diff --git a/-3ixsZ7fBUI.txt b/-3ixsZ7fBUI.txt new file mode 100644 index 0000000000000000000000000000000000000000..70111f1766a8635b457f0b90aab1b27a6d0990bb --- /dev/null +++ b/-3ixsZ7fBUI.txt @@ -0,0 +1,675 @@ +align:start position:0% + +uh my name is Miriam prosnit and I was + + align:start position:0% +uh my name is Miriam prosnit and I was + + + align:start position:0% +uh my name is Miriam prosnit and I was +on team Heatwave you play and there are + + align:start position:0% +on team Heatwave you play and there are + + + align:start position:0% +on team Heatwave you play and there are +characters moving around and different + + align:start position:0% +characters moving around and different + + + align:start position:0% +characters moving around and different +uh people who are at risk for being + + align:start position:0% +uh people who are at risk for being + + + align:start position:0% +uh people who are at risk for being +vulnerable to heat waves move around the + + align:start position:0% +vulnerable to heat waves move around the + + + align:start position:0% +vulnerable to heat waves move around the +screen so one person was in charge of + + align:start position:0% +screen so one person was in charge of + + + align:start position:0% +screen so one person was in charge of +researching who are those people and + + align:start position:0% +researching who are those people and + + + align:start position:0% +researching who are those people and +another person was in charge of okay I'm + + align:start position:0% +another person was in charge of okay I'm + + + align:start position:0% +another person was in charge of okay I'm +going to make a character object and we + + align:start position:0% +going to make a character object and we + + + align:start position:0% +going to make a character object and we +split up all of those actually right at + + align:start position:0% +split up all of those actually right at + + + align:start position:0% +split up all of those actually right at +the beginning so that we knew who to + + align:start position:0% +the beginning so that we knew who to + + + align:start position:0% +the beginning so that we knew who to +contact about what + + align:start position:0% +contact about what + + + align:start position:0% +contact about what +and then based off of that we would come + + align:start position:0% +and then based off of that we would come + + + align:start position:0% +and then based off of that we would come +together and say what needs to be done + + align:start position:0% +together and say what needs to be done + + + align:start position:0% +together and say what needs to be done +and whose job is it and is that still + + align:start position:0% +and whose job is it and is that still + + + align:start position:0% +and whose job is it and is that still +balanced in terms of who's working on + + align:start position:0% +balanced in terms of who's working on + + + align:start position:0% +balanced in terms of who's working on +what and it worked out really well + + align:start position:0% + + + + align:start position:0% + +actually actually funny enough I took + + align:start position:0% +actually actually funny enough I took + + + align:start position:0% +actually actually funny enough I took +this course solely because I had no + + align:start position:0% +this course solely because I had no + + + align:start position:0% +this course solely because I had no +course no computer science courses this + + align:start position:0% +course no computer science courses this + + + align:start position:0% +course no computer science courses this +semester uh because I was abroad last + + align:start position:0% +semester uh because I was abroad last + + + align:start position:0% +semester uh because I was abroad last +year I did a full year of engineering + + align:start position:0% +year I did a full year of engineering + + + align:start position:0% +year I did a full year of engineering +coursework and I was like don't need any + + align:start position:0% +coursework and I was like don't need any + + + align:start position:0% +coursework and I was like don't need any +more requirements might as well just + + align:start position:0% +more requirements might as well just + + + align:start position:0% +more requirements might as well just +take one for fun so here I am in + + align:start position:0% +take one for fun so here I am in + + + align:start position:0% +take one for fun so here I am in +creating video games and so my goal was + + align:start position:0% +creating video games and so my goal was + + + align:start position:0% +creating video games and so my goal was +to write code and the funniest thing I'm + + align:start position:0% +to write code and the funniest thing I'm + + + align:start position:0% +to write code and the funniest thing I'm +not representative of my team at all I'm + + align:start position:0% +not representative of my team at all I'm + + + align:start position:0% +not representative of my team at all I'm +like the one person in this class who's + + align:start position:0% +like the one person in this class who's + + + align:start position:0% +like the one person in this class who's +not written a single line of code this + + align:start position:0% +not written a single line of code this + + + align:start position:0% +not written a single line of code this +entire semester because I ended up being + + align:start position:0% +entire semester because I ended up being + + + align:start position:0% +entire semester because I ended up being +project manager a lot and so what I + + align:start position:0% +project manager a lot and so what I + + + align:start position:0% +project manager a lot and so what I +learned is a lot of the process a lot of + + align:start position:0% +learned is a lot of the process a lot of + + + align:start position:0% +learned is a lot of the process a lot of +making things work is really just + + align:start position:0% +making things work is really just + + + align:start position:0% +making things work is really just +emailing people calling them on the + + align:start position:0% +emailing people calling them on the + + + align:start position:0% +emailing people calling them on the +phone being like are you supposed to be + + align:start position:0% +phone being like are you supposed to be + + + align:start position:0% +phone being like are you supposed to be +at this meeting right now going and + + align:start position:0% +at this meeting right now going and + + + align:start position:0% +at this meeting right now going and +buying snacks for a meeeting you think + + align:start position:0% +buying snacks for a meeeting you think + + + align:start position:0% +buying snacks for a meeeting you think +it's like silly you know nobody really + + align:start position:0% +it's like silly you know nobody really + + + align:start position:0% +it's like silly you know nobody really +needs to get snacks but I've been told + + align:start position:0% +needs to get snacks but I've been told + + + align:start position:0% +needs to get snacks but I've been told +by my teammates that if I hadn't gotten + + align:start position:0% +by my teammates that if I hadn't gotten + + + align:start position:0% +by my teammates that if I hadn't gotten +snacks they wouldn't have come so um I + + align:start position:0% +snacks they wouldn't have come so um I + + + align:start position:0% +snacks they wouldn't have come so um I +learned a lot about the project + + align:start position:0% +learned a lot about the project + + + align:start position:0% +learned a lot about the project +management and the work that goes on + + align:start position:0% +management and the work that goes on + + + align:start position:0% +management and the work that goes on +behind the scenes which I've seen before + + align:start position:0% +behind the scenes which I've seen before + + + align:start position:0% +behind the scenes which I've seen before +but I just didn't realize the scale of + + align:start position:0% +but I just didn't realize the scale of + + + align:start position:0% +but I just didn't realize the scale of +it in games uh something I would give + + align:start position:0% +it in games uh something I would give + + + align:start position:0% +it in games uh something I would give +feedback about this class is I really + + align:start position:0% +feedback about this class is I really + + + align:start position:0% +feedback about this class is I really +like the fast paace of the first three + + align:start position:0% +like the fast paace of the first three + + + align:start position:0% +like the fast paace of the first three +project and this project uh because it + + align:start position:0% +project and this project uh because it + + + align:start position:0% +project and this project uh because it +was so much longer time the team was so + + align:start position:0% +was so much longer time the team was so + + + align:start position:0% +was so much longer time the team was so +much larger and we had this kind of set + + align:start position:0% +much larger and we had this kind of set + + + align:start position:0% +much larger and we had this kind of set +topic we had to deal with I didn't enjoy + + align:start position:0% +topic we had to deal with I didn't enjoy + + + align:start position:0% +topic we had to deal with I didn't enjoy +it as much as I mentioned one of the + + align:start position:0% +it as much as I mentioned one of the + + + align:start position:0% +it as much as I mentioned one of the +main issues for our team was passion at + + align:start position:0% +main issues for our team was passion at + + + align:start position:0% +main issues for our team was passion at +the end of the day I I can summarize + + align:start position:0% +the end of the day I I can summarize + + + align:start position:0% +the end of the day I I can summarize +what you should do in a heatwave in like + + align:start position:0% +what you should do in a heatwave in like + + + align:start position:0% +what you should do in a heatwave in like +two sentences that doesn't make for a + + align:start position:0% +two sentences that doesn't make for a + + + align:start position:0% +two sentences that doesn't make for a +very interesting game um so that's + + align:start position:0% +very interesting game um so that's + + + align:start position:0% +very interesting game um so that's +something I would say if I was to do it + + align:start position:0% +something I would say if I was to do it + + + align:start position:0% +something I would say if I was to do it +again I would I would have played the + + align:start position:0% +again I would I would have played the + + + align:start position:0% +again I would I would have played the +game where you play as the Heatwave and + + align:start position:0% +game where you play as the Heatwave and + + + align:start position:0% +game where you play as the Heatwave and +you like try to attack people cuz that + + align:start position:0% +you like try to attack people cuz that + + + align:start position:0% +you like try to attack people cuz that +sounds like more fun uh and I think + + align:start position:0% +sounds like more fun uh and I think + + + align:start position:0% +sounds like more fun uh and I think +that's the other thing I learned about + + align:start position:0% +that's the other thing I learned about + + + align:start position:0% +that's the other thing I learned about +games is that you really have to care + + align:start position:0% +games is that you really have to care + + + align:start position:0% +games is that you really have to care +about what you're + + align:start position:0% + + + + align:start position:0% + +making well somebody mentioned in one of + + align:start position:0% +making well somebody mentioned in one of + + + align:start position:0% +making well somebody mentioned in one of +the presentations that for the last + + align:start position:0% +the presentations that for the last + + + align:start position:0% +the presentations that for the last +project we would submit these Sprint + + align:start position:0% +project we would submit these Sprint + + + align:start position:0% +project we would submit these Sprint +task list and they wouldn't necessarily + + align:start position:0% +task list and they wouldn't necessarily + + + align:start position:0% +task list and they wouldn't necessarily +be what we like people actually would do + + align:start position:0% +be what we like people actually would do + + + align:start position:0% +be what we like people actually would do +because people were so busy at the end + + align:start position:0% +because people were so busy at the end + + + align:start position:0% +because people were so busy at the end +of the semester for my team if it was + + align:start position:0% +of the semester for my team if it was + + + align:start position:0% +of the semester for my team if it was +the case that we hadn't done something I + + align:start position:0% +the case that we hadn't done something I + + + align:start position:0% +the case that we hadn't done something I +would put it on the Sprint task list + + align:start position:0% +would put it on the Sprint task list + + + align:start position:0% +would put it on the Sprint task list +again uh but I didn't have to and that + + align:start position:0% +again uh but I didn't have to and that + + + align:start position:0% +again uh but I didn't have to and that +could have if I hadn't done that then + + align:start position:0% +could have if I hadn't done that then + + + align:start position:0% +could have if I hadn't done that then +there would have been a big Divergence + + align:start position:0% +there would have been a big Divergence + + + align:start position:0% +there would have been a big Divergence +between what we said we were doing and + + align:start position:0% +between what we said we were doing and + + + align:start position:0% +between what we said we were doing and +what we were actually doing so as an + + align:start position:0% +what we were actually doing so as an + + + align:start position:0% +what we were actually doing so as an +educator I would really say check in on + + align:start position:0% +educator I would really say check in on + + + align:start position:0% +educator I would really say check in on +your team see actually what they've done + + align:start position:0% +your team see actually what they've done + + + align:start position:0% +your team see actually what they've done +make sure they're setting realistic + + align:start position:0% +make sure they're setting realistic + + + align:start position:0% +make sure they're setting realistic +goals and following through on them \ No newline at end of file diff --git a/-OduZBd1aHw.txt b/-OduZBd1aHw.txt new file mode 100644 index 0000000000000000000000000000000000000000..82231cb1df5828d9ca1a803022829891231044fe --- /dev/null +++ b/-OduZBd1aHw.txt @@ -0,0 +1,260 @@ +There are a few MMU implementation details +we can tweak for more efficiency or functionality. + +In our simple page-map implementation, the +full page map occupies some number of physical + +pages. + +Using the numbers shown here, if each page +map entry occupies one word of main memory, + +we'd need 2^20 words (or 2^10 pages) to hold +the page table. + +If we have multiple contexts, we would need +multiple page tables, and the demands on our + +physical memory resources would start to get +large. + +The MMU implementation shown here uses a hierarchical +page map. + +The top 10 bits of virtual address are used +to access a "page directory", which indicates + +the physical page that holds the page map +for that segment of the virtual address space. + +The key idea is that the page map segments +are in virtual memory, i.e., they don't all + +have to be resident at any given time. + +If the running application is only actively +using a small portion of its virtual address + +space, we may only need a handful of pages +to hold the page directory and the necessary + +page map segments. + +The resultant savings really add up when there +are many applications, each with their own + +context. + +In this example, note that the middle entries +in the page directory, i.e., the entries corresponding + +to the as-yet unallocated virtual memory between +the stack and heap, are all marked as not + +resident. + +.133 So no page map resources need be devoted +to holding a zillion page map entries all + +marked "not resident". + +Accessing the page map now requires two access +to main memory (first to the page directory, + +then to the appropriate segment of the page +map), + +but the TLB makes the impact of that additional +access negligible. + +Normally when changing contexts, the OS would +reload the page-table pointer to point to + +the appropriate page table (or page table +directory if we adopt the scheme from the + +previous slide). + +Since this context switch in effect changes +all the entries in the page table, the OS + +would also have to invalidate all the entries +in the TLB cache. + +This naturally has a huge impact on the TLB +hit ratio and the average memory access time + +takes a huge hit because of the all page map +accesses that are now necessary until the + +TLB is refilled. + +To reduce the impact of context switches, +some MMUs include a context-number register + +whose contents are concatenated with the virtual +page number to form the query to the TLB. + +Essentially this means that the tag field +in the TLB cache entries will expand to include + +the context number provided at the time the +TLB entry was filled. + +To switch contexts, the OS would now reload +both the context-number register and the page-table + +pointer. + +With a new context number, entries in the +TLB for other contexts would no longer match, + +so no need to flush the TLB on a context switch. + +If the TLB has sufficient capacity to cache +the VPN-to-PPN mappings for several contexts, + +context switches would no longer have a substantial +impact on average memory access time. + +Finally, let's return to the question about +how to incorporate both a cache and an MMU + +into our memory system. + +The first choice is to place the cache between +the CPU and the MMU, i.e., the cache would + +work on virtual addresses. + +This seems good: the cost of the VPN-to-PPN +translation is only incurred on a cache miss. + +The difficulty comes when there's a context +switch, which changes the effective contents + +of virtual memory. + +After all that was the point of the context +switch, since we want to switch execution + +to another program. + +But that means the OS would have to invalidate +all the entries in the cache when performing + +a context switch, which makes the cache miss +ratio quite large until the cache is refilled. + +So once again the performance impact of a +context switch would be quite high. + +We can solve this problem by caching physical +addresses, i.e., placing the cache between + +the MMU and main memory. + +Thus the contents of the cache are unaffected +by context switches - + +the requested physical addresses will be different, +but the cache handles that in due course. + +The downside of this approach is that we have +to incur the cost of the MMU translation before + +we can start the cache access, slightly increasing +the average memory access time. + +But if we're clever we don't have to wait +for the MMU to finish before starting the + +access to the cache. + +To get started, the cache needs the line number +from the virtual address in order to fetch + +the appropriate cache line. + +If the address bits used for the line number +are completely contained in the page offset + +of the virtual address, these bits are unaffected +by the MMU translation, + +and so the cache lookup can happen in parallel +with the MMU operation. + +Once the cache lookup is complete, the tag +field of the cache line can be compared with + +the appropriate bits of the physical address +produced by the MMU. + +If there was a TLB hit in the MMU, the physical +address should be available at about the same + +time as the tag field produced by the cache +lookup. + +By performing the MMU translation and cache +lookup in parallel, there's usually no impact + +on the average memory access time! + +Voila, the best of both worlds: a physically +addressed cache that incurs no time penalty + +for MMU translation. + +One final detail: one way to increase the +capacity of the cache is to increase the number + +of cache lines and hence the number of bits +of address used as the line number. + +Since we want the line number to fit into +the page offset field of the virtual address, + +we're limited in how many cache lines we can +have. + +The same argument applies to increasing the +block size. + +So to increase the capacity of the cache our +only option is to increase the cache associativity, + +which adds capacity without affecting the +address bits used for the line number. + +That's it for our discussion of virtual memory. + +We use the MMU to provide the context for +mapping virtual addresses to physical addresses. + +By switching contexts we can create the illusion +of many virtual address spaces, so many programs + +can share a single CPU and physical memory +without interfering with each other. + +We discussed using a page map to translate +virtual page numbers to physical page numbers. + +To save costs, we located the page map in +physical memory and used a TLB to eliminate + +the cost of accessing the page map for most +virtual memory accesses. + +Access to a non-resident page causes a page +fault exception, allowing the OS to manage + +the complexities of equitably sharing physical +memory across many applications. + +We saw that providing contexts was the first +step towards creating virtual machines, which + +is the topic of our next lecture. \ No newline at end of file diff --git a/-QVENB3aEvY.txt b/-QVENB3aEvY.txt new file mode 100644 index 0000000000000000000000000000000000000000..e939a2f49ca60c5c3fb77cd012bc1b66852ad99d --- /dev/null +++ b/-QVENB3aEvY.txt @@ -0,0 +1,5323 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu get started um what do you + + align:start position:0% +ocw.mit.edu get started um what do you + + + align:start position:0% +ocw.mit.edu get started um what do you +think are some + + align:start position:0% +think are some + + + align:start position:0% +think are some +important new Concepts that we've been + + align:start position:0% +important new Concepts that we've been + + + align:start position:0% +important new Concepts that we've been +talking about in the last week + + align:start position:0% + + + + align:start position:0% + +make a list that's see ways + + align:start position:0% + + + + align:start position:0% + +toate + + align:start position:0% + + + + align:start position:0% + +okay all + + align:start position:0% +okay all + + + align:start position:0% +okay all +right virtual work virtual work + + align:start position:0% + + + + align:start position:0% + +something + + align:start position:0% + + + + align:start position:0% + +else all + + align:start position:0% + + + + align:start position:0% + +right concept of generalized coordinates + + align:start position:0% +right concept of generalized coordinates + + + align:start position:0% +right concept of generalized coordinates +generalized coordinates + + align:start position:0% + + + + align:start position:0% + +anything else on your + + align:start position:0% + + + + align:start position:0% + +list + + align:start position:0% + + + + align:start position:0% + +forces okay gr equations that's a pretty + + align:start position:0% +forces okay gr equations that's a pretty + + + align:start position:0% +forces okay gr equations that's a pretty +good list any now there we've talked + + align:start position:0% +good list any now there we've talked + + + align:start position:0% +good list any now there we've talked +about quite a few new things lately so + + align:start position:0% +about quite a few new things lately so + + + align:start position:0% +about quite a few new things lately so +is there any do you come in here today + + align:start position:0% +is there any do you come in here today + + + align:start position:0% +is there any do you come in here today +with any questions about something + + align:start position:0% +with any questions about something + + + align:start position:0% +with any questions about something +that's just does isn't sitting right you + + align:start position:0% +that's just does isn't sitting right you + + + align:start position:0% +that's just does isn't sitting right you +know on these topics or anything else + + align:start position:0% +know on these topics or anything else + + + align:start position:0% +know on these topics or anything else +and I think write up a couple extra + + align:start position:0% +and I think write up a couple extra + + + align:start position:0% +and I think write up a couple extra +questions that we may be able to cover + + align:start position:0% +questions that we may be able to cover + + + align:start position:0% +questions that we may be able to cover +them as we go along + + align:start position:0% +them as we go along + + + align:start position:0% +them as we go along +Stephen so + + align:start position:0% +Stephen so + + + align:start position:0% +Stephen so +you everything in general is coordinates + + align:start position:0% +you everything in general is coordinates + + + align:start position:0% +you everything in general is coordinates +right but say you want to plug in actual + + align:start position:0% +right but say you want to plug in actual + + + align:start position:0% +right but say you want to plug in actual +numbers you translate them + + align:start position:0% +numbers you translate them + + + align:start position:0% +numbers you translate them +to or + + align:start position:0% +to or + + + align:start position:0% +to or +you just more for + + align:start position:0% +you just more for + + + align:start position:0% +you just more for +practical so this is really how to so + + align:start position:0% +practical so this is really how to so + + + align:start position:0% +practical so this is really how to so +you come how to use the equations you + + align:start position:0% +you come how to use the equations you + + + align:start position:0% +you come how to use the equations you +end up with in in Practical situations + + align:start position:0% +end up with in in Practical situations + + + align:start position:0% +end up with in in Practical situations +okay the I'm just going to answer this + + align:start position:0% +okay the I'm just going to answer this + + + align:start position:0% +okay the I'm just going to answer this +one so when you choose your generalized + + align:start position:0% +one so when you choose your generalized + + + align:start position:0% +one so when you choose your generalized +coordinates you'll probably choose about + + align:start position:0% +coordinates you'll probably choose about + + + align:start position:0% +coordinates you'll probably choose about +the same ones you'd choose if you did + + align:start position:0% +the same ones you'd choose if you did + + + align:start position:0% +the same ones you'd choose if you did +the direct method so if you did direct + + align:start position:0% +the direct method so if you did direct + + + align:start position:0% +the direct method so if you did direct +method would you have the and got court + + align:start position:0% +method would you have the and got court + + + align:start position:0% +method would you have the and got court +it got I got equations of motion would + + align:start position:0% +it got I got equations of motion would + + + align:start position:0% +it got I got equations of motion would +you be asking the same + + align:start position:0% +you be asking the same + + + align:start position:0% +you be asking the same +question right okay so it really you + + align:start position:0% +question right okay so it really you + + + align:start position:0% +question right okay so it really you +want to choose coordinates that are + + align:start position:0% +want to choose coordinates that are + + + align:start position:0% +want to choose coordinates that are +going to be practically useful in the + + align:start position:0% +going to be practically useful in the + + + align:start position:0% +going to be practically useful in the +end okay and so it shouldn't matter + + align:start position:0% +end okay and so it shouldn't matter + + + align:start position:0% +end okay and so it shouldn't matter +whether you're doing it by lrange or + + align:start position:0% +whether you're doing it by lrange or + + + align:start position:0% +whether you're doing it by lrange or +doing it by the direct method to get to + + align:start position:0% +doing it by the direct method to get to + + + align:start position:0% +doing it by the direct method to get to +him you're going to use them the same + + align:start position:0% +him you're going to use them the same + + + align:start position:0% +him you're going to use them the same +way in the end and in fact how I now the + + align:start position:0% +way in the end and in fact how I now the + + + align:start position:0% +way in the end and in fact how I now the +we have two methods to get equations of + + align:start position:0% +we have two methods to get equations of + + + align:start position:0% +we have two methods to get equations of +motion now when you're doing tough + + align:start position:0% +motion now when you're doing tough + + + align:start position:0% +motion now when you're doing tough +problems complicated problems I would + + align:start position:0% +problems complicated problems I would + + + align:start position:0% +problems complicated problems I would +always do it one way and use the other + + align:start position:0% +always do it one way and use the other + + + align:start position:0% +always do it one way and use the other +way to check it I'd end up doing it both + + align:start position:0% +way to check it I'd end up doing it both + + + align:start position:0% +way to check it I'd end up doing it both +ways and if was really important you do + + align:start position:0% +ways and if was really important you do + + + align:start position:0% +ways and if was really important you do +it both ways and one will give you + + align:start position:0% +it both ways and one will give you + + + align:start position:0% +it both ways and one will give you +insight about the other you know + + align:start position:0% +insight about the other you know + + + align:start position:0% +insight about the other you know +yesterday I was in lecture talking about + + align:start position:0% +yesterday I was in lecture talking about + + + align:start position:0% +yesterday I was in lecture talking about +does it make sense to have a a + + align:start position:0% +does it make sense to have a a + + + align:start position:0% +does it make sense to have a a +um coriolis term in this equation you + + align:start position:0% +um coriolis term in this equation you + + + align:start position:0% +um coriolis term in this equation you +would you expect it you know in that + + align:start position:0% +would you expect it you know in that + + + align:start position:0% +would you expect it you know in that +kind of Common Sense checking all right + + align:start position:0% +kind of Common Sense checking all right + + + align:start position:0% +kind of Common Sense checking all right +any other questions good + + align:start position:0% +any other questions good + + + align:start position:0% +any other questions good +question generalize coordinates or + + align:start position:0% +question generalize coordinates or + + + align:start position:0% +question generalize coordinates or +forces or anything all right let's get + + align:start position:0% +forces or anything all right let's get + + + align:start position:0% +forces or anything all right let's get +on let's keep working + + align:start position:0% +on let's keep working + + + align:start position:0% +on let's keep working +here so I have an assignment for + + align:start position:0% +here so I have an assignment for + + + align:start position:0% +here so I have an assignment for +you and it's + + align:start position:0% + + + + align:start position:0% + +here this is a familiar problem that + + align:start position:0% +here this is a familiar problem that + + + align:start position:0% +here this is a familiar problem that +you've worked before by other methods + + align:start position:0% +you've worked before by other methods + + + align:start position:0% +you've worked before by other methods +and you did in fact even find the + + align:start position:0% +and you did in fact even find the + + + align:start position:0% +and you did in fact even find the +kinetic and potential energies I think + + align:start position:0% +kinetic and potential energies I think + + + align:start position:0% +kinetic and potential energies I think +last week for this so here's our cart + + align:start position:0% +last week for this so here's our cart + + + align:start position:0% +last week for this so here's our cart +with the rod uniform + + align:start position:0% +with the rod uniform + + + align:start position:0% +with the rod uniform +Rod no dash pot at the moment and no no + + align:start position:0% +Rod no dash pot at the moment and no no + + + align:start position:0% +Rod no dash pot at the moment and no no +external forces the I'm going to give + + align:start position:0% +external forces the I'm going to give + + + align:start position:0% +external forces the I'm going to give +you coordinates to use so here's our + + align:start position:0% +you coordinates to use so here's our + + + align:start position:0% +you coordinates to use so here's our +inertial system deflection of the cart X + + align:start position:0% +inertial system deflection of the cart X + + + align:start position:0% +inertial system deflection of the cart X +rotation of the rod Theta we're going to + + align:start position:0% +rotation of the rod Theta we're going to + + + align:start position:0% +rotation of the rod Theta we're going to +break you into groups boy we got about + + align:start position:0% +break you into groups boy we got about + + + align:start position:0% +break you into groups boy we got about +we got a big group here big five + + align:start position:0% + + + + align:start position:0% + +10 well that's we'll + + align:start position:0% +10 well that's we'll + + + align:start position:0% +10 well that's we'll +um just do I want break you into three + + align:start position:0% +um just do I want break you into three + + + align:start position:0% +um just do I want break you into three +groups kind of like five or six there + + align:start position:0% +groups kind of like five or six there + + + align:start position:0% +groups kind of like five or six there +five or six there and the same thing + + align:start position:0% +five or six there and the same thing + + + align:start position:0% +five or six there and the same thing +here and one group each so this group in + + align:start position:0% +here and one group each so this group in + + + align:start position:0% +here and one group each so this group in +the front left compute the kinetic + + align:start position:0% +the front left compute the kinetic + + + align:start position:0% +the front left compute the kinetic +energy of the system and the group + + align:start position:0% +energy of the system and the group + + + align:start position:0% +energy of the system and the group +behind them compute the potential in + + align:start position:0% +behind them compute the potential in + + + align:start position:0% +behind them compute the potential in +this group over here come up with the + + align:start position:0% +this group over here come up with the + + + align:start position:0% +this group over here come up with the +velocity of + + align:start position:0% +velocity of + + + align:start position:0% +velocity of +G + + align:start position:0% +G + + + align:start position:0% +G +and V g. VG the velocity + + align:start position:0% +and V g. VG the velocity + + + align:start position:0% +and V g. VG the velocity +squared okay and this won't take it long + + align:start position:0% +squared okay and this won't take it long + + + align:start position:0% +squared okay and this won't take it long +because you've done this stuff before + + align:start position:0% +because you've done this stuff before + + + align:start position:0% +because you've done this stuff before +and then when you get done somebody from + + align:start position:0% +and then when you get done somebody from + + + align:start position:0% +and then when you get done somebody from +your group just when you're done come up + + align:start position:0% +your group just when you're done come up + + + align:start position:0% +your group just when you're done come up +and write it down all right let's sort + + align:start position:0% +and write it down all right let's sort + + + align:start position:0% +and write it down all right let's sort +these out let's + + align:start position:0% + + + + align:start position:0% + +talk so let's start with the velocity + + align:start position:0% +talk so let's start with the velocity + + + align:start position:0% +talk so let's start with the velocity +we're going to we're going to need the + + align:start position:0% +we're going to we're going to need the + + + align:start position:0% +we're going to we're going to need the +velocity to be able to write to do the + + align:start position:0% +velocity to be able to write to do the + + + align:start position:0% +velocity to be able to write to do the +finish out the kinetic energy so the + + align:start position:0% +finish out the kinetic energy so the + + + align:start position:0% +finish out the kinetic energy so the +uh Vector right and you these and you've + + align:start position:0% +uh Vector right and you these and you've + + + align:start position:0% +uh Vector right and you these and you've +broken it into two + + align:start position:0% + + + + align:start position:0% + +pieces and since the others of you + + align:start position:0% +pieces and since the others of you + + + align:start position:0% +pieces and since the others of you +haven't worked on it are you guys can + + align:start position:0% +haven't worked on it are you guys can + + + align:start position:0% +haven't worked on it are you guys can +you switch the and ah I was about to ask + + align:start position:0% +you switch the and ah I was about to ask + + + align:start position:0% +you switch the and ah I was about to ask +you about + + align:start position:0% +you about + + + align:start position:0% +you about +that good I think that's that's better + + align:start position:0% +that good I think that's that's better + + + align:start position:0% +that good I think that's that's better +so this is sign right + + align:start position:0% +so this is sign right + + + align:start position:0% +so this is sign right +I just erased it okay that's + + align:start position:0% + + + + align:start position:0% + +coine right CU we've got this is your L + + align:start position:0% +coine right CU we've got this is your L + + + align:start position:0% +coine right CU we've got this is your L +Theta dot piece and you want it this way + + align:start position:0% +Theta dot piece and you want it this way + + + align:start position:0% +Theta dot piece and you want it this way +and that's sta so should be sin Theta J + + align:start position:0% +and that's sta so should be sin Theta J + + + align:start position:0% +and that's sta so should be sin Theta J +cosine Theta I + + align:start position:0% +cosine Theta I + + + align:start position:0% +cosine Theta I +yeah okay I think that's good for the + + align:start position:0% +yeah okay I think that's good for the + + + align:start position:0% +yeah okay I think that's good for the +velocity and then velocity squared just + + align:start position:0% +velocity and then velocity squared just + + + align:start position:0% +velocity and then velocity squared just +the square of each of + + align:start position:0% +the square of each of + + + align:start position:0% +the square of each of +the square of each of the pieces right + + align:start position:0% + + + + align:start position:0% + +okay so we have VV we need to put this + + align:start position:0% +okay so we have VV we need to put this + + + align:start position:0% +okay so we have VV we need to put this +into the kinetic energy expression but + + align:start position:0% +into the kinetic energy expression but + + + align:start position:0% +into the kinetic energy expression but +we let's one at a time here here the + + align:start position:0% +we let's one at a time here here the + + + align:start position:0% +we let's one at a time here here the +potential energy expression half kx^ s + + align:start position:0% +potential energy expression half kx^ s + + + align:start position:0% +potential energy expression half kx^ s +everybody good with that that looks like + + align:start position:0% +everybody good with that that looks like + + + align:start position:0% +everybody good with that that looks like +the spring kinetic spring potential + + align:start position:0% +the spring kinetic spring potential + + + align:start position:0% +the spring kinetic spring potential +energy and + + align:start position:0% +energy and + + + align:start position:0% +energy and +m2g a half L is the position on of the + + align:start position:0% +m2g a half L is the position on of the + + + align:start position:0% +m2g a half L is the position on of the +center of mass 1us cosine L that times 1 + + align:start position:0% +center of mass 1us cosine L that times 1 + + + align:start position:0% +center of mass 1us cosine L that times 1 +- cosine Theta is the amount that it + + align:start position:0% +- cosine Theta is the amount that it + + + align:start position:0% +- cosine Theta is the amount that it +changes height from the reference what's + + align:start position:0% +changes height from the reference what's + + + align:start position:0% +changes height from the reference what's +the reference + + align:start position:0% +the reference + + + align:start position:0% +the reference +position what have you assumed for the + + align:start position:0% +position what have you assumed for the + + + align:start position:0% +position what have you assumed for the +reference position in this formulation + + align:start position:0% +reference position in this formulation + + + align:start position:0% +reference position in this formulation +yeah when it's just down so your + + align:start position:0% +yeah when it's just down so your + + + align:start position:0% +yeah when it's just down so your +reference position is m center of mass + + align:start position:0% +reference position is m center of mass + + + align:start position:0% +reference position is m center of mass +when it's hanging straight down okay + + align:start position:0% +when it's hanging straight down okay + + + align:start position:0% +when it's hanging straight down okay +great so there's your potential energy + + align:start position:0% +great so there's your potential energy + + + align:start position:0% +great so there's your potential energy +expression that's pretty good kinetic + + align:start position:0% +expression that's pretty good kinetic + + + align:start position:0% +expression that's pretty good kinetic +energy expression uh how do people how + + align:start position:0% +energy expression uh how do people how + + + align:start position:0% +energy expression uh how do people how +everybody comfortable with + + align:start position:0% + + + + align:start position:0% + +that I'm not totally comfortable with it + + align:start position:0% +that I'm not totally comfortable with it + + + align:start position:0% +that I'm not totally comfortable with it +uh let's let's come up let's talk about + + align:start position:0% +uh let's let's come up let's talk about + + + align:start position:0% +uh let's let's come up let's talk about +a minute about kinetic energy and say + + align:start position:0% +a minute about kinetic energy and say + + + align:start position:0% +a minute about kinetic energy and say +what's what can we use what formulas can + + align:start position:0% +what's what can we use what formulas can + + + align:start position:0% +what's what can we use what formulas can +we use here for + + align:start position:0% +we use here for + + + align:start position:0% +we use here for +T you know there's totally General and + + align:start position:0% +T you know there's totally General and + + + align:start position:0% +T you know there's totally General and +then we can narrow it down yeah what do + + align:start position:0% +then we can narrow it down yeah what do + + + align:start position:0% +then we can narrow it down yeah what do +you + + align:start position:0% +you + + + align:start position:0% +you +suggest energy + + align:start position:0% +suggest energy + + + align:start position:0% +suggest energy +just you can take you have to take into + + align:start position:0% +just you can take you have to take into + + + align:start position:0% +just you can take you have to take into +account that it's not about MTH so you + + align:start position:0% +account that it's not about MTH so you + + + align:start position:0% +account that it's not about MTH so you +use the generalized + + align:start position:0% +use the generalized + + + align:start position:0% +use the generalized +formula2 um Omega dot it's angular + + align:start position:0% +formula2 um Omega dot it's angular + + + align:start position:0% +formula2 um Omega dot it's angular +Point okay so we have some general + + align:start position:0% +Point okay so we have some general + + + align:start position:0% +Point okay so we have some general +formulas and let's just let's kind of + + align:start position:0% +formulas and let's just let's kind of + + + align:start position:0% +formulas and let's just let's kind of +take a step-by-step approach to this we + + align:start position:0% +take a step-by-step approach to this we + + + align:start position:0% +take a step-by-step approach to this we +have how many rigid + + align:start position:0% +have how many rigid + + + align:start position:0% +have how many rigid +bodies two and what you compute the + + align:start position:0% +bodies two and what you compute the + + + align:start position:0% +bodies two and what you compute the +kinetic energy for each one + + align:start position:0% +kinetic energy for each one + + + align:start position:0% +kinetic energy for each one +individually is the safest way to go + + align:start position:0% +individually is the safest way to go + + + align:start position:0% +individually is the safest way to go +about this so uh I would stay away + + align:start position:0% +about this so uh I would stay away + + + align:start position:0% +about this so uh I would stay away +initially from doing this you're lumping + + align:start position:0% +initially from doing this you're lumping + + + align:start position:0% +initially from doing this you're lumping +the two together okay so I would take + + align:start position:0% +the two together okay so I would take + + + align:start position:0% +the two together okay so I would take +the two individ ually so if you take the + + align:start position:0% +the two individ ually so if you take the + + + align:start position:0% +the two individ ually so if you take the +the main + + align:start position:0% +the main + + + align:start position:0% +the main +Mass the big the block on Wheels what is + + align:start position:0% +Mass the big the block on Wheels what is + + + align:start position:0% +Mass the big the block on Wheels what is +its + + align:start position:0% + + + + align:start position:0% + +velocity it velocity is just X do right + + align:start position:0% +velocity it velocity is just X do right + + + align:start position:0% +velocity it velocity is just X do right +and its kinetic energy + + align:start position:0% +and its kinetic energy + + + align:start position:0% +and its kinetic energy +is okay so for the first block you have + + align:start position:0% +is okay so for the first block you have + + + align:start position:0% +is okay so for the first block you have +m1x do^ SAR and you're done that's the + + align:start position:0% +m1x do^ SAR and you're done that's the + + + align:start position:0% +m1x do^ SAR and you're done that's the +first block now you need the second + + align:start position:0% +first block now you need the second + + + align:start position:0% +first block now you need the second +rigid body so the second rigid body you + + align:start position:0% +rigid body so the second rigid body you + + + align:start position:0% +rigid body so the second rigid body you +could uh + + align:start position:0% + + + + align:start position:0% + +do I mean the full General expression is + + align:start position:0% +do I mean the full General expression is + + + align:start position:0% +do I mean the full General expression is +12 M to + + align:start position:0% +12 M to + + + align:start position:0% +12 M to +v g in O do VG in o plus a + + align:start position:0% +v g in O do VG in o plus a + + + align:start position:0% +v g in O do VG in o plus a +half + + align:start position:0% + + + + align:start position:0% + +Omega H right with respect to G you + + align:start position:0% +Omega H right with respect to G you + + + align:start position:0% +Omega H right with respect to G you +could good with that viente + + align:start position:0% +could good with that viente + + + align:start position:0% +could good with that viente +okay no you need to transpose need to + + align:start position:0% +okay no you need to transpose need to + + + align:start position:0% +okay no you need to transpose need to +transpose okay good all right that's and + + align:start position:0% +transpose okay good all right that's and + + + align:start position:0% +transpose okay good all right that's and +you and is can + + align:start position:0% +you and is can + + + align:start position:0% +you and is can +we can we simplify that at + + align:start position:0% + + + + align:start position:0% + +all you know there you know is it for + + align:start position:0% +all you know there you know is it for + + + align:start position:0% +all you know there you know is it for +example is it that Rod rotating about a + + align:start position:0% +example is it that Rod rotating about a + + + align:start position:0% +example is it that Rod rotating about a +fixed + + align:start position:0% + + + + align:start position:0% + +point it's not the point it rotates + + align:start position:0% +point it's not the point it rotates + + + align:start position:0% +point it's not the point it rotates +about moves right so you can't say it's + + align:start position:0% +about moves right so you can't say it's + + + align:start position:0% +about moves right so you can't say it's +just you can't use for example parallel + + align:start position:0% +just you can't use for example parallel + + + align:start position:0% +just you can't use for example parallel +axis theorem and just say it's 12 I with + + align:start position:0% +axis theorem and just say it's 12 I with + + + align:start position:0% +axis theorem and just say it's 12 I with +respect to that point Theta do^ squ + + align:start position:0% +respect to that point Theta do^ squ + + + align:start position:0% +respect to that point Theta do^ squ +won't + + align:start position:0% +won't + + + align:start position:0% +won't +work can't use that one uh you will find + + align:start position:0% +work can't use that one uh you will find + + + align:start position:0% +work can't use that one uh you will find +that if you work this out you can say 12 + + align:start position:0% +that if you work this out you can say 12 + + + align:start position:0% +that if you work this out you can say 12 +I with respect to G Omega squar and this + + align:start position:0% +I with respect to G Omega squar and this + + + align:start position:0% +I with respect to G Omega squar and this +problem will work out it will come out + + align:start position:0% +problem will work out it will come out + + + align:start position:0% +problem will work out it will come out +to that because this is a planer motion + + align:start position:0% +to that because this is a planer motion + + + align:start position:0% +to that because this is a planer motion +problem and there's only one component + + align:start position:0% +problem and there's only one component + + + align:start position:0% +problem and there's only one component +of rotation so this will work out to be + + align:start position:0% +of rotation so this will work out to be + + + align:start position:0% +of rotation so this will work out to be +uh a + + align:start position:0% +uh a + + + align:start position:0% +uh a +half I with respect ZZ of + + align:start position:0% +half I with respect ZZ of + + + align:start position:0% +half I with respect ZZ of +M2 with respect to G Omega z^ 2 in this + + align:start position:0% +M2 with respect to G Omega z^ 2 in this + + + align:start position:0% +M2 with respect to G Omega z^ 2 in this +case Theta do^ 2 that's what this term + + align:start position:0% +case Theta do^ 2 that's what this term + + + align:start position:0% +case Theta do^ 2 that's what this term +will reduce to but don't assume it just + + align:start position:0% +will reduce to but don't assume it just + + + align:start position:0% +will reduce to but don't assume it just +out of the box and then you need this + + align:start position:0% +out of the box and then you need this + + + align:start position:0% +out of the box and then you need this +term and that's why we need + + align:start position:0% +term and that's why we need + + + align:start position:0% +term and that's why we need +VG so you need to do + + align:start position:0% +VG so you need to do + + + align:start position:0% +VG so you need to do +that put that piece in over there okay + + align:start position:0% +that put that piece in over there okay + + + align:start position:0% +that put that piece in over there okay +so uh we have so we need + + align:start position:0% + + + + align:start position:0% + +to so what is izz about + + align:start position:0% + + + + align:start position:0% + +G for + + align:start position:0% + + + + align:start position:0% + +M2 for a rod cylender + + align:start position:0% + + + + align:start position:0% + +rod so + + align:start position:0% +rod so + + + align:start position:0% +rod so +M2 l^2 over 12 that's what you need to + + align:start position:0% +M2 l^2 over 12 that's what you need to + + + align:start position:0% +M2 l^2 over 12 that's what you need to +put in here we have an expression for V + + align:start position:0% +put in here we have an expression for V + + + align:start position:0% +put in here we have an expression for V +over there and we okay we have + + align:start position:0% +over there and we okay we have + + + align:start position:0% +over there and we okay we have +everything we we know everything now + + align:start position:0% +everything we we know everything now + + + align:start position:0% +everything we we know everything now +okay so now let's apply our lrange + + align:start position:0% + + + + align:start position:0% + +equations and I'm going to need to + + align:start position:0% +equations and I'm going to need to + + + align:start position:0% +equations and I'm going to need to +rearrange the board here a little + + align:start position:0% + + + + align:start position:0% + +bit I'm going to need that board space + + align:start position:0% +bit I'm going to need that board space + + + align:start position:0% +bit I'm going to need that board space +so our T is 12 M1 X1 do squar or X do + + align:start position:0% +so our T is 12 M1 X1 do squar or X do + + + align:start position:0% +so our T is 12 M1 X1 do squar or X do +s + + align:start position:0% + + + + align:start position:0% + +plus half M2 vg. + + align:start position:0% + + + + align:start position:0% + +VG okay and now I can cover this up + + align:start position:0% +VG okay and now I can cover this up + + + align:start position:0% +VG okay and now I can cover this up +all right now so the next task is let's + + align:start position:0% +all right now so the next task is let's + + + align:start position:0% +all right now so the next task is let's +work out let's try our do our lant + + align:start position:0% +work out let's try our do our lant + + + align:start position:0% +work out let's try our do our lant +equations work so how many generalized + + align:start position:0% +equations work so how many generalized + + + align:start position:0% +equations work so how many generalized +coordinates we have and what are + + align:start position:0% +coordinates we have and what are + + + align:start position:0% +coordinates we have and what are +they X and Theta right that we've chosen + + align:start position:0% +they X and Theta right that we've chosen + + + align:start position:0% +they X and Theta right that we've chosen +two degrees of freedom they're complete + + align:start position:0% +two degrees of freedom they're complete + + + align:start position:0% +two degrees of freedom they're complete +independent homic and we can use Lan + + align:start position:0% +independent homic and we can use Lan + + + align:start position:0% +independent homic and we can use Lan +equations we're going to come up with + + align:start position:0% +equations we're going to come up with + + + align:start position:0% +equations we're going to come up with +two equations in + + align:start position:0% +two equations in + + + align:start position:0% +two equations in +motion and we're going to apply this + + align:start position:0% +motion and we're going to apply this + + + align:start position:0% +motion and we're going to apply this +that's the gange equation we're going to + + align:start position:0% +that's the gange equation we're going to + + + align:start position:0% +that's the gange equation we're going to +apply it twice where L is defined as T + + align:start position:0% +apply it twice where L is defined as T + + + align:start position:0% +apply it twice where L is defined as T +minus + + align:start position:0% +minus + + + align:start position:0% +minus +V if you just plug in L into this + + align:start position:0% +V if you just plug in L into this + + + align:start position:0% +V if you just plug in L into this +expression and just expand it you get + + align:start position:0% +expression and just expand it you get + + + align:start position:0% +expression and just expand it you get +instead of two terms you get four terms + + align:start position:0% +instead of two terms you get four terms + + + align:start position:0% +instead of two terms you get four terms +because you have these two guys and this + + align:start position:0% +because you have these two guys and this + + + align:start position:0% +because you have these two guys and this +term what can you for mechanical systems + + align:start position:0% +term what can you for mechanical systems + + + align:start position:0% +term what can you for mechanical systems +what can you say about this term + + align:start position:0% +what can you say about this term + + + align:start position:0% +what can you say about this term +generally that's the derivative of V + + align:start position:0% +generally that's the derivative of V + + + align:start position:0% +generally that's the derivative of V +with respect to Q dots to + + align:start position:0% +with respect to Q dots to + + + align:start position:0% +with respect to Q dots to +velocities why + + align:start position:0% + + + + align:start position:0% + +conservative forces no just that you + + align:start position:0% +conservative forces no just that you + + + align:start position:0% +conservative forces no just that you +find that for mechanical system Springs + + align:start position:0% +find that for mechanical system Springs + + + align:start position:0% +find that for mechanical system Springs +and gravity you will + + align:start position:0% +and gravity you will + + + align:start position:0% +and gravity you will +never find that the potential energy is + + align:start position:0% +never find that the potential energy is + + + align:start position:0% +never find that the potential energy is +a function of time or + + align:start position:0% +a function of time or + + + align:start position:0% +a function of time or +velocity just isn't and if it's not a + + align:start position:0% +velocity just isn't and if it's not a + + + align:start position:0% +velocity just isn't and if it's not a +function of velocity you take a + + align:start position:0% +function of velocity you take a + + + align:start position:0% +function of velocity you take a +derivative with respect to Velocity you + + align:start position:0% +derivative with respect to Velocity you + + + align:start position:0% +derivative with respect to Velocity you +get zeros so this is this goes to zero + + align:start position:0% +get zeros so this is this goes to zero + + + align:start position:0% +get zeros so this is this goes to zero +for mechanical + + align:start position:0% + + + + align:start position:0% + +systems an exception for non-mechanical + + align:start position:0% +systems an exception for non-mechanical + + + align:start position:0% +systems an exception for non-mechanical +would be like a Charged particle in a + + align:start position:0% +would be like a Charged particle in a + + + align:start position:0% +would be like a Charged particle in a +magnetic field then the forces get + + align:start position:0% +magnetic field then the forces get + + + align:start position:0% +magnetic field then the forces get +involved with velocities and so forth it + + align:start position:0% +involved with velocities and so forth it + + + align:start position:0% +involved with velocities and so forth it +gets messy zero for mechanical system so + + align:start position:0% +gets messy zero for mechanical system so + + + align:start position:0% +gets messy zero for mechanical system so +we only only have to + + align:start position:0% +we only only have to + + + align:start position:0% +we only only have to +deal for with three terms that one that + + align:start position:0% +deal for with three terms that one that + + + align:start position:0% +deal for with three terms that one that +one and that one and then on the right + + align:start position:0% +one and that one and then on the right + + + align:start position:0% +one and that one and then on the right +hand side our generalized forces so we + + align:start position:0% +hand side our generalized forces so we + + + align:start position:0% +hand side our generalized forces so we +going to we have we can break into four + + align:start position:0% +going to we have we can break into four + + + align:start position:0% +going to we have we can break into four +smaller groups two groups are going to + + align:start position:0% +smaller groups two groups are going to + + + align:start position:0% +smaller groups two groups are going to +do the E the X equation you have to take + + align:start position:0% +do the E the X equation you have to take + + + align:start position:0% +do the E the X equation you have to take +these D qjs in this problem are + + align:start position:0% +these D qjs in this problem are + + + align:start position:0% +these D qjs in this problem are +q1 is X and Q2 is + + align:start position:0% +q1 is X and Q2 is + + + align:start position:0% +q1 is X and Q2 is +Theta so we need for the X equation we + + align:start position:0% +Theta so we need for the X equation we + + + align:start position:0% +Theta so we need for the X equation we +need to do these + + align:start position:0% +need to do these + + + align:start position:0% +need to do these +derivatives and for the Theta + + align:start position:0% + + + + align:start position:0% + +equation we need to do these + + align:start position:0% +equation we need to do these + + + align:start position:0% +equation we need to do these +computations so we've can let's have one + + align:start position:0% +computations so we've can let's have one + + + align:start position:0% +computations so we've can let's have one +group a do + + align:start position:0% +group a do + + + align:start position:0% +group a do +these and Group B do these and group + + align:start position:0% +these and Group B do these and group + + + align:start position:0% +these and Group B do these and group +grou C do these and a d group do those + + align:start position:0% + + + + align:start position:0% + +so break yourselves into four groups and + + align:start position:0% +so break yourselves into four groups and + + + align:start position:0% +so break yourselves into four groups and +we'll do a + + align:start position:0% + + + + align:start position:0% + +b c here in the center group here four + + align:start position:0% +b c here in the center group here four + + + align:start position:0% +b c here in the center group here four +five four five or group here the C group + + align:start position:0% +five four five or group here the C group + + + align:start position:0% +five four five or group here the C group +and D group over here okay do these + + align:start position:0% +and D group over here okay do these + + + align:start position:0% +and D group over here okay do these +calculations and let's get our two + + align:start position:0% +calculations and let's get our two + + + align:start position:0% +calculations and let's get our two +equations of motion and when you end up + + align:start position:0% +equations of motion and when you end up + + + align:start position:0% +equations of motion and when you end up +when you get your stuff done so the a + + align:start position:0% +when you get your stuff done so the a + + + align:start position:0% +when you get your stuff done so the a +group when you finish come up in right + + align:start position:0% +group when you finish come up in right + + + align:start position:0% +group when you finish come up in right +here right your stuff in the B group + + align:start position:0% +here right your stuff in the B group + + + align:start position:0% +here right your stuff in the B group +write your answer here the C group and + + align:start position:0% +write your answer here the C group and + + + align:start position:0% +write your answer here the C group and +the D group as soon as you get it done + + align:start position:0% +the D group as soon as you get it done + + + align:start position:0% +the D group as soon as you get it done +come up and put it + + align:start position:0% +come up and put it + + + align:start position:0% +come up and put it +down okay we + + align:start position:0% +down okay we + + + align:start position:0% +down okay we +got this term this term this term and + + align:start position:0% +got this term this term this term and + + + align:start position:0% +got this term this term this term and +this term + + align:start position:0% +this term + + + align:start position:0% +this term +okay did you guys check did you guys get + + align:start position:0% +okay did you guys check did you guys get + + + align:start position:0% +okay did you guys check did you guys get +a little time to the B group to check on + + align:start position:0% +a little time to the B group to check on + + + align:start position:0% +a little time to the B group to check on +the a + + align:start position:0% + + + + align:start position:0% + +group which one was it who's checking on + + align:start position:0% +group which one was it who's checking on + + + align:start position:0% +group which one was it who's checking on +whom here + + align:start position:0% +whom here + + + align:start position:0% +whom here +you're checking on it what do you + + align:start position:0% +you're checking on it what do you + + + align:start position:0% +you're checking on it what do you +think okay + + align:start position:0% +think okay + + + align:start position:0% +think okay +so main Mass + + align:start position:0% +so main Mass + + + align:start position:0% +so main Mass +acceleration the SEC second Mass it's + + align:start position:0% +acceleration the SEC second Mass it's + + + align:start position:0% +acceleration the SEC second Mass it's +total acceleration these + + align:start position:0% +total acceleration these + + + align:start position:0% +total acceleration these +pieces and there's an acceleration + + align:start position:0% +pieces and there's an acceleration + + + align:start position:0% +pieces and there's an acceleration +that's oil Arian and there's an + + align:start position:0% +that's oil Arian and there's an + + + align:start position:0% +that's oil Arian and there's an +acceleration that is what's this term + + align:start position:0% +acceleration that is what's this term + + + align:start position:0% +acceleration that is what's this term +related + + align:start position:0% +related + + + align:start position:0% +related +to you expect it to come up right okay + + align:start position:0% +to you expect it to come up right okay + + + align:start position:0% +to you expect it to come up right okay +and our KX term and all these are going + + align:start position:0% +and our KX term and all these are going + + + align:start position:0% +and our KX term and all these are going +to equal to the generalized forces of + + align:start position:0% +to equal to the generalized forces of + + + align:start position:0% +to equal to the generalized forces of +non any non-conservative forces so + + align:start position:0% +non any non-conservative forces so + + + align:start position:0% +non any non-conservative forces so +you're okay with this one let's move on + + align:start position:0% +you're okay with this one let's move on + + + align:start position:0% +you're okay with this one let's move on +to this one then uh who's the check + + align:start position:0% +to this one then uh who's the check + + + align:start position:0% +to this one then uh who's the check +group + + align:start position:0% +group + + + align:start position:0% +group +here what do you think I think they ter + + align:start position:0% +here what do you think I think they ter + + + align:start position:0% +here what do you think I think they ter +pardon you think there's a problem here + + align:start position:0% +pardon you think there's a problem here + + + align:start position:0% +pardon you think there's a problem here +um there might be all right um want it + + align:start position:0% +um there might be all right um want it + + + align:start position:0% +um there might be all right um want it +give me an alternative it may be that + + align:start position:0% +give me an alternative it may be that + + + align:start position:0% +give me an alternative it may be that +there DT D Theta there should be in the + + align:start position:0% +there DT D Theta there should be in the + + + align:start position:0% +there DT D Theta there should be in the +uh time derivative + + align:start position:0% + + + + align:start position:0% + +all right so we need D the the + + align:start position:0% +all right so we need D the the + + + align:start position:0% +all right so we need D the the +derivative of this with respect to Theta + + align:start position:0% + + + + align:start position:0% + +dot the first term doesn't give you + + align:start position:0% +dot the first term doesn't give you + + + align:start position:0% +dot the first term doesn't give you +anything right the MX do squ the second + + align:start position:0% +anything right the MX do squ the second + + + align:start position:0% +anything right the MX do squ the second +the third term gives you should give you + + align:start position:0% +the third term gives you should give you + + + align:start position:0% +the third term gives you should give you +an izz G Theta + + align:start position:0% +an izz G Theta + + + align:start position:0% +an izz G Theta +do theta double dot eventually right so + + align:start position:0% +do theta double dot eventually right so + + + align:start position:0% +do theta double dot eventually right so +for sure let's so this D by + + align:start position:0% + + + + align:start position:0% + +I DT the partial of t with respect to + + align:start position:0% +I DT the partial of t with respect to + + + align:start position:0% +I DT the partial of t with respect to +Theta dot so we just run through it the + + align:start position:0% +Theta dot so we just run through it the + + + align:start position:0% +Theta dot so we just run through it the +first term gives us nothing the second + + align:start position:0% +first term gives us nothing the second + + + align:start position:0% +first term gives us nothing the second +piece up there the third piece gives + + align:start position:0% +piece up there the third piece gives + + + align:start position:0% +piece up there the third piece gives +us with respect to Theta dot izz Theta + + align:start position:0% +us with respect to Theta dot izz Theta + + + align:start position:0% +us with respect to Theta dot izz Theta +Dot and no one wipes out the 1/2 the + + align:start position:0% +Dot and no one wipes out the 1/2 the + + + align:start position:0% +Dot and no one wipes out the 1/2 the +time derivative makes it Theta double + + align:start position:0% +time derivative makes it Theta double + + + align:start position:0% +time derivative makes it Theta double +dot so the third term is going to be an + + align:start position:0% +dot so the third term is going to be an + + + align:start position:0% +dot so the third term is going to be an +izz G Theta double dot and it's the + + align:start position:0% +izz G Theta double dot and it's the + + + align:start position:0% +izz G Theta double dot and it's the +second term that needs a derivative of + + align:start position:0% +second term that needs a derivative of + + + align:start position:0% +second term that needs a derivative of +this with respect to Theta + + align:start position:0% +this with respect to Theta + + + align:start position:0% +this with respect to Theta +dot + + align:start position:0% +dot + + + align:start position:0% +dot +okay + + align:start position:0% + + + + align:start position:0% + +so both terms are going to yield some + + align:start position:0% +so both terms are going to yield some + + + align:start position:0% +so both terms are going to yield some +stuff right a lot a lot of stuff okay + + align:start position:0% +stuff right a lot a lot of stuff okay + + + align:start position:0% +stuff right a lot a lot of stuff okay +all right I'm going to write down how + + align:start position:0% +all right I'm going to write down how + + + align:start position:0% +all right I'm going to write down how +this should work out rather than try to + + align:start position:0% +this should work out rather than try to + + + align:start position:0% +this should work out rather than try to +grind it out real time here + + align:start position:0% + + + + align:start position:0% + +all right ZZ + + align:start position:0% + + + + align:start position:0% + +all right these are the terms that + + align:start position:0% +all right these are the terms that + + + align:start position:0% +all right these are the terms that +should + + align:start position:0% +should + + + align:start position:0% +should +appear this is the piece about + + align:start position:0% +appear this is the piece about + + + align:start position:0% +appear this is the piece about +G this is + + align:start position:0% + + + + align:start position:0% + +the no that's not quite + + align:start position:0% + + + + align:start position:0% + +right that's the piece about G this + + align:start position:0% +right that's the piece about G this + + + align:start position:0% +right that's the piece about G this +should be about + + align:start position:0% + + + + align:start position:0% + +right and then this + + align:start position:0% + + + + align:start position:0% + +term that's how it actually should check + + align:start position:0% +term that's how it actually should check + + + align:start position:0% +term that's how it actually should check +out do you agree with me yeah that looks + + align:start position:0% +out do you agree with me yeah that looks + + + align:start position:0% +out do you agree with me yeah that looks +okay and then if we add to that the + + align:start position:0% + + + + align:start position:0% + +m2g l/ 2 sin Theta which is our + + align:start position:0% +m2g l/ 2 sin Theta which is our + + + align:start position:0% +m2g l/ 2 sin Theta which is our +gravitational potential energy all of + + align:start position:0% +gravitational potential energy all of + + + align:start position:0% +gravitational potential energy all of +that added together ought to be equal to + + align:start position:0% +that added together ought to be equal to + + + align:start position:0% +that added together ought to be equal to +Q Theta + + align:start position:0% +Q Theta + + + align:start position:0% +Q Theta +right so let's move on to looking at the + + align:start position:0% +right so let's move on to looking at the + + + align:start position:0% +right so let's move on to looking at the +generalized forces for this problem so I + + align:start position:0% +generalized forces for this problem so I + + + align:start position:0% +generalized forces for this problem so I +don't know where you guys + + align:start position:0% +don't know where you guys + + + align:start position:0% +don't know where you guys +went wrong on + + align:start position:0% +went wrong on + + + align:start position:0% +went wrong on +this but you have any + + align:start position:0% +this but you have any + + + align:start position:0% +this but you have any +question we can talk about this for a + + align:start position:0% +question we can talk about this for a + + + align:start position:0% +question we can talk about this for a +minute what what what + + align:start position:0% +minute what what what + + + align:start position:0% +minute what what what +your + + align:start position:0% +your + + + align:start position:0% +your +pardon d t d Theta so + + align:start position:0% +pardon d t d Theta so + + + align:start position:0% +pardon d t d Theta so +your final answer you got to take the + + align:start position:0% +your final answer you got to take the + + + align:start position:0% +your final answer you got to take the +partial derivative of this expression + + align:start position:0% +partial derivative of this expression + + + align:start position:0% +partial derivative of this expression +with respect to Theta dot this piece + + align:start position:0% +with respect to Theta dot this piece + + + align:start position:0% +with respect to Theta dot this piece +gives you a contribution right that will + + align:start position:0% +gives you a contribution right that will + + + align:start position:0% +gives you a contribution right that will +be izz Theta dot then you take its time + + align:start position:0% +be izz Theta dot then you take its time + + + align:start position:0% +be izz Theta dot then you take its time +derivative so that's pretty obvious why + + align:start position:0% +derivative so that's pretty obvious why + + + align:start position:0% +derivative so that's pretty obvious why +where why it gives you the first piece + + align:start position:0% +where why it gives you the first piece + + + align:start position:0% +where why it gives you the first piece +right I think the problem understanding + + align:start position:0% +right I think the problem understanding + + + align:start position:0% +right I think the problem understanding +the first place that D and it should + + align:start position:0% +the first place that D and it should + + + align:start position:0% +the first place that D and it should +have d dot oh + + align:start position:0% + + + + align:start position:0% + +first one but where's your like second + + align:start position:0% +first one but where's your like second + + + align:start position:0% +first one but where's your like second +okay then the second one when you take + + align:start position:0% +okay then the second one when you take + + + align:start position:0% +okay then the second one when you take +the derivative of this expression with + + align:start position:0% +the derivative of this expression with + + + align:start position:0% +the derivative of this expression with +respect to this is T with respect to + + align:start position:0% +respect to this is T with respect to + + + align:start position:0% +respect to this is T with respect to +Theta dot of this part this expression + + align:start position:0% +Theta dot of this part this expression + + + align:start position:0% +Theta dot of this part this expression +you get two times what's + + align:start position:0% +you get two times what's + + + align:start position:0% +you get two times what's +inside times the derivative of the + + align:start position:0% +inside times the derivative of the + + + align:start position:0% +inside times the derivative of the +inside with respect + + align:start position:0% +inside with respect + + + align:start position:0% +inside with respect +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +to uh Theta Dot and that'll give you + + align:start position:0% +to uh Theta Dot and that'll give you + + + align:start position:0% +to uh Theta Dot and that'll give you +another l over2 + + align:start position:0% + + + + align:start position:0% + +cosine Theta and I think you're done + + align:start position:0% +cosine Theta and I think you're done + + + align:start position:0% +cosine Theta and I think you're done +it's this times this stuff + + align:start position:0% +it's this times this stuff + + + align:start position:0% +it's this times this stuff +right 2 * this times the derivative of + + align:start position:0% +right 2 * this times the derivative of + + + align:start position:0% +right 2 * this times the derivative of +the inside which is well the derivative + + align:start position:0% +the inside which is well the derivative + + + align:start position:0% +the inside which is well the derivative +of the inside with respect to Theta dot + + align:start position:0% +of the inside with respect to Theta dot + + + align:start position:0% +of the inside with respect to Theta dot +should be L over2 cosine + + align:start position:0% +should be L over2 cosine + + + align:start position:0% +should be L over2 cosine +Theta so you get an x dot plus l/ 2 + + align:start position:0% +Theta so you get an x dot plus l/ 2 + + + align:start position:0% +Theta so you get an x dot plus l/ 2 +Theta dot cosine + + align:start position:0% +Theta dot cosine + + + align:start position:0% +Theta dot cosine +Theta 2 * that * + + align:start position:0% +Theta 2 * that * + + + align:start position:0% +Theta 2 * that * +the derivative of the inside with + + align:start position:0% +the derivative of the inside with + + + align:start position:0% +the derivative of the inside with +respect to Theta dot this is the only + + align:start position:0% +respect to Theta dot this is the only + + + align:start position:0% +respect to Theta dot this is the only +term that contributes is that and then + + align:start position:0% +term that contributes is that and then + + + align:start position:0% +term that contributes is that and then +you do the we've already done the + + align:start position:0% +you do the we've already done the + + + align:start position:0% +you do the we've already done the +derivative of this with respect to Theta + + align:start position:0% +derivative of this with respect to Theta + + + align:start position:0% +derivative of this with respect to Theta +dot wait a minute we haven't this one + + align:start position:0% +dot wait a minute we haven't this one + + + align:start position:0% +dot wait a minute we haven't this one +now we got another term here so this one + + align:start position:0% +now we got another term here so this one + + + align:start position:0% +now we got another term here so this one +gives you two + + align:start position:0% +gives you two + + + align:start position:0% +gives you two +times the expression times the the uh + + align:start position:0% + + + + align:start position:0% + +will give + + align:start position:0% +will give + + + align:start position:0% +will give +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +you Theta L Theta do sin Theta but now + + align:start position:0% +you Theta L Theta do sin Theta but now + + + align:start position:0% +you Theta L Theta do sin Theta but now +you have to take the derivative with + + align:start position:0% +you have to take the derivative with + + + align:start position:0% +you have to take the derivative with +respect to Theta + + align:start position:0% + + + + align:start position:0% + +dot which gives you + + align:start position:0% + + + + align:start position:0% + +what another L over 2 sin + + align:start position:0% + + + + align:start position:0% + +Theta comes out something like + + align:start position:0% +Theta comes out something like + + + align:start position:0% +Theta comes out something like +this so you end up with a Theta dot L + + align:start position:0% +this so you end up with a Theta dot L + + + align:start position:0% +this so you end up with a Theta dot L +over l^2 2 L Theta l^2 sin^2 and you + + align:start position:0% +over l^2 2 L Theta l^2 sin^2 and you + + + align:start position:0% +over l^2 2 L Theta l^2 sin^2 and you +probably get a Theta do l^2 cosine 2 + + align:start position:0% +probably get a Theta do l^2 cosine 2 + + + align:start position:0% +probably get a Theta do l^2 cosine 2 +over here and those two add together to + + align:start position:0% +over here and those two add together to + + + align:start position:0% +over here and those two add together to +give you a Theta dot l^2 + + align:start position:0% + + + + align:start position:0% + +over theta. l^2 I guess those collapse + + align:start position:0% +over theta. l^2 I guess those collapse + + + align:start position:0% +over theta. l^2 I guess those collapse +together and you end that's those come + + align:start position:0% +together and you end that's those come + + + align:start position:0% +together and you end that's those come +together to give you the other + + align:start position:0% +together to give you the other + + + align:start position:0% +together to give you the other +piece of this yeah we got that ter we + + align:start position:0% +piece of this yeah we got that ter we + + + align:start position:0% +piece of this yeah we got that ter we +just mess up one of the coefficients but + + align:start position:0% +just mess up one of the coefficients but + + + align:start position:0% +just mess up one of the coefficients but +where is like just don't have to do that + + align:start position:0% +where is like just don't have to do that + + + align:start position:0% +where is like just don't have to do that +no the derivative respected Theta only + + align:start position:0% +no the derivative respected Theta only + + + align:start position:0% +no the derivative respected Theta only +comes in in the potential energy + + align:start position:0% +comes in in the potential energy + + + align:start position:0% +comes in in the potential energy +term so what about number two like isn't + + align:start position:0% +term so what about number two like isn't + + + align:start position:0% +term so what about number two like isn't +that one just oh okay all right yep you + + align:start position:0% +that one just oh okay all right yep you + + + align:start position:0% +that one just oh okay all right yep you +need that and so t with respect to Theta + + align:start position:0% +need that and so t with respect to Theta + + + align:start position:0% +need that and so t with respect to Theta +yeah you have do have and you do have + + align:start position:0% +yeah you have do have and you do have + + + align:start position:0% +yeah you have do have and you do have +Theta pieces in there and it does kick + + align:start position:0% +Theta pieces in there and it does kick + + + align:start position:0% +Theta pieces in there and it does kick +out more pieces yeah did you put that + + align:start position:0% +out more pieces yeah did you put that + + + align:start position:0% +out more pieces yeah did you put that +one in here yet no I didn't haven't even + + align:start position:0% +one in here yet no I didn't haven't even + + + align:start position:0% +one in here yet no I didn't haven't even +done that piece yet okay so you do that + + align:start position:0% +done that piece yet okay so you do that + + + align:start position:0% +done that piece yet okay so you do that +piece a couple of things + + align:start position:0% +piece a couple of things + + + align:start position:0% +piece a couple of things +cancel and you end up + + align:start position:0% +cancel and you end up + + + align:start position:0% +cancel and you end up +with so rather than I don't have time to + + align:start position:0% +with so rather than I don't have time to + + + align:start position:0% +with so rather than I don't have time to +work it out to write it all up on the + + align:start position:0% +work it out to write it all up on the + + + align:start position:0% +work it out to write it all up on the +board but the complete solution for this + + align:start position:0% +board but the complete solution for this + + + align:start position:0% +board but the complete solution for this +is + + align:start position:0% +is + + + align:start position:0% +is +posted you know so all the the professor + + align:start position:0% +posted you know so all the the professor + + + align:start position:0% +posted you know so all the the professor +Gossard who teaches three of the other + + align:start position:0% +Gossard who teaches three of the other + + + align:start position:0% +Gossard who teaches three of the other +three recitation sections uh writes + + align:start position:0% +three recitation sections uh writes + + + align:start position:0% +three recitation sections uh writes +these up and posts the answers and so + + align:start position:0% +these up and posts the answers and so + + + align:start position:0% +these up and posts the answers and so +they're on Stellar so you get the the + + align:start position:0% +they're on Stellar so you get the the + + + align:start position:0% +they're on Stellar so you get the the +Gory details of each of these pieces + + align:start position:0% +Gory details of each of these pieces + + + align:start position:0% +Gory details of each of these pieces +okay let's go on to + + align:start position:0% +okay let's go on to + + + align:start position:0% +okay let's go on to +uh talk about + + align:start position:0% +uh talk about + + + align:start position:0% +uh talk about +generalized forces while we have a few + + align:start position:0% +generalized forces while we have a few + + + align:start position:0% +generalized forces while we have a few +minutes in this the way it was set up + + align:start position:0% +minutes in this the way it was set up + + + align:start position:0% +minutes in this the way it was set up +were there what are the right hand sides + + align:start position:0% +were there what are the right hand sides + + + align:start position:0% +were there what are the right hand sides +are there any general for generalized + + align:start position:0% +are there any general for generalized + + + align:start position:0% +are there any general for generalized +external non-conservative forces the way + + align:start position:0% +external non-conservative forces the way + + + align:start position:0% +external non-conservative forces the way +the problem was first + + align:start position:0% +the problem was first + + + align:start position:0% +the problem was first +posed none okay so let's put in a couple + + align:start position:0% +posed none okay so let's put in a couple + + + align:start position:0% +posed none okay so let's put in a couple +let's add a + + align:start position:0% +let's add a + + + align:start position:0% +let's add a +dashbot b here and an external Force + + align:start position:0% +dashbot b here and an external Force + + + align:start position:0% +dashbot b here and an external Force +here call it F1 of t + + align:start position:0% +here call it F1 of t + + + align:start position:0% +here call it F1 of t +so now what's Q QX and Q + + align:start position:0% +so now what's Q QX and Q + + + align:start position:0% +so now what's Q QX and Q +Theta which we'll + + align:start position:0% + + + + align:start position:0% + +uh that's an exercise I think you can + + align:start position:0% +uh that's an exercise I think you can + + + align:start position:0% +uh that's an exercise I think you can +all go through but just check with your + + align:start position:0% +all go through but just check with your + + + align:start position:0% +all go through but just check with your +groups figure out the generalized + + align:start position:0% +groups figure out the generalized + + + align:start position:0% +groups figure out the generalized +forces and do it you know do it by + + align:start position:0% +forces and do it you know do it by + + + align:start position:0% +forces and do it you know do it by +imagining as for this one for the X + + align:start position:0% +imagining as for this one for the X + + + align:start position:0% +imagining as for this one for the X +equation say okay you have a small + + align:start position:0% +equation say okay you have a small + + + align:start position:0% +equation say okay you have a small +virtual displacement Delta X what's + + align:start position:0% +virtual displacement Delta X what's + + + align:start position:0% +virtual displacement Delta X what's +virtual work that's done Delta W then + + align:start position:0% +virtual work that's done Delta W then + + + align:start position:0% +virtual work that's done Delta W then +will be uh thing you're looking for + + align:start position:0% +will be uh thing you're looking for + + + align:start position:0% +will be uh thing you're looking for +Delta X and the same thing with the this + + align:start position:0% +Delta X and the same thing with the this + + + align:start position:0% +Delta X and the same thing with the this +is the Theta one I mean the X1 and you + + align:start position:0% +is the Theta one I mean the X1 and you + + + align:start position:0% +is the Theta one I mean the X1 and you +get a similar X thing when you do the + + align:start position:0% +get a similar X thing when you do the + + + align:start position:0% +get a similar X thing when you do the +one for Theta it would be Q Theta Delta + + align:start position:0% +one for Theta it would be Q Theta Delta + + + align:start position:0% +one for Theta it would be Q Theta Delta +Theta figure out the work done and + + align:start position:0% +Theta figure out the work done and + + + align:start position:0% +Theta figure out the work done and +that'll tell you what QX and Q Theta + + align:start position:0% +that'll tell you what QX and Q Theta + + + align:start position:0% +that'll tell you what QX and Q Theta +are so the total work of the + + align:start position:0% +are so the total work of the + + + align:start position:0% +are so the total work of the +non-conservative + + align:start position:0% +non-conservative + + + align:start position:0% +non-conservative +forces through these virtual + + align:start position:0% +forces through these virtual + + + align:start position:0% +forces through these virtual +displacements you can just add them up + + align:start position:0% +displacements you can just add them up + + + align:start position:0% +displacements you can just add them up +so there's a contribution that comes + + align:start position:0% +so there's a contribution that comes + + + align:start position:0% +so there's a contribution that comes +from a Delta X and there'll be another + + align:start position:0% +from a Delta X and there'll be another + + + align:start position:0% +from a Delta X and there'll be another +contribution from the Delta Theta and we + + align:start position:0% +contribution from the Delta Theta and we + + + align:start position:0% +contribution from the Delta Theta and we +can figure out each piece and you assign + + align:start position:0% +can figure out each piece and you assign + + + align:start position:0% +can figure out each piece and you assign +each piece to the equation it goes with + + align:start position:0% +each piece to the equation it goes with + + + align:start position:0% +each piece to the equation it goes with +so what is the if you do a small virtual + + align:start position:0% +so what is the if you do a small virtual + + + align:start position:0% +so what is the if you do a small virtual +deflection in the X + + align:start position:0% +deflection in the X + + + align:start position:0% +deflection in the X +Direction how much work is + + align:start position:0% +Direction how much work is + + + align:start position:0% +Direction how much work is +done give me a term + + align:start position:0% + + + + align:start position:0% + +here so work remember is + + align:start position:0% +here so work remember is + + + align:start position:0% +here so work remember is +f.d. drr and this Dr is a function of + + align:start position:0% +f.d. drr and this Dr is a function of + + + align:start position:0% +f.d. drr and this Dr is a function of +our Delta x's and Delta thetas and so + + align:start position:0% +our Delta x's and Delta thetas and so + + + align:start position:0% +our Delta x's and Delta thetas and so +forth + + align:start position:0% + + + + align:start position:0% + +yeah DX Delta X yeah would be that'll be + + align:start position:0% +yeah DX Delta X yeah would be that'll be + + + align:start position:0% +yeah DX Delta X yeah would be that'll be +some work done so the for that Force + + align:start position:0% +some work done so the for that Force + + + align:start position:0% +some work done so the for that Force +external Force moves through the full + + align:start position:0% +external Force moves through the full + + + align:start position:0% +external Force moves through the full +Delta X huh okay and what else + + align:start position:0% +Delta X huh okay and what else + + + align:start position:0% +Delta X huh okay and what else +minus Del okay so that suggests then we + + align:start position:0% +minus Del okay so that suggests then we + + + align:start position:0% +minus Del okay so that suggests then we +have here this is F1 of T in the + + align:start position:0% +have here this is F1 of T in the + + + align:start position:0% +have here this is F1 of T in the +positive I Direction minus + + align:start position:0% +positive I Direction minus + + + align:start position:0% +positive I Direction minus +BX dot in the opposite direction times + + align:start position:0% +BX dot in the opposite direction times + + + align:start position:0% +BX dot in the opposite direction times +Delta X is a virtual work done by as you + + align:start position:0% +Delta X is a virtual work done by as you + + + align:start position:0% +Delta X is a virtual work done by as you +do that okay now how about the Delta + + align:start position:0% + + + + align:start position:0% + +Theta somebody else here how much + + align:start position:0% +Theta somebody else here how much + + + align:start position:0% +Theta somebody else here how much +virtual work is done by these forces F + + align:start position:0% +virtual work is done by these forces F + + + align:start position:0% +virtual work is done by these forces F +and minus BX so the only + + align:start position:0% +and minus BX so the only + + + align:start position:0% +and minus BX so the only +non-conservative external forces in the + + align:start position:0% +non-conservative external forces in the + + + align:start position:0% +non-conservative external forces in the +problem are the dashbot and that F + + align:start position:0% +problem are the dashbot and that F + + + align:start position:0% +problem are the dashbot and that F +whatever it is how much work is done by + + align:start position:0% +whatever it is how much work is done by + + + align:start position:0% +whatever it is how much work is done by +those forces in a virtual displacement + + align:start position:0% +those forces in a virtual displacement + + + align:start position:0% +those forces in a virtual displacement +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +Theta that a hand up back + + align:start position:0% +Theta that a hand up back + + + align:start position:0% +Theta that a hand up back +there I hear a bid for zero what do + + align:start position:0% +there I hear a bid for zero what do + + + align:start position:0% +there I hear a bid for zero what do +other people + + align:start position:0% +other people + + + align:start position:0% +other people +think do those forces move at all + + align:start position:0% +think do those forces move at all + + + align:start position:0% +think do those forces move at all +because you make a motion Delta Theta is + + align:start position:0% +because you make a motion Delta Theta is + + + align:start position:0% +because you make a motion Delta Theta is +there any Dr here that results because + + align:start position:0% +there any Dr here that results because + + + align:start position:0% +there any Dr here that results because +of Delta Theta in the direction of any + + align:start position:0% +of Delta Theta in the direction of any + + + align:start position:0% +of Delta Theta in the direction of any +of these applied forces at the point of + + align:start position:0% +of these applied forces at the point of + + + align:start position:0% +of these applied forces at the point of +application of these forces do they move + + align:start position:0% +application of these forces do they move + + + align:start position:0% +application of these forces do they move +so this force is right here does it move + + align:start position:0% +so this force is right here does it move + + + align:start position:0% +so this force is right here does it move +because you do Delta Theta nope and this + + align:start position:0% +because you do Delta Theta nope and this + + + align:start position:0% +because you do Delta Theta nope and this +Force it's applied right here does that + + align:start position:0% +Force it's applied right here does that + + + align:start position:0% +Force it's applied right here does that +point move because of Delta Theta no so + + align:start position:0% +point move because of Delta Theta no so + + + align:start position:0% +point move because of Delta Theta no so +in this problem then this piece here is + + align:start position:0% +in this problem then this piece here is + + + align:start position:0% +in this problem then this piece here is +z Delta Theta and total virtual work + + align:start position:0% +z Delta Theta and total virtual work + + + align:start position:0% +z Delta Theta and total virtual work +done as that and you assign each piece + + align:start position:0% +done as that and you assign each piece + + + align:start position:0% +done as that and you assign each piece +to its appropriate equation so QX this + + align:start position:0% +to its appropriate equation so QX this + + + align:start position:0% +to its appropriate equation so QX this +is QX right + + align:start position:0% +is QX right + + + align:start position:0% +is QX right +here Delta X QX + + align:start position:0% +here Delta X QX + + + align:start position:0% +here Delta X QX +belongs up here these some of these + + align:start position:0% +belongs up here these some of these + + + align:start position:0% +belongs up here these some of these +things equals QX and in the second case + + align:start position:0% +things equals QX and in the second case + + + align:start position:0% +things equals QX and in the second case +for the beta equation it's equal to zero + + align:start position:0% +for the beta equation it's equal to zero + + + align:start position:0% +for the beta equation it's equal to zero +so let's make it problem a little bit + + align:start position:0% +so let's make it problem a little bit + + + align:start position:0% +so let's make it problem a little bit +harder for a second let's + + align:start position:0% +harder for a second let's + + + align:start position:0% +harder for a second let's +put a force + + align:start position:0% +put a force + + + align:start position:0% +put a force +um apply a horizontal Force here we'll + + align:start position:0% +um apply a horizontal Force here we'll + + + align:start position:0% +um apply a horizontal Force here we'll +call this + + align:start position:0% + + + + align:start position:0% + +FS2 so + + align:start position:0% +FS2 so + + + align:start position:0% +FS2 so +now what is the + + align:start position:0% +now what is the + + + align:start position:0% +now what is the +work + + align:start position:0% +work + + + align:start position:0% +work +done in this system we now have an + + align:start position:0% +done in this system we now have an + + + align:start position:0% +done in this system we now have an +additional Force what's what's is there + + align:start position:0% +additional Force what's what's is there + + + align:start position:0% +additional Force what's what's is there +any work done because of Delta + + align:start position:0% + + + + align:start position:0% + +X this is the + + align:start position:0% +X this is the + + + align:start position:0% +X this is the +real you understand this this problem + + align:start position:0% +real you understand this this problem + + + align:start position:0% +real you understand this this problem +this piece then you're really beginning + + align:start position:0% +this piece then you're really beginning + + + align:start position:0% +this piece then you're really beginning +to understand how you do these + + align:start position:0% +to understand how you do these + + + align:start position:0% +to understand how you do these +generalized + + align:start position:0% +generalized + + + align:start position:0% +generalized +forces QX Delta X is there is the the + + align:start position:0% +forces QX Delta X is there is the the + + + align:start position:0% +forces QX Delta X is there is the the +generalized Force + + align:start position:0% +generalized Force + + + align:start position:0% +generalized Force +associated with Delta X is it affected + + align:start position:0% +associated with Delta X is it affected + + + align:start position:0% +associated with Delta X is it affected +by this new force does there any work + + align:start position:0% +by this new force does there any work + + + align:start position:0% +by this new force does there any work +done so I now cause this little Delta X + + align:start position:0% +done so I now cause this little Delta X + + + align:start position:0% +done so I now cause this little Delta X +to + + align:start position:0% +to + + + align:start position:0% +to +happen does that Force do any + + align:start position:0% +happen does that Force do any + + + align:start position:0% +happen does that Force do any +work assuming all no + + align:start position:0% +work assuming all no + + + align:start position:0% +work assuming all no +other deflections are happen right now + + align:start position:0% +other deflections are happen right now + + + align:start position:0% +other deflections are happen right now +right + + align:start position:0% + + + + align:start position:0% + +why it's almost rigid so is there yeah + + align:start position:0% +why it's almost rigid so is there yeah + + + align:start position:0% +why it's almost rigid so is there yeah +it means is not it's not allowed to move + + align:start position:0% +it means is not it's not allowed to move + + + align:start position:0% +it means is not it's not allowed to move +whatever instantaneous position it in + + align:start position:0% +whatever instantaneous position it in + + + align:start position:0% +whatever instantaneous position it in +it's frozen there and in its coordinate + + align:start position:0% +it's frozen there and in its coordinate + + + align:start position:0% +it's frozen there and in its coordinate +but if there's an X component it can it + + align:start position:0% +but if there's an X component it can it + + + align:start position:0% +but if there's an X component it can it +moves an X so it's angled like this off + + align:start position:0% +moves an X so it's angled like this off + + + align:start position:0% +moves an X so it's angled like this off +the cart but now Delta X does this to it + + align:start position:0% +the cart but now Delta X does this to it + + + align:start position:0% +the cart but now Delta X does this to it +does that Force F do any work how + + align:start position:0% + + + + align:start position:0% + +much okay so + + align:start position:0% +much okay so + + + align:start position:0% +much okay so +then when you add that one to it we end + + align:start position:0% +then when you add that one to it we end + + + align:start position:0% +then when you add that one to it we end +up with a and it's it in plus Direction + + align:start position:0% +up with a and it's it in plus Direction + + + align:start position:0% +up with a and it's it in plus Direction +and it's exactly in the same direction + + align:start position:0% +and it's exactly in the same direction + + + align:start position:0% +and it's exactly in the same direction +as Delta X there's no components it's + + align:start position:0% +as Delta X there's no components it's + + + align:start position:0% +as Delta X there's no components it's +fully it counts the dotproduct of F2 is + + align:start position:0% +fully it counts the dotproduct of F2 is + + + align:start position:0% +fully it counts the dotproduct of F2 is +in the I Direction dot Delta X which is + + align:start position:0% +in the I Direction dot Delta X which is + + + align:start position:0% +in the I Direction dot Delta X which is +also in the I so you get an additional + + align:start position:0% +also in the I so you get an additional + + + align:start position:0% +also in the I so you get an additional +contribution of F2 Delta X and so now + + align:start position:0% +contribution of F2 Delta X and so now + + + align:start position:0% +contribution of F2 Delta X and so now +this generalized Force has an F2 in it + + align:start position:0% +this generalized Force has an F2 in it + + + align:start position:0% +this generalized Force has an F2 in it +how about the other direction though how + + align:start position:0% +how about the other direction though how + + + align:start position:0% +how about the other direction though how +about the uh this now Q Theta Delta + + align:start position:0% +about the uh this now Q Theta Delta + + + align:start position:0% +about the uh this now Q Theta Delta +Theta what does it give you + + align:start position:0% + + + + align:start position:0% + +so now if you now freeze + + align:start position:0% +so now if you now freeze + + + align:start position:0% +so now if you now freeze +X and allow a slight angular variation + + align:start position:0% +X and allow a slight angular variation + + + align:start position:0% +X and allow a slight angular variation +Delta Theta does this guy do any work + + align:start position:0% +Delta Theta does this guy do any work + + + align:start position:0% +Delta Theta does this guy do any work +okay how how much and is it is it F2 + + align:start position:0% +okay how how much and is it is it F2 + + + align:start position:0% +okay how how much and is it is it F2 +Delta + + align:start position:0% + + + + align:start position:0% + +Theta that's wrong in two ways + + align:start position:0% +Theta that's wrong in two ways + + + align:start position:0% +Theta that's wrong in two ways +dimensions are + + align:start position:0% +dimensions are + + + align:start position:0% +dimensions are +wrong something else is wrong so let's + + align:start position:0% +wrong something else is wrong so let's + + + align:start position:0% +wrong something else is wrong so let's +draw it here's this thing here's FS2 + + align:start position:0% +draw it here's this thing here's FS2 + + + align:start position:0% +draw it here's this thing here's FS2 +Delta Theta causes a motion of this + + align:start position:0% +Delta Theta causes a motion of this + + + align:start position:0% +Delta Theta causes a motion of this +point in what + + align:start position:0% +point in what + + + align:start position:0% +point in what +direction kind of perpendicular to this + + align:start position:0% +direction kind of perpendicular to this + + + align:start position:0% +direction kind of perpendicular to this +right so you can think of it like this + + align:start position:0% +right so you can think of it like this + + + align:start position:0% +right so you can think of it like this +and this would be L Delta Theta is the + + align:start position:0% +and this would be L Delta Theta is the + + + align:start position:0% +and this would be L Delta Theta is the +actual distance that it + + align:start position:0% +actual distance that it + + + align:start position:0% +actual distance that it +moves right and so you can either say + + align:start position:0% +moves right and so you can either say + + + align:start position:0% +moves right and so you can either say +the component of that motion in the + + align:start position:0% +the component of that motion in the + + + align:start position:0% +the component of that motion in the +direction of the force or you can say + + align:start position:0% +direction of the force or you can say + + + align:start position:0% +direction of the force or you can say +the component of the force in the + + align:start position:0% +the component of the force in the + + + align:start position:0% +the component of the force in the +direction of that motion we on a DOT + + align:start position:0% +direction of that motion we on a DOT + + + align:start position:0% +direction of that motion we on a DOT +product between this and that and this + + align:start position:0% +product between this and that and this + + + align:start position:0% +product between this and that and this +is + + align:start position:0% +is + + + align:start position:0% +is +Theta so what is the component of L + + align:start position:0% +Theta so what is the component of L + + + align:start position:0% +Theta so what is the component of L +Delta Theta in the direction of the + + align:start position:0% +Delta Theta in the direction of the + + + align:start position:0% +Delta Theta in the direction of the +force that's this right + + align:start position:0% + + + + align:start position:0% + +here and that's now in the I hat dot + + align:start position:0% +here and that's now in the I hat dot + + + align:start position:0% +here and that's now in the I hat dot +F2 + + align:start position:0% +F2 + + + align:start position:0% +F2 +I so + + align:start position:0% +I so + + + align:start position:0% +I so +our Delta W in the Theta direction is Q + + align:start position:0% +our Delta W in the Theta direction is Q + + + align:start position:0% +our Delta W in the Theta direction is Q +Theta + + align:start position:0% +Theta + + + align:start position:0% +Theta +Delta theta equals my + + align:start position:0% +Delta theta equals my + + + align:start position:0% +Delta theta equals my +F2 + + align:start position:0% +F2 + + + align:start position:0% +F2 +L cine Theta Delta + + align:start position:0% +L cine Theta Delta + + + align:start position:0% +L cine Theta Delta +Theta and to solve for Q Theta now these + + align:start position:0% +Theta and to solve for Q Theta now these + + + align:start position:0% +Theta and to solve for Q Theta now these +can disappear and Q Theta is f2l cosine + + align:start position:0% +can disappear and Q Theta is f2l cosine + + + align:start position:0% +can disappear and Q Theta is f2l cosine +Theta are the units right what are the + + align:start position:0% +Theta are the units right what are the + + + align:start position:0% +Theta are the units right what are the +units of this generalized Force meaning + + align:start position:0% +units of this generalized Force meaning + + + align:start position:0% +units of this generalized Force meaning +go you got to think about that equation + + align:start position:0% +go you got to think about that equation + + + align:start position:0% +go you got to think about that equation +the Theta equation we talked about this + + align:start position:0% +the Theta equation we talked about this + + + align:start position:0% +the Theta equation we talked about this +before has units of what + + align:start position:0% + + + + align:start position:0% + +okay what are the dimensions of that of + + align:start position:0% +okay what are the dimensions of that of + + + align:start position:0% +okay what are the dimensions of that of +a term that looks like + + align:start position:0% +a term that looks like + + + align:start position:0% +a term that looks like +that this comes from you do it the + + align:start position:0% +that this comes from you do it the + + + align:start position:0% +that this comes from you do it the +direct way the summation of external Tor + + align:start position:0% +direct way the summation of external Tor + + + align:start position:0% +direct way the summation of external Tor +Tor this better have units of torque + + align:start position:0% +Tor this better have units of torque + + + align:start position:0% +Tor this better have units of torque +right which is units of force times + + align:start position:0% +right which is units of force times + + + align:start position:0% +right which is units of force times +distance so Force time distance it + + align:start position:0% +distance so Force time distance it + + + align:start position:0% +distance so Force time distance it +better be the units of this this + + align:start position:0% +better be the units of this this + + + align:start position:0% +better be the units of this this +equation and therefore that it better be + + align:start position:0% +equation and therefore that it better be + + + align:start position:0% +equation and therefore that it better be +a torque is force time length the torque + + align:start position:0% +a torque is force time length the torque + + + align:start position:0% +a torque is force time length the torque +have units of torque sure so that's the + + align:start position:0% +have units of torque sure so that's the + + + align:start position:0% +have units of torque sure so that's the +correct + + align:start position:0% +correct + + + align:start position:0% +correct +units and over here for the X equation + + align:start position:0% +units and over here for the X equation + + + align:start position:0% +units and over here for the X equation +do we come out with the correct + + align:start position:0% +do we come out with the correct + + + align:start position:0% +do we come out with the correct +unit yep comes out force and this + + align:start position:0% +unit yep comes out force and this + + + align:start position:0% +unit yep comes out force and this +naturally works because Delta Theta is + + align:start position:0% +naturally works because Delta Theta is + + + align:start position:0% +naturally works because Delta Theta is +dimensionless so the length the Dr the + + align:start position:0% +dimensionless so the length the Dr the + + + align:start position:0% +dimensionless so the length the Dr the +the length piece that comes in here + + align:start position:0% +the length piece that comes in here + + + align:start position:0% +the length piece that comes in here +stays with this to give you a torque + + align:start position:0% +stays with this to give you a torque + + + align:start position:0% +stays with this to give you a torque +over here Delta X has length in it and + + align:start position:0% +over here Delta X has length in it and + + + align:start position:0% +over here Delta X has length in it and +you're just left with the force so you + + align:start position:0% +you're just left with the force so you + + + align:start position:0% +you're just left with the force so you +get a force force ex this generalized + + align:start position:0% +get a force force ex this generalized + + + align:start position:0% +get a force force ex this generalized +Force for the X direction is a force the + + align:start position:0% +Force for the X direction is a force the + + + align:start position:0% +Force for the X direction is a force the +generalized force in the Theta direction + + align:start position:0% +generalized force in the Theta direction + + + align:start position:0% +generalized force in the Theta direction +is a moment a + + align:start position:0% +is a moment a + + + align:start position:0% +is a moment a +torque all right + + align:start position:0% +torque all right + + + align:start position:0% +torque all right +good + + align:start position:0% +good + + + align:start position:0% +good +so we're officially done but if you have + + align:start position:0% +so we're officially done but if you have + + + align:start position:0% +so we're officially done but if you have +any want last questions on this I'll + + align:start position:0% +any want last questions on this I'll + + + align:start position:0% +any want last questions on this I'll +stick around and we can chat about it \ No newline at end of file diff --git a/-pMowqywuIY.txt b/-pMowqywuIY.txt new file mode 100644 index 0000000000000000000000000000000000000000..6038da08c2f271d92def1b4220c1aaec77d1ed07 --- /dev/null +++ b/-pMowqywuIY.txt @@ -0,0 +1,619 @@ +align:start position:0% + +the left-hand side here is 0 because H 0 + + align:start position:0% +the left-hand side here is 0 because H 0 + + + align:start position:0% +the left-hand side here is 0 because H 0 +and 0 by taking the eigen state equation + + align:start position:0% +and 0 by taking the eigen state equation + + + align:start position:0% +and 0 by taking the eigen state equation +is equal to en 0 times and 0 so this + + align:start position:0% +is equal to en 0 times and 0 so this + + + align:start position:0% +is equal to en 0 times and 0 so this +really evaluates to en 0 and therefore + + align:start position:0% +really evaluates to en 0 and therefore + + + align:start position:0% +really evaluates to en 0 and therefore +the 2 cancels so this thing is 0 the + + align:start position:0% +the 2 cancels so this thing is 0 the + + + align:start position:0% +the 2 cancels so this thing is 0 the +right hand side this is a number + + align:start position:0% +right hand side this is a number + + + align:start position:0% +right hand side this is a number +en 1 it's a number it's in an + + align:start position:0% +en 1 it's a number it's in an + + + align:start position:0% +en 1 it's a number it's in an +expectation value n 0 has unit + + align:start position:0% +expectation value n 0 has unit + + + align:start position:0% +expectation value n 0 has unit +expectation value so this is e + 1 + + align:start position:0% +expectation value so this is e + 1 + + + align:start position:0% +expectation value so this is e + 1 +that's the number and then I have an + + align:start position:0% +that's the number and then I have an + + + align:start position:0% +that's the number and then I have an +operator here so this is minus and 0 + + align:start position:0% +operator here so this is minus and 0 + + + align:start position:0% +operator here so this is minus and 0 +Delta H and 0 so we get a very famous + + align:start position:0% +Delta H and 0 so we get a very famous + + + align:start position:0% +Delta H and 0 so we get a very famous +and important equation that e + 1 is + + align:start position:0% +and important equation that e + 1 is + + + align:start position:0% +and important equation that e + 1 is +equal to n 0 Delta H + 0 the first + + align:start position:0% +equal to n 0 Delta H + 0 the first + + + align:start position:0% +equal to n 0 Delta H + 0 the first +correction to the energy is obtained by + + align:start position:0% +correction to the energy is obtained by + + + align:start position:0% +correction to the energy is obtained by +finding the expectation value of the + + align:start position:0% +finding the expectation value of the + + + align:start position:0% +finding the expectation value of the +perturbation in the unperturbed State so + + align:start position:0% +perturbation in the unperturbed State so + + + align:start position:0% +perturbation in the unperturbed State so +you should be happy to hear that it says + + align:start position:0% +you should be happy to hear that it says + + + align:start position:0% +you should be happy to hear that it says +that to find the first correction in the + + align:start position:0% +that to find the first correction in the + + + align:start position:0% +that to find the first correction in the +energy you don't need to know what + + align:start position:0% +energy you don't need to know what + + + align:start position:0% +energy you don't need to know what +happens to the state I didn't need to + + align:start position:0% +happens to the state I didn't need to + + + align:start position:0% +happens to the state I didn't need to +know what N 1 was how the state changes + + align:start position:0% +know what N 1 was how the state changes + + + align:start position:0% +know what N 1 was how the state changes +to know how the energy changes the + + align:start position:0% +to know how the energy changes the + + + align:start position:0% +to know how the energy changes the +energy + + align:start position:0% +energy + + + align:start position:0% +energy +changed before and I just don't need it + + align:start position:0% +changed before and I just don't need it + + + align:start position:0% +changed before and I just don't need it +I just need the original state and the + + align:start position:0% +I just need the original state and the + + + align:start position:0% +I just need the original state and the +perturbation so it's a very nice result + + align:start position:0% +perturbation so it's a very nice result + + + align:start position:0% +perturbation so it's a very nice result +and it has a simple generalization the + + align:start position:0% +and it has a simple generalization the + + + align:start position:0% +and it has a simple generalization the +simple generalization is that + + align:start position:0% + + + + align:start position:0% + +I'm going to use another blackboard but + + align:start position:0% +I'm going to use another blackboard but + + + align:start position:0% +I'm going to use another blackboard but +let's look at it the simple + + align:start position:0% +let's look at it the simple + + + align:start position:0% +let's look at it the simple +generalization comes from doing the same + + align:start position:0% +generalization comes from doing the same + + + align:start position:0% +generalization comes from doing the same +exact thing with the order K equation so + + align:start position:0% +exact thing with the order K equation so + + + align:start position:0% +exact thing with the order K equation so +let's do that + + align:start position:0% +let's do that + + + align:start position:0% +let's do that +I put an N 0 to the left of this + + align:start position:0% +I put an N 0 to the left of this + + + align:start position:0% +I put an N 0 to the left of this +equation now what do we get from this + + align:start position:0% +equation now what do we get from this + + + align:start position:0% +equation now what do we get from this +term we get 0 for the same reason + + align:start position:0% +term we get 0 for the same reason + + + align:start position:0% +term we get 0 for the same reason +there's an N 0 now here and the H 0 is + + align:start position:0% +there's an N 0 now here and the H 0 is + + + align:start position:0% +there's an N 0 now here and the H 0 is +killed by this term gives you 0 and then + + align:start position:0% +killed by this term gives you 0 and then + + + align:start position:0% +killed by this term gives you 0 and then +we're going to continue with this and + + align:start position:0% +we're going to continue with this and + + + align:start position:0% +we're going to continue with this and +see what happens with these various + + align:start position:0% +see what happens with these various + + + align:start position:0% +see what happens with these various +terms let's look at it so put the N 0 0 + + align:start position:0% +terms let's look at it so put the N 0 0 + + + align:start position:0% +terms let's look at it so put the N 0 0 +and the left hand side was equal to 0 + + align:start position:0% +and the left hand side was equal to 0 + + + align:start position:0% +and the left hand side was equal to 0 +and on the right hand side what do we + + align:start position:0% +and on the right hand side what do we + + + align:start position:0% +and on the right hand side what do we +get well let me do a couple of terms n 0 + + align:start position:0% +get well let me do a couple of terms n 0 + + + align:start position:0% +get well let me do a couple of terms n 0 +e and 1 minus Delta H and K minus 1 plus + + align:start position:0% + + + + align:start position:0% + +all these other terms and ok so look + + align:start position:0% +all these other terms and ok so look + + + align:start position:0% +all these other terms and ok so look +what happens here let's do the next term + + align:start position:0% +what happens here let's do the next term + + + align:start position:0% +what happens here let's do the next term +for example + + align:start position:0% +for example + + + align:start position:0% +for example +em2 and 0 and K minus 2 well from here + + align:start position:0% +em2 and 0 and K minus 2 well from here + + + align:start position:0% +em2 and 0 and K minus 2 well from here +this is a number so I have here this + + align:start position:0% +this is a number so I have here this + + + align:start position:0% +this is a number so I have here this +goes out the overlap of n 0 with M + + align:start position:0% +goes out the overlap of n 0 with M + + + align:start position:0% +goes out the overlap of n 0 with M +- one but we said that all the higher + + align:start position:0% +- one but we said that all the higher + + + align:start position:0% +- one but we said that all the higher +corrections have no component along and + + align:start position:0% +corrections have no component along and + + + align:start position:0% +corrections have no component along and +zero so this thing will give you zero on + + align:start position:0% +zero so this thing will give you zero on + + + align:start position:0% +zero so this thing will give you zero on +the other hand here is an operator so + + align:start position:0% +the other hand here is an operator so + + + align:start position:0% +the other hand here is an operator so +there's nothing I can say so I'll write + + align:start position:0% +there's nothing I can say so I'll write + + + align:start position:0% +there's nothing I can say so I'll write +it - and zero Delta H and K minus one + + align:start position:0% + + + + align:start position:0% + +and then what else well you have n 0 + + align:start position:0% +and then what else well you have n 0 + + + align:start position:0% +and then what else well you have n 0 +then k minus 2 here that's zero because + + align:start position:0% +then k minus 2 here that's zero because + + + align:start position:0% +then k minus 2 here that's zero because +this is a higher state and all the terms + + align:start position:0% +this is a higher state and all the terms + + + align:start position:0% +this is a higher state and all the terms +give you zero until you get here where + + align:start position:0% +give you zero until you get here where + + + align:start position:0% +give you zero until you get here where +the end zero with the n zero give you + + align:start position:0% +the end zero with the n zero give you + + + align:start position:0% +the end zero with the n zero give you +one so the only term that survives is + + align:start position:0% +one so the only term that survives is + + + align:start position:0% +one so the only term that survives is +the last one and we get e and k so this + + align:start position:0% +the last one and we get e and k so this + + + align:start position:0% +the last one and we get e and k so this +gives you the result that e MK is equal + + align:start position:0% +gives you the result that e MK is equal + + + align:start position:0% +gives you the result that e MK is equal +to n 0 Delta H and K minus 1 I box it + + align:start position:0% +to n 0 Delta H and K minus 1 I box it + + + align:start position:0% +to n 0 Delta H and K minus 1 I box it +because it's another nice formula it + + align:start position:0% +because it's another nice formula it + + + align:start position:0% +because it's another nice formula it +tells you that the caithe order energy + + align:start position:0% +tells you that the caithe order energy + + + align:start position:0% +tells you that the caithe order energy +is given if you know the K minus 1 state + + align:start position:0% +is given if you know the K minus 1 state + + + align:start position:0% +is given if you know the K minus 1 state +if you have figured out the K minus one + + align:start position:0% +if you have figured out the K minus one + + + align:start position:0% +if you have figured out the K minus one +skir ection to the state then you know + + align:start position:0% +skir ection to the state then you know + + + align:start position:0% +skir ection to the state then you know +the energy of the caithe correction this + + align:start position:0% +the energy of the caithe correction this + + + align:start position:0% +the energy of the caithe correction this +formula certainly works when K is equal + + align:start position:0% +formula certainly works when K is equal + + + align:start position:0% +formula certainly works when K is equal +to 1 in which case it represents the + + align:start position:0% +to 1 in which case it represents the + + + align:start position:0% +to 1 in which case it represents the +formula we had on the blackboard to the + + align:start position:0% +formula we had on the blackboard to the + + + align:start position:0% +formula we had on the blackboard to the +right when K is equal to 1 you get the + + align:start position:0% +right when K is equal to 1 you get the + + + align:start position:0% +right when K is equal to 1 you get the +expectation value of Delta H around zero \ No newline at end of file diff --git a/0cmj5TfFCLY.txt b/0cmj5TfFCLY.txt new file mode 100644 index 0000000000000000000000000000000000000000..1ed659edea2a2e253e04f04be019fa61e232fe08 --- /dev/null +++ b/0cmj5TfFCLY.txt @@ -0,0 +1,15059 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right well I want to + + align:start position:0% +ocw.mit.edu all right well I want to + + + align:start position:0% +ocw.mit.edu all right well I want to +thank you all for coming to what I've + + align:start position:0% +thank you all for coming to what I've + + + align:start position:0% +thank you all for coming to what I've +advertised as the penultimate course in + + align:start position:0% +advertised as the penultimate course in + + + align:start position:0% +advertised as the penultimate course in +this lecture series everything else + + align:start position:0% +this lecture series everything else + + + align:start position:0% +this lecture series everything else +we've done up to this point has sort of + + align:start position:0% +we've done up to this point has sort of + + + align:start position:0% +we've done up to this point has sort of +been building up to actually finally + + align:start position:0% +been building up to actually finally + + + align:start position:0% +been building up to actually finally +really using databases you know and + + align:start position:0% +really using databases you know and + + + align:start position:0% +really using databases you know and +hopefully you haven't been too + + align:start position:0% +hopefully you haven't been too + + + align:start position:0% +hopefully you haven't been too +disappointed at how long I've sort of + + align:start position:0% +disappointed at how long I've sort of + + + align:start position:0% +disappointed at how long I've sort of +LED you uh LED you uh LED you along here + + align:start position:0% +LED you uh LED you uh LED you along here + + + align:start position:0% +LED you uh LED you uh LED you along here +to get to this point but the but the + + align:start position:0% +to get to this point but the but the + + + align:start position:0% +to get to this point but the but the +point being that if you have certain + + align:start position:0% +point being that if you have certain + + + align:start position:0% +point being that if you have certain +abstract Concepts in your + + align:start position:0% +abstract Concepts in your + + + align:start position:0% +abstract Concepts in your +mind that once we get to the database + + align:start position:0% +mind that once we get to the database + + + align:start position:0% +mind that once we get to the database +part it just feels sort of very + + align:start position:0% +part it just feels sort of very + + + align:start position:0% +part it just feels sort of very +straightforward um um if we do the + + align:start position:0% +straightforward um um if we do the + + + align:start position:0% +straightforward um um if we do the +database piece and you don't have those + + align:start position:0% +database piece and you don't have those + + + align:start position:0% +database piece and you don't have those +Concepts then you can easily get + + align:start position:0% +Concepts then you can easily get + + + align:start position:0% +Concepts then you can easily get +distracted by sort of extraneous + + align:start position:0% +distracted by sort of extraneous + + + align:start position:0% +distracted by sort of extraneous +information so today there's no no view + + align:start position:0% +information so today there's no no view + + + align:start position:0% +information so today there's no no view +graphs so I'm sure you're all thrilled + + align:start position:0% +graphs so I'm sure you're all thrilled + + + align:start position:0% +graphs so I'm sure you're all thrilled +about that um uh it's going to be all + + align:start position:0% +about that um uh it's going to be all + + + align:start position:0% +about that um uh it's going to be all +demos showing interacting with the + + align:start position:0% +demos showing interacting with the + + + align:start position:0% +demos showing interacting with the +actual technology that we have here + + align:start position:0% +actual technology that we have here + + + align:start position:0% +actual technology that we have here +everything I'm showing to is stuff that + + align:start position:0% +everything I'm showing to is stuff that + + + align:start position:0% +everything I'm showing to is stuff that +you can use I mean so everyone has been + + align:start position:0% +you can use I mean so everyone has been + + + align:start position:0% +you can use I mean so everyone has been +so I'm just GNA kind of + + align:start position:0% +so I'm just GNA kind of + + + align:start position:0% +so I'm just GNA kind of +get into this and let's just start with + + align:start position:0% +get into this and let's just start with + + + align:start position:0% +get into this and let's just start with +step one we're going to be using the + + align:start position:0% +step one we're going to be using the + + + align:start position:0% +step one we're going to be using the +accumulo databases that we've set up we + + align:start position:0% +accumulo databases that we've set up we + + + align:start position:0% +accumulo databases that we've set up we +have sort of a Clearing House of these + + align:start position:0% +have sort of a Clearing House of these + + + align:start position:0% +have sort of a Clearing House of these +databases on our elog grid system and + + align:start position:0% +databases on our elog grid system and + + + align:start position:0% +databases on our elog grid system and +you can get to that list by going to + + align:start position:0% +you can get to that list by going to + + + align:start position:0% +you can get to that list by going to +this web web page here DB status LL + + align:start position:0% +this web web page here DB status LL + + + align:start position:0% +this web web page here DB status LL +grid. l. mit.edu and when you go there + + align:start position:0% +grid. l. mit.edu and when you go there + + + align:start position:0% +grid. l. mit.edu and when you go there +it will prompt you for your one password + + align:start position:0% +it will prompt you for your one password + + + align:start position:0% +it will prompt you for your one password +and then it will show you the databases + + align:start position:0% +and then it will show you the databases + + + align:start position:0% +and then it will show you the databases +that you have access to + + align:start position:0% +that you have access to + + + align:start position:0% +that you have access to +now I have access to all the databases + + align:start position:0% +now I have access to all the databases + + + align:start position:0% +now I have access to all the databases +but you guys should only have C these + + align:start position:0% +but you guys should only have C these + + + align:start position:0% +but you guys should only have C these +class databases when you if you if you + + align:start position:0% +class databases when you if you if you + + + align:start position:0% +class databases when you if you if you +log into that and + + align:start position:0% +log into that and + + + align:start position:0% +log into that and +um um and so as you see here we have + + align:start position:0% +um um and so as you see here we have + + + align:start position:0% +um um and so as you see here we have +five databases that are set up these are + + align:start position:0% +five databases that are set up these are + + + align:start position:0% +five databases that are set up these are +five independent instances of accumulo + + align:start position:0% +five independent instances of accumulo + + + align:start position:0% +five independent instances of accumulo +and I've started a couple already and we + + align:start position:0% +and I've started a couple already and we + + + align:start position:0% +and I've started a couple already and we +can even take a look at + + align:start position:0% +can even take a look at + + + align:start position:0% +can even take a look at +them so this is what a running accumulo + + align:start position:0% +them so this is what a running accumulo + + + align:start position:0% +them so this is what a running accumulo +instance looks like this this is its + + align:start position:0% +instance looks like this this is its + + + align:start position:0% +instance looks like this this is its +main page here and it shows you kind of + + align:start position:0% +main page here and it shows you kind of + + + align:start position:0% +main page here and it shows you kind of +how much dis is used and the number of + + align:start position:0% +how much dis is used and the number of + + + align:start position:0% +how much dis is used and the number of +tables and all that type of stuff and it + + align:start position:0% +tables and all that type of stuff and it + + + align:start position:0% +tables and all that type of stuff and it +gives you a nice history that shows + + align:start position:0% +gives you a nice history that shows + + + align:start position:0% +gives you a nice history that shows +ingest rate you know over the last few + + align:start position:0% +ingest rate you know over the last few + + + align:start position:0% +ingest rate you know over the last few +bit and scan rate this is all in entries + + align:start position:0% +bit and scan rate this is all in entries + + + align:start position:0% +bit and scan rate this is all in entries +per second inest megabytes all different + + align:start position:0% +per second inest megabytes all different + + + align:start position:0% +per second inest megabytes all different +kinds of really useful information here + + align:start position:0% +kinds of really useful information here + + + align:start position:0% +kinds of really useful information here +and you'll see that this has got the URL + + align:start position:0% +and you'll see that this has got the URL + + + align:start position:0% +and you'll see that this has got the URL +of class + + align:start position:0% +of class + + + align:start position:0% +of class +DB1 cloud. LL grid that's been a you + + align:start position:0% +DB1 cloud. LL grid that's been a you + + + align:start position:0% +DB1 cloud. LL grid that's been a you +know when I started it was an actual + + align:start position:0% +know when I started it was an actual + + + align:start position:0% +know when I started it was an actual +machine that was allocated to that in + + align:start position:0% +machine that was allocated to that in + + + align:start position:0% +machine that was allocated to that in +fact just for fun here I could turn one + + align:start position:0% +fact just for fun here I could turn one + + + align:start position:0% +fact just for fun here I could turn one +of these on um you guys are free to + + align:start position:0% +of these on um you guys are free to + + + align:start position:0% +of these on um you guys are free to +start them I would encourage you to hit + + align:start position:0% +start them I would encourage you to hit + + + align:start position:0% +start them I would encourage you to hit +the stop button because if someone else + + align:start position:0% +the stop button because if someone else + + + align:start position:0% +the stop button because if someone else +is using it and you hit stop then you + + align:start position:0% +is using it and you hit stop then you + + + align:start position:0% +is using it and you hit stop then you +know that could be that could be uh that + + align:start position:0% +know that could be that could be uh that + + + align:start position:0% +know that could be that could be uh that +may not be something you want to do but + + align:start position:0% +may not be something you want to do but + + + align:start position:0% +may not be something you want to do but +it's the same setup for instance if you + + align:start position:0% +it's the same setup for instance if you + + + align:start position:0% +it's the same setup for instance if you +have a + + align:start position:0% +have a + + + align:start position:0% +have a +project everyone in the class can see + + align:start position:0% +project everyone in the class can see + + + align:start position:0% +project everyone in the class can see +this because we've made you all a part + + align:start position:0% +this because we've made you all a part + + + align:start position:0% +this because we've made you all a part +of the the class group but you can see + + align:start position:0% +of the the class group but you can see + + + align:start position:0% +of the the class group but you can see +here there's other classes we have a bio + + align:start position:0% +here there's other classes we have a bio + + + align:start position:0% +here there's other classes we have a bio +informatics group and they have a couple + + align:start position:0% +informatics group and they have a couple + + + align:start position:0% +informatics group and they have a couple +of databases those are theirs they're + + align:start position:0% +of databases those are theirs they're + + + align:start position:0% +of databases those are theirs they're +not running right now there's a very + + align:start position:0% +not running right now there's a very + + + align:start position:0% +not running right now there's a very +large graph database group it's running + + align:start position:0% +large graph database group it's running + + + align:start position:0% +large graph database group it's running +now and just to + + align:start position:0% +now and just to + + + align:start position:0% +now and just to +show this is it's running you see this + + align:start position:0% +show this is it's running you see this + + + align:start position:0% +show this is it's running you see this +has about 200 gigabytes data and then if + + align:start position:0% +has about 200 gigabytes data and then if + + + align:start position:0% +has about 200 gigabytes data and then if +we look in the tables here we see here + + align:start position:0% +we look in the tables here we see here + + + align:start position:0% +we look in the tables here we see here +we have a few tables here here are some + + align:start position:0% +we have a few tables here here are some + + + align:start position:0% +we have a few tables here here are some +tables with a a few billion entries that + + align:start position:0% +tables with a a few billion entries that + + + align:start position:0% +tables with a a few billion entries that +have been put in there and this is + + align:start position:0% +have been put in there and this is + + + align:start position:0% +have been put in there and this is +really what accumul does very very + + align:start position:0% +really what accumul does very very + + + align:start position:0% +really what accumul does very very +well but I'm going to start one just for + + align:start position:0% +well but I'm going to start one just for + + + align:start position:0% +well but I'm going to start one just for +fun here hope that works and so it will + + align:start position:0% +fun here hope that works and so it will + + + align:start position:0% +fun here hope that works and so it will +be starting that while that happens um + + align:start position:0% +be starting that while that happens um + + + align:start position:0% +be starting that while that happens um +and so you can and you can see it's + + align:start position:0% +and so you can and you can see it's + + + align:start position:0% +and so you can and you can see it's +starting and all those type of stuff so + + align:start position:0% +starting and all those type of stuff so + + + align:start position:0% +starting and all those type of stuff so +we're going to get going here now with + + align:start position:0% +we're going to get going here now with + + + align:start position:0% +we're going to get going here now with +these specific + + align:start position:0% + + + + align:start position:0% + +examples all right and I have + + align:start position:0% + + + + align:start position:0% + +these just so you know today's examples + + align:start position:0% +these just so you know today's examples + + + align:start position:0% +these just so you know today's examples +it's in the example directory in the + + align:start position:0% +it's in the example directory in the + + + align:start position:0% +it's in the example directory in the +scaling directory and two parallel + + align:start position:0% +scaling directory and two parallel + + + align:start position:0% +scaling directory and two parallel +database so this is the directory we're + + align:start position:0% +database so this is the directory we're + + + align:start position:0% +database so this is the directory we're +going to be going through today and um + + align:start position:0% +going to be going through today and um + + + align:start position:0% +going to be going through today and um +and we have a lot of examples to get + + align:start position:0% +and we have a lot of examples to get + + + align:start position:0% +and we have a lot of examples to get +through because we're going to be + + align:start position:0% +through because we're going to be + + + align:start position:0% +through because we're going to be +covering a lot of ground here about how + + align:start position:0% +covering a lot of ground here about how + + + align:start position:0% +covering a lot of ground here about how +you can take advantage of d4m and aumo + + align:start position:0% +you can take advantage of d4m and aumo + + + align:start position:0% +you can take advantage of d4m and aumo +uh together + + align:start position:0% +uh together + + + align:start position:0% +uh together +here + + align:start position:0% +here + + + align:start position:0% +here +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +the first thing I'm going to + + align:start position:0% +the first thing I'm going to + + + align:start position:0% +the first thing I'm going to +do + + align:start position:0% + + + + align:start position:0% + +is go here I'm going to run these I have + + align:start position:0% +is go here I'm going to run these I have + + + align:start position:0% +is go here I'm going to run these I have +essentially two versions of the code one + + align:start position:0% +essentially two versions of the code one + + + align:start position:0% +essentially two versions of the code one +that's going to do fairly smaller + + align:start position:0% +that's going to do fairly smaller + + + align:start position:0% +that's going to do fairly smaller +databases on my laptop and then I have + + align:start position:0% +databases on my laptop and then I have + + + align:start position:0% +databases on my laptop and then I have +another version that's sitting in my El + + align:start position:0% +another version that's sitting in my El + + + align:start position:0% +another version that's sitting in my El +grd account that I can do some bigger + + align:start position:0% +grd account that I can do some bigger + + + align:start position:0% +grd account that I can do some bigger +things with so so to get started we're + + align:start position:0% +things with so so to get started we're + + + align:start position:0% +things with so so to get started we're +going to do this first example pdb 01 + + align:start position:0% +going to do this first example pdb 01 + + + align:start position:0% +going to do this first example pdb 01 +data + + align:start position:0% +data + + + align:start position:0% +data +test okay + + align:start position:0% + + + + align:start position:0% + +all + + align:start position:0% +all + + + align:start position:0% +all +righty so in order to do database work + + align:start position:0% +righty so in order to do database work + + + align:start position:0% +righty so in order to do database work +and to test data we need to generate + + align:start position:0% +and to test data we need to generate + + + align:start position:0% +and to test data we need to generate +some data and uh so I'm using a built-in + + align:start position:0% +some data and uh so I'm using a built-in + + + align:start position:0% +some data and uh so I'm using a built-in +data generator that we have called uh + + align:start position:0% +data generator that we have called uh + + + align:start position:0% +data generator that we have called uh +the chroniker graph basically borrowed + + align:start position:0% +the chroniker graph basically borrowed + + + align:start position:0% +the chroniker graph basically borrowed +from a a benchmark called the graph 500 + + align:start position:0% +from a a benchmark called the graph 500 + + + align:start position:0% +from a a benchmark called the graph 500 +Benchmark there's actually a list called + + align:start position:0% +Benchmark there's actually a list called + + + align:start position:0% +Benchmark there's actually a list called +graph 500 and I helped write that + + align:start position:0% +graph 500 and I helped write that + + + align:start position:0% +graph 500 and I helped write that +Benchmark and in fact I actually the + + align:start position:0% +Benchmark and in fact I actually the + + + align:start position:0% +Benchmark and in fact I actually the +matlb code on that website is stuff that + + align:start position:0% +matlb code on that website is stuff that + + + align:start position:0% +matlb code on that website is stuff that +I originally voted uh uh wrote and other + + align:start position:0% +I originally voted uh uh wrote and other + + + align:start position:0% +I originally voted uh uh wrote and other +people have have since modified and so + + align:start position:0% +people have have since modified and so + + + align:start position:0% +people have have since modified and so +this is a graph generator it generates a + + align:start position:0% +this is a graph generator it generates a + + + align:start position:0% +this is a graph generator it generates a +very + + align:start position:0% +very + + + align:start position:0% +very +large power law graph uh using a a + + align:start position:0% +large power law graph uh using a a + + + align:start position:0% +large power law graph uh using a a +chroner product approach and it has a + + align:start position:0% +chroner product approach and it has a + + + align:start position:0% +chroner product approach and it has a +few parameters here a scale parameter + + align:start position:0% +few parameters here a scale parameter + + + align:start position:0% +few parameters here a scale parameter +which is basically the number of + + align:start position:0% +which is basically the number of + + + align:start position:0% +which is basically the number of +vertices so two to this scale parameter + + align:start position:0% +vertices so two to this scale parameter + + + align:start position:0% +vertices so two to this scale parameter +is approximately the number of vertices + + align:start position:0% +is approximately the number of vertices + + + align:start position:0% +is approximately the number of vertices +so 2 to the 12th gets you about what + + align:start position:0% +so 2 to the 12th gets you about what + + + align:start position:0% +so 2 to the 12th gets you about what +4,000 vertices it then creates a certain + + align:start position:0% +4,000 vertices it then creates a certain + + + align:start position:0% +4,000 vertices it then creates a certain +number of edges per vertex so 16 edges + + align:start position:0% +number of edges per vertex so 16 edges + + + align:start position:0% +number of edges per vertex so 16 edges +per vertex and so this cutes you know + + align:start position:0% +per vertex and so this cutes you know + + + align:start position:0% +per vertex and so this cutes you know +computes n Max as two to the scale here + + align:start position:0% +computes n Max as two to the scale here + + + align:start position:0% +computes n Max as two to the scale here +and then the number of edges is Edges + + align:start position:0% +and then the number of edges is Edges + + + align:start position:0% +and then the number of edges is Edges +per vertex times n Max this is the + + align:start position:0% +per vertex times n Max this is the + + + align:start position:0% +per vertex times n Max this is the +maximum number of edges and then it and + + align:start position:0% +maximum number of edges and then it and + + + align:start position:0% +maximum number of edges and then it and +then it generates this and it comes back + + align:start position:0% +then it generates this and it comes back + + + align:start position:0% +then it generates this and it comes back +with two + + align:start position:0% +with two + + + align:start position:0% +with two +vectors which is just the list of the + + align:start position:0% +vectors which is just the list of the + + + align:start position:0% +vectors which is just the list of the +the first list is a ver Vector is a list + + align:start position:0% +the first list is a ver Vector is a list + + + align:start position:0% +the first list is a ver Vector is a list +of starting vertices and the second + + align:start position:0% +of starting vertices and the second + + + align:start position:0% +of starting vertices and the second +Vector is a list of ending vertices and + + align:start position:0% +Vector is a list of ending vertices and + + + align:start position:0% +Vector is a list of ending vertices and +we're not really using any d4m here + + align:start position:0% +we're not really using any d4m here + + + align:start position:0% +we're not really using any d4m here +we're just creating a sparse adjacency + + align:start position:0% +we're just creating a sparse adjacency + + + align:start position:0% +we're just creating a sparse adjacency +Matrix of that data showing it uh and + + align:start position:0% +Matrix of that data showing it uh and + + + align:start position:0% +Matrix of that data showing it uh and +then plotting the degree distribution so + + align:start position:0% +then plotting the degree distribution so + + + align:start position:0% +then plotting the degree distribution so +if we look at that figure + + align:start position:0% +if we look at that figure + + + align:start position:0% +if we look at that figure +so this shows the uh adjacency Matrix of + + align:start position:0% +so this shows the uh adjacency Matrix of + + + align:start position:0% +so this shows the uh adjacency Matrix of +this graph start vertex n vertex uh + + align:start position:0% +this graph start vertex n vertex uh + + + align:start position:0% +this graph start vertex n vertex uh +these chroner graphs have this sort of + + align:start position:0% +these chroner graphs have this sort of + + + align:start position:0% +these chroner graphs have this sort of +recursive structure in if you kept + + align:start position:0% +recursive structure in if you kept + + + align:start position:0% +recursive structure in if you kept +zooming in you would see that the graph + + align:start position:0% +zooming in you would see that the graph + + + align:start position:0% +zooming in you would see that the graph +looked like itself uh sort of a in a + + align:start position:0% +looked like itself uh sort of a in a + + + align:start position:0% +looked like itself uh sort of a in a +recursive way here that's what gives us + + align:start position:0% +recursive way here that's what gives us + + + align:start position:0% +recursive way here that's what gives us +this uh this power law distribution and + + align:start position:0% +this uh this power law distribution and + + + align:start position:0% +this uh this power law distribution and +there's a relatively small graph um this + + align:start position:0% +there's a relatively small graph um this + + + align:start position:0% +there's a relatively small graph um this +particular data generator is chosen + + align:start position:0% +particular data generator is chosen + + + align:start position:0% +particular data generator is chosen +because you can make enormous graphs in + + align:start position:0% +because you can make enormous graphs in + + + align:start position:0% +because you can make enormous graphs in +parallel very easily uh which is + + align:start position:0% +parallel very easily uh which is + + + align:start position:0% +parallel very easily uh which is +something that if we had to pass around + + align:start position:0% +something that if we had to pass around + + + align:start position:0% +something that if we had to pass around +large data sets every single time we + + align:start position:0% +large data sets every single time we + + + align:start position:0% +large data sets every single time we +wanted to test our software it would be + + align:start position:0% +wanted to test our software it would be + + + align:start position:0% +wanted to test our software it would be +prohibitive because we'd be passing + + align:start position:0% +prohibitive because we'd be passing + + + align:start position:0% +prohibitive because we'd be passing +around you know gigabytes and terabytes + + align:start position:0% +around you know gigabytes and terabytes + + + align:start position:0% +around you know gigabytes and terabytes +and I think + + align:start position:0% +and I think + + + align:start position:0% +and I think +um I think the largest this has ever + + align:start position:0% +um I think the largest this has ever + + + align:start position:0% +um I think the largest this has ever +been run on is on a scale of 2 to the 37 + + align:start position:0% +been run on is on a scale of 2 to the 37 + + + align:start position:0% +been run on is on a scale of 2 to the 37 +so that's + + align:start position:0% +so that's + + + align:start position:0% +so that's +uh trillions of trillions of vertices or + + align:start position:0% +uh trillions of trillions of vertices or + + + align:start position:0% +uh trillions of trillions of vertices or +certainly B ions of vertices almost + + align:start position:0% +certainly B ions of vertices almost + + + align:start position:0% +certainly B ions of vertices almost +trillions of + + align:start position:0% +trillions of + + + align:start position:0% +trillions of +vertices um and then we do the degree + + align:start position:0% +vertices um and then we do the degree + + + align:start position:0% +vertices um and then we do the degree +distribution of this and you see here it + + align:start position:0% +distribution of this and you see here it + + + align:start position:0% +distribution of this and you see here it +creates a power law distribution we have + + align:start position:0% +creates a power law distribution we have + + + align:start position:0% +creates a power law distribution we have +a few vertices with only one connection + + align:start position:0% +a few vertices with only one connection + + + align:start position:0% +a few vertices with only one connection +and we always have a super node with a + + align:start position:0% +and we always have a super node with a + + + align:start position:0% +and we always have a super node with a +lot of connections and you can see + + align:start position:0% +lot of connections and you can see + + + align:start position:0% +lot of connections and you can see +actually here the the chroniker + + align:start position:0% +actually here the the chroniker + + + align:start position:0% +actually here the the chroniker +structure um in this in this uh in this + + align:start position:0% +structure um in this in this uh in this + + + align:start position:0% +structure um in this in this uh in this +data which is it creates this + + align:start position:0% +data which is it creates this + + + align:start position:0% +data which is it creates this +characteristic sort of Saw to pattern + + align:start position:0% +characteristic sort of Saw to pattern + + + align:start position:0% +characteristic sort of Saw to pattern +and there's ways to get rid of that if + + align:start position:0% +and there's ways to get rid of that if + + + align:start position:0% +and there's ways to get rid of that if +you want but for our purposes having + + align:start position:0% +you want but for our purposes having + + + align:start position:0% +you want but for our purposes having +that structure there there's no problem + + align:start position:0% +that structure there there's no problem + + + align:start position:0% +that structure there there's no problem +with that so this is kind of a exactly + + align:start position:0% +with that so this is kind of a exactly + + + align:start position:0% +with that so this is kind of a exactly +what this degree distribution looks + + align:start position:0% +what this degree distribution looks + + + align:start position:0% +what this degree distribution looks +like so that's just a small version to + + align:start position:0% +like so that's just a small version to + + + align:start position:0% +like so that's just a small version to +show you kind of what the data looks + + align:start position:0% +show you kind of what the data looks + + + align:start position:0% +show you kind of what the data looks +like now we're going to create a bigger + + align:start position:0% + + + + align:start position:0% + +version okay so this program which I'll + + align:start position:0% +version okay so this program which I'll + + + align:start position:0% +version okay so this program which I'll +now show + + align:start position:0% + + + + align:start position:0% + +you so this program + + align:start position:0% +you so this program + + + align:start position:0% +you so this program +uh creates uh essentially the same uh + + align:start position:0% +uh creates uh essentially the same uh + + + align:start position:0% +uh creates uh essentially the same uh +Chronicle graph and but it's going to do + + align:start position:0% +Chronicle graph and but it's going to do + + + align:start position:0% +Chronicle graph and but it's going to do +it uh eight times and the right one of + + align:start position:0% +it uh eight times and the right one of + + + align:start position:0% +it uh eight times and the right one of +the nice things about this generator is + + align:start position:0% +the nice things about this generator is + + + align:start position:0% +the nice things about this generator is +those will be you can if you just keep + + align:start position:0% +those will be you can if you just keep + + + align:start position:0% +those will be you can if you just keep +calling this it gives you more + + align:start position:0% +calling this it gives you more + + + align:start position:0% +calling this it gives you more +independent samples from the same graph + + align:start position:0% +independent samples from the same graph + + + align:start position:0% +independent samples from the same graph +so we're just sort of creating a a graph + + align:start position:0% +so we're just sort of creating a a graph + + + align:start position:0% +so we're just sort of creating a a graph +that's got eight times as many edges as + + align:start position:0% +that's got eight times as many edges as + + + align:start position:0% +that's got eight times as many edges as +the previous one just by calling it over + + align:start position:0% +the previous one just by calling it over + + + align:start position:0% +the previous one just by calling it over +and over again uh just from the random + + align:start position:0% +and over again uh just from the random + + + align:start position:0% +and over again uh just from the random +number + + align:start position:0% +number + + + align:start position:0% +number +generator um so I have eight I'm going + + align:start position:0% +generator um so I have eight I'm going + + + align:start position:0% +generator um so I have eight I'm going +to do do this eight times and I'm going + + align:start position:0% +to do do this eight times and I'm going + + + align:start position:0% +to do do this eight times and I'm going +to save each one of those to a separate + + align:start position:0% +to save each one of those to a separate + + + align:start position:0% +to save each one of those to a separate +file so I create a file name I'm + + align:start position:0% +file so I create a file name I'm + + + align:start position:0% +file so I create a file name I'm +actually setting the random number seed + + align:start position:0% +actually setting the random number seed + + + align:start position:0% +actually setting the random number seed +to be uh set by the the file name so + + align:start position:0% +to be uh set by the the file name so + + + align:start position:0% +to be uh set by the the file name so +that I can do this if I wanted uh you + + align:start position:0% +that I can do this if I wanted uh you + + + align:start position:0% +that I can do this if I wanted uh you +know I the the the seventh file will + + align:start position:0% +know I the the the seventh file will + + + align:start position:0% +know I the the the seventh file will +always have essentially the same random + + align:start position:0% +always have essentially the same random + + + align:start position:0% +always have essentially the same random +sequence regardless of when I run it and + + align:start position:0% +sequence regardless of when I run it and + + + align:start position:0% +sequence regardless of when I run it and +so I created my vertices and I'm going + + align:start position:0% +so I created my vertices and I'm going + + + align:start position:0% +so I created my vertices and I'm going +to convert these to Strings and then + + align:start position:0% +to convert these to Strings and then + + + align:start position:0% +to convert these to Strings and then +write the out write these out to files + + align:start position:0% +write the out write these out to files + + + align:start position:0% +write the out write these out to files +and so that's all that does here and one + + align:start position:0% +and so that's all that does here and one + + + align:start position:0% +and so that's all that does here and one +of the things I do throughout this + + align:start position:0% +of the things I do throughout this + + + align:start position:0% +of the things I do throughout this +process that you will see is I keep + + align:start position:0% +process that you will see is I keep + + + align:start position:0% +process that you will see is I keep +track of how many edges per second I'm + + align:start position:0% +track of how many edges per second I'm + + + align:start position:0% +track of how many edges per second I'm +generating things so here I'm generating + + align:start position:0% +generating things so here I'm generating + + + align:start position:0% +generating things so here I'm generating +you know about + + align:start position:0% +you know about + + + align:start position:0% +you know about +150,000 it varies in terms of the edges + + align:start position:0% +150,000 it varies in terms of the edges + + + align:start position:0% +150,000 it varies in terms of the edges +per second here uh um but you know + + align:start position:0% +per second here uh um but you know + + + align:start position:0% +per second here uh um but you know +between 30,000 and 150 or 180,000 edges + + align:start position:0% +between 30,000 and 150 or 180,000 edges + + + align:start position:0% +between 30,000 and 150 or 180,000 edges +per second because when you're creating + + align:start position:0% +per second because when you're creating + + + align:start position:0% +per second because when you're creating +a whole data processing pipeline that's + + align:start position:0% +a whole data processing pipeline that's + + + align:start position:0% +a whole data processing pipeline that's +essentially the kind of the metrics + + align:start position:0% +essentially the kind of the metrics + + + align:start position:0% +essentially the kind of the metrics +you're looking you know some some steps + + align:start position:0% +you're looking you know some some steps + + + align:start position:0% +you're looking you know some some steps +might generate you know process your + + align:start position:0% +might generate you know process your + + + align:start position:0% +might generate you know process your +edges extremely quickly and other steps + + align:start position:0% +edges extremely quickly and other steps + + + align:start position:0% +edges extremely quickly and other steps +might process your edges more slowly and + + align:start position:0% +might process your edges more slowly and + + + align:start position:0% +might process your edges more slowly and +that's obviously the ones where you want + + align:start position:0% +that's obviously the ones where you want + + + align:start position:0% +that's obviously the ones where you want +to put for energy and effort into + + align:start position:0% +to put for energy and effort into + + + align:start position:0% +to put for energy and effort into +it so we can actually now go and look + + align:start position:0% +it so we can actually now go and look + + + align:start position:0% +it so we can actually now go and look +it's stuck it in this data directory + + align:start position:0% +it's stuck it in this data directory + + + align:start position:0% +it's stuck it in this data directory +here and we just created that and so we + + align:start position:0% +here and we just created that and so we + + + align:start position:0% +here and we just created that and so we +basically we write it out on three files + + align:start position:0% +basically we write it out on three files + + + align:start position:0% +basically we write it out on three files +essentially each one of these holds one + + align:start position:0% +essentially each one of these holds one + + + align:start position:0% +essentially each one of these holds one +part of a triple so a column uh a row a + + align:start position:0% +part of a triple so a column uh a row a + + + align:start position:0% +part of a triple so a column uh a row a +column and a value so if we look at the + + align:start position:0% +column and a value so if we look at the + + + align:start position:0% +column and a value so if we look at the +uh the row + + align:start position:0% +uh the row + + + align:start position:0% +uh the row +you can just see it's a sequence of + + align:start position:0% +you can just see it's a sequence of + + + align:start position:0% +you can just see it's a sequence of +strings separated by + + align:start position:0% +strings separated by + + + align:start position:0% +strings separated by +commas same with the column just to + + align:start position:0% +commas same with the column just to + + + align:start position:0% +commas same with the column just to +separate a sequence of strings separated + + align:start position:0% +separate a sequence of strings separated + + + align:start position:0% +separate a sequence of strings separated +by by commas and then in this case the + + align:start position:0% +by by commas and then in this case the + + + align:start position:0% +by by commas and then in this case the +values we just made all ones nothing + + align:start position:0% +values we just made all ones nothing + + + align:start position:0% +values we just made all ones nothing +nothing fancy there so now we have eight + + align:start position:0% +nothing fancy there so now we have eight + + + align:start position:0% +nothing fancy there so now we have eight +files all right that's great we + + align:start position:0% +files all right that's great we + + + align:start position:0% +files all right that's great we +generated those very quickly and now we + + align:start position:0% +generated those very quickly and now we + + + align:start position:0% +generated those very quickly and now we +want to do a little processing on + + align:start position:0% + + + + align:start position:0% + +them so if we go p + + align:start position:0% +them so if we go p + + + align:start position:0% +them so if we go p +O3 the first thing we're going to do is + + align:start position:0% +O3 the first thing we're going to do is + + + align:start position:0% +O3 the first thing we're going to do is +read those files back in and construct + + align:start position:0% +read those files back in and construct + + + align:start position:0% +read those files back in and construct +associative arrays because the + + align:start position:0% +associative arrays because the + + + align:start position:0% +associative arrays because the +associative array construction time + + align:start position:0% +associative array construction time + + + align:start position:0% +associative array construction time +takes a little time and we're going to + + align:start position:0% +takes a little time and we're going to + + + align:start position:0% +takes a little time and we're going to +want to use it over and over again so we + + align:start position:0% +want to use it over and over again so we + + + align:start position:0% +want to use it over and over again so we +might as well take those triples and um + + align:start position:0% +might as well take those triples and um + + + align:start position:0% +might as well take those triples and um +and construct them into associative + + align:start position:0% +and construct them into associative + + + align:start position:0% +and construct them into associative +arrays and save them out as mat binary + + align:start position:0% +arrays and save them out as mat binary + + + align:start position:0% +arrays and save them out as mat binary +files and now that will be something + + align:start position:0% +files and now that will be something + + + align:start position:0% +files and now that will be something +that we can work with very + + align:start position:0% +that we can work with very + + + align:start position:0% +that we can work with very +quickly so we're going to do + + align:start position:0% +quickly so we're going to do + + + align:start position:0% +quickly so we're going to do +that all right so there you go it read + + align:start position:0% +that all right so there you go it read + + + align:start position:0% +that all right so there you go it read +them in and it shows you at the rate at + + align:start position:0% +them in and it shows you at the rate at + + + align:start position:0% +them in and it shows you at the rate at +which it reads them in and then + + align:start position:0% +which it reads them in and then + + + align:start position:0% +which it reads them in and then +essentially writes them out and gives us + + align:start position:0% +essentially writes them out and gives us + + + align:start position:0% +essentially writes them out and gives us +another example of the edges per second + + align:start position:0% +another example of the edges per second + + + align:start position:0% +another example of the edges per second +and now you see we have Matlab files for + + align:start position:0% +and now you see we have Matlab files for + + + align:start position:0% +and now you see we have Matlab files for +each one of those and not surprisingly + + align:start position:0% +each one of those and not surprisingly + + + align:start position:0% +each one of those and not surprisingly +the matlb file is smaller than the three + + align:start position:0% +the matlb file is smaller than the three + + + align:start position:0% +the matlb file is smaller than the three +input um triples that it gave so this is + + align:start position:0% +input um triples that it gave so this is + + + align:start position:0% +input um triples that it gave so this is +a 24 kilobyte Matlab file and you know + + align:start position:0% +a 24 kilobyte Matlab file and you know + + + align:start position:0% +a 24 kilobyte Matlab file and you know +it was probably about 80 kilobytes of + + align:start position:0% +it was probably about 80 kilobytes of + + + align:start position:0% +it was probably about 80 kilobytes of +input data and that's just because you + + align:start position:0% +input data and that's just because you + + + align:start position:0% +input data and that's just because you +know we've compressed all the row Keys + + align:start position:0% +know we've compressed all the row Keys + + + align:start position:0% +know we've compressed all the row Keys +into single vectors and we have the + + align:start position:0% +into single vectors and we have the + + + align:start position:0% +into single vectors and we have the +sparse adjacency Matrix which stores + + align:start position:0% +sparse adjacency Matrix which stores + + + align:start position:0% +sparse adjacency Matrix which stores +things and so that makes it a little bit + + align:start position:0% +things and so that makes it a little bit + + + align:start position:0% +things and so that makes it a little bit +uh a little bit better + + align:start position:0% + + + + align:start position:0% + +there we actually look at that program + + align:start position:0% +there we actually look at that program + + + align:start position:0% +there we actually look at that program +here so we can see we basically are + + align:start position:0% +here so we can see we basically are + + + align:start position:0% +here so we can see we basically are +reading it in and then what we're doing + + align:start position:0% +reading it in and then what we're doing + + + align:start position:0% +reading it in and then what we're doing +is we're basically creating an + + align:start position:0% +is we're basically creating an + + + align:start position:0% +is we're basically creating an +associative array we we read in each set + + align:start position:0% +associative array we we read in each set + + + align:start position:0% +associative array we we read in each set +of triples okay and then uh the + + align:start position:0% +of triples okay and then uh the + + + align:start position:0% +of triples okay and then uh the +Constructor takes the list of row + + align:start position:0% +Constructor takes the list of row + + + align:start position:0% +Constructor takes the list of row +strings column strings we just all want + + align:start position:0% +strings column strings we just all want + + + align:start position:0% +strings column strings we just all want +this since we knew they were all one + + align:start position:0% +this since we knew they were all one + + + align:start position:0% +this since we knew they were all one +we're just letting that be one and then + + align:start position:0% +we're just letting that be one and then + + + align:start position:0% +we're just letting that be one and then +there's a optional fourth argument that + + align:start position:0% +there's a optional fourth argument that + + + align:start position:0% +there's a optional fourth argument that +tells us what do we want to do if we put + + align:start position:0% +tells us what do we want to do if we put + + + align:start position:0% +tells us what do we want to do if we put +in two triples you know with the same + + align:start position:0% +in two triples you know with the same + + + align:start position:0% +in two triples you know with the same +row and column you know what to do the + + align:start position:0% +row and column you know what to do the + + + align:start position:0% +row and column you know what to do the +default is it will just do the Min so if + + align:start position:0% +default is it will just do the Min so if + + + align:start position:0% +default is it will just do the Min so if +I have a collision it will just do a Min + + align:start position:0% +I have a collision it will just do a Min + + + align:start position:0% +I have a collision it will just do a Min +if I give it this optional fourth + + align:start position:0% +if I give it this optional fourth + + + align:start position:0% +if I give it this optional fourth +argument at some in fact you can put in + + align:start position:0% +argument at some in fact you can put in + + + align:start position:0% +argument at some in fact you can put in +essentially any binary operation there + + align:start position:0% +essentially any binary operation there + + + align:start position:0% +essentially any binary operation there +but at some we'll just add the add them + + align:start position:0% +but at some we'll just add the add them + + + align:start position:0% +but at some we'll just add the add them +together so now we'll have at that in + + align:start position:0% +together so now we'll have at that in + + + align:start position:0% +together so now we'll have at that in +the in the in the associative array a + + align:start position:0% +the in the in the associative array a + + + align:start position:0% +the in the in the associative array a +particular row and column will have how + + align:start position:0% +particular row and column will have how + + + align:start position:0% +particular row and column will have how +many how many that that occurred and so + + align:start position:0% +many how many that that occurred and so + + + align:start position:0% +many how many that that occurred and so +you know we're we're summing up as we go + + align:start position:0% +you know we're we're summing up as we go + + + align:start position:0% +you know we're we're summing up as we go +here and then after we create the + + align:start position:0% +here and then after we create the + + + align:start position:0% +here and then after we create the +associate array we save them out to a + + align:start position:0% +associate array we save them out to a + + + align:start position:0% +associate array we save them out to a +file and so we have that step + + align:start position:0% + + + + align:start position:0% + +done all + + align:start position:0% +done all + + + align:start position:0% +done all +right now the whole reason I showed you + + align:start position:0% +right now the whole reason I showed you + + + align:start position:0% +right now the whole reason I showed you +this process is because now I'm actually + + align:start position:0% +this process is because now I'm actually + + + align:start position:0% +this process is because now I'm actually +in a position I can start doing + + align:start position:0% +in a position I can start doing + + + align:start position:0% +in a position I can start doing +computation just on the files as I said + + align:start position:0% +computation just on the files as I said + + + align:start position:0% +computation just on the files as I said +before I don't have to use the database + + align:start position:0% +before I don't have to use the database + + + align:start position:0% +before I don't have to use the database +I can if I'm going to do any kind of + + align:start position:0% +I can if I'm going to do any kind of + + + align:start position:0% +I can if I'm going to do any kind of +calculation that's going to involve + + align:start position:0% +calculation that's going to involve + + + align:start position:0% +calculation that's going to involve +traversing all the data it's going to be + + align:start position:0% +traversing all the data it's going to be + + + align:start position:0% +traversing all the data it's going to be +faster just to read in those matlb files + + align:start position:0% +faster just to read in those matlb files + + + align:start position:0% +faster just to read in those matlb files +and do my processing on that it's also + + align:start position:0% +and do my processing on that it's also + + + align:start position:0% +and do my processing on that it's also +very easy to make parallel I have a lot + + align:start position:0% +very easy to make parallel I have a lot + + + align:start position:0% +very easy to make parallel I have a lot +of files you know I just have different + + align:start position:0% +of files you know I just have different + + + align:start position:0% +of files you know I just have different +if I launch a parallel uh job I can just + + align:start position:0% +if I launch a parallel uh job I can just + + + align:start position:0% +if I launch a parallel uh job I can just +have different uh different uh processes + + align:start position:0% +have different uh different uh processes + + + align:start position:0% +have different uh different uh processes +reading separate files it will scale + + align:start position:0% +reading separate files it will scale + + + align:start position:0% +reading separate files it will scale +very well the the data rate read rates + + align:start position:0% +very well the the data rate read rates + + + align:start position:0% +very well the the data rate read rates +will be very fast all you know uh + + align:start position:0% +will be very fast all you know uh + + + align:start position:0% +will be very fast all you know uh +reading these files FES in parallel will + + align:start position:0% +reading these files FES in parallel will + + + align:start position:0% +reading these files FES in parallel will +take much less time than trying to pull + + align:start position:0% +take much less time than trying to pull + + + align:start position:0% +take much less time than trying to pull +out all the data from the database again + + align:start position:0% +out all the data from the database again + + + align:start position:0% +out all the data from the database again +so we're going to do a little analytic + + align:start position:0% + + + + align:start position:0% + +here4 so I'm going to basically compute + + align:start position:0% +here4 so I'm going to basically compute + + + align:start position:0% +here4 so I'm going to basically compute +I'm going to take those eight files read + + align:start position:0% +I'm going to take those eight files read + + + align:start position:0% +I'm going to take those eight files read +them all in and accumulate the results + + align:start position:0% +them all in and accumulate the results + + + align:start position:0% +them all in and accumulate the results +as we + + align:start position:0% +as we + + + align:start position:0% +as we +go right and there we go that's we get + + align:start position:0% +go right and there we go that's we get + + + align:start position:0% +go right and there we go that's we get +the the ingree distribution and the + + align:start position:0% +the the ingree distribution and the + + + align:start position:0% +the the ingree distribution and the +outdegree distribution of this of this + + align:start position:0% + + + + align:start position:0% + +result look at that program here you can + + align:start position:0% +result look at that program here you can + + + align:start position:0% +result look at that program here you can +see all we did is we looped over all the + + align:start position:0% +see all we did is we looped over all the + + + align:start position:0% +see all we did is we looped over all the +files just loaded them from in Matt mat + + align:start position:0% +files just loaded them from in Matt mat + + + align:start position:0% +files just loaded them from in Matt mat +lab and then basically summed the rows + + align:start position:0% +lab and then basically summed the rows + + + align:start position:0% +lab and then basically summed the rows +and added that to a a temp variable and + + align:start position:0% +and added that to a a temp variable and + + + align:start position:0% +and added that to a a temp variable and +sum The Columns and then plotted them + + align:start position:0% +sum The Columns and then plotted them + + + align:start position:0% +sum The Columns and then plotted them +out so we just sort of accumulated them + + align:start position:0% +out so we just sort of accumulated them + + + align:start position:0% +out so we just sort of accumulated them +as we went + + align:start position:0% +as we went + + + align:start position:0% +as we went +this actually this method of just + + align:start position:0% +this actually this method of just + + + align:start position:0% +this actually this method of just +summing on top of an associate array is + + align:start position:0% +summing on top of an associate array is + + + align:start position:0% +summing on top of an associate array is +something that you can certainly do it's + + align:start position:0% +something that you can certainly do it's + + + align:start position:0% +something that you can certainly do it's +a very convenient way to do it I should + + align:start position:0% +a very convenient way to do it I should + + + align:start position:0% +a very convenient way to do it I should +say though and you can kind of see it + + align:start position:0% +say though and you can kind of see it + + + align:start position:0% +say though and you can kind of see it +here a little bit you notice that the + + align:start position:0% +here a little bit you notice that the + + + align:start position:0% +here a little bit you notice that the +time is beginning to well it's not so + + align:start position:0% +time is beginning to well it's not so + + + align:start position:0% +time is beginning to well it's not so +clear here this took a little time but + + align:start position:0% +clear here this took a little time but + + + align:start position:0% +clear here this took a little time but +we on another larger example you what + + align:start position:0% +we on another larger example you what + + + align:start position:0% +we on another larger example you what +you would see is that every single time + + align:start position:0% +you would see is that every single time + + + align:start position:0% +you would see is that every single time +we did that because we're building and + + align:start position:0% +we did that because we're building and + + + align:start position:0% +we did that because we're building and +then adding we're basically redoing the + + align:start position:0% +then adding we're basically redoing the + + + align:start position:0% +then adding we're basically redoing the +construction process and So eventually + + align:start position:0% +construction process and So eventually + + + align:start position:0% +construction process and So eventually +this will become long longer and longer + + align:start position:0% +this will become long longer and longer + + + align:start position:0% +this will become long longer and longer +and longer and so it's okay for small + + align:start position:0% +and longer and so it's okay for small + + + align:start position:0% +and longer and so it's okay for small +stuff to do that or if you're only going + + align:start position:0% +stuff to do that or if you're only going + + + align:start position:0% +stuff to do that or if you're only going +to do it a few times but if you're going + + align:start position:0% +to do it a few times but if you're going + + + align:start position:0% +to do it a few times but if you're going +to be accumulating an enormous amount of + + align:start position:0% +to be accumulating an enormous amount of + + + align:start position:0% +to be accumulating an enormous amount of +of data then + + align:start position:0% +of data then + + + align:start position:0% +of data then +um what we can actually do is we have + + align:start position:0% +um what we can actually do is we have + + + align:start position:0% +um what we can actually do is we have +another version of this + + align:start position:0% +another version of this + + + align:start position:0% +another version of this +program PD + + align:start position:0% + + + + align:start position:0% + +boo4 cgre + + align:start position:0% +boo4 cgre + + + align:start position:0% +boo4 cgre +test and you could tell that was a + + align:start position:0% +test and you could tell that was a + + + align:start position:0% +test and you could tell that was a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +faster you see here it's all a + + align:start position:0% +faster you see here it's all a + + + align:start position:0% +faster you see here it's all a +milliseconds of time and so and the the + + align:start position:0% +milliseconds of time and so and the the + + + align:start position:0% +milliseconds of time and so and the the +way we did that and this is a little bit + + align:start position:0% +way we did that and this is a little bit + + + align:start position:0% +way we did that and this is a little bit +longer + + align:start position:0% + + + + align:start position:0% + +program what we're doing here + + align:start position:0% +program what we're doing here + + + align:start position:0% +program what we're doing here +is + + align:start position:0% +is + + + align:start position:0% +is +basically we're reading in doing the + + align:start position:0% +basically we're reading in doing the + + + align:start position:0% +basically we're reading in doing the +exact same thing we're loading our matlb + + align:start position:0% +exact same thing we're loading our matlb + + + align:start position:0% +exact same thing we're loading our matlb +file we're reading we're doing the sum + + align:start position:0% +file we're reading we're doing the sum + + + align:start position:0% +file we're reading we're doing the sum +okay and then since I know something + + align:start position:0% +okay and then since I know something + + + align:start position:0% +okay and then since I know something +about the structure of that that is + + align:start position:0% +about the structure of that that is + + + align:start position:0% +about the structure of that that is +basically I'm summing the rows + + align:start position:0% +basically I'm summing the rows + + + align:start position:0% +basically I'm summing the rows +okay I can just append that to a longer + + align:start position:0% +okay I can just append that to a longer + + + align:start position:0% +okay I can just append that to a longer +list okay and then at the end do + + align:start position:0% +list okay and then at the end do + + + align:start position:0% +list okay and then at the end do +one large sum and that's and then and + + align:start position:0% +one large sum and that's and then and + + + align:start position:0% +one large sum and that's and then and +that's that's obviously much much faster + + align:start position:0% +that's that's obviously much much faster + + + align:start position:0% +that's that's obviously much much faster +and so these kind of tricks you just + + align:start position:0% +and so these kind of tricks you just + + + align:start position:0% +and so these kind of tricks you just +need to be aware of if you're trying to + + align:start position:0% +need to be aware of if you're trying to + + + align:start position:0% +need to be aware of if you're trying to +do very you know people typically want + + align:start position:0% +do very you know people typically want + + + align:start position:0% +do very you know people typically want +to do large amount of data you just do + + align:start position:0% +to do large amount of data you just do + + + align:start position:0% +to do large amount of data you just do +the simp simp Le sum that'll be okay but + + align:start position:0% +the simp simp Le sum that'll be okay but + + + align:start position:0% +the simp simp Le sum that'll be okay but +if you're doing it a lot over a large + + align:start position:0% +if you're doing it a lot over a large + + + align:start position:0% +if you're doing it a lot over a large +list that essentially becomes almost an + + align:start position:0% +list that essentially becomes almost an + + + align:start position:0% +list that essentially becomes almost an +N squ operation with a number the loop + + align:start position:0% +N squ operation with a number the loop + + + align:start position:0% +N squ operation with a number the loop +loop variable and this is one that will + + align:start position:0% +loop variable and this is one that will + + + align:start position:0% +loop variable and this is one that will +be be even faster you can make it even + + align:start position:0% +be be even faster you can make it even + + + align:start position:0% +be be even faster you can make it even +faster uh because we are doing this + + align:start position:0% +faster uh because we are doing this + + + align:start position:0% +faster uh because we are doing this +concatenation here when you do a + + align:start position:0% +concatenation here when you do a + + + align:start position:0% +concatenation here when you do a +concatenation in M lab you're doing a + + align:start position:0% +concatenation in M lab you're doing a + + + align:start position:0% +concatenation in M lab you're doing a +Malik if you want to make it even faster + + align:start position:0% +Malik if you want to make it even faster + + + align:start position:0% +Malik if you want to make it even faster +you can preallocate a large buffer and + + align:start position:0% +you can preallocate a large buffer and + + + align:start position:0% +you can preallocate a large buffer and +then append into that buffer and then + + align:start position:0% +then append into that buffer and then + + + align:start position:0% +then append into that buffer and then +you hit the edge you know do do a sum + + align:start position:0% +you hit the edge you know do do a sum + + + align:start position:0% +you hit the edge you know do do a sum +then and and do it and do it that way + + align:start position:0% +then and and do it and do it that way + + + align:start position:0% +then and and do it and do it that way +and that that would even that's even F + + align:start position:0% +and that that would even that's even F + + + align:start position:0% +and that that would even that's even F +that's the fastest you can do so these + + align:start position:0% +that's the fastest you can do so these + + + align:start position:0% +that's the fastest you can do so these +are tricks doing very very large sums + + align:start position:0% +are tricks doing very very large sums + + + align:start position:0% +are tricks doing very very large sums +you can do them very quickly and all + + align:start position:0% +you can do them very quickly and all + + + align:start position:0% +you can do them very quickly and all +with files you don't need a database um + + align:start position:0% +with files you don't need a database um + + + align:start position:0% +with files you don't need a database um +uh and this is the way to go if you're + + align:start position:0% +uh and this is the way to go if you're + + + align:start position:0% +uh and this is the way to go if you're +going to be doing something where an + + align:start position:0% +going to be doing something where an + + + align:start position:0% +going to be doing something where an +analytic where you really want to + + align:start position:0% +analytic where you really want to + + + align:start position:0% +analytic where you really want to +Traverse most of the data in the + + align:start position:0% +Traverse most of the data in the + + + align:start position:0% +Traverse most of the data in the +database uh in your data set if if you + + align:start position:0% +database uh in your data set if if you + + + align:start position:0% +database uh in your data set if if you +just need to get pieces of the data in + + align:start position:0% +just need to get pieces of the data in + + + align:start position:0% +just need to get pieces of the data in +the database then the database will be + + align:start position:0% +the database then the database will be + + + align:start position:0% +the database then the database will be +be a better tool all right so + + align:start position:0% +be a better tool all right so + + + align:start position:0% +be a better tool all right so +um all right we did we did that so those + + align:start position:0% +um all right we did we did that so those + + + align:start position:0% +um all right we did we did that so those +show how we did worked with files all + + align:start position:0% +show how we did worked with files all + + + align:start position:0% +show how we did worked with files all +right and that's always a good place to + + align:start position:0% +right and that's always a good place to + + + align:start position:0% +right and that's always a good place to +start uh even if you are working with + + align:start position:0% +start uh even if you are working with + + + align:start position:0% +start uh even if you are working with +the database if you find that you're + + align:start position:0% +the database if you find that you're + + + align:start position:0% +the database if you find that you're +doing one query over and over again that + + align:start position:0% +doing one query over and over again that + + + align:start position:0% +doing one query over and over again that +you're going to be then working with + + align:start position:0% +you're going to be then working with + + + align:start position:0% +you're going to be then working with +that data a lot of times better just do + + align:start position:0% +that data a lot of times better just do + + + align:start position:0% +that data a lot of times better just do +that query and then save those results + + align:start position:0% +that query and then save those results + + + align:start position:0% +that query and then save those results +to a file and then just work with that + + align:start position:0% +to a file and then just work with that + + + align:start position:0% +to a file and then just work with that +file while you're doing it and again + + align:start position:0% +file while you're doing it and again + + + align:start position:0% +file while you're doing it and again +this is something that people often do + + align:start position:0% +this is something that people often do + + + align:start position:0% +this is something that people often do +in our business + + align:start position:0% +in our business + + + align:start position:0% +in our business +all right now we're going to get to the + + align:start position:0% +all right now we're going to get to the + + + align:start position:0% +all right now we're going to get to the +actual database part of it okay so first + + align:start position:0% +actual database part of it okay so first + + + align:start position:0% +actual database part of it okay so first +thing we're going to do is we have to + + align:start position:0% +thing we're going to do is we have to + + + align:start position:0% +thing we're going to do is we have to +set up our database we're going to + + align:start position:0% +set up our database we're going to + + + align:start position:0% +set up our database we're going to +create some tables in a + + align:start position:0% +create some tables in a + + + align:start position:0% +create some tables in a +cumulo and so we want to create those + + align:start position:0% +cumulo and so we want to create those + + + align:start position:0% +cumulo and so we want to create those +first so they're they're they're created + + align:start position:0% +first so they're they're they're created + + + align:start position:0% +first so they're they're they're created +properly and so I'm going to show you + + align:start position:0% +properly and so I'm going to show you + + + align:start position:0% +properly and so I'm going to show you +the program that does that the first + + align:start position:0% +the program that does that the first + + + align:start position:0% +the program that does that the first +thing you're going to do it's going to + + align:start position:0% +thing you're going to do it's going to + + + align:start position:0% +thing you're going to do it's going to +call a DB setup command and so let me + + align:start position:0% +call a DB setup command and so let me + + + align:start position:0% +call a DB setup command and so let me +this this program going to now show you + + align:start position:0% +this this program going to now show you + + + align:start position:0% +this this program going to now show you +that and so when you you run these + + align:start position:0% +that and so when you you run these + + + align:start position:0% +that and so when you you run these +examples you will have to modify this DB + + align:start position:0% +examples you will have to modify this DB + + + align:start position:0% +examples you will have to modify this DB +setup + + align:start position:0% +setup + + + align:start position:0% +setup +program + + align:start position:0% +program + + + align:start position:0% +program +okay so the first thing you you'll + + align:start position:0% +okay so the first thing you you'll + + + align:start position:0% +okay so the first thing you you'll +you'll notice is that uh we're all using + + align:start position:0% +you'll notice is that uh we're all using + + + align:start position:0% +you'll notice is that uh we're all using +the same or each + + align:start position:0% +the same or each + + + align:start position:0% +the same or each +group that's it's with those databases + + align:start position:0% +group that's it's with those databases + + + align:start position:0% +group that's it's with those databases +is all using one user account and you + + align:start position:0% +is all using one user account and you + + + align:start position:0% +is all using one user account and you +could say well that's not the the best + + align:start position:0% +could say well that's not the the best + + + align:start position:0% +could say well that's not the the best +way to do it well it's very consistent + + align:start position:0% +way to do it well it's very consistent + + + align:start position:0% +way to do it well it's very consistent +with the group structure in that is + + align:start position:0% +with the group structure in that is + + + align:start position:0% +with the group structure in that is +basically all users you're the datas is + + align:start position:0% +basically all users you're the datas is + + + align:start position:0% +basically all users you're the datas is +there to share data amongst your group + + align:start position:0% +there to share data amongst your group + + + align:start position:0% +there to share data amongst your group +and so it is not an uncommon practice to + + align:start position:0% +and so it is not an uncommon practice to + + + align:start position:0% +and so it is not an uncommon practice to +have a single user account in which you + + align:start position:0% +have a single user account in which you + + + align:start position:0% +have a single user account in which you +put that data so we have a bit of a + + align:start position:0% +put that data so we have a bit of a + + + align:start position:0% +put that data so we have a bit of a +namespace problem if you all just ran + + align:start position:0% +namespace problem if you all just ran + + + align:start position:0% +namespace problem if you all just ran +this example together you'd all create + + align:start position:0% +this example together you'd all create + + + align:start position:0% +this example together you'd all create +the exact same table and all you know + + align:start position:0% +the exact same table and all you know + + + align:start position:0% +the exact same table and all you know +fill it up so the first thing we're + + align:start position:0% +fill it up so the first thing we're + + + align:start position:0% +fill it up so the first thing we're +going to do is just Preen the tables and + + align:start position:0% +going to do is just Preen the tables and + + + align:start position:0% +going to do is just Preen the tables and +I would suggest you put your name you + + align:start position:0% +I would suggest you put your name you + + + align:start position:0% +I would suggest you put your name you +replace instead of having my name there + + align:start position:0% +replace instead of having my name there + + + align:start position:0% +replace instead of having my name there +you you put your name there and then we + + align:start position:0% +you you put your name there and then we + + + align:start position:0% +you you put your name there and then we +have a special command here called DB + + align:start position:0% +have a special command here called DB + + + align:start position:0% +have a special command here called DB +setup LL grid + + align:start position:0% +setup LL grid + + + align:start position:0% +setup LL grid +which basically creates a binding to a + + align:start position:0% +which basically creates a binding to a + + + align:start position:0% +which basically creates a binding to a +database just using the name of the + + align:start position:0% +database just using the name of the + + + align:start position:0% +database just using the name of the +database so it's a special function + + align:start position:0% +database so it's a special function + + + align:start position:0% +database so it's a special function +that's not a generic function only works + + align:start position:0% +that's not a generic function only works + + + align:start position:0% +that's not a generic function only works +with our elog grid system and it only + + align:start position:0% +with our elog grid system and it only + + + align:start position:0% +with our elog grid system and it only +works if you have mounted the elog grid + + align:start position:0% +works if you have mounted the elog grid + + + align:start position:0% +works if you have mounted the elog grid +file system + + align:start position:0% +file system + + + align:start position:0% +file system +so hide all this stuff + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +that so as you see here I have mounted + + align:start position:0% +that so as you see here I have mounted + + + align:start position:0% +that so as you see here I have mounted +the elog grid file system + + align:start position:0% + + + + align:start position:0% + +okay and uh and and you need to do that + + align:start position:0% +okay and uh and and you need to do that + + + align:start position:0% +okay and uh and and you need to do that +because the DB setup command when it + + align:start position:0% +because the DB setup command when it + + + align:start position:0% +because the DB setup command when it +binds to the database it actually goes + + align:start position:0% +binds to the database it actually goes + + + align:start position:0% +binds to the database it actually goes +get the keys from the log grid file + + align:start position:0% +get the keys from the log grid file + + + align:start position:0% +get the keys from the log grid file +system and those keys are sitting in the + + align:start position:0% +system and those keys are sitting in the + + + align:start position:0% +system and those keys are sitting in the +group directory for that so basically + + align:start position:0% +group directory for that so basically + + + align:start position:0% +group directory for that so basically +from a password management perspective + + align:start position:0% +from a password management perspective + + + align:start position:0% +from a password management perspective +all we need to do is add you to the + + align:start position:0% +all we need to do is add you to the + + + align:start position:0% +all we need to do is add you to the +group and then you have have access to + + align:start position:0% +group and then you have have access to + + + align:start position:0% +group and then you have have access to +the database or if we remove you from + + align:start position:0% +the database or if we remove you from + + + align:start position:0% +the database or if we remove you from +the group you no longer have access to + + align:start position:0% +the group you no longer have access to + + + align:start position:0% +the group you no longer have access to +the database so that's how we do + + align:start position:0% +the database so that's how we do + + + align:start position:0% +the database so that's how we do +otherwise we'd have to distribute uh uh + + align:start position:0% +otherwise we'd have to distribute uh uh + + + align:start position:0% +otherwise we'd have to distribute uh uh +uh keys to to to to every single user + + align:start position:0% +uh keys to to to to every single user + + + align:start position:0% +uh keys to to to to every single user +all the time and so this is this is why + + align:start position:0% +all the time and so this is this is why + + + align:start position:0% +all the time and so this is this is why +we do that so this greatly simplifies it + + align:start position:0% +we do that so this greatly simplifies it + + + align:start position:0% +we do that so this greatly simplifies it +but you will not be able to make a + + align:start position:0% +but you will not be able to make a + + + align:start position:0% +but you will not be able to make a +connection to the L to one of these + + align:start position:0% +connection to the L to one of these + + + align:start position:0% +connection to the L to one of these +databases unless you are either logged + + align:start position:0% +databases unless you are either logged + + + align:start position:0% +databases unless you are either logged +into your L grid account or if you're on + + align:start position:0% +into your L grid account or if you're on + + + align:start position:0% +into your L grid account or if you're on +your computer you've mounted the the the + + align:start position:0% +your computer you've mounted the the the + + + align:start position:0% +your computer you've mounted the the the +file system and d4m knows where to look + + align:start position:0% +file system and d4m knows where to look + + + align:start position:0% +file system and d4m knows where to look +for the keys uh when you when you pass + + align:start position:0% +for the keys uh when you when you pass + + + align:start position:0% +for the keys uh when you when you pass +in that setup + + align:start position:0% + + + + align:start position:0% + +command all right here + + align:start position:0% +command all right here + + + align:start position:0% +command all right here +so so if we look at that again so um and + + align:start position:0% +so so if we look at that again so um and + + + align:start position:0% +so so if we look at that again so um and +this is just a shorthand for the full DB + + align:start position:0% +this is just a shorthand for the full DB + + + align:start position:0% +this is just a shorthand for the full DB +server command so if you were connecting + + align:start position:0% +server command so if you were connecting + + + align:start position:0% +server command so if you were connecting +some to some database directly other + + align:start position:0% +some to some database directly other + + + align:start position:0% +some to some database directly other +than one of these or you could even do + + align:start position:0% +than one of these or you could even do + + + align:start position:0% +than one of these or you could even do +it with these you would have to pass in + + align:start position:0% +it with these you would have to pass in + + + align:start position:0% +it with these you would have to pass in +essentially a five argument thing which + + align:start position:0% +essentially a five argument thing which + + + align:start position:0% +essentially a five argument thing which +is the the uh the um the host name of + + align:start position:0% +is the the uh the um the host name of + + + align:start position:0% +is the the uh the um the host name of +the computer and the port the name of + + align:start position:0% +the computer and the port the name of + + + align:start position:0% +the computer and the port the name of +the instance um the name of the I guess + + align:start position:0% +the instance um the name of the I guess + + + align:start position:0% +the instance um the name of the I guess +there's a couple instance names here and + + align:start position:0% +there's a couple instance names here and + + + align:start position:0% +there's a couple instance names here and +then the name of the user and then an + + align:start position:0% +then the name of the user and then an + + + align:start position:0% +then the name of the user and then an +actual password and so that's the + + align:start position:0% +actual password and so that's the + + + align:start position:0% +actual password and so that's the +generic way to connect in general but + + align:start position:0% +generic way to connect in general but + + + align:start position:0% +generic way to connect in general but +for the uh those of you connected to L + + align:start position:0% +for the uh those of you connected to L + + + align:start position:0% +for the uh those of you connected to L +grid uh we can we can just use this + + align:start position:0% +grid uh we can we can just use this + + + align:start position:0% +grid uh we can we can just use this +shorthand which is very + + align:start position:0% +shorthand which is very + + + align:start position:0% +shorthand which is very +nice then we're going to build uh a + + align:start position:0% +nice then we're going to build uh a + + + align:start position:0% +nice then we're going to build uh a +couple of tables so we have these uh + + align:start position:0% +couple of tables so we have these uh + + + align:start position:0% +couple of tables so we have these uh +first thing we're going to do is we're + + align:start position:0% +first thing we're going to do is we're + + + align:start position:0% +first thing we're going to do is we're +going to want to create a table that's + + align:start position:0% +going to want to create a table that's + + + align:start position:0% +going to want to create a table that's +going to hold that adjacency Matrix that + + align:start position:0% +going to hold that adjacency Matrix that + + + align:start position:0% +going to hold that adjacency Matrix that +I just created in with the files and so + + align:start position:0% +I just created in with the files and so + + + align:start position:0% +I just created in with the files and so +um we're going to do that with a + + align:start position:0% +um we're going to do that with a + + + align:start position:0% +um we're going to do that with a +database pair so if we have our database + + align:start position:0% +database pair so if we have our database + + + align:start position:0% +database pair so if we have our database +object here we give it two string names + + align:start position:0% +object here we give it two string names + + + align:start position:0% +object here we give it two string names +it will know to create two tables in uh + + align:start position:0% +it will know to create two tables in uh + + + align:start position:0% +it will know to create two tables in uh +in the database and return a binding to + + align:start position:0% +in the database and return a binding to + + + align:start position:0% +in the database and return a binding to +that table that's a pair it's a + + align:start position:0% +that table that's a pair it's a + + + align:start position:0% +that table that's a pair it's a +transposed pair so whenever we do an + + align:start position:0% +transposed pair so whenever we do an + + + align:start position:0% +transposed pair so whenever we do an +insert into that that table it will + + align:start position:0% +insert into that that table it will + + + align:start position:0% +insert into that that table it will +insert you know the row and the column + + align:start position:0% +insert you know the row and the column + + + align:start position:0% +insert you know the row and the column +and in one table and then flip those and + + align:start position:0% +and in one table and then flip those and + + + align:start position:0% +and in one table and then flip those and +insert the column in the row in the + + align:start position:0% +insert the column in the row in the + + + align:start position:0% +insert the column in the row in the +other table and then whenever you do a + + align:start position:0% +other table and then whenever you do a + + + align:start position:0% +other table and then whenever you do a +lookup it will know if it's doing a row + + align:start position:0% +lookup it will know if it's doing a row + + + align:start position:0% +lookup it will know if it's doing a row +lookup to look on one table and if it's + + align:start position:0% +lookup to look on one table and if it's + + + align:start position:0% +lookup to look on one table and if it's +doing a column lookup to do on the other + + align:start position:0% +doing a column lookup to do on the other + + + align:start position:0% +doing a column lookup to do on the other +table and this allows you to do fast + + align:start position:0% +table and this allows you to do fast + + + align:start position:0% +table and this allows you to do fast +lookups of both rows and columns and + + align:start position:0% +lookups of both rows and columns and + + + align:start position:0% +lookups of both rows and columns and +makes it all nice for you we're also + + align:start position:0% +makes it all nice for you we're also + + + align:start position:0% +makes it all nice for you we're also +going to want to take advantage of a + + align:start position:0% +going to want to take advantage of a + + + align:start position:0% +going to want to take advantage of a +cumula built-in ability to sum as we + + align:start position:0% +cumula built-in ability to sum as we + + + align:start position:0% +cumula built-in ability to sum as we +insert and so we're going to create + + align:start position:0% +insert and so we're going to create + + + align:start position:0% +insert and so we're going to create +create something that's going to hold + + align:start position:0% +create something that's going to hold + + + align:start position:0% +create something that's going to hold +the the the the degree uh as as we go + + align:start position:0% +the the the the degree uh as as we go + + + align:start position:0% +the the the the degree uh as as we go +very useful to have these statistics uh + + align:start position:0% +very useful to have these statistics uh + + + align:start position:0% +very useful to have these statistics uh +because a lot of times you want to look + + align:start position:0% +because a lot of times you want to look + + + align:start position:0% +because a lot of times you want to look +up something and then you but the first + + align:start position:0% +up something and then you but the first + + + align:start position:0% +up something and then you but the first +thing you want to do is just see well + + align:start position:0% +thing you want to do is just see well + + + align:start position:0% +thing you want to do is just see well +how many of there are in there uh and so + + align:start position:0% +how many of there are in there uh and so + + + align:start position:0% +how many of there are in there uh and so +if you create a essentially a column + + align:start position:0% +if you create a essentially a column + + + align:start position:0% +if you create a essentially a column +Vector uh with that information very + + align:start position:0% +Vector uh with that information very + + + align:start position:0% +Vector uh with that information very +helpful later we're going to do + + align:start position:0% +helpful later we're going to do + + + align:start position:0% +helpful later we're going to do +something where we actually store the + + align:start position:0% +something where we actually store the + + + align:start position:0% +something where we actually store the +edges the raw edges that were created so + + align:start position:0% +edges the raw edges that were created so + + + align:start position:0% +edges the raw edges that were created so +when we create the uh uh uh The + + align:start position:0% +when we create the uh uh uh The + + + align:start position:0% +when we create the uh uh uh The +adjacency Matrix we actually lose a + + align:start position:0% +adjacency Matrix we actually lose a + + + align:start position:0% +adjacency Matrix we actually lose a +little bit of information and so when we + + align:start position:0% +little bit of information and so when we + + + align:start position:0% +little bit of information and so when we +create this Edge Matrix we'll be able to + + align:start position:0% +create this Edge Matrix we'll be able to + + + align:start position:0% +create this Edge Matrix we'll be able to +preserve that Matrix that information + + align:start position:0% +preserve that Matrix that information + + + align:start position:0% +preserve that Matrix that information +and um and likewise we'll be doing the + + align:start position:0% +and um and likewise we'll be doing the + + + align:start position:0% +and um and likewise we'll be doing the +tallies of the edges in that as well so + + align:start position:0% +tallies of the edges in that as well so + + + align:start position:0% +tallies of the edges in that as well so +that's what this does that's the setup + + align:start position:0% +that's what this does that's the setup + + + align:start position:0% +that's what this does that's the setup +you'll need to modify that and this + + align:start position:0% +you'll need to modify that and this + + + align:start position:0% +you'll need to modify that and this +program + + align:start position:0% +program + + + align:start position:0% +program +here actually uh uh basically in in + + align:start position:0% +here actually uh uh basically in in + + + align:start position:0% +here actually uh uh basically in in +after the setup is done it adds these + + align:start position:0% +after the setup is done it adds these + + + align:start position:0% +after the setup is done it adds these +accumulator things by designating + + align:start position:0% +accumulator things by designating + + + align:start position:0% +accumulator things by designating +certain columns to be com what they call + + align:start position:0% +certain columns to be com what they call + + + align:start position:0% +certain columns to be com what they call +combiners so in this adjacency degree + + align:start position:0% +combiners so in this adjacency degree + + + align:start position:0% +combiners so in this adjacency degree +table I've said I want to create two new + + align:start position:0% +table I've said I want to create two new + + + align:start position:0% +table I've said I want to create two new +columns an outdegree and ingree column + + align:start position:0% +columns an outdegree and ingree column + + + align:start position:0% +columns an outdegree and ingree column +and the operation that I want to be + + align:start position:0% +and the operation that I want to be + + + align:start position:0% +and the operation that I want to be +applied when there are collisions on + + align:start position:0% +applied when there are collisions on + + + align:start position:0% +applied when there are collisions on +those values is sum it will then sum the + + align:start position:0% +those values is sum it will then sum the + + + align:start position:0% +those values is sum it will then sum the +values and likewise with the edge I only + + align:start position:0% +values and likewise with the edge I only + + + align:start position:0% +values and likewise with the edge I only +have since since I only have one I'm + + align:start position:0% +have since since I only have one I'm + + + align:start position:0% +have since since I only have one I'm +going to have degree and sum + + align:start position:0% +going to have degree and sum + + + align:start position:0% +going to have degree and sum +there all right so that's how we do that + + align:start position:0% +there all right so that's how we do that + + + align:start position:0% +there all right so that's how we do that +so if we now go to our database page + + align:start position:0% +so if we now go to our database page + + + align:start position:0% +so if we now go to our database page +here so you can see class db3 it started + + align:start position:0% +here so you can see class db3 it started + + + align:start position:0% +here so you can see class db3 it started +we can actually view the info and this + + align:start position:0% +we can actually view the info and this + + + align:start position:0% +we can actually view the info and this +is what a nice fresh neverbe used a + + align:start position:0% +is what a nice fresh neverbe used a + + + align:start position:0% +is what a nice fresh neverbe used a +cumulo instant looks like has very + + align:start position:0% +cumulo instant looks like has very + + + align:start position:0% +cumulo instant looks like has very +little data it has one table a metadata + + align:start position:0% +little data it has one table a metadata + + + align:start position:0% +little data it has one table a metadata +table and a trace table this is what and + + align:start position:0% +table and a trace table this is what and + + + align:start position:0% +table and a trace table this is what and +and uh you know there's no no errors or + + align:start position:0% +and uh you know there's no no errors or + + + align:start position:0% +and uh you know there's no no errors or +anything like that it's a very clean + + align:start position:0% +anything like that it's a very clean + + + align:start position:0% +anything like that it's a very clean +instance and you can actually uh and and + + align:start position:0% +instance and you can actually uh and and + + + align:start position:0% +instance and you can actually uh and and +uh so so that's one one looks like we're + + align:start position:0% +uh so so that's one one looks like we're + + + align:start position:0% +uh so so that's one one looks like we're +going to use one that we've already + + align:start position:0% +going to use one that we've already + + + align:start position:0% +going to use one that we've already +started though which is uh + + align:start position:0% +started though which is uh + + + align:start position:0% +started though which is uh +DB1 and uh if we look at the tables + + align:start position:0% +DB1 and uh if we look at the tables + + + align:start position:0% +DB1 and uh if we look at the tables +here there's already some tables + + align:start position:0% +here there's already some tables + + + align:start position:0% +here there's already some tables +Michelle ran a practice run on this + + align:start position:0% +Michelle ran a practice run on this + + + align:start position:0% +Michelle ran a practice run on this +chance up ran a practice run I'm going + + align:start position:0% +chance up ran a practice run I'm going + + + align:start position:0% +chance up ran a practice run I'm going +to now create those tables + + align:start position:0% +to now create those tables + + + align:start position:0% +to now create those tables +by five set up + + align:start position:0% + + + + align:start position:0% + +test all right there creat all those + + align:start position:0% +test all right there creat all those + + + align:start position:0% +test all right there creat all those +tables you can now see did it actually + + align:start position:0% +tables you can now see did it actually + + + align:start position:0% +tables you can now see did it actually +work here so if I refresh that and you + + align:start position:0% +work here so if I refresh that and you + + + align:start position:0% +work here so if I refresh that and you +can see it's now created these six + + align:start position:0% +can see it's now created these six + + + align:start position:0% +can see it's now created these six +tables which are + + align:start position:0% +tables which are + + + align:start position:0% +tables which are +empty um we do have abilities to set the + + align:start position:0% +empty um we do have abilities to set the + + + align:start position:0% +empty um we do have abilities to set the +right and read permissions of these + + align:start position:0% +right and read permissions of these + + + align:start position:0% +right and read permissions of these +tables so right now everyone has the + + align:start position:0% +tables so right now everyone has the + + + align:start position:0% +tables so right now everyone has the +ability to read and write and delete + + align:start position:0% +ability to read and write and delete + + + align:start position:0% +ability to read and write and delete +everyone else's tables in this class + + align:start position:0% +everyone else's tables in this class + + + align:start position:0% +everyone else's tables in this class +database in a project that's not such a + + align:start position:0% +database in a project that's not such a + + + align:start position:0% +database in a project that's not such a +difficult thing to manage you all know + + align:start position:0% +difficult thing to manage you all know + + + align:start position:0% +difficult thing to manage you all know +that but you could imagine in situation + + align:start position:0% +that but you could imagine in situation + + + align:start position:0% +that but you could imagine in situation +where look we had a big inest this is a + + align:start position:0% +where look we had a big inest this is a + + + align:start position:0% +where look we had a big inest this is a +a corpus of data we don't want anybody + + align:start position:0% +a corpus of data we don't want anybody + + + align:start position:0% +a corpus of data we don't want anybody +we can actually make the permissions we + + align:start position:0% +we can actually make the permissions we + + + align:start position:0% +we can actually make the permissions we +can make it readon so that no one no one + + align:start position:0% +can make it readon so that no one no one + + + align:start position:0% +can make it readon so that no one no one +can delete or we can make it so it's + + align:start position:0% +can delete or we can make it so it's + + + align:start position:0% +can delete or we can make it so it's +still read and write but it can't be + + align:start position:0% +still read and write but it can't be + + + align:start position:0% +still read and write but it can't be +deleted whole cloth those permissions + + align:start position:0% +deleted whole cloth those permissions + + + align:start position:0% +deleted whole cloth those permissions +exist uh a feature we will add to this + + align:start position:0% +exist uh a feature we will add to this + + + align:start position:0% +exist uh a feature we will add to this +database manager will also be a + + align:start position:0% +database manager will also be a + + + align:start position:0% +database manager will also be a +checkpoint feature so for instance if + + align:start position:0% +checkpoint feature so for instance if + + + align:start position:0% +checkpoint feature so for instance if +you did a big ingest have a bunch of + + align:start position:0% +you did a big ingest have a bunch of + + + align:start position:0% +you did a big ingest have a bunch of +data that you're very happy with you can + + align:start position:0% +data that you're very happy with you can + + + align:start position:0% +data that you're very happy with you can +checkpoint it you know you will you'll + + align:start position:0% +checkpoint it you know you will you'll + + + align:start position:0% +checkpoint it you know you will you'll +have to stop the database then you can + + align:start position:0% +have to stop the database then you can + + + align:start position:0% +have to stop the database then you can +create a checkpoint of that stop + + align:start position:0% +create a checkpoint of that stop + + + align:start position:0% +create a checkpoint of that stop +database uh name checkpoint and then you + + align:start position:0% +database uh name checkpoint and then you + + + align:start position:0% +database uh name checkpoint and then you +can restart from that if for some reason + + align:start position:0% +can restart from that if for some reason + + + align:start position:0% +can restart from that if for some reason +your database gets corrupted as I like + + align:start position:0% +your database gets corrupted as I like + + + align:start position:0% +your database gets corrupted as I like +to say accumulo like all other databases + + align:start position:0% +to say accumulo like all other databases + + + align:start position:0% +to say accumulo like all other databases +it's stable for production but it can be + + align:start position:0% +it's stable for production but it can be + + + align:start position:0% +it's stable for production but it can be +unstable for development new databased + + align:start position:0% +unstable for development new databased + + + align:start position:0% +unstable for development new databased +users the database will train you in + + align:start position:0% +users the database will train you in + + + align:start position:0% +users the database will train you in +terms of the things that you should not + + align:start position:0% +terms of the things that you should not + + + align:start position:0% +terms of the things that you should not +do to it and so over time you will not + + align:start position:0% +do to it and so over time you will not + + + align:start position:0% +do to it and so over time you will not +do the things that destroy data or cause + + align:start position:0% +do the things that destroy data or cause + + + align:start position:0% +do the things that destroy data or cause +your database to be very unhappy and + + align:start position:0% +your database to be very unhappy and + + + align:start position:0% +your database to be very unhappy and +then you'll have a nice production + + align:start position:0% +then you'll have a nice production + + + align:start position:0% +then you'll have a nice production +database because you will only do things + + align:start position:0% +database because you will only do things + + + align:start position:0% +database because you will only do things +that make it happy but in that phase + + align:start position:0% +that make it happy but in that phase + + + align:start position:0% +that make it happy but in that phase +where you're learning or you're + + align:start position:0% +where you're learning or you're + + + align:start position:0% +where you're learning or you're +experimenting with things as with all + + align:start position:0% +experimenting with things as with all + + + align:start position:0% +experimenting with things as with all +databases any database it's easy to do + + align:start position:0% +databases any database it's easy to do + + + align:start position:0% +databases any database it's easy to do +commands that will put the database in a + + align:start position:0% +commands that will put the database in a + + + align:start position:0% +commands that will put the database in a +fairly unhappy State even to the point + + align:start position:0% +fairly unhappy State even to the point + + + align:start position:0% +fairly unhappy State even to the point +of corrupting or losing the data so um + + align:start position:0% +of corrupting or losing the data so um + + + align:start position:0% +of corrupting or losing the data so um +uh so so but for the most part once it's + + align:start position:0% +uh so so but for the most part once it's + + + align:start position:0% +uh so so but for the most part once it's +up and running in production and we have + + align:start position:0% +up and running in production and we have + + + align:start position:0% +up and running in production and we have +a a database that's been running for + + align:start position:0% +a a database that's been running for + + + align:start position:0% +a a database that's been running for +almost two years continuously using a + + align:start position:0% +almost two years continuously using a + + + align:start position:0% +almost two years continuously using a +very old version of this software so it + + align:start position:0% +very old version of this software so it + + + align:start position:0% +very old version of this software so it +just continues to hum away it's got + + align:start position:0% +just continues to hum away it's got + + + align:start position:0% +just continues to hum away it's got +billions of entries in it you know we're + + align:start position:0% +billions of entries in it you know we're + + + align:start position:0% +billions of entries in it you know we're +not really but it's on a single it's + + align:start position:0% +not really but it's on a single it's + + + align:start position:0% +not really but it's on a single it's +running on a single Mac you know and so + + align:start position:0% +running on a single Mac you know and so + + + align:start position:0% +running on a single Mac you know and so +it's uh so it definitely uh we've seen + + align:start position:0% +it's uh so it definitely uh we've seen + + + align:start position:0% +it's uh so it definitely uh we've seen +situations where it's like all other dat + + align:start position:0% +situations where it's like all other dat + + + align:start position:0% +situations where it's like all other dat +it has the same stability of as just + + align:start position:0% +it has the same stability of as just + + + align:start position:0% +it has the same stability of as just +about any other + + align:start position:0% +about any other + + + align:start position:0% +about any other +database so now we've created these + + align:start position:0% +database so now we've created these + + + align:start position:0% +database so now we've created these +tables and let's insert some data into + + align:start position:0% +tables and let's insert some data into + + + align:start position:0% +tables and let's insert some data into +them okay so I do + + align:start position:0% +them okay so I do + + + align:start position:0% +them okay so I do +pd6 so I'm now going to insert the + + align:start position:0% +pd6 so I'm now going to insert the + + + align:start position:0% +pd6 so I'm now going to insert the +adjacency + + align:start position:0% + + + + align:start position:0% + +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +there and now it's + + align:start position:0% +there and now it's + + + align:start position:0% +there and now it's +basically reading in each file and + + align:start position:0% +basically reading in each file and + + + align:start position:0% +basically reading in each file and +ingesting uh that that + + align:start position:0% +ingesting uh that that + + + align:start position:0% +ingesting uh that that +data it's not a lot of data it doesn't + + align:start position:0% +data it's not a lot of data it doesn't + + + align:start position:0% +data it's not a lot of data it doesn't +take very long and now you can + + align:start position:0% +take very long and now you can + + + align:start position:0% +take very long and now you can +see here here that data has been + + align:start position:0% +see here here that data has been + + + align:start position:0% +see here here that data has been +injested and you see there so we just + + align:start position:0% +injested and you see there so we just + + + align:start position:0% +injested and you see there so we just +inserted about 62,000 in each of those + + align:start position:0% +inserted about 62,000 in each of those + + + align:start position:0% +inserted about 62,000 in each of those +two tables and + + align:start position:0% +two tables and + + + align:start position:0% +two tables and +25,000 which for a cumula was a trivial + + align:start position:0% +25,000 which for a cumula was a trivial + + + align:start position:0% +25,000 which for a cumula was a trivial +amount you know we just inserted 150,000 + + align:start position:0% +amount you know we just inserted 150,000 + + + align:start position:0% +amount you know we just inserted 150,000 +entries into a a database which is + + align:start position:0% +entries into a a database which is + + + align:start position:0% +entries into a a database which is +pretty impressive you know to to be able + + align:start position:0% +pretty impressive you know to to be able + + + align:start position:0% +pretty impressive you know to to be able +to do that in you know essentially the + + align:start position:0% +to do that in you know essentially the + + + align:start position:0% +to do that in you know essentially the +blink of an eye and that's really the + + align:start position:0% +blink of an eye and that's really the + + + align:start position:0% +blink of an eye and that's really the +real power of a cumulo is this you know + + align:start position:0% +real power of a cumulo is this you know + + + align:start position:0% +real power of a cumulo is this you know +on a lot of other databases 150,000 + + align:start position:0% +on a lot of other databases 150,000 + + + align:start position:0% +on a lot of other databases 150,000 +entries you're talking about a few + + align:start position:0% +entries you're talking about a few + + + align:start position:0% +entries you're talking about a few +minutes and here it's just you wouldn't + + align:start position:0% +minutes and here it's just you wouldn't + + + align:start position:0% +minutes and here it's just you wouldn't +even think about doing that + + align:start position:0% +even think about doing that + + + align:start position:0% +even think about doing that +twice um all + + align:start position:0% +twice um all + + + align:start position:0% +twice um all +right so we can take a look at that + + align:start position:0% + + + + align:start position:0% + +program so here we go so we had eight + + align:start position:0% +program so here we go so we had eight + + + align:start position:0% +program so here we go so we had eight +files here and basically we loaded the + + align:start position:0% +files here and basically we loaded the + + + align:start position:0% +files here and basically we loaded the +data and basically one thing we have to + + align:start position:0% +data and basically one thing we have to + + + align:start position:0% +data and basically one thing we have to +remember is that our adjacency Matrix + + align:start position:0% +remember is that our adjacency Matrix + + + align:start position:0% +remember is that our adjacency Matrix +has numeric values in its in it in the + + align:start position:0% +has numeric values in its in it in the + + + align:start position:0% +has numeric values in its in it in the +associative array and a cumulo Can Only + + align:start position:0% +associative array and a cumulo Can Only + + + align:start position:0% +associative array and a cumulo Can Only +Hold strings so we have to call the num + + align:start position:0% +Hold strings so we have to call the num + + + align:start position:0% +Hold strings so we have to call the num +to string function which will convert + + align:start position:0% +to string function which will convert + + + align:start position:0% +to string function which will convert +those numbers into Strings uh to be to + + align:start position:0% +those numbers into Strings uh to be to + + + align:start position:0% +those numbers into Strings uh to be to +be stored so the first thing we do is we + + align:start position:0% +be stored so the first thing we do is we + + + align:start position:0% +be stored so the first thing we do is we +con we we do we read in we load our + + align:start position:0% +con we we do we read in we load our + + + align:start position:0% +con we we do we read in we load our +adjacency Matrix a we convert it the + + align:start position:0% +adjacency Matrix a we convert it the + + + align:start position:0% +adjacency Matrix a we convert it the +numeric values to Strings and then we + + align:start position:0% +numeric values to Strings and then we + + + align:start position:0% +numeric values to Strings and then we +just do a put so we can just insert the + + align:start position:0% +just do a put so we can just insert the + + + align:start position:0% +just do a put so we can just insert the +associative array directly into the + + align:start position:0% +associative array directly into the + + + align:start position:0% +associative array directly into the +adjacency Matrix and it knows it pulls + + align:start position:0% +adjacency Matrix and it knows it pulls + + + align:start position:0% +adjacency Matrix and it knows it pulls +apart the triples and it knows how to uh + + align:start position:0% +apart the triples and it knows how to uh + + + align:start position:0% +apart the triples and it knows how to uh +you know take care of the fact that it + + align:start position:0% +you know take care of the fact that it + + + align:start position:0% +you know take care of the fact that it +recognizes this is a transpose table + + align:start position:0% +recognizes this is a transpose table + + + align:start position:0% +recognizes this is a transpose table +pair and it does that that in in just + + align:start position:0% +pair and it does that that in in just + + + align:start position:0% +pair and it does that that in in just +for you and likewise same thing here now + + align:start position:0% +for you and likewise same thing here now + + + align:start position:0% +for you and likewise same thing here now +on these other things we pulled it out + + align:start position:0% +on these other things we pulled it out + + + align:start position:0% +on these other things we pulled it out +we we summed it converted to strings to + + align:start position:0% +we we summed it converted to strings to + + + align:start position:0% +we we summed it converted to strings to +do the outdegree and the same thing to + + align:start position:0% +do the outdegree and the same thing to + + + align:start position:0% +do the outdegree and the same thing to +do the IND degree and so this is + + align:start position:0% +do the IND degree and so this is + + + align:start position:0% +do the IND degree and so this is +actually where the adjacency Matrix + + align:start position:0% +actually where the adjacency Matrix + + + align:start position:0% +actually where the adjacency Matrix +comes in very handy because when we're + + align:start position:0% +comes in very handy because when we're + + + align:start position:0% +comes in very handy because when we're +we're doing accumulating if we didn't + + align:start position:0% +we're doing accumulating if we didn't + + + align:start position:0% +we're doing accumulating if we didn't +first sum it and then do it we would be + + align:start position:0% +first sum it and then do it we would be + + + align:start position:0% +first sum it and then do it we would be +if we put those raw triples into to to + + align:start position:0% +if we put those raw triples into to to + + + align:start position:0% +if we put those raw triples into to to +insert we're essentially redoing the + + align:start position:0% +insert we're essentially redoing the + + + align:start position:0% +insert we're essentially redoing the +complete insert and so this saves you + + align:start position:0% +complete insert and so this saves you + + + align:start position:0% +complete insert and so this saves you +know usually an order of magnitude and + + align:start position:0% +know usually an order of magnitude and + + + align:start position:0% +know usually an order of magnitude and +number of inserts by basically doing the + + align:start position:0% +number of inserts by basically doing the + + + align:start position:0% +number of inserts by basically doing the +sum in our D d4m program first and then + + align:start position:0% +sum in our D d4m program first and then + + + align:start position:0% +sum in our D d4m program first and then +just inserting those sum values just a + + align:start position:0% +just inserting those sum values just a + + + align:start position:0% +just inserting those sum values just a +nice way to to save the database a + + align:start position:0% +nice way to to save the database a + + + align:start position:0% +nice way to to save the database a +little bit of trouble in uh in doing + + align:start position:0% +little bit of trouble in uh in doing + + + align:start position:0% +little bit of trouble in uh in doing +that and so we certainly recommend this + + align:start position:0% +that and so we certainly recommend this + + + align:start position:0% +that and so we certainly recommend this +type of approach for doing + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +right that + + align:start position:0% +right that + + + align:start position:0% +right that +there so the next + + align:start position:0% +there so the next + + + align:start position:0% +there so the next +one7 so now we're going to do a query + + align:start position:0% +one7 so now we're going to do a query + + + align:start position:0% +one7 so now we're going to do a query +we're going to get some data out of that + + align:start position:0% +we're going to get some data out of that + + + align:start position:0% +we're going to get some data out of that +table + + align:start position:0% + + + + align:start position:0% + +that all right and so what we did here + + align:start position:0% +that all right and so what we did here + + + align:start position:0% +that all right and so what we did here +is we said I want to pick 100 random + + align:start position:0% +is we said I want to pick 100 random + + + align:start position:0% +is we said I want to pick 100 random +vertices okay so in this case I randomly + + align:start position:0% +vertices okay so in this case I randomly + + + align:start position:0% +vertices okay so in this case I randomly +generate uh 100 random vertices over the + + align:start position:0% +generate uh 100 random vertices over the + + + align:start position:0% +generate uh 100 random vertices over the +range 1 to a + + align:start position:0% +range 1 to a + + + align:start position:0% +range 1 to a +th okay and um I then convert those to a + + align:start position:0% +th okay and um I then convert those to a + + + align:start position:0% +th okay and um I then convert those to a +string because these are numeric values + + align:start position:0% +string because these are numeric values + + + align:start position:0% +string because these are numeric values +and I will look up strings and then the + + align:start position:0% +and I will look up strings and then the + + + align:start position:0% +and I will look up strings and then the +first thing I'm going to do is I'm going + + align:start position:0% +first thing I'm going to do is I'm going + + + align:start position:0% +first thing I'm going to do is I'm going +to look up the degrees essentially of + + align:start position:0% +to look up the degrees essentially of + + + align:start position:0% +to look up the degrees essentially of +those vertices so I have my sum table + + align:start position:0% +those vertices so I have my sum table + + + align:start position:0% +those vertices so I have my sum table +here called T adjacency degree I'm going + + align:start position:0% +here called T adjacency degree I'm going + + + align:start position:0% +here called T adjacency degree I'm going +to pass those strings in and then I'm + + align:start position:0% +to pass those strings in and then I'm + + + align:start position:0% +to pass those strings in and then I'm +going to get just the degrees so that's + + align:start position:0% +going to get just the degrees so that's + + + align:start position:0% +going to get just the degrees so that's +just a big long skinny Vector looking + + align:start position:0% +just a big long skinny Vector looking + + + align:start position:0% +just a big long skinny Vector looking +things up from that is it takes much + + align:start position:0% +things up from that is it takes much + + + align:start position:0% +things up from that is it takes much +less time than looking up whole rows and + + align:start position:0% +less time than looking up whole rows and + + + align:start position:0% +less time than looking up whole rows and +it and or columns and it stores all + + align:start position:0% +it and or columns and it stores all + + + align:start position:0% +it and or columns and it stores all +those values for me so that's a great + + align:start position:0% +those values for me so that's a great + + + align:start position:0% +those values for me so that's a great +place to start and then I want to say + + align:start position:0% +place to start and then I want to say + + + align:start position:0% +place to start and then I want to say +you know what I only care about degrees + + align:start position:0% +you know what I only care about degrees + + + align:start position:0% +you know what I only care about degrees +that are been a particular range this is + + align:start position:0% +that are been a particular range this is + + + align:start position:0% +that are been a particular range this is +a very common thing to do there'll be + + align:start position:0% +a very common thing to do there'll be + + + align:start position:0% +a very common thing to do there'll be +vertices that are so common you're like + + align:start position:0% +vertices that are so common you're like + + + align:start position:0% +vertices that are so common you're like +I don't care about those I don't I I + + align:start position:0% +I don't care about those I don't I I + + + align:start position:0% +I don't care about those I don't I I +have their tally and I these are + + align:start position:0% +have their tally and I these are + + + align:start position:0% +have their tally and I these are +sometimes called super nodes and and and + + align:start position:0% +sometimes called super nodes and and and + + + align:start position:0% +sometimes called super nodes and and and +and doing anything with those is a waste + + align:start position:0% +and doing anything with those is a waste + + + align:start position:0% +and doing anything with those is a waste +of my time and forces me to end up + + align:start position:0% +of my time and forces me to end up + + + align:start position:0% +of my time and forces me to end up +traversing enormous sads of the database + + align:start position:0% +traversing enormous sads of the database + + + align:start position:0% +traversing enormous sads of the database +so I'll set a uh an upper uh threshold + + align:start position:0% +so I'll set a uh an upper uh threshold + + + align:start position:0% +so I'll set a uh an upper uh threshold +here and a lower threshold so basically + + align:start position:0% +here and a lower threshold so basically + + + align:start position:0% +here and a lower threshold so basically +I take a degree I'm just going to look + + align:start position:0% +I take a degree I'm just going to look + + + align:start position:0% +I take a degree I'm just going to look +at the out degree I say I want things + + align:start position:0% +at the out degree I say I want things + + + align:start position:0% +at the out degree I say I want things +that are greater than the Min and less + + align:start position:0% +that are greater than the Min and less + + + align:start position:0% +that are greater than the Min and less +than the max and I want to get just + + align:start position:0% +than the max and I want to get just + + + align:start position:0% +than the max and I want to get just +those rows so that's this query a fairly + + align:start position:0% +those rows so that's this query a fairly + + + align:start position:0% +those rows so that's this query a fairly +complicated thing analytic here done in + + align:start position:0% +complicated thing analytic here done in + + + align:start position:0% +complicated thing analytic here done in +just sort of one line and now a new set + + align:start position:0% +just sort of one line and now a new set + + + align:start position:0% +just sort of one line and now a new set +of vertices which are just the rows that + + align:start position:0% +of vertices which are just the rows that + + + align:start position:0% +of vertices which are just the rows that +satisfy this requirement and then I'm + + align:start position:0% +satisfy this requirement and then I'm + + + align:start position:0% +satisfy this requirement and then I'm +going to look those up again so I'm just + + align:start position:0% +going to look those up again so I'm just + + + align:start position:0% +going to look those up again so I'm just +going to look up the ones that satisfy + + align:start position:0% +going to look up the ones that satisfy + + + align:start position:0% +going to look up the ones that satisfy +those I'm going to get the the whole row + + align:start position:0% +those I'm going to get the the whole row + + + align:start position:0% +those I'm going to get the the whole row +of those things so before I was just in + + align:start position:0% +of those things so before I was just in + + + align:start position:0% +of those things so before I was just in +looking up their counts now I'm going to + + align:start position:0% +looking up their counts now I'm going to + + + align:start position:0% +looking up their counts now I'm going to +get the whole row and I know that + + align:start position:0% +get the whole row and I know that + + + align:start position:0% +get the whole row and I know that +there's none that have more than this + + align:start position:0% +there's none that have more than this + + + align:start position:0% +there's none that have more than this +certain value or or have too few and + + align:start position:0% +certain value or or have too few and + + + align:start position:0% +certain value or or have too few and +then I'm going to + + align:start position:0% +then I'm going to + + + align:start position:0% +then I'm going to +um plot it and so if we look at the + + align:start position:0% +um plot it and so if we look at the + + + align:start position:0% +um plot it and so if we look at the +figure there we see so these are we + + align:start position:0% +figure there we see so these are we + + + align:start position:0% +figure there we see so these are we +ended up finding one two three + + align:start position:0% +ended up finding one two three + + + align:start position:0% +ended up finding one two three +four uh rows that had between let's see + + align:start position:0% +four uh rows that had between let's see + + + align:start position:0% +four uh rows that had between let's see +these should all write one two three + + align:start position:0% +these should all write one two three + + + align:start position:0% +these should all write one two three +four five six seven so that's between + + align:start position:0% +four five six seven so that's between + + + align:start position:0% +four five six seven so that's between +five and 10 these should all be between + + align:start position:0% +five and 10 these should all be between + + + align:start position:0% +five and 10 these should all be between +five and 10 and then this shows what + + align:start position:0% +five and 10 and then this shows what + + + align:start position:0% +five and 10 and then this shows what +their actual column column was and so + + align:start position:0% +their actual column column was and so + + + align:start position:0% +their actual column column was and so +that's a very uh quick example of that + + align:start position:0% +that's a very uh quick example of that + + + align:start position:0% +that's a very uh quick example of that +kind of analytic very and again very + + align:start position:0% +kind of analytic very and again very + + + align:start position:0% +kind of analytic very and again very +real bread and butter and this is + + align:start position:0% +real bread and butter and this is + + + align:start position:0% +real bread and butter and this is +basically standard from a signal Pro + + align:start position:0% +basically standard from a signal Pro + + + align:start position:0% +basically standard from a signal Pro +processing perspective the max is our + + align:start position:0% +processing perspective the max is our + + + align:start position:0% +processing perspective the max is our +clutter threshold we don't want want + + align:start position:0% +clutter threshold we don't want want + + + align:start position:0% +clutter threshold we don't want want +that it's too bright and then you know + + align:start position:0% +that it's too bright and then you know + + + align:start position:0% +that it's too bright and then you know +we'll have a noise threshold like we + + align:start position:0% +we'll have a noise threshold like we + + + align:start position:0% +we'll have a noise threshold like we +don't care anything that's below a + + align:start position:0% +don't care anything that's below a + + + align:start position:0% +don't care anything that's below a +certain value and this sort of Narrows + + align:start position:0% +certain value and this sort of Narrows + + + align:start position:0% +certain value and this sort of Narrows +in on the signal same kind of processing + + align:start position:0% +in on the signal same kind of processing + + + align:start position:0% +in on the signal same kind of processing +and Signal processing we're doing it + + align:start position:0% +and Signal processing we're doing it + + + align:start position:0% +and Signal processing we're doing it +here on graphs and a cumulo supports + + align:start position:0% +here on graphs and a cumulo supports + + + align:start position:0% +here on graphs and a cumulo supports +that very very nicely for + + align:start position:0% +that very very nicely for + + + align:start position:0% +that very very nicely for +us Al + + align:start position:0% + + + + align:start position:0% + +righty so let's move on to the next + + align:start position:0% +righty so let's move on to the next + + + align:start position:0% +righty so let's move on to the next +example and actually if we look + + align:start position:0% + + + + align:start position:0% + +here we go back to the + + align:start position:0% + + + + align:start position:0% + +overview so you see here that was that + + align:start position:0% +overview so you see here that was that + + + align:start position:0% +overview so you see here that was that +ingest I did this is the ingest so very + + align:start position:0% +ingest I did this is the ingest so very + + + align:start position:0% +ingest I did this is the ingest so very +quick was getting about 5,000 inserts a + + align:start position:0% +quick was getting about 5,000 inserts a + + + align:start position:0% +quick was getting about 5,000 inserts a +second but that was over a very short + + align:start position:0% +second but that was over a very short + + + align:start position:0% +second but that was over a very short +period of time you can't even doesn't + + align:start position:0% +period of time you can't even doesn't + + + align:start position:0% +period of time you can't even doesn't +even have time to get reach its full + + align:start position:0% +even have time to get reach its full + + + align:start position:0% +even have time to get reach its full +rise time there and then you can see the + + align:start position:0% +rise time there and then you can see the + + + align:start position:0% +rise time there and then you can see the +scan rate and it was very small it was a + + align:start position:0% +scan rate and it was very small it was a + + + align:start position:0% +scan rate and it was very small it was a +very tiny amount you know type of thing + + align:start position:0% +very tiny amount you know type of thing + + + align:start position:0% +very tiny amount you know type of thing +as we do larger data sets you'll really + + align:start position:0% +as we do larger data sets you'll really + + + align:start position:0% +as we do larger data sets you'll really +see that and this is a great tool here + + align:start position:0% +see that and this is a great tool here + + + align:start position:0% +see that and this is a great tool here +you know uh it really kind of shows you + + align:start position:0% +you know uh it really kind of shows you + + + align:start position:0% +you know uh it really kind of shows you +what's really going on + + align:start position:0% +what's really going on + + + align:start position:0% +what's really going on +um always before you use the database + + align:start position:0% +um always before you use the database + + + align:start position:0% +um always before you use the database +always check this + + align:start position:0% +always check this + + + align:start position:0% +always check this +page if you can't get to the page of the + + align:start position:0% +page if you can't get to the page of the + + + align:start position:0% +page if you can't get to the page of the +database you're not going to be able to + + align:start position:0% +database you're not going to be able to + + + align:start position:0% +database you're not going to be able to +get to the database there is no point in + + align:start position:0% +get to the database there is no point in + + + align:start position:0% +get to the database there is no point in +doing anything with d4m if the if this + + align:start position:0% +doing anything with d4m if the if this + + + align:start position:0% +doing anything with d4m if the if this +page is not responding okay likewise if + + align:start position:0% +page is not responding okay likewise if + + + align:start position:0% +page is not responding okay likewise if +you look at this and you see this thing + + align:start position:0% +you look at this and you see this thing + + + align:start position:0% +you look at this and you see this thing +is just hammering you know away and + + align:start position:0% +is just hammering you know away and + + + align:start position:0% +is just hammering you know away and +you're getting you seeing hundreds of + + align:start position:0% +you're getting you seeing hundreds of + + + align:start position:0% +you're getting you seeing hundreds of +thousands or millions of inserts a + + align:start position:0% +thousands or millions of inserts a + + + align:start position:0% +thousands or millions of inserts a +second it means that guess what someone + + align:start position:0% +second it means that guess what someone + + + align:start position:0% +second it means that guess what someone +is probably using your database and you + + align:start position:0% +is probably using your database and you + + + align:start position:0% +is probably using your database and you +might want to either pick check a + + align:start position:0% +might want to either pick check a + + + align:start position:0% +might want to either pick check a +different database or find out who that + + align:start position:0% +different database or find out who that + + + align:start position:0% +different database or find out who that +is and say hey when are you going to be + + align:start position:0% +is and say hey when are you going to be + + + align:start position:0% +is and say hey when are you going to be +done or something like that likewise on + + align:start position:0% +done or something like that likewise on + + + align:start position:0% +done or something like that likewise on +the scan side you know uh likewise when + + align:start position:0% +the scan side you know uh likewise when + + + align:start position:0% +the scan side you know uh likewise when +you do inserts you want to see well + + align:start position:0% +you do inserts you want to see well + + + align:start position:0% +you do inserts you want to see well +you'll get some examples here of the + + align:start position:0% +you'll get some examples here of the + + + align:start position:0% +you'll get some examples here of the +kinds of rates you should be seeing you + + align:start position:0% +kinds of rates you should be seeing you + + + align:start position:0% +kinds of rates you should be seeing you +want to make sure you're seeing those + + align:start position:0% +want to make sure you're seeing those + + + align:start position:0% +want to make sure you're seeing those +rates if you're not seeing those rates + + align:start position:0% +rates if you're not seeing those rates + + + align:start position:0% +rates if you're not seeing those rates +if you're basically just you know using + + align:start position:0% +if you're basically just you know using + + + align:start position:0% +if you're basically just you know using +the resource but only inserting at a low + + align:start position:0% +the resource but only inserting at a low + + + align:start position:0% +the resource but only inserting at a low +rate then you're actually doing yourself + + align:start position:0% +rate then you're actually doing yourself + + + align:start position:0% +rate then you're actually doing yourself +and everybody else's disservice you're + + align:start position:0% +and everybody else's disservice you're + + + align:start position:0% +and everybody else's disservice you're +you're using the database but you're + + align:start position:0% +you're using the database but you're + + + align:start position:0% +you're using the database but you're +using it inefficiently and it's much + + align:start position:0% +using it inefficiently and it's much + + + align:start position:0% +using it inefficiently and it's much +better to have your inserts go fast + + align:start position:0% +better to have your inserts go fast + + + align:start position:0% +better to have your inserts go fast +because then you're out of the way you + + align:start position:0% +because then you're out of the way you + + + align:start position:0% +because then you're out of the way you +know your work gets done quicker and + + align:start position:0% +know your work gets done quicker and + + + align:start position:0% +know your work gets done quicker and +then you're out of everybody else's way + + align:start position:0% +then you're out of everybody else's way + + + align:start position:0% +then you're out of everybody else's way +quicker too so so this is a very I I + + align:start position:0% +quicker too so so this is a very I I + + + align:start position:0% +quicker too so so this is a very I I +highly recommend people people look at + + align:start position:0% +highly recommend people people look at + + + align:start position:0% +highly recommend people people look at +this uh to see what's going on all right + + align:start position:0% +this uh to see what's going on all right + + + align:start position:0% +this uh to see what's going on all right +so I think the last one was seven so + + align:start position:0% +so I think the last one was seven so + + + align:start position:0% +so I think the last one was seven so +we'll move on to eight tier so now we're + + align:start position:0% +we'll move on to eight tier so now we're + + + align:start position:0% +we'll move on to eight tier so now we're +going to do another type of query we're + + align:start position:0% +going to do another type of query we're + + + align:start position:0% +going to do another type of query we're +going to do a little bit more + + align:start position:0% +going to do a little bit more + + + align:start position:0% +going to do a little bit more +sophisticated + + align:start position:0% +sophisticated + + + align:start position:0% +sophisticated +query that query used the degree tables + + align:start position:0% +query that query used the degree tables + + + align:start position:0% +query that query used the degree tables +to sort of prune our query so we didn't + + align:start position:0% +to sort of prune our query so we didn't + + + align:start position:0% +to sort of prune our query so we didn't +have to get you think about it like + + align:start position:0% +have to get you think about it like + + + align:start position:0% +have to get you think about it like +there was probably an Ed in there that + + align:start position:0% +there was probably an Ed in there that + + + align:start position:0% +there was probably an Ed in there that +had like 100 entries you know and we + + align:start position:0% +had like 100 entries you know and we + + + align:start position:0% +had like 100 entries you know and we +just were able to avoid that never had + + align:start position:0% +just were able to avoid that never had + + + align:start position:0% +just were able to avoid that never had +to touch that edge but if we had had + + align:start position:0% +to touch that edge but if we had had + + + align:start position:0% +to touch that edge but if we had had +touched it you know that could have been + + align:start position:0% +touched it you know that could have been + + + align:start position:0% +touched it you know that could have been +a much bigger query you like well 100 + + align:start position:0% +a much bigger query you like well 100 + + + align:start position:0% +a much bigger query you like well 100 +doesn't sound bad well it's easy to get + + align:start position:0% +doesn't sound bad well it's easy to get + + + align:start position:0% +doesn't sound bad well it's easy to get +databases where you'll have some some + + align:start position:0% +databases where you'll have some some + + + align:start position:0% +databases where you'll have some some +rows with a million entries or columns + + align:start position:0% +rows with a million entries or columns + + + align:start position:0% +rows with a million entries or columns +with a million um entries or a billion + + align:start position:0% +with a million um entries or a billion + + + align:start position:0% +with a million um entries or a billion +entries and you really don't want to + + align:start position:0% +entries and you really don't want to + + + align:start position:0% +entries and you really don't want to +have to query those rows or columns + + align:start position:0% +have to query those rows or columns + + + align:start position:0% +have to query those rows or columns +because they will just you know send + + align:start position:0% +because they will just you know send + + + align:start position:0% +because they will just you know send +back so much uh data but you can still + + align:start position:0% +back so much uh data but you can still + + + align:start position:0% +back so much uh data but you can still +have situations where you're doing + + align:start position:0% +have situations where you're doing + + + align:start position:0% +have situations where you're doing +queries that are going to take they're + + align:start position:0% +queries that are going to take they're + + + align:start position:0% +queries that are going to take they're +going to send back a lot of data more + + align:start position:0% +going to send back a lot of data more + + + align:start position:0% +going to send back a lot of data more +data that you can really handle uh uh + + align:start position:0% +data that you can really handle uh uh + + + align:start position:0% +data that you can really handle uh uh +you know in your in your memory segment + + align:start position:0% +you know in your in your memory segment + + + align:start position:0% +you know in your in your memory segment +so we have a thing called an iterator so + + align:start position:0% +so we have a thing called an iterator so + + + align:start position:0% +so we have a thing called an iterator so +we've created an iterator allowed you to + + align:start position:0% +we've created an iterator allowed you to + + + align:start position:0% +we've created an iterator allowed you to +set up a query and have it work through + + align:start position:0% +set up a query and have it work through + + + align:start position:0% +set up a query and have it work through +it now this table is so small that you + + align:start position:0% +it now this table is so small that you + + + align:start position:0% +it now this table is so small that you +only won't really get to see the + + align:start position:0% +only won't really get to see the + + + align:start position:0% +only won't really get to see the +iteration happening but uh but but I'll + + align:start position:0% +iteration happening but uh but but I'll + + + align:start position:0% +iteration happening but uh but but I'll +show you the setup so we'll do that all + + align:start position:0% +show you the setup so we'll do that all + + + align:start position:0% +show you the setup so we'll do that all +right so those very quick so essentially + + align:start position:0% +right so those very quick so essentially + + + align:start position:0% +right so those very quick so essentially +we're doing a similar thing we're + + align:start position:0% +we're doing a similar thing we're + + + align:start position:0% +we're doing a similar thing we're +creating a random set of vertices here + + align:start position:0% +creating a random set of vertices here + + + align:start position:0% +creating a random set of vertices here +about 100 + + align:start position:0% +about 100 + + + align:start position:0% +about 100 +getting creating you know bit over the + + align:start position:0% +getting creating you know bit over the + + + align:start position:0% +getting creating you know bit over the +range of 1 to + + align:start position:0% +range of 1 to + + + align:start position:0% +range of 1 to +1,000 and we're creating an iterator + + align:start position:0% +1,000 and we're creating an iterator + + + align:start position:0% +1,000 and we're creating an iterator +here called T adjacency iterator so the + + align:start position:0% +here called T adjacency iterator so the + + + align:start position:0% +here called T adjacency iterator so the +the we do we we it's this function here + + align:start position:0% +the we do we we it's this function here + + + align:start position:0% +the we do we we it's this function here +iterator we pass in the table then we + + align:start position:0% +iterator we pass in the table then we + + + align:start position:0% +iterator we pass in the table then we +have a flag which is element which is + + align:start position:0% +have a flag which is element which is + + + align:start position:0% +have a flag which is element which is +how many entries do we want this + + align:start position:0% +how many entries do we want this + + + align:start position:0% +how many entries do we want this +iterator it's the chunk size how many + + align:start position:0% +iterator it's the chunk size how many + + + align:start position:0% +iterator it's the chunk size how many +entries do we want this iterator to + + align:start position:0% +entries do we want this iterator to + + + align:start position:0% +entries do we want this iterator to +return every single time we call it and + + align:start position:0% +return every single time we call it and + + + align:start position:0% +return every single time we call it and +here we've set max to be a pretty small + + align:start position:0% +here we've set max to be a pretty small + + + align:start position:0% +here we've set max to be a pretty small +number to be a thousand okay so we're + + align:start position:0% +number to be a thousand okay so we're + + + align:start position:0% +number to be a thousand okay so we're +saying is every single time we do this + + align:start position:0% +saying is every single time we do this + + + align:start position:0% +saying is every single time we do this +query we want you to return a thousand + + align:start position:0% +query we want you to return a thousand + + + align:start position:0% +query we want you to return a thousand +at a + + align:start position:0% +at a + + + align:start position:0% +at a +time now for those of you who are mat + + align:start position:0% +time now for those of you who are mat + + + align:start position:0% +time now for those of you who are mat +lab of fici fishon AOS uh uh this should + + align:start position:0% +lab of fici fishon AOS uh uh this should + + + align:start position:0% +lab of fici fishon AOS uh uh this should +be you should be an awe because mat lab + + align:start position:0% +be you should be an awe because mat lab + + + align:start position:0% +be you should be an awe because mat lab +is supposed to be a stateless language + + align:start position:0% +is supposed to be a stateless language + + + align:start position:0% +is supposed to be a stateless language +and there's nothing more stateful than + + align:start position:0% +and there's nothing more stateful than + + + align:start position:0% +and there's nothing more stateful than +an iterator and so we have tricked mat + + align:start position:0% +an iterator and so we have tricked mat + + + align:start position:0% +an iterator and so we have tricked mat +lab with a combination of mat lab on the + + align:start position:0% +lab with a combination of mat lab on the + + + align:start position:0% +lab with a combination of mat lab on the +surface and some hidden Java under the + + align:start position:0% +surface and some hidden Java under the + + + align:start position:0% +surface and some hidden Java under the +covers to make it look have the feel of + + align:start position:0% +covers to make it look have the feel of + + + align:start position:0% +covers to make it look have the feel of +mat lab yet hold hold state so uh so now + + align:start position:0% +mat lab yet hold hold state so uh so now + + + align:start position:0% +mat lab yet hold hold state so uh so now +what we're going to do is we're going to + + align:start position:0% +what we're going to do is we're going to + + + align:start position:0% +what we're going to do is we're going to +this just creates the iterator um we + + align:start position:0% +this just creates the iterator um we + + + align:start position:0% +this just creates the iterator um we +then initialize the query by actually + + align:start position:0% +then initialize the query by actually + + + align:start position:0% +then initialize the query by actually +passing in a query so we now say okay + + align:start position:0% +passing in a query so we now say okay + + + align:start position:0% +passing in a query so we now say okay +the query we want is over this this uh + + align:start position:0% +the query we want is over this this uh + + + align:start position:0% +the query we want is over this this uh +set of rows here and so we're going to + + align:start position:0% +set of rows here and so we're going to + + + align:start position:0% +set of rows here and so we're going to +run the query the first time and do and + + align:start position:0% +run the query the first time and do and + + + align:start position:0% +run the query the first time and do and +since that thing returns string values + + align:start position:0% +since that thing returns string values + + + align:start position:0% +since that thing returns string values +and we want numbers we have to do a + + align:start position:0% +and we want numbers we have to do a + + + align:start position:0% +and we want numbers we have to do a +string to numb and that's our first + + align:start position:0% +string to numb and that's our first + + + align:start position:0% +string to numb and that's our first +associative array that's the result of + + align:start position:0% +associative array that's the result of + + + align:start position:0% +associative array that's the result of +the first query uh we then initialize + + align:start position:0% +the first query uh we then initialize + + + align:start position:0% +the first query uh we then initialize +our our tally uh here and then we just + + align:start position:0% +our our tally uh here and then we just + + + align:start position:0% +our our tally uh here and then we just +do a while on this result okay so we're + + align:start position:0% +do a while on this result okay so we're + + + align:start position:0% +do a while on this result okay so we're +going to say oh if there's something + + align:start position:0% +going to say oh if there's something + + + align:start position:0% +going to say oh if there's something +there then we want to sum that and add + + align:start position:0% +there then we want to sum that and add + + + align:start position:0% +there then we want to sum that and add +it to our tally to our ingree tally and + + align:start position:0% +it to our tally to our ingree tally and + + + align:start position:0% +it to our tally to our ingree tally and +then we call it again so we do the next + + align:start position:0% +then we call it again so we do the next + + + align:start position:0% +then we call it again so we do the next +round of the iteration by just calling + + align:start position:0% +round of the iteration by just calling + + + align:start position:0% +round of the iteration by just calling +the object with empty with no argument + + align:start position:0% +the object with empty with no argument + + + align:start position:0% +the object with empty with no argument +and it will just oh it'll just it'll + + align:start position:0% +and it will just oh it'll just it'll + + + align:start position:0% +and it will just oh it'll just it'll +just run it until the query is empty if + + align:start position:0% +just run it until the query is empty if + + + align:start position:0% +just run it until the query is empty if +we put in an argument it would + + align:start position:0% +we put in an argument it would + + + align:start position:0% +we put in an argument it would +reinitialize the iterator to that new + + align:start position:0% +reinitialize the iterator to that new + + + align:start position:0% +reinitialize the iterator to that new +query and so you don't have to create a + + align:start position:0% +query and so you don't have to create a + + + align:start position:0% +query and so you don't have to create a +new iterator every single time you want + + align:start position:0% +new iterator every single time you want + + + align:start position:0% +new iterator every single time you want +to put in a different query you can + + align:start position:0% +to put in a different query you can + + + align:start position:0% +to put in a different query you can +reuse the object but um not that it + + align:start position:0% +reuse the object but um not that it + + + align:start position:0% +reuse the object but um not that it +really matters um but this is how you + + align:start position:0% +really matters um but this is how you + + + align:start position:0% +really matters um but this is how you +get it to do again so it's a pretty + + align:start position:0% +get it to do again so it's a pretty + + + align:start position:0% +get it to do again so it's a pretty +elegant Syntax for basically doing an + + align:start position:0% +elegant Syntax for basically doing an + + + align:start position:0% +elegant Syntax for basically doing an +iterator and allows you to deal with uh + + align:start position:0% +iterator and allows you to deal with uh + + + align:start position:0% +iterator and allows you to deal with uh +uh uh things very nicely and uh as we + + align:start position:0% +uh uh things very nicely and uh as we + + + align:start position:0% +uh uh things very nicely and uh as we +see here then we did the calculation um + + align:start position:0% +see here then we did the calculation um + + + align:start position:0% +see here then we did the calculation um +here which is all right I wanted to then + + align:start position:0% +here which is all right I wanted to then + + + align:start position:0% +here which is all right I wanted to then +return the value with the um with the + + align:start position:0% +return the value with the um with the + + + align:start position:0% +return the value with the um with the +largest maximum degree so basically I + + align:start position:0% +largest maximum degree so basically I + + + align:start position:0% +largest maximum degree so basically I +compute the max I get the adjacency + + align:start position:0% +compute the max I get the adjacency + + + align:start position:0% +compute the max I get the adjacency +Matrix of the of the degree and I + + align:start position:0% +Matrix of the of the degree and I + + + align:start position:0% +Matrix of the of the degree and I +compute its maximum and then I set that + + align:start position:0% +compute its maximum and then I set that + + + align:start position:0% +compute its maximum and then I set that +equal to in degree and it tells me that + + align:start position:0% +equal to in degree and it tells me that + + + align:start position:0% +equal to in degree and it tells me that +the first vertex had a degree of 14 in + + align:start position:0% +the first vertex had a degree of 14 in + + + align:start position:0% +the first vertex had a degree of 14 in +this sare which makes sense in the + + align:start position:0% +this sare which makes sense in the + + + align:start position:0% +this sare which makes sense in the +chronicle Matrix that first that one one + + align:start position:0% +chronicle Matrix that first that one one + + + align:start position:0% +chronicle Matrix that first that one one +is always the largest and densest uh + + align:start position:0% +is always the largest and densest uh + + + align:start position:0% +is always the largest and densest uh +densest uh + + align:start position:0% +densest uh + + + align:start position:0% +densest uh +value so that's just how we use + + align:start position:0% + + + + align:start position:0% + +iterators let us continue on + + align:start position:0% + + + + align:start position:0% + +here all right now I'm going to use + + align:start position:0% +here all right now I'm going to use + + + align:start position:0% +here all right now I'm going to use +iterators in a more complicated way to + + align:start position:0% +iterators in a more complicated way to + + + align:start position:0% +iterators in a more complicated way to +do a a uh a join so a join is where I + + align:start position:0% +do a a uh a join so a join is where I + + + align:start position:0% +do a a uh a join so a join is where I +want to + + align:start position:0% +want to + + + align:start position:0% +want to +basically uh maybe there's a a row in + + align:start position:0% +basically uh maybe there's a a row in + + + align:start position:0% +basically uh maybe there's a a row in +the table and I only want the rows that + + align:start position:0% +the table and I only want the rows that + + + align:start position:0% +the table and I only want the rows that +have one type of you know have have have + + align:start position:0% +have one type of you know have have have + + + align:start position:0% +have one type of you know have have have +both of a certain type of value in them + + align:start position:0% +both of a certain type of value in them + + + align:start position:0% +both of a certain type of value in them +so for instance like if I had table of + + align:start position:0% +so for instance like if I had table of + + + align:start position:0% +so for instance like if I had table of +network records I might like look please + + align:start position:0% +network records I might like look please + + + align:start position:0% +network records I might like look please +only return records that have this + + align:start position:0% +only return records that have this + + + align:start position:0% +only return records that have this +Source IP and uh are talking to this + + align:start position:0% +Source IP and uh are talking to this + + + align:start position:0% +Source IP and uh are talking to this +domain name okay so we have to figure + + align:start position:0% +domain name okay so we have to figure + + + align:start position:0% +domain name okay so we have to figure +out how we do joins in this type of in + + align:start position:0% +out how we do joins in this type of in + + + align:start position:0% +out how we do joins in this type of in +this in this technology so I'm going to + + align:start position:0% +this in this technology so I'm going to + + + align:start position:0% +this in this technology so I'm going to +do that so let me run + + align:start position:0% + + + + align:start position:0% + +that all right our join so a little bit + + align:start position:0% +that all right our join so a little bit + + + align:start position:0% +that all right our join so a little bit +more complicated obviously we're + + align:start position:0% +more complicated obviously we're + + + align:start position:0% +more complicated obviously we're +building up sort of Fairly complicated + + align:start position:0% +building up sort of Fairly complicated + + + align:start position:0% +building up sort of Fairly complicated +analytics here so uh + + align:start position:0% +analytics here so uh + + + align:start position:0% +analytics here so uh +I uh create my uh my iterator limit here + + align:start position:0% +I uh create my uh my iterator limit here + + + align:start position:0% +I uh create my uh my iterator limit here +I'm going to pick two columns to join + + align:start position:0% +I'm going to pick two columns to join + + + align:start position:0% +I'm going to pick two columns to join +column one column two and this just does + + align:start position:0% +column one column two and this just does + + + align:start position:0% +column one column two and this just does +a simple join over those columns so + + align:start position:0% +a simple join over those columns so + + + align:start position:0% +a simple join over those columns so +basically what I'm doing is I'm getting + + align:start position:0% +basically what I'm doing is I'm getting + + + align:start position:0% +basically what I'm doing is I'm getting +I'm saying please return all the columns + + align:start position:0% +I'm saying please return all the columns + + + align:start position:0% +I'm saying please return all the columns +that contain this is an or basically + + align:start position:0% +that contain this is an or basically + + + align:start position:0% +that contain this is an or basically +either column one or two I'm going to + + align:start position:0% +either column one or two I'm going to + + + align:start position:0% +either column one or two I'm going to +then convert those values which would + + align:start position:0% +then convert those values which would + + + align:start position:0% +then convert those values which would +have been string values of numerics to + + align:start position:0% +have been string values of numerics to + + + align:start position:0% +have been string values of numerics to +just zeros or one then I'm going to sum + + align:start position:0% +just zeros or one then I'm going to sum + + + align:start position:0% +just zeros or one then I'm going to sum +that so I'm basically I got the two + + align:start position:0% +that so I'm basically I got the two + + + align:start position:0% +that so I'm basically I got the two +columns I converted all the values to + + align:start position:0% +columns I converted all the values to + + + align:start position:0% +columns I converted all the values to +one I'm going to sum them together okay + + align:start position:0% +one I'm going to sum them together okay + + + align:start position:0% +one I'm going to sum them together okay +and and then I'm going to ask the + + align:start position:0% +and and then I'm going to ask the + + + align:start position:0% +and and then I'm going to ask the +question where were those equal to + + align:start position:0% +question where were those equal to + + + align:start position:0% +question where were those equal to +two those show me the records so that's + + align:start position:0% +two those show me the records so that's + + + align:start position:0% +two those show me the records so that's +what I'm doing here I'm saying those + + align:start position:0% +what I'm doing here I'm saying those + + + align:start position:0% +what I'm doing here I'm saying those +equal to two so that shows me all the + + align:start position:0% +equal to two so that shows me all the + + + align:start position:0% +equal to two so that shows me all the +records where that value is equal to two + + align:start position:0% +records where that value is equal to two + + + align:start position:0% +records where that value is equal to two +and I can then get the row of those + + align:start position:0% +and I can then get the row of those + + + align:start position:0% +and I can then get the row of those +things and then pass that back in to the + + align:start position:0% +things and then pass that back in to the + + + align:start position:0% +things and then pass that back in to the +original + + align:start position:0% +original + + + align:start position:0% +original +Matrix okay and now I know now I will + + align:start position:0% +Matrix okay and now I know now I will + + + align:start position:0% +Matrix okay and now I know now I will +get back those rows with those things + + align:start position:0% +get back those rows with those things + + + align:start position:0% +get back those rows with those things +and so we can see that I think that's + + align:start position:0% +and so we can see that I think that's + + + align:start position:0% +and so we can see that I think that's +the first figure that we did here we go + + align:start position:0% +the first figure that we did here we go + + + align:start position:0% +the first figure that we did here we go +to figure one and those show + + align:start position:0% +to figure one and those show + + + align:start position:0% +to figure one and those show +basically what did we + + align:start position:0% +basically what did we + + + align:start position:0% +basically what did we +do + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% + + + + align:start position:0% + +this shows us the complete rows of all + + align:start position:0% +this shows us the complete rows of all + + + align:start position:0% +this shows us the complete rows of all +the records that had the value one so + + align:start position:0% +the records that had the value one so + + + align:start position:0% +the records that had the value one so +this is here one and I think it was 100 + + align:start position:0% +this is here one and I think it was 100 + + + align:start position:0% +this is here one and I think it was 100 +which is somewhere right like probably + + align:start position:0% +which is somewhere right like probably + + + align:start position:0% +which is somewhere right like probably +in there so there's you know basically + + align:start position:0% +in there so there's you know basically + + + align:start position:0% +in there so there's you know basically +every single one of these records had + + align:start position:0% +every single one of these records had + + + align:start position:0% +every single one of these records had +you know one and 100 in it and then it + + align:start position:0% +you know one and 100 in it and then it + + + align:start position:0% +you know one and 100 in it and then it +shows us all the rest of the values that + + align:start position:0% +shows us all the rest of the values that + + + align:start position:0% +shows us all the rest of the values that +are also in that that record if we just + + align:start position:0% +are also in that that record if we just + + + align:start position:0% +are also in that that record if we just +wanted those columns and those values + + align:start position:0% +wanted those columns and those values + + + align:start position:0% +wanted those columns and those values +then we were done when we just summed + + align:start position:0% +then we were done when we just summed + + + align:start position:0% +then we were done when we just summed +them and equals two we were done but + + align:start position:0% +them and equals two we were done but + + + align:start position:0% +them and equals two we were done but +this allowed us to then go back into the + + align:start position:0% +this allowed us to then go back into the + + + align:start position:0% +this allowed us to then go back into the +record and now into the into the full + + align:start position:0% +record and now into the into the full + + + align:start position:0% +record and now into the into the full +set and just get those records so this + + align:start position:0% +set and just get those records so this + + + align:start position:0% +set and just get those records so this +is a way to do a join if you can + + align:start position:0% +is a way to do a join if you can + + + align:start position:0% +is a way to do a join if you can +hold the complete results of both of + + align:start position:0% +hold the complete results of both of + + + align:start position:0% +hold the complete results of both of +those things like you know give me the + + align:start position:0% +those things like you know give me the + + + align:start position:0% +those things like you know give me the +whole column you know one and the whole + + align:start position:0% +whole column you know one and the whole + + + align:start position:0% +whole column you know one and the whole +column two that's one way to do a join + + align:start position:0% +column two that's one way to do a join + + + align:start position:0% +column two that's one way to do a join +um perfectly reasonable way to do a + + align:start position:0% +um perfectly reasonable way to do a + + + align:start position:0% +um perfectly reasonable way to do a +join I'm going to now do this again but + + align:start position:0% +join I'm going to now do this again but + + + align:start position:0% +join I'm going to now do this again but +with a column range so I'm going to say + + align:start position:0% +with a column range so I'm going to say + + + align:start position:0% +with a column range so I'm going to say +you know I want all columns I want to do + + align:start position:0% +you know I want all columns I want to do + + + align:start position:0% +you know I want all columns I want to do +a join of all columns that begin with + + align:start position:0% +a join of all columns that begin with + + + align:start position:0% +a join of all columns that begin with +111 and all columns that begin with 222 + + align:start position:0% +111 and all columns that begin with 222 + + + align:start position:0% +111 and all columns that begin with 222 +so so that would return more of and I'm + + align:start position:0% +so so that would return more of and I'm + + + align:start position:0% +so so that would return more of and I'm +going to create two iterators now to do + + align:start position:0% +going to create two iterators now to do + + + align:start position:0% +going to create two iterators now to do +that so I have initialized my iterator + + align:start position:0% +that so I have initialized my iterator + + + align:start position:0% +that so I have initialized my iterator +iterator one and iterator + + align:start position:0% +iterator one and iterator + + + align:start position:0% +iterator one and iterator +two all right and so now I'm going to + + align:start position:0% +two all right and so now I'm going to + + + align:start position:0% +two all right and so now I'm going to +start the first query iterator here by + + align:start position:0% +start the first query iterator here by + + + align:start position:0% +start the first query iterator here by +giving it its column range that + + align:start position:0% +giving it its column range that + + + align:start position:0% +giving it its column range that +initializes it and I get an A1 and then + + align:start position:0% +initializes it and I get an A1 and then + + + align:start position:0% +initializes it and I get an A1 and then +I check to see if A1 is not empty if it + + align:start position:0% +I check to see if A1 is not empty if it + + + align:start position:0% +I check to see if A1 is not empty if it +isn't empty I'm going to then sum it and + + align:start position:0% +isn't empty I'm going to then sum it and + + + align:start position:0% +isn't empty I'm going to then sum it and +then call it again until it's proceeds + + align:start position:0% +then call it again until it's proceeds + + + align:start position:0% +then call it again until it's proceeds +and since it's such a small thing it + + align:start position:0% +and since it's such a small thing it + + + align:start position:0% +and since it's such a small thing it +only went through that once + + align:start position:0% +only went through that once + + + align:start position:0% +only went through that once +okay and then now I'm going to do the + + align:start position:0% +okay and then now I'm going to do the + + + align:start position:0% +okay and then now I'm going to do the +same thing again with the other iterator + + align:start position:0% +same thing again with the other iterator + + + align:start position:0% +same thing again with the other iterator +and sum them get together + + align:start position:0% +and sum them get together + + + align:start position:0% +and sum them get together +again + + align:start position:0% + + + + align:start position:0% + +okay and now I'm going to + + align:start position:0% +okay and now I'm going to + + + align:start position:0% +okay and now I'm going to +join those + + align:start position:0% +join those + + + align:start position:0% +join those +two uh those two those two columns and + + align:start position:0% +two uh those two those two columns and + + + align:start position:0% +two uh those two those two columns and +that's a way of doing the join with + + align:start position:0% +that's a way of doing the join with + + + align:start position:0% +that's a way of doing the join with +essentially two nested iterators and + + align:start position:0% +essentially two nested iterators and + + + align:start position:0% +essentially two nested iterators and +doing doing the join that way so that's + + align:start position:0% +doing doing the join that way so that's + + + align:start position:0% +doing doing the join that way so that's +something you can do if you couldn't + + align:start position:0% +something you can do if you couldn't + + + align:start position:0% +something you can do if you couldn't +hold the whole column in memory and you + + align:start position:0% +hold the whole column in memory and you + + + align:start position:0% +hold the whole column in memory and you +wanted to sort of build it up as you + + align:start position:0% +wanted to sort of build it up as you + + + align:start position:0% +wanted to sort of build it up as you +went that's a way to do it with + + align:start position:0% +went that's a way to do it with + + + align:start position:0% +went that's a way to do it with +iterators then let's see + + align:start position:0% + + + + align:start position:0% + +here there's an example of the results + + align:start position:0% +here there's an example of the results + + + align:start position:0% +here there's an example of the results +from + + align:start position:0% +from + + + align:start position:0% +from +that + + align:start position:0% +that + + + align:start position:0% +that +right and just so you know I mean when + + align:start position:0% +right and just so you know I mean when + + + align:start position:0% +right and just so you know I mean when +you do an SQL query and an SQL database + + align:start position:0% +you do an SQL query and an SQL database + + + align:start position:0% +you do an SQL query and an SQL database +this is what it's doing under the covers + + align:start position:0% +this is what it's doing under the covers + + + align:start position:0% +this is what it's doing under the covers +it's trying to do whatever information + + align:start position:0% +it's trying to do whatever information + + + align:start position:0% +it's trying to do whatever information +it can it it will some lot of horror + + align:start position:0% +it can it it will some lot of horror + + + align:start position:0% +it can it it will some lot of horror +hold a lot of internal statistical + + align:start position:0% +hold a lot of internal statistical + + + align:start position:0% +hold a lot of internal statistical +information it's trying to figure out + + align:start position:0% +information it's trying to figure out + + + align:start position:0% +information it's trying to figure out +can I hold the results in memory or can + + align:start position:0% +can I hold the results in memory or can + + + align:start position:0% +can I hold the results in memory or can +I not do I have to go through them in + + align:start position:0% +I not do I have to go through them in + + + align:start position:0% +I not do I have to go through them in +chunks or or do I not do I have + + align:start position:0% +chunks or or do I not do I have + + + align:start position:0% +chunks or or do I not do I have +information about oh you know this query + + align:start position:0% +information about oh you know this query + + + align:start position:0% +information about oh you know this query +like you know do I have a a sum table + + align:start position:0% +like you know do I have a a sum table + + + align:start position:0% +like you know do I have a a sum table +you know sitting around that will tell + + align:start position:0% +you know sitting around that will tell + + + align:start position:0% +you know sitting around that will tell +me oh which which you know which column + + align:start position:0% +me oh which which you know which column + + + align:start position:0% +me oh which which you know which column +should I query first because it will + + align:start position:0% +should I query first because it will + + + align:start position:0% +should I query first because it will +return fewer results and then I can go + + align:start position:0% +return fewer results and then I can go + + + align:start position:0% +return fewer results and then I can go +from there type of thing so so this is + + align:start position:0% +from there type of thing so so this is + + + align:start position:0% +from there type of thing so so this is +sort of all going under the covers here + + align:start position:0% +sort of all going under the covers here + + + align:start position:0% +sort of all going under the covers here +you get the the power to do that + + align:start position:0% +you get the the power to do that + + + align:start position:0% +you get the the power to do that +directly uh on the database and it's + + align:start position:0% +directly uh on the database and it's + + + align:start position:0% +directly uh on the database and it's +pretty easy to do um so you have but you + + align:start position:0% +pretty easy to do um so you have but you + + + align:start position:0% +pretty easy to do um so you have but you +do have to understand these Concepts all + + align:start position:0% +do have to understand these Concepts all + + + align:start position:0% +do have to understand these Concepts all +right so now we're move + + align:start position:0% +right so now we're move + + + align:start position:0% +right so now we're move +on okay now we've done so that was all + + align:start position:0% +on okay now we've done so that was all + + + align:start position:0% +on okay now we've done so that was all +with the adjacency Matrix and as I said + + align:start position:0% +with the adjacency Matrix and as I said + + + align:start position:0% +with the adjacency Matrix and as I said +before when we formed the adjacency + + align:start position:0% +before when we formed the adjacency + + + align:start position:0% +before when we formed the adjacency +Matrix we threw away a little + + align:start position:0% +Matrix we threw away a little + + + align:start position:0% +Matrix we threw away a little +information right because if we had + + align:start position:0% +information right because if we had + + + align:start position:0% +information right because if we had +multiple we had a collision of any kind + + align:start position:0% +multiple we had a collision of any kind + + + align:start position:0% +multiple we had a collision of any kind +right we lost the distinctness of that + + align:start position:0% +right we lost the distinctness of that + + + align:start position:0% +right we lost the distinctness of that +that that record or that edge and a lot + + align:start position:0% +that that record or that edge and a lot + + + align:start position:0% +that that record or that edge and a lot +of times like no we want to keep keep + + align:start position:0% +of times like no we want to keep keep + + + align:start position:0% +of times like no we want to keep keep +these edges because you know yeah we'll + + align:start position:0% +these edges because you know yeah we'll + + + align:start position:0% +these edges because you know yeah we'll +have other information about those edges + + align:start position:0% +have other information about those edges + + + align:start position:0% +have other information about those edges +and we want to keep things so so so we + + align:start position:0% +and we want to keep things so so so we + + + align:start position:0% +and we want to keep things so so so we +want to we want to store that so we're + + align:start position:0% +want to we want to store that so we're + + + align:start position:0% +want to we want to store that so we're +going to + + align:start position:0% +going to + + + align:start position:0% +going to +now reinsert the data in the table and + + align:start position:0% +now reinsert the data in the table and + + + align:start position:0% +now reinsert the data in the table and +use essentially instead of an adjacency + + align:start position:0% +use essentially instead of an adjacency + + + align:start position:0% +use essentially instead of an adjacency +Matrix an incidence Matrix an incidence + + align:start position:0% +Matrix an incidence Matrix an incidence + + + align:start position:0% +Matrix an incidence Matrix an incidence +Matrix every single row is an edge and + + align:start position:0% +Matrix every single row is an edge and + + + align:start position:0% +Matrix every single row is an edge and +every + + align:start position:0% +every + + + align:start position:0% +every +single uh column is a verticy and so an + + align:start position:0% +single uh column is a verticy and so an + + + align:start position:0% +single uh column is a verticy and so an +edge can then connect multiple vertices + + align:start position:0% +edge can then connect multiple vertices + + + align:start position:0% +edge can then connect multiple vertices +it also allows us to store essentially + + align:start position:0% +it also allows us to store essentially + + + align:start position:0% +it also allows us to store essentially +what we call hyperedges so if you have + + align:start position:0% +what we call hyperedges so if you have + + + align:start position:0% +what we call hyperedges so if you have +an edge that connects multiple vertices + + align:start position:0% +an edge that connects multiple vertices + + + align:start position:0% +an edge that connects multiple vertices +at the same time uh we can do that so + + align:start position:0% +at the same time uh we can do that so + + + align:start position:0% +at the same time uh we can do that so +let's do + + align:start position:0% +let's do + + + align:start position:0% +let's do +that this this is inserting about twice + + align:start position:0% +that this this is inserting about twice + + + align:start position:0% +that this this is inserting about twice +as much data so uh it naturally takes a + + align:start position:0% +as much data so uh it naturally takes a + + + align:start position:0% +as much data so uh it naturally takes a +little bit longer + + align:start position:0% +little bit longer + + + align:start position:0% +little bit longer +there and you see the edge insertion + + align:start position:0% +there and you see the edge insertion + + + align:start position:0% +there and you see the edge insertion +rates that we're getting there uh you + + align:start position:0% +rates that we're getting there uh you + + + align:start position:0% +rates that we're getting there uh you +know 30 30,000 edges per second so let's + + align:start position:0% +know 30 30,000 edges per second so let's + + + align:start position:0% +know 30 30,000 edges per second so let's +go and see what it did to our um our + + align:start position:0% +go and see what it did to our um our + + + align:start position:0% +go and see what it did to our um our +data + + align:start position:0% +data + + + align:start position:0% +data +here so if we look at our + + align:start position:0% +here so if we look at our + + + align:start position:0% +here so if we look at our +tables we can see now that + + align:start position:0% +tables we can see now that + + + align:start position:0% +tables we can see now that +our there's our Edge data set and you + + align:start position:0% +our there's our Edge data set and you + + + align:start position:0% +our there's our Edge data set and you +see we've inserted about 270,000 + + align:start position:0% +see we've inserted about 270,000 + + + align:start position:0% +see we've inserted about 270,000 +distinct entries in this uh data there's + + align:start position:0% +distinct entries in this uh data there's + + + align:start position:0% +distinct entries in this uh data there's +the edge table and there's this + + align:start position:0% +the edge table and there's this + + + align:start position:0% +the edge table and there's this +transpose and there's the degree uh + + align:start position:0% +transpose and there's the degree uh + + + align:start position:0% +transpose and there's the degree uh +count and as you saw before you know we + + align:start position:0% +count and as you saw before you know we + + + align:start position:0% +count and as you saw before you know we +had 53,000 uh you know so that just + + align:start position:0% +had 53,000 uh you know so that just + + + align:start position:0% +had 53,000 uh you know so that just +shows you the additional + + align:start position:0% +shows you the additional + + + align:start position:0% +shows you the additional +information let me let's look at that uh + + align:start position:0% +information let me let's look at that uh + + + align:start position:0% +information let me let's look at that uh +that program + + align:start position:0% +that program + + + align:start position:0% +that program +here so again we're We're looping over + + align:start position:0% +here so again we're We're looping over + + + align:start position:0% +here so again we're We're looping over +all our files here um uh um we're + + align:start position:0% +all our files here um uh um we're + + + align:start position:0% +all our files here um uh um we're +reading them in I should say this case + + align:start position:0% +reading them in I should say this case + + + align:start position:0% +reading them in I should say this case +we are reading in the Raw text files + + align:start position:0% +we are reading in the Raw text files + + + align:start position:0% +we are reading in the Raw text files +again we're not reading in the + + align:start position:0% +again we're not reading in the + + + align:start position:0% +again we're not reading in the +associative array because we just want + + align:start position:0% +associative array because we just want + + + align:start position:0% +associative array because we just want +to insert those edges and then the only + + align:start position:0% +to insert those edges and then the only + + + align:start position:0% +to insert those edges and then the only +thing we've done is that basically to + + align:start position:0% +thing we've done is that basically to + + + align:start position:0% +thing we've done is that basically to +create our Edge we had to create this + + align:start position:0% +create our Edge we had to create this + + + align:start position:0% +create our Edge we had to create this +data didn't come with a record label so + + align:start position:0% +data didn't come with a record label so + + + align:start position:0% +data didn't come with a record label so +we we don't have any so we constructing + + align:start position:0% +we we don't have any so we constructing + + + align:start position:0% +we we don't have any so we constructing +a unique record label for each edge here + + align:start position:0% +a unique record label for each edge here + + + align:start position:0% +a unique record label for each edge here +just so that we have it for the row key + + align:start position:0% +just so that we have it for the row key + + + align:start position:0% +just so that we have it for the row key +and then we're prepending the word out + + align:start position:0% +and then we're prepending the word out + + + align:start position:0% +and then we're prepending the word out +and you know out into the row string and + + align:start position:0% +and you know out into the row string and + + + align:start position:0% +and you know out into the row string and +in into the column string so that we + + align:start position:0% +in into the column string so that we + + + align:start position:0% +in into the column string so that we +know you know when we create our record + + align:start position:0% +know you know when we create our record + + + align:start position:0% +know you know when we create our record +they'll be you know out is shows the + + align:start position:0% +they'll be you know out is shows the + + + align:start position:0% +they'll be you know out is shows the +direction it came from and in shows the + + align:start position:0% +direction it came from and in shows the + + + align:start position:0% +direction it came from and in shows the +direction it it left and so that's a way + + align:start position:0% +direction it it left and so that's a way + + + align:start position:0% +direction it it left and so that's a way +of sort of creating the edge and then + + align:start position:0% +of sort of creating the edge and then + + + align:start position:0% +of sort of creating the edge and then +likewise we do the count uh degree uh + + align:start position:0% +likewise we do the count uh degree uh + + + align:start position:0% +likewise we do the count uh degree uh +and such to preserve that information so + + align:start position:0% +and such to preserve that information so + + + align:start position:0% +and such to preserve that information so +we can summing the the total number of + + align:start position:0% +we can summing the the total number of + + + align:start position:0% +we can summing the the total number of +counts + + align:start position:0% + + + + align:start position:0% + +there all right + + align:start position:0% +there all right + + + align:start position:0% +there all right +right so let's do some queries on + + align:start position:0% + + + + align:start position:0% + +that all righty so I'm going to get I'm + + align:start position:0% +that all righty so I'm going to get I'm + + + align:start position:0% +that all righty so I'm going to get I'm +going to ask for 100 random vertices + + align:start position:0% +going to ask for 100 random vertices + + + align:start position:0% +going to ask for 100 random vertices +here so I get my random vertices and + + align:start position:0% +here so I get my random vertices and + + + align:start position:0% +here so I get my random vertices and +then I'm going to uh do my query of the + + align:start position:0% +then I'm going to uh do my query of the + + + align:start position:0% +then I'm going to uh do my query of the +strings but I have to preen the the this + + align:start position:0% +strings but I have to preen the the this + + + align:start position:0% +strings but I have to preen the the this +out slash then the value in it so I know + + align:start position:0% +out slash then the value in it so I know + + + align:start position:0% +out slash then the value in it so I know +I'm looking for for for uh uh you know + + align:start position:0% +I'm looking for for for uh uh you know + + + align:start position:0% +I'm looking for for for uh uh you know +vertices from which The Edge is + + align:start position:0% +vertices from which The Edge is + + + align:start position:0% +vertices from which The Edge is +departing and I'm going to get those + + align:start position:0% +departing and I'm going to get those + + + align:start position:0% +departing and I'm going to get those +edges so I get those Ed so I created the + + align:start position:0% +edges so I get those Ed so I created the + + + align:start position:0% +edges so I get those Ed so I created the +query I get the edges I'm going to do my + + align:start position:0% +query I get the edges I'm going to do my + + + align:start position:0% +query I get the edges I'm going to do my +thresholding again I want a certain uh + + align:start position:0% +thresholding again I want a certain uh + + + align:start position:0% +thresholding again I want a certain uh +uh Min and Max and then um I'm going to + + align:start position:0% +uh Min and Max and then um I'm going to + + + align:start position:0% +uh Min and Max and then um I'm going to +do the the the the the the the threshold + + align:start position:0% +do the the the the the the the threshold + + + align:start position:0% +do the the the the the the the threshold +so this just gave me the degree counts + + align:start position:0% +so this just gave me the degree counts + + + align:start position:0% +so this just gave me the degree counts +and I threshold it so that you know in + + align:start position:0% +and I threshold it so that you know in + + + align:start position:0% +and I threshold it so that you know in +this range and then now I then do the + + align:start position:0% +this range and then now I then do the + + + align:start position:0% +this range and then now I then do the +same thing back with the uh with the uh + + align:start position:0% +same thing back with the uh with the uh + + + align:start position:0% +same thing back with the uh with the uh +the I I I say give me everything greater + + align:start position:0% +the I I I say give me everything greater + + + align:start position:0% +the I I I say give me everything greater +than degree Min and less than degree Max + + align:start position:0% +than degree Min and less than degree Max + + + align:start position:0% +than degree Min and less than degree Max +I get a new set of rows so that will + + align:start position:0% +I get a new set of rows so that will + + + align:start position:0% +I get a new set of rows so that will +just return the edges that are a part of + + align:start position:0% +just return the edges that are a part of + + + align:start position:0% +just return the edges that are a part of +uh vertices with these degree range and + + align:start position:0% +uh vertices with these degree range and + + + align:start position:0% +uh vertices with these degree range and +then I'm going to get uh all those uh + + align:start position:0% +then I'm going to get uh all those uh + + + align:start position:0% +then I'm going to get uh all those uh +all those uh uh edges all the records + + align:start position:0% +all those uh uh edges all the records + + + align:start position:0% +all those uh uh edges all the records +that contain those those vertices + + align:start position:0% +that contain those those vertices + + + align:start position:0% +that contain those those vertices +through this uh nested queer + + align:start position:0% +through this uh nested queer + + + align:start position:0% +through this uh nested queer +here the result is this so basically + + align:start position:0% +here the result is this so basically + + + align:start position:0% +here the result is this so basically +this shows me all the edges that are + + align:start position:0% +this shows me all the edges that are + + + align:start position:0% +this shows me all the edges that are +part of um uh vertices this random set + + align:start position:0% +part of um uh vertices this random set + + + align:start position:0% +part of um uh vertices this random set +of vertices that have a degree range + + align:start position:0% +of vertices that have a degree range + + + align:start position:0% +of vertices that have a degree range +between five and + + align:start position:0% +between five and + + + align:start position:0% +between five and +10 this is a fairly sophisticated + + align:start position:0% +10 this is a fairly sophisticated + + + align:start position:0% +10 this is a fairly sophisticated +analytic uh in terms of you we got a lot + + align:start position:0% +analytic uh in terms of you we got a lot + + + align:start position:0% +analytic uh in terms of you we got a lot +of we're doing about seven or eight + + align:start position:0% +of we're doing about seven or eight + + + align:start position:0% +of we're doing about seven or eight +queries here doing a lot of mathematics + + align:start position:0% +queries here doing a lot of mathematics + + + align:start position:0% +queries here doing a lot of mathematics +and you see how how dense it is and + + align:start position:0% +and you see how how dense it is and + + + align:start position:0% +and you see how how dense it is and +hopefully uh from what we've learned + + align:start position:0% +hopefully uh from what we've learned + + + align:start position:0% +hopefully uh from what we've learned +prior prior has some some intuition for + + align:start position:0% +prior prior has some some intuition for + + + align:start position:0% +prior prior has some some intuition for +you all right we will continue + + align:start position:0% + + + + align:start position:0% + +on all right so now I'm going to do a + + align:start position:0% +on all right so now I'm going to do a + + + align:start position:0% +on all right so now I'm going to do a +query with the iterator again same type + + align:start position:0% +query with the iterator again same type + + + align:start position:0% +query with the iterator again same type +of drill I set the Maxum of elements of + + align:start position:0% +of drill I set the Maxum of elements of + + + align:start position:0% +of drill I set the Maxum of elements of +the iterator I get my random set of + + align:start position:0% +the iterator I get my random set of + + + align:start position:0% +the iterator I get my random set of +things I create an iterator again + + align:start position:0% +things I create an iterator again + + + align:start position:0% +things I create an iterator again +setting the number of + + align:start position:0% +setting the number of + + + align:start position:0% +setting the number of +elements I initialize the iterator to be + + align:start position:0% +elements I initialize the iterator to be + + + align:start position:0% +elements I initialize the iterator to be +over these vertices I then check to see + + align:start position:0% +over these vertices I then check to see + + + align:start position:0% +over these vertices I then check to see +if the if it returned anything if it did + + align:start position:0% +if the if it returned anything if it did + + + align:start position:0% +if the if it returned anything if it did +um I'm going to then actually pass that + + align:start position:0% +um I'm going to then actually pass that + + + align:start position:0% +um I'm going to then actually pass that +uh the the rows of that back into the uh + + align:start position:0% +uh the the rows of that back into the uh + + + align:start position:0% +uh the the rows of that back into the uh +the uh the uh uh into it to get the + + align:start position:0% +the uh the uh uh into it to get the + + + align:start position:0% +the uh the uh uh into it to get the +edges containing those vertices and then + + align:start position:0% +edges containing those vertices and then + + + align:start position:0% +edges containing those vertices and then +do a sum to compute the IND degree and + + align:start position:0% +do a sum to compute the IND degree and + + + align:start position:0% +do a sum to compute the IND degree and +so on and so forth and then I get here + + align:start position:0% +so on and so forth and then I get here + + + align:start position:0% +so on and so forth and then I get here +the maximum in degree of that set of + + align:start position:0% +the maximum in degree of that set of + + + align:start position:0% +the maximum in degree of that set of +vertices was 25 so that's just an + + align:start position:0% +vertices was 25 so that's just an + + + align:start position:0% +vertices was 25 so that's just an +example of + + align:start position:0% +example of + + + align:start position:0% +example of +that and that was 12 and I think 13 is + + align:start position:0% +that and that was 12 and I think 13 is + + + align:start position:0% +that and that was 12 and I think 13 is +our last + + align:start position:0% + + + + align:start position:0% + +one all + + align:start position:0% +one all + + + align:start position:0% +one all +right and again a more complicated + + align:start position:0% +right and again a more complicated + + + align:start position:0% +right and again a more complicated +example showing basically a a join over + + align:start position:0% +example showing basically a a join over + + + align:start position:0% +example showing basically a a join over +this space + + align:start position:0% +this space + + + align:start position:0% +this space +creating essentially uh a couple of uh + + align:start position:0% +creating essentially uh a couple of uh + + + align:start position:0% +creating essentially uh a couple of uh +of uh uh sets of edges a couple of + + align:start position:0% +of uh uh sets of edges a couple of + + + align:start position:0% +of uh uh sets of edges a couple of +column ranges uh iterators and so on and + + align:start position:0% +column ranges uh iterators and so on and + + + align:start position:0% +column ranges uh iterators and so on and +so forth and I won't belabor this point + + align:start position:0% +so forth and I won't belabor this point + + + align:start position:0% +so forth and I won't belabor this point +but this just shows how you can combine + + align:start position:0% +but this just shows how you can combine + + + align:start position:0% +but this just shows how you can combine +between using the degree table and + + align:start position:0% +between using the degree table and + + + align:start position:0% +between using the degree table and +iterators uh you should have you have + + align:start position:0% +iterators uh you should have you have + + + align:start position:0% +iterators uh you should have you have +all the tools at your disposal that uh + + align:start position:0% +all the tools at your disposal that uh + + + align:start position:0% +all the tools at your disposal that uh +any type of query planning system would + + align:start position:0% +any type of query planning system would + + + align:start position:0% +any type of query planning system would +have inside it that it would use to to + + align:start position:0% +have inside it that it would use to to + + + align:start position:0% +have inside it that it would use to to +make sure that you're not over uh taxing + + align:start position:0% +make sure that you're not over uh taxing + + + align:start position:0% +make sure that you're not over uh taxing +uh the results that you're returning you + + align:start position:0% +uh the results that you're returning you + + + align:start position:0% +uh the results that you're returning you +know to and that's a lot of times if you + + align:start position:0% +know to and that's a lot of times if you + + + align:start position:0% +know to and that's a lot of times if you +do a query on any database and you get + + align:start position:0% +do a query on any database and you get + + + align:start position:0% +do a query on any database and you get +the big spinning watch or whatever it's + + align:start position:0% +the big spinning watch or whatever it's + + + align:start position:0% +the big spinning watch or whatever it's +because the query you asked was was + + align:start position:0% +because the query you asked was was + + + align:start position:0% +because the query you asked was was +simply too too too long um it also gives + + align:start position:0% +simply too too too long um it also gives + + + align:start position:0% +simply too too too long um it also gives +a lot of nice places to if you're May + + align:start position:0% +a lot of nice places to if you're May + + + align:start position:0% +a lot of nice places to if you're May +making a query system to to um interrupt + + align:start position:0% +making a query system to to um interrupt + + + align:start position:0% +making a query system to to um interrupt +it so if you do the query against the + + align:start position:0% +it so if you do the query against the + + + align:start position:0% +it so if you do the query against the +counts you can quickly tell the user + + align:start position:0% +counts you can quickly tell the user + + + align:start position:0% +counts you can quickly tell the user +look you just did a query and this is + + align:start position:0% +look you just did a query and this is + + + align:start position:0% +look you just did a query and this is +going to return 10 million results do + + align:start position:0% +going to return 10 million results do + + + align:start position:0% +going to return 10 million results do +you want to proceed you know and so you + + align:start position:0% +you want to proceed you know and so you + + + align:start position:0% +you want to proceed you know and so you +of course could hold it or likewise uh + + align:start position:0% +of course could hold it or likewise uh + + + align:start position:0% +of course could hold it or likewise uh +you can set a maximum number of + + align:start position:0% +you can set a maximum number of + + + align:start position:0% +you can set a maximum number of +iterations it's like it says Okay I want + + align:start position:0% +iterations it's like it says Okay I want + + + align:start position:0% +iterations it's like it says Okay I want +to get them back in in in units of + + align:start position:0% +to get them back in in in units of + + + align:start position:0% +to get them back in in in units of +100,000 entries but I only want to go up + + align:start position:0% +100,000 entries but I only want to go up + + + align:start position:0% +100,000 entries but I only want to go up +to a million and then I'm going to pause + + align:start position:0% +to a million and then I'm going to pause + + + align:start position:0% +to a million and then I'm going to pause +and you know get some kind of additional + + align:start position:0% +and you know get some kind of additional + + + align:start position:0% +and you know get some kind of additional +guidance from the user to continue so + + align:start position:0% +guidance from the user to continue so + + + align:start position:0% +guidance from the user to continue so +those are the same tools and tricks that + + align:start position:0% +those are the same tools and tricks that + + + align:start position:0% +those are the same tools and tricks that +are in any query plan planner you know + + align:start position:0% +are in any query plan planner you know + + + align:start position:0% +are in any query plan planner you know +very elegantly exposed to you here for + + align:start position:0% +very elegantly exposed to you here for + + + align:start position:0% +very elegantly exposed to you here for +managing uh managing uh uh these types + + align:start position:0% +managing uh managing uh uh these types + + + align:start position:0% +managing uh managing uh uh these types +of + + align:start position:0% +of + + + align:start position:0% +of +queries all right with that I want to do + + align:start position:0% +queries all right with that I want to do + + + align:start position:0% +queries all right with that I want to do +some stuff where we do a little bit of + + align:start position:0% +some stuff where we do a little bit of + + + align:start position:0% +some stuff where we do a little bit of +bigger data set so kind of walked + + align:start position:0% +bigger data set so kind of walked + + + align:start position:0% +bigger data set so kind of walked +through the examples I want to kind of + + align:start position:0% +through the examples I want to kind of + + + align:start position:0% +through the examples I want to kind of +show you what this is like running on a + + align:start position:0% +show you what this is like running on a + + + align:start position:0% +show you what this is like running on a +bigger bigger data set so let's C let's + + align:start position:0% +bigger bigger data set so let's C let's + + + align:start position:0% +bigger bigger data set so let's C let's +close all + + align:start position:0% +close all + + + align:start position:0% +close all +that right + + align:start position:0% +that right + + + align:start position:0% +that right +close + + align:start position:0% +close + + + align:start position:0% +close +that and + + align:start position:0% + + + + align:start position:0% + +let's see here + + align:start position:0% + + + + align:start position:0% + +oops no that's what just did I want to + + align:start position:0% +oops no that's what just did I want to + + + align:start position:0% +oops no that's what just did I want to +do this one so now I'm logged + + align:start position:0% + + + + align:start position:0% + +into I just sshed into class + + align:start position:0% +into I just sshed into class + + + align:start position:0% +into I just sshed into class +dbo2 cloud. grid. + + align:start position:0% +dbo2 cloud. grid. + + + align:start position:0% +dbo2 cloud. grid. +l.m. uh which happens it tells you which + + align:start position:0% +l.m. uh which happens it tells you which + + + align:start position:0% +l.m. uh which happens it tells you which +node it's actually math to which is node + + align:start position:0% +node it's actually math to which is node + + + align:start position:0% +node it's actually math to which is node +F-1 15-11 in our cluster and this is a + + align:start position:0% +F-1 15-11 in our cluster and this is a + + + align:start position:0% +F-1 15-11 in our cluster and this is a +fairly powerful compute node these are + + align:start position:0% +fairly powerful compute node these are + + + align:start position:0% +fairly powerful compute node these are +our next Generation compute nodes for L + + align:start position:0% +our next Generation compute nodes for L + + + align:start position:0% +our next Generation compute nodes for L +grid so those who've been using El grid + + align:start position:0% +grid so those who've been using El grid + + + align:start position:0% +grid so those who've been using El grid +for all these past years may have notice + + align:start position:0% +for all these past years may have notice + + + align:start position:0% +for all these past years may have notice +that the they're getting a little long + + align:start position:0% +that the they're getting a little long + + + align:start position:0% +that the they're getting a little long +in the tooth these are the first set of + + align:start position:0% +in the tooth these are the first set of + + + align:start position:0% +in the tooth these are the first set of +the new nodes and we'll have about 500 + + align:start position:0% +the new nodes and we'll have about 500 + + + align:start position:0% +the new nodes and we'll have about 500 +of them total in various systems um and + + align:start position:0% +of them total in various systems um and + + + align:start position:0% +of them total in various systems um and +so here um I am uh doing something a + + align:start position:0% +so here um I am uh doing something a + + + align:start position:0% +so here um I am uh doing something a +little bit larger so let me see here so + + align:start position:0% +little bit larger so let me see here so + + + align:start position:0% +little bit larger so let me see here so +I see the volumes + + align:start position:0% +I see the volumes + + + align:start position:0% +I see the volumes +examples so I'm on my elegit account + + align:start position:0% +examples so I'm on my elegit account + + + align:start position:0% +examples so I'm on my elegit account +here and I'm going to go to three and + + align:start position:0% +here and I'm going to go to three and + + + align:start position:0% +here and I'm going to go to three and +two all right and I do open Dots all + + align:start position:0% +two all right and I do open Dots all + + + align:start position:0% +two all right and I do open Dots all +right so that's the + + align:start position:0% +right so that's the + + + align:start position:0% +right so that's the +directory and so the first thing I did + + align:start position:0% +directory and so the first thing I did + + + align:start position:0% +directory and so the first thing I did +is in my DB setup here you'll notice + + align:start position:0% +is in my DB setup here you'll notice + + + align:start position:0% +is in my DB setup here you'll notice +that I have uh done uh class + + align:start position:0% +that I have uh done uh class + + + align:start position:0% +that I have uh done uh class +db0 + + align:start position:0% +db0 + + + align:start position:0% +db0 +okay and also we don't need to do one + + align:start position:0% +okay and also we don't need to do one + + + align:start position:0% +okay and also we don't need to do one +but I will do two here I've made this + + align:start position:0% +but I will do two here I've made this + + + align:start position:0% +but I will do two here I've made this +bigger so I've made this now 2 to the + + align:start position:0% +bigger so I've made this now 2 to the + + + align:start position:0% +bigger so I've made this now 2 to the +18th vertices instead of what I had + + align:start position:0% +18th vertices instead of what I had + + + align:start position:0% +18th vertices instead of what I had +before so let's + + align:start position:0% +before so let's + + + align:start position:0% +before so let's +go that anymore if I do + + align:start position:0% +go that anymore if I do + + + align:start position:0% +go that anymore if I do +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +pdb2 it's going to now generate these + + align:start position:0% +pdb2 it's going to now generate these + + + align:start position:0% +pdb2 it's going to now generate these +things and so it's generating a lot more + + align:start position:0% +things and so it's generating a lot more + + + align:start position:0% +things and so it's generating a lot more +data and you see it's doing at about a + + align:start position:0% +data and you see it's doing at about a + + + align:start position:0% +data and you see it's doing at about a +couple hundred thousand veres per second + + align:start position:0% +couple hundred thousand veres per second + + + align:start position:0% +couple hundred thousand veres per second +just shows you a difference between the + + align:start position:0% +just shows you a difference between the + + + align:start position:0% +just shows you a difference between the +capability of my laptop and one of these + + align:start position:0% +capability of my laptop and one of these + + + align:start position:0% +capability of my laptop and one of these +one of these servers here okay and this + + align:start position:0% +one of these servers here okay and this + + + align:start position:0% +one of these servers here okay and this +will also I'm logged onto this system it + + align:start position:0% +will also I'm logged onto this system it + + + align:start position:0% +will also I'm logged onto this system it +has 32 cores I can do things in parallel + + align:start position:0% +has 32 cores I can do things in parallel + + + align:start position:0% +has 32 cores I can do things in parallel +and so for instance if I did eval prun + + align:start position:0% +and so for instance if I did eval prun + + + align:start position:0% +and so for instance if I did eval prun +for those of you who have had the + + align:start position:0% +for those of you who have had the + + + align:start position:0% +for those of you who have had the +parallel mat lab + + align:start position:0% + + + + align:start position:0% + +training I can say + + align:start position:0% +training I can say + + + align:start position:0% +training I can say +before and if I just since I'm logged + + align:start position:0% +before and if I just since I'm logged + + + align:start position:0% +before and if I just since I'm logged +into this node and I just do curly + + align:start position:0% +into this node and I just do curly + + + align:start position:0% +into this node and I just do curly +brackets it says Just Launch locally on + + align:start position:0% +brackets it says Just Launch locally on + + + align:start position:0% +brackets it says Just Launch locally on +that node don't launch onto the + + align:start position:0% + + + + align:start position:0% + +grid and now it's launching that in + + align:start position:0% +grid and now it's launching that in + + + align:start position:0% +grid and now it's launching that in +parallel on this node data one did that + + align:start position:0% +parallel on this node data one did that + + + align:start position:0% +parallel on this node data one did that +data two did that now it's done and the + + align:start position:0% +data two did that now it's done and the + + + align:start position:0% +data two did that now it's done and the +others finished their work to probably + + align:start position:0% +others finished their work to probably + + + align:start position:0% +others finished their work to probably +WR about now so that's just an example + + align:start position:0% +WR about now so that's just an example + + + align:start position:0% +WR about now so that's just an example +of being able to do things in parallel + + align:start position:0% +of being able to do things in parallel + + + align:start position:0% +of being able to do things in parallel +you know we've created here I mean you + + align:start position:0% +you know we've created here I mean you + + + align:start position:0% +you know we've created here I mean you +look at it and we did uh + + align:start position:0% +look at it and we did uh + + + align:start position:0% +look at it and we did uh +you know what 8 times 300, we did two + + align:start position:0% +you know what 8 times 300, we did two + + + align:start position:0% +you know what 8 times 300, we did two +and a half million edges in that in that + + align:start position:0% +and a half million edges in that in that + + + align:start position:0% +and a half million edges in that in that +essentially 5 Seconds type of thing so + + align:start position:0% +essentially 5 Seconds type of thing so + + + align:start position:0% +essentially 5 Seconds type of thing so +see you know a state mag multiply this + + align:start position:0% +see you know a state mag multiply this + + + align:start position:0% +see you know a state mag multiply this +by four you're doing like a million + + align:start position:0% +by four you're doing like a million + + + align:start position:0% +by four you're doing like a million +edges a second just in that one one type + + align:start position:0% +edges a second just in that one one type + + + align:start position:0% +edges a second just in that one one type +of of calculation + + align:start position:0% +of of calculation + + + align:start position:0% +of of calculation +there move on + + align:start position:0% + + + + align:start position:0% + +tpd3 and um oh I should say I did modify + + align:start position:0% +tpd3 and um oh I should say I did modify + + + align:start position:0% +tpd3 and um oh I should say I did modify +that program + + align:start position:0% +that program + + + align:start position:0% +that program +slightly let's see here here + + align:start position:0% +slightly let's see here here + + + align:start position:0% +slightly let's see here here +uh right so if I look + + align:start position:0% + + + + align:start position:0% + +at the the line enabled in big capital + + align:start position:0% +at the the line enabled in big capital + + + align:start position:0% +at the the line enabled in big capital +letters parallel I uncommented it that's + + align:start position:0% +letters parallel I uncommented it that's + + + align:start position:0% +letters parallel I uncommented it that's +what allows each one of the processors + + align:start position:0% +what allows each one of the processors + + + align:start position:0% +what allows each one of the processors +when they launch to then work on + + align:start position:0% +when they launch to then work on + + + align:start position:0% +when they launch to then work on +different files otherwise they all would + + align:start position:0% +different files otherwise they all would + + + align:start position:0% +different files otherwise they all would +have worked on the same the you know the + + align:start position:0% +have worked on the same the you know the + + + align:start position:0% +have worked on the same the you know the +same files so by uncommenting that + + align:start position:0% +same files so by uncommenting that + + + align:start position:0% +same files so by uncommenting that +parallel uh this now becomes a parallel + + align:start position:0% +parallel uh this now becomes a parallel + + + align:start position:0% +parallel uh this now becomes a parallel +program that I can run with the evlp Run + + align:start position:0% +program that I can run with the evlp Run + + + align:start position:0% +program that I can run with the evlp Run +command of course you have to have + + align:start position:0% +command of course you have to have + + + align:start position:0% +command of course you have to have +parallel malab installed which of course + + align:start position:0% +parallel malab installed which of course + + + align:start position:0% +parallel malab installed which of course +you all do since you're on L grid but um + + align:start position:0% +you all do since you're on L grid but um + + + align:start position:0% +you all do since you're on L grid but um +for anyone seeing this on the internet + + align:start position:0% +for anyone seeing this on the internet + + + align:start position:0% +for anyone seeing this on the internet +they would need to to have that software + + align:start position:0% +they would need to to have that software + + + align:start position:0% +they would need to to have that software +installed too which is also available on + + align:start position:0% +installed too which is also available on + + + align:start position:0% +installed too which is also available on +the web and and installable there so + + align:start position:0% +the web and and installable there so + + + align:start position:0% +the web and and installable there so +that's all we needed to do is uncomment + + align:start position:0% +that's all we needed to do is uncomment + + + align:start position:0% +that's all we needed to do is uncomment +that one line to make that program + + align:start position:0% +that one line to make that program + + + align:start position:0% +that one line to make that program +parallel and did the right thing for us + + align:start position:0% +parallel and did the right thing for us + + + align:start position:0% +parallel and did the right thing for us +as well and we're going to go on to the + + align:start position:0% +as well and we're going to go on to the + + + align:start position:0% +as well and we're going to go on to the +next example and we did the same thing + + align:start position:0% +next example and we did the same thing + + + align:start position:0% +next example and we did the same thing +there we did we just uncommented + + align:start position:0% +there we did we just uncommented + + + align:start position:0% +there we did we just uncommented +parallel and it's now going to you know + + align:start position:0% +parallel and it's now going to you know + + + align:start position:0% +parallel and it's now going to you know +create these associative arrays and + + align:start position:0% +create these associative arrays and + + + align:start position:0% +create these associative arrays and +parallel so if I do + + align:start position:0% + + + + align:start position:0% + +and again if we ran that in + + align:start position:0% + + + + align:start position:0% + +parallel it automatically tries to kill + + align:start position:0% +parallel it automatically tries to kill + + + align:start position:0% +parallel it automatically tries to kill +the last job you ran if you were in the + + align:start position:0% +the last job you ran if you were in the + + + align:start position:0% +the last job you ran if you were in the +same directory so that you're not + + align:start position:0% +same directory so that you're not + + + align:start position:0% +same directory so that you're not +stomping on to + + align:start position:0% +stomping on to + + + align:start position:0% +stomping on to +yourself and now you see it's doing that + + align:start position:0% +yourself and now you see it's doing that + + + align:start position:0% +yourself and now you see it's doing that +again and now it's done so again and the + + align:start position:0% +again and now it's done so again and the + + + align:start position:0% +again and now it's done so again and the +other ones have finished as well can + + align:start position:0% +other ones have finished as well can + + + align:start position:0% +other ones have finished as well can +actually check that if you really want + + align:start position:0% +actually check that if you really want + + + align:start position:0% +actually check that if you really want +to just control Z if I do + + align:start position:0% + + + + align:start position:0% + +more NPI star. out you can see those are + + align:start position:0% +more NPI star. out you can see those are + + + align:start position:0% +more NPI star. out you can see those are +the output files of each one of them I'm + + align:start position:0% +the output files of each one of them I'm + + + align:start position:0% +the output files of each one of them I'm +not lying they didn't take a ridiculous + + align:start position:0% +not lying they didn't take a ridiculous + + + align:start position:0% +not lying they didn't take a ridiculous +amount of time they all completed you + + align:start position:0% +amount of time they all completed you + + + align:start position:0% +amount of time they all completed you +know you always encourage people to + + align:start position:0% +know you always encourage people to + + + align:start position:0% +know you always encourage people to +check those dotout files in that Matt + + align:start position:0% +check those dotout files in that Matt + + + align:start position:0% +check those dotout files in that Matt +MPI directory that's where it sends all + + align:start position:0% +MPI directory that's where it sends all + + + align:start position:0% +MPI directory that's where it sends all +the standard out from all the other + + align:start position:0% +the standard out from all the other + + + align:start position:0% +the standard out from all the other +nodes it's probably the number one + + align:start position:0% +nodes it's probably the number one + + + align:start position:0% +nodes it's probably the number one +feedback we get from a user who says my + + align:start position:0% +feedback we get from a user who says my + + + align:start position:0% +feedback we get from a user who says my +job didn't run we're like what does it + + align:start position:0% +job didn't run we're like what does it + + + align:start position:0% +job didn't run we're like what does it +say in your dotout files and usually + + align:start position:0% +say in your dotout files and usually + + + align:start position:0% +say in your dotout files and usually +like oh there's an error on node three + + align:start position:0% +like oh there's an error on node three + + + align:start position:0% +like oh there's an error on node three +because this calculation is wrong on + + align:start position:0% +because this calculation is wrong on + + + align:start position:0% +because this calculation is wrong on +that particular node or something like + + align:start position:0% +that particular node or something like + + + align:start position:0% +that particular node or something like +that so just reminding reminding folks + + align:start position:0% +that so just reminding reminding folks + + + align:start position:0% +that so just reminding reminding folks +of that moving on let so that was uh + + align:start position:0% +of that moving on let so that was uh + + + align:start position:0% +of that moving on let so that was uh +what did we just do we did three so we + + align:start position:0% +what did we just do we did three so we + + + align:start position:0% +what did we just do we did three so we +did pdb + + align:start position:0% + + + + align:start position:0% + +four + + align:start position:0% + + + + align:start position:0% + +retest this is doing a little bit bigger + + align:start position:0% +retest this is doing a little bit bigger + + + align:start position:0% +retest this is doing a little bit bigger +calculation and so you can see here I + + align:start position:0% +calculation and so you can see here I + + + align:start position:0% +calculation and so you can see here I +told you it does begin to get bigger + + align:start position:0% +told you it does begin to get bigger + + + align:start position:0% +told you it does begin to get bigger +here so it started out you know the + + align:start position:0% +here so it started out you know the + + + align:start position:0% +here so it started out you know the +first iteration was about 6 seconds then + + align:start position:0% +first iteration was about 6 seconds then + + + align:start position:0% +first iteration was about 6 seconds then +it goes on to point8 seconds um if we + + align:start position:0% +it goes on to point8 seconds um if we + + + align:start position:0% +it goes on to point8 seconds um if we +did that cat approach um it would do it + + align:start position:0% +did that cat approach um it would do it + + + align:start position:0% +did that cat approach um it would do it +it would do it faster um + + align:start position:0% +it would do it faster um + + + align:start position:0% +it would do it faster um +I'll show you a little neat trick with + + align:start position:0% +I'll show you a little neat trick with + + + align:start position:0% +I'll show you a little neat trick with +this is also a parallel program when I + + align:start position:0% +this is also a parallel program when I + + + align:start position:0% +this is also a parallel program when I +run it and um basically I I Loop over + + align:start position:0% +run it and um basically I I Loop over + + + align:start position:0% +run it and um basically I I Loop over +each files here um I'm just doing this + + align:start position:0% +each files here um I'm just doing this + + + align:start position:0% +each files here um I'm just doing this +to this little a thing just to sync sync + + align:start position:0% +to this little a thing just to sync sync + + + align:start position:0% +to this little a thing just to sync sync +the processors just for fun so I don't + + align:start position:0% +the processors just for fun so I don't + + + align:start position:0% +the processors just for fun so I don't +have to wait for them to start um and + + align:start position:0% +have to wait for them to start um and + + + align:start position:0% +have to wait for them to start um and +then it's going to go and they're going + + align:start position:0% +then it's going to go and they're going + + + align:start position:0% +then it's going to go and they're going +to do their sums and then when they're + + align:start position:0% +to do their sums and then when they're + + + align:start position:0% +to do their sums and then when they're +all done they're going to call this glob + + align:start position:0% +all done they're going to call this glob + + + align:start position:0% +all done they're going to call this glob +so each one will have a local sum and it + + align:start position:0% +so each one will have a local sum and it + + + align:start position:0% +so each one will have a local sum and it +needs to be pulled together so we have + + align:start position:0% +needs to be pulled together so we have + + + align:start position:0% +needs to be pulled together so we have +this fun function called gag which + + align:start position:0% +this fun function called gag which + + + align:start position:0% +this fun function called gag which +basically takes associative arrays and + + align:start position:0% +basically takes associative arrays and + + + align:start position:0% +basically takes associative arrays and +we'll just sum them all together and + + align:start position:0% +we'll just sum them all together and + + + align:start position:0% +we'll just sum them all together and +very nice um um tool for doing that and + + align:start position:0% +very nice um um tool for doing that and + + + align:start position:0% +very nice um um tool for doing that and +of course we had to uncomment that in + + align:start position:0% +of course we had to uncomment that in + + + align:start position:0% +of course we had to uncomment that in +order for that to work and so let's go + + align:start position:0% +order for that to work and so let's go + + + align:start position:0% +order for that to work and so let's go +give that a try and so if we do + + align:start position:0% +give that a try and so if we do + + + align:start position:0% +give that a try and so if we do +eval + + align:start position:0% + + + + align:start position:0% + +prun so it's launching them + + align:start position:0% +prun so it's launching them + + + align:start position:0% +prun so it's launching them +and this reading and then I was going to + + align:start position:0% +and this reading and then I was going to + + + align:start position:0% +and this reading and then I was going to +have to wait a second okay so then it + + align:start position:0% +have to wait a second okay so then it + + + align:start position:0% +have to wait a second okay so then it +took about two seconds to pull them all + + align:start position:0% +took about two seconds to pull them all + + + align:start position:0% +took about two seconds to pull them all +together and do the sum across those + + align:start position:0% +together and do the sum across those + + + align:start position:0% +together and do the sum across those +processors so that's a parallel + + align:start position:0% +processors so that's a parallel + + + align:start position:0% +processors so that's a parallel +computation um you know a classic + + align:start position:0% +computation um you know a classic + + + align:start position:0% +computation um you know a classic +example of what people do with L grid + + align:start position:0% +example of what people do with L grid + + + align:start position:0% +example of what people do with L grid +and can do with d4m is they have a bunch + + align:start position:0% +and can do with d4m is they have a bunch + + + align:start position:0% +and can do with d4m is they have a bunch +of files each processor processes them + + align:start position:0% +of files each processor processes them + + + align:start position:0% +of files each processor processes them +independently and at the end they pull + + align:start position:0% +independently and at the end they pull + + + align:start position:0% +independently and at the end they pull +something all together using this uh + + align:start position:0% +something all together using this uh + + + align:start position:0% +something all together using this uh +either this this this uh gag gag + + align:start position:0% +either this this this uh gag gag + + + align:start position:0% +either this this this uh gag gag +command all right Right Moving + + align:start position:0% +command all right Right Moving + + + align:start position:0% +command all right Right Moving +On so now + + align:start position:0% + + + + align:start position:0% + +uh on database 2 here so I'm going to go + + align:start position:0% +uh on database 2 here so I'm going to go + + + align:start position:0% +uh on database 2 here so I'm going to go +to that let's look at our + + align:start position:0% +to that let's look at our + + + align:start position:0% +to that let's look at our +tables very little activity you see we + + align:start position:0% +tables very little activity you see we + + + align:start position:0% +tables very little activity you see we +have no tables there so I have to create + + align:start position:0% +have no tables there so I have to create + + + align:start position:0% +have no tables there so I have to create +them so I'm going to do PD pdb + + align:start position:0% +them so I'm going to do PD pdb + + + align:start position:0% +them so I'm going to do PD pdb +setup that's going to create those + + align:start position:0% +setup that's going to create those + + + align:start position:0% +setup that's going to create those +tables on that that + + align:start position:0% + + + + align:start position:0% + +database all right and we can now look + + align:start position:0% +database all right and we can now look + + + align:start position:0% +database all right and we can now look +and + + align:start position:0% +and + + + align:start position:0% +and +see voila I created all my table so now + + align:start position:0% +see voila I created all my table so now + + + align:start position:0% +see voila I created all my table so now +I'm ready to go and now we're going to + + align:start position:0% +I'm ready to go and now we're going to + + + align:start position:0% +I'm ready to go and now we're going to +do the insert again + + align:start position:0% +do the insert again + + + align:start position:0% +do the insert again +pdb six I'm going insert the adjacency + + align:start position:0% + + + + align:start position:0% + +Matrix and this obviously takes a little + + align:start position:0% +Matrix and this obviously takes a little + + + align:start position:0% +Matrix and this obviously takes a little +bit longer I just each one of these + + align:start position:0% +bit longer I just each one of these + + + align:start position:0% +bit longer I just each one of these +there's a parameter associated with the + + align:start position:0% +there's a parameter associated with the + + + align:start position:0% +there's a parameter associated with the +table which is you would think normally + + align:start position:0% +table which is you would think normally + + + align:start position:0% +table which is you would think normally +it should just send all its data to the + + align:start position:0% +it should just send all its data to the + + + align:start position:0% +it should just send all its data to the +database at once but it turns out one + + align:start position:0% +database at once but it turns out one + + + align:start position:0% +database at once but it turns out one +thing we found is that actually it + + align:start position:0% +thing we found is that actually it + + + align:start position:0% +thing we found is that actually it +prefers the database prefers to receive + + align:start position:0% +prefers the database prefers to receive + + + align:start position:0% +prefers the database prefers to receive +the data in a smaller increment + + align:start position:0% +the data in a smaller increment + + + align:start position:0% +the data in a smaller increment +typically around half a megabyte chunk + + align:start position:0% +typically around half a megabyte chunk + + + align:start position:0% +typically around half a megabyte chunk +so every single time it's calling this + + align:start position:0% +so every single time it's calling this + + + align:start position:0% +so every single time it's calling this +it's sending half a megabyte waiting to + + align:start position:0% +it's sending half a megabyte waiting to + + + align:start position:0% +it's sending half a megabyte waiting to +get the all clear again and then setting + + align:start position:0% +get the all clear again and then setting + + + align:start position:0% +get the all clear again and then setting +the next one and we've actually found + + align:start position:0% +the next one and we've actually found + + + align:start position:0% +the next one and we've actually found +that that makes a fairly significant so + + align:start position:0% +that that makes a fairly significant so + + + align:start position:0% +that that makes a fairly significant so +you can see here we're getting about + + align:start position:0% +you can see here we're getting about + + + align:start position:0% +you can see here we're getting about +60,000 inserts per second + + align:start position:0% +60,000 inserts per second + + + align:start position:0% +60,000 inserts per second +this is from one One + + align:start position:0% +this is from one One + + + align:start position:0% +this is from one One +processor and this takes a little while + + align:start position:0% +processor and this takes a little while + + + align:start position:0% +processor and this takes a little while +uh let's see we can go and look at it + + align:start position:0% +uh let's see we can go and look at it + + + align:start position:0% +uh let's see we can go and look at it +while it's going on go here we should + + align:start position:0% +while it's going on go here we should + + + align:start position:0% +while it's going on go here we should +begin to see some some there you go see + + align:start position:0% +begin to see some some there you go see + + + align:start position:0% +begin to see some some there you go see +that's that's what a real inserts + + align:start position:0% +that's that's what a real inserts + + + align:start position:0% +that's that's what a real inserts +beginning to look like it just changes + + align:start position:0% +beginning to look like it just changes + + + align:start position:0% +beginning to look like it just changes +its axis for you uh dynamically here but + + align:start position:0% +its axis for you uh dynamically here but + + + align:start position:0% +its axis for you uh dynamically here but +we're getting about 600 thou + + align:start position:0% +we're getting about 600 thou + + + align:start position:0% +we're getting about 600 thou +60,000 uh inserts a second there you + + align:start position:0% +60,000 uh inserts a second there you + + + align:start position:0% +60,000 uh inserts a second there you +just go along here it'll start leveling + + align:start position:0% +just go along here it'll start leveling + + + align:start position:0% +just go along here it'll start leveling +off a little bit + + align:start position:0% + + + + align:start position:0% + +and we'll show you what's going on in + + align:start position:0% +and we'll show you what's going on in + + + align:start position:0% +and we'll show you what's going on in +the tables + + align:start position:0% + + + + align:start position:0% + +there and just I mean you know not too + + align:start position:0% +there and just I mean you know not too + + + align:start position:0% +there and just I mean you know not too +many of you are probably database effici + + align:start position:0% +many of you are probably database effici + + + align:start position:0% +many of you are probably database effici +in Autos but + + align:start position:0% +in Autos but + + + align:start position:0% +in Autos but +60,000 inserts a second on a single node + + align:start position:0% +60,000 inserts a second on a single node + + + align:start position:0% +60,000 inserts a second on a single node +data base is pretty darn amazing I mean + + align:start position:0% +data base is pretty darn amazing I mean + + + align:start position:0% +data base is pretty darn amazing I mean +you would mostly have had to use a + + align:start position:0% +you would mostly have had to use a + + + align:start position:0% +you would mostly have had to use a +parallel database and that's actually + + align:start position:0% +parallel database and that's actually + + + align:start position:0% +parallel database and that's actually +one of the great powers of accumulators + + align:start position:0% +one of the great powers of accumulators + + + align:start position:0% +one of the great powers of accumulators +there's a lot of problem even though + + align:start position:0% +there's a lot of problem even though + + + align:start position:0% +there's a lot of problem even though +it's a parallel database there's a lot + + align:start position:0% +it's a parallel database there's a lot + + + align:start position:0% +it's a parallel database there's a lot +of problems you can now do with a single + + align:start position:0% +of problems you can now do with a single + + + align:start position:0% +of problems you can now do with a single +node database that you would have had to + + align:start position:0% +node database that you would have had to + + + align:start position:0% +node database that you would have had to +have a parallel system to do before and + + align:start position:0% +have a parallel system to do before and + + + align:start position:0% +have a parallel system to do before and +that's really because you know parallel + + align:start position:0% +that's really because you know parallel + + + align:start position:0% +that's really because you know parallel +Computing is a real pain I mean I should + + align:start position:0% +Computing is a real pain I mean I should + + + align:start position:0% +Computing is a real pain I mean I should +know and uh and so one of the best if + + align:start position:0% +know and uh and so one of the best if + + + align:start position:0% +know and uh and so one of the best if +you can make if you can make your + + align:start position:0% +you can make if you can make your + + + align:start position:0% +you can make if you can make your +parallel problem fast enough to Now work + + align:start position:0% +parallel problem fast enough to Now work + + + align:start position:0% +parallel problem fast enough to Now work +on a single one that's really uh a + + align:start position:0% +on a single one that's really uh a + + + align:start position:0% +on a single one that's really uh a +tremendously convenient uh + + align:start position:0% + + + + align:start position:0% + +capability all right so we inserted + + align:start position:0% +capability all right so we inserted + + + align:start position:0% +capability all right so we inserted +there what 8 + + align:start position:0% +there what 8 + + + align:start position:0% +there what 8 +million uh uh entries right so pretty + + align:start position:0% +million uh uh entries right so pretty + + + align:start position:0% +million uh uh entries right so pretty +impressive um but that did take a while + + align:start position:0% +impressive um but that did take a while + + + align:start position:0% +impressive um but that did take a while +you know and so maybe I want to do that + + align:start position:0% +you know and so maybe I want to do that + + + align:start position:0% +you know and so maybe I want to do that +in parallel so if I just do evil + + align:start position:0% +in parallel so if I just do evil + + + align:start position:0% +in parallel so if I just do evil +prun let's try let's try four see what + + align:start position:0% + + + + align:start position:0% + +happens now I would expect actually this + + align:start position:0% +happens now I would expect actually this + + + align:start position:0% +happens now I would expect actually this +to begin to top this thing out and so + + align:start position:0% +to begin to top this thing out and so + + + align:start position:0% +to begin to top this thing out and so +the individual ins search rates on each + + align:start position:0% +the individual ins search rates on each + + + align:start position:0% +the individual ins search rates on each +node probably go down a little + + align:start position:0% + + + + align:start position:0% + +bit and you'll see It'll get a little + + align:start position:0% +bit and you'll see It'll get a little + + + align:start position:0% +bit and you'll see It'll get a little +bit noisy here because now we have four + + align:start position:0% +bit noisy here because now we have four + + + align:start position:0% +bit noisy here because now we have four +separate processes all doing inserts you + + align:start position:0% +separate processes all doing inserts you + + + align:start position:0% +separate processes all doing inserts you +see there was one it took a little bit + + align:start position:0% +see there was one it took a little bit + + + align:start position:0% +see there was one it took a little bit +of almost a second you can get this + + align:start position:0% +of almost a second you can get this + + + align:start position:0% +of almost a second you can get this +noise beginning to happen here but we're + + align:start position:0% +noise beginning to happen here but we're + + + align:start position:0% +noise beginning to happen here but we're +getting 50,000 edges per second on one + + align:start position:0% +getting 50,000 edges per second on one + + + align:start position:0% +getting 50,000 edges per second on one +node which means we should be getting + + align:start position:0% +node which means we should be getting + + + align:start position:0% +node which means we should be getting +you know like close to four times that + + align:start position:0% +you know like close to four times that + + + align:start position:0% +you know like close to four times that +so let's go check what what's it seeing + + align:start position:0% +so let's go check what what's it seeing + + + align:start position:0% +so let's go check what what's it seeing +here so if we update that and there you + + align:start position:0% +here so if we update that and there you + + + align:start position:0% +here so if we update that and there you +see we're sort of now climbing the hill + + align:start position:0% +see we're sort of now climbing the hill + + + align:start position:0% +see we're sort of now climbing the hill +uh well over 100,000 that was our first + + align:start position:0% +uh well over 100,000 that was our first + + + align:start position:0% +uh well over 100,000 that was our first +insert there and now we're entering the + + align:start position:0% +insert there and now we're entering the + + + align:start position:0% +insert there and now we're entering the +second one + + align:start position:0% +second one + + + align:start position:0% +second one +here oops don't want to check my email + + align:start position:0% +here oops don't want to check my email + + + align:start position:0% +here oops don't want to check my email +do + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% +I + + + align:start position:0% +I +um let's see here so how we doing there + + align:start position:0% +um let's see here so how we doing there + + + align:start position:0% +um let's see here so how we doing there +oh it's done so uh I don't even know if + + align:start position:0% +oh it's done so uh I don't even know if + + + align:start position:0% +oh it's done so uh I don't even know if +we'll got we we may not even gotten the + + align:start position:0% +we'll got we we may not even gotten the + + + align:start position:0% +we'll got we we may not even gotten the +full rise time of that yeah so it + + align:start position:0% +full rise time of that yeah so it + + + align:start position:0% +full rise time of that yeah so it +basically finished before we could even + + align:start position:0% +basically finished before we could even + + + align:start position:0% +basically finished before we could even +hit the really hit the you know it has a + + align:start position:0% +hit the really hit the you know it has a + + + align:start position:0% +hit the really hit the you know it has a +little filter here has a certain + + align:start position:0% +little filter here has a certain + + + align:start position:0% +little filter here has a certain +resolution you really need to do an + + align:start position:0% +resolution you really need to do an + + + align:start position:0% +resolution you really need to do an +insert for about 10 minutes before you + + align:start position:0% +insert for about 10 minutes before you + + + align:start position:0% +insert for about 10 minutes before you +can get really a sense of that but uh + + align:start position:0% +can get really a sense of that but uh + + + align:start position:0% +can get really a sense of that but uh +you know there you you see you know we + + align:start position:0% +you know there you you see you know we + + + align:start position:0% +you know there you you see you know we +probably got over 200,000 inserts a + + align:start position:0% +probably got over 200,000 inserts a + + + align:start position:0% +probably got over 200,000 inserts a +second using four processes + + align:start position:0% +second using four processes + + + align:start position:0% +second using four processes +on on one note and so again and we could + + align:start position:0% +on on one note and so again and we could + + + align:start position:0% +on on one note and so again and we could +probably keep on going up this ramp you + + align:start position:0% +probably keep on going up this ramp you + + + align:start position:0% +probably keep on going up this ramp you +know for this data said I'd expect we'd + + align:start position:0% +know for this data said I'd expect we'd + + + align:start position:0% +know for this data said I'd expect we'd +be able to get maybe 500,000 inserts a + + align:start position:0% +be able to get maybe 500,000 inserts a + + + align:start position:0% +be able to get maybe 500,000 inserts a +second if I kept adding processors and + + align:start position:0% +second if I kept adding processors and + + + align:start position:0% +second if I kept adding processors and +stuff like that and again so and if you + + align:start position:0% +stuff like that and again so and if you + + + align:start position:0% +stuff like that and again so and if you +look at our data right you know what do + + align:start position:0% +look at our data right you know what do + + + align:start position:0% +look at our data right you know what do +we got + + align:start position:0% +we got + + + align:start position:0% +we got +here well we got like 15 million entries + + align:start position:0% +here well we got like 15 million entries + + + align:start position:0% +here well we got like 15 million entries +now in our database again one of the + + align:start position:0% +now in our database again one of the + + + align:start position:0% +now in our database again one of the +nice things is for typical databases a + + align:start position:0% +nice things is for typical databases a + + + align:start position:0% +nice things is for typical databases a +lot of times like you have to rein EST + + align:start position:0% +lot of times like you have to rein EST + + + align:start position:0% +lot of times like you have to rein EST +the whole database + + align:start position:0% +the whole database + + + align:start position:0% +the whole database +that's fine in our cyber program we have + + align:start position:0% +that's fine in our cyber program we have + + + align:start position:0% +that's fine in our cyber program we have +a month of data and we can reest it in a + + align:start position:0% +a month of data and we can reest it in a + + + align:start position:0% +a month of data and we can reest it in a +couple hours and that's a very powerful + + align:start position:0% +couple hours and that's a very powerful + + + align:start position:0% +couple hours and that's a very powerful +tool to be able to like oh you know what + + align:start position:0% +tool to be able to like oh you know what + + + align:start position:0% +tool to be able to like oh you know what +I didn't like the ingestion that's fine + + align:start position:0% +I didn't like the ingestion that's fine + + + align:start position:0% +I didn't like the ingestion that's fine +I'll just rewrite the ingestion and redo + + align:start position:0% +I'll just rewrite the ingestion and redo + + + align:start position:0% +I'll just rewrite the ingestion and redo +it and this is gives you a very powerful + + align:start position:0% +it and this is gives you a very powerful + + + align:start position:0% +it and this is gives you a very powerful +tool for exploring your data here so + + align:start position:0% +tool for exploring your data here so + + + align:start position:0% +tool for exploring your data here so +that's kind of what I want to do with + + align:start position:0% +that's kind of what I want to do with + + + align:start position:0% +that's kind of what I want to do with +that um one of our students here very + + align:start position:0% +that um one of our students here very + + + align:start position:0% +that um one of our students here very +generously um gave me some Twitter data + + align:start position:0% +generously um gave me some Twitter data + + + align:start position:0% +generously um gave me some Twitter data +and so I wanted to show you a little bit + + align:start position:0% +and so I wanted to show you a little bit + + + align:start position:0% +and so I wanted to show you a little bit +uh with that Twitter data because it's + + align:start position:0% +uh with that Twitter data because it's + + + align:start position:0% +uh with that Twitter data because it's +probably maybe a hair more meaningful + + align:start position:0% +probably maybe a hair more meaningful + + + align:start position:0% +probably maybe a hair more meaningful +than this uh abstract chronic graph uh + + align:start position:0% +than this uh abstract chronic graph uh + + + align:start position:0% +than this uh abstract chronic graph uh +data and by definition Twitter data is + + align:start position:0% +data and by definition Twitter data is + + + align:start position:0% +data and by definition Twitter data is +about the most public data that one + + align:start position:0% +about the most public data that one + + + align:start position:0% +about the most public data that one +could imagine I think no one who posts a + + align:start position:0% +could imagine I think no one who posts a + + + align:start position:0% +could imagine I think no one who posts a +Twitter is expecting any sense of of + + align:start position:0% +Twitter is expecting any sense of of + + + align:start position:0% +Twitter is expecting any sense of of +privacy there so I think we can we can + + align:start position:0% +privacy there so I think we can we can + + + align:start position:0% +privacy there so I think we can we can +use that + + align:start position:0% +use that + + + align:start position:0% +use that +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so let's see here let + + align:start position:0% +so let's see here let + + + align:start position:0% +so let's see here let +me out of + + align:start position:0% +me out of + + + align:start position:0% +me out of +that right and + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +desktop + + align:start position:0% +desktop + + + align:start position:0% +desktop +Twitter + + align:start position:0% + + + + align:start position:0% + +right all right and so basically just a + + align:start position:0% +right all right and so basically just a + + + align:start position:0% +right all right and so basically just a +few examples here the first thing we did + + align:start position:0% +few examples here the first thing we did + + + align:start position:0% +few examples here the first thing we did +is construct the associative array so + + align:start position:0% +is construct the associative array so + + + align:start position:0% +is construct the associative array so +let's start up + + align:start position:0% +let's start up + + + align:start position:0% +let's start up +here and I think it was like a million + + align:start position:0% +here and I think it was like a million + + + align:start position:0% +here and I think it was like a million +Twitter is that right million entries a + + align:start position:0% +Twitter is that right million entries a + + + align:start position:0% +Twitter is that right million entries a +million a million entries and how many + + align:start position:0% +million a million entries and how many + + + align:start position:0% +million a million entries and how many +Twitter how many tweets do you think + + align:start position:0% +Twitter how many tweets do you think + + + align:start position:0% +Twitter how many tweets do you think +that + + align:start position:0% +that + + + align:start position:0% +that +was oh we should be able to find out + + align:start position:0% +was oh we should be able to find out + + + align:start position:0% +was oh we should be able to find out +right we should be able to find out + + align:start position:0% + + + + align:start position:0% + +so so first thing + + align:start position:0% + + + + align:start position:0% + +here so it's reading these in chunk and + + align:start position:0% +here so it's reading these in chunk and + + + align:start position:0% +here so it's reading these in chunk and +writing them out to associative + + align:start position:0% + + + + align:start position:0% + +arrays that's going to be annoying isn't + + align:start position:0% +arrays that's going to be annoying isn't + + + align:start position:0% +arrays that's going to be annoying isn't +it let go to the faster + + align:start position:0% + + + + align:start position:0% + +system so this is running on the + + align:start position:0% +system so this is running on the + + + align:start position:0% +system so this is running on the +database + + align:start position:0% + + + + align:start position:0% + +system and I broke it up into chunks of + + align:start position:0% +system and I broke it up into chunks of + + + align:start position:0% +system and I broke it up into chunks of +10 I couldn't quite on my laptop fit the + + align:start position:0% +10 I couldn't quite on my laptop fit the + + + align:start position:0% +10 I couldn't quite on my laptop fit the +whole thing in one Associated race so I + + align:start position:0% +whole thing in one Associated race so I + + + align:start position:0% +whole thing in one Associated race so I +broke it up to chunks of + + align:start position:0% + + + + align:start position:0% + +10 yeah see we're still cruising + + align:start position:0% + + + + align:start position:0% + +there all right so that just reads it + + align:start position:0% +there all right so that just reads it + + + align:start position:0% +there all right so that just reads it +all in in fact we can take a look at + + align:start position:0% +all in in fact we can take a look at + + + align:start position:0% +all in in fact we can take a look at +that + + align:start position:0% +that + + + align:start position:0% +that +file go to + + align:start position:0% + + + + align:start position:0% + +desktop + + align:start position:0% +desktop + + + align:start position:0% +desktop +so I just took that exact same example + + align:start position:0% +so I just took that exact same example + + + align:start position:0% +so I just took that exact same example +and just put his data in so just to take + + align:start position:0% +and just put his data in so just to take + + + align:start position:0% +and just put his data in so just to take +a look at what that + + align:start position:0% +a look at what that + + + align:start position:0% +a look at what that +involved pretty much all the same I uh + + align:start position:0% +involved pretty much all the same I uh + + + align:start position:0% +involved pretty much all the same I uh +there was it was one big file but I + + align:start position:0% +there was it was one big file but I + + + align:start position:0% +there was it was one big file but I +couldn't process it I mean I could read + + align:start position:0% +couldn't process it I mean I could read + + + align:start position:0% +couldn't process it I mean I could read +it in each one of the the row he did a + + align:start position:0% +it in each one of the the row he did a + + + align:start position:0% +it in each one of the the row he did a +great job of creating into triples and I + + align:start position:0% +great job of creating into triples and I + + + align:start position:0% +great job of creating into triples and I +can easily hold those triples but I + + align:start position:0% +can easily hold those triples but I + + + align:start position:0% +can easily hold those triples but I +couldn't quite construct the associative + + align:start position:0% +couldn't quite construct the associative + + + align:start position:0% +couldn't quite construct the associative +array um and so I basically just go + + align:start position:0% +array um and so I basically just go + + + align:start position:0% +array um and so I basically just go +through and find all the separ operators + + align:start position:0% +through and find all the separ operators + + + align:start position:0% +through and find all the separ operators +and then basically take them out of the + + align:start position:0% +and then basically take them out of the + + + align:start position:0% +and then basically take them out of the +the the the vector in memory and so + + align:start position:0% +the the the vector in memory and so + + + align:start position:0% +the the the vector in memory and so +that's what I'm doing here is I'm + + align:start position:0% +that's what I'm doing here is I'm + + + align:start position:0% +that's what I'm doing here is I'm +looping over um um here so basically I + + align:start position:0% +looping over um um here so basically I + + + align:start position:0% +looping over um um here so basically I +get I read in all the data I find all + + align:start position:0% +get I read in all the data I find all + + + align:start position:0% +get I read in all the data I find all +the the separators and then I go through + + align:start position:0% +the the separators and then I go through + + + align:start position:0% +the the separators and then I go through +and it's a little bit of a messy + + align:start position:0% +and it's a little bit of a messy + + + align:start position:0% +and it's a little bit of a messy +calculation to basically do them in + + align:start position:0% +calculation to basically do them in + + + align:start position:0% +calculation to basically do them in +these particular blocks and then I can + + align:start position:0% +these particular blocks and then I can + + + align:start position:0% +these particular blocks and then I can +construct the associate array and save + + align:start position:0% +construct the associate array and save + + + align:start position:0% +construct the associate array and save +those out uh no + + align:start position:0% + + + + align:start position:0% + +problem then let's see here so what else + + align:start position:0% +problem then let's see here so what else + + + align:start position:0% +problem then let's see here so what else +did we do we did the we can do a little + + align:start position:0% +did we do we did the we can do a little + + + align:start position:0% +did we do we did the we can do a little +degree calculation from that + + align:start position:0% +degree calculation from that + + + align:start position:0% +degree calculation from that +data so it's now reading each one of + + align:start position:0% +data so it's now reading each one of + + + align:start position:0% +data so it's now reading each one of +those and Computing the + + align:start position:0% + + + + align:start position:0% + +degrees comparison do the same thing on + + align:start position:0% +degrees comparison do the same thing on + + + align:start position:0% +degrees comparison do the same thing on +this + + align:start position:0% + + + + align:start position:0% + +system pretty + + align:start position:0% + + + + align:start position:0% + +fast + + align:start position:0% + + + + align:start position:0% + +proceed then + + align:start position:0% +proceed then + + + align:start position:0% +proceed then +to Let's create some + + align:start position:0% +to Let's create some + + + align:start position:0% +to Let's create some +tables okay so I created a special class + + align:start position:0% +tables okay so I created a special class + + + align:start position:0% +tables okay so I created a special class +of tables for that just modify + + align:start position:0% +of tables for that just modify + + + align:start position:0% +of tables for that just modify +that can go over here it was on this + + align:start position:0% + + + + align:start position:0% + +one nope I did it on the other + + align:start position:0% + + + + align:start position:0% + +databee + + align:start position:0% +databee + + + align:start position:0% +databee +one tables + + align:start position:0% +one tables + + + align:start position:0% +one tables +there oh all right so all I was doing + + align:start position:0% +there oh all right so all I was doing + + + align:start position:0% +there oh all right so all I was doing +there was on the other one plotting the + + align:start position:0% +there was on the other one plotting the + + + align:start position:0% +there was on the other one plotting the +degree + + align:start position:0% +degree + + + align:start position:0% +degree +distribution so this shows us you know + + align:start position:0% +distribution so this shows us you know + + + align:start position:0% +distribution so this shows us you know +so for each tweet + + align:start position:0% +so for each tweet + + + align:start position:0% +so for each tweet +oops did a little anal there for each + + align:start position:0% +oops did a little anal there for each + + + align:start position:0% +oops did a little anal there for each +tweet uh let's go to + + align:start position:0% +tweet uh let's go to + + + align:start position:0% +tweet uh let's go to +figure one for each TW all + + align:start position:0% +figure one for each TW all + + + align:start position:0% +figure one for each TW all +right you done it's very twitter- like + + align:start position:0% +right you done it's very twitter- like + + + align:start position:0% +right you done it's very twitter- like +no no one has ever done in + + align:start position:0% +no no one has ever done in + + + align:start position:0% +no no one has ever done in +Twitter uh + + align:start position:0% +Twitter uh + + + align:start position:0% +Twitter uh +so wow what did I + + align:start position:0% + + + + align:start position:0% + +do I went to town didn't + + align:start position:0% +do I went to town didn't + + + align:start position:0% +do I went to town didn't +I done now all right so we go to figure + + align:start position:0% +I done now all right so we go to figure + + + align:start position:0% +I done now all right so we go to figure +one all right you see for each tweet + + align:start position:0% +one all right you see for each tweet + + + align:start position:0% +one all right you see for each tweet +this shows us how much information was + + align:start position:0% +this shows us how much information was + + + align:start position:0% +this shows us how much information was +in each tweet and you see that on + + align:start position:0% +in each tweet and you see that on + + + align:start position:0% +in each tweet and you see that on +average this because he basically ped + + align:start position:0% +average this because he basically ped + + + align:start position:0% +average this because he basically ped +out each word uniquely so this just + + align:start position:0% +out each word uniquely so this just + + + align:start position:0% +out each word uniquely so this just +shows there's about a thousand pieces of + + align:start position:0% +shows there's about a thousand pieces of + + + align:start position:0% +shows there's about a thousand pieces of +information associated with each uh each + + align:start position:0% +information associated with each uh each + + + align:start position:0% +information associated with each uh each +tweet which seems a little high so we + + align:start position:0% +tweet which seems a little high so we + + + align:start position:0% +tweet which seems a little high so we +should probably double check that + + align:start position:0% +should probably double check that + + + align:start position:0% +should probably double check that +um and then what did I do + + align:start position:0% + + + + align:start position:0% + +that so we loaded all them up we summ + + align:start position:0% +that so we loaded all them up we summ + + + align:start position:0% +that so we loaded all them up we summ +the degrees and then oh what I said I + + align:start position:0% +the degrees and then oh what I said I + + + align:start position:0% +the degrees and then oh what I said I +show me all the locations greater than + + align:start position:0% +show me all the locations greater than + + + align:start position:0% +show me all the locations greater than +with with that with crowns greater than + + align:start position:0% +with with that with crowns greater than + + + align:start position:0% +with with that with crowns greater than +100 and all the and then uh all the + + align:start position:0% +100 and all the and then uh all the + + + align:start position:0% +100 and all the and then uh all the +words with the at signs greater than 100 + + align:start position:0% +words with the at signs greater than 100 + + + align:start position:0% +words with the at signs greater than 100 +and all the hashtags greater than 50 so + + align:start position:0% +and all the hashtags greater than 50 so + + + align:start position:0% +and all the hashtags greater than 50 so +that's what these other guys are so so + + align:start position:0% +that's what these other guys are so so + + + align:start position:0% +that's what these other guys are so so +this was the essentially for each tweet + + align:start position:0% +this was the essentially for each tweet + + + align:start position:0% +this was the essentially for each tweet +how many you have um if we go to figure + + align:start position:0% +how many you have um if we go to figure + + + align:start position:0% +how many you have um if we go to figure +two this shows the degree distribution + + align:start position:0% +two this shows the degree distribution + + + align:start position:0% +two this shows the degree distribution +of all the words and other things in + + align:start position:0% +of all the words and other things in + + + align:start position:0% +of all the words and other things in +there so there's some guy here who's + + align:start position:0% +there so there's some guy here who's + + + align:start position:0% +there so there's some guy here who's +really really high in fact we can find + + align:start position:0% +really really high in fact we can find + + + align:start position:0% +really really high in fact we can find +him out um and so but as of course most + + align:start position:0% +him out um and so but as of course most + + + align:start position:0% +him out um and so but as of course most +things you know occur only once slighted + + align:start position:0% +things you know occur only once slighted + + + align:start position:0% +things you know occur only once slighted +once like there's a lot of unique keys + + align:start position:0% +once like there's a lot of unique keys + + + align:start position:0% +once like there's a lot of unique keys +in like the there's the message ID which + + align:start position:0% +in like the there's the message ID which + + + align:start position:0% +in like the there's the message ID which +of course is probably something that + + align:start position:0% +of course is probably something that + + + align:start position:0% +of course is probably something that +only appears once uh if we go to figure + + align:start position:0% +only appears once uh if we go to figure + + + align:start position:0% +only appears once uh if we go to figure +three so this just shows like the + + align:start position:0% +three so this just shows like the + + + align:start position:0% +three so this just shows like the +locations and this was tweets from the + + align:start position:0% +locations and this was tweets from the + + + align:start position:0% +locations and this was tweets from the +day before the hurricane or the week the + + align:start position:0% +day before the hurricane or the week the + + + align:start position:0% +day before the hurricane or the week the +Wednesday before the hurri Hurricane + + align:start position:0% +Wednesday before the hurri Hurricane + + + align:start position:0% +Wednesday before the hurri Hurricane +Sandy and so this shows us you know uh + + align:start position:0% +Sandy and so this shows us you know uh + + + align:start position:0% +Sandy and so this shows us you know uh +but in the limited to the kind of the + + align:start position:0% +but in the limited to the kind of the + + + align:start position:0% +but in the limited to the kind of the +New York area or something like that + + align:start position:0% +New York area or something like that + + + align:start position:0% +New York area or something like that +yeah 40 miles around yor C 40 miles + + align:start position:0% +yeah 40 miles around yor C 40 miles + + + align:start position:0% +yeah 40 miles around yor C 40 miles +around New York city so basically this + + align:start position:0% +around New York city so basically this + + + align:start position:0% +around New York city so basically this +shows us all the locations here and you + + align:start position:0% +shows us all the locations here and you + + + align:start position:0% +shows us all the locations here and you +see so this is a classic example the + + align:start position:0% +see so this is a classic example the + + + align:start position:0% +see so this is a classic example the +kind of things you want to do because + + align:start position:0% +kind of things you want to do because + + + align:start position:0% +kind of things you want to do because +the first thing that we see is that we + + align:start position:0% +the first thing that we see is that we + + + align:start position:0% +the first thing that we see is that we +have some problems with our data which + + align:start position:0% +have some problems with our data which + + + align:start position:0% +have some problems with our data which +is uh New York City and New York City + + align:start position:0% +is uh New York City and New York City + + + align:start position:0% +is uh New York City and New York City +space got to go in and correct all those + + align:start position:0% +space got to go in and correct all those + + + align:start position:0% +space got to go in and correct all those +right so that's a classic example this + + align:start position:0% +right so that's a classic example this + + + align:start position:0% +right so that's a classic example this +is really what + + align:start position:0% +is really what + + + align:start position:0% +is really what +d4m it's the number one thing that + + align:start position:0% +d4m it's the number one thing that + + + align:start position:0% +d4m it's the number one thing that +people do with d for m is it's the first + + align:start position:0% +people do with d for m is it's the first + + + align:start position:0% +people do with d for m is it's the first +time that you really can like do sums + + align:start position:0% +time that you really can like do sums + + + align:start position:0% +time that you really can like do sums +and tallies over the entire data set and + + align:start position:0% +and tallies over the entire data set and + + + align:start position:0% +and tallies over the entire data set and +these things just pop out they stick out + + align:start position:0% +these things just pop out they stick out + + + align:start position:0% +these things just pop out they stick out +like a sore thumb you know like oh got + + align:start position:0% +like a sore thumb you know like oh got + + + align:start position:0% +like a sore thumb you know like oh got +to correct that you know you can either + + align:start position:0% +to correct that you know you can either + + + align:start position:0% +to correct that you know you can either +correct in the database or correct it + + align:start position:0% +correct in the database or correct it + + + align:start position:0% +correct in the database or correct it +afterwards in the query but that just + + align:start position:0% +afterwards in the query but that just + + + align:start position:0% +afterwards in the query but that just +immediately improves the quality of + + align:start position:0% +immediately improves the quality of + + + align:start position:0% +immediately improves the quality of +everything else you have and then + + align:start position:0% +everything else you have and then + + + align:start position:0% +everything else you have and then +there's this clutter one like location + + align:start position:0% +there's this clutter one like location + + + align:start position:0% +there's this clutter one like location +none right well clearly you'd want to + + align:start position:0% +none right well clearly you'd want to + + + align:start position:0% +none right well clearly you'd want to +just kind of get rid of that or do + + align:start position:0% +just kind of get rid of that or do + + + align:start position:0% +just kind of get rid of that or do +something with that and then just plain + + align:start position:0% +something with that and then just plain + + + align:start position:0% +something with that and then just plain +old normal spelled New York so most + + align:start position:0% +old normal spelled New York so most + + + align:start position:0% +old normal spelled New York so most +people can spell correctly and so we're + + align:start position:0% +people can spell correctly and so we're + + + align:start position:0% +people can spell correctly and so we're +we're good but location iPhone I mean + + align:start position:0% +we're good but location iPhone I mean + + + align:start position:0% +we're good but location iPhone I mean +what's that about you know uh Jersey + + align:start position:0% +what's that about you know uh Jersey + + + align:start position:0% +what's that about you know uh Jersey +City well we don't care about that you + + align:start position:0% +City well we don't care about that you + + + align:start position:0% +City well we don't care about that you +know so uh South Jersey well + + align:start position:0% +know so uh South Jersey well + + + align:start position:0% +know so uh South Jersey well +what's South Jersey people don't know + + align:start position:0% +what's South Jersey people don't know + + + align:start position:0% +what's South Jersey people don't know +that they're 40 miles from New York I + + align:start position:0% +that they're 40 miles from New York I + + + align:start position:0% +that they're 40 miles from New York I +guess or whatever they have in their + + align:start position:0% +guess or whatever they have in their + + + align:start position:0% +guess or whatever they have in their +profile so a lot of people in South + + align:start position:0% +profile so a lot of people in South + + + align:start position:0% +profile so a lot of people in South +Jersey who uh say they're from New York + + align:start position:0% +Jersey who uh say they're from New York + + + align:start position:0% +Jersey who uh say they're from New York +so this uh what's her name from Jersey + + align:start position:0% +so this uh what's her name from Jersey + + + align:start position:0% +so this uh what's her name from Jersey +Shore Snookie right Snookie says she's + + align:start position:0% +Shore Snookie right Snookie says she's + + + align:start position:0% +Shore Snookie right Snookie says she's +actually from New York City not not + + align:start position:0% +actually from New York City not not + + + align:start position:0% +actually from New York City not not +Jersey not South Jersey so so uh so + + align:start position:0% +Jersey not South Jersey so so uh so + + + align:start position:0% +Jersey not South Jersey so so uh so +there's a great example of that and then + + align:start position:0% +there's a great example of that and then + + + align:start position:0% +there's a great example of that and then +um let's see here figure four so this + + align:start position:0% +um let's see here figure four so this + + + align:start position:0% +um let's see here figure four so this +just shows all the uh the at signs so + + align:start position:0% +just shows all the uh the at signs so + + + align:start position:0% +just shows all the uh the at signs so +you see + + align:start position:0% +you see + + + align:start position:0% +you see +basically uh damn it's true is like the + + align:start position:0% +basically uh damn it's true is like the + + + align:start position:0% +basically uh damn it's true is like the +most is this like like a retweeted thing + + align:start position:0% +most is this like like a retweeted thing + + + align:start position:0% +most is this like like a retweeted thing +or something or I don't know I don't + + align:start position:0% +or something or I don't know I don't + + + align:start position:0% +or something or I don't know I don't +know what the what does the at sign mean + + align:start position:0% +know what the what does the at sign mean + + + align:start position:0% +know what the what does the at sign mean +again it + + align:start position:0% +again it + + + align:start position:0% +again it +means another to a new to years so most + + align:start position:0% +means another to a new to years so most + + + align:start position:0% +means another to a new to years so most +people tweet to damn it's true in New + + align:start position:0% +people tweet to damn it's true in New + + + align:start position:0% +people tweet to damn it's true in New +York there you go uh funny + + align:start position:0% +York there you go uh funny + + + align:start position:0% +York there you go uh funny +fact uh relatable quote uh and then + + align:start position:0% +fact uh relatable quote uh and then + + + align:start position:0% +fact uh relatable quote uh and then +Donald Trump the real Donald Trump and + + align:start position:0% +Donald Trump the real Donald Trump and + + + align:start position:0% +Donald Trump the real Donald Trump and +then just word at sign so those are + + align:start position:0% +then just word at sign so those are + + + align:start position:0% +then just word at sign so those are +another example you know uh anything + + align:start position:0% +another example you know uh anything + + + align:start position:0% +another example you know uh anything +here is a hilarious idiot Bad Gal + + align:start position:0% +here is a hilarious idiot Bad Gal + + + align:start position:0% +here is a hilarious idiot Bad Gal +V then Marilyn Monroe ID I mean so there + + align:start position:0% +V then Marilyn Monroe ID I mean so there + + + align:start position:0% +V then Marilyn Monroe ID I mean so there +you go a lot of lot of lot of fun stuff + + align:start position:0% +you go a lot of lot of lot of fun stuff + + + align:start position:0% +you go a lot of lot of lot of fun stuff +there on Twitter um but this is sort of + + align:start position:0% +there on Twitter um but this is sort of + + + align:start position:0% +there on Twitter um but this is sort of +he's going to establish his background + + align:start position:0% +he's going to establish his background + + + align:start position:0% +he's going to establish his background +and let go back and look at during the + + align:start position:0% +and let go back and look at during the + + + align:start position:0% +and let go back and look at during the +hurricane so this is all basically the + + align:start position:0% +hurricane so this is all basically the + + + align:start position:0% +hurricane so this is all basically the +normal situation and then you know very + + align:start position:0% +normal situation and then you know very + + + align:start position:0% +normal situation and then you know very +clear clearly and then the uh the + + align:start position:0% +clear clearly and then the uh the + + + align:start position:0% +clear clearly and then the uh the +hashtags right so we can look at the + + align:start position:0% +hashtags right so we can look at the + + + align:start position:0% +hashtags right so we can look at the +hashtags so what do we got here uh + + align:start position:0% +hashtags so what do we got here uh + + + align:start position:0% +hashtags so what do we got here uh +favorite movie quotes favorite moves on + + align:start position:0% +favorite movie quotes favorite moves on + + + align:start position:0% +favorite movie quotes favorite moves on +and favorite movie quotes misspelled + + align:start position:0% +and favorite movie quotes misspelled + + + align:start position:0% +and favorite movie quotes misspelled +right up there the Knicks and then what + + align:start position:0% +right up there the Knicks and then what + + + align:start position:0% +right up there the Knicks and then what +I love the most and all this type team + + align:start position:0% +I love the most and all this type team + + + align:start position:0% +I love the most and all this type team +followback I don't know Team Auto no + + align:start position:0% +followback I don't know Team Auto no + + + align:start position:0% +followback I don't know Team Auto no +what's this word what's + + align:start position:0% +what's this word what's + + + align:start position:0% +what's this word what's +tfb no want know maybe we should don't + + align:start position:0% +tfb no want know maybe we should don't + + + align:start position:0% +tfb no want know maybe we should don't +want to know + + align:start position:0% +want to know + + + align:start position:0% +want to know +Soh so you can always look that up in + + align:start position:0% +Soh so you can always look that up in + + + align:start position:0% +Soh so you can always look that up in +Urban Dictionary and then it's a bad one + + align:start position:0% +Urban Dictionary and then it's a bad one + + + align:start position:0% +Urban Dictionary and then it's a bad one +all right okay good well then we'll + + align:start position:0% +all right okay good well then we'll + + + align:start position:0% +all right okay good well then we'll +leave it at that won't add that to the + + align:start position:0% +leave it at that won't add that to the + + + align:start position:0% +leave it at that won't add that to the +video um + + align:start position:0% + + + + align:start position:0% + +so continuing on here let's see + + align:start position:0% +so continuing on here let's see + + + align:start position:0% +so continuing on here let's see +um uh well you get the idea and so all + + align:start position:0% +um uh well you get the idea and so all + + + align:start position:0% +um uh well you get the idea and so all +these examples they work in parallel to + + align:start position:0% +these examples they work in parallel to + + + align:start position:0% +these examples they work in parallel to +uh you get a lot of speed up lots of + + align:start position:0% +uh you get a lot of speed up lots of + + + align:start position:0% +uh you get a lot of speed up lots of +interesting stuff like that but that's + + align:start position:0% +interesting stuff like that but that's + + + align:start position:0% +interesting stuff like that but that's +very classic the kind of thing you do + + align:start position:0% +very classic the kind of thing you do + + + align:start position:0% +very classic the kind of thing you do +you get data you parse it you maybe + + align:start position:0% +you get data you parse it you maybe + + + align:start position:0% +you get data you parse it you maybe +stick it in matlb files to do your + + align:start position:0% +stick it in matlb files to do your + + + align:start position:0% +stick it in matlb files to do your +initial sweep through it but then if it + + align:start position:0% +initial sweep through it but then if it + + + align:start position:0% +initial sweep through it but then if it +gets really really big and you want to + + align:start position:0% +gets really really big and you want to + + + align:start position:0% +gets really really big and you want to +do sort of more detailed things and you + + align:start position:0% +do sort of more detailed things and you + + + align:start position:0% +do sort of more detailed things and you +insert in the database can do queries + + align:start position:0% +insert in the database can do queries + + + align:start position:0% +insert in the database can do queries +there leverage using your counts so that + + align:start position:0% +there leverage using your counts so that + + + align:start position:0% +there leverage using your counts so that +you don't accidentally you know you can + + align:start position:0% +you don't accidentally you know you can + + + align:start position:0% +you don't accidentally you know you can +imagine if we put all the Tweets in the + + align:start position:0% +imagine if we put all the Tweets in the + + + align:start position:0% +imagine if we put all the Tweets in the +world and you had location New York City + + align:start position:0% +world and you had location New York City + + + align:start position:0% +world and you had location New York City +and you looked at you had to like give + + align:start position:0% +and you looked at you had to like give + + + align:start position:0% +and you looked at you had to like give +me all this set of locations and one of + + align:start position:0% +me all this set of locations and one of + + + align:start position:0% +me all this set of locations and one of +them was New York City you'd be like oh + + align:start position:0% +them was New York City you'd be like oh + + + align:start position:0% +them was New York City you'd be like oh +my god I've just you know done a query + + align:start position:0% +my god I've just you know done a query + + + align:start position:0% +my god I've just you know done a query +that's going to give me 5% of all the + + align:start position:0% +that's going to give me 5% of all the + + + align:start position:0% +that's going to give me 5% of all the +data back well it's going to just flush + + align:start position:0% +data back well it's going to just flush + + + align:start position:0% +data back well it's going to just flush +your system but if you can just do the + + align:start position:0% +your system but if you can just do the + + + align:start position:0% +your system but if you can just do the +count and be like Oh New York City's got + + align:start position:0% +count and be like Oh New York City's got + + + align:start position:0% +count and be like Oh New York City's got +a million entries don't touch that one + + align:start position:0% +a million entries don't touch that one + + + align:start position:0% +a million entries don't touch that one +you know or put an iterator on that one + + align:start position:0% +you know or put an iterator on that one + + + align:start position:0% +you know or put an iterator on that one +right you know so that uh so that I only + + align:start position:0% +right you know so that uh so that I only + + + align:start position:0% +right you know so that uh so that I only +handle it in manageable chunks so uh so + + align:start position:0% +handle it in manageable chunks so uh so + + + align:start position:0% +handle it in manageable chunks so uh so +I want to thank you so hopefully this + + align:start position:0% +I want to thank you so hopefully this + + + align:start position:0% +I want to thank you so hopefully this +was worth it uh we have one more class + + align:start position:0% +was worth it uh we have one more class + + + align:start position:0% +was worth it uh we have one more class +which deals with a little bit of + + align:start position:0% +which deals with a little bit of + + + align:start position:0% +which deals with a little bit of +wrapping up some of the theory uh kind + + align:start position:0% +wrapping up some of the theory uh kind + + + align:start position:0% +wrapping up some of the theory uh kind +of on this stuff and some stuff on + + align:start position:0% +of on this stuff and some stuff on + + + align:start position:0% +of on this stuff and some stuff on +performance metrics and then in two + + align:start position:0% +performance metrics and then in two + + + align:start position:0% +performance metrics and then in two +weeks for those of you who signed up we + + align:start position:0% +weeks for those of you who signed up we + + + align:start position:0% +weeks for those of you who signed up we +have the accumulo folks coming in + + align:start position:0% +have the accumulo folks coming in + + + align:start position:0% +have the accumulo folks coming in +showing you how to run your own uh + + align:start position:0% +showing you how to run your own uh + + + align:start position:0% +showing you how to run your own uh +database um you know all day on just you + + align:start position:0% +database um you know all day on just you + + + align:start position:0% +database um you know all day on just you +know um you know we're setting up a + + align:start position:0% +know um you know we're setting up a + + + align:start position:0% +know um you know we're setting up a +database for you for you guys on LL grid + + align:start position:0% +database for you for you guys on LL grid + + + align:start position:0% +database for you for you guys on LL grid +but you're definitely going to run in + + align:start position:0% +but you're definitely going to run in + + + align:start position:0% +but you're definitely going to run in +with your customers accumulo instances + + align:start position:0% +with your customers accumulo instances + + + align:start position:0% +with your customers accumulo instances +it's good to know some Basics about that + + align:start position:0% +it's good to know some Basics about that + + + align:start position:0% +it's good to know some Basics about that +because a lot of times you're not going + + align:start position:0% +because a lot of times you're not going + + + align:start position:0% +because a lot of times you're not going +to have all the kind of nice nice stuff + + align:start position:0% +to have all the kind of nice nice stuff + + + align:start position:0% +to have all the kind of nice nice stuff +that we've provided and it's good to + + align:start position:0% +that we've provided and it's good to + + + align:start position:0% +that we've provided and it's good to +know how to set up your own aimo and + + align:start position:0% +know how to set up your own aimo and + + + align:start position:0% +know how to set up your own aimo and +interact with that in the field so with + + align:start position:0% +interact with that in the field so with + + + align:start position:0% +interact with that in the field so with +that that brings the lecture to the end + + align:start position:0% +that that brings the lecture to the end + + + align:start position:0% +that that brings the lecture to the end +and happy to stay for any questions if + + align:start position:0% +and happy to stay for any questions if + + + align:start position:0% +and happy to stay for any questions if +anybody has + + align:start position:0% + + + + align:start position:0% + +them \ No newline at end of file diff --git a/0dJS3YUxeXI.txt b/0dJS3YUxeXI.txt new file mode 100644 index 0000000000000000000000000000000000000000..cdffd9caa657e6b087ae7e2b730d122b6ce9f456 --- /dev/null +++ b/0dJS3YUxeXI.txt @@ -0,0 +1,7043 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so last time we were talking about these + + align:start position:0% +so last time we were talking about these + + + align:start position:0% +so last time we were talking about these +aminoacyl trna synthetases that are + + align:start position:0% +aminoacyl trna synthetases that are + + + align:start position:0% +aminoacyl trna synthetases that are +responsible for attaching amino acid + + align:start position:0% +responsible for attaching amino acid + + + align:start position:0% +responsible for attaching amino acid +monomers to the three prime end of tRNAs + + align:start position:0% +monomers to the three prime end of tRNAs + + + align:start position:0% +monomers to the three prime end of tRNAs +and we were looking at the iso Lucille + + align:start position:0% +and we were looking at the iso Lucille + + + align:start position:0% +and we were looking at the iso Lucille +amino acyl tRNA synthetase as an example + + align:start position:0% +amino acyl tRNA synthetase as an example + + + align:start position:0% +amino acyl tRNA synthetase as an example +looking at experiments that were done to + + align:start position:0% +looking at experiments that were done to + + + align:start position:0% +looking at experiments that were done to +studying mechanisms so recall we left + + align:start position:0% +studying mechanisms so recall we left + + + align:start position:0% +studying mechanisms so recall we left +off having discussed a two step model + + align:start position:0% +off having discussed a two step model + + + align:start position:0% +off having discussed a two step model +right where there's an intermediate and + + align:start position:0% +right where there's an intermediate and + + + align:start position:0% +right where there's an intermediate and +amino adenylate formed and then in the + + align:start position:0% +amino adenylate formed and then in the + + + align:start position:0% +amino adenylate formed and then in the +second step there's transfer of that + + align:start position:0% +second step there's transfer of that + + + align:start position:0% +second step there's transfer of that +amino acid to the tRNA by the aar s and + + align:start position:0% +amino acid to the tRNA by the aar s and + + + align:start position:0% +amino acid to the tRNA by the aar s and +so we looked at some data from steady + + align:start position:0% +so we looked at some data from steady + + + align:start position:0% +so we looked at some data from steady +state kinetic experiments right recall + + align:start position:0% +state kinetic experiments right recall + + + align:start position:0% +state kinetic experiments right recall +that a c14 radio label was used to watch + + align:start position:0% +that a c14 radio label was used to watch + + + align:start position:0% +that a c14 radio label was used to watch +transfer and then we closed discussing + + align:start position:0% +transfer and then we closed discussing + + + align:start position:0% +transfer and then we closed discussing +an ATP PPI exchange assay which gave + + align:start position:0% +an ATP PPI exchange assay which gave + + + align:start position:0% +an ATP PPI exchange assay which gave +evidence for formation of that amino + + align:start position:0% +evidence for formation of that amino + + + align:start position:0% +evidence for formation of that amino +identity intermediate right and then + + align:start position:0% +identity intermediate right and then + + + align:start position:0% +identity intermediate right and then +lastly we talked about use of a stop + + align:start position:0% +lastly we talked about use of a stop + + + align:start position:0% +lastly we talked about use of a stop +flow to do experiments that allow you to + + align:start position:0% +flow to do experiments that allow you to + + + align:start position:0% +flow to do experiments that allow you to +look at early points within a reaction + + align:start position:0% +look at early points within a reaction + + + align:start position:0% +look at early points within a reaction +and so what we're going to do is to + + align:start position:0% +and so what we're going to do is to + + + align:start position:0% +and so what we're going to do is to +close these discussions of experiments + + align:start position:0% +close these discussions of experiments + + + align:start position:0% +close these discussions of experiments +and this AAA RS mechanism is just look + + align:start position:0% +and this AAA RS mechanism is just look + + + align:start position:0% +and this AAA RS mechanism is just look +at one more experiment that was done to + + align:start position:0% +at one more experiment that was done to + + + align:start position:0% +at one more experiment that was done to +further probe the rate determining step + + align:start position:0% +further probe the rate determining step + + + align:start position:0% +further probe the rate determining step +of this reaction using the stop flow + + align:start position:0% +of this reaction using the stop flow + + + align:start position:0% +of this reaction using the stop flow +okay and so this experiment pertains + + align:start position:0% +okay and so this experiment pertains + + + align:start position:0% +okay and so this experiment pertains +more to reaction kinetics and the + + align:start position:0% +more to reaction kinetics and the + + + align:start position:0% +more to reaction kinetics and the +question is let's monitor transfer of + + align:start position:0% +question is let's monitor transfer of + + + align:start position:0% +question is let's monitor transfer of +the amino acid to the tRNA by another + + align:start position:0% +the amino acid to the tRNA by another + + + align:start position:0% +the amino acid to the tRNA by another +method here and so + + align:start position:0% + + + + align:start position:0% + +these experiments were set up in two + + align:start position:0% +these experiments were set up in two + + + align:start position:0% +these experiments were set up in two +different ways + + align:start position:0% +different ways + + + align:start position:0% +different ways +depending on what components were mixed + + align:start position:0% +depending on what components were mixed + + + align:start position:0% +depending on what components were mixed +and if you just rewind to Monday and + + align:start position:0% +and if you just rewind to Monday and + + + align:start position:0% +and if you just rewind to Monday and +recall the ATP PPI exchange assay and + + align:start position:0% +recall the ATP PPI exchange assay and + + + align:start position:0% +recall the ATP PPI exchange assay and +the steps in that assay in that we + + align:start position:0% +the steps in that assay in that we + + + align:start position:0% +the steps in that assay in that we +showed that the immuno a generally + + align:start position:0% +showed that the immuno a generally + + + align:start position:0% +showed that the immuno a generally +intermediate remained bound to the + + align:start position:0% +intermediate remained bound to the + + + align:start position:0% +intermediate remained bound to the +enzyme there + + align:start position:0% +enzyme there + + + align:start position:0% +enzyme there +recall that only ppi was released in + + align:start position:0% +recall that only ppi was released in + + + align:start position:0% +recall that only ppi was released in +that assay and so in these experiments + + align:start position:0% +that assay and so in these experiments + + + align:start position:0% +that assay and so in these experiments +the fact that the immuno identity can + + align:start position:0% +the fact that the immuno identity can + + + align:start position:0% +the fact that the immuno identity can +remain bound was taken advantage of and + + align:start position:0% +remain bound was taken advantage of and + + + align:start position:0% +remain bound was taken advantage of and +the researchers were actually able to + + align:start position:0% +the researchers were actually able to + + + align:start position:0% +the researchers were actually able to +have a preform complex there so + + align:start position:0% +have a preform complex there so + + + align:start position:0% +have a preform complex there so +basically starting after step 2 so in + + align:start position:0% +basically starting after step 2 so in + + + align:start position:0% +basically starting after step 2 so in +experiment one how I'm going to show + + align:start position:0% +experiment one how I'm going to show + + + align:start position:0% +experiment one how I'm going to show +these is by drawing the two syringes and + + align:start position:0% +these is by drawing the two syringes and + + + align:start position:0% +these is by drawing the two syringes and +listing the components of each syringe + + align:start position:0% +listing the components of each syringe + + + align:start position:0% +listing the components of each syringe +and this is a good way for setting up + + align:start position:0% +and this is a good way for setting up + + + align:start position:0% +and this is a good way for setting up +problems within the problems that's + + align:start position:0% +problems within the problems that's + + + align:start position:0% +problems within the problems that's +thinking about stop flow experiments so + + align:start position:0% +thinking about stop flow experiments so + + + align:start position:0% +thinking about stop flow experiments so +the question is what are we going to mix + + align:start position:0% +the question is what are we going to mix + + + align:start position:0% +the question is what are we going to mix +we have syringe one and syringe two and + + align:start position:0% +we have syringe one and syringe two and + + + align:start position:0% +we have syringe one and syringe two and +recall that these go to some mixer so + + align:start position:0% +recall that these go to some mixer so + + + align:start position:0% +recall that these go to some mixer so +the two solutions can be rapidly mixed + + align:start position:0% +the two solutions can be rapidly mixed + + + align:start position:0% +the two solutions can be rapidly mixed +and that's where the chemistry is going + + align:start position:0% +and that's where the chemistry is going + + + align:start position:0% +and that's where the chemistry is going +to happen so in experiment one and + + align:start position:0% +to happen so in experiment one and + + + align:start position:0% +to happen so in experiment one and +syringe one what we have is the purified + + align:start position:0% +syringe one what we have is the purified + + + align:start position:0% +syringe one what we have is the purified +complex ok so we have C 14 labeled so + + align:start position:0% +complex ok so we have C 14 labeled so + + + align:start position:0% +complex ok so we have C 14 labeled so +we've seen a MP bound to the amino acyl + + align:start position:0% +we've seen a MP bound to the amino acyl + + + align:start position:0% +we've seen a MP bound to the amino acyl +tRNA synthetase + + align:start position:0% +tRNA synthetase + + + align:start position:0% +tRNA synthetase +okay purified complex + + align:start position:0% + + + + align:start position:0% + +here and then in this other syringe to + + align:start position:0% +here and then in this other syringe to + + + align:start position:0% +here and then in this other syringe to +what we have is the tRNA okay so imagine + + align:start position:0% +what we have is the tRNA okay so imagine + + + align:start position:0% +what we have is the tRNA okay so imagine +these are rapidly mixed they'll be + + align:start position:0% +these are rapidly mixed they'll be + + + align:start position:0% +these are rapidly mixed they'll be +transfer of the radio labeled isoleucine + + align:start position:0% +transfer of the radio labeled isoleucine + + + align:start position:0% +transfer of the radio labeled isoleucine +to the tRNA and so formation of that + + align:start position:0% +to the tRNA and so formation of that + + + align:start position:0% +to the tRNA and so formation of that +amino acyl tRNA can be monitored okay in + + align:start position:0% +amino acyl tRNA can be monitored okay in + + + align:start position:0% +amino acyl tRNA can be monitored okay in +the second experiment we have just kind + + align:start position:0% +the second experiment we have just kind + + + align:start position:0% +the second experiment we have just kind +of theme and variation and if you're + + align:start position:0% +of theme and variation and if you're + + + align:start position:0% +of theme and variation and if you're +interested in more details the reference + + align:start position:0% +interested in more details the reference + + + align:start position:0% +interested in more details the reference +is provided in the slides so again I'm + + align:start position:0% +is provided in the slides so again I'm + + + align:start position:0% +is provided in the slides so again I'm +syringe 2 we have the tRNA okay and in + + align:start position:0% +syringe 2 we have the tRNA okay and in + + + align:start position:0% +syringe 2 we have the tRNA okay and in +syringe 1 what will be combined or the + + align:start position:0% +syringe 1 what will be combined or the + + + align:start position:0% +syringe 1 what will be combined or the +components here ok so then the question + + align:start position:0% +components here ok so then the question + + + align:start position:0% +components here ok so then the question +is in each case what do we see and those + + align:start position:0% +is in each case what do we see and those + + + align:start position:0% +is in each case what do we see and those +data are prevented presented here from + + align:start position:0% +data are prevented presented here from + + + align:start position:0% +data are prevented presented here from +the paper and there's some additional + + align:start position:0% +the paper and there's some additional + + + align:start position:0% +the paper and there's some additional +details about the experimental setup so + + align:start position:0% +details about the experimental setup so + + + align:start position:0% +details about the experimental setup so +effectively what we're looking at on the + + align:start position:0% +effectively what we're looking at on the + + + align:start position:0% +effectively what we're looking at on the +y-axis is the amount of tRNA that's been + + align:start position:0% +y-axis is the amount of tRNA that's been + + + align:start position:0% +y-axis is the amount of tRNA that's been +modified so T RNA isolation measured by + + align:start position:0% +modified so T RNA isolation measured by + + + align:start position:0% +modified so T RNA isolation measured by +transfer of the radio label versus time + + align:start position:0% +transfer of the radio label versus time + + + align:start position:0% +transfer of the radio label versus time +okay and in the black circles we have + + align:start position:0% +okay and in the black circles we have + + + align:start position:0% +okay and in the black circles we have +the data from experiment one shown here + + align:start position:0% +the data from experiment one shown here + + + align:start position:0% +the data from experiment one shown here +and in the open circles we have the data + + align:start position:0% +and in the open circles we have the data + + + align:start position:0% +and in the open circles we have the data +from experiment 2 so what is the + + align:start position:0% +from experiment 2 so what is the + + + align:start position:0% +from experiment 2 so what is the +conclusion from these data and you know + + align:start position:0% +conclusion from these data and you know + + + align:start position:0% +conclusion from these data and you know +this value here is that similar to + + align:start position:0% +this value here is that similar to + + + align:start position:0% +this value here is that similar to +something we've seen before in this + + align:start position:0% +something we've seen before in this + + + align:start position:0% +something we've seen before in this +system + + align:start position:0% + + + + align:start position:0% + +both experimental setups are giving the + + align:start position:0% +both experimental setups are giving the + + + align:start position:0% +both experimental setups are giving the +same result + + align:start position:0% +same result + + + align:start position:0% +same result +right effectively these data are + + align:start position:0% +right effectively these data are + + + align:start position:0% +right effectively these data are +superimposable and they can be fit the + + align:start position:0% +superimposable and they can be fit the + + + align:start position:0% +superimposable and they can be fit the +same okay so what does that tell us + + align:start position:0% +same okay so what does that tell us + + + align:start position:0% +same okay so what does that tell us +about the rate determining step right + + align:start position:0% +about the rate determining step right + + + align:start position:0% +about the rate determining step right +aminoacylation of tRNAs the rate + + align:start position:0% +aminoacylation of tRNAs the rate + + + align:start position:0% +aminoacylation of tRNAs the rate +determining step so some of you + + align:start position:0% +determining step so some of you + + + align:start position:0% +determining step so some of you +suggested that in class on Monday right + + align:start position:0% +suggested that in class on Monday right + + + align:start position:0% +suggested that in class on Monday right +so that's the case here okay so + + align:start position:0% +so that's the case here okay so + + + align:start position:0% +so that's the case here okay so +formation of the intermediate is much + + align:start position:0% +formation of the intermediate is much + + + align:start position:0% +formation of the intermediate is much +more rapid than am you know a solution + + align:start position:0% +more rapid than am you know a solution + + + align:start position:0% +more rapid than am you know a solution +of the tRNA here so we examine now the + + align:start position:0% +of the tRNA here so we examine now the + + + align:start position:0% +of the tRNA here so we examine now the +mechanism in terms of getting the amino + + align:start position:0% +mechanism in terms of getting the amino + + + align:start position:0% +mechanism in terms of getting the amino +acid onto the tRNA what do we need to + + align:start position:0% +acid onto the tRNA what do we need to + + + align:start position:0% +acid onto the tRNA what do we need to +think about next here so what we need to + + align:start position:0% +think about next here so what we need to + + + align:start position:0% +think about next here so what we need to +think about is fidelity okay and we've + + align:start position:0% +think about is fidelity okay and we've + + + align:start position:0% +think about is fidelity okay and we've +looked at the overall rate of error in + + align:start position:0% +looked at the overall rate of error in + + + align:start position:0% +looked at the overall rate of error in +protein biosynthesis how often errors + + align:start position:0% +protein biosynthesis how often errors + + + align:start position:0% +protein biosynthesis how often errors +occur on the order of 10 to the 3 so how + + align:start position:0% +occur on the order of 10 to the 3 so how + + + align:start position:0% +occur on the order of 10 to the 3 so how +is the correct amino acid loaded onto + + align:start position:0% +is the correct amino acid loaded onto + + + align:start position:0% +is the correct amino acid loaded onto +the correct tRNA right each tRNA has an + + align:start position:0% +the correct tRNA right each tRNA has an + + + align:start position:0% +the correct tRNA right each tRNA has an +anticodon that is a cognate pair with a + + align:start position:0% +anticodon that is a cognate pair with a + + + align:start position:0% +anticodon that is a cognate pair with a +codon and so different tRNA s need to + + align:start position:0% +codon and so different tRNA s need to + + + align:start position:0% +codon and so different tRNA s need to +have different amino acids attached ok + + align:start position:0% +have different amino acids attached ok + + + align:start position:0% +have different amino acids attached ok +and what does that mean that means in + + align:start position:0% +and what does that mean that means in + + + align:start position:0% +and what does that mean that means in +general there's a dedicated amino acyl + + align:start position:0% +general there's a dedicated amino acyl + + + align:start position:0% +general there's a dedicated amino acyl +tRNA synthetase for each amino acid in + + align:start position:0% +tRNA synthetase for each amino acid in + + + align:start position:0% +tRNA synthetase for each amino acid in +general here so how are amino acids with + + align:start position:0% +general here so how are amino acids with + + + align:start position:0% +general here so how are amino acids with +similar side chains differentiated by + + align:start position:0% +similar side chains differentiated by + + + align:start position:0% +similar side chains differentiated by +these enzymes and is it possible for an + + align:start position:0% +these enzymes and is it possible for an + + + align:start position:0% +these enzymes and is it possible for an +incorrect amino acid to get loaded onto + + align:start position:0% +incorrect amino acid to get loaded onto + + + align:start position:0% +incorrect amino acid to get loaded onto +a tRNA and if that happens what are the + + align:start position:0% +a tRNA and if that happens what are the + + + align:start position:0% +a tRNA and if that happens what are the +consequences so we're going to examine + + align:start position:0% +consequences so we're going to examine + + + align:start position:0% +consequences so we're going to examine +fidelity some here and as background an + + align:start position:0% +fidelity some here and as background an + + + align:start position:0% +fidelity some here and as background an +observation made say from studies like + + align:start position:0% +observation made say from studies like + + + align:start position:0% +observation made say from studies like +that ATP PPI exchange assay is that some + + align:start position:0% +that ATP PPI exchange assay is that some + + + align:start position:0% +that ATP PPI exchange assay is that some +aminoacyl trna synthetases can activate + + align:start position:0% +aminoacyl trna synthetases can activate + + + align:start position:0% +aminoacyl trna synthetases can activate +multiple amino acids so not only the one + + align:start position:0% +multiple amino acids so not only the one + + + align:start position:0% +multiple amino acids so not only the one +they're supposed to activate but also + + align:start position:0% +they're supposed to activate but also + + + align:start position:0% +they're supposed to activate but also +others so what does that mean that means + + align:start position:0% +others so what does that mean that means + + + align:start position:0% +others so what does that mean that means +that the enzyme can bind and activate + + align:start position:0% +that the enzyme can bind and activate + + + align:start position:0% +that the enzyme can bind and activate +effectively the wrong you know + + align:start position:0% +effectively the wrong you know + + + align:start position:0% +effectively the wrong you know +amino acid and if we think about + + align:start position:0% +amino acid and if we think about + + + align:start position:0% +amino acid and if we think about +fidelity right we can think about this + + align:start position:0% +fidelity right we can think about this + + + align:start position:0% +fidelity right we can think about this +as being a problem here + + align:start position:0% +as being a problem here + + + align:start position:0% +as being a problem here +so what happens what happens is that + + align:start position:0% +so what happens what happens is that + + + align:start position:0% +so what happens what happens is that +these enzymes have an editing function + + align:start position:0% +these enzymes have an editing function + + + align:start position:0% +these enzymes have an editing function +okay and they're able to sense if a + + align:start position:0% +okay and they're able to sense if a + + + align:start position:0% +okay and they're able to sense if a +wrong amino acid is activated and then + + align:start position:0% +wrong amino acid is activated and then + + + align:start position:0% +wrong amino acid is activated and then +they have a way to deal with it and this + + align:start position:0% +they have a way to deal with it and this + + + align:start position:0% +they have a way to deal with it and this +is by hydrolysis okay and so let's + + align:start position:0% +is by hydrolysis okay and so let's + + + align:start position:0% +is by hydrolysis okay and so let's +consider an example for instance just + + align:start position:0% +consider an example for instance just + + + align:start position:0% +consider an example for instance just +similar side chains okay so if we just + + align:start position:0% +similar side chains okay so if we just + + + align:start position:0% +similar side chains okay so if we just +consider for instance valine isoleucine + + align:start position:0% +consider for instance valine isoleucine + + + align:start position:0% +consider for instance valine isoleucine +and threonine these will be the players + + align:start position:0% +and threonine these will be the players + + + align:start position:0% +and threonine these will be the players +for our discussion they're different but + + align:start position:0% +for our discussion they're different but + + + align:start position:0% +for our discussion they're different but +they're not two different right oops + + align:start position:0% +they're not two different right oops + + + align:start position:0% +they're not two different right oops +sorry about this we're missing a methyl + + align:start position:0% +sorry about this we're missing a methyl + + + align:start position:0% +sorry about this we're missing a methyl +right valine and isoleucine we have a + + align:start position:0% +right valine and isoleucine we have a + + + align:start position:0% +right valine and isoleucine we have a +difference of a methyl group + + align:start position:0% +difference of a methyl group + + + align:start position:0% +difference of a methyl group +okay threonine we have this this o H + + align:start position:0% +okay threonine we have this this o H + + + align:start position:0% +okay threonine we have this this o H +group right and we can just ask the + + align:start position:0% +group right and we can just ask the + + + align:start position:0% +group right and we can just ask the +question for instance how is valine + + align:start position:0% +question for instance how is valine + + + align:start position:0% +question for instance how is valine +differentiated but form isoleucine or + + align:start position:0% +differentiated but form isoleucine or + + + align:start position:0% +differentiated but form isoleucine or +threonine here okay and so as an example + + align:start position:0% +threonine here okay and so as an example + + + align:start position:0% +threonine here okay and so as an example +what's found is if we consider our + + align:start position:0% +what's found is if we consider our + + + align:start position:0% +what's found is if we consider our +friend that we've studied and for the + + align:start position:0% +friend that we've studied and for the + + + align:start position:0% +friend that we've studied and for the +mechanism here what we find is that this + + align:start position:0% +mechanism here what we find is that this + + + align:start position:0% +mechanism here what we find is that this +binds and activates isoleucine as we saw + + align:start position:0% + + + + align:start position:0% + +okay but it will also bind and activate + + align:start position:0% +okay but it will also bind and activate + + + align:start position:0% +okay but it will also bind and activate +bailing here okay and effectively if + + align:start position:0% +bailing here okay and effectively if + + + align:start position:0% +bailing here okay and effectively if +this happens right we have a mismatch + + align:start position:0% + + + + align:start position:0% + +because the end result will be + + align:start position:0% +because the end result will be + + + align:start position:0% +because the end result will be +isoleucine RS with valine am P bound + + align:start position:0% +isoleucine RS with valine am P bound + + + align:start position:0% +isoleucine RS with valine am P bound +here okay and what's found is that the + + align:start position:0% +here okay and what's found is that the + + + align:start position:0% +here okay and what's found is that the +catalytic efficiency or k-kat over km in + + align:start position:0% +catalytic efficiency or k-kat over km in + + + align:start position:0% +catalytic efficiency or k-kat over km in +this case is about a hundred and fifty + + align:start position:0% +this case is about a hundred and fifty + + + align:start position:0% +this case is about a hundred and fifty +fold less than the native substrate okay + + align:start position:0% +fold less than the native substrate okay + + + align:start position:0% +fold less than the native substrate okay +so that doesn't account for the 10 to + + align:start position:0% +so that doesn't account for the 10 to + + + align:start position:0% +so that doesn't account for the 10 to +the three error rate right here so we + + align:start position:0% +the three error rate right here so we + + + align:start position:0% +the three error rate right here so we +need more specificity so what what's + + align:start position:0% +need more specificity so what what's + + + align:start position:0% +need more specificity so what what's +going on so we're going to consider this + + align:start position:0% +going on so we're going to consider this + + + align:start position:0% +going on so we're going to consider this +editing function and a model that's + + align:start position:0% +editing function and a model that's + + + align:start position:0% +editing function and a model that's +often used to describe how these a a RS + + align:start position:0% +often used to describe how these a a RS + + + align:start position:0% +often used to describe how these a a RS +do editing is one of two sips these + + align:start position:0% +do editing is one of two sips these + + + align:start position:0% +do editing is one of two sips these +enzymes don't actually have a sieve it's + + align:start position:0% +enzymes don't actually have a sieve it's + + + align:start position:0% +enzymes don't actually have a sieve it's +just a conceptual way to think about it + + align:start position:0% +just a conceptual way to think about it + + + align:start position:0% +just a conceptual way to think about it +so this double sieve editing model + + align:start position:0% +so this double sieve editing model + + + align:start position:0% +so this double sieve editing model +involves a first v which is considered + + align:start position:0% +involves a first v which is considered + + + align:start position:0% +involves a first v which is considered +to be a course one so imagine if you + + align:start position:0% +to be a course one so imagine if you + + + align:start position:0% +to be a course one so imagine if you +have like a change sorter it will let + + align:start position:0% +have like a change sorter it will let + + + align:start position:0% +have like a change sorter it will let +the quarters through as well as the dime + + align:start position:0% +the quarters through as well as the dime + + + align:start position:0% +the quarters through as well as the dime +and the pennies there's some sort of + + align:start position:0% +and the pennies there's some sort of + + + align:start position:0% +and the pennies there's some sort of +discrimination of amino acids based on + + align:start position:0% +discrimination of amino acids based on + + + align:start position:0% +discrimination of amino acids based on +size and then depending what gets + + align:start position:0% +size and then depending what gets + + + align:start position:0% +size and then depending what gets +through this first silver gate there's a + + align:start position:0% +through this first silver gate there's a + + + align:start position:0% +through this first silver gate there's a +second sieve which is considered to be a + + align:start position:0% +second sieve which is considered to be a + + + align:start position:0% +second sieve which is considered to be a +fine one and this one can differentiate + + align:start position:0% +fine one and this one can differentiate + + + align:start position:0% +fine one and this one can differentiate +perhaps on the basis of size or maybe on + + align:start position:0% +perhaps on the basis of size or maybe on + + + align:start position:0% +perhaps on the basis of size or maybe on +hydrophilicity or hydrophobicity of the + + align:start position:0% +hydrophilicity or hydrophobicity of the + + + align:start position:0% +hydrophilicity or hydrophobicity of the +sidechain so effectively if an incorrect + + align:start position:0% +sidechain so effectively if an incorrect + + + align:start position:0% +sidechain so effectively if an incorrect +amino acid passes through this first + + align:start position:0% +amino acid passes through this first + + + align:start position:0% +amino acid passes through this first +sieve so in other words if it binds to + + align:start position:0% +sieve so in other words if it binds to + + + align:start position:0% +sieve so in other words if it binds to +the enzyme and becomes activated + + align:start position:0% +the enzyme and becomes activated + + + align:start position:0% +the enzyme and becomes activated +hydrolytic editing will occur okay so + + align:start position:0% +hydrolytic editing will occur okay so + + + align:start position:0% +hydrolytic editing will occur okay so +think about hydrolysis in terms of + + align:start position:0% +think about hydrolysis in terms of + + + align:start position:0% +think about hydrolysis in terms of +having break down of these species so if + + align:start position:0% +having break down of these species so if + + + align:start position:0% +having break down of these species so if +the incorrect amino acid passes through + + align:start position:0% +the incorrect amino acid passes through + + + align:start position:0% +the incorrect amino acid passes through +and is adenylate 'add there'll be + + align:start position:0% +and is adenylate 'add there'll be + + + align:start position:0% +and is adenylate 'add there'll be +hydrolysis so let's consider some + + align:start position:0% +hydrolysis so let's consider some + + + align:start position:0% +hydrolysis so let's consider some +examples so the first example here we + + align:start position:0% +examples so the first example here we + + + align:start position:0% +examples so the first example here we +can consider the sky and isoleucine and + + align:start position:0% +can consider the sky and isoleucine and + + + align:start position:0% +can consider the sky and isoleucine and +valine so as I mentioned this a ARS will + + align:start position:0% +valine so as I mentioned this a ARS will + + + align:start position:0% +valine so as I mentioned this a ARS will +activate both so in this case the first + + align:start position:0% +activate both so in this case the first + + + align:start position:0% +activate both so in this case the first +SIV can't differentiate isoleucine from + + align:start position:0% +SIV can't differentiate isoleucine from + + + align:start position:0% +SIV can't differentiate isoleucine from +valine they have similar sizes according + + align:start position:0% +valine they have similar sizes according + + + align:start position:0% +valine they have similar sizes according +to this a ARS but then what happens here + + align:start position:0% +to this a ARS but then what happens here + + + align:start position:0% +to this a ARS but then what happens here +in the second SIV isoleucine is too big + + align:start position:0% +in the second SIV isoleucine is too big + + + align:start position:0% +in the second SIV isoleucine is too big +and so there's no hydrolysis and it + + align:start position:0% +and so there's no hydrolysis and it + + + align:start position:0% +and so there's no hydrolysis and it +moves on to form the desired charged + + align:start position:0% +moves on to form the desired charged + + + align:start position:0% +moves on to form the desired charged +trna in contrast faylene's a bit smaller + + align:start position:0% +trna in contrast faylene's a bit smaller + + + align:start position:0% +trna in contrast faylene's a bit smaller +it passes through the sieve and in it + + align:start position:0% +it passes through the sieve and in it + + + align:start position:0% +it passes through the sieve and in it +end up being and ends up being + + align:start position:0% +end up being and ends up being + + + align:start position:0% +end up being and ends up being +hydrolyzed so these a ARS also have an + + align:start position:0% +hydrolyzed so these a ARS also have an + + + align:start position:0% +hydrolyzed so these a ARS also have an +editing domain and this editing domain + + align:start position:0% +editing domain and this editing domain + + + align:start position:0% +editing domain and this editing domain +as we'll see in a few slides and a + + align:start position:0% +as we'll see in a few slides and a + + + align:start position:0% +as we'll see in a few slides and a +structure is responsible for this + + align:start position:0% +structure is responsible for this + + + align:start position:0% +structure is responsible for this +hydrolysis so stated here right + + align:start position:0% +hydrolysis so stated here right + + + align:start position:0% +hydrolysis so stated here right +different sites so there's an amino acyl + + align:start position:0% +different sites so there's an amino acyl + + + align:start position:0% +different sites so there's an amino acyl +ation site and an editing site here so + + align:start position:0% +ation site and an editing site here so + + + align:start position:0% +ation site and an editing site here so +valine can reach the editing site but + + align:start position:0% +valine can reach the editing site but + + + align:start position:0% +valine can reach the editing site but +isoleucine cannot so how do you predict + + align:start position:0% +isoleucine cannot so how do you predict + + + align:start position:0% +isoleucine cannot so how do you predict +just to keep in mind every enzyme is + + align:start position:0% +just to keep in mind every enzyme is + + + align:start position:0% +just to keep in mind every enzyme is +different in terms of the model for + + align:start position:0% +different in terms of the model for + + + align:start position:0% +different in terms of the model for +discrimination and also when editing + + align:start position:0% +discrimination and also when editing + + + align:start position:0% +discrimination and also when editing +occurs so you really need to look at the + + align:start position:0% +occurs so you really need to look at the + + + align:start position:0% +occurs so you really need to look at the +data when the data is presented to you + + align:start position:0% +data when the data is presented to you + + + align:start position:0% +data when the data is presented to you +to sort out how how this works let's + + align:start position:0% +to sort out how how this works let's + + + align:start position:0% +to sort out how how this works let's +just look at another example with a + + align:start position:0% +just look at another example with a + + + align:start position:0% +just look at another example with a +cartoon depiction so this is for the + + align:start position:0% +cartoon depiction so this is for the + + + align:start position:0% +cartoon depiction so this is for the +valine RS and we're gonna consider the + + align:start position:0% +valine RS and we're gonna consider the + + + align:start position:0% +valine RS and we're gonna consider the +three amino acids here valine threonine + + align:start position:0% +three amino acids here valine threonine + + + align:start position:0% +three amino acids here valine threonine +and isoleucine + + align:start position:0% +and isoleucine + + + align:start position:0% +and isoleucine +so in green we have the first SIV and + + align:start position:0% +so in green we have the first SIV and + + + align:start position:0% +so in green we have the first SIV and +this is based on size so what do we see + + align:start position:0% +this is based on size so what do we see + + + align:start position:0% +this is based on size so what do we see +in this cartoon so threonine unbaling + + align:start position:0% +in this cartoon so threonine unbaling + + + align:start position:0% +in this cartoon so threonine unbaling +make it through but isoleucine does not + + align:start position:0% +make it through but isoleucine does not + + + align:start position:0% +make it through but isoleucine does not +it's rejected right away so it's never + + align:start position:0% +it's rejected right away so it's never + + + align:start position:0% +it's rejected right away so it's never +activated + + align:start position:0% +activated + + + align:start position:0% +activated +so if threonine and valine passed + + align:start position:0% +so if threonine and valine passed + + + align:start position:0% +so if threonine and valine passed +through what happens we see each one is + + align:start position:0% +through what happens we see each one is + + + align:start position:0% +through what happens we see each one is +activated as the amino adenylate and + + align:start position:0% +activated as the amino adenylate and + + + align:start position:0% +activated as the amino adenylate and +then what well valine we want to + + align:start position:0% +then what well valine we want to + + + align:start position:0% +then what well valine we want to +transfer the valine to the tRNA so it + + align:start position:0% +transfer the valine to the tRNA so it + + + align:start position:0% +transfer the valine to the tRNA so it +can move on and help with protein + + align:start position:0% +can move on and help with protein + + + align:start position:0% +can move on and help with protein +synthesis + + align:start position:0% +synthesis + + + align:start position:0% +synthesis +if threonine is activated and here we + + align:start position:0% +if threonine is activated and here we + + + align:start position:0% +if threonine is activated and here we +see that threonine is transferred to the + + align:start position:0% +see that threonine is transferred to the + + + align:start position:0% +see that threonine is transferred to the +tRNA as well + + align:start position:0% +tRNA as well + + + align:start position:0% +tRNA as well +this is hydrolyzed by the editing site + + align:start position:0% +this is hydrolyzed by the editing site + + + align:start position:0% +this is hydrolyzed by the editing site +in this case so the threonine is removed + + align:start position:0% +in this case so the threonine is removed + + + align:start position:0% +in this case so the threonine is removed +from the tRNA with the anticodon for + + align:start position:0% +from the tRNA with the anticodon for + + + align:start position:0% +from the tRNA with the anticodon for +valine right so think about the ester + + align:start position:0% +valine right so think about the ester + + + align:start position:0% +valine right so think about the ester +bonds right that we saw last time in + + align:start position:0% +bonds right that we saw last time in + + + align:start position:0% +bonds right that we saw last time in +terms of the three prime end of the tRNA + + align:start position:0% +terms of the three prime end of the tRNA + + + align:start position:0% +terms of the three prime end of the tRNA +being modified and the chemistry that + + align:start position:0% +being modified and the chemistry that + + + align:start position:0% +being modified and the chemistry that +will happen there to result in + + align:start position:0% +will happen there to result in + + + align:start position:0% +will happen there to result in +hydrolysis and the release of the amino + + align:start position:0% +hydrolysis and the release of the amino + + + align:start position:0% +hydrolysis and the release of the amino +acid here so what that cartoon hints to + + align:start position:0% +acid here so what that cartoon hints to + + + align:start position:0% +acid here so what that cartoon hints to +is that the hydrolysis can occur at + + align:start position:0% +is that the hydrolysis can occur at + + + align:start position:0% +is that the hydrolysis can occur at +different steps so we can have + + align:start position:0% +different steps so we can have + + + align:start position:0% +different steps so we can have +hydrolysis that is pre transfer which + + align:start position:0% +hydrolysis that is pre transfer which + + + align:start position:0% +hydrolysis that is pre transfer which +means the editing occurs before the tRNA + + align:start position:0% +means the editing occurs before the tRNA + + + align:start position:0% +means the editing occurs before the tRNA +is modified or we can have post transfer + + align:start position:0% +is modified or we can have post transfer + + + align:start position:0% +is modified or we can have post transfer +editing which is what we saw in the + + align:start position:0% +editing which is what we saw in the + + + align:start position:0% +editing which is what we saw in the +prior slide where the editing and + + align:start position:0% +prior slide where the editing and + + + align:start position:0% +prior slide where the editing and +hydrolysis occurs after the amino acid + + align:start position:0% +hydrolysis occurs after the amino acid + + + align:start position:0% +hydrolysis occurs after the amino acid +monomer is transferred to the tRNA okay + + align:start position:0% +monomer is transferred to the tRNA okay + + + align:start position:0% +monomer is transferred to the tRNA okay +and this schematic here depicts that so + + align:start position:0% +and this schematic here depicts that so + + + align:start position:0% +and this schematic here depicts that so +what do we have we have the aar s + + align:start position:0% +what do we have we have the aar s + + + align:start position:0% +what do we have we have the aar s +responsible for modifying tRNA for + + align:start position:0% +responsible for modifying tRNA for + + + align:start position:0% +responsible for modifying tRNA for +isoleucine and we combine that with + + align:start position:0% +isoleucine and we combine that with + + + align:start position:0% +isoleucine and we combine that with +valine the wrong amino acid and ATP what + + align:start position:0% +valine the wrong amino acid and ATP what + + + align:start position:0% +valine the wrong amino acid and ATP what +happens so E is for enzyme we have + + align:start position:0% +happens so E is for enzyme we have + + + align:start position:0% +happens so E is for enzyme we have +formation of the amino adenylate + + align:start position:0% +formation of the amino adenylate + + + align:start position:0% +formation of the amino adenylate +intermediate here's the tRNA with the + + align:start position:0% +intermediate here's the tRNA with the + + + align:start position:0% +intermediate here's the tRNA with the +anticodon for isoleucine what happens so + + align:start position:0% +anticodon for isoleucine what happens so + + + align:start position:0% +anticodon for isoleucine what happens so +we have this complex form in this + + align:start position:0% +we have this complex form in this + + + align:start position:0% +we have this complex form in this +depiction pre transfer editing would + + align:start position:0% +depiction pre transfer editing would + + + align:start position:0% +depiction pre transfer editing would +occur at this stage before the valine is + + align:start position:0% +occur at this stage before the valine is + + + align:start position:0% +occur at this stage before the valine is +transferred to the tRNA and so what do + + align:start position:0% +transferred to the tRNA and so what do + + + align:start position:0% +transferred to the tRNA and so what do +we see we see breakdown and these + + align:start position:0% +we see we see breakdown and these + + + align:start position:0% +we see we see breakdown and these +species if the valley is transferred to + + align:start position:0% +species if the valley is transferred to + + + align:start position:0% +species if the valley is transferred to +the tRNA we don't want this because that + + align:start position:0% +the tRNA we don't want this because that + + + align:start position:0% +the tRNA we don't want this because that +would result in this reading of the + + align:start position:0% +would result in this reading of the + + + align:start position:0% +would result in this reading of the +genetic code post transfer editing this + + align:start position:0% +genetic code post transfer editing this + + + align:start position:0% +genetic code post transfer editing this +species here is hydrolyzed so whether + + align:start position:0% +species here is hydrolyzed so whether + + + align:start position:0% +species here is hydrolyzed so whether +pre or post transfer editing occurs it's + + align:start position:0% +pre or post transfer editing occurs it's + + + align:start position:0% +pre or post transfer editing occurs it's +going to depend on the amino acyl tRNA + + align:start position:0% +going to depend on the amino acyl tRNA + + + align:start position:0% +going to depend on the amino acyl tRNA +synthetase and some can use both + + align:start position:0% +synthetase and some can use both + + + align:start position:0% +synthetase and some can use both +mechanisms + + align:start position:0% +mechanisms + + + align:start position:0% +mechanisms +that's what we're seeing here okay some + + align:start position:0% +that's what we're seeing here okay some + + + align:start position:0% +that's what we're seeing here okay some +only use one for instance the valine RS + + align:start position:0% +only use one for instance the valine RS + + + align:start position:0% +only use one for instance the valine RS +only uses a post transfer editing + + align:start position:0% +only uses a post transfer editing + + + align:start position:0% +only uses a post transfer editing +mechanism so when presented with the + + align:start position:0% +mechanism so when presented with the + + + align:start position:0% +mechanism so when presented with the +data look at the data and see what + + align:start position:0% +data look at the data and see what + + + align:start position:0% +data look at the data and see what +species is being hydrolyzed and if both + + align:start position:0% +species is being hydrolyzed and if both + + + align:start position:0% +species is being hydrolyzed and if both +are how do the steady-state kinetics for + + align:start position:0% +are how do the steady-state kinetics for + + + align:start position:0% +are how do the steady-state kinetics for +instance compare just to take a look in + + align:start position:0% +instance compare just to take a look in + + + align:start position:0% +instance compare just to take a look in +the context of a structure of one of + + align:start position:0% +the context of a structure of one of + + + align:start position:0% +the context of a structure of one of +these aar s so the sites where + + align:start position:0% +these aar s so the sites where + + + align:start position:0% +these aar s so the sites where +aminoacylation occur and editing occur + + align:start position:0% +aminoacylation occur and editing occur + + + align:start position:0% +aminoacylation occur and editing occur +are separated by about 30 angstroms and + + align:start position:0% +are separated by about 30 angstroms and + + + align:start position:0% +are separated by about 30 angstroms and +that's shown here where we have the + + align:start position:0% +that's shown here where we have the + + + align:start position:0% +that's shown here where we have the +aminoacylation site and here we have the + + align:start position:0% +aminoacylation site and here we have the + + + align:start position:0% +aminoacylation site and here we have the +editing site that's responsible for pre + + align:start position:0% +editing site that's responsible for pre + + + align:start position:0% +editing site that's responsible for pre +and or post transfer editing so in + + align:start position:0% +and or post transfer editing so in + + + align:start position:0% +and or post transfer editing so in +thinking about this and thinking about + + align:start position:0% +thinking about this and thinking about + + + align:start position:0% +thinking about this and thinking about +how one could leverage this 30 angstrom + + align:start position:0% +how one could leverage this 30 angstrom + + + align:start position:0% +how one could leverage this 30 angstrom +separation and these two distinct sites + + align:start position:0% +separation and these two distinct sites + + + align:start position:0% +separation and these two distinct sites +in terms of experiments right what does + + align:start position:0% +in terms of experiments right what does + + + align:start position:0% +in terms of experiments right what does +that allow one to do so imagine if you + + align:start position:0% +that allow one to do so imagine if you + + + align:start position:0% +that allow one to do so imagine if you +want to ask what are consequences of + + align:start position:0% +want to ask what are consequences of + + + align:start position:0% +want to ask what are consequences of +having a RS that have faulty editing + + align:start position:0% +having a RS that have faulty editing + + + align:start position:0% +having a RS that have faulty editing +function and effectively miss charge + + align:start position:0% +function and effectively miss charge + + + align:start position:0% +function and effectively miss charge +tRNAs or put the wrong amino acid on a + + align:start position:0% +tRNAs or put the wrong amino acid on a + + + align:start position:0% +tRNAs or put the wrong amino acid on a +tRNA what does that mean for a cell + + align:start position:0% +tRNA what does that mean for a cell + + + align:start position:0% +tRNA what does that mean for a cell +there's an opportunity to do that here + + align:start position:0% +there's an opportunity to do that here + + + align:start position:0% +there's an opportunity to do that here +so you could imagine mutating residues + + align:start position:0% +so you could imagine mutating residues + + + align:start position:0% +so you could imagine mutating residues +that are critical for editing function + + align:start position:0% +that are critical for editing function + + + align:start position:0% +that are critical for editing function +in the editing site such that you have + + align:start position:0% +in the editing site such that you have + + + align:start position:0% +in the editing site such that you have +an a a RS variant that can activate + + align:start position:0% +an a a RS variant that can activate + + + align:start position:0% +an a a RS variant that can activate +amino acids and transfer them to the + + align:start position:0% +amino acids and transfer them to the + + + align:start position:0% +amino acids and transfer them to the +tRNA but cannot edit when a mistake + + align:start position:0% +tRNA but cannot edit when a mistake + + + align:start position:0% +tRNA but cannot edit when a mistake +happens right so you can imagine + + align:start position:0% +happens right so you can imagine + + + align:start position:0% +happens right so you can imagine +site-directed mutagenesis purifying the + + align:start position:0% +site-directed mutagenesis purifying the + + + align:start position:0% +site-directed mutagenesis purifying the +enzyme and doing some in vitro + + align:start position:0% +enzyme and doing some in vitro + + + align:start position:0% +enzyme and doing some in vitro +characterization to see how it behaves + + align:start position:0% +characterization to see how it behaves + + + align:start position:0% +characterization to see how it behaves +and then you could also imagine + + align:start position:0% +and then you could also imagine + + + align:start position:0% +and then you could also imagine +translating this into a cellular context + + align:start position:0% +translating this into a cellular context + + + align:start position:0% +translating this into a cellular context +and asking say in cell culture what + + align:start position:0% +and asking say in cell culture what + + + align:start position:0% +and asking say in cell culture what +happens here so basically what are the + + align:start position:0% +happens here so basically what are the + + + align:start position:0% +happens here so basically what are the +consequences of faulty editing I mean + + align:start position:0% +consequences of faulty editing I mean + + + align:start position:0% +consequences of faulty editing I mean +these types of studies have been done + + align:start position:0% +these types of studies have been done + + + align:start position:0% +these types of studies have been done +we're not going to look at them + + align:start position:0% +we're not going to look at them + + + align:start position:0% +we're not going to look at them +in detail but just as an overview and + + align:start position:0% +in detail but just as an overview and + + + align:start position:0% +in detail but just as an overview and +some concepts that will come up within + + align:start position:0% +some concepts that will come up within + + + align:start position:0% +some concepts that will come up within +our folding section what's been shown is + + align:start position:0% +our folding section what's been shown is + + + align:start position:0% +our folding section what's been shown is +that a single point mutation in an + + align:start position:0% +that a single point mutation in an + + + align:start position:0% +that a single point mutation in an +editing domain of one of these aminoacyl + + align:start position:0% +editing domain of one of these aminoacyl + + + align:start position:0% +editing domain of one of these aminoacyl +trna synthetases + + align:start position:0% +trna synthetases + + + align:start position:0% +trna synthetases +may have deleterious consequences and we + + align:start position:0% +may have deleterious consequences and we + + + align:start position:0% +may have deleterious consequences and we +can imagine that these consequences + + align:start position:0% +can imagine that these consequences + + + align:start position:0% +can imagine that these consequences +could result from proteins or enzymes + + align:start position:0% +could result from proteins or enzymes + + + align:start position:0% +could result from proteins or enzymes +that gain a new function or don't do + + align:start position:0% +that gain a new function or don't do + + + align:start position:0% +that gain a new function or don't do +their correct function right so just + + align:start position:0% +their correct function right so just + + + align:start position:0% +their correct function right so just +imagine that some miss charge tRNAs + + align:start position:0% +imagine that some miss charge tRNAs + + + align:start position:0% +imagine that some miss charge tRNAs +where miss charged means the wrong and + + align:start position:0% +where miss charged means the wrong and + + + align:start position:0% +where miss charged means the wrong and +you know acid is attached are around + + align:start position:0% +you know acid is attached are around + + + align:start position:0% +you know acid is attached are around +because of some mutant aar s and these T + + align:start position:0% +because of some mutant aar s and these T + + + align:start position:0% +because of some mutant aar s and these T +RNAs that are Mis charged can be + + align:start position:0% +RNAs that are Mis charged can be + + + align:start position:0% +RNAs that are Mis charged can be +delivered to the ribosome which means + + align:start position:0% +delivered to the ribosome which means + + + align:start position:0% +delivered to the ribosome which means +that point mutations form within + + align:start position:0% +that point mutations form within + + + align:start position:0% +that point mutations form within +synthesized polypeptide change so + + align:start position:0% +synthesized polypeptide change so + + + align:start position:0% +synthesized polypeptide change so +there's some mixture where some of these + + align:start position:0% +there's some mixture where some of these + + + align:start position:0% +there's some mixture where some of these +proteins are native and others are + + align:start position:0% +proteins are native and others are + + + align:start position:0% +proteins are native and others are +mutant and what might happen here in + + align:start position:0% +mutant and what might happen here in + + + align:start position:0% +mutant and what might happen here in +terms of bless you consequences so + + align:start position:0% +terms of bless you consequences so + + + align:start position:0% +terms of bless you consequences so +native protein will go on and do its job + + align:start position:0% +native protein will go on and do its job + + + align:start position:0% +native protein will go on and do its job +imagine there's some mutant protein here + + align:start position:0% +imagine there's some mutant protein here + + + align:start position:0% +imagine there's some mutant protein here +that's altered in some way and these are + + align:start position:0% +that's altered in some way and these are + + + align:start position:0% +that's altered in some way and these are +just some examples of possible outcomes + + align:start position:0% +just some examples of possible outcomes + + + align:start position:0% +just some examples of possible outcomes +so maybe there's a breakdown of some + + align:start position:0% +so maybe there's a breakdown of some + + + align:start position:0% +so maybe there's a breakdown of some +essential cellular process you know here + + align:start position:0% +essential cellular process you know here + + + align:start position:0% +essential cellular process you know here +we have triggering of them audimute like + + align:start position:0% +we have triggering of them audimute like + + + align:start position:0% +we have triggering of them audimute like +responses things that are not good what + + align:start position:0% +responses things that are not good what + + + align:start position:0% +responses things that are not good what +if these mutant proteins miss fold so + + align:start position:0% +if these mutant proteins miss fold so + + + align:start position:0% +if these mutant proteins miss fold so +they can't form they're correct they're + + align:start position:0% +they can't form they're correct they're + + + align:start position:0% +they can't form they're correct they're +correct fold and fold is important for + + align:start position:0% +correct fold and fold is important for + + + align:start position:0% +correct fold and fold is important for +function + + align:start position:0% +function + + + align:start position:0% +function +maybe there's a Gregorio proteasome ER + + align:start position:0% +maybe there's a Gregorio proteasome ER + + + align:start position:0% +maybe there's a Gregorio proteasome ER +response + + align:start position:0% +response + + + align:start position:0% +response +unfolded protein response cell death so + + align:start position:0% +unfolded protein response cell death so + + + align:start position:0% +unfolded protein response cell death so +fidelity is important and just some + + align:start position:0% +fidelity is important and just some + + + align:start position:0% +fidelity is important and just some +things to think about as we close this + + align:start position:0% +things to think about as we close this + + + align:start position:0% +things to think about as we close this +section we can consider error rates of + + align:start position:0% +section we can consider error rates of + + + align:start position:0% +section we can consider error rates of +various biological polymerizations and + + align:start position:0% +various biological polymerizations and + + + align:start position:0% +various biological polymerizations and +whether that be DNA replication + + align:start position:0% +whether that be DNA replication + + + align:start position:0% +whether that be DNA replication +transcription or translation + + align:start position:0% +transcription or translation + + + align:start position:0% +transcription or translation +right and they vary quite a bit here + + align:start position:0% +right and they vary quite a bit here + + + align:start position:0% +right and they vary quite a bit here +from this and what the take home can be + + align:start position:0% +from this and what the take home can be + + + align:start position:0% +from this and what the take home can be +by comparing these error rates right is + + align:start position:0% +by comparing these error rates right is + + + align:start position:0% +by comparing these error rates right is +that infrequent mistakes in decoding the + + align:start position:0% +that infrequent mistakes in decoding the + + + align:start position:0% +that infrequent mistakes in decoding the +mRNA are accepted as a source of + + align:start position:0% +mRNA are accepted as a source of + + + align:start position:0% +mRNA are accepted as a source of +infidelity so they do occur and they + + align:start position:0% +infidelity so they do occur and they + + + align:start position:0% +infidelity so they do occur and they +occur more frequently than say an error + + align:start position:0% +occur more frequently than say an error + + + align:start position:0% +occur more frequently than say an error +and replicating the DNA and that makes + + align:start position:0% +and replicating the DNA and that makes + + + align:start position:0% +and replicating the DNA and that makes +sense right if an error occurs in DNA + + align:start position:0% +sense right if an error occurs in DNA + + + align:start position:0% +sense right if an error occurs in DNA +replication there's a huge problem + + align:start position:0% +replication there's a huge problem + + + align:start position:0% +replication there's a huge problem +likely compared to entire in translation + + align:start position:0% +likely compared to entire in translation + + + align:start position:0% +likely compared to entire in translation +so some questions just to think about + + align:start position:0% +so some questions just to think about + + + align:start position:0% +so some questions just to think about +answers aren't going to come up within + + align:start position:0% +answers aren't going to come up within + + + align:start position:0% +answers aren't going to come up within +the context of this course but higher + + align:start position:0% +the context of this course but higher + + + align:start position:0% +the context of this course but higher +accuracy is important but actually how + + align:start position:0% +accuracy is important but actually how + + + align:start position:0% +accuracy is important but actually how +much accuracy is enough and there is a + + align:start position:0% +much accuracy is enough and there is a + + + align:start position:0% +much accuracy is enough and there is a +cost in terms of cellular energy for + + align:start position:0% +cost in terms of cellular energy for + + + align:start position:0% +cost in terms of cellular energy for +accuracy and is it that this cell Tunes + + align:start position:0% +accuracy and is it that this cell Tunes + + + align:start position:0% +accuracy and is it that this cell Tunes +its accuracy to some some point that + + align:start position:0% +its accuracy to some some point that + + + align:start position:0% +its accuracy to some some point that +could be considered optimal and are + + align:start position:0% +could be considered optimal and are + + + align:start position:0% +could be considered optimal and are +there benefits to translational + + align:start position:0% +there benefits to translational + + + align:start position:0% +there benefits to translational +infidelity right so the prior slide + + align:start position:0% +infidelity right so the prior slide + + + align:start position:0% +infidelity right so the prior slide +showed negative consequences but but are + + align:start position:0% +showed negative consequences but but are + + + align:start position:0% +showed negative consequences but but are +there benefits so that discussion will + + align:start position:0% +there benefits so that discussion will + + + align:start position:0% +there benefits so that discussion will +close considering how the amino acids + + align:start position:0% +close considering how the amino acids + + + align:start position:0% +close considering how the amino acids +get attached to tRNAs and so where we're + + align:start position:0% +get attached to tRNAs and so where we're + + + align:start position:0% +get attached to tRNAs and so where we're +moving to now is the elongation cycle + + align:start position:0% + + + + align:start position:0% + +so I actually don't know but I think of + + align:start position:0% +so I actually don't know but I think of + + + align:start position:0% +so I actually don't know but I think of +them as being everywhere in terms of the + + align:start position:0% +them as being everywhere in terms of the + + + align:start position:0% +them as being everywhere in terms of the +tRNAs because as we'll see in a few + + align:start position:0% +tRNAs because as we'll see in a few + + + align:start position:0% +tRNAs because as we'll see in a few +slides ef-tu + + align:start position:0% +slides ef-tu + + + align:start position:0% +slides ef-tu +which is required for delivering the + + align:start position:0% +which is required for delivering the + + + align:start position:0% +which is required for delivering the +tRNAs to the ribosome is highly abundant + + align:start position:0% +tRNAs to the ribosome is highly abundant + + + align:start position:0% +tRNAs to the ribosome is highly abundant +at least that's my thinking for + + align:start position:0% +at least that's my thinking for + + + align:start position:0% +at least that's my thinking for +prokaryotes do you have anything to say + + align:start position:0% +prokaryotes do you have anything to say + + + align:start position:0% +prokaryotes do you have anything to say +this question was effectively are there + + align:start position:0% +this question was effectively are there + + + align:start position:0% +this question was effectively are there +certain regions of the cell where tRNAs + + align:start position:0% +certain regions of the cell where tRNAs + + + align:start position:0% +certain regions of the cell where tRNAs +get modified more than other regions + + align:start position:0% +get modified more than other regions + + + align:start position:0% +get modified more than other regions +I don't know million cells they of we're + + align:start position:0% +I don't know million cells they of we're + + + align:start position:0% +I don't know million cells they of we're +old complexes new some phases and + + align:start position:0% +old complexes new some phases and + + + align:start position:0% +old complexes new some phases and +they've been around forever and I still + + align:start position:0% +they've been around forever and I still + + + align:start position:0% +they've been around forever and I still +think we don't understand what the + + align:start position:0% +think we don't understand what the + + + align:start position:0% +think we don't understand what the +function is + + align:start position:0% + + + + align:start position:0% + +like that can you speak so the question + + align:start position:0% +like that can you speak so the question + + + align:start position:0% +like that can you speak so the question +is do we have information about made a + + align:start position:0% +is do we have information about made a + + + align:start position:0% +is do we have information about made a +distribution of tRNAs as being amino + + align:start position:0% +distribution of tRNAs as being amino + + + align:start position:0% +distribution of tRNAs as being amino +acid modified versus unmodified there's + + align:start position:0% +acid modified versus unmodified there's + + + align:start position:0% +acid modified versus unmodified there's +always a way probably right but I don't + + align:start position:0% +always a way probably right but I don't + + + align:start position:0% +always a way probably right but I don't +know what that distribution is either in + + align:start position:0% +know what that distribution is either in + + + align:start position:0% +know what that distribution is either in +terms of the percentage of T RNAs that + + align:start position:0% +terms of the percentage of T RNAs that + + + align:start position:0% +terms of the percentage of T RNAs that +are M you know I isolated at any one + + align:start position:0% +are M you know I isolated at any one + + + align:start position:0% +are M you know I isolated at any one +given time yeah just just don't know I + + align:start position:0% +given time yeah just just don't know I + + + align:start position:0% +given time yeah just just don't know I +think the key one key thing to think + + align:start position:0% +think the key one key thing to think + + + align:start position:0% +think the key one key thing to think +about us we come is that to the next + + align:start position:0% +about us we come is that to the next + + + align:start position:0% +about us we come is that to the next +part is that these T RNAs are are bound + + align:start position:0% +part is that these T RNAs are are bound + + + align:start position:0% +part is that these T RNAs are are bound +by ef-tu + + align:start position:0% +by ef-tu + + + align:start position:0% +by ef-tu +so to think of them as in complex with a + + align:start position:0% +so to think of them as in complex with a + + + align:start position:0% +so to think of them as in complex with a +translation factor as opposed to tRNA is + + align:start position:0% +translation factor as opposed to tRNA is + + + align:start position:0% +translation factor as opposed to tRNA is +floating around in the cytoplasm so I + + align:start position:0% +floating around in the cytoplasm so I + + + align:start position:0% +floating around in the cytoplasm so I +think that that's a key point of focus + + align:start position:0% +think that that's a key point of focus + + + align:start position:0% +think that that's a key point of focus +so moving into elongation what do we + + align:start position:0% +so moving into elongation what do we + + + align:start position:0% +so moving into elongation what do we +need to think about here so we need to + + align:start position:0% +need to think about here so we need to + + + align:start position:0% +need to think about here so we need to +think about delivery of the aminoacyl + + align:start position:0% +think about delivery of the aminoacyl + + + align:start position:0% +think about delivery of the aminoacyl +trnas how does the ribosome ensure that + + align:start position:0% +trnas how does the ribosome ensure that + + + align:start position:0% +trnas how does the ribosome ensure that +the correct amino acyl tRNA is delivered + + align:start position:0% +the correct amino acyl tRNA is delivered + + + align:start position:0% +the correct amino acyl tRNA is delivered +so we have the correct amino acid onto + + align:start position:0% +so we have the correct amino acid onto + + + align:start position:0% +so we have the correct amino acid onto +the tRNA but we also have to get the + + align:start position:0% +the tRNA but we also have to get the + + + align:start position:0% +the tRNA but we also have to get the +correct amino acid to the ribosome how + + align:start position:0% +correct amino acid to the ribosome how + + + align:start position:0% +correct amino acid to the ribosome how +is peptide bond formation catalyzed what + + align:start position:0% +is peptide bond formation catalyzed what + + + align:start position:0% +is peptide bond formation catalyzed what +is the method by which polypeptides + + align:start position:0% +is the method by which polypeptides + + + align:start position:0% +is the method by which polypeptides +leave the ribosome and how is + + align:start position:0% +leave the ribosome and how is + + + align:start position:0% +leave the ribosome and how is +translation terminated here so + + align:start position:0% +translation terminated here so + + + align:start position:0% +translation terminated here so +effectively these are all questions we + + align:start position:0% +effectively these are all questions we + + + align:start position:0% +effectively these are all questions we +need to address in terms of thinking + + align:start position:0% +need to address in terms of thinking + + + align:start position:0% +need to address in terms of thinking +about how the ribosome translates the + + align:start position:0% +about how the ribosome translates the + + + align:start position:0% +about how the ribosome translates the +genetic code and synthesizes the + + align:start position:0% +genetic code and synthesizes the + + + align:start position:0% +genetic code and synthesizes the +polypeptide so within the notes posted + + align:start position:0% +polypeptide so within the notes posted + + + align:start position:0% +polypeptide so within the notes posted +on stellar there's a number of pages of + + align:start position:0% +on stellar there's a number of pages of + + + align:start position:0% +on stellar there's a number of pages of +definitions so terminology that comes up + + align:start position:0% +definitions so terminology that comes up + + + align:start position:0% +definitions so terminology that comes up +within these discussions of the ribosome + + align:start position:0% +within these discussions of the ribosome + + + align:start position:0% +within these discussions of the ribosome +to refer to and in terms of our + + align:start position:0% +to refer to and in terms of our + + + align:start position:0% +to refer to and in terms of our +translation overview slide where we are + + align:start position:0% +translation overview slide where we are + + + align:start position:0% +translation overview slide where we are +now is here an elongation so we have the + + align:start position:0% +now is here an elongation so we have the + + + align:start position:0% +now is here an elongation so we have the +mRNA R 70s and we're gonna focus for the + + align:start position:0% +mRNA R 70s and we're gonna focus for the + + + align:start position:0% +mRNA R 70s and we're gonna focus for the +rest of today and thinking about ef-tu + + align:start position:0% +rest of today and thinking about ef-tu + + + align:start position:0% +rest of today and thinking about ef-tu +this elongation factor that's + + align:start position:0% +this elongation factor that's + + + align:start position:0% +this elongation factor that's +responsible for delivering the aminoacyl + + align:start position:0% +responsible for delivering the aminoacyl + + + align:start position:0% +responsible for delivering the aminoacyl +trnas to the ribosome here so as an + + align:start position:0% +trnas to the ribosome here so as an + + + align:start position:0% +trnas to the ribosome here so as an +overview in terms + + align:start position:0% +overview in terms + + + align:start position:0% +overview in terms +the cartoon where we going here we have + + align:start position:0% +the cartoon where we going here we have + + + align:start position:0% +the cartoon where we going here we have +our ribosome and in this depiction it + + align:start position:0% +our ribosome and in this depiction it + + + align:start position:0% +our ribosome and in this depiction it +has been translating so we have a + + align:start position:0% +has been translating so we have a + + + align:start position:0% +has been translating so we have a +nascent polypeptide emerging through the + + align:start position:0% +nascent polypeptide emerging through the + + + align:start position:0% +nascent polypeptide emerging through the +exit tunnel of the 50s so we see this + + align:start position:0% +exit tunnel of the 50s so we see this + + + align:start position:0% +exit tunnel of the 50s so we see this +peptidyl trna is in the p site and we + + align:start position:0% +peptidyl trna is in the p site and we + + + align:start position:0% +peptidyl trna is in the p site and we +have this D isolated tRNA in the e site + + align:start position:0% +have this D isolated tRNA in the e site + + + align:start position:0% +have this D isolated tRNA in the e site +so what happens the a site is empty and + + align:start position:0% +so what happens the a site is empty and + + + align:start position:0% +so what happens the a site is empty and +for another round of elongation to occur + + align:start position:0% +for another round of elongation to occur + + + align:start position:0% +for another round of elongation to occur +the amino acyl tRNA needs to be + + align:start position:0% +the amino acyl tRNA needs to be + + + align:start position:0% +the amino acyl tRNA needs to be +delivered and as we'll see today and in + + align:start position:0% +delivered and as we'll see today and in + + + align:start position:0% +delivered and as we'll see today and in +recitation this week ef-tu is + + align:start position:0% +recitation this week ef-tu is + + + align:start position:0% +recitation this week ef-tu is +responsible for that so there's a + + align:start position:0% +responsible for that so there's a + + + align:start position:0% +responsible for that so there's a +ternary complex that forms between ef-tu + + align:start position:0% +ternary complex that forms between ef-tu + + + align:start position:0% +ternary complex that forms between ef-tu +GTP so ef-tu is a GTP ace and the amino + + align:start position:0% +GTP so ef-tu is a GTP ace and the amino + + + align:start position:0% +GTP so ef-tu is a GTP ace and the amino +acyl tRNA and this ternary complex + + align:start position:0% +acyl tRNA and this ternary complex + + + align:start position:0% +acyl tRNA and this ternary complex +delivers the amino acyl tRNA to the a + + align:start position:0% +delivers the amino acyl tRNA to the a + + + align:start position:0% +delivers the amino acyl tRNA to the a +site okay this allows for peptide bond + + align:start position:0% +site okay this allows for peptide bond + + + align:start position:0% +site okay this allows for peptide bond +formation to occur in the catalytic + + align:start position:0% +formation to occur in the catalytic + + + align:start position:0% +formation to occur in the catalytic +center and then there's a process called + + align:start position:0% +center and then there's a process called + + + align:start position:0% +center and then there's a process called +translocation in which the elongation + + align:start position:0% +translocation in which the elongation + + + align:start position:0% +translocation in which the elongation +factor G in complex with gtp comes in + + align:start position:0% +factor G in complex with gtp comes in + + + align:start position:0% +factor G in complex with gtp comes in +and helps to reset the ribosome such + + align:start position:0% +and helps to reset the ribosome such + + + align:start position:0% +and helps to reset the ribosome such +that another amino acyl tRNA can come in + + align:start position:0% +that another amino acyl tRNA can come in + + + align:start position:0% +that another amino acyl tRNA can come in +okay so where we're going to focus for + + align:start position:0% +okay so where we're going to focus for + + + align:start position:0% +okay so where we're going to focus for +the rest of today is on this process + + align:start position:0% +the rest of today is on this process + + + align:start position:0% +the rest of today is on this process +here thinking about ef-tu + + align:start position:0% +here thinking about ef-tu + + + align:start position:0% +here thinking about ef-tu +and how that delivers amino acid + + align:start position:0% +and how that delivers amino acid + + + align:start position:0% +and how that delivers amino acid +attached to tRNAs to the a site + + align:start position:0% + + + + align:start position:0% + +okay so just in our cartoon where we + + align:start position:0% +okay so just in our cartoon where we + + + align:start position:0% +okay so just in our cartoon where we +left off with initiation process okay so + + align:start position:0% +left off with initiation process okay so + + + align:start position:0% +left off with initiation process okay so +we have that initiator tRNA in the P + + align:start position:0% +we have that initiator tRNA in the P + + + align:start position:0% +we have that initiator tRNA in the P +site and the a site is empty okay and + + align:start position:0% +site and the a site is empty okay and + + + align:start position:0% +site and the a site is empty okay and +one other thing I'll just show here we + + align:start position:0% +one other thing I'll just show here we + + + align:start position:0% +one other thing I'll just show here we +mentioned I mentioned when describing + + align:start position:0% +mentioned I mentioned when describing + + + align:start position:0% +mentioned I mentioned when describing +ribosome structure that some ribosomal + + align:start position:0% +ribosome structure that some ribosomal + + + align:start position:0% +ribosome structure that some ribosomal +proteins have additional jobs so it's + + align:start position:0% +proteins have additional jobs so it's + + + align:start position:0% +proteins have additional jobs so it's +not just that these proteins help with + + align:start position:0% +not just that these proteins help with + + + align:start position:0% +not just that these proteins help with +the overall structural integrity of the + + align:start position:0% +the overall structural integrity of the + + + align:start position:0% +the overall structural integrity of the +ribosome and there's two ribosomal + + align:start position:0% +ribosome and there's two ribosomal + + + align:start position:0% +ribosome and there's two ribosomal +proteins l 7 and 8 l 12 and these are + + align:start position:0% +proteins l 7 and 8 l 12 and these are + + + align:start position:0% +proteins l 7 and 8 l 12 and these are +involved in recruitment of that ternary + + align:start position:0% +involved in recruitment of that ternary + + + align:start position:0% +involved in recruitment of that ternary +complex between ef-tu the GTP and the + + align:start position:0% +complex between ef-tu the GTP and the + + + align:start position:0% +complex between ef-tu the GTP and the +immuno acyl tRNA + + align:start position:0% + + + + align:start position:0% + +so now we need to get the amino acyl + + align:start position:0% +so now we need to get the amino acyl + + + align:start position:0% +so now we need to get the amino acyl +tRNA to the a site okay and this + + align:start position:0% +tRNA to the a site okay and this + + + align:start position:0% +tRNA to the a site okay and this +requires ef-tu + + align:start position:0% + + + + align:start position:0% + +and when we think about this we always + + align:start position:0% +and when we think about this we always + + + align:start position:0% +and when we think about this we always +need to think about this ternary complex + + align:start position:0% +need to think about this ternary complex + + + align:start position:0% +need to think about this ternary complex +which is ef-tu down to the amino acyl + + align:start position:0% +which is ef-tu down to the amino acyl + + + align:start position:0% +which is ef-tu down to the amino acyl +tRNA bound to gtp so a little bit about + + align:start position:0% +tRNA bound to gtp so a little bit about + + + align:start position:0% +tRNA bound to gtp so a little bit about +ef-tu + + align:start position:0% +ef-tu + + + align:start position:0% +ef-tu +so in e.coli ef-tu is the most abundant + + align:start position:0% +so in e.coli ef-tu is the most abundant + + + align:start position:0% +so in e.coli ef-tu is the most abundant +protein so there's tons of ef-tu + + align:start position:0% +protein so there's tons of ef-tu + + + align:start position:0% +protein so there's tons of ef-tu +ok approximately here we have a hundred + + align:start position:0% +ok approximately here we have a hundred + + + align:start position:0% +ok approximately here we have a hundred +thousand copies per cell so it's about + + align:start position:0% +thousand copies per cell so it's about + + + align:start position:0% +thousand copies per cell so it's about +5% of total cellular protein and so as I + + align:start position:0% +5% of total cellular protein and so as I + + + align:start position:0% +5% of total cellular protein and so as I +just said in response to a question + + align:start position:0% +just said in response to a question + + + align:start position:0% +just said in response to a question +about these tRNAs in the cells we can + + align:start position:0% +about these tRNAs in the cells we can + + + align:start position:0% +about these tRNAs in the cells we can +think about this entire tRNA pool or + + align:start position:0% +think about this entire tRNA pool or + + + align:start position:0% +think about this entire tRNA pool or +amino acyl Aidid tRNA pool as being + + align:start position:0% +amino acyl Aidid tRNA pool as being + + + align:start position:0% +amino acyl Aidid tRNA pool as being +sequestered by ef-tu so ef-tu binds the + + align:start position:0% +sequestered by ef-tu so ef-tu binds the + + + align:start position:0% +sequestered by ef-tu so ef-tu binds the +amino acyl tRNA and it binds gtp + + align:start position:0% +amino acyl tRNA and it binds gtp + + + align:start position:0% +amino acyl tRNA and it binds gtp +to form the ternary complex and this + + align:start position:0% +to form the ternary complex and this + + + align:start position:0% +to form the ternary complex and this +allows the FTU to deliver these amino + + align:start position:0% +allows the FTU to deliver these amino + + + align:start position:0% +allows the FTU to deliver these amino +acids attached to the tRNAs to the a + + align:start position:0% +acids attached to the tRNAs to the a + + + align:start position:0% +acids attached to the tRNAs to the a +site and it's a GTP ace and we need to + + align:start position:0% +site and it's a GTP ace and we need to + + + align:start position:0% +site and it's a GTP ace and we need to +think a lot about how this activity + + align:start position:0% +think a lot about how this activity + + + align:start position:0% +think a lot about how this activity +relates to its function and fidelity so + + align:start position:0% +relates to its function and fidelity so + + + align:start position:0% +relates to its function and fidelity so +here is the depiction of the structure + + align:start position:0% +here is the depiction of the structure + + + align:start position:0% +here is the depiction of the structure +of a ternary complex so what we see is + + align:start position:0% +of a ternary complex so what we see is + + + align:start position:0% +of a ternary complex so what we see is +that we have a tRNA here and here we + + align:start position:0% +that we have a tRNA here and here we + + + align:start position:0% +that we have a tRNA here and here we +have ef-tu bound to the tRNA so here's + + align:start position:0% +have ef-tu bound to the tRNA so here's + + + align:start position:0% +have ef-tu bound to the tRNA so here's +the anticodon loop + + align:start position:0% +the anticodon loop + + + align:start position:0% +the anticodon loop +okay and if we consider this structure + + align:start position:0% +okay and if we consider this structure + + + align:start position:0% +okay and if we consider this structure +of the ternary complex bound to mRNA + + align:start position:0% +of the ternary complex bound to mRNA + + + align:start position:0% +of the ternary complex bound to mRNA +what do we see so we have an mRNA in + + align:start position:0% +what do we see so we have an mRNA in + + + align:start position:0% +what do we see so we have an mRNA in +green okay here's the tRNA and the + + align:start position:0% +green okay here's the tRNA and the + + + align:start position:0% +green okay here's the tRNA and the +anticodon end and here's ef-tu okay and + + align:start position:0% +anticodon end and here's ef-tu okay and + + + align:start position:0% +anticodon end and here's ef-tu okay and +as I said ef-tu is the gtp ace where is + + align:start position:0% +as I said ef-tu is the gtp ace where is + + + align:start position:0% +as I said ef-tu is the gtp ace where is +the gtp a center that's up here okay so + + align:start position:0% +the gtp a center that's up here okay so + + + align:start position:0% +the gtp a center that's up here okay so +this gtp a center of ef-tu + + align:start position:0% +this gtp a center of ef-tu + + + align:start position:0% +this gtp a center of ef-tu +is quite far from the tRNA anticodon + + align:start position:0% +is quite far from the tRNA anticodon + + + align:start position:0% +is quite far from the tRNA anticodon +down here this distance is about 17 + + align:start position:0% +down here this distance is about 17 + + + align:start position:0% +down here this distance is about 17 +angstroms and so this is something quite + + align:start position:0% +angstroms and so this is something quite + + + align:start position:0% +angstroms and so this is something quite +incredible to think about because as + + align:start position:0% +incredible to think about because as + + + align:start position:0% +incredible to think about because as +we'll see when there's codon recognition + + align:start position:0% +we'll see when there's codon recognition + + + align:start position:0% +we'll see when there's codon recognition +meaning this codon anticodon interaction + + align:start position:0% +meaning this codon anticodon interaction + + + align:start position:0% +meaning this codon anticodon interaction +that's a cognate pair GTP hydrolysis is + + align:start position:0% +that's a cognate pair GTP hydrolysis is + + + align:start position:0% +that's a cognate pair GTP hydrolysis is +stimulated so how is that communicated + + align:start position:0% +stimulated so how is that communicated + + + align:start position:0% +stimulated so how is that communicated +over 70 angstroms if there's a + + align:start position:0% +over 70 angstroms if there's a + + + align:start position:0% +over 70 angstroms if there's a +recognition event here between the mRNA + + align:start position:0% +recognition event here between the mRNA + + + align:start position:0% +recognition event here between the mRNA +and the tRNA anticodon and GTP + + align:start position:0% +and the tRNA anticodon and GTP + + + align:start position:0% +and the tRNA anticodon and GTP +hydrolysis happens up here how is that + + align:start position:0% +hydrolysis happens up here how is that + + + align:start position:0% +hydrolysis happens up here how is that +signaled over 70 angstroms right so + + align:start position:0% +signaled over 70 angstroms right so + + + align:start position:0% +signaled over 70 angstroms right so +clearly there's going to be some + + align:start position:0% +clearly there's going to be some + + + align:start position:0% +clearly there's going to be some +conformational changes that occur that + + align:start position:0% +conformational changes that occur that + + + align:start position:0% +conformational changes that occur that +allow this gtp ace activity to turn on + + align:start position:0% + + + + align:start position:0% + +just another view so here again we have + + align:start position:0% +just another view so here again we have + + + align:start position:0% +just another view so here again we have +the structure of the ternary complex + + align:start position:0% +the structure of the ternary complex + + + align:start position:0% +the structure of the ternary complex +bound to the mRNA and here we can look + + align:start position:0% +bound to the mRNA and here we can look + + + align:start position:0% +bound to the mRNA and here we can look +at the ternary complex bound to a 70s + + align:start position:0% +at the ternary complex bound to a 70s + + + align:start position:0% +at the ternary complex bound to a 70s +ribosome so we have the ribosome in this + + align:start position:0% +ribosome so we have the ribosome in this + + + align:start position:0% +ribosome so we have the ribosome in this +orange e gold color the 50s xxx here we + + align:start position:0% +orange e gold color the 50s xxx here we + + + align:start position:0% +orange e gold color the 50s xxx here we +have the PTC and decoding site the tRNA + + align:start position:0% +have the PTC and decoding site the tRNA + + + align:start position:0% +have the PTC and decoding site the tRNA +is in green and ef-tu + + align:start position:0% +is in green and ef-tu + + + align:start position:0% +is in green and ef-tu +is in this darker orange here okay to + + align:start position:0% +is in this darker orange here okay to + + + align:start position:0% +is in this darker orange here okay to +place that in the perspective of the 70s + + align:start position:0% +place that in the perspective of the 70s + + + align:start position:0% +place that in the perspective of the 70s +ribosome here so conformational change + + align:start position:0% +ribosome here so conformational change + + + align:start position:0% +ribosome here so conformational change +is required to signal codon recognition + + align:start position:0% +is required to signal codon recognition + + + align:start position:0% +is required to signal codon recognition +to the GTP a center and this is + + align:start position:0% +to the GTP a center and this is + + + align:start position:0% +to the GTP a center and this is +something and that we'll talk spoken + + align:start position:0% +something and that we'll talk spoken + + + align:start position:0% +something and that we'll talk spoken +about in quite some detail this week + + align:start position:0% +about in quite some detail this week + + + align:start position:0% +about in quite some detail this week +in recitation one other point of review + + align:start position:0% +in recitation one other point of review + + + align:start position:0% +in recitation one other point of review +before moving forward with delivery of + + align:start position:0% +before moving forward with delivery of + + + align:start position:0% +before moving forward with delivery of +the aminoacyl-trna we need to think + + align:start position:0% +the aminoacyl-trna we need to think + + + align:start position:0% +the aminoacyl-trna we need to think +about codon anticodon interactions here + + align:start position:0% +about codon anticodon interactions here + + + align:start position:0% +about codon anticodon interactions here +right for decoding + + align:start position:0% + + + + align:start position:0% + +okay so we have cognate verses near + + align:start position:0% +okay so we have cognate verses near + + + align:start position:0% +okay so we have cognate verses near +cognate versus non cognate okay and this + + align:start position:0% +cognate versus non cognate okay and this + + + align:start position:0% +cognate versus non cognate okay and this +is for the codon anticodon interaction + + align:start position:0% + + + + align:start position:0% + +okay and so if we imagine we have some + + align:start position:0% +okay and so if we imagine we have some + + + align:start position:0% +okay and so if we imagine we have some +mRNA and you need to think about the + + align:start position:0% +mRNA and you need to think about the + + + align:start position:0% +mRNA and you need to think about the +five Prime and three prime ends with + + align:start position:0% +five Prime and three prime ends with + + + align:start position:0% +five Prime and three prime ends with +this and then we have some tRNA okay + + align:start position:0% +this and then we have some tRNA okay + + + align:start position:0% +this and then we have some tRNA okay +three prime five prime right we need to + + align:start position:0% +three prime five prime right we need to + + + align:start position:0% +three prime five prime right we need to +ask how did these match so for instance + + align:start position:0% +ask how did these match so for instance + + + align:start position:0% +ask how did these match so for instance +here if we have a a G and we have + + align:start position:0% +here if we have a a G and we have + + + align:start position:0% +here if we have a a G and we have +positions 1 2 3 from left to right of + + align:start position:0% +positions 1 2 3 from left to right of + + + align:start position:0% +positions 1 2 3 from left to right of +the mRNA right here we have a cognate + + align:start position:0% +the mRNA right here we have a cognate + + + align:start position:0% +the mRNA right here we have a cognate +match ok so we have the AU match in + + align:start position:0% +match ok so we have the AU match in + + + align:start position:0% +match ok so we have the AU match in +positions one and two and then wobbles + + align:start position:0% +positions one and two and then wobbles + + + align:start position:0% +positions one and two and then wobbles +allowed in position three this this GU + + align:start position:0% +allowed in position three this this GU + + + align:start position:0% +allowed in position three this this GU +here so no no interaction ok just as + + align:start position:0% +here so no no interaction ok just as + + + align:start position:0% +here so no no interaction ok just as +another example here + + align:start position:0% + + + + align:start position:0% + +imagine we have ghe here right what we + + align:start position:0% +imagine we have ghe here right what we + + + align:start position:0% +imagine we have ghe here right what we +see is that there's only one match + + align:start position:0% +see is that there's only one match + + + align:start position:0% +see is that there's only one match +meaning what Stan Crick base pairing + + align:start position:0% +meaning what Stan Crick base pairing + + + align:start position:0% +meaning what Stan Crick base pairing +okay in position two okay here this GU + + align:start position:0% +okay in position two okay here this GU + + + align:start position:0% +okay in position two okay here this GU +that's not not a match + + align:start position:0% +that's not not a match + + + align:start position:0% +that's not not a match +based on Watson Crick base pairing and + + align:start position:0% +based on Watson Crick base pairing and + + + align:start position:0% +based on Watson Crick base pairing and +as a result the ribosome is going to + + align:start position:0% +as a result the ribosome is going to + + + align:start position:0% +as a result the ribosome is going to +want to reject this tRNA right if if + + align:start position:0% +want to reject this tRNA right if if + + + align:start position:0% +want to reject this tRNA right if if +this is what's happening in the a site + + align:start position:0% +this is what's happening in the a site + + + align:start position:0% +this is what's happening in the a site +here and then we can just imagine some + + align:start position:0% +here and then we can just imagine some + + + align:start position:0% +here and then we can just imagine some +situation where we have a tRNA and then + + align:start position:0% +situation where we have a tRNA and then + + + align:start position:0% +situation where we have a tRNA and then +RNA RNA where there's just no match okay + + align:start position:0% +RNA RNA where there's just no match okay + + + align:start position:0% +RNA RNA where there's just no match okay +no Watson and Crick base pairing here so + + align:start position:0% +no Watson and Crick base pairing here so + + + align:start position:0% +no Watson and Crick base pairing here so +bless you what we need to ask is as + + align:start position:0% +bless you what we need to ask is as + + + align:start position:0% +bless you what we need to ask is as +ef-tu is delivering these aminoacyl + + align:start position:0% +ef-tu is delivering these aminoacyl + + + align:start position:0% +ef-tu is delivering these aminoacyl +trnas what happens if it's a cognate + + align:start position:0% +trnas what happens if it's a cognate + + + align:start position:0% +trnas what happens if it's a cognate +match versus a near cognate versus a non + + align:start position:0% +match versus a near cognate versus a non + + + align:start position:0% +match versus a near cognate versus a non +cognate how does the ribosome deal with + + align:start position:0% +cognate how does the ribosome deal with + + + align:start position:0% +cognate how does the ribosome deal with +the wrong tRNA entering the a site right + + align:start position:0% +the wrong tRNA entering the a site right + + + align:start position:0% +the wrong tRNA entering the a site right +so again this is something important for + + align:start position:0% +so again this is something important for + + + align:start position:0% +so again this is something important for +fidelity okay and these both need to be + + align:start position:0% +fidelity okay and these both need to be + + + align:start position:0% +fidelity okay and these both need to be +rejected + + align:start position:0% + + + + align:start position:0% + +so why are we reviewing this we're + + align:start position:0% +so why are we reviewing this we're + + + align:start position:0% +so why are we reviewing this we're +reviewing this because it's important + + align:start position:0% +reviewing this because it's important + + + align:start position:0% +reviewing this because it's important +with terms of what happens during + + align:start position:0% +with terms of what happens during + + + align:start position:0% +with terms of what happens during +initial binding of aminoacyl trnas to + + align:start position:0% +initial binding of aminoacyl trnas to + + + align:start position:0% +initial binding of aminoacyl trnas to +the ribosome so we're going to go over + + align:start position:0% +the ribosome so we're going to go over + + + align:start position:0% +the ribosome so we're going to go over +some of this in words and then look at a + + align:start position:0% +some of this in words and then look at a + + + align:start position:0% +some of this in words and then look at a +cartoon that explains this process and + + align:start position:0% +cartoon that explains this process and + + + align:start position:0% +cartoon that explains this process and +what we're focused on is delivery of the + + align:start position:0% +what we're focused on is delivery of the + + + align:start position:0% +what we're focused on is delivery of the +amino acyl tRNA to the a site so what + + align:start position:0% +amino acyl tRNA to the a site so what + + + align:start position:0% +amino acyl tRNA to the a site so what +happens first okay first there needs to + + align:start position:0% +happens first okay first there needs to + + + align:start position:0% +happens first okay first there needs to +be an initial binding event where the + + align:start position:0% +be an initial binding event where the + + + align:start position:0% +be an initial binding event where the +ternary complex binds to the ribosome so + + align:start position:0% +ternary complex binds to the ribosome so + + + align:start position:0% +ternary complex binds to the ribosome so +initial binding it binds to the 70s and + + align:start position:0% +initial binding it binds to the 70s and + + + align:start position:0% +initial binding it binds to the 70s and +these ribosomal proteins are involved in + + align:start position:0% +these ribosomal proteins are involved in + + + align:start position:0% +these ribosomal proteins are involved in +recruitment of the ternary complex this + + align:start position:0% +recruitment of the ternary complex this + + + align:start position:0% +recruitment of the ternary complex this +initial binding event of the ternary + + align:start position:0% +initial binding event of the ternary + + + align:start position:0% +initial binding event of the ternary +complex to the ribosome is independent + + align:start position:0% +complex to the ribosome is independent + + + align:start position:0% +complex to the ribosome is independent +of the mRNA what happens next is that + + align:start position:0% +of the mRNA what happens next is that + + + align:start position:0% +of the mRNA what happens next is that +there's codon recognition so we need to + + align:start position:0% +there's codon recognition so we need to + + + align:start position:0% +there's codon recognition so we need to +think about that tRNA entering the a + + align:start position:0% +think about that tRNA entering the a + + + align:start position:0% +think about that tRNA entering the a +site and there's some sort of sampling + + align:start position:0% +site and there's some sort of sampling + + + align:start position:0% +site and there's some sort of sampling +that occurs in the decoding center so + + align:start position:0% +that occurs in the decoding center so + + + align:start position:0% +that occurs in the decoding center so +sampling of codon anticodon pairs in the + + align:start position:0% +sampling of codon anticodon pairs in the + + + align:start position:0% +sampling of codon anticodon pairs in the +a site and so what happens what happens + + align:start position:0% +a site and so what happens what happens + + + align:start position:0% +a site and so what happens what happens +if there's a cognate event or a non + + align:start position:0% +if there's a cognate event or a non + + + align:start position:0% +if there's a cognate event or a non +cognitive end so if a cognate anticodon + + align:start position:0% +cognitive end so if a cognate anticodon + + + align:start position:0% +cognitive end so if a cognate anticodon +recognition event occurs there's a + + align:start position:0% +recognition event occurs there's a + + + align:start position:0% +recognition event occurs there's a +series of steps that then happen so with + + align:start position:0% +series of steps that then happen so with + + + align:start position:0% +series of steps that then happen so with +a cognate codon anticodon interaction + + align:start position:0% +a cognate codon anticodon interaction + + + align:start position:0% +a cognate codon anticodon interaction +there will be a conformational change in + + align:start position:0% +there will be a conformational change in + + + align:start position:0% +there will be a conformational change in +ef-tu and this activates the GTP a + + align:start position:0% +ef-tu and this activates the GTP a + + + align:start position:0% +ef-tu and this activates the GTP a +center which allows for GTP hydrolysis + + align:start position:0% +center which allows for GTP hydrolysis + + + align:start position:0% +center which allows for GTP hydrolysis +okay and effectively this conformational + + align:start position:0% +okay and effectively this conformational + + + align:start position:0% +okay and effectively this conformational +change stabilizes the codon anticodon + + align:start position:0% +change stabilizes the codon anticodon + + + align:start position:0% +change stabilizes the codon anticodon +interaction here and that stabilization + + align:start position:0% +interaction here and that stabilization + + + align:start position:0% +interaction here and that stabilization +accelerates the GTP hydrolysis step so + + align:start position:0% +accelerates the GTP hydrolysis step so + + + align:start position:0% +accelerates the GTP hydrolysis step so +this is all building towards the + + align:start position:0% +this is all building towards the + + + align:start position:0% +this is all building towards the +kinetics scheme in terms of enhancements + + align:start position:0% +kinetics scheme in terms of enhancements + + + align:start position:0% +kinetics scheme in terms of enhancements +what's found is that the rate of GTP + + align:start position:0% +what's found is that the rate of GTP + + + align:start position:0% +what's found is that the rate of GTP +hydrolysis by ef-tu increases by about + + align:start position:0% +hydrolysis by ef-tu increases by about + + + align:start position:0% +hydrolysis by ef-tu increases by about +five times ten to the fourth with + + align:start position:0% +five times ten to the fourth with + + + align:start position:0% +five times ten to the fourth with +cognate anticodon recognition in the + + align:start position:0% +cognate anticodon recognition in the + + + align:start position:0% +cognate anticodon recognition in the +site so we have gtp hydrolysis and then + + align:start position:0% +site so we have gtp hydrolysis and then + + + align:start position:0% +site so we have gtp hydrolysis and then +there's another conformational change so + + align:start position:0% +there's another conformational change so + + + align:start position:0% +there's another conformational change so +we have ef-tu + + align:start position:0% +we have ef-tu + + + align:start position:0% +we have ef-tu +in its gdp-bound form an effectively eft + + align:start position:0% +in its gdp-bound form an effectively eft + + + align:start position:0% +in its gdp-bound form an effectively eft +you will dissociate from the amino acyl + + align:start position:0% +you will dissociate from the amino acyl + + + align:start position:0% +you will dissociate from the amino acyl +tRNA and the amino acyl tRNA will fully + + align:start position:0% +tRNA and the amino acyl tRNA will fully + + + align:start position:0% +tRNA and the amino acyl tRNA will fully +enter the a site okay so this process is + + align:start position:0% +enter the a site okay so this process is + + + align:start position:0% +enter the a site okay so this process is +called accommodation and once that + + align:start position:0% +called accommodation and once that + + + align:start position:0% +called accommodation and once that +happens peptide bond formation can occur + + align:start position:0% +happens peptide bond formation can occur + + + align:start position:0% +happens peptide bond formation can occur +so this is you know the good scenario + + align:start position:0% +so this is you know the good scenario + + + align:start position:0% +so this is you know the good scenario +the polypeptide can keep being made what + + align:start position:0% +the polypeptide can keep being made what + + + align:start position:0% +the polypeptide can keep being made what +if it's not a cognate so what if a near + + align:start position:0% +if it's not a cognate so what if a near + + + align:start position:0% +if it's not a cognate so what if a near +cognate tRNA is delivered to that a site + + align:start position:0% +cognate tRNA is delivered to that a site + + + align:start position:0% +cognate tRNA is delivered to that a site +during this initial binding event which + + align:start position:0% +during this initial binding event which + + + align:start position:0% +during this initial binding event which +is independent of the mRNA that that's + + align:start position:0% +is independent of the mRNA that that's + + + align:start position:0% +is independent of the mRNA that that's +why this can occur if it's a near code + + align:start position:0% +why this can occur if it's a near code + + + align:start position:0% +why this can occur if it's a near code +near cognate anticodon what we observe + + align:start position:0% +near cognate anticodon what we observe + + + align:start position:0% +near cognate anticodon what we observe +and this is all from experiments you'll + + align:start position:0% +and this is all from experiments you'll + + + align:start position:0% +and this is all from experiments you'll +be learning about this week the ternary + + align:start position:0% +be learning about this week the ternary + + + align:start position:0% +be learning about this week the ternary +complex rapidly dissociates from the + + align:start position:0% +complex rapidly dissociates from the + + + align:start position:0% +complex rapidly dissociates from the +ribosome and what's found from kinetic + + align:start position:0% +ribosome and what's found from kinetic + + + align:start position:0% +ribosome and what's found from kinetic +measurements is that the dissociation of + + align:start position:0% +measurements is that the dissociation of + + + align:start position:0% +measurements is that the dissociation of +the ternary complex when it's a near + + align:start position:0% +the ternary complex when it's a near + + + align:start position:0% +the ternary complex when it's a near +cognate situation is about 350 fold + + align:start position:0% +cognate situation is about 350 fold + + + align:start position:0% +cognate situation is about 350 fold +faster than cognate so let's look at + + align:start position:0% +faster than cognate so let's look at + + + align:start position:0% +faster than cognate so let's look at +this stepwise within a cartoon format + + align:start position:0% +this stepwise within a cartoon format + + + align:start position:0% +this stepwise within a cartoon format +you'll see another depiction of this + + align:start position:0% +you'll see another depiction of this + + + align:start position:0% +you'll see another depiction of this +scheme and the recitation notes and a + + align:start position:0% +scheme and the recitation notes and a + + + align:start position:0% +scheme and the recitation notes and a +problem set too so here we have multiple + + align:start position:0% +problem set too so here we have multiple + + + align:start position:0% +problem set too so here we have multiple +steps in this overall process all of + + align:start position:0% +steps in this overall process all of + + + align:start position:0% +steps in this overall process all of +these steps have some rate that's been + + align:start position:0% +these steps have some rate that's been + + + align:start position:0% +these steps have some rate that's been +measured by multiple types of methods + + align:start position:0% +measured by multiple types of methods + + + align:start position:0% +measured by multiple types of methods +and Joanne will be presenting this week + + align:start position:0% +and Joanne will be presenting this week + + + align:start position:0% +and Joanne will be presenting this week +on a lot of pre study state kinetic + + align:start position:0% +on a lot of pre study state kinetic + + + align:start position:0% +on a lot of pre study state kinetic +analyses that were done to measure these + + align:start position:0% +analyses that were done to measure these + + + align:start position:0% +analyses that were done to measure these +these rates here and basically the key + + align:start position:0% +these rates here and basically the key + + + align:start position:0% +these rates here and basically the key +point to keep in mind and that I'd like + + align:start position:0% +point to keep in mind and that I'd like + + + align:start position:0% +point to keep in mind and that I'd like +to stress from what was just said on the + + align:start position:0% +to stress from what was just said on the + + + align:start position:0% +to stress from what was just said on the +prior slide is that what you'll see + + align:start position:0% +prior slide is that what you'll see + + + align:start position:0% +prior slide is that what you'll see +throughout this is that conformational + + align:start position:0% +throughout this is that conformational + + + align:start position:0% +throughout this is that conformational +changes are coupled to these rapid + + align:start position:0% +changes are coupled to these rapid + + + align:start position:0% +changes are coupled to these rapid +chemical steps okay and the chemical + + align:start position:0% +chemical steps okay and the chemical + + + align:start position:0% +chemical steps okay and the chemical +steps are irreversible this GTP + + align:start position:0% +steps are irreversible this GTP + + + align:start position:0% +steps are irreversible this GTP +hydrolysis so what do we see we begin + + align:start position:0% +hydrolysis so what do we see we begin + + + align:start position:0% +hydrolysis so what do we see we begin +with initial selection + + align:start position:0% +with initial selection + + + align:start position:0% +with initial selection +here we have our ribosome and there's a + + align:start position:0% +here we have our ribosome and there's a + + + align:start position:0% +here we have our ribosome and there's a +polypeptide being synthesized here's the + + align:start position:0% +polypeptide being synthesized here's the + + + align:start position:0% +polypeptide being synthesized here's the +ternary complex the FTU GTP and the + + align:start position:0% +ternary complex the FTU GTP and the + + + align:start position:0% +ternary complex the FTU GTP and the +amino acyl tRNA so there's an initial + + align:start position:0% +amino acyl tRNA so there's an initial + + + align:start position:0% +amino acyl tRNA so there's an initial +binding step that's governed by k1 in + + align:start position:0% +binding step that's governed by k1 in + + + align:start position:0% +binding step that's governed by k1 in +the forward direction and K minus one in + + align:start position:0% +the forward direction and K minus one in + + + align:start position:0% +the forward direction and K minus one in +the back direction okay and I said + + align:start position:0% +the back direction okay and I said + + + align:start position:0% +the back direction okay and I said +before this is independent of the mRNA + + align:start position:0% +before this is independent of the mRNA + + + align:start position:0% +before this is independent of the mRNA +so what happens the ternary complex + + align:start position:0% +so what happens the ternary complex + + + align:start position:0% +so what happens the ternary complex +binds the ribosome they're sampling in + + align:start position:0% +binds the ribosome they're sampling in + + + align:start position:0% +binds the ribosome they're sampling in +the a site of the anticodon and then + + align:start position:0% +the a site of the anticodon and then + + + align:start position:0% +the a site of the anticodon and then +there's a step described as codon + + align:start position:0% +there's a step described as codon + + + align:start position:0% +there's a step described as codon +recognition with K 2 and K minus 2 okay + + align:start position:0% +recognition with K 2 and K minus 2 okay + + + align:start position:0% +recognition with K 2 and K minus 2 okay +in this scheme if an arrow is colored + + align:start position:0% +in this scheme if an arrow is colored + + + align:start position:0% +in this scheme if an arrow is colored +red arrow indicates the rate is greater + + align:start position:0% +red arrow indicates the rate is greater + + + align:start position:0% +red arrow indicates the rate is greater +for near cognate and cognate ok which + + align:start position:0% +for near cognate and cognate ok which + + + align:start position:0% +for near cognate and cognate ok which +means in the event here of a cognate + + align:start position:0% +means in the event here of a cognate + + + align:start position:0% +means in the event here of a cognate +pair this is going to push forward in + + align:start position:0% +pair this is going to push forward in + + + align:start position:0% +pair this is going to push forward in +the forward direction if it's near + + align:start position:0% +the forward direction if it's near + + + align:start position:0% +the forward direction if it's near +cognate this back step has a greater + + align:start position:0% +cognate this back step has a greater + + + align:start position:0% +cognate this back step has a greater +rate of about 350 fold okay so we're + + align:start position:0% +rate of about 350 fold okay so we're + + + align:start position:0% +rate of about 350 fold okay so we're +going to end up back here with cognate + + align:start position:0% +going to end up back here with cognate + + + align:start position:0% +going to end up back here with cognate +recognition next we have gtp ace + + align:start position:0% +recognition next we have gtp ace + + + align:start position:0% +recognition next we have gtp ace +activation again forward in Reverse + + align:start position:0% +activation again forward in Reverse + + + align:start position:0% +activation again forward in Reverse +green indicates the rate is greater for + + align:start position:0% +green indicates the rate is greater for + + + align:start position:0% +green indicates the rate is greater for +a cognate match than near cognate + + align:start position:0% +a cognate match than near cognate + + + align:start position:0% +a cognate match than near cognate +so if it's the correct anticodon it's + + align:start position:0% +so if it's the correct anticodon it's + + + align:start position:0% +so if it's the correct anticodon it's +going to plough through to here we have + + align:start position:0% +going to plough through to here we have + + + align:start position:0% +going to plough through to here we have +gtp ace activation and then what happens + + align:start position:0% +gtp ace activation and then what happens + + + align:start position:0% +gtp ace activation and then what happens +down here we have a GTP hydrolysis step + + align:start position:0% + + + + align:start position:0% + +we have a conformational change in ef-tu + + align:start position:0% +we have a conformational change in ef-tu + + + align:start position:0% +we have a conformational change in ef-tu +okay and then what we can have + + align:start position:0% +okay and then what we can have + + + align:start position:0% +okay and then what we can have +accommodation such that the trna is + + align:start position:0% +accommodation such that the trna is + + + align:start position:0% +accommodation such that the trna is +installed fully into the a site and then + + align:start position:0% +installed fully into the a site and then + + + align:start position:0% +installed fully into the a site and then +wrapped it peptide bond formation or + + align:start position:0% +wrapped it peptide bond formation or + + + align:start position:0% +wrapped it peptide bond formation or +peptide eel transfer the ribosome has + + align:start position:0% +peptide eel transfer the ribosome has + + + align:start position:0% +peptide eel transfer the ribosome has +one last chance to correct a mistake so + + align:start position:0% +one last chance to correct a mistake so + + + align:start position:0% +one last chance to correct a mistake so +you can imagine that after GTP + + align:start position:0% +you can imagine that after GTP + + + align:start position:0% +you can imagine that after GTP +hydrolysis after the conformational + + align:start position:0% +hydrolysis after the conformational + + + align:start position:0% +hydrolysis after the conformational +change in ef-tu and it's dissociation + + align:start position:0% +change in ef-tu and it's dissociation + + + align:start position:0% +change in ef-tu and it's dissociation +there's a last chance at rejection here + + align:start position:0% +there's a last chance at rejection here + + + align:start position:0% +there's a last chance at rejection here +okay realize that step is occurring at + + align:start position:0% +okay realize that step is occurring at + + + align:start position:0% +okay realize that step is occurring at +the expense of GTP here + + align:start position:0% + + + + align:start position:0% + +so in thinking about how to decon salute + + align:start position:0% +so in thinking about how to decon salute + + + align:start position:0% +so in thinking about how to decon salute +this model or how to design experiments + + align:start position:0% +this model or how to design experiments + + + align:start position:0% +this model or how to design experiments +to test this model there's a lot that + + align:start position:0% +to test this model there's a lot that + + + align:start position:0% +to test this model there's a lot that +needs to be done right a lot of rates + + align:start position:0% +needs to be done right a lot of rates + + + align:start position:0% +needs to be done right a lot of rates +that need to be measured a lot of + + align:start position:0% +that need to be measured a lot of + + + align:start position:0% +that need to be measured a lot of +different species along the way with the + + align:start position:0% +different species along the way with the + + + align:start position:0% +different species along the way with the +ribosome right so how do you get a + + align:start position:0% +ribosome right so how do you get a + + + align:start position:0% +ribosome right so how do you get a +readout of each of these steps that's + + align:start position:0% +readout of each of these steps that's + + + align:start position:0% +readout of each of these steps that's +what we'll be focused on in recitation + + align:start position:0% +what we'll be focused on in recitation + + + align:start position:0% +what we'll be focused on in recitation +this week and next here so here are some + + align:start position:0% +this week and next here so here are some + + + align:start position:0% +this week and next here so here are some +more details on this initial binding + + align:start position:0% +more details on this initial binding + + + align:start position:0% +more details on this initial binding +process okay with some information + + align:start position:0% +process okay with some information + + + align:start position:0% +process okay with some information +related to the K ones and K minus ones + + align:start position:0% +related to the K ones and K minus ones + + + align:start position:0% +related to the K ones and K minus ones +here that's provided to help navigate + + align:start position:0% +here that's provided to help navigate + + + align:start position:0% +here that's provided to help navigate +the reading this week for recitation + + align:start position:0% +the reading this week for recitation + + + align:start position:0% +the reading this week for recitation +here so what happens in the GTP a center + + align:start position:0% +here so what happens in the GTP a center + + + align:start position:0% +here so what happens in the GTP a center +of the FTU what are some of these + + align:start position:0% +of the FTU what are some of these + + + align:start position:0% +of the FTU what are some of these +conformational changes and effectively + + align:start position:0% +conformational changes and effectively + + + align:start position:0% +conformational changes and effectively +there are conformational changes in the + + align:start position:0% +there are conformational changes in the + + + align:start position:0% +there are conformational changes in the +decoding center that are critical on one + + align:start position:0% +decoding center that are critical on one + + + align:start position:0% +decoding center that are critical on one +hand so that's not at the GTP a center + + align:start position:0% +hand so that's not at the GTP a center + + + align:start position:0% +hand so that's not at the GTP a center +but first asking what's happening when + + align:start position:0% +but first asking what's happening when + + + align:start position:0% +but first asking what's happening when +the mRNA and T RNA codon interact and + + align:start position:0% +the mRNA and T RNA codon interact and + + + align:start position:0% +the mRNA and T RNA codon interact and +then what's happening in the GTP a + + align:start position:0% +then what's happening in the GTP a + + + align:start position:0% +then what's happening in the GTP a +center here so just to note not shown in + + align:start position:0% +center here so just to note not shown in + + + align:start position:0% +center here so just to note not shown in +the slide in terms of the gtp a center + + align:start position:0% +the slide in terms of the gtp a center + + + align:start position:0% +the slide in terms of the gtp a center +or sorry + + align:start position:0% + + + + align:start position:0% + +the decoding center okay what we need to + + align:start position:0% +the decoding center okay what we need to + + + align:start position:0% +the decoding center okay what we need to +be focusing on our changes in the 16s + + align:start position:0% + + + + align:start position:0% + +rRNA and effectively I'll just point out + + align:start position:0% +rRNA and effectively I'll just point out + + + align:start position:0% +rRNA and effectively I'll just point out +three of the positions so we have a one + + align:start position:0% +three of the positions so we have a one + + + align:start position:0% +three of the positions so we have a one +for nine to a one four nine three and G + + align:start position:0% +for nine to a one four nine three and G + + + align:start position:0% +for nine to a one four nine three and G +530 okay of the 16s here okay + + align:start position:0% +530 okay of the 16s here okay + + + align:start position:0% +530 okay of the 16s here okay +and what we find is that these bases + + align:start position:0% +and what we find is that these bases + + + align:start position:0% +and what we find is that these bases +effectively change conformation with the + + align:start position:0% +effectively change conformation with the + + + align:start position:0% +effectively change conformation with the +cognate match okay + + align:start position:0% +cognate match okay + + + align:start position:0% +cognate match okay +and they effectively flip and interact + + align:start position:0% +and they effectively flip and interact + + + align:start position:0% +and they effectively flip and interact +with that cognate anticodon okay to help + + align:start position:0% +with that cognate anticodon okay to help + + + align:start position:0% +with that cognate anticodon okay to help +stabilize the code on the anticodon + + align:start position:0% +stabilize the code on the anticodon + + + align:start position:0% +stabilize the code on the anticodon +interaction + + align:start position:0% + + + + align:start position:0% + +okay so this stabilizes the codon + + align:start position:0% +okay so this stabilizes the codon + + + align:start position:0% +okay so this stabilizes the codon +anticodon interaction and that + + align:start position:0% +anticodon interaction and that + + + align:start position:0% +anticodon interaction and that +stabilization accelerates the forward + + align:start position:0% +stabilization accelerates the forward + + + align:start position:0% +stabilization accelerates the forward +steps so that results in this + + align:start position:0% +steps so that results in this + + + align:start position:0% +steps so that results in this +acceleration of GTP hydrolysis so then + + align:start position:0% +acceleration of GTP hydrolysis so then + + + align:start position:0% +acceleration of GTP hydrolysis so then +the question is what's happening in the + + align:start position:0% +the question is what's happening in the + + + align:start position:0% +the question is what's happening in the +gtp a center of es tu because there has + + align:start position:0% +gtp a center of es tu because there has + + + align:start position:0% +gtp a center of es tu because there has +to be a change in conformation at that + + align:start position:0% +to be a change in conformation at that + + + align:start position:0% +to be a change in conformation at that +gtp a Center 70 angstroms away to allow + + align:start position:0% +gtp a Center 70 angstroms away to allow + + + align:start position:0% +gtp a Center 70 angstroms away to allow +for gtp hydrolysis to occur and somehow + + align:start position:0% +for gtp hydrolysis to occur and somehow + + + align:start position:0% +for gtp hydrolysis to occur and somehow +that all has to be signaled from here to + + align:start position:0% +that all has to be signaled from here to + + + align:start position:0% +that all has to be signaled from here to +there so what we're looking at here is + + align:start position:0% + + + + align:start position:0% + +an excerpt of the structure looking at + + align:start position:0% +an excerpt of the structure looking at + + + align:start position:0% +an excerpt of the structure looking at +this gtp a center ok and so what do we + + align:start position:0% +this gtp a center ok and so what do we + + + align:start position:0% +this gtp a center ok and so what do we +see effectively two residues so + + align:start position:0% +see effectively two residues so + + + align:start position:0% +see effectively two residues so +isoleucine 60 and valine 20 have been + + align:start position:0% +isoleucine 60 and valine 20 have been + + + align:start position:0% +isoleucine 60 and valine 20 have been +described as a hydrophobic gate in the + + align:start position:0% +described as a hydrophobic gate in the + + + align:start position:0% +described as a hydrophobic gate in the +gtp a Center okay and the idea is that + + align:start position:0% +gtp a Center okay and the idea is that + + + align:start position:0% +gtp a Center okay and the idea is that +if this gate is closed that prevents a + + align:start position:0% +if this gate is closed that prevents a + + + align:start position:0% +if this gate is closed that prevents a +certain histidine residue histidine 84 + + align:start position:0% +certain histidine residue histidine 84 + + + align:start position:0% +certain histidine residue histidine 84 +from activating a water molecule which + + align:start position:0% +from activating a water molecule which + + + align:start position:0% +from activating a water molecule which +then allows for the gtp to be hydrolyzed + + align:start position:0% +then allows for the gtp to be hydrolyzed + + + align:start position:0% +then allows for the gtp to be hydrolyzed +okay but if there's a change in + + align:start position:0% +okay but if there's a change in + + + align:start position:0% +okay but if there's a change in +conformation and this gate opens that + + align:start position:0% +conformation and this gate opens that + + + align:start position:0% +conformation and this gate opens that +chemistry can occur so what are we + + align:start position:0% +chemistry can occur so what are we + + + align:start position:0% +chemistry can occur so what are we +looking at here and these structures + + align:start position:0% +looking at here and these structures + + + align:start position:0% +looking at here and these structures +effectively here we have the two + + align:start position:0% +effectively here we have the two + + + align:start position:0% +effectively here we have the two +hydrophobic residues of the gate so + + align:start position:0% +hydrophobic residues of the gate so + + + align:start position:0% +hydrophobic residues of the gate so +valine xx isoleucine 60 and here's that + + align:start position:0% +valine xx isoleucine 60 and here's that + + + align:start position:0% +valine xx isoleucine 60 and here's that +histidine 84 I told you about and and + + align:start position:0% +histidine 84 I told you about and and + + + align:start position:0% +histidine 84 I told you about and and +what is this gdp CP so what we have + + align:start position:0% +what is this gdp CP so what we have + + + align:start position:0% +what is this gdp CP so what we have +there is a non-hydrolyzable GTP analogue + + align:start position:0% +there is a non-hydrolyzable GTP analogue + + + align:start position:0% +there is a non-hydrolyzable GTP analogue +okay these types of molecules are very + + align:start position:0% +okay these types of molecules are very + + + align:start position:0% +okay these types of molecules are very +helpful in terms of + + align:start position:0% +helpful in terms of + + + align:start position:0% +helpful in terms of +getting structural information in terms + + align:start position:0% +getting structural information in terms + + + align:start position:0% +getting structural information in terms +of doing certain types of biochemical + + align:start position:0% +of doing certain types of biochemical + + + align:start position:0% +of doing certain types of biochemical +experiments + + align:start position:0% +experiments + + + align:start position:0% +experiments +okay so effectively we can have an + + align:start position:0% +okay so effectively we can have an + + + align:start position:0% +okay so effectively we can have an +analogue bound that cannot hydrolyze + + align:start position:0% +analogue bound that cannot hydrolyze + + + align:start position:0% +analogue bound that cannot hydrolyze +what are we looking at here here we're + + align:start position:0% +what are we looking at here here we're + + + align:start position:0% +what are we looking at here here we're +looking at the say activated species and + + align:start position:0% +looking at the say activated species and + + + align:start position:0% +looking at the say activated species and +what do we see we see that this + + align:start position:0% +what do we see we see that this + + + align:start position:0% +what do we see we see that this +histidine has changed position + + align:start position:0% +histidine has changed position + + + align:start position:0% +histidine has changed position +so here it's flipped that way here this + + align:start position:0% +so here it's flipped that way here this + + + align:start position:0% +so here it's flipped that way here this +way okay and here what we see is a view + + align:start position:0% +way okay and here what we see is a view + + + align:start position:0% +way okay and here what we see is a view +with ef-tu + + align:start position:0% +with ef-tu + + + align:start position:0% +with ef-tu +in the gdp-bound form okay so the idea + + align:start position:0% +in the gdp-bound form okay so the idea + + + align:start position:0% +in the gdp-bound form okay so the idea +is that overall conformational changes + + align:start position:0% +is that overall conformational changes + + + align:start position:0% +is that overall conformational changes +that occur seventy angstroms away + + align:start position:0% +that occur seventy angstroms away + + + align:start position:0% +that occur seventy angstroms away +because of codon anticodon recognition + + align:start position:0% +because of codon anticodon recognition + + + align:start position:0% +because of codon anticodon recognition +effectively signal conformational + + align:start position:0% +effectively signal conformational + + + align:start position:0% +effectively signal conformational +changes in the GTP a center that allow + + align:start position:0% +changes in the GTP a center that allow + + + align:start position:0% +changes in the GTP a center that allow +for gtp hydrolysis to occur and things + + align:start position:0% +for gtp hydrolysis to occur and things + + + align:start position:0% +for gtp hydrolysis to occur and things +to move in the forward direction there + + align:start position:0% +to move in the forward direction there + + + align:start position:0% +to move in the forward direction there +okay so that's where we'll close for + + align:start position:0% +okay so that's where we'll close for + + + align:start position:0% +okay so that's where we'll close for +today on Friday we'll continue moving + + align:start position:0% +today on Friday we'll continue moving + + + align:start position:0% +today on Friday we'll continue moving +forward in this elongation cycle and + + align:start position:0% +forward in this elongation cycle and + + + align:start position:0% +forward in this elongation cycle and +starting in recitation tomorrow you'll + + align:start position:0% +starting in recitation tomorrow you'll + + + align:start position:0% +starting in recitation tomorrow you'll +look at experiments that allowed for + + align:start position:0% +look at experiments that allowed for + + + align:start position:0% +look at experiments that allowed for +this kinetic model to be analyzed and + + align:start position:0% +this kinetic model to be analyzed and + + + align:start position:0% +this kinetic model to be analyzed and +presented you really need to come to + + align:start position:0% +presented you really need to come to + + + align:start position:0% +presented you really need to come to +recitation this is it's a complicated + + align:start position:0% +recitation this is it's a complicated + + + align:start position:0% +recitation this is it's a complicated +paper which is why we have two weeks of + + align:start position:0% +paper which is why we have two weeks of + + + align:start position:0% +paper which is why we have two weeks of +recitation for it there's a lot of + + align:start position:0% +recitation for it there's a lot of + + + align:start position:0% +recitation for it there's a lot of +methods and I'll also point out that + + align:start position:0% +methods and I'll also point out that + + + align:start position:0% +methods and I'll also point out that +problem set 3 has very similar types of + + align:start position:0% +problem set 3 has very similar types of + + + align:start position:0% +problem set 3 has very similar types of +experiments but it's looking at EF G + + align:start position:0% +experiments but it's looking at EF G + + + align:start position:0% +experiments but it's looking at EF G +instead of ef-tu so spending the time on + + align:start position:0% +instead of ef-tu so spending the time on + + + align:start position:0% +instead of ef-tu so spending the time on +this paper in the upcoming weeks is + + align:start position:0% +this paper in the upcoming weeks is + + + align:start position:0% +this paper in the upcoming weeks is +really important + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/0pB2Wn6fvj4.txt b/0pB2Wn6fvj4.txt new file mode 100644 index 0000000000000000000000000000000000000000..a20456295f7469d3827cf7c080dd52175a19c536 --- /dev/null +++ b/0pB2Wn6fvj4.txt @@ -0,0 +1,12232 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay um social + + align:start position:0% +ocw.mit.edu okay um social + + + align:start position:0% +ocw.mit.edu okay um social +movements remind you of the picture we + + align:start position:0% +movements remind you of the picture we + + + align:start position:0% +movements remind you of the picture we +had the first day and once or twice I + + align:start position:0% +had the first day and once or twice I + + + align:start position:0% +had the first day and once or twice I +should have done it more often since but + + align:start position:0% +should have done it more often since but + + + align:start position:0% +should have done it more often since but +on the first day you know we've been + + align:start position:0% +on the first day you know we've been + + + align:start position:0% +on the first day you know we've been +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +policymaking uh we did on Monday we + + align:start position:0% +policymaking uh we did on Monday we + + + align:start position:0% +policymaking uh we did on Monday we +talked mainly about interest groups here + + align:start position:0% +talked mainly about interest groups here + + + align:start position:0% +talked mainly about interest groups here +a little bit about regulatory processes + + align:start position:0% +a little bit about regulatory processes + + + align:start position:0% +a little bit about regulatory processes +we'll come back to that uh on Wednesday + + align:start position:0% +we'll come back to that uh on Wednesday + + + align:start position:0% +we'll come back to that uh on Wednesday +but up here at the top is this vague + + align:start position:0% +but up here at the top is this vague + + + align:start position:0% +but up here at the top is this vague +sort of outside the box uh outside these + + align:start position:0% +sort of outside the box uh outside these + + + align:start position:0% +sort of outside the box uh outside these +boxes at least category of norms and + + align:start position:0% +boxes at least category of norms and + + + align:start position:0% +boxes at least category of norms and +customs and values and traditions and + + align:start position:0% +customs and values and traditions and + + + align:start position:0% +customs and values and traditions and +institutions that we had movements in + + align:start position:0% +institutions that we had movements in + + + align:start position:0% +institutions that we had movements in +there social + + align:start position:0% +there social + + + align:start position:0% +there social +movements and that's what we're going to + + align:start position:0% +movements and that's what we're going to + + + align:start position:0% +movements and that's what we're going to +talk about today we're going to talk + + align:start position:0% +talk about today we're going to talk + + + align:start position:0% +talk about today we're going to talk +about what they are how they differ from + + align:start position:0% +about what they are how they differ from + + + align:start position:0% +about what they are how they differ from +other policy actors how they + + align:start position:0% +other policy actors how they + + + align:start position:0% +other policy actors how they +work and briefly what impacts can we see + + align:start position:0% +work and briefly what impacts can we see + + + align:start position:0% +work and briefly what impacts can we see +on energy and environmental + + align:start position:0% +on energy and environmental + + + align:start position:0% +on energy and environmental +policy + + align:start position:0% +policy + + + align:start position:0% +policy +so if you think about who affects policy + + align:start position:0% +so if you think about who affects policy + + + align:start position:0% +so if you think about who affects policy +they're obviously individual firms or + + align:start position:0% +they're obviously individual firms or + + + align:start position:0% +they're obviously individual firms or +house + + align:start position:0% +house + + + align:start position:0% +house +holds and in the US setting you have to + + align:start position:0% +holds and in the US setting you have to + + + align:start position:0% +holds and in the US setting you have to +think + + align:start position:0% +think + + + align:start position:0% +think +about for federal policy you have to + + align:start position:0% +about for federal policy you have to + + + align:start position:0% +about for federal policy you have to +think about sub Federal governments and + + align:start position:0% +think about sub Federal governments and + + + align:start position:0% +think about sub Federal governments and +occasionally + + align:start position:0% +occasionally + + + align:start position:0% +occasionally +tribes what we talked about last time + + align:start position:0% +tribes what we talked about last time + + + align:start position:0% +tribes what we talked about last time +were all of these this alphabet soup of + + align:start position:0% +were all of these this alphabet soup of + + + align:start position:0% +were all of these this alphabet soup of +interest groups that you will find on K + + align:start position:0% +interest groups that you will find on K + + + align:start position:0% +interest groups that you will find on K +Street in Washington and you'll find + + align:start position:0% +Street in Washington and you'll find + + + align:start position:0% +Street in Washington and you'll find +various analoges in state capitals + + align:start position:0% +various analoges in state capitals + + + align:start position:0% +various analoges in state capitals +sometimes they fly in for those who + + align:start position:0% +sometimes they fly in for those who + + + align:start position:0% +sometimes they fly in for those who +don't live in this world that's the + + align:start position:0% +don't live in this world that's the + + + align:start position:0% +don't live in this world that's the +National Rifle Association the American + + align:start position:0% +National Rifle Association the American + + + align:start position:0% +National Rifle Association the American +Forest Products Association a the + + align:start position:0% +Forest Products Association a the + + + align:start position:0% +Forest Products Association a the +environmental defense fund the affl CIO + + align:start position:0% +environmental defense fund the affl CIO + + + align:start position:0% +environmental defense fund the affl CIO +the union organization the American + + align:start position:0% +the union organization the American + + + align:start position:0% +the union organization the American +Association of retired people which + + align:start position:0% +Association of retired people which + + + align:start position:0% +Association of retired people which +sends you mailings when you turn 50 to + + align:start position:0% +sends you mailings when you turn 50 to + + + align:start position:0% +sends you mailings when you turn 50 to +show you're really old uh the American + + align:start position:0% +show you're really old uh the American + + + align:start position:0% +show you're really old uh the American +petroleum Institute the national coal + + align:start position:0% +petroleum Institute the national coal + + + align:start position:0% +petroleum Institute the national coal +Institute and there are many + + align:start position:0% +Institute and there are many + + + align:start position:0% +Institute and there are many +more um then there are political + + align:start position:0% +more um then there are political + + + align:start position:0% +more um then there are political +parties Republican Democrat or + + align:start position:0% +parties Republican Democrat or + + + align:start position:0% +parties Republican Democrat or +Democratic depending on which party you + + align:start position:0% +Democratic depending on which party you + + + align:start position:0% +Democratic depending on which party you +affiliate with uh green parties a lot + + align:start position:0% +affiliate with uh green parties a lot + + + align:start position:0% +affiliate with uh green parties a lot +lots of places wig parties in US history + + align:start position:0% +lots of places wig parties in US history + + + align:start position:0% +lots of places wig parties in US history +plenty of other parties in various + + align:start position:0% +plenty of other parties in various + + + align:start position:0% +plenty of other parties in various +places and then social + + align:start position:0% +places and then social + + + align:start position:0% +places and then social +movements so the best way I find to + + align:start position:0% +movements so the best way I find to + + + align:start position:0% +movements so the best way I find to +think about a social movement is to + + align:start position:0% +think about a social movement is to + + + align:start position:0% +think about a social movement is to +think about + + align:start position:0% +think about + + + align:start position:0% +think about +examples so as I as I go back to my + + align:start position:0% +examples so as I as I go back to my + + + align:start position:0% +examples so as I as I go back to my +period of Consciousness there are a + + align:start position:0% +period of Consciousness there are a + + + align:start position:0% +period of Consciousness there are a +number of them that come to mind and let + + align:start position:0% +number of them that come to mind and let + + + align:start position:0% +number of them that come to mind and let +me just walk through a + + align:start position:0% +me just walk through a + + + align:start position:0% +me just walk through a +few there's the Civil Rights Movement + + align:start position:0% +few there's the Civil Rights Movement + + + align:start position:0% +few there's the Civil Rights Movement +that's the group Gathering to hear Dr + + align:start position:0% +that's the group Gathering to hear Dr + + + align:start position:0% +that's the group Gathering to hear Dr +Martin Luther King + + align:start position:0% + + + + align:start position:0% + +not all those people were paying dues to + + align:start position:0% +not all those people were paying dues to + + + align:start position:0% +not all those people were paying dues to +anything or had membership cards to + + align:start position:0% +anything or had membership cards to + + + align:start position:0% +anything or had membership cards to +anything but they had all come to + + align:start position:0% +anything but they had all come to + + + align:start position:0% +anything but they had all come to +Washington most people would probably + + align:start position:0% +Washington most people would probably + + + align:start position:0% +Washington most people would probably +call the Civil Rights Movement + + align:start position:0% +call the Civil Rights Movement + + + align:start position:0% +call the Civil Rights Movement +successful maybe + + align:start position:0% +successful maybe + + + align:start position:0% +successful maybe +not this is the anti-vietnam war + + align:start position:0% +not this is the anti-vietnam war + + + align:start position:0% +not this is the anti-vietnam war +movement um that of course is is at MIT + + align:start position:0% +movement um that of course is is at MIT + + + align:start position:0% +movement um that of course is is at MIT +this was in 1970 the picture and that's + + align:start position:0% +this was in 1970 the picture and that's + + + align:start position:0% +this was in 1970 the picture and that's +some other campus than this is + + align:start position:0% +some other campus than this is + + + align:start position:0% +some other campus than this is +Washington the picture I looked for very + + align:start position:0% +Washington the picture I looked for very + + + align:start position:0% +Washington the picture I looked for very +hard but couldn't find and I Know It + + align:start position:0% +hard but couldn't find and I Know It + + + align:start position:0% +hard but couldn't find and I Know It +exists is a picture of the then + + align:start position:0% +exists is a picture of the then + + + align:start position:0% +exists is a picture of the then +president of MIT Howard Johnson marching + + align:start position:0% +president of MIT Howard Johnson marching + + + align:start position:0% +president of MIT Howard Johnson marching +uh with a group of students down Mass + + align:start position:0% +uh with a group of students down Mass + + + align:start position:0% +uh with a group of students down Mass +Avenue with an antiwar + + align:start position:0% +Avenue with an antiwar + + + align:start position:0% +Avenue with an antiwar +Banner that movement you might call + + align:start position:0% +Banner that movement you might call + + + align:start position:0% +Banner that movement you might call +successful ultimately but I'm going to + + align:start position:0% +successful ultimately but I'm going to + + + align:start position:0% +successful ultimately but I'm going to +come back to this you might ask + + align:start position:0% +come back to this you might ask + + + align:start position:0% +come back to this you might ask +why most of those people are too young + + align:start position:0% +why most of those people are too young + + + align:start position:0% +why most of those people are too young +to + + align:start position:0% +to + + + align:start position:0% +to +vote so why was that movement successful + + align:start position:0% +vote so why was that movement successful + + + align:start position:0% +vote so why was that movement successful +or did the movement have anything to do + + align:start position:0% +or did the movement have anything to do + + + align:start position:0% +or did the movement have anything to do +with ending the war + + align:start position:0% +with ending the war + + + align:start position:0% +with ending the war +actually this is the Environmental + + align:start position:0% +actually this is the Environmental + + + align:start position:0% +actually this is the Environmental +movement that's an early rally Senator + + align:start position:0% +movement that's an early rally Senator + + + align:start position:0% +movement that's an early rally Senator +musky in Washington I think that's in + + align:start position:0% +musky in Washington I think that's in + + + align:start position:0% +musky in Washington I think that's in +Washington addressing a group and the + + align:start position:0% +Washington addressing a group and the + + + align:start position:0% +Washington addressing a group and the +tree hugger on the right I couldn't + + align:start position:0% +tree hugger on the right I couldn't + + + align:start position:0% +tree hugger on the right I couldn't +resist so there you you've got the uh + + align:start position:0% +resist so there you you've got the uh + + + align:start position:0% +resist so there you you've got the uh +the environmental movement successful + + align:start position:0% +the environmental movement successful + + + align:start position:0% +the environmental movement successful +maybe maybe not also you'll notice one + + align:start position:0% +maybe maybe not also you'll notice one + + + align:start position:0% +maybe maybe not also you'll notice one +of the interest groups I had up there + + align:start position:0% +of the interest groups I had up there + + + align:start position:0% +of the interest groups I had up there +was the environmental defense fund so + + align:start position:0% +was the environmental defense fund so + + + align:start position:0% +was the environmental defense fund so +one might want to think about where that + + align:start position:0% +one might want to think about where that + + + align:start position:0% +one might want to think about where that +boundary is and we'll come back to + + align:start position:0% +boundary is and we'll come back to + + + align:start position:0% +boundary is and we'll come back to +that the women's + + align:start position:0% +that the women's + + + align:start position:0% +that the women's +movement you see there the I think + + align:start position:0% +movement you see there the I think + + + align:start position:0% +movement you see there the I think +that's the + + align:start position:0% +that's the + + + align:start position:0% +that's the +entirety of the Equal Rights + + align:start position:0% +entirety of the Equal Rights + + + align:start position:0% +entirety of the Equal Rights +Amendment for which there was also + + align:start position:0% + + + + align:start position:0% + +opposition as regards the Equal Rights + + align:start position:0% +opposition as regards the Equal Rights + + + align:start position:0% +opposition as regards the Equal Rights +Amendment You could argue that was + + align:start position:0% +Amendment You could argue that was + + + align:start position:0% +Amendment You could argue that was +pretty successful those you don't see + + align:start position:0% +pretty successful those you don't see + + + align:start position:0% +pretty successful those you don't see +votes like that anymore + + align:start position:0% +votes like that anymore + + + align:start position:0% +votes like that anymore +the Equal Rights Amendment phrased on + + align:start position:0% +the Equal Rights Amendment phrased on + + + align:start position:0% +the Equal Rights Amendment phrased on +the left passed the house in 1972 354 to + + align:start position:0% +the left passed the house in 1972 354 to + + + align:start position:0% +the left passed the house in 1972 354 to +24 in the Senate 84 + + align:start position:0% +24 in the Senate 84 + + + align:start position:0% +24 in the Senate 84 +to8 that + + align:start position:0% +to8 that + + + align:start position:0% +to8 that +means there were a lot of Republican + + align:start position:0% +means there were a lot of Republican + + + align:start position:0% +means there were a lot of Republican +votes for + + align:start position:0% + + + + align:start position:0% + +it 30 states ratified it by the end of + + align:start position:0% +it 30 states ratified it by the end of + + + align:start position:0% +it 30 states ratified it by the end of +1973 but it + + align:start position:0% +1973 but it + + + align:start position:0% +1973 but it +failed they needed 38 to pass it got 35 + + align:start position:0% +failed they needed 38 to pass it got 35 + + + align:start position:0% +failed they needed 38 to pass it got 35 +By 1979 never got the 30 all of the + + align:start position:0% +By 1979 never got the 30 all of the + + + align:start position:0% +By 1979 never got the 30 all of the +pieces of leg just all of these + + align:start position:0% +pieces of leg just all of these + + + align:start position:0% +pieces of leg just all of these +Amendments have a deadline for + + align:start position:0% +Amendments have a deadline for + + + align:start position:0% +Amendments have a deadline for +ratification the deadline here was 79 + + align:start position:0% +ratification the deadline here was 79 + + + align:start position:0% +ratification the deadline here was 79 +and it didn't make it and some states + + align:start position:0% +and it didn't make it and some states + + + align:start position:0% +and it didn't make it and some states +rescinded + + align:start position:0% +rescinded + + + align:start position:0% +rescinded +ratification and I don't think you could + + align:start position:0% +ratification and I don't think you could + + + align:start position:0% +ratification and I don't think you could +get that I don't think you could get + + align:start position:0% +get that I don't think you could get + + + align:start position:0% +get that I don't think you could get +that Amendment voted on in Congress now + + align:start position:0% +that Amendment voted on in Congress now + + + align:start position:0% +that Amendment voted on in Congress now +let alone passed so you got to ask was + + align:start position:0% +let alone passed so you got to ask was + + + align:start position:0% +let alone passed so you got to ask was +that movement + + align:start position:0% +that movement + + + align:start position:0% +that movement +successful that was a movement I mean + + align:start position:0% +successful that was a movement I mean + + + align:start position:0% +successful that was a movement I mean +you got troops turning out you got + + align:start position:0% +you got troops turning out you got + + + align:start position:0% +you got troops turning out you got +rallies you got an anti- movement was + + align:start position:0% +rallies you got an anti- movement was + + + align:start position:0% +rallies you got an anti- movement was +that movement successful what did it + + align:start position:0% +that movement successful what did it + + + align:start position:0% +that movement successful what did it +do this is a more recent one you may + + align:start position:0% +do this is a more recent one you may + + + align:start position:0% +do this is a more recent one you may +recall the meetings of the World Trade + + align:start position:0% +recall the meetings of the World Trade + + + align:start position:0% +recall the meetings of the World Trade +Organization the international + + align:start position:0% +Organization the international + + + align:start position:0% +Organization the international +organization that basically sets trading + + align:start position:0% +organization that basically sets trading + + + align:start position:0% +organization that basically sets trading +rules for international trade um for a + + align:start position:0% +rules for international trade um for a + + + align:start position:0% +rules for international trade um for a +period those meetings were dangerous I + + align:start position:0% +period those meetings were dangerous I + + + align:start position:0% +period those meetings were dangerous I +don't know whether this is the one in + + align:start position:0% +don't know whether this is the one in + + + align:start position:0% +don't know whether this is the one in +Seattle but downtown Seattle got sort of + + align:start position:0% +Seattle but downtown Seattle got sort of + + + align:start position:0% +Seattle but downtown Seattle got sort of +Trashed by people who were protesting + + align:start position:0% +Trashed by people who were protesting + + + align:start position:0% +Trashed by people who were protesting +globalization protesting the WTO which + + align:start position:0% +globalization protesting the WTO which + + + align:start position:0% +globalization protesting the WTO which +is a bunch of bureaucrats who deal with + + align:start position:0% +is a bunch of bureaucrats who deal with + + + align:start position:0% +is a bunch of bureaucrats who deal with +trade + + align:start position:0% +trade + + + align:start position:0% +trade +disputes um and Associated it with + + align:start position:0% +disputes um and Associated it with + + + align:start position:0% +disputes um and Associated it with +global + + align:start position:0% +global + + + align:start position:0% +global +Injustice uh + + align:start position:0% +Injustice uh + + + align:start position:0% +Injustice uh + + align:start position:0% + + + align:start position:0% +um that movement failed I think that's + + align:start position:0% +um that movement failed I think that's + + + align:start position:0% +um that movement failed I think that's +fair to + + align:start position:0% +fair to + + + align:start position:0% +fair to +say right we have globalized uh trade + + align:start position:0% +say right we have globalized uh trade + + + align:start position:0% +say right we have globalized uh trade +has not turned back and that movement is + + align:start position:0% +has not turned back and that movement is + + + align:start position:0% +has not turned back and that movement is +pretty much vanished how come how come + + align:start position:0% +pretty much vanished how come how come + + + align:start position:0% +pretty much vanished how come how come +some succeed and some + + align:start position:0% +some succeed and some + + + align:start position:0% +some succeed and some +fail this is the anti-nuclear movement + + align:start position:0% +fail this is the anti-nuclear movement + + + align:start position:0% +fail this is the anti-nuclear movement +this is international this is is a + + align:start position:0% +this is international this is is a + + + align:start position:0% +this is international this is is a +that's Germany atom craft n Danka that's + + align:start position:0% +that's Germany atom craft n Danka that's + + + align:start position:0% +that's Germany atom craft n Danka that's +Japan and that of course is + + align:start position:0% +Japan and that of course is + + + align:start position:0% +Japan and that of course is +Vermont where the future of the Vermont + + align:start position:0% +Vermont where the future of the Vermont + + + align:start position:0% +Vermont where the future of the Vermont +Yankee nuclear plant is much + + align:start position:0% +Yankee nuclear plant is much + + + align:start position:0% +Yankee nuclear plant is much +debated is that movement successful that + + align:start position:0% +debated is that movement successful that + + + align:start position:0% +debated is that movement successful that +movement started well I'm going to come + + align:start position:0% +movement started well I'm going to come + + + align:start position:0% +movement started well I'm going to come +back to that movement because we'll talk + + align:start position:0% +back to that movement because we'll talk + + + align:start position:0% +back to that movement because we'll talk +about that actually at some length but + + align:start position:0% +about that actually at some length but + + + align:start position:0% +about that actually at some length but +that movement is + + align:start position:0% +that movement is + + + align:start position:0% +that movement is +global a lot of power plants have been + + align:start position:0% +global a lot of power plants have been + + + align:start position:0% +global a lot of power plants have been +built since that movement started + + align:start position:0% +built since that movement started + + + align:start position:0% +built since that movement started +a lot of nuclear + + align:start position:0% +a lot of nuclear + + + align:start position:0% +a lot of nuclear +plants still active this is the anti + + align:start position:0% +plants still active this is the anti + + + align:start position:0% +plants still active this is the anti +fracking movement more recently that's + + align:start position:0% +fracking movement more recently that's + + + align:start position:0% +fracking movement more recently that's +New York as you see that's somewhere in + + align:start position:0% +New York as you see that's somewhere in + + + align:start position:0% +New York as you see that's somewhere in +Paris and that I believe is + + align:start position:0% +Paris and that I believe is + + + align:start position:0% +Paris and that I believe is +Bulgaria uh so it it like the + + align:start position:0% +Bulgaria uh so it it like the + + + align:start position:0% +Bulgaria uh so it it like the +anti-nuclear movement is fairly broad + + align:start position:0% +anti-nuclear movement is fairly broad + + + align:start position:0% +anti-nuclear movement is fairly broad +geographically has succeeded in some + + align:start position:0% +geographically has succeeded in some + + + align:start position:0% +geographically has succeeded in some +places exceeded at least tentatively in + + align:start position:0% +places exceeded at least tentatively in + + + align:start position:0% +places exceeded at least tentatively in +New York and in France I have no idea + + align:start position:0% +New York and in France I have no idea + + + align:start position:0% +New York and in France I have no idea +what the status is in bulgar + + align:start position:0% +what the status is in bulgar + + + align:start position:0% +what the status is in bulgar +area + + align:start position:0% +area + + + align:start position:0% +area +um the Tea Party Movement look at those + + align:start position:0% +um the Tea Party Movement look at those + + + align:start position:0% +um the Tea Party Movement look at those +numbers as the Tea Party Movement + + align:start position:0% +numbers as the Tea Party Movement + + + align:start position:0% +numbers as the Tea Party Movement +succeeded will the Tea Party Movement + + align:start position:0% +succeeded will the Tea Party Movement + + + align:start position:0% +succeeded will the Tea Party Movement +last how does the Tea Party Movement + + align:start position:0% +last how does the Tea Party Movement + + + align:start position:0% +last how does the Tea Party Movement +work and of course on the other side by + + align:start position:0% +work and of course on the other side by + + + align:start position:0% +work and of course on the other side by +the way that's impressive that's + + align:start position:0% +the way that's impressive that's + + + align:start position:0% +the way that's impressive that's +Washington um that's Pennsylvania Avenue + + align:start position:0% +Washington um that's Pennsylvania Avenue + + + align:start position:0% +Washington um that's Pennsylvania Avenue +full of people uh this is the opposite + + align:start position:0% +full of people uh this is the opposite + + + align:start position:0% +full of people uh this is the opposite +side of the coin the Occupy + + align:start position:0% +side of the coin the Occupy + + + align:start position:0% +side of the coin the Occupy +Movement + + align:start position:0% +Movement + + + align:start position:0% +Movement +again jobs not Cuts whereas + + align:start position:0% + + + + align:start position:0% + +the that we want less over + + align:start position:0% +the that we want less over + + + align:start position:0% +the that we want less over +here and jobs not Cuts over here so you + + align:start position:0% +here and jobs not Cuts over here so you + + + align:start position:0% +here and jobs not Cuts over here so you +have two opposed social movements as we + + align:start position:0% + + + + align:start position:0% + +speak and then most dramatically this is + + align:start position:0% +speak and then most dramatically this is + + + align:start position:0% +speak and then most dramatically this is +a good time for this topic most + + align:start position:0% +a good time for this topic most + + + align:start position:0% +a good time for this topic most +dramatically the Arab + + align:start position:0% +dramatically the Arab + + + align:start position:0% +dramatically the Arab +Spring so as you go around + + align:start position:0% +Spring so as you go around + + + align:start position:0% +Spring so as you go around +there's tarir Square in Egypt there's + + align:start position:0% +there's tarir Square in Egypt there's + + + align:start position:0% +there's tarir Square in Egypt there's +Tunisia there's + + align:start position:0% +Tunisia there's + + + align:start position:0% +Tunisia there's +Yemen government toppled government + + align:start position:0% +Yemen government toppled government + + + align:start position:0% +Yemen government toppled government +toppled government toppled Bahrain + + align:start position:0% +toppled government toppled Bahrain + + + align:start position:0% +toppled government toppled Bahrain +protest + + align:start position:0% +protest + + + align:start position:0% +protest +continuing uh Syria civil war Libya + + align:start position:0% +continuing uh Syria civil war Libya + + + align:start position:0% +continuing uh Syria civil war Libya +government + + align:start position:0% +government + + + align:start position:0% +government +toppled social + + align:start position:0% + + + + align:start position:0% + +movements okay there are a lot of them + + align:start position:0% +movements okay there are a lot of them + + + align:start position:0% +movements okay there are a lot of them +this is just one slice of History a + + align:start position:0% +this is just one slice of History a + + + align:start position:0% +this is just one slice of History a +recent slice of History uh I'm going to + + align:start position:0% +recent slice of History uh I'm going to + + + align:start position:0% +recent slice of History uh I'm going to +come back and talk about some of + + align:start position:0% +come back and talk about some of + + + align:start position:0% +come back and talk about some of +them but the first thing we ought to + + align:start position:0% +them but the first thing we ought to + + + align:start position:0% +them but the first thing we ought to +worry about is + + align:start position:0% +worry about is + + + align:start position:0% +worry about is +um how what are these things how do how + + align:start position:0% +um how what are these things how do how + + + align:start position:0% +um how what are these things how do how +are they distinct from other other + + align:start position:0% +are they distinct from other other + + + align:start position:0% +are they distinct from other other +actors certainly they're trying to + + align:start position:0% +actors certainly they're trying to + + + align:start position:0% +actors certainly they're trying to +influence + + align:start position:0% +influence + + + align:start position:0% +influence +policy that's what they're there + + align:start position:0% +policy that's what they're there + + + align:start position:0% +policy that's what they're there +for not always in a coherent way not + + align:start position:0% +for not always in a coherent way not + + + align:start position:0% +for not always in a coherent way not +always in a well-defined way the + + align:start position:0% +always in a well-defined way the + + + align:start position:0% +always in a well-defined way the +anti-globalist ization + + align:start position:0% +anti-globalist ization + + + align:start position:0% +anti-globalist ization +movement what exactly did they + + align:start position:0% +movement what exactly did they + + + align:start position:0% +movement what exactly did they +want what's the Occupy Movement want but + + align:start position:0% +want what's the Occupy Movement want but + + + align:start position:0% +want what's the Occupy Movement want but +in any case they're trying to not + + align:start position:0% +in any case they're trying to not + + + align:start position:0% +in any case they're trying to not +necessarily with a specific agenda but + + align:start position:0% +necessarily with a specific agenda but + + + align:start position:0% +necessarily with a specific agenda but +they're trying to have some + + align:start position:0% + + + + align:start position:0% + +influence this is easy I listed these + + align:start position:0% +influence this is easy I listed these + + + align:start position:0% +influence this is easy I listed these +actors at the start they're not a formal + + align:start position:0% +actors at the start they're not a formal + + + align:start position:0% +actors at the start they're not a formal +part of the process they're not on the + + align:start position:0% +part of the process they're not on the + + + align:start position:0% +part of the process they're not on the +ballot they're not registered they don't + + align:start position:0% +ballot they're not registered they don't + + + align:start position:0% +ballot they're not registered they don't +they don't have National committees and + + align:start position:0% +they don't have National committees and + + + align:start position:0% +they don't have National committees and +slates of + + align:start position:0% +slates of + + + align:start position:0% +slates of +candidates + + align:start position:0% + + + + align:start position:0% + +formally the boundary between a social + + align:start position:0% +formally the boundary between a social + + + align:start position:0% +formally the boundary between a social +movement and an interest group though + + align:start position:0% +movement and an interest group though + + + align:start position:0% +movement and an interest group though +and Burstein talks about this is a + + align:start position:0% +and Burstein talks about this is a + + + align:start position:0% +and Burstein talks about this is a +little blurrier right + + align:start position:0% +little blurrier right + + + align:start position:0% +little blurrier right +um Loy whom we read earlier has this + + align:start position:0% +um Loy whom we read earlier has this + + + align:start position:0% +um Loy whom we read earlier has this +this italicized phrase which is sort of + + align:start position:0% +this italicized phrase which is sort of + + + align:start position:0% +this italicized phrase which is sort of +interesting all established interest + + align:start position:0% +interesting all established interest + + + align:start position:0% +interesting all established interest +groups are + + align:start position:0% +groups are + + + align:start position:0% +groups are +conservative and he means conservative + + align:start position:0% +conservative and he means conservative + + + align:start position:0% +conservative and he means conservative +not in the sense + + align:start position:0% +not in the sense + + + align:start position:0% +not in the sense +of uh left right in the sense of less + + align:start position:0% +of uh left right in the sense of less + + + align:start position:0% +of uh left right in the sense of less +government more government but in the + + align:start position:0% +government more government but in the + + + align:start position:0% +government more government but in the +oldfashioned sense of less change more + + align:start position:0% +oldfashioned sense of less change more + + + align:start position:0% +oldfashioned sense of less change more +change so he means they are conservative + + align:start position:0% +change so he means they are conservative + + + align:start position:0% +change so he means they are conservative +in the sense that interest groups tend + + align:start position:0% +in the sense that interest groups tend + + + align:start position:0% +in the sense that interest groups tend +to resist radical change they're part of + + align:start position:0% +to resist radical change they're part of + + + align:start position:0% +to resist radical change they're part of +the system the American Forest Products + + align:start position:0% +the system the American Forest Products + + + align:start position:0% +the system the American Forest Products +Association has some laws it likes has + + align:start position:0% +Association has some laws it likes has + + + align:start position:0% +Association has some laws it likes has +some laws it doesn't like lobbies here + + align:start position:0% +some laws it doesn't like lobbies here + + + align:start position:0% +some laws it doesn't like lobbies here +lobbies there if you said let's + + align:start position:0% +lobbies there if you said let's + + + align:start position:0% +lobbies there if you said let's +fundamentally 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has members + + align:start position:0% +environmental defense fund has members + + + align:start position:0% +environmental defense fund has members +has a budget has offices has + + align:start position:0% +has a budget has offices has + + + align:start position:0% +has a budget has offices has +lobbyists uh writes papers they do + + align:start position:0% +lobbyists uh writes papers they do + + + align:start position:0% +lobbyists uh writes papers they do +routine + + align:start position:0% +routine + + + align:start position:0% +routine +influence they Lobby they enter briefs + + align:start position:0% +influence they Lobby they enter briefs + + + align:start position:0% +influence they Lobby they enter briefs +in court they send in + + align:start position:0% + + + + align:start position:0% + +petitions social movements tend to be on + + align:start position:0% +petitions social movements tend to be on + + + align:start position:0% +petitions social movements tend to be on +the + + align:start position:0% +the + + + align:start position:0% +the +margins tend to be be on the margins of + + align:start position:0% +margins tend to be be on the margins of + + + align:start position:0% +margins tend to be be on the margins of +the system membership is not well + + align:start position:0% +the system membership is not well + + + align:start position:0% +the system membership is not well +defined who is a member of the Civil + + align:start position:0% +defined who is a member of the Civil + + + align:start position:0% +defined who is a member of the Civil +Rights Movement who was a member of the + + align:start position:0% +Rights Movement who was a member of the + + + align:start position:0% +Rights Movement who was a member of the +anti-war movement anti Vietnam movement + + align:start position:0% +anti-war movement anti Vietnam movement + + + align:start position:0% +anti-war movement anti Vietnam movement +almost everybody I knew did something + + align:start position:0% +almost everybody I knew did something + + + align:start position:0% +almost everybody I knew did something +none of us had + + align:start position:0% +none of us had + + + align:start position:0% +none of us had +cards um and they tend to engage in what + + align:start position:0% +cards um and they tend to engage in what + + + align:start position:0% +cards um and they tend to engage in what +you'd call non-routine actions like + + align:start position:0% +you'd call non-routine actions like + + + align:start position:0% +you'd call non-routine actions like +marches and demonstrations and chaining + + align:start position:0% +marches and demonstrations and chaining + + + align:start position:0% +marches and demonstrations and chaining +themselves to fences and all of that + + align:start position:0% +themselves to fences and all of that + + + align:start position:0% +themselves to fences and all of that +stuff they vary resources organization + + align:start position:0% +stuff they vary resources organization + + + align:start position:0% +stuff they vary resources organization +tactics Green Piece is an interesting + + align:start position:0% +tactics Green Piece is an interesting + + + align:start position:0% +tactics Green Piece is an interesting +example right Green Piece is noted for + + align:start position:0% +example right Green Piece is noted for + + + align:start position:0% +example right Green Piece is noted for +its anti- wailing activities has + + align:start position:0% +its anti- wailing activities has + + + align:start position:0% +its anti- wailing activities has +ships intercepts interferes with wailing + + align:start position:0% +ships intercepts interferes with wailing + + + align:start position:0% +ships intercepts interferes with wailing +that's a non-routine action it also has + + align:start position:0% +that's a non-routine action it also has + + + align:start position:0% +that's a non-routine action it also has +lobbyists in various in various capitals + + align:start position:0% +lobbyists in various in various capitals + + + align:start position:0% +lobbyists in various in various capitals +to push for various things so Greenpeace + + align:start position:0% +to push for various things so Greenpeace + + + align:start position:0% +to push for various things so Greenpeace +sort + + align:start position:0% +sort + + + align:start position:0% +sort +of is an interest group in the sense of + + align:start position:0% +of is an interest group in the sense of + + + align:start position:0% +of is an interest group in the sense of +being organized and having members and + + align:start position:0% +being organized and having members and + + + align:start position:0% +being organized and having members and +dos and + + align:start position:0% +dos and + + + align:start position:0% +dos and +stuff but + + align:start position:0% +stuff but + + + align:start position:0% +stuff but +it's it also engages in non-standard + + align:start position:0% +it's it also engages in non-standard + + + align:start position:0% +it's it also engages in non-standard +tactics so + + align:start position:0% +tactics so + + + align:start position:0% +tactics so +but all of the example social movements + + align:start position:0% +but all of the example social movements + + + align:start position:0% +but all of the example social movements +I had tend to + + align:start position:0% +I had tend to + + + align:start position:0% +I had tend to +be without a defined + + align:start position:0% +be without a defined + + + align:start position:0% +be without a defined +membership who was part of the Arab + + align:start position:0% +membership who was part of the Arab + + + align:start position:0% +membership who was part of the Arab +Spring varied from day to day who showed + + align:start position:0% +Spring varied from day to day who showed + + + align:start position:0% +Spring varied from day to day who showed +up for the + + align:start position:0% +up for the + + + align:start position:0% +up for the +demonstrations who's part of the the + + align:start position:0% +demonstrations who's part of the the + + + align:start position:0% +demonstrations who's part of the the +anti-putin movement to the extent it is + + align:start position:0% +anti-putin movement to the extent it is + + + align:start position:0% +anti-putin movement to the extent it is +a movement in Russia who + + align:start position:0% +a movement in Russia who + + + align:start position:0% +a movement in Russia who +comes um who was part of the the + + align:start position:0% +comes um who was part of the the + + + align:start position:0% +comes um who was part of the the +anti-war movement who was part of the + + align:start position:0% +anti-war movement who was part of the + + + align:start position:0% +anti-war movement who was part of the +Civil Rights Movement so the membership + + align:start position:0% +Civil Rights Movement so the membership + + + align:start position:0% +Civil Rights Movement so the membership +tends to be unclear the actions tend to + + align:start position:0% +tends to be unclear the actions tend to + + + align:start position:0% +tends to be unclear the actions tend to +be + + align:start position:0% +be + + + align:start position:0% +be +non-standard the anti-vietnam movement + + align:start position:0% +non-standard the anti-vietnam movement + + + align:start position:0% +non-standard the anti-vietnam movement +did engage in massive letter writing + + align:start position:0% +did engage in massive letter writing + + + align:start position:0% +did engage in massive letter writing +campaigns which is pretty + + align:start position:0% +campaigns which is pretty + + + align:start position:0% +campaigns which is pretty +standard but it also occupied the MIT + + align:start position:0% +standard but it also occupied the MIT + + + align:start position:0% +standard but it also occupied the MIT +president's office and various other + + align:start position:0% +president's office and various other + + + align:start position:0% +president's office and various other +university president's offices which is + + align:start position:0% +university president's offices which is + + + align:start position:0% +university president's offices which is +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +non-standard so it's a it's a + + align:start position:0% +non-standard so it's a it's a + + + align:start position:0% +non-standard so it's a it's a +mixture thoughts about this so + + align:start position:0% +mixture thoughts about this so + + + align:start position:0% +mixture thoughts about this so +far + + align:start position:0% +far + + + align:start position:0% +far +okay so how do they work when they + + align:start position:0% +okay so how do they work when they + + + align:start position:0% +okay so how do they work when they +work how might any of these affect + + align:start position:0% +work how might any of these affect + + + align:start position:0% +work how might any of these affect +public + + align:start position:0% +public + + + align:start position:0% +public +policy what are the mechanisms why do + + align:start position:0% +policy what are the mechanisms why do + + + align:start position:0% +policy what are the mechanisms why do +they matter why do they ever + + align:start position:0% +they matter why do they ever + + + align:start position:0% +they matter why do they ever +matter what are they + + align:start position:0% +matter what are they + + + align:start position:0% +matter what are they +doing + + align:start position:0% +doing + + + align:start position:0% +doing +yeah sometimes it's trying to show that + + align:start position:0% +yeah sometimes it's trying to show that + + + align:start position:0% +yeah sometimes it's trying to show that +if a politician does something with + + align:start position:0% +if a politician does something with + + + align:start position:0% +if a politician does something with +these social movements or back something + + align:start position:0% +these social movements or back something + + + align:start position:0% +these social movements or back something +the social movements find distasteful + + align:start position:0% +the social movements find distasteful + + + align:start position:0% +the social movements find distasteful +unpopular + + align:start position:0% +unpopular + + + align:start position:0% +unpopular +people will be disp them less likely to + + align:start position:0% +people will be disp them less likely to + + + align:start position:0% +people will be disp them less likely to +get + + align:start position:0% +get + + + align:start position:0% +get +elected recent example might be that so + + align:start position:0% +elected recent example might be that so + + + align:start position:0% +elected recent example might be that so +Bill people made it very clear that this + + align:start position:0% +Bill people made it very clear that this + + + align:start position:0% +Bill people made it very clear that this +is not something they supported and so + + align:start position:0% +is not something they supported and so + + + align:start position:0% +is not something they supported and so +politicians back so one mechanism is in + + align:start position:0% +politicians back so one mechanism is in + + + align:start position:0% +politicians back so one mechanism is in +a sense they provide information or they + + align:start position:0% + + + + align:start position:0% + +demonstrate + + align:start position:0% + + + + align:start position:0% + +salience salience salience is + + align:start position:0% + + + + align:start position:0% + +awareness so an issue is Salient to me + + align:start position:0% +awareness so an issue is Salient to me + + + align:start position:0% +awareness so an issue is Salient to me +if I'm aware of it and I consider it + + align:start position:0% +if I'm aware of it and I consider it + + + align:start position:0% +if I'm aware of it and I consider it +important so you could argue that the + + align:start position:0% +important so you could argue that the + + + align:start position:0% +important so you could argue that the +anti-vietnam protests made it + + align:start position:0% +anti-vietnam protests made it + + + align:start position:0% +anti-vietnam protests made it +clear that to at least a segment of the + + align:start position:0% +clear that to at least a segment of the + + + align:start position:0% +clear that to at least a segment of the +population all of us who could get + + align:start position:0% +population all of us who could get + + + align:start position:0% +population all of us who could get +drafted uh we were very aware of what + + align:start position:0% +drafted uh we were very aware of what + + + align:start position:0% +drafted uh we were very aware of what +was going on it was very important us we + + align:start position:0% +was going on it was very important us we + + + align:start position:0% +was going on it was very important us we +felt strongly okay so they can provide + + align:start position:0% +felt strongly okay so they can provide + + + align:start position:0% +felt strongly okay so they can provide +information about salience about the + + align:start position:0% +information about salience about the + + + align:start position:0% +information about salience about the +population's feelings how else might it + + align:start position:0% +population's feelings how else might it + + + align:start position:0% +population's feelings how else might it +work yeah Brendan you just Mo not + + align:start position:0% +work yeah Brendan you just Mo not + + + align:start position:0% +work yeah Brendan you just Mo not +necessarily motivate politician motivate + + align:start position:0% +necessarily motivate politician motivate + + + align:start position:0% +necessarily motivate politician motivate +other people like you know to like come + + align:start position:0% +other people like you know to like come + + + align:start position:0% +other people like you know to like come +on board so you + + align:start position:0% + + + + align:start position:0% + +might well there are two ways you might + + align:start position:0% +might well there are two ways you might + + + align:start position:0% +might well there are two ways you might +do + + align:start position:0% +do + + + align:start position:0% +do +that + + align:start position:0% +that + + + align:start position:0% +that +right one way is to change + + align:start position:0% + + + + align:start position:0% + +preferences right you could you could + + align:start position:0% +preferences right you could you could + + + align:start position:0% +preferences right you could you could +persuade people that by getting them to + + align:start position:0% +persuade people that by getting them to + + + align:start position:0% +persuade people that by getting them to +think about it that this group is right + + align:start position:0% +think about it that this group is right + + + align:start position:0% +think about it that this group is right +you could argue that was a large part of + + align:start position:0% +you could argue that was a large part of + + + align:start position:0% +you could argue that was a large part of +what Martin Luther King + + align:start position:0% +what Martin Luther King + + + align:start position:0% +what Martin Luther King +did uh and this the effective leadership + + align:start position:0% +did uh and this the effective leadership + + + align:start position:0% +did uh and this the effective leadership +of the Civil Rights Movement it + + align:start position:0% +of the Civil Rights Movement it + + + align:start position:0% +of the Civil Rights Movement it +persuaded a lot of people that the + + align:start position:0% +persuaded a lot of people that the + + + align:start position:0% +persuaded a lot of people that the +current state of Affairs was just wrong + + align:start position:0% +current state of Affairs was just wrong + + + align:start position:0% +current state of Affairs was just wrong +full stop + + align:start position:0% +full stop + + + align:start position:0% +full stop +wrong um it blurs with uh raay + + align:start position:0% + + + + align:start position:0% + +salans I think these two are are hard to + + align:start position:0% +salans I think these two are are hard to + + + align:start position:0% +salans I think these two are are hard to +separate right because because it it + + align:start position:0% +separate right because because it it + + + align:start position:0% +separate right because because it it +could be that an awful lot of people in + + align:start position:0% +could be that an awful lot of people in + + + align:start position:0% +could be that an awful lot of people in +the north were unaware of just how + + align:start position:0% +the north were unaware of just how + + + align:start position:0% +the north were unaware of just how +segregated The South + + align:start position:0% +segregated The South + + + align:start position:0% +segregated The South +was so you made people aware of it by by + + align:start position:0% +was so you made people aware of it by by + + + align:start position:0% +was so you made people aware of it by by +increasing + + align:start position:0% +increasing + + + align:start position:0% +increasing +awareness that works of course if they + + align:start position:0% +awareness that works of course if they + + + align:start position:0% +awareness that works of course if they +agree with you Charlotte I think that + + align:start position:0% +agree with you Charlotte I think that + + + align:start position:0% +agree with you Charlotte I think that +like going along with the trend of + + align:start position:0% +like going along with the trend of + + + align:start position:0% +like going along with the trend of +getting more people involved just having + + align:start position:0% +getting more people involved just having + + + align:start position:0% +getting more people involved just having +a group uh makes people who already have + + align:start position:0% +a group uh makes people who already have + + + align:start position:0% +a group uh makes people who already have +that belief maybe are already aware of + + align:start position:0% +that belief maybe are already aware of + + + align:start position:0% +that belief maybe are already aware of +the issue but just unaware of how they + + align:start position:0% +the issue but just unaware of how they + + + align:start position:0% +the issue but just unaware of how they +could affect it like join together and + + align:start position:0% +could affect it like join together and + + + align:start position:0% +could affect it like join together and +then it makes kind of more powerful just + + align:start position:0% +then it makes kind of more powerful just + + + align:start position:0% +then it makes kind of more powerful just +because they're more bodies so this is + + align:start position:0% +because they're more bodies so this is + + + align:start position:0% +because they're more bodies so this is +like attract people I guess + + align:start position:0% +like attract people I guess + + + align:start position:0% +like attract people I guess +like + + align:start position:0% +like + + + align:start position:0% +like +the yeah yeah the model bursting has is + + align:start position:0% +the yeah yeah the model bursting has is + + + align:start position:0% +the yeah yeah the model bursting has is +that works if it makes a politic + + align:start position:0% +that works if it makes a politic + + + align:start position:0% +that works if it makes a politic +rethink um rethink their um uh prospects + + align:start position:0% +rethink um rethink their um uh prospects + + + align:start position:0% +rethink um rethink their um uh prospects +and so I guess i' I'd sort of put that + + align:start position:0% +and so I guess i' I'd sort of put that + + + align:start position:0% +and so I guess i' I'd sort of put that +one in a way here but you'd say it not + + align:start position:0% +one in a way here but you'd say it not + + + align:start position:0% +one in a way here but you'd say it not +only demonstrates to politicians that a + + align:start position:0% +only demonstrates to politicians that a + + + align:start position:0% +only demonstrates to politicians that a +lot of people care about it demonstrates + + align:start position:0% +lot of people care about it demonstrates + + + align:start position:0% +lot of people care about it demonstrates +to a lot of other people that people + + align:start position:0% +to a lot of other people that people + + + align:start position:0% +to a lot of other people that people +care about it and that's a lot of the + + align:start position:0% +care about it and that's a lot of the + + + align:start position:0% +care about it and that's a lot of the +story of the Arab Spring I think is you + + align:start position:0% +story of the Arab Spring I think is you + + + align:start position:0% +story of the Arab Spring I think is you +got a few people who are just + + align:start position:0% +got a few people who are just + + + align:start position:0% +got a few people who are just +sufficiently outraged that they would + + align:start position:0% +sufficiently outraged that they would + + + align:start position:0% +sufficiently outraged that they would +risk getting shot at and other people + + align:start position:0% +risk getting shot at and other people + + + align:start position:0% +risk getting shot at and other people +say said well I feel that way too and if + + align:start position:0% +say said well I feel that way too and if + + + align:start position:0% +say said well I feel that way too and if +they're going to do that maybe I should + + align:start position:0% +they're going to do that maybe I should + + + align:start position:0% +they're going to do that maybe I should +do that um and at some point you + + align:start position:0% +do that um and at some point you + + + align:start position:0% +do that um and at some point you +demonstrate to the regime that it it + + align:start position:0% +demonstrate to the regime that it it + + + align:start position:0% +demonstrate to the regime that it it +lacks popular + + align:start position:0% +lacks popular + + + align:start position:0% +lacks popular +support and regimes that aren't + + align:start position:0% +support and regimes that aren't + + + align:start position:0% +support and regimes that aren't +Democratic tend to not have much idea + + align:start position:0% +Democratic tend to not have much idea + + + align:start position:0% +Democratic tend to not have much idea +how much support they have and it's easy + + align:start position:0% +how much support they have and it's easy + + + align:start position:0% +how much support they have and it's easy +to exaggerate how much support you have + + align:start position:0% +to exaggerate how much support you have + + + align:start position:0% +to exaggerate how much support you have +because every time you go out in public + + align:start position:0% +because every time you go out in public + + + align:start position:0% +because every time you go out in public +and have a parade people + + align:start position:0% +and have a parade people + + + align:start position:0% +and have a parade people +cheer because they why wouldn't you + + align:start position:0% +cheer because they why wouldn't you + + + align:start position:0% +cheer because they why wouldn't you +cheer uh the dictators going by so + + align:start position:0% +cheer uh the dictators going by so + + + align:start position:0% +cheer uh the dictators going by so +that's interesting you can say sort of + + align:start position:0% +that's interesting you can say sort of + + + align:start position:0% +that's interesting you can say sort of +rallies people um and I think those are + + align:start position:0% +rallies people um and I think those are + + + align:start position:0% +rallies people um and I think those are +the most plausible ways we we've got + + align:start position:0% +the most plausible ways we we've got + + + align:start position:0% +the most plausible ways we we've got +them + + align:start position:0% +them + + + align:start position:0% +them +um the uh + + align:start position:0% +um the uh + + + align:start position:0% +um the uh +others burin looks at people who argue + + align:start position:0% +others burin looks at people who argue + + + align:start position:0% +others burin looks at people who argue +that it that these somehow + + align:start position:0% +that it that these somehow + + + align:start position:0% +that it that these somehow +persuade as in a in a logical sense but + + align:start position:0% +persuade as in a in a logical sense but + + + align:start position:0% +persuade as in a in a logical sense but +that's not plausible he says and I agree + + align:start position:0% +that's not plausible he says and I agree + + + align:start position:0% +that's not plausible he says and I agree +with him + + align:start position:0% + + + + align:start position:0% + +that they're not going to you don't + + align:start position:0% +that they're not going to you don't + + + align:start position:0% +that they're not going to you don't +March in the streets to make an + + align:start position:0% +March in the streets to make an + + + align:start position:0% +March in the streets to make an +intellectual + + align:start position:0% +intellectual + + + align:start position:0% +intellectual +argument you mark March in the streets + + align:start position:0% +argument you mark March in the streets + + + align:start position:0% +argument you mark March in the streets +to do something else and if it isn't + + align:start position:0% +to do something else and if it isn't + + + align:start position:0% +to do something else and if it isn't +going to affect + + align:start position:0% +going to affect + + + align:start position:0% +going to affect +reelection uh why bother and if it is + + align:start position:0% +reelection uh why bother and if it is + + + align:start position:0% +reelection uh why bother and if it is +why is the group necessary uh if the + + align:start position:0% +why is the group necessary uh if the + + + align:start position:0% +why is the group necessary uh if the +person knows it you could argue that the + + align:start position:0% + + + + align:start position:0% + +anti-vietnam uh + + align:start position:0% + + + + align:start position:0% + +demonstrations simply made it uh + + align:start position:0% +demonstrations simply made it uh + + + align:start position:0% +demonstrations simply made it uh +inescapable that there was widespread + + align:start position:0% +inescapable that there was widespread + + + align:start position:0% +inescapable that there was widespread +opposition to the war public opinion + + align:start position:0% +opposition to the war public opinion + + + align:start position:0% +opposition to the war public opinion +polls said the same thing but Marching + + align:start position:0% +polls said the same thing but Marching + + + align:start position:0% +polls said the same thing but Marching +In the Streets uh made us all feel + + align:start position:0% +In the Streets uh made us all feel + + + align:start position:0% +In the Streets uh made us all feel +better of course but um uh also + + align:start position:0% +better of course but um uh also + + + align:start position:0% +better of course but um uh also +um uh brought it home the other point + + align:start position:0% +um uh brought it home the other point + + + align:start position:0% +um uh brought it home the other point +I'm making here in that second + + align:start position:0% +I'm making here in that second + + + align:start position:0% +I'm making here in that second +bullet is donors I mean gun control is + + align:start position:0% +bullet is donors I mean gun control is + + + align:start position:0% +bullet is donors I mean gun control is +an interesting example of the impact of + + align:start position:0% +an interesting example of the impact of + + + align:start position:0% +an interesting example of the impact of +salience and the impact of an interest + + align:start position:0% +salience and the impact of an interest + + + align:start position:0% +salience and the impact of an interest +group polls say that 70% of Americans + + align:start position:0% +group polls say that 70% of Americans + + + align:start position:0% +group polls say that 70% of Americans +typically the number varies a little bit + + align:start position:0% +typically the number varies a little bit + + + align:start position:0% +typically the number varies a little bit +but 70% of Americans would favor some + + align:start position:0% +but 70% of Americans would favor some + + + align:start position:0% +but 70% of Americans would favor some +gun control say limits on assault + + align:start position:0% +gun control say limits on assault + + + align:start position:0% +gun control say limits on assault +weapons on + + align:start position:0% +weapons on + + + align:start position:0% +weapons on +campus um you or or or some restrictions + + align:start position:0% +campus um you or or or some restrictions + + + align:start position:0% +campus um you or or or some restrictions +on on um carrying + + align:start position:0% + + + + align:start position:0% + +weapons but most people don't care much + + align:start position:0% +weapons but most people don't care much + + + align:start position:0% +weapons but most people don't care much +every police chief favors gun control + + align:start position:0% +every police chief favors gun control + + + align:start position:0% +every police chief favors gun control +most people don't care much people who + + align:start position:0% +most people don't care much people who + + + align:start position:0% +most people don't care much people who +support the National Rifle Association + + align:start position:0% +support the National Rifle Association + + + align:start position:0% +support the National Rifle Association +who oppose gun control care a + + align:start position:0% +who oppose gun control care a + + + align:start position:0% +who oppose gun control care a +lot and they + + align:start position:0% +lot and they + + + align:start position:0% +lot and they +win because the fact that I favor gun + + align:start position:0% +win because the fact that I favor gun + + + align:start position:0% +win because the fact that I favor gun +control is not going to cause me in most + + align:start position:0% +control is not going to cause me in most + + + align:start position:0% +control is not going to cause me in most +cases to change my vote on + + align:start position:0% +cases to change my vote on + + + align:start position:0% +cases to change my vote on +anything because that's rarely a big + + align:start position:0% +anything because that's rarely a big + + + align:start position:0% +anything because that's rarely a big +campaign issue if I'm elected I will + + align:start position:0% +campaign issue if I'm elected I will + + + align:start position:0% +campaign issue if I'm elected I will +enact no that's rarely a campaign issue + + align:start position:0% +enact no that's rarely a campaign issue + + + align:start position:0% +enact no that's rarely a campaign issue +um so so those of us who care a little + + align:start position:0% +um so so those of us who care a little + + + align:start position:0% +um so so those of us who care a little +bit don't do anything and those who care + + align:start position:0% +bit don't do anything and those who care + + + align:start position:0% +bit don't do anything and those who care +a lot have and have some money have + + align:start position:0% +a lot have and have some money have + + + align:start position:0% +a lot have and have some money have +control so that's a concentrated + + align:start position:0% +control so that's a concentrated + + + align:start position:0% +control so that's a concentrated +interest diffuse interest + + align:start position:0% +interest diffuse interest + + + align:start position:0% +interest diffuse interest +example of some + + align:start position:0% +example of some + + + align:start position:0% +example of some +importance so the other ways we talked + + align:start position:0% +importance so the other ways we talked + + + align:start position:0% +importance so the other ways we talked +about providing information you could + + align:start position:0% +about providing information you could + + + align:start position:0% +about providing information you could +argue that's what happened in + + align:start position:0% +argue that's what happened in + + + align:start position:0% +argue that's what happened in +Vietnam that's what happened in East + + align:start position:0% +Vietnam that's what happened in East + + + align:start position:0% +Vietnam that's what happened in East +Germany when the I didn't put out didn't + + align:start position:0% +Germany when the I didn't put out didn't + + + align:start position:0% +Germany when the I didn't put out didn't +put up the demonstrations that brought + + align:start position:0% +put up the demonstrations that brought + + + align:start position:0% +put up the demonstrations that brought +down the Berlin wall but as distinct + + align:start position:0% +down the Berlin wall but as distinct + + + align:start position:0% +down the Berlin wall but as distinct +from the Arab Spring nobody got + + align:start position:0% +from the Arab Spring nobody got + + + align:start position:0% +from the Arab Spring nobody got +shot right that happened quickly they + + align:start position:0% +shot right that happened quickly they + + + align:start position:0% +shot right that happened quickly they +talked about the Velvet Revolution in + + align:start position:0% + + + + align:start position:0% + +Czechoslovakia talked about in East in + + align:start position:0% +Czechoslovakia talked about in East in + + + align:start position:0% +Czechoslovakia talked about in East in +East Germany nothing much happened + + align:start position:0% +East Germany nothing much happened + + + align:start position:0% +East Germany nothing much happened +crowds turned out crowds turned out they + + align:start position:0% +crowds turned out crowds turned out they + + + align:start position:0% +crowds turned out crowds turned out they +didn't seize the government buildings + + align:start position:0% +didn't seize the government buildings + + + align:start position:0% +didn't seize the government buildings +they didn't overrun the the uh uh + + align:start position:0% +they didn't overrun the the uh uh + + + align:start position:0% +they didn't overrun the the uh uh +president's or prime minister's house + + align:start position:0% +president's or prime minister's house + + + align:start position:0% +president's or prime minister's house +the government just gave up and + + align:start position:0% +the government just gave up and + + + align:start position:0% +the government just gave up and +left so it I think the argument here is + + align:start position:0% +left so it I think the argument here is + + + align:start position:0% +left so it I think the argument here is +that they provided enormous amount of + + align:start position:0% +that they provided enormous amount of + + + align:start position:0% +that they provided enormous amount of +information to voters that um you have + + align:start position:0% +information to voters that um you have + + + align:start position:0% +information to voters that um you have +no support you're + + align:start position:0% +no support you're + + + align:start position:0% +no support you're +loathed changing preferences um this is + + align:start position:0% +loathed changing preferences um this is + + + align:start position:0% +loathed changing preferences um this is +of this often has to do with reframing + + align:start position:0% +of this often has to do with reframing + + + align:start position:0% +of this often has to do with reframing +an issue think about the pro-life + + align:start position:0% +an issue think about the pro-life + + + align:start position:0% +an issue think about the pro-life +movement uh which is a brilliant piece + + align:start position:0% +movement uh which is a brilliant piece + + + align:start position:0% +movement uh which is a brilliant piece +of + + align:start position:0% +of + + + align:start position:0% +of +reframing how can you be against + + align:start position:0% +reframing how can you be against + + + align:start position:0% +reframing how can you be against +life I mean you're for choice but what's + + align:start position:0% +life I mean you're for choice but what's + + + align:start position:0% +life I mean you're for choice but what's +more important choice or life so you + + align:start position:0% +more important choice or life so you + + + align:start position:0% +more important choice or life so you +could argue that reframing the issue as + + align:start position:0% +could argue that reframing the issue as + + + align:start position:0% +could argue that reframing the issue as +are you for or against life has an + + align:start position:0% +are you for or against life has an + + + align:start position:0% +are you for or against life has an +impact on + + align:start position:0% +impact on + + + align:start position:0% +impact on +preferences the the attacks on the + + align:start position:0% +preferences the the attacks on the + + + align:start position:0% +preferences the the attacks on the +healthc care legislation by by making it + + align:start position:0% +healthc care legislation by by making it + + + align:start position:0% +healthc care legislation by by making it +Obama's + + align:start position:0% +Obama's + + + align:start position:0% +Obama's +legislation as opposed to by the way no + + align:start position:0% +legislation as opposed to by the way no + + + align:start position:0% +legislation as opposed to by the way no +pre-existing condition Universal + + align:start position:0% +pre-existing condition Universal + + + align:start position:0% +pre-existing condition Universal +Insurance blah blah blah + + align:start position:0% +Insurance blah blah blah + + + align:start position:0% +Insurance blah blah blah +uh changes how it's thought of it's + + align:start position:0% +uh changes how it's thought of it's + + + align:start position:0% +uh changes how it's thought of it's +something Obama is shoving down our + + align:start position:0% +something Obama is shoving down our + + + align:start position:0% +something Obama is shoving down our +throats + + align:start position:0% +throats + + + align:start position:0% +throats +um and you can argue that this that + + align:start position:0% +um and you can argue that this that + + + align:start position:0% +um and you can argue that this that +civil rights did that that that was the + + align:start position:0% +civil rights did that that that was the + + + align:start position:0% +civil rights did that that that was the +essence of the civil rights + + align:start position:0% +essence of the civil rights + + + align:start position:0% +essence of the civil rights +movement that if you saw in in real time + + align:start position:0% +movement that if you saw in in real time + + + align:start position:0% +movement that if you saw in in real time +the the Marchers being taken down with + + align:start position:0% +the the Marchers being taken down with + + + align:start position:0% +the the Marchers being taken down with +fire hoses it was hard not to think + + align:start position:0% +fire hoses it was hard not to think + + + align:start position:0% +fire hoses it was hard not to think +that's just wrong these people are + + align:start position:0% +that's just wrong these people are + + + align:start position:0% +that's just wrong these people are +Marching how can they why is that right + + align:start position:0% +Marching how can they why is that right + + + align:start position:0% +Marching how can they why is that right +so + + align:start position:0% +so + + + align:start position:0% +so +a and you don't + + align:start position:0% +a and you don't + + + align:start position:0% +a and you don't +do king speeches were + + align:start position:0% +do king speeches were + + + align:start position:0% +do king speeches were +important but watching + + align:start position:0% +important but watching + + + align:start position:0% +important but watching +people peacefully protest being + + align:start position:0% +people peacefully protest being + + + align:start position:0% +people peacefully protest being +beaten changes your views of the people + + align:start position:0% +beaten changes your views of the people + + + align:start position:0% +beaten changes your views of the people +beating them and of the issue so part of + + align:start position:0% +beating them and of the issue so part of + + + align:start position:0% +beating them and of the issue so part of +what they do social movements is theater + + align:start position:0% +what they do social movements is theater + + + align:start position:0% +what they do social movements is theater +that changes preferences as well as + + align:start position:0% +that changes preferences as well as + + + align:start position:0% +that changes preferences as well as +signals uh signals + + align:start position:0% +signals uh signals + + + align:start position:0% +signals uh signals +information you can raise you can raise + + align:start position:0% +information you can raise you can raise + + + align:start position:0% +information you can raise you can raise +salience um by by making people aware of + + align:start position:0% +salience um by by making people aware of + + + align:start position:0% +salience um by by making people aware of +an issue but it it only works if they + + align:start position:0% +an issue but it it only works if they + + + align:start position:0% +an issue but it it only works if they +agree with + + align:start position:0% +agree with + + + align:start position:0% +agree with +you right I mean think about + + align:start position:0% +you right I mean think about + + + align:start position:0% +you right I mean think about +globalization the anti-globalization + + align:start position:0% +globalization the anti-globalization + + + align:start position:0% +globalization the anti-globalization +movement so they protested globalization + + align:start position:0% +movement so they protested globalization + + + align:start position:0% +movement so they protested globalization +they protested poor working conditions + + align:start position:0% +they protested poor working conditions + + + align:start position:0% +they protested poor working conditions +in poor countries and they trashed + + align:start position:0% +in poor countries and they trashed + + + align:start position:0% +in poor countries and they trashed +Starbucks and most people said + + align:start position:0% +Starbucks and most people said + + + align:start position:0% +Starbucks and most people said +what I'm sorry + + align:start position:0% +what I'm sorry + + + align:start position:0% +what I'm sorry +I if you're very very sympathetic to + + align:start position:0% +I if you're very very sympathetic to + + + align:start position:0% +I if you're very very sympathetic to +poor people you say yeah they should pay + + align:start position:0% +poor people you say yeah they should pay + + + align:start position:0% +poor people you say yeah they should pay +people more in poor countries and if + + align:start position:0% +people more in poor countries and if + + + align:start position:0% +people more in poor countries and if +you're not you say well they don't have + + align:start position:0% +you're not you say well they don't have + + + align:start position:0% +you're not you say well they don't have +to take the jobs you know I mean they're + + align:start position:0% +to take the jobs you know I mean they're + + + align:start position:0% +to take the jobs you know I mean they're +not being forced to work in these + + align:start position:0% +not being forced to work in these + + + align:start position:0% +not being forced to work in these +factories it's more fun than being in a + + align:start position:0% +factories it's more fun than being in a + + + align:start position:0% +factories it's more fun than being in a +village + + align:start position:0% +village + + + align:start position:0% +village +so it the + + align:start position:0% +so it the + + + align:start position:0% +so it the +example one of the optional readings uh + + align:start position:0% +example one of the optional readings uh + + + align:start position:0% +example one of the optional readings uh +C and G I forget now what their initials + + align:start position:0% +C and G I forget now what their initials + + + align:start position:0% +C and G I forget now what their initials +are make the point that among people who + + align:start position:0% +are make the point that among people who + + + align:start position:0% +are make the point that among people who +are for environmental change and who + + align:start position:0% +are for environmental change and who + + + align:start position:0% +are for environmental change and who +were opposed to EnV environmental change + + align:start position:0% +were opposed to EnV environmental change + + + align:start position:0% +were opposed to EnV environmental change +in a + + align:start position:0% +in a + + + align:start position:0% +in a +survey awareness of environmental issues + + align:start position:0% +survey awareness of environmental issues + + + align:start position:0% +survey awareness of environmental issues +was + + align:start position:0% +was + + + align:start position:0% +was +equal values + + align:start position:0% +equal values + + + align:start position:0% +equal values +differed so the policy implications + + align:start position:0% +differed so the policy implications + + + align:start position:0% +differed so the policy implications +differed so you make people aware that + + align:start position:0% +differed so you make people aware that + + + align:start position:0% +differed so you make people aware that +there's a lot of international trade and + + align:start position:0% +there's a lot of international trade and + + + align:start position:0% +there's a lot of international trade and +a lot of what you buy is uh uh produced + + align:start position:0% +a lot of what you buy is uh uh produced + + + align:start position:0% +a lot of what you buy is uh uh produced +by people in poor countries one response + + align:start position:0% +by people in poor countries one response + + + align:start position:0% +by people in poor countries one response +is that's really terrible and other + + align:start position:0% +is that's really terrible and other + + + align:start position:0% +is that's really terrible and other +response is well that's a + + align:start position:0% +response is well that's a + + + align:start position:0% +response is well that's a +market and if people mainly think that's + + align:start position:0% +market and if people mainly think that's + + + align:start position:0% +market and if people mainly think that's +a market because that's what they + + align:start position:0% +a market because that's what they + + + align:start position:0% +a market because that's what they +value making an ISS making them more + + align:start position:0% +value making an ISS making them more + + + align:start position:0% +value making an ISS making them more +aware of an issue won't + + align:start position:0% +aware of an issue won't + + + align:start position:0% +aware of an issue won't +help you could argue the same thing + + align:start position:0% +help you could argue the same thing + + + align:start position:0% +help you could argue the same thing +happens with climate change there's been + + align:start position:0% +happens with climate change there's been + + + align:start position:0% +happens with climate change there's been +a lot of work I wouldn't call it a + + align:start position:0% +a lot of work I wouldn't call it a + + + align:start position:0% +a lot of work I wouldn't call it a +movement but an awful lot of people have + + align:start position:0% +movement but an awful lot of people have + + + align:start position:0% +movement but an awful lot of people have +spent a lot of time trying to educate + + align:start position:0% +spent a lot of time trying to educate + + + align:start position:0% +spent a lot of time trying to educate +people about climate change it has not + + align:start position:0% +people about climate change it has not + + + align:start position:0% +people about climate change it has not +produced a ground swell quite the + + align:start position:0% +produced a ground swell quite the + + + align:start position:0% +produced a ground swell quite the +contrary and the argument is that uh it + + align:start position:0% +contrary and the argument is that uh it + + + align:start position:0% +contrary and the argument is that uh it +comes up against it's a conflict of + + align:start position:0% +comes up against it's a conflict of + + + align:start position:0% +comes up against it's a conflict of +values do you want to have economic + + align:start position:0% +values do you want to have economic + + + align:start position:0% +values do you want to have economic +growth or do you want to have + + align:start position:0% +growth or do you want to have + + + align:start position:0% +growth or do you want to have +Environmental Protection we can both be + + align:start position:0% +Environmental Protection we can both be + + + align:start position:0% +Environmental Protection we can both be +aware of climate change and its issues + + align:start position:0% +aware of climate change and its issues + + + align:start position:0% +aware of climate change and its issues +but reach very different policy + + align:start position:0% +but reach very different policy + + + align:start position:0% +but reach very different policy +conclusions so raising salience only + + align:start position:0% +conclusions so raising salience only + + + align:start position:0% +conclusions so raising salience only +works raising awareness only works if + + align:start position:0% +works raising awareness only works if + + + align:start position:0% +works raising awareness only works if +there's + + align:start position:0% +there's + + + align:start position:0% +there's +agreement or potential agreement or + + align:start position:0% +agreement or potential agreement or + + + align:start position:0% +agreement or potential agreement or +something like agreement + + align:start position:0% + + + + align:start position:0% + +and the final way and this is the + + align:start position:0% +and the final way and this is the + + + align:start position:0% +and the final way and this is the +borderline I this isn't really social + + align:start position:0% +borderline I this isn't really social + + + align:start position:0% +borderline I this isn't really social +movement I think the bur article is + + align:start position:0% +movement I think the bur article is + + + align:start position:0% +movement I think the bur article is +nonetheless a good + + align:start position:0% +nonetheless a good + + + align:start position:0% +nonetheless a good +article for interest groups how do + + align:start position:0% +article for interest groups how do + + + align:start position:0% +article for interest groups how do +interest groups affect policy well they + + align:start position:0% +interest groups affect policy well they + + + align:start position:0% +interest groups affect policy well they +do all this other + + align:start position:0% +do all this other + + + align:start position:0% +do all this other +stuff right the National Rifle + + align:start position:0% +stuff right the National Rifle + + + align:start position:0% +stuff right the National Rifle +Association does advertise does the + + align:start position:0% +Association does advertise does the + + + align:start position:0% +Association does advertise does the +environmental defense fund does send out + + align:start position:0% +environmental defense fund does send out + + + align:start position:0% +environmental defense fund does send out +mailings to people so these people do + + align:start position:0% +mailings to people so these people do + + + align:start position:0% +mailings to people so these people do +engage + + align:start position:0% +engage + + + align:start position:0% +engage +in they organize petition drives that + + align:start position:0% +in they organize petition drives that + + + align:start position:0% +in they organize petition drives that +that do all this but interest + + align:start position:0% +that do all this but interest + + + align:start position:0% +that do all this but interest +groups work on + + align:start position:0% +groups work on + + + align:start position:0% +groups work on +implementation that's inside + + align:start position:0% +implementation that's inside + + + align:start position:0% +implementation that's inside +baseball right + + align:start position:0% +baseball right + + + align:start position:0% +baseball right +so we'll talk about it in the + + align:start position:0% +so we'll talk about it in the + + + align:start position:0% +so we'll talk about it in the +environmental case next time when we + + align:start position:0% +environmental case next time when we + + + align:start position:0% +environmental case next time when we +talk about uh what EPA did to set + + align:start position:0% +talk about uh what EPA did to set + + + align:start position:0% +talk about uh what EPA did to set +standards a couple of + + align:start position:0% +standards a couple of + + + align:start position:0% +standards a couple of +times but the Dodd Frank law is the big + + align:start position:0% +times but the Dodd Frank law is the big + + + align:start position:0% +times but the Dodd Frank law is the big +current example right you can read about + + align:start position:0% +current example right you can read about + + + align:start position:0% +current example right you can read about +it in the paper all the time the law + + align:start position:0% +it in the paper all the time the law + + + align:start position:0% +it in the paper all the time the law +required lots of + + align:start position:0% +required lots of + + + align:start position:0% +required lots of +regulations set up some some new + + align:start position:0% +regulations set up some some new + + + align:start position:0% +regulations set up some some new +entities and it required this regulation + + align:start position:0% +entities and it required this regulation + + + align:start position:0% +entities and it required this regulation +that regulation spell this out make this + + align:start position:0% +that regulation spell this out make this + + + align:start position:0% +that regulation spell this out make this +clear hundreds thousands of regulations + + align:start position:0% +clear hundreds thousands of regulations + + + align:start position:0% +clear hundreds thousands of regulations +required no votes in + + align:start position:0% +required no votes in + + + align:start position:0% +required no votes in +Congress really really boring + + align:start position:0% +Congress really really boring + + + align:start position:0% +Congress really really boring +stuff who + + align:start position:0% +stuff who + + + align:start position:0% +stuff who +wins the people who + + align:start position:0% +wins the people who + + + align:start position:0% +wins the people who +have offices in Washington who have + + align:start position:0% +have offices in Washington who have + + + align:start position:0% +have offices in Washington who have +lawyers who have staff who have + + align:start position:0% +lawyers who have staff who have + + + align:start position:0% +lawyers who have staff who have +resources it's not a matter of buying + + align:start position:0% +resources it's not a matter of buying + + + align:start position:0% +resources it's not a matter of buying +votes in Regulatory Agencies it's a + + align:start position:0% +votes in Regulatory Agencies it's a + + + align:start position:0% +votes in Regulatory Agencies it's a +matter of providing information + + align:start position:0% +matter of providing information + + + align:start position:0% +matter of providing information +lobbying per the piece we had ass signed + + align:start position:0% +lobbying per the piece we had ass signed + + + align:start position:0% +lobbying per the piece we had ass signed +for last + + align:start position:0% + + + + align:start position:0% + +time + + align:start position:0% +time + + + align:start position:0% +time +when the issue has low salience to the + + align:start position:0% +when the issue has low salience to the + + + align:start position:0% +when the issue has low salience to the +public interchange fees on debit cards I + + align:start position:0% +public interchange fees on debit cards I + + + align:start position:0% +public interchange fees on debit cards I +will tell you exercise the entire + + align:start position:0% +will tell you exercise the entire + + + align:start position:0% +will tell you exercise the entire +banking + + align:start position:0% +banking + + + align:start position:0% +banking +industry and it may have been in the + + align:start position:0% +industry and it may have been in the + + + align:start position:0% +industry and it may have been in the +globe + + align:start position:0% +globe + + + align:start position:0% +globe +twice on the third business page + + align:start position:0% +twice on the third business page + + + align:start position:0% +twice on the third business page +every Banker in the country was up in + + align:start position:0% +every Banker in the country was up in + + + align:start position:0% +every Banker in the country was up in +arms um the Federal Reserve was required + + align:start position:0% +arms um the Federal Reserve was required + + + align:start position:0% +arms um the Federal Reserve was required +to to regulate that it had enormous + + align:start position:0% +to to regulate that it had enormous + + + align:start position:0% +to to regulate that it had enormous +discretion it it was required to + + align:start position:0% +discretion it it was required to + + + align:start position:0% +discretion it it was required to +regulate that fee paying due attention + + align:start position:0% +regulate that fee paying due attention + + + align:start position:0% +regulate that fee paying due attention +to incremental costs incremental costs + + align:start position:0% +to incremental costs incremental costs + + + align:start position:0% +to incremental costs incremental costs +varied all over the lot hundreds of + + align:start position:0% +varied all over the lot hundreds of + + + align:start position:0% +varied all over the lot hundreds of +submissions went into the Federal + + align:start position:0% +submissions went into the Federal + + + align:start position:0% +submissions went into the Federal +Reserve they made a decision yeah yeah + + align:start position:0% +Reserve they made a decision yeah yeah + + + align:start position:0% +Reserve they made a decision yeah yeah +so um that's the Der Amendment right of + + align:start position:0% +so um that's the Der Amendment right of + + + align:start position:0% +so um that's the Der Amendment right of +the the Durban Amendment y so when that + + align:start position:0% +the the Durban Amendment y so when that + + + align:start position:0% +the the Durban Amendment y so when that +so when that was approved uh the fact + + align:start position:0% +so when that was approved uh the fact + + + align:start position:0% +so when that was approved uh the fact +that for B up America started charging a + + align:start position:0% +that for B up America started charging a + + + align:start position:0% +that for B up America started charging a +monthly fee for people who would they + + align:start position:0% +monthly fee for people who would they + + + align:start position:0% +monthly fee for people who would they +use their debit card to kind of try to + + align:start position:0% +use their debit card to kind of try to + + + align:start position:0% +use their debit card to kind of try to +offset the fact that they couldn't make + + align:start position:0% +offset the fact that they couldn't make + + + align:start position:0% +offset the fact that they couldn't make +as much money from like the um from like + + align:start position:0% +as much money from like the um from like + + + align:start position:0% +as much money from like the um from like +the marginal C like the marginal revenue + + align:start position:0% +the marginal C like the marginal revenue + + + align:start position:0% +the marginal C like the marginal revenue +that they had before y but wouldn't that + + align:start position:0% +that they had before y but wouldn't that + + + align:start position:0% +that they had before y but wouldn't that +cause people to care a lot because at + + align:start position:0% +cause people to care a lot because at + + + align:start position:0% +cause people to care a lot because at +theend of the day the regular consum was + + align:start position:0% +theend of the day the regular consum was + + + align:start position:0% +theend of the day the regular consum was +the one who kind of got screwed over a + + align:start position:0% +the one who kind of got screwed over a + + + align:start position:0% +the one who kind of got screwed over a +little bit and the merchants were the + + align:start position:0% +little bit and the merchants were the + + + align:start position:0% +little bit and the merchants were the +ones who + + align:start position:0% +ones who + + + align:start position:0% +ones who +W uh but so wouldn't eventually like + + align:start position:0% +W uh but so wouldn't eventually like + + + align:start position:0% +W uh but so wouldn't eventually like +people be against the do Frank well you + + align:start position:0% +people be against the do Frank well you + + + align:start position:0% +people be against the do Frank well you +mean against that + + align:start position:0% +mean against that + + + align:start position:0% +mean against that +Amendment well well I mean here's + + align:start position:0% + + + + align:start position:0% + +here's here are the this this was a + + align:start position:0% +here's here are the this this was a + + + align:start position:0% +here's here are the this this was a +fight in which I I participated um + + align:start position:0% +fight in which I I participated um + + + align:start position:0% +fight in which I I participated um +here's sort of what happens in the short + + align:start position:0% +here's sort of what happens in the short + + + align:start position:0% +here's sort of what happens in the short +run what happens in the short run is + + align:start position:0% +run what happens in the short run is + + + align:start position:0% +run what happens in the short run is +Merchants save a little bit on debit + + align:start position:0% +Merchants save a little bit on debit + + + align:start position:0% +Merchants save a little bit on debit +card transactions not enough to C cause + + align:start position:0% +card transactions not enough to C cause + + + align:start position:0% +card transactions not enough to C cause +them to cut prices because it's only a + + align:start position:0% +them to cut prices because it's only a + + + align:start position:0% +them to cut prices because it's only a +little bit so one person one one uh + + align:start position:0% +little bit so one person one one uh + + + align:start position:0% +little bit so one person one one uh +large chain set on a conference call I + + align:start position:0% +large chain set on a conference call I + + + align:start position:0% +large chain set on a conference call I +it was Home Depot set on a conference + + align:start position:0% +it was Home Depot set on a conference + + + align:start position:0% +it was Home Depot set on a conference +call that that was worth about $100 + + align:start position:0% +call that that was worth about $100 + + + align:start position:0% +call that that was worth about $100 +million to them uh short run profits so + + align:start position:0% +million to them uh short run profits so + + + align:start position:0% +million to them uh short run profits so +prices don't go down what happens to + + align:start position:0% +prices don't go down what happens to + + + align:start position:0% +prices don't go down what happens to +Banks is checking accounts are now less + + align:start position:0% +Banks is checking accounts are now less + + + align:start position:0% +Banks is checking accounts are now less +profitable so they look to recoup in + + align:start position:0% +profitable so they look to recoup in + + + align:start position:0% +profitable so they look to recoup in +other ways they tried the the monthly + + align:start position:0% +other ways they tried the the monthly + + + align:start position:0% +other ways they tried the the monthly +fee that didn't work the easiest thing + + align:start position:0% +fee that didn't work the easiest thing + + + align:start position:0% +fee that didn't work the easiest thing +to do and what they've done quietly is + + align:start position:0% +to do and what they've done quietly is + + + align:start position:0% +to do and what they've done quietly is +they've raised the minimum balances + + align:start position:0% +they've raised the minimum balances + + + align:start position:0% +they've raised the minimum balances +required for free + + align:start position:0% +required for free + + + align:start position:0% +required for free +checking so and we'll see the numbers + + align:start position:0% +checking so and we'll see the numbers + + + align:start position:0% +checking so and we'll see the numbers +but checking because of these fees if + + align:start position:0% +but checking because of these fees if + + + align:start position:0% +but checking because of these fees if +you use the debit card a lot the bank is + + align:start position:0% +you use the debit card a lot the bank is + + + align:start position:0% +you use the debit card a lot the bank is +you are profitable to the bank even if + + align:start position:0% +you are profitable to the bank even if + + + align:start position:0% +you are profitable to the bank even if +you don't leave a lot of money on + + align:start position:0% +you don't leave a lot of money on + + + align:start position:0% +you don't leave a lot of money on +deposit take away those fees you're no + + align:start position:0% +deposit take away those fees you're no + + + align:start position:0% +deposit take away those fees you're no +longer profitable so they start raising + + align:start position:0% +longer profitable so they start raising + + + align:start position:0% +longer profitable so they start raising +the minimum requirement for free + + align:start position:0% +the minimum requirement for free + + + align:start position:0% +the minimum requirement for free +checking and the number of people + + align:start position:0% +checking and the number of people + + + align:start position:0% +checking and the number of people +without checking accounts goes goes + + align:start position:0% +without checking accounts goes goes + + + align:start position:0% +without checking accounts goes goes +up so I mean that's the predictable + + align:start position:0% +up so I mean that's the predictable + + + align:start position:0% +up so I mean that's the predictable +consequence of of the amendment uh it + + align:start position:0% +consequence of of the amendment uh it + + + align:start position:0% +consequence of of the amendment uh it +was pushed by + + align:start position:0% +was pushed by + + + align:start position:0% +was pushed by +Merchants um and + + align:start position:0% +Merchants um and + + + align:start position:0% +Merchants um and +um Senator Durban talked about his + + align:start position:0% +um Senator Durban talked about his + + + align:start position:0% +um Senator Durban talked about his +friend I think it was a hardware store + + align:start position:0% +friend I think it was a hardware store + + + align:start position:0% +friend I think it was a hardware store +owner or drugstore owner who was being + + align:start position:0% +owner or drugstore owner who was being + + + align:start position:0% +owner or drugstore owner who was being +being taken to the cleaners by these + + align:start position:0% +being taken to the cleaners by these + + + align:start position:0% +being taken to the cleaners by these +fees so he's presumably happy in the + + align:start position:0% +fees so he's presumably happy in the + + + align:start position:0% +fees so he's presumably happy in the +long run costs get passed through it's + + align:start position:0% +long run costs get passed through it's + + + align:start position:0% +long run costs get passed through it's +just their frictions to changing prices + + align:start position:0% +just their frictions to changing prices + + + align:start position:0% +just their frictions to changing prices +so in the short run they don't um + + align:start position:0% +so in the short run they don't um + + + align:start position:0% +so in the short run they don't um +in the long run prices adjust up people + + align:start position:0% +in the long run prices adjust up people + + + align:start position:0% +in the long run prices adjust up people +pay slightly more if they use use + + align:start position:0% +pay slightly more if they use use + + + align:start position:0% +pay slightly more if they use use +cash um + + align:start position:0% +cash um + + + align:start position:0% +cash um +so but this is a this is a typical this + + align:start position:0% +so but this is a this is a typical this + + + align:start position:0% +so but this is a this is a typical this +a this is an extreme piece of + + align:start position:0% +a this is an extreme piece of + + + align:start position:0% +a this is an extreme piece of +legislation it was not + + align:start position:0% +legislation it was not + + + align:start position:0% +legislation it was not +debated really you got a floor vote + + align:start position:0% +debated really you got a floor vote + + + align:start position:0% +debated really you got a floor vote +quick floor + + align:start position:0% +quick floor + + + align:start position:0% +quick floor +vote um not much material on it uh + + align:start position:0% +vote um not much material on it uh + + + align:start position:0% +vote um not much material on it uh +anywhere it it's said to the Federal + + align:start position:0% +anywhere it it's said to the Federal + + + align:start position:0% +anywhere it it's said to the Federal +Reserve neglect the fixed costs of + + align:start position:0% +Reserve neglect the fixed costs of + + + align:start position:0% +Reserve neglect the fixed costs of +running these programs when you set a + + align:start position:0% +running these programs when you set a + + + align:start position:0% +running these programs when you set a +price wait + + align:start position:0% +price wait + + + align:start position:0% +price wait +What they have to cover the fixed cost + + align:start position:0% +What they have to cover the fixed cost + + + align:start position:0% +What they have to cover the fixed cost +okay neglect the fixed costs and it it + + align:start position:0% +okay neglect the fixed costs and it it + + + align:start position:0% +okay neglect the fixed costs and it it +instructed the FED to consider marginal + + align:start position:0% +instructed the FED to consider marginal + + + align:start position:0% +instructed the FED to consider marginal +costs the FED ran a + + align:start position:0% +costs the FED ran a + + + align:start position:0% +costs the FED ran a +survey marginal costs varied by roughly + + align:start position:0% +survey marginal costs varied by roughly + + + align:start position:0% +survey marginal costs varied by roughly +in order of magnitude across + + align:start position:0% +in order of magnitude across + + + align:start position:0% +in order of magnitude across +Banks okay now what do you + + align:start position:0% +Banks okay now what do you + + + align:start position:0% +Banks okay now what do you +do and and they they came out with a + + align:start position:0% +do and and they they came out with a + + + align:start position:0% +do and and they they came out with a +proposed rule there was the expected + + align:start position:0% +proposed rule there was the expected + + + align:start position:0% +proposed rule there was the expected +howling they uh uh doubled the ceiling + + align:start position:0% +howling they uh uh doubled the ceiling + + + align:start position:0% +howling they uh uh doubled the ceiling +there was less howling life goes on but + + align:start position:0% +there was less howling life goes on but + + + align:start position:0% +there was less howling life goes on but +yeah it'll have the effect of of + + align:start position:0% +yeah it'll have the effect of of + + + align:start position:0% +yeah it'll have the effect of of +increasing the number of unbanked people + + align:start position:0% +increasing the number of unbanked people + + + align:start position:0% +increasing the number of unbanked people +it's not as serious as it used to be not + + align:start position:0% +it's not as serious as it used to be not + + + align:start position:0% +it's not as serious as it used to be not +to have a bank account but it's still + + align:start position:0% +to have a bank account but it's still + + + align:start position:0% +to have a bank account but it's still +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +serious so yeah the Durban Amendment you + + align:start position:0% +serious so yeah the Durban Amendment you + + + align:start position:0% +serious so yeah the Durban Amendment you +follow this stuff that's amazing it's + + align:start position:0% +follow this stuff that's amazing it's + + + align:start position:0% +follow this stuff that's amazing it's +not even + + align:start position:0% +not even + + + align:start position:0% +not even +energy uh anything else while I pause + + align:start position:0% +energy uh anything else while I pause + + + align:start position:0% +energy uh anything else while I pause +for breath and anecdote yeah could you + + align:start position:0% +for breath and anecdote yeah could you + + + align:start position:0% +for breath and anecdote yeah could you +tell us a little bit about the role that + + align:start position:0% +tell us a little bit about the role that + + + align:start position:0% +tell us a little bit about the role that +social media has played like how to + + align:start position:0% +social media has played like how to + + + align:start position:0% +social media has played like how to +mobilize all these different publics + + align:start position:0% +mobilize all these different publics + + + align:start position:0% +mobilize all these different publics +like I can see with Occupy Wall Street + + align:start position:0% +like I can see with Occupy Wall Street + + + align:start position:0% +like I can see with Occupy Wall Street +and like occupy everything um how how + + align:start position:0% +and like occupy everything um how how + + + align:start position:0% +and like occupy everything um how how +people have come together I saw that but + + align:start position:0% +people have come together I saw that but + + + align:start position:0% +people have come together I saw that but +but something like the Civil Rights + + align:start position:0% +but something like the Civil Rights + + + align:start position:0% +but something like the Civil Rights +Movement but it's a little less clear + + align:start position:0% +Movement but it's a little less clear + + + align:start position:0% +Movement but it's a little less clear +isn't it how the Occupy Movement I find + + align:start position:0% +isn't it how the Occupy Movement I find + + + align:start position:0% +isn't it how the Occupy Movement I find +mysterious is the Civil Rights Movement + + align:start position:0% +mysterious is the Civil Rights Movement + + + align:start position:0% +mysterious is the Civil Rights Movement +had a set of charismatic leaders it had + + align:start position:0% +had a set of charismatic leaders it had + + + align:start position:0% +had a set of charismatic leaders it had +some clear objectives and it had great + + align:start position:0% +some clear objectives and it had great + + + align:start position:0% +some clear objectives and it had great +media + + align:start position:0% +media + + + align:start position:0% +media +coverage right I mean when those kids + + align:start position:0% +coverage right I mean when those kids + + + align:start position:0% +coverage right I mean when those kids +went to where was it that the Civil + + align:start position:0% +went to where was it that the Civil + + + align:start position:0% +went to where was it that the Civil +Rights workers got shot Selma maybe boy + + align:start position:0% +Rights workers got shot Selma maybe boy + + + align:start position:0% +Rights workers got shot Selma maybe boy +that coverage of three college students + + align:start position:0% +that coverage of three college students + + + align:start position:0% +that coverage of three college students +go down to help the black community + + align:start position:0% +go down to help the black community + + + align:start position:0% +go down to help the black community +organized in Selma Alabama and get shot + + align:start position:0% +organized in Selma Alabama and get shot + + + align:start position:0% +organized in Selma Alabama and get shot +for their troubles that woke people up + + align:start position:0% +for their troubles that woke people up + + + align:start position:0% +for their troubles that woke people up +in an amazing way and and when you watch + + align:start position:0% +in an amazing way and and when you watch + + + align:start position:0% +in an amazing way and and when you watch +them fire hose the Marchers that was + + align:start position:0% +them fire hose the Marchers that was + + + align:start position:0% +them fire hose the Marchers that was +galvanizing and when Dr Martin Luther + + align:start position:0% +galvanizing and when Dr Martin Luther + + + align:start position:0% +galvanizing and when Dr Martin Luther +King spoke that was oh gee there is + + align:start position:0% +King spoke that was oh gee there is + + + align:start position:0% +King spoke that was oh gee there is +something here occupy was + + align:start position:0% +something here occupy was + + + align:start position:0% +something here occupy was +mysterious occupy just happened I I + + align:start position:0% +mysterious occupy just happened I I + + + align:start position:0% +mysterious occupy just happened I I +don't know + + align:start position:0% +don't know + + + align:start position:0% +don't know +I don't know these + + align:start position:0% +I don't know these + + + align:start position:0% +I don't know these +things and the anti globalization + + align:start position:0% +things and the anti globalization + + + align:start position:0% +things and the anti globalization +similarly what was what was the I can + + align:start position:0% +similarly what was what was the I can + + + align:start position:0% +similarly what was what was the I can +point to triggering + + align:start position:0% +point to triggering + + + align:start position:0% +point to triggering +events right you go back to the uh Rosa + + align:start position:0% +events right you go back to the uh Rosa + + + align:start position:0% +events right you go back to the uh Rosa +Parks refusing to sit in the back of the + + align:start position:0% +Parks refusing to sit in the back of the + + + align:start position:0% +Parks refusing to sit in the back of the +bus people moving into integrated lunch + + align:start position:0% +bus people moving into integrated lunch + + + align:start position:0% +bus people moving into integrated lunch +counters all of this getting media + + align:start position:0% +counters all of this getting media + + + align:start position:0% +counters all of this getting media +attention I can see the triggering + + align:start position:0% +attention I can see the triggering + + + align:start position:0% +attention I can see the triggering +events in civil rights were clear the + + align:start position:0% +events in civil rights were clear the + + + align:start position:0% +events in civil rights were clear the +triggering event in Vietnam was pretty + + align:start position:0% +triggering event in Vietnam was pretty + + + align:start position:0% +triggering event in Vietnam was pretty +clear it just went on and on and and uh + + align:start position:0% +clear it just went on and on and and uh + + + align:start position:0% +clear it just went on and on and and uh +thinking about thousands of people + + align:start position:0% +thinking about thousands of people + + + align:start position:0% +thinking about thousands of people +chanting hey hey LBJ how many kids did + + align:start position:0% +chanting hey hey LBJ how many kids did + + + align:start position:0% +chanting hey hey LBJ how many kids did +you kill today um those are pretty + + align:start position:0% +you kill today um those are pretty + + + align:start position:0% +you kill today um those are pretty +dramatic things but + + align:start position:0% +dramatic things but + + + align:start position:0% +dramatic things but +occupy I don't know what triggered + + align:start position:0% +occupy I don't know what triggered + + + align:start position:0% +occupy I don't know what triggered +occupy uh I also don't know what + + align:start position:0% +occupy uh I also don't know what + + + align:start position:0% +occupy uh I also don't know what +triggered the an globalization + + align:start position:0% +triggered the an globalization + + + align:start position:0% +triggered the an globalization +Movement we know the Arab Spring we know + + align:start position:0% +Movement we know the Arab Spring we know + + + align:start position:0% +Movement we know the Arab Spring we know +it was the normally there's something + + align:start position:0% +it was the normally there's something + + + align:start position:0% +it was the normally there's something +normally the guy in Tunisia who who + + align:start position:0% +normally the guy in Tunisia who who + + + align:start position:0% +normally the guy in Tunisia who who +burned himself to death in protest well + + align:start position:0% +burned himself to death in protest well + + + align:start position:0% +burned himself to death in protest well +not about just the trigger but like how + + align:start position:0% +not about just the trigger but like how + + + align:start position:0% +not about just the trigger but like how +people are mobilize and come together + + align:start position:0% +people are mobilize and come together + + + align:start position:0% +people are mobilize and come together +well now you now people point to + + align:start position:0% +well now you now people point to + + + align:start position:0% +well now you now people point to +particularly in the case of Egypt it was + + align:start position:0% +particularly in the case of Egypt it was + + + align:start position:0% +particularly in the case of Egypt it was +much discussed uh social + + align:start position:0% +much discussed uh social + + + align:start position:0% +much discussed uh social +media you can organize through through + + align:start position:0% +media you can organize through through + + + align:start position:0% +media you can organize through through +Twitter and Facebook and various other + + align:start position:0% +Twitter and Facebook and various other + + + align:start position:0% +Twitter and Facebook and various other +connections and just things going viral + + align:start position:0% +connections and just things going viral + + + align:start position:0% +connections and just things going viral +in a variety of ways through people's + + align:start position:0% +in a variety of ways through people's + + + align:start position:0% +in a variety of ways through people's +personal networks you can + + align:start position:0% +personal networks you can + + + align:start position:0% +personal networks you can +organize Vietnam was posters there will + + align:start position:0% +organize Vietnam was posters there will + + + align:start position:0% +organize Vietnam was posters there will +be a rally today there was a leader that + + align:start position:0% +be a rally today there was a leader that + + + align:start position:0% +be a rally today there was a leader that +called it all there were people who + + align:start position:0% +called it all there were people who + + + align:start position:0% +called it all there were people who +appointed themselves leaders you put up + + align:start position:0% +appointed themselves leaders you put up + + + align:start position:0% +appointed themselves leaders you put up +a poster and you say there's going to be + + align:start position:0% +a poster and you say there's going to be + + + align:start position:0% +a poster and you say there's going to be +a demonstration today in Killian well it + + align:start position:0% +a demonstration today in Killian well it + + + align:start position:0% +a demonstration today in Killian well it +was then the great Court um nobody had + + align:start position:0% +was then the great Court um nobody had + + + align:start position:0% +was then the great Court um nobody had +to show + + align:start position:0% +to show + + + align:start position:0% +to show +up if people weren't sort of ready to do + + align:start position:0% +up if people weren't sort of ready to do + + + align:start position:0% +up if people weren't sort of ready to do +something you know you could imagine + + align:start position:0% +something you know you could imagine + + + align:start position:0% +something you know you could imagine +calling a rally and nobody comes that + + align:start position:0% +calling a rally and nobody comes that + + + align:start position:0% +calling a rally and nobody comes that +happens often enough + + align:start position:0% +happens often enough + + + align:start position:0% +happens often enough +um uh + + align:start position:0% +um uh + + + align:start position:0% +um uh +it this as far as I know and undoubtedly + + align:start position:0% +it this as far as I know and undoubtedly + + + align:start position:0% +it this as far as I know and undoubtedly +there's there's people have written + + align:start position:0% +there's there's people have written + + + align:start position:0% +there's there's people have written +boring papers on it but it strikes me + + align:start position:0% +boring papers on it but it strikes me + + + align:start position:0% +boring papers on it but it strikes me +just as an observer of history that it's + + align:start position:0% +just as an observer of history that it's + + + align:start position:0% +just as an observer of history that it's +a bit mysterious what does it it's a bit + + align:start position:0% +a bit mysterious what does it it's a bit + + + align:start position:0% +a bit mysterious what does it it's a bit +mysterious + + align:start position:0% +mysterious + + + align:start position:0% +mysterious +so guy Burns himself to death in + + align:start position:0% +so guy Burns himself to death in + + + align:start position:0% +so guy Burns himself to death in +Tunisia why does that + + align:start position:0% +Tunisia why does that + + + align:start position:0% +Tunisia why does that +spread what triggers that did somebody + + align:start position:0% +spread what triggers that did somebody + + + align:start position:0% +spread what triggers that did somebody +in Egypt set himself up or herself up as + + align:start position:0% +in Egypt set himself up or herself up as + + + align:start position:0% +in Egypt set himself up or herself up as +a leader and begin saying hey we're + + align:start position:0% +a leader and begin saying hey we're + + + align:start position:0% +a leader and begin saying hey we're +going to meet in the Square tomorrow and + + align:start position:0% +going to meet in the Square tomorrow and + + + align:start position:0% +going to meet in the Square tomorrow and +then gradually it built I it did + + align:start position:0% +then gradually it built I it did + + + align:start position:0% +then gradually it built I it did +build uh from a relatively small group + + align:start position:0% +build uh from a relatively small group + + + align:start position:0% +build uh from a relatively small group +um + + align:start position:0% +um + + + align:start position:0% +um +but in Moscow there + + align:start position:0% +but in Moscow there + + + align:start position:0% +but in Moscow there +protests that have lost have plainly + + align:start position:0% +protests that have lost have plainly + + + align:start position:0% +protests that have lost have plainly +lost they're anti-putin protests in + + align:start position:0% +lost they're anti-putin protests in + + + align:start position:0% +lost they're anti-putin protests in +Russia they were small I don't know how + + align:start position:0% +Russia they were small I don't know how + + + align:start position:0% +Russia they were small I don't know how +they happened they weren't sufficient + + align:start position:0% +they happened they weren't sufficient + + + align:start position:0% +they happened they weren't sufficient +they + + align:start position:0% +they + + + align:start position:0% +they +dissipated so it doesn't always happen + + align:start position:0% +dissipated so it doesn't always happen + + + align:start position:0% +dissipated so it doesn't always happen +doesn't always happen + + align:start position:0% +doesn't always happen + + + align:start position:0% +doesn't always happen +Andrew um just as it might be an extreme + + align:start position:0% +Andrew um just as it might be an extreme + + + align:start position:0% +Andrew um just as it might be an extreme +but uh could someone argue that uh like + + align:start position:0% +but uh could someone argue that uh like + + + align:start position:0% +but uh could someone argue that uh like +especially in say for the arage spring + + align:start position:0% +especially in say for the arage spring + + + align:start position:0% +especially in say for the arage spring +movements uh that violence or like the + + align:start position:0% +movements uh that violence or like the + + + align:start position:0% +movements uh that violence or like the +threat of violence or blackmail or the + + align:start position:0% +threat of violence or blackmail or the + + + align:start position:0% +threat of violence or blackmail or the +threat of uh just like physically + + align:start position:0% +threat of uh just like physically + + + align:start position:0% +threat of uh just like physically +destroying something is a means of of of + + align:start position:0% +destroying something is a means of of of + + + align:start position:0% +destroying something is a means of of of +effective public policy so not not votes + + align:start position:0% +effective public policy so not not votes + + + align:start position:0% +effective public policy so not not votes +just the fact that uh there's a big body + + align:start position:0% +just the fact that uh there's a big body + + + align:start position:0% +just the fact that uh there's a big body +out there that will affect the way the + + align:start position:0% +out there that will affect the way the + + + align:start position:0% +out there that will affect the way the +country is run so like let's let's meet + + align:start position:0% +country is run so like let's let's meet + + + align:start position:0% +country is run so like let's let's meet +their demands well a standard a standard + + align:start position:0% +their demands well a standard a standard + + + align:start position:0% +their demands well a standard a standard +thing that happens although in France it + + align:start position:0% +thing that happens although in France it + + + align:start position:0% +thing that happens although in France it +tends to be well organized Mass + + align:start position:0% +tends to be well organized Mass + + + align:start position:0% +tends to be well organized Mass +strikes you can call you call it general + + align:start position:0% +strikes you can call you call it general + + + align:start position:0% +strikes you can call you call it general +strike and if the general strike's + + align:start position:0% +strike and if the general strike's + + + align:start position:0% +strike and if the general strike's +effective you've demonstrated that you + + align:start position:0% +effective you've demonstrated that you + + + align:start position:0% +effective you've demonstrated that you +have the that enough you've demonstrated + + align:start position:0% +have the that enough you've demonstrated + + + align:start position:0% +have the that enough you've demonstrated +that enough people care enough about the + + align:start position:0% +that enough people care enough about the + + + align:start position:0% +that enough people care enough about the +issue to do something I don't know if it + + align:start position:0% +issue to do something I don't know if it + + + align:start position:0% +issue to do something I don't know if it +has to be physical violence but I think + + align:start position:0% +has to be physical violence but I think + + + align:start position:0% +has to be physical violence but I think +it has to be an action because that's + + align:start position:0% +it has to be an action because that's + + + align:start position:0% +it has to be an action because that's +how you demonstrate that you + + align:start position:0% +how you demonstrate that you + + + align:start position:0% +how you demonstrate that you +care right I mean now of course you just + + align:start position:0% +care right I mean now of course you just + + + align:start position:0% +care right I mean now of course you just +send an email to Congress no that + + align:start position:0% +send an email to Congress no that + + + align:start position:0% +send an email to Congress no that +doesn't really say that you're very + + align:start position:0% +doesn't really say that you're very + + + align:start position:0% +doesn't really say that you're very +excited about the issue uh if you go out + + align:start position:0% +excited about the issue uh if you go out + + + align:start position:0% +excited about the issue uh if you go out +in March you stand in the hot sun for a + + align:start position:0% +in March you stand in the hot sun for a + + + align:start position:0% +in March you stand in the hot sun for a +few few hours it demonstrates it + + align:start position:0% + + + + align:start position:0% + +um the story of the Civil Rights + + align:start position:0% +um the story of the Civil Rights + + + align:start position:0% +um the story of the Civil Rights +Movement is kind of the reverse right + + align:start position:0% +Movement is kind of the reverse right + + + align:start position:0% +Movement is kind of the reverse right +there was no threat of + + align:start position:0% +there was no threat of + + + align:start position:0% +there was no threat of +violence from the activists it was the + + align:start position:0% +violence from the activists it was the + + + align:start position:0% +violence from the activists it was the +violence from those acting against them + + align:start position:0% +violence from those acting against them + + + align:start position:0% +violence from those acting against them +that really built support it was Dr + + align:start position:0% +that really built support it was Dr + + + align:start position:0% +that really built support it was Dr +King's nonviolence strategy which worked + + align:start position:0% +King's nonviolence strategy which worked + + + align:start position:0% +King's nonviolence strategy which worked +beyond anything I've seen um in Viet the + + align:start position:0% +beyond anything I've seen um in Viet the + + + align:start position:0% +beyond anything I've seen um in Viet the +vi anti Vietnam people were pretty non + + align:start position:0% +vi anti Vietnam people were pretty non + + + align:start position:0% +vi anti Vietnam people were pretty non +violent too I don't think it mattered + + align:start position:0% +violent too I don't think it mattered + + + align:start position:0% +violent too I don't think it mattered +much um occupy been nonviolent the Tea + + align:start position:0% +much um occupy been nonviolent the Tea + + + align:start position:0% +much um occupy been nonviolent the Tea +Party been a little shrill but + + align:start position:0% +Party been a little shrill but + + + align:start position:0% +Party been a little shrill but +nonviolent tea parties had some effect + + align:start position:0% +nonviolent tea parties had some effect + + + align:start position:0% +nonviolent tea parties had some effect +politically in the Republican Party the + + align:start position:0% +politically in the Republican Party the + + + align:start position:0% +politically in the Republican Party the +Occupy Movement seems to have vanished + + align:start position:0% +Occupy Movement seems to have vanished + + + align:start position:0% +Occupy Movement seems to have vanished +in the + + align:start position:0% +in the + + + align:start position:0% +in the +night so it's a little bit + + align:start position:0% +night so it's a little bit + + + align:start position:0% +night so it's a little bit +mysterious because you mentioned strikes + + align:start position:0% +mysterious because you mentioned strikes + + + align:start position:0% +mysterious because you mentioned strikes +because uh one other like where would + + align:start position:0% +because uh one other like where would + + + align:start position:0% +because uh one other like where would +that category get into the fact that so + + align:start position:0% +that category get into the fact that so + + + align:start position:0% +that category get into the fact that so +say as some people say I don't know like + + align:start position:0% +say as some people say I don't know like + + + align:start position:0% +say as some people say I don't know like +uh tomorrow all bus drivers decide they + + align:start position:0% +uh tomorrow all bus drivers decide they + + + align:start position:0% +uh tomorrow all bus drivers decide they +want to strike so like uh for some + + align:start position:0% +want to strike so like uh for some + + + align:start position:0% +want to strike so like uh for some +reason actually that's more pertinent in + + align:start position:0% +reason actually that's more pertinent in + + + align:start position:0% +reason actually that's more pertinent in +Europe where transportation is but + + align:start position:0% +Europe where transportation is but + + + align:start position:0% +Europe where transportation is but +because I've seen it happen so those are + + align:start position:0% +because I've seen it happen so those are + + + align:start position:0% +because I've seen it happen so those are +those tend to be very heavily unioned + + align:start position:0% +those tend to be very heavily unioned + + + align:start position:0% +those tend to be very heavily unioned +that's why I talked about a general + + align:start position:0% +that's why I talked about a general + + + align:start position:0% +that's why I talked about a general +strike yeah so so I was going to say + + align:start position:0% +strike yeah so so I was going to say + + + align:start position:0% +strike yeah so so I was going to say +even for a union uh so because it's a + + align:start position:0% +even for a union uh so because it's a + + + align:start position:0% +even for a union uh so because it's a +small relatively small body but because + + align:start position:0% +small relatively small body but because + + + align:start position:0% +small relatively small body but because +it it exhibits a big uh like a lot of + + align:start position:0% +it it exhibits a big uh like a lot of + + + align:start position:0% +it it exhibits a big uh like a lot of +power and like the fact that we won't + + align:start position:0% +power and like the fact that we won't + + + align:start position:0% +power and like the fact that we won't +have buses or the subway tomorrow will + + align:start position:0% +have buses or the subway tomorrow will + + + align:start position:0% +have buses or the subway tomorrow will +will + + align:start position:0% +will + + + align:start position:0% +will +um bother a lot of a bigger majority of + + align:start position:0% +um bother a lot of a bigger majority of + + + align:start position:0% +um bother a lot of a bigger majority of +people and basically that's almost like + + align:start position:0% +people and basically that's almost like + + + align:start position:0% +people and basically that's almost like +blackmail so like you're you're + + align:start position:0% +blackmail so like you're you're + + + align:start position:0% +blackmail so like you're you're +influencing what the majority of people + + align:start position:0% +influencing what the majority of people + + + align:start position:0% +influencing what the majority of people +is thinking about this issue it's not + + align:start position:0% +is thinking about this issue it's not + + + align:start position:0% +is thinking about this issue it's not +that that that it's directly influence + + align:start position:0% +that that that it's directly influence + + + align:start position:0% +that that that it's directly influence +in what you're asking for which could be + + align:start position:0% +in what you're asking for which could be + + + align:start position:0% +in what you're asking for which could be +wages for bus drivers but they're so + + align:start position:0% +wages for bus drivers but they're so + + + align:start position:0% +wages for bus drivers but they're so +frustrated that we don't have buses so + + align:start position:0% +frustrated that we don't have buses so + + + align:start position:0% +frustrated that we don't have buses so +okay let's give them the wages because + + align:start position:0% +okay let's give them the wages because + + + align:start position:0% +okay let's give them the wages because +they're causing all this but it can fail + + align:start position:0% +they're causing all this but it can fail + + + align:start position:0% +they're causing all this but it can fail +it can fail there was a I was reading + + align:start position:0% +it can fail there was a I was reading + + + align:start position:0% +it can fail there was a I was reading +recently a fictionalized treatment of + + align:start position:0% +recently a fictionalized treatment of + + + align:start position:0% +recently a fictionalized treatment of +the famous police strike in Boston in + + align:start position:0% +the famous police strike in Boston in + + + align:start position:0% +the famous police strike in Boston in +1919 that strike police hadn't been paid + + align:start position:0% +1919 that strike police hadn't been paid + + + align:start position:0% +1919 that strike police hadn't been paid +they were underpaid hadn't gotten a + + align:start position:0% +they were underpaid hadn't gotten a + + + align:start position:0% +they were underpaid hadn't gotten a +raise in 30 years kind of thing uh badly + + align:start position:0% +raise in 30 years kind of thing uh badly + + + align:start position:0% +raise in 30 years kind of thing uh badly +underpaid they struck there was a crime + + align:start position:0% +underpaid they struck there was a crime + + + align:start position:0% +underpaid they struck there was a crime +wave the police completely lost the + + align:start position:0% +wave the police completely lost the + + + align:start position:0% +wave the police completely lost the +popular sympathy and uh lots of them + + align:start position:0% +popular sympathy and uh lots of them + + + align:start position:0% +popular sympathy and uh lots of them +were fired and jailed and all kinds of + + align:start position:0% +were fired and jailed and all kinds of + + + align:start position:0% +were fired and jailed and all kinds of +things so you know that was a threat + + align:start position:0% +things so you know that was a threat + + + align:start position:0% +things so you know that was a threat +They carried out the threat people got + + align:start position:0% +They carried out the threat people got + + + align:start position:0% +They carried out the threat people got +very very + + align:start position:0% +very very + + + align:start position:0% +very very +angry uh Kelvin kulage president because + + align:start position:0% +angry uh Kelvin kulage president because + + + align:start position:0% +angry uh Kelvin kulage president because +of how drastically he he uh reacted + + align:start position:0% +of how drastically he he uh reacted + + + align:start position:0% +of how drastically he he uh reacted +against the strike so um it it doesn't + + align:start position:0% +against the strike so um it it doesn't + + + align:start position:0% +against the strike so um it it doesn't +it's not necessarily a winning strategy + + align:start position:0% +it's not necessarily a winning strategy + + + align:start position:0% +it's not necessarily a winning strategy +it's not necessarily a winning + + align:start position:0% +it's not necessarily a winning + + + align:start position:0% +it's not necessarily a winning +strategy um the other hand yeah I'm kind + + align:start position:0% +strategy um the other hand yeah I'm kind + + + align:start position:0% +strategy um the other hand yeah I'm kind +of confused about the difference between + + align:start position:0% +of confused about the difference between + + + align:start position:0% +of confused about the difference between +the first and the second strategies the + + align:start position:0% +the first and the second strategies the + + + align:start position:0% +the first and the second strategies the +first yeah I must say reading the + + align:start position:0% +first yeah I must say reading the + + + align:start position:0% +first yeah I must say reading the +reading the paper I was a little + + align:start position:0% +reading the paper I was a little + + + align:start position:0% +reading the paper I was a little +confused about his argument too he said + + align:start position:0% +confused about his argument too he said + + + align:start position:0% +confused about his argument too he said +well can you just walk in and say um I'm + + align:start position:0% +well can you just walk in and say um I'm + + + align:start position:0% +well can you just walk in and say um I'm +opposed to to the Vietnam War I've got + + align:start position:0% +opposed to to the Vietnam War I've got + + + align:start position:0% +opposed to to the Vietnam War I've got +uh there are a bunch of us and here are + + align:start position:0% +uh there are a bunch of us and here are + + + align:start position:0% +uh there are a bunch of us and here are +my + + align:start position:0% +my + + + align:start position:0% +my +arguments and I think what he's saying + + align:start position:0% +arguments and I think what he's saying + + + align:start position:0% +arguments and I think what he's saying +is that's not going to work social + + align:start position:0% +is that's not going to work social + + + align:start position:0% +is that's not going to work social +movements work by + + align:start position:0% +movements work by + + + align:start position:0% +movements work by +demonstrating that it matters to enough + + align:start position:0% +demonstrating that it matters to enough + + + align:start position:0% +demonstrating that it matters to enough +people that you have to take it into + + align:start position:0% +people that you have to take it into + + + align:start position:0% +people that you have to take it into +account that and if it if the if the + + align:start position:0% +account that and if it if the if the + + + align:start position:0% +account that and if it if the if the +policy maker knows that it matters + + align:start position:0% +policy maker knows that it matters + + + align:start position:0% +policy maker knows that it matters +enough to a lot of people you don't need + + align:start position:0% +enough to a lot of people you don't need + + + align:start position:0% +enough to a lot of people you don't need +a social movement and if it doesn't + + align:start position:0% +a social movement and if it doesn't + + + align:start position:0% +a social movement and if it doesn't +occupy if it doesn't the movement won't + + align:start position:0% +occupy if it doesn't the movement won't + + + align:start position:0% +occupy if it doesn't the movement won't +have any effect I think that's what he's + + align:start position:0% +have any effect I think that's what he's + + + align:start position:0% +have any effect I think that's what he's +saying in my money for so social + + align:start position:0% +saying in my money for so social + + + align:start position:0% +saying in my money for so social +movements what you want to think about + + align:start position:0% +movements what you want to think about + + + align:start position:0% +movements what you want to think about +is to think about these three are you + + align:start position:0% +is to think about these three are you + + + align:start position:0% +is to think about these three are you +are you persuading people that a lot of + + align:start position:0% +are you persuading people that a lot of + + + align:start position:0% +are you persuading people that a lot of +people care are you are you making + + align:start position:0% +people care are you are you making + + + align:start position:0% +people care are you are you making +changing people's preferences toward an + + align:start position:0% +changing people's preferences toward an + + + align:start position:0% +changing people's preferences toward an +issue or are you making them more aware + + align:start position:0% +issue or are you making them more aware + + + align:start position:0% +issue or are you making them more aware +of an issue and making it more important + + align:start position:0% +of an issue and making it more important + + + align:start position:0% +of an issue and making it more important +you could be aware of fracking you could + + align:start position:0% +you could be aware of fracking you could + + + align:start position:0% +you could be aware of fracking you could +make it more important in people's in + + align:start position:0% +make it more important in people's in + + + align:start position:0% +make it more important in people's in +people's minds by providing information + + align:start position:0% +people's minds by providing information + + + align:start position:0% +people's minds by providing information +you could raise salience either by + + align:start position:0% +you could raise salience either by + + + align:start position:0% +you could raise salience either by +awareness or on the important + + align:start position:0% +awareness or on the important + + + align:start position:0% +awareness or on the important +side um and this is an inside baseball + + align:start position:0% +side um and this is an inside baseball + + + align:start position:0% +side um and this is an inside baseball +story so I share I share your confusion + + align:start position:0% +story so I share I share your confusion + + + align:start position:0% +story so I share I share your confusion +about the first I confess I read his + + align:start position:0% +about the first I confess I read his + + + align:start position:0% +about the first I confess I read his +argument on the first one and I said + + align:start position:0% +argument on the first one and I said + + + align:start position:0% +argument on the first one and I said +well what would that look like uh the + + align:start position:0% +well what would that look like uh the + + + align:start position:0% +well what would that look like uh the +the closest thing I can I can think of + + align:start position:0% +the closest thing I can I can think of + + + align:start position:0% +the closest thing I can I can think of +is maybe in + + align:start position:0% +is maybe in + + + align:start position:0% +is maybe in +Vietnam uh there was some persuasion but + + align:start position:0% +Vietnam uh there was some persuasion but + + + align:start position:0% +Vietnam uh there was some persuasion but +I think what Vietnam was all about was + + align:start position:0% +I think what Vietnam was all about was + + + align:start position:0% +I think what Vietnam was all about was +this was letting people know that a + + align:start position:0% +this was letting people know that a + + + align:start position:0% +this was letting people know that a +large part of the population was + + align:start position:0% +large part of the population was + + + align:start position:0% +large part of the population was +passionate and that's what happened in + + align:start position:0% +passionate and that's what happened in + + + align:start position:0% +passionate and that's what happened in +in Czechoslovakia and East Germany and + + align:start position:0% +in Czechoslovakia and East Germany and + + + align:start position:0% +in Czechoslovakia and East Germany and +generally throughout Eastern Europe um + + align:start position:0% +generally throughout Eastern Europe um + + + align:start position:0% +generally throughout Eastern Europe um +once it became clear the Russians + + align:start position:0% +once it became clear the Russians + + + align:start position:0% +once it became clear the Russians +weren't going to intervene + + align:start position:0% +weren't going to intervene + + + align:start position:0% +weren't going to intervene +militarily and it became clear to the + + align:start position:0% +militarily and it became clear to the + + + align:start position:0% +militarily and it became clear to the +government that they had no popular + + align:start position:0% +government that they had no popular + + + align:start position:0% +government that they had no popular +support game over game over yeah I'm not + + align:start position:0% +support game over game over yeah I'm not + + + align:start position:0% +support game over game over yeah I'm not +sure if I'm correct but my theory My + + align:start position:0% +sure if I'm correct but my theory My + + + align:start position:0% +sure if I'm correct but my theory My +overall theory for like the occupi um + + align:start position:0% +overall theory for like the occupi um + + + align:start position:0% +overall theory for like the occupi um +movement is that it wasn't necessarily + + align:start position:0% +movement is that it wasn't necessarily + + + align:start position:0% +movement is that it wasn't necessarily +trigged by any particular EV however + + align:start position:0% +trigged by any particular EV however + + + align:start position:0% +trigged by any particular EV however +there was like since the financial + + align:start position:0% +there was like since the financial + + + align:start position:0% +there was like since the financial +crisis and and all the economic problems + + align:start position:0% +crisis and and all the economic problems + + + align:start position:0% +crisis and and all the economic problems +that were happening in the country I + + align:start position:0% +that were happening in the country I + + + align:start position:0% +that were happening in the country I +think there were just a lot of people + + align:start position:0% +think there were just a lot of people + + + align:start position:0% +think there were just a lot of people +unsatisfied in the current status but I + + align:start position:0% +unsatisfied in the current status but I + + + align:start position:0% +unsatisfied in the current status but I +don't think that that would have been + + align:start position:0% +don't think that that would have been + + + align:start position:0% +don't think that that would have been +enough to trigger the movement and for + + align:start position:0% +enough to trigger the movement and for + + + align:start position:0% +enough to trigger the movement and for +this particular case I think the actual + + align:start position:0% +this particular case I think the actual + + + align:start position:0% +this particular case I think the actual +people the initial leaders who who try + + align:start position:0% +people the initial leaders who who try + + + align:start position:0% +people the initial leaders who who try +to convince people those are really the + + align:start position:0% +to convince people those are really the + + + align:start position:0% +to convince people those are really the +key players I don't think that's + + align:start position:0% +key players I don't think that's + + + align:start position:0% +key players I don't think that's +something that would have that was bound + + align:start position:0% +something that would have that was bound + + + align:start position:0% +something that would have that was bound +to happen regardless of whether or not + + align:start position:0% +to happen regardless of whether or not + + + align:start position:0% +to happen regardless of whether or not +someone had had started I don't think it + + align:start position:0% +someone had had started I don't think it + + + align:start position:0% +someone had had started I don't think it +would have been something that if it + + align:start position:0% +would have been something that if it + + + align:start position:0% +would have been something that if it +didn't happen then it would have + + align:start position:0% +didn't happen then it would have + + + align:start position:0% +didn't happen then it would have +happened 2 months after I just think + + align:start position:0% +happened 2 months after I just think + + + align:start position:0% +happened 2 months after I just think +that the people who initially organized + + align:start position:0% +that the people who initially organized + + + align:start position:0% +that the people who initially organized +it did a really good job and kind of + + align:start position:0% +it did a really good job and kind of + + + align:start position:0% +it did a really good job and kind of +appealing to this sort of like an like + + align:start position:0% +appealing to this sort of like an like + + + align:start position:0% +appealing to this sort of like an like +Anarchy concept of know they had all + + align:start position:0% +Anarchy concept of know they had all + + + align:start position:0% +Anarchy concept of know they had all +those masks uh of that movie V V for + + align:start position:0% +those masks uh of that movie V V for + + + align:start position:0% +those masks uh of that movie V V for +Vendetta and you know they to that that + + align:start position:0% +Vendetta and you know they to that that + + + align:start position:0% +Vendetta and you know they to that that +image and you're just like very + + align:start position:0% +image and you're just like very + + + align:start position:0% +image and you're just like very +secretive about how they attracted + + align:start position:0% +secretive about how they attracted + + + align:start position:0% +secretive about how they attracted +people and they became viral and it + + align:start position:0% +people and they became viral and it + + + align:start position:0% +people and they became viral and it +became viral but but what interesting is + + align:start position:0% +became viral but but what interesting is + + + align:start position:0% +became viral but but what interesting is +you point to the the particular leaders + + align:start position:0% +you point to the the particular leaders + + + align:start position:0% +you point to the the particular leaders +I mean they occupied Portland Oregon for + + align:start position:0% +I mean they occupied Portland Oregon for + + + align:start position:0% +I mean they occupied Portland Oregon for +heaven's sakes what what was that about + + align:start position:0% +heaven's sakes what what was that about + + + align:start position:0% +heaven's sakes what what was that about +this was a protest against global + + align:start position:0% +this was a protest against global + + + align:start position:0% +this was a protest against global +capitalism have you been to Portland + + align:start position:0% +capitalism have you been to Portland + + + align:start position:0% +capitalism have you been to Portland +Oregon I mean this is not this is not + + align:start position:0% +Oregon I mean this is not this is not + + + align:start position:0% +Oregon I mean this is not this is not +the financial Hub of the western world + + align:start position:0% +the financial Hub of the western world + + + align:start position:0% +the financial Hub of the western world +with jillions of people getting rich on + + align:start position:0% +with jillions of people getting rich on + + + align:start position:0% +with jillions of people getting rich on +the backs of the masses right it's a + + align:start position:0% +the backs of the masses right it's a + + + align:start position:0% +the backs of the masses right it's a +pretty mellow place but they occupied + + align:start position:0% +pretty mellow place but they occupied + + + align:start position:0% +pretty mellow place but they occupied +Portland so I you know they occupied a + + align:start position:0% +Portland so I you know they occupied a + + + align:start position:0% +Portland so I you know they occupied a +lot of + + align:start position:0% +lot of + + + align:start position:0% +lot of +places uh I give up let me move on yeah + + align:start position:0% +places uh I give up let me move on yeah + + + align:start position:0% +places uh I give up let me move on yeah +Julian oh oh if you're moving + + align:start position:0% +Julian oh oh if you're moving + + + align:start position:0% +Julian oh oh if you're moving +I was going to try but undoubtedly it's + + align:start position:0% +I was going to try but undoubtedly it's + + + align:start position:0% +I was going to try but undoubtedly it's +profound give it a give it give it a + + align:start position:0% +profound give it a give it give it a + + + align:start position:0% +profound give it a give it give it a +shot I mean I think like like he said + + align:start position:0% +shot I mean I think like like he said + + + align:start position:0% +shot I mean I think like like he said +it's kind of the particip precipitation + + align:start position:0% +it's kind of the particip precipitation + + + align:start position:0% +it's kind of the particip precipitation +of like a general sentiment + + align:start position:0% +of like a general sentiment + + + align:start position:0% +of like a general sentiment +that the government isn't necessarily + + align:start position:0% +that the government isn't necessarily + + + align:start position:0% +that the government isn't necessarily +benefiting the great majority of the + + align:start position:0% +benefiting the great majority of the + + + align:start position:0% +benefiting the great majority of the +population I feel like which is exactly + + align:start position:0% +population I feel like which is exactly + + + align:start position:0% +population I feel like which is exactly +what the Tea Party People thought too + + align:start position:0% +what the Tea Party People thought too + + + align:start position:0% +what the Tea Party People thought too +which is interesting and know I mean + + align:start position:0% +which is interesting and know I mean + + + align:start position:0% +which is interesting and know I mean +that's it there's something wrong in + + align:start position:0% +that's it there's something wrong in + + + align:start position:0% +that's it there's something wrong in +Washington something wrong + + align:start position:0% +Washington something wrong + + + align:start position:0% +Washington something wrong +yeah with a different diagnosis + + align:start position:0% +yeah with a different diagnosis + + + align:start position:0% +yeah with a different diagnosis +different diagnosis I mean very + + align:start position:0% +different diagnosis I mean very + + + align:start position:0% +different diagnosis I mean very +different ideas in the Tea Party + + align:start position:0% +different ideas in the Tea Party + + + align:start position:0% +different ideas in the Tea Party +Movement but it's just a general + + align:start position:0% +Movement but it's just a general + + + align:start position:0% +Movement but it's just a general +precipitation of something's wrong and + + align:start position:0% +precipitation of something's wrong and + + + align:start position:0% +precipitation of something's wrong and +we don't necessarily like it from a + + align:start position:0% +we don't necessarily like it from a + + + align:start position:0% +we don't necessarily like it from a +financial standpoint I feel like the + + align:start position:0% +financial standpoint I feel like the + + + align:start position:0% +financial standpoint I feel like the +grand majority of people that took place + + align:start position:0% +grand majority of people that took place + + + align:start position:0% +grand majority of people that took place +in the movement don't necessarily know + + align:start position:0% +in the movement don't necessarily know + + + align:start position:0% +in the movement don't necessarily know +what is wrong or exactly how to fix it + + align:start position:0% +what is wrong or exactly how to fix it + + + align:start position:0% +what is wrong or exactly how to fix it +to begin with so I think that's one of + + align:start position:0% +to begin with so I think that's one of + + + align:start position:0% +to begin with so I think that's one of +reasons why it kind of died out is that + + align:start position:0% +reasons why it kind of died out is that + + + align:start position:0% +reasons why it kind of died out is that +it just became a general shout of I'm + + align:start position:0% +it just became a general shout of I'm + + + align:start position:0% +it just became a general shout of I'm +angry + + align:start position:0% +angry + + + align:start position:0% +angry +yeah nothing and you saw a lot of + + align:start position:0% +yeah nothing and you saw a lot of + + + align:start position:0% +yeah nothing and you saw a lot of +movements of the I'm angry variety + + align:start position:0% +movements of the I'm angry variety + + + align:start position:0% +movements of the I'm angry variety +during the Great Depression uh from both + + align:start position:0% +during the Great Depression uh from both + + + align:start position:0% +during the Great Depression uh from both +left and right so it does you do get + + align:start position:0% +left and right so it does you do get + + + align:start position:0% +left and right so it does you do get +this in hard times um uh there was + + align:start position:0% +this in hard times um uh there was + + + align:start position:0% +this in hard times um uh there was +a I think sometime in the 30s there was + + align:start position:0% +a I think sometime in the 30s there was + + + align:start position:0% +a I think sometime in the 30s there was +a uh World War I veterans March on + + align:start position:0% +a uh World War I veterans March on + + + align:start position:0% +a uh World War I veterans March on +Washington because pensions weren't w't + + align:start position:0% +Washington because pensions weren't w't + + + align:start position:0% +Washington because pensions weren't w't +adequate and you got the rise of both + + align:start position:0% +adequate and you got the rise of both + + + align:start position:0% +adequate and you got the rise of both +extreme left and extreme right political + + align:start position:0% +extreme left and extreme right political + + + align:start position:0% +extreme left and extreme right political +groups on the grounds that it's just not + + align:start position:0% +groups on the grounds that it's just not + + + align:start position:0% +groups on the grounds that it's just not +right the Tea Party + + align:start position:0% +right the Tea Party + + + align:start position:0% +right the Tea Party +Movement has more heft because it + + align:start position:0% +Movement has more heft because it + + + align:start position:0% +Movement has more heft because it +actually has clear clearer objectives + + align:start position:0% +actually has clear clearer objectives + + + align:start position:0% +actually has clear clearer objectives +right there there's a caucus in Congress + + align:start position:0% +right there there's a caucus in Congress + + + align:start position:0% +right there there's a caucus in Congress +there are relatively organized groups in + + align:start position:0% +there are relatively organized groups in + + + align:start position:0% +there are relatively organized groups in +some congressional + + align:start position:0% +some congressional + + + align:start position:0% +some congressional +districts uh tarty backing is a big deal + + align:start position:0% +districts uh tarty backing is a big deal + + + align:start position:0% +districts uh tarty backing is a big deal +they have a convention so they they've + + align:start position:0% +they have a convention so they they've + + + align:start position:0% +they have a convention so they they've +made themselves into an interest group + + align:start position:0% +made themselves into an interest group + + + align:start position:0% +made themselves into an interest group +from movement interestingly + + align:start position:0% +from movement interestingly + + + align:start position:0% +from movement interestingly +enough uh with a little + + align:start position:0% +enough uh with a little + + + align:start position:0% +enough uh with a little +incoherence there was a there was a + + align:start position:0% +incoherence there was a there was a + + + align:start position:0% +incoherence there was a there was a +split between the Boston Tea Party and + + align:start position:0% +split between the Boston Tea Party and + + + align:start position:0% +split between the Boston Tea Party and +the Worcester tea party recently uh so + + align:start position:0% +the Worcester tea party recently uh so + + + align:start position:0% +the Worcester tea party recently uh so +they had separate separate rallies the + + align:start position:0% +they had separate separate rallies the + + + align:start position:0% +they had separate separate rallies the +Worcester tea party said we're all about + + align:start position:0% +Worcester tea party said we're all about + + + align:start position:0% +Worcester tea party said we're all about +low taxes and limited government and + + align:start position:0% +low taxes and limited government and + + + align:start position:0% +low taxes and limited government and +stuff like that and the Boston Tea Party + + align:start position:0% +stuff like that and the Boston Tea Party + + + align:start position:0% +stuff like that and the Boston Tea Party +said yeah and we hate gay marriage too + + align:start position:0% +said yeah and we hate gay marriage too + + + align:start position:0% +said yeah and we hate gay marriage too +and the Worcester people said no maybe + + align:start position:0% +and the Worcester people said no maybe + + + align:start position:0% +and the Worcester people said no maybe +we ought to just stay focused so they + + align:start position:0% +we ought to just stay focused so they + + + align:start position:0% +we ought to just stay focused so they +split anyway um okay + + align:start position:0% +split anyway um okay + + + align:start position:0% +split anyway um okay +to get a little closer to this course + + align:start position:0% +to get a little closer to this course + + + align:start position:0% +to get a little closer to this course +and a little less abstract um there's an + + align:start position:0% +and a little less abstract um there's an + + + align:start position:0% +and a little less abstract um there's an +interesting the other assigned paper is + + align:start position:0% +interesting the other assigned paper is + + + align:start position:0% +interesting the other assigned paper is +unse and salt which is about nuclear + + align:start position:0% +unse and salt which is about nuclear + + + align:start position:0% +unse and salt which is about nuclear +power + + align:start position:0% +power + + + align:start position:0% +power +uh and they sort of trace the partial + + align:start position:0% +uh and they sort of trace the partial + + + align:start position:0% +uh and they sort of trace the partial +evolution of the politics here uh what + + align:start position:0% +evolution of the politics here uh what + + + align:start position:0% +evolution of the politics here uh what +did the politics of nuclear power look + + align:start position:0% +did the politics of nuclear power look + + + align:start position:0% +did the politics of nuclear power look +like in the 50s and 60s movements + + align:start position:0% +like in the 50s and 60s movements + + + align:start position:0% +like in the 50s and 60s movements +interest groups what + + align:start position:0% + + + + align:start position:0% + +that was a hand no I was not waving okay + + align:start position:0% +that was a hand no I was not waving okay + + + align:start position:0% +that was a hand no I was not waving okay +yeah Brendon you got it okay um I think + + align:start position:0% +yeah Brendon you got it okay um I think + + + align:start position:0% +yeah Brendon you got it okay um I think +it was kind of like let's do this like + + align:start position:0% +it was kind of like let's do this like + + + align:start position:0% +it was kind of like let's do this like +this is going to be like it's going to + + align:start position:0% +this is going to be like it's going to + + + align:start position:0% +this is going to be like it's going to +cost like pennies to like cost you Penny + + align:start position:0% +cost like pennies to like cost you Penny + + + align:start position:0% +cost like pennies to like cost you Penny +what too cheap to meter was the phrase + + align:start position:0% +what too cheap to meter was the phrase + + + align:start position:0% +what too cheap to meter was the phrase +too cheap to meter it was very + + align:start position:0% +too cheap to meter it was very + + + align:start position:0% +too cheap to meter it was very +enthusiastic Navy was going nuclear + + align:start position:0% +enthusiastic Navy was going nuclear + + + align:start position:0% +enthusiastic Navy was going nuclear +there's a lot of proliferation + + align:start position:0% +there's a lot of proliferation + + + align:start position:0% +there's a lot of proliferation +technology out there so these reactors + + align:start position:0% +technology out there so these reactors + + + align:start position:0% +technology out there so these reactors +were ready to build and the + + align:start position:0% +were ready to build and the + + + align:start position:0% +were ready to build and the +politics was industry interest groups + + align:start position:0% +politics was industry interest groups + + + align:start position:0% +politics was industry interest groups +right there was the the paper labeled a + + align:start position:0% +right there was the the paper labeled a + + + align:start position:0% +right there was the the paper labeled a +bunch of them um the big thing their big + + align:start position:0% +bunch of them um the big thing their big + + + align:start position:0% +bunch of them um the big thing their big +win was there's a limit still in force + + align:start position:0% +win was there's a limit still in force + + + align:start position:0% +win was there's a limit still in force +on the + + align:start position:0% +on the + + + align:start position:0% +on the +liability uh of any uh related to any + + align:start position:0% +liability uh of any uh related to any + + + align:start position:0% +liability uh of any uh related to any +nuclear facility the atomic energy + + align:start position:0% +nuclear facility the atomic energy + + + align:start position:0% +nuclear facility the atomic energy +commission was regulatory but it was + + align:start position:0% +commission was regulatory but it was + + + align:start position:0% +commission was regulatory but it was +also Pro it also was promoting atomic + + align:start position:0% +also Pro it also was promoting atomic + + + align:start position:0% +also Pro it also was promoting atomic +energy as well as regulating so it's + + align:start position:0% +energy as well as regulating so it's + + + align:start position:0% +energy as well as regulating so it's +like the early years of air airline + + align:start position:0% +like the early years of air airline + + + align:start position:0% +like the early years of air airline +travel where you know the what politics + + align:start position:0% +travel where you know the what politics + + + align:start position:0% +travel where you know the what politics +there was was positive industry groups + + align:start position:0% +there was was positive industry groups + + + align:start position:0% +there was was positive industry groups +dominated inside the Beltway + + align:start position:0% +dominated inside the Beltway + + + align:start position:0% +dominated inside the Beltway +stuff not much in the media except for + + align:start position:0% +stuff not much in the media except for + + + align:start position:0% +stuff not much in the media except for +cheap swell good clean + + align:start position:0% +cheap swell good clean + + + align:start position:0% +cheap swell good clean +Etc what happened in the + + align:start position:0% + + + + align:start position:0% + +70s yeah it was a combination of a movie + + align:start position:0% +70s yeah it was a combination of a movie + + + align:start position:0% +70s yeah it was a combination of a movie +called The China Syndrome that came out + + align:start position:0% +called The China Syndrome that came out + + + align:start position:0% +called The China Syndrome that came out +then three mile China Syndrome might + + align:start position:0% +then three mile China Syndrome might + + + align:start position:0% +then three mile China Syndrome might +been a little later but go ahead not + + align:start position:0% +been a little later but go ahead not + + + align:start position:0% +been a little later but go ahead not +much later it + + align:start position:0% +much later it + + + align:start position:0% +much later it +followe kind of frightening thene Island + + align:start position:0% +followe kind of frightening thene Island + + + align:start position:0% +followe kind of frightening thene Island +kind of seem to mimic the movie like oh + + align:start position:0% +kind of seem to mimic the movie like oh + + + align:start position:0% +kind of seem to mimic the movie like oh +jeez this is reality it's actually D and + + align:start position:0% +jeez this is reality it's actually D and + + + align:start position:0% +jeez this is reality it's actually D and +you began to get a different kind of + + align:start position:0% +you began to get a different kind of + + + align:start position:0% +you began to get a different kind of +politics right politically what did you + + align:start position:0% + + + + align:start position:0% + +get I showed you what was what was on + + align:start position:0% +get I showed you what was what was on + + + align:start position:0% +get I showed you what was what was on +that slide you got an anti-nuclear + + align:start position:0% +that slide you got an anti-nuclear + + + align:start position:0% +that slide you got an anti-nuclear +movement you got people marching you got + + align:start position:0% +movement you got people marching you got + + + align:start position:0% +movement you got people marching you got +protests all of a sudden you had these + + align:start position:0% +protests all of a sudden you had these + + + align:start position:0% +protests all of a sudden you had these +industry groups in Washington with guys + + align:start position:0% +industry groups in Washington with guys + + + align:start position:0% +industry groups in Washington with guys +in suits + + align:start position:0% +in suits + + + align:start position:0% +in suits +and other capitals for that matter it + + align:start position:0% +and other capitals for that matter it + + + align:start position:0% +and other capitals for that matter it +that wasn't just an American phenomenon + + align:start position:0% +that wasn't just an American phenomenon + + + align:start position:0% +that wasn't just an American phenomenon +and then you began to have those German + + align:start position:0% +and then you began to have those German + + + align:start position:0% +and then you began to have those German +Marchers and the Japanese Marchers and + + align:start position:0% +Marchers and the Japanese Marchers and + + + align:start position:0% +Marchers and the Japanese Marchers and +Vermont is recent but you had American + + align:start position:0% +Vermont is recent but you had American + + + align:start position:0% +Vermont is recent but you had American +Marchers you began to get an + + align:start position:0% +Marchers you began to get an + + + align:start position:0% +Marchers you began to get an +anti-nuclear movement with protests and + + align:start position:0% +anti-nuclear movement with protests and + + + align:start position:0% +anti-nuclear movement with protests and +after Three Mile Island the industry + + align:start position:0% +after Three Mile Island the industry + + + align:start position:0% +after Three Mile Island the industry +stopped now this is the neat part which + + align:start position:0% +stopped now this is the neat part which + + + align:start position:0% +stopped now this is the neat part which +I actually wasn't aware of until I saw + + align:start position:0% +I actually wasn't aware of until I saw + + + align:start position:0% +I actually wasn't aware of until I saw +the article what did the industry try to + + align:start position:0% +the article what did the industry try to + + + align:start position:0% +the article what did the industry try to +do to react back to + + align:start position:0% +do to react back to + + + align:start position:0% +do to react back to +this do you have the guys in suits in + + align:start position:0% +this do you have the guys in suits in + + + align:start position:0% +this do you have the guys in suits in +Washington are they a good reaction + + align:start position:0% +Washington are they a good reaction + + + align:start position:0% +Washington are they a good reaction +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +yeah they tried to do a pro-nuclear + + align:start position:0% +yeah they tried to do a pro-nuclear + + + align:start position:0% +yeah they tried to do a pro-nuclear +movement did did it work not really how + + align:start position:0% +movement did did it work not really how + + + align:start position:0% +movement did did it work not really how +come um well the article mentions like + + align:start position:0% +come um well the article mentions like + + + align:start position:0% +come um well the article mentions like +the the anti-nuclear movement came like + + align:start position:0% +the the anti-nuclear movement came like + + + align:start position:0% +the the anti-nuclear movement came like +from the people and they all felt like + + align:start position:0% +from the people and they all felt like + + + align:start position:0% +from the people and they all felt like +like + + align:start position:0% +like + + + align:start position:0% +like +the an industry back movement where + + align:start position:0% +the an industry back movement where + + + align:start position:0% +the an industry back movement where +people in s that were like set apart + + align:start position:0% +people in s that were like set apart + + + align:start position:0% +people in s that were like set apart +from the the m + + align:start position:0% +from the the m + + + align:start position:0% +from the the m +and + + align:start position:0% +and + + + align:start position:0% +and +then so they tried to do it but but they + + align:start position:0% +then so they tried to do it but but they + + + align:start position:0% +then so they tried to do it but but they +really had trouble making it + + align:start position:0% +really had trouble making it + + + align:start position:0% +really had trouble making it +authentic the the anti-nuclear movement + + align:start position:0% +authentic the the anti-nuclear movement + + + align:start position:0% +authentic the the anti-nuclear movement +was Mom and Pop and your uncle and + + align:start position:0% +was Mom and Pop and your uncle and + + + align:start position:0% +was Mom and Pop and your uncle and +people really upset and the pronuclear + + align:start position:0% +people really upset and the pronuclear + + + align:start position:0% +people really upset and the pronuclear +movement was kind of industry people + + align:start position:0% +movement was kind of industry people + + + align:start position:0% +movement was kind of industry people +with their ties + + align:start position:0% +with their ties + + + align:start position:0% +with their ties +off the the phrase they use in the + + align:start position:0% +off the the phrase they use in the + + + align:start position:0% +off the the phrase they use in the +business is to distinguish between + + align:start position:0% +business is to distinguish between + + + align:start position:0% +business is to distinguish between +Grassroots and + + align:start position:0% +Grassroots and + + + align:start position:0% +Grassroots and +AstroTurf uh Grassroots move movements + + align:start position:0% +AstroTurf uh Grassroots move movements + + + align:start position:0% +AstroTurf uh Grassroots move movements +are really genuine and reflect popular + + align:start position:0% +are really genuine and reflect popular + + + align:start position:0% +are really genuine and reflect popular +sentiment AstroTurf is + + align:start position:0% +sentiment AstroTurf is + + + align:start position:0% +sentiment AstroTurf is +created right you can see it when you + + align:start position:0% +created right you can see it when you + + + align:start position:0% +created right you can see it when you +get when you get emails when a + + align:start position:0% +get when you get emails when a + + + align:start position:0% +get when you get emails when a +congressional office gets emails on an + + align:start position:0% +congressional office gets emails on an + + + align:start position:0% +congressional office gets emails on an +issue and they're all + + align:start position:0% +issue and they're all + + + align:start position:0% +issue and they're all +identical you say oh that's + + align:start position:0% +identical you say oh that's + + + align:start position:0% +identical you say oh that's +AstroTurf somebody is is really pushing + + align:start position:0% +AstroTurf somebody is is really pushing + + + align:start position:0% +AstroTurf somebody is is really pushing +people to send somebody's saying to all + + align:start position:0% +people to send somebody's saying to all + + + align:start position:0% +people to send somebody's saying to all +their employees send this + + align:start position:0% +their employees send this + + + align:start position:0% +their employees send this +email um that's not people being + + align:start position:0% +email um that's not people being + + + align:start position:0% +email um that's not people being +passionate and it just didn't work + + align:start position:0% +passionate and it just didn't work + + + align:start position:0% +passionate and it just didn't work +didn't work it was an attempt to create + + align:start position:0% +didn't work it was an attempt to create + + + align:start position:0% +didn't work it was an attempt to create +a movement to affect energy policy + + align:start position:0% +a movement to affect energy policy + + + align:start position:0% +a movement to affect energy policy +didn't + + align:start position:0% +didn't + + + align:start position:0% +didn't +work there not a lot of social movements + + align:start position:0% +work there not a lot of social movements + + + align:start position:0% +work there not a lot of social movements +in energy directly you see the more on + + align:start position:0% +in energy directly you see the more on + + + align:start position:0% +in energy directly you see the more on +the environmental + + align:start position:0% +the environmental + + + align:start position:0% +the environmental +side and the piece by rooked uh but + + align:start position:0% +side and the piece by rooked uh but + + + align:start position:0% +side and the piece by rooked uh but +environmental movements affect energy so + + align:start position:0% +environmental movements affect energy so + + + align:start position:0% +environmental movements affect energy so +it's worth talking + + align:start position:0% + + + + align:start position:0% + +about that's a depressing article if you + + align:start position:0% +about that's a depressing article if you + + + align:start position:0% +about that's a depressing article if you +if you read the first part in a bad mood + + align:start position:0% +if you read the first part in a bad mood + + + align:start position:0% +if you read the first part in a bad mood +because he says the environment's gotten + + align:start position:0% +because he says the environment's gotten + + + align:start position:0% +because he says the environment's gotten +worse and species are getting extinct + + align:start position:0% +worse and species are getting extinct + + + align:start position:0% +worse and species are getting extinct +and we're we're depleting natural + + align:start position:0% +and we're we're depleting natural + + + align:start position:0% +and we're we're depleting natural +resources I would just argue that he's + + align:start position:0% +resources I would just argue that he's + + + align:start position:0% +resources I would just argue that he's +measuring against the past not against + + align:start position:0% +measuring against the past not against + + + align:start position:0% +measuring against the past not against +what would have happened but for the + + align:start position:0% +what would have happened but for the + + + align:start position:0% +what would have happened but for the +environmental movement since the air and + + align:start position:0% +environmental movement since the air and + + + align:start position:0% +environmental movement since the air and +the water in us and Europe and many + + align:start position:0% +the water in us and Europe and many + + + align:start position:0% +the water in us and Europe and many +other places has improved + + align:start position:0% +other places has improved + + + align:start position:0% +other places has improved +notably nobody believes that but those + + align:start position:0% +notably nobody believes that but those + + + align:start position:0% +notably nobody believes that but those +are the numbers um he argues so he's + + align:start position:0% +are the numbers um he argues so he's + + + align:start position:0% +are the numbers um he argues so he's +trying to be quantitative + + align:start position:0% +trying to be quantitative + + + align:start position:0% +trying to be quantitative +he says that + + align:start position:0% +he says that + + + align:start position:0% +he says that +um an environmental movement can work + + align:start position:0% +um an environmental movement can work + + + align:start position:0% +um an environmental movement can work +through lobbying can work through public + + align:start position:0% +through lobbying can work through public + + + align:start position:0% +through lobbying can work through public +opinion can work through + + align:start position:0% +opinion can work through + + + align:start position:0% +opinion can work through +individual uh individual attitudes or + + align:start position:0% +individual uh individual attitudes or + + + align:start position:0% +individual uh individual attitudes or +through a green party as exist in some + + align:start position:0% +through a green party as exist in some + + + align:start position:0% +through a green party as exist in some +countries and the reason he does + + align:start position:0% +countries and the reason he does + + + align:start position:0% +countries and the reason he does +this rather than thinking about the ways + + align:start position:0% +this rather than thinking about the ways + + + align:start position:0% +this rather than thinking about the ways +we just finished talking about the more + + align:start position:0% +we just finished talking about the more + + + align:start position:0% +we just finished talking about the more +General ways is he's got measures of all + + align:start position:0% +General ways is he's got measures of all + + + align:start position:0% +General ways is he's got measures of all +these things got measures of how big the + + align:start position:0% +these things got measures of how big the + + + align:start position:0% +these things got measures of how big the +the green movement is he's got measures + + align:start position:0% +the green movement is he's got measures + + + align:start position:0% +the green movement is he's got measures +of public opinion he's got measures of + + align:start position:0% +of public opinion he's got measures of + + + align:start position:0% +of public opinion he's got measures of +attitudes of various kinds and he + + align:start position:0% +attitudes of various kinds and he + + + align:start position:0% +attitudes of various kinds and he +certainly knows whether there's a green + + align:start position:0% +certainly knows whether there's a green + + + align:start position:0% +certainly knows whether there's a green +party that gets any votes so he can + + align:start position:0% +party that gets any votes so he can + + + align:start position:0% +party that gets any votes so he can +measure these channels and he gives you + + align:start position:0% +measure these channels and he gives you + + + align:start position:0% +measure these channels and he gives you +this + + align:start position:0% +this + + + align:start position:0% +this +nice this nice + + align:start position:0% +nice this nice + + + align:start position:0% +nice this nice +picture so environmental + + align:start position:0% +picture so environmental + + + align:start position:0% +picture so environmental +movements uh react to environmental + + align:start position:0% +movements uh react to environmental + + + align:start position:0% +movements uh react to environmental +problems I think interpreted largely via + + align:start position:0% +problems I think interpreted largely via + + + align:start position:0% +problems I think interpreted largely via +Sciences is a little too optimistic but + + align:start position:0% +Sciences is a little too optimistic but + + + align:start position:0% +Sciences is a little too optimistic but +perceived problems they can Lobby they + + align:start position:0% +perceived problems they can Lobby they + + + align:start position:0% +perceived problems they can Lobby they +can be an interest group the + + align:start position:0% +can be an interest group the + + + align:start position:0% +can be an interest group the +environmental defense fund the natural + + align:start position:0% +environmental defense fund the natural + + + align:start position:0% +environmental defense fund the natural +resources um defense Council the friends + + align:start position:0% +resources um defense Council the friends + + + align:start position:0% +resources um defense Council the friends +of the Earth the Sierra Club + + align:start position:0% +of the Earth the Sierra Club + + + align:start position:0% +of the Earth the Sierra Club +the there are more I'm trying to think + + align:start position:0% +the there are more I'm trying to think + + + align:start position:0% +the there are more I'm trying to think +of a few but uh they lobby as well as as + + align:start position:0% +of a few but uh they lobby as well as as + + + align:start position:0% +of a few but uh they lobby as well as as +do other things um uh and so here are + + align:start position:0% +do other things um uh and so here are + + + align:start position:0% +do other things um uh and so here are +his + + align:start position:0% +his + + + align:start position:0% +his +channels so he + + align:start position:0% +channels so he + + + align:start position:0% +channels so he +has this very + + align:start position:0% +has this very + + + align:start position:0% +has this very +interesting um table + + align:start position:0% +interesting um table + + + align:start position:0% +interesting um table +based on a set of measures he looks at + + align:start position:0% +based on a set of measures he looks at + + + align:start position:0% +based on a set of measures he looks at +the strength of environmental pressure + + align:start position:0% +the strength of environmental pressure + + + align:start position:0% +the strength of environmental pressure +pressure + + align:start position:0% +pressure + + + align:start position:0% +pressure +groups it looks based on opinion polls + + align:start position:0% +groups it looks based on opinion polls + + + align:start position:0% +groups it looks based on opinion polls +attitudes toward the environment is + + align:start position:0% +attitudes toward the environment is + + + align:start position:0% +attitudes toward the environment is +there a green + + align:start position:0% +there a green + + + align:start position:0% +there a green +party and how how strong is the policy + + align:start position:0% +party and how how strong is the policy + + + align:start position:0% +party and how how strong is the policy +and what's happened to the + + align:start position:0% +and what's happened to the + + + align:start position:0% +and what's happened to the +environment uh it's sort of interesting + + align:start position:0% +environment uh it's sort of interesting + + + align:start position:0% +environment uh it's sort of interesting +right the + + align:start position:0% +right the + + + align:start position:0% +right the +US scores high in terms of the + + align:start position:0% +US scores high in terms of the + + + align:start position:0% +US scores high in terms of the +environmental pressure group + + align:start position:0% +environmental pressure group + + + align:start position:0% +environmental pressure group +uh we're kind of in the middle in terms + + align:start position:0% +uh we're kind of in the middle in terms + + + align:start position:0% +uh we're kind of in the middle in terms +of attitudes we don't have a green party + + align:start position:0% +of attitudes we don't have a green party + + + align:start position:0% +of attitudes we don't have a green party +a lot of places don't have green parties + + align:start position:0% +a lot of places don't have green parties + + + align:start position:0% +a lot of places don't have green parties +and we're kind of in the middle on + + align:start position:0% +and we're kind of in the middle on + + + align:start position:0% +and we're kind of in the middle on +policy efforts which I think is compared + + align:start position:0% +policy efforts which I think is compared + + + align:start position:0% +policy efforts which I think is compared +to these countries I think is not not + + align:start position:0% +to these countries I think is not not + + + align:start position:0% +to these countries I think is not not +far off the + + align:start position:0% +far off the + + + align:start position:0% +far off the +mark + + align:start position:0% +mark + + + align:start position:0% +mark +roughly uh and we're kind of in the + + align:start position:0% +roughly uh and we're kind of in the + + + align:start position:0% +roughly uh and we're kind of in the +middle in terms of Environmental Quality + + align:start position:0% +middle in terms of Environmental Quality + + + align:start position:0% +middle in terms of Environmental Quality +I forget how he measures that that's a + + align:start position:0% +I forget how he measures that that's a + + + align:start position:0% +I forget how he measures that that's a +that's a tough one because he's got so + + align:start position:0% +that's a tough one because he's got so + + + align:start position:0% +that's a tough one because he's got so +many different + + align:start position:0% +many different + + + align:start position:0% +many different +things but this is the the summary his + + align:start position:0% +things but this is the the summary his + + + align:start position:0% +things but this is the the summary his +summary of of how these work and I must + + align:start position:0% +summary of of how these work and I must + + + align:start position:0% +summary of of how these work and I must +say so what he did was to be + + align:start position:0% +say so what he did was to be + + + align:start position:0% +say so what he did was to be +clear + + align:start position:0% +clear + + + align:start position:0% +clear +um the US gets a three here it gets a + + align:start position:0% +um the US gets a three here it gets a + + + align:start position:0% +um the US gets a three here it gets a +two here it gets a one here it gets a + + align:start position:0% +two here it gets a one here it gets a + + + align:start position:0% +two here it gets a one here it gets a +one there and and a one or sorry a two + + align:start position:0% +one there and and a one or sorry a two + + + align:start position:0% +one there and and a one or sorry a two +there and a two there this is three this + + align:start position:0% +there and a two there this is three this + + + align:start position:0% +there and a two there this is three this +is two this is one and then he looks at + + align:start position:0% +is two this is one and then he looks at + + + align:start position:0% +is two this is one and then he looks at +correlations which is not obvious ly the + + align:start position:0% +correlations which is not obvious ly the + + + align:start position:0% +correlations which is not obvious ly the +right way to do it it's not obviously + + align:start position:0% +right way to do it it's not obviously + + + align:start position:0% +right way to do it it's not obviously +the wrong way to do + + align:start position:0% +the wrong way to do + + + align:start position:0% +the wrong way to do +it but here they + + align:start position:0% + + + + align:start position:0% + +are okay so reading + + align:start position:0% +are okay so reading + + + align:start position:0% +are okay so reading +across an environmental pressure group + + align:start position:0% +across an environmental pressure group + + + align:start position:0% +across an environmental pressure group +is most strongly associated with the + + align:start position:0% +is most strongly associated with the + + + align:start position:0% +is most strongly associated with the +strength of policy across + + align:start position:0% +strength of policy across + + + align:start position:0% +strength of policy across +countries has very little to do with + + align:start position:0% +countries has very little to do with + + + align:start position:0% +countries has very little to do with +whether there's a green party or not the + + align:start position:0% +whether there's a green party or not the + + + align:start position:0% +whether there's a green party or not the +stars or statistical significance very + + align:start position:0% +stars or statistical significance very + + + align:start position:0% +stars or statistical significance very +little to do with whether there's a + + align:start position:0% +little to do with whether there's a + + + align:start position:0% +little to do with whether there's a +green party or + + align:start position:0% +green party or + + + align:start position:0% +green party or +not why don't we have a green party in + + align:start position:0% +not why don't we have a green party in + + + align:start position:0% +not why don't we have a green party in +the United + + align:start position:0% + + + + align:start position:0% + +States Brandon thought we did wasn't + + align:start position:0% +States Brandon thought we did wasn't + + + align:start position:0% +States Brandon thought we did wasn't +like + + align:start position:0% +like + + + align:start position:0% +like +that uh is that what he called it okay + + align:start position:0% +that uh is that what he called it okay + + + align:start position:0% +that uh is that what he called it okay +we might have once we don't have one now + + align:start position:0% +we might have once we don't have one now + + + align:start position:0% +we might have once we don't have one now +they do in Germany various other + + align:start position:0% +they do in Germany various other + + + align:start position:0% +they do in Germany various other +countries + + align:start position:0% +countries + + + align:start position:0% +countries +do + + align:start position:0% +do + + + align:start position:0% +do +well Julian we have just significant + + align:start position:0% +well Julian we have just significant + + + align:start position:0% +well Julian we have just significant +it's what it's just insignificant + + align:start position:0% +it's what it's just insignificant + + + align:start position:0% +it's what it's just insignificant +insignificant yeah well that maybe + + align:start position:0% +insignificant yeah well that maybe + + + align:start position:0% +insignificant yeah well that maybe +that's it why don't we have one that's + + align:start position:0% +that's it why don't we have one that's + + + align:start position:0% +that's it why don't we have one that's +significant we've always been heavily + + align:start position:0% +significant we've always been heavily + + + align:start position:0% +significant we've always been heavily +toiz party system of Democrats and + + align:start position:0% +toiz party system of Democrats and + + + align:start position:0% +toiz party system of Democrats and +Republicans it's really hard for any + + align:start position:0% +Republicans it's really hard for any + + + align:start position:0% +Republicans it's really hard for any +party to break into that and make it a + + align:start position:0% +party to break into that and make it a + + + align:start position:0% +party to break into that and make it a +free party system but especially a green + + align:start position:0% +free party system but especially a green + + + align:start position:0% +free party system but especially a green +which is sort of like a subset of the + + align:start position:0% +which is sort of like a subset of the + + + align:start position:0% +which is sort of like a subset of the +democratic + + align:start position:0% +democratic + + + align:start position:0% +democratic +party it's very important our electoral + + align:start position:0% +party it's very important our electoral + + + align:start position:0% +party it's very important our electoral +rules are pretty important as are as + + align:start position:0% +rules are pretty important as are as + + + align:start position:0% +rules are pretty important as are as +they are in some countries in in some + + align:start position:0% +they are in some countries in in some + + + align:start position:0% +they are in some countries in in some +countries uh you vote for the party not + + align:start position:0% +countries uh you vote for the party not + + + align:start position:0% +countries uh you vote for the party not +the candidate and you know the party has + + align:start position:0% +the candidate and you know the party has + + + align:start position:0% +the candidate and you know the party has +representation in Parliament depending + + align:start position:0% +representation in Parliament depending + + + align:start position:0% +representation in Parliament depending +on the percentage of the votes it gets + + align:start position:0% +on the percentage of the votes it gets + + + align:start position:0% +on the percentage of the votes it gets +in that case a green party could get + + align:start position:0% +in that case a green party could get + + + align:start position:0% +in that case a green party could get +five six% of the votes and have somebody + + align:start position:0% +five six% of the votes and have somebody + + + align:start position:0% +five six% of the votes and have somebody +in + + align:start position:0% +in + + + align:start position:0% +in +Washington here you've got to win a + + align:start position:0% +Washington here you've got to win a + + + align:start position:0% +Washington here you've got to win a +majority to get into the house to get + + align:start position:0% +majority to get into the house to get + + + align:start position:0% +majority to get into the house to get +into the + + align:start position:0% +into the + + + align:start position:0% +into the +Senate uh it's very tough for third + + align:start position:0% +Senate uh it's very tough for third + + + align:start position:0% +Senate uh it's very tough for third +parties of any kind in our system not in + + align:start position:0% +parties of any kind in our system not in + + + align:start position:0% +parties of any kind in our system not in +all systems I wouldn't say we're heavily + + align:start position:0% +all systems I wouldn't say we're heavily + + + align:start position:0% +all systems I wouldn't say we're heavily +we're heavily polarized now the + + align:start position:0% +we're heavily polarized now the + + + align:start position:0% +we're heavily polarized now the +Republican and Democratic parties used + + align:start position:0% +Republican and Democratic parties used + + + align:start position:0% +Republican and Democratic parties used +to overlap more you used to actually + + align:start position:0% +to overlap more you used to actually + + + align:start position:0% +to overlap more you used to actually +have conservative Democrats who were + + align:start position:0% +have conservative Democrats who were + + + align:start position:0% +have conservative Democrats who were +more conservative than Liberal + + align:start position:0% +more conservative than Liberal + + + align:start position:0% +more conservative than Liberal +Republicans believe it or not um so one + + align:start position:0% +Republicans believe it or not um so one + + + align:start position:0% +Republicans believe it or not um so one +of the reasons for + + align:start position:0% +of the reasons for + + + align:start position:0% +of the reasons for +this is um electoral laws but + + align:start position:0% + + + + align:start position:0% + +it's this is the strongest correlation + + align:start position:0% +it's this is the strongest correlation + + + align:start position:0% +it's this is the strongest correlation +he's got and that's between the + + align:start position:0% +he's got and that's between the + + + align:start position:0% +he's got and that's between the +importance of environmental pressure + + align:start position:0% +importance of environmental pressure + + + align:start position:0% +importance of environmental pressure +groups and the strength of policy + + align:start position:0% +groups and the strength of policy + + + align:start position:0% +groups and the strength of policy +efforts to preserve the + + align:start position:0% +efforts to preserve the + + + align:start position:0% +efforts to preserve the +environment which is sort of interesting + + align:start position:0% +environment which is sort of interesting + + + align:start position:0% +environment which is sort of interesting +says the environmental movement does + + align:start position:0% +says the environmental movement does + + + align:start position:0% +says the environmental movement does +matter uh he call environmental movement + + align:start position:0% +matter uh he call environmental movement + + + align:start position:0% +matter uh he call environmental movement +pressure if you think about it in the + + align:start position:0% +pressure if you think about it in the + + + align:start position:0% +pressure if you think about it in the +US we don't actually have a lot of + + align:start position:0% +US we don't actually have a lot of + + + align:start position:0% +US we don't actually have a lot of +marches and rallies for the + + align:start position:0% +marches and rallies for the + + + align:start position:0% +marches and rallies for the +environment we have interest groups in + + align:start position:0% +environment we have interest groups in + + + align:start position:0% +environment we have interest groups in +Washington the environmental defense + + align:start position:0% +Washington the environmental defense + + + align:start position:0% +Washington the environmental defense +fund the Sierra Club the this the that + + align:start position:0% +fund the Sierra Club the this the that + + + align:start position:0% +fund the Sierra Club the this the that +there not a lot of non-conventional + + align:start position:0% +there not a lot of non-conventional + + + align:start position:0% +there not a lot of non-conventional +actions being done to save the + + align:start position:0% +actions being done to save the + + + align:start position:0% +actions being done to save the +environment there was a time in the + + align:start position:0% +environment there was a time in the + + + align:start position:0% +environment there was a time in the +Pacific Northwest when people would + + align:start position:0% +Pacific Northwest when people would + + + align:start position:0% +Pacific Northwest when people would +drive iron spikes into trees to prevent + + align:start position:0% +drive iron spikes into trees to prevent + + + align:start position:0% +drive iron spikes into trees to prevent +logging you don't hear much of that + + align:start position:0% +logging you don't hear much of that + + + align:start position:0% +logging you don't hear much of that +anymore uh you don't hear people + + align:start position:0% +anymore uh you don't hear people + + + align:start position:0% +anymore uh you don't hear people +chaining themselves to nuclear power uh + + align:start position:0% +chaining themselves to nuclear power uh + + + align:start position:0% +chaining themselves to nuclear power uh +plants much anymore so at this point + + align:start position:0% +plants much anymore so at this point + + + align:start position:0% +plants much anymore so at this point +we're lobbying other places stronger the + + align:start position:0% +we're lobbying other places stronger the + + + align:start position:0% +we're lobbying other places stronger the +other interesting correlation is how + + align:start position:0% +other interesting correlation is how + + + align:start position:0% +other interesting correlation is how +much stronger the correlation between + + align:start position:0% +much stronger the correlation between + + + align:start position:0% +much stronger the correlation between +environmental movement pressure and + + align:start position:0% +environmental movement pressure and + + + align:start position:0% +environmental movement pressure and +policy is than between movement pressure + + align:start position:0% +policy is than between movement pressure + + + align:start position:0% +policy is than between movement pressure +and his measure at least of changes in + + align:start position:0% +and his measure at least of changes in + + + align:start position:0% +and his measure at least of changes in +the + + align:start position:0% + + + + align:start position:0% + +environment and part of that has to do + + align:start position:0% +environment and part of that has to do + + + align:start position:0% +environment and part of that has to do +with where you are and what the natural + + align:start position:0% +with where you are and what the natural + + + align:start position:0% +with where you are and what the natural +conditions are right policy efforts in + + align:start position:0% +conditions are right policy efforts in + + + align:start position:0% +conditions are right policy efforts in +Los Angeles are + + align:start position:0% +Los Angeles are + + + align:start position:0% +Los Angeles are +extraordinary Los Angeles has dirty + + align:start position:0% +extraordinary Los Angeles has dirty + + + align:start position:0% +extraordinary Los Angeles has dirty +air uh I don't don't think there's a + + align:start position:0% +air uh I don't don't think there's a + + + align:start position:0% +air uh I don't don't think there's a +European country that takes as much pain + + align:start position:0% +European country that takes as much pain + + + align:start position:0% +European country that takes as much pain +to preserve air quality as they as is + + align:start position:0% +to preserve air quality as they as is + + + align:start position:0% +to preserve air quality as they as is +done in the Los Angeles basin it's just + + align:start position:0% +done in the Los Angeles basin it's just + + + align:start position:0% +done in the Los Angeles basin it's just +really hard it just doesn't ventilate so + + align:start position:0% +really hard it just doesn't ventilate so + + + align:start position:0% +really hard it just doesn't ventilate so +the notion that and if you're if you're + + align:start position:0% +the notion that and if you're if you're + + + align:start position:0% +the notion that and if you're if you're +highly uh if it's a very dense country + + align:start position:0% +highly uh if it's a very dense country + + + align:start position:0% +highly uh if it's a very dense country +it's kind of hard to preserve species + + align:start position:0% +it's kind of hard to preserve species + + + align:start position:0% +it's kind of hard to preserve species +against development and so on and so + + align:start position:0% +against development and so on and so + + + align:start position:0% +against development and so on and so +forth so I don't know you you believe + + align:start position:0% +forth so I don't know you you believe + + + align:start position:0% +forth so I don't know you you believe +the AR are you persuaded by the article + + align:start position:0% +the AR are you persuaded by the article + + + align:start position:0% +the AR are you persuaded by the article +comments on it does that actually seem + + align:start position:0% +comments on it does that actually seem + + + align:start position:0% +comments on it does that actually seem +like a plausible description of interest + + align:start position:0% +like a plausible description of interest + + + align:start position:0% +like a plausible description of interest +group of + + align:start position:0% +group of + + + align:start position:0% +group of +environmental + + align:start position:0% +environmental + + + align:start position:0% +environmental +politics + + align:start position:0% +politics + + + align:start position:0% +politics +and I I would notice also that the the + + align:start position:0% +and I I would notice also that the the + + + align:start position:0% +and I I would notice also that the the +difference the the the link between and + + align:start position:0% +difference the the the link between and + + + align:start position:0% +difference the the the link between and +again causation is an inference it's + + align:start position:0% +again causation is an inference it's + + + align:start position:0% +again causation is an inference it's +correlation is all we all we measure the + + align:start position:0% +correlation is all we all we measure the + + + align:start position:0% +correlation is all we all we measure the +link between + + align:start position:0% +link between + + + align:start position:0% +link between +individual um between environmental + + align:start position:0% +individual um between environmental + + + align:start position:0% +individual um between environmental +pressure and attitudes isn't that + + align:start position:0% +pressure and attitudes isn't that + + + align:start position:0% +pressure and attitudes isn't that +great which makes sense in the US right + + align:start position:0% +great which makes sense in the US right + + + align:start position:0% +great which makes sense in the US right +because the Sierra Club isn't trying to + + align:start position:0% +because the Sierra Club isn't trying to + + + align:start position:0% +because the Sierra Club isn't trying to +persuade you and me it's trying to + + align:start position:0% +persuade you and me it's trying to + + + align:start position:0% +persuade you and me it's trying to +persuade Congress and the EPA + + align:start position:0% +persuade Congress and the EPA + + + align:start position:0% +persuade Congress and the EPA +so uh if it's successful there it wins + + align:start position:0% +so uh if it's successful there it wins + + + align:start position:0% +so uh if it's successful there it wins +um individual attitudes and policy not + + align:start position:0% +um individual attitudes and policy not + + + align:start position:0% +um individual attitudes and policy not +that strong either not that strong a + + align:start position:0% +that strong either not that strong a + + + align:start position:0% +that strong either not that strong a +correlation so this is sort of a picture + + align:start position:0% +correlation so this is sort of a picture + + + align:start position:0% +correlation so this is sort of a picture +of uh + + align:start position:0% +of uh + + + align:start position:0% +of uh +lobbying where the environmental + + align:start position:0% +lobbying where the environmental + + + align:start position:0% +lobbying where the environmental +movement acts directly on policy doesn't + + align:start position:0% +movement acts directly on policy doesn't + + + align:start position:0% +movement acts directly on policy doesn't +act indirectly seems to me through + + align:start position:0% +act indirectly seems to me through + + + align:start position:0% +act indirectly seems to me through +parades Mass marches demonstrations and + + align:start position:0% +parades Mass marches demonstrations and + + + align:start position:0% +parades Mass marches demonstrations and +any of those other mechanisms + + align:start position:0% +any of those other mechanisms + + + align:start position:0% +any of those other mechanisms +I think that's a fair description of the + + align:start position:0% +I think that's a fair description of the + + + align:start position:0% +I think that's a fair description of the +movement now in the US yeah seems to me + + align:start position:0% +movement now in the US yeah seems to me + + + align:start position:0% +movement now in the US yeah seems to me +it seems pretty reasonable even though + + align:start position:0% +it seems pretty reasonable even though + + + align:start position:0% +it seems pretty reasonable even though +it's correlation all compation right + + align:start position:0% +it's correlation all compation right + + + align:start position:0% +it's correlation all compation right +because uh although one can make the + + align:start position:0% +because uh although one can make the + + + align:start position:0% +because uh although one can make the +argument that interest groups would be + + align:start position:0% +argument that interest groups would be + + + align:start position:0% +argument that interest groups would be +would be would come out uh after certain + + align:start position:0% +would be would come out uh after certain + + + align:start position:0% +would be would come out uh after certain +policies made it seems to me that the + + align:start position:0% +policies made it seems to me that the + + + align:start position:0% +policies made it seems to me that the +the more logical flow would be for + + align:start position:0% +the more logical flow would be for + + + align:start position:0% +the more logical flow would be for +information uh for those groups be + + align:start position:0% +information uh for those groups be + + + align:start position:0% +information uh for those groups be +formed initially and then the policy is + + align:start position:0% +formed initially and then the policy is + + + align:start position:0% +formed initially and then the policy is +made um so even though he proved only + + align:start position:0% +made um so even though he proved only + + + align:start position:0% +made um so even though he proved only +correlation I think that that that flow + + align:start position:0% +correlation I think that that that flow + + + align:start position:0% +correlation I think that that that flow +makes more sense oh yeah no it's not + + align:start position:0% +makes more sense oh yeah no it's not + + + align:start position:0% +makes more sense oh yeah no it's not +it's not from in + + align:start position:0% +it's not from in + + + align:start position:0% +it's not from in +fact in fact it can go the other way + + align:start position:0% +fact in fact it can go the other way + + + align:start position:0% +fact in fact it can go the other way +because when Reagan basically declared + + align:start position:0% +because when Reagan basically declared + + + align:start position:0% +because when Reagan basically declared +war on Environmental Policy the + + align:start position:0% +war on Environmental Policy the + + + align:start position:0% +war on Environmental Policy the +memberships of those groups + + align:start position:0% +memberships of those groups + + + align:start position:0% +memberships of those groups +soared because they saw a + + align:start position:0% +soared because they saw a + + + align:start position:0% +soared because they saw a +threat and the groups you know s out + + align:start position:0% +threat and the groups you know s out + + + align:start position:0% +threat and the groups you know s out +mass mailing saying look what this guy's + + align:start position:0% +mass mailing saying look what this guy's + + + align:start position:0% +mass mailing saying look what this guy's +trying to do to the environment and the + + align:start position:0% +trying to do to the environment and the + + + align:start position:0% +trying to do to the environment and the +money flowed + + align:start position:0% +money flowed + + + align:start position:0% +money flowed +in um it's not so the question of are + + align:start position:0% +in um it's not so the question of are + + + align:start position:0% +in um it's not so the question of are +they are they exerting pressure yes but + + align:start position:0% +they are they exerting pressure yes but + + + align:start position:0% +they are they exerting pressure yes but +in that case they were exerting more + + align:start position:0% +in that case they were exerting more + + + align:start position:0% +in that case they were exerting more +pressure in a much more hostile + + align:start position:0% +pressure in a much more hostile + + + align:start position:0% +pressure in a much more hostile +environment politically so + + align:start position:0% +environment politically so + + + align:start position:0% +environment politically so +yeah um I I think + + align:start position:0% +yeah um I I think + + + align:start position:0% +yeah um I I think +that the direction is generally + + align:start position:0% +that the direction is generally + + + align:start position:0% +that the direction is generally +right any other + + align:start position:0% +right any other + + + align:start position:0% +right any other +comments yeah Charlotte I guess like I + + align:start position:0% +comments yeah Charlotte I guess like I + + + align:start position:0% +comments yeah Charlotte I guess like I +know he had a system for doing all this + + align:start position:0% +know he had a system for doing all this + + + align:start position:0% +know he had a system for doing all this +but it seems like you can come up with a + + align:start position:0% +but it seems like you can come up with a + + + align:start position:0% +but it seems like you can come up with a +different system and get different + + align:start position:0% +different system and get different + + + align:start position:0% +different system and get different +results and you're just not a natural + + align:start position:0% +results and you're just not a natural + + + align:start position:0% +results and you're just not a natural +sociologist numbers are weird to yeah + + align:start position:0% +sociologist numbers are weird to yeah + + + align:start position:0% +sociologist numbers are weird to yeah +well but this raises this raises a sort + + align:start position:0% +well but this raises this raises a sort + + + align:start position:0% +well but this raises this raises a sort +of a + + align:start position:0% +of a + + + align:start position:0% +of a +general a general problem in social + + align:start position:0% +general a general problem in social + + + align:start position:0% +general a general problem in social +science in economics we get lucky + + align:start position:0% +science in economics we get lucky + + + align:start position:0% +science in economics we get lucky +because you have dollars and quantities + + align:start position:0% +because you have dollars and quantities + + + align:start position:0% +because you have dollars and quantities +and tons and stuff this is sociology + + align:start position:0% +and tons and stuff this is sociology + + + align:start position:0% +and tons and stuff this is sociology +what have you got you've got attitudes + + align:start position:0% +what have you got you've got attitudes + + + align:start position:0% +what have you got you've got attitudes +you've got + + align:start position:0% +you've got + + + align:start position:0% +you've got +some IL defined measures of this that + + align:start position:0% +some IL defined measures of this that + + + align:start position:0% +some IL defined measures of this that +and the other you want to say are + + align:start position:0% +and the other you want to say are + + + align:start position:0% +and the other you want to say are +environmental groups + + align:start position:0% +environmental groups + + + align:start position:0% +environmental groups +effective uh it seems to me you're stuck + + align:start position:0% +effective uh it seems to me you're stuck + + + align:start position:0% +effective uh it seems to me you're stuck +doing something like this you can do it + + align:start position:0% +doing something like this you can do it + + + align:start position:0% +doing something like this you can do it +well or poorly I think this is pretty + + align:start position:0% +well or poorly I think this is pretty + + + align:start position:0% +well or poorly I think this is pretty +good um I'm still not I hadn't thought + + align:start position:0% +good um I'm still not I hadn't thought + + + align:start position:0% +good um I'm still not I hadn't thought +about it much but it just didn't strike + + align:start position:0% +about it much but it just didn't strike + + + align:start position:0% +about it much but it just didn't strike +me that just running ordinary + + align:start position:0% +me that just running ordinary + + + align:start position:0% +me that just running ordinary +correlations is quite the right way to + + align:start position:0% +correlations is quite the right way to + + + align:start position:0% +correlations is quite the right way to +do it but there's no obviously better + + align:start position:0% +do it but there's no obviously better + + + align:start position:0% +do it but there's no obviously better +way that comes to mind I know what would + + align:start position:0% +way that comes to mind I know what would + + + align:start position:0% +way that comes to mind I know what would +you do I think I'd be put more persuaded + + align:start position:0% +you do I think I'd be put more persuaded + + + align:start position:0% +you do I think I'd be put more persuaded +by case study where it did work in the + + align:start position:0% +by case study where it did work in the + + + align:start position:0% +by case study where it did work in the +case where there was like a green party + + align:start position:0% +case where there was like a green party + + + align:start position:0% +case where there was like a green party +or wasn't a green party or it didn't + + align:start position:0% +or wasn't a green party or it didn't + + + align:start position:0% +or wasn't a green party or it didn't +work in that sort of case like I think + + align:start position:0% +work in that sort of case like I think + + + align:start position:0% +work in that sort of case like I think +I'd be more I think I'd be able to + + align:start position:0% +I'd be more I think I'd be able to + + + align:start position:0% +I'd be more I think I'd be able to +relate to that more and I know that's + + align:start position:0% +relate to that more and I know that's + + + align:start position:0% +relate to that more and I know that's +not as general as what he's trying to do + + align:start position:0% +not as general as what he's trying to do + + + align:start position:0% +not as general as what he's trying to do +here but I think that maybe he makes it + + align:start position:0% +here but I think that maybe he makes it + + + align:start position:0% +here but I think that maybe he makes it +too General like what's the difference + + align:start position:0% +too General like what's the difference + + + align:start position:0% +too General like what's the difference +between like a 6 and a 7 on his little + + align:start position:0% +between like a 6 and a 7 on his little + + + align:start position:0% +between like a 6 and a 7 on his little +scale like that doesn't mean anything to + + align:start position:0% +scale like that doesn't mean anything to + + + align:start position:0% +scale like that doesn't mean anything to +me so no I'm I'm I'm I'm sort of with + + align:start position:0% +me so no I'm I'm I'm I'm sort of with + + + align:start position:0% +me so no I'm I'm I'm I'm sort of with +you uh I I'd prefer to I'd prefer to + + align:start position:0% +you uh I I'd prefer to I'd prefer to + + + align:start position:0% +you uh I I'd prefer to I'd prefer to +understand one or two two cases well + + align:start position:0% +understand one or two two cases well + + + align:start position:0% +understand one or two two cases well +than 18 cases badly um the issue + + align:start position:0% +than 18 cases badly um the issue + + + align:start position:0% +than 18 cases badly um the issue +he's well it's a general it's a general + + align:start position:0% +he's well it's a general it's a general + + + align:start position:0% +he's well it's a general it's a general +problem right um you do a case study you + + align:start position:0% +problem right um you do a case study you + + + align:start position:0% +problem right um you do a case study you +you you have a study where n equals 1 + + align:start position:0% +you you have a study where n equals 1 + + + align:start position:0% +you you have a study where n equals 1 +right you can't test a hypothesis with n + + align:start position:0% +right you can't test a hypothesis with n + + + align:start position:0% +right you can't test a hypothesis with n +equals 1 so if you're interested in + + align:start position:0% +equals 1 so if you're interested in + + + align:start position:0% +equals 1 so if you're interested in +testing a hypothesis say environmental + + align:start position:0% +testing a hypothesis say environmental + + + align:start position:0% +testing a hypothesis say environmental +movements operate mainly through + + align:start position:0% +movements operate mainly through + + + align:start position:0% +movements operate mainly through +individual + + align:start position:0% +individual + + + align:start position:0% +individual +attitudes you can't do n equals one you + + align:start position:0% +attitudes you can't do n equals one you + + + align:start position:0% +attitudes you can't do n equals one you +could probably do before and after in a + + align:start position:0% +could probably do before and after in a + + + align:start position:0% +could probably do before and after in a +case study you could try it but of + + align:start position:0% +case study you could try it but of + + + align:start position:0% +case study you could try it but of +course you can't hold everything else + + align:start position:0% +course you can't hold everything else + + + align:start position:0% +course you can't hold everything else +constant no I'm I'm I'm sympathetic I + + align:start position:0% +constant no I'm I'm I'm sympathetic I + + + align:start position:0% +constant no I'm I'm I'm sympathetic I +I'm I'm not excited about kind of + + align:start position:0% +I'm I'm not excited about kind of + + + align:start position:0% +I'm I'm not excited about kind of +unidimensional measures of policy + + align:start position:0% +unidimensional measures of policy + + + align:start position:0% +unidimensional measures of policy +efforts right I mean US policy is + + align:start position:0% +efforts right I mean US policy is + + + align:start position:0% +efforts right I mean US policy is +stronger than some of those other + + align:start position:0% +stronger than some of those other + + + align:start position:0% +stronger than some of those other +countries on some dimensions and weaker + + align:start position:0% +countries on some dimensions and weaker + + + align:start position:0% +countries on some dimensions and weaker +on + + align:start position:0% +on + + + align:start position:0% +on +others um Europe European tax systems + + align:start position:0% +others um Europe European tax systems + + + align:start position:0% +others um Europe European tax systems +favor use of diesels diesels produce + + align:start position:0% +favor use of diesels diesels produce + + + align:start position:0% +favor use of diesels diesels produce +small particulates small particulates + + align:start position:0% +small particulates small particulates + + + align:start position:0% +small particulates small particulates +have terrible health + + align:start position:0% +have terrible health + + + align:start position:0% +have terrible health +effects so are they more environmentally + + align:start position:0% +effects so are they more environmentally + + + align:start position:0% +effects so are they more environmentally +conscious than we are because they + + align:start position:0% +conscious than we are because they + + + align:start position:0% +conscious than we are because they +recycle or more or we more + + align:start position:0% +recycle or more or we more + + + align:start position:0% +recycle or more or we more +environmentally conscious because we + + align:start position:0% +environmentally conscious because we + + + align:start position:0% +environmentally conscious because we +avoid + + align:start position:0% +avoid + + + align:start position:0% +avoid +diesels very hard to do yeah no I I I I + + align:start position:0% +diesels very hard to do yeah no I I I I + + + align:start position:0% +diesels very hard to do yeah no I I I I +take the point anybody + + align:start position:0% + + + + align:start position:0% + +else + + align:start position:0% +else + + + align:start position:0% +else +okay we will Wednesday uh talk about uh + + align:start position:0% +okay we will Wednesday uh talk about uh + + + align:start position:0% +okay we will Wednesday uh talk about uh +us Environmental Policy walk through the + + align:start position:0% +us Environmental Policy walk through the + + + align:start position:0% +us Environmental Policy walk through the +case study and looking Beyond it so + + align:start position:0% +case study and looking Beyond it so + + + align:start position:0% +case study and looking Beyond it so +please read that um and for those of you + + align:start position:0% +please read that um and for those of you + + + align:start position:0% +please read that um and for those of you +who came late Monday we will see if we + + align:start position:0% +who came late Monday we will see if we + + + align:start position:0% +who came late Monday we will see if we +can find a guest speaker for an hour and + + align:start position:0% +can find a guest speaker for an hour and + + + align:start position:0% +can find a guest speaker for an hour and +we'll do an hour's soft shoe on a half + + align:start position:0% +we'll do an hour's soft shoe on a half + + + align:start position:0% +we'll do an hour's soft shoe on a half +an hour's soft shoe on green growth uh + + align:start position:0% +an hour's soft shoe on green growth uh + + + align:start position:0% +an hour's soft shoe on green growth uh +reflecting the will of a narrow + + align:start position:0% + + + + align:start position:0% + +majority \ No newline at end of file diff --git a/11iF2ovjKOg.txt b/11iF2ovjKOg.txt new file mode 100644 index 0000000000000000000000000000000000000000..11e796d9052d36f576523846e4cbe9d4eb0c04d0 --- /dev/null +++ b/11iF2ovjKOg.txt @@ -0,0 +1,1651 @@ +align:start position:0% + +we now move to the case of continuous + + align:start position:0% +we now move to the case of continuous + + + align:start position:0% +we now move to the case of continuous +random variables we will start with a + + align:start position:0% +random variables we will start with a + + + align:start position:0% +random variables we will start with a +special case where we want to find the + + align:start position:0% +special case where we want to find the + + + align:start position:0% +special case where we want to find the +PDF of a linear function of a continuous + + align:start position:0% +PDF of a linear function of a continuous + + + align:start position:0% +PDF of a linear function of a continuous +random variable we will start by + + align:start position:0% +random variable we will start by + + + align:start position:0% +random variable we will start by +considering a simple example and study + + align:start position:0% +considering a simple example and study + + + align:start position:0% +considering a simple example and study +it using an intuitive argument and + + align:start position:0% +it using an intuitive argument and + + + align:start position:0% +it using an intuitive argument and +afterwards we will justify our + + align:start position:0% +afterwards we will justify our + + + align:start position:0% +afterwards we will justify our +conclusions mathematically so we start + + align:start position:0% +conclusions mathematically so we start + + + align:start position:0% +conclusions mathematically so we start +with a random variable X that has a PDF + + align:start position:0% +with a random variable X that has a PDF + + + align:start position:0% +with a random variable X that has a PDF +over the form shown in this figure so + + align:start position:0% +over the form shown in this figure so + + + align:start position:0% +over the form shown in this figure so +that it is a piecewise constant PDF we + + align:start position:0% +that it is a piecewise constant PDF we + + + align:start position:0% +that it is a piecewise constant PDF we +then consider a random variable Z which + + align:start position:0% +then consider a random variable Z which + + + align:start position:0% +then consider a random variable Z which +is defined to be 2 times X the random + + align:start position:0% +is defined to be 2 times X the random + + + align:start position:0% +is defined to be 2 times X the random +variable X takes values between minus 1 + + align:start position:0% +variable X takes values between minus 1 + + + align:start position:0% +variable X takes values between minus 1 +and 1 so Z takes values between minus 2 + + align:start position:0% +and 1 so Z takes values between minus 2 + + + align:start position:0% +and 1 so Z takes values between minus 2 +and 2 now values of X between minus 1 + + align:start position:0% +and 2 now values of X between minus 1 + + + align:start position:0% +and 2 now values of X between minus 1 +and 0 correspond to values of Z between + + align:start position:0% +and 0 correspond to values of Z between + + + align:start position:0% +and 0 correspond to values of Z between +minus 2 and 0 the different values of x + + align:start position:0% +minus 2 and 0 the different values of x + + + align:start position:0% +minus 2 and 0 the different values of x +in this range are in some sense equally + + align:start position:0% +in this range are in some sense equally + + + align:start position:0% +in this range are in some sense equally +likely because we have a constant PDF + + align:start position:0% +likely because we have a constant PDF + + + align:start position:0% +likely because we have a constant PDF +and that argues that the corresponding + + align:start position:0% +and that argues that the corresponding + + + align:start position:0% +and that argues that the corresponding +values of Z should also be in some sense + + align:start position:0% +values of Z should also be in some sense + + + align:start position:0% +values of Z should also be in some sense +equally likely so the PDF should be + + align:start position:0% +equally likely so the PDF should be + + + align:start position:0% +equally likely so the PDF should be +constant over this range by a similar + + align:start position:0% +constant over this range by a similar + + + align:start position:0% +constant over this range by a similar +argument the PDF of Z should also be + + align:start position:0% +argument the PDF of Z should also be + + + align:start position:0% +argument the PDF of Z should also be +constant over the range from 0 to 2 and + + align:start position:0% +constant over the range from 0 to 2 and + + + align:start position:0% +constant over the range from 0 to 2 and +the PDF must of course be 0 outside this + + align:start position:0% +the PDF must of course be 0 outside this + + + align:start position:0% +the PDF must of course be 0 outside this +range because these are values of Z that + + align:start position:0% +range because these are values of Z that + + + align:start position:0% +range because these are values of Z that +are impossible let us now try to figure + + align:start position:0% +are impossible let us now try to figure + + + align:start position:0% +are impossible let us now try to figure +out the parameters of this PDF the + + align:start position:0% +out the parameters of this PDF the + + + align:start position:0% +out the parameters of this PDF the +probability that X is positive is the + + align:start position:0% +probability that X is positive is the + + + align:start position:0% +probability that X is positive is the +area of this rectangle and the area of + + align:start position:0% +area of this rectangle and the area of + + + align:start position:0% +area of this rectangle and the area of +this rectangle is 2/3 so the area of + + align:start position:0% +this rectangle is 2/3 so the area of + + + align:start position:0% +this rectangle is 2/3 so the area of +this rectangle should also be 2/3 and + + align:start position:0% +this rectangle should also be 2/3 and + + + align:start position:0% +this rectangle should also be 2/3 and +that means that the height of this + + align:start position:0% +that means that the height of this + + + align:start position:0% +that means that the height of this +rectangle should be equal to 1/3 + + align:start position:0% +rectangle should be equal to 1/3 + + + align:start position:0% +rectangle should be equal to 1/3 +similarly the probability that X is + + align:start position:0% +similarly the probability that X is + + + align:start position:0% +similarly the probability that X is +negative is the area of this rectangle + + align:start position:0% +negative is the area of this rectangle + + + align:start position:0% +negative is the area of this rectangle +and the area of this rectangle is equal + + align:start position:0% +and the area of this rectangle is equal + + + align:start position:0% +and the area of this rectangle is equal +to 1/3 when X is negative z is also + + align:start position:0% +to 1/3 when X is negative z is also + + + align:start position:0% +to 1/3 when X is negative z is also +negative so the probability of negative + + align:start position:0% +negative so the probability of negative + + + align:start position:0% +negative so the probability of negative +values should be equal to 1 + + align:start position:0% +values should be equal to 1 + + + align:start position:0% +values should be equal to 1 +and for the area of this rectangle to be + + align:start position:0% +and for the area of this rectangle to be + + + align:start position:0% +and for the area of this rectangle to be +1/3 it means that the height of this + + align:start position:0% +1/3 it means that the height of this + + + align:start position:0% +1/3 it means that the height of this +rectangle should be 1/6 so what happened + + align:start position:0% +rectangle should be 1/6 so what happened + + + align:start position:0% +rectangle should be 1/6 so what happened +here we started with a PDF of X and + + align:start position:0% +here we started with a PDF of X and + + + align:start position:0% +here we started with a PDF of X and +essentially stretched it out by a factor + + align:start position:0% +essentially stretched it out by a factor + + + align:start position:0% +essentially stretched it out by a factor +of 2 while keeping the same shape + + align:start position:0% +of 2 while keeping the same shape + + + align:start position:0% +of 2 while keeping the same shape +however we also scaled it down by a + + align:start position:0% +however we also scaled it down by a + + + align:start position:0% +however we also scaled it down by a +corresponding amount so 2/3 became 1/3 + + align:start position:0% +corresponding amount so 2/3 became 1/3 + + + align:start position:0% +corresponding amount so 2/3 became 1/3 +and 1/3 became 1/6 the reason for this + + align:start position:0% +and 1/3 became 1/6 the reason for this + + + align:start position:0% +and 1/3 became 1/6 the reason for this +scaling down is because we need the + + align:start position:0% +scaling down is because we need the + + + align:start position:0% +scaling down is because we need the +total probability the total area under + + align:start position:0% +total probability the total area under + + + align:start position:0% +total probability the total area under +this PDF to be equal to 1 if we now add + + align:start position:0% +this PDF to be equal to 1 if we now add + + + align:start position:0% +this PDF to be equal to 1 if we now add +a number let's say 3 to the random + + align:start position:0% +a number let's say 3 to the random + + + align:start position:0% +a number let's say 3 to the random +variable Z what is going to happen the + + align:start position:0% +variable Z what is going to happen the + + + align:start position:0% +variable Z what is going to happen the +random variable Y now will take values + + align:start position:0% +random variable Y now will take values + + + align:start position:0% +random variable Y now will take values +from minus 2 plus 3 this is plus 1 all + + align:start position:0% +from minus 2 plus 3 this is plus 1 all + + + align:start position:0% +from minus 2 plus 3 this is plus 1 all +the way up to 2 plus 3 which is plus 5 + + align:start position:0% +the way up to 2 plus 3 which is plus 5 + + + align:start position:0% +the way up to 2 plus 3 which is plus 5 +values in the range from 1 to 3 + + align:start position:0% +values in the range from 1 to 3 + + + align:start position:0% +values in the range from 1 to 3 +correspond to values of Z in the range + + align:start position:0% +correspond to values of Z in the range + + + align:start position:0% +correspond to values of Z in the range +from minus 2 to 0 these values are all + + align:start position:0% +from minus 2 to 0 these values are all + + + align:start position:0% +from minus 2 to 0 these values are all +in some sense equally likely so they + + align:start position:0% +in some sense equally likely so they + + + align:start position:0% +in some sense equally likely so they +should also be equally likely here and + + align:start position:0% +should also be equally likely here and + + + align:start position:0% +should also be equally likely here and +by a similar argument these values in + + align:start position:0% +by a similar argument these values in + + + align:start position:0% +by a similar argument these values in +the range from 3 to 5 should also be + + align:start position:0% +the range from 3 to 5 should also be + + + align:start position:0% +the range from 3 to 5 should also be +equally likely this rectangle + + align:start position:0% +equally likely this rectangle + + + align:start position:0% +equally likely this rectangle +corresponds to this rectangle here so + + align:start position:0% +corresponds to this rectangle here so + + + align:start position:0% +corresponds to this rectangle here so +the area should be the same and + + align:start position:0% +the area should be the same and + + + align:start position:0% +the area should be the same and +therefore the height should also be the + + align:start position:0% +therefore the height should also be the + + + align:start position:0% +therefore the height should also be the +same + + align:start position:0% +same + + + align:start position:0% +same +therefore the height here should be 1/6 + + align:start position:0% +therefore the height here should be 1/6 + + + align:start position:0% +therefore the height here should be 1/6 +and by the same argument the height here + + align:start position:0% +and by the same argument the height here + + + align:start position:0% +and by the same argument the height here +should be equal to 1/3 so what happens + + align:start position:0% +should be equal to 1/3 so what happens + + + align:start position:0% +should be equal to 1/3 so what happens +here is that when we add 3 to a random + + align:start position:0% +here is that when we add 3 to a random + + + align:start position:0% +here is that when we add 3 to a random +variable the PDF just gets shifted by 3 + + align:start position:0% +variable the PDF just gets shifted by 3 + + + align:start position:0% +variable the PDF just gets shifted by 3 +but otherwise retains the same shape so + + align:start position:0% +but otherwise retains the same shape so + + + align:start position:0% +but otherwise retains the same shape so +the story is entirely similar to what + + align:start position:0% +the story is entirely similar to what + + + align:start position:0% +the story is entirely similar to what +happened in the discrete case we start + + align:start position:0% +happened in the discrete case we start + + + align:start position:0% +happened in the discrete case we start +with a PDF of X we stretch it + + align:start position:0% +with a PDF of X we stretch it + + + align:start position:0% +with a PDF of X we stretch it +horizontally by a factor of 2 and then + + align:start position:0% +horizontally by a factor of 2 and then + + + align:start position:0% +horizontally by a factor of 2 and then +we shift it horizontally by 3 + + align:start position:0% +we shift it horizontally by 3 + + + align:start position:0% +we shift it horizontally by 3 +only difference is that here in the + + align:start position:0% +only difference is that here in the + + + align:start position:0% +only difference is that here in the +continuous case we also need to scale + + align:start position:0% +continuous case we also need to scale + + + align:start position:0% +continuous case we also need to scale +the plot in the vertical dimension by a + + align:start position:0% +the plot in the vertical dimension by a + + + align:start position:0% +the plot in the vertical dimension by a +factor of two actually make it smaller + + align:start position:0% +factor of two actually make it smaller + + + align:start position:0% +factor of two actually make it smaller +by a factor of two and this needs to be + + align:start position:0% +by a factor of two and this needs to be + + + align:start position:0% +by a factor of two and this needs to be +done in order to keep the total area + + align:start position:0% +done in order to keep the total area + + + align:start position:0% +done in order to keep the total area +under the PDF equal to one let us now go + + align:start position:0% +under the PDF equal to one let us now go + + + align:start position:0% +under the PDF equal to one let us now go +through a mathematical argument with the + + align:start position:0% +through a mathematical argument with the + + + align:start position:0% +through a mathematical argument with the +purpose of also finding a formula that + + align:start position:0% +purpose of also finding a formula that + + + align:start position:0% +purpose of also finding a formula that +represents what we just did in our + + align:start position:0% +represents what we just did in our + + + align:start position:0% +represents what we just did in our +previous example let Y be equal to ax + + align:start position:0% +previous example let Y be equal to ax + + + align:start position:0% +previous example let Y be equal to ax +plus B here X is a random variable with + + align:start position:0% +plus B here X is a random variable with + + + align:start position:0% +plus B here X is a random variable with +a given PDF a and B are given constants + + align:start position:0% +a given PDF a and B are given constants + + + align:start position:0% +a given PDF a and B are given constants +now if a is equal to zero then Y is + + align:start position:0% +now if a is equal to zero then Y is + + + align:start position:0% +now if a is equal to zero then Y is +identically equal to B so it is a + + align:start position:0% +identically equal to B so it is a + + + align:start position:0% +identically equal to B so it is a +constant random variable and does not + + align:start position:0% +constant random variable and does not + + + align:start position:0% +constant random variable and does not +have a PDF so let us exclude this case + + align:start position:0% +have a PDF so let us exclude this case + + + align:start position:0% +have a PDF so let us exclude this case +and start by assuming that a is a + + align:start position:0% +and start by assuming that a is a + + + align:start position:0% +and start by assuming that a is a +positive number we can try to work as in + + align:start position:0% +positive number we can try to work as in + + + align:start position:0% +positive number we can try to work as in +the discrete case and try it something + + align:start position:0% +the discrete case and try it something + + + align:start position:0% +the discrete case and try it something +like the following the probability that + + align:start position:0% +like the following the probability that + + + align:start position:0% +like the following the probability that +Y takes on a specific value is the same + + align:start position:0% +Y takes on a specific value is the same + + + align:start position:0% +Y takes on a specific value is the same +as the probability that a X plus B takes + + align:start position:0% +as the probability that a X plus B takes + + + align:start position:0% +as the probability that a X plus B takes +on a specific value which is the same as + + align:start position:0% +on a specific value which is the same as + + + align:start position:0% +on a specific value which is the same as +the probability that X takes on the + + align:start position:0% +the probability that X takes on the + + + align:start position:0% +the probability that X takes on the +specific value y minus B divided by a + + align:start position:0% +specific value y minus B divided by a + + + align:start position:0% +specific value y minus B divided by a +this equality was useful in the discrete + + align:start position:0% +this equality was useful in the discrete + + + align:start position:0% +this equality was useful in the discrete +case is it useful here unfortunately not + + align:start position:0% +case is it useful here unfortunately not + + + align:start position:0% +case is it useful here unfortunately not +when we're dealing with continuous + + align:start position:0% +when we're dealing with continuous + + + align:start position:0% +when we're dealing with continuous +random variables the probability that + + align:start position:0% +random variables the probability that + + + align:start position:0% +random variables the probability that +the continuous random variable is + + align:start position:0% +the continuous random variable is + + + align:start position:0% +the continuous random variable is +exactly equal to a given number this + + align:start position:0% +exactly equal to a given number this + + + align:start position:0% +exactly equal to a given number this +probability is going to be equal to zero + + align:start position:0% +probability is going to be equal to zero + + + align:start position:0% +probability is going to be equal to zero +and the same applies to this side as + + align:start position:0% +and the same applies to this side as + + + align:start position:0% +and the same applies to this side as +well so we have that zero is equal to + + align:start position:0% +well so we have that zero is equal to + + + align:start position:0% +well so we have that zero is equal to +zero and this is an informative and we + + align:start position:0% +zero and this is an informative and we + + + align:start position:0% +zero and this is an informative and we +have not made any progress so instead of + + align:start position:0% +have not made any progress so instead of + + + align:start position:0% +have not made any progress so instead of +working with probabilities of individual + + align:start position:0% +working with probabilities of individual + + + align:start position:0% +working with probabilities of individual +points which will always be 0 + + align:start position:0% +points which will always be 0 + + + align:start position:0% +points which will always be 0 +we will work with probabilities of + + align:start position:0% +we will work with probabilities of + + + align:start position:0% +we will work with probabilities of +intervals that generally have nonzero + + align:start position:0% +intervals that generally have nonzero + + + align:start position:0% +intervals that generally have nonzero +probability the trick is to work with + + align:start position:0% +probability the trick is to work with + + + align:start position:0% +probability the trick is to work with +CDF so let us try to find the CDF of Y + + align:start position:0% +CDF so let us try to find the CDF of Y + + + align:start position:0% +CDF so let us try to find the CDF of Y +the CDF of the random variable Y is + + align:start position:0% +the CDF of the random variable Y is + + + align:start position:0% +the CDF of the random variable Y is +defined as the probability that the + + align:start position:0% +defined as the probability that the + + + align:start position:0% +defined as the probability that the +random very + + align:start position:0% +random very + + + align:start position:0% +random very +is less than or equal to a certain + + align:start position:0% +is less than or equal to a certain + + + align:start position:0% +is less than or equal to a certain +number now in our case why is ax plus B + + align:start position:0% + + + + align:start position:0% + +we move B to the other side of the + + align:start position:0% +we move B to the other side of the + + + align:start position:0% +we move B to the other side of the +inequality and then divide both sides of + + align:start position:0% +inequality and then divide both sides of + + + align:start position:0% +inequality and then divide both sides of +the inequality by a and we get that this + + align:start position:0% +the inequality by a and we get that this + + + align:start position:0% +the inequality by a and we get that this +is the same as the probability that X is + + align:start position:0% +is the same as the probability that X is + + + align:start position:0% +is the same as the probability that X is +less than or equal to Y minus B divided + + align:start position:0% +less than or equal to Y minus B divided + + + align:start position:0% +less than or equal to Y minus B divided +by a which is the same as the CDF of X + + align:start position:0% +by a which is the same as the CDF of X + + + align:start position:0% +by a which is the same as the CDF of X +evaluated at y minus B over a so we have + + align:start position:0% +evaluated at y minus B over a so we have + + + align:start position:0% +evaluated at y minus B over a so we have +a formula for the CDF of Y in terms of + + align:start position:0% +a formula for the CDF of Y in terms of + + + align:start position:0% +a formula for the CDF of Y in terms of +the CDF of X how can we find the PDF + + align:start position:0% +the CDF of X how can we find the PDF + + + align:start position:0% +the CDF of X how can we find the PDF +simply by differentiating we + + align:start position:0% +simply by differentiating we + + + align:start position:0% +simply by differentiating we +differentiate both sides of this + + align:start position:0% +differentiate both sides of this + + + align:start position:0% +differentiate both sides of this +equation the derivative of a CDF is a + + align:start position:0% +equation the derivative of a CDF is a + + + align:start position:0% +equation the derivative of a CDF is a +PDF and therefore the PDF of Y is going + + align:start position:0% +PDF and therefore the PDF of Y is going + + + align:start position:0% +PDF and therefore the PDF of Y is going +to be equal to the derivative of this + + align:start position:0% +to be equal to the derivative of this + + + align:start position:0% +to be equal to the derivative of this +side here we need to use the chain rule + + align:start position:0% +side here we need to use the chain rule + + + align:start position:0% +side here we need to use the chain rule +first we take the derivative of this + + align:start position:0% +first we take the derivative of this + + + align:start position:0% +first we take the derivative of this +function and the derivative of the CDF + + align:start position:0% +function and the derivative of the CDF + + + align:start position:0% +function and the derivative of the CDF +is a PDF so the PDF of X evaluated at + + align:start position:0% +is a PDF so the PDF of X evaluated at + + + align:start position:0% +is a PDF so the PDF of X evaluated at +this particular number but then we also + + align:start position:0% +this particular number but then we also + + + align:start position:0% +this particular number but then we also +need to take the derivative of the + + align:start position:0% +need to take the derivative of the + + + align:start position:0% +need to take the derivative of the +argument inside with respect to Y and + + align:start position:0% +argument inside with respect to Y and + + + align:start position:0% +argument inside with respect to Y and +that derivative is equal to 1 over a and + + align:start position:0% +that derivative is equal to 1 over a and + + + align:start position:0% +that derivative is equal to 1 over a and +this gives us a formula for the PDF of Y + + align:start position:0% +this gives us a formula for the PDF of Y + + + align:start position:0% +this gives us a formula for the PDF of Y +in terms of the PDF of X how about the + + align:start position:0% +in terms of the PDF of X how about the + + + align:start position:0% +in terms of the PDF of X how about the +case where a is less than 0 what is + + align:start position:0% +case where a is less than 0 what is + + + align:start position:0% +case where a is less than 0 what is +going to change the first step up to + + align:start position:0% +going to change the first step up to + + + align:start position:0% +going to change the first step up to +here remains valid but now when we + + align:start position:0% +here remains valid but now when we + + + align:start position:0% +here remains valid but now when we +divide both sides of the inequality by a + + align:start position:0% +divide both sides of the inequality by a + + + align:start position:0% +divide both sides of the inequality by a +the direction of the inequality gets + + align:start position:0% +the direction of the inequality gets + + + align:start position:0% +the direction of the inequality gets +reversed so we obtain instead the + + align:start position:0% +reversed so we obtain instead the + + + align:start position:0% +reversed so we obtain instead the +probability that X is larger than or + + align:start position:0% +probability that X is larger than or + + + align:start position:0% +probability that X is larger than or +equal to Y minus B divided by a and this + + align:start position:0% +equal to Y minus B divided by a and this + + + align:start position:0% +equal to Y minus B divided by a and this +is 1 minus the probability that + + align:start position:0% +is 1 minus the probability that + + + align:start position:0% +is 1 minus the probability that +X is less than Y minus B over a now X is + + align:start position:0% +X is less than Y minus B over a now X is + + + align:start position:0% +X is less than Y minus B over a now X is +a continuous random variable so the + + align:start position:0% +a continuous random variable so the + + + align:start position:0% +a continuous random variable so the +probability is not going to change if + + align:start position:0% +probability is not going to change if + + + align:start position:0% +probability is not going to change if +here we make the inequality to be a less + + align:start position:0% +here we make the inequality to be a less + + + align:start position:0% +here we make the inequality to be a less +than or equal sign and what we have here + + align:start position:0% +than or equal sign and what we have here + + + align:start position:0% +than or equal sign and what we have here +is 1 minus the CDF of X evaluated at Y + + align:start position:0% +is 1 minus the CDF of X evaluated at Y + + + align:start position:0% +is 1 minus the CDF of X evaluated at Y +minus B over a we use the chain rule + + align:start position:0% +minus B over a we use the chain rule + + + align:start position:0% +minus B over a we use the chain rule +once more and we obtain that the PDF of + + align:start position:0% +once more and we obtain that the PDF of + + + align:start position:0% +once more and we obtain that the PDF of +Y in this case is equal to minus the PDF + + align:start position:0% +Y in this case is equal to minus the PDF + + + align:start position:0% +Y in this case is equal to minus the PDF +of X evaluated to Y minus B over a times + + align:start position:0% +of X evaluated to Y minus B over a times + + + align:start position:0% +of X evaluated to Y minus B over a times +1 over a now when a is positive a is the + + align:start position:0% +1 over a now when a is positive a is the + + + align:start position:0% +1 over a now when a is positive a is the +same as the absolute value of a when a + + align:start position:0% +same as the absolute value of a when a + + + align:start position:0% +same as the absolute value of a when a +is negative and we have this formula we + + align:start position:0% +is negative and we have this formula we + + + align:start position:0% +is negative and we have this formula we +have here a minus a which is the same as + + align:start position:0% +have here a minus a which is the same as + + + align:start position:0% +have here a minus a which is the same as +the absolute value of a so we can unify + + align:start position:0% +the absolute value of a so we can unify + + + align:start position:0% +the absolute value of a so we can unify +these two formulas by replacing the + + align:start position:0% +these two formulas by replacing the + + + align:start position:0% +these two formulas by replacing the +occurrences of a and that minus sign by + + align:start position:0% +occurrences of a and that minus sign by + + + align:start position:0% +occurrences of a and that minus sign by +just using the absolute value and this + + align:start position:0% +just using the absolute value and this + + + align:start position:0% +just using the absolute value and this +gives us this formula for the PDF of Y + + align:start position:0% +gives us this formula for the PDF of Y + + + align:start position:0% +gives us this formula for the PDF of Y +in terms of the PDF of X and it is a + + align:start position:0% +in terms of the PDF of X and it is a + + + align:start position:0% +in terms of the PDF of X and it is a +formula that's valid whether a is + + align:start position:0% +formula that's valid whether a is + + + align:start position:0% +formula that's valid whether a is +positive or negative what this formula + + align:start position:0% +positive or negative what this formula + + + align:start position:0% +positive or negative what this formula +represents is the following because of + + align:start position:0% +represents is the following because of + + + align:start position:0% +represents is the following because of +the factor of a that we have here we + + align:start position:0% +the factor of a that we have here we + + + align:start position:0% +the factor of a that we have here we +take the PDF of X and scale it + + align:start position:0% +take the PDF of X and scale it + + + align:start position:0% +take the PDF of X and scale it +horizontally by a factor of a because of + + align:start position:0% +horizontally by a factor of a because of + + + align:start position:0% +horizontally by a factor of a because of +the term B that we have here the PDF + + align:start position:0% +the term B that we have here the PDF + + + align:start position:0% +the term B that we have here the PDF +also gets shifted horizontally by B and + + align:start position:0% +also gets shifted horizontally by B and + + + align:start position:0% +also gets shifted horizontally by B and +finally this term here corresponds to a + + align:start position:0% +finally this term here corresponds to a + + + align:start position:0% +finally this term here corresponds to a +vertical scaling of the plot that we + + align:start position:0% +vertical scaling of the plot that we + + + align:start position:0% +vertical scaling of the plot that we +have and the reason that this term is + + align:start position:0% +have and the reason that this term is + + + align:start position:0% +have and the reason that this term is +present is so that the PDF of Y + + align:start position:0% +present is so that the PDF of Y + + + align:start position:0% +present is so that the PDF of Y +integrates to 1 it is interesting to + + align:start position:0% +integrates to 1 it is interesting to + + + align:start position:0% +integrates to 1 it is interesting to +also compare with the corresponding + + align:start position:0% +also compare with the corresponding + + + align:start position:0% +also compare with the corresponding +discrete formula that we derived earlier + + align:start position:0% +discrete formula that we derived earlier + + + align:start position:0% +discrete formula that we derived earlier +the discrete formula has exactly the + + align:start position:0% +the discrete formula has exactly the + + + align:start position:0% +the discrete formula has exactly the +same + + align:start position:0% +same + + + align:start position:0% +same +appearance except that the scaling + + align:start position:0% +appearance except that the scaling + + + align:start position:0% +appearance except that the scaling +factor is not present so for the case of + + align:start position:0% +factor is not present so for the case of + + + align:start position:0% +factor is not present so for the case of +continuous random variables we need to + + align:start position:0% +continuous random variables we need to + + + align:start position:0% +continuous random variables we need to +scale vertically the PDF but in the + + align:start position:0% +scale vertically the PDF but in the + + + align:start position:0% +scale vertically the PDF but in the +discrete case such as scaling is not + + align:start position:0% +discrete case such as scaling is not + + + align:start position:0% +discrete case such as scaling is not +present \ No newline at end of file diff --git a/1BU28txGAFI.txt b/1BU28txGAFI.txt new file mode 100644 index 0000000000000000000000000000000000000000..6b76a33d31dc08dd25975f5cc056b52010e3f0fb --- /dev/null +++ b/1BU28txGAFI.txt @@ -0,0 +1,339 @@ +align:start position:0% + +let's think about calculating torque I + + align:start position:0% +let's think about calculating torque I + + + align:start position:0% +let's think about calculating torque I +have a force F being applied to an + + align:start position:0% +have a force F being applied to an + + + align:start position:0% +have a force F being applied to an +object and that object is pivoted at a + + align:start position:0% +object and that object is pivoted at a + + + align:start position:0% +object and that object is pivoted at a +point Q I'll define R as the vector from + + align:start position:0% +point Q I'll define R as the vector from + + + align:start position:0% +point Q I'll define R as the vector from +the pivot point Q to the point of the + + align:start position:0% +the pivot point Q to the point of the + + + align:start position:0% +the pivot point Q to the point of the +application of the force torque is + + align:start position:0% +application of the force torque is + + + align:start position:0% +application of the force torque is +defined as the cross product R cross F + + align:start position:0% +defined as the cross product R cross F + + + align:start position:0% +defined as the cross product R cross F +which we can also write as R times F + + align:start position:0% +which we can also write as R times F + + + align:start position:0% +which we can also write as R times F +times the sine of theta but what does + + align:start position:0% +times the sine of theta but what does + + + align:start position:0% +times the sine of theta but what does +that mean + + align:start position:0% +that mean + + + align:start position:0% +that mean +I'll introduce two different intuitive + + align:start position:0% +I'll introduce two different intuitive + + + align:start position:0% +I'll introduce two different intuitive +ways of understanding this mathematical + + align:start position:0% +ways of understanding this mathematical + + + align:start position:0% +ways of understanding this mathematical +expression first we can think about this + + align:start position:0% +expression first we can think about this + + + align:start position:0% +expression first we can think about this +as the magnitude of F times the quantity + + align:start position:0% +as the magnitude of F times the quantity + + + align:start position:0% +as the magnitude of F times the quantity +R sine theta if we look at the direction + + align:start position:0% +R sine theta if we look at the direction + + + align:start position:0% +R sine theta if we look at the direction +of the force then it is easy to see that + + align:start position:0% +of the force then it is easy to see that + + + align:start position:0% +of the force then it is easy to see that +R sine theta is just the part of R that + + align:start position:0% +R sine theta is just the part of R that + + + align:start position:0% +R sine theta is just the part of R that +is perpendicular to the force so here + + align:start position:0% +is perpendicular to the force so here + + + align:start position:0% +is perpendicular to the force so here +the torque is equal to the magnitude of + + align:start position:0% +the torque is equal to the magnitude of + + + align:start position:0% +the torque is equal to the magnitude of +the force times the magnitude of this + + align:start position:0% +the force times the magnitude of this + + + align:start position:0% +the force times the magnitude of this +perpendicular part of the vector R this + + align:start position:0% +perpendicular part of the vector R this + + + align:start position:0% +perpendicular part of the vector R this +perpendicular portion of the distance + + align:start position:0% +perpendicular portion of the distance + + + align:start position:0% +perpendicular portion of the distance +vector R is often referred to as the + + align:start position:0% +vector R is often referred to as the + + + align:start position:0% +vector R is often referred to as the +moment arm we can instead group F with + + align:start position:0% +moment arm we can instead group F with + + + align:start position:0% +moment arm we can instead group F with +sine theta so this means that we're + + align:start position:0% +sine theta so this means that we're + + + align:start position:0% +sine theta so this means that we're +thinking of the cross-product as the + + align:start position:0% +thinking of the cross-product as the + + + align:start position:0% +thinking of the cross-product as the +distance R multiplied by F sine theta + + align:start position:0% +distance R multiplied by F sine theta + + + align:start position:0% +distance R multiplied by F sine theta +the component of the force F that's + + align:start position:0% +the component of the force F that's + + + align:start position:0% +the component of the force F that's +perpendicular to the position vector R + + align:start position:0% +perpendicular to the position vector R + + + align:start position:0% +perpendicular to the position vector R +here I'm calculating torque as the + + align:start position:0% +here I'm calculating torque as the + + + align:start position:0% +here I'm calculating torque as the +distance between the pivot point and + + align:start position:0% +distance between the pivot point and + + + align:start position:0% +distance between the pivot point and +where the force is applied times the + + align:start position:0% +where the force is applied times the + + + align:start position:0% +where the force is applied times the +perpendicular part of the force be very + + align:start position:0% +perpendicular part of the force be very + + + align:start position:0% +perpendicular part of the force be very +careful about the sine theta term in + + align:start position:0% +careful about the sine theta term in + + + align:start position:0% +careful about the sine theta term in +many cases the angle theta that is given + + align:start position:0% +many cases the angle theta that is given + + + align:start position:0% +many cases the angle theta that is given +in the problem is not the angle that is + + align:start position:0% +in the problem is not the angle that is + + + align:start position:0% +in the problem is not the angle that is +used in the expression in this example f + + align:start position:0% +used in the expression in this example f + + + align:start position:0% +used in the expression in this example f +times the sine of theta will actually + + align:start position:0% +times the sine of theta will actually + + + align:start position:0% +times the sine of theta will actually +give the parallel component of the force + + align:start position:0% +give the parallel component of the force + + + align:start position:0% +give the parallel component of the force +therefore it is much better to remember + + align:start position:0% +therefore it is much better to remember + + + align:start position:0% +therefore it is much better to remember +to take the perpendicular component + + align:start position:0% +to take the perpendicular component + + + align:start position:0% +to take the perpendicular component +rather than just memorizing sine of + + align:start position:0% +rather than just memorizing sine of + + + align:start position:0% +rather than just memorizing sine of +theta \ No newline at end of file diff --git a/1rgmGwAqMYc.txt b/1rgmGwAqMYc.txt new file mode 100644 index 0000000000000000000000000000000000000000..88586b5559d88a619db7450612acecf34a688963 --- /dev/null +++ b/1rgmGwAqMYc.txt @@ -0,0 +1,9683 @@ +align:start position:0% + +how is everyone doing today + + align:start position:0% +how is everyone doing today + + + align:start position:0% +how is everyone doing today +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +you know why there's a lot of excitement + + align:start position:0% +you know why there's a lot of excitement + + + align:start position:0% +you know why there's a lot of excitement +and i saw the silent praise + + align:start position:0% +and i saw the silent praise + + + align:start position:0% +and i saw the silent praise +because i know what this means recently + + align:start position:0% +because i know what this means recently + + + align:start position:0% +because i know what this means recently +and i'm doing it more and more um you + + align:start position:0% +and i'm doing it more and more um you + + + align:start position:0% +and i'm doing it more and more um you +guys are excited because + + align:start position:0% +guys are excited because + + + align:start position:0% +guys are excited because +we are celebrating something on friday + + align:start position:0% +we are celebrating something on friday + + + align:start position:0% +we are celebrating something on friday +we are celebrating knowledge we are + + align:start position:0% +we are celebrating knowledge we are + + + align:start position:0% +we are celebrating knowledge we are +celebrating + + align:start position:0% +celebrating + + + align:start position:0% +celebrating +uh uh chemistry + + align:start position:0% +uh uh chemistry + + + align:start position:0% +uh uh chemistry +and um we are we are celebrating how + + align:start position:0% +and um we are we are celebrating how + + + align:start position:0% +and um we are we are celebrating how +much we've learned in the last month + + align:start position:0% +much we've learned in the last month + + + align:start position:0% +much we've learned in the last month +it's called exam three it's a midterm + + align:start position:0% +it's called exam three it's a midterm + + + align:start position:0% +it's called exam three it's a midterm +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +thank you for that where over that and + + align:start position:0% +thank you for that where over that and + + + align:start position:0% +thank you for that where over that and +uh and and here oh and so so what you + + align:start position:0% +uh and and here oh and so so what you + + + align:start position:0% +uh and and here oh and so so what you +know + + align:start position:0% +know + + + align:start position:0% +know +what i thought we'd do today instead of + + align:start position:0% +what i thought we'd do today instead of + + + align:start position:0% +what i thought we'd do today instead of +uh again + + align:start position:0% +uh again + + + align:start position:0% +uh again +i mentioned this on monday i instead of + + align:start position:0% +i mentioned this on monday i instead of + + + align:start position:0% +i mentioned this on monday i instead of +it you know you + + align:start position:0% +it you know you + + + align:start position:0% +it you know you +you guys just had thanksgiving uh you're + + align:start position:0% +you guys just had thanksgiving uh you're + + + align:start position:0% +you guys just had thanksgiving uh you're +back and now we got a test + + align:start position:0% +back and now we got a test + + + align:start position:0% +back and now we got a test +and i know you got a lot of other stuff + + align:start position:0% +and i know you got a lot of other stuff + + + align:start position:0% +and i know you got a lot of other stuff +going on too at this time so instead of + + align:start position:0% +going on too at this time so instead of + + + align:start position:0% +going on too at this time so instead of +throwing something in that we're not + + align:start position:0% +throwing something in that we're not + + + align:start position:0% +throwing something in that we're not +going to test you on + + align:start position:0% +going to test you on + + + align:start position:0% +going to test you on +what i wanted to do with today was just + + align:start position:0% +what i wanted to do with today was just + + + align:start position:0% +what i wanted to do with today was just +to kind of feel our oneness + + align:start position:0% +to kind of feel our oneness + + + align:start position:0% +to kind of feel our oneness +with the concepts right and so i want to + + align:start position:0% +with the concepts right and so i want to + + + align:start position:0% +with the concepts right and so i want to +kind of go over the concepts that + + align:start position:0% +kind of go over the concepts that + + + align:start position:0% +kind of go over the concepts that +are going to be potentially on exam + + align:start position:0% +are going to be potentially on exam + + + align:start position:0% +are going to be potentially on exam +on the exam on friday and we'll do + + align:start position:0% +on the exam on friday and we'll do + + + align:start position:0% +on the exam on friday and we'll do +uh you know i'll talk about those + + align:start position:0% +uh you know i'll talk about those + + + align:start position:0% +uh you know i'll talk about those +concepts and we'll do a couple of + + align:start position:0% +concepts and we'll do a couple of + + + align:start position:0% +concepts and we'll do a couple of +problems here and there as we go + + align:start position:0% +problems here and there as we go + + + align:start position:0% +problems here and there as we go +okay so those are the the metrics the + + align:start position:0% +okay so those are the the metrics the + + + align:start position:0% +okay so those are the the metrics the +specs + + align:start position:0% +specs + + + align:start position:0% +specs +for exam three now i wanted before + + align:start position:0% +for exam three now i wanted before + + + align:start position:0% +for exam three now i wanted before +so that's what the top but on monday uh + + align:start position:0% +so that's what the top but on monday uh + + + align:start position:0% +so that's what the top but on monday uh +i finished with two minutes left and i + + align:start position:0% +i finished with two minutes left and i + + + align:start position:0% +i finished with two minutes left and i +said hey there's one more kind of + + align:start position:0% +said hey there's one more kind of + + + align:start position:0% +said hey there's one more kind of +acid-base definition + + align:start position:0% +acid-base definition + + + align:start position:0% +acid-base definition +you won't be tested on it but it's the + + align:start position:0% +you won't be tested on it but it's the + + + align:start position:0% +you won't be tested on it but it's the +most general and i got to give lewis his + + align:start position:0% +most general and i got to give lewis his + + + align:start position:0% +most general and i got to give lewis his +due + + align:start position:0% +due + + + align:start position:0% +due +so i just wanted to you know just show + + align:start position:0% +so i just wanted to you know just show + + + align:start position:0% +so i just wanted to you know just show +you like that + + align:start position:0% +you like that + + + align:start position:0% +you like that +you won't be tested on lewis acids and + + align:start position:0% +you won't be tested on lewis acids and + + + align:start position:0% +you won't be tested on lewis acids and +bases but but we did + + align:start position:0% +bases but but we did + + + align:start position:0% +bases but but we did +i did throw this in there and so i want + + align:start position:0% +i did throw this in there and so i want + + + align:start position:0% +i did throw this in there and so i want +to just for one or two more minutes talk + + align:start position:0% +to just for one or two more minutes talk + + + align:start position:0% +to just for one or two more minutes talk +about this + + align:start position:0% +about this + + + align:start position:0% +about this +right these are the things you are + + align:start position:0% +right these are the things you are + + + align:start position:0% +right these are the things you are +responsible for know yet so an arrhenius + + align:start position:0% +responsible for know yet so an arrhenius + + + align:start position:0% +responsible for know yet so an arrhenius +acid base + + align:start position:0% +acid base + + + align:start position:0% +acid base +oh h plus bronsted-lowry uh + + align:start position:0% +oh h plus bronsted-lowry uh + + + align:start position:0% +oh h plus bronsted-lowry uh +it's it's proton transfer and then + + align:start position:0% +it's it's proton transfer and then + + + align:start position:0% +it's it's proton transfer and then +there's lewis who broasted these guys + + align:start position:0% +there's lewis who broasted these guys + + + align:start position:0% +there's lewis who broasted these guys +because he said uh-uh and and this + + align:start position:0% +because he said uh-uh and and this + + + align:start position:0% +because he said uh-uh and and this +is the most general way to think about + + align:start position:0% +is the most general way to think about + + + align:start position:0% +is the most general way to think about +acids and bases + + align:start position:0% +acids and bases + + + align:start position:0% +acids and bases +it is the most general it is um it is it + + align:start position:0% +it is the most general it is um it is it + + + align:start position:0% +it is the most general it is um it is it +is quite powerful + + align:start position:0% +is quite powerful + + + align:start position:0% +is quite powerful +um because now you go back to say + + align:start position:0% +um because now you go back to say + + + align:start position:0% +um because now you go back to say +this one right and and so if this is a + + align:start position:0% +this one right and and so if this is a + + + align:start position:0% +this one right and and so if this is a +a uh what what if we mix this with this + + align:start position:0% +a uh what what if we mix this with this + + + align:start position:0% +a uh what what if we mix this with this +right uh so here we have h now remember + + align:start position:0% +right uh so here we have h now remember + + + align:start position:0% +right uh so here we have h now remember +lewis had all the dots all over the + + align:start position:0% +lewis had all the dots all over the + + + align:start position:0% +lewis had all the dots all over the +place he loved dots + + align:start position:0% +place he loved dots + + + align:start position:0% +place he loved dots +and so they're all over the place and + + align:start position:0% +and so they're all over the place and + + + align:start position:0% +and so they're all over the place and +that's what you know if you had this + + align:start position:0% +that's what you know if you had this + + + align:start position:0% +that's what you know if you had this +this is a lewis acid because + + align:start position:0% +this is a lewis acid because + + + align:start position:0% +this is a lewis acid because +it is ready to receive what is it ready + + align:start position:0% +it is ready to receive what is it ready + + + align:start position:0% +it is ready to receive what is it ready +to receive + + align:start position:0% +to receive + + + align:start position:0% +to receive +no more atoms only electrons it is the + + align:start position:0% +no more atoms only electrons it is the + + + align:start position:0% +no more atoms only electrons it is the +most + + align:start position:0% +most + + + align:start position:0% +most +general way to think about it right + + align:start position:0% +general way to think about it right + + + align:start position:0% +general way to think about it right +and this would be a lewis base because + + align:start position:0% +and this would be a lewis base because + + + align:start position:0% +and this would be a lewis base because +it is ready to give a pair of electrons + + align:start position:0% +it is ready to give a pair of electrons + + + align:start position:0% +it is ready to give a pair of electrons +and form a bond together and that's what + + align:start position:0% +and form a bond together and that's what + + + align:start position:0% +and form a bond together and that's what +they do or that's what they can do + + align:start position:0% +they do or that's what they can do + + + align:start position:0% +they do or that's what they can do +so lewis acid and a lewis base are the + + align:start position:0% +so lewis acid and a lewis base are the + + + align:start position:0% +so lewis acid and a lewis base are the +most general + + align:start position:0% +most general + + + align:start position:0% +most general +is the most general form and you really + + align:start position:0% +is the most general form and you really + + + align:start position:0% +is the most general form and you really +get rid of so for lewis you really + + align:start position:0% +get rid of so for lewis you really + + + align:start position:0% +get rid of so for lewis you really +it's all about electron transfer + + align:start position:0% +it's all about electron transfer + + + align:start position:0% +it's all about electron transfer +electron pair + + align:start position:0% +electron pair + + + align:start position:0% +electron pair +transfer pair transfer + + align:start position:0% +transfer pair transfer + + + align:start position:0% +transfer pair transfer +or bonds if you're well let's say elect + + align:start position:0% +or bonds if you're well let's say elect + + + align:start position:0% +or bonds if you're well let's say elect +i'm just going to make it as + + align:start position:0% +i'm just going to make it as + + + align:start position:0% +i'm just going to make it as +general as possible if you're going to + + align:start position:0% +general as possible if you're going to + + + align:start position:0% +general as possible if you're going to +mix an acid in a base which i'll do in a + + align:start position:0% +mix an acid in a base which i'll do in a + + + align:start position:0% +mix an acid in a base which i'll do in a +second + + align:start position:0% +second + + + align:start position:0% +second +it's a pair electron transfer + + align:start position:0% +it's a pair electron transfer + + + align:start position:0% +it's a pair electron transfer +is what it's all about and + + align:start position:0% +is what it's all about and + + + align:start position:0% +is what it's all about and +you know what what happens here well you + + align:start position:0% +you know what what happens here well you + + + align:start position:0% +you know what what happens here well you +don't you don't have any chemical + + align:start position:0% +don't you don't have any chemical + + + align:start position:0% +don't you don't have any chemical +identity + + align:start position:0% +identity + + + align:start position:0% +identity +no more chemical identity + + align:start position:0% + + + + align:start position:0% + +so it's it's full you don't need the + + align:start position:0% +so it's it's full you don't need the + + + align:start position:0% +so it's it's full you don't need the +hydrogens anymore you don't need the ohs + + align:start position:0% +hydrogens anymore you don't need the ohs + + + align:start position:0% +hydrogens anymore you don't need the ohs +it's totally general and and this really + + align:start position:0% +it's totally general and and this really + + + align:start position:0% +it's totally general and and this really +opens it up because now you can look at + + align:start position:0% +opens it up because now you can look at + + + align:start position:0% +opens it up because now you can look at +gases liquid solids all forms of matter + + align:start position:0% +gases liquid solids all forms of matter + + + align:start position:0% +gases liquid solids all forms of matter +all elements in the table and you can + + align:start position:0% +all elements in the table and you can + + + align:start position:0% +all elements in the table and you can +think about them as whether they're + + align:start position:0% +think about them as whether they're + + + align:start position:0% +think about them as whether they're +going to have + + align:start position:0% +going to have + + + align:start position:0% +going to have +an acid-like or a base like character in + + align:start position:0% +an acid-like or a base like character in + + + align:start position:0% +an acid-like or a base like character in +terms of electron transfer + + align:start position:0% +terms of electron transfer + + + align:start position:0% +terms of electron transfer +so you know here's the general if you + + align:start position:0% +so you know here's the general if you + + + align:start position:0% +so you know here's the general if you +had a lewis + + align:start position:0% +had a lewis + + + align:start position:0% +had a lewis +acid and a lewis base and you mix them + + align:start position:0% +acid and a lewis base and you mix them + + + align:start position:0% +acid and a lewis base and you mix them +together + + align:start position:0% +together + + + align:start position:0% +together +then you can see that if you got an + + align:start position:0% +then you can see that if you got an + + + align:start position:0% +then you can see that if you got an +electron pair + + align:start position:0% +electron pair + + + align:start position:0% +electron pair +that could then go that one of them + + align:start position:0% +that could then go that one of them + + + align:start position:0% +that could then go that one of them +wants it and the other can give it and + + align:start position:0% +wants it and the other can give it and + + + align:start position:0% +wants it and the other can give it and +they can form a bond + + align:start position:0% +they can form a bond + + + align:start position:0% +they can form a bond +then that would be how you think about + + align:start position:0% +then that would be how you think about + + + align:start position:0% +then that would be how you think about +mixing a lewis acid in a lewis base and + + align:start position:0% +mixing a lewis acid in a lewis base and + + + align:start position:0% +mixing a lewis acid in a lewis base and +again + + align:start position:0% +again + + + align:start position:0% +again +i'm not this won't be on the exam but i + + align:start position:0% +i'm not this won't be on the exam but i + + + align:start position:0% +i'm not this won't be on the exam but i +just had to + + align:start position:0% +just had to + + + align:start position:0% +just had to +give lewis his due okay + + align:start position:0% +give lewis his due okay + + + align:start position:0% +give lewis his due okay +lewis acids and bases are all about the + + align:start position:0% +lewis acids and bases are all about the + + + align:start position:0% +lewis acids and bases are all about the +electrons + + align:start position:0% +electrons + + + align:start position:0% +electrons +and then the other thing i didn't get to + + align:start position:0% +and then the other thing i didn't get to + + + align:start position:0% +and then the other thing i didn't get to +do on monday was my why this matters and + + align:start position:0% +do on monday was my why this matters and + + + align:start position:0% +do on monday was my why this matters and +so i want to do that now hair + + align:start position:0% +so i want to do that now hair + + + align:start position:0% +so i want to do that now hair +is very much affected by the softness of + + align:start position:0% +is very much affected by the softness of + + + align:start position:0% +is very much affected by the softness of +water + + align:start position:0% +water + + + align:start position:0% +water +and instead and and so but instead of + + align:start position:0% +and instead and and so but instead of + + + align:start position:0% +and instead and and so but instead of +you showing + + align:start position:0% +you showing + + + align:start position:0% +you showing +instead of me showing you lots of + + align:start position:0% +instead of me showing you lots of + + + align:start position:0% +instead of me showing you lots of +pictures of hair + + align:start position:0% +pictures of hair + + + align:start position:0% +pictures of hair +that i found randomly on the internet uh + + align:start position:0% +that i found randomly on the internet uh + + + align:start position:0% +that i found randomly on the internet uh +googling soft water hard water + + align:start position:0% +googling soft water hard water + + + align:start position:0% +googling soft water hard water +you know different forms of water hair + + align:start position:0% +you know different forms of water hair + + + align:start position:0% +you know different forms of water hair +i'm showing you pipes because that's + + align:start position:0% +i'm showing you pipes because that's + + + align:start position:0% +i'm showing you pipes because that's +much more actually uh + + align:start position:0% +much more actually uh + + + align:start position:0% +much more actually uh +relevant in terms of like for example + + align:start position:0% +relevant in terms of like for example + + + align:start position:0% +relevant in terms of like for example +whether you can get water into your + + align:start position:0% +whether you can get water into your + + + align:start position:0% +whether you can get water into your +house + + align:start position:0% +house + + + align:start position:0% +house +at all right and and this is a real + + align:start position:0% +at all right and and this is a real + + + align:start position:0% +at all right and and this is a real +problem + + align:start position:0% +problem + + + align:start position:0% +problem +if you have hard water what it means is + + align:start position:0% +if you have hard water what it means is + + + align:start position:0% +if you have hard water what it means is +you've got minerals + + align:start position:0% +you've got minerals + + + align:start position:0% +you've got minerals +in in the water right things like + + align:start position:0% +in in the water right things like + + + align:start position:0% +in in the water right things like +magnesium and calcium ions + + align:start position:0% +magnesium and calcium ions + + + align:start position:0% +magnesium and calcium ions +are in the water and what happens is if + + align:start position:0% +are in the water and what happens is if + + + align:start position:0% +are in the water and what happens is if +you run that through pipes + + align:start position:0% +you run that through pipes + + + align:start position:0% +you run that through pipes +they tend to react and form and deposit + + align:start position:0% +they tend to react and form and deposit + + + align:start position:0% +they tend to react and form and deposit +right and you get these deposits of very + + align:start position:0% +right and you get these deposits of very + + + align:start position:0% +right and you get these deposits of very +very hard mineral deposits around the + + align:start position:0% +very hard mineral deposits around the + + + align:start position:0% +very hard mineral deposits around the +edges that eventually + + align:start position:0% +edges that eventually + + + align:start position:0% +edges that eventually +look like this that's not a good thing + + align:start position:0% +look like this that's not a good thing + + + align:start position:0% +look like this that's not a good thing +and so you need to + + align:start position:0% +and so you need to + + + align:start position:0% +and so you need to +soften the water and that's something + + align:start position:0% +soften the water and that's something + + + align:start position:0% +soften the water and that's something +you may have heard of + + align:start position:0% +you may have heard of + + + align:start position:0% +you may have heard of +but now you really know how to think + + align:start position:0% +but now you really know how to think + + + align:start position:0% +but now you really know how to think +about it because you can think about it + + align:start position:0% +about it because you can think about it + + + align:start position:0% +about it because you can think about it +in terms of all of the things that + + align:start position:0% +in terms of all of the things that + + + align:start position:0% +in terms of all of the things that +you've learned + + align:start position:0% +you've learned + + + align:start position:0% +you've learned +and just as as an example if you it you + + align:start position:0% +and just as as an example if you it you + + + align:start position:0% +and just as as an example if you it you +know if one of those minerals that's a + + align:start position:0% +know if one of those minerals that's a + + + align:start position:0% +know if one of those minerals that's a +problem is calcium + + align:start position:0% +problem is calcium + + + align:start position:0% +problem is calcium +oh it is right magnesium is another one + + align:start position:0% +oh it is right magnesium is another one + + + align:start position:0% +oh it is right magnesium is another one +uh that that can cause this in pipes you + + align:start position:0% +uh that that can cause this in pipes you + + + align:start position:0% +uh that that can cause this in pipes you +you gotta you gotta somehow take it out + + align:start position:0% +you gotta you gotta somehow take it out + + + align:start position:0% +you gotta you gotta somehow take it out +of the water or at least + + align:start position:0% +of the water or at least + + + align:start position:0% +of the water or at least +make it into a form that uh that makes + + align:start position:0% +make it into a form that uh that makes + + + align:start position:0% +make it into a form that uh that makes +it like insoluble so it'll just flow + + align:start position:0% +it like insoluble so it'll just flow + + + align:start position:0% +it like insoluble so it'll just flow +and it won't have a chance to come + + align:start position:0% +and it won't have a chance to come + + + align:start position:0% +and it won't have a chance to come +around and and and deposit + + align:start position:0% +around and and and deposit + + + align:start position:0% +around and and and deposit +on on in you know on the edge there of + + align:start position:0% +on on in you know on the edge there of + + + align:start position:0% +on on in you know on the edge there of +the pipe and so + + align:start position:0% +the pipe and so + + + align:start position:0% +the pipe and so +what do you do well you add for example + + align:start position:0% +what do you do well you add for example + + + align:start position:0% +what do you do well you add for example +oh we've done this before right what if + + align:start position:0% +oh we've done this before right what if + + + align:start position:0% +oh we've done this before right what if +i add soda + + align:start position:0% +i add soda + + + align:start position:0% +i add soda +something called soda ash well we know + + align:start position:0% +something called soda ash well we know + + + align:start position:0% +something called soda ash well we know +what that is + + align:start position:0% +what that is + + + align:start position:0% +what that is +that's na2co3 + + align:start position:0% +that's na2co3 + + + align:start position:0% +that's na2co3 +and that will give me some ions + + align:start position:0% +and that will give me some ions + + + align:start position:0% +and that will give me some ions +it'll give me some n a pluses and it'll + + align:start position:0% +it'll give me some n a pluses and it'll + + + align:start position:0% +it'll give me some n a pluses and it'll +give me + + align:start position:0% +give me + + + align:start position:0% +give me +some co three two minuses + + align:start position:0% +some co three two minuses + + + align:start position:0% +some co three two minuses +and those are in aqueous solution you + + align:start position:0% +and those are in aqueous solution you + + + align:start position:0% +and those are in aqueous solution you +know this is this is all part of stuff + + align:start position:0% +know this is this is all part of stuff + + + align:start position:0% +know this is this is all part of stuff +that we've been talking about right + + align:start position:0% +that we've been talking about right + + + align:start position:0% +that we've been talking about right +you're dissociating this to get ions in + + align:start position:0% +you're dissociating this to get ions in + + + align:start position:0% +you're dissociating this to get ions in +solution but why do i want these ions + + align:start position:0% +solution but why do i want these ions + + + align:start position:0% +solution but why do i want these ions +that's a water softener why because now + + align:start position:0% +that's a water softener why because now + + + align:start position:0% +that's a water softener why because now +you you can see it right because this + + align:start position:0% +you you can see it right because this + + + align:start position:0% +you you can see it right because this +one here + + align:start position:0% +one here + + + align:start position:0% +one here +this one here is going to remove the + + align:start position:0% +this one here is going to remove the + + + align:start position:0% +this one here is going to remove the +calcium + + align:start position:0% +calcium + + + align:start position:0% +calcium +and so if i've got these calcium these + + align:start position:0% +and so if i've got these calcium these + + + align:start position:0% +and so if i've got these calcium these +minerals in the water making it hard + + align:start position:0% +minerals in the water making it hard + + + align:start position:0% +minerals in the water making it hard +water which leads to that + + align:start position:0% +water which leads to that + + + align:start position:0% +water which leads to that +and wreaks havoc on your hair then you + + align:start position:0% +and wreaks havoc on your hair then you + + + align:start position:0% +and wreaks havoc on your hair then you +you you get a little of this in there + + align:start position:0% +you you get a little of this in there + + + align:start position:0% +you you get a little of this in there +and you're gonna react with the calcium + + align:start position:0% +and you're gonna react with the calcium + + + align:start position:0% +and you're gonna react with the calcium +why but it's because of what we already + + align:start position:0% +why but it's because of what we already + + + align:start position:0% +why but it's because of what we already +saw right if i + + align:start position:0% +saw right if i + + + align:start position:0% +saw right if i +if i have this this is something we've + + align:start position:0% +if i have this this is something we've + + + align:start position:0% +if i have this this is something we've +already looked at if i have calcium + + align:start position:0% +already looked at if i have calcium + + + align:start position:0% +already looked at if i have calcium +two plus and i have some bicarbonate in + + align:start position:0% +two plus and i have some bicarbonate in + + + align:start position:0% +two plus and i have some bicarbonate in +there + + align:start position:0% +there + + + align:start position:0% +there +co3 minus then we know + + align:start position:0% +co3 minus then we know + + + align:start position:0% +co3 minus then we know +that i can get precipitates ca + + align:start position:0% +that i can get precipitates ca + + + align:start position:0% +that i can get precipitates ca +this is just what we looked at in the + + align:start position:0% +this is just what we looked at in the + + + align:start position:0% +this is just what we looked at in the +goody bag right plus + + align:start position:0% +goody bag right plus + + + align:start position:0% +goody bag right plus +co2 and plus h2o + + align:start position:0% +co2 and plus h2o + + + align:start position:0% +co2 and plus h2o +that's the same uh kind of reaction that + + align:start position:0% +that's the same uh kind of reaction that + + + align:start position:0% +that's the same uh kind of reaction that +we looked at already with calcium + + align:start position:0% +we looked at already with calcium + + + align:start position:0% +we looked at already with calcium +carbonate + + align:start position:0% +carbonate + + + align:start position:0% +carbonate +right calcium carbonate why well because + + align:start position:0% +right calcium carbonate why well because + + + align:start position:0% +right calcium carbonate why well because +this + + align:start position:0% +this + + + align:start position:0% +this +is going to give me these this is a + + align:start position:0% +is going to give me these this is a + + + align:start position:0% +is going to give me these this is a +source for those + + align:start position:0% +source for those + + + align:start position:0% +source for those +which then eats up some calcium + + align:start position:0% +which then eats up some calcium + + + align:start position:0% +which then eats up some calcium +and you say well now this can this can + + align:start position:0% +and you say well now this can this can + + + align:start position:0% +and you say well now this can this can +take the calcium ions out + + align:start position:0% +take the calcium ions out + + + align:start position:0% +take the calcium ions out +so that it runs through that's what you + + align:start position:0% +so that it runs through that's what you + + + align:start position:0% +so that it runs through that's what you +want to do here + + align:start position:0% +want to do here + + + align:start position:0% +want to do here +that's how you soften water well you can + + align:start position:0% +that's how you soften water well you can + + + align:start position:0% +that's how you soften water well you can +add lime + + align:start position:0% +add lime + + + align:start position:0% +add lime +which gives me a source of o h minus and + + align:start position:0% +which gives me a source of o h minus and + + + align:start position:0% +which gives me a source of o h minus and +that takes out the magnesium + + align:start position:0% +that takes out the magnesium + + + align:start position:0% +that takes out the magnesium +right and these are ways to change the + + align:start position:0% +right and these are ways to change the + + + align:start position:0% +right and these are ways to change the +chemistry of water so that you don't + + align:start position:0% +chemistry of water so that you don't + + + align:start position:0% +chemistry of water so that you don't +have as many ions + + align:start position:0% +have as many ions + + + align:start position:0% +have as many ions +mineral you know these calcium and + + align:start position:0% +mineral you know these calcium and + + + align:start position:0% +mineral you know these calcium and +magnesium ions floating around + + align:start position:0% +magnesium ions floating around + + + align:start position:0% +magnesium ions floating around +that cause problems so that was my why + + align:start position:0% +that cause problems so that was my why + + + align:start position:0% +that cause problems so that was my why +this matters + + align:start position:0% +this matters + + + align:start position:0% +this matters +and now we turn to what i started with + + align:start position:0% +and now we turn to what i started with + + + align:start position:0% +and now we turn to what i started with +which is exam three + + align:start position:0% +which is exam three + + + align:start position:0% +which is exam three +oh look at that i look at that and + + align:start position:0% +oh look at that i look at that and + + + align:start position:0% +oh look at that i look at that and +that's just + + align:start position:0% +that's just + + + align:start position:0% +that's just +you know that's happiness look at all + + align:start position:0% +you know that's happiness look at all + + + align:start position:0% +you know that's happiness look at all +those topics + + align:start position:0% +those topics + + + align:start position:0% +those topics +x-rays xrd defects + + align:start position:0% +x-rays xrd defects + + + align:start position:0% +x-rays xrd defects +glasses reaction rates solubility + + align:start position:0% +glasses reaction rates solubility + + + align:start position:0% +glasses reaction rates solubility +aqueous solutions acids bases + + align:start position:0% +aqueous solutions acids bases + + + align:start position:0% +aqueous solutions acids bases +it's all there it's all there and it's + + align:start position:0% +it's all there it's all there and it's + + + align:start position:0% +it's all there it's all there and it's +and it's all + + align:start position:0% +and it's all + + + align:start position:0% +and it's all +there in you wait and if not you've got + + align:start position:0% +there in you wait and if not you've got + + + align:start position:0% +there in you wait and if not you've got +two days + + align:start position:0% + + + + align:start position:0% + +so please make it be there + + align:start position:0% + + + + align:start position:0% + +let's go through this let's go through + + align:start position:0% +let's go through this let's go through + + + align:start position:0% +let's go through this let's go through +this i'm gonna go through this top right + + align:start position:0% +this i'm gonna go through this top right + + + align:start position:0% +this i'm gonna go through this top right +click so i'm gonna tell you kind of the + + align:start position:0% +click so i'm gonna tell you kind of the + + + align:start position:0% +click so i'm gonna tell you kind of the +concepts that i want to make sure you + + align:start position:0% +concepts that i want to make sure you + + + align:start position:0% +concepts that i want to make sure you +know + + align:start position:0% +know + + + align:start position:0% +know +and then uh and then we'll okay so + + align:start position:0% +and then uh and then we'll okay so + + + align:start position:0% +and then uh and then we'll okay so +here's the first one so it's x-rays + + align:start position:0% +here's the first one so it's x-rays + + + align:start position:0% +here's the first one so it's x-rays +and xrd so what do i want you to know + + align:start position:0% +and xrd so what do i want you to know + + + align:start position:0% +and xrd so what do i want you to know +well for example i want you to know + + align:start position:0% +well for example i want you to know + + + align:start position:0% +well for example i want you to know +about how you have + + align:start position:0% +about how you have + + + align:start position:0% +about how you have +characteristic characteristic + + align:start position:0% +characteristic characteristic + + + align:start position:0% +characteristic characteristic +characteristic uh + + align:start position:0% +characteristic uh + + + align:start position:0% +characteristic uh +x-rays and remember this this is + + align:start position:0% +x-rays and remember this this is + + + align:start position:0% +x-rays and remember this this is +this comes from those transitions right + + align:start position:0% +this comes from those transitions right + + + align:start position:0% +this comes from those transitions right +so you got like the k + + align:start position:0% +so you got like the k + + + align:start position:0% +so you got like the k +and the l and the m + + align:start position:0% +and the l and the m + + + align:start position:0% +and the l and the m +we say etc we never really did etc but + + align:start position:0% +we say etc we never really did etc but + + + align:start position:0% +we say etc we never really did etc but +you know we got a lot of k + + align:start position:0% +you know we got a lot of k + + + align:start position:0% +you know we got a lot of k +and l lines we looked at right + + align:start position:0% +and l lines we looked at right + + + align:start position:0% +and l lines we looked at right +alpha beta + + align:start position:0% + + + + align:start position:0% + +but there's also the continuous right so + + align:start position:0% +but there's also the continuous right so + + + align:start position:0% +but there's also the continuous right so +this was in + + align:start position:0% +this was in + + + align:start position:0% +this was in +if you want this would be in the topic + + align:start position:0% +if you want this would be in the topic + + + align:start position:0% +if you want this would be in the topic +of x-ray generation + + align:start position:0% +of x-ray generation + + + align:start position:0% +of x-ray generation +and there's that brim strolling + + align:start position:0% + + + + align:start position:0% + +word that means breaking + + align:start position:0% +word that means breaking + + + align:start position:0% +word that means breaking +right so if you if you just want to look + + align:start position:0% +right so if you if you just want to look + + + align:start position:0% +right so if you if you just want to look +at this + + align:start position:0% +at this + + + align:start position:0% +at this +you might have a curve that looks okay + + align:start position:0% +you might have a curve that looks okay + + + align:start position:0% +you might have a curve that looks okay +so we had things like this right + + align:start position:0% +so we had things like this right + + + align:start position:0% +so we had things like this right +oh i'm gonna try to make it not look + + align:start position:0% +oh i'm gonna try to make it not look + + + align:start position:0% +oh i'm gonna try to make it not look +too bad right and there's another one + + align:start position:0% +too bad right and there's another one + + + align:start position:0% +too bad right and there's another one +and so on and and remember + + align:start position:0% +and so on and and remember + + + align:start position:0% +and so on and and remember +yeah so this would be like intensity + + align:start position:0% +yeah so this would be like intensity + + + align:start position:0% +yeah so this would be like intensity +intensity and this would be like + + align:start position:0% +intensity and this would be like + + + align:start position:0% +intensity and this would be like +maybe uh lambda going that way or + + align:start position:0% +maybe uh lambda going that way or + + + align:start position:0% +maybe uh lambda going that way or +or maybe energy energy going that way or + + align:start position:0% +or maybe energy energy going that way or + + + align:start position:0% +or maybe energy energy going that way or +frequency + + align:start position:0% +frequency + + + align:start position:0% +frequency +right this would be like like the x-axis + + align:start position:0% +right this would be like like the x-axis + + + align:start position:0% +right this would be like like the x-axis +and and these are those lines those are + + align:start position:0% +and and these are those lines those are + + + align:start position:0% +and and these are those lines those are +the lines right and they come from the + + align:start position:0% +the lines right and they come from the + + + align:start position:0% +the lines right and they come from the +transitions + + align:start position:0% +transitions + + + align:start position:0% +transitions +that you get from like the k level to + + align:start position:0% +that you get from like the k level to + + + align:start position:0% +that you get from like the k level to +the l level to the m level right + + align:start position:0% +the l level to the m level right + + + align:start position:0% +the l level to the m level right +remember you're not + + align:start position:0% +remember you're not + + + align:start position:0% +remember you're not +you can if you get the energy high + + align:start position:0% +you can if you get the energy high + + + align:start position:0% +you can if you get the energy high +enough + + align:start position:0% +enough + + + align:start position:0% +enough +of an incident electron onto a target + + align:start position:0% +of an incident electron onto a target + + + align:start position:0% +of an incident electron onto a target +metal then you can knock out electrons + + align:start position:0% +metal then you can knock out electrons + + + align:start position:0% +metal then you can knock out electrons +from that 1s + + align:start position:0% +from that 1s + + + align:start position:0% +from that 1s +shell and then something cascades down + + align:start position:0% +shell and then something cascades down + + + align:start position:0% +shell and then something cascades down +and that emits these lines here + + align:start position:0% +and that emits these lines here + + + align:start position:0% +and that emits these lines here +right so it'll be like k alpha k alpha + + align:start position:0% +right so it'll be like k alpha k alpha + + + align:start position:0% +right so it'll be like k alpha k alpha +k beta et cetera but then you also even + + align:start position:0% +k beta et cetera but then you also even + + + align:start position:0% +k beta et cetera but then you also even +at lower energies + + align:start position:0% +at lower energies + + + align:start position:0% +at lower energies +even if you don't have enough energy to + + align:start position:0% +even if you don't have enough energy to + + + align:start position:0% +even if you don't have enough energy to +knock out a 1s electron + + align:start position:0% +knock out a 1s electron + + + align:start position:0% +knock out a 1s electron +you still can slow an electron down as + + align:start position:0% +you still can slow an electron down as + + + align:start position:0% +you still can slow an electron down as +it goes through a metal atom + + align:start position:0% +it goes through a metal atom + + + align:start position:0% +it goes through a metal atom +and that's where you get this continuous + + align:start position:0% +and that's where you get this continuous + + + align:start position:0% +and that's where you get this continuous +spectrum right + + align:start position:0% +spectrum right + + + align:start position:0% +spectrum right +and that that limit of how how much of + + align:start position:0% +and that that limit of how how much of + + + align:start position:0% +and that that limit of how how much of +that type of x-ray you get + + align:start position:0% +that type of x-ray you get + + + align:start position:0% +that type of x-ray you get +it just depends on the incident volt on + + align:start position:0% +it just depends on the incident volt on + + + align:start position:0% +it just depends on the incident volt on +the voltage right + + align:start position:0% +the voltage right + + + align:start position:0% +the voltage right +on the the maximum incident electron you + + align:start position:0% +on the the maximum incident electron you + + + align:start position:0% +on the the maximum incident electron you +fire at it so that's those first two + + align:start position:0% +fire at it so that's those first two + + + align:start position:0% +fire at it so that's those first two +topics + + align:start position:0% +topics + + + align:start position:0% +topics +okay uh well oh we also + + align:start position:0% +okay uh well oh we also + + + align:start position:0% +okay uh well oh we also +did uh x-ray diffraction + + align:start position:0% +did uh x-ray diffraction + + + align:start position:0% +did uh x-ray diffraction +oh that's fun diffraction + + align:start position:0% +oh that's fun diffraction + + + align:start position:0% +oh that's fun diffraction +okay and this involves understanding + + align:start position:0% +okay and this involves understanding + + + align:start position:0% +okay and this involves understanding +brag + + align:start position:0% +brag + + + align:start position:0% +brag +right the brag condition and + + align:start position:0% +right the brag condition and + + + align:start position:0% +right the brag condition and +also selection rules + + align:start position:0% + + + + align:start position:0% + +so let's do let's just take a look at an + + align:start position:0% +so let's do let's just take a look at an + + + align:start position:0% +so let's do let's just take a look at an +example of the of the diffraction and + + align:start position:0% +example of the of the diffraction and + + + align:start position:0% +example of the of the diffraction and +selection rules okay so what + + align:start position:0% +selection rules okay so what + + + align:start position:0% +selection rules okay so what +what would i want so these are like the + + align:start position:0% +what would i want so these are like the + + + align:start position:0% +what would i want so these are like the +kind of concepts that i want you to know + + align:start position:0% +kind of concepts that i want you to know + + + align:start position:0% +kind of concepts that i want you to know +about + + align:start position:0% +about + + + align:start position:0% +about +how might it play out so like um okay so + + align:start position:0% +how might it play out so like um okay so + + + align:start position:0% +how might it play out so like um okay so +here's like + + align:start position:0% +here's like + + + align:start position:0% +here's like +here's an example of a spectrum now + + align:start position:0% +here's an example of a spectrum now + + + align:start position:0% +here's an example of a spectrum now +that's an x-ray spectrum + + align:start position:0% +that's an x-ray spectrum + + + align:start position:0% +that's an x-ray spectrum +for uh mgfeo4 + + align:start position:0% +for uh mgfeo4 + + + align:start position:0% +for uh mgfeo4 +magnesium ferrite and and it's a kind of + + align:start position:0% +magnesium ferrite and and it's a kind of + + + align:start position:0% +magnesium ferrite and and it's a kind of +steel + + align:start position:0% +steel + + + align:start position:0% +steel +right and you put it in you make a + + align:start position:0% +right and you put it in you make a + + + align:start position:0% +right and you put it in you make a +powder of it and you and you throw some + + align:start position:0% +powder of it and you and you throw some + + + align:start position:0% +powder of it and you and you throw some +x-rays on + + align:start position:0% +x-rays on + + + align:start position:0% +x-rays on +it oh no you throw just one type of + + align:start position:0% +it oh no you throw just one type of + + + align:start position:0% +it oh no you throw just one type of +x-ray on it + + align:start position:0% +x-ray on it + + + align:start position:0% +x-ray on it +right so for these x-ray spectra what + + align:start position:0% +right so for these x-ray spectra what + + + align:start position:0% +right so for these x-ray spectra what +happened i threw some k + + align:start position:0% +happened i threw some k + + + align:start position:0% +happened i threw some k +alpha on it i showed right there you got + + align:start position:0% +alpha on it i showed right there you got + + + align:start position:0% +alpha on it i showed right there you got +to say what you got + + align:start position:0% +to say what you got + + + align:start position:0% +to say what you got +right there you got you got to know at + + align:start position:0% +right there you got you got to know at + + + align:start position:0% +right there you got you got to know at +least okay the source of x-rays + + align:start position:0% +least okay the source of x-rays + + + align:start position:0% +least okay the source of x-rays +has this has this wavelength good + + align:start position:0% +has this has this wavelength good + + + align:start position:0% +has this has this wavelength good +and if i have that spectrum and say + + align:start position:0% +and if i have that spectrum and say + + + align:start position:0% +and if i have that spectrum and say +what's the lattice constant + + align:start position:0% +what's the lattice constant + + + align:start position:0% +what's the lattice constant +well what's the structure i can get that + + align:start position:0% +well what's the structure i can get that + + + align:start position:0% +well what's the structure i can get that +how would i get that + + align:start position:0% +how would i get that + + + align:start position:0% +how would i get that +how would i get this so i would take + + align:start position:0% +how would i get this so i would take + + + align:start position:0% +how would i get this so i would take +this spectrum + + align:start position:0% +this spectrum + + + align:start position:0% +this spectrum +and notice something is very much + + align:start position:0% +and notice something is very much + + + align:start position:0% +and notice something is very much +pointed out to me + + align:start position:0% +pointed out to me + + + align:start position:0% +pointed out to me +a peak and a number 35.5 + + align:start position:0% +a peak and a number 35.5 + + + align:start position:0% +a peak and a number 35.5 +right that's the that's the two theta + + align:start position:0% +right that's the that's the two theta + + + align:start position:0% +right that's the that's the two theta +value for the three one one peak + + align:start position:0% +value for the three one one peak + + + align:start position:0% +value for the three one one peak +well i think i'll take that as a hint + + align:start position:0% +well i think i'll take that as a hint + + + align:start position:0% +well i think i'll take that as a hint +maybe i should think about that number + + align:start position:0% +maybe i should think about that number + + + align:start position:0% +maybe i should think about that number +and i show okay so let's see from bragg + + align:start position:0% +and i show okay so let's see from bragg + + + align:start position:0% +and i show okay so let's see from bragg +so from bragg + + align:start position:0% +so from bragg + + + align:start position:0% +so from bragg +you know that + + align:start position:0% +you know that + + + align:start position:0% +you know that +you got n lambda equals + + align:start position:0% +you got n lambda equals + + + align:start position:0% +you got n lambda equals +d equals 2d sine theta + + align:start position:0% +d equals 2d sine theta + + + align:start position:0% +d equals 2d sine theta +and remember that had to do with + + align:start position:0% +and remember that had to do with + + + align:start position:0% +and remember that had to do with +constructive and destructive uh + + align:start position:0% +constructive and destructive uh + + + align:start position:0% +constructive and destructive uh +interference of waves the waves being + + align:start position:0% +interference of waves the waves being + + + align:start position:0% +interference of waves the waves being +the x-rays and + + align:start position:0% +the x-rays and + + + align:start position:0% +the x-rays and +and then we said well n is n is one in + + align:start position:0% +and then we said well n is n is one in + + + align:start position:0% +and then we said well n is n is one in +our class okay so we're gonna + + align:start position:0% +our class okay so we're gonna + + + align:start position:0% +our class okay so we're gonna +that's just one in 309 one it doesn't + + align:start position:0% +that's just one in 309 one it doesn't + + + align:start position:0% +that's just one in 309 one it doesn't +have to be you could + + align:start position:0% +have to be you could + + + align:start position:0% +have to be you could +you could have interference off of two + + align:start position:0% +you could have interference off of two + + + align:start position:0% +you could have interference off of two +planes down three planes down but in + + align:start position:0% +planes down three planes down but in + + + align:start position:0% +planes down three planes down but in +this class we're just doing the two + + align:start position:0% +this class we're just doing the two + + + align:start position:0% +this class we're just doing the two +planes next to each other so n is one + + align:start position:0% +planes next to each other so n is one + + + align:start position:0% +planes next to each other so n is one +okay now i'll take that angle + + align:start position:0% +okay now i'll take that angle + + + align:start position:0% +okay now i'll take that angle +and i'll round it to 18 degrees so i'm + + align:start position:0% +and i'll round it to 18 degrees so i'm + + + align:start position:0% +and i'll round it to 18 degrees so i'm +going to say for theta + + align:start position:0% +going to say for theta + + + align:start position:0% +going to say for theta +equals 18 degrees + + align:start position:0% +equals 18 degrees + + + align:start position:0% +equals 18 degrees +then uh oh wait why is it 18 and not + + align:start position:0% +then uh oh wait why is it 18 and not + + + align:start position:0% +then uh oh wait why is it 18 and not +there + + align:start position:0% +there + + + align:start position:0% +there +because that's two theta right because + + align:start position:0% +because that's two theta right because + + + align:start position:0% +because that's two theta right because +remember we met we take spectra and two + + align:start position:0% +remember we met we take spectra and two + + + align:start position:0% +remember we met we take spectra and two +theta but the theta in brag is one theta + + align:start position:0% +theta but the theta in brag is one theta + + + align:start position:0% +theta but the theta in brag is one theta +okay that wasn't too hard and so then + + align:start position:0% +okay that wasn't too hard and so then + + + align:start position:0% +okay that wasn't too hard and so then +but now i got uh let's see + + align:start position:0% +but now i got uh let's see + + + align:start position:0% +but now i got uh let's see +uh sine theta + + align:start position:0% +uh sine theta + + + align:start position:0% +uh sine theta +is around 0.3 and so if you + + align:start position:0% +is around 0.3 and so if you + + + align:start position:0% +is around 0.3 and so if you +but oh i got lambda lambda equals + + align:start position:0% +but oh i got lambda lambda equals + + + align:start position:0% +but oh i got lambda lambda equals +1.54 nanometers and so i can actually + + align:start position:0% +1.54 nanometers and so i can actually + + + align:start position:0% +1.54 nanometers and so i can actually +plug in now + + align:start position:0% +plug in now + + + align:start position:0% +plug in now +i didn't even need the peak i'm just + + align:start position:0% +i didn't even need the peak i'm just + + + align:start position:0% +i didn't even need the peak i'm just +plugging in + + align:start position:0% +plugging in + + + align:start position:0% +plugging in +the brag condition right and i've got d + + align:start position:0% +the brag condition right and i've got d + + + align:start position:0% +the brag condition right and i've got d +d equals 2.5 to angstroms + + align:start position:0% +d equals 2.5 to angstroms + + + align:start position:0% +d equals 2.5 to angstroms +so i'm done no no + + align:start position:0% +so i'm done no no + + + align:start position:0% +so i'm done no no +i'm not done because the question says + + align:start position:0% +i'm not done because the question says + + + align:start position:0% +i'm not done because the question says +what's the lattice constant + + align:start position:0% +what's the lattice constant + + + align:start position:0% +what's the lattice constant +what's the lattice constant this d i + + align:start position:0% +what's the lattice constant this d i + + + align:start position:0% +what's the lattice constant this d i +didn't say + + align:start position:0% +didn't say + + + align:start position:0% +didn't say +i did something very bad i didn't say + + align:start position:0% +i did something very bad i didn't say + + + align:start position:0% +i did something very bad i didn't say +what d d is in h k l + + align:start position:0% +what d d is in h k l + + + align:start position:0% +what d d is in h k l +that's what an xrd does x + + align:start position:0% +that's what an xrd does x + + + align:start position:0% +that's what an xrd does x +xrd is that's a different d then + + align:start position:0% +xrd is that's a different d then + + + align:start position:0% +xrd is that's a different d then +diffraction but + + align:start position:0% +diffraction but + + + align:start position:0% +diffraction but +the d in brag is the distance between + + align:start position:0% +the d in brag is the distance between + + + align:start position:0% +the d in brag is the distance between +the the mirror planes that are + + align:start position:0% +the the mirror planes that are + + + align:start position:0% +the the mirror planes that are +scattering all right + + align:start position:0% +scattering all right + + + align:start position:0% +scattering all right +and so that's some cuts in the crystal + + align:start position:0% +and so that's some cuts in the crystal + + + align:start position:0% +and so that's some cuts in the crystal +that's some hkl and we know from that + + align:start position:0% +that's some hkl and we know from that + + + align:start position:0% +that's some hkl and we know from that +era that there is an equation + + align:start position:0% +era that there is an equation + + + align:start position:0% +era that there is an equation +for cubic crystals that gives us hkl + + align:start position:0% +for cubic crystals that gives us hkl + + + align:start position:0% +for cubic crystals that gives us hkl +which is a divided by the square root + + align:start position:0% +which is a divided by the square root + + + align:start position:0% +which is a divided by the square root +of h squared plus k + + align:start position:0% +of h squared plus k + + + align:start position:0% +of h squared plus k +squared plus l squared and that is + + align:start position:0% +squared plus l squared and that is + + + align:start position:0% +squared plus l squared and that is +the lattice constant of the crystal + + align:start position:0% + + + + align:start position:0% + +right and that would be the distance + + align:start position:0% +right and that would be the distance + + + align:start position:0% +right and that would be the distance +between any planes + + align:start position:0% +between any planes + + + align:start position:0% +between any planes +any set of planes in the crystal okay + + align:start position:0% +any set of planes in the crystal okay + + + align:start position:0% +any set of planes in the crystal okay +and that's what we need + + align:start position:0% +and that's what we need + + + align:start position:0% +and that's what we need +now i can i can use that combine it with + + align:start position:0% +now i can i can use that combine it with + + + align:start position:0% +now i can i can use that combine it with +with the the d and i can get that the + + align:start position:0% +with the the d and i can get that the + + + align:start position:0% +with the the d and i can get that the +lattice constant is 8.38 angstroms + + align:start position:0% +lattice constant is 8.38 angstroms + + + align:start position:0% +lattice constant is 8.38 angstroms +good the second question + + align:start position:0% +good the second question + + + align:start position:0% +good the second question +is you don't even need to do anything + + align:start position:0% +is you don't even need to do anything + + + align:start position:0% +is you don't even need to do anything +any math to answer that + + align:start position:0% +any math to answer that + + + align:start position:0% +any math to answer that +what is the lattice structure here + + align:start position:0% +what is the lattice structure here + + + align:start position:0% +what is the lattice structure here +we simply go to our selection rules and + + align:start position:0% +we simply go to our selection rules and + + + align:start position:0% +we simply go to our selection rules and +we know + + align:start position:0% +we know + + + align:start position:0% +we know +from before look if they're all you know + + align:start position:0% +from before look if they're all you know + + + align:start position:0% +from before look if they're all you know +if if they're all even or all odd + + align:start position:0% +if if they're all even or all odd + + + align:start position:0% +if if they're all even or all odd +so here we have let's see all these + + align:start position:0% +so here we have let's see all these + + + align:start position:0% +so here we have let's see all these +peaks 2 2 0 + + align:start position:0% +peaks 2 2 0 + + + align:start position:0% +peaks 2 2 0 +3 1 1 4 0 0. you can see they're always + + align:start position:0% +3 1 1 4 0 0. you can see they're always + + + align:start position:0% +3 1 1 4 0 0. you can see they're always +all even or they're always all odd + + align:start position:0% +all even or they're always all odd + + + align:start position:0% +all even or they're always all odd +from our selection rules what kind of + + align:start position:0% +from our selection rules what kind of + + + align:start position:0% +from our selection rules what kind of +crystal is that + + align:start position:0% + + + + align:start position:0% + +it's got to be fcc right + + align:start position:0% +it's got to be fcc right + + + align:start position:0% +it's got to be fcc right +it's got to be fcc so that that's that's + + align:start position:0% +it's got to be fcc so that that's that's + + + align:start position:0% +it's got to be fcc so that that's that's +the answer to that question + + align:start position:0% +the answer to that question + + + align:start position:0% +the answer to that question +right just from looking at the peaks + + align:start position:0% +right just from looking at the peaks + + + align:start position:0% +right just from looking at the peaks +that you get and + + align:start position:0% +that you get and + + + align:start position:0% +that you get and +and and matching them with the selection + + align:start position:0% +and and matching them with the selection + + + align:start position:0% +and and matching them with the selection +rules that you know + + align:start position:0% +rules that you know + + + align:start position:0% +rules that you know +that we've already talked about + + align:start position:0% + + + + align:start position:0% + +you could also you know if you didn't + + align:start position:0% +you could also you know if you didn't + + + align:start position:0% +you could also you know if you didn't +have the planes + + align:start position:0% +have the planes + + + align:start position:0% +have the planes +so this is the this is an example where + + align:start position:0% +so this is the this is an example where + + + align:start position:0% +so this is the this is an example where +you're given all these planes you're + + align:start position:0% +you're given all these planes you're + + + align:start position:0% +you're given all these planes you're +given all these hkls but what if instead + + align:start position:0% +given all these hkls but what if instead + + + align:start position:0% +given all these hkls but what if instead +it's like the one we had in class + + align:start position:0% +it's like the one we had in class + + + align:start position:0% +it's like the one we had in class +we went through this in class here i'm + + align:start position:0% +we went through this in class here i'm + + + align:start position:0% +we went through this in class here i'm +not given the planes i'm given + + align:start position:0% +not given the planes i'm given + + + align:start position:0% +not given the planes i'm given +instead just two theta values + + align:start position:0% +instead just two theta values + + + align:start position:0% +instead just two theta values +well now you got to go and use the + + align:start position:0% +well now you got to go and use the + + + align:start position:0% +well now you got to go and use the +procedure + + align:start position:0% +procedure + + + align:start position:0% +procedure +of xrd and i'm not going to do that + + align:start position:0% +of xrd and i'm not going to do that + + + align:start position:0% +of xrd and i'm not going to do that +again we've already done that + + align:start position:0% +again we've already done that + + + align:start position:0% +again we've already done that +pretty thoroughly um but but that's what + + align:start position:0% +pretty thoroughly um but but that's what + + + align:start position:0% +pretty thoroughly um but but that's what +you have to do here right + + align:start position:0% +you have to do here right + + + align:start position:0% +you have to do here right +where you create your columns remember + + align:start position:0% +where you create your columns remember + + + align:start position:0% +where you create your columns remember +the columns right + + align:start position:0% +the columns right + + + align:start position:0% +the columns right +so so so you would simply make your + + align:start position:0% +so so so you would simply make your + + + align:start position:0% +so so so you would simply make your +columns you make your sign + + align:start position:0% +columns you make your sign + + + align:start position:0% +columns you make your sign +your your thetas that is your two theta + + align:start position:0% +your your thetas that is your two theta + + + align:start position:0% +your your thetas that is your two theta +theta + + align:start position:0% +theta + + + align:start position:0% +theta +sine squared thetas and then you + + align:start position:0% +sine squared thetas and then you + + + align:start position:0% +sine squared thetas and then you +normalize right you take the lowest one + + align:start position:0% +normalize right you take the lowest one + + + align:start position:0% +normalize right you take the lowest one +and and you normalize to one + + align:start position:0% +and and you normalize to one + + + align:start position:0% +and and you normalize to one +clear fractions and then find the hkl + + align:start position:0% +clear fractions and then find the hkl + + + align:start position:0% +clear fractions and then find the hkl +combinations and that's how you would go + + align:start position:0% +combinations and that's how you would go + + + align:start position:0% +combinations and that's how you would go +from this to getting for example the the + + align:start position:0% +from this to getting for example the the + + + align:start position:0% +from this to getting for example the the +planes + + align:start position:0% +planes + + + align:start position:0% +planes +okay so those are some examples of + + align:start position:0% +okay so those are some examples of + + + align:start position:0% +okay so those are some examples of +things + + align:start position:0% +things + + + align:start position:0% +things +i want you to be able to do with x-rays + + align:start position:0% +i want you to be able to do with x-rays + + + align:start position:0% +i want you to be able to do with x-rays +and xrd let's move on + + align:start position:0% +and xrd let's move on + + + align:start position:0% +and xrd let's move on +let's go to the next topic let's do + + align:start position:0% +let's go to the next topic let's do + + + align:start position:0% +let's go to the next topic let's do +defects how about this + + align:start position:0% +defects how about this + + + align:start position:0% +defects how about this +defects because as we said + + align:start position:0% +defects because as we said + + + align:start position:0% +defects because as we said +it's just like life crystals defects are + + align:start position:0% +it's just like life crystals defects are + + + align:start position:0% +it's just like life crystals defects are +what make them interesting + + align:start position:0% +what make them interesting + + + align:start position:0% +what make them interesting +it's the same everything it's all about + + align:start position:0% +it's the same everything it's all about + + + align:start position:0% +it's the same everything it's all about +defects imperfections that those are + + align:start position:0% +defects imperfections that those are + + + align:start position:0% +defects imperfections that those are +the interesting and exciting things so + + align:start position:0% +the interesting and exciting things so + + + align:start position:0% +the interesting and exciting things so +we got to know about them in chemistry + + align:start position:0% +we got to know about them in chemistry + + + align:start position:0% +we got to know about them in chemistry +of course then so + + align:start position:0% +of course then so + + + align:start position:0% +of course then so +we we talked about a bunch of different + + align:start position:0% +we we talked about a bunch of different + + + align:start position:0% +we we talked about a bunch of different +kinds of defects the first one that we + + align:start position:0% +kinds of defects the first one that we + + + align:start position:0% +kinds of defects the first one that we +talked about + + align:start position:0% +talked about + + + align:start position:0% +talked about +were vacancies okay + + align:start position:0% +were vacancies okay + + + align:start position:0% +were vacancies okay +vacancies and these could be you know + + align:start position:0% +vacancies and these could be you know + + + align:start position:0% +vacancies and these could be you know +interstitial they you could also have + + align:start position:0% +interstitial they you could also have + + + align:start position:0% +interstitial they you could also have +these fall into the category of point + + align:start position:0% +these fall into the category of point + + + align:start position:0% +these fall into the category of point +defects + + align:start position:0% +defects + + + align:start position:0% +defects +point defects right + + align:start position:0% + + + + align:start position:0% + +you could also have also interstitial + + align:start position:0% +you could also have also interstitial + + + align:start position:0% +you could also have also interstitial +point defects + + align:start position:0% +point defects + + + align:start position:0% +point defects +interstitial or + + align:start position:0% +interstitial or + + + align:start position:0% +interstitial or +substitutional + + align:start position:0% + + + + align:start position:0% + +right those are the different kinds of + + align:start position:0% +right those are the different kinds of + + + align:start position:0% +right those are the different kinds of +defects we talked about + + align:start position:0% +defects we talked about + + + align:start position:0% +defects we talked about +for point defects also by the way if + + align:start position:0% +for point defects also by the way if + + + align:start position:0% +for point defects also by the way if +it's an ionic point defect + + align:start position:0% +it's an ionic point defect + + + align:start position:0% +it's an ionic point defect +ionic point defect + + align:start position:0% + + + + align:start position:0% + +you need to make sure you have charge + + align:start position:0% +you need to make sure you have charge + + + align:start position:0% +you need to make sure you have charge +neutrality charge neutrality + + align:start position:0% + + + + align:start position:0% + +plus two types + + align:start position:0% + + + + align:start position:0% + +there's frankel and there's shocky hey + + align:start position:0% +there's frankel and there's shocky hey + + + align:start position:0% +there's frankel and there's shocky hey +you think about + + align:start position:0% +you think about + + + align:start position:0% +you think about +is it shocky you remove + + align:start position:0% +is it shocky you remove + + + align:start position:0% +is it shocky you remove +but you got to remove them in a way + + align:start position:0% +but you got to remove them in a way + + + align:start position:0% +but you got to remove them in a way +that's charge balanced + + align:start position:0% +that's charge balanced + + + align:start position:0% +that's charge balanced +right so in shock you remove uh uh in an + + align:start position:0% +right so in shock you remove uh uh in an + + + align:start position:0% +right so in shock you remove uh uh in an +ionic crystal you got to keep charged + + align:start position:0% +ionic crystal you got to keep charged + + + align:start position:0% +ionic crystal you got to keep charged +that's the new thing + + align:start position:0% +that's the new thing + + + align:start position:0% +that's the new thing +you got to keep track of and so so if we + + align:start position:0% +you got to keep track of and so so if we + + + align:start position:0% +you got to keep track of and so so if we +had i'll go to the + + align:start position:0% +had i'll go to the + + + align:start position:0% +had i'll go to the +this uh this picture oh you should know + + align:start position:0% +this uh this picture oh you should know + + + align:start position:0% +this uh this picture oh you should know +this picture + + align:start position:0% +this picture + + + align:start position:0% +this picture +this is an important picture we showed + + align:start position:0% +this is an important picture we showed + + + align:start position:0% +this is an important picture we showed +it a lot right vacancy + + align:start position:0% +it a lot right vacancy + + + align:start position:0% +it a lot right vacancy +interstitial self-interstitial + + align:start position:0% +interstitial self-interstitial + + + align:start position:0% +interstitial self-interstitial +substitutional but and then if it's + + align:start position:0% +substitutional but and then if it's + + + align:start position:0% +substitutional but and then if it's +ionic + + align:start position:0% +ionic + + + align:start position:0% +ionic +now the sudden you got charges in there + + align:start position:0% +now the sudden you got charges in there + + + align:start position:0% +now the sudden you got charges in there +and so you just got to make sure things + + align:start position:0% +and so you just got to make sure things + + + align:start position:0% +and so you just got to make sure things +remain neutral right in shock you would + + align:start position:0% +remain neutral right in shock you would + + + align:start position:0% +remain neutral right in shock you would +remove + + align:start position:0% +remove + + + align:start position:0% +remove +atoms to balance the charge and in + + align:start position:0% +atoms to balance the charge and in + + + align:start position:0% +atoms to balance the charge and in +frankl + + align:start position:0% +frankl + + + align:start position:0% +frankl +you move an atom + + align:start position:0% +you move an atom + + + align:start position:0% +you move an atom +that shocky remove frankl move + + align:start position:0% +that shocky remove frankl move + + + align:start position:0% +that shocky remove frankl move +just occurred to me that that's + + align:start position:0% +just occurred to me that that's + + + align:start position:0% +just occurred to me that that's +the same word with just read in front of + + align:start position:0% +the same word with just read in front of + + + align:start position:0% +the same word with just read in front of +it + + align:start position:0% +it + + + align:start position:0% +it +that's exciting oh so if i were to ask + + align:start position:0% +that's exciting oh so if i were to ask + + + align:start position:0% +that's exciting oh so if i were to ask +you for example if i were to ask you + + align:start position:0% +you for example if i were to ask you + + + align:start position:0% +you for example if i were to ask you +this + + align:start position:0% +this + + + align:start position:0% +this +you diffuse chromium + + align:start position:0% + + + + align:start position:0% + +into one side of the ionic crystal + + align:start position:0% +into one side of the ionic crystal + + + align:start position:0% +into one side of the ionic crystal +alumina + + align:start position:0% +alumina + + + align:start position:0% +alumina +to make it red and titanium on the other + + align:start position:0% +to make it red and titanium on the other + + + align:start position:0% +to make it red and titanium on the other +would you expect + + align:start position:0% +would you expect + + + align:start position:0% +would you expect +oxygen vacancies illumina vacancies are + + align:start position:0% +oxygen vacancies illumina vacancies are + + + align:start position:0% +oxygen vacancies illumina vacancies are +no vacancies + + align:start position:0% +no vacancies + + + align:start position:0% +no vacancies +in each case just follow the + + align:start position:0% +in each case just follow the + + + align:start position:0% +in each case just follow the +follow oh follow the charge + + align:start position:0% +follow oh follow the charge + + + align:start position:0% +follow oh follow the charge +follow the charge so for example if i + + align:start position:0% +follow the charge so for example if i + + + align:start position:0% +follow the charge so for example if i +had aluminum + + align:start position:0% +had aluminum + + + align:start position:0% +had aluminum +alumina o3 well if i were lewis + + align:start position:0% +alumina o3 well if i were lewis + + + align:start position:0% +alumina o3 well if i were lewis +we started by time if i were lewis i + + align:start position:0% +we started by time if i were lewis i + + + align:start position:0% +we started by time if i were lewis i +would see this as + + align:start position:0% +would see this as + + + align:start position:0% +would see this as +2 al right 2 + + align:start position:0% +2 al right 2 + + + align:start position:0% +2 al right 2 +al 3 plus right this is how he saw + + align:start position:0% +al 3 plus right this is how he saw + + + align:start position:0% +al 3 plus right this is how he saw +ionic bonds uh three + + align:start position:0% + + + + align:start position:0% + +i want to make sure this is clear i'm + + align:start position:0% +i want to make sure this is clear i'm + + + align:start position:0% +i want to make sure this is clear i'm +gonna start over + + align:start position:0% +gonna start over + + + align:start position:0% +gonna start over +so i would have two + + align:start position:0% +so i would have two + + + align:start position:0% +so i would have two +al 3 plus and then i would have a 3 + + align:start position:0% +al 3 plus and then i would have a 3 + + + align:start position:0% +al 3 plus and then i would have a 3 +o 2 minus remember o likes to be 2 minus + + align:start position:0% + + + + align:start position:0% + +and so if i were to introduce something + + align:start position:0% +and so if i were to introduce something + + + align:start position:0% +and so if i were to introduce something +like + + align:start position:0% +like + + + align:start position:0% +like +cr203 well + + align:start position:0% +cr203 well + + + align:start position:0% +cr203 well +you know this also this is two + + align:start position:0% +you know this also this is two + + + align:start position:0% +you know this also this is two +cr three plus so this is two cr3 plus + + align:start position:0% +cr three plus so this is two cr3 plus + + + align:start position:0% +cr three plus so this is two cr3 plus +and three o two minus so + + align:start position:0% +and three o two minus so + + + align:start position:0% +and three o two minus so +you know if i if i substitute aluminum + + align:start position:0% +you know if i if i substitute aluminum + + + align:start position:0% +you know if i if i substitute aluminum +with chromium then i'm charge balance + + align:start position:0% +with chromium then i'm charge balance + + + align:start position:0% +with chromium then i'm charge balance +right i'm okay but if i substitute + + align:start position:0% +right i'm okay but if i substitute + + + align:start position:0% +right i'm okay but if i substitute +titanium + + align:start position:0% +titanium + + + align:start position:0% +titanium +right tio2 is ti + + align:start position:0% +right tio2 is ti + + + align:start position:0% +right tio2 is ti +4 plus and + + align:start position:0% +4 plus and + + + align:start position:0% +4 plus and +2 o 2 minus you know this just from the + + align:start position:0% +2 o 2 minus you know this just from the + + + align:start position:0% +2 o 2 minus you know this just from the +formula + + align:start position:0% +formula + + + align:start position:0% +formula +because if oxygen is 2 minus this + + align:start position:0% +because if oxygen is 2 minus this + + + align:start position:0% +because if oxygen is 2 minus this +thing's got to be neutral and so that's + + align:start position:0% +thing's got to be neutral and so that's + + + align:start position:0% +thing's got to be neutral and so that's +ti4 plus + + align:start position:0% +ti4 plus + + + align:start position:0% +ti4 plus +but now if i if i put a ti in there and + + align:start position:0% +but now if i if i put a ti in there and + + + align:start position:0% +but now if i if i put a ti in there and +i get one in for an aluminum + + align:start position:0% +i get one in for an aluminum + + + align:start position:0% +i get one in for an aluminum +i've knocked the charge by one + + align:start position:0% +i've knocked the charge by one + + + align:start position:0% +i've knocked the charge by one +right so this gives us + + align:start position:0% +right so this gives us + + + align:start position:0% +right so this gives us +an extra charge + + align:start position:0% + + + + align:start position:0% + +and that means you got to create + + align:start position:0% +and that means you got to create + + + align:start position:0% +and that means you got to create +vacancies create + + align:start position:0% +vacancies create + + + align:start position:0% +vacancies create +aluminum vacancies it's the only way to + + align:start position:0% +aluminum vacancies it's the only way to + + + align:start position:0% +aluminum vacancies it's the only way to +do + + align:start position:0% +do + + + align:start position:0% +do +it it so for every three titanium atoms + + align:start position:0% +it it so for every three titanium atoms + + + align:start position:0% +it it so for every three titanium atoms +that i put in i got to take an aluminum + + align:start position:0% +that i put in i got to take an aluminum + + + align:start position:0% +that i put in i got to take an aluminum +one out + + align:start position:0% +one out + + + align:start position:0% +one out +right otherwise i just i'm not going to + + align:start position:0% +right otherwise i just i'm not going to + + + align:start position:0% +right otherwise i just i'm not going to +have charge balance + + align:start position:0% +have charge balance + + + align:start position:0% +have charge balance +not going to have charge balance right + + align:start position:0% +not going to have charge balance right + + + align:start position:0% +not going to have charge balance right +so that would be an example + + align:start position:0% +so that would be an example + + + align:start position:0% +so that would be an example +of uh of of kind of playing with an + + align:start position:0% +of uh of of kind of playing with an + + + align:start position:0% +of uh of of kind of playing with an +ionic crystal but you know remember we + + align:start position:0% +ionic crystal but you know remember we + + + align:start position:0% +ionic crystal but you know remember we +also had stress strain curves + + align:start position:0% +also had stress strain curves + + + align:start position:0% +also had stress strain curves +because + + align:start position:0% + + + + align:start position:0% + +when we talked about line defects we + + align:start position:0% +when we talked about line defects we + + + align:start position:0% +when we talked about line defects we +talked about how that's a way for + + align:start position:0% +talked about how that's a way for + + + align:start position:0% +talked about how that's a way for +metals well and other materials to go to + + align:start position:0% +metals well and other materials to go to + + + align:start position:0% +metals well and other materials to go to +undergo deformation and then we said + + align:start position:0% +undergo deformation and then we said + + + align:start position:0% +undergo deformation and then we said +well how are we gonna + + align:start position:0% +well how are we gonna + + + align:start position:0% +well how are we gonna +how are we gonna conceptualize uh + + align:start position:0% +how are we gonna conceptualize uh + + + align:start position:0% +how are we gonna conceptualize uh +you know these things happening and we + + align:start position:0% +you know these things happening and we + + + align:start position:0% +you know these things happening and we +did it with the stress strain curve and + + align:start position:0% +did it with the stress strain curve and + + + align:start position:0% +did it with the stress strain curve and +the mechanical response of materials + + align:start position:0% +the mechanical response of materials + + + align:start position:0% +the mechanical response of materials +so we learned about stress strain curves + + align:start position:0% +so we learned about stress strain curves + + + align:start position:0% +so we learned about stress strain curves +and + + align:start position:0% +and + + + align:start position:0% +and +uh you know fracture points + + align:start position:0% +uh you know fracture points + + + align:start position:0% +uh you know fracture points +fracture and + + align:start position:0% +fracture and + + + align:start position:0% +fracture and +plastic versus elastic + + align:start position:0% + + + + align:start position:0% + +uh regimes okay i'll give an example in + + align:start position:0% +uh regimes okay i'll give an example in + + + align:start position:0% +uh regimes okay i'll give an example in +a sec + + align:start position:0% +a sec + + + align:start position:0% +a sec +okay + + align:start position:0% + + + + align:start position:0% + +and finally the last thing we did with + + align:start position:0% +and finally the last thing we did with + + + align:start position:0% +and finally the last thing we did with +defects is we talked about their + + align:start position:0% +defects is we talked about their + + + align:start position:0% +defects is we talked about their +activation + + align:start position:0% +activation + + + align:start position:0% +activation +and so we know if something is thermally + + align:start position:0% +and so we know if something is thermally + + + align:start position:0% +and so we know if something is thermally +activated + + align:start position:0% +activated + + + align:start position:0% +activated +as our point defects + + align:start position:0% +as our point defects + + + align:start position:0% +as our point defects +well the vacancies are are are thermally + + align:start position:0% +well the vacancies are are are thermally + + + align:start position:0% +well the vacancies are are are thermally +activated so are + + align:start position:0% +activated so are + + + align:start position:0% +activated so are +other types of point defects and and we + + align:start position:0% +other types of point defects and and we + + + align:start position:0% +other types of point defects and and we +said that we need an arrhenius + + align:start position:0% +said that we need an arrhenius + + + align:start position:0% +said that we need an arrhenius +relationship + + align:start position:0% +relationship + + + align:start position:0% +relationship +and that requires knowledge of an + + align:start position:0% +and that requires knowledge of an + + + align:start position:0% +and that requires knowledge of an +activation energy for the defect to form + + align:start position:0% +activation energy for the defect to form + + + align:start position:0% +activation energy for the defect to form +so that was another really important + + align:start position:0% +so that was another really important + + + align:start position:0% +so that was another really important +concept that we covered right and so + + align:start position:0% +concept that we covered right and so + + + align:start position:0% +concept that we covered right and so +so for example um here you know here's + + align:start position:0% +so for example um here you know here's + + + align:start position:0% +so for example um here you know here's +like a defect + + align:start position:0% +like a defect + + + align:start position:0% +like a defect +formation energy question + + align:start position:0% + + + + align:start position:0% + +so uh let me go over here stay with + + align:start position:0% +so uh let me go over here stay with + + + align:start position:0% +so uh let me go over here stay with +these + + align:start position:0% +these + + + align:start position:0% +these +this side where i've got some defects um + + align:start position:0% +this side where i've got some defects um + + + align:start position:0% +this side where i've got some defects um +so uh you know one thing i want to make + + align:start position:0% +so uh you know one thing i want to make + + + align:start position:0% +so uh you know one thing i want to make +clear + + align:start position:0% +clear + + + align:start position:0% +clear +the fraction of vacancies we talked + + align:start position:0% +the fraction of vacancies we talked + + + align:start position:0% +the fraction of vacancies we talked +about this the fr + + align:start position:0% +about this the fr + + + align:start position:0% +about this the fr +somewhat an arrhenius behavior arrhenius + + align:start position:0% +somewhat an arrhenius behavior arrhenius + + + align:start position:0% +somewhat an arrhenius behavior arrhenius +like behavior + + align:start position:0% +like behavior + + + align:start position:0% +like behavior +and the fraction of vacancies was the + + align:start position:0% +and the fraction of vacancies was the + + + align:start position:0% +and the fraction of vacancies was the +number of vacancies over + + align:start position:0% +number of vacancies over + + + align:start position:0% +number of vacancies over +the number of possible sites that makes + + align:start position:0% +the number of possible sites that makes + + + align:start position:0% +the number of possible sites that makes +a lot of sense + + align:start position:0% +a lot of sense + + + align:start position:0% +a lot of sense +now if it's a radius then this is some + + align:start position:0% +now if it's a radius then this is some + + + align:start position:0% +now if it's a radius then this is some +constant + + align:start position:0% +constant + + + align:start position:0% +constant +times e to the minus activation energy + + align:start position:0% +times e to the minus activation energy + + + align:start position:0% +times e to the minus activation energy +divided by kbt + + align:start position:0% +divided by kbt + + + align:start position:0% +divided by kbt +it where we use the boltzmann constant + + align:start position:0% +it where we use the boltzmann constant + + + align:start position:0% +it where we use the boltzmann constant +if it's per + + align:start position:0% +if it's per + + + align:start position:0% +if it's per +atom right so per vacancy + + align:start position:0% +atom right so per vacancy + + + align:start position:0% +atom right so per vacancy +that activation energy would be per + + align:start position:0% +that activation energy would be per + + + align:start position:0% +that activation energy would be per +vacancy uh but + + align:start position:0% +vacancy uh but + + + align:start position:0% +vacancy uh but +and when i first introduced this i + + align:start position:0% +and when i first introduced this i + + + align:start position:0% +and when i first introduced this i +simply let a be one + + align:start position:0% +simply let a be one + + + align:start position:0% +simply let a be one +but a is a constant this is a constant + + align:start position:0% + + + + align:start position:0% + +and it can be it can be whatever it's a + + align:start position:0% +and it can be it can be whatever it's a + + + align:start position:0% +and it can be it can be whatever it's a +constant it's called the entropic + + align:start position:0% +constant it's called the entropic + + + align:start position:0% +constant it's called the entropic +factor uh + + align:start position:0% +factor uh + + + align:start position:0% +factor uh +and it's a constant related to as you + + align:start position:0% +and it's a constant related to as you + + + align:start position:0% +and it's a constant related to as you +would have in any arrhenius-like + + align:start position:0% +would have in any arrhenius-like + + + align:start position:0% +would have in any arrhenius-like +behavior + + align:start position:0% +behavior + + + align:start position:0% +behavior +right remember how it's like a frequency + + align:start position:0% +right remember how it's like a frequency + + + align:start position:0% +right remember how it's like a frequency +factor + + align:start position:0% +factor + + + align:start position:0% +factor +right this is related to all sorts of + + align:start position:0% +right this is related to all sorts of + + + align:start position:0% +right this is related to all sorts of +complexities that we don't need to know + + align:start position:0% +complexities that we don't need to know + + + align:start position:0% +complexities that we don't need to know +about + + align:start position:0% +about + + + align:start position:0% +about +related to how vacancies form i mean + + align:start position:0% +related to how vacancies form i mean + + + align:start position:0% +related to how vacancies form i mean +it's a constant that's in there and i + + align:start position:0% +it's a constant that's in there and i + + + align:start position:0% +it's a constant that's in there and i +let it be one but i want to make sure + + align:start position:0% +let it be one but i want to make sure + + + align:start position:0% +let it be one but i want to make sure +we put it in explicitly now this yeah + + align:start position:0% +we put it in explicitly now this yeah + + + align:start position:0% +we put it in explicitly now this yeah +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so what's the this n + + align:start position:0% +so what's the this n + + + align:start position:0% +so what's the this n +is the number of possible sites right so + + align:start position:0% +is the number of possible sites right so + + + align:start position:0% +is the number of possible sites right so +maybe it's the number + + align:start position:0% +maybe it's the number + + + align:start position:0% +maybe it's the number +of lattice sites in the crystal + + align:start position:0% +of lattice sites in the crystal + + + align:start position:0% +of lattice sites in the crystal +a number of possible sites but you might + + align:start position:0% +a number of possible sites but you might + + + align:start position:0% +a number of possible sites but you might +get it + + align:start position:0% +get it + + + align:start position:0% +get it +this could be related to can relate + + align:start position:0% +this could be related to can relate + + + align:start position:0% +this could be related to can relate +to for example okay or to or from + + align:start position:0% +to for example okay or to or from + + + align:start position:0% +to for example okay or to or from +things like the grams that you have of + + align:start position:0% +things like the grams that you have of + + + align:start position:0% +things like the grams that you have of +something + + align:start position:0% +something + + + align:start position:0% +something +right or maybe the volume + + align:start position:0% + + + + align:start position:0% + +or the moles etc right so these are kind + + align:start position:0% +or the moles etc right so these are kind + + + align:start position:0% +or the moles etc right so these are kind +of the kinds of problems we've done + + align:start position:0% +of the kinds of problems we've done + + + align:start position:0% +of the kinds of problems we've done +now that gives you a sense of how many + + align:start position:0% +now that gives you a sense of how many + + + align:start position:0% +now that gives you a sense of how many +sites did you have + + align:start position:0% + + + + align:start position:0% + +right it could be per centimeter cubed + + align:start position:0% +right it could be per centimeter cubed + + + align:start position:0% +right it could be per centimeter cubed +it could be per you know per moles you + + align:start position:0% +it could be per you know per moles you + + + align:start position:0% +it could be per you know per moles you +can go back and forth it gives you + + align:start position:0% +can go back and forth it gives you + + + align:start position:0% +can go back and forth it gives you +how much stuff do i have right is that + + align:start position:0% +how much stuff do i have right is that + + + align:start position:0% +how much stuff do i have right is that +kind of back and forth + + align:start position:0% +kind of back and forth + + + align:start position:0% +kind of back and forth +if i had a problem like this then i know + + align:start position:0% +if i had a problem like this then i know + + + align:start position:0% +if i had a problem like this then i know +i've got + + align:start position:0% +i've got + + + align:start position:0% +i've got +i know i can set it up because i've got + + align:start position:0% +i know i can set it up because i've got + + + align:start position:0% +i know i can set it up because i've got +two temperatures + + align:start position:0% +two temperatures + + + align:start position:0% +two temperatures +you see the key here the concentration + + align:start position:0% +you see the key here the concentration + + + align:start position:0% +you see the key here the concentration +of 10 to the cube + + align:start position:0% +of 10 to the cube + + + align:start position:0% +of 10 to the cube +per centimeter cubed so don't let that + + align:start position:0% +per centimeter cubed so don't let that + + + align:start position:0% +per centimeter cubed so don't let that +throw you off it's simply + + align:start position:0% +throw you off it's simply + + + align:start position:0% +throw you off it's simply +two equations where a bunch of stuff + + align:start position:0% +two equations where a bunch of stuff + + + align:start position:0% +two equations where a bunch of stuff +cancels + + align:start position:0% +cancels + + + align:start position:0% +cancels +right so the fraction of vacancies + + align:start position:0% +right so the fraction of vacancies + + + align:start position:0% +right so the fraction of vacancies +fv one would be 10 to the third + + align:start position:0% +fv one would be 10 to the third + + + align:start position:0% +fv one would be 10 to the third +divided by fv2 and that's going to be 10 + + align:start position:0% +divided by fv2 and that's going to be 10 + + + align:start position:0% +divided by fv2 and that's going to be 10 +to the third + + align:start position:0% +to the third + + + align:start position:0% +to the third +over 10 to the 16th because + + align:start position:0% +over 10 to the 16th because + + + align:start position:0% +over 10 to the 16th because +the n the number of stuff cancels + + align:start position:0% +the n the number of stuff cancels + + + align:start position:0% +the n the number of stuff cancels +right i didn't change that oh but this + + align:start position:0% +right i didn't change that oh but this + + + align:start position:0% +right i didn't change that oh but this +pre-factor cancels two + + align:start position:0% +pre-factor cancels two + + + align:start position:0% +pre-factor cancels two +you can put it there right a times e to + + align:start position:0% +you can put it there right a times e to + + + align:start position:0% +you can put it there right a times e to +the minus e + + align:start position:0% +the minus e + + + align:start position:0% +the minus e +a divided by kb + + align:start position:0% +a divided by kb + + + align:start position:0% +a divided by kb +times 300 kelvin remember it so it was + + align:start position:0% +times 300 kelvin remember it so it was + + + align:start position:0% +times 300 kelvin remember it so it was +kelvin + + align:start position:0% +kelvin + + + align:start position:0% +kelvin +divided by a times e to the minus e a + + align:start position:0% +divided by a times e to the minus e a + + + align:start position:0% +divided by a times e to the minus e a +divided by kb + + align:start position:0% +divided by kb + + + align:start position:0% +divided by kb +times the other temperature 900 kelvin + + align:start position:0% +times the other temperature 900 kelvin + + + align:start position:0% +times the other temperature 900 kelvin +right and so those cancel the the + + align:start position:0% +right and so those cancel the the + + + align:start position:0% +right and so those cancel the the +you know the stuff related to n cancels + + align:start position:0% +you know the stuff related to n cancels + + + align:start position:0% +you know the stuff related to n cancels +and i can just take the number + + align:start position:0% +and i can just take the number + + + align:start position:0% +and i can just take the number +of vacancies right so that's what's nice + + align:start position:0% +of vacancies right so that's what's nice + + + align:start position:0% +of vacancies right so that's what's nice +about having something like this you + + align:start position:0% +about having something like this you + + + align:start position:0% +about having something like this you +have two temperatures + + align:start position:0% +have two temperatures + + + align:start position:0% +have two temperatures +and a whole bunch of stuff can cancel + + align:start position:0% +and a whole bunch of stuff can cancel + + + align:start position:0% +and a whole bunch of stuff can cancel +and you can figure out + + align:start position:0% +and you can figure out + + + align:start position:0% +and you can figure out +then the activation energy which doesn't + + align:start position:0% +then the activation energy which doesn't + + + align:start position:0% +then the activation energy which doesn't +change + + align:start position:0% +change + + + align:start position:0% +change +the activation energy is simply the + + align:start position:0% +the activation energy is simply the + + + align:start position:0% +the activation energy is simply the +energy that you need + + align:start position:0% +energy that you need + + + align:start position:0% +energy that you need +right so you can now solve + + align:start position:0% +right so you can now solve + + + align:start position:0% +right so you can now solve +for ea and i think you get something + + align:start position:0% +for ea and i think you get something + + + align:start position:0% +for ea and i think you get something +like 2.3 + + align:start position:0% +like 2.3 + + + align:start position:0% +like 2.3 +electron volts remember that you could + + align:start position:0% +electron volts remember that you could + + + align:start position:0% +electron volts remember that you could +also have plotted it + + align:start position:0% +also have plotted it + + + align:start position:0% +also have plotted it +you know that in this in this equation + + align:start position:0% +you know that in this in this equation + + + align:start position:0% +you know that in this in this equation +in the iranian relationship if you take + + align:start position:0% +in the iranian relationship if you take + + + align:start position:0% +in the iranian relationship if you take +the log + + align:start position:0% +the log + + + align:start position:0% +the log +right and then you have a minus 1 over t + + align:start position:0% +right and then you have a minus 1 over t + + + align:start position:0% +right and then you have a minus 1 over t +relationship so if i wanted to get the + + align:start position:0% +relationship so if i wanted to get the + + + align:start position:0% +relationship so if i wanted to get the +sl + + align:start position:0% +sl + + + align:start position:0% +sl +right so remember that so if you take + + align:start position:0% +right so remember that so if you take + + + align:start position:0% +right so remember that so if you take +the t + + align:start position:0% +the t + + + align:start position:0% +the t +versus the log then you're going to get + + align:start position:0% +versus the log then you're going to get + + + align:start position:0% +versus the log then you're going to get +that + + align:start position:0% +that + + + align:start position:0% +that +right we like plots + + align:start position:0% +right we like plots + + + align:start position:0% +right we like plots +when we think about arrhenius because it + + align:start position:0% +when we think about arrhenius because it + + + align:start position:0% +when we think about arrhenius because it +makes it easier we can make it linear + + align:start position:0% +makes it easier we can make it linear + + + align:start position:0% +makes it easier we can make it linear +right where the slope of this is minus e + + align:start position:0% +right where the slope of this is minus e + + + align:start position:0% +right where the slope of this is minus e +a + + align:start position:0% + + + + align:start position:0% + +the slope minus e a over kb + + align:start position:0% +the slope minus e a over kb + + + align:start position:0% +the slope minus e a over kb +in this case right so we talked about + + align:start position:0% +in this case right so we talked about + + + align:start position:0% +in this case right so we talked about +these are all kind of kinds of things + + align:start position:0% +these are all kind of kinds of things + + + align:start position:0% +these are all kind of kinds of things +that we talked about + + align:start position:0% +that we talked about + + + align:start position:0% +that we talked about +and finally getting to the stress strain + + align:start position:0% +and finally getting to the stress strain + + + align:start position:0% +and finally getting to the stress strain +what you know what if we looked at this + + align:start position:0% +what you know what if we looked at this + + + align:start position:0% +what you know what if we looked at this +this is the stress strain so now we're + + align:start position:0% +this is the stress strain so now we're + + + align:start position:0% +this is the stress strain so now we're +here + + align:start position:0% +here + + + align:start position:0% +here +we just did this we talked about that + + align:start position:0% +we just did this we talked about that + + + align:start position:0% +we just did this we talked about that +talk about this so + + align:start position:0% +talk about this so + + + align:start position:0% +talk about this so +stress strain so if you were to add you + + align:start position:0% +stress strain so if you were to add you + + + align:start position:0% +stress strain so if you were to add you +know if you were to be given floss like + + align:start position:0% +know if you were to be given floss like + + + align:start position:0% +know if you were to be given floss like +this you know + + align:start position:0% +this you know + + + align:start position:0% +this you know +which one is most brittle which one is + + align:start position:0% +which one is most brittle which one is + + + align:start position:0% +which one is most brittle which one is +the stiffest right + + align:start position:0% +the stiffest right + + + align:start position:0% +the stiffest right +the most resistant to changing uh + + align:start position:0% +the most resistant to changing uh + + + align:start position:0% +the most resistant to changing uh +elastically and which one is the most + + align:start position:0% +elastically and which one is the most + + + align:start position:0% +elastically and which one is the most +ductile + + align:start position:0% + + + + align:start position:0% + +well you can see that the stiffest one + + align:start position:0% +well you can see that the stiffest one + + + align:start position:0% +well you can see that the stiffest one +is going to be the + + align:start position:0% +is going to be the + + + align:start position:0% +is going to be the +one that's the most resistant + + align:start position:0% +one that's the most resistant + + + align:start position:0% +one that's the most resistant +to elastic deformation that's that + + align:start position:0% +to elastic deformation that's that + + + align:start position:0% +to elastic deformation that's that +linear part that first part + + align:start position:0% +linear part that first part + + + align:start position:0% +linear part that first part +so there it's going to be material a + + align:start position:0% +so there it's going to be material a + + + align:start position:0% +so there it's going to be material a +right it's going to be a because it's + + align:start position:0% +right it's going to be a because it's + + + align:start position:0% +right it's going to be a because it's +got the highest slope + + align:start position:0% +got the highest slope + + + align:start position:0% +got the highest slope +right okay how about the most brittle + + align:start position:0% +right okay how about the most brittle + + + align:start position:0% +right okay how about the most brittle +well that's the one that's going to + + align:start position:0% +well that's the one that's going to + + + align:start position:0% +well that's the one that's going to +break + + align:start position:0% +break + + + align:start position:0% +break +so it sort of looks like you know + + align:start position:0% +so it sort of looks like you know + + + align:start position:0% +so it sort of looks like you know +without deforming without being able to + + align:start position:0% +without deforming without being able to + + + align:start position:0% +without deforming without being able to +undergo deformation that's brittleness + + align:start position:0% +undergo deformation that's brittleness + + + align:start position:0% +undergo deformation that's brittleness +it's going to crack before doing + + align:start position:0% +it's going to crack before doing + + + align:start position:0% +it's going to crack before doing +anything so that's b + + align:start position:0% +anything so that's b + + + align:start position:0% +anything so that's b +right that's b and then the most ductile + + align:start position:0% +right that's b and then the most ductile + + + align:start position:0% +right that's b and then the most ductile +will be the one + + align:start position:0% +will be the one + + + align:start position:0% +will be the one +that has the most plastic deformation + + align:start position:0% +that has the most plastic deformation + + + align:start position:0% +that has the most plastic deformation +because that's what ductility is + + align:start position:0% +because that's what ductility is + + + align:start position:0% +because that's what ductility is +and so that's going to be c + + align:start position:0% +and so that's going to be c + + + align:start position:0% +and so that's going to be c +okay so remember stress strain curves + + align:start position:0% +okay so remember stress strain curves + + + align:start position:0% +okay so remember stress strain curves +right you got this + + align:start position:0% +right you got this + + + align:start position:0% +right you got this +this elastic part here that's linear and + + align:start position:0% +this elastic part here that's linear and + + + align:start position:0% +this elastic part here that's linear and +then + + align:start position:0% +then + + + align:start position:0% +then +if it's a material not all materials + + align:start position:0% +if it's a material not all materials + + + align:start position:0% +if it's a material not all materials +have + + align:start position:0% +have + + + align:start position:0% +have +plastic deformation some are going to + + align:start position:0% +plastic deformation some are going to + + + align:start position:0% +plastic deformation some are going to +break before they + + align:start position:0% +break before they + + + align:start position:0% +break before they +they start deforming plastically but if + + align:start position:0% +they start deforming plastically but if + + + align:start position:0% +they start deforming plastically but if +it can deform plastically then it's + + align:start position:0% +it can deform plastically then it's + + + align:start position:0% +it can deform plastically then it's +going to have + + align:start position:0% +going to have + + + align:start position:0% +going to have +that yield point right the yield stress + + align:start position:0% +that yield point right the yield stress + + + align:start position:0% +that yield point right the yield stress +where then it starts becoming non-linear + + align:start position:0% +where then it starts becoming non-linear + + + align:start position:0% +where then it starts becoming non-linear +and then finally it fractures somewhere + + align:start position:0% +and then finally it fractures somewhere + + + align:start position:0% +and then finally it fractures somewhere +else + + align:start position:0% +else + + + align:start position:0% +else +right okay so those are stress train + + align:start position:0% +right okay so those are stress train + + + align:start position:0% +right okay so those are stress train +curves + + align:start position:0% +curves + + + align:start position:0% +curves +okay let's move on + + align:start position:0% +okay let's move on + + + align:start position:0% +okay let's move on +now oh with uh + + align:start position:0% + + + + align:start position:0% + +the next topic oh boy i'm gonna run out + + align:start position:0% +the next topic oh boy i'm gonna run out + + + align:start position:0% +the next topic oh boy i'm gonna run out +of real estate we got glasses + + align:start position:0% + + + + align:start position:0% + +and here the most important thing to + + align:start position:0% +and here the most important thing to + + + align:start position:0% +and here the most important thing to +know about + + align:start position:0% +know about + + + align:start position:0% +know about +is the curve that's how it all started + + align:start position:0% +is the curve that's how it all started + + + align:start position:0% +is the curve that's how it all started +right i'm calling it the curve let's go + + align:start position:0% +right i'm calling it the curve let's go + + + align:start position:0% +right i'm calling it the curve let's go +all caps + + align:start position:0% +all caps + + + align:start position:0% +all caps +because it's the curve and + + align:start position:0% +because it's the curve and + + + align:start position:0% +because it's the curve and +what i mean by the curve is the volume + + align:start position:0% +what i mean by the curve is the volume + + + align:start position:0% +what i mean by the curve is the volume +per mole + + align:start position:0% + + + + align:start position:0% + +versus temperature we also talked about + + align:start position:0% +versus temperature we also talked about + + + align:start position:0% +versus temperature we also talked about +the the effects of cooling rate + + align:start position:0% + + + + align:start position:0% + +and we also talked about the effects + + align:start position:0% +and we also talked about the effects + + + align:start position:0% +and we also talked about the effects +of modifiers + + align:start position:0% + + + + align:start position:0% + +right and in particular how that how the + + align:start position:0% +right and in particular how that how the + + + align:start position:0% +right and in particular how that how the +modifier + + align:start position:0% + + + + align:start position:0% + +changes the viscosity because it cuts + + align:start position:0% +changes the viscosity because it cuts + + + align:start position:0% +changes the viscosity because it cuts +the pasta + + align:start position:0% +the pasta + + + align:start position:0% +the pasta +okay and so but that the framing of + + align:start position:0% +okay and so but that the framing of + + + align:start position:0% +okay and so but that the framing of +these concepts was in the curve + + align:start position:0% +these concepts was in the curve + + + align:start position:0% +these concepts was in the curve +and that's this one oh i have a pl i + + align:start position:0% +and that's this one oh i have a pl i + + + align:start position:0% +and that's this one oh i have a pl i +have a picture of it there it is + + align:start position:0% +have a picture of it there it is + + + align:start position:0% +have a picture of it there it is +okay okay they did specific we do volume + + align:start position:0% +okay okay they did specific we do volume + + + align:start position:0% +okay okay they did specific we do volume +per mole that's how we're looking at in + + align:start position:0% +per mole that's how we're looking at in + + + align:start position:0% +per mole that's how we're looking at in +this class so volume for mole versus + + align:start position:0% +this class so volume for mole versus + + + align:start position:0% +this class so volume for mole versus +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +now remember if it's a if it's a crystal + + align:start position:0% +now remember if it's a if it's a crystal + + + align:start position:0% +now remember if it's a if it's a crystal +where am i going to go let's go here if + + align:start position:0% +where am i going to go let's go here if + + + align:start position:0% +where am i going to go let's go here if +it's a crystal + + align:start position:0% +it's a crystal + + + align:start position:0% +it's a crystal +then you've got one melting point that + + align:start position:0% +then you've got one melting point that + + + align:start position:0% +then you've got one melting point that +only depends + + align:start position:0% +only depends + + + align:start position:0% +only depends +on the material okay it only depends on + + align:start position:0% +on the material okay it only depends on + + + align:start position:0% +on the material okay it only depends on +the material so that melting point is tm + + align:start position:0% + + + + align:start position:0% + +and and it's gonna have a big volume + + align:start position:0% +and and it's gonna have a big volume + + + align:start position:0% +and and it's gonna have a big volume +change + + align:start position:0% +change + + + align:start position:0% +change +as it goes from liquid to + + align:start position:0% +as it goes from liquid to + + + align:start position:0% +as it goes from liquid to +crystal solid okay and so for example + + align:start position:0% +crystal solid okay and so for example + + + align:start position:0% +crystal solid okay and so for example +you know i'm just basically re-plotting + + align:start position:0% +you know i'm just basically re-plotting + + + align:start position:0% +you know i'm just basically re-plotting +it but + + align:start position:0% +it but + + + align:start position:0% +it but +you would have something like this and + + align:start position:0% +you would have something like this and + + + align:start position:0% +you would have something like this and +something like this + + align:start position:0% +something like this + + + align:start position:0% +something like this +and something like this and that's your + + align:start position:0% +and something like this and that's your + + + align:start position:0% +and something like this and that's your +melting point + + align:start position:0% +melting point + + + align:start position:0% +melting point +right and this would be the liquid and + + align:start position:0% +right and this would be the liquid and + + + align:start position:0% +right and this would be the liquid and +this would be the solid + + align:start position:0% +this would be the solid + + + align:start position:0% +this would be the solid +and you know that if it's going to + + align:start position:0% +and you know that if it's going to + + + align:start position:0% +and you know that if it's going to +undergo this big volume change + + align:start position:0% +undergo this big volume change + + + align:start position:0% +undergo this big volume change +then it's the melting point it's a + + align:start position:0% +then it's the melting point it's a + + + align:start position:0% +then it's the melting point it's a +crystal all right + + align:start position:0% +crystal all right + + + align:start position:0% +crystal all right +uh but then we say well but if it can't + + align:start position:0% +uh but then we say well but if it can't + + + align:start position:0% +uh but then we say well but if it can't +fight chris by crystal + + align:start position:0% +fight chris by crystal + + + align:start position:0% +fight chris by crystal +i mean in opposition to glass which we + + align:start position:0% +i mean in opposition to glass which we + + + align:start position:0% +i mean in opposition to glass which we +know + + align:start position:0% +know + + + align:start position:0% +know +doesn't just mean your windows it means + + align:start position:0% +doesn't just mean your windows it means + + + align:start position:0% +doesn't just mean your windows it means +any amorphous material + + align:start position:0% +any amorphous material + + + align:start position:0% +any amorphous material +meaning it's not crystalline it didn't + + align:start position:0% +meaning it's not crystalline it didn't + + + align:start position:0% +meaning it's not crystalline it didn't +find the lattice structure + + align:start position:0% +find the lattice structure + + + align:start position:0% +find the lattice structure +the atoms remember those three reasons + + align:start position:0% +the atoms remember those three reasons + + + align:start position:0% +the atoms remember those three reasons +the musical chairs + + align:start position:0% +the musical chairs + + + align:start position:0% +the musical chairs +whatever you're trying to crystallize + + align:start position:0% +whatever you're trying to crystallize + + + align:start position:0% +whatever you're trying to crystallize +atoms or molecules they weren't able to + + align:start position:0% +atoms or molecules they weren't able to + + + align:start position:0% +atoms or molecules they weren't able to +find all the lattice sites + + align:start position:0% +find all the lattice sites + + + align:start position:0% +find all the lattice sites +not even withstanding some defects here + + align:start position:0% +not even withstanding some defects here + + + align:start position:0% +not even withstanding some defects here +and there they simply couldn't do it and + + align:start position:0% +and there they simply couldn't do it and + + + align:start position:0% +and there they simply couldn't do it and +so it's amorphous + + align:start position:0% +so it's amorphous + + + align:start position:0% +so it's amorphous +and it's a glass and in that case + + align:start position:0% +and it's a glass and in that case + + + align:start position:0% +and it's a glass and in that case +what happens is it super cools and + + align:start position:0% +what happens is it super cools and + + + align:start position:0% +what happens is it super cools and +then becomes a solid + + align:start position:0% +then becomes a solid + + + align:start position:0% +then becomes a solid +at something called the glass transition + + align:start position:0% +at something called the glass transition + + + align:start position:0% +at something called the glass transition +temperature which unlike the crystal + + align:start position:0% +temperature which unlike the crystal + + + align:start position:0% +temperature which unlike the crystal +can have different values and those + + align:start position:0% +can have different values and those + + + align:start position:0% +can have different values and those +values can depend on things + + align:start position:0% +values can depend on things + + + align:start position:0% +values can depend on things +like the cooling rate right so if i cool + + align:start position:0% +like the cooling rate right so if i cool + + + align:start position:0% +like the cooling rate right so if i cool +it slower + + align:start position:0% +it slower + + + align:start position:0% +it slower +ah if i cool it slower + + align:start position:0% +ah if i cool it slower + + + align:start position:0% +ah if i cool it slower +right this remember this is faster + + align:start position:0% +right this remember this is faster + + + align:start position:0% +right this remember this is faster +faster slower and please + + align:start position:0% +faster slower and please + + + align:start position:0% +faster slower and please +do not confuse time with this axis this + + align:start position:0% +do not confuse time with this axis this + + + align:start position:0% +do not confuse time with this axis this +is just temperature + + align:start position:0% +is just temperature + + + align:start position:0% +is just temperature +so we can use the same this is volume + + align:start position:0% +so we can use the same this is volume + + + align:start position:0% +so we can use the same this is volume +per mole + + align:start position:0% +per mole + + + align:start position:0% +per mole +we can use the same the plot you know to + + align:start position:0% +we can use the same the plot you know to + + + align:start position:0% +we can use the same the plot you know to +think about modifiers + + align:start position:0% +think about modifiers + + + align:start position:0% +think about modifiers +as well because it's not this this is + + align:start position:0% +as well because it's not this this is + + + align:start position:0% +as well because it's not this this is +just + + align:start position:0% +just + + + align:start position:0% +just +one plot one curve and another this + + align:start position:0% +one plot one curve and another this + + + align:start position:0% +one plot one curve and another this +happened to be cooled slower because and + + align:start position:0% +happened to be cooled slower because and + + + align:start position:0% +happened to be cooled slower because and +so it was able to super cool + + align:start position:0% +so it was able to super cool + + + align:start position:0% +so it was able to super cool +more before it locked in the disorder + + align:start position:0% +more before it locked in the disorder + + + align:start position:0% +more before it locked in the disorder +and the other one was faster but if you + + align:start position:0% +and the other one was faster but if you + + + align:start position:0% +and the other one was faster but if you +you could also imagine if you cut the + + align:start position:0% +you could also imagine if you cut the + + + align:start position:0% +you could also imagine if you cut the +pasta + + align:start position:0% +pasta + + + align:start position:0% +pasta +you you change the viscosity right + + align:start position:0% +you you change the viscosity right + + + align:start position:0% +you you change the viscosity right +and and so now you're changing something + + align:start position:0% +and and so now you're changing something + + + align:start position:0% +and and so now you're changing something +else about the glass using chemistry + + align:start position:0% +else about the glass using chemistry + + + align:start position:0% +else about the glass using chemistry +and you're allowing it to find those + + align:start position:0% +and you're allowing it to find those + + + align:start position:0% +and you're allowing it to find those +lattice sites more easily you're + + align:start position:0% +lattice sites more easily you're + + + align:start position:0% +lattice sites more easily you're +allowing it to try to become crystalline + + align:start position:0% +allowing it to try to become crystalline + + + align:start position:0% +allowing it to try to become crystalline +to try to close pack just a little bit + + align:start position:0% +to try to close pack just a little bit + + + align:start position:0% +to try to close pack just a little bit +more + + align:start position:0% +more + + + align:start position:0% +more +so you can also get this by cutting the + + align:start position:0% +so you can also get this by cutting the + + + align:start position:0% +so you can also get this by cutting the +pasta you can get these kinds of changes + + align:start position:0% +pasta you can get these kinds of changes + + + align:start position:0% +pasta you can get these kinds of changes +right so those are the things + + align:start position:0% +right so those are the things + + + align:start position:0% +right so those are the things +we talked about with glass now + + align:start position:0% + + + + align:start position:0% + +next we talked about reactions + + align:start position:0% +next we talked about reactions + + + align:start position:0% +next we talked about reactions +okay + + align:start position:0% + + + + align:start position:0% + +what do we need to know about reactions + + align:start position:0% + + + + align:start position:0% + +reaction rates + + align:start position:0% +reaction rates + + + align:start position:0% +reaction rates +so we want to know the order + + align:start position:0% + + + + align:start position:0% + +right of some general reaction like a a + + align:start position:0% +right of some general reaction like a a + + + align:start position:0% +right of some general reaction like a a +plus b b remember this goes to + + align:start position:0% +plus b b remember this goes to + + + align:start position:0% +plus b b remember this goes to +c c plus d d + + align:start position:0% + + + + align:start position:0% + +and we want to know the rate + + align:start position:0% + + + + align:start position:0% + +the rate from basically it's the the + + align:start position:0% +the rate from basically it's the the + + + align:start position:0% +the rate from basically it's the the +mass conservation right so from the + + align:start position:0% +mass conservation right so from the + + + align:start position:0% +mass conservation right so from the +coefficients + + align:start position:0% + + + + align:start position:0% + +okay so that would be for example like + + align:start position:0% +okay so that would be for example like + + + align:start position:0% +okay so that would be for example like +minus 1 over + + align:start position:0% +minus 1 over + + + align:start position:0% +minus 1 over +a d a dt that's a rate equals minus 1 + + align:start position:0% +a d a dt that's a rate equals minus 1 + + + align:start position:0% +a d a dt that's a rate equals minus 1 +over b + + align:start position:0% +over b + + + align:start position:0% +over b +db dt etc + + align:start position:0% + + + + align:start position:0% + +now those come from the coefficients but + + align:start position:0% +now those come from the coefficients but + + + align:start position:0% +now those come from the coefficients but +the rate law does not + + align:start position:0% +the rate law does not + + + align:start position:0% +the rate law does not +the rate law does not so + + align:start position:0% +the rate law does not so + + + align:start position:0% +the rate law does not so +these are simply instantaneous rates but + + align:start position:0% +these are simply instantaneous rates but + + + align:start position:0% +these are simply instantaneous rates but +now i say no i want to rate + + align:start position:0% +now i say no i want to rate + + + align:start position:0% +now i say no i want to rate +law that gives me the dependence on + + align:start position:0% +law that gives me the dependence on + + + align:start position:0% +law that gives me the dependence on +these + + align:start position:0% +these + + + align:start position:0% +these +on these uh uh + + align:start position:0% + + + + align:start position:0% + +these concentrations at any time + + align:start position:0% +these concentrations at any time + + + align:start position:0% +these concentrations at any time +and so the rate law so the rate law + + align:start position:0% + + + + align:start position:0% + +would be for example uh okay like rate + + align:start position:0% +would be for example uh okay like rate + + + align:start position:0% +would be for example uh okay like rate +equals k times let's say a to the m + + align:start position:0% +equals k times let's say a to the m + + + align:start position:0% +equals k times let's say a to the m +b to the n now here's the thing + + align:start position:0% +b to the n now here's the thing + + + align:start position:0% +b to the n now here's the thing +these these + + align:start position:0% + + + + align:start position:0% + +come from experiments + + align:start position:0% + + + + align:start position:0% + +very important distinction right those + + align:start position:0% +very important distinction right those + + + align:start position:0% +very important distinction right those +come from experiments + + align:start position:0% +come from experiments + + + align:start position:0% +come from experiments +and and so you could get the rate with + + align:start position:0% +and and so you could get the rate with + + + align:start position:0% +and and so you could get the rate with +respect to a which would be + + align:start position:0% +respect to a which would be + + + align:start position:0% +respect to a which would be +i'm sorry the order with respect to a + + align:start position:0% +i'm sorry the order with respect to a + + + align:start position:0% +i'm sorry the order with respect to a +would be m + + align:start position:0% +would be m + + + align:start position:0% +would be m +the order with respect to b would be n + + align:start position:0% +the order with respect to b would be n + + + align:start position:0% +the order with respect to b would be n +and the overall order of the reaction is + + align:start position:0% +and the overall order of the reaction is + + + align:start position:0% +and the overall order of the reaction is +m plus n + + align:start position:0% +m plus n + + + align:start position:0% +m plus n +right the overall order + + align:start position:0% + + + + align:start position:0% + +so that's why and then we had one more + + align:start position:0% +so that's why and then we had one more + + + align:start position:0% +so that's why and then we had one more +item here of you know conceptually what + + align:start position:0% +item here of you know conceptually what + + + align:start position:0% +item here of you know conceptually what +i want you to know about + + align:start position:0% +i want you to know about + + + align:start position:0% +i want you to know about +which is that the rate also depends on + + align:start position:0% +which is that the rate also depends on + + + align:start position:0% +which is that the rate also depends on +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +sorry the rate constant rate constant + + align:start position:0% + + + + align:start position:0% + +depends on temperature so + + align:start position:0% +depends on temperature so + + + align:start position:0% +depends on temperature so +if i were to now say well okay i want to + + align:start position:0% +if i were to now say well okay i want to + + + align:start position:0% +if i were to now say well okay i want to +know something about the order of a + + align:start position:0% +know something about the order of a + + + align:start position:0% +know something about the order of a +reaction + + align:start position:0% +reaction + + + align:start position:0% +reaction +you might get a table like this and we + + align:start position:0% +you might get a table like this and we + + + align:start position:0% +you might get a table like this and we +did this you know in class + + align:start position:0% +did this you know in class + + + align:start position:0% +did this you know in class +you might get a table just like this + + align:start position:0% +you might get a table just like this + + + align:start position:0% +you might get a table just like this +here's a reaction it's w + + align:start position:0% +here's a reaction it's w + + + align:start position:0% +here's a reaction it's w +and x and y and it goes to z + + align:start position:0% + + + + align:start position:0% + +don't let the fact that you have three + + align:start position:0% +don't let the fact that you have three + + + align:start position:0% +don't let the fact that you have three +reactants throw you obviously + + align:start position:0% +reactants throw you obviously + + + align:start position:0% +reactants throw you obviously +you've got a certain number of reactants + + align:start position:0% +you've got a certain number of reactants + + + align:start position:0% +you've got a certain number of reactants +they've got their coefficients and they + + align:start position:0% +they've got their coefficients and they + + + align:start position:0% +they've got their coefficients and they +go to some product + + align:start position:0% +go to some product + + + align:start position:0% +go to some product +okay and now you're given experimental + + align:start position:0% +okay and now you're given experimental + + + align:start position:0% +okay and now you're given experimental +data + + align:start position:0% +data + + + align:start position:0% +data +so from this data you can get the order + + align:start position:0% +so from this data you can get the order + + + align:start position:0% +so from this data you can get the order +of the reaction + + align:start position:0% +of the reaction + + + align:start position:0% +of the reaction +with respect to each one of these right + + align:start position:0% +with respect to each one of these right + + + align:start position:0% +with respect to each one of these right +and that would then give you of course + + align:start position:0% +and that would then give you of course + + + align:start position:0% +and that would then give you of course +the overall order + + align:start position:0% +the overall order + + + align:start position:0% +the overall order +right so let's see if we were to look at + + align:start position:0% +right so let's see if we were to look at + + + align:start position:0% +right so let's see if we were to look at +that data + + align:start position:0% +that data + + + align:start position:0% +that data +then what what would we get + + align:start position:0% +then what what would we get + + + align:start position:0% +then what what would we get +so what you want to do in these kinds of + + align:start position:0% +so what you want to do in these kinds of + + + align:start position:0% +so what you want to do in these kinds of +situations + + align:start position:0% +situations + + + align:start position:0% +situations +is + + align:start position:0% + + + + align:start position:0% + +first of all don't panic oh by the way + + align:start position:0% +first of all don't panic oh by the way + + + align:start position:0% +first of all don't panic oh by the way +on an exam + + align:start position:0% +on an exam + + + align:start position:0% +on an exam +in general don't panic and if you have a + + align:start position:0% +in general don't panic and if you have a + + + align:start position:0% +in general don't panic and if you have a +question you can ask a question + + align:start position:0% +question you can ask a question + + + align:start position:0% +question you can ask a question +and but also show us what you know + + align:start position:0% +and but also show us what you know + + + align:start position:0% +and but also show us what you know +we will give you as you i hope have seen + + align:start position:0% +we will give you as you i hope have seen + + + align:start position:0% +we will give you as you i hope have seen +already we will give you as much credit + + align:start position:0% +already we will give you as much credit + + + align:start position:0% +already we will give you as much credit +as we can + + align:start position:0% +as we can + + + align:start position:0% +as we can +for sharing what you know you don't have + + align:start position:0% +for sharing what you know you don't have + + + align:start position:0% +for sharing what you know you don't have +to get everything right to get a lot of + + align:start position:0% +to get everything right to get a lot of + + + align:start position:0% +to get everything right to get a lot of +points + + align:start position:0% +points + + + align:start position:0% +points +please share your knowledge + + align:start position:0% +please share your knowledge + + + align:start position:0% +please share your knowledge +so in this case what would the knowledge + + align:start position:0% +so in this case what would the knowledge + + + align:start position:0% +so in this case what would the knowledge +be well it'd be that i want to compare + + align:start position:0% +be well it'd be that i want to compare + + + align:start position:0% +be well it'd be that i want to compare +stuff like trial one and two + + align:start position:0% +stuff like trial one and two + + + align:start position:0% +stuff like trial one and two +and and if i do that you see okay trial + + align:start position:0% +and and if i do that you see okay trial + + + align:start position:0% +and and if i do that you see okay trial +one trial two + + align:start position:0% +one trial two + + + align:start position:0% +one trial two +then two of them stay constant but w + + align:start position:0% +then two of them stay constant but w + + + align:start position:0% +then two of them stay constant but w +doubles + + align:start position:0% +doubles + + + align:start position:0% +doubles +okay so comparing + + align:start position:0% + + + + align:start position:0% + +one versus two you got + + align:start position:0% +one versus two you got + + + align:start position:0% +one versus two you got +w goes to two + + align:start position:0% +w goes to two + + + align:start position:0% +w goes to two +two times but the rate is same + + align:start position:0% +two times but the rate is same + + + align:start position:0% +two times but the rate is same +so you know the order the order is zero + + align:start position:0% +so you know the order the order is zero + + + align:start position:0% +so you know the order the order is zero +with respect to w but if i compare + + align:start position:0% +with respect to w but if i compare + + + align:start position:0% +with respect to w but if i compare +1 versus 3 then + + align:start position:0% +1 versus 3 then + + + align:start position:0% +1 versus 3 then +you know that let's see x + + align:start position:0% +you know that let's see x + + + align:start position:0% +you know that let's see x +goes to 3x and the rate + + align:start position:0% +goes to 3x and the rate + + + align:start position:0% +goes to 3x and the rate +goes to 3x and so the order + + align:start position:0% +goes to 3x and so the order + + + align:start position:0% +goes to 3x and so the order +is 1 and then finally for y + + align:start position:0% +is 1 and then finally for y + + + align:start position:0% +is 1 and then finally for y +i will just jump to it the order + + align:start position:0% +i will just jump to it the order + + + align:start position:0% +i will just jump to it the order +is 2. and you can do that just by + + align:start position:0% +is 2. and you can do that just by + + + align:start position:0% +is 2. and you can do that just by +find one where only y changes you don't + + align:start position:0% +find one where only y changes you don't + + + align:start position:0% +find one where only y changes you don't +have to necessarily + + align:start position:0% +have to necessarily + + + align:start position:0% +have to necessarily +find one where just one changes right + + align:start position:0% +find one where just one changes right + + + align:start position:0% +find one where just one changes right +because if you knew one + + align:start position:0% +because if you knew one + + + align:start position:0% +because if you knew one +is first or you know if you knew one and + + align:start position:0% +is first or you know if you knew one and + + + align:start position:0% +is first or you know if you knew one and +then you had another one and they both + + align:start position:0% +then you had another one and they both + + + align:start position:0% +then you had another one and they both +changed but maybe the rate didn't change + + align:start position:0% +changed but maybe the rate didn't change + + + align:start position:0% +changed but maybe the rate didn't change +then you know they must have the both + + align:start position:0% +then you know they must have the both + + + align:start position:0% +then you know they must have the both +the same order if they change in + + align:start position:0% +the same order if they change in + + + align:start position:0% +the same order if they change in +opposite ways + + align:start position:0% +opposite ways + + + align:start position:0% +opposite ways +right so you can get into this in + + align:start position:0% +right so you can get into this in + + + align:start position:0% +right so you can get into this in +different ways just looking at + + align:start position:0% +different ways just looking at + + + align:start position:0% +different ways just looking at +these changes from one to another and + + align:start position:0% +these changes from one to another and + + + align:start position:0% +these changes from one to another and +thinking about + + align:start position:0% +thinking about + + + align:start position:0% +thinking about +what must happen in terms of the rate + + align:start position:0% +what must happen in terms of the rate + + + align:start position:0% +what must happen in terms of the rate +law in terms of what you wrote out + + align:start position:0% +law in terms of what you wrote out + + + align:start position:0% +law in terms of what you wrote out +here okay + + align:start position:0% +here okay + + + align:start position:0% +here okay +but you could also you could also ask + + align:start position:0% +but you could also you could also ask + + + align:start position:0% +but you could also you could also ask +questions like + + align:start position:0% +questions like + + + align:start position:0% +questions like +like you know with reactions like okay + + align:start position:0% +like you know with reactions like okay + + + align:start position:0% +like you know with reactions like okay +this is first order + + align:start position:0% +this is first order + + + align:start position:0% +this is first order +what's the dependence of the + + align:start position:0% +what's the dependence of the + + + align:start position:0% +what's the dependence of the +concentration over time as a function of + + align:start position:0% +concentration over time as a function of + + + align:start position:0% +concentration over time as a function of +the rate constant + + align:start position:0% +the rate constant + + + align:start position:0% +the rate constant +well that's uh you know that just goes + + align:start position:0% +well that's uh you know that just goes + + + align:start position:0% +well that's uh you know that just goes +back to our + + align:start position:0% +back to our + + + align:start position:0% +back to our +understanding of the integrated rate + + align:start position:0% +understanding of the integrated rate + + + align:start position:0% +understanding of the integrated rate +equation right + + align:start position:0% +equation right + + + align:start position:0% +equation right +and so let's see oh boy + + align:start position:0% +and so let's see oh boy + + + align:start position:0% +and so let's see oh boy +now i need to find i'm gonna go + + align:start position:0% +now i need to find i'm gonna go + + + align:start position:0% +now i need to find i'm gonna go +i hate to do this xrd i hate to do this + + align:start position:0% +i hate to do this xrd i hate to do this + + + align:start position:0% +i hate to do this xrd i hate to do this +but + + align:start position:0% + + + + align:start position:0% + +sometimes being first carries a + + align:start position:0% +sometimes being first carries a + + + align:start position:0% +sometimes being first carries a +consequence + + align:start position:0% + + + + align:start position:0% + +okay uh so you know in this case + + align:start position:0% +okay uh so you know in this case + + + align:start position:0% +okay uh so you know in this case +first of all by the way you look at + + align:start position:0% +first of all by the way you look at + + + align:start position:0% +first of all by the way you look at +reaction like that you're like well okay + + align:start position:0% +reaction like that you're like well okay + + + align:start position:0% +reaction like that you're like well okay +from the coefficients in the mass + + align:start position:0% +from the coefficients in the mass + + + align:start position:0% +from the coefficients in the mass +balance stuff + + align:start position:0% +balance stuff + + + align:start position:0% +balance stuff +you know you know that the change in + + align:start position:0% +you know you know that the change in + + + align:start position:0% +you know you know that the change in +oxygen for example with time + + align:start position:0% +oxygen for example with time + + + align:start position:0% +oxygen for example with time +the instantaneous rate would equal minus + + align:start position:0% +the instantaneous rate would equal minus + + + align:start position:0% +the instantaneous rate would equal minus +the change + + align:start position:0% +the change + + + align:start position:0% +the change +in mo2 right + + align:start position:0% +in mo2 right + + + align:start position:0% +in mo2 right +with time well that's not what the + + align:start position:0% +with time well that's not what the + + + align:start position:0% +with time well that's not what the +question asks the question says it's + + align:start position:0% +question asks the question says it's + + + align:start position:0% +question asks the question says it's +first order + + align:start position:0% +first order + + + align:start position:0% +first order +so that's enough because + + align:start position:0% +so that's enough because + + + align:start position:0% +so that's enough because +the in the the rate law if you integrate + + align:start position:0% +the in the the rate law if you integrate + + + align:start position:0% +the in the the rate law if you integrate +a first order this means + + align:start position:0% +a first order this means + + + align:start position:0% +a first order this means +that if i integrate the rate law + + align:start position:0% +that if i integrate the rate law + + + align:start position:0% +that if i integrate the rate law +then first of all if it's first order + + align:start position:0% +then first of all if it's first order + + + align:start position:0% +then first of all if it's first order +then d + + align:start position:0% +then d + + + align:start position:0% +then d +of m o two with respect to time + + align:start position:0% +of m o two with respect to time + + + align:start position:0% +of m o two with respect to time +must equal some constant times the + + align:start position:0% +must equal some constant times the + + + align:start position:0% +must equal some constant times the +concentration + + align:start position:0% +concentration + + + align:start position:0% +concentration +of mo2 to the one + + align:start position:0% +of mo2 to the one + + + align:start position:0% +of mo2 to the one +right first order and so now if i + + align:start position:0% +right first order and so now if i + + + align:start position:0% +right first order and so now if i +integrate this + + align:start position:0% +integrate this + + + align:start position:0% +integrate this +i take this concentration over here i + + align:start position:0% +i take this concentration over here i + + + align:start position:0% +i take this concentration over here i +put the dt over there you integrate it + + align:start position:0% +put the dt over there you integrate it + + + align:start position:0% +put the dt over there you integrate it +right you've got all the integrated rate + + align:start position:0% +right you've got all the integrated rate + + + align:start position:0% +right you've got all the integrated rate +laws + + align:start position:0% +laws + + + align:start position:0% +laws +we've gone through this already you know + + align:start position:0% +we've gone through this already you know + + + align:start position:0% +we've gone through this already you know +that you get + + align:start position:0% +that you get + + + align:start position:0% +that you get +that the log oh we do logs + + align:start position:0% +that the log oh we do logs + + + align:start position:0% +that the log oh we do logs +of this mo2 + + align:start position:0% +of this mo2 + + + align:start position:0% +of this mo2 +equals the log of some starting + + align:start position:0% +equals the log of some starting + + + align:start position:0% +equals the log of some starting +concentration + + align:start position:0% +concentration + + + align:start position:0% +concentration +minus kt okay + + align:start position:0% +minus kt okay + + + align:start position:0% +minus kt okay +why do we do that because we like + + align:start position:0% +why do we do that because we like + + + align:start position:0% +why do we do that because we like +plotting things linear things + + align:start position:0% +plotting things linear things + + + align:start position:0% +plotting things linear things +we love linear + + align:start position:0% +we love linear + + + align:start position:0% +we love linear +so you know you remember we did this we + + align:start position:0% +so you know you remember we did this we + + + align:start position:0% +so you know you remember we did this we +went from these these integrated rate + + align:start position:0% +went from these these integrated rate + + + align:start position:0% +went from these these integrated rate +laws to plots + + align:start position:0% +laws to plots + + + align:start position:0% +laws to plots +and back and forth and so that's also + + align:start position:0% +and back and forth and so that's also + + + align:start position:0% +and back and forth and so that's also +very important + + align:start position:0% +very important + + + align:start position:0% +very important +okay now finally okay so the last couple + + align:start position:0% +okay now finally okay so the last couple + + + align:start position:0% +okay now finally okay so the last couple +of things + + align:start position:0% +of things + + + align:start position:0% +of things +so and and these i'm purposely giving + + align:start position:0% +so and and these i'm purposely giving + + + align:start position:0% +so and and these i'm purposely giving +these last ones a little less time + + align:start position:0% +these last ones a little less time + + + align:start position:0% +these last ones a little less time +because + + align:start position:0% +because + + + align:start position:0% +because +they're the ones that we've seen very + + align:start position:0% +they're the ones that we've seen very + + + align:start position:0% +they're the ones that we've seen very +recently and these are the ones that we + + align:start position:0% +recently and these are the ones that we + + + align:start position:0% +recently and these are the ones that we +haven't seen for almost a month + + align:start position:0% +haven't seen for almost a month + + + align:start position:0% +haven't seen for almost a month +right yeah but you still got to know + + align:start position:0% +right yeah but you still got to know + + + align:start position:0% +right yeah but you still got to know +about + + align:start position:0% +about + + + align:start position:0% +about +solubility + + align:start position:0% + + + + align:start position:0% + +and so for solubility remember what we + + align:start position:0% +and so for solubility remember what we + + + align:start position:0% +and so for solubility remember what we +did is + + align:start position:0% +did is + + + align:start position:0% +did is +we did equilibrium and + + align:start position:0% +we did equilibrium and + + + align:start position:0% +we did equilibrium and +le chatelier + + align:start position:0% + + + + align:start position:0% + +and we did the equilibrium constants + + align:start position:0% +and we did the equilibrium constants + + + align:start position:0% +and we did the equilibrium constants +the k's like for example + + align:start position:0% +the k's like for example + + + align:start position:0% +the k's like for example +ksp is the solubility product solubility + + align:start position:0% +ksp is the solubility product solubility + + + align:start position:0% +ksp is the solubility product solubility +product constant right + + align:start position:0% +product constant right + + + align:start position:0% +product constant right +and then we also did ice tables + + align:start position:0% + + + + align:start position:0% + +and then we talked about the common ion + + align:start position:0% + + + + align:start position:0% + +right and so as an example + + align:start position:0% +right and so as an example + + + align:start position:0% +right and so as an example +you know if i were to say well okay i'm + + align:start position:0% +you know if i were to say well okay i'm + + + align:start position:0% +you know if i were to say well okay i'm +going to take uh why is bacl2 i might + + align:start position:0% +going to take uh why is bacl2 i might + + + align:start position:0% +going to take uh why is bacl2 i might +have done this one in class + + align:start position:0% +have done this one in class + + + align:start position:0% +have done this one in class +why if i add bacl2 to a saturated + + align:start position:0% +why if i add bacl2 to a saturated + + + align:start position:0% +why if i add bacl2 to a saturated +solution of baso4 + + align:start position:0% +solution of baso4 + + + align:start position:0% +solution of baso4 +why does it cause precipitation that's + + align:start position:0% +why does it cause precipitation that's + + + align:start position:0% +why does it cause precipitation that's +the + + align:start position:0% +the + + + align:start position:0% +the +common because answer because of the + + align:start position:0% +common because answer because of the + + + align:start position:0% +common because answer because of the +common ion effect + + align:start position:0% +common ion effect + + + align:start position:0% +common ion effect +well you could write these out right so + + align:start position:0% +well you could write these out right so + + + align:start position:0% +well you could write these out right so +you write out your + + align:start position:0% +you write out your + + + align:start position:0% +you write out your +your saturated solution right so you + + align:start position:0% +your saturated solution right so you + + + align:start position:0% +your saturated solution right so you +write out your baso4 + + align:start position:0% +write out your baso4 + + + align:start position:0% +write out your baso4 +and you see that ba so4 solid + + align:start position:0% +and you see that ba so4 solid + + + align:start position:0% +and you see that ba so4 solid +will go to ba + + align:start position:0% +will go to ba + + + align:start position:0% +will go to ba +two plus in solution plus + + align:start position:0% +two plus in solution plus + + + align:start position:0% +two plus in solution plus +so4 two minus in solution and + + align:start position:0% +so4 two minus in solution and + + + align:start position:0% +so4 two minus in solution and +and so the common ion effect tells you + + align:start position:0% +and so the common ion effect tells you + + + align:start position:0% +and so the common ion effect tells you +that if i + + align:start position:0% +that if i + + + align:start position:0% +that if i +if i now add something else that has + + align:start position:0% +if i now add something else that has + + + align:start position:0% +if i now add something else that has +something in common with one of these + + align:start position:0% +something in common with one of these + + + align:start position:0% +something in common with one of these +that gives me + + align:start position:0% +that gives me + + + align:start position:0% +that gives me +an ion in common then because of le + + align:start position:0% +an ion in common then because of le + + + align:start position:0% +an ion in common then because of le +chatelier you're going to drive + + align:start position:0% +chatelier you're going to drive + + + align:start position:0% +chatelier you're going to drive +the reaction the other way that + + align:start position:0% +the reaction the other way that + + + align:start position:0% +the reaction the other way that +precipitates because it forms a solid + + align:start position:0% +precipitates because it forms a solid + + + align:start position:0% +precipitates because it forms a solid +bso4 so i've just done that right i've + + align:start position:0% +bso4 so i've just done that right i've + + + align:start position:0% +bso4 so i've just done that right i've +given you bacl2 which gives you a source + + align:start position:0% +given you bacl2 which gives you a source + + + align:start position:0% +given you bacl2 which gives you a source +of ba2 plus + + align:start position:0% +of ba2 plus + + + align:start position:0% +of ba2 plus +and how do you figure out if you were + + align:start position:0% +and how do you figure out if you were + + + align:start position:0% +and how do you figure out if you were +given amounts + + align:start position:0% +given amounts + + + align:start position:0% +given amounts +what happens what the new equilibrium is + + align:start position:0% +what happens what the new equilibrium is + + + align:start position:0% +what happens what the new equilibrium is +you use ice right you use the ice tables + + align:start position:0% +you use ice right you use the ice tables + + + align:start position:0% +you use ice right you use the ice tables +right okay and then finally + + align:start position:0% +right okay and then finally + + + align:start position:0% +right okay and then finally +we talked about acids and bases oh + + align:start position:0% +we talked about acids and bases oh + + + align:start position:0% +we talked about acids and bases oh +i really hate to erase defects but here + + align:start position:0% +i really hate to erase defects but here + + + align:start position:0% +i really hate to erase defects but here +we go + + align:start position:0% +we go + + + align:start position:0% +we go +defects are gone arrhenius i'm so sorry + + align:start position:0% +defects are gone arrhenius i'm so sorry + + + align:start position:0% +defects are gone arrhenius i'm so sorry +that was painful and the last + + align:start position:0% +that was painful and the last + + + align:start position:0% +that was painful and the last +topic here is acids and bases and this + + align:start position:0% +topic here is acids and bases and this + + + align:start position:0% +topic here is acids and bases and this +is the most recent one + + align:start position:0% + + + + align:start position:0% + +and so what do we have well we've got + + align:start position:0% +and so what do we have well we've got + + + align:start position:0% +and so what do we have well we've got +the + + align:start position:0% +the + + + align:start position:0% +the +acid equilibrium constant the base + + align:start position:0% +acid equilibrium constant the base + + + align:start position:0% +acid equilibrium constant the base +right we did water we did ph + + align:start position:0% +right we did water we did ph + + + align:start position:0% +right we did water we did ph +oh we did p anything right p + + align:start position:0% +oh we did p anything right p + + + align:start position:0% +oh we did p anything right p +equals negative log of the thing + + align:start position:0% +equals negative log of the thing + + + align:start position:0% +equals negative log of the thing +uh pka pkb + + align:start position:0% +uh pka pkb + + + align:start position:0% +uh pka pkb +so so okay so we could have uh + + align:start position:0% +so so okay so we could have uh + + + align:start position:0% +so so okay so we could have uh +and then we did like for example the + + align:start position:0% +and then we did like for example the + + + align:start position:0% +and then we did like for example the +definitions right so + + align:start position:0% +definitions right so + + + align:start position:0% +definitions right so +arrhenius versus bronsted-lowry + + align:start position:0% +arrhenius versus bronsted-lowry + + + align:start position:0% +arrhenius versus bronsted-lowry +lowry definitions + + align:start position:0% +lowry definitions + + + align:start position:0% +lowry definitions +right and so so for example if you're + + align:start position:0% +right and so so for example if you're + + + align:start position:0% +right and so so for example if you're +given a solution this is one just simple + + align:start position:0% +given a solution this is one just simple + + + align:start position:0% +given a solution this is one just simple +example right + + align:start position:0% +example right + + + align:start position:0% +example right +of an acid and you and it's hocn and + + align:start position:0% +of an acid and you and it's hocn and + + + align:start position:0% +of an acid and you and it's hocn and +you're given the acid and you know the + + align:start position:0% +you're given the acid and you know the + + + align:start position:0% +you're given the acid and you know the +ph + + align:start position:0% +ph + + + align:start position:0% +ph +so you're given that then the ph + + align:start position:0% +so you're given that then the ph + + + align:start position:0% +so you're given that then the ph +the ph from that information you can get + + align:start position:0% +the ph from that information you can get + + + align:start position:0% +the ph from that information you can get +that the concentration of h plus which + + align:start position:0% +that the concentration of h plus which + + + align:start position:0% +that the concentration of h plus which +is also h3o plus + + align:start position:0% +is also h3o plus + + + align:start position:0% +is also h3o plus +is 1.7 times 10 to the minus 3 + + align:start position:0% +is 1.7 times 10 to the minus 3 + + + align:start position:0% +is 1.7 times 10 to the minus 3 +moles per liter right that's from the ph + + align:start position:0% + + + + align:start position:0% + +and if you have that then you can go to + + align:start position:0% +and if you have that then you can go to + + + align:start position:0% +and if you have that then you can go to +the + + align:start position:0% +the + + + align:start position:0% +the +ka definition which is + + align:start position:0% +ka definition which is + + + align:start position:0% +ka definition which is +h plus concentration + + align:start position:0% +h plus concentration + + + align:start position:0% +h plus concentration +ocn minus divided by + + align:start position:0% +ocn minus divided by + + + align:start position:0% +ocn minus divided by +the acid ohcn concentration + + align:start position:0% +the acid ohcn concentration + + + align:start position:0% +the acid ohcn concentration +and you got it all because if you write + + align:start position:0% +and you got it all because if you write + + + align:start position:0% +and you got it all because if you write +the the equilibrium + + align:start position:0% +the the equilibrium + + + align:start position:0% +the the equilibrium +equation which is what ka describes + + align:start position:0% +equation which is what ka describes + + + align:start position:0% +equation which is what ka describes +the equilibrium of this acid + + align:start position:0% +the equilibrium of this acid + + + align:start position:0% +the equilibrium of this acid +dissociating into ions right + + align:start position:0% +dissociating into ions right + + + align:start position:0% +dissociating into ions right +dissociating into h plus and oc and + + align:start position:0% +dissociating into h plus and oc and + + + align:start position:0% +dissociating into h plus and oc and +minus and so you can get ka + + align:start position:0% +minus and so you can get ka + + + align:start position:0% +minus and so you can get ka +okay so what i hope is that this got us + + align:start position:0% +okay so what i hope is that this got us + + + align:start position:0% +okay so what i hope is that this got us +in the mood that this got us all kind of + + align:start position:0% +in the mood that this got us all kind of + + + align:start position:0% +in the mood that this got us all kind of +on the right page with respect to these + + align:start position:0% +on the right page with respect to these + + + align:start position:0% +on the right page with respect to these +topics you've got two days + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/2BttG14vI7c.txt b/2BttG14vI7c.txt new file mode 100644 index 0000000000000000000000000000000000000000..288a690d6915f94337853a6fec66e3169fc28e0f --- /dev/null +++ b/2BttG14vI7c.txt @@ -0,0 +1,1123 @@ +align:start position:0% + +in this segment we point out and discuss + + align:start position:0% +in this segment we point out and discuss + + + align:start position:0% +in this segment we point out and discuss +some important but also intuitive + + align:start position:0% +some important but also intuitive + + + align:start position:0% +some important but also intuitive +properties of conditional expectations + + align:start position:0% +properties of conditional expectations + + + align:start position:0% +properties of conditional expectations +the first property is the one that is + + align:start position:0% +the first property is the one that is + + + align:start position:0% +the first property is the one that is +written up here what is the intuitive + + align:start position:0% +written up here what is the intuitive + + + align:start position:0% +written up here what is the intuitive +meaning if you condition on Y then the + + align:start position:0% +meaning if you condition on Y then the + + + align:start position:0% +meaning if you condition on Y then the +value of y is known and so G of Y is + + align:start position:0% +value of y is known and so G of Y is + + + align:start position:0% +value of y is known and so G of Y is +also known there's no randomness in it + + align:start position:0% +also known there's no randomness in it + + + align:start position:0% +also known there's no randomness in it +it can be treated as a constant and + + align:start position:0% +it can be treated as a constant and + + + align:start position:0% +it can be treated as a constant and +therefore it can be pulled outside the + + align:start position:0% +therefore it can be pulled outside the + + + align:start position:0% +therefore it can be pulled outside the +expectation so that's the intuition how + + align:start position:0% +expectation so that's the intuition how + + + align:start position:0% +expectation so that's the intuition how +does one establish such a result + + align:start position:0% +does one establish such a result + + + align:start position:0% +does one establish such a result +formally let us take the discrete case + + align:start position:0% +formally let us take the discrete case + + + align:start position:0% +formally let us take the discrete case +so let us assume that x and y are both + + align:start position:0% +so let us assume that x and y are both + + + align:start position:0% +so let us assume that x and y are both +discrete what does it take to establish + + align:start position:0% +discrete what does it take to establish + + + align:start position:0% +discrete what does it take to establish +a fact of this kind we want to show that + + align:start position:0% +a fact of this kind we want to show that + + + align:start position:0% +a fact of this kind we want to show that +two random variables are equal and that + + align:start position:0% +two random variables are equal and that + + + align:start position:0% +two random variables are equal and that +amounts to the following we consider an + + align:start position:0% +amounts to the following we consider an + + + align:start position:0% +amounts to the following we consider an +outcome of the experiment and we want to + + align:start position:0% +outcome of the experiment and we want to + + + align:start position:0% +outcome of the experiment and we want to +show that whatever the outcome of the + + align:start position:0% +show that whatever the outcome of the + + + align:start position:0% +show that whatever the outcome of the +experiment is these two random variables + + align:start position:0% +experiment is these two random variables + + + align:start position:0% +experiment is these two random variables +will be the same so let us consider an + + align:start position:0% +will be the same so let us consider an + + + align:start position:0% +will be the same so let us consider an +outcome for which the random variable Y + + align:start position:0% +outcome for which the random variable Y + + + align:start position:0% +outcome for which the random variable Y +takes a specific value little Y and of + + align:start position:0% +takes a specific value little Y and of + + + align:start position:0% +takes a specific value little Y and of +course this has to be a specific little + + align:start position:0% +course this has to be a specific little + + + align:start position:0% +course this has to be a specific little +Y that is possible otherwise + + align:start position:0% +Y that is possible otherwise + + + align:start position:0% +Y that is possible otherwise +conditioning on that event would not be + + align:start position:0% +conditioning on that event would not be + + + align:start position:0% +conditioning on that event would not be +meaningful so if an outcome has this + + align:start position:0% +meaningful so if an outcome has this + + + align:start position:0% +meaningful so if an outcome has this +value for the random variable Y then + + align:start position:0% +value for the random variable Y then + + + align:start position:0% +value for the random variable Y then +what does this random variable do this + + align:start position:0% +what does this random variable do this + + + align:start position:0% +what does this random variable do this +is by definition the random variable + + align:start position:0% +is by definition the random variable + + + align:start position:0% +is by definition the random variable +that takes the value expected value of G + + align:start position:0% +that takes the value expected value of G + + + align:start position:0% +that takes the value expected value of G +Y X conditional expectation given that + + align:start position:0% +Y X conditional expectation given that + + + align:start position:0% +Y X conditional expectation given that +capital y took on this value this was + + align:start position:0% +capital y took on this value this was + + + align:start position:0% +capital y took on this value this was +our definition of the concept of the + + align:start position:0% +our definition of the concept of the + + + align:start position:0% +our definition of the concept of the +abstract conditional expectation as a + + align:start position:0% +abstract conditional expectation as a + + + align:start position:0% +abstract conditional expectation as a +random variable this is the random + + align:start position:0% +random variable this is the random + + + align:start position:0% +random variable this is the random +variable that they + + align:start position:0% +variable that they + + + align:start position:0% +variable that they +this specific numerical value whenever + + align:start position:0% +this specific numerical value whenever + + + align:start position:0% +this specific numerical value whenever +the random variable capital Y takes the + + align:start position:0% +the random variable capital Y takes the + + + align:start position:0% +the random variable capital Y takes the +value little Y and similarly if the + + align:start position:0% +value little Y and similarly if the + + + align:start position:0% +value little Y and similarly if the +random variable capital Y takes the + + align:start position:0% +random variable capital Y takes the + + + align:start position:0% +random variable capital Y takes the +value little Y this random variable here + + align:start position:0% +value little Y this random variable here + + + align:start position:0% +value little Y this random variable here +is the expected value of x given that Y + + align:start position:0% +is the expected value of x given that Y + + + align:start position:0% +is the expected value of x given that Y +is little Y and when capital Y takes the + + align:start position:0% +is little Y and when capital Y takes the + + + align:start position:0% +is little Y and when capital Y takes the +value little Y this function G of Y + + align:start position:0% +value little Y this function G of Y + + + align:start position:0% +value little Y this function G of Y +takes on this particular numerical value + + align:start position:0% +takes on this particular numerical value + + + align:start position:0% +takes on this particular numerical value +so we want to show that these two + + align:start position:0% +so we want to show that these two + + + align:start position:0% +so we want to show that these two +expressions will be equal no matter what + + align:start position:0% +expressions will be equal no matter what + + + align:start position:0% +expressions will be equal no matter what +Capital y is now when we place ourselves + + align:start position:0% +Capital y is now when we place ourselves + + + align:start position:0% +Capital y is now when we place ourselves +in a conditional universe where capital + + align:start position:0% +in a conditional universe where capital + + + align:start position:0% +in a conditional universe where capital +y takes a value little Y then the joint + + align:start position:0% +y takes a value little Y then the joint + + + align:start position:0% +y takes a value little Y then the joint +PMF of X and y gets concentrated on + + align:start position:0% +PMF of X and y gets concentrated on + + + align:start position:0% +PMF of X and y gets concentrated on +those values of capital y that obey this + + align:start position:0% +those values of capital y that obey this + + + align:start position:0% +those values of capital y that obey this +relation so conditioned on this event + + align:start position:0% +relation so conditioned on this event + + + align:start position:0% +relation so conditioned on this event +Capital y is with certainty equal to + + align:start position:0% +Capital y is with certainty equal to + + + align:start position:0% +Capital y is with certainty equal to +little Y therefore this random variable + + align:start position:0% +little Y therefore this random variable + + + align:start position:0% +little Y therefore this random variable +here in the conditional universe is the + + align:start position:0% +here in the conditional universe is the + + + align:start position:0% +here in the conditional universe is the +same as this number but now since this + + align:start position:0% +same as this number but now since this + + + align:start position:0% +same as this number but now since this +is a number it can be pulled outside the + + align:start position:0% +is a number it can be pulled outside the + + + align:start position:0% +is a number it can be pulled outside the +expectation + + align:start position:0% + + + + align:start position:0% + +so we have concluded that for any + + align:start position:0% +so we have concluded that for any + + + align:start position:0% +so we have concluded that for any +outcome for which the random variable + + align:start position:0% +outcome for which the random variable + + + align:start position:0% +outcome for which the random variable +Capital y takes this specific value + + align:start position:0% +Capital y takes this specific value + + + align:start position:0% +Capital y takes this specific value +little Y this random variable takes this + + align:start position:0% +little Y this random variable takes this + + + align:start position:0% +little Y this random variable takes this +value this random variable takes this + + align:start position:0% +value this random variable takes this + + + align:start position:0% +value this random variable takes this +value they are the same so no matter + + align:start position:0% +value they are the same so no matter + + + align:start position:0% +value they are the same so no matter +what the outcome is these two random + + align:start position:0% +what the outcome is these two random + + + align:start position:0% +what the outcome is these two random +variables take the same value and + + align:start position:0% +variables take the same value and + + + align:start position:0% +variables take the same value and +therefore they are the same random + + align:start position:0% +therefore they are the same random + + + align:start position:0% +therefore they are the same random +variables now this is a correct proof if + + align:start position:0% +variables now this is a correct proof if + + + align:start position:0% +variables now this is a correct proof if +the random variables are discrete if the + + align:start position:0% +the random variables are discrete if the + + + align:start position:0% +the random variables are discrete if the +random variables are continuous or + + align:start position:0% +random variables are continuous or + + + align:start position:0% +random variables are continuous or +general then carrying out a rigorous + + align:start position:0% +general then carrying out a rigorous + + + align:start position:0% +general then carrying out a rigorous +proof is actually quite subtle and it is + + align:start position:0% +proof is actually quite subtle and it is + + + align:start position:0% +proof is actually quite subtle and it is +beyond our scope + + align:start position:0% +beyond our scope + + + align:start position:0% +beyond our scope +however the intuition is still correct + + align:start position:0% +however the intuition is still correct + + + align:start position:0% +however the intuition is still correct +and the result is correct and we will be + + align:start position:0% +and the result is correct and we will be + + + align:start position:0% +and the result is correct and we will be +using it freely whenever we need to let + + align:start position:0% +using it freely whenever we need to let + + + align:start position:0% +using it freely whenever we need to let +us now move to a second observation + + align:start position:0% +us now move to a second observation + + + align:start position:0% +us now move to a second observation +suppose that H is an invertible function + + align:start position:0% +suppose that H is an invertible function + + + align:start position:0% +suppose that H is an invertible function +what does that mean that if I give you + + align:start position:0% +what does that mean that if I give you + + + align:start position:0% +what does that mean that if I give you +the value of H you can tell me the value + + align:start position:0% +the value of H you can tell me the value + + + align:start position:0% +the value of H you can tell me the value +of the argument + + align:start position:0% +of the argument + + + align:start position:0% +of the argument +so in some sense Y and H of Y can be + + align:start position:0% +so in some sense Y and H of Y can be + + + align:start position:0% +so in some sense Y and H of Y can be +recovered from each other if I give you + + align:start position:0% +recovered from each other if I give you + + + align:start position:0% +recovered from each other if I give you +Y you can calculate H of Y but also if I + + align:start position:0% +Y you can calculate H of Y but also if I + + + align:start position:0% +Y you can calculate H of Y but also if I +give you H of Y you can figure out what + + align:start position:0% +give you H of Y you can figure out what + + + align:start position:0% +give you H of Y you can figure out what +Y was an example could be the function H + + align:start position:0% +Y was an example could be the function H + + + align:start position:0% +Y was an example could be the function H +of y equals y to the third power if I + + align:start position:0% +of y equals y to the third power if I + + + align:start position:0% +of y equals y to the third power if I +tell you the value of y you know Y cube + + align:start position:0% +tell you the value of y you know Y cube + + + align:start position:0% +tell you the value of y you know Y cube +but if I tell you why cube you can also + + align:start position:0% +but if I tell you why cube you can also + + + align:start position:0% +but if I tell you why cube you can also +figure out y so Y and y tube carry + + align:start position:0% +figure out y so Y and y tube carry + + + align:start position:0% +figure out y so Y and y tube carry +exactly the same information in that + + align:start position:0% +exactly the same information in that + + + align:start position:0% +exactly the same information in that +case the conditional expectation what + + align:start position:0% +case the conditional expectation what + + + align:start position:0% +case the conditional expectation what +you expect on the average X to be if I + + align:start position:0% +you expect on the average X to be if I + + + align:start position:0% +you expect on the average X to be if I +tell you the value of Y should be the + + align:start position:0% +tell you the value of Y should be the + + + align:start position:0% +tell you the value of Y should be the +same as what you would expect X to be if + + align:start position:0% +same as what you would expect X to be if + + + align:start position:0% +same as what you would expect X to be if +I give you the value of let's say Y cube + + align:start position:0% +I give you the value of let's say Y cube + + + align:start position:0% +I give you the value of let's say Y cube +in both cases I am giving you the same + + align:start position:0% +in both cases I am giving you the same + + + align:start position:0% +in both cases I am giving you the same +amount of information so the conditional + + align:start position:0% +amount of information so the conditional + + + align:start position:0% +amount of information so the conditional +distribution of X should be the same and + + align:start position:0% +distribution of X should be the same and + + + align:start position:0% +distribution of X should be the same and +the conditional + + align:start position:0% +the conditional + + + align:start position:0% +the conditional +stations should also be the same so this + + align:start position:0% +stations should also be the same so this + + + align:start position:0% +stations should also be the same so this +is again a very intuitive fact how do we + + align:start position:0% +is again a very intuitive fact how do we + + + align:start position:0% +is again a very intuitive fact how do we +verify that this fact is true + + align:start position:0% +verify that this fact is true + + + align:start position:0% +verify that this fact is true +using the same method as before so fix + + align:start position:0% +using the same method as before so fix + + + align:start position:0% +using the same method as before so fix +some particular outcome for which the + + align:start position:0% +some particular outcome for which the + + + align:start position:0% +some particular outcome for which the +random variable capital Y takes a + + align:start position:0% +random variable capital Y takes a + + + align:start position:0% +random variable capital Y takes a +specific value little Y when that + + align:start position:0% +specific value little Y when that + + + align:start position:0% +specific value little Y when that +happens this random variable will take + + align:start position:0% +happens this random variable will take + + + align:start position:0% +happens this random variable will take +this value here that's just by the + + align:start position:0% +this value here that's just by the + + + align:start position:0% +this value here that's just by the +definition of conditional expectation + + align:start position:0% +definition of conditional expectation + + + align:start position:0% +definition of conditional expectation +this is the random variable that takes + + align:start position:0% +this is the random variable that takes + + + align:start position:0% +this is the random variable that takes +this value whenever capital Y happens to + + align:start position:0% +this value whenever capital Y happens to + + + align:start position:0% +this value whenever capital Y happens to +be equal to little Y in that case we + + align:start position:0% +be equal to little Y in that case we + + + align:start position:0% +be equal to little Y in that case we +also have that H of capital y takes on a + + align:start position:0% +also have that H of capital y takes on a + + + align:start position:0% +also have that H of capital y takes on a +specific value H of little why when this + + align:start position:0% +specific value H of little why when this + + + align:start position:0% +specific value H of little why when this +random variable takes this specific + + align:start position:0% +random variable takes this specific + + + align:start position:0% +random variable takes this specific +value this random variable here will + + align:start position:0% +value this random variable here will + + + align:start position:0% +value this random variable here will +take a value of this kind + + align:start position:0% + + + + align:start position:0% + +so this is the random variable that + + align:start position:0% +so this is the random variable that + + + align:start position:0% +so this is the random variable that +takes this value whenever age of capital + + align:start position:0% +takes this value whenever age of capital + + + align:start position:0% +takes this value whenever age of capital +y happens to be this specific number but + + align:start position:0% +y happens to be this specific number but + + + align:start position:0% +y happens to be this specific number but +now the event that H of Y takes this + + align:start position:0% +now the event that H of Y takes this + + + align:start position:0% +now the event that H of Y takes this +specific value because the function H is + + align:start position:0% +specific value because the function H is + + + align:start position:0% +specific value because the function H is +invertible is identical to the event + + align:start position:0% +invertible is identical to the event + + + align:start position:0% +invertible is identical to the event +that Y takes that particular value and + + align:start position:0% +that Y takes that particular value and + + + align:start position:0% +that Y takes that particular value and +so since this event is identical to that + + align:start position:0% +so since this event is identical to that + + + align:start position:0% +so since this event is identical to that +event the conditional probability is + + align:start position:0% +event the conditional probability is + + + align:start position:0% +event the conditional probability is +given this event would be the same as + + align:start position:0% +given this event would be the same as + + + align:start position:0% +given this event would be the same as +the conditional probabilities given that + + align:start position:0% +the conditional probabilities given that + + + align:start position:0% +the conditional probabilities given that +event and therefore the conditional + + align:start position:0% +event and therefore the conditional + + + align:start position:0% +event and therefore the conditional +expectations would also be the same once + + align:start position:0% +expectations would also be the same once + + + align:start position:0% +expectations would also be the same once +more this is a proof that entirely + + align:start position:0% +more this is a proof that entirely + + + align:start position:0% +more this is a proof that entirely +rigorous if we are dealing with discrete + + align:start position:0% +rigorous if we are dealing with discrete + + + align:start position:0% +rigorous if we are dealing with discrete +random variables although in the + + align:start position:0% +random variables although in the + + + align:start position:0% +random variables although in the +continuous case there would be some + + align:start position:0% +continuous case there would be some + + + align:start position:0% +continuous case there would be some +subtleties involved however the result + + align:start position:0% +subtleties involved however the result + + + align:start position:0% +subtleties involved however the result +is true in general the technical details + + align:start position:0% +is true in general the technical details + + + align:start position:0% +is true in general the technical details +are beyond our scope \ No newline at end of file diff --git a/2Gk4Vg2tuRQ.txt b/2Gk4Vg2tuRQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..269d965e542efeea224502ec511a06046ff0bfee --- /dev/null +++ b/2Gk4Vg2tuRQ.txt @@ -0,0 +1,4803 @@ +align:start position:0% + +the major component of a relationship of + + align:start position:0% +the major component of a relationship of + + + align:start position:0% +the major component of a relationship of +a a faculty to a student is the death + + align:start position:0% +a a faculty to a student is the death + + + align:start position:0% +a a faculty to a student is the death +side Crypt critique where uh you sit + + align:start position:0% +side Crypt critique where uh you sit + + + align:start position:0% +side Crypt critique where uh you sit +down with a student the student explains + + align:start position:0% +down with a student the student explains + + + align:start position:0% +down with a student the student explains +where they are in the + + align:start position:0% +where they are in the + + + align:start position:0% +where they are in the +process a drawing our model and you make + + align:start position:0% +process a drawing our model and you make + + + align:start position:0% +process a drawing our model and you make +comments and it's a very fascinating + + align:start position:0% +comments and it's a very fascinating + + + align:start position:0% +comments and it's a very fascinating +process because you're very + + align:start position:0% +process because you're very + + + align:start position:0% +process because you're very +quickly understanding what the student + + align:start position:0% +quickly understanding what the student + + + align:start position:0% +quickly understanding what the student +is trying to + + align:start position:0% +is trying to + + + align:start position:0% +is trying to +do um and you have to select what + + align:start position:0% +do um and you have to select what + + + align:start position:0% +do um and you have to select what +criticism you can give that's going to + + align:start position:0% +criticism you can give that's going to + + + align:start position:0% +criticism you can give that's going to +be helpful for the next step happens + + align:start position:0% +be helpful for the next step happens + + + align:start position:0% +be helpful for the next step happens +very + + align:start position:0% +very + + + align:start position:0% +very +quickly but it's an essential one-on-one + + align:start position:0% +quickly but it's an essential one-on-one + + + align:start position:0% +quickly but it's an essential one-on-one +process between myself and the + + align:start position:0% +process between myself and the + + + align:start position:0% +process between myself and the +students guiding the work through the + + align:start position:0% +students guiding the work through the + + + align:start position:0% +students guiding the work through the +semester + + align:start position:0% +semester + + + align:start position:0% +semester +perhaps uh during the semester there are + + align:start position:0% +perhaps uh during the semester there are + + + align:start position:0% +perhaps uh during the semester there are +hundreds of crits deide crits that take + + align:start position:0% +hundreds of crits deide crits that take + + + align:start position:0% +hundreds of crits deide crits that take +place um often if there's uh in this + + align:start position:0% +place um often if there's uh in this + + + align:start position:0% +place um often if there's uh in this +class there's 13 + + align:start position:0% +class there's 13 + + + align:start position:0% +class there's 13 +people uh I will try to see 13 people in + + align:start position:0% +people uh I will try to see 13 people in + + + align:start position:0% +people uh I will try to see 13 people in +one + + align:start position:0% +one + + + align:start position:0% +one +afternoon and sometimes uh once or twice + + align:start position:0% +afternoon and sometimes uh once or twice + + + align:start position:0% +afternoon and sometimes uh once or twice +a week so by the end of the semester the + + align:start position:0% +a week so by the end of the semester the + + + align:start position:0% +a week so by the end of the semester the +student has received maybe uh 20 25 + + align:start position:0% +student has received maybe uh 20 25 + + + align:start position:0% +student has received maybe uh 20 25 +death side crits so today you're seeing + + align:start position:0% +death side crits so today you're seeing + + + align:start position:0% +death side crits so today you're seeing +one of + + align:start position:0% +one of + + + align:start position:0% +one of +those so uh last time I talked with you + + align:start position:0% +those so uh last time I talked with you + + + align:start position:0% +those so uh last time I talked with you +I had um this model uh in that spot yep + + align:start position:0% +I had um this model uh in that spot yep + + + align:start position:0% +I had um this model uh in that spot yep +and + + align:start position:0% +and + + + align:start position:0% +and +uh I have the idea of of creating a sort + + align:start position:0% +uh I have the idea of of creating a sort + + + align:start position:0% +uh I have the idea of of creating a sort +of wall but um making penetrations + + align:start position:0% +of wall but um making penetrations + + + align:start position:0% +of wall but um making penetrations +within it and + + align:start position:0% +within it and + + + align:start position:0% +within it and +um what I started to do was um go from + + align:start position:0% +um what I started to do was um go from + + + align:start position:0% +um what I started to do was um go from +from a very sort of square form or + + align:start position:0% +from a very sort of square form or + + + align:start position:0% +from a very sort of square form or +orthogonal form to creating + + align:start position:0% +orthogonal form to creating + + + align:start position:0% +orthogonal form to creating +um + + align:start position:0% +um + + + align:start position:0% +um +more nicer shapes and the just creating + + align:start position:0% +more nicer shapes and the just creating + + + align:start position:0% +more nicer shapes and the just creating +a stepping here for example + + align:start position:0% +a stepping here for example + + + align:start position:0% +a stepping here for example +um we also discussed the the idea of an + + align:start position:0% +um we also discussed the the idea of an + + + align:start position:0% +um we also discussed the the idea of an +Alleyway here and um the trees that are + + align:start position:0% +Alleyway here and um the trees that are + + + align:start position:0% +Alleyway here and um the trees that are +on the site right now are the ones that + + align:start position:0% +on the site right now are the ones that + + + align:start position:0% +on the site right now are the ones that +I put up um sort of to figure + + align:start position:0% +I put up um sort of to figure + + + align:start position:0% +I put up um sort of to figure +out whether I want to cut down a tree or + + align:start position:0% +out whether I want to cut down a tree or + + + align:start position:0% +out whether I want to cut down a tree or +not or how I can work with a trees and + + align:start position:0% +not or how I can work with a trees and + + + align:start position:0% +not or how I can work with a trees and +mhm um you know me pretty well by now + + align:start position:0% +mhm um you know me pretty well by now + + + align:start position:0% +mhm um you know me pretty well by now +and you know that I don't want to cut + + align:start position:0% +and you know that I don't want to cut + + + align:start position:0% +and you know that I don't want to cut +down trees + + align:start position:0% +down trees + + + align:start position:0% +down trees +so um so I I'm working to to preserve + + align:start position:0% +so um so I I'm working to to preserve + + + align:start position:0% +so um so I I'm working to to preserve +them and in this case I I cut into it a + + align:start position:0% +them and in this case I I cut into it a + + + align:start position:0% +them and in this case I I cut into it a +little bit and instead of having an + + align:start position:0% +little bit and instead of having an + + + align:start position:0% +little bit and instead of having an +Alleyway I just I decided that I'd have + + align:start position:0% +Alleyway I just I decided that I'd have + + + align:start position:0% +Alleyway I just I decided that I'd have +a secret garden sort of in the back here + + align:start position:0% +a secret garden sort of in the back here + + + align:start position:0% +a secret garden sort of in the back here +um and then create a balcony in in there + + align:start position:0% +um and then create a balcony in in there + + + align:start position:0% +um and then create a balcony in in there +so + + align:start position:0% + + + + align:start position:0% + +um so that there' be a sort of balcony + + align:start position:0% +um so that there' be a sort of balcony + + + align:start position:0% +um so that there' be a sort of balcony +here from the second floor and uh and + + align:start position:0% +here from the second floor and uh and + + + align:start position:0% +here from the second floor and uh and +out here would be a secret garden sort + + align:start position:0% +out here would be a secret garden sort + + + align:start position:0% +out here would be a secret garden sort +of thing and this idea of having + + align:start position:0% +of thing and this idea of having + + + align:start position:0% +of thing and this idea of having +um sort of a arcade um would be present + + align:start position:0% +um sort of a arcade um would be present + + + align:start position:0% +um sort of a arcade um would be present +here as well would be in would be here + + align:start position:0% +here as well would be in would be here + + + align:start position:0% +here as well would be in would be here +also here too okay here as well and on + + align:start position:0% +also here too okay here as well and on + + + align:start position:0% +also here too okay here as well and on +one of + + align:start position:0% + + + + align:start position:0% + +my um I was I was working with that sort + + align:start position:0% +my um I was I was working with that sort + + + align:start position:0% +my um I was I was working with that sort +of idea and seeing how it can just flow + + align:start position:0% +of idea and seeing how it can just flow + + + align:start position:0% +of idea and seeing how it can just flow +through the space Maybe + + align:start position:0% +through the space Maybe + + + align:start position:0% +through the space Maybe +um and so one of one of the ideas that + + align:start position:0% +um and so one of one of the ideas that + + + align:start position:0% +um and so one of one of the ideas that +this this model here this um shape + + align:start position:0% +this this model here this um shape + + + align:start position:0% +this this model here this um shape +suggested to me was the idea of a foot + + align:start position:0% +suggested to me was the idea of a foot + + + align:start position:0% +suggested to me was the idea of a foot +Bridge just crossing that and uh since + + align:start position:0% +Bridge just crossing that and uh since + + + align:start position:0% +Bridge just crossing that and uh since +I'm working with elderly um I think it + + align:start position:0% +I'm working with elderly um I think it + + + align:start position:0% +I'm working with elderly um I think it +would be very nice to have a foot Bridge + + align:start position:0% +would be very nice to have a foot Bridge + + + align:start position:0% +would be very nice to have a foot Bridge +here so that they won't have to go all + + align:start position:0% +here so that they won't have to go all + + + align:start position:0% +here so that they won't have to go all +the way down and then get another + + align:start position:0% +the way down and then get another + + + align:start position:0% +the way down and then get another +elevator or or take another ramp up they + + align:start position:0% +elevator or or take another ramp up they + + + align:start position:0% +elevator or or take another ramp up they +can just cut across here and since I'm + + align:start position:0% +can just cut across here and since I'm + + + align:start position:0% +can just cut across here and since I'm +thinking of having uh a screen here or a + + align:start position:0% +thinking of having uh a screen here or a + + + align:start position:0% +thinking of having uh a screen here or a +sort of theater space out here for + + align:start position:0% +sort of theater space out here for + + + align:start position:0% +sort of theater space out here for +outdoors um I could have people lining + + align:start position:0% +outdoors um I could have people lining + + + align:start position:0% +outdoors um I could have people lining +up here and looking in there or + + align:start position:0% +up here and looking in there or + + + align:start position:0% +up here and looking in there or +screenings of films and things like that + + align:start position:0% +screenings of films and things like that + + + align:start position:0% +screenings of films and things like that +I could have people this would be + + align:start position:0% +I could have people this would be + + + align:start position:0% +I could have people this would be +another sort of seating area and we + + align:start position:0% +another sort of seating area and we + + + align:start position:0% +another sort of seating area and we +could have speaker system or something + + align:start position:0% +could have speaker system or something + + + align:start position:0% +could have speaker system or something +um picks up there + + align:start position:0% +um picks up there + + + align:start position:0% +um picks up there +um so right now I feel um I feel sort of + + align:start position:0% +um so right now I feel um I feel sort of + + + align:start position:0% +um so right now I feel um I feel sort of +set on how I'm doing this something + + align:start position:0% +set on how I'm doing this something + + + align:start position:0% +set on how I'm doing this something +actually minor detail that was suggested + + align:start position:0% +actually minor detail that was suggested + + + align:start position:0% +actually minor detail that was suggested +to me simply from the shapes that I had + + align:start position:0% +to me simply from the shapes that I had + + + align:start position:0% +to me simply from the shapes that I had +um was sort of having a lower window + + align:start position:0% +um was sort of having a lower window + + + align:start position:0% +um was sort of having a lower window +here um and since this is going to be my + + align:start position:0% +here um and since this is going to be my + + + align:start position:0% +here um and since this is going to be my +more private space private building + + align:start position:0% +more private space private building + + + align:start position:0% +more private space private building +versus the um and quieter building uh + + align:start position:0% +versus the um and quieter building uh + + + align:start position:0% +versus the um and quieter building uh +versus a louder sort of um more social + + align:start position:0% +versus a louder sort of um more social + + + align:start position:0% +versus a louder sort of um more social +space here um I like the idea of having + + align:start position:0% +space here um I like the idea of having + + + align:start position:0% +space here um I like the idea of having +those windows be right at the very + + align:start position:0% +those windows be right at the very + + + align:start position:0% +those windows be right at the very +bottom um in that + + align:start position:0% +bottom um in that + + + align:start position:0% +bottom um in that +level which means that this is a + + align:start position:0% +level which means that this is a + + + align:start position:0% +level which means that this is a +two-story + + align:start position:0% +two-story + + + align:start position:0% +two-story +space uh that would be one story that + + align:start position:0% +space uh that would be one story that + + + align:start position:0% +space uh that would be one story that +but light's going down in below yeah so + + align:start position:0% +but light's going down in below yeah so + + + align:start position:0% +but light's going down in below yeah so +in this inside this is there space there + + align:start position:0% +in this inside this is there space there + + + align:start position:0% +in this inside this is there space there +will be yeah I I imagine that being um + + align:start position:0% +will be yeah I I imagine that being um + + + align:start position:0% +will be yeah I I imagine that being um +either the uh the where the infants + + align:start position:0% +either the uh the where the infants + + + align:start position:0% +either the uh the where the infants +would be um in my daycare center or uh + + align:start position:0% +would be um in my daycare center or uh + + + align:start position:0% +would be um in my daycare center or uh +just a place where people can go and + + align:start position:0% +just a place where people can go and + + + align:start position:0% +just a place where people can go and +sleep uh children elderly um and sleep + + align:start position:0% +sleep uh children elderly um and sleep + + + align:start position:0% +sleep uh children elderly um and sleep +and I don't know it's just a minor touch + + align:start position:0% +and I don't know it's just a minor touch + + + align:start position:0% +and I don't know it's just a minor touch +but just the shape that I had from that + + align:start position:0% +but just the shape that I had from that + + + align:start position:0% +but just the shape that I had from that +cardboard because they didn't match I I + + align:start position:0% +cardboard because they didn't match I I + + + align:start position:0% +cardboard because they didn't match I I +just put it in and and I realized that + + align:start position:0% +just put it in and and I realized that + + + align:start position:0% +just put it in and and I realized that +it suggested something to me but the + + align:start position:0% +it suggested something to me but the + + + align:start position:0% +it suggested something to me but the +point is there be a a slot of light + + align:start position:0% +point is there be a a slot of light + + + align:start position:0% +point is there be a a slot of light +behind that or you or you're just + + align:start position:0% +behind that or you or you're just + + + align:start position:0% +behind that or you or you're just +getting light into this + + align:start position:0% +getting light into this + + + align:start position:0% +getting light into this +yeah the only the only light will be + + align:start position:0% +yeah the only the only light will be + + + align:start position:0% +yeah the only the only light will be +coming natural light will be coming in + + align:start position:0% +coming natural light will be coming in + + + align:start position:0% +coming natural light will be coming in +from the floor sort of that was a minor + + align:start position:0% +from the floor sort of that was a minor + + + align:start position:0% +from the floor sort of that was a minor +detail okay but uh in terms of I don't + + align:start position:0% +detail okay but uh in terms of I don't + + + align:start position:0% +detail okay but uh in terms of I don't +know penetrating sort of this this space + + align:start position:0% +know penetrating sort of this this space + + + align:start position:0% +know penetrating sort of this this space +I decided I would probably include this + + align:start position:0% +I decided I would probably include this + + + align:start position:0% +I decided I would probably include this +tree into the actual building um having + + align:start position:0% +tree into the actual building um having + + + align:start position:0% +tree into the actual building um having +people from the street level um this + + align:start position:0% +people from the street level um this + + + align:start position:0% +people from the street level um this +being North Street um well power sort of + + align:start position:0% +being North Street um well power sort of + + + align:start position:0% +being North Street um well power sort of +um the tourist coming that way this um I + + align:start position:0% +um the tourist coming that way this um I + + + align:start position:0% +um the tourist coming that way this um I +I like the way that taking this out a + + align:start position:0% +I like the way that taking this out a + + + align:start position:0% +I like the way that taking this out a +little bit um invited people in here and + + align:start position:0% +little bit um invited people in here and + + + align:start position:0% +little bit um invited people in here and +sort of showed them the way of how to + + align:start position:0% +sort of showed them the way of how to + + + align:start position:0% +sort of showed them the way of how to +enter this building um and including the + + align:start position:0% +enter this building um and including the + + + align:start position:0% +enter this building um and including the +tree and and here I had the same sort of + + align:start position:0% +tree and and here I had the same sort of + + + align:start position:0% +tree and and here I had the same sort of +concept that I could I could include + + align:start position:0% +concept that I could I could include + + + align:start position:0% +concept that I could I could include +this trees the trees um before before + + align:start position:0% +this trees the trees um before before + + + align:start position:0% +this trees the trees um before before +Tuesday I hadn't um put the trees in and + + align:start position:0% +Tuesday I hadn't um put the trees in and + + + align:start position:0% +Tuesday I hadn't um put the trees in and +and I just sort of plunked all my my + + align:start position:0% +and I just sort of plunked all my my + + + align:start position:0% +and I just sort of plunked all my my +objects here but once that I put the + + align:start position:0% +objects here but once that I put the + + + align:start position:0% +objects here but once that I put the +trees I started thinking well maybe I + + align:start position:0% +trees I started thinking well maybe I + + + align:start position:0% +trees I started thinking well maybe I +could do something like that + + align:start position:0% +could do something like that + + + align:start position:0% +could do something like that +and and I realized that I would just + + align:start position:0% +and and I realized that I would just + + + align:start position:0% +and and I realized that I would just +lose the whole idea I had of of relating + + align:start position:0% +lose the whole idea I had of of relating + + + align:start position:0% +lose the whole idea I had of of relating +to the street and having that right + + align:start position:0% +to the street and having that right + + + align:start position:0% +to the street and having that right +angle right there + + align:start position:0% +angle right there + + + align:start position:0% +angle right there +so I I see that the only solution for + + align:start position:0% +so I I see that the only solution for + + + align:start position:0% +so I I see that the only solution for +those trees would be to just include + + align:start position:0% +those trees would be to just include + + + align:start position:0% +those trees would be to just include +them in the building create um one of my + + align:start position:0% +them in the building create um one of my + + + align:start position:0% +them in the building create um one of my +ideas is to create a patio + + align:start position:0% + + + + align:start position:0% + +area and that One MH that would be a + + align:start position:0% +area and that One MH that would be a + + + align:start position:0% +area and that One MH that would be a +patio area for eating and things like + + align:start position:0% +patio area for eating and things like + + + align:start position:0% +patio area for eating and things like +that and you you mentioned to me um + + align:start position:0% +that and you you mentioned to me um + + + align:start position:0% +that and you you mentioned to me um +creating a secret garden here on the + + align:start position:0% +creating a secret garden here on the + + + align:start position:0% +creating a secret garden here on the +left and the entrance would be somehow + + align:start position:0% +left and the entrance would be somehow + + + align:start position:0% +left and the entrance would be somehow +have having to do with entering through + + align:start position:0% +have having to do with entering through + + + align:start position:0% +have having to do with entering through +here and going through the building and + + align:start position:0% +here and going through the building and + + + align:start position:0% +here and going through the building and +looking at these two trees they it just + + align:start position:0% +looking at these two trees they it just + + + align:start position:0% +looking at these two trees they it just +was a Gateway sort of to enter into this + + align:start position:0% +was a Gateway sort of to enter into this + + + align:start position:0% +was a Gateway sort of to enter into this +space um so I'm I'm imagining that + + align:start position:0% +space um so I'm I'm imagining that + + + align:start position:0% +space um so I'm I'm imagining that +um that they will create a sort of + + align:start position:0% +um that they will create a sort of + + + align:start position:0% +um that they will create a sort of +gateway to enter in here where there'll + + align:start position:0% +gateway to enter in here where there'll + + + align:start position:0% +gateway to enter in here where there'll +be a playground some swing steps um + + align:start position:0% +be a playground some swing steps um + + + align:start position:0% +be a playground some swing steps um +tables for I don't know two elderly + + align:start position:0% +tables for I don't know two elderly + + + align:start position:0% +tables for I don't know two elderly +gentlemen to play chess um just these + + align:start position:0% +gentlemen to play chess um just these + + + align:start position:0% +gentlemen to play chess um just these +images I have in my head right now and I + + align:start position:0% +images I have in my head right now and I + + + align:start position:0% +images I have in my head right now and I +I just imagine bushes right now + + align:start position:0% +I just imagine bushes right now + + + align:start position:0% +I just imagine bushes right now +separating that space so that people + + align:start position:0% +separating that space so that people + + + align:start position:0% +separating that space so that people +walking by know it's there and then + + align:start position:0% +walking by know it's there and then + + + align:start position:0% +walking by know it's there and then +question how do I how do I get in there + + align:start position:0% +question how do I how do I get in there + + + align:start position:0% +question how do I how do I get in there +and realize that they they actually have + + align:start position:0% +and realize that they they actually have + + + align:start position:0% +and realize that they they actually have +a the right to go in there because this + + align:start position:0% +a the right to go in there because this + + + align:start position:0% +a the right to go in there because this +is a public space um so those are my + + align:start position:0% +is a public space um so those are my + + + align:start position:0% +is a public space um so those are my +basic ideas right now if you if I'm + + align:start position:0% +basic ideas right now if you if I'm + + + align:start position:0% +basic ideas right now if you if I'm +coming down the street for the first + + align:start position:0% +coming down the street for the first + + + align:start position:0% +coming down the street for the first +time do you see me coming into this + + align:start position:0% +time do you see me coming into this + + + align:start position:0% +time do you see me coming into this +space or into here + + align:start position:0% +space or into here + + + align:start position:0% +space or into here +as the entrance well I think this would + + align:start position:0% +as the entrance well I think this would + + + align:start position:0% +as the entrance well I think this would +be more prominent and I think more more + + align:start position:0% +be more prominent and I think more more + + + align:start position:0% +be more prominent and I think more more +people will will enter into here at + + align:start position:0% +people will will enter into here at + + + align:start position:0% +people will will enter into here at +first and then find out what this is + + align:start position:0% +first and then find out what this is + + + align:start position:0% +first and then find out what this is +this this is going to be the central + + align:start position:0% +this this is going to be the central + + + align:start position:0% +this this is going to be the central +space to my design and yes I I think + + align:start position:0% +space to my design and yes I I think + + + align:start position:0% +space to my design and yes I I think +that I I had to stick the wall out a + + align:start position:0% +that I I had to stick the wall out a + + + align:start position:0% +that I I had to stick the wall out a +little bit here + + align:start position:0% +little bit here + + + align:start position:0% +little bit here +because there had to be a sort of way to + + align:start position:0% +because there had to be a sort of way to + + + align:start position:0% +because there had to be a sort of way to +invite people into this building as well + + align:start position:0% +invite people into this building as well + + + align:start position:0% +invite people into this building as well +even though it's my my quieter building + + align:start position:0% +even though it's my my quieter building + + + align:start position:0% +even though it's my my quieter building +um for study for um sleeping and uh + + align:start position:0% +um for study for um sleeping and uh + + + align:start position:0% +um for study for um sleeping and uh +taking care of infants whereas here is + + align:start position:0% +taking care of infants whereas here is + + + align:start position:0% +taking care of infants whereas here is +the dining and the um teaching kids more + + align:start position:0% +the dining and the um teaching kids more + + + align:start position:0% +the dining and the um teaching kids more +uh creative arts things like that um so + + align:start position:0% +uh creative arts things like that um so + + + align:start position:0% +uh creative arts things like that um so +I am hoping people enter here but I do I + + align:start position:0% +I am hoping people enter here but I do I + + + align:start position:0% +I am hoping people enter here but I do I +do see that that that is prominent there + + align:start position:0% +do see that that that is prominent there + + + align:start position:0% +do see that that that is prominent there +and that maybe I should suppress that a + + align:start position:0% +and that maybe I should suppress that a + + + align:start position:0% +and that maybe I should suppress that a +little all right I got + + align:start position:0% +little all right I got + + + align:start position:0% +little all right I got +it uh first of all the evolution from + + align:start position:0% +it uh first of all the evolution from + + + align:start position:0% +it uh first of all the evolution from +this to this is very successful because + + align:start position:0% +this to this is very successful because + + + align:start position:0% +this to this is very successful because +I think you're starting to develop I + + align:start position:0% +I think you're starting to develop I + + + align:start position:0% +I think you're starting to develop I +architecture language in this um which + + align:start position:0% +architecture language in this um which + + + align:start position:0% +architecture language in this um which +needs obviously more work but it's + + align:start position:0% +needs obviously more work but it's + + + align:start position:0% +needs obviously more work but it's +nevertheless it's taking the rough form + + align:start position:0% +nevertheless it's taking the rough form + + + align:start position:0% +nevertheless it's taking the rough form +into something that's more precise and I + + align:start position:0% +into something that's more precise and I + + + align:start position:0% +into something that's more precise and I +think it's good the notion of a ramp + + align:start position:0% +think it's good the notion of a ramp + + + align:start position:0% +think it's good the notion of a ramp +that moves through this um and across + + align:start position:0% +that moves through this um and across + + + align:start position:0% +that moves through this um and across +and over which is a new idea since + + align:start position:0% +and over which is a new idea since + + + align:start position:0% +and over which is a new idea since +before is very powerful just so you know + + align:start position:0% +before is very powerful just so you know + + + align:start position:0% +before is very powerful just so you know +the normal ramp is 1 to 12 and this is + + align:start position:0% +the normal ramp is 1 to 12 and this is + + + align:start position:0% +the normal ramp is 1 to 12 and this is +probably not that but that's okay that's + + align:start position:0% +probably not that but that's okay that's + + + align:start position:0% +probably not that but that's okay that's +a handicap that's not necessarily okay + + align:start position:0% +a handicap that's not necessarily okay + + + align:start position:0% +a handicap that's not necessarily okay +uh but the notion of the ramp being the + + align:start position:0% +uh but the notion of the ramp being the + + + align:start position:0% +uh but the notion of the ramp being the +thing that moves me through + + align:start position:0% +thing that moves me through + + + align:start position:0% +thing that moves me through +this um at least to a certain extent I + + align:start position:0% +this um at least to a certain extent I + + + align:start position:0% +this um at least to a certain extent I +think is a very powerful + + align:start position:0% +think is a very powerful + + + align:start position:0% +think is a very powerful +notion um some + + align:start position:0% +notion um some + + + align:start position:0% +notion um some +comments the idea that this is still + + align:start position:0% +comments the idea that this is still + + + align:start position:0% +comments the idea that this is still +covered and lights coming into this I + + align:start position:0% +covered and lights coming into this I + + + align:start position:0% +covered and lights coming into this I +think is + + align:start position:0% +think is + + + align:start position:0% +think is +powerful but I'm not so sure it's + + align:start position:0% +powerful but I'm not so sure it's + + + align:start position:0% +powerful but I'm not so sure it's +necessary to continue it uh in the same + + align:start position:0% +necessary to continue it uh in the same + + + align:start position:0% +necessary to continue it uh in the same +way for instance here it could be + + align:start position:0% +way for instance here it could be + + + align:start position:0% +way for instance here it could be +outside this this walkway or slightly + + align:start position:0% +outside this this walkway or slightly + + + align:start position:0% +outside this this walkway or slightly +covered okay but not necessarily heated + + align:start position:0% +covered okay but not necessarily heated + + + align:start position:0% +covered okay but not necessarily heated +so you'd have where this one might be a + + align:start position:0% +so you'd have where this one might be a + + + align:start position:0% +so you'd have where this one might be a +heated space so I could come in into a + + align:start position:0% +heated space so I could come in into a + + + align:start position:0% +heated space so I could come in into a +heated building and then I'm covered and + + align:start position:0% +heated building and then I'm covered and + + + align:start position:0% +heated building and then I'm covered and +I come out and maybe I go back into it + + align:start position:0% +I come out and maybe I go back into it + + + align:start position:0% +I come out and maybe I go back into it +as opposed to it completely being uh + + align:start position:0% +as opposed to it completely being uh + + + align:start position:0% +as opposed to it completely being uh +covered as you show it here and here I + + align:start position:0% +covered as you show it here and here I + + + align:start position:0% +covered as you show it here and here I +showed it in section to idea yeah well + + align:start position:0% +showed it in section to idea yeah well + + + align:start position:0% +showed it in section to idea yeah well +it could be that you need first of all + + align:start position:0% +it could be that you need first of all + + + align:start position:0% +it could be that you need first of all +you need this continuity which I think + + align:start position:0% +you need this continuity which I think + + + align:start position:0% +you need this continuity which I think +is very powerful of the of the the path + + align:start position:0% +is very powerful of the of the the path + + + align:start position:0% +is very powerful of the of the the path +through or the journey through the + + align:start position:0% +through or the journey through the + + + align:start position:0% +through or the journey through the +building to hold together the the pieces + + align:start position:0% +building to hold together the the pieces + + + align:start position:0% +building to hold together the the pieces +so that's very positive then the + + align:start position:0% +so that's very positive then the + + + align:start position:0% +so that's very positive then the +question is the magnitude of it and it + + align:start position:0% +question is the magnitude of it and it + + + align:start position:0% +question is the magnitude of it and it +could be that this is overboard just a + + align:start position:0% +could be that this is overboard just a + + + align:start position:0% +could be that this is overboard just a +little bit and you could draw back on + + align:start position:0% +little bit and you could draw back on + + + align:start position:0% +little bit and you could draw back on +it um at the same time I think you very + + align:start position:0% +it um at the same time I think you very + + + align:start position:0% +it um at the same time I think you very +ingeniously have figured out a way of + + align:start position:0% +ingeniously have figured out a way of + + + align:start position:0% +ingeniously have figured out a way of +meeting this to this by making this + + align:start position:0% +meeting this to this by making this + + + align:start position:0% +meeting this to this by making this +little place for the tree which I think + + align:start position:0% +little place for the tree which I think + + + align:start position:0% +little place for the tree which I think +is terrific and producing the Little + + align:start position:0% +is terrific and producing the Little + + + align:start position:0% +is terrific and producing the Little +Secret + + align:start position:0% +Secret + + + align:start position:0% +Secret +Garden but where I don't think it works + + align:start position:0% +Garden but where I don't think it works + + + align:start position:0% +Garden but where I don't think it works +is where you think of this as being + + align:start position:0% +is where you think of this as being + + + align:start position:0% +is where you think of this as being +covered okay I think the building + + align:start position:0% +covered okay I think the building + + + align:start position:0% +covered okay I think the building +somewhere in here stops and you go + + align:start position:0% +somewhere in here stops and you go + + + align:start position:0% +somewhere in here stops and you go +outside into this space okay and this + + align:start position:0% +outside into this space okay and this + + + align:start position:0% +outside into this space okay and this +guy this little space is to the street + + align:start position:0% +guy this little space is to the street + + + align:start position:0% +guy this little space is to the street +this one is to the building okay so + + align:start position:0% +this one is to the building okay so + + + align:start position:0% +this one is to the building okay so +maybe in there there's a bench or two so + + align:start position:0% +maybe in there there's a bench or two so + + + align:start position:0% +maybe in there there's a bench or two so +I can sit on or in fact all along this + + align:start position:0% +I can sit on or in fact all along this + + + align:start position:0% +I can sit on or in fact all along this +might be benches as a public place this + + align:start position:0% +might be benches as a public place this + + + align:start position:0% +might be benches as a public place this +is given over to the to the uh Street + + align:start position:0% +is given over to the to the uh Street + + + align:start position:0% +is given over to the to the uh Street +the other is given over to the building + + align:start position:0% +the other is given over to the building + + + align:start position:0% +the other is given over to the building +okay so you move in + + align:start position:0% +okay so you move in + + + align:start position:0% +okay so you move in +now that brings me to the and that's why + + align:start position:0% +now that brings me to the and that's why + + + align:start position:0% +now that brings me to the and that's why +I ask you the question you have a very + + align:start position:0% +I ask you the question you have a very + + + align:start position:0% +I ask you the question you have a very +subtle but important problem of + + align:start position:0% +subtle but important problem of + + + align:start position:0% +subtle but important problem of +architecture and that is that you do + + align:start position:0% +architecture and that is that you do + + + align:start position:0% +architecture and that is that you do +have two entrances really there's this + + align:start position:0% +have two entrances really there's this + + + align:start position:0% +have two entrances really there's this +which is very + + align:start position:0% +which is very + + + align:start position:0% +which is very +major and there's this that's important + + align:start position:0% +major and there's this that's important + + + align:start position:0% +major and there's this that's important +for you but is not as major probably as + + align:start position:0% +for you but is not as major probably as + + + align:start position:0% +for you but is not as major probably as +this that would say for me that because + + align:start position:0% +this that would say for me that because + + + align:start position:0% +this that would say for me that because +there's a directionality here that + + align:start position:0% +there's a directionality here that + + + align:start position:0% +there's a directionality here that +you're working with that you need to + + align:start position:0% +you're working with that you need to + + + align:start position:0% +you're working with that you need to +make some forms can I do something with + + align:start position:0% +make some forms can I do something with + + + align:start position:0% +make some forms can I do something with +this you need to do something with + + align:start position:0% +this you need to do something with + + + align:start position:0% +this you need to do something with +this not that necessarily but something + + align:start position:0% +this not that necessarily but something + + + align:start position:0% +this not that necessarily but something +like that that directs me into this + + align:start position:0% +like that that directs me into this + + + align:start position:0% +like that that directs me into this +space a little bit more forceful okay uh + + align:start position:0% +space a little bit more forceful okay uh + + + align:start position:0% +space a little bit more forceful okay uh +even to the point where in the most + + align:start position:0% +even to the point where in the most + + + align:start position:0% +even to the point where in the most +extreme can I have a piece of uh some + + align:start position:0% +extreme can I have a piece of uh some + + + align:start position:0% +extreme can I have a piece of uh some +toys + + align:start position:0% +toys + + + align:start position:0% +toys +yeah this is Extreme but even to the + + align:start position:0% +yeah this is Extreme but even to the + + + align:start position:0% +yeah this is Extreme but even to the +point I don't mean it like this even to + + align:start position:0% +point I don't mean it like this even to + + + align:start position:0% +point I don't mean it like this even to +the point where it says I come to this + + align:start position:0% +the point where it says I come to this + + + align:start position:0% +the point where it says I come to this +point and I'm directed in into slipping + + align:start position:0% +point and I'm directed in into slipping + + + align:start position:0% +point and I'm directed in into slipping +into the space here at the same time I + + align:start position:0% +into the space here at the same time I + + + align:start position:0% +into the space here at the same time I +can go in here but this is probably the + + align:start position:0% +can go in here but this is probably the + + + align:start position:0% +can go in here but this is probably the +one that I think I'm going to go into if + + align:start position:0% +one that I think I'm going to go into if + + + align:start position:0% +one that I think I'm going to go into if +I don't know the building so I think you + + align:start position:0% +I don't know the building so I think you + + + align:start position:0% +I don't know the building so I think you +need to pronounce that more and I'm + + align:start position:0% +need to pronounce that more and I'm + + + align:start position:0% +need to pronounce that more and I'm +going to be leading up to something here + + align:start position:0% +going to be leading up to something here + + + align:start position:0% +going to be leading up to something here +because the directionality of this could + + align:start position:0% +because the directionality of this could + + + align:start position:0% +because the directionality of this could +be exploited more than what you've done + + align:start position:0% +be exploited more than what you've done + + + align:start position:0% +be exploited more than what you've done +because there is this to work with just + + align:start position:0% +because there is this to work with just + + + align:start position:0% +because there is this to work with just +as you've been working with that however + + align:start position:0% +as you've been working with that however + + + align:start position:0% +as you've been working with that however +at the same time that I say that it + + align:start position:0% +at the same time that I say that it + + + align:start position:0% +at the same time that I say that it +seems to me that coming into this space + + align:start position:0% +seems to me that coming into this space + + + align:start position:0% +seems to me that coming into this space +with this wonderful ramp which is a + + align:start position:0% +with this wonderful ramp which is a + + + align:start position:0% +with this wonderful ramp which is a +twostory or three-story space I can + + align:start position:0% +twostory or three-story space I can + + + align:start position:0% +twostory or three-story space I can +imagine light slipping down alongside of + + align:start position:0% +imagine light slipping down alongside of + + + align:start position:0% +imagine light slipping down alongside of +it uh is also important and even to the + + align:start position:0% +it uh is also important and even to the + + + align:start position:0% +it uh is also important and even to the +point where this ramp might have just + + align:start position:0% +point where this ramp might have just + + + align:start position:0% +point where this ramp might have just +slightly turned to pick me up so I come + + align:start position:0% +slightly turned to pick me up so I come + + + align:start position:0% +slightly turned to pick me up so I come +in when I know the building or come out + + align:start position:0% +in when I know the building or come out + + + align:start position:0% +in when I know the building or come out +by the way it's not only going in it's + + align:start position:0% +by the way it's not only going in it's + + + align:start position:0% +by the way it's not only going in it's +coming out so I come in or I go out + + align:start position:0% +coming out so I come in or I go out + + + align:start position:0% +coming out so I come in or I go out +through this ramp that is a clear kind + + align:start position:0% +through this ramp that is a clear kind + + + align:start position:0% +through this ramp that is a clear kind +of definition I talked to you other day + + align:start position:0% +of definition I talked to you other day + + + align:start position:0% +of definition I talked to you other day +about paths and places this is the clear + + align:start position:0% +about paths and places this is the clear + + + align:start position:0% +about paths and places this is the clear +journey of a path + + align:start position:0% +journey of a path + + + align:start position:0% +journey of a path +moving through your environment and + + align:start position:0% +moving through your environment and + + + align:start position:0% +moving through your environment and +coming down into something so all I'm + + align:start position:0% +coming down into something so all I'm + + + align:start position:0% +coming down into something so all I'm +saying is watch out here that you + + align:start position:0% +saying is watch out here that you + + + align:start position:0% +saying is watch out here that you +don't overdo it yeah you need to get us + + align:start position:0% +don't overdo it yeah you need to get us + + + align:start position:0% +don't overdo it yeah you need to get us +in but you need us to get us in there + + align:start position:0% +in but you need us to get us in there + + + align:start position:0% +in but you need us to get us in there +even more okay and you're not there yet + + align:start position:0% +even more okay and you're not there yet + + + align:start position:0% +even more okay and you're not there yet +in the sense that you haven't worked + + align:start position:0% +in the sense that you haven't worked + + + align:start position:0% +in the sense that you haven't worked +over there yet so it probably will + + align:start position:0% +over there yet so it probably will + + + align:start position:0% +over there yet so it probably will +happen incidentally I think it's + + align:start position:0% +happen incidentally I think it's + + + align:start position:0% +happen incidentally I think it's +incredibly uh uh sensitive of you to try + + align:start position:0% +incredibly uh uh sensitive of you to try + + + align:start position:0% +incredibly uh uh sensitive of you to try +to save the trees and and that's a + + align:start position:0% +to save the trees and and that's a + + + align:start position:0% +to save the trees and and that's a +that's a + + align:start position:0% +that's a + + + align:start position:0% +that's a +plus and not always very easy now the + + align:start position:0% +plus and not always very easy now the + + + align:start position:0% +plus and not always very easy now the +form that you're working with in here um + + align:start position:0% +form that you're working with in here um + + + align:start position:0% +form that you're working with in here um +the forms is terrific except the next go + + align:start position:0% +the forms is terrific except the next go + + + align:start position:0% +the forms is terrific except the next go +around you may find that this is not all + + align:start position:0% +around you may find that this is not all + + + align:start position:0% +around you may find that this is not all +glass Y and for the kids this is a + + align:start position:0% +glass Y and for the kids this is a + + + align:start position:0% +glass Y and for the kids this is a +daycare up here this may be a playground + + align:start position:0% +daycare up here this may be a playground + + + align:start position:0% +daycare up here this may be a playground +for them oh and therefore I can move out + + align:start position:0% +for them oh and therefore I can move out + + + align:start position:0% +for them oh and therefore I can move out +into that space from there oh okay and + + align:start position:0% +into that space from there oh okay and + + + align:start position:0% +into that space from there oh okay and +maybe it's so it doesn't mean you don't + + align:start position:0% +maybe it's so it doesn't mean you don't + + + align:start position:0% +maybe it's so it doesn't mean you don't +do this it may mean that at this corner + + align:start position:0% +do this it may mean that at this corner + + + align:start position:0% +do this it may mean that at this corner +the corner is a good place I go out into + + align:start position:0% +the corner is a good place I go out into + + + align:start position:0% +the corner is a good place I go out into +a a roof Garden here for the kids + + align:start position:0% +a a roof Garden here for the kids + + + align:start position:0% +a a roof Garden here for the kids +otherwise they don't have a place to + + align:start position:0% +otherwise they don't have a place to + + + align:start position:0% +otherwise they don't have a place to +play or they might play down there um + + align:start position:0% +play or they might play down there um + + + align:start position:0% +play or they might play down there um +but they could still have a place here + + align:start position:0% +but they could still have a place here + + + align:start position:0% +but they could still have a place here +as long as it's protected obviously but + + align:start position:0% +as long as it's protected obviously but + + + align:start position:0% +as long as it's protected obviously but +it's a it's a kid little hangout or a + + align:start position:0% +it's a it's a kid little hangout or a + + + align:start position:0% +it's a it's a kid little hangout or a +little secret place which is kind of + + align:start position:0% +little secret place which is kind of + + + align:start position:0% +little secret place which is kind of +neat up in the sky if I were a kid and + + align:start position:0% +neat up in the sky if I were a kid and + + + align:start position:0% +neat up in the sky if I were a kid and +you can look out and watch people + + align:start position:0% +you can look out and watch people + + + align:start position:0% +you can look out and watch people +parties like that yeah so there's a lot + + align:start position:0% +parties like that yeah so there's a lot + + + align:start position:0% +parties like that yeah so there's a lot +of privacy + + align:start position:0% +of privacy + + + align:start position:0% +of privacy +and as we said before as you go up + + align:start position:0% +and as we said before as you go up + + + align:start position:0% +and as we said before as you go up +things are more private so this makes + + align:start position:0% +things are more private so this makes + + + align:start position:0% +things are more private so this makes +this daycare for the kids very private + + align:start position:0% +this daycare for the kids very private + + + align:start position:0% +this daycare for the kids very private +and almost like if you wish they are + + align:start position:0% +and almost like if you wish they are + + + align:start position:0% +and almost like if you wish they are +viewers of the street they watch people + + align:start position:0% +viewers of the street they watch people + + + align:start position:0% +viewers of the street they watch people +go back and forth now let's move over to + + align:start position:0% +go back and forth now let's move over to + + + align:start position:0% +go back and forth now let's move over to +here because I think that's important my + + align:start position:0% +here because I think that's important my + + + align:start position:0% +here because I think that's important my +problem area well it's not yet your + + align:start position:0% +problem area well it's not yet your + + + align:start position:0% +problem area well it's not yet your +problem area but it's your problem area + + align:start position:0% +problem area but it's your problem area + + + align:start position:0% +problem area but it's your problem area +because you haven't done it but I think + + align:start position:0% +because you haven't done it but I think + + + align:start position:0% +because you haven't done it but I think +there's a major uh piece here if I'm + + align:start position:0% +there's a major uh piece here if I'm + + + align:start position:0% +there's a major uh piece here if I'm +reading this + + align:start position:0% +reading this + + + align:start position:0% +reading this +right uh this is still that wall right + + align:start position:0% +right uh this is still that wall right + + + align:start position:0% +right uh this is still that wall right +yes and the tree is here right and the + + align:start position:0% +yes and the tree is here right and the + + + align:start position:0% +yes and the tree is here right and the +other tree is in + + align:start position:0% +other tree is in + + + align:start position:0% +other tree is in +here and there's another tree back here + + align:start position:0% +here and there's another tree back here + + + align:start position:0% +here and there's another tree back here +right and then there's a little bit a + + align:start position:0% +right and then there's a little bit a + + + align:start position:0% +right and then there's a little bit a +little another little tree okay good and + + align:start position:0% +little another little tree okay good and + + + align:start position:0% +little another little tree okay good and +then there's a wall back in here two + + align:start position:0% +then there's a wall back in here two + + + align:start position:0% +then there's a wall back in here two +things that you might consider you have + + align:start position:0% +things that you might consider you have + + + align:start position:0% +things that you might consider you have +this the wall that we talked about and + + align:start position:0% +this the wall that we talked about and + + + align:start position:0% +this the wall that we talked about and +then the opening I'm going through and + + align:start position:0% +then the opening I'm going through and + + + align:start position:0% +then the opening I'm going through and +we talked about all this and I'm going + + align:start position:0% +we talked about all this and I'm going + + + align:start position:0% +we talked about all this and I'm going +under and I mentioned that we need to + + align:start position:0% +under and I mentioned that we need to + + + align:start position:0% +under and I mentioned that we need to +have some kind of a way + + align:start position:0% +have some kind of a way + + + align:start position:0% +have some kind of a way +of getting us there's a tree in here by + + align:start position:0% +of getting us there's a tree in here by + + + align:start position:0% +of getting us there's a tree in here by +the way somewhere into this space all + + align:start position:0% +the way somewhere into this space all + + + align:start position:0% +the way somewhere into this space all +that's + + align:start position:0% +that's + + + align:start position:0% +that's +fine and I'm above it then is this + + align:start position:0% +fine and I'm above it then is this + + + align:start position:0% +fine and I'm above it then is this +passage way that is coming to a point + + align:start position:0% +passage way that is coming to a point + + + align:start position:0% +passage way that is coming to a point +and then either by ramp in the same way + + align:start position:0% +and then either by ramp in the same way + + + align:start position:0% +and then either by ramp in the same way +it comes down into this and it would be + + align:start position:0% +it comes down into this and it would be + + + align:start position:0% +it comes down into this and it would be +interesting if there's a way you could + + align:start position:0% +interesting if there's a way you could + + + align:start position:0% +interesting if there's a way you could +make that ramp then part of + + align:start position:0% +make that ramp then part of + + + align:start position:0% +make that ramp then part of +seats which then relates to your + + align:start position:0% +seats which then relates to your + + + align:start position:0% +seats which then relates to your +Amphitheater which is here if you you + + align:start position:0% +Amphitheater which is here if you you + + + align:start position:0% +Amphitheater which is here if you you +can do that um so then I have a + + align:start position:0% +can do that um so then I have a + + + align:start position:0% +can do that um so then I have a +continuous experience coming down if you + + align:start position:0% +continuous experience coming down if you + + + align:start position:0% +continuous experience coming down if you +can't make that happen then maybe this + + align:start position:0% +can't make that happen then maybe this + + + align:start position:0% +can't make that happen then maybe this +ramp comes along across and there's some + + align:start position:0% +ramp comes along across and there's some + + + align:start position:0% +ramp comes along across and there's some +major kind of spal stairs like the uh + + align:start position:0% +major kind of spal stairs like the uh + + + align:start position:0% +major kind of spal stairs like the uh +one over the memorial uh Star Drive that + + align:start position:0% +one over the memorial uh Star Drive that + + + align:start position:0% +one over the memorial uh Star Drive that +gets me down and out into this space + + align:start position:0% +gets me down and out into this space + + + align:start position:0% +gets me down and out into this space +because this is really the center of the + + align:start position:0% +because this is really the center of the + + + align:start position:0% +because this is really the center of the +life for you an outside this is inside + + align:start position:0% +life for you an outside this is inside + + + align:start position:0% +life for you an outside this is inside +but the point that I want to make is + + align:start position:0% +but the point that I want to make is + + + align:start position:0% +but the point that I want to make is +that the building is + + align:start position:0% +that the building is + + + align:start position:0% +that the building is +let me just move this slightly is + + align:start position:0% +let me just move this slightly is + + + align:start position:0% +let me just move this slightly is +here and you have this space that we + + align:start position:0% +here and you have this space that we + + + align:start position:0% +here and you have this space that we +talked about + + align:start position:0% +talked about + + + align:start position:0% +talked about +before it seems to me still that since + + align:start position:0% +before it seems to me still that since + + + align:start position:0% +before it seems to me still that since +there's a tremendous notion here that + + align:start position:0% +there's a tremendous notion here that + + + align:start position:0% +there's a tremendous notion here that +there's a wall of different kinds that + + align:start position:0% +there's a wall of different kinds that + + + align:start position:0% +there's a wall of different kinds that +are coming along the street that we + + align:start position:0% +are coming along the street that we + + + align:start position:0% +are coming along the street that we +still might see something here that is + + align:start position:0% +still might see something here that is + + + align:start position:0% +still might see something here that is +not obviously nearly as opaque as is + + align:start position:0% +not obviously nearly as opaque as is + + + align:start position:0% +not obviously nearly as opaque as is +maybe much lower but is collected to + + align:start position:0% +maybe much lower but is collected to + + + align:start position:0% +maybe much lower but is collected to +this in some way so that the corner is + + align:start position:0% +this in some way so that the corner is + + + align:start position:0% +this in some way so that the corner is +not turned + + align:start position:0% +not turned + + + align:start position:0% +not turned +drastically maybe this is low maybe this + + align:start position:0% +drastically maybe this is low maybe this + + + align:start position:0% +drastically maybe this is low maybe this +is translucent I can see through and + + align:start position:0% +is translucent I can see through and + + + align:start position:0% +is translucent I can see through and +then this becomes which is what I think + + align:start position:0% +then this becomes which is what I think + + + align:start position:0% +then this becomes which is what I think +you want something of a secret uh Garden + + align:start position:0% +you want something of a secret uh Garden + + + align:start position:0% +you want something of a secret uh Garden +to hang out in yeah which is not + + align:start position:0% +to hang out in yeah which is not + + + align:start position:0% +to hang out in yeah which is not +necessarily connected to this or could + + align:start position:0% +necessarily connected to this or could + + + align:start position:0% +necessarily connected to this or could +be now here comes the piece that I think + + align:start position:0% +be now here comes the piece that I think + + + align:start position:0% +be now here comes the piece that I think +could be + + align:start position:0% +could be + + + align:start position:0% +could be +interesting if these guys these trees + + align:start position:0% +interesting if these guys these trees + + + align:start position:0% +interesting if these guys these trees +are here then maybe this building does + + align:start position:0% +are here then maybe this building does + + + align:start position:0% +are here then maybe this building does +this + + align:start position:0% +this + + + align:start position:0% +this +and this part is + + align:start position:0% +and this part is + + + align:start position:0% +and this part is +outside so that when I'm in this + + align:start position:0% +outside so that when I'm in this + + + align:start position:0% +outside so that when I'm in this +space I'm let letting the trees to be + + align:start position:0% +space I'm let letting the trees to be + + + align:start position:0% +space I'm let letting the trees to be +outside and I'm also providing a way of + + align:start position:0% +outside and I'm also providing a way of + + + align:start position:0% +outside and I'm also providing a way of +getting into this building or + + align:start position:0% +getting into this building or + + + align:start position:0% +getting into this building or +out from the street or this would still + + align:start position:0% +out from the street or this would still + + + align:start position:0% +out from the street or this would still +be cut off no this would still be here + + align:start position:0% +be cut off no this would still be here + + + align:start position:0% +be cut off no this would still be here +but all I'm saying is that in order to + + align:start position:0% +but all I'm saying is that in order to + + + align:start position:0% +but all I'm saying is that in order to +keep that tree which you want to do yeah + + align:start position:0% +keep that tree which you want to do yeah + + + align:start position:0% +keep that tree which you want to do yeah +maybe it's part of this space and it's + + align:start position:0% +maybe it's part of this space and it's + + + align:start position:0% +maybe it's part of this space and it's +also a way of making the transition as + + align:start position:0% +also a way of making the transition as + + + align:start position:0% +also a way of making the transition as +another entrance or exit from this + + align:start position:0% +another entrance or exit from this + + + align:start position:0% +another entrance or exit from this +building into this + + align:start position:0% +building into this + + + align:start position:0% +building into this +space as opposed to which is what you + + align:start position:0% +space as opposed to which is what you + + + align:start position:0% +space as opposed to which is what you +were suggesting which was to Coral + + align:start position:0% +were suggesting which was to Coral + + + align:start position:0% +were suggesting which was to Coral +it or build something around it + + align:start position:0% +it or build something around it + + + align:start position:0% +it or build something around it +basically and then hope that um it's + + align:start position:0% +basically and then hope that um it's + + + align:start position:0% +basically and then hope that um it's +going to be uh it's it's not going to + + align:start position:0% +going to be uh it's it's not going to + + + align:start position:0% +going to be uh it's it's not going to +live inside by the way it has to be + + align:start position:0% +live inside by the way it has to be + + + align:start position:0% +live inside by the way it has to be +outside somehow you could make a + + align:start position:0% +outside somehow you could make a + + + align:start position:0% +outside somehow you could make a +courtyard out of it but I think the you + + align:start position:0% +courtyard out of it but I think the you + + + align:start position:0% +courtyard out of it but I think the you +got a bum pencil hand I think the + + align:start position:0% +got a bum pencil hand I think the + + + align:start position:0% +got a bum pencil hand I think the +courtyard is + + align:start position:0% +courtyard is + + + align:start position:0% +courtyard is +um is too close close to the other + + align:start position:0% +um is too close close to the other + + + align:start position:0% +um is too close close to the other +Courtyard yeah to make any sense um so + + align:start position:0% +Courtyard yeah to make any sense um so + + + align:start position:0% +Courtyard yeah to make any sense um so +instead of a courtyard here and a + + align:start position:0% +instead of a courtyard here and a + + + align:start position:0% +instead of a courtyard here and a +courtyard here it might be combined okay + + align:start position:0% +courtyard here it might be combined okay + + + align:start position:0% +courtyard here it might be combined okay +now in the vest + + align:start position:0% +now in the vest + + + align:start position:0% +now in the vest +World maybe this tree if you more + + align:start position:0% +World maybe this tree if you more + + + align:start position:0% +World maybe this tree if you more +accurate the two trees so that this is + + align:start position:0% +accurate the two trees so that this is + + + align:start position:0% +accurate the two trees so that this is +more of a tiny triangle or chunk out of + + align:start position:0% +more of a tiny triangle or chunk out of + + + align:start position:0% +more of a tiny triangle or chunk out of +this yeah as opposed to the one I just + + align:start position:0% +this yeah as opposed to the one I just + + + align:start position:0% +this yeah as opposed to the one I just +drew but I don't know we have to see + + align:start position:0% +drew but I don't know we have to see + + + align:start position:0% +drew but I don't know we have to see +what it is and then you still have that + + align:start position:0% +what it is and then you still have that + + + align:start position:0% +what it is and then you still have that +so now I have this kind of relationship + + align:start position:0% +so now I have this kind of relationship + + + align:start position:0% +so now I have this kind of relationship +from this and by the way you you said + + align:start position:0% +from this and by the way you you said + + + align:start position:0% +from this and by the way you you said +there'd be a hedge here so now I'm + + align:start position:0% +there'd be a hedge here so now I'm + + + align:start position:0% +there'd be a hedge here so now I'm +saying there's some kind of translucent + + align:start position:0% +saying there's some kind of translucent + + + align:start position:0% +saying there's some kind of translucent +wall in here I can see through I can see + + align:start position:0% +wall in here I can see through I can see + + + align:start position:0% +wall in here I can see through I can see +people they're playing chess Etc but + + align:start position:0% +people they're playing chess Etc but + + + align:start position:0% +people they're playing chess Etc but +maybe there's something else in here + + align:start position:0% +maybe there's something else in here + + + align:start position:0% +maybe there's something else in here +there's water I don't know what that + + align:start position:0% +there's water I don't know what that + + + align:start position:0% +there's water I don't know what that +acts as a focus of this but because the + + align:start position:0% +acts as a focus of this but because the + + + align:start position:0% +acts as a focus of this but because the +trees are Marching along I'm putting + + align:start position:0% +trees are Marching along I'm putting + + + align:start position:0% +trees are Marching along I'm putting +another one here MH this space is + + align:start position:0% +another one here MH this space is + + + align:start position:0% +another one here MH this space is +marching into this one yeah and then I'm + + align:start position:0% +marching into this one yeah and then I'm + + + align:start position:0% +marching into this one yeah and then I'm +into that and by the way even better if + + align:start position:0% +into that and by the way even better if + + + align:start position:0% +into that and by the way even better if +I could figure out a way that I can at + + align:start position:0% +I could figure out a way that I can at + + + align:start position:0% +I could figure out a way that I can at +this point see right through this + + align:start position:0% +this point see right through this + + + align:start position:0% +this point see right through this +building and out into the amphitheater + + align:start position:0% +building and out into the amphitheater + + + align:start position:0% +building and out into the amphitheater +so then I get a continuous experience + + align:start position:0% +so then I get a continuous experience + + + align:start position:0% +so then I get a continuous experience +between the hardness I'll say for the + + align:start position:0% +between the hardness I'll say for the + + + align:start position:0% +between the hardness I'll say for the +moment of the amphitheater to the inside + + align:start position:0% +moment of the amphitheater to the inside + + + align:start position:0% +moment of the amphitheater to the inside +to a transition into this very quiet + + align:start position:0% +to a transition into this very quiet + + + align:start position:0% +to a transition into this very quiet +Garden which might have water I guess we + + align:start position:0% +Garden which might have water I guess we + + + align:start position:0% +Garden which might have water I guess we +talked about that before um so there's + + align:start position:0% +talked about that before um so there's + + + align:start position:0% +talked about that before um so there's +different experiences along the way but + + align:start position:0% +different experiences along the way but + + + align:start position:0% +different experiences along the way but +they're all connected there's two + + align:start position:0% +they're all connected there's two + + + align:start position:0% +they're all connected there's two +connections that you got one is the the + + align:start position:0% +connections that you got one is the the + + + align:start position:0% +connections that you got one is the the +screen will caught along the street and + + align:start position:0% +screen will caught along the street and + + + align:start position:0% +screen will caught along the street and +the other one is your ingenious ramp + + align:start position:0% +the other one is your ingenious ramp + + + align:start position:0% +the other one is your ingenious ramp +that was Ming through down and around + + align:start position:0% +that was Ming through down and around + + + align:start position:0% +that was Ming through down and around +into + + align:start position:0% +into + + + align:start position:0% +into +this now tell me again is this I + + align:start position:0% +this now tell me again is this I + + + align:start position:0% +this now tell me again is this I +forgotten is this guy two stories + + align:start position:0% +forgotten is this guy two stories + + + align:start position:0% +forgotten is this guy two stories +building it'll be two or three I'm not + + align:start position:0% +building it'll be two or three I'm not + + + align:start position:0% +building it'll be two or three I'm not +sure yet um I was I was envisioning + + align:start position:0% +sure yet um I was I was envisioning + + + align:start position:0% +sure yet um I was I was envisioning +three because I was seeing again this of + + align:start position:0% +three because I was seeing again this of + + + align:start position:0% +three because I was seeing again this of +stepping I wanted to to mimic that here + + align:start position:0% +stepping I wanted to to mimic that here + + + align:start position:0% +stepping I wanted to to mimic that here +sort of an echo of it um and and also + + align:start position:0% +sort of an echo of it um and and also + + + align:start position:0% +sort of an echo of it um and and also +mimic sort of the the as a stadium as a + + align:start position:0% +mimic sort of the the as a stadium as a + + + align:start position:0% +mimic sort of the the as a stadium as a +Amphitheater um but I'm I'm until I sort + + align:start position:0% +Amphitheater um but I'm I'm until I sort + + + align:start position:0% +Amphitheater um but I'm I'm until I sort +of tackle that I don't know um but I was + + align:start position:0% +of tackle that I don't know um but I was + + + align:start position:0% +of tackle that I don't know um but I was +envisioning three stories I I talked to + + align:start position:0% +envisioning three stories I I talked to + + + align:start position:0% +envisioning three stories I I talked to +you last time about hierarchy and I was + + align:start position:0% +you last time about hierarchy and I was + + + align:start position:0% +you last time about hierarchy and I was +worried that um I was missing out on on + + align:start position:0% +worried that um I was missing out on on + + + align:start position:0% +worried that um I was missing out on on +the hierarchy if the two buildings are + + align:start position:0% +the hierarchy if the two buildings are + + + align:start position:0% +the hierarchy if the two buildings are +the same sort of height um so I might + + align:start position:0% +the same sort of height um so I might + + + align:start position:0% +the same sort of height um so I might +lose that but maybe if if I can if I can + + align:start position:0% +lose that but maybe if if I can if I can + + + align:start position:0% +lose that but maybe if if I can if I can +emphasize this as being space then that + + align:start position:0% +emphasize this as being space then that + + + align:start position:0% +emphasize this as being space then that +would be my hierarchy and I won't need + + align:start position:0% +would be my hierarchy and I won't need + + + align:start position:0% +would be my hierarchy and I won't need +to um but what we talked about before + + align:start position:0% +to um but what we talked about before + + + align:start position:0% +to um but what we talked about before +too is that + + align:start position:0% +too is that + + + align:start position:0% +too is that +the the roofs if it's a second story + + align:start position:0% +the the roofs if it's a second story + + + align:start position:0% +the the roofs if it's a second story +building which is going to interfere + + align:start position:0% +building which is going to interfere + + + align:start position:0% +building which is going to interfere +with this thing coming across so this + + align:start position:0% +with this thing coming across so this + + + align:start position:0% +with this thing coming across so this +thing May slip behind it could be seats + + align:start position:0% +thing May slip behind it could be seats + + + align:start position:0% +thing May slip behind it could be seats +for the Ampitheater and then there's + + align:start position:0% +for the Ampitheater and then there's + + + align:start position:0% +for the Ampitheater and then there's +seats down here also for the + + align:start position:0% +seats down here also for the + + + align:start position:0% +seats down here also for the +Ampitheater so that the side of this + + align:start position:0% +Ampitheater so that the side of this + + + align:start position:0% +Ampitheater so that the side of this +building although it's got transparency + + align:start position:0% +building although it's got transparency + + + align:start position:0% +building although it's got transparency +moving into the space but the side of + + align:start position:0% +moving into the space but the side of + + + align:start position:0% +moving into the space but the side of +that building is actually moving up from + + align:start position:0% +that building is actually moving up from + + + align:start position:0% +that building is actually moving up from +the + + align:start position:0% +the + + + align:start position:0% +the +landscape making a kind of a bowl shape + + align:start position:0% +landscape making a kind of a bowl shape + + + align:start position:0% +landscape making a kind of a bowl shape +and I think that's very powerful because + + align:start position:0% +and I think that's very powerful because + + + align:start position:0% +and I think that's very powerful because +you're putting an incredible amount of + + align:start position:0% +you're putting an incredible amount of + + + align:start position:0% +you're putting an incredible amount of +of U energy or um activity on this in + + align:start position:0% +of U energy or um activity on this in + + + align:start position:0% +of U energy or um activity on this in +other words when we're all done this is + + align:start position:0% +other words when we're all done this is + + + align:start position:0% +other words when we're all done this is +probably the place where you come uh to + + align:start position:0% +probably the place where you come uh to + + + align:start position:0% +probably the place where you come uh to +have an event obviously but also kind of + + align:start position:0% +have an event obviously but also kind of + + + align:start position:0% +have an event obviously but also kind of +a meeting place this is a place uh where + + align:start position:0% +a meeting place this is a place uh where + + + align:start position:0% +a meeting place this is a place uh where +and the kids might play in here and run + + align:start position:0% +and the kids might play in here and run + + + align:start position:0% +and the kids might play in here and run +around yeah this is probably the quiet + + align:start position:0% +around yeah this is probably the quiet + + + align:start position:0% +around yeah this is probably the quiet +place m uh whether as you said play + + align:start position:0% +place m uh whether as you said play + + + align:start position:0% +place m uh whether as you said play +checkers or whatever and it's wonderful + + align:start position:0% +checkers or whatever and it's wonderful + + + align:start position:0% +checkers or whatever and it's wonderful +and in + + align:start position:0% +and in + + + align:start position:0% +and in +fact maybe this even becomes more green + + align:start position:0% +fact maybe this even becomes more green + + + align:start position:0% +fact maybe this even becomes more green +in relationship to this I'm somewhat of + + align:start position:0% +in relationship to this I'm somewhat of + + + align:start position:0% +in relationship to this I'm somewhat of +the sunlight since most of the sunlight + + align:start position:0% +the sunlight since most of the sunlight + + + align:start position:0% +the sunlight since most of the sunlight +would be coming in through here right um + + align:start position:0% +would be coming in through here right um + + + align:start position:0% +would be coming in through here right um +I'm I'm also thinking of stepping it + + align:start position:0% +I'm I'm also thinking of stepping it + + + align:start position:0% +I'm I'm also thinking of stepping it +down towards this building so that maybe + + align:start position:0% +down towards this building so that maybe + + + align:start position:0% +down towards this building so that maybe +the sunlight could go right in that + + align:start position:0% +the sunlight could go right in that + + + align:start position:0% +the sunlight could go right in that +corner and and enter into this space + + align:start position:0% +corner and and enter into this space + + + align:start position:0% +corner and and enter into this space +well I'd be careful I'll tell you why + + align:start position:0% +well I'd be careful I'll tell you why + + + align:start position:0% +well I'd be careful I'll tell you why +you're defining this space and it does + + align:start position:0% +you're defining this space and it does + + + align:start position:0% +you're defining this space and it does +have two good + + align:start position:0% +have two good + + + align:start position:0% +have two good +definitions this by having the wall up + + align:start position:0% +definitions this by having the wall up + + + align:start position:0% +definitions this by having the wall up +at that point there's a slippage there + + align:start position:0% +at that point there's a slippage there + + + align:start position:0% +at that point there's a slippage there +which is fine um makes it more contained + + align:start position:0% +which is fine um makes it more contained + + + align:start position:0% +which is fine um makes it more contained +if you start stepping it down you may + + align:start position:0% +if you start stepping it down you may + + + align:start position:0% +if you start stepping it down you may +start to lose some of that containment + + align:start position:0% +start to lose some of that containment + + + align:start position:0% +start to lose some of that containment +okay and this is different kind of a + + align:start position:0% +okay and this is different kind of a + + + align:start position:0% +okay and this is different kind of a +space in this I don't think this is uh + + align:start position:0% +space in this I don't think this is uh + + + align:start position:0% +space in this I don't think this is uh +here this backyard space Little Secret + + align:start position:0% +here this backyard space Little Secret + + + align:start position:0% +here this backyard space Little Secret +Garden is fine that slips out I'm not so + + align:start position:0% +Garden is fine that slips out I'm not so + + + align:start position:0% +Garden is fine that slips out I'm not so +sure that this one wants to slip out as + + align:start position:0% +sure that this one wants to slip out as + + + align:start position:0% +sure that this one wants to slip out as +much but I would invite you to to take + + align:start position:0% +much but I would invite you to to take + + + align:start position:0% +much but I would invite you to to take +the model and a luxa lamp or any light + + align:start position:0% +the model and a luxa lamp or any light + + + align:start position:0% +the model and a luxa lamp or any light +and follow the sun yeah just want that's + + align:start position:0% +and follow the sun yeah just want that's + + + align:start position:0% +and follow the sun yeah just want that's +that's perfect that's a sun and follow + + align:start position:0% +that's perfect that's a sun and follow + + + align:start position:0% +that's perfect that's a sun and follow +the Sun and see what it does because the + + align:start position:0% +the Sun and see what it does because the + + + align:start position:0% +the Sun and see what it does because the +next step would be to + + align:start position:0% +next step would be to + + + align:start position:0% +next step would be to +consider if the Sun for instance is + + align:start position:0% +consider if the Sun for instance is + + + align:start position:0% +consider if the Sun for instance is +coming over the + + align:start position:0% +coming over the + + + align:start position:0% +coming over the +building then on this side of the where + + align:start position:0% +building then on this side of the where + + + align:start position:0% +building then on this side of the where +am I am I no I + + align:start position:0% +am I am I no I + + + align:start position:0% +am I am I no I +got the vent building + + align:start position:0% +got the vent building + + + align:start position:0% +got the vent building +there might be panels that can divert + + align:start position:0% +there might be panels that can divert + + + align:start position:0% +there might be panels that can divert +the light down into here or if the sun + + align:start position:0% +the light down into here or if the sun + + + align:start position:0% +the light down into here or if the sun +is coming this way there might be panels + + align:start position:0% +is coming this way there might be panels + + + align:start position:0% +is coming this way there might be panels +that on the side of the building that's + + align:start position:0% +that on the side of the building that's + + + align:start position:0% +that on the side of the building that's +vertical that can divert bounce the + + align:start position:0% +vertical that can divert bounce the + + + align:start position:0% +vertical that can divert bounce the +light down we talked + + align:start position:0% +light down we talked + + + align:start position:0% +light down we talked +about um I doubt you're going to get + + align:start position:0% +about um I doubt you're going to get + + + align:start position:0% +about um I doubt you're going to get +much sun down into here period but you + + align:start position:0% +much sun down into here period but you + + + align:start position:0% +much sun down into here period but you +are going to probably get sun up above + + align:start position:0% +are going to probably get sun up above + + + align:start position:0% +are going to probably get sun up above +so these + + align:start position:0% +so these + + + align:start position:0% +so these +panels or even yeah so these panels + + align:start position:0% +panels or even yeah so these panels + + + align:start position:0% +panels or even yeah so these panels +maybe are up here that are catching the + + align:start position:0% +maybe are up here that are catching the + + + align:start position:0% +maybe are up here that are catching the +Sun and bringing it down so there's + + align:start position:0% +Sun and bringing it down so there's + + + align:start position:0% +Sun and bringing it down so there's +another uhhuh so there's a whole another + + align:start position:0% +another uhhuh so there's a whole another + + + align:start position:0% +another uhhuh so there's a whole another +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +design notion here that we haven't + + align:start position:0% +design notion here that we haven't + + + align:start position:0% +design notion here that we haven't +talked + + align:start position:0% +talked + + + align:start position:0% +talked +about all this is this let's assume it's + + align:start position:0% +about all this is this let's assume it's + + + align:start position:0% +about all this is this let's assume it's +all done then there may be up around + + align:start position:0% +all done then there may be up around + + + align:start position:0% +all done then there may be up around +this building which is there's going to + + align:start position:0% +this building which is there's going to + + + align:start position:0% +this building which is there's going to +be uh a streen on this right but even + + align:start position:0% +be uh a streen on this right but even + + + align:start position:0% +be uh a streen on this right but even +above that there might be panels that + + align:start position:0% +above that there might be panels that + + + align:start position:0% +above that there might be panels that +are bouncing light all the way around at + + align:start position:0% +are bouncing light all the way around at + + + align:start position:0% +are bouncing light all the way around at +a certain hype which is another form of + + align:start position:0% +a certain hype which is another form of + + + align:start position:0% +a certain hype which is another form of +architecture sky form actually and I'm + + align:start position:0% +architecture sky form actually and I'm + + + align:start position:0% +architecture sky form actually and I'm +catching the sun bouncing like down into + + align:start position:0% +catching the sun bouncing like down into + + + align:start position:0% +catching the sun bouncing like down into +what I think is your major place this + + align:start position:0% +what I think is your major place this + + + align:start position:0% +what I think is your major place this +one not here this is cool green Shady + + align:start position:0% +one not here this is cool green Shady + + + align:start position:0% +one not here this is cool green Shady +quiet this is alive light hot sunny just + + align:start position:0% +quiet this is alive light hot sunny just + + + align:start position:0% +quiet this is alive light hot sunny just +the opposite yeah but beyond that and of + + align:start position:0% +the opposite yeah but beyond that and of + + + align:start position:0% +the opposite yeah but beyond that and of +course we should be using the Sun as + + align:start position:0% +course we should be using the Sun as + + + align:start position:0% +course we should be using the Sun as +much as we can beyond that um this is an + + align:start position:0% +much as we can beyond that um this is an + + + align:start position:0% +much as we can beyond that um this is an +architectural never AR another + + align:start position:0% +architectural never AR another + + + align:start position:0% +architectural never AR another +architectural + + align:start position:0% +architectural + + + align:start position:0% +architectural +continuity so it's not only bouncing the + + align:start position:0% +continuity so it's not only bouncing the + + + align:start position:0% +continuity so it's not only bouncing the +Sun but it's it's something else I I + + align:start position:0% +Sun but it's it's something else I I + + + align:start position:0% +Sun but it's it's something else I I +like the way that the the site or the + + align:start position:0% +like the way that the the site or the + + + align:start position:0% +like the way that the the site or the +the way that this is laid out right now + + align:start position:0% +the way that this is laid out right now + + + align:start position:0% +the way that this is laid out right now +is is sort of hugging itself like this + + align:start position:0% +is is sort of hugging itself like this + + + align:start position:0% +is is sort of hugging itself like this +is quiet here's Qui and then there the + + align:start position:0% +is quiet here's Qui and then there the + + + align:start position:0% +is quiet here's Qui and then there the +busy activities s of in the summer + + align:start position:0% +busy activities s of in the summer + + + align:start position:0% +busy activities s of in the summer +and it it feels like it's getting there + + align:start position:0% +and it it feels like it's getting there + + + align:start position:0% +and it it feels like it's getting there +contining a little + + align:start position:0% +contining a little + + + align:start position:0% +contining a little +bit I think the organization is just + + align:start position:0% +bit I think the organization is just + + + align:start position:0% +bit I think the organization is just +right um the the way you have fed it I + + align:start position:0% +right um the the way you have fed it I + + + align:start position:0% +right um the the way you have fed it I +think the architectural language that + + align:start position:0% +think the architectural language that + + + align:start position:0% +think the architectural language that +you're starting to develop is the + + align:start position:0% +you're starting to develop is the + + + align:start position:0% +you're starting to develop is the +beginning I would move on now quickly to + + align:start position:0% +beginning I would move on now quickly to + + + align:start position:0% +beginning I would move on now quickly to +here y uh and I happen to know from + + align:start position:0% +here y uh and I happen to know from + + + align:start position:0% +here y uh and I happen to know from +experience that this ramp is not going + + align:start position:0% +experience that this ramp is not going + + + align:start position:0% +experience that this ramp is not going +to be as nice as you think it's going to + + align:start position:0% +to be as nice as you think it's going to + + + align:start position:0% +to be as nice as you think it's going to +take a little working to make it work + + align:start position:0% +take a little working to make it work + + + align:start position:0% +take a little working to make it work +but is it powerful notion that the ramp + + align:start position:0% +but is it powerful notion that the ramp + + + align:start position:0% +but is it powerful notion that the ramp +is is an + + align:start position:0% + + + + align:start position:0% + +organizer \ No newline at end of file diff --git a/2P-yW7LQr08.txt b/2P-yW7LQr08.txt new file mode 100644 index 0000000000000000000000000000000000000000..4745658af1d5318170d8d42e5192e9b772332ac3 --- /dev/null +++ b/2P-yW7LQr08.txt @@ -0,0 +1,12978 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so uh welcome to + + align:start position:0% +ocw.mit.edu so uh welcome to + + + align:start position:0% +ocw.mit.edu so uh welcome to +6046 my name is shini deas I'm a + + align:start position:0% +6046 my name is shini deas I'm a + + + align:start position:0% +6046 my name is shini deas I'm a +professor of computer science uh this is + + align:start position:0% +professor of computer science uh this is + + + align:start position:0% +professor of computer science uh this is +my 27th year at + + align:start position:0% +my 27th year at + + + align:start position:0% +my 27th year at +MIT I'm uh teaching this class with the + + align:start position:0% +MIT I'm uh teaching this class with the + + + align:start position:0% +MIT I'm uh teaching this class with the +great core staff uh with uh co- + + align:start position:0% +great core staff uh with uh co- + + + align:start position:0% +great core staff uh with uh co- +lecturers Eric Dain over + + align:start position:0% +lecturers Eric Dain over + + + align:start position:0% +lecturers Eric Dain over +here and uh Nancy Lynch who's over there + + align:start position:0% +here and uh Nancy Lynch who's over there + + + align:start position:0% +here and uh Nancy Lynch who's over there +and a whole bunch of Tas who you will + + align:start position:0% +and a whole bunch of Tas who you will + + + align:start position:0% +and a whole bunch of Tas who you will +meet through the term uh we just signed + + align:start position:0% +meet through the term uh we just signed + + + align:start position:0% +meet through the term uh we just signed +up our uh uh last ta yesterday so at + + align:start position:0% +up our uh uh last ta yesterday so at + + + align:start position:0% +up our uh uh last ta yesterday so at +this point even I don't know their + + align:start position:0% +this point even I don't know their + + + align:start position:0% +this point even I don't know their +names uh but uh we hope to have a great + + align:start position:0% +names uh but uh we hope to have a great + + + align:start position:0% +names uh but uh we hope to have a great +semester I I'm very excited to be + + align:start position:0% +semester I I'm very excited to be + + + align:start position:0% +semester I I'm very excited to be +teaching this class with Eric and Nancy + + align:start position:0% +teaching this class with Eric and Nancy + + + align:start position:0% +teaching this class with Eric and Nancy +I recognize some of you folks from 006 + + align:start position:0% +I recognize some of you folks from 006 + + + align:start position:0% +I recognize some of you folks from 006 +from a year ago uh so hello again and + + align:start position:0% +from a year ago uh so hello again and + + + align:start position:0% +from a year ago uh so hello again and +from other classes uh and so uh let's + + align:start position:0% +from other classes uh and so uh let's + + + align:start position:0% +from other classes uh and so uh let's +get started um I mentioned 006 uh6 is a + + align:start position:0% +get started um I mentioned 006 uh6 is a + + + align:start position:0% +get started um I mentioned 006 uh6 is a +prerequisite for this class uh so if uh + + align:start position:0% +prerequisite for this class uh so if uh + + + align:start position:0% +prerequisite for this class uh so if uh +by chance you've skip the class uh MIT + + align:start position:0% +by chance you've skip the class uh MIT + + + align:start position:0% +by chance you've skip the class uh MIT +or ECS has allowed you to skip that uh + + align:start position:0% +or ECS has allowed you to skip that uh + + + align:start position:0% +or ECS has allowed you to skip that uh +make sure um you check in with us uh to + + align:start position:0% +make sure um you check in with us uh to + + + align:start position:0% +make sure um you check in with us uh to +see that U you are ready for uh 6046 + + align:start position:0% +see that U you are ready for uh 6046 + + + align:start position:0% +see that U you are ready for uh 6046 +because we will assume that you know the + + align:start position:0% +because we will assume that you know the + + + align:start position:0% +because we will assume that you know the + + align:start position:0% + + + align:start position:0% +material and by that I mean uh basic + + align:start position:0% +material and by that I mean uh basic + + + align:start position:0% +material and by that I mean uh basic +material on uh data structures classical + + align:start position:0% +material on uh data structures classical + + + align:start position:0% +material on uh data structures classical +algorithms like + + align:start position:0% +algorithms like + + + align:start position:0% +algorithms like +sorting uh algorithms for um uh for + + align:start position:0% +sorting uh algorithms for um uh for + + + align:start position:0% +sorting uh algorithms for um uh for +dynamic programming or algorithms that + + align:start position:0% +dynamic programming or algorithms that + + + align:start position:0% +dynamic programming or algorithms that +use dynamic programming I should say + + align:start position:0% +use dynamic programming I should say + + + align:start position:0% +use dynamic programming I should say +algorithms for shortest paths uh Etc uh + + align:start position:0% +algorithms for shortest paths uh Etc uh + + + align:start position:0% +algorithms for shortest paths uh Etc uh +6046 itself uh we're going to run this + + align:start position:0% +6046 itself uh we're going to run this + + + align:start position:0% +6046 itself uh we're going to run this +course uh pretty much off the Stellar + + align:start position:0% +course uh pretty much off the Stellar + + + align:start position:0% +course uh pretty much off the Stellar +website uh in the sense that uh that'll + + align:start position:0% +website uh in the sense that uh that'll + + + align:start position:0% +website uh in the sense that uh that'll +be your uh One-Stop shop for getting + + align:start position:0% +be your uh One-Stop shop for getting + + + align:start position:0% +be your uh One-Stop shop for getting +everything including uh lecture handouts + + align:start position:0% +everything including uh lecture handouts + + + align:start position:0% +everything including uh lecture handouts +uh problem sets turning in your problem + + align:start position:0% +uh problem sets turning in your problem + + + align:start position:0% +uh problem sets turning in your problem +sets uh + + align:start position:0% +sets uh + + + align:start position:0% +sets uh +Etc and uh I should mention that uh this + + align:start position:0% +Etc and uh I should mention that uh this + + + align:start position:0% +Etc and uh I should mention that uh this +course is being taped uh for open + + align:start position:0% +course is being taped uh for open + + + align:start position:0% +course is being taped uh for open +courseware and uh while it'll take a + + align:start position:0% +courseware and uh while it'll take a + + + align:start position:0% +courseware and uh while it'll take a +little bit of time for the videos uh to + + align:start position:0% +little bit of time for the videos uh to + + + align:start position:0% +little bit of time for the videos uh to +be put online uh we hope to do that uh + + align:start position:0% +be put online uh we hope to do that uh + + + align:start position:0% +be put online uh we hope to do that uh +perhaps in uh in clumps uh before uh uh + + align:start position:0% +perhaps in uh in clumps uh before uh uh + + + align:start position:0% +perhaps in uh in clumps uh before uh uh +the exams the the quizzes that you will + + align:start position:0% +the exams the the quizzes that you will + + + align:start position:0% +the exams the the quizzes that you will +have as we have to have in uh in our + + align:start position:0% +have as we have to have in uh in our + + + align:start position:0% +have as we have to have in uh in our +class uh so let me uh just say a couple + + align:start position:0% +class uh so let me uh just say a couple + + + align:start position:0% +class uh so let me uh just say a couple +more things about uh Logistics and then + + align:start position:0% +more things about uh Logistics and then + + + align:start position:0% +more things about uh Logistics and then +we'll get started with the technical + + align:start position:0% +we'll get started with the technical + + + align:start position:0% +we'll get started with the technical +content uh as I mentioned uh we're going + + align:start position:0% +content uh as I mentioned uh we're going + + + align:start position:0% +content uh as I mentioned uh we're going +to be running this course of Stellar uh + + align:start position:0% +to be running this course of Stellar uh + + + align:start position:0% +to be running this course of Stellar uh +please sign up for a registration + + align:start position:0% +please sign up for a registration + + + align:start position:0% +please sign up for a registration +section by going to the Stellar website + + align:start position:0% +section by going to the Stellar website + + + align:start position:0% +section by going to the Stellar website +and choosing a section that works for + + align:start position:0% +and choosing a section that works for + + + align:start position:0% +and choosing a section that works for +your schedule uh sections go from 10 + + align:start position:0% +your schedule uh sections go from 10 + + + align:start position:0% +your schedule uh sections go from 10 +a.m. all the way to uh 300 p.m. I think + + align:start position:0% +a.m. all the way to uh 300 p.m. I think + + + align:start position:0% +a.m. all the way to uh 300 p.m. I think +uh and uh uh We've placed a limit on uh + + align:start position:0% +uh and uh uh We've placed a limit on uh + + + align:start position:0% +uh and uh uh We've placed a limit on uh +the number of students per section be + + align:start position:0% +the number of students per section be + + + align:start position:0% +the number of students per section be +want the sections to be manageable in + + align:start position:0% +want the sections to be manageable in + + + align:start position:0% +want the sections to be manageable in +size but there's plenty of room for + + align:start position:0% +size but there's plenty of room for + + + align:start position:0% +size but there's plenty of room for +everybody and uh the schedule + + align:start position:0% +everybody and uh the schedule + + + align:start position:0% +everybody and uh the schedule +flexibility should allow you to uh + + align:start position:0% +flexibility should allow you to uh + + + align:start position:0% +flexibility should allow you to uh +choose a section uh pretty easily uh we + + align:start position:0% +choose a section uh pretty easily uh we + + + align:start position:0% +choose a section uh pretty easily uh we +have a course information document and + + align:start position:0% +have a course information document and + + + align:start position:0% +have a course information document and +an objectives document on the website + + align:start position:0% +an objectives document on the website + + + align:start position:0% +an objectives document on the website +that has a lot of details on uh the + + align:start position:0% +that has a lot of details on uh the + + + align:start position:0% +that has a lot of details on uh the +grading policy the collaboration policy + + align:start position:0% +grading policy the collaboration policy + + + align:start position:0% +grading policy the collaboration policy +Etc please read it very carefully uh + + align:start position:0% +Etc please read it very carefully uh + + + align:start position:0% +Etc please read it very carefully uh +from the first page all the way to the + + align:start position:0% +from the first page all the way to the + + + align:start position:0% +from the first page all the way to the +end and I will mention one thing that uh + + align:start position:0% +end and I will mention one thing that uh + + + align:start position:0% +end and I will mention one thing that uh +you should be uh careful about uh which + + align:start position:0% +you should be uh careful about uh which + + + align:start position:0% +you should be uh careful about uh which +is that uh while problem sets are only + + align:start position:0% +is that uh while problem sets are only + + + align:start position:0% +is that uh while problem sets are only +uh 30% of the grade I we do require you + + align:start position:0% +uh 30% of the grade I we do require you + + + align:start position:0% +uh 30% of the grade I we do require you +to attempt the problems and there's + + align:start position:0% +to attempt the problems and there's + + + align:start position:0% +to attempt the problems and there's +actually a penalty associated with not + + align:start position:0% +actually a penalty associated with not + + + align:start position:0% +actually a penalty associated with not +attempting problems and not turning + + align:start position:0% +attempting problems and not turning + + + align:start position:0% +attempting problems and not turning +problem sets in that is way more than + + align:start position:0% +problem sets in that is way more than + + + align:start position:0% +problem sets in that is way more than +30% right so keep that in mind and uh + + align:start position:0% +30% right so keep that in mind and uh + + + align:start position:0% +30% right so keep that in mind and uh +please read the collaboration policy uh + + align:start position:0% +please read the collaboration policy uh + + + align:start position:0% +please read the collaboration policy uh +as well as the grading policy carefully + + align:start position:0% +as well as the grading policy carefully + + + align:start position:0% +as well as the grading policy carefully +and uh feel free to ask us questions uh + + align:start position:0% +and uh feel free to ask us questions uh + + + align:start position:0% +and uh feel free to ask us questions uh +you can ask us questions anonymously uh + + align:start position:0% +you can ask us questions anonymously uh + + + align:start position:0% +you can ask us questions anonymously uh +through Piaza or you could suddenly send + + align:start position:0% +through Piaza or you could suddenly send + + + align:start position:0% +through Piaza or you could suddenly send +us email all the information is on + + align:start position:0% +us email all the information is on + + + align:start position:0% +us email all the information is on +Stellar so that's all I really had to + + align:start position:0% +Stellar so that's all I really had to + + + align:start position:0% +Stellar so that's all I really had to +say uh about course Logistics um let me + + align:start position:0% +say uh about course Logistics um let me + + + align:start position:0% +say uh about course Logistics um let me +tell you a little bit about U how the + + align:start position:0% +tell you a little bit about U how the + + + align:start position:0% +tell you a little bit about U how the +content of this course is + + align:start position:0% +content of this course is + + + align:start position:0% +content of this course is +structured um we have uh several modules + + align:start position:0% +structured um we have uh several modules + + + align:start position:0% +structured um we have uh several modules +and uh Eric Nancy and I will be + + align:start position:0% +and uh Eric Nancy and I will be + + + align:start position:0% +and uh Eric Nancy and I will be +uh in charge of each of these different + + align:start position:0% +uh in charge of each of these different + + + align:start position:0% +uh in charge of each of these different +modules as the term goes on our very + + align:start position:0% +modules as the term goes on our very + + + align:start position:0% +modules as the term goes on our very +first module um is uh going to start + + align:start position:0% +first module um is uh going to start + + + align:start position:0% +first module um is uh going to start +really next time today is really an + + align:start position:0% +really next time today is really an + + + align:start position:0% +really next time today is really an +overview lecture + + align:start position:0% +overview lecture + + + align:start position:0% +overview lecture +but it's a module on divide and conquer + + align:start position:0% +but it's a module on divide and conquer + + + align:start position:0% +but it's a module on divide and conquer +and uh you uh learned about this divide + + align:start position:0% +and uh you uh learned about this divide + + + align:start position:0% +and uh you uh learned about this divide +and conquer Paradigm in6 or equivalent + + align:start position:0% +and conquer Paradigm in6 or equivalent + + + align:start position:0% +and conquer Paradigm in6 or equivalent +classes uh it's breaking up a problem + + align:start position:0% +classes uh it's breaking up a problem + + + align:start position:0% +classes uh it's breaking up a problem +into smaller problems and uh getting + + align:start position:0% +into smaller problems and uh getting + + + align:start position:0% +into smaller problems and uh getting +efficiency that way merge sort is a + + align:start position:0% +efficiency that way merge sort is a + + + align:start position:0% +efficiency that way merge sort is a +classic algorithm that follows the + + align:start position:0% +classic algorithm that follows the + + + align:start position:0% +classic algorithm that follows the +divide and conquer Paradigm we're going + + align:start position:0% +divide and conquer Paradigm we're going + + + align:start position:0% +divide and conquer Paradigm we're going +to take it to a new level and I guess + + align:start position:0% +to take it to a new level and I guess + + + align:start position:0% +to take it to a new level and I guess +that's sort of uh the theme of 046 you + + align:start position:0% +that's sort of uh the theme of 046 you + + + align:start position:0% +that's sort of uh the theme of 046 you +know take the material in6 and raise the + + align:start position:0% +know take the material in6 and raise the + + + align:start position:0% +know take the material in6 and raise the +stakes a little bit raise the level of + + align:start position:0% +stakes a little bit raise the level of + + + align:start position:0% +stakes a little bit raise the level of +sophistication and you'll see things + + align:start position:0% +sophistication and you'll see things + + + align:start position:0% +sophistication and you'll see things +like Fast for8 transform uh uh finding + + align:start position:0% +like Fast for8 transform uh uh finding + + + align:start position:0% +like Fast for8 transform uh uh finding +an algorithm for a convex Hull we'll do + + align:start position:0% +an algorithm for a convex Hull we'll do + + + align:start position:0% +an algorithm for a convex Hull we'll do +that next time that uses the divide and + + align:start position:0% +that next time that uses the divide and + + + align:start position:0% +that next time that uses the divide and +conquer Paradigm uh we're going to do a + + align:start position:0% +conquer Paradigm uh we're going to do a + + + align:start position:0% +conquer Paradigm uh we're going to do a +ton of + + align:start position:0% +ton of + + + align:start position:0% +ton of +optimization divide and conquer can + + align:start position:0% +optimization divide and conquer can + + + align:start position:0% +optimization divide and conquer can +obviously be used for search and also + + align:start position:0% +obviously be used for search and also + + + align:start position:0% +obviously be used for search and also +for + + align:start position:0% +for + + + align:start position:0% +for +optimization um in particular uh we look + + align:start position:0% +optimization um in particular uh we look + + + align:start position:0% +optimization um in particular uh we look +at uh strategies corresponding to uh + + align:start position:0% +at uh strategies corresponding to uh + + + align:start position:0% +at uh strategies corresponding to uh +greedy algorithms dyra which uh + + align:start position:0% +greedy algorithms dyra which uh + + + align:start position:0% +greedy algorithms dyra which uh +hopefully you remember shortest path + + align:start position:0% +hopefully you remember shortest path + + + align:start position:0% +hopefully you remember shortest path +algorithm uh from 006 is a example of a + + align:start position:0% +algorithm uh from 006 is a example of a + + + align:start position:0% +algorithm uh from 006 is a example of a +greedy algorithm we'll see a bunch of + + align:start position:0% +greedy algorithm we'll see a bunch of + + + align:start position:0% +greedy algorithm we'll see a bunch of +other examples um and we we'll look at + + align:start position:0% +other examples um and we we'll look at + + + align:start position:0% +other examples um and we we'll look at +one today and dynamic programming It's a + + align:start position:0% +one today and dynamic programming It's a + + + align:start position:0% +one today and dynamic programming It's a +Wonderful uh hammer uh algorithmic + + align:start position:0% +Wonderful uh hammer uh algorithmic + + + align:start position:0% +Wonderful uh hammer uh algorithmic +hammer that you can apply to a wide + + align:start position:0% +hammer that you can apply to a wide + + + align:start position:0% +hammer that you can apply to a wide +variety of problems certainly to + + align:start position:0% +variety of problems certainly to + + + align:start position:0% +variety of problems certainly to +shortest Pats as well we'll look at it + + align:start position:0% +shortest Pats as well we'll look at it + + + align:start position:0% +shortest Pats as well we'll look at it +in many different contexts and then + + align:start position:0% +in many different contexts and then + + + align:start position:0% +in many different contexts and then +really quickly + + align:start position:0% +really quickly + + + align:start position:0% +really quickly +uh Network flow which is uh a problem + + align:start position:0% +uh Network flow which is uh a problem + + + align:start position:0% +uh Network flow which is uh a problem +that's associated with here's a network + + align:start position:0% +that's associated with here's a network + + + align:start position:0% +that's associated with here's a network +there's capacities associated with the + + align:start position:0% +there's capacities associated with the + + + align:start position:0% +there's capacities associated with the +network uh the capacities could + + align:start position:0% +network uh the capacities could + + + align:start position:0% +network uh the capacities could +correspond to uh uh the width of the + + align:start position:0% +correspond to uh uh the width of the + + + align:start position:0% +correspond to uh uh the width of the +roads uh in a uh in in in a highway + + align:start position:0% +roads uh in a uh in in in a highway + + + align:start position:0% +roads uh in a uh in in in a highway +system the or the number of lanes the + + align:start position:0% +system the or the number of lanes the + + + align:start position:0% +system the or the number of lanes the +amount of traffic that can go through + + align:start position:0% +amount of traffic that can go through + + + align:start position:0% +amount of traffic that can go through +how do I maximize the set of Commodities + + align:start position:0% +how do I maximize the set of Commodities + + + align:start position:0% +how do I maximize the set of Commodities +or the amount of Commodities that I can + + align:start position:0% +or the amount of Commodities that I can + + + align:start position:0% +or the amount of Commodities that I can +push through the network that it turns + + align:start position:0% +push through the network that it turns + + + align:start position:0% +push through the network that it turns +out is again a + + align:start position:0% +out is again a + + + align:start position:0% +out is again a +a a problem that has many different + + align:start position:0% +a a problem that has many different + + + align:start position:0% +a a problem that has many different +applications so it's really a collection + + align:start position:0% +applications so it's really a collection + + + align:start position:0% +applications so it's really a collection +of problems um we're going to spend some + + align:start position:0% +of problems um we're going to spend some + + + align:start position:0% +of problems um we're going to spend some +time a little bit today but a little + + align:start position:0% +time a little bit today but a little + + + align:start position:0% +time a little bit today but a little +more than in + + align:start position:0% +more than in + + + align:start position:0% +more than in +66 talking about + + align:start position:0% +66 talking about + + + align:start position:0% +66 talking about +intractability so a lot of the + + align:start position:0% +intractability so a lot of the + + + align:start position:0% +intractability so a lot of the +algorithms that we're going to talk + + align:start position:0% +algorithms that we're going to talk + + + align:start position:0% +algorithms that we're going to talk +about are efficient in the sense that + + align:start position:0% +about are efficient in the sense that + + + align:start position:0% +about are efficient in the sense that +they're polinomial time solvable and uh + + align:start position:0% +they're polinomial time solvable and uh + + + align:start position:0% +they're polinomial time solvable and uh +I of course you know polinomial time + + align:start position:0% +I of course you know polinomial time + + + align:start position:0% +I of course you know polinomial time +solvable doesn't imply efficiency in the + + align:start position:0% +solvable doesn't imply efficiency in the + + + align:start position:0% +solvable doesn't imply efficiency in the +practical sense so if you have an N + + align:start position:0% +practical sense so if you have an N + + + align:start position:0% +practical sense so if you have an N +raised to 8 algorithm it's polinomial + + align:start position:0% +raised to 8 algorithm it's polinomial + + + align:start position:0% +raised to 8 algorithm it's polinomial +time but really it's not something that + + align:start position:0% +time but really it's not something that + + + align:start position:0% +time but really it's not something that +you can use on real world problems where + + align:start position:0% +you can use on real world problems where + + + align:start position:0% +you can use on real world problems where +n is relatively large but I generally in + + align:start position:0% +n is relatively large but I generally in + + + align:start position:0% +n is relatively large but I generally in +a theoretical computer science class + + align:start position:0% +a theoretical computer science class + + + align:start position:0% +a theoretical computer science class +we'll think about U tractable problems + + align:start position:0% +we'll think about U tractable problems + + + align:start position:0% +we'll think about U tractable problems +as being those that have Pol polinomial + + align:start position:0% +as being those that have Pol polinomial + + + align:start position:0% +as being those that have Pol polinomial +time algorithms uh that can solve them + + align:start position:0% +time algorithms uh that can solve them + + + align:start position:0% +time algorithms uh that can solve them +exactly or optimally + + align:start position:0% +exactly or optimally + + + align:start position:0% +exactly or optimally +but uh intractability then corresponds + + align:start position:0% +but uh intractability then corresponds + + + align:start position:0% +but uh intractability then corresponds +to problems that uh at the moment uh we + + align:start position:0% +to problems that uh at the moment uh we + + + align:start position:0% +to problems that uh at the moment uh we +don't know of a polinomial Time + + align:start position:0% +don't know of a polinomial Time + + + align:start position:0% +don't know of a polinomial Time +algorithm to solve them and the best + + align:start position:0% +algorithm to solve them and the best + + + align:start position:0% +algorithm to solve them and the best +algorithms we have take worst case + + align:start position:0% +algorithms we have take worst case + + + align:start position:0% +algorithms we have take worst case +exponential time and so the question is + + align:start position:0% +exponential time and so the question is + + + align:start position:0% +exponential time and so the question is +what happens for those problems and + + align:start position:0% +what happens for those problems and + + + align:start position:0% +what happens for those problems and +we'll look at things like approximation + + align:start position:0% +we'll look at things like approximation + + + align:start position:0% +we'll look at things like approximation +algorithms uh that U can get us in the + + align:start position:0% +algorithms uh that U can get us in the + + + align:start position:0% +algorithms uh that U can get us in the +case of + + align:start position:0% +case of + + + align:start position:0% +case of +optimization problems i' get us uh with + + align:start position:0% +optimization problems i' get us uh with + + + align:start position:0% +optimization problems i' get us uh with +to within a certain fraction of optimal + + align:start position:0% +to within a certain fraction of optimal + + + align:start position:0% +to within a certain fraction of optimal +guaranteed and run in polinomial time so + + align:start position:0% +guaranteed and run in polinomial time so + + + align:start position:0% +guaranteed and run in polinomial time so +you can't get the absolute best but you + + align:start position:0% +you can't get the absolute best but you + + + align:start position:0% +you can't get the absolute best but you +can get within 10% or we can get within + + align:start position:0% +can get within 10% or we can get within + + + align:start position:0% +can get within 10% or we can get within +a factor of two that may be enough for + + align:start position:0% +a factor of two that may be enough for + + + align:start position:0% +a factor of two that may be enough for +um a particular instance of a problem or + + align:start position:0% +um a particular instance of a problem or + + + align:start position:0% +um a particular instance of a problem or +or a set of instances of a problem and + + align:start position:0% +or a set of instances of a problem and + + + align:start position:0% +or a set of instances of a problem and +we'll do a bunch of advanced topics I + + align:start position:0% +we'll do a bunch of advanced topics I + + + align:start position:0% +we'll do a bunch of advanced topics I +think we have distributed algorithms + + align:start position:0% +think we have distributed algorithms + + + align:start position:0% +think we have distributed algorithms +plan Nancy Works in that area uh and uh + + align:start position:0% +plan Nancy Works in that area uh and uh + + + align:start position:0% +plan Nancy Works in that area uh and uh +uh uh we'll also talk about cryptography + + align:start position:0% +uh uh we'll also talk about cryptography + + + align:start position:0% +uh uh we'll also talk about cryptography +there's a deep connection between number + + align:start position:0% +there's a deep connection between number + + + align:start position:0% +there's a deep connection between number +Theory algorithms and cryptography that + + align:start position:0% +Theory algorithms and cryptography that + + + align:start position:0% +Theory algorithms and cryptography that +uh towards the end of the lecture or I + + align:start position:0% +uh towards the end of the lecture or I + + + align:start position:0% +uh towards the end of the lecture or I +should say towards the end of uh the + + align:start position:0% +should say towards the end of uh the + + + align:start position:0% +should say towards the end of uh the +course I will look at a little more + + align:start position:0% +course I will look at a little more + + + align:start position:0% +course I will look at a little more +closely so so much for overview uh let's + + align:start position:0% +closely so so much for overview uh let's + + + align:start position:0% +closely so so much for overview uh let's +get started with the today's lecture for + + align:start position:0% +get started with the today's lecture for + + + align:start position:0% +get started with the today's lecture for +real and here's the theme of today's + + align:start position:0% +real and here's the theme of today's + + + align:start position:0% +real and here's the theme of today's +lecture um + + align:start position:0% +lecture um + + + align:start position:0% +lecture um +I talked a bit about tractability and + + align:start position:0% +I talked a bit about tractability and + + + align:start position:0% +I talked a bit about tractability and +intractability and what is fascinating + + align:start position:0% +intractability and what is fascinating + + + align:start position:0% +intractability and what is fascinating +about algorithms is that you might see a + + align:start position:0% +about algorithms is that you might see a + + + align:start position:0% +about algorithms is that you might see a +problem that has a fairly obvious Pol + + align:start position:0% +problem that has a fairly obvious Pol + + + align:start position:0% +problem that has a fairly obvious Pol +polinomial time solution or a linear + + align:start position:0% +polinomial time solution or a linear + + + align:start position:0% +polinomial time solution or a linear +time solution then you change it ever so + + align:start position:0% +time solution then you change it ever so + + + align:start position:0% +time solution then you change it ever so +slightly and the linear time algorithm + + align:start position:0% +slightly and the linear time algorithm + + + align:start position:0% +slightly and the linear time algorithm +doesn't work maybe you can find a cubic + + align:start position:0% +doesn't work maybe you can find a cubic + + + align:start position:0% +doesn't work maybe you can find a cubic +algorithm uh and then you change it a + + align:start position:0% +algorithm uh and then you change it a + + + align:start position:0% +algorithm uh and then you change it a +little more little more for and uh you + + align:start position:0% +little more little more for and uh you + + + align:start position:0% +little more little more for and uh you +end up with something that you can't + + align:start position:0% +end up with something that you can't + + + align:start position:0% +end up with something that you can't +find you can't find a polinomial Time + + align:start position:0% +find you can't find a polinomial Time + + + align:start position:0% +find you can't find a polinomial Time +algorithm for you can't prove that uh + + align:start position:0% +algorithm for you can't prove that uh + + + align:start position:0% +algorithm for you can't prove that uh +the polinomial time algorithm or any + + align:start position:0% +the polinomial time algorithm or any + + + align:start position:0% +the polinomial time algorithm or any +polinomial time algorithm gives you the + + align:start position:0% +polinomial time algorithm gives you the + + + align:start position:0% +polinomial time algorithm gives you the +optimal solution in all cases and and + + align:start position:0% +optimal solution in all cases and and + + + align:start position:0% +optimal solution in all cases and and +then you go off into complexity Theory + + align:start position:0% +then you go off into complexity Theory + + + align:start position:0% +then you go off into complexity Theory +uh you maybe discover that uh or show + + align:start position:0% +uh you maybe discover that uh or show + + + align:start position:0% +uh you maybe discover that uh or show +that this Al this problem is NP complete + + align:start position:0% +that this Al this problem is NP complete + + + align:start position:0% +that this Al this problem is NP complete +and now you're in the intractability + + align:start position:0% +and now you're in the intractability + + + align:start position:0% +and now you're in the intractability +domain so very small changes + + align:start position:0% +domain so very small changes + + + align:start position:0% +domain so very small changes +in problem + + align:start position:0% +in problem + + + align:start position:0% +in problem +statements can end up + + align:start position:0% +statements can end up + + + align:start position:0% +statements can end up +with very different situations from a + + align:start position:0% +with very different situations from a + + + align:start position:0% +with very different situations from a +standpoint of algorithm complexity and + + align:start position:0% +standpoint of algorithm complexity and + + + align:start position:0% +standpoint of algorithm complexity and +so that's really what I want + + align:start position:0% +so that's really what I want + + + align:start position:0% +so that's really what I want +to point out to you in some + + align:start position:0% +to point out to you in some + + + align:start position:0% +to point out to you in some +detail with a concrete + + align:start position:0% + + + + align:start position:0% + +example so I want to get a little bit + + align:start position:0% +example so I want to get a little bit + + + align:start position:0% +example so I want to get a little bit +pedantic here with respect to + + align:start position:0% +pedantic here with respect to + + + align:start position:0% +pedantic here with respect to +intractability and tractability uh + + align:start position:0% +intractability and tractability uh + + + align:start position:0% +intractability and tractability uh +you've + + align:start position:0% +you've + + + align:start position:0% +you've +seen I think these terms before in the + + align:start position:0% +seen I think these terms before in the + + + align:start position:0% +seen I think these terms before in the +one lecture + + align:start position:0% +one lecture + + + align:start position:0% +one lecture +in6 uh but we'll go over this in some + + align:start position:0% +in6 uh but we'll go over this in some + + + align:start position:0% +in6 uh but we'll go over this in some +detail today and more later on in this + + align:start position:0% +detail today and more later on in this + + + align:start position:0% +detail today and more later on in this +semester but for now uh let's recall + + align:start position:0% +semester but for now uh let's recall + + + align:start position:0% +semester but for now uh let's recall +some uh basic terminology associated + + align:start position:0% +some uh basic terminology associated + + + align:start position:0% +some uh basic terminology associated +with tractability and intract ility or + + align:start position:0% +with tractability and intract ility or + + + align:start position:0% +with tractability and intract ility or +complexity Theory broadly speaking + + align:start position:0% +complexity Theory broadly speaking + + + align:start position:0% +complexity Theory broadly speaking +capital P is the class of + + align:start position:0% +capital P is the class of + + + align:start position:0% +capital P is the class of +problems + + align:start position:0% +problems + + + align:start position:0% +problems +solvable in polinomial + + align:start position:0% + + + + align:start position:0% + +time and think of that as Big O N raised + + align:start position:0% +time and think of that as Big O N raised + + + align:start position:0% +time and think of that as Big O N raised +to K for + + align:start position:0% +to K for + + + align:start position:0% +to K for +some constant + + align:start position:0% +some constant + + + align:start position:0% +some constant +K now you can have log factors in there + + align:start position:0% +K now you can have log factors in there + + + align:start position:0% +K now you can have log factors in there +but once you put a big O in there uh + + align:start position:0% +but once you put a big O in there uh + + + align:start position:0% +but once you put a big O in there uh +you're good you can always say uh uh or + + align:start position:0% +you're good you can always say uh uh or + + + align:start position:0% +you're good you can always say uh uh or +or n even if it's a logarithmic problem + + align:start position:0% +or n even if it's a logarithmic problem + + + align:start position:0% +or n even if it's a logarithmic problem +and bigo lets you be sloppy like that uh + + align:start position:0% +and bigo lets you be sloppy like that uh + + + align:start position:0% +and bigo lets you be sloppy like that uh +and uh there are many examples of + + align:start position:0% +and uh there are many examples of + + + align:start position:0% +and uh there are many examples of +polinomial time algorithms of course for + + align:start position:0% +polinomial time algorithms of course for + + + align:start position:0% +polinomial time algorithms of course for +interesting problems like shortest paths + + align:start position:0% +interesting problems like shortest paths + + + align:start position:0% +interesting problems like shortest paths +so the shortest path problem is order V + + align:start position:0% +so the shortest path problem is order V + + + align:start position:0% +so the shortest path problem is order V +Square where V is the number of vertices + + align:start position:0% +Square where V is the number of vertices + + + align:start position:0% +Square where V is the number of vertices +in the graph there's algorithms for that + + align:start position:0% +in the graph there's algorithms for that + + + align:start position:0% +in the graph there's algorithms for that +uh you can do a little bit better uh if + + align:start position:0% +uh you can do a little bit better uh if + + + align:start position:0% +uh you can do a little bit better uh if +you to um uh use fancier data structures + + align:start position:0% +you to um uh use fancier data structures + + + align:start position:0% +you to um uh use fancier data structures +but that's an example + + align:start position:0% +but that's an example + + + align:start position:0% +but that's an example +NP is uh another class of problems + + align:start position:0% +NP is uh another class of problems + + + align:start position:0% +NP is uh another class of problems +that's very interesting uh this is the + + align:start position:0% +that's very interesting uh this is the + + + align:start position:0% +that's very interesting uh this is the +class of + + align:start position:0% +class of + + + align:start position:0% +class of +problems that are whose + + align:start position:0% +problems that are whose + + + align:start position:0% +problems that are whose +solution is + + align:start position:0% +solution is + + + align:start position:0% +solution is +verifiable in polinomial + + align:start position:0% + + + + align:start position:0% + +time U so an example of a problem in NP + + align:start position:0% +time U so an example of a problem in NP + + + align:start position:0% +time U so an example of a problem in NP +uh that uh + + align:start position:0% +uh that uh + + + align:start position:0% +uh that uh +is not known to be in P is the + + align:start position:0% +is not known to be in P is the + + + align:start position:0% +is not known to be in P is the +hamiltonian cycle + + align:start position:0% +hamiltonian cycle + + + align:start position:0% +hamiltonian cycle +problem and the hamiltonian cycle + + align:start position:0% +problem and the hamiltonian cycle + + + align:start position:0% +problem and the hamiltonian cycle +problem corresponds + + align:start position:0% + + + + align:start position:0% + +to given a directed + + align:start position:0% + + + + align:start position:0% + +graph + + align:start position:0% + + + + align:start position:0% + +find + + align:start position:0% +find + + + align:start position:0% +find +a simple cycle so you can't repeat + + align:start position:0% +a simple cycle so you can't repeat + + + align:start position:0% +a simple cycle so you can't repeat +vertices but you need the simple cycle + + align:start position:0% +vertices but you need the simple cycle + + + align:start position:0% +vertices but you need the simple cycle +to + + align:start position:0% +to + + + align:start position:0% +to +contain each vertex in + + align:start position:0% + + + + align:start position:0% + +v + + align:start position:0% +v + + + align:start position:0% +v +and + + align:start position:0% +and + + + align:start position:0% +and +determining whether a given cycle is a + + align:start position:0% +determining whether a given cycle is a + + + align:start position:0% +determining whether a given cycle is a +hamiltonian cycle or not is simple you + + align:start position:0% +hamiltonian cycle or not is simple you + + + align:start position:0% +hamiltonian cycle or not is simple you +just uh Traverse the cycle make sure + + align:start position:0% +just uh Traverse the cycle make sure + + + align:start position:0% +just uh Traverse the cycle make sure +that you've touched all the vertices + + align:start position:0% +that you've touched all the vertices + + + align:start position:0% +that you've touched all the vertices +exactly once and you're done clearly + + align:start position:0% +exactly once and you're done clearly + + + align:start position:0% +exactly once and you're done clearly +doable in polinomial time so therefore + + align:start position:0% +doable in polinomial time so therefore + + + align:start position:0% +doable in polinomial time so therefore +hamiltonian cycle is an NP + + align:start position:0% +hamiltonian cycle is an NP + + + align:start position:0% +hamiltonian cycle is an NP +but uh determining whether a graph has a + + align:start position:0% +but uh determining whether a graph has a + + + align:start position:0% +but uh determining whether a graph has a +hamiltonian cycle or not is a is a hard + + align:start position:0% +hamiltonian cycle or not is a is a hard + + + align:start position:0% +hamiltonian cycle or not is a is a hard +problem and + + align:start position:0% +problem and + + + align:start position:0% +problem and +U in + + align:start position:0% +U in + + + align:start position:0% +U in +particular uh the notion of NP + + align:start position:0% +particular uh the notion of NP + + + align:start position:0% +particular uh the notion of NP +completeness + + align:start position:0% + + + + align:start position:0% + +um is something that U defines the level + + align:start position:0% +um is something that U defines the level + + + align:start position:0% +um is something that U defines the level +of + + align:start position:0% +of + + + align:start position:0% +of +intractability + + align:start position:0% +intractability + + + align:start position:0% +intractability +for NP the NP complete problems are the + + align:start position:0% +for NP the NP complete problems are the + + + align:start position:0% +for NP the NP complete problems are the +hardest problems in NP and hamiltonian + + align:start position:0% +hardest problems in NP and hamiltonian + + + align:start position:0% +hardest problems in NP and hamiltonian +cycle is one of them if you can + + align:start position:0% + + + + align:start position:0% + +solve any NP complete problem in + + align:start position:0% +solve any NP complete problem in + + + align:start position:0% +solve any NP complete problem in +polinomial time you can solve all + + align:start position:0% +polinomial time you can solve all + + + align:start position:0% +polinomial time you can solve all +problems in NP in polom time so that's + + align:start position:0% +problems in NP in polom time so that's + + + align:start position:0% +problems in NP in polom time so that's +what I meant by saying that NP complete + + align:start position:0% +what I meant by saying that NP complete + + + align:start position:0% +what I meant by saying that NP complete +problems are in some sense the hardest + + align:start position:0% +problems are in some sense the hardest + + + align:start position:0% +problems are in some sense the hardest +problems in NP because solving one of + + align:start position:0% +problems in NP because solving one of + + + align:start position:0% +problems in NP because solving one of +them gives you everything so the + + align:start position:0% +them gives you everything so the + + + align:start position:0% +them gives you everything so the +definition of NP completeness is that + + align:start position:0% +definition of NP completeness is that + + + align:start position:0% +definition of NP completeness is that +the problem is in + + align:start position:0% +the problem is in + + + align:start position:0% +the problem is in +NP and is as + + align:start position:0% +NP and is as + + + align:start position:0% +NP and is as +hard an informal definition + + align:start position:0% +hard an informal definition + + + align:start position:0% +hard an informal definition +as any problem in + + align:start position:0% +as any problem in + + + align:start position:0% +as any problem in +NP + + align:start position:0% + + + + align:start position:0% + +and so hamiltonian + + align:start position:0% +and so hamiltonian + + + align:start position:0% +and so hamiltonian +cycle is an NP complete problem + + align:start position:0% +cycle is an NP complete problem + + + align:start position:0% +cycle is an NP complete problem +satisfiability is an NP complete problem + + align:start position:0% +satisfiability is an NP complete problem + + + align:start position:0% +satisfiability is an NP complete problem +and there's a whole bunch of them so + + align:start position:0% +and there's a whole bunch of them so + + + align:start position:0% +and there's a whole bunch of them so +going back to our theme Here what I want + + align:start position:0% +going back to our theme Here what I want + + + align:start position:0% +going back to our theme Here what I want +to show you is how for an interval + + align:start position:0% +to show you is how for an interval + + + align:start position:0% +to show you is how for an interval +scheduling problem that I'll Define in a + + align:start position:0% +scheduling problem that I'll Define in a + + + align:start position:0% +scheduling problem that I'll Define in a +couple of minutes how we move + + align:start position:0% +couple of minutes how we move + + + align:start position:0% +couple of minutes how we move +from linear time therefore p + + align:start position:0% +from linear time therefore p + + + align:start position:0% +from linear time therefore p +to something that's still in P but it's + + align:start position:0% +to something that's still in P but it's + + + align:start position:0% +to something that's still in P but it's +a little more complicated if I change + + align:start position:0% +a little more complicated if I change + + + align:start position:0% +a little more complicated if I change +the constraints of a problem a little + + align:start position:0% +the constraints of a problem a little + + + align:start position:0% +the constraints of a problem a little +bit and finally if I add more + + align:start position:0% +bit and finally if I add more + + + align:start position:0% +bit and finally if I add more +constraints to the problem generalize it + + align:start position:0% +constraints to the problem generalize it + + + align:start position:0% +constraints to the problem generalize it +and you can think of it as adding + + align:start position:0% +and you can think of it as adding + + + align:start position:0% +and you can think of it as adding +constraints or general generalizing the + + align:start position:0% +constraints or general generalizing the + + + align:start position:0% +constraints or general generalizing the +problem uh you you get with small + + align:start position:0% +problem uh you you get with small + + + align:start position:0% +problem uh you you get with small +changes to something that becomes NP + + align:start position:0% +changes to something that becomes NP + + + align:start position:0% +changes to something that becomes NP +complete right so this is something that + + align:start position:0% +complete right so this is something that + + + align:start position:0% +complete right so this is something that +algorithm designers have to keep in mind + + align:start position:0% +algorithm designers have to keep in mind + + + align:start position:0% +algorithm designers have to keep in mind +because uh before you go off and try to + + align:start position:0% +because uh before you go off and try to + + + align:start position:0% +because uh before you go off and try to +design an algorithm for a problem you'd + + align:start position:0% +design an algorithm for a problem you'd + + + align:start position:0% +design an algorithm for a problem you'd +like to know where in the Spectrum your + + align:start position:0% +like to know where in the Spectrum your + + + align:start position:0% +like to know where in the Spectrum your +problem resides and uh in order to do + + align:start position:0% +problem resides and uh in order to do + + + align:start position:0% +problem resides and uh in order to do +that uh you need to understand algorithm + + align:start position:0% +that uh you need to understand algorithm + + + align:start position:0% +that uh you need to understand algorithm +paradigms obviously and be able to apply + + align:start position:0% +paradigms obviously and be able to apply + + + align:start position:0% +paradigms obviously and be able to apply +them but you also have to understand + + align:start position:0% +them but you also have to understand + + + align:start position:0% +them but you also have to understand +reductions where you can try and + + align:start position:0% +reductions where you can try and + + + align:start position:0% +reductions where you can try and +translate one problem to another and if + + align:start position:0% +translate one problem to another and if + + + align:start position:0% +translate one problem to another and if +you can do that and U the first problem + + align:start position:0% +you can do that and U the first problem + + + align:start position:0% +you can do that and U the first problem +um is is is is known to be hard then you + + align:start position:0% +um is is is is known to be hard then you + + + align:start position:0% +um is is is is known to be hard then you +can make arguments about the hardness of + + align:start position:0% +can make arguments about the hardness of + + + align:start position:0% +can make arguments about the hardness of +the of your problem so these are the + + align:start position:0% +the of your problem so these are the + + + align:start position:0% +the of your problem so these are the +kinds of things that we'll touch upon + + align:start position:0% +kinds of things that we'll touch upon + + + align:start position:0% +kinds of things that we'll touch upon +today the an analysis of of of an + + align:start position:0% +today the an analysis of of of an + + + align:start position:0% +today the an analysis of of of an +algorithm the design of an algorithm and + + align:start position:0% +algorithm the design of an algorithm and + + + align:start position:0% +algorithm the design of an algorithm and +also uh the complexity analysis of an + + align:start position:0% +also uh the complexity analysis of an + + + align:start position:0% +also uh the complexity analysis of an +algorithm which may not just be an asmic + + align:start position:0% +algorithm which may not just be an asmic + + + align:start position:0% +algorithm which may not just be an asmic +well this is order n cubed or order n + + align:start position:0% +well this is order n cubed or order n + + + align:start position:0% +well this is order n cubed or order n +square but more in the realm of NP + + align:start position:0% +square but more in the realm of NP + + + align:start position:0% +square but more in the realm of NP +completeness as well + + align:start position:0% +completeness as well + + + align:start position:0% +completeness as well +okay so so so much for context Let's uh + + align:start position:0% +okay so so so much for context Let's uh + + + align:start position:0% +okay so so so much for context Let's uh +dive into our interval scheduling + + align:start position:0% +dive into our interval scheduling + + + align:start position:0% +dive into our interval scheduling +problem + + align:start position:0% +problem + + + align:start position:0% +problem +which is something that you can imagine + + align:start position:0% +which is something that you can imagine + + + align:start position:0% +which is something that you can imagine +doing for + + align:start position:0% +doing for + + + align:start position:0% +doing for +classes uh tasks you know particular + + align:start position:0% +classes uh tasks you know particular + + + align:start position:0% +classes uh tasks you know particular +schedule during a day know life in + + align:start position:0% +schedule during a day know life in + + + align:start position:0% +schedule during a day know life in +general uh and in general setting we + + align:start position:0% +general uh and in general setting we + + + align:start position:0% +general uh and in general setting we +have resources and + + align:start position:0% +have resources and + + + align:start position:0% +have resources and +requests + + align:start position:0% +requests + + + align:start position:0% +requests +and we're going to have a single + + align:start position:0% +and we're going to have a single + + + align:start position:0% +and we're going to have a single +resource for our first version of the + + align:start position:0% +resource for our first version of the + + + align:start position:0% +resource for our first version of the +problem and our requests + + align:start position:0% +problem and our requests + + + align:start position:0% +problem and our requests +are going to be 1 through n and we can + + align:start position:0% +are going to be 1 through n and we can + + + align:start position:0% +are going to be 1 through n and we can +think of these requests as requiring + + align:start position:0% +think of these requests as requiring + + + align:start position:0% +think of these requests as requiring +time corresponding to the resource so + + align:start position:0% +time corresponding to the resource so + + + align:start position:0% +time corresponding to the resource so +the request is for the resource and you + + align:start position:0% +the request is for the resource and you + + + align:start position:0% +the request is for the resource and you +want time on the resource maybe it's + + align:start position:0% +want time on the resource maybe it's + + + align:start position:0% +want time on the resource maybe it's +computation time maybe it's your time I + + align:start position:0% +computation time maybe it's your time I + + + align:start position:0% +computation time maybe it's your time I +could be anything um each of these press + + align:start position:0% +could be anything um each of these press + + + align:start position:0% +could be anything um each of these press +corresponds to an interval of time and + + align:start position:0% +corresponds to an interval of time and + + + align:start position:0% +corresponds to an interval of time and +that's where the name comes from SI is + + align:start position:0% +that's where the name comes from SI is + + + align:start position:0% +that's where the name comes from SI is +the start + + align:start position:0% + + + + align:start position:0% + +time + + align:start position:0% +time + + + align:start position:0% +time +fi is the finish + + align:start position:0% + + + + align:start position:0% + +time and we're going to say si is + + align:start position:0% +time and we're going to say si is + + + align:start position:0% +time and we're going to say si is +strictly less than + + align:start position:0% +strictly less than + + + align:start position:0% +strictly less than +fi okay so I didn't put less than or + + align:start position:0% +fi okay so I didn't put less than or + + + align:start position:0% +fi okay so I didn't put less than or +equal to there because I want these + + align:start position:0% +equal to there because I want these + + + align:start position:0% +equal to there because I want these +requests to be non-null nonzero so + + align:start position:0% +requests to be non-null nonzero so + + + align:start position:0% +requests to be non-null nonzero so +otherwise they're uninteresting and + + align:start position:0% +otherwise they're uninteresting and + + + align:start position:0% +otherwise they're uninteresting and +we're going to have a start time and + + align:start position:0% +we're going to have a start time and + + + align:start position:0% +we're going to have a start time and +we're going to have an end time and + + align:start position:0% +we're going to have an end time and + + + align:start position:0% +we're going to have an end time and +they're not equal so that's + + align:start position:0% +they're not equal so that's + + + align:start position:0% +they're not equal so that's +uh the first part of the specification + + align:start position:0% +uh the first part of the specification + + + align:start position:0% +uh the first part of the specification +of the problem and then the second part + + align:start position:0% +of the problem and then the second part + + + align:start position:0% +of the problem and then the second part +uh which + + align:start position:0% +uh which + + + align:start position:0% +uh which +is intuitive is that two requests we + + align:start position:0% +is intuitive is that two requests we + + + align:start position:0% +is intuitive is that two requests we +have a single resource here remember um + + align:start position:0% +have a single resource here remember um + + + align:start position:0% +have a single resource here remember um +I and + + align:start position:0% +I and + + + align:start position:0% +I and +J are considered to be + + align:start position:0% +J are considered to be + + + align:start position:0% +J are considered to be +compatible which means you can satisfy + + align:start position:0% +compatible which means you can satisfy + + + align:start position:0% +compatible which means you can satisfy +both these requests they're compatible + + align:start position:0% +both these requests they're compatible + + + align:start position:0% +both these requests they're compatible +incompatible requests you can't satisfy + + align:start position:0% +incompatible requests you can't satisfy + + + align:start position:0% +incompatible requests you can't satisfy +with your single resource + + align:start position:0% +with your single resource + + + align:start position:0% +with your single resource +simultaneously provided they uh don't + + align:start position:0% + + + + align:start position:0% + +overlap and an overlapping condition + + align:start position:0% +overlap and an overlapping condition + + + align:start position:0% +overlap and an overlapping condition +might be that + + align:start position:0% +might be that + + + align:start position:0% +might be that +fi is less than or equal to + + align:start position:0% +fi is less than or equal to + + + align:start position:0% +fi is less than or equal to +SJ + + align:start position:0% +SJ + + + align:start position:0% +SJ +and R + + align:start position:0% +and R + + + align:start position:0% +and R +FJ less than equal to SI so again I put + + align:start position:0% +FJ less than equal to SI so again I put + + + align:start position:0% +FJ less than equal to SI so again I put +less than or equal to here which is um + + align:start position:0% +less than or equal to here which is um + + + align:start position:0% +less than or equal to here which is um +important to spend uh a minute on what + + align:start position:0% +important to spend uh a minute on what + + + align:start position:0% +important to spend uh a minute on what +I'm saying here that in in this context + + align:start position:0% +I'm saying here that in in this context + + + align:start position:0% +I'm saying here that in in this context +is that I really have um open-ended + + align:start position:0% +is that I really have um open-ended + + + align:start position:0% +is that I really have um open-ended +intervals on the on the right hand side + + align:start position:0% +intervals on the on the right hand side + + + align:start position:0% +intervals on the on the right hand side +corresponding to the uh fi so + + align:start position:0% +corresponding to the uh fi so + + + align:start position:0% +corresponding to the uh fi so +pictorially you could look at it this + + align:start position:0% +pictorially you could look at it this + + + align:start position:0% +pictorially you could look at it this +way let's say I + + align:start position:0% +way let's say I + + + align:start position:0% +way let's say I +have intervals like + + align:start position:0% +have intervals like + + + align:start position:0% +have intervals like +this so this is interval number one + + align:start position:0% +this so this is interval number one + + + align:start position:0% +this so this is interval number one +that's interval number two right here I + + align:start position:0% +that's interval number two right here I + + + align:start position:0% +that's interval number two right here I +have S of + + align:start position:0% +have S of + + + align:start position:0% +have S of +one out here F of one out here s of two + + align:start position:0% +one out here F of one out here s of two + + + align:start position:0% +one out here F of one out here s of two +out here and F of two out here so this + + align:start position:0% +out here and F of two out here so this + + + align:start position:0% +out here and F of two out here so this +is s uh F of one for that that and S of2 + + align:start position:0% +is s uh F of one for that that and S of2 + + + align:start position:0% +is s uh F of one for that that and S of2 +for this I'm allowing S of2 and F of one + + align:start position:0% +for this I'm allowing S of2 and F of one + + + align:start position:0% +for this I'm allowing S of2 and F of one +to be exactly equal and I + + align:start position:0% +to be exactly equal and I + + + align:start position:0% +to be exactly equal and I +still agree that these two are + + align:start position:0% +still agree that these two are + + + align:start position:0% +still agree that these two are +compatible requests okay so this is just + + align:start position:0% +compatible requests okay so this is just + + + align:start position:0% +compatible requests okay so this is just +I guess it's terminology it's uh it's + + align:start position:0% +I guess it's terminology it's uh it's + + + align:start position:0% +I guess it's terminology it's uh it's +it's it's our definition of + + align:start position:0% +it's it's our definition of + + + align:start position:0% +it's it's our definition of +compatibility + + align:start position:0% +compatibility + + + align:start position:0% +compatibility +so you can imagine now an optimization + + align:start position:0% +so you can imagine now an optimization + + + align:start position:0% +so you can imagine now an optimization +problem + + align:start position:0% +problem + + + align:start position:0% +problem +that is associated with interval + + align:start position:0% +that is associated with interval + + + align:start position:0% +that is associated with interval +scheduling where in a different example + + align:start position:0% +scheduling where in a different example + + + align:start position:0% +scheduling where in a different example +I have this interval corresponding to S1 + + align:start position:0% +I have this interval corresponding to S1 + + + align:start position:0% +I have this interval corresponding to S1 +and F1 I might + + align:start position:0% +and F1 I might + + + align:start position:0% +and F1 I might +have a different interval here + + align:start position:0% +have a different interval here + + + align:start position:0% +have a different interval here +corresponding to two then corresponding + + align:start position:0% +corresponding to two then corresponding + + + align:start position:0% +corresponding to two then corresponding +to three and then maybe I got four + + align:start position:0% +to three and then maybe I got four + + + align:start position:0% +to three and then maybe I got four +here + + align:start position:0% +here + + + align:start position:0% +here +five and six right so those are my six + + align:start position:0% +five and six right so those are my six + + + align:start position:0% +five and six right so those are my six +intervals corresponding to my input I + + align:start position:0% +intervals corresponding to my input I + + + align:start position:0% +intervals corresponding to my input I +have a single resource I've just drawn + + align:start position:0% +have a single resource I've just drawn + + + align:start position:0% +have a single resource I've just drawn +out in a two-dimensional form the six + + align:start position:0% +out in a two-dimensional form the six + + + align:start position:0% +out in a two-dimensional form the six +different requests that I have the six + + align:start position:0% +different requests that I have the six + + + align:start position:0% +different requests that I have the six +different intervals intervals and + + align:start position:0% +different intervals intervals and + + + align:start position:0% +different intervals intervals and +requests are + + align:start position:0% +requests are + + + align:start position:0% +requests are +synonyms uh and my goal here and it's + + align:start position:0% +synonyms uh and my goal here and it's + + + align:start position:0% +synonyms uh and my goal here and it's +kind of obvious in this example is + + align:start position:0% +kind of obvious in this example is + + + align:start position:0% +kind of obvious in this example is +to + + align:start position:0% + + + + align:start position:0% + +select a compatible + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +subset of + + align:start position:0% +subset of + + + align:start position:0% +subset of +requests or + + align:start position:0% + + + + align:start position:0% + +intervals that is of maximum + + align:start position:0% + + + + align:start position:0% + +size and I'd like to do this + + align:start position:0% +size and I'd like to do this + + + align:start position:0% +size and I'd like to do this +efficiently so we'll always consider + + align:start position:0% +efficiently so we'll always consider + + + align:start position:0% +efficiently so we'll always consider +efficiency here but in terms of the + + align:start position:0% +efficiency here but in terms of the + + + align:start position:0% +efficiency here but in terms of the +specification of the problem as opposed + + align:start position:0% +specification of the problem as opposed + + + align:start position:0% +specification of the problem as opposed +to a requirement on the the complexity + + align:start position:0% +to a requirement on the the complexity + + + align:start position:0% +to a requirement on the the complexity +of the algorithm I I want maximum size + + align:start position:0% +of the algorithm I I want maximum size + + + align:start position:0% +of the algorithm I I want maximum size +for this subset so as I showed you or I + + align:start position:0% +for this subset so as I showed you or I + + + align:start position:0% +for this subset so as I showed you or I +mentioned earlier uh in this + + align:start position:0% +mentioned earlier uh in this + + + align:start position:0% +mentioned earlier uh in this +case it is clear from uh the drawing + + align:start position:0% +case it is clear from uh the drawing + + + align:start position:0% +case it is clear from uh the drawing +that I put up there that the maximum + + align:start position:0% +that I put up there that the maximum + + + align:start position:0% +that I put up there that the maximum +size for that six request example that I + + align:start position:0% +size for that six request example that I + + + align:start position:0% +size for that six request example that I +have is three okay so that's the setup + + align:start position:0% +have is three okay so that's the setup + + + align:start position:0% +have is three okay so that's the setup +now we're going to spend the next few + + align:start position:0% +now we're going to spend the next few + + + align:start position:0% +now we're going to spend the next few +minutes talking about uh a greedy + + align:start position:0% +minutes talking about uh a greedy + + + align:start position:0% +minutes talking about uh a greedy +strategy for solving this particular + + align:start position:0% +strategy for solving this particular + + + align:start position:0% +strategy for solving this particular +problem we don't know if the greedy + + align:start position:0% +problem we don't know if the greedy + + + align:start position:0% +problem we don't know if the greedy +strategy is going + + align:start position:0% +strategy is going + + + align:start position:0% +strategy is going +to always produce the maximum size or + + align:start position:0% +to always produce the maximum size or + + + align:start position:0% +to always produce the maximum size or +not in fact it depends on the + + align:start position:0% +not in fact it depends on the + + + align:start position:0% +not in fact it depends on the +particular greedy heuristic the the + + align:start position:0% +particular greedy heuristic the the + + + align:start position:0% +particular greedy heuristic the the +selection heuristic that a greedy + + align:start position:0% +selection heuristic that a greedy + + + align:start position:0% +selection heuristic that a greedy +algorithm uses + + align:start position:0% +algorithm uses + + + align:start position:0% +algorithm uses +so that's going to be important and + + align:start position:0% +so that's going to be important and + + + align:start position:0% +so that's going to be important and +we'll take a look and hopefully you can + + align:start position:0% +we'll take a look and hopefully you can + + + align:start position:0% +we'll take a look and hopefully you can +suggest some at uh a few different + + align:start position:0% +suggest some at uh a few different + + + align:start position:0% +suggest some at uh a few different +greedy + + align:start position:0% +greedy + + + align:start position:0% +greedy +heuristics but my claim overall claim + + align:start position:0% +heuristics but my claim overall claim + + + align:start position:0% +heuristics but my claim overall claim +that I'm going to have to spend a bunch + + align:start position:0% +that I'm going to have to spend a bunch + + + align:start position:0% +that I'm going to have to spend a bunch +of time here justifying and eventually + + align:start position:0% +of time here justifying and eventually + + + align:start position:0% +of time here justifying and eventually +proving is that we can + + align:start position:0% + + + + align:start position:0% + +solve this + + align:start position:0% + + + + align:start position:0% + +problem + + align:start position:0% +problem + + + align:start position:0% +problem +using a greedy Al + + align:start position:0% + + + + align:start position:0% + +now what is a greedy algorithm you've + + align:start position:0% +now what is a greedy algorithm you've + + + align:start position:0% +now what is a greedy algorithm you've +seen some examples um as the name + + align:start position:0% +seen some examples um as the name + + + align:start position:0% +seen some examples um as the name +implies it's something that's + + align:start position:0% +implies it's something that's + + + align:start position:0% +implies it's something that's +uh myopic it's doesn't look ahead it + + align:start position:0% +uh myopic it's doesn't look ahead it + + + align:start position:0% +uh myopic it's doesn't look ahead it +looks to + + align:start position:0% +looks to + + + align:start position:0% +looks to +maximize the the very first thing that + + align:start position:0% +maximize the the very first thing that + + + align:start position:0% +maximize the the very first thing that +you can maximize uh it uh it + + align:start position:0% +you can maximize uh it uh it + + + align:start position:0% +you can maximize uh it uh it +says you traffic is a good example uh + + align:start position:0% +says you traffic is a good example uh + + + align:start position:0% +says you traffic is a good example uh +don't let anybody cut in front of you + + align:start position:0% +don't let anybody cut in front of you + + + align:start position:0% +don't let anybody cut in front of you +uh you got some room up there you know + + align:start position:0% +uh you got some room up there you know + + + align:start position:0% +uh you got some room up there you know +get up there + + align:start position:0% +get up there + + + align:start position:0% +get up there +as generally people um are greedy when + + align:start position:0% +as generally people um are greedy when + + + align:start position:0% +as generally people um are greedy when +it comes to uh you know getting to work + + align:start position:0% +it comes to uh you know getting to work + + + align:start position:0% +it comes to uh you know getting to work +uh trying to uh minimize the time in + + align:start position:0% +uh trying to uh minimize the time in + + + align:start position:0% +uh trying to uh minimize the time in +this case on the time that they spend on + + align:start position:0% +this case on the time that they spend on + + + align:start position:0% +this case on the time that they spend on +the road but uh we've had other examples + + align:start position:0% +the road but uh we've had other examples + + + align:start position:0% +the road but uh we've had other examples +uh for example when you uh look at + + align:start position:0% +uh for example when you uh look at + + + align:start position:0% +uh for example when you uh look at +interval scheduling uh you might say I'm + + align:start position:0% +interval scheduling uh you might say I'm + + + align:start position:0% +interval scheduling uh you might say I'm +going to pick uh uh the smallest request + + align:start position:0% +going to pick uh uh the smallest request + + + align:start position:0% +going to pick uh uh the smallest request +and I'm going to pick the smallest + + align:start position:0% +and I'm going to pick the smallest + + + align:start position:0% +and I'm going to pick the smallest +request first and I'm going to try and + + align:start position:0% +request first and I'm going to try and + + + align:start position:0% +request first and I'm going to try and +collect together as many requests as + + align:start position:0% +collect together as many requests as + + + align:start position:0% +collect together as many requests as +possible and if the requests are small + + align:start position:0% +possible and if the requests are small + + + align:start position:0% +possible and if the requests are small +in the sense that SI and fi for the two + + align:start position:0% +in the sense that SI and fi for the two + + + align:start position:0% +in the sense that SI and fi for the two +requests are uh close to each other then + + align:start position:0% +requests are uh close to each other then + + + align:start position:0% +requests are uh close to each other then +maybe that's the best strategy right so + + align:start position:0% +maybe that's the best strategy right so + + + align:start position:0% +maybe that's the best strategy right so +that's an example of uh a greedy + + align:start position:0% +that's an example of uh a greedy + + + align:start position:0% +that's an example of uh a greedy +strategy for our particular example but + + align:start position:0% +strategy for our particular example but + + + align:start position:0% +strategy for our particular example but +just + + align:start position:0% +just + + + align:start position:0% +just +to give you a slightly better definition + + align:start position:0% +to give you a slightly better definition + + + align:start position:0% +to give you a slightly better definition +of of greedy then what I've said so + + align:start position:0% + + + + align:start position:0% + +far a greedy algorithm is + + align:start position:0% + + + + align:start position:0% + +uh myopic + + align:start position:0% + + + + align:start position:0% + +algorithm that does two things it + + align:start position:0% + + + + align:start position:0% + +processes the + + align:start position:0% + + + + align:start position:0% + +input one piece at a time + + align:start position:0% + + + + align:start position:0% + +with no apparent look + + align:start position:0% + + + + align:start position:0% + +ahead so what happens is that read + + align:start position:0% +ahead so what happens is that read + + + align:start position:0% +ahead so what happens is that read +algorithms are typically quite + + align:start position:0% +algorithms are typically quite + + + align:start position:0% +algorithms are typically quite +efficient um what you end up doing is um + + align:start position:0% +efficient um what you end up doing is um + + + align:start position:0% +efficient um what you end up doing is um +looking at a small part of the problem + + align:start position:0% +looking at a small part of the problem + + + align:start position:0% +looking at a small part of the problem +instance and deciding what to do uh when + + align:start position:0% +instance and deciding what to do uh when + + + align:start position:0% +instance and deciding what to do uh when +once you've done that uh then you're in + + align:start position:0% +once you've done that uh then you're in + + + align:start position:0% +once you've done that uh then you're in +a situation where the problem has gotten + + align:start position:0% +a situation where the problem has gotten + + + align:start position:0% +a situation where the problem has gotten +a little bit simpler because you've + + align:start position:0% +a little bit simpler because you've + + + align:start position:0% +a little bit simpler because you've +already solved part of it and then you + + align:start position:0% +already solved part of it and then you + + + align:start position:0% +already solved part of it and then you +move + + align:start position:0% +move + + + align:start position:0% +move +on so what would a template for a greedy + + align:start position:0% +on so what would a template for a greedy + + + align:start position:0% +on so what would a template for a greedy +algorithm look like for our interval + + align:start position:0% +algorithm look like for our interval + + + align:start position:0% +algorithm look like for our interval +scheduling + + align:start position:0% +scheduling + + + align:start position:0% +scheduling +problem here's here's a template that + + align:start position:0% +problem here's here's a template that + + + align:start position:0% +problem here's here's a template that +hopefully puts it all together and gives + + align:start position:0% +hopefully puts it all together and gives + + + align:start position:0% +hopefully puts it all together and gives +you a a good sense of what I mean by + + align:start position:0% +you a a good sense of what I mean by + + + align:start position:0% +you a a good sense of what I mean by +greedy at least in this + + align:start position:0% +greedy at least in this + + + align:start position:0% +greedy at least in this +context + + align:start position:0% +context + + + align:start position:0% +context +so before we even get into + + align:start position:0% +so before we even get into + + + align:start position:0% +so before we even get into +particulars of uh selection + + align:start position:0% +particulars of uh selection + + + align:start position:0% +particulars of uh selection +strategies let me give you a template + + align:start position:0% +strategies let me give you a template + + + align:start position:0% +strategies let me give you a template +for greedy interval + + align:start position:0% + + + + align:start position:0% + +scheduling so step one use a simple + + align:start position:0% + + + + align:start position:0% + +rule to select a + + align:start position:0% +rule to select a + + + align:start position:0% +rule to select a +request + + align:start position:0% + + + + align:start position:0% + +and once you do + + align:start position:0% +and once you do + + + align:start position:0% +and once you do +that if you've selected a particular + + align:start position:0% +that if you've selected a particular + + + align:start position:0% +that if you've selected a particular +request let's say you've selected + + align:start position:0% +request let's say you've selected + + + align:start position:0% +request let's say you've selected +one what happens + + align:start position:0% +one what happens + + + align:start position:0% +one what happens +now once you've selected + + align:start position:0% +now once you've selected + + + align:start position:0% +now once you've selected +one well you're done you can select two + + align:start position:0% +one well you're done you can select two + + + align:start position:0% +one well you're done you can select two +you can select three you can't select + + align:start position:0% +you can select three you can't select + + + align:start position:0% +you can select three you can't select +four you can select five you can select + + align:start position:0% +four you can select five you can select + + + align:start position:0% +four you can select five you can select +six right so if you selected one in this + + align:start position:0% +six right so if you selected one in this + + + align:start position:0% +six right so if you selected one in this +case uh your done but we have to codify + + align:start position:0% +case uh your done but we have to codify + + + align:start position:0% +case uh your done but we have to codify +that in a step here and what that means + + align:start position:0% +that in a step here and what that means + + + align:start position:0% +that in a step here and what that means +is that we have to reject all + + align:start position:0% +is that we have to reject all + + + align:start position:0% +is that we have to reject all +requests that are + + align:start position:0% + + + + align:start position:0% + +incompatible with + + align:start position:0% +incompatible with + + + align:start position:0% +incompatible with +I okay and at this point because we've + + align:start position:0% +I okay and at this point because we've + + + align:start position:0% +I okay and at this point because we've +rejected a bunch of requests our problem + + align:start position:0% +rejected a bunch of requests our problem + + + align:start position:0% +rejected a bunch of requests our problem +got + + align:start position:0% +got + + + align:start position:0% +got +smaller okay and + + align:start position:0% +smaller okay and + + + align:start position:0% +smaller okay and +so you now + + align:start position:0% +so you now + + + align:start position:0% +so you now +have a smaller problem and you just + + align:start position:0% +have a smaller problem and you just + + + align:start position:0% +have a smaller problem and you just +repeat go back to step one until all + + align:start position:0% +repeat go back to step one until all + + + align:start position:0% +repeat go back to step one until all +requests are + + align:start position:0% + + + + align:start position:0% + +processed right so that's a classical + + align:start position:0% +processed right so that's a classical + + + align:start position:0% +processed right so that's a classical +template for a greedy + + align:start position:0% +template for a greedy + + + align:start position:0% +template for a greedy +algorithm uh you just + + align:start position:0% +algorithm uh you just + + + align:start position:0% +algorithm uh you just +go through these really simple steps and + + align:start position:0% +go through these really simple steps and + + + align:start position:0% +go through these really simple steps and +the reason this is a template is because + + align:start position:0% +the reason this is a template is because + + + align:start position:0% +the reason this is a template is because +I haven't specified a particular Rule + + align:start position:0% +I haven't specified a particular Rule + + + align:start position:0% +I haven't specified a particular Rule +and so it's not quite + + align:start position:0% +and so it's not quite + + + align:start position:0% +and so it's not quite +an algorithm that you can code yet + + align:start position:0% +an algorithm that you can code yet + + + align:start position:0% +an algorithm that you can code yet +because we need a + + align:start position:0% +because we need a + + + align:start position:0% +because we need a +rule + + align:start position:0% +rule + + + align:start position:0% +rule +so with all of that context let me ask + + align:start position:0% +so with all of that context let me ask + + + align:start position:0% +so with all of that context let me ask +you uh what is a rule + + align:start position:0% +you uh what is a rule + + + align:start position:0% +you uh what is a rule +that you think would work well for an + + align:start position:0% +that you think would work well for an + + + align:start position:0% +that you think would work well for an +interval scheduling problem yeah go + + align:start position:0% +interval scheduling problem yeah go + + + align:start position:0% +interval scheduling problem yeah go +ahead one with the select one with the + + align:start position:0% +ahead one with the select one with the + + + align:start position:0% +ahead one with the select one with the +earliest finish time all right well I + + align:start position:0% +earliest finish time all right well I + + + align:start position:0% +earliest finish time all right well I +did not want that + + align:start position:0% +did not want that + + + align:start position:0% +did not want that +answer but now that uh you've given me + + align:start position:0% +answer but now that uh you've given me + + + align:start position:0% +answer but now that uh you've given me +the answer I have to do something about + + align:start position:0% +the answer I have to do something about + + + align:start position:0% +the answer I have to do something about +this right so I want a different answer + + align:start position:0% +this right so I want a different answer + + + align:start position:0% +this right so I want a different answer +but uh so we'll go to a different person + + align:start position:0% +but uh so we'll go to a different person + + + align:start position:0% +but uh so we'll go to a different person +but before I do that um let me uh uh uh + + align:start position:0% +but before I do that um let me uh uh uh + + + align:start position:0% +but before I do that um let me uh uh uh +reward you for that answer I did not + + align:start position:0% +reward you for that answer I did not + + + align:start position:0% +reward you for that answer I did not +want um with a a limited edition + + align:start position:0% +want um with a a limited edition + + + align:start position:0% +want um with a a limited edition + + align:start position:0% + + + align:start position:0% +frisbee okay all right you need to stand + + align:start position:0% +frisbee okay all right you need to stand + + + align:start position:0% +frisbee okay all right you need to stand +up because uh I don't want to take + + align:start position:0% +up because uh I don't want to take + + + align:start position:0% +up because uh I don't want to take +people's heads off yeah sorry right so + + align:start position:0% +people's heads off yeah sorry right so + + + align:start position:0% +people's heads off yeah sorry right so +here you go all right + + align:start position:0% +here you go all right + + + align:start position:0% +here you go all right +good so people do uh people do cookies + + align:start position:0% +good so people do uh people do cookies + + + align:start position:0% +good so people do uh people do cookies +and Candy I think uh Eric Nancy and I + + align:start position:0% +and Candy I think uh Eric Nancy and I + + + align:start position:0% +and Candy I think uh Eric Nancy and I +are + + align:start position:0% +are + + + align:start position:0% +are +cooler so we do + + align:start position:0% +cooler so we do + + + align:start position:0% +cooler so we do +frisbee okay all right good so uh the + + align:start position:0% +frisbee okay all right good so uh the + + + align:start position:0% +frisbee okay all right good so uh the +fact of the matter was that uh this + + align:start position:0% +fact of the matter was that uh this + + + align:start position:0% +fact of the matter was that uh this +class was scheduled for 9:30 to + + align:start position:0% +class was scheduled for 9:30 to + + + align:start position:0% +class was scheduled for 9:30 to +11: on Tuesdays and Thursdays that's + + align:start position:0% +11: on Tuesdays and Thursdays that's + + + align:start position:0% +11: on Tuesdays and Thursdays that's +when we decided to do + + align:start position:0% +when we decided to do + + + align:start position:0% +when we decided to do +frisbees uh and then it got shifted over + + align:start position:0% +frisbees uh and then it got shifted over + + + align:start position:0% +frisbees uh and then it got shifted over +to 11 to 12:30 but then we bought all + + align:start position:0% +to 11 to 12:30 but then we bought all + + + align:start position:0% +to 11 to 12:30 but then we bought all +these frisbees so we said whatever right + + align:start position:0% +these frisbees so we said whatever right + + + align:start position:0% +these frisbees so we said whatever right +it's not like we could use all of them + + align:start position:0% +it's not like we could use all of them + + + align:start position:0% +it's not like we could use all of them +all right good so I don't like that + + align:start position:0% +all right good so I don't like that + + + align:start position:0% +all right good so I don't like that +answer uh uh and uh I want a different + + align:start position:0% +answer uh uh and uh I want a different + + + align:start position:0% +answer uh uh and uh I want a different +one give me give me another one yeah go + + align:start position:0% +one give me give me another one yeah go + + + align:start position:0% +one give me give me another one yeah go +ahead I'm + + align:start position:0% +ahead I'm + + + align:start position:0% +ahead I'm +sorry iterate through in numerical order + + align:start position:0% +sorry iterate through in numerical order + + + align:start position:0% +sorry iterate through in numerical order +is that going to + + align:start position:0% +is that going to + + + align:start position:0% +is that going to +work and what's an example where it + + align:start position:0% +work and what's an example where it + + + align:start position:0% +work and what's an example where it +didn't work the one right there right + + align:start position:0% +didn't work the one right there right + + + align:start position:0% +didn't work the one right there right +right should I get her of + + align:start position:0% +right should I get her of + + + align:start position:0% +right should I get her of +frisbee we should I'm going to be + + align:start position:0% +frisbee we should I'm going to be + + + align:start position:0% +frisbee we should I'm going to be +generous at the beginning you can just + + align:start position:0% +generous at the beginning you can just + + + align:start position:0% +generous at the beginning you can just +right but that's an answer I liked yeah + + align:start position:0% +right but that's an answer I liked yeah + + + align:start position:0% +right but that's an answer I liked yeah +oh there you + + align:start position:0% +oh there you + + + align:start position:0% +oh there you +go + + align:start position:0% +go + + + align:start position:0% +go +so uh iterate through a numeric order + + align:start position:0% +so uh iterate through a numeric order + + + align:start position:0% +so uh iterate through a numeric order +isn't going to work this is a great + + align:start position:0% +isn't going to work this is a great + + + align:start position:0% +isn't going to work this is a great +example right right there right uh um + + align:start position:0% +example right right there right uh um + + + align:start position:0% +example right right there right uh um +give me another + + align:start position:0% + + + + align:start position:0% + +one I'm going to run out of frisbee + + align:start position:0% +one I'm going to run out of frisbee + + + align:start position:0% +one I'm going to run out of frisbee +right here over there yeah um try the + + align:start position:0% +right here over there yeah um try the + + + align:start position:0% +right here over there yeah um try the +one with the shortest time ah try the + + align:start position:0% +one with the shortest time ah try the + + + align:start position:0% +one with the shortest time ah try the +one with the shortest time okay so um so + + align:start position:0% +one with the shortest time okay so um so + + + align:start position:0% +one with the shortest time okay so um so +the shortest time in this case might be + + align:start position:0% +the shortest time in this case might be + + + align:start position:0% +the shortest time in this case might be +this one right uh the shortest time + + align:start position:0% +this one right uh the shortest time + + + align:start position:0% +this one right uh the shortest time +might be this one and hey may that might + + align:start position:0% +might be this one and hey may that might + + + align:start position:0% +might be this one and hey may that might +work in this case because you pick this + + align:start position:0% +work in this case because you pick this + + + align:start position:0% +work in this case because you pick this +one which is the shortest or maybe it's + + align:start position:0% +one which is the shortest or maybe it's + + + align:start position:0% +one which is the shortest or maybe it's +five which is the shortest uh either way + + align:start position:0% +five which is the shortest uh either way + + + align:start position:0% +five which is the shortest uh either way +you could get two five and six you know + + align:start position:0% +you could get two five and six you know + + + align:start position:0% +you could get two five and six you know +looking at this picture seems to work uh + + align:start position:0% +looking at this picture seems to work uh + + + align:start position:0% +looking at this picture seems to work uh +maybe four five and six uh if you pick + + align:start position:0% +maybe four five and six uh if you pick + + + align:start position:0% +maybe four five and six uh if you pick +five first Etc right I'll give you a + + align:start position:0% +five first Etc right I'll give you a + + + align:start position:0% +five first Etc right I'll give you a +frisbee if you can take that same + + align:start position:0% +frisbee if you can take that same + + + align:start position:0% +frisbee if you can take that same +algorithm and give me a counter + + align:start position:0% + + + + align:start position:0% + +example let's say you have two requests + + align:start position:0% +example let's say you have two requests + + + align:start position:0% +example let's say you have two requests +which don't and then there's there's one + + align:start position:0% +which don't and then there's there's one + + + align:start position:0% +which don't and then there's there's one +right in the middle exactly right yeah + + align:start position:0% +right in the middle exactly right yeah + + + align:start position:0% +right in the middle exactly right yeah +so uh let's see where what do I do oh + + align:start position:0% + + + + align:start position:0% + +here so pict tally you can look at + + align:start position:0% +here so pict tally you can look at + + + align:start position:0% +here so pict tally you can look at +this and you can actually figure out + + align:start position:0% +this and you can actually figure out + + + align:start position:0% +this and you can actually figure out +whether your heuristic works or not but + + align:start position:0% +whether your heuristic works or not but + + + align:start position:0% +whether your heuristic works or not but +this is I think what you were thinking + + align:start position:0% + + + + align:start position:0% + +about there you go + + align:start position:0% +about there you go + + + align:start position:0% +about there you go +right so you get + + align:start position:0% + + + + align:start position:0% + +one so that clearly doesn't work so this + + align:start position:0% +one so that clearly doesn't work so this + + + align:start position:0% +one so that clearly doesn't work so this +one was + + align:start position:0% + + + + align:start position:0% + +smallest doesn't work uh the suggestion + + align:start position:0% +smallest doesn't work uh the suggestion + + + align:start position:0% +smallest doesn't work uh the suggestion +here was uh numeric + + align:start position:0% + + + + align:start position:0% + +doesn't + + align:start position:0% +doesn't + + + align:start position:0% +doesn't +work + + align:start position:0% +work + + + align:start position:0% +work +um here's one that + + align:start position:0% +um here's one that + + + align:start position:0% +um here's one that +uh might actually + + align:start position:0% +uh might actually + + + align:start position:0% +uh might actually +work uh for each + + align:start position:0% + + + + align:start position:0% + +request find the number of incompatible + + align:start position:0% + + + + align:start position:0% + +requests so you got a request you can + + align:start position:0% +requests so you got a request you can + + + align:start position:0% +requests so you got a request you can +always intersect the other requests with + + align:start position:0% +always intersect the other requests with + + + align:start position:0% +always intersect the other requests with +it and decide whether the the the second + + align:start position:0% +it and decide whether the the the second + + + align:start position:0% +it and decide whether the the the second +request is compatible or not right and + + align:start position:0% +request is compatible or not right and + + + align:start position:0% +request is compatible or not right and +you do this for every other request and + + align:start position:0% +you do this for every other request and + + + align:start position:0% +you do this for every other request and +you can collect together uh numbers + + align:start position:0% +you can collect together uh numbers + + + align:start position:0% +you can collect together uh numbers +associated with how many incompatible + + align:start position:0% +associated with how many incompatible + + + align:start position:0% +associated with how many incompatible +requests a particular request has and + + align:start position:0% +requests a particular request has and + + + align:start position:0% +requests a particular request has and +you say well uh let me use that as a + + align:start position:0% +you say well uh let me use that as a + + + align:start position:0% +you say well uh let me use that as a +heuristic right so each request find + + align:start position:0% +heuristic right so each request find + + + align:start position:0% +heuristic right so each request find +number of incompatible requests and + + align:start position:0% +number of incompatible requests and + + + align:start position:0% +number of incompatible requests and +select the + + align:start position:0% + + + + align:start position:0% + +one with the + + align:start position:0% +one with the + + + align:start position:0% +one with the +minimum number of + + align:start position:0% + + + + align:start position:0% + +incompatibles + + align:start position:0% +incompatibles + + + align:start position:0% +incompatibles +right so just to be clear in this case + + align:start position:0% +right so just to be clear in this case + + + align:start position:0% +right so just to be clear in this case +you would not select one uh because + + align:start position:0% +you would not select one uh because + + + align:start position:0% +you would not select one uh because +clearly one is incompatible with every + + align:start position:0% +clearly one is incompatible with every + + + align:start position:0% +clearly one is incompatible with every +other request right so that clearly is + + align:start position:0% +other request right so that clearly is + + + align:start position:0% +other request right so that clearly is +not numeric order in this case you would + + align:start position:0% +not numeric order in this case you would + + + align:start position:0% +not numeric order in this case you would +not select this one because it's + + align:start position:0% +not select this one because it's + + + align:start position:0% +not select this one because it's +incompatible with this one and that one + + align:start position:0% +incompatible with this one and that one + + + align:start position:0% +incompatible with this one and that one +right so you select the one which has + + align:start position:0% +right so you select the one which has + + + align:start position:0% +right so you select the one which has +the minimum number of incompatibles + + align:start position:0% +the minimum number of incompatibles + + + align:start position:0% +the minimum number of incompatibles +right so do you think this is going to + + align:start position:0% +right so do you think this is going to + + + align:start position:0% +right so do you think this is going to +produce the the correct answer the + + align:start position:0% +produce the the correct answer the + + + align:start position:0% +produce the the correct answer the +maximum answer in every possible + + align:start position:0% +maximum answer in every possible + + + align:start position:0% +maximum answer in every possible +case no who said + + align:start position:0% +case no who said + + + align:start position:0% +case no who said +no well anybody who said no should give + + align:start position:0% +no well anybody who said no should give + + + align:start position:0% +no well anybody who said no should give +me a counter example yeah go go for it + + align:start position:0% +me a counter example yeah go go for it + + + align:start position:0% +me a counter example yeah go go for it +if the one that it selects has mutually + + align:start position:0% +if the one that it selects has mutually + + + align:start position:0% +if the one that it selects has mutually +incompatible collection of intervals + + align:start position:0% +incompatible collection of intervals + + + align:start position:0% +incompatible collection of intervals +with right so that's that's a good + + align:start position:0% +with right so that's that's a good + + + align:start position:0% +with right so that's that's a good +thought uh um we'll have to concretize + + align:start position:0% +thought uh um we'll have to concretize + + + align:start position:0% +thought uh um we'll have to concretize +that and uh I think this particular + + align:start position:0% +that and uh I think this particular + + + align:start position:0% +that and uh I think this particular +example does exactly what you said um + + align:start position:0% +example does exactly what you said um + + + align:start position:0% +example does exactly what you said um +which is + + align:start position:0% +which is + + + align:start position:0% +which is +instantiates your U notion of mutual + + align:start position:0% +instantiates your U notion of mutual + + + align:start position:0% +instantiates your U notion of mutual +incompatibility so here's here's an + + align:start position:0% +incompatibility so here's here's an + + + align:start position:0% +incompatibility so here's here's an +example where I have something it's a + + align:start position:0% +example where I have something it's a + + + align:start position:0% +example where I have something it's a +little more complicated as you can see + + align:start position:0% +little more complicated as you can see + + + align:start position:0% +little more complicated as you can see +this is a pretty good heuristic it's not + + align:start position:0% +this is a pretty good heuristic it's not + + + align:start position:0% +this is a pretty good heuristic it's not +perfect as you can see from this + + align:start position:0% +perfect as you can see from this + + + align:start position:0% +perfect as you can see from this +example where I have + + align:start position:0% + + + + align:start position:0% + +something like + + align:start position:0% + + + + align:start position:0% + +this so if you look at + + align:start position:0% + + + + align:start position:0% + +this what I have here is I have just a + + align:start position:0% +this what I have here is I have just a + + + align:start position:0% +this what I have here is I have just a +bunch of + + align:start position:0% +bunch of + + + align:start position:0% +bunch of +requests uh which have uh this is + + align:start position:0% +requests uh which have uh this is + + + align:start position:0% +requests uh which have uh this is +incompatible with this and that and + + align:start position:0% +incompatible with this and that and + + + align:start position:0% +incompatible with this and that and +these two so clearly a lot of + + align:start position:0% +these two so clearly a lot of + + + align:start position:0% +these two so clearly a lot of +incompatibilities for these lot of + + align:start position:0% +incompatibilities for these lot of + + + align:start position:0% +incompatibilities for these lot of +incompatibilities for these which is the + + align:start position:0% +incompatibilities for these which is the + + + align:start position:0% +incompatibilities for these which is the +minimum the one in here right but you + + align:start position:0% +minimum the one in here right but you + + + align:start position:0% +minimum the one in here right but you +what happens if you select that well + + align:start position:0% +what happens if you select that well + + + align:start position:0% +what happens if you select that well +clearly you don't get this solution + + align:start position:0% +clearly you don't get this solution + + + align:start position:0% +clearly you don't get this solution +which is optimal right the one on + + align:start position:0% +which is optimal right the one on + + + align:start position:0% +which is optimal right the one on +top right so this is a bad + + align:start position:0% + + + + align:start position:0% + +selection so this doesn't work either + + align:start position:0% +selection so this doesn't work either + + + align:start position:0% +selection so this doesn't work either +okay here you + + align:start position:0% + + + + align:start position:0% + +go so as it turns out uh the reason I + + align:start position:0% +go so as it turns out uh the reason I + + + align:start position:0% +go so as it turns out uh the reason I +didn't like that first answer was it was + + align:start position:0% +didn't like that first answer was it was + + + align:start position:0% +didn't like that first answer was it was +it was correct uh it it's actually a a + + align:start position:0% +it was correct uh it it's actually a a + + + align:start position:0% +it was correct uh it it's actually a a +beautiful heuristic earliest finish + + align:start position:0% +beautiful heuristic earliest finish + + + align:start position:0% +beautiful heuristic earliest finish +time is a huris uh that is well it's not + + align:start position:0% +time is a huris uh that is well it's not + + + align:start position:0% +time is a huris uh that is well it's not +really a heuristic in the sense that if + + align:start position:0% +really a heuristic in the sense that if + + + align:start position:0% +really a heuristic in the sense that if +you use that selection rule uh then it + + align:start position:0% +you use that selection rule uh then it + + + align:start position:0% +you use that selection rule uh then it +works + + align:start position:0% +works + + + align:start position:0% +works +in every + + align:start position:0% +in every + + + align:start position:0% +in every +case uh in every case it's going to get + + align:start position:0% +case uh in every case it's going to get + + + align:start position:0% +case uh in every case it's going to get +you the maximum number okay earliest + + align:start position:0% +you the maximum number okay earliest + + + align:start position:0% +you the maximum number okay earliest +finish time right + + align:start position:0% +finish time right + + + align:start position:0% +finish time right +so what does that mean well it just + + align:start position:0% +so what does that mean well it just + + + align:start position:0% +so what does that mean well it just +means that I'm going to + + align:start position:0% + + + + align:start position:0% + +scan the F of I associated with the list + + align:start position:0% +scan the F of I associated with the list + + + align:start position:0% +scan the F of I associated with the list +of requests that I have and I'm going to + + align:start position:0% +of requests that I have and I'm going to + + + align:start position:0% +of requests that I have and I'm going to +pick the one that is + + align:start position:0% +pick the one that is + + + align:start position:0% +pick the one that is +minimum minimum ffi means earliest + + align:start position:0% +minimum minimum ffi means earliest + + + align:start position:0% +minimum minimum ffi means earliest +finish time right now you can just step + + align:start position:0% +finish time right now you can just step + + + align:start position:0% +finish time right now you can just step +back and I'm not going to do this for + + align:start position:0% +back and I'm not going to do this for + + + align:start position:0% +back and I'm not going to do this for +every diagram that I have up here but + + align:start position:0% +every diagram that I have up here but + + + align:start position:0% +every diagram that I have up here but +look at every example that I've put up + + align:start position:0% +look at every example that I've put up + + + align:start position:0% +look at every example that I've put up +apply the selection rule associated with + + align:start position:0% +apply the selection rule associated with + + + align:start position:0% +apply the selection rule associated with +earliest finish + + align:start position:0% +earliest finish + + + align:start position:0% +earliest finish +time and you'll see that it works and + + align:start position:0% +time and you'll see that it works and + + + align:start position:0% +time and you'll see that it works and +gets you the maximum number for + + align:start position:0% +gets you the maximum number for + + + align:start position:0% +gets you the maximum number for +example uh over + + align:start position:0% +example uh over + + + align:start position:0% +example uh over +here this has the earliest finish time + + align:start position:0% +here this has the earliest finish time + + + align:start position:0% +here this has the earliest finish time +okay + + align:start position:0% +okay + + + align:start position:0% +okay +not this not this it's over here so you + + align:start position:0% +not this not this it's over here so you + + + align:start position:0% +not this not this it's over here so you +pick that and then you use the the + + align:start position:0% +pick that and then you use the the + + + align:start position:0% +pick that and then you use the the +greedy algorithm step two to eliminate + + align:start position:0% +greedy algorithm step two to eliminate + + + align:start position:0% +greedy algorithm step two to eliminate +all of the intervals that are + + align:start position:0% +all of the intervals that are + + + align:start position:0% +all of the intervals that are +incompatible so these go away right once + + align:start position:0% +incompatible so these go away right once + + + align:start position:0% +incompatible so these go away right once +this goes away this one has the earliest + + align:start position:0% +this goes away this one has the earliest + + + align:start position:0% +this goes away this one has the earliest +finish time right and so on and so forth + + align:start position:0% +finish time right and so on and so forth + + + align:start position:0% +finish time right and so on and so forth +so this is something that you can prove + + align:start position:0% +so this is something that you can prove + + + align:start position:0% +so this is something that you can prove +through examples right that's not really + + align:start position:0% +through examples right that's not really + + + align:start position:0% +through examples right that's not really +a good notion but you can prove to + + align:start position:0% +a good notion but you can prove to + + + align:start position:0% +a good notion but you can prove to +yourself uh using examples and this is + + align:start position:0% +yourself uh using examples and this is + + + align:start position:0% +yourself uh using examples and this is +where I I guess the essence of essence + + align:start position:0% +where I I guess the essence of essence + + + align:start position:0% +where I I guess the essence of essence +of 6046 to some extent 006 uh comes into + + align:start position:0% +of 6046 to some extent 006 uh comes into + + + align:start position:0% +of 6046 to some extent 006 uh comes into +play we will have to prove beyond a + + align:start position:0% +play we will have to prove beyond a + + + align:start position:0% +play we will have to prove beyond a +shadow of a + + align:start position:0% +shadow of a + + + align:start position:0% +shadow of a +doubt using mathematical rigor that the + + align:start position:0% +doubt using mathematical rigor that the + + + align:start position:0% +doubt using mathematical rigor that the +earliest finish + + align:start position:0% +earliest finish + + + align:start position:0% +earliest finish +time selection rule always gives + + align:start position:0% +time selection rule always gives + + + align:start position:0% +time selection rule always gives +the maximum number of requests okay and + + align:start position:0% +the maximum number of requests okay and + + + align:start position:0% +the maximum number of requests okay and +we're going to do that it's going to + + align:start position:0% +we're going to do that it's going to + + + align:start position:0% +we're going to do that it's going to +take us a little bit of time but that's + + align:start position:0% +take us a little bit of time but that's + + + align:start position:0% +take us a little bit of time but that's +the kind of thing you will be expected + + align:start position:0% +the kind of thing you will be expected + + + align:start position:0% +the kind of thing you will be expected +to do and you'll see a lot of in + + align:start position:0% +to do and you'll see a lot of in + + + align:start position:0% +to do and you'll see a lot of in + + align:start position:0% + + + align:start position:0% +okay so everyone by by earliest finish + + align:start position:0% +okay so everyone by by earliest finish + + + align:start position:0% +okay so everyone by by earliest finish +time y go + + align:start position:0% + + + + align:start position:0% + +ahead + + align:start position:0% +ahead + + + align:start position:0% +ahead +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +uh well then you get one for if there's + + align:start position:0% +uh well then you get one for if there's + + + align:start position:0% +uh well then you get one for if there's +only two requests and uh your maximum + + align:start position:0% +only two requests and uh your maximum + + + align:start position:0% +only two requests and uh your maximum +number is one so you pick it doesn't + + align:start position:0% +number is one so you pick it doesn't + + + align:start position:0% +number is one so you pick it doesn't +matter it's not like you want efficiency + + align:start position:0% +matter it's not like you want efficiency + + + align:start position:0% +matter it's not like you want efficiency +of your resource in this particular case + + align:start position:0% +of your resource in this particular case + + + align:start position:0% +of your resource in this particular case +we will look at uh cases where uh you + + align:start position:0% +we will look at uh cases where uh you + + + align:start position:0% +we will look at uh cases where uh you +might have an extra consideration + + align:start position:0% +might have an extra consideration + + + align:start position:0% +might have an extra consideration +associated with your problem which + + align:start position:0% +associated with your problem which + + + align:start position:0% +associated with your problem which +changes the problem that says I want my + + align:start position:0% +changes the problem that says I want my + + + align:start position:0% +changes the problem that says I want my +resource to be maximally utilized if you + + align:start position:0% +resource to be maximally utilized if you + + + align:start position:0% +resource to be maximally utilized if you +do that then this doesn't work and + + align:start position:0% +do that then this doesn't work and + + + align:start position:0% +do that then this doesn't work and +that's exactly it's a great question + + align:start position:0% +that's exactly it's a great question + + + align:start position:0% +that's exactly it's a great question +asked uh but I did say that uh uh that + + align:start position:0% +asked uh but I did say that uh uh that + + + align:start position:0% +asked uh but I did say that uh uh that +we were going to uh look at the theme + + align:start position:0% +we were going to uh look at the theme + + + align:start position:0% +we were going to uh look at the theme +here uh which I don't have anymore but + + align:start position:0% +here uh which I don't have anymore but + + + align:start position:0% +here uh which I don't have anymore but +of how problems changes change + + align:start position:0% +of how problems changes change + + + align:start position:0% +of how problems changes change +algorithms right and so that's a problem + + align:start position:0% +algorithms right and so that's a problem + + + align:start position:0% +algorithms right and so that's a problem +change okay you got + + align:start position:0% + + + + align:start position:0% + +question + + align:start position:0% +question + + + align:start position:0% +question +right + + align:start position:0% + + + + align:start position:0% + +inters okay so you're are you claiming + + align:start position:0% +inters okay so you're are you claiming + + + align:start position:0% +inters okay so you're are you claiming +that there's going to be a counter + + align:start position:0% +that there's going to be a counter + + + align:start position:0% +that there's going to be a counter +example to earliest finish time all + + align:start position:0% +example to earliest finish time all + + + align:start position:0% +example to earliest finish time all +right I would write it down on a sheet + + align:start position:0% +right I would write it down on a sheet + + + align:start position:0% +right I would write it down on a sheet +of paper right uh and get me a concrete + + align:start position:0% +of paper right uh and get me a concrete + + + align:start position:0% +of paper right uh and get me a concrete +example and you can just slide it by and + + align:start position:0% +example and you can just slide it by and + + + align:start position:0% +example and you can just slide it by and +if you get that before I finish my proof + + align:start position:0% +if you get that before I finish my proof + + + align:start position:0% +if you get that before I finish my proof +right uh you win okay uh um uh so I + + align:start position:0% +right uh you win okay uh um uh so I + + + align:start position:0% +right uh you win okay uh um uh so I +would write it down right just write it + + align:start position:0% +would write it down right just write it + + + align:start position:0% +would write it down right just write it +down right so good all right so this is + + align:start position:0% +down right so good all right so this is + + + align:start position:0% +down right so good all right so this is +a contest now + + align:start position:0% +a contest now + + + align:start position:0% +a contest now +okay all right so we're going to try and + + align:start position:0% +okay all right so we're going to try and + + + align:start position:0% +okay all right so we're going to try and +prove + + align:start position:0% + + + + align:start position:0% + +this so uh there's many ways you could + + align:start position:0% +this so uh there's many ways you could + + + align:start position:0% +this so uh there's many ways you could +prove things and I mean prove things + + align:start position:0% +prove things and I mean prove things + + + align:start position:0% +prove things and I mean prove things +properly uh I don't know if you've read + + align:start position:0% +properly uh I don't know if you've read + + + align:start position:0% +properly uh I don't know if you've read +the old + + align:start position:0% +the old + + + align:start position:0% +the old +6042 uh proof techniques that are + + align:start position:0% +6042 uh proof techniques that are + + + align:start position:0% +6042 uh proof techniques that are +invalid you know which is things like + + align:start position:0% +invalid you know which is things like + + + align:start position:0% +invalid you know which is things like +proof by + + align:start position:0% +proof by + + + align:start position:0% +proof by +intimidation um you know proof uh + + align:start position:0% +intimidation um you know proof uh + + + align:start position:0% +intimidation um you know proof uh +because the lecturer said so you know + + align:start position:0% +because the lecturer said so you know + + + align:start position:0% +because the lecturer said so you know +things like that uh this is going to be + + align:start position:0% +things like that uh this is going to be + + + align:start position:0% +things like that uh this is going to be +a classical proof technique it's going + + align:start position:0% +a classical proof technique it's going + + + align:start position:0% +a classical proof technique it's going +to be a proof by induction right we're + + align:start position:0% +to be a proof by induction right we're + + + align:start position:0% +to be a proof by induction right we're +going to go into it in some detail um + + align:start position:0% +going to go into it in some detail um + + + align:start position:0% +going to go into it in some detail um +later on in the term we're going to put + + align:start position:0% +later on in the term we're going to put + + + align:start position:0% +later on in the term we're going to put +out uh sketches of proofs we're going to + + align:start position:0% +out uh sketches of proofs we're going to + + + align:start position:0% +out uh sketches of proofs we're going to +be skipping steps in lecture uh that are + + align:start position:0% +be skipping steps in lecture uh that are + + + align:start position:0% +be skipping steps in lecture uh that are +obvious uh or maybe not so obvious but + + align:start position:0% +obvious uh or maybe not so obvious but + + + align:start position:0% +obvious uh or maybe not so obvious but +if you paid attention uh then uh you can + + align:start position:0% +if you paid attention uh then uh you can + + + align:start position:0% +if you paid attention uh then uh you can +infer uh the middle step for example and + + align:start position:0% +infer uh the middle step for example and + + + align:start position:0% +infer uh the middle step for example and +so we'll be doing uh proof sketches + + align:start position:0% +so we'll be doing uh proof sketches + + + align:start position:0% +so we'll be doing uh proof sketches +right right and proof sketches are not + + align:start position:0% +right right and proof sketches are not + + + align:start position:0% +right right and proof sketches are not +sketchy proofs okay so uh keep that in + + align:start position:0% +sketchy proofs okay so uh keep that in + + + align:start position:0% +sketchy proofs okay so uh keep that in +mind but this particular proof that + + align:start position:0% +mind but this particular proof that + + + align:start position:0% +mind but this particular proof that +we're going to do I'm going to put in + + align:start position:0% +we're going to do I'm going to put in + + + align:start position:0% +we're going to do I'm going to put in +all the steps because it's our first one + + align:start position:0% +all the steps because it's our first one + + + align:start position:0% +all the steps because it's our first one +okay and so what we're going to do here + + align:start position:0% +okay and so what we're going to do here + + + align:start position:0% +okay and so what we're going to do here +is prove a + + align:start position:0% +is prove a + + + align:start position:0% +is prove a +claim and the claim is + + align:start position:0% +claim and the claim is + + + align:start position:0% +claim and the claim is +simply + + align:start position:0% + + + + align:start position:0% + +that oops this is + + align:start position:0% +that oops this is + + + align:start position:0% +that oops this is +not writing very + + align:start position:0% + + + + align:start position:0% + +well what is going on + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +okay back to the + + align:start position:0% + + + + align:start position:0% + +white given a + + align:start position:0% +white given a + + + align:start position:0% +white given a +list of interval + + align:start position:0% + + + + align:start position:0% + +L are greedy + + align:start position:0% + + + + align:start position:0% + +algorithm with earliest finish + + align:start position:0% + + + + align:start position:0% + +time + + align:start position:0% + + + + align:start position:0% + +produces + + align:start position:0% +produces + + + align:start position:0% +produces +Kar + + align:start position:0% + + + + align:start position:0% + +intervals where Kar is minimum + + align:start position:0% + + + + align:start position:0% + +so that's what we'd like to + + align:start position:0% + + + + align:start position:0% + +prove sorry what + + align:start position:0% +prove sorry what + + + align:start position:0% +prove sorry what +happened oh + + align:start position:0% +happened oh + + + align:start position:0% +happened oh +right good + + align:start position:0% +right good + + + align:start position:0% +right good +point + + align:start position:0% + + + + align:start position:0% + +Max what we're going to do is prove this + + align:start position:0% +Max what we're going to do is prove this + + + align:start position:0% +Max what we're going to do is prove this +by induction and it's going to be + + align:start position:0% +by induction and it's going to be + + + align:start position:0% +by induction and it's going to be +induction on K + + align:start position:0% + + + + align:start position:0% + +star and so the base + + align:start position:0% +star and so the base + + + align:start position:0% +star and so the base +case is almost always with induction + + align:start position:0% +case is almost always with induction + + + align:start position:0% +case is almost always with induction +proofs trivial and it's similar here as + + align:start position:0% +proofs trivial and it's similar here as + + + align:start position:0% +proofs trivial and it's similar here as +well and in the base case + + align:start position:0% +well and in the base case + + + align:start position:0% +well and in the base case +if you have a single interval in your + + align:start position:0% +if you have a single interval in your + + + align:start position:0% +if you have a single interval in your +list then obviously that's a trivial + + align:start position:0% +list then obviously that's a trivial + + + align:start position:0% +list then obviously that's a trivial +example but what I'm saying here for the + + align:start position:0% +example but what I'm saying here for the + + + align:start position:0% +example but what I'm saying here for the +base case is slightly different it says + + align:start position:0% +base case is slightly different it says + + + align:start position:0% +base case is slightly different it says +that the optimal solution has a single + + align:start position:0% +that the optimal solution has a single + + + align:start position:0% +that the optimal solution has a single +interval right and so now if your + + align:start position:0% +interval right and so now if your + + + align:start position:0% +interval right and so now if your +problem has one interval or two + + align:start position:0% +problem has one interval or two + + + align:start position:0% +problem has one interval or two +intervals or three intervals you can + + align:start position:0% +intervals or three intervals you can + + + align:start position:0% +intervals or three intervals you can +always pick one and it's clearly going + + align:start position:0% +always pick one and it's clearly going + + + align:start position:0% +always pick one and it's clearly going +to be a valid schedule because you don't + + align:start position:0% +to be a valid schedule because you don't + + + align:start position:0% +to be a valid schedule because you don't +have to check compatibility and so the + + align:start position:0% +have to check compatibility and so the + + + align:start position:0% +have to check compatibility and so the +base case is Trivial even in the case + + align:start position:0% +base case is Trivial even in the case + + + align:start position:0% +base case is Trivial even in the case +where we're not talking about necess not + + align:start position:0% +where we're not talking about necess not + + + align:start position:0% +where we're not talking about necess not +we're not talking just of intervals that + + align:start position:0% +we're not talking just of intervals that + + + align:start position:0% +we're not talking just of intervals that +have cardinality one but the optimal + + align:start position:0% +have cardinality one but the optimal + + + align:start position:0% +have cardinality one but the optimal +schedule has cardinality one so that's a + + align:start position:0% +schedule has cardinality one so that's a + + + align:start position:0% +schedule has cardinality one so that's a +trivial + + align:start position:0% +trivial + + + align:start position:0% +trivial +case so the hard work of course in + + align:start position:0% +case so the hard work of course in + + + align:start position:0% +case so the hard work of course in +uh induction proves + + align:start position:0% +uh induction proves + + + align:start position:0% +uh induction proves +this assuming the hypothesis and proving + + align:start position:0% +this assuming the hypothesis and proving + + + align:start position:0% +this assuming the hypothesis and proving +the n + one or in this case the K star + + + align:start position:0% +the n + one or in this case the K star + + + + align:start position:0% +the n + one or in this case the K star + +one k + + align:start position:0% +one k + + + align:start position:0% +one k +and that's what we'll have to work + + align:start position:0% +and that's what we'll have to work + + + align:start position:0% +and that's what we'll have to work +on so let's say + + align:start position:0% + + + + align:start position:0% + +that the + + align:start position:0% +that the + + + align:start position:0% +that the +claim + + align:start position:0% +claim + + + align:start position:0% +claim +holds + + align:start position:0% +holds + + + align:start position:0% +holds +for K + + align:start position:0% +for K + + + align:start position:0% +for K +star + + align:start position:0% +star + + + align:start position:0% +star +and we are + + align:start position:0% + + + + align:start position:0% + +given a + + align:start position:0% +given a + + + align:start position:0% +given a +list of intervals + + align:start position:0% + + + + align:start position:0% + +whose optimal + + align:start position:0% + + + + align:start position:0% + +schedule is Kar + + + align:start position:0% + + + + align:start position:0% + +one it + + align:start position:0% +one it + + + align:start position:0% +one it +has Kar + one intervals in the optimal + + align:start position:0% +has Kar + one intervals in the optimal + + + align:start position:0% +has Kar + one intervals in the optimal +schedule so L may be some large number + + align:start position:0% +schedule so L may be some large number + + + align:start position:0% +schedule so L may be some large number +capital L maybe in the hundreds and K + + align:start position:0% +capital L maybe in the hundreds and K + + + align:start position:0% +capital L maybe in the hundreds and K +star maybe 10 what have you they they're + + align:start position:0% +star maybe 10 what have you they they're + + + align:start position:0% +star maybe 10 what have you they they're +different I want to point that out so + + align:start position:0% +different I want to point that out so + + + align:start position:0% +different I want to point that out so +our optimal schedule we're going to + + align:start position:0% +our optimal schedule we're going to + + + align:start position:0% +our optimal schedule we're going to +write out as as + + align:start position:0% + + + + align:start position:0% + +this uh s + + align:start position:0% +this uh s + + + align:start position:0% +this uh s +star so usually we use star for optimal + + align:start position:0% +star so usually we use star for optimal + + + align:start position:0% +star so usually we use star for optimal +in 046 and it's got uh K star + one + + align:start position:0% +in 046 and it's got uh K star + one + + + align:start position:0% +in 046 and it's got uh K star + one +entries and those entries look like uh s + + align:start position:0% +entries and those entries look like uh s + + + align:start position:0% +entries and those entries look like uh s +uh F in uh pairs so I'm going to be + + align:start position:0% +uh F in uh pairs so I'm going to be + + + align:start position:0% +uh F in uh pairs so I'm going to be +using the subscript + + align:start position:0% +using the subscript + + + align:start position:0% +using the subscript +J1 through uh J Kar + + + align:start position:0% +J1 through uh J Kar + + + + align:start position:0% +J1 through uh J Kar + +one + + align:start position:0% +one + + + align:start position:0% +one +to denote these uh these intervals so + + align:start position:0% +to denote these uh these intervals so + + + align:start position:0% +to denote these uh these intervals so +the first one is sj1 fj1 that's an + + align:start position:0% +the first one is sj1 fj1 that's an + + + align:start position:0% +the first one is sj1 fj1 that's an +interval that's been selected and is + + align:start position:0% +interval that's been selected and is + + + align:start position:0% +interval that's been selected and is +part of our optimal solution and then if + + align:start position:0% +part of our optimal solution and then if + + + align:start position:0% +part of our optimal solution and then if +we keep going and we + + align:start position:0% +we keep going and we + + + align:start position:0% +we keep going and we +have um + + align:start position:0% +have um + + + align:start position:0% +have um +SJ K star + 1 comma f j + + align:start position:0% +SJ K star + 1 comma f j + + + align:start position:0% +SJ K star + 1 comma f j +Kar + one right so + + align:start position:0% +Kar + one right so + + + align:start position:0% +Kar + one right so +um no getting away from subscripts here + + align:start position:0% +um no getting away from subscripts here + + + align:start position:0% +um no getting away from subscripts here +in + + align:start position:0% +in + + + align:start position:0% +in +046 so that's + + align:start position:0% +046 so that's + + + align:start position:0% +046 so that's +our uh uh that's that's what we have in + + align:start position:0% +our uh uh that's that's what we have in + + + align:start position:0% +our uh uh that's that's what we have in +terms of this is what the optimal + + align:start position:0% +terms of this is what the optimal + + + align:start position:0% +terms of this is what the optimal +schedule list it's got size K star of + + align:start position:0% +schedule list it's got size K star of + + + align:start position:0% +schedule list it's got size K star of +course what we have to show is that the + + align:start position:0% +course what we have to show is that the + + + align:start position:0% +course what we have to show is that the +greedy + + align:start position:0% +greedy + + + align:start position:0% +greedy +algorithm with the earliest finish time + + align:start position:0% +algorithm with the earliest finish time + + + align:start position:0% +algorithm with the earliest finish time +is going to produce something that is K + + align:start position:0% +is going to produce something that is K + + + align:start position:0% +is going to produce something that is K +star + one in size and so that's the + + align:start position:0% +star + one in size and so that's the + + + align:start position:0% +star + one in size and so that's the +that's the hard part we can assume the + + align:start position:0% +that's the hard part we can assume the + + + align:start position:0% +that's the hard part we can assume the +inductive hypothesis and we'll have to + + align:start position:0% +inductive hypothesis and we'll have to + + + align:start position:0% +inductive hypothesis and we'll have to +do that but there's a couple of steps in + + align:start position:0% +do that but there's a couple of steps in + + + align:start position:0% +do that but there's a couple of steps in +between right + + align:start position:0% +between right + + + align:start position:0% +between right +so let's say that what we have + + align:start position:0% +so let's say that what we have + + + align:start position:0% +so let's say that what we have +is S1 through + + align:start position:0% +is S1 through + + + align:start position:0% +is S1 through +K is what the greedy algorithm produces + + align:start position:0% +K is what the greedy algorithm produces + + + align:start position:0% +K is what the greedy algorithm produces +with the earliest finish time so I'm + + align:start position:0% +with the earliest finish time so I'm + + + align:start position:0% +with the earliest finish time so I'm +going to write that + + align:start position:0% + + + + align:start position:0% + +down s i k f i + + align:start position:0% +down s i k f i + + + align:start position:0% +down s i k f i +k right so notice I've have K here and K + + align:start position:0% +k right so notice I've have K here and K + + + align:start position:0% +k right so notice I've have K here and K +and K + + align:start position:0% +and K + + + align:start position:0% +and K +star at this + + align:start position:0% +star at this + + + align:start position:0% +star at this +point are not + + align:start position:0% + + + + align:start position:0% + +comparable I'm just making a statement + + align:start position:0% +comparable I'm just making a statement + + + align:start position:0% +comparable I'm just making a statement +that I took um this + + align:start position:0% + + + + align:start position:0% + +particular problem that has K star + one + + align:start position:0% +particular problem that has K star + one + + + align:start position:0% +particular problem that has K star + one +in terms of its uh optimal solution size + + align:start position:0% +in terms of its uh optimal solution size + + + align:start position:0% +in terms of its uh optimal solution size +and for that problem I have K intervals + + align:start position:0% +and for that problem I have K intervals + + + align:start position:0% +and for that problem I have K intervals +that are produced by the earliest finish + + align:start position:0% +that are produced by the earliest finish + + + align:start position:0% +that are produced by the earliest finish +time greedy heuristic okay and so that's + + align:start position:0% +time greedy heuristic okay and so that's + + + align:start position:0% +time greedy heuristic okay and so that's +why the subscripts + + align:start position:0% +why the subscripts + + + align:start position:0% +why the subscripts +here are different well I have i1 here + + align:start position:0% +here are different well I have i1 here + + + align:start position:0% +here are different well I have i1 here +and ik and then over here I have the JS + + align:start position:0% +and ik and then over here I have the JS + + + align:start position:0% +and ik and then over here I have the JS +right so that these intervals are + + align:start position:0% +right so that these intervals are + + + align:start position:0% +right so that these intervals are +different um if I look at u f of I plus + + align:start position:0% +different um if I look at u f of I plus + + + align:start position:0% +different um if I look at u f of I plus +F of i1 and if I look at F + + align:start position:0% +F of i1 and if I look at F + + + align:start position:0% +F of i1 and if I look at F +of + + align:start position:0% +of + + + align:start position:0% +of +J1 what can I say about F of i1 and F of + + align:start position:0% + + + + align:start position:0% + +J1 is there a relationship between F of + + align:start position:0% +J1 is there a relationship between F of + + + align:start position:0% +J1 is there a relationship between F of +i1 and F of + + align:start position:0% + + + + align:start position:0% + +J1 they're equal do they have to be + + align:start position:0% +J1 they're equal do they have to be + + + align:start position:0% +J1 they're equal do they have to be +equal + + align:start position:0% +equal + + + align:start position:0% +equal +yeah L equal less than equal to exactly + + align:start position:0% +yeah L equal less than equal to exactly + + + align:start position:0% +yeah L equal less than equal to exactly +right so they're they're less than equal + + align:start position:0% +right so they're they're less than equal + + + align:start position:0% +right so they're they're less than equal +to uh it's possible that uh you might + + align:start position:0% +to uh it's possible that uh you might + + + align:start position:0% +to uh it's possible that uh you might +end up with a different optimal solution + + align:start position:0% +end up with a different optimal solution + + + align:start position:0% +end up with a different optimal solution +uh that uh doesn't uh use the earliest + + align:start position:0% +uh that uh doesn't uh use the earliest + + + align:start position:0% +uh that uh doesn't uh use the earliest +finish time we think earliest finish + + align:start position:0% +finish time we think earliest finish + + + align:start position:0% +finish time we think earliest finish +time is optimal at this point we haven't + + align:start position:0% +time is optimal at this point we haven't + + + align:start position:0% +time is optimal at this point we haven't +proven it yet but it's quite possible + + align:start position:0% +proven it yet but it's quite possible + + + align:start position:0% +proven it yet but it's quite possible +that you may have other solutions that + + align:start position:0% +that you may have other solutions that + + + align:start position:0% +that you may have other solutions that +are optimal that aren't necessarily the + + align:start position:0% +are optimal that aren't necessarily the + + + align:start position:0% +are optimal that aren't necessarily the +ones that earliest finish time gives you + + align:start position:0% +ones that earliest finish time gives you + + + align:start position:0% +ones that earliest finish time gives you +right so that's really why the less than + + align:start position:0% +right so that's really why the less than + + + align:start position:0% +right so that's really why the less than +or equal to is important + + align:start position:0% +or equal to is important + + + align:start position:0% +or equal to is important +here um now what I'm going to do is + + align:start position:0% +here um now what I'm going to do is + + + align:start position:0% +here um now what I'm going to do is +create a schedule s star + + align:start position:0% +create a schedule s star + + + align:start position:0% +create a schedule s star +star that essentially is going to be + + align:start position:0% +star that essentially is going to be + + + align:start position:0% +star that essentially is going to be +taking s star and pulling out the + + align:start position:0% +taking s star and pulling out the + + + align:start position:0% +taking s star and pulling out the +first interval from s star and + + align:start position:0% +first interval from s star and + + + align:start position:0% +first interval from s star and +substituting it with the first interval + + align:start position:0% +substituting it with the first interval + + + align:start position:0% +substituting it with the first interval +from my greedy algorithms schedule so + + align:start position:0% +from my greedy algorithms schedule so + + + align:start position:0% +from my greedy algorithms schedule so +I'm just going to replace that and so s + + align:start position:0% +I'm just going to replace that and so s + + + align:start position:0% +I'm just going to replace that and so s +star star is um s + + align:start position:0% +star star is um s + + + align:start position:0% +star star is um s +i1 + + align:start position:0% +i1 + + + align:start position:0% +i1 +f + + align:start position:0% +f + + + align:start position:0% +f +J1 and then I'm going to be going back + + align:start position:0% +J1 and then I'm going to be going back + + + align:start position:0% +J1 and then I'm going to be going back +to + + align:start position:0% +to + + + align:start position:0% +to +sj2 fj2 because I'm going back to S + + align:start position:0% +sj2 fj2 because I'm going back to S + + + align:start position:0% +sj2 fj2 because I'm going back to S +star and all the other ones are are + + align:start position:0% +star and all the other ones are are + + + align:start position:0% +star and all the other ones are are +coming from s star so they're going to + + align:start position:0% +coming from s star so they're going to + + + align:start position:0% +coming from s star so they're going to +be s j k star + + + align:start position:0% +be s j k star + + + + align:start position:0% +be s j k star + +one + + align:start position:0% +one + + + align:start position:0% +one +uh comma + + align:start position:0% +uh comma + + + align:start position:0% +uh comma +f j k + + align:start position:0% +f j k + + + align:start position:0% +f j k +star + + + align:start position:0% +star + + + + align:start position:0% +star + +one okay so I just did a little + + align:start position:0% +one okay so I just did a little + + + align:start position:0% +one okay so I just did a little +substitution there um associated with uh + + align:start position:0% +substitution there um associated with uh + + + align:start position:0% +substitution there um associated with uh +the the optimal solution and I stuck in + + align:start position:0% +the the optimal solution and I stuck in + + + align:start position:0% +the the optimal solution and I stuck in +part of the greedy algorithm solution in + + align:start position:0% +part of the greedy algorithm solution in + + + align:start position:0% +part of the greedy algorithm solution in +fact the very first schedule + + align:start position:0% + + + + align:start position:0% + +okay oh this should be uh I I want thank + + align:start position:0% +okay oh this should be uh I I want thank + + + align:start position:0% +okay oh this should be uh I I want thank +you + + align:start position:0% + + + + align:start position:0% + +y good + + align:start position:0% +y good + + + align:start position:0% +y good +so we got a couple of things to do a + + align:start position:0% +so we got a couple of things to do a + + + align:start position:0% +so we got a couple of things to do a +couple of observations to make and we're + + align:start position:0% +couple of observations to make and we're + + + align:start position:0% +couple of observations to make and we're +going to be able + + align:start position:0% + + + + align:start position:0% + +to + + align:start position:0% +to + + + align:start position:0% +to +prove some relationship between K and K + + align:start position:0% +prove some relationship between K and K + + + align:start position:0% +prove some relationship between K and K +star that is going to give us our the + + align:start position:0% +star that is going to give us our the + + + align:start position:0% +star that is going to give us our the +proof for our + + align:start position:0% + + + + align:start position:0% + +claim + + align:start position:0% +claim + + + align:start position:0% +claim +so clearly s + + align:start position:0% +so clearly s + + + align:start position:0% +so clearly s +star is also + + align:start position:0% +star is also + + + align:start position:0% +star is also +optimal all I've done is taken one + + align:start position:0% +optimal all I've done is taken one + + + align:start position:0% +optimal all I've done is taken one +interval out and replaced it with + + align:start position:0% +interval out and replaced it with + + + align:start position:0% +interval out and replaced it with +another one hasn't changed the size it + + align:start position:0% +another one hasn't changed the size it + + + align:start position:0% +another one hasn't changed the size it +goes up to K star + one so s star is + + align:start position:0% +goes up to K star + one so s star is + + + align:start position:0% +goes up to K star + one so s star is +also optimal s star is optimal s double + + align:start position:0% +also optimal s star is optimal s double + + + align:start position:0% +also optimal s star is optimal s double +star is + + align:start position:0% +star is + + + align:start position:0% +star is +optimal now I'm going to + + align:start position:0% +optimal now I'm going to + + + align:start position:0% +optimal now I'm going to +Define l + + align:start position:0% +Define l + + + align:start position:0% +Define l +Prime as the set of + + align:start position:0% + + + + align:start position:0% + +intervals with s of I greater than or + + align:start position:0% +intervals with s of I greater than or + + + align:start position:0% +intervals with s of I greater than or +equal to F of + + align:start position:0% +equal to F of + + + align:start position:0% +equal to F of +i1 right so what is L Prime well L Prime + + align:start position:0% +i1 right so what is L Prime well L Prime + + + align:start position:0% +i1 right so what is L Prime well L Prime +is what happens in the second step of + + align:start position:0% +is what happens in the second step of + + + align:start position:0% +is what happens in the second step of +the greedy + + align:start position:0% +the greedy + + + align:start position:0% +the greedy +algorithm where in the second step of + + align:start position:0% +algorithm where in the second step of + + + align:start position:0% +algorithm where in the second step of +the greedy algorithm once I've selected + + align:start position:0% +the greedy algorithm once I've selected + + + align:start position:0% +the greedy algorithm once I've selected +this particular interval and I've pulled + + align:start position:0% +this particular interval and I've pulled + + + align:start position:0% +this particular interval and I've pulled +it in I have to reject all of the other + + align:start position:0% +it in I have to reject all of the other + + + align:start position:0% +it in I have to reject all of the other +intervals that are incomp compatible + + align:start position:0% +intervals that are incomp compatible + + + align:start position:0% +intervals that are incomp compatible +with this one right so I'm going to have + + align:start position:0% +with this one right so I'm going to have + + + align:start position:0% +with this one right so I'm going to have +to take only those intervals for which s + + align:start position:0% +to take only those intervals for which s + + + align:start position:0% +to take only those intervals for which s +ofi is greater than or equal to F of i1 + + align:start position:0% +ofi is greater than or equal to F of i1 + + + align:start position:0% +ofi is greater than or equal to F of i1 +because uh those + + align:start position:0% +because uh those + + + align:start position:0% +because uh those +are those are the ones that are + + align:start position:0% +are those are the ones that are + + + align:start position:0% +are those are the ones that are +compatible okay so that's what L Prime + + align:start position:0% +compatible okay so that's what L Prime + + + align:start position:0% +compatible okay so that's what L Prime +is + + align:start position:0% +is + + + align:start position:0% +is +and I'm going to be able to say that + + align:start position:0% +and I'm going to be able to say that + + + align:start position:0% +and I'm going to be able to say that +since + + align:start position:0% +since + + + align:start position:0% +since +s double + + align:start position:0% +s double + + + align:start position:0% +s double +star is op + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% +for + + + align:start position:0% +for +l + + align:start position:0% +l + + + align:start position:0% +l +s double star + + align:start position:0% +s double star + + + align:start position:0% +s double star +2 to Kar + + + align:start position:0% +2 to Kar + + + + align:start position:0% +2 to Kar + +1 is optimal for L + + align:start position:0% + + + + align:start position:0% + +Prime right so I'm making a statement + + align:start position:0% +Prime right so I'm making a statement + + + align:start position:0% +Prime right so I'm making a statement +about this optimal solution I know + + align:start position:0% +about this optimal solution I know + + + align:start position:0% +about this optimal solution I know +that's optimal and basically what I'm + + align:start position:0% +that's optimal and basically what I'm + + + align:start position:0% +that's optimal and basically what I'm +saying is subset sets of the optimal + + align:start position:0% +saying is subset sets of the optimal + + + align:start position:0% +saying is subset sets of the optimal +solution are going to have to be optimal + + align:start position:0% +solution are going to have to be optimal + + + align:start position:0% +solution are going to have to be optimal +because if that's not the case I could + + align:start position:0% +because if that's not the case I could + + + align:start position:0% +because if that's not the case I could +uh always + + align:start position:0% +uh always + + + align:start position:0% +uh always +substitute the something better and + + align:start position:0% +substitute the something better and + + + align:start position:0% +substitute the something better and +shrink the size of + + align:start position:0% +shrink the size of + + + align:start position:0% +shrink the size of +the the K Star Plus One optimal solution + + align:start position:0% +the the K Star Plus One optimal solution + + + align:start position:0% +the the K Star Plus One optimal solution +which obviously would be a contradiction + + align:start position:0% +which obviously would be a contradiction + + + align:start position:0% +which obviously would be a contradiction +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so s double star is going to is optimal + + align:start position:0% +so s double star is going to is optimal + + + align:start position:0% +so s double star is going to is optimal +for L and therefore s star 2 through K + + align:start position:0% +for L and therefore s star 2 through K + + + align:start position:0% +for L and therefore s star 2 through K +star + 1 is optimal for L Prime right + + align:start position:0% +star + 1 is optimal for L Prime right + + + align:start position:0% +star + 1 is optimal for L Prime right +everybody buy that y + + align:start position:0% +everybody buy that y + + + align:start position:0% +everybody buy that y +good and so what this means of course is + + align:start position:0% +good and so what this means of course is + + + align:start position:0% +good and so what this means of course is +that the optimal + + align:start position:0% + + + + align:start position:0% + +schedule for L + + align:start position:0% +schedule for L + + + align:start position:0% +schedule for L +Prime has + + align:start position:0% +Prime has + + + align:start position:0% +Prime has +Kar + + align:start position:0% +Kar + + + align:start position:0% +Kar +size I'm starting with two I've taken + + align:start position:0% +size I'm starting with two I've taken + + + align:start position:0% +size I'm starting with two I've taken +away one so now I have L Prime which is + + align:start position:0% +away one so now I have L Prime which is + + + align:start position:0% +away one so now I have L Prime which is +a smaller problem now you see where the + + align:start position:0% +a smaller problem now you see where the + + + align:start position:0% +a smaller problem now you see where the +proof is headed um if you didn't already + + align:start position:0% +proof is headed um if you didn't already + + + align:start position:0% +proof is headed um if you didn't already +uh I have a smaller problem which is L + + align:start position:0% +uh I have a smaller problem which is L + + + align:start position:0% +uh I have a smaller problem which is L +Prime clearly it's got fewer requests + + align:start position:0% +Prime clearly it's got fewer requests + + + align:start position:0% +Prime clearly it's got fewer requests +and I I have constructed an optimal + + align:start position:0% +and I I have constructed an optimal + + + align:start position:0% +and I I have constructed an optimal +schedule for that problem by pulling it + + align:start position:0% +schedule for that problem by pulling it + + + align:start position:0% +schedule for that problem by pulling it +out of the original optimal schedule I + + align:start position:0% +out of the original optimal schedule I + + + align:start position:0% +out of the original optimal schedule I +was given and that size of that optimal + + align:start position:0% +was given and that size of that optimal + + + align:start position:0% +was given and that size of that optimal +schedule is Kar right um and now I get + + align:start position:0% +schedule is Kar right um and now I get + + + align:start position:0% +schedule is Kar right um and now I get +to invoke my inductive hypoth is because + + align:start position:0% +to invoke my inductive hypoth is because + + + align:start position:0% +to invoke my inductive hypoth is because +my inductive + + align:start position:0% +my inductive + + + align:start position:0% +my inductive +hypothesis says that this claim that I + + align:start position:0% +hypothesis says that this claim that I + + + align:start position:0% +hypothesis says that this claim that I +have up there holds for any set of + + align:start position:0% +have up there holds for any set of + + + align:start position:0% +have up there holds for any set of +problems that have an optimal schedule + + align:start position:0% +problems that have an optimal schedule + + + align:start position:0% +problems that have an optimal schedule +of size K Star right that's what the + + align:start position:0% +of size K Star right that's what the + + + align:start position:0% +of size K Star right that's what the +inductive hypothesis gives me and so by + + align:start position:0% +inductive hypothesis gives me and so by + + + align:start position:0% +inductive hypothesis gives me and so by +the inductive + + align:start position:0% + + + + align:start position:0% + +hypothesis + + align:start position:0% +hypothesis + + + align:start position:0% +hypothesis +when I + + align:start position:0% + + + + align:start position:0% + +run the greedy + + align:start position:0% + + + + align:start position:0% + +algorithm on L + + align:start position:0% + + + + align:start position:0% + +Prime I'm going to + + align:start position:0% + + + + align:start position:0% + +get a schedule of size case + + align:start position:0% + + + + align:start position:0% + +star + + align:start position:0% + + + + align:start position:0% + +right now can you tell me based on what + + align:start position:0% +right now can you tell me based on what + + + align:start position:0% +right now can you tell me based on what +you see on the board by + + align:start position:0% +you see on the board by + + + align:start position:0% +you see on the board by +construction when I run the greedy + + align:start position:0% +construction when I run the greedy + + + align:start position:0% +construction when I run the greedy +algorithm what am I getting on + + align:start position:0% + + + + align:start position:0% + +lar by construction when I run the + + align:start position:0% +lar by construction when I run the + + + align:start position:0% +lar by construction when I run the +greedy algorithm on L uh I'm sorry L + + align:start position:0% +greedy algorithm on L uh I'm sorry L + + + align:start position:0% +greedy algorithm on L uh I'm sorry L +Prime there's too many uh superscripts + + align:start position:0% +Prime there's too many uh superscripts + + + align:start position:0% +Prime there's too many uh superscripts +here when I when I run the greedy + + align:start position:0% +here when I when I run the greedy + + + align:start position:0% +here when I when I run the greedy +algorithm on L Prime what do I + + align:start position:0% +algorithm on L Prime what do I + + + align:start position:0% +algorithm on L Prime what do I +get + + align:start position:0% +get + + + align:start position:0% +get +someone + + align:start position:0% + + + + align:start position:0% + +yeah exactly right I get um everything + + align:start position:0% +yeah exactly right I get um everything + + + align:start position:0% +yeah exactly right I get um everything +from the the second thing here all the + + align:start position:0% +from the the second thing here all the + + + align:start position:0% +from the the second thing here all the +way to the nend right because that's + + align:start position:0% +way to the nend right because that's + + + align:start position:0% +way to the nend right because that's +exactly what the greedy algorithm does + + align:start position:0% +exactly what the greedy algorithm does + + + align:start position:0% +exactly what the greedy algorithm does +remember the greedy algorithm picked si1 + + align:start position:0% +remember the greedy algorithm picked si1 + + + align:start position:0% +remember the greedy algorithm picked si1 +fi1 and then rejected all requests that + + align:start position:0% +fi1 and then rejected all requests that + + + align:start position:0% +fi1 and then rejected all requests that +were incompatible and and then moved on + + align:start position:0% +were incompatible and and then moved on + + + align:start position:0% +were incompatible and and then moved on +then you rejected all requests that were + + align:start position:0% +then you rejected all requests that were + + + align:start position:0% +then you rejected all requests that were +incompatible here you got exactly L + + align:start position:0% +incompatible here you got exactly L + + + align:start position:0% +incompatible here you got exactly L +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +and uh by construction uh the greedy + + align:start position:0% +and uh by construction uh the greedy + + + align:start position:0% +and uh by construction uh the greedy +algorithm should have given me uh all + + align:start position:0% +algorithm should have given me uh all + + + align:start position:0% +algorithm should have given me uh all +the way from si2 to uh SI ik right thank + + align:start position:0% +the way from si2 to uh SI ik right thank + + + align:start position:0% +the way from si2 to uh SI ik right thank +you + + align:start position:0% + + + + align:start position:0% + +so by + + align:start position:0% + + + + align:start position:0% + +construction the + + align:start position:0% +construction the + + + align:start position:0% +construction the +greedy on L + + align:start position:0% +greedy on L + + + align:start position:0% +greedy on L +Prime gives + + align:start position:0% + + + + align:start position:0% + +S2 to K right and what is the size of + + align:start position:0% +S2 to K right and what is the size of + + + align:start position:0% +S2 to K right and what is the size of +this 2 to K gives me a size of K minus + + align:start position:0% +this 2 to K gives me a size of K minus + + + align:start position:0% +this 2 to K gives me a size of K minus +one right this is K minus + + align:start position:0% +one right this is K minus + + + align:start position:0% +one right this is K minus +one + + align:start position:0% + + + + align:start position:0% + +so so if I put the if I put these two + + align:start position:0% +so so if I put the if I put these two + + + align:start position:0% +so so if I put the if I put these two +things + + align:start position:0% +things + + + align:start position:0% +things +together what what do I have what is the + + align:start position:0% +together what what do I have what is the + + + align:start position:0% +together what what do I have what is the +next step I have the inductive + + align:start position:0% +next step I have the inductive + + + align:start position:0% +next step I have the inductive +hypothesis + + align:start position:0% +hypothesis + + + align:start position:0% +hypothesis +giving me a fact I have the construction + + align:start position:0% +giving me a fact I have the construction + + + align:start position:0% +giving me a fact I have the construction +giving me something now I can relate K + + align:start position:0% +giving me something now I can relate K + + + align:start position:0% +giving me something now I can relate K +and K star what's the + + align:start position:0% + + + + align:start position:0% + +relationship K star is equal to K minus + + align:start position:0% +relationship K star is equal to K minus + + + align:start position:0% +relationship K star is equal to K minus +one right do people see + + align:start position:0% +one right do people see + + + align:start position:0% +one right do people see +that right so size K star which + + align:start position:0% +that right so size K star which + + + align:start position:0% +that right so size K star which +is K minus one right so what that means + + align:start position:0% +is K minus one right so what that means + + + align:start position:0% +is K minus one right so what that means +is um given that s + + align:start position:0% +is um given that s + + + align:start position:0% +is um given that s +2K is of size K star it means that + + align:start position:0% +2K is of size K star it means that + + + align:start position:0% +2K is of size K star it means that +s1k is of size K star + one which uh is + + align:start position:0% +s1k is of size K star + one which uh is + + + align:start position:0% +s1k is of size K star + one which uh is +exactly what I want that's uh optimal + + align:start position:0% +exactly what I want that's uh optimal + + + align:start position:0% +exactly what I want that's uh optimal +because I said in the beginning that we + + align:start position:0% +because I said in the beginning that we + + + align:start position:0% +because I said in the beginning that we +had K star + one in our uh inductive + + align:start position:0% +had K star + one in our uh inductive + + + align:start position:0% +had K star + one in our uh inductive +hypothesis case as being the optimal + + align:start position:0% +hypothesis case as being the optimal + + + align:start position:0% +hypothesis case as being the optimal +solution so this last step here um is + + align:start position:0% +solution so this last step here um is + + + align:start position:0% +solution so this last step here um is +all you need to to argue now that uh + + align:start position:0% +all you need to to argue now that uh + + + align:start position:0% +all you need to to argue now that uh +um s of 1K going back up here um this is + + align:start position:0% +um s of 1K going back up here um this is + + + align:start position:0% +um s of 1K going back up here um this is +optimal + + align:start position:0% +optimal + + + align:start position:0% +optimal +because k equal K star + 1 + + align:start position:0% +because k equal K star + 1 + + + align:start position:0% +because k equal K star + 1 +right there you + + align:start position:0% + + + + align:start position:0% + +go so so that's the kind of argument + + align:start position:0% +go so so that's the kind of argument + + + align:start position:0% +go so so that's the kind of argument +that you'd like have to make um in order + + align:start position:0% +that you'd like have to make um in order + + + align:start position:0% +that you'd like have to make um in order +to prove something like this in 046 and + + align:start position:0% +to prove something like this in 046 and + + + align:start position:0% +to prove something like this in 046 and +what you'll see in your problem sets uh + + align:start position:0% +what you'll see in your problem sets uh + + + align:start position:0% +what you'll see in your problem sets uh +uh including the one that's going to + + align:start position:0% +uh including the one that's going to + + + align:start position:0% +uh including the one that's going to +come out on Thursday is a different uh + + align:start position:0% +come out on Thursday is a different uh + + + align:start position:0% +come out on Thursday is a different uh +problem that you'd have to have approv + + align:start position:0% +problem that you'd have to have approv + + + align:start position:0% +problem that you'd have to have approv +for a greedy algorithm for I forget + + align:start position:0% +for a greedy algorithm for I forget + + + align:start position:0% +for a greedy algorithm for I forget +exactly what technique you'll have to + + align:start position:0% +exactly what technique you'll have to + + + align:start position:0% +exactly what technique you'll have to +use there perhaps induction perhaps + + align:start position:0% +use there perhaps induction perhaps + + + align:start position:0% +use there perhaps induction perhaps +contradiction and these are the kinds of + + align:start position:0% +contradiction and these are the kinds of + + + align:start position:0% +contradiction and these are the kinds of +things that uh get you to the point + + align:start position:0% +things that uh get you to the point + + + align:start position:0% +things that uh get you to the point +where you've analyzed the correctness of + + align:start position:0% +where you've analyzed the correctness of + + + align:start position:0% +where you've analyzed the correctness of +algorithms uh not just the fact that + + align:start position:0% +algorithms uh not just the fact that + + + align:start position:0% +algorithms uh not just the fact that +you're getting a valid schedule but + + align:start position:0% +you're getting a valid schedule but + + + align:start position:0% +you're getting a valid schedule but +you're getting a valid uh maximum + + align:start position:0% +you're getting a valid uh maximum + + + align:start position:0% +you're getting a valid uh maximum +schedule in terms of the maximum number + + align:start position:0% +schedule in terms of the maximum number + + + align:start position:0% +schedule in terms of the maximum number +of requests okay any questions about + + align:start position:0% +of requests okay any questions about + + + align:start position:0% +of requests okay any questions about +this do people buy the + + align:start position:0% +this do people buy the + + + align:start position:0% +this do people buy the +proof yep good um so that was greedy for + + align:start position:0% +proof yep good um so that was greedy for + + + align:start position:0% +proof yep good um so that was greedy for +a particular problem I told you that the + + align:start position:0% +a particular problem I told you that the + + + align:start position:0% +a particular problem I told you that the +theme of our lecture here was uh + + align:start position:0% +theme of our lecture here was uh + + + align:start position:0% +theme of our lecture here was uh +changing the problem and uh + + align:start position:0% +changing the problem and uh + + + align:start position:0% +changing the problem and uh +getting + + align:start position:0% + + + + align:start position:0% + +different different algorithms that had + + align:start position:0% +different different algorithms that had + + + align:start position:0% +different different algorithms that had +different + + align:start position:0% +different + + + align:start position:0% +different +complexities so let's go ahead and do + + align:start position:0% +complexities so let's go ahead and do + + + align:start position:0% +complexities so let's go ahead and do +that so for the rest of this uh lecture + + align:start position:0% +that so for the rest of this uh lecture + + + align:start position:0% +that so for the rest of this uh lecture +we'll just take a look at different + + align:start position:0% +we'll just take a look at different + + + align:start position:0% +we'll just take a look at different +kinds of problems and talk a little more + + align:start position:0% +kinds of problems and talk a little more + + + align:start position:0% +kinds of problems and talk a little more +superficially about uh what the problem + + align:start position:0% +superficially about uh what the problem + + + align:start position:0% +superficially about uh what the problem +complexities are and so one thing that + + align:start position:0% +complexities are and so one thing that + + + align:start position:0% +complexities are and so one thing that +might come to mind is that you'd like to + + align:start position:0% +might come to mind is that you'd like to + + + align:start position:0% +might come to mind is that you'd like to +do weighted interval + + align:start position:0% + + + + align:start position:0% + +scheduling and + + align:start position:0% +scheduling and + + + align:start position:0% +scheduling and +what happens here is each + + align:start position:0% + + + + align:start position:0% + +request has + + align:start position:0% +request has + + + align:start position:0% +request has +weight + + align:start position:0% +weight + + + align:start position:0% +weight +wi and what we want to do is + + align:start position:0% + + + + align:start position:0% + +schedule a subset of + + align:start position:0% + + + + align:start position:0% + +requests with maximum weight so + + align:start position:0% +requests with maximum weight so + + + align:start position:0% +requests with maximum weight so +previously it was just all weights were + + align:start position:0% +previously it was just all weights were + + + align:start position:0% +previously it was just all weights were +one so maximum cut ality was what we + + align:start position:0% +one so maximum cut ality was what we + + + align:start position:0% +one so maximum cut ality was what we +wanted but now we want to schedule a + + align:start position:0% +wanted but now we want to schedule a + + + align:start position:0% +wanted but now we want to schedule a +subset of requests with maximum weight + + align:start position:0% +subset of requests with maximum weight + + + align:start position:0% +subset of requests with maximum weight +um someone give + + align:start position:0% +um someone give + + + align:start position:0% +um someone give +me an argument as to whether the greedy + + align:start position:0% +me an argument as to whether the greedy + + + align:start position:0% +me an argument as to whether the greedy +algorithm earliest finish time first is + + align:start position:0% +algorithm earliest finish time first is + + + align:start position:0% +algorithm earliest finish time first is +optimal for this weighted case or give + + align:start position:0% +optimal for this weighted case or give + + + align:start position:0% +optimal for this weighted case or give +me a counter + + align:start position:0% +me a counter + + + align:start position:0% +me a counter +example yeah uh go + + align:start position:0% + + + + align:start position:0% + +ahead + + align:start position:0% + + + + align:start position:0% + +right exactly exactly right all right I + + align:start position:0% +right exactly exactly right all right I + + + align:start position:0% +right exactly exactly right all right I +owe you one too you + + align:start position:0% +owe you one too you + + + align:start position:0% +owe you one too you +go um so it's a fairly trivial example + + align:start position:0% +go um so it's a fairly trivial example + + + align:start position:0% +go um so it's a fairly trivial example +all you do + + align:start position:0% +all you do + + + align:start position:0% +all you do +is W = 1 W = + + align:start position:0% +is W = 1 W = + + + align:start position:0% +is W = 1 W = +1 wal 3 right so there you go um so + + align:start position:0% +1 wal 3 right so there you go um so + + + align:start position:0% +1 wal 3 right so there you go um so +clearly the earliest finish time would + + align:start position:0% +clearly the earliest finish time would + + + align:start position:0% +clearly the earliest finish time would +pick this one and then this one which is + + align:start position:0% +pick this one and then this one which is + + + align:start position:0% +pick this one and then this one which is +fine you get two of these but this was + + align:start position:0% +fine you get two of these but this was + + + align:start position:0% +fine you get two of these but this was +important you know this is I don't know + + align:start position:0% +important you know this is I don't know + + + align:start position:0% +important you know this is I don't know +sleep party + + align:start position:0% +sleep party + + + align:start position:0% +sleep party +6046 right so there you go so the weight + + align:start position:0% +6046 right so there you go so the weight + + + align:start position:0% +6046 right so there you go so the weight +is I should make that uh infinity + + align:start position:0% +is I should make that uh infinity + + + align:start position:0% +is I should make that uh infinity +right right most important thing in the + + align:start position:0% +right right most important thing in the + + + align:start position:0% +right right most important thing in the +world at least for the next uh 6 + + align:start position:0% + + + + align:start position:0% + +months um so uh how does it work + + align:start position:0% + + + + align:start position:0% + +now so it turns out at the + + align:start position:0% +now so it turns out at the + + + align:start position:0% +now so it turns out at the +greedy strategy the template that I had + + align:start position:0% +greedy strategy the template that I had + + + align:start position:0% +greedy strategy the template that I had +uh fails okay uh there's nothing that + + align:start position:0% +uh fails okay uh there's nothing that + + + align:start position:0% +uh fails okay uh there's nothing that +exists on this planet that at least I + + align:start position:0% +exists on this planet that at least I + + + align:start position:0% +exists on this planet that at least I +know of uh where you can have a simple + + align:start position:0% +know of uh where you can have a simple + + + align:start position:0% +know of uh where you can have a simple +rule and use that template to get the + + align:start position:0% +rule and use that template to get the + + + align:start position:0% +rule and use that template to get the +optimum solution in this case maximum + + align:start position:0% +optimum solution in this case maximum + + + align:start position:0% +optimum solution in this case maximum +weight solution + + align:start position:0% +weight solution + + + align:start position:0% +weight solution +for every problem instance right so that + + align:start position:0% +for every problem instance right so that + + + align:start position:0% +for every problem instance right so that +template just fails okay + + align:start position:0% +template just fails okay + + + align:start position:0% +template just fails okay +um what other programming Paradigm do + + align:start position:0% +um what other programming Paradigm do + + + align:start position:0% +um what other programming Paradigm do +you think would be useful + + align:start position:0% + + + + align:start position:0% + +here yeah go ahead DP right so you you + + align:start position:0% +here yeah go ahead DP right so you you + + + align:start position:0% +here yeah go ahead DP right so you you +want to take a stab at uh a potential DP + + align:start position:0% +want to take a stab at uh a potential DP + + + align:start position:0% +want to take a stab at uh a potential DP +solution here yeah + + align:start position:0% +solution here yeah + + + align:start position:0% +solution here yeah +either or discard it and + + align:start position:0% +either or discard it and + + + align:start position:0% +either or discard it and +yeah that's that's the perfect divide + + align:start position:0% +yeah that's that's the perfect divide + + + align:start position:0% +yeah that's that's the perfect divide +and conquer and then when you include it + + align:start position:0% +and conquer and then when you include it + + + align:start position:0% +and conquer and then when you include it +what do you have to do + + align:start position:0% +what do you have to do + + + align:start position:0% +what do you have to do +elim right how many sub problems do you + + align:start position:0% +elim right how many sub problems do you + + + align:start position:0% +elim right how many sub problems do you +think there are I I want to make you + + align:start position:0% +think there are I I want to make you + + + align:start position:0% +think there are I I want to make you +earn your Frisbee + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% + + + + align:start position:0% + +probably number + + align:start position:0% +probably number + + + align:start position:0% +probably number +of number inters you have well that's a + + align:start position:0% +of number inters you have well that's a + + + align:start position:0% +of number inters you have well that's a +that's a number of sub sets that you + + align:start position:0% +that's a number of sub sets that you + + + align:start position:0% +that's a number of sub sets that you +have uh so you have n intervals then you + + align:start position:0% +have uh so you have n intervals then you + + + align:start position:0% +have uh so you have n intervals then you +have two rais to n subsets right but + + align:start position:0% +have two rais to n subsets right but + + + align:start position:0% +have two rais to n subsets right but +remember you want to go uh you know you + + align:start position:0% +remember you want to go uh you know you + + + align:start position:0% +remember you want to go uh you know you +want to be smarter than that right you + + align:start position:0% +want to be smarter than that right you + + + align:start position:0% +want to be smarter than that right you +want to be a little bit smarter than + + align:start position:0% +want to be a little bit smarter than + + + align:start position:0% +want to be a little bit smarter than +that uh and uh uh so here you get a FR + + align:start position:0% +that uh and uh uh so here you get a FR + + + align:start position:0% +that uh and uh uh so here you get a FR +be anyway no not anyway here you + + align:start position:0% +be anyway no not anyway here you + + + align:start position:0% +be anyway no not anyway here you +go right um so uh anybody else uh so + + align:start position:0% +go right um so uh anybody else uh so + + + align:start position:0% +go right um so uh anybody else uh so +what I want to use uh is dynamic + + align:start position:0% +what I want to use uh is dynamic + + + align:start position:0% +what I want to use uh is dynamic +programming we've established that right + + align:start position:0% +programming we've established that right + + + align:start position:0% +programming we've established that right +I want to use Dynamic program in and + + align:start position:0% +I want to use Dynamic program in and + + + align:start position:0% +I want to use Dynamic program in and +with dynamic programming you have some + + align:start position:0% +with dynamic programming you have some + + + align:start position:0% +with dynamic programming you have some +experience with that + + align:start position:0% +experience with that + + + align:start position:0% +experience with that +in6 uh the name of the game is to figure + + align:start position:0% +in6 uh the name of the game is to figure + + + align:start position:0% +in6 uh the name of the game is to figure +out what the sub problems are right um + + align:start position:0% +out what the sub problems are right um + + + align:start position:0% +out what the sub problems are right um +the sub problems are kind of going to + + align:start position:0% +the sub problems are kind of going to + + + align:start position:0% +the sub problems are kind of going to +look like a collection of requests I + + align:start position:0% +look like a collection of requests I + + + align:start position:0% +look like a collection of requests I +mean there's no two things about it + + align:start position:0% +mean there's no two things about it + + + align:start position:0% +mean there's no two things about it +they're going to be a collection of + + align:start position:0% +they're going to be a collection of + + + align:start position:0% +they're going to be a collection of +requests right and so uh the challenge + + align:start position:0% +requests right and so uh the challenge + + + align:start position:0% +requests right and so uh the challenge +here is not to go to the 2 ra to n okay + + align:start position:0% +here is not to go to the 2 ra to n okay + + + align:start position:0% +here is not to go to the 2 ra to n okay +because 2 ra to n is bad right um for uh + + align:start position:0% +because 2 ra to n is bad right um for uh + + + align:start position:0% +because 2 ra to n is bad right um for uh +we want efficiency so we have to have a + + align:start position:0% +we want efficiency so we have to have a + + + align:start position:0% +we want efficiency so we have to have a +polinomial number of sub problems so + + align:start position:0% +polinomial number of sub problems so + + + align:start position:0% +polinomial number of sub problems so +someone who hasn't answered yeah go + + align:start position:0% +someone who hasn't answered yeah go + + + align:start position:0% +someone who hasn't answered yeah go +ahead + + align:start position:0% + + + + align:start position:0% + +so so you're looking at every pairs of I + + align:start position:0% +so so you're looking at every pairs of I + + + align:start position:0% +so so you're looking at every pairs of I +and JS uh and uh uh well not all of them + + align:start position:0% +and JS uh and uh uh well not all of them + + + align:start position:0% +and JS uh and uh uh well not all of them +are going to be valid they won't be + + align:start position:0% +are going to be valid they won't be + + + align:start position:0% +are going to be valid they won't be +intervals associated with that right but + + align:start position:0% +intervals associated with that right but + + + align:start position:0% +intervals associated with that right but +you know that's a that's that's a + + align:start position:0% +you know that's a that's that's a + + + align:start position:0% +you know that's a that's that's a +reasonable start right someone + + align:start position:0% +reasonable start right someone + + + align:start position:0% +reasonable start right someone +else uh someone who hasn't answered yeah + + align:start position:0% +else uh someone who hasn't answered yeah + + + align:start position:0% +else uh someone who hasn't answered yeah +back there um you could go the best from + + align:start position:0% +back there um you could go the best from + + + align:start position:0% +back there um you could go the best from +the start to some point answer there + + align:start position:0% +the start to some point answer there + + + align:start position:0% +the start to some point answer there +those ah best from the start to any + + align:start position:0% +those ah best from the start to any + + + align:start position:0% +those ah best from the start to any +given point all right well you got you + + align:start position:0% +given point all right well you got you + + + align:start position:0% +given point all right well you got you +got close uh Michael there you go uh you + + align:start position:0% +got close uh Michael there you go uh you + + + align:start position:0% +got close uh Michael there you go uh you +need to stand + + align:start position:0% +need to stand + + + align:start position:0% +need to stand +up oh bad throw that's a bad throw I got + + align:start position:0% +up oh bad throw that's a bad throw I got + + + align:start position:0% +up oh bad throw that's a bad throw I got +to + + align:start position:0% +to + + + align:start position:0% +to +practice okay so um as you can see with + + align:start position:0% +practice okay so um as you can see with + + + align:start position:0% +practice okay so um as you can see with +dynamic programming the challenge is to + + align:start position:0% +dynamic programming the challenge is to + + + align:start position:0% +dynamic programming the challenge is to +figure out what the sub problems are uh + + align:start position:0% +figure out what the sub problems are uh + + + align:start position:0% +figure out what the sub problems are uh +the fact of the matter is that there's + + align:start position:0% +the fact of the matter is that there's + + + align:start position:0% +the fact of the matter is that there's +going to be many different uh possible + + align:start position:0% +going to be many different uh possible + + + align:start position:0% +going to be many different uh possible +algorithms that are all DP for this + + align:start position:0% +algorithms that are all DP for this + + + align:start position:0% +algorithms that are all DP for this +weighted problem there's at least two + + align:start position:0% +weighted problem there's at least two + + + align:start position:0% +weighted problem there's at least two +interesting ones we're going to do a + + align:start position:0% +interesting ones we're going to do a + + + align:start position:0% +interesting ones we're going to do a +simple one which is based on the answer + + align:start position:0% +simple one which is based on the answer + + + align:start position:0% +simple one which is based on the answer +that uh the gentleman just here just + + align:start position:0% +that uh the gentleman just here just + + + align:start position:0% +that uh the gentleman just here just +gave uh but uh it turns out you can be a + + align:start position:0% +gave uh but uh it turns out you can be a + + + align:start position:0% +gave uh but uh it turns out you can be a +little smarter than that and uh most + + align:start position:0% +little smarter than that and uh most + + + align:start position:0% +little smarter than that and uh most +likely you'll hear that the smarter way + + align:start position:0% +likely you'll hear that the smarter way + + + align:start position:0% +likely you'll hear that the smarter way +in the section okay but let's do the + + align:start position:0% +in the section okay but let's do the + + + align:start position:0% +in the section okay but let's do the +simple one because that's all I have + + align:start position:0% +simple one because that's all I have + + + align:start position:0% +simple one because that's all I have +time here for and the key is to define + + align:start position:0% +time here for and the key is to define + + + align:start position:0% +time here for and the key is to define +the sub problems and then once you do + + align:start position:0% +the sub problems and then once you do + + + align:start position:0% +the sub problems and then once you do +that uh the actual recursion ends up + + align:start position:0% +that uh the actual recursion ends up + + + align:start position:0% +that uh the actual recursion ends up +being a fairly straightforward and + + align:start position:0% +being a fairly straightforward and + + + align:start position:0% +being a fairly straightforward and +intuitive + + align:start position:0% +intuitive + + + align:start position:0% +intuitive +step so let's + + align:start position:0% + + + + align:start position:0% + +uh look + + align:start position:0% +uh look + + + align:start position:0% +uh look +at + + align:start position:0% +at + + + align:start position:0% +at +dynamic programming one particular way + + align:start position:0% +dynamic programming one particular way + + + align:start position:0% +dynamic programming one particular way +of solving this problem using the DP + + align:start position:0% +of solving this problem using the DP + + + align:start position:0% +of solving this problem using the DP +Paradigm so what I'm going to do is + + align:start position:0% +Paradigm so what I'm going to do is + + + align:start position:0% +Paradigm so what I'm going to do is +Define sub problems R + + align:start position:0% +Define sub problems R + + + align:start position:0% +Define sub problems R +star so R is the total number of + + align:start position:0% +star so R is the total number of + + + align:start position:0% +star so R is the total number of +requests that we + + align:start position:0% +requests that we + + + align:start position:0% +requests that we +have and the sub problems are going to + + align:start position:0% +have and the sub problems are going to + + + align:start position:0% +have and the sub problems are going to +correspond to I'm going to pick request + + align:start position:0% +correspond to I'm going to pick request + + + align:start position:0% +correspond to I'm going to pick request +J belonging to R such + + align:start position:0% +J belonging to R such + + + align:start position:0% +J belonging to R such +that oh I'm sorry this was R of x + + align:start position:0% +that oh I'm sorry this was R of x + + + align:start position:0% +that oh I'm sorry this was R of x +X um such that s SJ is greater than or + + align:start position:0% +X um such that s SJ is greater than or + + + align:start position:0% +X um such that s SJ is greater than or +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +X right so um what I'm doing here is um + + align:start position:0% +X right so um what I'm doing here is um + + + align:start position:0% +X right so um what I'm doing here is um +given a particular X I can always shrink + + align:start position:0% +given a particular X I can always shrink + + + align:start position:0% +given a particular X I can always shrink +the number of requests that I have based + + align:start position:0% +the number of requests that I have based + + + align:start position:0% +the number of requests that I have based +on this rule okay and then you might ask + + align:start position:0% +on this rule okay and then you might ask + + + align:start position:0% +on this rule okay and then you might ask +you know what is X and now you can apply + + align:start position:0% +you know what is X and now you can apply + + + align:start position:0% +you know what is X and now you can apply +the + + align:start position:0% +the + + + align:start position:0% +the +same subsetting + + align:start position:0% +same subsetting + + + align:start position:0% +same subsetting +property by choosing the X's to + + align:start position:0% +property by choosing the X's to + + + align:start position:0% +property by choosing the X's to +be the finishing times of all of the + + align:start position:0% +be the finishing times of all of the + + + align:start position:0% +be the finishing times of all of the +other + + align:start position:0% +other + + + align:start position:0% +other +requests right so uh x equals F ofi so + + align:start position:0% +requests right so uh x equals F ofi so + + + align:start position:0% +requests right so uh x equals F ofi so +what this means + + align:start position:0% +what this means + + + align:start position:0% +what this means +is um when I put uh F ofi over here it + + align:start position:0% +is um when I put uh F ofi over here it + + + align:start position:0% +is um when I put uh F ofi over here it +means all of the requests that come + + align:start position:0% +means all of the requests that come + + + align:start position:0% +means all of the requests that come +after the I request finished are part of + + align:start position:0% +after the I request finished are part of + + + align:start position:0% +after the I request finished are part of +R of fi so R of fi would simply + + align:start position:0% + + + + align:start position:0% + +be + + align:start position:0% +be + + + align:start position:0% +be +requests + + align:start position:0% +requests + + + align:start position:0% +requests +later than F of I okay and there's + + align:start position:0% +later than F of I okay and there's + + + align:start position:0% +later than F of I okay and there's +something subtle here that I want to + + align:start position:0% +something subtle here that I want to + + + align:start position:0% +something subtle here that I want to +point out which is R of fi is not the + + align:start position:0% +point out which is R of fi is not the + + + align:start position:0% +point out which is R of fi is not the +set of requests that are compatible with + + align:start position:0% +set of requests that are compatible with + + + align:start position:0% +set of requests that are compatible with +the I request + + align:start position:0% +the I request + + + align:start position:0% +the I request +okay it's it's not exactly that it's the + + align:start position:0% +okay it's it's not exactly that it's the + + + align:start position:0% +okay it's it's not exactly that it's the +set of requests that are later than F + + align:start position:0% +set of requests that are later than F + + + align:start position:0% +set of requests that are later than F +ofi okay so keep that in mind because + + align:start position:0% +ofi okay so keep that in mind because + + + align:start position:0% +ofi okay so keep that in mind because +what happens here is we're going to + + align:start position:0% +what happens here is we're going to + + + align:start position:0% +what happens here is we're going to +solve this problem uh step by step we're + + align:start position:0% +solve this problem uh step by step we're + + + align:start position:0% +solve this problem uh step by step we're +going to construct the dynamic + + align:start position:0% +going to construct the dynamic + + + align:start position:0% +going to construct the dynamic +programming solution um + + align:start position:0% +programming solution um + + + align:start position:0% +programming solution um +essentially by picking a request and + + align:start position:0% +essentially by picking a request and + + + align:start position:0% +essentially by picking a request and +then just like in the greedy case and + + align:start position:0% +then just like in the greedy case and + + + align:start position:0% +then just like in the greedy case and +then picking the request that comes + + align:start position:0% +then picking the request that comes + + + align:start position:0% +then picking the request that comes +after that so if we're going to pick + + align:start position:0% +after that so if we're going to pick + + + align:start position:0% +after that so if we're going to pick +pick an early request and then we're + + align:start position:0% +pick an early request and then we're + + + align:start position:0% +pick an early request and then we're +going to subset the solution pick the + + align:start position:0% +going to subset the solution pick the + + + align:start position:0% +going to subset the solution pick the +next one just like we did with the + + align:start position:0% +next one just like we did with the + + + align:start position:0% +next one just like we did with the +greedy um and so uh the sub problems + + align:start position:0% +greedy um and so uh the sub problems + + + align:start position:0% +greedy um and so uh the sub problems +that we will actually solve potentially + + align:start position:0% +that we will actually solve potentially + + + align:start position:0% +that we will actually solve potentially +bottom up if we doing recursion um are + + align:start position:0% +bottom up if we doing recursion um are + + + align:start position:0% +bottom up if we doing recursion um are +going to correspond to a set of requests + + align:start position:0% +going to correspond to a set of requests + + + align:start position:0% +going to correspond to a set of requests +that come later than the + + align:start position:0% +that come later than the + + + align:start position:0% +that come later than the +particular subset that we're looking at + + align:start position:0% +particular subset that we're looking at + + + align:start position:0% +particular subset that we're looking at +which is defined by a particular + + align:start position:0% +which is defined by a particular + + + align:start position:0% +which is defined by a particular +interval all right so requests that are + + align:start position:0% +interval all right so requests that are + + + align:start position:0% +interval all right so requests that are +later than ffi not necessarily all of + + align:start position:0% +later than ffi not necessarily all of + + + align:start position:0% +later than ffi not necessarily all of +the requests that are compatible with + + align:start position:0% +the requests that are compatible with + + + align:start position:0% +the requests that are compatible with +the I + + align:start position:0% +the I + + + align:start position:0% +the I +request and so if you do + + align:start position:0% +request and so if you do + + + align:start position:0% +request and so if you do +that then the number of sub problems + + align:start position:0% +that then the number of sub problems + + + align:start position:0% +that then the number of sub problems +here are small n where n is the number + + align:start position:0% +here are small n where n is the number + + + align:start position:0% +here are small n where n is the number +of requests so if n is + + align:start position:0% +of requests so if n is + + + align:start position:0% +of requests so if n is +the number of requests in the original + + align:start position:0% +the number of requests in the original + + + align:start position:0% +the number of requests in the original +problem the number of sub + + align:start position:0% +problem the number of sub + + + align:start position:0% +problem the number of sub +problems + + align:start position:0% + + + + align:start position:0% + +equals n because all I do is plug in an + + align:start position:0% +equals n because all I do is plug in an + + + align:start position:0% +equals n because all I do is plug in an +appropriate I find the F ofi for it and + + align:start position:0% +appropriate I find the F ofi for it and + + + align:start position:0% +appropriate I find the F ofi for it and +generate the r of f ofi for each of + + align:start position:0% +generate the r of f ofi for each of + + + align:start position:0% +generate the r of f ofi for each of +those so there's going to be n of those + + align:start position:0% +those so there's going to be n of those + + + align:start position:0% +those so there's going to be n of those +sub + + align:start position:0% +sub + + + align:start position:0% +sub +problems + + align:start position:0% +problems + + + align:start position:0% +problems +and we're going to + + align:start position:0% +and we're going to + + + align:start position:0% +and we're going to +solve each sub problem + + align:start position:0% + + + + align:start position:0% + +once and then + + align:start position:0% +once and then + + + align:start position:0% +once and then +memorize + + align:start position:0% + + + + align:start position:0% + +and so the work that we have to do is uh + + align:start position:0% +and so the work that we have to do is uh + + + align:start position:0% +and so the work that we have to do is uh +the basic rule corresponding to the + + align:start position:0% +the basic rule corresponding to the + + + align:start position:0% +the basic rule corresponding to the +complexity of a DP which is number of + + align:start position:0% +complexity of a DP which is number of + + + align:start position:0% +complexity of a DP which is number of +sub + + align:start position:0% + + + + align:start position:0% + +problems + + align:start position:0% + + + + align:start position:0% + +times the + + align:start position:0% +times the + + + align:start position:0% +times the +time to + + align:start position:0% +time to + + + align:start position:0% +time to +solve um each sub problem or a single + + align:start position:0% +solve um each sub problem or a single + + + align:start position:0% +solve um each sub problem or a single +sub + + align:start position:0% +sub + + + align:start position:0% +sub +problem + + align:start position:0% +problem + + + align:start position:0% +problem +and this + + align:start position:0% + + + + align:start position:0% + +assumes order one + + align:start position:0% +assumes order one + + + align:start position:0% +assumes order one +for uh + + align:start position:0% +for uh + + + align:start position:0% +for uh +lookups so you can you can think of the + + align:start position:0% +lookups so you can you can think of the + + + align:start position:0% +lookups so you can you can think of the +recursive calls as being order + + align:start position:0% + + + + align:start position:0% + +one because you're assuming you're doing + + align:start position:0% +one because you're assuming you're doing + + + align:start position:0% +one because you're assuming you're doing +memorization okay so I haven't really + + align:start position:0% +memorization okay so I haven't really + + + align:start position:0% +memorization okay so I haven't really +told you anything here that uh you + + align:start position:0% +told you anything here that uh you + + + align:start position:0% +told you anything here that uh you +haven't seen in6 and likely applied + + align:start position:0% +haven't seen in6 and likely applied + + + align:start position:0% +haven't seen in6 and likely applied +bunch of times um over here we've just + + align:start position:0% +bunch of times um over here we've just + + + align:start position:0% +bunch of times um over here we've just +defined what our sub problems are for + + align:start position:0% +defined what our sub problems are for + + + align:start position:0% +defined what our sub problems are for +our particular DP and we argued that the + + align:start position:0% +our particular DP and we argued that the + + + align:start position:0% +our particular DP and we argued that the +number of sub problems that are + + align:start position:0% +number of sub problems that are + + + align:start position:0% +number of sub problems that are +associated with this particular choice + + align:start position:0% +associated with this particular choice + + + align:start position:0% +associated with this particular choice +of of sub problems corresponds to n if + + align:start position:0% +of of sub problems corresponds to n if + + + align:start position:0% +of of sub problems corresponds to n if +you have n requests in the original + + align:start position:0% +you have n requests in the original + + + align:start position:0% +you have n requests in the original +problem instance that you're + + align:start position:0% +problem instance that you're + + + align:start position:0% +problem instance that you're +given so the last thing that we have to + + align:start position:0% +given so the last thing that we have to + + + align:start position:0% +given so the last thing that we have to +do here to solve our DP is of course to + + align:start position:0% +do here to solve our DP is of course to + + + align:start position:0% +do here to solve our DP is of course to +write our recursion out + + align:start position:0% +write our recursion out + + + align:start position:0% +write our recursion out +and to convince ourselves that this + + align:start position:0% +and to convince ourselves that this + + + align:start position:0% +and to convince ourselves that this +actually all works + + align:start position:0% +actually all works + + + align:start position:0% +actually all works +out and let's do + + align:start position:0% + + + + align:start position:0% + +that and so what we have here + + align:start position:0% +that and so what we have here + + + align:start position:0% +that and so what we have here +is our DP + + align:start position:0% + + + + align:start position:0% + +guessing and we're going to + + align:start position:0% +guessing and we're going to + + + align:start position:0% +guessing and we're going to +try each + + align:start position:0% +try each + + + align:start position:0% +try each +request + + align:start position:0% +request + + + align:start position:0% +request +I and as a possible first + + align:start position:0% + + + + align:start position:0% + +request right and so that's where this + + align:start position:0% +request right and so that's where this + + + align:start position:0% +request right and so that's where this +works you might be thinking boy I mean + + align:start position:0% +works you might be thinking boy I mean + + + align:start position:0% +works you might be thinking boy I mean +this R of fi looks a little strange why + + align:start position:0% +this R of fi looks a little strange why + + + align:start position:0% +this R of fi looks a little strange why +doesn't it include all of the requests + + align:start position:0% +doesn't it include all of the requests + + + align:start position:0% +doesn't it include all of the requests +that are compatible with the with the + + align:start position:0% +that are compatible with the with the + + + align:start position:0% +that are compatible with the with the +with the I request I mean I'm somehow + + align:start position:0% +with the I request I mean I'm somehow + + + align:start position:0% +with the I request I mean I'm somehow +shrinking my my subsequent problem size + + align:start position:0% +shrinking my my subsequent problem size + + + align:start position:0% +shrinking my my subsequent problem size +if I'm ignoring some requests that are + + align:start position:0% +if I'm ignoring some requests that are + + + align:start position:0% +if I'm ignoring some requests that are +earlier that really should be part of + + align:start position:0% +earlier that really should be part of + + + align:start position:0% +earlier that really should be part of +the or are part of the compatible set + + align:start position:0% +the or are part of the compatible set + + + align:start position:0% +the or are part of the compatible set +but they're not part of the RF fi set + + align:start position:0% +but they're not part of the RF fi set + + + align:start position:0% +but they're not part of the RF fi set +right and so some of you may be thinking + + align:start position:0% +right and so some of you may be thinking + + + align:start position:0% +right and so some of you may be thinking +that well the reason this is going to + + align:start position:0% +that well the reason this is going to + + + align:start position:0% +that well the reason this is going to +work out is because we're going to + + align:start position:0% +work out is because we're going to + + + align:start position:0% +work out is because we're going to +construct our solution as I said before + + align:start position:0% +construct our solution as I said before + + + align:start position:0% +construct our solution as I said before +from the beginning to the end so we're + + align:start position:0% +from the beginning to the end so we're + + + align:start position:0% +from the beginning to the end so we're +going to try each request as a possible + + align:start position:0% +going to try each request as a possible + + + align:start position:0% +going to try each request as a possible +first request okay so even though this + + align:start position:0% +first request okay so even though this + + + align:start position:0% +first request okay so even though this +request might be in our chart you know + + align:start position:0% +request might be in our chart you know + + + align:start position:0% +request might be in our chart you know +all the way to the right uh it might + + align:start position:0% +all the way to the right uh it might + + + align:start position:0% +all the way to the right uh it might +have a huge weight okay and so I'm going + + align:start position:0% +have a huge weight okay and so I'm going + + + align:start position:0% +have a huge weight okay and so I'm going +to have to try that out as my first + + align:start position:0% +to have to try that out as my first + + + align:start position:0% +to have to try that out as my first +selection and when I try that out as my + + align:start position:0% +selection and when I try that out as my + + + align:start position:0% +selection and when I try that out as my +first selection then the definition of + + align:start position:0% +first selection then the definition of + + + align:start position:0% +first selection then the definition of +my sub problem says that this will work + + align:start position:0% +my sub problem says that this will work + + + align:start position:0% +my sub problem says that this will work +I only have to look at requests that + + align:start position:0% +I only have to look at requests that + + + align:start position:0% +I only have to look at requests that +come later than that because the ones + + align:start position:0% +come later than that because the ones + + + align:start position:0% +come later than that because the ones +that came earlier I've tried them out + + align:start position:0% +that came earlier I've tried them out + + + align:start position:0% +that came earlier I've tried them out +too okay so that's something that you + + align:start position:0% +too okay so that's something that you + + + align:start position:0% +too okay so that's something that you +need to keep in mind I in order to argue + + align:start position:0% +need to keep in mind I in order to argue + + + align:start position:0% +need to keep in mind I in order to argue +correctness of this recursion that I'm + + align:start position:0% +correctness of this recursion that I'm + + + align:start position:0% +correctness of this recursion that I'm +going to write out now + + align:start position:0% +going to write out now + + + align:start position:0% +going to write out now +and so the + + align:start position:0% +and so the + + + align:start position:0% +and so the +recursion and I have opt + + align:start position:0% +recursion and I have opt + + + align:start position:0% +recursion and I have opt +R what is the first thing that I'm going + + align:start position:0% +R what is the first thing that I'm going + + + align:start position:0% +R what is the first thing that I'm going +to have on the right hand side of this + + align:start position:0% +to have on the right hand side of this + + + align:start position:0% +to have on the right hand side of this +recursive formulation what uh + + align:start position:0% +recursive formulation what uh + + + align:start position:0% +recursive formulation what uh +mathematical construct am I going to + + align:start position:0% +mathematical construct am I going to + + + align:start position:0% +mathematical construct am I going to +have to do here when I when you see + + align:start position:0% +have to do here when I when you see + + + align:start position:0% +have to do here when I when you see +something like guessing and seeing + + align:start position:0% +something like guessing and seeing + + + align:start position:0% +something like guessing and seeing +something like try each request is a + + align:start position:0% +something like try each request is a + + + align:start position:0% +something like try each request is a +possible first what mathematical + + align:start position:0% +possible first what mathematical + + + align:start position:0% +possible first what mathematical +construct am I going to have to put up + + align:start position:0% +construct am I going to have to put up + + + align:start position:0% +construct am I going to have to put up +here Max who said + + align:start position:0% +here Max who said + + + align:start position:0% +here Max who said +max + + align:start position:0% +max + + + align:start position:0% +max +no one wants to take credit for Max it's + + align:start position:0% +no one wants to take credit for Max it's + + + align:start position:0% +no one wants to take credit for Max it's +Max right so I'm going to have + + align:start position:0% +Max right so I'm going to have + + + align:start position:0% +Max right so I'm going to have +Max um 1 less than equal to I less than + + align:start position:0% +Max um 1 less than equal to I less than + + + align:start position:0% +Max um 1 less than equal to I less than +or equal to + + align:start position:0% +or equal to + + + align:start position:0% +or equal to +n and I'm going to um uh someone want to + + align:start position:0% +n and I'm going to um uh someone want to + + + align:start position:0% +n and I'm going to um uh someone want to +tell me what the rest of this looks + + align:start position:0% +tell me what the rest of this looks + + + align:start position:0% +tell me what the rest of this looks +like someone someone + + align:start position:0% +like someone someone + + + align:start position:0% +like someone someone +else couple of Frisbees left + + align:start position:0% +else couple of Frisbees left + + + align:start position:0% +else couple of Frisbees left +guys what do the rest of this look + + align:start position:0% + + + + align:start position:0% + +like yep + + align:start position:0% +like yep + + + align:start position:0% +like yep +optim uh not one just we have what what + + align:start position:0% +optim uh not one just we have what what + + + align:start position:0% +optim uh not one just we have what what +kind of problem do we have here it's not + + align:start position:0% +kind of problem do we have here it's not + + + align:start position:0% +kind of problem do we have here it's not +one + + align:start position:0% +one + + + align:start position:0% +one +anymore the weight the weight yeah so wi + + align:start position:0% +anymore the weight the weight yeah so wi + + + align:start position:0% +anymore the weight the weight yeah so wi +plus the + + align:start position:0% +plus the + + + align:start position:0% +plus the +optimal uh + + align:start position:0% +optimal uh + + + align:start position:0% +optimal uh +R + + align:start position:0% +R + + + align:start position:0% +R +fi right + + align:start position:0% +fi right + + + align:start position:0% +fi right +okay so we got wi plus optimal of R of + + align:start position:0% +okay so we got wi plus optimal of R of + + + align:start position:0% +okay so we got wi plus optimal of R of +fi okay so and the reason you said one + + align:start position:0% +fi okay so and the reason you said one + + + align:start position:0% +fi okay so and the reason you said one +but I that close enough if it was one + + align:start position:0% +but I that close enough if it was one + + + align:start position:0% +but I that close enough if it was one +You' use greedy and so that's why we're + + align:start position:0% +You' use greedy and so that's why we're + + + align:start position:0% +You' use greedy and so that's why we're +in the wi mode and we end up getting + + align:start position:0% +in the wi mode and we end up getting + + + align:start position:0% +in the wi mode and we end up getting +this here so that's it you try every + + align:start position:0% +this here so that's it you try every + + + align:start position:0% +this here so that's it you try every +request as a possible first you + + align:start position:0% +request as a possible first you + + + align:start position:0% +request as a possible first you +obviously pick that request so it's part + + align:start position:0% +obviously pick that request so it's part + + + align:start position:0% +obviously pick that request so it's part +of your weight in terms of your uh the + + align:start position:0% +of your weight in terms of your uh the + + + align:start position:0% +of your weight in terms of your uh the +weight for your solution when you do + + align:start position:0% +weight for your solution when you do + + + align:start position:0% +weight for your solution when you do +that because it was the first request + + align:start position:0% +that because it was the first request + + + align:start position:0% +that because it was the first request +you get to prune the set of requests + + align:start position:0% +you get to prune the set of requests + + + align:start position:0% +you get to prune the set of requests +that come later corresponding to um R of + + align:start position:0% +that come later corresponding to um R of + + + align:start position:0% +that come later corresponding to um R of +fi that you see here and then you uh go + + align:start position:0% +fi that you see here and then you uh go + + + align:start position:0% +fi that you see here and then you uh go +ahead and simply uh find the optimum for + + align:start position:0% +ahead and simply uh find the optimum for + + + align:start position:0% +ahead and simply uh find the optimum for +a smaller problem clearly has a fewer + + align:start position:0% +a smaller problem clearly has a fewer + + + align:start position:0% +a smaller problem clearly has a fewer +requests and uh as long as you maximize + + align:start position:0% +requests and uh as long as you maximize + + + align:start position:0% +requests and uh as long as you maximize +over the set of guesses that you've + + align:start position:0% +over the set of guesses that you've + + + align:start position:0% +over the set of guesses that you've +taken and there's n guesses up at the + + align:start position:0% +taken and there's n guesses up at the + + + align:start position:0% +taken and there's n guesses up at the +top level obviously at the lower levels + + align:start position:0% +top level obviously at the lower levels + + + align:start position:0% +top level obviously at the lower levels +you're going to have fewer requests uh + + align:start position:0% +you're going to have fewer requests uh + + + align:start position:0% +you're going to have fewer requests uh +in your R of fi and you'll have + + align:start position:0% +in your R of fi and you'll have + + + align:start position:0% +in your R of fi and you'll have +fewer uh iterations of the Max and but + + align:start position:0% +fewer uh iterations of the Max and but + + + align:start position:0% +fewer uh iterations of the Max and but +it's n at the top level okay so um one + + align:start position:0% +it's n at the top level okay so um one + + + align:start position:0% +it's n at the top level okay so um one +last + + align:start position:0% +last + + + align:start position:0% +last +question uh what is the complexity of + + align:start position:0% +question uh what is the complexity of + + + align:start position:0% +question uh what is the complexity of +what we see + + align:start position:0% + + + + align:start position:0% + +here n square right and the reason is n + + align:start position:0% +here n square right and the reason is n + + + align:start position:0% +here n square right and the reason is n +square is you simply use you can be very + + align:start position:0% +square is you simply use you can be very + + + align:start position:0% +square is you simply use you can be very +mechanical about this you you you say if + + align:start position:0% +mechanical about this you you you say if + + + align:start position:0% +mechanical about this you you you say if +this was order one I'm doing a Max Over + + align:start position:0% +this was order one I'm doing a Max Over + + + align:start position:0% +this was order one I'm doing a Max Over +N items and therefore that's order end + + align:start position:0% +N items and therefore that's order end + + + align:start position:0% +N items and therefore that's order end +time to solve one sub problem and uh uh + + align:start position:0% +time to solve one sub problem and uh uh + + + align:start position:0% +time to solve one sub problem and uh uh +since I have N Sub problems I I get n + + align:start position:0% +since I have N Sub problems I I get n + + + align:start position:0% +since I have N Sub problems I I get n +time order n which is order n s okay so + + align:start position:0% +time order n which is order n s okay so + + + align:start position:0% +time order n which is order n s okay so +um the last thing I will do and I just + + align:start position:0% +um the last thing I will do and I just + + + align:start position:0% +um the last thing I will do and I just +have one more minute is H give you a + + align:start position:0% +have one more minute is H give you a + + + align:start position:0% +have one more minute is H give you a +sense of a small change to uh interval + + align:start position:0% +sense of a small change to uh interval + + + align:start position:0% +sense of a small change to uh interval +scheduling that puts us in the NP + + align:start position:0% +scheduling that puts us in the NP + + + align:start position:0% +scheduling that puts us in the NP +complete domain okay so so far we've + + align:start position:0% +complete domain okay so so far we've + + + align:start position:0% +complete domain okay so so far we've +just done two problems there's many + + align:start position:0% +just done two problems there's many + + + align:start position:0% +just done two problems there's many +others we did interval scheduling there + + align:start position:0% +others we did interval scheduling there + + + align:start position:0% +others we did interval scheduling there +was greedy linear time weighted interval + + align:start position:0% +was greedy linear time weighted interval + + + align:start position:0% +was greedy linear time weighted interval +scheduling is order and square according + + align:start position:0% +scheduling is order and square according + + + align:start position:0% +scheduling is order and square according +to this particular DP formulation turns + + align:start position:0% +to this particular DP formulation turns + + + align:start position:0% +to this particular DP formulation turns +out there's a smarter DP formulation + + align:start position:0% +out there's a smarter DP formulation + + + align:start position:0% +out there's a smarter DP formulation +that runs an order n log end time uh + + align:start position:0% +that runs an order n log end time uh + + + align:start position:0% +that runs an order n log end time uh +that uh you'll hear about in section on + + align:start position:0% +that uh you'll hear about in section on + + + align:start position:0% +that uh you'll hear about in section on +Friday uh but still polinomial time um + + align:start position:0% +Friday uh but still polinomial time um + + + align:start position:0% +Friday uh but still polinomial time um +let's make make one reasonable change to + + align:start position:0% +let's make make one reasonable change to + + + align:start position:0% +let's make make one reasonable change to +this which is to say that we may have + + align:start position:0% +this which is to say that we may have + + + align:start position:0% +this which is to say that we may have +multiple + + align:start position:0% +multiple + + + align:start position:0% +multiple +resources and they may be + + align:start position:0% +resources and they may be + + + align:start position:0% +resources and they may be +non-identical right so turns out + + align:start position:0% +non-identical right so turns out + + + align:start position:0% +non-identical right so turns out +everything that we've done kind of + + align:start position:0% +everything that we've done kind of + + + align:start position:0% +everything that we've done kind of +extrapolates very well to um uh to + + align:start position:0% +extrapolates very well to um uh to + + + align:start position:0% +extrapolates very well to um uh to +identical machines even though there's + + align:start position:0% +identical machines even though there's + + + align:start position:0% +identical machines even though there's +many identical machines but if you have + + align:start position:0% +many identical machines but if you have + + + align:start position:0% +many identical machines but if you have +non-identical machines what that means + + align:start position:0% +non-identical machines what that means + + + align:start position:0% +non-identical machines what that means +is you have uh resources or machine + + align:start position:0% +is you have uh resources or machine + + + align:start position:0% +is you have uh resources or machine +that have different uh types so maybe + + align:start position:0% +that have different uh types so maybe + + + align:start position:0% +that have different uh types so maybe +your your your machines are + + align:start position:0% +your your your machines are + + + align:start position:0% +your your your machines are +T1 to three + + align:start position:0% +T1 to three + + + align:start position:0% +T1 to three +TM okay and + + align:start position:0% +TM okay and + + + align:start position:0% +TM okay and +um it's uh essentially a situation where + + align:start position:0% +um it's uh essentially a situation where + + + align:start position:0% +um it's uh essentially a situation where +you say uh this particular task can only + + align:start position:0% +you say uh this particular task can only + + + align:start position:0% +you say uh this particular task can only +be run on this machine or this other + + align:start position:0% +be run on this machine or this other + + + align:start position:0% +be run on this machine or this other +machine some subset of machines so um + + align:start position:0% +machine some subset of machines so um + + + align:start position:0% +machine some subset of machines so um +you can still have a weight of one for + + align:start position:0% +you can still have a weight of one for + + + align:start position:0% +you can still have a weight of one for +all requests + + align:start position:0% +all requests + + + align:start position:0% +all requests +but you have something like Q of I + + align:start position:0% +but you have something like Q of I + + + align:start position:0% +but you have something like Q of I +belonging subset of + + align:start position:0% +belonging subset of + + + align:start position:0% +belonging subset of +T is a set of + + align:start position:0% + + + + align:start position:0% + +machines that I runs + + align:start position:0% + + + + align:start position:0% + +on okay that's it that's the change we + + align:start position:0% +on okay that's it that's the change we + + + align:start position:0% +on okay that's it that's the change we +make + + align:start position:0% +make + + + align:start position:0% +make +qfi is going to be specified for each of + + align:start position:0% +qfi is going to be specified for each of + + + align:start position:0% +qfi is going to be specified for each of +the eyes so you could even have two + + align:start position:0% +the eyes so you could even have two + + + align:start position:0% +the eyes so you could even have two +machines and you could say here's a a + + align:start position:0% +machines and you could say here's a a + + + align:start position:0% +machines and you could say here's a a +set of requests that could run on both + + align:start position:0% +set of requests that could run on both + + + align:start position:0% +set of requests that could run on both +machines here's a set that only runs on + + align:start position:0% +machines here's a set that only runs on + + + align:start position:0% +machines here's a set that only runs on +the first machine and here's another set + + align:start position:0% +the first machine and here's another set + + + align:start position:0% +the first machine and here's another set +that runs on the second machine right + + align:start position:0% +that runs on the second machine right + + + align:start position:0% +that runs on the second machine right +that's a a simple example of this + + align:start position:0% +that's a a simple example of this + + + align:start position:0% +that's a a simple example of this +generalization um if you do this this + + align:start position:0% + + + + align:start position:0% + +problem has been shown to be NP + + align:start position:0% +problem has been shown to be NP + + + align:start position:0% +problem has been shown to be NP +complete and by that I mean NP complete + + align:start position:0% +complete and by that I mean NP complete + + + align:start position:0% +complete and by that I mean NP complete +problems are decision problems and so + + align:start position:0% +problems are decision problems and so + + + align:start position:0% +problems are decision problems and so +you + + align:start position:0% +you + + + align:start position:0% +you +say can some specific number number K + + align:start position:0% +say can some specific number number K + + + align:start position:0% +say can some specific number number K +less than n + + align:start position:0% +less than n + + + align:start position:0% +less than n +requests P + + align:start position:0% + + + + align:start position:0% + +schedule this decision problem is NP + + align:start position:0% +schedule this decision problem is NP + + + align:start position:0% +schedule this decision problem is NP +complete okay and so what happens when + + align:start position:0% +complete okay and so what happens when + + + align:start position:0% +complete okay and so what happens when +you have NP complete problems well we're + + align:start position:0% +you have NP complete problems well we're + + + align:start position:0% +you have NP complete problems well we're +going to have a little module in the + + align:start position:0% +going to have a little module in the + + + align:start position:0% +going to have a little module in the +class that deals with intractability + + align:start position:0% +class that deals with intractability + + + align:start position:0% +class that deals with intractability +we're going to look at U cases where we + + align:start position:0% +we're going to look at U cases where we + + + align:start position:0% +we're going to look at U cases where we +could apply approximation algorithms and + + align:start position:0% +could apply approximation algorithms and + + + align:start position:0% +could apply approximation algorithms and +maybe uh in the case of the optimization + + align:start position:0% +maybe uh in the case of the optimization + + + align:start position:0% +maybe uh in the case of the optimization +problem uh if the optimum uh for this is + + align:start position:0% +problem uh if the optimum uh for this is + + + align:start position:0% +problem uh if the optimum uh for this is +K star we'll say that we can get within + + align:start position:0% +K star we'll say that we can get within + + + align:start position:0% +K star we'll say that we can get within +10% of K star um the other way is to + + align:start position:0% +10% of K star um the other way is to + + + align:start position:0% +10% of K star um the other way is to +just deal with intractability by uh + + align:start position:0% +just deal with intractability by uh + + + align:start position:0% +just deal with intractability by uh +hoping that your exponential time + + align:start position:0% +hoping that your exponential time + + + align:start position:0% +hoping that your exponential time +algorithm runs in reasonable amount of + + align:start position:0% +algorithm runs in reasonable amount of + + + align:start position:0% +algorithm runs in reasonable amount of +time for common cases so in the worst + + align:start position:0% +time for common cases so in the worst + + + align:start position:0% +time for common cases so in the worst +case uh you uh might end up taking a + + align:start position:0% +case uh you uh might end up taking a + + + align:start position:0% +case uh you uh might end up taking a +long time but you just sort of back off + + align:start position:0% +long time but you just sort of back off + + + align:start position:0% +long time but you just sort of back off +after an hour and take what you get from + + align:start position:0% +after an hour and take what you get from + + + align:start position:0% +after an hour and take what you get from +the output of the algorithm but uh in + + align:start position:0% +the output of the algorithm but uh in + + + align:start position:0% +the output of the algorithm but uh in +many cases uh the algorithm might + + align:start position:0% +many cases uh the algorithm might + + + align:start position:0% +many cases uh the algorithm might +actually complete uh and they give you + + align:start position:0% +actually complete uh and they give you + + + align:start position:0% +actually complete uh and they give you +the optimum solution okay so done here + + align:start position:0% +the optimum solution okay so done here + + + align:start position:0% +the optimum solution okay so done here +make sure to uh sign up for the + + align:start position:0% +make sure to uh sign up for the + + + align:start position:0% +make sure to uh sign up for the +resistration section and see you guys + + align:start position:0% +resistration section and see you guys + + + align:start position:0% +resistration section and see you guys +next + + align:start position:0% +next + + + align:start position:0% +next +time \ No newline at end of file diff --git a/2TZa151GC-0.txt b/2TZa151GC-0.txt new file mode 100644 index 0000000000000000000000000000000000000000..0468b22027f12afff56a09189cfee01a01b58798 --- /dev/null +++ b/2TZa151GC-0.txt @@ -0,0 +1,1083 @@ +align:start position:0% + +we now would like to generalize our + + align:start position:0% +we now would like to generalize our + + + align:start position:0% +we now would like to generalize our +concept of work to the motion of an + + align:start position:0% +concept of work to the motion of an + + + align:start position:0% +concept of work to the motion of an +object that goes in more than one + + align:start position:0% +object that goes in more than one + + + align:start position:0% +object that goes in more than one +dimension and so if we have our object + + align:start position:0% +dimension and so if we have our object + + + align:start position:0% +dimension and so if we have our object +here and we're applying a force and the + + align:start position:0% +here and we're applying a force and the + + + align:start position:0% +here and we're applying a force and the +object is moving and let's say the path + + align:start position:0% +object is moving and let's say the path + + + align:start position:0% +object is moving and let's say the path +is a little bit more complicated so our + + align:start position:0% +is a little bit more complicated so our + + + align:start position:0% +is a little bit more complicated so our +object a little bit later has + + align:start position:0% +object a little bit later has + + + align:start position:0% +object a little bit later has +moved and we're going to call that the + + align:start position:0% +moved and we're going to call that the + + + align:start position:0% +moved and we're going to call that the +displacement we now want to generalize + + align:start position:0% +displacement we now want to generalize + + + align:start position:0% +displacement we now want to generalize +our concept of work to handle this type + + align:start position:0% +our concept of work to handle this type + + + align:start position:0% +our concept of work to handle this type +of motion in more than one dimension in + + align:start position:0% +of motion in more than one dimension in + + + align:start position:0% +of motion in more than one dimension in +order to do that we'll need a new + + align:start position:0% +order to do that we'll need a new + + + align:start position:0% +order to do that we'll need a new +mathematical operation which we're going + + align:start position:0% +mathematical operation which we're going + + + align:start position:0% +mathematical operation which we're going +to call the scalar + + align:start position:0% +to call the scalar + + + align:start position:0% +to call the scalar +product so what I'd like to do first is + + align:start position:0% +product so what I'd like to do first is + + + align:start position:0% +product so what I'd like to do first is +Define this in terms of vectors and then + + align:start position:0% +Define this in terms of vectors and then + + + align:start position:0% +Define this in terms of vectors and then +we'll apply it to the concept of work so + + align:start position:0% +we'll apply it to the concept of work so + + + align:start position:0% +we'll apply it to the concept of work so +suppose I have two vectors + + align:start position:0% +suppose I have two vectors + + + align:start position:0% +suppose I have two vectors +A and another Vector B and they're + + align:start position:0% +A and another Vector B and they're + + + align:start position:0% +A and another Vector B and they're +separated by an angle Theta and in this + + align:start position:0% +separated by an angle Theta and in this + + + align:start position:0% +separated by an angle Theta and in this +case + + align:start position:0% +case + + + align:start position:0% +case +oura we're going to just take it between + + align:start position:0% +oura we're going to just take it between + + + align:start position:0% +oura we're going to just take it between +0 and + + align:start position:0% +0 and + + + align:start position:0% +0 and +Pi + + align:start position:0% +Pi + + + align:start position:0% +Pi +now i' like to talk about how much one + + align:start position:0% +now i' like to talk about how much one + + + align:start position:0% +now i' like to talk about how much one +vector projects in the direction of the + + align:start position:0% +vector projects in the direction of the + + + align:start position:0% +vector projects in the direction of the +other so if I call this the parallel + + align:start position:0% +other so if I call this the parallel + + + align:start position:0% +other so if I call this the parallel +component of b then I want to define a + + align:start position:0% +component of b then I want to define a + + + align:start position:0% +component of b then I want to define a +quantity which we're going to call the + + align:start position:0% +quantity which we're going to call the + + + align:start position:0% +quantity which we're going to call the +scalar product of a do B + + align:start position:0% +scalar product of a do B + + + align:start position:0% +scalar product of a do B +which is the magnitude of a times the + + align:start position:0% +which is the magnitude of a times the + + + align:start position:0% +which is the magnitude of a times the +amount of B that is in the direction + + align:start position:0% +amount of B that is in the direction + + + align:start position:0% +amount of B that is in the direction +parallel to a now from our geometric + + align:start position:0% +parallel to a now from our geometric + + + align:start position:0% +parallel to a now from our geometric +diagram you can see that b + + align:start position:0% +diagram you can see that b + + + align:start position:0% +diagram you can see that b +parallel is equal to the magnitude of B + + align:start position:0% +parallel is equal to the magnitude of B + + + align:start position:0% +parallel is equal to the magnitude of B +time cosine of thet now remember Theta + + align:start position:0% +time cosine of thet now remember Theta + + + align:start position:0% +time cosine of thet now remember Theta +is going from 0 to Pi so this quantity + + align:start position:0% +is going from 0 to Pi so this quantity + + + align:start position:0% +is going from 0 to Pi so this quantity +be parallel can both be positive or + + align:start position:0% +be parallel can both be positive or + + + align:start position:0% +be parallel can both be positive or +negative if + + align:start position:0% +negative if + + + align:start position:0% +negative if +Theta is between + + align:start position:0% +Theta is between + + + align:start position:0% +Theta is between +0 and pi over two then in that range the + + align:start position:0% +0 and pi over two then in that range the + + + align:start position:0% +0 and pi over two then in that range the +cosine goes from 1 to zero and this + + align:start position:0% +cosine goes from 1 to zero and this + + + align:start position:0% +cosine goes from 1 to zero and this +quantity B will be greater or equal to + + align:start position:0% +quantity B will be greater or equal to + + + align:start position:0% +quantity B will be greater or equal to +zero be parallel if Theta is going from + + align:start position:0% +zero be parallel if Theta is going from + + + align:start position:0% +zero be parallel if Theta is going from +Pi / 2 Theta to + + align:start position:0% +Pi / 2 Theta to + + + align:start position:0% +Pi / 2 Theta to +Pi then we have that b + + align:start position:0% +Pi then we have that b + + + align:start position:0% +Pi then we have that b +parallel is less than or equal to + + align:start position:0% +parallel is less than or equal to + + + align:start position:0% +parallel is less than or equal to +zero and in particular at the value pi/ + + align:start position:0% +zero and in particular at the value pi/ + + + align:start position:0% +zero and in particular at the value pi/ +2 be parallel to zero because when Theta + + align:start position:0% +2 be parallel to zero because when Theta + + + align:start position:0% +2 be parallel to zero because when Theta +is Pi / 2 the B Vector is completely + + align:start position:0% +is Pi / 2 the B Vector is completely + + + align:start position:0% +is Pi / 2 the B Vector is completely +perpendicular to a and this is what + + align:start position:0% +perpendicular to a and this is what + + + align:start position:0% +perpendicular to a and this is what +we're going to Define to be the scalar + + align:start position:0% +we're going to Define to be the scalar + + + align:start position:0% +we're going to Define to be the scalar +product but geometrically we can also + + align:start position:0% +product but geometrically we can also + + + align:start position:0% +product but geometrically we can also +look at let's draw our pictures again A + + align:start position:0% +look at let's draw our pictures again A + + + align:start position:0% +look at let's draw our pictures again A +and B and now let's consider how much of + + align:start position:0% +and B and now let's consider how much of + + + align:start position:0% +and B and now let's consider how much of +a is parallel to B so that's a + + align:start position:0% +a is parallel to B so that's a + + + align:start position:0% +a is parallel to B so that's a +parallel and if this is the angle Theta + + align:start position:0% +parallel and if this is the angle Theta + + + align:start position:0% +parallel and if this is the angle Theta +we see that a + + align:start position:0% +we see that a + + + align:start position:0% +we see that a +parallel here and I'll write it as a + + align:start position:0% +parallel here and I'll write it as a + + + align:start position:0% +parallel here and I'll write it as a +parallel is the magnitude of a Time + + align:start position:0% +parallel is the magnitude of a Time + + + align:start position:0% +parallel is the magnitude of a Time +cosine of theta and so I can also Define + + align:start position:0% +cosine of theta and so I can also Define + + + align:start position:0% +cosine of theta and so I can also Define +a. + + align:start position:0% +a. + + + align:start position:0% +a. +b + + align:start position:0% +b + + + align:start position:0% +b +as equal to how much of a is parallel to + + align:start position:0% +as equal to how much of a is parallel to + + + align:start position:0% +as equal to how much of a is parallel to +B time the magnitude of B now in both of + + align:start position:0% +B time the magnitude of B now in both of + + + align:start position:0% +B time the magnitude of B now in both of +these instances because B parallel is + + align:start position:0% +these instances because B parallel is + + + align:start position:0% +these instances because B parallel is +the magnitude of B cosine Theta and a + + align:start position:0% +the magnitude of B cosine Theta and a + + + align:start position:0% +the magnitude of B cosine Theta and a +parallel is the magnitude of a cosine + + align:start position:0% +parallel is the magnitude of a cosine + + + align:start position:0% +parallel is the magnitude of a cosine +Theta what we're writing is is that a b + + align:start position:0% +Theta what we're writing is is that a b + + + align:start position:0% +Theta what we're writing is is that a b +is the magnitude of a cosine Theta + + align:start position:0% +is the magnitude of a cosine Theta + + + align:start position:0% +is the magnitude of a cosine Theta +magnitude of B and now you can see that + + align:start position:0% +magnitude of B and now you can see that + + + align:start position:0% +magnitude of B and now you can see that +this quantity is a + + align:start position:0% +this quantity is a + + + align:start position:0% +this quantity is a +parallel and this quantity is B parallel + + align:start position:0% +parallel and this quantity is B parallel + + + align:start position:0% +parallel and this quantity is B parallel +and this is our geometric definition of + + align:start position:0% +and this is our geometric definition of + + + align:start position:0% +and this is our geometric definition of +a DOT + + align:start position:0% +a DOT + + + align:start position:0% +a DOT +product now one thing that we want to + + align:start position:0% +product now one thing that we want to + + + align:start position:0% +product now one thing that we want to +consider are two important rules for DOT + + align:start position:0% +consider are two important rules for DOT + + + align:start position:0% +consider are two important rules for DOT +products and they're the following that + + align:start position:0% +products and they're the following that + + + align:start position:0% +products and they're the following that +if we take a vector and multiply a by a + + align:start position:0% +if we take a vector and multiply a by a + + + align:start position:0% +if we take a vector and multiply a by a +quantity of C here here is a scalar + + align:start position:0% +quantity of C here here is a scalar + + + align:start position:0% +quantity of C here here is a scalar +quantity then this is equal to C + + align:start position:0% +quantity then this is equal to C + + + align:start position:0% +quantity then this is equal to C +* a do + + align:start position:0% +* a do + + + align:start position:0% +* a do +B now geometrically this is very easy to + + align:start position:0% +B now geometrically this is very easy to + + + align:start position:0% +B now geometrically this is very easy to +see because if we draw + + align:start position:0% +see because if we draw + + + align:start position:0% +see because if we draw +a and we draw + + align:start position:0% +a and we draw + + + align:start position:0% +a and we draw +B and If I multiply a by a scalar and + + align:start position:0% +B and If I multiply a by a scalar and + + + align:start position:0% +B and If I multiply a by a scalar and +let's make in this particular picture + + align:start position:0% +let's make in this particular picture + + + align:start position:0% +let's make in this particular picture +our scalar bigger than one then the new + + align:start position:0% +our scalar bigger than one then the new + + + align:start position:0% +our scalar bigger than one then the new +Vector a + + align:start position:0% +Vector a + + + align:start position:0% +Vector a +is multiplied by C and it's C * a and + + align:start position:0% +is multiplied by C and it's C * a and + + + align:start position:0% +is multiplied by C and it's C * a and +the scalar product is + + align:start position:0% +the scalar product is + + + align:start position:0% +the scalar product is +just + + align:start position:0% +just + + + align:start position:0% +just +ca. B is the + + align:start position:0% +ca. B is the + + + align:start position:0% +ca. B is the +magnitude of CA times how much of B is + + align:start position:0% +magnitude of CA times how much of B is + + + align:start position:0% +magnitude of CA times how much of B is +parallel and when you multiply this + + align:start position:0% +parallel and when you multiply this + + + align:start position:0% +parallel and when you multiply this +together you get C * a * B + + align:start position:0% +together you get C * a * B + + + align:start position:0% +together you get C * a * B +parallel + + align:start position:0% +parallel + + + align:start position:0% +parallel +now C of a. + + align:start position:0% +now C of a. + + + align:start position:0% +now C of a. +B is equal to c times the magnitude of a + + align:start position:0% +B is equal to c times the magnitude of a + + + align:start position:0% +B is equal to c times the magnitude of a +Time B + + align:start position:0% +Time B + + + align:start position:0% +Time B +parallel and you can see that these two + + align:start position:0% +parallel and you can see that these two + + + align:start position:0% +parallel and you can see that these two +expressions are equal so if you + + align:start position:0% +expressions are equal so if you + + + align:start position:0% +expressions are equal so if you +multiply a DOT product by a + + align:start position:0% +multiply a DOT product by a + + + align:start position:0% +multiply a DOT product by a +scalar it satisfies this Rule and + + align:start position:0% +scalar it satisfies this Rule and + + + align:start position:0% +scalar it satisfies this Rule and +there's one other crucial rule that + + align:start position:0% +there's one other crucial rule that + + + align:start position:0% +there's one other crucial rule that +we'll need when we look at vectors that + + align:start position:0% +we'll need when we look at vectors that + + + align:start position:0% +we'll need when we look at vectors that +if you take a vector a + + align:start position:0% +if you take a vector a + + + align:start position:0% +if you take a vector a +and you add to it a vector B and you dot + + align:start position:0% +and you add to it a vector B and you dot + + + align:start position:0% +and you add to it a vector B and you dot +it into a vector C then that's this is + + align:start position:0% +it into a vector C then that's this is + + + align:start position:0% +it into a vector C then that's this is +vector addition and Vector + + align:start position:0% +vector addition and Vector + + + align:start position:0% +vector addition and Vector +multiplication this vector addition + + align:start position:0% +multiplication this vector addition + + + align:start position:0% +multiplication this vector addition +distributes over Vector multiplication + + align:start position:0% +distributes over Vector multiplication + + + align:start position:0% +distributes over Vector multiplication +by a do c plus b do c so these two facts + + align:start position:0% +by a do c plus b do c so these two facts + + + align:start position:0% +by a do c plus b do c so these two facts +are crucial to our development of + + align:start position:0% +are crucial to our development of + + + align:start position:0% +are crucial to our development of +vectors and one thing that we can say is + + align:start position:0% +vectors and one thing that we can say is + + + align:start position:0% +vectors and one thing that we can say is +we'll leave this as a little + + align:start position:0% +we'll leave this as a little + + + align:start position:0% +we'll leave this as a little +exercise for you to prove this result + + align:start position:0% +exercise for you to prove this result + + + align:start position:0% +exercise for you to prove this result +it's a pretty straightforward Vector + + align:start position:0% +it's a pretty straightforward Vector + + + align:start position:0% +it's a pretty straightforward Vector +construction and to just give you a + + align:start position:0% +construction and to just give you a + + + align:start position:0% +construction and to just give you a +little bit of a hint if we have a vector + + align:start position:0% +little bit of a hint if we have a vector + + + align:start position:0% +little bit of a hint if we have a vector +a and another Vector + + align:start position:0% +a and another Vector + + + align:start position:0% +a and another Vector +B and we have a similar Vector + + align:start position:0% +B and we have a similar Vector + + + align:start position:0% +B and we have a similar Vector +C then if I draw the + + align:start position:0% +C then if I draw the + + + align:start position:0% +C then if I draw the +vector a do B plus + + align:start position:0% +vector a do B plus + + + align:start position:0% +vector a do B plus +b and I want to take a do c so I have + + align:start position:0% +b and I want to take a do c so I have + + + align:start position:0% +b and I want to take a do c so I have +how much of a is parallel to C and if I + + align:start position:0% +how much of a is parallel to C and if I + + + align:start position:0% +how much of a is parallel to C and if I +look at how much of B is parallel to C + + align:start position:0% +look at how much of B is parallel to C + + + align:start position:0% +look at how much of B is parallel to C +then as part of the exercise make sure + + align:start position:0% +then as part of the exercise make sure + + + align:start position:0% +then as part of the exercise make sure +that you can see that how much of a plus + + align:start position:0% +that you can see that how much of a plus + + + align:start position:0% +that you can see that how much of a plus +b parallel to C agrees to this + + align:start position:0% +b parallel to C agrees to this + + + align:start position:0% +b parallel to C agrees to this +distributive rule so these are our + + align:start position:0% +distributive rule so these are our + + + align:start position:0% +distributive rule so these are our +definition of a scalar product and the + + align:start position:0% +definition of a scalar product and the + + + align:start position:0% +definition of a scalar product and the +two key facts that we'll need when we + + align:start position:0% +two key facts that we'll need when we + + + align:start position:0% +two key facts that we'll need when we +apply it in our example of + + align:start position:0% + + + + align:start position:0% + +work \ No newline at end of file diff --git a/2bF6H_xu0ao.txt b/2bF6H_xu0ao.txt new file mode 100644 index 0000000000000000000000000000000000000000..14a39b60a0328fe345179b7f5bb39297a255f7bf --- /dev/null +++ b/2bF6H_xu0ao.txt @@ -0,0 +1,1851 @@ +align:start position:0% + +hello and welcome back to recitation uh + + align:start position:0% +hello and welcome back to recitation uh + + + align:start position:0% +hello and welcome back to recitation uh +today the problem I'd like to work with + + align:start position:0% +today the problem I'd like to work with + + + align:start position:0% +today the problem I'd like to work with +you is about uh Computing partial + + align:start position:0% +you is about uh Computing partial + + + align:start position:0% +you is about uh Computing partial +derivatives and uh and the total + + align:start position:0% +derivatives and uh and the total + + + align:start position:0% +derivatives and uh and the total +differential so we have a function Z + + align:start position:0% +differential so we have a function Z + + + align:start position:0% +differential so we have a function Z +which is uh x^2 + y^2 so it depends on + + align:start position:0% +which is uh x^2 + y^2 so it depends on + + + align:start position:0% +which is uh x^2 + y^2 so it depends on +the two variables X and Y now the + + align:start position:0% +the two variables X and Y now the + + + align:start position:0% +the two variables X and Y now the +variables X and Y themselves depend on + + align:start position:0% +variables X and Y themselves depend on + + + align:start position:0% +variables X and Y themselves depend on +two auxiliary variables u and v so + + align:start position:0% +two auxiliary variables u and v so + + + align:start position:0% +two auxiliary variables u and v so +that's the setup that we have so in part + + align:start position:0% +that's the setup that we have so in part + + + align:start position:0% +that's the setup that we have so in part +A we just want to compute the total + + align:start position:0% +A we just want to compute the total + + + align:start position:0% +A we just want to compute the total +differential uh DZ in terms of DX and Dy + + align:start position:0% +differential uh DZ in terms of DX and Dy + + + align:start position:0% +differential uh DZ in terms of DX and Dy +so u and v aren't going to enter into + + align:start position:0% +so u and v aren't going to enter into + + + align:start position:0% +so u and v aren't going to enter into +the picture and then uh in Part B we're + + align:start position:0% +the picture and then uh in Part B we're + + + align:start position:0% +the picture and then uh in Part B we're +going to compute the partial derivative + + align:start position:0% +going to compute the partial derivative + + + align:start position:0% +going to compute the partial derivative +partial Z partial u in two different + + align:start position:0% +partial Z partial u in two different + + + align:start position:0% +partial Z partial u in two different +ways um first we're going to compute it + + align:start position:0% +ways um first we're going to compute it + + + align:start position:0% +ways um first we're going to compute it +using the chain Rule and then we're + + align:start position:0% +using the chain Rule and then we're + + + align:start position:0% +using the chain Rule and then we're +going to compute it using total + + align:start position:0% +going to compute it using total + + + align:start position:0% +going to compute it using total +differentials uh and so we'll substitute + + align:start position:0% +differentials uh and so we'll substitute + + + align:start position:0% +differentials uh and so we'll substitute +in some of the work that we had in a to + + align:start position:0% +in some of the work that we had in a to + + + align:start position:0% +in some of the work that we had in a to +solve that part so uh why don't I uh + + align:start position:0% +solve that part so uh why don't I uh + + + align:start position:0% +solve that part so uh why don't I uh +pause why don't you pause the video now + + align:start position:0% +pause why don't you pause the video now + + + align:start position:0% +pause why don't you pause the video now +and work on the problem we'll check back + + align:start position:0% +and work on the problem we'll check back + + + align:start position:0% +and work on the problem we'll check back +and we'll do it + + align:start position:0% + + + + align:start position:0% + +together I and welcome back let's get + + align:start position:0% +together I and welcome back let's get + + + align:start position:0% +together I and welcome back let's get +started + + align:start position:0% +started + + + align:start position:0% +started +so first Computing a is not so + + align:start position:0% +so first Computing a is not so + + + align:start position:0% +so first Computing a is not so +bad so we just need to first remember + + align:start position:0% +bad so we just need to first remember + + + align:start position:0% +bad so we just need to first remember +what does it mean the total differential + + align:start position:0% +what does it mean the total differential + + + align:start position:0% +what does it mean the total differential +so we need to uh so the total + + align:start position:0% +so we need to uh so the total + + + align:start position:0% +so we need to uh so the total +differential DZ is + + align:start position:0% +differential DZ is + + + align:start position:0% +differential DZ is +just the partial derivative of Z in the + + align:start position:0% +just the partial derivative of Z in the + + + align:start position:0% +just the partial derivative of Z in the +X Direction + + align:start position:0% +X Direction + + + align:start position:0% +X Direction +DX plus Z in the y direction + + align:start position:0% +DX plus Z in the y direction + + + align:start position:0% +DX plus Z in the y direction +Dy okay so now looking at uh our formula + + align:start position:0% +Dy okay so now looking at uh our formula + + + align:start position:0% +Dy okay so now looking at uh our formula +here for Z we have uh so the partial + + align:start position:0% +here for Z we have uh so the partial + + + align:start position:0% +here for Z we have uh so the partial +derivative of Z in the X direction is 2x + + align:start position:0% +derivative of Z in the X direction is 2x + + + align:start position:0% +derivative of Z in the X direction is 2x +so this is + + align:start position:0% +so this is + + + align:start position:0% +so this is +2x + + align:start position:0% +2x + + + align:start position:0% +2x +DX and the partial derivative of Z and + + align:start position:0% +DX and the partial derivative of Z and + + + align:start position:0% +DX and the partial derivative of Z and +the Y is 2 y so we have 2 y + + align:start position:0% +the Y is 2 y so we have 2 y + + + align:start position:0% +the Y is 2 y so we have 2 y +Dy okay and that's all we have to do for + + align:start position:0% +Dy okay and that's all we have to do for + + + align:start position:0% +Dy okay and that's all we have to do for +a now for + + align:start position:0% +a now for + + + align:start position:0% +a now for +B we want + + align:start position:0% +B we want + + + align:start position:0% +B we want +to compute this partial derivative in + + align:start position:0% +to compute this partial derivative in + + + align:start position:0% +to compute this partial derivative in +two different ways first using the chain + + align:start position:0% +two different ways first using the chain + + + align:start position:0% +two different ways first using the chain +rule so let's remember what the chain + + align:start position:0% +rule so let's remember what the chain + + + align:start position:0% +rule so let's remember what the chain +rule says so whenever I think about the + + align:start position:0% +rule says so whenever I think about the + + + align:start position:0% +rule says so whenever I think about the +chain rule I like to draw this + + align:start position:0% + + + + align:start position:0% + +uh dependency graph + + align:start position:0% +uh dependency graph + + + align:start position:0% +uh dependency graph +okay and this is just a way for me to + + align:start position:0% +okay and this is just a way for me to + + + align:start position:0% +okay and this is just a way for me to +organize how the different variables + + align:start position:0% +organize how the different variables + + + align:start position:0% +organize how the different variables +depend on one another so at the top we + + align:start position:0% +depend on one another so at the top we + + + align:start position:0% +depend on one another so at the top we +have Z and + + align:start position:0% +have Z and + + + align:start position:0% +have Z and +Z is a + + align:start position:0% +Z is a + + + align:start position:0% +Z is a +function of X and Y but X and Y X is + + align:start position:0% +function of X and Y but X and Y X is + + + align:start position:0% +function of X and Y but X and Y X is +itself a function of both u and v and y + + align:start position:0% +itself a function of both u and v and y + + + align:start position:0% +itself a function of both u and v and y +is also a function of u and v so Z + + align:start position:0% +is also a function of u and v so Z + + + align:start position:0% +is also a function of u and v so Z +depends on X and Y and X and Y each + + align:start position:0% +depends on X and Y and X and Y each + + + align:start position:0% +depends on X and Y and X and Y each +jointly depend on u and v so it's a + + align:start position:0% +jointly depend on u and v so it's a + + + align:start position:0% +jointly depend on u and v so it's a +little bit complicated the relationships + + align:start position:0% +little bit complicated the relationships + + + align:start position:0% +little bit complicated the relationships +here so now uh what the chain rule says + + align:start position:0% +here so now uh what the chain rule says + + + align:start position:0% +here so now uh what the chain rule says +is it says that if we take a partial + + align:start position:0% + + + + align:start position:0% + +derivative partial Z partial U we have + + align:start position:0% +derivative partial Z partial U we have + + + align:start position:0% +derivative partial Z partial U we have +to uh go through our dependency graph + + align:start position:0% +to uh go through our dependency graph + + + align:start position:0% +to uh go through our dependency graph +every way that we can get from Z to U uh + + align:start position:0% +every way that we can get from Z to U uh + + + align:start position:0% +every way that we can get from Z to U uh +we get a a term in our summation for for + + align:start position:0% +we get a a term in our summation for for + + + align:start position:0% +we get a a term in our summation for for +each one of those so for instance Z goes + + align:start position:0% +each one of those so for instance Z goes + + + align:start position:0% +each one of those so for instance Z goes +to X goes to U so that means that we + + align:start position:0% +to X goes to U so that means that we + + + align:start position:0% +to X goes to U so that means that we +have partial Z partial X partial X + + align:start position:0% +have partial Z partial X partial X + + + align:start position:0% +have partial Z partial X partial X +partial U and + + align:start position:0% +partial U and + + + align:start position:0% +partial U and +then we can also go Z goes to Y goes to + + align:start position:0% +then we can also go Z goes to Y goes to + + + align:start position:0% +then we can also go Z goes to Y goes to +U and that will give us partial Z + + align:start position:0% +U and that will give us partial Z + + + align:start position:0% +U and that will give us partial Z +partial y partial y partial U and now + + align:start position:0% +partial y partial y partial U and now + + + align:start position:0% +partial y partial y partial U and now +these uh these partials are are ones + + align:start position:0% +these uh these partials are are ones + + + align:start position:0% +these uh these partials are are ones +that we can just compute from our our + + align:start position:0% +that we can just compute from our our + + + align:start position:0% +that we can just compute from our our +formulas so for instance partial Z + + align:start position:0% +formulas so for instance partial Z + + + align:start position:0% +formulas so for instance partial Z +partial X that's two X which we + + align:start position:0% + + + + align:start position:0% + +computed now partial X partial U we have + + align:start position:0% +computed now partial X partial U we have + + + align:start position:0% +computed now partial X partial U we have +to remember that X is defined as U ^2 + + align:start position:0% +to remember that X is defined as U ^2 + + + align:start position:0% +to remember that X is defined as U ^2 +minus V ^2 and so partial X partial U + + align:start position:0% +minus V ^2 and so partial X partial U + + + align:start position:0% +minus V ^2 and so partial X partial U +that's 2 + + align:start position:0% + + + + align:start position:0% + +U uh partial Z partial y uh again is + + align:start position:0% +U uh partial Z partial y uh again is + + + align:start position:0% +U uh partial Z partial y uh again is +this 2 y that we + + align:start position:0% +this 2 y that we + + + align:start position:0% +this 2 y that we +computed and partial y partial + + align:start position:0% +computed and partial y partial + + + align:start position:0% +computed and partial y partial +U is uh + + align:start position:0% +U is uh + + + align:start position:0% +U is uh +V this V is just because y was UV and we + + align:start position:0% +V this V is just because y was UV and we + + + align:start position:0% +V this V is just because y was UV and we +take a partial in the U Direction okay + + align:start position:0% +take a partial in the U Direction okay + + + align:start position:0% +take a partial in the U Direction okay +so so in fact this is uh so Al together + + align:start position:0% +so so in fact this is uh so Al together + + + align:start position:0% +so so in fact this is uh so Al together +this is 4 uxx + 2 uh + + align:start position:0% +this is 4 uxx + 2 uh + + + align:start position:0% +this is 4 uxx + 2 uh +VY and uh and and that's our partial + + align:start position:0% +VY and uh and and that's our partial + + + align:start position:0% +VY and uh and and that's our partial +derivative so notice that you know U is + + align:start position:0% +derivative so notice that you know U is + + + align:start position:0% +derivative so notice that you know U is +excuse me X is a function of u and v so + + align:start position:0% +excuse me X is a function of u and v so + + + align:start position:0% +excuse me X is a function of u and v so +I could if I really wanted to I could + + align:start position:0% +I could if I really wanted to I could + + + align:start position:0% +I could if I really wanted to I could +substitute for X it's formula for u and + + align:start position:0% +substitute for X it's formula for u and + + + align:start position:0% +substitute for X it's formula for u and +v but that's not really necessary this + + align:start position:0% +v but that's not really necessary this + + + align:start position:0% +v but that's not really necessary this +you know what's interesting about these + + align:start position:0% +you know what's interesting about these + + + align:start position:0% +you know what's interesting about these +problems is how the the differentials + + align:start position:0% +problems is how the the differentials + + + align:start position:0% +problems is how the the differentials +depend on one each other on one another + + align:start position:0% +depend on one each other on one another + + + align:start position:0% +depend on one each other on one another +and uh I'm perfectly happy with an + + align:start position:0% +and uh I'm perfectly happy with an + + + align:start position:0% +and uh I'm perfectly happy with an +answer that has mixed variables like + + align:start position:0% +answer that has mixed variables like + + + align:start position:0% +answer that has mixed variables like +this that's fine so now + + align:start position:0% + + + + align:start position:0% + +let's go over here and let's see if we + + align:start position:0% +let's go over here and let's see if we + + + align:start position:0% +let's go over here and let's see if we +can uh get the same answer by uh using + + align:start position:0% +can uh get the same answer by uh using + + + align:start position:0% +can uh get the same answer by uh using +total differentials now I have to say + + align:start position:0% +total differentials now I have to say + + + align:start position:0% +total differentials now I have to say +that the chain rule that we used uh on + + align:start position:0% +that the chain rule that we used uh on + + + align:start position:0% +that the chain rule that we used uh on +the + + align:start position:0% +the + + + align:start position:0% +the +previous uh + + align:start position:0% +previous uh + + + align:start position:0% +previous uh +problem it's it's the quickest way to do + + align:start position:0% +problem it's it's the quickest way to do + + + align:start position:0% +problem it's it's the quickest way to do +these sorts of things um I I I like to + + align:start position:0% +these sorts of things um I I I like to + + + align:start position:0% +these sorts of things um I I I like to +do total differentials if I really want + + align:start position:0% +do total differentials if I really want + + + align:start position:0% +do total differentials if I really want +if I have the some time to actually + + align:start position:0% +if I have the some time to actually + + + align:start position:0% +if I have the some time to actually +explore the problem and get comfortable + + align:start position:0% +explore the problem and get comfortable + + + align:start position:0% +explore the problem and get comfortable +with it I prefer to use total + + align:start position:0% +with it I prefer to use total + + + align:start position:0% +with it I prefer to use total +differentials because I think it's a + + align:start position:0% +differentials because I think it's a + + + align:start position:0% +differentials because I think it's a +little bit clearer somehow this chain + + align:start position:0% +little bit clearer somehow this chain + + + align:start position:0% +little bit clearer somehow this chain +rule it's just uh to me it's just a + + align:start position:0% +rule it's just uh to me it's just a + + + align:start position:0% +rule it's just uh to me it's just a +prescription it's not a it's not an + + align:start position:0% +prescription it's not a it's not an + + + align:start position:0% +prescription it's not a it's not an +explanation so why don't we uh compute + + align:start position:0% +explanation so why don't we uh compute + + + align:start position:0% +explanation so why don't we uh compute +some total differentials so we already + + align:start position:0% +some total differentials so we already + + + align:start position:0% +some total differentials so we already +saw + + align:start position:0% + + + + align:start position:0% + +let me just repeat uh over here we + + align:start position:0% +let me just repeat uh over here we + + + align:start position:0% +let me just repeat uh over here we +already saw that DZ is 2x + + align:start position:0% +already saw that DZ is 2x + + + align:start position:0% +already saw that DZ is 2x +DX plus 2 y + + align:start position:0% +DX plus 2 y + + + align:start position:0% +DX plus 2 y +Dy + + align:start position:0% +Dy + + + align:start position:0% +Dy +okay now now we want to use the fact + + align:start position:0% +okay now now we want to use the fact + + + align:start position:0% +okay now now we want to use the fact +that X is itself a function of u and v + + align:start position:0% +that X is itself a function of u and v + + + align:start position:0% +that X is itself a function of u and v +so that's what we need to do now so that + + align:start position:0% +so that's what we need to do now so that + + + align:start position:0% +so that's what we need to do now so that +tells us that + + align:start position:0% +tells us that + + + align:start position:0% +tells us that +DX is uh so 2 + + align:start position:0% +DX is uh so 2 + + + align:start position:0% +DX is uh so 2 +U du minus 2v DV in the same way and + + align:start position:0% +U du minus 2v DV in the same way and + + + align:start position:0% +U du minus 2v DV in the same way and +Dy so remember y was UV so taking D of + + align:start position:0% +Dy so remember y was UV so taking D of + + + align:start position:0% +Dy so remember y was UV so taking D of +UV we get V + + align:start position:0% +UV we get V + + + align:start position:0% +UV we get V +duu plus u + + align:start position:0% +duu plus u + + + align:start position:0% +duu plus u +DV okay so now so what we've done is + + align:start position:0% +DV okay so now so what we've done is + + + align:start position:0% +DV okay so now so what we've done is +we've just listed out all the partial uh + + align:start position:0% +we've just listed out all the partial uh + + + align:start position:0% +we've just listed out all the partial uh +different excuse me all of the total + + align:start position:0% +different excuse me all of the total + + + align:start position:0% +different excuse me all of the total +differentials and uh the nice thing + + align:start position:0% +differentials and uh the nice thing + + + align:start position:0% +differentials and uh the nice thing +about this is once you've done these + + align:start position:0% +about this is once you've done these + + + align:start position:0% +about this is once you've done these +computations now it's just just uh it's + + align:start position:0% +computations now it's just just uh it's + + + align:start position:0% +computations now it's just just uh it's +just substitution so what we really want + + align:start position:0% +just substitution so what we really want + + + align:start position:0% +just substitution so what we really want +to know is we want to know how does Z + + align:start position:0% +to know is we want to know how does Z + + + align:start position:0% +to know is we want to know how does Z +depend on u and v and so all we need to + + align:start position:0% +depend on u and v and so all we need to + + + align:start position:0% +depend on u and v and so all we need to +do is uh substitute in our formulas for + + align:start position:0% +do is uh substitute in our formulas for + + + align:start position:0% +do is uh substitute in our formulas for +DX here so this tells us that + + align:start position:0% +DX here so this tells us that + + + align:start position:0% +DX here so this tells us that +DZ is okay so we have + + align:start position:0% +DZ is okay so we have + + + align:start position:0% +DZ is okay so we have +2X now instead of DX we just uh plug in + + align:start position:0% +2X now instead of DX we just uh plug in + + + align:start position:0% +2X now instead of DX we just uh plug in +here so we have 2 U du minus 2 V DV + + align:start position:0% +here so we have 2 U du minus 2 V DV + + + align:start position:0% +here so we have 2 U du minus 2 V DV +uh so that was this term and now we have + + align:start position:0% +uh so that was this term and now we have + + + align:start position:0% +uh so that was this term and now we have +plus 2 + + align:start position:0% +plus 2 + + + align:start position:0% +plus 2 +Y and uh now we have we just plug in + + align:start position:0% +Y and uh now we have we just plug in + + + align:start position:0% +Y and uh now we have we just plug in +this so + + align:start position:0% + + + + align:start position:0% + +VD plus udv you see it's just + + align:start position:0% +VD plus udv you see it's just + + + align:start position:0% +VD plus udv you see it's just +substitution so then uh now we just + + align:start position:0% +substitution so then uh now we just + + + align:start position:0% +substitution so then uh now we just +expand everything out using um just just + + align:start position:0% +expand everything out using um just just + + + align:start position:0% +expand everything out using um just just +uh expanding these out and so we get + + align:start position:0% +uh expanding these out and so we get + + + align:start position:0% +uh expanding these out and so we get +okay so let's collect all the things + + align:start position:0% +okay so let's collect all the things + + + align:start position:0% +okay so let's collect all the things +involv in Du so if we collect all the + + align:start position:0% +involv in Du so if we collect all the + + + align:start position:0% +involv in Du so if we collect all the +things involving du we have + + align:start position:0% +things involving du we have + + + align:start position:0% +things involving du we have +4 2 * 2 * x * U 4X + + align:start position:0% +4 2 * 2 * x * U 4X + + + align:start position:0% +4 2 * 2 * x * U 4X +U plus 2 y + + align:start position:0% + + + + align:start position:0% + +v this whole quantity times + + align:start position:0% +v this whole quantity times + + + align:start position:0% +v this whole quantity times +du and then if we collect the terms in + + align:start position:0% +du and then if we collect the terms in + + + align:start position:0% +du and then if we collect the terms in +DV we have uh so we have 2 + + align:start position:0% + + + + align:start position:0% + +Yu + + align:start position:0% +Yu + + + align:start position:0% +Yu +so that's uh coming from here and then + + align:start position:0% +so that's uh coming from here and then + + + align:start position:0% +so that's uh coming from here and then +we have a minus + + align:start position:0% + + + + align:start position:0% + +4xv okay and now what that tells us is + + align:start position:0% +4xv okay and now what that tells us is + + + align:start position:0% +4xv okay and now what that tells us is +that uh so so let's just remember that + + align:start position:0% +that uh so so let's just remember that + + + align:start position:0% +that uh so so let's just remember that +uh the the the one definition of the of + + align:start position:0% +uh the the the one definition of the of + + + align:start position:0% +uh the the the one definition of the of +the partial derivative partial Z partial + + align:start position:0% +the partial derivative partial Z partial + + + align:start position:0% +the partial derivative partial Z partial +U is this coefficient so if we write so + + align:start position:0% +U is this coefficient so if we write so + + + align:start position:0% +U is this coefficient so if we write so +if I go over here if we write uh the + + align:start position:0% +if I go over here if we write uh the + + + align:start position:0% +if I go over here if we write uh the +total differential DZ we can write that + + align:start position:0% +total differential DZ we can write that + + + align:start position:0% +total differential DZ we can write that +as uh partial Z partial U + + align:start position:0% +as uh partial Z partial U + + + align:start position:0% +as uh partial Z partial U +du plus uh partial Z partial V + + align:start position:0% +du plus uh partial Z partial V + + + align:start position:0% +du plus uh partial Z partial V +DV right so well look what we have here + + align:start position:0% +DV right so well look what we have here + + + align:start position:0% +DV right so well look what we have here +on these two sides is this is uh is + + align:start position:0% +on these two sides is this is uh is + + + align:start position:0% +on these two sides is this is uh is +essentially the same expression so that + + align:start position:0% +essentially the same expression so that + + + align:start position:0% +essentially the same expression so that +means if we want to compute partial Z + + align:start position:0% +means if we want to compute partial Z + + + align:start position:0% +means if we want to compute partial Z +partial U + + align:start position:0% +partial U + + + align:start position:0% +partial U +then that's just equal to this + + align:start position:0% +then that's just equal to this + + + align:start position:0% +then that's just equal to this +coefficient + + align:start position:0% +coefficient + + + align:start position:0% +coefficient +here so we get that partial Z partial U + + align:start position:0% +here so we get that partial Z partial U + + + align:start position:0% +here so we get that partial Z partial U +is + + align:start position:0% +is + + + align:start position:0% +is +4xu plus uh two that should be V one of + + align:start position:0% +4xu plus uh two that should be V one of + + + align:start position:0% +4xu plus uh two that should be V one of +those is an x uh let's see so what where + + align:start position:0% +those is an x uh let's see so what where + + + align:start position:0% +those is an x uh let's see so what where +did this come from yeah one of those is + + align:start position:0% +did this come from yeah one of those is + + + align:start position:0% +did this come from yeah one of those is +an X sorry Y is a + + align:start position:0% +an X sorry Y is a + + + align:start position:0% +an X sorry Y is a +y 2 VY okay now uh you know just as a as + + align:start position:0% +y 2 VY okay now uh you know just as a as + + + align:start position:0% +y 2 VY okay now uh you know just as a as +a sanity check why don't we go back to + + align:start position:0% +a sanity check why don't we go back to + + + align:start position:0% +a sanity check why don't we go back to +to the middle of the board and uh we'll + + align:start position:0% +to the middle of the board and uh we'll + + + align:start position:0% +to the middle of the board and uh we'll +see that we got the same thing so 4xu + + + align:start position:0% +see that we got the same thing so 4xu + + + + align:start position:0% +see that we got the same thing so 4xu + +2 VY that's what we concluded for + + align:start position:0% +2 VY that's what we concluded for + + + align:start position:0% +2 VY that's what we concluded for +partial Z partial U and then going back + + align:start position:0% +partial Z partial U and then going back + + + align:start position:0% +partial Z partial U and then going back +to the middle of the board uh that's + + align:start position:0% +to the middle of the board uh that's + + + align:start position:0% +to the middle of the board uh that's +what we found + + align:start position:0% +what we found + + + align:start position:0% +what we found +again so uh let's just go over the two + + align:start position:0% +again so uh let's just go over the two + + + align:start position:0% +again so uh let's just go over the two +different methods and uh and compare + + align:start position:0% +different methods and uh and compare + + + align:start position:0% +different methods and uh and compare +them so if if I'm if I'm in a rush to do + + align:start position:0% +them so if if I'm if I'm in a rush to do + + + align:start position:0% +them so if if I'm if I'm in a rush to do +a computation uh maybe I'm taking an + + align:start position:0% +a computation uh maybe I'm taking an + + + align:start position:0% +a computation uh maybe I'm taking an +exam uh I definitely think it's it's the + + align:start position:0% +exam uh I definitely think it's it's the + + + align:start position:0% +exam uh I definitely think it's it's the +quickest to just compute uh to figure + + align:start position:0% +quickest to just compute uh to figure + + + align:start position:0% +quickest to just compute uh to figure +out what the dependenc of the variables + + align:start position:0% +out what the dependenc of the variables + + + align:start position:0% +out what the dependenc of the variables +is and I use this dependency graph and + + align:start position:0% +is and I use this dependency graph and + + + align:start position:0% +is and I use this dependency graph and +then I just Trace all the paths from Z + + align:start position:0% +then I just Trace all the paths from Z + + + align:start position:0% +then I just Trace all the paths from Z +to the uh independent variable U that + + align:start position:0% +to the uh independent variable U that + + + align:start position:0% +to the uh independent variable U that +I'm interested in and uh and then uh + + align:start position:0% +I'm interested in and uh and then uh + + + align:start position:0% +I'm interested in and uh and then uh +this and I multiply all of the partial + + align:start position:0% +this and I multiply all of the partial + + + align:start position:0% +this and I multiply all of the partial +derivatives that correspond to each Edge + + align:start position:0% +derivatives that correspond to each Edge + + + align:start position:0% +derivatives that correspond to each Edge +and I get uh I get an expression now if + + align:start position:0% +and I get uh I get an expression now if + + + align:start position:0% +and I get uh I get an expression now if +I have more time uh then I I really + + align:start position:0% +I have more time uh then I I really + + + align:start position:0% +I have more time uh then I I really +prefer to use the method of total + + align:start position:0% +prefer to use the method of total + + + align:start position:0% +prefer to use the method of total +differentials that we did on the third + + align:start position:0% +differentials that we did on the third + + + align:start position:0% +differentials that we did on the third +board um I like it because uh once do + + align:start position:0% +board um I like it because uh once do + + + align:start position:0% +board um I like it because uh once do +some simple calculus and then after that + + align:start position:0% +some simple calculus and then after that + + + align:start position:0% +some simple calculus and then after that +it's just it's basic algebra so um it it + + align:start position:0% +it's just it's basic algebra so um it it + + + align:start position:0% +it's just it's basic algebra so um it it +it's + + align:start position:0% +it's + + + align:start position:0% +it's +uh I I find that I'm less likely to make + + align:start position:0% +uh I I find that I'm less likely to make + + + align:start position:0% +uh I I find that I'm less likely to make +a mistake doing that method um but as + + align:start position:0% +a mistake doing that method um but as + + + align:start position:0% +a mistake doing that method um but as +you saw it involves Computing a lot more + + align:start position:0% +you saw it involves Computing a lot more + + + align:start position:0% +you saw it involves Computing a lot more +derivatives that we didn't actually use + + align:start position:0% +derivatives that we didn't actually use + + + align:start position:0% +derivatives that we didn't actually use +in the final answer for instance when we + + align:start position:0% +in the final answer for instance when we + + + align:start position:0% +in the final answer for instance when we +computed the partial uh when we computed + + align:start position:0% +computed the partial uh when we computed + + + align:start position:0% +computed the partial uh when we computed +total differentials we got an expression + + align:start position:0% +total differentials we got an expression + + + align:start position:0% +total differentials we got an expression +for partial Z partial V at the end of + + align:start position:0% +for partial Z partial V at the end of + + + align:start position:0% +for partial Z partial V at the end of +the day even though we weren't asked to + + align:start position:0% +the day even though we weren't asked to + + + align:start position:0% +the day even though we weren't asked to +do that so it it um it it's it's + + align:start position:0% +do that so it it um it it's it's + + + align:start position:0% +do that so it it um it it's it's +lengthier but I think more conceptually + + align:start position:0% +lengthier but I think more conceptually + + + align:start position:0% +lengthier but I think more conceptually +straightforward so I think I'll leave it + + align:start position:0% +straightforward so I think I'll leave it + + + align:start position:0% +straightforward so I think I'll leave it +at that \ No newline at end of file diff --git a/3HIV4MnLGCw.txt b/3HIV4MnLGCw.txt new file mode 100644 index 0000000000000000000000000000000000000000..e9a158c7535ba10584d544e485ea22e2b0e8ce7b --- /dev/null +++ b/3HIV4MnLGCw.txt @@ -0,0 +1,253 @@ +In this chapter our goal is to introduce some +metrics for measuring the performance of a + +circuit and then investigate ways to improve +that performance. + +We'll start by putting aside circuits for +a moment and look at an everyday example that + +will help us understand the proposed performance +metrics. + +Laundry is a processing task we all have to +face at some point! + +The input to our laundry "system" is some +number of loads of dirty laundry and the output + +is the same loads, but washed, dried, and +folded. + +There two system components: a washer that +washes a load of laundry in 30 minutes, and + +a dryer that dries a load in 60 minutes. + +You may be used to laundry system components +with different propagation delays, but let's + +go with these delays for our example. + +Our laundry follows a simple path through +the system: + +each load is first washed in the washer and +afterwards moved to the dryer for drying. + +There can, of course, be delays between the +steps of loading the washer, or moving wet, + +washed loads to the dryer, or in taking dried +loads out of the dryer. + +Let's assume we move the laundry through the +system as fast as possible, moving loads to + +the next processing step as soon as we can. + +Most of us wait to do laundry until we've +accumulated several loads. + +That turns out to be a good strategy! + +Let's see why… + +To process a single load of laundry, we first +run it through the washer, which takes 30 + +minutes. + +Then we run it through the dryer, which takes +60 minutes. + +So the total amount of time from system input +to system output is 90 minutes. + +If this were a combinational logic circuit, +we'd say the circuit's propagation delay is + +90 minutes from valid inputs to valid outputs. + +Okay, that's the performance analysis for +a single load of laundry. + +Now let's think about doing N loads of laundry. + +Here at MIT we like to make gentle fun of +our colleagues at the prestigious institution + +just up the river from us. + +So here's how we imagine they do N loads of +laundry at Harvard. + +They follow the combinational recipe of supplying +new system inputs after the system generates + +the correct output from the previous set of +inputs. + +So in step 1 the first load is washed and +in step 2, the first load is dried, taking + +a total of 90 minutes. + +Once those steps complete, Harvard students +move on to step 3, starting the processing + +of the second load of laundry. + +And so on… + +The total time for the system to process N +laundry loads is just N times the time it + +takes to process a single load. + +So the total time is N*90 minutes. + +Of course, we're being silly here! + +Harvard students don't actually do laundry. + +Mummy sends the family butler over on Wednesday +mornings to collect the dirty loads and return + +them starched and pressed in time for afternoon +tea. + +But I hope you're seeing the analogy we're +making between the Harvard approach to laundry + +and combinational circuits. + +We can all see that the washer is sitting +idle while the dryer is running and that inefficiency + +has a cost in terms of the rate at which N +load of laundry can move through the system. + +As engineering students here in 6.004, we +see that it makes sense to overlap washing + +and drying. + +So in step 1 we wash the first load. + +And in step 2, we dry the first load as before, +but, in addition, we start washing the second + +load of laundry. + +We have to allocate 60 minutes for step 2 +in order to give the dryer time to finish. + +There's a slight inefficiency in that the +washer finishes its work early, but with only + +one dryer, it's the dryer that determines +how quickly laundry moves through the system. + +Systems that overlap the processing of a sequence +of inputs are called pipelined systems and + +each of the processing steps is called a stage +of the pipeline. + +The rate at which inputs move through the +pipeline is determined by the slowest pipeline + +stage. + +Our laundry system is a 2-stage pipeline with +a 60-minute processing time for each stage. + +We repeat the overlapped wash/dry step until +all N loads of laundry have been processed. + +We're starting a new washer load every 60 +minutes and getting a new load of dried laundry + +from the dryer every 60 minutes. + +In other words, the effective processing rate +of our overlapped laundry system is one load + +every 60 minutes. + +So once the process is underway N loads of +laundry takes N*60 minutes. + +And a particular load of laundry, which requires +two stages of processing time, takes 120 minutes. + +The timing for the first load of laundry is +a little different since the timing of Step + +1 can be shorter with no dryer to wait for. + +But in the performance analysis of pipelined +systems, we're interested in the steady state + +where we're assuming that we have an infinite +supply of inputs. + +We see that there are two interesting performance +metrics. + +The first is the latency of the system, the +time it takes for the system to process a + +particular input. + +In the Harvard laundry system, it takes 90 +minutes to wash and dry a load. + +In the 6.004 laundry, it takes 120 minutes +to wash and dry a load, assuming that it's + +not the first load. + +The second performance measure is throughput, +the rate at which the system produces outputs. + +In many systems, we get one set of outputs +for each set of inputs, and in such systems, + +the throughput also tells us the rate at inputs +are consumed. + +In the Harvard laundry system, the throughput +is 1 load of laundry every 90 minutes. + +In the 6.004 laundry, the throughput is 1 +load of laundry every 60 minutes. + +The Harvard laundry has lower latency, the +6.004 laundry has better throughput. + +Which is the better system? + +That depends on your goals! + +If you need to wash 100 loads of laundry, +you'd prefer to use the system with higher + +throughput. + +If, on the other hand, you want clean underwear +for your date in 90 minutes, you're much more + +concerned about the latency. + +The laundry example also illustrates a common +tradeoff between latency and throughput. + +If we increase throughput by using pipelined +processing, the latency usually increases + +since all pipeline stages must operate in +lock-step and the rate of processing is thus + +determined by the slowest stage. \ No newline at end of file diff --git a/3WrHSdaC9-A.txt b/3WrHSdaC9-A.txt new file mode 100644 index 0000000000000000000000000000000000000000..f77e294fd4de73bf36dbf2d7fa6a53b7ef89da60 --- /dev/null +++ b/3WrHSdaC9-A.txt @@ -0,0 +1,683 @@ +align:start position:0% + +so so the waiter makes a beautiful + + align:start position:0% +so so the waiter makes a beautiful + + + align:start position:0% +so so the waiter makes a beautiful +thesis that calls the knife is it's huge + + align:start position:0% +thesis that calls the knife is it's huge + + + align:start position:0% +thesis that calls the knife is it's huge +it's six volumes and it's on it's called + + align:start position:0% +it's six volumes and it's on it's called + + + align:start position:0% +it's six volumes and it's on it's called +the add class of evasion creo so it's + + align:start position:0% +the add class of evasion creo so it's + + + align:start position:0% +the add class of evasion creo so it's +online so I'd be happy to share the + + align:start position:0% +online so I'd be happy to share the + + + align:start position:0% +online so I'd be happy to share the +reference with you + + align:start position:0% +reference with you + + + align:start position:0% +reference with you +I mean I shouldn't only it's it has Maps + + align:start position:0% +I mean I shouldn't only it's it has Maps + + + align:start position:0% +I mean I shouldn't only it's it has Maps +because as recordings can actually go + + align:start position:0% +because as recordings can actually go + + + align:start position:0% +because as recordings can actually go +and listen to the various dialects of + + align:start position:0% +and listen to the various dialects of + + + align:start position:0% +and listen to the various dialects of +evasion Creole and what what people have + + align:start position:0% +evasion Creole and what what people have + + + align:start position:0% +evasion Creole and what what people have +found striking is the fact that in terms + + align:start position:0% +found striking is the fact that in terms + + + align:start position:0% +found striking is the fact that in terms +of variation it's quite restricted so + + align:start position:0% +of variation it's quite restricted so + + + align:start position:0% +of variation it's quite restricted so +anyway you are in hate you can speak to + + align:start position:0% +anyway you are in hate you can speak to + + + align:start position:0% +anyway you are in hate you can speak to +someone who speaks Creole you speak + + align:start position:0% +someone who speaks Creole you speak + + + align:start position:0% +someone who speaks Creole you speak +Creole so there'll be some words that + + align:start position:0% +Creole so there'll be some words that + + + align:start position:0% +Creole so there'll be some words that +are kind of Shibboleth of certain + + align:start position:0% +are kind of Shibboleth of certain + + + align:start position:0% +are kind of Shibboleth of certain +regions but overall there is no issue + + align:start position:0% +regions but overall there is no issue + + + align:start position:0% +regions but overall there is no issue +with mutual understanding you know + + align:start position:0% +with mutual understanding you know + + + align:start position:0% +with mutual understanding you know +Asians understand each other when they + + align:start position:0% +Asians understand each other when they + + + align:start position:0% +Asians understand each other when they +speak Creole even though at first I + + align:start position:0% +speak Creole even though at first I + + + align:start position:0% +speak Creole even though at first I +might be a bit of a station if you come + + align:start position:0% +might be a bit of a station if you come + + + align:start position:0% +might be a bit of a station if you come +from different regions and in that atlas + + align:start position:0% +from different regions and in that atlas + + + align:start position:0% +from different regions and in that atlas +actually taught me that very well that + + align:start position:0% +actually taught me that very well that + + + align:start position:0% +actually taught me that very well that +you have lots of lexical idiosyncrasies + + align:start position:0% +you have lots of lexical idiosyncrasies + + + align:start position:0% +you have lots of lexical idiosyncrasies +across regions but but the grammar + + align:start position:0% +across regions but but the grammar + + + align:start position:0% +across regions but but the grammar +itself is pretty much similar which one + + align:start position:0% +itself is pretty much similar which one + + + align:start position:0% +itself is pretty much similar which one +might say is surprising even that she + + align:start position:0% +might say is surprising even that she + + + align:start position:0% +might say is surprising even that she +had all these influx of Africans from + + align:start position:0% +had all these influx of Africans from + + + align:start position:0% +had all these influx of Africans from +various language groups right will + + align:start position:0% +various language groups right will + + + align:start position:0% +various language groups right will +expect more variation but but I was so + + align:start position:0% +expect more variation but but I was so + + + align:start position:0% +expect more variation but but I was so +lucky that the fact that you look at the + + align:start position:0% +lucky that the fact that you look at the + + + align:start position:0% +lucky that the fact that you look at the +hits of Haiti the country was for for a + + align:start position:0% +hits of Haiti the country was for for a + + + align:start position:0% +hits of Haiti the country was for for a +long time pretty isolated + + align:start position:0% +long time pretty isolated + + + align:start position:0% +long time pretty isolated +right after independence it's like + + align:start position:0% +right after independence it's like + + + align:start position:0% +right after independence it's like +that's something that we can talk about + + align:start position:0% +that's something that we can talk about + + + align:start position:0% +that's something that we can talk about +later the the European forces and the + + align:start position:0% +later the the European forces and the + + + align:start position:0% +later the the European forces and the +American forces even though Haiti helped + + align:start position:0% +American forces even though Haiti helped + + + align:start position:0% +American forces even though Haiti helped +the u.s. in terms of its independence + + align:start position:0% +the u.s. in terms of its independence + + + align:start position:0% +the u.s. in terms of its independence +getting more territory like I don't know + + align:start position:0% +getting more territory like I don't know + + + align:start position:0% +getting more territory like I don't know +you've heard about the region approaches + + align:start position:0% +you've heard about the region approaches + + + align:start position:0% +you've heard about the region approaches +which was create calls because of + + align:start position:0% +which was create calls because of + + + align:start position:0% +which was create calls because of +Napoleon losing 80 because of the + + align:start position:0% +Napoleon losing 80 because of the + + + align:start position:0% +Napoleon losing 80 because of the +involution but yet the u.s. quarantine + + align:start position:0% +involution but yet the u.s. quarantine + + + align:start position:0% +involution but yet the u.s. quarantine +Haiti very quickly why because it was an + + align:start position:0% +Haiti very quickly why because it was an + + + align:start position:0% +Haiti very quickly why because it was an +example of of black liberty which was a + + align:start position:0% +example of of black liberty which was a + + + align:start position:0% +example of of black liberty which was a +threat to the world order back back then + + align:start position:0% +threat to the world order back back then + + + align:start position:0% +threat to the world order back back then +so he was was unthinkable and + + align:start position:0% +so he was was unthinkable and + + + align:start position:0% +so he was was unthinkable and +unacceptable so it had to be embargoed + + align:start position:0% +unacceptable so it had to be embargoed + + + align:start position:0% +unacceptable so it had to be embargoed +and that embargo + + align:start position:0% +and that embargo + + + align:start position:0% +and that embargo +people have argued is what actually + + align:start position:0% +people have argued is what actually + + + align:start position:0% +people have argued is what actually +created this isolation that in turn gave + + align:start position:0% +created this isolation that in turn gave + + + align:start position:0% +created this isolation that in turn gave +fish and Creole it's pretty much its + + align:start position:0% +fish and Creole it's pretty much its + + + align:start position:0% +fish and Creole it's pretty much its +uniformity because it was little traffic + + align:start position:0% +uniformity because it was little traffic + + + align:start position:0% +uniformity because it was little traffic +from outside to heat if + + align:start position:0% +from outside to heat if + + + align:start position:0% +from outside to heat if +long time he was pretty much self + + align:start position:0% +long time he was pretty much self + + + align:start position:0% +long time he was pretty much self +contained and that helped the language + + align:start position:0% +contained and that helped the language + + + align:start position:0% +contained and that helped the language +jail as if you know pretty uniform + + align:start position:0% +jail as if you know pretty uniform + + + align:start position:0% +jail as if you know pretty uniform +system well over time the date I thought + + align:start position:0% +system well over time the date I thought + + + align:start position:0% +system well over time the date I thought +so it will have enough data to document + + align:start position:0% +so it will have enough data to document + + + align:start position:0% +so it will have enough data to document +that weather over time there was more or + + align:start position:0% +that weather over time there was more or + + + align:start position:0% +that weather over time there was more or +less variation because what we have is + + align:start position:0% +less variation because what we have is + + + align:start position:0% +less variation because what we have is +purified fragmentary we will have lots + + align:start position:0% +purified fragmentary we will have lots + + + align:start position:0% +purified fragmentary we will have lots +of evidence about you know say + + align:start position:0% +of evidence about you know say + + + align:start position:0% +of evidence about you know say +eighteenth-century + + align:start position:0% +eighteenth-century + + + align:start position:0% +eighteenth-century +Asian Creole we have some archival data + + align:start position:0% +Asian Creole we have some archival data + + + align:start position:0% +Asian Creole we have some archival data +but not enough to be able to compare + + align:start position:0% +but not enough to be able to compare + + + align:start position:0% +but not enough to be able to compare +what happened in different regions of + + align:start position:0% +what happened in different regions of + + + align:start position:0% +what happened in different regions of +the country but what we do have say + + align:start position:0% +the country but what we do have say + + + align:start position:0% +the country but what we do have say +going to do 17 eighteenth-century + + align:start position:0% +going to do 17 eighteenth-century + + + align:start position:0% +going to do 17 eighteenth-century +no strikers has pretty similar you know + + align:start position:0% +no strikers has pretty similar you know + + + align:start position:0% +no strikers has pretty similar you know +to the to the Haitian spoken now so they + + align:start position:0% +to the to the Haitian spoken now so they + + + align:start position:0% +to the to the Haitian spoken now so they +were French scholars were writing down + + align:start position:0% +were French scholars were writing down + + + align:start position:0% +were French scholars were writing down +what they would hear they were writing + + align:start position:0% +what they would hear they were writing + + + align:start position:0% +what they would hear they were writing +down you know varieties of Haitian + + align:start position:0% +down you know varieties of Haitian + + + align:start position:0% +down you know varieties of Haitian +Creole from the H 19th century and I can + + align:start position:0% +Creole from the H 19th century and I can + + + align:start position:0% +Creole from the H 19th century and I can +still read those texts no of course you + + align:start position:0% +still read those texts no of course you + + + align:start position:0% +still read those texts no of course you +are written with French orthography and + + align:start position:0% +are written with French orthography and + + + align:start position:0% +are written with French orthography and +maybe that's a that's another confound + + align:start position:0% +maybe that's a that's another confound + + + align:start position:0% +maybe that's a that's another confound +you know they were probably imposing + + align:start position:0% +you know they were probably imposing + + + align:start position:0% +you know they were probably imposing +their French onto onto the Creole that + + align:start position:0% +their French onto onto the Creole that + + + align:start position:0% +their French onto onto the Creole that +were transcribing but if you read that + + align:start position:0% +were transcribing but if you read that + + + align:start position:0% +were transcribing but if you read that +Creole back then the structures were + + align:start position:0% +Creole back then the structures were + + + align:start position:0% +Creole back then the structures were +pretty similar to the Creole of today + + align:start position:0% +pretty similar to the Creole of today + + + align:start position:0% +pretty similar to the Creole of today +which also is fracking as compared to + + align:start position:0% +which also is fracking as compared to + + + align:start position:0% +which also is fracking as compared to +English which which has evolved much + + align:start position:0% +English which which has evolved much + + + align:start position:0% +English which which has evolved much +faster \ No newline at end of file diff --git a/42TnAE67iaE.txt b/42TnAE67iaE.txt new file mode 100644 index 0000000000000000000000000000000000000000..6c5225c1628595ae66d5732022b97439a124a744 --- /dev/null +++ b/42TnAE67iaE.txt @@ -0,0 +1,4599 @@ +NARRATOR: The following content +is provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high-quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: All right. + +You guys ready for +some more games? + +Today, we will finish off +two-player games in particular. + +So last time, we were in this +world of two-player games + +with a polynomial-bounded +number of moves. + +We proved that Othello +reversi is PSPACE complete. + +All these games live in PSPACE. + +And we ended with constraint +logic in the two-player case. + +We proved that's +PSPACE complete. + +I'll just show you +that again in a moment. + +And then, in the +rest of today, we'll + +talk about various other games +that don't fit in this table, + +but in particular two-player +and unbounded number of moves. + +So exponential number of +moves, where you get x time + +completeness for +constraint logic + +and for various practical games +like checkers, chess, and go. + +But I won't prove all of this. + +So this is bounded to +player constraint logic. + +Remember, we could +simulate these formulas, + +where here the setup was you +can only flip each edge once. + +And in particular, +players could take + +turns deciding whether +to-- white player + +can set variables to true +by flipping these edges. + +Black player can set variables +false by flipping those edges. + +Then, if the formula +satisfied, white wins. + +And that was hard and in +particular constraint logic + +could simulate that problem. + +So what I want to show you +next is three real-life games + +that can be reduced from bounded +to player constraint logic. + +And for those, we'll need +two additional facts. + +One is that planar-bounded +two-player constraint + +logic is PSPACE complete +with this crossover gadget. + +We just need the addition +of a choice variable + +with three red edges, +two in, one out. + +This is what we will need. + +And also that we can +make protected ORs, + +an OR where you're guaranteed +at most one of these + +comes in by allowing an +additional gadget which + +is a free edge. + +So only one of our +constructions will use this. + +But in that setting, +we can make a free edge + +and we need the protected OR. + +So they go together well . + +And so this is review +from last class. + +So first real game +we're going to look at + +is called Amazons +from the late '80s + +but became popular in the +common material game theory + +world I think in the +mid-2000s, at least that's + +when I heard about it. + +So the usual game is played +on an 8x8 checkerboard-- + +chessboard, I should say-- +with four black queens and four + +white queens. + +Those are the Amazons. + +The Amazons, as you may +know, carry bows and arrows. + +So a move in this game is to +take a queen of your color, + +move it in a queen-like way. + +So in this example, we're moving +the clean up to this position. + +And then, you fire an arrow by +another queen move from there. + +So from here, we're +shooting an arrow + +to this position +diagonally visible. + +You're not allowed to +move through other players + +or through arrows. + +And you're not allowed to +shoot through other players + +or through arrows. + +So this the square +is destroyed forever. + +So this is clearly +a bounded game. + +Every move we destroy square. + +You have to do both +of those things, + +move between by +a non-zero amount + +and then shoot an arrow +somewhere other than yourself. + +You're never allowed to +land on a dead square. + +So a typical game. + +After you play it for a +while, it's really fun. + +You should try it. + +We'll end up the situation where +you've partitioned the queens + +into independent components. + +And so then, it's basically +a bunch of Hamiltonian cycle + +problems, or longest path. + +Now, these guys +have to walk around. + +It's a little bit weird, because +you can shoot not exactly where + +you're landing. + +But in particular, you could +shoot where you just came from. + +So if each of these +components-- usually they're + +Hamiltonian or have +a Hamiltonian path-- + +and then with the queen moves. + +And then, you just +sum up the areas then, + +and whether white or black +has more area is the winner. + +Because in general, once you +can't move, you lose the game. + +The goal is to move last. + +So in general, your goal is +to partition up the space + +so you have more territory. + +So we're going to prove PSPACE +completeness of this game using + +bounded two-player +constraint logic. + +So here's the basic gadgets, in +particular the idea of a wire. + +We're imagining this is an +upward traveling signal. + +And for it to travel +up-- think of this + +as an edge reversing +from downward + +pointing to upward pointing. + +If the A queen has to move +down and also shoot down, + +so leaving two black squares, +in that situation B can + +move down and shoot down one or +move down two and shoot up one, + +either way consume +these two squares + +but leave two for the next guy. + +This is a parity shift. + +It also works if this guy +moves down, shoots down, + +leaving these two squares. + +Then, B can move down and +shoot diagonally and so on. + +So that's our wire. + +That's how we're +going to propagate + +the signal, because we only +need single-use gadgets you + +can do a turn, A moves +down, shoots down. + +B moves down, shoots down. + +C moves over, shoots diagonally. + +D moves over, shoots +diagonally, and so on. + +Variable gadget, +so this is what we + +had on the bottom +of the construction. + +This is a white or black edge. + +And we'll never have to connect +black edges to anything, + +so they're just hanging out. + +Here, if black moves first +here and obliterates these two + +squares, this wire's dead. + +If white moves first then, the +white can activate the chain. + +So that's going to simulate +the usual setup, where + +white and black are taking +turns, setting their variables + +the way they want them. + +And then, if white can succeed +and satisfy the formula-- + +we have to get to +AND and OR gadgets. + +But if white can succeed +and this guy can move down, + +then B can move to this place +and shoot here, and then + +move over here and shoot +into this giant room. + +And then, we'll spend +tons of moves in here. + +And then, come back here, +shoot there, back there, + +shoot there, ther, shoot there, +and get to the other room + +But if this guy does +not move down first, + +this guy-- whichever +way he goes-- he'll + +have to either destroy +the room he is walking to + +or destroy the other room +that he could have gone. + +So you only get +half of the points + +if this is not activated. + +And we're going to set +it up so that black + +has a bunch of other moves and +some other room that's already + +been cut off. + +And it will be roughly +equal to one of these rooms. + +And so only if you get +both of them do you win. + +And because we can't +control which way B goes, + +these two rooms have +to be the same size. + +So you happen to win by a factor +of 2 and the number of moves. + +But that's not essential to +the proof, just for symmetry. + +So those are the basic gadgets. + +Now, we have AND and OR +and SPLIT and CHOICE. + +Usually, in NCL, we +think of AND and SPLIT + +as being the same thing. + +But in this setting, especially +in the bounded situation, + +they're really different. + +Remember, it corresponds +to whether initially + +the red things are pointing in +or the blue things are pointing + +in, red edges or the blue edge. + +And they behave quite +differently in this setting. + +So for the AND gate, +these are the two inputs. + +If both of them move out of +the way, then C can move here, + +shoot here. + +And D can move here +and shoot there. + +And if you only +move one of the two, + +you won't have enough room. + +AUDIENCE: Wait. + +Why? + +PROFESSOR: Why? + +If B moves out of the way, +C can move and shoot here. + +But D only has one one square. + +If A moves out if the +way, C can't move. + +On the other hand, an OR +gadget, these are the two inputs + +and this is the output. + +If either one of these +moves, we sort of already + +have one square. + +We just need a second +square for C to shoot into. + +It could be here or here. + +As long as one of them moves +out of the way, we are happy. + +As a CHOICE gadget, so this +is three blues coming in + +but the orientations +are different. + +So a CHOICE is we have an input +coming up from the bottom. + +And we want to activate one +of the two but only one. + +So that corresponds +to A moving out + +of the way leaving two squares. + +Either B can take it and hit +those two squares or C can + +take it, but only one of them. + +So the same gadget does both. + +That makes sense +because we're not + +really distinguishing between +red and blue very much here. + +SPLIT is a little bit trickier. + +Let's walk through it. + +A moves down. + +B moves over and shoots here. + +Then, C can move down +here and shoot here. + +And then, D can move over +here and shoot there. + +Using our queen +moves, so that leaves + +these four spaces unoccupied. + +Now, E can move down +here and shoot there. + +F can move here and shoot there. + +And now, we've got +the four squares + +necessary to trigger +both H and G. + +So that's a SPLIT. + +And that is Amazons. + +Therefore Amazons +is PSPACE complete. + +Done. + +Question. + +AUDIENCE: What is +CHOICE needed for? + +PROFESSOR: CHOICE is needed +for the crossover gadget + +in particular. + +Next game we'll look +at-- these proofs + +are going to start +to look similar. + +But I think it's helpful +to see a few examples. + +This is Konane. + +It's a very old game-- we +don't know how old-- invented + +by Hawaiian Polynesians. + +First documented in +1778 by Captain Cook. + +And this was a +world championship. + +No. + +This is a regional +championship in 2005 + +that I probably lost at. + +But we like to play +it with go stones. + +That's not the +original formulation. + +But you have two colors of +stones on a square grid. + +And it's something like peg +solitaire, but with two colors. + +So let me maybe show +you a bigger image. + +The type of move you +can do, if you're + +white you can jump over a +sequence of black stones. + +You can only jump +over one at a time. + +So if I had two in a row, you +wouldn't be able to jump it. + +And furthermore, you're not +allowed to change directions + +in a single move. + +In a single move, +I could jump over + +any chain of black blank +blank blank things. + +And they are removed. + +I captured them. + +And it has to be +in a straight line. + +So that's the rules. + +And of course, every move +I make I capture somebody, + +so it's a polynomial-bounded +number of moves. + +This is the general +idea for a wire + +is that with white will be +doing most of the action here. + +And so white will +be jumping here. + +At this point, I have +to change directions. + +But luckily after I +obliterate those two pieces, + +black can't do anything to me. + +I'm safe between these +two black squares. + +So black will do something +else, and then white + +is free to start jumping in +the direction they want to. + +That will be critical. + +Here is a variable +where if black moves + +first in this scenario, it +can capture the white thing + +and prevent it from +activating this wire. + +If white moves first, they +can activate the wire. + +So whoever goes there +first sets the variable. + +AUDIENCE: What's the start +configuration for this game? + +PROFESSOR: Oh, in +the original game, + +the whole board is filled +where the color of your pieces + +equal the color of the +square of the checkerboard, + +except for the center +two places are blank. + +But we're not considering +it from the actual initial + +configuration. + +We're considering it from a +half-played configuration. + +Because the original +configuration, + +the answer is the function +of the board size. + +And that's not +enough information + +to be interesting from +a complexity standpoint. + +Yeah? + +AUDIENCE: Do you +have any problems + +that have significant +hardness results for sort + +of the standard start +but generalized? + +PROFESSOR: No. + +In general, none +of those problems + +can be hard in the sense that +we want, because they're sparse. + +They have very few +inputs of a given size, + +so there is no such result. + +Unless you have a +variable initial setup, + +like maybe games where +you-- what do you + +call it-- draft your +deck in the beginning. + +I mean, if you consider that +part of the initial setup, + +then that could be +much more interesting. + +Right. + +Haven't done the +OR and the CHOICE. + +So again if we-- +let's do the OR. + +If we are activating from +here, we can just keep going. + +It'd be bad to stop here, +because then black could + +capture us. + +But we can go straight. + +On the other hand, if we +come from this position, + +we killed those two +guys who were safe + +and then we can go up. + +And a CHOICE gadget would +be coming-- the input + +for a CHOICE would be here. + +So you can jump here and +then you have a choice + +whether to go up or down. + +So again, same gadget +does OR and CHOICE. + +And here's one gadget +that does AND, SPLIT, + +and a SHIFT, which is convenient +for various ways to use it. + +But what if what +it really does is + +there's two traversal +paths, input 1 to output 1 + +and input 2 to output 2. + +And they have to +happen in that order. + +If you try to activate path +2, you have to stop here. + +I mean, I guess you +could jump here and then + +be captured that way. + +If you stop here, you'll +be captured by that guy. + +So that's bad news. + +But if we first do the input +1 traversal-- this is safe-- + +and then go to the output +traversal, this guy's gone. + +And so then we can +do input 2, pause, + +and then go up to output 2. + +So that's what the +gadget does by itself. + +If we ignore what +happens out here, + +then we can think of +this as an AND gate, + +where first this input has +to come in, kill that guy, + +and then go off Neverneverland. + +And then, if the +second input comes in, + +then we activate the output. + +So that would be the +output of the AND gate. + +That's garbage. + +And these are the two inputs. + +Now, there is an issue of +you have to make this one + +trigger before this one. + +But in all these setups, +we have these posits + +where the piece can wait. + +So if we have a turn gadget +right before the input, + +it can just sit there and wait +for the other input to the AND + +to activate. + +And then, this one can go ahead +and activate the second one. + +So we're very +flexible on timing. + +So we can make input 1 go +before input 2 for AND. + +For a SPLIT, we can just have +a white token sitting here + +ready to go in that's +in a safe position. + +And then, once this input +comes in, it gets output there. + +Then, this one can +trigger an output there. + +So we get both of the +outputs for one input. + +And for a SHIFT, we do +both of these things. + +We treat this is garbage. + +And we have a safe +white token here. + +So if this comes in, +then that can go out. + +So we end up shifting by one. + +And that fixes +any parity issues. + +Cool. + +So that's Konane +PSPACE complete. + +AUDIENCE: How do you guarantee +that black doesn't screw you? + +PROFESSOR: By checking +all the cases. + +In general, I mean, +there's a question + +of what black is doing. + +Basically, within +all these gadgets, + +we're preventing black +from doing anything. + +So the main place where we care +about black's motion is here. + +So there's going to be an +initial phase where everyone's + +setting variables. + +We're taking turns. + +And white's going +to set half of them. + +Black's going to +set half of them. + +Their black is screwing you, +but in a controlled fashion. + +After that, there's going +to be a pile of extra moves + +that black can just do. + +And black will always be forced +to do those extra useless + +moves. + +If we happen to satisfy +the final output + +to the overall thing, +then white will + +have a zillion free moves +and then white will win. + +That's the idea. + +But within these +gadgets, as long + +as we don't do +something intelligent + +like going here and then +getting captured by black, + +and therefore destroying +the whole construction. + +Then, white will lose, probably. + +We're always careful to go +to positions that are safe. + +Black cannot jump +us if we're there. + +So by checking all +those cases, you + +can guarantee black +doesn't hurt you. + +I didn't mention what's +black doing when we're not + +allowing it to play at all. + +Cool. + +So that's Konane. + +Next, is a game +called Cross Purposes. + +This is a fairly new +game by Michael Albert + +who's a fun guy in the common +material game theory scene. + +So again we're going +to play with go stones, + +but what you should imagine +is that black stones + +are towers of two blocks. + +And then, you can +push them over. + +So in this case, we took +this tower, pushed it up, + +and so it occupied +those two spots. + +But once it's pushed +over, it's kind of dead. + +So we draw it in white. + +And then, for example, we could +take this tower pop it over + +to the right and get those two. + +Now, to make this a fun +two-player game-- this + +would be a natural +enough solitaire game. + +But to make it a +two-player game, + +we're going to have two players, +one called horizontal, which + +can only do this type of +move, and another player + +called vertical, which can +only do this type of move. + +So what's fun here is that +it's the same black pieces used + +by both players. + +But one of them can +tip them left to right. + +And the other can +tip them up or down. + +But again it's bounded, because +once you top over a tower + +it's dead. + +So this is going to be +PSPACE complete by reduction + +from bounded two-player +constraint logic. + +So some-- question. + +AUDIENCE: What's the +goal of the game? + +PROFESSOR: The goal the +game is to move last. + +If you can't move, you lose. + +And that can be asymmetric. + +Some pieces are only going +to be flippable up or down. + +A lot of games +have that feature. + +It's called normal play, +in fact, it's so common. + +That the last +player to move wins. + +So a wire is going to +look something like this. + +In general, I think vertical +is the player that we're + +rooting for, and +we're trying to decide + +whether vertical can win. + +And we're going to +set up horizontal-- + +unlike the previous game-- +we're going to set up horizontal + +in a position that it never +has any moves except the one + +that you give it right then. + +So the idea is that as +soon as we move A down, + +then horizontal has a +move, namely the playing B. + +And then, we have +a move and so on. + +So that will trigger. + +That better not +stop at any point. + +We always want to set it up so +when we're switching gadgets, + +it's our turn to move, +because the horizontal player + +will never have +another move to make. + +This is what it +looks like after. + +I mean, things are +just filling in + +if you've partially +filled in this thing. + +Here's how we make a variable. + +So here in the initial +phase of the game, + +horizontal will have moves. + +Horizontal could play this, +filling those two squares, + +preventing us from +playing this wire. + +So whoever goes here first +will claim the thing. + +And if it's vertical, then +it triggers the true value. + +We can also terminate +a wire like this. + +This is always good for us. + +We can just trigger it +whenever we want as vertical. + +So we need that for +free edges, which + +we need for the protected OR. + +So to clarify or to fix what I +said before, for the initial n + +moves, horizontal +and vertical are + +going to exchange variables, +take turns picking them. + +At that point onwards, +horizontal has no moves + +except the one +right after-- we're + +forcing horizontal to +always play the way we want. + +So after this is done, then +as soon as you move this, + +then horizontal +has a unique move. + +So it will cooperate. + +Horizontal has to cooperate +with us to fill in wires. + +So here is a protected OR. + +So if we trigger this, then this +triggers, then this triggers, + +then this triggers, then +that triggers, and so on. + +So that's all good. + +The reason it's a +protected OR-- the trouble + +if we activated this twice, so +first we activate through here, + +and then we activate +here, and then here. + +And then, as vertical, +we move B down. + +Now, horizontal has no move. + +So that would be bad +news, if we sort of waste + +a trigger like that. + +And so that's why we +need a protected OR, + +where only at most one of +the two sides will trigger. + +CHOICE gadget is the same, +but rotated 90 degrees. + +And that makes a big difference, +because horizontal and vertical + +are flipped. + +So input is here. + +So if we trigger this, and +then this, and then this, + +and then this. + +Then, as vertical, +we get to choose + +whether this one activates +or this one activates. + +So it's important to +make it the right player. + +And here's the omega gadget +that does AND, SPLIT, and SHIFT. + +If we try to activate +input 2, these topple over. + +This topples down. + +And now, horizontal +gets a choice. + +And horizontal's going +to be mean and push B + +over and prevent this thing +from activating, because it + +wants to prevent you from +doing whatever you're doing. + +Because eventually, you're +going to get to a place + +where you win, where +you have a single move + +and then horizontal +doesn't have a move. + +So that's in horizontal's +interest to block you. + +But if you first did +all of these toppling, + +topple this down, over down, +over down, over down, over. + +Then, in particular, you +put a white token here + +and so B won't be +able to do that. + +So when you activate these +guys, D will have to go over + +and out you go. + +So and then, it's the +same thing either putting + +a free wire in input 2 and/or +ignoring the output from output + +1, we get AND, SPLIT, and SHIFT. + +And I think that's it +for Cross Purposes. + +Question. + +AUDIENCE: I probably +misinterpreted. + +Did you show TURN gadget? + +PROFESSOR: I maybe did +not show a TURN gadget. + +There's a TURN gadget. + +Good. + +I didn't talk about it. + +It works in the obvious way. + +But, yeah, it is +definitely a little tricky + +to make sure you can do it. + +But it works. + +AUDIENCE: Back to the +normal play condition, + +if you use games different +from the [INAUDIBLE] + +version of the rule set? + +PROFESSOR: In +general, those games + +are different when you +can't move then you win. + +But from a PSPACE +completeness perspective, + +it should be the same. + +It's really whether you are +starting the quantifying + +sequence with an +exists or a for all. + +And both end up with +the class PSPACE. + +So there may be a +way to distinguish. + +But at our level of granularity, +we're not distinguishing. + +Yeah. + +AUDIENCE: Do you know +whether it's PSPACE + +complete for arbitrary setups +with only black starting + +tokens? + +PROFESSOR: Oh. + +I see. + +No obstacles. + +AUDIENCE: It's a more +natural starting place, + +than starting with a-- + +PROFESSOR: Yeah. + +That's definitely not known. + +I think it would be cool to +think about only black tokens, + +no initial whites. + +All right. + +So that's all I want +to say about PSPACE. + +I think we're done with PSPACE. + +We first did PSPACE here, +then PSPACE here last class, + +and then PSPACE here. + +So now we're going to move +up to EXPTIME, 2 players, + +unbounded number of moves. + +EXPTIME turns out to +be the right class. + +Oh. + +I lied. + +I have one more PSPACE class, +which I don't have slides for. + +This is a short topic, +but it's a cool one, + +I think something that +deserves more study. + +But at the moment there +are no natural games + +like real-life +games that have been + +shown to fall into this class +or to be complete in this class. + +So this is stochastic games. + +The idea is you're playing +against a random opponent. + +So you have two players, and +one of the players is random. + +So it's hard to identify +with randomness. + +So the other player is you. + +Your goal is to win the game. + +And you know that your player's +just flipping a coin every time + +and playing randomly, +say uniformly + +or some distribution +that's known to you. + +Think of games where you're +rolling dice, or drawing cards, + +or there's some random +aspect to the game. + +How hard are these games? + +Well, what's been studied-- +this is a [INAUDIBLE] paper-- + +is for bounded two-player +stochastic games. + +The answer is PSPACE again. + +So, for example, here's a game, +a formula game, stochastic SAT. + +We want to know is +there a move such + +that for a randomly chosen +move-- I like this notation. + +We have exist and for all. + +Backwards R is a +random quantifier. + +There exists an x3 +such that a random x4, + +so this is uniform random over +0 and 1, the binary choice 01. + +We want the probability-- +this gives a distribution. + +We want the probability of +the formula being satisfied + +being greater than a half. + +I'm guessing you could pump that +up to be with high probability. + +But just deciding +whether you could + +win by probability strictly more +than half, is PSPACE complete. + +So this is cool. + +And to me intuitively +randomness should be weaker + +than an adversarial +player, where + +you replace these with for all. + +But it turns out they behave +roughly the same essentially + +by a probability +amplification argument. + +It's a little too +detailed to go into here. + +And so far, there +are no reductions + +from this to what I +would call natural games. + +There are a few +examples in the paper, + +but none around rolling dice. + +I would love to apply this +to like playing Tetris, + +or in the paper they +mention backgammon + +as a candidate, +something like that, + +where you'd like to +get PSPACE completeness + +in a bounded setting. + +So throwing that out there is an +interesting direction to study, + +but I'll end it there. + +Now, we can go to EXPTIME, +two players, unbounded game, + +adversarial player, +no randomness. + +And we get EXPTIME completeness. + +So we're going to start +out with-- I guess, + +similar to what we do it down +here-- I'm going to start + +with some formula games +which are EXPTIME complete + +and then some graph games +that are EXPTIME complete, + +then constraint logic game +which is EXPTIME complete. + +And along the way will prove +something some hardness. + +There are fewer results here, +in general, I would say. + +In particular, I don't +have a good example + +of using constraint logic +to prove a fun game hard, + +though they probably exist. + +We just haven't +gotten there yet. + +So it's more open problems. + +But there are a lot of cool +base problems out there. + +And this field started by a +paper by Stockmeyer and Chandra + +in 1979. + +And it's been the basis +for pretty much all + +EXPTIME hardness proofs. + +EXPTIME hardness is +really cool, because it + +implies exponential time. + +Any problems EXPTIME hard +cannot be solved faster than + +exponential time. + +Whereas all these +other classes, we + +need to assume P does not equal +NP or P is not equal to PSPACE. + +P we know does +not equal EXPTIME. + +So these games require +exponential time. + +It's kind of fun. + +And I'm pretty sure the first +results in this category + +were these games. + +So it's power of games. + +So in general, we're going +to have some formula, maybe + +a couple formulas. + +But definitely we have +a variable assignment. + +And the state of +the game is going + +to be a variable +assignment and who's + +going to move next, player 1 +or player 2, black or white. + +Again, we'll use that notation. + +And we're going to start +with some variable arbitrary + +variable assignment. + +That's part of the initial state +of the game, the board if you + +will. + +And in general, you can +set variables to 0 or 1 + +as many times as you like. + +That's what distinguishes +this from bounded games. + +And all of these games +are going to be partisan, + +a term we used last +class, so meaning + +we're going to have black +and white variables. + +And I'm going to +cheat a little bit. + +There's going to be +one variable that's + +black and white, but +only in one of the games. + +So we'll get there. + +So black player can only +change the black variables. + +The white player can only +change the white variables, + +except for how I'm +going to cheat. + +So let's start. + +These games are very +creatively named. + +First one's called G1. + +And it's amazing how +consistent the literature + +is about the naming +of these games. + +So in G1, I move my +player is to set all + +the variables of your color. + +So if you're white, you're going +to set all the white variables. + +If black, you're going to +set all black variables. + +And set here means you get to +choose whether it's 0 or 1. + +So you're just going to +completely rewrite all + +of the variables of your color. + +And then, here's the cheat. + +We're also going to have +a single variable that's + +shared between black and white. + +Call it t. + +And it's going to be 0 if +it's a player 2's move, + +1 if it's player 1's move. + +I mean, it doesn't +really matter. + +But I guess 1 and 1 is nice. + +So that's the moves. + +What's the goal of the game? + +You're going to lose the +game if, by making your move, + +you satisfy a common between +the two players 4DNF formula. + +So there's one +formula in the game. + +It's DNF, which is very +simple to think about. + +It's just a bunch of options. + +If this happens, you lose. + +It's an OR with +various conditions. + +So you want to +move in such a way + +that you do not satisfy +that formula every time. + +And in each move, you can +rewrite all your variables. + +But this formula +does involve t, which + +lets you care about +who's turn it was. + +So that's cool, very clean. + +I mean, the players have +a lot of power here. + +This is the first +game proved hard. + +A little tricky to work +with, because in most games + +you can't set all the +variables at once. + +Generally, you're only setting +one variable at a time. + +So all the other +games are going to be + +setting one variable at a time. + +At this point, +we're just defining. + +Then, we'll use these games +to prove some hardness. + +G2, the next game, is +a move was going to be + +set one variable of your color. + +So in particular, if you set the +variable to its original value, + +that's like passing. + +So passing is +allowed in this game. + +Passing is also allowed here. + +You could not change +any of the variables. + +You wouldn't win in that case. + +You only win if your +opponent loses in this setup. + +When the question +is can you win. + +In this case, we're going +to have a win condition. + +In this case, white +and black have + +their own winning formulas. + +They're in 12DNF, still +DNF but a little bigger. + +And if you satisfy your formula +at the end of your turn, + +you win and vice versa. + +And move is just change +one variable at a time. + +So that's a very useful game. + +Next is G3. + +A slight variation +to G3, we're going + +to flip one variable +of your color. + +And then, we're going to lose if +you satisfy your 12DNF formula. + +One thing to keep in mind. + +Losing and winning +are quite different, + +because losing is essentially +negating the formula, which + +turns DNF into DNF. + +So you can think +of this as winning. + +In the CNF condition, +you could think of this + +as losing in a DNF condition. + +But they're not interchangeable. + +So here we flipped +between DNF and DNF. + +But we've also changed +the definition of a move. + +A flip, you're not +allowed to pass. + +You must change a variable +to its opposite value. + +Here, we're allowed +to just pass. + +So we changed the move +definition and the win + +condition. + +That is also hard. + +This is a common one. + +I would say most EXPTIME +hardness proofs use this one. + +G4. + +Move is going to be like this. + +You can set one +variable of your color. + +And here, we're going to +have a common win condition. + +This is nice. + +You win if satisfy a +common 12DNF formula. + +Whoops. + +13DNF. + +We need a little more. + +So every move, +we're both checking + +the same formula in this case. + +And here, the set +happens to win. + +So it's a variation of G2. + +G5 does not exist. + +G6-- there is a G5 in +the paper, but it's + +a generalization of G6. + +So I'll tell you +what is in a second. + +Not important. + +So G6, same thing for the move. + +You set one of your variables +to whatever you want. + +But we're going to make +it asymmetric in the sense + +that-- and this will be very +helpful for constraint logic-- + +player 1 wins-- player 1 is +the one that we care about. + +We're trying to decide whether +they win-- if anyone satisfies + +a particular formula. + +So there's one CNF formula. + +If it's ever satisfied, +player 1 wins. + +If it's never satisfied, +you get a tie. + +And we want to know whether +player 1 can force a win. + +So this is very compatible +with this sort of thing + +we were doing before +with it was the game + +problem from last class, but in +particular the constraint logic + +games. + +So we'll use G6 for +constraint logic. + +G3 is most other proofs. + +So these are all EXPTIME +complete formula games. + +Yeah? + +AUDIENCE: All right. + +I'm a know; little +confused about G1. + +So I can pass by just setting +down any of my variables, + +right? + +PROFESSOR: Yes. + +AUDIENCE: So then, +how could I ever lose? + +Because if-- + +AUDIENCE: You can lose if +the turn variable changed + +satisfies the [INAUDIBLE]. + +AUDIENCE: Oh. + +Yeah. + +[INTERPOSING VOICES] + +AUDIENCE: Sorry. + +PROFESSOR: Well, it changes +every time so, yeah, right. + +I think you could set your +variables in such a way when + +it's the opponents turn, +no matter what they do, + +the formula becomes +satisfied and then they lose. + +Yeah. + +Good. + +AUDIENCE: But then it +became satisfied on my turn. + +Sorry. + +PROFESSOR: But t was +a different value. + +So when it's your turn, you +set t to 0 or set t to 1. + +And so then, maybe the +formula's not satisfied. + +When it's the opponents +turn, even if they pass, + +t is set to 0. + +Yes. t is part of the formula. + +AUDIENCE: Where +does the 12 come up? + +Is that from the previous? + +PROFESSOR: I think it's +from the previous result. + +Yeah. + +Didn't we have an 11 or 12? + +AUDIENCE: It was 12. + +PROFESSOR: Yeah. + +All right. + +In case, you prefer +real games, as I do. + +Here is a physical +instantiation-- + +it could be many of the games. + +The one they chose +to highlight was G4. + +So this is a game called Peek. + +And that name has +been reappropriated + +for many other games, which +we'll talk about in a moment. + +But the idea is you +have a bunch of trays. + +Each tray has a +bunch of holes in it. + +Everybody knows where +all the holes are. + +Each tray has +exactly two positions + +in all the way and +out all the way. + +It's like here. + +And there are white +trays and black trays. + +So G4, white player can take any +of the trays of their variable, + +and if they want to, +toggle its state. + +They can either push it in +or pull it out or leave it + +as it is. + +And then, you're going to +win if, viewed from above, + +there's a hole that sees all +the way down to the ground. + +So you could put +something red here. + +And if you see red at +the top, then you've + +satisfied the DNF formula. + +It's common between the two. + +So the first player +to make a move + +where you could see a +hole the way through, + +that is expressing DNF formula. + +So that's kind of a +fun way, geometric way, + +to think about these games. + +And you could adapt it +to all of these games, + +just with slightly +different geometric setups. + +We'll see one in a little bit. + +Cool. + +I have here the next +thing to mention + +is why are all these +games in EXPTIME. + +I think that's +worth talking about. + +The idea is pretty simple. + +All these games-- I mean, +you can represent a state + +in a polynomial number of bits. + +It's just the current setting +of the variables and maybe + +whose turn it is. + +Therefore, there are +an exponential number + +of possible states. + +And the approach is basically +to build the entire state graph + +and then rank for each +position whether it's + +a win for one player or a +win for the other player. + +And I think the +easiest way to think + +about this is you start +with all the configurations + +that satisfy the win condition. + +You call those +mate-in-0 positions. + +And then, from there +in exponential time + +you can compute, find +all of the moves, where + +all the places where you can +make a move in any response + +lead you to a win position. + +And those are the +mate-in-1 positions. + +Or in two ply, one +move, one pair of moves. + +And so on and so forth. + +And so then, at +most you are going + +to be mate in exponential, +because they're only + +exponentially many states. + +So the longest mate path +is going to be exponential. + +So you can do like 4k equals 0 +to the total number of states, + +which is an exponential +compute mate-in-k. + +And then, you've characterized +the whole state space + +in nearly exponential time. + +And now you know which +ones are winning states. + +And then, you check whether +yours is one of them. + +So there's probably +other ways to do it. + +You could probably start from +your initial configuration. + +But this makes it clear that +it's at most exponential time + +that you'll be spending. + +Not polynomial space, because +we're building the entire graph + +here for this to work. + +We have to remember for all +the states that we visited, + +so we can check for duplicates. + +So that's intuitively why we're +an exponential time bigger + +than PSPACE, assuming +PSPACE does not equal + +EXPTIME, which we believe. + +Cool. + +So let's do some +graph games next. + +I have two games to mention +and a proof for one of them. + +First game is based +on Hamiltonian cycle. + +So this is a funny kind of game. + +And the claim is that you can do +this for a lot of different NP + +complete problems. + +But in general, we have a graph. + +Every edge of the graph +is either black or white. + +And black player can +only play black edges. + +White player can only +play black edges. + +In addition, every edge +either in or out, in the graph + +or currently out of the graph. + +And that's what these variables +are going to correspond to. + +I mean, we're going to convert +into a corresponding game. + +In this case, it's going +to be a G6 style game. + +So the winning condition +is that the set of in edges + +form a Hamiltonian +cycle in the graph. + +So you could think in +means in the cycle, + +out means not in the cycle. + +If we ever get to a +state where the in edges + +form a Hamiltonian +cycle, player 1 wins. + +Player 2's goal is +to try to avoid that. + +Player 2 can only +control the black edges. + +Player 1 can only +control the white edges. + +At the end of each turn, you +can change, if you want to, + +one of the edges +between in and out + +and one of the +edges of your color. + +So I'm just going to leave it at +that, because the proof is not + +terribly interesting. + +No gadgets, but +this next game is + +I think a lot more fun, +more surprisingly hard. + +And it has a nice clean +reduction also from G3. + +So what's the game? + +We are given three graphs +on the same vertices. + +So really you can think of this +as a three-edge colored graph. + +There's the red graph, the +blue graph, the green graph, + +same set of vertices. + +And we are going to +have tokens on vertices. + +And we're going to have +at most one per vertex. + +There are white tokens +and black tokens. + +A move by a player +is going to, call it, + +slide a token, exactly one of +them, of your color along path + +in one of the graphs. + +There's three of them. + +And that slide has to +satisfy a few conditions. + +One condition which is +that the target vertex + +you get to and all intermediate +vertices that you follow + +along the path must be empty. + +They should have no tokens. + +So you pick up any +token of your color-- + +you pick a color +red, green, or blue-- + +and you follow a red path +or you follow a green path + +or you follow a blue path. + +As long as that path doesn't +hit any other tokens, + +then you drop your +token, erase it + +from where it was +originally, and you + +keep making moves like that. + +What about the win condition? + +We look at a player-- I'm going +to come the players 1 and 2. + +Player i will win if they +get one of their tokens + +to a node in the win set WI. + +So also we're going to color +the nodes as winning for white + +or winning for black. + +And if you ever get a token to +a winning spot for your color, + +games over. + +You win. + +So this is a pretty +natural token-sliding game. + +As EXPTIME complete, very hard. + +And this one we're +going to proof. + +So this is a variable gadget. + +So we're going to +reduce from G3. + +I think I said that. + +This one. + +So G3, a move +corresponds to you're + +forced to flip a +variable of your color. + +Although we could switch +that to the other version. + +And you're going to lose the +game if you satisfy your DNF + +formula. + +So there's lots of edges here. + +But in particular, there's +solid edges, dashed edges, + +and the dotted edges. + +That's red, green, and blue. + +This is before color journals. + +Question. + +AUDIENCE: I didn't +catch what the purpose + +of coloring the edges is. + +PROFESSOR: Oh. + +It's basically to +decompose the graph + +into a bunch of +different types of paths. + +So when you follow +a path, it must + +be a path of a single color. + +AUDIENCE: Oh. + +OK. + +PROFESSOR: Yes. + +So you can only follow the solid +path or follow a dashed path + +or follow a dotted path. + +You can't mix edges +of different colors. + +So that's the three graphs. + +So what's going on? + +We've got a white token +here, black token here, + +white token here. + +This is a win +position for white. + +These are win +positions for black. + +So there's a lot of +things going on here. + +But the main idea is that white +can move the token to here. + +That corresponds to +EXPTIME being false. + +Or it can move it to here. + +That corresponds to +EXPTIME being true. + +And that's essentially all +you can do in this picture. + +Why? + +Because if this guy moves +to here, for example, + +then black can win. + +Black can go along this +path and get to a win state. + +And symmetrically, if white +also goes off the track, + +then black can go +to the win state. + +Also, we had to put this vertex +here, put this token here, + +to make that true. + +You might worry, +maybe black tries + +to move out of that position to +there or to there or to there. + +But then white will +win by going like that. + +So under optimal play, if you +don't make silly losing moves, + +all you can do is move the white +token between here and here. + +And I didn't say it, +but the path here + +is supposed to be a +non-zero length path. + +So you have to move your token. + +And therefore, that +represents this constraint + +that you must put the variable. + +You must flip exactly one +variable of your color. + +So that's the variable gadget. + +And for a while, that's +just going to happen. + +But now we have to +implement the win condition + +or the lose condition. + +So that's this thing. + +This is a clause. + +This is a DNF clause. + +Is it x3 is false +and y5 is true. + +In that case, we +want to lose or win. + +It doesn't particularly +matter here. + +We want to lose, I guess. + +Obviously, black can't move +first in this configuration, + +because then white +could just win. + +So black can't move first, so +what can happen in this gadget + +is that white must move +here because you're not + +allowed to collide. + +Once you move there, +the threat is that white + +will win in the next turn. + +So black must move up. + +And then, if this is +empty, white can move here. + +It could actually move to +here, because that's a path. + +And then, the threat +is white will win. + +So black must move up. + +Also, there's a black win +there, but we'll get to that. + +Actually, I'll do it now. + +So if this was blocked by +x3, because x3 is currently + +set to true, then you won't +be able to move this way. + +So you'll basically +be stuck here. + +And then, black +can win like that. + +So you don't want to +activate this gadget + +unless this is clear. + +Similarly, we don't +want to activate it + +unless this is clear. + +So if we're up to +here, then white + +can move up, threatening to win. + +Therefore, black must move up. + +And then, if this is clear, +white can move up to there. + +And then, black has to go +there to prevent this win. + +But white can win that way. + +So white is going to +win if this clause was + +satisfied or unsatisfied. + +And I'm a little confused about +how many times we negated. + +But I think you get the spirit. + +And if this DNF clause is +satisfied, then white wins. + +And you can have a bunch of +these clauses just sitting + +around. + +These are all vertices +unique to the clause, + +except for these +guys, which are shared + +with the variable gadgets here. + +So those are the same +as these vertices. + +They're all glued together. + +No planarity here. + +Cool. + +So that's EXPTIME completeness +of this game called Block. + +All right. + +This is a little ambitious. + +But the next one +I'd like to prove + +is a real-life classic +game, namely checkers. + +This is most of the +proof in one slide. + +It's a little bit complicated. + +But let me give you +the high level idea. + +It's actually a +really cool proof. + +It's also from my birth years. + +So it's cool. + +So don't worry +about this too much, + +but our construction is going +to be this little square + +inside this little square. + +And then there's +this giant spiral + +outside that will cause +everything to self-destruct + +when the game ends. + +I'll talk about that later. + +Let's focus in first +on what's happening + +within this little square. + +But that will be the context, +and we'll get to that again. + +So inside the square +is this thing. + +So I mean, I think the +perspective is from white. + +So the goal is for white to win. + +And in checkers, there's +two types of pieces. + +And the circles are +going to be pieces + +that are going this way for +white and that way for black. + +And the squares are +going to be kings. + +They can move up or down. + +So white and has some +variables that it can set + +between true and false up here. + +Black has some +variables that can + +be set between true or false. + +I didn't mention, but we +are going to be playing G3. + +We are going to +be simulating G3. + +So a move is going to be +forcing to flip something. + +And we're going to lose +if the formula ends up + +being satisfied. + +So then there's this +computation done in the middle. + +Basically, each of +these boxes is going + +to correspond to a DNF clause. + +What makes it tricky +is each clause + +involves some black variables +and some white variables. + +And those are going to +behave quite differently. + +But this construction is +going to make that happen. + +And overall, let's see. + +Where to go? + +Let's start with +the variable gadget. + +So this is a white +variable gadget. + +Black variable +gadget is symmetric + +with all the colors +flipped I believe. + +Yeah. + +That should be fine. + +And the key actor is +this king right here. + +I've drawn it at +the intersection. + +But it could be on the t +position or the f position. + +t corresponds to +variables being said true. + +f corresponds to the +variables being set false. + +And so most of the game is going +to be all the players moving + +their kings back and +forth between these t + +and f positions. + +Those will correspond +to flipping + +a variable of your color. + +Now, constantly you're +worrying about the threats. + +These attack zones and +defend paths are the threats. + +And if ever a +threat is satisfied, + +somebody's going to win. + +And the game will end. + +So when that happens, players +in the variable position + +can choose to activate a +variable of their color. + +And the way you would +do that, a key rule + +which you may have +forgotten about checkers, + +is that if you can +capture you must capture. + +So that's how we're going +to force the opponent + +to do lots of things +we want them to do. + +If we move this white token up +and to the right, then suddenly + +this black token can capture. + +And it must capture along the +unique path boom, boom, boom, + +boom. + +Assuming that we're +in the true position, + +he must jump there, jump +there, jump there, and activate + +some stuff down here. + +Conversely, if we're +in the false position, + +we're going to move this +B guy up and to the left. + +And then, black token will have +to go off into this position. + +So far so good. + +Now, so this variable may occur +in several different clauses. + +There's one clause that matters, +because this is a DNF thing. + +We're just trying to prove that +one clause has been satisfied. + +So white's going to want to +send things that satisfy it. + +Black is going to want to +send its variables that + +cause it to be not satisfied. + +So there's going to be +some white variables + +and some black variables +involved in this one clause. + +But we need the ability to +send the copy of this variable + +to the clause that matters. + +So the threatening +player, white, + +is going to be sending their +thing to a particular cause. + +They do that using +this fork gadget. + +So if you're coming +from up here, + +you jump here, and jump here. + +Black jumps here. + +And that's the end +of black's turn. + +Now, white is going to move +this position to either H or I, + +forcing black to go +follow the next path. + +So white's always in +control for this path. + +There's going to be a +symmetric thing where + +black is in control. + +And black and send their token +to where they want it to go, + +one of these squares. + +Cool. + +Now, maybe at this +point I should + +mention that there are these +letters here, MWD and MBD. + +And this is relevant to +the overall architecture + +of the game. + +What we're essentially trying +to do is get free moves. + +Free moves will win +the game, because + +of the spiral on the outside. + +But before I get to +the spiral, here's + +a way to generate free moves. + +Suppose right here I'm going +to throw in a whole bunch-- + +think of infinity-- copies of +this gadget, so-called white + +delay. + +So black is forced to jump here +and just keeps going through. + +There's no options for black. + +It just has to keep going. + +But after that move, +white has a penalty, + +because white is forced +to capture that token. + +So white essentially lost a +move sometime in the future. + +As long as there are still +capture moves it's OK. + +But that's kind +of bad for white. + +And there's a symmetric +version for black. + +I didn't bring the picture, +but it's pretty similar. + +And black will be forced +afterwards to jump. + +So the point is if we +essentially stopped + +here, black would win actually. + +Because there's +so many moves here + +that white is forced +to waste, they'll + +end up being able to win +the whole game in a way + +that I will get to. + +For that reason, you better +not trigger this thing + +unless the king is +in the right spot. + +Otherwise, black will stop +there and then black will win. + +But there's a matching +MBD down here for black. + +And so we're forced +to use both of them. + +Then, they cancel +each other out. + +Because if black +has n free moves + +and white as n +free moves, they'll + +just make all those captures +and then get back to the game. + +So, in general, the +gadgets use these things + +to force you to not stop in +the middle of the construction. + +The heart of the matter is +this gadget, the clause. + +So there's numbers here. + +If you look closely, these +are 1's and then these are + +2's and then these are 3's. + +So the idea is let's +suppose that there + +are three white variables +and two black variables + +in this clause that +you can generalize. + +That's what the figure shows. + +So the idea is that first +white's trying to win. + +So it's going to +send its variables + +of the appropriate truth +assignment into the one clause. + +It's going to +activate whichever one + +happens to be glued to the +one clause first or the one + +position. + +And what will happen is the +white token will go here. + +I forgot to mention +we've switched colors + +from white to black. + +That's because +there's a color change + +gadget, where you can convert +white wires into black wires. + +So don't worry about it. + +So now we have a white token +that captures all these pieces. + +Notice it captures +this one, which will + +enable the two path next time. + +So it is first you send in this. + +It just stops, +nothing to do there. + +Then, we send in the 2's. + +And if this has +been done already, + +so this is basically a +conjunction of 1 and 2. + +2 will be able to get here +if and only if both 1 and 2 + +are set. + +Also capture this position +and this position, + +enabling both of these 3's. + +Basically, we have two +copies of the 3 wire + +just because the opponent +could mess things up + +for us by moving one of these. + +Black can move this over here. + +And then, we're kind of annoyed. + +But we have two +copies for redundancy. + +So even if black messes up +one of them, we'll be OK. + +The worry is after you activate +this thing black has a turn. + +And so maybe instead of +doing something else, black + +could just move this. + +But we have enough redundancy. + +That won't hurt us. + +Finally, if we can send +1, 2, and 3 together, + +then black will waste n moves. + +And so white is in the lead. + +And then, white will +win the game in a way + +that I haven't shown you. + +Conversely, black has a blocking +strategy, a defense strategy, + +which is after 2 has +activated, if black + +has either of these variable +set to the right value, + +they can trigger them with a +corresponding black variable + +gadget. + +And then, the white +token will come up here + +and hit this gadget MWD, which +is a whole bunch of these. + +And then, white is behind. + +And then, black will +immediately win. + +Before white gets to do +this, black will win. + +So overall structure make sense? + +Basically, this gadget +is active as soon + +as the white player +sends down the one thing + +and then sends +down the two thing. + +And then, if black happens +to have a response which + +blocks it, what +that corresponds to + +is that one of the +black variables + +is in the wrong setting +for this clause. + +Then, black will have a defense +strategy and win the game. + +And so you only want +to activate a thing + +if all the black variables +are in the correct setting + +currently and the +white variables + +in the correct setting, so you +could do the 1, 2, 3, and then + +win. + +And symmetrically, there are +things like this for black. + +But that is the game. + +Now, let me tell +you how once you + +have n free moves, how +you could win the game. + +This is the outer spiral. + +So everything +we're talking about + +was in here very far away from +the spiral, like n squared away + +or something. + +And the spiral in more +detail looks like this. + +We have a whole bunch of kings, +and white king, black king. + +And if you have a +bunch of free moves-- + +you don't actually need +very many free moves. + +It's like five or something. + +But they didn't feel +like computing it, + +so they just called it x +and then figured out for x. + +You can make a few moves +and get from this position + +to this position. + +So far so good. + +Still have a free move. + +Iam going to move this A +king to the B position. + +At that point, black +has a forced jump. + +Now, they may have +other forced jumps. + +We'll just just sit +there and wait for them + +to do all their forced jumps. + +And then, black will have +to make this jump, capturing + +one of these kings. + +So this guy's basically +to prevent you + +from jumping that way. + +So this guy moves down, which +forces this guy to jump here. + +And then, from here, you +can jump here, here, here, + +here, here, so satisfying. + +Take all the black +kings on the outside. + +Now, you own the +entire spiral, which + +is a huge number of things. + +The number of +rings of the spiral + +is greater than the +number of pieces in there. + +And also, these things +are very far away. + +So you have plenty of moves. + +So whatever's +happening in here-- + +chaos could be +happening-- you can + +rearrange the white spiral into +a bunch of white rectangles. + +And it's already been shown +conveniently that if you have + +n white rectangles +in this sense, less + +or equal to n +pieces, then you win. + +So it doesn't matter +what's in here. + +You can come in +and use each ring + +to destroy one black +token at a time. + +And game over. + +[LAUGHTER] + +PROFESSOR: Isn't that fun? + +So that's checkers +EXPTIME complete. + +A very cool proof. + +There are details I didn't show. + +There's a parity shift, +a few other things. + +But that's pretty +much everything. + +And that's the power of G3. + +I'll just show +pictures for chess. + +It's even more complicated. + +But chess is also +EXPTIME complete. + +Now, I mean, both +checkers and chess + +in the real game sometimes +in some versions of the rules + +it says you can make at +most 200 moves or 500 + +moves or something. + +Those games are of +course PSPACE complete, + +if you add an artificial +move bound of n or something. + +But if you don't, the +natural game I think + +is when you don't bound +the number of moves, + +then they become +EXPTIME complete. + +This is also from G3. + +That's I'll say about chess. + +AUDIENCE: Do you know in +chess what pieces are used? + +PROFESSOR: I think it's just +pawns and bishops, which + +is pretty cool. + +One of these figures-- + +AUDIENCE: Oh. + +It's on the left. + +PROFESSOR: Yeah. + +White pawn, black pawn, +white bishop, black bishop. + +I'm pretty sure +that's all of them. + +But it's a little hard to +tell him from this figure. + +I think you need a better +scan to know which are which. + +And + +This paper's a little hard to +find, but I got a scanned copy. + +Go is EXPTIME hard. + +So how many people know Go? + +Good. + +Almost everyone. + +So Go is a little +funny, because you might + +think it's a bounded game. + +Every time you place a +token, you consume area. + +But captures remove area, and +furthermore kos are the action. + +So kos are these threats that +when I capture and someone else + +can capture me back. + +And you can flip back and forth +from those types of states. + +There are actually +different rules for Go. + +The Japanese rule set +says that you are not + +allowed to repeat the +position you were just at. + +And this is the +subtlety of a ko. + +So this is the +canonical simplest ko. + +So if you move white here, +you capture this stone. + +And under Japanese +rules, you're not + +allowed to repeat the +previous position, which + +means you're not allowed +to immediately play back + +here and capture this stone. + +You can see why. + +It'd be kind of a boring game +if you just went back and forth + +capturing the same guy. + +But as long as you +play anywhere else, + +then you can come +back and capture. + +That's the ko threat. + +That game is in EXPTIME. + +And Go is EXPTIME complete +under Japanese rules. + +In some sense, because +the number of states + +is still only +exponential, you just + +need to remember the +current state and the very + +previous state. + +Because the ko rule is +that you're not allowed + +to repeat the previous state. + +In the USA and China, there +is something called a super ko + +rule, which is that +you're not allowed + +to repeat any previous +state of the game ever seen. + +That means that you are not +necessarily still in EXPTIME, + +because you might need to +remember all past states, which + +could be exponentially long. + +So it's like double +the exponential size. + +In general, you are in EXPSPACE. + +And it's an open problem +whether Go with super ko + +is EXPSPACE complete. + +Currently, best known lower +bound is EXPTIME hardness. + +I won't cover the gadgets here. + +I mean, it's even more subtle, +because you can't really + +be capturing. + +It's all about ko threats. + +Or you can't really +be adding pieces. + +You have to constantly +be capturing, + +because you must +conserve volume. + +You're running for +exponential time. + +It would be quite an +interesting game to watch. + +But it's a reduction +I think from G3 again. + +That's Go. + +Let me tell you a little +bit about constraint logic. + +So we got a question. + +AUDIENCE: Sorry. + +I was just wondering +if you're allowed + +to use superpolynomial +reductions for EXPTIME purpose. + +PROFESSOR: So in +fact, all the proofs + +I've seen in this world +use LOGSPACE, which is even + +stronger than polynomial time. + +I don't know why. + +Probably just because they can. + +And it's slightly better. + +It makes sense to use LOGSPACE +reductions for PSPACE hardness. + +But they ended up still +doing LOGSPACE reductions + +for EXPTIME hardness. + +For my purposes, I think +polynomial time would be fine. + +You could imagine using +a little bit more time. + +Definitely you don't want +to use exponential time, + +because that wouldn't +preserve a lower bound. + +But you could use +quasi-polynomial or polynomial + +spaces or some crazy thing. + +But all the claims +I've made don't even + +need polynomial time reductions. + +It's pretty strong. + +Yeah. + +AUDIENCE: That rule +confuses me a lot. + +So that means I can't ever +go in the erased area? + +PROFESSOR: Well, no. + +You could play here as long +as something else changed. + +You cannot repeat the +entire board configuration. + +So the local +configuration can repeat. + +So as long as something +else has changed, + +then you can play here. + +AUDIENCE: But then it's +the same rule, right? + +PROFESSOR: It's the same rule. + +But if you have five of +these, so in the ko rule, + +as long as you're +basically playing them + +in a different order, you +can keep playing around + +and ko, ko, ko. + +But in the super-ko +rule, at some point, + +you're going to run +out of ko patterns. + +And at some point, you won't +be able to repeat something. + +And that changes how +the game behaves. + +Of course, we don't have a +hardness proof for that case, + +or a stronger hardness proof. + +It's subtle. + +Two-player constraint +logic unbounded + +is also EXPTIME complete. + +This is a reduction from G6. + +You can set one of your +variables however you want. + +And player 1 is going to win +if we satisfy a CNF formula. + +So the formula is out +here or here or here. + +This is a white variable. + +This is a black variable. + +The only difference is +this edge is white here. + +This edge is black there. + +So the idea is this can +be set left to right. + +If it's left, that +corresponds to false. + +If it's to the right, +it corresponds to true. + +And so most of the +time, players are just + +going to be flipping their +edges back and forth. + +It'd be a pretty boring game. + +But at some point, there's +this constant threat network, + +which is if the +formula is satisfied, + +then the white player is +going to be able to win. + +How do they win? + +First thing they do +is lock a variable. + +So this is pointing to the +true state-- sorry, also left + +and right pictures are +symmetric, so symmetric + +that we didn't even +draw it in the book. + +So I reflected the image and +all the letters are backwards. + +So let's say the variable's +pointing to the right. + +So white is going to +lock the variable, + +prevent it from flipping +anymore, by flipping this edge. + +Now, we enter attack face. + +And lots of things happen. + +So this is a SPLIT gadget. + +So immediately, +for example, black + +could flip here and +start winning the game. + +There's a long path here. + +It's slow, so it's a long path. + +But eventually black +will win the game. + +The timer starts +ticking now potentially, + +if black chooses to +follow that path. + +Simultaneously, white is +going to flip this guy, + +then flip this guy, +and then flip this guy + +and activate the formula. + +Now, it's a little +awkward, because we + +needed 1, 2, 3, 4 moves +to trigger the formula. + +We basically want to +consume four moves of black + +so that things remain balanced. + +And that's this +1, 2, 3, 4 flips. + +If black does not +flip all these edges, + +then white can flip this +and then flip this and then + +flip this and then +instantly win. + +That's the fast win track. + +So to prevent that, black +must flip this edge. + +It can't flip this edge +until it's flipped this one. + +It can't flip this one +until it's flipped this one. + +So as soon as you +lock a variable, + +black must respond +with A. At that point, + +white can afford to flip here. + +And black must respond +with B. And then flip here, + +black must respond with +C. And then flip here, + +black must respond-- I guess, +flip here first and then + +flip B. And then you can +activate the formula. + +So then white and black +are balanced again. + +What's cool about that is it +means white cannot only lock + +this variable but lock +all of the variables. + +Every variable +behaves the same way. + +And the goal for white is to +get all the variables locked + +so it can start +triggering the formula. + +So every time you +lock a variable, + +black is forced to respond +in a particular way. + +And so after that, white can +lock the next variable, both + +the white ones and the black +ones, locks all of them. + +And now, the formula's +basically primed, ready to go. + +The variables can't +change anymore. + +And now, we're in +full attack mode. + +Cool. + +And then, the formula happens. + +Meanwhile, this slow win is +probably happening, fusing. + +And we set up the formula +so that if it's satisfied, + +you end up flipping the win edge +in a certain amount of time. + +And this is slightly longer. + +So if you don't end up +satisfying the formula, + +black wins. + +And then, it was +not a valid threat. + +You shouldn't have +triggered this attack mode. + +There's another threat +here, the slower win. + +So I assume that people +were flipping these edges. + +But it could be actually +black flips A early. + +If it does that, then +white will eventually + +win through that path. + +So this win path is just +to prevent A from flipping + +before it's locked. + +And the timing is +to setup right. + +Obviously, lots of +timing issues here, + +so we have to build an +equalizer gadget that ends up + +slowing down the traversal +of an edge basically + +in a particular way. + +And these are all of +the vertices need. + +It's a fair number, including +some white and black edges, + +which is a little bit annoying. + +It'd be nice to simplify +instead of gadgets. + +But that's the best +we have so far. + +And you can use the regular +NCL crossover appropriately, + +making everything else slower +so that crossover doesn't + +slow things down too much. + +Cool. + +A couple more minutes. + +I want to mention +a couple of games + +that do not fit into the table. + +In some sense, they are +higher than the table. + +So we have polynomial +bounded number of moves. + +And then, above that, we have +exponential number of moves. + +But if you take those +exponential number of moves + +and add an extra rule, so this +is entirely motivated by Go + +with super-ko rule. + +And you take any of these +games like G1 through G6. + +So you have the same win rule. + +But in addition you will lose +if you ever repeat a past game + +configuration. + +So it's forbidden to do that. + +Then, Robson, same guy who +proved Go is EXPTIME hard, + +proved that G1, G2, and +G3, and chess and checkers + +become EXPSPACE +complete, which is cool. + +That's a little harder. + +And it makes sense +they're in EXPSPACE + +because it can sort of walk +the graph in exponential space. + +But they actually +become that hard. + +And even crazier +to me is this rule. + +It seems almost the same. + +So we're going to have two +extra variables x and y, which + +can appear in the formula. + +And instead of +this lose rule, we + +add this lose rule which is +if you ever repeat a past game + +configuration-- and between +now and that past configuration + +at most one of x and y have +changed and that in turn-- then + +you lose. + +So if both of them +get changed, you're + +allowed to repeat it again. + +I don't have a great intuition +why this makes the game even + +harder, but it pushes it +up to the next level which + +is double the exponential time. + +AUDIENCE: This is +change and changed + +back [INAUDIBLE] configuration? + +PROFESSOR: Well, right. + +One of them will +have changed, x or y. + +Hm. + +You're repeating +the configuration. + +So you changed something-- +it be some other variable z-- + +and then change it back. + +As long as you didn't +also change both x and y, + +that's considered invalid. + +Once you change x and y, you +are free to repeat everything + +again, until the next time +something gets repeated. + +So I guess you have +to keep track of when + +the x and y changes are. + +So it's even harder to know +the history of the game, + +which repeats are valid +and which are invalid. + +In this case, all +that he could prove + +is the G1 becomes double +the exponential time. + +Cool. + +I could say a little more. + +In this world, it's probably +good to know this fun fact. + +Normally, when we think +of non-determinism, + +we think of an NP. + +We have existential +quantifiers on the guesses. + +If there's at least one branch +that works, then we're happy. + +Then, we return, yes. + +You could also think of +universal quantifiers, where + +if all of the paths going out +of here end up with yes, then + +we're happy. + +You can also think of an +alternating guess machine, + +or alternating lucky machine, +where every other time + +it's an existential guess +branch and the opposite times + +it's a universal guess branch. + +That corresponds to two-player +games in a natural way. + +Alternating polynomial time +thing corresponds to queue set. + +So that would give you PSPACE. + +Alternating polynomial time +gives you polynomial space. + +Alternating polynomial space +gives you exponential time. + +Alternating exponential time +gives you exponential space. + +Alternating exponential +space gives you + +double the exponential time. + +So in fact, this +result is stated + +as alternating exponential +space complete, + +which is the same as +double exponential time. + +So time and space are +interleaved in the natural way. + +And if you add +alternation to one layer, + +you get to the next layer. + +So it's just fun facts. + +And it's useful for +reasoning about these games. + +One more class. + +We've so far talked about +perfect information games, + +where everybody knows all the +states of all the variables. + +You can define a +private information + +game, where you can +see some but not + +all of your opponent's state. + +You know all of your +variable settings. + +In this setting, a slight +variation on G1 and G2. + +We have to generalize the +formula's a little bit, + +become double the exponential +time complete, just as hard + +as the weird repeat rule. + +Private information gives +you a very hard thing. + +A more restricted form is when +player 1 can't see anything + +about player 2. + +But player 2 can see a +little bit of player 1. + +This is sort of a +semi-blind game. + +In this case, G2 at least is +exponential space complete. + +That's weaker than here. + +So lots of weird +separations here. + +There are no well-known +games in these categories + +that have been proofed hard. + +But here is the version of Peek. + +You can redesign +the Peek structure. + +So you have some walls here. + +So you can't see whether this +guy's in or this guy's out. + +Player 0 can only +play on these guys. + +Player 1 can only +plan on these guys. + +Player 1 can see +all of this state, + +a little bit of the state. + +In the blind version, you can't +see anything to the right. + +And because they +couldn't do G4, this + +is the G2 version, which is +there's also a wall here. + +And you can only see +red through these holes. + +And your opponent can see +red through these holes. + +So you've got two +different win conditions. + +That's G2. + +And so that's a version of Peek. + +This one is double +the exponential time + +hard and complete. + +And this one is +exponential space complete. + +So these are like +way in the deep end. + +But next class we'll talk +about this category of team + +imperfect information games. + +And then, we even +get undecidability, + +which is the ultimate hardness. + +But that's all for today. \ No newline at end of file diff --git a/47yJ7g6DzkA.txt b/47yJ7g6DzkA.txt new file mode 100644 index 0000000000000000000000000000000000000000..56e57cac5bceebf1369ebf27aa2bad049affb609 --- /dev/null +++ b/47yJ7g6DzkA.txt @@ -0,0 +1,3337 @@ +PROFESSOR: So if you want to +hand in your problem sets, we + +have three handouts. + +The old problem set solutions, +the new problem set, and we're + +also handing out chapter +eight today. + +Of course, these are +all on the web. + +Reminders of previously +announced events. + +Next week I'm going +to be away. + +Ralf Koetter will be a +much-improved substitute. + +He'll be talking about +Reed-Solomon codes and + +Reed-Solomon decoding. + +He's one of the world experts +on these things. + +He's a great lecturer. + +So you're really lucky, +I believe. + +I will, of course, look at the +video afterwards and see how + +he did, but I'm sure he'll +do it better than I + +would have done it. + +And midterm is in two weeks. + +That's just a reminder. + +When I come back, we'll have +a Monday class to go over + +anything that Ralf may have +missed, or really anything in + +the whole course up through +chapter eight. + +You can bring questions +in to that. + +I don't know how much I feel +I'll need to embellish and + +cover, so I don't know +how much time + +there will be for questions. + +But that can be a fairly +free form lecture. + +And then Ashish is going to run +a review session on the + +Tuesday with exactly +the same purpose. + +So hopefully that'll put you in +good shape for the midterm. + +We have to make up +the midterm. + +No idea what's going to +be on the midterm yet. + +OK. + +Any questions about +these things? + +Homework processes going OK? + +Office hours? + +Solutions? + +Everything seems to be +all right so far? + +Good. + +We're in chapter seven. + +I certainly plan to +complete it today. + +I'm not going to cover all of +chapter seven, but the key + +elements that I want +you to know. + +You're responsible only +for what's covered in + +class, by the way. + +We've talked about a lot +of algebraic objects. + +Our main emphasis has been to +get the finite field, and at + +this point, we have +prime fields. + +Fields with a prime number +p of elements. + +And we find that we can +construct such a field by + +taking the integers mod p. + +You can write that +as z mod p z. + +You can equally well consider +this as the equivalence + +classes of integers of the +cosets of pz nz which are each + +identified by a remainder +or residue r between + +0 and p minus 1. + +OK. + +So basically, the elements of +the field are these remainders + +or these cosets. + +There are p of them. + +We do arithmetic by simply +doing mod p addition and + +multiplication. + +So if you understand arithmetic +mod p, you + +understand this field. + +Yes? + +AUDIENCE: Is Fp and +Zp isomorphic? + +PROFESSOR: As an additive group, +it's isomorphic to Zp. + +Zp we use that notation +for the group. + +We use this notation +for the field. + +And I write Zp is isomorphic +to Z mod pZ + +as a quotient group. + +Here I've added in the +multiplication operation mod p + +to make this a field. + +So this is somewhat more than +just a quotient group. + +Sorry. + +The notation is supposed to be +more suggestive than precise. + +This is not a math class. + +I hope it's helpful rather +than otherwise. + +OK. + +So today, we're going to +construct all the rest of the + +finite fields. + +By the way, we showed that these +are the only fields with + +a prime number of elements. + +Today we're going to construct +fields with a prime power + +number of elements in a very +analogous way, and it will + +turn out -- although I'm not +going to prove this -- that + +these are the only +finite fields. + +Well, these are generalization +of this, so all finite fields + +have a prime power number of +elements and are basically + +isomorphic to one +of these fields. + +How do we construct +this field? + +To give you a preview, very +analogously to the way we + +constructed this field. + +You'll see that the character +of the arguments is + +very much the same. + +And that's because there is a +great algebraic similarity + +between the integers and the +polynomials over a field. + +And we'll talk about +that in a second. + +Basically, they're both +countably infinite rings, or + +infinite rings. + +Countably infinite if it's +over a finite field. + +And they both have analogous +factorization properties. + +They're both unique +factorization domains, would + +be one characterization, +algebraically. + +All right. + +How do we construct +this field? + +We're basically going to +construct it by taking the set + +of all polynomials over Fp which +is denoted by Fp square + +brackets x. + +And we're going to take that mod +the set of all polynomials + +that are divisible by G of x, or +G of x times the set of all + +polynomials. + +The set of all multiples +of G of x. + +Or more simply, just +mod G of x. + +Where we're going to take G of +x to be a prime polynomial. + +And I guess I have to add that +the degree of G of x is going + +to be equal to m. + +So we basically need to find a +prime polynomial degree m. + +Then we take the set of all +polynomials modulo this prime + +polynomial. + +They're going to be exactly p +to the m residue classes, or + +equivalence classes, or +remainders modulo g of x. + +And we'll use the arithmetic +operations from mod G of x + +arithmetic, addition mod G of x, +multiplication mod G of x, + +and we'll find that the +resulting object has satisfied + +the axioms of the field. + +OK? + +So that's where we're going. + +You with me? + +OK. + +So let's talk about +factorization. + +And I think it makes it easy to +understand polynomials if + +we understand the analogies +to the integers. + +In particular where I'm headed +is unique factorization. + +Both the integers and the +polynomials have unique + +factorizations. + +The integers into product of +integers, and any polynomial + +is uniquely factorizable into +a product of polynomials. + +Now I wasn't quite precise +when I said that. + +We have to be a little bit +more precise when we talk + +about factorization. + +In particular, we have a +certain kind of trivial + +factorization that +involves units. + +Units, if you remember, are +the invertible elements. + +We're in a ring, so not every +element has an inverse, but + +some of them do. + +And in the integers, what were +the invertible integers under + +multiplication? + +Everything here is about +multiplication, you know? + +A ring is something that +satisfies all of the + +properties of the field, +except that some of the + +elements don't have inverses, +so that division is not + +necessarily well-defined, even +for non-zero elements. + +OK? + +Sorry. + +I think I said that before. + +But we're not emphasizing +that these are rings, + +although they are. + +That's an informal definition. + +So in the integers, of course +12 doesn't have a + +multiplicative inverse, +but it's an integer. + +But which integers do have +multiplicative inverses? + +Plus or minus 1. + +So if an integer is divisible +by n, it's also + +divisible by minus n. + +All right? + +Trivially. + +These are the only ones +in the integers. + +And last time we actually +talked, if I remember + +correctly, about the units +and the polynomials. + +Which polynomials +have inverses? + +Excuse me. + +The degree 0. + +Thank you. + +The degree 0 polynomials have +inverses because they are + +basically the non-zero elements +of the field. + +OK? + +It's slight abuse of notation. + +We identify the field elements +with the degree zero + +polynomials. + +These are polynomials just of +the form F of x equals F_0 a + +constant, where the constant +is non-zero. + +OK. + +So similarly, we will have to +have representatives of + +equivalence classes with +respect to the units. + +So if both plus or minus n +divide something, what we take + +as the representative is we take +the positive integers. + +When we talk about divisibility, +we talk only + +about divisibility by positive +integers or factorization by + +positive integers. + +It's trivial that if something +is divisible by n, it's also + +divisible by minus n. + +Similarly for polynomials, the +representatives are taken as + +mnemonic polynomials. + +And this means that the highest +order term, Fm is + +equal to 1. + +So we can take any polynomial, +and by multiplying it by one + +of these invertible elements, +basically by a non-zero + +constant in the ground field, we +can make the highest order + +term equal to 1. + +Right? + +So if a polynomial is divisible +by F of x, it's also + +divisible by alpha F of x, where +alpha is any non-zero + +field element, right? + +And so we may as well fix the +highest order coefficient + +equal to 1. + +Actually, for some purposes in +the literature, like you've + +probably seen this in filter +design, or we always make the + +lowest order coefficient +equal to one. + +F0 equal to 1. + +You could also adopt that +convention, and say that + +that's going to be a mnemonic +polynomial. + +Here we'll focus on the high +order coefficient, but you + +could do it either way. + +And these both have the nice +property that the product of + +positive integers is +a positive integer. + +The product of monic polynomials +is a monic + +polynomial, right? + +The highest order term of the +product is going to have a + +highest order term equal to 1. + +Or if you chose the +lowest order one, + +that would work, too. + +The lowest order term of the +product would be equal to 1. + +All right. + +So having recognized this, +when we talk about unique + +factorization, just as with the +integers, what we really + +mean is factorization of a +positive integer into a + +product of positive integers. + +It's unique up to units. + +We can always put units either +on the integer that we're + +factoring or on any of the +factors, and we can freely + +multiply any of these things by +units, and it won't affect + +the factorization. + +Similarly over here, when +we talk about unique + +factorization, we mean +unique up to units. + +We're basically going to talk +about the factorization of + +monic polynomials into a product +of monic polynomials. + +Not getting a real positive +feeling that everybody's + +following me. + +Would it help if I wrote +down more things, + +or wrote some examples? + +In F2 of x, for instance, +we have -- + +well, this isn't a very +good example. + +Let's write R of x. + +OK? + +We're going to talk about +factorizations like this. x + +squared minus 1 equals x +minus 1 times x plus 1. + +That's a factorization of a +monic polynomial into a + +product of monic polynomials +of a lower degree. + +Happens in F2 of x. + +Since there is only one non-zero +field element, then + +all polynomials are monic, +except for the 0 polynomial. + +The only non-zero term we +have play with is one. + +So the highest order non-zero +term is always 1. + +All right. + +OK. + +So that's what we're going to +mean by unique factorization. + +Now, there's one other +qualifier. + +There's some trivial factors. + +We took some care to use the +standard mathematical + +terminology in the notes, so if +it says trivial devisors, + +then that's what I mean. + +What would the trivial divisors +of integer n be? + +1 and n are always going +to divide in. + +And we're really not interested +in those when we + +talk about factorization. + +Similarly, over here, the +trivial divisor of a + +polynomial F of x are +1 and F of x. + +We're not interested in those. + +So when we talk about unique +factorization, we mean up to + +units and nontrivial factors. + +And for the integers, that means +that we're going to talk + +about divisors d, let's +say, such that d is + +between 1 and n. + +And for polynomials, what this +means is we're not interested + +in degree 0 factors. + +The only factor of degree the +same as F of x is going to be + +F of x up to units. + +We're interested in divisors d +of x such that the degree that + +0 is less than the degree of +the divisor less than the + +degree of what it's +dividing into. + +Sorry. + +I'm not defining everything, +but I hope that's clear. + +We're just interested in factors +that have degree less + +than the polynomial that we're +factoring, but we're not + +interested in degree +0 factors. + +So that's what's meant by +unique factorization. + +It also shows you the +analogy in general. + +In the case of integers, the key +thing in a divisor is that + +it have magnitude +between 1 and n. + +The key thing in a polynomial +is it have degree between 0 + +and the degree of F of x. + +Basically, we want to factor +something into + +smaller things here. + +And when we say smaller, we +talk about magnitude. + +Here when we say smaller, we're +talking about degrees. + +In general, we go between +these two things. + +The concept of magnitude is +replaced by the concept of + +degree, to say how +big something is. + +In both of these, the key to +all proofs is the Euclidean + +division algorithm. + +Suppose we want to see if +n is a divisor of m. + +I've forgotten what I +put in the notes. + +Then we go through division, and +we find that m is equal to + +q, some quotient times n, +plus a remainder r. + +This is standard grade +school division. + +But it's really the key in the +universe in talking about + +these two domains. + +And this is what we've used, +really, to prove everything + +about the factorization +properties of integers. + +And how would you actually prove +that everything can be + +written this way? + +There's an important caveat. + +That the remainder we can always +choose to have to be in + +the range from 0 less +than r less than or + +equal to n minus 1. + +And the remainder is what +we call m mod n. + +We divide and we get a remainder +that's one of these + +n things, and that's the main +thing we get out of this + +division, is m mod n, which is +equal to the remainder r. + +And there are precisely +n remainders. + +Now, how do you actually +prove this? + +You prove this, if +you want, very + +easily, just by recursion. + +You take m, and you ask, is +it already in this range? + +If it is, you're done. + +m is the remainder +and q is zero. + +If not, then you subtract n from +m, thereby reducing the + +magnitude of m. + +You can use the magnitude as an +indicator of how far you've + +gotten in this process. + +You reduce the magnitude, and +then you ask, is the result in + +this range? + +OK. + +If it's in that range, fine, +you finish this and q is 1. + +Otherwise, you continue. + +And in the recursion, you're +continually reducing the + +magnitude, and it's easy to +show that eventually, the + +magnitude has to fall into this +range and be one of these + +n remainder numbers, and +then you're done. + +OK? + +So it's a descending chain +where the chain + +has a bottom at 0. + +If you start with a positive +integer, you can't go below 0. + +And this is the only way +it can come out. + +Very easy to prove that. + +All right. + +Similarly in polynomials, we get +an analogous expression. + +If we want to take F of x and +see if G of x is a divisor, we + +take F of x, and we can always +write this as some quotient + +times G of x plus +some remainder. + +Where the important thing here +about the remainder is that + +the degree of the remainder +is less than the + +degree of G of x. + +And here the remainder is called +F of x mod G of x. + +Just as the remainder here +is called m mod n. + +And there's a unique +remainder. + +And again, how would +you prove this? + +You could just take any long +division algorithm that you + +know for dividing G +of x into F of x. + +Basically long division amounts +to taking F of x. + +You can always choose some +scalar multiple of G of x such + +that F of x minus alpha G of x +has degree less than F of x. + +So you pick the top term to +reduce the degree, all right? + +Let's take G of x to be monic. + +We're only interested in +monic polynomials. + +If the top term of F of x is -- +well, we're only going to + +divide it into monic +polynomials. + +But as we go along, we may +get non-monic ones. + +So you take the top +term, whatever it + +is over here, f(m). + +You multiply f(m) +times g of x. + +You subtract f(m) g +of x from f of x. + +You reduce the degree. + +OK? + +AUDIENCE: [INAUDIBLE PHRASE]. + +PROFESSOR: Correct. + +Thank you very much. + +You need also a term x to +whatever the difference in + +degrees is here to move the +degree up to the top. + +When we're actually doing long +division, we write f(m) f(m + +minus 1) down to f(0). + +We divide g(n) down to g(1). + +And the first term, g(n) is +going to be equal to 1. + +We take f(m) up here. + +We implicitly move it over to +get f(m) dot dot dot dot, down + +to f(m) alpha. + +We subtract, and we're down +to something that only has + +degree m minus 1. + +That's what polynomial long +division is shorthand for. + +So you all know how +to do this. + +OK. + +Again, similar kind of proof, +that you must be able to get a + +remainder in this range, +and furthermore, the + +remainder is unique. + +You basically can go through +this process. + +You reduce the degree by at +least one every time. + +Therefore, degree must +eventually be reduced to where + +it's less than degree g of x. + +At that point, you can't +continue this process. + +You're stuck. + +And that's your remainder. + +There's no way of taking +something of lesser degree of + +g of x and then subtracting some +multiple from g of x from + +it to still further +reduce the degree. + +All right. + +So similar proof. + +Uniqueness is pretty obvious. + +So you get a unique remainder of +lesser degree than g of x. + +And so you can reduce any f of +x to some remainder r of x, + +which is called f +of x mod g of x. + +And if we do arithmetic, the way +we do arithmetic over here + +for addition is we just, if we +want to add two remainders mod + +n, we take the sum of them, and +then if necessary, reduce + +them mod n. + +Similarly with multiplication. + +If we want to multiply them, +we take the product of two + +remainders, and if necessary, +reduce them again to a + +legitimate remainder which is +in this range or to mod n. + +It's the same over here. + +If we want to add two + +remainders, that's easy enough. + +We can do that and we won't +increase the degree, so we + +automatically get something +when we add two remainders + +that satisfies this +degree property. + +We don't have to reduce +mod g of x. + +If we multiply, you do have to +check that when you multiply + +two remainders, then all you +need to do is reduce + +the mod g of x. + +And basically, the assertion +is that -- + +let's see. r of x, s of x -- + +it's hard to write this without +being tautological. + +r of x, s of x. + +Reduced mod n, I'm sorry, +mod g of x. + +I'm sorry. + +This is not worth writing. + +r of x, s of x, mod g of x. + +Something like that. + +Bah. + +It's a total tautology. + +Forget it. + +Said correctly in the notes. + +I'd rather think of it +as residue classes. + +If we, say, we talk about this +as a coset, f of x plus r of + +x, and we want to multiply +any element. + +This coset times any element +of the coset f + +of x plus s of x. + +Then the result is just +multiplying out symbolically + +the polynomials times the +polynomials are the + +polynomials. + +Any polynomial times a +polynomial is a polynomial. + +Plus r of x f of x. + +We could get some multiple +of r of x, + +some polynomial multiple. + +We could get some polynomial +multiple of s of x. + +Plus r of x s of x. + +But this is a polynomial that's +included in here. + +We don't need to +say that again. + +Similarly here. + +And so this is equal +to f of x. + +It's equal to the coset f +of x plus r of x s of x. + +But this is another +polynomial that + +probably has higher degree. + +This is equal to the coset +f of x plus r of x s + +of x mod g of x. + +OK. + +So this tells us that to +multiply cosets, coset with + +representative r of x times the +coset with representative + +s of x, we're going to get +something in the coset whose + +representative is r of +x, s of x mod g of x. + +So this is a sketch of a proof +that basically mod g of x + +commutes with multiplication. + +To multiply r of +x times s of x. + +All right. + +So -- + +AUDIENCE: [INAUDIBLE PHRASE]. + +PROFESSOR: Yeah. + +You're quite correct. + +What I mean is the cosets +of g of x of f of x. + +So I now understand all +the blank looks. + +Are we better off now? + +We have a group consisting of +the set of all multiples of g + +of x, which I write as g of x +times all the polynomials. + +The cosets of the group +are precisely -- + +there's one remainder of degree +less than g of x in + +every coset. + +So this is the representative +of the coset. + +This is a sketch of a proof that +multiplication basically + +just amounts to multiplying +the remainders. + +The representative of the +product coset is the product + +of the representatives +modulo g of x. + +I think I said it correctly +for once. + +Please read the notes if you are +still confused, as I can + +see some of you are. + +Maybe it would help +to do an example. + +Let's take g of x to be equal +to x squared plus x + +plus 1 in f2 of x. + +It's a binary polynomial. + +Then r of x. + +The remainders are +equal to 0,1. + +This was degree minus infinity, +this is degree 0. + +They're x or x plus one. + +OK? + +These are the possible +remainders when I take any + +polynomial modulo g of x. + +Divide it by g of x, and I'm +going to get a polynomial in + +f2 of x of degree less than or +equal to 1, and those are all + +of the polynomials that are +decisively for degree less + +than or equal to 1. + +All right? + +So what's the addition table? + +Addition is pretty easy. + +0 plus anything is itself. + +1 plus 1 in F2 is simply 0. + +1 plus x is 1 plus x, sorry, +x plus 1 as I've written. + +And 1 plus x plus 1 is x. + +x, x plus 1. + +x plus x is what? + +Hello? + +0. + +Thank you. + +x plus x plus 1? + +Thank you. + +x plus 1, x. + +x plus x plus 1, 1, and 0. + +So that's what the addition +table looks like. + +Actually you could think of +these as being just written as + +binary pairs, 0 0, 0 1, 1 0, +1 1, where this pair is + +basically F1 F0. + +And then the addition table is +precisely the same as the + +addition table for these +binary 2-tuples. + +You just add, component-wise, +the lowest order coefficient, + +the F1 coefficient. + +So addition is just like +addition in F2 squared. + +Or z2 squared, if you like. + +OK. + +That's actually an +additive group. + +Check it out. + +It's not z4 by the way. + +The other abelian group, or the +other group of size four, + +sometimes called the Klein +four-group, but it's really + +just the addition table for +the set of all binary + +[UNINTELLIGIBLE] + +two-tuples. + +OK? + +Multiplication. + +One very nice thing about +finite fields is + +you can simply -- + +sorry. + +This was supposed to be +addition, this was supposed to + +be multiplication. + +You know can simply write out +what all the rules are in a + +finite space. + +OK. + +So what's 0 times anything? + +What's 1 times anything? + +Itself. + +1 is the multiplicative +identity. + +But you know. + +You could formally do this +by doing polynomial + +multiplication. + +All right. + +Here's an interesting one. + +What's x times x? + +Do x times x. + +What is that going +to be equal to? + +x plus 1. + +How did you do that? + +We did the modulo. + +First of all, we write that +that's x squared. + +But then we have to do x +squared modulo g of x. + +x squared plus x plus 1. + +So we have to go through a +little long division process. + +We have to subtract this +out from that. + +And that gives us x plus 1. + +So that's the key rule. + +Whenever we see something of +degree two or higher, we can + +always reduce it by subtracting +out some multiple + +of g of x down to something +of lower degree. + +Right? + +So this is what I've +been talking about. + +So x times x is x plus 1. + +What's x times x plus 1? + +Equals what? + +Good. + +You can do that in your heads. + +And what's x plus 1 +times x plus 1? + +Remember, we're doing +mod-2 arithmetic in + +our base field here. + +So this equals what? + +x squared plus 1. + +We reduce that, we get x. + +OK. + +Let me check right now. + +Is this a field? + +These four elements with these +rules for addition and + +multiplication. + +Does that form a field? + +What do I have to check, apart +from formalities like the + +distributive law? + +Which follows from the +distributive law for + +polynomials. + +That's always going to hold +through mod x arithmetic. + +What do I have to check? + +What are my field axioms? + +Anybody? + +Closure under multiplication. + +That's getting towards a very +crisp statement of the -- + +I'm looking for two +group axioms. + +One has to do with something we +have to check for addition. + +Something has to do with +something we have to check for + +multiplication. + +Inverses? + +AUDIENCE: [INAUDIBLE PHRASE]. + +PROFESSOR: OK. + +Between the two of you I heard +the two answers that I want. + +We have to check that +this forms an + +abelian group under addition. + +So we have to check that the +addition table is the addition + +table of an abelian group. + +And under multiplication, we +have to check that the + +non-zero elements form +a billion group. + +So just this part of the table +has to form an abelian group, + +and both these have to have +an identity, of course. + +But the identity in mod g of x +arithmetic is always going to + +be 0 for addition and it's +always going to be 1 for + +multiplication. + +All right. + +So I check this. + +Is this a group table? + +Basically, I just have to check +whether every row and + +column is a permutation +of the elements. + +And it is. + +And 0 acts as 0 should act. + +Has the additive identity. + +All right? + +Here what I have to check is +that the nonzero elements, + +these three, form an abelian +group under multiplication. + +Well, there really is only +one group of size three. + +It is isomorphic to Z3. + +If I replace -- + +let's remember what Z3 looks +like under addition. + +This looks like 0 1 2, +0 1 2, 0 1 2, 0 1 2. + +It's mod-3. + +1 plus 1 is 2, 1 plus 2 is 3, +which is 0, 1 plus 2 is 3, + +which is 0, 2 plus 2 equals 1. + +So gee whiz. + +This is isomorphic to that if I +relabel 1 by 0, x by 1, and + +x plus 1 by 2. + +That's the only thing +it could be. + +The only group table in which +every row and column is a + +permutation of every other. + +OK? + +So we verified that we +now have a finite + +field with four elements. + +Prime power number +of elements. + +Right? + +The elements of my field are +these four remainders, or you + +can think of them as +representatives for their + +cosets, modulo g of x. + +The addition rule is addition +modulo g of x, and the + +multiplication rule is +multiplication modulo g of x. + +And it satisfies the field +axioms, therefore, it's a + +finite field. + +All right? + +I can add, subtract. + +Addition and subtraction +basically looks like addition + +and subtraction of binary +two-tuples, just + +component-wise. + +Multiplication is a little +bit more mysterious + +right now, but it works. + +Let me tell you where we're +going to go on multiplication. + +In this case, I can write x +plus 1 in a different way. + +I note that x plus 1 is +equal to x squared. + +All right? + +So let me write a little +log table over here for + +multiplication purposes. + +I'm going to write x -- + +I'm going to call that alpha. + +And x plus 1 is equal +to x squared, + +or it's alpha squared. + +What's alpha cubed? + +Alpha cubed is x times +this again. + +Let me look in the table. x +times x plus 1 is equal to 1. + +So 1 equals alpha cubed. + +Or I could write that +as alpha to 0. + +If I multiply by x again, +I just cycle. + +So I'm going to get a +cyclic group here. + +And now I'm going to write the + +multiplication table as follows. + +I'm going to write the elements +of the group as 1, + +alpha, alpha squared, 0, 1, +alpha, alpha squared. + +Again, 0 times anything is 0. + +We never have to worry +about that. + +1, alpha, alpha squared. + +Alpha times alpha is +alpha squared. + +Alpha times alpha squared +is alpha cubed. + +But that's equal to 1. + +Same here. + +Alpha squared times +alpha squared -- + +what's that? + +Alpha to the fourth, but what +does alpha fourth equal to if + +alpha cubed is equal to 1? + +This has to be equal to alpha. + +Point is, because of this +relationship here, I can + +always reduce the exponents +modulo 3. + +I've basically got a little +multiplicative cyclic group of + +order three that's, of course, +isomorphic to the + +additive group, Z3. + +So there are two ways I +can do multiplication. + +One is, I can do it by +this mod g of x way. + +I can represent things by these +which basically stand + +for polynomials of degree +one or less. + +And I can multiply two of these +by simply going through + +standard polynomial +multiplication over the + +appropriate field. + +And then I'll likely get some +powers of x squared or higher, + +and I reduce those to modulo +x squared plus x plus 1. + +That's legitimate and that +gives me this statement. + +Well, the other thing I can do +is for multiplication, I can + +have a different +representation. + +This is basically just +a log table. + +OK? + +For each, I would have in my +little computer a separate + +table where I'd write that this +corresponds to 0, 0 1 + +corresponds to 1, 1 0 +corresponds to alpha, and 1 1 + +corresponds to alpha squared. + +Or of course, I would just +represent these by their + +exponents that have some +special value for 0. + +And then all I have to do is +add exponents modulo 3 for + +multiplication. + +So log of x is 1, log of x plus +1 is 2, log of 1 is 0, + +and then I just use this for my +multiplication operation, + +or equivalently this cyclic +multiplicative group. + +Then I go through some inverse +log operation to get back to + +the other representation, +if I wanted to. + +And in fact, in finite field +arithmetic, this is what's + +typically done. + +There's just a little table +lookup such that you can go + +back and forth between this +representation, which we use + +for addition, and this +representation, which we use + +for multiplication. + +Yeah? + +AUDIENCE: [INAUDIBLE PHRASE]. + +PROFESSOR: You have to represent +it as being special + +in some way. + +So if, in fact, literally, I +made log x equal to 1, log x + +plus 1 equal to 2, log +1 equal to 0 -- + +one thing I suggest in the +notes, you can make log 0 + +equal to minus infinity. + +That will always work. + +If you ever multiply +by 0, you'll be + +adding minus infinity. + +The result will be minus +infinity, so the + +inverse log is 0. + +So that's one way +you can do it. + +Or you could do what you do in +ordinary real and complex + +arithmetic. + +You could just, say, have +some special routine for + +multiplication by +0 is always 0. + +Division by 0 is illegal. + +Put out some error message. + +All right? + +So that's how you actually build +a little finite field + +computer for this +finite field. + +OK. + +Now, I chose this advisedly. + +Suppose I have chosen g of x +equal to x squared plus 1. + +OK? + +I can do mod g of x arithmetic +for x squared plus 1. + +Again, my four field elements +are going to be the four + +binary polynomials of +degree 1 or less. + +The addition table is going +to be exactly the same. + +So let's just write the + +multiplication table over here. + +0, 1, x, x plus 1, 0, +1, x, x plus 1. + +0 times anything is 0 in +ordinary polynomial + +multiplication, and therefore +also in mod g of x + +for any g of x. + +1 times anything is itself. + +No problem there. + +x, x plus 1. + +So we again have to give a +little bit care to x squared. + +What's that going +to be equal to? + +1. + +And x times x plus 1 +is equal to what? + +x squared plus x is +equal to what? + +Looks like there's a problem. + +x plus 1 times x squared x plus +1 is equal to x squared + +plus 1, what's that equal? + +0. + +Yuck. + +Didn't work. + +What's the essential +problem here? + +Yeah. + +This clearly is not a group. + +It's not even closed under +multiplication. + +Because x plus 1 times x +plus 1 is equal to 0. + +The essential problem is that +there are two polynomials of + +degree less than two whose +product is x squared plus 1. + +In other words, this +is factorizable. + +OK? + +In F2 of x. + +All right? + +So whereas x squared +plus x plus 1. + +Does that have any factors +of degree 1 or less? + +Any nontrivial factors +of degree 1 or less? + +Well, basically we proved that +it didn't, when we wrote this + +multiplication table. + +We tried all products of degree +1 or less polynomials + +where they're both non-zero, +and we never got 0. + +So this will work if and only if +g of x is irreducible, has + +no nontrivial factors, is +a prime polynomial. + +These are all equivalent +in F2 of x. + +There's this distinction in +other fields that irreducible + +just means has no nontrivial +factors. + +Prime means there's a monic +polynomial with + +no non-trivial factors. + +So that's what I +said back here. + +That the way we're ultimately +going to have to construct + +finite fields is take the +polynomials in Fp, Fp of x -- + +we've been looking +at F2 of x -- + +modulo a prime polynomial +g of x. + +So what we're going to need to +find is prime polynomials. + +Let's see. + +Can I already prove that this is +going to work for any prime + +polynomial? + +So I'm going to force the g of +x to be equal to a prime + +polynomial in Fp of +x of degree m. + +All right + +For example, x squared plus x +plus 1 is a prime polynomial. + +And I'm going to ask if the +remainders mod g of x form a + +field under mod g +of x arithmetic. + +OK. + +Let's flow this out +a little bit. + +Again, what are the remainders +going to be of any polynomial + +of degree m? + +So this is basically going to +be the polynomials of degree + +less than m in Fp of x. + +How many of them are +there, by the way? + +p to the m. + +So the size of this +is p to the m. + +And one of the representations +for these polynomials is just + +to write out F0, F1, +up to m minus 1. + +So this just basically looks +like the polynomial m-tuples. + +Set of F0, F1 up to F minus 1, +for each of these an element + +of the field. + +OK? + +I can make a one-to-one +correspondence between the + +polynomials of degree less +than m and the set of all + +coefficient m-tuples over Fp. + +These are just m-tuples +over Fp. + +So there are p to +the m of them. + +And so it's a finite set, +size p to the m. + +Does it form a field under +mod g of x arithmetic? + +AUDIENCE: [INAUDIBLE PHRASE]. + +PROFESSOR: Correct. + +And that's a homework problem. + +So I'm not going to do it in +class, but I will sketch here + +how it's going to be done. + +But I'm glad that you +instantly see that. + +Because again, we just model +everything we do on what we + +did for integers. + +If you remember how we proved +it for integers. + +First of all, we really need +to check two things. + +Addition. + +Just as we did for this specific +example up here, we + +first have to check that the +addition table is that of an + +abelian group, that these +supposed field elements form + +an abelian group +under addition. + +And we've already observed +several times that addition is + +just basically component-wise +addition of these m-tuples. + +So it's just like +vector addition. + +And vector addition, of course, + +has the group property. + +So addition is basically just +like vector addition. + +Or I could write, perhaps more +precisely, Zp over m. + +Distinction without a +difference, really. + +So it's just component-wise +addition of the coefficients. + +That's how we do polynomial +addition. + +And it will give us a remainder +that has a degree of + +less than m, so we don't have +to have ever reduce it. + +Modulo g of x, we just simply +add component-wise. + +OK. + +So that's easy to verify. + +The addition table is always +going to be OK. + +So what do we have +to prove now? + +We have to -- + +what am I going to call these? + +Rg of x. + +The remainders mod g of x. + +For multiplication, we have to +prove that Rg of x star -- + +the non-zero polynomials form an +abelian group, which, as I + +say, it's a homework problem. + +Let me sketch the proof. + +It's precisely analogous +to the proof that + +we made for Zp star. + +We basically have to +check closure. + +If we multiply two non-zero +polynomials, do we get another + +non-zero polynomial? + +Asking another way, is it +possible to multiply two + +polynomials of degree less than +m and get a result which + +is a multiple of g of x, which +is either equal to g of x or a + +multiple of g of x? + +And it's, I think, easy to +convince yourself if this has + +no factors -- + +its only factors are +itself and 1, no + +non-trivial factors -- + +then you can't multiply two +lesser degree polynomials and + +get either g of x, of course, +or any multiple of g of x. + +And it's an exercise +for the student to + +write that proof out. + +OK? + +But it's just exactly analogous +to the proof that + +you can't multiply two integers +less than a prime p + +and get a multiple of p. + +So use that as a model, if you +want to, in your proof. + +That of course depends +on this being prime. + +If this is factorizable, +non-prime, then of course + +there are going to be two +nontrivial factors, two + +remainders of degree less than +m, whose product is equal to g + +of x itself, if it's +factorizable. + +So you can't possibly +get closure. + +So this is why non-prime +polynomials don't work, just + +like non-prime integers don't +work when we constructed Fp. + +Exactly analogous reasons. + +All right. + +Second question is, when we go +through this multiplication, + +suppose we take r +of x times -- + +let's construct a multiplication +table. + +Let's take a particular row. + +Let's take r of x times all +the non-zero things. + +Can we possibly get +any repeats? + +Can r of x times s of x equal +r of x times t of x? + +And again, it's easy to convince +yourself that that's + +not possible. + +If that were possible, then r of +x times s of x minus t of x + +would be equal to 0. + +And so we're back to where +we were before -- + +mod g of x. + +And this is impossible. + +These are both degrees +less than m. + +We can't multiply two things +of lower degree together to + +get a multiple of g of x. + +So it can't equal 0. + +That means there can't +be any repeats. + +That means that each row +is a permutation + +of every other row. + +Similarly for columns. + +If you want to do that, +all you have to + +actually prove is one. + +So every row or column is a +permutations of every other + +one, if we just look at the +non-zero polynomials, star. + +And therefore, this forms an +abelian group whose identity + +is always one. + +Just as we proved up here. + +So this depends on +irreducibility. + +Depends on no nontrivial +factors of g of x. + +OK. + +And that's all we +have to check. + +So I claim that by this process, +I can, given a prime + +polynomial in Fp of x of degree +m, I can construct a + +finite field with p to the m +elements, that the addition + +and multiplication rules can +be taken as mod g of x + +arithmetic, and they will +satisfy the field axioms. + +So you can now construct a +finite field for any prime + +power p to the m, right? + +There's actually still +a hole in this. + +AUDIENCE: [INAUDIBLE PHRASE]. + +PROFESSOR: Define prime +polynomial? + +The term, or -- + +AUDIENCE: Define the +[UNINTELLIGIBLE] of degree m. + +PROFESSOR: Correct. + +Is there going to be a prime +polynomial of every degree? + +I don't know. + +Suppose you want to define an +irreducible polynomial over, + +say, F2 of x or F3 +of x of degree 4. + +Could you do that? + +AUDIENCE: [INAUDIBLE PHRASE]. + +PROFESSOR: Beautiful. + +I mean, that's an excellent +suggestion. + +So the question is, does there +exist a prime polynomial in Fp + +of x of every degree? + +Or of a given degree? + +And there are various ways of +attacking this question. + +First of all, I'll tell +you the answer is yes. + +For every p and every m, there +does exist a prime polynomial. + +Which is fortunate. + +So from that, we conclude there +is a finite field with p + +to the m elements for every +prime p and every m greater + +than or equal to 1. + +Now, how might we prove that? + +One is, look it up on Google. + +You can certainly formulate a +question that will lead you to + +a webpage that will have a +listing of all the prime + +polynomials of all degrees over +any field that you're + +interested in. + +So perhaps that will +suffice for you. + +Two. + +What I'm going to talk about +is the sieve method. + +Three. + +You could do a bound on the +number of polynomials of each + +degree in d, and show that +it's greater than + +or equal to 1, always. + +And this is done in the notes. + +Section 7.9 I think. + +Or four, you can do what Mr. +Agarwal has suggested. + +You can actually do the closed +form combinatoric + +formula, which -- + +I haven't done any number +theory here. + +There's a little bit of +elementary number + +theory in the notes. + +Euler numbers, this +sort of thing. + +We get formulas for the number +of integers degree d that -- + +well, number of integers that +have multiplicative orders d + +mod n, and so forth. + +It's a lovely combinatoric +field. + +There is a lovely closed form +for this that you get from the + +Mobius inversion formula. + +And it can be found in +combinatoric books. + +I know it's in Berlekamp's +Algebraic Coding Theory book. + +And it's extremely pretty. + +And then of course, given the +formula, you have to prove to + +all of the -- + +again, n of d is greater +than or equal to 1. + +But there is a closed form +expression for it that you get + +out of combinatorics. + +We're not going to +do that here. + +I'll be satisfied -- + +well, this is the real +engineering solution here. + +This is the mathematical +engineering solution. + +And what do I mean by +the sieve method? + +Again, take the analogy +with the integers. + +One of the first mathematical +accomplishments was + +Eratosthenes' sieve for +finding prime numbers. + +How does it work? + +You start to write +down all the -- + +well. + +Imagine first writing down +all the integers. + +All right? + +Cross off 1. + +Start with 2. + +All right. + +So the first prime is 2. + +Then you cross off all +multiples of 2. + +4,6,8, so forth. + +OK? + +So what's the next number that +you haven't crossed off? + +It's 3, so that's +the next prime. + +You cross off all the +multiples of 3. + +3,6,9. + +So forth. + +15. + +And thereby you continue. + +So the steps are, find the +next integer on the list. + +That's going to be a prime, +because it won't have been + +crossed off by any +previous steps. + +It's not a multiple of any +integer of lower degree. + +Then cross off all of its +multiples, up to however long + +your scribe has written +this on the tablet. + +And this way, you can find +the primes up to + +any number you want. + +Gets kind of tedious after a +while, but you can certainly + +find all the primes +up to 100 in a few + +minutes doing this, right? + +Well, it's the same for +integers, and it's the same + +for polynomials. + +So let's, for instance, +do a polynomial sieve. + +Of course, what we're most +interested in is the + +polynomials with binary +coefficients, F2 of x. + +And how do we do it? + +Let's write down -- + +let's forget about 0 and 1. + +Those are not considered +to be prime. + +Let's start with the degree +1 polynomials. + +What are the degree +one polynomials? + +They're x, x plus 1. + +Are these factorizable? + +Obviously their only factors +are one and themselves. + +They have no nontrivial +factors. + +So these are primes. + +OK. + +So now let's write down all the +polynomials of degree two. + +I'm sort of doing this in +an interleaved manner. + +There are going to be two of +degree 1, four of degree 2. + +All I'm going to do is -- well, +the only polynomials are + +monic in F2 of x, so I don't +have to make that + +qualification. + +All right. + +So here are the four +of degree 2, right? + +Now I go through with my sieve +and we take out all + +multiples of x. + +Multiples of x are polynomials +with 0 constant term, right? + +A lowest order term. + +So obviously this is a multiple +of x, this is a + +multiple of x. + +Multiples of x plus 1. + +How do you recognize those +over the binary field? + +This is basically the polynomial +whose root is 1. + +That means the mod-2 sum of the + +coefficients is equal to 0. + +So any polynomial that has an +even number of non-zero + +coefficients is divisible +by x plus 1. + +Did you all get that? + +If not, try that at home. + +That's the easy way to recognize +whether something is + +a multiple of x plus 1. + +It has an even number of +non-zero coefficients. + +So this is a multiple +of x plus 1. + +We wrote it out explicitly. + +It's x plus 1 squared in F2 +of x, and this is not. + +So there is only one prime +polynomial over F2 of x + +that's degree 2. + +So this is our only possible +choice if we want to construct + +a finite field with +four elements, + +due to the two elements. + +OK. + +So that might begin +to get us scared. + +Is it possible that +there are no prime + +polynomials of degree three? + +Well, we had two +here, one here. + +Is it going down? + +Let's write down the polynomials +of degree 3. + +x third, x third plus 1, x to +the three plus x, to the three + +plus x plus 1, x to the three +plus x squared, x to the three + +plus x squared plus 1, x to the +three plus x squared plus + +x, x to the three plus x +squared plus x plus 1. + +Eight of them. + +So that's working +in our favor. + +There's double the number +of polynomials as we + +go up one in degree. + +And again, let's go +through the sieve. + +Which are multiples of x, +non-zero constant term? + +Which are multiples of x plus +1, even number of non-zero + +coefficients? + +If you doubt that, +write it out. + +Which are multiples of x +squared plus x plus 1? + +Well, they're going to have to +be x squared plus x plus 1 + +times x plus 1 or times x, so +we've already got them. + +If we take this times itself, +we're going to get a + +polynomial of degree 4. + +Not going to be on this list. + +So we have to multiply +this by these. + +We've already got those. + +So whew. + +We found two. + +We could use either of these +to construct a finite field + +with eight elements. + +And so forth. + +And it turns out as you go up +to higher degrees, that the + +number now increases very +nicely, and there's no problem + +finding a prime polynomial +of each degree. + +And in fact, you could be cute +about it and try to find one + +with only three non-zero terms, +or has some other nice + +property that makes it easy +to calculate with. + +And so forth. + +So do you understand +the sieve method? + +If you do, then I believe +you could find a -- + +suppose you want to construct +a field with 64 elements. + +What do you need? + +64 is 2 to the sixth, so +you're going to need a + +polynomial with p equals +2 and m equals 6. + +You're going to need a binary +polynomial of degree 6 that is + +prime, irreducible. + +And again, in a few minutes +by going through the sieve + +process, you can quickly find +one, or you could look it up + +in Google, or in Peterson's +book, or any algebraic coding + +theory book, or probably +a lot of other places. + +So this is a practical solution +for the problem for + +any given p and m. + +Of course, it hardly proves +that there's one of every + +degree, because they're +kind of an + +infinite number of degrees. + +Yeah? + +AUDIENCE: So there's two order +3 polynomials that are prime. + +Will it generate two separate +fields, or are they going to + +be isomorphic to each other? + +PROFESSOR: Great question. + +All fields with p to the m +elements are isomorphic to + +each other. + +That's proved in the notes. + +I'm not going to +do it in class. + +And the other thing that's +proved in the notes is the + +analog to Zp. + +There are no other finite fields +with other than p to + +the m number of elements. + +OK? + +So this is it. + +Now, if you explicitly write +out these two, and + +write out their -- + +well, the addition tables are +always look the same, because + +it's always just binary +three-tuples, in this case. + +But multiplication tables are +going to look different. + +But there is some isomorphism. + +x and 1 may be equivalent to x +squared plus 1 on the other + +one, or something. + +But if you go through that +isomorphism, you'll find that + +the field tables are the same. + +Actually, I guess I'm going to +prove that, because I'm going + +to prove that the +multiplication + +table is always cyclic. + +That the group to which it's +isomorphic is z mod p + +to the m minus 1. + +Just as it was to Z3 here. + +And I guess that's sufficient +with the addition table + +isomorphism. + +I guess you have to prove +they're equivalent. + +You saw it in a different +way in the notes. + +But you're going to see that all +the multiplication group + +is always a cyclic group, with +p to the m minus 1 elements, + +and that goes a long way towards +suggesting that these + +are always going to be +isomorphic to each other. + +Yeah? + +AUDIENCE: Identify +roots, right? + +PROFESSOR: Identify roots? + +If I understand what you're +saying, that's basically the + +way it's done in the notes. + +You first show there's always +going to be some primitive + +element that generates +the cyclic group. + +Some single generator such that +alpha alpha squared, so + +forth, is the entire +non-zero set. + +You're going to show that +alpha has some minimal + +polynomial, and the set of all +linear combinations of powers + +of alpha is basically equal +to the whole field. + +And so this allows you to +establish the isomorphism. + +and I think that's what +you're suggesting. + +So you're well equipped to read +the notes, but I'm not + +going to do that in class. + +Yeah. + +I'm very interested +in your questions. + +Please ask more, as many +questions as you like. + +What I'm getting from it is, +you know, you all come from + +different backgrounds. + +Some of you have seen this in +perhaps a math context, or + +some other context, or you've +seen parts of it, or some of + +the words are familiar. + +And of course, there are many +different ways to present this + +and to make the proofs +and so forth. + +So I'm trying to pick a line +that works for the particular + +results that I want to get to. + +I don't think you would do +anything much different if you + +wanted to develop +finite fields. + +But the class has a very +different set of backgrounds, + +and I'm trying to reach +all of you. + +Don't be alarmed if +you've never seen + +anything like this before. + +You're not way behind everybody +else, either. + +I think it's pretty easy +to understand. + +Maybe it would take you a +couple hours longer than + +somebody who has more +background, but + +not more than that. + +OK. + +So that's how we construct +finite fields. + +You have an example of it. + +Goodness. + +Is it really 11 o'clock? + +OK. + +So I'm not even -- + +so I've simply asserted, +but not proved. + +You saw in this case that the +multiplicative group was a + +cyclic group. + +And we could always, for +multiplication, represent + +grouped elements by +this log table. + +So I'd hoped to prove +that in class. + +I'm not going to be able +to prove that in class. + +And I'll simply ask you +to read that, too. + +This is important for working +with finite fields, because it + +is the way, probably the +preferred way, to implement + +multiplication. + +So you ought to be thinking of +how you would program up a + +finite field multiplier. + +One way is polynomial +multiplication. + +The other way is just use the +fact that the multiplicative + +group is cyclic. + +And then it's easy. + +Just add exponents and reduce +modulo q minus 1. + +OK. + +I'm sorry not to have had a +chance to go over that. + +Next time, Ralf Koetter will +start to get into chapter + +eight, Reed-Solomon codes. \ No newline at end of file diff --git a/4XfaGkNEE9g.txt b/4XfaGkNEE9g.txt new file mode 100644 index 0000000000000000000000000000000000000000..b21d4920a3bba41e11088cc0f4957f94a8f01794 --- /dev/null +++ b/4XfaGkNEE9g.txt @@ -0,0 +1,1251 @@ +align:start position:0% + +hello as the last element in our + + align:start position:0% +hello as the last element in our + + + align:start position:0% +hello as the last element in our +discussion of musical representations I + + align:start position:0% +discussion of musical representations I + + + align:start position:0% +discussion of musical representations I +want to talk about two different + + align:start position:0% +want to talk about two different + + + align:start position:0% +want to talk about two different +fundamental ways that we can represent + + align:start position:0% +fundamental ways that we can represent + + + align:start position:0% +fundamental ways that we can represent +musical + + align:start position:0% +musical + + + align:start position:0% +musical +scores TimeWise and partwise and these + + align:start position:0% +scores TimeWise and partwise and these + + + align:start position:0% +scores TimeWise and partwise and these +really matter in anything that has more + + align:start position:0% +really matter in anything that has more + + + align:start position:0% +really matter in anything that has more +than one note or more than one independ + + align:start position:0% +than one note or more than one independ + + + align:start position:0% +than one note or more than one independ +part going s once and I want to + + align:start position:0% +part going s once and I want to + + + align:start position:0% +part going s once and I want to +acknowledge I'm going to be using slides + + align:start position:0% +acknowledge I'm going to be using slides + + + align:start position:0% +acknowledge I'm going to be using slides +from a presentation called notation as + + align:start position:0% +from a presentation called notation as + + + align:start position:0% +from a presentation called notation as +composition by William Andrew burnson + + align:start position:0% +composition by William Andrew burnson + + + align:start position:0% +composition by William Andrew burnson +creator of the B bage notation + + align:start position:0% +creator of the B bage notation + + + align:start position:0% +creator of the B bage notation +package one of the ways that we can look + + align:start position:0% +package one of the ways that we can look + + + align:start position:0% +package one of the ways that we can look +at musical notes is as musical scores is + + align:start position:0% +at musical notes is as musical scores is + + + align:start position:0% +at musical notes is as musical scores is +as a series of containers so that we can + + align:start position:0% +as a series of containers so that we can + + + align:start position:0% +as a series of containers so that we can +think of uh and part based containers so + + align:start position:0% +think of uh and part based containers so + + + align:start position:0% +think of uh and part based containers so +we have a score and within that score as + + align:start position:0% +we have a score and within that score as + + + align:start position:0% +we have a score and within that score as +the first element we have two parts in + + align:start position:0% +the first element we have two parts in + + + align:start position:0% +the first element we have two parts in +this case and within those parts we have + + align:start position:0% +this case and within those parts we have + + + align:start position:0% +this case and within those parts we have +measures and we might even go further + + align:start position:0% +measures and we might even go further + + + align:start position:0% +measures and we might even go further +and think that within those measures we + + align:start position:0% +and think that within those measures we + + + align:start position:0% +and think that within those measures we +have voices but first when we think + + align:start position:0% +have voices but first when we think + + + align:start position:0% +have voices but first when we think +about dividing a score into parts let's + + align:start position:0% +about dividing a score into parts let's + + + align:start position:0% +about dividing a score into parts let's +say it's you know the score of um a + + align:start position:0% +say it's you know the score of um a + + + align:start position:0% +say it's you know the score of um a +massive three-hour Opera well you start + + align:start position:0% +massive three-hour Opera well you start + + + align:start position:0% +massive three-hour Opera well you start +with you whatever's at the top of the + + align:start position:0% +with you whatever's at the top of the + + + align:start position:0% +with you whatever's at the top of the +piccolo or something like that and you + + align:start position:0% +piccolo or something like that and you + + + align:start position:0% +piccolo or something like that and you +go with the piccolo part from measure + + align:start position:0% +go with the piccolo part from measure + + + align:start position:0% +go with the piccolo part from measure +one all the way to the end of the three + + align:start position:0% +one all the way to the end of the three + + + align:start position:0% +one all the way to the end of the three +hours then you go to the second part + + align:start position:0% +hours then you go to the second part + + + align:start position:0% +hours then you go to the second part +probably the flute and you go all the + + align:start position:0% +probably the flute and you go all the + + + align:start position:0% +probably the flute and you go all the +way from one to the end and so on and so + + align:start position:0% +way from one to the end and so on and so + + + align:start position:0% +way from one to the end and so on and so +you have everything in one part from the + + align:start position:0% +you have everything in one part from the + + + align:start position:0% +you have everything in one part from the +beginning to the end and it makes it + + align:start position:0% +beginning to the end and it makes it + + + align:start position:0% +beginning to the end and it makes it +very easy to do the kinds of analysis + + align:start position:0% +very easy to do the kinds of analysis + + + align:start position:0% +very easy to do the kinds of analysis +that look at what happens in the + + align:start position:0% +that look at what happens in the + + + align:start position:0% +that look at what happens in the +part the other principal way of looking + + align:start position:0% +part the other principal way of looking + + + align:start position:0% +part the other principal way of looking +at musical notation representation is + + align:start position:0% +at musical notation representation is + + + align:start position:0% +at musical notation representation is +you have a score and within that you + + align:start position:0% +you have a score and within that you + + + align:start position:0% +you have a score and within that you +have all the things that happen at a + + align:start position:0% +have all the things that happen at a + + + align:start position:0% +have all the things that happen at a +certain moment so that be getting you + + align:start position:0% +certain moment so that be getting you + + + align:start position:0% +certain moment so that be getting you +know you might say well there's all the + + align:start position:0% +know you might say well there's all the + + + align:start position:0% +know you might say well there's all the +clubs and if it's a 10 bar score you + + align:start position:0% +clubs and if it's a 10 bar score you + + + align:start position:0% +clubs and if it's a 10 bar score you +might have trouble trouble trouble + + align:start position:0% +might have trouble trouble trouble + + + align:start position:0% +might have trouble trouble trouble +trouble trouble Alto base base Bas base + + align:start position:0% +trouble trouble Alto base base Bas base + + + align:start position:0% +trouble trouble Alto base base Bas base +Bas so on and then you have all the time + + align:start position:0% +Bas so on and then you have all the time + + + align:start position:0% +Bas so on and then you have all the time +signature key signatures all the time + + align:start position:0% +signature key signatures all the time + + + align:start position:0% +signature key signatures all the time +signatures and then every note + + align:start position:0% +signatures and then every note + + + align:start position:0% +signatures and then every note +everything that happens at the beginning + + align:start position:0% +everything that happens at the beginning + + + align:start position:0% +everything that happens at the beginning +of the + + align:start position:0% +of the + + + align:start position:0% +of the +piece and then you have everything that + + align:start position:0% +piece and then you have everything that + + + align:start position:0% +piece and then you have everything that +happens at the next instant the next + + align:start position:0% +happens at the next instant the next + + + align:start position:0% +happens at the next instant the next +time that something happens here + + align:start position:0% +time that something happens here + + + align:start position:0% +time that something happens here +and in this particular case when we get + + align:start position:0% +and in this particular case when we get + + + align:start position:0% +and in this particular case when we get +to the third instant um which is the E + + align:start position:0% +to the third instant um which is the E + + + align:start position:0% +to the third instant um which is the E +quarter note in the base and then the c + + align:start position:0% +quarter note in the base and then the c + + + align:start position:0% +quarter note in the base and then the c +u the C eighth note in the E there there + + align:start position:0% +u the C eighth note in the E there there + + + align:start position:0% +u the C eighth note in the E there there +is something that's happening in the top + + align:start position:0% +is something that's happening in the top + + + align:start position:0% +is something that's happening in the top +part that that g half note that is not + + align:start position:0% +part that that g half note that is not + + + align:start position:0% +part that that g half note that is not +represented in that instant but is + + align:start position:0% +represented in that instant but is + + + align:start position:0% +represented in that instant but is +thought to be continuing from before and + + align:start position:0% +thought to be continuing from before and + + + align:start position:0% +thought to be continuing from before and +in the next instant the there was just a + + align:start position:0% +in the next instant the there was just a + + + align:start position:0% +in the next instant the there was just a +an eighth note with nothing else + + align:start position:0% +an eighth note with nothing else + + + align:start position:0% +an eighth note with nothing else +happening and so this makes it very nice + + align:start position:0% +happening and so this makes it very nice + + + align:start position:0% +happening and so this makes it very nice +to see what's happening at every attack + + align:start position:0% +to see what's happening at every attack + + + align:start position:0% +to see what's happening at every attack +and you might be able to + + align:start position:0% +and you might be able to + + + align:start position:0% +and you might be able to +programmatically go back and see what's + + align:start position:0% +programmatically go back and see what's + + + align:start position:0% +programmatically go back and see what's +happening at every instant but it makes + + align:start position:0% +happening at every instant but it makes + + + align:start position:0% +happening at every instant but it makes +it very hard instead to figure out + + align:start position:0% +it very hard instead to figure out + + + align:start position:0% +it very hard instead to figure out +what's happening from one uh beginning + + align:start position:0% +what's happening from one uh beginning + + + align:start position:0% +what's happening from one uh beginning +of the score to the + + align:start position:0% +of the score to the + + + align:start position:0% +of the score to the +End by the way we call these instance uh + + align:start position:0% +End by the way we call these instance uh + + + align:start position:0% +End by the way we call these instance uh +instance or uh offset moments or you + + align:start position:0% +instance or uh offset moments or you + + + align:start position:0% +instance or uh offset moments or you +know cuts through hierarchies generally + + align:start position:0% +know cuts through hierarchies generally + + + align:start position:0% +know cuts through hierarchies generally +speaking but often we Cally call these + + align:start position:0% +speaking but often we Cally call these + + + align:start position:0% +speaking but often we Cally call these +salami slices in the process of creating + + align:start position:0% +salami slices in the process of creating + + + align:start position:0% +salami slices in the process of creating +these things salami + + align:start position:0% +these things salami + + + align:start position:0% +these things salami +slicing it's just kind of something + + align:start position:0% +slicing it's just kind of something + + + align:start position:0% +slicing it's just kind of something +that's come out in music 21 we call this + + align:start position:0% +that's come out in music 21 we call this + + + align:start position:0% +that's come out in music 21 we call this +process codification and so you'll see + + align:start position:0% +process codification and so you'll see + + + align:start position:0% +process codification and so you'll see +the cify happens a lot so which is + + align:start position:0% +the cify happens a lot so which is + + + align:start position:0% +the cify happens a lot so which is +better part-based containers or time + + align:start position:0% +better part-based containers or time + + + align:start position:0% +better part-based containers or time +based + + align:start position:0% +based + + + align:start position:0% +based +containers each of these formats has + + align:start position:0% +containers each of these formats has + + + align:start position:0% +containers each of these formats has +their own POS positive things and + + align:start position:0% +their own POS positive things and + + + align:start position:0% +their own POS positive things and +drawbacks as I said part-based + + align:start position:0% +drawbacks as I said part-based + + + align:start position:0% +drawbacks as I said part-based +containers make it very easy for us to + + align:start position:0% +containers make it very easy for us to + + + align:start position:0% +containers make it very easy for us to +follow an entire part from beginning to + + align:start position:0% +follow an entire part from beginning to + + + align:start position:0% +follow an entire part from beginning to +end an entire line from beginning to end + + align:start position:0% +end an entire line from beginning to end + + + align:start position:0% +end an entire line from beginning to end +time based containers let us see what + + align:start position:0% +time based containers let us see what + + + align:start position:0% +time based containers let us see what +chords are happening in a certain moment + + align:start position:0% +chords are happening in a certain moment + + + align:start position:0% +chords are happening in a certain moment +but very hard to follow + + align:start position:0% +but very hard to follow + + + align:start position:0% +but very hard to follow +Melody but each of them has certain uh + + align:start position:0% +Melody but each of them has certain uh + + + align:start position:0% +Melody but each of them has certain uh +certain difficult to encode things for + + align:start position:0% +certain difficult to encode things for + + + align:start position:0% +certain difficult to encode things for +instance in alia staff uh a staff where + + align:start position:0% +instance in alia staff uh a staff where + + + align:start position:0% +instance in alia staff uh a staff where +something uh optional is happening or or + + align:start position:0% +something uh optional is happening or or + + + align:start position:0% +something uh optional is happening or or +you can do this instead of something + + align:start position:0% +you can do this instead of something + + + align:start position:0% +you can do this instead of something +else what part is that in how do you + + align:start position:0% +else what part is that in how do you + + + align:start position:0% +else what part is that in how do you +encode that uh do you put a part with + + align:start position:0% +encode that uh do you put a part with + + + align:start position:0% +encode that uh do you put a part with +hidden measures all the way up to this + + align:start position:0% +hidden measures all the way up to this + + + align:start position:0% +hidden measures all the way up to this +moment and hidden measures all the way + + align:start position:0% +moment and hidden measures all the way + + + align:start position:0% +moment and hidden measures all the way +to the end and how do we indicate that + + align:start position:0% +to the end and how do we indicate that + + + align:start position:0% +to the end and how do we indicate that +the player could do this so this is + + align:start position:0% +the player could do this so this is + + + align:start position:0% +the player could do this so this is +something that's very hard to encode + + align:start position:0% +something that's very hard to encode + + + align:start position:0% +something that's very hard to encode +when we do part-based representations so + + align:start position:0% +when we do part-based representations so + + + align:start position:0% +when we do part-based representations so +instead let's move to time based + + align:start position:0% +instead let's move to time based + + + align:start position:0% +instead let's move to time based +representations because it doesn't have + + align:start position:0% +representations because it doesn't have + + + align:start position:0% +representations because it doesn't have +this they don't have this problem but + + align:start position:0% +this they don't have this problem but + + + align:start position:0% +this they don't have this problem but +instead they have other problems where + + align:start position:0% +instead they have other problems where + + + align:start position:0% +instead they have other problems where +do we put these Grace notes uh in you + + align:start position:0% +do we put these Grace notes uh in you + + + align:start position:0% +do we put these Grace notes uh in you +know in in encoding like this especially + + align:start position:0% +know in in encoding like this especially + + + align:start position:0% +know in in encoding like this especially +when you know we know that not all five + + align:start position:0% +when you know we know that not all five + + + align:start position:0% +when you know we know that not all five +of those Grace notes come after that + + align:start position:0% +of those Grace notes come after that + + + align:start position:0% +of those Grace notes come after that +last let's assum it's trouble in base + + align:start position:0% +last let's assum it's trouble in base + + + align:start position:0% +last let's assum it's trouble in base +Club after that last B of the sub tuplet + + align:start position:0% +Club after that last B of the sub tuplet + + + align:start position:0% +Club after that last B of the sub tuplet +within the triplet you know where do we + + align:start position:0% +within the triplet you know where do we + + + align:start position:0% +within the triplet you know where do we +go how do we encode Grace notes do they + + align:start position:0% +go how do we encode Grace notes do they + + + align:start position:0% +go how do we encode Grace notes do they +attach to the note next to them or or + + align:start position:0% +attach to the note next to them or or + + + align:start position:0% +attach to the note next to them or or +what and both of the representations + + align:start position:0% +what and both of the representations + + + align:start position:0% +what and both of the representations +have maj problems when we want to look + + align:start position:0% +have maj problems when we want to look + + + align:start position:0% +have maj problems when we want to look +at things that involve horizontal and + + align:start position:0% +at things that involve horizontal and + + + align:start position:0% +at things that involve horizontal and +vertical at the same time things like + + align:start position:0% +vertical at the same time things like + + + align:start position:0% +vertical at the same time things like +voice leading here's a common uh voice + + align:start position:0% +voice leading here's a common uh voice + + + align:start position:0% +voice leading here's a common uh voice +leading error in uh in sort of very + + align:start position:0% +leading error in uh in sort of very + + + align:start position:0% +leading error in uh in sort of very +strict traditional uh harmonic writing + + align:start position:0% +strict traditional uh harmonic writing + + + align:start position:0% +strict traditional uh harmonic writing +where we have um and we have a overlap + + align:start position:0% +where we have um and we have a overlap + + + align:start position:0% +where we have um and we have a overlap +where the low G crosses the boundary + + align:start position:0% +where the low G crosses the boundary + + + align:start position:0% +where the low G crosses the boundary +established by the B before and goes up + + align:start position:0% +established by the B before and goes up + + + align:start position:0% +established by the B before and goes up +to the C above it which form format + + align:start position:0% +to the C above it which form format + + + align:start position:0% +to the C above it which form format +makes this possible to see if you're + + align:start position:0% +makes this possible to see if you're + + + align:start position:0% +makes this possible to see if you're +just look at each part alone you see + + align:start position:0% +just look at each part alone you see + + + align:start position:0% +just look at each part alone you see +okay there's a b going to an E then we + + align:start position:0% +okay there's a b going to an E then we + + + align:start position:0% +okay there's a b going to an E then we +get to the next part there's a g going + + align:start position:0% +get to the next part there's a g going + + + align:start position:0% +get to the next part there's a g going +to a c but you don't see that the G + + align:start position:0% +to a c but you don't see that the G + + + align:start position:0% +to a c but you don't see that the G +Going to the C overlap the B going to an + + align:start position:0% +Going to the C overlap the B going to an + + + align:start position:0% +Going to the C overlap the B going to an +e on the other hand if we look at it in + + align:start position:0% +e on the other hand if we look at it in + + + align:start position:0% +e on the other hand if we look at it in +time based we have a g and a b and we + + align:start position:0% +time based we have a g and a b and we + + + align:start position:0% +time based we have a g and a b and we +look at that then the next part we see + + align:start position:0% +look at that then the next part we see + + + align:start position:0% +look at that then the next part we see +there's a c and an e but it's hard to + + align:start position:0% +there's a c and an e but it's hard to + + + align:start position:0% +there's a c and an e but it's hard to +tell well did the G go to the C did the + + align:start position:0% +tell well did the G go to the C did the + + + align:start position:0% +tell well did the G go to the C did the +G go to the E did the you what what + + align:start position:0% +G go to the E did the you what what + + + align:start position:0% +G go to the E did the you what what +happened how's the voice leading happen + + align:start position:0% +happened how's the voice leading happen + + + align:start position:0% +happened how's the voice leading happen +so these are the problems in musical + + align:start position:0% +so these are the problems in musical + + + align:start position:0% +so these are the problems in musical +representations and we'll quite often + + align:start position:0% +representations and we'll quite often + + + align:start position:0% +representations and we'll quite often +find that we have to convert from + + align:start position:0% +find that we have to convert from + + + align:start position:0% +find that we have to convert from +part-based representation to time based + + align:start position:0% +part-based representation to time based + + + align:start position:0% +part-based representation to time based +representation and back or in the case + + align:start position:0% +representation and back or in the case + + + align:start position:0% +representation and back or in the case +of a voice leading moment we have to + + align:start position:0% +of a voice leading moment we have to + + + align:start position:0% +of a voice leading moment we have to +keep both the part and the time based + + align:start position:0% +keep both the part and the time based + + + align:start position:0% +keep both the part and the time based +representations in in our head in the + + align:start position:0% +representations in in our head in the + + + align:start position:0% +representations in in our head in the +musical memory in the representation at + + align:start position:0% +musical memory in the representation at + + + align:start position:0% +musical memory in the representation at +the same time in order to find these + + align:start position:0% +the same time in order to find these + + + align:start position:0% +the same time in order to find these +things I find these problems really cool + + align:start position:0% +things I find these problems really cool + + + align:start position:0% +things I find these problems really cool +and hope you guys do too and solving + + align:start position:0% +and hope you guys do too and solving + + + align:start position:0% +and hope you guys do too and solving +them is is another one of the great + + align:start position:0% +them is is another one of the great + + + align:start position:0% +them is is another one of the great +choice of this class \ No newline at end of file diff --git a/4fTOrb1yBFU.txt b/4fTOrb1yBFU.txt new file mode 100644 index 0000000000000000000000000000000000000000..f9983d45be05786a7efada6284db61dd985615bb --- /dev/null +++ b/4fTOrb1yBFU.txt @@ -0,0 +1,202 @@ +Now let's think a bit about what happens if +there's an error and one or more of the bits + +in our encoded data gets corrupted. + +We'll focus on single-bit errors, but much +of what we discuss can be generalized to multi-bit + +errors. + +For example, consider encoding the results +of some unpredictable event, e.g., flipping + +a fair coin. + +There are two outcomes: "heads", encoded as, +say, 0, and "tails" encoded as 1. + +Now suppose some error occurs during processing +- for example, the data is corrupted while + +being transmitted from Bob to Alice: +Bob intended to send the message "heads", + +but the 0 was corrupted and become a 1 during +transmission, so Alice receives 1, which she + +interprets as "tails". + +So this simple encoding doesn't work very +well if there's the possibility of single-bit + +errors. + +To help with our discussion, we'll introduce +the notion of "Hamming distance", defined + +as the number of positions in which the corresponding +digits differ in two encodings of the same + +length. + +For example, here are two 7-bit encodings, +which differ in their third and fifth positions, + +so the Hamming distance between the encodings +is 2. + +If someone tells us the Hamming distance of +two encodings is 0, then the two encodings + +are identical. + +Hamming distance is a handy tool for measuring +how encodings differ. + +How does this help us think about single-bit +errors? + +A single-bit error changes exactly one of +the bits of an encoding, so the Hamming distance + +between a valid binary code word and the same +code word with a single-bit error is 1. + +The difficulty with our simple encoding is +that the two valid code words ("0" and "1") + +also have a Hamming distance of 1. + +So a single-bit error changes one valid code +word into another valid code word. + +We'll show this graphically, using an arrow +to indicate that two encodings differ by a + +single bit, i.e., that the Hamming distance +between the encodings is 1. + +The real issue here is that when Alice receives +a 1, she can't distinguish between an uncorrupted + +encoding of tails and a corrupted encoding +of heads - she can't detect that an error + +occurred. + +Let's figure how to solve her problem! + +The insight is to come up with a set of valid +code words such that a single-bit error does + +NOT produce another valid code word. + +What we need are code words that differ by +at least two bits, i.e., we want the minimum + +Hamming distance between any two code words +to be at least 2. + +If we have a set of code words where the minimum +Hamming distance is 1, we can generate the + +set we want by adding a parity bit to each +of the original code words. + +There's "even parity" and "odd parity." + +Using even parity, the additional parity bit +is chosen so that the total number of 1 bits + +in the new code word are even. + +For example, our original encoding for "heads" +was 0, adding an even parity bit gives us + +00. + +Adding an even parity bit to our original +encoding for "tails" gives us 11. + +The minimum Hamming distance between code +words has increased from 1 to 2. + +How does this help? + +Consider what happens when there's a single-bit +error: 00 would be corrupted to 01 or 10, + +neither of which is a valid code word. + +Aha! + +We can detect that a single-bit error has +occurred. + +Similarly, single-bit errors for 11 would +also be detected. + +Note that the valid code words 00 and 11 both +have an even number of 1-bits, but that the + +corrupted code words 01 or 10 have an odd +number of 1-bits. + +We say that corrupted code words have a "parity +error". + +It's easy to perform a parity check: simply +count the number of 1s in the code word. + +If it's even, a single-bit error has NOT occurred; +if it's odd, a single-bit error HAS occurred. + +We'll see in a couple of chapters that the +Boolean function exclusive-or can be used + +to perform parity checks. + +Note that parity won't help us if there's +an even number of bit errors, where a corrupted + +code word would have an even number of 1-bits +and hence appear to be okay. + +Parity is useful for detecting single-bit +errors; we'll need a more sophisticated encoding + +to detect more errors. + +In general, to detect some number E of errors, +we need a minimum Hamming distance of E+1 + +between code words. + +We can see this graphically below which shows +how errors can corrupt the valid code words + +000 and 111, which have a Hamming distance +of 3. + +In theory this means we should be able to +detect up to 2-bit errors. + +Each arrow represents a single-bit error and +we can see from the diagram that following + +any path of length 2 from either 000 or 111 +doesn't get us to the other valid code word. + +In other words, assuming we start with either +000 or 111, we can detect the occurrence of + +up to 2 errors. + +Basically our error detection scheme relies +on choosing code words far enough apart, as + +measured by Hamming distance, so that E errors +can't corrupt one valid code word so that + +it looks like another valid code word. \ No newline at end of file diff --git a/4i9jRsZlqUs.txt b/4i9jRsZlqUs.txt new file mode 100644 index 0000000000000000000000000000000000000000..52cebe9612186537f6a09a64da45d5a5c8230445 --- /dev/null +++ b/4i9jRsZlqUs.txt @@ -0,0 +1,12883 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following content is provided by MIT +open courseware under a Creative Commons + + align:start position:0% +open courseware under a Creative Commons + + + align:start position:0% +open courseware under a Creative Commons +license additional information about our + + align:start position:0% +license additional information about our + + + align:start position:0% +license additional information about our +license and MIT open courseware in + + align:start position:0% +license and MIT open courseware in + + + align:start position:0% +license and MIT open courseware in +general is available at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu in in the last lecture I was + + align:start position:0% +ocw.mit.edu in in the last lecture I was + + + align:start position:0% +ocw.mit.edu in in the last lecture I was +talking about the fact + + align:start position:0% +talking about the fact + + + align:start position:0% +talking about the fact +that people + + align:start position:0% +that people + + + align:start position:0% +that people +um kids go through roughly the Stag of + + align:start position:0% +um kids go through roughly the Stag of + + + align:start position:0% +um kids go through roughly the Stag of +language development they go through the + + align:start position:0% +language development they go through the + + + align:start position:0% +language development they go through the +same set of language developments stages + + align:start position:0% +same set of language developments stages + + + align:start position:0% +same set of language developments stages +o did it + + align:start position:0% +o did it + + + align:start position:0% +o did it +stop + + align:start position:0% +stop + + + align:start position:0% +stop +no + + align:start position:0% +no + + + align:start position:0% +no +um a babbling sort of preverbal stage + + align:start position:0% +um a babbling sort of preverbal stage + + + align:start position:0% +um a babbling sort of preverbal stage +one word two word and then more than uh + + align:start position:0% +one word two word and then more than uh + + + align:start position:0% +one word two word and then more than uh +two word stages and uh the question + + align:start position:0% +two word stages and uh the question + + + align:start position:0% +two word stages and uh the question +we're left with at the moment is well + + align:start position:0% +we're left with at the moment is well + + + align:start position:0% +we're left with at the moment is well +what is it that they're actually + + align:start position:0% +what is it that they're actually + + + align:start position:0% +what is it that they're actually +learning when they're learning language + + align:start position:0% +learning when they're learning language + + + align:start position:0% +learning when they're learning language +there's lots of stuff that they're + + align:start position:0% +there's lots of stuff that they're + + + align:start position:0% +there's lots of stuff that they're +that's got to be learned one of the + + align:start position:0% +that's got to be learned one of the + + + align:start position:0% +that's got to be learned one of the +things that I saw in the handout + + align:start position:0% +things that I saw in the handout + + + align:start position:0% +things that I saw in the handout +somewhere there as I recall is they got + + align:start position:0% +somewhere there as I recall is they got + + + align:start position:0% +somewhere there as I recall is they got +to do a remarkable job of learning words + + align:start position:0% +to do a remarkable job of learning words + + + align:start position:0% +to do a remarkable job of learning words +and word meaning between about a year + + align:start position:0% +and word meaning between about a year + + + align:start position:0% +and word meaning between about a year +and a half and six years of age in order + + align:start position:0% +and a half and six years of age in order + + + align:start position:0% +and a half and six years of age in order +to explain what the + + align:start position:0% +to explain what the + + + align:start position:0% +to explain what the +um uh in order to account for the + + align:start position:0% +um uh in order to account for the + + + align:start position:0% +um uh in order to account for the +vocabulary that a six-year-old has you + + align:start position:0% +vocabulary that a six-year-old has you + + + align:start position:0% +vocabulary that a six-year-old has you +have to assume that children are + + align:start position:0% +have to assume that children are + + + align:start position:0% +have to assume that children are +learning five to 10 words a day every + + align:start position:0% +learning five to 10 words a day every + + + align:start position:0% +learning five to 10 words a day every +day so you know that that that's that's + + align:start position:0% +day so you know that that that's that's + + + align:start position:0% +day so you know that that that's that's +a rate sort of approaching a + + align:start position:0% +a rate sort of approaching a + + + align:start position:0% +a rate sort of approaching a +word a word an hour or so and they're + + align:start position:0% +word a word an hour or so and they're + + + align:start position:0% +word a word an hour or so and they're +not doing it in school right it's not + + align:start position:0% +not doing it in school right it's not + + + align:start position:0% +not doing it in school right it's not +that they're going to school and every + + align:start position:0% +that they're going to school and every + + + align:start position:0% +that they're going to school and every +day they're being handed long vocabulary + + align:start position:0% +day they're being handed long vocabulary + + + align:start position:0% +day they're being handed long vocabulary +list they're just picking this stuff up + + align:start position:0% +list they're just picking this stuff up + + + align:start position:0% +list they're just picking this stuff up +it's it's an amazing um and not trivial + + align:start position:0% +it's it's an amazing um and not trivial + + + align:start position:0% +it's it's an amazing um and not trivial +feat for figuring out how you do that + + align:start position:0% +feat for figuring out how you do that + + + align:start position:0% +feat for figuring out how you do that +you know + + align:start position:0% +you know + + + align:start position:0% +you know +you um somebody says oh oh look there's + + align:start position:0% +you um somebody says oh oh look there's + + + align:start position:0% +you um somebody says oh oh look there's +the + + align:start position:0% +the + + + align:start position:0% +the +chalk and the kid not only has to learn + + align:start position:0% +chalk and the kid not only has to learn + + + align:start position:0% +chalk and the kid not only has to learn +this new word chalk but has to figure + + align:start position:0% +this new word chalk but has to figure + + + align:start position:0% +this new word chalk but has to figure +out that it somehow refers to um you + + align:start position:0% +out that it somehow refers to um you + + + align:start position:0% +out that it somehow refers to um you +know this box of stuff and not to the + + align:start position:0% +know this box of stuff and not to the + + + align:start position:0% +know this box of stuff and not to the +color yellow or to the letter c or to um + + align:start position:0% +color yellow or to the letter c or to um + + + align:start position:0% +color yellow or to the letter c or to um +the uh uh you know small boxes when Bush + + align:start position:0% +the uh uh you know small boxes when Bush + + + align:start position:0% +the uh uh you know small boxes when Bush +is president or any of a vast number of + + align:start position:0% +is president or any of a vast number of + + + align:start position:0% +is president or any of a vast number of +other possibilities it's a very daunting + + align:start position:0% +other possibilities it's a very daunting + + + align:start position:0% +other possibilities it's a very daunting +problem I'm going to focus rather um + + align:start position:0% +problem I'm going to focus rather um + + + align:start position:0% +problem I'm going to focus rather um +than on the word meaning problem on a + + align:start position:0% +than on the word meaning problem on a + + + align:start position:0% +than on the word meaning problem on a +different problem um which is the + + align:start position:0% +different problem um which is the + + + align:start position:0% +different problem um which is the +problem of learning uh grammar and that + + align:start position:0% +problem of learning uh grammar and that + + + align:start position:0% +problem of learning uh grammar and that +is is uh there there are sort of two + + align:start position:0% +is is uh there there are sort of two + + + align:start position:0% +is is uh there there are sort of two +large scale classes of theory that I + + align:start position:0% +large scale classes of theory that I + + + align:start position:0% +large scale classes of theory that I +have uh Cartoon I cartooned them on the + + align:start position:0% +have uh Cartoon I cartooned them on the + + + align:start position:0% +have uh Cartoon I cartooned them on the +board and describe them on the + + align:start position:0% +board and describe them on the + + + align:start position:0% +board and describe them on the +um on the handout as the East Coast View + + align:start position:0% +um on the handout as the East Coast View + + + align:start position:0% +um on the handout as the East Coast View +and the West Coast view um this this is + + align:start position:0% +and the West Coast view um this this is + + + align:start position:0% +and the West Coast view um this this is +uh the East Coast view could really be + + align:start position:0% +uh the East Coast view could really be + + + align:start position:0% +uh the East Coast view could really be +called the MIT view originally it really + + align:start position:0% +called the MIT view originally it really + + + align:start position:0% +called the MIT view originally it really +starts with people like Chomsky here and + + align:start position:0% +starts with people like Chomsky here and + + + align:start position:0% +starts with people like Chomsky here and +and is uh nicely wrapped up in Steve + + align:start position:0% +and is uh nicely wrapped up in Steve + + + align:start position:0% +and is uh nicely wrapped up in Steve +pinker's book called The Language + + align:start position:0% +pinker's book called The Language + + + align:start position:0% +pinker's book called The Language +instinct which if you turn out to be + + align:start position:0% +instinct which if you turn out to be + + + align:start position:0% +instinct which if you turn out to be +interested in the topic of language and + + align:start position:0% +interested in the topic of language and + + + align:start position:0% +interested in the topic of language and +language learning I strongly recommend + + align:start position:0% +language learning I strongly recommend + + + align:start position:0% +language learning I strongly recommend +you read it among other things Pinker is + + align:start position:0% +you read it among other things Pinker is + + + align:start position:0% +you read it among other things Pinker is +one of the better writers in our field + + align:start position:0% +one of the better writers in our field + + + align:start position:0% +one of the better writers in our field +and uh it's a it's a good read um the uh + + align:start position:0% +and uh it's a it's a good read um the uh + + + align:start position:0% +and uh it's a it's a good read um the uh +and and and the West Coast view was a a + + align:start position:0% +and and and the West Coast view was a a + + + align:start position:0% +and and and the West Coast view was a a +view held by oh people like Mark + + align:start position:0% +view held by oh people like Mark + + + align:start position:0% +view held by oh people like Mark +Seidenberg at at UCLA well Mark + + align:start position:0% +Seidenberg at at UCLA well Mark + + + align:start position:0% +Seidenberg at at UCLA well Mark +Seidenberg is now at Minnesota so this + + align:start position:0% +Seidenberg is now at Minnesota so this + + + align:start position:0% +Seidenberg is now at Minnesota so this +ge geographical thing doesn't work so + + align:start position:0% +ge geographical thing doesn't work so + + + align:start position:0% +ge geographical thing doesn't work so +well anymore um but here's here's the + + align:start position:0% +well anymore um but here's here's the + + + align:start position:0% +well anymore um but here's here's the +distinction the the notion the the East + + align:start position:0% +distinction the the notion the the East + + + align:start position:0% +distinction the the notion the the East +Coast guys so so let's start with a + + align:start position:0% +Coast guys so so let's start with a + + + align:start position:0% +Coast guys so so let's start with a +specific problem specific problem might + + align:start position:0% +specific problem specific problem might + + + align:start position:0% +specific problem specific problem might +be something like how do you well as it + + align:start position:0% +be something like how do you well as it + + + align:start position:0% +be something like how do you well as it +says on the handout how do you make the + + align:start position:0% +says on the handout how do you make the + + + align:start position:0% +says on the handout how do you make the +past tense in uh in in English um I mean + + align:start position:0% +past tense in uh in in English um I mean + + + align:start position:0% +past tense in uh in in English um I mean +you'd obviously have to learn how to + + align:start position:0% +you'd obviously have to learn how to + + + align:start position:0% +you'd obviously have to learn how to +make the past tense in some other + + align:start position:0% +make the past tense in some other + + + align:start position:0% +make the past tense in some other +language if you were going to learn + + align:start position:0% +language if you were going to learn + + + align:start position:0% +language if you were going to learn +learn yourself some other language um + + align:start position:0% +learn yourself some other language um + + + align:start position:0% +learn yourself some other language um +but uh I walk to the store yet yesterday + + align:start position:0% +but uh I walk to the store yet yesterday + + + align:start position:0% +but uh I walk to the store yet yesterday +I did + + align:start position:0% +I did + + + align:start position:0% +I did +what I I I I walked to the store okay um + + align:start position:0% +what I I I I walked to the store okay um + + + align:start position:0% +what I I I I walked to the store okay um +uh today I plan uh to uh I don't know I + + align:start position:0% +uh today I plan uh to uh I don't know I + + + align:start position:0% +uh today I plan uh to uh I don't know I +plan to go to the airport actually right + + align:start position:0% +plan to go to the airport actually right + + + align:start position:0% +plan to go to the airport actually right +after this lecture um yesterday I did + + align:start position:0% +after this lecture um yesterday I did + + + align:start position:0% +after this lecture um yesterday I did +what all right okay so how do we uh how + + align:start position:0% +what all right okay so how do we uh how + + + align:start position:0% +what all right okay so how do we uh how +do we go and make the past tense in + + align:start position:0% + + + + align:start position:0% + +English + + align:start position:0% +English + + + align:start position:0% +English +huh yeah I stick an ed on things most of + + align:start position:0% +huh yeah I stick an ed on things most of + + + align:start position:0% +huh yeah I stick an ed on things most of +the time um except uh today I'm going to + + align:start position:0% +the time um except uh today I'm going to + + + align:start position:0% +the time um except uh today I'm going to +sing yesterday I I didn't singed and uh + + align:start position:0% +sing yesterday I I didn't singed and uh + + + align:start position:0% +sing yesterday I I didn't singed and uh +today we ring the bell + + align:start position:0% +today we ring the bell + + + align:start position:0% +today we ring the bell +yesterday we rang the bell or we rung + + align:start position:0% +yesterday we rang the bell or we rung + + + align:start position:0% +yesterday we rang the bell or we rung +the no we didn't rung the Bell + + align:start position:0% +the no we didn't rung the Bell + + + align:start position:0% +the no we didn't rung the Bell +yesterday the Bell was rung yesterday + + align:start position:0% +yesterday the Bell was rung yesterday + + + align:start position:0% +yesterday the Bell was rung yesterday +but we rang it yesterday anyway it gets + + align:start position:0% +but we rang it yesterday anyway it gets + + + align:start position:0% +but we rang it yesterday anyway it gets +complicated and uh + + align:start position:0% +complicated and uh + + + align:start position:0% +complicated and uh +today um I bring you all this + + align:start position:0% +today um I bring you all this + + + align:start position:0% +today um I bring you all this +information about language yesterday I + + align:start position:0% +information about language yesterday I + + + align:start position:0% +information about language yesterday I +brought it's not even brang so it's a + + align:start position:0% +brought it's not even brang so it's a + + + align:start position:0% +brought it's not even brang so it's a +rule there's a sort of a sub Sing sang + + align:start position:0% +rule there's a sort of a sub Sing sang + + + align:start position:0% +rule there's a sort of a sub Sing sang +kind of rule there's a bring brang brang + + align:start position:0% +kind of rule there's a bring brang brang + + + align:start position:0% +kind of rule there's a bring brang brang +no brang doesn't work brought um so you + + align:start position:0% +no brang doesn't work brought um so you + + + align:start position:0% +no brang doesn't work brought um so you +you have to learn uh well so kids behave + + align:start position:0% +you have to learn uh well so kids behave + + + align:start position:0% +you have to learn uh well so kids behave +as though they have learned a rule and a + + align:start position:0% +as though they have learned a rule and a + + + align:start position:0% +as though they have learned a rule and a +set of exceptions the East Coast view of + + align:start position:0% +set of exceptions the East Coast view of + + + align:start position:0% +set of exceptions the East Coast view of +this is that they really have learned a + + align:start position:0% +this is that they really have learned a + + + align:start position:0% +this is that they really have learned a +rule that somewhere + + align:start position:0% +rule that somewhere + + + align:start position:0% +rule that somewhere +uh deep in their little brains it you + + align:start position:0% +uh deep in their little brains it you + + + align:start position:0% +uh deep in their little brains it you +could hypothetically go in and find the + + align:start position:0% +could hypothetically go in and find the + + + align:start position:0% +could hypothetically go in and find the +rule that it is that it is written um in + + align:start position:0% +rule that it is that it is written um in + + + align:start position:0% +rule that it is that it is written um in +there one of the lines of evidence for + + align:start position:0% +there one of the lines of evidence for + + + align:start position:0% +there one of the lines of evidence for +this is that at a certain point during + + align:start position:0% +this is that at a certain point during + + + align:start position:0% +this is that at a certain point during +development as they're learning this + + align:start position:0% +development as they're learning this + + + align:start position:0% +development as they're learning this +they start to overuse the rule um and a + + align:start position:0% +they start to overuse the rule um and a + + + align:start position:0% +they start to overuse the rule um and a +child will uh say things like I goed to + + align:start position:0% +child will uh say things like I goed to + + + align:start position:0% +child will uh say things like I goed to +the store yet + + align:start position:0% +the store yet + + + align:start position:0% +the store yet +yesterday and um you know or or or or I + + align:start position:0% +yesterday and um you know or or or or I + + + align:start position:0% +yesterday and um you know or or or or I +bringed the ball home from school + + align:start position:0% +bringed the ball home from school + + + align:start position:0% +bringed the ball home from school +yesterday or something like that they'll + + align:start position:0% +yesterday or something like that they'll + + + align:start position:0% +yesterday or something like that they'll +start to overgeneralize they don't do it + + align:start position:0% +start to overgeneralize they don't do it + + + align:start position:0% +start to overgeneralize they don't do it +all the time but they start to behave as + + align:start position:0% +all the time but they start to behave as + + + align:start position:0% +all the time but they start to behave as +though they are saying aha got this verb + + align:start position:0% +though they are saying aha got this verb + + + align:start position:0% +though they are saying aha got this verb +here I know I need to make it into the + + align:start position:0% +here I know I need to make it into the + + + align:start position:0% +here I know I need to make it into the +past tense what's the rule for making + + align:start position:0% +past tense what's the rule for making + + + align:start position:0% +past tense what's the rule for making +the past tense um I I got to I I got to + + align:start position:0% +the past tense um I I got to I I got to + + + align:start position:0% +the past tense um I I got to I I got to +stick an ed on the end of it even though + + align:start position:0% +stick an ed on the end of it even though + + + align:start position:0% +stick an ed on the end of it even though +a few months earlier they might have + + align:start position:0% +a few months earlier they might have + + + align:start position:0% +a few months earlier they might have +successfully said when + + align:start position:0% +successfully said when + + + align:start position:0% +successfully said when +um it is as if they learn a rule and + + align:start position:0% +um it is as if they learn a rule and + + + align:start position:0% +um it is as if they learn a rule and +they learn a set of + + align:start position:0% +they learn a set of + + + align:start position:0% +they learn a set of +exceptions the job uh and and when you + + align:start position:0% +exceptions the job uh and and when you + + + align:start position:0% +exceptions the job uh and and when you +go in and look for what you're trying to + + align:start position:0% +go in and look for what you're trying to + + + align:start position:0% +go in and look for what you're trying to +say past tense of go if the past tense + + align:start position:0% +say past tense of go if the past tense + + + align:start position:0% +say past tense of go if the past tense +of go you know I went doesn't get there + + align:start position:0% +of go you know I went doesn't get there + + + align:start position:0% +of go you know I went doesn't get there +fast enough you default to the rule you + + align:start position:0% +fast enough you default to the rule you + + + align:start position:0% +fast enough you default to the rule you +say I I I goed + + align:start position:0% +say I I I goed + + + align:start position:0% +say I I I goed +um this + + align:start position:0% +um this + + + align:start position:0% +um this +assumes or this this assumes a certain + + align:start position:0% +assumes or this this assumes a certain + + + align:start position:0% +assumes or this this assumes a certain +amount of stuffff in the head ahead of + + align:start position:0% +amount of stuffff in the head ahead of + + + align:start position:0% +amount of stuffff in the head ahead of +time that's what this cartoon is about + + align:start position:0% +time that's what this cartoon is about + + + align:start position:0% +time that's what this cartoon is about +doesn't need to be + + align:start position:0% +doesn't need to be + + + align:start position:0% +doesn't need to be +uh doesn't need to be exactly this kind + + align:start position:0% +uh doesn't need to be exactly this kind + + + align:start position:0% +uh doesn't need to be exactly this kind +of stuff but this is the sort of stuff + + align:start position:0% +of stuff but this is the sort of stuff + + + align:start position:0% +of stuff but this is the sort of stuff +that you might have in the head um let + + align:start position:0% +that you might have in the head um let + + + align:start position:0% +that you might have in the head um let +let's let's think actually going back to + + align:start position:0% +let's let's think actually going back to + + + align:start position:0% +let's let's think actually going back to +the um lectures I was giving on + + align:start position:0% +the um lectures I was giving on + + + align:start position:0% +the um lectures I was giving on +cognitive development a couple last last + + align:start position:0% +cognitive development a couple last last + + + align:start position:0% +cognitive development a couple last last +week remember uh there's pretty good + + align:start position:0% +week remember uh there's pretty good + + + align:start position:0% +week remember uh there's pretty good +evidence that little kids have in their + + align:start position:0% +evidence that little kids have in their + + + align:start position:0% +evidence that little kids have in their +head an idea about objects they know + + align:start position:0% +head an idea about objects they know + + + align:start position:0% +head an idea about objects they know +there are such things about objects so + + align:start position:0% +there are such things about objects so + + + align:start position:0% +there are such things about objects so +oops I didn't put objects in + + align:start position:0% +oops I didn't put objects in + + + align:start position:0% +oops I didn't put objects in +here let's assume that there are such + + align:start position:0% +here let's assume that there are such + + + align:start position:0% +here let's assume that there are such +things as objects um well uh and and + + align:start position:0% +things as objects um well uh and and + + + align:start position:0% +things as objects um well uh and and +also we saw that little kids um know + + align:start position:0% +also we saw that little kids um know + + + align:start position:0% +also we saw that little kids um know +something about number like they can do + + align:start position:0% +something about number like they can do + + + align:start position:0% +something about number like they can do +that Karen wi Style baby math they know + + align:start position:0% +that Karen wi Style baby math they know + + + align:start position:0% +that Karen wi Style baby math they know +that there's um one and more than one + + align:start position:0% +that there's um one and more than one + + + align:start position:0% +that there's um one and more than one +certainly um and now let's assume that + + align:start position:0% +certainly um and now let's assume that + + + align:start position:0% +certainly um and now let's assume that +they've got some innate idea um that + + align:start position:0% +they've got some innate idea um that + + + align:start position:0% +they've got some innate idea um that +some innate capability to learn language + + align:start position:0% +some innate capability to learn language + + + align:start position:0% +some innate capability to learn language +well if I'm going to learn a language of + + align:start position:0% +well if I'm going to learn a language of + + + align:start position:0% +well if I'm going to learn a language of +any use it's going to have to be able to + + align:start position:0% +any use it's going to have to be able to + + + align:start position:0% +any use it's going to have to be able to +talk about these object things so I'm + + align:start position:0% +talk about these object things so I'm + + + align:start position:0% +talk about these object things so I'm +going to have some sort of innate idea + + align:start position:0% +going to have some sort of innate idea + + + align:start position:0% +going to have some sort of innate idea +that there will be nouns I don't know + + align:start position:0% +that there will be nouns I don't know + + + align:start position:0% +that there will be nouns I don't know +what the nouns are going to look like in + + align:start position:0% +what the nouns are going to look like in + + + align:start position:0% +what the nouns are going to look like in +this language but but but I come into + + align:start position:0% +this language but but but I come into + + + align:start position:0% +this language but but but I come into +the world in this view knowing that + + align:start position:0% +the world in this view knowing that + + + align:start position:0% +the world in this view knowing that +there have to be noun likee things not + + align:start position:0% +there have to be noun likee things not + + + align:start position:0% +there have to be noun likee things not +only that I know that there can be one + + align:start position:0% +only that I know that there can be one + + + align:start position:0% +only that I know that there can be one +thing and there can be more than one + + align:start position:0% +thing and there can be more than one + + + align:start position:0% +thing and there can be more than one +thing it therefore follows that I need + + align:start position:0% +thing it therefore follows that I need + + + align:start position:0% +thing it therefore follows that I need +to be able to talk about that too and so + + align:start position:0% +to be able to talk about that too and so + + + align:start position:0% +to be able to talk about that too and so +my job as a little + + align:start position:0% +my job as a little + + + align:start position:0% +my job as a little +language learner is to figure out what + + align:start position:0% +language learner is to figure out what + + + align:start position:0% +language learner is to figure out what +do the L nouns look like and and and how + + align:start position:0% +do the L nouns look like and and and how + + + align:start position:0% +do the L nouns look like and and and how +do I make those into + + align:start position:0% +do I make those into + + + align:start position:0% +do I make those into +plurals in in my + + align:start position:0% +plurals in in my + + + align:start position:0% +plurals in in my +language and what I will do I said + + align:start position:0% +language and what I will do I said + + + align:start position:0% +language and what I will do I said +there's a infinite number of ways in + + align:start position:0% +there's a infinite number of ways in + + + align:start position:0% +there's a infinite number of ways in +principle that I could designate a + + align:start position:0% +principle that I could designate a + + + align:start position:0% +principle that I could designate a +plural but I will learn that for the + + align:start position:0% +plural but I will learn that for the + + + align:start position:0% +plural but I will learn that for the +most part in English it's going to be + + align:start position:0% +most part in English it's going to be + + + align:start position:0% +most part in English it's going to be +add + + align:start position:0% +add + + + align:start position:0% +add +s right oh look there's the cat um oh + + align:start position:0% +s right oh look there's the cat um oh + + + align:start position:0% +s right oh look there's the cat um oh +look there are the cats and so on and + + align:start position:0% +look there are the cats and so on and + + + align:start position:0% +look there are the cats and so on and +I'm going to have to do the same thing + + align:start position:0% +I'm going to have to do the same thing + + + align:start position:0% +I'm going to have to do the same thing +as I was talking about in the past tense + + align:start position:0% +as I was talking about in the past tense + + + align:start position:0% +as I was talking about in the past tense +I'm going to have to learn there are are + + align:start position:0% +I'm going to have to learn there are are + + + align:start position:0% +I'm going to have to learn there are are +are exceptions yeah cat cats rat rats + + align:start position:0% +are exceptions yeah cat cats rat rats + + + align:start position:0% +are exceptions yeah cat cats rat rats +chair chairs + + align:start position:0% +chair chairs + + + align:start position:0% +chair chairs +Mouse mice fish for some reason fish is + + align:start position:0% +Mouse mice fish for some reason fish is + + + align:start position:0% +Mouse mice fish for some reason fish is +fish One Fish Two Fish Red Fish Blue + + align:start position:0% +fish One Fish Two Fish Red Fish Blue + + + align:start position:0% +fish One Fish Two Fish Red Fish Blue +Fish all that kind of stuff um so again + + align:start position:0% +Fish all that kind of stuff um so again + + + align:start position:0% +Fish all that kind of stuff um so again +I'll learn a rule I'll overgeneralize + + align:start position:0% +I'll learn a rule I'll overgeneralize + + + align:start position:0% +I'll learn a rule I'll overgeneralize +that rule when I get to be three or four + + align:start position:0% +that rule when I get to be three or four + + + align:start position:0% +that rule when I get to be three or four +years old um + + align:start position:0% +years old um + + + align:start position:0% +years old um +and I'll learn a set of + + align:start position:0% +and I'll learn a set of + + + align:start position:0% +and I'll learn a set of +exceptions and I will find uh when I + + align:start position:0% +exceptions and I will find uh when I + + + align:start position:0% +exceptions and I will find uh when I +become a a literature Professor later on + + align:start position:0% +become a a literature Professor later on + + + align:start position:0% +become a a literature Professor later on +and and and and study the history of of + + align:start position:0% +and and and and study the history of of + + + align:start position:0% +and and and and study the history of of +English literature that the that that + + align:start position:0% +English literature that the that that + + + align:start position:0% +English literature that the that that +that things shift over time things that + + align:start position:0% +that things shift over time things that + + + align:start position:0% +that things shift over time things that +were exceptions or things that were + + align:start position:0% +were exceptions or things that were + + + align:start position:0% +were exceptions or things that were +ungrammatical once upon a time might + + align:start position:0% +ungrammatical once upon a time might + + + align:start position:0% +ungrammatical once upon a time might +become grammatical it's it's a moving + + align:start position:0% +become grammatical it's it's a moving + + + align:start position:0% +become grammatical it's it's a moving +it's a moving target language you have + + align:start position:0% +it's a moving target language you have + + + align:start position:0% +it's a moving target language you have +to figure out what the current state of + + align:start position:0% +to figure out what the current state of + + + align:start position:0% +to figure out what the current state of +your + + align:start position:0% +your + + + align:start position:0% +your +language might be um the + + align:start position:0% +language might be um the + + + align:start position:0% +language might be um the +alternative is to say the West Coast + + align:start position:0% +alternative is to say the West Coast + + + align:start position:0% +alternative is to say the West Coast +view which is really a sort of a neural + + align:start position:0% +view which is really a sort of a neural + + + align:start position:0% +view which is really a sort of a neural +net parallel distributed processing kind + + align:start position:0% +net parallel distributed processing kind + + + align:start position:0% +net parallel distributed processing kind +of view is to say that we don't have to + + align:start position:0% +of view is to say that we don't have to + + + align:start position:0% +of view is to say that we don't have to +propose that there's all this stuff + + align:start position:0% +propose that there's all this stuff + + + align:start position:0% +propose that there's all this stuff +these these structures in the head in + + align:start position:0% +these these structures in the head in + + + align:start position:0% +these these structures in the head in +quite the same way what we can say is + + align:start position:0% +quite the same way what we can say is + + + align:start position:0% +quite the same way what we can say is +look there's this very powerful um + + align:start position:0% +look there's this very powerful um + + + align:start position:0% +look there's this very powerful um +Association Learner in here and + + align:start position:0% +Association Learner in here and + + + align:start position:0% +Association Learner in here and +statistic a device out there looking for + + align:start position:0% +statistic a device out there looking for + + + align:start position:0% +statistic a device out there looking for +statistical regularity there's evidence + + align:start position:0% +statistical regularity there's evidence + + + align:start position:0% +statistical regularity there's evidence +I think I mentioned last time that that + + align:start position:0% +I think I mentioned last time that that + + + align:start position:0% +I think I mentioned last time that that +little kids long before they can speak a + + align:start position:0% +little kids long before they can speak a + + + align:start position:0% +little kids long before they can speak a +language are already um sensitive to the + + align:start position:0% +language are already um sensitive to the + + + align:start position:0% +language are already um sensitive to the +statistical regularities of What + + align:start position:0% +statistical regularities of What + + + align:start position:0% +statistical regularities of What +syllables can follow what other + + align:start position:0% +syllables can follow what other + + + align:start position:0% +syllables can follow what other +syllables in um in the noises that they + + align:start position:0% +syllables in um in the noises that they + + + align:start position:0% +syllables in um in the noises that they +are are hearing so you've got this very + + align:start position:0% +are are hearing so you've got this very + + + align:start position:0% +are are hearing so you've got this very +powerful um statistical learning device + + align:start position:0% +powerful um statistical learning device + + + align:start position:0% +powerful um statistical learning device +in your head and it ends up behaving as + + align:start position:0% +in your head and it ends up behaving as + + + align:start position:0% +in your head and it ends up behaving as +if it had a rule but the rule is not um + + align:start position:0% +if it had a rule but the rule is not um + + + align:start position:0% +if it had a rule but the rule is not um +explicitly is is is not written out + + align:start position:0% +explicitly is is is not written out + + + align:start position:0% +explicitly is is is not written out +anywhere in in in brainware it's just + + align:start position:0% +anywhere in in in brainware it's just + + + align:start position:0% +anywhere in in in brainware it's just +the way the network behaves in the same + + align:start position:0% +the way the network behaves in the same + + + align:start position:0% +the way the network behaves in the same +way that um that this hunk of chalk + + align:start position:0% +way that um that this hunk of chalk + + + align:start position:0% +way that um that this hunk of chalk +where's somebody who looks reasonably + + align:start position:0% +where's somebody who looks reasonably + + + align:start position:0% +where's somebody who looks reasonably +alert do you look reasonably alert no + + align:start position:0% +alert do you look reasonably alert no + + + align:start position:0% +alert do you look reasonably alert no +now she's looking elsewhere to see if + + align:start position:0% +now she's looking elsewhere to see if + + + align:start position:0% +now she's looking elsewhere to see if +she + + align:start position:0% +she + + + align:start position:0% +she +can no no all right how about if I just + + align:start position:0% +can no no all right how about if I just + + + align:start position:0% +can no no all right how about if I just +throw it out there there we go look at + + align:start position:0% +throw it out there there we go look at + + + align:start position:0% +throw it out there there we go look at +that see that oh very good send it back + + align:start position:0% +that see that oh very good send it back + + + align:start position:0% +that see that oh very good send it back +that's a smart hunk of chalk it knew to + + align:start position:0% +that's a smart hunk of chalk it knew to + + + align:start position:0% +that's a smart hunk of chalk it knew to +fly on a parabolic path + + align:start position:0% +fly on a parabolic path + + + align:start position:0% +fly on a parabolic path +KN knew a whole bunch of like 801 style + + align:start position:0% +KN knew a whole bunch of like 801 style + + + align:start position:0% +KN knew a whole bunch of like 801 style +physics it didn't know it in any real + + align:start position:0% +physics it didn't know it in any real + + + align:start position:0% +physics it didn't know it in any real +sense of course it behaves as if because + + align:start position:0% +sense of course it behaves as if because + + + align:start position:0% +sense of course it behaves as if because +you know it's operating under under + + align:start position:0% +you know it's operating under under + + + align:start position:0% +you know it's operating under under +simple physical forces in the world and + + align:start position:0% +simple physical forces in the world and + + + align:start position:0% +simple physical forces in the world and +ends up behaving as if it knows physics + + align:start position:0% +ends up behaving as if it knows physics + + + align:start position:0% +ends up behaving as if it knows physics +it's a it's a it's a somewhat stretched + + align:start position:0% +it's a it's a it's a somewhat stretched + + + align:start position:0% +it's a it's a it's a somewhat stretched +analogy but the same sort of thing is + + align:start position:0% +analogy but the same sort of thing is + + + align:start position:0% +analogy but the same sort of thing is +going on here the uh you learn about the + + align:start position:0% +going on here the uh you learn about the + + + align:start position:0% +going on here the uh you learn about the +linguistic world you are in and then you + + align:start position:0% +linguistic world you are in and then you + + + align:start position:0% +linguistic world you are in and then you +behave as if you knew uh these the these + + align:start position:0% +behave as if you knew uh these the these + + + align:start position:0% +behave as if you knew uh these the these +rules rather than having some sort of + + align:start position:0% +rules rather than having some sort of + + + align:start position:0% +rules rather than having some sort of +mechanism by which you actually in a + + align:start position:0% +mechanism by which you actually in a + + + align:start position:0% +mechanism by which you actually in a +sense before uh be you know at Birth + + align:start position:0% +sense before uh be you know at Birth + + + align:start position:0% +sense before uh be you know at Birth +knew that there should be such rules and + + align:start position:0% +knew that there should be such rules and + + + align:start position:0% +knew that there should be such rules and +merely needed to figure out um the + + align:start position:0% +merely needed to figure out um the + + + align:start position:0% +merely needed to figure out um the +particular form that the rule took in in + + align:start position:0% +particular form that the rule took in in + + + align:start position:0% +particular form that the rule took in in +your language these are in a sense um + + align:start position:0% +your language these are in a sense um + + + align:start position:0% +your language these are in a sense um +modern and uh and and not hugely + + align:start position:0% +modern and uh and and not hugely + + + align:start position:0% +modern and uh and and not hugely +different views of initial positions + + align:start position:0% +different views of initial positions + + + align:start position:0% +different views of initial positions +that are radically different so if if + + align:start position:0% +that are radically different so if if + + + align:start position:0% +that are radically different so if if +this is a Continuum here um way over + + align:start position:0% +this is a Continuum here um way over + + + align:start position:0% +this is a Continuum here um way over +here somewhere would be radical nativist + + align:start position:0% +here somewhere would be radical nativist + + + align:start position:0% +here somewhere would be radical nativist +views of language and way over here + + align:start position:0% +views of language and way over here + + + align:start position:0% +views of language and way over here +somewhere would be radical empiricist + + align:start position:0% +somewhere would be radical empiricist + + + align:start position:0% +somewhere would be radical empiricist +views of language um + + align:start position:0% +views of language um + + + align:start position:0% +views of language um +empir the + + align:start position:0% +empir the + + + align:start position:0% +empir the +um the most radical nativist views + + align:start position:0% +um the most radical nativist views + + + align:start position:0% +um the most radical nativist views +nobody particularly H held except I + + align:start position:0% +nobody particularly H held except I + + + align:start position:0% +nobody particularly H held except I +think I mentioned little children are + + align:start position:0% +think I mentioned little children are + + + align:start position:0% +think I mentioned little children are +subject to this as as a as an erroneous + + align:start position:0% +subject to this as as a as an erroneous + + + align:start position:0% +subject to this as as a as an erroneous +thought and that's the view that you are + + align:start position:0% +thought and that's the view that you are + + + align:start position:0% +thought and that's the view that you are +not only + + align:start position:0% +not only + + + align:start position:0% +not only +born um to have language but you're born + + align:start position:0% +born um to have language but you're born + + + align:start position:0% +born um to have language but you're born +to have a specific language so that if + + align:start position:0% +to have a specific language so that if + + + align:start position:0% +to have a specific language so that if +if you are um you know a Saudi kid that + + align:start position:0% +if you are um you know a Saudi kid that + + + align:start position:0% +if you are um you know a Saudi kid that +you are born to speak Arabic and that + + align:start position:0% +you are born to speak Arabic and that + + + align:start position:0% +you are born to speak Arabic and that +all else being equal well even all else + + align:start position:0% +all else being equal well even all else + + + align:start position:0% +all else being equal well even all else +not being equal you're a Saudi kid you + + align:start position:0% +not being equal you're a Saudi kid you + + + align:start position:0% +not being equal you're a Saudi kid you +get + + align:start position:0% +get + + + align:start position:0% +get +transplanted uh to Sweden + + align:start position:0% +transplanted uh to Sweden + + + align:start position:0% +transplanted uh to Sweden +and at the right moment Arabic appears + + align:start position:0% +and at the right moment Arabic appears + + + align:start position:0% +and at the right moment Arabic appears +um you know that that's not true nobody + + align:start position:0% +um you know that that's not true nobody + + + align:start position:0% +um you know that that's not true nobody +uh nobody other than a small kid I think + + align:start position:0% +uh nobody other than a small kid I think + + + align:start position:0% +uh nobody other than a small kid I think +ever particularly believed this because + + align:start position:0% +ever particularly believed this because + + + align:start position:0% +ever particularly believed this because +it was clearly + + align:start position:0% +it was clearly + + + align:start position:0% +it was clearly +falsifiable um but uh but what the the + + align:start position:0% +falsifiable um but uh but what the the + + + align:start position:0% +falsifiable um but uh but what the the +earliest experiment I know in this area + + align:start position:0% +earliest experiment I know in this area + + + align:start position:0% +earliest experiment I know in this area +and I don't know if the experiment was + + align:start position:0% +and I don't know if the experiment was + + + align:start position:0% +and I don't know if the experiment was +ever done is something reported by + + align:start position:0% +ever done is something reported by + + + align:start position:0% +ever done is something reported by +Herodotus in uh in in his book about his + + align:start position:0% +Herodotus in uh in in his book about his + + + align:start position:0% +Herodotus in uh in in his book about his +about traveling in Egypt and he says + + align:start position:0% +about traveling in Egypt and he says + + + align:start position:0% +about traveling in Egypt and he says +that king simus of Egypt 2500 years ago + + align:start position:0% +that king simus of Egypt 2500 years ago + + + align:start position:0% +that king simus of Egypt 2500 years ago +um + + align:start position:0% +um + + + align:start position:0% +um +believed that there was an original + + align:start position:0% +believed that there was an original + + + align:start position:0% +believed that there was an original +language of of + + align:start position:0% +language of of + + + align:start position:0% +language of of +humankind um where where King simus uh + + align:start position:0% +humankind um where where King simus uh + + + align:start position:0% +humankind um where where King simus uh +you know grown up in in the sort of + + align:start position:0% +you know grown up in in the sort of + + + align:start position:0% +you know grown up in in the sort of +judeo-christian tradition he might have + + align:start position:0% +judeo-christian tradition he might have + + + align:start position:0% +judeo-christian tradition he might have +called it the language of the Garden of + + align:start position:0% +called it the language of the Garden of + + + align:start position:0% +called it the language of the Garden of +Eden you know what language did Adam and + + align:start position:0% +Eden you know what language did Adam and + + + align:start position:0% +Eden you know what language did Adam and +Eve speak in the garden well it be the + + align:start position:0% +Eve speak in the garden well it be the + + + align:start position:0% +Eve speak in the garden well it be the +original language of of of of of + + align:start position:0% +original language of of of of of + + + align:start position:0% +original language of of of of of +humankind and cedus figured he would uh + + align:start position:0% +humankind and cedus figured he would uh + + + align:start position:0% +humankind and cedus figured he would uh +go and + + align:start position:0% +go and + + + align:start position:0% +go and +figure out what that language was he + + align:start position:0% +figure out what that language was he + + + align:start position:0% +figure out what that language was he +actually had a hypothesis about what it + + align:start position:0% +actually had a hypothesis about what it + + + align:start position:0% +actually had a hypothesis about what it +was he was king of Egypt it stood to + + align:start position:0% +was he was king of Egypt it stood to + + + align:start position:0% +was he was king of Egypt it stood to +reason that the original language of of + + align:start position:0% +reason that the original language of of + + + align:start position:0% +reason that the original language of of +of uh Humanity was Egyptian um and so + + align:start position:0% +of uh Humanity was Egyptian um and so + + + align:start position:0% +of uh Humanity was Egyptian um and so +what he is alleged to have done is to + + align:start position:0% +what he is alleged to have done is to + + + align:start position:0% +what he is alleged to have done is to +take two children give them to a + + align:start position:0% +take two children give them to a + + + align:start position:0% +take two children give them to a +Shepherd tell the shepherd to raise them + + align:start position:0% +Shepherd tell the shepherd to raise them + + + align:start position:0% +Shepherd tell the shepherd to raise them +with sheep and uh not talk to them and + + align:start position:0% +with sheep and uh not talk to them and + + + align:start position:0% +with sheep and uh not talk to them and +to report to the king what the first + + align:start position:0% +to report to the king what the first + + + align:start position:0% +to report to the king what the first +word was that these children + + align:start position:0% +word was that these children + + + align:start position:0% +word was that these children +spoke and um + + align:start position:0% +spoke and um + + + align:start position:0% +spoke and um +the report is that When the Children + + align:start position:0% +the report is that When the Children + + + align:start position:0% +the report is that When the Children +First spoke their first word was + + align:start position:0% +First spoke their first word was + + + align:start position:0% +First spoke their first word was +beckos um which sounds suspiciously like + + align:start position:0% +beckos um which sounds suspiciously like + + + align:start position:0% +beckos um which sounds suspiciously like +they were imitating the Sheep I think + + align:start position:0% +they were imitating the Sheep I think + + + align:start position:0% +they were imitating the Sheep I think +but anyway um beckos Turned out to mean + + align:start position:0% +but anyway um beckos Turned out to mean + + + align:start position:0% +but anyway um beckos Turned out to mean +bread um and that that seemed like a + + align:start position:0% +bread um and that that seemed like a + + + align:start position:0% +bread um and that that seemed like a +pretty encouraging thing except that it + + align:start position:0% +pretty encouraging thing except that it + + + align:start position:0% +pretty encouraging thing except that it +meant bread in + + align:start position:0% +meant bread in + + + align:start position:0% +meant bread in +frian uh the language of Fria which is + + align:start position:0% +frian uh the language of Fria which is + + + align:start position:0% +frian uh the language of Fria which is +in modern-day turkey it didn't it wasn't + + align:start position:0% +in modern-day turkey it didn't it wasn't + + + align:start position:0% +in modern-day turkey it didn't it wasn't +word for bread in Egyptian at all um and + + align:start position:0% +word for bread in Egyptian at all um and + + + align:start position:0% +word for bread in Egyptian at all um and +so cicus is reputed to have been + + align:start position:0% +so cicus is reputed to have been + + + align:start position:0% +so cicus is reputed to have been +disappointed by the results of the + + align:start position:0% +disappointed by the results of the + + + align:start position:0% +disappointed by the results of the +experiment look we don't know that the + + align:start position:0% +experiment look we don't know that the + + + align:start position:0% +experiment look we don't know that the +experiment was ever done we do know or + + align:start position:0% +experiment was ever done we do know or + + + align:start position:0% +experiment was ever done we do know or +we're pretty sure we know how the + + align:start position:0% +we're pretty sure we know how the + + + align:start position:0% +we're pretty sure we know how the +experiment would have come out had it + + align:start position:0% +experiment would have come out had it + + + align:start position:0% +experiment would have come out had it +actually been done um which is that they + + align:start position:0% +actually been done um which is that they + + + align:start position:0% +actually been done um which is that they +wouldn't have spoken a language at all + + align:start position:0% +wouldn't have spoken a language at all + + + align:start position:0% +wouldn't have spoken a language at all +that in the absence of a linguistic + + align:start position:0% +that in the absence of a linguistic + + + align:start position:0% +that in the absence of a linguistic +environment even if you come into the + + align:start position:0% +environment even if you come into the + + + align:start position:0% +environment even if you come into the +world with some native endowment to + + align:start position:0% +world with some native endowment to + + + align:start position:0% +world with some native endowment to +learn a language which does seem to be + + align:start position:0% +learn a language which does seem to be + + + align:start position:0% +learn a language which does seem to be +the case you do not speak a normal human + + align:start position:0% +the case you do not speak a normal human + + + align:start position:0% +the case you do not speak a normal human +language unless you are raised in a + + align:start position:0% +language unless you are raised in a + + + align:start position:0% +language unless you are raised in a +linguistic environment uh at at at some + + align:start position:0% +linguistic environment uh at at at some + + + align:start position:0% +linguistic environment uh at at at some +point the re we think we know this from + + align:start position:0% +point the re we think we know this from + + + align:start position:0% +point the re we think we know this from +a an isolated set of cases over uh over + + align:start position:0% +a an isolated set of cases over uh over + + + align:start position:0% +a an isolated set of cases over uh over +the course of um you know historical + + align:start position:0% +the course of um you know historical + + + align:start position:0% +the course of um you know historical +record where kids are somehow uh + + align:start position:0% +record where kids are somehow uh + + + align:start position:0% +record where kids are somehow uh +deprived of linguistic input now that + + align:start position:0% +deprived of linguistic input now that + + + align:start position:0% +deprived of linguistic input now that +happens typically in in odd and and + + align:start position:0% +happens typically in in odd and and + + + align:start position:0% +happens typically in in odd and and +disturbing kinds of + + align:start position:0% +disturbing kinds of + + + align:start position:0% +disturbing kinds of +circumstances um and so it's it's it's + + align:start position:0% +circumstances um and so it's it's it's + + + align:start position:0% +circumstances um and so it's it's it's +nothing like a a real experiment because + + align:start position:0% +nothing like a a real experiment because + + + align:start position:0% +nothing like a a real experiment because +of course you'd never do the real + + align:start position:0% +of course you'd never do the real + + + align:start position:0% +of course you'd never do the real +experiment it wouldn't be even close to + + align:start position:0% +experiment it wouldn't be even close to + + + align:start position:0% +experiment it wouldn't be even close to +ethical um the uh the this this class of + + align:start position:0% +ethical um the uh the this this class of + + + align:start position:0% +ethical um the uh the this this class of +children are known as wolf children a + + align:start position:0% +children are known as wolf children a + + + align:start position:0% +children are known as wolf children a +term that has always Disturbed me + + align:start position:0% +term that has always Disturbed me + + + align:start position:0% +term that has always Disturbed me +personally + + align:start position:0% +personally + + + align:start position:0% +personally +um but the the uh the illusion is is not + + align:start position:0% +um but the the uh the illusion is is not + + + align:start position:0% +um but the the uh the illusion is is not +to Wolf with an e but to the uh + + align:start position:0% +to Wolf with an e but to the uh + + + align:start position:0% +to Wolf with an e but to the uh +legendary + + align:start position:0% +legendary + + + align:start position:0% +legendary +story of the founding of Rome where the + + align:start position:0% +story of the founding of Rome where the + + + align:start position:0% +story of the founding of Rome where the +twins Romulus and Remis are abandoned I + + align:start position:0% +twins Romulus and Remis are abandoned I + + + align:start position:0% +twins Romulus and Remis are abandoned I +can't remember why but anyway they get + + align:start position:0% +can't remember why but anyway they get + + + align:start position:0% +can't remember why but anyway they get +suckled by a She Wolf and so if you look + + align:start position:0% +suckled by a She Wolf and so if you look + + + align:start position:0% +suckled by a She Wolf and so if you look +at Roman coins and things you'll see + + align:start position:0% +at Roman coins and things you'll see + + + align:start position:0% +at Roman coins and things you'll see +this picture of a great big wolf and and + + align:start position:0% +this picture of a great big wolf and and + + + align:start position:0% +this picture of a great big wolf and and +and two little babies suckling + + align:start position:0% +and two little babies suckling + + + align:start position:0% +and two little babies suckling +underneath you know is this is and and + + align:start position:0% +underneath you know is this is and and + + + align:start position:0% +underneath you know is this is and and +presumably the wolf wasn't speaking good + + align:start position:0% +presumably the wolf wasn't speaking good + + + align:start position:0% +presumably the wolf wasn't speaking good +Latin um but presumably ramulus and + + align:start position:0% +Latin um but presumably ramulus and + + + align:start position:0% +Latin um but presumably ramulus and +Remis managed to come up with good Latin + + align:start position:0% +Remis managed to come up with good Latin + + + align:start position:0% +Remis managed to come up with good Latin +somehow out of all this + + align:start position:0% +somehow out of all this + + + align:start position:0% +somehow out of all this +um there are uh occasionally it happens + + align:start position:0% +um there are uh occasionally it happens + + + align:start position:0% +um there are uh occasionally it happens +that some kid gets abandoned in the + + align:start position:0% +that some kid gets abandoned in the + + + align:start position:0% +that some kid gets abandoned in the +woods and somehow survives I think + + align:start position:0% +woods and somehow survives I think + + + align:start position:0% +woods and somehow survives I think +there's a case of an Indian child who + + align:start position:0% +there's a case of an Indian child who + + + align:start position:0% +there's a case of an Indian child who +described in Gman um there was a very + + align:start position:0% +described in Gman um there was a very + + + align:start position:0% +described in Gman um there was a very +disturbing book interesting but + + align:start position:0% +disturbing book interesting but + + + align:start position:0% +disturbing book interesting but +disturbing book called Genie written a + + align:start position:0% +disturbing book called Genie written a + + + align:start position:0% +disturbing book called Genie written a +few years ago about a child of deeply + + align:start position:0% +few years ago about a child of deeply + + + align:start position:0% +few years ago about a child of deeply +Disturbed parents who had taken her and + + align:start position:0% +Disturbed parents who had taken her and + + + align:start position:0% +Disturbed parents who had taken her and +basically locked her in a closet for all + + align:start position:0% +basically locked her in a closet for all + + + align:start position:0% +basically locked her in a closet for all +of her childhood um and the the the the + + align:start position:0% +of her childhood um and the the the the + + + align:start position:0% +of her childhood um and the the the the +the bottom line is that this is not + + align:start position:0% +the bottom line is that this is not + + + align:start position:0% +the bottom line is that this is not +going to be good for any aspect of your + + align:start position:0% +going to be good for any aspect of your + + + align:start position:0% +going to be good for any aspect of your +development but you don't develop a + + align:start position:0% +development but you don't develop a + + + align:start position:0% +development but you don't develop a +normal language if you don't get exposed + + align:start position:0% +normal language if you don't get exposed + + + align:start position:0% +normal language if you don't get exposed +to language during a so-called critical + + align:start position:0% +to language during a so-called critical + + + align:start position:0% +to language during a so-called critical +period which for language um is + + align:start position:0% +period which for language um is + + + align:start position:0% +period which for language um is +certainly over by early adolescence and + + align:start position:0% +certainly over by early adolescence and + + + align:start position:0% +certainly over by early adolescence and +and is is is getting pretty much over + + align:start position:0% +and is is is getting pretty much over + + + align:start position:0% +and is is is getting pretty much over +six seven eight years old you'd better + + align:start position:0% +six seven eight years old you'd better + + + align:start position:0% +six seven eight years old you'd better +get your language + + align:start position:0% +get your language + + + align:start position:0% +get your language +experience in there before before that + + align:start position:0% +experience in there before before that + + + align:start position:0% +experience in there before before that +um you're just never going to speak a + + align:start position:0% +um you're just never going to speak a + + + align:start position:0% +um you're just never going to speak a +normal grammatic language the door + + align:start position:0% +normal grammatic language the door + + + align:start position:0% +normal grammatic language the door +closed on it so Genie this this uh poor + + align:start position:0% +closed on it so Genie this this uh poor + + + align:start position:0% +closed on it so Genie this this uh poor +girl who was raised in the closet you + + align:start position:0% +girl who was raised in the closet you + + + align:start position:0% +girl who was raised in the closet you +could be taught could could be taught a + + align:start position:0% +could be taught could could be taught a + + + align:start position:0% +could be taught could could be taught a +certain amount of of vocabulary and + + align:start position:0% +certain amount of of vocabulary and + + + align:start position:0% +certain amount of of vocabulary and +things like that but but could never + + align:start position:0% +things like that but but could never + + + align:start position:0% +things like that but but could never +somehow get a real grip on um on the uh + + align:start position:0% +somehow get a real grip on um on the uh + + + align:start position:0% +somehow get a real grip on um on the uh +the grammar of a language it also turns + + align:start position:0% +the grammar of a language it also turns + + + align:start position:0% +the grammar of a language it also turns +out to be easier to learn a second + + align:start position:0% +out to be easier to learn a second + + + align:start position:0% +out to be easier to learn a second +language during the critical period but + + align:start position:0% +language during the critical period but + + + align:start position:0% +language during the critical period but +not impossible to learn one afterwards + + align:start position:0% +not impossible to learn one afterwards + + + align:start position:0% +not impossible to learn one afterwards +as those of you who are you know have + + align:start position:0% +as those of you who are you know have + + + align:start position:0% +as those of you who are you know have +just started learning French or + + align:start position:0% +just started learning French or + + + align:start position:0% +just started learning French or +something will be happy to know uh the + + align:start position:0% +something will be happy to know uh the + + + align:start position:0% +something will be happy to know uh the +is that that uh it's it's very difficult + + align:start position:0% +is that that uh it's it's very difficult + + + align:start position:0% +is that that uh it's it's very difficult +to become a truly + + align:start position:0% +to become a truly + + + align:start position:0% +to become a truly +fluent um speaker uh of of a uh Second + + align:start position:0% +fluent um speaker uh of of a uh Second + + + align:start position:0% +fluent um speaker uh of of a uh Second +Language later in life um but uh but + + align:start position:0% +Language later in life um but uh but + + + align:start position:0% +Language later in life um but uh but +it's not impossible in the way it + + align:start position:0% +it's not impossible in the way it + + + align:start position:0% +it's not impossible in the way it +appears to be impossible to learn a + + align:start position:0% +appears to be impossible to learn a + + + align:start position:0% +appears to be impossible to learn a +first language after the after the end + + align:start position:0% +first language after the after the end + + + align:start position:0% +first language after the after the end +of a critical period + + align:start position:0% +of a critical period + + + align:start position:0% +of a critical period +um + + align:start position:0% + + + + align:start position:0% + +the alternative the radical alternative + + align:start position:0% +the alternative the radical alternative + + + align:start position:0% +the alternative the radical alternative +to uh King cicus on on one side if we're + + align:start position:0% +to uh King cicus on on one side if we're + + + align:start position:0% +to uh King cicus on on one side if we're +sticking with classical references um on + + align:start position:0% +sticking with classical references um on + + + align:start position:0% +sticking with classical references um on +this side would be somebody like St + + align:start position:0% +this side would be somebody like St + + + align:start position:0% +this side would be somebody like St +Augustine who writes that he learned + + align:start position:0% +Augustine who writes that he learned + + + align:start position:0% +Augustine who writes that he learned +Lang he knows how he learned language he + + align:start position:0% +Lang he knows how he learned language he + + + align:start position:0% +Lang he knows how he learned language he +learned language um by being by being + + align:start position:0% +learned language um by being by being + + + align:start position:0% +learned language um by being by being +explicitly taught that the same way + + align:start position:0% +explicitly taught that the same way + + + align:start position:0% +explicitly taught that the same way +you'd learn anything else that uh uh + + align:start position:0% +you'd learn anything else that uh uh + + + align:start position:0% +you'd learn anything else that uh uh +people said uh you know that's chalk + + align:start position:0% +people said uh you know that's chalk + + + align:start position:0% +people said uh you know that's chalk +that's a chair um you know that's your + + align:start position:0% +that's a chair um you know that's your + + + align:start position:0% +that's a chair um you know that's your +your your your ta and and you learned + + align:start position:0% +your your your ta and and you learned + + + align:start position:0% +your your your ta and and you learned +this sort of stuff um and that it was an + + align:start position:0% +this sort of stuff um and that it was an + + + align:start position:0% +this sort of stuff um and that it was an +act of learning not unlike other acts of + + align:start position:0% +act of learning not unlike other acts of + + + align:start position:0% +act of learning not unlike other acts of +learning now this this gets developed um + + align:start position:0% +learning now this this gets developed um + + + align:start position:0% +learning now this this gets developed um +St St Augustine was not particularly + + align:start position:0% +St St Augustine was not particularly + + + align:start position:0% +St St Augustine was not particularly +working on on learning theory but by the + + align:start position:0% +working on on learning theory but by the + + + align:start position:0% +working on on learning theory but by the +time you get + + align:start position:0% +time you get + + + align:start position:0% +time you get +to the mid uh 20th century and the + + align:start position:0% +to the mid uh 20th century and the + + + align:start position:0% +to the mid uh 20th century and the +Heyday of behaviorism and all that good + + align:start position:0% +Heyday of behaviorism and all that good + + + align:start position:0% +Heyday of behaviorism and all that good +skinnerian pigeons in the box kind of + + align:start position:0% +skinnerian pigeons in the box kind of + + + align:start position:0% +skinnerian pigeons in the box kind of +thing um you get uh theories of language + + align:start position:0% +thing um you get uh theories of language + + + align:start position:0% +thing um you get uh theories of language +learning that say well look language + + align:start position:0% +learning that say well look language + + + align:start position:0% +learning that say well look language +learning is just a fancy variety of any + + align:start position:0% +learning is just a fancy variety of any + + + align:start position:0% +learning is just a fancy variety of any +other kind of learning you want your kid + + align:start position:0% +other kind of learning you want your kid + + + align:start position:0% +other kind of learning you want your kid +to speak English and so you reward him + + align:start position:0% +to speak English and so you reward him + + + align:start position:0% +to speak English and so you reward him +for speaking English you shape the + + align:start position:0% +for speaking English you shape the + + + align:start position:0% +for speaking English you shape the +behavior um you know and at the same + + align:start position:0% +behavior um you know and at the same + + + align:start position:0% +behavior um you know and at the same +time you're trying to get the kid to do + + align:start position:0% +time you're trying to get the kid to do + + + align:start position:0% +time you're trying to get the kid to do +some sort of complicated thing like like + + align:start position:0% +some sort of complicated thing like like + + + align:start position:0% +some sort of complicated thing like like +being toilet trained you're also trying + + align:start position:0% +being toilet trained you're also trying + + + align:start position:0% +being toilet trained you're also trying +to get them to do things like saying um + + align:start position:0% +to get them to do things like saying um + + + align:start position:0% +to get them to do things like saying um +you know I go to the store yesterday I + + align:start position:0% +you know I go to the store yesterday I + + + align:start position:0% +you know I go to the store yesterday I +went to the store and and you know it's + + align:start position:0% +went to the store and and you know it's + + + align:start position:0% +went to the store and and you know it's +it's just the same thing more or less um + + align:start position:0% +it's just the same thing more or less um + + + align:start position:0% +it's just the same thing more or less um +the one of the great efforts to make + + align:start position:0% +the one of the great efforts to make + + + align:start position:0% +the one of the great efforts to make +that into a single coherent story is BF + + align:start position:0% +that into a single coherent story is BF + + + align:start position:0% +that into a single coherent story is BF +Skinner's book called verb uh verbal + + align:start position:0% +Skinner's book called verb uh verbal + + + align:start position:0% +Skinner's book called verb uh verbal +behavior um good name for from a good + + align:start position:0% +behavior um good name for from a good + + + align:start position:0% +behavior um good name for from a good +behaviorist it's just another kind of + + align:start position:0% +behaviorist it's just another kind of + + + align:start position:0% +behaviorist it's just another kind of +behavior and uh s the start of the East + + align:start position:0% +behavior and uh s the start of the East + + + align:start position:0% +behavior and uh s the start of the East +Coast um story and the start of um + + align:start position:0% +Coast um story and the start of um + + + align:start position:0% +Coast um story and the start of um +modern cognitive science in some ways is + + align:start position:0% +modern cognitive science in some ways is + + + align:start position:0% +modern cognitive science in some ways is +Nome Chomsky then a young Professor at + + align:start position:0% +Nome Chomsky then a young Professor at + + + align:start position:0% +Nome Chomsky then a young Professor at +MIT writing a scathing review of that + + align:start position:0% +MIT writing a scathing review of that + + + align:start position:0% +MIT writing a scathing review of that +book which still Bears reading it's + + align:start position:0% +book which still Bears reading it's + + + align:start position:0% +book which still Bears reading it's +still fun to it's still fun to read that + + align:start position:0% +still fun to it's still fun to read that + + + align:start position:0% +still fun to it's still fun to read that +or you can go read the summary of it in + + align:start position:0% +or you can go read the summary of it in + + + align:start position:0% +or you can go read the summary of it in +the the the the recap of it in in in + + align:start position:0% +the the the the recap of it in in in + + + align:start position:0% +the the the the recap of it in in in +pinker's book but you have to imagine + + align:start position:0% +pinker's book but you have to imagine + + + align:start position:0% +pinker's book but you have to imagine +this as a sort of a cultural event + + align:start position:0% +this as a sort of a cultural event + + + align:start position:0% +this as a sort of a cultural event +Skinner is the leading American + + align:start position:0% +Skinner is the leading American + + + align:start position:0% +Skinner is the leading American +psychologist of the the time and this + + align:start position:0% +psychologist of the the time and this + + + align:start position:0% +psychologist of the the time and this +young uh gnome Chomsky guy is going + + align:start position:0% +young uh gnome Chomsky guy is going + + + align:start position:0% +young uh gnome Chomsky guy is going +after him um with with with a bat and + + align:start position:0% +after him um with with with a bat and + + + align:start position:0% +after him um with with with a bat and +and and both barrels blazing and any + + align:start position:0% +and and both barrels blazing and any + + + align:start position:0% +and and both barrels blazing and any +other Weaponry you can think of it is + + align:start position:0% +other Weaponry you can think of it is + + + align:start position:0% +other Weaponry you can think of it is +not a temperate review um it is + + align:start position:0% +not a temperate review um it is + + + align:start position:0% +not a temperate review um it is +insulting in many ways um and it's an + + align:start position:0% +insulting in many ways um and it's an + + + align:start position:0% +insulting in many ways um and it's an +insulting uh piece written by a young + + align:start position:0% +insulting uh piece written by a young + + + align:start position:0% +insulting uh piece written by a young +guy about a very senior established + + align:start position:0% +guy about a very senior established + + + align:start position:0% +guy about a very senior established +important guy and it started it's it + + align:start position:0% +important guy and it started it's it + + + align:start position:0% +important guy and it started it's it +starts a revolution anyway I'm not going + + align:start position:0% +starts a revolution anyway I'm not going + + + align:start position:0% +starts a revolution anyway I'm not going +to go through the whole argument but the + + align:start position:0% +to go through the whole argument but the + + + align:start position:0% +to go through the whole argument but the +sorts of uh things that Chomsky points + + align:start position:0% +sorts of uh things that Chomsky points + + + align:start position:0% +sorts of uh things that Chomsky points +out is that um the you know Skinner's + + align:start position:0% +out is that um the you know Skinner's + + + align:start position:0% +out is that um the you know Skinner's +talking about schedules of reinforcement + + align:start position:0% +talking about schedules of reinforcement + + + align:start position:0% +talking about schedules of reinforcement +the rein the patterns of reinforcement + + align:start position:0% +the rein the patterns of reinforcement + + + align:start position:0% +the rein the patterns of reinforcement +for language just aren't there this has + + align:start position:0% +for language just aren't there this has + + + align:start position:0% +for language just aren't there this has +been extensively developed since + + align:start position:0% +been extensively developed since + + + align:start position:0% +been extensively developed since +chomsky's time but yeah let me you can + + align:start position:0% +chomsky's time but yeah let me you can + + + align:start position:0% +chomsky's time but yeah let me you can +imagine this from a sort of an ex just + + align:start position:0% +imagine this from a sort of an ex just + + + align:start position:0% +imagine this from a sort of an ex just +an example imagine yourself back home as + + align:start position:0% +an example imagine yourself back home as + + + align:start position:0% +an example imagine yourself back home as +a little kid and you go up to your + + align:start position:0% +a little kid and you go up to your + + + align:start position:0% +a little kid and you go up to your +mother and you say Mommy I loves you so + + align:start position:0% +mother and you say Mommy I loves you so + + + align:start position:0% +mother and you say Mommy I loves you so +much what's the chance that she's going + + align:start position:0% +much what's the chance that she's going + + + align:start position:0% +much what's the chance that she's going +to say bad child bad child it's I love + + align:start position:0% +to say bad child bad child it's I love + + + align:start position:0% +to say bad child bad child it's I love +you and by the same token what's the + + align:start position:0% +you and by the same token what's the + + + align:start position:0% +you and by the same token what's the +chance that if you go up and say you + + align:start position:0% +chance that if you go up and say you + + + align:start position:0% +chance that if you go up and say you +know as a precocious + + align:start position:0% +know as a precocious + + + align:start position:0% +know as a precocious +three-year-old Mother + + align:start position:0% +three-year-old Mother + + + align:start position:0% +three-year-old Mother +dear I'm sorry to have to say this but + + align:start position:0% +dear I'm sorry to have to say this but + + + align:start position:0% +dear I'm sorry to have to say this but +it turns out that I actually loathe you + + align:start position:0% +it turns out that I actually loathe you + + + align:start position:0% +it turns out that I actually loathe you +and despise the ground on which you + + align:start position:0% +and despise the ground on which you + + + align:start position:0% +and despise the ground on which you +walk right your mother is not going to + + align:start position:0% +walk right your mother is not going to + + + align:start position:0% +walk right your mother is not going to +say that's a very sophisticated + + align:start position:0% +say that's a very sophisticated + + + align:start position:0% +say that's a very sophisticated +utterance for a three-year-old good job + + align:start position:0% +utterance for a three-year-old good job + + + align:start position:0% +utterance for a three-year-old good job +right you're not going to get and and + + align:start position:0% +right you're not going to get and and + + + align:start position:0% +right you're not going to get and and +and look that's a cartoon version but + + align:start position:0% +and look that's a cartoon version but + + + align:start position:0% +and look that's a cartoon version but +when you go and look at substantial + + align:start position:0% +when you go and look at substantial + + + align:start position:0% +when you go and look at substantial +bodies of child language and their + + align:start position:0% +bodies of child language and their + + + align:start position:0% +bodies of child language and their +interaction with with the grown-ups in + + align:start position:0% +interaction with with the grown-ups in + + + align:start position:0% +interaction with with the grown-ups in +their life you don't find good evidence + + align:start position:0% +their life you don't find good evidence + + + align:start position:0% +their life you don't find good evidence +for systematic correction of language or + + align:start position:0% +for systematic correction of language or + + + align:start position:0% +for systematic correction of language or +systematic reinforcement for for + + align:start position:0% +systematic reinforcement for for + + + align:start position:0% +systematic reinforcement for for +grammatical structure you don't find any + + align:start position:0% +grammatical structure you don't find any + + + align:start position:0% +grammatical structure you don't find any +great + + align:start position:0% +great + + + align:start position:0% +great +sensitivity on the part of the kid in + + align:start position:0% +sensitivity on the part of the kid in + + + align:start position:0% +sensitivity on the part of the kid in +that to that correction when it's given + + align:start position:0% +that to that correction when it's given + + + align:start position:0% +that to that correction when it's given +the the the sorts of things that uh that + + align:start position:0% +the the the sorts of things that uh that + + + align:start position:0% +the the the sorts of things that uh that +every parent has they show up in the in + + align:start position:0% +every parent has they show up in the in + + + align:start position:0% +every parent has they show up in the in +in the child language uh uh you know + + align:start position:0% +in the child language uh uh you know + + + align:start position:0% +in the child language uh uh you know +literature but any parent can tell you + + align:start position:0% +literature but any parent can tell you + + + align:start position:0% +literature but any parent can tell you +that you know you kid comes up to you + + align:start position:0% +that you know you kid comes up to you + + + align:start position:0% +that you know you kid comes up to you +and says uh mommy I loves you um and and + + align:start position:0% +and says uh mommy I loves you um and and + + + align:start position:0% +and says uh mommy I loves you um and and +you say oh that's sweet honey but it's + + align:start position:0% +you say oh that's sweet honey but it's + + + align:start position:0% +you say oh that's sweet honey but it's +really Mommy I love you um and the kid + + align:start position:0% +really Mommy I love you um and the kid + + + align:start position:0% +really Mommy I love you um and the kid +says yeah that's right Mommy I loves you + + align:start position:0% +says yeah that's right Mommy I loves you + + + align:start position:0% +says yeah that's right Mommy I loves you +um they don't show an awful lot of + + align:start position:0% +um they don't show an awful lot of + + + align:start position:0% +um they don't show an awful lot of +sensitivity to what to to this sort of + + align:start position:0% +sensitivity to what to to this sort of + + + align:start position:0% +sensitivity to what to to this sort of +negative the the negative support for + + align:start position:0% +negative the the negative support for + + + align:start position:0% +negative the the negative support for +what they're saying how they actually + + align:start position:0% +what they're saying how they actually + + + align:start position:0% +what they're saying how they actually +figure out eventually that it's wrong is + + align:start position:0% +figure out eventually that it's wrong is + + + align:start position:0% +figure out eventually that it's wrong is +is is an interesting and important + + align:start position:0% +is is an interesting and important + + + align:start position:0% +is is an interesting and important +problem but what is pretty clearly the + + align:start position:0% +problem but what is pretty clearly the + + + align:start position:0% +problem but what is pretty clearly the +case is that a story that will explain + + align:start position:0% +case is that a story that will explain + + + align:start position:0% +case is that a story that will explain +how it is that I persuaded my pigeon in + + align:start position:0% +how it is that I persuaded my pigeon in + + + align:start position:0% +how it is that I persuaded my pigeon in +my intro site class to do ballet I think + + align:start position:0% +my intro site class to do ballet I think + + + align:start position:0% +my intro site class to do ballet I think +I told that story here but anyway you + + align:start position:0% +I told that story here but anyway you + + + align:start position:0% +I told that story here but anyway you +know I shaped my pigeon to do ballet + + align:start position:0% +know I shaped my pigeon to do ballet + + + align:start position:0% +know I shaped my pigeon to do ballet +that was great um that such a story uh + + align:start position:0% +that was great um that such a story uh + + + align:start position:0% +that was great um that such a story uh +does not cash out well as a story for + + align:start position:0% +does not cash out well as a story for + + + align:start position:0% +does not cash out well as a story for +how you're trying to explain language it + + align:start position:0% +how you're trying to explain language it + + + align:start position:0% +how you're trying to explain language it +does not seem to be possible to explain + + align:start position:0% +does not seem to be possible to explain + + + align:start position:0% +does not seem to be possible to explain +language in um in those terms + + align:start position:0% +language in um in those terms + + + align:start position:0% +language in um in those terms +um as noted if you want to know more + + align:start position:0% +um as noted if you want to know more + + + align:start position:0% +um as noted if you want to know more +about this particular argument I really + + align:start position:0% +about this particular argument I really + + + align:start position:0% +about this particular argument I really +would recommend pinker's um pinker's + + align:start position:0% +would recommend pinker's um pinker's + + + align:start position:0% +would recommend pinker's um pinker's +book um it it it it's it's good stuff um + + align:start position:0% +book um it it it it's it's good stuff um + + + align:start position:0% +book um it it it it's it's good stuff um +so what what do we got we got the notion + + align:start position:0% +so what what do we got we got the notion + + + align:start position:0% +so what what do we got we got the notion +that specific languages are learned you + + align:start position:0% +that specific languages are learned you + + + align:start position:0% +that specific languages are learned you +didn't come into the world pre-wired for + + align:start position:0% +didn't come into the world pre-wired for + + + align:start position:0% +didn't come into the world pre-wired for +English Arabic Chinese or whatever + + align:start position:0% +English Arabic Chinese or whatever + + + align:start position:0% +English Arabic Chinese or whatever +language in the abstract it's not + + align:start position:0% +language in the abstract it's not + + + align:start position:0% +language in the abstract it's not +exactly clear what it is that's innate + + align:start position:0% +exactly clear what it is that's innate + + + align:start position:0% +exactly clear what it is that's innate +but something is innate that allows you + + align:start position:0% +but something is innate that allows you + + + align:start position:0% +but something is innate that allows you +to learn uh + + align:start position:0% +to learn uh + + + align:start position:0% +to learn uh +language and that's + + align:start position:0% +language and that's + + + align:start position:0% +language and that's +something could be as specific as as as + + align:start position:0% +something could be as specific as as as + + + align:start position:0% +something could be as specific as as as +having in a sense the grammar written + + align:start position:0% +having in a sense the grammar written + + + align:start position:0% +having in a sense the grammar written +out in in some sort of abstract form in + + align:start position:0% +out in in some sort of abstract form in + + + align:start position:0% +out in in some sort of abstract form in +your head and you're filling in the + + align:start position:0% +your head and you're filling in the + + + align:start position:0% +your head and you're filling in the +blanks it could be something a as + + align:start position:0% +blanks it could be something a as + + + align:start position:0% +blanks it could be something a as +non-specific as having a device that's + + align:start position:0% +non-specific as having a device that's + + + align:start position:0% +non-specific as having a device that's +uh that's designed to look for + + align:start position:0% +uh that's designed to look for + + + align:start position:0% +uh that's designed to look for +regularities in um in linguistic input + + align:start position:0% +regularities in um in linguistic input + + + align:start position:0% +regularities in um in linguistic input +um but something is um is in there that + + align:start position:0% +um but something is um is in there that + + + align:start position:0% +um but something is um is in there that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh that that predisposes you and any + + align:start position:0% +uh that that predisposes you and any + + + align:start position:0% +uh that that predisposes you and any +linguistically normal + + align:start position:0% +linguistically normal + + + align:start position:0% +linguistically normal +um a human to learn language and in fact + + align:start position:0% +um a human to learn language and in fact + + + align:start position:0% +um a human to learn language and in fact +it doesn't have to be it's it's not just + + align:start position:0% +it doesn't have to be it's it's not just + + + align:start position:0% +it doesn't have to be it's it's not just +something that's that that's + + align:start position:0% +something that's that that's + + + align:start position:0% +something that's that that's +predisposing you to learn um a a spoken + + align:start position:0% +predisposing you to learn um a a spoken + + + align:start position:0% +predisposing you to learn um a a spoken +language one of the most interesting + + align:start position:0% +language one of the most interesting + + + align:start position:0% +language one of the most interesting +bits of uh + + align:start position:0% +bits of uh + + + align:start position:0% +bits of uh +uh work in recent years in this area um + + align:start position:0% +uh work in recent years in this area um + + + align:start position:0% +uh work in recent years in this area um +is the development of what really boils + + align:start position:0% +is the development of what really boils + + + align:start position:0% +is the development of what really boils +down to a brand new language uh that we + + align:start position:0% +down to a brand new language uh that we + + + align:start position:0% +down to a brand new language uh that we +can uh growing up as much as anything + + align:start position:0% +can uh growing up as much as anything + + + align:start position:0% +can uh growing up as much as anything +out of whatever this innate endowment is + + align:start position:0% +out of whatever this innate endowment is + + + align:start position:0% +out of whatever this innate endowment is +uh this is the story of Nicaraguan sign + + align:start position:0% +uh this is the story of Nicaraguan sign + + + align:start position:0% +uh this is the story of Nicaraguan sign +language um before the sandanista + + align:start position:0% +language um before the sandanista + + + align:start position:0% +language um before the sandanista +Revolution in the 70s in + + align:start position:0% +Revolution in the 70s in + + + align:start position:0% +Revolution in the 70s in +Nicaragua uh I gather that that deaf + + align:start position:0% +Nicaragua uh I gather that that deaf + + + align:start position:0% +Nicaragua uh I gather that that deaf +kids were typically raised at home and + + align:start position:0% +kids were typically raised at home and + + + align:start position:0% +kids were typically raised at home and +um and treated as though they were uh + + align:start position:0% +um and treated as though they were uh + + + align:start position:0% +um and treated as though they were uh +not just deaf but you not not bright + + align:start position:0% +not just deaf but you not not bright + + + align:start position:0% +not just deaf but you not not bright +they weren't going to learn much um when + + align:start position:0% +they weren't going to learn much um when + + + align:start position:0% +they weren't going to learn much um when +the I don't know if this is universally + + align:start position:0% +the I don't know if this is universally + + + align:start position:0% +the I don't know if this is universally +true but there was a population of such + + align:start position:0% +true but there was a population of such + + + align:start position:0% +true but there was a population of such +kids when when the revolution happened + + align:start position:0% +kids when when the revolution happened + + + align:start position:0% +kids when when the revolution happened +one of the things that happened was a a + + align:start position:0% +one of the things that happened was a a + + + align:start position:0% +one of the things that happened was a a +school for the deaf was set up in managa + + align:start position:0% +school for the deaf was set up in managa + + + align:start position:0% +school for the deaf was set up in managa +in the capital and a bunch of deaf kids + + align:start position:0% +in the capital and a bunch of deaf kids + + + align:start position:0% +in the capital and a bunch of deaf kids +were brought together for the um for the + + align:start position:0% +were brought together for the um for the + + + align:start position:0% +were brought together for the um for the +first time what happened was that de + + align:start position:0% +first time what happened was that de + + + align:start position:0% +first time what happened was that de +deaf deaf kids even in in uh in the + + align:start position:0% +deaf deaf kids even in in uh in the + + + align:start position:0% +deaf deaf kids even in in uh in the +absence of other uh members of a deaf + + align:start position:0% +absence of other uh members of a deaf + + + align:start position:0% +absence of other uh members of a deaf +community will produce signs uh gestures + + align:start position:0% +community will produce signs uh gestures + + + align:start position:0% +community will produce signs uh gestures +that uh called home signs that indicate + + align:start position:0% +that uh called home signs that indicate + + + align:start position:0% +that uh called home signs that indicate +certain things you know that you know + + align:start position:0% +certain things you know that you know + + + align:start position:0% +certain things you know that you know +it's sort of a basic vocabulary not a + + align:start position:0% +it's sort of a basic vocabulary not a + + + align:start position:0% +it's sort of a basic vocabulary not a +language but a sort of a core vocabulary + + align:start position:0% +language but a sort of a core vocabulary + + + align:start position:0% +language but a sort of a core vocabulary +that you can use to communicate with + + align:start position:0% +that you can use to communicate with + + + align:start position:0% +that you can use to communicate with +with your hearing parents for instance + + align:start position:0% +with your hearing parents for instance + + + align:start position:0% +with your hearing parents for instance +um what happened was that uh all these + + align:start position:0% +um what happened was that uh all these + + + align:start position:0% +um what happened was that uh all these +deaf kids got + + align:start position:0% +deaf kids got + + + align:start position:0% +deaf kids got +together and um I don't know what was + + align:start position:0% +together and um I don't know what was + + + align:start position:0% +together and um I don't know what was +going on in school but I think what was + + align:start position:0% +going on in school but I think what was + + + align:start position:0% +going on in school but I think what was +going on at night and you know up in up + + align:start position:0% +going on at night and you know up in up + + + align:start position:0% +going on at night and you know up in up +in the dormitories was they were working + + align:start position:0% +in the dormitories was they were working + + + align:start position:0% +in the dormitories was they were working +something out so they could they they + + align:start position:0% +something out so they could they they + + + align:start position:0% +something out so they could they they +they could communicate with each other + + align:start position:0% +they could communicate with each other + + + align:start position:0% +they could communicate with each other +and they put together a a sort of a + + align:start position:0% +and they put together a a sort of a + + + align:start position:0% +and they put together a a sort of a +Proto + + align:start position:0% +Proto + + + align:start position:0% +Proto +language then the Next Generation the + + align:start position:0% +language then the Next Generation the + + + align:start position:0% +language then the Next Generation the +next cohort of kids come and now there's + + align:start position:0% +next cohort of kids come and now there's + + + align:start position:0% +next cohort of kids come and now there's +a a a a crude linguistic environment and + + align:start position:0% +a a a a crude linguistic environment and + + + align:start position:0% +a a a a crude linguistic environment and +what has happened over the next few + + align:start position:0% +what has happened over the next few + + + align:start position:0% +what has happened over the next few +cohorts of kids is that these the the + + align:start position:0% +cohorts of kids is that these the the + + + align:start position:0% +cohorts of kids is that these the the +next round of language learning kids + + align:start position:0% +next round of language learning kids + + + align:start position:0% +next round of language learning kids +have systematically developed a language + + align:start position:0% +have systematically developed a language + + + align:start position:0% +have systematically developed a language +that now has grammatical structures in + + align:start position:0% +that now has grammatical structures in + + + align:start position:0% +that now has grammatical structures in +it that look like the grammatical + + align:start position:0% +it that look like the grammatical + + + align:start position:0% +it that look like the grammatical +structures of other languages American + + align:start position:0% +structures of other languages American + + + align:start position:0% +structures of other languages American +sign language which is the common + + align:start position:0% +sign language which is the common + + + align:start position:0% +sign language which is the common +language used in the deaf Community the + + align:start position:0% +language used in the deaf Community the + + + align:start position:0% +language used in the deaf Community the +signing deaf Community here is a + + align:start position:0% +signing deaf Community here is a + + + align:start position:0% +signing deaf Community here is a +language like French English Chinese or + + align:start position:0% +language like French English Chinese or + + + align:start position:0% +language like French English Chinese or +whatever it's not English translated + + align:start position:0% +whatever it's not English translated + + + align:start position:0% +whatever it's not English translated +into hand gestures um Nicaraguan sign + + align:start position:0% +into hand gestures um Nicaraguan sign + + + align:start position:0% +into hand gestures um Nicaraguan sign +language is not American Sign Language + + align:start position:0% +language is not American Sign Language + + + align:start position:0% +language is not American Sign Language +it's a new sign language with its own + + align:start position:0% +it's a new sign language with its own + + + align:start position:0% +it's a new sign language with its own +set of vocabulary and its own + + align:start position:0% +set of vocabulary and its own + + + align:start position:0% +set of vocabulary and its own +grammatical structure but that + + align:start position:0% +grammatical structure but that + + + align:start position:0% +grammatical structure but that +grammatical structure seems to + + align:start position:0% +grammatical structure seems to + + + align:start position:0% +grammatical structure seems to +reflect um an underlying tendency for + + align:start position:0% +reflect um an underlying tendency for + + + align:start position:0% +reflect um an underlying tendency for +all languages to have certain structures + + align:start position:0% +all languages to have certain structures + + + align:start position:0% +all languages to have certain structures +to them let me give you one example + + align:start position:0% +to them let me give you one example + + + align:start position:0% +to them let me give you one example +because brand new this uh this year's + + align:start position:0% +because brand new this uh this year's + + + align:start position:0% +because brand new this uh this year's +Discovery in this realm um suppose + + align:start position:0% +Discovery in this realm um suppose + + + align:start position:0% +Discovery in this realm um suppose +you're you're you're telling the Jack + + align:start position:0% +you're you're you're telling the Jack + + + align:start position:0% +you're you're you're telling the Jack +and Jill story right Jack and Jill went + + align:start position:0% +and Jill story right Jack and Jill went + + + align:start position:0% +and Jill story right Jack and Jill went +up the hill and and then stuff happens + + align:start position:0% +up the hill and and then stuff happens + + + align:start position:0% +up the hill and and then stuff happens +and they fall down the hill right in + + align:start position:0% +and they fall down the hill right in + + + align:start position:0% +and they fall down the hill right in +English the fall down part and the hill + + align:start position:0% +English the fall down part and the hill + + + align:start position:0% +English the fall down part and the hill +part are are are separate they are + + align:start position:0% +part are are are separate they are + + + align:start position:0% +part are are are separate they are +obligatorily separate there's the verb + + align:start position:0% +obligatorily separate there's the verb + + + align:start position:0% +obligatorily separate there's the verb +part and there's the object of that verb + + align:start position:0% +part and there's the object of that verb + + + align:start position:0% +part and there's the object of that verb +what you fell down and you fell down the + + align:start position:0% +what you fell down and you fell down the + + + align:start position:0% +what you fell down and you fell down the +hill there's no reason that would need + + align:start position:0% +hill there's no reason that would need + + + align:start position:0% +hill there's no reason that would need +to be the case in a sign language right + + align:start position:0% +to be the case in a sign language right + + + align:start position:0% +to be the case in a sign language right +you could perfectly have a gesture that + + align:start position:0% +you could perfectly have a gesture that + + + align:start position:0% +you could perfectly have a gesture that +was that designates the act of falling + + align:start position:0% +was that designates the act of falling + + + align:start position:0% +was that designates the act of falling +down a hill and indeed apparently the um + + align:start position:0% +down a hill and indeed apparently the um + + + align:start position:0% +down a hill and indeed apparently the um +first generations of signers in nicar in + + align:start position:0% +first generations of signers in nicar in + + + align:start position:0% +first generations of signers in nicar in +in this Nicaraguan school have signs + + align:start position:0% +in this Nicaraguan school have signs + + + align:start position:0% +in this Nicaraguan school have signs +like that but the new kids the kids who + + align:start position:0% +like that but the new kids the kids who + + + align:start position:0% +like that but the new kids the kids who +came in young and are learning + + align:start position:0% +came in young and are learning + + + align:start position:0% +came in young and are learning +developing this new uh grammatical + + align:start position:0% +developing this new uh grammatical + + + align:start position:0% +developing this new uh grammatical +version of sign language have now + + align:start position:0% +version of sign language have now + + + align:start position:0% +version of sign language have now +separated those signs out and have a + + align:start position:0% +separated those signs out and have a + + + align:start position:0% +separated those signs out and have a +falling sign and a hill sign I'm not I + + align:start position:0% +falling sign and a hill sign I'm not I + + + align:start position:0% +falling sign and a hill sign I'm not I +don't know that the signs look like that + + align:start position:0% +don't know that the signs look like that + + + align:start position:0% +don't know that the signs look like that +at all the important piece of it though + + align:start position:0% +at all the important piece of it though + + + align:start position:0% +at all the important piece of it though +that's another misconception about signs + + align:start position:0% +that's another misconception about signs + + + align:start position:0% +that's another misconception about signs +is that the signs necessarily need to be + + align:start position:0% +is that the signs necessarily need to be + + + align:start position:0% +is that the signs necessarily need to be +sort of pictographic there's no + + align:start position:0% +sort of pictographic there's no + + + align:start position:0% +sort of pictographic there's no +requirement that hill sign look like a + + align:start position:0% +requirement that hill sign look like a + + + align:start position:0% +requirement that hill sign look like a +hill but for those of us who are + + align:start position:0% +hill but for those of us who are + + + align:start position:0% +hill but for those of us who are +complete illiterates in anything like a + + align:start position:0% +complete illiterates in anything like a + + + align:start position:0% +complete illiterates in anything like a +sign language it might as well be + + align:start position:0% +sign language it might as well be + + + align:start position:0% +sign language it might as well be +because it gives you the idea so they + + align:start position:0% +because it gives you the idea so they + + + align:start position:0% +because it gives you the idea so they +have developed instead of a falling down + + align:start position:0% +have developed instead of a falling down + + + align:start position:0% +have developed instead of a falling down +the hill sign a + + align:start position:0% +the hill sign a + + + align:start position:0% +the hill sign a +falling Hill grammar that corresponds to + + align:start position:0% +falling Hill grammar that corresponds to + + + align:start position:0% +falling Hill grammar that corresponds to +the same sort of constraints that show + + align:start position:0% +the same sort of constraints that show + + + align:start position:0% +the same sort of constraints that show +up in other languages um strong evidence + + align:start position:0% +up in other languages um strong evidence + + + align:start position:0% +up in other languages um strong evidence +this whole project has been interesting + + align:start position:0% +this whole project has been interesting + + + align:start position:0% +this whole project has been interesting +evidence for the the powerful sense in + + align:start position:0% +evidence for the the powerful sense in + + + align:start position:0% +evidence for the the powerful sense in +which the human brain is there to uh to + + align:start position:0% +which the human brain is there to uh to + + + align:start position:0% +which the human brain is there to uh to +learn and even if necessary to to create + + align:start position:0% +learn and even if necessary to to create + + + align:start position:0% +learn and even if necessary to to create +language well I that raises the + + align:start position:0% +language well I that raises the + + + align:start position:0% +language well I that raises the +interesting question of well what about + + align:start position:0% +interesting question of well what about + + + align:start position:0% +interesting question of well what about +nonhuman brains do animals have um have + + align:start position:0% +nonhuman brains do animals have um have + + + align:start position:0% +nonhuman brains do animals have um have +language and this has been a question + + align:start position:0% +language and this has been a question + + + align:start position:0% +language and this has been a question +for a long long + + align:start position:0% +for a long long + + + align:start position:0% +for a long long +time it's been a scientific question for + + align:start position:0% +time it's been a scientific question for + + + align:start position:0% +time it's been a scientific question for +reasonably + + align:start position:0% +reasonably + + + align:start position:0% +reasonably +uh reasonably long time um it's we're + + align:start position:0% +uh reasonably long time um it's we're + + + align:start position:0% +uh reasonably long time um it's we're +going to talk about it's important to + + align:start position:0% +going to talk about it's important to + + + align:start position:0% +going to talk about it's important to +distinguish + + align:start position:0% +distinguish + + + align:start position:0% +distinguish +between uh two different sorts of + + align:start position:0% +between uh two different sorts of + + + align:start position:0% +between uh two different sorts of +language one would be the natural any + + align:start position:0% +language one would be the natural any + + + align:start position:0% +language one would be the natural any +natural language that the animals might + + align:start position:0% +natural language that the animals might + + + align:start position:0% +natural language that the animals might +have on their own do animals talk to + + align:start position:0% +have on their own do animals talk to + + + align:start position:0% +have on their own do animals talk to +each other in the absence of humans + + align:start position:0% +each other in the absence of humans + + + align:start position:0% +each other in the absence of humans +intervening um and the other question is + + align:start position:0% +intervening um and the other question is + + + align:start position:0% +intervening um and the other question is +can we teach them our language can we + + align:start position:0% +can we teach them our language can we + + + align:start position:0% +can we teach them our language can we +teach them how to how to talk like us in + + align:start position:0% +teach them how to how to talk like us in + + + align:start position:0% +teach them how to how to talk like us in +in uh in some + + align:start position:0% +in uh in some + + + align:start position:0% +in uh in some +fashion within this natural and trained + + align:start position:0% +fashion within this natural and trained + + + align:start position:0% +fashion within this natural and trained +language dichotomy then it's important + + align:start position:0% +language dichotomy then it's important + + + align:start position:0% +language dichotomy then it's important +to to break this the question of + + align:start position:0% +to to break this the question of + + + align:start position:0% +to to break this the question of +language down into smaller pieces um + + align:start position:0% +language down into smaller pieces um + + + align:start position:0% +language down into smaller pieces um +because otherwise you end up in an + + align:start position:0% +because otherwise you end up in an + + + align:start position:0% +because otherwise you end up in an +endless sterile argument about well what + + align:start position:0% +endless sterile argument about well what + + + align:start position:0% +endless sterile argument about well what +exactly do you mean by language um you + + align:start position:0% +exactly do you mean by language um you + + + align:start position:0% +exactly do you mean by language um you +can if I write a question on the final + + align:start position:0% +can if I write a question on the final + + + align:start position:0% +can if I write a question on the final +exam because it won't be on the midterm + + align:start position:0% +exam because it won't be on the midterm + + + align:start position:0% +exam because it won't be on the midterm +because today's topic is not on the + + align:start position:0% +because today's topic is not on the + + + align:start position:0% +because today's topic is not on the +midterm if it write on if I write a + + align:start position:0% +midterm if it write on if I write a + + + align:start position:0% +midterm if it write on if I write a +question on the on the final exam that + + align:start position:0% +question on the on the final exam that + + + align:start position:0% +question on the on the final exam that +basically says do animals have language + + align:start position:0% +basically says do animals have language + + + align:start position:0% +basically says do animals have language +it would be perfectly possible to write + + align:start position:0% +it would be perfectly possible to write + + + align:start position:0% +it would be perfectly possible to write +a coherent answer for either the yes or + + align:start position:0% +a coherent answer for either the yes or + + + align:start position:0% +a coherent answer for either the yes or +no + + align:start position:0% +no + + + align:start position:0% +no +position um but that would depend on + + align:start position:0% +position um but that would depend on + + + align:start position:0% +position um but that would depend on +what it is that you mean by language so + + align:start position:0% +what it is that you mean by language so + + + align:start position:0% +what it is that you mean by language so +let's break this down a little bit for + + align:start position:0% +let's break this down a little bit for + + + align:start position:0% +let's break this down a little bit for +starters do animals have something that + + align:start position:0% +starters do animals have something that + + + align:start position:0% +starters do animals have something that +um we could call signals + + align:start position:0% +um we could call signals + + + align:start position:0% +um we could call signals +um do they have sensory stimuli that are + + align:start position:0% +um do they have sensory stimuli that are + + + align:start position:0% +um do they have sensory stimuli that are +um communicative in their uh intent well + + align:start position:0% +um communicative in their uh intent well + + + align:start position:0% +um communicative in their uh intent well +look the answer to that is is is clearly + + align:start position:0% +look the answer to that is is is clearly + + + align:start position:0% +look the answer to that is is is clearly +yes um there's no problem with that with + + align:start position:0% +yes um there's no problem with that with + + + align:start position:0% +yes um there's no problem with that with +with figuring that out at all um you + + align:start position:0% +with figuring that out at all um you + + + align:start position:0% +with figuring that out at all um you +know a peacock's tail is a signal to uh + + align:start position:0% +know a peacock's tail is a signal to uh + + + align:start position:0% +know a peacock's tail is a signal to uh +to the peen um and tropical fish why are + + align:start position:0% +to the peen um and tropical fish why are + + + align:start position:0% +to the peen um and tropical fish why are +tropical fish do do do tropical fish + + align:start position:0% +tropical fish do do do tropical fish + + + align:start position:0% +tropical fish do do do tropical fish +have all these beautiful colors all over + + align:start position:0% +have all these beautiful colors all over + + + align:start position:0% +have all these beautiful colors all over +them well the idea is that I'm a + + align:start position:0% +them well the idea is that I'm a + + + align:start position:0% +them well the idea is that I'm a +tropical fish with oh I guess with + + align:start position:0% +tropical fish with oh I guess with + + + align:start position:0% +tropical fish with oh I guess with +stripes on and and um and I got to look + + align:start position:0% +stripes on and and um and I got to look + + + align:start position:0% +stripes on and and um and I got to look +for another tropical fish with stripes + + align:start position:0% +for another tropical fish with stripes + + + align:start position:0% +for another tropical fish with stripes +on because if I mate with one with spots + + align:start position:0% +on because if I mate with one with spots + + + align:start position:0% +on because if I mate with one with spots +on nothing's going to happen but if I + + align:start position:0% +on nothing's going to happen but if I + + + align:start position:0% +on nothing's going to happen but if I +mate with one with stripes on you know + + align:start position:0% +mate with one with stripes on you know + + + align:start position:0% +mate with one with stripes on you know +we we we we get more little stripy fish + + align:start position:0% +we we we we get more little stripy fish + + + align:start position:0% +we we we we get more little stripy fish +um that the peacock tale story is + + align:start position:0% +um that the peacock tale story is + + + align:start position:0% +um that the peacock tale story is +supposed to be slightly more complicated + + align:start position:0% +supposed to be slightly more complicated + + + align:start position:0% +supposed to be slightly more complicated +the standard evolutionary story story + + align:start position:0% +the standard evolutionary story story + + + align:start position:0% +the standard evolutionary story story +for peacock Tales is that peacock Tales + + align:start position:0% +for peacock Tales is that peacock Tales + + + align:start position:0% +for peacock Tales is that peacock Tales +are really stupid right that they don't + + align:start position:0% +are really stupid right that they don't + + + align:start position:0% +are really stupid right that they don't +help you fly they drag they they make + + align:start position:0% +help you fly they drag they they make + + + align:start position:0% +help you fly they drag they they make +you more likely to get chomped on by a + + align:start position:0% +you more likely to get chomped on by a + + + align:start position:0% +you more likely to get chomped on by a +predator and stuff but they a huge + + align:start position:0% +predator and stuff but they a huge + + + align:start position:0% +predator and stuff but they a huge +investment and and and what this is is + + align:start position:0% +investment and and and what this is is + + + align:start position:0% +investment and and and what this is is +the male peacock saying I am so fit my + + align:start position:0% +the male peacock saying I am so fit my + + + align:start position:0% +the male peacock saying I am so fit my +jeans are so good that I grew this whole + + align:start position:0% +jeans are so good that I grew this whole + + + align:start position:0% +jeans are so good that I grew this whole +thing just for you honey um and and you + + align:start position:0% +thing just for you honey um and and you + + + align:start position:0% +thing just for you honey um and and you +really ought to come and check this out + + align:start position:0% +really ought to come and check this out + + + align:start position:0% +really ought to come and check this out +um um so you know that it's it's a + + align:start position:0% +um um so you know that it's it's a + + + align:start position:0% +um um so you know that it's it's a +signal there's there and it's not just + + align:start position:0% +signal there's there and it's not just + + + align:start position:0% +signal there's there and it's not just +an awful lot of animal signals seem to + + align:start position:0% +an awful lot of animal signals seem to + + + align:start position:0% +an awful lot of animal signals seem to +be about um sex and mating uh issues not + + align:start position:0% +be about um sex and mating uh issues not + + + align:start position:0% +be about um sex and mating uh issues not +all of them so uh vervet monkeys for + + align:start position:0% +all of them so uh vervet monkeys for + + + align:start position:0% +all of them so uh vervet monkeys for +instance have uh three distinct alarm + + align:start position:0% +instance have uh three distinct alarm + + + align:start position:0% +instance have uh three distinct alarm +calls um how do you know they're + + align:start position:0% +calls um how do you know they're + + + align:start position:0% +calls um how do you know they're +distinct alarm calls well you go off and + + align:start position:0% +distinct alarm calls well you go off and + + + align:start position:0% +distinct alarm calls well you go off and +record them and then you get your your + + align:start position:0% +record them and then you get your your + + + align:start position:0% +record them and then you get your your +your uh uh not your iPod because they + + align:start position:0% +your uh uh not your iPod because they + + + align:start position:0% +your uh uh not your iPod because they +don't have the little ear you got your + + align:start position:0% +don't have the little ear you got your + + + align:start position:0% +don't have the little ear you got your +boom box or something and you play them + + align:start position:0% +boom box or something and you play them + + + align:start position:0% +boom box or something and you play them +to a bunch of vervent monkeys if you + + align:start position:0% +to a bunch of vervent monkeys if you + + + align:start position:0% +to a bunch of vervent monkeys if you +play uh um call number one all the + + align:start position:0% +play uh um call number one all the + + + align:start position:0% +play uh um call number one all the +vervent monkeys jump up a tree if you + + align:start position:0% +vervent monkeys jump up a tree if you + + + align:start position:0% +vervent monkeys jump up a tree if you +play call number two all the vervent + + align:start position:0% +play call number two all the vervent + + + align:start position:0% +play call number two all the vervent +monkeys jump down a hole and if you play + + align:start position:0% +monkeys jump down a hole and if you play + + + align:start position:0% +monkeys jump down a hole and if you play +number three they all stand up and look + + align:start position:0% +number three they all stand up and look + + + align:start position:0% +number three they all stand up and look +all around and + + align:start position:0% +all around and + + + align:start position:0% +all around and +apparently um what this is about is if + + align:start position:0% +apparently um what this is about is if + + + align:start position:0% +apparently um what this is about is if +you give if you see if you're a veret + + align:start position:0% +you give if you see if you're a veret + + + align:start position:0% +you give if you see if you're a veret +monkey and you see um a leopard you give + + align:start position:0% +monkey and you see um a leopard you give + + + align:start position:0% +monkey and you see um a leopard you give +one scream and everybody jumps up the + + align:start position:0% +one scream and everybody jumps up the + + + align:start position:0% +one scream and everybody jumps up the +tree because the leopard can't go up the + + align:start position:0% +tree because the leopard can't go up the + + + align:start position:0% +tree because the leopard can't go up the +tree + + align:start position:0% +tree + + + align:start position:0% +tree +um if you if you see a hawk or whatever + + align:start position:0% +um if you if you see a hawk or whatever + + + align:start position:0% +um if you if you see a hawk or whatever +the big predator bird is who eats veret + + align:start position:0% +the big predator bird is who eats veret + + + align:start position:0% +the big predator bird is who eats veret +monkeys um you give a different scream + + align:start position:0% +monkeys um you give a different scream + + + align:start position:0% +monkeys um you give a different scream +you should jump down the hole because + + align:start position:0% +you should jump down the hole because + + + align:start position:0% +you should jump down the hole because +the bird ain't going down the hole and + + align:start position:0% +the bird ain't going down the hole and + + + align:start position:0% +the bird ain't going down the hole and +snakes you want to just keep an eye out + + align:start position:0% +snakes you want to just keep an eye out + + + align:start position:0% +snakes you want to just keep an eye out +for them um if so if somebody thinks + + align:start position:0% +for them um if so if somebody thinks + + + align:start position:0% +for them um if so if somebody thinks +they see a snake everybody else is just + + align:start position:0% +they see a snake everybody else is just + + + align:start position:0% +they see a snake everybody else is just +GNA look around so you got that sort of + + align:start position:0% +GNA look around so you got that sort of + + + align:start position:0% +GNA look around so you got that sort of +a three-word vocabulary there it also + + align:start position:0% +a three-word vocabulary there it also + + + align:start position:0% +a three-word vocabulary there it also +gets on to the second issue on the + + align:start position:0% +gets on to the second issue on the + + + align:start position:0% +gets on to the second issue on the +handout I assume oh yes sir no that's + + align:start position:0% +handout I assume oh yes sir no that's + + + align:start position:0% +handout I assume oh yes sir no that's +not the handout this is the handout yes + + align:start position:0% +not the handout this is the handout yes + + + align:start position:0% +not the handout this is the handout yes +it should say meaning do these signals + + align:start position:0% +it should say meaning do these signals + + + align:start position:0% +it should say meaning do these signals +have meaning well sure there's no point + + align:start position:0% +have meaning well sure there's no point + + + align:start position:0% +have meaning well sure there's no point +to having a + + align:start position:0% +to having a + + + align:start position:0% +to having a +signal um of this sort if it doesn't + + align:start position:0% +signal um of this sort if it doesn't + + + align:start position:0% +signal um of this sort if it doesn't +have meaning well you could have a + + align:start position:0% +have meaning well you could have a + + + align:start position:0% +have meaning well you could have a +signal without meaning look got a rock + + align:start position:0% +signal without meaning look got a rock + + + align:start position:0% +signal without meaning look got a rock +here you know this this Crystal has a + + align:start position:0% +here you know this this Crystal has a + + + align:start position:0% +here you know this this Crystal has a +partic you know could be thought of as + + align:start position:0% +partic you know could be thought of as + + + align:start position:0% +partic you know could be thought of as +signaling its its uh you know sapphir or + + align:start position:0% +signaling its its uh you know sapphir or + + + align:start position:0% +signaling its its uh you know sapphir or +something like that but no other + + align:start position:0% +something like that but no other + + + align:start position:0% +something like that but no other +Sapphire gives a hoot about it there's + + align:start position:0% +Sapphire gives a hoot about it there's + + + align:start position:0% +Sapphire gives a hoot about it there's +no meaning there from the point of view + + align:start position:0% +no meaning there from the point of view + + + align:start position:0% +no meaning there from the point of view +of the rock it just is whereas um and + + align:start position:0% +of the rock it just is whereas um and + + + align:start position:0% +of the rock it just is whereas um and +animals signals of the sort that we've + + align:start position:0% +animals signals of the sort that we've + + + align:start position:0% +animals signals of the sort that we've +been talking about clearly have + + align:start position:0% +been talking about clearly have + + + align:start position:0% +been talking about clearly have +communicative intent there is a a a + + align:start position:0% +communicative intent there is a a a + + + align:start position:0% +communicative intent there is a a a +purpose here and it's not even confined + + align:start position:0% +purpose here and it's not even confined + + + align:start position:0% +purpose here and it's not even confined +just to animals it turns out um there + + align:start position:0% +just to animals it turns out um there + + + align:start position:0% +just to animals it turns out um there +are trees who respond to Predator + + align:start position:0% +are trees who respond to Predator + + + align:start position:0% +are trees who respond to Predator +attacks by releasing a uh a chemical in + + align:start position:0% +attacks by releasing a uh a chemical in + + + align:start position:0% +attacks by releasing a uh a chemical in +and it's all quite a passive kind of + + align:start position:0% +and it's all quite a passive kind of + + + align:start position:0% +and it's all quite a passive kind of +thing the uh um the the the bug chews on + + align:start position:0% +thing the uh um the the the bug chews on + + + align:start position:0% +thing the uh um the the the bug chews on +the leaves that ruptures the cells which + + align:start position:0% +the leaves that ruptures the cells which + + + align:start position:0% +the leaves that ruptures the cells which +causes a chemical to be released which + + align:start position:0% +causes a chemical to be released which + + + align:start position:0% +causes a chemical to be released which +can then be uh picked up by the next + + align:start position:0% +can then be uh picked up by the next + + + align:start position:0% +can then be uh picked up by the next +tree over the next tree over in response + + align:start position:0% +tree over the next tree over in response + + + align:start position:0% +tree over the next tree over in response +now mobilizes a defense against that + + align:start position:0% +now mobilizes a defense against that + + + align:start position:0% +now mobilizes a defense against that +Predator so in a sense the trees are + + align:start position:0% +Predator so in a sense the trees are + + + align:start position:0% +Predator so in a sense the trees are +talking to uh to each other there's a + + align:start position:0% +talking to uh to each other there's a + + + align:start position:0% +talking to uh to each other there's a +signal there and it's being uh it's + + align:start position:0% +signal there and it's being uh it's + + + align:start position:0% +signal there and it's being uh it's +being + + align:start position:0% +being + + + align:start position:0% +being +received um so no doubt that the animal + + align:start position:0% +received um so no doubt that the animal + + + align:start position:0% +received um so no doubt that the animal +kingdom has uh signals the equivalent in + + align:start position:0% +kingdom has uh signals the equivalent in + + + align:start position:0% +kingdom has uh signals the equivalent in +human language would be phones um a and + + align:start position:0% +human language would be phones um a and + + + align:start position:0% +human language would be phones um a and +uh no doubt that uh that these signals + + align:start position:0% +uh no doubt that uh that these signals + + + align:start position:0% +uh no doubt that uh that these signals +have um meaning uh at least in some + + align:start position:0% +have um meaning uh at least in some + + + align:start position:0% +have um meaning uh at least in some +cases and and that could be considered + + align:start position:0% +cases and and that could be considered + + + align:start position:0% +cases and and that could be considered +to be sort of the equivalent of + + align:start position:0% +to be sort of the equivalent of + + + align:start position:0% +to be sort of the equivalent of +morphemes what about um what about human + + align:start position:0% +morphemes what about um what about human + + + align:start position:0% +morphemes what about um what about human +language what about training an animal + + align:start position:0% +language what about training an animal + + + align:start position:0% +language what about training an animal +to use human language could be the case + + align:start position:0% +to use human language could be the case + + + align:start position:0% +to use human language could be the case +that the only + + align:start position:0% +that the only + + + align:start position:0% +that the only +reason that a chimp who is a close + + align:start position:0% +reason that a chimp who is a close + + + align:start position:0% +reason that a chimp who is a close +relation of ours hasn't talked to us is + + align:start position:0% +relation of ours hasn't talked to us is + + + align:start position:0% +relation of ours hasn't talked to us is +because nobody talked to him + + align:start position:0% +because nobody talked to him + + + align:start position:0% +because nobody talked to him +so back in the 30s the hazes uh couple + + align:start position:0% +so back in the 30s the hazes uh couple + + + align:start position:0% +so back in the 30s the hazes uh couple +in Salt Lake City as I recall tried this + + align:start position:0% +in Salt Lake City as I recall tried this + + + align:start position:0% +in Salt Lake City as I recall tried this +out what they did was they had a kid + + align:start position:0% +out what they did was they had a kid + + + align:start position:0% +out what they did was they had a kid +Mara could try this they they had a kid + + align:start position:0% +Mara could try this they they had a kid + + + align:start position:0% +Mara could try this they they had a kid +they got a chimp they said we'll raise + + align:start position:0% +they got a chimp they said we'll raise + + + align:start position:0% +they got a chimp they said we'll raise +the two of them identically I don't know + + align:start position:0% +the two of them identically I don't know + + + align:start position:0% +the two of them identically I don't know +the chimp might sleep through the night + + align:start position:0% +the chimp might sleep through the night + + + align:start position:0% +the chimp might sleep through the night +sooner the um but they you know they'll + + align:start position:0% +sooner the um but they you know they'll + + + align:start position:0% +sooner the um but they you know they'll +talk to the kid they'll talk to the + + align:start position:0% +talk to the kid they'll talk to the + + + align:start position:0% +talk to the kid they'll talk to the +chimp and and + + align:start position:0% +chimp and and + + + align:start position:0% +chimp and and +after how + + align:start position:0% +after how + + + align:start position:0% +after how +long oh I didn't it doesn't say how long + + align:start position:0% +long oh I didn't it doesn't say how long + + + align:start position:0% +long oh I didn't it doesn't say how long +they were at it you don't want to do + + align:start position:0% +they were at it you don't want to do + + + align:start position:0% +they were at it you don't want to do +this for too long because after a while + + align:start position:0% +this for too long because after a while + + + align:start position:0% +this for too long because after a while +um raising your chimp with your just + + align:start position:0% +um raising your chimp with your just + + + align:start position:0% +um raising your chimp with your just +hanging around in the in in the playroom + + align:start position:0% +hanging around in the in in the playroom + + + align:start position:0% +hanging around in the in in the playroom +with your uh kid is not going to be good + + align:start position:0% +with your uh kid is not going to be good + + + align:start position:0% +with your uh kid is not going to be good +for the kid because the chimp may not + + align:start position:0% +for the kid because the chimp may not + + + align:start position:0% +for the kid because the chimp may not +talk a lot but the chimp grows big and + + align:start position:0% +talk a lot but the chimp grows big and + + + align:start position:0% +talk a lot but the chimp grows big and +strong um and uh will play with your kid + + align:start position:0% +strong um and uh will play with your kid + + + align:start position:0% +strong um and uh will play with your kid +in ways that your kid will not + + align:start position:0% +in ways that your kid will not + + + align:start position:0% +in ways that your kid will not +enjoy but um the kid the chimp didn't + + align:start position:0% +enjoy but um the kid the chimp didn't + + + align:start position:0% +enjoy but um the kid the chimp didn't +talk any nor and this is important + + align:start position:0% +talk any nor and this is important + + + align:start position:0% +talk any nor and this is important +because any neurologically normal child + + align:start position:0% +because any neurologically normal child + + + align:start position:0% +because any neurologically normal child +raised in a linguistic environment um + + align:start position:0% +raised in a linguistic environment um + + + align:start position:0% +raised in a linguistic environment um +will will talk we'll we'll we'll learn + + align:start position:0% +will will talk we'll we'll we'll learn + + + align:start position:0% +will will talk we'll we'll we'll learn +to we'll learn to talk um and and or or + + align:start position:0% +to we'll learn to talk um and and or or + + + align:start position:0% +to we'll learn to talk um and and or or +if if DEA will communicate um you know + + align:start position:0% +if if DEA will communicate um you know + + + align:start position:0% +if if DEA will communicate um you know +and give given an appropriate input + + align:start position:0% +and give given an appropriate input + + + align:start position:0% +and give given an appropriate input +will'll communicate in in in other ways + + align:start position:0% +will'll communicate in in in other ways + + + align:start position:0% +will'll communicate in in in other ways +um the um the chimp is reputed to have + + align:start position:0% +um the um the chimp is reputed to have + + + align:start position:0% +um the um the chimp is reputed to have +said I think Mama what what do we got + + align:start position:0% +said I think Mama what what do we got + + + align:start position:0% +said I think Mama what what do we got +here mama papa and cup you know okay + + align:start position:0% +here mama papa and cup you know okay + + + align:start position:0% +here mama papa and cup you know okay +that and and and and and that was it now + + align:start position:0% +that and and and and and that was it now + + + align:start position:0% +that and and and and and that was it now +one of the problems here that was + + align:start position:0% +one of the problems here that was + + + align:start position:0% +one of the problems here that was +quickly identified is that the chimp's + + align:start position:0% +quickly identified is that the chimp's + + + align:start position:0% +quickly identified is that the chimp's +vocal apparatus is not like yours and + + align:start position:0% +vocal apparatus is not like yours and + + + align:start position:0% +vocal apparatus is not like yours and +mine and is poorly designed to make the + + align:start position:0% +mine and is poorly designed to make the + + + align:start position:0% +mine and is poorly designed to make the +range of human phones that are important + + align:start position:0% +range of human phones that are important + + + align:start position:0% +range of human phones that are important +in human language um so the uh um uh it + + align:start position:0% +in human language um so the uh um uh it + + + align:start position:0% +in human language um so the uh um uh it +occurred to subsequent researchers to + + align:start position:0% +occurred to subsequent researchers to + + + align:start position:0% +occurred to subsequent researchers to +try using sign language with with chimps + + align:start position:0% +try using sign language with with chimps + + + align:start position:0% +try using sign language with with chimps +or uh because um The Chimps are very + + align:start position:0% +or uh because um The Chimps are very + + + align:start position:0% +or uh because um The Chimps are very +good with their hands there's no problem + + align:start position:0% +good with their hands there's no problem + + + align:start position:0% +good with their hands there's no problem +making the sort of gestures there's no + + align:start position:0% +making the sort of gestures there's no + + + align:start position:0% +making the sort of gestures there's no +physical limitation on the on on the + + align:start position:0% +physical limitation on the on on the + + + align:start position:0% +physical limitation on the on on the +sort of gestures that uh that The Chimps + + align:start position:0% +sort of gestures that uh that The Chimps + + + align:start position:0% +sort of gestures that uh that The Chimps +could make or gorillas um limited work + + align:start position:0% +could make or gorillas um limited work + + + align:start position:0% +could make or gorillas um limited work +with oranga tangs who turn out to be uh + + align:start position:0% +with oranga tangs who turn out to be uh + + + align:start position:0% +with oranga tangs who turn out to be uh +uh big and lazy I understand um but + + align:start position:0% +uh big and lazy I understand um but + + + align:start position:0% +uh big and lazy I understand um but +gorillas chimps bonabo chimps uh and and + + align:start position:0% +gorillas chimps bonabo chimps uh and and + + + align:start position:0% +gorillas chimps bonabo chimps uh and and +gorillas are all make good signers um + + align:start position:0% +gorillas are all make good signers um + + + align:start position:0% +gorillas are all make good signers um +the uh and and and so most of the effort + + align:start position:0% +the uh and and and so most of the effort + + + align:start position:0% +the uh and and and so most of the effort +to teach human language to um primates + + align:start position:0% +to teach human language to um primates + + + align:start position:0% +to teach human language to um primates +has involved sign language or uh + + align:start position:0% +has involved sign language or uh + + + align:start position:0% +has involved sign language or uh +computer keyboard Arrangements where you + + align:start position:0% +computer keyboard Arrangements where you + + + align:start position:0% +computer keyboard Arrangements where you +teach you're sort of teaching the the uh + + align:start position:0% +teach you're sort of teaching the the uh + + + align:start position:0% +teach you're sort of teaching the the uh +animal to to type in a sense rather than + + align:start position:0% +animal to to type in a sense rather than + + + align:start position:0% +animal to to type in a sense rather than +to uh um rather than to sign um now it's + + align:start position:0% +to uh um rather than to sign um now it's + + + align:start position:0% +to uh um rather than to sign um now it's +true that chimps are not don't have the + + align:start position:0% +true that chimps are not don't have the + + + align:start position:0% +true that chimps are not don't have the +vocal apparatus to talk the way you and + + align:start position:0% +vocal apparatus to talk the way you and + + + align:start position:0% +vocal apparatus to talk the way you and +I talk talk but that couldn't be the + + align:start position:0% +I talk talk but that couldn't be the + + + align:start position:0% +I talk talk but that couldn't be the +whole story because if you have a child + + align:start position:0% +whole story because if you have a child + + + align:start position:0% +whole story because if you have a child +born with some congenital malformation + + align:start position:0% +born with some congenital malformation + + + align:start position:0% +born with some congenital malformation +that makes it impossible for them to + + align:start position:0% +that makes it impossible for them to + + + align:start position:0% +that makes it impossible for them to +talk properly that child will talk badly + + align:start position:0% +talk properly that child will talk badly + + + align:start position:0% +talk properly that child will talk badly +but will talk and will learn a language + + align:start position:0% +but will talk and will learn a language + + + align:start position:0% +but will talk and will learn a language +a chimp um in the same situation will + + align:start position:0% +a chimp um in the same situation will + + + align:start position:0% +a chimp um in the same situation will +simply not talk there is a fundamental + + align:start position:0% +simply not talk there is a fundamental + + + align:start position:0% +simply not talk there is a fundamental +difference in the way that uh that that + + align:start position:0% +difference in the way that uh that that + + + align:start position:0% +difference in the way that uh that that +the chimp and the child are responding + + align:start position:0% +the chimp and the child are responding + + + align:start position:0% +the chimp and the child are responding +to uh two linguistic input + + align:start position:0% +to uh two linguistic input + + + align:start position:0% +to uh two linguistic input +um + + align:start position:0% +um + + + align:start position:0% +um +so can you teach them to sign yeah + + align:start position:0% +so can you teach them to sign yeah + + + align:start position:0% +so can you teach them to sign yeah +actually you can teach them to sign + + align:start position:0% +actually you can teach them to sign + + + align:start position:0% +actually you can teach them to sign +there a whole string of chimps um who + + align:start position:0% +there a whole string of chimps um who + + + align:start position:0% +there a whole string of chimps um who +really do really quite well uh with + + align:start position:0% +really do really quite well uh with + + + align:start position:0% +really do really quite well uh with +vocabularies on the order of of uh + + align:start position:0% +vocabularies on the order of of uh + + + align:start position:0% +vocabularies on the order of of uh +hundreds of signs that um that seem to + + align:start position:0% +hundreds of signs that um that seem to + + + align:start position:0% +hundreds of signs that um that seem to +have discreet meaning and it's not it's + + align:start position:0% +have discreet meaning and it's not it's + + + align:start position:0% +have discreet meaning and it's not it's +not limited even to uh to chimps um + + align:start position:0% +not limited even to uh to chimps um + + + align:start position:0% +not limited even to uh to chimps um +Irene pepperberg who um was here for a + + align:start position:0% +Irene pepperberg who um was here for a + + + align:start position:0% +Irene pepperberg who um was here for a +while is now a fellow at Harvard this + + align:start position:0% +while is now a fellow at Harvard this + + + align:start position:0% +while is now a fellow at Harvard this +year has made a career out of studying + + align:start position:0% +year has made a career out of studying + + + align:start position:0% +year has made a career out of studying +uh African gray parrots you know it's a + + align:start position:0% +uh African gray parrots you know it's a + + + align:start position:0% +uh African gray parrots you know it's a +not terribly dramatic nice looking + + align:start position:0% +not terribly dramatic nice looking + + + align:start position:0% +not terribly dramatic nice looking +little parrot with a nice little bird + + align:start position:0% +little parrot with a nice little bird + + + align:start position:0% +little parrot with a nice little bird +brain and uh the nice thing of course + + align:start position:0% +brain and uh the nice thing of course + + + align:start position:0% +brain and uh the nice thing of course +about parrots is that they they can form + + align:start position:0% +about parrots is that they they can form + + + align:start position:0% +about parrots is that they they can form +uh the sounds that they're they're + + align:start position:0% +uh the sounds that they're they're + + + align:start position:0% +uh the sounds that they're they're +pretty good with the phon names right + + align:start position:0% +pretty good with the phon names right + + + align:start position:0% +pretty good with the phon names right +you probably want a cracker and all that + + align:start position:0% +you probably want a cracker and all that + + + align:start position:0% +you probably want a cracker and all that +sort of stuff but they're also + + align:start position:0% +sort of stuff but they're also + + + align:start position:0% +sort of stuff but they're also +remarkably bright and and um uh Alex her + + align:start position:0% +remarkably bright and and um uh Alex her + + + align:start position:0% +remarkably bright and and um uh Alex her +great African gray um has a vocabulary + + align:start position:0% +great African gray um has a vocabulary + + + align:start position:0% +great African gray um has a vocabulary +on the order of I 50 to 100 words I I + + align:start position:0% +on the order of I 50 to 100 words I I + + + align:start position:0% +on the order of I 50 to 100 words I I +think um that it can use in uh I suppose + + align:start position:0% +think um that it can use in uh I suppose + + + align:start position:0% +think um that it can use in uh I suppose +he can use in various and uh uh + + align:start position:0% +he can use in various and uh uh + + + align:start position:0% +he can use in various and uh uh +reasonable ways so if you if if Irene + + align:start position:0% +reasonable ways so if you if if Irene + + + align:start position:0% +reasonable ways so if you if if Irene +says to Alex pick up the blue thing um + + align:start position:0% +says to Alex pick up the blue thing um + + + align:start position:0% +says to Alex pick up the blue thing um +or the blue one that you Alex will + + align:start position:0% +or the blue one that you Alex will + + + align:start position:0% +or the blue one that you Alex will +toddle over and and and and grab a blue + + align:start position:0% +toddle over and and and and grab a blue + + + align:start position:0% +toddle over and and and and grab a blue +thing and and and if you say uh get the + + align:start position:0% +thing and and and if you say uh get the + + + align:start position:0% +thing and and and if you say uh get the +truck it'll go get the truck and stuff + + align:start position:0% +truck it'll go get the truck and stuff + + + align:start position:0% +truck it'll go get the truck and stuff +like that it clearly has a grasp of a + + align:start position:0% +like that it clearly has a grasp of a + + + align:start position:0% +like that it clearly has a grasp of a +vocabulary and an ability to use it in + + align:start position:0% +vocabulary and an ability to use it in + + + align:start position:0% +vocabulary and an ability to use it in +um in in some fashion uh or other mostly + + align:start position:0% +um in in some fashion uh or other mostly + + + align:start position:0% +um in in some fashion uh or other mostly +trained almost all the examples of + + align:start position:0% +trained almost all the examples of + + + align:start position:0% +trained almost all the examples of +animal use of of of a human language uh + + align:start position:0% +animal use of of of a human language uh + + + align:start position:0% +animal use of of of a human language uh +you know any any aspects of a human + + align:start position:0% +you know any any aspects of a human + + + align:start position:0% +you know any any aspects of a human +language are heavily Tred trained again + + align:start position:0% +language are heavily Tred trained again + + + align:start position:0% +language are heavily Tred trained again +that's different from a little kid um + + align:start position:0% +that's different from a little kid um + + + align:start position:0% +that's different from a little kid um +where a little kid will pick up a + + align:start position:0% +where a little kid will pick up a + + + align:start position:0% +where a little kid will pick up a +language just by being around speakers + + align:start position:0% +language just by being around speakers + + + align:start position:0% +language just by being around speakers +um there + + align:start position:0% +um there + + + align:start position:0% +um there +is uh there are a couple of instances + + align:start position:0% +is uh there are a couple of instances + + + align:start position:0% +is uh there are a couple of instances +now in the literature where um + + align:start position:0% +now in the literature where um + + + align:start position:0% +now in the literature where um +children The Offspring of signing Apes + + align:start position:0% +children The Offspring of signing Apes + + + align:start position:0% +children The Offspring of signing Apes +have picked up signing on their own so + + align:start position:0% +have picked up signing on their own so + + + align:start position:0% +have picked up signing on their own so +it may in fact be the case that they + + align:start position:0% +it may in fact be the case that they + + + align:start position:0% +it may in fact be the case that they +don't that you don't need explicit um + + align:start position:0% +don't that you don't need explicit um + + + align:start position:0% +don't that you don't need explicit um +training but what is what what does seem + + align:start position:0% +training but what is what what does seem + + + align:start position:0% +training but what is what what does seem +to be the case is that you can + + align:start position:0% +to be the case is that you can + + + align:start position:0% +to be the case is that you can +um uh that that chimps and parrots can + + align:start position:0% +um uh that that chimps and parrots can + + + align:start position:0% +um uh that that chimps and parrots can +use + + align:start position:0% +use + + + align:start position:0% +use +um what what you'd probably consider to + + align:start position:0% +um what what you'd probably consider to + + + align:start position:0% +um what what you'd probably consider to +be morphemes signs with with meaning of + + align:start position:0% +be morphemes signs with with meaning of + + + align:start position:0% +be morphemes signs with with meaning of +some sort there are issues about the + + align:start position:0% +some sort there are issues about the + + + align:start position:0% +some sort there are issues about the +data quality so if you uh point to + + align:start position:0% +data quality so if you uh point to + + + align:start position:0% +data quality so if you uh point to +something you know if you point to this + + align:start position:0% +something you know if you point to this + + + align:start position:0% +something you know if you point to this +banana and uh ask one of the signing + + align:start position:0% +banana and uh ask one of the signing + + + align:start position:0% +banana and uh ask one of the signing +Apes what it is you'll probably get + + align:start position:0% +Apes what it is you'll probably get + + + align:start position:0% +Apes what it is you'll probably get +banana but you might get something out + + align:start position:0% +banana but you might get something out + + + align:start position:0% +banana but you might get something out +like you know banana banana me tickle + + align:start position:0% +like you know banana banana me tickle + + + align:start position:0% +like you know banana banana me tickle +banana you tickle me banana banana or + + align:start position:0% +banana you tickle me banana banana or + + + align:start position:0% +banana you tickle me banana banana or +something and you might wonder whether + + align:start position:0% +something and you might wonder whether + + + align:start position:0% +something and you might wonder whether +or not you should code that as as banana + + align:start position:0% +or not you should code that as as banana + + + align:start position:0% +or not you should code that as as banana +um the uh the the as I saw one + + align:start position:0% +um the uh the the as I saw one + + + align:start position:0% +um the uh the the as I saw one +description that said that uh chimps + + align:start position:0% +description that said that uh chimps + + + align:start position:0% +description that said that uh chimps +tend to run on at the hands you know the + + align:start position:0% +tend to run on at the hands you know the + + + align:start position:0% +tend to run on at the hands you know the +expression to that somebody runs on at + + align:start position:0% +expression to that somebody runs on at + + + align:start position:0% +expression to that somebody runs on at +the mouth well chimps sign a lot these + + align:start position:0% +the mouth well chimps sign a lot these + + + align:start position:0% +the mouth well chimps sign a lot these +signing chimps BEC perhaps because + + align:start position:0% +signing chimps BEC perhaps because + + + align:start position:0% +signing chimps BEC perhaps because +they're playing the same guessing game + + align:start position:0% +they're playing the same guessing game + + + align:start position:0% +they're playing the same guessing game +that we're all playing with language + + align:start position:0% +that we're all playing with language + + + align:start position:0% +that we're all playing with language +what does this guy want from me you know + + align:start position:0% +what does this guy want from me you know + + + align:start position:0% +what does this guy want from me you know +what's he trying to con pointing at that + + align:start position:0% +what's he trying to con pointing at that + + + align:start position:0% +what's he trying to con pointing at that +thing oh yeah if if I make these banana + + align:start position:0% +thing oh yeah if if I make these banana + + + align:start position:0% +thing oh yeah if if I make these banana +signs maybe a few other signs in there + + align:start position:0% +signs maybe a few other signs in there + + + align:start position:0% +signs maybe a few other signs in there +you know good things will happen he'll + + align:start position:0% +you know good things will happen he'll + + + align:start position:0% +you know good things will happen he'll +be happy with me and maybe we'll get + + align:start position:0% +be happy with me and maybe we'll get + + + align:start position:0% +be happy with me and maybe we'll get +good stuff so in any case we've got + + align:start position:0% +good stuff so in any case we've got + + + align:start position:0% +good stuff so in any case we've got +evidence for um signals we've got + + align:start position:0% +evidence for um signals we've got + + + align:start position:0% +evidence for um signals we've got +evidence that they have meaning how + + align:start position:0% +evidence that they have meaning how + + + align:start position:0% +evidence that they have meaning how +about grammar is there any evidence for + + align:start position:0% +about grammar is there any evidence for + + + align:start position:0% +about grammar is there any evidence for +uh grammar in in animals um things get + + align:start position:0% +uh grammar in in animals um things get + + + align:start position:0% +uh grammar in in animals um things get +thinner there recall that you can use uh + + align:start position:0% +thinner there recall that you can use uh + + + align:start position:0% +thinner there recall that you can use uh +grammatical + + align:start position:0% +grammatical + + + align:start position:0% +grammatical +information um to get yourself into the + + align:start position:0% +information um to get yourself into the + + + align:start position:0% +information um to get yourself into the +meaning of an utterance even if you + + align:start position:0% +meaning of an utterance even if you + + + align:start position:0% +meaning of an utterance even if you +don't really well I I think did I put on + + align:start position:0% +don't really well I I think did I put on + + + align:start position:0% +don't really well I I think did I put on +the handout colorless green ideas sleep + + align:start position:0% +the handout colorless green ideas sleep + + + align:start position:0% +the handout colorless green ideas sleep +furiously which I think is a a Chomsky + + align:start position:0% +furiously which I think is a a Chomsky + + + align:start position:0% +furiously which I think is a a Chomsky +ISM originally designed to point out + + align:start position:0% +ISM originally designed to point out + + + align:start position:0% +ISM originally designed to point out +that purely + + align:start position:0% +that purely + + + align:start position:0% +that purely +syntactic information tells you do + + align:start position:0% +syntactic information tells you do + + + align:start position:0% +syntactic information tells you do +something even without um much in the + + align:start position:0% +something even without um much in the + + + align:start position:0% +something even without um much in the +way of you know how that sentence put + + align:start position:0% +way of you know how that sentence put + + + align:start position:0% +way of you know how that sentence put +together actually this goes back before + + align:start position:0% +together actually this goes back before + + + align:start position:0% +together actually this goes back before +that uh how many of you are great + + align:start position:0% +that uh how many of you are great + + + align:start position:0% +that uh how many of you are great +Allison Wonderland fans from your youth + + align:start position:0% +Allison Wonderland fans from your youth + + + align:start position:0% +Allison Wonderland fans from your youth +at some point oh very limited you're + + align:start position:0% +at some point oh very limited you're + + + align:start position:0% +at some point oh very limited you're +you're so most people cannot sit here + + align:start position:0% +you're so most people cannot sit here + + + align:start position:0% +you're so most people cannot sit here +and quote back to me TW brillig and the + + align:start position:0% +and quote back to me TW brillig and the + + + align:start position:0% +and quote back to me TW brillig and the +slyy toes did guy and gimbal in the wave + + align:start position:0% +slyy toes did guy and gimbal in the wave + + + align:start position:0% +slyy toes did guy and gimbal in the wave +all Mimsy were the borrow Groves and the + + align:start position:0% +all Mimsy were the borrow Groves and the + + + align:start position:0% +all Mimsy were the borrow Groves and the +mom rats + + align:start position:0% +mom rats + + + align:start position:0% +mom rats +outra um you have no idea what that's + + align:start position:0% +outra um you have no idea what that's + + + align:start position:0% +outra um you have no idea what that's +about yeah it's it's a it's the + + align:start position:0% +about yeah it's it's a it's the + + + align:start position:0% +about yeah it's it's a it's the +Jabberwocky poem in in in uh it's + + align:start position:0% +Jabberwocky poem in in in uh it's + + + align:start position:0% +Jabberwocky poem in in in uh it's +through the looking glass or I think + + align:start position:0% +through the looking glass or I think + + + align:start position:0% +through the looking glass or I think +it's through looking glass ra rather + + align:start position:0% +it's through looking glass ra rather + + + align:start position:0% +it's through looking glass ra rather +than anyway it's it's it's in it's in uh + + align:start position:0% +than anyway it's it's it's in it's in uh + + + align:start position:0% +than anyway it's it's it's in it's in uh +in one of the two Alice books but the + + align:start position:0% +in one of the two Alice books but the + + + align:start position:0% +in one of the two Alice books but the +interesting thing about it is even + + align:start position:0% +interesting thing about it is even + + + align:start position:0% +interesting thing about it is even +though you have no idea um you know twas + + align:start position:0% +though you have no idea um you know twas + + + align:start position:0% +though you have no idea um you know twas +brillig and the slidy toes did guy and + + align:start position:0% +brillig and the slidy toes did guy and + + + align:start position:0% +brillig and the slidy toes did guy and +gimbal in the wave + + align:start position:0% +gimbal in the wave + + + align:start position:0% +gimbal in the wave +you well but you know that now that + + align:start position:0% +you well but you know that now that + + + align:start position:0% +you well but you know that now that +there are some things called toes they + + align:start position:0% +there are some things called toes they + + + align:start position:0% +there are some things called toes they +have the attribute of + + align:start position:0% +have the attribute of + + + align:start position:0% +have the attribute of +sness they can do things that um are + + align:start position:0% +sness they can do things that um are + + + align:start position:0% +sness they can do things that um are +apparently uh uh guying and gimal you + + align:start position:0% +apparently uh uh guying and gimal you + + + align:start position:0% +apparently uh uh guying and gimal you +can say things like guing and gimb + + align:start position:0% +can say things like guing and gimb + + + align:start position:0% +can say things like guing and gimb +inging these things even though you + + align:start position:0% +inging these things even though you + + + align:start position:0% +inging these things even though you +never you not got no idea what this verb + + align:start position:0% +never you not got no idea what this verb + + + align:start position:0% +never you not got no idea what this verb +means you just know it's a verb so + + align:start position:0% +means you just know it's a verb so + + + align:start position:0% +means you just know it's a verb so +that's the sort of power of the grammar + + align:start position:0% +that's the sort of power of the grammar + + + align:start position:0% +that's the sort of power of the grammar +of the syntax of the language to what + + align:start position:0% +of the syntax of the language to what + + + align:start position:0% +of the syntax of the language to what +extent do animals have a grip on on that + + align:start position:0% +extent do animals have a grip on on that + + + align:start position:0% +extent do animals have a grip on on that +uh the answer seems to be a pretty + + align:start position:0% +uh the answer seems to be a pretty + + + align:start position:0% +uh the answer seems to be a pretty +limited grip there is evidence for word + + align:start position:0% +limited grip there is evidence for word + + + align:start position:0% +limited grip there is evidence for word +order um sensitivity in in uh animal + + align:start position:0% +order um sensitivity in in uh animal + + + align:start position:0% +order um sensitivity in in uh animal +signing for instance so um you can uh + + align:start position:0% +signing for instance so um you can uh + + + align:start position:0% +signing for instance so um you can uh +you can have you know the the the the uh + + align:start position:0% +you can have you know the the the the uh + + + align:start position:0% +you can have you know the the the the uh +chimp equivalent of John hit Mary being + + align:start position:0% +chimp equivalent of John hit Mary being + + + align:start position:0% +chimp equivalent of John hit Mary being +different from Mary hit John um those + + align:start position:0% +different from Mary hit John um those + + + align:start position:0% +different from Mary hit John um those +are two the you know same + + align:start position:0% +are two the you know same + + + align:start position:0% +are two the you know same +words um different order different + + align:start position:0% +words um different order different + + + align:start position:0% +words um different order different +meaning and and chimps will show his + + align:start position:0% +meaning and and chimps will show his + + + align:start position:0% +meaning and and chimps will show his +sensitivity to that in fact uh when this + + align:start position:0% +sensitivity to that in fact uh when this + + + align:start position:0% +sensitivity to that in fact uh when this +was a hot issue + + align:start position:0% +was a hot issue + + + align:start position:0% +was a hot issue +um and and and people were arguing about + + align:start position:0% +um and and and people were arguing about + + + align:start position:0% +um and and and people were arguing about +it vociferously uh Epstein up at Harvard + + align:start position:0% +it vociferously uh Epstein up at Harvard + + + align:start position:0% +it vociferously uh Epstein up at Harvard +who was one of Skinner's last students + + align:start position:0% +who was one of Skinner's last students + + + align:start position:0% +who was one of Skinner's last students +used to have a great time trying to do + + align:start position:0% +used to have a great time trying to do + + + align:start position:0% +used to have a great time trying to do +chimp you know these fancy chimp + + align:start position:0% +chimp you know these fancy chimp + + + align:start position:0% +chimp you know these fancy chimp +language demonstrations with pigeons and + + align:start position:0% +language demonstrations with pigeons and + + + align:start position:0% +language demonstrations with pigeons and +he showed that sure enough you could get + + align:start position:0% +he showed that sure enough you could get + + + align:start position:0% +he showed that sure enough you could get +a pigeon to understand and that uh you + + align:start position:0% +a pigeon to understand and that uh you + + + align:start position:0% +a pigeon to understand and that uh you +got got a bunch of colored keys in your + + align:start position:0% +got got a bunch of colored keys in your + + + align:start position:0% +got got a bunch of colored keys in your +your Skinner box that if I pick red + + align:start position:0% +your Skinner box that if I pick red + + + align:start position:0% +your Skinner box that if I pick red +green blue I get food but if I do blue + + align:start position:0% +green blue I get food but if I do blue + + + align:start position:0% +green blue I get food but if I do blue +green red I get water and the pigeon + + align:start position:0% +green red I get water and the pigeon + + + align:start position:0% +green red I get water and the pigeon +would respond appropriately to that so + + align:start position:0% +would respond appropriately to that so + + + align:start position:0% +would respond appropriately to that so +order information is is uh there in + + align:start position:0% +order information is is uh there in + + + align:start position:0% +order information is is uh there in +chimp signing and it's in there in other + + align:start position:0% +chimp signing and it's in there in other + + + align:start position:0% +chimp signing and it's in there in other +behaviors too it's also there's there's + + align:start position:0% +behaviors too it's also there's there's + + + align:start position:0% +behaviors too it's also there's there's +order information structural information + + align:start position:0% +order information structural information + + + align:start position:0% +order information structural information +in natural animal language too it's not + + align:start position:0% +in natural animal language too it's not + + + align:start position:0% +in natural animal language too it's not +just um you know means snake or + + align:start position:0% +just um you know means snake or + + + align:start position:0% +just um you know means snake or +something like that so for + + align:start position:0% +something like that so for + + + align:start position:0% +something like that so for +example bees how many of you have been + + align:start position:0% +example bees how many of you have been + + + align:start position:0% +example bees how many of you have been +to the uh uh well how many of you seen + + align:start position:0% +to the uh uh well how many of you seen + + + align:start position:0% +to the uh uh well how many of you seen +have seen uh the waggle dance of + + align:start position:0% +have seen uh the waggle dance of + + + align:start position:0% +have seen uh the waggle dance of +bees no all it's pretty thin stuff here + + align:start position:0% +bees no all it's pretty thin stuff here + + + align:start position:0% +bees no all it's pretty thin stuff here +um you get in free to the Science Museum + + align:start position:0% +um you get in free to the Science Museum + + + align:start position:0% +um you get in free to the Science Museum +here I believe as MIT students + + align:start position:0% +here I believe as MIT students + + + align:start position:0% +here I believe as MIT students +sometime like Friday when you're done + + align:start position:0% +sometime like Friday when you're done + + + align:start position:0% +sometime like Friday when you're done +with the midterm + + align:start position:0% +with the midterm + + + align:start position:0% +with the midterm +or something you want to go over to the + + align:start position:0% +or something you want to go over to the + + + align:start position:0% +or something you want to go over to the +Science Museum you go up to the third + + align:start position:0% +Science Museum you go up to the third + + + align:start position:0% +Science Museum you go up to the third +floor fourth floor where the library is + + align:start position:0% +floor fourth floor where the library is + + + align:start position:0% +floor fourth floor where the library is +they got a beehive there and if you look + + align:start position:0% +they got a beehive there and if you look + + + align:start position:0% +they got a beehive there and if you look +at this beehive it's a big glass plane + + align:start position:0% +at this beehive it's a big glass plane + + + align:start position:0% +at this beehive it's a big glass plane +so you can you know look in on it what + + align:start position:0% +so you can you know look in on it what + + + align:start position:0% +so you can you know look in on it what +you will see not so much at this time of + + align:start position:0% +you will see not so much at this time of + + + align:start position:0% +you will see not so much at this time of +year because they're all going to bed at + + align:start position:0% +year because they're all going to bed at + + + align:start position:0% +year because they're all going to bed at +this point but anyway um what you'll see + + align:start position:0% +this point but anyway um what you'll see + + + align:start position:0% +this point but anyway um what you'll see +is is a bee who will be + + align:start position:0% +is is a bee who will be + + + align:start position:0% +is is a bee who will be +marching up the uh + + align:start position:0% +marching up the uh + + + align:start position:0% +marching up the uh +Hive uh with a with a characteristic + + align:start position:0% +Hive uh with a with a characteristic + + + align:start position:0% +Hive uh with a with a characteristic +waggle of of of her backside + + align:start position:0% +waggle of of of her backside + + + align:start position:0% +waggle of of of her backside +um and then looping back down and and + + align:start position:0% +um and then looping back down and and + + + align:start position:0% +um and then looping back down and and +and repeating this while a whole bunch + + align:start position:0% +and repeating this while a whole bunch + + + align:start position:0% +and repeating this while a whole bunch +of other bees are gathered around it's + + align:start position:0% +of other bees are gathered around it's + + + align:start position:0% +of other bees are gathered around it's +easy to find because there's typically a + + align:start position:0% +easy to find because there's typically a + + + align:start position:0% +easy to find because there's typically a +sort of a circle of bees watching + + align:start position:0% +sort of a circle of bees watching + + + align:start position:0% +sort of a circle of bees watching +this and this is a highly structured bit + + align:start position:0% +this and this is a highly structured bit + + + align:start position:0% +this and this is a highly structured bit +of + + align:start position:0% +of + + + align:start position:0% +of +communication um about where to go to + + align:start position:0% +communication um about where to go to + + + align:start position:0% +communication um about where to go to +look for food my I I I didn't go off and + + align:start position:0% +look for food my I I I didn't go off and + + + align:start position:0% +look for food my I I I didn't go off and +review my waggle dance information but + + align:start position:0% +review my waggle dance information but + + + align:start position:0% +review my waggle dance information but +um I'm pretty sure that I that memory + + align:start position:0% +um I'm pretty sure that I that memory + + + align:start position:0% +um I'm pretty sure that I that memory +serves correctly to say that um the + + align:start position:0% +serves correctly to say that um the + + + align:start position:0% +serves correctly to say that um the +length of the vector here uh gives + + align:start position:0% +length of the vector here uh gives + + + align:start position:0% +length of the vector here uh gives +information about how far you've got to + + align:start position:0% +information about how far you've got to + + + align:start position:0% +information about how far you've got to +go that the direction of the vector is + + align:start position:0% +go that the direction of the vector is + + + align:start position:0% +go that the direction of the vector is +giving you orientation relative to the + + align:start position:0% +giving you orientation relative to the + + + align:start position:0% +giving you orientation relative to the +sun about which direction to fly and I + + align:start position:0% +sun about which direction to fly and I + + + align:start position:0% +sun about which direction to fly and I +think amplitude of the waggle is telling + + align:start position:0% +think amplitude of the waggle is telling + + + align:start position:0% +think amplitude of the waggle is telling +you about the uh uh the the magnitude of + + align:start position:0% +you about the uh uh the the magnitude of + + + align:start position:0% +you about the uh uh the the magnitude of +the food source + + align:start position:0% +the food source + + + align:start position:0% +the food source +how good is this stuff um and I can't + + align:start position:0% +how good is this stuff um and I can't + + + align:start position:0% +how good is this stuff um and I can't +and and got any waggle dance + + align:start position:0% +and and got any waggle dance + + + align:start position:0% +and and got any waggle dance +experts + + align:start position:0% +experts + + + align:start position:0% +experts +I'm an + + align:start position:0% +I'm an + + + align:start position:0% +I'm an +altitude how + + align:start position:0% +altitude how + + + align:start position:0% +altitude how +what's how the signaling how high you + + align:start position:0% +what's how the signaling how high you + + + align:start position:0% +what's how the signaling how high you +should + + align:start position:0% + + + + align:start position:0% + +fly that's cool I didn't know that why + + align:start position:0% +fly that's cool I didn't know that why + + + align:start position:0% +fly that's cool I didn't know that why +would they + + align:start position:0% +would they + + + align:start position:0% +would they +care so they + + align:start position:0% +care so they + + + align:start position:0% +care so they +don't oh oh I suppose yes of course yeah + + align:start position:0% +don't oh oh I suppose yes of course yeah + + + align:start position:0% +don't oh oh I suppose yes of course yeah +yeah if if if if the if the not not all + + align:start position:0% +yeah if if if if the if the not not all + + + align:start position:0% +yeah if if if if the if the not not all +the flowers are just lying on the ground + + align:start position:0% +the flowers are just lying on the ground + + + align:start position:0% +the flowers are just lying on the ground +it could particularly in Boston could be + + align:start position:0% +it could particularly in Boston could be + + + align:start position:0% +it could particularly in Boston could be +a roof Garden okay in any case that's + + align:start position:0% +a roof Garden okay in any case that's + + + align:start position:0% +a roof Garden okay in any case that's +cool but you don't remember what the + + align:start position:0% +cool but you don't remember what the + + + align:start position:0% +cool but you don't remember what the +signal is okay you don't and you don't + + align:start position:0% +signal is okay you don't and you don't + + + align:start position:0% +signal is okay you don't and you don't +remember what the the the the looping + + align:start position:0% +remember what the the the the looping + + + align:start position:0% +remember what the the the the looping +back piece contains information too but + + align:start position:0% +back piece contains information too but + + + align:start position:0% +back piece contains information too but +I don't remember what that very clever + + align:start position:0% +I don't remember what that very clever + + + align:start position:0% +I don't remember what that very clever +research that people do on on this it's + + align:start position:0% +research that people do on on this it's + + + align:start position:0% +research that people do on on this it's +it's it's love lovely a lovely body of + + align:start position:0% +it's it's love lovely a lovely body of + + + align:start position:0% +it's it's love lovely a lovely body of +literature but in any case very + + align:start position:0% +literature but in any case very + + + align:start position:0% +literature but in any case very +structured um You full full of uh um a + + align:start position:0% +structured um You full full of uh um a + + + align:start position:0% +structured um You full full of uh um a +sort of um + + align:start position:0% +sort of um + + + align:start position:0% +sort of um +native grammar + + align:start position:0% +native grammar + + + align:start position:0% +native grammar +um but + + align:start position:0% +um but + + + align:start position:0% +um but +it's it's it's pretty limited stuff um + + align:start position:0% +it's it's it's pretty limited stuff um + + + align:start position:0% +it's it's it's pretty limited stuff um +the perhaps the uh well this the newest + + align:start position:0% +the perhaps the uh well this the newest + + + align:start position:0% +the perhaps the uh well this the newest +evidence for what the limitation might + + align:start position:0% +evidence for what the limitation might + + + align:start position:0% +evidence for what the limitation might +be um that makes animal + + align:start position:0% +be um that makes animal + + + align:start position:0% +be um that makes animal +grammar fundamentally different from + + align:start position:0% +grammar fundamentally different from + + + align:start position:0% +grammar fundamentally different from +your grammar and and my grammar comes + + align:start position:0% +your grammar and and my grammar comes + + + align:start position:0% +your grammar and and my grammar comes +from uh an experiment um by that I think + + align:start position:0% +from uh an experiment um by that I think + + + align:start position:0% +from uh an experiment um by that I think +I put on the handout yeah new paper by + + align:start position:0% +I put on the handout yeah new paper by + + + align:start position:0% +I put on the handout yeah new paper by +fit and er um where they basically were + + align:start position:0% +fit and er um where they basically were + + + align:start position:0% +fit and er um where they basically were +teaching grammatical structures to uh to + + align:start position:0% +teaching grammatical structures to uh to + + + align:start position:0% +teaching grammatical structures to uh to +primates to non-human primates um and + + align:start position:0% +primates to non-human primates um and + + + align:start position:0% +primates to non-human primates um and +um they were pretty good they were they + + align:start position:0% +um they were pretty good they were they + + + align:start position:0% +um they were pretty good they were they +were they were doing fine on the John + + align:start position:0% +were they were doing fine on the John + + + align:start position:0% +were they were doing fine on the John +hit Mary is different from the Mary hit + + align:start position:0% +hit Mary is different from the Mary hit + + + align:start position:0% +hit Mary is different from the Mary hit +John part but it was nested + + align:start position:0% +John part but it was nested + + + align:start position:0% +John part but it was nested +constructions that they simply never + + align:start position:0% +constructions that they simply never + + + align:start position:0% +constructions that they simply never +managed to get um so um you know Mary + + align:start position:0% +managed to get um so um you know Mary + + + align:start position:0% +managed to get um so um you know Mary +who was engaged to Sam hit John that's + + align:start position:0% +who was engaged to Sam hit John that's + + + align:start position:0% +who was engaged to Sam hit John that's +perfectly fine for you that sticking one + + align:start position:0% +perfectly fine for you that sticking one + + + align:start position:0% +perfectly fine for you that sticking one +Clause inside another that was stuff + + align:start position:0% +Clause inside another that was stuff + + + align:start position:0% +Clause inside another that was stuff +that they could just never manage to get + + align:start position:0% +that they could just never manage to get + + + align:start position:0% +that they could just never manage to get +their um their primates to um to pick up + + align:start position:0% +their um their primates to um to pick up + + + align:start position:0% +their um their primates to um to pick up +on now this is not an argument Hower um + + align:start position:0% +on now this is not an argument Hower um + + + align:start position:0% +on now this is not an argument Hower um +in particular is not somebody who spends + + align:start position:0% +in particular is not somebody who spends + + + align:start position:0% +in particular is not somebody who spends +a lot of time arguing um that that apes + + align:start position:0% +a lot of time arguing um that that apes + + + align:start position:0% +a lot of time arguing um that that apes +are stupid or something like that um the + + align:start position:0% +are stupid or something like that um the + + + align:start position:0% +are stupid or something like that um the +great apes are remarkably clever beasts + + align:start position:0% +great apes are remarkably clever beasts + + + align:start position:0% +great apes are remarkably clever beasts +uh and and in in studying them you find + + align:start position:0% +uh and and in in studying them you find + + + align:start position:0% +uh and and in in studying them you find +uh cognitive abilities not unlike a lot + + align:start position:0% +uh cognitive abilities not unlike a lot + + + align:start position:0% +uh cognitive abilities not unlike a lot +of our our our cognitive abilities I + + align:start position:0% +of our our our cognitive abilities I + + + align:start position:0% +of our our our cognitive abilities I +don't think it's a Hower experiment but + + align:start position:0% +don't think it's a Hower experiment but + + + align:start position:0% +don't think it's a Hower experiment but +one of the ones that comes to mind is + + align:start position:0% +one of the ones that comes to mind is + + + align:start position:0% +one of the ones that comes to mind is +that I could have talked about in the + + align:start position:0% +that I could have talked about in the + + + align:start position:0% +that I could have talked about in the +context of egocentric behavior before is + + align:start position:0% +context of egocentric behavior before is + + + align:start position:0% +context of egocentric behavior before is +that an important landmark in the + + align:start position:0% +that an important landmark in the + + + align:start position:0% +that an important landmark in the +development of um in in your mental + + align:start position:0% +development of um in in your mental + + + align:start position:0% +development of um in in your mental +development was when you learned how to + + align:start position:0% +development was when you learned how to + + + align:start position:0% +development was when you learned how to +lie I you know it was it's another one + + align:start position:0% +lie I you know it was it's another one + + + align:start position:0% +lie I you know it was it's another one +of these ones that didn't necessarily + + align:start position:0% +of these ones that didn't necessarily + + + align:start position:0% +of these ones that didn't necessarily +get uh a lot of positive reinforcement + + align:start position:0% +get uh a lot of positive reinforcement + + + align:start position:0% +get uh a lot of positive reinforcement +from your parents when you demonstrated + + align:start position:0% +from your parents when you demonstrated + + + align:start position:0% +from your parents when you demonstrated +it to them but it is an important + + align:start position:0% +it to them but it is an important + + + align:start position:0% +it to them but it is an important +cognitive Landmark because it says I + + align:start position:0% +cognitive Landmark because it says I + + + align:start position:0% +cognitive Landmark because it says I +know that what's in here is not what's + + align:start position:0% +know that what's in here is not what's + + + align:start position:0% +know that what's in here is not what's +in there in your head I can tell you + + align:start position:0% +in there in your head I can tell you + + + align:start position:0% +in there in your head I can tell you +something that I know is + + align:start position:0% +something that I know is + + + align:start position:0% +something that I know is +bogus and you'll believe + + align:start position:0% +bogus and you'll believe + + + align:start position:0% +bogus and you'll believe +it monkeys can do that too how do you + + align:start position:0% +it monkeys can do that too how do you + + + align:start position:0% +it monkeys can do that too how do you +know this well I I I can't remember who + + align:start position:0% +know this well I I I can't remember who + + + align:start position:0% +know this well I I I can't remember who +did the experiment but you set up this + + align:start position:0% +did the experiment but you set up this + + + align:start position:0% +did the experiment but you set up this +clever experiment with um a good uh you + + align:start position:0% +clever experiment with um a good uh you + + + align:start position:0% +clever experiment with um a good uh you +know person and a bad person the monkey + + align:start position:0% +know person and a bad person the monkey + + + align:start position:0% +know person and a bad person the monkey +knows both of these people the good + + align:start position:0% +knows both of these people the good + + + align:start position:0% +knows both of these people the good +person so but both of these + + align:start position:0% +person so but both of these + + + align:start position:0% +person so but both of these +people have access to uh you to + + align:start position:0% +people have access to uh you to + + + align:start position:0% +people have access to uh you to +these you know boxes of stuff the monkey + + align:start position:0% +these you know boxes of stuff the monkey + + + align:start position:0% +these you know boxes of stuff the monkey +sometimes has access to the boxes of + + align:start position:0% +sometimes has access to the boxes of + + + align:start position:0% +sometimes has access to the boxes of +stuff when the monkey gets access you + + align:start position:0% +stuff when the monkey gets access you + + + align:start position:0% +stuff when the monkey gets access you +you know he can look under under the box + + align:start position:0% +you know he can look under under the box + + + align:start position:0% +you know he can look under under the box +and he finds the banana you know oh cool + + align:start position:0% +and he finds the banana you know oh cool + + + align:start position:0% +and he finds the banana you know oh cool +great or you know the grapes or or + + align:start position:0% +great or you know the grapes or or + + + align:start position:0% +great or you know the grapes or or +there's nothing under there that's + + align:start position:0% +there's nothing under there that's + + + align:start position:0% +there's nothing under there that's +boring okay now now the monkey's on the + + align:start position:0% +boring okay now now the monkey's on the + + + align:start position:0% +boring okay now now the monkey's on the +other side of the cage and here's the + + align:start position:0% +other side of the cage and here's the + + + align:start position:0% +other side of the cage and here's the +stuff and if the good guy comes in he + + align:start position:0% +stuff and if the good guy comes in he + + + align:start position:0% +stuff and if the good guy comes in he +looks under one of these things finds + + align:start position:0% +looks under one of these things finds + + + align:start position:0% +looks under one of these things finds +the banana and he shares it with the + + align:start position:0% +the banana and he shares it with the + + + align:start position:0% +the banana and he shares it with the +monkey if the bad guy comes in looks + + align:start position:0% +monkey if the bad guy comes in looks + + + align:start position:0% +monkey if the bad guy comes in looks +finds the banana he eats it and doesn't + + align:start position:0% +finds the banana he eats it and doesn't + + + align:start position:0% +finds the banana he eats it and doesn't +give the monkey any so now do this a few + + align:start position:0% +give the monkey any so now do this a few + + + align:start position:0% +give the monkey any so now do this a few +times monkey monkeys got this bit down + + align:start position:0% +times monkey monkeys got this bit down + + + align:start position:0% +times monkey monkeys got this bit down +now um a third party comes in and and + + align:start position:0% +now um a third party comes in and and + + + align:start position:0% +now um a third party comes in and and +baits one of these two uh Wells you know + + align:start position:0% +baits one of these two uh Wells you know + + + align:start position:0% +baits one of these two uh Wells you know +puts the banana under one of them and + + align:start position:0% +puts the banana under one of them and + + + align:start position:0% +puts the banana under one of them and +now if the good guy comes + + align:start position:0% +now if the good guy comes + + + align:start position:0% +now if the good guy comes +in what does the monkey do the monkey + + align:start position:0% +in what does the monkey do the monkey + + + align:start position:0% +in what does the monkey do the monkey +basically says look there you only get + + align:start position:0% +basically says look there you only get + + + align:start position:0% +basically says look there you only get +the look there that's that's where you + + align:start position:0% +the look there that's that's where you + + + align:start position:0% +the look there that's that's where you +want to look the bad guy comes in what's + + align:start position:0% +want to look the bad guy comes in what's + + + align:start position:0% +want to look the bad guy comes in what's +the monkey do he says look there + + align:start position:0% +the monkey do he says look there + + + align:start position:0% +the monkey do he says look there +and and and um monkeys will also do this + + align:start position:0% +and and and um monkeys will also do this + + + align:start position:0% +and and and um monkeys will also do this +um to each other apparently in in the uh + + align:start position:0% +um to each other apparently in in the uh + + + align:start position:0% +um to each other apparently in in the uh +in the wild there's a version where you + + align:start position:0% +in the wild there's a version where you + + + align:start position:0% +in the wild there's a version where you +uh um stash stuff around a + + align:start position:0% +uh um stash stuff around a + + + align:start position:0% +uh um stash stuff around a +field and um how does it work that the + + align:start position:0% +field and um how does it work that the + + + align:start position:0% +field and um how does it work that the +monkey lies to his + + align:start position:0% +monkey lies to his + + + align:start position:0% +monkey lies to his +friends but the monkey you arrange for + + align:start position:0% +friends but the monkey you arrange for + + + align:start position:0% +friends but the monkey you arrange for +monkey one to discover the good stash + + align:start position:0% +monkey one to discover the good stash + + + align:start position:0% +monkey one to discover the good stash +and then this monkey in some fashion + + align:start position:0% +and then this monkey in some fashion + + + align:start position:0% +and then this monkey in some fashion +goes off and tells his buddies to go + + align:start position:0% +goes off and tells his buddies to go + + + align:start position:0% +goes off and tells his buddies to go +look over there the good stuff's over + + align:start position:0% +look over there the good stuff's over + + + align:start position:0% +look over there the good stuff's over +here and the monkey's busy you guys go + + align:start position:0% +here and the monkey's busy you guys go + + + align:start position:0% +here and the monkey's busy you guys go +over there and and he goes and eats all + + align:start position:0% +over there and and he goes and eats all + + + align:start position:0% +over there and and he goes and eats all +the bananas so you know they they're + + align:start position:0% +the bananas so you know they they're + + + align:start position:0% +the bananas so you know they they're +they're they're clever animals but there + + align:start position:0% +they're they're clever animals but there + + + align:start position:0% +they're they're clever animals but there +does seem to be there do seem to be + + align:start position:0% +does seem to be there do seem to be + + + align:start position:0% +does seem to be there do seem to be +fundamental differences that you don't + + align:start position:0% +fundamental differences that you don't + + + align:start position:0% +fundamental differences that you don't +get around that no at least nobody's + + align:start position:0% +get around that no at least nobody's + + + align:start position:0% +get around that no at least nobody's +figured out how to get around them yet + + align:start position:0% +figured out how to get around them yet + + + align:start position:0% +figured out how to get around them yet +nobody has figured around way how to get + + align:start position:0% +nobody has figured around way how to get + + + align:start position:0% +nobody has figured around way how to get +monkeys to anything like the richness of + + align:start position:0% +monkeys to anything like the richness of + + + align:start position:0% +monkeys to anything like the richness of +the grammar that that human language has + + align:start position:0% +the grammar that that human language has + + + align:start position:0% +the grammar that that human language has +the result of this is that even if you + + align:start position:0% +the result of this is that even if you + + + align:start position:0% +the result of this is that even if you +want to concede that this is why you can + + align:start position:0% +want to concede that this is why you can + + + align:start position:0% +want to concede that this is why you can +answer both both ways to the do animals + + align:start position:0% +answer both both ways to the do animals + + + align:start position:0% +answer both both ways to the do animals +have language suppose you decide that + + align:start position:0% +have language suppose you decide that + + + align:start position:0% +have language suppose you decide that +all you want is some evidence for um + + align:start position:0% +all you want is some evidence for um + + + align:start position:0% +all you want is some evidence for um +phones morphemes and and and and an + + align:start position:0% +phones morphemes and and and and an + + + align:start position:0% +phones morphemes and and and and an +ability to be sensitive to structure + + align:start position:0% +ability to be sensitive to structure + + + align:start position:0% +ability to be sensitive to structure +well yeah there's some evidence that + + align:start position:0% +well yeah there's some evidence that + + + align:start position:0% +well yeah there's some evidence that +that that that chimps can do that for + + align:start position:0% +that that that chimps can do that for + + + align:start position:0% +that that that chimps can do that for +instance but the the the hurdle of + + align:start position:0% +instance but the the the hurdle of + + + align:start position:0% +instance but the the the hurdle of +developing a productive language a + + align:start position:0% +developing a productive language a + + + align:start position:0% +developing a productive language a +language where you can say new stuff um + + align:start position:0% +language where you can say new stuff um + + + align:start position:0% +language where you can say new stuff um +that does not seem to be + + align:start position:0% +that does not seem to be + + + align:start position:0% +that does not seem to be +something that uh that not seem to be a + + align:start position:0% +something that uh that not seem to be a + + + align:start position:0% +something that uh that not seem to be a +hurdle that any non-human species gets + + align:start position:0% +hurdle that any non-human species gets + + + align:start position:0% +hurdle that any non-human species gets +over in either natural language or in um + + align:start position:0% +over in either natural language or in um + + + align:start position:0% +over in either natural language or in um +in trained language so you know bees + + align:start position:0% +in trained language so you know bees + + + align:start position:0% +in trained language so you know bees +great sophisticated stuff but no + + align:start position:0% +great sophisticated stuff but no + + + align:start position:0% +great sophisticated stuff but no +evidence that the bee ever learns to + + align:start position:0% +evidence that the bee ever learns to + + + align:start position:0% +evidence that the bee ever learns to +talk about anything new with this right + + align:start position:0% +talk about anything new with this right + + + align:start position:0% +talk about anything new with this right +the the bee doesn't get to they don't + + align:start position:0% +the the bee doesn't get to they don't + + + align:start position:0% +the the bee doesn't get to they don't +get to sit around and apparently Muse + + align:start position:0% +get to sit around and apparently Muse + + + align:start position:0% +get to sit around and apparently Muse +about remember last year remember that + + align:start position:0% +about remember last year remember that + + + align:start position:0% +about remember last year remember that +honey not the honey you know remember + + align:start position:0% +honey not the honey you know remember + + + align:start position:0% +honey not the honey you know remember +remember that patch of flowers that was + + align:start position:0% +remember that patch of flowers that was + + + align:start position:0% +remember that patch of flowers that was +over there um at least nobody to my + + align:start position:0% +over there um at least nobody to my + + + align:start position:0% +over there um at least nobody to my +knowledge has ever found the past tense + + align:start position:0% +knowledge has ever found the past tense + + + align:start position:0% +knowledge has ever found the past tense +in waggle or anything like it there's + + align:start position:0% +in waggle or anything like it there's + + + align:start position:0% +in waggle or anything like it there's +it's there up to a limit but but not uh + + align:start position:0% +it's there up to a limit but but not uh + + + align:start position:0% +it's there up to a limit but but not uh +not further now uh what I will do is + + align:start position:0% +not further now uh what I will do is + + + align:start position:0% +not further now uh what I will do is +take a momentary break here say a word + + align:start position:0% +take a momentary break here say a word + + + align:start position:0% +take a momentary break here say a word +about why does this matter um and then + + align:start position:0% +about why does this matter um and then + + + align:start position:0% +about why does this matter um and then +what I'll do is + + align:start position:0% +what I'll do is + + + align:start position:0% +what I'll do is +entertain um midterm questions for a few + + align:start position:0% +entertain um midterm questions for a few + + + align:start position:0% +entertain um midterm questions for a few +minutes before the uh before the end of + + align:start position:0% +minutes before the uh before the end of + + + align:start position:0% +minutes before the uh before the end of +the hour + + align:start position:0% +the hour + + + align:start position:0% +the hour +so take a take a quick stretch and then + + align:start position:0% +so take a take a quick stretch and then + + + align:start position:0% +so take a take a quick stretch and then +let's come back and finish things up + + align:start position:0% + + + + align:start position:0% + +here um why does this matter + + align:start position:0% +here um why does this matter + + + align:start position:0% +here um why does this matter +um this has been a very + + align:start position:0% +um this has been a very + + + align:start position:0% +um this has been a very +contentious uh a very contentious topic + + align:start position:0% +contentious uh a very contentious topic + + + align:start position:0% +contentious uh a very contentious topic +um and you know more more so than many + + align:start position:0% +um and you know more more so than many + + + align:start position:0% +um and you know more more so than many +you know people argue about visual + + align:start position:0% +you know people argue about visual + + + align:start position:0% +you know people argue about visual +attention but people don't get like + + align:start position:0% +attention but people don't get like + + + align:start position:0% +attention but people don't get like +really agitated about it like it's a + + align:start position:0% +really agitated about it like it's a + + + align:start position:0% +really agitated about it like it's a +moral issue people get agitated about um + + align:start position:0% +moral issue people get agitated about um + + + align:start position:0% +moral issue people get agitated about um +animal language like it is a moral issue + + align:start position:0% +animal language like it is a moral issue + + + align:start position:0% +animal language like it is a moral issue +um because in some fashion it is it or + + align:start position:0% +um because in some fashion it is it or + + + align:start position:0% +um because in some fashion it is it or +it is not itself a moral issue but it it + + align:start position:0% +it is not itself a moral issue but it it + + + align:start position:0% +it is not itself a moral issue but it it +it impinges on issues that have more to + + align:start position:0% +it impinges on issues that have more to + + + align:start position:0% +it impinges on issues that have more to +do with morality than um than with + + align:start position:0% +do with morality than um than with + + + align:start position:0% +do with morality than um than with +science well you could couch it in + + align:start position:0% +science well you could couch it in + + + align:start position:0% +science well you could couch it in +theological terms if you like in in in + + align:start position:0% +theological terms if you like in in in + + + align:start position:0% +theological terms if you like in in in +Psalms um the the psalmist asks + + align:start position:0% +Psalms um the the psalmist asks + + + align:start position:0% +Psalms um the the psalmist asks +rhetorically at some point of God um you + + align:start position:0% +rhetorically at some point of God um you + + + align:start position:0% +rhetorically at some point of God um you +know what is man that you are mindful of + + align:start position:0% +know what is man that you are mindful of + + + align:start position:0% +know what is man that you are mindful of +him what is it that makes us so special + + align:start position:0% +him what is it that makes us so special + + + align:start position:0% +him what is it that makes us so special +that um that we're different from all + + align:start position:0% +that um that we're different from all + + + align:start position:0% +that um that we're different from all +these animal things out there um + + align:start position:0% +these animal things out there um + + + align:start position:0% +these animal things out there um +and that's a + + align:start position:0% +and that's a + + + align:start position:0% +and that's a +question that becomes difficult if there + + align:start position:0% +question that becomes difficult if there + + + align:start position:0% +question that becomes difficult if there +is not a nice clean qualitative + + align:start position:0% +is not a nice clean qualitative + + + align:start position:0% +is not a nice clean qualitative +difference between what an animal is and + + align:start position:0% +difference between what an animal is and + + + align:start position:0% +difference between what an animal is and +what US is the uh this was one of the + + align:start position:0% +what US is the uh this was one of the + + + align:start position:0% +what US is the uh this was one of the +reasons why the Advent of the theory of + + align:start position:0% +reasons why the Advent of the theory of + + + align:start position:0% +reasons why the Advent of the theory of +reev Revolution the theory of evolution + + align:start position:0% +reev Revolution the theory of evolution + + + align:start position:0% +reev Revolution the theory of evolution +was so uh so problematic because it + + align:start position:0% +was so uh so problematic because it + + + align:start position:0% +was so uh so problematic because it +suggested that um that species were not + + align:start position:0% +suggested that um that species were not + + + align:start position:0% +suggested that um that species were not +you know completely distinct and and + + align:start position:0% +you know completely distinct and and + + + align:start position:0% +you know completely distinct and and +that we were somehow a completely + + align:start position:0% +that we were somehow a completely + + + align:start position:0% +that we were somehow a completely +separate sort of creation but that that + + align:start position:0% +separate sort of creation but that that + + + align:start position:0% +separate sort of creation but that that +there was a continuity between all forms + + align:start position:0% +there was a continuity between all forms + + + align:start position:0% +there was a continuity between all forms +of animal life up to an including + + align:start position:0% +of animal life up to an including + + + align:start position:0% +of animal life up to an including +us um if that's the case who is it that + + align:start position:0% +us um if that's the case who is it that + + + align:start position:0% +us um if that's the case who is it that +gets the sort of uh rights and + + align:start position:0% +gets the sort of uh rights and + + + align:start position:0% +gets the sort of uh rights and +privileges that we would arrogate to + + align:start position:0% +privileges that we would arrogate to + + + align:start position:0% +privileges that we would arrogate to +ourselves and who is it that we get to + + align:start position:0% +ourselves and who is it that we get to + + + align:start position:0% +ourselves and who is it that we get to +treat well who we get to treat like + + align:start position:0% +treat well who we get to treat like + + + align:start position:0% +treat well who we get to treat like +animals and the search for a nice clear + + align:start position:0% +animals and the search for a nice clear + + + align:start position:0% +animals and the search for a nice clear +answer I'm not going to give you the + + align:start position:0% +answer I'm not going to give you the + + + align:start position:0% +answer I'm not going to give you the +answer to this because there is at least + + align:start position:0% +answer to this because there is at least + + + align:start position:0% +answer to this because there is at least +in my view there is no nice sharp + + align:start position:0% +in my view there is no nice sharp + + + align:start position:0% +in my view there is no nice sharp +dividing line that that that gives you a + + align:start position:0% +dividing line that that that gives you a + + + align:start position:0% +dividing line that that that gives you a +nice clean answer answer to this but the + + align:start position:0% +nice clean answer answer to this but the + + + align:start position:0% +nice clean answer answer to this but the +search for a nice clean answer could + + align:start position:0% +search for a nice clean answer could + + + align:start position:0% +search for a nice clean answer could +include well who can talk to us maybe + + align:start position:0% +include well who can talk to us maybe + + + align:start position:0% +include well who can talk to us maybe +that's may maybe maybe the ability to + + align:start position:0% +that's may maybe maybe the ability to + + + align:start position:0% +that's may maybe maybe the ability to +speak or communicate in a in a + + align:start position:0% +speak or communicate in a in a + + + align:start position:0% +speak or communicate in a in a +linguistic way is the is the critical + + align:start position:0% +linguistic way is the is the critical + + + align:start position:0% +linguistic way is the is the critical +division because I mean look think about + + align:start position:0% +division because I mean look think about + + + align:start position:0% +division because I mean look think about +it in terms of what you'll what you + + align:start position:0% +it in terms of what you'll what you + + + align:start position:0% +it in terms of what you'll what you +would eat if it were the case that um + + align:start position:0% +would eat if it were the case that um + + + align:start position:0% +would eat if it were the case that um +you walk out into the + + align:start position:0% +you walk out into the + + + align:start position:0% +you walk out into the +field and the cow can talk to you right + + align:start position:0% +field and the cow can talk to you right + + + align:start position:0% +field and the cow can talk to you right +and and carry on a conversation even a + + align:start position:0% +and and carry on a conversation even a + + + align:start position:0% +and and carry on a conversation even a +sort of a simple conversation a + + align:start position:0% +sort of a simple conversation a + + + align:start position:0% +sort of a simple conversation a +childlike conversation good grass like + + align:start position:0% +childlike conversation good grass like + + + align:start position:0% +childlike conversation good grass like +grass nice grass you know what's the + + align:start position:0% +grass nice grass you know what's the + + + align:start position:0% +grass nice grass you know what's the +chance that you're going to eat him it + + align:start position:0% +chance that you're going to eat him it + + + align:start position:0% +chance that you're going to eat him it +doesn't feel quite right anymore right + + align:start position:0% +doesn't feel quite right anymore right + + + align:start position:0% +doesn't feel quite right anymore right +this and and this it's not just language + + align:start position:0% +this and and this it's not just language + + + align:start position:0% +this and and this it's not just language +we don't like to eat things that we get + + align:start position:0% +we don't like to eat things that we get + + + align:start position:0% +we don't like to eat things that we get +to know language is a good way to get to + + align:start position:0% +to know language is a good way to get to + + + align:start position:0% +to know language is a good way to get to +know something but but um oh third grade + + align:start position:0% +know something but but um oh third grade + + + align:start position:0% +know something but but um oh third grade +at the moment reading charlott's web + + align:start position:0% +at the moment reading charlott's web + + + align:start position:0% +at the moment reading charlott's web +right how many of you read Charlotte's + + align:start position:0% +right how many of you read Charlotte's + + + align:start position:0% +right how many of you read Charlotte's +Web at some point oh good still a + + align:start position:0% +Web at some point oh good still a + + + align:start position:0% +Web at some point oh good still a +classic out there uh lot of the ISS it's + + align:start position:0% +classic out there uh lot of the ISS it's + + + align:start position:0% +classic out there uh lot of the ISS it's +an issue about language and who you're + + align:start position:0% +an issue about language and who you're + + + align:start position:0% +an issue about language and who you're +going to get to eat um there's a there's + + align:start position:0% +going to get to eat um there's a there's + + + align:start position:0% +going to get to eat um there's a there's +a great one in in uh um in in the little + + align:start position:0% +a great one in in uh um in in the little + + + align:start position:0% +a great one in in uh um in in the little +Jewish kid uh repertoire called uh the + + align:start position:0% +Jewish kid uh repertoire called uh the + + + align:start position:0% +Jewish kid uh repertoire called uh the +carp in the bathtub where uh a big carp + + align:start position:0% +carp in the bathtub where uh a big carp + + + align:start position:0% +carp in the bathtub where uh a big carp +is basically an overgrown goldfish thing + + align:start position:0% +is basically an overgrown goldfish thing + + + align:start position:0% +is basically an overgrown goldfish thing +comes home and is living in the bathtub + + align:start position:0% +comes home and is living in the bathtub + + + align:start position:0% +comes home and is living in the bathtub +and and and the kids love it but this + + align:start position:0% +and and and the kids love it but this + + + align:start position:0% +and and and the kids love it but this +thing is intended to be food and sad + + align:start position:0% +thing is intended to be food and sad + + + align:start position:0% +thing is intended to be food and sad +things happen to the carp um you know + + align:start position:0% +things happen to the carp um you know + + + align:start position:0% +things happen to the carp um you know +the it's it's hard things that are close + + align:start position:0% +the it's it's hard things that are close + + + align:start position:0% +the it's it's hard things that are close +to you are not things that you want to + + align:start position:0% +to you are not things that you want to + + + align:start position:0% +to you are not things that you want to +kill not things that you want uh + + align:start position:0% +kill not things that you want uh + + + align:start position:0% +kill not things that you want uh +necessarily want to hurt and and + + align:start position:0% +necessarily want to hurt and and + + + align:start position:0% +necessarily want to hurt and and +so how you draw that + + align:start position:0% +so how you draw that + + + align:start position:0% +so how you draw that +line is + + align:start position:0% +line is + + + align:start position:0% +line is +important if you could argue that it is + + align:start position:0% +important if you could argue that it is + + + align:start position:0% +important if you could argue that it is +absolutely the case that there is human + + align:start position:0% +absolutely the case that there is human + + + align:start position:0% +absolutely the case that there is human +language ability and animal uh animals + + align:start position:0% +language ability and animal uh animals + + + align:start position:0% +language ability and animal uh animals +just don't got it at all another realm + + align:start position:0% +just don't got it at all another realm + + + align:start position:0% +just don't got it at all another realm +word this was tried was humans are tool + + align:start position:0% +word this was tried was humans are tool + + + align:start position:0% +word this was tried was humans are tool +users and animals just aren't there's a + + align:start position:0% +users and animals just aren't there's a + + + align:start position:0% +users and animals just aren't there's a +sharp division there we can see it it + + align:start position:0% +sharp division there we can see it it + + + align:start position:0% +sharp division there we can see it it +makes these sorts of discussions + + align:start position:0% +makes these sorts of discussions + + + align:start position:0% +makes these sorts of discussions +somewhat easier it doesn't make them a + + align:start position:0% +somewhat easier it doesn't make them a + + + align:start position:0% +somewhat easier it doesn't make them a +lot easier necessarily because look if + + align:start position:0% +lot easier necessarily because look if + + + align:start position:0% +lot easier necessarily because look if +you have a a a a human child who has um + + align:start position:0% +you have a a a a human child who has um + + + align:start position:0% +you have a a a a human child who has um +a congenital uh neurological problem + + align:start position:0% +a congenital uh neurological problem + + + align:start position:0% +a congenital uh neurological problem +that means that that child will never + + align:start position:0% +that means that that child will never + + + align:start position:0% +that means that that child will never +speak right the kids kid's mentally + + align:start position:0% +speak right the kids kid's mentally + + + align:start position:0% +speak right the kids kid's mentally + in some fashion is never going + + align:start position:0% + in some fashion is never going + + + align:start position:0% + in some fashion is never going +to speak that doesn't mean you can eat + + align:start position:0% +to speak that doesn't mean you can eat + + + align:start position:0% +to speak that doesn't mean you can eat +him or anything of the sort that's + + align:start position:0% +him or anything of the sort that's + + + align:start position:0% +him or anything of the sort that's +obvious sick nonsense right so it's it's + + align:start position:0% +obvious sick nonsense right so it's it's + + + align:start position:0% +obvious sick nonsense right so it's it's +there's it's not a simple division but + + align:start position:0% +there's it's not a simple division but + + + align:start position:0% +there's it's not a simple division but +the efforts to figure out what makes um + + align:start position:0% +the efforts to figure out what makes um + + + align:start position:0% +the efforts to figure out what makes um +you know what makes us distinctively + + align:start position:0% +you know what makes us distinctively + + + align:start position:0% +you know what makes us distinctively +human and as a result who do human + + align:start position:0% +human and as a result who do human + + + align:start position:0% +human and as a result who do human +rights extend to is is is is + + align:start position:0% +rights extend to is is is is + + + align:start position:0% +rights extend to is is is is +a is a serious problem one that I'm not + + align:start position:0% +a is a serious problem one that I'm not + + + align:start position:0% +a is a serious problem one that I'm not +going to attempt to uh to solve here but + + align:start position:0% +going to attempt to uh to solve here but + + + align:start position:0% +going to attempt to uh to solve here but +one that is is certainly worth your uh + + align:start position:0% +one that is is certainly worth your uh + + + align:start position:0% +one that is is certainly worth your uh +your ongoing uh your ongoing + + align:start position:0% +your ongoing uh your ongoing + + + align:start position:0% +your ongoing uh your ongoing +consideration um what I will attempt to + + align:start position:0% +consideration um what I will attempt to + + + align:start position:0% +consideration um what I will attempt to +solve here for the remaining 10 15 + + align:start position:0% +solve here for the remaining 10 15 + + + align:start position:0% +solve here for the remaining 10 15 +minutes or so is I will uh dutifully + + align:start position:0% +minutes or so is I will uh dutifully + + + align:start position:0% +minutes or so is I will uh dutifully +attempt to answer any questions about + + align:start position:0% +attempt to answer any questions about + + + align:start position:0% +attempt to answer any questions about +the midterm uh that you might have at + + align:start position:0% +the midterm uh that you might have at + + + align:start position:0% +the midterm uh that you might have at +the present moment um and + + align:start position:0% + + + + align:start position:0% + +uh somebody's asked a couple of people + + align:start position:0% +uh somebody's asked a couple of people + + + align:start position:0% +uh somebody's asked a couple of people +asked me is it a hard + + align:start position:0% +asked me is it a hard + + + align:start position:0% +asked me is it a hard +midterm and the answer is that the first + + align:start position:0% +midterm and the answer is that the first + + + align:start position:0% +midterm and the answer is that the first +two Tas who read it said boy this is + + align:start position:0% +two Tas who read it said boy this is + + + align:start position:0% +two Tas who read it said boy this is +easy and the second two Tas who read it + + align:start position:0% +easy and the second two Tas who read it + + + align:start position:0% +easy and the second two Tas who read it +said boy this is + + align:start position:0% +said boy this is + + + align:start position:0% +said boy this is +hard um but and sadly the distinction + + align:start position:0% +hard um but and sadly the distinction + + + align:start position:0% +hard um but and sadly the distinction +between the first two Tas and the second + + align:start position:0% +between the first two Tas and the second + + + align:start position:0% +between the first two Tas and the second +two Tas in this case was the first two + + align:start position:0% +two Tas in this case was the first two + + + align:start position:0% +two Tas in this case was the first two +Tas had ta the course last year um and + + align:start position:0% +Tas had ta the course last year um and + + + align:start position:0% +Tas had ta the course last year um and +had been through this once before and + + align:start position:0% +had been through this once before and + + + align:start position:0% +had been through this once before and +the other ones hadn't so you may use + + align:start position:0% +the other ones hadn't so you may use + + + align:start position:0% +the other ones hadn't so you may use +that tidbit of information in any way + + align:start position:0% +that tidbit of information in any way + + + align:start position:0% +that tidbit of information in any way +you see fit uh what other tidbits of + + align:start position:0% +you see fit uh what other tidbits of + + + align:start position:0% +you see fit uh what other tidbits of +information can I provide for you + + align:start position:0% +information can I provide for you + + + align:start position:0% +information can I provide for you +oh yeah right yeah yeah close class and + + align:start position:0% +oh yeah right yeah yeah close class and + + + align:start position:0% +oh yeah right yeah yeah close class and +open class uh words it's on it's it's on + + align:start position:0% +open class uh words it's on it's it's on + + + align:start position:0% +open class uh words it's on it's it's on +today's handout I think I mentioned it + + align:start position:0% +today's handout I think I mentioned it + + + align:start position:0% +today's handout I think I mentioned it +last time but let me reiterate that + + align:start position:0% +last time but let me reiterate that + + + align:start position:0% +last time but let me reiterate that +closed class so it was on last time so + + align:start position:0% +closed class so it was on last time so + + + align:start position:0% +closed class so it was on last time so +it's fair game for the midterm um closed + + align:start position:0% +it's fair game for the midterm um closed + + + align:start position:0% +it's fair game for the midterm um closed +class words are words that uh + + align:start position:0% +class words are words that uh + + + align:start position:0% +class words are words that uh +serve um grammatical + + align:start position:0% +serve um grammatical + + + align:start position:0% +serve um grammatical +syntactical roles and do not uh you know + + align:start position:0% +syntactical roles and do not uh you know + + + align:start position:0% +syntactical roles and do not uh you know +the + + align:start position:0% +the + + + align:start position:0% +the +and um uh you know words that don't have + + align:start position:0% +and um uh you know words that don't have + + + align:start position:0% +and um uh you know words that don't have +a definition um in any straightforward + + align:start position:0% +a definition um in any straightforward + + + align:start position:0% +a definition um in any straightforward +sense except to explain that the' means + + align:start position:0% +sense except to explain that the' means + + + align:start position:0% +sense except to explain that the' means +noun is a common and means I'm joining a + + align:start position:0% +noun is a common and means I'm joining a + + + align:start position:0% +noun is a common and means I'm joining a +couple of things together + + align:start position:0% +couple of things together + + + align:start position:0% +couple of things together +um and open class words are the other + + align:start position:0% +um and open class words are the other + + + align:start position:0% +um and open class words are the other +ones closed class they're it's a much + + align:start position:0% +ones closed class they're it's a much + + + align:start position:0% +ones closed class they're it's a much +smaller set the closed class words are + + align:start position:0% +smaller set the closed class words are + + + align:start position:0% +smaller set the closed class words are +are a um a a very small set and the Open + + align:start position:0% +are a um a a very small set and the Open + + + align:start position:0% +are a um a a very small set and the Open +Class set is is the set of all other + + align:start position:0% +Class set is is the set of all other + + + align:start position:0% +Class set is is the set of all other +words that fill up the dictionary and + + align:start position:0% +words that fill up the dictionary and + + + align:start position:0% +words that fill up the dictionary and +everything else + + align:start position:0% +everything else + + + align:start position:0% +everything else +um so I think that's what you need to + + align:start position:0% +um so I think that's what you need to + + + align:start position:0% +um so I think that's what you need to +know about that oh the other thing to + + align:start position:0% +know about that oh the other thing to + + + align:start position:0% +know about that oh the other thing to +know about it is the closed class words + + align:start position:0% +know about it is the closed class words + + + align:start position:0% +know about it is the closed class words +are what shows up when you get beyond + + align:start position:0% +are what shows up when you get beyond + + + align:start position:0% +are what shows up when you get beyond +the two-word stage in language + + align:start position:0% +the two-word stage in language + + + align:start position:0% +the two-word stage in language +development right little kids two-word + + align:start position:0% +development right little kids two-word + + + align:start position:0% +development right little kids two-word +stage kids don't say the ball they say + + align:start position:0% +stage kids don't say the ball they say + + + align:start position:0% +stage kids don't say the ball they say +go ball or something like that but um + + align:start position:0% +go ball or something like that but um + + + align:start position:0% +go ball or something like that but um +you know when they start to say I see + + align:start position:0% +you know when they start to say I see + + + align:start position:0% +you know when they start to say I see +the cat um you know longer utterances + + align:start position:0% +the cat um you know longer utterances + + + align:start position:0% +the cat um you know longer utterances +that that's when you start getting these + + align:start position:0% +that that's when you start getting these + + + align:start position:0% +that that's when you start getting these +closed class things coming in okay what + + align:start position:0% +closed class things coming in okay what + + + align:start position:0% +closed class things coming in okay what +else do you need to + + align:start position:0% +else do you need to + + + align:start position:0% +else do you need to +know everybody knows everything this is + + align:start position:0% +know everybody knows everything this is + + + align:start position:0% +know everybody knows everything this is +great no okay + + align:start position:0% + + + + align:start position:0% + +what uh you if you look at the exam from + + align:start position:0% +what uh you if you look at the exam from + + + align:start position:0% +what uh you if you look at the exam from +years past the mix is roughly comparable + + align:start position:0% +years past the mix is roughly comparable + + + align:start position:0% +years past the mix is roughly comparable +I I didn't actually check it's it's i' + + align:start position:0% +I I didn't actually check it's it's i' + + + align:start position:0% +I I didn't actually check it's it's i' +I've there there there's a sort of an + + align:start position:0% +I've there there there's a sort of an + + + align:start position:0% +I've there there there's a sort of an +interesting Push Pull here the the the + + align:start position:0% +interesting Push Pull here the the the + + + align:start position:0% +interesting Push Pull here the the the +the the long longer answers are worth 10 + + align:start position:0% +the the long longer answers are worth 10 + + + align:start position:0% +the the long longer answers are worth 10 +points so if I write long answer + + align:start position:0% +points so if I write long answer + + + align:start position:0% +points so if I write long answer +questions um they uh I I can get done + + align:start position:0% +questions um they uh I I can get done + + + align:start position:0% +questions um they uh I I can get done +writing the exam faster I don't have to + + align:start position:0% +writing the exam faster I don't have to + + + align:start position:0% +writing the exam faster I don't have to +write as many questions the short answer + + align:start position:0% +write as many questions the short answer + + + align:start position:0% +write as many questions the short answer +questions the multiple choice questions + + align:start position:0% +questions the multiple choice questions + + + align:start position:0% +questions the multiple choice questions +are a lot easier to grade so if I write + + align:start position:0% +are a lot easier to grade so if I write + + + align:start position:0% +are a lot easier to grade so if I write +a lot of those it's an easier an easier + + align:start position:0% +a lot of those it's an easier an easier + + + align:start position:0% +a lot of those it's an easier an easier +test to grade and and and so the mix of + + align:start position:0% +test to grade and and and so the mix of + + + align:start position:0% +test to grade and and and so the mix of +those two + + align:start position:0% +those two + + + align:start position:0% +those two +pressures leads me to sort of the usual + + align:start position:0% +pressures leads me to sort of the usual + + + align:start position:0% +pressures leads me to sort of the usual +mix I think does it didn't look weird + + align:start position:0% +mix I think does it didn't look weird + + + align:start position:0% +mix I think does it didn't look weird +did it in any no it's about this kind of + + align:start position:0% +did it in any no it's about this kind of + + + align:start position:0% +did it in any no it's about this kind of +the usual some of + + align:start position:0% + + + + align:start position:0% + +each + + align:start position:0% + + + + align:start position:0% + +yes um the ones of you who come here + + align:start position:0% +yes um the ones of you who come here + + + align:start position:0% +yes um the ones of you who come here +will the ones who sleep late well + + align:start position:0% +will the ones who sleep late well + + + align:start position:0% +will the ones who sleep late well +actually this is at least it's start in + + align:start position:0% +actually this is at least it's start in + + + align:start position:0% +actually this is at least it's start in +the afternoon here mostly people make it + + align:start position:0% +the afternoon here mostly people make it + + + align:start position:0% +the afternoon here mostly people make it +awake it's when is the is the final in + + align:start position:0% +awake it's when is the is the final in + + + align:start position:0% +awake it's when is the is the final in +the morning or in the afternoon any it's + + align:start position:0% +the morning or in the afternoon any it's + + + align:start position:0% +the morning or in the afternoon any it's +morning afternoon oh good whenever it's + + align:start position:0% +morning afternoon oh good whenever it's + + + align:start position:0% +morning afternoon oh good whenever it's +in the morning there's all these sad + + align:start position:0% +in the morning there's all these sad + + + align:start position:0% +in the morning there's all these sad +people who trapes in an hour and a half + + align:start position:0% +people who trapes in an hour and a half + + + align:start position:0% +people who trapes in an hour and a half +late with some great story about I woke + + align:start position:0% +late with some great story about I woke + + + align:start position:0% +late with some great story about I woke +up when my alarm clock woke me up but + + align:start position:0% +up when my alarm clock woke me up but + + + align:start position:0% +up when my alarm clock woke me up but +then I went back to sleep and I had a + + align:start position:0% +then I went back to sleep and I had a + + + align:start position:0% +then I went back to sleep and I had a +dream that I was awake taking the exam + + align:start position:0% +dream that I was awake taking the exam + + + align:start position:0% +dream that I was awake taking the exam +can't I get credit for the answers I was + + align:start position:0% +can't I get credit for the answers I was + + + align:start position:0% +can't I get credit for the answers I was +writing um but um yeah it's it's it's + + align:start position:0% +writing um but um yeah it's it's it's + + + align:start position:0% +writing um but um yeah it's it's it's +here it's here everybody's taking it + + align:start position:0% +here it's here everybody's taking it + + + align:start position:0% +here it's here everybody's taking it +here and and look you know do me a favor + + align:start position:0% +here and and look you know do me a favor + + + align:start position:0% +here and and look you know do me a favor +do your best to put a seat between each + + align:start position:0% +do your best to put a seat between each + + + align:start position:0% +do your best to put a seat between each +of you and if you're not putting a seat + + align:start position:0% +of you and if you're not putting a seat + + + align:start position:0% +of you and if you're not putting a seat +between each of you because we've run + + align:start position:0% +between each of you because we've run + + + align:start position:0% +between each of you because we've run +out you know because there are 300 of + + align:start position:0% +out you know because there are 300 of + + + align:start position:0% +out you know because there are 300 of +you and not 600 seats um you know it's + + align:start position:0% +you and not 600 seats um you know it's + + + align:start position:0% +you and not 600 seats um you know it's +consider considered good form not to + + align:start position:0% +consider considered good form not to + + + align:start position:0% +consider considered good form not to +take the exam like + + align:start position:0% +take the exam like + + + align:start position:0% +take the exam like +this particularly since the guy sitting + + align:start position:0% +this particularly since the guy sitting + + + align:start position:0% +this particularly since the guy sitting +next to you is probably is just as + + align:start position:0% +next to you is probably is just as + + + align:start position:0% +next to you is probably is just as +clueless as you are um and it's really + + align:start position:0% +clueless as you are um and it's really + + + align:start position:0% +clueless as you are um and it's really +really + + align:start position:0% +really + + + align:start position:0% +really +embarrassing when your wrong answer is + + align:start position:0% +embarrassing when your wrong answer is + + + align:start position:0% +embarrassing when your wrong answer is +exactly the same as the wrong answer + + align:start position:0% +exactly the same as the wrong answer + + + align:start position:0% +exactly the same as the wrong answer +sitting next to you that's I mean it's + + align:start position:0% +sitting next to you that's I mean it's + + + align:start position:0% +sitting next to you that's I mean it's +okay on a multiple choice thing but the + + align:start position:0% +okay on a multiple choice thing but the + + + align:start position:0% +okay on a multiple choice thing but the +this + + align:start position:0% +this + + + align:start position:0% +this +happened actually this happened to me + + align:start position:0% +happened actually this happened to me + + + align:start position:0% +happened actually this happened to me +once upon a time in in grade school I + + align:start position:0% +once upon a time in in grade school I + + + align:start position:0% +once upon a time in in grade school I +was accused of plagiarizing of a a + + align:start position:0% +was accused of plagiarizing of a a + + + align:start position:0% +was accused of plagiarizing of a a +report and they showed it to me and uh + + align:start position:0% +report and they showed it to me and uh + + + align:start position:0% +report and they showed it to me and uh +you you know here's this kid's report + + align:start position:0% +you you know here's this kid's report + + + align:start position:0% +you you know here's this kid's report +here's your report these are identical + + align:start position:0% +here's your report these are identical + + + align:start position:0% +here's your report these are identical +which was true um and arrogant smart kid + + align:start position:0% +which was true um and arrogant smart kid + + + align:start position:0% +which was true um and arrogant smart kid +that I was I said do you think I'd + + align:start position:0% +that I was I said do you think I'd + + + align:start position:0% +that I was I said do you think I'd +plagarized from him I mean it was it + + align:start position:0% +plagarized from him I mean it was it + + + align:start position:0% +plagarized from him I mean it was it +didn't take much of a brain to figure + + align:start position:0% +didn't take much of a brain to figure + + + align:start position:0% +didn't take much of a brain to figure +out who'd plagiarized from whom because + + align:start position:0% +out who'd plagiarized from whom because + + + align:start position:0% +out who'd plagiarized from whom because +this was a kid who was you know still + + align:start position:0% +this was a kid who was you know still + + + align:start position:0% +this was a kid who was you know still +reading the books with the print that + + align:start position:0% +reading the books with the print that + + + align:start position:0% +reading the books with the print that +you could read across the room and + + align:start position:0% +you could read across the room and + + + align:start position:0% +you could read across the room and +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +it was I wasn't going to plagiarize his + + align:start position:0% +it was I wasn't going to plagiarize his + + + align:start position:0% +it was I wasn't going to plagiarize his +I was sort of flattered that he took my + + align:start position:0% +I was sort of flattered that he took my + + + align:start position:0% +I was sort of flattered that he took my +paper I guess anyway does anybody + + align:start position:0% +paper I guess anyway does anybody + + + align:start position:0% +paper I guess anyway does anybody +actually have a question I should answer + + align:start position:0% +actually have a question I should answer + + + align:start position:0% +actually have a question I should answer +here yeah all + + align:start position:0% +here yeah all + + + align:start position:0% +here yeah all +right can I go over + + align:start position:0% +right can I go over + + + align:start position:0% +right can I go over +who the logic of perception well the + + align:start position:0% +who the logic of perception well the + + + align:start position:0% +who the logic of perception well the +logic of perception is irn Rock's uh + + align:start position:0% +logic of perception is irn Rock's uh + + + align:start position:0% +logic of perception is irn Rock's uh +jargon for what I was really talking + + align:start position:0% +jargon for what I was really talking + + + align:start position:0% +jargon for what I was really talking +about in lecture for instance as as um + + align:start position:0% +about in lecture for instance as as um + + + align:start position:0% +about in lecture for instance as as um +as inference and I think maybe in the + + align:start position:0% +as inference and I think maybe in the + + + align:start position:0% +as inference and I think maybe in the +book also Al is Helm hold's idea of + + align:start position:0% +book also Al is Helm hold's idea of + + + align:start position:0% +book also Al is Helm hold's idea of +unconscious inference it's this idea + + align:start position:0% +unconscious inference it's this idea + + + align:start position:0% +unconscious inference it's this idea +that you're you're continuously making + + align:start position:0% +that you're you're continuously making + + + align:start position:0% +that you're you're continuously making +the + + align:start position:0% +the + + + align:start position:0% +the +best guess you can from an + + align:start position:0% +best guess you can from an + + + align:start position:0% +best guess you can from an +impoverished stimulus that you've got a + + align:start position:0% +impoverished stimulus that you've got a + + + align:start position:0% +impoverished stimulus that you've got a +set of uh of rules built into you that + + align:start position:0% +set of uh of rules built into you that + + + align:start position:0% +set of uh of rules built into you that +say um that that help you to try to + + align:start position:0% +say um that that help you to try to + + + align:start position:0% +say um that that help you to try to +figure out what it is that you're you're + + align:start position:0% +figure out what it is that you're you're + + + align:start position:0% +figure out what it is that you're you're +um you're looking at there's more to Lo + + align:start position:0% +um you're looking at there's more to Lo + + + align:start position:0% +um you're looking at there's more to Lo +to to Rock's argument than that but not + + align:start position:0% +to to Rock's argument than that but not + + + align:start position:0% +to to Rock's argument than that but not +much more in the book as I recall + + align:start position:0% +much more in the book as I recall + + + align:start position:0% +much more in the book as I recall +something about like that there was + + align:start position:0% +something about like that there was + + + align:start position:0% +something about like that there was +another hand over there a moment ago + + align:start position:0% +another hand over there a moment ago + + + align:start position:0% +another hand over there a moment ago +well now there's one + + align:start position:0% + + + + align:start position:0% + +here so oh so lectures or book this is + + align:start position:0% +here so oh so lectures or book this is + + + align:start position:0% +here so oh so lectures or book this is +the triage question I haven't read the + + align:start position:0% +the triage question I haven't read the + + + align:start position:0% +the triage question I haven't read the +book I wasn't at the lectures now what + + align:start position:0% +book I wasn't at the lectures now what + + + align:start position:0% +book I wasn't at the lectures now what +do I do um the uh I the answer is that + + align:start position:0% +do I do um the uh I the answer is that + + + align:start position:0% +do I do um the uh I the answer is that +um the intersection of book and lecture + + align:start position:0% +um the intersection of book and lecture + + + align:start position:0% +um the intersection of book and lecture +is the best place to devote your energy + + align:start position:0% +is the best place to devote your energy + + + align:start position:0% +is the best place to devote your energy +so things that were covered in both are + + align:start position:0% +so things that were covered in both are + + + align:start position:0% +so things that were covered in both are +probably important enough that well you + + align:start position:0% +probably important enough that well you + + + align:start position:0% +probably important enough that well you +know they're important enough that glan + + align:start position:0% +know they're important enough that glan + + + align:start position:0% +know they're important enough that glan +thought it was important I thought it + + align:start position:0% +thought it was important I thought it + + + align:start position:0% +thought it was important I thought it +was important that sounds important um + + align:start position:0% +was important that sounds important um + + + align:start position:0% +was important that sounds important um +beyond that I used to say that because I + + align:start position:0% +beyond that I used to say that because I + + + align:start position:0% +beyond that I used to say that because I +you know am as uh you know egocentric as + + align:start position:0% +you know am as uh you know egocentric as + + + align:start position:0% +you know am as uh you know egocentric as +the next person that things that are in + + align:start position:0% +the next person that things that are in + + + align:start position:0% +the next person that things that are in +my lectures but not in the book are more + + align:start position:0% +my lectures but not in the book are more + + + align:start position:0% +my lectures but not in the book are more +likely to show up than things that are + + align:start position:0% +likely to show up than things that are + + + align:start position:0% +likely to show up than things that are +in the book but not in the lecture but + + align:start position:0% +in the book but not in the lecture but + + + align:start position:0% +in the book but not in the lecture but +I'm not really sure that's + + align:start position:0% +I'm not really sure that's + + + align:start position:0% +I'm not really sure that's +true um anymore and and so I would say + + align:start position:0% +true um anymore and and so I would say + + + align:start position:0% +true um anymore and and so I would say +that you know after that if I was trying + + align:start position:0% +that you know after that if I was trying + + + align:start position:0% +that you know after that if I was trying +to figure out how to ration my precious + + align:start position:0% +to figure out how to ration my precious + + + align:start position:0% +to figure out how to ration my precious +time I would look at the set of kind of + + align:start position:0% +time I would look at the set of kind of + + + align:start position:0% +time I would look at the set of kind of +bullet questions that I put on most of + + align:start position:0% +bullet questions that I put on most of + + + align:start position:0% +bullet questions that I put on most of +the handouts until I ran out of time um + + align:start position:0% +the handouts until I ran out of time um + + + align:start position:0% +the handouts until I ran out of time um +for the chapter + + align:start position:0% +for the chapter + + + align:start position:0% +for the chapter +readings because you know what you've + + align:start position:0% +readings because you know what you've + + + align:start position:0% +readings because you know what you've +got there is what I think is important + + align:start position:0% +got there is what I think is important + + + align:start position:0% +got there is what I think is important +in the chapters and that's a pretty good + + align:start position:0% +in the chapters and that's a pretty good + + + align:start position:0% +in the chapters and that's a pretty good +bet on things that I might ask about um + + align:start position:0% +bet on things that I might ask about um + + + align:start position:0% +bet on things that I might ask about um +I'm you know I I got no particular stake + + align:start position:0% +I'm you know I I got no particular stake + + + align:start position:0% +I'm you know I I got no particular stake +in + + align:start position:0% +in + + + align:start position:0% +in +being arbitrarily evil and saying can I + + align:start position:0% +being arbitrarily evil and saying can I + + + align:start position:0% +being arbitrarily evil and saying can I +find some really teeny little piece of + + align:start position:0% +find some really teeny little piece of + + + align:start position:0% +find some really teeny little piece of +the book that I can quiz you about and + + align:start position:0% +the book that I can quiz you about and + + + align:start position:0% +the book that I can quiz you about and +yeah nobody got it um you know the + + align:start position:0% +yeah nobody got it um you know the + + + align:start position:0% +yeah nobody got it um you know the +amusement of that wears off after the + + align:start position:0% +amusement of that wears off after the + + + align:start position:0% +amusement of that wears off after the +first 20 years of teaching the course it + + align:start position:0% +first 20 years of teaching the course it + + + align:start position:0% +first 20 years of teaching the course it +turns out um so I so another way of + + align:start position:0% +turns out um so I so another way of + + + align:start position:0% +turns out um so I so another way of +looking at it is I I tend to ask + + align:start position:0% +looking at it is I I tend to ask + + + align:start position:0% +looking at it is I I tend to ask +question if when I'm going for stuff + + align:start position:0% +question if when I'm going for stuff + + + align:start position:0% +question if when I'm going for stuff +that's just in the book I tend to go for + + align:start position:0% +that's just in the book I tend to go for + + + align:start position:0% +that's just in the book I tend to go for +stuff that's covered in more than one + + align:start position:0% +stuff that's covered in more than one + + + align:start position:0% +stuff that's covered in more than one +sentence in the book so if something is + + align:start position:0% +sentence in the book so if something is + + + align:start position:0% +sentence in the book so if something is +worth a page to + + align:start position:0% +worth a page to + + + align:start position:0% +worth a page to +glan you know you might as well pay more + + align:start position:0% +glan you know you might as well pay more + + + align:start position:0% +glan you know you might as well pay more +attention to that than than a than a + + align:start position:0% +attention to that than than a than a + + + align:start position:0% +attention to that than than a than a +passing figure + + align:start position:0% +passing figure + + + align:start position:0% +passing figure +caption you'll be fine all right we'll + + align:start position:0% +caption you'll be fine all right we'll + + + align:start position:0% +caption you'll be fine all right we'll +take one more back + + align:start position:0% +take one more back + + + align:start position:0% +take one more back +there hour and a + + align:start position:0% +there hour and a + + + align:start position:0% +there hour and a +half and you should know that it's no + + align:start position:0% +half and you should know that it's no + + + align:start position:0% +half and you should know that it's no +longer than it used to be when it was an + + align:start position:0% +longer than it used to be when it was an + + + align:start position:0% +longer than it used to be when it was an +hour long so you'll be fine + + align:start position:0% +hour long so you'll be fine + + + align:start position:0% +hour long so you'll be fine +what genre of book is it based on + + align:start position:0% + + + + align:start position:0% + +printed good luck \ No newline at end of file diff --git a/5BvE_WSDt74.txt b/5BvE_WSDt74.txt new file mode 100644 index 0000000000000000000000000000000000000000..bf58246fc442fc8dac96eccce760aae1aa91932c --- /dev/null +++ b/5BvE_WSDt74.txt @@ -0,0 +1,2291 @@ +align:start position:0% + +And so next we have Susan. Um, + + align:start position:0% + + + + align:start position:0% + +>> you need the clicker. + + align:start position:0% +>> you need the clicker. + + + align:start position:0% +>> you need the clicker. +>> I do need the clicker. I don't need the + + align:start position:0% +>> I do need the clicker. I don't need the + + + align:start position:0% +>> I do need the clicker. I don't need the +pen. + + align:start position:0% +pen. + + + align:start position:0% +pen. +>> It's about the MIT project. Wow, that + + align:start position:0% +>> It's about the MIT project. Wow, that + + + align:start position:0% +>> It's about the MIT project. Wow, that +was fantastic. Uh, I also want to add my + + align:start position:0% +was fantastic. Uh, I also want to add my + + + align:start position:0% +was fantastic. Uh, I also want to add my +voice uh to this chorus, my voice and my + + align:start position:0% +voice uh to this chorus, my voice and my + + + align:start position:0% +voice uh to this chorus, my voice and my +colleagues voice. And to start by + + align:start position:0% +colleagues voice. And to start by + + + align:start position:0% +colleagues voice. And to start by +thanking uh Zenab and this incredible + + align:start position:0% +thanking uh Zenab and this incredible + + + align:start position:0% +thanking uh Zenab and this incredible +group that's joined here today and to + + align:start position:0% +group that's joined here today and to + + + align:start position:0% +group that's joined here today and to +say that you all are pioneers. You know, + + align:start position:0% +say that you all are pioneers. You know, + + + align:start position:0% +say that you all are pioneers. You know, +we've been I've been so moved by so much + + align:start position:0% +we've been I've been so moved by so much + + + align:start position:0% +we've been I've been so moved by so much +creative work by so many leaders in the + + align:start position:0% +creative work by so many leaders in the + + + align:start position:0% +creative work by so many leaders in the +field that have been brought together. + + align:start position:0% +field that have been brought together. + + + align:start position:0% +field that have been brought together. +It's truly remarkable. And so thank you. + + align:start position:0% +It's truly remarkable. And so thank you. + + + align:start position:0% +It's truly remarkable. And so thank you. +Uh I'm going to introduce to you the MIT + + align:start position:0% +Uh I'm going to introduce to you the MIT + + + align:start position:0% +Uh I'm going to introduce to you the MIT +thermal energy network or mitten plan + + align:start position:0% +thermal energy network or mitten plan + + + align:start position:0% +thermal energy network or mitten plan +for rapid costeffective decarbonization + + align:start position:0% +for rapid costeffective decarbonization + + + align:start position:0% +for rapid costeffective decarbonization +of MIT campus. Uh it is the work of MACA + + align:start position:0% +of MIT campus. Uh it is the work of MACA + + + align:start position:0% +of MIT campus. Uh it is the work of MACA +MIT campus group. MAC stands for MIT + + align:start position:0% +MIT campus group. MAC stands for MIT + + + align:start position:0% +MIT campus group. MAC stands for MIT +alumni for climate action in + + align:start position:0% +alumni for climate action in + + + align:start position:0% +alumni for climate action in +collaboration with GIO at MIT which is + + align:start position:0% +collaboration with GIO at MIT which is + + + align:start position:0% +collaboration with GIO at MIT which is +the student group that we've worked + + align:start position:0% +the student group that we've worked + + + align:start position:0% +the student group that we've worked +with. Maka was founded in 2018. The idea + + align:start position:0% +with. Maka was founded in 2018. The idea + + + align:start position:0% +with. Maka was founded in 2018. The idea +for a thermal energy network for MIT + + align:start position:0% +for a thermal energy network for MIT + + + align:start position:0% +for a thermal energy network for MIT +campus uh uh goes to Rick Clemensy, a + + align:start position:0% +campus uh uh goes to Rick Clemensy, a + + + align:start position:0% +campus uh uh goes to Rick Clemensy, a +colleague of uh uh Garen um Eubank, who + + align:start position:0% +colleague of uh uh Garen um Eubank, who + + + align:start position:0% +colleague of uh uh Garen um Eubank, who +we heard from earlier. Uh Rick and Judy + + align:start position:0% +we heard from earlier. Uh Rick and Judy + + + align:start position:0% +we heard from earlier. Uh Rick and Judy +uh won a climate collab competition uh + + align:start position:0% +uh won a climate collab competition uh + + + align:start position:0% +uh won a climate collab competition uh +that MIT sponsored in 2016. Um but it + + align:start position:0% +that MIT sponsored in 2016. Um but it + + + align:start position:0% +that MIT sponsored in 2016. Um but it +didn't go anywhere. MIT wasn't + + align:start position:0% +didn't go anywhere. MIT wasn't + + + align:start position:0% +didn't go anywhere. MIT wasn't +interested at the time in listening to + + align:start position:0% +interested at the time in listening to + + + align:start position:0% +interested at the time in listening to +that. Um we we picked that up at MIT. Uh + + align:start position:0% +that. Um we we picked that up at MIT. Uh + + + align:start position:0% +that. Um we we picked that up at MIT. Uh +the Maka group picked up that idea and + + align:start position:0% +the Maka group picked up that idea and + + + align:start position:0% +the Maka group picked up that idea and +have built on it for the past three + + align:start position:0% +have built on it for the past three + + + align:start position:0% +have built on it for the past three +years and we just introduced it formally + + align:start position:0% +years and we just introduced it formally + + + align:start position:0% +years and we just introduced it formally +in a class that I t taught um this past + + align:start position:0% +in a class that I t taught um this past + + + align:start position:0% +in a class that I t taught um this past +week uh and in an hourong presentation + + align:start position:0% +week uh and in an hourong presentation + + + align:start position:0% +week uh and in an hourong presentation +which has been reduced to 10 minutes for + + align:start position:0% +which has been reduced to 10 minutes for + + + align:start position:0% +which has been reduced to 10 minutes for +today. So, moving along, MIT's + + align:start position:0% +today. So, moving along, MIT's + + + align:start position:0% +today. So, moving along, MIT's +decarbonization challenge is that 97% of + + align:start position:0% +decarbonization challenge is that 97% of + + + align:start position:0% +decarbonization challenge is that 97% of +MIT's greenhouse gas emissions are from + + align:start position:0% +MIT's greenhouse gas emissions are from + + + align:start position:0% +MIT's greenhouse gas emissions are from +the operation of its buildings and 26% + + align:start position:0% +the operation of its buildings and 26% + + + align:start position:0% +the operation of its buildings and 26% +of all of Cambridge's greenhouse gases + + align:start position:0% +of all of Cambridge's greenhouse gases + + + align:start position:0% +of all of Cambridge's greenhouse gases +are from MIT. + + align:start position:0% +are from MIT. + + + align:start position:0% +are from MIT. +Um, MIT has had two climate action plans + + align:start position:0% +Um, MIT has had two climate action plans + + + align:start position:0% +Um, MIT has had two climate action plans +in 2016 and 2021 um which postponed + + align:start position:0% +in 2016 and 2021 um which postponed + + + align:start position:0% +in 2016 and 2021 um which postponed +significant investment in direct campus + + align:start position:0% +significant investment in direct campus + + + align:start position:0% +significant investment in direct campus +decarbonization until later. uh its + + align:start position:0% +decarbonization until later. uh its + + + align:start position:0% +decarbonization until later. uh its +emphasis in the early years 2020 up to + + align:start position:0% +emphasis in the early years 2020 up to + + + align:start position:0% +emphasis in the early years 2020 up to +2040 and going on is uh power purchase + + align:start position:0% +2040 and going on is uh power purchase + + + align:start position:0% +2040 and going on is uh power purchase +agreements uh in the Midwest uh and um + + align:start position:0% +agreements uh in the Midwest uh and um + + + align:start position:0% +agreements uh in the Midwest uh and um +and mainly the power purchase agreements + + align:start position:0% +and mainly the power purchase agreements + + + align:start position:0% +and mainly the power purchase agreements +um but uh it it hopes for um some major + + align:start position:0% +um but uh it it hopes for um some major + + + align:start position:0% +um but uh it it hopes for um some major +breakthroughs uh in the future um and is + + align:start position:0% +breakthroughs uh in the future um and is + + + align:start position:0% +breakthroughs uh in the future um and is +going to put you know is is there there + + align:start position:0% +going to put you know is is there there + + + align:start position:0% +going to put you know is is there there +are voices uh among this chorus at MIT + + align:start position:0% +are voices uh among this chorus at MIT + + + align:start position:0% +are voices uh among this chorus at MIT +who would like to see um uh small + + align:start position:0% +who would like to see um uh small + + + align:start position:0% +who would like to see um uh small +nuclear reactors or deep geothermal uh + + align:start position:0% +nuclear reactors or deep geothermal uh + + + align:start position:0% +nuclear reactors or deep geothermal uh +at some future point when it becomes uh + + align:start position:0% +at some future point when it becomes uh + + + align:start position:0% +at some future point when it becomes uh +a reality. + + align:start position:0% +a reality. + + + align:start position:0% +a reality. +The MIT thermal energy decarbonization + + align:start position:0% +The MIT thermal energy decarbonization + + + align:start position:0% +The MIT thermal energy decarbonization +plan is an all electric campus fueled by + + align:start position:0% +plan is an all electric campus fueled by + + + align:start position:0% +plan is an all electric campus fueled by +carbon-f free power. It implements + + align:start position:0% +carbon-f free power. It implements + + + align:start position:0% +carbon-f free power. It implements +energy conservation measures including + + align:start position:0% +energy conservation measures including + + + align:start position:0% +energy conservation measures including +waste heat recovery from ventilation + + align:start position:0% +waste heat recovery from ventilation + + + align:start position:0% +waste heat recovery from ventilation +systems to reduce heating and cooling. + + align:start position:0% +systems to reduce heating and cooling. + + + align:start position:0% +systems to reduce heating and cooling. +We're installing high efficiency water + + align:start position:0% +We're installing high efficiency water + + + align:start position:0% +We're installing high efficiency water +source heat pumps in each building + + align:start position:0% +source heat pumps in each building + + + align:start position:0% +source heat pumps in each building +distributed + + align:start position:0% +distributed + + + align:start position:0% +distributed +um for heating and cooling. It + + align:start position:0% +um for heating and cooling. It + + + align:start position:0% +um for heating and cooling. It +repurposes the existing chiller loop to + + align:start position:0% +repurposes the existing chiller loop to + + + align:start position:0% +repurposes the existing chiller loop to +an ambient loop circulating 45 to 85 + + align:start position:0% +an ambient loop circulating 45 to 85 + + + align:start position:0% +an ambient loop circulating 45 to 85 +degree water year round to water source + + align:start position:0% +degree water year round to water source + + + align:start position:0% +degree water year round to water source +heat pumps in each building. It + + align:start position:0% +heat pumps in each building. It + + + align:start position:0% +heat pumps in each building. It +repurposes the oil tanks at the CUP + + align:start position:0% +repurposes the oil tanks at the CUP + + + align:start position:0% +repurposes the oil tanks at the CUP +central utilities plant for thermal + + align:start position:0% +central utilities plant for thermal + + + align:start position:0% +central utilities plant for thermal +storage. And there are energy transfer + + align:start position:0% +storage. And there are energy transfer + + + align:start position:0% +storage. And there are energy transfer +stations operated by the Cambridge Water + + align:start position:0% +stations operated by the Cambridge Water + + + align:start position:0% +stations operated by the Cambridge Water +Department exchanging heat with the + + align:start position:0% +Department exchanging heat with the + + + align:start position:0% +Department exchanging heat with the +ambient loop where possible and if not + + align:start position:0% +ambient loop where possible and if not + + + align:start position:0% +ambient loop where possible and if not +then looking to the MWR and and the + + align:start position:0% +then looking to the MWR and and the + + + align:start position:0% +then looking to the MWR and and the +wastewater sewage or drilling uh + + align:start position:0% +wastewater sewage or drilling uh + + + align:start position:0% +wastewater sewage or drilling uh +geothermal bore holes. + + align:start position:0% +geothermal bore holes. + + + align:start position:0% +geothermal bore holes. +The plan is the most cost-effective and + + align:start position:0% +The plan is the most cost-effective and + + + align:start position:0% +The plan is the most cost-effective and +energyefficient way to decarbonize the + + align:start position:0% +energyefficient way to decarbonize the + + + align:start position:0% +energyefficient way to decarbonize the +campus. It demonstrates MIT leadership. + + align:start position:0% +campus. It demonstrates MIT leadership. + + + align:start position:0% +campus. It demonstrates MIT leadership. +It leverages MIT's investment in + + align:start position:0% +It leverages MIT's investment in + + + align:start position:0% +It leverages MIT's investment in +existing infrastructure. It eliminates + + align:start position:0% +existing infrastructure. It eliminates + + + align:start position:0% +existing infrastructure. It eliminates +the cost impact of maintaining separate + + align:start position:0% +the cost impact of maintaining separate + + + align:start position:0% +the cost impact of maintaining separate +systems because the water source heat + + align:start position:0% +systems because the water source heat + + + align:start position:0% +systems because the water source heat +pumps uh provide both heating and + + align:start position:0% +pumps uh provide both heating and + + + align:start position:0% +pumps uh provide both heating and +cooling. It eliminates energy + + align:start position:0% +cooling. It eliminates energy + + + align:start position:0% +cooling. It eliminates energy +transmission losses, enables the capture + + align:start position:0% +transmission losses, enables the capture + + + align:start position:0% +transmission losses, enables the capture +of free energy where there is concurrent + + align:start position:0% +of free energy where there is concurrent + + + align:start position:0% +of free energy where there is concurrent +heating and cooling on campus and + + align:start position:0% +heating and cooling on campus and + + + align:start position:0% +heating and cooling on campus and +perhaps will tap into future um + + align:start position:0% +perhaps will tap into future um + + + align:start position:0% +perhaps will tap into future um +subsidies. Uh the Met building already + + align:start position:0% +subsidies. Uh the Met building already + + + align:start position:0% +subsidies. Uh the Met building already +demonstrates this uh and this that that + + align:start position:0% +demonstrates this uh and this that that + + + align:start position:0% +demonstrates this uh and this that that +demonstration is underway. + + align:start position:0% +demonstration is underway. + + + align:start position:0% +demonstration is underway. +How is the campus heated and cooled now? + + align:start position:0% +How is the campus heated and cooled now? + + + align:start position:0% +How is the campus heated and cooled now? +It has a central utilities plant with + + align:start position:0% +It has a central utilities plant with + + + align:start position:0% +It has a central utilities plant with +co-generation. It produces steam and hot + + align:start position:0% +co-generation. It produces steam and hot + + + align:start position:0% +co-generation. It produces steam and hot +water. It operates on a steamdriven + + align:start position:0% +water. It operates on a steamdriven + + + align:start position:0% +water. It operates on a steamdriven +chiller. It generates over 22 megawatts + + align:start position:0% +chiller. It generates over 22 megawatts + + + align:start position:0% +chiller. It generates over 22 megawatts +of electric power connected to steam + + align:start position:0% +of electric power connected to steam + + + align:start position:0% +of electric power connected to steam +distribution connected to chilled water + + align:start position:0% +distribution connected to chilled water + + + align:start position:0% +distribution connected to chilled water +distribution to most buildings and the + + align:start position:0% +distribution to most buildings and the + + + align:start position:0% +distribution to most buildings and the +cooling load is high and most affected + + align:start position:0% +cooling load is high and most affected + + + align:start position:0% +cooling load is high and most affected +by global warming. + + align:start position:0% +by global warming. + + + align:start position:0% +by global warming. +Decarbonization issues with the existing + + align:start position:0% +Decarbonization issues with the existing + + + align:start position:0% +Decarbonization issues with the existing +plant. The the grid decarbonization is + + align:start position:0% +plant. The the grid decarbonization is + + + align:start position:0% +plant. The the grid decarbonization is +rapidly reducing carbon once added for a + + align:start position:0% +rapidly reducing carbon once added for a + + + align:start position:0% +rapidly reducing carbon once added for a +combined heat and power. + + align:start position:0% +combined heat and power. + + + align:start position:0% +combined heat and power. +Fossil fuel backup is necessary. + + align:start position:0% +Fossil fuel backup is necessary. + + + align:start position:0% +Fossil fuel backup is necessary. +Efficiency of 50 to 55% source to + + align:start position:0% +Efficiency of 50 to 55% source to + + + align:start position:0% +Efficiency of 50 to 55% source to +output. Low turndown rate of about 30%. + + align:start position:0% +output. Low turndown rate of about 30%. + + + align:start position:0% +output. Low turndown rate of about 30%. +High thermal losses in the seam + + align:start position:0% +High thermal losses in the seam + + + align:start position:0% +High thermal losses in the seam +distribution system of 10 to 20%. + + align:start position:0% +distribution system of 10 to 20%. + + + align:start position:0% +distribution system of 10 to 20%. +nonzero losses in the chilled water + + align:start position:0% +nonzero losses in the chilled water + + + align:start position:0% +nonzero losses in the chilled water +system of 5 to 15% and also the hot + + align:start position:0% +system of 5 to 15% and also the hot + + + align:start position:0% +system of 5 to 15% and also the hot +water district system have losses also + + align:start position:0% +water district system have losses also + + + align:start position:0% +water district system have losses also +um and hot water is what MIT's + + align:start position:0% +um and hot water is what MIT's + + + align:start position:0% +um and hot water is what MIT's +administration is currently uh seeming + + align:start position:0% +administration is currently uh seeming + + + align:start position:0% +administration is currently uh seeming +to embrace for its uh favored uh + + align:start position:0% +to embrace for its uh favored uh + + + align:start position:0% +to embrace for its uh favored uh +geothermal um pathway pathway option. + + align:start position:0% +geothermal um pathway pathway option. + + + align:start position:0% +geothermal um pathway pathway option. +How would the mitten plan heat and cool + + align:start position:0% +How would the mitten plan heat and cool + + + align:start position:0% +How would the mitten plan heat and cool +the campus? Uh, distributed heat pumps + + align:start position:0% +the campus? Uh, distributed heat pumps + + + align:start position:0% +the campus? Uh, distributed heat pumps +connected to a network of sources and + + align:start position:0% +connected to a network of sources and + + + align:start position:0% +connected to a network of sources and +sinks. No one solution since the + + align:start position:0% +sinks. No one solution since the + + + align:start position:0% +sinks. No one solution since the +buildings range over a history of + + align:start position:0% +buildings range over a history of + + + align:start position:0% +buildings range over a history of +hundred years. Use of building + + align:start position:0% +hundred years. Use of building + + + align:start position:0% +hundred years. Use of building +tobuilding and building inbuilding + + align:start position:0% +tobuilding and building inbuilding + + + align:start position:0% +tobuilding and building inbuilding +sources and sinks. Use of thermal energy + + align:start position:0% +sources and sinks. Use of thermal energy + + + align:start position:0% +sources and sinks. Use of thermal energy +storage and ground coupling with as I've + + align:start position:0% +storage and ground coupling with as I've + + + align:start position:0% +storage and ground coupling with as I've +said Cambridge water, sewer or uh ground + + align:start position:0% +said Cambridge water, sewer or uh ground + + + align:start position:0% +said Cambridge water, sewer or uh ground +thermal exchanges. + + align:start position:0% +thermal exchanges. + + + align:start position:0% +thermal exchanges. +We consider this a fifth or sixth + + align:start position:0% +We consider this a fifth or sixth + + + align:start position:0% +We consider this a fifth or sixth +generation district HVAC decarbonization + + align:start position:0% +generation district HVAC decarbonization + + + align:start position:0% +generation district HVAC decarbonization +transition with an ambient loop, + + align:start position:0% +transition with an ambient loop, + + + align:start position:0% +transition with an ambient loop, +two-pipe system, exhaust recovery, + + align:start position:0% +two-pipe system, exhaust recovery, + + + align:start position:0% +two-pipe system, exhaust recovery, +distributed water source heat pumps, + + align:start position:0% +distributed water source heat pumps, + + + align:start position:0% +distributed water source heat pumps, +thermal storage, air source heat pumps + + align:start position:0% +thermal storage, air source heat pumps + + + align:start position:0% +thermal storage, air source heat pumps +and ground heat exchange, municipal + + align:start position:0% +and ground heat exchange, municipal + + + align:start position:0% +and ground heat exchange, municipal +water thermal and other + + align:start position:0% +water thermal and other + + + align:start position:0% +water thermal and other +uh and the chiller loop to the ambient + + align:start position:0% +uh and the chiller loop to the ambient + + + align:start position:0% +uh and the chiller loop to the ambient +loop conversion. uh we would use the + + align:start position:0% +loop conversion. uh we would use the + + + align:start position:0% +loop conversion. uh we would use the +same two pipes that exist already. Uh + + align:start position:0% +same two pipes that exist already. Uh + + + align:start position:0% +same two pipes that exist already. Uh +first of all the blue uh buildings have + + align:start position:0% +first of all the blue uh buildings have + + + align:start position:0% +first of all the blue uh buildings have +currently chiller loop. Uh oh and I + + align:start position:0% +currently chiller loop. Uh oh and I + + + align:start position:0% +currently chiller loop. Uh oh and I +didn't say we have um MIT administration + + align:start position:0% +didn't say we have um MIT administration + + + align:start position:0% +didn't say we have um MIT administration +uh provided us with a memorandum of + + align:start position:0% +uh provided us with a memorandum of + + + align:start position:0% +uh provided us with a memorandum of +understanding uh to test fit our idea to + + align:start position:0% +understanding uh to test fit our idea to + + + align:start position:0% +understanding uh to test fit our idea to +six buildings and those six buildings + + align:start position:0% +six buildings and those six buildings + + + align:start position:0% +six buildings and those six buildings +are uh here uh W20 is the student center + + align:start position:0% +are uh here uh W20 is the student center + + + align:start position:0% +are uh here uh W20 is the student center +and the rest are the athletic complex + + align:start position:0% +and the rest are the athletic complex + + + align:start position:0% +and the rest are the athletic complex +W31 to W35 + + align:start position:0% +W31 to W35 + + + align:start position:0% +W31 to W35 +and three of those buildings have the + + align:start position:0% +and three of those buildings have the + + + align:start position:0% +and three of those buildings have the +blue buildings have the Chillerloop loop + + align:start position:0% +blue buildings have the Chillerloop loop + + + align:start position:0% +blue buildings have the Chillerloop loop +uh but the other three do not. So our + + align:start position:0% +uh but the other three do not. So our + + + align:start position:0% +uh but the other three do not. So our +plan would for the test fit would + + align:start position:0% +plan would for the test fit would + + + align:start position:0% +plan would for the test fit would +require the chiller loop to be added to + + align:start position:0% +require the chiller loop to be added to + + + align:start position:0% +require the chiller loop to be added to +these three excuse me the ambient loop + + align:start position:0% +these three excuse me the ambient loop + + + align:start position:0% +these three excuse me the ambient loop +to be added to these three buildings as + + align:start position:0% +to be added to these three buildings as + + + align:start position:0% +to be added to these three buildings as +represented by the green dots were our + + align:start position:0% +represented by the green dots were our + + + align:start position:0% +represented by the green dots were our +our uh proposal for these buildings + + align:start position:0% +our uh proposal for these buildings + + + align:start position:0% +our uh proposal for these buildings +expanded to the whole campus. It's we + + align:start position:0% +expanded to the whole campus. It's we + + + align:start position:0% +expanded to the whole campus. It's we +would also need an ambient loop here. Uh + + align:start position:0% +would also need an ambient loop here. Uh + + + align:start position:0% +would also need an ambient loop here. Uh +those are the only two places that we + + align:start position:0% +those are the only two places that we + + + align:start position:0% +those are the only two places that we +would need to do work. And I meant to + + align:start position:0% +would need to do work. And I meant to + + + align:start position:0% +would need to do work. And I meant to +say uh that here are the six buildings + + align:start position:0% +say uh that here are the six buildings + + + align:start position:0% +say uh that here are the six buildings +um on a graph of the EUIs of a number of + + align:start position:0% +um on a graph of the EUIs of a number of + + + align:start position:0% +um on a graph of the EUIs of a number of +the buildings, not all the buildings, + + align:start position:0% +the buildings, not all the buildings, + + + align:start position:0% +the buildings, not all the buildings, +but most of the buildings. And MIT has + + align:start position:0% +but most of the buildings. And MIT has + + + align:start position:0% +but most of the buildings. And MIT has +very high EUIs with the lab build oops + + align:start position:0% +very high EUIs with the lab build oops + + + align:start position:0% +very high EUIs with the lab build oops +with the lab buildings being uh + + align:start position:0% +with the lab buildings being uh + + + align:start position:0% +with the lab buildings being uh +backwards. Uh the + + align:start position:0% +backwards. Uh the + + + align:start position:0% +backwards. Uh the +um the the worst the worst uh performing + + align:start position:0% +um the the worst the worst uh performing + + + align:start position:0% +um the the worst the worst uh performing +buildings. Uh and what's interesting is + + align:start position:0% +buildings. Uh and what's interesting is + + + align:start position:0% +buildings. Uh and what's interesting is +that these six buildings represent a + + align:start position:0% +that these six buildings represent a + + + align:start position:0% +that these six buildings represent a +quite + + align:start position:0% +quite + + + align:start position:0% +quite +uh the huge a huge span of uh the campus + + align:start position:0% +uh the huge a huge span of uh the campus + + + align:start position:0% +uh the huge a huge span of uh the campus +uh current u EUIS. + + align:start position:0% +uh current u EUIS. + + + align:start position:0% +uh current u EUIS. +So + + align:start position:0% +So + + + align:start position:0% +So +uh this is where uh in W33 the ambient + + align:start position:0% +uh this is where uh in W33 the ambient + + + align:start position:0% +uh this is where uh in W33 the ambient +loop would run + + align:start position:0% +loop would run + + + align:start position:0% +loop would run +and this is uh the cluster from above um + + align:start position:0% +and this is uh the cluster from above um + + + align:start position:0% +and this is uh the cluster from above um +uh on which uh the ambient loop that you + + align:start position:0% +uh on which uh the ambient loop that you + + + align:start position:0% +uh on which uh the ambient loop that you +just saw would be running uh from the uh + + align:start position:0% +just saw would be running uh from the uh + + + align:start position:0% +just saw would be running uh from the uh +chilled water loop uh connection through + + align:start position:0% +chilled water loop uh connection through + + + align:start position:0% +chilled water loop uh connection through +uh what you just saw and through this + + align:start position:0% +uh what you just saw and through this + + + align:start position:0% +uh what you just saw and through this +building and into this building and also + + align:start position:0% +building and into this building and also + + + align:start position:0% +building and into this building and also +into W20. We would also put uh solar + + align:start position:0% +into W20. We would also put uh solar + + + align:start position:0% +into W20. We would also put uh solar +collectors on these wonderful flat roofs + + align:start position:0% +collectors on these wonderful flat roofs + + + align:start position:0% +collectors on these wonderful flat roofs +that are uh hidden from view. Uh and we + + align:start position:0% +that are uh hidden from view. Uh and we + + + align:start position:0% +that are uh hidden from view. Uh and we +would + + align:start position:0% +would + + + align:start position:0% +would +um put on the roof of W20, the student + + align:start position:0% +um put on the roof of W20, the student + + + align:start position:0% +um put on the roof of W20, the student +center u multistack heat pump units + + align:start position:0% +center u multistack heat pump units + + + align:start position:0% +center u multistack heat pump units +where there's already space for that. We + + align:start position:0% +where there's already space for that. We + + + align:start position:0% +where there's already space for that. We +would put as one option multistacks in + + align:start position:0% +would put as one option multistacks in + + + align:start position:0% +would put as one option multistacks in +W34 as well. Uh perhaps another option + + align:start position:0% +W34 as well. Uh perhaps another option + + + align:start position:0% +W34 as well. Uh perhaps another option +would be the AON SA23 in W34. + + align:start position:0% +would be the AON SA23 in W34. + + + align:start position:0% +would be the AON SA23 in W34. +And then uh to compare um a central + + align:start position:0% +And then uh to compare um a central + + + align:start position:0% +And then uh to compare um a central +plant fourpipe distribution system as is + + align:start position:0% +plant fourpipe distribution system as is + + + align:start position:0% +plant fourpipe distribution system as is +being proposed. You can see uh that + + align:start position:0% +being proposed. You can see uh that + + + align:start position:0% +being proposed. You can see uh that +um MIT currently has uh installed hot + + align:start position:0% +um MIT currently has uh installed hot + + + align:start position:0% +um MIT currently has uh installed hot +water pipes in the Sloan complex. It + + align:start position:0% +water pipes in the Sloan complex. It + + + align:start position:0% +water pipes in the Sloan complex. It +represents about 15% of the campus. Um + + align:start position:0% +represents about 15% of the campus. Um + + + align:start position:0% +represents about 15% of the campus. Um +and the consultants plan would require + + align:start position:0% +and the consultants plan would require + + + align:start position:0% +and the consultants plan would require +hot water pipes uh with I believe 180 to + + align:start position:0% +hot water pipes uh with I believe 180 to + + + align:start position:0% +hot water pipes uh with I believe 180 to +they call it low + + align:start position:0% +they call it low + + + align:start position:0% +they call it low +temperature pipes but not so low. Um 180 + + align:start position:0% +temperature pipes but not so low. Um 180 + + + align:start position:0% +temperature pipes but not so low. Um 180 +to 240 I believe uh degrees Fahrenheit + + align:start position:0% +to 240 I believe uh degrees Fahrenheit + + + align:start position:0% +to 240 I believe uh degrees Fahrenheit +hot water in these pipes and all of this + + align:start position:0% +hot water in these pipes and all of this + + + align:start position:0% +hot water in these pipes and all of this +would need to be um uh installed. And of + + align:start position:0% +would need to be um uh installed. And of + + + align:start position:0% +would need to be um uh installed. And of +course that would need need steel pipes + + align:start position:0% +course that would need need steel pipes + + + align:start position:0% +course that would need need steel pipes +and insulated pipes uh as opposed to the + + align:start position:0% +and insulated pipes uh as opposed to the + + + align:start position:0% +and insulated pipes uh as opposed to the +ambient loop uh small areas here. + + align:start position:0% +ambient loop uh small areas here. + + + align:start position:0% +ambient loop uh small areas here. +The + + align:start position:0% +The + + + align:start position:0% +The +central thermal plant has heat losses in + + align:start position:0% +central thermal plant has heat losses in + + + align:start position:0% +central thermal plant has heat losses in +transmission. Uh it starts off with a + + align:start position:0% +transmission. Uh it starts off with a + + + align:start position:0% +transmission. Uh it starts off with a +lower CO cop + + align:start position:0% +lower CO cop + + + align:start position:0% +lower CO cop +uh and Mittens has uh limited um heat + + align:start position:0% +uh and Mittens has uh limited um heat + + + align:start position:0% +uh and Mittens has uh limited um heat +losses because of each heat pump being + + align:start position:0% +losses because of each heat pump being + + + align:start position:0% +losses because of each heat pump being +in the building itself. + + align:start position:0% + + + + align:start position:0% + +So to sum up uh a kind of topline + + align:start position:0% +So to sum up uh a kind of topline + + + align:start position:0% +So to sum up uh a kind of topline +comparison of approaches um both + + align:start position:0% +comparison of approaches um both + + + align:start position:0% +comparison of approaches um both +approaches meet building HVAC specs. + + align:start position:0% +approaches meet building HVAC specs. + + + align:start position:0% +approaches meet building HVAC specs. +Both approaches achieve zero emissions. + + align:start position:0% +Both approaches achieve zero emissions. + + + align:start position:0% +Both approaches achieve zero emissions. +uh our approach achieves those emissions + + align:start position:0% +uh our approach achieves those emissions + + + align:start position:0% +uh our approach achieves those emissions +by 2035 were we to start this year uh + + align:start position:0% +by 2035 were we to start this year uh + + + align:start position:0% +by 2035 were we to start this year uh +with a pilot on the existing six + + align:start position:0% +with a pilot on the existing six + + + align:start position:0% +with a pilot on the existing six +building complex. + + align:start position:0% +building complex. + + + align:start position:0% +building complex. +Uh ours is minimally disruptive as you + + align:start position:0% +Uh ours is minimally disruptive as you + + + align:start position:0% +Uh ours is minimally disruptive as you +saw with the ambient loop only needing + + align:start position:0% +saw with the ambient loop only needing + + + align:start position:0% +saw with the ambient loop only needing +to be extended in a few places. Uh we + + align:start position:0% +to be extended in a few places. Uh we + + + align:start position:0% +to be extended in a few places. Uh we +need a pilot to confirm our projections + + align:start position:0% +need a pilot to confirm our projections + + + align:start position:0% +need a pilot to confirm our projections +and to learn as the heat ever source uh + + align:start position:0% +and to learn as the heat ever source uh + + + align:start position:0% +and to learn as the heat ever source uh +demonstration has learned uh a + + align:start position:0% +demonstration has learned uh a + + + align:start position:0% +demonstration has learned uh a +tremendous amount. We need to do that + + align:start position:0% +tremendous amount. We need to do that + + + align:start position:0% +tremendous amount. We need to do that +learning on the MIT campus by a real + + align:start position:0% +learning on the MIT campus by a real + + + align:start position:0% +learning on the MIT campus by a real +project. It's easy to upgrade over time. + + align:start position:0% +project. It's easy to upgrade over time. + + + align:start position:0% +project. It's easy to upgrade over time. +It's fiscally responsible and it's unc + + align:start position:0% +It's fiscally responsible and it's unc + + + align:start position:0% +It's fiscally responsible and it's unc +clear whether MIT will seriously + + align:start position:0% +clear whether MIT will seriously + + + align:start position:0% +clear whether MIT will seriously +consider our our proposal. + + align:start position:0% +consider our our proposal. + + + align:start position:0% +consider our our proposal. +Uh our proposal we call a thermal + + align:start position:0% +Uh our proposal we call a thermal + + + align:start position:0% +Uh our proposal we call a thermal +transition um leapfrog and we'll take + + align:start position:0% +transition um leapfrog and we'll take + + + align:start position:0% +transition um leapfrog and we'll take +would go from the existing chiller plant + + align:start position:0% +would go from the existing chiller plant + + + align:start position:0% +would go from the existing chiller plant +to a distributed energy network. So + + align:start position:0% +to a distributed energy network. So + + + align:start position:0% +to a distributed energy network. So +finally, at the end of the day, the + + align:start position:0% +finally, at the end of the day, the + + + align:start position:0% +finally, at the end of the day, the +project is not just about public + + align:start position:0% +project is not just about public + + + align:start position:0% +project is not just about public +relations, but it should result in real + + align:start position:0% +relations, but it should result in real + + + align:start position:0% +relations, but it should result in real +progress. The central utility plant will + + align:start position:0% +progress. The central utility plant will + + + align:start position:0% +progress. The central utility plant will +play an important role in the mitten + + align:start position:0% +play an important role in the mitten + + + align:start position:0% +play an important role in the mitten +solution. Our plan is available now. + + align:start position:0% +solution. Our plan is available now. + + + align:start position:0% +solution. Our plan is available now. +We're using off-the-shelf equipment. + + align:start position:0% +We're using off-the-shelf equipment. + + + align:start position:0% +We're using off-the-shelf equipment. +It's cost-effective. It will eliminate + + align:start position:0% +It's cost-effective. It will eliminate + + + align:start position:0% +It's cost-effective. It will eliminate +carbon emissions and be minimally + + align:start position:0% +carbon emissions and be minimally + + + align:start position:0% +carbon emissions and be minimally +disruptive. We feel that we can show the + + align:start position:0% +disruptive. We feel that we can show the + + + align:start position:0% +disruptive. We feel that we can show the +world and demonstrate to other campuses + + align:start position:0% +world and demonstrate to other campuses + + + align:start position:0% +world and demonstrate to other campuses +not only in Boston area or across the + + align:start position:0% +not only in Boston area or across the + + + align:start position:0% +not only in Boston area or across the +North America but around the world that + + align:start position:0% +North America but around the world that + + + align:start position:0% +North America but around the world that +this is a an approach that is + + align:start position:0% +this is a an approach that is + + + align:start position:0% +this is a an approach that is +cost-effective, rapid and doable. um + + align:start position:0% +cost-effective, rapid and doable. um + + + align:start position:0% +cost-effective, rapid and doable. um +MIT's the world's leading research + + align:start position:0% +MIT's the world's leading research + + + align:start position:0% +MIT's the world's leading research +institute and should do something that's + + align:start position:0% +institute and should do something that's + + + align:start position:0% +institute and should do something that's +not just uh cut cookie cutter um that + + align:start position:0% +not just uh cut cookie cutter um that + + + align:start position:0% +not just uh cut cookie cutter um that +other campuses have already done um like + + align:start position:0% +other campuses have already done um like + + + align:start position:0% +other campuses have already done um like +Princeton or like Stanford um and um + + align:start position:0% +Princeton or like Stanford um and um + + + align:start position:0% +Princeton or like Stanford um and um +that is a centralized approach um and we + + align:start position:0% +that is a centralized approach um and we + + + align:start position:0% +that is a centralized approach um and we +need to do a pilot and advocate for that + + align:start position:0% +need to do a pilot and advocate for that + + + align:start position:0% +need to do a pilot and advocate for that +um for 2020 2025 so that we can get to + + align:start position:0% +um for 2020 2025 so that we can get to + + + align:start position:0% +um for 2020 2025 so that we can get to +net zero by 2035. + + align:start position:0% +net zero by 2035. + + + align:start position:0% +net zero by 2035. +And I'll close with uh words of Sally + + align:start position:0% +And I'll close with uh words of Sally + + + align:start position:0% +And I'll close with uh words of Sally +Cornblath at her inauguration. Climate + + align:start position:0% +Cornblath at her inauguration. Climate + + + align:start position:0% +Cornblath at her inauguration. Climate +change and its mounting consequence is + + align:start position:0% +change and its mounting consequence is + + + align:start position:0% +change and its mounting consequence is +the greatest scientific and societal + + align:start position:0% +the greatest scientific and societal + + + align:start position:0% +the greatest scientific and societal +challenge of this or any age. We need + + align:start position:0% +challenge of this or any age. We need + + + align:start position:0% +challenge of this or any age. We need +energy and expertise from every MIT + + align:start position:0% +energy and expertise from every MIT + + + align:start position:0% +energy and expertise from every MIT +school and college and from every lab + + align:start position:0% +school and college and from every lab + + + align:start position:0% +school and college and from every lab +and every center from every member of + + align:start position:0% +and every center from every member of + + + align:start position:0% +and every center from every member of +the faculty and from every one of you. + + align:start position:0% +the faculty and from every one of you. + + + align:start position:0% +the faculty and from every one of you. +Um so um thank you and uh I think I want + + align:start position:0% +Um so um thank you and uh I think I want + + + align:start position:0% +Um so um thank you and uh I think I want +to end really with this slide. We want + + align:start position:0% +to end really with this slide. We want + + + align:start position:0% +to end really with this slide. We want +to get there by 2035. + + align:start position:0% +to get there by 2035. + + + align:start position:0% +to get there by 2035. +And uh we're asking MIT when can we + + align:start position:0% +And uh we're asking MIT when can we + + + align:start position:0% +And uh we're asking MIT when can we +start \ No newline at end of file diff --git a/5e5PPseWX6Y.txt b/5e5PPseWX6Y.txt new file mode 100644 index 0000000000000000000000000000000000000000..8265eae0d449dc3eb5c86bdaed220b5b88ef63e2 --- /dev/null +++ b/5e5PPseWX6Y.txt @@ -0,0 +1,10651 @@ +align:start position:0% + +uh lecture + + align:start position:0% +uh lecture + + + align:start position:0% +uh lecture +13 um and uh moving back now from from + + align:start position:0% +13 um and uh moving back now from from + + + align:start position:0% +13 um and uh moving back now from from +differential + + align:start position:0% +differential + + + align:start position:0% +differential +equations um which isn't my specialty uh + + align:start position:0% +equations um which isn't my specialty uh + + + align:start position:0% +equations um which isn't my specialty uh +the pl heat equation wave equation back + + align:start position:0% +the pl heat equation wave equation back + + + align:start position:0% +the pl heat equation wave equation back +towards uh dealing with data probably + + align:start position:0% +towards uh dealing with data probably + + + align:start position:0% +towards uh dealing with data probably +closer to problems that uh are Central + + align:start position:0% +closer to problems that uh are Central + + + align:start position:0% +closer to problems that uh are Central +for the lab um and uh part of its linear + + align:start position:0% +for the lab um and uh part of its linear + + + align:start position:0% +for the lab um and uh part of its linear +algebra of course um + + align:start position:0% +algebra of course um + + + align:start position:0% +algebra of course um +kelman filter and other estimation + + align:start position:0% +kelman filter and other estimation + + + align:start position:0% +kelman filter and other estimation +problems coming up and and by the way on + + align:start position:0% +problems coming up and and by the way on + + + align:start position:0% +problems coming up and and by the way on +those I'm not an expert I'm G to be + + align:start position:0% +those I'm not an expert I'm G to be + + + align:start position:0% +those I'm not an expert I'm G to be +learning as fast as I can and I will + + align:start position:0% +learning as fast as I can and I will + + + align:start position:0% +learning as fast as I can and I will +appreciate uh + + align:start position:0% +appreciate uh + + + align:start position:0% +appreciate uh +suggestions uh advice guidance on uh + + align:start position:0% +suggestions uh advice guidance on uh + + + align:start position:0% +suggestions uh advice guidance on uh +what would be most useful there uh and + + align:start position:0% +what would be most useful there uh and + + + align:start position:0% +what would be most useful there uh and +then uh of course further in the future + + align:start position:0% +then uh of course further in the future + + + align:start position:0% +then uh of course further in the future +come signal processing image processing + + align:start position:0% +come signal processing image processing + + + align:start position:0% +come signal processing image processing +wavelet ideas that all coming so today + + align:start position:0% +wavelet ideas that all coming so today + + + align:start position:0% +wavelet ideas that all coming so today +is + + align:start position:0% +is + + + align:start position:0% +is +two this lecture is this um fundamental + + align:start position:0% +two this lecture is this um fundamental + + + align:start position:0% +two this lecture is this um fundamental +problem of H of dealing with of getting + + align:start position:0% +problem of H of dealing with of getting + + + align:start position:0% +problem of H of dealing with of getting +of using uh or orthogonal or orthonormal + + align:start position:0% +of using uh or orthogonal or orthonormal + + + align:start position:0% +of using uh or orthogonal or orthonormal +vectors so I'm in finite Dimensions + + align:start position:0% +vectors so I'm in finite Dimensions + + + align:start position:0% +vectors so I'm in finite Dimensions +mostly also I I better make a remark + + align:start position:0% +mostly also I I better make a remark + + + align:start position:0% +mostly also I I better make a remark +about how nice it is when functions are + + align:start position:0% +about how nice it is when functions are + + + align:start position:0% +about how nice it is when functions are +orthonormal too but for the most most + + align:start position:0% +orthonormal too but for the most most + + + align:start position:0% +orthonormal too but for the most most +part vectors and we've seen already the + + align:start position:0% +part vectors and we've seen already the + + + align:start position:0% +part vectors and we've seen already the +meaning of orthonormal that their inner + + align:start position:0% +meaning of orthonormal that their inner + + + align:start position:0% +meaning of orthonormal that their inner +products are one that's the + + align:start position:0% +products are one that's the + + + align:start position:0% +products are one that's the +normalization length one and but the + + align:start position:0% +normalization length one and but the + + + align:start position:0% +normalization length one and but the +main point is of course that the they're + + align:start position:0% +main point is of course that the they're + + + align:start position:0% +main point is of course that the they're +mutually + + align:start position:0% +mutually + + + align:start position:0% +mutually +orthogonal and then the good way to + + align:start position:0% +orthogonal and then the good way to + + + align:start position:0% +orthogonal and then the good way to +express that this fact is to put those + + align:start position:0% +express that this fact is to put those + + + align:start position:0% +express that this fact is to put those +cues into a matrix so I don't know if + + align:start position:0% +cues into a matrix so I don't know if + + + align:start position:0% +cues into a matrix so I don't know if +I've made that clear the columns here's + + align:start position:0% +I've made that clear the columns here's + + + align:start position:0% +I've made that clear the columns here's +my Matrix Q + + align:start position:0% +my Matrix Q + + + align:start position:0% +my Matrix Q +I've just put these in the the vectors + + align:start position:0% +I've just put these in the the vectors + + + align:start position:0% +I've just put these in the the vectors +in The Columns of the Matrix here's my + + align:start position:0% +in The Columns of the Matrix here's my + + + align:start position:0% +in The Columns of the Matrix here's my +Matrix Q + + align:start position:0% +Matrix Q + + + align:start position:0% +Matrix Q +transpose the qes are in the rows and + + align:start position:0% +transpose the qes are in the rows and + + + align:start position:0% +transpose the qes are in the rows and +then I do the matrix multiplication and + + align:start position:0% +then I do the matrix multiplication and + + + align:start position:0% +then I do the matrix multiplication and +the I one against the jth one gives me a + + align:start position:0% +the I one against the jth one gives me a + + + align:start position:0% +the I one against the jth one gives me a +zero a higher up I one against a later J + + align:start position:0% +zero a higher up I one against a later J + + + align:start position:0% +zero a higher up I one against a later J +one would give me a zero there and of + + align:start position:0% +one would give me a zero there and of + + + align:start position:0% +one would give me a zero there and of +course I get ones on the identity when + + align:start position:0% +course I get ones on the identity when + + + align:start position:0% +course I get ones on the identity when +I'm when the row and column match in + + align:start position:0% +I'm when the row and column match in + + + align:start position:0% +I'm when the row and column match in +other words I'm getting the identity + + align:start position:0% +other words I'm getting the identity + + + align:start position:0% +other words I'm getting the identity +Matrix so this is the + + align:start position:0% +Matrix so this is the + + + align:start position:0% +Matrix so this is the +shorthand for and the and the neat fact + + align:start position:0% +shorthand for and the and the neat fact + + + align:start position:0% +shorthand for and the and the neat fact +that uh uh that uh says I've got a + + align:start position:0% +that uh uh that uh says I've got a + + + align:start position:0% +that uh uh that uh says I've got a +Matrix Matrix with orth orthonormal + + align:start position:0% +Matrix Matrix with orth orthonormal + + + align:start position:0% +Matrix Matrix with orth orthonormal +columns that's a heck of a long + + align:start position:0% +columns that's a heck of a long + + + align:start position:0% +columns that's a heck of a long +expression and I'm sorry we don't have a + + align:start position:0% +expression and I'm sorry we don't have a + + + align:start position:0% +expression and I'm sorry we don't have a +totally conventional word for that maybe + + align:start position:0% +totally conventional word for that maybe + + + align:start position:0% +totally conventional word for that maybe +I'll just call it orthogonal + + align:start position:0% +I'll just call it orthogonal + + + align:start position:0% +I'll just call it orthogonal +Matrix so Q transpose Q equal ey that's + + align:start position:0% +Matrix so Q transpose Q equal ey that's + + + align:start position:0% +Matrix so Q transpose Q equal ey that's +going to stay on the board whatever else + + align:start position:0% +going to stay on the board whatever else + + + align:start position:0% +going to stay on the board whatever else +might disappear okay + + align:start position:0% +might disappear okay + + + align:start position:0% +might disappear okay +now so what are my thoughts for the + + align:start position:0% +now so what are my thoughts for the + + + align:start position:0% +now so what are my thoughts for the +lecture first of + + align:start position:0% +lecture first of + + + align:start position:0% +lecture first of +all to say why is orthogonality good + + align:start position:0% +all to say why is orthogonality good + + + align:start position:0% +all to say why is orthogonality good +what what are the virtues of of having + + align:start position:0% +what what are the virtues of of having + + + align:start position:0% +what what are the virtues of of having +an orthonormal + + align:start position:0% +an orthonormal + + + align:start position:0% +an orthonormal +basis and I can only probably mention + + align:start position:0% +basis and I can only probably mention + + + align:start position:0% +basis and I can only probably mention +some of them but uh it's certainly + + align:start position:0% +some of them but uh it's certainly + + + align:start position:0% +some of them but uh it's certainly +desirable + + align:start position:0% +desirable + + + align:start position:0% +desirable +then how do you get it if you have a + + align:start position:0% +then how do you get it if you have a + + + align:start position:0% +then how do you get it if you have a +basis of of uh of vectors that aren't + + align:start position:0% +basis of of uh of vectors that aren't + + + align:start position:0% +basis of of uh of vectors that aren't +orthogonal how do you straighten them + + align:start position:0% +orthogonal how do you straighten them + + + align:start position:0% +orthogonal how do you straighten them +out to get right angles so that's this + + align:start position:0% +out to get right angles so that's this + + + align:start position:0% +out to get right angles so that's this +that's the + + align:start position:0% +that's the + + + align:start position:0% +that's the +orthogonalization another heck of a long + + align:start position:0% +orthogonalization another heck of a long + + + align:start position:0% +orthogonalization another heck of a long +word for the uh for the uh subject of + + align:start position:0% +word for the uh for the uh subject of + + + align:start position:0% +word for the uh for the uh subject of +the lecture so the virtues of it + + align:start position:0% +the lecture so the virtues of it + + + align:start position:0% +the lecture so the virtues of it +how to get there and then because there + + align:start position:0% +how to get there and then because there + + + align:start position:0% +how to get there and then because there +are several ways to do it Graham Schmidt + + align:start position:0% +are several ways to do it Graham Schmidt + + + align:start position:0% +are several ways to do it Graham Schmidt +the most famous but uh not the only and + + align:start position:0% +the most famous but uh not the only and + + + align:start position:0% +the most famous but uh not the only and +um and then the costs so I've I've + + align:start position:0% +um and then the costs so I've I've + + + align:start position:0% +um and then the costs so I've I've +listed here in the this list we've we + + align:start position:0% +listed here in the this list we've we + + + align:start position:0% +listed here in the this list we've we +know what orthogonal matrices are so + + align:start position:0% +know what orthogonal matrices are so + + + align:start position:0% +know what orthogonal matrices are so +something about the virtues something + + align:start position:0% +something about the virtues something + + + align:start position:0% +something about the virtues something +about getting there something about the + + align:start position:0% +about getting there something about the + + + align:start position:0% +about getting there something about the +costs and then uh + + align:start position:0% +costs and then uh + + + align:start position:0% +costs and then uh +some some + + align:start position:0% +some some + + + align:start position:0% +some some +applications some of the applications of + + align:start position:0% +applications some of the applications of + + + align:start position:0% +applications some of the applications of +QR right okay so uh I use the words QR + + align:start position:0% +QR right okay so uh I use the words QR + + + align:start position:0% +QR right okay so uh I use the words QR +there which is the the shorthand + + align:start position:0% +there which is the the shorthand + + + align:start position:0% +there which is the the shorthand +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +for um this process of + + align:start position:0% +for um this process of + + + align:start position:0% +for um this process of +orthogonalization okay now virtues + + align:start position:0% +orthogonalization okay now virtues + + + align:start position:0% +orthogonalization okay now virtues +first well maybe one way to + + align:start position:0% +first well maybe one way to + + + align:start position:0% +first well maybe one way to +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +say one one virtue to point to is that + + align:start position:0% +say one one virtue to point to is that + + + align:start position:0% +say one one virtue to point to is that +when I multiply by an orthogonal Matrix + + align:start position:0% +when I multiply by an orthogonal Matrix + + + align:start position:0% +when I multiply by an orthogonal Matrix +I don't change the length of the vector + + align:start position:0% +I don't change the length of the vector + + + align:start position:0% +I don't change the length of the vector +let's just see that point so crucial + + align:start position:0% +let's just see that point so crucial + + + align:start position:0% +let's just see that point so crucial +point is that the what's the length of a + + align:start position:0% +point is that the what's the length of a + + + align:start position:0% +point is that the what's the length of a +vector first I have to say what's the + + align:start position:0% +vector first I have to say what's the + + + align:start position:0% +vector first I have to say what's the +length and then we'll check that it + + align:start position:0% +length and then we'll check that it + + + align:start position:0% +length and then we'll check that it +doesn't change so what's the length of a + + align:start position:0% +doesn't change so what's the length of a + + + align:start position:0% +doesn't change so what's the length of a +vector it's I'm I'm taking the + + align:start position:0% +vector it's I'm I'm taking the + + + align:start position:0% +vector it's I'm I'm taking the +ordinary ukian length it's often called + + align:start position:0% +ordinary ukian length it's often called + + + align:start position:0% +ordinary ukian length it's often called +or L2 it might be sometimes referred to + + align:start position:0% +or L2 it might be sometimes referred to + + + align:start position:0% +or L2 it might be sometimes referred to +but that sounds a little uh + + align:start position:0% +but that sounds a little uh + + + align:start position:0% +but that sounds a little uh +exotic uh it's just the sum of the + + align:start position:0% +exotic uh it's just the sum of the + + + align:start position:0% +exotic uh it's just the sum of the +squares the sum of the squares well if I + + align:start position:0% +squares the sum of the squares well if I + + + align:start position:0% +squares the sum of the squares well if I +make it a square then I don't have to + + align:start position:0% +make it a square then I don't have to + + + align:start position:0% +make it a square then I don't have to +take the square root so it's the sum of + + align:start position:0% +take the square root so it's the sum of + + + align:start position:0% +take the square root so it's the sum of +the + + align:start position:0% +the + + + align:start position:0% +the +components + + align:start position:0% +components + + + align:start position:0% +components +squared and it's also X transpose X I + + align:start position:0% +squared and it's also X transpose X I + + + align:start position:0% +squared and it's also X transpose X I +mean that's what x transpose X is like a + + align:start position:0% +mean that's what x transpose X is like a + + + align:start position:0% +mean that's what x transpose X is like a +shorthand the it the matrix + + align:start position:0% +shorthand the it the matrix + + + align:start position:0% +shorthand the it the matrix +multiplication does it for us and of + + align:start position:0% +multiplication does it for us and of + + + align:start position:0% +multiplication does it for us and of +course that's exactly what we did here + + align:start position:0% +course that's exactly what we did here + + + align:start position:0% +course that's exactly what we did here +when we took Q q i transposed Qi and got + + align:start position:0% +when we took Q q i transposed Qi and got + + + align:start position:0% +when we took Q q i transposed Qi and got +one that was saying that the length was + + align:start position:0% +one that was saying that the length was + + + align:start position:0% +one that was saying that the length was +one okay now uh oh okay now here I I + + align:start position:0% +one okay now uh oh okay now here I I + + + align:start position:0% +one okay now uh oh okay now here I I +claimed that if I multiply by + + align:start position:0% +claimed that if I multiply by + + + align:start position:0% +claimed that if I multiply by +Q I don't change that length so how how + + align:start position:0% +Q I don't change that length so how how + + + align:start position:0% +Q I don't change that length so how how +would I prove that let me Square it + + align:start position:0% +would I prove that let me Square it + + + align:start position:0% +would I prove that let me Square it +again just to avoid having to write + + align:start position:0% +again just to avoid having to write + + + align:start position:0% +again just to avoid having to write +square roots why is it that the length + + align:start position:0% +square roots why is it that the length + + + align:start position:0% +square roots why is it that the length +of QX I want to say that the length that + + align:start position:0% +of QX I want to say that the length that + + + align:start position:0% +of QX I want to say that the length that +this is the same as + + align:start position:0% +this is the same as + + + align:start position:0% +this is the same as +that + + align:start position:0% +that + + + align:start position:0% +that +and the reason I like that the reason + + align:start position:0% +and the reason I like that the reason + + + align:start position:0% +and the reason I like that the reason +that's good is that it + + align:start position:0% +that's good is that it + + + align:start position:0% +that's good is that it +means M vectors can't get out of control + + align:start position:0% +means M vectors can't get out of control + + + align:start position:0% +means M vectors can't get out of control +numerical stability is terrific if I'm + + align:start position:0% +numerical stability is terrific if I'm + + + align:start position:0% +numerical stability is terrific if I'm +working with orthogonal matrices so + + align:start position:0% +working with orthogonal matrices so + + + align:start position:0% +working with orthogonal matrices so +that's one virtue is the sort of + + align:start position:0% +that's one virtue is the sort of + + + align:start position:0% +that's one virtue is the sort of +numerical stability there's the + + align:start position:0% +numerical stability there's the + + + align:start position:0% +numerical stability there's the +condition number which I'll speak more + + align:start position:0% +condition number which I'll speak more + + + align:start position:0% +condition number which I'll speak more +about this afternoon the condition + + align:start position:0% +about this afternoon the condition + + + align:start position:0% +about this afternoon the condition +number of an orthogonal Matrix couldn't + + align:start position:0% +number of an orthogonal Matrix couldn't + + + align:start position:0% +number of an orthogonal Matrix couldn't +be better it's + + align:start position:0% +be better it's + + + align:start position:0% +be better it's +one that those are the matrices that + + align:start position:0% +one that those are the matrices that + + + align:start position:0% +one that those are the matrices that +have condition number one and uh other + + align:start position:0% +have condition number one and uh other + + + align:start position:0% +have condition number one and uh other +matrices have higher condition numbers + + align:start position:0% +matrices have higher condition numbers + + + align:start position:0% +matrices have higher condition numbers +and and uh and uh so errors could blow + + align:start position:0% +and and uh and uh so errors could blow + + + align:start position:0% +and and uh and uh so errors could blow +up and if we iterate they could blow up + + align:start position:0% +up and if we iterate they could blow up + + + align:start position:0% +up and if we iterate they could blow up +a lot but nothing can blow up with this + + align:start position:0% +a lot but nothing can blow up with this + + + align:start position:0% +a lot but nothing can blow up with this +it's okay now why is this so the length + + align:start position:0% +it's okay now why is this so the length + + + align:start position:0% +it's okay now why is this so the length +of QX by this same formula should be QX + + align:start position:0% +of QX by this same formula should be QX + + + align:start position:0% +of QX by this same formula should be QX +transpose QX that's the we just using + + align:start position:0% +transpose QX that's the we just using + + + align:start position:0% +transpose QX that's the we just using +the length formula for uh for the vector + + align:start position:0% +the length formula for uh for the vector + + + align:start position:0% +the length formula for uh for the vector +QX now okay so what do I do to make it + + align:start position:0% +QX now okay so what do I do to make it + + + align:start position:0% +QX now okay so what do I do to make it +to make everything clear sort of + + align:start position:0% +to make everything clear sort of + + + align:start position:0% +to make everything clear sort of +multiply it out so that's X transpose Q + + align:start position:0% +multiply it out so that's X transpose Q + + + align:start position:0% +multiply it out so that's X transpose Q +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +QX and now the key step is I put the + + align:start position:0% +QX and now the key step is I put the + + + align:start position:0% +QX and now the key step is I put the +parentheses in a smart place I mean + + align:start position:0% +parentheses in a smart place I mean + + + align:start position:0% +parentheses in a smart place I mean +that's uh so many of the of the basic + + align:start position:0% +that's uh so many of the of the basic + + + align:start position:0% +that's uh so many of the of the basic +linear algebra arguments are simply do + + align:start position:0% +linear algebra arguments are simply do + + + align:start position:0% +linear algebra arguments are simply do +that multiplication + + align:start position:0% +that multiplication + + + align:start position:0% +that multiplication +first keep them in the right order of + + align:start position:0% +first keep them in the right order of + + + align:start position:0% +first keep them in the right order of +course but do the + + align:start position:0% +course but do the + + + align:start position:0% +course but do the +multiplication there in the middle first + + align:start position:0% +multiplication there in the middle first + + + align:start position:0% +multiplication there in the middle first +and of course that's the identity so + + align:start position:0% +and of course that's the identity so + + + align:start position:0% +and of course that's the identity so +that's just X transpose X which + + align:start position:0% +that's just X transpose X which + + + align:start position:0% +that's just X transpose X which +is X + + align:start position:0% +is X + + + align:start position:0% +is X +squ so am I + + align:start position:0% +squ so am I + + + align:start position:0% +squ so am I +there okay + + align:start position:0% +there okay + + + align:start position:0% +there okay +oops so uh lengths don't change uh also + + align:start position:0% +oops so uh lengths don't change uh also + + + align:start position:0% +oops so uh lengths don't change uh also +angles don't change we could check that + + align:start position:0% +angles don't change we could check that + + + align:start position:0% +angles don't change we could check that +too that might be maybe I'll try to put + + align:start position:0% +too that might be maybe I'll try to put + + + align:start position:0% +too that might be maybe I'll try to put +that include that in the notes that the + + align:start position:0% +that include that in the notes that the + + + align:start position:0% +that include that in the notes that the +angle between two + + align:start position:0% +angle between two + + + align:start position:0% +angle between two +vectors doesn't change if the vectors + + align:start position:0% +vectors doesn't change if the vectors + + + align:start position:0% +vectors doesn't change if the vectors +are if if two vectors are orthogonal and + + align:start position:0% +are if if two vectors are orthogonal and + + + align:start position:0% +are if if two vectors are orthogonal and +I do a Q on both of them they're still + + align:start position:0% +I do a Q on both of them they're still + + + align:start position:0% +I do a Q on both of them they're still +orthogonal how do we actually think of I + + align:start position:0% +orthogonal how do we actually think of I + + + align:start position:0% +orthogonal how do we actually think of I +mean give me some examples of of Q's + + align:start position:0% +mean give me some examples of of Q's + + + align:start position:0% +mean give me some examples of of Q's +that uh of of orthogonal + + align:start position:0% +that uh of of orthogonal + + + align:start position:0% +that uh of of orthogonal +matrices uh let's take some examples so + + align:start position:0% +matrices uh let's take some examples so + + + align:start position:0% +matrices uh let's take some examples so +so we don't we know + + align:start position:0% +so we don't we know + + + align:start position:0% +so we don't we know +this fact so this might be a good spot + + align:start position:0% +this fact so this might be a good spot + + + align:start position:0% +this fact so this might be a good spot +to put in some examples give me a simple + + align:start position:0% +to put in some examples give me a simple + + + align:start position:0% +to put in some examples give me a simple +2x two + + align:start position:0% +2x two + + + align:start position:0% +2x two +example of uh an orthogonal Matrix or + + align:start position:0% +example of uh an orthogonal Matrix or + + + align:start position:0% +example of uh an orthogonal Matrix or +yeah 2 by + + align:start position:0% +yeah 2 by + + + align:start position:0% +yeah 2 by +two so what's a what's a typical + + align:start position:0% +two so what's a what's a typical + + + align:start position:0% +two so what's a what's a typical +orthogonal Matrix that's 2 by + + align:start position:0% +orthogonal Matrix that's 2 by + + + align:start position:0% +orthogonal Matrix that's 2 by +two it's a rotation + + align:start position:0% +two it's a rotation + + + align:start position:0% +two it's a rotation +now that we know orthogonal matrices are + + align:start position:0% +now that we know orthogonal matrices are + + + align:start position:0% +now that we know orthogonal matrices are +the ones that don't change length we + + align:start position:0% +the ones that don't change length we + + + align:start position:0% +the ones that don't change length we +just have we can sort of think + + align:start position:0% +just have we can sort of think + + + align:start position:0% +just have we can sort of think +geometrically what can we do to the + + align:start position:0% +geometrically what can we do to the + + + align:start position:0% +geometrically what can we do to the +plane that won't change the length of + + align:start position:0% +plane that won't change the length of + + + align:start position:0% +plane that won't change the length of +any vector and one thing we can do is to + + align:start position:0% +any vector and one thing we can do is to + + + align:start position:0% +any vector and one thing we can do is to +rotate it so Q the rotation Matrix is + + align:start position:0% +rotate it so Q the rotation Matrix is + + + align:start position:0% +rotate it so Q the rotation Matrix is +cos Theta sin Theta that's where that's + + align:start position:0% +cos Theta sin Theta that's where that's + + + align:start position:0% +cos Theta sin Theta that's where that's +the that's a unit Vector of course in + + align:start position:0% +the that's a unit Vector of course in + + + align:start position:0% +the that's a unit Vector of course in +the Theta Direction and now I want to + + align:start position:0% +the Theta Direction and now I want to + + + align:start position:0% +the Theta Direction and now I want to +perpendicular to it so that will be + + align:start position:0% +perpendicular to it so that will be + + + align:start position:0% +perpendicular to it so that will be +minus sin Theta cos + + align:start position:0% +minus sin Theta cos + + + align:start position:0% +minus sin Theta cos +Theta that's a that's a you see those + + align:start position:0% +Theta that's a that's a you see those + + + align:start position:0% +Theta that's a that's a you see those +are those that's orthogonal to + + align:start position:0% +are those that's orthogonal to + + + align:start position:0% +are those that's orthogonal to +that they're unit vectors we've got a + + align:start position:0% +that they're unit vectors we've got a + + + align:start position:0% +that they're unit vectors we've got a +this is a rotation this is a rotation of + + align:start position:0% + + + + align:start position:0% + +course maybe I + + align:start position:0% +course maybe I + + + align:start position:0% +course maybe I +mention oh two little as two two two + + align:start position:0% +mention oh two little as two two two + + + align:start position:0% +mention oh two little as two two two +things come to mind uh I I could mention + + align:start position:0% +things come to mind uh I I could mention + + + align:start position:0% +things come to mind uh I I could mention +another + + align:start position:0% +another + + + align:start position:0% +another +um uh unitary Matrix another rather + + align:start position:0% +um uh unitary Matrix another rather + + + align:start position:0% +um uh unitary Matrix another rather +simple one um but these are maybe the + + align:start position:0% +simple one um but these are maybe the + + + align:start position:0% +simple one um but these are maybe the +most basic building blocks I I guess + + align:start position:0% +most basic building blocks I I guess + + + align:start position:0% +most basic building blocks I I guess +it's probably true that if I take a 6x6 + + align:start position:0% +it's probably true that if I take a 6x6 + + + align:start position:0% +it's probably true that if I take a 6x6 +orthogonal Matrix say 6 by I just made + + align:start position:0% +orthogonal Matrix say 6 by I just made + + + align:start position:0% +orthogonal Matrix say 6 by I just made +up six 6x6 orthogonal Matrix probably it + + align:start position:0% +up six 6x6 orthogonal Matrix probably it + + + align:start position:0% +up six 6x6 orthogonal Matrix probably it +can I think that's true could be written + + align:start position:0% +can I think that's true could be written + + + align:start position:0% +can I think that's true could be written +as a product of these 2 by two + + align:start position:0% +as a product of these 2 by two + + + align:start position:0% +as a product of these 2 by two +rotations um you know rotating in the + + align:start position:0% +rotations um you know rotating in the + + + align:start position:0% +rotations um you know rotating in the +one two position and the one three + + align:start position:0% +one two position and the one three + + + align:start position:0% +one two position and the one three +position and the two three positions uh + + align:start position:0% +position and the two three positions uh + + + align:start position:0% +position and the two three positions uh +so all the all the I so how many + + align:start position:0% +so all the all the I so how many + + + align:start position:0% +so all the all the I so how many +rotations are we likely to + + align:start position:0% +rotations are we likely to + + + align:start position:0% +rotations are we likely to +need um if it's + + align:start position:0% +need um if it's + + + align:start position:0% +need um if it's +6x6 let's let's just figure it 6x6 I'm + + align:start position:0% +6x6 let's let's just figure it 6x6 I'm + + + align:start position:0% +6x6 let's let's just figure it 6x6 I'm +figuring I can make it a product of + + align:start position:0% +figuring I can make it a product of + + + align:start position:0% +figuring I can make it a product of +things that are are the these plain + + align:start position:0% +things that are are the these plain + + + align:start position:0% +things that are are the these plain +rotations say in here's a rotation in + + align:start position:0% +rotations say in here's a rotation in + + + align:start position:0% +rotations say in here's a rotation in +the + + align:start position:0% +the + + + align:start position:0% +the +two five position I just makebe can I + + align:start position:0% +two five position I just makebe can I + + + align:start position:0% +two five position I just makebe can I +just write C in C in row two s in row + + align:start position:0% +just write C in C in row two s in row + + + align:start position:0% +just write C in C in row two s in row +five minus s in in row two c and row + + align:start position:0% +five minus s in in row two c and row + + + align:start position:0% +five minus s in in row two c and row +five that would be a + + align:start position:0% +five that would be a + + + align:start position:0% +five that would be a +two5 in the that would be a rotation in + + align:start position:0% +two5 in the that would be a rotation in + + + align:start position:0% +two5 in the that would be a rotation in +the two5 + + align:start position:0% + + + + align:start position:0% + +plane and uh it seems reasonable + + align:start position:0% +plane and uh it seems reasonable + + + align:start position:0% +plane and uh it seems reasonable +that uh if that uh how many different + + align:start position:0% +that uh if that uh how many different + + + align:start position:0% +that uh if that uh how many different +planes are there how many pairs I guess + + align:start position:0% +planes are there how many pairs I guess + + + align:start position:0% +planes are there how many pairs I guess +yeah how many pairs are + + align:start position:0% +yeah how many pairs are + + + align:start position:0% +yeah how many pairs are +there + + align:start position:0% +there + + + align:start position:0% +there +uh yeah choose any of them so let's see + + align:start position:0% +uh yeah choose any of them so let's see + + + align:start position:0% +uh yeah choose any of them so let's see +I've got six choices for the + + align:start position:0% +I've got six choices for the + + + align:start position:0% +I've got six choices for the +first um row to use and five choices + + align:start position:0% +first um row to use and five choices + + + align:start position:0% +first um row to use and five choices +maybe 30 maybe there 30 30 + + align:start position:0% +maybe 30 maybe there 30 30 + + + align:start position:0% +maybe 30 maybe there 30 30 +rotations uh produce a uh + + align:start position:0% +rotations uh produce a uh + + + align:start position:0% +rotations uh produce a uh +a more General orthogonal Matrix uh + + align:start position:0% +a more General orthogonal Matrix uh + + + align:start position:0% +a more General orthogonal Matrix uh +probably it's almost every let's see the + + align:start position:0% +probably it's almost every let's see the + + + align:start position:0% +probably it's almost every let's see the +only thing I noticed is that the + + align:start position:0% +only thing I noticed is that the + + + align:start position:0% +only thing I noticed is that the +determinant of that is plus one and if I + + align:start position:0% +determinant of that is plus one and if I + + + align:start position:0% +determinant of that is plus one and if I +changed a couple of signs I could have + + align:start position:0% +changed a couple of signs I could have + + + align:start position:0% +changed a couple of signs I could have +made the determinant minus one so that + + align:start position:0% +made the determinant minus one so that + + + align:start position:0% +made the determinant minus one so that +pretty minor difference um but uh anyway + + align:start position:0% +pretty minor difference um but uh anyway + + + align:start position:0% +pretty minor difference um but uh anyway +these it's numerically this is important + + align:start position:0% +these it's numerically this is important + + + align:start position:0% +these it's numerically this is important +too we'll see that that that uh a way to + + align:start position:0% +too we'll see that that that uh a way to + + + align:start position:0% +too we'll see that that that uh a way to +construct + + align:start position:0% +construct + + + align:start position:0% +construct +uh orthogonal Matrix is by a product of + + align:start position:0% +uh orthogonal Matrix is by a product of + + + align:start position:0% +uh orthogonal Matrix is by a product of +these plane rotations + + align:start position:0% +these plane rotations + + + align:start position:0% +these plane rotations +okay for 6 by six + + align:start position:0% + + + + align:start position:0% + +well yeah I think well let's see yeah + + align:start position:0% +well yeah I think well let's see yeah + + + align:start position:0% +well yeah I think well let's see yeah +it's a good question what can we + + align:start position:0% +it's a good question what can we + + + align:start position:0% +it's a good question what can we +achieve like suppose we have this full + + align:start position:0% +achieve like suppose we have this full + + + align:start position:0% +achieve like suppose we have this full +6x6 + + align:start position:0% +6x6 + + + align:start position:0% +6x6 +Matrix what can we achieve with one + + align:start position:0% +Matrix what can we achieve with one + + + align:start position:0% +Matrix what can we achieve with one +rotation that's a that's a good question + + align:start position:0% +rotation that's a that's a good question + + + align:start position:0% +rotation that's a that's a good question +and it'll come up what what so like in + + align:start position:0% +and it'll come up what what so like in + + + align:start position:0% +and it'll come up what what so like in +the one two POS say I do it in the one + + align:start position:0% +the one two POS say I do it in the one + + + align:start position:0% +the one two POS say I do it in the one +two up in this up in this corner what + + align:start position:0% +two up in this up in this corner what + + + align:start position:0% +two up in this up in this corner what +could I do to my orthogonal Matrix if I + + align:start position:0% +could I do to my orthogonal Matrix if I + + + align:start position:0% +could I do to my orthogonal Matrix if I +suppose I + + align:start position:0% +suppose I + + + align:start position:0% +suppose I +multiply uh this orthogonal Matrix say + + align:start position:0% +multiply uh this orthogonal Matrix say + + + align:start position:0% +multiply uh this orthogonal Matrix say +it's 6 by + + align:start position:0% +it's 6 by + + + align:start position:0% +it's 6 by +six and so this is what what's what's + + align:start position:0% +six and so this is what what's what's + + + align:start position:0% +six and so this is what what's what's +going to happen when I multip so this is + + align:start position:0% +going to happen when I multip so this is + + + align:start position:0% +going to happen when I multip so this is +really 6 by but it's all the rest is + + align:start position:0% +really 6 by but it's all the rest is + + + align:start position:0% +really 6 by but it's all the rest is +zeros what so sorry it's not very that's + + align:start position:0% +zeros what so sorry it's not very that's + + + align:start position:0% +zeros what so sorry it's not very that's +meant to be up in the left corner of + + align:start position:0% +meant to be up in the left corner of + + + align:start position:0% +meant to be up in the left corner of +this 6x6 and here's my + + align:start position:0% +this 6x6 and here's my + + + align:start position:0% +this 6x6 and here's my +original uh one what could I do what + + align:start position:0% +original uh one what could I do what + + + align:start position:0% +original uh one what could I do what +could I achieve like it's like + + align:start position:0% + + + + align:start position:0% + +elimination but and probably yeah very + + align:start position:0% +elimination but and probably yeah very + + + align:start position:0% +elimination but and probably yeah very +like elimination I can probably get a z + + align:start position:0% +like elimination I can probably get a z + + + align:start position:0% +like elimination I can probably get a z +a zero in the answer in + + align:start position:0% +a zero in the answer in + + + align:start position:0% +a zero in the answer in +that one two position for + + align:start position:0% +that one two position for + + + align:start position:0% +that one two position for +example I I think I could do this so + + align:start position:0% +example I I think I could do this so + + + align:start position:0% +example I I think I could do this so +here's my here's my orthogonal Matrix + + align:start position:0% +here's my here's my orthogonal Matrix + + + align:start position:0% +here's my here's my orthogonal Matrix +orthogonal + + align:start position:0% +orthogonal + + + align:start position:0% +orthogonal +Matrix and I'm trying to I'm trying + + align:start position:0% +Matrix and I'm trying to I'm trying + + + align:start position:0% +Matrix and I'm trying to I'm trying +to simplify it I'm trying to like do + + align:start position:0% +to simplify it I'm trying to like do + + + align:start position:0% +to simplify it I'm trying to like do +elimination but with these Special + + align:start position:0% +elimination but with these Special + + + align:start position:0% +elimination but with these Special +rotations and if I rotate in the one two + + align:start position:0% +rotations and if I rotate in the one two + + + align:start position:0% +rotations and if I rotate in the one two +plane I think I could like realign these + + align:start position:0% +plane I think I could like realign these + + + align:start position:0% +plane I think I could like realign these +uh things to get a zero there and we + + align:start position:0% +uh things to get a zero there and we + + + align:start position:0% +uh things to get a zero there and we +could figure out what Theta would do the + + align:start position:0% +could figure out what Theta would do the + + + align:start position:0% +could figure out what Theta would do the +job but I I think what to follow up I + + align:start position:0% +job but I I think what to follow up I + + + align:start position:0% +job but I I think what to follow up I +think I can probably only get one zero + + align:start position:0% +think I can probably only get one zero + + + align:start position:0% +think I can probably only get one zero +there and then I'll need another guy to + + align:start position:0% +there and then I'll need another guy to + + + align:start position:0% +there and then I'll need another guy to +get another zero somewhere else uh and + + align:start position:0% +get another zero somewhere else uh and + + + align:start position:0% +get another zero somewhere else uh and +then I'll have to think yeah so then I + + align:start position:0% +then I'll have to think yeah so then I + + + align:start position:0% +then I'll have to think yeah so then I +keep I keep getting a whole lot of guys + + align:start position:0% +keep I keep getting a whole lot of guys + + + align:start position:0% +keep I keep getting a whole lot of guys +that produce zeros and in the end I have + + align:start position:0% +that produce zeros and in the end I have + + + align:start position:0% +that produce zeros and in the end I have +the identity Matrix so then all these + + align:start position:0% +the identity Matrix so then all these + + + align:start position:0% +the identity Matrix so then all these +all these little + + align:start position:0% +all these little + + + align:start position:0% +all these little +rotations + + align:start position:0% +rotations + + + align:start position:0% +rotations +are well I guess the inverse of that and + + align:start position:0% +are well I guess the inverse of that and + + + align:start position:0% +are well I guess the inverse of that and +I sry if I transpose them i' I've got + + align:start position:0% +I sry if I transpose them i' I've got + + + align:start position:0% +I sry if I transpose them i' I've got +the thing itself so are you kind of + + align:start position:0% +the thing itself so are you kind of + + + align:start position:0% +the thing itself so are you kind of +seeing what this is what + + align:start position:0% +seeing what this is what + + + align:start position:0% +seeing what this is what +numerical linear algebra people like go + + align:start position:0% +numerical linear algebra people like go + + + align:start position:0% +numerical linear algebra people like go +to sleep thinking about uh can they can + + align:start position:0% +to sleep thinking about uh can they can + + + align:start position:0% +to sleep thinking about uh can they can +they do a bunch of rotations and reduce + + align:start position:0% +they do a bunch of rotations and reduce + + + align:start position:0% +they do a bunch of rotations and reduce +the Matrix well while I'm on that + + align:start position:0% +the Matrix well while I'm on that + + + align:start position:0% +the Matrix well while I'm on that +subject + + align:start position:0% +subject + + + align:start position:0% +subject +they have a what what bothers them what + + align:start position:0% +they have a what what bothers them what + + + align:start position:0% +they have a what what bothers them what +what they lose sleep over is this that + + align:start position:0% +what they lose sleep over is this that + + + align:start position:0% +what they lose sleep over is this that +suppose I now want suppose The Next Step + + align:start position:0% +suppose I now want suppose The Next Step + + + align:start position:0% +suppose I now want suppose The Next Step +would be to try to get a zero there so + + align:start position:0% +would be to try to get a zero there so + + + align:start position:0% +would be to try to get a zero there so +here's here's uh you know my usual it's + + align:start position:0% +here's here's uh you know my usual it's + + + align:start position:0% +here's here's uh you know my usual it's +like elimination I get a zero there can + + align:start position:0% +like elimination I get a zero there can + + + align:start position:0% +like elimination I get a zero there can +do we could figure out what the angle + + align:start position:0% +do we could figure out what the angle + + + align:start position:0% +do we could figure out what the angle +should be no + + align:start position:0% +should be no + + + align:start position:0% +should be no +problem then we go to get the next + + align:start position:0% + + + + align:start position:0% + +zero so how are we going to get get a + + align:start position:0% +zero so how are we going to get get a + + + align:start position:0% +zero so how are we going to get get a +zero in the 31 + + align:start position:0% +zero in the 31 + + + align:start position:0% +zero in the 31 +position well we're going to do a + + align:start position:0% +position well we're going to do a + + + align:start position:0% +position well we're going to do a +rotation in the 31 we're going to do a + + align:start position:0% +rotation in the 31 we're going to do a + + + align:start position:0% +rotation in the 31 we're going to do a +31 right this will be a c minus s s c in + + align:start position:0% +31 right this will be a c minus s s c in + + + align:start position:0% +31 right this will be a c minus s s c in +the one three in rows and columns one + + align:start position:0% +the one three in rows and columns one + + + align:start position:0% +the one three in rows and columns one +and + + align:start position:0% +and + + + align:start position:0% +and +three + + align:start position:0% +three + + + align:start position:0% +three +but do you see that the I I haven't + + align:start position:0% +but do you see that the I I haven't + + + align:start position:0% +but do you see that the I I haven't +really done giving you much to look at + + align:start position:0% +really done giving you much to look at + + + align:start position:0% +really done giving you much to look at +here but maybe you could + + align:start position:0% +here but maybe you could + + + align:start position:0% +here but maybe you could +guess what's going to happen I do a + + align:start position:0% +guess what's going to happen I do a + + + align:start position:0% +guess what's going to happen I do a +rotation in the one and three position + + align:start position:0% +rotation in the one and three position + + + align:start position:0% +rotation in the one and three position +so it changes rows one and three and + + align:start position:0% +so it changes rows one and three and + + + align:start position:0% +so it changes rows one and three and +columns one and three and what's the + + align:start position:0% +columns one and three and what's the + + + align:start position:0% +columns one and three and what's the +danger here that I can you anticipate + + align:start position:0% +danger here that I can you anticipate + + + align:start position:0% +danger here that I can you anticipate +what yeah I'm gonna mess it up I don't + + align:start position:0% +what yeah I'm gonna mess it up I don't + + + align:start position:0% +what yeah I'm gonna mess it up I don't +want to mess it up but it's certainly a + + align:start position:0% +want to mess it up but it's certainly a + + + align:start position:0% +want to mess it up but it's certainly a +danger that I + + align:start position:0% +danger that I + + + align:start position:0% +danger that I +will that I will right and uh uh + + align:start position:0% +will that I will right and uh uh + + + align:start position:0% +will that I will right and uh uh +actually I should be yeah uh uh if you + + align:start position:0% +actually I should be yeah uh uh if you + + + align:start position:0% +actually I should be yeah uh uh if you +want to right yeah + + align:start position:0% +want to right yeah + + + align:start position:0% +want to right yeah +so the danger is I mess it + + align:start position:0% +so the danger is I mess it + + + align:start position:0% +so the danger is I mess it +up in fact I will mess it + + align:start position:0% +up in fact I will mess it + + + align:start position:0% +up in fact I will mess it +up okay so then you have to think is + + align:start position:0% +up okay so then you have to think is + + + align:start position:0% +up okay so then you have to think is +there a way to do it so that you don't + + align:start position:0% +there a way to do it so that you don't + + + align:start position:0% +there a way to do it so that you don't +mess things up and so I've got into this + + align:start position:0% +mess things up and so I've got into this + + + align:start position:0% +mess things up and so I've got into this +topic earlier than I intended to in the + + align:start position:0% +topic earlier than I intended to in the + + + align:start position:0% +topic earlier than I intended to in the +lecture but just just so you sort of see + + align:start position:0% +lecture but just just so you sort of see + + + align:start position:0% +lecture but just just so you sort of see +what what enters in the linear algebra + + align:start position:0% +what what enters in the linear algebra + + + align:start position:0% +what what enters in the linear algebra +here well suppose + + align:start position:0% +here well suppose + + + align:start position:0% +here well suppose +I here's the here's the trick that I can + + align:start position:0% +I here's the here's the trick that I can + + + align:start position:0% +I here's the here's the trick that I can +do do it without messing up if I'm not + + align:start position:0% +do do it without messing up if I'm not + + + align:start position:0% +do do it without messing up if I'm not +quite so ambitious if I say okay I'll + + align:start position:0% +quite so ambitious if I say okay I'll + + + align:start position:0% +quite so ambitious if I say okay I'll +live with + + align:start position:0% +live with + + + align:start position:0% +live with +stuff also I I won't shoot for that to + + align:start position:0% +stuff also I I won't shoot for that to + + + align:start position:0% +stuff also I I won't shoot for that to +be zero I'll I'll start my zeros down + + align:start position:0% +be zero I'll I'll start my zeros down + + + align:start position:0% +be zero I'll I'll start my zeros down +lower and and and just you see what's + + align:start position:0% +lower and and and just you see what's + + + align:start position:0% +lower and and and just you see what's +happening here I the claim is that I can + + align:start position:0% +happening here I the claim is that I can + + + align:start position:0% +happening here I the claim is that I can +get those zeros so that's a matrix is + + align:start position:0% +get those zeros so that's a matrix is + + + align:start position:0% +get those zeros so that's a matrix is +that is that Matrix upper + + align:start position:0% +that is that Matrix upper + + + align:start position:0% +that is that Matrix upper +triangular no I didn't get that far if I + + align:start position:0% +triangular no I didn't get that far if I + + + align:start position:0% +triangular no I didn't get that far if I +could have got that far I that would + + align:start position:0% +could have got that far I that would + + + align:start position:0% +could have got that far I that would +that's more than more than uh man can do + + align:start position:0% +that's more than more than uh man can do + + + align:start position:0% +that's more than more than uh man can do +here uh there's I've got to allow myself + + align:start position:0% +here uh there's I've got to allow myself + + + align:start position:0% +here uh there's I've got to allow myself +one diagonal below the diagonal then + + align:start position:0% +one diagonal below the diagonal then + + + align:start position:0% +one diagonal below the diagonal then +it's possible so how would I get that + + align:start position:0% +it's possible so how would I get that + + + align:start position:0% +it's possible so how would I get that +zero let's see if we can imagine how to + + align:start position:0% +zero let's see if we can imagine how to + + + align:start position:0% +zero let's see if we can imagine how to +do it I'll get that Zero by a one two + + align:start position:0% +do it I'll get that Zero by a one two + + + align:start position:0% +do it I'll get that Zero by a one two +rotation I can get that Zero by a one + + align:start position:0% +rotation I can get that Zero by a one + + + align:start position:0% +rotation I can get that Zero by a one +two rotation because the one two + + align:start position:0% +two rotation because the one two + + + align:start position:0% +two rotation because the one two +rotation Alters column one and probably + + align:start position:0% +rotation Alters column one and probably + + + align:start position:0% +rotation Alters column one and probably +I can get it then I'll get this Zero by + + align:start position:0% +I can get it then I'll get this Zero by + + + align:start position:0% +I can get it then I'll get this Zero by +a 13 rotation you see I'm sort of sort + + align:start position:0% +a 13 rotation you see I'm sort of sort + + + align:start position:0% +a 13 rotation you see I'm sort of sort +of chasing these nonzeros out of the out + + align:start position:0% +of chasing these nonzeros out of the out + + + align:start position:0% +of chasing these nonzeros out of the out +of the Matrix but it's leaving me a + + align:start position:0% +of the Matrix but it's leaving me a + + + align:start position:0% +of the Matrix but it's leaving me a +little more okay can I + + align:start position:0% +little more okay can I + + + align:start position:0% +little more okay can I +not um go beyond that but it's a highly + + align:start position:0% +not um go beyond that but it's a highly + + + align:start position:0% +not um go beyond that but it's a highly +important Point uh and if I the same + + align:start position:0% +important Point uh and if I the same + + + align:start position:0% +important Point uh and if I the same +thing thing if I had a symmetric Matrix + + align:start position:0% +thing thing if I had a symmetric Matrix + + + align:start position:0% +thing thing if I had a symmetric Matrix +if I had a symmetric Matrix I might want + + align:start position:0% +if I had a symmetric Matrix I might want + + + align:start position:0% +if I had a symmetric Matrix I might want +to do these rotations and get zeros but + + align:start position:0% +to do these rotations and get zeros but + + + align:start position:0% +to do these rotations and get zeros but +I would have to accept a + + align:start position:0% +I would have to accept a + + + align:start position:0% +I would have to accept a +diagonal below the main diagonal still + + align:start position:0% +diagonal below the main diagonal still + + + align:start position:0% +diagonal below the main diagonal still +non zero yeah right okay that's a so + + align:start position:0% +non zero yeah right okay that's a so + + + align:start position:0% +non zero yeah right okay that's a so +that's a that's a a point of uh interest + + align:start position:0% +that's a that's a a point of uh interest + + + align:start position:0% +that's a that's a a point of uh interest +all right + + align:start position:0% +all right + + + align:start position:0% +all right +um let's see I wanted to say one more + + align:start position:0% +um let's see I wanted to say one more + + + align:start position:0% +um let's see I wanted to say one more +thing about these + + align:start position:0% +thing about these + + + align:start position:0% +thing about these +rotations and to connect them with yeah + + align:start position:0% +rotations and to connect them with yeah + + + align:start position:0% +rotations and to connect them with yeah +so here's my other point about + + align:start position:0% + + + + align:start position:0% + +rotations um Can a rotation be yeah + + align:start position:0% +rotations um Can a rotation be yeah + + + align:start position:0% +rotations um Can a rotation be yeah +here's a this this is like coming up + + align:start position:0% +here's a this this is like coming up + + + align:start position:0% +here's a this this is like coming up +quite a bit in in applications uh can I + + align:start position:0% +quite a bit in in applications uh can I + + + align:start position:0% +quite a bit in in applications uh can I +write a rotation so is it all right just + + align:start position:0% +write a rotation so is it all right just + + + align:start position:0% +write a rotation so is it all right just +to write + + align:start position:0% +to write + + + align:start position:0% +to write +CNS for cos Theta and sin Theta and + + align:start position:0% +CNS for cos Theta and sin Theta and + + + align:start position:0% +CNS for cos Theta and sin Theta and +minus sin Theta and cos Theta + + align:start position:0% +minus sin Theta and cos Theta + + + align:start position:0% +minus sin Theta and cos Theta +now so here's like a separate question + + align:start position:0% +now so here's like a separate question + + + align:start position:0% +now so here's like a separate question +could I write it + + align:start position:0% +could I write it + + + align:start position:0% +could I write it +as + + align:start position:0% +as + + + align:start position:0% +as +a + + align:start position:0% +a + + + align:start position:0% +a +product + + align:start position:0% +product + + + align:start position:0% +product +of matrices of of this of this of the + + align:start position:0% +of matrices of of this of this of the + + + align:start position:0% +of matrices of of this of this of the +kind we've sort of come to know and love + + align:start position:0% +kind we've sort of come to know and love + + + align:start position:0% +kind we've sort of come to know and love +something up here zero there something + + align:start position:0% +something up here zero there something + + + align:start position:0% +something up here zero there something +there one one zero and something + + align:start position:0% +there one one zero and something + + + align:start position:0% +there one one zero and something +here one one + + align:start position:0% +here one one + + + align:start position:0% +here one one +one zero and something + + align:start position:0% +one zero and something + + + align:start position:0% +one zero and something +here and and and the answer is yes that + + align:start position:0% +here and and and the answer is yes that + + + align:start position:0% +here and and and the answer is yes that +can be done let me see I think I can + + align:start position:0% +can be done let me see I think I can + + + align:start position:0% +can be done let me see I think I can +tell you what those things are I think + + align:start position:0% +tell you what those things are I think + + + align:start position:0% +tell you what those things are I think +it's cosine -1 over s and I think this + + align:start position:0% +it's cosine -1 over s and I think this + + + align:start position:0% +it's cosine -1 over s and I think this +one is s and I think this one is cosine + + align:start position:0% +one is s and I think this one is cosine + + + align:start position:0% +one is s and I think this one is cosine +- one over + + align:start position:0% +- one over + + + align:start position:0% +- one over +s + + align:start position:0% +s + + + align:start position:0% +s +now what's good about this and what's a + + align:start position:0% +now what's good about this and what's a + + + align:start position:0% +now what's good about this and what's a +little un usual what's good is that + + align:start position:0% +little un usual what's good is that + + + align:start position:0% +little un usual what's good is that +these three matrices are particularly + + align:start position:0% +these three matrices are particularly + + + align:start position:0% +these three matrices are particularly +simple to + + align:start position:0% +simple to + + + align:start position:0% +simple to +execute uh what kind of a what does that + + align:start position:0% +execute uh what kind of a what does that + + + align:start position:0% +execute uh what kind of a what does that +do if I had a if I had a good picture I + + align:start position:0% +do if I had a if I had a good picture I + + + align:start position:0% +do if I had a if I had a good picture I +could show you suppose we have a picture + + align:start position:0% +could show you suppose we have a picture + + + align:start position:0% +could show you suppose we have a picture +here an image and we want to rotate it + + align:start position:0% +here an image and we want to rotate it + + + align:start position:0% +here an image and we want to rotate it +so we want to multiply it by this + + align:start position:0% +so we want to multiply it by this + + + align:start position:0% +so we want to multiply it by this +rotation mate we want to multiply uh we + + align:start position:0% +rotation mate we want to multiply uh we + + + align:start position:0% +rotation mate we want to multiply uh we +want to apply that rot ation Matrix to + + align:start position:0% +want to apply that rot ation Matrix to + + + align:start position:0% +want to apply that rot ation Matrix to +to all the little pixels and turn the + + align:start position:0% +to all the little pixels and turn the + + + align:start position:0% +to all the little pixels and turn the +face you can see computer Graphics is + + align:start position:0% +face you can see computer Graphics is + + + align:start position:0% +face you can see computer Graphics is +going to want to do this so + + align:start position:0% +going to want to do this so + + + align:start position:0% +going to want to do this so +so so uh the question + + align:start position:0% +so so uh the question + + + align:start position:0% +so so uh the question +is can we turn a can we do a + + align:start position:0% +is can we turn a can we do a + + + align:start position:0% +is can we turn a can we do a +rotation as a sequence of these guys and + + align:start position:0% +rotation as a sequence of these guys and + + + align:start position:0% +rotation as a sequence of these guys and +this formula is saying yes we can okay + + align:start position:0% +this formula is saying yes we can okay + + + align:start position:0% +this formula is saying yes we can okay +now what are these what do the what kind + + align:start position:0% +now what are these what do the what kind + + + align:start position:0% +now what are these what do the what kind +of a matri what does this do to the to + + align:start position:0% +of a matri what does this do to the to + + + align:start position:0% +of a matri what does this do to the to +the plane I said that the that this + + align:start position:0% +the plane I said that the that this + + + align:start position:0% +the plane I said that the that this +thing rotates the plane we have a really + + align:start position:0% +thing rotates the plane we have a really + + + align:start position:0% +thing rotates the plane we have a really +good image of what that does now let me + + align:start position:0% +good image of what that does now let me + + + align:start position:0% +good image of what that does now let me +ask you what does so I've lost + + align:start position:0% +ask you what does so I've lost + + + align:start position:0% +ask you what does so I've lost +orthogonality here and that's part of + + align:start position:0% +orthogonality here and that's part of + + + align:start position:0% +orthogonality here and that's part of +the point suppose I suppose I have a one + + align:start position:0% +the point suppose I suppose I have a one + + + align:start position:0% +the point suppose I suppose I have a one +suppose I have a matrix like that what + + align:start position:0% +suppose I have a matrix like that what + + + align:start position:0% +suppose I have a matrix like that what +does that do to to the plane do you do + + align:start position:0% +does that do to to the plane do you do + + + align:start position:0% +does that do to to the plane do you do +you think of a matrix + + align:start position:0% +you think of a matrix + + + align:start position:0% +you think of a matrix +as as a transformation it it takes every + + align:start position:0% +as as a transformation it it takes every + + + align:start position:0% +as as a transformation it it takes every +Vector in the plane and multiplies by + + align:start position:0% +Vector in the plane and multiplies by + + + align:start position:0% +Vector in the plane and multiplies by +The Matrix and so it moves all those + + align:start position:0% +The Matrix and so it moves all those + + + align:start position:0% +The Matrix and so it moves all those +vectors let's see what will happen if + + align:start position:0% +vectors let's see what will happen if + + + align:start position:0% +vectors let's see what will happen if +the vector is say in the X Direction so + + align:start position:0% +the vector is say in the X Direction so + + + align:start position:0% +the vector is say in the X Direction so +if I start with a vector X is one Z and + + align:start position:0% +if I start with a vector X is one Z and + + + align:start position:0% +if I start with a vector X is one Z and +let me call this this s for example I'll + + align:start position:0% +let me call this this s for example I'll + + + align:start position:0% +let me call this this s for example I'll +call that Matrix S what is + + align:start position:0% +call that Matrix S what is + + + align:start position:0% +call that Matrix S what is +SX + + align:start position:0% +SX + + + align:start position:0% +SX +it's is it still one zero yes okay so + + align:start position:0% +it's is it still one zero yes okay so + + + align:start position:0% +it's is it still one zero yes okay so +this is SX didn't move actually so it's + + align:start position:0% +this is SX didn't move actually so it's + + + align:start position:0% +this is SX didn't move actually so it's +an igen Vector I value one okay let me + + align:start position:0% +an igen Vector I value one okay let me + + + align:start position:0% +an igen Vector I value one okay let me +take another guy because if I take two + + align:start position:0% +take another guy because if I take two + + + align:start position:0% +take another guy because if I take two +I'll know everything right if I if I + + align:start position:0% +I'll know everything right if I if I + + + align:start position:0% +I'll know everything right if I if I +know what it does to two vectors I know + + align:start position:0% +know what it does to two vectors I know + + + align:start position:0% +know what it does to two vectors I know +everything okay what does it do to y + + align:start position:0% +everything okay what does it do to y + + + align:start position:0% +everything okay what does it do to y +equal + + align:start position:0% + + + + align:start position:0% + +01 well I multiply s by Y and what do I + + align:start position:0% +01 well I multiply s by Y and what do I + + + align:start position:0% +01 well I multiply s by Y and what do I +get see1 so it goes it's it goes + + align:start position:0% +get see1 so it goes it's it goes + + + align:start position:0% +get see1 so it goes it's it goes +there now what kind of a do you do you + + align:start position:0% +there now what kind of a do you do you + + + align:start position:0% +there now what kind of a do you do you +know the word for a transformation that + + align:start position:0% +know the word for a transformation that + + + align:start position:0% +know the word for a transformation that +so what is it doing here see I'm not are + + align:start position:0% +so what is it doing here see I'm not are + + + align:start position:0% +so what is it doing here see I'm not are +we are you seeing what it does to the + + align:start position:0% +we are you seeing what it does to the + + + align:start position:0% +we are you seeing what it does to the +whole plane + + align:start position:0% +whole plane + + + align:start position:0% +whole plane +it vectors that are in this direction + + align:start position:0% +it vectors that are in this direction + + + align:start position:0% +it vectors that are in this direction +stay put vectors that are here kind of + + align:start position:0% +stay put vectors that are here kind of + + + align:start position:0% +stay put vectors that are here kind of +Shear over a little bit all these + + align:start position:0% +Shear over a little bit all these + + + align:start position:0% +Shear over a little bit all these +vectors could tilt + + align:start position:0% +vectors could tilt + + + align:start position:0% +vectors could tilt +vectors here go so so um the the uh it's + + align:start position:0% +vectors here go so so um the the uh it's + + + align:start position:0% +vectors here go so so um the the uh it's +the word is a + + align:start position:0% + + + + align:start position:0% + +Shear I I I what it does is like + + align:start position:0% +Shear I I I what it does is like + + + align:start position:0% +Shear I I I what it does is like +it these these matrices will one of them + + align:start position:0% +it these these matrices will one of them + + + align:start position:0% +it these these matrices will one of them +will Shear the thing it's like it pushes + + align:start position:0% +will Shear the thing it's like it pushes + + + align:start position:0% +will Shear the thing it's like it pushes +this edge up like like so + + align:start position:0% +this edge up like like so + + + align:start position:0% +this edge up like like so +somehow and then the second one shear in + + align:start position:0% +somehow and then the second one shear in + + + align:start position:0% +somehow and then the second one shear in +the other direction and my my art is + + align:start position:0% +the other direction and my my art is + + + align:start position:0% +the other direction and my my art is +going to let me down now and the third + + align:start position:0% +going to let me down now and the third + + + align:start position:0% +going to let me down now and the third +one shares again and the result is a + + align:start position:0% +one shares again and the result is a + + + align:start position:0% +one shares again and the result is a +rotation I'm remembering vividly a a + + align:start position:0% +rotation I'm remembering vividly a a + + + align:start position:0% +rotation I'm remembering vividly a a +visit my only visit to National + + align:start position:0% +visit my only visit to National + + + align:start position:0% +visit my only visit to National +Institutes of Health well it didn't have + + align:start position:0% +Institutes of Health well it didn't have + + + align:start position:0% +Institutes of Health well it didn't have +anything to do with medicine or or + + align:start position:0% +anything to do with medicine or or + + + align:start position:0% +anything to do with medicine or or +anything but there were a few + + align:start position:0% +anything but there were a few + + + align:start position:0% +anything but there were a few +mathematicians there I hadn't met and + + align:start position:0% +mathematicians there I hadn't met and + + + align:start position:0% +mathematicians there I hadn't met and +wanted to uh in Maryland and they had + + align:start position:0% +wanted to uh in Maryland and they had + + + align:start position:0% +wanted to uh in Maryland and they had +just uh implemented this idea in a very + + align:start position:0% +just uh implemented this idea in a very + + + align:start position:0% +just uh implemented this idea in a very +elegant way and uh we're we're very uh + + align:start position:0% +elegant way and uh we're we're very uh + + + align:start position:0% +elegant way and uh we're we're very uh +excited about the stability and the and + + align:start position:0% +excited about the stability and the and + + + align:start position:0% +excited about the stability and the and +the efficiency of their + + align:start position:0% +the efficiency of their + + + align:start position:0% +the efficiency of their +rotation uh part of my point I guess is + + align:start position:0% +rotation uh part of my point I guess is + + + align:start position:0% +rotation uh part of my point I guess is +just that factoring + + align:start position:0% +just that factoring + + + align:start position:0% +just that factoring +matrices in interesting ways is is + + align:start position:0% +matrices in interesting ways is is + + + align:start position:0% +matrices in interesting ways is is +pretty uh is is a piece of Applied math + + align:start position:0% +pretty uh is is a piece of Applied math + + + align:start position:0% +pretty uh is is a piece of Applied math +and what's interesting a little about + + align:start position:0% +and what's interesting a little about + + + align:start position:0% +and what's interesting a little about +this factorization is you you see we'll + + align:start position:0% +this factorization is you you see we'll + + + align:start position:0% +this factorization is you you see we'll +we'll see this again in in uh future + + align:start position:0% +we'll see this again in in uh future + + + align:start position:0% +we'll see this again in in uh future +things this these these matrices are + + align:start position:0% +things this these these matrices are + + + align:start position:0% +things this these these matrices are +particularly simple this is this + + align:start position:0% +particularly simple this is this + + + align:start position:0% +particularly simple this is this +involves sort of a butterfly in a in a + + align:start position:0% +involves sort of a butterfly in a in a + + + align:start position:0% +involves sort of a butterfly in a in a +as in the fast 4 a transform you may + + align:start position:0% +as in the fast 4 a transform you may + + + align:start position:0% +as in the fast 4 a transform you may +have seen that butterfly picture because + + align:start position:0% +have seen that butterfly picture because + + + align:start position:0% +have seen that butterfly picture because +I have two inputs and two outputs so so + + align:start position:0% +I have two inputs and two outputs so so + + + align:start position:0% +I have two inputs and two outputs so so +the the m + + align:start position:0% +the the m + + + align:start position:0% +the the m +for this two inputs then the C and S and + + align:start position:0% +for this two inputs then the C and S and + + + align:start position:0% +for this two inputs then the C and S and +minus s and C affect the two outputs so + + align:start position:0% +minus s and C affect the two outputs so + + + align:start position:0% +minus s and C affect the two outputs so +then I get two outputs so each output is + + align:start position:0% +then I get two outputs so each output is + + + align:start position:0% +then I get two outputs so each output is +involved with both + + align:start position:0% +involved with both + + + align:start position:0% +involved with both +inputs What's Happening Here I have + + align:start position:0% +inputs What's Happening Here I have + + + align:start position:0% +inputs What's Happening Here I have +input in the first coordinate input in + + align:start position:0% +input in the first coordinate input in + + + align:start position:0% +input in the first coordinate input in +the second coordinate now when I + + align:start position:0% +the second coordinate now when I + + + align:start position:0% +the second coordinate now when I +multiply by this guy which was this sort + + align:start position:0% +multiply by this guy which was this sort + + + align:start position:0% +multiply by this guy which was this sort +of thing the the thing in the xord + + align:start position:0% +of thing the the thing in the xord + + + align:start position:0% +of thing the the thing in the xord +coordinate didn't change the thing in + + align:start position:0% +coordinate didn't change the thing in + + + align:start position:0% +coordinate didn't change the thing in +the + + align:start position:0% +the + + + align:start position:0% +the +y-coordinate was affected by you see + + align:start position:0% +y-coordinate was affected by you see + + + align:start position:0% +y-coordinate was affected by you see +what happened when we the thing in the + + align:start position:0% +what happened when we the thing in the + + + align:start position:0% +what happened when we the thing in the +y-coordinate was was changed to C1 it + + align:start position:0% +y-coordinate was was changed to C1 it + + + align:start position:0% +y-coordinate was was changed to C1 it +was affected by it by the x coordinate + + align:start position:0% +was affected by it by the x coordinate + + + align:start position:0% +was affected by it by the x coordinate +so it's like these these involve like a + + align:start position:0% +so it's like these these involve like a + + + align:start position:0% +so it's like these these involve like a +one so can I say a One-Winged + + align:start position:0% +one so can I say a One-Winged + + + align:start position:0% +one so can I say a One-Winged +butterfly and then then the next step + + align:start position:0% +butterfly and then then the next step + + + align:start position:0% +butterfly and then then the next step +here + + align:start position:0% +here + + + align:start position:0% +here +will be this this one now gets affected + + align:start position:0% +will be this this one now gets affected + + + align:start position:0% +will be this this one now gets affected +by this one but this guy goes + + align:start position:0% +by this one but this guy goes + + + align:start position:0% +by this one but this guy goes +through and then the last step will be + + align:start position:0% +through and then the last step will be + + + align:start position:0% +through and then the last step will be +this guy goes through and this one is + + align:start position:0% +this guy goes through and this one is + + + align:start position:0% +this guy goes through and this one is +affected by this one so we have produced + + align:start position:0% +affected by this one so we have produced + + + align:start position:0% +affected by this one so we have produced +a + + align:start position:0% +a + + + align:start position:0% +a +butterfly out of + + align:start position:0% +butterfly out of + + + align:start position:0% +butterfly out of +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +three One-Winged + + align:start position:0% +three One-Winged + + + align:start position:0% +three One-Winged +butterflies what a what a weird + + align:start position:0% +butterflies what a what a weird + + + align:start position:0% +butterflies what a what a weird +description but it it's + + align:start position:0% +description but it it's + + + align:start position:0% +description but it it's +uh there there are simple ideas like + + align:start position:0% +uh there there are simple ideas like + + + align:start position:0% +uh there there are simple ideas like +that have uh applications that that were + + align:start position:0% +that have uh applications that that were + + + align:start position:0% +that have uh applications that that were +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +unexpectedly uh simple but + + align:start position:0% +unexpectedly uh simple but + + + align:start position:0% +unexpectedly uh simple but +important and uh but there's a little + + align:start position:0% +important and uh but there's a little + + + align:start position:0% +important and uh but there's a little +bit of linear algebra here that that uh + + align:start position:0% +bit of linear algebra here that that uh + + + align:start position:0% +bit of linear algebra here that that uh +I I I don't feel I have completely clear + + align:start position:0% +I I I don't feel I have completely clear + + + align:start position:0% +I I I don't feel I have completely clear +what's what's we're factoring an + + align:start position:0% +what's what's we're factoring an + + + align:start position:0% +what's what's we're factoring an +orthogonal Matrix and these guys are + + align:start position:0% +orthogonal Matrix and these guys are + + + align:start position:0% +orthogonal Matrix and these guys are +simple but they're certainly not + + align:start position:0% +simple but they're certainly not + + + align:start position:0% +simple but they're certainly not +orthogonal so there's a there's some + + align:start position:0% +orthogonal so there's a there's some + + + align:start position:0% +orthogonal so there's a there's some +there's some linear algebra there of + + align:start position:0% +there's some linear algebra there of + + + align:start position:0% +there's some linear algebra there of +what what how if I start with an + + align:start position:0% +what what how if I start with an + + + align:start position:0% +what what how if I start with an +orthogonal Matrix and I factor it into + + align:start position:0% +orthogonal Matrix and I factor it into + + + align:start position:0% +orthogonal Matrix and I factor it into +these these um elimination type + + align:start position:0% +these these um elimination type + + + align:start position:0% +these these um elimination type +matrices uh we've lost orthogonality but + + align:start position:0% +matrices uh we've lost orthogonality but + + + align:start position:0% +matrices uh we've lost orthogonality but +but if we do it right the product will + + align:start position:0% +but if we do it right the product will + + + align:start position:0% +but if we do it right the product will +will the product will come out + + align:start position:0% +will the product will come out + + + align:start position:0% +will the product will come out +orthogonal okay that's I've I've now I + + align:start position:0% +orthogonal okay that's I've I've now I + + + align:start position:0% +orthogonal okay that's I've I've now I +really digressed now twice because of + + align:start position:0% +really digressed now twice because of + + + align:start position:0% +really digressed now twice because of +these the Simplicity of these 2 by two + + align:start position:0% +these the Simplicity of these 2 by two + + + align:start position:0% +these the Simplicity of these 2 by two +rotations and uh this was a digression + + align:start position:0% +rotations and uh this was a digression + + + align:start position:0% +rotations and uh this was a digression +into what are called Oiler angles when + + align:start position:0% +into what are called Oiler angles when + + + align:start position:0% +into what are called Oiler angles when +I'm creating a matrix as a operating on + + align:start position:0% +I'm creating a matrix as a operating on + + + align:start position:0% +I'm creating a matrix as a operating on +a matrix by these plane + + align:start position:0% +a matrix by these plane + + + align:start position:0% +a matrix by these plane +rotations and this was a digression uh + + align:start position:0% +rotations and this was a digression uh + + + align:start position:0% +rotations and this was a digression uh +that we'll appreciate later but it's + + align:start position:0% +that we'll appreciate later but it's + + + align:start position:0% +that we'll appreciate later but it's +sort of like simple enough to see the + + align:start position:0% +sort of like simple enough to see the + + + align:start position:0% +sort of like simple enough to see the +see it happen Okay can I come back to + + align:start position:0% +see it happen Okay can I come back to + + + align:start position:0% +see it happen Okay can I come back to +the main + + align:start position:0% +the main + + + align:start position:0% +the main +theme which is right now the virtues of + + align:start position:0% +theme which is right now the virtues of + + + align:start position:0% +theme which is right now the virtues of +orthogonality all right let let me do + + align:start position:0% +orthogonality all right let let me do + + + align:start position:0% +orthogonality all right let let me do +that the virtues of + + align:start position:0% + + + + align:start position:0% + +orthogonality + + align:start position:0% + + + + align:start position:0% + +okay well all right take that guy out of + + align:start position:0% +okay well all right take that guy out of + + + align:start position:0% +okay well all right take that guy out of +it + + align:start position:0% +it + + + align:start position:0% +it +too + + align:start position:0% +too + + + align:start position:0% +too +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +we okay the virtues of orthogonality all + + align:start position:0% +we okay the virtues of orthogonality all + + + align:start position:0% +we okay the virtues of orthogonality all +right suppose I have an orthogonal basis + + align:start position:0% +right suppose I have an orthogonal basis + + + align:start position:0% +right suppose I have an orthogonal basis +I've got these guys and I've got a + + align:start position:0% +I've got these guys and I've got a + + + align:start position:0% +I've got these guys and I've got a +vector which I would like to express as + + align:start position:0% +vector which I would like to express as + + + align:start position:0% +vector which I would like to express as +some combination of these orthogonal + + align:start position:0% + + + + align:start position:0% + +vectors my question is what is C1 + + align:start position:0% + + + + align:start position:0% + +what what if I have an orthogonal basis + + align:start position:0% +what what if I have an orthogonal basis + + + align:start position:0% +what what if I have an orthogonal basis +I one of its virtues is that I can I + + align:start position:0% +I one of its virtues is that I can I + + + align:start position:0% +I one of its virtues is that I can I +mean if it's a basis then any Vector is + + align:start position:0% +mean if it's a basis then any Vector is + + + align:start position:0% +mean if it's a basis then any Vector is +a combination of those basis vectors one + + align:start position:0% +a combination of those basis vectors one + + + align:start position:0% +a combination of those basis vectors one +of the virtues is important virtue is + + align:start position:0% +of the virtues is important virtue is + + + align:start position:0% +of the virtues is important virtue is +that these the coefficients C1 C2 CN I + + align:start position:0% +that these the coefficients C1 C2 CN I + + + align:start position:0% +that these the coefficients C1 C2 CN I +can find quickly and how do I do it can + + align:start position:0% +can find quickly and how do I do it can + + + align:start position:0% +can find quickly and how do I do it can +you take that inner product right take + + align:start position:0% +you take that inner product right take + + + align:start position:0% +you take that inner product right take +the inner product with how will I find + + align:start position:0% +the inner product with how will I find + + + align:start position:0% +the inner product with how will I find +C1 take the inner product with + + align:start position:0% +C1 take the inner product with + + + align:start position:0% +C1 take the inner product with +q1 + + align:start position:0% +q1 + + + align:start position:0% +q1 +right then all this stuff will disappear + + align:start position:0% +right then all this stuff will disappear + + + align:start position:0% +right then all this stuff will disappear +so q1 transpose X that's the inner + + align:start position:0% +so q1 transpose X that's the inner + + + align:start position:0% +so q1 transpose X that's the inner +product you wanted is C1 * q1 transpose + + align:start position:0% +product you wanted is C1 * q1 transpose + + + align:start position:0% +product you wanted is C1 * q1 transpose +q1 which + + align:start position:0% +q1 which + + + align:start position:0% +q1 which +is one C1 * 1 and all that stuff is zero + + align:start position:0% +is one C1 * 1 and all that stuff is zero + + + align:start position:0% +is one C1 * 1 and all that stuff is zero +so you see we immediately get those + + align:start position:0% +so you see we immediately get those + + + align:start position:0% +so you see we immediately get those +coefficients can I write that + + align:start position:0% +coefficients can I write that + + + align:start position:0% +coefficients can I write that +in Matrix + + align:start position:0% +in Matrix + + + align:start position:0% +in Matrix +language can I can just you're going to + + align:start position:0% +language can I can just you're going to + + + align:start position:0% +language can I can just you're going to +see the same thing but it's so so + + align:start position:0% +see the same thing but it's so so + + + align:start position:0% +see the same thing but it's so so +important and by the way yeah okay let's + + align:start position:0% +important and by the way yeah okay let's + + + align:start position:0% +important and by the way yeah okay let's +just see the same thing in Matrix + + align:start position:0% +just see the same thing in Matrix + + + align:start position:0% +just see the same thing in Matrix +language here I have a vector + + align:start position:0% +language here I have a vector + + + align:start position:0% +language here I have a vector +X and and and when you see a combination + + align:start position:0% +X and and and when you see a combination + + + align:start position:0% +X and and and when you see a combination +of + + align:start position:0% +of + + + align:start position:0% +of +vectors how do you see that in Matrix + + align:start position:0% +vectors how do you see that in Matrix + + + align:start position:0% +vectors how do you see that in Matrix +language I I I uh + + align:start position:0% +language I I I uh + + + align:start position:0% +language I I I uh +uh I want to express it using the Matrix + + align:start position:0% +uh I want to express it using the Matrix + + + align:start position:0% +uh I want to express it using the Matrix +Q of course the Matrix Q is going to be + + align:start position:0% +Q of course the Matrix Q is going to be + + + align:start position:0% +Q of course the Matrix Q is going to be +always stand for my my uh Matrix with + + align:start position:0% +always stand for my my uh Matrix with + + + align:start position:0% +always stand for my my uh Matrix with +these Q's in its columns + + align:start position:0% +these Q's in its columns + + + align:start position:0% +these Q's in its columns +Q2 + + align:start position:0% +Q2 + + + align:start position:0% +Q2 +qn okay and I've got coefficients C1 C2 + + align:start position:0% +qn okay and I've got coefficients C1 C2 + + + align:start position:0% +qn okay and I've got coefficients C1 C2 +up to + + align:start position:0% +up to + + + align:start position:0% +up to +CN what's that right hand side in Matrix + + align:start position:0% +CN what's that right hand side in Matrix + + + align:start position:0% +CN what's that right hand side in Matrix +language QC thanks QC it's Q * C + + align:start position:0% +language QC thanks QC it's Q * C + + + align:start position:0% +language QC thanks QC it's Q * C +because if I take q and multiply by now + + align:start position:0% +because if I take q and multiply by now + + + align:start position:0% +because if I take q and multiply by now +let me put in the C If I multiply by + + align:start position:0% +let me put in the C If I multiply by + + + align:start position:0% +let me put in the C If I multiply by +C12 down to + + align:start position:0% +C12 down to + + + align:start position:0% +C12 down to +CN it's ex this is exactly what that + + align:start position:0% +CN it's ex this is exactly what that + + + align:start position:0% +CN it's ex this is exactly what that +does it takes C1 * q1 C2 * Q2 CN * qn so + + align:start position:0% +does it takes C1 * q1 C2 * Q2 CN * qn so + + + align:start position:0% +does it takes C1 * q1 C2 * Q2 CN * qn so +X is QC all right now what's + + align:start position:0% +X is QC all right now what's + + + align:start position:0% +X is QC all right now what's +C if I have an equation xal QC what is + + align:start position:0% +C if I have an equation xal QC what is + + + align:start position:0% +C if I have an equation xal QC what is +uh uh the answer what's the solution C + + align:start position:0% +uh uh the answer what's the solution C + + + align:start position:0% +uh uh the answer what's the solution C +what are the coefficients in Matrix + + align:start position:0% +what are the coefficients in Matrix + + + align:start position:0% +what are the coefficients in Matrix +language what do I do to this what do I + + align:start position:0% +language what do I do to this what do I + + + align:start position:0% +language what do I do to this what do I +do to this equation to make it uh to + + align:start position:0% +do to this equation to make it uh to + + + align:start position:0% +do to this equation to make it uh to +produce + + align:start position:0% +produce + + + align:start position:0% +produce +C multiply by Q transpose thanks + + align:start position:0% +C multiply by Q transpose thanks + + + align:start position:0% +C multiply by Q transpose thanks +multiply by Q transpose and I have q + + align:start position:0% +multiply by Q transpose and I have q + + + align:start position:0% +multiply by Q transpose and I have q +transpose x equals + + align:start position:0% +transpose x equals + + + align:start position:0% +transpose x equals +c and you see that that's exactly what + + align:start position:0% +c and you see that that's exactly what + + + align:start position:0% +c and you see that that's exactly what +we did here the first C was the first + + align:start position:0% +we did here the first C was the first + + + align:start position:0% +we did here the first C was the first +row of Q transpose if I write more C's + + align:start position:0% +row of Q transpose if I write more C's + + + align:start position:0% +row of Q transpose if I write more C's +all at once you see that that did it all + + align:start position:0% +all at once you see that that did it all + + + align:start position:0% +all at once you see that that did it all +at once here I'm doing them like one at + + align:start position:0% +at once here I'm doing them like one at + + + align:start position:0% +at once here I'm doing them like one at +a time to get + + align:start position:0% +a time to get + + + align:start position:0% +a time to get +C2 I'm doing Q transpose Q2 transpose X + + align:start position:0% +C2 I'm doing Q transpose Q2 transpose X + + + align:start position:0% +C2 I'm doing Q transpose Q2 transpose X +for the same reason that would give me + + align:start position:0% +for the same reason that would give me + + + align:start position:0% +for the same reason that would give me +C2 and that's just the second row of Q + + align:start position:0% +C2 and that's just the second row of Q + + + align:start position:0% +C2 and that's just the second row of Q +transpose xal + + align:start position:0% +transpose xal + + + align:start position:0% +transpose xal +C2 okay so that's that's great uh now + + align:start position:0% +C2 okay so that's that's great uh now + + + align:start position:0% +C2 okay so that's that's great uh now +actually I'm I'm I'm + + align:start position:0% +actually I'm I'm I'm + + + align:start position:0% +actually I'm I'm I'm +uh I'm + + align:start position:0% +uh I'm + + + align:start position:0% +uh I'm +uh ready to start so this these are like + + align:start position:0% +uh ready to start so this these are like + + + align:start position:0% +uh ready to start so this these are like +great advantages of having orthogonal + + align:start position:0% +great advantages of having orthogonal + + + align:start position:0% +great advantages of having orthogonal +bases that lengths don't + + align:start position:0% +bases that lengths don't + + + align:start position:0% +bases that lengths don't +change that I'm working with simple + + align:start position:0% +change that I'm working with simple + + + align:start position:0% +change that I'm working with simple +rotations that I can do projections and + + align:start position:0% +rotations that I can do projections and + + + align:start position:0% +rotations that I can do projections and +I can do change of coordinates very + + align:start position:0% +I can do change of coordinates very + + + align:start position:0% +I can do change of coordinates very +quickly because always because of this + + align:start position:0% +quickly because always because of this + + + align:start position:0% +quickly because always because of this +formula which is which is firmly on the + + align:start position:0% +formula which is which is firmly on the + + + align:start position:0% +formula which is which is firmly on the +board okay + + align:start position:0% +board okay + + + align:start position:0% +board okay +now oh yeah okay let me ask you a let me + + align:start position:0% +now oh yeah okay let me ask you a let me + + + align:start position:0% +now oh yeah okay let me ask you a let me +go back to leas squares let me go back + + align:start position:0% +go back to leas squares let me go back + + + align:start position:0% +go back to leas squares let me go back +to these + + align:start position:0% +to these + + + align:start position:0% +to these +squares uh well I have to I yeah I guess + + align:start position:0% +squares uh well I have to I yeah I guess + + + align:start position:0% +squares uh well I have to I yeah I guess +yeah yeah let me go back to least + + align:start position:0% +yeah yeah let me go back to least + + + align:start position:0% +yeah yeah let me go back to least +squares so here's here's a here's a + + align:start position:0% +squares so here's here's a here's a + + + align:start position:0% +squares so here's here's a here's a +question okay so remember how Le squares + + align:start position:0% +question okay so remember how Le squares + + + align:start position:0% +question okay so remember how Le squares +started we had an a system ax equal + + align:start position:0% + + + + align:start position:0% + +B + + align:start position:0% + + + + align:start position:0% + +which had too many + + align:start position:0% +which had too many + + + align:start position:0% +which had too many +equations which had too many equations + + align:start position:0% +equations which had too many equations + + + align:start position:0% +equations which had too many equations +for the number of unknowns so there + + align:start position:0% +for the number of unknowns so there + + + align:start position:0% +for the number of unknowns so there +wasn't a + + align:start position:0% +wasn't a + + + align:start position:0% +wasn't a +solution and how did we get the + + align:start position:0% +solution and how did we get the + + + align:start position:0% +solution and how did we get the +solution what was the best X everybody + + align:start position:0% +solution what was the best X everybody + + + align:start position:0% +solution what was the best X everybody +remembering that the the equation for + + align:start position:0% +remembering that the the equation for + + + align:start position:0% +remembering that the the equation for +the best + + align:start position:0% +the best + + + align:start position:0% +the best +X the equation for the multiply by a + + align:start position:0% +X the equation for the multiply by a + + + align:start position:0% +X the equation for the multiply by a +transpose we took a transpose a for the + + align:start position:0% +transpose we took a transpose a for the + + + align:start position:0% +transpose we took a transpose a for the +best X + + align:start position:0% +best X + + + align:start position:0% +best X +was a oops a transposed B + + align:start position:0% + + + + align:start position:0% + +okay this is the best + + align:start position:0% + + + + align:start position:0% + +X best meaning it makes the error as + + align:start position:0% +X best meaning it makes the error as + + + align:start position:0% +X best meaning it makes the error as +small as possible best X means we're + + align:start position:0% +small as possible best X means we're + + + align:start position:0% +small as possible best X means we're +we're + + align:start position:0% +we're + + + align:start position:0% +we're +minimizing the distance between ax and B + + align:start position:0% +minimizing the distance between ax and B + + + align:start position:0% +minimizing the distance between ax and B +and that minimum is is achieved at X hat + + align:start position:0% +and that minimum is is achieved at X hat + + + align:start position:0% +and that minimum is is achieved at X hat +that's what this meant + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +well let's see if I can make my point + + align:start position:0% +well let's see if I can make my point + + + align:start position:0% +well let's see if I can make my point +here suppose + + align:start position:0% +here suppose + + + align:start position:0% +here suppose +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +we this is this is the way it's usually + + align:start position:0% +we this is this is the way it's usually + + + align:start position:0% +we this is this is the way it's usually +done solving those equations but there's + + align:start position:0% +done solving those equations but there's + + + align:start position:0% +done solving those equations but there's +another way to do it it would I I guess + + align:start position:0% +another way to do it it would I I guess + + + align:start position:0% +another way to do it it would I I guess +here's the way to make my point how + + align:start position:0% +here's the way to make my point how + + + align:start position:0% +here's the way to make my point how +simple this would be if a had if a was + + align:start position:0% +simple this would be if a had if a was + + + align:start position:0% +simple this would be if a had if a was +Q if a was Q what would be the best + + align:start position:0% +Q if a was Q what would be the best + + + align:start position:0% +Q if a was Q what would be the best +choice so let me just put over here if a + + align:start position:0% +choice so let me just put over here if a + + + align:start position:0% +choice so let me just put over here if a +was Q if a should I say was or were was + + align:start position:0% +was Q if a should I say was or were was + + + align:start position:0% +was Q if a should I say was or were was +were were is the subjunctive right if a + + align:start position:0% +were were is the subjunctive right if a + + + align:start position:0% +were were is the subjunctive right if a +were + + align:start position:0% +were + + + align:start position:0% +were +Q if a were if a in other words if a had + + align:start position:0% +Q if a were if a in other words if a had + + + align:start position:0% +Q if a were if a in other words if a had +orthonormal columns and wasn't just some + + align:start position:0% +orthonormal columns and wasn't just some + + + align:start position:0% +orthonormal columns and wasn't just some +uh some rectangular Matrix it was a + + align:start position:0% +uh some rectangular Matrix it was a + + + align:start position:0% +uh some rectangular Matrix it was a +rectangular Matrix with orthogonal + + align:start position:0% +rectangular Matrix with orthogonal + + + align:start position:0% +rectangular Matrix with orthogonal +columns then what would how would that + + align:start position:0% +columns then what would how would that + + + align:start position:0% +columns then what would how would that +what would be the best + + align:start position:0% +what would be the best + + + align:start position:0% +what would be the best +X well be just Q transpose B because + + align:start position:0% +X well be just Q transpose B because + + + align:start position:0% +X well be just Q transpose B because +this would be the identity right so the + + align:start position:0% +this would be the identity right so the + + + align:start position:0% +this would be the identity right so the +the beauty again another way to say the + + align:start position:0% +the beauty again another way to say the + + + align:start position:0% +the beauty again another way to say the +beauty of orthogonality is it prod it + + align:start position:0% +beauty of orthogonality is it prod it + + + align:start position:0% +beauty of orthogonality is it prod it +makes that Matrix the identity and then + + align:start position:0% +makes that Matrix the identity and then + + + align:start position:0% +makes that Matrix the identity and then +the best X becomes a trans ose well it + + align:start position:0% +the best X becomes a trans ose well it + + + align:start position:0% +the best X becomes a trans ose well it +be Q transpose + + align:start position:0% +be Q transpose + + + align:start position:0% +be Q transpose +B actually this is just the kind of + + align:start position:0% +B actually this is just the kind of + + + align:start position:0% +B actually this is just the kind of +thing we did here just the kind of thing + + align:start position:0% +thing we did here just the kind of thing + + + align:start position:0% +thing we did here just the kind of thing +we did here we're we're trying to + + align:start position:0% +we did here we're we're trying to + + + align:start position:0% +we did here we're we're trying to +minimize this and uh oh yeah here's a + + align:start position:0% +minimize this and uh oh yeah here's a + + + align:start position:0% +minimize this and uh oh yeah here's a +quick way to see + + align:start position:0% + + + + align:start position:0% + +that well okay if if a was + + align:start position:0% +that well okay if if a was + + + align:start position:0% +that well okay if if a was +Q yeah should we just just like some + + align:start position:0% +Q yeah should we just just like some + + + align:start position:0% +Q yeah should we just just like some +practice we're trying to minimize + + align:start position:0% +practice we're trying to minimize + + + align:start position:0% +practice we're trying to minimize +I if a were Q we we would be trying to + + align:start position:0% +I if a were Q we we would be trying to + + + align:start position:0% +I if a were Q we we would be trying to +minimize QX minus B and the claim is + + align:start position:0% +minimize QX minus B and the claim is + + + align:start position:0% +minimize QX minus B and the claim is +that that's the winner now I would like + + align:start position:0% +that that's the winner now I would like + + + align:start position:0% +that that's the winner now I would like +to see that really quickly suppose uh Q + + align:start position:0% +to see that really quickly suppose uh Q + + + align:start position:0% +to see that really quickly suppose uh Q +is one of my Q will always stand for the + + align:start position:0% +is one of my Q will always stand for the + + + align:start position:0% +is one of my Q will always stand for the +Matrix with Q transfers Q equal I if H + + align:start position:0% +Matrix with Q transfers Q equal I if H + + + align:start position:0% +Matrix with Q transfers Q equal I if H +how can I see that the right thing to do + + align:start position:0% +how can I see that the right thing to do + + + align:start position:0% +how can I see that the right thing to do +that this is the winning + + align:start position:0% +that this is the winning + + + align:start position:0% +that this is the winning +choice it's a projection that's true + + align:start position:0% +choice it's a projection that's true + + + align:start position:0% +choice it's a projection that's true +that's a good way to see it um um + + align:start position:0% +that's a good way to see it um um + + + align:start position:0% +that's a good way to see it um um +geometrically I was going to suggest + + align:start position:0% +geometrically I was going to suggest + + + align:start position:0% +geometrically I was going to suggest +also an algebraic way to see this + + align:start position:0% +also an algebraic way to see this + + + align:start position:0% +also an algebraic way to see this +suppose I multiply this thing by Q + + align:start position:0% + + + + align:start position:0% + +transpose suppose I multiply this is the + + align:start position:0% +transpose suppose I multiply this is the + + + align:start position:0% +transpose suppose I multiply this is the +error right suppose I multiply by Q + + align:start position:0% +error right suppose I multiply by Q + + + align:start position:0% +error right suppose I multiply by Q +transpose then what do I have when if I + + align:start position:0% +transpose then what do I have when if I + + + align:start position:0% +transpose then what do I have when if I +when I multiply that thing by Q + + align:start position:0% +when I multiply that thing by Q + + + align:start position:0% +when I multiply that thing by Q +transpose I have x minus Q transpose + + align:start position:0% +transpose I have x minus Q transpose + + + align:start position:0% +transpose I have x minus Q transpose +B + + align:start position:0% +B + + + align:start position:0% +B +and what's the connection between that + + align:start position:0% +and what's the connection between that + + + align:start position:0% +and what's the connection between that +one and this + + align:start position:0% + + + + align:start position:0% + +one they're the + + align:start position:0% +one they're the + + + align:start position:0% +one they're the +same why is + + align:start position:0% +same why is + + + align:start position:0% +same why is +that because I multiplied by a q + + align:start position:0% +that because I multiplied by a q + + + align:start position:0% +that because I multiplied by a q +transpose which is one of my orthogonal + + align:start position:0% +transpose which is one of my orthogonal + + + align:start position:0% +transpose which is one of my orthogonal +guys Q transposes is yeah it it it's the + + align:start position:0% +guys Q transposes is yeah it it it's the + + + align:start position:0% +guys Q transposes is yeah it it it's the +same so uh + + align:start position:0% +same so uh + + + align:start position:0% +same so uh +um so then I okay well yeah I'm I'm I'm + + align:start position:0% +um so then I okay well yeah I'm I'm I'm + + + align:start position:0% +um so then I okay well yeah I'm I'm I'm +slightly messed up here between + + align:start position:0% +slightly messed up here between + + + align:start position:0% +slightly messed up here between +rectangular and square matrices but uh + + align:start position:0% +rectangular and square matrices but uh + + + align:start position:0% +rectangular and square matrices but uh +so let me just say that that conclusion + + align:start position:0% +so let me just say that that conclusion + + + align:start position:0% +so let me just say that that conclusion +is correct okay all right I won't pursue + + align:start position:0% +is correct okay all right I won't pursue + + + align:start position:0% +is correct okay all right I won't pursue +that totally because I'm gonna do + + align:start position:0% +that totally because I'm gonna do + + + align:start position:0% +that totally because I'm gonna do +something similar here okay + + align:start position:0% +something similar here okay + + + align:start position:0% +something similar here okay +now here back to our leas squares + + align:start position:0% +now here back to our leas squares + + + align:start position:0% +now here back to our leas squares +problem this is a very very basic + + align:start position:0% +problem this is a very very basic + + + align:start position:0% +problem this is a very very basic +problem and constantly being solved okay + + align:start position:0% +problem and constantly being solved okay + + + align:start position:0% +problem and constantly being solved okay +and then and what are the ways to solve + + align:start position:0% +and then and what are the ways to solve + + + align:start position:0% +and then and what are the ways to solve +it way way one is + + align:start position:0% +it way way one is + + + align:start position:0% +it way way one is +headon just solve the normal + + align:start position:0% +headon just solve the normal + + + align:start position:0% +headon just solve the normal +equations way two + + align:start position:0% +equations way two + + + align:start position:0% +equations way two +is take your Matrix and orthogonalize + + align:start position:0% +is take your Matrix and orthogonalize + + + align:start position:0% +is take your Matrix and orthogonalize +those + + align:start position:0% +those + + + align:start position:0% +those +columns make it into a Q and then you + + align:start position:0% +columns make it into a Q and then you + + + align:start position:0% +columns make it into a Q and then you +got an easy easy + + align:start position:0% +got an easy easy + + + align:start position:0% +got an easy easy +problem so can I can I follow through on + + align:start position:0% +problem so can I can I follow through on + + + align:start position:0% +problem so can I can I follow through on +that because that that's like a decision + + align:start position:0% +that because that that's like a decision + + + align:start position:0% +that because that that's like a decision +that people are still arguing about + + align:start position:0% +that people are still arguing about + + + align:start position:0% +that people are still arguing about +what's the best way do you tackle it + + align:start position:0% +what's the best way do you tackle it + + + align:start position:0% +what's the best way do you tackle it +headon or do you first + + align:start position:0% +headon or do you first + + + align:start position:0% +headon or do you first +orthogonalize and let me + + align:start position:0% +orthogonalize and let me + + + align:start position:0% +orthogonalize and let me +say orthogonalize The Columns of + + align:start position:0% +say orthogonalize The Columns of + + + align:start position:0% +say orthogonalize The Columns of +a and now I have to say what that does + + align:start position:0% +a and now I have to say what that does + + + align:start position:0% +a and now I have to say what that does +that's this famous QR this is the this + + align:start position:0% +that's this famous QR this is the this + + + align:start position:0% +that's this famous QR this is the this +this gram Schmid process which my uh + + align:start position:0% +this gram Schmid process which my uh + + + align:start position:0% +this gram Schmid process which my uh +linear algebra lectures would have + + align:start position:0% +linear algebra lectures would have + + + align:start position:0% +linear algebra lectures would have +described but I'm I'm I'm going to + + align:start position:0% +described but I'm I'm I'm going to + + + align:start position:0% +described but I'm I'm I'm going to +recall it here so I'm going to take my + + align:start position:0% +recall it here so I'm going to take my + + + align:start position:0% +recall it here so I'm going to take my +a and I'm going to produce out of it a + + align:start position:0% +a and I'm going to produce out of it a + + + align:start position:0% +a and I'm going to produce out of it a +Q and there's going to be half to be + + align:start position:0% +Q and there's going to be half to be + + + align:start position:0% +Q and there's going to be half to be +some Matrix + + align:start position:0% +some Matrix + + + align:start position:0% +some Matrix +r + + align:start position:0% +r + + + align:start position:0% +r +that + + align:start position:0% +that + + + align:start position:0% +that +that does the job that does the job so + + align:start position:0% +that does the job that does the job so + + + align:start position:0% +that does the job that does the job so +these The Columns of a were not + + align:start position:0% +these The Columns of a were not + + + align:start position:0% +these The Columns of a were not +orthogonal The Columns of Q are + + align:start position:0% +orthogonal The Columns of Q are + + + align:start position:0% +orthogonal The Columns of Q are +orthogonal and there's an invertible + + align:start position:0% +orthogonal and there's an invertible + + + align:start position:0% +orthogonal and there's an invertible +Matrix r that connects them okay + + align:start position:0% +Matrix r that connects them okay + + + align:start position:0% +Matrix r that connects them okay +so this is what Graham Schmid + + align:start position:0% +so this is what Graham Schmid + + + align:start position:0% +so this is what Graham Schmid +achieves and I I'll come back to that + + align:start position:0% +achieves and I I'll come back to that + + + align:start position:0% +achieves and I I'll come back to that +what I want to do is use it + + align:start position:0% +what I want to do is use it + + + align:start position:0% +what I want to do is use it +suppose suppose I've orthogonalized The + + align:start position:0% +suppose suppose I've orthogonalized The + + + align:start position:0% +suppose suppose I've orthogonalized The +Columns of a to get q and the r has done + + align:start position:0% +Columns of a to get q and the r has done + + + align:start position:0% +Columns of a to get q and the r has done +it this is this is this is M byn this is + + align:start position:0% +it this is this is this is M byn this is + + + align:start position:0% +it this is this is this is M byn this is +n byn and this is n byn nice and square + + align:start position:0% +n byn and this is n byn nice and square + + + align:start position:0% +n byn and this is n byn nice and square +and invertible and everything in fact + + align:start position:0% +and invertible and everything in fact + + + align:start position:0% +and invertible and everything in fact +triangular that's that's a that's a r is + + align:start position:0% +triangular that's that's a that's a r is + + + align:start position:0% +triangular that's that's a that's a r is +a nice + + align:start position:0% +a nice + + + align:start position:0% +a nice +Matrix we we've taken a un a not nice + + align:start position:0% +Matrix we we've taken a un a not nice + + + align:start position:0% +Matrix we we've taken a un a not nice +Matrix and we've factored it into a nice + + align:start position:0% +Matrix and we've factored it into a nice + + + align:start position:0% +Matrix and we've factored it into a nice +rectangular Matrix + + align:start position:0% +rectangular Matrix + + + align:start position:0% +rectangular Matrix +and a very nice uh Square Matrix but it + + align:start position:0% +and a very nice uh Square Matrix but it + + + align:start position:0% +and a very nice uh Square Matrix but it +cost something to do that we had to I + + align:start position:0% +cost something to do that we had to I + + + align:start position:0% +cost something to do that we had to I +I'm going to be very practical + + align:start position:0% +I'm going to be very practical + + + align:start position:0% +I'm going to be very practical +here what's because I'm asking what's + + align:start position:0% +here what's because I'm asking what's + + + align:start position:0% +here what's because I'm asking what's +the best way to solve this fundamental + + align:start position:0% +the best way to solve this fundamental + + + align:start position:0% +the best way to solve this fundamental +problem should we tackle it this + + align:start position:0% + + + + align:start position:0% + +way and what would be the cost there or + + align:start position:0% +way and what would be the cost there or + + + align:start position:0% +way and what would be the cost there or +should we tackle it this way all right + + align:start position:0% +should we tackle it this way all right + + + align:start position:0% +should we tackle it this way all right +now if we tackle it this way what will + + align:start position:0% +now if we tackle it this way what will + + + align:start position:0% +now if we tackle it this way what will +we get + + align:start position:0% +we get + + + align:start position:0% +we get +so now I'm + + align:start position:0% +so now I'm + + + align:start position:0% +so now I'm +minimizing yeah so so what does it mean + + align:start position:0% +minimizing yeah so so what does it mean + + + align:start position:0% +minimizing yeah so so what does it mean +what if if a is QR what's my answer + + align:start position:0% +what if if a is QR what's my answer + + + align:start position:0% +what if if a is QR what's my answer +here let's see that I'm I'm + + align:start position:0% +here let's see that I'm I'm + + + align:start position:0% +here let's see that I'm I'm +minimizing axus + + align:start position:0% +minimizing axus + + + align:start position:0% +minimizing axus +B but that's QR x- + + align:start position:0% +B but that's QR x- + + + align:start position:0% +B but that's QR x- +B and now again I can multiply by Q + + align:start position:0% +B and now again I can multiply by Q + + + align:start position:0% +B and now again I can multiply by Q +transpose and I get I'm I'm minimizing + + align:start position:0% +transpose and I get I'm I'm minimizing + + + align:start position:0% +transpose and I get I'm I'm minimizing +I'm I get uh RX minus Q transpose + + align:start position:0% +I'm I get uh RX minus Q transpose + + + align:start position:0% +I'm I get uh RX minus Q transpose +B and now I look for the best X but R is + + align:start position:0% +B and now I look for the best X but R is + + + align:start position:0% +B and now I look for the best X but R is +invertible so the best X is let me let + + align:start position:0% +invertible so the best X is let me let + + + align:start position:0% +invertible so the best X is let me let +me just put it here is R inverse Q + + align:start position:0% +me just put it here is R inverse Q + + + align:start position:0% +me just put it here is R inverse Q +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +B that's an that's another another way + + align:start position:0% +B that's an that's another another way + + + align:start position:0% +B that's an that's another another way +to to do + + align:start position:0% +to to do + + + align:start position:0% +to to do +estimation another way to do estimation + + align:start position:0% +estimation another way to do estimation + + + align:start position:0% +estimation another way to do estimation +and I guess this so this is way 2 and + + align:start position:0% +and I guess this so this is way 2 and + + + align:start position:0% +and I guess this so this is way 2 and +this is way one and the choice between + + align:start position:0% +this is way one and the choice between + + + align:start position:0% +this is way one and the choice between +those two ways is sort of quite + + align:start position:0% +those two ways is sort of quite + + + align:start position:0% +those two ways is sort of quite +fundamental it it comes up in kelman + + align:start position:0% +fundamental it it comes up in kelman + + + align:start position:0% +fundamental it it comes up in kelman +filters every time because common + + align:start position:0% +filters every time because common + + + align:start position:0% +filters every time because common +filters are all the so many filters are + + align:start position:0% +filters are all the so many filters are + + + align:start position:0% +filters are all the so many filters are +doing these + + align:start position:0% +doing these + + + align:start position:0% +doing these +squares and what's how's a way to + + align:start position:0% +squares and what's how's a way to + + + align:start position:0% +squares and what's how's a way to +describe that choice maybe you've heard + + align:start position:0% +describe that choice maybe you've heard + + + align:start position:0% +describe that choice maybe you've heard +heard of it in in this filter + + align:start position:0% +heard of it in in this filter + + + align:start position:0% +heard of it in in this filter +connection here we're basically working + + align:start position:0% +connection here we're basically working + + + align:start position:0% +connection here we're basically working +with a + + align:start position:0% +with a + + + align:start position:0% +with a +squared somehow a transpose a is the + + align:start position:0% +squared somehow a transpose a is the + + + align:start position:0% +squared somehow a transpose a is the +Matrix version of a squared we're we're + + align:start position:0% +Matrix version of a squared we're we're + + + align:start position:0% +Matrix version of a squared we're we're +things are being + + align:start position:0% +things are being + + + align:start position:0% +things are being +squared here we + + align:start position:0% +squared here we + + + align:start position:0% +squared here we +aren't here we didn't work with a + + align:start position:0% +aren't here we didn't work with a + + + align:start position:0% +aren't here we didn't work with a +transpose a we only stayed with a so + + align:start position:0% +transpose a we only stayed with a so + + + align:start position:0% +transpose a we only stayed with a so +this is like the square root + + align:start position:0% +this is like the square root + + + align:start position:0% +this is like the square root +filter have you heard that expression in + + align:start position:0% +filter have you heard that expression in + + + align:start position:0% +filter have you heard that expression in +in in connection with + + align:start position:0% +in in connection with + + + align:start position:0% +in in connection with +filtering because it was like a + + align:start position:0% +filtering because it was like a + + + align:start position:0% +filtering because it was like a +bombshell in the world of calman filters + + align:start position:0% +bombshell in the world of calman filters + + + align:start position:0% +bombshell in the world of calman filters +the suggestion of a square root filter + + align:start position:0% +the suggestion of a square root filter + + + align:start position:0% +the suggestion of a square root filter +and why was it a bombshell because when + + align:start position:0% +and why was it a bombshell because when + + + align:start position:0% +and why was it a bombshell because when +I Square + + align:start position:0% +I Square + + + align:start position:0% +I Square +stuff I'm messing I can mess up the + + align:start position:0% +stuff I'm messing I can mess up the + + + align:start position:0% +stuff I'm messing I can mess up the +condition number I can mess up the + + align:start position:0% +condition number I can mess up the + + + align:start position:0% +condition number I can mess up the +stability so these square root filters + + align:start position:0% +stability so these square root filters + + + align:start position:0% +stability so these square root filters +became very important because they're + + align:start position:0% +became very important because they're + + + align:start position:0% +became very important because they're +more + + align:start position:0% +more + + + align:start position:0% +more +stable and uh condition number is I'll + + align:start position:0% +stable and uh condition number is I'll + + + align:start position:0% +stable and uh condition number is I'll +come to in the second lecture this + + align:start position:0% +come to in the second lecture this + + + align:start position:0% +come to in the second lecture this +afternoon as a measure of stability so + + align:start position:0% +afternoon as a measure of stability so + + + align:start position:0% +afternoon as a measure of stability so +but here we're + + align:start position:0% +but here we're + + + align:start position:0% +but here we're +seeing I mean once we get to kman + + align:start position:0% +seeing I mean once we get to kman + + + align:start position:0% +seeing I mean once we get to kman +filters we're going to get buried by by + + align:start position:0% +filters we're going to get buried by by + + + align:start position:0% +filters we're going to get buried by by +um uh so many important ideas I thought + + align:start position:0% +um uh so many important ideas I thought + + + align:start position:0% +um uh so many important ideas I thought +maybe to to see it in this simple case + + align:start position:0% +maybe to to see it in this simple case + + + align:start position:0% +maybe to to see it in this simple case +simple being the cleanest possible case + + align:start position:0% +simple being the cleanest possible case + + + align:start position:0% +simple being the cleanest possible case +of a linear system no solution one + + align:start position:0% +of a linear system no solution one + + + align:start position:0% +of a linear system no solution one +option is go to a transpose + + align:start position:0% +option is go to a transpose + + + align:start position:0% +option is go to a transpose +a second option is is orthogonalize the + + align:start position:0% +a second option is is orthogonalize the + + + align:start position:0% +a second option is is orthogonalize the +columns and then you have so this is + + align:start position:0% +columns and then you have so this is + + + align:start position:0% +columns and then you have so this is +triangular no no work is involved in + + align:start position:0% +triangular no no work is involved in + + + align:start position:0% +triangular no no work is involved in +that no work that's a simple matrix + + align:start position:0% +that no work that's a simple matrix + + + align:start position:0% +that no work that's a simple matrix +multiplication that's really + + align:start position:0% +multiplication that's really + + + align:start position:0% +multiplication that's really +fast why wouldn't you just do number two + + align:start position:0% +fast why wouldn't you just do number two + + + align:start position:0% +fast why wouldn't you just do number two +every + + align:start position:0% + + + + align:start position:0% + +time yeah you're really on the ball + + align:start position:0% +time yeah you're really on the ball + + + align:start position:0% +time yeah you're really on the ball +that's it you have to you'd have to + + align:start position:0% +that's it you have to you'd have to + + + align:start position:0% +that's it you have to you'd have to +because you can't do it until you've + + align:start position:0% +because you can't do it until you've + + + align:start position:0% +because you can't do it until you've +done this + + align:start position:0% +done this + + + align:start position:0% +done this +step so the question is what cost more + + align:start position:0% +step so the question is what cost more + + + align:start position:0% +step so the question is what cost more +to do this step and then you had + + align:start position:0% +to do this step and then you had + + + align:start position:0% +to do this step and then you had +triangular Matrix transpose I mean the + + align:start position:0% +triangular Matrix transpose I mean the + + + align:start position:0% +triangular Matrix transpose I mean the +the the solution of the system was no + + align:start position:0% +the the solution of the system was no + + + align:start position:0% +the the solution of the system was no +work the work is in there where here was + + align:start position:0% +work the work is in there where here was + + + align:start position:0% +work the work is in there where here was +the the we have a linear system to + + align:start position:0% +the the we have a linear system to + + + align:start position:0% +the the we have a linear system to +solve and + + align:start position:0% +solve and + + + align:start position:0% +solve and +so it's a regretable fact it's a pretty + + align:start position:0% +so it's a regretable fact it's a pretty + + + align:start position:0% +so it's a regretable fact it's a pretty +it's a pretty close race but this one is + + align:start position:0% +it's a pretty close race but this one is + + + align:start position:0% +it's a pretty close race but this one is +faster + + align:start position:0% +faster + + + align:start position:0% +faster +and this one is + + align:start position:0% +and this one is + + + align:start position:0% +and this one is +safer so it depends if you're a risk + + align:start position:0% +safer so it depends if you're a risk + + + align:start position:0% +safer so it depends if you're a risk +averse uh do that + + align:start position:0% +averse uh do that + + + align:start position:0% +averse uh do that +one uh if you're if you figure let's + + align:start position:0% +one uh if you're if you figure let's + + + align:start position:0% +one uh if you're if you figure let's +just get the answer here uh this one and + + align:start position:0% +just get the answer here uh this one and + + + align:start position:0% +just get the answer here uh this one and +maybe I could I noticed in + + align:start position:0% +maybe I could I noticed in + + + align:start position:0% +maybe I could I noticed in +this important Bible in this subject is + + align:start position:0% +this important Bible in this subject is + + + align:start position:0% +this important Bible in this subject is +the book by gallb and Van loone do + + align:start position:0% +the book by gallb and Van loone do + + + align:start position:0% +the book by gallb and Van loone do +you let me let me just copy down some uh + + align:start position:0% +you let me let me just copy down some uh + + + align:start position:0% +you let me let me just copy down some uh +numbers from their from their + + align:start position:0% + + + + align:start position:0% + +book I I I feel it's first useful to + + align:start position:0% +book I I I feel it's first useful to + + + align:start position:0% +book I I I feel it's first useful to +mention who are some of the leaders in + + align:start position:0% +mention who are some of the leaders in + + + align:start position:0% +mention who are some of the leaders in +this field uh Jean gallb is certainly + + align:start position:0% +this field uh Jean gallb is certainly + + + align:start position:0% +this field uh Jean gallb is certainly +one and Charlie van loone probably wrote + + align:start position:0% +one and Charlie van loone probably wrote + + + align:start position:0% +one and Charlie van loone probably wrote +most of the + + align:start position:0% +most of the + + + align:start position:0% +most of the +book uh and he's he's at Cornell and and + + align:start position:0% +book uh and he's he's at Cornell and and + + + align:start position:0% +book uh and he's he's at Cornell and and +gallb is at Stanford + + align:start position:0% +gallb is at Stanford + + + align:start position:0% +gallb is at Stanford +and uh it's now in its second edition it + + align:start position:0% +and uh it's now in its second edition it + + + align:start position:0% +and uh it's now in its second edition it +just happened that at home I had this + + align:start position:0% +just happened that at home I had this + + + align:start position:0% +just happened that at home I had this +first edition so I I've brought that + + align:start position:0% +first edition so I I've brought that + + + align:start position:0% +first edition so I I've brought that +today to tell you the the uh + + align:start position:0% +today to tell you the the uh + + + align:start position:0% +today to tell you the the uh +costs of the different ways that you + + align:start position:0% +costs of the different ways that you + + + align:start position:0% +costs of the different ways that you +could solve these squares okay uh so + + align:start position:0% +could solve these squares okay uh so + + + align:start position:0% +could solve these squares okay uh so +this book is called matrix computations + + align:start position:0% +this book is called matrix computations + + + align:start position:0% +this book is called matrix computations +it's pretty + + align:start position:0% +it's pretty + + + align:start position:0% +it's pretty +dense uh but it gives the basic + + align:start position:0% +dense uh but it gives the basic + + + align:start position:0% +dense uh but it gives the basic +algorithms for for numerical linear + + align:start position:0% +algorithms for for numerical linear + + + align:start position:0% +algorithms for for numerical linear +algebra so it's it's kind of become the + + align:start position:0% +algebra so it's it's kind of become the + + + align:start position:0% +algebra so it's it's kind of become the +Bible in this subject okay um gallab is + + align:start position:0% +Bible in this subject okay um gallab is + + + align:start position:0% +Bible in this subject okay um gallab is +especially associated with the SVD which + + align:start position:0% +especially associated with the SVD which + + + align:start position:0% +especially associated with the SVD which +is my next lecture so he actually his + + align:start position:0% +is my next lecture so he actually his + + + align:start position:0% +is my next lecture so he actually his +his license plate is Dr + + align:start position:0% +his license plate is Dr + + + align:start position:0% +his license plate is Dr +SVD uh California Plate and uh I think + + align:start position:0% +SVD uh California Plate and uh I think + + + align:start position:0% +SVD uh California Plate and uh I think +he's quite quite proud of it of course + + align:start position:0% +he's quite quite proud of it of course + + + align:start position:0% +he's quite quite proud of it of course +um + + align:start position:0% +um + + + align:start position:0% +um +but he's + + align:start position:0% +but he's + + + align:start position:0% +but he's +a he's a good guy a pretty good guy he's + + align:start position:0% +a he's a good guy a pretty good guy he's + + + align:start position:0% +a he's a good guy a pretty good guy he's +he's U okay so I was going to write down + + align:start position:0% +he's U okay so I was going to write down + + + align:start position:0% +he's U okay so I was going to write down +the table + + align:start position:0% +the table + + + align:start position:0% +the table +of okay how + + align:start position:0% +of okay how + + + align:start position:0% +of okay how +many uh flops so a flop is a floating + + align:start position:0% +many uh flops so a flop is a floating + + + align:start position:0% +many uh flops so a flop is a floating +Point + + align:start position:0% +Point + + + align:start position:0% +Point +operation + + align:start position:0% +operation + + + align:start position:0% +operation +and + + align:start position:0% +and + + + align:start position:0% +and +um well either for solving a square + + align:start position:0% +um well either for solving a square + + + align:start position:0% +um well either for solving a square +system yeah I don't know if I've got all + + align:start position:0% +system yeah I don't know if I've got all + + + align:start position:0% +system yeah I don't know if I've got all +the the yeah + + align:start position:0% + + + + align:start position:0% + +the this is n + + align:start position:0% + + + + align:start position:0% + +byn and do you know how many operations + + align:start position:0% +byn and do you know how many operations + + + align:start position:0% +byn and do you know how many operations +it takes to + + align:start position:0% +it takes to + + + align:start position:0% +it takes to +solve it's + + align:start position:0% +solve it's + + + align:start position:0% +solve it's +symmetric which will cut the operation + + align:start position:0% +symmetric which will cut the operation + + + align:start position:0% +symmetric which will cut the operation +count in half how many operations to + + align:start position:0% +count in half how many operations to + + + align:start position:0% +count in half how many operations to +solve uh an N byend symmetric + + align:start position:0% +solve uh an N byend symmetric + + + align:start position:0% +solve uh an N byend symmetric +system anybody know it goes up like n + + align:start position:0% +system anybody know it goes up like n + + + align:start position:0% +system anybody know it goes up like n +cubed and then now we have to get what's + + align:start position:0% +cubed and then now we have to get what's + + + align:start position:0% +cubed and then now we have to get what's +the what's what number multiplies that n + + align:start position:0% +the what's what number multiplies that n + + + align:start position:0% +the what's what number multiplies that n +Cube because all these ways are going to + + align:start position:0% +Cube because all these ways are going to + + + align:start position:0% +Cube because all these ways are going to +turn out to be n Cube ways and the so + + align:start position:0% +turn out to be n Cube ways and the so + + + align:start position:0% +turn out to be n Cube ways and the so +the coefficient is what tells us whether + + align:start position:0% +the coefficient is what tells us whether + + + align:start position:0% +the coefficient is what tells us whether +one wins or another and let's see it's + + align:start position:0% +one wins or another and let's see it's + + + align:start position:0% +one wins or another and let's see it's +uh for a normal n byn Matrix it would be + + align:start position:0% +uh for a normal n byn Matrix it would be + + + align:start position:0% +uh for a normal n byn Matrix it would be +1/3 n cubed multiplies and 1/3 n cubed + + align:start position:0% +1/3 n cubed multiplies and 1/3 n cubed + + + align:start position:0% +1/3 n cubed multiplies and 1/3 n cubed +adds + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +2/3 but for symmetric Matrix half of the + + align:start position:0% +2/3 but for symmetric Matrix half of the + + + align:start position:0% +2/3 but for symmetric Matrix half of the +work is not necessary we don't have to + + align:start position:0% +work is not necessary we don't have to + + + align:start position:0% +work is not necessary we don't have to +worry about above the diagonal if we + + align:start position:0% +worry about above the diagonal if we + + + align:start position:0% +worry about above the diagonal if we +follow below the diagonal so this this + + align:start position:0% +follow below the diagonal so this this + + + align:start position:0% +follow below the diagonal so this this +method is takes one well I was going to + + align:start position:0% +method is takes one well I was going to + + + align:start position:0% +method is takes one well I was going to +write it over here this method uh + + align:start position:0% +write it over here this method uh + + + align:start position:0% +write it over here this method uh +elimination takes one3 of n Cub flops + + align:start position:0% +elimination takes one3 of n Cub flops + + + align:start position:0% +elimination takes one3 of n Cub flops +okay and uh then there are other ways + + align:start position:0% +okay and uh then there are other ways + + + align:start position:0% +okay and uh then there are other ways +but let me let me mention Graham + + align:start position:0% + + + + align:start position:0% + +Schmidt which is a equal + + align:start position:0% +Schmidt which is a equal + + + align:start position:0% +Schmidt which is a equal +QR that + + align:start position:0% +QR that + + + align:start position:0% +QR that +idea by by the Graham Schmidt method + + align:start position:0% +idea by by the Graham Schmidt method + + + align:start position:0% +idea by by the Graham Schmidt method +well it turned out to be n + + align:start position:0% +well it turned out to be n + + + align:start position:0% +well it turned out to be n +cubed and using the SVD ah is worse in + + align:start position:0% +cubed and using the SVD ah is worse in + + + align:start position:0% +cubed and using the SVD ah is worse in +this case the SVD is more more still inq + + align:start position:0% +this case the SVD is more more still inq + + + align:start position:0% +this case the SVD is more more still inq +but but higher H there are other + + align:start position:0% +but but higher H there are other + + + align:start position:0% +but but higher H there are other +possibilities won't list people just + + align:start position:0% +possibilities won't list people just + + + align:start position:0% +possibilities won't list people just +spend a lot of time thinking H what's + + align:start position:0% +spend a lot of time thinking H what's + + + align:start position:0% +spend a lot of time thinking H what's +the efficient way to do these things so + + align:start position:0% +the efficient way to do these things so + + + align:start position:0% +the efficient way to do these things so +there there we see it uh in this choice + + align:start position:0% +there there we see it uh in this choice + + + align:start position:0% +there there we see it uh in this choice +of taking squaring or a square root one + + align:start position:0% +of taking squaring or a square root one + + + align:start position:0% +of taking squaring or a square root one +in that simple context and one of the + + align:start position:0% +in that simple context and one of the + + + align:start position:0% +in that simple context and one of the +things I I hope to learn maybe in + + align:start position:0% +things I I hope to learn maybe in + + + align:start position:0% +things I I hope to learn maybe in +conversation + + align:start position:0% +conversation + + + align:start position:0% +conversation +is in + + align:start position:0% +is in + + + align:start position:0% +is in +filtering have the square root filters + + align:start position:0% +filtering have the square root filters + + + align:start position:0% +filtering have the square root filters +triumphed I don't know what the standard + + align:start position:0% +triumphed I don't know what the standard + + + align:start position:0% +triumphed I don't know what the standard +software is in in that in that world in + + align:start position:0% +software is in in that in that world in + + + align:start position:0% +software is in in that in that world in +this world this simpler world the + + align:start position:0% +this world this simpler world the + + + align:start position:0% +this world this simpler world the +standard most people just go with that + + align:start position:0% +standard most people just go with that + + + align:start position:0% +standard most people just go with that +one because it's so + + align:start position:0% +one because it's so + + + align:start position:0% +one because it's so +simple uh and uh and it's faster okay so + + align:start position:0% +simple uh and uh and it's faster okay so + + + align:start position:0% +simple uh and uh and it's faster okay so +that's some comment about about uh these + + align:start position:0% +that's some comment about about uh these + + + align:start position:0% +that's some comment about about uh these +squares and this a equal QR from Graham + + align:start position:0% +squares and this a equal QR from Graham + + + align:start position:0% +squares and this a equal QR from Graham +Schmidt let's see I had one more topic + + align:start position:0% +Schmidt let's see I had one more topic + + + align:start position:0% +Schmidt let's see I had one more topic +that I didn't want to to uh + + align:start position:0% +that I didn't want to to uh + + + align:start position:0% +that I didn't want to to uh +um miss out on so I've oh okay so I'm + + align:start position:0% +um miss out on so I've oh okay so I'm + + + align:start position:0% +um miss out on so I've oh okay so I'm +going down the list here I've spoken + + align:start position:0% +going down the list here I've spoken + + + align:start position:0% +going down the list here I've spoken +about costs and now I wanted to speak + + align:start position:0% +about costs and now I wanted to speak + + + align:start position:0% +about costs and now I wanted to speak +about the igen value problem and then I + + align:start position:0% +about the igen value problem and then I + + + align:start position:0% +about the igen value problem and then I +really should say more about QR but let + + align:start position:0% +really should say more about QR but let + + + align:start position:0% +really should say more about QR but let +me say something about the igen value + + align:start position:0% + + + + align:start position:0% + +problem + + align:start position:0% +problem + + + align:start position:0% +problem +because finding igen values let's take a + + align:start position:0% +because finding igen values let's take a + + + align:start position:0% +because finding igen values let's take a +Matrix so a equal a + + align:start position:0% + + + + align:start position:0% + +transpose + + align:start position:0% + + + + align:start position:0% + +find the igen + + align:start position:0% +find the igen + + + align:start position:0% +find the igen +values okay that's my that's one of the + + align:start position:0% +values okay that's my that's one of the + + + align:start position:0% +values okay that's my that's one of the +fundamental Computing jobs and it's not + + align:start position:0% +fundamental Computing jobs and it's not + + + align:start position:0% +fundamental Computing jobs and it's not +at all clear how to do it I've mentioned + + align:start position:0% +at all clear how to do it I've mentioned + + + align:start position:0% +at all clear how to do it I've mentioned +when we spoke about when we introduced + + align:start position:0% +when we spoke about when we introduced + + + align:start position:0% +when we spoke about when we introduced +igen values that you would never want to + + align:start position:0% +igen values that you would never want to + + + align:start position:0% +igen values that you would never want to +use the determinant of a minus Lambda I + + align:start position:0% +use the determinant of a minus Lambda I + + + align:start position:0% +use the determinant of a minus Lambda I +that figure out that polinomial and find + + align:start position:0% +that figure out that polinomial and find + + + align:start position:0% +that figure out that polinomial and find +its + + align:start position:0% +its + + + align:start position:0% +its +roots yeah I mean the roots of + + align:start position:0% +roots yeah I mean the roots of + + + align:start position:0% +roots yeah I mean the roots of +polinomial are are are quite difficult + + align:start position:0% +polinomial are are are quite difficult + + + align:start position:0% +polinomial are are are quite difficult +to find actually I had a case in in an + + align:start position:0% +to find actually I had a case in in an + + + align:start position:0% +to find actually I had a case in in an +event of that kind uh in a week ago uh + + align:start position:0% +event of that kind uh in a week ago uh + + + align:start position:0% +event of that kind uh in a week ago uh +we + + align:start position:0% +we + + + align:start position:0% +we +were using + + align:start position:0% +were using + + + align:start position:0% +were using +matlb which of course does it to does + + align:start position:0% +matlb which of course does it to does + + + align:start position:0% +matlb which of course does it to does +computes to 16 + + align:start position:0% +computes to 16 + + + align:start position:0% +computes to 16 +digits + + align:start position:0% +digits + + + align:start position:0% +digits +and forgive me if I mentioned this + + align:start position:0% +and forgive me if I mentioned this + + + align:start position:0% +and forgive me if I mentioned this +before just say it again we had a + + align:start position:0% +before just say it again we had a + + + align:start position:0% +before just say it again we had a +polinomial of degree six and we knew + + align:start position:0% +polinomial of degree six and we knew + + + align:start position:0% +polinomial of degree six and we knew +that four roots were at one or at minus + + align:start position:0% +that four roots were at one or at minus + + + align:start position:0% +that four roots were at one or at minus +one we knew it had our we knew that our + + align:start position:0% +one we knew it had our we knew that our + + + align:start position:0% +one we knew it had our we knew that our +polinomial had four roots at minus + + align:start position:0% + + + + align:start position:0% + +one and the other two Roots were real so + + align:start position:0% +one and the other two Roots were real so + + + align:start position:0% +one and the other two Roots were real so +we knew what it was and we'll actually + + align:start position:0% +we knew what it was and we'll actually + + + align:start position:0% +we knew what it was and we'll actually +see that polinomial in the wavelet + + align:start position:0% +see that polinomial in the wavelet + + + align:start position:0% +see that polinomial in the wavelet +lectures and so we gave it to mat lab + + align:start position:0% +lectures and so we gave it to mat lab + + + align:start position:0% +lectures and so we gave it to mat lab +The Roots command to find the roots + + align:start position:0% +The Roots command to find the roots + + + align:start position:0% +The Roots command to find the roots +and I was disappointed actually I was + + align:start position:0% +and I was disappointed actually I was + + + align:start position:0% +and I was disappointed actually I was +speaking to Cle moly yesterday but I + + align:start position:0% +speaking to Cle moly yesterday but I + + + align:start position:0% +speaking to Cle moly yesterday but I +didn't mention this uh that it found + + align:start position:0% +didn't mention this uh that it found + + + align:start position:0% +didn't mention this uh that it found +imaginary Roots complex + + align:start position:0% +imaginary Roots complex + + + align:start position:0% +imaginary Roots complex +Roots uh with quite a significant + + align:start position:0% +Roots uh with quite a significant + + + align:start position:0% +Roots uh with quite a significant +imaginary part in other words the the so + + align:start position:0% +imaginary part in other words the the so + + + align:start position:0% +imaginary part in other words the the so +I I'll come back to this but here is the + + align:start position:0% +I I'll come back to this but here is the + + + align:start position:0% +I I'll come back to this but here is the +complex plane yeah I I may have + + align:start position:0% +complex plane yeah I I may have + + + align:start position:0% +complex plane yeah I I may have +mentioned this here's the complex plane + + align:start position:0% +mentioned this here's the complex plane + + + align:start position:0% +mentioned this here's the complex plane +our polinomial had four roots here at + + align:start position:0% +our polinomial had four roots here at + + + align:start position:0% +our polinomial had four roots here at +minus1 and what mat lab produced were + + align:start position:0% +minus1 and what mat lab produced were + + + align:start position:0% +minus1 and what mat lab produced were +four roots in a little circle around + + align:start position:0% +four roots in a little circle around + + + align:start position:0% +four roots in a little circle around +minus one and partly complex okay so all + + align:start position:0% +minus one and partly complex okay so all + + + align:start position:0% +minus one and partly complex okay so all +that's just to say Do + + align:start position:0% +that's just to say Do + + + align:start position:0% +that's just to say Do +not if you can avoid it don't get + + align:start position:0% +not if you can avoid it don't get + + + align:start position:0% +not if you can avoid it don't get +polinomial of high degree and look for + + align:start position:0% +polinomial of high degree and look for + + + align:start position:0% +polinomial of high degree and look for +their Roots got to find a better way + + align:start position:0% +their Roots got to find a better way + + + align:start position:0% +their Roots got to find a better way +okay got to find a better way so so what + + align:start position:0% +okay got to find a better way so so what + + + align:start position:0% +okay got to find a better way so so what +what's a better way + + align:start position:0% +what's a better way + + + align:start position:0% +what's a better way +well here's a here's here's this QR + + align:start position:0% +well here's a here's here's this QR + + + align:start position:0% +well here's a here's here's this QR +method so so somehow out of uh this is + + align:start position:0% +method so so somehow out of uh this is + + + align:start position:0% +method so so somehow out of uh this is +this is all uh numerical linear algebra + + align:start position:0% +this is all uh numerical linear algebra + + + align:start position:0% +this is all uh numerical linear algebra +in my lifetime and maybe some of yours + + align:start position:0% +in my lifetime and maybe some of yours + + + align:start position:0% +in my lifetime and maybe some of yours +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the like when we were doing well I + + align:start position:0% +the like when we were doing well I + + + align:start position:0% +the like when we were doing well I +wasn't doing calculations in World War + + align:start position:0% +wasn't doing calculations in World War + + + align:start position:0% +wasn't doing calculations in World War +II but uh when calculations were being + + align:start position:0% +II but uh when calculations were being + + + align:start position:0% +II but uh when calculations were being +done in World War II there was no good + + align:start position:0% +done in World War II there was no good + + + align:start position:0% +done in World War II there was no good +way to find the igen values of a matrix + + align:start position:0% +way to find the igen values of a matrix + + + align:start position:0% +way to find the igen values of a matrix +even of order 20 which mat lab will now + + align:start position:0% +even of order 20 which mat lab will now + + + align:start position:0% +even of order 20 which mat lab will now +just do in an + + align:start position:0% +just do in an + + + align:start position:0% +just do in an +instant uh and uh because people thought + + align:start position:0% +instant uh and uh because people thought + + + align:start position:0% +instant uh and uh because people thought +well we take that polinomial of degree + + align:start position:0% +well we take that polinomial of degree + + + align:start position:0% +well we take that polinomial of degree +20 find its roots and and it was + + align:start position:0% +20 find its roots and and it was + + + align:start position:0% +20 find its roots and and it was +ridiculous okay so out of that out of + + align:start position:0% +ridiculous okay so out of that out of + + + align:start position:0% +ridiculous okay so out of that out of +that need to find igen values gradually + + align:start position:0% +that need to find igen values gradually + + + align:start position:0% +that need to find igen values gradually +emerged something called the QR method + + align:start position:0% +emerged something called the QR method + + + align:start position:0% +emerged something called the QR method +so here's the QR method + + align:start position:0% +so here's the QR method + + + align:start position:0% +so here's the QR method +in a nutshell you you this you + + align:start position:0% +in a nutshell you you this you + + + align:start position:0% +in a nutshell you you this you +orthogonalize you orthogonalize so you + + align:start position:0% +orthogonalize you orthogonalize so you + + + align:start position:0% +orthogonalize you orthogonalize so you +write you you you factor a into + + align:start position:0% + + + + align:start position:0% + +QR and then the next step of the method + + align:start position:0% +QR and then the next step of the method + + + align:start position:0% +QR and then the next step of the method +is you form you + + align:start position:0% +is you form you + + + align:start position:0% +is you form you +form r q you reverse the order of those + + align:start position:0% +form r q you reverse the order of those + + + align:start position:0% +form r q you reverse the order of those +two of those two uh + + align:start position:0% +two of those two uh + + + align:start position:0% +two of those two uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +factors and H how is that Matrix related + + align:start position:0% +factors and H how is that Matrix related + + + align:start position:0% +factors and H how is that Matrix related +to that one so let let me let me give + + align:start position:0% +to that one so let let me let me give + + + align:start position:0% +to that one so let let me let me give +this name this Matrix a name a two say + + align:start position:0% +this name this Matrix a name a two say + + + align:start position:0% +this name this Matrix a name a two say +this is A1 QR this is our starting + + align:start position:0% +this is A1 QR this is our starting + + + align:start position:0% +this is A1 QR this is our starting +Matrix okay so you form this Matrix and + + align:start position:0% +Matrix okay so you form this Matrix and + + + align:start position:0% +Matrix okay so you form this Matrix and +this is A2 and how is it related to A1 + + align:start position:0% +this is A2 and how is it related to A1 + + + align:start position:0% +this is A2 and how is it related to A1 +can you see what we've done + + align:start position:0% +can you see what we've done + + + align:start position:0% +can you see what we've done +we've yeah we've sort of rotated + + align:start position:0% + + + + align:start position:0% + +so if I started with + + align:start position:0% +so if I started with + + + align:start position:0% +so if I started with +A1 which was the QR what have I done to + + align:start position:0% +A1 which was the QR what have I done to + + + align:start position:0% +A1 which was the QR what have I done to +get r + + align:start position:0% +get r + + + align:start position:0% +get r +q well I guess I've multiplied by maybe + + align:start position:0% +q well I guess I've multiplied by maybe + + + align:start position:0% +q well I guess I've multiplied by maybe +a q inverse which is a q transpose on + + align:start position:0% +a q inverse which is a q transpose on + + + align:start position:0% +a q inverse which is a q transpose on +one side and by Q on the other is that + + align:start position:0% +one side and by Q on the other is that + + + align:start position:0% +one side and by Q on the other is that +right if I if I had QR and I multiplied + + align:start position:0% +right if I if I had QR and I multiplied + + + align:start position:0% +right if I if I had QR and I multiplied +by Q inverse on the left and Q on the + + align:start position:0% +by Q inverse on the left and Q on the + + + align:start position:0% +by Q inverse on the left and Q on the +right then that gave me + + align:start position:0% +right then that gave me + + + align:start position:0% +right then that gave me +RQ + + align:start position:0% + + + + align:start position:0% + +okay that's one + + align:start position:0% +okay that's one + + + align:start position:0% +okay that's one +step that doesn't get you too far but it + + align:start position:0% +step that doesn't get you too far but it + + + align:start position:0% +step that doesn't get you too far but it +and the cost was well we've just seen + + align:start position:0% +and the cost was well we've just seen + + + align:start position:0% +and the cost was well we've just seen +what the cost is now so now we've got A2 + + align:start position:0% +what the cost is now so now we've got A2 + + + align:start position:0% +what the cost is now so now we've got A2 +okay now we Factor + + align:start position:0% +okay now we Factor + + + align:start position:0% +okay now we Factor +A2 the new guy into QR that'll be a + + align:start position:0% +A2 the new guy into QR that'll be a + + + align:start position:0% +A2 the new guy into QR that'll be a +different QR oh I've got to put ones on + + align:start position:0% +different QR oh I've got to put ones on + + + align:start position:0% +different QR oh I've got to put ones on +these things so these were the + + align:start position:0% + + + + align:start position:0% + +ones ones were the subscripts all along + + align:start position:0% +ones ones were the subscripts all along + + + align:start position:0% +ones ones were the subscripts all along +there okay now take A2 take + + align:start position:0% +there okay now take A2 take + + + align:start position:0% +there okay now take A2 take +A2 and Factor it into the the + + align:start position:0% +A2 and Factor it into the the + + + align:start position:0% +A2 and Factor it into the the +normal this factorization that I keep + + align:start position:0% +normal this factorization that I keep + + + align:start position:0% +normal this factorization that I keep +referring to it's it's the gram Schmid + + align:start position:0% +referring to it's it's the gram Schmid + + + align:start position:0% +referring to it's it's the gram Schmid +idea it's we could we could uh create + + align:start position:0% +idea it's we could we could uh create + + + align:start position:0% +idea it's we could we could uh create +the algorithm that does it and here it + + align:start position:0% +the algorithm that does it and here it + + + align:start position:0% +the algorithm that does it and here it +is in Matrix language we Factor it like + + align:start position:0% +is in Matrix language we Factor it like + + + align:start position:0% +is in Matrix language we Factor it like +that now what what's the next step + + align:start position:0% +that now what what's the next step + + + align:start position:0% +that now what what's the next step +you're going to now now you can carry it + + align:start position:0% +you're going to now now you can carry it + + + align:start position:0% +you're going to now now you can carry it +on from here what what will be + + align:start position:0% + + + + align:start position:0% + +A3 reverse the r and the Q put the r and + + align:start position:0% +A3 reverse the r and the Q put the r and + + + align:start position:0% +A3 reverse the r and the Q put the r and +the Q in the opposite + + align:start position:0% +the Q in the opposite + + + align:start position:0% +the Q in the opposite +order and that will be A3 and again + + align:start position:0% +order and that will be A3 and again + + + align:start position:0% +order and that will be A3 and again +that's the same as Q2 inverse + + align:start position:0% +that's the same as Q2 inverse + + + align:start position:0% +that's the same as Q2 inverse +A2 + + align:start position:0% +A2 + + + align:start position:0% +A2 +Q2 right when we when we put the Q on + + align:start position:0% +Q2 right when we when we put the Q on + + + align:start position:0% +Q2 right when we when we put the Q on +the other side we've multiplied by Q + + align:start position:0% +the other side we've multiplied by Q + + + align:start position:0% +the other side we've multiplied by Q +from the right and by Q inverse from the + + align:start position:0% +from the right and by Q inverse from the + + + align:start position:0% +from the right and by Q inverse from the +left okay now what first of all what's + + align:start position:0% +left okay now what first of all what's + + + align:start position:0% +left okay now what first of all what's +this got to do with igen values and + + align:start position:0% +this got to do with igen values and + + + align:start position:0% +this got to do with igen values and +second is it getting us + + align:start position:0% +second is it getting us + + + align:start position:0% +second is it getting us +anywhere all right first question what + + align:start position:0% +anywhere all right first question what + + + align:start position:0% +anywhere all right first question what +does it have to do with igen values + + align:start position:0% +does it have to do with igen values + + + align:start position:0% +does it have to do with igen values +well my claim is that the igen values + + align:start position:0% +well my claim is that the igen values + + + align:start position:0% +well my claim is that the igen values +aren't changing that A2 and A3 and A4 + + align:start position:0% +aren't changing that A2 and A3 and A4 + + + align:start position:0% +aren't changing that A2 and A3 and A4 +and the whole sequence of numbers of + + align:start position:0% +and the whole sequence of numbers of + + + align:start position:0% +and the whole sequence of numbers of +matrices has the same igen values as the + + align:start position:0% +matrices has the same igen values as the + + + align:start position:0% +matrices has the same igen values as the +original so that's 0.1 so that I'm + + align:start position:0% +original so that's 0.1 so that I'm + + + align:start position:0% +original so that's 0.1 so that I'm +speaking now of of of of Left + + align:start position:0% +speaking now of of of of Left + + + align:start position:0% +speaking now of of of of Left +orthogonality for the moment and and + + align:start position:0% +orthogonality for the moment and and + + + align:start position:0% +orthogonality for the moment and and +talking about this famous method for + + align:start position:0% +talking about this famous method for + + + align:start position:0% +talking about this famous method for +finding igen values can you tell me why + + align:start position:0% +finding igen values can you tell me why + + + align:start position:0% +finding igen values can you tell me why +A1 and A2 have the same igen + + align:start position:0% + + + + align:start position:0% + +values that that's a very important + + align:start position:0% +values that that's a very important + + + align:start position:0% +values that that's a very important +point and why is if a vector is we have + + align:start position:0% +point and why is if a vector is we have + + + align:start position:0% +point and why is if a vector is we have +a vector that's being say stretched + + align:start position:0% +a vector that's being say stretched + + + align:start position:0% +a vector that's being say stretched +along line all right let's let's take + + align:start position:0% +along line all right let's let's take + + + align:start position:0% +along line all right let's let's take +rting right we're Ro + + align:start position:0% + + + + align:start position:0% + +right rotate right that's right so + + align:start position:0% +right rotate right that's right so + + + align:start position:0% +right rotate right that's right so +you're not exactly we had a vector the + + align:start position:0% +you're not exactly we had a vector the + + + align:start position:0% +you're not exactly we had a vector the +original a which I guess we're now + + align:start position:0% +original a which I guess we're now + + + align:start position:0% +original a which I guess we're now +calling + + align:start position:0% +calling + + + align:start position:0% +calling +A1 had a vector X right that was being + + align:start position:0% +A1 had a vector X right that was being + + + align:start position:0% +A1 had a vector X right that was being +stretched + + align:start position:0% +stretched + + + align:start position:0% +stretched +good + + align:start position:0% +good + + + align:start position:0% +good +now uh what about a let's see what If I + + align:start position:0% +now uh what about a let's see what If I + + + align:start position:0% +now uh what about a let's see what If I +multiply do this as you said I should + + align:start position:0% +multiply do this as you said I should + + + align:start position:0% +multiply do this as you said I should +just now rotate everything so shall I + + align:start position:0% +just now rotate everything so shall I + + + align:start position:0% +just now rotate everything so shall I +rotate it by q1 + + align:start position:0% +rotate it by q1 + + + align:start position:0% +rotate it by q1 +inverse so I'll rotate everything by q1 + + align:start position:0% + + + + align:start position:0% + +inverse and now my + + align:start position:0% +inverse and now my + + + align:start position:0% +inverse and now my +X + + align:start position:0% +X + + + align:start position:0% +X +let me call that q1 y let me just change + + align:start position:0% +let me call that q1 y let me just change + + + align:start position:0% +let me call that q1 y let me just change +again I'm rotating so let this x be q1 + + align:start position:0% + + + + align:start position:0% + +y so this x is q1 y I'm doing a proof by + + align:start position:0% +y so this x is q1 y I'm doing a proof by + + + align:start position:0% +y so this x is q1 y I'm doing a proof by +a ratier here which is easy on the + + align:start position:0% +a ratier here which is easy on the + + + align:start position:0% +a ratier here which is easy on the +Blackboard what have I got well q1 + + align:start position:0% +Blackboard what have I got well q1 + + + align:start position:0% +Blackboard what have I got well q1 +inverse q1 is + + align:start position:0% +inverse q1 is + + + align:start position:0% +inverse q1 is +identity so I've learned that q1 inverse + + align:start position:0% +identity so I've learned that q1 inverse + + + align:start position:0% +identity so I've learned that q1 inverse +A1 q1 y this is the igen vector + + align:start position:0% +A1 q1 y this is the igen vector + + + align:start position:0% +A1 q1 y this is the igen vector +but this igen value is the same you you + + align:start position:0% +but this igen value is the same you you + + + align:start position:0% +but this igen value is the same you you +said it and I and I probably didn't do + + align:start position:0% +said it and I and I probably didn't do + + + align:start position:0% +said it and I and I probably didn't do +it as clearly as you said it uh that + + align:start position:0% +it as clearly as you said it uh that + + + align:start position:0% +it as clearly as you said it uh that +that if uh if I have an i Vector of A1 + + align:start position:0% +that if uh if I have an i Vector of A1 + + + align:start position:0% +that if uh if I have an i Vector of A1 +it's a vector that's just stretched when + + align:start position:0% +it's a vector that's just stretched when + + + align:start position:0% +it's a vector that's just stretched when +I + + align:start position:0% +I + + + align:start position:0% +I +rotate it rotates into a vector that's + + align:start position:0% +rotate it rotates into a vector that's + + + align:start position:0% +rotate it rotates into a vector that's +also just + + align:start position:0% +also just + + + align:start position:0% +also just +stretched that that's the that's the key + + align:start position:0% +stretched that that's the that's the key + + + align:start position:0% +stretched that that's the that's the key +idea so uh the Aon values don't change + + align:start position:0% +idea so uh the Aon values don't change + + + align:start position:0% +idea so uh the Aon values don't change +and remember from the very beginning the + + align:start position:0% +and remember from the very beginning the + + + align:start position:0% +and remember from the very beginning the +matrices aren't getting any + + align:start position:0% +matrices aren't getting any + + + align:start position:0% +matrices aren't getting any +Wilder and in fact they're getting + + align:start position:0% +Wilder and in fact they're getting + + + align:start position:0% +Wilder and in fact they're getting +better that's what that's somewhat of a + + align:start position:0% +better that's what that's somewhat of a + + + align:start position:0% +better that's what that's somewhat of a +mystery but it's it's it it's uh true + + align:start position:0% +mystery but it's it's it it's uh true + + + align:start position:0% +mystery but it's it's it it's uh true +that that these this sequence of + + align:start position:0% +that that these this sequence of + + + align:start position:0% +that that these this sequence of +matrices gets more and more + + align:start position:0% +matrices gets more and more + + + align:start position:0% +matrices gets more and more +diagonal the igen values in about four + + align:start position:0% +diagonal the igen values in about four + + + align:start position:0% +diagonal the igen values in about four +or five steps or the at least one of the + + align:start position:0% +or five steps or the at least one of the + + + align:start position:0% +or five steps or the at least one of the +igen values will show up on the main + + align:start position:0% +igen values will show up on the main + + + align:start position:0% +igen values will show up on the main +diagonal with just little off diagonal + + align:start position:0% +diagonal with just little off diagonal + + + align:start position:0% +diagonal with just little off diagonal +entries so it's slightly wrong I I can't + + align:start position:0% +entries so it's slightly wrong I I can't + + + align:start position:0% +entries so it's slightly wrong I I can't +get it exactly right + + align:start position:0% +get it exactly right + + + align:start position:0% +get it exactly right +but I can get it as accurately as + + align:start position:0% +but I can get it as accurately as + + + align:start position:0% +but I can get it as accurately as +possible so that's this famous QR method + + align:start position:0% +possible so that's this famous QR method + + + align:start position:0% +possible so that's this famous QR method +you see why it's named QR because at + + align:start position:0% +you see why it's named QR because at + + + align:start position:0% +you see why it's named QR because at +every step we're doing a QR + + align:start position:0% +every step we're doing a QR + + + align:start position:0% +every step we're doing a QR +factorization we're doing we're doing a + + align:start position:0% +factorization we're doing we're doing a + + + align:start position:0% +factorization we're doing we're doing a +matrix multiplication to get the new + + align:start position:0% +matrix multiplication to get the new + + + align:start position:0% +matrix multiplication to get the new +Matrix we're doing QR on that a matrix + + align:start position:0% +Matrix we're doing QR on that a matrix + + + align:start position:0% +Matrix we're doing QR on that a matrix +multiplication to get A3 and so forth + + align:start position:0% +multiplication to get A3 and so forth + + + align:start position:0% +multiplication to get A3 and so forth +and quite efficiently the igen values + + align:start position:0% +and quite efficiently the igen values + + + align:start position:0% +and quite efficiently the igen values +come out that's uh and which that second + + align:start position:0% +come out that's uh and which that second + + + align:start position:0% +come out that's uh and which that second +part I + + align:start position:0% +part I + + + align:start position:0% +part I +haven't uh explained here that why this + + align:start position:0% +haven't uh explained here that why this + + + align:start position:0% +haven't uh explained here that why this +thing should get closer and closer to + + align:start position:0% +thing should get closer and closer to + + + align:start position:0% +thing should get closer and closer to +the igen values we could test it if we + + align:start position:0% +the igen values we could test it if we + + + align:start position:0% +the igen values we could test it if we +wanted uh on uh on a particular on a 2 + + align:start position:0% +wanted uh on uh on a particular on a 2 + + + align:start position:0% +wanted uh on uh on a particular on a 2 +by two model to see why that would + + align:start position:0% +by two model to see why that would + + + align:start position:0% +by two model to see why that would +happen uh + + align:start position:0% +happen uh + + + align:start position:0% +happen uh +if if we uh maybe maybe I'll just I mean + + align:start position:0% +if if we uh maybe maybe I'll just I mean + + + align:start position:0% +if if we uh maybe maybe I'll just I mean +the so there's a discussion of this in + + align:start position:0% +the so there's a discussion of this in + + + align:start position:0% +the so there's a discussion of this in +the uh in the + + align:start position:0% +the uh in the + + + align:start position:0% +the uh in the +textbook uh so some of this lecture is + + align:start position:0% +textbook uh so some of this lecture is + + + align:start position:0% +textbook uh so some of this lecture is +is dis quite a bit of this lecture is + + align:start position:0% +is dis quite a bit of this lecture is + + + align:start position:0% +is dis quite a bit of this lecture is +discussed in chapter five of the applied + + align:start position:0% +discussed in chapter five of the applied + + + align:start position:0% +discussed in chapter five of the applied +math book The the blue + + align:start position:0% +math book The the blue + + + align:start position:0% +math book The the blue +book um so I've covered the topics that + + align:start position:0% +book um so I've covered the topics that + + + align:start position:0% +book um so I've covered the topics that +that uh I promised and uh in a what I + + align:start position:0% +that uh I promised and uh in a what I + + + align:start position:0% +that uh I promised and uh in a what I +feel is slightly uh + + align:start position:0% +feel is slightly uh + + + align:start position:0% +feel is slightly uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um + + align:start position:0% +um + + + align:start position:0% +um +noisy um uh manner more maybe less + + align:start position:0% +noisy um uh manner more maybe less + + + align:start position:0% +noisy um uh manner more maybe less +smooth and uh I wish uh can I recap + + align:start position:0% +smooth and uh I wish uh can I recap + + + align:start position:0% +smooth and uh I wish uh can I recap +the the virtues of orthogonal matrices + + align:start position:0% +the the virtues of orthogonal matrices + + + align:start position:0% +the the virtues of orthogonal matrices +are lengths don't change angles don't + + align:start position:0% +are lengths don't change angles don't + + + align:start position:0% +are lengths don't change angles don't +change igen values don't change + + align:start position:0% +change igen values don't change + + + align:start position:0% +change igen values don't change +and uh and therefore this question + + align:start position:0% +and uh and therefore this question + + + align:start position:0% +and uh and therefore this question +arises if we have a bunch of vectors in + + align:start position:0% +arises if we have a bunch of vectors in + + + align:start position:0% +arises if we have a bunch of vectors in +a should + + align:start position:0% +a should + + + align:start position:0% +a should +we straighten them out to be + + align:start position:0% +we straighten them out to be + + + align:start position:0% +we straighten them out to be +orthogonal by uh a matrix R and that + + align:start position:0% +orthogonal by uh a matrix R and that + + + align:start position:0% +orthogonal by uh a matrix R and that +process that's one of the the the most + + align:start position:0% +process that's one of the the the most + + + align:start position:0% +process that's one of the the the most +important uh uh factorizations in uh in + + align:start position:0% +important uh uh factorizations in uh in + + + align:start position:0% +important uh uh factorizations in uh in +u v algebra so uh I might say one more + + align:start position:0% +u v algebra so uh I might say one more + + + align:start position:0% +u v algebra so uh I might say one more +word about that at the beginning of the + + align:start position:0% +word about that at the beginning of the + + + align:start position:0% +word about that at the beginning of the +next lecture this a equal QR because I + + align:start position:0% +next lecture this a equal QR because I + + + align:start position:0% +next lecture this a equal QR because I +pupped it up there without saying where + + align:start position:0% +pupped it up there without saying where + + + align:start position:0% +pupped it up there without saying where +it came from uh but uh the main point is + + align:start position:0% +it came from uh but uh the main point is + + + align:start position:0% +it came from uh but uh the main point is +that then leas squares projections all + + align:start position:0% +that then leas squares projections all + + + align:start position:0% +that then leas squares projections all +the operations of uh linear algebra + + align:start position:0% +the operations of uh linear algebra + + + align:start position:0% +the operations of uh linear algebra +become so simple when we have orthogonal + + align:start position:0% +become so simple when we have orthogonal + + + align:start position:0% +become so simple when we have orthogonal +matrices uh so I hope that's uh okay as + + align:start position:0% +matrices uh so I hope that's uh okay as + + + align:start position:0% +matrices uh so I hope that's uh okay as +a as a uh justification for uh + + align:start position:0% +a as a uh justification for uh + + + align:start position:0% +a as a uh justification for uh +concentrating on these on these + + align:start position:0% +concentrating on these on these + + + align:start position:0% +concentrating on these on these +orthonormal + + align:start position:0% +orthonormal + + + align:start position:0% +orthonormal +guys I could take a question or two but + + align:start position:0% +guys I could take a question or two but + + + align:start position:0% +guys I could take a question or two but +or yes thanks and I'll repeat comp + + align:start position:0% +or yes thanks and I'll repeat comp + + + align:start position:0% +or yes thanks and I'll repeat comp +comp yes comparing the + + align:start position:0% + + + + align:start position:0% + +cost uh I will but actually my next so + + align:start position:0% +cost uh I will but actually my next so + + + align:start position:0% +cost uh I will but actually my next so +the question was should I uh introduce + + align:start position:0% +the question was should I uh introduce + + + align:start position:0% +the question was should I uh introduce +what safety means well could we how + + align:start position:0% +what safety means well could we how + + + align:start position:0% +what safety means well could we how +could we estimate the the uh numer how + + align:start position:0% +could we estimate the the uh numer how + + + align:start position:0% +could we estimate the the uh numer how +how can we estimate numerical errors how + + align:start position:0% +how can we estimate numerical errors how + + + align:start position:0% +how can we estimate numerical errors how +which problems + + align:start position:0% +which problems + + + align:start position:0% +which problems +are ill conditioned which problems are + + align:start position:0% +are ill conditioned which problems are + + + align:start position:0% +are ill conditioned which problems are +well conditioned and yeah so maybe the + + align:start position:0% +well conditioned and yeah so maybe the + + + align:start position:0% +well conditioned and yeah so maybe the +next leor is the perfect one to to pin + + align:start position:0% +next leor is the perfect one to to pin + + + align:start position:0% +next leor is the perfect one to to pin +down that idea of conditioning condition + + align:start position:0% +down that idea of conditioning condition + + + align:start position:0% +down that idea of conditioning condition +numbers okay so let's take our break + + align:start position:0% +numbers okay so let's take our break + + + align:start position:0% +numbers okay so let's take our break +another question how do you know when to + + align:start position:0% +another question how do you know when to + + + align:start position:0% +another question how do you know when to +stop here you oh how do you know when to + + align:start position:0% +stop here you oh how do you know when to + + + align:start position:0% +stop here you oh how do you know when to +stop well what you + + align:start position:0% +stop well what you + + + align:start position:0% +stop well what you +see in this QR method so the question is + + align:start position:0% +see in this QR method so the question is + + + align:start position:0% +see in this QR method so the question is +when to stop what you'll see in this QR + + align:start position:0% +when to stop what you'll see in this QR + + + align:start position:0% +when to stop what you'll see in this QR +method is uh it it happens first down + + align:start position:0% +method is uh it it happens first down + + + align:start position:0% +method is uh it it happens first down +here we get a tiny little number which + + align:start position:0% +here we get a tiny little number which + + + align:start position:0% +here we get a tiny little number which +of course I'm going to call Epsilon + + align:start position:0% +of course I'm going to call Epsilon + + + align:start position:0% +of course I'm going to call Epsilon +meaning Tiny uh shows up there and and + + align:start position:0% +meaning Tiny uh shows up there and and + + + align:start position:0% +meaning Tiny uh shows up there and and +we'll keep we'll stay we actually will + + align:start position:0% +we'll keep we'll stay we actually will + + + align:start position:0% +we'll keep we'll stay we actually will +stay symmetric so we'll we'll have still + + align:start position:0% +stay symmetric so we'll we'll have still + + + align:start position:0% +stay symmetric so we'll we'll have still +significant numbers beside the D + + align:start position:0% +significant numbers beside the D + + + align:start position:0% +significant numbers beside the D +diagonal but but the first ones to get + + align:start position:0% +diagonal but but the first ones to get + + + align:start position:0% +diagonal but but the first ones to get +small are that so when that's below some + + align:start position:0% +small are that so when that's below some + + + align:start position:0% +small are that so when that's below some +tolerance then this is an igen value + + align:start position:0% +tolerance then this is an igen value + + + align:start position:0% +tolerance then this is an igen value +because if that was a zero that really + + align:start position:0% +because if that was a zero that really + + + align:start position:0% +because if that was a zero that really +would be an igen value and then you + + align:start position:0% +would be an igen value and then you + + + align:start position:0% +would be an igen value and then you +could if you liked uh knock that part of + + align:start position:0% +could if you liked uh knock that part of + + + align:start position:0% +could if you liked uh knock that part of +the Matrix out keep going deflation + + align:start position:0% +the Matrix out keep going deflation + + + align:start position:0% +the Matrix out keep going deflation +that's called another three or four this + + align:start position:0% +that's called another three or four this + + + align:start position:0% +that's called another three or four this +guy will have been getting smaller + + align:start position:0% +guy will have been getting smaller + + + align:start position:0% +guy will have been getting smaller +another three or four steps it'll be an + + align:start position:0% +another three or four steps it'll be an + + + align:start position:0% +another three or four steps it'll be an +Epsilon and you'll see sitting there the + + align:start position:0% +Epsilon and you'll see sitting there the + + + align:start position:0% +Epsilon and you'll see sitting there the +next igen value it's quite like uh + + align:start position:0% +next igen value it's quite like uh + + + align:start position:0% +next igen value it's quite like uh +wonderful uh and and and actually it's + + align:start position:0% +wonderful uh and and and actually it's + + + align:start position:0% +wonderful uh and and and actually it's +it has been the winning method for igen + + align:start position:0% +it has been the winning method for igen + + + align:start position:0% +it has been the winning method for igen +values until somebody came up with an + + align:start position:0% +values until somebody came up with an + + + align:start position:0% +values until somebody came up with an +alternative just a year a couple of + + align:start position:0% +alternative just a year a couple of + + + align:start position:0% +alternative just a year a couple of +years ago uh which I won't attempt to + + align:start position:0% +years ago uh which I won't attempt to + + + align:start position:0% +years ago uh which I won't attempt to +describe time already having run out but + + align:start position:0% +describe time already having run out but + + + align:start position:0% +describe time already having run out but +I can say roughly what happens he he the + + align:start position:0% +I can say roughly what happens he he the + + + align:start position:0% +I can say roughly what happens he he the +suggest this new algorithm is called + + align:start position:0% +suggest this new algorithm is called + + + align:start position:0% +suggest this new algorithm is called +divide and conquer so this time just as + + align:start position:0% +divide and conquer so this time just as + + + align:start position:0% +divide and conquer so this time just as +there's so much Ingenuity in this stuff + + align:start position:0% +there's so much Ingenuity in this stuff + + + align:start position:0% +there's so much Ingenuity in this stuff +so we let's say we have one of our + + align:start position:0% +so we let's say we have one of our + + + align:start position:0% +so we let's say we have one of our +tridiagonal matrices which is actually + + align:start position:0% +tridiagonal matrices which is actually + + + align:start position:0% +tridiagonal matrices which is actually +the good way the first thing to do in in + + align:start position:0% +the good way the first thing to do in in + + + align:start position:0% +the good way the first thing to do in in +all these methods is to get get these + + align:start position:0% +all these methods is to get get these + + + align:start position:0% +all these methods is to get get these +zeros that I spoke about at the + + align:start position:0% +zeros that I spoke about at the + + + align:start position:0% +zeros that I spoke about at the +beginning of the lecture we can get + + align:start position:0% +beginning of the lecture we can get + + + align:start position:0% +beginning of the lecture we can get +zeros here no problem what we can can't + + align:start position:0% +zeros here no problem what we can can't + + + align:start position:0% +zeros here no problem what we can can't +do is make those zeros because if we + + align:start position:0% +do is make those zeros because if we + + + align:start position:0% +do is make those zeros because if we +could do that then the igen values would + + align:start position:0% +could do that then the igen values would + + + align:start position:0% +could do that then the igen values would +would be sitting there we can't do that + + align:start position:0% +would be sitting there we can't do that + + + align:start position:0% +would be sitting there we can't do that +except by some idea so this QR idea + + align:start position:0% +except by some idea so this QR idea + + + align:start position:0% +except by some idea so this QR idea +makes gets + + align:start position:0% +makes gets + + + align:start position:0% +makes gets +zeros like gradually but pretty + + align:start position:0% +zeros like gradually but pretty + + + align:start position:0% +zeros like gradually but pretty +quickly here's this divide and conquer + + align:start position:0% +quickly here's this divide and conquer + + + align:start position:0% +quickly here's this divide and conquer +idea the divide and conquer idea is deal + + align:start position:0% +idea the divide and conquer idea is deal + + + align:start position:0% +idea the divide and conquer idea is deal +with that Matrix and this + + align:start position:0% +with that Matrix and this + + + align:start position:0% +with that Matrix and this +one find suppose we knew the igen value + + align:start position:0% +one find suppose we knew the igen value + + + align:start position:0% +one find suppose we knew the igen value +of this half siiz guy that's going to be + + align:start position:0% +of this half siiz guy that's going to be + + + align:start position:0% +of this half siiz guy that's going to be +faster and the IG values of this half + + align:start position:0% +faster and the IG values of this half + + + align:start position:0% +faster and the IG values of this half +siiz guy + + align:start position:0% +siiz guy + + + align:start position:0% +siiz guy +then what's what's well we haven't got + + align:start position:0% +then what's what's well we haven't got + + + align:start position:0% +then what's what's well we haven't got +those aren't IG values of the whole + + align:start position:0% +those aren't IG values of the whole + + + align:start position:0% +those aren't IG values of the whole +thing why not because of this little + + align:start position:0% +thing why not because of this little + + + align:start position:0% +thing why not because of this little +rank two + + align:start position:0% +rank two + + + align:start position:0% +rank two +Matrix that's connecting them + + align:start position:0% +Matrix that's connecting them + + + align:start position:0% +Matrix that's connecting them +so there's an iteration of course to + + align:start position:0% +so there's an iteration of course to + + + align:start position:0% +so there's an iteration of course to +gradually work connect + + align:start position:0% +gradually work connect + + + align:start position:0% +gradually work connect +so you see the idea of you see why the + + align:start position:0% +so you see the idea of you see why the + + + align:start position:0% +so you see the idea of you see why the +name divide and conquer you you divide + + align:start position:0% +name divide and conquer you you divide + + + align:start position:0% +name divide and conquer you you divide +the Matrix into half you work on this + + align:start position:0% +the Matrix into half you work on this + + + align:start position:0% +the Matrix into half you work on this +half work on this half and then make the + + align:start position:0% +half work on this half and then make the + + + align:start position:0% +half work on this half and then make the +the adjustment which of course is going + + align:start position:0% +the adjustment which of course is going + + + align:start position:0% +the adjustment which of course is going +to be the serious part to deal with that + + align:start position:0% +to be the serious part to deal with that + + + align:start position:0% +to be the serious part to deal with that +and then of course how do you do this + + align:start position:0% +and then of course how do you do this + + + align:start position:0% +and then of course how do you do this +one yeah Divine conquer again right you + + align:start position:0% +one yeah Divine conquer again right you + + + align:start position:0% +one yeah Divine conquer again right you +we've got the idea uh except for knowing + + align:start position:0% +we've got the idea uh except for knowing + + + align:start position:0% +we've got the idea uh except for knowing +what to do with this and seems such a + + align:start position:0% +what to do with this and seems such a + + + align:start position:0% +what to do with this and seems such a +natural idea it's amazing that uh uh it + + align:start position:0% +natural idea it's amazing that uh uh it + + + align:start position:0% +natural idea it's amazing that uh uh it +it didn't come until pretty + + align:start position:0% +it didn't come until pretty + + + align:start position:0% +it didn't come until pretty +recently okay you're seeing like + + align:start position:0% +recently okay you're seeing like + + + align:start position:0% +recently okay you're seeing like +numerical linear algebra uh uh in in + + align:start position:0% +numerical linear algebra uh uh in in + + + align:start position:0% +numerical linear algebra uh uh in in +commotion here and uh the second lecture + + align:start position:0% +commotion here and uh the second lecture + + + align:start position:0% +commotion here and uh the second lecture +today will + + align:start position:0% +today will + + + align:start position:0% +today will +be uh the other great factorization some + + align:start position:0% +be uh the other great factorization some + + + align:start position:0% +be uh the other great factorization some +people say the greatest the singular + + align:start position:0% +people say the greatest the singular + + + align:start position:0% +people say the greatest the singular +value decomposition uh Jean goab would + + align:start position:0% +value decomposition uh Jean goab would + + + align:start position:0% +value decomposition uh Jean goab would +say the greatest yes okay + + align:start position:0% + + + + align:start position:0% + +thanks \ No newline at end of file diff --git a/5ucfHd8FWKw.txt b/5ucfHd8FWKw.txt new file mode 100644 index 0000000000000000000000000000000000000000..f6be13473165cf9a2dd602e483f17686358e5246 --- /dev/null +++ b/5ucfHd8FWKw.txt @@ -0,0 +1,195 @@ +align:start position:0% + +here we will learn to distinguish + + align:start position:0% +here we will learn to distinguish + + + align:start position:0% +here we will learn to distinguish +between vectors and scalars vectors are + + align:start position:0% +between vectors and scalars vectors are + + + align:start position:0% +between vectors and scalars vectors are +objects that have both a magnitude a + + align:start position:0% +objects that have both a magnitude a + + + align:start position:0% +objects that have both a magnitude a +single number and a + + align:start position:0% +single number and a + + + align:start position:0% +single number and a +direction whereas scalers have only a + + align:start position:0% +direction whereas scalers have only a + + + align:start position:0% +direction whereas scalers have only a +magnitude let's see some examples of + + align:start position:0% +magnitude let's see some examples of + + + align:start position:0% +magnitude let's see some examples of +each the length of something is a scalar + + align:start position:0% +each the length of something is a scalar + + + align:start position:0% +each the length of something is a scalar +because it's just the + + align:start position:0% +because it's just the + + + align:start position:0% +because it's just the +magnitude a force exerted by someone + + align:start position:0% +magnitude a force exerted by someone + + + align:start position:0% +magnitude a force exerted by someone +pulling something is a vector because we + + align:start position:0% +pulling something is a vector because we + + + align:start position:0% +pulling something is a vector because we +care about the strength of the force the + + align:start position:0% +care about the strength of the force the + + + align:start position:0% +care about the strength of the force the +magnitude and the direction in which the + + align:start position:0% +magnitude and the direction in which the + + + align:start position:0% +magnitude and the direction in which the +force is + + align:start position:0% +force is + + + align:start position:0% +force is +acting + + align:start position:0% +acting + + + align:start position:0% +acting +temperature it's a + + align:start position:0% +temperature it's a + + + align:start position:0% +temperature it's a +scalar if we display temperature on a + + align:start position:0% +scalar if we display temperature on a + + + align:start position:0% +scalar if we display temperature on a +weather map where the value of the + + align:start position:0% +weather map where the value of the + + + align:start position:0% +weather map where the value of the +temperature is different at each point + + align:start position:0% +temperature is different at each point + + + align:start position:0% +temperature is different at each point +in space this is a scalar + + align:start position:0% +in space this is a scalar + + + align:start position:0% +in space this is a scalar +field in comparison this weather map of + + align:start position:0% +field in comparison this weather map of + + + align:start position:0% +field in comparison this weather map of +wind where the value of the wind + + align:start position:0% +wind where the value of the wind + + + align:start position:0% +wind where the value of the wind +velocity at each point in space is + + align:start position:0% +velocity at each point in space is + + + align:start position:0% +velocity at each point in space is +represented by a + + align:start position:0% +represented by a + + + align:start position:0% +represented by a +vector is a vector + + align:start position:0% +vector is a vector + + + align:start position:0% +vector is a vector +field \ No newline at end of file diff --git a/6Ee1tj3_4xQ.txt b/6Ee1tj3_4xQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..9ebbb479b59872d1ba157caf2576760f6c4ced16 --- /dev/null +++ b/6Ee1tj3_4xQ.txt @@ -0,0 +1,16043 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +so where we left it last time is that we + + align:start position:0% +so where we left it last time is that we + + + align:start position:0% +so where we left it last time is that we +found some you know theoretical + + align:start position:0% +found some you know theoretical + + + align:start position:0% +found some you know theoretical +justification for why people might be + + align:start position:0% +justification for why people might be + + + align:start position:0% +justification for why people might be +able to tell you + + align:start position:0% +able to tell you + + + align:start position:0% +able to tell you +who the influential people in a network + + align:start position:0% +who the influential people in a network + + + align:start position:0% +who the influential people in a network +has + + align:start position:0% +has + + + align:start position:0% +has +ah even if they have no idea already of + + align:start position:0% +ah even if they have no idea already of + + + align:start position:0% +ah even if they have no idea already of +the shape of the network + + align:start position:0% +the shape of the network + + + align:start position:0% +the shape of the network +simply because it happens to be that + + align:start position:0% +simply because it happens to be that + + + align:start position:0% +simply because it happens to be that +there is a natural link between how many + + align:start position:0% +there is a natural link between how many + + + align:start position:0% +there is a natural link between how many +times we hear about someone and the + + align:start position:0% +times we hear about someone and the + + + align:start position:0% +times we hear about someone and the +ability from this from any message + + align:start position:0% +ability from this from any message + + + align:start position:0% +ability from this from any message +originating from that person to reach a + + align:start position:0% +originating from that person to reach a + + + align:start position:0% +originating from that person to reach a +lot of people + + align:start position:0% +lot of people + + + align:start position:0% +lot of people +so although it's not the same object + + align:start position:0% +so although it's not the same object + + + align:start position:0% +so although it's not the same object +they are related and potentially quite + + align:start position:0% +they are related and potentially quite + + + align:start position:0% +they are related and potentially quite +closely related if they are once we are + + align:start position:0% +closely related if they are once we are + + + align:start position:0% +closely related if they are once we are +starting to look at processes that + + align:start position:0% +starting to look at processes that + + + align:start position:0% +starting to look at processes that +continue for a long time + + align:start position:0% +continue for a long time + + + align:start position:0% +continue for a long time +so the first uh now have let's put that + + align:start position:0% +so the first uh now have let's put that + + + align:start position:0% +so the first uh now have let's put that +in a context of thinking about + + align:start position:0% +in a context of thinking about + + + align:start position:0% +in a context of thinking about +immunization + + align:start position:0% +immunization + + + align:start position:0% +immunization +so that was in fact only the second the + + align:start position:0% +so that was in fact only the second the + + + align:start position:0% +so that was in fact only the second the +second time we tested it we tested this + + align:start position:0% +second time we tested it we tested this + + + align:start position:0% +second time we tested it we tested this +idea for immunization was so in a + + align:start position:0% +idea for immunization was so in a + + + align:start position:0% +idea for immunization was so in a +large-scale project undertaken in + + align:start position:0% +large-scale project undertaken in + + + align:start position:0% +large-scale project undertaken in +collaboration with the government of + + align:start position:0% +collaboration with the government of + + + align:start position:0% +collaboration with the government of +haryana in India + + align:start position:0% +haryana in India + + + align:start position:0% +haryana in India +and the objective was to increase our + + align:start position:0% +and the objective was to increase our + + + align:start position:0% +and the objective was to increase our +immunization in a context where a + + align:start position:0% +immunization in a context where a + + + align:start position:0% +immunization in a context where a +musician rate was low and the demand was + + align:start position:0% +musician rate was low and the demand was + + + align:start position:0% +musician rate was low and the demand was +quite good the supply was quite good + + align:start position:0% +quite good the supply was quite good + + + align:start position:0% +quite good the supply was quite good +they invested in a lot of + + align:start position:0% +they invested in a lot of + + + align:start position:0% +they invested in a lot of +infrastructure to make it easy going + + align:start position:0% +infrastructure to make it easy going + + + align:start position:0% +infrastructure to make it easy going +back to the points you made about about + + align:start position:0% +back to the points you made about about + + + align:start position:0% +back to the points you made about about +Chile to make it easy for people to go + + align:start position:0% +Chile to make it easy for people to go + + + align:start position:0% +Chile to make it easy for people to go +and yet it got stuck at full elimination + + align:start position:0% +and yet it got stuck at full elimination + + + align:start position:0% +and yet it got stuck at full elimination +rate in the high 40s uh + + align:start position:0% +rate in the high 40s uh + + + align:start position:0% +rate in the high 40s uh +according to the report by the parents + + align:start position:0% +according to the report by the parents + + + align:start position:0% +according to the report by the parents +which are probably overestimated anyways + + align:start position:0% +which are probably overestimated anyways + + + align:start position:0% +which are probably overestimated anyways +so + + align:start position:0% +so + + + align:start position:0% +so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +we + + align:start position:0% + + + + align:start position:0% + +what we had in our hands was this thing + + align:start position:0% +what we had in our hands was this thing + + + align:start position:0% +what we had in our hands was this thing +that maybe gossips would work as well as + + align:start position:0% +that maybe gossips would work as well as + + + align:start position:0% +that maybe gossips would work as well as +the previous experiment that already + + align:start position:0% +the previous experiment that already + + + align:start position:0% +the previous experiment that already +showed you on the impact of small + + align:start position:0% +showed you on the impact of small + + + align:start position:0% +showed you on the impact of small +incentives on immunization + + align:start position:0% +incentives on immunization + + + align:start position:0% +incentives on immunization +and so we decided that we could put the + + align:start position:0% +and so we decided that we could put the + + + align:start position:0% +and so we decided that we could put the +two things together as well as a third + + align:start position:0% +two things together as well as a third + + + align:start position:0% +two things together as well as a third +Intervention which is very frequent + + align:start position:0% +Intervention which is very frequent + + + align:start position:0% +Intervention which is very frequent +uh probably you know even for your own + + align:start position:0% +uh probably you know even for your own + + + align:start position:0% +uh probably you know even for your own +health you get reminders you know of + + align:start position:0% +health you get reminders you know of + + + align:start position:0% +health you get reminders you know of +going to the doctor if you've gone once + + align:start position:0% +going to the doctor if you've gone once + + + align:start position:0% +going to the doctor if you've gone once +to the eye doctor you will get a + + align:start position:0% +to the eye doctor you will get a + + + align:start position:0% +to the eye doctor you will get a +reminder once a year that it is time to + + align:start position:0% +reminder once a year that it is time to + + + align:start position:0% +reminder once a year that it is time to +go to the high eye doctor so SMS + + align:start position:0% +go to the high eye doctor so SMS + + + align:start position:0% +go to the high eye doctor so SMS +reminder I've also become quite popular + + align:start position:0% +reminder I've also become quite popular + + + align:start position:0% +reminder I've also become quite popular +so we wanted to try the three things + + align:start position:0% +so we wanted to try the three things + + + align:start position:0% +so we wanted to try the three things +um + + align:start position:0% +um + + + align:start position:0% +um +and to do that we first had to set up + + align:start position:0% +and to do that we first had to set up + + + align:start position:0% +and to do that we first had to set up +the like an Mis they didn't have a way + + align:start position:0% +the like an Mis they didn't have a way + + + align:start position:0% +the like an Mis they didn't have a way +of collecting immunization in a reliable + + align:start position:0% +of collecting immunization in a reliable + + + align:start position:0% +of collecting immunization in a reliable +way it was done in Registries that uh + + align:start position:0% +way it was done in Registries that uh + + + align:start position:0% +way it was done in Registries that uh +paper registry that were not collected + + align:start position:0% +paper registry that were not collected + + + align:start position:0% +paper registry that were not collected +so the first thing we did is to work + + align:start position:0% +so the first thing we did is to work + + + align:start position:0% +so the first thing we did is to work +with a group here at MIT to set up a + + align:start position:0% +with a group here at MIT to set up a + + + align:start position:0% +with a group here at MIT to set up a +small M Health platform I'm saying small + + align:start position:0% +small M Health platform I'm saying small + + + align:start position:0% +small M Health platform I'm saying small +in that it was very bare bone it was + + align:start position:0% +in that it was very bare bone it was + + + align:start position:0% +in that it was very bare bone it was +just for immunization + + align:start position:0% +just for immunization + + + align:start position:0% +just for immunization +incidentally I thought this would be + + align:start position:0% +incidentally I thought this would be + + + align:start position:0% +incidentally I thought this would be +really easy and for whatever reason it's + + align:start position:0% +really easy and for whatever reason it's + + + align:start position:0% +really easy and for whatever reason it's +not it took them a long time and it + + align:start position:0% +not it took them a long time and it + + + align:start position:0% +not it took them a long time and it +wasn't working first and so it took like + + align:start position:0% +wasn't working first and so it took like + + + align:start position:0% +wasn't working first and so it took like +months to develop that thing which is + + align:start position:0% +months to develop that thing which is + + + align:start position:0% +months to develop that thing which is +really busy it's like an Android + + align:start position:0% +really busy it's like an Android + + + align:start position:0% +really busy it's like an Android +an Android + + align:start position:0% + + + + align:start position:0% + +form there is a registration aspect and + + align:start position:0% +form there is a registration aspect and + + + align:start position:0% +form there is a registration aspect and +then for for a new kid and then the + + align:start position:0% +then for for a new kid and then the + + + align:start position:0% +then for for a new kid and then the +follow-up as kids come up + + align:start position:0% +follow-up as kids come up + + + align:start position:0% +follow-up as kids come up +for whatever reason it's harder than you + + align:start position:0% +for whatever reason it's harder than you + + + align:start position:0% +for whatever reason it's harder than you +think + + align:start position:0% +think + + + align:start position:0% +think +I'm not I still don't understand why but + + align:start position:0% +I'm not I still don't understand why but + + + align:start position:0% +I'm not I still don't understand why but +it's it's worth keeping that in mind if + + align:start position:0% +it's it's worth keeping that in mind if + + + align:start position:0% +it's it's worth keeping that in mind if +you want to get into any things like + + align:start position:0% +you want to get into any things like + + + align:start position:0% +you want to get into any things like +that involving software it's always + + align:start position:0% +that involving software it's always + + + align:start position:0% +that involving software it's always +harder than you think uh + + align:start position:0% +harder than you think uh + + + align:start position:0% +harder than you think uh +uh maybe also we wanted to work at at + + align:start position:0% +uh maybe also we wanted to work at at + + + align:start position:0% +uh maybe also we wanted to work at at +scale so we + + align:start position:0% +scale so we + + + align:start position:0% +scale so we +we worked in seven districts + + align:start position:0% +we worked in seven districts + + + align:start position:0% +we worked in seven districts +um a little over 2000 villages in total + + align:start position:0% +um a little over 2000 villages in total + + + align:start position:0% +um a little over 2000 villages in total +we had three hundred thousand uh unique + + align:start position:0% +we had three hundred thousand uh unique + + + align:start position:0% +we had three hundred thousand uh unique +children in our system + + align:start position:0% +children in our system + + + align:start position:0% +children in our system +uh and uh almost 500 000 vaccines + + align:start position:0% +uh and uh almost 500 000 vaccines + + + align:start position:0% +uh and uh almost 500 000 vaccines +what I'm going to present today it's all + + align:start position:0% +what I'm going to present today it's all + + + align:start position:0% +what I'm going to present today it's all +based on the administrative data from + + align:start position:0% +based on the administrative data from + + + align:start position:0% +based on the administrative data from +that system that we kind of owned so one + + align:start position:0% +that system that we kind of owned so one + + + align:start position:0% +that system that we kind of owned so one +issue is whether that system that that + + align:start position:0% +issue is whether that system that that + + + align:start position:0% +issue is whether that system that that +data is reliable or whether people lie + + align:start position:0% +data is reliable or whether people lie + + + align:start position:0% +data is reliable or whether people lie +about you know for example with our kids + + align:start position:0% +about you know for example with our kids + + + align:start position:0% +about you know for example with our kids +that have never been immunized that are + + align:start position:0% +that have never been immunized that are + + + align:start position:0% +that have never been immunized that are +registered as being immunized that's + + align:start position:0% +registered as being immunized that's + + + align:start position:0% +registered as being immunized that's +particularly relevant for the incentive + + align:start position:0% +particularly relevant for the incentive + + + align:start position:0% +particularly relevant for the incentive +but because + + align:start position:0% +but because + + + align:start position:0% +but because +you could imagine a nurse deciding that + + align:start position:0% +you could imagine a nurse deciding that + + + align:start position:0% +you could imagine a nurse deciding that +they are going to immunize a lot of + + align:start position:0% +they are going to immunize a lot of + + + align:start position:0% +they are going to immunize a lot of +children giving their phone number or + + align:start position:0% +children giving their phone number or + + + align:start position:0% +children giving their phone number or +their cousin's phone number or you know + + align:start position:0% +their cousin's phone number or you know + + + align:start position:0% +their cousin's phone number or you know +everyone their friends phone number and + + align:start position:0% +everyone their friends phone number and + + + align:start position:0% +everyone their friends phone number and +in this way uh collecting the small + + align:start position:0% +in this way uh collecting the small + + + align:start position:0% +in this way uh collecting the small +incentives which were airtime on the + + align:start position:0% +incentives which were airtime on the + + + align:start position:0% +incentives which were airtime on the +phone so + + align:start position:0% + + + + align:start position:0% + +what we did there is we we sent the + + align:start position:0% +what we did there is we we sent the + + + align:start position:0% +what we did there is we we sent the +um people to the field to collect + + align:start position:0% +um people to the field to collect + + + align:start position:0% +um people to the field to collect +to to contact all of the families that + + align:start position:0% +to to contact all of the families that + + + align:start position:0% +to to contact all of the families that +had + + align:start position:0% +had + + + align:start position:0% +had +um not all some random sample of the + + align:start position:0% +um not all some random sample of the + + + align:start position:0% +um not all some random sample of the +feminists that had been registered in + + align:start position:0% +feminists that had been registered in + + + align:start position:0% +feminists that had been registered in +the system + + align:start position:0% +the system + + + align:start position:0% +the system +find them check that they existed and + + align:start position:0% +find them check that they existed and + + + align:start position:0% +find them check that they existed and +then if they existed whether they + + align:start position:0% +then if they existed whether they + + + align:start position:0% +then if they existed whether they +remembered going to the camp and the + + align:start position:0% +remembered going to the camp and the + + + align:start position:0% +remembered going to the camp and the +kind of vaccinations they got + + align:start position:0% +kind of vaccinations they got + + + align:start position:0% +kind of vaccinations they got +and the good news is that we could find + + align:start position:0% +and the good news is that we could find + + + align:start position:0% +and the good news is that we could find +everyone + + align:start position:0% +everyone + + + align:start position:0% +everyone +unlike in similar exercises that have + + align:start position:0% +unlike in similar exercises that have + + + align:start position:0% +unlike in similar exercises that have +been performed for the energy program or + + align:start position:0% +been performed for the energy program or + + + align:start position:0% +been performed for the energy program or +for a welfare program where you go to + + align:start position:0% +for a welfare program where you go to + + + align:start position:0% +for a welfare program where you go to +the Village to look for the + + align:start position:0% +the Village to look for the + + + align:start position:0% +the Village to look for the +beneficiaries of the welfare program and + + align:start position:0% +beneficiaries of the welfare program and + + + align:start position:0% +beneficiaries of the welfare program and +you find like half of them so we find + + align:start position:0% +you find like half of them so we find + + + align:start position:0% +you find like half of them so we find +all of them + + align:start position:0% +all of them + + + align:start position:0% +all of them +and then when we find them they sort of + + align:start position:0% +and then when we find them they sort of + + + align:start position:0% +and then when we find them they sort of +at least remember going to the camp + + align:start position:0% +at least remember going to the camp + + + align:start position:0% +at least remember going to the camp +although sometimes they don't remember + + align:start position:0% +although sometimes they don't remember + + + align:start position:0% +although sometimes they don't remember +which shot they got but then it's not + + align:start position:0% +which shot they got but then it's not + + + align:start position:0% +which shot they got but then it's not +clear who is wrong at this point so + + align:start position:0% +clear who is wrong at this point so + + + align:start position:0% +clear who is wrong at this point so +our takeaway from that is by and large + + align:start position:0% +our takeaway from that is by and large + + + align:start position:0% +our takeaway from that is by and large +the data is is the administrative data + + align:start position:0% +the data is is the administrative data + + + align:start position:0% +the data is is the administrative data +is reliable enough and that's what we + + align:start position:0% +is reliable enough and that's what we + + + align:start position:0% +is reliable enough and that's what we +are going to use as a as our measure + + align:start position:0% +are going to use as a as our measure + + + align:start position:0% +are going to use as a as our measure +yeah + + align:start position:0% + + + + align:start position:0% + +it's an excellent question uh and I + + align:start position:0% +it's an excellent question uh and I + + + align:start position:0% +it's an excellent question uh and I +thank you very much for asking to me and + + align:start position:0% +thank you very much for asking to me and + + + align:start position:0% +thank you very much for asking to me and +that's basically what I'm going to talk + + align:start position:0% +that's basically what I'm going to talk + + + align:start position:0% +that's basically what I'm going to talk +about in five minutes in fact I + + align:start position:0% + + + + align:start position:0% + +I uh + + align:start position:0% +I uh + + + align:start position:0% +I uh +I hope you're gonna read that paper one + + align:start position:0% +I hope you're gonna read that paper one + + + align:start position:0% +I hope you're gonna read that paper one +day this is the people I should have put + + align:start position:0% +day this is the people I should have put + + + align:start position:0% +day this is the people I should have put +on the syllabus uh for you to read now + + align:start position:0% +on the syllabus uh for you to read now + + + align:start position:0% +on the syllabus uh for you to read now +is it asking exactly that question + + align:start position:0% +is it asking exactly that question + + + align:start position:0% +is it asking exactly that question +instead I put the question paper which + + align:start position:0% +instead I put the question paper which + + + align:start position:0% +instead I put the question paper which +is fine too and then it's + + align:start position:0% +is fine too and then it's + + + align:start position:0% +is fine too and then it's +but which kind of highlights just one + + align:start position:0% +but which kind of highlights just one + + + align:start position:0% +but which kind of highlights just one +part of that and not this pre this + + align:start position:0% +part of that and not this pre this + + + align:start position:0% +part of that and not this pre this +question about there are many treatments + + align:start position:0% +question about there are many treatments + + + align:start position:0% +question about there are many treatments +there but let me come back to that in a + + align:start position:0% +there but let me come back to that in a + + + align:start position:0% +there but let me come back to that in a +minute just close the gossip parts that + + align:start position:0% +minute just close the gossip parts that + + + align:start position:0% +minute just close the gossip parts that +we are done with that + + align:start position:0% +we are done with that + + + align:start position:0% +we are done with that +so in the gaussian part uh + + align:start position:0% +so in the gaussian part uh + + + align:start position:0% +so in the gaussian part uh +so in our first gossip experiment which + + align:start position:0% +so in our first gossip experiment which + + + align:start position:0% +so in our first gossip experiment which +in the paper you read comes second but + + align:start position:0% +in the paper you read comes second but + + + align:start position:0% +in the paper you read comes second but +chronologically is is was first uh we + + align:start position:0% +chronologically is is was first uh we + + + align:start position:0% +chronologically is is was first uh we +just had got we just have this question + + align:start position:0% +just had got we just have this question + + + align:start position:0% +just had got we just have this question +of if I want to see people for her for + + align:start position:0% +of if I want to see people for her for + + + align:start position:0% +of if I want to see people for her for +fair how you know who should I go see so + + align:start position:0% +fair how you know who should I go see so + + + align:start position:0% +fair how you know who should I go see so +the idea was to capture something which + + align:start position:0% +the idea was to capture something which + + + align:start position:0% +the idea was to capture something which +is not loaded and is all about diffusion + + align:start position:0% +is not loaded and is all about diffusion + + + align:start position:0% +is not loaded and is all about diffusion +of information + + align:start position:0% +of information + + + align:start position:0% +of information +but and then in that first experiment + + align:start position:0% +but and then in that first experiment + + + align:start position:0% +but and then in that first experiment +the experiment was a bit artificial we + + align:start position:0% +the experiment was a bit artificial we + + + align:start position:0% +the experiment was a bit artificial we +were trying to transfer information + + align:start position:0% +were trying to transfer information + + + align:start position:0% +were trying to transfer information +about a cell phone self you know cell + + align:start position:0% +about a cell phone self you know cell + + + align:start position:0% +about a cell phone self you know cell +phone offer okay + + align:start position:0% + + + + align:start position:0% + +but here when we are now in a real world + + align:start position:0% +but here when we are now in a real world + + + align:start position:0% +but here when we are now in a real world +setting and in particular Health setting + + align:start position:0% +setting and in particular Health setting + + + align:start position:0% +setting and in particular Health setting +there might be there is this trust issue + + align:start position:0% +there might be there is this trust issue + + + align:start position:0% +there might be there is this trust issue +which is the people whom you would know + + align:start position:0% +which is the people whom you would know + + + align:start position:0% +which is the people whom you would know +you you might trust to tell you when the + + align:start position:0% +you you might trust to tell you when the + + + align:start position:0% +you you might trust to tell you when the +next Affair is or when an Excel phone + + align:start position:0% +next Affair is or when an Excel phone + + + align:start position:0% +next Affair is or when an Excel phone +rifle is might not know might not be the + + align:start position:0% +rifle is might not know might not be the + + + align:start position:0% +rifle is might not know might not be the +one you're going to talk to about health + + align:start position:0% +one you're going to talk to about health + + + align:start position:0% +one you're going to talk to about health +and although we have a theory for saying + + align:start position:0% +and although we have a theory for saying + + + align:start position:0% +and although we have a theory for saying +people might be good at knowing who is + + align:start position:0% +people might be good at knowing who is + + + align:start position:0% +people might be good at knowing who is +good at spreading information + + align:start position:0% +good at spreading information + + + align:start position:0% +good at spreading information +we don't have a similarity to tell us + + align:start position:0% +we don't have a similarity to tell us + + + align:start position:0% +we don't have a similarity to tell us +whether people are good at spreading at + + align:start position:0% +whether people are good at spreading at + + + align:start position:0% +whether people are good at spreading at +spreading information that people will + + align:start position:0% +spreading information that people will + + + align:start position:0% +spreading information that people will +believe + + align:start position:0% +believe + + + align:start position:0% +believe +that people Trust + + align:start position:0% +that people Trust + + + align:start position:0% +that people Trust +so what we decided to do is to just test + + align:start position:0% +so what we decided to do is to just test + + + align:start position:0% +so what we decided to do is to just test +it + + align:start position:0% +it + + + align:start position:0% +it +so we asked people either were randomly + + align:start position:0% +so we asked people either were randomly + + + align:start position:0% +so we asked people either were randomly +at random random seeds someone asked by + + align:start position:0% +at random random seeds someone asked by + + + align:start position:0% +at random random seeds someone asked by +the way in the paper or should you have + + align:start position:0% +the way in the paper or should you have + + + align:start position:0% +the way in the paper or should you have +had random seeds so we had random seeds + + align:start position:0% +had random seeds so we had random seeds + + + align:start position:0% +had random seeds so we had random seeds +or seeds that were + + align:start position:0% +or seeds that were + + + align:start position:0% +or seeds that were +where we elicited gossips where we + + align:start position:0% +where we elicited gossips where we + + + align:start position:0% +where we elicited gossips where we +listed the trusted people of trusted + + align:start position:0% +listed the trusted people of trusted + + + align:start position:0% +listed the trusted people of trusted +gossips + + align:start position:0% +gossips + + + align:start position:0% +gossips +so how do we elicit the the + + align:start position:0% +so how do we elicit the the + + + align:start position:0% +so how do we elicit the the +any of these people we go and find out + + align:start position:0% +any of these people we go and find out + + + align:start position:0% +any of these people we go and find out +talk to 15 people and we ask them so for + + align:start position:0% +talk to 15 people and we ask them so for + + + align:start position:0% +talk to 15 people and we ask them so for +gossip uh that's the question if they + + align:start position:0% +gossip uh that's the question if they + + + align:start position:0% +gossip uh that's the question if they +share information about the music + + align:start position:0% +share information about the music + + + align:start position:0% +share information about the music +festival Street play fair many people + + align:start position:0% +festival Street play fair many people + + + align:start position:0% +festival Street play fair many people +would learn about it + + align:start position:0% +would learn about it + + + align:start position:0% +would learn about it +that's because and then we kind of put + + align:start position:0% +that's because and then we kind of put + + + align:start position:0% +that's because and then we kind of put +the theory for how why uh could you name + + align:start position:0% +the theory for how why uh could you name + + + align:start position:0% +the theory for how why uh could you name +these people + + align:start position:0% +these people + + + align:start position:0% +these people +then for trusted people is who are the + + align:start position:0% +then for trusted people is who are the + + + align:start position:0% +then for trusted people is who are the +people in this Village that you and many + + align:start position:0% +people in this Village that you and many + + + align:start position:0% +people in this Village that you and many +Village uh villagers trust within and + + align:start position:0% +Village uh villagers trust within and + + + align:start position:0% +Village uh villagers trust within and +outside this neighborhood + + align:start position:0% +outside this neighborhood + + + align:start position:0% +outside this neighborhood +that means when I give advice on + + align:start position:0% +that means when I give advice on + + + align:start position:0% +that means when I give advice on +something many people believe that it's + + align:start position:0% +something many people believe that it's + + + align:start position:0% +something many people believe that it's +correct and they tend to follow it + + align:start position:0% +correct and they tend to follow it + + + align:start position:0% +correct and they tend to follow it +uh so choosing the right fertilizer for + + align:start position:0% +uh so choosing the right fertilizer for + + + align:start position:0% +uh so choosing the right fertilizer for +the crop and keeping your child healthy + + align:start position:0% +the crop and keeping your child healthy + + + align:start position:0% +the crop and keeping your child healthy +so we specifically at the health example + + align:start position:0% +so we specifically at the health example + + + align:start position:0% +so we specifically at the health example +because we were going to transmit + + align:start position:0% +because we were going to transmit + + + align:start position:0% +because we were going to transmit +information about about health + + align:start position:0% +information about about health + + + align:start position:0% +information about about health +and then finally trusted gossip it's a + + align:start position:0% +and then finally trusted gossip it's a + + + align:start position:0% +and then finally trusted gossip it's a +mouthful + + align:start position:0% +mouthful + + + align:start position:0% +mouthful +but + + align:start position:0% +but + + + align:start position:0% +but +many people get to know about a piece of + + align:start position:0% +many people get to know about a piece of + + + align:start position:0% +many people get to know about a piece of +information and among those people who + + align:start position:0% +information and among those people who + + + align:start position:0% +information and among those people who +are trusted + + align:start position:0% +are trusted + + + align:start position:0% +are trusted +so you need to First be a gossip and + + align:start position:0% +so you need to First be a gossip and + + + align:start position:0% +so you need to First be a gossip and +then also be trusted + + align:start position:0% + + + + align:start position:0% + +and then the intervention was once these + + align:start position:0% +and then the intervention was once these + + + align:start position:0% +and then the intervention was once these +people were named so we found the these + + align:start position:0% +people were named so we found the these + + + align:start position:0% +people were named so we found the these +results that very few people are unnamed + + align:start position:0% +results that very few people are unnamed + + + align:start position:0% +results that very few people are unnamed +and there is a lot of consensus of who + + align:start position:0% +and there is a lot of consensus of who + + + align:start position:0% +and there is a lot of consensus of who +they might be we picked the five on that + + align:start position:0% +they might be we picked the five on that + + + align:start position:0% +they might be we picked the five on that +come on top of the 15 uh out of all the + + align:start position:0% +come on top of the 15 uh out of all the + + + align:start position:0% +come on top of the 15 uh out of all the +domination from the 15 random people we + + align:start position:0% +domination from the 15 random people we + + + align:start position:0% +domination from the 15 random people we +interviewed + + align:start position:0% +interviewed + + + align:start position:0% +interviewed +um and we uh and we go for that so + + align:start position:0% +um and we uh and we go for that so + + + align:start position:0% +um and we uh and we go for that so +someone was asking also whether it's + + align:start position:0% +someone was asking also whether it's + + + align:start position:0% +someone was asking also whether it's +it's pretty expensive to go visit 15 + + align:start position:0% +it's pretty expensive to go visit 15 + + + align:start position:0% +it's pretty expensive to go visit 15 +people but it's not really expensive to + + align:start position:0% +people but it's not really expensive to + + + align:start position:0% +people but it's not really expensive to +go visit 15 people especially if we + + align:start position:0% +go visit 15 people especially if we + + + align:start position:0% +go visit 15 people especially if we +don't really care who they are + + align:start position:0% +don't really care who they are + + + align:start position:0% +don't really care who they are +because it's not that we are under this + + align:start position:0% +because it's not that we are under this + + + align:start position:0% +because it's not that we are under this +Theory it's kind of anybody would be + + align:start position:0% +Theory it's kind of anybody would be + + + align:start position:0% +Theory it's kind of anybody would be +fine it doesn't need to be random random + + align:start position:0% +fine it doesn't need to be random random + + + align:start position:0% +fine it doesn't need to be random random +it could be just you know anyone uh + + align:start position:0% +it could be just you know anyone uh + + + align:start position:0% +it could be just you know anyone uh +so it goes quite quickly to go visit 15 + + align:start position:0% +so it goes quite quickly to go visit 15 + + + align:start position:0% +so it goes quite quickly to go visit 15 +people that said we are now interested + + align:start position:0% +people that said we are now interested + + + align:start position:0% +people that said we are now interested +in the scale up of um of this program + + align:start position:0% +in the scale up of um of this program + + + align:start position:0% +in the scale up of um of this program +which I'm shortcutting but which turned + + align:start position:0% +which I'm shortcutting but which turned + + + align:start position:0% +which I'm shortcutting but which turned +out to be effective and cost effective + + align:start position:0% +out to be effective and cost effective + + + align:start position:0% +out to be effective and cost effective +and there we actually exactly stumbled + + align:start position:0% +and there we actually exactly stumbled + + + align:start position:0% +and there we actually exactly stumbled +upon this issue which is for us it's + + align:start position:0% +upon this issue which is for us it's + + + align:start position:0% +upon this issue which is for us it's +pretty easy to go see 15 people and + + align:start position:0% +pretty easy to go see 15 people and + + + align:start position:0% +pretty easy to go see 15 people and +record the answer and and be done in our + + align:start position:0% +record the answer and and be done in our + + + align:start position:0% +record the answer and and be done in our +gossips but for the government if you + + align:start position:0% +gossips but for the government if you + + + align:start position:0% +gossips but for the government if you +want to do that for every single Village + + align:start position:0% +want to do that for every single Village + + + align:start position:0% +want to do that for every single Village +it becomes like a thing so who is going + + align:start position:0% +it becomes like a thing so who is going + + + align:start position:0% +it becomes like a thing so who is going +to do it and how they're gonna do it and + + align:start position:0% +to do it and how they're gonna do it and + + + align:start position:0% +to do it and how they're gonna do it and +are they going you know if we ask the + + align:start position:0% +are they going you know if we ask the + + + align:start position:0% +are they going you know if we ask the +Frontline Health worker to do it the + + align:start position:0% +Frontline Health worker to do it the + + + align:start position:0% +Frontline Health worker to do it the +ashes are they just going to make up the + + align:start position:0% +ashes are they just going to make up the + + + align:start position:0% +ashes are they just going to make up the +names + + align:start position:0% +names + + + align:start position:0% +names +and so basically it's a huge stumbling + + align:start position:0% +and so basically it's a huge stumbling + + + align:start position:0% +and so basically it's a huge stumbling +block so in fact you know when I write + + align:start position:0% +block so in fact you know when I write + + + align:start position:0% +block so in fact you know when I write +the the your question I was like well + + align:start position:0% +the the your question I was like well + + + align:start position:0% +the the your question I was like well +you know it's not that expensive and + + align:start position:0% +you know it's not that expensive and + + + align:start position:0% +you know it's not that expensive and +then I thought tomorrow and say well + + align:start position:0% +then I thought tomorrow and say well + + + align:start position:0% +then I thought tomorrow and say well +actually it is uh logistically a + + align:start position:0% +actually it is uh logistically a + + + align:start position:0% +actually it is uh logistically a +nightmare and so + + align:start position:0% +nightmare and so + + + align:start position:0% +nightmare and so +what we are trying to do in the scale up + + align:start position:0% +what we are trying to do in the scale up + + + align:start position:0% +what we are trying to do in the scale up +of that is we are not + + align:start position:0% +of that is we are not + + + align:start position:0% +of that is we are not +doing that anymore we are + + align:start position:0% +doing that anymore we are + + + align:start position:0% +doing that anymore we are +asking the parents + + align:start position:0% +asking the parents + + + align:start position:0% +asking the parents +when they're since now they have a + + align:start position:0% +when they're since now they have a + + + align:start position:0% +when they're since now they have a +little better mhealth intervention + + align:start position:0% +little better mhealth intervention + + + align:start position:0% +little better mhealth intervention +we are asking the parents to tell us + + align:start position:0% +we are asking the parents to tell us + + + align:start position:0% +we are asking the parents to tell us +so that's what we were hoping to do is + + align:start position:0% +so that's what we were hoping to do is + + + align:start position:0% +so that's what we were hoping to do is +to using to add a module to the to their + + align:start position:0% +to using to add a module to the to their + + + align:start position:0% +to using to add a module to the to their +registration Camp when when people come + + align:start position:0% +registration Camp when when people come + + + align:start position:0% +registration Camp when when people come +to say hey by the way do you know + + align:start position:0% +to say hey by the way do you know + + + align:start position:0% +to say hey by the way do you know +someone who is + + align:start position:0% +someone who is + + + align:start position:0% +someone who is +a gossip uh you know some and so we + + align:start position:0% +a gossip uh you know some and so we + + + align:start position:0% +a gossip uh you know some and so we +thought that would be very smart but + + align:start position:0% +thought that would be very smart but + + + align:start position:0% +thought that would be very smart but +that in + + align:start position:0% +that in + + + align:start position:0% +that in +so that was the idea that it's going to + + align:start position:0% +so that was the idea that it's going to + + + align:start position:0% +so that was the idea that it's going to +be very cheap it's it would in fact be + + align:start position:0% +be very cheap it's it would in fact be + + + align:start position:0% +be very cheap it's it would in fact be +very cheap but it involves + + align:start position:0% +very cheap but it involves + + + align:start position:0% +very cheap but it involves +modifying the the software + + align:start position:0% +modifying the the software + + + align:start position:0% +modifying the the software +which turns out to be a huge nightmare + + align:start position:0% +which turns out to be a huge nightmare + + + align:start position:0% +which turns out to be a huge nightmare +and getting the nurse to use the + + align:start position:0% +and getting the nurse to use the + + + align:start position:0% +and getting the nurse to use the +software and to you know to use that + + align:start position:0% +software and to you know to use that + + + align:start position:0% +software and to you know to use that +modified version + + align:start position:0% +modified version + + + align:start position:0% +modified version +so we've also been stuck on that + + align:start position:0% +so we've also been stuck on that + + + align:start position:0% +so we've also been stuck on that +for uh + + align:start position:0% +for uh + + + align:start position:0% +for uh +some month + + align:start position:0% +some month + + + align:start position:0% +some month +so the current version so this was + + align:start position:0% +so the current version so this was + + + align:start position:0% +so the current version so this was +version two so the current version is + + align:start position:0% +version two so the current version is + + + align:start position:0% +version two so the current version is +that + + align:start position:0% + + + + align:start position:0% + +we have a large database of phone + + align:start position:0% +we have a large database of phone + + + align:start position:0% +we have a large database of phone +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +because there is a huge health insurance + + align:start position:0% +because there is a huge health insurance + + + align:start position:0% +because there is a huge health insurance +programs where many people are in it and + + align:start position:0% +programs where many people are in it and + + + align:start position:0% +programs where many people are in it and +they have phone numbers + + align:start position:0% +they have phone numbers + + + align:start position:0% +they have phone numbers +and this health insurance people have a + + align:start position:0% +and this health insurance people have a + + + align:start position:0% +and this health insurance people have a +call center + + align:start position:0% +call center + + + align:start position:0% +call center +they call them for buyers you know + + align:start position:0% +they call them for buyers you know + + + align:start position:0% +they call them for buyers you know +people call them to ask for insurance + + align:start position:0% +people call them to ask for insurance + + + align:start position:0% +people call them to ask for insurance +stuff and they're cool people in turn + + align:start position:0% +stuff and they're cool people in turn + + + align:start position:0% +stuff and they're cool people in turn +and these people in the call center can + + align:start position:0% +and these people in the call center can + + + align:start position:0% +and these people in the call center can +do a survey + + align:start position:0% +do a survey + + + align:start position:0% +do a survey +can do a short survey to a few people in + + align:start position:0% +can do a short survey to a few people in + + + align:start position:0% +can do a short survey to a few people in +each Village + + align:start position:0% +each Village + + + align:start position:0% +each Village +on the phone + + align:start position:0% +on the phone + + + align:start position:0% +on the phone +so that's where we are now to uh that's + + align:start position:0% +so that's where we are now to uh that's + + + align:start position:0% +so that's where we are now to uh that's +what we that's what seems feasible uh + + align:start position:0% +what we that's what seems feasible uh + + + align:start position:0% +what we that's what seems feasible uh +stay tuned I'll tell you because we + + align:start position:0% +stay tuned I'll tell you because we + + + align:start position:0% +stay tuned I'll tell you because we +haven't yet tried and therefore failed + + align:start position:0% +haven't yet tried and therefore failed + + + align:start position:0% +haven't yet tried and therefore failed +but that might be an issue out there + + align:start position:0% +but that might be an issue out there + + + align:start position:0% +but that might be an issue out there +anyway so that seems simple but it's not + + align:start position:0% +anyway so that seems simple but it's not + + + align:start position:0% +anyway so that seems simple but it's not +that simple but once we find them then + + align:start position:0% +that simple but once we find them then + + + align:start position:0% +that simple but once we find them then +we go and uh and and visit them try to + + align:start position:0% +we go and uh and and visit them try to + + + align:start position:0% +we go and uh and and visit them try to +enroll them in the program + + align:start position:0% +enroll them in the program + + + align:start position:0% +enroll them in the program +and we tell them that we will send them + + align:start position:0% +and we tell them that we will send them + + + align:start position:0% +and we tell them that we will send them +these messages so we have incentive and + + align:start position:0% +these messages so we have incentive and + + + align:start position:0% +these messages so we have incentive and +non-incentive villages we saw that in + + align:start position:0% +non-incentive villages we saw that in + + + align:start position:0% +non-incentive villages we saw that in +incentive Villages they were well they + + align:start position:0% +incentive Villages they were well they + + + align:start position:0% +incentive Villages they were well they +would be well placed to mention that + + align:start position:0% +would be well placed to mention that + + + align:start position:0% +would be well placed to mention that +there is an incentive program + + align:start position:0% +there is an incentive program + + + align:start position:0% +there is an incentive program +that's a concrete piece of information + + align:start position:0% +that's a concrete piece of information + + + align:start position:0% +that's a concrete piece of information +people probably don't know because the + + align:start position:0% +people probably don't know because the + + + align:start position:0% +people probably don't know because the +the advertising of the incentive program + + align:start position:0% +the advertising of the incentive program + + + align:start position:0% +the advertising of the incentive program +is not huge and then in no incentive + + align:start position:0% +is not huge and then in no incentive + + + align:start position:0% +is not huge and then in no incentive +Villages it's just a general you know + + align:start position:0% +Villages it's just a general you know + + + align:start position:0% +Villages it's just a general you know +immunition it's good for you go ahead + + align:start position:0% +immunition it's good for you go ahead + + + align:start position:0% +immunition it's good for you go ahead +and and do it + + align:start position:0% + + + + align:start position:0% + +so here is the basic basic results I'll + + align:start position:0% +so here is the basic basic results I'll + + + align:start position:0% +so here is the basic basic results I'll +tell you about more results when I get + + align:start position:0% +tell you about more results when I get + + + align:start position:0% +tell you about more results when I get +to Kayla's questions in more details + + align:start position:0% +to Kayla's questions in more details + + + align:start position:0% +to Kayla's questions in more details +but the basic result is that if we look + + align:start position:0% +but the basic result is that if we look + + + align:start position:0% +but the basic result is that if we look +at measles that's gonna be my uh my main + + align:start position:0% +at measles that's gonna be my uh my main + + + align:start position:0% +at measles that's gonna be my uh my main +outcomes because that's the last + + align:start position:0% +outcomes because that's the last + + + align:start position:0% +outcomes because that's the last +vaccination in the sequence uh that's + + align:start position:0% +vaccination in the sequence uh that's + + + align:start position:0% +vaccination in the sequence uh that's +the log number of people who receive the + + align:start position:0% +the log number of people who receive the + + + align:start position:0% +the log number of people who receive the +missile vaccine in any uh in any in any + + align:start position:0% +missile vaccine in any uh in any in any + + + align:start position:0% +missile vaccine in any uh in any in any +monthly camp in a village + + align:start position:0% +monthly camp in a village + + + align:start position:0% +monthly camp in a village +and it's uh so here it's in logs later + + align:start position:0% +and it's uh so here it's in logs later + + + align:start position:0% +and it's uh so here it's in logs later +I'm going to show you results in levels + + align:start position:0% +I'm going to show you results in levels + + + align:start position:0% +I'm going to show you results in levels +but for some reason in these people we + + align:start position:0% +but for some reason in these people we + + + align:start position:0% +but for some reason in these people we +show them in logs and it's 18 percent + + align:start position:0% +show them in logs and it's 18 percent + + + align:start position:0% +show them in logs and it's 18 percent +higher in places in a village that have + + align:start position:0% +higher in places in a village that have + + + align:start position:0% +higher in places in a village that have +a gossip uh these two the trusted and + + align:start position:0% +a gossip uh these two the trusted and + + + align:start position:0% +a gossip uh these two the trusted and +trusted gossip are not individual + + align:start position:0% +trusted gossip are not individual + + + align:start position:0% +trusted gossip are not individual +neither of them is actually significant + + align:start position:0% +neither of them is actually significant + + + align:start position:0% +neither of them is actually significant +they're also not significantly different + + align:start position:0% +they're also not significantly different + + + align:start position:0% +they're also not significantly different +so I can't say that it's worth but what + + align:start position:0% +so I can't say that it's worth but what + + + align:start position:0% +so I can't say that it's worth but what +is per what is relevant is that it's no + + align:start position:0% +is per what is relevant is that it's no + + + align:start position:0% +is per what is relevant is that it's no +better + + align:start position:0% +better + + + align:start position:0% +better +um and in particular you might think + + align:start position:0% +um and in particular you might think + + + align:start position:0% +um and in particular you might think +that the trusted gossip would be + + align:start position:0% +that the trusted gossip would be + + + align:start position:0% +that the trusted gossip would be +obviously better because it's both a + + align:start position:0% +obviously better because it's both a + + + align:start position:0% +obviously better because it's both a +gossip and it's trusted but of course + + align:start position:0% +gossip and it's trusted but of course + + + align:start position:0% +gossip and it's trusted but of course +when you're trying to find a trusted + + align:start position:0% +when you're trying to find a trusted + + + align:start position:0% +when you're trying to find a trusted +gossip you you lose some on regressive + + align:start position:0% +gossip you you lose some on regressive + + + align:start position:0% +gossip you you lose some on regressive +dimension + + align:start position:0% +dimension + + + align:start position:0% +dimension +so if in fact it turns out that you + + align:start position:0% +so if in fact it turns out that you + + + align:start position:0% +so if in fact it turns out that you +don't get the most gossiping gossip + + align:start position:0% +don't get the most gossiping gossip + + + align:start position:0% +don't get the most gossiping gossip +potentially because they are not + + align:start position:0% +potentially because they are not + + + align:start position:0% +potentially because they are not +necessarily the most trusted so if in + + align:start position:0% +necessarily the most trusted so if in + + + align:start position:0% +necessarily the most trusted so if in +fact the trust Dimension is not that + + align:start position:0% +fact the trust Dimension is not that + + + align:start position:0% +fact the trust Dimension is not that +important compared to repeating the + + align:start position:0% +important compared to repeating the + + + align:start position:0% +important compared to repeating the +thing then you might lose something + + align:start position:0% +thing then you might lose something + + + align:start position:0% +thing then you might lose something +so we can say that they look they all + + align:start position:0% +so we can say that they look they all + + + align:start position:0% +so we can say that they look they all +look fairly similar + + align:start position:0% +look fairly similar + + + align:start position:0% +look fairly similar +and then these are the incentive results + + align:start position:0% +and then these are the incentive results + + + align:start position:0% +and then these are the incentive results +that I'll come to that in a in a second + + align:start position:0% +that I'll come to that in a in a second + + + align:start position:0% +that I'll come to that in a in a second +so putting it all together uh uh and so + + align:start position:0% +so putting it all together uh uh and so + + + align:start position:0% +so putting it all together uh uh and so +that's the other people written on the + + align:start position:0% +that's the other people written on the + + + align:start position:0% +that's the other people written on the +same uh on the same experiment so the + + align:start position:0% +same uh on the same experiment so the + + + align:start position:0% +same uh on the same experiment so the +first one really just it was more of + + align:start position:0% +first one really just it was more of + + + align:start position:0% +first one really just it was more of +used this experiment just for the gossip + + align:start position:0% +used this experiment just for the gossip + + + align:start position:0% +used this experiment just for the gossip +aspect + + align:start position:0% +aspect + + + align:start position:0% +aspect +but then we exactly have kailash's + + align:start position:0% +but then we exactly have kailash's + + + align:start position:0% +but then we exactly have kailash's +question is there are a lot of treatment + + align:start position:0% +question is there are a lot of treatment + + + align:start position:0% +question is there are a lot of treatment +here + + align:start position:0% +here + + + align:start position:0% +here +um you know but and why are there a lot + + align:start position:0% +um you know but and why are there a lot + + + align:start position:0% +um you know but and why are there a lot +of treatment + + align:start position:0% +of treatment + + + align:start position:0% +of treatment +now another treatment because we are not + + align:start position:0% +now another treatment because we are not + + + align:start position:0% +now another treatment because we are not +in this case we didn't go to this + + align:start position:0% +in this case we didn't go to this + + + align:start position:0% +in this case we didn't go to this +project for testing a particular Theory + + align:start position:0% +project for testing a particular Theory + + + align:start position:0% +project for testing a particular Theory +sometimes you go on and you have + + align:start position:0% +sometimes you go on and you have + + + align:start position:0% +sometimes you go on and you have +something very simple in mind very clear + + align:start position:0% +something very simple in mind very clear + + + align:start position:0% +something very simple in mind very clear +in mind you want to test a particular + + align:start position:0% +in mind you want to test a particular + + + align:start position:0% +in mind you want to test a particular +Theory or you want to test + + align:start position:0% +Theory or you want to test + + + align:start position:0% +Theory or you want to test +whether intervention a works + + align:start position:0% +whether intervention a works + + + align:start position:0% +whether intervention a works +but I'll mandate here with the gun was a + + align:start position:0% +but I'll mandate here with the gun was a + + + align:start position:0% +but I'll mandate here with the gun was a +bit different which is that can you come + + align:start position:0% +bit different which is that can you come + + + align:start position:0% +bit different which is that can you come +up with the best possible intervention + + align:start position:0% +up with the best possible intervention + + + align:start position:0% +up with the best possible intervention +for us in terms of increasing + + align:start position:0% +for us in terms of increasing + + + align:start position:0% +for us in terms of increasing +immunization rates + + align:start position:0% +immunization rates + + + align:start position:0% +immunization rates +based only on the main intervention at + + align:start position:0% +based only on the main intervention at + + + align:start position:0% +based only on the main intervention at +least they are taking care of the supply + + align:start position:0% +least they are taking care of the supply + + + align:start position:0% +least they are taking care of the supply +so we had the supply sorted out but + + align:start position:0% +so we had the supply sorted out but + + + align:start position:0% +so we had the supply sorted out but +based on what you know on the literature + + align:start position:0% +based on what you know on the literature + + + align:start position:0% +based on what you know on the literature +what's the best we can do both for + + align:start position:0% +what's the best we can do both for + + + align:start position:0% +what's the best we can do both for +increasing a musician overall and also + + align:start position:0% +increasing a musician overall and also + + + align:start position:0% +increasing a musician overall and also +in terms of cost Effectiveness and cost + + align:start position:0% +in terms of cost Effectiveness and cost + + + align:start position:0% +in terms of cost Effectiveness and cost +per dollar + + align:start position:0% +per dollar + + + align:start position:0% +per dollar +and when we started brainstorming with + + align:start position:0% +and when we started brainstorming with + + + align:start position:0% +and when we started brainstorming with +them + + align:start position:0% +them + + + align:start position:0% +them +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the the uncaring thing on social so the + + align:start position:0% +the the uncaring thing on social so the + + + align:start position:0% +the the uncaring thing on social so the +bracelet was not there yet so we didn't + + align:start position:0% +bracelet was not there yet so we didn't + + + align:start position:0% +bracelet was not there yet so we didn't +have that part of it but what we had was + + align:start position:0% +have that part of it but what we had was + + + align:start position:0% +have that part of it but what we had was +the idea of cash incentive which we had + + align:start position:0% +the idea of cash incentive which we had + + + align:start position:0% +the idea of cash incentive which we had +found to be effective in udaipur the + + align:start position:0% +found to be effective in udaipur the + + + align:start position:0% +found to be effective in udaipur the +reminders which everybody is using which + + align:start position:0% +reminders which everybody is using which + + + align:start position:0% +reminders which everybody is using which +has been on you know endorsed by the + + align:start position:0% +has been on you know endorsed by the + + + align:start position:0% +has been on you know endorsed by the +Indian Academy of Pediatrics and + + align:start position:0% +Indian Academy of Pediatrics and + + + align:start position:0% +Indian Academy of Pediatrics and +and the this new idea of gossips + + align:start position:0% +and the this new idea of gossips + + + align:start position:0% +and the this new idea of gossips +and then + + align:start position:0% +and then + + + align:start position:0% +and then +uh so there is evidence uh from from the + + align:start position:0% +uh so there is evidence uh from from the + + + align:start position:0% +uh so there is evidence uh from from the +rest of the literature that each of the + + align:start position:0% +rest of the literature that each of the + + + align:start position:0% +rest of the literature that each of the +strategy May improve take up + + align:start position:0% +strategy May improve take up + + + align:start position:0% +strategy May improve take up +but we don't know + + align:start position:0% +but we don't know + + + align:start position:0% +but we don't know +which one is the most effective which + + align:start position:0% +which one is the most effective which + + + align:start position:0% +which one is the most effective which +one is the most cost effective + + align:start position:0% +one is the most cost effective + + + align:start position:0% +one is the most cost effective +we don't how they should be used for + + align:start position:0% +we don't how they should be used for + + + align:start position:0% +we don't how they should be used for +example in udaipo we tried one + + align:start position:0% +example in udaipo we tried one + + + align:start position:0% +example in udaipo we tried one +type of incentive lentils and then an + + align:start position:0% +type of incentive lentils and then an + + + align:start position:0% +type of incentive lentils and then an +increase so it was sloppy + + align:start position:0% +increase so it was sloppy + + + align:start position:0% +increase so it was sloppy +and you know the equivalent of maybe + + align:start position:0% +and you know the equivalent of maybe + + + align:start position:0% +and you know the equivalent of maybe +about a dollar a shot uh in in today's + + align:start position:0% +about a dollar a shot uh in in today's + + + align:start position:0% +about a dollar a shot uh in in today's +term in PPP town + + align:start position:0% +term in PPP town + + + align:start position:0% +term in PPP town +uh maybe we could get you know we could + + align:start position:0% +uh maybe we could get you know we could + + + align:start position:0% +uh maybe we could get you know we could +get less maybe you could just use less + + align:start position:0% +get less maybe you could just use less + + + align:start position:0% +get less maybe you could just use less +money maybe it doesn't need to be sloppy + + align:start position:0% +money maybe it doesn't need to be sloppy + + + align:start position:0% +money maybe it doesn't need to be sloppy +with SMS do you need to SMS everyone or + + align:start position:0% +with SMS do you need to SMS everyone or + + + align:start position:0% +with SMS do you need to SMS everyone or +you SMS some people + + align:start position:0% +you SMS some people + + + align:start position:0% +you SMS some people +with the gossip you know as you know we + + align:start position:0% +with the gossip you know as you know we + + + align:start position:0% +with the gossip you know as you know we +don't know if we should use gossips or + + align:start position:0% +don't know if we should use gossips or + + + align:start position:0% +don't know if we should use gossips or +trusted people or trusted gossips so + + align:start position:0% +trusted people or trusted gossips so + + + align:start position:0% +trusted people or trusted gossips so +they are kind of different type of + + align:start position:0% +they are kind of different type of + + + align:start position:0% +they are kind of different type of +variants + + align:start position:0% +variants + + + align:start position:0% +variants +and then you start asking yourself + + align:start position:0% +and then you start asking yourself + + + align:start position:0% +and then you start asking yourself +whether the combination of this variant + + align:start position:0% +whether the combination of this variant + + + align:start position:0% +whether the combination of this variant +would work well so for example the + + align:start position:0% +would work well so for example the + + + align:start position:0% +would work well so for example the +gossip might work better when there is + + align:start position:0% +gossip might work better when there is + + + align:start position:0% +gossip might work better when there is +incentive as well because there is a + + align:start position:0% +incentive as well because there is a + + + align:start position:0% +incentive as well because there is a +clear message to + + align:start position:0% +clear message to + + + align:start position:0% +clear message to +to convert and not so at least this one + + align:start position:0% +to convert and not so at least this one + + + align:start position:0% +to convert and not so at least this one +was a you know potentially a clear + + align:start position:0% +was a you know potentially a clear + + + align:start position:0% +was a you know potentially a clear +hypothesis + + align:start position:0% +hypothesis + + + align:start position:0% +hypothesis +but it's like a mess like there is a + + align:start position:0% +but it's like a mess like there is a + + + align:start position:0% +but it's like a mess like there is a +chamber of things and so here it comes + + align:start position:0% +chamber of things and so here it comes + + + align:start position:0% +chamber of things and so here it comes +to careless questions how do you proceed + + align:start position:0% +to careless questions how do you proceed + + + align:start position:0% +to careless questions how do you proceed +so + + align:start position:0% +so + + + align:start position:0% +so +in the literature the way you typically + + align:start position:0% +in the literature the way you typically + + + align:start position:0% +in the literature the way you typically +get to that and that's you know that's + + align:start position:0% +get to that and that's you know that's + + + align:start position:0% +get to that and that's you know that's +kind of the best way we have most of the + + align:start position:0% +kind of the best way we have most of the + + + align:start position:0% +kind of the best way we have most of the +time is you are collecting estimate from + + align:start position:0% +time is you are collecting estimate from + + + align:start position:0% +time is you are collecting estimate from +a lot of different papers and putting + + align:start position:0% +a lot of different papers and putting + + + align:start position:0% +a lot of different papers and putting +them on a common scale so that's really + + align:start position:0% +them on a common scale so that's really + + + align:start position:0% +them on a common scale so that's really +the Campbell collaborative and the + + align:start position:0% +the Campbell collaborative and the + + + align:start position:0% +the Campbell collaborative and the +coconut review is what they do for for + + align:start position:0% +coconut review is what they do for for + + + align:start position:0% +coconut review is what they do for for +health intervention and now also for + + align:start position:0% +health intervention and now also for + + + align:start position:0% +health intervention and now also for +some social science intervention they're + + align:start position:0% +some social science intervention they're + + + align:start position:0% +some social science intervention they're +basically saying you know on vitamin A + + align:start position:0% +basically saying you know on vitamin A + + + align:start position:0% +basically saying you know on vitamin A +we have like 20 studies and we can put + + align:start position:0% +we have like 20 studies and we can put + + + align:start position:0% +we have like 20 studies and we can put +them on a scale + + align:start position:0% +them on a scale + + + align:start position:0% +them on a scale +in fact once you have that you can try + + align:start position:0% +in fact once you have that you can try + + + align:start position:0% +in fact once you have that you can try +to do meta-analysis like the ones that + + align:start position:0% +to do meta-analysis like the ones that + + + align:start position:0% +to do meta-analysis like the ones that +um we found for the we discussed for the + + align:start position:0% +um we found for the we discussed for the + + + align:start position:0% +um we found for the we discussed for the +Ultra Pro paper + + align:start position:0% +Ultra Pro paper + + + align:start position:0% +Ultra Pro paper +uh Japan is doing that uh + + align:start position:0% +uh Japan is doing that uh + + + align:start position:0% +uh Japan is doing that uh +trying to accumulate different different + + align:start position:0% +trying to accumulate different different + + + align:start position:0% +trying to accumulate different different +the impact of different intervention on + + align:start position:0% +the impact of different intervention on + + + align:start position:0% +the impact of different intervention on +something and then put them on a common + + align:start position:0% +something and then put them on a common + + + align:start position:0% +something and then put them on a common +scale to find out you know what seems to + + align:start position:0% +scale to find out you know what seems to + + + align:start position:0% +scale to find out you know what seems to +be more most cost effective to increase + + align:start position:0% +be more most cost effective to increase + + + align:start position:0% +be more most cost effective to increase +test scores or attendance or anything + + align:start position:0% +test scores or attendance or anything + + + align:start position:0% +test scores or attendance or anything +you're interested in + + align:start position:0% +you're interested in + + + align:start position:0% +you're interested in +the problem of course is the population + + align:start position:0% +the problem of course is the population + + + align:start position:0% +the problem of course is the population +intervention very considerably across + + align:start position:0% +intervention very considerably across + + + align:start position:0% +intervention very considerably across +studies so it's it's comparable or not + + align:start position:0% +studies so it's it's comparable or not + + + align:start position:0% +studies so it's it's comparable or not +uh when you test different intervention + + align:start position:0% +uh when you test different intervention + + + align:start position:0% +uh when you test different intervention +in different contexts you can't get to + + align:start position:0% +in different contexts you can't get to + + + align:start position:0% +in different contexts you can't get to +the interaction + + align:start position:0% +the interaction + + + align:start position:0% +the interaction +which makes running you know if you want + + align:start position:0% +which makes running you know if you want + + + align:start position:0% +which makes running you know if you want +to answer a question in particular in + + align:start position:0% +to answer a question in particular in + + + align:start position:0% +to answer a question in particular in +this case with harriera which is their + + align:start position:0% +this case with harriera which is their + + + align:start position:0% +this case with harriera which is their +viewers that whatever you tell us we're + + align:start position:0% +viewers that whatever you tell us we're + + + align:start position:0% +viewers that whatever you tell us we're +gonna try and scale it up + + align:start position:0% +gonna try and scale it up + + + align:start position:0% +gonna try and scale it up +is I you know the idea and experiment + + align:start position:0% +is I you know the idea and experiment + + + align:start position:0% +is I you know the idea and experiment +then is not one experiment with one + + align:start position:0% +then is not one experiment with one + + + align:start position:0% +then is not one experiment with one +treatment is to run a single large RCT + + align:start position:0% +treatment is to run a single large RCT + + + align:start position:0% +treatment is to run a single large RCT +which has everything we can think of + + align:start position:0% + + + + align:start position:0% + +the problem is that + + align:start position:0% +the problem is that + + + align:start position:0% +the problem is that +and even though the experiment this + + align:start position:0% +and even though the experiment this + + + align:start position:0% +and even though the experiment this +experiment was pretty large + + align:start position:0% +experiment was pretty large + + + align:start position:0% +experiment was pretty large +so it's two Thousand Villages but in + + align:start position:0% +so it's two Thousand Villages but in + + + align:start position:0% +so it's two Thousand Villages but in +fact + + align:start position:0% +fact + + + align:start position:0% +fact +900 Villages where we did the the + + align:start position:0% +900 Villages where we did the the + + + align:start position:0% +900 Villages where we did the the +centers where we could do the gossips + + align:start position:0% +centers where we could do the gossips + + + align:start position:0% +centers where we could do the gossips +um + + align:start position:0% +um + + + align:start position:0% +um +but it's not infinite + + align:start position:0% +but it's not infinite + + + align:start position:0% +but it's not infinite +and the number of possible combination + + align:start position:0% +and the number of possible combination + + + align:start position:0% +and the number of possible combination +is large + + align:start position:0% +is large + + + align:start position:0% +is large +so what did you do so uh + + align:start position:0% +so what did you do so uh + + + align:start position:0% +so what did you do so uh +the first thing you could do is to say + + align:start position:0% +the first thing you could do is to say + + + align:start position:0% +the first thing you could do is to say +well you know it's too large uh that's + + align:start position:0% +well you know it's too large uh that's + + + align:start position:0% +well you know it's too large uh that's +going to be too many things to look at + + align:start position:0% +going to be too many things to look at + + + align:start position:0% +going to be too many things to look at +you're never going to be power to look + + align:start position:0% +you're never going to be power to look + + + align:start position:0% +you're never going to be power to look +at every single cell of interaction so + + align:start position:0% +at every single cell of interaction so + + + align:start position:0% +at every single cell of interaction so +run very few treatments + + align:start position:0% +run very few treatments + + + align:start position:0% +run very few treatments +so that's the uh um there was there is a + + align:start position:0% +so that's the uh um there was there is a + + + align:start position:0% +so that's the uh um there was there is a +paper by Karthik muralidan and others + + align:start position:0% +paper by Karthik muralidan and others + + + align:start position:0% +paper by Karthik muralidan and others +that point out that once you have + + align:start position:0% +that point out that once you have + + + align:start position:0% +that point out that once you have +interaction + + align:start position:0% +interaction + + + align:start position:0% +interaction +if you have say two treatment and their + + align:start position:0% +if you have say two treatment and their + + + align:start position:0% +if you have say two treatment and their +interaction it gets messy to ignore the + + align:start position:0% +interaction it gets messy to ignore the + + + align:start position:0% +interaction it gets messy to ignore the +interaction which is what a lot of + + align:start position:0% +interaction which is what a lot of + + + align:start position:0% +interaction which is what a lot of +people do + + align:start position:0% +people do + + + align:start position:0% +people do +and then therefore it's confusing so the + + align:start position:0% +and then therefore it's confusing so the + + + align:start position:0% +and then therefore it's confusing so the +Mackenzie solution is just don't do it + + align:start position:0% +Mackenzie solution is just don't do it + + + align:start position:0% +Mackenzie solution is just don't do it +run one treatment + + align:start position:0% +run one treatment + + + align:start position:0% +run one treatment +that's nice + + align:start position:0% +that's nice + + + align:start position:0% +that's nice +but uh + + align:start position:0% + + + + align:start position:0% + +that means like which one like how will + + align:start position:0% +that means like which one like how will + + + align:start position:0% +that means like which one like how will +you pick which one + + align:start position:0% +you pick which one + + + align:start position:0% +you pick which one +or you could include all combos + + align:start position:0% +or you could include all combos + + + align:start position:0% +or you could include all combos +but potentially lose power because you + + align:start position:0% +but potentially lose power because you + + + align:start position:0% +but potentially lose power because you +have a lot of different cells and the + + align:start position:0% +have a lot of different cells and the + + + align:start position:0% +have a lot of different cells and the +cells can become quite small + + align:start position:0% +cells can become quite small + + + align:start position:0% +cells can become quite small +uh + + align:start position:0% +uh + + + align:start position:0% +uh +I'll tell you exactly how small in our + + align:start position:0% +I'll tell you exactly how small in our + + + align:start position:0% +I'll tell you exactly how small in our +case for example when I get to that so + + align:start position:0% +case for example when I get to that so + + + align:start position:0% +case for example when I get to that so +in practice what people do is sometimes + + align:start position:0% +in practice what people do is sometimes + + + align:start position:0% +in practice what people do is sometimes +run many experiments and then pull + + align:start position:0% +run many experiments and then pull + + + align:start position:0% +run many experiments and then pull +exposed if it looks like the + + align:start position:0% +exposed if it looks like the + + + align:start position:0% +exposed if it looks like the +interactions are not significant + + align:start position:0% +interactions are not significant + + + align:start position:0% +interactions are not significant +but then that poses a problem of + + align:start position:0% +but then that poses a problem of + + + align:start position:0% +but then that poses a problem of +Statistics which is if you first run all + + align:start position:0% +Statistics which is if you first run all + + + align:start position:0% +Statistics which is if you first run all +interaction then remove them when they + + align:start position:0% +interaction then remove them when they + + + align:start position:0% +interaction then remove them when they +are not significant then + + align:start position:0% +are not significant then + + + align:start position:0% +are not significant then +it's not clear how to read the the test + + align:start position:0% +it's not clear how to read the the test + + + align:start position:0% +it's not clear how to read the the test +statistics right because you might it + + align:start position:0% +statistics right because you might it + + + align:start position:0% +statistics right because you might it +might just have been a fluke that it was + + align:start position:0% +might just have been a fluke that it was + + + align:start position:0% +might just have been a fluke that it was +or wasn't significant so we can't + + align:start position:0% +or wasn't significant so we can't + + + align:start position:0% +or wasn't significant so we can't +interpret these statistics unless we go + + align:start position:0% +interpret these statistics unless we go + + + align:start position:0% +interpret these statistics unless we go +with a clear frame in mind + + align:start position:0% + + + + align:start position:0% + +so in the literature uh there is a lot + + align:start position:0% +so in the literature uh there is a lot + + + align:start position:0% +so in the literature uh there is a lot +of push towards uh you know going simple + + align:start position:0% +of push towards uh you know going simple + + + align:start position:0% +of push towards uh you know going simple +and pre-analysis plan and therefore + + align:start position:0% +and pre-analysis plan and therefore + + + align:start position:0% +and pre-analysis plan and therefore +going towards like one or saying in + + align:start position:0% +going towards like one or saying in + + + align:start position:0% +going towards like one or saying in +advance exactly what you're gonna run + + align:start position:0% +advance exactly what you're gonna run + + + align:start position:0% +advance exactly what you're gonna run +um + + align:start position:0% +um + + + align:start position:0% +um +the issue is that that's uh it's + + align:start position:0% +the issue is that that's uh it's + + + align:start position:0% +the issue is that that's uh it's +assuming the conclusion + + align:start position:0% +assuming the conclusion + + + align:start position:0% +assuming the conclusion +so this is a an image from The Matrix + + align:start position:0% +so this is a an image from The Matrix + + + align:start position:0% +so this is a an image from The Matrix +where uh the Oracle so this is the + + align:start position:0% +where uh the Oracle so this is the + + + align:start position:0% +where uh the Oracle so this is the +Oracle problem like the Oracle point is + + align:start position:0% +Oracle problem like the Oracle point is + + + align:start position:0% +Oracle problem like the Oracle point is +that if you have if you know what it is + + align:start position:0% +that if you have if you know what it is + + + align:start position:0% +that if you have if you know what it is +that you want to test + + align:start position:0% +that you want to test + + + align:start position:0% +that you want to test +then first of all there is a question of + + align:start position:0% +then first of all there is a question of + + + align:start position:0% +then first of all there is a question of +whether you should test it anyway + + align:start position:0% +whether you should test it anyway + + + align:start position:0% +whether you should test it anyway +uh but uh you uh you kind of want the + + align:start position:0% +uh but uh you uh you kind of want the + + + align:start position:0% +uh but uh you uh you kind of want the +experiment to justify your your your + + align:start position:0% +experiment to justify your your your + + + align:start position:0% +experiment to justify your your your +prior so you you didn't come here to + + align:start position:0% +prior so you you didn't come here to + + + align:start position:0% +prior so you you didn't come here to +make the choice you've already made it + + align:start position:0% +make the choice you've already made it + + + align:start position:0% +make the choice you've already made it +you have to understand why you made it + + align:start position:0% +you have to understand why you made it + + + align:start position:0% +you have to understand why you made it +so that's the issue with Oracle and in a + + align:start position:0% +so that's the issue with Oracle and in a + + + align:start position:0% +so that's the issue with Oracle and in a +lot of cases for example in this case I + + align:start position:0% +lot of cases for example in this case I + + + align:start position:0% +lot of cases for example in this case I +you know we didn't have an argument + + align:start position:0% +you know we didn't have an argument + + + align:start position:0% +you know we didn't have an argument +so that's that's the problem so that's + + align:start position:0% +so that's that's the problem so that's + + + align:start position:0% +so that's that's the problem so that's +the tension that kailash's question was + + align:start position:0% +the tension that kailash's question was + + + align:start position:0% +the tension that kailash's question was +uh was asking + + align:start position:0% +uh was asking + + + align:start position:0% +uh was asking +and then there is another problem which + + align:start position:0% +and then there is another problem which + + + align:start position:0% +and then there is another problem which +is when you even if you had a large + + align:start position:0% +is when you even if you had a large + + + align:start position:0% +is when you even if you had a large +large + + align:start position:0% +large + + + align:start position:0% +large +set of sample size so you could run many + + align:start position:0% +set of sample size so you could run many + + + align:start position:0% +set of sample size so you could run many +many things individually you can think + + align:start position:0% +many things individually you can think + + + align:start position:0% +many things individually you can think +of them all of the Combos and variants + + align:start position:0% +of them all of the Combos and variants + + + align:start position:0% +of them all of the Combos and variants +and variant combos or variants as uh + + align:start position:0% +and variant combos or variants as uh + + + align:start position:0% +and variant combos or variants as uh +individual treatment + + align:start position:0% +individual treatment + + + align:start position:0% +individual treatment +and then you tell the government this is + + align:start position:0% +and then you tell the government this is + + + align:start position:0% +and then you tell the government this is +the best policy you go for it this is + + align:start position:0% +the best policy you go for it this is + + + align:start position:0% +the best policy you go for it this is +the effect you're going to get for it + + align:start position:0% +the effect you're going to get for it + + + align:start position:0% +the effect you're going to get for it +okay that's nice except that it will + + align:start position:0% +okay that's nice except that it will + + + align:start position:0% +okay that's nice except that it will +make uh the policy + + align:start position:0% +make uh the policy + + + align:start position:0% +make uh the policy +is chosen to be the best in that sample + + align:start position:0% +is chosen to be the best in that sample + + + align:start position:0% +is chosen to be the best in that sample +so by definition it performs pretty well + + align:start position:0% +so by definition it performs pretty well + + + align:start position:0% +so by definition it performs pretty well +in that sample and it could be a fluke + + align:start position:0% +in that sample and it could be a fluke + + + align:start position:0% +in that sample and it could be a fluke +as you know it's like the best uh + + align:start position:0% +as you know it's like the best uh + + + align:start position:0% +as you know it's like the best uh +basketball player + + align:start position:0% +basketball player + + + align:start position:0% +basketball player +if you rank people with a basketball + + align:start position:0% +if you rank people with a basketball + + + align:start position:0% +if you rank people with a basketball +player the best basketball player is + + align:start position:0% +player the best basketball player is + + + align:start position:0% +player the best basketball player is +someone who's on the day you were + + align:start position:0% +someone who's on the day you were + + + align:start position:0% +someone who's on the day you were +ranking as Scott many many goals but it + + align:start position:0% +ranking as Scott many many goals but it + + + align:start position:0% +ranking as Scott many many goals but it +might not be that that much best overall + + align:start position:0% +might not be that that much best overall + + + align:start position:0% +might not be that that much best overall +it's just a that day it performed so + + align:start position:0% +it's just a that day it performed so + + + align:start position:0% +it's just a that day it performed so +well that it looks absolutely fabulous + + align:start position:0% +well that it looks absolutely fabulous + + + align:start position:0% +well that it looks absolutely fabulous +that's not his you might be + + align:start position:0% +that's not his you might be + + + align:start position:0% +that's not his you might be +very disappointed once you get him to + + align:start position:0% +very disappointed once you get him to + + + align:start position:0% +very disappointed once you get him to +your team that on most days is not as + + align:start position:0% +your team that on most days is not as + + + align:start position:0% +your team that on most days is not as +fabulous + + align:start position:0% +fabulous + + + align:start position:0% +fabulous +similarly for a policy if you picked it + + align:start position:0% +similarly for a policy if you picked it + + + align:start position:0% +similarly for a policy if you picked it +along among a big range of policy to be + + align:start position:0% +along among a big range of policy to be + + + align:start position:0% +along among a big range of policy to be +the best it will look really great + + align:start position:0% +the best it will look really great + + + align:start position:0% +the best it will look really great +by definition it performs really well in + + align:start position:0% +by definition it performs really well in + + + align:start position:0% +by definition it performs really well in +your small sample + + align:start position:0% +your small sample + + + align:start position:0% +your small sample +the question is you're giving it credit + + align:start position:0% +the question is you're giving it credit + + + align:start position:0% +the question is you're giving it credit +for + + align:start position:0% +for + + + align:start position:0% +for +the Epsilon + + align:start position:0% +the Epsilon + + + align:start position:0% +the Epsilon +and so that's not a conceptually + + align:start position:0% +and so that's not a conceptually + + + align:start position:0% +and so that's not a conceptually +difficult problem + + align:start position:0% +difficult problem + + + align:start position:0% +difficult problem +it's a very nice paper by Isaiah and + + align:start position:0% +it's a very nice paper by Isaiah and + + + align:start position:0% +it's a very nice paper by Isaiah and +quarters that looks at that and + + align:start position:0% +quarters that looks at that and + + + align:start position:0% +quarters that looks at that and +basically disease can be it just can be + + align:start position:0% +basically disease can be it just can be + + + align:start position:0% +basically disease can be it just can be +corrected and so this is they have a + + align:start position:0% +corrected and so this is they have a + + + align:start position:0% +corrected and so this is they have a +paper called influence on winners + + align:start position:0% +paper called influence on winners + + + align:start position:0% +paper called influence on winners +now the problem is the more policies you + + align:start position:0% +now the problem is the more policies you + + + align:start position:0% +now the problem is the more policies you +are trying to test against + + align:start position:0% +are trying to test against + + + align:start position:0% +are trying to test against +and the more + + align:start position:0% +and the more + + + align:start position:0% +and the more +similar there to each other + + align:start position:0% +similar there to each other + + + align:start position:0% +similar there to each other +the more you're going to be penalized by + + align:start position:0% +the more you're going to be penalized by + + + align:start position:0% +the more you're going to be penalized by +the inference on winners + + align:start position:0% +the inference on winners + + + align:start position:0% +the inference on winners +so naturally because they you have to be + + align:start position:0% +so naturally because they you have to be + + + align:start position:0% +so naturally because they you have to be +the best you'd have to you have to be + + align:start position:0% +the best you'd have to you have to be + + + align:start position:0% +the best you'd have to you have to be +particularly lucky + + align:start position:0% +particularly lucky + + + align:start position:0% +particularly lucky +so that means that that's one more + + align:start position:0% +so that means that that's one more + + + align:start position:0% +so that means that that's one more +reason to not have a lot a lot a lot of + + align:start position:0% +reason to not have a lot a lot a lot of + + + align:start position:0% +reason to not have a lot a lot a lot of +treatments uh in principle but then we + + align:start position:0% +treatments uh in principle but then we + + + align:start position:0% +treatments uh in principle but then we +still would sometimes we would like to + + align:start position:0% +still would sometimes we would like to + + + align:start position:0% +still would sometimes we would like to +have a lot a lot of treatments because + + align:start position:0% +have a lot a lot of treatments because + + + align:start position:0% +have a lot a lot of treatments because +we really don't know and we would like + + align:start position:0% +we really don't know and we would like + + + align:start position:0% +we really don't know and we would like +to run one experiment and have a you + + align:start position:0% +to run one experiment and have a you + + + align:start position:0% +to run one experiment and have a you +know coherent answer that doesn't assume + + align:start position:0% +know coherent answer that doesn't assume + + + align:start position:0% +know coherent answer that doesn't assume +the solution in advance + + align:start position:0% + + + + align:start position:0% + +yeah so it's just like you happen to in + + align:start position:0% +yeah so it's just like you happen to in + + + align:start position:0% +yeah so it's just like you happen to in +that sample you happen to do quite well + + align:start position:0% +that sample you happen to do quite well + + + align:start position:0% +that sample you happen to do quite well +so it's just imagine for example a + + align:start position:0% +so it's just imagine for example a + + + align:start position:0% +so it's just imagine for example a +setting where in fact all of the + + align:start position:0% +setting where in fact all of the + + + align:start position:0% +setting where in fact all of the +policies have the same effect + + align:start position:0% +policies have the same effect + + + align:start position:0% +policies have the same effect +you're still gonna rank them + + align:start position:0% +you're still gonna rank them + + + align:start position:0% +you're still gonna rank them +according to the Epsilon + + align:start position:0% +according to the Epsilon + + + align:start position:0% +according to the Epsilon +so that's the that's what we have to get + + align:start position:0% +so that's the that's what we have to get + + + align:start position:0% +so that's the that's what we have to get +rid of so this is not like the scale-up + + align:start position:0% +rid of so this is not like the scale-up + + + align:start position:0% +rid of so this is not like the scale-up +problem that's not the scalar problem + + align:start position:0% +problem that's not the scalar problem + + + align:start position:0% +problem that's not the scalar problem +it's just I have tested a lot of policy + + align:start position:0% +it's just I have tested a lot of policy + + + align:start position:0% +it's just I have tested a lot of policy +I'm picking the best + + align:start position:0% +I'm picking the best + + + align:start position:0% +I'm picking the best +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +and this is kind of a standard thing + + align:start position:0% +and this is kind of a standard thing + + + align:start position:0% +and this is kind of a standard thing +that's exactly what we're going to do + + align:start position:0% +that's exactly what we're going to do + + + align:start position:0% +that's exactly what we're going to do +here that's exactly what we want to do + + align:start position:0% +here that's exactly what we want to do + + + align:start position:0% +here that's exactly what we want to do +here and that's a common way to think + + align:start position:0% +here and that's a common way to think + + + align:start position:0% +here and that's a common way to think +about policy problems is you know what's + + align:start position:0% +about policy problems is you know what's + + + align:start position:0% +about policy problems is you know what's +the best and then the best is also the + + align:start position:0% +the best and then the best is also the + + + align:start position:0% +the best and then the best is also the +one who performed the best in that + + align:start position:0% +one who performed the best in that + + + align:start position:0% +one who performed the best in that +sample and hence + + align:start position:0% +sample and hence + + + align:start position:0% +sample and hence +that has kind of benefited from the most + + align:start position:0% +that has kind of benefited from the most + + + align:start position:0% +that has kind of benefited from the most +fluke by construction so this is + + align:start position:0% +fluke by construction so this is + + + align:start position:0% +fluke by construction so this is +collectible + + align:start position:0% +collectible + + + align:start position:0% +collectible +this is pretty easy to correct actually + + align:start position:0% +this is pretty easy to correct actually + + + align:start position:0% +this is pretty easy to correct actually +there is nothing it's just it's very + + align:start position:0% +there is nothing it's just it's very + + + align:start position:0% +there is nothing it's just it's very +classical statistics in there the + + align:start position:0% +classical statistics in there the + + + align:start position:0% +classical statistics in there the +problem is the correction is going to + + align:start position:0% +problem is the correction is going to + + + align:start position:0% +problem is the correction is going to +penalize you for having a lot of options + + align:start position:0% +penalize you for having a lot of options + + + align:start position:0% +penalize you for having a lot of options +you're trying against each other as well + + align:start position:0% +you're trying against each other as well + + + align:start position:0% +you're trying against each other as well +as for having options that that are in + + align:start position:0% +as for having options that that are in + + + align:start position:0% +as for having options that that are in +fact similar yep + + align:start position:0% + + + + align:start position:0% + +between each other no + + align:start position:0% +between each other no + + + align:start position:0% +between each other no +I don't know like if I can see the two + + align:start position:0% +I don't know like if I can see the two + + + align:start position:0% +I don't know like if I can see the two +interventions are one is + + align:start position:0% +interventions are one is + + + align:start position:0% +interventions are one is +yeah so the control here doesn't the + + align:start position:0% +yeah so the control here doesn't the + + + align:start position:0% +yeah so the control here doesn't the +control here is the same for everyone so + + align:start position:0% +control here is the same for everyone so + + + align:start position:0% +control here is the same for everyone so +so when you crank again to when you it's + + align:start position:0% +so when you crank again to when you it's + + + align:start position:0% +so when you crank again to when you it's +if you do the treatment effect you're + + align:start position:0% +if you do the treatment effect you're + + + align:start position:0% +if you do the treatment effect you're +gonna do the treatment effect against + + align:start position:0% +gonna do the treatment effect against + + + align:start position:0% +gonna do the treatment effect against +the control and you're saying + + align:start position:0% +the control and you're saying + + + align:start position:0% +the control and you're saying +intervention a as the biggest treatment + + align:start position:0% +intervention a as the biggest treatment + + + align:start position:0% +intervention a as the biggest treatment +effect b as the second biggest treatment + + align:start position:0% +effect b as the second biggest treatment + + + align:start position:0% +effect b as the second biggest treatment +effect Etc they're all ranked again to + + align:start position:0% +effect Etc they're all ranked again to + + + align:start position:0% +effect Etc they're all ranked again to +the same control + + align:start position:0% +the same control + + + align:start position:0% +the same control +yeah but then but then for example the + + align:start position:0% +yeah but then but then for example the + + + align:start position:0% +yeah but then but then for example the +first the best front and the second + + align:start position:0% +first the best front and the second + + + align:start position:0% +first the best front and the second +round between each other not the + + align:start position:0% + + + + align:start position:0% + +they could be I couldn't rule out that + + align:start position:0% +they could be I couldn't rule out that + + + align:start position:0% +they could be I couldn't rule out that +one is better than the other two is that + + align:start position:0% +one is better than the other two is that + + + align:start position:0% +one is better than the other two is that +that that's possible but is it so in + + align:start position:0% +that that's possible but is it so in + + + align:start position:0% +that that's possible but is it so in +that case you don't know which is the + + align:start position:0% +that case you don't know which is the + + + align:start position:0% +that case you don't know which is the +best but even if they are it it might be + + align:start position:0% +best but even if they are it it might be + + + align:start position:0% +best but even if they are it it might be +because it is in part because your first + + align:start position:0% +because it is in part because your first + + + align:start position:0% +because it is in part because your first +one happened to do well in the sample + + align:start position:0% +one happened to do well in the sample + + + align:start position:0% +one happened to do well in the sample +compared to the second one + + align:start position:0% +compared to the second one + + + align:start position:0% +compared to the second one +if they are if they are suppose they are + + align:start position:0% +if they are if they are suppose they are + + + align:start position:0% +if they are if they are suppose they are +statistically different it could still + + align:start position:0% +statistically different it could still + + + align:start position:0% +statistically different it could still +be impact because the first one happened + + align:start position:0% +be impact because the first one happened + + + align:start position:0% +be impact because the first one happened +to have a very good draw of the epsilons + + align:start position:0% +to have a very good draw of the epsilons + + + align:start position:0% +to have a very good draw of the epsilons +in the treatment comp and the two didn't + + align:start position:0% +in the treatment comp and the two didn't + + + align:start position:0% +in the treatment comp and the two didn't +so that's the that's the problem that's + + align:start position:0% +so that's the that's the problem that's + + + align:start position:0% +so that's the that's the problem that's +not it's not a problem that you might + + align:start position:0% +not it's not a problem that you might + + + align:start position:0% +not it's not a problem that you might +think they are different but in fact + + align:start position:0% +think they are different but in fact + + + align:start position:0% +think they are different but in fact +they are not statistically different + + align:start position:0% +they are not statistically different + + + align:start position:0% +they are not statistically different +which is a good point + + align:start position:0% +which is a good point + + + align:start position:0% +which is a good point +but then even if they are it could be + + align:start position:0% +but then even if they are it could be + + + align:start position:0% +but then even if they are it could be +just for a fluke performance in that + + align:start position:0% +just for a fluke performance in that + + + align:start position:0% +just for a fluke performance in that +sample so that's not it's it's not a + + align:start position:0% +sample so that's not it's it's not a + + + align:start position:0% +sample so that's not it's it's not a +conceptually difficult at all + + align:start position:0% +conceptually difficult at all + + + align:start position:0% +conceptually difficult at all +but uh oh oh it's not difficult to deal + + align:start position:0% +but uh oh oh it's not difficult to deal + + + align:start position:0% +but uh oh oh it's not difficult to deal +with at all + + align:start position:0% +with at all + + + align:start position:0% +with at all +um even in in stata but + + align:start position:0% +um even in in stata but + + + align:start position:0% +um even in in stata but +it's just that how you know how much you + + align:start position:0% +it's just that how you know how much you + + + align:start position:0% +it's just that how you know how much you +penalize yourself it depends on how many + + align:start position:0% +penalize yourself it depends on how many + + + align:start position:0% +penalize yourself it depends on how many +policies you run against each other + + align:start position:0% +policies you run against each other + + + align:start position:0% +policies you run against each other +which makes sense because you have more + + align:start position:0% +which makes sense because you have more + + + align:start position:0% +which makes sense because you have more +ignorance so that's the tension that's + + align:start position:0% +ignorance so that's the tension that's + + + align:start position:0% +ignorance so that's the tension that's +where your question needed more than a + + align:start position:0% +where your question needed more than a + + + align:start position:0% +where your question needed more than a +one minute answer is what do you do + + align:start position:0% +one minute answer is what do you do + + + align:start position:0% +one minute answer is what do you do +so what we did is that we tried + + align:start position:0% +so what we did is that we tried + + + align:start position:0% +so what we did is that we tried +basically we tried to navigate getting + + align:start position:0% +basically we tried to navigate getting + + + align:start position:0% +basically we tried to navigate getting +the best of both world + + align:start position:0% +the best of both world + + + align:start position:0% +the best of both world +by saying look + + align:start position:0% +by saying look + + + align:start position:0% +by saying look +most policies don't work anyways and + + align:start position:0% +most policies don't work anyways and + + + align:start position:0% +most policies don't work anyways and +most policy variation might not matter + + align:start position:0% +most policy variation might not matter + + + align:start position:0% +most policy variation might not matter +so for example dosage + + align:start position:0% +so for example dosage + + + align:start position:0% +so for example dosage +those age might not be that relevant in + + align:start position:0% +those age might not be that relevant in + + + align:start position:0% +those age might not be that relevant in +the gossip world you know the fact that + + align:start position:0% +the gossip world you know the fact that + + + align:start position:0% +the gossip world you know the fact that +the gossip is trusted or trusted gossip + + align:start position:0% +the gossip is trusted or trusted gossip + + + align:start position:0% +the gossip is trusted or trusted gossip +might be you know + + align:start position:0% +might be you know + + + align:start position:0% +might be you know +similar + + align:start position:0% +similar + + + align:start position:0% +similar +you don't know whether it's similar that + + align:start position:0% +you don't know whether it's similar that + + + align:start position:0% +you don't know whether it's similar that +you say maybe it is so maybe a lot of my + + align:start position:0% +you say maybe it is so maybe a lot of my + + + align:start position:0% +you say maybe it is so maybe a lot of my +possible treatments can be + + align:start position:0% +possible treatments can be + + + align:start position:0% +possible treatments can be +eliminated from my from my consideration + + align:start position:0% +eliminated from my from my consideration + + + align:start position:0% +eliminated from my from my consideration +set + + align:start position:0% +set + + + align:start position:0% +set +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and therefore I can run many many + + align:start position:0% +and therefore I can run many many + + + align:start position:0% +and therefore I can run many many +treatments + + align:start position:0% +treatments + + + align:start position:0% +treatments +and get rid of anything that doesn't + + align:start position:0% +and get rid of anything that doesn't + + + align:start position:0% +and get rid of anything that doesn't +work at all + + align:start position:0% +work at all + + + align:start position:0% +work at all +and then + + align:start position:0% +and then + + + align:start position:0% +and then +pull together + + align:start position:0% +pull together + + + align:start position:0% +pull together +what is similar + + align:start position:0% +what is similar + + + align:start position:0% +what is similar +and then uh be left only with uh + + align:start position:0% +and then uh be left only with uh + + + align:start position:0% +and then uh be left only with uh +intervention that seems promising at the + + align:start position:0% +intervention that seems promising at the + + + align:start position:0% +intervention that seems promising at the +end of the day and estimate my + + align:start position:0% +end of the day and estimate my + + + align:start position:0% +end of the day and estimate my +congression in that set of promising + + align:start position:0% +congression in that set of promising + + + align:start position:0% +congression in that set of promising +policies + + align:start position:0% +policies + + + align:start position:0% +policies +so what do I mean by pulling + + align:start position:0% +so what do I mean by pulling + + + align:start position:0% +so what do I mean by pulling +we're only going to pull uh and that's + + align:start position:0% +we're only going to pull uh and that's + + + align:start position:0% +we're only going to pull uh and that's +the + + align:start position:0% +the + + + align:start position:0% +the +you know that why is why can you pull in + + align:start position:0% +you know that why is why can you pull in + + + align:start position:0% +you know that why is why can you pull in +some setting that and not get uh uh full + + align:start position:0% +some setting that and not get uh uh full + + + align:start position:0% +some setting that and not get uh uh full +prayer of the of the problem that + + align:start position:0% +prayer of the of the problem that + + + align:start position:0% +prayer of the of the problem that +Karthik molidarana identified which is + + align:start position:0% +Karthik molidarana identified which is + + + align:start position:0% +Karthik molidarana identified which is +if I pool exposed + + align:start position:0% +if I pool exposed + + + align:start position:0% +if I pool exposed +when the interaction is negative that's + + align:start position:0% +when the interaction is negative that's + + + align:start position:0% +when the interaction is negative that's +a little that's that's fishy + + align:start position:0% + + + + align:start position:0% + +we only going to pull or we're only + + align:start position:0% +we only going to pull or we're only + + + align:start position:0% +we only going to pull or we're only +going to ask the data whether they want + + align:start position:0% +going to ask the data whether they want + + + align:start position:0% +going to ask the data whether they want +to pull things that that that that are + + align:start position:0% +to pull things that that that that are + + + align:start position:0% +to pull things that that that that are +dosages of the same or variants of the + + align:start position:0% +dosages of the same or variants of the + + + align:start position:0% +dosages of the same or variants of the +same treatment + + align:start position:0% +same treatment + + + align:start position:0% +same treatment +so I'm putting in some Theory it's not + + align:start position:0% +so I'm putting in some Theory it's not + + + align:start position:0% +so I'm putting in some Theory it's not +really Theory or some amount of + + align:start position:0% +really Theory or some amount of + + + align:start position:0% +really Theory or some amount of +structure there + + align:start position:0% +structure there + + + align:start position:0% +structure there +to say well any sort of incentives I + + align:start position:0% +to say well any sort of incentives I + + + align:start position:0% +to say well any sort of incentives I +want to try different incentives + + align:start position:0% +want to try different incentives + + + align:start position:0% +want to try different incentives +because who knows they might differ + + align:start position:0% +because who knows they might differ + + + align:start position:0% +because who knows they might differ +but I'm going to allow the data to pull + + align:start position:0% +but I'm going to allow the data to pull + + + align:start position:0% +but I'm going to allow the data to pull +them if it turns out that all the + + align:start position:0% +them if it turns out that all the + + + align:start position:0% +them if it turns out that all the +effects are the same + + align:start position:0% +effects are the same + + + align:start position:0% +effects are the same +for example high and low incentive will + + align:start position:0% +for example high and low incentive will + + + align:start position:0% +for example high and low incentive will +be allowed to pull slope and flat and + + align:start position:0% +be allowed to pull slope and flat and + + + align:start position:0% +be allowed to pull slope and flat and +incentive will be allowed to pull the + + align:start position:0% +incentive will be allowed to pull the + + + align:start position:0% +incentive will be allowed to pull the +slope and flat and high and low will be + + align:start position:0% +slope and flat and high and low will be + + + align:start position:0% +slope and flat and high and low will be +allowed to pull + + align:start position:0% +allowed to pull + + + align:start position:0% +allowed to pull +and so that creates a treatment profile + + align:start position:0% +and so that creates a treatment profile + + + align:start position:0% +and so that creates a treatment profile +of like any sort of incentives + + align:start position:0% +of like any sort of incentives + + + align:start position:0% +of like any sort of incentives +then similarly any sorts of gossips + + align:start position:0% +then similarly any sorts of gossips + + + align:start position:0% +then similarly any sorts of gossips +and then any sort of reminder + + align:start position:0% +and then any sort of reminder + + + align:start position:0% +and then any sort of reminder +uh a lot of Commander versus fewer + + align:start position:0% +uh a lot of Commander versus fewer + + + align:start position:0% +uh a lot of Commander versus fewer +reminders + + align:start position:0% +reminders + + + align:start position:0% +reminders +so I'm telling the data that they can + + align:start position:0% +so I'm telling the data that they can + + + align:start position:0% +so I'm telling the data that they can +pull I'm going to parametrize telling + + align:start position:0% +pull I'm going to parametrize telling + + + align:start position:0% +pull I'm going to parametrize telling +the data they can pull that way + + align:start position:0% +the data they can pull that way + + + align:start position:0% +the data they can pull that way +and then uh you run I last saw on that + + align:start position:0% +and then uh you run I last saw on that + + + align:start position:0% +and then uh you run I last saw on that +you run into a small problem which is + + align:start position:0% +you run into a small problem which is + + + align:start position:0% +you run into a small problem which is +that when you run a last one that by + + align:start position:0% +that when you run a last one that by + + + align:start position:0% +that when you run a last one that by +definition you have a lot of correlation + + align:start position:0% +definition you have a lot of correlation + + + align:start position:0% +definition you have a lot of correlation +between you're going to structure so + + align:start position:0% +between you're going to structure so + + + align:start position:0% +between you're going to structure so +think of writing the regression in order + + align:start position:0% +think of writing the regression in order + + + align:start position:0% +think of writing the regression in order +to pulling allowing pulling is instead + + align:start position:0% +to pulling allowing pulling is instead + + + align:start position:0% +to pulling allowing pulling is instead +of you know you have now run all of your + + align:start position:0% +of you know you have now run all of your + + + align:start position:0% +of you know you have now run all of your +different possible treatments and + + align:start position:0% +different possible treatments and + + + align:start position:0% +different possible treatments and +interactions + + align:start position:0% +interactions + + + align:start position:0% +interactions +instead of running one regression for + + align:start position:0% +instead of running one regression for + + + align:start position:0% +instead of running one regression for +each possible treatment you run a + + align:start position:0% +each possible treatment you run a + + + align:start position:0% +each possible treatment you run a +regression of the form + + align:start position:0% +regression of the form + + + align:start position:0% +regression of the form +any incentive and then marginal effect + + align:start position:0% +any incentive and then marginal effect + + + align:start position:0% +any incentive and then marginal effect +of high incentive so then that might be + + align:start position:0% +of high incentive so then that might be + + + align:start position:0% +of high incentive so then that might be +that might become zero right as opposed + + align:start position:0% +that might become zero right as opposed + + + align:start position:0% +that might become zero right as opposed +to high incentive low incentive and then + + align:start position:0% +to high incentive low incentive and then + + + align:start position:0% +to high incentive low incentive and then +you test the difference why it's + + align:start position:0% +you test the difference why it's + + + align:start position:0% +you test the difference why it's +relevant to write it this way it's + + align:start position:0% +relevant to write it this way it's + + + align:start position:0% +relevant to write it this way it's +because you are going to run a lasso on + + align:start position:0% +because you are going to run a lasso on + + + align:start position:0% +because you are going to run a lasso on +this regression and lasso is going to uh + + align:start position:0% +this regression and lasso is going to uh + + + align:start position:0% +this regression and lasso is going to uh +penalize you for having a lot of terms + + align:start position:0% +penalize you for having a lot of terms + + + align:start position:0% +penalize you for having a lot of terms +and it's going to just ask you to curl a + + align:start position:0% +and it's going to just ask you to curl a + + + align:start position:0% +and it's going to just ask you to curl a +bunch of them saying they are completely + + align:start position:0% +bunch of them saying they are completely + + + align:start position:0% +bunch of them saying they are completely +relevant they shouldn't even be there + + align:start position:0% +relevant they shouldn't even be there + + + align:start position:0% +relevant they shouldn't even be there +so it it is so if you are two policies + + align:start position:0% +so it it is so if you are two policies + + + align:start position:0% +so it it is so if you are two policies +high and low incentive that in fact had + + align:start position:0% +high and low incentive that in fact had + + + align:start position:0% +high and low incentive that in fact had +the same effect lasso would want them + + align:start position:0% +the same effect lasso would want them + + + align:start position:0% +the same effect lasso would want them +both if they were both effective + + align:start position:0% +both if they were both effective + + + align:start position:0% +both if they were both effective +if you have if you write it as any + + align:start position:0% +if you have if you write it as any + + + align:start position:0% +if you have if you write it as any +incentive and an incentive + + align:start position:0% +incentive and an incentive + + + align:start position:0% +incentive and an incentive +the extra effect of uh High versus low + + align:start position:0% +the extra effect of uh High versus low + + + align:start position:0% +the extra effect of uh High versus low +then lasso is gonna + + align:start position:0% +then lasso is gonna + + + align:start position:0% +then lasso is gonna +get rid of that so it will allow get rid + + align:start position:0% +get rid of that so it will allow get rid + + + align:start position:0% +get rid of that so it will allow get rid +but there is a problem with doing that + + align:start position:0% +but there is a problem with doing that + + + align:start position:0% +but there is a problem with doing that +which is as soon as you do that + + align:start position:0% +which is as soon as you do that + + + align:start position:0% +which is as soon as you do that +you create a lot of correlation between + + align:start position:0% +you create a lot of correlation between + + + align:start position:0% +you create a lot of correlation between +the variable + + align:start position:0% +the variable + + + align:start position:0% +the variable +because + + align:start position:0% +because + + + align:start position:0% +because +and by definition any incentive and + + align:start position:0% +and by definition any incentive and + + + align:start position:0% +and by definition any incentive and +incentive high are very correlated + + align:start position:0% +incentive high are very correlated + + + align:start position:0% +incentive high are very correlated +right because incentive high will have a + + align:start position:0% +right because incentive high will have a + + + align:start position:0% +right because incentive high will have a +one every time incentive will have a one + + align:start position:0% +one every time incentive will have a one + + + align:start position:0% +one every time incentive will have a one +every time incentive one as a a high as + + align:start position:0% +every time incentive one as a a high as + + + align:start position:0% +every time incentive one as a a high as +a one and in addition it will have some + + align:start position:0% +a one and in addition it will have some + + + align:start position:0% +a one and in addition it will have some +zeros when the incentive is in fact low + + align:start position:0% +zeros when the incentive is in fact low + + + align:start position:0% +zeros when the incentive is in fact low +so by construction you're going to have + + align:start position:0% +so by construction you're going to have + + + align:start position:0% +so by construction you're going to have +a lot of Coalition which is precisely + + align:start position:0% +a lot of Coalition which is precisely + + + align:start position:0% +a lot of Coalition which is precisely +when you cannot run lasso intuitively is + + align:start position:0% +when you cannot run lasso intuitively is + + + align:start position:0% +when you cannot run lasso intuitively is +that you know the intuition for it being + + align:start position:0% +that you know the intuition for it being + + + align:start position:0% +that you know the intuition for it being +that you lasso is not going to know what + + align:start position:0% +that you lasso is not going to know what + + + align:start position:0% +that you lasso is not going to know what +to pick if the two things are correlated + + align:start position:0% +to pick if the two things are correlated + + + align:start position:0% +to pick if the two things are correlated +statistically it's it's uh it fails + + align:start position:0% +statistically it's it's uh it fails + + + align:start position:0% +statistically it's it's uh it fails +irrepresentability from TVA which is + + align:start position:0% +irrepresentability from TVA which is + + + align:start position:0% +irrepresentability from TVA which is +saying you cannot uh the + + align:start position:0% +saying you cannot uh the + + + align:start position:0% +saying you cannot uh the +irrepresentability is that you can only + + align:start position:0% +irrepresentability is that you can only + + + align:start position:0% +irrepresentability is that you can only +run lasso if if no variable can be + + align:start position:0% +run lasso if if no variable can be + + + align:start position:0% +run lasso if if no variable can be +approximated very well by a combination + + align:start position:0% +approximated very well by a combination + + + align:start position:0% +approximated very well by a combination +of other ones + + align:start position:0% +of other ones + + + align:start position:0% +of other ones +so but there is a solution for this + + align:start position:0% +so but there is a solution for this + + + align:start position:0% +so but there is a solution for this +problem so which is a preconditioning + + align:start position:0% +problem so which is a preconditioning + + + align:start position:0% +problem so which is a preconditioning +like preconditioning of the variable + + align:start position:0% +like preconditioning of the variable + + + align:start position:0% +like preconditioning of the variable +that basically orthogonalizes them it + + align:start position:0% +that basically orthogonalizes them it + + + align:start position:0% +that basically orthogonalizes them it +penalizes you for doing that but you get + + align:start position:0% +penalizes you for doing that but you get + + + align:start position:0% +penalizes you for doing that but you get +it works + + align:start position:0% +it works + + + align:start position:0% +it works +and then once you've done that so you + + align:start position:0% +and then once you've done that so you + + + align:start position:0% +and then once you've done that so you +run your lasso the lasso is going to + + align:start position:0% +run your lasso the lasso is going to + + + align:start position:0% +run your lasso the lasso is going to +select some variable + + align:start position:0% +select some variable + + + align:start position:0% +select some variable +it's going to kick out everything that + + align:start position:0% +it's going to kick out everything that + + + align:start position:0% +it's going to kick out everything that +is ineffective and it's going to also + + align:start position:0% +is ineffective and it's going to also + + + align:start position:0% +is ineffective and it's going to also +kick out uh things that are marginal + + align:start position:0% +kick out uh things that are marginal + + + align:start position:0% +kick out uh things that are marginal +difference that are not pertinent + + align:start position:0% +difference that are not pertinent + + + align:start position:0% +difference that are not pertinent +and once you have that you have very few + + align:start position:0% +and once you have that you have very few + + + align:start position:0% +and once you have that you have very few +variable left and you can do your post + + align:start position:0% +variable left and you can do your post + + + align:start position:0% +variable left and you can do your post +processing uh that is running which is + + align:start position:0% +processing uh that is running which is + + + align:start position:0% +processing uh that is running which is +basically running your wireless + + align:start position:0% +basically running your wireless + + + align:start position:0% +basically running your wireless +regression happily on a very small set + + align:start position:0% +regression happily on a very small set + + + align:start position:0% +regression happily on a very small set +of variable + + align:start position:0% +of variable + + + align:start position:0% +of variable +and now you can find your uh + + align:start position:0% +and now you can find your uh + + + align:start position:0% +and now you can find your uh +your Andrew's correction + + align:start position:0% +your Andrew's correction + + + align:start position:0% +your Andrew's correction +without being penalized by the fact that + + align:start position:0% +without being penalized by the fact that + + + align:start position:0% +without being penalized by the fact that +there was a lot of variables in the + + align:start position:0% +there was a lot of variables in the + + + align:start position:0% +there was a lot of variables in the +first place and you and you go ahead + + align:start position:0% +first place and you and you go ahead + + + align:start position:0% +first place and you and you go ahead +so that's that strategy Works uh you uh + + align:start position:0% +so that's that strategy Works uh you uh + + + align:start position:0% +so that's that strategy Works uh you uh +and it's sort of nicely compatible + + align:start position:0% +and it's sort of nicely compatible + + + align:start position:0% +and it's sort of nicely compatible +uh you are just uh you you don't have a + + align:start position:0% +uh you are just uh you you don't have a + + + align:start position:0% +uh you are just uh you you don't have a +fluke that's too too high because you've + + align:start position:0% +fluke that's too too high because you've + + + align:start position:0% +fluke that's too too high because you've +you've got so you you with Untold it's + + align:start position:0% +you've got so you you with Untold it's + + + align:start position:0% +you've got so you you with Untold it's +like if you wanted to really say this + + align:start position:0% +like if you wanted to really say this + + + align:start position:0% +like if you wanted to really say this +goes going back to uh salo's point which + + align:start position:0% +goes going back to uh salo's point which + + + align:start position:0% +goes going back to uh salo's point which +is suppose you have high incentive and + + align:start position:0% +is suppose you have high incentive and + + + align:start position:0% +is suppose you have high incentive and +low incentive and in fact they have the + + align:start position:0% +low incentive and in fact they have the + + + align:start position:0% +low incentive and in fact they have the +same effect + + align:start position:0% +same effect + + + align:start position:0% +same effect +they are not statistically different so + + align:start position:0% +they are not statistically different so + + + align:start position:0% +they are not statistically different so +one of them will come out ahead and will + + align:start position:0% +one of them will come out ahead and will + + + align:start position:0% +one of them will come out ahead and will +be penalized a lot + + align:start position:0% +be penalized a lot + + + align:start position:0% +be penalized a lot +by the fact that it's very close to the + + align:start position:0% +by the fact that it's very close to the + + + align:start position:0% +by the fact that it's very close to the +other one + + align:start position:0% +other one + + + align:start position:0% +other one +but in fact if you know that they should + + align:start position:0% +but in fact if you know that they should + + + align:start position:0% +but in fact if you know that they should +be pulled and you won't have that + + align:start position:0% +be pulled and you won't have that + + + align:start position:0% +be pulled and you won't have that +problem you just have incentives + + align:start position:0% +problem you just have incentives + + + align:start position:0% +problem you just have incentives +so that's that's that's why we run it in + + align:start position:0% +so that's that's that's why we run it in + + + align:start position:0% +so that's that's that's why we run it in +these steps so if we go back now so with + + align:start position:0% +these steps so if we go back now so with + + + align:start position:0% +these steps so if we go back now so with +how many treatment we have + + align:start position:0% +how many treatment we have + + + align:start position:0% +how many treatment we have +so incentives are cost Two by Two by + + align:start position:0% +so incentives are cost Two by Two by + + + align:start position:0% +so incentives are cost Two by Two by +high and low and flat and slope + + align:start position:0% +high and low and flat and slope + + + align:start position:0% +high and low and flat and slope +reminders of two uh + + align:start position:0% +reminders of two uh + + + align:start position:0% +reminders of two uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +smaller a few versus a lot + + align:start position:0% +smaller a few versus a lot + + + align:start position:0% +smaller a few versus a lot +the ambassadors have random Plus + + align:start position:0% +the ambassadors have random Plus + + + align:start position:0% +the ambassadors have random Plus +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um + + align:start position:0% +um + + + align:start position:0% +um +information seed plus trusted seed plus + + align:start position:0% +information seed plus trusted seed plus + + + align:start position:0% +information seed plus trusted seed plus +I think this went from the from the + + align:start position:0% +I think this went from the from the + + + align:start position:0% +I think this went from the from the +board information time stress that's + + align:start position:0% +board information time stress that's + + + align:start position:0% +board information time stress that's +makes four + + align:start position:0% +makes four + + + align:start position:0% +makes four +so in total that 75 unique policy + + align:start position:0% +so in total that 75 unique policy + + + align:start position:0% +so in total that 75 unique policy +combination everything is interacted + + align:start position:0% +combination everything is interacted + + + align:start position:0% +combination everything is interacted +with everything so it's 75 unique policy + + align:start position:0% +with everything so it's 75 unique policy + + + align:start position:0% +with everything so it's 75 unique policy +combination so with 914 which actually + + align:start position:0% +combination so with 914 which actually + + + align:start position:0% +combination so with 914 which actually +used this is useful this is a sample + + align:start position:0% +used this is useful this is a sample + + + align:start position:0% +used this is useful this is a sample +that where we do a reminder in incentive + + align:start position:0% +that where we do a reminder in incentive + + + align:start position:0% +that where we do a reminder in incentive +but the gossip is not only done in 900 + + align:start position:0% +but the gossip is not only done in 900 + + + align:start position:0% +but the gossip is not only done in 900 +the the resulting sample size would + + align:start position:0% +the the resulting sample size would + + + align:start position:0% +the the resulting sample size would +actually be quite low + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +that's the the + + align:start position:0% + + + + align:start position:0% + +how everything is caused with everything + + align:start position:0% +how everything is caused with everything + + + align:start position:0% +how everything is caused with everything +doesn't really matter + + align:start position:0% +doesn't really matter + + + align:start position:0% +doesn't really matter +so we could start we start by doing if + + align:start position:0% +so we could start we start by doing if + + + align:start position:0% +so we could start we start by doing if +we start by doing the kind of naive + + align:start position:0% +we start by doing the kind of naive + + + align:start position:0% +we start by doing the kind of naive +thing of not interacting with everything + + align:start position:0% +thing of not interacting with everything + + + align:start position:0% +thing of not interacting with everything +uh you run this uh this regression so + + align:start position:0% +uh you run this uh this regression so + + + align:start position:0% +uh you run this uh this regression so +this is a dummy for each thing + + align:start position:0% +this is a dummy for each thing + + + align:start position:0% +this is a dummy for each thing +it's already giving you giving you some + + align:start position:0% +it's already giving you giving you some + + + align:start position:0% +it's already giving you giving you some +interesting results we already saw the + + align:start position:0% +interesting results we already saw the + + + align:start position:0% +interesting results we already saw the +gossip results + + align:start position:0% +gossip results + + + align:start position:0% +gossip results +ah and then the in terms of incentives + + align:start position:0% +ah and then the in terms of incentives + + + align:start position:0% +ah and then the in terms of incentives +it looks like the high slope incentive + + align:start position:0% +it looks like the high slope incentive + + + align:start position:0% +it looks like the high slope incentive +Works although maybe you know you can + + align:start position:0% +Works although maybe you know you can + + + align:start position:0% +Works although maybe you know you can +say that it's so statistically different + + align:start position:0% +say that it's so statistically different + + + align:start position:0% +say that it's so statistically different +from low slope + + align:start position:0% +from low slope + + + align:start position:0% +from low slope +however giving flat incentive doesn't + + align:start position:0% +however giving flat incentive doesn't + + + align:start position:0% +however giving flat incentive doesn't +seem to work + + align:start position:0% +seem to work + + + align:start position:0% +seem to work +SMS uh is uh the + + align:start position:0% +SMS uh is uh the + + + align:start position:0% +SMS uh is uh the +there's a not significant impact this is + + align:start position:0% +there's a not significant impact this is + + + align:start position:0% +there's a not significant impact this is +in the entire sample and that's in the + + align:start position:0% +in the entire sample and that's in the + + + align:start position:0% +in the entire sample and that's in the +in the smaller in the smaller sample + + align:start position:0% +in the smaller in the smaller sample + + + align:start position:0% +in the smaller in the smaller sample +so if you just looked at that + + align:start position:0% +so if you just looked at that + + + align:start position:0% +so if you just looked at that +you would say well you know gossip you + + align:start position:0% +you would say well you know gossip you + + + align:start position:0% +you would say well you know gossip you +look effective perhaps as effective as + + align:start position:0% +look effective perhaps as effective as + + + align:start position:0% +look effective perhaps as effective as +giving highest Loop incentive and for + + align:start position:0% +giving highest Loop incentive and for + + + align:start position:0% +giving highest Loop incentive and for +otherwise we are not very sure what will + + align:start position:0% +otherwise we are not very sure what will + + + align:start position:0% +otherwise we are not very sure what will +pull what we not pull and of course we + + align:start position:0% +pull what we not pull and of course we + + + align:start position:0% +pull what we not pull and of course we +have nothing to say about the + + align:start position:0% +have nothing to say about the + + + align:start position:0% +have nothing to say about the +interaction from looking in that + + align:start position:0% +interaction from looking in that + + + align:start position:0% +interaction from looking in that +so that's the procedure you you define + + align:start position:0% +so that's the procedure you you define + + + align:start position:0% +so that's the procedure you you define +what's allowed to pull + + align:start position:0% +what's allowed to pull + + + align:start position:0% +what's allowed to pull +potentially so in our case it's pretty + + align:start position:0% +potentially so in our case it's pretty + + + align:start position:0% +potentially so in our case it's pretty +simple because it's by category of + + align:start position:0% +simple because it's by category of + + + align:start position:0% +simple because it's by category of +intervention + + align:start position:0% +intervention + + + align:start position:0% +intervention +once you do that you define you specify + + align:start position:0% +once you do that you define you specify + + + align:start position:0% +once you do that you define you specify +the regression in this Marginal Way so + + align:start position:0% +the regression in this Marginal Way so + + + align:start position:0% +the regression in this Marginal Way so +to me that looks super intrigued that + + align:start position:0% +to me that looks super intrigued that + + + align:start position:0% +to me that looks super intrigued that +looks very intuitive + + align:start position:0% +looks very intuitive + + + align:start position:0% +looks very intuitive +but in fact it's a bit tricky uh when + + align:start position:0% +but in fact it's a bit tricky uh when + + + align:start position:0% +but in fact it's a bit tricky uh when +you have a lot of possibilities if if + + align:start position:0% +you have a lot of possibilities if if + + + align:start position:0% +you have a lot of possibilities if if +two by two it's pretty clear there is + + align:start position:0% +two by two it's pretty clear there is + + + align:start position:0% +two by two it's pretty clear there is +only there is only one way to do it + + align:start position:0% +only there is only one way to do it + + + align:start position:0% +only there is only one way to do it +if it's if you start having many you + + align:start position:0% +if it's if you start having many you + + + align:start position:0% +if it's if you start having many you +know potentially a large number of + + align:start position:0% +know potentially a large number of + + + align:start position:0% +know potentially a large number of +different treatment different treatment + + align:start position:0% +different treatment different treatment + + + align:start position:0% +different treatment different treatment +profile + + align:start position:0% +profile + + + align:start position:0% +profile +uh it takes a bit of combinatorics to + + align:start position:0% +uh it takes a bit of combinatorics to + + + align:start position:0% +uh it takes a bit of combinatorics to +say you know how to make sure not to + + align:start position:0% +say you know how to make sure not to + + + align:start position:0% +say you know how to make sure not to +forget some and how they should be + + align:start position:0% +forget some and how they should be + + + align:start position:0% +forget some and how they should be +pulled and why it still works and that's + + align:start position:0% +pulled and why it still works and that's + + + align:start position:0% +pulled and why it still works and that's +described in the in the paper + + align:start position:0% +described in the in the paper + + + align:start position:0% +described in the in the paper +then you use the perfect transformation + + align:start position:0% +then you use the perfect transformation + + + align:start position:0% +then you use the perfect transformation +to make to make it less so compatible so + + align:start position:0% +to make to make it less so compatible so + + + align:start position:0% +to make to make it less so compatible so +that's just a way of the basically + + align:start position:0% +that's just a way of the basically + + + align:start position:0% +that's just a way of the basically +changing the expression of the variable + + align:start position:0% +changing the expression of the variable + + + align:start position:0% +changing the expression of the variable +to uh to make them orthogonal to each + + align:start position:0% +to uh to make them orthogonal to each + + + align:start position:0% +to uh to make them orthogonal to each +other it doesn't come for free by the + + align:start position:0% +other it doesn't come for free by the + + + align:start position:0% +other it doesn't come for free by the +way it adds noise to the detail of the + + align:start position:0% +way it adds noise to the detail of the + + + align:start position:0% +way it adds noise to the detail of the +tool then you run your your so you make + + align:start position:0% +tool then you run your your so you make + + + align:start position:0% +tool then you run your your so you make +your lasso then your post lasso and + + align:start position:0% +your lasso then your post lasso and + + + align:start position:0% +your lasso then your post lasso and +finally the winner cost correction + + align:start position:0% + + + + align:start position:0% + +so that's the the the the pulling + + align:start position:0% +so that's the the the the pulling + + + align:start position:0% +so that's the the the the pulling +specification looks something like that + + align:start position:0% +specification looks something like that + + + align:start position:0% +specification looks something like that +where you have for example SMS any SMS + + align:start position:0% +where you have for example SMS any SMS + + + align:start position:0% +where you have for example SMS any SMS +and then the marginal effect of SMS + + align:start position:0% +and then the marginal effect of SMS + + + align:start position:0% +and then the marginal effect of SMS +uh any slope and then whether it's high + + align:start position:0% +uh any slope and then whether it's high + + + align:start position:0% +uh any slope and then whether it's high +any flat incentive and whether it's a + + align:start position:0% +any flat incentive and whether it's a + + + align:start position:0% +any flat incentive and whether it's a +flat incentive + + align:start position:0% +flat incentive + + + align:start position:0% +flat incentive +random is separate + + align:start position:0% +random is separate + + + align:start position:0% +random is separate +uh in full Hub is separate trust is + + align:start position:0% +uh in full Hub is separate trust is + + + align:start position:0% +uh in full Hub is separate trust is +separate and then trusted in four is on + + align:start position:0% +separate and then trusted in four is on + + + align:start position:0% +separate and then trusted in four is on +top of is on top of trust + + align:start position:0% +top of is on top of trust + + + align:start position:0% +top of is on top of trust +and then all of the interaction that are + + align:start position:0% +and then all of the interaction that are + + + align:start position:0% +and then all of the interaction that are +in the axes of all of these things so + + align:start position:0% +in the axes of all of these things so + + + align:start position:0% +in the axes of all of these things so +it's not kind of the main effect as in + + align:start position:0% +it's not kind of the main effect as in + + + align:start position:0% +it's not kind of the main effect as in +the main treatment profile + + align:start position:0% +the main treatment profile + + + align:start position:0% +the main treatment profile +so you see that we already took some + + align:start position:0% +so you see that we already took some + + + align:start position:0% +so you see that we already took some +decisions in some sense uh big for + + align:start position:0% +decisions in some sense uh big for + + + align:start position:0% +decisions in some sense uh big for +example we don't allow + + align:start position:0% +example we don't allow + + + align:start position:0% +example we don't allow +we're not doing anything + + align:start position:0% +we're not doing anything + + + align:start position:0% +we're not doing anything +random it's its own condom to pull with + + align:start position:0% +random it's its own condom to pull with + + + align:start position:0% +random it's its own condom to pull with +the rest + + align:start position:0% +the rest + + + align:start position:0% +the rest +because we think that uh see this is + + align:start position:0% +because we think that uh see this is + + + align:start position:0% +because we think that uh see this is +different than a chosen seed is + + align:start position:0% +different than a chosen seed is + + + align:start position:0% +different than a chosen seed is +different than a random seed so there is + + align:start position:0% +different than a random seed so there is + + + align:start position:0% +different than a random seed so there is +already a little bit of theory in their + + align:start position:0% +already a little bit of theory in their + + + align:start position:0% +already a little bit of theory in their +theory in there structured in there + + align:start position:0% +theory in there structured in there + + + align:start position:0% +theory in there structured in there +even in doing just that + + align:start position:0% + + + + align:start position:0% + +so what do we find when we find when we + + align:start position:0% +so what do we find when we find when we + + + align:start position:0% +so what do we find when we find when we +do all this so very few things survive + + align:start position:0% +do all this so very few things survive + + + align:start position:0% +do all this so very few things survive +lasso only four of four combination + + align:start position:0% +lasso only four of four combination + + + align:start position:0% +lasso only four of four combination +survive lasso + + align:start position:0% +survive lasso + + + align:start position:0% +survive lasso +in terms of uh + + align:start position:0% +in terms of uh + + + align:start position:0% +in terms of uh +increase of immunization so this which + + align:start position:0% +increase of immunization so this which + + + align:start position:0% +increase of immunization so this which +we do it very simple it's in number it's + + align:start position:0% +we do it very simple it's in number it's + + + align:start position:0% +we do it very simple it's in number it's +number of shots given number of missile + + align:start position:0% +number of shots given number of missile + + + align:start position:0% +number of shots given number of missile +shot given in the village every month + + align:start position:0% +shot given in the village every month + + + align:start position:0% +shot given in the village every month +so the average it's 7.32 in the control + + align:start position:0% +so the average it's 7.32 in the control + + + align:start position:0% +so the average it's 7.32 in the control +group + + align:start position:0% +group + + + align:start position:0% +group +what appears to be the most effective is + + align:start position:0% +what appears to be the most effective is + + + align:start position:0% +what appears to be the most effective is +to do everything + + align:start position:0% +to do everything + + + align:start position:0% +to do everything +so that I mean after all this work maybe + + align:start position:0% +so that I mean after all this work maybe + + + align:start position:0% +so that I mean after all this work maybe +you could have known it but you know + + align:start position:0% +you could have known it but you know + + + align:start position:0% +you could have known it but you know +that was not obvious and um we um all of + + align:start position:0% +that was not obvious and um we um all of + + + align:start position:0% +that was not obvious and um we um all of +the incentives pool there's no all of + + align:start position:0% +the incentives pool there's no all of + + + align:start position:0% +the incentives pool there's no all of +the sloppy incentive pool so high and + + align:start position:0% +the sloppy incentive pool so high and + + + align:start position:0% +the sloppy incentive pool so high and +low incentive pull + + align:start position:0% +low incentive pull + + + align:start position:0% +low incentive pull +the info have pulled so the trusted + + align:start position:0% +the info have pulled so the trusted + + + align:start position:0% +the info have pulled so the trusted +gossip and trusted gossip pull together + + align:start position:0% +gossip and trusted gossip pull together + + + align:start position:0% +gossip and trusted gossip pull together +uh and uh and the SMS put + + align:start position:0% +uh and uh and the SMS put + + + align:start position:0% +uh and uh and the SMS put +so it's pretty nice that the variant + + align:start position:0% +so it's pretty nice that the variant + + + align:start position:0% +so it's pretty nice that the variant +seems to make no difference uh so you + + align:start position:0% +seems to make no difference uh so you + + + align:start position:0% +seems to make no difference uh so you +could go with uh you know if you want to + + align:start position:0% +could go with uh you know if you want to + + + align:start position:0% +could go with uh you know if you want to +pick the cheapest you could pick low + + align:start position:0% +pick the cheapest you could pick low + + + align:start position:0% +pick the cheapest you could pick low +sloppy insensive SMS a low level of SMS + + align:start position:0% +sloppy insensive SMS a low level of SMS + + + align:start position:0% +sloppy insensive SMS a low level of SMS +and and gossips + + align:start position:0% +and and gossips + + + align:start position:0% +and and gossips +uh but because + + align:start position:0% +uh but because + + + align:start position:0% +uh but because +that pulls with the the more ambitious + + align:start position:0% +that pulls with the the more ambitious + + + align:start position:0% +that pulls with the the more ambitious +version of it and that increases + + align:start position:0% +version of it and that increases + + + align:start position:0% +version of it and that increases +immediation level by by four + + align:start position:0% +immediation level by by four + + + align:start position:0% +immediation level by by four +relative to control which was a + + align:start position:0% +relative to control which was a + + + align:start position:0% +relative to control which was a +732 so it's very pretty large + + align:start position:0% +732 so it's very pretty large + + + align:start position:0% +732 so it's very pretty large +proportional increase + + align:start position:0% + + + + align:start position:0% + +the other things so this the other thing + + align:start position:0% +the other things so this the other thing + + + align:start position:0% +the other things so this the other thing +that also works is something very + + align:start position:0% +that also works is something very + + + align:start position:0% +that also works is something very +similar + + align:start position:0% +similar + + + align:start position:0% +similar +but using the trusted seed instead of + + align:start position:0% +but using the trusted seed instead of + + + align:start position:0% +but using the trusted seed instead of +the info hubs + + align:start position:0% +the info hubs + + + align:start position:0% +the info hubs +that's also significant these other two + + align:start position:0% +that's also significant these other two + + + align:start position:0% +that's also significant these other two +although they were selected by lasso in + + align:start position:0% +although they were selected by lasso in + + + align:start position:0% +although they were selected by lasso in +the postlasso appears to be + + align:start position:0% +the postlasso appears to be + + + align:start position:0% +the postlasso appears to be +insignificant on their own although you + + align:start position:0% +insignificant on their own although you + + + align:start position:0% +insignificant on their own although you +couldn't make them you couldn't set a + + align:start position:0% +couldn't make them you couldn't set a + + + align:start position:0% +couldn't make them you couldn't set a +difference which is no seed at all and + + align:start position:0% +difference which is no seed at all and + + + align:start position:0% +difference which is no seed at all and +high slope and SMS and then this one is + + align:start position:0% +high slope and SMS and then this one is + + + align:start position:0% +high slope and SMS and then this one is +is + + align:start position:0% +is + + + align:start position:0% +is +actually has a negative impact it's + + align:start position:0% +actually has a negative impact it's + + + align:start position:0% +actually has a negative impact it's +selected by lasso but it doesn't have a + + align:start position:0% +selected by lasso but it doesn't have a + + + align:start position:0% +selected by lasso but it doesn't have a +negative impact here + + align:start position:0% + + + + align:start position:0% + +once you look at yeah + + align:start position:0% + + + + align:start position:0% + +all other treatments + + align:start position:0% +all other treatments + + + align:start position:0% +all other treatments +yes all of the treatment are pulled with + + align:start position:0% +yes all of the treatment are pulled with + + + align:start position:0% +yes all of the treatment are pulled with +the control + + align:start position:0% +the control + + + align:start position:0% +the control +because + + align:start position:0% +because + + + align:start position:0% +because +lasso doesn't want them so basically + + align:start position:0% +lasso doesn't want them so basically + + + align:start position:0% +lasso doesn't want them so basically +they are they become the + + align:start position:0% +they are they become the + + + align:start position:0% +they are they become the +just + + align:start position:0% + + + + align:start position:0% + +select some variable and then you push + + align:start position:0% +select some variable and then you push + + + align:start position:0% +select some variable and then you push +pause you you run your or less + + align:start position:0% +pause you you run your or less + + + align:start position:0% +pause you you run your or less +regression + + align:start position:0% +regression + + + align:start position:0% +regression +and then it's not uh it doesn't turn out + + align:start position:0% +and then it's not uh it doesn't turn out + + + align:start position:0% +and then it's not uh it doesn't turn out +to be significant yeah + + align:start position:0% +to be significant yeah + + + align:start position:0% +to be significant yeah +Lazo penalizes you basically what blasto + + align:start position:0% +Lazo penalizes you basically what blasto + + + align:start position:0% +Lazo penalizes you basically what blasto +does is that it penalizes you for every + + align:start position:0% +does is that it penalizes you for every + + + align:start position:0% +does is that it penalizes you for every +variable you add you you introduce + + align:start position:0% +variable you add you you introduce + + + align:start position:0% +variable you add you you introduce +and then it it lets you keep so so at + + align:start position:0% +and then it it lets you keep so so at + + + align:start position:0% +and then it it lets you keep so so at +some point depending on how you know you + + align:start position:0% +some point depending on how you know you + + + align:start position:0% +some point depending on how you know you +you depending on the penalty level you + + align:start position:0% +you depending on the penalty level you + + + align:start position:0% +you depending on the penalty level you +choose uh it's going to say it says how + + align:start position:0% +choose uh it's going to say it says how + + + align:start position:0% +choose uh it's going to say it says how +many variables you should introduce and + + align:start position:0% +many variables you should introduce and + + + align:start position:0% +many variables you should introduce and +then you introduce them by the fact that + + align:start position:0% +then you introduce them by the fact that + + + align:start position:0% +then you introduce them by the fact that +they contribute more to the variants to + + align:start position:0% +they contribute more to the variants to + + + align:start position:0% +they contribute more to the variants to +this case so after that which doesn't + + align:start position:0% +this case so after that which doesn't + + + align:start position:0% +this case so after that which doesn't +mean they are they are that secret it + + align:start position:0% +mean they are they are that secret it + + + align:start position:0% +mean they are they are that secret it +means these other things have even + + align:start position:0% +means these other things have even + + + align:start position:0% +means these other things have even +smaller coefficients + + align:start position:0% +smaller coefficients + + + align:start position:0% +smaller coefficients +um + + align:start position:0% + + + + align:start position:0% + +also once you re-run the regression with + + align:start position:0% +also once you re-run the regression with + + + align:start position:0% +also once you re-run the regression with +only the four + + align:start position:0% +only the four + + + align:start position:0% +only the four +you get different coefficient you get + + align:start position:0% +you get different coefficient you get + + + align:start position:0% +you get different coefficient you get +you don't get the same coefficient as + + align:start position:0% +you don't get the same coefficient as + + + align:start position:0% +you don't get the same coefficient as +when you run if you had attempted to run + + align:start position:0% +when you run if you had attempted to run + + + align:start position:0% +when you run if you had attempted to run +the full regression + + align:start position:0% +the full regression + + + align:start position:0% +the full regression +because all of the rest is sent to + + align:start position:0% +because all of the rest is sent to + + + align:start position:0% +because all of the rest is sent to +control yeah + + align:start position:0% + + + + align:start position:0% + +as all is very significant and very + + align:start position:0% +as all is very significant and very + + + align:start position:0% +as all is very significant and very +positive and then just changing your + + align:start position:0% +positive and then just changing your + + + align:start position:0% +positive and then just changing your +whole house with translation for us + + align:start position:0% + + + + align:start position:0% + +through the mixed plan + + align:start position:0% +through the mixed plan + + + align:start position:0% +through the mixed plan +this one to this one yeah I don't think + + align:start position:0% +this one to this one yeah I don't think + + + align:start position:0% +this one to this one yeah I don't think +they trusted the the yeah I don't I + + align:start position:0% +they trusted the the yeah I don't I + + + align:start position:0% +they trusted the the yeah I don't I +don't know that's the I don't think that + + align:start position:0% +don't know that's the I don't think that + + + align:start position:0% +don't know that's the I don't think that +the trust + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +it's the trusted one are not trusted in + + align:start position:0% +it's the trusted one are not trusted in + + + align:start position:0% +it's the trusted one are not trusted in +so let me think + + align:start position:0% + + + + align:start position:0% + +yeah it's just trusted by The Trusted + + align:start position:0% +yeah it's just trusted by The Trusted + + + align:start position:0% +yeah it's just trusted by The Trusted +info on their own + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um + + align:start position:0% +um + + + align:start position:0% +um +yeah I don't have a I don't have a great + + align:start position:0% +yeah I don't have a I don't have a great + + + align:start position:0% +yeah I don't have a I don't have a great +interpretation for why you know they + + align:start position:0% +interpretation for why you know they + + + align:start position:0% +interpretation for why you know they +seem to pull with the other one but + + align:start position:0% +seem to pull with the other one but + + + align:start position:0% +seem to pull with the other one but +that's they produce no effect uh on + + align:start position:0% +that's they produce no effect uh on + + + align:start position:0% +that's they produce no effect uh on +their own + + align:start position:0% +their own + + + align:start position:0% +their own +this is by the way that's the result we + + align:start position:0% +this is by the way that's the result we + + + align:start position:0% +this is by the way that's the result we +had earlier that the trusted gossip on + + align:start position:0% +had earlier that the trusted gossip on + + + align:start position:0% +had earlier that the trusted gossip on +their own seems to have no effect but + + align:start position:0% +their own seems to have no effect but + + + align:start position:0% +their own seems to have no effect but +they have no effect in a way that is not + + align:start position:0% +they have no effect in a way that is not + + + align:start position:0% +they have no effect in a way that is not +significantly different from + + align:start position:0% +significantly different from + + + align:start position:0% +significantly different from +putting them with the other uh with the + + align:start position:0% +putting them with the other uh with the + + + align:start position:0% +putting them with the other uh with the +other info hubs so um + + align:start position:0% + + + + align:start position:0% + +yeah exactly + + align:start position:0% + + + + align:start position:0% + +oh incidentally when you run this + + align:start position:0% +oh incidentally when you run this + + + align:start position:0% +oh incidentally when you run this +regression you re-run it now as in each + + align:start position:0% +regression you re-run it now as in each + + + align:start position:0% +regression you re-run it now as in each +each of them is an individual package so + + align:start position:0% +each of them is an individual package so + + + align:start position:0% +each of them is an individual package so +it's the effect of the combo of each of + + align:start position:0% +it's the effect of the combo of each of + + + align:start position:0% +it's the effect of the combo of each of +this is the effect of the combo policy + + align:start position:0% +this is the effect of the combo policy + + + align:start position:0% +this is the effect of the combo policy +not the marginal effects + + align:start position:0% + + + + align:start position:0% + +when you look at immunization peradatas + + align:start position:0% +when you look at immunization peradatas + + + align:start position:0% +when you look at immunization peradatas +lasso selects a few more things but most + + align:start position:0% +lasso selects a few more things but most + + + align:start position:0% +lasso selects a few more things but most +of them are negative + + align:start position:0% +of them are negative + + + align:start position:0% +of them are negative +why because you're spending money on + + align:start position:0% +why because you're spending money on + + + align:start position:0% +why because you're spending money on +these programs so and we are now + + align:start position:0% +these programs so and we are now + + + align:start position:0% +these programs so and we are now +comparing to the control group so you + + align:start position:0% +comparing to the control group so you + + + align:start position:0% +comparing to the control group so you +could well say that you are perfectly + + align:start position:0% +could well say that you are perfectly + + + align:start position:0% +could well say that you are perfectly +willing to spend money on getting + + align:start position:0% +willing to spend money on getting + + + align:start position:0% +willing to spend money on getting +markets immunized even if the cost per + + align:start position:0% +markets immunized even if the cost per + + + align:start position:0% +markets immunized even if the cost per +ammunition increases + + align:start position:0% +ammunition increases + + + align:start position:0% +ammunition increases +but it could also be like we had a new + + align:start position:0% +but it could also be like we had a new + + + align:start position:0% +but it could also be like we had a new +day Pro setting that there is some + + align:start position:0% +day Pro setting that there is some + + + align:start position:0% +day Pro setting that there is some +treatment where the cost per + + align:start position:0% +treatment where the cost per + + + align:start position:0% +treatment where the cost per +immunization decreases because there are + + align:start position:0% +immunization decreases because there are + + + align:start position:0% +immunization decreases because there are +fixed cost of running new program + + align:start position:0% +fixed cost of running new program + + + align:start position:0% +fixed cost of running new program +so in the cost per ammunition we include + + align:start position:0% +so in the cost per ammunition we include + + + align:start position:0% +so in the cost per ammunition we include +both fixed cost and viable cost any + + align:start position:0% +both fixed cost and viable cost any + + + align:start position:0% +both fixed cost and viable cost any +intervention like incentives Etc + + align:start position:0% +intervention like incentives Etc + + + align:start position:0% +intervention like incentives Etc +increases the viable cost + + align:start position:0% +increases the viable cost + + + align:start position:0% +increases the viable cost +but means that those fixed cost is + + align:start position:0% +but means that those fixed cost is + + + align:start position:0% +but means that those fixed cost is +spread over a larger a group of people + + align:start position:0% +spread over a larger a group of people + + + align:start position:0% +spread over a larger a group of people +so in the Uday that's why in the day + + align:start position:0% +so in the Uday that's why in the day + + + align:start position:0% +so in the Uday that's why in the day +four results we had that seemingly + + align:start position:0% +four results we had that seemingly + + + align:start position:0% +four results we had that seemingly +paradoxical result that is cheaper to + + align:start position:0% +paradoxical result that is cheaper to + + + align:start position:0% +paradoxical result that is cheaper to +give incentive not to give them but it + + align:start position:0% +give incentive not to give them but it + + + align:start position:0% +give incentive not to give them but it +didn't have to be the case and in fact + + align:start position:0% +didn't have to be the case and in fact + + + align:start position:0% +didn't have to be the case and in fact +in the entire sample all of the + + align:start position:0% +in the entire sample all of the + + + align:start position:0% +in the entire sample all of the +incentive results are all of the + + align:start position:0% +incentive results are all of the + + + align:start position:0% +incentive results are all of the +incentive effects have are + + align:start position:0% +incentive effects have are + + + align:start position:0% +incentive effects have are +selected because they have this very + + align:start position:0% +selected because they have this very + + + align:start position:0% +selected because they have this very +negative treatment effect they are + + align:start position:0% +negative treatment effect they are + + + align:start position:0% +negative treatment effect they are +expensive the cost per dollar but what + + align:start position:0% +expensive the cost per dollar but what + + + align:start position:0% +expensive the cost per dollar but what +emerges and in fact in this case is the + + align:start position:0% +emerges and in fact in this case is the + + + align:start position:0% +emerges and in fact in this case is the +only policy that is that is cost + + align:start position:0% +only policy that is that is cost + + + align:start position:0% +only policy that is that is cost +effective compared to doing nothing + + align:start position:0% +effective compared to doing nothing + + + align:start position:0% +effective compared to doing nothing +in the sense that it increased the cost + + align:start position:0% +in the sense that it increased the cost + + + align:start position:0% +in the sense that it increased the cost +on ammunition per dollars is the uh + + align:start position:0% +on ammunition per dollars is the uh + + + align:start position:0% +on ammunition per dollars is the uh +doing SMS combined with uh within four + + align:start position:0% +doing SMS combined with uh within four + + + align:start position:0% +doing SMS combined with uh within four +hubs + + align:start position:0% + + + + align:start position:0% + +so it's gossip plus plus SMS + + align:start position:0% + + + + align:start position:0% + +that makes sense it's cheap to do uh and + + align:start position:0% +that makes sense it's cheap to do uh and + + + align:start position:0% +that makes sense it's cheap to do uh and +therefore it's uh + + align:start position:0% +therefore it's uh + + + align:start position:0% +therefore it's uh +um the the marginal cost is not very + + align:start position:0% +um the the marginal cost is not very + + + align:start position:0% +um the the marginal cost is not very +large and to the extent there are + + align:start position:0% +large and to the extent there are + + + align:start position:0% +large and to the extent there are +impacts + + align:start position:0% +impacts + + + align:start position:0% +impacts +uh the impact means that all your fixed + + align:start position:0% +uh the impact means that all your fixed + + + align:start position:0% +uh the impact means that all your fixed +infrastructure is used more effectively + + align:start position:0% + + + + align:start position:0% + +so now we can do the best policy + + align:start position:0% +so now we can do the best policy + + + align:start position:0% +so now we can do the best policy +correction so if you remember we have we + + align:start position:0% +correction so if you remember we have we + + + align:start position:0% +correction so if you remember we have we +had an initial effect of about four uh + + align:start position:0% +had an initial effect of about four uh + + + align:start position:0% +had an initial effect of about four uh +for the combination for the best policy + + align:start position:0% +for the combination for the best policy + + + align:start position:0% +for the combination for the best policy +in case of number of shots which was the + + align:start position:0% +in case of number of shots which was the + + + align:start position:0% +in case of number of shots which was the +combo of everything + + align:start position:0% +combo of everything + + + align:start position:0% +combo of everything +so we penalized it for being close to + + align:start position:0% +so we penalized it for being close to + + + align:start position:0% +so we penalized it for being close to +the next one and we arrived therefore at + + align:start position:0% +the next one and we arrived therefore at + + + align:start position:0% +the next one and we arrived therefore at +the effect of an increase in + + align:start position:0% +the effect of an increase in + + + align:start position:0% +the effect of an increase in +immunization compared to control of + + align:start position:0% +immunization compared to control of + + + align:start position:0% +immunization compared to control of +about three + + align:start position:0% +about three + + + align:start position:0% +about three +for Millions per dollar since there is + + align:start position:0% +for Millions per dollar since there is + + + align:start position:0% +for Millions per dollar since there is +only one policy that is that has a + + align:start position:0% +only one policy that is that has a + + + align:start position:0% +only one policy that is that has a +positive impact it doesn't get penalized + + align:start position:0% +positive impact it doesn't get penalized + + + align:start position:0% +positive impact it doesn't get penalized +it's on its own so the uh the the the + + align:start position:0% +it's on its own so the uh the the the + + + align:start position:0% +it's on its own so the uh the the the +Pinellas impact is the impact + + align:start position:0% + + + + align:start position:0% + +so that's the summary of the result but + + align:start position:0% +so that's the summary of the result but + + + align:start position:0% +so that's the summary of the result but +uh I think we went through this already + + align:start position:0% +uh I think we went through this already + + + align:start position:0% +uh I think we went through this already +so what's the policy prescription so at + + align:start position:0% +so what's the policy prescription so at + + + align:start position:0% +so what's the policy prescription so at +some point all these people from high + + align:start position:0% +some point all these people from high + + + align:start position:0% +some point all these people from high +and actually they came here on the + + align:start position:0% +and actually they came here on the + + + align:start position:0% +and actually they came here on the +delegation we present them the results + + align:start position:0% +delegation we present them the results + + + align:start position:0% +delegation we present them the results +and uh so the the obviously it's uh it + + align:start position:0% +and uh so the the obviously it's uh it + + + align:start position:0% +and uh so the the obviously it's uh it +would be they could do Gusty plus SMS + + align:start position:0% +would be they could do Gusty plus SMS + + + align:start position:0% +would be they could do Gusty plus SMS +everywhere it's cheap and it's effective + + align:start position:0% +everywhere it's cheap and it's effective + + + align:start position:0% +everywhere it's cheap and it's effective +and it's cost effective so fine + + align:start position:0% +and it's cost effective so fine + + + align:start position:0% +and it's cost effective so fine +uh but but if they're also interested in + + align:start position:0% +uh but but if they're also interested in + + + align:start position:0% +uh but but if they're also interested in +increasing in in some places doing the + + align:start position:0% +increasing in in some places doing the + + + align:start position:0% +increasing in in some places doing the +you know really adding a big push on the + + align:start position:0% +you know really adding a big push on the + + + align:start position:0% +you know really adding a big push on the +mission they're willing to pay for it + + align:start position:0% +mission they're willing to pay for it + + + align:start position:0% +mission they're willing to pay for it +the most effective policy is the is the + + align:start position:0% +the most effective policy is the is the + + + align:start position:0% +the most effective policy is the is the +combination + + align:start position:0% +combination + + + align:start position:0% +combination +so then you know are there places they + + align:start position:0% +so then you know are there places they + + + align:start position:0% +so then you know are there places they +can identify + + align:start position:0% +can identify + + + align:start position:0% +can identify +where this policy would be effective + + align:start position:0% +where this policy would be effective + + + align:start position:0% +where this policy would be effective +and that's the certain people that you + + align:start position:0% +and that's the certain people that you + + + align:start position:0% +and that's the certain people that you +read which is + + align:start position:0% +read which is + + + align:start position:0% +read which is +trying to do this like predictive + + align:start position:0% +trying to do this like predictive + + + align:start position:0% +trying to do this like predictive +medicine which is kind of figure out a + + align:start position:0% +medicine which is kind of figure out a + + + align:start position:0% +medicine which is kind of figure out a +group of people for whom this + + align:start position:0% +group of people for whom this + + + align:start position:0% +group of people for whom this +intervention will work + + align:start position:0% +intervention will work + + + align:start position:0% +intervention will work +and the issue with predictive medicine + + align:start position:0% +and the issue with predictive medicine + + + align:start position:0% +and the issue with predictive medicine +is even more than with multiple + + align:start position:0% +is even more than with multiple + + + align:start position:0% +is even more than with multiple +treatment is this possibility of + + align:start position:0% +treatment is this possibility of + + + align:start position:0% +treatment is this possibility of +specification searching which is exposed + + align:start position:0% +specification searching which is exposed + + + align:start position:0% +specification searching which is exposed +you will always you know find a group + + align:start position:0% +you will always you know find a group + + + align:start position:0% +you will always you know find a group +for which it looks like the uh the + + align:start position:0% +for which it looks like the uh the + + + align:start position:0% +for which it looks like the uh the +treatment was working so that's why the + + align:start position:0% +treatment was working so that's why the + + + align:start position:0% +treatment was working so that's why the +FDA does not allow you to do any + + align:start position:0% +FDA does not allow you to do any + + + align:start position:0% +FDA does not allow you to do any +storyboard any subgroup that were not + + align:start position:0% +storyboard any subgroup that were not + + + align:start position:0% +storyboard any subgroup that were not +pre-specified + + align:start position:0% +pre-specified + + + align:start position:0% +pre-specified +you just cannot otherwise you say well + + align:start position:0% +you just cannot otherwise you say well + + + align:start position:0% +you just cannot otherwise you say well +you know my drug doesn't work on average + + align:start position:0% +you know my drug doesn't work on average + + + align:start position:0% +you know my drug doesn't work on average +but it worked on people which have + + align:start position:0% +but it worked on people which have + + + align:start position:0% +but it worked on people which have +red shirts on the day of the trial and + + align:start position:0% +red shirts on the day of the trial and + + + align:start position:0% +red shirts on the day of the trial and +then you can always come up with the + + align:start position:0% +then you can always come up with the + + + align:start position:0% +then you can always come up with the +reason so in economics we are less a + + align:start position:0% +reason so in economics we are less a + + + align:start position:0% +reason so in economics we are less a +little less stressed about that probably + + align:start position:0% +little less stressed about that probably + + + align:start position:0% +little less stressed about that probably +because the you know they are less + + align:start position:0% +because the you know they are less + + + align:start position:0% +because the you know they are less +Financial incentive reasons to push a + + align:start position:0% +Financial incentive reasons to push a + + + align:start position:0% +Financial incentive reasons to push a +particular results and there is always + + align:start position:0% +particular results and there is always + + + align:start position:0% +particular results and there is always +we have more tolerance I think for + + align:start position:0% +we have more tolerance I think for + + + align:start position:0% +we have more tolerance I think for +theorizing exposed about results partly + + align:start position:0% +theorizing exposed about results partly + + + align:start position:0% +theorizing exposed about results partly +because we like Theory and we should and + + align:start position:0% +because we like Theory and we should and + + + align:start position:0% +because we like Theory and we should and +you know we've learned something about + + align:start position:0% +you know we've learned something about + + + align:start position:0% +you know we've learned something about +the world and even if the subgroups are + + align:start position:0% +the world and even if the subgroups are + + + align:start position:0% +the world and even if the subgroups are +exposed you may have learned something + + align:start position:0% +exposed you may have learned something + + + align:start position:0% +exposed you may have learned something +about them + + align:start position:0% +about them + + + align:start position:0% +about them +so it would be a bit sad not to use them + + align:start position:0% +so it would be a bit sad not to use them + + + align:start position:0% +so it would be a bit sad not to use them +so that's kind of the exact same it's + + align:start position:0% +so that's kind of the exact same it's + + + align:start position:0% +so that's kind of the exact same it's +not exactly the same trade-off as before + + align:start position:0% +not exactly the same trade-off as before + + + align:start position:0% +not exactly the same trade-off as before +but there is a trade-off of that nature + + align:start position:0% +but there is a trade-off of that nature + + + align:start position:0% +but there is a trade-off of that nature +so going all the way to the medicine + + align:start position:0% +so going all the way to the medicine + + + align:start position:0% +so going all the way to the medicine +standard and say we are just gonna allow + + align:start position:0% +standard and say we are just gonna allow + + + align:start position:0% +standard and say we are just gonna allow +very few you know pre-analysis plan and + + align:start position:0% +very few you know pre-analysis plan and + + + align:start position:0% +very few you know pre-analysis plan and +and penalize multiple comparison with uh + + align:start position:0% + + + + align:start position:0% + +Q values or other form of adjusting for + + align:start position:0% +Q values or other form of adjusting for + + + align:start position:0% +Q values or other form of adjusting for +multiple comparisons then you would get + + align:start position:0% +multiple comparisons then you would get + + + align:start position:0% +multiple comparisons then you would get +a bit + + align:start position:0% +a bit + + + align:start position:0% +a bit +boy like you wouldn't be able to get as + + align:start position:0% +boy like you wouldn't be able to get as + + + align:start position:0% +boy like you wouldn't be able to get as +much information + + align:start position:0% + + + + align:start position:0% + +uh and and often we have a lot of data + + align:start position:0% +uh and and often we have a lot of data + + + align:start position:0% +uh and and often we have a lot of data +and we kind of would like to use it but + + align:start position:0% +and we kind of would like to use it but + + + align:start position:0% +and we kind of would like to use it but +we would like to use it in a disciplined + + align:start position:0% +we would like to use it in a disciplined + + + align:start position:0% +we would like to use it in a disciplined +way + + align:start position:0% +way + + + align:start position:0% +way +hence machine learning has the advantage + + align:start position:0% +hence machine learning has the advantage + + + align:start position:0% +hence machine learning has the advantage +of potentially giving you some rules + + align:start position:0% +of potentially giving you some rules + + + align:start position:0% +of potentially giving you some rules +some algorithm that you can specify in + + align:start position:0% +some algorithm that you can specify in + + + align:start position:0% +some algorithm that you can specify in +advance that you could put in your + + align:start position:0% +advance that you could put in your + + + align:start position:0% +advance that you could put in your +prayer in this plan I'm going to use + + align:start position:0% +prayer in this plan I'm going to use + + + align:start position:0% +prayer in this plan I'm going to use +so-and-so's machine learning technique + + align:start position:0% +so-and-so's machine learning technique + + + align:start position:0% +so-and-so's machine learning technique +to look for possible for whether they + + align:start position:0% +to look for possible for whether they + + + align:start position:0% +to look for possible for whether they +are heterogeneous effect and who seem to + + align:start position:0% +are heterogeneous effect and who seem to + + + align:start position:0% +are heterogeneous effect and who seem to +be the most affected + + align:start position:0% +be the most affected + + + align:start position:0% +be the most affected +so in principle The Hope is you get the + + align:start position:0% +so in principle The Hope is you get the + + + align:start position:0% +so in principle The Hope is you get the +best of both War because you have the + + align:start position:0% +best of both War because you have the + + + align:start position:0% +best of both War because you have the +ability to look for differences in a + + align:start position:0% +ability to look for differences in a + + + align:start position:0% +ability to look for differences in a +statistically disciplined way and you + + align:start position:0% +statistically disciplined way and you + + + align:start position:0% +statistically disciplined way and you +won't do too much determining + + align:start position:0% +won't do too much determining + + + align:start position:0% +won't do too much determining +the problem is by no problem + + align:start position:0% +the problem is by no problem + + + align:start position:0% +the problem is by no problem +is really not a tool for uh for uh + + align:start position:0% +is really not a tool for uh for uh + + + align:start position:0% +is really not a tool for uh for uh +saying it's a tool for prediction + + align:start position:0% +saying it's a tool for prediction + + + align:start position:0% +saying it's a tool for prediction +it's a tool for predicting what's going + + align:start position:0% +it's a tool for predicting what's going + + + align:start position:0% +it's a tool for predicting what's going +to happen but it's not a tool to + + align:start position:0% +to happen but it's not a tool to + + + align:start position:0% +to happen but it's not a tool to +interpret any differences in treatment + + align:start position:0% +interpret any differences in treatment + + + align:start position:0% +interpret any differences in treatment +effect we find and in particular in the + + align:start position:0% +effect we find and in particular in the + + + align:start position:0% +effect we find and in particular in the +absence of very strict + + align:start position:0% +absence of very strict + + + align:start position:0% +absence of very strict +conditions to be met we don't know how + + align:start position:0% +conditions to be met we don't know how + + + align:start position:0% +conditions to be met we don't know how +to estimate the causal average treatment + + align:start position:0% +to estimate the causal average treatment + + + align:start position:0% +to estimate the causal average treatment +effect in a way that is interpretable + + align:start position:0% +effect in a way that is interpretable + + + align:start position:0% +effect in a way that is interpretable +so the idea that okay I'm gonna the full + + align:start position:0% +so the idea that okay I'm gonna the full + + + align:start position:0% +so the idea that okay I'm gonna the full +predictive medicine ideal of for anybody + + align:start position:0% +predictive medicine ideal of for anybody + + + align:start position:0% +predictive medicine ideal of for anybody +with any set of X characteristic and I + + align:start position:0% +with any set of X characteristic and I + + + align:start position:0% +with any set of X characteristic and I +can predict that treatment effect + + align:start position:0% +can predict that treatment effect + + + align:start position:0% +can predict that treatment effect +we just don't know how to do that unless + + align:start position:0% +we just don't know how to do that unless + + + align:start position:0% +we just don't know how to do that unless +we are willing to be super restrictive + + align:start position:0% +we are willing to be super restrictive + + + align:start position:0% +we are willing to be super restrictive +and then sudanate here + + align:start position:0% +and then sudanate here + + + align:start position:0% +and then sudanate here +has a paper with Stephen Vega with + + align:start position:0% +has a paper with Stephen Vega with + + + align:start position:0% +has a paper with Stephen Vega with +enough you know with enough under + + align:start position:0% +enough you know with enough under + + + align:start position:0% +enough you know with enough under +sufficiently harsh condition you can do + + align:start position:0% +sufficiently harsh condition you can do + + + align:start position:0% +sufficiently harsh condition you can do +things like trees to give an answer to + + align:start position:0% +things like trees to give an answer to + + + align:start position:0% +things like trees to give an answer to +this question + + align:start position:0% +this question + + + align:start position:0% +this question +but these conditions are pretty hard and + + align:start position:0% +but these conditions are pretty hard and + + + align:start position:0% +but these conditions are pretty hard and +they are not really testable + + align:start position:0% +they are not really testable + + + align:start position:0% +they are not really testable +so what can you do + + align:start position:0% +so what can you do + + + align:start position:0% +so what can you do +well you can say let's give up on + + align:start position:0% +well you can say let's give up on + + + align:start position:0% +well you can say let's give up on +estimate the whole function + + align:start position:0% +estimate the whole function + + + align:start position:0% +estimate the whole function +can we say at least a few things + + align:start position:0% +can we say at least a few things + + + align:start position:0% +can we say at least a few things +so we give up on the estimating the full + + align:start position:0% +so we give up on the estimating the full + + + align:start position:0% +so we give up on the estimating the full +conditional average treatment effect as + + align:start position:0% +conditional average treatment effect as + + + align:start position:0% +conditional average treatment effect as +opposed and restricted as a function of + + align:start position:0% +opposed and restricted as a function of + + + align:start position:0% +opposed and restricted as a function of +all those X's that people or villagers + + align:start position:0% +all those X's that people or villagers + + + align:start position:0% +all those X's that people or villagers +might have + + align:start position:0% +might have + + + align:start position:0% +might have +but I want to answer a few simple + + align:start position:0% +but I want to answer a few simple + + + align:start position:0% +but I want to answer a few simple +questions number one is there any + + align:start position:0% +questions number one is there any + + + align:start position:0% +questions number one is there any +heterogeneity + + align:start position:0% +heterogeneity + + + align:start position:0% +heterogeneity +so that's like one parameter number two + + align:start position:0% +so that's like one parameter number two + + + align:start position:0% +so that's like one parameter number two +if there is if there is any or is it + + align:start position:0% +if there is if there is any or is it + + + align:start position:0% +if there is if there is any or is it +just any idea that I think is there is + + align:start position:0% +just any idea that I think is there is + + + align:start position:0% +just any idea that I think is there is +in fact not there number two if there + + align:start position:0% +in fact not there number two if there + + + align:start position:0% +in fact not there number two if there +isn't it any heterogeneity can I put can + + align:start position:0% +isn't it any heterogeneity can I put can + + + align:start position:0% +isn't it any heterogeneity can I put can +I make + + align:start position:0% +I make + + + align:start position:0% +I make +say five groups + + align:start position:0% +say five groups + + + align:start position:0% +say five groups +where I estimate the treatment effect + + align:start position:0% +where I estimate the treatment effect + + + align:start position:0% +where I estimate the treatment effect +for these five groups so it's now five + + align:start position:0% +for these five groups so it's now five + + + align:start position:0% +for these five groups so it's now five +parameters still a small number of + + align:start position:0% +parameters still a small number of + + + align:start position:0% +parameters still a small number of +parameters + + align:start position:0% +parameters + + + align:start position:0% +parameters +and then maybe one more step is saying + + align:start position:0% +and then maybe one more step is saying + + + align:start position:0% +and then maybe one more step is saying +well you know now that I have these five + + align:start position:0% +well you know now that I have these five + + + align:start position:0% +well you know now that I have these five +group maybe I can describe the + + align:start position:0% +group maybe I can describe the + + + align:start position:0% +group maybe I can describe the +characteristics of these five groups + + align:start position:0% +characteristics of these five groups + + + align:start position:0% +characteristics of these five groups +it's not going to be causal it's going + + align:start position:0% +it's not going to be causal it's going + + + align:start position:0% +it's not going to be causal it's going +to be productive but maybe it's + + align:start position:0% +to be productive but maybe it's + + + align:start position:0% +to be productive but maybe it's +interesting anyway + + align:start position:0% +interesting anyway + + + align:start position:0% +interesting anyway +so that's kind of what with in a paper + + align:start position:0% +so that's kind of what with in a paper + + + align:start position:0% +so that's kind of what with in a paper +with a vector we use the Machinery of + + align:start position:0% +with a vector we use the Machinery of + + + align:start position:0% +with a vector we use the Machinery of +double machine learning that Victor + + align:start position:0% +double machine learning that Victor + + + align:start position:0% +double machine learning that Victor +Whitney and Co developed that we already + + align:start position:0% +Whitney and Co developed that we already + + + align:start position:0% +Whitney and Co developed that we already +discussed in the Gana paper to apply to + + align:start position:0% +discussed in the Gana paper to apply to + + + align:start position:0% +discussed in the Gana paper to apply to +this problem to + + align:start position:0% +this problem to + + + align:start position:0% +this problem to +not important to answer to one + + align:start position:0% +not important to answer to one + + + align:start position:0% +not important to answer to one +understand the detail of how it works + + align:start position:0% +understand the detail of how it works + + + align:start position:0% +understand the detail of how it works +the most important thing is what I + + align:start position:0% +the most important thing is what I + + + align:start position:0% +the most important thing is what I +already told you is well if you reduce + + align:start position:0% +already told you is well if you reduce + + + align:start position:0% +already told you is well if you reduce +your ambitions + + align:start position:0% +your ambitions + + + align:start position:0% +your ambitions +the second most important thing is as in + + align:start position:0% +the second most important thing is as in + + + align:start position:0% +the second most important thing is as in +the first thing as in in that first + + align:start position:0% +the first thing as in in that first + + + align:start position:0% +the first thing as in in that first +paper use samples sample splitting + + align:start position:0% +paper use samples sample splitting + + + align:start position:0% +paper use samples sample splitting +and basically + + align:start position:0% +and basically + + + align:start position:0% +and basically +think for example is there any + + align:start position:0% +think for example is there any + + + align:start position:0% +think for example is there any +heterogeneity how is it going to work + + align:start position:0% +heterogeneity how is it going to work + + + align:start position:0% +heterogeneity how is it going to work +well in I split my sample in two + + align:start position:0% +well in I split my sample in two + + + align:start position:0% +well in I split my sample in two +in half of the sample I use any any + + align:start position:0% +in half of the sample I use any any + + + align:start position:0% +in half of the sample I use any any +machine learning tool I like to come up + + align:start position:0% +machine learning tool I like to come up + + + align:start position:0% +machine learning tool I like to come up +with my best guess for the causal + + align:start position:0% +with my best guess for the causal + + + align:start position:0% +with my best guess for the causal +average treatment effect + + align:start position:0% +average treatment effect + + + align:start position:0% +average treatment effect +that is you know think of it if you + + align:start position:0% +that is you know think of it if you + + + align:start position:0% +that is you know think of it if you +think of it in some version of lasso for + + align:start position:0% +think of it in some version of lasso for + + + align:start position:0% +think of it in some version of lasso for +example is interacting All My Exes and + + align:start position:0% +example is interacting All My Exes and + + + align:start position:0% +example is interacting All My Exes and +all of the interaction possible uh with + + align:start position:0% +all of the interaction possible uh with + + + align:start position:0% +all of the interaction possible uh with +the + + align:start position:0% +the + + + align:start position:0% +the +with the treatment + + align:start position:0% +with the treatment + + + align:start position:0% +with the treatment +and then that gives in principle a + + align:start position:0% +and then that gives in principle a + + + align:start position:0% +and then that gives in principle a +prediction for each person of what the + + align:start position:0% +prediction for each person of what the + + + align:start position:0% +prediction for each person of what the +treatment effect should be + + align:start position:0% +treatment effect should be + + + align:start position:0% +treatment effect should be +I know that this is unlikely to be great + + align:start position:0% +I know that this is unlikely to be great + + + align:start position:0% +I know that this is unlikely to be great +because it's full of flukes and noise + + align:start position:0% +because it's full of flukes and noise + + + align:start position:0% +because it's full of flukes and noise +and stuff like that that I'm going that + + align:start position:0% +and stuff like that that I'm going that + + + align:start position:0% +and stuff like that that I'm going that +are going to be wrongly attributed to + + align:start position:0% +are going to be wrongly attributed to + + + align:start position:0% +are going to be wrongly attributed to +the to to the effect of the actors + + align:start position:0% +the to to the effect of the actors + + + align:start position:0% +the to to the effect of the actors +but you know I still do it + + align:start position:0% +but you know I still do it + + + align:start position:0% +but you know I still do it +could use lasso on them Forest neural + + align:start position:0% +could use lasso on them Forest neural + + + align:start position:0% +could use lasso on them Forest neural +network anything you like to make that + + align:start position:0% +network anything you like to make that + + + align:start position:0% +network anything you like to make that +prediction for each + + align:start position:0% +prediction for each + + + align:start position:0% +prediction for each +combination of covariates + + align:start position:0% +combination of covariates + + + align:start position:0% +combination of covariates +and then in the sample that you left + + align:start position:0% +and then in the sample that you left + + + align:start position:0% +and then in the sample that you left +behind + + align:start position:0% +behind + + + align:start position:0% +behind +so note that it's different from sample + + align:start position:0% +so note that it's different from sample + + + align:start position:0% +so note that it's different from sample +splitting as it's used in ml typically + + align:start position:0% +splitting as it's used in ml typically + + + align:start position:0% +splitting as it's used in ml typically +because for example in order to do even + + align:start position:0% +because for example in order to do even + + + align:start position:0% +because for example in order to do even +the exercise that I'm doing usually you + + align:start position:0% +the exercise that I'm doing usually you + + + align:start position:0% +the exercise that I'm doing usually you +will need sample splitting to tune the + + align:start position:0% +will need sample splitting to tune the + + + align:start position:0% +will need sample splitting to tune the +parameter and all that so that's not + + align:start position:0% +parameter and all that so that's not + + + align:start position:0% +parameter and all that so that's not +that's sample splitting my sample + + align:start position:0% +that's sample splitting my sample + + + align:start position:0% +that's sample splitting my sample +splitting is that + + align:start position:0% +splitting is that + + + align:start position:0% +splitting is that +in my half of the example I you know put + + align:start position:0% +in my half of the example I you know put + + + align:start position:0% +in my half of the example I you know put +my best foot forward to estimate the + + align:start position:0% +my best foot forward to estimate the + + + align:start position:0% +my best foot forward to estimate the +thing + + align:start position:0% +thing + + + align:start position:0% +thing +and then in the half of the sample that + + align:start position:0% +and then in the half of the sample that + + + align:start position:0% +and then in the half of the sample that +I kept + + align:start position:0% +I kept + + + align:start position:0% +I kept +I'm going to regress the treatment + + align:start position:0% +I'm going to regress the treatment + + + align:start position:0% +I'm going to regress the treatment +effect on this characteristic and see + + align:start position:0% +effect on this characteristic and see + + + align:start position:0% +effect on this characteristic and see +whether I get on a linear linearly + + align:start position:0% +whether I get on a linear linearly + + + align:start position:0% +whether I get on a linear linearly +and say if there is any effect I should + + align:start position:0% +and say if there is any effect I should + + + align:start position:0% +and say if there is any effect I should +find one if the two effect was as + + align:start position:0% +find one if the two effect was as + + + align:start position:0% +find one if the two effect was as +estimated in the + + align:start position:0% +estimated in the + + + align:start position:0% +estimated in the +if the if the the two uh heterogeneity + + align:start position:0% +if the if the the two uh heterogeneity + + + align:start position:0% +if the if the the two uh heterogeneity +in effect was as estimated in my machine + + align:start position:0% +in effect was as estimated in my machine + + + align:start position:0% +in effect was as estimated in my machine +learning sample in the test sample I + + align:start position:0% +learning sample in the test sample I + + + align:start position:0% +learning sample in the test sample I +should find a coefficient of 1 when I + + align:start position:0% +should find a coefficient of 1 when I + + + align:start position:0% +should find a coefficient of 1 when I +try to predict it for each person + + align:start position:0% +try to predict it for each person + + + align:start position:0% +try to predict it for each person +it should line up in the same way + + align:start position:0% +it should line up in the same way + + + align:start position:0% +it should line up in the same way +and if in fact it was all noise it's not + + align:start position:0% +and if in fact it was all noise it's not + + + align:start position:0% +and if in fact it was all noise it's not +going to line up in the same way so I'm + + align:start position:0% +going to line up in the same way so I'm + + + align:start position:0% +going to line up in the same way so I'm +going to find a big fat zero + + align:start position:0% +going to find a big fat zero + + + align:start position:0% +going to find a big fat zero +empirically in my experience of trying + + align:start position:0% +empirically in my experience of trying + + + align:start position:0% +empirically in my experience of trying +this most of the time you stop there + + align:start position:0% +this most of the time you stop there + + + align:start position:0% +this most of the time you stop there +because you find zero that where you + + align:start position:0% +because you find zero that where you + + + align:start position:0% +because you find zero that where you +think that you had it towards an 80s + + align:start position:0% +think that you had it towards an 80s + + + align:start position:0% +think that you had it towards an 80s +like you know and maybe you even told + + align:start position:0% +like you know and maybe you even told + + + align:start position:0% +like you know and maybe you even told +yourself some nice stories about why you + + align:start position:0% +yourself some nice stories about why you + + + align:start position:0% +yourself some nice stories about why you +would be heterogeneous and in fact once + + align:start position:0% +would be heterogeneous and in fact once + + + align:start position:0% +would be heterogeneous and in fact once +you do it in the other sample and you + + align:start position:0% +you do it in the other sample and you + + + align:start position:0% +you do it in the other sample and you +regress the predicted treatment effect + + align:start position:0% +regress the predicted treatment effect + + + align:start position:0% +regress the predicted treatment effect +on on the actual treatment effect + + align:start position:0% +on on the actual treatment effect + + + align:start position:0% +on on the actual treatment effect +uh for um for the person in with those + + align:start position:0% +uh for um for the person in with those + + + align:start position:0% +uh for um for the person in with those +characteristics you don't find you don't + + align:start position:0% +characteristics you don't find you don't + + + align:start position:0% +characteristics you don't find you don't +find any difference + + align:start position:0% +find any difference + + + align:start position:0% +find any difference +if you do then you can say oh great then + + align:start position:0% +if you do then you can say oh great then + + + align:start position:0% +if you do then you can say oh great then +now I can uh + + align:start position:0% +now I can uh + + + align:start position:0% +now I can uh +um separate my groups into who is the + + align:start position:0% +um separate my groups into who is the + + + align:start position:0% +um separate my groups into who is the +most likely to be affected by the + + align:start position:0% +most likely to be affected by the + + + align:start position:0% +most likely to be affected by the +treatment or by quintile and run + + align:start position:0% +treatment or by quintile and run + + + align:start position:0% +treatment or by quintile and run +and and calculate the treatment effect + + align:start position:0% +and and calculate the treatment effect + + + align:start position:0% +and and calculate the treatment effect +for the people who are predicted to be + + align:start position:0% +for the people who are predicted to be + + + align:start position:0% +for the people who are predicted to be +the the least affected and the second + + align:start position:0% +the the least affected and the second + + + align:start position:0% +the the least affected and the second +least affected and the third least + + align:start position:0% +least affected and the third least + + + align:start position:0% +least affected and the third least +affected and so I I make the separation + + align:start position:0% +affected and so I I make the separation + + + align:start position:0% +affected and so I I make the separation +based on my machine learning sample and + + align:start position:0% +based on my machine learning sample and + + + align:start position:0% +based on my machine learning sample and +then I I estimate the treatment effect + + align:start position:0% +then I I estimate the treatment effect + + + align:start position:0% +then I I estimate the treatment effect +in that group + + align:start position:0% +in that group + + + align:start position:0% +in that group +so this is a treatment effect in that + + align:start position:0% +so this is a treatment effect in that + + + align:start position:0% +so this is a treatment effect in that +group in the leftover sample + + align:start position:0% +group in the leftover sample + + + align:start position:0% +group in the leftover sample +and then once you've done that once well + + align:start position:0% +and then once you've done that once well + + + align:start position:0% +and then once you've done that once well +you can do it many many many times many + + align:start position:0% +you can do it many many many times many + + + align:start position:0% +you can do it many many many times many +of the splits many times and then you + + align:start position:0% +of the splits many times and then you + + + align:start position:0% +of the splits many times and then you +even get a standard offer for that + + align:start position:0% +even get a standard offer for that + + + align:start position:0% +even get a standard offer for that +effect that reflects both the actual + + align:start position:0% +effect that reflects both the actual + + + align:start position:0% +effect that reflects both the actual +noise you have in your data set and the + + align:start position:0% +noise you have in your data set and the + + + align:start position:0% +noise you have in your data set and the +fact that it's a your sample split so + + align:start position:0% +fact that it's a your sample split so + + + align:start position:0% +fact that it's a your sample split so +each sample still introduce its own + + align:start position:0% +each sample still introduce its own + + + align:start position:0% +each sample still introduce its own +noise that needs to be taken into + + align:start position:0% +noise that needs to be taken into + + + align:start position:0% +noise that needs to be taken into +account yep + + align:start position:0% + + + + align:start position:0% + +so the train set like this is the first + + align:start position:0% +so the train set like this is the first + + + align:start position:0% +so the train set like this is the first +time you estimate the treatment you + + align:start position:0% +time you estimate the treatment you + + + align:start position:0% +time you estimate the treatment you +estimate the treatment effect + + align:start position:0% +estimate the treatment effect + + + align:start position:0% +estimate the treatment effect +the interactive regression for example + + align:start position:0% +the interactive regression for example + + + align:start position:0% +the interactive regression for example +think of it this way + + align:start position:0% +think of it this way + + + align:start position:0% +think of it this way +in the second uh set you + + align:start position:0% +in the second uh set you + + + align:start position:0% +in the second uh set you +um you you predict for each person + + align:start position:0% + + + + align:start position:0% + +as a function of your estimating the Z + + align:start position:0% +as a function of your estimating the Z + + + align:start position:0% +as a function of your estimating the Z +what their treatment effect would have + + align:start position:0% +what their treatment effect would have + + + align:start position:0% +what their treatment effect would have +been + + align:start position:0% +been + + + align:start position:0% +been +and then you regress for example you you + + align:start position:0% +and then you regress for example you you + + + align:start position:0% +and then you regress for example you you +do you you run a linear regression + + align:start position:0% + + + + align:start position:0% + +of uh your uh + + align:start position:0% +of uh your uh + + + align:start position:0% +of uh your uh +why your outcome + + align:start position:0% +why your outcome + + + align:start position:0% +why your outcome +uh in so think of uh running the + + align:start position:0% +uh in so think of uh running the + + + align:start position:0% +uh in so think of uh running the +following regression your new outcome on + + align:start position:0% +following regression your new outcome on + + + align:start position:0% +following regression your new outcome on +treatment treatment interaction + + align:start position:0% +treatment treatment interaction + + + align:start position:0% +treatment treatment interaction +interacted with this predicted effect + + align:start position:0% +interacted with this predicted effect + + + align:start position:0% +interacted with this predicted effect +and the predicted effect + + align:start position:0% +and the predicted effect + + + align:start position:0% +and the predicted effect +so this is now a linear coefficient and + + align:start position:0% +so this is now a linear coefficient and + + + align:start position:0% +so this is now a linear coefficient and +just asking + + align:start position:0% +just asking + + + align:start position:0% +just asking +is the people are the people that I + + align:start position:0% +is the people are the people that I + + + align:start position:0% +is the people are the people that I +predict to be to have the largest + + align:start position:0% +predict to be to have the largest + + + align:start position:0% +predict to be to have the largest +treatment effect do they in fact have a + + align:start position:0% +treatment effect do they in fact have a + + + align:start position:0% +treatment effect do they in fact have a +larger treatment effect + + align:start position:0% +larger treatment effect + + + align:start position:0% +larger treatment effect +that linear parameter is of no interest + + align:start position:0% +that linear parameter is of no interest + + + align:start position:0% +that linear parameter is of no interest +in and of itself it just say + + align:start position:0% +in and of itself it just say + + + align:start position:0% +in and of itself it just say +you know it should be ideally if that + + align:start position:0% +you know it should be ideally if that + + + align:start position:0% +you know it should be ideally if that +estimate was very very precise it would + + align:start position:0% +estimate was very very precise it would + + + align:start position:0% +estimate was very very precise it would +that coefficient would be one + + align:start position:0% +that coefficient would be one + + + align:start position:0% +that coefficient would be one +if that estimate is junk that estimate + + align:start position:0% +if that estimate is junk that estimate + + + align:start position:0% +if that estimate is junk that estimate +would be zero + + align:start position:0% +would be zero + + + align:start position:0% +would be zero +so that's the that's the + + align:start position:0% +so that's the that's the + + + align:start position:0% +so that's the that's the +that's the main use of that linear thing + + align:start position:0% +that's the main use of that linear thing + + + align:start position:0% +that's the main use of that linear thing +then what you're doing here + + align:start position:0% +then what you're doing here + + + align:start position:0% +then what you're doing here +is similar but but domified dummified + + align:start position:0% +is similar but but domified dummified + + + align:start position:0% +is similar but but domified dummified +version + + align:start position:0% +version + + + align:start position:0% +version +you basically on the basis of your uh of + + align:start position:0% +you basically on the basis of your uh of + + + align:start position:0% +you basically on the basis of your uh of +your + + align:start position:0% +your + + + align:start position:0% +your +the estimate in your in your machine + + align:start position:0% +the estimate in your in your machine + + + align:start position:0% +the estimate in your in your machine +learning sample + + align:start position:0% +learning sample + + + align:start position:0% +learning sample +you've made uh five groups of the people + + align:start position:0% +you've made uh five groups of the people + + + align:start position:0% +you've made uh five groups of the people +who are predicted to be the most + + align:start position:0% +who are predicted to be the most + + + align:start position:0% +who are predicted to be the most +affected based on their uh + + align:start position:0% +affected based on their uh + + + align:start position:0% +affected based on their uh +X characteristics on their Baseline + + align:start position:0% +X characteristics on their Baseline + + + align:start position:0% +X characteristics on their Baseline +characteristics + + align:start position:0% +characteristics + + + align:start position:0% +characteristics +and then in your test sample + + align:start position:0% +and then in your test sample + + + align:start position:0% +and then in your test sample +you are actually estimating the + + align:start position:0% +you are actually estimating the + + + align:start position:0% +you are actually estimating the +treatment effect in for the people who + + align:start position:0% +treatment effect in for the people who + + + align:start position:0% +treatment effect in for the people who +have these characteristics this + + align:start position:0% +have these characteristics this + + + align:start position:0% +have these characteristics this +combination of characteristics + + align:start position:0% +combination of characteristics + + + align:start position:0% +combination of characteristics +do you in that quintile of the people + + align:start position:0% +do you in that quintile of the people + + + align:start position:0% +do you in that quintile of the people +who are predicted to have the lowest + + align:start position:0% +who are predicted to have the lowest + + + align:start position:0% +who are predicted to have the lowest +treatment effect so again if the if it + + align:start position:0% +treatment effect so again if the if it + + + align:start position:0% +treatment effect so again if the if it +was on the journey it would be it would + + align:start position:0% +was on the journey it would be it would + + + align:start position:0% +was on the journey it would be it would +just be a line + + align:start position:0% +just be a line + + + align:start position:0% +just be a line +because the people who have the lowest + + align:start position:0% +because the people who have the lowest + + + align:start position:0% +because the people who have the lowest +treatment effect in your machine + + align:start position:0% +treatment effect in your machine + + + align:start position:0% +treatment effect in your machine +learning sample in fact don't in in real + + align:start position:0% +learning sample in fact don't in in real + + + align:start position:0% +learning sample in fact don't in in real +life + + align:start position:0% + + + + align:start position:0% + +make sense + + align:start position:0% +make sense + + + align:start position:0% +make sense +and then once you so you you can do that + + align:start position:0% +and then once you so you you can do that + + + align:start position:0% +and then once you so you you can do that +so here these are the results for the + + align:start position:0% +so here these are the results for the + + + align:start position:0% +so here these are the results for the +immunization sample + + align:start position:0% +immunization sample + + + align:start position:0% +immunization sample +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so they are + + align:start position:0% +so they are + + + align:start position:0% +so they are +exceptionally nice in that they actually + + align:start position:0% +exceptionally nice in that they actually + + + align:start position:0% +exceptionally nice in that they actually +something comes out of it + + align:start position:0% +something comes out of it + + + align:start position:0% +something comes out of it +um it's not always the case as I said + + align:start position:0% +um it's not always the case as I said + + + align:start position:0% +um it's not always the case as I said +and what you find is very very strong + + align:start position:0% +and what you find is very very strong + + + align:start position:0% +and what you find is very very strong +heterogeneity to the point that the + + align:start position:0% +heterogeneity to the point that the + + + align:start position:0% +heterogeneity to the point that the +people the place that are the most + + align:start position:0% +people the place that are the most + + + align:start position:0% +people the place that are the most +affected are really affected you have + + align:start position:0% +affected are really affected you have + + + align:start position:0% +affected are really affected you have +huge treatment effect + + align:start position:0% +huge treatment effect + + + align:start position:0% +huge treatment effect +and the places which are not which are + + align:start position:0% +and the places which are not which are + + + align:start position:0% +and the places which are not which are +least effective as negative treatment + + align:start position:0% +least effective as negative treatment + + + align:start position:0% +least effective as negative treatment +effect + + align:start position:0% + + + + align:start position:0% + +uh so then what you can do is to two + + align:start position:0% +uh so then what you can do is to two + + + align:start position:0% +uh so then what you can do is to two +things first that I will discuss that + + align:start position:0% +things first that I will discuss that + + + align:start position:0% +things first that I will discuss that +for a minute of why is that why is it + + align:start position:0% +for a minute of why is that why is it + + + align:start position:0% +for a minute of why is that why is it +even plausible to have negative + + align:start position:0% +even plausible to have negative + + + align:start position:0% +even plausible to have negative +treatment effect + + align:start position:0% +treatment effect + + + align:start position:0% +treatment effect +and only you could say uh that the last + + align:start position:0% +and only you could say uh that the last + + + align:start position:0% +and only you could say uh that the last +thing that we do + + align:start position:0% +thing that we do + + + align:start position:0% +thing that we do +is to say well + + align:start position:0% +is to say well + + + align:start position:0% +is to say well +we can do a sort of classification + + align:start position:0% +we can do a sort of classification + + + align:start position:0% +we can do a sort of classification +analysis which is to say what are the + + align:start position:0% +analysis which is to say what are the + + + align:start position:0% +analysis which is to say what are the +characters this is like a bunch of these + + align:start position:0% +characters this is like a bunch of these + + + align:start position:0% +characters this is like a bunch of these +interacted with certain complicated way + + align:start position:0% +interacted with certain complicated way + + + align:start position:0% +interacted with certain complicated way +but you know if I just run a summary + + align:start position:0% +but you know if I just run a summary + + + align:start position:0% +but you know if I just run a summary +statistics just a summary statistics + + align:start position:0% +statistics just a summary statistics + + + align:start position:0% +statistics just a summary statistics +table of the some characteristic of + + align:start position:0% +table of the some characteristic of + + + align:start position:0% +table of the some characteristic of +these different groups + + align:start position:0% +these different groups + + + align:start position:0% +these different groups +I do they look different in the groups + + align:start position:0% +I do they look different in the groups + + + align:start position:0% +I do they look different in the groups +so there you have to be careful not to + + align:start position:0% +so there you have to be careful not to + + + align:start position:0% +so there you have to be careful not to +over interpret this difference because + + align:start position:0% +over interpret this difference because + + + align:start position:0% +over interpret this difference because +again they are not causal but at least + + align:start position:0% +again they are not causal but at least + + + align:start position:0% +again they are not causal but at least +it gives you a description and what we + + align:start position:0% +it gives you a description and what we + + + align:start position:0% +it gives you a description and what we +find that's pretty interesting is that + + align:start position:0% +find that's pretty interesting is that + + + align:start position:0% +find that's pretty interesting is that +the places that are the most affected + + align:start position:0% +the places that are the most affected + + + align:start position:0% +the places that are the most affected +are the ones where immunization rates + + align:start position:0% +are the ones where immunization rates + + + align:start position:0% +are the ones where immunization rates +were very very low to start with + + align:start position:0% +were very very low to start with + + + align:start position:0% +were very very low to start with +and the places that were the least + + align:start position:0% +and the places that were the least + + + align:start position:0% +and the places that were the least +affected are the places that have high + + align:start position:0% +affected are the places that have high + + + align:start position:0% +affected are the places that have high +ammunition rate to start with + + align:start position:0% +ammunition rate to start with + + + align:start position:0% +ammunition rate to start with +so I remember I first presented that in + + align:start position:0% +so I remember I first presented that in + + + align:start position:0% +so I remember I first presented that in +the bank and in the world bank and uh + + align:start position:0% +the bank and in the world bank and uh + + + align:start position:0% +the bank and in the world bank and uh +uh my transitional death was work we are + + align:start position:0% +uh my transitional death was work we are + + + align:start position:0% +uh my transitional death was work we are +going to talk a lot about in the rest of + + align:start position:0% +going to talk a lot about in the rest of + + + align:start position:0% +going to talk a lot about in the rest of +today and next week + + align:start position:0% +today and next week + + + align:start position:0% +today and next week +I was like come on you cannot write a + + align:start position:0% +I was like come on you cannot write a + + + align:start position:0% +I was like come on you cannot write a +paper or you do this whole things and + + align:start position:0% +paper or you do this whole things and + + + align:start position:0% +paper or you do this whole things and +you just tell me the people who are most + + align:start position:0% +you just tell me the people who are most + + + align:start position:0% +you just tell me the people who are most +affected by any images are the people + + align:start position:0% +affected by any images are the people + + + align:start position:0% +affected by any images are the people +whose ammunition level were allowed to + + align:start position:0% +whose ammunition level were allowed to + + + align:start position:0% +whose ammunition level were allowed to +start with + + align:start position:0% +start with + + + align:start position:0% +start with +and first I was like yeah yeah you're + + align:start position:0% +and first I was like yeah yeah you're + + + align:start position:0% +and first I was like yeah yeah you're +right that sounds that sounds a bit + + align:start position:0% +right that sounds that sounds a bit + + + align:start position:0% +right that sounds that sounds a bit +silly but then I thought about it it's + + align:start position:0% +silly but then I thought about it it's + + + align:start position:0% +silly but then I thought about it it's +like why + + align:start position:0% +like why + + + align:start position:0% +like why +even the people with high ammunition + + align:start position:0% +even the people with high ammunition + + + align:start position:0% +even the people with high ammunition +rate it's not that they have super high + + align:start position:0% +rate it's not that they have super high + + + align:start position:0% +rate it's not that they have super high +musician right they have plenty of scope + + align:start position:0% +musician right they have plenty of scope + + + align:start position:0% +musician right they have plenty of scope +to improve + + align:start position:0% +to improve + + + align:start position:0% +to improve +so it's not mechanical they are not + + align:start position:0% +so it's not mechanical they are not + + + align:start position:0% +so it's not mechanical they are not +bounded they are not at all in the range + + align:start position:0% +bounded they are not at all in the range + + + align:start position:0% +bounded they are not at all in the range +where they would be bounded so nothing + + align:start position:0% +where they would be bounded so nothing + + + align:start position:0% +where they would be bounded so nothing +says that the impact of intervention are + + align:start position:0% +says that the impact of intervention are + + + align:start position:0% +says that the impact of intervention are +concave in general + + align:start position:0% +concave in general + + + align:start position:0% +concave in general +in fact in in many cases it's for + + align:start position:0% +in fact in in many cases it's for + + + align:start position:0% +in fact in in many cases it's for +example in the ultra poor program the + + align:start position:0% +example in the ultra poor program the + + + align:start position:0% +example in the ultra poor program the +people who benefit the most are the + + align:start position:0% +people who benefit the most are the + + + align:start position:0% +people who benefit the most are the +richest of the El Chapo + + align:start position:0% +richest of the El Chapo + + + align:start position:0% +richest of the El Chapo +so + + align:start position:0% +so + + + align:start position:0% +so +I don't think it is mechanical but maybe + + align:start position:0% +I don't think it is mechanical but maybe + + + align:start position:0% +I don't think it is mechanical but maybe +it's true that a little bit like the + + align:start position:0% +it's true that a little bit like the + + + align:start position:0% +it's true that a little bit like the +first paper it sounds a bit + + align:start position:0% +first paper it sounds a bit + + + align:start position:0% +first paper it sounds a bit +um sad after all this exercise to come + + align:start position:0% +um sad after all this exercise to come + + + align:start position:0% +um sad after all this exercise to come +up with something obvious + + align:start position:0% +up with something obvious + + + align:start position:0% +up with something obvious +and then the other thing that that is + + align:start position:0% +and then the other thing that that is + + + align:start position:0% +and then the other thing that that is +clearly not mechanical is that you get a + + align:start position:0% +clearly not mechanical is that you get a + + + align:start position:0% +clearly not mechanical is that you get a +negative impact uh you know why so I + + align:start position:0% +negative impact uh you know why so I + + + align:start position:0% +negative impact uh you know why so I +which might be sort of the most + + align:start position:0% +which might be sort of the most + + + align:start position:0% +which might be sort of the most +interesting or is probably the most + + align:start position:0% +interesting or is probably the most + + + align:start position:0% +interesting or is probably the most +interesting and scary results of here so + + align:start position:0% +interesting and scary results of here so + + + align:start position:0% +interesting and scary results of here so +why do you think the the result might be + + align:start position:0% + + + + align:start position:0% + +why do you think some people might be + + align:start position:0% +why do you think some people might be + + + align:start position:0% +why do you think some people might be +negatively affected + + align:start position:0% + + + + align:start position:0% + +some Villages or and therefore some + + align:start position:0% +some Villages or and therefore some + + + align:start position:0% +some Villages or and therefore some +people + + align:start position:0% +people + + + align:start position:0% +people +might be + + align:start position:0% +might be + + + align:start position:0% +might be +negatively affected by by a program like + + align:start position:0% +negatively affected by by a program like + + + align:start position:0% +negatively affected by by a program like +that + + align:start position:0% + + + + align:start position:0% + +so you mean they were already doing + + align:start position:0% +so you mean they were already doing + + + align:start position:0% +so you mean they were already doing +something and not liking other people + + align:start position:0% + + + + align:start position:0% + +it's the number of shots that are given + + align:start position:0% +it's the number of shots that are given + + + align:start position:0% +it's the number of shots that are given +by in the month that's the outcome so + + align:start position:0% +by in the month that's the outcome so + + + align:start position:0% +by in the month that's the outcome so +they might be counting out of other + + align:start position:0% +they might be counting out of other + + + align:start position:0% +they might be counting out of other +things but here for example if people + + align:start position:0% +things but here for example if people + + + align:start position:0% +things but here for example if people +come from other Villages they would be + + align:start position:0% +come from other Villages they would be + + + align:start position:0% +come from other Villages they would be +counted + + align:start position:0% +counted + + + align:start position:0% +counted +so any this is including any crowding of + + align:start position:0% +so any this is including any crowding of + + + align:start position:0% +so any this is including any crowding of +other people + + align:start position:0% +other people + + + align:start position:0% +other people +from other villages + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +one hypothesis I guess that was + + align:start position:0% +one hypothesis I guess that was + + + align:start position:0% +one hypothesis I guess that was +mentioned briefly in the paper which is + + align:start position:0% +mentioned briefly in the paper which is + + + align:start position:0% +mentioned briefly in the paper which is +that some people are very intrinsically + + align:start position:0% +that some people are very intrinsically + + + align:start position:0% +that some people are very intrinsically +motivated to get vaccinated and once you + + align:start position:0% +motivated to get vaccinated and once you + + + align:start position:0% +motivated to get vaccinated and once you +introduce this external encouragement + + align:start position:0% +introduce this external encouragement + + + align:start position:0% +introduce this external encouragement +then the kind of you know + + align:start position:0% +then the kind of you know + + + align:start position:0% +then the kind of you know +behavioral explanation of actually + + align:start position:0% +behavioral explanation of actually + + + align:start position:0% +behavioral explanation of actually +yes maybe this is one of these uh + + align:start position:0% +yes maybe this is one of these uh + + + align:start position:0% +yes maybe this is one of these uh +example of + + align:start position:0% +example of + + + align:start position:0% +example of +weaknesses as a series of series of + + align:start position:0% +weaknesses as a series of series of + + + align:start position:0% +weaknesses as a series of series of +people one is called the fine is a price + + align:start position:0% +people one is called the fine is a price + + + align:start position:0% +people one is called the fine is a price +that shows that when when a school + + align:start position:0% +that shows that when when a school + + + align:start position:0% +that shows that when when a school +penalizes parents give it a fine to + + align:start position:0% +penalizes parents give it a fine to + + + align:start position:0% +penalizes parents give it a fine to +people for parents when they collect + + align:start position:0% +people for parents when they collect + + + align:start position:0% +people for parents when they collect +their kids late at daycare + + align:start position:0% +their kids late at daycare + + + align:start position:0% +their kids late at daycare +the number of parents who send their + + align:start position:0% +the number of parents who send their + + + align:start position:0% +the number of parents who send their +kids who pick up their kids late + + align:start position:0% +kids who pick up their kids late + + + align:start position:0% +kids who pick up their kids late +actually increases + + align:start position:0% +actually increases + + + align:start position:0% +actually increases +because before people thought like oh + + align:start position:0% +because before people thought like oh + + + align:start position:0% +because before people thought like oh +this is the deadline I have to pick I + + align:start position:0% +this is the deadline I have to pick I + + + align:start position:0% +this is the deadline I have to pick I +have to pick up my kids and now it's + + align:start position:0% +have to pick up my kids and now it's + + + align:start position:0% +have to pick up my kids and now it's +like + + align:start position:0% +like + + + align:start position:0% +like +you're actually sending a signal that + + align:start position:0% +you're actually sending a signal that + + + align:start position:0% +you're actually sending a signal that +you um + + align:start position:0% +you um + + + align:start position:0% +you um +uh you know you can do it against some + + align:start position:0% +uh you know you can do it against some + + + align:start position:0% +uh you know you can do it against some +price + + align:start position:0% +price + + + align:start position:0% +price +other effect of other + + align:start position:0% +other effect of other + + + align:start position:0% +other effect of other +example yeah + + align:start position:0% +example yeah + + + align:start position:0% +example yeah +me like another + + align:start position:0% +me like another + + + align:start position:0% +me like another +violence + + align:start position:0% + + + + align:start position:0% + +everyone in the village + + align:start position:0% +everyone in the village + + + align:start position:0% +everyone in the village +me feels like the easiest people for + + align:start position:0% +me feels like the easiest people for + + + align:start position:0% +me feels like the easiest people for +vaccinations that's what everyone else + + align:start position:0% +vaccinations that's what everyone else + + + align:start position:0% +vaccinations that's what everyone else +needs like lots of like information or + + align:start position:0% +needs like lots of like information or + + + align:start position:0% +needs like lots of like information or +nothing but the financial incentive they + + align:start position:0% +nothing but the financial incentive they + + + align:start position:0% +nothing but the financial incentive they +might might wonder like why is the + + align:start position:0% +might might wonder like why is the + + + align:start position:0% +might might wonder like why is the +government or whoever it is trying to + + align:start position:0% +government or whoever it is trying to + + + align:start position:0% +government or whoever it is trying to +get the money + + align:start position:0% + + + + align:start position:0% + +I'm sure people can actually get it yeah + + align:start position:0% +I'm sure people can actually get it yeah + + + align:start position:0% +I'm sure people can actually get it yeah +exactly so the people uh so some version + + align:start position:0% +exactly so the people uh so some version + + + align:start position:0% +exactly so the people uh so some version +of it which you know Behavioral or not + + align:start position:0% +of it which you know Behavioral or not + + + align:start position:0% +of it which you know Behavioral or not +could be that people were already doing + + align:start position:0% +could be that people were already doing + + + align:start position:0% +could be that people were already doing +it + + align:start position:0% +it + + + align:start position:0% +it +and then suddenly uh there is an + + align:start position:0% +and then suddenly uh there is an + + + align:start position:0% +and then suddenly uh there is an +incentive it's like why do they need + + align:start position:0% +incentive it's like why do they need + + + align:start position:0% +incentive it's like why do they need +meat why do they need to pay me to do + + align:start position:0% +meat why do they need to pay me to do + + + align:start position:0% +meat why do they need to pay me to do +that + + align:start position:0% + + + + align:start position:0% + +um you know it must be really bad if + + align:start position:0% +um you know it must be really bad if + + + align:start position:0% +um you know it must be really bad if +they need to pay me to do that I + + align:start position:0% +they need to pay me to do that I + + + align:start position:0% +they need to pay me to do that I +shouldn't want to do it by myself in the + + align:start position:0% +shouldn't want to do it by myself in the + + + align:start position:0% +shouldn't want to do it by myself in the +context of the covid-19 vaccine for + + align:start position:0% +context of the covid-19 vaccine for + + + align:start position:0% +context of the covid-19 vaccine for +example in discussion in France of + + align:start position:0% +example in discussion in France of + + + align:start position:0% +example in discussion in France of +making it mandatory and or + + align:start position:0% +making it mandatory and or + + + align:start position:0% +making it mandatory and or +you know quasi mandatory which is what + + align:start position:0% +you know quasi mandatory which is what + + + align:start position:0% +you know quasi mandatory which is what +it is now + + align:start position:0% +it is now + + + align:start position:0% +it is now +uh it certainly wasn't it was there that + + align:start position:0% +uh it certainly wasn't it was there that + + + align:start position:0% +uh it certainly wasn't it was there that +if you make something mandatory then + + align:start position:0% +if you make something mandatory then + + + align:start position:0% +if you make something mandatory then +it's it says it sends a signal that it's + + align:start position:0% +it's it says it sends a signal that it's + + + align:start position:0% +it's it says it sends a signal that it's +not something you should desire + + align:start position:0% +not something you should desire + + + align:start position:0% +not something you should desire +and instead in fact people were + + align:start position:0% +and instead in fact people were + + + align:start position:0% +and instead in fact people were +extremely suspicious of the vaccine in + + align:start position:0% +extremely suspicious of the vaccine in + + + align:start position:0% +extremely suspicious of the vaccine in +France it was one of the highest + + align:start position:0% +France it was one of the highest + + + align:start position:0% +France it was one of the highest +before the vaccination campaign even + + align:start position:0% +before the vaccination campaign even + + + align:start position:0% +before the vaccination campaign even +started it was one of the highest + + align:start position:0% +started it was one of the highest + + + align:start position:0% +started it was one of the highest +suspicion + + align:start position:0% +suspicion + + + align:start position:0% +suspicion +uh country + + align:start position:0% +uh country + + + align:start position:0% +uh country +and then the the beginning of the + + align:start position:0% +and then the the beginning of the + + + align:start position:0% +and then the the beginning of the +campaign was totally but it was really + + align:start position:0% +campaign was totally but it was really + + + align:start position:0% +campaign was totally but it was really +slow in the first two weeks they they + + align:start position:0% +slow in the first two weeks they they + + + align:start position:0% +slow in the first two weeks they they +immunized like 12 people since they even + + align:start position:0% +immunized like 12 people since they even + + + align:start position:0% +immunized like 12 people since they even +immunized some woman called Morissette + + align:start position:0% +immunized some woman called Morissette + + + align:start position:0% +immunized some woman called Morissette +and uh in an old age home person maybe + + align:start position:0% +and uh in an old age home person maybe + + + align:start position:0% +and uh in an old age home person maybe +like 12 people in two weeks it was a + + align:start position:0% +like 12 people in two weeks it was a + + + align:start position:0% +like 12 people in two weeks it was a +disaster the whole thing was about there + + align:start position:0% +disaster the whole thing was about there + + + align:start position:0% +disaster the whole thing was about there +is not going to be enough vaccine and we + + align:start position:0% +is not going to be enough vaccine and we + + + align:start position:0% +is not going to be enough vaccine and we +are not going to be able to do it + + align:start position:0% +are not going to be able to do it + + + align:start position:0% +are not going to be able to do it +and then + + align:start position:0% +and then + + + align:start position:0% +and then +the The View on whether people wanted to + + align:start position:0% +the The View on whether people wanted to + + + align:start position:0% +the The View on whether people wanted to +get vaccinated changed and one possible + + align:start position:0% +get vaccinated changed and one possible + + + align:start position:0% +get vaccinated changed and one possible +interpretation is that that became to be + + align:start position:0% +interpretation is that that became to be + + + align:start position:0% +interpretation is that that became to be +seen like something rare that you should + + align:start position:0% +seen like something rare that you should + + + align:start position:0% +seen like something rare that you should +desire because there is not enough of it + + align:start position:0% +desire because there is not enough of it + + + align:start position:0% +desire because there is not enough of it +and there is not and this these idiots + + align:start position:0% +and there is not and this these idiots + + + align:start position:0% +and there is not and this these idiots +of the government they are not able to + + align:start position:0% +of the government they are not able to + + + align:start position:0% +of the government they are not able to +deliver this good that we really need + + align:start position:0% +deliver this good that we really need + + + align:start position:0% +deliver this good that we really need +and uh therefore you know the your + + align:start position:0% +and uh therefore you know the your + + + align:start position:0% +and uh therefore you know the your +mistrusting the government paradoxically + + align:start position:0% +mistrusting the government paradoxically + + + align:start position:0% +mistrusting the government paradoxically +I think pleading now in in the favor of + + align:start position:0% +I think pleading now in in the favor of + + + align:start position:0% +I think pleading now in in the favor of +generating a consensus more than + + align:start position:0% +generating a consensus more than + + + align:start position:0% +generating a consensus more than +anything else + + align:start position:0% +anything else + + + align:start position:0% +anything else +and then + + align:start position:0% +and then + + + align:start position:0% +and then +I'm not saying they did that on purpose + + align:start position:0% +I'm not saying they did that on purpose + + + align:start position:0% +I'm not saying they did that on purpose +I know they didn't uh but and and I + + align:start position:0% +I know they didn't uh but and and I + + + align:start position:0% +I know they didn't uh but and and I +don't know whether my expansion is + + align:start position:0% +don't know whether my expansion is + + + align:start position:0% +don't know whether my expansion is +correct but it could be + + align:start position:0% +correct but it could be + + + align:start position:0% +correct but it could be +what I know they didn't do on purpose is + + align:start position:0% +what I know they didn't do on purpose is + + + align:start position:0% +what I know they didn't do on purpose is +to not have a mandator anything looking + + align:start position:0% +to not have a mandator anything looking + + + align:start position:0% +to not have a mandator anything looking +like that or incentives or until quite + + align:start position:0% +like that or incentives or until quite + + + align:start position:0% +like that or incentives or until quite +late + + align:start position:0% +late + + + align:start position:0% +late +because they were worried about that + + align:start position:0% +because they were worried about that + + + align:start position:0% +because they were worried about that +backlash effect that if you put an + + align:start position:0% +backlash effect that if you put an + + + align:start position:0% +backlash effect that if you put an +incentive people are just gonna + + align:start position:0% +incentive people are just gonna + + + align:start position:0% +incentive people are just gonna +not do it just to spite just to spite + + align:start position:0% +not do it just to spite just to spite + + + align:start position:0% +not do it just to spite just to spite +despite the Garment + + align:start position:0% +despite the Garment + + + align:start position:0% +despite the Garment +and here there might be a bit like that + + align:start position:0% +and here there might be a bit like that + + + align:start position:0% +and here there might be a bit like that +it's like why do they need to pay me to + + align:start position:0% +it's like why do they need to pay me to + + + align:start position:0% +it's like why do they need to pay me to +do the thing I was gonna do it anywhere + + align:start position:0% +do the thing I was gonna do it anywhere + + + align:start position:0% +do the thing I was gonna do it anywhere +but it must really be good but if they + + align:start position:0% +but it must really be good but if they + + + align:start position:0% +but it must really be good but if they +if they pay me to do it + + align:start position:0% + + + + align:start position:0% + +um and and that's consistent with the + + align:start position:0% +um and and that's consistent with the + + + align:start position:0% +um and and that's consistent with the +fact that the effects are the are the + + align:start position:0% +fact that the effects are the are the + + + align:start position:0% +fact that the effects are the are the +smallest in places that have a lot of + + align:start position:0% +smallest in places that have a lot of + + + align:start position:0% +smallest in places that have a lot of +immunization already because it it + + align:start position:0% +immunization already because it it + + + align:start position:0% +immunization already because it it +leaves a bunch of people who + + align:start position:0% +leaves a bunch of people who + + + align:start position:0% +leaves a bunch of people who +would otherwise have done it who can be + + align:start position:0% +would otherwise have done it who can be + + + align:start position:0% +would otherwise have done it who can be +unconvinced a lot of people are aware it + + align:start position:0% +unconvinced a lot of people are aware it + + + align:start position:0% +unconvinced a lot of people are aware it +was in the effect in the places where + + align:start position:0% +was in the effect in the places where + + + align:start position:0% +was in the effect in the places where +nobody gets vaccinated + + align:start position:0% +nobody gets vaccinated + + + align:start position:0% +nobody gets vaccinated +there is nobody who has intrinsically + + align:start position:0% +there is nobody who has intrinsically + + + align:start position:0% +there is nobody who has intrinsically +motivated to start with so you you your + + align:start position:0% +motivated to start with so you you your + + + align:start position:0% +motivated to start with so you you your +expressing motivation is helping helping + + align:start position:0% +expressing motivation is helping helping + + + align:start position:0% +expressing motivation is helping helping +it yeah in this particular setting do + + align:start position:0% +it yeah in this particular setting do + + + align:start position:0% +it yeah in this particular setting do +you have any uh evidence or prior to + + align:start position:0% +you have any uh evidence or prior to + + + align:start position:0% +you have any uh evidence or prior to +this intervention + + align:start position:0% +this intervention + + + align:start position:0% +this intervention +um when people were getting immunized + + align:start position:0% +um when people were getting immunized + + + align:start position:0% +um when people were getting immunized +was it was it previously associated with + + align:start position:0% +was it was it previously associated with + + + align:start position:0% +was it was it previously associated with +the government so could it be that you + + align:start position:0% +the government so could it be that you + + + align:start position:0% +the government so could it be that you +know now the government wants to give me + + align:start position:0% +know now the government wants to give me + + + align:start position:0% +know now the government wants to give me +the previously you know I was happy to + + align:start position:0% +the previously you know I was happy to + + + align:start position:0% +the previously you know I was happy to +go to my doctor you know there wasn't as + + align:start position:0% +go to my doctor you know there wasn't as + + + align:start position:0% +go to my doctor you know there wasn't as +much of a limit between immunizations + + align:start position:0% +much of a limit between immunizations + + + align:start position:0% +much of a limit between immunizations +and the government wanting to do it so + + align:start position:0% +and the government wanting to do it so + + + align:start position:0% +and the government wanting to do it so +it's specifically about + + align:start position:0% +it's specifically about + + + align:start position:0% +it's specifically about +I mistrustful of the government but not + + align:start position:0% +I mistrustful of the government but not + + + align:start position:0% +I mistrustful of the government but not +necessarily at medicine but now that the + + align:start position:0% +necessarily at medicine but now that the + + + align:start position:0% +necessarily at medicine but now that the +government is kind of imposing itself I + + align:start position:0% +government is kind of imposing itself I + + + align:start position:0% +government is kind of imposing itself I +I don't know if yeah I don't know + + align:start position:0% +I don't know if yeah I don't know + + + align:start position:0% +I don't know if yeah I don't know +because the the the the incentive was + + align:start position:0% +because the the the the incentive was + + + align:start position:0% +because the the the the incentive was +done as part of the government + + align:start position:0% +done as part of the government + + + align:start position:0% +done as part of the government +structures anyway okay so it could be a + + align:start position:0% +structures anyway okay so it could be a + + + align:start position:0% +structures anyway okay so it could be a +instance of keep the government out of + + align:start position:0% +instance of keep the government out of + + + align:start position:0% +instance of keep the government out of +my medicare + + align:start position:0% +my medicare + + + align:start position:0% +my medicare +uh that is you know suddenly people + + align:start position:0% +uh that is you know suddenly people + + + align:start position:0% +uh that is you know suddenly people +realize the importance of the of the + + align:start position:0% +realize the importance of the of the + + + align:start position:0% +realize the importance of the of the +government in ordering their care but uh + + align:start position:0% +government in ordering their care but uh + + + align:start position:0% +government in ordering their care but uh +I'm not I'm not sure it could be yeah + + align:start position:0% + + + + align:start position:0% + +you kind of translate it back into some + + align:start position:0% +you kind of translate it back into some + + + align:start position:0% +you kind of translate it back into some +like simple demographics + + align:start position:0% +like simple demographics + + + align:start position:0% +like simple demographics +yes the way that this one translates + + align:start position:0% +yes the way that this one translates + + + align:start position:0% +yes the way that this one translates +nicely + + align:start position:0% +nicely + + + align:start position:0% +nicely +basically your + + align:start position:0% +basically your + + + align:start position:0% +basically your +you have a table sort of like that + + align:start position:0% +you have a table sort of like that + + + align:start position:0% +you have a table sort of like that +except you can express it in a express + + align:start position:0% +except you can express it in a express + + + align:start position:0% +except you can express it in a express +it in graphs you say well you get the + + align:start position:0% +it in graphs you say well you get the + + + align:start position:0% +it in graphs you say well you get the +biggest effect in places where there is + + align:start position:0% +biggest effect in places where there is + + + align:start position:0% +biggest effect in places where there is +a lot of vaccination already + + align:start position:0% +a lot of vaccination already + + + align:start position:0% +a lot of vaccination already +this in these are side side dimension of + + align:start position:0% +this in these are side side dimension of + + + align:start position:0% +this in these are side side dimension of +vaccination but you can think just one + + align:start position:0% +vaccination but you can think just one + + + align:start position:0% +vaccination but you can think just one +and none of the other you know and then + + align:start position:0% +and none of the other you know and then + + + align:start position:0% +and none of the other you know and then +that's the one thing that comes out and + + align:start position:0% +that's the one thing that comes out and + + + align:start position:0% +that's the one thing that comes out and +for example for the government very + + align:start position:0% +for example for the government very + + + align:start position:0% +for example for the government very +important to tell them that it's not + + align:start position:0% +important to tell them that it's not + + + align:start position:0% +important to tell them that it's not +about religion this is haryana that's + + align:start position:0% +about religion this is haryana that's + + + align:start position:0% +about religion this is haryana that's +like Hindu + + align:start position:0% + + + + align:start position:0% + +the government is like + + align:start position:0% +the government is like + + + align:start position:0% +the government is like +hindutva dominated + + align:start position:0% +hindutva dominated + + + align:start position:0% +hindutva dominated +so they are very pumped to say that this + + align:start position:0% +so they are very pumped to say that this + + + align:start position:0% +so they are very pumped to say that this +is our Muslims who don't want to get + + align:start position:0% +is our Muslims who don't want to get + + + align:start position:0% +is our Muslims who don't want to get +immunized so you can show this effect it + + align:start position:0% +immunized so you can show this effect it + + + align:start position:0% +immunized so you can show this effect it +doesn't vary but it must be in Hindu + + align:start position:0% + + + + align:start position:0% + +that kind of things + + align:start position:0% + + + + align:start position:0% + +but you're right that's why we want to + + align:start position:0% +but you're right that's why we want to + + + align:start position:0% +but you're right that's why we want to +kind of get to the Sea land to give + + align:start position:0% +kind of get to the Sea land to give + + + align:start position:0% +kind of get to the Sea land to give +something that is kind of concretely + + align:start position:0% +something that is kind of concretely + + + align:start position:0% +something that is kind of concretely +actionable understandable + + align:start position:0% + + + + align:start position:0% + +but they are still not so they are still + + align:start position:0% +but they are still not so they are still + + + align:start position:0% +but they are still not so they are still +not doing it this full one + + align:start position:0% +not doing it this full one + + + align:start position:0% +not doing it this full one +it's not there are they were very keen + + align:start position:0% +it's not there are they were very keen + + + align:start position:0% +it's not there are they were very keen +to scale up the gossip plus SMS + + align:start position:0% +to scale up the gossip plus SMS + + + align:start position:0% +to scale up the gossip plus SMS +but this one is + + align:start position:0% +but this one is + + + align:start position:0% +but this one is +more complicated the fact that it costs + + align:start position:0% +more complicated the fact that it costs + + + align:start position:0% +more complicated the fact that it costs +money even though so even though another + + align:start position:0% +money even though so even though another + + + align:start position:0% +money even though so even though another +important message for for policies that + + align:start position:0% +important message for for policies that + + + align:start position:0% +important message for for policies that +if you focus on the places that are the + + align:start position:0% +if you focus on the places that are the + + + align:start position:0% +if you focus on the places that are the +most + + align:start position:0% +most + + + align:start position:0% +most +that are that have the largest effect it + + align:start position:0% +that are that have the largest effect it + + + align:start position:0% +that are that have the largest effect it +becomes cost effective in those places + + align:start position:0% +becomes cost effective in those places + + + align:start position:0% +becomes cost effective in those places +uh not uh not tremendously so it's not + + align:start position:0% +uh not uh not tremendously so it's not + + + align:start position:0% +uh not uh not tremendously so it's not +terribly uh + + align:start position:0% +terribly uh + + + align:start position:0% +terribly uh +it's not terribly + + align:start position:0% +it's not terribly + + + align:start position:0% +it's not terribly +um + + align:start position:0% + + + + align:start position:0% + +much cheaper than the control which is + + align:start position:0% +much cheaper than the control which is + + + align:start position:0% +much cheaper than the control which is +what we do in which we find in udaipur + + align:start position:0% +what we do in which we find in udaipur + + + align:start position:0% +what we do in which we find in udaipur +but in the top groups you know you + + align:start position:0% +but in the top groups you know you + + + align:start position:0% +but in the top groups you know you +cannot project that it's uh you don't + + align:start position:0% +cannot project that it's uh you don't + + + align:start position:0% +cannot project that it's uh you don't +lose any money per shot compared to not + + align:start position:0% +lose any money per shot compared to not + + + align:start position:0% +lose any money per shot compared to not +doing the incentives + + align:start position:0% +doing the incentives + + + align:start position:0% +doing the incentives +so that's also why it's important + + align:start position:0% +so that's also why it's important + + + align:start position:0% +so that's also why it's important +important to have that + + align:start position:0% +important to have that + + + align:start position:0% +important to have that +to have that analysis because the policy + + align:start position:0% +to have that analysis because the policy + + + align:start position:0% +to have that analysis because the policy +message becomes a little bit more + + align:start position:0% +message becomes a little bit more + + + align:start position:0% +message becomes a little bit more +centered it's a you don't want to do it + + align:start position:0% +centered it's a you don't want to do it + + + align:start position:0% +centered it's a you don't want to do it +where it's going to backfire but be in + + align:start position:0% +where it's going to backfire but be in + + + align:start position:0% +where it's going to backfire but be in +places where it actually works you know + + align:start position:0% +places where it actually works you know + + + align:start position:0% +places where it actually works you know +you might as well do it + + align:start position:0% +you might as well do it + + + align:start position:0% +you might as well do it +it's not it's not even going to consume + + align:start position:0% +it's not it's not even going to consume + + + align:start position:0% +it's not it's not even going to consume +operation + + align:start position:0% +operation + + + align:start position:0% +operation +but I I I totally take you to point that + + align:start position:0% +but I I I totally take you to point that + + + align:start position:0% +but I I I totally take you to point that +my empirical observation is that that's + + align:start position:0% +my empirical observation is that that's + + + align:start position:0% +my empirical observation is that that's +a message that's harder to convey than + + align:start position:0% +a message that's harder to convey than + + + align:start position:0% +a message that's harder to convey than +the simple message this is what you can + + align:start position:0% +the simple message this is what you can + + + align:start position:0% +the simple message this is what you can +do everywhere and this is cheap to do + + align:start position:0% +do everywhere and this is cheap to do + + + align:start position:0% +do everywhere and this is cheap to do +and go for it + + align:start position:0% + + + + align:start position:0% + +so all of that means that so first of + + align:start position:0% +so all of that means that so first of + + + align:start position:0% +so all of that means that so first of +all there is lots with unstainfully you + + align:start position:0% +all there is lots with unstainfully you + + + align:start position:0% +all there is lots with unstainfully you +understand what the meant for health but + + align:start position:0% +understand what the meant for health but + + + align:start position:0% +understand what the meant for health but +uh it's very a great + + align:start position:0% +uh it's very a great + + + align:start position:0% +uh it's very a great +set of topics many of them still open + + align:start position:0% +set of topics many of them still open + + + align:start position:0% +set of topics many of them still open +and then it makes for a pretty + + align:start position:0% +and then it makes for a pretty + + + align:start position:0% +and then it makes for a pretty +complicated supply of response in an + + align:start position:0% +complicated supply of response in an + + + align:start position:0% +complicated supply of response in an +environment where the demand is + + align:start position:0% +environment where the demand is + + + align:start position:0% +environment where the demand is +complicated is + + align:start position:0% +complicated is + + + align:start position:0% +complicated is +as all of these things going on the + + align:start position:0% +as all of these things going on the + + + align:start position:0% +as all of these things going on the +trust the public discounting the + + align:start position:0% +trust the public discounting the + + + align:start position:0% +trust the public discounting the +misinformation + + align:start position:0% +misinformation + + + align:start position:0% +misinformation +Etc you might expect that where the + + align:start position:0% +Etc you might expect that where the + + + align:start position:0% +Etc you might expect that where the +supply is going to be hard to to + + align:start position:0% +supply is going to be hard to to + + + align:start position:0% +supply is going to be hard to to +discipline + + align:start position:0% +discipline + + + align:start position:0% +discipline +so we don't really have time to cover + + align:start position:0% +so we don't really have time to cover + + + align:start position:0% +so we don't really have time to cover +all of the supply today + + align:start position:0% +all of the supply today + + + align:start position:0% +all of the supply today +but I can just start a little bit and + + align:start position:0% +but I can just start a little bit and + + + align:start position:0% +but I can just start a little bit and +then continue I do want to teach about + + align:start position:0% +then continue I do want to teach about + + + align:start position:0% +then continue I do want to teach about +healthcare supplies so I'm going to + + align:start position:0% +healthcare supplies so I'm going to + + + align:start position:0% +healthcare supplies so I'm going to +continue continue later + + align:start position:0% +continue continue later + + + align:start position:0% +continue continue later +but let me start + + align:start position:0% + + + + align:start position:0% + +so the motivation is from our + + align:start position:0% +so the motivation is from our + + + align:start position:0% +so the motivation is from our +uh Healthcare is a Credence good + + align:start position:0% +uh Healthcare is a Credence good + + + align:start position:0% +uh Healthcare is a Credence good +with a lot of asymmetric information to + + align:start position:0% +with a lot of asymmetric information to + + + align:start position:0% +with a lot of asymmetric information to +provide a news moment than the patient + + align:start position:0% +provide a news moment than the patient + + + align:start position:0% +provide a news moment than the patient +for all of the reason we described + + align:start position:0% +for all of the reason we described + + + align:start position:0% +for all of the reason we described +that's clearly two learning is very + + align:start position:0% +that's clearly two learning is very + + + align:start position:0% +that's clearly two learning is very +difficult + + align:start position:0% +difficult + + + align:start position:0% +difficult +and there are a lot of externalities so + + align:start position:0% +and there are a lot of externalities so + + + align:start position:0% +and there are a lot of externalities so +even if you knew everything you should + + align:start position:0% +even if you knew everything you should + + + align:start position:0% +even if you knew everything you should +you will have fairly low demand for some + + align:start position:0% +you will have fairly low demand for some + + + align:start position:0% +you will have fairly low demand for some +Goods like prevention and they went too + + align:start position:0% +Goods like prevention and they went too + + + align:start position:0% +Goods like prevention and they went too +high for some other Goods like + + align:start position:0% +high for some other Goods like + + + align:start position:0% +high for some other Goods like +antibiotic even if you understand + + align:start position:0% +antibiotic even if you understand + + + align:start position:0% +antibiotic even if you understand +everything + + align:start position:0% +everything + + + align:start position:0% +everything +just because the antibiotic is going to + + align:start position:0% +just because the antibiotic is going to + + + align:start position:0% +just because the antibiotic is going to +help you now whereas the immunization is + + align:start position:0% +help you now whereas the immunization is + + + align:start position:0% +help you now whereas the immunization is +going to help all sorts of other people + + align:start position:0% +going to help all sorts of other people + + + align:start position:0% +going to help all sorts of other people +so you cannot rely on the individuals to + + align:start position:0% +so you cannot rely on the individuals to + + + align:start position:0% +so you cannot rely on the individuals to +follow the right to to choose the right + + align:start position:0% +follow the right to to choose the right + + + align:start position:0% +follow the right to to choose the right +outcome + + align:start position:0% +outcome + + + align:start position:0% +outcome +for all of these reasons unregulated + + align:start position:0% +for all of these reasons unregulated + + + align:start position:0% +for all of these reasons unregulated +Private health care will tend to treat + + align:start position:0% +Private health care will tend to treat + + + align:start position:0% +Private health care will tend to treat +badly and to over provide some + + align:start position:0% +badly and to over provide some + + + align:start position:0% +badly and to over provide some +medication and to under provide some + + align:start position:0% +medication and to under provide some + + + align:start position:0% +medication and to under provide some +medication + + align:start position:0% +medication + + + align:start position:0% +medication +hence Arrow Arrow's conclusion is not + + align:start position:0% +hence Arrow Arrow's conclusion is not + + + align:start position:0% +hence Arrow Arrow's conclusion is not +talking about India is talking about the + + align:start position:0% +talking about India is talking about the + + + align:start position:0% +talking about India is talking about the +us but that applies to India it is the + + align:start position:0% +us but that applies to India it is the + + + align:start position:0% +us but that applies to India it is the +General Social consensus clearly not the + + align:start position:0% +General Social consensus clearly not the + + + align:start position:0% +General Social consensus clearly not the +Lesser Fair solution for medicine is + + align:start position:0% +Lesser Fair solution for medicine is + + + align:start position:0% +Lesser Fair solution for medicine is +intolerable + + align:start position:0% +intolerable + + + align:start position:0% +intolerable +we agree + + align:start position:0% + + + + align:start position:0% + +except that + + align:start position:0% +except that + + + align:start position:0% +except that +uh + + align:start position:0% + + + + align:start position:0% + +and I'm going to skip that + + align:start position:0% + + + + align:start position:0% + +well maybe not uh + + align:start position:0% +well maybe not uh + + + align:start position:0% +well maybe not uh +so + + align:start position:0% + + + + align:start position:0% + +indeed learning about the quality of + + align:start position:0% +indeed learning about the quality of + + + align:start position:0% +indeed learning about the quality of +healthcare you receive is very difficult + + align:start position:0% +healthcare you receive is very difficult + + + align:start position:0% +healthcare you receive is very difficult +both because of what we discussed of + + align:start position:0% +both because of what we discussed of + + + align:start position:0% +both because of what we discussed of +self-limiting diseases + + align:start position:0% +self-limiting diseases + + + align:start position:0% +self-limiting diseases +uh and because of externalities + + align:start position:0% +uh and because of externalities + + + align:start position:0% +uh and because of externalities +as a result people have a very poor + + align:start position:0% +as a result people have a very poor + + + align:start position:0% +as a result people have a very poor +understanding of the health and they are + + align:start position:0% +understanding of the health and they are + + + align:start position:0% +understanding of the health and they are +very poor understanding of whether they + + align:start position:0% +very poor understanding of whether they + + + align:start position:0% +very poor understanding of whether they +are getting good health care so we + + align:start position:0% +are getting good health care so we + + + align:start position:0% +are getting good health care so we +discuss self-limited diseases already + + align:start position:0% +discuss self-limited diseases already + + + align:start position:0% +discuss self-limited diseases already +and that leads potentially to overuse of + + align:start position:0% +and that leads potentially to overuse of + + + align:start position:0% +and that leads potentially to overuse of +antibiotic or invermectin for covert + + align:start position:0% +antibiotic or invermectin for covert + + + align:start position:0% +antibiotic or invermectin for covert +because you think that they have been + + align:start position:0% +because you think that they have been + + + align:start position:0% +because you think that they have been +effective when in fact it's just that + + align:start position:0% +effective when in fact it's just that + + + align:start position:0% +effective when in fact it's just that +the disease became little the other + + align:start position:0% +the disease became little the other + + + align:start position:0% +the disease became little the other +problem is is externalities that when + + align:start position:0% +problem is is externalities that when + + + align:start position:0% +problem is is externalities that when +you get when a lot of people get + + align:start position:0% +you get when a lot of people get + + + align:start position:0% +you get when a lot of people get +immunized or get dewormed nobody gets + + align:start position:0% +immunized or get dewormed nobody gets + + + align:start position:0% +immunized or get dewormed nobody gets +sick and you don't get less sick because + + align:start position:0% +sick and you don't get less sick because + + + align:start position:0% +sick and you don't get less sick because +you got the ammunition of the deworming + + align:start position:0% +you got the ammunition of the deworming + + + align:start position:0% +you got the ammunition of the deworming +the result is that there is a lot of + + align:start position:0% +the result is that there is a lot of + + + align:start position:0% +the result is that there is a lot of +it's very easy for a provider to take + + align:start position:0% +it's very easy for a provider to take + + + align:start position:0% +it's very easy for a provider to take +advantage of the situation to give very + + align:start position:0% +advantage of the situation to give very + + + align:start position:0% +advantage of the situation to give very +very bad care and in particular to give + + align:start position:0% +very bad care and in particular to give + + + align:start position:0% +very bad care and in particular to give +very very bad medicines + + align:start position:0% +very very bad medicines + + + align:start position:0% +very very bad medicines +uh in an environment where many people + + align:start position:0% +uh in an environment where many people + + + align:start position:0% +uh in an environment where many people +take malaria treatment even when they + + align:start position:0% +take malaria treatment even when they + + + align:start position:0% +take malaria treatment even when they +don't have malaria and people are very + + align:start position:0% +don't have malaria and people are very + + + align:start position:0% +don't have malaria and people are very +naive about the model there is very + + align:start position:0% +naive about the model there is very + + + align:start position:0% +naive about the model there is very +strong incentive to sell fake treatment + + align:start position:0% +strong incentive to sell fake treatment + + + align:start position:0% +strong incentive to sell fake treatment +because usually you can get away with it + + align:start position:0% +because usually you can get away with it + + + align:start position:0% +because usually you can get away with it +uh so to investigate that bjorkman + + align:start position:0% +uh so to investigate that bjorkman + + + align:start position:0% +uh so to investigate that bjorkman +Svenson and janakisawa + + align:start position:0% +Svenson and janakisawa + + + align:start position:0% +Svenson and janakisawa +uh send mystery shopper to buy uh anti + + align:start position:0% +uh send mystery shopper to buy uh anti + + + align:start position:0% +uh send mystery shopper to buy uh anti +Malaya drug the new one acting + + align:start position:0% +Malaya drug the new one acting + + + align:start position:0% +Malaya drug the new one acting +commission therapy + + align:start position:0% +commission therapy + + + align:start position:0% +commission therapy +at 99 Market in Uganda and then test + + align:start position:0% +at 99 Market in Uganda and then test + + + align:start position:0% +at 99 Market in Uganda and then test +them in the lab + + align:start position:0% +them in the lab + + + align:start position:0% +them in the lab +and what they find is that 37 of the + + align:start position:0% +and what they find is that 37 of the + + + align:start position:0% +and what they find is that 37 of the +shop sells some counterfeits + + align:start position:0% +shop sells some counterfeits + + + align:start position:0% +shop sells some counterfeits +that the price is unrelated with whether + + align:start position:0% +that the price is unrelated with whether + + + align:start position:0% +that the price is unrelated with whether +it's counterfeits or not + + align:start position:0% +it's counterfeits or not + + + align:start position:0% +it's counterfeits or not +and that the share the production of + + align:start position:0% +and that the share the production of + + + align:start position:0% +and that the share the production of +counterfeits is increasing in the share + + align:start position:0% +counterfeits is increasing in the share + + + align:start position:0% +counterfeits is increasing in the share +of naive consumers so people who + + align:start position:0% +of naive consumers so people who + + + align:start position:0% +of naive consumers so people who +misunderstand malaria so they ask people + + align:start position:0% +misunderstand malaria so they ask people + + + align:start position:0% +misunderstand malaria so they ask people +questions about whether what you think + + align:start position:0% +questions about whether what you think + + + align:start position:0% +questions about whether what you think +causes malaria so some people think that + + align:start position:0% +causes malaria so some people think that + + + align:start position:0% +causes malaria so some people think that +rain causes malaria + + align:start position:0% +rain causes malaria + + + align:start position:0% +rain causes malaria +and some people know that it's + + align:start position:0% +and some people know that it's + + + align:start position:0% +and some people know that it's +mosquitoes uh and that they're more + + align:start position:0% +mosquitoes uh and that they're more + + + align:start position:0% +mosquitoes uh and that they're more +mosquito when it rains and the more of + + align:start position:0% +mosquito when it rains and the more of + + + align:start position:0% +mosquito when it rains and the more of +these naive households you have + + align:start position:0% +these naive households you have + + + align:start position:0% +these naive households you have +the more counterfeit there is uh people + + align:start position:0% +the more counterfeit there is uh people + + + align:start position:0% +the more counterfeit there is uh people +are more likely to to uh to have people + + align:start position:0% +are more likely to to uh to have people + + + align:start position:0% +are more likely to to uh to have people +are + + align:start position:0% +are + + + align:start position:0% +are +um so the more this is here the more + + align:start position:0% +um so the more this is here the more + + + align:start position:0% +um so the more this is here the more +naive people you have the more uh the + + align:start position:0% +naive people you have the more uh the + + + align:start position:0% +naive people you have the more uh the +more likely it is that please sell + + align:start position:0% +more likely it is that please sell + + + align:start position:0% +more likely it is that please sell +counterfeits malaria + + align:start position:0% +counterfeits malaria + + + align:start position:0% +counterfeits malaria +and that's related to the fact that the + + align:start position:0% +and that's related to the fact that the + + + align:start position:0% +and that's related to the fact that the +more native people are the more people + + align:start position:0% +more native people are the more people + + + align:start position:0% +more native people are the more people +are convinced that the drug they get is + + align:start position:0% +are convinced that the drug they get is + + + align:start position:0% +are convinced that the drug they get is +good + + align:start position:0% +good + + + align:start position:0% +good +perhaps because they tried it and it + + align:start position:0% +perhaps because they tried it and it + + + align:start position:0% +perhaps because they tried it and it +worked as far as they're concerned + + align:start position:0% +worked as far as they're concerned + + + align:start position:0% +worked as far as they're concerned +so what they do in this paper + + align:start position:0% +so what they do in this paper + + + align:start position:0% +so what they do in this paper +is that they ask themselves whether a + + align:start position:0% +is that they ask themselves whether a + + + align:start position:0% +is that they ask themselves whether a +good quality can drive bad ones so they + + align:start position:0% +good quality can drive bad ones so they + + + align:start position:0% +good quality can drive bad ones so they +work with black the same + + align:start position:0% +work with black the same + + + align:start position:0% +work with black the same +of alcapore Fame and otherwise uh + + align:start position:0% +of alcapore Fame and otherwise uh + + + align:start position:0% +of alcapore Fame and otherwise uh +extremely reputable and competent + + align:start position:0% +extremely reputable and competent + + + align:start position:0% +extremely reputable and competent +organization + + align:start position:0% +organization + + + align:start position:0% +organization +who now doesn't work just in Bangladesh + + align:start position:0% +who now doesn't work just in Bangladesh + + + align:start position:0% +who now doesn't work just in Bangladesh +but also in Uganda and other East + + align:start position:0% +but also in Uganda and other East + + + align:start position:0% +but also in Uganda and other East +African countries + + align:start position:0% +African countries + + + align:start position:0% +African countries +and the black sets up pharmacies which + + align:start position:0% +and the black sets up pharmacies which + + + align:start position:0% +and the black sets up pharmacies which +sells bonded malaria Medicine of good + + align:start position:0% +sells bonded malaria Medicine of good + + + align:start position:0% +sells bonded malaria Medicine of good +quality and their question is is it + + align:start position:0% +quality and their question is is it + + + align:start position:0% +quality and their question is is it +going to lead the other people to + + align:start position:0% +going to lead the other people to + + + align:start position:0% +going to lead the other people to +disappear + + align:start position:0% +disappear + + + align:start position:0% +disappear +and the question the answer is in two uh + + align:start position:0% +and the question the answer is in two uh + + + align:start position:0% +and the question the answer is in two uh +is in two steps + + align:start position:0% +is in two steps + + + align:start position:0% +is in two steps +on average the quality in the shop + + align:start position:0% +on average the quality in the shop + + + align:start position:0% +on average the quality in the shop +increases and the price of the Malaya + + align:start position:0% +increases and the price of the Malaya + + + align:start position:0% +increases and the price of the Malaya +medicine decreases so on average the + + align:start position:0% +medicine decreases so on average the + + + align:start position:0% +medicine decreases so on average the +competition effect in fact works out if + + align:start position:0% +competition effect in fact works out if + + + align:start position:0% +competition effect in fact works out if +you introduce this bonded product people + + align:start position:0% +you introduce this bonded product people + + + align:start position:0% +you introduce this bonded product people +will flock to that and then put pressure + + align:start position:0% +will flock to that and then put pressure + + + align:start position:0% +will flock to that and then put pressure +on the other guys and they will tend to + + align:start position:0% +on the other guys and they will tend to + + + align:start position:0% +on the other guys and they will tend to +either go for good medicine or and + + align:start position:0% +either go for good medicine or and + + + align:start position:0% +either go for good medicine or and +reduce the prices + + align:start position:0% +reduce the prices + + + align:start position:0% +reduce the prices +however this works less in villages + + align:start position:0% +however this works less in villages + + + align:start position:0% +however this works less in villages +where there are more naive customers so + + align:start position:0% +where there are more naive customers so + + + align:start position:0% +where there are more naive customers so +when you interact + + align:start position:0% +when you interact + + + align:start position:0% +when you interact +to use this table + + align:start position:0% +to use this table + + + align:start position:0% +to use this table +when you interact at the fraction the + + align:start position:0% +when you interact at the fraction the + + + align:start position:0% +when you interact at the fraction the +the NGO cells drug on average there is + + align:start position:0% +the NGO cells drug on average there is + + + align:start position:0% +the NGO cells drug on average there is +less likely to be a + + align:start position:0% +less likely to be a + + + align:start position:0% +less likely to be a +to be fake drug in the village + + align:start position:0% +to be fake drug in the village + + + align:start position:0% +to be fake drug in the village +if there are more native people as we + + align:start position:0% +if there are more native people as we + + + align:start position:0% +if there are more native people as we +saw before + + align:start position:0% +saw before + + + align:start position:0% +saw before +that's this one there are more fake + + align:start position:0% +that's this one there are more fake + + + align:start position:0% +that's this one there are more fake +drugs and then if there is more naive + + align:start position:0% +drugs and then if there is more naive + + + align:start position:0% +drugs and then if there is more naive +people in the village the treatment + + align:start position:0% +people in the village the treatment + + + align:start position:0% +people in the village the treatment +effect is less strong + + align:start position:0% +effect is less strong + + + align:start position:0% +effect is less strong +so the uh even + + align:start position:0% +so the uh even + + + align:start position:0% +so the uh even +so number one when you have more naive + + align:start position:0% +so number one when you have more naive + + + align:start position:0% +so number one when you have more naive +people in the village who don't + + align:start position:0% +people in the village who don't + + + align:start position:0% +people in the village who don't +understand the model you have more fake + + align:start position:0% +understand the model you have more fake + + + align:start position:0% +understand the model you have more fake +drugs number two it makes it difficult + + align:start position:0% +drugs number two it makes it difficult + + + align:start position:0% +drugs number two it makes it difficult +to a more difficult to address it by + + align:start position:0% +to a more difficult to address it by + + + align:start position:0% +to a more difficult to address it by +putting good drugs + + align:start position:0% +putting good drugs + + + align:start position:0% +putting good drugs +so that's just to say that uh sort of uh + + align:start position:0% +so that's just to say that uh sort of uh + + + align:start position:0% +so that's just to say that uh sort of uh +to to uh + + align:start position:0% +to to uh + + + align:start position:0% +to to uh +Comfort the the point that Arrow made + + align:start position:0% +Comfort the the point that Arrow made + + + align:start position:0% +Comfort the the point that Arrow made +um + + align:start position:0% +um + + + align:start position:0% +um +it's hard to learn about health + + align:start position:0% +it's hard to learn about health + + + align:start position:0% +it's hard to learn about health +and providers take advantage of it + + align:start position:0% +and providers take advantage of it + + + align:start position:0% +and providers take advantage of it +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +the Private health care sector in two + + align:start position:0% +the Private health care sector in two + + + align:start position:0% +the Private health care sector in two +countries is really awful and I'll tell + + align:start position:0% +countries is really awful and I'll tell + + + align:start position:0% +countries is really awful and I'll tell +you a bit more about our authorities uh + + align:start position:0% +you a bit more about our authorities uh + + + align:start position:0% +you a bit more about our authorities uh +next + + align:start position:0% + + + + align:start position:0% + +so we'll stop here + + align:start position:0% +so we'll stop here + + + align:start position:0% +so we'll stop here +um I think we'll have time to to finish + + align:start position:0% +um I think we'll have time to to finish + + + align:start position:0% +um I think we'll have time to to finish +that in a in about a half lecture which + + align:start position:0% +that in a in about a half lecture which + + + align:start position:0% +that in a in about a half lecture which +still will give us a half one and a half + + align:start position:0% +still will give us a half one and a half + + + align:start position:0% +still will give us a half one and a half +lecture on gender so that will be fine + + align:start position:0% +lecture on gender so that will be fine + + + align:start position:0% +lecture on gender so that will be fine +but on Monday Ben is teaching + + align:start position:0% +but on Monday Ben is teaching + + + align:start position:0% +but on Monday Ben is teaching +So you you're gonna leave that in the + + align:start position:0% +So you you're gonna leave that in the + + + align:start position:0% +So you you're gonna leave that in the +fridge for a minute for for one lecture + + align:start position:0% +fridge for a minute for for one lecture + + + align:start position:0% +fridge for a minute for for one lecture +and we'll go back together \ No newline at end of file diff --git a/75Q0ZN2njGQ.txt b/75Q0ZN2njGQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..e4875c5c5ac92ee935a29f3f9f6f3ed3ca10c3dc --- /dev/null +++ b/75Q0ZN2njGQ.txt @@ -0,0 +1,1193 @@ +align:start position:0% + +hi welcome today's problem is about + + align:start position:0% +hi welcome today's problem is about + + + align:start position:0% +hi welcome today's problem is about +finding Solutions of this + + align:start position:0% +finding Solutions of this + + + align:start position:0% +finding Solutions of this +non-homogeneous linear system x - 2 y - + + align:start position:0% +non-homogeneous linear system x - 2 y - + + + align:start position:0% +non-homogeneous linear system x - 2 y - +2 Z = B1 2x - 5 y - 4 Z = B2 and 4x - 9 + + align:start position:0% +2 Z = B1 2x - 5 y - 4 Z = B2 and 4x - 9 + + + align:start position:0% +2 Z = B1 2x - 5 y - 4 Z = B2 and 4x - 9 +y - 8 zal B3 and as you can see the + + align:start position:0% +y - 8 zal B3 and as you can see the + + + align:start position:0% +y - 8 zal B3 and as you can see the +system doesn't only have numbers and + + align:start position:0% +system doesn't only have numbers and + + + align:start position:0% +system doesn't only have numbers and +unknowns it also has parameters B1 B2 + + align:start position:0% +unknowns it also has parameters B1 B2 + + + align:start position:0% +unknowns it also has parameters B1 B2 +and B3 and the solution will depend on + + align:start position:0% +and B3 and the solution will depend on + + + align:start position:0% +and B3 and the solution will depend on +these parameters but also the existence + + align:start position:0% +these parameters but also the existence + + + align:start position:0% +these parameters but also the existence +of the solution will depend on these + + align:start position:0% +of the solution will depend on these + + + align:start position:0% +of the solution will depend on these +parameters and we're asked to find the + + align:start position:0% +parameters and we're asked to find the + + + align:start position:0% +parameters and we're asked to find the +solution and find when it exists + + align:start position:0% +solution and find when it exists + + + align:start position:0% +solution and find when it exists +depending on the values of B1 B2 and B3 + + align:start position:0% +depending on the values of B1 B2 and B3 + + + align:start position:0% +depending on the values of B1 B2 and B3 +so now you should pause the video solve + + align:start position:0% +so now you should pause the video solve + + + align:start position:0% +so now you should pause the video solve +the problem and come back and compare + + align:start position:0% +the problem and come back and compare + + + align:start position:0% +the problem and come back and compare +Your solution with + + align:start position:0% + + + + align:start position:0% + +mine and we're back let's try let's + + align:start position:0% +mine and we're back let's try let's + + + align:start position:0% +mine and we're back let's try let's +start by solving this system as if + + align:start position:0% +start by solving this system as if + + + align:start position:0% +start by solving this system as if +though B1 B2 and B3 were numbers + + align:start position:0% + + + + align:start position:0% + +so we write the Matrix of the system + + align:start position:0% +so we write the Matrix of the system + + + align:start position:0% +so we write the Matrix of the system +which is 1 - 2 - + + align:start position:0% +which is 1 - 2 - + + + align:start position:0% +which is 1 - 2 - + + align:start position:0% + + + align:start position:0% +B1 sorry + + align:start position:0% +B1 sorry + + + align:start position:0% +B1 sorry +again 2 - 5 - 4 + + align:start position:0% +again 2 - 5 - 4 + + + align:start position:0% +again 2 - 5 - 4 +B2 and 4 - 9 minus + + align:start position:0% +B2 and 4 - 9 minus + + + align:start position:0% +B2 and 4 - 9 minus + + align:start position:0% + + + align:start position:0% +B3 and we do + + align:start position:0% +B3 and we do + + + align:start position:0% +B3 and we do +elimination so we multip multiply the + + align:start position:0% +elimination so we multip multiply the + + + align:start position:0% +elimination so we multip multiply the +first row by minus two and add it to the + + align:start position:0% +first row by minus two and add it to the + + + align:start position:0% +first row by minus two and add it to the +second + + align:start position:0% +second + + + align:start position:0% +second +row and we multiplied by minus 4 and add + + align:start position:0% +row and we multiplied by minus 4 and add + + + align:start position:0% +row and we multiplied by minus 4 and add +it to the four to the third + + align:start position:0% +it to the four to the third + + + align:start position:0% +it to the four to the third +row and we get 1 - 2 minus + + align:start position:0% +row and we get 1 - 2 minus + + + align:start position:0% +row and we get 1 - 2 minus + + align:start position:0% + + + align:start position:0% +B1 zero + + align:start position:0% + + + + align:start position:0% + +um 4 - 5 is + + align:start position:0% +um 4 - 5 is + + + align:start position:0% +um 4 - 5 is +-1 4 - 4 is0 and - 2 * B1 + + + align:start position:0% + + + + align:start position:0% + +B2 and here we get + + align:start position:0% +B2 and here we get + + + align:start position:0% +B2 and here we get +0 8 - 9 is + + align:start position:0% +0 8 - 9 is + + + align:start position:0% +0 8 - 9 is +-1 and 8 - 8 is zero finally on the + + align:start position:0% +-1 and 8 - 8 is zero finally on the + + + align:start position:0% +-1 and 8 - 8 is zero finally on the +right hand side Min - 4 B1 + + align:start position:0% +right hand side Min - 4 B1 + + + align:start position:0% +right hand side Min - 4 B1 +plus + + align:start position:0% + + + + align:start position:0% + +B3 and you can already see that + + align:start position:0% +B3 and you can already see that + + + align:start position:0% +B3 and you can already see that +something's going to happen here but + + align:start position:0% +something's going to happen here but + + + align:start position:0% +something's going to happen here but +let's do one more + + align:start position:0% +let's do one more + + + align:start position:0% +let's do one more +step + + align:start position:0% +step + + + align:start position:0% +step +so eliminating further we get one - 2 - + + align:start position:0% +so eliminating further we get one - 2 - + + + align:start position:0% +so eliminating further we get one - 2 - + + align:start position:0% + + + align:start position:0% +B1 0 -1 0 - 2 B1 + + + align:start position:0% +B1 0 -1 0 - 2 B1 + + + + align:start position:0% +B1 0 -1 0 - 2 B1 + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +B2 and in the last row we replace it + + align:start position:0% +B2 and in the last row we replace it + + + align:start position:0% +B2 and in the last row we replace it +with the last row minus the second row + + align:start position:0% +with the last row minus the second row + + + align:start position:0% +with the last row minus the second row +and we get 0 0 0 minus 4 + + align:start position:0% +and we get 0 0 0 minus 4 + + + align:start position:0% +and we get 0 0 0 minus 4 +B1 + 2 or so minus minus 2 B2 is um Min + + align:start position:0% +B1 + 2 or so minus minus 2 B2 is um Min + + + align:start position:0% +B1 + 2 or so minus minus 2 B2 is um Min +- 2 + + align:start position:0% +- 2 + + + align:start position:0% +- 2 +B1 minus B2 and plus B3 + + align:start position:0% +B1 minus B2 and plus B3 + + + align:start position:0% +B1 minus B2 and plus B3 +I hope I did this + + align:start position:0% +I hope I did this + + + align:start position:0% +I hope I did this +right okay so now let's think of it as a + + align:start position:0% +right okay so now let's think of it as a + + + align:start position:0% +right okay so now let's think of it as a +system again the last equation says + + align:start position:0% +system again the last equation says + + + align:start position:0% +system again the last equation says +zero equals this expression in B1 B2 and + + align:start position:0% +zero equals this expression in B1 B2 and + + + align:start position:0% +zero equals this expression in B1 B2 and +B3 so this is something this is + + align:start position:0% +B3 so this is something this is + + + align:start position:0% +B3 so this is something this is +something to note down if - 2 B1 minus + + align:start position:0% +something to note down if - 2 B1 minus + + + align:start position:0% +something to note down if - 2 B1 minus +B2 + + + align:start position:0% +B2 + + + + align:start position:0% +B2 + +B3 is some number that's not zero then + + align:start position:0% +B3 is some number that's not zero then + + + align:start position:0% +B3 is some number that's not zero then +the last equation is going to say 0 + + align:start position:0% +the last equation is going to say 0 + + + align:start position:0% +the last equation is going to say 0 +equals non Zer it's never going to be + + align:start position:0% +equals non Zer it's never going to be + + + align:start position:0% +equals non Zer it's never going to be +satisfied and the entire system is never + + align:start position:0% +satisfied and the entire system is never + + + align:start position:0% +satisfied and the entire system is never +going to have a solution so in this + + align:start position:0% + + + + align:start position:0% + +case we have no + + align:start position:0% + + + + align:start position:0% + +Solutions if this is equal to Z so - 2 + + align:start position:0% +Solutions if this is equal to Z so - 2 + + + align:start position:0% +Solutions if this is equal to Z so - 2 +B1 - B2 + V3 is equal to zero then let's + + align:start position:0% +B1 - B2 + V3 is equal to zero then let's + + + align:start position:0% +B1 - B2 + V3 is equal to zero then let's +do one more step in this uh on this + + align:start position:0% +do one more step in this uh on this + + + align:start position:0% +do one more step in this uh on this +Matrix here let's turn this number into + + align:start position:0% +Matrix here let's turn this number into + + + align:start position:0% +Matrix here let's turn this number into +one by multiplying this row by negative + + align:start position:0% +one by multiplying this row by negative + + + align:start position:0% +one by multiplying this row by negative +1 and let's use it to eliminate this + + align:start position:0% +1 and let's use it to eliminate this + + + align:start position:0% +1 and let's use it to eliminate this +number here as + + align:start position:0% +number here as + + + align:start position:0% +number here as +well so in this case we + + align:start position:0% +well so in this case we + + + align:start position:0% +well so in this case we +get let me write it from the last row + + align:start position:0% +get let me write it from the last row + + + align:start position:0% +get let me write it from the last row +which now becomes 0 0 0 equals 0 which + + align:start position:0% +which now becomes 0 0 0 equals 0 which + + + align:start position:0% +which now becomes 0 0 0 equals 0 which +is fine the second row becomes 0 1 0 2 + + align:start position:0% +is fine the second row becomes 0 1 0 2 + + + align:start position:0% +is fine the second row becomes 0 1 0 2 +B1 minus + + align:start position:0% +B1 minus + + + align:start position:0% +B1 minus +B2 and the first one to get rid of this + + align:start position:0% +B2 and the first one to get rid of this + + + align:start position:0% +B2 and the first one to get rid of this +minus two we multiply this row by -2 and + + align:start position:0% +minus two we multiply this row by -2 and + + + align:start position:0% +minus two we multiply this row by -2 and +add it to the to the first one we get 1 + + align:start position:0% +add it to the to the first one we get 1 + + + align:start position:0% +add it to the to the first one we get 1 + + align:start position:0% + + + align:start position:0% +-2 and here we get U B1 + 4 B1 which is + + align:start position:0% +-2 and here we get U B1 + 4 B1 which is + + + align:start position:0% +-2 and here we get U B1 + 4 B1 which is +5 B1 + + align:start position:0% +5 B1 + + + align:start position:0% +5 B1 +minus + + align:start position:0% +minus + + + align:start position:0% +minus + + align:start position:0% + + + align:start position:0% +B2 the reason why we did this was to get + + align:start position:0% +B2 the reason why we did this was to get + + + align:start position:0% +B2 the reason why we did this was to get +the identity Matrix here and now let's + + align:start position:0% +the identity Matrix here and now let's + + + align:start position:0% +the identity Matrix here and now let's +solve this these two columns + + align:start position:0% +solve this these two columns + + + align:start position:0% +solve this these two columns +corresponding to variables X and Y um + + align:start position:0% +corresponding to variables X and Y um + + + align:start position:0% +corresponding to variables X and Y um +have pivots in them so these are the + + align:start position:0% +have pivots in them so these are the + + + align:start position:0% +have pivots in them so these are the +pivot + + align:start position:0% + + + + align:start position:0% + +variables this column here has no pivot + + align:start position:0% +variables this column here has no pivot + + + align:start position:0% +variables this column here has no pivot +in it so it's a free + + align:start position:0% + + + + align:start position:0% + +variable and now we're going to + + align:start position:0% +variable and now we're going to + + + align:start position:0% +variable and now we're going to +calculate the solutions but by picking + + align:start position:0% +calculate the solutions but by picking + + + align:start position:0% +calculate the solutions but by picking +particular values for Z and then + + align:start position:0% +particular values for Z and then + + + align:start position:0% +particular values for Z and then +calculating the values for X and + + align:start position:0% +calculating the values for X and + + + align:start position:0% +calculating the values for X and +Y which we have two kinds of solution + + align:start position:0% +Y which we have two kinds of solution + + + align:start position:0% +Y which we have two kinds of solution +one kind is the particular + + align:start position:0% + + + + align:start position:0% + +solution so this one solves ax equals + + align:start position:0% +solution so this one solves ax equals + + + align:start position:0% +solution so this one solves ax equals +B there's only one of them and we get it + + align:start position:0% +B there's only one of them and we get it + + + align:start position:0% +B there's only one of them and we get it +by setting the free + + align:start position:0% +by setting the free + + + align:start position:0% +by setting the free +variable equal to + + align:start position:0% +variable equal to + + + align:start position:0% +variable equal to +zero setting the free variable equal to + + align:start position:0% +zero setting the free variable equal to + + + align:start position:0% +zero setting the free variable equal to +zero we + + align:start position:0% +zero we + + + align:start position:0% +zero we +get + + align:start position:0% +get + + + align:start position:0% +get +well this is equal to zero the second + + align:start position:0% +well this is equal to zero the second + + + align:start position:0% +well this is equal to zero the second +equation says y equals this thing here + + align:start position:0% +equation says y equals this thing here + + + align:start position:0% +equation says y equals this thing here +so 2 B1 minus B2 and the first equation + + align:start position:0% +so 2 B1 minus B2 and the first equation + + + align:start position:0% +so 2 B1 minus B2 and the first equation +says x - 2 * 0 equals this expression + + align:start position:0% +says x - 2 * 0 equals this expression + + + align:start position:0% +says x - 2 * 0 equals this expression +here so 5 B1 minus 2 + + align:start position:0% +here so 5 B1 minus 2 + + + align:start position:0% +here so 5 B1 minus 2 +B2 that's our particular + + align:start position:0% +B2 that's our particular + + + align:start position:0% +B2 that's our particular +solution the next kind is the uh special + + align:start position:0% + + + + align:start position:0% + +solution so remember those solve ax + + align:start position:0% +solution so remember those solve ax + + + align:start position:0% +solution so remember those solve ax +equal + + align:start position:0% +equal + + + align:start position:0% +equal +Z there's as many of them as free as + + align:start position:0% +Z there's as many of them as free as + + + align:start position:0% +Z there's as many of them as free as +there are three variables in our case + + align:start position:0% +there are three variables in our case + + + align:start position:0% +there are three variables in our case +there's only + + align:start position:0% +there's only + + + align:start position:0% +there's only +one and we get it by setting all three + + align:start position:0% +one and we get it by setting all three + + + align:start position:0% +one and we get it by setting all three +variables equal to zero except one equal + + align:start position:0% +variables equal to zero except one equal + + + align:start position:0% +variables equal to zero except one equal +to one and do it for every free variable + + align:start position:0% +to one and do it for every free variable + + + align:start position:0% +to one and do it for every free variable +so in our case there's only one free + + align:start position:0% +so in our case there's only one free + + + align:start position:0% +so in our case there's only one free +variable and we set Z equal to + + align:start position:0% +variable and we set Z equal to + + + align:start position:0% +variable and we set Z equal to +1 the + + align:start position:0% +1 the + + + align:start position:0% +1 the +solution that we get in this case and + + align:start position:0% +solution that we get in this case and + + + align:start position:0% +solution that we get in this case and +remember we're solving ax equals z we + + align:start position:0% +remember we're solving ax equals z we + + + align:start position:0% +remember we're solving ax equals z we +don't care about the right hand side + + align:start position:0% +don't care about the right hand side + + + align:start position:0% +don't care about the right hand side +anymore so Z is one this second equation + + align:start position:0% +anymore so Z is one this second equation + + + align:start position:0% +anymore so Z is one this second equation +says y equal + + align:start position:0% +says y equal + + + align:start position:0% +says y equal +0 and the first equation says x - 2 * 1 + + align:start position:0% +0 and the first equation says x - 2 * 1 + + + align:start position:0% +0 and the first equation says x - 2 * 1 += 0 in other + + align:start position:0% += 0 in other + + + align:start position:0% += 0 in other +words x = two uh x equals 2 so the + + align:start position:0% +words x = two uh x equals 2 so the + + + align:start position:0% +words x = two uh x equals 2 so the +special solution solution is 2 1 and now + + align:start position:0% +special solution solution is 2 1 and now + + + align:start position:0% +special solution solution is 2 1 and now +all + + align:start position:0% + + + + align:start position:0% + +solutions + + align:start position:0% +solutions + + + align:start position:0% +solutions +are of the form X + + align:start position:0% +are of the form X + + + align:start position:0% +are of the form X +equals a particular solution plus any + + align:start position:0% +equals a particular solution plus any + + + align:start position:0% +equals a particular solution plus any +multiple of the special + + align:start position:0% +multiple of the special + + + align:start position:0% +multiple of the special +solution let me recap in case this + + align:start position:0% +solution let me recap in case this + + + align:start position:0% +solution let me recap in case this +particular combination of parameters is + + align:start position:0% +particular combination of parameters is + + + align:start position:0% +particular combination of parameters is +not zero there's no Solutions in case + + align:start position:0% +not zero there's no Solutions in case + + + align:start position:0% +not zero there's no Solutions in case +this particular combination of + + align:start position:0% +this particular combination of + + + align:start position:0% +this particular combination of +parameters is equal to zero there are + + align:start position:0% +parameters is equal to zero there are + + + align:start position:0% +parameters is equal to zero there are +solutions there's as there are as many + + align:start position:0% +solutions there's as there are as many + + + align:start position:0% +solutions there's as there are as many +of them as there are real numbers C and + + align:start position:0% +of them as there are real numbers C and + + + align:start position:0% +of them as there are real numbers C and +they're all of this form for these two + + align:start position:0% +they're all of this form for these two + + + align:start position:0% +they're all of this form for these two +vectors and that's all I wanted to say + + align:start position:0% +vectors and that's all I wanted to say + + + align:start position:0% +vectors and that's all I wanted to say +today \ No newline at end of file diff --git a/7LLUz7A1--Q.txt b/7LLUz7A1--Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..eae36a241760a5d3dd1def19eaa72408a268efb0 --- /dev/null +++ b/7LLUz7A1--Q.txt @@ -0,0 +1,12605 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a creative commons license + + align:start position:0% +a creative commons license + + + align:start position:0% +a creative commons license +your support will help mit + + align:start position:0% +your support will help mit + + + align:start position:0% +your support will help mit +opencourseware continue to offer high + + align:start position:0% +opencourseware continue to offer high + + + align:start position:0% +opencourseware continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of mit courses + + align:start position:0% +materials from hundreds of mit courses + + + align:start position:0% +materials from hundreds of mit courses +visit mit open courseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +uh welcome back + + align:start position:0% +uh welcome back + + + align:start position:0% +uh welcome back +so + + align:start position:0% +so + + + align:start position:0% +so +today we get to + + align:start position:0% + + + + align:start position:0% + +finish our discussion + + align:start position:0% +finish our discussion + + + align:start position:0% +finish our discussion +at least the first wave of value-based + + align:start position:0% +at least the first wave of value-based + + + align:start position:0% +at least the first wave of value-based +methods + + align:start position:0% +methods + + + align:start position:0% +methods +for trying to find optimal control + + align:start position:0% +for trying to find optimal control + + + align:start position:0% +for trying to find optimal control +policies + + align:start position:0% +policies + + + align:start position:0% +policies +without a model + + align:start position:0% +without a model + + + align:start position:0% +without a model +so + + align:start position:0% +so + + + align:start position:0% +so +we started last time + + align:start position:0% +we started last time + + + align:start position:0% +we started last time +talking about these uh + + align:start position:0% +talking about these uh + + + align:start position:0% +talking about these uh +model 3 methods + + align:start position:0% +model 3 methods + + + align:start position:0% +model 3 methods +and + + align:start position:0% +and + + + align:start position:0% +and +just a picture where + + align:start position:0% +just a picture where + + + align:start position:0% +just a picture where +we're all synced up here so + + align:start position:0% +we're all synced up here so + + + align:start position:0% +we're all synced up here so +big picture right + + align:start position:0% +big picture right + + + align:start position:0% +big picture right +is that uh + + align:start position:0% + + + + align:start position:0% + +we're trying to + + align:start position:0% +we're trying to + + + align:start position:0% +we're trying to +learn an optimal policy + + align:start position:0% + + + + align:start position:0% + +approximate policy + + align:start position:0% + + + + align:start position:0% + +without a model + + align:start position:0% + + + + align:start position:0% + +by just learning an approximate value + + align:start position:0% + + + + align:start position:0% + +the claim is + + align:start position:0% +the claim is + + + align:start position:0% +the claim is +that value functions are a good thing to + + align:start position:0% +that value functions are a good thing to + + + align:start position:0% +that value functions are a good thing to +learn + + align:start position:0% +learn + + + align:start position:0% +learn +for a couple reasons + + align:start position:0% +for a couple reasons + + + align:start position:0% +for a couple reasons +first of all they should describe + + align:start position:0% +first of all they should describe + + + align:start position:0% +first of all they should describe +everything + + align:start position:0% +everything + + + align:start position:0% +everything +you need to know + + align:start position:0% +you need to know + + + align:start position:0% +you need to know +about + + align:start position:0% +about + + + align:start position:0% +about +the optimal control + + align:start position:0% +the optimal control + + + align:start position:0% +the optimal control +second of all they're actually + + align:start position:0% +second of all they're actually + + + align:start position:0% +second of all they're actually +they're fairly compact i'm going to say + + align:start position:0% +they're fairly compact i'm going to say + + + align:start position:0% +they're fairly compact i'm going to say +more about that in a minute but if you + + align:start position:0% +more about that in a minute but if you + + + align:start position:0% +more about that in a minute but if you +think about it + + align:start position:0% +think about it + + + align:start position:0% +think about it +probably the value function might + + align:start position:0% +probably the value function might + + + align:start position:0% +probably the value function might +actually be a simpler thing to represent + + align:start position:0% +actually be a simpler thing to represent + + + align:start position:0% +actually be a simpler thing to represent +in the policy + + align:start position:0% +in the policy + + + align:start position:0% +in the policy +a smaller + + align:start position:0% +a smaller + + + align:start position:0% +a smaller +thing because it's just a scalar value + + align:start position:0% +thing because it's just a scalar value + + + align:start position:0% +thing because it's just a scalar value +over all states + + align:start position:0% +over all states + + + align:start position:0% +over all states +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and the um + + align:start position:0% +and the um + + + align:start position:0% +and the um +the third legal innovation i tried to + + align:start position:0% +the third legal innovation i tried to + + + align:start position:0% +the third legal innovation i tried to +get last time was that + + align:start position:0% +get last time was that + + + align:start position:0% +get last time was that +so these temporal difference methods + + align:start position:0% +so these temporal difference methods + + + align:start position:0% +so these temporal difference methods +which bootstrap + + align:start position:0% +which bootstrap + + + align:start position:0% +which bootstrap +based on previous experience + + align:start position:0% +based on previous experience + + + align:start position:0% +based on previous experience +their light value duration and dynamic + + align:start position:0% +their light value duration and dynamic + + + align:start position:0% +their light value duration and dynamic +programming can be very efficient in + + align:start position:0% +programming can be very efficient in + + + align:start position:0% +programming can be very efficient in +terms of reusing + + align:start position:0% +terms of reusing + + + align:start position:0% +terms of reusing +um their computation or reusing the + + align:start position:0% +um their computation or reusing the + + + align:start position:0% +um their computation or reusing the +samples that you've gotten by using + + align:start position:0% +samples that you've gotten by using + + + align:start position:0% +samples that you've gotten by using +estimates that you've already made of + + align:start position:0% +estimates that you've already made of + + + align:start position:0% +estimates that you've already made of +your value function to make better + + align:start position:0% +your value function to make better + + + align:start position:0% +your value function to make better +fast estimates of your value function as + + align:start position:0% +fast estimates of your value function as + + + align:start position:0% +fast estimates of your value function as +you go + + align:start position:0% + + + + align:start position:0% + +these are all going to come up again but + + align:start position:0% +these are all going to come up again but + + + align:start position:0% +these are all going to come up again but +that's just that's the high level of + + align:start position:0% +that's just that's the high level of + + + align:start position:0% +that's just that's the high level of +motivation for why we care about trying + + align:start position:0% +motivation for why we care about trying + + + align:start position:0% +motivation for why we care about trying +to run value functions okay and the + + align:start position:0% +to run value functions okay and the + + + align:start position:0% +to run value functions okay and the +first thing we did was really all we did + + align:start position:0% +first thing we did was really all we did + + + align:start position:0% +first thing we did was really all we did +last time + + align:start position:0% + + + + align:start position:0% + +the first thing we had to + + align:start position:0% +the first thing we had to + + + align:start position:0% +the first thing we had to +achieve + + align:start position:0% +achieve + + + align:start position:0% +achieve +was just + + align:start position:0% +was just + + + align:start position:0% +was just +estimate a value function for a fixed + + align:start position:0% +estimate a value function for a fixed + + + align:start position:0% +estimate a value function for a fixed +policy + + align:start position:0% + + + + align:start position:0% + +we did it just from sample trajectories + + align:start position:0% + + + + align:start position:0% + +in discrete state in action we call them + + align:start position:0% +in discrete state in action we call them + + + align:start position:0% +in discrete state in action we call them +s + + align:start position:0% + + + + align:start position:0% + +take a bunch of + + align:start position:0% +take a bunch of + + + align:start position:0% +take a bunch of +trajectories + + align:start position:0% +trajectories + + + align:start position:0% +trajectories +and you need to be + + align:start position:0% +and you need to be + + + align:start position:0% +and you need to be +able from those trajectories to try to + + align:start position:0% +able from those trajectories to try to + + + align:start position:0% +able from those trajectories to try to +back out + + align:start position:0% + + + + align:start position:0% + +j-pop and those trajectories are + + align:start position:0% +j-pop and those trajectories are + + + align:start position:0% +j-pop and those trajectories are +generated using policy + + align:start position:0% + + + + align:start position:0% + +so i actually tried to argue that that + + align:start position:0% +so i actually tried to argue that that + + + align:start position:0% +so i actually tried to argue that that +was useful even in the so if you just + + align:start position:0% +was useful even in the so if you just + + + align:start position:0% +was useful even in the so if you just +want if you have a robot out there + + align:start position:0% +want if you have a robot out there + + + align:start position:0% +want if you have a robot out there +that's already executing a policy or a + + align:start position:0% +that's already executing a policy or a + + + align:start position:0% +that's already executing a policy or a +passive walker or something like this + + align:start position:0% +passive walker or something like this + + + align:start position:0% +passive walker or something like this +that doesn't have a policy and you just + + align:start position:0% +that doesn't have a policy and you just + + + align:start position:0% +that doesn't have a policy and you just +want to see how well it's doing + + align:start position:0% +want to see how well it's doing + + + align:start position:0% +want to see how well it's doing +estimated stability is one example that + + align:start position:0% +estimated stability is one example that + + + align:start position:0% +estimated stability is one example that +you can actually + + align:start position:0% +you can actually + + + align:start position:0% +you can actually +this might be enough for you it might + + align:start position:0% +this might be enough for you it might + + + align:start position:0% +this might be enough for you it might +just try to evaluate + + align:start position:0% +just try to evaluate + + + align:start position:0% +just try to evaluate +how well that policy is doing + + align:start position:0% +how well that policy is doing + + + align:start position:0% +how well that policy is doing +we call that policy evaluation + + align:start position:0% + + + + align:start position:0% + +what we're actually interested is not + + align:start position:0% +what we're actually interested is not + + + align:start position:0% +what we're actually interested is not +bad right that's just + + align:start position:0% +bad right that's just + + + align:start position:0% +bad right that's just +the first step + + align:start position:0% +the first step + + + align:start position:0% +the first step +what we care about now is given if we + + align:start position:0% +what we care about now is given if we + + + align:start position:0% +what we care about now is given if we +can estimate um + + align:start position:0% +can estimate um + + + align:start position:0% +can estimate um +the value for a + + align:start position:0% +the value for a + + + align:start position:0% +the value for a +stationary policy + + align:start position:0% +stationary policy + + + align:start position:0% +stationary policy +can we now do something smarter + + align:start position:0% +can we now do something smarter + + + align:start position:0% +can we now do something smarter +more involved and try to estimate + + align:start position:0% +more involved and try to estimate + + + align:start position:0% +more involved and try to estimate +well the optimal value function + + align:start position:0% +well the optimal value function + + + align:start position:0% +well the optimal value function +or you might think of it as um + + align:start position:0% +or you might think of it as um + + + align:start position:0% +or you might think of it as um +continuing to to estimate the value + + align:start position:0% +continuing to to estimate the value + + + align:start position:0% +continuing to to estimate the value +function as we change pi towards + + align:start position:0% +function as we change pi towards + + + align:start position:0% +function as we change pi towards +the optimum cost + + align:start position:0% + + + + align:start position:0% + +okay we talked about a a couple ways to + + align:start position:0% +okay we talked about a a couple ways to + + + align:start position:0% +okay we talked about a a couple ways to +estimate the value function for a fixed + + align:start position:0% +estimate the value function for a fixed + + + align:start position:0% +estimate the value function for a fixed +pi right um even for function + + align:start position:0% +pi right um even for function + + + align:start position:0% +pi right um even for function +approximation + + align:start position:0% +approximation + + + align:start position:0% +approximation +we did first mark all the chains + + align:start position:0% + + + + align:start position:0% + +then we went to function approximation + + align:start position:0% + + + + align:start position:0% + +and we have + + align:start position:0% +and we have + + + align:start position:0% +and we have +convergence results + + align:start position:0% + + + + align:start position:0% + +for linear function approximators + + align:start position:0% + + + + align:start position:0% + +and we went back and looked up elmore's + + align:start position:0% +and we went back and looked up elmore's + + + align:start position:0% +and we went back and looked up elmore's +had a question + + align:start position:0% +had a question + + + align:start position:0% +had a question +about whether if you used lambda in your + + align:start position:0% +about whether if you used lambda in your + + + align:start position:0% +about whether if you used lambda in your +update it always got to the same + + align:start position:0% +update it always got to the same + + + align:start position:0% +update it always got to the same +estimate of j i think the answer is yes + + align:start position:0% +estimate of j i think the answer is yes + + + align:start position:0% +estimate of j i think the answer is yes +it always gets there's a the convergence + + align:start position:0% +it always gets there's a the convergence + + + align:start position:0% +it always gets there's a the convergence +proof has an error bound + + align:start position:0% +proof has an error bound + + + align:start position:0% +proof has an error bound +and that error bound does depend on + + align:start position:0% +and that error bound does depend on + + + align:start position:0% +and that error bound does depend on +lambda + + align:start position:0% +lambda + + + align:start position:0% +lambda +the discussion um + + align:start position:0% +the discussion um + + + align:start position:0% +the discussion um +and but if you set your learning rate + + align:start position:0% +and but if you set your learning rate + + + align:start position:0% +and but if you set your learning rate +smaller and smaller as you go it should + + align:start position:0% +smaller and smaller as you go it should + + + align:start position:0% +smaller and smaller as you go it should +converge to the they should all converge + + align:start position:0% +converge to the they should all converge + + + align:start position:0% +converge to the they should all converge +to the same + + align:start position:0% +to the same + + + align:start position:0% +to the same +estimate of j + + align:start position:0% +estimate of j + + + align:start position:0% +estimate of j +okay + + align:start position:0% + + + + align:start position:0% + +so if you think about it + + align:start position:0% +so if you think about it + + + align:start position:0% +so if you think about it +learning j pi + + align:start position:0% +learning j pi + + + align:start position:0% +learning j pi +shouldn't involve any any new machinery + + align:start position:0% +shouldn't involve any any new machinery + + + align:start position:0% +shouldn't involve any any new machinery +right if i'm just experiencing cost + + align:start position:0% +right if i'm just experiencing cost + + + align:start position:0% +right if i'm just experiencing cost +and i'm experiencing states and i'm + + align:start position:0% +and i'm experiencing states and i'm + + + align:start position:0% +and i'm experiencing states and i'm +trying to learn a function of cost to go + + align:start position:0% +trying to learn a function of cost to go + + + align:start position:0% +trying to learn a function of cost to go +given states i should just be able to do + + align:start position:0% +given states i should just be able to do + + + align:start position:0% +given states i should just be able to do +a least squares function it's just a + + align:start position:0% +a least squares function it's just a + + + align:start position:0% +a least squares function it's just a +standard + + align:start position:0% +standard + + + align:start position:0% +standard +function approximation task + + align:start position:0% +function approximation task + + + align:start position:0% +function approximation task +i could just do + + align:start position:0% + + + + align:start position:0% + +just be squares function approximately + + align:start position:0% +just be squares function approximately + + + align:start position:0% +just be squares function approximately +squares estimation + + align:start position:0% + + + + align:start position:0% + +and what we call the monte carlo error + + align:start position:0% + + + + align:start position:0% + +just run a bunch of trials + + align:start position:0% +just run a bunch of trials + + + align:start position:0% +just run a bunch of trials +figure out you know estimates of what + + align:start position:0% +figure out you know estimates of what + + + align:start position:0% +figure out you know estimates of what +the cost of gold was at every time then + + align:start position:0% +the cost of gold was at every time then + + + align:start position:0% +the cost of gold was at every time then +just + + align:start position:0% +just + + + align:start position:0% +just +do these squares estimation + + align:start position:0% +do these squares estimation + + + align:start position:0% +do these squares estimation +the other the machinery we developed + + align:start position:0% +the other the machinery we developed + + + align:start position:0% +the other the machinery we developed +last time + + align:start position:0% +last time + + + align:start position:0% +last time +was because + + align:start position:0% +was because + + + align:start position:0% +was because +it's actually a lot faster to use these + + align:start position:0% + + + + align:start position:0% + +bootstraps are much faster + + align:start position:0% + + + + align:start position:0% + +right so we talked about the tv + + align:start position:0% + + + + align:start position:0% + +including for function approximation + + align:start position:0% + + + + align:start position:0% + +the only reason we had to develop any + + align:start position:0% +the only reason we had to develop any + + + align:start position:0% +the only reason we had to develop any +new machinery is because we wanted to be + + align:start position:0% +new machinery is because we wanted to be + + + align:start position:0% +new machinery is because we wanted to be +able to + + align:start position:0% +able to + + + align:start position:0% +able to +essentially do that least squares + + align:start position:0% +essentially do that least squares + + + align:start position:0% +essentially do that least squares +estimation but we wanted to reuse our + + align:start position:0% +estimation but we wanted to reuse our + + + align:start position:0% +estimation but we wanted to reuse our +current estimate as we build up the + + align:start position:0% +current estimate as we build up the + + + align:start position:0% +current estimate as we build up the +estimate + + align:start position:0% +estimate + + + align:start position:0% +estimate +and that's why it's not just + + align:start position:0% +and that's why it's not just + + + align:start position:0% +and that's why it's not just +uh standard function approximation tasks + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +machinery + + align:start position:0% + + + + align:start position:0% + +so that's the simple + + align:start position:0% +so that's the simple + + + align:start position:0% +so that's the simple +policy evaluation story + + align:start position:0% + + + + align:start position:0% + +now the question is how do we + + align:start position:0% +now the question is how do we + + + align:start position:0% +now the question is how do we +how do we use the ability to do policy + + align:start position:0% +how do we use the ability to do policy + + + align:start position:0% +how do we use the ability to do policy +evaluation to get towards a more optimal + + align:start position:0% +evaluation to get towards a more optimal + + + align:start position:0% +evaluation to get towards a more optimal +policy okay + + align:start position:0% + + + + align:start position:0% + +so today + + align:start position:0% + + + + align:start position:0% + +given we can do policy evaluation + + align:start position:0% + + + + align:start position:0% + +we want to improve the policy + + align:start position:0% + + + + align:start position:0% + +the idea is + + align:start position:0% +the idea is + + + align:start position:0% +the idea is +the first idea you have to have you had + + align:start position:0% +the first idea you have to have you had + + + align:start position:0% +the first idea you have to have you had +very reasonable + + align:start position:0% + + + + align:start position:0% + +call policy iteration + + align:start position:0% + + + + align:start position:0% + +so given i start off with some initial + + align:start position:0% +so given i start off with some initial + + + align:start position:0% +so given i start off with some initial +guess for a policy + + align:start position:0% +guess for a policy + + + align:start position:0% +guess for a policy +right + + align:start position:0% +right + + + align:start position:0% +right +and i run it for a little while + + align:start position:0% +and i run it for a little while + + + align:start position:0% +and i run it for a little while +i can do policy evaluation until i'm + + align:start position:0% +i can do policy evaluation until i'm + + + align:start position:0% +i can do policy evaluation until i'm +converged on a nice + + align:start position:0% +converged on a nice + + + align:start position:0% +converged on a nice +estimate to get + + align:start position:0% +estimate to get + + + align:start position:0% +estimate to get +j pi + + align:start position:0% +j pi + + + align:start position:0% +j pi +one + + align:start position:0% + + + + align:start position:0% + +and now i'd like to take j pi one + + align:start position:0% +and now i'd like to take j pi one + + + align:start position:0% +and now i'd like to take j pi one +my + + align:start position:0% +my + + + align:start position:0% +my +estimate + + align:start position:0% +estimate + + + align:start position:0% +estimate +and come up with a new + + align:start position:0% + + + + align:start position:0% + +pi 2. + + align:start position:0% + + + + align:start position:0% + +let's talk about how to be how to how + + align:start position:0% +let's talk about how to be how to how + + + align:start position:0% +let's talk about how to be how to how +the value function confirms the policy + + align:start position:0% +the value function confirms the policy + + + align:start position:0% +the value function confirms the policy +and if i repeat and i do it properly + + align:start position:0% + + + + align:start position:0% + +then it all goes well + + align:start position:0% +then it all goes well + + + align:start position:0% +then it all goes well +i should by myself + + align:start position:0% +i should by myself + + + align:start position:0% +i should by myself +if it's always increasing in performance + + align:start position:0% +if it's always increasing in performance + + + align:start position:0% +if it's always increasing in performance +if we can show that + + align:start position:0% +if we can show that + + + align:start position:0% +if we can show that +i should find myself + + align:start position:0% +i should find myself + + + align:start position:0% +i should find myself +eventually + + align:start position:0% +eventually + + + align:start position:0% +eventually +at the uh + + align:start position:0% +at the uh + + + align:start position:0% +at the uh +optimal + + align:start position:0% + + + + align:start position:0% + +policy and optimal body function + + align:start position:0% + + + + align:start position:0% + +so we said td lambda + + align:start position:0% +so we said td lambda + + + align:start position:0% +so we said td lambda +is a candidate for sitting there + + align:start position:0% +is a candidate for sitting there + + + align:start position:0% +is a candidate for sitting there +evaluating + + align:start position:0% +evaluating + + + align:start position:0% +evaluating +policy which talked about a couple + + align:start position:0% +policy which talked about a couple + + + align:start position:0% +policy which talked about a couple +different ways to do policy evaluation + + align:start position:0% +different ways to do policy evaluation + + + align:start position:0% +different ways to do policy evaluation +so the question now is how do we do this + + align:start position:0% +so the question now is how do we do this + + + align:start position:0% +so the question now is how do we do this +step + + align:start position:0% +step + + + align:start position:0% +step +that's the first question + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +given your policy given your value + + align:start position:0% +given your policy given your value + + + align:start position:0% +given your policy given your value +function + + align:start position:0% +function + + + align:start position:0% +function +how do you compute + + align:start position:0% +how do you compute + + + align:start position:0% +how do you compute +a new policy that's at least as good as + + align:start position:0% +a new policy that's at least as good as + + + align:start position:0% +a new policy that's at least as good as +your own about + + align:start position:0% +your own about + + + align:start position:0% +your own about +policy but being better + + align:start position:0% + + + + align:start position:0% + +it's a + + align:start position:0% +it's a + + + align:start position:0% +it's a +good + + align:start position:0% +good + + + align:start position:0% +good +in fact that's sort of + + align:start position:0% +in fact that's sort of + + + align:start position:0% +in fact that's sort of +next week's idea + + align:start position:0% +next week's idea + + + align:start position:0% +next week's idea +all right + + align:start position:0% +all right + + + align:start position:0% +all right +we've been buying some guests + + align:start position:0% +we've been buying some guests + + + align:start position:0% +we've been buying some guests +and + + align:start position:0% +and + + + align:start position:0% +and +evaluation to do after critic + + align:start position:0% + + + + align:start position:0% + +but there's a simpler sort of idea + + align:start position:0% + + + + align:start position:0% + +i guess i think it requires anything to + + align:start position:0% +i guess i think it requires anything to + + + align:start position:0% +i guess i think it requires anything to +think about as well as making the notes + + align:start position:0% +think about as well as making the notes + + + align:start position:0% +think about as well as making the notes +but i guess it requires + + align:start position:0% +but i guess it requires + + + align:start position:0% +but i guess it requires +an observation that + + align:start position:0% + + + + align:start position:0% + +so the + + align:start position:0% +so the + + + align:start position:0% +so the +the optimal value function and the + + align:start position:0% +the optimal value function and the + + + align:start position:0% +the optimal value function and the +output policy + + align:start position:0% +output policy + + + align:start position:0% +output policy +at the property that the policy is going + + align:start position:0% +at the property that the policy is going + + + align:start position:0% +at the property that the policy is going +to + + align:start position:0% +to + + + align:start position:0% +to +take the fastest descent down the value + + align:start position:0% +take the fastest descent down the value + + + align:start position:0% +take the fastest descent down the value +function + + align:start position:0% +function + + + align:start position:0% +function +right your job is to go down and + + align:start position:0% +right your job is to go down and + + + align:start position:0% +right your job is to go down and +function as fast as possible + + align:start position:0% + + + + align:start position:0% + +um but if you're not optimal yet right + + align:start position:0% +um but if you're not optimal yet right + + + align:start position:0% +um but if you're not optimal yet right +i've got some random policy and i figure + + align:start position:0% +i've got some random policy and i figure + + + align:start position:0% +i've got some random policy and i figure +out + + align:start position:0% +out + + + align:start position:0% +out +my + + align:start position:0% +my + + + align:start position:0% +my +value of executing that policy + + align:start position:0% +value of executing that policy + + + align:start position:0% +value of executing that policy +that's actually not true yet + + align:start position:0% + + + + align:start position:0% + +so so what i need to say is if you if + + align:start position:0% +so so what i need to say is if you if + + + align:start position:0% +so so what i need to say is if you if +you start giving your value function + + align:start position:0% +you start giving your value function + + + align:start position:0% +you start giving your value function +you come up with a new policy which + + align:start position:0% +you come up with a new policy which + + + align:start position:0% +you come up with a new policy which +tries to be as aggressive as possible on + + align:start position:0% +tries to be as aggressive as possible on + + + align:start position:0% +tries to be as aggressive as possible on +this value function which in our + + align:start position:0% +this value function which in our + + + align:start position:0% +this value function which in our +continuous sense is just going down the + + align:start position:0% +continuous sense is just going down the + + + align:start position:0% +continuous sense is just going down the +gradient of the value function as fast + + align:start position:0% +gradient of the value function as fast + + + align:start position:0% +gradient of the value function as fast +as possible + + align:start position:0% +as possible + + + align:start position:0% +as possible +and that should be at least as good in + + align:start position:0% +and that should be at least as good in + + + align:start position:0% +and that should be at least as good in +the case of the optimal + + align:start position:0% +the case of the optimal + + + align:start position:0% +the case of the optimal +policy it should be the same it should + + align:start position:0% +policy it should be the same it should + + + align:start position:0% +policy it should be the same it should +return the output policy + + align:start position:0% +return the output policy + + + align:start position:0% +return the output policy +in the case where the value estimate is + + align:start position:0% +in the case where the value estimate is + + + align:start position:0% +in the case where the value estimate is +from + + align:start position:0% +from + + + align:start position:0% +from +another original policy it should be + + align:start position:0% +another original policy it should be + + + align:start position:0% +another original policy it should be +better + + align:start position:0% +better + + + align:start position:0% +better +okay + + align:start position:0% + + + + align:start position:0% + +so the basic story that's the continuous + + align:start position:0% +so the basic story that's the continuous + + + align:start position:0% +so the basic story that's the continuous +thing + + align:start position:0% +thing + + + align:start position:0% +thing +you want to come up with the greedy + + align:start position:0% +you want to come up with the greedy + + + align:start position:0% +you want to come up with the greedy +policy + + align:start position:0% + + + + align:start position:0% + +that moves down + + align:start position:0% +that moves down + + + align:start position:0% +that moves down +that does the best it can with + + align:start position:0% +that does the best it can with + + + align:start position:0% +that does the best it can with +this j-pop + + align:start position:0% + + + + align:start position:0% + +right so + + align:start position:0% +right so + + + align:start position:0% +right so +pi 2 let's say + + align:start position:0% +pi 2 let's say + + + align:start position:0% +pi 2 let's say +which is a function of s + + align:start position:0% +which is a function of s + + + align:start position:0% +which is a function of s +should be for instance + + align:start position:0% + + + + align:start position:0% + +sentence here + + align:start position:0% +sentence here + + + align:start position:0% +sentence here +street state connection minimize the + + align:start position:0% +street state connection minimize the + + + align:start position:0% +street state connection minimize the +expected value + + align:start position:0% +expected value + + + align:start position:0% +expected value +value first + + align:start position:0% +value first + + + align:start position:0% +value first +one step here + + align:start position:0% +one step here + + + align:start position:0% +one step here +plus + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so i've got the cost that i + + align:start position:0% +so i've got the cost that i + + + align:start position:0% +so i've got the cost that i +incur here + + align:start position:0% +incur here + + + align:start position:0% +incur here +plus the longer cost here i want to pick + + align:start position:0% +plus the longer cost here i want to pick + + + align:start position:0% +plus the longer cost here i want to pick +the new + + align:start position:0% +the new + + + align:start position:0% +the new +middle 8 + + align:start position:0% + + + + align:start position:0% + +the best thing i can do given that + + align:start position:0% +the best thing i can do given that + + + align:start position:0% +the best thing i can do given that +estimate of the value function + + align:start position:0% +estimate of the value function + + + align:start position:0% +estimate of the value function +right and that's going to give me a new + + align:start position:0% +right and that's going to give me a new + + + align:start position:0% +right and that's going to give me a new +policy actually + + align:start position:0% +policy actually + + + align:start position:0% +policy actually +i2 which is greedy + + align:start position:0% +i2 which is greedy + + + align:start position:0% +i2 which is greedy +with respect to this estimate of the + + align:start position:0% +with respect to this estimate of the + + + align:start position:0% +with respect to this estimate of the +language + + align:start position:0% + + + + align:start position:0% + +what does that look like + + align:start position:0% + + + + align:start position:0% + +yeah okay + + align:start position:0% +yeah okay + + + align:start position:0% +yeah okay +so + + align:start position:0% +so + + + align:start position:0% +so +value iteration for dynamic programming + + align:start position:0% +value iteration for dynamic programming + + + align:start position:0% +value iteration for dynamic programming +is exactly + + align:start position:0% +is exactly + + + align:start position:0% +is exactly +policy iteration + + align:start position:0% +policy iteration + + + align:start position:0% +policy iteration +in the case where you do a sweep through + + align:start position:0% +in the case where you do a sweep through + + + align:start position:0% +in the case where you do a sweep through +your entire state + + align:start position:0% +your entire state + + + align:start position:0% +your entire state +space every time + + align:start position:0% +space every time + + + align:start position:0% +space every time +and then do an update just sweep your + + align:start position:0% +and then do an update just sweep your + + + align:start position:0% +and then do an update just sweep your +entire state space you do an update + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +absolutely + + align:start position:0% +absolutely + + + align:start position:0% +absolutely +but it's a more general idea than just + + align:start position:0% +but it's a more general idea than just + + + align:start position:0% +but it's a more general idea than just +value iteration you don't have to + + align:start position:0% +value iteration you don't have to + + + align:start position:0% +value iteration you don't have to +actually evaluate all s + + align:start position:0% +actually evaluate all s + + + align:start position:0% +actually evaluate all s +you might call it asynchronous value + + align:start position:0% + + + + align:start position:0% + +oh good thank you + + align:start position:0% +oh good thank you + + + align:start position:0% +oh good thank you +this + + align:start position:0% + + + + align:start position:0% + +is like + + align:start position:0% + + + + align:start position:0% + +right i always minimize things so g is + + align:start position:0% +right i always minimize things so g is + + + align:start position:0% +right i always minimize things so g is +bad + + align:start position:0% + + + + align:start position:0% + +well i don't promise that i will never + + align:start position:0% +well i don't promise that i will never + + + align:start position:0% +well i don't promise that i will never +make mistake the sign because i try to + + align:start position:0% +make mistake the sign because i try to + + + align:start position:0% +make mistake the sign because i try to +use reinforcement + + align:start position:0% +use reinforcement + + + align:start position:0% +use reinforcement +with costs + + align:start position:0% +with costs + + + align:start position:0% +with costs +sometimes i get myself in control i + + align:start position:0% +sometimes i get myself in control i + + + align:start position:0% +sometimes i get myself in control i +never write audio + + align:start position:0% +never write audio + + + align:start position:0% +never write audio +okay + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% + + + + align:start position:0% + +okay um this is the argument the min is + + align:start position:0% +okay um this is the argument the min is + + + align:start position:0% +okay um this is the argument the min is +is the + + align:start position:0% +is the + + + align:start position:0% +is the +is the value in the case of value + + align:start position:0% +is the value in the case of value + + + align:start position:0% +is the value in the case of value +duration but in general you don't have + + align:start position:0% +duration but in general you don't have + + + align:start position:0% +duration but in general you don't have +to wait till you sweep the entire state + + align:start position:0% +to wait till you sweep the entire state + + + align:start position:0% +to wait till you sweep the entire state +space you can just + + align:start position:0% +space you can just + + + align:start position:0% +space you can just +take a single trajectory through update + + align:start position:0% +take a single trajectory through update + + + align:start position:0% +take a single trajectory through update +your value + + align:start position:0% +your value + + + align:start position:0% +your value +j or you can take lots of trajectories + + align:start position:0% +j or you can take lots of trajectories + + + align:start position:0% +j or you can take lots of trajectories +through and do + + align:start position:0% +through and do + + + align:start position:0% +through and do +get an improved estimate for j + + align:start position:0% + + + + align:start position:0% + +and then do this and get a new policy + + align:start position:0% +and then do this and get a new policy + + + align:start position:0% +and then do this and get a new policy +right + + align:start position:0% +right + + + align:start position:0% +right +in this policy iteration the original + + align:start position:0% +in this policy iteration the original + + + align:start position:0% +in this policy iteration the original +idea + + align:start position:0% +idea + + + align:start position:0% +idea +is you should really do this policy + + align:start position:0% +is you should really do this policy + + + align:start position:0% +is you should really do this policy +evaluation step until your estimate of j + + align:start position:0% +evaluation step until your estimate of j + + + align:start position:0% +evaluation step until your estimate of j +pi converges + + align:start position:0% +pi converges + + + align:start position:0% +pi converges +and then move on + + align:start position:0% +and then move on + + + align:start position:0% +and then move on +but in fact value iteration and other + + align:start position:0% +but in fact value iteration and other + + + align:start position:0% +but in fact value iteration and other +many algorithms show that you can it + + align:start position:0% +many algorithms show that you can it + + + align:start position:0% +many algorithms show that you can it +actually is still stable if you don't + + align:start position:0% +actually is still stable if you don't + + + align:start position:0% +actually is still stable if you don't +wait for it to converge + + align:start position:0% + + + + align:start position:0% + +but there's a problem with what i wrote + + align:start position:0% +but there's a problem with what i wrote + + + align:start position:0% +but there's a problem with what i wrote +here + + align:start position:0% + + + + align:start position:0% + +hopefully there's not a technical + + align:start position:0% +hopefully there's not a technical + + + align:start position:0% +hopefully there's not a technical +problem but why is that not quite what + + align:start position:0% +problem but why is that not quite what + + + align:start position:0% +problem but why is that not quite what +we need for today's lunch + + align:start position:0% + + + + align:start position:0% + +you can't do that with a value function + + align:start position:0% +you can't do that with a value function + + + align:start position:0% +you can't do that with a value function +you can have a model right + + align:start position:0% +you can have a model right + + + align:start position:0% +you can have a model right +that's actually exactly that you're + + align:start position:0% +that's actually exactly that you're + + + align:start position:0% +that's actually exactly that you're +answering the question that was asking + + align:start position:0% +answering the question that was asking + + + align:start position:0% +answering the question that was asking +that's perfect right + + align:start position:0% +that's perfect right + + + align:start position:0% +that's perfect right +so + + align:start position:0% +so + + + align:start position:0% +so +the problem is i said model free model + + align:start position:0% +the problem is i said model free model + + + align:start position:0% +the problem is i said model free model +free model 3 but then i i wrote down a + + align:start position:0% +free model 3 but then i i wrote down a + + + align:start position:0% +free model 3 but then i i wrote down a +model here right + + align:start position:0% +model here right + + + align:start position:0% +model here right +so how can i do you and the in the + + align:start position:0% +so how can i do you and the in the + + + align:start position:0% +so how can i do you and the in the +steepest sense or continuous sense by + + align:start position:0% +steepest sense or continuous sense by + + + align:start position:0% +steepest sense or continuous sense by +that + + align:start position:0% +that + + + align:start position:0% +that +this isn't sort of + + align:start position:0% +this isn't sort of + + + align:start position:0% +this isn't sort of +in the discrete sentence argument over a + + align:start position:0% +in the discrete sentence argument over a + + + align:start position:0% +in the discrete sentence argument over a +is typically done with a search over all + + align:start position:0% +is typically done with a search over all + + + align:start position:0% +is typically done with a search over all +actions in the continuous state in + + align:start position:0% +actions in the continuous state in + + + align:start position:0% +actions in the continuous state in +action i think it was finding the + + align:start position:0% +action i think it was finding the + + + align:start position:0% +action i think it was finding the +gradient down the slope + + align:start position:0% +gradient down the slope + + + align:start position:0% +gradient down the slope +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but right both of those required + + align:start position:0% +but right both of those required + + + align:start position:0% +but right both of those required +the model to actually do that policy + + align:start position:0% +the model to actually do that policy + + + align:start position:0% +the model to actually do that policy +so the first question for today is how + + align:start position:0% +so the first question for today is how + + + align:start position:0% +so the first question for today is how +do we do + + align:start position:0% +do we do + + + align:start position:0% +do we do +how do we come up with our greedy policy + + align:start position:0% +how do we come up with our greedy policy + + + align:start position:0% +how do we come up with our greedy policy +basically + + align:start position:0% +basically + + + align:start position:0% +basically +without having + + align:start position:0% + + + + align:start position:0% + +how can i possibly come up with + + align:start position:0% + + + + align:start position:0% + +a new policy + + align:start position:0% +a new policy + + + align:start position:0% +a new policy +without having them + + align:start position:0% + + + + align:start position:0% + +it turns out i didn't actually have the + + align:start position:0% +it turns out i didn't actually have the + + + align:start position:0% +it turns out i didn't actually have the +question in a way that i even imagined + + align:start position:0% +question in a way that i even imagined + + + align:start position:0% +question in a way that i even imagined +the way i wanted so um it turns out if + + align:start position:0% +the way i wanted so um it turns out if + + + align:start position:0% +the way i wanted so um it turns out if +we change the thing we store just a + + align:start position:0% +we change the thing we store just a + + + align:start position:0% +we change the thing we store just a +little bit okay + + align:start position:0% +little bit okay + + + align:start position:0% +little bit okay +then it turns out to be contributed + + align:start position:0% +then it turns out to be contributed + + + align:start position:0% +then it turns out to be contributed +to + + align:start position:0% +to + + + align:start position:0% +to +do model 3 + + align:start position:0% + + + + align:start position:0% + +3d policy + + align:start position:0% + + + + align:start position:0% + +okay so the way we do that is our cue + + align:start position:0% + + + + align:start position:0% + +q function + + align:start position:0% +q function + + + align:start position:0% +q function +it's a lot like a value function + + align:start position:0% +it's a lot like a value function + + + align:start position:0% +it's a lot like a value function +okay but now it's a function of state + + align:start position:0% +okay but now it's a function of state + + + align:start position:0% +okay but now it's a function of state +and action + + align:start position:0% + + + + align:start position:0% + +and also + + align:start position:0% +and also + + + align:start position:0% +and also +this is still + + align:start position:0% + + + + align:start position:0% + +going this way + + align:start position:0% + + + + align:start position:0% + +okay so what's a q function a q function + + align:start position:0% +okay so what's a q function a q function + + + align:start position:0% +okay so what's a q function a q function +is the + + align:start position:0% +is the + + + align:start position:0% +is the +cost you should expect to take to incur + + align:start position:0% +cost you should expect to take to incur + + + align:start position:0% +cost you should expect to take to incur +given you're in a current state and you + + align:start position:0% +given you're in a current state and you + + + align:start position:0% +given you're in a current state and you +take a particular action + + align:start position:0% +take a particular action + + + align:start position:0% +take a particular action +right so it's a lot like a value + + align:start position:0% +right so it's a lot like a value + + + align:start position:0% +right so it's a lot like a value +function but now you're actually + + align:start position:0% +function but now you're actually + + + align:start position:0% +function but now you're actually +learning a function over both state and + + align:start position:0% +learning a function over both state and + + + align:start position:0% +learning a function over both state and +actions so in any state + + align:start position:0% + + + + align:start position:0% + +j cube pi is the is the cost that you + + align:start position:0% +j cube pi is the is the cost that you + + + align:start position:0% +j cube pi is the is the cost that you +expect to incur okay when i take + + align:start position:0% +expect to incur okay when i take + + + align:start position:0% +expect to incur okay when i take +action 80 for one step and i follow + + align:start position:0% +action 80 for one step and i follow + + + align:start position:0% +action 80 for one step and i follow +policy pi for the rest of time + + align:start position:0% + + + + align:start position:0% + +makes sense + + align:start position:0% +makes sense + + + align:start position:0% +makes sense +all right so i could have my uh + + align:start position:0% +all right so i could have my uh + + + align:start position:0% +all right so i could have my uh +my acrobatic controller or something + + align:start position:0% +my acrobatic controller or something + + + align:start position:0% +my acrobatic controller or something +like this and then current state and + + align:start position:0% +like this and then current state and + + + align:start position:0% +like this and then current state and +i've got a policy that + + align:start position:0% +i've got a policy that + + + align:start position:0% +i've got a policy that +mostly gets me up but i'm learning more + + align:start position:0% +mostly gets me up but i'm learning more + + + align:start position:0% +mostly gets me up but i'm learning more +than just what that policy would be from + + align:start position:0% +than just what that policy would be from + + + align:start position:0% +than just what that policy would be from +this state i'm learning what that policy + + align:start position:0% +this state i'm learning what that policy + + + align:start position:0% +this state i'm learning what that policy +would have done if i for once that + + align:start position:0% +would have done if i for once that + + + align:start position:0% +would have done if i for once that +executed any random action i want a + + align:start position:0% +executed any random action i want a + + + align:start position:0% +executed any random action i want a +function for any random action and then + + align:start position:0% +function for any random action and then + + + align:start position:0% +function for any random action and then +what would i do from the + + align:start position:0% +what would i do from the + + + align:start position:0% +what would i do from the +given i ran that controller + + align:start position:0% + + + + align:start position:0% + +okay algebraically it's going to make a + + align:start position:0% +okay algebraically it's going to make a + + + align:start position:0% +okay algebraically it's going to make a +lot of sense if i just restore this but + + align:start position:0% +lot of sense if i just restore this but + + + align:start position:0% +lot of sense if i just restore this but +it's actually interesting to think a + + align:start position:0% +it's actually interesting to think a + + + align:start position:0% +it's actually interesting to think a +little bit about what that q function + + align:start position:0% +little bit about what that q function + + + align:start position:0% +little bit about what that q function +should look like + + align:start position:0% + + + + align:start position:0% + +and if you have a q function you + + align:start position:0% +and if you have a q function you + + + align:start position:0% +and if you have a q function you +certainly can also get the + + align:start position:0% +certainly can also get the + + + align:start position:0% +certainly can also get the +um + + align:start position:0% + + + + align:start position:0% + +because you can look up + + align:start position:0% +because you can look up + + + align:start position:0% +because you can look up +for a given pie + + align:start position:0% +for a given pie + + + align:start position:0% +for a given pie +what action that policy would have taken + + align:start position:0% +what action that policy would have taken + + + align:start position:0% +what action that policy would have taken +you can always pull out your current + + align:start position:0% +you can always pull out your current + + + align:start position:0% +you can always pull out your current +value function from + + align:start position:0% +value function from + + + align:start position:0% +value function from +q + + align:start position:0% + + + + align:start position:0% + +but you can also + + align:start position:0% + + + + align:start position:0% + +compare the simple relationship + + align:start position:0% + + + + align:start position:0% + +the optimal + + align:start position:0% + + + + align:start position:0% + +flip any signs + + align:start position:0% + + + + align:start position:0% + +okay we're roboticists in this room + + align:start position:0% +okay we're roboticists in this room + + + align:start position:0% +okay we're roboticists in this room +what does it mean + + align:start position:0% +what does it mean + + + align:start position:0% +what does it mean +to learn a q function + + align:start position:0% +to learn a q function + + + align:start position:0% +to learn a q function +what are the implications of learning a + + align:start position:0% +what are the implications of learning a + + + align:start position:0% +what are the implications of learning a +q function right + + align:start position:0% + + + + align:start position:0% + +well i guess i didn't say so so given + + align:start position:0% +well i guess i didn't say so so given + + + align:start position:0% +well i guess i didn't say so so given +the q function pi as its trivial notice + + align:start position:0% +the q function pi as its trivial notice + + + align:start position:0% +the q function pi as its trivial notice +having a q function makes + + align:start position:0% +having a q function makes + + + align:start position:0% +having a q function makes +action + + align:start position:0% + + + + align:start position:0% + +collection easy + + align:start position:0% + + + + align:start position:0% + +pi 2 of s is now just + + align:start position:0% +pi 2 of s is now just + + + align:start position:0% +pi 2 of s is now just +a min over a + + align:start position:0% + + + + align:start position:0% + +s + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% + + + + align:start position:0% + +okay if i was willing to + + align:start position:0% +okay if i was willing to + + + align:start position:0% +okay if i was willing to +the reason to learn a q function in one + + align:start position:0% +the reason to learn a q function in one + + + align:start position:0% +the reason to learn a q function in one +case here is that it tells me about the + + align:start position:0% +case here is that it tells me about the + + + align:start position:0% +case here is that it tells me about the +other actions i could have taken + + align:start position:0% +other actions i could have taken + + + align:start position:0% +other actions i could have taken +and if i want to now improve my policy + + align:start position:0% +and if i want to now improve my policy + + + align:start position:0% +and if i want to now improve my policy +then i'll just look at my q function at + + align:start position:0% +then i'll just look at my q function at + + + align:start position:0% +then i'll just look at my q function at +every state i'm in instead of taking the + + align:start position:0% +every state i'm in instead of taking the + + + align:start position:0% +every state i'm in instead of taking the +one + + align:start position:0% +one + + + align:start position:0% +one +at pi a i'll go ahead and take the best + + align:start position:0% +at pi a i'll go ahead and take the best + + + align:start position:0% +at pi a i'll go ahead and take the best +one + + align:start position:0% +one + + + align:start position:0% +one +right if pi a + + align:start position:0% +right if pi a + + + align:start position:0% +right if pi a +if pi one was optimal then i'll just get + + align:start position:0% +if pi one was optimal then i'll just get + + + align:start position:0% +if pi one was optimal then i'll just get +back + + align:start position:0% + + + + align:start position:0% + +the same policy + + align:start position:0% +the same policy + + + align:start position:0% +the same policy +but if pi one wasn't optimal then i'll + + align:start position:0% +but if pi one wasn't optimal then i'll + + + align:start position:0% +but if pi one wasn't optimal then i'll +get back somewhere + + align:start position:0% +get back somewhere + + + align:start position:0% +get back somewhere +given my + + align:start position:0% +given my + + + align:start position:0% +given my +q + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +what does it mean to run q and this is + + align:start position:0% +what does it mean to run q and this is + + + align:start position:0% +what does it mean to run q and this is +actually + + align:start position:0% +actually + + + align:start position:0% +actually +all you need to learn + + align:start position:0% +all you need to learn + + + align:start position:0% +all you need to learn +to do + + align:start position:0% +to do + + + align:start position:0% +to do +model three value learning to about four + + align:start position:0% +model three value learning to about four + + + align:start position:0% +model three value learning to about four +columns + + align:start position:0% + + + + align:start position:0% + +that's actually really big + + align:start position:0% +that's actually really big + + + align:start position:0% +that's actually really big +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +it's a little bit more to learn + + align:start position:0% +it's a little bit more to learn + + + align:start position:0% +it's a little bit more to learn +than + + align:start position:0% +than + + + align:start position:0% +than +learning a value function right so + + align:start position:0% + + + + align:start position:0% + +you're learning about your + + align:start position:0% + + + + align:start position:0% + +all row if i had to learn + + align:start position:0% +all row if i had to learn + + + align:start position:0% +all row if i had to learn +j pi + + align:start position:0% +j pi + + + align:start position:0% +j pi +how big is that if i'm going to say + + align:start position:0% + + + + align:start position:0% + +i've got + + align:start position:0% +i've got + + + align:start position:0% +i've got +n dimensional states + + align:start position:0% + + + + align:start position:0% + +i have to learn j pi + + align:start position:0% +i have to learn j pi + + + align:start position:0% +i have to learn j pi +how big is that what's that what's that + + align:start position:0% +how big is that what's that what's that + + + align:start position:0% +how big is that what's that what's that +function + + align:start position:0% + + + + align:start position:0% + +learning a scalar function over the + + align:start position:0% +learning a scalar function over the + + + align:start position:0% +learning a scalar function over the +state space + + align:start position:0% +state space + + + align:start position:0% +state space +to + + align:start position:0% + + + + align:start position:0% + +just really a scalar function + + align:start position:0% +just really a scalar function + + + align:start position:0% +just really a scalar function +if i was learning a policy + + align:start position:0% +if i was learning a policy + + + align:start position:0% +if i was learning a policy +would that mean right + + align:start position:0% +would that mean right + + + align:start position:0% +would that mean right +there's a stationary policy + + align:start position:0% + + + + align:start position:0% + +that might be + + align:start position:0% +that might be + + + align:start position:0% +that might be +that + + align:start position:0% + + + + align:start position:0% + +so how bad is it to learn q + + align:start position:0% + + + + align:start position:0% + +looks cute + + align:start position:0% + + + + align:start position:0% + +let's keep a deterministic policy for + + align:start position:0% +let's keep a deterministic policy for + + + align:start position:0% +let's keep a deterministic policy for +now + + align:start position:0% + + + + align:start position:0% + +now i've suddenly got to learn something + + align:start position:0% +now i've suddenly got to learn something + + + align:start position:0% +now i've suddenly got to learn something +over + + align:start position:0% + + + + align:start position:0% + +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +yeah + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% +for + + + align:start position:0% +for +for friends + + align:start position:0% +for friends + + + align:start position:0% +for friends +what would it be to learn a modeling + + align:start position:0% +what would it be to learn a modeling + + + align:start position:0% +what would it be to learn a modeling +system + + align:start position:0% + + + + align:start position:0% + +i wanted to use this idea + + align:start position:0% +i wanted to use this idea + + + align:start position:0% +i wanted to use this idea +what does that mean + + align:start position:0% + + + + align:start position:0% + +so let's just think about how much you + + align:start position:0% +so let's just think about how much you + + + align:start position:0% +so let's just think about how much you +have to learn so the easiness of + + align:start position:0% +have to learn so the easiness of + + + align:start position:0% +have to learn so the easiness of +learning this is not direct not only + + align:start position:0% +learning this is not direct not only + + + align:start position:0% +learning this is not direct not only +related to the size but it does does + + align:start position:0% +related to the size but it does does + + + align:start position:0% +related to the size but it does does +matter + + align:start position:0% +matter + + + align:start position:0% +matter +okay so most of the time as control guys + + align:start position:0% +okay so most of the time as control guys + + + align:start position:0% +okay so most of the time as control guys +as as + + align:start position:0% +as as + + + align:start position:0% +as as +robotics guys who probably try to learn + + align:start position:0% +robotics guys who probably try to learn + + + align:start position:0% +robotics guys who probably try to learn +a model first + + align:start position:0% +a model first + + + align:start position:0% +a model first +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then do model based control the last + + align:start position:0% +and then do model based control the last + + + align:start position:0% +and then do model based control the last +few days have been saying let's try to + + align:start position:0% +few days have been saying let's try to + + + align:start position:0% +few days have been saying let's try to +do something right now + + align:start position:0% +do something right now + + + align:start position:0% +do something right now +here's one + + align:start position:0% +here's one + + + align:start position:0% +here's one +interesting reason why + + align:start position:0% +interesting reason why + + + align:start position:0% +interesting reason why +it's actually learning a model is sort + + align:start position:0% +it's actually learning a model is sort + + + align:start position:0% +it's actually learning a model is sort +of a tall order it's a lot to learn + + align:start position:0% +of a tall order it's a lot to learn + + + align:start position:0% +of a tall order it's a lot to learn +right you got to learn from every + + align:start position:0% +right you got to learn from every + + + align:start position:0% +right you got to learn from every +possible state in action what's my + + align:start position:0% +possible state in action what's my + + + align:start position:0% +possible state in action what's my +you know + + align:start position:0% +you know + + + align:start position:0% +you know +x dot + + align:start position:0% +x dot + + + align:start position:0% +x dot +this is only learning + + align:start position:0% +this is only learning + + + align:start position:0% +this is only learning +from every possible state in action + + align:start position:0% +from every possible state in action + + + align:start position:0% +from every possible state in action +what's the expected cost to go + + align:start position:0% +what's the expected cost to go + + + align:start position:0% +what's the expected cost to go +in this scalar + + align:start position:0% +in this scalar + + + align:start position:0% +in this scalar +so it's loading one output + + align:start position:0% +so it's loading one output + + + align:start position:0% +so it's loading one output +and the beautiful thing about optimal + + align:start position:0% +and the beautiful thing about optimal + + + align:start position:0% +and the beautiful thing about optimal +control + + align:start position:0% +control + + + align:start position:0% +control +with the sort of additive cost functions + + align:start position:0% +with the sort of additive cost functions + + + align:start position:0% +with the sort of additive cost functions +and everything like that + + align:start position:0% +and everything like that + + + align:start position:0% +and everything like that +the beautiful thing + + align:start position:0% +the beautiful thing + + + align:start position:0% +the beautiful thing +is that this is all you need to know + + align:start position:0% +is that this is all you need to know + + + align:start position:0% +is that this is all you need to know +to make operable decisions + + align:start position:0% +to make operable decisions + + + align:start position:0% +to make operable decisions +you don't need to know your model that + + align:start position:0% +you don't need to know your model that + + + align:start position:0% +you don't need to know your model that +model is extra + + align:start position:0% +model is extra + + + align:start position:0% +model is extra +informational + + align:start position:0% +informational + + + align:start position:0% +informational +all you need to know to make optimal + + align:start position:0% +all you need to know to make optimal + + + align:start position:0% +all you need to know to make optimal +decisions + + align:start position:0% +decisions + + + align:start position:0% +decisions +give these additive cost function + + align:start position:0% +give these additive cost function + + + align:start position:0% +give these additive cost function +performance + + align:start position:0% +performance + + + align:start position:0% +performance +is given an + + align:start position:0% +is given an + + + align:start position:0% +is given an +administration how much do i expect to + + align:start position:0% +administration how much do i expect to + + + align:start position:0% +administration how much do i expect to +incur possible + + align:start position:0% +incur possible + + + align:start position:0% +incur possible +it's a beautiful thing + + align:start position:0% +it's a beautiful thing + + + align:start position:0% +it's a beautiful thing +okay so if we make it stochastic it gets + + align:start position:0% +okay so if we make it stochastic it gets + + + align:start position:0% +okay so if we make it stochastic it gets +even sort of you know learning a + + align:start position:0% +even sort of you know learning a + + + align:start position:0% +even sort of you know learning a +stochastic model if your dynamics are + + align:start position:0% +stochastic model if your dynamics are + + + align:start position:0% +stochastic model if your dynamics are +variable and that's important you don't + + align:start position:0% +variable and that's important you don't + + + align:start position:0% +variable and that's important you don't +do stochastic output control learning + + align:start position:0% +do stochastic output control learning + + + align:start position:0% +do stochastic output control learning +the stochastic model is probably even + + align:start position:0% +the stochastic model is probably even + + + align:start position:0% +the stochastic model is probably even +harder than that + + align:start position:0% +harder than that + + + align:start position:0% +harder than that +right maybe i have to learn uh + + align:start position:0% +right maybe i have to learn uh + + + align:start position:0% +right maybe i have to learn uh +the mean of x dot plus the covariance + + align:start position:0% +the mean of x dot plus the covariance + + + align:start position:0% +the mean of x dot plus the covariance +matrix of x dot or something like this + + align:start position:0% +matrix of x dot or something like this + + + align:start position:0% +matrix of x dot or something like this +okay + + align:start position:0% +okay + + + align:start position:0% +okay +running a statistic model will be even + + align:start position:0% +running a statistic model will be even + + + align:start position:0% +running a statistic model will be even +more + + align:start position:0% +more + + + align:start position:0% +more +expensive + + align:start position:0% +expensive + + + align:start position:0% +expensive +q + + align:start position:0% +q + + + align:start position:0% +q +in the q sense + + align:start position:0% +in the q sense + + + align:start position:0% +in the q sense +i left it off in the first pass just to + + align:start position:0% +i left it off in the first pass just to + + + align:start position:0% +i left it off in the first pass just to +keep it clean but + + align:start position:0% +keep it clean but + + + align:start position:0% +keep it clean but +q is just going to be the expected value + + align:start position:0% +q is just going to be the expected value + + + align:start position:0% +q is just going to be the expected value +around this okay + + align:start position:0% + + + + align:start position:0% + +so q is always going to be a scale + + align:start position:0% +so q is always going to be a scale + + + align:start position:0% +so q is always going to be a scale +even in a stochastic and output control + + align:start position:0% +even in a stochastic and output control + + + align:start position:0% +even in a stochastic and output control +sense + + align:start position:0% + + + + align:start position:0% + +so maybe this is the biggest point of + + align:start position:0% +so maybe this is the biggest point of + + + align:start position:0% +so maybe this is the biggest point of +optimal control honestly + + align:start position:0% +optimal control honestly + + + align:start position:0% +optimal control honestly +optimal control related to learning is + + align:start position:0% +optimal control related to learning is + + + align:start position:0% +optimal control related to learning is +that if you're willing to do the uh + + align:start position:0% +that if you're willing to do the uh + + + align:start position:0% +that if you're willing to do the uh +the + + align:start position:0% +the + + + align:start position:0% +the +additive expected value + + align:start position:0% +additive expected value + + + align:start position:0% +additive expected value +optimization problems which i think + + align:start position:0% +optimization problems which i think + + + align:start position:0% +optimization problems which i think +we've seen lots of interesting problems + + align:start position:0% +we've seen lots of interesting problems + + + align:start position:0% +we've seen lots of interesting problems +that follow that category + + align:start position:0% +that follow that category + + + align:start position:0% +that follow that category +then all you need to make know to make + + align:start position:0% +then all you need to make know to make + + + align:start position:0% +then all you need to make know to make +decisions is to build the value function + + align:start position:0% +decisions is to build the value function + + + align:start position:0% +decisions is to build the value function +the the q function here + + align:start position:0% +the the q function here + + + align:start position:0% +the the q function here +right + + align:start position:0% +right + + + align:start position:0% +right +the expected value of future numbers + + align:start position:0% +the expected value of future numbers + + + align:start position:0% +the expected value of future numbers +for everything else weight away + + align:start position:0% + + + + align:start position:0% + +okay important point + + align:start position:0% + + + + align:start position:0% + +now just to soften it a little bit + + align:start position:0% +now just to soften it a little bit + + + align:start position:0% +now just to soften it a little bit +um + + align:start position:0% +um + + + align:start position:0% +um +you know in practice that you might not + + align:start position:0% +you know in practice that you might not + + + align:start position:0% +you know in practice that you might not +get away without doing that right if you + + align:start position:0% +get away without doing that right if you + + + align:start position:0% +get away without doing that right if you +have to somehow build an observer to do + + align:start position:0% +have to somehow build an observer to do + + + align:start position:0% +have to somehow build an observer to do +state estimation or an estimated queue + + align:start position:0% +state estimation or an estimated queue + + + align:start position:0% +state estimation or an estimated queue +you know + + align:start position:0% +you know + + + align:start position:0% +you know +there might be other reasons floating + + align:start position:0% +there might be other reasons floating + + + align:start position:0% +there might be other reasons floating +around in your robot that might require + + align:start position:0% +around in your robot that might require + + + align:start position:0% +around in your robot that might require +you to learn this okay + + align:start position:0% +you to learn this okay + + + align:start position:0% +you to learn this okay +but + + align:start position:0% +but + + + align:start position:0% +but +in a pure sense that's really what you + + align:start position:0% +in a pure sense that's really what you + + + align:start position:0% +in a pure sense that's really what you +need to know + + align:start position:0% + + + + align:start position:0% + +number of states + + align:start position:0% + + + + align:start position:0% + +if you want to make an analogy back here + + align:start position:0% +if you want to make an analogy back here + + + align:start position:0% +if you want to make an analogy back here +that it would actually be just the + + align:start position:0% +that it would actually be just the + + + align:start position:0% +that it would actually be just the +number of elements in s but i wanted to + + align:start position:0% +number of elements in s but i wanted to + + + align:start position:0% +number of elements in s but i wanted to +sort of feel about it for a little bit + + align:start position:0% +sort of feel about it for a little bit + + + align:start position:0% +sort of feel about it for a little bit +okay + + align:start position:0% +okay + + + align:start position:0% +okay +this is just the + + align:start position:0% +this is just the + + + align:start position:0% +this is just the +computer scientists that did this + + align:start position:0% +computer scientists that did this + + + align:start position:0% +computer scientists that did this +but it doesn't even be precisely + + align:start position:0% +but it doesn't even be precisely + + + align:start position:0% +but it doesn't even be precisely +okay so i meant + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +okay so now how do we learn q i told you + + align:start position:0% +okay so now how do we learn q i told you + + + align:start position:0% +okay so now how do we learn q i told you +how to learn j + + align:start position:0% +how to learn j + + + align:start position:0% +how to learn j +um q looks pretty close to j + + align:start position:0% +um q looks pretty close to j + + + align:start position:0% +um q looks pretty close to j +how do i learn q i told you about temple + + align:start position:0% +how do i learn q i told you about temple + + + align:start position:0% +how do i learn q i told you about temple +difference learning probably wouldn't + + align:start position:0% +difference learning probably wouldn't + + + align:start position:0% +difference learning probably wouldn't +wasted your time talking about temporal + + align:start position:0% +wasted your time talking about temporal + + + align:start position:0% +wasted your time talking about temporal +difference learning that wasn't also + + align:start position:0% +difference learning that wasn't also + + + align:start position:0% +difference learning that wasn't also +relevant for + + align:start position:0% +relevant for + + + align:start position:0% +relevant for +what we needed to do these model free + + align:start position:0% + + + + align:start position:0% + +value methods so let's just see + + align:start position:0% +value methods so let's just see + + + align:start position:0% +value methods so let's just see +that temporal difference learning also + + align:start position:0% +that temporal difference learning also + + + align:start position:0% +that temporal difference learning also +works for learning these functions + + align:start position:0% + + + + align:start position:0% + +let's do + + align:start position:0% +let's do + + + align:start position:0% +let's do +just a simple case first where + + align:start position:0% +just a simple case first where + + + align:start position:0% +just a simple case first where +i'm just doing remember td 0 was just + + align:start position:0% +i'm just doing remember td 0 was just + + + align:start position:0% +i'm just doing remember td 0 was just +bootstrapping it wasn't carrying around + + align:start position:0% +bootstrapping it wasn't carrying around + + + align:start position:0% +bootstrapping it wasn't carrying around +long term awards it was just saying i'm + + align:start position:0% +long term awards it was just saying i'm + + + align:start position:0% +long term awards it was just saying i'm +going to do one step and i'm going to + + align:start position:0% +going to do one step and i'm going to + + + align:start position:0% +going to do one step and i'm going to +use my value estimate for the rest of + + align:start position:0% +use my value estimate for the rest of + + + align:start position:0% +use my value estimate for the rest of +time as my new update + + align:start position:0% +time as my new update + + + align:start position:0% +time as my new update +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and i'll go ahead since we're + + align:start position:0% +and i'll go ahead since we're + + + align:start position:0% +and i'll go ahead since we're +we talked about last time how the + + align:start position:0% +we talked about last time how the + + + align:start position:0% +we talked about last time how the +function approximator is getting reduced + + align:start position:0% +function approximator is getting reduced + + + align:start position:0% +function approximator is getting reduced +to the + + align:start position:0% +to the + + + align:start position:0% +to the +markov chain case let's just do it like + + align:start position:0% + + + + align:start position:0% + +let's say q prime of s is + + align:start position:0% +let's say q prime of s is + + + align:start position:0% +let's say q prime of s is +f i + + align:start position:0% +f i + + + align:start position:0% +f i +v i + + align:start position:0% +v i + + + align:start position:0% +v i +and linear function approximators + + align:start position:0% + + + + align:start position:0% + +okay then the + + align:start position:0% +okay then the + + + align:start position:0% +okay then the +td lambda update + + align:start position:0% +td lambda update + + + align:start position:0% +td lambda update +is going to be td 0 is + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +gradient here in linear function + + align:start position:0% +gradient here in linear function + + + align:start position:0% +gradient here in linear function +approximately is just + + align:start position:0% + + + + align:start position:0% + +so if you look back in your notes that's + + align:start position:0% +so if you look back in your notes that's + + + align:start position:0% +so if you look back in your notes that's +exactly what we had before + + align:start position:0% +exactly what we had before + + + align:start position:0% +exactly what we had before +where this used to be j + + align:start position:0% +where this used to be j + + + align:start position:0% +where this used to be j +right we're going to use as our new + + align:start position:0% +right we're going to use as our new + + + align:start position:0% +right we're going to use as our new +update we're going to say that our new + + align:start position:0% +update we're going to say that our new + + + align:start position:0% +update we're going to say that our new +estimate for + + align:start position:0% +estimate for + + + align:start position:0% +estimate for +for j is basically the one step cost + + align:start position:0% +for j is basically the one step cost + + + align:start position:0% +for j is basically the one step cost +plus the long term look ahead + + align:start position:0% +plus the long term look ahead + + + align:start position:0% +plus the long term look ahead +a n plus one in the case of + + align:start position:0% +a n plus one in the case of + + + align:start position:0% +a n plus one in the case of +doing a + + align:start position:0% +doing a + + + align:start position:0% +doing a +i'm non-policy trying to do policy + + align:start position:0% +i'm non-policy trying to do policy + + + align:start position:0% +i'm non-policy trying to do policy +evaluation is going to be + + align:start position:0% +evaluation is going to be + + + align:start position:0% +evaluation is going to be +pi + + align:start position:0% + + + + align:start position:0% + +one step prediction minus my current + + align:start position:0% +one step prediction minus my current + + + align:start position:0% +one step prediction minus my current +prediction and try to make that go to + + align:start position:0% +prediction and try to make that go to + + + align:start position:0% +prediction and try to make that go to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +and in order to do it in a function + + align:start position:0% +and in order to do it in a function + + + align:start position:0% +and in order to do it in a function +approximator sense that means + + align:start position:0% +approximator sense that means + + + align:start position:0% +approximator sense that means +multiplying that error the temporal + + align:start position:0% +multiplying that error the temporal + + + align:start position:0% +multiplying that error the temporal +difference error by your gradient + + align:start position:0% +difference error by your gradient + + + align:start position:0% +difference error by your gradient +and that does + + align:start position:0% +and that does + + + align:start position:0% +and that does +something like creating this + + align:start position:0% +something like creating this + + + align:start position:0% +something like creating this +on your temporal difference cost + + align:start position:0% +on your temporal difference cost + + + align:start position:0% +on your temporal difference cost +but not exactly because it's + + align:start position:0% + + + + align:start position:0% + +this whole + + align:start position:0% +this whole + + + align:start position:0% +this whole +recursive dependence thing + + align:start position:0% + + + + align:start position:0% + +people get why + + align:start position:0% +people get why + + + align:start position:0% +people get why +you get that it's not quite getting + + align:start position:0% +you get that it's not quite getting + + + align:start position:0% +you get that it's not quite getting +percent but + + align:start position:0% + + + + align:start position:0% + +this looks a lot like what i would get + + align:start position:0% +this looks a lot like what i would get + + + align:start position:0% +this looks a lot like what i would get +if i was + + align:start position:0% +if i was + + + align:start position:0% +if i was +trying to do um + + align:start position:0% + + + + align:start position:0% + +creating the sent on something right + + align:start position:0% + + + + align:start position:0% + +but only in the case of td1 it would + + align:start position:0% +but only in the case of td1 it would + + + align:start position:0% +but only in the case of td1 it would +actually read but normally i have a + + align:start position:0% + + + + align:start position:0% + +y minus + + align:start position:0% +y minus + + + align:start position:0% +y minus +f of x i'm going to do + + align:start position:0% +f of x i'm going to do + + + align:start position:0% +f of x i'm going to do +the gradient with respect to this + + align:start position:0% +the gradient with respect to this + + + align:start position:0% +the gradient with respect to this +i'm going to minimize this + + align:start position:0% + + + + align:start position:0% + +i'll get something if i take the + + align:start position:0% +i'll get something if i take the + + + align:start position:0% +i'll get something if i take the +gradient respect to alpha + + align:start position:0% +gradient respect to alpha + + + align:start position:0% +gradient respect to alpha +i get + + align:start position:0% +i get + + + align:start position:0% +i get +that error + + align:start position:0% +that error + + + align:start position:0% +that error +without the + + align:start position:0% +without the + + + align:start position:0% +without the +x + + align:start position:0% + + + + align:start position:0% + +which is what we've got here this is our + + align:start position:0% +which is what we've got here this is our + + + align:start position:0% +which is what we've got here this is our +error if we assume that this is just my + + align:start position:0% +error if we assume that this is just my + + + align:start position:0% +error if we assume that this is just my +my desire + + align:start position:0% +my desire + + + align:start position:0% +my desire +and this is my actual this is great + + align:start position:0% +and this is my actual this is great + + + align:start position:0% +and this is my actual this is great +but it's not quite that because this + + align:start position:0% +but it's not quite that because this + + + align:start position:0% +but it's not quite that because this +depends on alpha these all depend on + + align:start position:0% +depends on alpha these all depend on + + + align:start position:0% +depends on alpha these all depend on +alpha so by virtue of having this one in + + align:start position:0% +alpha so by virtue of having this one in + + + align:start position:0% +alpha so by virtue of having this one in +the alpha it's not exactly agreeing to + + align:start position:0% +the alpha it's not exactly agreeing to + + + align:start position:0% +the alpha it's not exactly agreeing to +that algorithm + + align:start position:0% + + + + align:start position:0% + +but it still works + + align:start position:0% + + + + align:start position:0% + +and actually in the case where + + align:start position:0% +and actually in the case where + + + align:start position:0% +and actually in the case where +td is one + + align:start position:0% +td is one + + + align:start position:0% +td is one +these things actually um go through it + + align:start position:0% +these things actually um go through it + + + align:start position:0% +these things actually um go through it +um + + align:start position:0% +um + + + align:start position:0% +um +and cancel each other out with whatever + + align:start position:0% +and cancel each other out with whatever + + + align:start position:0% +and cancel each other out with whatever +it is + + align:start position:0% + + + + align:start position:0% + +but i want you to see + + align:start position:0% +but i want you to see + + + align:start position:0% +but i want you to see +this is my error i'm trying to make + + align:start position:0% +this is my error i'm trying to make + + + align:start position:0% +this is my error i'm trying to make +q and my current statement action look + + align:start position:0% +q and my current statement action look + + + align:start position:0% +q and my current statement action look +like my + + align:start position:0% +like my + + + align:start position:0% +like my +one step cost plus q of my next state in + + align:start position:0% +one step cost plus q of my next state in + + + align:start position:0% +one step cost plus q of my next state in +action and i'm going to do that and + + align:start position:0% +action and i'm going to do that and + + + align:start position:0% +action and i'm going to do that and +multiply my error by my gradient + + align:start position:0% +multiply my error by my gradient + + + align:start position:0% +multiply my error by my gradient +and agree to send kind of + + align:start position:0% + + + + align:start position:0% + +okay you can still do + + align:start position:0% +okay you can still do + + + align:start position:0% +okay you can still do +td lambda + + align:start position:0% + + + + align:start position:0% + +if you like + + align:start position:0% +if you like + + + align:start position:0% +if you like +also + + align:start position:0% + + + + align:start position:0% + +functions + + align:start position:0% + + + + align:start position:0% + +and the big idea there was to use an + + align:start position:0% +and the big idea there was to use an + + + align:start position:0% +and the big idea there was to use an +eligibility trace + + align:start position:0% +eligibility trace + + + align:start position:0% +eligibility trace +which in the + + align:start position:0% + + + + align:start position:0% + +um function approximated case + + align:start position:0% +um function approximated case + + + align:start position:0% +um function approximated case +was + + align:start position:0% +was + + + align:start position:0% +was +gamma + + align:start position:0% +gamma + + + align:start position:0% +gamma +lambda + + align:start position:0% +lambda + + + align:start position:0% +lambda +e i n + + align:start position:0% + + + + align:start position:0% + +plus + + align:start position:0% + + + + align:start position:0% + +and then my update is + + align:start position:0% +and then my update is + + + align:start position:0% +and then my update is +the same thing + + align:start position:0% + + + + align:start position:0% + +this is my big temporal difference here + + align:start position:0% +this is my big temporal difference here + + + align:start position:0% +this is my big temporal difference here +instead of multiplying my degrees + + align:start position:0% + + + + align:start position:0% + +eligibility + + align:start position:0% +eligibility + + + align:start position:0% +eligibility +and magically through an algebraic trick + + align:start position:0% +and magically through an algebraic trick + + + align:start position:0% +and magically through an algebraic trick +that membrane remembering the gradient + + align:start position:0% +that membrane remembering the gradient + + + align:start position:0% +that membrane remembering the gradient +computes the + + align:start position:0% +computes the + + + align:start position:0% +computes the +the + + align:start position:0% +the + + + align:start position:0% +the +bootstrapping case when i know zero + + align:start position:0% +bootstrapping case when i know zero + + + align:start position:0% +bootstrapping case when i know zero +the monte carlo case from lambda is one + + align:start position:0% +the monte carlo case from lambda is one + + + align:start position:0% +the monte carlo case from lambda is one +and something in between them + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so you can still do temporal difference + + align:start position:0% +so you can still do temporal difference + + + align:start position:0% +so you can still do temporal difference +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +eight point number two + + align:start position:0% + + + + align:start position:0% + +big idea number one we have to use + + align:start position:0% +big idea number one we have to use + + + align:start position:0% +big idea number one we have to use +two functions to do + + align:start position:0% +two functions to do + + + align:start position:0% +two functions to do +to do action selection + + align:start position:0% + + + + align:start position:0% + +point number two + + align:start position:0% + + + + align:start position:0% + +is off policy policy evaluation + + align:start position:0% +is off policy policy evaluation + + + align:start position:0% +is off policy policy evaluation +so once we start using q + + align:start position:0% +so once we start using q + + + align:start position:0% +so once we start using q +you could do this trick that i mentioned + + align:start position:0% +you could do this trick that i mentioned + + + align:start position:0% +you could do this trick that i mentioned +the first day we're doing + + align:start position:0% +the first day we're doing + + + align:start position:0% +the first day we're doing +value methods + + align:start position:0% +value methods + + + align:start position:0% +value methods +and that is to + + align:start position:0% + + + + align:start position:0% + +execute + + align:start position:0% + + + + align:start position:0% + +i'll see high one + + align:start position:0% +i'll see high one + + + align:start position:0% +i'll see high one +but learn + + align:start position:0% + + + + align:start position:0% + +q + + align:start position:0% +q + + + align:start position:0% +q +two + + align:start position:0% + + + + align:start position:0% + +you see how we do that + + align:start position:0% + + + + align:start position:0% + +i virtue of having this extra dimension + + align:start position:0% +i virtue of having this extra dimension + + + align:start position:0% +i virtue of having this extra dimension +we know + + align:start position:0% +we know + + + align:start position:0% +we know +we're learning + + align:start position:0% +we're learning + + + align:start position:0% +we're learning +not only what happens when i take calls + + align:start position:0% +not only what happens when i take calls + + + align:start position:0% +not only what happens when i take calls +pi + + align:start position:0% +pi + + + align:start position:0% +pi +um from state s + + align:start position:0% +um from state s + + + align:start position:0% +um from state s +i'm learning what happens if i take any + + align:start position:0% +i'm learning what happens if i take any + + + align:start position:0% +i'm learning what happens if i take any +action like this + + align:start position:0% + + + + align:start position:0% + +gives me a lot more + + align:start position:0% +gives me a lot more + + + align:start position:0% +gives me a lot more +power + + align:start position:0% +power + + + align:start position:0% +power +because for instance when i'm making my + + align:start position:0% +because for instance when i'm making my + + + align:start position:0% +because for instance when i'm making my +temporal difference error + + align:start position:0% + + + + align:start position:0% + +i don't need to necessarily use my + + align:start position:0% +i don't need to necessarily use my + + + align:start position:0% +i don't need to necessarily use my +one-step prediction + + align:start position:0% +one-step prediction + + + align:start position:0% +one-step prediction +as the current policy + + align:start position:0% +as the current policy + + + align:start position:0% +as the current policy +right i can just look up + + align:start position:0% +right i can just look up + + + align:start position:0% +right i can just look up +what would policy 2 have done + + align:start position:0% + + + + align:start position:0% + +because i'm + + align:start position:0% +because i'm + + + align:start position:0% +because i'm +um + + align:start position:0% +um + + + align:start position:0% +um +i'm storing every state action pair it's + + align:start position:0% +i'm storing every state action pair it's + + + align:start position:0% +i'm storing every state action pair it's +mortality it's more work + + align:start position:0% +mortality it's more work + + + align:start position:0% +mortality it's more work +but it means i can say + + align:start position:0% +but it means i can say + + + align:start position:0% +but it means i can say +i'd like my new + + align:start position:0% +i'd like my new + + + align:start position:0% +i'd like my new +q pi 2 + + align:start position:0% +q pi 2 + + + align:start position:0% +q pi 2 +to be the one step cost i got for taking + + align:start position:0% +to be the one step cost i got for taking + + + align:start position:0% +to be the one step cost i got for taking +a + + align:start position:0% +a + + + align:start position:0% +a +plus the long term cost of taking policy + + align:start position:0% +plus the long term cost of taking policy + + + align:start position:0% +plus the long term cost of taking policy +iq + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% +and then + + + align:start position:0% +and then +all the same equations play out and you + + align:start position:0% +all the same equations play out and you + + + align:start position:0% +all the same equations play out and you +get a + + align:start position:0% + + + + align:start position:0% + +you got an estimate for policy too + + align:start position:0% + + + + align:start position:0% + +does it count like + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +does he have more than the first step of + + align:start position:0% +does he have more than the first step of + + + align:start position:0% +does he have more than the first step of +policy two and then like take the cost + + align:start position:0% +policy two and then like take the cost + + + align:start position:0% +policy two and then like take the cost +to go policy with them or + + align:start position:0% +to go policy with them or + + + align:start position:0% +to go policy with them or +does it somehow + + align:start position:0% + + + + align:start position:0% + +so i can't switch + + align:start position:0% +so i can't switch + + + align:start position:0% +so i can't switch +um well we'll talk about another you can + + align:start position:0% +um well we'll talk about another you can + + + align:start position:0% +um well we'll talk about another you can +switch halfway through but once i commit + + align:start position:0% +switch halfway through but once i commit + + + align:start position:0% +switch halfway through but once i commit +to learning um + + align:start position:0% +to learning um + + + align:start position:0% +to learning um +cube pi too + + align:start position:0% +cube pi too + + + align:start position:0% +cube pi too +right that actually this whole thing + + align:start position:0% +right that actually this whole thing + + + align:start position:0% +right that actually this whole thing +is built up of experience of executing + + align:start position:0% +is built up of experience of executing + + + align:start position:0% +is built up of experience of executing +policies too + + align:start position:0% +policies too + + + align:start position:0% +policies too +even though i've only generated sample + + align:start position:0% +even though i've only generated sample + + + align:start position:0% +even though i've only generated sample +paths with policy one + + align:start position:0% +paths with policy one + + + align:start position:0% +paths with policy one +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +so it's a completely consistent + + align:start position:0% +so it's a completely consistent + + + align:start position:0% +so it's a completely consistent +estimator of + + align:start position:0% +estimator of + + + align:start position:0% +estimator of +powers of q pi two right if i halfway + + align:start position:0% +powers of q pi two right if i halfway + + + align:start position:0% +powers of q pi two right if i halfway +through decided i wanted to start + + align:start position:0% +through decided i wanted to start + + + align:start position:0% +through decided i wanted to start +evaluating pi three then i'm going to + + align:start position:0% +evaluating pi three then i'm going to + + + align:start position:0% +evaluating pi three then i'm going to +have to wait for those + + align:start position:0% +have to wait for those + + + align:start position:0% +have to wait for those +cancel out or play some tricks to do + + align:start position:0% +cancel out or play some tricks to do + + + align:start position:0% +cancel out or play some tricks to do +that but + + align:start position:0% +that but + + + align:start position:0% +that but +it actually rehearsally builds up to the + + align:start position:0% +it actually rehearsally builds up to the + + + align:start position:0% +it actually rehearsally builds up to the +estimate of class + + align:start position:0% + + + + align:start position:0% + +2. um + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +so why isn't it true reading the seven + + align:start position:0% + + + + align:start position:0% + +that's that's that's exactly what i + + align:start position:0% +that's that's that's exactly what i + + + align:start position:0% +that's that's that's exactly what i +proposed you do but the only problem is + + align:start position:0% +proposed you do but the only problem is + + + align:start position:0% +proposed you do but the only problem is +this isn't what we have + + align:start position:0% +this isn't what we have + + + align:start position:0% +this isn't what we have +right but we actually have this + + align:start position:0% + + + + align:start position:0% + +right which means this is not true i can + + align:start position:0% +right which means this is not true i can + + + align:start position:0% +right which means this is not true i can +also have a term for the for partial y + + align:start position:0% +also have a term for the for partial y + + + align:start position:0% +also have a term for the for partial y +partial suggestion so instead of one + + align:start position:0% +partial suggestion so instead of one + + + align:start position:0% +partial suggestion so instead of one +alpha + + align:start position:0% +alpha + + + align:start position:0% +alpha +g plus + + align:start position:0% +g plus + + + align:start position:0% +g plus +the approximation of y so this g plus + + align:start position:0% +the approximation of y so this g plus + + + align:start position:0% +the approximation of y so this g plus +gamma q is another approximation for y + + align:start position:0% +gamma q is another approximation for y + + + align:start position:0% +gamma q is another approximation for y +right + + align:start position:0% +right + + + align:start position:0% +right +i'm trying to perfectly make the analogy + + align:start position:0% +i'm trying to perfectly make the analogy + + + align:start position:0% +i'm trying to perfectly make the analogy +that this looks like that + + align:start position:0% +that this looks like that + + + align:start position:0% +that this looks like that +and this + + align:start position:0% +and this + + + align:start position:0% +and this +looks like that + + align:start position:0% +looks like that + + + align:start position:0% +looks like that +okay but when you're taking the + + align:start position:0% +okay but when you're taking the + + + align:start position:0% +okay but when you're taking the +derivative from that function using the + + align:start position:0% +derivative from that function using the + + + align:start position:0% +derivative from that function using the +y constant yes and then solve this yes + + align:start position:0% +y constant yes and then solve this yes + + + align:start position:0% +y constant yes and then solve this yes +you can actually assume that y is + + align:start position:0% +you can actually assume that y is + + + align:start position:0% +you can actually assume that y is +dependent on alpha + + align:start position:0% +dependent on alpha + + + align:start position:0% +dependent on alpha +as well yeah + + align:start position:0% +as well yeah + + + align:start position:0% +as well yeah +so you could do that okay so you're + + align:start position:0% +so you could do that okay so you're + + + align:start position:0% +so you could do that okay so you're +saying why don't we actually have a + + align:start position:0% +saying why don't we actually have a + + + align:start position:0% +saying why don't we actually have a +different update which has the greater + + align:start position:0% +different update which has the greater + + + align:start position:0% +different update which has the greater +than that + + align:start position:0% +than that + + + align:start position:0% +than that +okay good so um in the case of td 0 or + + align:start position:0% +okay good so um in the case of td 0 or + + + align:start position:0% +okay good so um in the case of td 0 or +dd1 you actually do have that + + align:start position:0% +dd1 you actually do have that + + + align:start position:0% +dd1 you actually do have that +and i think what's true i've actually + + align:start position:0% +and i think what's true i've actually + + + align:start position:0% +and i think what's true i've actually +worked this out a number of years ago + + align:start position:0% +worked this out a number of years ago + + + align:start position:0% +worked this out a number of years ago +but i think it's true that if you start + + align:start position:0% +but i think it's true that if you start + + + align:start position:0% +but i think it's true that if you start +including that + + align:start position:0% +including that + + + align:start position:0% +including that +if you look at the sum over a chain + + align:start position:0% +if you look at the sum over a chain + + + align:start position:0% +if you look at the sum over a chain +the + + align:start position:0% +the + + + align:start position:0% +the +for this standard update with td + + align:start position:0% +for this standard update with td + + + align:start position:0% +for this standard update with td +not the t 0 for instance that those + + align:start position:0% +not the t 0 for instance that those + + + align:start position:0% +not the t 0 for instance that those +terms this term now will actually cancel + + align:start position:0% +terms this term now will actually cancel + + + align:start position:0% +terms this term now will actually cancel +itself out in this term + + align:start position:0% +itself out in this term + + + align:start position:0% +itself out in this term +here + + align:start position:0% +here + + + align:start position:0% +here +for instance it doesn't work it doesn't + + align:start position:0% +for instance it doesn't work it doesn't + + + align:start position:0% +for instance it doesn't work it doesn't +work nicely it would give you it gives + + align:start position:0% +work nicely it would give you it gives + + + align:start position:0% +work nicely it would give you it gives +you back the monte carlo error right it + + align:start position:0% +you back the monte carlo error right it + + + align:start position:0% +you back the monte carlo error right it +doesn't do temporary it doesn't do the + + align:start position:0% +doesn't do temporary it doesn't do the + + + align:start position:0% +doesn't do temporary it doesn't do the +bootstrap + + align:start position:0% +bootstrap + + + align:start position:0% +bootstrap +so basically if you start including that + + align:start position:0% +so basically if you start including that + + + align:start position:0% +so basically if you start including that +then you you do get at least squares + + align:start position:0% +then you you do get at least squares + + + align:start position:0% +then you you do get at least squares +algorithm of course + + align:start position:0% +algorithm of course + + + align:start position:0% +algorithm of course +but it's it's um effectively doing money + + align:start position:0% +but it's it's um effectively doing money + + + align:start position:0% +but it's it's um effectively doing money +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you have to sort of ignore that + + align:start position:0% + + + + align:start position:0% + +all right you're actually saying i'm + + align:start position:0% +all right you're actually saying i'm + + + align:start position:0% +all right you're actually saying i'm +going to believe this estimate + + align:start position:0% +going to believe this estimate + + + align:start position:0% +going to believe this estimate +in order to do that + + align:start position:0% +in order to do that + + + align:start position:0% +in order to do that +okay + + align:start position:0% + + + + align:start position:0% + +several differences if you actually + + align:start position:0% +several differences if you actually + + + align:start position:0% +several differences if you actually +actually want to prove any of these + + align:start position:0% +actually want to prove any of these + + + align:start position:0% +actually want to prove any of these +things + + align:start position:0% +things + + + align:start position:0% +things +i have one example of it though i think + + align:start position:0% +i have one example of it though i think + + + align:start position:0% +i have one example of it though i think +that i put in um + + align:start position:0% +that i put in um + + + align:start position:0% +that i put in um +td one is is creating the side of the + + align:start position:0% +td one is is creating the side of the + + + align:start position:0% +td one is is creating the side of the +notes just to so you see an example the + + align:start position:0% +notes just to so you see an example the + + + align:start position:0% +notes just to so you see an example the +story the rule of the game in temporal + + align:start position:0% +story the rule of the game in temporal + + + align:start position:0% +story the rule of the game in temporal +lobes learning + + align:start position:0% +lobes learning + + + align:start position:0% +lobes learning +derivations improves + + align:start position:0% +derivations improves + + + align:start position:0% +derivations improves +is you start expanding these sums + + align:start position:0% +is you start expanding these sums + + + align:start position:0% +is you start expanding these sums +in terms from time + + align:start position:0% +in terms from time + + + align:start position:0% +in terms from time +n + + align:start position:0% +n + + + align:start position:0% +n +in terms of time n plus one + + align:start position:0% +in terms of time n plus one + + + align:start position:0% +in terms of time n plus one +cancel each other out in a major way + + align:start position:0% +cancel each other out in a major way + + + align:start position:0% +cancel each other out in a major way +and you're left with you know something + + align:start position:0% +and you're left with you know something + + + align:start position:0% +and you're left with you know something +much more compact that's why we call it + + align:start position:0% +much more compact that's why we call it + + + align:start position:0% +much more compact that's why we call it +algebraic trick why these things work + + align:start position:0% +algebraic trick why these things work + + + align:start position:0% +algebraic trick why these things work +okay but + + align:start position:0% +okay but + + + align:start position:0% +okay but +because these are not random + + align:start position:0% +because these are not random + + + align:start position:0% +because these are not random +um samples drawn + + align:start position:0% +um samples drawn + + + align:start position:0% +um samples drawn +one at a time and they're actually + + align:start position:0% +one at a time and they're actually + + + align:start position:0% +one at a time and they're actually +trajectory to relate to each other + + align:start position:0% +trajectory to relate to each other + + + align:start position:0% +trajectory to relate to each other +that's what makes them + + align:start position:0% + + + + align:start position:0% + +okay so we said off policy evaluation + + align:start position:0% +okay so we said off policy evaluation + + + align:start position:0% +okay so we said off policy evaluation +says um execute policy pi one to get um + + align:start position:0% +says um execute policy pi one to get um + + + align:start position:0% +says um execute policy pi one to get um +pi one generates sn + + align:start position:0% +pi one generates sn + + + align:start position:0% +pi one generates sn +am trajectories right + + align:start position:0% +am trajectories right + + + align:start position:0% +am trajectories right +but you're going to do the update + + align:start position:0% +but you're going to do the update + + + align:start position:0% +but you're going to do the update +alpha + + align:start position:0% + + + + align:start position:0% + +alpha plus + + align:start position:0% +alpha plus + + + align:start position:0% +alpha plus +right quickly here gsa + + align:start position:0% +right quickly here gsa + + + align:start position:0% +right quickly here gsa +plus m q i it's going to be an estimator + + align:start position:0% +plus m q i it's going to be an estimator + + + align:start position:0% +plus m q i it's going to be an estimator +of 2 pi 2 + + align:start position:0% +of 2 pi 2 + + + align:start position:0% +of 2 pi 2 +s n plus + + align:start position:0% +s n plus + + + align:start position:0% +s n plus + + align:start position:0% + + + align:start position:0% +um pi 2. + + align:start position:0% +um pi 2. + + + align:start position:0% +um pi 2. +what would pi 2 have done kind of + + align:start position:0% +what would pi 2 have done kind of + + + align:start position:0% +what would pi 2 have done kind of +sn plus 1. + + align:start position:0% + + + + align:start position:0% + +in general multiplied + + align:start position:0% +in general multiplied + + + align:start position:0% +in general multiplied +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so that's a good trick that's + + align:start position:0% +all right so that's a good trick that's + + + align:start position:0% +all right so that's a good trick that's +a really really nice trick let's learn + + align:start position:0% +a really really nice trick let's learn + + + align:start position:0% +a really really nice trick let's learn +about policy one or policy two while we + + align:start position:0% +about policy one or policy two while we + + + align:start position:0% +about policy one or policy two while we +execute policy + + align:start position:0% + + + + align:start position:0% + +okay so what policy two should we learn + + align:start position:0% +okay so what policy two should we learn + + + align:start position:0% +okay so what policy two should we learn +about + + align:start position:0% + + + + align:start position:0% + +again these are + + align:start position:0% +again these are + + + align:start position:0% +again these are +asking the questions if there's our ways + + align:start position:0% +asking the questions if there's our ways + + + align:start position:0% +asking the questions if there's our ways +and there's a specific answer but + + align:start position:0% +and there's a specific answer but + + + align:start position:0% +and there's a specific answer but +there's a better way to ask that + + align:start position:0% +there's a better way to ask that + + + align:start position:0% +there's a better way to ask that +question + + align:start position:0% +question + + + align:start position:0% +question +our ultimate goal is to not to learn + + align:start position:0% +our ultimate goal is to not to learn + + + align:start position:0% +our ultimate goal is to not to learn +about stuff arbitrary high too + + align:start position:0% +about stuff arbitrary high too + + + align:start position:0% +about stuff arbitrary high too +i want to learn about the optimal policy + + align:start position:0% +i want to learn about the optimal policy + + + align:start position:0% +i want to learn about the optimal policy +right + + align:start position:0% + + + + align:start position:0% + +i don't have the optimal policy + + align:start position:0% +i don't have the optimal policy + + + align:start position:0% +i don't have the optimal policy +but i have an estimate of it + + align:start position:0% +but i have an estimate of it + + + align:start position:0% +but i have an estimate of it +so actually a perfectly reasonable + + align:start position:0% +so actually a perfectly reasonable + + + align:start position:0% +so actually a perfectly reasonable +update to do + + align:start position:0% +update to do + + + align:start position:0% +update to do +um + + align:start position:0% +um + + + align:start position:0% +um +and the way you might describe it is + + align:start position:0% +and the way you might describe it is + + + align:start position:0% +and the way you might describe it is +um + + align:start position:0% +um + + + align:start position:0% +um +let's execute and put it in quotes + + align:start position:0% +let's execute and put it in quotes + + + align:start position:0% +let's execute and put it in quotes +because it's not + + align:start position:0% +because it's not + + + align:start position:0% +because it's not +entirely accurate but it's the right + + align:start position:0% +entirely accurate but it's the right + + + align:start position:0% +entirely accurate but it's the right +idea + + align:start position:0% + + + + align:start position:0% + +execute policy one + + align:start position:0% +execute policy one + + + align:start position:0% +execute policy one +but learn about + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and how we can do that well + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +that makes some sense might as well + + align:start position:0% +that makes some sense might as well + + + align:start position:0% +that makes some sense might as well +um as i'm learning + + align:start position:0% +um as i'm learning + + + align:start position:0% +um as i'm learning +always trying to learn about policy + + align:start position:0% +always trying to learn about policy + + + align:start position:0% +always trying to learn about policy +which is optimal with respect to my + + align:start position:0% +which is optimal with respect to my + + + align:start position:0% +which is optimal with respect to my +current estimate + + align:start position:0% +current estimate + + + align:start position:0% +current estimate +j hat + + align:start position:0% +j hat + + + align:start position:0% +j hat +and this algorithm is called keyboarding + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +it's the + + align:start position:0% +it's the + + + align:start position:0% +it's the +crown jewel of the value + + align:start position:0% +crown jewel of the value + + + align:start position:0% +crown jewel of the value +based + + align:start position:0% + + + + align:start position:0% + +methods + + align:start position:0% +methods + + + align:start position:0% +methods +i would say it was the it was the gold + + align:start position:0% +i would say it was the it was the gold + + + align:start position:0% +i would say it was the it was the gold +standard until probably about 90 + + align:start position:0% +standard until probably about 90 + + + align:start position:0% +standard until probably about 90 +or something like that and people + + align:start position:0% +or something like that and people + + + align:start position:0% +or something like that and people +started doing college grading stuff more + + align:start position:0% +started doing college grading stuff more + + + align:start position:0% +started doing college grading stuff more +often + + align:start position:0% +often + + + align:start position:0% +often +okay even even probably halfway through + + align:start position:0% +okay even even probably halfway through + + + align:start position:0% +okay even even probably halfway through +the night because people are still + + align:start position:0% +the night because people are still + + + align:start position:0% +the night because people are still +mostly about writing papers about q + + align:start position:0% +mostly about writing papers about q + + + align:start position:0% +mostly about writing papers about q +learning um + + align:start position:0% + + + + align:start position:0% + +is based on data from five one + + align:start position:0% +is based on data from five one + + + align:start position:0% +is based on data from five one +but if i always make my update + + align:start position:0% +but if i always make my update + + + align:start position:0% +but if i always make my update +making this this update that it really + + align:start position:0% +making this this update that it really + + + align:start position:0% +making this this update that it really +is + + align:start position:0% +is + + + align:start position:0% +is +learning about + + align:start position:0% +learning about + + + align:start position:0% +learning about +how to + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +okay good so there's a couple ways that + + align:start position:0% +okay good so there's a couple ways that + + + align:start position:0% +okay good so there's a couple ways that +i can um do this so in the policy the + + align:start position:0% +i can um do this so in the policy the + + + align:start position:0% +i can um do this so in the policy the +simple + + align:start position:0% +simple + + + align:start position:0% +simple +policy + + align:start position:0% +policy + + + align:start position:0% +policy +iteration you + + align:start position:0% +iteration you + + + align:start position:0% +iteration you +evaluate for a long time and then you + + align:start position:0% +evaluate for a long time and then you + + + align:start position:0% +evaluate for a long time and then you +you make an + + align:start position:0% +you make an + + + align:start position:0% +you make an +update you evaluate for a long time to + + align:start position:0% +update you evaluate for a long time to + + + align:start position:0% +update you evaluate for a long time to +make an update + + align:start position:0% +make an update + + + align:start position:0% +make an update +this is always sort of updating right + + align:start position:0% +this is always sort of updating right + + + align:start position:0% +this is always sort of updating right +that's the type + + align:start position:0% +that's the type + + + align:start position:0% +that's the type +and then + + align:start position:0% +and then + + + align:start position:0% +and then +you can prove that it's still a sound + + align:start position:0% +you can prove that it's still a sound + + + align:start position:0% +you can prove that it's still a sound +algorithm despite doing that but yes + + align:start position:0% +algorithm despite doing that but yes + + + align:start position:0% +algorithm despite doing that but yes +this is always sort of updating it's + + align:start position:0% +this is always sort of updating it's + + + align:start position:0% +this is always sort of updating it's +it's uh it's policy as it goes + + align:start position:0% + + + + align:start position:0% + +compared to this which is more of the + + align:start position:0% +compared to this which is more of the + + + align:start position:0% +compared to this which is more of the +to learn about how to tie two for a + + align:start position:0% +to learn about how to tie two for a + + + align:start position:0% +to learn about how to tie two for a +while stop + + align:start position:0% +while stop + + + align:start position:0% +while stop +by three throw livestock + + align:start position:0% + + + + align:start position:0% + +okay good so what is it + + align:start position:0% +okay good so what is it + + + align:start position:0% +okay good so what is it +um + + align:start position:0% +um + + + align:start position:0% +um +what's required for someone for a q + + align:start position:0% +what's required for someone for a q + + + align:start position:0% +what's required for someone for a q +learning algorithm to converge + + align:start position:0% +learning algorithm to converge + + + align:start position:0% +learning algorithm to converge +so even for this however + + align:start position:0% +so even for this however + + + align:start position:0% +so even for this however +in order for pi + + align:start position:0% +in order for pi + + + align:start position:0% +in order for pi +1 to really teach me everything there is + + align:start position:0% +1 to really teach me everything there is + + + align:start position:0% +1 to really teach me everything there is +to know about i2 + + align:start position:0% +to know about i2 + + + align:start position:0% +to know about i2 +there's some + + align:start position:0% +there's some + + + align:start position:0% +there's some +important + + align:start position:0% +important + + + align:start position:0% +important +feature which is that pi 1 and pi 2 have + + align:start position:0% +feature which is that pi 1 and pi 2 have + + + align:start position:0% +feature which is that pi 1 and pi 2 have +better pick + + align:start position:0% +better pick + + + align:start position:0% +better pick +same actions with some low probability + + align:start position:0% + + + + align:start position:0% + +so off policy works + + align:start position:0% + + + + align:start position:0% + +let's just even think about i'll even + + align:start position:0% +let's just even think about i'll even + + + align:start position:0% +let's just even think about i'll even +restrict my + + align:start position:0% +restrict my + + + align:start position:0% +restrict my +session first in the + + align:start position:0% +session first in the + + + align:start position:0% +session first in the +state discrete actions the markov + + align:start position:0% + + + + align:start position:0% + +confirmations + + align:start position:0% +confirmations + + + align:start position:0% +confirmations +off policy + + align:start position:0% +off policy + + + align:start position:0% +off policy +works + + align:start position:0% +works + + + align:start position:0% +works +if + + align:start position:0% +if + + + align:start position:0% +if +pi one + + align:start position:0% +pi one + + + align:start position:0% +pi one +takes in general all + + align:start position:0% +takes in general all + + + align:start position:0% +takes in general all +state action pairs + + align:start position:0% + + + + align:start position:0% + +with some small probability + + align:start position:0% + + + + align:start position:0% + +all right if pi + + align:start position:0% +all right if pi + + + align:start position:0% +all right if pi + + align:start position:0% + + + align:start position:0% +took + + align:start position:0% +took + + + align:start position:0% +took +action 3 and state 1 and pi 1 never did + + align:start position:0% +action 3 and state 1 and pi 1 never did + + + align:start position:0% +action 3 and state 1 and pi 1 never did +there's no way i'm going to learn + + align:start position:0% +there's no way i'm going to learn + + + align:start position:0% +there's no way i'm going to learn +really what pie 2 is all about + + align:start position:0% + + + + align:start position:0% + +i like that + + align:start position:0% + + + + align:start position:0% + +okay so how do you do that if you just + + align:start position:0% +okay so how do you do that if you just + + + align:start position:0% +okay so how do you do that if you just +if you're thinking about + + align:start position:0% +if you're thinking about + + + align:start position:0% +if you're thinking about +greedy policies on our robot if you've + + align:start position:0% +greedy policies on our robot if you've + + + align:start position:0% +greedy policies on our robot if you've +got your current estimate of the value + + align:start position:0% +got your current estimate of the value + + + align:start position:0% +got your current estimate of the value +and you do + + align:start position:0% +and you do + + + align:start position:0% +and you do +the most aggressive action on the + + align:start position:0% +the most aggressive action on the + + + align:start position:0% +the most aggressive action on the +acrobat i'll tell you what's going to + + align:start position:0% +acrobat i'll tell you what's going to + + + align:start position:0% +acrobat i'll tell you what's going to +happen + + align:start position:0% +happen + + + align:start position:0% +happen +you're going to visit + + align:start position:0% +you're going to visit + + + align:start position:0% +you're going to visit +the state's near the bottom when you + + align:start position:0% +the state's near the bottom when you + + + align:start position:0% +the state's near the bottom when you +start learning a lot + + align:start position:0% +start learning a lot + + + align:start position:0% +start learning a lot +right and you're never going to visit + + align:start position:0% +right and you're never going to visit + + + align:start position:0% +right and you're never going to visit +the states at the time right when you're + + align:start position:0% +the states at the time right when you're + + + align:start position:0% +the states at the time right when you're +learning + + align:start position:0% +learning + + + align:start position:0% +learning +so how are you going to get around that + + align:start position:0% +so how are you going to get around that + + + align:start position:0% +so how are you going to get around that +in the acrobat and the acronym is top + + align:start position:0% +in the acrobat and the acronym is top + + + align:start position:0% +in the acrobat and the acronym is top +actually right + + align:start position:0% +actually right + + + align:start position:0% +actually right +but the idea is + + align:start position:0% +but the idea is + + + align:start position:0% +but the idea is +you better add some randomness right so + + align:start position:0% +you better add some randomness right so + + + align:start position:0% +you better add some randomness right so +that you explore more and more state and + + align:start position:0% +that you explore more and more state and + + + align:start position:0% +that you explore more and more state and +actions + + align:start position:0% +actions + + + align:start position:0% +actions +and the hope is that if you had enough + + align:start position:0% +and the hope is that if you had enough + + + align:start position:0% +and the hope is that if you had enough +for a long enough time you're going to + + align:start position:0% +for a long enough time you're going to + + + align:start position:0% +for a long enough time you're going to +learn better and better policies and + + align:start position:0% +learn better and better policies and + + + align:start position:0% +learn better and better policies and +you're going to find your way up to the + + align:start position:0% +you're going to find your way up to the + + + align:start position:0% +you're going to find your way up to the +top + + align:start position:0% +top + + + align:start position:0% +top +so the acrobat is actually almost + + align:start position:0% +so the acrobat is actually almost + + + align:start position:0% +so the acrobat is actually almost +as hard as it gets with these things + + align:start position:0% +as hard as it gets with these things + + + align:start position:0% +as hard as it gets with these things +right where you really have to find your + + align:start position:0% +right where you really have to find your + + + align:start position:0% +right where you really have to find your +way into this region to learn about the + + align:start position:0% +way into this region to learn about the + + + align:start position:0% +way into this region to learn about the +region + + align:start position:0% +region + + + align:start position:0% +region +um + + align:start position:0% +um + + + align:start position:0% +um +in fact my beef with the enforcement + + align:start position:0% +in fact my beef with the enforcement + + + align:start position:0% +in fact my beef with the enforcement +learning community is that they they + + align:start position:0% +learning community is that they they + + + align:start position:0% +learning community is that they they +learn only to + + align:start position:0% +learn only to + + + align:start position:0% +learn only to +swing up to some threshold they never + + align:start position:0% +swing up to some threshold they never + + + align:start position:0% +swing up to some threshold they never +actually balance at the top + + align:start position:0% +actually balance at the top + + + align:start position:0% +actually balance at the top +if you look there's lots of pages + + align:start position:0% +if you look there's lots of pages + + + align:start position:0% +if you look there's lots of pages +there's countless papers written about + + align:start position:0% +there's countless papers written about + + + align:start position:0% +there's countless papers written about +being personal learning q learning for + + align:start position:0% +being personal learning q learning for + + + align:start position:0% +being personal learning q learning for +um the acrobatic things like this and to + + align:start position:0% +um the acrobatic things like this and to + + + align:start position:0% +um the acrobatic things like this and to +ever actually solve the problem you just + + align:start position:0% +ever actually solve the problem you just + + + align:start position:0% +ever actually solve the problem you just +try to do it who are the top but + + align:start position:0% +try to do it who are the top but + + + align:start position:0% +try to do it who are the top but +they don't do it they just get off the + + align:start position:0% +they don't do it they just get off the + + + align:start position:0% +they don't do it they just get off the +side because it is sort of a tough case + + align:start position:0% + + + + align:start position:0% + +so how do you do it so yeah like i said + + align:start position:0% +so how do you do it so yeah like i said + + + align:start position:0% +so how do you do it so yeah like i said +in order to start exploring that space + + align:start position:0% +in order to start exploring that space + + + align:start position:0% +in order to start exploring that space +you better add some + + align:start position:0% +you better add some + + + align:start position:0% +you better add some +some randomness + + align:start position:0% +some randomness + + + align:start position:0% +some randomness +so + + align:start position:0% +so + + + align:start position:0% +so +one of the standard approaches is these + + align:start position:0% +one of the standard approaches is these + + + align:start position:0% +one of the standard approaches is these +epsilon ingredients + + align:start position:0% + + + + align:start position:0% + +so i said let's make pi2 exactly the + + align:start position:0% +so i said let's make pi2 exactly the + + + align:start position:0% +so i said let's make pi2 exactly the +minimizing thing + + align:start position:0% +minimizing thing + + + align:start position:0% +minimizing thing +that's true but if you execute that + + align:start position:0% +that's true but if you execute that + + + align:start position:0% +that's true but if you execute that +you're probably gonna + + align:start position:0% +you're probably gonna + + + align:start position:0% +you're probably gonna +get stuck + + align:start position:0% +get stuck + + + align:start position:0% +get stuck +much better to + + align:start position:0% +much better to + + + align:start position:0% +much better to +execute a policy + + align:start position:0% + + + + align:start position:0% + +by us + + align:start position:0% +by us + + + align:start position:0% +by us +for the let's say + + align:start position:0% +for the let's say + + + align:start position:0% +for the let's say +policy i care about i'm going to execute + + align:start position:0% +policy i care about i'm going to execute + + + align:start position:0% +policy i care about i'm going to execute +with probability + + align:start position:0% +with probability + + + align:start position:0% +with probability +um + + align:start position:0% +um + + + align:start position:0% +um +sort of to flip a coin if uh + + align:start position:0% +sort of to flip a coin if uh + + + align:start position:0% +sort of to flip a coin if uh +pull a random number between zero and + + align:start position:0% +pull a random number between zero and + + + align:start position:0% +pull a random number between zero and +one if it's greater than epsilon then go + + align:start position:0% +one if it's greater than epsilon then go + + + align:start position:0% +one if it's greater than epsilon then go +ahead and execute the policy that you're + + align:start position:0% +ahead and execute the policy that you're + + + align:start position:0% +ahead and execute the policy that you're +trying to learn about + + align:start position:0% +trying to learn about + + + align:start position:0% +trying to learn about +but + + align:start position:0% +but + + + align:start position:0% +but +execute some random action + + align:start position:0% + + + + align:start position:0% + +otherwise + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +every time i'm every dt i'm going to + + align:start position:0% +every time i'm every dt i'm going to + + + align:start position:0% +every time i'm every dt i'm going to +flip a coin keep it well not a point + + align:start position:0% +flip a coin keep it well not a point + + + align:start position:0% +flip a coin keep it well not a point +hundred times + + align:start position:0% + + + + align:start position:0% + +a continuous thing if it comes out less + + align:start position:0% +a continuous thing if it comes out less + + + align:start position:0% +a continuous thing if it comes out less +than + + align:start position:0% +than + + + align:start position:0% +than +then + + align:start position:0% +then + + + align:start position:0% +then +um + + align:start position:0% +um + + + align:start position:0% +um +epsilon i'm going to do a random action + + align:start position:0% +epsilon i'm going to do a random action + + + align:start position:0% +epsilon i'm going to do a random action +just forget about my current policy pick + + align:start position:0% +just forget about my current policy pick + + + align:start position:0% +just forget about my current policy pick +a random action the uniform distribution + + align:start position:0% +a random action the uniform distribution + + + align:start position:0% +a random action the uniform distribution +over + + align:start position:0% +over + + + align:start position:0% +over +actions + + align:start position:0% +actions + + + align:start position:0% +actions +otherwise i'll take this + + align:start position:0% +otherwise i'll take this + + + align:start position:0% +otherwise i'll take this +the action from my policy + + align:start position:0% +the action from my policy + + + align:start position:0% +the action from my policy +and by virtue of having this off policy + + align:start position:0% +and by virtue of having this off policy + + + align:start position:0% +and by virtue of having this off policy +learning things i can still learn about + + align:start position:0% +learning things i can still learn about + + + align:start position:0% +learning things i can still learn about +pi too even about taking this pi epsilon + + align:start position:0% + + + + align:start position:0% + +but i have the advantage of exploring + + align:start position:0% +but i have the advantage of exploring + + + align:start position:0% +but i have the advantage of exploring +all the state nations + + align:start position:0% + + + + align:start position:0% + +he's + + align:start position:0% + + + + align:start position:0% + +there's a couple different candidates um + + align:start position:0% +there's a couple different candidates um + + + align:start position:0% +there's a couple different candidates um +the softmax is another one people use a + + align:start position:0% +the softmax is another one people use a + + + align:start position:0% +the softmax is another one people use a +lot + + align:start position:0% + + + + align:start position:0% + +and a lot of people i mean in the off + + align:start position:0% +and a lot of people i mean in the off + + + align:start position:0% +and a lot of people i mean in the off +policy sense it's actually quite robust + + align:start position:0% +policy sense it's actually quite robust + + + align:start position:0% +policy sense it's actually quite robust +right so + + align:start position:0% +right so + + + align:start position:0% +right so +um a lot of people will talk about um + + align:start position:0% +um a lot of people will talk about um + + + align:start position:0% +um a lot of people will talk about um +using behavioral policy which is just + + align:start position:0% +using behavioral policy which is just + + + align:start position:0% +using behavioral policy which is just +sort of something that trump is designed + + align:start position:0% +sort of something that trump is designed + + + align:start position:0% +sort of something that trump is designed +to explore the state space uh actually + + align:start position:0% +to explore the state space uh actually + + + align:start position:0% +to explore the state space uh actually +my candidate for behavioral policy + + align:start position:0% +my candidate for behavioral policy + + + align:start position:0% +my candidate for behavioral policy +something like an rrt + + align:start position:0% +something like an rrt + + + align:start position:0% +something like an rrt +right we should really try to do + + align:start position:0% +right we should really try to do + + + align:start position:0% +right we should really try to do +something that gets me into all areas of + + align:start position:0% +something that gets me into all areas of + + + align:start position:0% +something that gets me into all areas of +state space for instance + + align:start position:0% +state space for instance + + + align:start position:0% +state space for instance +um and then maybe that's a good way to + + align:start position:0% +um and then maybe that's a good way to + + + align:start position:0% +um and then maybe that's a good way to +design to sample these state action + + align:start position:0% +design to sample these state action + + + align:start position:0% +design to sample these state action +pairs + + align:start position:0% +pairs + + + align:start position:0% +pairs +and all the while you try to learn about + + align:start position:0% +and all the while you try to learn about + + + align:start position:0% +and all the while you try to learn about +i2 so it is robust + + align:start position:0% + + + + align:start position:0% + +when i say works here i have to be a + + align:start position:0% +when i say works here i have to be a + + + align:start position:0% +when i say works here i have to be a +little careful + + align:start position:0% +little careful + + + align:start position:0% +little careful +this is + + align:start position:0% +this is + + + align:start position:0% +this is +only for the mvp + + align:start position:0% +only for the mvp + + + align:start position:0% +only for the mvp +that's really guaranteed to work there's + + align:start position:0% +that's really guaranteed to work there's + + + align:start position:0% +that's really guaranteed to work there's +more recent work + + align:start position:0% + + + + align:start position:0% + +doing off policy and function + + align:start position:0% +doing off policy and function + + + align:start position:0% +doing off policy and function +approximators + + align:start position:0% +approximators + + + align:start position:0% +approximators +and you can do that + + align:start position:0% + + + + align:start position:0% + +i don't want to bear you guys + + align:start position:0% +i don't want to bear you guys + + + align:start position:0% +i don't want to bear you guys +with um + + align:start position:0% +with um + + + align:start position:0% +with um +but you can do + + align:start position:0% +but you can do + + + align:start position:0% +but you can do +off policy + + align:start position:0% + + + + align:start position:0% + +function with linear function + + align:start position:0% +function with linear function + + + align:start position:0% +function with linear function +approximators safely + + align:start position:0% + + + + align:start position:0% + +using a important sampling + + align:start position:0% + + + + align:start position:0% + +let's work by doing a pre-cut + + align:start position:0% + + + + align:start position:0% + +the basic idea is you have to if your + + align:start position:0% +the basic idea is you have to if your + + + align:start position:0% +the basic idea is you have to if your +policy is changing like this thing is + + align:start position:0% +policy is changing like this thing is + + + align:start position:0% +policy is changing like this thing is +changing over time you better wait your + + align:start position:0% +changing over time you better wait your + + + align:start position:0% +changing over time you better wait your +updates based on the relative + + align:start position:0% + + + + align:start position:0% + +the probability of taking this action + + align:start position:0% +the probability of taking this action + + + align:start position:0% +the probability of taking this action +from one step and the next q a by two + + align:start position:0% +from one step and the next q a by two + + + align:start position:0% +from one step and the next q a by two +and that's still multiplied either by + + align:start position:0% +and that's still multiplied either by + + + align:start position:0% +and that's still multiplied either by +two will never take that action + + align:start position:0% + + + + align:start position:0% + +so i think it's good the thing that has + + align:start position:0% +so i think it's good the thing that has + + + align:start position:0% +so i think it's good the thing that has +to happen is that pi two has to + + align:start position:0% +to happen is that pi two has to + + + align:start position:0% +to happen is that pi two has to +be well-defined for every possible step + + align:start position:0% +be well-defined for every possible step + + + align:start position:0% +be well-defined for every possible step +okay so the key thing that q pi 2 is + + align:start position:0% +okay so the key thing that q pi 2 is + + + align:start position:0% +okay so the key thing that q pi 2 is +take a certain from a certain state take + + align:start position:0% +take a certain from a certain state take + + + align:start position:0% +take a certain from a certain state take +a certain action then execute + + align:start position:0% +a certain action then execute + + + align:start position:0% +a certain action then execute +yes okay sorry i lost that definition + + align:start position:0% +yes okay sorry i lost that definition + + + align:start position:0% +yes okay sorry i lost that definition +okay sorry + + align:start position:0% +okay sorry + + + align:start position:0% +okay sorry +yes so cool + + align:start position:0% +yes so cool + + + align:start position:0% +yes so cool +so i think that still works + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +so this is good so let me tell you + + align:start position:0% +so this is good so let me tell you + + + align:start position:0% +so this is good so let me tell you +where where you are so far so we've now + + align:start position:0% +where where you are so far so we've now + + + align:start position:0% +where where you are so far so we've now +switched from doing temporal difference + + align:start position:0% +switched from doing temporal difference + + + align:start position:0% +switched from doing temporal difference +learning um value functions to tempo + + align:start position:0% +learning um value functions to tempo + + + align:start position:0% +learning um value functions to tempo +difference function learning and + + align:start position:0% +difference function learning and + + + align:start position:0% +difference function learning and +q functions and the major thing we got + + align:start position:0% +q functions and the major thing we got + + + align:start position:0% +q functions and the major thing we got +out of that was + + align:start position:0% +out of that was + + + align:start position:0% +out of that was +that we could do this off policy + + align:start position:0% + + + + align:start position:0% + +you put it all together into my back + + align:start position:0% +you put it all together into my back + + + align:start position:0% +you put it all together into my back +into my policy consideration + + align:start position:0% +into my policy consideration + + + align:start position:0% +into my policy consideration +diagram + + align:start position:0% +diagram + + + align:start position:0% +diagram +and what we have we've defined the + + align:start position:0% +and what we have we've defined the + + + align:start position:0% +and what we have we've defined the +policy evaluation that's the tb lambda + + align:start position:0% +policy evaluation that's the tb lambda + + + align:start position:0% +policy evaluation that's the tb lambda +we defined now our our update which + + align:start position:0% +we defined now our our update which + + + align:start position:0% +we defined now our our update which +could be this in the general sense + + align:start position:0% +could be this in the general sense + + + align:start position:0% +could be this in the general sense +this one is + + align:start position:0% + + + + align:start position:0% + +if i use pi one again if i really did on + + align:start position:0% +if i use pi one again if i really did on + + + align:start position:0% +if i use pi one again if i really did on +policy if i use pi one everywhere + + align:start position:0% +policy if i use pi one everywhere + + + align:start position:0% +policy if i use pi one everywhere +while i'm executing pi one then this + + align:start position:0% +while i'm executing pi one then this + + + align:start position:0% +while i'm executing pi one then this +would be called sarsa + + align:start position:0% + + + + align:start position:0% + +on policy key learning on policy + + align:start position:0% +on policy key learning on policy + + + align:start position:0% +on policy key learning on policy +updating and and q learning is this is + + align:start position:0% +updating and and q learning is this is + + + align:start position:0% +updating and and q learning is this is +where you use the mineral grade + + align:start position:0% +where you use the mineral grade + + + align:start position:0% +where you use the mineral grade +and what we know + + align:start position:0% +and what we know + + + align:start position:0% +and what we know +people have proven + + align:start position:0% +people have proven + + + align:start position:0% +people have proven +the algorithms were in use for years and + + align:start position:0% +the algorithms were in use for years and + + + align:start position:0% +the algorithms were in use for years and +years and years before it was actually + + align:start position:0% +years and years before it was actually + + + align:start position:0% +years and years before it was actually +proven that they converted even in the + + align:start position:0% +proven that they converted even in the + + + align:start position:0% +proven that they converted even in the +tabular case where you're where you have + + align:start position:0% +tabular case where you're where you have + + + align:start position:0% +tabular case where you're where you have +finite state actions but now we know + + align:start position:0% +finite state actions but now we know + + + align:start position:0% +finite state actions but now we know +that + + align:start position:0% +that + + + align:start position:0% +that +this thing is guaranteed to converge to + + align:start position:0% +this thing is guaranteed to converge to + + + align:start position:0% +this thing is guaranteed to converge to +the optimal policy that policy iteration + + align:start position:0% +the optimal policy that policy iteration + + + align:start position:0% +the optimal policy that policy iteration +even if it's updated on every step + + align:start position:0% +even if it's updated on every step + + + align:start position:0% +even if it's updated on every step +is going to converge to the optimal + + align:start position:0% +is going to converge to the optimal + + + align:start position:0% +is going to converge to the optimal +policy and the optimal + + align:start position:0% +policy and the optimal + + + align:start position:0% +policy and the optimal +q function given that all state action + + align:start position:0% +q function given that all state action + + + align:start position:0% +q function given that all state action +terms are visible + + align:start position:0% +terms are visible + + + align:start position:0% +terms are visible +in the tabular case okay + + align:start position:0% + + + + align:start position:0% + +if we go to function approximation um + + align:start position:0% +if we go to function approximation um + + + align:start position:0% +if we go to function approximation um +if you just do policy evaluation but not + + align:start position:0% +if you just do policy evaluation but not + + + align:start position:0% +if you just do policy evaluation but not +update + + align:start position:0% +update + + + align:start position:0% +update +then we have a + + align:start position:0% +then we have a + + + align:start position:0% +then we have a +an example where where + + align:start position:0% +an example where where + + + align:start position:0% +an example where where +this is actually in in + + align:start position:0% +this is actually in in + + + align:start position:0% +this is actually in in +two or something like this + + align:start position:0% +two or something like this + + + align:start position:0% +two or something like this +ii + + align:start position:0% + + + + align:start position:0% + +and finally we finally proved that all + + align:start position:0% +and finally we finally proved that all + + + align:start position:0% +and finally we finally proved that all +policy was linear function approximation + + align:start position:0% +policy was linear function approximation + + + align:start position:0% +policy was linear function approximation +would + + align:start position:0% +would + + + align:start position:0% +would +converge when the cup when the policy is + + align:start position:0% +converge when the cup when the policy is + + + align:start position:0% +converge when the cup when the policy is +not changing + + align:start position:0% +not changing + + + align:start position:0% +not changing +no control + + align:start position:0% +no control + + + align:start position:0% +no control +so the thing i need to give you before + + align:start position:0% +so the thing i need to give you before + + + align:start position:0% +so the thing i need to give you before +we + + align:start position:0% +we + + + align:start position:0% +we +consider this a complete + + align:start position:0% +consider this a complete + + + align:start position:0% +consider this a complete +story here is can we do + + align:start position:0% +story here is can we do + + + align:start position:0% +story here is can we do +off policy learning + + align:start position:0% +off policy learning + + + align:start position:0% +off policy learning +right can we can we do our policy + + align:start position:0% +right can we can we do our policy + + + align:start position:0% +right can we can we do our policy +improvement update + + align:start position:0% +improvement update + + + align:start position:0% +improvement update +stably with function approximation + + align:start position:0% +stably with function approximation + + + align:start position:0% +stably with function approximation +okay and the the algorithm we have for + + align:start position:0% +okay and the the algorithm we have for + + + align:start position:0% +okay and the the algorithm we have for +that is our least squares policy + + align:start position:0% +that is our least squares policy + + + align:start position:0% +that is our least squares policy +iteration + + align:start position:0% + + + + align:start position:0% + +remember these squares double difference + + align:start position:0% +remember these squares double difference + + + align:start position:0% +remember these squares double difference +right + + align:start position:0% +right + + + align:start position:0% +right +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +the idea was that + + align:start position:0% +the idea was that + + + align:start position:0% +the idea was that +if we look at the stationary update + + align:start position:0% + + + + align:start position:0% + +i look at the stationary update if i + + align:start position:0% +i look at the stationary update if i + + + align:start position:0% +i look at the stationary update if i +were to run an entire + + align:start position:0% +were to run an entire + + + align:start position:0% +were to run an entire +batch of i mean the big idea that you + + align:start position:0% +batch of i mean the big idea that you + + + align:start position:0% +batch of i mean the big idea that you +can do with these squares is that we're + + align:start position:0% +can do with these squares is that we're + + + align:start position:0% +can do with these squares is that we're +going to try to reuse all that we're not + + align:start position:0% +going to try to reuse all that we're not + + + align:start position:0% +going to try to reuse all that we're not +going to just make a single update spit + + align:start position:0% +going to just make a single update spit + + + align:start position:0% +going to just make a single update spit +it out throw it away we're going to + + align:start position:0% +it out throw it away we're going to + + + align:start position:0% +it out throw it away we're going to +remember a bunch of old + + align:start position:0% +remember a bunch of old + + + align:start position:0% +remember a bunch of old +state action pairs and trying to make a + + align:start position:0% +state action pairs and trying to make a + + + align:start position:0% +state action pairs and trying to make a +least squares update which does the same + + align:start position:0% +least squares update which does the same + + + align:start position:0% +least squares update which does the same +thing as development + + align:start position:0% +thing as development + + + align:start position:0% +thing as development +in the monte carlo sense it's easy it's + + align:start position:0% +in the monte carlo sense it's easy it's + + + align:start position:0% +in the monte carlo sense it's easy it's +just function approximation but with + + align:start position:0% +just function approximation but with + + + align:start position:0% +just function approximation but with +this td term floating floating around + + align:start position:0% +this td term floating floating around + + + align:start position:0% +this td term floating floating around +it's harder to come up with these + + align:start position:0% +it's harder to come up with these + + + align:start position:0% +it's harder to come up with these +squares be this + + align:start position:0% +squares be this + + + align:start position:0% +squares be this +and in the + + align:start position:0% +and in the + + + align:start position:0% +and in the +lstb case + + align:start position:0% +lstb case + + + align:start position:0% +lstb case +the story was we could uh + + align:start position:0% +the story was we could uh + + + align:start position:0% +the story was we could uh +we could build up a matrix um + + align:start position:0% + + + + align:start position:0% + +using + + align:start position:0% +using + + + align:start position:0% +using +something that looked like + + align:start position:0% + + + + align:start position:0% + +5s + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +sum of these terms + + align:start position:0% + + + + align:start position:0% + +you know if i did + + align:start position:0% +you know if i did + + + align:start position:0% +you know if i did +this least square solution + + align:start position:0% +this least square solution + + + align:start position:0% +this least square solution +or i could invert that carefully with + + align:start position:0% +or i could invert that carefully with + + + align:start position:0% +or i could invert that carefully with +svd or something like that then what i + + align:start position:0% +svd or something like that then what i + + + align:start position:0% +svd or something like that then what i +get out is the + + align:start position:0% + + + + align:start position:0% + +jumps immediately + + align:start position:0% + + + + align:start position:0% + +to the steady state solution + + align:start position:0% + + + + align:start position:0% + +of td brandon + + align:start position:0% + + + + align:start position:0% + +so this is essentially the + + align:start position:0% +so this is essentially the + + + align:start position:0% +so this is essentially the +big piece of the td lambda update + + align:start position:0% +big piece of the td lambda update + + + align:start position:0% +big piece of the td lambda update +um broken into the front depends on + + align:start position:0% +um broken into the front depends on + + + align:start position:0% +um broken into the front depends on +alpha part it doesn't depend on alpha + + align:start position:0% +alpha part it doesn't depend on alpha + + + align:start position:0% +alpha part it doesn't depend on alpha +i can write my batch + + align:start position:0% +i can write my batch + + + align:start position:0% +i can write my batch +td lambda update as + + align:start position:0% +td lambda update as + + + align:start position:0% +td lambda update as +alpha equals alpha plus + + align:start position:0% +alpha equals alpha plus + + + align:start position:0% +alpha equals alpha plus +gamma alpha + + align:start position:0% +gamma alpha + + + align:start position:0% +gamma alpha +and i can solve for that at steady state + + align:start position:0% +and i can solve for that at steady state + + + align:start position:0% +and i can solve for that at steady state +basis + + align:start position:0% + + + + align:start position:0% + +all right so least squares policy least + + align:start position:0% +all right so least squares policy least + + + align:start position:0% +all right so least squares policy least +squares temporal difference learning is + + align:start position:0% +squares temporal difference learning is + + + align:start position:0% +squares temporal difference learning is +about reusing lots of trajectories to + + align:start position:0% +about reusing lots of trajectories to + + + align:start position:0% +about reusing lots of trajectories to +make a single update that was going to + + align:start position:0% +make a single update that was going to + + + align:start position:0% +make a single update that was going to +jump right to the + + align:start position:0% +jump right to the + + + align:start position:0% +jump right to the +case where + + align:start position:0% + + + + align:start position:0% + +the temporal difference learning would + + align:start position:0% +the temporal difference learning would + + + align:start position:0% +the temporal difference learning would +have gotten to it we just replayed it a + + align:start position:0% +have gotten to it we just replayed it a + + + align:start position:0% +have gotten to it we just replayed it a +bunch of times + + align:start position:0% + + + + align:start position:0% + +now the question is + + align:start position:0% + + + + align:start position:0% + +the policy is going to be moving + + align:start position:0% +the policy is going to be moving + + + align:start position:0% +the policy is going to be moving +while we're doing this + + align:start position:0% +while we're doing this + + + align:start position:0% +while we're doing this +how can we + + align:start position:0% +how can we + + + align:start position:0% +how can we +do + + align:start position:0% +do + + + align:start position:0% +do +the sort of least squares method + + align:start position:0% +the sort of least squares method + + + align:start position:0% +the sort of least squares method +to do a policy iteration + + align:start position:0% + + + + align:start position:0% + +again + + align:start position:0% +again + + + align:start position:0% +again +the trick is pretty simple + + align:start position:0% +the trick is pretty simple + + + align:start position:0% +the trick is pretty simple +it's learning we're just going to learn + + align:start position:0% +it's learning we're just going to learn + + + align:start position:0% +it's learning we're just going to learn +the q function instead it's the biggest + + align:start position:0% +the q function instead it's the biggest + + + align:start position:0% +the q function instead it's the biggest +trick + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so in order to do + + align:start position:0% +so in order to do + + + align:start position:0% +so in order to do +control not just the value of single + + align:start position:0% +control not just the value of single + + + align:start position:0% +control not just the value of single +policy but actually try to find the + + align:start position:0% +policy but actually try to find the + + + align:start position:0% +policy but actually try to find the +optimal policy + + align:start position:0% + + + + align:start position:0% + +first thing we have to do is figure out + + align:start position:0% +first thing we have to do is figure out + + + align:start position:0% +first thing we have to do is figure out +how to do + + align:start position:0% +how to do + + + align:start position:0% +how to do +lstd on a q function okay + + align:start position:0% + + + + align:start position:0% + +and it turns out + + align:start position:0% +and it turns out + + + align:start position:0% +and it turns out +it's a little harder + + align:start position:0% + + + + align:start position:0% + +it turns out if you uh + + align:start position:0% +it turns out if you uh + + + align:start position:0% +it turns out if you uh +keep along a matrix in exactly the same + + align:start position:0% +keep along a matrix in exactly the same + + + align:start position:0% +keep along a matrix in exactly the same +form as we did in least squares + + align:start position:0% +form as we did in least squares + + + align:start position:0% +form as we did in least squares +temporal difference learning + + align:start position:0% +temporal difference learning + + + align:start position:0% +temporal difference learning +but now we do everything with + + align:start position:0% +but now we do everything with + + + align:start position:0% +but now we do everything with +functions of smt + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +this whole time we're representing our q + + align:start position:0% +this whole time we're representing our q + + + align:start position:0% +this whole time we're representing our q +function + + align:start position:0% + + + + align:start position:0% + +q hat + + align:start position:0% +q hat + + + align:start position:0% +q hat +is now + + align:start position:0% +is now + + + align:start position:0% +is now +a linear combination + + align:start position:0% + + + + align:start position:0% + +of nonlinear basis functions on sma + + align:start position:0% + + + + align:start position:0% + +i tried to put a transpose with my + + align:start position:0% +i tried to put a transpose with my + + + align:start position:0% +i tried to put a transpose with my +poorly + + align:start position:0% +poorly + + + align:start position:0% +poorly +throughout everything + + align:start position:0% +throughout everything + + + align:start position:0% +throughout everything +so you're saying this one of these + + align:start position:0% +so you're saying this one of these + + + align:start position:0% +so you're saying this one of these +shouldn't be cancelled + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +good so i'm gonna + + align:start position:0% +good so i'm gonna + + + align:start position:0% +good so i'm gonna +flip + + align:start position:0% +flip + + + align:start position:0% +flip +this one + + align:start position:0% +this one + + + align:start position:0% +this one +i wrote this whole update as the + + align:start position:0% +i wrote this whole update as the + + + align:start position:0% +i wrote this whole update as the +transpose of the other of what i just + + align:start position:0% +transpose of the other of what i just + + + align:start position:0% +transpose of the other of what i just +read + + align:start position:0% + + + + align:start position:0% + +well actually it's um + + align:start position:0% +well actually it's um + + + align:start position:0% +well actually it's um +the alpha is really not there + + align:start position:0% + + + + align:start position:0% + +it's eight times alpha so it makes the + + align:start position:0% +it's eight times alpha so it makes the + + + align:start position:0% +it's eight times alpha so it makes the +update + + align:start position:0% + + + + align:start position:0% + +yeah so that is actually + + align:start position:0% +yeah so that is actually + + + align:start position:0% +yeah so that is actually +this is the one i had + + align:start position:0% + + + + align:start position:0% + +okay good + + align:start position:0% +okay good + + + align:start position:0% +okay good +so it turns out you can learn q function + + align:start position:0% +so it turns out you can learn q function + + + align:start position:0% +so it turns out you can learn q function +just like you could learn a um a value + + align:start position:0% +just like you could learn a um a value + + + align:start position:0% +just like you could learn a um a value +function with + + align:start position:0% +function with + + + align:start position:0% +function with +storing up these matrices which are what + + align:start position:0% +storing up these matrices which are what + + + align:start position:0% +storing up these matrices which are what +td learning would have done + + align:start position:0% +td learning would have done + + + align:start position:0% +td learning would have done +in a batch sense okay + + align:start position:0% +in a batch sense okay + + + align:start position:0% +in a batch sense okay +and then just making a one-step shot to + + align:start position:0% +and then just making a one-step shot to + + + align:start position:0% +and then just making a one-step shot to +get directly to the solution for + + align:start position:0% +get directly to the solution for + + + align:start position:0% +get directly to the solution for +temporal differences on your q function + + align:start position:0% + + + + align:start position:0% + +and again i put in here + + align:start position:0% +and again i put in here + + + align:start position:0% +and again i put in here +s prime + + align:start position:0% +s prime + + + align:start position:0% +s prime +and i left this a little bit ambiguous + + align:start position:0% +and i left this a little bit ambiguous + + + align:start position:0% +and i left this a little bit ambiguous +so i can evaluate any + + align:start position:0% + + + + align:start position:0% + +policy + + align:start position:0% +policy + + + align:start position:0% +policy +by just putting in + + align:start position:0% +by just putting in + + + align:start position:0% +by just putting in +that policy in here and doing the replay + + align:start position:0% + + + + align:start position:0% + +it turns out + + align:start position:0% + + + + align:start position:0% + +if i now do this + + align:start position:0% +if i now do this + + + align:start position:0% +if i now do this +in a policy + + align:start position:0% +in a policy + + + align:start position:0% +in a policy +iteration sense + + align:start position:0% + + + + align:start position:0% + +lspi these first policy iterations + + align:start position:0% +lspi these first policy iterations + + + align:start position:0% +lspi these first policy iterations +basically start off with an initial + + align:start position:0% +basically start off with an initial + + + align:start position:0% +basically start off with an initial +guess + + align:start position:0% +guess + + + align:start position:0% +guess +you do + + align:start position:0% +you do + + + align:start position:0% +you do +ls + + align:start position:0% + + + + align:start position:0% + +q + + align:start position:0% + + + + align:start position:0% + +to get + + align:start position:0% +to get + + + align:start position:0% +to get +q pi + + align:start position:0% +q pi + + + align:start position:0% +q pi +and then you repeat + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +then this thing + + align:start position:0% +then this thing + + + align:start position:0% +then this thing +that's enough + + align:start position:0% +that's enough + + + align:start position:0% +that's enough +to get + + align:start position:0% +to get + + + align:start position:0% +to get +you to um + + align:start position:0% + + + + align:start position:0% + +converges + + align:start position:0% + + + + align:start position:0% + +and be careful about it how it converges + + align:start position:0% +and be careful about it how it converges + + + align:start position:0% +and be careful about it how it converges +it converges with some error bound + + align:start position:0% + + + + align:start position:0% + +to 5 star + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the error bound depends on a couple of + + align:start position:0% +the error bound depends on a couple of + + + align:start position:0% +the error bound depends on a couple of +the parameters + + align:start position:0% +the parameters + + + align:start position:0% +the parameters +so technically it could get close to + + align:start position:0% +so technically it could get close to + + + align:start position:0% +so technically it could get close to +your solution and oscillate or something + + align:start position:0% +your solution and oscillate or something + + + align:start position:0% +your solution and oscillate or something +like that but it's pretty strong + + align:start position:0% +like that but it's pretty strong + + + align:start position:0% +like that but it's pretty strong +conversation for this for a policy + + align:start position:0% +conversation for this for a policy + + + align:start position:0% +conversation for this for a policy +improvement + + align:start position:0% +improvement + + + align:start position:0% +improvement +with a value it's an approximate value + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +in the pure sense + + align:start position:0% +in the pure sense + + + align:start position:0% +in the pure sense +it is + + align:start position:0% +it is + + + align:start position:0% +it is +you should run this for a while + + align:start position:0% +you should run this for a while + + + align:start position:0% +you should run this for a while +to + + align:start position:0% +to + + + align:start position:0% +to +until you get a good estimate throughout + + align:start position:0% +until you get a good estimate throughout + + + align:start position:0% +until you get a good estimate throughout +td and then you get to your new + + align:start position:0% +td and then you get to your new + + + align:start position:0% +td and then you get to your new +um + + align:start position:0% + + + + align:start position:0% + +but by virtue of + + align:start position:0% +but by virtue of + + + align:start position:0% +but by virtue of +using q functions + + align:start position:0% +using q functions + + + align:start position:0% +using q functions +when you do switch to your new policy pi + + align:start position:0% +when you do switch to your new policy pi + + + align:start position:0% +when you do switch to your new policy pi +2 let's say + + align:start position:0% +2 let's say + + + align:start position:0% +2 let's say +you don't have to throw away all your + + align:start position:0% +you don't have to throw away all your + + + align:start position:0% +you don't have to throw away all your +old data + + align:start position:0% +old data + + + align:start position:0% +old data +just take your old tapes and actually + + align:start position:0% +just take your old tapes and actually + + + align:start position:0% +just take your old tapes and actually +regenerate a and b + + align:start position:0% +regenerate a and b + + + align:start position:0% +regenerate a and b +as if you had played out those new those + + align:start position:0% +as if you had played out those new those + + + align:start position:0% +as if you had played out those new those +old groups + + align:start position:0% +old groups + + + align:start position:0% +old groups +with the + + align:start position:0% +with the + + + align:start position:0% +with the +as if you had seen the old tapes + + align:start position:0% +as if you had seen the old tapes + + + align:start position:0% +as if you had seen the old tapes +executing the new policy + + align:start position:0% + + + + align:start position:0% + +and you can reuse all your old data + + align:start position:0% +and you can reuse all your old data + + + align:start position:0% +and you can reuse all your old data +and make an efficient update to get + + align:start position:0% +and make an efficient update to get + + + align:start position:0% +and make an efficient update to get +couponing + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +these squares + + align:start position:0% + + + + align:start position:0% + +okay i know that was a little dry a + + align:start position:0% +okay i know that was a little dry a + + + align:start position:0% +okay i know that was a little dry a +little bit and a lot but let's make sure + + align:start position:0% +little bit and a lot but let's make sure + + + align:start position:0% +little bit and a lot but let's make sure +we know + + align:start position:0% +we know + + + align:start position:0% +we know +how we got where we + + align:start position:0% +how we got where we + + + align:start position:0% +how we got where we +got so + + align:start position:0% +got so + + + align:start position:0% +got so +um + + align:start position:0% + + + + align:start position:0% + +there's an in there's another route + + align:start position:0% +there's an in there's another route + + + align:start position:0% +there's an in there's another route +besides paul's pure policy search to do + + align:start position:0% +besides paul's pure policy search to do + + + align:start position:0% +besides paul's pure policy search to do +model-free learning all you have to do + + align:start position:0% +model-free learning all you have to do + + + align:start position:0% +model-free learning all you have to do +is take a bunch of trajectories + + align:start position:0% +is take a bunch of trajectories + + + align:start position:0% +is take a bunch of trajectories +okay + + align:start position:0% +okay + + + align:start position:0% +okay +learn a value function from those + + align:start position:0% +learn a value function from those + + + align:start position:0% +learn a value function from those +trajectories that's how you don't even + + align:start position:0% +trajectories that's how you don't even + + + align:start position:0% +trajectories that's how you don't even +actually have to take the + + align:start position:0% +actually have to take the + + + align:start position:0% +actually have to take the +perfect + + align:start position:0% +perfect + + + align:start position:0% +perfect +your best controller yet you can take + + align:start position:0% +your best controller yet you can take + + + align:start position:0% +your best controller yet you can take +some + + align:start position:0% +some + + + align:start position:0% +some +rrt control something that's going to + + align:start position:0% +rrt control something that's going to + + + align:start position:0% +rrt control something that's going to +explore the space you try to learn about + + align:start position:0% +explore the space you try to learn about + + + align:start position:0% +explore the space you try to learn about +your value function + + align:start position:0% +your value function + + + align:start position:0% +your value function +okay + + align:start position:0% +okay + + + align:start position:0% +okay +learn q pi uh through these + + align:start position:0% +learn q pi uh through these + + + align:start position:0% +learn q pi uh through these +ls tv algorithms you can do a pretty + + align:start position:0% +ls tv algorithms you can do a pretty + + + align:start position:0% +ls tv algorithms you can do a pretty +efficient update for doing q pi + + align:start position:0% +efficient update for doing q pi + + + align:start position:0% +efficient update for doing q pi +you can improve it efficiently by just + + align:start position:0% +you can improve it efficiently by just + + + align:start position:0% +you can improve it efficiently by just +looking over the + + align:start position:0% +looking over the + + + align:start position:0% +looking over the +min over q + + align:start position:0% +min over q + + + align:start position:0% +min over q +and pretty quickly iterate to an optimal + + align:start position:0% +and pretty quickly iterate to an optimal + + + align:start position:0% +and pretty quickly iterate to an optimal +policy and optimal value function + + align:start position:0% +policy and optimal value function + + + align:start position:0% +policy and optimal value function +only storing the only thing you have to + + align:start position:0% +only storing the only thing you have to + + + align:start position:0% +only storing the only thing you have to +store in that whole process is the key + + align:start position:0% +store in that whole process is the key + + + align:start position:0% +store in that whole process is the key +function + + align:start position:0% +function + + + align:start position:0% +function +and in the ls case the lstd cases you + + align:start position:0% +and in the ls case the lstd cases you + + + align:start position:0% +and in the ls case the lstd cases you +remember the + + align:start position:0% +remember the + + + align:start position:0% +remember the +history of tapes just you can use them + + align:start position:0% +history of tapes just you can use them + + + align:start position:0% +history of tapes just you can use them +more efficiently + + align:start position:0% +more efficiently + + + align:start position:0% +more efficiently +okay yeah + + align:start position:0% +okay yeah + + + align:start position:0% +okay yeah +so could you use this on the + + align:start position:0% +so could you use this on the + + + align:start position:0% +so could you use this on the +clapper that + + align:start position:0% +clapper that + + + align:start position:0% +clapper that +john showed + + align:start position:0% +john showed + + + align:start position:0% +john showed +or + + align:start position:0% +or + + + align:start position:0% +or +so + + align:start position:0% +so + + + align:start position:0% +so +good very good question so + + align:start position:0% +good very good question so + + + align:start position:0% +good very good question so +um + + align:start position:0% +um + + + align:start position:0% +um +that's an excellent question + + align:start position:0% +that's an excellent question + + + align:start position:0% +that's an excellent question +so in fact the last um data class what + + align:start position:0% +so in fact the last um data class what + + + align:start position:0% +so in fact the last um data class what +we're going to do is is going to last a + + align:start position:0% +we're going to do is is going to last a + + + align:start position:0% +we're going to do is is going to last a +high present advice um we're going to go + + align:start position:0% +high present advice um we're going to go + + + align:start position:0% +high present advice um we're going to go +through a couple of sort of case studies + + align:start position:0% +through a couple of sort of case studies + + + align:start position:0% +through a couple of sort of case studies +and different problems with people who + + align:start position:0% +and different problems with people who + + + align:start position:0% +and different problems with people who +had success and tell you why we think + + align:start position:0% +had success and tell you why we think + + + align:start position:0% +had success and tell you why we think +the algorithm we picked things like that + + align:start position:0% +the algorithm we picked things like that + + + align:start position:0% +the algorithm we picked things like that +so why didn't we do this on the on the + + align:start position:0% +so why didn't we do this on the on the + + + align:start position:0% +so why didn't we do this on the on the +flat verb + + align:start position:0% +flat verb + + + align:start position:0% +flat verb +the simplest reason is that we don't + + align:start position:0% +the simplest reason is that we don't + + + align:start position:0% +the simplest reason is that we don't +know the state space + + align:start position:0% +know the state space + + + align:start position:0% +know the state space +it's infinite dimensional in + + align:start position:0% +it's infinite dimensional in + + + align:start position:0% +it's infinite dimensional in +general + + align:start position:0% +general + + + align:start position:0% +general +so + + align:start position:0% +so + + + align:start position:0% +so +that would have been a big thing to + + align:start position:0% +that would have been a big thing to + + + align:start position:0% +that would have been a big thing to +represent a few folks before + + align:start position:0% +represent a few folks before + + + align:start position:0% +represent a few folks before +it doesn't mean it doesn't make it + + align:start position:0% +it doesn't mean it doesn't make it + + + align:start position:0% +it doesn't mean it doesn't make it +invalid + + align:start position:0% +invalid + + + align:start position:0% +invalid +we could have learned we could have + + align:start position:0% +we could have learned we could have + + + align:start position:0% +we could have learned we could have +tried to approximate the state space + + align:start position:0% +tried to approximate the state space + + + align:start position:0% +tried to approximate the state space +with + + align:start position:0% +with + + + align:start position:0% +with +even a handful of features learned a + + align:start position:0% +even a handful of features learned a + + + align:start position:0% +even a handful of features learned a +very approximate + + align:start position:0% + + + + align:start position:0% + +q function and done something like + + align:start position:0% +q function and done something like + + + align:start position:0% +q function and done something like +acrocritic like we're going to do next + + align:start position:0% +acrocritic like we're going to do next + + + align:start position:0% +acrocritic like we're going to do next +time but i think in cases where you + + align:start position:0% +time but i think in cases where you + + + align:start position:0% +time but i think in cases where you +don't know the state space or the state + + align:start position:0% +don't know the state space or the state + + + align:start position:0% +don't know the state space or the state +space is very very large and you can + + align:start position:0% +space is very very large and you can + + + align:start position:0% +space is very very large and you can +write a simple controller then it makes + + align:start position:0% +write a simple controller then it makes + + + align:start position:0% +write a simple controller then it makes +more sense to parameterize the policy + + align:start position:0% +more sense to parameterize the policy + + + align:start position:0% +more sense to parameterize the policy +it really goes down to that being the + + align:start position:0% +it really goes down to that being the + + + align:start position:0% +it really goes down to that being the +accounting game in some ways of + + align:start position:0% + + + + align:start position:0% + +how many dimensions things are but in + + align:start position:0% +how many dimensions things are but in + + + align:start position:0% +how many dimensions things are but in +the fluids case you could have a pretty + + align:start position:0% +the fluids case you could have a pretty + + + align:start position:0% +the fluids case you could have a pretty +simple policy from sensors to actions + + align:start position:0% +simple policy from sensors to actions + + + align:start position:0% +simple policy from sensors to actions +so you could twiddle + + align:start position:0% +so you could twiddle + + + align:start position:0% +so you could twiddle +you couldn't have a uh + + align:start position:0% +you couldn't have a uh + + + align:start position:0% +you couldn't have a uh +efficient value function + + align:start position:0% + + + + align:start position:0% + +now there are there are other cases + + align:start position:0% +now there are there are other cases + + + align:start position:0% +now there are there are other cases +where the obvious is true the opposite + + align:start position:0% +where the obvious is true the opposite + + + align:start position:0% +where the obvious is true the opposite +is true where you create + + align:start position:0% +is true where you create + + + align:start position:0% +is true where you create +you have a small state space let's say + + align:start position:0% +you have a small state space let's say + + + align:start position:0% +you have a small state space let's say +but the + + align:start position:0% +but the + + + align:start position:0% +but the +resulting policies would require a lot + + align:start position:0% +resulting policies would require a lot + + + align:start position:0% +resulting policies would require a lot +of features for entertainers + + align:start position:0% +of features for entertainers + + + align:start position:0% +of features for entertainers +but i think in general the strength of + + align:start position:0% +but i think in general the strength of + + + align:start position:0% +but i think in general the strength of +these algorithms is that they are + + align:start position:0% +these algorithms is that they are + + + align:start position:0% +these algorithms is that they are +efficient with reusing + + align:start position:0% +efficient with reusing + + + align:start position:0% +efficient with reusing +the weakness is that um + + align:start position:0% +the weakness is that um + + + align:start position:0% +the weakness is that um +well the weakness a few years ago would + + align:start position:0% +well the weakness a few years ago would + + + align:start position:0% +well the weakness a few years ago would +have been that they blow up all the time + + align:start position:0% +have been that they blow up all the time + + + align:start position:0% +have been that they blow up all the time +but organs have gotten better + + align:start position:0% + + + + align:start position:0% + +we have some convergence guarantees not + + align:start position:0% +we have some convergence guarantees not + + + align:start position:0% +we have some convergence guarantees not +the general thing i have i never told + + align:start position:0% +the general thing i have i never told + + + align:start position:0% +the general thing i have i never told +you that it converged if you have a + + align:start position:0% +you that it converged if you have a + + + align:start position:0% +you that it converged if you have a +non-linear functional calculator we'd + + align:start position:0% +non-linear functional calculator we'd + + + align:start position:0% +non-linear functional calculator we'd +love to have that result we don't have + + align:start position:0% +love to have that result we don't have + + + align:start position:0% +love to have that result we don't have +maybe we won't do it for a while + + align:start position:0% +maybe we won't do it for a while + + + align:start position:0% +maybe we won't do it for a while +but if we in linear function + + align:start position:0% +but if we in linear function + + + align:start position:0% +but if we in linear function +approximation sense we have those + + align:start position:0% + + + + align:start position:0% + +but there's a lot of success stories + + align:start position:0% +but there's a lot of success stories + + + align:start position:0% +but there's a lot of success stories +with this + + align:start position:0% +with this + + + align:start position:0% +with this +these are the kind of algorithms that + + align:start position:0% +these are the kind of algorithms that + + + align:start position:0% +these are the kind of algorithms that +were used to play backgammon right + + align:start position:0% +were used to play backgammon right + + + align:start position:0% +were used to play backgammon right +there are examples of them working on + + align:start position:0% +there are examples of them working on + + + align:start position:0% +there are examples of them working on +things like the acrobat + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +the domains that i care about most in my + + align:start position:0% +the domains that i care about most in my + + + align:start position:0% +the domains that i care about most in my +lab we tend to call it \ No newline at end of file diff --git a/7WwuKAvtdq8.txt b/7WwuKAvtdq8.txt new file mode 100644 index 0000000000000000000000000000000000000000..6530edfaf0213e97530a666ec71dd6a704ea01c8 --- /dev/null +++ b/7WwuKAvtdq8.txt @@ -0,0 +1,4827 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer high quality educational + + align:start position:0% +to offer high quality educational + + + align:start position:0% +to offer high quality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu we're V1 + + align:start position:0% + + + + align:start position:0% + +UHS um just quick history of this uh + + align:start position:0% +UHS um just quick history of this uh + + + align:start position:0% +UHS um just quick history of this uh +this vehicle that we're working on this + + align:start position:0% +this vehicle that we're working on this + + + align:start position:0% +this vehicle that we're working on this +to our vehicle was made in the summer in + + align:start position:0% +to our vehicle was made in the summer in + + + align:start position:0% +to our vehicle was made in the summer in +8 weeks and uh it runs and everything + + align:start position:0% +8 weeks and uh it runs and everything + + + align:start position:0% +8 weeks and uh it runs and everything +but it didn't have a door or a + + align:start position:0% +but it didn't have a door or a + + + align:start position:0% +but it didn't have a door or a +windshield and so that was our job um + + align:start position:0% +windshield and so that was our job um + + + align:start position:0% +windshield and so that was our job um +and our goal was to getting prepared for + + align:start position:0% +and our goal was to getting prepared for + + + align:start position:0% +and our goal was to getting prepared for +solid works World action starting on + + align:start position:0% +solid works World action starting on + + + align:start position:0% +solid works World action starting on +Monday and um so to be shown there as an + + align:start position:0% +Monday and um so to be shown there as an + + + align:start position:0% +Monday and um so to be shown there as an +example Sol is one of the sponsors of + + align:start position:0% +example Sol is one of the sponsors of + + + align:start position:0% +example Sol is one of the sponsors of +BDS so the vehicle is going to go there + + align:start position:0% +BDS so the vehicle is going to go there + + + align:start position:0% +BDS so the vehicle is going to go there +to show sort of as a what solid works + + align:start position:0% +to show sort of as a what solid works + + + align:start position:0% +to show sort of as a what solid works +can do project type thing and u COO + + align:start position:0% +can do project type thing and u COO + + + align:start position:0% +can do project type thing and u COO +solid works will be driving on stage + + align:start position:0% +solid works will be driving on stage + + + align:start position:0% +solid works will be driving on stage +later in the week is that still your + + align:start position:0% +later in the week is that still your + + + align:start position:0% +later in the week is that still your +plan that's + + align:start position:0% + + + + align:start position:0% + +still um so I'd like to introduce the + + align:start position:0% +still um so I'd like to introduce the + + + align:start position:0% +still um so I'd like to introduce the +team I'm me this is + + align:start position:0% + + + + align:start position:0% + +anas so so + + align:start position:0% +anas so so + + + align:start position:0% +anas so so +likey about the entry and exit the the + + align:start position:0% +likey about the entry and exit the the + + + align:start position:0% +likey about the entry and exit the the +the entry to the car was only through + + align:start position:0% +the entry to the car was only through + + + align:start position:0% +the entry to the car was only through +shield from in front there was no other + + align:start position:0% +shield from in front there was no other + + + align:start position:0% +shield from in front there was no other +way of entering the car uh it was pretty + + align:start position:0% +way of entering the car uh it was pretty + + + align:start position:0% +way of entering the car uh it was pretty +hard to + + align:start position:0% +hard to + + + align:start position:0% +hard to +basically or app we were trying to + + align:start position:0% +basically or app we were trying to + + + align:start position:0% +basically or app we were trying to +define a methodology of really designing + + align:start position:0% +define a methodology of really designing + + + align:start position:0% +define a methodology of really designing +a system that could provide some sort of + + align:start position:0% +a system that could provide some sort of + + + align:start position:0% +a system that could provide some sort of +that exit uh we did we we we started + + align:start position:0% +that exit uh we did we we we started + + + align:start position:0% +that exit uh we did we we we started +with um a few um defining our objectives + + align:start position:0% +with um a few um defining our objectives + + + align:start position:0% +with um a few um defining our objectives +we had initially a a multiobjective + + align:start position:0% +we had initially a a multiobjective + + + align:start position:0% +we had initially a a multiobjective +problem we had quantifiable criterias + + align:start position:0% +problem we had quantifiable criterias + + + align:start position:0% +problem we had quantifiable criterias +cost visibility uh which we wanted to + + align:start position:0% +cost visibility uh which we wanted to + + + align:start position:0% +cost visibility uh which we wanted to +increase compared to the previous car uh + + align:start position:0% +increase compared to the previous car uh + + + align:start position:0% +increase compared to the previous car uh +the amount of of time that takes us to + + align:start position:0% +the amount of of time that takes us to + + + align:start position:0% +the amount of of time that takes us to +get in and out of the car which was + + align:start position:0% +get in and out of the car which was + + + align:start position:0% +get in and out of the car which was +although Define as aial criteria what + + align:start position:0% +although Define as aial criteria what + + + align:start position:0% +although Define as aial criteria what +very hard to model we had to do it + + align:start position:0% +very hard to model we had to do it + + + align:start position:0% +very hard to model we had to do it +basically test the unquantifiable + + align:start position:0% +basically test the unquantifiable + + + align:start position:0% +basically test the unquantifiable +criteria is eom + + align:start position:0% +criteria is eom + + + align:start position:0% +criteria is eom +manufactury uh the reason we specified + + align:start position:0% +manufactury uh the reason we specified + + + align:start position:0% +manufactury uh the reason we specified +it as unquantifiable because our design + + align:start position:0% +it as unquantifiable because our design + + + align:start position:0% +it as unquantifiable because our design +was changing so much at the time that we + + align:start position:0% +was changing so much at the time that we + + + align:start position:0% +was changing so much at the time that we +pushed it more + + align:start position:0% +pushed it more + + + align:start position:0% +pushed it more +of of an unquantifiable criteria + + align:start position:0% +of of an unquantifiable criteria + + + align:start position:0% +of of an unquantifiable criteria +Aesthetics was also definitely an + + align:start position:0% +Aesthetics was also definitely an + + + align:start position:0% +Aesthetics was also definitely an +quantifiable criteria which which we + + align:start position:0% +quantifiable criteria which which we + + + align:start position:0% +quantifiable criteria which which we +were U had not no model really of of + + align:start position:0% +were U had not no model really of of + + + align:start position:0% +were U had not no model really of of +building on uh our constraints were the + + align:start position:0% +building on uh our constraints were the + + + align:start position:0% +building on uh our constraints were the +existing U shell the shape of the + + align:start position:0% +existing U shell the shape of the + + + align:start position:0% +existing U shell the shape of the +existing shell we were uh we were + + align:start position:0% +existing shell we were uh we were + + + align:start position:0% +existing shell we were uh we were +constrained not to to change anything + + align:start position:0% +constrained not to to change anything + + + align:start position:0% +constrained not to to change anything +and um basically just maintain the same + + align:start position:0% +and um basically just maintain the same + + + align:start position:0% +and um basically just maintain the same +form the weight of of the new shell uh + + align:start position:0% +form the weight of of the new shell uh + + + align:start position:0% +form the weight of of the new shell uh +should not exceed U uh double the the + + align:start position:0% +should not exceed U uh double the the + + + align:start position:0% +should not exceed U uh double the the +the amount of of whatever material we + + align:start position:0% +the amount of of whatever material we + + + align:start position:0% +the amount of of whatever material we +were taking cost uh was we had also + + align:start position:0% +were taking cost uh was we had also + + + align:start position:0% +were taking cost uh was we had also +constraints on cost I can't + + align:start position:0% +constraints on cost I can't + + + align:start position:0% +constraints on cost I can't +remember how much we were constrained + + align:start position:0% + + + + align:start position:0% + +I design variables uh we had we had + + align:start position:0% +I design variables uh we had we had + + + align:start position:0% +I design variables uh we had we had +three major design variables geometry + + align:start position:0% +three major design variables geometry + + + align:start position:0% +three major design variables geometry +numbering of positions of joints + + align:start position:0% +numbering of positions of joints + + + align:start position:0% +numbering of positions of joints +material and kinematics as as as + + align:start position:0% +material and kinematics as as as + + + align:start position:0% +material and kinematics as as as +different methodologies uh these three + + align:start position:0% +different methodologies uh these three + + + align:start position:0% +different methodologies uh these three +basically were + + align:start position:0% +basically were + + + align:start position:0% +basically were +were we started with a few sketches I'll + + align:start position:0% +were we started with a few sketches I'll + + + align:start position:0% +were we started with a few sketches I'll +go back to the Des variables we started + + align:start position:0% +go back to the Des variables we started + + + align:start position:0% +go back to the Des variables we started +with just a few sketches and ideas of + + align:start position:0% +with just a few sketches and ideas of + + + align:start position:0% +with just a few sketches and ideas of +how do we want this thing to and and we + + align:start position:0% +how do we want this thing to and and we + + + align:start position:0% +how do we want this thing to and and we +were trying to increase the size of the + + align:start position:0% +were trying to increase the size of the + + + align:start position:0% +were trying to increase the size of the +area of uh of the glass and and + + align:start position:0% +area of uh of the glass and and + + + align:start position:0% +area of uh of the glass and and +basically use both the windshield and + + align:start position:0% +basically use both the windshield and + + + align:start position:0% +basically use both the windshield and +the uh U the door as as one compon + + align:start position:0% +the uh U the door as as one compon + + + align:start position:0% +the uh U the door as as one compon +um we we started with with some sort of + + align:start position:0% +um we we started with with some sort of + + + align:start position:0% +um we we started with with some sort of +a design system and our design system + + align:start position:0% +a design system and our design system + + + align:start position:0% +a design system and our design system +was was broken down given the design + + align:start position:0% +was was broken down given the design + + + align:start position:0% +was was broken down given the design +variables we had so we had geometry at + + align:start position:0% +variables we had so we had geometry at + + + align:start position:0% +variables we had so we had geometry at +one level of tree uh the materials uh + + align:start position:0% +one level of tree uh the materials uh + + + align:start position:0% +one level of tree uh the materials uh +transparency versus opness on another + + align:start position:0% +transparency versus opness on another + + + align:start position:0% +transparency versus opness on another +andics and based on that we started + + align:start position:0% +andics and based on that we started + + + align:start position:0% +andics and based on that we started +building uh our own design tree just + + align:start position:0% +building uh our own design tree just + + + align:start position:0% +building uh our own design tree just +just basically FL out some of the + + align:start position:0% +just basically FL out some of the + + + align:start position:0% +just basically FL out some of the +possible solutions so and we started + + align:start position:0% +possible solutions so and we started + + + align:start position:0% +possible solutions so and we started +generating really huge amount again + + align:start position:0% +generating really huge amount again + + + align:start position:0% +generating really huge amount again +small version of the tree yeah which was + + align:start position:0% +small version of the tree yeah which was + + + align:start position:0% +small version of the tree yeah which was +there this is definitely a small version + + align:start position:0% +there this is definitely a small version + + + align:start position:0% +there this is definitely a small version +of of the tree something like 200 just + + align:start position:0% +of of the tree something like 200 just + + + align:start position:0% +of of the tree something like 200 just +little sketches and and the idea was + + align:start position:0% +little sketches and and the idea was + + + align:start position:0% +little sketches and and the idea was +basically we would try we start geometry + + align:start position:0% +basically we would try we start geometry + + + align:start position:0% +basically we would try we start geometry +with one line add start adding different + + align:start position:0% +with one line add start adding different + + + align:start position:0% +with one line add start adding different +lines of breakage of of joints and uh on + + align:start position:0% +lines of breakage of of joints and uh on + + + align:start position:0% +lines of breakage of of joints and uh on +one level uh based on on the geometry I + + align:start position:0% +one level uh based on on the geometry I + + + align:start position:0% +one level uh based on on the geometry I +generated there on a different level we + + align:start position:0% +generated there on a different level we + + + align:start position:0% +generated there on a different level we +start choosing zones and areas of that + + align:start position:0% +start choosing zones and areas of that + + + align:start position:0% +start choosing zones and areas of that +uh to uh to basically change the + + align:start position:0% +uh to uh to basically change the + + + align:start position:0% +uh to uh to basically change the +material and see what and and then + + align:start position:0% +material and see what and and then + + + align:start position:0% +material and see what and and then +pneumatics on those joints choose what + + align:start position:0% +pneumatics on those joints choose what + + + align:start position:0% +pneumatics on those joints choose what +are the types of is this the fixed + + align:start position:0% +are the types of is this the fixed + + + align:start position:0% +are the types of is this the fixed +jointing sler uh hatch and the + + align:start position:0% +jointing sler uh hatch and the + + + align:start position:0% +jointing sler uh hatch and the +like uh we eventually start even + + align:start position:0% +like uh we eventually start even + + + align:start position:0% +like uh we eventually start even +generating hybrids this was we have to + + align:start position:0% +generating hybrids this was we have to + + + align:start position:0% +generating hybrids this was we have to +connect few tables and just spread the + + align:start position:0% +connect few tables and just spread the + + + align:start position:0% +connect few tables and just spread the +whole thing on it and just start mapping + + align:start position:0% +whole thing on it and just start mapping + + + align:start position:0% +whole thing on it and just start mapping +looking at the different + + align:start position:0% +looking at the different + + + align:start position:0% +looking at the different +possibilities um we came up with with + + align:start position:0% +possibilities um we came up with with + + + align:start position:0% +possibilities um we came up with with +this solution can real quick how did you + + align:start position:0% +this solution can real quick how did you + + + align:start position:0% +this solution can real quick how did you +screen all this uh we truly by + + align:start position:0% +screen all this uh we truly by + + + align:start position:0% +screen all this uh we truly by +elimination um we just went on based on + + align:start position:0% +elimination um we just went on based on + + + align:start position:0% +elimination um we just went on based on +the initial criterias we had and given + + align:start position:0% +the initial criterias we had and given + + + align:start position:0% +the initial criterias we had and given +the time we had we there was no way of + + align:start position:0% +the time we had we there was no way of + + + align:start position:0% +the time we had we there was no way of +timating this so we were looking at a + + align:start position:0% +timating this so we were looking at a + + + align:start position:0% +timating this so we were looking at a +different possibilities at that level + + align:start position:0% +different possibilities at that level + + + align:start position:0% +different possibilities at that level +and looking at all the different designs + + align:start position:0% +and looking at all the different designs + + + align:start position:0% +and looking at all the different designs +we didn't actually sit down and talk + + align:start position:0% +we didn't actually sit down and talk + + + align:start position:0% +we didn't actually sit down and talk +about all to intent we started talking + + align:start position:0% +about all to intent we started talking + + + align:start position:0% +about all to intent we started talking +you know about everyone but you get + + align:start position:0% +you know about everyone but you get + + + align:start position:0% +you know about everyone but you get +repeating sequences basically where the + + align:start position:0% +repeating sequences basically where the + + + align:start position:0% +repeating sequences basically where the +only you get highle concept + + align:start position:0% +only you get highle concept + + + align:start position:0% +only you get highle concept +sort of like a door that slides board + + align:start position:0% +sort of like a door that slides board + + + align:start position:0% +sort of like a door that slides board +and then you know so sliding board + + align:start position:0% +and then you know so sliding board + + + align:start position:0% +and then you know so sliding board +that's that's a two line geometry and it + + align:start position:0% +that's that's a two line geometry and it + + + align:start position:0% +that's that's a two line geometry and it +slides forward and then the M where you + + align:start position:0% +slides forward and then the M where you + + + align:start position:0% +slides forward and then the M where you +put the material which part's okay which + + align:start position:0% +put the material which part's okay which + + + align:start position:0% +put the material which part's okay which +part is clear didn't really change the + + align:start position:0% +part is clear didn't really change the + + + align:start position:0% +part is clear didn't really change the +concept that much it's just kind of like + + align:start position:0% +concept that much it's just kind of like + + + align:start position:0% +concept that much it's just kind of like +that but it was good to see all of them + + align:start position:0% +that but it was good to see all of them + + + align:start position:0% +that but it was good to see all of them +because we really helped us think about + + align:start position:0% +because we really helped us think about + + + align:start position:0% +because we really helped us think about +all the compal problems I think this is + + align:start position:0% +all the compal problems I think this is + + + align:start position:0% +all the compal problems I think this is +what Engineers call by + + align:start position:0% +what Engineers call by + + + align:start position:0% +what Engineers call by +inspection + + align:start position:0% +inspection + + + align:start position:0% +inspection +inspection uh yeah this was + + align:start position:0% + + + + align:start position:0% + +this was the uh the idea behind our + + align:start position:0% +this was the uh the idea behind our + + + align:start position:0% +this was the uh the idea behind our +design we started with really just + + align:start position:0% +design we started with really just + + + align:start position:0% +design we started with really just +defining a line uh one of the lines we + + align:start position:0% +defining a line uh one of the lines we + + + align:start position:0% +defining a line uh one of the lines we +started with the geometry here uh + + align:start position:0% +started with the geometry here uh + + + align:start position:0% +started with the geometry here uh +basically producing a hybrid of a few + + align:start position:0% +basically producing a hybrid of a few + + + align:start position:0% +basically producing a hybrid of a few +Solutions we we came up with and + + align:start position:0% +Solutions we we came up with and + + + align:start position:0% +Solutions we we came up with and +generating this Arc uh that the the + + align:start position:0% +generating this Arc uh that the the + + + align:start position:0% +generating this Arc uh that the the +basically the windshield at windshield + + align:start position:0% +basically the windshield at windshield + + + align:start position:0% +basically the windshield at windshield +door uh basically slides on top of and + + align:start position:0% +door uh basically slides on top of and + + + align:start position:0% +door uh basically slides on top of and +and and basically the idea was really to + + align:start position:0% +and and basically the idea was really to + + + align:start position:0% +and and basically the idea was really to +to uh to look at at the at the + + align:start position:0% +to uh to look at at the at the + + + align:start position:0% +to uh to look at at the at the +windshield as as being uh minimizing to + + align:start position:0% +windshield as as being uh minimizing to + + + align:start position:0% +windshield as as being uh minimizing to +the maximum any any complexities in in + + align:start position:0% +the maximum any any complexities in in + + + align:start position:0% +the maximum any any complexities in in +in in the IDE so it just basically um + + align:start position:0% +in in the IDE so it just basically um + + + align:start position:0% +in in the IDE so it just basically um +moves on that rail which is a clear neat + + align:start position:0% +moves on that rail which is a clear neat + + + align:start position:0% +moves on that rail which is a clear neat +Arc and and basically just rotates + + align:start position:0% +Arc and and basically just rotates + + + align:start position:0% +Arc and and basically just rotates +around it and by its own weight just + + align:start position:0% +around it and by its own weight just + + + align:start position:0% +around it and by its own weight just +goes down so the only force that was + + align:start position:0% +goes down so the only force that was + + + align:start position:0% +goes down so the only force that was +there was just the pushing of of of the + + align:start position:0% +there was just the pushing of of of the + + + align:start position:0% +there was just the pushing of of of the +of the windshield the mechanics where + + align:start position:0% +of the windshield the mechanics where + + + align:start position:0% +of the windshield the mechanics where +where intent was really to simplify to + + align:start position:0% +where intent was really to simplify to + + + align:start position:0% +where intent was really to simplify to +to the maximum we just had two rails on + + align:start position:0% +to the maximum we just had two rails on + + + align:start position:0% +to the maximum we just had two rails on +both sides and handles that run within + + align:start position:0% +both sides and handles that run within + + + align:start position:0% +both sides and handles that run within +those rails and the handles actually + + align:start position:0% +those rails and the handles actually + + + align:start position:0% +those rails and the handles actually +connect to the to the windshield um and + + align:start position:0% +connect to the to the windshield um and + + + align:start position:0% +connect to the to the windshield um and +basically just by pushing it up upwards + + align:start position:0% +basically just by pushing it up upwards + + + align:start position:0% +basically just by pushing it up upwards +uh we had a a small well just hold it in + + align:start position:0% +uh we had a a small well just hold it in + + + align:start position:0% +uh we had a a small well just hold it in +place when it pushes and releasing it + + align:start position:0% +place when it pushes and releasing it + + + align:start position:0% +place when it pushes and releasing it +from its position just basically lets it + + align:start position:0% +from its position just basically lets it + + + align:start position:0% +from its position just basically lets it +by by by its own weight to drop and lock + + align:start position:0% +by by by its own weight to drop and lock + + + align:start position:0% +by by by its own weight to drop and lock +in + + align:start position:0% +in + + + align:start position:0% +in +um + + align:start position:0% +um + + + align:start position:0% +um +that's again just just a zoom in on the + + align:start position:0% +that's again just just a zoom in on the + + + align:start position:0% +that's again just just a zoom in on the +rail itself and and the handles uh and + + align:start position:0% +rail itself and and the handles uh and + + + align:start position:0% +rail itself and and the handles uh and +this is from the right side and this is + + align:start position:0% +this is from the right side and this is + + + align:start position:0% +this is from the right side and this is +where the windshield really connects + + align:start position:0% +where the windshield really connects + + + align:start position:0% +where the windshield really connects +these handles that the driver basically + + align:start position:0% +these handles that the driver basically + + + align:start position:0% +these handles that the driver basically +holds and PES + + align:start position:0% + + + + align:start position:0% + +up that's that's again with with the + + align:start position:0% +up that's that's again with with the + + + align:start position:0% +up that's that's again with with the +with the + + align:start position:0% +with the + + + align:start position:0% +with the +canopy and close + + align:start position:0% + + + + align:start position:0% + +that uh so we had to look because was + + align:start position:0% +that uh so we had to look because was + + + align:start position:0% +that uh so we had to look because was +made have plexy glass we had to sort of + + align:start position:0% +made have plexy glass we had to sort of + + + align:start position:0% +made have plexy glass we had to sort of +analyze the loads we're going to put on + + align:start position:0% +analyze the loads we're going to put on + + + align:start position:0% +analyze the loads we're going to put on +it see how strong it would be um + + align:start position:0% +it see how strong it would be um + + + align:start position:0% +it see how strong it would be um +plexiglass tends to uh stress crack and + + align:start position:0% +plexiglass tends to uh stress crack and + + + align:start position:0% +plexiglass tends to uh stress crack and +then it starts just splitting basically + + align:start position:0% +then it starts just splitting basically + + + align:start position:0% +then it starts just splitting basically +so it won't you know catastrophically + + align:start position:0% +so it won't you know catastrophically + + + align:start position:0% +so it won't you know catastrophically +deform but it'll over time sort of wear + + align:start position:0% +deform but it'll over time sort of wear + + + align:start position:0% +deform but it'll over time sort of wear +out and so we had a few tests the first + + align:start position:0% +out and so we had a few tests the first + + + align:start position:0% +out and so we had a few tests the first +test was the hard opening so this is + + align:start position:0% +test was the hard opening so this is + + + align:start position:0% +test was the hard opening so this is +when someone sitting in the car and they + + align:start position:0% +when someone sitting in the car and they + + + align:start position:0% +when someone sitting in the car and they +want to get out they sort of overdo it + + align:start position:0% +want to get out they sort of overdo it + + + align:start position:0% +want to get out they sort of overdo it +and slam it to the end of the rail and + + align:start position:0% +and slam it to the end of the rail and + + + align:start position:0% +and slam it to the end of the rail and +so this is mod + + align:start position:0% +so this is mod + + + align:start position:0% +so this is mod +um as as this part + + align:start position:0% +um as as this part + + + align:start position:0% +um as as this part +fixed because that's the part that + + align:start position:0% +fixed because that's the part that + + + align:start position:0% +fixed because that's the part that +slides in the rail that's attached the + + align:start position:0% +slides in the rail that's attached the + + + align:start position:0% +slides in the rail that's attached the +rail so it's more or less fixed and this + + align:start position:0% +rail so it's more or less fixed and this + + + align:start position:0% +rail so it's more or less fixed and this +U you know up and forward motion which + + align:start position:0% +U you know up and forward motion which + + + align:start position:0% +U you know up and forward motion which +is what happens when we slide it in and + + align:start position:0% +is what happens when we slide it in and + + + align:start position:0% +is what happens when we slide it in and +this is force of 2G mass count so there + + align:start position:0% +this is force of 2G mass count so there + + + align:start position:0% +this is force of 2G mass count so there +it is um you see the stress is + + align:start position:0% +it is um you see the stress is + + + align:start position:0% +it is um you see the stress is +concentrated around the joint um but + + align:start position:0% +concentrated around the joint um but + + + align:start position:0% +concentrated around the joint um but +more or less you know we're seeing lots + + align:start position:0% +more or less you know we're seeing lots + + + align:start position:0% +more or less you know we're seeing lots +of blue and green which is + + align:start position:0% +of blue and green which is + + + align:start position:0% +of blue and green which is +okay but um the displacements are also + + align:start position:0% +okay but um the displacements are also + + + align:start position:0% +okay but um the displacements are also +acceptable the canopy deforms quite a + + align:start position:0% +acceptable the canopy deforms quite a + + + align:start position:0% +acceptable the canopy deforms quite a +bit but it always comes back to shape + + align:start position:0% +bit but it always comes back to shape + + + align:start position:0% +bit but it always comes back to shape +Reon and so that part was + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +one this is a driving pressure force uh + + align:start position:0% +one this is a driving pressure force uh + + + align:start position:0% +one this is a driving pressure force uh +theoretically the HPV can go up to 60 M + + align:start position:0% +theoretically the HPV can go up to 60 M + + + align:start position:0% +theoretically the HPV can go up to 60 M +hour no one's ever doing it that fast as + + align:start position:0% +hour no one's ever doing it that fast as + + + align:start position:0% +hour no one's ever doing it that fast as +far as I know but we want to see what + + align:start position:0% +far as I know but we want to see what + + + align:start position:0% +far as I know but we want to see what +pressure distribution sort of would be + + align:start position:0% +pressure distribution sort of would be + + + align:start position:0% +pressure distribution sort of would be +on the caterine at the speed just to see + + align:start position:0% +on the caterine at the speed just to see + + + align:start position:0% +on the caterine at the speed just to see +how strong C be we were experimenting + + align:start position:0% +how strong C be we were experimenting + + + align:start position:0% +how strong C be we were experimenting +with different thicknesses and we ended + + align:start position:0% +with different thicknesses and we ended + + + align:start position:0% +with different thicknesses and we ended +up with something that's about a 16th of + + align:start position:0% +up with something that's about a 16th of + + + align:start position:0% +up with something that's about a 16th of +an inch between + + align:start position:0% +an inch between + + + align:start position:0% +an inch between +16 and um so we're looking at P + + align:start position:0% +16 and um so we're looking at P + + + align:start position:0% +16 and um so we're looking at P +distribution and see + + align:start position:0% +distribution and see + + + align:start position:0% +distribution and see +how basically feel strong enough and + + align:start position:0% +how basically feel strong enough and + + + align:start position:0% +how basically feel strong enough and +also do we get any sort of resonant + + align:start position:0% +also do we get any sort of resonant + + + align:start position:0% +also do we get any sort of resonant +frequencies as it starts bubbling and + + align:start position:0% +frequencies as it starts bubbling and + + + align:start position:0% +frequencies as it starts bubbling and +all that kind of stuff um you see the + + align:start position:0% +all that kind of stuff um you see the + + + align:start position:0% +all that kind of stuff um you see the +first one at 05z and the Cy displacement + + align:start position:0% +first one at 05z and the Cy displacement + + + align:start position:0% +first one at 05z and the Cy displacement +was about 3 mm Max 60 MPH um + + align:start position:0% +was about 3 mm Max 60 MPH um + + + align:start position:0% +was about 3 mm Max 60 MPH um +which again not so bad uh the two things + + align:start position:0% +which again not so bad uh the two things + + + align:start position:0% +which again not so bad uh the two things +to look at here is that sort of for for + + align:start position:0% +to look at here is that sort of for for + + + align:start position:0% +to look at here is that sort of for for +show the canopy dis Wasing 3 mm not so + + align:start position:0% +show the canopy dis Wasing 3 mm not so + + + align:start position:0% +show the canopy dis Wasing 3 mm not so +bad because it's just you know for sure + + align:start position:0% +bad because it's just you know for sure + + + align:start position:0% +bad because it's just you know for sure +if we were to enter it in sort of like + + align:start position:0% +if we were to enter it in sort of like + + + align:start position:0% +if we were to enter it in sort of like +EC Marathon or something like that we'd + + align:start position:0% +EC Marathon or something like that we'd + + + align:start position:0% +EC Marathon or something like that we'd +actually want to probably use the + + align:start position:0% +actually want to probably use the + + + align:start position:0% +actually want to probably use the +original hard copy so that the + + align:start position:0% +original hard copy so that the + + + align:start position:0% +original hard copy so that the +aerodynamics were strin very well + + align:start position:0% +aerodynamics were strin very well + + + align:start position:0% +aerodynamics were strin very well +flopping + + align:start position:0% +flopping + + + align:start position:0% +flopping +around but that's not in future next + + align:start position:0% +around but that's not in future next + + + align:start position:0% +around but that's not in future next +slide uh rail optimization and so we had + + align:start position:0% +slide uh rail optimization and so we had + + + align:start position:0% +slide uh rail optimization and so we had +the rails as everyone saw and the guy + + align:start position:0% +the rails as everyone saw and the guy + + + align:start position:0% +the rails as everyone saw and the guy +thing and we were looking sort of at um + + align:start position:0% +thing and we were looking sort of at um + + + align:start position:0% +thing and we were looking sort of at um +the thickness of the rail they need to + + align:start position:0% +the thickness of the rail they need to + + + align:start position:0% +the thickness of the rail they need to +be the main issue with the rail is that + + align:start position:0% +be the main issue with the rail is that + + + align:start position:0% +be the main issue with the rail is that +it's that kind of shape as you see here + + align:start position:0% +it's that kind of shape as you see here + + + align:start position:0% +it's that kind of shape as you see here +and it's mounted just here and here + + align:start position:0% +and it's mounted just here and here + + + align:start position:0% +and it's mounted just here and here +which means if you hit it here + + align:start position:0% +which means if you hit it here + + + align:start position:0% +which means if you hit it here +especially into the pl the board you're + + align:start position:0% +especially into the pl the board you're + + + align:start position:0% +especially into the pl the board you're +getting a huge moment at the base and + + align:start position:0% +getting a huge moment at the base and + + + align:start position:0% +getting a huge moment at the base and +that's I think the really the + + align:start position:0% +that's I think the really the + + + align:start position:0% +that's I think the really the +constraining issue with our rail um um + + align:start position:0% +constraining issue with our rail um um + + + align:start position:0% +constraining issue with our rail um um +so we bu the thickness in the rail to + + align:start position:0% +so we bu the thickness in the rail to + + + align:start position:0% +so we bu the thickness in the rail to +find the optimum sizes and and um the + + align:start position:0% +find the optimum sizes and and um the + + + align:start position:0% +find the optimum sizes and and um the +side note load we did was 40 Ms uh which + + align:start position:0% +side note load we did was 40 Ms uh which + + + align:start position:0% +side note load we did was 40 Ms uh which +is basically someone leing on the copy + + align:start position:0% +is basically someone leing on the copy + + + align:start position:0% +is basically someone leing on the copy +accidentally or when you're getting the + + align:start position:0% +accidentally or when you're getting the + + + align:start position:0% +accidentally or when you're getting the +car accidentally kicking the rail that + + align:start position:0% +car accidentally kicking the rail that + + + align:start position:0% +car accidentally kicking the rail that +kind of thing and um so we tried at + + align:start position:0% +kind of thing and um so we tried at + + + align:start position:0% +kind of thing and um so we tried at +first making this two ways the numbers + + align:start position:0% +first making this two ways the numbers + + + align:start position:0% +first making this two ways the numbers +came out to be fairly thick at first um + + align:start position:0% +came out to be fairly thick at first um + + + align:start position:0% +came out to be fairly thick at first um +us I think it just came out to be half + + align:start position:0% +us I think it just came out to be half + + + align:start position:0% +us I think it just came out to be half +an inch or something there and like wow + + align:start position:0% +an inch or something there and like wow + + + align:start position:0% +an inch or something there and like wow +half inch a little bit of block that's + + align:start position:0% +half inch a little bit of block that's + + + align:start position:0% +half inch a little bit of block that's +kind of thick so we tried making a + + align:start position:0% +kind of thick so we tried making a + + + align:start position:0% +kind of thick so we tried making a +sandwich material and it's like this is + + align:start position:0% +sandwich material and it's like this is + + + align:start position:0% +sandwich material and it's like this is +not you know didn't work too well El + + align:start position:0% +not you know didn't work too well El + + + align:start position:0% +not you know didn't work too well El +laminated especially didn't tried to + + align:start position:0% +laminated especially didn't tried to + + + align:start position:0% +laminated especially didn't tried to +glue it after water ding + + align:start position:0% +glue it after water ding + + + align:start position:0% +glue it after water ding +it um and so that worked but now we're + + align:start position:0% +it um and so that worked but now we're + + + align:start position:0% +it um and so that worked but now we're +using a 0.25 aluminum Rail and what we + + align:start position:0% +using a 0.25 aluminum Rail and what we + + + align:start position:0% +using a 0.25 aluminum Rail and what we +did to to to allow ourselves to go to + + align:start position:0% +did to to to allow ourselves to go to + + + align:start position:0% +did to to to allow ourselves to go to +that thinner amount is we increased the + + align:start position:0% +that thinner amount is we increased the + + + align:start position:0% +that thinner amount is we increased the +thickness of this part uh the next to + + align:start position:0% +thickness of this part uh the next to + + + align:start position:0% +thickness of this part uh the next to +the sort of the margin between the slot + + align:start position:0% +the sort of the margin between the slot + + + align:start position:0% +the sort of the margin between the slot +and the rail and what that we found was + + align:start position:0% +and the rail and what that we found was + + + align:start position:0% +and the rail and what that we found was +there's a lot of twisting in the rail in + + align:start position:0% +there's a lot of twisting in the rail in + + + align:start position:0% +there's a lot of twisting in the rail in +the first one we made so we increased + + align:start position:0% +the first one we made so we increased + + + align:start position:0% +the first one we made so we increased +that thickness and that helped us + + align:start position:0% +that thickness and that helped us + + + align:start position:0% +that thickness and that helped us +improve the S um next slide okay I'm + + align:start position:0% +improve the S um next slide okay I'm + + + align:start position:0% +improve the S um next slide okay I'm +sorry I didn't quite catch that um based + + align:start position:0% +sorry I didn't quite catch that um based + + + align:start position:0% +sorry I didn't quite catch that um based +on your safety Factor first you had half + + align:start position:0% +on your safety Factor first you had half + + + align:start position:0% +on your safety Factor first you had half +an inch and that caused + + align:start position:0% +an inch and that caused + + + align:start position:0% +an inch and that caused +delamination then you said no we're + + align:start position:0% +delamination then you said no we're + + + align:start position:0% +delamination then you said no we're +going to go to + + align:start position:0% +going to go to + + + align:start position:0% +going to go to +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +0.25 uh but now the rail is a of + + align:start position:0% +0.25 uh but now the rail is a of + + + align:start position:0% +0.25 uh but now the rail is a of +non-uniform thickness uh no um say so + + align:start position:0% +non-uniform thickness uh no um say so + + + align:start position:0% +non-uniform thickness uh no um say so +first we had half an inch and we thought + + align:start position:0% +first we had half an inch and we thought + + + align:start position:0% +first we had half an inch and we thought +wow this is really heavy so we made that + + align:start position:0% +wow this is really heavy so we made that + + + align:start position:0% +wow this is really heavy so we made that +laminate which was aluminum wood + + align:start position:0% +laminate which was aluminum wood + + + align:start position:0% +laminate which was aluminum wood +aluminum plywood and it didn't work very + + align:start position:0% +aluminum plywood and it didn't work very + + + align:start position:0% +aluminum plywood and it didn't work very +well it's very twisty all that so then + + align:start position:0% +well it's very twisty all that so then + + + align:start position:0% +well it's very twisty all that so then +we said well I mean I guess me airace + + align:start position:0% +we said well I mean I guess me airace + + + align:start position:0% +we said well I mean I guess me airace +engine thought Happ in M it's a really + + align:start position:0% +engine thought Happ in M it's a really + + + align:start position:0% +engine thought Happ in M it's a really +thick rail do we really need that thick + + align:start position:0% +thick rail do we really need that thick + + + align:start position:0% +thick rail do we really need that thick +and so what we did was made a design + + align:start position:0% +and so what we did was made a design + + + align:start position:0% +and so what we did was made a design +change where we found that this is the + + align:start position:0% +change where we found that this is the + + + align:start position:0% +change where we found that this is the +weaker as you can see this is the the + + align:start position:0% +weaker as you can see this is the the + + + align:start position:0% +weaker as you can see this is the the +weak area and here and so we thickened + + align:start position:0% +weak area and here and so we thickened + + + align:start position:0% +weak area and here and so we thickened +these parts made the rail this wide and + + align:start position:0% +these parts made the rail this wide and + + + align:start position:0% +these parts made the rail this wide and +we made this one wider too same Groove + + align:start position:0% +we made this one wider too same Groove + + + align:start position:0% +we made this one wider too same Groove +size but more more material this way + + align:start position:0% +size but more more material this way + + + align:start position:0% +size but more more material this way +into into the but still uh 25 thickness + + align:start position:0% +into into the but still uh 25 thickness + + + align:start position:0% +into into the but still uh 25 thickness +you just broaden the rail right exactly + + align:start position:0% +you just broaden the rail right exactly + + + align:start position:0% +you just broaden the rail right exactly +and that that helped a lot + + align:start position:0% +and that that helped a lot + + + align:start position:0% +and that that helped a lot +yeah um this is our solid work + + align:start position:0% +yeah um this is our solid work + + + align:start position:0% +yeah um this is our solid work +optimization we use the optimization + + align:start position:0% +optimization we use the optimization + + + align:start position:0% +optimization we use the optimization +feature pretty interesting um sort of uh + + align:start position:0% +feature pretty interesting um sort of uh + + + align:start position:0% +feature pretty interesting um sort of uh +it go this is a design variable which is + + align:start position:0% +it go this is a design variable which is + + + align:start position:0% +it go this is a design variable which is +our case thickness so we basically asked + + align:start position:0% +our case thickness so we basically asked + + + align:start position:0% +our case thickness so we basically asked +solid works we had the rail and we said + + align:start position:0% +solid works we had the rail and we said + + + align:start position:0% +solid works we had the rail and we said +this is actually prior to the + + align:start position:0% +this is actually prior to the + + + align:start position:0% +this is actually prior to the +manufacturing we had the rail and we + + align:start position:0% +manufacturing we had the rail and we + + + align:start position:0% +manufacturing we had the rail and we +said how th should the rail be for these + + align:start position:0% +said how th should the rail be for these + + + align:start position:0% +said how th should the rail be for these +loads and it goes through all its + + align:start position:0% +loads and it goes through all its + + + align:start position:0% +loads and it goes through all its +different points and you see points here + + align:start position:0% +different points and you see points here + + + align:start position:0% +different points and you see points here +again yeah and what this shows you is + + align:start position:0% +again yeah and what this shows you is + + + align:start position:0% +again yeah and what this shows you is +that um this is like optimality so lower + + align:start position:0% +that um this is like optimality so lower + + + align:start position:0% +that um this is like optimality so lower +is better Until It Breaks so what this + + align:start position:0% +is better Until It Breaks so what this + + + align:start position:0% +is better Until It Breaks so what this +shows you solid works optimization path + + align:start position:0% +shows you solid works optimization path + + + align:start position:0% +shows you solid works optimization path +which it first suggested a one in rail + + align:start position:0% +which it first suggested a one in rail + + + align:start position:0% +which it first suggested a one in rail +it just iterates to get the right number + + align:start position:0% +it just iterates to get the right number + + + align:start position:0% +it just iterates to get the right number +and it went down + + align:start position:0% +and it went down + + + align:start position:0% +and it went down +went back up went down and finally set + + align:start position:0% +went back up went down and finally set + + + align:start position:0% +went back up went down and finally set +at a 23 in rail which is why I went to + + align:start position:0% + + + + align:start position:0% + +25 okay uh having just come from the + + align:start position:0% +25 okay uh having just come from the + + + align:start position:0% +25 okay uh having just come from the +workshop that was thought I should talk + + align:start position:0% +workshop that was thought I should talk + + + align:start position:0% +workshop that was thought I should talk +about + + align:start position:0% +about + + + align:start position:0% +about +cation uh our + + align:start position:0% +cation uh our + + + align:start position:0% +cation uh our +cany uh we tried to heat form it + + align:start position:0% +cany uh we tried to heat form it + + + align:start position:0% +cany uh we tried to heat form it +ourselves just using heat guns and the + + align:start position:0% +ourselves just using heat guns and the + + + align:start position:0% +ourselves just using heat guns and the +existing mold that didn't work at all + + align:start position:0% +existing mold that didn't work at all + + + align:start position:0% +existing mold that didn't work at all +probably didn't really match the shell + + align:start position:0% +probably didn't really match the shell + + + align:start position:0% +probably didn't really match the shell +very well so we ordered a counter from a + + align:start position:0% +very well so we ordered a counter from a + + + align:start position:0% +very well so we ordered a counter from a +professional manufacturer in Florida + + align:start position:0% +professional manufacturer in Florida + + + align:start position:0% +professional manufacturer in Florida +uh the handles which they're made out of + + align:start position:0% +uh the handles which they're made out of + + + align:start position:0% +uh the handles which they're made out of +aluminum 2 and they're being welded onto + + align:start position:0% +aluminum 2 and they're being welded onto + + + align:start position:0% +aluminum 2 and they're being welded onto +water Jed guide rails uh which will then + + align:start position:0% +water Jed guide rails uh which will then + + + align:start position:0% +water Jed guide rails uh which will then +be attached by UK clamp to the existing + + align:start position:0% +be attached by UK clamp to the existing + + + align:start position:0% +be attached by UK clamp to the existing +chassi and then to attach to keep the + + align:start position:0% +chassi and then to attach to keep the + + + align:start position:0% +chassi and then to attach to keep the +canop in this we're going to use + + align:start position:0% +canop in this we're going to use + + + align:start position:0% +canop in this we're going to use +adhesive back magnetic strip which is + + align:start position:0% +adhesive back magnetic strip which is + + + align:start position:0% +adhesive back magnetic strip which is +mounted on of the canop and + + align:start position:0% +mounted on of the canop and + + + align:start position:0% +mounted on of the canop and +shell uh + + align:start position:0% +shell uh + + + align:start position:0% +shell uh +so right there these uh these are reals + + align:start position:0% +so right there these uh these are reals + + + align:start position:0% +so right there these uh these are reals +uh you can see we mounted those on the + + align:start position:0% +uh you can see we mounted those on the + + + align:start position:0% +uh you can see we mounted those on the +chassis just using clamps last night and + + align:start position:0% +chassis just using clamps last night and + + + align:start position:0% +chassis just using clamps last night and +in order to draw a line on the shell + + align:start position:0% +in order to draw a line on the shell + + + align:start position:0% +in order to draw a line on the shell +which is one of the fundamental + + align:start position:0% +which is one of the fundamental + + + align:start position:0% +which is one of the fundamental +manufacturing problems we had how do you + + align:start position:0% +manufacturing problems we had how do you + + + align:start position:0% +manufacturing problems we had how do you +get an exact curve cut on the shell we + + align:start position:0% +get an exact curve cut on the shell we + + + align:start position:0% +get an exact curve cut on the shell we +came up with this say genius hydraulic + + align:start position:0% +came up with this say genius hydraulic + + + align:start position:0% +came up with this say genius hydraulic +mechanism where we matched the two + + align:start position:0% +mechanism where we matched the two + + + align:start position:0% +mechanism where we matched the two +rails like so the same level and same + + align:start position:0% +rails like so the same level and same + + + align:start position:0% +rails like so the same level and same +distance apart and then and that's use + + align:start position:0% +distance apart and then and that's use + + + align:start position:0% +distance apart and then and that's use +the horizontal marking fill to draw a + + align:start position:0% +the horizontal marking fill to draw a + + + align:start position:0% +the horizontal marking fill to draw a +curve on the + + align:start position:0% +curve on the + + + align:start position:0% +curve on the +shell uh now you have a curve on one + + align:start position:0% +shell uh now you have a curve on one + + + align:start position:0% +shell uh now you have a curve on one +side of the + + align:start position:0% +side of the + + + align:start position:0% +side of the +shell uh how do you replicate the exact + + align:start position:0% +shell uh how do you replicate the exact + + + align:start position:0% +shell uh how do you replicate the exact +same curve on the other side uh one + + align:start position:0% +same curve on the other side uh one + + + align:start position:0% +same curve on the other side uh one +answer probably not the most efficient + + align:start position:0% +answer probably not the most efficient + + + align:start position:0% +answer probably not the most efficient +answer is to draw a grid on your shell + + align:start position:0% +answer is to draw a grid on your shell + + + align:start position:0% +answer is to draw a grid on your shell +like so so this this line here it's a + + align:start position:0% +like so so this this line here it's a + + + align:start position:0% +like so so this this line here it's a +fixed distance from the these lines are + + align:start position:0% +fixed distance from the these lines are + + + align:start position:0% +fixed distance from the these lines are +all all have exactly the same which was + + align:start position:0% +all all have exactly the same which was + + + align:start position:0% +all all have exactly the same which was +100 mm and you can see on the other + + align:start position:0% +100 mm and you can see on the other + + + align:start position:0% +100 mm and you can see on the other +sides we the same a image of this line + + align:start position:0% +sides we the same a image of this line + + + align:start position:0% +sides we the same a image of this line +image of the grid and then we just + + align:start position:0% +image of the grid and then we just + + + align:start position:0% +image of the grid and then we just +measured these distances using string + + align:start position:0% +measured these distances using string + + + align:start position:0% +measured these distances using string +and transferred them across and that was + + align:start position:0% +and transferred them across and that was + + + align:start position:0% +and transferred them across and that was +surprisingly accurate to within about 2 + + align:start position:0% +surprisingly accurate to within about 2 + + + align:start position:0% +surprisingly accurate to within about 2 +or 3 + + align:start position:0% +or 3 + + + align:start position:0% +or 3 +mm and uh from there we went to cutting + + align:start position:0% +mm and uh from there we went to cutting + + + align:start position:0% +mm and uh from there we went to cutting +it and is that the actual canopy from + + align:start position:0% +it and is that the actual canopy from + + + align:start position:0% +it and is that the actual canopy from +Florida yes that is oh so so that was a + + align:start position:0% +Florida yes that is oh so so that was a + + + align:start position:0% +Florida yes that is oh so so that was a +fairly quick delivery time oh yes + + align:start position:0% +fairly quick delivery time oh yes + + + align:start position:0% +fairly quick delivery time oh yes +absolutely + + align:start position:0% +absolutely + + + align:start position:0% +absolutely +within about three four days of ordering + + align:start position:0% +within about three four days of ordering + + + align:start position:0% +within about three four days of ordering +it five days of ordering it we had a + + align:start position:0% +it five days of ordering it we had a + + + align:start position:0% +it five days of ordering it we had a +that's very + + align:start position:0% +that's very + + + align:start position:0% +that's very +impressive well the canopy was not + + align:start position:0% +impressive well the canopy was not + + + align:start position:0% +impressive well the canopy was not +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +shap yeah part of the the trick of + + align:start position:0% +shap yeah part of the the trick of + + + align:start position:0% +shap yeah part of the the trick of +canopies we use this guy hand forms + + align:start position:0% +canopies we use this guy hand forms + + + align:start position:0% +canopies we use this guy hand forms +canopies as opposed to everyone else + + align:start position:0% +canopies as opposed to everyone else + + + align:start position:0% +canopies as opposed to everyone else +that's like where's your CNC mold well + + align:start position:0% +that's like where's your CNC mold well + + + align:start position:0% +that's like where's your CNC mold well +we don't have one it's not going to make + + align:start position:0% +we don't have one it's not going to make + + + align:start position:0% +we don't have one it's not going to make +one for $20,000 so um the result of that + + align:start position:0% +one for $20,000 so um the result of that + + + align:start position:0% +one for $20,000 so um the result of that +is exact shape but it actually turned + + align:start position:0% +is exact shape but it actually turned + + + align:start position:0% +is exact shape but it actually turned +out pretty + + align:start position:0% +out pretty + + + align:start position:0% +out pretty +good over hang the + + align:start position:0% +good over hang the + + + align:start position:0% +good over hang the +edge so we uh yeah we we cut it uh and + + align:start position:0% +edge so we uh yeah we we cut it uh and + + + align:start position:0% +edge so we uh yeah we we cut it uh and +we found that to be actually quite + + align:start position:0% +we found that to be actually quite + + + align:start position:0% +we found that to be actually quite +awkward and our accuracy of 2 or 3 mm + + align:start position:0% +awkward and our accuracy of 2 or 3 mm + + + align:start position:0% +awkward and our accuracy of 2 or 3 mm +was perfectly + + align:start position:0% +was perfectly + + + align:start position:0% +was perfectly +te the + + align:start position:0% +te the + + + align:start position:0% +te the +measurements uh so we took the plunge + + align:start position:0% +measurements uh so we took the plunge + + + align:start position:0% +measurements uh so we took the plunge +cut a big ho out of the shell and + + align:start position:0% +cut a big ho out of the shell and + + + align:start position:0% +cut a big ho out of the shell and +there's no going back now uh this is + + align:start position:0% +there's no going back now uh this is + + + align:start position:0% +there's no going back now uh this is +kind of the will look uh you can see we + + align:start position:0% +kind of the will look uh you can see we + + + align:start position:0% +kind of the will look uh you can see we +have a + + align:start position:0% +have a + + + align:start position:0% +have a +here we do have extra pieces of plastic + + align:start position:0% +here we do have extra pieces of plastic + + + align:start position:0% +here we do have extra pieces of plastic +which we can uh form to person can + + align:start position:0% +which we can uh form to person can + + + align:start position:0% +which we can uh form to person can +couldn't go down into this area and ni + + align:start position:0% +couldn't go down into this area and ni + + + align:start position:0% +couldn't go down into this area and ni +curve how are you going to are you going + + align:start position:0% +curve how are you going to are you going + + + align:start position:0% +curve how are you going to are you going +to double them up or how you going uh + + align:start position:0% +to double them up or how you going uh + + + align:start position:0% +to double them up or how you going uh +yeah we plan to either we have a couple + + align:start position:0% +yeah we plan to either we have a couple + + + align:start position:0% +yeah we plan to either we have a couple +options we're thinking perhaps using the + + align:start position:0% +options we're thinking perhaps using the + + + align:start position:0% +options we're thinking perhaps using the +Shell that we cut + + align:start position:0% +Shell that we cut + + + align:start position:0% +Shell that we cut +out Bring it across there and that would + + align:start position:0% +out Bring it across there and that would + + + align:start position:0% +out Bring it across there and that would +give reinforcement uh and then either + + align:start position:0% +give reinforcement uh and then either + + + align:start position:0% +give reinforcement uh and then either +glue or + + align:start position:0% +glue or + + + align:start position:0% +glue or +toach the or we have extra plastic that + + align:start position:0% +toach the or we have extra plastic that + + + align:start position:0% +toach the or we have extra plastic that +we can form using the volts and again + + align:start position:0% +we can form using the volts and again + + + align:start position:0% +we can form using the volts and again +just reinforce a + + align:start position:0% +just reinforce a + + + align:start position:0% +just reinforce a +bit + + align:start position:0% +bit + + + align:start position:0% +bit +bolts uh so what's next the handles are + + align:start position:0% +bolts uh so what's next the handles are + + + align:start position:0% +bolts uh so what's next the handles are +being bu to the reels as we + + align:start position:0% +being bu to the reels as we + + + align:start position:0% +being bu to the reels as we +speak to the chassis + + align:start position:0% +speak to the chassis + + + align:start position:0% +speak to the chassis +refor + + align:start position:0% +refor + + + align:start position:0% +refor +reinforcement handles test mechanism + + align:start position:0% +reinforcement handles test mechanism + + + align:start position:0% +reinforcement handles test mechanism +might come after we drive solid works + + align:start position:0% +might come after we drive solid works + + + align:start position:0% +might come after we drive solid works +World be on stage by the CEO contested + + align:start position:0% +World be on stage by the CEO contested + + + align:start position:0% +World be on stage by the CEO contested +for us and uh magnetic sh is not so + + align:start position:0% +for us and uh magnetic sh is not so + + + align:start position:0% +for us and uh magnetic sh is not so +important uh if you're not going to be + + align:start position:0% +important uh if you're not going to be + + + align:start position:0% +important uh if you're not going to be +driving + + align:start position:0% +driving + + + align:start position:0% +driving +around uh cost estimation uh the major + + align:start position:0% +around uh cost estimation uh the major + + + align:start position:0% +around uh cost estimation uh the major +cost was uh labor for us uh obviously we + + align:start position:0% +cost was uh labor for us uh obviously we + + + align:start position:0% +cost was uh labor for us uh obviously we +had we were very constrained with the + + align:start position:0% +had we were very constrained with the + + + align:start position:0% +had we were very constrained with the +existing shell and the existing chassis + + align:start position:0% +existing shell and the existing chassis + + + align:start position:0% +existing shell and the existing chassis +so they had whenever it was originally + + align:start position:0% +so they had whenever it was originally + + + align:start position:0% +so they had whenever it was originally +designed it wasn't really how you're + + align:start position:0% +designed it wasn't really how you're + + + align:start position:0% +designed it wasn't really how you're +going to get in the night uh and + + align:start position:0% +going to get in the night uh and + + + align:start position:0% +going to get in the night uh and +especially not how you going to get in + + align:start position:0% +especially not how you going to get in + + + align:start position:0% +especially not how you going to get in +the night in an elegant way so you can + + align:start position:0% +the night in an elegant way so you can + + + align:start position:0% +the night in an elegant way so you can +get in front of the crowd so that was + + align:start position:0% +get in front of the crowd so that was + + + align:start position:0% +get in front of the crowd so that was +quite a big problem for us we spent a + + align:start position:0% +quite a big problem for us we spent a + + + align:start position:0% +quite a big problem for us we spent a +lot of time designing and different + + align:start position:0% +lot of time designing and different + + + align:start position:0% +lot of time designing and different +solutions uh and that's that's the main + + align:start position:0% +solutions uh and that's that's the main + + + align:start position:0% +solutions uh and that's that's the main +cost if you to do again would be a lot + + align:start position:0% +cost if you to do again would be a lot + + + align:start position:0% +cost if you to do again would be a lot +less uh so the lessons we've + + align:start position:0% +less uh so the lessons we've + + + align:start position:0% +less uh so the lessons we've +learned are set realistic goals and I + + align:start position:0% +learned are set realistic goals and I + + + align:start position:0% +learned are set realistic goals and I +think perhaps going for such a + + align:start position:0% +think perhaps going for such a + + + align:start position:0% +think perhaps going for such a +complicated ship May may have been a + + align:start position:0% +complicated ship May may have been a + + + align:start position:0% +complicated ship May may have been a +mistake we will see later on uh better + + align:start position:0% +mistake we will see later on uh better + + + align:start position:0% +mistake we will see later on uh better +use of FDA uh as you see we went for + + align:start position:0% +use of FDA uh as you see we went for + + + align:start position:0% +use of FDA uh as you see we went for +quite chunky reel I think if we' have + + align:start position:0% +quite chunky reel I think if we' have + + + align:start position:0% +quite chunky reel I think if we' have +worked it that a bit more we could have + + align:start position:0% +worked it that a bit more we could have + + + align:start position:0% +worked it that a bit more we could have +got the mass down more which would be + + align:start position:0% +got the mass down more which would be + + + align:start position:0% +got the mass down more which would be +good if thep used for + + align:start position:0% +good if thep used for + + + align:start position:0% +good if thep used for +racing uh as I said we're still + + align:start position:0% +racing uh as I said we're still + + + align:start position:0% +racing uh as I said we're still +manufacturing so we should have started + + align:start position:0% +manufacturing so we should have started + + + align:start position:0% +manufacturing so we should have started +earlier uh having the right tools making + + align:start position:0% +earlier uh having the right tools making + + + align:start position:0% +earlier uh having the right tools making +the right decisions at the right + + align:start position:0% +the right decisions at the right + + + align:start position:0% +the right decisions at the right +time things that here you can just see + + align:start position:0% +time things that here you can just see + + + align:start position:0% +time things that here you can just see +this is what we started with this is as + + align:start position:0% +this is what we started with this is as + + + align:start position:0% +this is what we started with this is as +it was a couple of hours ago to be + + align:start position:0% + + + + align:start position:0% + +continu that's it thank + + align:start position:0% + + + + align:start position:0% + +you okay so is there any + + align:start position:0% +you okay so is there any + + + align:start position:0% +you okay so is there any +questions um I'm not quite clear did you + + align:start position:0% +questions um I'm not quite clear did you + + + align:start position:0% +questions um I'm not quite clear did you +send in like a model and was that shell + + align:start position:0% +send in like a model and was that shell + + + align:start position:0% +send in like a model and was that shell +manufactured or can you say it was an + + align:start position:0% +manufactured or can you say it was an + + + align:start position:0% +manufactured or can you say it was an +already designed shap that you just + + align:start position:0% +already designed shap that you just + + + align:start position:0% +already designed shap that you just +how did that + + align:start position:0% +how did that + + + align:start position:0% +how did that +work you talking about the canopy + + align:start position:0% +work you talking about the canopy + + + align:start position:0% +work you talking about the canopy +yeah we we did we developed a Model A + + align:start position:0% +yeah we we did we developed a Model A + + + align:start position:0% +yeah we we did we developed a Model A +cat model and he did send it but he + + align:start position:0% +cat model and he did send it but he + + + align:start position:0% +cat model and he did send it but he +basically does not deal with + + align:start position:0% +basically does not deal with + + + align:start position:0% +basically does not deal with +cat so so we we had to basically start + + align:start position:0% +cat so so we we had to basically start + + + align:start position:0% +cat so so we we had to basically start +producing points and and just dimensions + + align:start position:0% +producing points and and just dimensions + + + align:start position:0% +producing points and and just dimensions +for him and uh + + align:start position:0% +for him and uh + + + align:start position:0% +for him and uh +approximate okay so that's + + align:start position:0% + + + + align:start position:0% + +why question I have is um as far as like + + align:start position:0% +why question I have is um as far as like + + + align:start position:0% +why question I have is um as far as like +air flow coming in from the front um is + + align:start position:0% +air flow coming in from the front um is + + + align:start position:0% +air flow coming in from the front um is +there some mounting point in the front I + + align:start position:0% +there some mounting point in the front I + + + align:start position:0% +there some mounting point in the front I +mean is air just kind of flowing in it + + align:start position:0% +mean is air just kind of flowing in it + + + align:start position:0% +mean is air just kind of flowing in it +seems like uh intuitively like the copy + + align:start position:0% +seems like uh intuitively like the copy + + + align:start position:0% +seems like uh intuitively like the copy +might want to fly out because the low + + align:start position:0% +might want to fly out because the low + + + align:start position:0% +might want to fly out because the low +pressure inside the cab the high + + align:start position:0% + + + + align:start position:0% + +pressure uh well basically at the minute + + align:start position:0% +pressure uh well basically at the minute + + + align:start position:0% +pressure uh well basically at the minute +there's overlap um we intend to heat + + align:start position:0% +there's overlap um we intend to heat + + + align:start position:0% +there's overlap um we intend to heat +form the just the lip of the C which we + + align:start position:0% +form the just the lip of the C which we + + + align:start position:0% +form the just the lip of the C which we +tried we can't do that just to get a + + align:start position:0% +tried we can't do that just to get a + + + align:start position:0% +tried we can't do that just to get a +flush with the the shell the point at + + align:start position:0% +flush with the the shell the point at + + + align:start position:0% +flush with the the shell the point at +which the shell on the canopy be + + align:start position:0% +which the shell on the canopy be + + + align:start position:0% +which the shell on the canopy be +although you can't tell in the picture + + align:start position:0% +although you can't tell in the picture + + + align:start position:0% +although you can't tell in the picture +is about this angle if you're able to + + align:start position:0% +is about this angle if you're able to + + + align:start position:0% +is about this angle if you're able to +get the flush and so it kind of wraps + + align:start position:0% +get the flush and so it kind of wraps + + + align:start position:0% +get the flush and so it kind of wraps +around the bottom if the shell was a + + align:start position:0% +around the bottom if the shell was a + + + align:start position:0% +around the bottom if the shell was a +better shape it' be easier for us but + + align:start position:0% +better shape it' be easier for us but + + + align:start position:0% +better shape it' be easier for us but +now we have to do more to make it Happ + + align:start position:0% +now we have to do more to make it Happ + + + align:start position:0% +now we have to do more to make it Happ +uh but it's held down pretty well by the + + align:start position:0% +uh but it's held down pretty well by the + + + align:start position:0% +uh but it's held down pretty well by the +rails and uh yeah we'll see it's not + + align:start position:0% +rails and uh yeah we'll see it's not + + + align:start position:0% +rails and uh yeah we'll see it's not +going that fast yet + + align:start position:0% +going that fast yet + + + align:start position:0% +going that fast yet +so oh + + align:start position:0% + + + + align:start position:0% + +was one more your U like original your + + align:start position:0% +was one more your U like original your + + + align:start position:0% +was one more your U like original your +few models at the very beginning are + + align:start position:0% +few models at the very beginning are + + + align:start position:0% +few models at the very beginning are +really excellent were those in Sol work + + align:start position:0% +really excellent were those in Sol work + + + align:start position:0% +really excellent were those in Sol work +you had I mean did you start from + + align:start position:0% +you had I mean did you start from + + + align:start position:0% +you had I mean did you start from +scratch there exactly okay you know I've + + align:start position:0% +scratch there exactly okay you know I've + + + align:start position:0% +scratch there exactly okay you know I've +asked him that question before this is + + align:start position:0% +asked him that question before this is + + + align:start position:0% +asked him that question before this is +an architectural secret I think you're + + align:start position:0% +an architectural secret I think you're + + + align:start position:0% +an architectural secret I think you're +rendering you're rendering software in + + align:start position:0% +rendering you're rendering software in + + + align:start position:0% +rendering you're rendering software in +depends I mean rendering here the movie + + align:start position:0% +depends I mean rendering here the movie + + + align:start position:0% +depends I mean rendering here the movie +was in 3D + + align:start position:0% +was in 3D + + + align:start position:0% +was in 3D +Max software + + align:start position:0% +Max software + + + align:start position:0% +Max software +and the modeling was done in RH and + + align:start position:0% +and the modeling was done in RH and + + + align:start position:0% +and the modeling was done in RH and +solid so it depends which solid works + + align:start position:0% +solid so it depends which solid works + + + align:start position:0% +solid so it depends which solid works +was the one we used for like di + + align:start position:0% +was the one we used for like di + + + align:start position:0% +was the one we used for like di +mentioning when you're actually testing + + align:start position:0% +mentioning when you're actually testing + + + align:start position:0% +mentioning when you're actually testing +something apparently RH easier for + + align:start position:0% +something apparently RH easier for + + + align:start position:0% +something apparently RH easier for +testing out + + align:start position:0% +testing out + + + align:start position:0% +testing out +shapes is good for things and other + + align:start position:0% +shapes is good for things and other + + + align:start position:0% +shapes is good for things and other +software are + + align:start position:0% + + + + align:start position:0% + +definitely um I had a couple of points + + align:start position:0% +definitely um I had a couple of points + + + align:start position:0% +definitely um I had a couple of points +one was U the dynamic load that you + + align:start position:0% +one was U the dynamic load that you + + + align:start position:0% +one was U the dynamic load that you +assume the 2 GS times the uh + + align:start position:0% +assume the 2 GS times the uh + + + align:start position:0% +assume the 2 GS times the uh +weight of the canopy right um if you + + align:start position:0% +weight of the canopy right um if you + + + align:start position:0% +weight of the canopy right um if you +really slam things hard into a into a + + align:start position:0% +really slam things hard into a into a + + + align:start position:0% +really slam things hard into a into a +dead stop the the dynamic load can be + + align:start position:0% +dead stop the the dynamic load can be + + + align:start position:0% +dead stop the the dynamic load can be +significantly higher than 2 days and so + + align:start position:0% +significantly higher than 2 days and so + + + align:start position:0% +significantly higher than 2 days and so +it's a tough problem how to estimate + + align:start position:0% +it's a tough problem how to estimate + + + align:start position:0% +it's a tough problem how to estimate +that but I'm wondering if you can + + align:start position:0% +that but I'm wondering if you can + + + align:start position:0% +that but I'm wondering if you can +um if you put in some some rubber stops + + align:start position:0% +um if you put in some some rubber stops + + + align:start position:0% +um if you put in some some rubber stops +or a spring at the end of the rail + + align:start position:0% +or a spring at the end of the rail + + + align:start position:0% +or a spring at the end of the rail +travel can you can you in other words if + + align:start position:0% +travel can you can you in other words if + + + align:start position:0% +travel can you can you in other words if +you push up the canopy can you dampen + + align:start position:0% +you push up the canopy can you dampen + + + align:start position:0% +you push up the canopy can you dampen +out out that that that end Lo by putting + + align:start position:0% +out out that that that end Lo by putting + + + align:start position:0% +out out that that that end Lo by putting +in some some spring or damper or + + align:start position:0% +in some some spring or damper or + + + align:start position:0% +in some some spring or damper or +something at the end of the rail travel + + align:start position:0% +something at the end of the rail travel + + + align:start position:0% +something at the end of the rail travel +you thought about that um yeah we + + align:start position:0% +you thought about that um yeah we + + + align:start position:0% +you thought about that um yeah we +thought about that um one thing we + + align:start position:0% +thought about that um one thing we + + + align:start position:0% +thought about that um one thing we +thought about was actually mounting + + align:start position:0% +thought about was actually mounting + + + align:start position:0% +thought about was actually mounting +Hydraulics onto the can so it would do + + align:start position:0% +Hydraulics onto the can so it would do + + + align:start position:0% +Hydraulics onto the can so it would do +it nicely and slowly but we just + + align:start position:0% +it nicely and slowly but we just + + + align:start position:0% +it nicely and slowly but we just +couldn't get the geometry quite right in + + align:start position:0% +couldn't get the geometry quite right in + + + align:start position:0% +couldn't get the geometry quite right in +time mostly was really the time had to + + align:start position:0% +time mostly was really the time had to + + + align:start position:0% +time mostly was really the time had to +really zoom + + align:start position:0% +really zoom + + + align:start position:0% +really zoom +in and to I mean I think that's + + align:start position:0% +in and to I mean I think that's + + + align:start position:0% +in and to I mean I think that's +something to look look forward to + + align:start position:0% +something to look look forward to + + + align:start position:0% +something to look look forward to +definitely when it comes back from solid + + align:start position:0% +definitely when it comes back from solid + + + align:start position:0% +definitely when it comes back from solid +works world right now it does have a + + align:start position:0% +works world right now it does have a + + + align:start position:0% +works world right now it does have a +little dip at the end which is like + + align:start position:0% +little dip at the end which is like + + + align:start position:0% +little dip at the end which is like +potential hold it there and so like when + + align:start position:0% +potential hold it there and so like when + + + align:start position:0% +potential hold it there and so like when +you slam it it + + align:start position:0% +you slam it it + + + align:start position:0% +you slam it it +should go down which willand it from a + + align:start position:0% +should go down which willand it from a + + + align:start position:0% +should go down which willand it from a +direct slam but still so maybe you can + + align:start position:0% +direct slam but still so maybe you can + + + align:start position:0% +direct slam but still so maybe you can +just put in some some rubber things at + + align:start position:0% +just put in some some rubber things at + + + align:start position:0% +just put in some some rubber things at +the end of the Rails just to and then + + align:start position:0% +the end of the Rails just to and then + + + align:start position:0% +the end of the Rails just to and then +the second question was this is an + + align:start position:0% +the second question was this is an + + + align:start position:0% +the second question was this is an +ahpv + + align:start position:0% +ahpv + + + align:start position:0% +ahpv +so okay now it's cold outside so that + + align:start position:0% +so okay now it's cold outside so that + + + align:start position:0% +so okay now it's cold outside so that +won't be a big problem but uh if someone + + align:start position:0% +won't be a big problem but uh if someone + + + align:start position:0% +won't be a big problem but uh if someone +is really pedling hard on this uh going + + align:start position:0% +is really pedling hard on this uh going + + + align:start position:0% +is really pedling hard on this uh going +to + + align:start position:0% +to + + + align:start position:0% +to +work uh a lot of heat is going to + + align:start position:0% +work uh a lot of heat is going to + + + align:start position:0% +work uh a lot of heat is going to +develop in there uh how does that + + align:start position:0% +develop in there uh how does that + + + align:start position:0% +develop in there uh how does that +internal air flow management uh you know + + align:start position:0% +internal air flow management uh you know + + + align:start position:0% +internal air flow management uh you know +before it was no problem because it was + + align:start position:0% +before it was no problem because it was + + + align:start position:0% +before it was no problem because it was +open we had free air + + align:start position:0% +open we had free air + + + align:start position:0% +open we had free air +flow + + align:start position:0% +flow + + + align:start position:0% +flow +um you know now you have really nice + + align:start position:0% +um you know now you have really nice + + + align:start position:0% +um you know now you have really nice +Aesthetics but what about the heat + + align:start position:0% +Aesthetics but what about the heat + + + align:start position:0% +Aesthetics but what about the heat +management + + align:start position:0% + + + + align:start position:0% + +and okay um + + align:start position:0% +and okay um + + + align:start position:0% +and okay um +um well so the bottom part of the canopy + + align:start position:0% +um well so the bottom part of the canopy + + + align:start position:0% +um well so the bottom part of the canopy +which is sorry of the shell there's a + + align:start position:0% +which is sorry of the shell there's a + + + align:start position:0% +which is sorry of the shell there's a +bottom part which attaches the HPV it's + + align:start position:0% +bottom part which attaches the HPV it's + + + align:start position:0% +bottom part which attaches the HPV it's +not quite flush and there are holes in + + align:start position:0% +not quite flush and there are holes in + + + align:start position:0% +not quite flush and there are holes in +it actually specifically for the wheel + + align:start position:0% +it actually specifically for the wheel + + + align:start position:0% +it actually specifically for the wheel +well there's there's a gap around the + + align:start position:0% +well there's there's a gap around the + + + align:start position:0% +well there's there's a gap around the +wheel well on both sides and the back of + + align:start position:0% +wheel well on both sides and the back of + + + align:start position:0% +wheel well on both sides and the back of +the motor so we thought about that and + + align:start position:0% +the motor so we thought about that and + + + align:start position:0% +the motor so we thought about that and +um we didn't calculate out the exact + + align:start position:0% +um we didn't calculate out the exact + + + align:start position:0% +um we didn't calculate out the exact +amount of air flow we needed um where it + + align:start position:0% +amount of air flow we needed um where it + + + align:start position:0% +amount of air flow we needed um where it +has more focus on getting it completed + + align:start position:0% +has more focus on getting it completed + + + align:start position:0% +has more focus on getting it completed +but we could cut out some parts for from + + align:start position:0% +but we could cut out some parts for from + + + align:start position:0% +but we could cut out some parts for from +the canopy um on the canopy for air flow + + align:start position:0% +the canopy um on the canopy for air flow + + + align:start position:0% +the canopy um on the canopy for air flow +and but right now there is quite a lot + + align:start position:0% +and but right now there is quite a lot + + + align:start position:0% +and but right now there is quite a lot +of air coming from the wheel well if you + + align:start position:0% +of air coming from the wheel well if you + + + align:start position:0% +of air coming from the wheel well if you +see the wheel walls here the wheel takes + + align:start position:0% +see the wheel walls here the wheel takes + + + align:start position:0% +see the wheel walls here the wheel takes +it's a bicycle wheel and it's all the + + align:start position:0% +it's a bicycle wheel and it's all the + + + align:start position:0% +it's a bicycle wheel and it's all the +space is open and so it really covers + + align:start position:0% +space is open and so it really covers + + + align:start position:0% +space is open and so it really covers +very little of the Wheel wall either + + align:start position:0% +very little of the Wheel wall either + + + align:start position:0% +very little of the Wheel wall either +configuration so I guess we're on that + + align:start position:0% +configuration so I guess we're on that + + + align:start position:0% +configuration so I guess we're on that +right + + align:start position:0% + + + + align:start position:0% + +now okay thank you very + + align:start position:0% + + + + align:start position:0% + +much + + align:start position:0% + + + + align:start position:0% + +okay so that's the end of the + + align:start position:0% +okay so that's the end of the + + + align:start position:0% +okay so that's the end of the +class I get some sleep uh upload + + align:start position:0% +class I get some sleep uh upload + + + align:start position:0% +class I get some sleep uh upload +anything that you haven't uploaded yet + + align:start position:0% +anything that you haven't uploaded yet + + + align:start position:0% +anything that you haven't uploaded yet +and check your email and then have a + + align:start position:0% +and check your email and then have a + + + align:start position:0% +and check your email and then have a +good start and I'm hoping I I don't know + + align:start position:0% +good start and I'm hoping I I don't know + + + align:start position:0% +good start and I'm hoping I I don't know +exactly what everyone's plans are but if + + align:start position:0% +exactly what everyone's plans are but if + + + align:start position:0% +exactly what everyone's plans are but if +if some of you are are interested that + + align:start position:0% +if some of you are are interested that + + + align:start position:0% +if some of you are are interested that +are not part of EDS or midet and you're + + align:start position:0% +are not part of EDS or midet and you're + + + align:start position:0% +are not part of EDS or midet and you're +continuing to you're interested in + + align:start position:0% +continuing to you're interested in + + + align:start position:0% +continuing to you're interested in +continuing to help out by all means uh I + + align:start position:0% +continuing to help out by all means uh I + + + align:start position:0% +continuing to help out by all means uh I +encourage you to sort of I'm assuming + + align:start position:0% +encourage you to sort of I'm assuming + + + align:start position:0% +encourage you to sort of I'm assuming +that they're welcome interest to to + + align:start position:0% +that they're welcome interest to to + + + align:start position:0% +that they're welcome interest to to +immigrate yourself into those teams + + align:start position:0% +immigrate yourself into those teams + + + align:start position:0% +immigrate yourself into those teams +it'll run a little bit differently than + + align:start position:0% +it'll run a little bit differently than + + + align:start position:0% +it'll run a little bit differently than +this class but \ No newline at end of file diff --git a/8hcWKoPR6DI.txt b/8hcWKoPR6DI.txt new file mode 100644 index 0000000000000000000000000000000000000000..33f3bb31c982baafbe8fad32ae37613496fcb814 --- /dev/null +++ b/8hcWKoPR6DI.txt @@ -0,0 +1,6819 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +equilibrium in a unary heterogeneous + + align:start position:0% +equilibrium in a unary heterogeneous + + + align:start position:0% +equilibrium in a unary heterogeneous +system so let me let me give you the + + align:start position:0% +system so let me let me give you the + + + align:start position:0% +system so let me let me give you the +reason why + + align:start position:0% +reason why + + + align:start position:0% +reason why +um we are not talking about phase + + align:start position:0% +um we are not talking about phase + + + align:start position:0% +um we are not talking about phase +diagrams + + align:start position:0% +diagrams + + + align:start position:0% +diagrams +in exam one + + align:start position:0% + + + + align:start position:0% + +but that comes next + + align:start position:0% +but that comes next + + + align:start position:0% +but that comes next +that's what we cover next after the exam + + align:start position:0% +that's what we cover next after the exam + + + align:start position:0% +that's what we cover next after the exam +so today's lecture is like a bridging + + align:start position:0% +so today's lecture is like a bridging + + + align:start position:0% +so today's lecture is like a bridging +lecture we're going to talk about + + align:start position:0% +lecture we're going to talk about + + + align:start position:0% +lecture we're going to talk about +applying equilibrium which we've learned + + align:start position:0% +applying equilibrium which we've learned + + + align:start position:0% +applying equilibrium which we've learned +about + + align:start position:0% + + + + align:start position:0% + +in unary + + align:start position:0% +in unary + + + align:start position:0% +in unary +heterogeneous systems + + align:start position:0% + + + + align:start position:0% + +and of course this will lead into unary + + align:start position:0% +and of course this will lead into unary + + + align:start position:0% +and of course this will lead into unary +phase diagrams + + align:start position:0% +phase diagrams + + + align:start position:0% +phase diagrams +so let's set up the problem this problem + + align:start position:0% +so let's set up the problem this problem + + + align:start position:0% +so let's set up the problem this problem +is as follows we're going to isolate our + + align:start position:0% +is as follows we're going to isolate our + + + align:start position:0% +is as follows we're going to isolate our +system so we have a box + + align:start position:0% +system so we have a box + + + align:start position:0% +system so we have a box +and it's going to have + + align:start position:0% +and it's going to have + + + align:start position:0% +and it's going to have +uh thermal insulation + + align:start position:0% +uh thermal insulation + + + align:start position:0% +uh thermal insulation +imagine the thermal insulation all + + align:start position:0% +imagine the thermal insulation all + + + align:start position:0% +imagine the thermal insulation all +around there and we're going to have two + + align:start position:0% +around there and we're going to have two + + + align:start position:0% +around there and we're going to have two +phases in this box we're going to have + + align:start position:0% +phases in this box we're going to have + + + align:start position:0% +phases in this box we're going to have +an alpha phase + + align:start position:0% + + + + align:start position:0% + +and then over here in a different region + + align:start position:0% +and then over here in a different region + + + align:start position:0% +and then over here in a different region +we're going to have a beta phase + + align:start position:0% + + + + align:start position:0% + +and we're going to have a phase boundary + + align:start position:0% +and we're going to have a phase boundary + + + align:start position:0% +and we're going to have a phase boundary +between them and this is unary so one + + align:start position:0% +between them and this is unary so one + + + align:start position:0% +between them and this is unary so one +component okay so system + + align:start position:0% + + + + align:start position:0% + +with one component + + align:start position:0% + + + + align:start position:0% + +and two phases + + align:start position:0% + + + + align:start position:0% + +we're isolating the system + + align:start position:0% + + + + align:start position:0% + +so if it's isolated from the + + align:start position:0% +so if it's isolated from the + + + align:start position:0% +so if it's isolated from the +surroundings what is going to be its um + + align:start position:0% +surroundings what is going to be its um + + + align:start position:0% +surroundings what is going to be its um +condition for equilibrium + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +for + + align:start position:0% +for + + + align:start position:0% +for +what's the condition for equilibrium for + + align:start position:0% +what's the condition for equilibrium for + + + align:start position:0% +what's the condition for equilibrium for +an isolated system + + align:start position:0% + + + + align:start position:0% + +is it that entropy is that at maximum s + + align:start position:0% +is it that entropy is that at maximum s + + + align:start position:0% +is it that entropy is that at maximum s +Max right maximum entropy condition that + + align:start position:0% +Max right maximum entropy condition that + + + align:start position:0% +Max right maximum entropy condition that +was right isolated system + + align:start position:0% +was right isolated system + + + align:start position:0% +was right isolated system +thank you okay the internal + + align:start position:0% + + + + align:start position:0% + +something + + align:start position:0% + + + + align:start position:0% + +and this is part of the problem + + align:start position:0% +and this is part of the problem + + + align:start position:0% +and this is part of the problem +statement this isn't always true + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +there's a boundary between the phases + + align:start position:0% +there's a boundary between the phases + + + align:start position:0% +there's a boundary between the phases +internally think + + align:start position:0% +internally think + + + align:start position:0% +internally think +the boundary between the ice and the + + align:start position:0% +the boundary between the ice and the + + + align:start position:0% +the boundary between the ice and the +water in your glass of ice water that's + + align:start position:0% +water in your glass of ice water that's + + + align:start position:0% +water in your glass of ice water that's +an example + + align:start position:0% + + + + align:start position:0% + +that internal boundary is non-rigid it's + + align:start position:0% +that internal boundary is non-rigid it's + + + align:start position:0% +that internal boundary is non-rigid it's +open + + align:start position:0% +open + + + align:start position:0% +open +and it's diathermal so + + align:start position:0% +and it's diathermal so + + + align:start position:0% +and it's diathermal so +it's the opposite of the external + + align:start position:0% +it's the opposite of the external + + + align:start position:0% +it's the opposite of the external +boundary so that's the problem setup + + align:start position:0% +boundary so that's the problem setup + + + align:start position:0% +boundary so that's the problem setup +and + + align:start position:0% +and + + + align:start position:0% +and +our goal + + align:start position:0% + + + + align:start position:0% + +is to evaluate the equilibrium condition + + align:start position:0% + + + + align:start position:0% + +so that's it evaluate the equilibrium + + align:start position:0% +so that's it evaluate the equilibrium + + + align:start position:0% +so that's it evaluate the equilibrium +condition + + align:start position:0% +condition + + + align:start position:0% +condition +so let's see what we mean by that + + align:start position:0% + + + + align:start position:0% + +so let's write an expression + + align:start position:0% + + + + align:start position:0% + +all right if we want to evaluate the + + align:start position:0% +all right if we want to evaluate the + + + align:start position:0% +all right if we want to evaluate the +condition DS we have to write an + + align:start position:0% +condition DS we have to write an + + + align:start position:0% +condition DS we have to write an +expression for DS + + align:start position:0% +expression for DS + + + align:start position:0% +expression for DS +so let's start with phase Alpha + + align:start position:0% + + + + align:start position:0% + +for phase Alpha + + align:start position:0% +for phase Alpha + + + align:start position:0% +for phase Alpha +d u of alpha we're going to do combined + + align:start position:0% +d u of alpha we're going to do combined + + + align:start position:0% +d u of alpha we're going to do combined +statement equals T Alpha DS Alpha + + align:start position:0% +statement equals T Alpha DS Alpha + + + align:start position:0% +statement equals T Alpha DS Alpha +minus P Alpha + + align:start position:0% +minus P Alpha + + + align:start position:0% +minus P Alpha +DV Alpha + + align:start position:0% +DV Alpha + + + align:start position:0% +DV Alpha +plus Mu Alpha d n Alpha + + align:start position:0% + + + + align:start position:0% + +here we call a couple lectures ago + + align:start position:0% +here we call a couple lectures ago + + + align:start position:0% +here we call a couple lectures ago +we introduced briefly + + align:start position:0% + + + + align:start position:0% + +superscript phase labels + + align:start position:0% + + + + align:start position:0% + +and now we're going to start using them + + align:start position:0% +and now we're going to start using them + + + align:start position:0% +and now we're going to start using them +now we're going to start using them a + + align:start position:0% +now we're going to start using them a + + + align:start position:0% +now we're going to start using them a +lot + + align:start position:0% +lot + + + align:start position:0% +lot +cost me about a penny okay + + align:start position:0% +cost me about a penny okay + + + align:start position:0% +cost me about a penny okay +all right so this is combined statement + + align:start position:0% +all right so this is combined statement + + + align:start position:0% +all right so this is combined statement +you've seen this before we've just + + align:start position:0% +you've seen this before we've just + + + align:start position:0% +you've seen this before we've just +adding superscript phase labels so we're + + align:start position:0% +adding superscript phase labels so we're + + + align:start position:0% +adding superscript phase labels so we're +going to rearrange this is a pretty uh + + align:start position:0% +going to rearrange this is a pretty uh + + + align:start position:0% +going to rearrange this is a pretty uh +easy algebra operation we're going to + + align:start position:0% +easy algebra operation we're going to + + + align:start position:0% +easy algebra operation we're going to +rearrange and write DS equals + + align:start position:0% +rearrange and write DS equals + + + align:start position:0% +rearrange and write DS equals +1 over T Alpha d u Alpha + + align:start position:0% +1 over T Alpha d u Alpha + + + align:start position:0% +1 over T Alpha d u Alpha +plus P Alpha T Alpha + + align:start position:0% +plus P Alpha T Alpha + + + align:start position:0% +plus P Alpha T Alpha +d v Alpha + + align:start position:0% +d v Alpha + + + align:start position:0% +d v Alpha +minus Mu Alpha T Alpha d n Alpha + + align:start position:0% + + + + align:start position:0% + +likewise + + align:start position:0% + + + + align:start position:0% + +likewise for the beta phase we're going + + align:start position:0% +likewise for the beta phase we're going + + + align:start position:0% +likewise for the beta phase we're going +to have DS of beta + + align:start position:0% +to have DS of beta + + + align:start position:0% +to have DS of beta +equals 1 over T beta + + align:start position:0% +equals 1 over T beta + + + align:start position:0% +equals 1 over T beta +d u beta plus P beta T beta + + align:start position:0% +d u beta plus P beta T beta + + + align:start position:0% +d u beta plus P beta T beta +d v beta minus mu Theta T beta + + align:start position:0% +d v beta minus mu Theta T beta + + + align:start position:0% +d v beta minus mu Theta T beta +DN beta + + align:start position:0% +DN beta + + + align:start position:0% +DN beta +I'm going to try using + + align:start position:0% +I'm going to try using + + + align:start position:0% +I'm going to try using +this pen for a while Center + + align:start position:0% +this pen for a while Center + + + align:start position:0% +this pen for a while Center +you guys can tell me which one you like + + align:start position:0% +you guys can tell me which one you like + + + align:start position:0% +you guys can tell me which one you like +better so we have made an assumption + + align:start position:0% +better so we have made an assumption + + + align:start position:0% +better so we have made an assumption +here which is that + + align:start position:0% +here which is that + + + align:start position:0% +here which is that +the alpha phase is everywhere at the + + align:start position:0% +the alpha phase is everywhere at the + + + align:start position:0% +the alpha phase is everywhere at the +same temperature + + align:start position:0% + + + + align:start position:0% + +also it's everywhere at the same + + align:start position:0% +also it's everywhere at the same + + + align:start position:0% +also it's everywhere at the same +pressure and it's everywhere the same + + align:start position:0% +pressure and it's everywhere the same + + + align:start position:0% +pressure and it's everywhere the same +chemical potential + + align:start position:0% +chemical potential + + + align:start position:0% +chemical potential +similarly we've assumed that the beta + + align:start position:0% +similarly we've assumed that the beta + + + align:start position:0% +similarly we've assumed that the beta +phase is everywhere at the same + + align:start position:0% +phase is everywhere at the same + + + align:start position:0% +phase is everywhere at the same +temperature everywhere at the same + + align:start position:0% +temperature everywhere at the same + + + align:start position:0% +temperature everywhere at the same +pressure and everywhere at the same + + align:start position:0% +pressure and everywhere at the same + + + align:start position:0% +pressure and everywhere at the same +chemical potential + + align:start position:0% +chemical potential + + + align:start position:0% +chemical potential +okay so just I want you know you have to + + align:start position:0% +okay so just I want you know you have to + + + align:start position:0% +okay so just I want you know you have to +State your assumptions it's good to know + + align:start position:0% +State your assumptions it's good to know + + + align:start position:0% +State your assumptions it's good to know +what they are + + align:start position:0% +what they are + + + align:start position:0% +what they are +all right so um + + align:start position:0% + + + + align:start position:0% + +now entropy + + align:start position:0% + + + + align:start position:0% + +I'll ask is it extensive + + align:start position:0% +I'll ask is it extensive + + + align:start position:0% +I'll ask is it extensive +or intensive + + align:start position:0% + + + + align:start position:0% + +extensive extensive right entropy is + + align:start position:0% +extensive extensive right entropy is + + + align:start position:0% +extensive extensive right entropy is +extensive + + align:start position:0% +extensive + + + align:start position:0% +extensive +not intensive + + align:start position:0% +not intensive + + + align:start position:0% +not intensive +so + + align:start position:0% +so + + + align:start position:0% +so +the total DS the thing we're trying to + + align:start position:0% +the total DS the thing we're trying to + + + align:start position:0% +the total DS the thing we're trying to +write + + align:start position:0% +write + + + align:start position:0% +write +equals + + align:start position:0% +equals + + + align:start position:0% +equals +DS Alpha + + align:start position:0% +DS Alpha + + + align:start position:0% +DS Alpha +plus DS + + align:start position:0% +plus DS + + + align:start position:0% +plus DS +beta + + align:start position:0% + + + + align:start position:0% + +I want to make sure that people + + align:start position:0% +I want to make sure that people + + + align:start position:0% +I want to make sure that people +understand that + + align:start position:0% +understand that + + + align:start position:0% +understand that +if there are questions about that + + align:start position:0% +if there are questions about that + + + align:start position:0% +if there are questions about that +concept let's tackle them now + + align:start position:0% +concept let's tackle them now + + + align:start position:0% +concept let's tackle them now +okay + + align:start position:0% +okay + + + align:start position:0% +okay +no questions about that so + + align:start position:0% +no questions about that so + + + align:start position:0% +no questions about that so +that means the total change of entropy + + align:start position:0% +that means the total change of entropy + + + align:start position:0% +that means the total change of entropy +in the system + + align:start position:0% +in the system + + + align:start position:0% +in the system +equals the sum + + align:start position:0% +equals the sum + + + align:start position:0% +equals the sum +of the things where Jesus wrote down so + + align:start position:0% +of the things where Jesus wrote down so + + + align:start position:0% +of the things where Jesus wrote down so +I'm going to take the pains to write it + + align:start position:0% +I'm going to take the pains to write it + + + align:start position:0% +I'm going to take the pains to write it +out + + align:start position:0% + + + + align:start position:0% + +thank you + + align:start position:0% + + + + align:start position:0% + +all right so this is a big differential + + align:start position:0% +all right so this is a big differential + + + align:start position:0% +all right so this is a big differential +equation + + align:start position:0% +equation + + + align:start position:0% +equation +um + + align:start position:0% + + + + align:start position:0% + +let's count variables + + align:start position:0% +let's count variables + + + align:start position:0% +let's count variables +how many variables are there + + align:start position:0% + + + + align:start position:0% + +independent variables how many + + align:start position:0% +independent variables how many + + + align:start position:0% +independent variables how many +independent variables are there + + align:start position:0% + + + + align:start position:0% + +three all right + + align:start position:0% +three all right + + + align:start position:0% +three all right +so there are six here + + align:start position:0% +so there are six here + + + align:start position:0% +so there are six here +U Alpha V Alpha and Alpha U beta V beta + + align:start position:0% +U Alpha V Alpha and Alpha U beta V beta + + + align:start position:0% +U Alpha V Alpha and Alpha U beta V beta +and beta + + align:start position:0% + + + + align:start position:0% + +six variables + + align:start position:0% +six variables + + + align:start position:0% +six variables +and six coefficients + + align:start position:0% + + + + align:start position:0% + +so we're we're learning to identify + + align:start position:0% +so we're we're learning to identify + + + align:start position:0% +so we're we're learning to identify +variables and coefficients from + + align:start position:0% +variables and coefficients from + + + align:start position:0% +variables and coefficients from +differential equations that was + + align:start position:0% +differential equations that was + + + align:start position:0% +differential equations that was +that was a + + align:start position:0% +that was a + + + align:start position:0% +that was a +you know where we were working on for + + align:start position:0% +you know where we were working on for + + + align:start position:0% +you know where we were working on for +the last two lectures so you + + align:start position:0% +the last two lectures so you + + + align:start position:0% +the last two lectures so you +differential form independent dependent + + align:start position:0% +differential form independent dependent + + + align:start position:0% +differential form independent dependent +variable independent variables + + align:start position:0% +variable independent variables + + + align:start position:0% +variable independent variables +coefficients + + align:start position:0% +coefficients + + + align:start position:0% +coefficients +right I want you to really get to the + + align:start position:0% +right I want you to really get to the + + + align:start position:0% +right I want you to really get to the +point where you don't have to think to + + align:start position:0% +point where you don't have to think to + + + align:start position:0% +point where you don't have to think to +pick those off + + align:start position:0% +pick those off + + + align:start position:0% +pick those off +all right so now we're going to talk + + align:start position:0% +all right so now we're going to talk + + + align:start position:0% +all right so now we're going to talk +about optimization + + align:start position:0% + + + + align:start position:0% + +for the case + + align:start position:0% +for the case + + + align:start position:0% +for the case +of unconstrained + + align:start position:0% + + + + align:start position:0% + +unconstrained optimization + + align:start position:0% + + + + align:start position:0% + +DS equals zero + + align:start position:0% + + + + align:start position:0% + +requires + + align:start position:0% +requires + + + align:start position:0% +requires +that all + + align:start position:0% +that all + + + align:start position:0% +that all +six + + align:start position:0% + + + + align:start position:0% + +coefficients + + align:start position:0% +coefficients + + + align:start position:0% +coefficients +equals zero + + align:start position:0% + + + + align:start position:0% + +so those of you who have done a lot of + + align:start position:0% +so those of you who have done a lot of + + + align:start position:0% +so those of you who have done a lot of +mathematical optimization + + align:start position:0% +mathematical optimization + + + align:start position:0% +mathematical optimization +are probably familiar with this + + align:start position:0% +are probably familiar with this + + + align:start position:0% +are probably familiar with this +those of you who have not which is + + align:start position:0% +those of you who have not which is + + + align:start position:0% +those of you who have not which is +probably most of you might take a minute + + align:start position:0% +probably most of you might take a minute + + + align:start position:0% +probably most of you might take a minute +to think about what that means so I'm + + align:start position:0% +to think about what that means so I'm + + + align:start position:0% +to think about what that means so I'm +going to draw that in one dimension we + + align:start position:0% +going to draw that in one dimension we + + + align:start position:0% +going to draw that in one dimension we +have a six-dimensional problem but I'm + + align:start position:0% +have a six-dimensional problem but I'm + + + align:start position:0% +have a six-dimensional problem but I'm +not very good at drawing in Six + + align:start position:0% +not very good at drawing in Six + + + align:start position:0% +not very good at drawing in Six +Dimensions but I can draw in one + + align:start position:0% +Dimensions but I can draw in one + + + align:start position:0% +Dimensions but I can draw in one +so let's draw a curve in one dimension + + align:start position:0% +so let's draw a curve in one dimension + + + align:start position:0% +so let's draw a curve in one dimension +I have + + align:start position:0% +I have + + + align:start position:0% +I have +X + + align:start position:0% +X + + + align:start position:0% +X +and I have + + align:start position:0% +and I have + + + align:start position:0% +and I have +y + + align:start position:0% +y + + + align:start position:0% +y +Where is the + + align:start position:0% +Where is the + + + align:start position:0% +Where is the +Optimum of this curve + + align:start position:0% +Optimum of this curve + + + align:start position:0% +Optimum of this curve +optimization means finding the object + + align:start position:0% +optimization means finding the object + + + align:start position:0% +optimization means finding the object +the maximum point right right just just + + align:start position:0% +the maximum point right right just just + + + align:start position:0% +the maximum point right right just just +the maximum point right right so so what + + align:start position:0% +the maximum point right right so so what + + + align:start position:0% +the maximum point right right so so what +would the condition for that be + + align:start position:0% +would the condition for that be + + + align:start position:0% +would the condition for that be +say it in calculus language + + align:start position:0% +say it in calculus language + + + align:start position:0% +say it in calculus language +the slope to be zero yeah the x d sorry + + align:start position:0% +the slope to be zero yeah the x d sorry + + + align:start position:0% +the slope to be zero yeah the x d sorry +d y d x equals zero + + align:start position:0% +d y d x equals zero + + + align:start position:0% +d y d x equals zero +sorry I messed up my y there but at that + + align:start position:0% +sorry I messed up my y there but at that + + + align:start position:0% +sorry I messed up my y there but at that +point the slope is zero right + + align:start position:0% +point the slope is zero right + + + align:start position:0% +point the slope is zero right +so what that means is + + align:start position:0% +so what that means is + + + align:start position:0% +so what that means is +um + + align:start position:0% +um + + + align:start position:0% +um +let's say x is unconstrained + + align:start position:0% + + + + align:start position:0% + +as X Wiggles around + + align:start position:0% + + + + align:start position:0% + +the value of y doesn't change + + align:start position:0% +the value of y doesn't change + + + align:start position:0% +the value of y doesn't change +only + + align:start position:0% +only + + + align:start position:0% +only +as long as I'm at that point with zero + + align:start position:0% +as long as I'm at that point with zero + + + align:start position:0% +as long as I'm at that point with zero +slope + + align:start position:0% +slope + + + align:start position:0% +slope +if I'm at a point with non-zero slope + + align:start position:0% +if I'm at a point with non-zero slope + + + align:start position:0% +if I'm at a point with non-zero slope +as X Wiggles around y will change + + align:start position:0% +as X Wiggles around y will change + + + align:start position:0% +as X Wiggles around y will change +so if there is a potential + + align:start position:0% +so if there is a potential + + + align:start position:0% +so if there is a potential +which tries to maximize y it's going to + + align:start position:0% +which tries to maximize y it's going to + + + align:start position:0% +which tries to maximize y it's going to +force the system to the right right if + + align:start position:0% +force the system to the right right if + + + align:start position:0% +force the system to the right right if +I'm here or if I'm over here if there's + + align:start position:0% +I'm here or if I'm over here if there's + + + align:start position:0% +I'm here or if I'm over here if there's +a potential that tries to maximize y + + align:start position:0% +a potential that tries to maximize y + + + align:start position:0% +a potential that tries to maximize y +it's going to force the system + + align:start position:0% +it's going to force the system + + + align:start position:0% +it's going to force the system +to the left + + align:start position:0% +to the left + + + align:start position:0% +to the left +so the only condition for which the + + align:start position:0% +so the only condition for which the + + + align:start position:0% +so the only condition for which the +system is stationary + + align:start position:0% +system is stationary + + + align:start position:0% +system is stationary +or you might say at equilibrium + + align:start position:0% +or you might say at equilibrium + + + align:start position:0% +or you might say at equilibrium +is the condition for which that slope is + + align:start position:0% +is the condition for which that slope is + + + align:start position:0% +is the condition for which that slope is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +now Imagine This in Six Dimensions right + + align:start position:0% +now Imagine This in Six Dimensions right + + + align:start position:0% +now Imagine This in Six Dimensions right +this is this is this is one plus one + + align:start position:0% +this is this is this is one plus one + + + align:start position:0% +this is this is this is one plus one +Dimensions now imagine it in six plus + + align:start position:0% +Dimensions now imagine it in six plus + + + align:start position:0% +Dimensions now imagine it in six plus +one dimension so I can't draw in seven + + align:start position:0% +one dimension so I can't draw in seven + + + align:start position:0% +one dimension so I can't draw in seven +dimensions any better than I can draw in + + align:start position:0% +dimensions any better than I can draw in + + + align:start position:0% +dimensions any better than I can draw in +six + + align:start position:0% +six + + + align:start position:0% +six +by the same thinking applies that for + + align:start position:0% +by the same thinking applies that for + + + align:start position:0% +by the same thinking applies that for +unconstrained optimization + + align:start position:0% +unconstrained optimization + + + align:start position:0% +unconstrained optimization +I would need all six coefficients those + + align:start position:0% +I would need all six coefficients those + + + align:start position:0% +I would need all six coefficients those +are the partial differentials to be zero + + align:start position:0% + + + + align:start position:0% + +so the way to solve this problem + + align:start position:0% +so the way to solve this problem + + + align:start position:0% +so the way to solve this problem +and figure out the equilibrium + + align:start position:0% +and figure out the equilibrium + + + align:start position:0% +and figure out the equilibrium +conditions is to identify + + align:start position:0% + + + + align:start position:0% + +what + + align:start position:0% +what + + + align:start position:0% +what +are + + align:start position:0% +are + + + align:start position:0% +are +relevant + + align:start position:0% +relevant + + + align:start position:0% +relevant +constraints + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +reduce the dimensionality of the problem + + align:start position:0% + + + + align:start position:0% + +so that's what we're going to do next + + align:start position:0% +so that's what we're going to do next + + + align:start position:0% +so that's what we're going to do next +we're going to think about what + + align:start position:0% +we're going to think about what + + + align:start position:0% +we're going to think about what +constraints apply in this case + + align:start position:0% +constraints apply in this case + + + align:start position:0% +constraints apply in this case +and the constraints change + + align:start position:0% +and the constraints change + + + align:start position:0% +and the constraints change +from case to case let me show you what I + + align:start position:0% +from case to case let me show you what I + + + align:start position:0% +from case to case let me show you what I +mean + + align:start position:0% +mean + + + align:start position:0% +mean +let's talk about constraints + + align:start position:0% + + + + align:start position:0% + +you know a constrained optimization is + + align:start position:0% +you know a constrained optimization is + + + align:start position:0% +you know a constrained optimization is +is + + align:start position:0% +is + + + align:start position:0% +is +um + + align:start position:0% +um + + + align:start position:0% +um +you can you could + + align:start position:0% + + + + align:start position:0% + +now if you went into business Consulting + + align:start position:0% +now if you went into business Consulting + + + align:start position:0% +now if you went into business Consulting +you're sort of doing constrained + + align:start position:0% +you're sort of doing constrained + + + align:start position:0% +you're sort of doing constrained +optimization + + align:start position:0% +optimization + + + align:start position:0% +optimization +operations research + + align:start position:0% +operations research + + + align:start position:0% +operations research +a lot of engineering problems boil down + + align:start position:0% +a lot of engineering problems boil down + + + align:start position:0% +a lot of engineering problems boil down +to constrained optimization we're just + + align:start position:0% +to constrained optimization we're just + + + align:start position:0% +to constrained optimization we're just +sort of scratching the surface here + + align:start position:0% +sort of scratching the surface here + + + align:start position:0% +sort of scratching the surface here +the constraints come from physical + + align:start position:0% +the constraints come from physical + + + align:start position:0% +the constraints come from physical +things let's start for conservation of + + align:start position:0% +things let's start for conservation of + + + align:start position:0% +things let's start for conservation of +energy + + align:start position:0% + + + + align:start position:0% + +I seem to have switched back to the fat + + align:start position:0% +I seem to have switched back to the fat + + + align:start position:0% +I seem to have switched back to the fat +pen + + align:start position:0% +pen + + + align:start position:0% +pen +I'm going to switch Midstream here I + + align:start position:0% +I'm going to switch Midstream here I + + + align:start position:0% +I'm going to switch Midstream here I +want a vote + + align:start position:0% +want a vote + + + align:start position:0% +want a vote +at some point you guys tell me which + + align:start position:0% +at some point you guys tell me which + + + align:start position:0% +at some point you guys tell me which +which one you like better conservation + + align:start position:0% +which one you like better conservation + + + align:start position:0% +which one you like better conservation +of energy so conservation of energy + + align:start position:0% +of energy so conservation of energy + + + align:start position:0% +of energy so conservation of energy +this is an isolated system + + align:start position:0% +this is an isolated system + + + align:start position:0% +this is an isolated system +so what can we say about d u of alpha + + align:start position:0% +so what can we say about d u of alpha + + + align:start position:0% +so what can we say about d u of alpha +if Alpha gains energy where does it have + + align:start position:0% +if Alpha gains energy where does it have + + + align:start position:0% +if Alpha gains energy where does it have +to come from + + align:start position:0% +to come from + + + align:start position:0% +to come from +from beta has to come from beta + + align:start position:0% +from beta has to come from beta + + + align:start position:0% +from beta has to come from beta +so d u of alpha has to equal minus the U + + align:start position:0% +so d u of alpha has to equal minus the U + + + align:start position:0% +so d u of alpha has to equal minus the U +of beta + + align:start position:0% + + + + align:start position:0% + +right again coming back to our picture + + align:start position:0% +right again coming back to our picture + + + align:start position:0% +right again coming back to our picture +we have an alpha phase + + align:start position:0% +we have an alpha phase + + + align:start position:0% +we have an alpha phase +we have a beta phase + + align:start position:0% +we have a beta phase + + + align:start position:0% +we have a beta phase +they're separated by a very porous + + align:start position:0% +they're separated by a very porous + + + align:start position:0% +they're separated by a very porous +almost non-material boundary + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +and that boundary allows + + align:start position:0% + + + + align:start position:0% + +energy to pass back and forth right they + + align:start position:0% +energy to pass back and forth right they + + + align:start position:0% +energy to pass back and forth right they +can do work on each other and they can + + align:start position:0% +can do work on each other and they can + + + align:start position:0% +can do work on each other and they can +heat each other + + align:start position:0% +heat each other + + + align:start position:0% +heat each other +okay that's good this reduces our number + + align:start position:0% +okay that's good this reduces our number + + + align:start position:0% +okay that's good this reduces our number +of Dimensions by one right we have an + + align:start position:0% +of Dimensions by one right we have an + + + align:start position:0% +of Dimensions by one right we have an +additional equation + + align:start position:0% +additional equation + + + align:start position:0% +additional equation +there's another constraint + + align:start position:0% + + + + align:start position:0% + +conservation of volume I said the the + + align:start position:0% +conservation of volume I said the the + + + align:start position:0% +conservation of volume I said the the +system was rigid it was in a box and the + + align:start position:0% +system was rigid it was in a box and the + + + align:start position:0% +system was rigid it was in a box and the +Box's size wasn't changing so if we have + + align:start position:0% +Box's size wasn't changing so if we have + + + align:start position:0% +Box's size wasn't changing so if we have +volume conserved + + align:start position:0% + + + + align:start position:0% + +what do we know about DV of alpha + + align:start position:0% + + + + align:start position:0% + +like minus DV beta Minus TV of beta + + align:start position:0% +like minus DV beta Minus TV of beta + + + align:start position:0% +like minus DV beta Minus TV of beta +right + + align:start position:0% +right + + + align:start position:0% +right +if one side is getting bigger it has to + + align:start position:0% +if one side is getting bigger it has to + + + align:start position:0% +if one side is getting bigger it has to +be because the other side is getting + + align:start position:0% +be because the other side is getting + + + align:start position:0% +be because the other side is getting +smaller + + align:start position:0% +smaller + + + align:start position:0% +smaller +there's nothing else in the Box + + align:start position:0% + + + + align:start position:0% + +and the third conservation law we're + + align:start position:0% +and the third conservation law we're + + + align:start position:0% +and the third conservation law we're +going to apply is conservation of mass + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% +if + + + align:start position:0% +if +if phage Alpha gains particles + + align:start position:0% +if phage Alpha gains particles + + + align:start position:0% +if phage Alpha gains particles +has to come at the expense + + align:start position:0% +has to come at the expense + + + align:start position:0% +has to come at the expense +a phase beta + + align:start position:0% +a phase beta + + + align:start position:0% +a phase beta +because the box is closed the mass of + + align:start position:0% +because the box is closed the mass of + + + align:start position:0% +because the box is closed the mass of +the overall system is fixed + + align:start position:0% +the overall system is fixed + + + align:start position:0% +the overall system is fixed +so these three conditions + + align:start position:0% +so these three conditions + + + align:start position:0% +so these three conditions +which are constraints + + align:start position:0% + + + + align:start position:0% + +they simplify + + align:start position:0% + + + + align:start position:0% + +the equilibrium condition + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +DS equals zero + + align:start position:0% +DS equals zero + + + align:start position:0% +DS equals zero +to + + align:start position:0% +to + + + align:start position:0% +to +three + + align:start position:0% +three + + + align:start position:0% +three +independent + + align:start position:0% + + + + align:start position:0% + +variables + + align:start position:0% +variables + + + align:start position:0% +variables +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +with three coefficients + + align:start position:0% + + + + align:start position:0% + +that we set to zero + + align:start position:0% +that we set to zero + + + align:start position:0% +that we set to zero +so now instead of worrying about six + + align:start position:0% +so now instead of worrying about six + + + align:start position:0% +so now instead of worrying about six +slopes + + align:start position:0% +slopes + + + align:start position:0% +slopes +small space now we only have to worry + + align:start position:0% +small space now we only have to worry + + + align:start position:0% +small space now we only have to worry +about it in a three plus one dimensional + + align:start position:0% +about it in a three plus one dimensional + + + align:start position:0% +about it in a three plus one dimensional +space + + align:start position:0% +space + + + align:start position:0% +space +I still can't drive but we'll see that + + align:start position:0% +I still can't drive but we'll see that + + + align:start position:0% +I still can't drive but we'll see that +the math is relatively simple + + align:start position:0% +the math is relatively simple + + + align:start position:0% +the math is relatively simple +okay so let's talk about + + align:start position:0% +okay so let's talk about + + + align:start position:0% +okay so let's talk about +let's talk about those + + align:start position:0% +let's talk about those + + + align:start position:0% +let's talk about those +constrained optimization + + align:start position:0% +constrained optimization + + + align:start position:0% +constrained optimization +[Music] + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +optimization + + align:start position:0% +optimization + + + align:start position:0% +optimization +down + + align:start position:0% +down + + + align:start position:0% +down +we're down to three we're down to three + + align:start position:0% +we're down to three we're down to three + + + align:start position:0% +we're down to three we're down to three +terms DS equals + + align:start position:0% +terms DS equals + + + align:start position:0% +terms DS equals +1 over temperature of alpha minus 1 over + + align:start position:0% +1 over temperature of alpha minus 1 over + + + align:start position:0% +1 over temperature of alpha minus 1 over +temperature of beta + + align:start position:0% +temperature of beta + + + align:start position:0% +temperature of beta +d u of alpha see I didn't I eliminated + + align:start position:0% +d u of alpha see I didn't I eliminated + + + align:start position:0% +d u of alpha see I didn't I eliminated +the U of beta I eliminated the energy of + + align:start position:0% +the U of beta I eliminated the energy of + + + align:start position:0% +the U of beta I eliminated the energy of +the beta phase + + align:start position:0% + + + + align:start position:0% + +okay likewise P of alpha over T of alpha + + align:start position:0% +okay likewise P of alpha over T of alpha + + + align:start position:0% +okay likewise P of alpha over T of alpha +minus P of beta T of beta + + align:start position:0% + + + + align:start position:0% + +d v of alpha right I eliminated DV of + + align:start position:0% +d v of alpha right I eliminated DV of + + + align:start position:0% +d v of alpha right I eliminated DV of +beta + + align:start position:0% +beta + + + align:start position:0% +beta +and similarly + + align:start position:0% +and similarly + + + align:start position:0% +and similarly +mu of alpha T of alpha minus mu beta T + + align:start position:0% +mu of alpha T of alpha minus mu beta T + + + align:start position:0% +mu of alpha T of alpha minus mu beta T +of beta + + align:start position:0% +of beta + + + align:start position:0% +of beta +d n of alpha + + align:start position:0% +d n of alpha + + + align:start position:0% +d n of alpha +right + + align:start position:0% +right + + + align:start position:0% +right +so now this is my problem and this whole + + align:start position:0% +so now this is my problem and this whole + + + align:start position:0% +so now this is my problem and this whole +thing has to be equal + + align:start position:0% +thing has to be equal + + + align:start position:0% +thing has to be equal +to zero + + align:start position:0% +to zero + + + align:start position:0% +to zero +okay so now we've we've applied our + + align:start position:0% +okay so now we've we've applied our + + + align:start position:0% +okay so now we've we've applied our +constraints + + align:start position:0% + + + + align:start position:0% + +how can I guarantee that this whole term + + align:start position:0% +how can I guarantee that this whole term + + + align:start position:0% +how can I guarantee that this whole term +equals zero + + align:start position:0% +equals zero + + + align:start position:0% +equals zero +under what conditions can I be + + align:start position:0% +under what conditions can I be + + + align:start position:0% +under what conditions can I be +guaranteed that that term will be zero + + align:start position:0% + + + + align:start position:0% + +if all the coefficients are zero again + + align:start position:0% +if all the coefficients are zero again + + + align:start position:0% +if all the coefficients are zero again +that's exactly right the only way I can + + align:start position:0% +that's exactly right the only way I can + + + align:start position:0% +that's exactly right the only way I can +guarantee that zero is if the + + align:start position:0% +guarantee that zero is if the + + + align:start position:0% +guarantee that zero is if the +coefficients are zeroed out + + align:start position:0% +coefficients are zeroed out + + + align:start position:0% +coefficients are zeroed out +why is that + + align:start position:0% +why is that + + + align:start position:0% +why is that +because I can't set + + align:start position:0% +because I can't set + + + align:start position:0% +because I can't set +the independent parameters to be zero + + align:start position:0% + + + + align:start position:0% + +why is that + + align:start position:0% + + + + align:start position:0% + +these two phases can exchange generally + + align:start position:0% +these two phases can exchange generally + + + align:start position:0% +these two phases can exchange generally +energy freely + + align:start position:0% +energy freely + + + align:start position:0% +energy freely +they can exchange volume + + align:start position:0% +they can exchange volume + + + align:start position:0% +they can exchange volume +freely + + align:start position:0% +freely + + + align:start position:0% +freely +and they can exchange uh particle number + + align:start position:0% +and they can exchange uh particle number + + + align:start position:0% +and they can exchange uh particle number +freely + + align:start position:0% +freely + + + align:start position:0% +freely +it's an open boundary + + align:start position:0% +it's an open boundary + + + align:start position:0% +it's an open boundary +I Can't Stop Those processes + + align:start position:0% + + + + align:start position:0% + +so d u of Alpha and DV of Alpha and DNA + + align:start position:0% +so d u of Alpha and DV of Alpha and DNA + + + align:start position:0% +so d u of Alpha and DV of Alpha and DNA +of alpha in general can be non-zero so + + align:start position:0% +of alpha in general can be non-zero so + + + align:start position:0% +of alpha in general can be non-zero so +the only way that I can guarantee that + + align:start position:0% +the only way that I can guarantee that + + + align:start position:0% +the only way that I can guarantee that +I'm at equilibrium is to set the + + align:start position:0% +I'm at equilibrium is to set the + + + align:start position:0% +I'm at equilibrium is to set the +coefficients equal to zero + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +let's do that 1 over T of alpha minus 1 + + align:start position:0% +let's do that 1 over T of alpha minus 1 + + + align:start position:0% +let's do that 1 over T of alpha minus 1 +over T of beta equals zero what does + + align:start position:0% +over T of beta equals zero what does + + + align:start position:0% +over T of beta equals zero what does +that give me + + align:start position:0% +that give me + + + align:start position:0% +that give me +that gives me temperature of alpha + + align:start position:0% +that gives me temperature of alpha + + + align:start position:0% +that gives me temperature of alpha +equals temperature of beta + + align:start position:0% + + + + align:start position:0% + +this is known as + + align:start position:0% +this is known as + + + align:start position:0% +this is known as +thermal equilibrium + + align:start position:0% + + + + align:start position:0% + +so let's remember how we got thermal + + align:start position:0% +so let's remember how we got thermal + + + align:start position:0% +so let's remember how we got thermal +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +two subsystems that could exchange + + align:start position:0% +two subsystems that could exchange + + + align:start position:0% +two subsystems that could exchange +energy + + align:start position:0% + + + + align:start position:0% + +reach thermal equilibrium + + align:start position:0% + + + + align:start position:0% + +what's the next one p of alpha over T of + + align:start position:0% +what's the next one p of alpha over T of + + + align:start position:0% +what's the next one p of alpha over T of +alpha + + align:start position:0% +alpha + + + align:start position:0% +alpha +minus P of beta over T of beta + + align:start position:0% +minus P of beta over T of beta + + + align:start position:0% +minus P of beta over T of beta +equals zero + + align:start position:0% + + + + align:start position:0% + +well given thermal equilibrium from this + + align:start position:0% +well given thermal equilibrium from this + + + align:start position:0% +well given thermal equilibrium from this +I get P of alpha + + align:start position:0% +I get P of alpha + + + align:start position:0% +I get P of alpha +equals P of beta + + align:start position:0% +equals P of beta + + + align:start position:0% +equals P of beta +this is known as mechanical equilibrium + + align:start position:0% + + + + align:start position:0% + +and the third one is U of alpha over T + + align:start position:0% +and the third one is U of alpha over T + + + align:start position:0% +and the third one is U of alpha over T +of alpha minus mu of beta over T of beta + + align:start position:0% +of alpha minus mu of beta over T of beta + + + align:start position:0% +of alpha minus mu of beta over T of beta +equals zero and + + align:start position:0% +equals zero and + + + align:start position:0% +equals zero and +again given thermal equilibrium this + + align:start position:0% +again given thermal equilibrium this + + + align:start position:0% +again given thermal equilibrium this +gives me + + align:start position:0% +gives me + + + align:start position:0% +gives me +mu of alpha + + align:start position:0% +mu of alpha + + + align:start position:0% +mu of alpha +equals mu of beta and this is known as + + align:start position:0% +equals mu of beta and this is known as + + + align:start position:0% +equals mu of beta and this is known as +does anybody know what this is known as + + align:start position:0% + + + + align:start position:0% + +equilibrium + + align:start position:0% + + + + align:start position:0% + +so there are three different + + align:start position:0% +so there are three different + + + align:start position:0% +so there are three different +sort of subsets of equilibrium + + align:start position:0% +sort of subsets of equilibrium + + + align:start position:0% +sort of subsets of equilibrium +three subsets of equilibrium each can be + + align:start position:0% +three subsets of equilibrium each can be + + + align:start position:0% +three subsets of equilibrium each can be +achieved on its own + + align:start position:0% +achieved on its own + + + align:start position:0% +achieved on its own +each can be engineered + + align:start position:0% +each can be engineered + + + align:start position:0% +each can be engineered +to be achieved on its own but if you add + + align:start position:0% +to be achieved on its own but if you add + + + align:start position:0% +to be achieved on its own but if you add +them up + + align:start position:0% +them up + + + align:start position:0% +them up +this equals thermodynamic equilibrium + + align:start position:0% +this equals thermodynamic equilibrium + + + align:start position:0% +this equals thermodynamic equilibrium +so that's the meaning + + align:start position:0% + + + + align:start position:0% + +this is the equilibrium + + align:start position:0% +this is the equilibrium + + + align:start position:0% +this is the equilibrium +right in fat written conditions + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% +for + + + align:start position:0% +for +two phase + + align:start position:0% +two phase + + + align:start position:0% +two phase +coexistence + + align:start position:0% + + + + align:start position:0% + +so if two phases are going to coexist in + + align:start position:0% +so if two phases are going to coexist in + + + align:start position:0% +so if two phases are going to coexist in +equilibrium in the unary system + + align:start position:0% +equilibrium in the unary system + + + align:start position:0% +equilibrium in the unary system +you must have all three of these thermal + + align:start position:0% +you must have all three of these thermal + + + align:start position:0% +you must have all three of these thermal +mechanical and chemical + + align:start position:0% + + + + align:start position:0% + +and the the structure the mathematical + + align:start position:0% +and the the structure the mathematical + + + align:start position:0% +and the the structure the mathematical +structure of this will come up again + + align:start position:0% +structure of this will come up again + + + align:start position:0% +structure of this will come up again +in more complicated scenarios + + align:start position:0% + + + + align:start position:0% + +but if we can see past the mass I want + + align:start position:0% +but if we can see past the mass I want + + + align:start position:0% +but if we can see past the mass I want +you to see the physical origin of this + + align:start position:0% +you to see the physical origin of this + + + align:start position:0% +you to see the physical origin of this +when systems can exchange energy they + + align:start position:0% +when systems can exchange energy they + + + align:start position:0% +when systems can exchange energy they +come to Thermo equilibrium + + align:start position:0% +come to Thermo equilibrium + + + align:start position:0% +come to Thermo equilibrium +when systems can exchange volume they + + align:start position:0% +when systems can exchange volume they + + + align:start position:0% +when systems can exchange volume they +come to Mechanical equilibrium and + + align:start position:0% +come to Mechanical equilibrium and + + + align:start position:0% +come to Mechanical equilibrium and +kinetic systems can exchange particles + + align:start position:0% +kinetic systems can exchange particles + + + align:start position:0% +kinetic systems can exchange particles +they come to chemical equilibrium + + align:start position:0% +they come to chemical equilibrium + + + align:start position:0% +they come to chemical equilibrium +and you as Engineers can engineer + + align:start position:0% +and you as Engineers can engineer + + + align:start position:0% +and you as Engineers can engineer +processes to achieve selective + + align:start position:0% +processes to achieve selective + + + align:start position:0% +processes to achieve selective +equilibrium you can allow systems to + + align:start position:0% +equilibrium you can allow systems to + + + align:start position:0% +equilibrium you can allow systems to +exchange volume but have impermeable + + align:start position:0% +exchange volume but have impermeable + + + align:start position:0% +exchange volume but have impermeable +membrane membrane so they can't exchange + + align:start position:0% +membrane membrane so they can't exchange + + + align:start position:0% +membrane membrane so they can't exchange +particles you could allow systems to + + align:start position:0% +particles you could allow systems to + + + align:start position:0% +particles you could allow systems to +exchange energy by heating but have + + align:start position:0% +exchange energy by heating but have + + + align:start position:0% +exchange energy by heating but have +rigid and impermeable membranes or you + + align:start position:0% +rigid and impermeable membranes or you + + + align:start position:0% +rigid and impermeable membranes or you +could have membranes that allow some + + align:start position:0% +could have membranes that allow some + + + align:start position:0% +could have membranes that allow some +particles to equilibrate and others not + + align:start position:0% +particles to equilibrate and others not + + + align:start position:0% +particles to equilibrate and others not +to so let's say you're making a + + align:start position:0% +to so let's say you're making a + + + align:start position:0% +to so let's say you're making a +desalination system right you want water + + align:start position:0% +desalination system right you want water + + + align:start position:0% +desalination system right you want water +to equilibrate but dissolve solids not + + align:start position:0% +to equilibrate but dissolve solids not + + + align:start position:0% +to equilibrate but dissolve solids not +to lots of examples here so um this + + align:start position:0% +to lots of examples here so um this + + + align:start position:0% +to lots of examples here so um this +seems really theoretical it actually + + align:start position:0% +seems really theoretical it actually + + + align:start position:0% +seems really theoretical it actually +presents a lot of opportunity for + + align:start position:0% +presents a lot of opportunity for + + + align:start position:0% +presents a lot of opportunity for +engineering + + align:start position:0% +engineering + + + align:start position:0% +engineering +selective equilibrium + + align:start position:0% +selective equilibrium + + + align:start position:0% +selective equilibrium +okay + + align:start position:0% +okay + + + align:start position:0% +okay +let's highlight some assumptions to this + + align:start position:0% +let's highlight some assumptions to this + + + align:start position:0% +let's highlight some assumptions to this +point + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% +oh + + + align:start position:0% +oh +assumptions + + align:start position:0% +assumptions + + + align:start position:0% +assumptions +to this + + align:start position:0% + + + + align:start position:0% + +so assumptions to this point are + + align:start position:0% +so assumptions to this point are + + + align:start position:0% +so assumptions to this point are +the Intensive parameters + + align:start position:0% + + + + align:start position:0% + +that is T and P mu + + align:start position:0% +that is T and P mu + + + align:start position:0% +that is T and P mu +our uniform + + align:start position:0% + + + + align:start position:0% + +within each phase + + align:start position:0% + + + + align:start position:0% + +that's been an assumption + + align:start position:0% +that's been an assumption + + + align:start position:0% +that's been an assumption +we also assume that the boundary + + align:start position:0% + + + + align:start position:0% + +has + + align:start position:0% +has + + + align:start position:0% +has +no substance + + align:start position:0% + + + + align:start position:0% + +or effect + + align:start position:0% + + + + align:start position:0% + +on properties + + align:start position:0% +on properties + + + align:start position:0% +on properties +of either phase + + align:start position:0% + + + + align:start position:0% + +so this is relatively straightforward + + align:start position:0% +so this is relatively straightforward + + + align:start position:0% +so this is relatively straightforward +this this gets complicated + + align:start position:0% +this this gets complicated + + + align:start position:0% +this this gets complicated +so we've assumed the boundary is a + + align:start position:0% +so we've assumed the boundary is a + + + align:start position:0% +so we've assumed the boundary is a +dashed line + + align:start position:0% +dashed line + + + align:start position:0% +dashed line +with no substance + + align:start position:0% +with no substance + + + align:start position:0% +with no substance +in the real world whether that's a good + + align:start position:0% +in the real world whether that's a good + + + align:start position:0% +in the real world whether that's a good +assumption depends a lot on the size + + align:start position:0% +assumption depends a lot on the size + + + align:start position:0% +assumption depends a lot on the size +scale you're talking about so some of + + align:start position:0% +scale you're talking about so some of + + + align:start position:0% +scale you're talking about so some of +you may have been involved in + + align:start position:0% +you may have been involved in + + + align:start position:0% +you may have been involved in +nanoscience + + align:start position:0% +nanoscience + + + align:start position:0% +nanoscience +um When Things trinked interphasis + + align:start position:0% +um When Things trinked interphasis + + + align:start position:0% +um When Things trinked interphasis +become more and more important it's a + + align:start position:0% +become more and more important it's a + + + align:start position:0% +become more and more important it's a +geometrical fact + + align:start position:0% + + + + align:start position:0% + +the thermodynamics of systems with + + align:start position:0% +the thermodynamics of systems with + + + align:start position:0% +the thermodynamics of systems with +you know with boundary effects is a + + align:start position:0% +you know with boundary effects is a + + + align:start position:0% +you know with boundary effects is a +really interesting topic that goes + + align:start position:0% +really interesting topic that goes + + + align:start position:0% +really interesting topic that goes +beyond O2L + + align:start position:0% +beyond O2L + + + align:start position:0% +beyond O2L +but it becomes important for those of + + align:start position:0% +but it becomes important for those of + + + align:start position:0% +but it becomes important for those of +you who might work on colloidal systems + + align:start position:0% +you who might work on colloidal systems + + + align:start position:0% +you who might work on colloidal systems +or semiconductor Quantum dots or + + align:start position:0% +or semiconductor Quantum dots or + + + align:start position:0% +or semiconductor Quantum dots or +Coatings lots of useful + + align:start position:0% +Coatings lots of useful + + + align:start position:0% +Coatings lots of useful +materials that that um where you know + + align:start position:0% +materials that that um where you know + + + align:start position:0% +materials that that um where you know +you don't get the right answer if you + + align:start position:0% +you don't get the right answer if you + + + align:start position:0% +you don't get the right answer if you +don't consider the boundary but in this + + align:start position:0% +don't consider the boundary but in this + + + align:start position:0% +don't consider the boundary but in this +class we don't consider the boundary + + align:start position:0% +class we don't consider the boundary + + + align:start position:0% +class we don't consider the boundary +a corollary of this assumption is that + + align:start position:0% +a corollary of this assumption is that + + + align:start position:0% +a corollary of this assumption is that +the spatial + + align:start position:0% +the spatial + + + align:start position:0% +the spatial +distribution + + align:start position:0% + + + + align:start position:0% + +doesn't matter + + align:start position:0% + + + + align:start position:0% + +spatial distribution doesn't matter so + + align:start position:0% + + + + align:start position:0% + +I could have two versions + + align:start position:0% +I could have two versions + + + align:start position:0% +I could have two versions +of this system + + align:start position:0% + + + + align:start position:0% + +what colors did I use to my phases + + align:start position:0% +what colors did I use to my phases + + + align:start position:0% +what colors did I use to my phases +orange and purple I think + + align:start position:0% +orange and purple I think + + + align:start position:0% +orange and purple I think +are the matters + + align:start position:0% +are the matters + + + align:start position:0% +are the matters +one with let's say + + align:start position:0% +one with let's say + + + align:start position:0% +one with let's say +Orange + + align:start position:0% +Orange + + + align:start position:0% +Orange +and purple + + align:start position:0% + + + + align:start position:0% + +and a single phase boundary separating + + align:start position:0% +and a single phase boundary separating + + + align:start position:0% +and a single phase boundary separating +them + + align:start position:0% +them + + + align:start position:0% +them +or I could have + + align:start position:0% + + + + align:start position:0% + +purple + + align:start position:0% +purple + + + align:start position:0% +purple +you know particles or filaments or or + + align:start position:0% +you know particles or filaments or or + + + align:start position:0% +you know particles or filaments or or +um + + align:start position:0% + + + + align:start position:0% + +dispersed right in an orange Matrix + + align:start position:0% +dispersed right in an orange Matrix + + + align:start position:0% +dispersed right in an orange Matrix +right because this situation + + align:start position:0% + + + + align:start position:0% + +as long as my total quantities are the + + align:start position:0% +as long as my total quantities are the + + + align:start position:0% +as long as my total quantities are the +same in both cases + + align:start position:0% +same in both cases + + + align:start position:0% +same in both cases +there's no difference + + align:start position:0% +there's no difference + + + align:start position:0% +there's no difference +there's no difference if the boundary + + align:start position:0% +there's no difference if the boundary + + + align:start position:0% +there's no difference if the boundary +has no substance right you can create or + + align:start position:0% +has no substance right you can create or + + + align:start position:0% +has no substance right you can create or +destroy boundaries if they're free + + align:start position:0% +destroy boundaries if they're free + + + align:start position:0% +destroy boundaries if they're free +um so when we start caring about the + + align:start position:0% +um so when we start caring about the + + + align:start position:0% +um so when we start caring about the +differences between these we have to + + align:start position:0% +differences between these we have to + + + align:start position:0% +differences between these we have to +start accounting for boundaries all + + align:start position:0% +start accounting for boundaries all + + + align:start position:0% +start accounting for boundaries all +right enough about boundaries because we + + align:start position:0% +right enough about boundaries because we + + + align:start position:0% +right enough about boundaries because we +don't cover them in this class but I + + align:start position:0% +don't cover them in this class but I + + + align:start position:0% +don't cover them in this class but I +want to make clear that you know where + + align:start position:0% +want to make clear that you know where + + + align:start position:0% +want to make clear that you know where +we are and where we're not + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +I just sort of finish here this + + align:start position:0% +I just sort of finish here this + + + align:start position:0% +I just sort of finish here this +is the same same + + align:start position:0% + + + + align:start position:0% + +if if and only if + + align:start position:0% +if if and only if + + + align:start position:0% +if if and only if +boundaries are free + + align:start position:0% + + + + align:start position:0% + +no cost + + align:start position:0% +no cost + + + align:start position:0% +no cost +got it okay moving on + + align:start position:0% + + + + align:start position:0% + +and make something kind of abundantly it + + align:start position:0% +and make something kind of abundantly it + + + align:start position:0% +and make something kind of abundantly it +might be sort of beating a horse here + + align:start position:0% +might be sort of beating a horse here + + + align:start position:0% +might be sort of beating a horse here +but boundary conditions + + align:start position:0% + + + + align:start position:0% + +affect equilibrium + + align:start position:0% + + + + align:start position:0% + +the boundary conditions affect + + align:start position:0% +the boundary conditions affect + + + align:start position:0% +the boundary conditions affect +equilibrium so for example here's a + + align:start position:0% +equilibrium so for example here's a + + + align:start position:0% +equilibrium so for example here's a +simplified case + + align:start position:0% + + + + align:start position:0% + +here's an isolated system + + align:start position:0% + + + + align:start position:0% + +I think I used brown here for a thermal + + align:start position:0% +I think I used brown here for a thermal + + + align:start position:0% +I think I used brown here for a thermal +insulation giving you an idea really is + + align:start position:0% +insulation giving you an idea really is + + + align:start position:0% +insulation giving you an idea really is +isolated + + align:start position:0% +isolated + + + align:start position:0% +isolated +and I'm going to have + + align:start position:0% + + + + align:start position:0% + +an alpha phase + + align:start position:0% +an alpha phase + + + align:start position:0% +an alpha phase +then I'm going to have a rigid but + + align:start position:0% +then I'm going to have a rigid but + + + align:start position:0% +then I'm going to have a rigid but +thermally conductive box + + align:start position:0% +thermally conductive box + + + align:start position:0% +thermally conductive box +containing + + align:start position:0% +containing + + + align:start position:0% +containing +the beta phase + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +um in this case + + align:start position:0% + + + + align:start position:0% + +Alpha and beta separated + + align:start position:0% + + + + align:start position:0% + +by boundary + + align:start position:0% + + + + align:start position:0% + +that is rigid + + align:start position:0% + + + + align:start position:0% + +no volume Exchange + + align:start position:0% + + + + align:start position:0% + +closed + + align:start position:0% + + + + align:start position:0% + +no Mass Exchange + + align:start position:0% + + + + align:start position:0% + +but diathermal + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +Heat + + align:start position:0% +Heat + + + align:start position:0% +Heat +heating is okay + + align:start position:0% +heating is okay + + + align:start position:0% +heating is okay +so this is um you know this is you + + align:start position:0% +so this is um you know this is you + + + align:start position:0% +so this is um you know this is you +grabbing a uh you know a Coke out of the + + align:start position:0% +grabbing a uh you know a Coke out of the + + + align:start position:0% +grabbing a uh you know a Coke out of the +freezer out of the cooler right it's + + align:start position:0% +freezer out of the cooler right it's + + + align:start position:0% +freezer out of the cooler right it's +it's it might be pressurized but it's + + align:start position:0% +it's it might be pressurized but it's + + + align:start position:0% +it's it might be pressurized but it's +going to come to feminine equilibrium + + align:start position:0% +going to come to feminine equilibrium + + + align:start position:0% +going to come to feminine equilibrium +with your hand if you wait long enough + + align:start position:0% +with your hand if you wait long enough + + + align:start position:0% +with your hand if you wait long enough +so this is a case of selective + + align:start position:0% +so this is a case of selective + + + align:start position:0% +so this is a case of selective +equilibrium you're going to get thermal + + align:start position:0% +equilibrium you're going to get thermal + + + align:start position:0% +equilibrium you're going to get thermal +equilibrium but not chemical and not + + align:start position:0% +equilibrium but not chemical and not + + + align:start position:0% +equilibrium but not chemical and not +mechanical + + align:start position:0% + + + + align:start position:0% + +in such a case + + align:start position:0% +in such a case + + + align:start position:0% +in such a case +DS + + align:start position:0% +DS + + + align:start position:0% +DS +simplifies all you have + + align:start position:0% + + + + align:start position:0% + +no DV + + align:start position:0% +no DV + + + align:start position:0% +no DV +no DN terms + + align:start position:0% + + + + align:start position:0% + +and T Alpha equals T beta + + align:start position:0% +and T Alpha equals T beta + + + align:start position:0% +and T Alpha equals T beta +at equilibrium + + align:start position:0% +at equilibrium + + + align:start position:0% +at equilibrium +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +now physically you know that right you + + align:start position:0% +now physically you know that right you + + + align:start position:0% +now physically you know that right you +know you take a pressurized bottle out + + align:start position:0% +know you take a pressurized bottle out + + + align:start position:0% +know you take a pressurized bottle out +of the cooler it will come to your you + + align:start position:0% +of the cooler it will come to your you + + + align:start position:0% +of the cooler it will come to your you +know room temperature the temperature of + + align:start position:0% +know room temperature the temperature of + + + align:start position:0% +know room temperature the temperature of +your hand but until you release the cap + + align:start position:0% +your hand but until you release the cap + + + align:start position:0% +your hand but until you release the cap +it will stay pressurized and you won't + + align:start position:0% +it will stay pressurized and you won't + + + align:start position:0% +it will stay pressurized and you won't +have any mixing + + align:start position:0% +have any mixing + + + align:start position:0% +have any mixing +um so I'm trying to use these examples + + align:start position:0% +um so I'm trying to use these examples + + + align:start position:0% +um so I'm trying to use these examples +which are very physically familiar with + + align:start position:0% +which are very physically familiar with + + + align:start position:0% +which are very physically familiar with +um and illustrate them in this way this + + align:start position:0% +um and illustrate them in this way this + + + align:start position:0% +um and illustrate them in this way this +mathematical optimization framework that + + align:start position:0% +mathematical optimization framework that + + + align:start position:0% +mathematical optimization framework that +you're maybe less familiar with so you + + align:start position:0% +you're maybe less familiar with so you + + + align:start position:0% +you're maybe less familiar with so you +so you can become more familiar with it + + align:start position:0% + + + + align:start position:0% + +and why does all of this happen why does + + align:start position:0% +and why does all of this happen why does + + + align:start position:0% +and why does all of this happen why does +all of this happen + + align:start position:0% +all of this happen + + + align:start position:0% +all of this happen +all this happens + + align:start position:0% +all this happens + + + align:start position:0% +all this happens +because of entropy generation + + align:start position:0% + + + + align:start position:0% + +during a spontaneous + + align:start position:0% +during a spontaneous + + + align:start position:0% +during a spontaneous +spontaneous + + align:start position:0% + + + + align:start position:0% + +processes + + align:start position:0% + + + + align:start position:0% + +and this is where we need to keep our + + align:start position:0% +and this is where we need to keep our + + + align:start position:0% +and this is where we need to keep our +eyes on generation of entropy during + + align:start position:0% +eyes on generation of entropy during + + + align:start position:0% +eyes on generation of entropy during +spontaneous processes so let's write out + + align:start position:0% +spontaneous processes so let's write out + + + align:start position:0% +spontaneous processes so let's write out +DS again + + align:start position:0% + + + + align:start position:0% + +T alpha 1 over minus t beta 1 over + + align:start position:0% +T alpha 1 over minus t beta 1 over + + + align:start position:0% +T alpha 1 over minus t beta 1 over +d u Alpha + + align:start position:0% +d u Alpha + + + align:start position:0% +d u Alpha +plus P Alpha T Alpha minus P beta T beta + + align:start position:0% + + + + align:start position:0% + +TV Alpha sorry that's messy + + align:start position:0% +TV Alpha sorry that's messy + + + align:start position:0% +TV Alpha sorry that's messy +minus Mu Alpha T Alpha minus mu beta t + + align:start position:0% +minus Mu Alpha T Alpha minus mu beta t + + + align:start position:0% +minus Mu Alpha T Alpha minus mu beta t +beta + + align:start position:0% +beta + + + align:start position:0% +beta +V and Alpha okay so this is our + + align:start position:0% + + + + align:start position:0% + +at equilibrium + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so let's consider + + align:start position:0% + + + + align:start position:0% + +T Alpha + + align:start position:0% +T Alpha + + + align:start position:0% +T Alpha +greater than T beta let's consider you + + align:start position:0% +greater than T beta let's consider you + + + align:start position:0% +greater than T beta let's consider you +drop a hot particle of alpha phase into + + align:start position:0% +drop a hot particle of alpha phase into + + + align:start position:0% +drop a hot particle of alpha phase into +a bath with beta phase + + align:start position:0% +a bath with beta phase + + + align:start position:0% +a bath with beta phase +in this case + + align:start position:0% + + + + align:start position:0% + +1 over T Alpha + + align:start position:0% +1 over T Alpha + + + align:start position:0% +1 over T Alpha +minus 1 over t + + align:start position:0% +minus 1 over t + + + align:start position:0% +minus 1 over t +beta is less than zero + + align:start position:0% + + + + align:start position:0% + +if the temperature of alpha is greater + + align:start position:0% +if the temperature of alpha is greater + + + align:start position:0% +if the temperature of alpha is greater +than the temperature beta what can you + + align:start position:0% +than the temperature beta what can you + + + align:start position:0% +than the temperature beta what can you +say about which what will happen + + align:start position:0% +say about which what will happen + + + align:start position:0% +say about which what will happen +spontaneously the hotter phase + + align:start position:0% + + + + align:start position:0% + +Alpha + + align:start position:0% +Alpha + + + align:start position:0% +Alpha +it will heat or it will cool the cooler + + align:start position:0% +it will heat or it will cool the cooler + + + align:start position:0% +it will heat or it will cool the cooler +phase + + align:start position:0% +phase + + + align:start position:0% +phase +it will spontaneously what + + align:start position:0% + + + + align:start position:0% + +yeah Heat + + align:start position:0% + + + + align:start position:0% + +the colder phase + + align:start position:0% + + + + align:start position:0% + +right that's actually another statement + + align:start position:0% +right that's actually another statement + + + align:start position:0% +right that's actually another statement +of the second one that's clausius + + align:start position:0% +of the second one that's clausius + + + align:start position:0% +of the second one that's clausius +statement of the second law of + + align:start position:0% +statement of the second law of + + + align:start position:0% +statement of the second law of +Thermodynamics is hot material + + align:start position:0% +Thermodynamics is hot material + + + align:start position:0% +Thermodynamics is hot material +spontaneously heat colder materials + + align:start position:0% +spontaneously heat colder materials + + + align:start position:0% +spontaneously heat colder materials +it's equivalent to the other ones the + + align:start position:0% +it's equivalent to the other ones the + + + align:start position:0% +it's equivalent to the other ones the +other statements we've seen so that + + align:start position:0% +other statements we've seen so that + + + align:start position:0% +other statements we've seen so that +means + + align:start position:0% +means + + + align:start position:0% +means +d u Alpha is less than zero or + + align:start position:0% +d u Alpha is less than zero or + + + align:start position:0% +d u Alpha is less than zero or +d u beta is greater than zero right + + align:start position:0% +d u beta is greater than zero right + + + align:start position:0% +d u beta is greater than zero right +those are the same thing + + align:start position:0% +those are the same thing + + + align:start position:0% +those are the same thing +so if d u of alpha is less than zero + + align:start position:0% +so if d u of alpha is less than zero + + + align:start position:0% +so if d u of alpha is less than zero +and this coefficient is less than zero + + align:start position:0% + + + + align:start position:0% + +then d s + + align:start position:0% + + + + align:start position:0% + +is greater than zero + + align:start position:0% +is greater than zero + + + align:start position:0% +is greater than zero +right good + + align:start position:0% +right good + + + align:start position:0% +right good +entropy is generated + + align:start position:0% + + + + align:start position:0% + +entropy is generated + + align:start position:0% + + + + align:start position:0% + +during heat transfer + + align:start position:0% + + + + align:start position:0% + +from + + align:start position:0% +from + + + align:start position:0% +from +hot + + align:start position:0% +hot + + + align:start position:0% +hot +too cold + + align:start position:0% + + + + align:start position:0% + +this is again uh + + align:start position:0% +this is again uh + + + align:start position:0% +this is again uh +a state a restatement of the second law + + align:start position:0% +a state a restatement of the second law + + + align:start position:0% +a state a restatement of the second law +super important + + align:start position:0% +super important + + + align:start position:0% +super important +so when a hot object spontaneously Heats + + align:start position:0% +so when a hot object spontaneously Heats + + + align:start position:0% +so when a hot object spontaneously Heats +a cold object entropy is generated + + align:start position:0% +a cold object entropy is generated + + + align:start position:0% +a cold object entropy is generated +that's what we want to see based on + + align:start position:0% +that's what we want to see based on + + + align:start position:0% +that's what we want to see based on +everything that we've postulated and + + align:start position:0% +everything that we've postulated and + + + align:start position:0% +everything that we've postulated and +that's what the math gives us so it's + + align:start position:0% +that's what the math gives us so it's + + + align:start position:0% +that's what the math gives us so it's +all consistent that's good + + align:start position:0% +all consistent that's good + + + align:start position:0% +all consistent that's good +let's consider another case + + align:start position:0% +let's consider another case + + + align:start position:0% +let's consider another case +[Applause] + + align:start position:0% + + + + align:start position:0% + +consider + + align:start position:0% + + + + align:start position:0% + +T of alpha equals T of beta so they're + + align:start position:0% +T of alpha equals T of beta so they're + + + align:start position:0% +T of alpha equals T of beta so they're +already thermally equilibrated but + + align:start position:0% + + + + align:start position:0% + +they're mechanically out of equilibrium + + align:start position:0% + + + + align:start position:0% + +or in other words P of alpha or t of + + align:start position:0% +or in other words P of alpha or t of + + + align:start position:0% +or in other words P of alpha or t of +alpha minus P of beta over T of beta is + + align:start position:0% +alpha minus P of beta over T of beta is + + + align:start position:0% +alpha minus P of beta over T of beta is +greater than zero okay so what's going + + align:start position:0% +greater than zero okay so what's going + + + align:start position:0% +greater than zero okay so what's going +to happen the higher + + align:start position:0% +to happen the higher + + + align:start position:0% +to happen the higher +pressure + + align:start position:0% + + + + align:start position:0% + +phase + + align:start position:0% +phase + + + align:start position:0% +phase +will spontaneously + + align:start position:0% + + + + align:start position:0% + +you'll either expand + + align:start position:0% +you'll either expand + + + align:start position:0% +you'll either expand +or contract + + align:start position:0% + + + + align:start position:0% + +so the higher pressure phase will + + align:start position:0% +so the higher pressure phase will + + + align:start position:0% +so the higher pressure phase will +spontaneously expand or contract + + align:start position:0% + + + + align:start position:0% + +and yeah expand right this is + + align:start position:0% +and yeah expand right this is + + + align:start position:0% +and yeah expand right this is +not going to contract we'll spontaneous + + align:start position:0% +not going to contract we'll spontaneous + + + align:start position:0% +not going to contract we'll spontaneous +expand + + align:start position:0% +expand + + + align:start position:0% +expand +and I could say + + align:start position:0% +and I could say + + + align:start position:0% +and I could say +at the expense + + align:start position:0% + + + + align:start position:0% + +of the lower pressure + + align:start position:0% + + + + align:start position:0% + +so it's elbowing the lower pressure + + align:start position:0% +so it's elbowing the lower pressure + + + align:start position:0% +so it's elbowing the lower pressure +phase out of the way right + + align:start position:0% +phase out of the way right + + + align:start position:0% +phase out of the way right +that means DV of alpha is greater than + + align:start position:0% +that means DV of alpha is greater than + + + align:start position:0% +that means DV of alpha is greater than +zero or DV of beta Less Than Zero and + + align:start position:0% +zero or DV of beta Less Than Zero and + + + align:start position:0% +zero or DV of beta Less Than Zero and +again + + align:start position:0% +again + + + align:start position:0% +again +from the previous page + + align:start position:0% +from the previous page + + + align:start position:0% +from the previous page +and from these + + align:start position:0% +and from these + + + align:start position:0% +and from these +I get d s + + align:start position:0% +I get d s + + + align:start position:0% +I get d s +greater than zero + + align:start position:0% + + + + align:start position:0% + +so it's not just heat transfer + + align:start position:0% +so it's not just heat transfer + + + align:start position:0% +so it's not just heat transfer +that um that can increase entropy + + align:start position:0% +that um that can increase entropy + + + align:start position:0% +that um that can increase entropy +it's also mechanical work + + align:start position:0% +it's also mechanical work + + + align:start position:0% +it's also mechanical work +that can increase entropy + + align:start position:0% +that can increase entropy + + + align:start position:0% +that can increase entropy +why is that by the way let's let's go + + align:start position:0% +why is that by the way let's let's go + + + align:start position:0% +why is that by the way let's let's go +back to the baby book picture why is it + + align:start position:0% +back to the baby book picture why is it + + + align:start position:0% +back to the baby book picture why is it +the mechanical work can increase entropy + + align:start position:0% +the mechanical work can increase entropy + + + align:start position:0% +the mechanical work can increase entropy +what's going on let me draw a picture + + align:start position:0% +what's going on let me draw a picture + + + align:start position:0% +what's going on let me draw a picture +let's start + + align:start position:0% +let's start + + + align:start position:0% +let's start +at T equals zero + + align:start position:0% +at T equals zero + + + align:start position:0% +at T equals zero +with a high pressure phase + + align:start position:0% +with a high pressure phase + + + align:start position:0% +with a high pressure phase +and let's imagine these are gases + + align:start position:0% + + + + align:start position:0% + +and let's draw a low pressure phase + + align:start position:0% + + + + align:start position:0% + +so this is high pressure and this is low + + align:start position:0% +so this is high pressure and this is low + + + align:start position:0% +so this is high pressure and this is low +pressure T equals zero and then I remove + + align:start position:0% +pressure T equals zero and then I remove + + + align:start position:0% +pressure T equals zero and then I remove +the partition so you know the high + + align:start position:0% +the partition so you know the high + + + align:start position:0% +the partition so you know the high +pressure phase expands into the lower + + align:start position:0% +pressure phase expands into the lower + + + align:start position:0% +pressure phase expands into the lower +pressure phase + + align:start position:0% + + + + align:start position:0% + +why does that increase the entropy + + align:start position:0% + + + + align:start position:0% + +maybe because particles are more + + align:start position:0% +maybe because particles are more + + + align:start position:0% +maybe because particles are more +randomly distributed and go out further + + align:start position:0% +randomly distributed and go out further + + + align:start position:0% +randomly distributed and go out further +from each other yeah yeah it's like that + + align:start position:0% +from each other yeah yeah it's like that + + + align:start position:0% +from each other yeah yeah it's like that +these can be more mixed up in the whole + + align:start position:0% +these can be more mixed up in the whole + + + align:start position:0% +these can be more mixed up in the whole +volume + + align:start position:0% +volume + + + align:start position:0% +volume +there's a more random distribution of + + align:start position:0% +there's a more random distribution of + + + align:start position:0% +there's a more random distribution of +more particles + + align:start position:0% +more particles + + + align:start position:0% +more particles +yeah that's that's that's sort of it + + align:start position:0% + + + + align:start position:0% + +good okay + + align:start position:0% +good okay + + + align:start position:0% +good okay +um + + align:start position:0% +um + + + align:start position:0% +um +last example here + + align:start position:0% + + + + align:start position:0% + +consider + + align:start position:0% +consider + + + align:start position:0% +consider +temperature Alpha equals temperature + + align:start position:0% +temperature Alpha equals temperature + + + align:start position:0% +temperature Alpha equals temperature +beta + + align:start position:0% +beta + + + align:start position:0% +beta +but mu of alpha is greater than mu + + align:start position:0% +but mu of alpha is greater than mu + + + align:start position:0% +but mu of alpha is greater than mu +of beta + + align:start position:0% +of beta + + + align:start position:0% +of beta +so in this Con situation mu of alpha + + align:start position:0% +so in this Con situation mu of alpha + + + align:start position:0% +so in this Con situation mu of alpha +over temperature of alpha minus U of + + align:start position:0% +over temperature of alpha minus U of + + + align:start position:0% +over temperature of alpha minus U of +beta over temperature beta is of course + + align:start position:0% +beta over temperature beta is of course + + + align:start position:0% +beta over temperature beta is of course +greater than zero + + align:start position:0% + + + + align:start position:0% + +so we have + + align:start position:0% +so we have + + + align:start position:0% +so we have +phase boundary + + align:start position:0% +phase boundary + + + align:start position:0% +phase boundary +we have the alpha phase + + align:start position:0% +we have the alpha phase + + + align:start position:0% +we have the alpha phase +you imagine particles in the alpha phase + + align:start position:0% + + + + align:start position:0% + +I shouldn't have used the color I should + + align:start position:0% +I shouldn't have used the color I should + + + align:start position:0% +I shouldn't have used the color I should +have used + + align:start position:0% +have used + + + align:start position:0% +have used +the same black + + align:start position:0% +the same black + + + align:start position:0% +the same black +because it's unary we only have one type + + align:start position:0% +because it's unary we only have one type + + + align:start position:0% +because it's unary we only have one type +of + + align:start position:0% +of + + + align:start position:0% +of +all right and then we have uh + + align:start position:0% +all right and then we have uh + + + align:start position:0% +all right and then we have uh +the beta phase + + align:start position:0% + + + + align:start position:0% + +and again more of the same + + align:start position:0% +and again more of the same + + + align:start position:0% +and again more of the same +component + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +so + + align:start position:0% + + + + align:start position:0% + +matter + + align:start position:0% +matter + + + align:start position:0% +matter +in phase + + align:start position:0% + + + + align:start position:0% + +at higher chemical potential + + align:start position:0% + + + + align:start position:0% + +will spontaneously + + align:start position:0% + + + + align:start position:0% + +convert + + align:start position:0% + + + + align:start position:0% + +two phase + + align:start position:0% + + + + align:start position:0% + +at lower chemical potential + + align:start position:0% + + + + align:start position:0% + +in other words the N of alpha is going + + align:start position:0% +in other words the N of alpha is going + + + align:start position:0% +in other words the N of alpha is going +to be less than zero or d n of beta is + + align:start position:0% +to be less than zero or d n of beta is + + + align:start position:0% +to be less than zero or d n of beta is +going to be greater than zero + + align:start position:0% +going to be greater than zero + + + align:start position:0% +going to be greater than zero +how did this actually happen + + align:start position:0% +how did this actually happen + + + align:start position:0% +how did this actually happen +each individual little particle and + + align:start position:0% +each individual little particle and + + + align:start position:0% +each individual little particle and +anthropomorphize here each individual + + align:start position:0% +anthropomorphize here each individual + + + align:start position:0% +anthropomorphize here each individual +little particle samples its local + + align:start position:0% +little particle samples its local + + + align:start position:0% +little particle samples its local +environment + + align:start position:0% +environment + + + align:start position:0% +environment +and it asks itself where can I where can + + align:start position:0% +and it asks itself where can I where can + + + align:start position:0% +and it asks itself where can I where can +I get the cheapest Gibbs free energy + + align:start position:0% +I get the cheapest Gibbs free energy + + + align:start position:0% +I get the cheapest Gibbs free energy +it's Gibbs free energy price shopping + + align:start position:0% +it's Gibbs free energy price shopping + + + align:start position:0% +it's Gibbs free energy price shopping +right it goes Price shopping + + align:start position:0% +right it goes Price shopping + + + align:start position:0% +right it goes Price shopping +and it sees that uh + + align:start position:0% +and it sees that uh + + + align:start position:0% +and it sees that uh +that it's it's it's in a more expensive + + align:start position:0% +that it's it's it's in a more expensive + + + align:start position:0% +that it's it's it's in a more expensive +region it actually would like to + + align:start position:0% +region it actually would like to + + + align:start position:0% +region it actually would like to +transform into a cheaper region + + align:start position:0% +transform into a cheaper region + + + align:start position:0% +transform into a cheaper region +so it it transforms + + align:start position:0% +so it it transforms + + + align:start position:0% +so it it transforms +and when it does so the phase boundary + + align:start position:0% +and when it does so the phase boundary + + + align:start position:0% +and when it does so the phase boundary +moves a little bit right now that + + align:start position:0% +moves a little bit right now that + + + align:start position:0% +moves a little bit right now that +particle has transformed from alpha to + + align:start position:0% +particle has transformed from alpha to + + + align:start position:0% +particle has transformed from alpha to +Beta + + align:start position:0% +Beta + + + align:start position:0% +Beta +the beta phase has grown a little bit at + + align:start position:0% +the beta phase has grown a little bit at + + + align:start position:0% +the beta phase has grown a little bit at +the expense of the alpha phase + + align:start position:0% +the expense of the alpha phase + + + align:start position:0% +the expense of the alpha phase +right and then the next particle gets to + + align:start position:0% +right and then the next particle gets to + + + align:start position:0% +right and then the next particle gets to +ask itself + + align:start position:0% +ask itself + + + align:start position:0% +ask itself +right what would I like would rather be + + align:start position:0% +right what would I like would rather be + + + align:start position:0% +right what would I like would rather be +and the phase boundary moves a little + + align:start position:0% +and the phase boundary moves a little + + + align:start position:0% +and the phase boundary moves a little +bit more + + align:start position:0% +bit more + + + align:start position:0% +bit more +and so on until chemical equilibrium is + + align:start position:0% +and so on until chemical equilibrium is + + + align:start position:0% +and so on until chemical equilibrium is +reached + + align:start position:0% + + + + align:start position:0% + +and again from the combined statement + + align:start position:0% +and again from the combined statement + + + align:start position:0% +and again from the combined statement +we find that this spontaneous process + + align:start position:0% +we find that this spontaneous process + + + align:start position:0% +we find that this spontaneous process +increases the entropy as we expect + + align:start position:0% + + + + align:start position:0% + +so this process here by which particles + + align:start position:0% +so this process here by which particles + + + align:start position:0% +so this process here by which particles +transformed between their phase right + + align:start position:0% +transformed between their phase right + + + align:start position:0% +transformed between their phase right +sometimes in this class they call it + + align:start position:0% +sometimes in this class they call it + + + align:start position:0% +sometimes in this class they call it +Gibbs free energy price shopping that's + + align:start position:0% +Gibbs free energy price shopping that's + + + align:start position:0% +Gibbs free energy price shopping that's +most of what we deal with in Material + + align:start position:0% +most of what we deal with in Material + + + align:start position:0% +most of what we deal with in Material +Science + + align:start position:0% +Science + + + align:start position:0% +Science +it's it's less intuitive than high + + align:start position:0% +it's it's less intuitive than high + + + align:start position:0% +it's it's less intuitive than high +pressure things pushing into low + + align:start position:0% +pressure things pushing into low + + + align:start position:0% +pressure things pushing into low +pressure things + + align:start position:0% +pressure things + + + align:start position:0% +pressure things +but you know we're not mechanical + + align:start position:0% +but you know we're not mechanical + + + align:start position:0% +but you know we're not mechanical +engineers and uh it's less intuitive + + align:start position:0% +engineers and uh it's less intuitive + + + align:start position:0% +engineers and uh it's less intuitive +than than uh than hot things right + + align:start position:0% +than than uh than hot things right + + + align:start position:0% +than than uh than hot things right +heating cold things + + align:start position:0% +heating cold things + + + align:start position:0% +heating cold things +so of these three examples uh it's it's + + align:start position:0% +so of these three examples uh it's it's + + + align:start position:0% +so of these three examples uh it's it's +the least intuitive maybe it's at least + + align:start position:0% +the least intuitive maybe it's at least + + + align:start position:0% +the least intuitive maybe it's at least +every day + + align:start position:0% +every day + + + align:start position:0% +every day +um but uh + + align:start position:0% +um but uh + + + align:start position:0% +um but uh +it provides the most rich Behavior right + + align:start position:0% +it provides the most rich Behavior right + + + align:start position:0% +it provides the most rich Behavior right +so this is what we're going to be + + align:start position:0% +so this is what we're going to be + + + align:start position:0% +so this is what we're going to be +worrying about + + align:start position:0% +worrying about + + + align:start position:0% +worrying about +um + + align:start position:0% +um + + + align:start position:0% +um +and of course the particles don't sit + + align:start position:0% +and of course the particles don't sit + + + align:start position:0% +and of course the particles don't sit +down and think right + + align:start position:0% +down and think right + + + align:start position:0% +down and think right +um + + align:start position:0% +um + + + align:start position:0% +um +but through spontaneous random thermal + + align:start position:0% +but through spontaneous random thermal + + + align:start position:0% +but through spontaneous random thermal +fluctuations they sample different + + align:start position:0% +fluctuations they sample different + + + align:start position:0% +fluctuations they sample different +environments + + align:start position:0% +environments + + + align:start position:0% +environments +and they will stay in the environment + + align:start position:0% +and they will stay in the environment + + + align:start position:0% +and they will stay in the environment +that's more stable + + align:start position:0% +that's more stable + + + align:start position:0% +that's more stable +so + + align:start position:0% +so + + + align:start position:0% +so +um that sort of gets towards kinetics + + align:start position:0% +um that sort of gets towards kinetics + + + align:start position:0% +um that sort of gets towards kinetics +again another topic which we don't quite + + align:start position:0% +again another topic which we don't quite + + + align:start position:0% +again another topic which we don't quite +have time for this semester + + align:start position:0% +have time for this semester + + + align:start position:0% +have time for this semester +or we worry about this semester is + + align:start position:0% +or we worry about this semester is + + + align:start position:0% +or we worry about this semester is +chemical potential + + align:start position:0% +chemical potential + + + align:start position:0% +chemical potential +and reaching equilibrium + + align:start position:0% +and reaching equilibrium + + + align:start position:0% +and reaching equilibrium +now I always say you should never + + align:start position:0% +now I always say you should never + + + align:start position:0% +now I always say you should never +anthropomorphize atoms they hate it when + + align:start position:0% +anthropomorphize atoms they hate it when + + + align:start position:0% +anthropomorphize atoms they hate it when +you do that + + align:start position:0% +you do that + + + align:start position:0% +you do that +now that note + + align:start position:0% +now that note + + + align:start position:0% +now that note +um I think I'll stop recording and + + align:start position:0% +um I think I'll stop recording and + + + align:start position:0% +um I think I'll stop recording and +we can leave here for the weekend I'll + + align:start position:0% +we can leave here for the weekend I'll + + + align:start position:0% +we can leave here for the weekend I'll +stick around till 11 or Beyond uh happy + + align:start position:0% +stick around till 11 or Beyond uh happy + + + align:start position:0% +stick around till 11 or Beyond uh happy +to answer questions + + align:start position:0% +to answer questions + + + align:start position:0% +to answer questions +foreign \ No newline at end of file diff --git a/8hdBSfisyxg.txt b/8hdBSfisyxg.txt new file mode 100644 index 0000000000000000000000000000000000000000..ed363fd9a24b126705aae7b816059bf1d69d576e --- /dev/null +++ b/8hdBSfisyxg.txt @@ -0,0 +1,11632 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +openware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu uh we introduced the uh ther + + align:start position:0% +ocw.mit.edu uh we introduced the uh ther + + + align:start position:0% +ocw.mit.edu uh we introduced the uh ther +effects this including C + + align:start position:0% +effects this including C + + + align:start position:0% +effects this including C +effect when we have a temperature + + align:start position:0% +effect when we have a temperature + + + align:start position:0% +effect when we have a temperature +difference of voltage generated that's + + align:start position:0% +difference of voltage generated that's + + + align:start position:0% +difference of voltage generated that's +the phenomen right and then we give a + + align:start position:0% +the phenomen right and then we give a + + + align:start position:0% +the phenomen right and then we give a +microscop a picture of the what + + align:start position:0% +microscop a picture of the what + + + align:start position:0% +microscop a picture of the what +happens diffusion of CH one side of thep + + align:start position:0% +happens diffusion of CH one side of thep + + + align:start position:0% +happens diffusion of CH one side of thep +the the other + + align:start position:0% +the the other + + + align:start position:0% +the the other +side and the C effect uh is when we have + + align:start position:0% +side and the C effect uh is when we have + + + align:start position:0% +side and the C effect uh is when we have +a junction that made of two different + + align:start position:0% +a junction that made of two different + + + align:start position:0% +a junction that made of two different +material will pass current through it + + align:start position:0% +material will pass current through it + + + align:start position:0% +material will pass current through it +you will have either cooling or heating + + align:start position:0% +you will have either cooling or heating + + + align:start position:0% +you will have either cooling or heating +effect depends on the direction of the + + align:start position:0% +effect depends on the direction of the + + + align:start position:0% +effect depends on the direction of the +current FL and this is because the + + align:start position:0% +current FL and this is because the + + + align:start position:0% +current FL and this is because the +charge itself also carry heat so when + + align:start position:0% +charge itself also carry heat so when + + + align:start position:0% +charge itself also carry heat so when +the charge flow from one material to the + + align:start position:0% +the charge flow from one material to the + + + align:start position:0% +the charge flow from one material to the +another material if there more heat + + align:start position:0% +another material if there more heat + + + align:start position:0% +another material if there more heat +flows out then the junction PS down and + + align:start position:0% +flows out then the junction PS down and + + + align:start position:0% +flows out then the junction PS down and +if more that flows in the J up and you + + align:start position:0% +if more that flows in the J up and you + + + align:start position:0% +if more that flows in the J up and you +reverse the current direction you can + + align:start position:0% +reverse the current direction you can + + + align:start position:0% +reverse the current direction you can +see that effect is + + align:start position:0% +see that effect is + + + align:start position:0% +see that effect is +revers and the thant effect is when we + + align:start position:0% +revers and the thant effect is when we + + + align:start position:0% +revers and the thant effect is when we +have a uniform + + align:start position:0% +have a uniform + + + align:start position:0% +have a uniform +conductor or semiconductor we have a c + + align:start position:0% +conductor or semiconductor we have a c + + + align:start position:0% +conductor or semiconductor we have a c +differ + + align:start position:0% +differ + + + align:start position:0% +differ +post and FL a current through then along + + align:start position:0% +post and FL a current through then along + + + align:start position:0% +post and FL a current through then along +the material there is uniform cooling + + align:start position:0% +the material there is uniform cooling + + + align:start position:0% +the material there is uniform cooling +there there's a distributed cooling or + + align:start position:0% +there there's a distributed cooling or + + + align:start position:0% +there there's a distributed cooling or +heting uh that happens around material + + align:start position:0% +heting uh that happens around material + + + align:start position:0% +heting uh that happens around material +and this is because really at each + + align:start position:0% +and this is because really at each + + + align:start position:0% +and this is because really at each +section of the + + align:start position:0% +section of the + + + align:start position:0% +section of the +material because of temperature + + align:start position:0% +material because of temperature + + + align:start position:0% +material because of temperature +difference the charge the electron carry + + align:start position:0% +difference the charge the electron carry + + + align:start position:0% +difference the charge the electron carry +different amount of uh heat so that's + + align:start position:0% +different amount of uh heat so that's + + + align:start position:0% +different amount of uh heat so that's +the com that and then we did a uh + + align:start position:0% +the com that and then we did a uh + + + align:start position:0% +the com that and then we did a uh +analysis simple analysis of a device we + + align:start position:0% +analysis simple analysis of a device we + + + align:start position:0% +analysis simple analysis of a device we +have a real device with pass Curr + + align:start position:0% +have a real device with pass Curr + + + align:start position:0% +have a real device with pass Curr +through it there is a the therm electric + + align:start position:0% +through it there is a the therm electric + + + align:start position:0% +through it there is a the therm electric +effect but there also + + align:start position:0% +effect but there also + + + align:start position:0% +effect but there also +undesirable side effects those side + + align:start position:0% +undesirable side effects those side + + + align:start position:0% +undesirable side effects those side +effects is one there's jar Heating and + + align:start position:0% +effects is one there's jar Heating and + + + align:start position:0% +effects is one there's jar Heating and +two there is reverse heat flow + + align:start position:0% +two there is reverse heat flow + + + align:start position:0% +two there is reverse heat flow +conduction and this diminish uh degree + + align:start position:0% +conduction and this diminish uh degree + + + align:start position:0% +conduction and this diminish uh degree +the device performance and if we do the + + align:start position:0% +the device performance and if we do the + + + align:start position:0% +the device performance and if we do the +device analysis and you find out the uh + + align:start position:0% +device analysis and you find out the uh + + + align:start position:0% +device analysis and you find out the uh +efficiency or the coefficient + + align:start position:0% +efficiency or the coefficient + + + align:start position:0% +efficiency or the coefficient +performance uh we found that those + + align:start position:0% +performance uh we found that those + + + align:start position:0% +performance uh we found that those +depends on eventually the material + + align:start position:0% +depends on eventually the material + + + align:start position:0% +depends on eventually the material +property uh which for the figure + + align:start position:0% +property uh which for the figure + + + align:start position:0% +property uh which for the figure +Z and of course those are heat engines + + align:start position:0% +Z and of course those are heat engines + + + align:start position:0% +Z and of course those are heat engines +so the uh pre factor is the car Factor + + align:start position:0% +so the uh pre factor is the car Factor + + + align:start position:0% +so the uh pre factor is the car Factor +times something that's less than one at + + align:start position:0% +times something that's less than one at + + + align:start position:0% +times something that's less than one at +this less than one is depending on the + + align:start position:0% +this less than one is depending on the + + + align:start position:0% +this less than one is depending on the +material property and Z want to be larg + + align:start position:0% +material property and Z want to be larg + + + align:start position:0% +material property and Z want to be larg +as large as possible and then we + + align:start position:0% +as large as possible and then we + + + align:start position:0% +as large as possible and then we +discuss applications um I mentioned that + + align:start position:0% +discuss applications um I mentioned that + + + align:start position:0% +discuss applications um I mentioned that +like at this stage the materials is not + + align:start position:0% +like at this stage the materials is not + + + align:start position:0% +like at this stage the materials is not +competitive to replace the main + + align:start position:0% +competitive to replace the main + + + align:start position:0% +competitive to replace the main +refrigerators or main power generator + + align:start position:0% +refrigerators or main power generator + + + align:start position:0% +refrigerators or main power generator +like internal compus engine so uh there + + align:start position:0% +like internal compus engine so uh there + + + align:start position:0% +like internal compus engine so uh there +are two directions to go why if your + + align:start position:0% +are two directions to go why if your + + + align:start position:0% +are two directions to go why if your +engineer uh think about really using + + align:start position:0% +engineer uh think about really using + + + align:start position:0% +engineer uh think about really using +those there you have to look at the + + align:start position:0% +those there you have to look at the + + + align:start position:0% +those there you have to look at the +system and The Innovation where it makes + + align:start position:0% +system and The Innovation where it makes + + + align:start position:0% +system and The Innovation where it makes +sense uh from both the efficiency and + + align:start position:0% +sense uh from both the efficiency and + + + align:start position:0% +sense uh from both the efficiency and +the particularly Cost commercial product + + align:start position:0% +the particularly Cost commercial product + + + align:start position:0% +the particularly Cost commercial product +on The View and the other direction is + + align:start position:0% +on The View and the other direction is + + + align:start position:0% +on The View and the other direction is +go to improve the materials so what we + + align:start position:0% +go to improve the materials so what we + + + align:start position:0% +go to improve the materials so what we +will be talking in the next today's + + align:start position:0% +will be talking in the next today's + + + align:start position:0% +will be talking in the next today's +lecture and the next lecture is um + + align:start position:0% +lecture and the next lecture is um + + + align:start position:0% +lecture and the next lecture is um +understanding what really determin the + + align:start position:0% +understanding what really determin the + + + align:start position:0% +understanding what really determin the +microscopic uh aspects of the materials + + align:start position:0% +microscopic uh aspects of the materials + + + align:start position:0% +microscopic uh aspects of the materials +and what are the directions we should go + + align:start position:0% +and what are the directions we should go + + + align:start position:0% +and what are the directions we should go +to improve the materials what are the + + align:start position:0% +to improve the materials what are the + + + align:start position:0% +to improve the materials what are the +ideas uh so let me uh uh again uh start + + align:start position:0% +ideas uh so let me uh uh again uh start + + + align:start position:0% +ideas uh so let me uh uh again uh start +with this the figure of Mer ZT um I said + + align:start position:0% +with this the figure of Mer ZT um I said + + + align:start position:0% +with this the figure of Mer ZT um I said +that when you do thero electrics people + + align:start position:0% +that when you do thero electrics people + + + align:start position:0% +that when you do thero electrics people +you say I work on Thermo electrics of + + align:start position:0% +you say I work on Thermo electrics of + + + align:start position:0% +you say I work on Thermo electrics of +people ask what's your ZT right uh that + + align:start position:0% +people ask what's your ZT right uh that + + + align:start position:0% +people ask what's your ZT right uh that +shows you know something about it and uh + + align:start position:0% +shows you know something about it and uh + + + align:start position:0% +shows you know something about it and uh +it has three parameters the electrical + + align:start position:0% +it has three parameters the electrical + + + align:start position:0% +it has three parameters the electrical +conductivity the cack + + align:start position:0% +conductivity the cack + + + align:start position:0% +conductivity the cack +coefficient and the seral + + align:start position:0% +coefficient and the seral + + + align:start position:0% +coefficient and the seral +conductivity and the seral conductivity + + align:start position:0% +conductivity and the seral conductivity + + + align:start position:0% +conductivity and the seral conductivity +the heat conduction in the material will + + align:start position:0% +the heat conduction in the material will + + + align:start position:0% +the heat conduction in the material will +consist of two parts one is atomical + + align:start position:0% +consist of two parts one is atomical + + + align:start position:0% +consist of two parts one is atomical +vibration the lce in the material the + + align:start position:0% +vibration the lce in the material the + + + align:start position:0% +vibration the lce in the material the +atoms in the material vibrate and + + align:start position:0% +atoms in the material vibrate and + + + align:start position:0% +atoms in the material vibrate and +conduct it and the other is when charge + + align:start position:0% +conduct it and the other is when charge + + + align:start position:0% +conduct it and the other is when charge +itself right it carries St also conduct + + align:start position:0% +itself right it carries St also conduct + + + align:start position:0% +itself right it carries St also conduct +it so here we uh decompose this K into + + align:start position:0% +it so here we uh decompose this K into + + + align:start position:0% +it so here we uh decompose this K into +Fon and + + align:start position:0% +Fon and + + + align:start position:0% +Fon and +electron so those are the uh uh when you + + align:start position:0% +electron so those are the uh uh when you + + + align:start position:0% +electron so those are the uh uh when you +think about ZT you look at those + + align:start position:0% +think about ZT you look at those + + + align:start position:0% +think about ZT you look at those +parameter Electric conductivity cack + + align:start position:0% +parameter Electric conductivity cack + + + align:start position:0% +parameter Electric conductivity cack +coefficient and the F contribution to + + align:start position:0% +coefficient and the F contribution to + + + align:start position:0% +coefficient and the F contribution to +ther conductivity electron contribution + + align:start position:0% +ther conductivity electron contribution + + + align:start position:0% +ther conductivity electron contribution +th + + align:start position:0% +th + + + align:start position:0% +th +conductivity and what I want to do next + + align:start position:0% +conductivity and what I want to do next + + + align:start position:0% +conductivity and what I want to do next +is to give you a go dive into more + + align:start position:0% +is to give you a go dive into more + + + align:start position:0% +is to give you a go dive into more +details so what are the microscopic + + align:start position:0% +details so what are the microscopic + + + align:start position:0% +details so what are the microscopic +pictures determine those + + align:start position:0% +pictures determine those + + + align:start position:0% +pictures determine those +properties and what are the physical uh + + align:start position:0% +properties and what are the physical uh + + + align:start position:0% +properties and what are the physical uh +more of the uh together with some + + align:start position:0% +more of the uh together with some + + + align:start position:0% +more of the uh together with some +mathematical formulation for those + + align:start position:0% +mathematical formulation for those + + + align:start position:0% +mathematical formulation for those +properties + + align:start position:0% + + + + align:start position:0% + +so uh today we uh hope I hope you power + + align:start position:0% +so uh today we uh hope I hope you power + + + align:start position:0% +so uh today we uh hope I hope you power +uh those topics uh we will first review + + align:start position:0% +uh those topics uh we will first review + + + align:start position:0% +uh those topics uh we will first review +uh some basic concepts uh in solid + + align:start position:0% +uh some basic concepts uh in solid + + + align:start position:0% +uh some basic concepts uh in solid +States and then uh using the simplest + + align:start position:0% +States and then uh using the simplest + + + align:start position:0% +States and then uh using the simplest +picture that's the same picture I talked + + align:start position:0% +picture that's the same picture I talked + + + align:start position:0% +picture that's the same picture I talked +in the first lecture how we use three + + align:start position:0% +in the first lecture how we use three + + + align:start position:0% +in the first lecture how we use three +step I derive F right really partic + + align:start position:0% +step I derive F right really partic + + + align:start position:0% +step I derive F right really partic +going from left minus partic going from + + align:start position:0% +going from left minus partic going from + + + align:start position:0% +going from left minus partic going from +uh from left to right master from right + + align:start position:0% +uh from left to right master from right + + + align:start position:0% +uh from left to right master from right +to left so with that imbalance you will + + align:start position:0% +to left so with that imbalance you will + + + align:start position:0% +to left so with that imbalance you will +see we can come up with expressions for + + align:start position:0% +see we can come up with expressions for + + + align:start position:0% +see we can come up with expressions for +the electric conductivity cback thermal + + align:start position:0% +the electric conductivity cback thermal + + + align:start position:0% +the electric conductivity cback thermal +conductive ERS and then I will uh to + + align:start position:0% +conductive ERS and then I will uh to + + + align:start position:0% +conductive ERS and then I will uh to +leave a pH I'm not going to Der detail + + align:start position:0% +leave a pH I'm not going to Der detail + + + align:start position:0% +leave a pH I'm not going to Der detail +deration from this you you you know we + + align:start position:0% +deration from this you you you know we + + + align:start position:0% +deration from this you you you know we +go we can go to more form more transort + + align:start position:0% +go we can go to more form more transort + + + align:start position:0% +go we can go to more form more transort +Theory and uh have the uh more rigorous + + align:start position:0% +Theory and uh have the uh more rigorous + + + align:start position:0% +Theory and uh have the uh more rigorous +expressions for the transport + + align:start position:0% + + + + align:start position:0% + +coefficient so uh let me uh start like I + + align:start position:0% +coefficient so uh let me uh start like I + + + align:start position:0% +coefficient so uh let me uh start like I +said this is a review but I know for + + align:start position:0% +said this is a review but I know for + + + align:start position:0% +said this is a review but I know for +most of you it's new because if you are + + align:start position:0% +most of you it's new because if you are + + + align:start position:0% +most of you it's new because if you are +for example from mechanic engineering + + align:start position:0% +for example from mechanic engineering + + + align:start position:0% +for example from mechanic engineering +you have not seen this so uh don't worry + + align:start position:0% +you have not seen this so uh don't worry + + + align:start position:0% +you have not seen this so uh don't worry +about it uh you just follow let's follow + + align:start position:0% +about it uh you just follow let's follow + + + align:start position:0% +about it uh you just follow let's follow +through some you take say those are the + + align:start position:0% +through some you take say those are the + + + align:start position:0% +through some you take say those are the +results from physics others I hope they + + align:start position:0% +results from physics others I hope they + + + align:start position:0% +results from physics others I hope they +picture is simple enough for you to + + align:start position:0% +picture is simple enough for you to + + + align:start position:0% +picture is simple enough for you to +appreciate uh uh those + + align:start position:0% +appreciate uh uh those + + + align:start position:0% +appreciate uh uh those +pictures uh so let's start with the + + align:start position:0% +pictures uh so let's start with the + + + align:start position:0% +pictures uh so let's start with the +basic concepts first uh in terms of the + + align:start position:0% +basic concepts first uh in terms of the + + + align:start position:0% +basic concepts first uh in terms of the +uh atomical vibration I because atomical + + align:start position:0% +uh atomical vibration I because atomical + + + align:start position:0% +uh atomical vibration I because atomical +vibration in the solid carries key right + + align:start position:0% +vibration in the solid carries key right + + + align:start position:0% +vibration in the solid carries key right +so now I think about the the bonding + + align:start position:0% +so now I think about the the bonding + + + align:start position:0% +so now I think about the the bonding +between atoms you can think this either + + align:start position:0% +between atoms you can think this either + + + align:start position:0% +between atoms you can think this either +solid or even just a hydrogen molecule + + align:start position:0% +solid or even just a hydrogen molecule + + + align:start position:0% +solid or even just a hydrogen molecule +the bonding between the two two at two + + align:start position:0% +the bonding between the two two at two + + + align:start position:0% +the bonding between the two two at two +hydrogen atoms in the molecule when they + + align:start position:0% +hydrogen atoms in the molecule when they + + + align:start position:0% +hydrogen atoms in the molecule when they +are far apart they + + align:start position:0% +are far apart they + + + align:start position:0% +are far apart they +attractive and then are two close the + + align:start position:0% +attractive and then are two close the + + + align:start position:0% +attractive and then are two close the +repell should are because the electron + + align:start position:0% +repell should are because the electron + + + align:start position:0% +repell should are because the electron +start to overlap and the P mechanics say + + align:start position:0% +start to overlap and the P mechanics say + + + align:start position:0% +start to overlap and the P mechanics say +the uh the basic principle is Exclusion + + align:start position:0% +the uh the basic principle is Exclusion + + + align:start position:0% +the uh the basic principle is Exclusion +Principle it doesn't allow the electron + + align:start position:0% +Principle it doesn't allow the electron + + + align:start position:0% +Principle it doesn't allow the electron +take the same op so uh we have a typical + + align:start position:0% +take the same op so uh we have a typical + + + align:start position:0% +take the same op so uh we have a typical +of potential curve in the far separation + + align:start position:0% +of potential curve in the far separation + + + align:start position:0% +of potential curve in the far separation +between the atoms uh it's attractive and + + align:start position:0% +between the atoms uh it's attractive and + + + align:start position:0% +between the atoms uh it's attractive and +when they close uh it's repulsive and + + align:start position:0% +when they close uh it's repulsive and + + + align:start position:0% +when they close uh it's repulsive and +the atoms sits in uh the equilibrium + + align:start position:0% +the atoms sits in uh the equilibrium + + + align:start position:0% +the atoms sits in uh the equilibrium +position here so when we have many atoms + + align:start position:0% +position here so when we have many atoms + + + align:start position:0% +position here so when we have many atoms +they will have constraints on both sides + + align:start position:0% +they will have constraints on both sides + + + align:start position:0% +they will have constraints on both sides +so they have most stable position that's + + align:start position:0% +so they have most stable position that's + + + align:start position:0% +so they have most stable position that's +where the energy uh is the minimum right + + align:start position:0% +where the energy uh is the minimum right + + + align:start position:0% +where the energy uh is the minimum right +now because this curve the energy is + + align:start position:0% +now because this curve the energy is + + + align:start position:0% +now because this curve the energy is +minimum if you look at the uh the + + align:start position:0% +minimum if you look at the uh the + + + align:start position:0% +minimum if you look at the uh the +mathematics when I have a curve minimum + + align:start position:0% +mathematics when I have a curve minimum + + + align:start position:0% +mathematics when I have a curve minimum +or maximum the first derivative is zero + + align:start position:0% +or maximum the first derivative is zero + + + align:start position:0% +or maximum the first derivative is zero +so when I look at the uh uh expansion I + + align:start position:0% +so when I look at the uh uh expansion I + + + align:start position:0% +so when I look at the uh uh expansion I +can expand this potential uh into the + + align:start position:0% +can expand this potential uh into the + + + align:start position:0% +can expand this potential uh into the +minimum point plus the first derivative + + align:start position:0% +minimum point plus the first derivative + + + align:start position:0% +minimum point plus the first derivative +zero then I go to second derivative so + + align:start position:0% +zero then I go to second derivative so + + + align:start position:0% +zero then I go to second derivative so +you can go to higher order but for the + + align:start position:0% +you can go to higher order but for the + + + align:start position:0% +you can go to higher order but for the +understanding here we just go to second + + align:start position:0% +understanding here we just go to second + + + align:start position:0% +understanding here we just go to second +order and then the + + align:start position:0% +order and then the + + + align:start position:0% +order and then the +force between the ATS is just the D + + align:start position:0% +force between the ATS is just the D + + + align:start position:0% +force between the ATS is just the D +derivative of the potential right so f + + align:start position:0% +derivative of the potential right so f + + + align:start position:0% +derivative of the potential right so f +equals the potential derivative so I get + + align:start position:0% +equals the potential derivative so I get + + + align:start position:0% +equals the potential derivative so I get +a force equals the Sprint + + align:start position:0% +a force equals the Sprint + + + align:start position:0% +a force equals the Sprint +constant the uh so now we can take this + + align:start position:0% +constant the uh so now we can take this + + + align:start position:0% +constant the uh so now we can take this +two atom vibration as a Sprint so it's a + + align:start position:0% +two atom vibration as a Sprint so it's a + + + align:start position:0% +two atom vibration as a Sprint so it's a +maass and spring + + align:start position:0% +maass and spring + + + align:start position:0% +maass and spring +system and for maass spring system uh we + + align:start position:0% +system and for maass spring system uh we + + + align:start position:0% +system and for maass spring system uh we +all know the simplest picture is mass + + align:start position:0% +all know the simplest picture is mass + + + align:start position:0% +all know the simplest picture is mass +frint right and there is a leral fre + + align:start position:0% +frint right and there is a leral fre + + + align:start position:0% +frint right and there is a leral fre +frequency for this vibration the + + align:start position:0% +frequency for this vibration the + + + align:start position:0% +frequency for this vibration the +vibration frequency is the spring + + align:start position:0% +vibration frequency is the spring + + + align:start position:0% +vibration frequency is the spring +constant and divided by the mass of the + + align:start position:0% +constant and divided by the mass of the + + + align:start position:0% +constant and divided by the mass of the +atom this is a very relevant when you + + align:start position:0% +atom this is a very relevant when you + + + align:start position:0% +atom this is a very relevant when you +think about uh what what what material + + align:start position:0% +think about uh what what what material + + + align:start position:0% +think about uh what what what material +you want to choose for thero + + align:start position:0% +you want to choose for thero + + + align:start position:0% +you want to choose for thero +electrics and uh typically the larger is + + align:start position:0% +electrics and uh typically the larger is + + + align:start position:0% +electrics and uh typically the larger is +the string constant between the atoms + + align:start position:0% +the string constant between the atoms + + + align:start position:0% +the string constant between the atoms +right look at this the higher is the + + align:start position:0% +right look at this the higher is the + + + align:start position:0% +right look at this the higher is the +frequency the uh more vibrational energy + + align:start position:0% +frequency the uh more vibrational energy + + + align:start position:0% +frequency the uh more vibrational energy +the more uh the bending of the atom is + + align:start position:0% +the more uh the bending of the atom is + + + align:start position:0% +the more uh the bending of the atom is +stronger it is larger spring constant + + align:start position:0% +stronger it is larger spring constant + + + align:start position:0% +stronger it is larger spring constant +and this will lead to high thermal + + align:start position:0% +and this will lead to high thermal + + + align:start position:0% +and this will lead to high thermal +conductivity and diamond for example has + + align:start position:0% +conductivity and diamond for example has + + + align:start position:0% +conductivity and diamond for example has +the highest theral conductivity among + + align:start position:0% +the highest theral conductivity among + + + align:start position:0% +the highest theral conductivity among +materials and that's because the bonding + + align:start position:0% +materials and that's because the bonding + + + align:start position:0% +materials and that's because the bonding +between carbon in diamond is very strong + + align:start position:0% +between carbon in diamond is very strong + + + align:start position:0% +between carbon in diamond is very strong +and the carbon atom is very + + align:start position:0% +and the carbon atom is very + + + align:start position:0% +and the carbon atom is very +light okay so that's just a uh uh uh uh + + align:start position:0% +light okay so that's just a uh uh uh uh + + + align:start position:0% +light okay so that's just a uh uh uh uh +it has + + align:start position:0% +it has + + + align:start position:0% +it has +implications uh for this even though + + align:start position:0% +implications uh for this even though + + + align:start position:0% +implications uh for this even though +it's very simple and this is what they + + align:start position:0% +it's very simple and this is what they + + + align:start position:0% +it's very simple and this is what they +learn in + + align:start position:0% +learn in + + + align:start position:0% +learn in +classical mechanics Dynamics right the + + align:start position:0% +classical mechanics Dynamics right the + + + align:start position:0% +classical mechanics Dynamics right the +Lal frequency of + + align:start position:0% +Lal frequency of + + + align:start position:0% +Lal frequency of +vibration and if you go to Quantum + + align:start position:0% +vibration and if you go to Quantum + + + align:start position:0% +vibration and if you go to Quantum +Mechanics what it tells you it's just a + + align:start position:0% +Mechanics what it tells you it's just a + + + align:start position:0% +Mechanics what it tells you it's just a +small addition you know say the + + align:start position:0% +small addition you know say the + + + align:start position:0% +small addition you know say the +frequency is still same new is still the + + align:start position:0% +frequency is still same new is still the + + + align:start position:0% +frequency is still same new is still the +same but what it tells you is that + + align:start position:0% +same but what it tells you is that + + + align:start position:0% +same but what it tells you is that +energy cannot be any value we all know + + align:start position:0% +energy cannot be any value we all know + + + align:start position:0% +energy cannot be any value we all know +Quantum mechanic basic the en comp right + + align:start position:0% +Quantum mechanic basic the en comp right + + + align:start position:0% +Quantum mechanic basic the en comp right +so if your illation is either this + + align:start position:0% +so if your illation is either this + + + align:start position:0% +so if your illation is either this +frequency in classical mechanics the + + align:start position:0% +frequency in classical mechanics the + + + align:start position:0% +frequency in classical mechanics the +illation amplitude the velocity can be + + align:start position:0% +illation amplitude the velocity can be + + + align:start position:0% +illation amplitude the velocity can be +any value and in Quant mechanics we say + + align:start position:0% +any value and in Quant mechanics we say + + + align:start position:0% +any value and in Quant mechanics we say +and uh the the energy must be integer of + + align:start position:0% +and uh the the energy must be integer of + + + align:start position:0% +and uh the the energy must be integer of +this H + + align:start position:0% +this H + + + align:start position:0% +this H +new okay so that's the new the new thing + + align:start position:0% +new okay so that's the new the new thing + + + align:start position:0% +new okay so that's the new the new thing +coming from uh quantum mechanics so must + + align:start position:0% +coming from uh quantum mechanics so must + + + align:start position:0% +coming from uh quantum mechanics so must +be multipl of the H new and so this H + + align:start position:0% +be multipl of the H new and so this H + + + align:start position:0% +be multipl of the H new and so this H +new you can think this as a Basic Energy + + align:start position:0% +new you can think this as a Basic Energy + + + align:start position:0% +new you can think this as a Basic Energy +Quant and that's uh in solid is called a + + align:start position:0% +Quant and that's uh in solid is called a + + + align:start position:0% +Quant and that's uh in solid is called a +f and this one half is also is related + + align:start position:0% +f and this one half is also is related + + + align:start position:0% +f and this one half is also is related +to the soal uncertainty principle in + + align:start position:0% +to the soal uncertainty principle in + + + align:start position:0% +to the soal uncertainty principle in +mechanics it's also called Zero Point + + align:start position:0% +mechanics it's also called Zero Point + + + align:start position:0% +mechanics it's also called Zero Point +Energy so uh if you if you recall before + + align:start position:0% +Energy so uh if you if you recall before + + + align:start position:0% +Energy so uh if you if you recall before +I talk about the photon right when we + + align:start position:0% +I talk about the photon right when we + + + align:start position:0% +I talk about the photon right when we +through electromagnetic wave and this + + align:start position:0% +through electromagnetic wave and this + + + align:start position:0% +through electromagnetic wave and this +Atomic vibration is an analogous to the + + align:start position:0% +Atomic vibration is an analogous to the + + + align:start position:0% +Atomic vibration is an analogous to the +electromagnetic wave so those are all + + align:start position:0% +electromagnetic wave so those are all + + + align:start position:0% +electromagnetic wave so those are all +waves uh we extend this more to waves in + + align:start position:0% +waves uh we extend this more to waves in + + + align:start position:0% +waves uh we extend this more to waves in +The Next Step so that's where the L + + align:start position:0% +The Next Step so that's where the L + + + align:start position:0% +The Next Step so that's where the L +coming from Photon for electromagnetic + + align:start position:0% +coming from Photon for electromagnetic + + + align:start position:0% +coming from Photon for electromagnetic +wave and poon for lce vibration and + + align:start position:0% +wave and poon for lce vibration and + + + align:start position:0% +wave and poon for lce vibration and +that's the Basic Energy cont of + + align:start position:0% +that's the Basic Energy cont of + + + align:start position:0% +that's the Basic Energy cont of +vibration okay so this this is we're + + align:start position:0% +vibration okay so this this is we're + + + align:start position:0% +vibration okay so this this is we're +talking about the individual + + align:start position:0% +talking about the individual + + + align:start position:0% +talking about the individual +oscillator and now uh I look at the uh + + align:start position:0% +oscillator and now uh I look at the uh + + + align:start position:0% +oscillator and now uh I look at the uh +Atomic ch right so uh when I think about + + align:start position:0% +Atomic ch right so uh when I think about + + + align:start position:0% +Atomic ch right so uh when I think about +solid the most uh simple picture is + + align:start position:0% +solid the most uh simple picture is + + + align:start position:0% +solid the most uh simple picture is +crystals Crystal are periodical + + align:start position:0% +crystals Crystal are periodical + + + align:start position:0% +crystals Crystal are periodical +arrangement of atoms so now I started + + align:start position:0% +arrangement of atoms so now I started + + + align:start position:0% +arrangement of atoms so now I started +with a one dimension of atomic + + align:start position:0% +with a one dimension of atomic + + + align:start position:0% +with a one dimension of atomic +chain and uh uh uh the distance between + + align:start position:0% +chain and uh uh uh the distance between + + + align:start position:0% +chain and uh uh uh the distance between +the atoms is the L constant a so we have + + align:start position:0% +the atoms is the L constant a so we have + + + align:start position:0% +the atoms is the L constant a so we have +n atoms so the length of this chain is + + align:start position:0% +n atoms so the length of this chain is + + + align:start position:0% +n atoms so the length of this chain is +n now again you recall uh in the uh + + align:start position:0% +n now again you recall uh in the uh + + + align:start position:0% +n now again you recall uh in the uh +electromagnetic wave the last lecture I + + align:start position:0% +electromagnetic wave the last lecture I + + + align:start position:0% +electromagnetic wave the last lecture I +derive the uh pl's black body radiation + + align:start position:0% +derive the uh pl's black body radiation + + + align:start position:0% +derive the uh pl's black body radiation +La uh I said that when we consider + + align:start position:0% +La uh I said that when we consider + + + align:start position:0% +La uh I said that when we consider +cavity in the lens Direction I have + + align:start position:0% +cavity in the lens Direction I have + + + align:start position:0% +cavity in the lens Direction I have +standing W now I'm going to make the + + align:start position:0% +standing W now I'm going to make the + + + align:start position:0% +standing W now I'm going to make the +same argument if I clamp the two ends of + + align:start position:0% +same argument if I clamp the two ends of + + + align:start position:0% +same argument if I clamp the two ends of +this Atomic chain do not move right + + align:start position:0% +this Atomic chain do not move right + + + align:start position:0% +this Atomic chain do not move right +again take a rubber band as an + + align:start position:0% +again take a rubber band as an + + + align:start position:0% +again take a rubber band as an +example right you fix this end you + + align:start position:0% +example right you fix this end you + + + align:start position:0% +example right you fix this end you +oscillate it you'll see the waves + + align:start position:0% +oscillate it you'll see the waves + + + align:start position:0% +oscillate it you'll see the waves +different waves right and the violin is + + align:start position:0% +different waves right and the violin is + + + align:start position:0% +different waves right and the violin is +another example right so the length give + + align:start position:0% +another example right so the length give + + + align:start position:0% +another example right so the length give +me those are the wave uh the constraint + + align:start position:0% +me those are the wave uh the constraint + + + align:start position:0% +me those are the wave uh the constraint +the wave has to be multiple + + align:start position:0% +the wave has to be multiple + + + align:start position:0% +the wave has to be multiple +of Lambda which is the wav length over + + align:start position:0% +of Lambda which is the wav length over + + + align:start position:0% +of Lambda which is the wav length over +two so I have the length must be mle two + + align:start position:0% +two so I have the length must be mle two + + + align:start position:0% +two so I have the length must be mle two +you could be + + align:start position:0% +you could be + + + align:start position:0% +you could be +here and then the V Vector again I'm + + align:start position:0% +here and then the V Vector again I'm + + + align:start position:0% +here and then the V Vector again I'm +talking about because it's the wave so + + align:start position:0% +talking about because it's the wave so + + + align:start position:0% +talking about because it's the wave so +the uh the inverse of the wavess is the + + align:start position:0% +the uh the inverse of the wavess is the + + + align:start position:0% +the uh the inverse of the wavess is the +wave Vector is 2 pi/ Lambda that's the + + align:start position:0% +wave Vector is 2 pi/ Lambda that's the + + + align:start position:0% +wave Vector is 2 pi/ Lambda that's the +definition and fundamentally is like the + + align:start position:0% +definition and fundamentally is like the + + + align:start position:0% +definition and fundamentally is like the +F transform trans for right if you're + + align:start position:0% +F transform trans for right if you're + + + align:start position:0% +F transform trans for right if you're +electric engineer the time signal or + + align:start position:0% +electric engineer the time signal or + + + align:start position:0% +electric engineer the time signal or +sign Omega T signal the p is T and + + align:start position:0% +sign Omega T signal the p is T and + + + align:start position:0% +sign Omega T signal the p is T and +frequency is Omega the relation is Omega + + align:start position:0% +frequency is Omega the relation is Omega + + + align:start position:0% +frequency is Omega the relation is Omega += 2 pi/ T the same this is a a specially + + align:start position:0% += 2 pi/ T the same this is a a specially + + + align:start position:0% += 2 pi/ T the same this is a a specially +periodic vibration so the wave vector + + align:start position:0% +periodic vibration so the wave vector + + + align:start position:0% +periodic vibration so the wave vector +and wave L relation is to five over + + align:start position:0% +and wave L relation is to five over + + + align:start position:0% +and wave L relation is to five over +Lambda that's a FAL + + align:start position:0% +Lambda that's a FAL + + + align:start position:0% +Lambda that's a FAL +transform and uh so this is this sending + + align:start position:0% +transform and uh so this is this sending + + + align:start position:0% +transform and uh so this is this sending +me picture when I climb the two end of + + align:start position:0% +me picture when I climb the two end of + + + align:start position:0% +me picture when I climb the two end of +the uh L chain I have those are the + + align:start position:0% +the uh L chain I have those are the + + + align:start position:0% +the uh L chain I have those are the +loable uh wave + + align:start position:0% +loable uh wave + + + align:start position:0% +loable uh wave +vectors and uh I went this pretty fast + + align:start position:0% +vectors and uh I went this pretty fast + + + align:start position:0% +vectors and uh I went this pretty fast +in the uh last time I talk about + + align:start position:0% +in the uh last time I talk about + + + align:start position:0% +in the uh last time I talk about +electromagnetic wave but I did say the + + align:start position:0% +electromagnetic wave but I did say the + + + align:start position:0% +electromagnetic wave but I did say the +standing W I read write the mathematics + + align:start position:0% +standing W I read write the mathematics + + + align:start position:0% +standing W I read write the mathematics +you go to check when say I wrote + + align:start position:0% +you go to check when say I wrote + + + align:start position:0% +you go to check when say I wrote +mathematics I say I can do the summation + + align:start position:0% +mathematics I say I can do the summation + + + align:start position:0% +mathematics I say I can do the summation +of two traveling w + + align:start position:0% +of two traveling w + + + align:start position:0% +of two traveling w +one goes from left to right the other is + + align:start position:0% +one goes from left to right the other is + + + align:start position:0% +one goes from left to right the other is +go from uh right to left so here K is 2 + + align:start position:0% +go from uh right to left so here K is 2 + + + align:start position:0% +go from uh right to left so here K is 2 +pi Lambda those are the values so uh now + + align:start position:0% +pi Lambda those are the values so uh now + + + align:start position:0% +pi Lambda those are the values so uh now +I uh uh do the traveling wave so rather + + align:start position:0% +I uh uh do the traveling wave so rather + + + align:start position:0% +I uh uh do the traveling wave so rather +than clim the two ends I say okay I + + align:start position:0% +than clim the two ends I say okay I + + + align:start position:0% +than clim the two ends I say okay I +don't have that constraint the waves can + + align:start position:0% +don't have that constraint the waves can + + + align:start position:0% +don't have that constraint the waves can +go both positive direction negative + + align:start position:0% +go both positive direction negative + + + align:start position:0% +go both positive direction negative +Direction okay so in this case the V + + align:start position:0% +Direction okay so in this case the V + + + align:start position:0% +Direction okay so in this case the V +vector + + align:start position:0% +vector + + + align:start position:0% +vector +is pi over from minus pi/ a to plus pi/ + + align:start position:0% +is pi over from minus pi/ a to plus pi/ + + + align:start position:0% +is pi over from minus pi/ a to plus pi/ +a and two traveling a w will make the + + align:start position:0% +a and two traveling a w will make the + + + align:start position:0% +a and two traveling a w will make the +standing wave so if you have the same + + align:start position:0% +standing wave so if you have the same + + + align:start position:0% +standing wave so if you have the same +wav there and uh but also if you compare + + align:start position:0% +wav there and uh but also if you compare + + + align:start position:0% +wav there and uh but also if you compare +what I wrote + + align:start position:0% +what I wrote + + + align:start position:0% +what I wrote +before okay I didn't put the L limit + + align:start position:0% +before okay I didn't put the L limit + + + align:start position:0% +before okay I didn't put the L limit +right so this way we Vector can have any + + align:start position:0% +right so this way we Vector can have any + + + align:start position:0% +right so this way we Vector can have any +value on the other hand when I think + + align:start position:0% +value on the other hand when I think + + + align:start position:0% +value on the other hand when I think +about + + align:start position:0% +about + + + align:start position:0% +about +very large we Vector what it means in a + + align:start position:0% +very large we Vector what it means in a + + + align:start position:0% +very large we Vector what it means in a +crystal because the two ATS the smallest + + align:start position:0% +crystal because the two ATS the smallest + + + align:start position:0% +crystal because the two ATS the smallest +distance is here now if you have W + + align:start position:0% +distance is here now if you have W + + + align:start position:0% +distance is here now if you have W +wavelength shorter than that doesn't + + align:start position:0% +wavelength shorter than that doesn't + + + align:start position:0% +wavelength shorter than that doesn't +mean much okay so that's why I say my + + align:start position:0% +mean much okay so that's why I say my + + + align:start position:0% +mean much okay so that's why I say my +wavelength is limited to uh here if you + + align:start position:0% +wavelength is limited to uh here if you + + + align:start position:0% +wavelength is limited to uh here if you +look at this this is a 2 a the two uh + + align:start position:0% +look at this this is a 2 a the two uh + + + align:start position:0% +look at this this is a 2 a the two uh +one Atomic distance is a so this is the + + align:start position:0% +one Atomic distance is a so this is the + + + align:start position:0% +one Atomic distance is a so this is the +minimum + + align:start position:0% +minimum + + + align:start position:0% +minimum +you can have in terms of Wess so those + + align:start position:0% +you can have in terms of Wess so those + + + align:start position:0% +you can have in terms of Wess so those +are the reg the region of my we Vector + + align:start position:0% +are the reg the region of my we Vector + + + align:start position:0% +are the reg the region of my we Vector +going + + align:start position:0% +going + + + align:start position:0% +going +from a to plus + + align:start position:0% +from a to plus + + + align:start position:0% +from a to plus +a now you think about the uh frequency + + align:start position:0% +a now you think about the uh frequency + + + align:start position:0% +a now you think about the uh frequency +right when I talk about the one atom + + align:start position:0% +right when I talk about the one atom + + + align:start position:0% +right when I talk about the one atom +vibrating the frequency is k/ M square + + align:start position:0% +vibrating the frequency is k/ M square + + + align:start position:0% +vibrating the frequency is k/ M square +root of k/ + + align:start position:0% +root of k/ + + + align:start position:0% +root of k/ +M now I have the whole lce right + + align:start position:0% +M now I have the whole lce right + + + align:start position:0% +M now I have the whole lce right +different wave Vector so each wave + + align:start position:0% +different wave Vector so each wave + + + align:start position:0% +different wave Vector so each wave +length corresponding to one mod of those + + align:start position:0% +length corresponding to one mod of those + + + align:start position:0% +length corresponding to one mod of those +vibration and think about if my whole + + align:start position:0% +vibration and think about if my whole + + + align:start position:0% +vibration and think about if my whole +Atomic CH is one wave right one w w pure + + align:start position:0% +Atomic CH is one wave right one w w pure + + + align:start position:0% +Atomic CH is one wave right one w w pure +one + + align:start position:0% +one + + + align:start position:0% +one +pure the frequency is a higher or lower + + align:start position:0% +pure the frequency is a higher or lower + + + align:start position:0% +pure the frequency is a higher or lower +or same as my + + align:start position:0% +or same as my + + + align:start position:0% +or same as my +individual K Over M square root + + align:start position:0% + + + + align:start position:0% + +anybody's youing + + align:start position:0% +anybody's youing + + + align:start position:0% +anybody's youing +guesss + + align:start position:0% +guesss + + + align:start position:0% +guesss +move yes i' say it's the same + + align:start position:0% +move yes i' say it's the same + + + align:start position:0% +move yes i' say it's the same +Asal well let's suppose again let me + + align:start position:0% +Asal well let's suppose again let me + + + align:start position:0% +Asal well let's suppose again let me +take this as a right now all the atoms + + align:start position:0% +take this as a right now all the atoms + + + align:start position:0% +take this as a right now all the atoms +mov in just one one pure + + align:start position:0% +mov in just one one pure + + + align:start position:0% +mov in just one one pure +all the moves and the next is qu + + align:start position:0% +all the moves and the next is qu + + + align:start position:0% +all the moves and the next is qu +pure okay and uh more P so in terms of + + align:start position:0% +pure okay and uh more P so in terms of + + + align:start position:0% +pure okay and uh more P so in terms of +frequency do they + + align:start position:0% +frequency do they + + + align:start position:0% +frequency do they +change or they + + align:start position:0% + + + + align:start position:0% + +don't well you probably can go back and + + align:start position:0% +don't well you probably can go back and + + + align:start position:0% +don't well you probably can go back and +do an experiment put some p over say + + align:start position:0% +do an experiment put some p over say + + + align:start position:0% +do an experiment put some p over say +rubber B and then you will find out + + align:start position:0% +rubber B and then you will find out + + + align:start position:0% +rubber B and then you will find out +right the uh uh the + + align:start position:0% +right the uh uh the + + + align:start position:0% +right the uh uh the +uh relation between the uh + + align:start position:0% +uh relation between the uh + + + align:start position:0% +uh relation between the uh +frequency and the wi + + align:start position:0% +frequency and the wi + + + align:start position:0% +frequency and the wi +BL in this case is changing right when + + align:start position:0% +BL in this case is changing right when + + + align:start position:0% +BL in this case is changing right when +all the atoms move in + + align:start position:0% +all the atoms move in + + + align:start position:0% +all the atoms move in +you let say one only one period it looks + + align:start position:0% +you let say one only one period it looks + + + align:start position:0% +you let say one only one period it looks +like the whole atoms whole all the atoms + + align:start position:0% +like the whole atoms whole all the atoms + + + align:start position:0% +like the whole atoms whole all the atoms +in the chain is moving same time right + + align:start position:0% +in the chain is moving same time right + + + align:start position:0% +in the chain is moving same time right +so it's slower + + align:start position:0% +so it's slower + + + align:start position:0% +so it's slower +frequency is smaller so that's in the + + align:start position:0% +frequency is smaller so that's in the + + + align:start position:0% +frequency is smaller so that's in the +long wave L this is W Vector long wave L + + align:start position:0% +long wave L this is W Vector long wave L + + + align:start position:0% +long wave L this is W Vector long wave L +frequency is smaller and when you go to + + align:start position:0% +frequency is smaller and when you go to + + + align:start position:0% +frequency is smaller and when you go to +a larger wance and at the end it's close + + align:start position:0% +a larger wance and at the end it's close + + + align:start position:0% +a larger wance and at the end it's close +coming back to here you can see here is + + align:start position:0% +coming back to here you can see here is + + + align:start position:0% +coming back to here you can see here is +a k over M square root so come come back + + align:start position:0% +a k over M square root so come come back + + + align:start position:0% +a k over M square root so come come back +to individual atom attach a spr high + + align:start position:0% +to individual atom attach a spr high + + + align:start position:0% +to individual atom attach a spr high +frequency + + align:start position:0% +frequency + + + align:start position:0% +frequency +the okay so this is the relation between + + align:start position:0% +the okay so this is the relation between + + + align:start position:0% +the okay so this is the relation between +the V vector + + align:start position:0% +the V vector + + + align:start position:0% +the V vector +and the frequency is again the + + align:start position:0% +and the frequency is again the + + + align:start position:0% +and the frequency is again the +dispersion remember for foron for + + align:start position:0% +dispersion remember for foron for + + + align:start position:0% +dispersion remember for foron for +magnetic way Omega equals c k that's a + + align:start position:0% +magnetic way Omega equals c k that's a + + + align:start position:0% +magnetic way Omega equals c k that's a +linear dispersion and + + align:start position:0% +linear dispersion and + + + align:start position:0% +linear dispersion and +here the real one we have is is + + align:start position:0% +here the real one we have is is + + + align:start position:0% +here the real one we have is is +approximately the half of a sign this is + + align:start position:0% +approximately the half of a sign this is + + + align:start position:0% +approximately the half of a sign this is +like a sign function and often we do a + + align:start position:0% +like a sign function and often we do a + + + align:start position:0% +like a sign function and often we do a +linear approximation pick this slope + + align:start position:0% +linear approximation pick this slope + + + align:start position:0% +linear approximation pick this slope +so the speed of sound is that that's the + + align:start position:0% +so the speed of sound is that that's the + + + align:start position:0% +so the speed of sound is that that's the +this slope is for the longitudinal wave + + align:start position:0% +this slope is for the longitudinal wave + + + align:start position:0% +this slope is for the longitudinal wave +that's the speed of s so in solid okay + + align:start position:0% +that's the speed of s so in solid okay + + + align:start position:0% +that's the speed of s so in solid okay +you lock one end prob to the other end + + align:start position:0% +you lock one end prob to the other end + + + align:start position:0% +you lock one end prob to the other end +that's the speed of s and that's this + + align:start position:0% +that's the speed of s and that's this + + + align:start position:0% +that's the speed of s and that's this +slope here + + align:start position:0% +slope here + + + align:start position:0% +slope here +okay and very high frequency when you go + + align:start position:0% +okay and very high frequency when you go + + + align:start position:0% +okay and very high frequency when you go +to look at the uh uh see the put the + + align:start position:0% +to look at the uh uh see the put the + + + align:start position:0% +to look at the uh uh see the put the +mass of atom you can see this quency can + + align:start position:0% +mass of atom you can see this quency can + + + align:start position:0% +mass of atom you can see this quency can +go as high as terz or t of terz so very + + align:start position:0% +go as high as terz or t of terz so very + + + align:start position:0% +go as high as terz or t of terz so very +high frequency of course the acoustic + + align:start position:0% +high frequency of course the acoustic + + + align:start position:0% +high frequency of course the acoustic +wave that we get here is only few + + align:start position:0% +wave that we get here is only few + + + align:start position:0% +wave that we get here is only few +hundred okay so this is a a simple one + + align:start position:0% +hundred okay so this is a a simple one + + + align:start position:0% +hundred okay so this is a a simple one +uh + + align:start position:0% +uh + + + align:start position:0% +uh +monom CH and now if I uh extend this a + + align:start position:0% +monom CH and now if I uh extend this a + + + align:start position:0% +monom CH and now if I uh extend this a +little bit suppose my CH has two + + align:start position:0% +little bit suppose my CH has two + + + align:start position:0% +little bit suppose my CH has two +different + + align:start position:0% +different + + + align:start position:0% +different +atoms right Dum oite as a crystal right + + align:start position:0% +atoms right Dum oite as a crystal right + + + align:start position:0% +atoms right Dum oite as a crystal right +one atom is G the other atom is + + align:start position:0% +one atom is G the other atom is + + + align:start position:0% +one atom is G the other atom is +oate and I have uh so in this case this + + align:start position:0% +oate and I have uh so in this case this + + + align:start position:0% +oate and I have uh so in this case this +is a one one p uh so uh from between the + + align:start position:0% +is a one one p uh so uh from between the + + + align:start position:0% +is a one one p uh so uh from between the +two atoms the same atom that's one + + align:start position:0% +two atoms the same atom that's one + + + align:start position:0% +two atoms the same atom that's one +p of course see one simple picture is + + align:start position:0% +p of course see one simple picture is + + + align:start position:0% +p of course see one simple picture is +the other atom is moving in unison with + + align:start position:0% +the other atom is moving in unison with + + + align:start position:0% +the other atom is moving in unison with +this atom to + + align:start position:0% +this atom to + + + align:start position:0% +this atom to +forms uh the same + + align:start position:0% +forms uh the same + + + align:start position:0% +forms uh the same +phas in the two sets of sub atom that is + + align:start position:0% +phas in the two sets of sub atom that is + + + align:start position:0% +phas in the two sets of sub atom that is +and this in this case the dispersion the + + align:start position:0% +and this in this case the dispersion the + + + align:start position:0% +and this in this case the dispersion the +relation between the wave length wave + + align:start position:0% +relation between the wave length wave + + + align:start position:0% +relation between the wave length wave +VOR and frequency is similar to what we + + align:start position:0% +VOR and frequency is similar to what we + + + align:start position:0% +VOR and frequency is similar to what we +draw + + align:start position:0% +draw + + + align:start position:0% +draw +before and in the other + + align:start position:0% +before and in the other + + + align:start position:0% +before and in the other +case we could have this set of atom + + align:start position:0% +case we could have this set of atom + + + align:start position:0% +case we could have this set of atom +moving up the other set of atom moving + + align:start position:0% +moving up the other set of atom moving + + + align:start position:0% +moving up the other set of atom moving +down so it's a much harder stretching + + align:start position:0% +down so it's a much harder stretching + + + align:start position:0% +down so it's a much harder stretching +right they are very close + + align:start position:0% +right they are very close + + + align:start position:0% +right they are very close +you are forcing them in terms of a + + align:start position:0% +you are forcing them in terms of a + + + align:start position:0% +you are forcing them in terms of a +different face there it's much harder + + align:start position:0% +different face there it's much harder + + + align:start position:0% +different face there it's much harder +stretching and the higher frequency + + align:start position:0% +stretching and the higher frequency + + + align:start position:0% +stretching and the higher frequency +stiffer so in this case we have uh two + + align:start position:0% +stiffer so in this case we have uh two + + + align:start position:0% +stiffer so in this case we have uh two +type uh when I have two ATS uh one is + + align:start position:0% +type uh when I have two ATS uh one is + + + align:start position:0% +type uh when I have two ATS uh one is +the acoustic Branch that's the bottom + + align:start position:0% +the acoustic Branch that's the bottom + + + align:start position:0% +the acoustic Branch that's the bottom +part that's this picture here roughly + + align:start position:0% +part that's this picture here roughly + + + align:start position:0% +part that's this picture here roughly +the other is the other face + + align:start position:0% +the other is the other face + + + align:start position:0% +the other is the other face +that's the opio + + align:start position:0% +that's the opio + + + align:start position:0% +that's the opio +branch okay so that's the atomic + + align:start position:0% +branch okay so that's the atomic + + + align:start position:0% +branch okay so that's the atomic +vibration in one + + align:start position:0% +vibration in one + + + align:start position:0% +vibration in one +dimension and of course a crystal is not + + align:start position:0% +dimension and of course a crystal is not + + + align:start position:0% +dimension and of course a crystal is not +one one dimension as solid is not just + + align:start position:0% +one one dimension as solid is not just + + + align:start position:0% +one one dimension as solid is not just +one dimension it's three + + align:start position:0% +one dimension it's three + + + align:start position:0% +one dimension it's three +dimension right so any direction you + + align:start position:0% +dimension right so any direction you + + + align:start position:0% +dimension right so any direction you +look it look like you got a one + + align:start position:0% +look it look like you got a one + + + align:start position:0% +look it look like you got a one +dimension periodical Arrangement it's + + align:start position:0% +dimension periodical Arrangement it's + + + align:start position:0% +dimension periodical Arrangement it's +just that space between the atoms to be + + align:start position:0% +just that space between the atoms to be + + + align:start position:0% +just that space between the atoms to be +different so how we express + + align:start position:0% +different so how we express + + + align:start position:0% +different so how we express +it + + align:start position:0% +it + + + align:start position:0% +it +right so here uh we'll go back to what I + + align:start position:0% +right so here uh we'll go back to what I + + + align:start position:0% +right so here uh we'll go back to what I +said before uh fori + + align:start position:0% +said before uh fori + + + align:start position:0% +said before uh fori +transform and periodic signal if the + + align:start position:0% +transform and periodic signal if the + + + align:start position:0% +transform and periodic signal if the +period is + + align:start position:0% +period is + + + align:start position:0% +period is +T we see the frequency is 2 pi over T + + align:start position:0% +T we see the frequency is 2 pi over T + + + align:start position:0% +T we see the frequency is 2 pi over T +right and uh uh in terms of wave in one + + align:start position:0% +right and uh uh in terms of wave in one + + + align:start position:0% +right and uh uh in terms of wave in one +dimension we this is + + align:start position:0% +dimension we this is + + + align:start position:0% +dimension we this is +Lambda and the full transfer is 2 pi + + align:start position:0% +Lambda and the full transfer is 2 pi + + + align:start position:0% +Lambda and the full transfer is 2 pi +Lambda but in three + + align:start position:0% +Lambda but in three + + + align:start position:0% +Lambda but in three +dimension each Direction has a Lambda + + align:start position:0% +dimension each Direction has a Lambda + + + align:start position:0% +dimension each Direction has a Lambda +right if I look at a crystal a cube + + align:start position:0% +right if I look at a crystal a cube + + + align:start position:0% +right if I look at a crystal a cube +simple take a simple Cube put in + + align:start position:0% +simple take a simple Cube put in + + + align:start position:0% +simple take a simple Cube put in +periodical range you look at diagonal + + align:start position:0% +periodical range you look at diagonal + + + align:start position:0% +periodical range you look at diagonal +Direction the period is cubic three no + + align:start position:0% +Direction the period is cubic three no + + + align:start position:0% +Direction the period is cubic three no +square root of three times the L + + align:start position:0% +square root of three times the L + + + align:start position:0% +square root of three times the L +constant a so that's your + + align:start position:0% +constant a so that's your + + + align:start position:0% +constant a so that's your +ficity you look at say uh different plan + + align:start position:0% +ficity you look at say uh different plan + + + align:start position:0% +ficity you look at say uh different plan +Crystal plan you have different + + align:start position:0% +Crystal plan you have different + + + align:start position:0% +Crystal plan you have different +periodicity so what I do is I transform + + align:start position:0% +periodicity so what I do is I transform + + + align:start position:0% +periodicity so what I do is I transform +this periodicity in + + align:start position:0% +this periodicity in + + + align:start position:0% +this periodicity in +space okay let's say I take a a + + align:start position:0% +space okay let's say I take a a + + + align:start position:0% +space okay let's say I take a a +crystal as say here is a say face Center + + align:start position:0% +crystal as say here is a say face Center + + + align:start position:0% +crystal as say here is a say face Center +structure face Center Cube and we add a + + align:start position:0% +structure face Center Cube and we add a + + + align:start position:0% +structure face Center Cube and we add a +face on the surface there's also + + align:start position:0% +face on the surface there's also + + + align:start position:0% +face on the surface there's also +atom uh and uh I do Fuller transform of + + align:start position:0% +atom uh and uh I do Fuller transform of + + + align:start position:0% +atom uh and uh I do Fuller transform of +this space in three dimension + + align:start position:0% +this space in three dimension + + + align:start position:0% +this space in three dimension +that's what it looks like now it looks a + + align:start position:0% +that's what it looks like now it looks a + + + align:start position:0% +that's what it looks like now it looks a +little bit ugly okay but I can say each + + align:start position:0% +little bit ugly okay but I can say each + + + align:start position:0% +little bit ugly okay but I can say each +Crystal graphic Direction here is a k + + align:start position:0% +Crystal graphic Direction here is a k + + + align:start position:0% +Crystal graphic Direction here is a k +direction right and uh uh the shortest + + align:start position:0% +direction right and uh uh the shortest + + + align:start position:0% +direction right and uh uh the shortest +distance L this point is the longest + + align:start position:0% +distance L this point is the longest + + + align:start position:0% +distance L this point is the longest +real space + + align:start position:0% +real space + + + align:start position:0% +real space +right because the K is 2 pi over + + align:start position:0% +right because the K is 2 pi over + + + align:start position:0% +right because the K is 2 pi over +Lambda so if I think about + + align:start position:0% +Lambda so if I think about + + + align:start position:0% +Lambda so if I think about +this from Center to this point of the + + align:start position:0% +this from Center to this point of the + + + align:start position:0% +this from Center to this point of the +shortest and now for Cube that's a 111 + + align:start position:0% +shortest and now for Cube that's a 111 + + + align:start position:0% +shortest and now for Cube that's a 111 +Direction the inverse of the atomic + + align:start position:0% +Direction the inverse of the atomic + + + align:start position:0% +Direction the inverse of the atomic +space so this is this is way that the uh + + align:start position:0% +space so this is this is way that the uh + + + align:start position:0% +space so this is this is way that the uh +physes like to uh use the reciprocal + + align:start position:0% +physes like to uh use the reciprocal + + + align:start position:0% +physes like to uh use the reciprocal +space joku is you guys don't live in the + + align:start position:0% +space joku is you guys don't live in the + + + align:start position:0% +space joku is you guys don't live in the +real world they like to express things + + align:start position:0% +real world they like to express things + + + align:start position:0% +real world they like to express things +in the reciprocal space so so um now + + align:start position:0% +in the reciprocal space so so um now + + + align:start position:0% +in the reciprocal space so so um now +let's look at it simple in terms of + + align:start position:0% +let's look at it simple in terms of + + + align:start position:0% +let's look at it simple in terms of +mathematics expression things right you + + align:start position:0% +mathematics expression things right you + + + align:start position:0% +mathematics expression things right you +go to Electric Engineers they like to do + + align:start position:0% +go to Electric Engineers they like to do + + + align:start position:0% +go to Electric Engineers they like to do +signal analysis in + + align:start position:0% +signal analysis in + + + align:start position:0% +signal analysis in +frequency they don't do time signal + + align:start position:0% +frequency they don't do time signal + + + align:start position:0% +frequency they don't do time signal +right time signal you have to PL at time + + align:start position:0% +right time signal you have to PL at time + + + align:start position:0% +right time signal you have to PL at time +you do hard spectral analysis you get to + + align:start position:0% +you do hard spectral analysis you get to + + + align:start position:0% +you do hard spectral analysis you get to +use frequency it's much simpler + + align:start position:0% +use frequency it's much simpler + + + align:start position:0% +use frequency it's much simpler +mathematical + + align:start position:0% +mathematical + + + align:start position:0% +mathematical +language okay so now you get to the real + + align:start position:0% +language okay so now you get to the real + + + align:start position:0% +language okay so now you get to the real +world because that before it look very + + align:start position:0% +world because that before it look very + + + align:start position:0% +world because that before it look very +simple now you start to look at the + + align:start position:0% +simple now you start to look at the + + + align:start position:0% +simple now you start to look at the +string for most mechanic engineer you + + align:start position:0% +string for most mechanic engineer you + + + align:start position:0% +string for most mechanic engineer you +look at this you'll get the uh what is + + align:start position:0% +look at this you'll get the uh what is + + + align:start position:0% +look at this you'll get the uh what is +that see it's really look at a different + + align:start position:0% +that see it's really look at a different + + + align:start position:0% +that see it's really look at a different +cryst graphic Direction the vibration + + align:start position:0% +cryst graphic Direction the vibration + + + align:start position:0% +cryst graphic Direction the vibration +frequen and uh uh if you look at this + + align:start position:0% +frequen and uh uh if you look at this + + + align:start position:0% +frequen and uh uh if you look at this +all silicon g m or face Center cubic as + + align:start position:0% +all silicon g m or face Center cubic as + + + align:start position:0% +all silicon g m or face Center cubic as +I do before different Crystal has + + align:start position:0% +I do before different Crystal has + + + align:start position:0% +I do before different Crystal has +different uh those different directions + + align:start position:0% +different uh those different directions + + + align:start position:0% +different uh those different directions +different reciprocal the shape of this + + align:start position:0% +different reciprocal the shape of this + + + align:start position:0% +different reciprocal the shape of this +basic UN in reciprocal space so I look + + align:start position:0% +basic UN in reciprocal space so I look + + + align:start position:0% +basic UN in reciprocal space so I look +at the uh gamma Direction that's so one + + align:start position:0% +at the uh gamma Direction that's so one + + + align:start position:0% +at the uh gamma Direction that's so one +Z say z z so this Diagon from this to + + align:start position:0% +Z say z z so this Diagon from this to + + + align:start position:0% +Z say z z so this Diagon from this to +this diagonal Direction so if I look at + + align:start position:0% +this diagonal Direction so if I look at + + + align:start position:0% +this diagonal Direction so if I look at +that direction what's the vibrational + + align:start position:0% +that direction what's the vibrational + + + align:start position:0% +that direction what's the vibrational +situation Spectrum so if I have the lest + + align:start position:0% +situation Spectrum so if I have the lest + + + align:start position:0% +situation Spectrum so if I have the lest +we propagating in the diagonal Direction + + align:start position:0% +we propagating in the diagonal Direction + + + align:start position:0% +we propagating in the diagonal Direction +so that's a from GMA to l + + align:start position:0% + + + + align:start position:0% + +right and this is the those are the op F + + align:start position:0% +right and this is the those are the op F + + + align:start position:0% +right and this is the those are the op F +those are theous Fons F start from zero + + align:start position:0% +those are theous Fons F start from zero + + + align:start position:0% +those are theous Fons F start from zero +here optic + + align:start position:0% +here optic + + + align:start position:0% +here optic +is from the top of the acoustic and why + + align:start position:0% +is from the top of the acoustic and why + + + align:start position:0% +is from the top of the acoustic and why +I have different branches I have + + align:start position:0% +I have different branches I have + + + align:start position:0% +I have different branches I have +different branches because the vibration + + align:start position:0% +different branches because the vibration + + + align:start position:0% +different branches because the vibration +the sound wave you're receiving is + + align:start position:0% +the sound wave you're receiving is + + + align:start position:0% +the sound wave you're receiving is +longitudinal air is it's longital wave + + align:start position:0% +longitudinal air is it's longital wave + + + align:start position:0% +longitudinal air is it's longital wave +only but in solid you can have lital as + + align:start position:0% +only but in solid you can have lital as + + + align:start position:0% +only but in solid you can have lital as +well as transverse you can experience + + align:start position:0% +well as transverse you can experience + + + align:start position:0% +well as transverse you can experience +you can sustain the + + align:start position:0% +you can sustain the + + + align:start position:0% +you can sustain the +share so uh I have longitudinal way + + align:start position:0% +share so uh I have longitudinal way + + + align:start position:0% +share so uh I have longitudinal way +transverse + + align:start position:0% +transverse + + + align:start position:0% +transverse +way and really transvers if you look at + + align:start position:0% +way and really transvers if you look at + + + align:start position:0% +way and really transvers if you look at +the electromagnetic wave I said there + + align:start position:0% +the electromagnetic wave I said there + + + align:start position:0% +the electromagnetic wave I said there +are two polarization + + align:start position:0% +are two polarization + + + align:start position:0% +are two polarization +right see acis way transvers also too + + align:start position:0% +right see acis way transvers also too + + + align:start position:0% +right see acis way transvers also too +but the entirely symmetri Direction like + + align:start position:0% +but the entirely symmetri Direction like + + + align:start position:0% +but the entirely symmetri Direction like +uh uh from gamma to L in this case it's + + align:start position:0% +uh uh from gamma to L in this case it's + + + align:start position:0% +uh uh from gamma to L in this case it's +symmetric so the two direction this + + align:start position:0% +symmetric so the two direction this + + + align:start position:0% +symmetric so the two direction this +direction and this direction the same + + align:start position:0% +direction and this direction the same + + + align:start position:0% +direction and this direction the same +Vector they have same + + align:start position:0% +Vector they have same + + + align:start position:0% +Vector they have same +frequency so they become degenerate just + + align:start position:0% +frequency so they become degenerate just + + + align:start position:0% +frequency so they become degenerate just +PL + + align:start position:0% +PL + + + align:start position:0% +PL +one but in some other direction it's not + + align:start position:0% +one but in some other direction it's not + + + align:start position:0% +one but in some other direction it's not +high symmetric you can see clearly three + + align:start position:0% +high symmetric you can see clearly three + + + align:start position:0% +high symmetric you can see clearly three +polarizations non one + + align:start position:0% +polarizations non one + + + align:start position:0% +polarizations non one +two so acoustic branches + + align:start position:0% +two so acoustic branches + + + align:start position:0% +two so acoustic branches +op + + align:start position:0% +op + + + align:start position:0% +op +branches that's the + + align:start position:0% +branches that's the + + + align:start position:0% +branches that's the +extension from 1D to + + align:start position:0% + + + + align:start position:0% + +3D uh different W Vector the space those + + align:start position:0% +3D uh different W Vector the space those + + + align:start position:0% +3D uh different W Vector the space those +first those are experiments the the data + + align:start position:0% +first those are experiments the the data + + + align:start position:0% +first those are experiments the the data +is comp compar experiment they should + + align:start position:0% +is comp compar experiment they should + + + align:start position:0% +is comp compar experiment they should +frequen should be in like or huh + + align:start position:0% +frequen should be in like or huh + + + align:start position:0% +frequen should be in like or huh +frequency frequency is in like hearts + + align:start position:0% +frequency frequency is in like hearts + + + align:start position:0% +frequency frequency is in like hearts +frequency is if it's Omega so so this is + + align:start position:0% +frequency is if it's Omega so so this is + + + align:start position:0% +frequency is if it's Omega so so this is +another thing that very often you people + + align:start position:0% +another thing that very often you people + + + align:start position:0% +another thing that very often you people +get really confused because depends on + + align:start position:0% +get really confused because depends on + + + align:start position:0% +get really confused because depends on +who likes to PL on + + align:start position:0% + + + + align:start position:0% + +what + + align:start position:0% +what + + + align:start position:0% +what +right and sometimes here is + + align:start position:0% +right and sometimes here is + + + align:start position:0% +right and sometimes here is +K Omega and sometimes you see this one + + align:start position:0% +K Omega and sometimes you see this one + + + align:start position:0% +K Omega and sometimes you see this one +is not terms of the frequency this cim + + align:start position:0% +is not terms of the frequency this cim + + + align:start position:0% +is not terms of the frequency this cim +inverse + + align:start position:0% +inverse + + + align:start position:0% +inverse +all this is that's not a frequency + + align:start position:0% +all this is that's not a frequency + + + align:start position:0% +all this is that's not a frequency +unit right so what they do what they + + align:start position:0% +unit right so what they do what they + + + align:start position:0% +unit right so what they do what they +mean and in this case if you want to + + align:start position:0% +mean and in this case if you want to + + + align:start position:0% +mean and in this case if you want to +look at the first frequency is 2 pi mu + + align:start position:0% +look at the first frequency is 2 pi mu + + + align:start position:0% +look at the first frequency is 2 pi mu +angular + + align:start position:0% +angular + + + align:start position:0% +angular +frequency right you have to see what + + align:start position:0% +frequency right you have to see what + + + align:start position:0% +frequency right you have to see what +exactly that whether PL the angular + + align:start position:0% +exactly that whether PL the angular + + + align:start position:0% +exactly that whether PL the angular +frequency or + + align:start position:0% +frequency or + + + align:start position:0% +frequency or +frequency and mu is if the we Vector + + align:start position:0% +frequency and mu is if the we Vector + + + align:start position:0% +frequency and mu is if the we Vector +inverse they prodct one Lambda + + align:start position:0% +inverse they prodct one Lambda + + + align:start position:0% +inverse they prodct one Lambda +okay so you have to convert the + + align:start position:0% +okay so you have to convert the + + + align:start position:0% +okay so you have to convert the +frequency equals + + align:start position:0% + + + + align:start position:0% + +c so the people have different habit yes + + align:start position:0% +c so the people have different habit yes + + + align:start position:0% +c so the people have different habit yes +this a speed of sound or speed of light + + align:start position:0% +this a speed of sound or speed of light + + + align:start position:0% +this a speed of sound or speed of light +huh speed of sound or speed of light + + align:start position:0% +huh speed of sound or speed of light + + + align:start position:0% +huh speed of sound or speed of light +this is a speed of + + align:start position:0% +this is a speed of + + + align:start position:0% +this is a speed of +sound oh I'm sorry I'm sorry speed of + + align:start position:0% +sound oh I'm sorry I'm sorry speed of + + + align:start position:0% +sound oh I'm sorry I'm sorry speed of +light yeah uh not speed of sound when + + align:start position:0% +light yeah uh not speed of sound when + + + align:start position:0% +light yeah uh not speed of sound when +they do this kind of expression they + + align:start position:0% +they do this kind of expression they + + + align:start position:0% +they do this kind of expression they +always go to speed of like + + align:start position:0% +always go to speed of like + + + align:start position:0% +always go to speed of like +black speed of sound is different for + + align:start position:0% +black speed of sound is different for + + + align:start position:0% +black speed of sound is different for +different + + align:start position:0% +different + + + align:start position:0% +different +materials okay so uh uh What uh you + + align:start position:0% +materials okay so uh uh What uh you + + + align:start position:0% +materials okay so uh uh What uh you +asking what are the W Vector l so uh + + align:start position:0% +asking what are the W Vector l so uh + + + align:start position:0% +asking what are the W Vector l so uh +this is where right the L of waves when + + align:start position:0% +this is where right the L of waves when + + + align:start position:0% +this is where right the L of waves when +I go from here to here what this is + + align:start position:0% +I go from here to here what this is + + + align:start position:0% +I go from here to here what this is +called from pi/ a minus Pi a to plus pi + + align:start position:0% +called from pi/ a minus Pi a to plus pi + + + align:start position:0% +called from pi/ a minus Pi a to plus pi +that's called the + + align:start position:0% +that's called the + + + align:start position:0% +that's called the +first and the number of V vectors k + + align:start position:0% +first and the number of V vectors k + + + align:start position:0% +first and the number of V vectors k +equals the L of atoms you + + align:start position:0% +equals the L of atoms you + + + align:start position:0% +equals the L of atoms you +have okay so so this points so from here + + align:start position:0% +have okay so so this points so from here + + + align:start position:0% +have okay so so this points so from here +to here the L is + + align:start position:0% + + + + align:start position:0% + +it that's actually important when I + + align:start position:0% +it that's actually important when I + + + align:start position:0% +it that's actually important when I +later this is all this L is all + + align:start position:0% +later this is all this L is all + + + align:start position:0% +later this is all this L is all +important when you do counting once you + + align:start position:0% +important when you do counting once you + + + align:start position:0% +important when you do counting once you +go to microscopic picture you do + + align:start position:0% +go to microscopic picture you do + + + align:start position:0% +go to microscopic picture you do +um in in Silicon U dispersion relation + + align:start position:0% +um in in Silicon U dispersion relation + + + align:start position:0% +um in in Silicon U dispersion relation +we we have a mode that um seemingly + + align:start position:0% +we we have a mode that um seemingly + + + align:start position:0% +we we have a mode that um seemingly +correspond to the optical mode + + align:start position:0% +correspond to the optical mode + + + align:start position:0% +correspond to the optical mode +inite then what will be the mode will + + align:start position:0% +inite then what will be the mode will + + + align:start position:0% +inite then what will be the mode will +look like for the Silicon at the top oh + + align:start position:0% +look like for the Silicon at the top oh + + + align:start position:0% +look like for the Silicon at the top oh +me Optical modes uh Well turns out + + align:start position:0% +me Optical modes uh Well turns out + + + align:start position:0% +me Optical modes uh Well turns out +silicon those a uh it's a one ni Point + + align:start position:0% +silicon those a uh it's a one ni Point + + + align:start position:0% +silicon those a uh it's a one ni Point +how many + + align:start position:0% +how many + + + align:start position:0% +how many +atoms okay and + + align:start position:0% +atoms okay and + + + align:start position:0% +atoms okay and +silicon is in one lat point you have two + + align:start position:0% +silicon is in one lat point you have two + + + align:start position:0% +silicon is in one lat point you have two +atoms so there is another atom say that + + align:start position:0% +atoms so there is another atom say that + + + align:start position:0% +atoms so there is another atom say that +one quarter one quarter one quarter if + + align:start position:0% +one quarter one quarter one quarter if + + + align:start position:0% +one quarter one quarter one quarter if +you think this is one right there's + + align:start position:0% +you think this is one right there's + + + align:start position:0% +you think this is one right there's +another this is a l this is a point lce + + align:start position:0% +another this is a l this is a point lce + + + align:start position:0% +another this is a l this is a point lce +point so there's another atom at the one + + align:start position:0% +point so there's another atom at the one + + + align:start position:0% +point so there's another atom at the one +quarter one quarter one quter it's not + + align:start position:0% +quarter one quarter one quter it's not + + + align:start position:0% +quarter one quarter one quter it's not +it's FCC but there's two two atoms if + + align:start position:0% +it's FCC but there's two two atoms if + + + align:start position:0% +it's FCC but there's two two atoms if +there are two atoms then say uh in the + + align:start position:0% +there are two atoms then say uh in the + + + align:start position:0% +there are two atoms then say uh in the +latest point if there are two atoms then + + align:start position:0% +latest point if there are two atoms then + + + align:start position:0% +latest point if there are two atoms then +there are three acoustic + + align:start position:0% +there are three acoustic + + + align:start position:0% +there are three acoustic +Branch three acoustic branch and then + + align:start position:0% +Branch three acoustic branch and then + + + align:start position:0% +Branch three acoustic branch and then +there are another n so two atoms right n + + align:start position:0% +there are another n so two atoms right n + + + align:start position:0% +there are another n so two atoms right n +minus one so time three so there there + + align:start position:0% +minus one so time three so there there + + + align:start position:0% +minus one so time three so there there +three op Branch if you have three atoms + + align:start position:0% +three op Branch if you have three atoms + + + align:start position:0% +three op Branch if you have three atoms +you have three acoustic Point Branch you + + align:start position:0% +you have three acoustic Point Branch you + + + align:start position:0% +you have three acoustic Point Branch you +have six opio Branch right so the total + + align:start position:0% +have six opio Branch right so the total + + + align:start position:0% +have six opio Branch right so the total +is three + + align:start position:0% +is three + + + align:start position:0% +is three +time n that's n is at every Point how + + align:start position:0% +time n that's n is at every Point how + + + align:start position:0% +time n that's n is at every Point how +many ATS you + + align:start position:0% +many ATS you + + + align:start position:0% +many ATS you +have what's what's the direction of the + + align:start position:0% +have what's what's the direction of the + + + align:start position:0% +have what's what's the direction of the +two + + align:start position:0% +two + + + align:start position:0% +two +transpar roughly roughly is + + align:start position:0% +transpar roughly roughly is + + + align:start position:0% +transpar roughly roughly is +perpendicular but when you actually do + + align:start position:0% +perpendicular but when you actually do + + + align:start position:0% +perpendicular but when you actually do +it you have to solve the uh uh the The + + align:start position:0% +it you have to solve the uh uh the The + + + align:start position:0% +it you have to solve the uh uh the The +dyamic Matrix you have to solve The + + align:start position:0% +dyamic Matrix you have to solve The + + + align:start position:0% +dyamic Matrix you have to solve The +Matrix to find out the exact direction + + align:start position:0% +Matrix to find out the exact direction + + + align:start position:0% +Matrix to find out the exact direction +of the vibration the is vectors you can + + align:start position:0% +of the vibration the is vectors you can + + + align:start position:0% +of the vibration the is vectors you can +you can always decomposed right but + + align:start position:0% +you can always decomposed right but + + + align:start position:0% +you can always decomposed right but +there's a i Vector that we should do to + + align:start position:0% +there's a i Vector that we should do to + + + align:start position:0% +there's a i Vector that we should do to +solve the equation of motion you can + + align:start position:0% +solve the equation of motion you can + + + align:start position:0% +solve the equation of motion you can +solve Neal equation motion to get + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% +this + + + align:start position:0% +this +okay that's all about Crystal + + align:start position:0% +okay that's all about Crystal + + + align:start position:0% +okay that's all about Crystal +vibration and now let's say the + + align:start position:0% +vibration and now let's say the + + + align:start position:0% +vibration and now let's say the +electrons right I started with Crystal + + align:start position:0% +electrons right I started with Crystal + + + align:start position:0% +electrons right I started with Crystal +vibration by hydrogen + + align:start position:0% +vibration by hydrogen + + + align:start position:0% +vibration by hydrogen +molecule have the two two atoms and the + + align:start position:0% +molecule have the two two atoms and the + + + align:start position:0% +molecule have the two two atoms and the +separation Springs Mass + + align:start position:0% +separation Springs Mass + + + align:start position:0% +separation Springs Mass +Sprint and when I talk about electron + + align:start position:0% +Sprint and when I talk about electron + + + align:start position:0% +Sprint and when I talk about electron +let's also start with hydrogen let's + + align:start position:0% +let's also start with hydrogen let's + + + align:start position:0% +let's also start with hydrogen let's +this time I'm starting hydrogen + + align:start position:0% +this time I'm starting hydrogen + + + align:start position:0% +this time I'm starting hydrogen +atom right and hydrogen atom again you + + align:start position:0% +atom right and hydrogen atom again you + + + align:start position:0% +atom right and hydrogen atom again you +go common mechanics this is the energy + + align:start position:0% +go common mechanics this is the energy + + + align:start position:0% +go common mechanics this is the energy +levels of hydrogen at electrons in this + + align:start position:0% +levels of hydrogen at electrons in this + + + align:start position:0% +levels of hydrogen at electrons in this +case I'm + + align:start position:0% +case I'm + + + align:start position:0% +case I'm +talk and and uh uh the electron the + + align:start position:0% +talk and and uh uh the electron the + + + align:start position:0% +talk and and uh uh the electron the +energy + + align:start position:0% +energy + + + align:start position:0% +energy +level uh I didn't even write it + + align:start position:0% + + + + align:start position:0% + +down you can say I + + align:start position:0% + + + + align:start position:0% + +wrote so + + align:start position:0% +wrote so + + + align:start position:0% +wrote so +e of the + + align:start position:0% +e of the + + + align:start position:0% +e of the +electron is depends on the N isus 13 .6 + + align:start position:0% +electron is depends on the N isus 13 .6 + + + align:start position:0% +electron is depends on the N isus 13 .6 +electron volt + + align:start position:0% + + + + align:start position:0% + +n² + + align:start position:0% +n² + + + align:start position:0% +n² +okay so uh what is one so let me say one + + align:start position:0% +okay so uh what is one so let me say one + + + align:start position:0% +okay so uh what is one so let me say one +electron volt is when electron move in + + align:start position:0% +electron volt is when electron move in + + + align:start position:0% +electron volt is when electron move in +one charge electron in one one voltage + + align:start position:0% +one charge electron in one one voltage + + + align:start position:0% +one charge electron in one one voltage +electric field one voltage and that's + + align:start position:0% +electric field one voltage and that's + + + align:start position:0% +electric field one voltage and that's +the energy of the electron and this is + + align:start position:0% +the energy of the electron and this is + + + align:start position:0% +the energy of the electron and this is +equals 1.6 Theus 19 uh jar so that's the + + align:start position:0% +equals 1.6 Theus 19 uh jar so that's the + + + align:start position:0% +equals 1.6 Theus 19 uh jar so that's the +uh energy uh of the uh + + align:start position:0% +uh energy uh of the uh + + + align:start position:0% +uh energy uh of the uh +electrons in the uh hydrogen + + align:start position:0% +electrons in the uh hydrogen + + + align:start position:0% +electrons in the uh hydrogen +at and uh uh it's electrons moving in + + align:start position:0% +at and uh uh it's electrons moving in + + + align:start position:0% +at and uh uh it's electrons moving in +three + + align:start position:0% +three + + + align:start position:0% +three +dimension right and so when I solve the + + align:start position:0% +dimension right and so when I solve the + + + align:start position:0% +dimension right and so when I solve the +uh equation I'll find the wave function + + align:start position:0% +uh equation I'll find the wave function + + + align:start position:0% +uh equation I'll find the wave function +again uh this is going qu mechanics we + + align:start position:0% +again uh this is going qu mechanics we + + + align:start position:0% +again uh this is going qu mechanics we +not going do any Quantum I'm just + + align:start position:0% +not going do any Quantum I'm just + + + align:start position:0% +not going do any Quantum I'm just +introducing the uh basic + + align:start position:0% +introducing the uh basic + + + align:start position:0% +introducing the uh basic +concept and uh it turns out because we + + align:start position:0% +concept and uh it turns out because we + + + align:start position:0% +concept and uh it turns out because we +have three dimension Reta 5 in in three + + align:start position:0% +have three dimension Reta 5 in in three + + + align:start position:0% +have three dimension Reta 5 in in three +dimensional space so there is three + + align:start position:0% +dimensional space so there is three + + + align:start position:0% +dimensional space so there is three +quantum numbers n + + align:start position:0% +quantum numbers n + + + align:start position:0% +quantum numbers n +Ln okay those are all results of qu + + align:start position:0% +Ln okay those are all results of qu + + + align:start position:0% +Ln okay those are all results of qu +mechanics except that's in s you have to + + align:start position:0% +mechanics except that's in s you have to + + + align:start position:0% +mechanics except that's in s you have to +go the even relativistic F + + align:start position:0% +go the even relativistic F + + + align:start position:0% +go the even relativistic F +mechanics and this n you can see now all + + align:start position:0% +mechanics and this n you can see now all + + + align:start position:0% +mechanics and this n you can see now all +integers those are the the quantum + + align:start position:0% +integers those are the the quantum + + + align:start position:0% +integers those are the the quantum +number n is allow with 1 2 three all + + align:start position:0% +number n is allow with 1 2 three all + + + align:start position:0% +number n is allow with 1 2 three all +those integers L must be less than n n + + align:start position:0% +those integers L must be less than n n + + + align:start position:0% +those integers L must be less than n n +must be less than L those is all + + align:start position:0% +must be less than L those is all + + + align:start position:0% +must be less than L those is all +mathematics coming from + + align:start position:0% +mathematics coming from + + + align:start position:0% +mathematics coming from +mathematics but what it really mean is I + + align:start position:0% +mathematics but what it really mean is I + + + align:start position:0% +mathematics but what it really mean is I +wrote down the I forgot to write the + + align:start position:0% +wrote down the I forgot to write the + + + align:start position:0% +wrote down the I forgot to write the +energy energy is + + align:start position:0% +energy energy is + + + align:start position:0% +energy energy is +-3.6 electron was divide n² so energy + + align:start position:0% +-3.6 electron was divide n² so energy + + + align:start position:0% +-3.6 electron was divide n² so energy +doesn't depend on + + align:start position:0% +doesn't depend on + + + align:start position:0% +doesn't depend on +L and N depends only on + + align:start position:0% +L and N depends only on + + + align:start position:0% +L and N depends only on +N right so when Nal + + align:start position:0% +N right so when Nal + + + align:start position:0% +N right so when Nal +one I have uh uh L has you look at it l + + align:start position:0% +one I have uh uh L has you look at it l + + + align:start position:0% +one I have uh uh L has you look at it l +has to be zero M has to be + + align:start position:0% +has to be zero M has to be + + + align:start position:0% +has to be zero M has to be +zero and S could be plus and minus 12 so + + align:start position:0% +zero and S could be plus and minus 12 so + + + align:start position:0% +zero and S could be plus and minus 12 so +there are two qualum St so here I have + + align:start position:0% +there are two qualum St so here I have + + + align:start position:0% +there are two qualum St so here I have +two qualum states so you look at thetic + + align:start position:0% +two qualum states so you look at thetic + + + align:start position:0% +two qualum states so you look at thetic +table that's why you have + + align:start position:0% +table that's why you have + + + align:start position:0% +table that's why you have +hydrogen helium + + align:start position:0% +hydrogen helium + + + align:start position:0% +hydrogen helium +fi state two field and the next quum + + align:start position:0% +fi state two field and the next quum + + + align:start position:0% +fi state two field and the next quum +level you go to n = 2 is pretty pretty + + align:start position:0% +level you go to n = 2 is pretty pretty + + + align:start position:0% +level you go to n = 2 is pretty pretty +far away from from first level right so + + align:start position:0% +far away from from first level right so + + + align:start position:0% +far away from from first level right so +you look at the table again you feel + + align:start position:0% +you look at the table again you feel + + + align:start position:0% +you look at the table again you feel +this is a one Quantum + + align:start position:0% +this is a one Quantum + + + align:start position:0% +this is a one Quantum +State one Quantum State can only have + + align:start position:0% +State one Quantum State can only have + + + align:start position:0% +State one Quantum State can only have +one electron + + align:start position:0% +one electron + + + align:start position:0% +one electron +much right that's when I count spin as a + + align:start position:0% +much right that's when I count spin as a + + + align:start position:0% +much right that's when I count spin as a +different state + + align:start position:0% +different state + + + align:start position:0% +different state +so uh uh + + align:start position:0% +so uh uh + + + align:start position:0% +so uh uh +hydrogen lithium + + align:start position:0% +hydrogen lithium + + + align:start position:0% +hydrogen lithium +lithium okay this still one say 2 s now + + align:start position:0% +lithium okay this still one say 2 s now + + + align:start position:0% +lithium okay this still one say 2 s now +so you go to continue look at the + + align:start position:0% +so you go to continue look at the + + + align:start position:0% +so you go to continue look at the +periodical table you fill in here uh the + + align:start position:0% +periodical table you fill in here uh the + + + align:start position:0% +periodical table you fill in here uh the +each energy level is 2 N uh say uh uh + + align:start position:0% +each energy level is 2 N uh say uh uh + + + align:start position:0% +each energy level is 2 N uh say uh uh +once you go toal two the number toal + + align:start position:0% +once you go toal two the number toal + + + align:start position:0% +once you go toal two the number toal +number of electron you can have up to F + + align:start position:0% +number of electron you can have up to F + + + align:start position:0% +number of electron you can have up to F +the all the orbital the con state is2 is + + align:start position:0% +the all the orbital the con state is2 is + + + align:start position:0% +the all the orbital the con state is2 is +what + + align:start position:0% +what + + + align:start position:0% +what +um uh eight + + align:start position:0% + + + + align:start position:0% + +right okay so that's the uh hydrogen + + align:start position:0% +right okay so that's the uh hydrogen + + + align:start position:0% +right okay so that's the uh hydrogen +atom and this is this is a basic model + + align:start position:0% +atom and this is this is a basic model + + + align:start position:0% +atom and this is this is a basic model +for the periodic table you look at the + + align:start position:0% +for the periodic table you look at the + + + align:start position:0% +for the periodic table you look at the +periodic table you can use this uh and + + align:start position:0% +periodic table you can use this uh and + + + align:start position:0% +periodic table you can use this uh and +pretty much interpret lot of those + + align:start position:0% +pretty much interpret lot of those + + + align:start position:0% +pretty much interpret lot of those + + align:start position:0% + + + align:start position:0% +atom + + align:start position:0% +atom + + + align:start position:0% +atom +now I'm going to again since stting from + + align:start position:0% +now I'm going to again since stting from + + + align:start position:0% +now I'm going to again since stting from +here I'm going into Atomic chain because + + align:start position:0% +here I'm going into Atomic chain because + + + align:start position:0% +here I'm going into Atomic chain because +I want to understand electrons in + + align:start position:0% +I want to understand electrons in + + + align:start position:0% +I want to understand electrons in +solid + + align:start position:0% +solid + + + align:start position:0% +solid +right so aom CH uh thinking + + align:start position:0% +right so aom CH uh thinking + + + align:start position:0% +right so aom CH uh thinking +about hydrogen as a as a simple example + + align:start position:0% +about hydrogen as a as a simple example + + + align:start position:0% +about hydrogen as a as a simple example +but the hydrogen of course + + align:start position:0% +but the hydrogen of course + + + align:start position:0% +but the hydrogen of course +the gas I'm thinking about solid and so + + align:start position:0% +the gas I'm thinking about solid and so + + + align:start position:0% +the gas I'm thinking about solid and so +uh electrons they are waves in quantum + + align:start position:0% +uh electrons they are waves in quantum + + + align:start position:0% +uh electrons they are waves in quantum +mechanics it's both waves and Par + + align:start position:0% +mechanics it's both waves and Par + + + align:start position:0% +mechanics it's both waves and Par +characteristics right so waves each + + align:start position:0% +characteristics right so waves each + + + align:start position:0% +characteristics right so waves each +electron has those wave function I pled + + align:start position:0% +electron has those wave function I pled + + + align:start position:0% +electron has those wave function I pled +before this is the this is the wave + + align:start position:0% +before this is the this is the wave + + + align:start position:0% +before this is the this is the wave +function like all the mechanics will + + align:start position:0% +function like all the mechanics will + + + align:start position:0% +function like all the mechanics will +give you this + + align:start position:0% +give you this + + + align:start position:0% +give you this +function + + align:start position:0% +function + + + align:start position:0% +function +and now the are WS + + align:start position:0% +and now the are WS + + + align:start position:0% +and now the are WS +so let's plal one + + align:start position:0% +so let's plal one + + + align:start position:0% +so let's plal one +approximately and they spread out not + + align:start position:0% +approximately and they spread out not + + + align:start position:0% +approximately and they spread out not +just confine to one electron and now + + align:start position:0% +just confine to one electron and now + + + align:start position:0% +just confine to one electron and now +this is the next atom + + align:start position:0% +this is the next atom + + + align:start position:0% +this is the next atom +and they start to overlap with each + + align:start position:0% +and they start to overlap with each + + + align:start position:0% +and they start to overlap with each +other right what + + align:start position:0% +other right what + + + align:start position:0% +other right what +happens and these two electrons from the + + align:start position:0% +happens and these two electrons from the + + + align:start position:0% +happens and these two electrons from the +two atom want to have the same States + + align:start position:0% +two atom want to have the same States + + + align:start position:0% +two atom want to have the same States +because once they start overlap with + + align:start position:0% +because once they start overlap with + + + align:start position:0% +because once they start overlap with +once they start overlapping the state of + + align:start position:0% +once they start overlapping the state of + + + align:start position:0% +once they start overlapping the state of +the two atoms are the identical + + align:start position:0% +the two atoms are the identical + + + align:start position:0% +the two atoms are the identical +States and the basic quantum mechanics + + align:start position:0% +States and the basic quantum mechanics + + + align:start position:0% +States and the basic quantum mechanics +doesn't allow + + align:start position:0% +doesn't allow + + + align:start position:0% +doesn't allow +it okay so the state was start + + align:start position:0% +it okay so the state was start + + + align:start position:0% +it okay so the state was start +to uh adjust a little + + align:start position:0% +to uh adjust a little + + + align:start position:0% +to uh adjust a little +bit + + align:start position:0% +bit + + + align:start position:0% +bit +and form that so now n = + + align:start position:0% +and form that so now n = + + + align:start position:0% +and form that so now n = +1 this is original n 2 three four I + + align:start position:0% +1 this is original n 2 three four I + + + align:start position:0% +1 this is original n 2 three four I +think now they start to forming bands so + + align:start position:0% +think now they start to forming bands so + + + align:start position:0% +think now they start to forming bands so +those there are if you have n atoms + + align:start position:0% +those there are if you have n atoms + + + align:start position:0% +those there are if you have n atoms +again in the chair from between here and + + align:start position:0% +again in the chair from between here and + + + align:start position:0% +again in the chair from between here and +here I have n point and each point now + + align:start position:0% +here I have n point and each point now + + + align:start position:0% +here I have n point and each point now +they start to to uh you can see here + + align:start position:0% +they start to to uh you can see here + + + align:start position:0% +they start to to uh you can see here +side different and those same allowable + + align:start position:0% +side different and those same allowable + + + align:start position:0% +side different and those same allowable +wave Vector now electron is a wave + + align:start position:0% +wave Vector now electron is a wave + + + align:start position:0% +wave Vector now electron is a wave +extended through the whole l + + align:start position:0% +extended through the whole l + + + align:start position:0% +extended through the whole l +a simple this is a one qu mechanical + + align:start position:0% +a simple this is a one qu mechanical + + + align:start position:0% +a simple this is a one qu mechanical +state so the waves can have different we + + align:start position:0% +state so the waves can have different we + + + align:start position:0% +state so the waves can have different we +vectors different P same as we + + align:start position:0% +vectors different P same as we + + + align:start position:0% +vectors different P same as we +argu for uh the + + align:start position:0% +argu for uh the + + + align:start position:0% +argu for uh the +L + + align:start position:0% +L + + + align:start position:0% +L +right so that's a basic Quant mechanics + + align:start position:0% +right so that's a basic Quant mechanics + + + align:start position:0% +right so that's a basic Quant mechanics +dictate the energy has to split a little + + align:start position:0% +dictate the energy has to split a little + + + align:start position:0% +dictate the energy has to split a little +bit forming now a + + align:start position:0% +bit forming now a + + + align:start position:0% +bit forming now a +band course I continue + + align:start position:0% +band course I continue + + + align:start position:0% +band course I continue +we pl continuous because that K there + + align:start position:0% +we pl continuous because that K there + + + align:start position:0% +we pl continuous because that K there +are many ke points but there still + + align:start position:0% +are many ke points but there still + + + align:start position:0% +are many ke points but there still +between here to here they are end + + align:start position:0% +between here to here they are end + + + align:start position:0% +between here to here they are end +point and the end is your L of AD in + + align:start position:0% +point and the end is your L of AD in + + + align:start position:0% +point and the end is your L of AD in +ch okay this is a uh very + + align:start position:0% +ch okay this is a uh very + + + align:start position:0% +ch okay this is a uh very +interesting because even this simple + + align:start position:0% +interesting because even this simple + + + align:start position:0% +interesting because even this simple +picture I said the hydrogen picture + + align:start position:0% +picture I said the hydrogen picture + + + align:start position:0% +picture I said the hydrogen picture +tells you the periodic table what this + + align:start position:0% +tells you the periodic table what this + + + align:start position:0% +tells you the periodic table what this +picture tells you whether you have + + align:start position:0% +picture tells you whether you have + + + align:start position:0% +picture tells you whether you have +insulator or + + align:start position:0% +insulator or + + + align:start position:0% +insulator or +conductor let's think + + align:start position:0% +conductor let's think + + + align:start position:0% +conductor let's think +about if again if I take + + align:start position:0% +about if again if I take + + + align:start position:0% +about if again if I take +hydrogen as a support + + align:start position:0% +hydrogen as a support + + + align:start position:0% +hydrogen as a support +extreme each hydrogen has one + + align:start position:0% +extreme each hydrogen has one + + + align:start position:0% +extreme each hydrogen has one +electron right so when the electron fail + + align:start position:0% +electron right so when the electron fail + + + align:start position:0% +electron right so when the electron fail +go to the + + align:start position:0% +go to the + + + align:start position:0% +go to the +energy they lowest the energy level + + align:start position:0% +energy they lowest the energy level + + + align:start position:0% +energy they lowest the energy level +fails first they're + + align:start position:0% +fails first they're + + + align:start position:0% +fails first they're +lazying okay now that's the first the + + align:start position:0% +lazying okay now that's the first the + + + align:start position:0% +lazying okay now that's the first the +thermodynamics tells + + align:start position:0% +thermodynamics tells + + + align:start position:0% +thermodynamics tells +you right everybody wants to go to + + align:start position:0% +you right everybody wants to go to + + + align:start position:0% +you right everybody wants to go to +minimum energy + + align:start position:0% +minimum energy + + + align:start position:0% +minimum energy +state so the if I have n + + align:start position:0% +state so the if I have n + + + align:start position:0% +state so the if I have n +atoms I have between here and here N + + align:start position:0% +atoms I have between here and here N + + + align:start position:0% +atoms I have between here and here N +Point each + + align:start position:0% +Point each + + + align:start position:0% +Point each +point as a spin I didn't the spin is not + + align:start position:0% +point as a spin I didn't the spin is not + + + align:start position:0% +point as a spin I didn't the spin is not +reflected in this + + align:start position:0% +reflected in this + + + align:start position:0% +reflected in this +curve + + align:start position:0% +curve + + + align:start position:0% +curve +okay so each point has two states two + + align:start position:0% +okay so each point has two states two + + + align:start position:0% +okay so each point has two states two +spin S = Plus half so now I start to + + align:start position:0% +spin S = Plus half so now I start to + + + align:start position:0% +spin S = Plus half so now I start to +feel the bottom electron if I have + + align:start position:0% +feel the bottom electron if I have + + + align:start position:0% +feel the bottom electron if I have +hydrogen I feel there are really two n + + align:start position:0% +hydrogen I feel there are really two n + + + align:start position:0% +hydrogen I feel there are really two n +Quantum States I have only n electron + + align:start position:0% +Quantum States I have only n electron + + + align:start position:0% +Quantum States I have only n electron +where it + + align:start position:0% +where it + + + align:start position:0% +where it +goes feels about half + + align:start position:0% +goes feels about half + + + align:start position:0% +goes feels about half +right so the electron maximum number I + + align:start position:0% +right so the electron maximum number I + + + align:start position:0% +right so the electron maximum number I +say energy will be the this will be + + align:start position:0% +say energy will be the this will be + + + align:start position:0% +say energy will be the this will be +where somewhere in between the + + align:start position:0% +where somewhere in between the + + + align:start position:0% +where somewhere in between the +B okay + + align:start position:0% +B okay + + + align:start position:0% +B okay +so this is where depends on hydrogen I + + align:start position:0% +so this is where depends on hydrogen I + + + align:start position:0% +so this is where depends on hydrogen I +set a f here depends on how many + + align:start position:0% +set a f here depends on how many + + + align:start position:0% +set a f here depends on how many +electron you can feel to we in the + + align:start position:0% +electron you can feel to we in the + + + align:start position:0% +electron you can feel to we in the +B and if it's either zero + + align:start position:0% +B and if it's either zero + + + align:start position:0% +B and if it's either zero +temperature 0 + + align:start position:0% +temperature 0 + + + align:start position:0% +temperature 0 +Kelvin this point where the top most + + align:start position:0% +Kelvin this point where the top most + + + align:start position:0% +Kelvin this point where the top most +just think about the water bucket right + + align:start position:0% +just think about the water bucket right + + + align:start position:0% +just think about the water bucket right +the comos Sur uh energy level is called + + align:start position:0% +the comos Sur uh energy level is called + + + align:start position:0% +the comos Sur uh energy level is called +the + + align:start position:0% + + + + align:start position:0% + +th + + align:start position:0% +th + + + align:start position:0% +th +and so if it's a nonzero + + align:start position:0% +and so if it's a nonzero + + + align:start position:0% +and so if it's a nonzero +temperature those electron cannot move + + align:start position:0% +temperature those electron cannot move + + + align:start position:0% +temperature those electron cannot move +it Le a lot of energy to move right + + align:start position:0% +it Le a lot of energy to move right + + + align:start position:0% +it Le a lot of energy to move right +because there's no quum States in this + + align:start position:0% +because there's no quum States in this + + + align:start position:0% +because there's no quum States in this +here mechan no State allow this energy + + align:start position:0% +here mechan no State allow this energy + + + align:start position:0% +here mechan no State allow this energy +to move to when they move they change + + align:start position:0% +to move to when they move they change + + + align:start position:0% +to move to when they move they change +State the state has to be AJ allowable + + align:start position:0% +State the state has to be AJ allowable + + + align:start position:0% +State the state has to be AJ allowable +in the solid so only electron in this + + align:start position:0% +in the solid so only electron in this + + + align:start position:0% +in the solid so only electron in this +reg are + + align:start position:0% + + + + align:start position:0% + +movable and in metal because the Le + + align:start position:0% +movable and in metal because the Le + + + align:start position:0% +movable and in metal because the Le +State just close to this point is very + + align:start position:0% +State just close to this point is very + + + align:start position:0% +State just close to this point is very +close the energy difference is very + + align:start position:0% +close the energy difference is very + + + align:start position:0% +close the energy difference is very +close right so the thermal energy is + + align:start position:0% +close right so the thermal energy is + + + align:start position:0% +close right so the thermal energy is +large enough to allow them to go to the + + align:start position:0% +large enough to allow them to go to the + + + align:start position:0% +large enough to allow them to go to the +next + + align:start position:0% +next + + + align:start position:0% +next +state so only when your electron fail to + + align:start position:0% +state so only when your electron fail to + + + align:start position:0% +state so only when your electron fail to +level their empty St in the in the band + + align:start position:0% +level their empty St in the in the band + + + align:start position:0% +level their empty St in the in the band +it's a condu it's a it's me that's + + align:start position:0% +it's a condu it's a it's me that's + + + align:start position:0% +it's a condu it's a it's me that's +matter + + align:start position:0% +matter + + + align:start position:0% +matter +okay and what + + align:start position:0% +okay and what + + + align:start position:0% +okay and what +happens if my L of electron field to + + align:start position:0% + + + + align:start position:0% + +here then it needs a lot of energy right + + align:start position:0% +here then it needs a lot of energy right + + + align:start position:0% +here then it needs a lot of energy right +depends on the difference of the energy + + align:start position:0% +depends on the difference of the energy + + + align:start position:0% +depends on the difference of the energy +here and + + align:start position:0% +here and + + + align:start position:0% +here and +here if this difference is very + + align:start position:0% +here if this difference is very + + + align:start position:0% +here if this difference is very +large you got a insulator electron + + align:start position:0% +large you got a insulator electron + + + align:start position:0% +large you got a insulator electron +cannot + + align:start position:0% +cannot + + + align:start position:0% +cannot +move + + align:start position:0% +move + + + align:start position:0% +move +so + + align:start position:0% +so + + + align:start position:0% +so +this from the uh the + + align:start position:0% +this from the uh the + + + align:start position:0% +this from the uh the +topmost of the electron to the Le + + align:start position:0% +topmost of the electron to the Le + + + align:start position:0% +topmost of the electron to the Le +F St that's the + + align:start position:0% + + + + align:start position:0% + +bank okay and this Bank Gap is very + + align:start position:0% +bank okay and this Bank Gap is very + + + align:start position:0% +bank okay and this Bank Gap is very +large that's an insulator how large is + + align:start position:0% +large that's an insulator how large is + + + align:start position:0% +large that's an insulator how large is +large few electron volts + + align:start position:0% +large few electron volts + + + align:start position:0% +large few electron volts +and this is because a room + + align:start position:0% +and this is because a room + + + align:start position:0% +and this is because a room +temperature the we said that at the + + align:start position:0% +temperature the we said that at the + + + align:start position:0% +temperature the we said that at the +first class the energy is about KBT K is + + align:start position:0% +first class the energy is about KBT K is + + + align:start position:0% +first class the energy is about KBT K is +a b constant times temperature thermal + + align:start position:0% +a b constant times temperature thermal + + + align:start position:0% +a b constant times temperature thermal +energy and that's about 26 M electron + + align:start position:0% +energy and that's about 26 M electron + + + align:start position:0% +energy and that's about 26 M electron +volts + + align:start position:0% +volts + + + align:start position:0% +volts +right and uh so if this one is a few + + align:start position:0% +right and uh so if this one is a few + + + align:start position:0% +right and uh so if this one is a few +electron volts much larger than + + align:start position:0% +electron volts much larger than + + + align:start position:0% +electron volts much larger than +KBT so very very few chance the electron + + align:start position:0% +KBT so very very few chance the electron + + + align:start position:0% +KBT so very very few chance the electron +can come over here due to + + align:start position:0% +can come over here due to + + + align:start position:0% +can come over here due to +ser and it's + + align:start position:0% +ser and it's + + + align:start position:0% +ser and it's +insulated but if this Gap is not large + + align:start position:0% +insulated but if this Gap is not large + + + align:start position:0% +insulated but if this Gap is not large +glass for example is + + align:start position:0% +glass for example is + + + align:start position:0% +glass for example is +insulated right and the Gap is a few of + + align:start position:0% +insulated right and the Gap is a few of + + + align:start position:0% +insulated right and the Gap is a few of +about four to five electron + + align:start position:0% +about four to five electron + + + align:start position:0% +about four to five electron +Vols now + + align:start position:0% +Vols now + + + align:start position:0% +Vols now +silicon that Gap is about 1.12 electron + + align:start position:0% +silicon that Gap is about 1.12 electron + + + align:start position:0% +silicon that Gap is about 1.12 electron +Vol by room + + align:start position:0% +Vol by room + + + align:start position:0% +Vol by room +temperature so silicon become a + + align:start position:0% +temperature so silicon become a + + + align:start position:0% +temperature so silicon become a +semiconductor because this Gap is not + + align:start position:0% +semiconductor because this Gap is not + + + align:start position:0% +semiconductor because this Gap is not +very + + align:start position:0% +very + + + align:start position:0% +very +large and if you cool silicon to zero K + + align:start position:0% +large and if you cool silicon to zero K + + + align:start position:0% +large and if you cool silicon to zero K +it should be + + align:start position:0% + + + + align:start position:0% + +insulator because there's not enough + + align:start position:0% +insulator because there's not enough + + + align:start position:0% +insulator because there's not enough +thermal energy to kick the electron from + + align:start position:0% +thermal energy to kick the electron from + + + align:start position:0% +thermal energy to kick the electron from +here to here but at room + + align:start position:0% +here to here but at room + + + align:start position:0% +here to here but at room +temperature the thermal energy + + align:start position:0% +temperature the thermal energy + + + align:start position:0% +temperature the thermal energy +KBT because of the thermal energy some + + align:start position:0% +KBT because of the thermal energy some + + + align:start position:0% +KBT because of the thermal energy some +electron kicked from + + align:start position:0% +electron kicked from + + + align:start position:0% +electron kicked from +here to here and if they are kick from + + align:start position:0% +here to here and if they are kick from + + + align:start position:0% +here to here and if they are kick from +here to here what's left behind are some + + align:start position:0% +here to here what's left behind are some + + + align:start position:0% +here to here what's left behind are some +empty States right now those electrons + + align:start position:0% +empty States right now those electrons + + + align:start position:0% +empty States right now those electrons +those other electron feel happy know + + align:start position:0% +those other electron feel happy know + + + align:start position:0% +those other electron feel happy know +there are some states they can + + align:start position:0% +there are some states they can + + + align:start position:0% +there are some states they can +move and this other electrons that + + align:start position:0% +move and this other electrons that + + + align:start position:0% +move and this other electrons that +picked up is also happy because there + + align:start position:0% +picked up is also happy because there + + + align:start position:0% +picked up is also happy because there +are also empty States they can + + align:start position:0% +are also empty States they can + + + align:start position:0% +are also empty States they can +move right so the motion of those + + align:start position:0% +move right so the motion of those + + + align:start position:0% +move right so the motion of those +electron those + + align:start position:0% +electron those + + + align:start position:0% +electron those +electrons it's much easier so you can + + align:start position:0% +electrons it's much easier so you can + + + align:start position:0% +electrons it's much easier so you can +think this the real the thing that's + + align:start position:0% +think this the real the thing that's + + + align:start position:0% +think this the real the thing that's +really MO is the electron moving because + + align:start position:0% +really MO is the electron moving because + + + align:start position:0% +really MO is the electron moving because +they are empty States but it's much + + align:start position:0% +they are empty States but it's much + + + align:start position:0% +they are empty States but it's much +easier to + + align:start position:0% +easier to + + + align:start position:0% +easier to +think then as a positive charge so don't + + align:start position:0% +think then as a positive charge so don't + + + align:start position:0% +think then as a positive charge so don't +think those as electron just think those + + align:start position:0% +think those as electron just think those + + + align:start position:0% +think those as electron just think those +empty things as holes there's no + + align:start position:0% +empty things as holes there's no + + + align:start position:0% +empty things as holes there's no +hole okay no positive + + align:start position:0% +hole okay no positive + + + align:start position:0% +hole okay no positive +charge it's electron that's + + align:start position:0% +charge it's electron that's + + + align:start position:0% +charge it's electron that's +M but but we just say this as whole + + align:start position:0% +M but but we just say this as whole + + + align:start position:0% +M but but we just say this as whole +positive charge and those + + align:start position:0% +positive charge and those + + + align:start position:0% +positive charge and those +electrons and you can even put a so + + align:start position:0% +electrons and you can even put a so + + + align:start position:0% +electrons and you can even put a so +that's intrinsic silicon I said right + + align:start position:0% +that's intrinsic silicon I said right + + + align:start position:0% +that's intrinsic silicon I said right +but you put even put the + + align:start position:0% +but you put even put the + + + align:start position:0% +but you put even put the +impurities into silicon into + + align:start position:0% +impurities into silicon into + + + align:start position:0% +impurities into silicon into +semiconductors to add more electron or + + align:start position:0% +semiconductors to add more electron or + + + align:start position:0% +semiconductors to add more electron or +add more holes so when I add for example + + align:start position:0% +add more holes so when I add for example + + + align:start position:0% +add more holes so when I add for example +if I put the phosphor in + + align:start position:0% +if I put the phosphor in + + + align:start position:0% +if I put the phosphor in +silicon phosphor has five charge silicon + + align:start position:0% +silicon phosphor has five charge silicon + + + align:start position:0% +silicon phosphor has five charge silicon +four in the outer Shield so there's one + + align:start position:0% +four in the outer Shield so there's one + + + align:start position:0% +four in the outer Shield so there's one +extra compared silicon so that extra + + align:start position:0% +extra compared silicon so that extra + + + align:start position:0% +extra compared silicon so that extra +because it's very close the energy level + + align:start position:0% +because it's very close the energy level + + + align:start position:0% +because it's very close the energy level +of fos very close to the here so that + + align:start position:0% +of fos very close to the here so that + + + align:start position:0% +of fos very close to the here so that +electron can easily be excited to this + + align:start position:0% +electron can easily be excited to this + + + align:start position:0% +electron can easily be excited to this +region so it's a n type + + align:start position:0% + + + + align:start position:0% + +semiconductor and on the other hand if I + + align:start position:0% +semiconductor and on the other hand if I + + + align:start position:0% +semiconductor and on the other hand if I +put the + + align:start position:0% +put the + + + align:start position:0% +put the +Boron into + + align:start position:0% +Boron into + + + align:start position:0% +Boron into +cicon the outer has + + align:start position:0% +cicon the outer has + + + align:start position:0% +cicon the outer has +three right so the foron energy level is + + align:start position:0% +three right so the foron energy level is + + + align:start position:0% +three right so the foron energy level is +somewhere + + align:start position:0% +somewhere + + + align:start position:0% +somewhere +here close to the bottom of this B here + + align:start position:0% +here close to the bottom of this B here + + + align:start position:0% +here close to the bottom of this B here +this is a valence band this conduction + + align:start position:0% +this is a valence band this conduction + + + align:start position:0% +this is a valence band this conduction +band so the energy level is here those + + align:start position:0% +band so the energy level is here those + + + align:start position:0% +band so the energy level is here those +electrons are much happier to go here so + + align:start position:0% +electrons are much happier to go here so + + + align:start position:0% +electrons are much happier to go here so +left behind + + align:start position:0% +left behind + + + align:start position:0% +left behind +hles so Boron become acceptor trap that + + align:start position:0% +hles so Boron become acceptor trap that + + + align:start position:0% +hles so Boron become acceptor trap that +electron and they uh they uh they create + + align:start position:0% +electron and they uh they uh they create + + + align:start position:0% +electron and they uh they uh they create +the holes in those BS and this B that + + align:start position:0% +the holes in those BS and this B that + + + align:start position:0% +the holes in those BS and this B that +happy to know so that's how you do + + align:start position:0% +happy to know so that's how you do + + + align:start position:0% +happy to know so that's how you do +doping in semiconductor you add you + + align:start position:0% +doping in semiconductor you add you + + + align:start position:0% +doping in semiconductor you add you +create the energy State sometimes even + + align:start position:0% +create the energy State sometimes even + + + align:start position:0% +create the energy State sometimes even +impur even vacany could create those + + align:start position:0% +impur even vacany could create those + + + align:start position:0% +impur even vacany could create those +additional States depends on in cicon we + + align:start position:0% +additional States depends on in cicon we + + + align:start position:0% +additional States depends on in cicon we +do artificial doping when we ther + + align:start position:0% +do artificial doping when we ther + + + align:start position:0% +do artificial doping when we ther +electric materials we can State missing + + align:start position:0% +electric materials we can State missing + + + align:start position:0% +electric materials we can State missing +atom to create this kind of situation so + + align:start position:0% +atom to create this kind of situation so + + + align:start position:0% +atom to create this kind of situation so +the doping in material in thermics do is + + align:start position:0% +the doping in material in thermics do is + + + align:start position:0% +the doping in material in thermics do is +very important of course this is a tool + + align:start position:0% +very important of course this is a tool + + + align:start position:0% +very important of course this is a tool +for all + + align:start position:0% +for all + + + align:start position:0% +for all +device okay any questions + + align:start position:0% + + + + align:start position:0% + +here now let's move + + align:start position:0% +here now let's move + + + align:start position:0% +here now let's move +on look at the real here now right see + + align:start position:0% +on look at the real here now right see + + + align:start position:0% +on look at the real here now right see +that's a one dimensional picture and I + + align:start position:0% +that's a one dimensional picture and I + + + align:start position:0% +that's a one dimensional picture and I +Noti again three dimension go to the uh + + align:start position:0% +Noti again three dimension go to the uh + + + align:start position:0% +Noti again three dimension go to the uh +virtual reciprocal + + align:start position:0% +virtual reciprocal + + + align:start position:0% +virtual reciprocal +space and 111 is the gamma to L Point + + align:start position:0% +space and 111 is the gamma to L Point + + + align:start position:0% +space and 111 is the gamma to L Point +direction 111 I only draw a half of it + + align:start position:0% +direction 111 I only draw a half of it + + + align:start position:0% +direction 111 I only draw a half of it +because it's + + align:start position:0% +because it's + + + align:start position:0% +because it's +symmetric positive we Vector netive we + + align:start position:0% +symmetric positive we Vector netive we + + + align:start position:0% +symmetric positive we Vector netive we +Vector symmetric I draw half to save + + align:start position:0% +Vector symmetric I draw half to save + + + align:start position:0% +Vector symmetric I draw half to save +space okay so this is a to X One z z + + align:start position:0% +space okay so this is a to X One z z + + + align:start position:0% +space okay so this is a to X One z z +Direction and it turns out the cic the + + align:start position:0% +Direction and it turns out the cic the + + + align:start position:0% +Direction and it turns out the cic the +maximum point where this electron the F + + align:start position:0% +maximum point where this electron the F + + + align:start position:0% +maximum point where this electron the F +to as Valance + + align:start position:0% +to as Valance + + + align:start position:0% +to as Valance +band and the minimum Point that's the + + align:start position:0% +band and the minimum Point that's the + + + align:start position:0% +band and the minimum Point that's the +conduction band they do not agree in + + align:start position:0% +conduction band they do not agree in + + + align:start position:0% +conduction band they do not agree in +terms of the we Vector so this is the + + align:start position:0% +terms of the we Vector so this is the + + + align:start position:0% +terms of the we Vector so this is the +indirect sem + + align:start position:0% +indirect sem + + + align:start position:0% +indirect sem +conductor and on the other hand is a + + align:start position:0% +conductor and on the other hand is a + + + align:start position:0% +conductor and on the other hand is a +direct sign + + align:start position:0% +direct sign + + + align:start position:0% +direct sign +okay there's a big + + align:start position:0% +okay there's a big + + + align:start position:0% +okay there's a big +difference in these two materials direct + + align:start position:0% +difference in these two materials direct + + + align:start position:0% +difference in these two materials direct +indirect micro electronics Industry is + + align:start position:0% +indirect micro electronics Industry is + + + align:start position:0% +indirect micro electronics Industry is +established on + + align:start position:0% +established on + + + align:start position:0% +established on +Silicon but the lasers semic + + align:start position:0% +Silicon but the lasers semic + + + align:start position:0% +Silicon but the lasers semic +lasers you nobody can use cicon to make + + align:start position:0% +lasers you nobody can use cicon to make + + + align:start position:0% +lasers you nobody can use cicon to make +sem Las people are making progress It's + + align:start position:0% +sem Las people are making progress It's + + + align:start position:0% +sem Las people are making progress It's +much much more difficult to make a laser + + align:start position:0% +much much more difficult to make a laser + + + align:start position:0% +much much more difficult to make a laser +out of silicon it's a direct Gap + + align:start position:0% +out of silicon it's a direct Gap + + + align:start position:0% +out of silicon it's a direct Gap +semiconductor is much easier the reason + + align:start position:0% +semiconductor is much easier the reason + + + align:start position:0% +semiconductor is much easier the reason +is that in G device Micron device you + + align:start position:0% +is that in G device Micron device you + + + align:start position:0% +is that in G device Micron device you +inject the electron here you inject C + + align:start position:0% +inject the electron here you inject C + + + align:start position:0% +inject the electron here you inject C +that's by device design you put a c you + + align:start position:0% +that's by device design you put a c you + + + align:start position:0% +that's by device design you put a c you +actually inject into the material and + + align:start position:0% +actually inject into the material and + + + align:start position:0% +actually inject into the material and +then electron fall up to uh the bottom + + align:start position:0% +then electron fall up to uh the bottom + + + align:start position:0% +then electron fall up to uh the bottom +of the uh so from we combine from turn + + align:start position:0% +of the uh so from we combine from turn + + + align:start position:0% +of the uh so from we combine from turn +here and here give off a + + align:start position:0% +here and here give off a + + + align:start position:0% +here and here give off a +vol right it's much easier to do that in + + align:start position:0% +vol right it's much easier to do that in + + + align:start position:0% +vol right it's much easier to do that in +directly G because there's say no we VOR + + align:start position:0% +directly G because there's say no we VOR + + + align:start position:0% +directly G because there's say no we VOR +mismatch and here it's very difficult + + align:start position:0% +mismatch and here it's very difficult + + + align:start position:0% +mismatch and here it's very difficult +for electron Rec combine with the + + align:start position:0% +for electron Rec combine with the + + + align:start position:0% +for electron Rec combine with the +whole or you say that's good for solar + + align:start position:0% +whole or you say that's good for solar + + + align:start position:0% +whole or you say that's good for solar +cells right solar cell you don't want + + align:start position:0% +cells right solar cell you don't want + + + align:start position:0% +cells right solar cell you don't want +recombination uh really you you want to + + align:start position:0% +recombination uh really you you want to + + + align:start position:0% +recombination uh really you you want to +get the + + align:start position:0% +get the + + + align:start position:0% +get the +charge uh uh but there are there are + + align:start position:0% +charge uh uh but there are there are + + + align:start position:0% +charge uh uh but there are there are +various uh points the this one solar + + align:start position:0% +various uh points the this one solar + + + align:start position:0% +various uh points the this one solar +cell is not good it doesn't absorb well + + align:start position:0% +cell is not good it doesn't absorb well + + + align:start position:0% +cell is not good it doesn't absorb well +can't create where Photon comes in right + + align:start position:0% +can't create where Photon comes in right + + + align:start position:0% +can't create where Photon comes in right +a photon the wave Vector uh the wence is + + align:start position:0% +a photon the wave Vector uh the wence is + + + align:start position:0% +a photon the wave Vector uh the wence is +about one + + align:start position:0% +about one + + + align:start position:0% +about one +micron right of half mic let think about + + align:start position:0% +micron right of half mic let think about + + + align:start position:0% +micron right of half mic let think about +visible like half Micon + + align:start position:0% +visible like half Micon + + + align:start position:0% +visible like half Micon +right and the V Vector of phon is 2 pi + + align:start position:0% +right and the V Vector of phon is 2 pi + + + align:start position:0% +right and the V Vector of phon is 2 pi +over + + align:start position:0% +over + + + align:start position:0% +over +Lambda 2 pi over half + + align:start position:0% +Lambda 2 pi over half + + + align:start position:0% +Lambda 2 pi over half +mic and here is two pi/ a a is l a f + + align:start position:0% +mic and here is two pi/ a a is l a f + + + align:start position:0% +mic and here is two pi/ a a is l a f +Armstrong right so between so this is a + + align:start position:0% +Armstrong right so between so this is a + + + align:start position:0% +Armstrong right so between so this is a +f Armstrong if it's a two + + align:start position:0% +f Armstrong if it's a two + + + align:start position:0% +f Armstrong if it's a two +pi over half Micron that's exactly + + align:start position:0% +pi over half Micron that's exactly + + + align:start position:0% +pi over half Micron that's exactly +almost right at the + + align:start position:0% +almost right at the + + + align:start position:0% +almost right at the +center right the V Vector of full very + + align:start position:0% +center right the V Vector of full very + + + align:start position:0% +center right the V Vector of full very +small V Vector h k h or Lambda is + + align:start position:0% +small V Vector h k h or Lambda is + + + align:start position:0% +small V Vector h k h or Lambda is +momentum momentum photon is very + + align:start position:0% +momentum momentum photon is very + + + align:start position:0% +momentum momentum photon is very +small + + align:start position:0% +small + + + align:start position:0% +small +so in G the photon comes in can go you + + align:start position:0% +so in G the photon comes in can go you + + + align:start position:0% +so in G the photon comes in can go you +go from here to if the energy is large + + align:start position:0% +go from here to if the energy is large + + + align:start position:0% +go from here to if the energy is large +enough you can lift electron from here + + align:start position:0% +enough you can lift electron from here + + + align:start position:0% +enough you can lift electron from here +to here get + + align:start position:0% +to here get + + + align:start position:0% +to here get +absor but in Silicon because indirect + + align:start position:0% +absor but in Silicon because indirect + + + align:start position:0% +absor but in Silicon because indirect +semiconductor the photon momentum is + + align:start position:0% +semiconductor the photon momentum is + + + align:start position:0% +semiconductor the photon momentum is +here you cannot LIF the electron from + + align:start position:0% +here you cannot LIF the electron from + + + align:start position:0% +here you cannot LIF the electron from +here to here doesn't have enough + + align:start position:0% +here to here doesn't have enough + + + align:start position:0% +here to here doesn't have enough +momentum it has enough + + align:start position:0% + + + + align:start position:0% + +energy one can solve that problem + + align:start position:0% +energy one can solve that problem + + + align:start position:0% +energy one can solve that problem +some through some method you make a big + + align:start position:0% +some through some method you make a big + + + align:start position:0% +some through some method you make a big +you solve a huge problem okay see this + + align:start position:0% +you solve a huge problem okay see this + + + align:start position:0% +you solve a huge problem okay see this +is really even in the microscopical + + align:start position:0% +is really even in the microscopical + + + align:start position:0% +is really even in the microscopical +world the energy conservation momentum + + align:start position:0% +world the energy conservation momentum + + + align:start position:0% +world the energy conservation momentum +conservation you learn either in + + align:start position:0% +conservation you learn either in + + + align:start position:0% +conservation you learn either in +continum or in display that always + + align:start position:0% +continum or in display that always + + + align:start position:0% +continum or in display that always +true okay so cic absorb well G absorb if + + align:start position:0% +true okay so cic absorb well G absorb if + + + align:start position:0% +true okay so cic absorb well G absorb if +you look at g s people use the S fil + + align:start position:0% +you look at g s people use the S fil + + + align:start position:0% +you look at g s people use the S fil +they absorb well C it's very hard to use + + align:start position:0% +they absorb well C it's very hard to use + + + align:start position:0% +they absorb well C it's very hard to use +S film because they don't absorb you get + + align:start position:0% +S film because they don't absorb you get + + + align:start position:0% +S film because they don't absorb you get +so your compromises make make thicker + + align:start position:0% +so your compromises make make thicker + + + align:start position:0% +so your compromises make make thicker +for that chance to + + align:start position:0% + + + + align:start position:0% + +happen uh yes but uh that's exactly how + + align:start position:0% +happen uh yes but uh that's exactly how + + + align:start position:0% +happen uh yes but uh that's exactly how +it absorb PS you need a + + align:start position:0% +it absorb PS you need a + + + align:start position:0% +it absorb PS you need a +colon right F has that we + + align:start position:0% +colon right F has that we + + + align:start position:0% +colon right F has that we +Vector F doesn't have enough energy that + + align:start position:0% +Vector F doesn't have enough energy that + + + align:start position:0% +Vector F doesn't have enough energy that +the guys is too + + align:start position:0% +the guys is too + + + align:start position:0% +the guys is too +small so Fon plus + + align:start position:0% +small so Fon plus + + + align:start position:0% +small so Fon plus +phon Fon give you the V Vector phon give + + align:start position:0% +phon Fon give you the V Vector phon give + + + align:start position:0% +phon Fon give you the V Vector phon give +you the energy can lift from here to + + align:start position:0% +you the energy can lift from here to + + + align:start position:0% +you the energy can lift from here to +here you got the three part work + + align:start position:0% +here you got the three part work + + + align:start position:0% +here you got the three part work +together right think about your + + align:start position:0% +together right think about your + + + align:start position:0% +together right think about your +coordination at MIT get three Professor + + align:start position:0% +coordination at MIT get three Professor + + + align:start position:0% +coordination at MIT get three Professor +together much less + + align:start position:0% +together much less + + + align:start position:0% +together much less +chance the probability + + align:start position:0% +chance the probability + + + align:start position:0% +chance the probability +issue right you all have that experience + + align:start position:0% + + + + align:start position:0% + +okay uh now we're going to do a little B + + align:start position:0% +okay uh now we're going to do a little B + + + align:start position:0% +okay uh now we're going to do a little B +more that's the that's a basic idea of + + align:start position:0% +more that's the that's a basic idea of + + + align:start position:0% +more that's the that's a basic idea of +the energy levels vibrational energy + + align:start position:0% +the energy levels vibrational energy + + + align:start position:0% +the energy levels vibrational energy +level and uh the uh electronic energy + + align:start position:0% +level and uh the uh electronic energy + + + align:start position:0% +level and uh the uh electronic energy +level in + + align:start position:0% +level in + + + align:start position:0% +level in +solids and I'm going to do a little more + + align:start position:0% +solids and I'm going to do a little more + + + align:start position:0% +solids and I'm going to do a little more +uh uh and I approximate first I think + + align:start position:0% +uh uh and I approximate first I think + + + align:start position:0% +uh uh and I approximate first I think +about the free electron the kinetic + + align:start position:0% +about the free electron the kinetic + + + align:start position:0% +about the free electron the kinetic +energy 12 MV s + + align:start position:0% +energy 12 MV s + + + align:start position:0% +energy 12 MV s +right and m s uh quantum + + align:start position:0% +right and m s uh quantum + + + align:start position:0% +right and m s uh quantum +mechanics uh say say first m m * we is + + align:start position:0% +mechanics uh say say first m m * we is + + + align:start position:0% +mechanics uh say say first m m * we is +momentum so p² to M that's still just a + + align:start position:0% +momentum so p² to M that's still just a + + + align:start position:0% +momentum so p² to M that's still just a +relation from p is M + + align:start position:0% +relation from p is M + + + align:start position:0% +relation from p is M +we and in quantum mechanics p is + + align:start position:0% +we and in quantum mechanics p is + + + align:start position:0% +we and in quantum mechanics p is +HK so oh I forgot h s sorry should be x² + + align:start position:0% +HK so oh I forgot h s sorry should be x² + + + align:start position:0% +HK so oh I forgot h s sorry should be x² +t + + align:start position:0% +t + + + align:start position:0% +t +s so that's a free electr + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and for electron in this + + align:start position:0% +and for electron in this + + + align:start position:0% +and for electron in this +solid I'm going to do a similar + + align:start position:0% +solid I'm going to do a similar + + + align:start position:0% +solid I'm going to do a similar +treatment because this here is maximum + + align:start position:0% +treatment because this here is maximum + + + align:start position:0% +treatment because this here is maximum +here is + + align:start position:0% +here is + + + align:start position:0% +here is +minimum right again the first order + + align:start position:0% +minimum right again the first order + + + align:start position:0% +minimum right again the first order +derivative is zero unless this is a very + + align:start position:0% +derivative is zero unless this is a very + + + align:start position:0% +derivative is zero unless this is a very +shock there are some cases is not the + + align:start position:0% +shock there are some cases is not the + + + align:start position:0% +shock there are some cases is not the +derivative is not + + align:start position:0% +derivative is not + + + align:start position:0% +derivative is not +continuous so the band is not a par I + + align:start position:0% +continuous so the band is not a par I + + + align:start position:0% +continuous so the band is not a par I +say is not a continuous curvature + + align:start position:0% +say is not a continuous curvature + + + align:start position:0% +say is not a continuous curvature +there but say most of case this maximum + + align:start position:0% +there but say most of case this maximum + + + align:start position:0% +there but say most of case this maximum +minimum the first derivative is zero so + + align:start position:0% +minimum the first derivative is zero so + + + align:start position:0% +minimum the first derivative is zero so +I have second order in + + align:start position:0% +I have second order in + + + align:start position:0% +I have second order in +10 right mathematics T expansion so here + + align:start position:0% +10 right mathematics T expansion so here + + + align:start position:0% +10 right mathematics T expansion so here +if I for example take it e e say of + + align:start position:0% +if I for example take it e e say of + + + align:start position:0% +if I for example take it e e say of +course I put a k I didn't put a k this + + align:start position:0% +course I put a k I didn't put a k this + + + align:start position:0% +course I put a k I didn't put a k this +is not zero so I should kx- + + align:start position:0% +is not zero so I should kx- + + + align:start position:0% +is not zero so I should kx- +k0 Square + + align:start position:0% +k0 Square + + + align:start position:0% +k0 Square +here I put the center at at the center + + align:start position:0% +here I put the center at at the center + + + align:start position:0% +here I put the center at at the center +so this is the uh uh semi general not + + align:start position:0% +so this is the uh uh semi general not + + + align:start position:0% +so this is the uh uh semi general not +the most general form of doing the + + align:start position:0% +the most general form of doing the + + + align:start position:0% +the most general form of doing the +mathematics + + align:start position:0% + + + + align:start position:0% + +right and here it looks very similar to + + align:start position:0% +right and here it looks very similar to + + + align:start position:0% +right and here it looks very similar to +free electron this is just a second + + align:start position:0% +free electron this is just a second + + + align:start position:0% +free electron this is just a second +order derivative of the + + align:start position:0% +order derivative of the + + + align:start position:0% +order derivative of the +curvature now if I treat that just as a + + align:start position:0% +curvature now if I treat that just as a + + + align:start position:0% +curvature now if I treat that just as a +mass equivalent Mass I the effective + + align:start position:0% +mass equivalent Mass I the effective + + + align:start position:0% +mass equivalent Mass I the effective +mess then it's a free electron I can + + align:start position:0% +mess then it's a free electron I can + + + align:start position:0% +mess then it's a free electron I can +then do the rest of my work as a free + + align:start position:0% +then do the rest of my work as a free + + + align:start position:0% +then do the rest of my work as a free +electron so mathematical simplification + + align:start position:0% +electron so mathematical simplification + + + align:start position:0% +electron so mathematical simplification +here are the effective + + align:start position:0% +here are the effective + + + align:start position:0% +here are the effective +mass of the uh in electron in the + + align:start position:0% +mass of the uh in electron in the + + + align:start position:0% +mass of the uh in electron in the +crystal if I take that effective Mass I + + align:start position:0% +crystal if I take that effective Mass I + + + align:start position:0% +crystal if I take that effective Mass I +write this pretty much like a three Elon + + align:start position:0% +write this pretty much like a three Elon + + + align:start position:0% +write this pretty much like a three Elon +so I'm going to do three electron most + + align:start position:0% +so I'm going to do three electron most + + + align:start position:0% +so I'm going to do three electron most +of the + + align:start position:0% +of the + + + align:start position:0% +of the +time with the except the replace the + + align:start position:0% +time with the except the replace the + + + align:start position:0% +time with the except the replace the +mass so this is again my dispersion + + align:start position:0% +mass so this is again my dispersion + + + align:start position:0% +mass so this is again my dispersion +relation right before I said dispersion + + align:start position:0% +relation right before I said dispersion + + + align:start position:0% +relation right before I said dispersion +relation between + + align:start position:0% +relation between + + + align:start position:0% +relation between +frequency and W vector and now if you + + align:start position:0% +frequency and W vector and now if you + + + align:start position:0% +frequency and W vector and now if you +think about energy related to frequency + + align:start position:0% +think about energy related to frequency + + + align:start position:0% +think about energy related to frequency +H new so frequency we Vector except that + + align:start position:0% +H new so frequency we Vector except that + + + align:start position:0% +H new so frequency we Vector except that +for electron people don't talk for + + align:start position:0% +for electron people don't talk for + + + align:start position:0% +for electron people don't talk for +frequency people like to talk about + + align:start position:0% +frequency people like to talk about + + + align:start position:0% +frequency people like to talk about +energy those relation between V Vector + + align:start position:0% +energy those relation between V Vector + + + align:start position:0% +energy those relation between V Vector +frequency or V vector and energy are + + align:start position:0% + + + + align:start position:0% + +dispersion it could be different for + + align:start position:0% +dispersion it could be different for + + + align:start position:0% +dispersion it could be different for +every direction could be uh in some + + align:start position:0% +every direction could be uh in some + + + align:start position:0% +every direction could be uh in some +cases it could be + + align:start position:0% +cases it could be + + + align:start position:0% +cases it could be +isotop okay actually let one let me show + + align:start position:0% +isotop okay actually let one let me show + + + align:start position:0% +isotop okay actually let one let me show +you now if we take energ as Conant I dra + + align:start position:0% +you now if we take energ as Conant I dra + + + align:start position:0% +you now if we take energ as Conant I dra +this right if you look at this this is a + + align:start position:0% +this right if you look at this this is a + + + align:start position:0% +this right if you look at this this is a +okay what's a constant energy surface + + align:start position:0% +okay what's a constant energy surface + + + align:start position:0% +okay what's a constant energy surface +looking like in 3D if this are the same + + align:start position:0% +looking like in 3D if this are the same + + + align:start position:0% +looking like in 3D if this are the same +it's a sphere they are different they + + align:start position:0% +it's a sphere they are different they + + + align:start position:0% +it's a sphere they are different they +are + + align:start position:0% + + + + align:start position:0% + +right so this is what's + + align:start position:0% + + + + align:start position:0% + +in this is a c + + align:start position:0% + + + + align:start position:0% + +electr + + align:start position:0% +electr + + + align:start position:0% +electr +right so in this case we say okay there + + align:start position:0% +right so in this case we say okay there + + + align:start position:0% +right so in this case we say okay there +you got us six PA + + align:start position:0% +you got us six PA + + + align:start position:0% +you got us six PA +Pockets different + + align:start position:0% +Pockets different + + + align:start position:0% +Pockets different +directions okay + + align:start position:0% + + + + align:start position:0% + +and this is just a review uh I showed + + align:start position:0% +and this is just a review uh I showed + + + align:start position:0% +and this is just a review uh I showed +this before now we know what is pH now + + align:start position:0% +this before now we know what is pH now + + + align:start position:0% +this before now we know what is pH now +what is + + align:start position:0% +what is + + + align:start position:0% +what is +electron and per distribution is for + + align:start position:0% +electron and per distribution is for + + + align:start position:0% +electron and per distribution is for +electron stand distribution for Fon and + + align:start position:0% +electron stand distribution for Fon and + + + align:start position:0% +electron stand distribution for Fon and +phon most of the time this me is zero + + align:start position:0% +phon most of the time this me is zero + + + align:start position:0% +phon most of the time this me is zero +because Fon and phon lot real + + align:start position:0% +because Fon and phon lot real + + + align:start position:0% +because Fon and phon lot real +particles it's another way they're not + + align:start position:0% +particles it's another way they're not + + + align:start position:0% +particles it's another way they're not +real you can disappear + + align:start position:0% +real you can disappear + + + align:start position:0% +real you can disappear +right + + align:start position:0% +right + + + align:start position:0% +right +electron also disappear but most of the + + align:start position:0% +electron also disappear but most of the + + + align:start position:0% +electron also disappear but most of the +time and not disappear electron can not + + align:start position:0% +time and not disappear electron can not + + + align:start position:0% +time and not disappear electron can not +disappear electron is real + + align:start position:0% +disappear electron is real + + + align:start position:0% +disappear electron is real +part we go from conduction band to + + align:start position:0% +part we go from conduction band to + + + align:start position:0% +part we go from conduction band to +Valance band we combine just you will + + align:start position:0% +Valance band we combine just you will + + + align:start position:0% +Valance band we combine just you will +the electron still is there + + align:start position:0% +the electron still is there + + + align:start position:0% +the electron still is there +okay okay now I'm going to do math uh + + align:start position:0% +okay okay now I'm going to do math uh + + + align:start position:0% +okay okay now I'm going to do math uh +say uh the uh comp I'm going to do + + align:start position:0% +say uh the uh comp I'm going to do + + + align:start position:0% +say uh the uh comp I'm going to do +detail more detail comp + + align:start position:0% +detail more detail comp + + + align:start position:0% +detail more detail comp +I say okay I I for semiconduct + + align:start position:0% + + + + align:start position:0% + +yes uh Mass conservation + + align:start position:0% +yes uh Mass conservation + + + align:start position:0% +yes uh Mass conservation +for + + align:start position:0% +for + + + align:start position:0% +for +question I don't I don't think we can + + align:start position:0% +question I don't I don't think we can + + + align:start position:0% +question I don't I don't think we can +talk about + + align:start position:0% +talk about + + + align:start position:0% +talk about +mass + + align:start position:0% +mass + + + align:start position:0% +mass +for under the effective Mass picture I'm + + align:start position:0% +for under the effective Mass picture I'm + + + align:start position:0% +for under the effective Mass picture I'm +sure about the this is only from I think + + align:start position:0% +sure about the this is only from I think + + + align:start position:0% +sure about the this is only from I think +the most system from trans view electron + + align:start position:0% +the most system from trans view electron + + + align:start position:0% +the most system from trans view electron +of course the the true math is still the + + align:start position:0% +of course the the true math is still the + + + align:start position:0% +of course the the true math is still the +the1 31 but in the solid when you look + + align:start position:0% +the1 31 but in the solid when you look + + + align:start position:0% +the1 31 but in the solid when you look +at the transport I see three electron + + align:start position:0% +at the transport I see three electron + + + align:start position:0% +at the transport I see three electron +then uh due to the feel the drag of the + + align:start position:0% +then uh due to the feel the drag of the + + + align:start position:0% +then uh due to the feel the drag of the +background lce so th the feel either + + align:start position:0% +background lce so th the feel either + + + align:start position:0% +background lce so th the feel either +heavier or lighter than that free + + align:start position:0% +heavier or lighter than that free + + + align:start position:0% +heavier or lighter than that free +electron Mass which is line1 + + align:start position:0% + + + + align:start position:0% + +yes when when people do theu cation + + align:start position:0% +yes when when people do theu cation + + + align:start position:0% +yes when when people do theu cation +electrons do they uh + + align:start position:0% +electrons do they uh + + + align:start position:0% +electrons do they uh +assume independent electron + + align:start position:0% +assume independent electron + + + align:start position:0% +assume independent electron +transation give they + + align:start position:0% +transation give they + + + align:start position:0% +transation give they +include I think they should include the + + align:start position:0% +include I think they should include the + + + align:start position:0% +include I think they should include the +electron the this is for example do uh + + align:start position:0% +electron the this is for example do uh + + + align:start position:0% +electron the this is for example do uh +this function Theory calculation uh they + + align:start position:0% +this function Theory calculation uh they + + + align:start position:0% +this function Theory calculation uh they +will include the other electron + + align:start position:0% + + + + align:start position:0% + +and you don't do a three just + + align:start position:0% +and you don't do a three just + + + align:start position:0% +and you don't do a three just +independent electron you you have + + align:start position:0% +independent electron you you have + + + align:start position:0% +independent electron you you have +electron inflence other electron even + + align:start position:0% +electron inflence other electron even + + + align:start position:0% +electron inflence other electron even +the same + + align:start position:0% + + + + align:start position:0% + +atom okay so now I'm going to do a + + align:start position:0% +atom okay so now I'm going to do a + + + align:start position:0% +atom okay so now I'm going to do a +spherical I'm not going to do parabolic + + align:start position:0% +spherical I'm not going to do parabolic + + + align:start position:0% +spherical I'm not going to do parabolic +elliptical bands I'm going to do + + align:start position:0% +elliptical bands I'm going to do + + + align:start position:0% +elliptical bands I'm going to do +spherical band uh and is the same in all + + align:start position:0% +spherical band uh and is the same in all + + + align:start position:0% +spherical band uh and is the same in all +directions okay so that's like a really + + align:start position:0% +directions okay so that's like a really + + + align:start position:0% +directions okay so that's like a really +like a fre + + align:start position:0% +like a fre + + + align:start position:0% +like a fre +except that this MK could be different + + align:start position:0% +except that this MK could be different + + + align:start position:0% +except that this MK could be different +like I said it's good for G last night + + align:start position:0% +like I said it's good for G last night + + + align:start position:0% +like I said it's good for G last night +right let me suppose I want to find out + + align:start position:0% +right let me suppose I want to find out + + + align:start position:0% +right let me suppose I want to find out +if I do the + + align:start position:0% +if I do the + + + align:start position:0% +if I do the +material how many electron I have in + + align:start position:0% +material how many electron I have in + + + align:start position:0% +material how many electron I have in +this + + align:start position:0% + + + + align:start position:0% + +conduction and uh I'm going to do + + align:start position:0% +conduction and uh I'm going to do + + + align:start position:0% +conduction and uh I'm going to do +counting this is a strategy that I use + + align:start position:0% +counting this is a strategy that I use + + + align:start position:0% +counting this is a strategy that I use +and uh uh it's a uh I use before same + + align:start position:0% +and uh uh it's a uh I use before same + + + align:start position:0% +and uh uh it's a uh I use before same +for Photon I did that Photon in a cavity + + align:start position:0% +for Photon I did that Photon in a cavity + + + align:start position:0% +for Photon I did that Photon in a cavity +I count how many photons in the + + align:start position:0% +I count how many photons in the + + + align:start position:0% +I count how many photons in the +cavity right so now if you remember each + + align:start position:0% +cavity right so now if you remember each + + + align:start position:0% +cavity right so now if you remember each +quantum mechanical + + align:start position:0% +quantum mechanical + + + align:start position:0% +quantum mechanical +State can have one + + align:start position:0% +State can have one + + + align:start position:0% +State can have one +electron and uh they they State what's + + align:start position:0% +electron and uh they they State what's + + + align:start position:0% +electron and uh they they State what's +the average number of electron is given + + align:start position:0% +the average number of electron is given + + + align:start position:0% +the average number of electron is given +by F Rock maximum one electron right we + + align:start position:0% +by F Rock maximum one electron right we + + + align:start position:0% +by F Rock maximum one electron right we +said in the this is the + + align:start position:0% +said in the this is the + + + align:start position:0% +said in the this is the +average given at certain temperature + + align:start position:0% +average given at certain temperature + + + align:start position:0% +average given at certain temperature +potential every L of electron in one + + align:start position:0% +potential every L of electron in one + + + align:start position:0% +potential every L of electron in one +state now I just need to see how many + + align:start position:0% +state now I just need to see how many + + + align:start position:0% +state now I just need to see how many +Quantum States I have + + align:start position:0% +Quantum States I have + + + align:start position:0% +Quantum States I have +right one Quantum State this is the + + align:start position:0% +right one Quantum State this is the + + + align:start position:0% +right one Quantum State this is the +area number of + + align:start position:0% +area number of + + + align:start position:0% +area number of +electrons so I just need to really all + + align:start position:0% +electrons so I just need to really all + + + align:start position:0% +electrons so I just need to really all +this C looking very complicated it's + + align:start position:0% +this C looking very complicated it's + + + align:start position:0% +this C looking very complicated it's +just a counting qualum state and before + + align:start position:0% +just a counting qualum state and before + + + align:start position:0% +just a counting qualum state and before +when I do electromagnetic wave I was + + align:start position:0% +when I do electromagnetic wave I was + + + align:start position:0% +when I do electromagnetic wave I was +counting Counting electr magnetic mes + + align:start position:0% +counting Counting electr magnetic mes + + + align:start position:0% +counting Counting electr magnetic mes +same same way right so all that com in + + align:start position:0% +same same way right so all that com in + + + align:start position:0% +same same way right so all that com in +come in how many mes the m is + + align:start position:0% +come in how many mes the m is + + + align:start position:0% +come in how many mes the m is +essentially a state right so I'm + + align:start position:0% +essentially a state right so I'm + + + align:start position:0% +essentially a state right so I'm +counting so in the X so 3 KX KY + + align:start position:0% +counting so in the X so 3 KX KY + + + align:start position:0% +counting so in the X so 3 KX KY +KZ and KX I have NX + + align:start position:0% +KZ and KX I have NX + + + align:start position:0% +KZ and KX I have NX +l and add in the X Direction K Y and Y + + align:start position:0% +l and add in the X Direction K Y and Y + + + align:start position:0% +l and add in the X Direction K Y and Y +number k z and Z + + align:start position:0% + + + + align:start position:0% + +number okay and the factor of two is + + align:start position:0% +number okay and the factor of two is + + + align:start position:0% +number okay and the factor of two is +because I have spin electron spin one + + align:start position:0% +because I have spin electron spin one + + + align:start position:0% +because I have spin electron spin one +positive minus + + align:start position:0% +positive minus + + + align:start position:0% +positive minus +netive electromagnetic wave is a factor + + align:start position:0% +netive electromagnetic wave is a factor + + + align:start position:0% +netive electromagnetic wave is a factor +two if I want to do full maybe it's a + + align:start position:0% +two if I want to do full maybe it's a + + + align:start position:0% +two if I want to do full maybe it's a +fact of three right because my trans if + + align:start position:0% +fact of three right because my trans if + + + align:start position:0% +fact of three right because my trans if +they are all the same + + align:start position:0% + + + + align:start position:0% + +okay and so this is the L of quantum + + align:start position:0% +okay and so this is the L of quantum + + + align:start position:0% +okay and so this is the L of quantum +States and this is at each Quantum State + + align:start position:0% +States and this is at each Quantum State + + + align:start position:0% +States and this is at each Quantum State +what's the average L of + + align:start position:0% +what's the average L of + + + align:start position:0% +what's the average L of +electron you can think that for f or for + + align:start position:0% +electron you can think that for f or for + + + align:start position:0% +electron you can think that for f or for +full it's all the same + + align:start position:0% +full it's all the same + + + align:start position:0% +full it's all the same +way + + align:start position:0% + + + + align:start position:0% + +right real Vector number well number + + align:start position:0% +right real Vector number well number + + + align:start position:0% +right real Vector number well number +minus Z or two this is a this is + + align:start position:0% +minus Z or two this is a this is + + + align:start position:0% +minus Z or two this is a this is +the yes it's the counting the lumber but + + align:start position:0% +the yes it's the counting the lumber but + + + align:start position:0% +the yes it's the counting the lumber but +say then I do the integration + + align:start position:0% +say then I do the integration + + + align:start position:0% +say then I do the integration +conversion okay here iting + + align:start position:0% +conversion okay here iting + + + align:start position:0% +conversion okay here iting +the okay here is a uh I'm counting n + + align:start position:0% +the okay here is a uh I'm counting n + + + align:start position:0% +the okay here is a uh I'm counting n +these are the discrete + + align:start position:0% +these are the discrete + + + align:start position:0% +these are the discrete +States + + align:start position:0% +States + + + align:start position:0% +States +right uh and this is a standing wave + + align:start position:0% +right uh and this is a standing wave + + + align:start position:0% +right uh and this is a standing wave +picture so everything is positive + + align:start position:0% +picture so everything is positive + + + align:start position:0% +picture so everything is positive +and when I do traveling with two + + align:start position:0% +and when I do traveling with two + + + align:start position:0% +and when I do traveling with two +directions it's I said that this are + + align:start position:0% +directions it's I said that this are + + + align:start position:0% +directions it's I said that this are +equivalent okay so that's why I go from + + align:start position:0% +equivalent okay so that's why I go from + + + align:start position:0% +equivalent okay so that's why I go from +negative and to positive and it's just a + + align:start position:0% + + + + align:start position:0% + +equivalent okay why I count the lers + + align:start position:0% +equivalent okay why I count the lers + + + align:start position:0% +equivalent okay why I count the lers +because my next step is convert that + + align:start position:0% +because my next step is convert that + + + align:start position:0% +because my next step is convert that +Lumber into integration it's counting + + align:start position:0% +Lumber into integration it's counting + + + align:start position:0% +Lumber into integration it's counting +States right it's better to do integral + + align:start position:0% +States right it's better to do integral + + + align:start position:0% +States right it's better to do integral +States rather than fraction of + + align:start position:0% +States rather than fraction of + + + align:start position:0% +States rather than fraction of +Lum this is the the Lum State that's + + align:start position:0% +Lum this is the the Lum State that's + + + align:start position:0% +Lum this is the the Lum State that's +where I convert + + align:start position:0% +where I convert + + + align:start position:0% +where I convert +this if I think about we vector k is a + + align:start position:0% +this if I think about we vector k is a + + + align:start position:0% +this if I think about we vector k is a +continuous + + align:start position:0% +continuous + + + align:start position:0% +continuous +function and between two + + align:start position:0% +function and between two + + + align:start position:0% +function and between two +states that Delta K is 2 pi/ + + align:start position:0% +states that Delta K is 2 pi/ + + + align:start position:0% +states that Delta K is 2 pi/ +L so this is converting this integer + + align:start position:0% +L so this is converting this integer + + + align:start position:0% +L so this is converting this integer +summation + + align:start position:0% +summation + + + align:start position:0% +summation +into uh no the summation into + + align:start position:0% +into uh no the summation into + + + align:start position:0% +into uh no the summation into +integration + + align:start position:0% + + + + align:start position:0% + +right I did that same thing when I do + + align:start position:0% +right I did that same thing when I do + + + align:start position:0% +right I did that same thing when I do +electr magnetic + + align:start position:0% +electr magnetic + + + align:start position:0% +electr magnetic +mode so in the X Direction This is if + + align:start position:0% +mode so in the X Direction This is if + + + align:start position:0% +mode so in the X Direction This is if +this is the length but the the leg two + + align:start position:0% +this is the length but the the leg two + + + align:start position:0% +this is the length but the the leg two +adjacent the k n is 2 pi LX so this is + + align:start position:0% +adjacent the k n is 2 pi LX so this is + + + align:start position:0% +adjacent the k n is 2 pi LX so this is +the L convert into here CR down here so + + align:start position:0% +the L convert into here CR down here so + + + align:start position:0% +the L convert into here CR down here so +here I have the integration KX KY KZ + + align:start position:0% + + + + align:start position:0% + +those are all mathematics + + align:start position:0% +those are all mathematics + + + align:start position:0% +those are all mathematics +converting and say the conversion and + + align:start position:0% +converting and say the conversion and + + + align:start position:0% +converting and say the conversion and +the + + align:start position:0% +the + + + align:start position:0% +the +counting and the reason I want to do + + align:start position:0% +counting and the reason I want to do + + + align:start position:0% +counting and the reason I want to do +this now is I have integration dkx dky + + align:start position:0% +this now is I have integration dkx dky + + + align:start position:0% +this now is I have integration dkx dky +DK Z and 2 pi now I have is 8 Pi cubic + + align:start position:0% +DK Z and 2 pi now I have is 8 Pi cubic + + + align:start position:0% +DK Z and 2 pi now I have is 8 Pi cubic +LX l y l z is the + + align:start position:0% +LX l y l z is the + + + align:start position:0% +LX l y l z is the +volume + + align:start position:0% +volume + + + align:start position:0% +volume +two and uh now the + + align:start position:0% +two and uh now the + + + align:start position:0% +two and uh now the +f i I'm going to just ignore that one + + align:start position:0% +f i I'm going to just ignore that one + + + align:start position:0% +f i I'm going to just ignore that one +plus one that's a b approximation for + + align:start position:0% +plus one that's a b approximation for + + + align:start position:0% +plus one that's a b approximation for +theer Dra + + align:start position:0% + + + + align:start position:0% + +distribution okay so I plug in this F + + align:start position:0% +distribution okay so I plug in this F + + + align:start position:0% +distribution okay so I plug in this F +already here so that's my L of + + align:start position:0% +already here so that's my L of + + + align:start position:0% +already here so that's my L of +electrons in this region in the in the + + align:start position:0% +electrons in this region in the in the + + + align:start position:0% +electrons in this region in the in the +conduction + + align:start position:0% + + + + align:start position:0% + +B + + align:start position:0% +B + + + align:start position:0% +B +okay I encounter this classical problem + + align:start position:0% +okay I encounter this classical problem + + + align:start position:0% +okay I encounter this classical problem +my integration is over weight + + align:start position:0% +my integration is over weight + + + align:start position:0% +my integration is over weight +Vector my function is over + + align:start position:0% +Vector my function is over + + + align:start position:0% +Vector my function is over +energy right same thing in + + align:start position:0% +energy right same thing in + + + align:start position:0% +energy right same thing in +electromagnetic way my function my + + align:start position:0% +electromagnetic way my function my + + + align:start position:0% +electromagnetic way my function my +integration is over KX k k z my function + + align:start position:0% +integration is over KX k k z my function + + + align:start position:0% +integration is over KX k k z my function +is our energy and I have to choose + + align:start position:0% +is our energy and I have to choose + + + align:start position:0% +is our energy and I have to choose +either energy or we Vector as my + + align:start position:0% +either energy or we Vector as my + + + align:start position:0% +either energy or we Vector as my +variable to do this + + align:start position:0% +variable to do this + + + align:start position:0% +variable to do this +integration I already have the relation + + align:start position:0% +integration I already have the relation + + + align:start position:0% +integration I already have the relation +between e and K that's my Parabola here + + align:start position:0% +between e and K that's my Parabola here + + + align:start position:0% +between e and K that's my Parabola here +e and + + align:start position:0% + + + + align:start position:0% + +K + + align:start position:0% +K + + + align:start position:0% +K +right so I'm going to do that conversion + + align:start position:0% +right so I'm going to do that conversion + + + align:start position:0% +right so I'm going to do that conversion +I in this case it's much easier for me + + align:start position:0% +I in this case it's much easier for me + + + align:start position:0% +I in this case it's much easier for me +to + + align:start position:0% +to + + + align:start position:0% +to +convert dkx dky DK Z into e because you + + align:start position:0% +convert dkx dky DK Z into e because you + + + align:start position:0% +convert dkx dky DK Z into e because you +can say that's a partition coordinate I + + align:start position:0% +can say that's a partition coordinate I + + + align:start position:0% +can say that's a partition coordinate I +into spal + + align:start position:0% +into spal + + + align:start position:0% +into spal +coordinate and + + align:start position:0% +coordinate and + + + align:start position:0% +coordinate and +uh so I doing this conversion I now I do + + align:start position:0% +uh so I doing this conversion I now I do + + + align:start position:0% +uh so I doing this conversion I now I do +per unit volume Lumber + + align:start position:0% +per unit volume Lumber + + + align:start position:0% +per unit volume Lumber +density and I do that the dkx dky DK Z + + align:start position:0% +density and I do that the dkx dky DK Z + + + align:start position:0% +density and I do that the dkx dky DK Z +in spherical coordinate K is the + + align:start position:0% +in spherical coordinate K is the + + + align:start position:0% +in spherical coordinate K is the +magnitude right so it's 4 Pi k + + align:start position:0% + + + + align:start position:0% + +s right so that's from Cici to + + align:start position:0% +s right so that's from Cici to + + + align:start position:0% +s right so that's from Cici to +sperical function and Par + + align:start position:0% + + + + align:start position:0% + +now I replace because I know the k k + + align:start position:0% +now I replace because I know the k k + + + align:start position:0% +now I replace because I know the k k +square is 2 m h² right that's the + + align:start position:0% +square is 2 m h² right that's the + + + align:start position:0% +square is 2 m h² right that's the +expression this is h² * K squ that's K + + align:start position:0% +expression this is h² * K squ that's K + + + align:start position:0% +expression this is h² * K squ that's K +is my radius like R + + align:start position:0% +is my radius like R + + + align:start position:0% +is my radius like R +right so I replace this K + + align:start position:0% + + + + align:start position:0% + +Square k = 2 e h Square DK becomes this + + align:start position:0% +Square k = 2 e h Square DK becomes this + + + align:start position:0% +Square k = 2 e h Square DK becomes this +D and everything is in + + align:start position:0% +D and everything is in + + + align:start position:0% +D and everything is in +energ it's the pick you do all the time + + align:start position:0% +energ it's the pick you do all the time + + + align:start position:0% +energ it's the pick you do all the time +in counting the numbers in Crystal you + + align:start position:0% +in counting the numbers in Crystal you + + + align:start position:0% +in counting the numbers in Crystal you +convert the states L of States summation + + align:start position:0% +convert the states L of States summation + + + align:start position:0% +convert the states L of States summation +into integration you choose your either + + align:start position:0% +into integration you choose your either + + + align:start position:0% +into integration you choose your either +integration variable either in energy or + + align:start position:0% +integration variable either in energy or + + + align:start position:0% +integration variable either in energy or +V + + align:start position:0% + + + + align:start position:0% + +vector and if I group everything all + + align:start position:0% +vector and if I group everything all + + + align:start position:0% +vector and if I group everything all +together + + align:start position:0% +together + + + align:start position:0% +together +this is my + + align:start position:0% +this is my + + + align:start position:0% +this is my +f and this one I call the density of + + align:start position:0% +f and this one I call the density of + + + align:start position:0% +f and this one I call the density of +St + + align:start position:0% +St + + + align:start position:0% +St +okay it's used it's mathematics then + + align:start position:0% +okay it's used it's mathematics then + + + align:start position:0% +okay it's used it's mathematics then +still stays + + align:start position:0% +still stays + + + align:start position:0% +still stays +nothing the physics wise is don't have + + align:start position:0% +nothing the physics wise is don't have + + + align:start position:0% +nothing the physics wise is don't have +much physics it's just a mathematical + + align:start position:0% +much physics it's just a mathematical + + + align:start position:0% +much physics it's just a mathematical +way of saying doing converting my + + align:start position:0% +way of saying doing converting my + + + align:start position:0% +way of saying doing converting my +summation into equation so this is the L + + align:start position:0% +summation into equation so this is the L + + + align:start position:0% +summation into equation so this is the L +of f States per unit volume because I + + align:start position:0% +of f States per unit volume because I + + + align:start position:0% +of f States per unit volume because I +normalize volume and per energy interval + + align:start position:0% +normalize volume and per energy interval + + + align:start position:0% +normalize volume and per energy interval +because here is + + align:start position:0% +because here is + + + align:start position:0% +because here is +B right that's a physical interpretation + + align:start position:0% +B right that's a physical interpretation + + + align:start position:0% +B right that's a physical interpretation +of my + + align:start position:0% + + + + align:start position:0% + +deration and in fact you go to look at + + align:start position:0% +deration and in fact you go to look at + + + align:start position:0% +deration and in fact you go to look at +this one you can do the integration + + align:start position:0% +this one you can do the integration + + + align:start position:0% +this one you can do the integration +analytic that's why I use bman + + align:start position:0% +analytic that's why I use bman + + + align:start position:0% +analytic that's why I use bman +distribution if I put a affir rock if I + + align:start position:0% +distribution if I put a affir rock if I + + + align:start position:0% +distribution if I put a affir rock if I +put say say one over this not this plus + + align:start position:0% +put say say one over this not this plus + + + align:start position:0% +put say say one over this not this plus +one I can do this integration + + align:start position:0% +one I can do this integration + + + align:start position:0% +one I can do this integration +okay so the reason I use board M + + align:start position:0% +okay so the reason I use board M + + + align:start position:0% +okay so the reason I use board M +distribution is I can do this + + align:start position:0% +distribution is I can do this + + + align:start position:0% +distribution is I can do this +integration and this integration gives + + align:start position:0% +integration and this integration gives + + + align:start position:0% +integration and this integration gives +me here is + + align:start position:0% +me here is + + + align:start position:0% +me here is +KBT and here + + align:start position:0% + + + + align:start position:0% + +is so how I determine the capit + + align:start position:0% +is so how I determine the capit + + + align:start position:0% +is so how I determine the capit +potential mu if you give me the L of + + align:start position:0% +potential mu if you give me the L of + + + align:start position:0% +potential mu if you give me the L of +toen so I put a phospher in the + + align:start position:0% +toen so I put a phospher in the + + + align:start position:0% +toen so I put a phospher in the +semiconductor + + align:start position:0% +semiconductor + + + align:start position:0% +semiconductor +per unit volume I put how much I know + + align:start position:0% +per unit volume I put how much I know + + + align:start position:0% +per unit volume I put how much I know +that and if I assume each + + align:start position:0% +that and if I assume each + + + align:start position:0% +that and if I assume each +phosphor Del the one + + align:start position:0% +phosphor Del the one + + + align:start position:0% +phosphor Del the one +electron assumption right and there are + + align:start position:0% +electron assumption right and there are + + + align:start position:0% +electron assumption right and there are +most rigorous statistical way to say how + + align:start position:0% +most rigorous statistical way to say how + + + align:start position:0% +most rigorous statistical way to say how +many electron activated but because + + align:start position:0% +many electron activated but because + + + align:start position:0% +many electron activated but because +phosphor energy is so close to Silicon + + align:start position:0% +phosphor energy is so close to Silicon + + + align:start position:0% +phosphor energy is so close to Silicon +so you can roughly approximate this + + align:start position:0% +so you can roughly approximate this + + + align:start position:0% +so you can roughly approximate this +every atom you put in there to the one + + align:start position:0% +every atom you put in there to the one + + + align:start position:0% +every atom you put in there to the one +electron so with that I know the left + + align:start position:0% +electron so with that I know the left + + + align:start position:0% +electron so with that I know the left +hand side + + align:start position:0% +hand side + + + align:start position:0% +hand side +I can do the inversion I do this is + + align:start position:0% +I can do the inversion I do this is + + + align:start position:0% +I can do the inversion I do this is +where my chal potential is so chal + + align:start position:0% +where my chal potential is so chal + + + align:start position:0% +where my chal potential is so chal +potential it's determined by the number + + align:start position:0% +potential it's determined by the number + + + align:start position:0% +potential it's determined by the number +of carriers you put + + align:start position:0% +of carriers you put + + + align:start position:0% +of carriers you put +there and then you will seeing therm + + align:start position:0% +there and then you will seeing therm + + + align:start position:0% +there and then you will seeing therm +Elric you have to optimize this carrier + + align:start position:0% +Elric you have to optimize this carrier + + + align:start position:0% +Elric you have to optimize this carrier +dity to get the maximum + + align:start position:0% + + + + align:start position:0% + +performance + + align:start position:0% +performance + + + align:start position:0% +performance +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so let me summarize this right + + align:start position:0% +so let me summarize this right + + + align:start position:0% +so let me summarize this right +uh this way of doing the uh conver the + + align:start position:0% +uh this way of doing the uh conver the + + + align:start position:0% +uh this way of doing the uh conver the +to the lb accounting you can always + + align:start position:0% +to the lb accounting you can always + + + align:start position:0% +to the lb accounting you can always +start with that summation I said but at + + align:start position:0% +start with that summation I said but at + + + align:start position:0% +start with that summation I said but at +the end most most time you end up with + + align:start position:0% +the end most most time you end up with + + + align:start position:0% +the end most most time you end up with +this dens of State it's just you der of + + align:start position:0% +this dens of State it's just you der of + + + align:start position:0% +this dens of State it's just you der of +state every time if you don't if you + + align:start position:0% +state every time if you don't if you + + + align:start position:0% +state every time if you don't if you +once you become comfortable you can say + + align:start position:0% +once you become comfortable you can say + + + align:start position:0% +once you become comfortable you can say +okay this is I can write it directly the + + align:start position:0% +okay this is I can write it directly the + + + align:start position:0% +okay this is I can write it directly the +number of electrons per quum state this + + align:start position:0% +number of electrons per quum state this + + + align:start position:0% +number of electrons per quum state this +is the lambra of quantum State per unit + + align:start position:0% +is the lambra of quantum State per unit + + + align:start position:0% +is the lambra of quantum State per unit +volume per energy interval that's L of + + align:start position:0% +volume per energy interval that's L of + + + align:start position:0% +volume per energy interval that's L of +quantum states there and that gives me + + align:start position:0% +quantum states there and that gives me + + + align:start position:0% +quantum states there and that gives me +the number of electrons near energy e + + align:start position:0% +the number of electrons near energy e + + + align:start position:0% +the number of electrons near energy e +and i integrate over all possible energy + + align:start position:0% +and i integrate over all possible energy + + + align:start position:0% +and i integrate over all possible energy +states that should give me the number of + + align:start position:0% +states that should give me the number of + + + align:start position:0% +states that should give me the number of +charg right so once you gone through a + + align:start position:0% +charg right so once you gone through a + + + align:start position:0% +charg right so once you gone through a +few times you can just start from + + align:start position:0% + + + + align:start position:0% + +those and I wrote down for + + align:start position:0% +those and I wrote down for + + + align:start position:0% +those and I wrote down for +my under both my + + align:start position:0% +my under both my + + + align:start position:0% +my under both my +distribution I can do this + + align:start position:0% +distribution I can do this + + + align:start position:0% +distribution I can do this +integration and that's what we + + align:start position:0% +integration and that's what we + + + align:start position:0% +integration and that's what we +have and what it + + align:start position:0% + + + + align:start position:0% + +means + + align:start position:0% +means + + + align:start position:0% +means +is if I gave a l of dop to the like + + align:start position:0% +is if I gave a l of dop to the like + + + align:start position:0% +is if I gave a l of dop to the like +foser I can see where my potential is H + + align:start position:0% +foser I can see where my potential is H + + + align:start position:0% +foser I can see where my potential is H +Po from here G and I inverse I know e + + align:start position:0% +Po from here G and I inverse I know e + + + align:start position:0% +Po from here G and I inverse I know e +you see and the statistics the only + + align:start position:0% +you see and the statistics the only + + + align:start position:0% +you see and the statistics the only +valid when this m is far below + + align:start position:0% +valid when this m is far below + + + align:start position:0% +valid when this m is far below +E once the M gets into here you have to + + align:start position:0% +E once the M gets into here you have to + + + align:start position:0% +E once the M gets into here you have to +use the per + + align:start position:0% +use the per + + + align:start position:0% +use the per +Ro that's degenerate + + align:start position:0% +Ro that's degenerate + + + align:start position:0% +Ro that's degenerate +semic this is only + + align:start position:0% +semic this is only + + + align:start position:0% +semic this is only +approximation but here is G you can + + align:start position:0% +approximation but here is G you can + + + align:start position:0% +approximation but here is G you can +always do that math to inverse the G a + + align:start position:0% +always do that math to inverse the G a + + + align:start position:0% +always do that math to inverse the G a +given number you can get the + + align:start position:0% + + + + align:start position:0% + +C and the density of States it's + + align:start position:0% +C and the density of States it's + + + align:start position:0% +C and the density of States it's +mathematical concept but say it's very + + align:start position:0% +mathematical concept but say it's very + + + align:start position:0% +mathematical concept but say it's very +Convent and uh really is a number of + + align:start position:0% +Convent and uh really is a number of + + + align:start position:0% +Convent and uh really is a number of +quantum States per energy interval the + + align:start position:0% +quantum States per energy interval the + + + align:start position:0% +quantum States per energy interval the +we and in the parabolic B it's a parab + + align:start position:0% +we and in the parabolic B it's a parab + + + align:start position:0% +we and in the parabolic B it's a parab +it's a square root + + align:start position:0% + + + + align:start position:0% + +relation square root + + align:start position:0% +relation square root + + + align:start position:0% +relation square root +and of course below EC this is where EC + + align:start position:0% +and of course below EC this is where EC + + + align:start position:0% +and of course below EC this is where EC +is the bottom here there's no space in + + align:start position:0% +is the bottom here there's no space in + + + align:start position:0% +is the bottom here there's no space in +this region in the forid time + + align:start position:0% +this region in the forid time + + + align:start position:0% +this region in the forid time +Gap so that's a typical bulk material + + align:start position:0% +Gap so that's a typical bulk material + + + align:start position:0% +Gap so that's a typical bulk material +dens of Stace and when you fill and it + + align:start position:0% +dens of Stace and when you fill and it + + + align:start position:0% +dens of Stace and when you fill and it +turns out most of time is only a small + + align:start position:0% +turns out most of time is only a small + + + align:start position:0% +turns out most of time is only a small +region because this here is KT so + + align:start position:0% +region because this here is KT so + + + align:start position:0% +region because this here is KT so +electrons are mostly in this region you + + align:start position:0% +electrons are mostly in this region you + + + align:start position:0% +electrons are mostly in this region you +do while n becomes very large that + + align:start position:0% +do while n becomes very large that + + + align:start position:0% +do while n becomes very large that +exponential Factor very small much + + align:start position:0% +exponential Factor very small much + + + align:start position:0% +exponential Factor very small much +larger than K this is very + + align:start position:0% + + + + align:start position:0% + +small okay so that's what uh uh uh we + + align:start position:0% +small okay so that's what uh uh uh we + + + align:start position:0% +small okay so that's what uh uh uh we +went + + align:start position:0% +went + + + align:start position:0% +went +through and uh I saw that I was doing + + align:start position:0% +through and uh I saw that I was doing + + + align:start position:0% +through and uh I saw that I was doing +much faster we'll do the next time this + + align:start position:0% +much faster we'll do the next time this + + + align:start position:0% +much faster we'll do the next time this +is actually just write on my project + + align:start position:0% +is actually just write on my project + + + align:start position:0% +is actually just write on my project +original syllabus any questions here + + align:start position:0% + + + + align:start position:0% + +now mechanical engineer again I'm sure + + align:start position:0% +now mechanical engineer again I'm sure + + + align:start position:0% +now mechanical engineer again I'm sure +this + + align:start position:0% +this + + + align:start position:0% +this +isal mechan talk about this and you I + + align:start position:0% +isal mechan talk about this and you I + + + align:start position:0% +isal mechan talk about this and you I +don't expect you complete mastering but + + align:start position:0% +don't expect you complete mastering but + + + align:start position:0% +don't expect you complete mastering but +I think what you'll get is say oh I know + + align:start position:0% +I think what you'll get is say oh I know + + + align:start position:0% +I think what you'll get is say oh I know +periodic table I know the metal and the + + align:start position:0% +periodic table I know the metal and the + + + align:start position:0% +periodic table I know the metal and the +uh dialectric difference right and then + + align:start position:0% +uh dialectric difference right and then + + + align:start position:0% +uh dialectric difference right and then +now theal vibration in the crystal it's + + align:start position:0% +now theal vibration in the crystal it's + + + align:start position:0% +now theal vibration in the crystal it's +quti and the basic unit of that + + align:start position:0% +quti and the basic unit of that + + + align:start position:0% +quti and the basic unit of that +quantization + + align:start position:0% +quantization + + + align:start position:0% +quantization +F now you know electron you know F and + + align:start position:0% +F now you know electron you know F and + + + align:start position:0% +F now you know electron you know F and +the Thal conductivity Remember come from + + align:start position:0% +the Thal conductivity Remember come from + + + align:start position:0% +the Thal conductivity Remember come from +electron and phon and in Thal electrics + + align:start position:0% +electron and phon and in Thal electrics + + + align:start position:0% +electron and phon and in Thal electrics +the S Square come from electron so you + + align:start position:0% +the S Square come from electron so you + + + align:start position:0% +the S Square come from electron so you +have to really got this basic picture + + align:start position:0% +have to really got this basic picture + + + align:start position:0% +have to really got this basic picture +before + + align:start position:0% + + + + align:start position:0% + +talk and other + + align:start position:0% + + + + align:start position:0% + +question okay \ No newline at end of file diff --git a/8yO2FBBfaB0.txt b/8yO2FBBfaB0.txt new file mode 100644 index 0000000000000000000000000000000000000000..56dc3d93250c2cd7bcf9f34e50bc3303466f958c --- /dev/null +++ b/8yO2FBBfaB0.txt @@ -0,0 +1,441 @@ +Here's how our virtual memory system will +work. + +The memory addresses generated by the CPU +are called virtual addresses to distinguish + +them from the physical addresses used by main +memory. + +In between the CPU and main memory there's +a new piece of hardware called the memory + +management unit (MMU). + +The MMU's job is to translate virtual addresses +to physical addresses. + +"But wait!" you say. + +"Doesn't the cache go between the CPU and +main memory?" + +You're right and at the end of this lecture +we'll talk about how to use both an MMU and + +a cache. + +But for now, let's assume there's only an +MMU and no cache. + +The MMU hardware translates virtual addresses +to physical addresses using a simple table + +lookup. + +This table is called the page map or page +table. + +Conceptually, the MMU uses the virtual address +as index to select an entry in the table, + +which tells us the corresponding physical +address. + +The table allows a particular virtual address +to be found anywhere in main memory. + +In normal operation we'd want to ensure that +two virtual addresses don't map to the same + +physical address. + +But it would be okay if some of the virtual +addresses did not have a translation to a + +physical address. + +This would indicate that the contents of the +requested virtual address haven't yet been + +loaded into main memory, so the MMU would +signal a memory-management exception to the + +CPU, +which could assign a location in physical + +memory and perform the required I/O operation +to initialize that location from secondary + +storage. + +The MMU table gives the system a lot of control +over how physical memory is accessed by the + +program running on the CPU. + +For example, we could arrange to run multiple +programs in quick succession (a technique + +called time sharing) by changing the page +map when we change programs. + +Main memory locations accessible to one program +could be made inaccessible to another program + +by proper management of their respective page +maps. + +And we could use memory-management exceptions +to load program contents into main memory + +on demand instead of having to load the entire +program before execution starts. + +In fact, we only need to ensure the current +working set of a program is actually resident + +in main memory. + +Locations not currently being used could live +in secondary storage until needed. + +In this lecture and next, we'll see how the +MMU plays a central role in the design of + +a modern timesharing computer system. + +Of course, we'd need an impossibly large table +to separately map each virtual address to + +a physical address. + +So instead we divide both the virtual and +physical address spaces into fixed-sized blocks, + +called pages. + +Page sizes are always a power-of-2 bytes, +say 2^p bytes, so p is the number address + +bits needed to select a particular location +on the page. + +We'll the use low-order p bits of the virtual +or physical address as the page offset. + +The remaining address bits tell us which page +is being accessed and are called the page + +number. + +A typical page size is 4KB to 16KB, which +correspond to p=12 and p=14 respectively. + +Suppose p=12. + +If the CPU produces a 32-bit virtual address, +the low-order 12 bits of the virtual address + +are the page offset and the high-order 20 +bits are the virtual page number. + +Similarly, the low-order p bits of the physical +address are the page offset and the remaining + +physical address bits are the physical page +number. + +The key idea is that the MMU will manage pages, +not individual locations. + +We'll move entire pages from secondary storage +into main memory. + +By the principal of locality, if a program +access one location on a page, we expect it + +will soon access other nearby locations. + +By choosing the page offset from the low-order +address bits, we'll ensure that nearby locations + +live on the same page (unless of course we're +near one end of the page or the other). + +So pages naturally capture the notion of locality. + +And since pages are large, by dealing with +pages when accessing secondary storage, + +we'll take advantage that reading or writing +many locations is only slightly more time + +consuming than accessing the first location. + +The MMU will map virtual page numbers to physical +page numbers. + +It does this by using the virtual page number +(VPN) as an index into the page table. + +Each entry in the page table indicates if +the page is resident in main memory and, if + +it is, provides the appropriate physical page +number (PPN). + +The PPN is combined with the page offset to +form the physical address for main memory. + +If the requested virtual page is NOT resident +in main memory, the MMU signals a memory-management + +exception, called a page fault, to the CPU +so it can load the appropriate page from secondary + +storage and set up the appropriate mapping +in the MMU. + +Our plan to use main memory as page cache +is called "paging" or sometimes "demand paging" + +since movements of pages to and from secondary +storage is determined by the demands of the + +program. + +So here's the plan. + +Initially all the virtual pages for a program +reside in secondary storage and the MMU is + +empty, i.e., there are no pages resident in +physical memory. + +The CPU starts running the program and each +virtual address it generates, either for an + +instruction fetch or data access, is passed +to the MMU to be mapped to a physical address + +in main memory. + +If the virtual address is resident in physical +memory, the main memory hardware can complete + +the access. + +If the virtual address in NOT resident in +physical memory, the MMU signals a page fault + +exception, forcing the CPU to switch execution +to special code called the page fault handler. + +The handler allocates a physical page to hold +the requested virtual page and loads the virtual + +page from secondary storage into main memory. + +It then adjusts the page map entry for the +requested virtual page to show that it is + +now resident and to indicate the physical +page number for the newly allocated and initialized + +physical page. + +When trying to allocate a physical page, the +handler may discover that all physical pages + +are currently in use. + +In this case it chooses an existing page to +replace, e.g., a resident virtual page that + +hasn't been recently accessed. + +It swaps the contents of the chosen virtual +page out to secondary storage and updates + +the page map entry for the replaced virtual +page to indicate it is no longer resident. + +Now there's a free physical page to re-use +to hold the contents of the virtual page that + +was missing. + +The working set of the program, i.e., the +set of pages the program is currently accessing, + +is loaded into main memory through a series +of page faults. + +After a flurry of page faults when the program +starts running, the working set changes slowly, + +so the frequency of page faults drops dramatically, +perhaps close to zero if the program is small + +and well-behaved. + +It is possible to write programs that consistently +generate page faults, a phenomenon called + +thrashing. + +Given the long access times of secondary storage, +a program that's thrashing runs *very* slowly, + +usually so slowly that users give up and rewrite +the program to behave more sensibly. + +The design of the page map is straightforward. + +There's one entry in the page map for each +virtual page. + +For example, if the CPU generates a 32-bit +virtual address and the page size is 2^12 + +bytes, the virtual page number has 32-12 = 20 +bits and the page table will have 2^20 entries. + +Each entry in the page table contains a "resident +bit" (R) which is set to 1 when the virtual + +page is resident in physical memory. + +If R is 0, an access to that virtual page +will cause a page fault. + +If R is 1, the entry also contains the PPN, +indicating where to find the virtual page + +in main memory. + +There's one additional state bit called the +"dirty bit" (D). + +When a page has just been loaded from secondary +storage, it's "clean", i.e, the contents of + +physical memory match the contents of the +page in secondary storage. + +So the D bit is set to 0. + +If subsequently the CPU stores into a location +on the page, the D bit for the page is set + +to 1, indicating the page is "dirty", i.e., +the contents of memory now differ from the + +contents of secondary storage. + +If a dirty page is ever chosen for replacement, +its contents must be written to secondary + +storage in order to save the changes before +the page gets reused. + +Some MMUs have additional state bits in each +page table entry. + +For example, there could be a "read-only" +bit which, when set, would generate an exception + +if the program attempts to store into the +page. + +This would be useful for protecting code pages +from accidentally being corrupted by errant + +data accesses, a very handy debugging feature. + +Here's an example of the MMU in action. + +To make things simple, assume that the virtual +address is 12 bits, consisting of an 8-bit + +page offset and a 4-bit virtual page number. + +So there are 2^4 = 16 virtual pages. + +The physical address is 11 bits, divided into +the same 8-bit page offset and a 3-bit physical + +page number. + +So there are 2^3 = 8 physical pages. + +On the left we see a diagram showing the contents +of the 16-entry page map, i.e., an entry for + +each virtual page. + +Each page table entry includes a dirty bit +(D), a resident bit (R) and a 3-bit physical + +page number, for a total of 5 bits. + +So the page map has 16 entries, each with +5-bits, for a total of 16*5 = 80 bits. + +The first entry in the table is for virtual +page 0, the second entry for virtual page + +1, and so on. + +In the middle of the slide there's a diagram +of physical memory showing the 8 physical + +pages. + +The annotation for each physical page shows +the virtual page number of its contents. + +Note that there's no particular order to how +virtual pages are stored in physical memory + +- +which page holds what is determined by which + +pages are free at the time of a page fault. + +In general, after the program has run for +a while, we'd expected to find the sort of + +jumbled ordering we see here. + +Let's follow along as the MMU handles the +request for virtual address 0x2C8, generated + +by the execution of the LD instruction shown +here. + +Splitting the virtual address into page number +and offset, we see that the VPN is 2 and the + +offset is 0xC8. + +Looking at the page map entry with index 2, +we see that the R bit is 1, indicating that + +virtual page 2 is resident in physical memory. + +The PPN field of entry tells us that virtual +page 2 can be found in physical page 4. + +Combining the PPN with the 8-bit offset, we +find that the contents of virtual address + +0x2C8 can be found in main memory location +0x4C8. + +Note that the offset is unchanged by the translation +process - + +the offset into the physical page is always +the same as the offset into the virtual page. \ No newline at end of file diff --git a/8yvmHBGcNbg.txt b/8yvmHBGcNbg.txt new file mode 100644 index 0000000000000000000000000000000000000000..cf4fe9fc3c05b1b8791ca5d1cd46db6210607581 --- /dev/null +++ b/8yvmHBGcNbg.txt @@ -0,0 +1,3092 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation, or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +ARAM HARROW: So +let's get started. + +This week Professor +Zwiebach is away, + +and I'll be doing +today's lecture. + +And Will Detmold will +do the one on Wednesday. + +The normal office +hours, unfortunately, + +will not be held today. + +One of us will cover his +hours on Wednesday though. + +And you should also just email +either me or Professor Detmold + +if you want to set +up an appointment + +to talk to in the next few days. + +What I'm going to +talk about today + +will be more about the +linear algebra that's + +behind all of quantum mechanics. + +And, at the end of last +time-- last lecture + +you heard about vector +spaces from a more abstract + +perspective than +the usual vectors + +are columns of +numbers perspective. + +Today we're going to +look at operators, + +which act on vector +spaces, which + +are linear maps from a +vector space to itself. + +And they're, in a +sense, equivalent + +to the familiar +idea of matrices, + +which are squares or +rectangles of numbers. + +But are work in this +more abstract setting + +of vector spaces, which +has a number of advantages. + +For example, of +being able to deal + +with infinite dimensional +vector spaces and also + +of being able to talk about +basis independent properties. + +And so I'll tell you +all about that today. + +So we'll talk about how +to define operators, + +some examples, some of +their properties, and then + +finally how to relate them to +the familiar idea of matrices. + +I'll then talk about +eigenvectors and eigenvalues + +from this operator prospective. + +And, depending on time +today, a little bit + +about inner products, +which you'll + +hear more about the future. + +These numbers here correspond +to the sections of the notes + +that these refer to. + +So let me first-- this is +a little bit mathematical + +and perhaps dry at first. + +The payoff is more +distant than usual + +for things you'll hear +in quantum mechanics. + +I just want to +mention a little bit + +about the motivation for it. + +So operators, of course, are +how we define observables. + +And so if we want to know what +the properties of observables, + +of which a key example +are of Hamiltonians, + +then we need to know +about operators. + +They also, as you will +see in the future, + +are useful for +talking about states. + +Right now, states are described +as elements of a vector space, + +but in the future you'll +learn a different formalism + +in which states are also +described as dense operators. + +What are called density +operators or density matrices. + +And finally, operators are +also useful in describing + +symmetries of quantum systems. + +So already in +classical mechanics, + +symmetries have been very +important for understanding + +things like momentum +conservation and energy + +conservation so on. + +They'll be even more +important in quantum mechanics + +and will be understood through +the formalism of operators. + +So these are not things +that I will talk about today + +but are sort of the +motivation for understanding + +very well the structure +of operators now. + +So at the end of +the last lecture, + +Professor Zwiebach +defined linear maps. + +So this is the set of linear +maps from a vector space, v, + +to a vector space w. + +And just to remind you +what it means for a map + +to be linear, so T is linear if +for all pairs of vectors in v, + +the way T acts on their +sum is given by just T of u + +plus T of v. That's +the first property. + +And second, for all vectors +u and for all scalars a-- + +so f is the field that +we're working over, + +it could be reals are +complexes-- we have that + +if T acts on a times u, that's +equal to a times t acting on u. + +So if you put these +together what this means + +is that t essentially +looks like multiplication. + +The way T acts on vectors is +precisely what you would expect + +from the multiplication +map, right? + +It has the distributive property +and it commutes with scalars. + +So this is sort of +informal-- I mean, + +the formal definition is +here, but the informal idea + +is that T acts like +multiplication. + +So if the map that squares +every entry of a vector + +does not act like this, +but linear operators do. + +And for this reason we often +neglect the parentheses. + +So we just write TU to mean T +of u, which is justified because + +of this analogy +with multiplication. + +So an important special case of +this is when v is equal to w. + +And so we just write l of +v to denote the maps from v + +to itself. + +Which you could also +write like this. + +And these are called +operators on v. + +So when we talk about +operators on a vector space, + +v, we mean linear maps from +that vector space to itself. + +So let me illustrate +this with a few examples. + +Starting with some of the +examples of vector spaces + +that you saw from last time. + +So one example of a +vector space is an example + +you've seen before but +a different notation. + +This is the vector space +of all real polynomials + +in one variable. + +So real polynomials +over some variable, x. + +And over-- this is an infinite +dimensional vector space-- + +and we can define various +operators over it. + +For example, we can +define one operator, T, + +to be like differentiation. + +So what you might +write as ddx hat, + +and it's defined for any +polynomial, p, to map + +p to p prime. + +So this is certainly a +function from polynomials + +to polynomials. + +And you can check +that it's also linear + +if you multiply the +polynomial by a scalar, then + +the derivative multiplied +by the same scale. + +If I take the derivative of +a sum of two polynomials, + +then I get the sum +of the derivatives + +of those polynomials. + +I won't write that +down, but you can + +check that the +properties are true. + +And this is indeed +a linear operator. + +Another operator, which +you've seen before, + +is multiplication by x. + +So this is defined +as the map that + +simply multiplies +the polynomial by x. + +Of course, this gives +you another polynomial. + +And, again, you can check easily +that it satisfies these two + +conditions. + +So this gives you a +sense of why things + +that don't appear +to be matrix-like + +can still be viewed in +this operator picture. + +Another example, +which you'll see + +later shows some of the +slightly paradoxical features + +of infinite dimensional +vector spaces, + +comes from the vector space +of infinite sequences. + +So these are all the infinite +sequences of reals or complexes + +or whatever f is. + +One operator we can define +is the left shift operator, + +which is simply defined by +shifting this entire infinite + +sequence left by one +place and throwing away + +the first position. + +So you start with +x2, x3, and so. + +Still goes to +infinity so it still + +gives you an infinite sequence. + +So it is indeed a map-- that's +the first thing you should + +check that this is indeed +a map from v to itself-- + +and you can also check +that it's linear, + +that it satisfies +these two products. + +Another example is right shift. + +And here-- Yeah? + +AUDIENCE: So left shift +was the first one or-- + +ARAM HARROW: That's right. + +So there's no back, really. + +It's a good point. + +So you'd like to not throw +out the first one, perhaps, + +but there's no canonical +place to put it in. + +This just goes off to infinity +and just falls off the edge. + +It's a little bit +like differentiation. + +Right? + +AUDIENCE: Yeah. + +I guess it loses +some information. + +ARAM HARROW: It loses +some information. + +That's right. + +It's a little bit weird, right? + +Because how many +numbers do you have + +before you applied +the left shift? + +Infinity. + +How many do you have after +you applied the left shift? + +Infinity. + +But you lost some information. + +So you have to be a little +careful with the infinities. + +OK + +The right shift. + +Here it's not so +obvious what to do. + +We've kind of made space +for another number, + +and so we have to put something +in that first position. + +So this will be question +mark x1, x2, dot, dot, dot. + +Any guesses what should +go in the question mark? + +AUDIENCE: 0? + +ARAM HARROW: 0. + +Right. + +And why should that be 0? + +AUDIENCE: [INAUDIBLE]. + +ARAM HARROW: What's that? + +AUDIENCE: So it's linear. + +ARAM HARROW: Otherwise +it wouldn't be linear. + +Right. + +So imagine what +happens if you apply + +the right shift to +the all 0 string. + +If you were to get +something non-zero here, + +then you would map to the 0 +vector to a non-zero vector. + +But, by linearity, +that's impossible. + +Because I could take any vector +and multiply it by the scalar + +0 and I get the vector 0. + +And that should be +equal to the scalar + +0 multiplied by +the output of it. + +And so that means that T +should always map 0 to 0. + +T should always map the +vector 0 to the vector 0. + +And so if we want right shift +to be a linear operator, + +we have to put a 0 in there. + +And this one is strange also +because it creates more space + +but still preserves +all of the information. + +So two other small examples +of linear operators + +that come up very often. + +There's, of course, +the 0 operator, + +which takes any vector +to the 0 vector. + +Here I'm not distinguishing +between-- here + +the 0 means an operator, +here it means a vector. + +I guess I can +clarify it that way. + +And this is, of course, linear +and sends any vector space + +to itself. + +One important thing +is that the output + +doesn't have to be the +entire vector space. + +The fact that it sends +a vector space to itself + +only means that the output is +contained within the vector + +space. + +It could be something +as boring is + +0 that just sends all the +vectors to a single point. + +And finally, one other +important operator + +is the identity operator +that sends-- actually I + +won't use the arrows here. + +We'll get used to +the mathematical way + +of writing it-- that sends +any vector to itself. + +Those are a few +examples of operators. + +I guess you've seen already +kind of the more familiar + +matrix-type of operators, +but these show you + +also the range of +what is possible. + +So the space l of v +of all operators-- + +I want to talk now +about its properties. + +So l of v is the space of all +linear maps from v to itself. + +So this is the space of +maps on a vector space, + +but itself is also +a vector space. + +So the set of operators +satisfies all the axioms + +of a vector space. + +It contains a 0 operator. + +That's this one right here. + +It's closed under a +linear combination. + +If I add together +two linear operators, + +I get another linear operator. + +It's closed under a +scalar multiplication. + +If I multiply a linear +operator by a scalar, + +I get another linear +operator, et cetera. + +And so everything we can +do on a vector space, + +like finding a +basis and so on, we + +can do for the space +of linear operators. + +However, in addition to having +the vector space structure, + +it has an additional structure, +which is multiplication. + +And here we're finally +making use of the fact + +that we're talking about +linear maps from a vector space + +to itself. + +If we were talking +about maps from v to w, + +we couldn't necessarily multiply +them by other maps from v to w, + +we could only multiply them by +maps from w to something else. + +Just like how, if +you're multiplying + +rectangular matrices, +the multiplication is not + +always defined if the +dimensions don't match up, + +But since these operators +are like square matrices, + +multiplication is +always defined, + +and this can be used to prove +many nice things about them. + +So this type of +structure being a vector + +space of multiplication +makes it, in many ways, + +like a field-- like real +numbers or complexes-- + +but without all +of the properties. + +So the properties that the +multiplication does have first + +is that it's associative. + +So let's see what +this looks like. + +So if we have a times bc +is equal to ab times c. + +And the way we can +check this is just + +by verifying the action +of this on any vector. + +So an operator is defined +by its action and all + +of the vectors in +a vector space. + +So the definition +of ab can be thought + +of as asking how does it act +on all the possible vectors? + +And this is defined just in +terms of the action of a and b + +as you first apply b +and then you apply A. + +So this can be thought +of as the definition + +of how to multiply operators. + +And then from this, +you can easily + +check the associativity property +that in both cases, however + +you write it out, you +obtain A of B of C of v. + +I'm writing out +all the parentheses + +just to sort of emphasize +this is C acting on v, + +and then B acting on C of v, and +then A acting on all of this. + +The fact that this is equal-- +that this is the same no matter + +how A, B, and C are +grouped is again + +part of what let's us +justify this right here, + +where we drop-- we just +don't use parentheses + +when we have operators acting. + +So, yes, we have the +associative property. + +Another property of +multiplication that operators + +satisfy is the existence +of an identity. + +That's just the +identity operator, here, + +which for any vector space +can always be defined. + +But there are other +properties of multiplication + +that it doesn't have. + +So inverses are +not always defined. + +They sometimes are. + +I can't say that a matrix +is never invertible, + +but for things like the +reals and the complexes, + +every nonzero element +has an inverse. + +And for matrices, +that's not true. + +And another property-- a +more interesting one that + +these lack-- is that the +multiplication is not + +commutative. + +So this is something that +you've seen for matrices. + +If you multiply two +matrices, the order matters, + +and so it's not surprising that +same is true for operators. + +And just to give a +quick example of that, + +let's look at this example +one here with polynomials. + +And let's consider S times +T acting on the monomial x + +to the n. + +So T is differentiation +so it sends + +this to n times x +to the n minus 1. + +So we get S times n, +x to the n minus 1. + +Linearity means we can move +the n past the S. S acting here + +multiplies by x, and so +we get n times x to the n. + +Whereas if we did +the other order, + +we get T times S acting +on x to the n, which + +is x to the n plus 1. + +When you differentiate this you +get n plus 1 times x to the n. + +So these numbers are +different meaning + +that S and T do not commute. + +And it's kind of cute to +measure to what extent do they + +not commute. + +This is done by the commutator. + +And what these equations say +is that if the commutator acts + +on x to the n, then +you get n plus 1 times + +x to the n minus n +times x to the n, + +which is just x to the n. + +And we can write this +another way as identity + +times x to the n. + +And since this is true +for any choice of n, + +it's true for what +turns out to be + +a basis for the +space of polynomials. + +So 1x, x squared, +x cubed, et cetera, + +these span the space +of polynomials. + +So if you know what an +operator does and all + +of the x to the +n's, you know what + +it does on all the polynomials. + +And so this means, actually, +that the commutator + +of these two is the identity. + +And so the significance +of this is-- well, + +I won't dwell on the physical +significance of this, + +but it's related to what you've +seen for position and momentum. + +And essentially the fact +that these don't commute + +is actually an important +feature of the theory. + +So these are some of +the key properties + +of the space of operators. + +I want to also now +tell you about some + +of the key properties +of individual operators. + +And basically, if +you're given an operator + +and want to know the +gross features of it, + +what should you look at? + +So one of these things is the +null space of an operator. + +So this is the set of +all v, of all vectors, + +that are killed by the operator. + +They're sent to 0. + +In some case-- so this will +always include the vector 0. + +So this always at least includes +the vector 0, but in some cases + +it will be a lot bigger. + +So for the identity +operator, the null space + +is only the vector 0. + +The only thing that gets +sent to 0 is 0 itself. + +Whereas, for the 0 operator, +everything gets sent to 0. + +So the null space is +the entire vector space. + +For left shift, the null space +is only 0 itself-- sorry, + +for right shift the null +space is only 0 itself. + +And what about for left shift? + +What's the null space here? + +Yeah? + +AUDIENCE: Some numer with a +string of 0s following it. + +ARAM HARROW: Right. + +Any sequence where +the first number + +is arbitrary, but everything +after the first number is 0. + +And so from all +of these examples + +you might guess that this +is a linear subspace, + +because in every case it's been +a vector space, and, in fact, + +this is correct. + +So this is a subspace +of v because, if there's + +a vector that gets sent +to 0, any multiple of it + +also will be sent to 0. + +And of the two vectors +that get sent to 0, + +their sum will +also be sent to 0. + +So the fact that it's +a linear subspace + +can be a helpful way of +understanding this set. + +And it's related to the +properties of T as a function. + +So for a function we often want +to know whether it's 1 to 1, + +or injective, or whether it's +[? onto ?] or surjective. + +And you can check that +if T is injective, + +meaning that if u is not +equal to v, then T of u + +is not equal to T of +v. So this property, + +that T maps distinct vectors +two distinct vectors, + +turns out to be equivalent +to the null space + +being only the 0 vector. + +So why is that? + +This statement here, that +whenever u is not equal to v, + +T of u is not equal +to T of v, another way + +to write that is whenever u is +not equal to v, T of u minus v + +is not equal to 0. + +And if you look +at this statement + +a little more carefully, +you'll realize + +that all we cared about on +both sides was u minus v. Here, + +obviously, we care +about u minus v. Here + +we only care if u +is not equal to v. + +So that's the same as saying +if u minus v is non-zero, + +then T of u minus v is non-zero. + +And this in turn is +equivalent to saying + +that the null space +of T is only 0. + +In other words, the set of +vectors that get sent to 0 + +consists only of +the 0 vector itself. + +So the null space +for linear operators + +is how we can characterize +whether they're 1 to 1, + +whether they destroy +any information. + +The other subspace that will +be important that we will use + +is the range of an operator. + +So the range of an operator, +which we can also just + +write as T of v, is the set of +all points that vectors in v + +get mapped to. + +So the set of all Tv +for some vector, v. + +So this, too, can be +shown to be a subspace. + +And that's because-- it takes +a little more work to show it, + +but not very much-- if there's +something in the output of T, + +then whatever the +corresponding input is + +we could have multiplied +that by a scalar. + +And then the +corresponding output also + +would get multiplied +by a scalar, + +and so that, too, +would be in the range. + +And so that means that +for anything in the range, + +we can multiply it by +any scalar and again get + +something in the range. + +Similarly for addition. + +A similar argument +shows that the range + +is closed under addition. + +So indeed, it's a +linear subspace. + +Again, since it's a linear +subspace, it always contains 0. + +And depending on the operator, +may contain a lot more. + +So whereas the null +space determined + +whether T was +injective, the range + +determines whether +T is surjective. + +So the range of T equals v if +and only if T is surjective. + +And here this is simply the +definition of being surjective. + +It's not really a theorem +like it was in the case of T + +being injective. + +Here that's really what +it means to be surjective + +is that your output +is the entire space. + +So one important +property of the range + +of the null space whenever +v is finite dimensional + +is that the dimension of v +is equal to the dimension + +of the null space plus the +dimension of the range. + +And this is actually +not trivial to prove. + +And I'm actually not going +to prove it right now. + +But the intuition +of it is as follows. + +Imagine that v is some +n dimensional space + +and the null space +has dimension k. + +So that means you have input +of n degrees of freedom, + +but T kills k of n. + +And so k at different +degrees of freedom, + +no matter how you vary them, +have no effect on the output. + +They just get mapped to 0. + +And so what's left are n +minus k degrees of freedom + +that do affect the outcome. + +Where, if you vary them, it does +change the output in some way. + +And those correspond to +the n minus k dimensions + +of the range. + +And if you want +to get formal, you + +have to formalize +what I was saying + +about what's left is n minus k. + +If you talk about something +like the orthogonal + +complement or completing +a basis or in some way + +formalize that intuition. + +And, in fact, you can +do a little further, + +and you can decompose the space. + +So this is just +dimensions counting. + +You can even decompose the +space into the null space + +and the complement of that +and show that T is 1 to 1 + +on the complement +of the null space. + +But for now, I think this is +all that we'll need for now. + +Any questions so far? + +Yeah? + +AUDIENCE: Why isn't the null +space part of the range? + +ARAM HARROW: Why isn't +it part of the range? + +AUDIENCE: So you're +taking T of v + +and null space is just the +special case when T of v + +is equal to 0. + +ARAM HARROW: Right. + +So the null space are all +of the-- This theorem, + +I guess, would be a little bit +more surprising if you realized + +that it works not +only for operators, + +but for general linear maps. + +And in that case, the range +is a subset space of w. + +Because the range +is about the output. + +And the null space is +a [? subset ?] space + +of v, which is +part of the input. + +And so in that case, +they're not even comparable. + +The vectors might just +have different lengths. + +And so it can never-- like +the null space in a range, + +in that case, would live in +totally different spaces. + +So let me give you a +very simple example. + +Let's suppose that T is +equal to 3, 0, minus 1, 4. + +So just a diagonal +4 by 4 matrix. + +Then the null space +would be the span + +of e2, that's the vector with +a 1 in the second position. + +And the range would be +the span of e1, e3, in e4. + +So in fact, usually it's +the opposite that happens. + +The null space in +the range are-- + +in this case they're actually +orthogonal subspaces. + +But this picture is +actually a little bit + +deceptive in how nice it is. + +So if you look at +this, total space + +is 4, four dimensions, +it divides up + +into one dimension +that gets killed, + +and three dimensions where +the output still tells you + +something about the +input, where there's + +some variation of the output. + +But this picture makes it seem-- +the simplicity of this picture + +does not always exist. + +A much more horrible +example is this matrix. + +So what's the null +space of this matrix? + +Yeah? + +AUDIENCE: You just don't care +about the upper [INAUDIBLE]. + +ARAM HARROW: You don't care +about the-- informally, + +it's everything of this form. + +Everything with something +in the first position, + +0 in the second position. + +In other words, +it's the span of e1. + +What about the range? + +AUDIENCE: [INAUDIBLE]. + +ARAM HARROW: What's that? + +Yeah? + +AUDIENCE: [INAUDIBLE]. + +ARAM HARROW: It's actually-- + +AUDIENCE: Isn't it e1? + +ARAM HARROW: It's also e1. + +It's the same thing. + +So you have this intuition +that some degrees of freedom + +are preserved and +some are killed. + +And here they look +totally different. + +And there they look the same. + +So you should be a +little bit nervous + +about trying to +apply that intuition. + +You should be reassured that +at least the theorem is still + +true. + +At least 1 plus 1 is equal to 2. + +We still have that. + +But the null space and the +range are the same thing here. + +And the way around +that paradox-- Yeah? + +AUDIENCE: So can you +just change the basis-- + +is there always +a way of changing + +the basis of the matrix? + +In this case it +becomes [INAUDIBLE]? + +Or not necessarily? + +ARAM HARROW: No. + +It turns out that, even +with the change of basis, + +you cannot guarantee that the +null space and the range will + +be perpendicular. + +Yeah? + +AUDIENCE: What if you reduce +it to only measures on the-- + +or what if you reduce the +matrix of-- [? usability ?] + +on only [INAUDIBLE] +on the diagonal? + +ARAM HARROW: Right Good. + +So if you do that, then-- if you +do row [? eduction ?] with two + +different row and +column operations, + +then what you've done is +you have a different input + +and output basis. + +And so that would-- then +once you kind of unpack + +what's going on in +terms of the basis, + +then it would turn out +that you could still + +have strange behavior like this. + +What your intuition +is based on is + +that if the matrix is +diagonal in some basis, + +then you don't +have this trouble. + +But the problem is that not all +matrices can be diagonalized. + +Yeah? + +AUDIENCE: So is it +just the trouble + +that the null is +what you're acting on + +and the range is +what results from it? + +ARAM HARROW: Exactly. + +And they could even +live in different space. + +And so they really just don't-- +to compare them is dangerous. + +So it turns out that the +degrees of freedom corresponding + +to the range-- what +you should think about + +are the degrees of freedom +that get sent to the range. + +And in this case, +that would be e2. + +And so then you can say that +e1 gets sent to 0 and e2 + +gets sent to the range. + +And now you really have +decomposed the input space + +into two orthogonal parts. + +And because we're talking +about a single space, the input + +space, it actually makes +sense to break it up + +into these parts. + +Whereas here, they look like +they're the same, but really + +input and output +spaces you should + +think of as +potentially different. + +So this is just a mild +warning about reading too much + +into this formula, even +though it's the rough idea + +it counting degrees of freedom +is still roughly accurate. + +So I want to say one more thing +about properties of operators, + +which is about invertibility. + +And maybe I'll leave +this up for now. + +So we say that a +linear operator, T, + +has a left inverse, S, if +multiplying T on the left by s + +will give you the identity. + +And T has a right +inverse, S prime, + +you can guess what +will happen here + +if multiplying T on the right +by S prime gives you identity. + +And what if T has both? + +Then in that next +case, it turns out + +that S and S prime +have to be the same. + +So here's the proof. + +So if both exist, then S is +equal to s times identity-- + +by the definition +of the identity. + +And then we can replace +identity with TS prime. + +Then we can group these and +cancel them and get S prime. + +So if a matrix has both a +left and a right inverse, + +then it turns out that the left +and right inverse are the same. + +And in this case, we say +that T is invertible, + +and we define T inverse to be S. + +One question that +you often want to ask + +is when do left to +right inverses exist? + +Actually, maybe +I'll write it here. + +Intuitively, there should +exist a left inverse + +when, after we've +applied T, we haven't + +done irreparable damage. + +So whatever we're +left with, there's + +still enough information +that some linear operator + +can restore our original vector +and give us back the identity. + +And so that condition +is when-- of not doing + +irreparable damage, of +not losing information, + +is asking essentially +whether T is injective. + +So there exists a left inverse +if and only if T is injective. + +Now for a right +inverse the situation + +is sort of dual to this. + +And here what we +want-- we can multiply + +on the right by +whatever we like, + +but there won't be +anything on the left. + +So after the action of T, +there won't be any further room + +to explore the +whole vector space. + +So the output of T had better +cover all of the possibilities + +if we want to be able to achieve +identity by multiplying T + +by something on the right. + +So any guesses for +what the condition + +is for having a right inverse? + +AUDIENCE: Surjective. + +ARAM HARROW: Surjective. + +Right. + +So there exists a right inverse +if and only if T is surjective. + +Technically, I've only +proved one direction. + +My hand waving just now proved +that, if T is not injective, + +there's no way it will +have a left inverse. + +If it's not surjective, +there's no way + +it'll have a right inverse. + +I haven't actually proved +that, if it is injective, + +there is such a left inverse. + +And if it is surjective, there +is such a right universe. + +But those I think +are good exercises + +for you to do to make sure you +understand what's going on. + +This takes us part +of the way there. + +In some cases our lives +become much easier. + +In particular, if v +is finite dimensional, + +it turns out that all +of these are equivalent. + +So T is injective if and +only if T is surjective if + +and only if T is invertible. + +And why is this? + +Why should it be true +that T is surjective if + +and only if T is injective? + +Why should those be +equivalent statements? + +Yeah? + +AUDIENCE: This isn't really +a rigorous statement, + +but if the intuition of it is +a little bit that you're taking + +vectors in v to vectors in v. + +ARAM HARROW: Yeah. + +AUDIENCE: And so your +mapping is 1 to 1 + +if and only if every vector +is mapped to, because then + +you're not leaving anything out. + +ARAM HARROW: That's right. + +In failing to be injective +and failing to be surjective + +both look like +losing information. + +Failing to be +injective means I'm + +sending a whole non-zero +vector and its multiples + +to 0, that's a degree +of freedom lost. + +Failing to be surjective +means once I look + +at all the degrees +of freedom I reach, + +I haven't reached everything. + +So they intuitively +look the same. + +So that's the right intuition. + +There's a proof, +actually, that makes + +use of something on a +current blackboard though. + +Yeah? + +AUDIENCE: Well, you +need the dimensions + +of-- so if the +[INAUDIBLE] space is 0, + +you need dimensions of +[? the range to p. ?] + +ARAM HARROW: Right. + +Right. + +So from this dimensions +formula you immediately get + +because if this is 0, then +this is the whole vector space. + +And if this is non-zero, this +is not the whole vector space. + +And this proof is sort +of non-illuminating + +if you don't know the +proof of that thing-- which + +I apologize for. + +But also, you can see +immediately from that + +that we've used the fact +that v is finite dimensional. + +And it turns out this +equivalence breaks down + +if the vector space is +infinite dimensional. + +Which is pretty weird. + +There's a lot of subtleties +of infinite dimensional vector + +spaces that it's easy to +overlook if you build up + +your intuition from matrices. + +So does anyone have an +idea of a-- so let's think + +of an example of a +vector of something + +that is on an infinite +dimensional space that's + +surjective but not injective. + +Any guesses for +such an operation? + +Yeah? + +AUDIENCE: The left shift. + +ARAM HARROW: Yes. + +You'll notice I didn't erase +this blackboard strategically. + +Yes. + +The left shift +operator is surjective. + +I can prepare any +vector here I like just + +by putting it into the x2, +x3, dot, dot, dot parts. + +So the range is everything, +but it's not injective + +because it throws away +the first register. + +It's maps things with +it a non-zero element + +in the first position and +0's everywhere else to 0. + +So this is surjective +not injective. + +On the other hand, +if you want something + +that's injective +and not surjective, + +you don't have to look +very far, the right shift + +is injective and not surjective. + +It's pretty obvious +it's not surjective. + +There's that 0 there which +definitely means it cannot + +achieve any vector. + +And it's not too hard +to see it's injective. + +It hasn't lost any information. + +It's like you're in the +hotel that's infinitely long + +and all the rooms are full and +the person at the front desk + +says, no problem. + +I'll just move everyone +down one room to the right, + +and you can take the first room. + +So that policy is +injective-- you'll + +always get a room to +yourself-- and made + +possible by having an infinite +dimensional vector space. + +So in infinite dimensions +we cannot say this. + +Instead, we can say +that T is invertible if + +and only if T is +injective and surjective. + +So this statement +is true in general + +for infinite dimensional, +whatever, vector spaces. + +And only in the nice special +case of finite dimensions + +do we get this equivalence. + +Yeah? + +AUDIENCE: Can the range and null +space of T a [INAUDIBLE] of T + +the operator again use a +vector space [INAUDIBLE]? + +ARAM HARROW: Yes. +the question was + +do the null space in a range +are they properties just of T + +or also of v? + +And definitely you +also need to know + +v. The way I've +been writing it, T + +is implicitly defined +in terms of v, + +which in turn is +implicitly defined + +in terms of the field, f. + +And all these things +can make a difference. + +Yes? + +AUDIENCE: So do you have to +be a bijection for it to be-- + +ARAM HARROW: That's right. + +That's right. + +Invertible is the +same a bijection. + +So let me now try and +relate this to matrices. + +I've been saying +that operators are + +like the fancy mathematician's +form of matrices. + +If you're Arrested +Development fans, + +it's like magic trick +versus an illusion. + +But are they different or not +depends on your perspective. + +There are advantages to +seeing it both ways, I think. + +So let me tell you +how you can view + +an operator in a matrix form. + +The way to do this-- +and the reason + +why matrices are not universally +loved by mathematicians + +is I haven't specified +a basis this whole time. + +But if I want a +matrix, all I needed + +was a vector space +and a function-- + +a linear function between +two vector spaces-- + +or, sorry, from a +vector space to itself. + +But if I want a matrix, I +need additional structure. + +And mathematicians try to +avoid that whenever possible. + +But if you're willing to take +this additional structure-- so + +if you choose a +basis v1 through vn-- + +it turns out you +can get a simpler + +form of the operator that's +useful to compute with. + +So why is that? + +Well, the fact that +it's a basis that + +means that any v can be +written as linear combinations + +of these basis elements where a1 +though an belong to the field. + +And since T is linear, +if T acts on v, + +we can rewrite it +in this way, and you + +see that the entire +action is determined + +by T acting on v1 through vn. + +So think about-- if +you wanted to represent + +an operator in a +computer, you'd say, + +well, there's an infinite +number of input vectors. + +And for each input vector +I have to write down + +the output vector. + +And this says, no, you don't. + +You only need to restore +on your computer what + +does T do to v1, what does +T do to v2, et cetera. + +So that's good. + +Now you only have to +write down n vectors, + +and since these +factors in turn can + +be expressed in +terms of the basis, + +you can express this just in +terms of a bunch of numbers. + +So let's further expand +Tvj in this basis. + +And so there's some coefficient. + +So it's something times v1 plus +something times v2 something + +times vn. + +And I'm going to-- these +somethings are a function of T + +so I'm just going to call this +T sub 1j, T sub 2j, T sub nj. + +And this whole thing I can write +more succinctly in this way. + +And now all I need +are these T's of ij, + +and that can completely +determine for me the action + +of T because this +Tv here-- so Tv + +we can write as a sum +over j of T times ajvj. + +And we can move +the aj past the T. + +And then if we +expand this out, we + +get that it's a sum over i from +1 to n, sum over j from 1 to n, + +of Tijajvi. + +And so if we act on +in general vector, v, + +and we know the coefficients +of v in some basis, + +then we can re-express it +in that basis as follows. + +And this output in +general can always + +be written in the basis +with some coefficients. + +So we could always +write it like this. + +And this formula tells you what +those coefficients should be. + +They say, if your input vector +has coefficients a1 through an, + +then your output vector has +coefficients b1 through bn, + +where the b sub i are +defined by this sum. + +And of course there's a +more-- this formula is one + +that you've seen +before, and it's often + +written in this +more familiar form. + +So this is now the familiar +matrix-vector multiplication. + +And it says that the b vector +is obtained from the a vector + +by multiplying it by +the matrix of these Tij. + +And so this T is +the matrix form-- + +this is a matrix form +of the operator T. + +And you might find this +not very impressive. + +You say, well, +look I already knew + +how to multiply a +matrix by vector. + +But what I think is nice about +this is that the usual way + +you learn linear +algebra if someone says, + +a vector is a list of numbers. + +A matrix is a +rectangle of numbers. + +Here's are the rules for +what you do with them. + +If you want to +put them together, + +you do it in this way. + +Here this was not an axiom +of the theory at all. + +We just started with linear +maps from one vector space + +to another one and +the idea of a basis + +as something that you +can prove has to exist + +and you can derive +matrix multiplication. + +So matrix +multiplication emerges-- + +or matrix-vector +multiplication emerges + +as a consequence of the theory +rather than as something + +that you have to put in. + +So that, I think, is what's +kind of cute about this + +even if it comes back +on the end to something + +that you had been taught before. + +Any questions about that? + +So this is matrix-vector +multiplication. + +You can similarly derive +matrix-matrix multiplication. + +So if we have two +operators, T and S, + +and we act on a +vector, v sub k-- + +and by what I +argued before, it's + +enough just to know how they +act on the basis vectors. + +You don't need to +know-- and once you + +do that, you can figure out +how they act on any vector. + +So if we just expand out +what we wrote before, + +this is equal to T times +the sum over j of Sjkvj. + +So Svk can be +re-expressed in terms + +of the basis with +some coefficients. + +And those coefficients +will depend + +on the vector you start +with, k, and the part + +of the basis that you're +using to express it with j. + +Then we apply the same +thing again with T. + +We get-- this is sum over +i, sum over j TijSjkvi. + +And now, what have we done? + +TS is an operator and +when you act of vk + +it spat out something that's +a linear combination of all + +the basis states, v sub i, +and the coefficient of v sub i + +is this part in the parentheses. + +And so this is the +matrix element of TS. + +So the ik matrix element of ts +is the sum over j of Tijsjk. + +And so just like we derived +matrix-vector multiplication, + +here we can derive +matrix-matrix multiplication. + +And so what was originally just +sort of an axiom of the theory + +is now the only +possible way it could + +be if you want to define +operator multiplication is + +first one operator acts, +than the other operator acts. + +So in terms of this-- +so this, I think, + +justifies why you +can think of matrices + +as a faithful +representation of operators. + +And once you've chosen +a basis, they can-- + +the square full +of numbers becomes + +equivalent to the abstract +map between vector spaces. + +And the equivalent-- they're +so equivalent that I'm just + +going to write things +like equal signs. + +Like I'll write identity +equals a bunch of 1's + +down the diagonal, right? + +And not worry about the +fact that technically this + +is an operator and +this is a matrix. + +And similarly, the 0 matrix +equals a matrix full of 0's. + +Technically, we +should write-- if you + +want to express the +basis dependence, + +you can write things like +T parentheses-- sorry, + +let me write it like this. + +If you really want to be very +explicit about the basis, + +you could use this to +refer to the matrix. + +Just to really emphasize +that the matrix depends + +not only on the operator, but +also on your choice of basis. + +But we'll almost never +bothered to do this. + +We usually just sort of say +it in words what the basis is. + +So matrices are an important +calculational tool, + +and we ultimately want to +compute numbers of physical + +quantities so we cannot always +spend our lives in abstract + +vector spaces. + +But the basis dependence +is an unfortunate thing. + +A basis is like a choice +of coordinate systems, + +and you really don't want +your physics to depend on it, + +and you don't want quantity if +you compute to be dependent on. + +And so we often +want to formulate-- + +we're interested in quantities +that are basis independent. + +And in fact, that's a big +point of the whole operator + +picture is that because +the quantities we want + +are ultimately +basis independent, + +it's nice to have language that +is itself basis independent. + +Terminology and theorems +that do not refer to a basis. + +I'll mention a few basis +independent quantities, + +and I won't say too +much more about them + +because you will prove +properties [INAUDIBLE] + +on your p set, but one +of them is the trace + +and another one is +the determinant. + +And when you first +look at them-- OK, + +you can check that each +one is basis independent, + +and it really looks +kind of mysterious. + +I mean, like, who pulled +these out of the hat? + +They look totally +different, right? + +They don't look remotely +related to each other. + +And are these all there is? + +Are there many more? + +And it turns out that, at least +for matrices with eigenvalues, + +these can be seen as members +of a much larger family. + +And the reason is that +the trace turns out + +to be the sum of +all the eigenvalues + +and the determinant +turns out to be + +the product of all +of the eigenvalues. + +And in general, we'll see +in a minute, that basis + +independent things-- +actually, not in a minute. + +In a future lecture-- that +basis independent things + +are functions of eigenvalues. + +And furthermore, that don't +care about the ordering + +of the eigenvalues. + +So they're symmetric +functions of eigenvalues. + +And then it starts to make +a little bit more sense. + +Because if you talk about +symmetric polynomials, + +those are two of the most +important ones where you just + +add up all the things and when +you multiply all the things. + +And then, if you +add this perspective + +of symmetric polynomial +of the eigenvalue, + +then you can cook up other +basis independent quantities. + +So this is actually +not the approach + +you should take on the p set. + +The [? p set ?] +asks you to prove + +more directly that the +trace is basis independent, + +but the sort of framework +that these fit into + +is symmetric functions +of eigenvalues. + +So I want to say a little +bit about eigenvalues. + +Any questions about +matrices before I do? + +So eigenvalues-- +I guess, these are + +basis independent quantities. + +Another important basis +independent quantity, + +or property of a matrix, is +its eigenvalue-eigenvector + +structure. + +The place where +eigenvectors come from + +is by considering a slightly +more general thing, which + +is the idea of an +invariant subspace. + +So we say that U is a +T invariant subspace + +if T of U-- this is an operator +acting on an entire subspace. + +So what do I mean by that? + +I mean the set of all TU +for vectors in the subspace. + +If T of U is contained in U. + +So I take a vector in this +subspace, act on it with T, + +and then I'm still +in the subspace + +no matter which vector I had. + +So some examples +that always work. + +The 0 subspace is invariant. + +T always maps it to itself. + +And the entire space, v, T +is a linear operator on v + +so by definition it +maps v to itself. + +These are called the +trivial examples. + +And usually when people talk +about non-trivial invariant + +subspaces they mean +not one of these two. + +The particular type that +we will be interested in + +are one dimensional ones. + +So this corresponds to a +direction that T fixes. + +So U-- this vector space +now can be written just + +as the span of a single vector, +U, and U being T invariant + +is equivalent to TU being +a mu, because they're just + +a single vector. + +So all I have to do is get +that single vector right + +and I'll get the +whole subspace right. + +And that, in turn, is equivalent +to TU being some multiple of U. + +And this equation +you've seen before. + +This is the familiar +eigenvector equation. + +And if it's a very, +very important equation + +it might be named +after a mathematician, + +but this one is so important +that two of the pieces of it + +have their own special name. + +So these are called-- lambda +is called an eigenvalue + +and U is called an eigenvector. + +And more or less it's true that +all of the solutions to this + +are called eigenvalues, +and all the solutions + +are called eigenvectors. + +There's one exception, +which is there's + +one kind of trivial solution +to this equation, which + +is when U is 0 this +equation is always true. + +And that's not very +interesting, but it's + +true for all values of lambda. + +And so that doesn't count +as being an eigenvalue. + +And you can tell a doesn't +correspond to 1D invariant + +subspace, right? + +It corresponds to a 0 +dimensional subspace, + +which is the trivial case. + +So we say that lambda +is an eigenvalue of T + +if Tu equals lambda U for +some non-zero vector, U. + +So the non 0 is crucial. + +And then the spectrum +of T is the collection + +of all eigenvalues. + +So there's something a little +bit asymmetric about this, + +which is we still +say that 0 vector is + +an eigenvector with all +the various eigenvalues, + +but we had to put this +here or everything + +would be an eigenvalue and it +wouldn't be very interesting. + +So the-- + +Oh, also I want to say this term +spectrum you'll see it other + +[INAUDIBLE]. + +You'll see spectral theory +or spectral this or that, + +and that means essentially +making use of the eigenvalues. + +So people talk about +partitioning a graph using + +eigenvalues of the +associated matrix, that's + +called spectral partitioning. + +And so throughout math, +this term is used a lot. + +So I have only +about three minutes + +left to tell-- so +I think I will not + +finish the eigenvalue discussion +but will just show you + +a few examples of +how it's not always + +as nice as you might expect. + +So one example +that I'll consider + +is the vector space will be +the reals, 3D real space, + +and the operator, T, will +be rotation about the z-axis + +by some small angle. + +Let's call it a theta +rotation about the z-axis. + +Turns out, if you write +this in matrix form, + +it looks like this. + +Cosine theta minus sine theta +0 sine theta cosine theta 0, 0, + +0, 0, 1. + +That 1 is because it +leaves the z-axis alone + +and then x and y get rotated. + +You can tell if theta +is 0 it does nothing + +so that's reassuring. + +And if theta does a +little bit, then it + +starts mixing the +x and y components. + +So that is the rotation matrix. + +So what is an +eigenvalue-- and anyone + +say what an eigenvalue +is of this matrix? + +AUDIENCE: 1. + +ARAM HARROW: 1. + +Good. + +And what's the eigenvector? + +AUDIENCE: The z basis vector. + +ARAM HARROW: The z basis vector. + +Right. + +So it fixes a z +basis vector so this + +is an eigenvector +with eigenvalue 1. + +Does it have any +other eigenvectors? + +Yeah? + +AUDIENCE: If you go to the +complex plane, then yes. + +ARAM HARROW: If you are talking +about complex numbers, then + +yes, it has complex eigenvalues. + +But if we're talking +about a real vector space, + +then it doesn't. + +And so this just has one +eigenvalue and one eigenvector. + +And if we were to get rid +of the third dimension-- + +so if we just had T-- and +let's be even simpler, + +let's just take theta +to be pi over 2. + +So let's just take a 90 +degree rotation in the plane. + +Now T has no eigenvalues. + +There are no vectors other +than 0 that it sends to itself. + +And so this is a +slightly unfortunate note + +to end the lecture on. + +You think, well, these +eigenvalues are great, + +but maybe they exist, +maybe they don't. + +And you'll see next +time part of the reason + +why we use complex numbers, +even though it looks + +like real space isn't complex, +is because any polynomial can + +be completely factored +in complex numbers, + +and every matrix has +a complex egeinvalue. + +OK, I'll stop here. \ No newline at end of file diff --git a/933cBlGFDcs.txt b/933cBlGFDcs.txt new file mode 100644 index 0000000000000000000000000000000000000000..0aaeac8e4336c954992f04c45eea90e7693f0130 --- /dev/null +++ b/933cBlGFDcs.txt @@ -0,0 +1,15571 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu right so you can see it's me + + align:start position:0% +ocw.mit.edu right so you can see it's me + + + align:start position:0% +ocw.mit.edu right so you can see it's me +again so George George can have a + + align:start position:0% +again so George George can have a + + + align:start position:0% +again so George George can have a +holiday again but it's he's not really + + align:start position:0% +holiday again but it's he's not really + + + align:start position:0% +holiday again but it's he's not really +having a real holiday because he's still + + align:start position:0% +having a real holiday because he's still + + + align:start position:0% +having a real holiday because he's still +he's actually sitting in and I guess one + + align:start position:0% +he's actually sitting in and I guess one + + + align:start position:0% +he's actually sitting in and I guess one +reason why we decided that he had to do + + align:start position:0% +reason why we decided that he had to do + + + align:start position:0% +reason why we decided that he had to do +that was because I I have to use his + + align:start position:0% +that was because I I have to use his + + + align:start position:0% +that was because I I have to use his +computer because he's he's written these + + align:start position:0% +computer because he's he's written these + + + align:start position:0% +computer because he's he's written these +talks in this + + align:start position:0% +talks in this + + + align:start position:0% +talks in this +strange uh application that I that + + align:start position:0% +strange uh application that I that + + + align:start position:0% +strange uh application that I that +doesn't run on my + + align:start position:0% +doesn't run on my + + + align:start position:0% +doesn't run on my +computer okay so now we're getting to uh + + align:start position:0% +computer okay so now we're getting to uh + + + align:start position:0% +computer okay so now we're getting to uh +today we're get we're just about getting + + align:start position:0% +today we're get we're just about getting + + + align:start position:0% +today we're get we're just about getting +into interesting stuff now seems rather + + align:start position:0% +into interesting stuff now seems rather + + + align:start position:0% +into interesting stuff now seems rather +a long time since the beginning of this + + align:start position:0% +a long time since the beginning of this + + + align:start position:0% +a long time since the beginning of this +course uh before we get into the real + + align:start position:0% +course uh before we get into the real + + + align:start position:0% +course uh before we get into the real +wave Optics uh which I'm sure everyone + + align:start position:0% +wave Optics uh which I'm sure everyone + + + align:start position:0% +wave Optics uh which I'm sure everyone +would agree is the most interesting part + + align:start position:0% +would agree is the most interesting part + + + align:start position:0% +would agree is the most interesting part +uh so this this this lecture uh is uh + + align:start position:0% +uh so this this this lecture uh is uh + + + align:start position:0% +uh so this this this lecture uh is uh +about + + align:start position:0% +about + + + align:start position:0% +about +interferometry uh and uh and then the + + align:start position:0% +interferometry uh and uh and then the + + + align:start position:0% +interferometry uh and uh and then the +next lecture I don't know how how much + + align:start position:0% +next lecture I don't know how how much + + + align:start position:0% +next lecture I don't know how how much +I'm going to get through today but uh + + align:start position:0% +I'm going to get through today but uh + + + align:start position:0% +I'm going to get through today but uh +the next lecture is about + + align:start position:0% +the next lecture is about + + + align:start position:0% +the next lecture is about +defraction uh so these are two + + align:start position:0% +defraction uh so these are two + + + align:start position:0% +defraction uh so these are two +techniques two two uh phenomena that are + + align:start position:0% +techniques two two uh phenomena that are + + + align:start position:0% +techniques two two uh phenomena that are +obviously very closely related to each + + align:start position:0% +obviously very closely related to each + + + align:start position:0% +obviously very closely related to each +other so so in this talk uh really two + + align:start position:0% +other so so in this talk uh really two + + + align:start position:0% +other so so in this talk uh really two +types of interferometer the Micon + + align:start position:0% +types of interferometer the Micon + + + align:start position:0% +types of interferometer the Micon +interferometer and the max Zander + + align:start position:0% + + + + align:start position:0% + +interferometer okay + + align:start position:0% +interferometer okay + + + align:start position:0% +interferometer okay +so um it took me a few minutes to + + align:start position:0% +so um it took me a few minutes to + + + align:start position:0% +so um it took me a few minutes to +understand this picture but anyway it + + align:start position:0% +understand this picture but anyway it + + + align:start position:0% +understand this picture but anyway it +looks a bit sort of messy but I but in + + align:start position:0% +looks a bit sort of messy but I but in + + + align:start position:0% +looks a bit sort of messy but I but in +the end I George Drew this obviously but + + align:start position:0% +the end I George Drew this obviously but + + + align:start position:0% +the end I George Drew this obviously but +otherwise I wouldn't be saying that uh + + align:start position:0% +otherwise I wouldn't be saying that uh + + + align:start position:0% +otherwise I wouldn't be saying that uh +but what this is showing then is trying + + align:start position:0% +but what this is showing then is trying + + + align:start position:0% +but what this is showing then is trying +to show how a wave varies both in + + align:start position:0% +to show how a wave varies both in + + + align:start position:0% +to show how a wave varies both in +distance and in time uh so the waves + + align:start position:0% +distance and in time uh so the waves + + + align:start position:0% +distance and in time uh so the waves +propagating along this Z Direction so if + + align:start position:0% +propagating along this Z Direction so if + + + align:start position:0% +propagating along this Z Direction so if +you look along this Zed axis you will + + align:start position:0% +you look along this Zed axis you will + + + align:start position:0% +you look along this Zed axis you will +see this uh amplitude variation given by + + align:start position:0% +see this uh amplitude variation given by + + + align:start position:0% +see this uh amplitude variation given by +the black line so a cosine type uh + + align:start position:0% +the black line so a cosine type uh + + + align:start position:0% +the black line so a cosine type uh +variation uh and then at any point any + + align:start position:0% +variation uh and then at any point any + + + align:start position:0% +variation uh and then at any point any +value of + + align:start position:0% +value of + + + align:start position:0% +value of +Zed uh you can see ploted in red how + + align:start position:0% +Zed uh you can see ploted in red how + + + align:start position:0% +Zed uh you can see ploted in red how +that how the amplitude will change with + + align:start position:0% +that how the amplitude will change with + + + align:start position:0% +that how the amplitude will change with +time along this axis here okay so you + + align:start position:0% +time along this axis here okay so you + + + align:start position:0% +time along this axis here okay so you +can see that you get a A sinusoidal + + align:start position:0% +can see that you get a A sinusoidal + + + align:start position:0% +can see that you get a A sinusoidal +variation in uh both in time and in + + align:start position:0% +variation in uh both in time and in + + + align:start position:0% +variation in uh both in time and in +space uh and uh and uh reminder here + + align:start position:0% +space uh and uh and uh reminder here + + + align:start position:0% +space uh and uh and uh reminder here +then how you can express this wave this + + align:start position:0% +then how you can express this wave this + + + align:start position:0% +then how you can express this wave this +is this is a + + align:start position:0% +is this is a + + + align:start position:0% +is this is a +wave uh a sinusoidal shaped wave which + + align:start position:0% +wave uh a sinusoidal shaped wave which + + + align:start position:0% +wave uh a sinusoidal shaped wave which +is moving in the positive Zed Direction + + align:start position:0% +is moving in the positive Zed Direction + + + align:start position:0% +is moving in the positive Zed Direction +and you can either express it in this + + align:start position:0% +and you can either express it in this + + + align:start position:0% +and you can either express it in this +form uh which is uh what you would + + align:start position:0% +form uh which is uh what you would + + + align:start position:0% +form uh which is uh what you would +actually measure if you could really + + align:start position:0% +actually measure if you could really + + + align:start position:0% +actually measure if you could really +measure it except that as we said before + + align:start position:0% +measure it except that as we said before + + + align:start position:0% +measure it except that as we said before +you can't really measure it because it's + + align:start position:0% +you can't really measure it because it's + + + align:start position:0% +you can't really measure it because it's +moving too quickly uh but normally we uh + + align:start position:0% +moving too quickly uh but normally we uh + + + align:start position:0% +moving too quickly uh but normally we uh +manipulate do the manipulations on the + + align:start position:0% +manipulate do the manipulations on the + + + align:start position:0% +manipulate do the manipulations on the +expressions using this complex + + align:start position:0% +expressions using this complex + + + align:start position:0% +expressions using this complex +notation uh because it makes it easier + + align:start position:0% +notation uh because it makes it easier + + + align:start position:0% +notation uh because it makes it easier +to do the the the sums uh and um yeah so + + align:start position:0% +to do the the the sums uh and um yeah so + + + align:start position:0% +to do the the the sums uh and um yeah so +this is showing + + align:start position:0% +this is showing + + + align:start position:0% +this is showing +then uh this is a particular value of + + align:start position:0% +then uh this is a particular value of + + + align:start position:0% +then uh this is a particular value of +distance then uh and showing how it + + align:start position:0% +distance then uh and showing how it + + + align:start position:0% +distance then uh and showing how it +changes here the value of the phase of + + align:start position:0% +changes here the value of the phase of + + + align:start position:0% +changes here the value of the phase of +this cosine wave uh at the time T equals + + align:start position:0% +this cosine wave uh at the time T equals + + + align:start position:0% +this cosine wave uh at the time T equals +not according to the value of Zed I + + align:start position:0% +not according to the value of Zed I + + + align:start position:0% +not according to the value of Zed I +guess that's what that's trying to + + align:start position:0% + + + + align:start position:0% + +show okay and then uh let's think now + + align:start position:0% +show okay and then uh let's think now + + + align:start position:0% +show okay and then uh let's think now +what happens if we've got some wave a + + align:start position:0% +what happens if we've got some wave a + + + align:start position:0% +what happens if we've got some wave a +plane wave propagating a along at some + + align:start position:0% +plane wave propagating a along at some + + + align:start position:0% +plane wave propagating a along at some +at an angle with the axis uh so here's + + align:start position:0% +at an angle with the axis uh so here's + + + align:start position:0% +at an angle with the axis uh so here's +this wave coming along uh which is um it + + align:start position:0% +this wave coming along uh which is um it + + + align:start position:0% +this wave coming along uh which is um it +it's going along a uh an axis a line the + + align:start position:0% +it's going along a uh an axis a line the + + + align:start position:0% +it's going along a uh an axis a line the +direction of of um propagation of the + + align:start position:0% +direction of of um propagation of the + + + align:start position:0% +direction of of um propagation of the +wave is along uh this direction which is + + align:start position:0% +wave is along uh this direction which is + + + align:start position:0% +wave is along uh this direction which is +an angle Theta uh with the axis uh and + + align:start position:0% +an angle Theta uh with the axis uh and + + + align:start position:0% +an angle Theta uh with the axis uh and +uh so you can see that when this wave uh + + align:start position:0% +uh so you can see that when this wave uh + + + align:start position:0% +uh so you can see that when this wave uh +reaches this plane's Z equals fixed here + + align:start position:0% +reaches this plane's Z equals fixed here + + + align:start position:0% +reaches this plane's Z equals fixed here +here so this is some plane where we + + align:start position:0% +here so this is some plane where we + + + align:start position:0% +here so this is some plane where we +might put a screen or detector or + + align:start position:0% +might put a screen or detector or + + + align:start position:0% +might put a screen or detector or +something uh you can see that the + + align:start position:0% +something uh you can see that the + + + align:start position:0% +something uh you can see that the +different parts of this pH front uh are + + align:start position:0% +different parts of this pH front uh are + + + align:start position:0% +different parts of this pH front uh are +going to strike uh this plane at + + align:start position:0% +going to strike uh this plane at + + + align:start position:0% +going to strike uh this plane at +different times uh or equivalent you you + + align:start position:0% +different times uh or equivalent you you + + + align:start position:0% +different times uh or equivalent you you +can say that if you uh look at this + + align:start position:0% +can say that if you uh look at this + + + align:start position:0% +can say that if you uh look at this +plane here uh this wave will experience + + align:start position:0% +plane here uh this wave will experience + + + align:start position:0% +plane here uh this wave will experience +exhibit different phase uh at different + + align:start position:0% +exhibit different phase uh at different + + + align:start position:0% +exhibit different phase uh at different +points along this line uh and um so this + + align:start position:0% +points along this line uh and um so this + + + align:start position:0% +points along this line uh and um so this +is what we're looking at here then uh as + + align:start position:0% +is what we're looking at here then uh as + + + align:start position:0% +is what we're looking at here then uh as +it says here the the path delay + + align:start position:0% +it says here the the path delay + + + align:start position:0% +it says here the the path delay +increases linearly with x uh so there'll + + align:start position:0% +increases linearly with x uh so there'll + + + align:start position:0% +increases linearly with x uh so there'll +be somewhere where uh this arrives at a + + align:start position:0% +be somewhere where uh this arrives at a + + + align:start position:0% +be somewhere where uh this arrives at a +phase of zero I guess is this point here + + align:start position:0% +phase of zero I guess is this point here + + + align:start position:0% +phase of zero I guess is this point here +uh and then on one side the phase is + + align:start position:0% +uh and then on one side the phase is + + + align:start position:0% +uh and then on one side the phase is +going to be uh positive and negative + + align:start position:0% +going to be uh positive and negative + + + align:start position:0% +going to be uh positive and negative +According to which way you go uh so + + align:start position:0% +According to which way you go uh so + + + align:start position:0% +According to which way you go uh so +mathematically this is how we express + + align:start position:0% +mathematically this is how we express + + + align:start position:0% +mathematically this is how we express +this uh so this is our wave the same as + + align:start position:0% +this uh so this is our wave the same as + + + align:start position:0% +this uh so this is our wave the same as +the previous uh uh slide uh but now the + + align:start position:0% +the previous uh uh slide uh but now the + + + align:start position:0% +the previous uh uh slide uh but now the +wave is moving at this angle Theta to + + align:start position:0% +wave is moving at this angle Theta to + + + align:start position:0% +wave is moving at this angle Theta to +the axis uh so we get this term this is + + align:start position:0% +the axis uh so we get this term this is + + + align:start position:0% +the axis uh so we get this term this is +our you remember we expressed this + + align:start position:0% +our you remember we expressed this + + + align:start position:0% +our you remember we expressed this +before as + + align:start position:0% +before as + + + align:start position:0% +before as +k.r uh for a wave moving in general in a + + align:start position:0% +k.r uh for a wave moving in general in a + + + align:start position:0% +k.r uh for a wave moving in general in a +direction uh R uh and um + + align:start position:0% +direction uh R uh and um + + + align:start position:0% +direction uh R uh and um +so um so this uh this so we can write + + align:start position:0% +so um so this uh this so we can write + + + align:start position:0% +so um so this uh this so we can write +this then this this is what uh + + align:start position:0% +this then this this is what uh + + + align:start position:0% +this then this this is what uh +uh is is in terms of our phaser + + align:start position:0% +uh is is in terms of our phaser + + + align:start position:0% +uh is is in terms of our phaser +representation right so we as before we + + align:start position:0% +representation right so we as before we + + + align:start position:0% +representation right so we as before we +write this as an e to the ey type thing + + align:start position:0% +write this as an e to the ey type thing + + + align:start position:0% +write this as an e to the ey type thing +uh and then we also this e to the minus + + align:start position:0% +uh and then we also this e to the minus + + + align:start position:0% +uh and then we also this e to the minus +I Omega t uh we just missed that out uh + + align:start position:0% +I Omega t uh we just missed that out uh + + + align:start position:0% +I Omega t uh we just missed that out uh +for clarity uh just because we don't + + align:start position:0% +for clarity uh just because we don't + + + align:start position:0% +for clarity uh just because we don't +want to have to write that every time uh + + align:start position:0% +want to have to write that every time uh + + + align:start position:0% +want to have to write that every time uh +so we we there's an e to the minus I Oma + + align:start position:0% +so we we there's an e to the minus I Oma + + + align:start position:0% +so we we there's an e to the minus I Oma +understood that we don't write uh and K + + align:start position:0% +understood that we don't write uh and K + + + align:start position:0% +understood that we don't write uh and K +of course is 2 pi over Lambda right so K + + align:start position:0% +of course is 2 pi over Lambda right so K + + + align:start position:0% +of course is 2 pi over Lambda right so K +is related inversely to the the um the + + align:start position:0% +is related inversely to the the um the + + + align:start position:0% +is related inversely to the the um the +um wavelength of the light uh and uh so + + align:start position:0% +um wavelength of the light uh and uh so + + + align:start position:0% +um wavelength of the light uh and uh so +this thing here this complex number here + + align:start position:0% +this thing here this complex number here + + + align:start position:0% +this thing here this complex number here +uh you can write this as e to the I + + align:start position:0% +uh you can write this as e to the I + + + align:start position:0% +uh you can write this as e to the I +fi like this uh where fi is the phase of + + align:start position:0% +fi like this uh where fi is the phase of + + + align:start position:0% +fi like this uh where fi is the phase of +the wave as a function which is a + + align:start position:0% +the wave as a function which is a + + + align:start position:0% +the wave as a function which is a +function of of of of position uh and uh + + align:start position:0% +function of of of of position uh and uh + + + align:start position:0% +function of of of of position uh and uh +and it can be written like this right so + + align:start position:0% +and it can be written like this right so + + + align:start position:0% +and it can be written like this right so +if we look at a particular value of Zed + + align:start position:0% +if we look at a particular value of Zed + + + align:start position:0% +if we look at a particular value of Zed +then this Zed is going to be fixed uh so + + align:start position:0% +then this Zed is going to be fixed uh so + + + align:start position:0% +then this Zed is going to be fixed uh so +uh so this this this part e to the i 2 + + align:start position:0% +uh so this this this part e to the i 2 + + + align:start position:0% +uh so this this this part e to the i 2 +pi over Lambda Z cos Theta is going to + + align:start position:0% +pi over Lambda Z cos Theta is going to + + + align:start position:0% +pi over Lambda Z cos Theta is going to +be fixed uh and the phase variation is + + align:start position:0% +be fixed uh and the phase variation is + + + align:start position:0% +be fixed uh and the phase variation is +only going to be because of this other + + align:start position:0% +only going to be because of this other + + + align:start position:0% +only going to be because of this other +part + + align:start position:0% + + + + align:start position:0% + +here so uh this is another + + align:start position:0% +here so uh this is another + + + align:start position:0% +here so uh this is another +example uh and uh so this uh shows uh + + align:start position:0% +example uh and uh so this uh shows uh + + + align:start position:0% +example uh and uh so this uh shows uh +spherical waves or rather distorted + + align:start position:0% +spherical waves or rather distorted + + + align:start position:0% +spherical waves or rather distorted +spherical waves they become because of + + align:start position:0% +spherical waves they become because of + + + align:start position:0% +spherical waves they become because of +uh the the advances in modern technology + + align:start position:0% +uh the the advances in modern technology + + + align:start position:0% +uh the the advances in modern technology +that love to distort everything you draw + + align:start position:0% +that love to distort everything you draw + + + align:start position:0% +that love to distort everything you draw +uh and make it so that it's not the + + align:start position:0% +uh and make it so that it's not the + + + align:start position:0% +uh and make it so that it's not the +right shape anymore uh but anyway this + + align:start position:0% +right shape anymore uh but anyway this + + + align:start position:0% +right shape anymore uh but anyway this +is a point + + align:start position:0% +is a point + + + align:start position:0% +is a point +source uh which is giving out spherical + + align:start position:0% +source uh which is giving out spherical + + + align:start position:0% +source uh which is giving out spherical +waves uh and you can see that uh here we + + align:start position:0% +waves uh and you can see that uh here we + + + align:start position:0% +waves uh and you can see that uh here we +put our screen again or whatever it is + + align:start position:0% +put our screen again or whatever it is + + + align:start position:0% +put our screen again or whatever it is +at Z equal + + align:start position:0% +at Z equal + + + align:start position:0% +at Z equal +z uh so you can see that these waves as + + align:start position:0% +z uh so you can see that these waves as + + + align:start position:0% +z uh so you can see that these waves as +they travel out here they're traveling a + + align:start position:0% +they travel out here they're traveling a + + + align:start position:0% +they travel out here they're traveling a +different distance in in before they get + + align:start position:0% +different distance in in before they get + + + align:start position:0% +different distance in in before they get +to the screen right so uh you can see + + align:start position:0% +to the screen right so uh you can see + + + align:start position:0% +to the screen right so uh you can see +that's going to do two things uh one is + + align:start position:0% +that's going to do two things uh one is + + + align:start position:0% +that's going to do two things uh one is +of course the ampl amplitude is going to + + align:start position:0% +of course the ampl amplitude is going to + + + align:start position:0% +of course the ampl amplitude is going to +Decay as 1 / R so the amplitude of the + + align:start position:0% +Decay as 1 / R so the amplitude of the + + + align:start position:0% +Decay as 1 / R so the amplitude of the +wave when it reaches out here is going + + align:start position:0% +wave when it reaches out here is going + + + align:start position:0% +wave when it reaches out here is going +to be smaller uh than the amplitude here + + align:start position:0% +to be smaller uh than the amplitude here + + + align:start position:0% +to be smaller uh than the amplitude here +uh but much more important is the phase + + align:start position:0% +uh but much more important is the phase + + + align:start position:0% +uh but much more important is the phase +effect because you can see um the phase + + align:start position:0% +effect because you can see um the phase + + + align:start position:0% +effect because you can see um the phase +actually might change tremendously + + align:start position:0% +actually might change tremendously + + + align:start position:0% +actually might change tremendously +because you see the because the + + align:start position:0% +because you see the because the + + + align:start position:0% +because you see the because the +wavelength is so small compared with + + align:start position:0% +wavelength is so small compared with + + + align:start position:0% +wavelength is so small compared with +these distances it means that you only + + align:start position:0% +these distances it means that you only + + + align:start position:0% +these distances it means that you only +have to go quite a small distance before + + align:start position:0% +have to go quite a small distance before + + + align:start position:0% +have to go quite a small distance before +you get a big change in the phase right + + align:start position:0% +you get a big change in the phase right + + + align:start position:0% +you get a big change in the phase right +so that's what we want to be able to + + align:start position:0% +so that's what we want to be able to + + + align:start position:0% +so that's what we want to be able to +quantify uh and uh so so here we're + + align:start position:0% +quantify uh and uh so so here we're + + + align:start position:0% +quantify uh and uh so so here we're +riding our spherical wave just like we + + align:start position:0% +riding our spherical wave just like we + + + align:start position:0% +riding our spherical wave just like we +did before so this is um George has kept + + align:start position:0% +did before so this is um George has kept + + + align:start position:0% +did before so this is um George has kept +this the same as he's said before you'll + + align:start position:0% +this the same as he's said before you'll + + + align:start position:0% +this the same as he's said before you'll +notice that it's got this funny pi over + + align:start position:0% +notice that it's got this funny pi over + + + align:start position:0% +notice that it's got this funny pi over +two in there uh which um he he + + align:start position:0% +two in there uh which um he he + + + align:start position:0% +two in there uh which um he he +introduced that before it has the effect + + align:start position:0% +introduced that before it has the effect + + + align:start position:0% +introduced that before it has the effect +of making this like a sign of course + + align:start position:0% +of making this like a sign of course + + + align:start position:0% +of making this like a sign of course +something minus Pi by two is like sign + + align:start position:0% +something minus Pi by two is like sign + + + align:start position:0% +something minus Pi by two is like sign +so it's it's like this is actually like + + align:start position:0% +so it's it's like this is actually like + + + align:start position:0% +so it's it's like this is actually like +a syn type + + align:start position:0% +a syn type + + + align:start position:0% +a syn type +function uh and um the that's the reason + + align:start position:0% +function uh and um the that's the reason + + + align:start position:0% +function uh and um the that's the reason +why that pi over is there it's so that + + align:start position:0% +why that pi over is there it's so that + + + align:start position:0% +why that pi over is there it's so that +uh it doesn't blow up when you look at + + align:start position:0% +uh it doesn't blow up when you look at + + + align:start position:0% +uh it doesn't blow up when you look at +what happens at x y = z tals + + align:start position:0% +what happens at x y = z tals + + + align:start position:0% +what happens at x y = z tals +n um if you didn't have the Pi / 2 there + + align:start position:0% +n um if you didn't have the Pi / 2 there + + + align:start position:0% +n um if you didn't have the Pi / 2 there +you'd have horrible Infinities so you + + align:start position:0% +you'd have horrible Infinities so you + + + align:start position:0% +you'd have horrible Infinities so you +avoid those by putting this Pi / 2 + + align:start position:0% +avoid those by putting this Pi / 2 + + + align:start position:0% +avoid those by putting this Pi / 2 +there and yeah so this is the radius R + + align:start position:0% +there and yeah so this is the radius R + + + align:start position:0% +there and yeah so this is the radius R +is just the sare < TK of X2 + y^2 + Z 2 + + align:start position:0% +is just the sare < TK of X2 + y^2 + Z 2 + + + align:start position:0% +is just the sare < TK of X2 + y^2 + Z 2 +and we get so this is K Rus Omega t + + align:start position:0% +and we get so this is K Rus Omega t + + + align:start position:0% +and we get so this is K Rus Omega t +and this is our r at the + + align:start position:0% +and this is our r at the + + + align:start position:0% +and this is our r at the +bottom and now we uh now we make an + + align:start position:0% +bottom and now we uh now we make an + + + align:start position:0% +bottom and now we uh now we make an +approximation which the approximation + + align:start position:0% +approximation which the approximation + + + align:start position:0% +approximation which the approximation +we're going to make uh is that we're not + + align:start position:0% +we're going to make uh is that we're not + + + align:start position:0% +we're going to make uh is that we're not +actually really looking at this geometry + + align:start position:0% +actually really looking at this geometry + + + align:start position:0% +actually really looking at this geometry +as shown in the picture uh but we're + + align:start position:0% +as shown in the picture uh but we're + + + align:start position:0% +as shown in the picture uh but we're +looking at the geometry when actually + + align:start position:0% +looking at the geometry when actually + + + align:start position:0% +looking at the geometry when actually +we're only looking in a small region + + align:start position:0% +we're only looking in a small region + + + align:start position:0% +we're only looking in a small region +near to the axis uh what that really in + + align:start position:0% +near to the axis uh what that really in + + + align:start position:0% +near to the axis uh what that really in +in practice in physical practice that + + align:start position:0% +in practice in physical practice that + + + align:start position:0% +in practice in physical practice that +means uh is that this this + + align:start position:0% +means uh is that this this + + + align:start position:0% +means uh is that this this +Zed znot becomes very large we're a long + + align:start position:0% +Zed znot becomes very large we're a long + + + align:start position:0% +Zed znot becomes very large we're a long +way away from the the the source and so + + align:start position:0% +way away from the the the source and so + + + align:start position:0% +way away from the the the source and so +uh we can think of this this value of + + align:start position:0% +uh we can think of this this value of + + + align:start position:0% +uh we can think of this this value of +Zed being uh very + + align:start position:0% +Zed being uh very + + + align:start position:0% +Zed being uh very +large sorry you understand my uh funny + + align:start position:0% +large sorry you understand my uh funny + + + align:start position:0% +large sorry you understand my uh funny +English language don't you when I talk + + align:start position:0% +English language don't you when I talk + + + align:start position:0% +English language don't you when I talk +about Zeds what you call Z's I've just + + align:start position:0% +about Zeds what you call Z's I've just + + + align:start position:0% +about Zeds what you call Z's I've just +suddenly realized that uh anyway uh so + + align:start position:0% +suddenly realized that uh anyway uh so + + + align:start position:0% +suddenly realized that uh anyway uh so +that so we've already had this before in + + align:start position:0% +that so we've already had this before in + + + align:start position:0% +that so we've already had this before in +earlier lectures as well this is a um a + + align:start position:0% +earlier lectures as well this is a um a + + + align:start position:0% +earlier lectures as well this is a um a +square root that we can expand by the + + align:start position:0% +square root that we can expand by the + + + align:start position:0% +square root that we can expand by the +binomial uh and assume that Zed is L + + align:start position:0% +binomial uh and assume that Zed is L + + + align:start position:0% +binomial uh and assume that Zed is L +much larger than X and Y uh so you you + + align:start position:0% +much larger than X and Y uh so you you + + + align:start position:0% +much larger than X and Y uh so you you +take out a factor of Zed and the square + + align:start position:0% +take out a factor of Zed and the square + + + align:start position:0% +take out a factor of Zed and the square +root becomes one uh becomes 1 plus a + + align:start position:0% +root becomes one uh becomes 1 plus a + + + align:start position:0% +root becomes one uh becomes 1 plus a +half + + align:start position:0% +half + + + align:start position:0% +half +something uh and uh So eventually you + + align:start position:0% +something uh and uh So eventually you + + + align:start position:0% +something uh and uh So eventually you +get this sort of thing uh so that's what + + align:start position:0% +get this sort of thing uh so that's what + + + align:start position:0% +get this sort of thing uh so that's what +we do at the inside this um phase term + + align:start position:0% +we do at the inside this um phase term + + + align:start position:0% +we do at the inside this um phase term +uh but the thing at the + + align:start position:0% +uh but the thing at the + + + align:start position:0% +uh but the thing at the +bottom uh we say uh we don't have to be + + align:start position:0% +bottom uh we say uh we don't have to be + + + align:start position:0% +bottom uh we say uh we don't have to be +so careful with that because uh it's not + + align:start position:0% +so careful with that because uh it's not + + + align:start position:0% +so careful with that because uh it's not +so sensitive to this this amplitude + + align:start position:0% +so sensitive to this this amplitude + + + align:start position:0% +so sensitive to this this amplitude +because all it does uh all it does uh is + + align:start position:0% +because all it does uh all it does uh is + + + align:start position:0% +because all it does uh all it does uh is +just changes the uh the magnitude of the + + align:start position:0% +just changes the uh the magnitude of the + + + align:start position:0% +just changes the uh the magnitude of the +of the wave by a small amount right + + align:start position:0% +of the wave by a small amount right + + + align:start position:0% +of the wave by a small amount right +because we've said X and Y is small but + + align:start position:0% +because we've said X and Y is small but + + + align:start position:0% +because we've said X and Y is small but +up here you have to be more + + align:start position:0% +up here you have to be more + + + align:start position:0% +up here you have to be more +careful uh because we're talking about + + align:start position:0% +careful uh because we're talking about + + + align:start position:0% +careful uh because we're talking about +phases right uh uh so anyway at the + + align:start position:0% +phases right uh uh so anyway at the + + + align:start position:0% +phases right uh uh so anyway at the +bottom we can just neglect the X and Y + + align:start position:0% +bottom we can just neglect the X and Y + + + align:start position:0% +bottom we can just neglect the X and Y +so that's where the Zs come from there + + align:start position:0% +so that's where the Zs come from there + + + align:start position:0% +so that's where the Zs come from there +uh and when we do this binomial thing on + + align:start position:0% +uh and when we do this binomial thing on + + + align:start position:0% +uh and when we do this binomial thing on +the top we get this expression here then + + align:start position:0% +the top we get this expression here then + + + align:start position:0% +the top we get this expression here then +uh so the um the dependence on X and Y + + align:start position:0% +uh so the um the dependence on X and Y + + + align:start position:0% +uh so the um the dependence on X and Y +uh you can see just becomes a quadratic + + align:start position:0% +uh you can see just becomes a quadratic + + + align:start position:0% +uh you can see just becomes a quadratic +type term x^2 + y^2 over 2 Z uh and uh + + align:start position:0% +type term x^2 + y^2 over 2 Z uh and uh + + + align:start position:0% +type term x^2 + y^2 over 2 Z uh and uh +so this is what this picture's drawing + + align:start position:0% +so this is what this picture's drawing + + + align:start position:0% +so this is what this picture's drawing +here uh the path delay uh increases quad + + align:start position:0% +here uh the path delay uh increases quad + + + align:start position:0% +here uh the path delay uh increases quad +I atically with X right so if as you go + + align:start position:0% +I atically with X right so if as you go + + + align:start position:0% +I atically with X right so if as you go +further this point here corresponds to + + align:start position:0% +further this point here corresponds to + + + align:start position:0% +further this point here corresponds to +the center of the screen and then as you + + align:start position:0% +the center of the screen and then as you + + + align:start position:0% +the center of the screen and then as you +go further + + align:start position:0% +go further + + + align:start position:0% +go further +away uh this + + align:start position:0% +away uh this + + + align:start position:0% +away uh this +uh increases with some + + align:start position:0% +uh increases with some + + + align:start position:0% +uh increases with some +parabolic uh variation like + + align:start position:0% +parabolic uh variation like + + + align:start position:0% +parabolic uh variation like +this uh okay so that's right that's + + align:start position:0% +this uh okay so that's right that's + + + align:start position:0% +this uh okay so that's right that's +doing it in terms of the uh uh cosiness + + align:start position:0% +doing it in terms of the uh uh cosiness + + + align:start position:0% +doing it in terms of the uh uh cosiness +if we go in terms of the + + align:start position:0% +if we go in terms of the + + + align:start position:0% +if we go in terms of the +complex uh complex exponential + + align:start position:0% +complex uh complex exponential + + + align:start position:0% +complex uh complex exponential +much the same sort of approach uh you + + align:start position:0% +much the same sort of approach uh you + + + align:start position:0% +much the same sort of approach uh you +can just um uh expand again this square + + align:start position:0% +can just um uh expand again this square + + + align:start position:0% +can just um uh expand again this square +root inside the exponential now exactly + + align:start position:0% +root inside the exponential now exactly + + + align:start position:0% +root inside the exponential now exactly +the same really uh and you end up + + align:start position:0% +the same really uh and you end up + + + align:start position:0% +the same really uh and you end up +getting this expression here uh and um + + align:start position:0% +getting this expression here uh and um + + + align:start position:0% +getting this expression here uh and um +so this is an example now you can see of + + align:start position:0% +so this is an example now you can see of + + + align:start position:0% +so this is an example now you can see of +the uh of the power of this complex + + align:start position:0% +the uh of the power of this complex + + + align:start position:0% +the uh of the power of this complex +exponential form though uh + + align:start position:0% +exponential form though uh + + + align:start position:0% +exponential form though uh +because uh because this complex + + align:start position:0% +because uh because this complex + + + align:start position:0% +because uh because this complex +exponential + + align:start position:0% +exponential + + + align:start position:0% +exponential +of here two terms or it might be more + + align:start position:0% +of here two terms or it might be more + + + align:start position:0% +of here two terms or it might be more +terms in general uh you can just expand + + align:start position:0% +terms in general uh you can just expand + + + align:start position:0% +terms in general uh you can just expand +them can't you they just be you can just + + align:start position:0% +them can't you they just be you can just + + + align:start position:0% +them can't you they just be you can just +say that multiply together uh whereas if + + align:start position:0% +say that multiply together uh whereas if + + + align:start position:0% +say that multiply together uh whereas if +it was cosine of course you'd have to + + align:start position:0% +it was cosine of course you'd have to + + + align:start position:0% +it was cosine of course you'd have to +remember uh all these things C of a plus + + align:start position:0% +remember uh all these things C of a plus + + + align:start position:0% +remember uh all these things C of a plus +b plus + + align:start position:0% +b plus + + + align:start position:0% +b plus +C + + align:start position:0% +C + + + align:start position:0% +C +horrible I don't know why I'm making + + align:start position:0% +horrible I don't know why I'm making + + + align:start position:0% +horrible I don't know why I'm making +funny + + align:start position:0% +funny + + + align:start position:0% +funny +noises maybe I shouldn't keep get + + align:start position:0% +noises maybe I shouldn't keep get + + + align:start position:0% +noises maybe I shouldn't keep get +getting too near the spe speakers is + + align:start position:0% +getting too near the spe speakers is + + + align:start position:0% +getting too near the spe speakers is +that what it is uh okay so yeah so uh + + align:start position:0% +that what it is uh okay so yeah so uh + + + align:start position:0% +that what it is uh okay so yeah so uh +with the complex exponentials we can + + align:start position:0% +with the complex exponentials we can + + + align:start position:0% +with the complex exponentials we can +break it up very simply uh and this + + align:start position:0% +break it up very simply uh and this + + + align:start position:0% +break it up very simply uh and this +thing in inside the braces then is our + + align:start position:0% +thing in inside the braces then is our + + + align:start position:0% +thing in inside the braces then is our +fire before or IFI so we can say this is + + align:start position:0% +fire before or IFI so we can say this is + + + align:start position:0% +fire before or IFI so we can say this is +e e e to the I5 where the phase five has + + align:start position:0% +e e e to the I5 where the phase five has + + + align:start position:0% +e e e to the I5 where the phase five has +just got this parabolic um uh term uh + + align:start position:0% +just got this parabolic um uh term uh + + + align:start position:0% +just got this parabolic um uh term uh +plus some constant term which + + align:start position:0% +plus some constant term which + + + align:start position:0% +plus some constant term which +corresponds to this which corresponds of + + align:start position:0% +corresponds to this which corresponds of + + + align:start position:0% +corresponds to this which corresponds of +course to this distance the that you get + + align:start position:0% +course to this distance the that you get + + + align:start position:0% +course to this distance the that you get +through traveling that distance + + align:start position:0% +through traveling that distance + + + align:start position:0% +through traveling that distance +there okay so that's how you get a phase + + align:start position:0% +there okay so that's how you get a phase + + + align:start position:0% +there okay so that's how you get a phase +delay I've got a question yeah what + + align:start position:0% +delay I've got a question yeah what + + + align:start position:0% +delay I've got a question yeah what +happened to the pi over 2 in the + + align:start position:0% +happened to the pi over 2 in the + + + align:start position:0% +happened to the pi over 2 in the +phaser what happened to the pi over 2 in + + align:start position:0% +phaser what happened to the pi over 2 in + + + align:start position:0% +phaser what happened to the pi over 2 in +the + + align:start position:0% +the + + + align:start position:0% +the +phaser which uh so we got a + + align:start position:0% +phaser which uh so we got a + + + align:start position:0% +phaser which uh so we got a +good + + align:start position:0% + + + + align:start position:0% + +uh it's there isn't it and and then it's + + align:start position:0% + + + + align:start position:0% + +disappeared oh the eye out the side + + align:start position:0% +disappeared oh the eye out the side + + + align:start position:0% +disappeared oh the eye out the side +there it is it's that + + align:start position:0% +there it is it's that + + + align:start position:0% +there it is it's that +one yeah okay so it's an eye it's an eye + + align:start position:0% +one yeah okay so it's an eye it's an eye + + + align:start position:0% +one yeah okay so it's an eye it's an eye +outside and + + align:start position:0% +outside and + + + align:start position:0% +outside and +uh yeah that's that's that's an + + align:start position:0% +uh yeah that's that's that's an + + + align:start position:0% +uh yeah that's that's that's an +interesting I think George said + + align:start position:0% +interesting I think George said + + + align:start position:0% +interesting I think George said +something about that before because + + align:start position:0% +something about that before because + + + align:start position:0% +something about that before because +effectively it makes um it makes this uh + + align:start position:0% +effectively it makes um it makes this uh + + + align:start position:0% +effectively it makes um it makes this uh +wave 90 de out of phase and + + align:start position:0% +wave 90 de out of phase and + + + align:start position:0% +wave 90 de out of phase and +um uh you know I I like to think of that + + align:start position:0% +um uh you know I I like to think of that + + + align:start position:0% +um uh you know I I like to think of that +as being related to some sort of + + align:start position:0% +as being related to some sort of + + + align:start position:0% +as being related to some sort of +resonance type + + align:start position:0% +resonance type + + + align:start position:0% +resonance type +phenomenon um you know if you excite + + align:start position:0% +phenomenon um you know if you excite + + + align:start position:0% +phenomenon um you know if you excite +something uh that resonates then it's + + align:start position:0% +something uh that resonates then it's + + + align:start position:0% +something uh that resonates then it's +going to resonate at 90° out of phase + + align:start position:0% +going to resonate at 90° out of phase + + + align:start position:0% +going to resonate at 90° out of phase +isn't it so if you if you got a a point + + align:start position:0% +isn't it so if you if you got a a point + + + align:start position:0% +isn't it so if you if you got a a point +source and you excite it with + + align:start position:0% +source and you excite it with + + + align:start position:0% +source and you excite it with +a a wave uh then the the scattered wave + + align:start position:0% +a a wave uh then the the scattered wave + + + align:start position:0% +a a wave uh then the the scattered wave +is going to be 90° out of phase uh with + + align:start position:0% +is going to be 90° out of phase uh with + + + align:start position:0% +is going to be 90° out of phase uh with +with the the driving force just because + + align:start position:0% +with the the driving force just because + + + align:start position:0% +with the the driving force just because +it's like a resonance and um I guess + + align:start position:0% +it's like a resonance and um I guess + + + align:start position:0% +it's like a resonance and um I guess +that's also true in the hyan thing that + + align:start position:0% +that's also true in the hyan thing that + + + align:start position:0% +that's also true in the hyan thing that +we we come on in the next lecture uh but + + align:start position:0% +we we come on in the next lecture uh but + + + align:start position:0% +we we come on in the next lecture uh but +yeah okay thanks for pointing that out + + align:start position:0% +yeah okay thanks for pointing that out + + + align:start position:0% +yeah okay thanks for pointing that out +I'd forgotten + + align:start position:0% +I'd forgotten + + + align:start position:0% +I'd forgotten +that uh okay uh so all this other than + + align:start position:0% +that uh okay uh so all this other than + + + align:start position:0% +that uh okay uh so all this other than +that it's it's it's fine isn't it I + + align:start position:0% + + + + align:start position:0% + +hope so we're now going on to uh discuss + + align:start position:0% +hope so we're now going on to uh discuss + + + align:start position:0% +hope so we're now going on to uh discuss +something about the significance there + + align:start position:0% +something about the significance there + + + align:start position:0% +something about the significance there +uh yeah so the point is I mentioned that + + align:start position:0% +uh yeah so the point is I mentioned that + + + align:start position:0% +uh yeah so the point is I mentioned that +the the there is this modulus term + + align:start position:0% +the the there is this modulus term + + + align:start position:0% +the the there is this modulus term +intensity type + + align:start position:0% +intensity type + + + align:start position:0% +intensity type +term uh but this is a very weak change + + align:start position:0% +term uh but this is a very weak change + + + align:start position:0% +term uh but this is a very weak change +so you can imagine if you trying to do + + align:start position:0% +so you can imagine if you trying to do + + + align:start position:0% +so you can imagine if you trying to do +an experiment uh to actually measure the + + align:start position:0% +an experiment uh to actually measure the + + + align:start position:0% +an experiment uh to actually measure the +properties of that wave field uh by + + align:start position:0% +properties of that wave field uh by + + + align:start position:0% +properties of that wave field uh by +looking at the intensity would be quite + + align:start position:0% +looking at the intensity would be quite + + + align:start position:0% +looking at the intensity would be quite +tough because we said that the these two + + align:start position:0% +tough because we said that the these two + + + align:start position:0% +tough because we said that the these two +terms are very much smaller than that + + align:start position:0% +terms are very much smaller than that + + + align:start position:0% +terms are very much smaller than that +one right so uh looking at the phase of + + align:start position:0% +one right so uh looking at the phase of + + + align:start position:0% +one right so uh looking at the phase of +signal is a much more sensitive way for + + align:start position:0% +signal is a much more sensitive way for + + + align:start position:0% +signal is a much more sensitive way for +to look at that uh at that + + align:start position:0% +to look at that uh at that + + + align:start position:0% +to look at that uh at that +wavefront uh and um as it says the the + + align:start position:0% +wavefront uh and um as it says the the + + + align:start position:0% +wavefront uh and um as it says the the +phase can tell us all sorts of things + + align:start position:0% +phase can tell us all sorts of things + + + align:start position:0% +phase can tell us all sorts of things +about the wave uh like where the where + + align:start position:0% +about the wave uh like where the where + + + align:start position:0% +about the wave uh like where the where +the wave has come from how far it's + + align:start position:0% +the wave has come from how far it's + + + align:start position:0% +the wave has come from how far it's +traveled the materials it's gone through + + align:start position:0% +traveled the materials it's gone through + + + align:start position:0% +traveled the materials it's gone through +uh and uh the well in generally the + + align:start position:0% +uh and uh the well in generally the + + + align:start position:0% +uh and uh the well in generally the +optical + + align:start position:0% +optical + + + align:start position:0% +optical +path uh right which is you remember we + + align:start position:0% +path uh right which is you remember we + + + align:start position:0% +path uh right which is you remember we +had optical path before integral ndz so + + align:start position:0% +had optical path before integral ndz so + + + align:start position:0% +had optical path before integral ndz so +that will change the phase uh and so if + + align:start position:0% +that will change the phase uh and so if + + + align:start position:0% +that will change the phase uh and so if +we can measure the phase uh we can find + + align:start position:0% +we can measure the phase uh we can find + + + align:start position:0% +we can measure the phase uh we can find +out information about those things um + + align:start position:0% +out information about those things um + + + align:start position:0% +out information about those things um +the problem though as we've said before + + align:start position:0% +the problem though as we've said before + + + align:start position:0% +the problem though as we've said before +is that the phase is not something you + + align:start position:0% +is that the phase is not something you + + + align:start position:0% +is that the phase is not something you +can actually see directly because it + + align:start position:0% +can actually see directly because it + + + align:start position:0% +can actually see directly because it +it's so fast so 10 the minus uh 10^ the + + align:start position:0% +it's so fast so 10 the minus uh 10^ the + + + align:start position:0% +it's so fast so 10 the minus uh 10^ the +15 Hertz is typical uh very very F much + + align:start position:0% +15 Hertz is typical uh very very F much + + + align:start position:0% +15 Hertz is typical uh very very F much +faster than you can measure with any + + align:start position:0% +faster than you can measure with any + + + align:start position:0% +faster than you can measure with any +Electronics so how do we do this we do + + align:start position:0% +Electronics so how do we do this we do + + + align:start position:0% +Electronics so how do we do this we do +it uh by uh some form of + + align:start position:0% +it uh by uh some form of + + + align:start position:0% +it uh by uh some form of +interferometry uh which is + + align:start position:0% +interferometry uh which is + + + align:start position:0% +interferometry uh which is +basically uh mixing it with a reference + + align:start position:0% +basically uh mixing it with a reference + + + align:start position:0% +basically uh mixing it with a reference +beam uh and then you look at the + + align:start position:0% +beam uh and then you look at the + + + align:start position:0% +beam uh and then you look at the +intensity of the uh of the um + + align:start position:0% +intensity of the uh of the um + + + align:start position:0% +intensity of the uh of the um +interference between the two waves so + + align:start position:0% +interference between the two waves so + + + align:start position:0% +interference between the two waves so +this is uh how we do it uh so I said + + align:start position:0% +this is uh how we do it uh so I said + + + align:start position:0% +this is uh how we do it uh so I said +that we're going to look at two two + + align:start position:0% +that we're going to look at two two + + + align:start position:0% +that we're going to look at two two +types of interferometer the first one is + + align:start position:0% +types of interferometer the first one is + + + align:start position:0% +types of interferometer the first one is +the microson interferometer so this is + + align:start position:0% +the microson interferometer so this is + + + align:start position:0% +the microson interferometer so this is +how you make a microson interferometer + + align:start position:0% +how you make a microson interferometer + + + align:start position:0% +how you make a microson interferometer +you get get light from some Source uh + + align:start position:0% +you get get light from some Source uh + + + align:start position:0% +you get get light from some Source uh +and split it into two parts with a beam + + align:start position:0% +and split it into two parts with a beam + + + align:start position:0% +and split it into two parts with a beam +splitter uh and one one of those one of + + align:start position:0% +splitter uh and one one of those one of + + + align:start position:0% +splitter uh and one one of those one of +those beams is what we call the signal + + align:start position:0% +those beams is what we call the signal + + + align:start position:0% +those beams is what we call the signal +arm this is what we're going to try and + + align:start position:0% +arm this is what we're going to try and + + + align:start position:0% +arm this is what we're going to try and +measure so here this shows uh this light + + align:start position:0% +measure so here this shows uh this light + + + align:start position:0% +measure so here this shows uh this light +going through some object uh and um then + + align:start position:0% +going through some object uh and um then + + + align:start position:0% +going through some object uh and um then +being reflected uh by a mirror and then + + align:start position:0% +being reflected uh by a mirror and then + + + align:start position:0% +being reflected uh by a mirror and then +coming back to a detector and then the + + align:start position:0% +coming back to a detector and then the + + + align:start position:0% +coming back to a detector and then the +other arm uh is the reference arm uh so + + align:start position:0% +other arm uh is the reference arm uh so + + + align:start position:0% +other arm uh is the reference arm uh so +this is a going to produce a reference + + align:start position:0% +this is a going to produce a reference + + + align:start position:0% +this is a going to produce a reference +signal so effectively we're going to be + + align:start position:0% +signal so effectively we're going to be + + + align:start position:0% +signal so effectively we're going to be +comparing the phases in those two arms + + align:start position:0% +comparing the phases in those two arms + + + align:start position:0% +comparing the phases in those two arms +uh so the reference beam comes down also + + align:start position:0% +uh so the reference beam comes down also + + + align:start position:0% +uh so the reference beam comes down also +so these add + + align:start position:0% +so these add + + + align:start position:0% +so these add +together uh so we can add them as phases + + align:start position:0% +together uh so we can add them as phases + + + align:start position:0% +together uh so we can add them as phases +we've got this is for the reference beam + + align:start position:0% +we've got this is for the reference beam + + + align:start position:0% +we've got this is for the reference beam +a e to the I fire uh for this for the + + align:start position:0% +a e to the I fire uh for this for the + + + align:start position:0% +a e to the I fire uh for this for the +signal beam we've got as e to the i f s + + align:start position:0% +signal beam we've got as e to the i f s + + + align:start position:0% +signal beam we've got as e to the i f s +we add the amplitudes cuz we're assuming + + align:start position:0% +we add the amplitudes cuz we're assuming + + + align:start position:0% +we add the amplitudes cuz we're assuming +it's + + align:start position:0% +it's + + + align:start position:0% +it's +coherent maybe I'll to stress that a bit + + align:start position:0% +coherent maybe I'll to stress that a bit + + + align:start position:0% +coherent maybe I'll to stress that a bit +of course U so this is assuming that + + align:start position:0% +of course U so this is assuming that + + + align:start position:0% +of course U so this is assuming that +this is um this is a coherent these two + + align:start position:0% +this is um this is a coherent these two + + + align:start position:0% +this is um this is a coherent these two +beams are coherent with respect to each + + align:start position:0% +beams are coherent with respect to each + + + align:start position:0% +beams are coherent with respect to each +other right so if you had light here + + align:start position:0% +other right so if you had light here + + + align:start position:0% +other right so if you had light here +from a laser uh that would be that would + + align:start position:0% +from a laser uh that would be that would + + + align:start position:0% +from a laser uh that would be that would +be true okay uh and uh we'll probably + + align:start position:0% +be true okay uh and uh we'll probably + + + align:start position:0% +be true okay uh and uh we'll probably +come on to cases where it might not be + + align:start position:0% +come on to cases where it might not be + + + align:start position:0% +come on to cases where it might not be +true later on and once we got the + + align:start position:0% +true later on and once we got the + + + align:start position:0% +true later on and once we got the +amplitude then we just have to find the + + align:start position:0% +amplitude then we just have to find the + + + align:start position:0% +amplitude then we just have to find the +modulus Square to find the intensity and + + align:start position:0% +modulus Square to find the intensity and + + + align:start position:0% +modulus Square to find the intensity and +if you remember there's actually a + + align:start position:0% +if you remember there's actually a + + + align:start position:0% +if you remember there's actually a +proportional sign here there's some + + align:start position:0% +proportional sign here there's some + + + align:start position:0% +proportional sign here there's some +funny constants with Epsilon and a half + + align:start position:0% +funny constants with Epsilon and a half + + + align:start position:0% +funny constants with Epsilon and a half +and things which we just don't usually + + align:start position:0% +and things which we just don't usually + + + align:start position:0% +and things which we just don't usually +worry about okay so these these + + align:start position:0% +worry about okay so these these + + + align:start position:0% +worry about okay so these these +phases uh tell us um the optical path + + align:start position:0% +phases uh tell us um the optical path + + + align:start position:0% +phases uh tell us um the optical path +that the light has gone through in these + + align:start position:0% +that the light has gone through in these + + + align:start position:0% +that the light has gone through in these +two arms in order to get to the detector + + align:start position:0% +two arms in order to get to the detector + + + align:start position:0% +two arms in order to get to the detector +uh and uh so what we're measuring is the + + align:start position:0% +uh and uh so what we're measuring is the + + + align:start position:0% +uh and uh so what we're measuring is the +difference in the optical path in those + + align:start position:0% +difference in the optical path in those + + + align:start position:0% +difference in the optical path in those +two + + align:start position:0% +two + + + align:start position:0% +two +arms uh and so this shows how that can + + align:start position:0% +arms uh and so this shows how that can + + + align:start position:0% +arms uh and so this shows how that can +work uh so this is an example where + + align:start position:0% +work uh so this is an example where + + + align:start position:0% +work uh so this is an example where +these two waves arrive in Phase with + + align:start position:0% +these two waves arrive in Phase with + + + align:start position:0% +these two waves arrive in Phase with +each other so then they'll add uh + + align:start position:0% +each other so then they'll add uh + + + align:start position:0% +each other so then they'll add uh +constructively and you'll get a big + + align:start position:0% +constructively and you'll get a big + + + align:start position:0% +constructively and you'll get a big +signal like that uh on the other hand + + align:start position:0% +signal like that uh on the other hand + + + align:start position:0% +signal like that uh on the other hand +you could imagine that they might not + + align:start position:0% +you could imagine that they might not + + + align:start position:0% +you could imagine that they might not +arrive like that they might arrive uh in + + align:start position:0% +arrive like that they might arrive uh in + + + align:start position:0% +arrive like that they might arrive uh in +antiphase like this in which case um you + + align:start position:0% +antiphase like this in which case um you + + + align:start position:0% +antiphase like this in which case um you +can see that the the two ways now are + + align:start position:0% +can see that the the two ways now are + + + align:start position:0% +can see that the the two ways now are +going to cancel out and you're not going + + align:start position:0% +going to cancel out and you're not going + + + align:start position:0% +going to cancel out and you're not going +to see now uh any interference in + + align:start position:0% +to see now uh any interference in + + + align:start position:0% +to see now uh any interference in +practice of course it could be anything + + align:start position:0% +practice of course it could be anything + + + align:start position:0% +practice of course it could be anything +in between here right so as you change + + align:start position:0% +in between here right so as you change + + + align:start position:0% +in between here right so as you change +you can change uh the the relative phase + + align:start position:0% +you can change uh the the relative phase + + + align:start position:0% +you can change uh the the relative phase +of this light by changing the position + + align:start position:0% +of this light by changing the position + + + align:start position:0% +of this light by changing the position +of this mirror or the the the size or uh + + align:start position:0% +of this mirror or the the the size or uh + + + align:start position:0% +of this mirror or the the the size or uh +refractive index of this object that's + + align:start position:0% +refractive index of this object that's + + + align:start position:0% +refractive index of this object that's +in there or the wavelength of the light + + align:start position:0% +in there or the wavelength of the light + + + align:start position:0% +in there or the wavelength of the light +or whatever it's going to depend on all + + align:start position:0% +or whatever it's going to depend on all + + + align:start position:0% +or whatever it's going to depend on all +of these + + align:start position:0% + + + + align:start position:0% + +things and uh so example uh measuring + + align:start position:0% +things and uh so example uh measuring + + + align:start position:0% +things and uh so example uh measuring +distance uh so we've said that + + align:start position:0% +distance uh so we've said that + + + align:start position:0% +distance uh so we've said that +effectively what we're doing is + + align:start position:0% +effectively what we're doing is + + + align:start position:0% +effectively what we're doing is +measuring the optical + + align:start position:0% +measuring the optical + + + align:start position:0% +measuring the optical +path uh so Optical path depends on a few + + align:start position:0% +path uh so Optical path depends on a few + + + align:start position:0% +path uh so Optical path depends on a few +things doesn't it Optical path depends + + align:start position:0% +things doesn't it Optical path depends + + + align:start position:0% +things doesn't it Optical path depends +on the distance it depends on the + + align:start position:0% +on the distance it depends on the + + + align:start position:0% +on the distance it depends on the +wavelength and it depends on the + + align:start position:0% +wavelength and it depends on the + + + align:start position:0% +wavelength and it depends on the +refractive index uh so these are all + + align:start position:0% +refractive index uh so these are all + + + align:start position:0% +refractive index uh so these are all +things that you can measure using this + + align:start position:0% +things that you can measure using this + + + align:start position:0% +things that you can measure using this +sort of system uh so so here it's + + align:start position:0% +sort of system uh so so here it's + + + align:start position:0% +sort of system uh so so here it's +talking as an example there's no object + + align:start position:0% +talking as an example there's no object + + + align:start position:0% +talking as an example there's no object +in this one anymore so this is just free + + align:start position:0% +in this one anymore so this is just free + + + align:start position:0% +in this one anymore so this is just free +space uh and uh so in this case then + + align:start position:0% +space uh and uh so in this case then + + + align:start position:0% +space uh and uh so in this case then +what you what you can measure is the + + align:start position:0% +what you what you can measure is the + + + align:start position:0% +what you what you can measure is the +difference in the optical path in this + + align:start position:0% +difference in the optical path in this + + + align:start position:0% +difference in the optical path in this +arm and this arm and the optical path + + align:start position:0% +arm and this arm and the optical path + + + align:start position:0% +arm and this arm and the optical path +well the refractive index is now the + + align:start position:0% +well the refractive index is now the + + + align:start position:0% +well the refractive index is now the +same in each the wavelength is the same + + align:start position:0% +same in each the wavelength is the same + + + align:start position:0% +same in each the wavelength is the same +in each uh so you could measure uh the + + align:start position:0% +in each uh so you could measure uh the + + + align:start position:0% +in each uh so you could measure uh the +distance right so so this is a um an + + align:start position:0% +distance right so so this is a um an + + + align:start position:0% +distance right so so this is a um an +interferometer for measuring distance uh + + align:start position:0% +interferometer for measuring distance uh + + + align:start position:0% +interferometer for measuring distance uh +so you might where could you use this + + align:start position:0% +so you might where could you use this + + + align:start position:0% +so you might where could you use this +well imagine this this might not + + align:start position:0% +well imagine this this might not + + + align:start position:0% +well imagine this this might not +actually be a a a flat mirror it might + + align:start position:0% +actually be a a a flat mirror it might + + + align:start position:0% +actually be a a a flat mirror it might +actually have some structure there uh in + + align:start position:0% +actually have some structure there uh in + + + align:start position:0% +actually have some structure there uh in +which case you could actually measure + + align:start position:0% +which case you could actually measure + + + align:start position:0% +which case you could actually measure +what that structure is right or you + + align:start position:0% +what that structure is right or you + + + align:start position:0% +what that structure is right or you +could use if it was a mirror you could + + align:start position:0% +could use if it was a mirror you could + + + align:start position:0% +could use if it was a mirror you could +actually use this to accurately measure + + align:start position:0% +actually use this to accurately measure + + + align:start position:0% +actually use this to accurately measure +the distance of this mirror how far away + + align:start position:0% +the distance of this mirror how far away + + + align:start position:0% +the distance of this mirror how far away +is um from from the the instrument so to + + align:start position:0% +is um from from the the instrument so to + + + align:start position:0% +is um from from the the instrument so to +speak right so + + align:start position:0% +speak right so + + + align:start position:0% +speak right so +uh the interesting thing another + + align:start position:0% +uh the interesting thing another + + + align:start position:0% +uh the interesting thing another +interesting thing this is the Michaelson + + align:start position:0% +interesting thing this is the Michaelson + + + align:start position:0% +interesting thing this is the Michaelson +ineter and the Michaelson interferometer + + align:start position:0% +ineter and the Michaelson interferometer + + + align:start position:0% +ineter and the Michaelson interferometer +was as the name says was in invented by + + align:start position:0% +was as the name says was in invented by + + + align:start position:0% +was as the name says was in invented by +Michaelson well I think he probably + + align:start position:0% +Michaelson well I think he probably + + + align:start position:0% +Michaelson well I think he probably +invented it he certainly has his name + + align:start position:0% +invented it he certainly has his name + + + align:start position:0% +invented it he certainly has his name +attached to it uh but he mainly used it + + align:start position:0% +attached to it uh but he mainly used it + + + align:start position:0% +attached to it uh but he mainly used it +for measuring + + align:start position:0% +for measuring + + + align:start position:0% +for measuring +wavelength uh so um we'll come back to + + align:start position:0% +wavelength uh so um we'll come back to + + + align:start position:0% +wavelength uh so um we'll come back to +that after I've gone through the mat a + + align:start position:0% +that after I've gone through the mat a + + + align:start position:0% +that after I've gone through the mat a +bit actually I think it's probably best + + align:start position:0% +bit actually I think it's probably best + + + align:start position:0% +bit actually I think it's probably best +uh anyway so what we said is this we add + + align:start position:0% +uh anyway so what we said is this we add + + + align:start position:0% +uh anyway so what we said is this we add +together these two phases find the + + align:start position:0% +together these two phases find the + + + align:start position:0% +together these two phases find the +modulus square and then we got to expand + + align:start position:0% +modulus square and then we got to expand + + + align:start position:0% +modulus square and then we got to expand +that so this is a a square of a sum of + + align:start position:0% +that so this is a a square of a sum of + + + align:start position:0% +that so this is a a square of a sum of +two things so we're going to get the + + align:start position:0% +two things so we're going to get the + + + align:start position:0% +two things so we're going to get the +square of this the square of this and + + align:start position:0% +square of this the square of this and + + + align:start position:0% +square of this the square of this and +then uh we're going to get some uh uh + + align:start position:0% +then uh we're going to get some uh uh + + + align:start position:0% +then uh we're going to get some uh uh +cross uh cross terms and this is what it + + align:start position:0% +cross uh cross terms and this is what it + + + align:start position:0% +cross uh cross terms and this is what it +comes out to be the two cross terms uh + + align:start position:0% +comes out to be the two cross terms uh + + + align:start position:0% +comes out to be the two cross terms uh +one is the complex conjugate of the + + align:start position:0% +one is the complex conjugate of the + + + align:start position:0% +one is the complex conjugate of the +other uh and which means means that when + + align:start position:0% +other uh and which means means that when + + + align:start position:0% +other uh and which means means that when +you add them together the final result + + align:start position:0% +you add them together the final result + + + align:start position:0% +you add them together the final result +is real uh that has to be true of course + + align:start position:0% +is real uh that has to be true of course + + + align:start position:0% +is real uh that has to be true of course +because this is an expression for + + align:start position:0% +because this is an expression for + + + align:start position:0% +because this is an expression for +intensity and intensity has to be + + align:start position:0% +intensity and intensity has to be + + + align:start position:0% +intensity and intensity has to be +real uh and uh so we've written it in + + align:start position:0% +real uh and uh so we've written it in + + + align:start position:0% +real uh and uh so we've written it in +this nice form AR 2 + a s 2 plus 2 a r a + + align:start position:0% +this nice form AR 2 + a s 2 plus 2 a r a + + + align:start position:0% +this nice form AR 2 + a s 2 plus 2 a r a +s c of something uh and this this thing + + align:start position:0% +s c of something uh and this this thing + + + align:start position:0% +s c of something uh and this this thing +here the something is the difference + + align:start position:0% +here the something is the difference + + + align:start position:0% +here the something is the difference +between the phases of the two beams + + align:start position:0% +between the phases of the two beams + + + align:start position:0% +between the phases of the two beams +right and uh so this next + + align:start position:0% +right and uh so this next + + + align:start position:0% +right and uh so this next +line uh puts it into a sort of general + + align:start position:0% +line uh puts it into a sort of general + + + align:start position:0% +line uh puts it into a sort of general +term general form it's of the forms a + + align:start position:0% +term general form it's of the forms a + + + align:start position:0% +term general form it's of the forms a +constant plus a + + align:start position:0% +constant plus a + + + align:start position:0% +constant plus a +cosine uh and uh and then uh these + + align:start position:0% +cosine uh and uh and then uh these + + + align:start position:0% +cosine uh and uh and then uh these +quantities I not M and Delta fi you can + + align:start position:0% +quantities I not M and Delta fi you can + + + align:start position:0% +quantities I not M and Delta fi you can +also write in terms of these other + + align:start position:0% +also write in terms of these other + + + align:start position:0% +also write in terms of these other +parameters we had + + align:start position:0% +parameters we had + + + align:start position:0% +parameters we had +earlier right + + align:start position:0% +earlier right + + + align:start position:0% +earlier right +so um it as it says when both paths are + + align:start position:0% +so um it as it says when both paths are + + + align:start position:0% +so um it as it says when both paths are +clear + + align:start position:0% +clear + + + align:start position:0% +clear +uh then these phases are just directly + + align:start position:0% +uh then these phases are just directly + + + align:start position:0% +uh then these phases are just directly +proportional to the + + align:start position:0% +proportional to the + + + align:start position:0% +proportional to the +distance LS and LR uh and so the phase + + align:start position:0% +distance LS and LR uh and so the phase + + + align:start position:0% +distance LS and LR uh and so the phase +diff difference is just K times the + + align:start position:0% +diff difference is just K times the + + + align:start position:0% +diff difference is just K times the +difference in the two + + align:start position:0% +difference in the two + + + align:start position:0% +difference in the two +parts right so therefore if you measured + + align:start position:0% +parts right so therefore if you measured + + + align:start position:0% +parts right so therefore if you measured +the + + align:start position:0% +the + + + align:start position:0% +the +signal uh you can if you know what the + + align:start position:0% +signal uh you can if you know what the + + + align:start position:0% +signal uh you can if you know what the +wavelength + + align:start position:0% +wavelength + + + align:start position:0% +wavelength +is uh you can measure what the + + align:start position:0% +is uh you can measure what the + + + align:start position:0% +is uh you can measure what the +difference in those two distances is um + + align:start position:0% +difference in those two distances is um + + + align:start position:0% +difference in those two distances is um +there's there's a a bit of a Proviso + + align:start position:0% +there's there's a a bit of a Proviso + + + align:start position:0% +there's there's a a bit of a Proviso +there which is quite a big Proviso uh + + align:start position:0% +there which is quite a big Proviso uh + + + align:start position:0% +there which is quite a big Proviso uh +that you can only do this of course + + align:start position:0% +that you can only do this of course + + + align:start position:0% +that you can only do this of course +modulo 2 pi right so uh because this is + + align:start position:0% +modulo 2 pi right so uh because this is + + + align:start position:0% +modulo 2 pi right so uh because this is +a cosine that's going to keep repeating + + align:start position:0% +a cosine that's going to keep repeating + + + align:start position:0% +a cosine that's going to keep repeating +uh and you won't know which of the + + align:start position:0% +uh and you won't know which of the + + + align:start position:0% +uh and you won't know which of the +Cycles you're on uh but so it means + + align:start position:0% +Cycles you're on uh but so it means + + + align:start position:0% +Cycles you're on uh but so it means +interferometry is usually very sensitive + + align:start position:0% +interferometry is usually very sensitive + + + align:start position:0% +interferometry is usually very sensitive +you can measure uh you can measure very + + align:start position:0% +you can measure uh you can measure very + + + align:start position:0% +you can measure uh you can measure very +very small distances uh easily much + + align:start position:0% +very small distances uh easily much + + + align:start position:0% +very small distances uh easily much +smaller than the wavelength uh and + + align:start position:0% +smaller than the wavelength uh and + + + align:start position:0% +smaller than the wavelength uh and +people sometimes talk about measuring + + align:start position:0% +people sometimes talk about measuring + + + align:start position:0% +people sometimes talk about measuring +100th of an angstrom and amazing small + + align:start position:0% +100th of an angstrom and amazing small + + + align:start position:0% +100th of an angstrom and amazing small +quantities using + + align:start position:0% +quantities using + + + align:start position:0% +quantities using +interferometry uh the um ligo project I + + align:start position:0% +interferometry uh the um ligo project I + + + align:start position:0% +interferometry uh the um ligo project I +don't know what they're + + align:start position:0% +don't know what they're + + + align:start position:0% +don't know what they're +claiming um 10 Theus 15 M or something + + align:start position:0% +claiming um 10 Theus 15 M or something + + + align:start position:0% +claiming um 10 Theus 15 M or something +isn't it they're they're trying + + align:start position:0% +isn't it they're they're trying + + + align:start position:0% +isn't it they're they're trying +to um measure to to detect these + + align:start position:0% +to um measure to to detect these + + + align:start position:0% +to um measure to to detect these +gravitational + + align:start position:0% +gravitational + + + align:start position:0% +gravitational +waves uh and anyway yeah so + + align:start position:0% +waves uh and anyway yeah so + + + align:start position:0% +waves uh and anyway yeah so +uh so you only measure it modulo 2 pi uh + + align:start position:0% +uh so you only measure it modulo 2 pi uh + + + align:start position:0% +uh so you only measure it modulo 2 pi uh +so that means then if you're you're + + align:start position:0% +so that means then if you're you're + + + align:start position:0% +so that means then if you're you're +trying to use this method to measure for + + align:start position:0% +trying to use this method to measure for + + + align:start position:0% +trying to use this method to measure for +example uh I'm looking at the door at + + align:start position:0% +example uh I'm looking at the door at + + + align:start position:0% +example uh I'm looking at the door at +the back of the lecture theater if I'm + + align:start position:0% +the back of the lecture theater if I'm + + + align:start position:0% +the back of the lecture theater if I'm +trying to use this to measure the + + align:start position:0% +trying to use this to measure the + + + align:start position:0% +trying to use this to measure the +distance of that door uh I can measure + + align:start position:0% +distance of that door uh I can measure + + + align:start position:0% +distance of that door uh I can measure +the distance so an accuracy maybe of + + align:start position:0% +the distance so an accuracy maybe of + + + align:start position:0% +the distance so an accuracy maybe of +something smaller than a micron but I + + align:start position:0% +something smaller than a micron but I + + + align:start position:0% +something smaller than a micron but I +wouldn't really know whether it had + + align:start position:0% +wouldn't really know whether it had + + + align:start position:0% +wouldn't really know whether it had +added to that um 10 meters or + + align:start position:0% +added to that um 10 meters or + + + align:start position:0% +added to that um 10 meters or +whatever so that actually has been what + + align:start position:0% +whatever so that actually has been what + + + align:start position:0% +whatever so that actually has been what +a lot of people have put effort into + + align:start position:0% +a lot of people have put effort into + + + align:start position:0% +a lot of people have put effort into +trying to develop interferometric + + align:start position:0% +trying to develop interferometric + + + align:start position:0% +trying to develop interferometric +methods that you can get that extra + + align:start position:0% +methods that you can get that extra + + + align:start position:0% +methods that you can get that extra +information so that you can actually uh + + align:start position:0% +information so that you can actually uh + + + align:start position:0% +information so that you can actually uh +do what we call unwrapping because this + + align:start position:0% +do what we call unwrapping because this + + + align:start position:0% +do what we call unwrapping because this +this is like they sometimes call this + + align:start position:0% +this is like they sometimes call this + + + align:start position:0% +this is like they sometimes call this +phase + + align:start position:0% +phase + + + align:start position:0% +phase +wrapping the the phase wraps because of + + align:start position:0% +wrapping the the phase wraps because of + + + align:start position:0% +wrapping the the phase wraps because of +the cosine and so you don't know which + + align:start position:0% +the cosine and so you don't know which + + + align:start position:0% +the cosine and so you don't know which +of these loes you're + + align:start position:0% +of these loes you're + + + align:start position:0% +of these loes you're +on yeah well going back to uh Michaelson + + align:start position:0% +on yeah well going back to uh Michaelson + + + align:start position:0% +on yeah well going back to uh Michaelson +so Michaelson uh did this the other way + + align:start position:0% +so Michaelson uh did this the other way + + + align:start position:0% +so Michaelson uh did this the other way +around he he knows his distance uh and + + align:start position:0% +around he he knows his distance uh and + + + align:start position:0% +around he he knows his distance uh and +uses this expression to uh to find the + + align:start position:0% +uses this expression to uh to find the + + + align:start position:0% +uses this expression to uh to find the +wavelength or the K value or whatever uh + + align:start position:0% +wavelength or the K value or whatever uh + + + align:start position:0% +wavelength or the K value or whatever uh +that's of course what you do in a in an + + align:start position:0% +that's of course what you do in a in an + + + align:start position:0% +that's of course what you do in a in an +interferometer isn't it uh if you do a f + + align:start position:0% +interferometer isn't it uh if you do a f + + + align:start position:0% +interferometer isn't it uh if you do a f +a transform interferometer you're using + + align:start position:0% +a transform interferometer you're using + + + align:start position:0% +a transform interferometer you're using +that as a uh as a way of measuring uh + + align:start position:0% +that as a uh as a way of measuring uh + + + align:start position:0% +that as a uh as a way of measuring uh +the the wavelength of the light right uh + + align:start position:0% +the the wavelength of the light right uh + + + align:start position:0% +the the wavelength of the light right uh +in in the case of um uh Michaelson he + + align:start position:0% +in in the case of um uh Michaelson he + + + align:start position:0% +in in the case of um uh Michaelson he +was looking he looked at various things + + align:start position:0% +was looking he looked at various things + + + align:start position:0% +was looking he looked at various things +he didn't look at lasers because he + + align:start position:0% +he didn't look at lasers because he + + + align:start position:0% +he didn't look at lasers because he +there weren't any lasers there uh but he + + align:start position:0% +there weren't any lasers there uh but he + + + align:start position:0% +there weren't any lasers there uh but he +looked at light from uh discharge tubes + + align:start position:0% +looked at light from uh discharge tubes + + + align:start position:0% +looked at light from uh discharge tubes +and various different types of lamp and + + align:start position:0% +and various different types of lamp and + + + align:start position:0% +and various different types of lamp and +so on uh and uh he looked at how the + + align:start position:0% +so on uh and uh he looked at how the + + + align:start position:0% +so on uh and uh he looked at how the +signal would vary As you move this + + align:start position:0% +signal would vary As you move this + + + align:start position:0% +signal would vary As you move this +mirror and it turns out that if you do + + align:start position:0% +mirror and it turns out that if you do + + + align:start position:0% +mirror and it turns out that if you do +move the mirror and you know accurately + + align:start position:0% +move the mirror and you know accurately + + + align:start position:0% +move the mirror and you know accurately +how you're moving the mirror you can + + align:start position:0% +how you're moving the mirror you can + + + align:start position:0% +how you're moving the mirror you can +actually work out from that uh what the + + align:start position:0% +actually work out from that uh what the + + + align:start position:0% +actually work out from that uh what the +spectral distribution of the source is + + align:start position:0% +spectral distribution of the source is + + + align:start position:0% +spectral distribution of the source is +right uh that also uh + + align:start position:0% +right uh that also uh + + + align:start position:0% +right uh that also uh +suggests uh a way around this this + + align:start position:0% +suggests uh a way around this this + + + align:start position:0% +suggests uh a way around this this +wrapping + + align:start position:0% +wrapping + + + align:start position:0% +wrapping +problem the the way around the wrap or a + + align:start position:0% +problem the the way around the wrap or a + + + align:start position:0% +problem the the way around the wrap or a +way around the wrapping problem is to + + align:start position:0% +way around the wrapping problem is to + + + align:start position:0% +way around the wrapping problem is to +use not just one wavelength but many + + align:start position:0% +use not just one wavelength but many + + + align:start position:0% +use not just one wavelength but many +wavelengths so uh even two wavelengths + + align:start position:0% +wavelengths so uh even two wavelengths + + + align:start position:0% +wavelengths so uh even two wavelengths +is a big help + + align:start position:0% +is a big help + + + align:start position:0% +is a big help +actually + + align:start position:0% + + + + align:start position:0% + +yeah it's quite interesting that + + align:start position:0% +yeah it's quite interesting that + + + align:start position:0% +yeah it's quite interesting that +Michaelson I think I've spoken about + + align:start position:0% +Michaelson I think I've spoken about + + + align:start position:0% +Michaelson I think I've spoken about +this with some of my students before + + align:start position:0% +this with some of my students before + + + align:start position:0% +this with some of my students before +that Michaelson he wrote quite a lot + + align:start position:0% +that Michaelson he wrote quite a lot + + + align:start position:0% +that Michaelson he wrote quite a lot +about measuring wavelengths using that + + align:start position:0% +about measuring wavelengths using that + + + align:start position:0% +about measuring wavelengths using that +interferometer uh and then many many + + align:start position:0% +interferometer uh and then many many + + + align:start position:0% +interferometer uh and then many many +years later uh people came up with this + + align:start position:0% +years later uh people came up with this + + + align:start position:0% +years later uh people came up with this +bright idea of + + align:start position:0% +bright idea of + + + align:start position:0% +bright idea of +using um what they call the low + + align:start position:0% +using um what they call the low + + + align:start position:0% +using um what they call the low +coherence interferometer or the white + + align:start position:0% +coherence interferometer or the white + + + align:start position:0% +coherence interferometer or the white +light inter ometer uh to measure + + align:start position:0% +light inter ometer uh to measure + + + align:start position:0% +light inter ometer uh to measure +distances but as far as I know + + align:start position:0% +distances but as far as I know + + + align:start position:0% +distances but as far as I know +Michaelson never never suggested this + + align:start position:0% +Michaelson never never suggested this + + + align:start position:0% +Michaelson never never suggested this +I've never found it in any of these + + align:start position:0% +I've never found it in any of these + + + align:start position:0% +I've never found it in any of these +papers right anyway so this is another + + align:start position:0% +papers right anyway so this is another + + + align:start position:0% +papers right anyway so this is another +application uh here we're going to look + + align:start position:0% +application uh here we're going to look + + + align:start position:0% +application uh here we're going to look +at a a real uh object that we put in + + align:start position:0% +at a a real uh object that we put in + + + align:start position:0% +at a a real uh object that we put in +there and try and find out something + + align:start position:0% +there and try and find out something + + + align:start position:0% +there and try and find out something +about it so we put in this um um lump of + + align:start position:0% +about it so we put in this um um lump of + + + align:start position:0% +about it so we put in this um um lump of +material a l length L A Certain + + align:start position:0% +material a l length L A Certain + + + align:start position:0% +material a l length L A Certain +refractive index uh and you can see now + + align:start position:0% +refractive index uh and you can see now + + + align:start position:0% +refractive index uh and you can see now +then that the uh the phase of this light + + align:start position:0% +then that the uh the phase of this light + + + align:start position:0% +then that the uh the phase of this light +when it gets there uh is going to be + + align:start position:0% +when it gets there uh is going to be + + + align:start position:0% +when it gets there uh is going to be +changed uh by the uh By the Light + + align:start position:0% +changed uh by the uh By the Light + + + align:start position:0% +changed uh by the uh By the Light +traveling through that material uh and + + align:start position:0% + + + + align:start position:0% + +um have we taken into account George + + align:start position:0% +um have we taken into account George + + + align:start position:0% +um have we taken into account George +that it's gone through twice here that + + align:start position:0% +that it's gone through twice here that + + + align:start position:0% +that it's gone through twice here that +the or even on the previous + + align:start position:0% +the or even on the previous + + + align:start position:0% +the or even on the previous +one uh + + align:start position:0% +one uh + + + align:start position:0% +one uh +there there ought to be a two in there + + align:start position:0% +there there ought to be a two in there + + + align:start position:0% +there there ought to be a two in there +there ought to be a two in here AR there + + align:start position:0% +there ought to be a two in here AR there + + + align:start position:0% +there ought to be a two in here AR there +all right so uh this the phase + + align:start position:0% +all right so uh this the phase + + + align:start position:0% +all right so uh this the phase +difference is is is actually twice this + + align:start position:0% +difference is is is actually twice this + + + align:start position:0% +difference is is is actually twice this +because this it makes it has this amount + + align:start position:0% +because this it makes it has this amount + + + align:start position:0% +because this it makes it has this amount +of phase difference on the way in and on + + align:start position:0% +of phase difference on the way in and on + + + align:start position:0% +of phase difference on the way in and on +the way + + align:start position:0% +the way + + + align:start position:0% +the way +out uh so I had noticed that before + + align:start position:0% +out uh so I had noticed that before + + + align:start position:0% +out uh so I had noticed that before +either so but it applies to this next + + align:start position:0% +either so but it applies to this next + + + align:start position:0% +either so but it applies to this next +one as well uh so so this this one the + + align:start position:0% +one as well uh so so this this one the + + + align:start position:0% +one as well uh so so this this one the +light goes through this uh object here + + align:start position:0% +light goes through this uh object here + + + align:start position:0% +light goes through this uh object here +uh and so there's this extra phased + + align:start position:0% +uh and so there's this extra phased + + + align:start position:0% +uh and so there's this extra phased +delay that comes because of this object + + align:start position:0% +delay that comes because of this object + + + align:start position:0% +delay that comes because of this object +which is this bit here so again there + + align:start position:0% +which is this bit here so again there + + + align:start position:0% +which is this bit here so again there +ought to be a factor of two for all all + + align:start position:0% +ought to be a factor of two for all all + + + align:start position:0% +ought to be a factor of two for all all +of these terms uh and um so so there we + + align:start position:0% +of these terms uh and um so so there we + + + align:start position:0% +of these terms uh and um so so there we +are though we've got this extra um + + align:start position:0% +are though we've got this extra um + + + align:start position:0% +are though we've got this extra um +Optical path uh and uh so now we can uh + + align:start position:0% +Optical path uh and uh so now we can uh + + + align:start position:0% +Optical path uh and uh so now we can uh +measure the optical path of that object + + align:start position:0% +measure the optical path of that object + + + align:start position:0% +measure the optical path of that object +again modulo 2 + + align:start position:0% +again modulo 2 + + + align:start position:0% +again modulo 2 +pi uh so if this is if if if this is um + + align:start position:0% +pi uh so if this is if if if this is um + + + align:start position:0% +pi uh so if this is if if if this is um +many wavelengths you might have trouble + + align:start position:0% +many wavelengths you might have trouble + + + align:start position:0% +many wavelengths you might have trouble +to to know uh exactly how long it is of + + align:start position:0% +to to know uh exactly how long it is of + + + align:start position:0% +to to know uh exactly how long it is of +course because of the the the wrapping + + align:start position:0% +course because of the the the wrapping + + + align:start position:0% +course because of the the the wrapping +of the phase again uh + + align:start position:0% +of the phase again uh + + + align:start position:0% +of the phase again uh +so uh so so if if to this modulo 2 pi we + + align:start position:0% +so uh so so if if to this modulo 2 pi we + + + align:start position:0% +so uh so so if if to this modulo 2 pi we +can actually measure uh the uh this is + + align:start position:0% +can actually measure uh the uh this is + + + align:start position:0% +can actually measure uh the uh this is +the optical path difference n -1 * L the + + align:start position:0% +the optical path difference n -1 * L the + + + align:start position:0% +the optical path difference n -1 * L the +minus one of course is because the other + + align:start position:0% +minus one of course is because the other + + + align:start position:0% +minus one of course is because the other +but the reference has gone through air + + align:start position:0% +but the reference has gone through air + + + align:start position:0% +but the reference has gone through air +when this has gone through this material + + align:start position:0% +when this has gone through this material + + + align:start position:0% +when this has gone through this material +right so what we measure is nus1 * L if + + align:start position:0% +right so what we measure is nus1 * L if + + + align:start position:0% +right so what we measure is nus1 * L if +we knew what n is we could know what L + + align:start position:0% +we knew what n is we could know what L + + + align:start position:0% +we knew what n is we could know what L +is if we knew what L is we could know + + align:start position:0% +is if we knew what L is we could know + + + align:start position:0% +is if we knew what L is we could know +what n + + align:start position:0% +what n + + + align:start position:0% +what n +is uh but as it says there but if you + + align:start position:0% +is uh but as it says there but if you + + + align:start position:0% +is uh but as it says there but if you +don't know either then you can't find + + align:start position:0% +don't know either then you can't find + + + align:start position:0% +don't know either then you can't find +either you all you know is what n minus + + align:start position:0% +either you all you know is what n minus + + + align:start position:0% +either you all you know is what n minus +one L is um anyone got any ideas about + + align:start position:0% +one L is um anyone got any ideas about + + + align:start position:0% +one L is um anyone got any ideas about +how you might what what might you do to + + align:start position:0% +how you might what what might you do to + + + align:start position:0% +how you might what what might you do to +get + + align:start position:0% +get + + + align:start position:0% +get +both of those if you if you wanted to + + align:start position:0% +both of those if you if you wanted to + + + align:start position:0% +both of those if you if you wanted to +know both of + + align:start position:0% +know both of + + + align:start position:0% +know both of +those any ideas how you could do + + align:start position:0% + + + + align:start position:0% + +that based on what though you'd have to + + align:start position:0% +that based on what though you'd have to + + + align:start position:0% +that based on what though you'd have to +have two + + align:start position:0% +have two + + + align:start position:0% +have two +measurements press the button + + align:start position:0% + + + + align:start position:0% + +please uh yeah someone suggested that + + align:start position:0% +please uh yeah someone suggested that + + + align:start position:0% +please uh yeah someone suggested that +use two wav length to set up + + align:start position:0% +use two wav length to set up + + + align:start position:0% +use two wav length to set up +simultaneous equations exactly good one + + align:start position:0% +simultaneous equations exactly good one + + + align:start position:0% +simultaneous equations exactly good one +yeah who who said it + + align:start position:0% +yeah who who said it + + + align:start position:0% +yeah who who said it +someone in the said it you're not + + align:start position:0% +someone in the said it you're not + + + align:start position:0% +someone in the said it you're not +getting the full credit for that sh yeah + + align:start position:0% +getting the full credit for that sh yeah + + + align:start position:0% +getting the full credit for that sh yeah +yeah anyway someone got it uh so yeah so + + align:start position:0% +yeah anyway someone got it uh so yeah so + + + align:start position:0% +yeah anyway someone got it uh so yeah so +if you measured this for two different + + align:start position:0% +if you measured this for two different + + + align:start position:0% +if you measured this for two different +wavelengths uh then you could have a + + align:start position:0% +wavelengths uh then you could have a + + + align:start position:0% +wavelengths uh then you could have a +pair of simultaneous equations and you + + align:start position:0% +pair of simultaneous equations and you + + + align:start position:0% +pair of simultaneous equations and you +could solve uh solve for both of those + + align:start position:0% +could solve uh solve for both of those + + + align:start position:0% +could solve uh solve for both of those +that of course assuming there there's no + + align:start position:0% +that of course assuming there there's no + + + align:start position:0% +that of course assuming there there's no +dispersion if the if if the if n changes + + align:start position:0% +dispersion if the if if the if n changes + + + align:start position:0% +dispersion if the if if the if n changes +with wavelength then you're still back + + align:start position:0% +with wavelength then you're still back + + + align:start position:0% +with wavelength then you're still back +to square one + + align:start position:0% +to square one + + + align:start position:0% +to square one +unless you do some more wavelengths I + + align:start position:0% +unless you do some more wavelengths I + + + align:start position:0% +unless you do some more wavelengths I +guess but anyway yeah so it just shows + + align:start position:0% +guess but anyway yeah so it just shows + + + align:start position:0% +guess but anyway yeah so it just shows +you that you can um do a lot of these + + align:start position:0% +you that you can um do a lot of these + + + align:start position:0% +you that you can um do a lot of these +experiments very easily uh so now the + + align:start position:0% +experiments very easily uh so now the + + + align:start position:0% +experiments very easily uh so now the +sort of these are used this um Micron + + align:start position:0% +sort of these are used this um Micron + + + align:start position:0% +sort of these are used this um Micron +interferometer is used a lot in uh + + align:start position:0% +interferometer is used a lot in uh + + + align:start position:0% +interferometer is used a lot in uh +Metrology industrial sort of Metrology + + align:start position:0% +Metrology industrial sort of Metrology + + + align:start position:0% +Metrology industrial sort of Metrology +and uh you know all countries have their + + align:start position:0% +and uh you know all countries have their + + + align:start position:0% +and uh you know all countries have their +um well you in the US it used to be + + align:start position:0% +um well you in the US it used to be + + + align:start position:0% +um well you in the US it used to be +called The National Bureau of Standards + + align:start position:0% +called The National Bureau of Standards + + + align:start position:0% +called The National Bureau of Standards +didn't it but I don't I don't know that + + align:start position:0% +didn't it but I don't I don't know that + + + align:start position:0% +didn't it but I don't I don't know that +that exists anymore does it nist nist + + align:start position:0% +that exists anymore does it nist nist + + + align:start position:0% +that exists anymore does it nist nist +that's right it changed I don't know why + + align:start position:0% +that's right it changed I don't know why + + + align:start position:0% +that's right it changed I don't know why +it changed its name but anyway uh so all + + align:start position:0% +it changed its name but anyway uh so all + + + align:start position:0% +it changed its name but anyway uh so all +countries have got this they uh they + + align:start position:0% +countries have got this they uh they + + + align:start position:0% +countries have got this they uh they +they have this uh standard measures that + + align:start position:0% +they have this uh standard measures that + + + align:start position:0% +they have this uh standard measures that +they have procedures for + + align:start position:0% +they have procedures for + + + align:start position:0% +they have procedures for +calibrating uh distances and so on uh + + align:start position:0% +calibrating uh distances and so on uh + + + align:start position:0% +calibrating uh distances and so on uh +and uh the idea is that you know if a + + align:start position:0% +and uh the idea is that you know if a + + + align:start position:0% +and uh the idea is that you know if a +company uh like General Motors is making + + align:start position:0% +company uh like General Motors is making + + + align:start position:0% +company uh like General Motors is making +uh um parts for a + + align:start position:0% +uh um parts for a + + + align:start position:0% +uh um parts for a +car uh that they will those those parts + + align:start position:0% +car uh that they will those those parts + + + align:start position:0% +car uh that they will those those parts +will + + align:start position:0% +will + + + align:start position:0% +will +fit uh as a spare for another car that's + + align:start position:0% +fit uh as a spare for another car that's + + + align:start position:0% +fit uh as a spare for another car that's +made by another Factory right so if if + + align:start position:0% +made by another Factory right so if if + + + align:start position:0% +made by another Factory right so if if +if um they know if you say say you make + + align:start position:0% +if um they know if you say say you make + + + align:start position:0% +if um they know if you say say you make +some um shaft that's got that's supposed + + align:start position:0% +some um shaft that's got that's supposed + + + align:start position:0% +some um shaft that's got that's supposed +to be 1 in in + + align:start position:0% +to be 1 in in + + + align:start position:0% +to be 1 in in +diameter and uh you you you want it to + + align:start position:0% +diameter and uh you you you want it to + + + align:start position:0% +diameter and uh you you you want it to +be accurately 1 in + + align:start position:0% +be accurately 1 in + + + align:start position:0% +be accurately 1 in +diameter uh otherwise the the bit from + + align:start position:0% +diameter uh otherwise the the bit from + + + align:start position:0% +diameter uh otherwise the the bit from +one place wouldn't fit the bit from the + + align:start position:0% +one place wouldn't fit the bit from the + + + align:start position:0% +one place wouldn't fit the bit from the +other uh there is actually a true story + + align:start position:0% +other uh there is actually a true story + + + align:start position:0% +other uh there is actually a true story +about that uh a thing called the Vicor + + align:start position:0% +about that uh a thing called the Vicor + + + align:start position:0% +about that uh a thing called the Vicor +inch Vicor is an engineering company in + + align:start position:0% +inch Vicor is an engineering company in + + + align:start position:0% +inch Vicor is an engineering company in +the UK uh and um this this Vicor inch + + align:start position:0% +the UK uh and um this this Vicor inch + + + align:start position:0% +the UK uh and um this this Vicor inch +was a big thing that came up during the + + align:start position:0% +was a big thing that came up during the + + + align:start position:0% +was a big thing that came up during the +second World War uh where uh lots of + + align:start position:0% +second World War uh where uh lots of + + + align:start position:0% +second World War uh where uh lots of +factories all over UK were converted to + + align:start position:0% +factories all over UK were converted to + + + align:start position:0% +factories all over UK were converted to +make + + align:start position:0% +make + + + align:start position:0% +make +Munitions uh and um some somewhere down + + align:start position:0% +Munitions uh and um some somewhere down + + + align:start position:0% +Munitions uh and um some somewhere down +down the line people realized that + + align:start position:0% +down the line people realized that + + + align:start position:0% +down the line people realized that +Vickers had a different inch from + + align:start position:0% +Vickers had a different inch from + + + align:start position:0% +Vickers had a different inch from +everyone + + align:start position:0% +everyone + + + align:start position:0% +everyone +else uh so you know when when they made + + align:start position:0% +else uh so you know when when they made + + + align:start position:0% +else uh so you know when when they made +a shell and tried putting it in the + + align:start position:0% +a shell and tried putting it in the + + + align:start position:0% +a shell and tried putting it in the +barrel of the gun it didn't quite fit So + + align:start position:0% +barrel of the gun it didn't quite fit So + + + align:start position:0% +barrel of the gun it didn't quite fit So +eventually that was sorted out they they + + align:start position:0% +eventually that was sorted out they they + + + align:start position:0% +eventually that was sorted out they they +they worked out what the problem was and + + align:start position:0% +they worked out what the problem was and + + + align:start position:0% +they worked out what the problem was and +I guess it's that sort of problem that + + align:start position:0% +I guess it's that sort of problem that + + + align:start position:0% +I guess it's that sort of problem that +makes it uh so that the companies now uh + + align:start position:0% +makes it uh so that the companies now uh + + + align:start position:0% +makes it uh so that the companies now uh +obviously uh you know the countries keep + + align:start position:0% +obviously uh you know the countries keep + + + align:start position:0% +obviously uh you know the countries keep +these standards and so on so the sort of + + align:start position:0% +these standards and so on so the sort of + + + align:start position:0% +these standards and so on so the sort of +thing you might do uh is measure the + + align:start position:0% +thing you might do uh is measure the + + + align:start position:0% +thing you might do uh is measure the +height of this uh let's say you you you + + align:start position:0% +height of this uh let's say you you you + + + align:start position:0% +height of this uh let's say you you you +put in that you they have these things + + align:start position:0% +put in that you they have these things + + + align:start position:0% +put in that you they have these things +called gauge blocks the lot of you are + + align:start position:0% +called gauge blocks the lot of you are + + + align:start position:0% +called gauge blocks the lot of you are +mechanical engineer so you must know + + align:start position:0% +mechanical engineer so you must know + + + align:start position:0% +mechanical engineer so you must know +about gauge blocks so these are uh you + + align:start position:0% +about gauge blocks so these are uh you + + + align:start position:0% +about gauge blocks so these are uh you +can buy these standard lumps of metal + + align:start position:0% +can buy these standard lumps of metal + + + align:start position:0% +can buy these standard lumps of metal +that have got a certain thickness uh and + + align:start position:0% +that have got a certain thickness uh and + + + align:start position:0% +that have got a certain thickness uh and +uh so you put this lamp of metal in here + + align:start position:0% +uh so you put this lamp of metal in here + + + align:start position:0% +uh so you put this lamp of metal in here +and measure the thickness of it using an + + align:start position:0% +and measure the thickness of it using an + + + align:start position:0% +and measure the thickness of it using an +interferometer uh and uh and then um so + + align:start position:0% +interferometer uh and uh and then um so + + + align:start position:0% +interferometer uh and uh and then um so +the you know these standards of course + + align:start position:0% +the you know these standards of course + + + align:start position:0% +the you know these standards of course +they have the what they call primary + + align:start position:0% +they have the what they call primary + + + align:start position:0% +they have the what they call primary +standards and then they're handed down + + align:start position:0% +standards and then they're handed down + + + align:start position:0% +standards and then they're handed down +uh the actual I'm not quite sure how the + + align:start position:0% +uh the actual I'm not quite sure how the + + + align:start position:0% +uh the actual I'm not quite sure how the +thing the length works anymore but it's + + align:start position:0% +thing the length works anymore but it's + + + align:start position:0% +thing the length works anymore but it's +all defined in terms of the wavelength + + align:start position:0% +all defined in terms of the wavelength + + + align:start position:0% +all defined in terms of the wavelength +of something isn't it uh and uh and then + + align:start position:0% +of something isn't it uh and uh and then + + + align:start position:0% +of something isn't it uh and uh and then +all the countries around the world they + + align:start position:0% +all the countries around the world they + + + align:start position:0% +all the countries around the world they +all have to compare uh their meter to + + align:start position:0% +all have to compare uh their meter to + + + align:start position:0% +all have to compare uh their meter to +make sure that they've all got the same + + align:start position:0% +make sure that they've all got the same + + + align:start position:0% +make sure that they've all got the same +meter uh and then within each country so + + align:start position:0% +meter uh and then within each country so + + + align:start position:0% +meter uh and then within each country so +in the US nist uh would then uh be + + align:start position:0% +in the US nist uh would then uh be + + + align:start position:0% +in the US nist uh would then uh be +measuring these gauge blocks that would + + align:start position:0% +measuring these gauge blocks that would + + + align:start position:0% +measuring these gauge blocks that would +be sent to them from other + + align:start position:0% +be sent to them from other + + + align:start position:0% +be sent to them from other +companies uh to make sure that they've + + align:start position:0% +companies uh to make sure that they've + + + align:start position:0% +companies uh to make sure that they've +got the right size and then in the + + align:start position:0% +got the right size and then in the + + + align:start position:0% +got the right size and then in the +companies then they would compare those + + align:start position:0% +companies then they would compare those + + + align:start position:0% +companies then they would compare those +gauge blocks against other uh other um + + align:start position:0% +gauge blocks against other uh other um + + + align:start position:0% +gauge blocks against other uh other um +gauge blocks and other + + align:start position:0% +gauge blocks and other + + + align:start position:0% +gauge blocks and other +things so that this is what you one of + + align:start position:0% +things so that this is what you one of + + + align:start position:0% +things so that this is what you one of +the things you use this + + align:start position:0% +the things you use this + + + align:start position:0% +the things you use this +for okay so now uh Fringe visibility + + align:start position:0% +for okay so now uh Fringe visibility + + + align:start position:0% +for okay so now uh Fringe visibility +yeah so we've said that you get these + + align:start position:0% +yeah so we've said that you get these + + + align:start position:0% +yeah so we've said that you get these +fringes um perhaps I have to go back + + align:start position:0% +fringes um perhaps I have to go back + + + align:start position:0% +fringes um perhaps I have to go back +back and explain that a bit + + align:start position:0% +back and explain that a bit + + + align:start position:0% +back and explain that a bit +more + + align:start position:0% +more + + + align:start position:0% +more +uh back to this + + align:start position:0% +uh back to this + + + align:start position:0% +uh back to this +one so you can see here uh we've got a + + align:start position:0% +one so you can see here uh we've got a + + + align:start position:0% +one so you can see here uh we've got a +constant term plus a sinusoidal type + + align:start position:0% +constant term plus a sinusoidal type + + + align:start position:0% +constant term plus a sinusoidal type +term or cosinusoidal type term uh and + + align:start position:0% +term or cosinusoidal type term uh and + + + align:start position:0% +term or cosinusoidal type term uh and +the you can see that what this term m is + + align:start position:0% +the you can see that what this term m is + + + align:start position:0% +the you can see that what this term m is +called the contrast or Fringe + + align:start position:0% +called the contrast or Fringe + + + align:start position:0% +called the contrast or Fringe +visibility so if m is one uh then you + + align:start position:0% +visibility so if m is one uh then you + + + align:start position:0% +visibility so if m is one uh then you +can see that there are going to be + + align:start position:0% +can see that there are going to be + + + align:start position:0% +can see that there are going to be +particular values of Del to five uh this + + align:start position:0% +particular values of Del to five uh this + + + align:start position:0% +particular values of Del to five uh this +intensity is going to go to + + align:start position:0% +intensity is going to go to + + + align:start position:0% +intensity is going to go to +zero right so that's when you get uh + + align:start position:0% +zero right so that's when you get uh + + + align:start position:0% +zero right so that's when you get uh +you've got very high uh Fringe + + align:start position:0% +you've got very high uh Fringe + + + align:start position:0% +you've got very high uh Fringe +visibility and you can see that this + + align:start position:0% +visibility and you can see that this + + + align:start position:0% +visibility and you can see that this +visibility depends on this a 2 a as over + + align:start position:0% +visibility depends on this a 2 a as over + + + align:start position:0% +visibility depends on this a 2 a as over +a r 2 + a s and you can show quite + + align:start position:0% +a r 2 + a s and you can show quite + + + align:start position:0% +a r 2 + a s and you can show quite +easily that that is going to uh reach a + + align:start position:0% +easily that that is going to uh reach a + + + align:start position:0% +easily that that is going to uh reach a +maximum going to is going to be equal to + + align:start position:0% +maximum going to is going to be equal to + + + align:start position:0% +maximum going to is going to be equal to +1 when AR R equals a s so if you ensure + + align:start position:0% +1 when AR R equals a s so if you ensure + + + align:start position:0% +1 when AR R equals a s so if you ensure +that a equals as uh then you're going to + + align:start position:0% +that a equals as uh then you're going to + + + align:start position:0% +that a equals as uh then you're going to +get your your visibility of one I guess + + align:start position:0% +get your your visibility of one I guess + + + align:start position:0% +get your your visibility of one I guess +it can't be bigger than one because that + + align:start position:0% +it can't be bigger than one because that + + + align:start position:0% +it can't be bigger than one because that +would mean that the intensity go + + align:start position:0% +would mean that the intensity go + + + align:start position:0% +would mean that the intensity go +negative which is not possible right so + + align:start position:0% +negative which is not possible right so + + + align:start position:0% +negative which is not possible right so +this this plots what it is what what you + + align:start position:0% +this this plots what it is what what you + + + align:start position:0% +this this plots what it is what what you +would see as a function of Delta + + align:start position:0% +would see as a function of Delta + + + align:start position:0% +would see as a function of Delta +F uh and um uh for a particular value of + + align:start position:0% +F uh and um uh for a particular value of + + + align:start position:0% +F uh and um uh for a particular value of +M so there some + + align:start position:0% +M so there some + + + align:start position:0% +M so there some +background sometimes called the bias uh + + align:start position:0% +background sometimes called the bias uh + + + align:start position:0% +background sometimes called the bias uh +and then you've got some Wiggles on top + + align:start position:0% +and then you've got some Wiggles on top + + + align:start position:0% +and then you've got some Wiggles on top +of that uh and so this plot is plotted + + align:start position:0% +of that uh and so this plot is plotted + + + align:start position:0% +of that uh and so this plot is plotted +against Delta fi uh Delta fi could + + align:start position:0% +against Delta fi uh Delta fi could + + + align:start position:0% +against Delta fi uh Delta fi could +change by a number of different ways of + + align:start position:0% +change by a number of different ways of + + + align:start position:0% +change by a number of different ways of +course one way it could change is if you + + align:start position:0% +course one way it could change is if you + + + align:start position:0% +course one way it could change is if you +actually move the mirror another way it + + align:start position:0% +actually move the mirror another way it + + + align:start position:0% +actually move the mirror another way it +could change is if if you tilted the + + align:start position:0% +could change is if if you tilted the + + + align:start position:0% +could change is if if you tilted the +mirror if you tilted the mirror then + + align:start position:0% +mirror if you tilted the mirror then + + + align:start position:0% +mirror if you tilted the mirror then +there'd be different Delta fi at + + align:start position:0% +there'd be different Delta fi at + + + align:start position:0% +there'd be different Delta fi at +different transverse positions on the + + align:start position:0% +different transverse positions on the + + + align:start position:0% +different transverse positions on the +mirror uh and if we take a r equal as + + align:start position:0% +mirror uh and if we take a r equal as + + + align:start position:0% +mirror uh and if we take a r equal as +s then you've got perfect contrast uh m + + align:start position:0% +s then you've got perfect contrast uh m + + + align:start position:0% +s then you've got perfect contrast uh m +equal 1 uh you see it goes right down to + + align:start position:0% +equal 1 uh you see it goes right down to + + + align:start position:0% +equal 1 uh you see it goes right down to +zero uh and that's the the the um + + align:start position:0% +zero uh and that's the the the um + + + align:start position:0% +zero uh and that's the the the um +highest visibility of the fringes that + + align:start position:0% +highest visibility of the fringes that + + + align:start position:0% +highest visibility of the fringes that +you can get if on the other hand uh you + + align:start position:0% +you can get if on the other hand uh you + + + align:start position:0% +you can get if on the other hand uh you +you find uh that if you take let's say + + align:start position:0% +you find uh that if you take let's say + + + align:start position:0% +you find uh that if you take let's say +uh the reference beam to be much + + align:start position:0% +uh the reference beam to be much + + + align:start position:0% +uh the reference beam to be much +stronger than the signal beam uh then + + align:start position:0% +stronger than the signal beam uh then + + + align:start position:0% +stronger than the signal beam uh then +you can see that m is going to tend to + + align:start position:0% +you can see that m is going to tend to + + + align:start position:0% +you can see that m is going to tend to +zero the contrast is going to be become + + align:start position:0% +zero the contrast is going to be become + + + align:start position:0% +zero the contrast is going to be become +very weak uh actually uh sometimes + + align:start position:0% +very weak uh actually uh sometimes + + + align:start position:0% +very weak uh actually uh sometimes +people do do that um contrast is not + + align:start position:0% +people do do that um contrast is not + + + align:start position:0% +people do do that um contrast is not +necessarily the most important thing uh + + align:start position:0% +necessarily the most important thing uh + + + align:start position:0% +necessarily the most important thing uh +because if you notice what we had + + align:start position:0% +because if you notice what we had + + + align:start position:0% +because if you notice what we had +before + + align:start position:0% + + + + align:start position:0% + +uh you see + + align:start position:0% +uh you see + + + align:start position:0% +uh you see +that um the the U + + align:start position:0% +that um the the U + + + align:start position:0% +that um the the U +the let's go back to the previous + + align:start position:0% +the let's go back to the previous + + + align:start position:0% +the let's go back to the previous +one + + align:start position:0% +one + + + align:start position:0% +one +yeah let's go back to this one here you + + align:start position:0% +yeah let's go back to this one here you + + + align:start position:0% +yeah let's go back to this one here you +can see that youve got these three + + align:start position:0% +can see that youve got these three + + + align:start position:0% +can see that youve got these three +terms uh so what we're saying is if you + + align:start position:0% +terms uh so what we're saying is if you + + + align:start position:0% +terms uh so what we're saying is if you +make AR much bigger than as uh then you + + align:start position:0% +make AR much bigger than as uh then you + + + align:start position:0% +make AR much bigger than as uh then you +you you you make the contrast is going + + align:start position:0% +you you you make the contrast is going + + + align:start position:0% +you you you make the contrast is going +to get smaller and smaller because + + align:start position:0% +to get smaller and smaller because + + + align:start position:0% +to get smaller and smaller because +obviously this term is going to become + + align:start position:0% +obviously this term is going to become + + + align:start position:0% +obviously this term is going to become +much bigger than this one uh but + + align:start position:0% +much bigger than this one uh but + + + align:start position:0% +much bigger than this one uh but +nevertheless it does actually make this + + align:start position:0% +nevertheless it does actually make this + + + align:start position:0% +nevertheless it does actually make this +term bigger so if actually what you're + + align:start position:0% +term bigger so if actually what you're + + + align:start position:0% +term bigger so if actually what you're +trying to do uh is measure this signal + + align:start position:0% +trying to do uh is measure this signal + + + align:start position:0% +trying to do uh is measure this signal +in in in some background of noise it's + + align:start position:0% +in in in some background of noise it's + + + align:start position:0% +in in in some background of noise it's +sometimes it's sometimes a good thing to + + align:start position:0% +sometimes it's sometimes a good thing to + + + align:start position:0% +sometimes it's sometimes a good thing to +make AR bigger than as because if as you + + align:start position:0% +make AR bigger than as because if as you + + + align:start position:0% +make AR bigger than as because if as you +increase AR it increases the strength of + + align:start position:0% +increase AR it increases the strength of + + + align:start position:0% +increase AR it increases the strength of +this uh of of this interference term uh + + align:start position:0% +this uh of of this interference term uh + + + align:start position:0% +this uh of of this interference term uh +and that's that's the principle that's + + align:start position:0% +and that's that's the principle that's + + + align:start position:0% +and that's that's the principle that's +used in in hod + + align:start position:0% +used in in hod + + + align:start position:0% +used in in hod +interferometry uh so not always true + + align:start position:0% +interferometry uh so not always true + + + align:start position:0% +interferometry uh so not always true +that you you try and make it the the the + + align:start position:0% +that you you try and make it the the the + + + align:start position:0% +that you you try and make it the the the +contrast as big as possible yeah um + + align:start position:0% +contrast as big as possible yeah um + + + align:start position:0% +contrast as big as possible yeah um +there is one more + + align:start position:0% +there is one more + + + align:start position:0% +there is one more +factor of two missing here at the on the + + align:start position:0% +factor of two missing here at the on the + + + align:start position:0% +factor of two missing here at the on the +left hand side bottom the swing of the + + align:start position:0% +left hand side bottom the swing of the + + + align:start position:0% +left hand side bottom the swing of the +fringes should be 2 m * I not not M + + align:start position:0% +fringes should be 2 m * I not not M + + + align:start position:0% +fringes should be 2 m * I not not M +times yeah there a fact of two Miss + + align:start position:0% +times yeah there a fact of two Miss + + + align:start position:0% +times yeah there a fact of two Miss +right that's quite unusual three slides + + align:start position:0% +right that's quite unusual three slides + + + align:start position:0% +right that's quite unusual three slides +in a row they're all missing a factor of + + align:start position:0% +in a row they're all missing a factor of + + + align:start position:0% +in a row they're all missing a factor of +two and they don't cancel out yeah I + + align:start position:0% +two and they don't cancel out yeah I + + + align:start position:0% +two and they don't cancel out yeah I +guess + + align:start position:0% + + + + align:start position:0% + +so okay so that's the microen + + align:start position:0% +so okay so that's the microen + + + align:start position:0% +so okay so that's the microen +interferometer um so so the micro + + align:start position:0% +interferometer um so so the micro + + + align:start position:0% +interferometer um so so the micro +interferometer is basically you can see + + align:start position:0% +interferometer is basically you can see + + + align:start position:0% +interferometer is basically you can see +a sort of reflection + + align:start position:0% +a sort of reflection + + + align:start position:0% +a sort of reflection +interferometer uh and we're now going to + + align:start position:0% +interferometer uh and we're now going to + + + align:start position:0% +interferometer uh and we're now going to +go onto the max Zander interferometer + + align:start position:0% +go onto the max Zander interferometer + + + align:start position:0% +go onto the max Zander interferometer +which is basically a transmission + + align:start position:0% +which is basically a transmission + + + align:start position:0% +which is basically a transmission +interferometer so it's the principle is + + align:start position:0% +interferometer so it's the principle is + + + align:start position:0% +interferometer so it's the principle is +very + + align:start position:0% +very + + + align:start position:0% +very +similar uh you split the light into two + + align:start position:0% +similar uh you split the light into two + + + align:start position:0% +similar uh you split the light into two +paths the two paths uh two light beams + + align:start position:0% +paths the two paths uh two light beams + + + align:start position:0% +paths the two paths uh two light beams +go through different path and then you + + align:start position:0% +go through different path and then you + + + align:start position:0% +go through different path and then you +combine them uh onto onto a detector um + + align:start position:0% +combine them uh onto onto a detector um + + + align:start position:0% +combine them uh onto onto a detector um +but so so this works in transmission + + align:start position:0% +but so so this works in transmission + + + align:start position:0% +but so so this works in transmission +mode + + align:start position:0% +mode + + + align:start position:0% +mode +here you got you're looking through an + + align:start position:0% +here you got you're looking through an + + + align:start position:0% +here you got you're looking through an +object uh so so now you're not going to + + align:start position:0% +object uh so so now you're not going to + + + align:start position:0% +object uh so so now you're not going to +get that factor of two of course because + + align:start position:0% +get that factor of two of course because + + + align:start position:0% +get that factor of two of course because +the light is only going through it + + align:start position:0% +the light is only going through it + + + align:start position:0% +the light is only going through it +once uh so the light goes through here + + align:start position:0% +once uh so the light goes through here + + + align:start position:0% +once uh so the light goes through here +uh you notice that the way this has been + + align:start position:0% +uh you notice that the way this has been + + + align:start position:0% +uh you notice that the way this has been +drawn uh it's been drawn so that this + + align:start position:0% +drawn uh it's been drawn so that this + + + align:start position:0% +drawn uh it's been drawn so that this +light is going like this this light is + + align:start position:0% +light is going like this this light is + + + align:start position:0% +light is going like this this light is +going like this so you can see this path + + align:start position:0% +going like this so you can see this path + + + align:start position:0% +going like this so you can see this path +and this path are roughly + + align:start position:0% +and this path are roughly + + + align:start position:0% +and this path are roughly +equal um you might you might equally + + align:start position:0% +equal um you might you might equally + + + align:start position:0% +equal um you might you might equally +well you you you could have thought of + + align:start position:0% +well you you you could have thought of + + + align:start position:0% +well you you you could have thought of +made making this by by by doing it more + + align:start position:0% +made making this by by by doing it more + + + align:start position:0% +made making this by by by doing it more +like couldn't you you could have done + + align:start position:0% +like couldn't you you could have done + + + align:start position:0% +like couldn't you you could have done +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +it like + + align:start position:0% + + + + align:start position:0% + +that um so where now you can see if we'd + + align:start position:0% +that um so where now you can see if we'd + + + align:start position:0% +that um so where now you can see if we'd +have made it like + + align:start position:0% +have made it like + + + align:start position:0% +have made it like +that this this path is obviously longer + + align:start position:0% +that this this path is obviously longer + + + align:start position:0% +that this this path is obviously longer +than that path + + align:start position:0% +than that path + + + align:start position:0% +than that path +right so + + align:start position:0% +right so + + + align:start position:0% +right so +um I I guess nowadays if you if you did + + align:start position:0% +um I I guess nowadays if you if you did + + + align:start position:0% +um I I guess nowadays if you if you did +that experiment with a a with a a laser + + align:start position:0% +that experiment with a a with a a laser + + + align:start position:0% +that experiment with a a with a a laser +which has got a very long coherence + + align:start position:0% +which has got a very long coherence + + + align:start position:0% +which has got a very long coherence +length something like a frequency double + + align:start position:0% +length something like a frequency double + + + align:start position:0% +length something like a frequency double +yag laser this would work fine if you + + align:start position:0% +yag laser this would work fine if you + + + align:start position:0% +yag laser this would work fine if you +tried doing this + + align:start position:0% +tried doing this + + + align:start position:0% +tried doing this +with uh an ark lamp or something like + + align:start position:0% +with uh an ark lamp or something like + + + align:start position:0% +with uh an ark lamp or something like +that it wouldn't work uh because uh this + + align:start position:0% +that it wouldn't work uh because uh this + + + align:start position:0% +that it wouldn't work uh because uh this +distance is much longer uh than the + + align:start position:0% +distance is much longer uh than the + + + align:start position:0% +distance is much longer uh than the +coherence length of the source so you're + + align:start position:0% +coherence length of the source so you're + + + align:start position:0% +coherence length of the source so you're +you're you're all used to the idea uh + + align:start position:0% +you're you're all used to the idea uh + + + align:start position:0% +you're you're all used to the idea uh +that actually you don't see interference + + align:start position:0% +that actually you don't see interference + + + align:start position:0% +that actually you don't see interference +fringes all the time in the in the + + align:start position:0% +fringes all the time in the in the + + + align:start position:0% +fringes all the time in the in the +normal regular everyday life you don't + + align:start position:0% +normal regular everyday life you don't + + + align:start position:0% +normal regular everyday life you don't +see interference fringes very much uh + + align:start position:0% +see interference fringes very much uh + + + align:start position:0% +see interference fringes very much uh +and that's because in in everyday life + + align:start position:0% +and that's because in in everyday life + + + align:start position:0% +and that's because in in everyday life +normally the light is incoherent rather + + align:start position:0% +normally the light is incoherent rather + + + align:start position:0% +normally the light is incoherent rather +than coherent uh so uh if you make if + + align:start position:0% +than coherent uh so uh if you make if + + + align:start position:0% +than coherent uh so uh if you make if +you make this system here or the or the + + align:start position:0% +you make this system here or the or the + + + align:start position:0% +you make this system here or the or the +microson interferometer we showed before + + align:start position:0% +microson interferometer we showed before + + + align:start position:0% +microson interferometer we showed before +uh and you make it so that these paths + + align:start position:0% +uh and you make it so that these paths + + + align:start position:0% +uh and you make it so that these paths +are accurately the same + + align:start position:0% +are accurately the same + + + align:start position:0% +are accurately the same +length uh then you could get + + align:start position:0% +length uh then you could get + + + align:start position:0% +length uh then you could get +interference uh even with light from a + + align:start position:0% +interference uh even with light from a + + + align:start position:0% +interference uh even with light from a +you can get interference even from light + + align:start position:0% +you can get interference even from light + + + align:start position:0% +you can get interference even from light +from a Tungsten lamp Bol uh and U and + + align:start position:0% +from a Tungsten lamp Bol uh and U and + + + align:start position:0% +from a Tungsten lamp Bol uh and U and +they look they they produce really nice + + align:start position:0% +they look they they produce really nice + + + align:start position:0% +they look they they produce really nice +beautiful fringes with uh different + + align:start position:0% +beautiful fringes with uh different + + + align:start position:0% +beautiful fringes with uh different +colors maybe my students may have seen + + align:start position:0% +colors maybe my students may have seen + + + align:start position:0% +colors maybe my students may have seen +these in the lab um but anyway so here + + align:start position:0% +these in the lab um but anyway so here + + + align:start position:0% +these in the lab um but anyway so here +you can use this to measure the optical + + align:start position:0% +you can use this to measure the optical + + + align:start position:0% +you can use this to measure the optical +path path of some + + align:start position:0% +path path of some + + + align:start position:0% +path path of some +object uh and + + align:start position:0% +object uh and + + + align:start position:0% +object uh and +um yeah so so this is um yeah so this is + + align:start position:0% +um yeah so so this is um yeah so this is + + + align:start position:0% +um yeah so so this is um yeah so this is +now again looking at this um idea of + + align:start position:0% +now again looking at this um idea of + + + align:start position:0% +now again looking at this um idea of +tilting something I mentioned about + + align:start position:0% +tilting something I mentioned about + + + align:start position:0% +tilting something I mentioned about +tilting uh with regard to the microen + + align:start position:0% +tilting uh with regard to the microen + + + align:start position:0% +tilting uh with regard to the microen +interferometer I said if you tilt one of + + align:start position:0% +interferometer I said if you tilt one of + + + align:start position:0% +interferometer I said if you tilt one of +those mirrors you would actually get uh + + align:start position:0% +those mirrors you would actually get uh + + + align:start position:0% +those mirrors you would actually get uh +you would actually get the uh Optical + + align:start position:0% +you would actually get the uh Optical + + + align:start position:0% +you would actually get the uh Optical +path varying linearly with transverse + + align:start position:0% +path varying linearly with transverse + + + align:start position:0% +path varying linearly with transverse +distance so if you actually looked at an + + align:start position:0% +distance so if you actually looked at an + + + align:start position:0% +distance so if you actually looked at an +image of that interference what you + + align:start position:0% +image of that interference what you + + + align:start position:0% +image of that interference what you +would see would be a a a series of + + align:start position:0% +would see would be a a a series of + + + align:start position:0% +would see would be a a a series of +fringes and the uh spacing between the + + align:start position:0% +fringes and the uh spacing between the + + + align:start position:0% +fringes and the uh spacing between the +fringes would uh increase as you CH as + + align:start position:0% +fringes would uh increase as you CH as + + + align:start position:0% +fringes would uh increase as you CH as +you increase the angle so this is the + + align:start position:0% +you increase the angle so this is the + + + align:start position:0% +you increase the angle so this is the +same here we're we're getting the uh the + + align:start position:0% +same here we're we're getting the uh the + + + align:start position:0% +same here we're we're getting the uh the +offset between these two paths these + + align:start position:0% +offset between these two paths these + + + align:start position:0% +offset between these two paths these +these two beams by rotating uh this uh + + align:start position:0% +these two beams by rotating uh this uh + + + align:start position:0% +these two beams by rotating uh this uh +mirror + + align:start position:0% +mirror + + + align:start position:0% +mirror +slightly uh so and and then as you can + + align:start position:0% +slightly uh so and and then as you can + + + align:start position:0% +slightly uh so and and then as you can +see uh these two beams arrive on a CCD + + align:start position:0% +see uh these two beams arrive on a CCD + + + align:start position:0% +see uh these two beams arrive on a CCD +camera it shows here so you would + + align:start position:0% +camera it shows here so you would + + + align:start position:0% +camera it shows here so you would +actually in this case you would get some + + align:start position:0% +actually in this case you would get some + + + align:start position:0% +actually in this case you would get some +uh variation in intensity on this + + align:start position:0% +uh variation in intensity on this + + + align:start position:0% +uh variation in intensity on this +detector which you could actually + + align:start position:0% +detector which you could actually + + + align:start position:0% +detector which you could actually +measure with the detector so it would + + align:start position:0% +measure with the detector so it would + + + align:start position:0% +measure with the detector so it would +look something like this this would now + + align:start position:0% +look something like this this would now + + + align:start position:0% +look something like this this would now +be then a function of x uh rather than + + align:start position:0% +be then a function of x uh rather than + + + align:start position:0% +be then a function of x uh rather than +just being a function of the optical + + align:start position:0% +just being a function of the optical + + + align:start position:0% +just being a function of the optical +path uh difference so uh so this bit + + align:start position:0% +path uh difference so uh so this bit + + + align:start position:0% +path uh difference so uh so this bit +here I guess is uh is explaining is + + align:start position:0% +here I guess is uh is explaining is + + + align:start position:0% +here I guess is uh is explaining is +deriving that + + align:start position:0% +deriving that + + + align:start position:0% +deriving that +uh so we're adding two waves together + + align:start position:0% +uh so we're adding two waves together + + + align:start position:0% +uh so we're adding two waves together +one is arriving normally uh the other + + align:start position:0% +one is arriving normally uh the other + + + align:start position:0% +one is arriving normally uh the other +one is tilted through an angle + + align:start position:0% +one is tilted through an angle + + + align:start position:0% +one is tilted through an angle +Theta uh and so this this one here is + + align:start position:0% +Theta uh and so this this one here is + + + align:start position:0% +Theta uh and so this this one here is +going to have a a + + align:start position:0% +going to have a a + + + align:start position:0% +going to have a a +phase uh a linear phase variation as a + + align:start position:0% +phase uh a linear phase variation as a + + + align:start position:0% +phase uh a linear phase variation as a +function of x uh which will then appear + + align:start position:0% +function of x uh which will then appear + + + align:start position:0% +function of x uh which will then appear +inside this + + align:start position:0% + + + + align:start position:0% + +cosine right so uh finally what we get + + align:start position:0% +cosine right so uh finally what we get + + + align:start position:0% +cosine right so uh finally what we get +here then the the value of the uh this + + align:start position:0% +here then the the value of the uh this + + + align:start position:0% +here then the the value of the uh this +bit here the Z cos Theta is the is just + + align:start position:0% +bit here the Z cos Theta is the is just + + + align:start position:0% +bit here the Z cos Theta is the is just +this constant here uh so all that does + + align:start position:0% +this constant here uh so all that does + + + align:start position:0% +this constant here uh so all that does +is is shifts these these fringes this + + align:start position:0% +is is shifts these these fringes this + + + align:start position:0% +is is shifts these these fringes this +way uh but normally what if you were + + align:start position:0% +way uh but normally what if you were + + + align:start position:0% +way uh but normally what if you were +doing this experiment um one thing you + + align:start position:0% +doing this experiment um one thing you + + + align:start position:0% +doing this experiment um one thing you +could do then is very simply is to + + align:start position:0% +could do then is very simply is to + + + align:start position:0% +could do then is very simply is to +measure what this spatial wavelength of + + align:start position:0% +measure what this spatial wavelength of + + + align:start position:0% +measure what this spatial wavelength of +these fringes is uh and from that you + + align:start position:0% +these fringes is uh and from that you + + + align:start position:0% +these fringes is uh and from that you +could for example uh if you knew all the + + align:start position:0% +could for example uh if you knew all the + + + align:start position:0% +could for example uh if you knew all the +other things you could measure what this + + align:start position:0% +other things you could measure what this + + + align:start position:0% +other things you could measure what this +rotation Theta was couldn't you if you + + align:start position:0% +rotation Theta was couldn't you if you + + + align:start position:0% +rotation Theta was couldn't you if you +knew what the rotation Theta is uh then + + align:start position:0% +knew what the rotation Theta is uh then + + + align:start position:0% +knew what the rotation Theta is uh then +uh I don't know what you could measure + + align:start position:0% +uh I don't know what you could measure + + + align:start position:0% +uh I don't know what you could measure +but you could measure something + + align:start position:0% +but you could measure something + + + align:start position:0% +but you could measure something +probably right so um so the max Zender I + + align:start position:0% +probably right so um so the max Zender I + + + align:start position:0% +probably right so um so the max Zender I +mentioned that this is like a + + align:start position:0% +mentioned that this is like a + + + align:start position:0% +mentioned that this is like a +transmission uh inter perometer the + + align:start position:0% +transmission uh inter perometer the + + + align:start position:0% +transmission uh inter perometer the +Michaelson uh is like a a reflection + + align:start position:0% +Michaelson uh is like a a reflection + + + align:start position:0% +Michaelson uh is like a a reflection +interferometer both of these sorts of + + align:start position:0% +interferometer both of these sorts of + + + align:start position:0% +interferometer both of these sorts of +interferometers are used in microscopy + + align:start position:0% +interferometers are used in microscopy + + + align:start position:0% +interferometers are used in microscopy +actually um and so you can make a an + + align:start position:0% +actually um and so you can make a an + + + align:start position:0% +actually um and so you can make a an +interference microscope based on this + + align:start position:0% +interference microscope based on this + + + align:start position:0% +interference microscope based on this +technique and if you could put in here + + align:start position:0% +technique and if you could put in here + + + align:start position:0% +technique and if you could put in here +let's say a biological slide with a bit + + align:start position:0% +let's say a biological slide with a bit + + + align:start position:0% +let's say a biological slide with a bit +of um tissue or something on it and you + + align:start position:0% +of um tissue or something on it and you + + + align:start position:0% +of um tissue or something on it and you +could use this to measure the optical + + align:start position:0% +could use this to measure the optical + + + align:start position:0% +could use this to measure the optical +path in going through that that object + + align:start position:0% +path in going through that that object + + + align:start position:0% +path in going through that that object +uh it's not trivial to do that uh you + + align:start position:0% +uh it's not trivial to do that uh you + + + align:start position:0% +uh it's not trivial to do that uh you +normally to do if you want to do it in a + + align:start position:0% +normally to do if you want to do it in a + + + align:start position:0% +normally to do if you want to do it in a +microscope you'd have to place some + + align:start position:0% +microscope you'd have to place some + + + align:start position:0% +microscope you'd have to place some +microscope objectives and things in here + + align:start position:0% +microscope objectives and things in here + + + align:start position:0% +microscope objectives and things in here +uh and usually it's found that if you do + + align:start position:0% +uh and usually it's found that if you do + + + align:start position:0% +uh and usually it's found that if you do +that that messes everything up so you + + align:start position:0% +that that messes everything up so you + + + align:start position:0% +that that messes everything up so you +normally have to put the microscope + + align:start position:0% +normally have to put the microscope + + + align:start position:0% +normally have to put the microscope +objectives in this one as well so you + + align:start position:0% +objectives in this one as well so you + + + align:start position:0% +objectives in this one as well so you +end up really having to have two + + align:start position:0% +end up really having to have two + + + align:start position:0% +end up really having to have two +microscopes uh and the whole thing + + align:start position:0% +microscopes uh and the whole thing + + + align:start position:0% +microscopes uh and the whole thing +becomes very expensive so uh that sort + + align:start position:0% +becomes very expensive so uh that sort + + + align:start position:0% +becomes very expensive so uh that sort +of method has really gone out of fashion + + align:start position:0% +of method has really gone out of fashion + + + align:start position:0% +of method has really gone out of fashion +although many years ago Ze and people + + align:start position:0% +although many years ago Ze and people + + + align:start position:0% +although many years ago Ze and people +used to make instruments like that um + + align:start position:0% +used to make instruments like that um + + + align:start position:0% +used to make instruments like that um +the uh same goes for a michelon type + + align:start position:0% +the uh same goes for a michelon type + + + align:start position:0% +the uh same goes for a michelon type +interferometer you can measure that for + + align:start position:0% +interferometer you can measure that for + + + align:start position:0% +interferometer you can measure that for +looking use that for uh in a microscope + + align:start position:0% +looking use that for uh in a microscope + + + align:start position:0% +looking use that for uh in a microscope +for looking at + + align:start position:0% +for looking at + + + align:start position:0% +for looking at +surfaces uh surf surface height changes + + align:start position:0% +surfaces uh surf surface height changes + + + align:start position:0% +surfaces uh surf surface height changes +and so + + align:start position:0% + + + + align:start position:0% + +on okay so uh so this shows again this + + align:start position:0% +on okay so uh so this shows again this + + + align:start position:0% +on okay so uh so this shows again this +how this comes about then you got this + + align:start position:0% +how this comes about then you got this + + + align:start position:0% +how this comes about then you got this +one wave which is coming along this + + align:start position:0% +one wave which is coming along this + + + align:start position:0% +one wave which is coming along this +angle here uh and so this represents the + + align:start position:0% +angle here uh and so this represents the + + + align:start position:0% +angle here uh and so this represents the +phases this is a + + align:start position:0% +phases this is a + + + align:start position:0% +phases this is a +movie I just click it again it it will + + align:start position:0% +movie I just click it again it it will + + + align:start position:0% +movie I just click it again it it will +do something will + + align:start position:0% +do something will + + + align:start position:0% +do something will +it yes there we are so okay so oh it + + align:start position:0% +it yes there we are so okay so oh it + + + align:start position:0% +it yes there we are so okay so oh it +didn't go very it didn't go very far uh + + align:start position:0% +didn't go very it didn't go very far uh + + + align:start position:0% +didn't go very it didn't go very far uh +anyway you you probably was quick enough + + align:start position:0% +anyway you you probably was quick enough + + + align:start position:0% +anyway you you probably was quick enough +to see uh it it was a wave that's moving + + align:start position:0% +to see uh it it was a wave that's moving + + + align:start position:0% +to see uh it it was a wave that's moving +this way uh but the important + + align:start position:0% + + + + align:start position:0% + +thing if I go back and do it + + align:start position:0% +thing if I go back and do it + + + align:start position:0% +thing if I go back and do it +again now okay so so you all got to + + align:start position:0% +again now okay so so you all got to + + + align:start position:0% +again now okay so so you all got to +watch this time and and you you'll see + + align:start position:0% +watch this time and and you you'll see + + + align:start position:0% +watch this time and and you you'll see +there's two things I want you to watch + + align:start position:0% +there's two things I want you to watch + + + align:start position:0% +there's two things I want you to watch +one is the the wave moving this way but + + align:start position:0% +one is the the wave moving this way but + + + align:start position:0% +one is the the wave moving this way but +more importantly uh look what happens on + + align:start position:0% +more importantly uh look what happens on + + + align:start position:0% +more importantly uh look what happens on +on this line here where you've got the + + align:start position:0% +on this line here where you've got the + + + align:start position:0% +on this line here where you've got the +uh camera + + align:start position:0% + + + + align:start position:0% + +placed ah right yeah yeah yeah otherwise + + align:start position:0% +placed ah right yeah yeah yeah otherwise + + + align:start position:0% +placed ah right yeah yeah yeah otherwise +I think people have to be very + + align:start position:0% + + + + align:start position:0% + +quick + + align:start position:0% + + + + align:start position:0% + +yes look at + + align:start position:0% +yes look at + + + align:start position:0% +yes look at +that okay so good + + align:start position:0% + + + + align:start position:0% + +so so this this wave is is moving out + + align:start position:0% +so so this this wave is is moving out + + + align:start position:0% +so so this this wave is is moving out +here uh but you can see if you look at + + align:start position:0% +here uh but you can see if you look at + + + align:start position:0% +here uh but you can see if you look at +where the detector is it's as though the + + align:start position:0% +where the detector is it's as though the + + + align:start position:0% +where the detector is it's as though the +fringes are the the the phase is + + align:start position:0% +fringes are the the the phase is + + + align:start position:0% +fringes are the the the phase is +actually + + align:start position:0% +actually + + + align:start position:0% +actually +moving um continuously in One Direction + + align:start position:0% +moving um continuously in One Direction + + + align:start position:0% +moving um continuously in One Direction +like that right so um + + align:start position:0% + + + + align:start position:0% + +right so the point is that the reference + + align:start position:0% +right so the point is that the reference + + + align:start position:0% +right so the point is that the reference +has a constant + + align:start position:0% +has a constant + + + align:start position:0% +has a constant +phase uh because it is normal on the on + + align:start position:0% +phase uh because it is normal on the on + + + align:start position:0% +phase uh because it is normal on the on +the vertical axis + + align:start position:0% +the vertical axis + + + align:start position:0% +the vertical axis +so as the as the incident wave is + + align:start position:0% +so as the as the incident wave is + + + align:start position:0% +so as the as the incident wave is +passing through + + align:start position:0% +passing through + + + align:start position:0% +passing through +the + + align:start position:0% +the + + + align:start position:0% +the +uh the the Peaks are the locations where + + align:start position:0% +uh the the Peaks are the locations where + + + align:start position:0% +uh the the Peaks are the locations where +the the intensity accumulates right so + + align:start position:0% +the the intensity accumulates right so + + + align:start position:0% +the the intensity accumulates right so +you end up getting a uh a peak whereas + + align:start position:0% +you end up getting a uh a peak whereas + + + align:start position:0% +you end up getting a uh a peak whereas +in the in the nulls it means that the as + + align:start position:0% +in the in the nulls it means that the as + + + align:start position:0% +in the in the nulls it means that the as +the wave is passing through the phases + + align:start position:0% +the wave is passing through the phases + + + align:start position:0% +the wave is passing through the phases +are are not lining up so you end up + + align:start position:0% +are are not lining up so you end up + + + align:start position:0% +are are not lining up so you end up +getting a null that's how you yeah yeah + + align:start position:0% +getting a null that's how you yeah yeah + + + align:start position:0% +getting a null that's how you yeah yeah +okay they yeah so I guess the reference + + align:start position:0% +okay they yeah so I guess the reference + + + align:start position:0% +okay they yeah so I guess the reference +beam as you say is coming along this way + + align:start position:0% +beam as you say is coming along this way + + + align:start position:0% +beam as you say is coming along this way +but of course that's got fringes as well + + align:start position:0% +but of course that's got fringes as well + + + align:start position:0% +but of course that's got fringes as well +so that's right the uh the peaks of that + + align:start position:0% +so that's right the uh the peaks of that + + + align:start position:0% +so that's right the uh the peaks of that +when they match up with the peaks of the + + align:start position:0% +when they match up with the peaks of the + + + align:start position:0% +when they match up with the peaks of the +other would would uh uh give the Maxima + + align:start position:0% +other would would uh uh give the Maxima + + + align:start position:0% +other would would uh uh give the Maxima +in the yeah there's locations where the + + align:start position:0% +in the yeah there's locations where the + + + align:start position:0% +in the yeah there's locations where the +the Peaks always arrive at the same time + + align:start position:0% +the Peaks always arrive at the same time + + + align:start position:0% +the Peaks always arrive at the same time +right yeah but a little bit below the + + align:start position:0% +right yeah but a little bit below the + + + align:start position:0% +right yeah but a little bit below the +pigs will be actually out of phase so + + align:start position:0% +pigs will be actually out of phase so + + + align:start position:0% +pigs will be actually out of phase so +they end up getting a + + align:start position:0% +they end up getting a + + + align:start position:0% +they end up getting a +null + + align:start position:0% + + + + align:start position:0% + +end of + + align:start position:0% +end of + + + align:start position:0% +end of +show so that's the end of that that + + align:start position:0% +show so that's the end of that that + + + align:start position:0% +show so that's the end of that that +sounds like a good place for a + + align:start position:0% +sounds like a good place for a + + + align:start position:0% +sounds like a good place for a +break so uh so let's let's make a break + + align:start position:0% +break so uh so let's let's make a break + + + align:start position:0% +break so uh so let's let's make a break +uh unless anyone's got some questions of + + align:start position:0% +uh unless anyone's got some questions of + + + align:start position:0% +uh unless anyone's got some questions of +course yeah of course sh question um in + + align:start position:0% +course yeah of course sh question um in + + + align:start position:0% +course yeah of course sh question um in +Michaelson interferometer the uh object + + align:start position:0% +Michaelson interferometer the uh object + + + align:start position:0% +Michaelson interferometer the uh object +would affect the + + align:start position:0% +would affect the + + + align:start position:0% +would affect the +intensity um according to whatever phase + + align:start position:0% +intensity um according to whatever phase + + + align:start position:0% +intensity um according to whatever phase +delay introduces but in the uh maender + + align:start position:0% +delay introduces but in the uh maender + + + align:start position:0% +delay introduces but in the uh maender +interference + + align:start position:0% +interference + + + align:start position:0% +interference +it will affect the spacing of the + + align:start position:0% +it will affect the spacing of the + + + align:start position:0% +it will affect the spacing of the +fringes is that correct uh it will + + align:start position:0% +fringes is that correct uh it will + + + align:start position:0% +fringes is that correct uh it will +change the spacing we we added this + + align:start position:0% +change the spacing we we added this + + + align:start position:0% +change the spacing we we added this +constant slope uh in the signal + + align:start position:0% +constant slope uh in the signal + + + align:start position:0% +constant slope uh in the signal +beam the I think this this this tilting + + align:start position:0% +beam the I think this this this tilting + + + align:start position:0% +beam the I think this this this tilting +the tilting the one beam relative to + + align:start position:0% +the tilting the one beam relative to + + + align:start position:0% +the tilting the one beam relative to +another you can doing either sort of + + align:start position:0% +another you can doing either sort of + + + align:start position:0% +another you can doing either sort of +interferometer so that's not a + + align:start position:0% +interferometer so that's not a + + + align:start position:0% +interferometer so that's not a +fundamental difference between the two + + align:start position:0% +fundamental difference between the two + + + align:start position:0% +fundamental difference between the two +types oh so so the I was thinking when + + align:start position:0% +types oh so so the I was thinking when + + + align:start position:0% +types oh so so the I was thinking when +you have a tilted uh plane a tilted + + align:start position:0% +you have a tilted uh plane a tilted + + + align:start position:0% +you have a tilted uh plane a tilted +mirror then uh you would measure the + + align:start position:0% +mirror then uh you would measure the + + + align:start position:0% +mirror then uh you would measure the +spacing between fringes to find out the + + align:start position:0% +spacing between fringes to find out the + + + align:start position:0% +spacing between fringes to find out the +object object's Optical path length but + + align:start position:0% +object object's Optical path length but + + + align:start position:0% +object object's Optical path length but +if you didn't have that then uh you + + align:start position:0% +if you didn't have that then uh you + + + align:start position:0% +if you didn't have that then uh you +would just measure the the intensity + + align:start position:0% +would just measure the the intensity + + + align:start position:0% +would just measure the the intensity +change in + + align:start position:0% +change in + + + align:start position:0% +change in +intensity uh to get the wrapped phase + + align:start position:0% +intensity uh to get the wrapped phase + + + align:start position:0% +intensity uh to get the wrapped phase +and then apply on + + align:start position:0% +and then apply on + + + align:start position:0% +and then apply on +wrapping is that + + align:start position:0% + + + + align:start position:0% + +correct well it depends what you're + + align:start position:0% +correct well it depends what you're + + + align:start position:0% +correct well it depends what you're +trying to do to find out the object phas + + align:start position:0% +trying to do to find out the object phas + + + align:start position:0% +trying to do to find out the object phas +yeah yeah yeah yeah but you know if um + + align:start position:0% +yeah yeah yeah yeah but you know if um + + + align:start position:0% +yeah yeah yeah yeah but you know if um +you're thinking of it varying it's a + + align:start position:0% +you're thinking of it varying it's a + + + align:start position:0% +you're thinking of it varying it's a +spatially varing quantity that you're + + align:start position:0% +spatially varing quantity that you're + + + align:start position:0% +spatially varing quantity that you're +trying to measure isn't it yeah yeah so + + align:start position:0% +trying to measure isn't it yeah yeah so + + + align:start position:0% +trying to measure isn't it yeah yeah so +I mean very often what you do of course + + align:start position:0% +I mean very often what you do of course + + + align:start position:0% +I mean very often what you do of course +is you actually very often you want the + + align:start position:0% +is you actually very often you want the + + + align:start position:0% +is you actually very often you want the +fringes because they give you something + + align:start position:0% +fringes because they give you something + + + align:start position:0% +fringes because they give you something +to actually look at you know so normally + + align:start position:0% +to actually look at you know so normally + + + align:start position:0% +to actually look at you know so normally +um if you if you don't do the tilting + + align:start position:0% +um if you if you don't do the tilting + + + align:start position:0% +um if you if you don't do the tilting +thing you what you'd see if if if the + + align:start position:0% +thing you what you'd see if if if the + + + align:start position:0% +thing you what you'd see if if if the +two paths were equal would be let's say + + align:start position:0% +two paths were equal would be let's say + + + align:start position:0% +two paths were equal would be let's say +completely yeah feature this bright + + align:start position:0% +completely yeah feature this bright + + + align:start position:0% +completely yeah feature this bright +wouldn't wouldn't it right yeah uh and + + align:start position:0% +wouldn't wouldn't it right yeah uh and + + + align:start position:0% +wouldn't wouldn't it right yeah uh and +so let's say you put some objects in + + align:start position:0% +so let's say you put some objects in + + + align:start position:0% +so let's say you put some objects in +there which has got some face change you + + align:start position:0% +there which has got some face change you + + + align:start position:0% +there which has got some face change you +you would just see a small change from + + align:start position:0% +you would just see a small change from + + + align:start position:0% +you would just see a small change from +that bright right which might not be + + align:start position:0% +that bright right which might not be + + + align:start position:0% +that bright right which might not be +very visible I see yeah uh but for + + align:start position:0% +very visible I see yeah uh but for + + + align:start position:0% +very visible I see yeah uh but for +example then if you um uh tilted yeah + + align:start position:0% +example then if you um uh tilted yeah + + + align:start position:0% +example then if you um uh tilted yeah +then you would get some fringes and you + + align:start position:0% +then you would get some fringes and you + + + align:start position:0% +then you would get some fringes and you +the sort of thing you might see of + + align:start position:0% +the sort of thing you might see of + + + align:start position:0% +the sort of thing you might see of +course let's say you in a disc of + + align:start position:0% +course let's say you in a disc of + + + align:start position:0% +course let's say you in a disc of +material uh like this and you're trying + + align:start position:0% +material uh like this and you're trying + + + align:start position:0% +material uh like this and you're trying +to measure the thickness of this disc of + + align:start position:0% +to measure the thickness of this disc of + + + align:start position:0% +to measure the thickness of this disc of +material uh so what you would find is if + + align:start position:0% +material uh so what you would find is if + + + align:start position:0% +material uh so what you would find is if +it was nicely uniformly thick you you + + align:start position:0% +it was nicely uniformly thick you you + + + align:start position:0% +it was nicely uniformly thick you you +you'd find that you got these regular + + align:start position:0% +you'd find that you got these regular + + + align:start position:0% +you'd find that you got these regular +sort of fringes across here right + + align:start position:0% +sort of fringes across here right + + + align:start position:0% +sort of fringes across here right +whereas um if it wasn't then you might + + align:start position:0% +whereas um if it wasn't then you might + + + align:start position:0% +whereas um if it wasn't then you might +find that you get fringes that have got + + align:start position:0% +find that you get fringes that have got + + + align:start position:0% +find that you get fringes that have got +some shape that look something like this + + align:start position:0% +some shape that look something like this + + + align:start position:0% +some shape that look something like this +right so by looking at the the ometry of + + align:start position:0% +right so by looking at the the ometry of + + + align:start position:0% +right so by looking at the the ometry of +those fringes you can quite easily + + align:start position:0% +those fringes you can quite easily + + + align:start position:0% +those fringes you can quite easily +measure the the the changes in the the + + align:start position:0% +measure the the the changes in the the + + + align:start position:0% +measure the the the changes in the the +deformations in the in the shape of it + + align:start position:0% +deformations in the in the shape of it + + + align:start position:0% +deformations in the in the shape of it +yeah but but to so so you know and as + + align:start position:0% +yeah but but to so so you know and as + + + align:start position:0% +yeah but but to so so you know and as +you change the the Tilt it would change + + align:start position:0% +you change the the Tilt it would change + + + align:start position:0% +you change the the Tilt it would change +the separation between these + + align:start position:0% +the separation between these + + + align:start position:0% +the separation between these +fringes uh and um so if you make the + + align:start position:0% +fringes uh and um so if you make the + + + align:start position:0% +fringes uh and um so if you make the +Tilt very small then you just + + align:start position:0% +Tilt very small then you just + + + align:start position:0% +Tilt very small then you just +effectively be looking at just a single + + align:start position:0% +effectively be looking at just a single + + + align:start position:0% +effectively be looking at just a single +Fringe you you what no fringes really + + align:start position:0% +Fringe you you what no fringes really + + + align:start position:0% +Fringe you you what no fringes really +right so then it would be actually very + + align:start position:0% +right so then it would be actually very + + + align:start position:0% +right so then it would be actually very +difficult to to see the the the the + + align:start position:0% +difficult to to see the the the the + + + align:start position:0% +difficult to to see the the the the +changes in the thickness unless you + + align:start position:0% +changes in the thickness unless you + + + align:start position:0% +changes in the thickness unless you +actually made you know very sensitive + + align:start position:0% + + + + align:start position:0% + +measurements okay so everyone back + + align:start position:0% + + + + align:start position:0% + +again yeah I thought of something else + + align:start position:0% +again yeah I thought of something else + + + align:start position:0% +again yeah I thought of something else +that perhaps um I I could mention uh + + align:start position:0% +that perhaps um I I could mention uh + + + align:start position:0% +that perhaps um I I could mention uh +following on from this + + align:start position:0% +following on from this + + + align:start position:0% +following on from this +diagram uh you so so in the in the + + align:start position:0% +diagram uh you so so in the in the + + + align:start position:0% +diagram uh you so so in the in the +lectures uh the the system as you + + align:start position:0% +lectures uh the the system as you + + + align:start position:0% +lectures uh the the system as you +remember uh was arranged to do this sort + + align:start position:0% +remember uh was arranged to do this sort + + + align:start position:0% +remember uh was arranged to do this sort +of + + align:start position:0% +of + + + align:start position:0% +of +thing so the idea here is that the two + + align:start position:0% +thing so the idea here is that the two + + + align:start position:0% +thing so the idea here is that the two +parts now um this path and this path are + + align:start position:0% +parts now um this path and this path are + + + align:start position:0% +parts now um this path and this path are +roughly equal in size um in the old days + + align:start position:0% +roughly equal in size um in the old days + + + align:start position:0% +roughly equal in size um in the old days +when people were trying to do this with + + align:start position:0% +when people were trying to do this with + + + align:start position:0% +when people were trying to do this with +um non non-coherent + + align:start position:0% +um non non-coherent + + + align:start position:0% +um non non-coherent +sources uh then you had to be really + + align:start position:0% +sources uh then you had to be really + + + align:start position:0% +sources uh then you had to be really +careful and for example this is a beam + + align:start position:0% +careful and for example this is a beam + + + align:start position:0% +careful and for example this is a beam +splitter which is actually of course a + + align:start position:0% +splitter which is actually of course a + + + align:start position:0% +splitter which is actually of course a +lump of glass maybe with some coating on + + align:start position:0% +lump of glass maybe with some coating on + + + align:start position:0% +lump of glass maybe with some coating on +it on one side uh but you can see this + + align:start position:0% +it on one side uh but you can see this + + + align:start position:0% +it on one side uh but you can see this +this beam has gone through this glass + + align:start position:0% +this beam has gone through this glass + + + align:start position:0% +this beam has gone through this glass +but this beam hasn't gone through that + + align:start position:0% +but this beam hasn't gone through that + + + align:start position:0% +but this beam hasn't gone through that +glass uh and so the these are all things + + align:start position:0% +glass uh and so the these are all things + + + align:start position:0% +glass uh and so the these are all things +that you also have to take into account + + align:start position:0% +that you also have to take into account + + + align:start position:0% +that you also have to take into account +and um so in order to correct uh for the + + align:start position:0% +and um so in order to correct uh for the + + + align:start position:0% +and um so in order to correct uh for the +optical effects of say for instance that + + align:start position:0% +optical effects of say for instance that + + + align:start position:0% +optical effects of say for instance that +that slab of glass there uh you might + + align:start position:0% +that slab of glass there uh you might + + + align:start position:0% +that slab of glass there uh you might +actually uh end up putting a slab of + + align:start position:0% +actually uh end up putting a slab of + + + align:start position:0% +actually uh end up putting a slab of +glass in + + align:start position:0% +glass in + + + align:start position:0% +glass in +here some sort of um compensating um + + align:start position:0% +here some sort of um compensating um + + + align:start position:0% +here some sort of um compensating um +piece of glass to so that this this + + align:start position:0% +piece of glass to so that this this + + + align:start position:0% +piece of glass to so that this this +would produce the same uh dispersion in + + align:start position:0% +would produce the same uh dispersion in + + + align:start position:0% +would produce the same uh dispersion in +the two arms uh so there was a lot of um + + align:start position:0% +the two arms uh so there was a lot of um + + + align:start position:0% +the two arms uh so there was a lot of um +uh effort put into trying to design + + align:start position:0% +uh effort put into trying to design + + + align:start position:0% +uh effort put into trying to design +these systems so that they would work + + align:start position:0% +these systems so that they would work + + + align:start position:0% +these systems so that they would work +with the Broadband sources and so on + + align:start position:0% +with the Broadband sources and so on + + + align:start position:0% +with the Broadband sources and so on +nowadays I guess most of the time we're + + align:start position:0% +nowadays I guess most of the time we're + + + align:start position:0% +nowadays I guess most of the time we're +doing it with lasers and we don't have + + align:start position:0% +doing it with lasers and we don't have + + + align:start position:0% +doing it with lasers and we don't have +to worry about any of these things but + + align:start position:0% +to worry about any of these things but + + + align:start position:0% +to worry about any of these things but +if you look in any of the standard books + + align:start position:0% +if you look in any of the standard books + + + align:start position:0% +if you look in any of the standard books +on uh on interferometry there are a + + align:start position:0% +on uh on interferometry there are a + + + align:start position:0% +on uh on interferometry there are a +number of textbooks on interferometry + + align:start position:0% +number of textbooks on interferometry + + + align:start position:0% +number of textbooks on interferometry +that will give you all the information + + align:start position:0% +that will give you all the information + + + align:start position:0% +that will give you all the information +if you want to go more into it okay so + + align:start position:0% +if you want to go more into it okay so + + + align:start position:0% +if you want to go more into it okay so +now we're going to uh + + align:start position:0% +now we're going to uh + + + align:start position:0% +now we're going to uh +change uh step slightly uh from + + align:start position:0% +change uh step slightly uh from + + + align:start position:0% +change uh step slightly uh from +interference to + + align:start position:0% +interference to + + + align:start position:0% +interference to +defraction uh and uh so what's the + + align:start position:0% +defraction uh and uh so what's the + + + align:start position:0% +defraction uh and uh so what's the +difference between interference and + + align:start position:0% +difference between interference and + + + align:start position:0% +difference between interference and +defraction uh the answer is really not a + + align:start position:0% +defraction uh the answer is really not a + + + align:start position:0% +defraction uh the answer is really not a +lot except that normally + + align:start position:0% +lot except that normally + + + align:start position:0% +lot except that normally +interference uh we're we're talking + + align:start position:0% +interference uh we're we're talking + + + align:start position:0% +interference uh we're we're talking +about two beams interfering whereas in + + align:start position:0% +about two beams interfering whereas in + + + align:start position:0% +about two beams interfering whereas in +defraction we're normally talking about + + align:start position:0% +defraction we're normally talking about + + + align:start position:0% +defraction we're normally talking about +uh lots of beams interfering so you can + + align:start position:0% +uh lots of beams interfering so you can + + + align:start position:0% +uh lots of beams interfering so you can +uh think of um the two as really being + + align:start position:0% +uh think of um the two as really being + + + align:start position:0% +uh think of um the two as really being +uh effectively the same same phenomenon + + align:start position:0% +uh effectively the same same phenomenon + + + align:start position:0% +uh effectively the same same phenomenon +actually uh and um so we're going to + + align:start position:0% +actually uh and um so we're going to + + + align:start position:0% +actually uh and um so we're going to +look at huan's + + align:start position:0% +look at huan's + + + align:start position:0% +look at huan's +principle uh we're then going to go on + + align:start position:0% +principle uh we're then going to go on + + + align:start position:0% +principle uh we're then going to go on +to the young Young's interferometer so + + align:start position:0% +to the young Young's interferometer so + + + align:start position:0% +to the young Young's interferometer so +this this really does show doesn't it + + align:start position:0% +this this really does show doesn't it + + + align:start position:0% +this this really does show doesn't it +how interferometry is related to + + align:start position:0% +how interferometry is related to + + + align:start position:0% +how interferometry is related to +defraction uh because this lecture is + + align:start position:0% +defraction uh because this lecture is + + + align:start position:0% +defraction uh because this lecture is +really about defraction uh and then + + align:start position:0% +really about defraction uh and then + + + align:start position:0% +really about defraction uh and then +we're going to go to a more complicated + + align:start position:0% +we're going to go to a more complicated + + + align:start position:0% +we're going to go to a more complicated +case uh of frenel uh + + align:start position:0% + + + + align:start position:0% + +defraction okay so uh first of all hen's + + align:start position:0% +defraction okay so uh first of all hen's + + + align:start position:0% +defraction okay so uh first of all hen's +principle uh so I think uh at the + + align:start position:0% +principle uh so I think uh at the + + + align:start position:0% +principle uh so I think uh at the +beginning of the lecture course uh + + align:start position:0% +beginning of the lecture course uh + + + align:start position:0% +beginning of the lecture course uh +George said bit about the + + align:start position:0% +George said bit about the + + + align:start position:0% +George said bit about the +history uh of of how Hans came up with + + align:start position:0% +history uh of of how Hans came up with + + + align:start position:0% +history uh of of how Hans came up with +this idea uh quite a long time ago + + align:start position:0% +this idea uh quite a long time ago + + + align:start position:0% +this idea uh quite a long time ago +wasn't it it was even before Newton or + + align:start position:0% +wasn't it it was even before Newton or + + + align:start position:0% +wasn't it it was even before Newton or +around I think slightly before but + + align:start position:0% +around I think slightly before but + + + align:start position:0% +around I think slightly before but +around the same time as Newton so uh + + align:start position:0% +around the same time as Newton so uh + + + align:start position:0% +around the same time as Newton so uh +when people were were still hadn't + + align:start position:0% +when people were were still hadn't + + + align:start position:0% +when people were were still hadn't +really decided whether light or was a + + align:start position:0% +really decided whether light or was a + + + align:start position:0% +really decided whether light or was a +wave or a particle uh and of course we + + align:start position:0% +wave or a particle uh and of course we + + + align:start position:0% +wave or a particle uh and of course we +still haven't decided so times don't + + align:start position:0% +still haven't decided so times don't + + + align:start position:0% +still haven't decided so times don't +change really uh but anyway so probably + + align:start position:0% +change really uh but anyway so probably + + + align:start position:0% +change really uh but anyway so probably +probably now we looking back we could + + align:start position:0% +probably now we looking back we could + + + align:start position:0% +probably now we looking back we could +say that Newton was the first Quantum + + align:start position:0% +say that Newton was the first Quantum + + + align:start position:0% +say that Newton was the first Quantum +optic uh but uh anyway so but this was + + align:start position:0% +optic uh but uh anyway so but this was + + + align:start position:0% +optic uh but uh anyway so but this was +this was huan's idea he was saying uh + + align:start position:0% +this was huan's idea he was saying uh + + + align:start position:0% +this was huan's idea he was saying uh +that if you think of a light beam a wave + + align:start position:0% +that if you think of a light beam a wave + + + align:start position:0% +that if you think of a light beam a wave +propagating in space then at some moment + + align:start position:0% +propagating in space then at some moment + + + align:start position:0% +propagating in space then at some moment +in time this is a a a + + align:start position:0% +in time this is a a a + + + align:start position:0% +in time this is a a a +wavefront the wavefront is a a surface + + align:start position:0% +wavefront the wavefront is a a surface + + + align:start position:0% +wavefront the wavefront is a a surface +of constant phase right uh and uh you + + align:start position:0% +of constant phase right uh and uh you + + + align:start position:0% +of constant phase right uh and uh you +could uh he came up with this model for + + align:start position:0% +could uh he came up with this model for + + + align:start position:0% +could uh he came up with this model for +how light propagates uh where he he + + align:start position:0% +how light propagates uh where he he + + + align:start position:0% +how light propagates uh where he he +assumed that all the points all all all + + align:start position:0% +assumed that all the points all all all + + + align:start position:0% +assumed that all the points all all all +the points on this wavefront can be + + align:start position:0% +the points on this wavefront can be + + + align:start position:0% +the points on this wavefront can be +thought of as being a source of what he + + align:start position:0% +thought of as being a source of what he + + + align:start position:0% +thought of as being a source of what he +called secondary wavelets so each of + + align:start position:0% +called secondary wavelets so each of + + + align:start position:0% +called secondary wavelets so each of +these points radiates like a spherical + + align:start position:0% +these points radiates like a spherical + + + align:start position:0% +these points radiates like a spherical +wave uh and uh and then if you sum those + + align:start position:0% +wave uh and uh and then if you sum those + + + align:start position:0% +wave uh and uh and then if you sum those +all up and calculate what the what the + + align:start position:0% +all up and calculate what the what the + + + align:start position:0% +all up and calculate what the what the +effect is at some distance in front here + + align:start position:0% +effect is at some distance in front here + + + align:start position:0% +effect is at some distance in front here +uh then that would then predict uh what + + align:start position:0% +uh then that would then predict uh what + + + align:start position:0% +uh then that would then predict uh what +that wave front uh what what the what + + align:start position:0% +that wave front uh what what the what + + + align:start position:0% +that wave front uh what what the what +the um the the wave had done at slightly + + align:start position:0% +the um the the wave had done at slightly + + + align:start position:0% +the um the the wave had done at slightly +later time so that's the principle uh + + align:start position:0% +later time so that's the principle uh + + + align:start position:0% +later time so that's the principle uh +and um so quite a simple idea really uh + + align:start position:0% +and um so quite a simple idea really uh + + + align:start position:0% +and um so quite a simple idea really uh +and to you can come up with a very + + align:start position:0% +and to you can come up with a very + + + align:start position:0% +and to you can come up with a very +simple uh + + align:start position:0% +simple uh + + + align:start position:0% +simple uh +mathematical um description of it uh + + align:start position:0% +mathematical um description of it uh + + + align:start position:0% +mathematical um description of it uh +unfortunately it doesn't work + + align:start position:0% +unfortunately it doesn't work + + + align:start position:0% +unfortunately it doesn't work +marvelously well and people put a lot of + + align:start position:0% +marvelously well and people put a lot of + + + align:start position:0% +marvelously well and people put a lot of +effort into trying to improve the theory + + align:start position:0% +effort into trying to improve the theory + + + align:start position:0% +effort into trying to improve the theory +and they came up with some rather uh you + + align:start position:0% +and they came up with some rather uh you + + + align:start position:0% +and they came up with some rather uh you +know um arbitrary they seem rather + + align:start position:0% +know um arbitrary they seem rather + + + align:start position:0% +know um arbitrary they seem rather +arbitrary factors that they had to in + + align:start position:0% +arbitrary factors that they had to in + + + align:start position:0% +arbitrary factors that they had to in +include in order to get it to work + + align:start position:0% +include in order to get it to work + + + align:start position:0% +include in order to get it to work +properly so I think nowadays uh we + + align:start position:0% +properly so I think nowadays uh we + + + align:start position:0% +properly so I think nowadays uh we +probably look back at all this and think + + align:start position:0% +probably look back at all this and think + + + align:start position:0% +probably look back at all this and think +it was just history uh and um you know + + align:start position:0% +it was just history uh and um you know + + + align:start position:0% +it was just history uh and um you know +there are better ways of really tackling + + align:start position:0% +there are better ways of really tackling + + + align:start position:0% +there are better ways of really tackling +the problem but uh anyway from the very + + align:start position:0% +the problem but uh anyway from the very + + + align:start position:0% +the problem but uh anyway from the very +at the very simple level though uh it's + + align:start position:0% +at the very simple level though uh it's + + + align:start position:0% +at the very simple level though uh it's +still a nice Simple Theory uh for for + + align:start position:0% +still a nice Simple Theory uh for for + + + align:start position:0% +still a nice Simple Theory uh for for +how you would do that uh so if you want + + align:start position:0% +how you would do that uh so if you want + + + align:start position:0% +how you would do that uh so if you want +to calculate what the field is at this + + align:start position:0% +to calculate what the field is at this + + + align:start position:0% +to calculate what the field is at this +point here say you look at all these + + align:start position:0% +point here say you look at all these + + + align:start position:0% +point here say you look at all these +waves that come from all these points on + + align:start position:0% +waves that come from all these points on + + + align:start position:0% +waves that come from all these points on +the wave front add them all together as + + align:start position:0% +the wave front add them all together as + + + align:start position:0% +the wave front add them all together as +phases of course uh and that will give + + align:start position:0% +phases of course uh and that will give + + + align:start position:0% +phases of course uh and that will give +you the the field at that + + align:start position:0% + + + + align:start position:0% + +point and there's it's showing how you + + align:start position:0% +point and there's it's showing how you + + + align:start position:0% +point and there's it's showing how you +do that and then you do it you can do it + + align:start position:0% +do that and then you do it you can do it + + + align:start position:0% +do that and then you do it you can do it +again and again and again and show how + + align:start position:0% +again and again and again and show how + + + align:start position:0% +again and again and again and show how +the wave + + align:start position:0% +the wave + + + align:start position:0% +the wave +propagates okay so example a hole in an + + align:start position:0% +propagates okay so example a hole in an + + + align:start position:0% +propagates okay so example a hole in an +opaque screen so I guess this is pretty + + align:start position:0% +opaque screen so I guess this is pretty + + + align:start position:0% +opaque screen so I guess this is pretty +well the simplest example you could + + align:start position:0% +well the simplest example you could + + + align:start position:0% +well the simplest example you could +possibly think of uh well no I suppose + + align:start position:0% +possibly think of uh well no I suppose + + + align:start position:0% +possibly think of uh well no I suppose +the opaque screen with no ho holding + + align:start position:0% +the opaque screen with no ho holding + + + align:start position:0% +the opaque screen with no ho holding +would be even simpler then you wouldn't + + align:start position:0% +would be even simpler then you wouldn't + + + align:start position:0% +would be even simpler then you wouldn't +see + + align:start position:0% +see + + + align:start position:0% +see +anything but what we do is we just have + + align:start position:0% +anything but what we do is we just have + + + align:start position:0% +anything but what we do is we just have +a very small hole in this uh and so this + + align:start position:0% +a very small hole in this uh and so this + + + align:start position:0% +a very small hole in this uh and so this +is going to act like a source uh that's + + align:start position:0% +is going to act like a source uh that's + + + align:start position:0% +is going to act like a source uh that's +going to radiate like a a a spherical + + align:start position:0% +going to radiate like a a a spherical + + + align:start position:0% +going to radiate like a a a spherical +wave uh and what we'd see on this screen + + align:start position:0% +wave uh and what we'd see on this screen + + + align:start position:0% +wave uh and what we'd see on this screen +that we place here uh you you you'd see + + align:start position:0% +that we place here uh you you you'd see + + + align:start position:0% +that we place here uh you you you'd see +uh + + align:start position:0% +uh + + + align:start position:0% +uh +that that is virtually what we've been + + align:start position:0% +that that is virtually what we've been + + + align:start position:0% +that that is virtually what we've been +looking at before anyway we've done that + + align:start position:0% +looking at before anyway we've done that + + + align:start position:0% +looking at before anyway we've done that +before so here we are there's the + + align:start position:0% +before so here we are there's the + + + align:start position:0% +before so here we are there's the +spherical + + align:start position:0% +spherical + + + align:start position:0% +spherical +wave uh and and then we can are we going + + align:start position:0% +wave uh and and then we can are we going + + + align:start position:0% +wave uh and and then we can are we going +to get some more on + + align:start position:0% +to get some more on + + + align:start position:0% +to get some more on +that did something happen then + + align:start position:0% + + + + align:start position:0% + +George ah e to the I right sorry I + + align:start position:0% +George ah e to the I right sorry I + + + align:start position:0% +George ah e to the I right sorry I +couldn't see anything happening okay so + + align:start position:0% +couldn't see anything happening okay so + + + align:start position:0% +couldn't see anything happening okay so +this this is the plane wave coming + + align:start position:0% +this this is the plane wave coming + + + align:start position:0% +this this is the plane wave coming +in uh and uh + + align:start position:0% +in uh and uh + + + align:start position:0% +in uh and uh +and now something's come up uh the the + + align:start position:0% +and now something's come up uh the the + + + align:start position:0% +and now something's come up uh the the +the hold is a Delta function did that + + align:start position:0% +the hold is a Delta function did that + + + align:start position:0% +the hold is a Delta function did that +just come + + align:start position:0% + + + + align:start position:0% + +up and now something else has come up + + align:start position:0% +up and now something else has come up + + + align:start position:0% +up and now something else has come up +this is the spherical wave now and this + + align:start position:0% +this is the spherical wave now and this + + + align:start position:0% +this is the spherical wave now and this +is the same expression we had for the + + align:start position:0% +is the same expression we had for the + + + align:start position:0% +is the same expression we had for the +spherical wave in the previous lecture + + align:start position:0% +spherical wave in the previous lecture + + + align:start position:0% +spherical wave in the previous lecture +then uh so um you remember this um + + align:start position:0% +then uh so um you remember this um + + + align:start position:0% +then uh so um you remember this um +parabolic type um approximation we made + + align:start position:0% +parabolic type um approximation we made + + + align:start position:0% +parabolic type um approximation we made +uh for a for a spherical wave uh this is + + align:start position:0% +uh for a for a spherical wave uh this is + + + align:start position:0% +uh for a for a spherical wave uh this is +called the frenel approxim + + align:start position:0% +called the frenel approxim + + + align:start position:0% +called the frenel approxim +uh B based based named after the guy + + align:start position:0% +uh B based based named after the guy + + + align:start position:0% +uh B based based named after the guy +forel who I guess must have come up with + + align:start position:0% +forel who I guess must have come up with + + + align:start position:0% +forel who I guess must have come up with +this in the first place uh and you + + align:start position:0% +this in the first place uh and you + + + align:start position:0% +this in the first place uh and you +remember it's true uh it's going to be + + align:start position:0% +remember it's true uh it's going to be + + + align:start position:0% +remember it's true uh it's going to be +approximately true if uh if if the X and + + align:start position:0% +approximately true if uh if if the X and + + + align:start position:0% +approximately true if uh if if the X and +Y are small compared with the distance L + + align:start position:0% +Y are small compared with the distance L + + + align:start position:0% +Y are small compared with the distance L +right so you need that in order to apply + + align:start position:0% +right so you need that in order to apply + + + align:start position:0% +right so you need that in order to apply +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +binomial uh and uh right so there it is + + align:start position:0% +binomial uh and uh right so there it is + + + align:start position:0% +binomial uh and uh right so there it is +uh I just mention again this this eye + + align:start position:0% +uh I just mention again this this eye + + + align:start position:0% +uh I just mention again this this eye +that someone from from MIT asked about + + align:start position:0% +that someone from from MIT asked about + + + align:start position:0% +that someone from from MIT asked about +earlier so that I then at the bottom uh + + align:start position:0% +earlier so that I then at the bottom uh + + + align:start position:0% +earlier so that I then at the bottom uh +is saying that this spherical wave uh is + + align:start position:0% +is saying that this spherical wave uh is + + + align:start position:0% +is saying that this spherical wave uh is +actually 90 degrees out of phase with + + align:start position:0% +actually 90 degrees out of phase with + + + align:start position:0% +actually 90 degrees out of phase with +the the wave that arrives at this point + + align:start position:0% +the the wave that arrives at this point + + + align:start position:0% +the the wave that arrives at this point +uh so that's quite interesting so it's + + align:start position:0% +uh so that's quite interesting so it's + + + align:start position:0% +uh so that's quite interesting so it's +you can think of it being like a a a + + align:start position:0% +you can think of it being like a a a + + + align:start position:0% +you can think of it being like a a a +resonance sort of effect I + + align:start position:0% +resonance sort of effect I + + + align:start position:0% +resonance sort of effect I +think and uh and um I guess this is + + align:start position:0% +think and uh and um I guess this is + + + align:start position:0% +think and uh and um I guess this is +something that hen's principle cannot + + align:start position:0% +something that hen's principle cannot + + + align:start position:0% +something that hen's principle cannot +really explain right + + align:start position:0% +really explain right + + + align:start position:0% +really explain right +this is why you have to do more than + + align:start position:0% +this is why you have to do more than + + + align:start position:0% +this is why you have to do more than +hens but we take it for granted in the + + align:start position:0% +hens but we take it for granted in the + + + align:start position:0% +hens but we take it for granted in the +class so we don't get into + + align:start position:0% +class so we don't get into + + + align:start position:0% +class so we don't get into +the yeah okay yeah yeah so I think + + align:start position:0% +the yeah okay yeah yeah so I think + + + align:start position:0% +the yeah okay yeah yeah so I think +George is really saying that hens didn't + + align:start position:0% +George is really saying that hens didn't + + + align:start position:0% +George is really saying that hens didn't +actually have that eye + + align:start position:0% +actually have that eye + + + align:start position:0% +actually have that eye +there so uh so we're clever than he + + align:start position:0% +there so uh so we're clever than he + + + align:start position:0% +there so uh so we're clever than he +is don't know + + align:start position:0% + + + + align:start position:0% + +why okay uh so so there we are then uh + + align:start position:0% +why okay uh so so there we are then uh + + + align:start position:0% +why okay uh so so there we are then uh +and + + align:start position:0% +and + + + align:start position:0% +and +uh uh oh now we got two holes I knew + + align:start position:0% +uh uh oh now we got two holes I knew + + + align:start position:0% +uh uh oh now we got two holes I knew +something had happened and the spherical + + align:start position:0% +something had happened and the spherical + + + align:start position:0% +something had happened and the spherical +wave is Now hidden behind here + + align:start position:0% +wave is Now hidden behind here + + + align:start position:0% +wave is Now hidden behind here +partly oh more will come okay so now + + align:start position:0% +partly oh more will come okay so now + + + align:start position:0% +partly oh more will come okay so now +we've got two holes each of these is a + + align:start position:0% +we've got two holes each of these is a + + + align:start position:0% +we've got two holes each of these is a +spherical wave uh and of course when we + + align:start position:0% +spherical wave uh and of course when we + + + align:start position:0% +spherical wave uh and of course when we +get two of them there's going to be two + + align:start position:0% +get two of them there's going to be two + + + align:start position:0% +get two of them there's going to be two +spherical waves which I think is going + + align:start position:0% +spherical waves which I think is going + + + align:start position:0% +spherical waves which I think is going +to oh yes another spherical wave and + + align:start position:0% +to oh yes another spherical wave and + + + align:start position:0% +to oh yes another spherical wave and +another equation look there we are so + + align:start position:0% +another equation look there we are so + + + align:start position:0% +another equation look there we are so +these are the + + align:start position:0% +these are the + + + align:start position:0% +these are the +equations uh of the what you'd see on + + align:start position:0% +equations uh of the what you'd see on + + + align:start position:0% +equations uh of the what you'd see on +the screen for each of these two + + align:start position:0% +the screen for each of these two + + + align:start position:0% +the screen for each of these two +spherical waves + + align:start position:0% +spherical waves + + + align:start position:0% +spherical waves +and if you look at them you'll notice + + align:start position:0% +and if you look at them you'll notice + + + align:start position:0% +and if you look at them you'll notice +that see these are um a distance X and + + align:start position:0% +that see these are um a distance X and + + + align:start position:0% +that see these are um a distance X and +minus X relative to the axis uh and you + + align:start position:0% +minus X relative to the axis uh and you + + + align:start position:0% +minus X relative to the axis uh and you +can see the only difference in these + + align:start position:0% +can see the only difference in these + + + align:start position:0% +can see the only difference in these +Expressions is this sign plus and minus + + align:start position:0% +Expressions is this sign plus and minus + + + align:start position:0% +Expressions is this sign plus and minus +there uh so we now now want to add those + + align:start position:0% +there uh so we now now want to add those + + + align:start position:0% +there uh so we now now want to add those +together uh and um uh so here we're + + align:start position:0% +together uh and um uh so here we're + + + align:start position:0% +together uh and um uh so here we're +looking at some observation Point uh you + + align:start position:0% +looking at some observation Point uh you + + + align:start position:0% +looking at some observation Point uh you +got to add those things together + + align:start position:0% + + + + align:start position:0% + +yeah so uh of course as it explains here + + align:start position:0% +yeah so uh of course as it explains here + + + align:start position:0% +yeah so uh of course as it explains here +if this distance we look at this + + align:start position:0% +if this distance we look at this + + + align:start position:0% +if this distance we look at this +distance and this distance if the path + + align:start position:0% +distance and this distance if the path + + + align:start position:0% +distance and this distance if the path +difference between those uh is an exact + + align:start position:0% +difference between those uh is an exact + + + align:start position:0% +difference between those uh is an exact +number of wavelengths then they're going + + align:start position:0% +number of wavelengths then they're going + + + align:start position:0% +number of wavelengths then they're going +to add up in Phase if they're if they're + + align:start position:0% +to add up in Phase if they're if they're + + + align:start position:0% +to add up in Phase if they're if they're +exact number of half wavelengths then + + align:start position:0% +exact number of half wavelengths then + + + align:start position:0% +exact number of half wavelengths then +then you're you're going to get + + align:start position:0% +then you're you're going to get + + + align:start position:0% +then you're you're going to get +destructive interference and you're + + align:start position:0% +destructive interference and you're + + + align:start position:0% +destructive interference and you're +going to get uh a black + + align:start position:0% +going to get uh a black + + + align:start position:0% +going to get uh a black +region + + align:start position:0% + + + + align:start position:0% + +uh so there they are there's the + + align:start position:0% +uh so there they are there's the + + + align:start position:0% +uh so there they are there's the +distances D1 and D2 uh this is the + + align:start position:0% +distances D1 and D2 uh this is the + + + align:start position:0% +distances D1 and D2 uh this is the +expressions for + + align:start position:0% +expressions for + + + align:start position:0% +expressions for +those uh and again we can use this Fel + + align:start position:0% +those uh and again we can use this Fel + + + align:start position:0% +those uh and again we can use this Fel +approximation to expand the square root + + align:start position:0% +approximation to expand the square root + + + align:start position:0% +approximation to expand the square root +and then D2 minus D1 is going to be this + + align:start position:0% +and then D2 minus D1 is going to be this + + + align:start position:0% +and then D2 minus D1 is going to be this +minus this uh and you can see the only + + align:start position:0% +minus this uh and you can see the only + + + align:start position:0% +minus this uh and you can see the only +difference uh there's a sign there + + align:start position:0% + + + + align:start position:0% + +George uh and uh and so + + align:start position:0% +George uh and uh and so + + + align:start position:0% +George uh and uh and so +yeah so there's going to be 4 x x- over + + align:start position:0% +yeah so there's going to be 4 x x- over + + + align:start position:0% +yeah so there's going to be 4 x x- over +2 L so the one of the twos cancels and + + align:start position:0% +2 L so the one of the twos cancels and + + + align:start position:0% +2 L so the one of the twos cancels and +you get this right so the optical path + + align:start position:0% +you get this right so the optical path + + + align:start position:0% +you get this right so the optical path +uh length Optical path + + align:start position:0% +uh length Optical path + + + align:start position:0% +uh length Optical path +difference uh is is this 2 X x- over L + + align:start position:0% +difference uh is is this 2 X x- over L + + + align:start position:0% +difference uh is is this 2 X x- over L +right so X is this this distance here x + + align:start position:0% +right so X is this this distance here x + + + align:start position:0% +right so X is this this distance here x +dashed is this distance here so both of + + align:start position:0% +dashed is this distance here so both of + + + align:start position:0% +dashed is this distance here so both of +those are small quantities + + align:start position:0% +those are small quantities + + + align:start position:0% +those are small quantities +uh and uh L of course is a big + + align:start position:0% +uh and uh L of course is a big + + + align:start position:0% +uh and uh L of course is a big +quantity uh so this is actually then in + + align:start position:0% +quantity uh so this is actually then in + + + align:start position:0% +quantity uh so this is actually then in +terms of uh distance of course you know + + align:start position:0% +terms of uh distance of course you know + + + align:start position:0% +terms of uh distance of course you know +two distances at the top and a distance + + align:start position:0% +two distances at the top and a distance + + + align:start position:0% +two distances at the top and a distance +at the bottom this has got the right + + align:start position:0% +at the bottom this has got the right + + + align:start position:0% +at the bottom this has got the right +dimensions of of of um length for + + align:start position:0% +dimensions of of of um length for + + + align:start position:0% +dimensions of of of um length for +optical + + align:start position:0% + + + + align:start position:0% + +path right so as we said let's give + + align:start position:0% +path right so as we said let's give + + + align:start position:0% +path right so as we said let's give +constructive and destructive interfer + + align:start position:0% +constructive and destructive interfer + + + align:start position:0% +constructive and destructive interfer +what you're going to see uh is just um + + align:start position:0% +what you're going to see uh is just um + + + align:start position:0% +what you're going to see uh is just um +fringes like this so there's going to be + + align:start position:0% +fringes like this so there's going to be + + + align:start position:0% +fringes like this so there's going to be +positions where uh these two add up in + + align:start position:0% +positions where uh these two add up in + + + align:start position:0% +positions where uh these two add up in +phase and positions where they uh you + + align:start position:0% +phase and positions where they uh you + + + align:start position:0% +phase and positions where they uh you +get destructive + + align:start position:0% + + + + align:start position:0% + +interference right so if um if the + + align:start position:0% +interference right so if um if the + + + align:start position:0% +interference right so if um if the +optical path difference is equal to + + align:start position:0% +optical path difference is equal to + + + align:start position:0% +optical path difference is equal to +Lambda uh then you if you put Lambda + + align:start position:0% +Lambda uh then you if you put Lambda + + + align:start position:0% +Lambda uh then you if you put Lambda +equal to this thing uh then you get that + + align:start position:0% +equal to this thing uh then you get that + + + align:start position:0% +equal to this thing uh then you get that +x- is Lambda L / 2 + + align:start position:0% +x- is Lambda L / 2 + + + align:start position:0% +x- is Lambda L / 2 +x right so this this then tells you if + + align:start position:0% +x right so this this then tells you if + + + align:start position:0% +x right so this this then tells you if +you made this n Lambda of course you'd + + align:start position:0% +you made this n Lambda of course you'd + + + align:start position:0% +you made this n Lambda of course you'd +have an n in here so but this distance + + align:start position:0% +have an n in here so but this distance + + + align:start position:0% +have an n in here so but this distance +here to uh to this distance to there is + + align:start position:0% +here to uh to this distance to there is + + + align:start position:0% +here to uh to this distance to there is +given by this Lambda L over 2 x so you + + align:start position:0% +given by this Lambda L over 2 x so you + + + align:start position:0% +given by this Lambda L over 2 x so you +can + + align:start position:0% +can + + + align:start position:0% +can +see the the smaller X not is uh the + + align:start position:0% +see the the smaller X not is uh the + + + align:start position:0% +see the the smaller X not is uh the +bigger uh X dashed is the smaller you + + align:start position:0% +bigger uh X dashed is the smaller you + + + align:start position:0% +bigger uh X dashed is the smaller you +make this the bigger you make + + align:start position:0% + + + + align:start position:0% + +this what + + align:start position:0% + + + + align:start position:0% + +happened ah that spacing there right + + align:start position:0% +happened ah that spacing there right + + + align:start position:0% +happened ah that spacing there right +okay so this + + align:start position:0% +okay so this + + + align:start position:0% +okay so this +is this is the uh the the the the the + + align:start position:0% +is this is the uh the the the the the + + + align:start position:0% +is this is the uh the the the the the +spacing of the fringes then yeah is this + + align:start position:0% +spacing of the fringes then yeah is this + + + align:start position:0% +spacing of the fringes then yeah is this +Lambda uh Lambda l/ 2 x + + align:start position:0% + + + + align:start position:0% + +right okay and uh so this is going + + align:start position:0% +right okay and uh so this is going + + + align:start position:0% +right okay and uh so this is going +through the maths of that uh so these + + align:start position:0% +through the maths of that uh so these + + + align:start position:0% +through the maths of that uh so these +are the two waves we've added together + + align:start position:0% +are the two waves we've added together + + + align:start position:0% +are the two waves we've added together +uh the only difference between them is + + align:start position:0% +uh the only difference between them is + + + align:start position:0% +uh the only difference between them is +this sign uh so we can take out the + + align:start position:0% +this sign uh so we can take out the + + + align:start position:0% +this sign uh so we can take out the +other things as factors uh and so these + + align:start position:0% +other things as factors uh and so these + + + align:start position:0% +other things as factors uh and so these +are the two terms with the sign + + align:start position:0% +are the two terms with the sign + + + align:start position:0% +are the two terms with the sign +difference uh so e to the minus I + + align:start position:0% +difference uh so e to the minus I + + + align:start position:0% +difference uh so e to the minus I +something plus C to the I something + + align:start position:0% +something plus C to the I something + + + align:start position:0% +something plus C to the I something +gives + + align:start position:0% +gives + + + align:start position:0% +gives +cosine and so there's our final answer + + align:start position:0% +cosine and so there's our final answer + + + align:start position:0% +cosine and so there's our final answer +what you see uh the intensity is the + + align:start position:0% +what you see uh the intensity is the + + + align:start position:0% +what you see uh the intensity is the +modulus square of this these are all + + align:start position:0% +modulus square of this these are all + + + align:start position:0% +modulus square of this these are all +phase terms so we don't worry about them + + align:start position:0% +phase terms so we don't worry about them + + + align:start position:0% +phase terms so we don't worry about them +uh and uh I guess in this expression + + align:start position:0% +uh and uh I guess in this expression + + + align:start position:0% +uh and uh I guess in this expression +here we don't worry about any of these + + align:start position:0% +here we don't worry about any of these + + + align:start position:0% +here we don't worry about any of these +other things either these constants the + + align:start position:0% +other things either these constants the + + + align:start position:0% +other things either these constants the +only thing that's important uh is is + + align:start position:0% +only thing that's important uh is is + + + align:start position:0% +only thing that's important uh is is +This this term + + align:start position:0% +This this term + + + align:start position:0% +This this term +here uh and but we seem to have kept the + + align:start position:0% +here uh and but we seem to have kept the + + + align:start position:0% +here uh and but we seem to have kept the +four 2^ + + align:start position:0% +four 2^ + + + align:start position:0% +four 2^ +squared uh I guess yeah why we kept + + align:start position:0% +squared uh I guess yeah why we kept + + + align:start position:0% +squared uh I guess yeah why we kept +that anyway 4 cos squ something and then + + align:start position:0% +that anyway 4 cos squ something and then + + + align:start position:0% +that anyway 4 cos squ something and then +we say that COS squar of something is + + align:start position:0% +we say that COS squar of something is + + + align:start position:0% +we say that COS squar of something is +equal to 1 + cos 2 + + align:start position:0% +equal to 1 + cos 2 + + + align:start position:0% +equal to 1 + cos 2 +Theta uh and uh so therefore our final + + align:start position:0% +Theta uh and uh so therefore our final + + + align:start position:0% +Theta uh and uh so therefore our final +result then uh this is then uh our + + align:start position:0% +result then uh this is then uh our + + + align:start position:0% +result then uh this is then uh our +expression very similar to what we had + + align:start position:0% +expression very similar to what we had + + + align:start position:0% +expression very similar to what we had +before of course for the + + align:start position:0% +before of course for the + + + align:start position:0% +before of course for the +interferometry uh a + + align:start position:0% +interferometry uh a + + + align:start position:0% +interferometry uh a +background uh with a cosine fringes on + + align:start position:0% +background uh with a cosine fringes on + + + align:start position:0% +background uh with a cosine fringes on +top of it right so here it here it is + + align:start position:0% +top of it right so here it here it is + + + align:start position:0% +top of it right so here it here it is +it's very similar to what we had before + + align:start position:0% +it's very similar to what we had before + + + align:start position:0% +it's very similar to what we had before +um the M here is is one uh and that of + + align:start position:0% +um the M here is is one uh and that of + + + align:start position:0% +um the M here is is one uh and that of +course is just like with the case of the + + align:start position:0% +course is just like with the case of the + + + align:start position:0% +course is just like with the case of the +uh interferometer that we described + + align:start position:0% +uh interferometer that we described + + + align:start position:0% +uh interferometer that we described +before you remember we got m equals 1 + + align:start position:0% +before you remember we got m equals 1 + + + align:start position:0% +before you remember we got m equals 1 +when the strength of the object beam and + + align:start position:0% +when the strength of the object beam and + + + align:start position:0% +when the strength of the object beam and +the reference beam were equal so in this + + align:start position:0% +the reference beam were equal so in this + + + align:start position:0% +the reference beam were equal so in this +case uh they're equal aren't they + + align:start position:0% +case uh they're equal aren't they + + + align:start position:0% +case uh they're equal aren't they +because the two the two + + align:start position:0% +because the two the two + + + align:start position:0% +because the two the two +uh slits in the screen are equal if you + + align:start position:0% +uh slits in the screen are equal if you + + + align:start position:0% +uh slits in the screen are equal if you +made those two slightly different width + + align:start position:0% +made those two slightly different width + + + align:start position:0% +made those two slightly different width +or something then that would not be true + + align:start position:0% +or something then that would not be true + + + align:start position:0% +or something then that would not be true +right so then then you might end up with + + align:start position:0% +right so then then you might end up with + + + align:start position:0% +right so then then you might end up with +something where which didn't have this + + align:start position:0% +something where which didn't have this + + + align:start position:0% +something where which didn't have this +um uh uh visibility of of + + align:start position:0% + + + + align:start position:0% + +one okay so that's the uh first example + + align:start position:0% +one okay so that's the uh first example + + + align:start position:0% +one okay so that's the uh first example +so that that one really was showing how + + align:start position:0% +so that that one really was showing how + + + align:start position:0% +so that that one really was showing how +interferometry and defraction are really + + align:start position:0% +interferometry and defraction are really + + + align:start position:0% +interferometry and defraction are really +the same uh now we're going to go on to + + align:start position:0% +the same uh now we're going to go on to + + + align:start position:0% +the same uh now we're going to go on to +some more about um uh fraction uh and uh + + align:start position:0% +some more about um uh fraction uh and uh + + + align:start position:0% +some more about um uh fraction uh and uh +introduce the idea of a of a + + align:start position:0% +introduce the idea of a of a + + + align:start position:0% +introduce the idea of a of a +transparency so all we all we're doing + + align:start position:0% +transparency so all we all we're doing + + + align:start position:0% +transparency so all we all we're doing +here is we're we're introducing the + + align:start position:0% +here is we're we're introducing the + + + align:start position:0% +here is we're we're introducing the +concept of a transparency that can + + align:start position:0% +concept of a transparency that can + + + align:start position:0% +concept of a transparency that can +change uh the uh the magnitude and phase + + align:start position:0% +change uh the uh the magnitude and phase + + + align:start position:0% +change uh the uh the magnitude and phase +of a wave by it transmitting through it + + align:start position:0% +of a wave by it transmitting through it + + + align:start position:0% +of a wave by it transmitting through it +and uh so this shows + + align:start position:0% +and uh so this shows + + + align:start position:0% +and uh so this shows +here our + + align:start position:0% +here our + + + align:start position:0% +here our +transparency uh and you can see here it + + align:start position:0% +transparency uh and you can see here it + + + align:start position:0% +transparency uh and you can see here it +shows that the um uh the I don't know + + align:start position:0% +shows that the um uh the I don't know + + + align:start position:0% +shows that the um uh the I don't know +what what this color whether it + + align:start position:0% + + + + align:start position:0% + +means right so this means the yeah the + + align:start position:0% +means right so this means the yeah the + + + align:start position:0% +means right so this means the yeah the +absorption of the screen uh and but it + + align:start position:0% +absorption of the screen uh and but it + + + align:start position:0% +absorption of the screen uh and but it +might I guess also change the phase it + + align:start position:0% +might I guess also change the phase it + + + align:start position:0% +might I guess also change the phase it +might have some refractive index as well + + align:start position:0% +might have some refractive index as well + + + align:start position:0% +might have some refractive index as well +yeah and and and it changes in thickness + + align:start position:0% +yeah and and and it changes in thickness + + + align:start position:0% +yeah and and and it changes in thickness +as well right so um so you have to work + + align:start position:0% +as well right so um so you have to work + + + align:start position:0% +as well right so um so you have to work +out just like before the optical path as + + align:start position:0% +out just like before the optical path as + + + align:start position:0% +out just like before the optical path as +the light goes through the structure and + + align:start position:0% +the light goes through the structure and + + + align:start position:0% +the light goes through the structure and +it might change both the amplitude and + + align:start position:0% +it might change both the amplitude and + + + align:start position:0% +it might change both the amplitude and +the phase of the of the light right so + + align:start position:0% +the phase of the of the light right so + + + align:start position:0% +the phase of the of the light right so +um we can think of this uh thin + + align:start position:0% +um we can think of this uh thin + + + align:start position:0% +um we can think of this uh thin +transparency as just having a sort of + + align:start position:0% +transparency as just having a sort of + + + align:start position:0% +transparency as just having a sort of +multiplying effect uh if uh if it's thin + + align:start position:0% +multiplying effect uh if uh if it's thin + + + align:start position:0% +multiplying effect uh if uh if it's thin +enough so you can use your um you can + + align:start position:0% +enough so you can use your um you can + + + align:start position:0% +enough so you can use your um you can +use your um hyan type principle uh to + + align:start position:0% +use your um hyan type principle uh to + + + align:start position:0% +use your um hyan type principle uh to +say that when the light has gone through + + align:start position:0% +say that when the light has gone through + + + align:start position:0% +say that when the light has gone through +there it it it produces some wave fr on + + align:start position:0% +there it it it produces some wave fr on + + + align:start position:0% +there it it it produces some wave fr on +the far side uh so okay so the + + align:start position:0% +the far side uh so okay so the + + + align:start position:0% +the far side uh so okay so the +assumptions the thickness I've just said + + align:start position:0% +assumptions the thickness I've just said + + + align:start position:0% +assumptions the thickness I've just said +also the features on the + + align:start position:0% +also the features on the + + + align:start position:0% +also the features on the +transparency uh what's that mean what's + + align:start position:0% +transparency uh what's that mean what's + + + align:start position:0% +transparency uh what's that mean what's +that mean the features on the + + align:start position:0% +that mean the features on the + + + align:start position:0% +that mean the features on the +transparency are smaller than + + align:start position:0% + + + + align:start position:0% + +Lambda ah right okay that's why I was + + align:start position:0% +Lambda ah right okay that's why I was + + + align:start position:0% +Lambda ah right okay that's why I was +confused okay right so yeah so this so + + align:start position:0% +confused okay right so yeah so this so + + + align:start position:0% +confused okay right so yeah so this so +This transparency can change the + + align:start position:0% +This transparency can change the + + + align:start position:0% +This transparency can change the +attenuation right so the the black bits + + align:start position:0% +attenuation right so the the black bits + + + align:start position:0% +attenuation right so the the black bits +are going to absorb the light uh but it + + align:start position:0% +are going to absorb the light uh but it + + + align:start position:0% +are going to absorb the light uh but it +can also change the + + align:start position:0% +can also change the + + + align:start position:0% +can also change the +phase uh so phase delay uh and both of + + align:start position:0% +phase uh so phase delay uh and both of + + + align:start position:0% +phase uh so phase delay uh and both of +these are going to be uh both of these + + align:start position:0% +these are going to be uh both of these + + + align:start position:0% +these are going to be uh both of these +effects are going to be dependent on the + + align:start position:0% +effects are going to be dependent on the + + + align:start position:0% +effects are going to be dependent on the +material properties of this transparen + + align:start position:0% +material properties of this transparen + + + align:start position:0% +material properties of this transparen +transparency of course and also its + + align:start position:0% +transparency of course and also its + + + align:start position:0% +transparency of course and also its +thickness uh and uh as it points out + + align:start position:0% +thickness uh and uh as it points out + + + align:start position:0% +thickness uh and uh as it points out +here in some cases uh you might be able + + align:start position:0% +here in some cases uh you might be able + + + align:start position:0% +here in some cases uh you might be able +to think of these uh quantities the + + align:start position:0% +to think of these uh quantities the + + + align:start position:0% +to think of these uh quantities the +attenuation and the phase delay as being + + align:start position:0% +attenuation and the phase delay as being + + + align:start position:0% +attenuation and the phase delay as being +being uh binary quantities they might + + align:start position:0% +being uh binary quantities they might + + + align:start position:0% +being uh binary quantities they might +only have two two two different values + + align:start position:0% +only have two two two different values + + + align:start position:0% +only have two two two different values +for example you might have black and + + align:start position:0% +for example you might have black and + + + align:start position:0% +for example you might have black and +white or they might be uh grayscale type + + align:start position:0% +white or they might be uh grayscale type + + + align:start position:0% +white or they might be uh grayscale type +continuously varying type quantities and + + align:start position:0% +continuously varying type quantities and + + + align:start position:0% +continuously varying type quantities and +uh and then the phase also you can think + + align:start position:0% +uh and then the phase also you can think + + + align:start position:0% +uh and then the phase also you can think +of that uh maybe it's it's continuously + + align:start position:0% +of that uh maybe it's it's continuously + + + align:start position:0% +of that uh maybe it's it's continuously +varying phase change uh or it might have + + align:start position:0% +varying phase change uh or it might have + + + align:start position:0% +varying phase change uh or it might have +uh just two values binary values or it + + align:start position:0% +uh just two values binary values or it + + + align:start position:0% +uh just two values binary values or it +might even have mult multiple values + + align:start position:0% +might even have mult multiple values + + + align:start position:0% +might even have mult multiple values +maybe um say eight values you can code + + align:start position:0% +maybe um say eight values you can code + + + align:start position:0% +maybe um say eight values you can code +uh people often use uh transparencies + + align:start position:0% +uh people often use uh transparencies + + + align:start position:0% +uh people often use uh transparencies +like this to code binary uh numbers like + + align:start position:0% +like this to code binary uh numbers like + + + align:start position:0% +like this to code binary uh numbers like +uh uh up to some you know um basis of + + align:start position:0% +uh uh up to some you know um basis of + + + align:start position:0% +uh uh up to some you know um basis of +eight or something like + + align:start position:0% +eight or something like + + + align:start position:0% +eight or something like +that okay so if if these assumptions are + + align:start position:0% +that okay so if if these assumptions are + + + align:start position:0% +that okay so if if these assumptions are +true uh then uh according to hen's + + align:start position:0% +true uh then uh according to hen's + + + align:start position:0% +true uh then uh according to hen's +principle this uh the propagation + + align:start position:0% +principle this uh the propagation + + + align:start position:0% +principle this uh the propagation +through this all it's going to do + + align:start position:0% +through this all it's going to do + + + align:start position:0% +through this all it's going to do +basically is change uh the uh the this + + align:start position:0% +basically is change uh the uh the this + + + align:start position:0% +basically is change uh the uh the this +is going to change to this this is going + + align:start position:0% +is going to change to this this is going + + + align:start position:0% +is going to change to this this is going +to change to this and you're not going + + align:start position:0% +to change to this and you're not going + + + align:start position:0% +to change to this and you're not going +to get uh this affecting this very much + + align:start position:0% +to get uh this affecting this very much + + + align:start position:0% +to get uh this affecting this very much +if this Assumption of this thickness uh + + align:start position:0% +if this Assumption of this thickness uh + + + align:start position:0% +if this Assumption of this thickness uh +being very um thin is is valid in which + + align:start position:0% +being very um thin is is valid in which + + + align:start position:0% +being very um thin is is valid in which +case uh all it does all this + + align:start position:0% +case uh all it does all this + + + align:start position:0% +case uh all it does all this +transparency does is + + align:start position:0% +transparency does is + + + align:start position:0% +transparency does is +multiplies uh the field going in by the + + align:start position:0% +multiplies uh the field going in by the + + + align:start position:0% +multiplies uh the field going in by the +transmission of the grating to give the + + align:start position:0% +transmission of the grating to give the + + + align:start position:0% +transmission of the grating to give the +the uh the amplitude of the wave as it + + align:start position:0% +the uh the amplitude of the wave as it + + + align:start position:0% +the uh the amplitude of the wave as it +comes out right so G minus is the wave + + align:start position:0% +comes out right so G minus is the wave + + + align:start position:0% +comes out right so G minus is the wave +is the amplitude on the way in G Plus is + + align:start position:0% +is the amplitude on the way in G Plus is + + + align:start position:0% +is the amplitude on the way in G Plus is +the way amplitude of the wave on the way + + align:start position:0% +the way amplitude of the wave on the way + + + align:start position:0% +the way amplitude of the wave on the way +out uh and this um transmit + + align:start position:0% +out uh and this um transmit + + + align:start position:0% +out uh and this um transmit +transmittance we call this the amplitude + + align:start position:0% +transmittance we call this the amplitude + + + align:start position:0% +transmittance we call this the amplitude +transmittance of the grating uh and you + + align:start position:0% +transmittance of the grating uh and you + + + align:start position:0% +transmittance of the grating uh and you +see it's a function of position uh and + + align:start position:0% +see it's a function of position uh and + + + align:start position:0% +see it's a function of position uh and +as we just described uh it can be broken + + align:start position:0% +as we just described uh it can be broken + + + align:start position:0% +as we just described uh it can be broken +up into uh an absorption term and a + + align:start position:0% +up into uh an absorption term and a + + + align:start position:0% +up into uh an absorption term and a +phase + + align:start position:0% +phase + + + align:start position:0% +phase +term right and and as we just said those + + align:start position:0% +term right and and as we just said those + + + align:start position:0% +term right and and as we just said those +two might either be they could be binary + + align:start position:0% +two might either be they could be binary + + + align:start position:0% +two might either be they could be binary +or they could be continuously + + align:start position:0% + + + + align:start position:0% + +variable + + align:start position:0% +variable + + + align:start position:0% +variable +right um yeah so this is saying how um + + align:start position:0% +right um yeah so this is saying how um + + + align:start position:0% +right um yeah so this is saying how um +you can think of it being very similar + + align:start position:0% +you can think of it being very similar + + + align:start position:0% +you can think of it being very similar +to the to the to the Young's + + align:start position:0% +to the to the to the Young's + + + align:start position:0% +to the to the to the Young's +interferometer the two slit + + align:start position:0% +interferometer the two slit + + + align:start position:0% +interferometer the two slit +experiment uh but + + align:start position:0% + + + + align:start position:0% + +um now you can see it here is we're + + align:start position:0% +um now you can see it here is we're + + + align:start position:0% +um now you can see it here is we're +thinking of it as being many beams so so + + align:start position:0% +thinking of it as being many beams so so + + + align:start position:0% +thinking of it as being many beams so so +you've broken this up into not not just + + align:start position:0% +you've broken this up into not not just + + + align:start position:0% +you've broken this up into not not just +two uh two beams but many beams and each + + align:start position:0% +two uh two beams but many beams and each + + + align:start position:0% +two uh two beams but many beams and each +of these is going to + + align:start position:0% +of these is going to + + + align:start position:0% +of these is going to +propagate uh but + + align:start position:0% +propagate uh but + + + align:start position:0% +propagate uh but +um I'm not quite sure what this is + + align:start position:0% +um I'm not quite sure what this is + + + align:start position:0% +um I'm not quite sure what this is +trying to + + align:start position:0% +trying to + + + align:start position:0% +trying to +show + + align:start position:0% +show + + + align:start position:0% +show +yeah okay so it's pretty well what I + + align:start position:0% +yeah okay so it's pretty well what I + + + align:start position:0% +yeah okay so it's pretty well what I +said before uh so if if this thing is + + align:start position:0% +said before uh so if if this thing is + + + align:start position:0% +said before uh so if if this thing is +thin enough uh then then this point here + + align:start position:0% +thin enough uh then then this point here + + + align:start position:0% +thin enough uh then then this point here +is only going to be affected by this one + + align:start position:0% +is only going to be affected by this one + + + align:start position:0% +is only going to be affected by this one +and not by the others right so so then + + align:start position:0% +and not by the others right so so then + + + align:start position:0% +and not by the others right so so then +you will get this simple uh mult + + align:start position:0% +you will get this simple uh mult + + + align:start position:0% +you will get this simple uh mult +multiplicative sort of uh + + align:start position:0% + + + + align:start position:0% + +relationship okay so you can think of um + + align:start position:0% +relationship okay so you can think of um + + + align:start position:0% +relationship okay so you can think of um +uh defraction then as being like uh + + align:start position:0% +uh defraction then as being like uh + + + align:start position:0% +uh defraction then as being like uh +interference with many many + + align:start position:0% + + + + align:start position:0% + +beams okay uh and + + align:start position:0% + + + + align:start position:0% + +um yeah so this is saying just like we + + align:start position:0% +um yeah so this is saying just like we + + + align:start position:0% +um yeah so this is saying just like we +said before we we um putting this + + align:start position:0% +said before we we um putting this + + + align:start position:0% +said before we we um putting this +describing this uh interference of these + + align:start position:0% +describing this uh interference of these + + + align:start position:0% +describing this uh interference of these +many many beams now when we did the uh + + align:start position:0% +many many beams now when we did the uh + + + align:start position:0% +many many beams now when we did the uh +the Young's experiment each of the uh + + align:start position:0% +the Young's experiment each of the uh + + + align:start position:0% +the Young's experiment each of the uh +slits uh was described by a Delta + + align:start position:0% +slits uh was described by a Delta + + + align:start position:0% +slits uh was described by a Delta +function at a particular position uh and + + align:start position:0% +function at a particular position uh and + + + align:start position:0% +function at a particular position uh and +now we're saying that in general we can + + align:start position:0% +now we're saying that in general we can + + + align:start position:0% +now we're saying that in general we can +uh think of this as not being just two + + align:start position:0% +uh think of this as not being just two + + + align:start position:0% +uh think of this as not being just two +slits but an integral uh over many uh + + align:start position:0% +slits but an integral uh over many uh + + + align:start position:0% +slits but an integral uh over many uh +many uh apertures very small apertures + + align:start position:0% +many uh apertures very small apertures + + + align:start position:0% +many uh apertures very small apertures +placed at these points X1 uh y1 uh and + + align:start position:0% +placed at these points X1 uh y1 uh and + + + align:start position:0% +placed at these points X1 uh y1 uh and +uh sorry placed at the points XY I guess + + align:start position:0% +uh sorry placed at the points XY I guess + + + align:start position:0% +uh sorry placed at the points XY I guess +and then we're integrating over all + + align:start position:0% +and then we're integrating over all + + + align:start position:0% +and then we're integrating over all +those uh points uh in order to get the + + align:start position:0% +those uh points uh in order to get the + + + align:start position:0% +those uh points uh in order to get the +total effect of + + align:start position:0% + + + + align:start position:0% + +like our a single point on the wave + + align:start position:0% +like our a single point on the wave + + + align:start position:0% +like our a single point on the wave +front going in uh and this gives rise to + + align:start position:0% +front going in uh and this gives rise to + + + align:start position:0% +front going in uh and this gives rise to +a wave that comes out a spherical wave + + align:start position:0% +a wave that comes out a spherical wave + + + align:start position:0% +a wave that comes out a spherical wave +that comes out uh which is of this form + + align:start position:0% +that comes out uh which is of this form + + + align:start position:0% +that comes out uh which is of this form +is the same as this multiplied by the + + align:start position:0% +is the same as this multiplied by the + + + align:start position:0% +is the same as this multiplied by the +transmission of the source uh and then + + align:start position:0% +transmission of the source uh and then + + + align:start position:0% +transmission of the source uh and then +this then radiates like a spherical wave + + align:start position:0% +this then radiates like a spherical wave + + + align:start position:0% +this then radiates like a spherical wave +and then you're going to get some + + align:start position:0% +and then you're going to get some + + + align:start position:0% +and then you're going to get some +distribution of amplitude on this + + align:start position:0% +distribution of amplitude on this + + + align:start position:0% +distribution of amplitude on this +observation plane which is going to be + + align:start position:0% +observation plane which is going to be + + + align:start position:0% +observation plane which is going to be +exactly the same as we had before uh and + + align:start position:0% +exactly the same as we had before uh and + + + align:start position:0% +exactly the same as we had before uh and +we've got the this uh again we've got + + align:start position:0% +we've got the this uh again we've got + + + align:start position:0% +we've got the this uh again we've got +this parabolic phase function uh that + + align:start position:0% +this parabolic phase function uh that + + + align:start position:0% +this parabolic phase function uh that +comes from the the frel uh + + align:start position:0% +comes from the the frel uh + + + align:start position:0% +comes from the the frel uh +approximation so assumes that x x dashed + + align:start position:0% +approximation so assumes that x x dashed + + + align:start position:0% +approximation so assumes that x x dashed +y dashed is much smaller than Zed + + align:start position:0% + + + + align:start position:0% + +so okay so that's for a single point and + + align:start position:0% +so okay so that's for a single point and + + + align:start position:0% +so okay so that's for a single point and +now we do now we integrate over all of + + align:start position:0% +now we do now we integrate over all of + + + align:start position:0% +now we do now we integrate over all of +these uh and the final result for the + + align:start position:0% +these uh and the final result for the + + + align:start position:0% +these uh and the final result for the +amplitude we'll we'll see on the screen + + align:start position:0% +amplitude we'll we'll see on the screen + + + align:start position:0% +amplitude we'll we'll see on the screen +is given by this expression then so this + + align:start position:0% +is given by this expression then so this + + + align:start position:0% +is given by this expression then so this +is the incident wave this is the + + align:start position:0% +is the incident wave this is the + + + align:start position:0% +is the incident wave this is the +transmission of the screen uh and this + + align:start position:0% +transmission of the screen uh and this + + + align:start position:0% +transmission of the screen uh and this +is the bit that + + align:start position:0% +is the bit that + + + align:start position:0% +is the bit that +describes uh the uh propagation of the + + align:start position:0% +describes uh the uh propagation of the + + + align:start position:0% +describes uh the uh propagation of the +spherical waves according to the uh Fel + + align:start position:0% + + + + align:start position:0% + +approximation okay so yeah so this this + + align:start position:0% +approximation okay so yeah so this this + + + align:start position:0% +approximation okay so yeah so this this +result is known as the frel defraction + + align:start position:0% +result is known as the frel defraction + + + align:start position:0% +result is known as the frel defraction +integral or simply the frel integral and + + align:start position:0% +integral or simply the frel integral and + + + align:start position:0% +integral or simply the frel integral and +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +um we I mentioned earlier that this + + align:start position:0% +um we I mentioned earlier that this + + + align:start position:0% +um we I mentioned earlier that this +approximation of replacing these the + + align:start position:0% +approximation of replacing these the + + + align:start position:0% +approximation of replacing these the +square root by the square terms is + + align:start position:0% +square root by the square terms is + + + align:start position:0% +square root by the square terms is +called the frenel approximation right so + + align:start position:0% +called the frenel approximation right so + + + align:start position:0% +called the frenel approximation right so +all of these frenel gets the name of all + + align:start position:0% +all of these frenel gets the name of all + + + align:start position:0% +all of these frenel gets the name of all +of these + + align:start position:0% + + + + align:start position:0% + +things okay yeah this is just pointing + + align:start position:0% +things okay yeah this is just pointing + + + align:start position:0% +things okay yeah this is just pointing +out that um this expression we've just + + align:start position:0% +out that um this expression we've just + + + align:start position:0% +out that um this expression we've just +written down the form of this is exactly + + align:start position:0% +written down the form of this is exactly + + + align:start position:0% +written down the form of this is exactly +the form of of a + + align:start position:0% +the form of of a + + + align:start position:0% +the form of of a +convolution uh and uh so what that + + align:start position:0% +convolution uh and uh so what that + + + align:start position:0% +convolution uh and uh so what that +that's a very important + + align:start position:0% +that's a very important + + + align:start position:0% +that's a very important +result um a convolution of course means + + align:start position:0% +result um a convolution of course means + + + align:start position:0% +result um a convolution of course means +it's it's space invariant doesn't it it + + align:start position:0% +it's it's space invariant doesn't it it + + + align:start position:0% +it's it's space invariant doesn't it it +means that you can write this it it's + + align:start position:0% +means that you can write this it it's + + + align:start position:0% +means that you can write this it it's +some it's something it's what goes in + + align:start position:0% +some it's something it's what goes in + + + align:start position:0% +some it's something it's what goes in +convolved with something which is + + align:start position:0% +convolved with something which is + + + align:start position:0% +convolved with something which is +independent of the coordinates uh and um + + align:start position:0% +independent of the coordinates uh and um + + + align:start position:0% +independent of the coordinates uh and um +so if you think of this as a + + align:start position:0% +so if you think of this as a + + + align:start position:0% +so if you think of this as a +convolution the thing you have to + + align:start position:0% +convolution the thing you have to + + + align:start position:0% +convolution the thing you have to +convolve with is this thing uh so you + + align:start position:0% +convolve with is this thing uh so you + + + align:start position:0% +convolve with is this thing uh so you +can think of this as as being um uh like + + align:start position:0% +can think of this as as being um uh like + + + align:start position:0% +can think of this as as being um uh like +like a what it's called the the point + + align:start position:0% +like a what it's called the the point + + + align:start position:0% +like a what it's called the the point +spread function or the amplitude point + + align:start position:0% +spread function or the amplitude point + + + align:start position:0% +spread function or the amplitude point +spread function so if you put in some + + align:start position:0% +spread function so if you put in some + + + align:start position:0% +spread function so if you put in some +amplitude and convolve it with this uh + + align:start position:0% +amplitude and convolve it with this uh + + + align:start position:0% +amplitude and convolve it with this uh +then you'll get something + + align:start position:0% + + + + align:start position:0% + +out + + align:start position:0% + + + + align:start position:0% + +okay so this is explaining what I just + + align:start position:0% +okay so this is explaining what I just + + + align:start position:0% +okay so this is explaining what I just +said uh so this this this is um the sort + + align:start position:0% +said uh so this this this is um the sort + + + align:start position:0% +said uh so this this this is um the sort +of uh behavior that you think of uh when + + align:start position:0% +of uh behavior that you think of uh when + + + align:start position:0% +of uh behavior that you think of uh when +you're looking at um you know mechanical + + align:start position:0% +you're looking at um you know mechanical + + + align:start position:0% +you're looking at um you know mechanical +or electrical systems you can think of a + + align:start position:0% +or electrical systems you can think of a + + + align:start position:0% +or electrical systems you can think of a +a system of being like a a black box or + + align:start position:0% +a system of being like a a black box or + + + align:start position:0% +a system of being like a a black box or +in this case a blue + + align:start position:0% +in this case a blue + + + align:start position:0% +in this case a blue +box uh and something goes in and + + align:start position:0% +box uh and something goes in and + + + align:start position:0% +box uh and something goes in and +something comes out and we don't have to + + align:start position:0% +something comes out and we don't have to + + + align:start position:0% +something comes out and we don't have to +worry too much about what's in here uh + + align:start position:0% +worry too much about what's in here uh + + + align:start position:0% +worry too much about what's in here uh +but you can Express what goes in of + + align:start position:0% +but you can Express what goes in of + + + align:start position:0% +but you can Express what goes in of +course either in terms of uh uh some + + align:start position:0% +course either in terms of uh uh some + + + align:start position:0% +course either in terms of uh uh some +sort of impulse response function uh or + + align:start position:0% +sort of impulse response function uh or + + + align:start position:0% +sort of impulse response function uh or +as we'll come to in later lectures as + + align:start position:0% +as we'll come to in later lectures as + + + align:start position:0% +as we'll come to in later lectures as +some sort of transfer function uh type + + align:start position:0% +some sort of transfer function uh type + + + align:start position:0% +some sort of transfer function uh type +Behavior but at the moment we do it in + + align:start position:0% +Behavior but at the moment we do it in + + + align:start position:0% +Behavior but at the moment we do it in +the the spatial domain so if we uh if we + + align:start position:0% +the the spatial domain so if we uh if we + + + align:start position:0% +the the spatial domain so if we uh if we +convolve this with this point spread + + align:start position:0% +convolve this with this point spread + + + align:start position:0% +convolve this with this point spread +function uh then we'll get this uh + + align:start position:0% +function uh then we'll get this uh + + + align:start position:0% +function uh then we'll get this uh +output like + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% + + + + align:start position:0% + +okay now we go on to do some examples of + + align:start position:0% +okay now we go on to do some examples of + + + align:start position:0% +okay now we go on to do some examples of +this uh and this is probably the most + + align:start position:0% +this uh and this is probably the most + + + align:start position:0% +this uh and this is probably the most +important example comes up all the time + + align:start position:0% +important example comes up all the time + + + align:start position:0% +important example comes up all the time +uh because you know lots of optical + + align:start position:0% +uh because you know lots of optical + + + align:start position:0% +uh because you know lots of optical +components are circular uh so lenses and + + align:start position:0% +components are circular uh so lenses and + + + align:start position:0% +components are circular uh so lenses and +so on uh very often they've got this + + align:start position:0% +so on uh very often they've got this + + + align:start position:0% +so on uh very often they've got this +circular form uh and uh so this is comes + + align:start position:0% +circular form uh and uh so this is comes + + + align:start position:0% +circular form uh and uh so this is comes +up time and time again uh and uh so all + + align:start position:0% +up time and time again uh and uh so all + + + align:start position:0% +up time and time again uh and uh so all +we got to do now then is we we put in uh + + align:start position:0% +we got to do now then is we we put in uh + + + align:start position:0% +we got to do now then is we we put in uh +we we say that + + align:start position:0% +we we say that + + + align:start position:0% +we we say that +our um s our amplitude after the light's + + align:start position:0% +our um s our amplitude after the light's + + + align:start position:0% +our um s our amplitude after the light's +gone through this this circle circular + + align:start position:0% +gone through this this circle circular + + + align:start position:0% +gone through this this circle circular +aperture is one inside the circle and + + align:start position:0% +aperture is one inside the circle and + + + align:start position:0% +aperture is one inside the circle and +zero outside the + + align:start position:0% +zero outside the + + + align:start position:0% +zero outside the +circle uh and uh and so that frenel + + align:start position:0% +circle uh and uh and so that frenel + + + align:start position:0% +circle uh and uh and so that frenel +defraction integral that we have to work + + align:start position:0% +defraction integral that we have to work + + + align:start position:0% +defraction integral that we have to work +out for this circular aperture is just + + align:start position:0% +out for this circular aperture is just + + + align:start position:0% +out for this circular aperture is just +um it's just one inside and zero outside + + align:start position:0% +um it's just one inside and zero outside + + + align:start position:0% +um it's just one inside and zero outside +so it's just this is you just have to do + + align:start position:0% +so it's just this is you just have to do + + + align:start position:0% +so it's just this is you just have to do +the integral over the inside so you this + + align:start position:0% +the integral over the inside so you this + + + align:start position:0% +the integral over the inside so you this +is just over the values of X and Y that + + align:start position:0% +is just over the values of X and Y that + + + align:start position:0% +is just over the values of X and Y that +are inside the right part + + align:start position:0% +are inside the right part + + + align:start position:0% +are inside the right part +here uh and uh now so unfortunately that + + align:start position:0% +here uh and uh now so unfortunately that + + + align:start position:0% +here uh and uh now so unfortunately that +integral is a bit hard to do so we're + + align:start position:0% +integral is a bit hard to do so we're + + + align:start position:0% +integral is a bit hard to do so we're +not going to do it at the moment uh in + + align:start position:0% +not going to do it at the moment uh in + + + align:start position:0% +not going to do it at the moment uh in +general uh but we we'll do a very simple + + align:start position:0% +general uh but we we'll do a very simple + + + align:start position:0% +general uh but we we'll do a very simple +example a special case of what happens + + align:start position:0% +example a special case of what happens + + + align:start position:0% +example a special case of what happens +along the axis + + align:start position:0% +along the axis + + + align:start position:0% +along the axis +so if we put uh X and Y both + + align:start position:0% +so if we put uh X and Y both + + + align:start position:0% +so if we put uh X and Y both +zero uh now we get uh we put x x- equals + + align:start position:0% +zero uh now we get uh we put x x- equals + + + align:start position:0% +zero uh now we get uh we put x x- equals +not y- equals not the integral comes + + align:start position:0% +not y- equals not the integral comes + + + align:start position:0% +not y- equals not the integral comes +down to this uh and uh and now that is + + align:start position:0% +down to this uh and uh and now that is + + + align:start position:0% +down to this uh and uh and now that is +an integral we can do uh and it's an + + align:start position:0% +an integral we can do uh and it's an + + + align:start position:0% +an integral we can do uh and it's an +integral that probably a lot of you have + + align:start position:0% +integral that probably a lot of you have + + + align:start position:0% +integral that probably a lot of you have +come come across before the way to solve + + align:start position:0% +come come across before the way to solve + + + align:start position:0% +come come across before the way to solve +that is to go into Polar + + align:start position:0% +that is to go into Polar + + + align:start position:0% +that is to go into Polar +coordinates uh and uh so if you if you + + align:start position:0% +coordinates uh and uh so if you if you + + + align:start position:0% +coordinates uh and uh so if you if you +change into Polar + + align:start position:0% +change into Polar + + + align:start position:0% +change into Polar +coordinates uh you you've got a Theta + + align:start position:0% +coordinates uh you you've got a Theta + + + align:start position:0% +coordinates uh you you've got a Theta +and a fi a Theta and a row + + align:start position:0% +and a fi a Theta and a row + + + align:start position:0% +and a fi a Theta and a row +part uh the the Theta part is just an + + align:start position:0% +part uh the the Theta part is just an + + + align:start position:0% +part uh the the Theta part is just an +integral of a constant so that just + + align:start position:0% +integral of a constant so that just + + + align:start position:0% +integral of a constant so that just +becomes 2 pi and the integral of this + + align:start position:0% +becomes 2 pi and the integral of this + + + align:start position:0% +becomes 2 pi and the integral of this +other thing you can now + + align:start position:0% +other thing you can now + + + align:start position:0% +other thing you can now +do uh integral of row e to the I Row 2 + + align:start position:0% +do uh integral of row e to the I Row 2 + + + align:start position:0% +do uh integral of row e to the I Row 2 +over something you can do because the + + align:start position:0% +over something you can do because the + + + align:start position:0% +over something you can do because the +the row outside is the diff uh + + align:start position:0% +the row outside is the diff uh + + + align:start position:0% +the row outside is the diff uh +differential of the bit + + align:start position:0% +differential of the bit + + + align:start position:0% +differential of the bit +inside uh so to actually do that + + align:start position:0% +inside uh so to actually do that + + + align:start position:0% +inside uh so to actually do that +properly um you can make a substitution + + align:start position:0% +properly um you can make a substitution + + + align:start position:0% +properly um you can make a substitution +then make uh substitution that Z is + + align:start position:0% +then make uh substitution that Z is + + + align:start position:0% +then make uh substitution that Z is +equal to this thing inside here uh and + + align:start position:0% +equal to this thing inside here uh and + + + align:start position:0% +equal to this thing inside here uh and +after you've made that + + align:start position:0% +after you've made that + + + align:start position:0% +after you've made that +substitution uh you now just get + + align:start position:0% +substitution uh you now just get + + + align:start position:0% +substitution uh you now just get +integral of e to the i + + align:start position:0% +integral of e to the i + + + align:start position:0% +integral of e to the i +z uh so it's that's something you can + + align:start position:0% +z uh so it's that's something you can + + + align:start position:0% +z uh so it's that's something you can +just um uh + + align:start position:0% +just um uh + + + align:start position:0% +just um uh +do uh and uh you get an answer uh so + + align:start position:0% +do uh and uh you get an answer uh so + + + align:start position:0% +do uh and uh you get an answer uh so +notice + + align:start position:0% + + + + align:start position:0% + +um yeah notice that you get so this this + + align:start position:0% +um yeah notice that you get so this this + + + align:start position:0% +um yeah notice that you get so this this +final result here uh this term here is + + align:start position:0% +final result here uh this term here is + + + align:start position:0% +final result here uh this term here is +just the phase term uh as a function of + + align:start position:0% +just the phase term uh as a function of + + + align:start position:0% +just the phase term uh as a function of +Zed so that's just just what you would + + align:start position:0% +Zed so that's just just what you would + + + align:start position:0% +Zed so that's just just what you would +get if if it was just a a wave moving in + + align:start position:0% +get if if it was just a a wave moving in + + + align:start position:0% +get if if it was just a a wave moving in +free space uh and and then these other + + align:start position:0% +free space uh and and then these other + + + align:start position:0% +free space uh and and then these other +two terms notice they're exactly the + + align:start position:0% +two terms notice they're exactly the + + + align:start position:0% +two terms notice they're exactly the +same form this is an X an e to the I + + align:start position:0% +same form this is an X an e to the I + + + align:start position:0% +same form this is an X an e to the I +something and this is a sign of the + + align:start position:0% +something and this is a sign of the + + + align:start position:0% +something and this is a sign of the +exactly the same + + align:start position:0% + + + + align:start position:0% + +thing okay so so that's what we + + align:start position:0% +thing okay so so that's what we + + + align:start position:0% +thing okay so so that's what we +get um as I say if you if you go back to + + align:start position:0% +get um as I say if you if you go back to + + + align:start position:0% +get um as I say if you if you go back to +this if you wanted to do this integral + + align:start position:0% +this if you wanted to do this integral + + + align:start position:0% +this if you wanted to do this integral +here it's a bit more + + align:start position:0% +here it's a bit more + + + align:start position:0% +here it's a bit more +complicated uh and so we're not going to + + align:start position:0% +complicated uh and so we're not going to + + + align:start position:0% +complicated uh and so we're not going to +do that at the moment but I guess + + align:start position:0% +do that at the moment but I guess + + + align:start position:0% +do that at the moment but I guess +eventually we have to do something about + + align:start position:0% +eventually we have to do something about + + + align:start position:0% +eventually we have to do something about +it + + align:start position:0% +it + + + align:start position:0% +it +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +right so if we look at the um this + + align:start position:0% +right so if we look at the um this + + + align:start position:0% +right so if we look at the um this +amplitude along the axis then you can + + align:start position:0% +amplitude along the axis then you can + + + align:start position:0% +amplitude along the axis then you can +see it's got this sinusoidal sort of + + align:start position:0% +see it's got this sinusoidal sort of + + + align:start position:0% +see it's got this sinusoidal sort of +behavior uh if you look at the intensity + + align:start position:0% +behavior uh if you look at the intensity + + + align:start position:0% +behavior uh if you look at the intensity +this would just go and you just get sin + + align:start position:0% +this would just go and you just get sin + + + align:start position:0% +this would just go and you just get sin +squar of something sin squar is a + + align:start position:0% +squar of something sin squar is a + + + align:start position:0% +squar of something sin squar is a +function of a constant over Zed uh so uh + + align:start position:0% +function of a constant over Zed uh so uh + + + align:start position:0% +function of a constant over Zed uh so uh +as it points out here then it's going to + + align:start position:0% +as it points out here then it's going to + + + align:start position:0% +as it points out here then it's going to +have um Peaks and nulls Maxima or Minima + + align:start position:0% +have um Peaks and nulls Maxima or Minima + + + align:start position:0% +have um Peaks and nulls Maxima or Minima +corresponding to these particular values + + align:start position:0% +corresponding to these particular values + + + align:start position:0% +corresponding to these particular values +of Zed so you'll get the get a um like a + + align:start position:0% +of Zed so you'll get the get a um like a + + + align:start position:0% +of Zed so you'll get the get a um like a +sinusoidal variation in in amplitude + + align:start position:0% +sinusoidal variation in in amplitude + + + align:start position:0% +sinusoidal variation in in amplitude +along the + + align:start position:0% +along the + + + align:start position:0% +along the +axis right the other thing to note uh is + + align:start position:0% +axis right the other thing to note uh is + + + align:start position:0% +axis right the other thing to note uh is +that + + align:start position:0% +that + + + align:start position:0% +that +um where's it gone + + align:start position:0% + + + + align:start position:0% + +uh yeah notice that this this Zed + + align:start position:0% +uh yeah notice that this this Zed + + + align:start position:0% +uh yeah notice that this this Zed +and this Z canceled out this Z here + + align:start position:0% +and this Z canceled out this Z here + + + align:start position:0% +and this Z canceled out this Z here +appeared when we made this + + align:start position:0% +appeared when we made this + + + align:start position:0% +appeared when we made this +substitution uh and uh so these Zeds uh + + align:start position:0% +substitution uh and uh so these Zeds uh + + + align:start position:0% +substitution uh and uh so these Zeds uh +finally cancel uh and uh so the final + + align:start position:0% +finally cancel uh and uh so the final + + + align:start position:0% +finally cancel uh and uh so the final +result has got no Zed in it no no sorry + + align:start position:0% +result has got no Zed in it no no sorry + + + align:start position:0% +result has got no Zed in it no no sorry +no Zed in the modulus part term so + + align:start position:0% +no Zed in the modulus part term so + + + align:start position:0% +no Zed in the modulus part term so +you've got this series of + + align:start position:0% +you've got this series of + + + align:start position:0% +you've got this series of +fringes uh which are of constant uh + + align:start position:0% +fringes uh which are of constant uh + + + align:start position:0% +fringes uh which are of constant uh +amplitude + + align:start position:0% +amplitude + + + align:start position:0% +amplitude +uh far away from this aperture you go + + align:start position:0% +uh far away from this aperture you go + + + align:start position:0% +uh far away from this aperture you go +which might seem rather surprising you + + align:start position:0% +which might seem rather surprising you + + + align:start position:0% +which might seem rather surprising you +might think that as you got closer to + + align:start position:0% +might think that as you got closer to + + + align:start position:0% +might think that as you got closer to +the aperture it would get + + align:start position:0% +the aperture it would get + + + align:start position:0% +the aperture it would get +brighter might you uh but it doesn't it + + align:start position:0% + + + + align:start position:0% + +seems I'm just trying to think quickly + + align:start position:0% +seems I'm just trying to think quickly + + + align:start position:0% +seems I'm just trying to think quickly +why that should be the + + align:start position:0% + + + + align:start position:0% + +case but I'm sure it is is + + align:start position:0% + + + + align:start position:0% + +true notice also the bio Two Face shift + + align:start position:0% +true notice also the bio Two Face shift + + + align:start position:0% +true notice also the bio Two Face shift +has + + align:start position:0% + + + + align:start position:0% + +disappeared it got e up by the sign yeah + + align:start position:0% +disappeared it got e up by the sign yeah + + + align:start position:0% +disappeared it got e up by the sign yeah +that's true sorry I didn't mention that + + align:start position:0% +that's true sorry I didn't mention that + + + align:start position:0% +that's true sorry I didn't mention that +yeah okay so when when you put in the + + align:start position:0% +yeah okay so when when you put in the + + + align:start position:0% +yeah okay so when when you put in the +limits of the + + align:start position:0% +limits of the + + + align:start position:0% +limits of the +integration uh then you got this minus + + align:start position:0% +integration uh then you got this minus + + + align:start position:0% +integration uh then you got this minus +this and this you we replaced by sign + + align:start position:0% +this and this you we replaced by sign + + + align:start position:0% +this and this you we replaced by sign +but of course we need to get an extra IE + + align:start position:0% +but of course we need to get an extra IE + + + align:start position:0% +but of course we need to get an extra IE +to get the sign so yeah so the pi the pi + + align:start position:0% +to get the sign so yeah so the pi the pi + + + align:start position:0% +to get the sign so yeah so the pi the pi +over two face shift is also gone oh the + + align:start position:0% +over two face shift is also gone oh the + + + align:start position:0% +over two face shift is also gone oh the +other thing that perhaps is worth + + align:start position:0% +other thing that perhaps is worth + + + align:start position:0% +other thing that perhaps is worth +mentioning also is that when we got down + + align:start position:0% +mentioning also is that when we got down + + + align:start position:0% +mentioning also is that when we got down +to this integral of course this is just + + align:start position:0% +to this integral of course this is just + + + align:start position:0% +to this integral of course this is just +this is just the fer transform of one + + align:start position:0% +this is just the fer transform of one + + + align:start position:0% +this is just the fer transform of one +isn't it within this region it's the fer + + align:start position:0% +isn't it within this region it's the fer + + + align:start position:0% +isn't it within this region it's the fer +transform of a of a rect + + align:start position:0% +transform of a of a rect + + + align:start position:0% +transform of a of a rect +function uh and um so you know even if + + align:start position:0% +function uh and um so you know even if + + + align:start position:0% +function uh and um so you know even if +you look at more complicated example if + + align:start position:0% +you look at more complicated example if + + + align:start position:0% +you look at more complicated example if +it had this circular symmetry whatever + + align:start position:0% +it had this circular symmetry whatever + + + align:start position:0% +it had this circular symmetry whatever +this uh amplitude uh transmittance of + + align:start position:0% +this uh amplitude uh transmittance of + + + align:start position:0% +this uh amplitude uh transmittance of +this aperture would been uh all we'd + + align:start position:0% +this aperture would been uh all we'd + + + align:start position:0% +this aperture would been uh all we'd +have to do is to do the fer transform of + + align:start position:0% +have to do is to do the fer transform of + + + align:start position:0% +have to do is to do the fer transform of +that amplitude transmittance of that + + align:start position:0% +that amplitude transmittance of that + + + align:start position:0% +that amplitude transmittance of that +aperture as a function of this + + align:start position:0% +aperture as a function of this + + + align:start position:0% +aperture as a function of this +coordinate + + align:start position:0% +coordinate + + + align:start position:0% +coordinate +Z right so that's a a sort of trick you + + align:start position:0% +Z right so that's a a sort of trick you + + + align:start position:0% +Z right so that's a a sort of trick you +can use to calculate these things easily + + align:start position:0% +can use to calculate these things easily + + + align:start position:0% +can use to calculate these things easily +sometimes right I think we're here for + + align:start position:0% +sometimes right I think we're here for + + + align:start position:0% +sometimes right I think we're here for +the movies now uh so uh Matt lab has + + align:start position:0% +the movies now uh so uh Matt lab has + + + align:start position:0% +the movies now uh so uh Matt lab has +calculated these things for us uh and uh + + align:start position:0% +calculated these things for us uh and uh + + + align:start position:0% +calculated these things for us uh and uh +when I press the button it will go but + + align:start position:0% +when I press the button it will go but + + + align:start position:0% +when I press the button it will go but +I'm not going to press it until you're + + align:start position:0% +I'm not going to press it until you're + + + align:start position:0% +I'm not going to press it until you're +ready just in case it's very quick uh so + + align:start position:0% +ready just in case it's very quick uh so + + + align:start position:0% +ready just in case it's very quick uh so +this is a big aperture right so now so + + align:start position:0% +this is a big aperture right so now so + + + align:start position:0% +this is a big aperture right so now so +what you'll see is how the wave + + align:start position:0% +what you'll see is how the wave + + + align:start position:0% +what you'll see is how the wave +propagates uh from that aperture this is + + align:start position:0% +propagates uh from that aperture this is + + + align:start position:0% +propagates uh from that aperture this is +actually quite a big aperture so you + + align:start position:0% +actually quite a big aperture so you + + + align:start position:0% +actually quite a big aperture so you +don't expect to see a lot of defraction + + align:start position:0% +don't expect to see a lot of defraction + + + align:start position:0% +don't expect to see a lot of defraction +in this case when we come to this one + + align:start position:0% +in this case when we come to this one + + + align:start position:0% +in this case when we come to this one +this is a small aperture and as we said + + align:start position:0% +this is a small aperture and as we said + + + align:start position:0% +this is a small aperture and as we said +before the smaller it is to start the + + align:start position:0% +before the smaller it is to start the + + + align:start position:0% +before the smaller it is to start the +more it's going to spread right so + + align:start position:0% +more it's going to spread right so + + + align:start position:0% +more it's going to spread right so +you're going to see a lot more effect on + + align:start position:0% +you're going to see a lot more effect on + + + align:start position:0% +you're going to see a lot more effect on +that one uh and uh so you have to look + + align:start position:0% +that one uh and uh so you have to look + + + align:start position:0% +that one uh and uh so you have to look +quite closely to see what happens as it + + align:start position:0% +quite closely to see what happens as it + + + align:start position:0% +quite closely to see what happens as it +propagates so this is is a radius of 40 + + align:start position:0% +propagates so this is is a radius of 40 + + + align:start position:0% +propagates so this is is a radius of 40 +Lambda now you can see some sort of + + align:start position:0% +Lambda now you can see some sort of + + + align:start position:0% +Lambda now you can see some sort of +fringes appearing and it becomes a like + + align:start position:0% +fringes appearing and it becomes a like + + + align:start position:0% +fringes appearing and it becomes a like +like a bright halo around the + + align:start position:0% +like a bright halo around the + + + align:start position:0% +like a bright halo around the +edges uh and if you look very closely + + align:start position:0% +edges uh and if you look very closely + + + align:start position:0% +edges uh and if you look very closely +you'll see quite a lot of fine structure + + align:start position:0% +you'll see quite a lot of fine structure + + + align:start position:0% +you'll see quite a lot of fine structure +on + + align:start position:0% + + + + align:start position:0% + +this and then the small one this is 10 + + align:start position:0% +this and then the small one this is 10 + + + align:start position:0% +this and then the small one this is 10 +wavelengths so this one changes a lot + + align:start position:0% +wavelengths so this one changes a lot + + + align:start position:0% +wavelengths so this one changes a lot +quicker you see it's doing quite drastic + + align:start position:0% +quicker you see it's doing quite drastic + + + align:start position:0% +quicker you see it's doing quite drastic +things and now you by the time it gets + + align:start position:0% +things and now you by the time it gets + + + align:start position:0% +things and now you by the time it gets +to the end you've even got a black spot + + align:start position:0% +to the end you've even got a black spot + + + align:start position:0% +to the end you've even got a black spot +in the center right + + align:start position:0% +in the center right + + + align:start position:0% +in the center right +so + + align:start position:0% + + + + align:start position:0% + +uh the the fact that uh of course + + align:start position:0% +uh the the fact that uh of course + + + align:start position:0% +uh the the fact that uh of course +um we said before that the smaller the + + align:start position:0% +um we said before that the smaller the + + + align:start position:0% +um we said before that the smaller the +aperture the more it spreads but also + + align:start position:0% +aperture the more it spreads but also + + + align:start position:0% +aperture the more it spreads but also +the quicker it spreads so you can see + + align:start position:0% +the quicker it spreads so you can see + + + align:start position:0% +the quicker it spreads so you can see +that actually this one has got a lot + + align:start position:0% +that actually this one has got a lot + + + align:start position:0% +that actually this one has got a lot +further in the development of the + + align:start position:0% +further in the development of the + + + align:start position:0% +further in the development of the +pattern than this one this one still + + align:start position:0% +pattern than this one this one still + + + align:start position:0% +pattern than this one this one still +looks roughly similar to what what what + + align:start position:0% +looks roughly similar to what what what + + + align:start position:0% +looks roughly similar to what what what +it started it has this one is looking + + align:start position:0% +it started it has this one is looking + + + align:start position:0% +it started it has this one is looking +very very + + align:start position:0% + + + + align:start position:0% + +different right it calls this the + + align:start position:0% +different right it calls this the + + + align:start position:0% +different right it calls this the +blinking spot I've never heard of it + + align:start position:0% +blinking spot I've never heard of it + + + align:start position:0% +blinking spot I've never heard of it +called the blinking spot but + + align:start position:0% + + + + align:start position:0% + +anyway well yeah I'm not even sure I um + + align:start position:0% +anyway well yeah I'm not even sure I um + + + align:start position:0% +anyway well yeah I'm not even sure I um +I always think of the pon spot as being + + align:start position:0% +I always think of the pon spot as being + + + align:start position:0% +I always think of the pon spot as being +what you get from a um an opaque object + + align:start position:0% +what you get from a um an opaque object + + + align:start position:0% +what you get from a um an opaque object +rather than for a uh uh but maybe that's + + align:start position:0% +rather than for a uh uh but maybe that's + + + align:start position:0% +rather than for a uh uh but maybe that's +the arrow goes for but B says that the + + align:start position:0% +the arrow goes for but B says that the + + + align:start position:0% +the arrow goes for but B says that the +two are the same right yeah yeah + + align:start position:0% +two are the same right yeah yeah + + + align:start position:0% +two are the same right yeah yeah +yeah okay so now the rectangular + + align:start position:0% +yeah okay so now the rectangular + + + align:start position:0% +yeah okay so now the rectangular +aperture uh the rectangular + + align:start position:0% +aperture uh the rectangular + + + align:start position:0% +aperture uh the rectangular +aperture uh actually it turns out you + + align:start position:0% +aperture uh actually it turns out you + + + align:start position:0% +aperture uh actually it turns out you +can't get a simple expression for what + + align:start position:0% +can't get a simple expression for what + + + align:start position:0% +can't get a simple expression for what +happens along the axis of the + + align:start position:0% +happens along the axis of the + + + align:start position:0% +happens along the axis of the +rectangular case uh unlike the circular + + align:start position:0% +rectangular case uh unlike the circular + + + align:start position:0% +rectangular case uh unlike the circular +case uh so that's probably why George + + align:start position:0% +case uh so that's probably why George + + + align:start position:0% +case uh so that's probably why George +hasn't done it uh and uh so you can get + + align:start position:0% +hasn't done it uh and uh so you can get + + + align:start position:0% +hasn't done it uh and uh so you can get +expressions in terms of frel integrals + + align:start position:0% +expressions in terms of frel integrals + + + align:start position:0% +expressions in terms of frel integrals +for everywhere in fact for this case so + + align:start position:0% +for everywhere in fact for this case so + + + align:start position:0% +for everywhere in fact for this case so +the square case then let's see what that + + align:start position:0% +the square case then let's see what that + + + align:start position:0% +the square case then let's see what that +does the big Square yeah again you can + + align:start position:0% +does the big Square yeah again you can + + + align:start position:0% +does the big Square yeah again you can +see you can see some sort of + + align:start position:0% +see you can see some sort of + + + align:start position:0% +see you can see some sort of +fringes uh all by the by the time it's + + align:start position:0% +fringes uh all by the by the time it's + + + align:start position:0% +fringes uh all by the by the time it's +got to the end here you can see um a + + align:start position:0% +got to the end here you can see um a + + + align:start position:0% +got to the end here you can see um a +bright lines around the edges and also + + align:start position:0% +bright lines around the edges and also + + + align:start position:0% +bright lines around the edges and also +bright spots in the four + + align:start position:0% +bright spots in the four + + + align:start position:0% +bright spots in the four +corners and and then if we look at the + + align:start position:0% +corners and and then if we look at the + + + align:start position:0% +corners and and then if we look at the +small + + align:start position:0% + + + + align:start position:0% + +square uh again it's changing more + + align:start position:0% +square uh again it's changing more + + + align:start position:0% +square uh again it's changing more +quickly and you'll notice that uh you + + align:start position:0% +quickly and you'll notice that uh you + + + align:start position:0% +quickly and you'll notice that uh you +we've developed by then we've got quite + + align:start position:0% +we've developed by then we've got quite + + + align:start position:0% +we've developed by then we've got quite +strong sort of streaking along these two + + align:start position:0% +strong sort of streaking along these two + + + align:start position:0% +strong sort of streaking along these two +axes here uh and uh in fact um so you + + align:start position:0% +axes here uh and uh in fact um so you + + + align:start position:0% +axes here uh and uh in fact um so you +see this final uh pattern there that + + align:start position:0% +see this final uh pattern there that + + + align:start position:0% +see this final uh pattern there that +that's um is the defraction pattern of + + align:start position:0% +that's um is the defraction pattern of + + + align:start position:0% +that's um is the defraction pattern of +the of the square + + align:start position:0% +the of the square + + + align:start position:0% +the of the square +aperture um what does it say um we + + align:start position:0% +aperture um what does it say um we + + + align:start position:0% +aperture um what does it say um we +have we haven't done fra defraction yet + + align:start position:0% +have we haven't done fra defraction yet + + + align:start position:0% +have we haven't done fra defraction yet +have + + align:start position:0% +have + + + align:start position:0% +have +we this is an introduction to yeah this + + align:start position:0% +we this is an introduction to yeah this + + + align:start position:0% +we this is an introduction to yeah this +is an example of frown off a defraction + + align:start position:0% +is an example of frown off a defraction + + + align:start position:0% +is an example of frown off a defraction +then if you're a long way away you get + + align:start position:0% +then if you're a long way away you get + + + align:start position:0% +then if you're a long way away you get +what's called frown off a defraction + + align:start position:0% +what's called frown off a defraction + + + align:start position:0% +what's called frown off a defraction +this is what it looks like uh and uh as + + align:start position:0% +this is what it looks like uh and uh as + + + align:start position:0% +this is what it looks like uh and uh as +we're going to show later uh this is + + align:start position:0% +we're going to show later uh this is + + + align:start position:0% +we're going to show later uh this is +very simply related to the Foria + + align:start position:0% +very simply related to the Foria + + + align:start position:0% +very simply related to the Foria +transform of the of the structure the + + align:start position:0% +transform of the of the structure the + + + align:start position:0% +transform of the of the structure the +object that we're going to look + + align:start position:0% +object that we're going to look + + + align:start position:0% +object that we're going to look +at um okay yeah so this case here if if + + align:start position:0% +at um okay yeah so this case here if if + + + align:start position:0% +at um okay yeah so this case here if if +we eventually this one would look like + + align:start position:0% +we eventually this one would look like + + + align:start position:0% +we eventually this one would look like +this but we haven't gone anywhere near + + align:start position:0% +this but we haven't gone anywhere near + + + align:start position:0% +this but we haven't gone anywhere near +far enough uh for it to to to look like + + align:start position:0% +far enough uh for it to to to look like + + + align:start position:0% +far enough uh for it to to to look like +that but eventually it would get like + + align:start position:0% +that but eventually it would get like + + + align:start position:0% +that but eventually it would get like +that the distance you have to go uh + + align:start position:0% +that the distance you have to go uh + + + align:start position:0% +that the distance you have to go uh +depends on how big the aperture + + align:start position:0% + + + + align:start position:0% + +is end of + + align:start position:0% +is end of + + + align:start position:0% +is end of +show \ No newline at end of file diff --git a/9FLItlbBUPY.txt b/9FLItlbBUPY.txt new file mode 100644 index 0000000000000000000000000000000000000000..abfd6a525b2c50bc0abb6d5ae1b4ffe4a1e1aad7 --- /dev/null +++ b/9FLItlbBUPY.txt @@ -0,0 +1,7744 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu thank you + + align:start position:0% +ocw.mit.edu thank you + + + align:start position:0% +ocw.mit.edu thank you +so okay let's + + align:start position:0% +so okay let's + + + align:start position:0% +so okay let's +continue with vector + + align:start position:0% +continue with vector + + + align:start position:0% +continue with vector +and operations on them so remember + + align:start position:0% +and operations on them so remember + + + align:start position:0% +and operations on them so remember +yesterday we saw the topic yesterday was + + align:start position:0% +yesterday we saw the topic yesterday was + + + align:start position:0% +yesterday we saw the topic yesterday was +dot + + align:start position:0% +dot + + + align:start position:0% +dot +product + + align:start position:0% + + + + align:start position:0% + +and remember the definition of dot + + align:start position:0% +and remember the definition of dot + + + align:start position:0% +and remember the definition of dot +product well the dot product of two + + align:start position:0% +product well the dot product of two + + + align:start position:0% +product well the dot product of two +vectors is obtained + + align:start position:0% +vectors is obtained + + + align:start position:0% +vectors is obtained +by multiplying the first component with + + align:start position:0% +by multiplying the first component with + + + align:start position:0% +by multiplying the first component with +the first component the second with the + + align:start position:0% +the first component the second with the + + + align:start position:0% +the first component the second with the +second and so on and summing these and + + align:start position:0% +second and so on and summing these and + + + align:start position:0% +second and so on and summing these and +you get the scalar and the geometric + + align:start position:0% +you get the scalar and the geometric + + + align:start position:0% +you get the scalar and the geometric +interpretation of + + align:start position:0% +interpretation of + + + align:start position:0% +interpretation of +that is that you can also take the + + align:start position:0% +that is that you can also take the + + + align:start position:0% +that is that you can also take the +length of a take the length of B + + align:start position:0% +length of a take the length of B + + + align:start position:0% +length of a take the length of B +multiply them and multiply that by the + + align:start position:0% +multiply them and multiply that by the + + + align:start position:0% +multiply them and multiply that by the +coine of the angle between the two + + align:start position:0% + + + + align:start position:0% + +vectors so we've seen several + + align:start position:0% +vectors so we've seen several + + + align:start position:0% +vectors so we've seen several +applications of + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +so one application is to + + align:start position:0% +so one application is to + + + align:start position:0% +so one application is to +find lengths and + + align:start position:0% + + + + align:start position:0% + +angles + + align:start position:0% +angles + + + align:start position:0% +angles +so for example well you can use this + + align:start position:0% +so for example well you can use this + + + align:start position:0% +so for example well you can use this +relation to give you that the cosine of + + align:start position:0% +relation to give you that the cosine of + + + align:start position:0% +relation to give you that the cosine of +the angle between two vectors + + align:start position:0% +the angle between two vectors + + + align:start position:0% +the angle between two vectors +is their dot product divided by + + align:start position:0% +is their dot product divided by + + + align:start position:0% +is their dot product divided by +the product of the + + align:start position:0% + + + + align:start position:0% + +lengths another application that we + + align:start position:0% + + + + align:start position:0% + +have is to + + align:start position:0% +have is to + + + align:start position:0% +have is to +detect whether two vectors are + + align:start position:0% +detect whether two vectors are + + + align:start position:0% +detect whether two vectors are +perpendicular so to decide if two + + align:start position:0% +perpendicular so to decide if two + + + align:start position:0% +perpendicular so to decide if two +vectors are perpendicular to each other + + align:start position:0% +vectors are perpendicular to each other + + + align:start position:0% +vectors are perpendicular to each other +all we have to do is compute their dot + + align:start position:0% +all we have to do is compute their dot + + + align:start position:0% +all we have to do is compute their dot +product and see if we get + + align:start position:0% + + + + align:start position:0% + +zero + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and well one third application that we + + align:start position:0% +and well one third application that we + + + align:start position:0% +and well one third application that we +didn't have time to discuss yesterday + + align:start position:0% +didn't have time to discuss yesterday + + + align:start position:0% +didn't have time to discuss yesterday +that I will mention very quickly is to + + align:start position:0% +that I will mention very quickly is to + + + align:start position:0% +that I will mention very quickly is to +find + + align:start position:0% + + + + align:start position:0% + +components of so let's say find the + + align:start position:0% +components of so let's say find the + + + align:start position:0% +components of so let's say find the +component of a vector a + + align:start position:0% +component of a vector a + + + align:start position:0% +component of a vector a +along a + + align:start position:0% + + + + align:start position:0% + +Direction + + align:start position:0% +Direction + + + align:start position:0% +Direction +U so some unit + + align:start position:0% +U so some unit + + + align:start position:0% +U so some unit +Vector so let me + + align:start position:0% +Vector so let me + + + align:start position:0% +Vector so let me +explain let's say that I have some + + align:start position:0% +explain let's say that I have some + + + align:start position:0% +explain let's say that I have some +direction for example the horizontal + + align:start position:0% +direction for example the horizontal + + + align:start position:0% +direction for example the horizontal +axis on this Blackboard but it could be + + align:start position:0% +axis on this Blackboard but it could be + + + align:start position:0% +axis on this Blackboard but it could be +any direction in space and to describe + + align:start position:0% +any direction in space and to describe + + + align:start position:0% +any direction in space and to describe +this direction maybe I have a unit + + align:start position:0% +this direction maybe I have a unit + + + align:start position:0% +this direction maybe I have a unit +Vector along this + + align:start position:0% +Vector along this + + + align:start position:0% +Vector along this +axis let's say that I + + align:start position:0% +axis let's say that I + + + align:start position:0% +axis let's say that I +have any other Vector a and I want to + + align:start position:0% +have any other Vector a and I want to + + + align:start position:0% +have any other Vector a and I want to +find out what is the component of a + + align:start position:0% +find out what is the component of a + + + align:start position:0% +find out what is the component of a +along U so that means what is the + + align:start position:0% +along U so that means what is the + + + align:start position:0% +along U so that means what is the +length of this projection of a to the + + align:start position:0% +length of this projection of a to the + + + align:start position:0% +length of this projection of a to the +given + + align:start position:0% +given + + + align:start position:0% +given +Direction okay so this thing here is the + + align:start position:0% + + + + align:start position:0% + +component of + + align:start position:0% +component of + + + align:start position:0% +component of +a along + + align:start position:0% +a along + + + align:start position:0% +a along +U well how do we find + + align:start position:0% +U well how do we find + + + align:start position:0% +U well how do we find +that + + align:start position:0% +that + + + align:start position:0% +that +well + + align:start position:0% + + + + align:start position:0% + +we know that here we have a right angle + + align:start position:0% +we know that here we have a right angle + + + align:start position:0% +we know that here we have a right angle +so this component is just length a times + + align:start position:0% +so this component is just length a times + + + align:start position:0% +so this component is just length a times +cosine of the angle between a and + + align:start position:0% +cosine of the angle between a and + + + align:start position:0% +cosine of the angle between a and +u but now that means actually we can + + align:start position:0% +u but now that means actually we can + + + align:start position:0% +u but now that means actually we can +compute it very + + align:start position:0% +compute it very + + + align:start position:0% +compute it very +easily because well I could you know + + align:start position:0% +easily because well I could you know + + + align:start position:0% +easily because well I could you know +that's the same as length a time length + + align:start position:0% +that's the same as length a time length + + + align:start position:0% +that's the same as length a time length +U * cosine Theta because U is a unit + + align:start position:0% +U * cosine Theta because U is a unit + + + align:start position:0% +U * cosine Theta because U is a unit +Vector it's a unit Vector that means + + align:start position:0% +Vector it's a unit Vector that means + + + align:start position:0% +Vector it's a unit Vector that means +this is equal to + + align:start position:0% +this is equal to + + + align:start position:0% +this is equal to +one and so that's the same as the dot + + align:start position:0% +one and so that's the same as the dot + + + align:start position:0% +one and so that's the same as the dot +product between a and + + align:start position:0% +product between a and + + + align:start position:0% +product between a and +u okay so that's very easy and of course + + align:start position:0% +u okay so that's very easy and of course + + + align:start position:0% +u okay so that's very easy and of course +the most obvious cases of that is say + + align:start position:0% +the most obvious cases of that is say + + + align:start position:0% +the most obvious cases of that is say +for example we want just to find the + + align:start position:0% +for example we want just to find the + + + align:start position:0% +for example we want just to find the +component along I hat the first axis you + + align:start position:0% +component along I hat the first axis you + + + align:start position:0% +component along I hat the first axis you +know the unit Vector along the x axis + + align:start position:0% +know the unit Vector along the x axis + + + align:start position:0% +know the unit Vector along the x axis +then you do the dot product with IH hat + + align:start position:0% +then you do the dot product with IH hat + + + align:start position:0% +then you do the dot product with IH hat +which is 1 0 0 what you get is the first + + align:start position:0% +which is 1 0 0 what you get is the first + + + align:start position:0% +which is 1 0 0 what you get is the first +component and that's in the X component + + align:start position:0% +component and that's in the X component + + + align:start position:0% +component and that's in the X component +of the vector similarly say you want the + + align:start position:0% +of the vector similarly say you want the + + + align:start position:0% +of the vector similarly say you want the +Z component you do the dot product with + + align:start position:0% +Z component you do the dot product with + + + align:start position:0% +Z component you do the dot product with +K that gives you the last component of + + align:start position:0% +K that gives you the last component of + + + align:start position:0% +K that gives you the last component of +your + + align:start position:0% +your + + + align:start position:0% +your +vector but the same works with a unit + + align:start position:0% +vector but the same works with a unit + + + align:start position:0% +vector but the same works with a unit +Vector in any + + align:start position:0% +Vector in any + + + align:start position:0% +Vector in any +direction okay so what's an application + + align:start position:0% +direction okay so what's an application + + + align:start position:0% +direction okay so what's an application +of + + align:start position:0% + + + + align:start position:0% + +that well for example in physics maybe + + align:start position:0% +that well for example in physics maybe + + + align:start position:0% +that well for example in physics maybe +you have seen situations where you have + + align:start position:0% +you have seen situations where you have + + + align:start position:0% +you have seen situations where you have +a pendulum that swings so you have maybe + + align:start position:0% +a pendulum that swings so you have maybe + + + align:start position:0% +a pendulum that swings so you have maybe +some mass at the end of a string and + + align:start position:0% +some mass at the end of a string and + + + align:start position:0% +some mass at the end of a string and +that mass swings back and forth on a + + align:start position:0% +that mass swings back and forth on a + + + align:start position:0% +that mass swings back and forth on a +circle and to analyze this mechanically + + align:start position:0% +circle and to analyze this mechanically + + + align:start position:0% +circle and to analyze this mechanically +you want to use of course Newton lows of + + align:start position:0% +you want to use of course Newton lows of + + + align:start position:0% +you want to use of course Newton lows of +mechanics and you want to use well you + + align:start position:0% +mechanics and you want to use well you + + + align:start position:0% +mechanics and you want to use well you +know forces and so on but I claim that + + align:start position:0% +know forces and so on but I claim that + + + align:start position:0% +know forces and so on but I claim that +components of vectors are useful here to + + align:start position:0% +components of vectors are useful here to + + + align:start position:0% +components of vectors are useful here to +understand what happens + + align:start position:0% +understand what happens + + + align:start position:0% +understand what happens +geometrically + + align:start position:0% +geometrically + + + align:start position:0% +geometrically +so what are the forces exerted on this + + align:start position:0% +so what are the forces exerted on this + + + align:start position:0% +so what are the forces exerted on this +pendulum well there's its + + align:start position:0% +pendulum well there's its + + + align:start position:0% +pendulum well there's its +weight which usually points + + align:start position:0% + + + + align:start position:0% + +downwards and there's the tension of the + + align:start position:0% + + + + align:start position:0% + +string and these two forces together are + + align:start position:0% +string and these two forces together are + + + align:start position:0% +string and these two forces together are +what explains how this pendulum is going + + align:start position:0% +what explains how this pendulum is going + + + align:start position:0% +what explains how this pendulum is going +to move back and forth + + align:start position:0% +to move back and forth + + + align:start position:0% +to move back and forth +now you could try to understand the + + align:start position:0% +now you could try to understand the + + + align:start position:0% +now you could try to understand the +equations of motion using X Y + + align:start position:0% +equations of motion using X Y + + + align:start position:0% +equations of motion using X Y +coordinates or maybe XZ or whatever you + + align:start position:0% +coordinates or maybe XZ or whatever you + + + align:start position:0% +coordinates or maybe XZ or whatever you +want to call them let's say + + align:start position:0% +want to call them let's say + + + align:start position:0% +want to call them let's say +XY + + align:start position:0% +XY + + + align:start position:0% +XY +but really what causes the pendulum to + + align:start position:0% +but really what causes the pendulum to + + + align:start position:0% +but really what causes the pendulum to +swing back and + + align:start position:0% +swing back and + + + align:start position:0% +swing back and +forth and also to somehow stay at + + align:start position:0% +forth and also to somehow stay at + + + align:start position:0% +forth and also to somehow stay at +constant + + align:start position:0% +constant + + + align:start position:0% +constant +distance are phenomena relative to this + + align:start position:0% +distance are phenomena relative to this + + + align:start position:0% +distance are phenomena relative to this +circular trajectory so for example maybe + + align:start position:0% +circular trajectory so for example maybe + + + align:start position:0% +circular trajectory so for example maybe +instead of taking components along the X + + align:start position:0% +instead of taking components along the X + + + align:start position:0% +instead of taking components along the X +and Y axis we want to look at two other + + align:start position:0% +and Y axis we want to look at two other + + + align:start position:0% +and Y axis we want to look at two other +unit vectors so we can look + + align:start position:0% +unit vectors so we can look + + + align:start position:0% +unit vectors so we can look +at a vector let's call it t that's + + align:start position:0% +at a vector let's call it t that's + + + align:start position:0% +at a vector let's call it t that's +tangent to the + + align:start position:0% + + + + align:start position:0% + +trajectory sorry can you read that maybe + + align:start position:0% +trajectory sorry can you read that maybe + + + align:start position:0% +trajectory sorry can you read that maybe +it's not very readable + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +T is + + align:start position:0% +T is + + + align:start position:0% +T is +tangent to the trajectory + + align:start position:0% + + + + align:start position:0% + +and on the other hand we can introduce + + align:start position:0% +and on the other hand we can introduce + + + align:start position:0% +and on the other hand we can introduce +another Vector it's call that + + align:start position:0% + + + + align:start position:0% + +n and that one + + align:start position:0% +n and that one + + + align:start position:0% +n and that one +is normal or perpendicular to the + + align:start position:0% + + + + align:start position:0% + +trajectory and so now if you think about + + align:start position:0% +trajectory and so now if you think about + + + align:start position:0% +trajectory and so now if you think about +it you can look at the components of the + + align:start position:0% +it you can look at the components of the + + + align:start position:0% +it you can look at the components of the +weight along the tensent direction and + + align:start position:0% +weight along the tensent direction and + + + align:start position:0% +weight along the tensent direction and +along the normal + + align:start position:0% + + + + align:start position:0% + +Direction and + + align:start position:0% + + + + align:start position:0% + +so the component of + + align:start position:0% +so the component of + + + align:start position:0% +so the component of +f along the tension direction is what + + align:start position:0% +f along the tension direction is what + + + align:start position:0% +f along the tension direction is what +causes acceleration in the direction + + align:start position:0% +causes acceleration in the direction + + + align:start position:0% +causes acceleration in the direction +along the trajectory it's what causes + + align:start position:0% +along the trajectory it's what causes + + + align:start position:0% +along the trajectory it's what causes +the pendulum to swing back and + + align:start position:0% + + + + align:start position:0% + +forth + + align:start position:0% + + + + align:start position:0% + +and the + + align:start position:0% +and the + + + align:start position:0% +and the +component along n on the other + + align:start position:0% + + + + align:start position:0% + +hand so that's the part of the weight + + align:start position:0% +hand so that's the part of the weight + + + align:start position:0% +hand so that's the part of the weight +that tends to + + align:start position:0% +that tends to + + + align:start position:0% +that tends to +pull our Mass away from this point is + + align:start position:0% +pull our Mass away from this point is + + + align:start position:0% +pull our Mass away from this point is +what's going to be responsible for the + + align:start position:0% +what's going to be responsible for the + + + align:start position:0% +what's going to be responsible for the +tension of the string it's why the + + align:start position:0% +tension of the string it's why the + + + align:start position:0% +tension of the string it's why the +string is tot and not + + align:start position:0% +string is tot and not + + + align:start position:0% +string is tot and not +slack and you know with things moving + + align:start position:0% +slack and you know with things moving + + + align:start position:0% +slack and you know with things moving +all over the place uh so that one is + + align:start position:0% + + + + align:start position:0% + +responsible for the tension of a + + align:start position:0% + + + + align:start position:0% + +string and now of course if you want to + + align:start position:0% +string and now of course if you want to + + + align:start position:0% +string and now of course if you want to +compute things well maybe you will call + + align:start position:0% +compute things well maybe you will call + + + align:start position:0% +compute things well maybe you will call +this angle Theta and then you will + + align:start position:0% +this angle Theta and then you will + + + align:start position:0% +this angle Theta and then you will +Express things explicitly using SS and + + align:start position:0% +Express things explicitly using SS and + + + align:start position:0% +Express things explicitly using SS and +cosines and you will solve for the + + align:start position:0% +cosines and you will solve for the + + + align:start position:0% +cosines and you will solve for the +equations of motion okay that be very + + align:start position:0% +equations of motion okay that be very + + + align:start position:0% +equations of motion okay that be very +interesting physics problem but to save + + align:start position:0% +interesting physics problem but to save + + + align:start position:0% +interesting physics problem but to save +time we're not going to do it I'm sure + + align:start position:0% +time we're not going to do it I'm sure + + + align:start position:0% +time we're not going to do it I'm sure +you've seen that in 801 or similar + + align:start position:0% +you've seen that in 801 or similar + + + align:start position:0% +you've seen that in 801 or similar +classes + + align:start position:0% + + + + align:start position:0% + +but and so to find these components we + + align:start position:0% +but and so to find these components we + + + align:start position:0% +but and so to find these components we +would just do dot + + align:start position:0% + + + + align:start position:0% + +products okay any + + align:start position:0% + + + + align:start position:0% + +questions no okay so let's move on to + + align:start position:0% +questions no okay so let's move on to + + + align:start position:0% +questions no okay so let's move on to +our next topic + + align:start position:0% +our next topic + + + align:start position:0% +our next topic +so here we have found things about + + align:start position:0% +so here we have found things about + + + align:start position:0% +so here we have found things about +lengths + + align:start position:0% +lengths + + + align:start position:0% +lengths +angles and uh stuff like that one + + align:start position:0% +angles and uh stuff like that one + + + align:start position:0% +angles and uh stuff like that one +important concept that we haven't + + align:start position:0% +important concept that we haven't + + + align:start position:0% +important concept that we haven't +understood yet in terms of vectors is + + align:start position:0% +understood yet in terms of vectors is + + + align:start position:0% +understood yet in terms of vectors is +area so let's say that you know we want + + align:start position:0% +area so let's say that you know we want + + + align:start position:0% +area so let's say that you know we want +to + + align:start position:0% +to + + + align:start position:0% +to +find the area of this Pentagon well how + + align:start position:0% +find the area of this Pentagon well how + + + align:start position:0% +find the area of this Pentagon well how +do we compute that using vectors can we + + align:start position:0% +do we compute that using vectors can we + + + align:start position:0% +do we compute that using vectors can we +do it using vectors + + align:start position:0% +do it using vectors + + + align:start position:0% +do it using vectors +yes we can and uh that's going to be the + + align:start position:0% +yes we can and uh that's going to be the + + + align:start position:0% +yes we can and uh that's going to be the +goal but how so the first thing we + + align:start position:0% +goal but how so the first thing we + + + align:start position:0% +goal but how so the first thing we +should do is probably simplify the + + align:start position:0% +should do is probably simplify the + + + align:start position:0% +should do is probably simplify the +problem you know we don't actually need + + align:start position:0% +problem you know we don't actually need + + + align:start position:0% +problem you know we don't actually need +to bother with pentagons all we need to + + align:start position:0% +to bother with pentagons all we need to + + + align:start position:0% +to bother with pentagons all we need to +know are triangles because for example + + align:start position:0% +know are triangles because for example + + + align:start position:0% +know are triangles because for example +you can cut that into three triangles + + align:start position:0% +you can cut that into three triangles + + + align:start position:0% +you can cut that into three triangles +and then sum the areas of the + + align:start position:0% +and then sum the areas of the + + + align:start position:0% +and then sum the areas of the +triangles okay + + align:start position:0% +triangles okay + + + align:start position:0% +triangles okay +so perhaps + + align:start position:0% +so perhaps + + + align:start position:0% +so perhaps +easier what's the area of a + + align:start position:0% + + + + align:start position:0% + +triangle so let's start with you know a + + align:start position:0% +triangle so let's start with you know a + + + align:start position:0% +triangle so let's start with you know a +triangle in the + + align:start position:0% + + + + align:start position:0% + +plane and well then we need two vectors + + align:start position:0% +plane and well then we need two vectors + + + align:start position:0% +plane and well then we need two vectors +to describe it say A and B + + align:start position:0% +to describe it say A and B + + + align:start position:0% +to describe it say A and B +here how do we find the area of a + + align:start position:0% +here how do we find the area of a + + + align:start position:0% +here how do we find the area of a +triangle well we all know base time + + align:start position:0% +triangle well we all know base time + + + align:start position:0% +triangle well we all know base time +height over two so what's the base + + align:start position:0% +height over two so what's the base + + + align:start position:0% +height over two so what's the base +what's the height well so the area of + + align:start position:0% +what's the height well so the area of + + + align:start position:0% +what's the height well so the area of +this triangle is going to be 1/2 of the + + align:start position:0% +this triangle is going to be 1/2 of the + + + align:start position:0% +this triangle is going to be 1/2 of the +base is going to be the length of a and + + align:start position:0% +base is going to be the length of a and + + + align:start position:0% +base is going to be the length of a and +the + + align:start position:0% +the + + + align:start position:0% +the +height well if you call Theta this angle + + align:start position:0% +height well if you call Theta this angle + + + align:start position:0% +height well if you call Theta this angle +then this is length B sin + + align:start position:0% + + + + align:start position:0% + +Theta now that looks a lot like the + + align:start position:0% +Theta now that looks a lot like the + + + align:start position:0% +Theta now that looks a lot like the +formula we had there except for one + + align:start position:0% +formula we had there except for one + + + align:start position:0% +formula we had there except for one +little catch this is a sign instead of a + + align:start position:0% +little catch this is a sign instead of a + + + align:start position:0% +little catch this is a sign instead of a +cosine how do we deal with that + + align:start position:0% +cosine how do we deal with that + + + align:start position:0% +cosine how do we deal with that +well what we could + + align:start position:0% +well what we could + + + align:start position:0% +well what we could +do is first find the cosine of the angle + + align:start position:0% +do is first find the cosine of the angle + + + align:start position:0% +do is first find the cosine of the angle +we know how to find the cosine of the + + align:start position:0% +we know how to find the cosine of the + + + align:start position:0% +we know how to find the cosine of the +angle using dot + + align:start position:0% + + + + align:start position:0% + +product then solve for S + + align:start position:0% +product then solve for S + + + align:start position:0% +product then solve for S +using sin square plus cosine Square = + + align:start position:0% +using sin square plus cosine Square = + + + align:start position:0% +using sin square plus cosine Square = +1 and then plug that back into here well + + align:start position:0% +1 and then plug that back into here well + + + align:start position:0% +1 and then plug that back into here well +that works but it's kind of a very + + align:start position:0% +that works but it's kind of a very + + + align:start position:0% +that works but it's kind of a very +complicated way of doing it so there's + + align:start position:0% +complicated way of doing it so there's + + + align:start position:0% +complicated way of doing it so there's +an easier way and that's going to be + + align:start position:0% +an easier way and that's going to be + + + align:start position:0% +an easier way and that's going to be +determinants but let me explain how we + + align:start position:0% +determinants but let me explain how we + + + align:start position:0% +determinants but let me explain how we +get to that maybe still doing Elementary + + align:start position:0% +get to that maybe still doing Elementary + + + align:start position:0% +get to that maybe still doing Elementary +geometry and Dot products + + align:start position:0% + + + + align:start position:0% + +first + + align:start position:0% + + + + align:start position:0% + +so let's + + align:start position:0% +so let's + + + align:start position:0% +so let's +see what we can do is instead of finding + + align:start position:0% +see what we can do is instead of finding + + + align:start position:0% +see what we can do is instead of finding +the S of theta well we're not good at + + align:start position:0% +the S of theta well we're not good at + + + align:start position:0% +the S of theta well we're not good at +finding signs of angles but we are very + + align:start position:0% +finding signs of angles but we are very + + + align:start position:0% +finding signs of angles but we are very +good now at finding cosines angles so + + align:start position:0% +good now at finding cosines angles so + + + align:start position:0% +good now at finding cosines angles so +maybe we can find another angle whose + + align:start position:0% +maybe we can find another angle whose + + + align:start position:0% +maybe we can find another angle whose +cosine is the same as the S of + + align:start position:0% +cosine is the same as the S of + + + align:start position:0% +cosine is the same as the S of +theta well you probably heard about + + align:start position:0% +theta well you probably heard about + + + align:start position:0% +theta well you probably heard about +complimentary angles and how you know if + + align:start position:0% +complimentary angles and how you know if + + + align:start position:0% +complimentary angles and how you know if +I take my Vector + + align:start position:0% +I take my Vector + + + align:start position:0% +I take my Vector +a have my Vector B here I have an angle + + align:start position:0% +a have my Vector B here I have an angle + + + align:start position:0% +a have my Vector B here I have an angle +Theta well let's say that I rotate my + + align:start position:0% +Theta well let's say that I rotate my + + + align:start position:0% +Theta well let's say that I rotate my +Vector a by 90° to get a new Vector a + + align:start position:0% +Vector a by 90° to get a new Vector a + + + align:start position:0% +Vector a by 90° to get a new Vector a +prime okay so a + + align:start position:0% +prime okay so a + + + align:start position:0% +prime okay so a +prime + + align:start position:0% +prime + + + align:start position:0% +prime +is just a + + align:start position:0% +is just a + + + align:start position:0% +is just a +rotated by + + align:start position:0% +rotated by + + + align:start position:0% +rotated by +90° then the angle between these two + + align:start position:0% +90° then the angle between these two + + + align:start position:0% +90° then the angle between these two +guys let's say Theta + + align:start position:0% +guys let's say Theta + + + align:start position:0% +guys let's say Theta +Prime well Theta Prime is 90 Dees of 2 + + align:start position:0% +Prime well Theta Prime is 90 Dees of 2 + + + align:start position:0% +Prime well Theta Prime is 90 Dees of 2 +radians minus Theta so in particular + + align:start position:0% +radians minus Theta so in particular + + + align:start position:0% +radians minus Theta so in particular +cosine of theta Prime is equal to S of + + align:start position:0% + + + + align:start position:0% + +theta so in + + align:start position:0% +theta so in + + + align:start position:0% +theta so in +particular that means + + align:start position:0% +particular that means + + + align:start position:0% +particular that means +that length a length + + align:start position:0% +that length a length + + + align:start position:0% +that length a length +B sin Theta which is what we would need + + align:start position:0% +B sin Theta which is what we would need + + + align:start position:0% +B sin Theta which is what we would need +to know in order to find the area of + + align:start position:0% +to know in order to find the area of + + + align:start position:0% +to know in order to find the area of +this triangle is equal to well a and a + + align:start position:0% +this triangle is equal to well a and a + + + align:start position:0% +this triangle is equal to well a and a +prime have the same length so let me + + align:start position:0% +prime have the same length so let me + + + align:start position:0% +prime have the same length so let me +replace that by length of a prime okay + + align:start position:0% +replace that by length of a prime okay + + + align:start position:0% +replace that by length of a prime okay +I'm not changing + + align:start position:0% +I'm not changing + + + align:start position:0% +I'm not changing +anything length B cosine Theta + + align:start position:0% +anything length B cosine Theta + + + align:start position:0% +anything length B cosine Theta +Prim and now with have something that's + + align:start position:0% +Prim and now with have something that's + + + align:start position:0% +Prim and now with have something that's +much easier for us because that's just a + + align:start position:0% +much easier for us because that's just a + + + align:start position:0% +much easier for us because that's just a +prime + + align:start position:0% + + + + align:start position:0% + +B okay so that looks like a very good + + align:start position:0% +B okay so that looks like a very good + + + align:start position:0% +B okay so that looks like a very good +plan there's only one small thing which + + align:start position:0% +plan there's only one small thing which + + + align:start position:0% +plan there's only one small thing which +is we don't know yet how to find this a + + align:start position:0% +is we don't know yet how to find this a + + + align:start position:0% +is we don't know yet how to find this a +prime well I claim it's not very + + align:start position:0% +prime well I claim it's not very + + + align:start position:0% +prime well I claim it's not very +hard let's + + align:start position:0% +hard let's + + + align:start position:0% +hard let's +see why don't you guys do do the hard + + align:start position:0% +see why don't you guys do do the hard + + + align:start position:0% +see why don't you guys do do the hard +work + + align:start position:0% +work + + + align:start position:0% +work +so let's say that I have a plain Vector + + align:start position:0% +so let's say that I have a plain Vector + + + align:start position:0% +so let's say that I have a plain Vector +a with two components A1 A2 and I want + + align:start position:0% +a with two components A1 A2 and I want + + + align:start position:0% +a with two components A1 A2 and I want +to rotate it counterclockwise by + + align:start position:0% +to rotate it counterclockwise by + + + align:start position:0% +to rotate it counterclockwise by +90° + + align:start position:0% +90° + + + align:start position:0% +90° +so it looks like maybe we should change + + align:start position:0% +so it looks like maybe we should change + + + align:start position:0% +so it looks like maybe we should change +some signs somewhere maybe we should do + + align:start position:0% +some signs somewhere maybe we should do + + + align:start position:0% +some signs somewhere maybe we should do +something with the + + align:start position:0% +something with the + + + align:start position:0% +something with the +components um can you come up with an + + align:start position:0% +components um can you come up with an + + + align:start position:0% +components um can you come up with an +idea of what it might + + align:start position:0% + + + + align:start position:0% + +be okay so I I see a lot of people + + align:start position:0% +be okay so I I see a lot of people + + + align:start position:0% +be okay so I I see a lot of people +answering + + align:start position:0% +answering + + + align:start position:0% +answering +fre I see some other answers but the + + align:start position:0% +fre I see some other answers but the + + + align:start position:0% +fre I see some other answers but the +majority vot seems to be number + + align:start position:0% +majority vot seems to be number + + + align:start position:0% +majority vot seems to be number +three minus A2 and A1 I think I agree so + + align:start position:0% +three minus A2 and A1 I think I agree so + + + align:start position:0% +three minus A2 and A1 I think I agree so +let's + + align:start position:0% +let's + + + align:start position:0% +let's +see let's say that we + + align:start position:0% + + + + align:start position:0% + +have this Vector + + align:start position:0% +have this Vector + + + align:start position:0% +have this Vector +a with + + align:start position:0% +a with + + + align:start position:0% +a with +components + + align:start position:0% +components + + + align:start position:0% +components +A1 so A1 is here and A2 so A2 is here + + align:start position:0% +A1 so A1 is here and A2 so A2 is here + + + align:start position:0% +A1 so A1 is here and A2 so A2 is here +okay let's rotate this box by 90° + + align:start position:0% + + + + align:start position:0% + +counterclockwise + + align:start position:0% +counterclockwise + + + align:start position:0% +counterclockwise +so this rectangular box ends up there + + align:start position:0% +so this rectangular box ends up there + + + align:start position:0% +so this rectangular box ends up there +it's the same box just flipped on its + + align:start position:0% +it's the same box just flipped on its + + + align:start position:0% +it's the same box just flipped on its +side so this length here becomes A1 and + + align:start position:0% +side so this length here becomes A1 and + + + align:start position:0% +side so this length here becomes A1 and +this length here becomes A2 and that + + align:start position:0% +this length here becomes A2 and that + + + align:start position:0% +this length here becomes A2 and that +means our new Vector a prime + + align:start position:0% + + + + align:start position:0% + +is going to be well the first component + + align:start position:0% +is going to be well the first component + + + align:start position:0% +is going to be well the first component +looks like an A2 but it's pointing to + + align:start position:0% +looks like an A2 but it's pointing to + + + align:start position:0% +looks like an A2 but it's pointing to +the left when A2 is positive so actually + + align:start position:0% +the left when A2 is positive so actually + + + align:start position:0% +the left when A2 is positive so actually +it's minus + + align:start position:0% +it's minus + + + align:start position:0% +it's minus +A2 and the Y component is going to be + + align:start position:0% +A2 and the Y component is going to be + + + align:start position:0% +A2 and the Y component is going to be +the same as this guy so it's going to be + + align:start position:0% +the same as this guy so it's going to be + + + align:start position:0% +the same as this guy so it's going to be +A1 + + align:start position:0% + + + + align:start position:0% + +okay if you wanted instead to rotate + + align:start position:0% +okay if you wanted instead to rotate + + + align:start position:0% +okay if you wanted instead to rotate +clockwise then you would do the opposite + + align:start position:0% +clockwise then you would do the opposite + + + align:start position:0% +clockwise then you would do the opposite +you would do A2 minus A1 + + align:start position:0% +you would do A2 minus A1 + + + align:start position:0% +you would do A2 minus A1 +okay is that reasonably clear for + + align:start position:0% + + + + align:start position:0% + +everyone + + align:start position:0% +everyone + + + align:start position:0% +everyone +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so well let's continue that calculation + + align:start position:0% +so well let's continue that calculation + + + align:start position:0% +so well let's continue that calculation +there a prime we've + + align:start position:0% +there a prime we've + + + align:start position:0% +there a prime we've +decided is minus A2 A1 so minus A2 A1 + + align:start position:0% +decided is minus A2 A1 so minus A2 A1 + + + align:start position:0% +decided is minus A2 A1 so minus A2 A1 +dot product with let's call B1 and B2 + + align:start position:0% +dot product with let's call B1 and B2 + + + align:start position:0% +dot product with let's call B1 and B2 +the components of B + + align:start position:0% +the components of B + + + align:start position:0% +the components of B +then that will + + align:start position:0% +then that will + + + align:start position:0% +then that will +be well minus A2 B1 plus A1 B2 let me + + align:start position:0% +be well minus A2 B1 plus A1 B2 let me + + + align:start position:0% +be well minus A2 B1 plus A1 B2 let me +write that the other way around A1 B2 + + align:start position:0% +write that the other way around A1 B2 + + + align:start position:0% +write that the other way around A1 B2 +minus A2 + + align:start position:0% + + + + align:start position:0% + +B1 and that's a quantity that you may + + align:start position:0% +B1 and that's a quantity that you may + + + align:start position:0% +B1 and that's a quantity that you may +already know under the name of + + align:start position:0% +already know under the name of + + + align:start position:0% +already know under the name of +determinant of vectors A and + + align:start position:0% +determinant of vectors A and + + + align:start position:0% +determinant of vectors A and +B which we write + + align:start position:0% +B which we write + + + align:start position:0% +B which we write +symbolically using this notations so we + + align:start position:0% +symbolically using this notations so we + + + align:start position:0% +symbolically using this notations so we +put a and b next to each other inside a + + align:start position:0% +put a and b next to each other inside a + + + align:start position:0% +put a and b next to each other inside a +2X two table and we put this vertical + + align:start position:0% +2X two table and we put this vertical + + + align:start position:0% +2X two table and we put this vertical +bars and that means the determinant of + + align:start position:0% +bars and that means the determinant of + + + align:start position:0% +bars and that means the determinant of +these numbers it means this guy times + + align:start position:0% +these numbers it means this guy times + + + align:start position:0% +these numbers it means this guy times +this guy minus this guy time this + + align:start position:0% +this guy minus this guy time this + + + align:start position:0% +this guy minus this guy time this +guy okay so that's called the + + align:start position:0% + + + + align:start position:0% + +determinant + + align:start position:0% +determinant + + + align:start position:0% +determinant +and geometrically what it + + align:start position:0% +and geometrically what it + + + align:start position:0% +and geometrically what it +measures is the area well not of a + + align:start position:0% +measures is the area well not of a + + + align:start position:0% +measures is the area well not of a +triangle because we didn't divide by two + + align:start position:0% +triangle because we didn't divide by two + + + align:start position:0% +triangle because we didn't divide by two +but of a parallelogram formed by A and B + + align:start position:0% +but of a parallelogram formed by A and B + + + align:start position:0% +but of a parallelogram formed by A and B +so it measures the + + align:start position:0% +so it measures the + + + align:start position:0% +so it measures the +area of the parallelogram with + + align:start position:0% +area of the parallelogram with + + + align:start position:0% +area of the parallelogram with +sides A and + + align:start position:0% +sides A and + + + align:start position:0% +sides A and +B and of course if you want the triangle + + align:start position:0% +B and of course if you want the triangle + + + align:start position:0% +B and of course if you want the triangle +then you will just divide by two the + + align:start position:0% +then you will just divide by two the + + + align:start position:0% +then you will just divide by two the +triangle is half a + + align:start position:0% +triangle is half a + + + align:start position:0% +triangle is half a +parallelogram + + align:start position:0% +parallelogram + + + align:start position:0% +parallelogram +uh there's one small catch the area + + align:start position:0% +uh there's one small catch the area + + + align:start position:0% +uh there's one small catch the area +usually is something that's going to be + + align:start position:0% +usually is something that's going to be + + + align:start position:0% +usually is something that's going to be +positive this guy here has no reason to + + align:start position:0% +positive this guy here has no reason to + + + align:start position:0% +positive this guy here has no reason to +be positive or negative + + align:start position:0% +be positive or negative + + + align:start position:0% +be positive or negative +because in + + align:start position:0% + + + + align:start position:0% + +fact well if you compute things you will + + align:start position:0% +fact well if you compute things you will + + + align:start position:0% +fact well if you compute things you will +see that whether it's positive or + + align:start position:0% +see that whether it's positive or + + + align:start position:0% +see that whether it's positive or +negative depends on + + align:start position:0% +negative depends on + + + align:start position:0% +negative depends on +whether A and B are clockwise or + + align:start position:0% +whether A and B are clockwise or + + + align:start position:0% +whether A and B are clockwise or +counterclockwise from each other I mean + + align:start position:0% +counterclockwise from each other I mean + + + align:start position:0% +counterclockwise from each other I mean +the issue that we have well when we say + + align:start position:0% +the issue that we have well when we say + + + align:start position:0% +the issue that we have well when we say +the area is 12 length a length B sin + + align:start position:0% +the area is 12 length a length B sin + + + align:start position:0% +the area is 12 length a length B sin +Theta that was assuming that Theta is + + align:start position:0% +Theta that was assuming that Theta is + + + align:start position:0% +Theta that was assuming that Theta is +positive that it's s is positive + + align:start position:0% +positive that it's s is positive + + + align:start position:0% +positive that it's s is positive +otherwise if Theta is negative maybe we + + align:start position:0% +otherwise if Theta is negative maybe we + + + align:start position:0% +otherwise if Theta is negative maybe we +need actually to take the absolute value + + align:start position:0% +need actually to take the absolute value + + + align:start position:0% +need actually to take the absolute value +of this so just to be more truful I will + + align:start position:0% +of this so just to be more truful I will + + + align:start position:0% +of this so just to be more truful I will +say the determinant is either plus or + + align:start position:0% +say the determinant is either plus or + + + align:start position:0% +say the determinant is either plus or +minus the + + align:start position:0% + + + + align:start position:0% + +area okay any questions about this + + align:start position:0% + + + + align:start position:0% + +yes uh uh oh sorry that's not the dot + + align:start position:0% +yes uh uh oh sorry that's not the dot + + + align:start position:0% +yes uh uh oh sorry that's not the dot +product that's a usual multiplication + + align:start position:0% +product that's a usual multiplication + + + align:start position:0% +product that's a usual multiplication +okay that's a length a * length B * sin + + align:start position:0% + + + + align:start position:0% + +Theta what is that equal and so that's + + align:start position:0% +Theta what is that equal and so that's + + + align:start position:0% +Theta what is that equal and so that's +equal to the area of a parallelogram so + + align:start position:0% +equal to the area of a parallelogram so + + + align:start position:0% +equal to the area of a parallelogram so +let me explain that again + + align:start position:0% +let me explain that again + + + align:start position:0% +let me explain that again +so if I have two vectors A and + + align:start position:0% + + + + align:start position:0% + +B so I can form a parallelogram with + + align:start position:0% +B so I can form a parallelogram with + + + align:start position:0% +B so I can form a parallelogram with +them or I can form a triangle okay and + + align:start position:0% +them or I can form a triangle okay and + + + align:start position:0% +them or I can form a triangle okay and +so the area of a + + align:start position:0% +so the area of a + + + align:start position:0% +so the area of a +parallelogram is equal to length a + + align:start position:0% +parallelogram is equal to length a + + + align:start position:0% +parallelogram is equal to length a +length B sin Theta is equal to the + + align:start position:0% +length B sin Theta is equal to the + + + align:start position:0% +length B sin Theta is equal to the +determinant of A and + + align:start position:0% +determinant of A and + + + align:start position:0% +determinant of A and +B while the + + align:start position:0% +B while the + + + align:start position:0% +B while the +area of a + + align:start position:0% +area of a + + + align:start position:0% +area of a +triangle is2 of + + align:start position:0% + + + + align:start position:0% + +that and again to be hopeful I should + + align:start position:0% +that and again to be hopeful I should + + + align:start position:0% +that and again to be hopeful I should +say these things can be positive or + + align:start position:0% +say these things can be positive or + + + align:start position:0% +say these things can be positive or +negative so depending on whether you + + align:start position:0% +negative so depending on whether you + + + align:start position:0% +negative so depending on whether you +count the angle positively or negatively + + align:start position:0% +count the angle positively or negatively + + + align:start position:0% +count the angle positively or negatively +you will get either the area or minus + + align:start position:0% +you will get either the area or minus + + + align:start position:0% +you will get either the area or minus +the area the area is actually the + + align:start position:0% +the area the area is actually the + + + align:start position:0% +the area the area is actually the +absolute value of this + + align:start position:0% +absolute value of this + + + align:start position:0% +absolute value of this +quantities okay is that + + align:start position:0% + + + + align:start position:0% + +clear + + align:start position:0% + + + + align:start position:0% + +okay yes + + align:start position:0% + + + + align:start position:0% + +sorry so if you want to compute the area + + align:start position:0% +sorry so if you want to compute the area + + + align:start position:0% +sorry so if you want to compute the area +you will just take the absolute value of + + align:start position:0% +you will just take the absolute value of + + + align:start position:0% +you will just take the absolute value of +a determinant okay + + align:start position:0% + + + + align:start position:0% + +so our here will + + align:start position:0% + + + + align:start position:0% + +be well I should say the area of the + + align:start position:0% +be well I should say the area of the + + + align:start position:0% +be well I should say the area of the +parallelogram so that it's completely + + align:start position:0% +parallelogram so that it's completely + + + align:start position:0% +parallelogram so that it's completely +clear um sorry you have a + + align:start position:0% + + + + align:start position:0% + +question + + align:start position:0% + + + + align:start position:0% + +explain again sorry what's the question + + align:start position:0% +explain again sorry what's the question + + + align:start position:0% +explain again sorry what's the question +how the determinant equals the area of a + + align:start position:0% +how the determinant equals the area of a + + + align:start position:0% +how the determinant equals the area of a +parallelogram okay so the area of a + + align:start position:0% +parallelogram okay so the area of a + + + align:start position:0% +parallelogram okay so the area of a +parallelogram it's going to be the base + + align:start position:0% +parallelogram it's going to be the base + + + align:start position:0% +parallelogram it's going to be the base +times the height right so the base let's + + align:start position:0% +times the height right so the base let's + + + align:start position:0% +times the height right so the base let's +take this guy to be the base so the + + align:start position:0% +take this guy to be the base so the + + + align:start position:0% +take this guy to be the base so the +length of the base will be length of a + + align:start position:0% +length of the base will be length of a + + + align:start position:0% +length of the base will be length of a +then the height will be obtained by + + align:start position:0% +then the height will be obtained by + + + align:start position:0% +then the height will be obtained by +taking B but only looking at the + + align:start position:0% +taking B but only looking at the + + + align:start position:0% +taking B but only looking at the +vertical part so that will be length of + + align:start position:0% +vertical part so that will be length of + + + align:start position:0% +vertical part so that will be length of +B times the S of theta okay so that's + + align:start position:0% +B times the S of theta okay so that's + + + align:start position:0% +B times the S of theta okay so that's +how I got that the area of a + + align:start position:0% +how I got that the area of a + + + align:start position:0% +how I got that the area of a +parallelogram is length a length b s + + align:start position:0% +parallelogram is length a length b s + + + align:start position:0% +parallelogram is length a length b s +Theta and then I did this manipulation + + align:start position:0% +Theta and then I did this manipulation + + + align:start position:0% +Theta and then I did this manipulation +and this trick of rotating to find a + + align:start position:0% +and this trick of rotating to find a + + + align:start position:0% +and this trick of rotating to find a +nice + + align:start position:0% + + + + align:start position:0% + +formula uh + + align:start position:0% + + + + align:start position:0% + +yes uh so you're asking ahead of what + + align:start position:0% +yes uh so you're asking ahead of what + + + align:start position:0% +yes uh so you're asking ahead of what +I'm going to do in a few minutes um so + + align:start position:0% +I'm going to do in a few minutes um so + + + align:start position:0% +I'm going to do in a few minutes um so +you're asking about magnitude of A cross + + align:start position:0% +you're asking about magnitude of A cross + + + align:start position:0% +you're asking about magnitude of A cross +B so going to learn about cross product + + align:start position:0% +B so going to learn about cross product + + + align:start position:0% +B so going to learn about cross product +in a few minutes and the answer is yes + + align:start position:0% +in a few minutes and the answer is yes + + + align:start position:0% +in a few minutes and the answer is yes +but cross product is for vectors in + + align:start position:0% +but cross product is for vectors in + + + align:start position:0% +but cross product is for vectors in +space here I was simplifying things by + + align:start position:0% +space here I was simplifying things by + + + align:start position:0% +space here I was simplifying things by +doing things just in the + + align:start position:0% +doing things just in the + + + align:start position:0% +doing things just in the +plane okay so just bear with me for five + + align:start position:0% +plane okay so just bear with me for five + + + align:start position:0% +plane okay so just bear with me for five +more minutes and we'll do things in + + align:start position:0% + + + + align:start position:0% + +space uh + + align:start position:0% + + + + align:start position:0% + +yes that's correct the way you compute + + align:start position:0% +yes that's correct the way you compute + + + align:start position:0% +yes that's correct the way you compute +this in practice is you just do this + + align:start position:0% +this in practice is you just do this + + + align:start position:0% +this in practice is you just do this +okay that's how you compute to + + align:start position:0% + + + + align:start position:0% + +determinant + + align:start position:0% +determinant + + + align:start position:0% +determinant +yes what + + align:start position:0% +yes what + + + align:start position:0% +yes what +about so three dimensions we are going + + align:start position:0% +about so three dimensions we are going + + + align:start position:0% +about so three dimensions we are going +to do now okay more questions should we + + align:start position:0% +to do now okay more questions should we + + + align:start position:0% +to do now okay more questions should we +move to okay let's move to + + align:start position:0% + + + + align:start position:0% + +space + + align:start position:0% + + + + align:start position:0% + +so so there's two things we can do in + + align:start position:0% +so so there's two things we can do in + + + align:start position:0% +so so there's two things we can do in +space + + align:start position:0% + + + + align:start position:0% + +case and you know you can find you can + + align:start position:0% +case and you know you can find you can + + + align:start position:0% +case and you know you can find you can +look for the volume of solid or you can + + align:start position:0% +look for the volume of solid or you can + + + align:start position:0% +look for the volume of solid or you can +look for the area of surfaces so let me + + align:start position:0% +look for the area of surfaces so let me + + + align:start position:0% +look for the area of surfaces so let me +start with easier of the two let me + + align:start position:0% +start with easier of the two let me + + + align:start position:0% +start with easier of the two let me +start with volumes of solids and we'll + + align:start position:0% +start with volumes of solids and we'll + + + align:start position:0% +start with volumes of solids and we'll +go back to area I + + align:start position:0% + + + + align:start position:0% + +promise so I claim that there's also a + + align:start position:0% +promise so I claim that there's also a + + + align:start position:0% +promise so I claim that there's also a +notion of determinant in space and + + align:start position:0% +notion of determinant in space and + + + align:start position:0% +notion of determinant in space and +that's going to tell us how to find + + align:start position:0% +that's going to tell us how to find + + + align:start position:0% +that's going to tell us how to find +volumes so let's say that we have three + + align:start position:0% +volumes so let's say that we have three + + + align:start position:0% +volumes so let's say that we have three +vectors A B and + + align:start position:0% + + + + align:start position:0% + +C and then the definition of their + + align:start position:0% + + + + align:start position:0% + +determinant is going to be so the + + align:start position:0% +determinant is going to be so the + + + align:start position:0% +determinant is going to be so the +notation for that in terms of the + + align:start position:0% +notation for that in terms of the + + + align:start position:0% +notation for that in terms of the +components is the same as of there we + + align:start position:0% +components is the same as of there we + + + align:start position:0% +components is the same as of there we +put the components of a the components + + align:start position:0% +put the components of a the components + + + align:start position:0% +put the components of a the components +of B and the components of C + + align:start position:0% + + + + align:start position:0% + +inside vertical bars + + align:start position:0% +inside vertical bars + + + align:start position:0% +inside vertical bars +okay and of course I have to give a + + align:start position:0% +okay and of course I have to give a + + + align:start position:0% +okay and of course I have to give a +meaning to this so this will be a number + + align:start position:0% +meaning to this so this will be a number + + + align:start position:0% +meaning to this so this will be a number +and what is that number well the + + align:start position:0% +and what is that number well the + + + align:start position:0% +and what is that number well the +definition I will take is that this is + + align:start position:0% +definition I will take is that this is + + + align:start position:0% +definition I will take is that this is +A1 times the determinant of what I get + + align:start position:0% +A1 times the determinant of what I get + + + align:start position:0% +A1 times the determinant of what I get +by looking in this lower right corner so + + align:start position:0% +by looking in this lower right corner so + + + align:start position:0% +by looking in this lower right corner so +the 2x2 determinant 2 B3 C2 + + align:start position:0% +the 2x2 determinant 2 B3 C2 + + + align:start position:0% +the 2x2 determinant 2 B3 C2 +C3 then I will subtract A2 * the + + align:start position:0% +C3 then I will subtract A2 * the + + + align:start position:0% +C3 then I will subtract A2 * the +determinant of B1 B3 C1 + + align:start position:0% + + + + align:start position:0% + +C3 and then I will add A3 times the + + align:start position:0% +C3 and then I will add A3 times the + + + align:start position:0% +C3 and then I will add A3 times the +determinant B1 B2 C1 + + align:start position:0% +determinant B1 B2 C1 + + + align:start position:0% +determinant B1 B2 C1 +C2 and each of these guys means again + + align:start position:0% +C2 and each of these guys means again + + + align:start position:0% +C2 and each of these guys means again +you take B2 * C3 minus C 2 * B3 and this + + align:start position:0% +you take B2 * C3 minus C 2 * B3 and this + + + align:start position:0% +you take B2 * C3 minus C 2 * B3 and this +* that minus this * that and so on so in + + align:start position:0% +* that minus this * that and so on so in + + + align:start position:0% +* that minus this * that and so on so in +fact there's a total of six terms in + + align:start position:0% +fact there's a total of six terms in + + + align:start position:0% +fact there's a total of six terms in +here okay and maybe some of you have + + align:start position:0% +here okay and maybe some of you have + + + align:start position:0% +here okay and maybe some of you have +already seen a different formula for 3x3 + + align:start position:0% +already seen a different formula for 3x3 + + + align:start position:0% +already seen a different formula for 3x3 +determinants where you directly have the + + align:start position:0% +determinants where you directly have the + + + align:start position:0% +determinants where you directly have the +six terms it's the same it's the same + + align:start position:0% +six terms it's the same it's the same + + + align:start position:0% +six terms it's the same it's the same +definition so how to remember the + + align:start position:0% +definition so how to remember the + + + align:start position:0% +definition so how to remember the +structure of this + + align:start position:0% +structure of this + + + align:start position:0% +structure of this +formula well it's called an this is + + align:start position:0% +formula well it's called an this is + + + align:start position:0% +formula well it's called an this is +called an expansion according to the + + align:start position:0% +called an expansion according to the + + + align:start position:0% +called an expansion according to the +first row so we're going to take the + + align:start position:0% +first row so we're going to take the + + + align:start position:0% +first row so we're going to take the +entries in the first row A1 A2 A3 and + + align:start position:0% +entries in the first row A1 A2 A3 and + + + align:start position:0% +entries in the first row A1 A2 A3 and +for each of them we get a term namely we + + align:start position:0% +for each of them we get a term namely we + + + align:start position:0% +for each of them we get a term namely we +multiply it by a 2 by2 determinant that + + align:start position:0% +multiply it by a 2 by2 determinant that + + + align:start position:0% +multiply it by a 2 by2 determinant that +we get by + + align:start position:0% +we get by + + + align:start position:0% +we get by +deleting the first row and the column + + align:start position:0% +deleting the first row and the column + + + align:start position:0% +deleting the first row and the column +where we are okay so here the + + align:start position:0% +where we are okay so here the + + + align:start position:0% +where we are okay so here the +coefficient next to A1 is well we delete + + align:start position:0% +coefficient next to A1 is well we delete + + + align:start position:0% +coefficient next to A1 is well we delete +this column and this row and we're left + + align:start position:0% +this column and this row and we're left + + + align:start position:0% +this column and this row and we're left +with B2 B3 C2 + + align:start position:0% +with B2 B3 C2 + + + align:start position:0% +with B2 B3 C2 +C3 next the next one we take A2 we + + align:start position:0% +C3 next the next one we take A2 we + + + align:start position:0% +C3 next the next one we take A2 we +delete the row that's in it and the + + align:start position:0% +delete the row that's in it and the + + + align:start position:0% +delete the row that's in it and the +column that it's in and we left with B1 + + align:start position:0% +column that it's in and we left with B1 + + + align:start position:0% +column that it's in and we left with B1 +B3 C1 C3 and similarly with A3 we take + + align:start position:0% +B3 C1 C3 and similarly with A3 we take + + + align:start position:0% +B3 C1 C3 and similarly with A3 we take +what remains that's B1 B2 C1 C2 finally + + align:start position:0% +what remains that's B1 B2 C1 C2 finally + + + align:start position:0% +what remains that's B1 B2 C1 C2 finally +last but not least there's a minus sign + + align:start position:0% +last but not least there's a minus sign + + + align:start position:0% +last but not least there's a minus sign +here for the second + + align:start position:0% +here for the second + + + align:start position:0% +here for the second +guy + + align:start position:0% +guy + + + align:start position:0% +guy +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so well it looks like a weird + + align:start position:0% +so well it looks like a weird + + + align:start position:0% +so well it looks like a weird +formula and + + align:start position:0% +formula and + + + align:start position:0% +formula and +I mean it is a little bit weird but it's + + align:start position:0% +I mean it is a little bit weird but it's + + + align:start position:0% +I mean it is a little bit weird but it's +a formula that you should learn because + + align:start position:0% +a formula that you should learn because + + + align:start position:0% +a formula that you should learn because +it's really really useful for a lot of + + align:start position:0% +it's really really useful for a lot of + + + align:start position:0% +it's really really useful for a lot of +things um so I should say if this looks + + align:start position:0% +things um so I should say if this looks + + + align:start position:0% +things um so I should say if this looks +very artificial to you and you like to + + align:start position:0% +very artificial to you and you like to + + + align:start position:0% +very artificial to you and you like to +know more there's more in the notes so + + align:start position:0% +know more there's more in the notes so + + + align:start position:0% +know more there's more in the notes so +read the notes they will tell you a bit + + align:start position:0% +read the notes they will tell you a bit + + + align:start position:0% +read the notes they will tell you a bit +more about what this means where it + + align:start position:0% +more about what this means where it + + + align:start position:0% +more about what this means where it +comes from and so on if you want to know + + align:start position:0% +comes from and so on if you want to know + + + align:start position:0% +comes from and so on if you want to know +a lot more then someday you should take + + align:start position:0% +a lot more then someday you should take + + + align:start position:0% +a lot more then someday you should take +1806 linear algebra where you will learn + + align:start position:0% +1806 linear algebra where you will learn + + + align:start position:0% +1806 linear algebra where you will learn +a lot more about determinance in nend + + align:start position:0% +a lot more about determinance in nend + + + align:start position:0% +a lot more about determinance in nend +dimensional space with n vectors and um + + align:start position:0% +dimensional space with n vectors and um + + + align:start position:0% +dimensional space with n vectors and um +there's a generalization of this in + + align:start position:0% +there's a generalization of this in + + + align:start position:0% +there's a generalization of this in +arbitrary dimensions in this class we + + align:start position:0% +arbitrary dimensions in this class we + + + align:start position:0% +arbitrary dimensions in this class we +only deal with two or three + + align:start position:0% +only deal with two or three + + + align:start position:0% +only deal with two or three +dimensions + + align:start position:0% +dimensions + + + align:start position:0% +dimensions +yes sorry why is why is the negative + + align:start position:0% +yes sorry why is why is the negative + + + align:start position:0% +yes sorry why is why is the negative +there well that's a very good question + + align:start position:0% +there well that's a very good question + + + align:start position:0% +there well that's a very good question +it has to be there so that this will + + align:start position:0% +it has to be there so that this will + + + align:start position:0% +it has to be there so that this will +actually equal well what I'm going to + + align:start position:0% +actually equal well what I'm going to + + + align:start position:0% +actually equal well what I'm going to +say right now is that this will give us + + align:start position:0% +say right now is that this will give us + + + align:start position:0% +say right now is that this will give us +the volume of the box with sides a b c + + align:start position:0% +the volume of the box with sides a b c + + + align:start position:0% +the volume of the box with sides a b c +and the formula just doesn't work if you + + align:start position:0% +and the formula just doesn't work if you + + + align:start position:0% +and the formula just doesn't work if you +don't put the negative + + align:start position:0% +don't put the negative + + + align:start position:0% +don't put the negative +uh there's a more fundamental reason + + align:start position:0% +uh there's a more fundamental reason + + + align:start position:0% +uh there's a more fundamental reason +which has to do with orientation of + + align:start position:0% +which has to do with orientation of + + + align:start position:0% +which has to do with orientation of +space and the fact that if you switch + + align:start position:0% +space and the fact that if you switch + + + align:start position:0% +space and the fact that if you switch +two coordinates in space then basically + + align:start position:0% +two coordinates in space then basically + + + align:start position:0% +two coordinates in space then basically +you change What's called the handedness + + align:start position:0% +you change What's called the handedness + + + align:start position:0% +you change What's called the handedness +of the coordinates um if you look at + + align:start position:0% +of the coordinates um if you look at + + + align:start position:0% +of the coordinates um if you look at +your right hand and your left hand they + + align:start position:0% +your right hand and your left hand they + + + align:start position:0% +your right hand and your left hand they +are not actually the same they're mirror + + align:start position:0% +are not actually the same they're mirror + + + align:start position:0% +are not actually the same they're mirror +images and if you swap two coordinate + + align:start position:0% +images and if you swap two coordinate + + + align:start position:0% +images and if you swap two coordinate +axes that's what you get that's the + + align:start position:0% +axes that's what you get that's the + + + align:start position:0% +axes that's what you get that's the +fundamental reason for the minus but + + align:start position:0% +fundamental reason for the minus but + + + align:start position:0% +fundamental reason for the minus but +again I mean we don't need to think too + + align:start position:0% +again I mean we don't need to think too + + + align:start position:0% +again I mean we don't need to think too +much about that all we need in this + + align:start position:0% +much about that all we need in this + + + align:start position:0% +much about that all we need in this +class is the formula + + align:start position:0% + + + + align:start position:0% + +so why do we care about this formula + + align:start position:0% +so why do we care about this formula + + + align:start position:0% +so why do we care about this formula +it's because of a + + align:start position:0% +it's because of a + + + align:start position:0% +it's because of a +theorem that says + + align:start position:0% +theorem that says + + + align:start position:0% +theorem that says +that + + align:start position:0% + + + + align:start position:0% + +geometrically the + + align:start position:0% +geometrically the + + + align:start position:0% +geometrically the +determinant of the three vectors A B + + align:start position:0% +determinant of the three vectors A B + + + align:start position:0% +determinant of the three vectors A B +C is again plus or minus this + + align:start position:0% +C is again plus or minus this + + + align:start position:0% +C is again plus or minus this +determinant could be positive or + + align:start position:0% +determinant could be positive or + + + align:start position:0% +determinant could be positive or +negative see there's minuses and there's + + align:start position:0% +negative see there's minuses and there's + + + align:start position:0% +negative see there's minuses and there's +all sorts of stuff plus or minus the + + align:start position:0% +all sorts of stuff plus or minus the + + + align:start position:0% +all sorts of stuff plus or minus the +volume of the + + align:start position:0% + + + + align:start position:0% + +parallelepiped that's just a fancy name + + align:start position:0% +parallelepiped that's just a fancy name + + + align:start position:0% +parallelepiped that's just a fancy name +for a box with parallelogram sides in + + align:start position:0% +for a box with parallelogram sides in + + + align:start position:0% +for a box with parallelogram sides in +case you + + align:start position:0% +case you + + + align:start position:0% +case you +wonder with sides a b and c okay so you + + align:start position:0% +wonder with sides a b and c okay so you + + + align:start position:0% +wonder with sides a b and c okay so you +take your three vectors A B and C + + align:start position:0% +take your three vectors A B and C + + + align:start position:0% +take your three vectors A B and C +and you form a box whose sides are all + + align:start position:0% + + + + align:start position:0% + +parallelograms and then its volume is + + align:start position:0% +parallelograms and then its volume is + + + align:start position:0% +parallelograms and then its volume is +going to be the + + align:start position:0% + + + + align:start position:0% + +determinant + + align:start position:0% +determinant + + + align:start position:0% +determinant +okay um are + + align:start position:0% +okay um are + + + align:start position:0% +okay um are +questions oh uh + + align:start position:0% + + + + align:start position:0% + +back + + align:start position:0% +back + + + align:start position:0% +back +I'm sorry I can't quite hear + + align:start position:0% + + + + align:start position:0% + +you uh yes we are going to see how to do + + align:start position:0% +you uh yes we are going to see how to do + + + align:start position:0% +you uh yes we are going to see how to do +it geometrically without a determinant + + align:start position:0% +it geometrically without a determinant + + + align:start position:0% +it geometrically without a determinant +but then you'll see that you actually + + align:start position:0% +but then you'll see that you actually + + + align:start position:0% +but then you'll see that you actually +need a determinant to compute it no + + align:start position:0% +need a determinant to compute it no + + + align:start position:0% +need a determinant to compute it no +matter what so we're going to go back to + + align:start position:0% +matter what so we're going to go back to + + + align:start position:0% +matter what so we're going to go back to +this and see another formula for volume + + align:start position:0% +this and see another formula for volume + + + align:start position:0% +this and see another formula for volume +but you'll see that really I'm cheating + + align:start position:0% +but you'll see that really I'm cheating + + + align:start position:0% +but you'll see that really I'm cheating +I mean the important way I mean somehow + + align:start position:0% +I mean the important way I mean somehow + + + align:start position:0% +I mean the important way I mean somehow +computationally the only way to compute + + align:start position:0% +computationally the only way to compute + + + align:start position:0% +computationally the only way to compute +it is really to use a + + align:start position:0% +it is really to use a + + + align:start position:0% +it is really to use a +determinant + + align:start position:0% +determinant + + + align:start position:0% +determinant +yes the + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +determin that's correct in + + align:start position:0% +determin that's correct in + + + align:start position:0% +determin that's correct in +general I mean actually I should say if + + align:start position:0% +general I mean actually I should say if + + + align:start position:0% +general I mean actually I should say if +you look at the 2x two determinant see + + align:start position:0% +you look at the 2x two determinant see + + + align:start position:0% +you look at the 2x two determinant see +you can also explain it in terms of this + + align:start position:0% +you can also explain it in terms of this + + + align:start position:0% +you can also explain it in terms of this +expansion you take A1 and multiply by + + align:start position:0% +expansion you take A1 and multiply by + + + align:start position:0% +expansion you take A1 and multiply by +this one by one determinant B2 then you + + align:start position:0% +this one by one determinant B2 then you + + + align:start position:0% +this one by one determinant B2 then you +take A2 you multiply it by this 1 by one + + align:start position:0% +take A2 you multiply it by this 1 by one + + + align:start position:0% +take A2 you multiply it by this 1 by one +determinant B1 but you put a minus sign + + align:start position:0% +determinant B1 but you put a minus sign + + + align:start position:0% +determinant B1 but you put a minus sign +and in general indeed when you expand + + align:start position:0% +and in general indeed when you expand + + + align:start position:0% +and in general indeed when you expand +you would start putting plus minus plus + + align:start position:0% +you would start putting plus minus plus + + + align:start position:0% +you would start putting plus minus plus +minus + + align:start position:0% +minus + + + align:start position:0% +minus +alternatingly um more about that in 1806 + + align:start position:0% + + + + align:start position:0% + +yes there's a way to do it based on + + align:start position:0% +yes there's a way to do it based on + + + align:start position:0% +yes there's a way to do it based on +other rows as well but then you have to + + align:start position:0% +other rows as well but then you have to + + + align:start position:0% +other rows as well but then you have to +be very careful with the sign factors so + + align:start position:0% +be very careful with the sign factors so + + + align:start position:0% +be very careful with the sign factors so +I'll refer you to the notes for that + + align:start position:0% +I'll refer you to the notes for that + + + align:start position:0% +I'll refer you to the notes for that +okay if you did it with I mean you could + + align:start position:0% +okay if you did it with I mean you could + + + align:start position:0% +okay if you did it with I mean you could +also do it with a column by the way just + + align:start position:0% +also do it with a column by the way just + + + align:start position:0% +also do it with a column by the way just +I mean be careful about the sign rules + + align:start position:0% +I mean be careful about the sign rules + + + align:start position:0% +I mean be careful about the sign rules +so given how how little we'll use + + align:start position:0% +so given how how little we'll use + + + align:start position:0% +so given how how little we'll use +determinants in this class I mean we'll + + align:start position:0% +determinants in this class I mean we'll + + + align:start position:0% +determinants in this class I mean we'll +use them in a way that's fundamental but + + align:start position:0% +use them in a way that's fundamental but + + + align:start position:0% +use them in a way that's fundamental but +we won't compute much so let's say this + + align:start position:0% +we won't compute much so let's say this + + + align:start position:0% +we won't compute much so let's say this +is going to be enough for us for + + align:start position:0% + + + + align:start position:0% + +now okay + + align:start position:0% + + + + align:start position:0% + +so after determinant now I can tell you + + align:start position:0% +so after determinant now I can tell you + + + align:start position:0% +so after determinant now I can tell you +about cross product and cross product is + + align:start position:0% +about cross product and cross product is + + + align:start position:0% +about cross product and cross product is +going to be the answer to your question + + align:start position:0% +going to be the answer to your question + + + align:start position:0% +going to be the answer to your question +about + + align:start position:0% + + + + align:start position:0% + +area + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so okay so let me move on to cross + + align:start position:0% + + + + align:start position:0% + +product so cross product is something + + align:start position:0% +product so cross product is something + + + align:start position:0% +product so cross product is something +that you can apply to two + + align:start position:0% +that you can apply to two + + + align:start position:0% +that you can apply to two +vectors in + + align:start position:0% + + + + align:start position:0% + +space and by that I mean really in three + + align:start position:0% +space and by that I mean really in three + + + align:start position:0% +space and by that I mean really in three +dimensional space okay this is something + + align:start position:0% +dimensional space okay this is something + + + align:start position:0% +dimensional space okay this is something +that's specific to three + + align:start position:0% +that's specific to three + + + align:start position:0% +that's specific to three +dimensions so the + + align:start position:0% + + + + align:start position:0% + +definition A cross + + align:start position:0% +definition A cross + + + align:start position:0% +definition A cross +B so it's important to really do your + + align:start position:0% +B so it's important to really do your + + + align:start position:0% +B so it's important to really do your +multiplication symbol well so that you + + align:start position:0% +multiplication symbol well so that you + + + align:start position:0% +multiplication symbol well so that you +don't mistake it with a DOT + + align:start position:0% +don't mistake it with a DOT + + + align:start position:0% +don't mistake it with a DOT +product well that's going to be a + + align:start position:0% + + + + align:start position:0% + +vector okay so that's another reason not + + align:start position:0% +vector okay so that's another reason not + + + align:start position:0% +vector okay so that's another reason not +to confuse it with DOT product dot + + align:start position:0% +to confuse it with DOT product dot + + + align:start position:0% +to confuse it with DOT product dot +product gives you a number + + align:start position:0% +product gives you a number + + + align:start position:0% +product gives you a number +cross product gives you a vector so + + align:start position:0% +cross product gives you a vector so + + + align:start position:0% +cross product gives you a vector so +they're really completely different + + align:start position:0% +they're really completely different + + + align:start position:0% +they're really completely different +operations they're both called Product + + align:start position:0% +operations they're both called Product + + + align:start position:0% +operations they're both called Product +because well somehow one couldn't come + + align:start position:0% +because well somehow one couldn't come + + + align:start position:0% +because well somehow one couldn't come +up with a better name but they're + + align:start position:0% +up with a better name but they're + + + align:start position:0% +up with a better name but they're +completely different operations okay so + + align:start position:0% +completely different operations okay so + + + align:start position:0% +completely different operations okay so +what do we do to do the cross product of + + align:start position:0% +what do we do to do the cross product of + + + align:start position:0% +what do we do to do the cross product of +A and B well we do something very + + align:start position:0% +A and B well we do something very + + + align:start position:0% +A and B well we do something very +strange just after I've told you that a + + align:start position:0% +strange just after I've told you that a + + + align:start position:0% +strange just after I've told you that a +determinant is something where we put + + align:start position:0% +determinant is something where we put + + + align:start position:0% +determinant is something where we put +numbers and we get a number I'm going to + + align:start position:0% +numbers and we get a number I'm going to + + + align:start position:0% +numbers and we get a number I'm going to +violate my own role I'm going + + align:start position:0% +violate my own role I'm going + + + align:start position:0% +violate my own role I'm going +to put + + align:start position:0% +to put + + + align:start position:0% +to put +together a + + align:start position:0% +together a + + + align:start position:0% +together a +determinant in + + align:start position:0% +determinant in + + + align:start position:0% +determinant in +which well the last two rows are the + + align:start position:0% +which well the last two rows are the + + + align:start position:0% +which well the last two rows are the +components of the vectors A and B but + + align:start position:0% +components of the vectors A and B but + + + align:start position:0% +components of the vectors A and B but +the first row strangely consists of the + + align:start position:0% +the first row strangely consists of the + + + align:start position:0% +the first row strangely consists of the +unit vectors i j k what does that mean + + align:start position:0% +unit vectors i j k what does that mean + + + align:start position:0% +unit vectors i j k what does that mean +well that certainly is not a determinant + + align:start position:0% +well that certainly is not a determinant + + + align:start position:0% +well that certainly is not a determinant +in the usual sense you cannot you know + + align:start position:0% +in the usual sense you cannot you know + + + align:start position:0% +in the usual sense you cannot you know +if you try to put that into your + + align:start position:0% +if you try to put that into your + + + align:start position:0% +if you try to put that into your +calculator it will tell you there's an + + align:start position:0% +calculator it will tell you there's an + + + align:start position:0% +calculator it will tell you there's an +error I don't know how to put vectors in + + align:start position:0% +error I don't know how to put vectors in + + + align:start position:0% +error I don't know how to put vectors in +there I want numbers + + align:start position:0% +there I want numbers + + + align:start position:0% +there I want numbers +uh what it means is it's a symbolic + + align:start position:0% +uh what it means is it's a symbolic + + + align:start position:0% +uh what it means is it's a symbolic +notation that helps you remember what + + align:start position:0% +notation that helps you remember what + + + align:start position:0% +notation that helps you remember what +the formula is so the actual formula is + + align:start position:0% +the formula is so the actual formula is + + + align:start position:0% +the formula is so the actual formula is +well you use this definition and you + + align:start position:0% +well you use this definition and you + + + align:start position:0% +well you use this definition and you +know if you use this + + align:start position:0% +know if you use this + + + align:start position:0% +know if you use this +definition you see that it's IH hat + + align:start position:0% +definition you see that it's IH hat + + + align:start position:0% +definition you see that it's IH hat +times some + + align:start position:0% +times some + + + align:start position:0% +times some +number okay so let me write it as + + align:start position:0% +number okay so let me write it as + + + align:start position:0% +number okay so let me write it as +determinant of A2 A3 B2 B3 * I + + align:start position:0% +determinant of A2 A3 B2 B3 * I + + + align:start position:0% +determinant of A2 A3 B2 B3 * I +hat + + align:start position:0% +hat + + + align:start position:0% +hat +minus determinant A1 A3 B1 + + align:start position:0% +minus determinant A1 A3 B1 + + + align:start position:0% +minus determinant A1 A3 B1 +B3 J hat plus A1 A2 B1 + + align:start position:0% +B3 J hat plus A1 A2 B1 + + + align:start position:0% +B3 J hat plus A1 A2 B1 +B2 K + + align:start position:0% +B2 K + + + align:start position:0% +B2 K +hat okay and so that's the actual + + align:start position:0% +hat okay and so that's the actual + + + align:start position:0% +hat okay and so that's the actual +definition in a way that makes complete + + align:start position:0% +definition in a way that makes complete + + + align:start position:0% +definition in a way that makes complete +sense but to remember this formula + + align:start position:0% +sense but to remember this formula + + + align:start position:0% +sense but to remember this formula +without too much trouble it's much + + align:start position:0% +without too much trouble it's much + + + align:start position:0% +without too much trouble it's much +easier to think of it to think about it + + align:start position:0% +easier to think of it to think about it + + + align:start position:0% +easier to think of it to think about it +in these terms + + align:start position:0% +in these terms + + + align:start position:0% +in these terms +here okay so that's a definition and it + + align:start position:0% +here okay so that's a definition and it + + + align:start position:0% +here okay so that's a definition and it +gives you a vector + + align:start position:0% +gives you a vector + + + align:start position:0% +gives you a vector +now as usual with definitions the + + align:start position:0% +now as usual with definitions the + + + align:start position:0% +now as usual with definitions the +question is what is it good for what is + + align:start position:0% +question is what is it good for what is + + + align:start position:0% +question is what is it good for what is +the geometric meaning of this very + + align:start position:0% +the geometric meaning of this very + + + align:start position:0% +the geometric meaning of this very +strange operation why do we bother to do + + align:start position:0% + + + + align:start position:0% + +that so here's what it does + + align:start position:0% + + + + align:start position:0% + +geometrically so remember a vector has + + align:start position:0% +geometrically so remember a vector has + + + align:start position:0% +geometrically so remember a vector has +two different things it has a length and + + align:start position:0% +two different things it has a length and + + + align:start position:0% +two different things it has a length and +it has a direction okay let's start with + + align:start position:0% +it has a direction okay let's start with + + + align:start position:0% +it has a direction okay let's start with +a length + + align:start position:0% + + + + align:start position:0% + +the length of a cross + + align:start position:0% + + + + align:start position:0% + +product is the + + align:start position:0% +product is the + + + align:start position:0% +product is the +area of the + + align:start position:0% +area of the + + + align:start position:0% +area of the +parallelogram in + + align:start position:0% +parallelogram in + + + align:start position:0% +parallelogram in +space formed by the vectors A and + + align:start position:0% + + + + align:start position:0% + +B okay so now if you have a + + align:start position:0% +B okay so now if you have a + + + align:start position:0% +B okay so now if you have a +parallelogram in space you can find it + + align:start position:0% +parallelogram in space you can find it + + + align:start position:0% +parallelogram in space you can find it +area just by doing this calculation when + + align:start position:0% +area just by doing this calculation when + + + align:start position:0% +area just by doing this calculation when +you know the coordinates of a + + align:start position:0% +you know the coordinates of a + + + align:start position:0% +you know the coordinates of a +point you do this calculation and then + + align:start position:0% +point you do this calculation and then + + + align:start position:0% +point you do this calculation and then +you take the length so the length you + + align:start position:0% +you take the length so the length you + + + align:start position:0% +you take the length so the length you +know you take this square plus that + + align:start position:0% +know you take this square plus that + + + align:start position:0% +know you take this square plus that +square plus that squar square + + align:start position:0% +square plus that squar square + + + align:start position:0% +square plus that squar square +root it looks like a very complicated + + align:start position:0% +root it looks like a very complicated + + + align:start position:0% +root it looks like a very complicated +formula but it works and actually it's + + align:start position:0% +formula but it works and actually it's + + + align:start position:0% +formula but it works and actually it's +the simplest way to do + + align:start position:0% + + + + align:start position:0% + +it okay this time we don't actually need + + align:start position:0% +it okay this time we don't actually need + + + align:start position:0% +it okay this time we don't actually need +to put plus or minus because the length + + align:start position:0% +to put plus or minus because the length + + + align:start position:0% +to put plus or minus because the length +of a vector is always positive we don't + + align:start position:0% +of a vector is always positive we don't + + + align:start position:0% +of a vector is always positive we don't +have to worry about that + + align:start position:0% + + + + align:start position:0% + +and what's even more magical is that not + + align:start position:0% +and what's even more magical is that not + + + align:start position:0% +and what's even more magical is that not +only is the length remarkable but the + + align:start position:0% +only is the length remarkable but the + + + align:start position:0% +only is the length remarkable but the +direction is also remarkable so the + + align:start position:0% +direction is also remarkable so the + + + align:start position:0% +direction is also remarkable so the +direction of A cross + + align:start position:0% +direction of A cross + + + align:start position:0% +direction of A cross +B is perpendicular to the plane of the + + align:start position:0% + + + + align:start position:0% + +parallelogram + + align:start position:0% +parallelogram + + + align:start position:0% +parallelogram +so you know our two vectors A and B + + align:start position:0% +so you know our two vectors A and B + + + align:start position:0% +so you know our two vectors A and B +together the determine a + + align:start position:0% + + + + align:start position:0% + +plane and what what I'm telling you is + + align:start position:0% +plane and what what I'm telling you is + + + align:start position:0% +plane and what what I'm telling you is +that the vector A cross B will + + align:start position:0% +that the vector A cross B will + + + align:start position:0% +that the vector A cross B will +point will stick straight out of that + + align:start position:0% +point will stick straight out of that + + + align:start position:0% +point will stick straight out of that +plane perpendicularly to + + align:start position:0% + + + + align:start position:0% + +it + + align:start position:0% +it + + + align:start position:0% +it +okay so in fact I have to be more + + align:start position:0% +okay so in fact I have to be more + + + align:start position:0% +okay so in fact I have to be more +precise there's two ways is that you can + + align:start position:0% +precise there's two ways is that you can + + + align:start position:0% +precise there's two ways is that you can +be perpendic perpendicular to this plane + + align:start position:0% +be perpendic perpendicular to this plane + + + align:start position:0% +be perpendic perpendicular to this plane +right you can be perpendicular pointing + + align:start position:0% +right you can be perpendicular pointing + + + align:start position:0% +right you can be perpendicular pointing +up or pointing + + align:start position:0% +up or pointing + + + align:start position:0% +up or pointing +down how do I decide + + align:start position:0% +down how do I decide + + + align:start position:0% +down how do I decide +which + + align:start position:0% + + + + align:start position:0% + +well there's something called the right + + align:start position:0% +well there's something called the right + + + align:start position:0% +well there's something called the right +hand + + align:start position:0% + + + + align:start position:0% + +rule okay so what does the right hand + + align:start position:0% +rule okay so what does the right hand + + + align:start position:0% +rule okay so what does the right hand +rule say well there's various versions + + align:start position:0% +rule say well there's various versions + + + align:start position:0% +rule say well there's various versions +of the right hand rule depending on in + + align:start position:0% +of the right hand rule depending on in + + + align:start position:0% +of the right hand rule depending on in +which country you learn about it uh in + + align:start position:0% +which country you learn about it uh in + + + align:start position:0% +which country you learn about it uh in +France given the culture you even learn + + align:start position:0% +France given the culture you even learn + + + align:start position:0% +France given the culture you even learn +about it in terms of a crew and one + + align:start position:0% +about it in terms of a crew and one + + + align:start position:0% +about it in terms of a crew and one +bottle but I think uh I'll just use the + + align:start position:0% +bottle but I think uh I'll just use the + + + align:start position:0% +bottle but I think uh I'll just use the +usual version here um so you take your + + align:start position:0% +usual version here um so you take your + + + align:start position:0% +usual version here um so you take your +right hand if you're left handed + + align:start position:0% +right hand if you're left handed + + + align:start position:0% +right hand if you're left handed +remember to take your right hand not the + + align:start position:0% +remember to take your right hand not the + + + align:start position:0% +remember to take your right hand not the +left one the other the other right okay + + align:start position:0% +left one the other the other right okay + + + align:start position:0% +left one the other the other right okay +um and then place your hand to point in + + align:start position:0% +um and then place your hand to point in + + + align:start position:0% +um and then place your hand to point in +the direction of a so let's say my right + + align:start position:0% +the direction of a so let's say my right + + + align:start position:0% +the direction of a so let's say my right +hand is going in that direction now curl + + align:start position:0% +hand is going in that direction now curl + + + align:start position:0% +hand is going in that direction now curl +your fingers so that they Point towards + + align:start position:0% +your fingers so that they Point towards + + + align:start position:0% +your fingers so that they Point towards +B so here that would be kind of into the + + align:start position:0% +B so here that would be kind of into the + + + align:start position:0% +B so here that would be kind of into the +Blackboard okay don't snap any bones if + + align:start position:0% +Blackboard okay don't snap any bones if + + + align:start position:0% +Blackboard okay don't snap any bones if +it doesn't quite work and rotate your + + align:start position:0% +it doesn't quite work and rotate your + + + align:start position:0% +it doesn't quite work and rotate your +arm so that you know you can actually + + align:start position:0% +arm so that you know you can actually + + + align:start position:0% +arm so that you know you can actually +physically do + + align:start position:0% +physically do + + + align:start position:0% +physically do +it then you know get your firm to stick + + align:start position:0% +it then you know get your firm to stick + + + align:start position:0% +it then you know get your firm to stick +straight out well here my f is going to + + align:start position:0% +straight out well here my f is going to + + + align:start position:0% +straight out well here my f is going to +go up and that tells me that A cross B + + align:start position:0% +go up and that tells me that A cross B + + + align:start position:0% +go up and that tells me that A cross B +will go + + align:start position:0% +will go + + + align:start position:0% +will go +up okay so let me write that down while + + align:start position:0% +up okay so let me write that down while + + + align:start position:0% +up okay so let me write that down while +you experiment with + + align:start position:0% +you experiment with + + + align:start position:0% +you experiment with +it again try not to injure + + align:start position:0% + + + + align:start position:0% + +yourselves + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +first your right + + align:start position:0% +first your right + + + align:start position:0% +first your right +hand + + align:start position:0% +hand + + + align:start position:0% +hand +points parallel to Vector + + align:start position:0% +points parallel to Vector + + + align:start position:0% +points parallel to Vector +a + + align:start position:0% +a + + + align:start position:0% +a +then + + align:start position:0% + + + + align:start position:0% + +fingers point in the direction of B then + + align:start position:0% +fingers point in the direction of B then + + + align:start position:0% +fingers point in the direction of B then +your fum when you stick it out is going + + align:start position:0% +your fum when you stick it out is going + + + align:start position:0% +your fum when you stick it out is going +to + + align:start position:0% +to + + + align:start position:0% +to +point in the direction of A cross + + align:start position:0% +point in the direction of A cross + + + align:start position:0% +point in the direction of A cross +B + + align:start position:0% + + + + align:start position:0% + +okay let's do a quick + + align:start position:0% +okay let's do a quick + + + align:start position:0% +okay let's do a quick +example what's my quick + + align:start position:0% +example what's my quick + + + align:start position:0% +example what's my quick +example + + align:start position:0% +example + + + align:start position:0% +example +here let's + + align:start position:0% + + + + align:start position:0% + +take I cross + + align:start position:0% + + + + align:start position:0% + +J + + align:start position:0% + + + + align:start position:0% + +so I see some of you well most of you + + align:start position:0% +so I see some of you well most of you + + + align:start position:0% +so I see some of you well most of you +have it going in the right + + align:start position:0% +have it going in the right + + + align:start position:0% +have it going in the right +direction uh if you have it pointing in + + align:start position:0% +direction uh if you have it pointing in + + + align:start position:0% +direction uh if you have it pointing in +the wrong direction it might mean that + + align:start position:0% +the wrong direction it might mean that + + + align:start position:0% +the wrong direction it might mean that +you're using your left hand for example + + align:start position:0% +you're using your left hand for example + + + align:start position:0% +you're using your left hand for example +Okay + + align:start position:0% + + + + align:start position:0% + +so example I claim that I cross J equals + + align:start position:0% +so example I claim that I cross J equals + + + align:start position:0% +so example I claim that I cross J equals +K okay let's see I points toward us J + + align:start position:0% +K okay let's see I points toward us J + + + align:start position:0% +K okay let's see I points toward us J +points to our right so I guess this is + + align:start position:0% +points to our right so I guess this is + + + align:start position:0% +points to our right so I guess this is +your right right I think it's kind of + + align:start position:0% +your right right I think it's kind of + + + align:start position:0% +your right right I think it's kind of +hard to and then your Thum is going to + + align:start position:0% +hard to and then your Thum is going to + + + align:start position:0% +hard to and then your Thum is going to +point up okay so that tells us it's + + align:start position:0% +point up okay so that tells us it's + + + align:start position:0% +point up okay so that tells us it's +roughly pointing up uh and of course the + + align:start position:0% +roughly pointing up uh and of course the + + + align:start position:0% +roughly pointing up uh and of course the +length should be one because if you take + + align:start position:0% +length should be one because if you take + + + align:start position:0% +length should be one because if you take +the unit Square in the XY plane its area + + align:start position:0% +the unit Square in the XY plane its area + + + align:start position:0% +the unit Square in the XY plane its area +is one and the direction should indeed + + align:start position:0% +is one and the direction should indeed + + + align:start position:0% +is one and the direction should indeed +be vertical because it should be + + align:start position:0% +be vertical because it should be + + + align:start position:0% +be vertical because it should be +perpendicular to the XY + + align:start position:0% +perpendicular to the XY + + + align:start position:0% +perpendicular to the XY +plane + + align:start position:0% +plane + + + align:start position:0% +plane +so looks like I cross J will be K well + + align:start position:0% +so looks like I cross J will be K well + + + align:start position:0% +so looks like I cross J will be K well +let's check with a definition you + + align:start position:0% +let's check with a definition you + + + align:start position:0% +let's check with a definition you +know I J K what is I I is 1 0 0 J is 0 1 + + align:start position:0% +know I J K what is I I is 1 0 0 J is 0 1 + + + align:start position:0% +know I J K what is I I is 1 0 0 J is 0 1 +0 well so the coefficient of I will be 0 + + align:start position:0% +0 well so the coefficient of I will be 0 + + + align:start position:0% +0 well so the coefficient of I will be 0 +* 0 - 0 * 1 that's + + align:start position:0% +* 0 - 0 * 1 that's + + + align:start position:0% +* 0 - 0 * 1 that's +0 coefficient of J will be 1 * 0 - 0 * 0 + + align:start position:0% +0 coefficient of J will be 1 * 0 - 0 * 0 + + + align:start position:0% +0 coefficient of J will be 1 * 0 - 0 * 0 +that's + + align:start position:0% +that's + + + align:start position:0% +that's +0us 0 J doesn't matter but and the + + align:start position:0% +0us 0 J doesn't matter but and the + + + align:start position:0% +0us 0 J doesn't matter but and the +coefficient of + + align:start position:0% +coefficient of + + + align:start position:0% +coefficient of +K will be 1 * 1 that's 1 minus 0 * 0 so + + align:start position:0% +K will be 1 * 1 that's 1 minus 0 * 0 so + + + align:start position:0% +K will be 1 * 1 that's 1 minus 0 * 0 so + + align:start position:0% + + + align:start position:0% +K okay so we do get i+ Jal K both + + align:start position:0% +K okay so we do get i+ Jal K both + + + align:start position:0% +K okay so we do get i+ Jal K both +ways uh in this case it's easier to do + + align:start position:0% +ways uh in this case it's easier to do + + + align:start position:0% +ways uh in this case it's easier to do +geometrically if I give you more + + align:start position:0% +geometrically if I give you more + + + align:start position:0% +geometrically if I give you more +complicated vectors probably you will + + align:start position:0% +complicated vectors probably you will + + + align:start position:0% +complicated vectors probably you will +actually want to do the + + align:start position:0% + + + + align:start position:0% + +calculation okay any questions uh + + align:start position:0% + + + + align:start position:0% + +yes ah so the coefficient of K remember + + align:start position:0% +yes ah so the coefficient of K remember + + + align:start position:0% +yes ah so the coefficient of K remember +I take so I delete the first row and the + + align:start position:0% +I take so I delete the first row and the + + + align:start position:0% +I take so I delete the first row and the +last column so I get this 2x two + + align:start position:0% +last column so I get this 2x two + + + align:start position:0% +last column so I get this 2x two +determinant okay that 2x2 determinant is + + align:start position:0% +determinant okay that 2x2 determinant is + + + align:start position:0% +determinant okay that 2x2 determinant is +1 * 1- 0 * 0 so that gives me 1 + + align:start position:0% +1 * 1- 0 * 0 so that gives me 1 + + + align:start position:0% +1 * 1- 0 * 0 so that gives me 1 +okay that's what you do with 2x two + + align:start position:0% +okay that's what you do with 2x two + + + align:start position:0% +okay that's what you do with 2x two +determinants similarly for vs but vs + + align:start position:0% +determinants similarly for vs but vs + + + align:start position:0% +determinants similarly for vs but vs +turn out to be + + align:start position:0% + + + + align:start position:0% + +zero um more + + align:start position:0% + + + + align:start position:0% + +questions uh yes let me repeat how I got + + align:start position:0% +questions uh yes let me repeat how I got + + + align:start position:0% +questions uh yes let me repeat how I got +the one in front of K so remember the + + align:start position:0% +the one in front of K so remember the + + + align:start position:0% +the one in front of K so remember the +definition of a + + align:start position:0% +definition of a + + + align:start position:0% +definition of a +determinant I expand according to the + + align:start position:0% +determinant I expand according to the + + + align:start position:0% +determinant I expand according to the +entries in the first row when I get to K + + align:start position:0% +entries in the first row when I get to K + + + align:start position:0% +entries in the first row when I get to K +what I do is I delete the first row and + + align:start position:0% +what I do is I delete the first row and + + + align:start position:0% +what I do is I delete the first row and +I delete the last column the column that + + align:start position:0% +I delete the last column the column that + + + align:start position:0% +I delete the last column the column that +contains K okay so I delete these guys + + align:start position:0% +contains K okay so I delete these guys + + + align:start position:0% +contains K okay so I delete these guys +and these guys I'm left with this 2x two + + align:start position:0% +and these guys I'm left with this 2x two + + + align:start position:0% +and these guys I'm left with this 2x two +determinant now a 2X two determinant you + + align:start position:0% +determinant now a 2X two determinant you + + + align:start position:0% +determinant now a 2X two determinant you +multiply according to this downward + + align:start position:0% +multiply according to this downward + + + align:start position:0% +multiply according to this downward +diagonal and then minus this * that okay + + align:start position:0% +diagonal and then minus this * that okay + + + align:start position:0% +diagonal and then minus this * that okay +so 1 * + + align:start position:0% +so 1 * + + + align:start position:0% +so 1 * +1 let me say here I got 1K because + + align:start position:0% +1 let me say here I got 1K because + + + align:start position:0% +1 let me say here I got 1K because +that's 1 * 1 minus 0 * 0 equals 1 sorry + + align:start position:0% +that's 1 * 1 minus 0 * 0 equals 1 sorry + + + align:start position:0% +that's 1 * 1 minus 0 * 0 equals 1 sorry +and that's really hard to read maybe it + + align:start position:0% +and that's really hard to read maybe it + + + align:start position:0% +and that's really hard to read maybe it +will be easier that + + align:start position:0% + + + + align:start position:0% + +way + + align:start position:0% +way + + + align:start position:0% +way +okay uh + + align:start position:0% + + + + align:start position:0% + +yes ah okay so let's try if I do the + + align:start position:0% +yes ah okay so let's try if I do the + + + align:start position:0% +yes ah okay so let's try if I do the +same for I I think I will also get zero + + align:start position:0% +same for I I think I will also get zero + + + align:start position:0% +same for I I think I will also get zero +okay so let's do the same for I so I + + align:start position:0% +okay so let's do the same for I so I + + + align:start position:0% +okay so let's do the same for I so I +take I I delete the first row I delete + + align:start position:0% +take I I delete the first row I delete + + + align:start position:0% +take I I delete the first row I delete +the First Column I get this 2x two + + align:start position:0% +the First Column I get this 2x two + + + align:start position:0% +the First Column I get this 2x two +determinant here and I get 0 * 0 that's + + align:start position:0% +determinant here and I get 0 * 0 that's + + + align:start position:0% +determinant here and I get 0 * 0 that's +0us 0 * 1 that's here the trick question + + align:start position:0% +0us 0 * 1 that's here the trick question + + + align:start position:0% +0us 0 * 1 that's here the trick question +0 * 1 is 0 as well so that's 0 minus 0 + + align:start position:0% +0 * 1 is 0 as well so that's 0 minus 0 + + + align:start position:0% +0 * 1 is 0 as well so that's 0 minus 0 +is + + align:start position:0% +is + + + align:start position:0% +is +z + + align:start position:0% + + + + align:start position:0% + +okay so I hope in Monday you should get + + align:start position:0% +okay so I hope in Monday you should get + + + align:start position:0% +okay so I hope in Monday you should get +more practice in recitation about how to + + align:start position:0% +more practice in recitation about how to + + + align:start position:0% +more practice in recitation about how to +compute determinants so hopefully will + + align:start position:0% +compute determinants so hopefully will + + + align:start position:0% +compute determinants so hopefully will +become very easy for you all to compute + + align:start position:0% +become very easy for you all to compute + + + align:start position:0% +become very easy for you all to compute +this + + align:start position:0% +this + + + align:start position:0% +this +things I know the first time it's kind + + align:start position:0% +things I know the first time it's kind + + + align:start position:0% +things I know the first time it's kind +of a shock because there's a lot of + + align:start position:0% +of a shock because there's a lot of + + + align:start position:0% +of a shock because there's a lot of +numbers and a lot of things to + + align:start position:0% + + + + align:start position:0% + +do + + align:start position:0% + + + + align:start position:0% + +not + + align:start position:0% +not + + + align:start position:0% +not +good + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so okay so let me return to the question + + align:start position:0% +so okay so let me return to the question + + + align:start position:0% +so okay so let me return to the question +that you asked a bit earlier about how + + align:start position:0% +that you asked a bit earlier about how + + + align:start position:0% +that you asked a bit earlier about how +do I find actually volume if I don't + + align:start position:0% +do I find actually volume if I don't + + + align:start position:0% +do I find actually volume if I don't +want to know about + + align:start position:0% +want to know about + + + align:start position:0% +want to know about +determinants + + align:start position:0% +determinants + + + align:start position:0% +determinants +well so let's have another + + align:start position:0% + + + + align:start position:0% + +look and for + + align:start position:0% + + + + align:start position:0% + +volum okay + + align:start position:0% +volum okay + + + align:start position:0% +volum okay +so let's say that I have three + + align:start position:0% +so let's say that I have three + + + align:start position:0% +so let's say that I have three +vectors let me put them this way + + align:start position:0% +vectors let me put them this way + + + align:start position:0% +vectors let me put them this way +a + + align:start position:0% +a + + + align:start position:0% +a +b and c and let's try to see how else I + + align:start position:0% +b and c and let's try to see how else I + + + align:start position:0% +b and c and let's try to see how else I +could think + + align:start position:0% +could think + + + align:start position:0% +could think +about the volume of this + + align:start position:0% +about the volume of this + + + align:start position:0% +about the volume of this +box + + align:start position:0% +box + + + align:start position:0% +box +okay so probably you know that the + + align:start position:0% +okay so probably you know that the + + + align:start position:0% +okay so probably you know that the +volume of a parallelepiped is the area + + align:start position:0% +volume of a parallelepiped is the area + + + align:start position:0% +volume of a parallelepiped is the area +of a base times the + + align:start position:0% +of a base times the + + + align:start position:0% +of a base times the +height okay + + align:start position:0% +height okay + + + align:start position:0% +height okay +so sorry the + + align:start position:0% + + + + align:start position:0% + +volume is the area of the + + align:start position:0% +volume is the area of the + + + align:start position:0% +volume is the area of the +base times the + + align:start position:0% +base times the + + + align:start position:0% +base times the +height how do we do that in practice + + align:start position:0% +height how do we do that in practice + + + align:start position:0% +height how do we do that in practice +well what's the area of the base so the + + align:start position:0% +well what's the area of the base so the + + + align:start position:0% +well what's the area of the base so the +base is a parallelogram in space with + + align:start position:0% +base is a parallelogram in space with + + + align:start position:0% +base is a parallelogram in space with +sides B and C how do we find the area of + + align:start position:0% +sides B and C how do we find the area of + + + align:start position:0% +sides B and C how do we find the area of +a parallelogram in space well we just + + align:start position:0% +a parallelogram in space well we just + + + align:start position:0% +a parallelogram in space well we just +discovered that we can do it by taking + + align:start position:0% +discovered that we can do it by taking + + + align:start position:0% +discovered that we can do it by taking +the cross product so the area of a base + + align:start position:0% +the cross product so the area of a base + + + align:start position:0% +the cross product so the area of a base +well we take the cross product of B and + + align:start position:0% +well we take the cross product of B and + + + align:start position:0% +well we take the cross product of B and +C that's not quite it because this is a + + align:start position:0% +C that's not quite it because this is a + + + align:start position:0% +C that's not quite it because this is a +vector we would like a number well we + + align:start position:0% +vector we would like a number well we + + + align:start position:0% +vector we would like a number well we +take its length Okay that's pretty good + + align:start position:0% +take its length Okay that's pretty good + + + align:start position:0% +take its length Okay that's pretty good +what about the height well the height is + + align:start position:0% +what about the height well the height is + + + align:start position:0% +what about the height well the height is +going to be the component of a in the + + align:start position:0% +going to be the component of a in the + + + align:start position:0% +going to be the component of a in the +direction that's perpendicular to the + + align:start position:0% +direction that's perpendicular to the + + + align:start position:0% +direction that's perpendicular to the +base so let's take a Direction that's + + align:start position:0% +base so let's take a Direction that's + + + align:start position:0% +base so let's take a Direction that's +perpendicular to the base let's call + + align:start position:0% +perpendicular to the base let's call + + + align:start position:0% +perpendicular to the base let's call +that n a unit Vector in that direction + + align:start position:0% +that n a unit Vector in that direction + + + align:start position:0% +that n a unit Vector in that direction +then we can get the height by taking a + + align:start position:0% +then we can get the height by taking a + + + align:start position:0% +then we can get the height by taking a +do n that's what we saw at the beginning + + align:start position:0% +do n that's what we saw at the beginning + + + align:start position:0% +do n that's what we saw at the beginning +of class okay that a. n will tell me how + + align:start position:0% +of class okay that a. n will tell me how + + + align:start position:0% +of class okay that a. n will tell me how +much a goes in the direction of + + align:start position:0% +much a goes in the direction of + + + align:start position:0% +much a goes in the direction of +n okay are you still with + + align:start position:0% +n okay are you still with + + + align:start position:0% +n okay are you still with +me okay let's keep + + align:start position:0% + + + + align:start position:0% + +going + + align:start position:0% +going + + + align:start position:0% +going +so let's think about this Vector n how + + align:start position:0% +so let's think about this Vector n how + + + align:start position:0% +so let's think about this Vector n how +do I get + + align:start position:0% +do I get + + + align:start position:0% +do I get +it well I can get it by actually using + + align:start position:0% +it well I can get it by actually using + + + align:start position:0% +it well I can get it by actually using +cross product as well because I said the + + align:start position:0% +cross product as well because I said the + + + align:start position:0% +cross product as well because I said the +direction perpendicular to two vectors I + + align:start position:0% +direction perpendicular to two vectors I + + + align:start position:0% +direction perpendicular to two vectors I +can get by taking the cross product and + + align:start position:0% +can get by taking the cross product and + + + align:start position:0% +can get by taking the cross product and +looking at that direction so this is + + align:start position:0% +looking at that direction so this is + + + align:start position:0% +looking at that direction so this is +still B Cross C length and this one + + align:start position:0% +still B Cross C length and this one + + + align:start position:0% +still B Cross C length and this one +is so I + + align:start position:0% +is so I + + + align:start position:0% +is so I +claim I should do an aside here n can be + + align:start position:0% +claim I should do an aside here n can be + + + align:start position:0% +claim I should do an aside here n can be +obtained by taking B Cross C well that + + align:start position:0% +obtained by taking B Cross C well that + + + align:start position:0% +obtained by taking B Cross C well that +point in the right direction but it's + + align:start position:0% +point in the right direction but it's + + + align:start position:0% +point in the right direction but it's +not a unit Vector how do I get a unit + + align:start position:0% +not a unit Vector how do I get a unit + + + align:start position:0% +not a unit Vector how do I get a unit +Vector I divide by the + + align:start position:0% + + + + align:start position:0% + +length thanks so I take B Cross C and I + + align:start position:0% +length thanks so I take B Cross C and I + + + align:start position:0% +length thanks so I take B Cross C and I +divide by length B Cross + + align:start position:0% +divide by length B Cross + + + align:start position:0% +divide by length B Cross +C well now I can probably simplify + + align:start position:0% +C well now I can probably simplify + + + align:start position:0% +C well now I can probably simplify +between these two + + align:start position:0% +between these two + + + align:start position:0% +between these two +guys and so what I will + + align:start position:0% + + + + align:start position:0% + +get + + align:start position:0% + + + + align:start position:0% + +oops it's going to be the last think for + + align:start position:0% +oops it's going to be the last think for + + + align:start position:0% +oops it's going to be the last think for +today what I get out of this + + align:start position:0% +today what I get out of this + + + align:start position:0% +today what I get out of this +is that my volume equals a DOT product + + align:start position:0% +is that my volume equals a DOT product + + + align:start position:0% +is that my volume equals a DOT product +with the vector B Cross C and of course + + align:start position:0% +with the vector B Cross C and of course + + + align:start position:0% +with the vector B Cross C and of course +I have to be careful in which order I do + + align:start position:0% +I have to be careful in which order I do + + + align:start position:0% +I have to be careful in which order I do +it if I do it the other way around + + align:start position:0% +it if I do it the other way around + + + align:start position:0% +it if I do it the other way around +a B I get a number I cannot cross that + + align:start position:0% +a B I get a number I cannot cross that + + + align:start position:0% +a B I get a number I cannot cross that +so I mean I really have to do the cross + + align:start position:0% +so I mean I really have to do the cross + + + align:start position:0% +so I mean I really have to do the cross +product first I get a new vector and + + align:start position:0% +product first I get a new vector and + + + align:start position:0% +product first I get a new vector and +then I do + + align:start position:0% +then I do + + + align:start position:0% +then I do +product okay so the fact is that the + + align:start position:0% +product okay so the fact is that the + + + align:start position:0% +product okay so the fact is that the +determinant of + + align:start position:0% +determinant of + + + align:start position:0% +determinant of +ABC is equal to this so-called triple + + align:start position:0% +ABC is equal to this so-called triple + + + align:start position:0% +ABC is equal to this so-called triple +product well that looks good + + align:start position:0% +product well that looks good + + + align:start position:0% +product well that looks good +geometrically let's try to check whether + + align:start position:0% +geometrically let's try to check whether + + + align:start position:0% +geometrically let's try to check whether +it makes sense with the formulas just + + align:start position:0% +it makes sense with the formulas just + + + align:start position:0% +it makes sense with the formulas just +one small thing so we saw the + + align:start position:0% +one small thing so we saw the + + + align:start position:0% +one small thing so we saw the +determinant is A1 * determinant B2 B3 C2 + + align:start position:0% +determinant is A1 * determinant B2 B3 C2 + + + align:start position:0% +determinant is A1 * determinant B2 B3 C2 +C3 minus A2 * something plus A3 * + + align:start position:0% +C3 minus A2 * something plus A3 * + + + align:start position:0% +C3 minus A2 * something plus A3 * +something I let you fill in the + + align:start position:0% +something I let you fill in the + + + align:start position:0% +something I let you fill in the +numbers okay that's this + + align:start position:0% +numbers okay that's this + + + align:start position:0% +numbers okay that's this +guy what about this guy well dot product + + align:start position:0% +guy what about this guy well dot product + + + align:start position:0% +guy what about this guy well dot product +we take the first component of a that's + + align:start position:0% +we take the first component of a that's + + + align:start position:0% +we take the first component of a that's +A1 we multiply by the first component of + + align:start position:0% +A1 we multiply by the first component of + + + align:start position:0% +A1 we multiply by the first component of +b Cross C what's the first component of + + align:start position:0% +b Cross C what's the first component of + + + align:start position:0% +b Cross C what's the first component of +b Cross C well it's this determinant + + align:start position:0% + + + + align:start position:0% + +B2 B3 C2 C3 right if you look at if you + + align:start position:0% +B2 B3 C2 C3 right if you look at if you + + + align:start position:0% +B2 B3 C2 C3 right if you look at if you +put B and C instead of A and B into + + align:start position:0% +put B and C instead of A and B into + + + align:start position:0% +put B and C instead of A and B into +there you will get that the I component + + align:start position:0% +there you will get that the I component + + + align:start position:0% +there you will get that the I component +is this guy minus well plus A2 * the + + align:start position:0% +is this guy minus well plus A2 * the + + + align:start position:0% +is this guy minus well plus A2 * the +second component which is minus some + + align:start position:0% +second component which is minus some + + + align:start position:0% +second component which is minus some +determinant plus A3 * the third + + align:start position:0% +determinant plus A3 * the third + + + align:start position:0% +determinant plus A3 * the third +component which is again a determinant + + align:start position:0% +component which is again a determinant + + + align:start position:0% +component which is again a determinant +and you can check you get exactly the + + align:start position:0% +and you can check you get exactly the + + + align:start position:0% +and you can check you get exactly the +same expression so everything is fine uh + + align:start position:0% +same expression so everything is fine uh + + + align:start position:0% +same expression so everything is fine uh +there's no contradiction in meth just + + align:start position:0% +there's no contradiction in meth just + + + align:start position:0% +there's no contradiction in meth just +yet + + align:start position:0% +yet + + + align:start position:0% +yet +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so well on Tuesday we'll continue with + + align:start position:0% +so well on Tuesday we'll continue with + + + align:start position:0% +so well on Tuesday we'll continue with +this and we'll start going into matrices + + align:start position:0% +this and we'll start going into matrices + + + align:start position:0% +this and we'll start going into matrices +equations of planes and so on uh + + align:start position:0% +equations of planes and so on uh + + + align:start position:0% +equations of planes and so on uh +meanwhile have a good weekend and please + + align:start position:0% +meanwhile have a good weekend and please + + + align:start position:0% +meanwhile have a good weekend and please +start working on your problem sets so + + align:start position:0% +start working on your problem sets so + + + align:start position:0% +start working on your problem sets so +that you can ask lots of questions to + + align:start position:0% +that you can ask lots of questions to + + + align:start position:0% +that you can ask lots of questions to +your Tas on + + align:start position:0% +your Tas on + + + align:start position:0% +your Tas on +Monday \ No newline at end of file diff --git a/A2WFReES8CY.txt b/A2WFReES8CY.txt new file mode 100644 index 0000000000000000000000000000000000000000..a146dc87f0ccc608424a611df8fcc9e4814f9f87 --- /dev/null +++ b/A2WFReES8CY.txt @@ -0,0 +1,2501 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Now today's +lecture. + +First I want to talk a little +bit about what computer + +scientists do. + +This whole course has been +about computer science. + +And I hope that at least for +many of you, it might have + +persuaded you that there's an +interesting career out there + +for you as a computer +scientist. + +And then I'll finish up with an +overview of what I think we + +covered this term. + +So what do computer +scientists do? + +Well, they look a lot like +that as you all know. + +In fact, it's amazing. + +There's almost nothing that +computer scientists don't do. + +So here I've just collected a +few of the different pictures + +related to what computer +scientists in EECS are doing + +these days, things like working +on the software that + +keeps airplanes from falling +out of the skies. + +Quite a few people working in +the movie industry these days + +doing animations in 3D and +that sort of thing. + +These days, computer scientists +don't get paid as + +much as the actors. + +But they get paid a lot +to produce movies. + +Robots, of course. + +A lot of medical work, +particularly medical imaging. + +This is a picture where someone +has written software + +to try and identify the tumors +in the human brain, and then + +will draw little lines telling +the surgeon where to cut so as + +to do the least damage +and the most good. + +A lot of work in genetics. + +And of course, core things +like making the internet + +actually not crash. + +Fundamentally, what computer +scientists do is they think + +computationally. + +And I hope that you've +understood that that's been + +the theme of 6.00, is how to +formulate problems and think + +computationally. + +This will be, I think, the most +important skill used by + +certainly scientists and +engineers but, in fact, + +everybody by the middle of the +21st century or sooner. + +People will just do everything +computationally. + +And just as once upon a time +maybe it's still important + +everyone learn to read and +write and do a little + +arithmetic, people will think +that computation is exactly as + +important and that you'll have +to know how to formulate + +problems computationally +to survive in society. + +The process, and this is what +we've been doing all term, is + +not an easy one. + +But it's not an impossible +one either. + +We begin by identifying and +inventing useful abstractions. + +Everything we do is an +abstraction of reality. + +And as we've gone through the +second half of the term, + +almost every interesting +computation we've designed + +starts with inventing classes +that give us useful data + +abstraction or functions that +compute useful things. + +And that's sort of what +we start with. + +We start with some existing set +of abstractions, and we + +invent new ones that +will help us think + +about the current problem. + +We then formulate the solution +to the problem as a + +computational experiment and +then design and construct a + +sufficiently efficient +implementation. + +It doesn't have to be the most +efficient one possible. + +It just has to be efficient +enough that we can run it and + +get an answer. + +Of course, before we trust +the answer, as with any + +experimental apparatus-- + +and it is an experimental +apparatus, a program-- + +we need to validate the +experiment, convince ourselves + +that when we run it, we should +believe the answer. + +That's the process +of debugging. + +And I'm sure it's a process +that all of you have spent + +more time on this term then +you might have liked. + +I hope by now you feel you are a +little bit better at it than + +you used to be. + +Once we think we've got the +experiment put together + +properly, we run it. + +We then evaluate the results. + +And then we repeat as +needed, the classic + +iterative style of science. + +And a lot of this, of course, is +what you would have learned + +in your chemistry lab or your +physics lab or the bio lab in + +designing any experiment. + +You have to go through +a lot of these steps. + +And the difference is these +are all computational + +experiments. + +So we think of there +are two ways of + +computational thinking. + +There's abstraction. + +You have to choose the +right abstraction. + +Typically, we operate in terms +of multiple layers of + +abstraction simultaneously. + +And this is an important part +of thinking computationally. + +We have to be able to not worry +about, say, the details + +of how floating point numbers +were implemented, but just + +assume it's a good + +approximation of the real numbers. + +That's one level +of abstraction. + +And another level of +abstraction, we think about + +bus stop queues. + +And maybe we have to implement +those ourselves. + +And then we have to think about +the relationships among + +the layers. + +A key thing that makes +computational abstractions + +different from so many others +is we can automate them. + +So we often think about +abstractions as we go through + +life and think about how to cope +with things that are too + +complex to understand. + +We have these various +abstractions. + +Newton gave us some good +abstractions of the physical + +world that let us understand +how things like levers and + +such almost how they work. + +But here we get the big +advantage that we not only can + +invent an abstraction, +we can mechanize it. + +We can do this for +two reasons. + +One, we have a precise and +exacting notation for + +expressing the abstractions +for building our + +computational models. + +This term, that has been Python +and PyLab and NumPy. + +But it could have been Java. + +It could have been C++. + +It could have been MATLAB. + +Doesn't matter very much. + +What matters is that we have a +notation that's precise enough + +that we can actually describe +a computation. + +And we have some machine that +can take a computation written + +in that notation, or a set of +computations actually written + +in that notation, and execute +them and give us results. + +And that's been the big +transformation that has made + +computation so important. + +We've had the notion of +computation long before we had + +machines that could +execute them. + +The Greeks, the Egyptians +understood notions of + +computation, as we've seen +before when we looked at some + +early algorithms. + +Algorithms have been +around a long time. + +But nobody cared very much +until we had machines and + +notations that would let us +actually run the algorithms. + +That came along in +the late '40s. + +And then the world changed +dramatically. + +So some examples of +computational thinking. + +How difficult is this problem, +and how best can I solve it? + +And that's what theoretical +computer scientists spend + +their time thinking about. + +They try to give precise +meanings to these kinds of + +questions so that we can ask +them in the context of, say, + +random access machines or +parallel machines or, more + +lately, quantum machines, how +do we formulate those + +questions precisely? + +And how can we answer them? + +And of course, thinking +recursively is very important. + +Fundamentally, it's the key in +that what we try and do is we + +try and reformulate a seemingly +difficult problem + +into one we already +know how to solve. + +This is what we talked about +before, reduction to a + +previously solved problem. + +And we've looked at different +ways of doing this. + +There is reduction, +as I mentioned. + +There's embedding, where, OK, +our problem is complex. + +We can't reduce it to +a different problem. + +But we can embed a different +problem in it as at least part + +of the solution. + +We can do some transformations, +take one + +problem and transform it +to a different problem. + +Usually, a simpler problem that +we know how to solve. + +We've seen a lot of that. + +That's, of course, what you've +seen in the bus simulation + +you're studying, I hope as-- + +I hope not as I speak, but as +soon as I finish speaking, + +you'll be studying it. + +We've taken a complex problem +and simplified it by + +transforming it into +a simpler problem + +that we can then attack. + +And we've used a lot of +simulation as a mechanism for + +dealing with problems. + +So here's a little recursive +picture. + +Here's one of my favorite +illustrations of recursion. + +I don't know how they +did that, but I + +think it's pretty cool. + +All right. + +That's a very quick +introduction, at a very + +abstract level, what computer +scientists might do. + +I'm gonna spend some time now +on what one particular + +computer scientist does, +and that's me. + +Why did I choose me? + +Well, not because I'm the most +interesting, but because I'm + +the one I know the best. + +So it's kind of easier for me +to talk about my work than + +about somebody else's. + +And the truth be told, it's +not actually my work. + +Like all professors, I claim +credit for the work that my + +students do. + +So all of the work you're going +to see is actually work + +that my students have done. + +Mostly graduate students, +but also some + +very productive UROPs. + +So, I won't give them as much +credit as I should, but you + +should know in your heart that +I didn't do any of this + +actually myself. + +All right. + +What do we do? + +The goals of our research group +is the rather modest one + +of helping people live longer +and better quality lives. + +Other than that, we don't intend +to accomplish anything. + +And we do this mostly in the +medical area by collaborating + +with clinical researchers and +practicing clinicians. + +Along the way we have a lot of +fun pushing the frontiers, the + +state of the art in computer +science, electrical + +engineering, and certainly +medicine. + +We use a lot of the technical +kind of ideas you've seen this + +semester and that you'll see in +almost any computer science + +course you take. + +We do a lot of machine learning +and data mining. + +I'll explain why shortly. + +We do a lot of algorithm design +because a lot of the + +problems we're trying to solve +are too complex to solve if + +you're not clever about +how you solve them. + +We do some signal processing. + +I'll explain why we do that. + +And a lot of just plain-old +software systems are needed. + +Do we use databases? + +How we build software that +injects electrical signals + +into people's brains? + +So we spend a fair amount of +time trying to convince + +ourselves it actually works, +doesn't inject the wrong + +signals at the wrong time. + +But that might be fun too. + +And these are just the +logos of some of the + +hospitals we work with. + +So what are some of the problems +we try and deal with? + +Probably our longest standing +project has to do with medical + +telepresence. + +These hands do not belong +to a basketball player. + +These are normal sized hands +like yours or mine. + +That is not a normal +sized baby. + +This is not a Photoshop photo. + +This is a real photo. + +This is a very small +premature baby. + +And we have spent a lot of +time working with groups + +figuring out how to provide +better outcomes for these tiny + +little, very delicate people. + +A problem is that a lot of +these babies are born-- + +if these babies are born in the +right hospital, Brigham + +and Women's Hospital or +something close to Children's + +Hospital or MGH, they have +very good outcomes. + +They tend to survive, and they +tend to grow up to be + +relatively normal. + +If these babies are born in a +community hospital that does + +not know how to take care of +these kinds of babies, they + +have very bad outcomes. + +A lot of them die. + +Many of them who survive end up +being permanently disabled. + +Very sad. + +One of the shocking statistics +is that globally there's a + +neonatal death every +10 seconds. + +Shocking number, I think. + +It's just tragic. + +And many of these +are unnecessary. + +And they occur because there's +not adequate care at the point + +where the baby is born. + +And so we've been trying to use +technology to link places + +where these babies might be born +to places where people + +can advise how to take +care of them. + +And it turns out to be a very +interesting set of computer + +networking communications +problems. + +You can't just use Skype +for reasons I won't + +have time to go into. + +But it's very exciting. + +It uses a lot of computer +science, a lot of medicine, + +but mostly computer science, +in this case. + +And we're actually currently +running some trials in + +conjunction with Children's +Hospital Boston where they're + +actually trying to look at +babies born elsewhere. + +Another problem we've been +looking at is health-care + +associated infections. + +Approximately 1 in 20 hospital +visits results in the patient + +contracting an infection totally +unrelated to the + +reason they entered +the hospital. + +And today it's among the top ten +leading causes of death in + +the United States. + +Somebody enters a hospital for +a reason x, picks up an + +infection unrelated +to x, and dies. + +Not a very good outcome. + +And it's particularly +discouraging because, in + +principle, these infections +should be preventable. + +You shouldn't acquire a +life-threatening infection + +while you're in the hospital. + +But people do. + +We've been trying to +understand why. + +We've been working on this +project with Microsoft, which + +has provided us with data from +4.5 million different hospital + +visits and about 2000 pieces of +information per visit, lab + +tests, drug tests, who the +doctors were, who the nurses + +were, what rooms they were in. + +And we're trying to study-- +these are pictures of some of + +the most obnoxious of +these infections-- + +and we've been trying to figure +out what's causing them + +and what can be done +not to cause them. + +This has been primarily a +machine learning project. + +We've been struggling with it. + +We've been dealing with exactly +some of the issues we + +talked about in class. + +Which features are +most important? + +How should you weight the +different features? + +How can we reduce the number +of features so that we can + +actually finish our +computations? + +We've been using different kinds +of clustering, different + +kinds of supervised learning, +many different techniques. + +And we're beginning to get a +handle here on, in fact, what + +are some of the causes of these +infections and what + +could they be done. + +Some of the things are +very disturbing. + +Some of them, a lot of them, +seem to be caused by drugs + +that are given in +the hospital. + +And maybe we can substitute +one drug for another if we + +understand that. + +At least in some cases they seem +to be related to things + +like what room you happen to be +placed in, suggesting that + +maybe they're not cleaning +the rooms adequately. + +Things like that. + +All right. + +Another project, probably our +biggest sets of projects, have + +to do with extracting +information from + +physiological signals. + +We've been focusing on the +heart, the brain, and the + +connected anatomy. + +For those of you who don't +happen to be biology or course + +20 majors, here's where the +heart and the brain are + +located and what +they look like. + +Some of the examples we're +interested in are predicting + +adverse cardiac events. + +And for that you can think +about death from a heart + +event, heart attack. + +And we spent a lot of time +dealing with epilepsy. + +So let me give a little bit more +detail about these two + +examples because each of +them relate to things + +we've covered in 6.00. + +So epilepsy, an interesting +disease. + +Surprisingly, it affects about +1% of the world's population. + +When I first heard this, +I was astounded. + +Because gee, 1 out +of 100 people + +that I know have epilepsy? + +And the truth is, yes. + +I just didn't know it. + +I've been amazed, since it's +become known that I do + +research in this area, the +number of people I've known + +for years who come up to me +say, you know, I never + +mentioned this before, but I +have epilepsy, or my kid has + +epilepsy or my parent has +epilepsy, and I have some + +questions now that you're +supposed to be + +an expert on this. + +And I give them the usual +caveats, you know, I'm not a + +doctor, I just play +one on television. + +But then I tell them go talk +to one of my students. + +They're not doctors either, +but they're really smart. + +Probably smarter than +your doctor. + +All right. + +Why is it underestimated when +we do it ourselves? + +Well, because they're +still some stigmas. + +A few hundred years ago, they +burned women in Salem, + +Massachusetts, who had epilepsy +because they thought + +the seizures meant they were +possessed by the devil. + +Today, if you tell the Registry +of Motor Vehicles + +that you have epilepsy, they +won't let you drive an + +automobile. + +So people tend not +to announce it. + +What's it characterized by +is a recurrent seizure. + +A seizure is abnormal electrical +activity that + +originates and persists +in the brain. + +Number of causes. + +It can be acquired. + +It can be inherited. + +There's manifest different +symptoms. + +Most of them do not +look like what's + +portrayed on the Simpsons. + +Slightly more realistically, +and maybe more horrifying. + +Here's a picture of a young +girl, a movie, you're gonna + +see a seizure. + +It's not pleasant, I'm +gonna warn you. + +What I want you to notice +is two things. + +(1) She's all happy, and +the seizure seems + +to come out of nowhere. + +She doesn't expect it. + +She doesn't know she's +going to have. + +It just hits. + +That's very important. + +(2) She happened to be in the +clinic at the time wearing + +this funny looking cap, with +it has electrodes in it. + +Just sits on the scalp. + +And here is a record of the +electrical activity at the + +surface of her scalp. + +And what you'll see is a quick +slight change on it just + +before the seizure hits, and +then enormous changes during + +the seizure. + +Turns out that the enormous +changes during the seizure + +have nothing really to +do with the seizure. + +They have to do with +muscle activity. + +As you'll see once the seizure +hits, there's a lot of ugly + +muscle activity. + +All right. + +Let's look at it. + +Uh oh. + +All right. + +Let's look at it-- + +I thought I had put the links in +here that should have done + +it, but who knows. + +I know where to find them. + +[VIDEO PLAYBACK] + +[SINGING IN FOREIGN LANGUAGE] + +[SPEAKING FOREIGN LANGUAGE] + +[END VIDEO PLAYBACK] + +PROFESSOR: So kind of scary. + +Certainly when I've been seeing +them actually happen, + +I've found it terrifying +to watch. + +That kind of-- it's called +a tonic-clonic seizure. + +They seem- I emphasize the word +'seem' -- unpredictable. + +The interesting thing about +these seizures, or an + +interesting thing, is they're +self-limiting. + +In a few minutes, that young +lady or girl's seizure will be + +over, not because anybody +intervened but because the + +brain resets itself. + +Then it will take-- + +in this case, probably took her +about an hour to recover + +and get back to normal, +which is not good. + +But after that, everything was +as before the seizure. + +The difficulty is because +they're unpredictable, there + +are huge injuries. + +Imagine she'd been riding +a bicycle when that hit. + +Well, something catastrophic. + +Or more simply, imagine she'd +been going down a flight of + +stairs or in a bathtub. + +Any one of a number of things +would have resulted in this + +potentially catastrophic +collateral damage after the + +seizure or during the seizure. + +And indeed people who +have epilepsy, you + +can see their scars. + +It's awful. + +It can result in death, about +1 per 100 patient years. + +It's called the sudden +unexpected + +death in epilepsy patients. + +So what we wanted to do is see +whether we could detect the + +seizures and give a +little warning. + +The notion being that even if +you couldn't do anything about + +the seizure, if you could give +somebody, say, even five + +seconds warning, they +could sit down + +before they fell down. + +They could get out of the tub. + +They could back away +from the stove. + +All sorts of things. + +Furthermore, if you could use +technology to signal to + +someone else that there was +about to be a seizure, help + +could arrive. + +Also potentially a good thing. + +Turns out there are now some +fast-acting drugs that if you + +put under the tongue can +ameliorate the seizure. + +These have not yet been approved +by the FDA, but soon. + +And we were particularly +interested in neural + +stimulation. + +If we ejected electrical current +into the brain at + +exactly the right moment, could +we offset essentially + +the effect of the seizure +and do a reset? + +And maybe stop the seizure or +abort it, prevent it, or at + +least reduce the long +term recovery time. + +The thing to keep in mind for +the seizure is there were two + +distinct onset times. + +What you saw if you're looking +at the girl was what's called + +the clinical onset, when there's +some clinical event. + +If you were able to not look at +the person and instead look + +at the EEG, not so easy, you +would have seen that there was + +an electrographic onset that +preceded the clinical onset. + +We know, in fact, since the +clinical effects are caused by + +the electrical activity, there +will always be abnormal + +electrical activity +prior to any + +abnormal clinical activity. + +And so the hope was that we +could detect the electrical + +activity early. + +Now that's not so easy. + +What makes it hard is +that the EEG, the + +electroencephalograph, differs +greatly across patients. + +First of all, people with +epilepsy have abnormal + +baseline EEG. + +Even when they're not having a +seizure, bizarre things are + +going on in their brains + +electrically, all unusual things. + +And so they don't +look like people + +who don't have epilepsy. + +And it varies tremendously +across patients. + +So for about 35 years, people +attempted to build generic + +detectors that would detect +seizures in everybody. + +And they've not worked +well at all. + +Every time a hospital buys an +EEG machine, it comes with a + +detector built in. + +And usually the first thing they +do is they turn them off + +because the false alarm rate is +so high that it's like the + +boy who cried wolf. + +They're just saying seizure, +seizure, seizure, and people + +start ignoring it. + +The good news is it's pretty +consistent seizure onset for a + +particular individual. + +That suggests you should build +not generic detectors, but + +patient specific detectors. + +And we've been working +on using machine + +learning to do that. + +And in fact, it's been +highly successful. + +We've done several retrospective +studies + +indicating that it works +really well. + +And we're now doing +a substantial + +prospective study -- + +in progress at MGH. + +And as part of that, we're +actually working at turning on + +a neuro-stimulator that we hope +will attenuate the effect + +of the seizure. + +And I emphasize hope because we +don't have enough data to + +know if it works. + +It's part of what goes +on in this business. + +But it's certainly been an +interesting project. + +All right. + +Heart attacks. + +Let's look at that. + +And I'll go to the easy +way to show them. + +I should warn you, you're gonna +see something that's not + +very pleasant. + +You're actually gonna +see somebody die. + +This was actually a person who +was playing in a soccer game + +and died while the game +was being televised. + +All right. + +What I want to show you is this +didn't have to happen. + +We're now gonna see another +televised soccer game where + +the player had exactly the same +event but with a rather + +different outcome. + +So look at the upper center of +field and you'll see the + +person has collapsed, much the +same way it happened before. + +Now watch the body convulse. + +You'll see the knees +kick up there. + +And now comes the miracle. + +He sits up. + +He leaves the field and, in +fact, he later asked if he can + +reenter the game. + +The coach, to the coach's +everlasting credit, said no. + +Clearly the right decision. + +So it's amazing really +that this happens. + +So what was the difference +between the two? + +well, we see this here. + +There are things you can do. + +So in acute coronary syndrome, +think of it as some sort of a + +heart attack. + +They're very common, about +one and a quarter million + +per year in the US. + +15% to 20% of these people will +suffer a cardiac-related + +death within the next +four years. + +If you could figure out who +were the people at highest + +risk of different events and +choose the treatment properly, + +for example, implant an +implantable cardiac + +defibrillator, you could +save these lives. + +And that was what we +saw in our movies. + +That the first patient, first +person, the one who died, did + +not have a defibrillator. + +The second person, the one +who survived, did. + +So he collapsed on the field. + +The defibrillator sensed that +his heart had stopped, gave it + +an electric shock. + +You've all seen this in +television where they put the + +paddles on and they +say, clear. + +And then there's this moment of +drama where everyone stares + +at the EKG machine, and it +goes from a flat line to + +suddenly up and down, and +everyone goes, ah. + +Well that's exactly what +happened here. + +And that convulsion was this +huge electrical shock getting + +sent through the person's body +which restarted the heart, + +saved his life. + +Probably, if the other player +had had an ICD, he would not + +have died either. + +So great technology. + +Well, yes and no. + +This was a study in the New +England Journal of Medicine + +not so long ago, a very good +control study, where they + +matched patients with ICDs and +patients without ICDs and over + +72 months tracked which ones +lived and which ones died. + +Well, the disturbing news is +there isn't much difference + +between the red line +and the blue line. + +So these people had what was +essentially a, well, which was + +about a $50,000 implant and +various kinds of risks and + +inconvenience and discomfort, +et cetera, and on average it + +didn't save lives. + +Oh, dear. + +In fact, 90% of the people who +got them-- and this is not + +just in this study. + +This is in every study- receives +zero, actually less + +than zero medical benefit +from the ICD. + +How do we know that? + +Well, remember, it only turns on +when it senses the heart is + +in trouble. + +For 90% of the people who get +it, it never energizes because + +the heart doesn't +get in trouble, + +or detectable trouble. + +So what we see, if we look at +a little more detail in this + +study, is that for sudden +cardiac death, the kind of + +death we saw in those videos, +or non-death, + +the ICD reduces that. + +Unfortunately, it increases +other causes of death, for + +example, infections related to +the surgery, et cetera, those + +unfortunate hospital acquired +infections, for example, we + +talked about earlier. + +So what we see here is we have +a technology that if we knew + +whose heart was likely to +stop or go into serious + +fibrillation, beating +uncontrollably, and we only + +gave those people ICDs, +we could save an + +enormous number of lives. + +But currently we don't know +who's in that population, and + +therefore we don't know +who should get them. + +So we use other mechanisms +deciding who should get them. + +And we're wrong most of the +time, doing more harm than + +good on those patients +for whom we're wrong. + +OK. + +Well, how do the people +predict it today? + +The usual things. + +Are you male or female? + +Do you have high +blood pressure? + +Diabetes? + +What's your cholesterol level? + +BMP? + +Various other kinds of things. + +Electrocardiograms, +which look at-- + +it's an echo cardiogram +that looks at the + +activity of the heart. + +Is the blood flowing +through it OK? + +EKGs. + +Many different methods for +analyzing the electrical + +activity, et cetera. + +We played with many of +these techniques. + +The one I want to tell you about +today, because it's the + +most closely related to 6.00 +material, is what we think of + +the Tolstoy approach to +risk stratification. + +So Tolstoy is famous for saying +that happy families are + +all alike, but every +unhappy family is + +unhappy in its own way. + +So we generalize that, or +specialized it maybe, to say + +that happy hearts are all alike, +but every unhappy heart + +is different, and then did some +fairly simple work to + +quantify the difference between +electrical activities + +in different people's hearts, +converting it to symbols. + +You don't have to worry +about that. + +We used dynamic programming as +an important part because we + +were looking at roughly a +billion heart beats and so we + +needed to make it run fast. + +And then we used clustering to +identify patients whose hearts + +we thought were similar +to one another. + +Here are some results. + +These are people who had an +acute coronary syndrome. + +So the dominant group, the +biggest group, the quote + +"people who we thought were +most likely to be fine"-- + +because remember, most +people are fine + +after a heart attack-- + +457 patients in this particular +data set. + +And you can see that they +did pretty well. + +A very small fraction +of them died. + +Can't see it from this angle, +but come out here. + +Yeah, less than 1%. + +But then we looked at +people who were + +in these other clusters. + +And in fact, we used a glomerate +of hierarchical + +clustering to do this. + +And in cluster A, which had 53 +patients, well, 3.77% died. + +If you happened to fall +in cluster C, you were + +at very high risk. + +And we can just see that there's +a big difference here. + +And so the notion is could we +have used this to predict in + +advance who was most likely to +benefit from the various kinds + +of treatments? + +All right. + +Again, very quick just to +give you the details-- + +not the details, the overview +that the kinds of things that + +we cover in this course are +actually quite useful in + +solving real practical +problems. + +All right. + +Let me wrap up the term. + +So I hope most of you feel +you've come a long way-- + +maybe you prefer this picture. + +That if you think about the +kinds of problems and + +struggles you had three months +ago in getting tiny little + +programs to work and think about +how easy those would be + +for you today, you should have +some appreciation that you've + +really taught yourself a lot. + +And you really taught it to +yourself, by doing the problem + +sets, in many ways, right. + +We've tried to help, but +learning is very much up to + +the individual who's +doing the learning. + +But I'm certainly impressed in +looking at the kinds of really + +pretty complicated problems +you guys can now solve. + +We looked at six major topics. + +Clearly, you learned a notation +for expressing + +computations, and +that was Python. + +And I hope you don't think +that's the only notation you + +can use and that if you take +a course that uses MATLAB, + +you'll say, oh, this +is just the same. + +It's easy. + +Or Java or anything else. + +Learning programming +languages is easy. + +Once you've learned one, the +next one is much easier. + +Harder was learning about the +process of writing and + +debugging programs. + +You've learned that, I think, +largely through experience. + +You've learned about the process +of moving from a + +problem statement, something +as vague as should shuttle + +buses be bigger or faster +to improve service, to a + +computational formulation of the +problem and a method for + +solving a problem. + +And we've looked at lots +of different methods. + +You've learned basic recipes, +algorithms, things like + +dynamic programming, things +like depth-first search, + +things like decision trees, +that you'll be able to use + +again and again. + +The good news is there are only +a really small number of + +important recipes. + +And once you've mastered those, +you just use them over + +and over again to solve +new problems. + +Spent a lot of time on using +simulations to shed light on + +problems that don't +easily succumb + +to closed form solutions. + +And I think that's really +the place where + +computation is so important. + +There are a lot of problems +where you can turn them into a + +set of differential equations, +maybe solve the equations, and + +you're done. + +Oh, we'll write programs to do +those because we're lazy. + +But in principle, +you could solve + +those without a computer. + +But in fact, the thing you can't +do without a computer is + +these messy problems that are +most of what goes on in the + +real world, where there's +randomness, and things like + +that, and there is no +simple formula that + +gives you the answer. + +And what you have to do is write +a simulation and run it + +and see what goes on. + +And that's why we spent so +much time on simulation + +because it really is +increasingly the + +thing people use. + +And we learned about how to +use computational tools to + +help model and understand data, +how to do [?] plots, a + +small amount of statistics, +machine learning, just + +dealing with data. + +Why Python? + +It's pretty easy to +learn to use. + +Compared to most other +programming languages like, + +say, C++ or Java, +Python is easy. + +The syntax is simple. + +It's interpretive, which +makes debugging easier. + +You don't have to worry about +managing memory as you do in, + +say, C, right. + +You get a big list or +dictionary, and + +magically it exists. + +And when you don't need it +any more, it's gone. + +It's modern. + +It supports the currently +stylish mode of + +object-oriented programming in +a nice way with its classes + +and things like that. + +So indeed what you would hear +about in a Java class, we can + +cover almost all the + +interesting things with Python. + +And it's increasingly popular. + +It's used in an increasing +number of subjects at MIT. + +A lot of course 6 subjects, but +also a lot of course 20 + +subjects, course 9 subjects, +over and over again. + +It's becoming, probably, the +most popular language at MIT + +and at other universities. + +Increasingly it's used +in industry. + +And as you've seen with PyLab, +the libraries are amazing. + +And so PyLab, Random, et cetera, +there's just a lot of + +stuff you can get for free +if you're living in + +the world of Python. + +The main thing in writing, +testing, and bugging programs, + +I hope you've learned, is to +take it a step at a time. + +Understand the problem. + +Think about the overall +structure and algorithms + +separately of how you express +them in the programming + +language, right. + +We can talk about dynamic +programming conceptually + +without worrying about +how to code it up. + +Always break the problem +into small parts. + +Identify useful abstractions. + +Code and test each unit +independently. + +Worry about functionality +first. + +Get it to work. + +Get it to give you +the right answer. + +Then worry about making it +do that more quickly. + +But separate those things. + +Start with some pseudo code. + +Then above all, be systematic. + +When debugging, think about +the scientific method of + +forming hypotheses, forming +experiments that can test the + +hypotheses, running +the experiment, + +checking the results. + +Don't try and do +it too quickly. + +Just be slow and careful. + +Slow and steady will win +the race in debugging. + +And when your program +behaves badly-- + +and the sad news is no matter +how many years you spend at + +it, you will write programs that +don't work the way you + +think they should +the first time-- + +ask yourself why it did what it +did, not why didn't it do + +what you wanted to do. + +It's a lot easier to debug +from the how come it's + +behaving the way it is then why +isn't it behaving the way + +I want it to behave. + +In going from problem statement +to computation, + +break the problem into +smaller problems. + +Try and relate your problem to +a problem that somebody else, + +ideally, has already solved. + +For example, is it a +knapsack problem? + +Is it a shortest path problem? + +If so, good, I know how +to solve those. + +Think about what kind of output +you might want to see. + +What should the plots be like? + +I usually design the output +before I design the program. + +Often you can formulate things +as an optimization problem. + +Pull back. + +Say, well, can I formulate this +as finding the minimum or + +maximum values satisfying an +objective function and some + +set of constraints? + +If I can, it's an optimization +problem, and therefore I know + +how to attack it. + +And don't be afraid to think +about approximate solutions. + +Sometimes you're just gonna not +actually be able to solve + +the problem you want to solve. + +And so you'll find a solution to +a simpler problem, and that + +will be good enough. + +Sometimes you can actually solve +the problem by finding a + +series of solutions that +approaches, but may never + +reach, a perfect answer. + +Probably the third week in the +course, we looked at Newton's + +method as an example of +that kind of problem. + +And then there are algorithms. + +We looked at big O notation, +various kinds of algorithms, a + +lot of kinds. + +You've already - I sent a list +of specific algorithms. + +And particularly, we looked +at optimization problems. + +We spent a lot of time on +modeling the world, keeping in + +mind that the models +are always wrong. + +But nevertheless, they're +often useful. + +They provide abstractions +of reality. + +So we looked at two kinds of +simulation models, Monte Carlo + +and queuing networks. + +We looked at statistical models, +for example, linear + +regression. + +And we looked at some graph +theoretic models. + +Those are not the only +techniques, but they're very + +useful techniques. + +We looked at making +sense of data. + +We talked about statistical +techniques. + +How to use them well. + +How to use them badly. + +We looked at plotting. + +And we spent some time on +machine learning, supervised + +and unsupervised and feature +vectors, and spent a lot of + +time talking about how do you +choose the features, because + +fundamentally that's typically +the difference between success + +and failure in the world +of machine learning. + +Throughout it all, the pervasive +themes were the + +power of abstraction and +systematic problem solving. + +So what's next? + +Many of you have worked really +hard this semester. + +We know that. + +And the TAs and LAs and +I all appreciate that. + +And I thank you sincerely +for the effort you + +put into the course. + +Only you know your return +on the investment. + +I hope it's good. + +Remember as you go forward in +your careers that you can now + +write programs to solve problems +you need to solve. + +Don't be afraid to do it. + +If you like this, there are +plenty of other CS courses + +that you now could take. + +You're actually equipped, +probably, to take any one of + +these four courses based upon +what you've learned in 6.00. + +You could major in course 6 or +think about the new major in + +computer science and +molecular biology. + +And you're certainly qualified +to go off and to look for + +UROPs that involve serious +programming. + +All right. + +Wrapping up with some famous +last words, these were words + +that some famous people said +as they were about to die. + +An actor, Douglas Fairbanks +senior, was asked by a family + +member, how are you feeling? + +He said, never felt better. + +And then that was the last +thing he ever said. + +In contrast, the last thing +Luther Burbank was reported to + +have said, a famous scientist, +was, I don't feel so good. + +He was a scientist rather +than actor. + +He had a better appreciation +of the state of the world. + +Conrad Hilton, who you probably +think of as Paris + +Hilton's grandfather, but +actually is more well known in + +some circles for running the +Hilton hotels, his last words + +when his family asked him-- they +knew he was dying-- is + +there anything you +want us to know + +about running the business? + +And he said, yes, leave the +shower curtain on the inside + +of the tub. + +And that's advice, I have to +confess, my wife has given me + +on several occasions. + +Archimedes, basically before +he was taken away and + +executed, asked, could he please +finish solving the + +problem he was working on. + +You know, I could imagine some +poor 6.00 student who's about + +to be carted away by the police +saying, can I finish my + +problem set first, please? + +Actually, I can't +imagine that. + +And finally, this US Civil War +general, John Sedgwick, was + +reputedly-- + +and this is, I believe, a true +story-- said, talking about + +the snipers from the other side +who were quite far away, + +that telling his people, don't +be afraid, they couldn't get + +an elephant at this distance. + +And if you go to the site of the +battle, you'll find this + +plaque describing the death of +John Sedgwick who was shot and + +killed immediately upon saying +this by one of said snipers. + +It says something about generals +that probably is + +still true today. + +All right, quick reminders +and then we're done. + +There's a final exam. + +If you haven't done the +underground guide, go do it. + +These are things I said at the +beginning of the lecture. + +I'm just repeating them. + +Thanks a lot. + +Good luck in the final 6.00, +all your finals. + +And then more importantly, +have a great summer. \ No newline at end of file diff --git a/A76FlzncnbU.txt b/A76FlzncnbU.txt new file mode 100644 index 0000000000000000000000000000000000000000..0d7faf05ee6486001d678c51f419f7a3752a6f6d --- /dev/null +++ b/A76FlzncnbU.txt @@ -0,0 +1,1283 @@ +align:start position:0% + +I'm here to talk to you today about why + + align:start position:0% +I'm here to talk to you today about why + + + align:start position:0% +I'm here to talk to you today about why +the mission of the World Bank's new + + align:start position:0% +the mission of the World Bank's new + + + align:start position:0% +the mission of the World Bank's new +office of sustainable development should + + align:start position:0% +office of sustainable development should + + + align:start position:0% +office of sustainable development should +be to promote sustainable economic + + align:start position:0% +be to promote sustainable economic + + + align:start position:0% +be to promote sustainable economic +development first I will explain what + + align:start position:0% +development first I will explain what + + + align:start position:0% +development first I will explain what +sustainable development means in the + + align:start position:0% +sustainable development means in the + + + align:start position:0% +sustainable development means in the +context of global investment in + + align:start position:0% +context of global investment in + + + align:start position:0% +context of global investment in +developing countries then I will discuss + + align:start position:0% +developing countries then I will discuss + + + align:start position:0% +developing countries then I will discuss +why the World Bank ought to put a + + align:start position:0% +why the World Bank ought to put a + + + align:start position:0% +why the World Bank ought to put a +premium on these particular kinds of + + align:start position:0% +premium on these particular kinds of + + + align:start position:0% +premium on these particular kinds of +investments and why I ought to promote + + align:start position:0% +investments and why I ought to promote + + + align:start position:0% +investments and why I ought to promote +environmental protection in its work to + + align:start position:0% +environmental protection in its work to + + + align:start position:0% +environmental protection in its work to +understand sustainable development we + + align:start position:0% +understand sustainable development we + + + align:start position:0% +understand sustainable development we +must first understand that the + + align:start position:0% +must first understand that the + + + align:start position:0% +must first understand that the +well-being of the economic system is + + align:start position:0% +well-being of the economic system is + + + align:start position:0% +well-being of the economic system is +intrinsically tied to the well-being of + + align:start position:0% +intrinsically tied to the well-being of + + + align:start position:0% +intrinsically tied to the well-being of +the environment the economy's + + align:start position:0% +the environment the economy's + + + align:start position:0% +the environment the economy's +functioning depends on inputs from + + align:start position:0% +functioning depends on inputs from + + + align:start position:0% +functioning depends on inputs from +nature which are then exchanged among + + align:start position:0% +nature which are then exchanged among + + + align:start position:0% +nature which are then exchanged among +various market actors and eventually + + align:start position:0% +various market actors and eventually + + + align:start position:0% +various market actors and eventually +output as waste into the environment the + + align:start position:0% +output as waste into the environment the + + + align:start position:0% +output as waste into the environment the +economy grows at an unsustainable rate + + align:start position:0% +economy grows at an unsustainable rate + + + align:start position:0% +economy grows at an unsustainable rate +when the rate of resource consumption + + align:start position:0% +when the rate of resource consumption + + + align:start position:0% +when the rate of resource consumption +and waste production exceeds the rate in + + align:start position:0% +and waste production exceeds the rate in + + + align:start position:0% +and waste production exceeds the rate in +which the environment can regenerate and + + align:start position:0% +which the environment can regenerate and + + + align:start position:0% +which the environment can regenerate and +absorb waste products + + align:start position:0% +absorb waste products + + + align:start position:0% +absorb waste products +it is also important to note here that + + align:start position:0% +it is also important to note here that + + + align:start position:0% +it is also important to note here that +economic growth is simply a measure of + + align:start position:0% +economic growth is simply a measure of + + + align:start position:0% +economic growth is simply a measure of +total resource throughput it says + + align:start position:0% +total resource throughput it says + + + align:start position:0% +total resource throughput it says +nothing about happiness health safety or + + align:start position:0% +nothing about happiness health safety or + + + align:start position:0% +nothing about happiness health safety or +sense of community within the region now + + align:start position:0% +sense of community within the region now + + + align:start position:0% +sense of community within the region now +that we've defined growth it can + + align:start position:0% +that we've defined growth it can + + + align:start position:0% +that we've defined growth it can +contrast it the concept of development + + align:start position:0% +contrast it the concept of development + + + align:start position:0% +contrast it the concept of development +development is the qualitative + + align:start position:0% +development is the qualitative + + + align:start position:0% +development is the qualitative +improvement of resource efficiency + + align:start position:0% +improvement of resource efficiency + + + align:start position:0% +improvement of resource efficiency +within a region to invest in projects + + align:start position:0% +within a region to invest in projects + + + align:start position:0% +within a region to invest in projects +that promote development in poor + + align:start position:0% +that promote development in poor + + + align:start position:0% +that promote development in poor +countries is to invest in projects that + + align:start position:0% +countries is to invest in projects that + + + align:start position:0% +countries is to invest in projects that +allow people to produce more but the + + align:start position:0% +allow people to produce more but the + + + align:start position:0% +allow people to produce more but the +resources they already have these kinds + + align:start position:0% +resources they already have these kinds + + + align:start position:0% +resources they already have these kinds +of projects might involve investing in + + align:start position:0% +of projects might involve investing in + + + align:start position:0% +of projects might involve investing in +education investing in the construction + + align:start position:0% +education investing in the construction + + + align:start position:0% +education investing in the construction +of local hospitals and clinics or + + align:start position:0% +of local hospitals and clinics or + + + align:start position:0% +of local hospitals and clinics or +investing in research and development of + + align:start position:0% +investing in research and development of + + + align:start position:0% +investing in research and development of +crop seeds that are less resource + + align:start position:0% +crop seeds that are less resource + + + align:start position:0% +crop seeds that are less resource +intensive while projects that promote + + align:start position:0% +intensive while projects that promote + + + align:start position:0% +intensive while projects that promote +growth simply increase production and + + align:start position:0% +growth simply increase production and + + + align:start position:0% +growth simply increase production and +consumption products projects that + + align:start position:0% +consumption products projects that + + + align:start position:0% +consumption products projects that +promote development increase the + + align:start position:0% +promote development increase the + + + align:start position:0% +promote development increase the +efficiency in production production + + align:start position:0% +efficiency in production production + + + align:start position:0% +efficiency in production production +consumption towards some end that + + align:start position:0% +consumption towards some end that + + + align:start position:0% +consumption towards some end that +enhances human welfare economic growth + + align:start position:0% +enhances human welfare economic growth + + + align:start position:0% +enhances human welfare economic growth +is less important than economic + + align:start position:0% +is less important than economic + + + align:start position:0% +is less important than economic +development because growth usually + + align:start position:0% +development because growth usually + + + align:start position:0% +development because growth usually +measured in terms of GDP is a flawed + + align:start position:0% +measured in terms of GDP is a flawed + + + align:start position:0% +measured in terms of GDP is a flawed +measure of progress there is nothing + + align:start position:0% +measure of progress there is nothing + + + align:start position:0% +measure of progress there is nothing +inherently beneficial about economic + + align:start position:0% +inherently beneficial about economic + + + align:start position:0% +inherently beneficial about economic +this is because growth only implies an + + align:start position:0% +this is because growth only implies an + + + align:start position:0% +this is because growth only implies an +increase in resources throughput it + + align:start position:0% +increase in resources throughput it + + + align:start position:0% +increase in resources throughput it +doesn't take into account whether the + + align:start position:0% +doesn't take into account whether the + + + align:start position:0% +doesn't take into account whether the +resources are being used in ways that + + align:start position:0% +resources are being used in ways that + + + align:start position:0% +resources are being used in ways that +efficiently maximize well-being while + + align:start position:0% +efficiently maximize well-being while + + + align:start position:0% +efficiently maximize well-being while +minimizing resource consumption on the + + align:start position:0% +minimizing resource consumption on the + + + align:start position:0% +minimizing resource consumption on the +other hand economic development is a far + + align:start position:0% +other hand economic development is a far + + + align:start position:0% +other hand economic development is a far +better job of indicating economic + + align:start position:0% +better job of indicating economic + + + align:start position:0% +better job of indicating economic +progress development implies that + + align:start position:0% +progress development implies that + + + align:start position:0% +progress development implies that +resources are being used increasingly + + align:start position:0% +resources are being used increasingly + + + align:start position:0% +resources are being used increasingly +efficient ways the more developed the + + align:start position:0% +efficient ways the more developed the + + + align:start position:0% +efficient ways the more developed the +country is the more benefits from the + + align:start position:0% +country is the more benefits from the + + + align:start position:0% +country is the more benefits from the +resources it has while minimizing its + + align:start position:0% +resources it has while minimizing its + + + align:start position:0% +resources it has while minimizing its +total consumption of these resources as + + align:start position:0% +total consumption of these resources as + + + align:start position:0% +total consumption of these resources as +it becomes more and more clear that + + align:start position:0% +it becomes more and more clear that + + + align:start position:0% +it becomes more and more clear that +people across the world that development + + align:start position:0% +people across the world that development + + + align:start position:0% +people across the world that development +not growth should be our top priorities + + align:start position:0% +not growth should be our top priorities + + + align:start position:0% +not growth should be our top priorities +then the bank's investment goals of the + + align:start position:0% +then the bank's investment goals of the + + + align:start position:0% +then the bank's investment goals of the +in line meet the goals of the rest of + + align:start position:0% +in line meet the goals of the rest of + + + align:start position:0% +in line meet the goals of the rest of +the world this is because investors will + + align:start position:0% +the world this is because investors will + + + align:start position:0% +the world this is because investors will +want the same thing as anyone else the + + align:start position:0% +want the same thing as anyone else the + + + align:start position:0% +want the same thing as anyone else the +maximum amount of benefit they can get + + align:start position:0% +maximum amount of benefit they can get + + + align:start position:0% +maximum amount of benefit they can get +at the lowest cost + + align:start position:0% +at the lowest cost + + + align:start position:0% +at the lowest cost +likewise individuals from recognized + + align:start position:0% +likewise individuals from recognized + + + align:start position:0% +likewise individuals from recognized +development as their goal want to + + align:start position:0% +development as their goal want to + + + align:start position:0% +development as their goal want to +receive the greatest benefit through + + align:start position:0% +receive the greatest benefit through + + + align:start position:0% +receive the greatest benefit through +natural resources they use while + + align:start position:0% +natural resources they use while + + + align:start position:0% +natural resources they use while +minimizing resource consumption as the + + align:start position:0% +minimizing resource consumption as the + + + align:start position:0% +minimizing resource consumption as the +UN's international financial institution + + align:start position:0% +UN's international financial institution + + + align:start position:0% +UN's international financial institution +the World Bank's mission is to reduce + + align:start position:0% +the World Bank's mission is to reduce + + + align:start position:0% +the World Bank's mission is to reduce +property it should do this by promoting + + align:start position:0% +property it should do this by promoting + + + align:start position:0% +property it should do this by promoting +economic development which insurance the + + align:start position:0% +economic development which insurance the + + + align:start position:0% +economic development which insurance the +long run integrity of economic systems + + align:start position:0% +long run integrity of economic systems + + + align:start position:0% +long run integrity of economic systems +if the bank instead chooses to promote + + align:start position:0% +if the bank instead chooses to promote + + + align:start position:0% +if the bank instead chooses to promote +economic growth it will be investing in + + align:start position:0% +economic growth it will be investing in + + + align:start position:0% +economic growth it will be investing in +projects that contribute to constructing + + align:start position:0% +projects that contribute to constructing + + + align:start position:0% +projects that contribute to constructing +an unsustainable economic and social + + align:start position:0% +an unsustainable economic and social + + + align:start position:0% +an unsustainable economic and social +paradigm with incredible inertia the + + align:start position:0% +paradigm with incredible inertia the + + + align:start position:0% +paradigm with incredible inertia the +longer economic growth remains the + + align:start position:0% +longer economic growth remains the + + + align:start position:0% +longer economic growth remains the +dominant measure of progress the more + + align:start position:0% +dominant measure of progress the more + + + align:start position:0% +dominant measure of progress the more +difficult it will be to change our + + align:start position:0% +difficult it will be to change our + + + align:start position:0% +difficult it will be to change our +consumption patterns in business + + align:start position:0% +consumption patterns in business + + + align:start position:0% +consumption patterns in business +practices the ones to ones that are more + + align:start position:0% +practices the ones to ones that are more + + + align:start position:0% +practices the ones to ones that are more +sustainable the world bank need not look + + align:start position:0% +sustainable the world bank need not look + + + align:start position:0% +sustainable the world bank need not look +very far in seeking out philosophical + + align:start position:0% +very far in seeking out philosophical + + + align:start position:0% +very far in seeking out philosophical +justification for taking this measure + + align:start position:0% +justification for taking this measure + + + align:start position:0% +justification for taking this measure +utilitarianism the common philosophical + + align:start position:0% +utilitarianism the common philosophical + + + align:start position:0% +utilitarianism the common philosophical +foundation for much of existing + + align:start position:0% +foundation for much of existing + + + align:start position:0% +foundation for much of existing +environmental policy tells us that we + + align:start position:0% +environmental policy tells us that we + + + align:start position:0% +environmental policy tells us that we +should take the forward-looking utility + + align:start position:0% +should take the forward-looking utility + + + align:start position:0% +should take the forward-looking utility +maximizing actions choosing to make + + align:start position:0% +maximizing actions choosing to make + + + align:start position:0% +maximizing actions choosing to make +investments that promote developments + + align:start position:0% +investments that promote developments + + + align:start position:0% +investments that promote developments +not + + align:start position:0% +not + + + align:start position:0% +not +it's just such an action this is because + + align:start position:0% +it's just such an action this is because + + + align:start position:0% +it's just such an action this is because +human wellbeing in the long run is + + align:start position:0% +human wellbeing in the long run is + + + align:start position:0% +human wellbeing in the long run is +maximized from the very goal of the + + align:start position:0% +maximized from the very goal of the + + + align:start position:0% +maximized from the very goal of the +economic system is to provide to human + + align:start position:0% +economic system is to provide to human + + + align:start position:0% +economic system is to provide to human +needs while maintaining the integrity of + + align:start position:0% +needs while maintaining the integrity of + + + align:start position:0% +needs while maintaining the integrity of +the environment in the long run human + + align:start position:0% +the environment in the long run human + + + align:start position:0% +the environment in the long run human +welfare certainly not maximized when the + + align:start position:0% +welfare certainly not maximized when the + + + align:start position:0% +welfare certainly not maximized when the +goal of the economic system is to simply + + align:start position:0% +goal of the economic system is to simply + + + align:start position:0% +goal of the economic system is to simply +maximize consumption without regard to + + align:start position:0% +maximize consumption without regard to + + + align:start position:0% +maximize consumption without regard to +the system's longer in viability such + + align:start position:0% +the system's longer in viability such + + + align:start position:0% +the system's longer in viability such +economic protocol uses our collective + + align:start position:0% +economic protocol uses our collective + + + align:start position:0% +economic protocol uses our collective +welfare because it leads to depletion of + + align:start position:0% +welfare because it leads to depletion of + + + align:start position:0% +welfare because it leads to depletion of +economic inputs Natural Resources then + + align:start position:0% +economic inputs Natural Resources then + + + align:start position:0% +economic inputs Natural Resources then +uses raw materials as well as the + + align:start position:0% +uses raw materials as well as the + + + align:start position:0% +uses raw materials as well as the +accumulation of economic outputs which + + align:start position:0% +accumulation of economic outputs which + + + align:start position:0% +accumulation of economic outputs which +are manifested by landfills and garbage + + align:start position:0% +are manifested by landfills and garbage + + + align:start position:0% +are manifested by landfills and garbage +patches neither of these outcomes at + + align:start position:0% +patches neither of these outcomes at + + + align:start position:0% +patches neither of these outcomes at +once anyone would want if the road + + align:start position:0% +once anyone would want if the road + + + align:start position:0% +once anyone would want if the road +bank's goal is to reduce poverty in the + + align:start position:0% +bank's goal is to reduce poverty in the + + + align:start position:0% +bank's goal is to reduce poverty in the +long run you must take a long-run view + + align:start position:0% +long run you must take a long-run view + + + align:start position:0% +long run you must take a long-run view +of success as UI initiative with what + + align:start position:0% +of success as UI initiative with what + + + align:start position:0% +of success as UI initiative with what +with a moral imperative + + align:start position:0% +with a moral imperative + + + align:start position:0% +with a moral imperative +the World Bank should work to ensure + + align:start position:0% +the World Bank should work to ensure + + + align:start position:0% +the World Bank should work to ensure +that its investment decisions are based + + align:start position:0% +that its investment decisions are based + + + align:start position:0% +that its investment decisions are based +on the utility maximizing philosophy + + align:start position:0% +on the utility maximizing philosophy + + + align:start position:0% +on the utility maximizing philosophy +that promotes long run human welfare + + align:start position:0% +that promotes long run human welfare + + + align:start position:0% +that promotes long run human welfare +indeed investments in development + + align:start position:0% +indeed investments in development + + + align:start position:0% +indeed investments in development +related projects pay dividends over many + + align:start position:0% +related projects pay dividends over many + + + align:start position:0% +related projects pay dividends over many +years while investments in growth + + align:start position:0% +years while investments in growth + + + align:start position:0% +years while investments in growth +related projects may only provide for + + align:start position:0% +related projects may only provide for + + + align:start position:0% +related projects may only provide for +human needs for a short period of time + + align:start position:0% +human needs for a short period of time + + + align:start position:0% +human needs for a short period of time +it is a road bank's responsibility to + + align:start position:0% +it is a road bank's responsibility to + + + align:start position:0% +it is a road bank's responsibility to +take into account long run water in the + + align:start position:0% +take into account long run water in the + + + align:start position:0% +take into account long run water in the +environment because the viability of + + align:start position:0% +environment because the viability of + + + align:start position:0% +environment because the viability of +economic systems depend on its and + + align:start position:0% +economic systems depend on its and + + + align:start position:0% +economic systems depend on its and +sustained integrity to promote growth is + + align:start position:0% +sustained integrity to promote growth is + + + align:start position:0% +sustained integrity to promote growth is +to promote the idea that the economy can + + align:start position:0% +to promote the idea that the economy can + + + align:start position:0% +to promote the idea that the economy can +continue to flourish independently of + + align:start position:0% +continue to flourish independently of + + + align:start position:0% +continue to flourish independently of +the environment an idea that is a + + align:start position:0% +the environment an idea that is a + + + align:start position:0% +the environment an idea that is a +fiction however to promote development + + align:start position:0% +fiction however to promote development + + + align:start position:0% +fiction however to promote development +means to promote human progress that is + + align:start position:0% +means to promote human progress that is + + + align:start position:0% +means to promote human progress that is +sensitive to the environments carrying + + align:start position:0% +sensitive to the environments carrying + + + align:start position:0% +sensitive to the environments carrying +capacity and actively works to promote + + align:start position:0% +capacity and actively works to promote + + + align:start position:0% +capacity and actively works to promote +environmental stewardship while tending + + align:start position:0% +environmental stewardship while tending + + + align:start position:0% +environmental stewardship while tending +to human needs this is the goal on which + + align:start position:0% +to human needs this is the goal on which + + + align:start position:0% +to human needs this is the goal on which +all economies should be based that and + + align:start position:0% +all economies should be based that and + + + align:start position:0% +all economies should be based that and +the World Bank should work to promote + + align:start position:0% +the World Bank should work to promote + + + align:start position:0% +the World Bank should work to promote +this idea in our newest economies so + + align:start position:0% +this idea in our newest economies so + + + align:start position:0% +this idea in our newest economies so +that they take no time in choosing the + + align:start position:0% +that they take no time in choosing the + + + align:start position:0% +that they take no time in choosing the +best method to promote the progress of + + align:start position:0% +best method to promote the progress of + + + align:start position:0% +best method to promote the progress of +their people \ No newline at end of file diff --git a/A77qVe-U0iw.txt b/A77qVe-U0iw.txt new file mode 100644 index 0000000000000000000000000000000000000000..a1b48483282e2cb23ec9d6c6c3d96ed42fd77434 --- /dev/null +++ b/A77qVe-U0iw.txt @@ -0,0 +1,307 @@ +align:start position:0% + +so when you're teaching students to + + align:start position:0% +so when you're teaching students to + + + align:start position:0% +so when you're teaching students to +communicate orally effectively giving + + align:start position:0% +communicate orally effectively giving + + + align:start position:0% +communicate orally effectively giving +them a real living large audience ups + + align:start position:0% +them a real living large audience ups + + + align:start position:0% +them a real living large audience ups +their game considerably obviously like + + align:start position:0% +their game considerably obviously like + + + align:start position:0% +their game considerably obviously like +nobody wants to do a bad job in front of + + align:start position:0% +nobody wants to do a bad job in front of + + + align:start position:0% +nobody wants to do a bad job in front of +their peers in front of a group and + + align:start position:0% +their peers in front of a group and + + + align:start position:0% +their peers in front of a group and +obviously that's important because it + + align:start position:0% +obviously that's important because it + + + align:start position:0% +obviously that's important because it +replicates the kind of talks that + + align:start position:0% +replicates the kind of talks that + + + align:start position:0% +replicates the kind of talks that +they're likely to be giving say at + + align:start position:0% +they're likely to be giving say at + + + align:start position:0% +they're likely to be giving say at +conferences however it may not be wise + + align:start position:0% +conferences however it may not be wise + + + align:start position:0% +conferences however it may not be wise +to throw them in the deep end right away + + align:start position:0% +to throw them in the deep end right away + + + align:start position:0% +to throw them in the deep end right away +and a lot of times in classes that do + + align:start position:0% +and a lot of times in classes that do + + + align:start position:0% +and a lot of times in classes that do +have an oral communication component + + align:start position:0% +have an oral communication component + + + align:start position:0% +have an oral communication component +that's what happens you know somebody + + align:start position:0% +that's what happens you know somebody + + + align:start position:0% +that's what happens you know somebody +isn't necessarily an experienced speaker + + align:start position:0% +isn't necessarily an experienced speaker + + + align:start position:0% +isn't necessarily an experienced speaker +and their first experience of it is an + + align:start position:0% +and their first experience of it is an + + + align:start position:0% +and their first experience of it is an +end of the semester presentation and + + align:start position:0% +end of the semester presentation and + + + align:start position:0% +end of the semester presentation and +that's very very difficult for a lot of + + align:start position:0% +that's very very difficult for a lot of + + + align:start position:0% +that's very very difficult for a lot of +students so what I think has worked + + align:start position:0% +students so what I think has worked + + + align:start position:0% +students so what I think has worked +really well in this class is giving them + + align:start position:0% +really well in this class is giving them + + + align:start position:0% +really well in this class is giving them +that practice over and over again in a + + align:start position:0% +that practice over and over again in a + + + align:start position:0% +that practice over and over again in a +slightly safer setting where it's just a + + align:start position:0% +slightly safer setting where it's just a + + + align:start position:0% +slightly safer setting where it's just a +couple of people where the you know when + + align:start position:0% +couple of people where the you know when + + + align:start position:0% +couple of people where the you know when +you when they give the original practice + + align:start position:0% +you when they give the original practice + + + align:start position:0% +you when they give the original practice +oral presentation it's not even graded + + align:start position:0% +oral presentation it's not even graded + + + align:start position:0% +oral presentation it's not even graded +so it's safe to fail and that sense of + + align:start position:0% +so it's safe to fail and that sense of + + + align:start position:0% +so it's safe to fail and that sense of +safety in that sense of really building + + align:start position:0% +safety in that sense of really building + + + align:start position:0% +safety in that sense of really building +up stage by stage your skills is what + + align:start position:0% +up stage by stage your skills is what + + + align:start position:0% +up stage by stage your skills is what +gives them the confidence to be skilled + + align:start position:0% +gives them the confidence to be skilled + + + align:start position:0% +gives them the confidence to be skilled +communicators by the end of the semester + + align:start position:0% +communicators by the end of the semester + + + align:start position:0% +communicators by the end of the semester +you know by the time they finish 8:13 + + align:start position:0% +you know by the time they finish 8:13 + + + align:start position:0% +you know by the time they finish 8:13 +there is nobody in the class who doesn't + + align:start position:0% +there is nobody in the class who doesn't + + + align:start position:0% +there is nobody in the class who doesn't +understand what they need to do to make + + align:start position:0% +understand what they need to do to make + + + align:start position:0% +understand what they need to do to make +their presentation work and that makes + + align:start position:0% +their presentation work and that makes + + + align:start position:0% +their presentation work and that makes +it you know the moment of going into the + + align:start position:0% +it you know the moment of going into the + + + align:start position:0% +it you know the moment of going into the +you know the conference room or the or + + align:start position:0% +you know the conference room or the or + + + align:start position:0% +you know the conference room or the or +the classroom and standing up in front + + align:start position:0% +the classroom and standing up in front + + + align:start position:0% +the classroom and standing up in front +of their peers that makes it possible + + align:start position:0% +of their peers that makes it possible + + + align:start position:0% +of their peers that makes it possible +that makes it maybe even fun \ No newline at end of file diff --git a/AMLekTJR5_U.txt b/AMLekTJR5_U.txt new file mode 100644 index 0000000000000000000000000000000000000000..de22d65b522a932a6c09b917dbc7ce8f51e06506 --- /dev/null +++ b/AMLekTJR5_U.txt @@ -0,0 +1,1512 @@ +align:start position:0% + +hi everyone okay so for the first part + + align:start position:0% +hi everyone okay so for the first part + + + align:start position:0% +hi everyone okay so for the first part +of this course we've learned basically + + align:start position:0% +of this course we've learned basically + + + align:start position:0% +of this course we've learned basically +the ins and outs of solving linear + + align:start position:0% +the ins and outs of solving linear + + + align:start position:0% +the ins and outs of solving linear +systems of equations today we're gonna + + align:start position:0% +systems of equations today we're gonna + + + align:start position:0% +systems of equations today we're gonna +do a little review of the basic concepts + + align:start position:0% +do a little review of the basic concepts + + + align:start position:0% +do a little review of the basic concepts +hopefully we'll see a few of them in the + + align:start position:0% +hopefully we'll see a few of them in the + + + align:start position:0% +hopefully we'll see a few of them in the +in the following problem we're given a + + align:start position:0% +in the following problem we're given a + + + align:start position:0% +in the following problem we're given a +square matrix a a 3x3 square matrix a + + align:start position:0% +square matrix a a 3x3 square matrix a + + + align:start position:0% +square matrix a a 3x3 square matrix a +where the last entry is a parameter K + + align:start position:0% +where the last entry is a parameter K + + + align:start position:0% +where the last entry is a parameter K +and this parameter will vary and we'll + + align:start position:0% +and this parameter will vary and we'll + + + align:start position:0% +and this parameter will vary and we'll +see how the system whether what happens + + align:start position:0% +see how the system whether what happens + + + align:start position:0% +see how the system whether what happens +to the system of equations ax equal to 2 + + align:start position:0% +to the system of equations ax equal to 2 + + + align:start position:0% +to the system of equations ax equal to 2 +3 7 whether for which K it has a unique + + align:start position:0% +3 7 whether for which K it has a unique + + + align:start position:0% +3 7 whether for which K it has a unique +solution for which K has infinitely many + + align:start position:0% +solution for which K has infinitely many + + + align:start position:0% +solution for which K has infinitely many +solutions then we'll find the Lu + + align:start position:0% +solutions then we'll find the Lu + + + align:start position:0% +solutions then we'll find the Lu +decomposition and finally write down the + + align:start position:0% +decomposition and finally write down the + + + align:start position:0% +decomposition and finally write down the +complete solution to the system so I'll + + align:start position:0% +complete solution to the system so I'll + + + align:start position:0% +complete solution to the system so I'll +give you a few minutes to work this + + align:start position:0% +give you a few minutes to work this + + + align:start position:0% +give you a few minutes to work this +problem on your own and then please come + + align:start position:0% +problem on your own and then please come + + + align:start position:0% +problem on your own and then please come +back and see how I do it alright welcome + + align:start position:0% +back and see how I do it alright welcome + + + align:start position:0% +back and see how I do it alright welcome +back so let's start with Part A for + + align:start position:0% +back so let's start with Part A for + + + align:start position:0% +back so let's start with Part A for +which K does this system ax equal to 3 7 + + align:start position:0% +which K does this system ax equal to 3 7 + + + align:start position:0% +which K does this system ax equal to 3 7 +have a unique solution so what do we + + align:start position:0% +have a unique solution so what do we + + + align:start position:0% +have a unique solution so what do we +know about square systems of square + + align:start position:0% +know about square systems of square + + + align:start position:0% +know about square systems of square +systems of linear equations they have a + + align:start position:0% +systems of linear equations they have a + + + align:start position:0% +systems of linear equations they have a +unique solution when the matrix a is + + align:start position:0% +unique solution when the matrix a is + + + align:start position:0% +unique solution when the matrix a is +invertible ok so now when is a + + align:start position:0% +invertible ok so now when is a + + + align:start position:0% +invertible ok so now when is a +invertible it is invertible when it is a + + align:start position:0% +invertible it is invertible when it is a + + + align:start position:0% +invertible it is invertible when it is a +full rank and how do we figure this this + + align:start position:0% +full rank and how do we figure this this + + + align:start position:0% +full rank and how do we figure this this +out we do it by performing row + + align:start position:0% +out we do it by performing row + + + align:start position:0% +out we do it by performing row +operations we do it by doing + + align:start position:0% +operations we do it by doing + + + align:start position:0% +operations we do it by doing +eliminations on the matrix ok but since + + align:start position:0% +eliminations on the matrix ok but since + + + align:start position:0% +eliminations on the matrix ok but since +we want to simulate an exam setting it + + align:start position:0% +we want to simulate an exam setting it + + + align:start position:0% +we want to simulate an exam setting it +always pays off to see what tasks lie + + align:start position:0% +always pays off to see what tasks lie + + + align:start position:0% +always pays off to see what tasks lie +ahead of us so in in Part C we'll + + align:start position:0% +ahead of us so in in Part C we'll + + + align:start position:0% +ahead of us so in in Part C we'll +we're asked to find the Lu decomposition + + align:start position:0% +we're asked to find the Lu decomposition + + + align:start position:0% +we're asked to find the Lu decomposition +this means that when we do row + + align:start position:0% +this means that when we do row + + + align:start position:0% +this means that when we do row +operations we'd better keep track what + + align:start position:0% +operations we'd better keep track what + + + align:start position:0% +operations we'd better keep track what +row operations we're doing exactly + + align:start position:0% +row operations we're doing exactly + + + align:start position:0% +row operations we're doing exactly +in particular we'll write them down as + + align:start position:0% +in particular we'll write them down as + + + align:start position:0% +in particular we'll write them down as +elementary matrices and in Part D we + + align:start position:0% +elementary matrices and in Part D we + + + align:start position:0% +elementary matrices and in Part D we +will be asked to compute the complete + + align:start position:0% +will be asked to compute the complete + + + align:start position:0% +will be asked to compute the complete +solution and therefore it's good to do + + align:start position:0% +solution and therefore it's good to do + + + align:start position:0% +solution and therefore it's good to do +row operations on the Augmented matrix a + + align:start position:0% +row operations on the Augmented matrix a + + + align:start position:0% +row operations on the Augmented matrix a +ok so let's do this all right well + + align:start position:0% +ok so let's do this all right well + + + align:start position:0% +ok so let's do this all right well +mantich matrix is following beasts + + align:start position:0% + + + + align:start position:0% + +one two three okay and then two three + + align:start position:0% +one two three okay and then two three + + + align:start position:0% +one two three okay and then two three +seven okay so first thing we we subtract + + align:start position:0% +seven okay so first thing we we subtract + + + align:start position:0% +seven okay so first thing we we subtract +row by multiple of Row one from Row two + + align:start position:0% +row by multiple of Row one from Row two + + + align:start position:0% +row by multiple of Row one from Row two +and it's exactly negative 1 times the + + align:start position:0% +and it's exactly negative 1 times the + + + align:start position:0% +and it's exactly negative 1 times the +first row plus the second right so let + + align:start position:0% +first row plus the second right so let + + + align:start position:0% +first row plus the second right so let +me write down the corresponding + + align:start position:0% +me write down the corresponding + + + align:start position:0% +me write down the corresponding +elementary elementary matrix that does + + align:start position:0% +elementary elementary matrix that does + + + align:start position:0% +elementary elementary matrix that does +this + + align:start position:0% +this + + + align:start position:0% +this +it's e 2 1 and it's lower diagonal with + + align:start position:0% +it's e 2 1 and it's lower diagonal with + + + align:start position:0% +it's e 2 1 and it's lower diagonal with +ones on the diagonal and it's gonna be + + align:start position:0% +ones on the diagonal and it's gonna be + + + align:start position:0% +ones on the diagonal and it's gonna be +exactly minus 1 and the first entry of + + align:start position:0% +exactly minus 1 and the first entry of + + + align:start position:0% +exactly minus 1 and the first entry of +the second row okay so we get 1 1 1 2 0 + + align:start position:0% +the second row okay so we get 1 1 1 2 0 + + + align:start position:0% +the second row okay so we get 1 1 1 2 0 +1 2 1 and we copy down third row ok + + align:start position:0% +1 2 1 and we copy down third row ok + + + align:start position:0% +1 2 1 and we copy down third row ok +no we subtract a multiple of the first + + align:start position:0% +no we subtract a multiple of the first + + + align:start position:0% +no we subtract a multiple of the first +row from the third one and write this + + align:start position:0% +row from the third one and write this + + + align:start position:0% +row from the third one and write this +here it's precisely Wilmot yeah we'll + + align:start position:0% +here it's precisely Wilmot yeah we'll + + + align:start position:0% +here it's precisely Wilmot yeah we'll +multiply the first row by negative three + + align:start position:0% +multiply the first row by negative three + + + align:start position:0% +multiply the first row by negative three +and add it to the third one this is + + align:start position:0% +and add it to the third one this is + + + align:start position:0% +and add it to the third one this is +accomplished by the elementary matrix + + align:start position:0% +accomplished by the elementary matrix + + + align:start position:0% +accomplished by the elementary matrix +III 1 which is 1 1 1 negative 3 and then + + align:start position:0% +III 1 which is 1 1 1 negative 3 and then + + + align:start position:0% +III 1 which is 1 1 1 negative 3 and then +0 0 ok 1 1 1 2 0 1 2 1 we copy the first + + align:start position:0% +0 0 ok 1 1 1 2 0 1 2 1 we copy the first + + + align:start position:0% +0 0 ok 1 1 1 2 0 1 2 1 we copy the first +two rows and then the third one will be + + align:start position:0% +two rows and then the third one will be + + + align:start position:0% +two rows and then the third one will be +0 1 K minus 3 and 7 minus 3 x - 7 - 6 1 + + align:start position:0% +0 1 K minus 3 and 7 minus 3 x - 7 - 6 1 + + + align:start position:0% +0 1 K minus 3 and 7 minus 3 x - 7 - 6 1 +ok we have essentially well one last of + + align:start position:0% +ok we have essentially well one last of + + + align:start position:0% +ok we have essentially well one last of +row operations to perform here so we'll + + align:start position:0% +row operations to perform here so we'll + + + align:start position:0% +row operations to perform here so we'll +subtract the second row from the third + + align:start position:0% +subtract the second row from the third + + + align:start position:0% +subtract the second row from the third +one and get 1 1 1 2 0 1 2 1 0 0 K minus + + align:start position:0% +one and get 1 1 1 2 0 1 2 1 0 0 K minus + + + align:start position:0% +one and get 1 1 1 2 0 1 2 1 0 0 K minus +5 and then 0 and this was achieved by + + align:start position:0% +5 and then 0 and this was achieved by + + + align:start position:0% +5 and then 0 and this was achieved by +the elementary matrix III 2 which was 1 + + align:start position:0% +the elementary matrix III 2 which was 1 + + + align:start position:0% +the elementary matrix III 2 which was 1 +1 and then negative 1 + + align:start position:0% +1 and then negative 1 + + + align:start position:0% +1 and then negative 1 +ok because we multiplied the second row + + align:start position:0% +ok because we multiplied the second row + + + align:start position:0% +ok because we multiplied the second row +by a negative 1 and edited to the third + + align:start position:0% +by a negative 1 and edited to the third + + + align:start position:0% +by a negative 1 and edited to the third +one + + align:start position:0% +one + + + align:start position:0% +one +ok so we have the we have we got 2 + + align:start position:0% +ok so we have the we have we got 2 + + + align:start position:0% +ok so we have the we have we got 2 +matrix which was which is upper + + align:start position:0% +matrix which was which is upper + + + align:start position:0% +matrix which was which is upper +triangular and we want to hear we want + + align:start position:0% +triangular and we want to hear we want + + + align:start position:0% +triangular and we want to hear we want +to figure out for which value of the + + align:start position:0% +to figure out for which value of the + + + align:start position:0% +to figure out for which value of the +parameter K is this matrix may + + align:start position:0% +parameter K is this matrix may + + + align:start position:0% +parameter K is this matrix may +full rank well this pivot is this is a + + align:start position:0% +full rank well this pivot is this is a + + + align:start position:0% +full rank well this pivot is this is a +pivot this is a pivot and we want this + + align:start position:0% +pivot this is a pivot and we want this + + + align:start position:0% +pivot this is a pivot and we want this +one to be a pivot as well and that + + align:start position:0% +one to be a pivot as well and that + + + align:start position:0% +one to be a pivot as well and that +happens when K minus five is not zero + + align:start position:0% +happens when K minus five is not zero + + + align:start position:0% +happens when K minus five is not zero +okay so when K is different from five + + align:start position:0% +okay so when K is different from five + + + align:start position:0% +okay so when K is different from five +the matrix a is a full rank and + + align:start position:0% +the matrix a is a full rank and + + + align:start position:0% +the matrix a is a full rank and +therefore the system ax equals two to + + align:start position:0% +therefore the system ax equals two to + + + align:start position:0% +therefore the system ax equals two to +three seven has a unique solution now + + align:start position:0% +three seven has a unique solution now + + + align:start position:0% +three seven has a unique solution now +Part B for which K do we have infinitely + + align:start position:0% +Part B for which K do we have infinitely + + + align:start position:0% +Part B for which K do we have infinitely +many solutions so when when when the + + align:start position:0% +many solutions so when when when the + + + align:start position:0% +many solutions so when when when the +when are we in such a situation we are + + align:start position:0% +when are we in such a situation we are + + + align:start position:0% +when are we in such a situation we are +in such a situation when the null space + + align:start position:0% +in such a situation when the null space + + + align:start position:0% +in such a situation when the null space +of the matrix a is non-trivial + + align:start position:0% +of the matrix a is non-trivial + + + align:start position:0% +of the matrix a is non-trivial +so the null space will be known as + + align:start position:0% +so the null space will be known as + + + align:start position:0% +so the null space will be known as +non-trivial when this K minus 5 number + + align:start position:0% +non-trivial when this K minus 5 number + + + align:start position:0% +non-trivial when this K minus 5 number +here which is was the pivots in the + + align:start position:0% +here which is was the pivots in the + + + align:start position:0% +here which is was the pivots in the +first case is 0 so can a minus 5 equals + + align:start position:0% +first case is 0 so can a minus 5 equals + + + align:start position:0% +first case is 0 so can a minus 5 equals +to 0 you see yeah there is a little + + align:start position:0% +to 0 you see yeah there is a little + + + align:start position:0% +to 0 you see yeah there is a little +caveat here when yeah K is equal to 5 we + + align:start position:0% +caveat here when yeah K is equal to 5 we + + + align:start position:0% +caveat here when yeah K is equal to 5 we +get the third row of the Augmented + + align:start position:0% +get the third row of the Augmented + + + align:start position:0% +get the third row of the Augmented +matrix 0 0 0 equal to 0 this means that + + align:start position:0% +matrix 0 0 0 equal to 0 this means that + + + align:start position:0% +matrix 0 0 0 equal to 0 this means that +the matrix is actually consistent and we + + align:start position:0% +the matrix is actually consistent and we + + + align:start position:0% +the matrix is actually consistent and we +indeed have a solution but if this entry + + align:start position:0% +indeed have a solution but if this entry + + + align:start position:0% +indeed have a solution but if this entry +were nonzero then we would get no + + align:start position:0% +were nonzero then we would get no + + + align:start position:0% +were nonzero then we would get no +solutions okay + + align:start position:0% +solutions okay + + + align:start position:0% +solutions okay +now off to Part C + + align:start position:0% + + + + align:start position:0% + +we want to compute the Lu decomposition + + align:start position:0% +we want to compute the Lu decomposition + + + align:start position:0% +we want to compute the Lu decomposition +well we already got what the matrix U is + + align:start position:0% +well we already got what the matrix U is + + + align:start position:0% +well we already got what the matrix U is +through a performing grow operations it + + align:start position:0% +through a performing grow operations it + + + align:start position:0% +through a performing grow operations it +is this guy here let me write it down 1 + + align:start position:0% +is this guy here let me write it down 1 + + + align:start position:0% +is this guy here let me write it down 1 +1 1 0 1 2 0 0 K minus 5 and when K is + + align:start position:0% +1 1 0 1 2 0 0 K minus 5 and when K is + + + align:start position:0% +1 1 0 1 2 0 0 K minus 5 and when K is +equal to 4 this entry is negative 1 ok + + align:start position:0% +equal to 4 this entry is negative 1 ok + + + align:start position:0% +equal to 4 this entry is negative 1 ok +and now what about the matrix L well how + + align:start position:0% +and now what about the matrix L well how + + + align:start position:0% +and now what about the matrix L well how +did we get to this you we had the matrix + + align:start position:0% +did we get to this you we had the matrix + + + align:start position:0% +did we get to this you we had the matrix +a we got the matrix U and what we did + + align:start position:0% +a we got the matrix U and what we did + + + align:start position:0% +a we got the matrix U and what we did +was first we applied a to 1 then we + + align:start position:0% +was first we applied a to 1 then we + + + align:start position:0% +was first we applied a to 1 then we +applied a 3 1 III one and then III to so + + align:start position:0% +applied a 3 1 III one and then III to so + + + align:start position:0% +applied a 3 1 III one and then III to so +a a is we get a by inverting this + + align:start position:0% +a a is we get a by inverting this + + + align:start position:0% +a a is we get a by inverting this +equation so it's gonna be e to 1 inverse + + align:start position:0% +equation so it's gonna be e to 1 inverse + + + align:start position:0% +equation so it's gonna be e to 1 inverse +e 3 1 inverse e 3 2 inverse times u and + + align:start position:0% +e 3 1 inverse e 3 2 inverse times u and + + + align:start position:0% +e 3 1 inverse e 3 2 inverse times u and +this is our matrix L and we know it's + + align:start position:0% +this is our matrix L and we know it's + + + align:start position:0% +this is our matrix L and we know it's +fairly easy to invert these elementary + + align:start position:0% +fairly easy to invert these elementary + + + align:start position:0% +fairly easy to invert these elementary +matrices e we just yeah we flip the + + align:start position:0% +matrices e we just yeah we flip the + + + align:start position:0% +matrices e we just yeah we flip the +signs of the abdominal entries okay so + + align:start position:0% +signs of the abdominal entries okay so + + + align:start position:0% +signs of the abdominal entries okay so +I'm not gonna write down the the again + + align:start position:0% +I'm not gonna write down the the again + + + align:start position:0% +I'm not gonna write down the the again +the inverses of these guys I'm oh yeah + + align:start position:0% +the inverses of these guys I'm oh yeah + + + align:start position:0% +the inverses of these guys I'm oh yeah +I'm just gonna write the product of the + + align:start position:0% +I'm just gonna write the product of the + + + align:start position:0% +I'm just gonna write the product of the +inverses and that's also very easy to + + align:start position:0% +inverses and that's also very easy to + + + align:start position:0% +inverses and that's also very easy to +compute because one we invert the signs + + align:start position:0% +compute because one we invert the signs + + + align:start position:0% +compute because one we invert the signs +we just send the numbers in their + + align:start position:0% +we just send the numbers in their + + + align:start position:0% +we just send the numbers in their +corresponding entry Avella I mean the + + align:start position:0% +corresponding entry Avella I mean the + + + align:start position:0% +corresponding entry Avella I mean the +following thing so minus 1 becomes a 1 + + align:start position:0% +following thing so minus 1 becomes a 1 + + + align:start position:0% +following thing so minus 1 becomes a 1 +and + + align:start position:0% + + + + align:start position:0% + +it comes here in its respective entry + + align:start position:0% +it comes here in its respective entry + + + align:start position:0% +it comes here in its respective entry +for eath vf4 e31 this becomes we flip + + align:start position:0% +for eath vf4 e31 this becomes we flip + + + align:start position:0% +for eath vf4 e31 this becomes we flip +the sign first three and we plug it in + + align:start position:0% +the sign first three and we plug it in + + + align:start position:0% +the sign first three and we plug it in +here and four III 2 we flip the sign of + + align:start position:0% +here and four III 2 we flip the sign of + + + align:start position:0% +here and four III 2 we flip the sign of +this guy it comes one and we plug it in + + align:start position:0% +this guy it comes one and we plug it in + + + align:start position:0% +this guy it comes one and we plug it in +here okay + + align:start position:0% +here okay + + + align:start position:0% +here okay +so give me a few moments do you raise + + align:start position:0% +so give me a few moments do you raise + + + align:start position:0% +so give me a few moments do you raise +the board and then I'll do part four + + align:start position:0% + + + + align:start position:0% + +okay we're back and we're gonna do Part + + align:start position:0% +okay we're back and we're gonna do Part + + + align:start position:0% +okay we're back and we're gonna do Part +D now okay so we need to find the + + align:start position:0% +D now okay so we need to find the + + + align:start position:0% +D now okay so we need to find the +complete solution of the system for all + + align:start position:0% +complete solution of the system for all + + + align:start position:0% +complete solution of the system for all +K and we saw that for k equal to five + + align:start position:0% +K and we saw that for k equal to five + + + align:start position:0% +K and we saw that for k equal to five +the system had many many solutions and + + align:start position:0% +the system had many many solutions and + + + align:start position:0% +the system had many many solutions and +for K not equal to five it has only one + + align:start position:0% +for K not equal to five it has only one + + + align:start position:0% +for K not equal to five it has only one +okay so first let's look at the case + + align:start position:0% +okay so first let's look at the case + + + align:start position:0% +okay so first let's look at the case +okay nacht equal to five when the matrix + + align:start position:0% +okay nacht equal to five when the matrix + + + align:start position:0% +okay nacht equal to five when the matrix +a will was invertible that well we can + + align:start position:0% +a will was invertible that well we can + + + align:start position:0% +a will was invertible that well we can +it's it's not hard to see what the + + align:start position:0% +it's it's not hard to see what the + + + align:start position:0% +it's it's not hard to see what the +solution of the system then is it's + + align:start position:0% +solution of the system then is it's + + + align:start position:0% +solution of the system then is it's +gonna be let me just write it down so + + align:start position:0% +gonna be let me just write it down so + + + align:start position:0% +gonna be let me just write it down so +when K is not equal to 5 this was non + + align:start position:0% +when K is not equal to 5 this was non + + + align:start position:0% +when K is not equal to 5 this was non +zero therefore X 3 needs to be 0 right + + align:start position:0% +zero therefore X 3 needs to be 0 right + + + align:start position:0% +zero therefore X 3 needs to be 0 right +when X 3 is 0 we have X 2 plus 2 times X + + align:start position:0% +when X 3 is 0 we have X 2 plus 2 times X + + + align:start position:0% +when X 3 is 0 we have X 2 plus 2 times X +3 so X 2 plus 0 equals 1 therefore X 2 + + align:start position:0% +3 so X 2 plus 0 equals 1 therefore X 2 + + + align:start position:0% +3 so X 2 plus 0 equals 1 therefore X 2 +is 1 and then we go back to the first + + align:start position:0% +is 1 and then we go back to the first + + + align:start position:0% +is 1 and then we go back to the first +row we have X 1 plus X 2 plus X 3 equals + + align:start position:0% +row we have X 1 plus X 2 plus X 3 equals + + + align:start position:0% +row we have X 1 plus X 2 plus X 3 equals + + align:start position:0% + + + align:start position:0% +so X 1 plus 1 plus 0 equals 2 so X 1 + + align:start position:0% +so X 1 plus 1 plus 0 equals 2 so X 1 + + + align:start position:0% +so X 1 plus 1 plus 0 equals 2 so X 1 +plus 1 equals 2 and therefore X 1 is 1 + + align:start position:0% +plus 1 equals 2 and therefore X 1 is 1 + + + align:start position:0% +plus 1 equals 2 and therefore X 1 is 1 +good now what about K equals to five + + align:start position:0% +good now what about K equals to five + + + align:start position:0% +good now what about K equals to five +then we see that X 3 is a free variable + + align:start position:0% +then we see that X 3 is a free variable + + + align:start position:0% +then we see that X 3 is a free variable +okay so the solution will be X 1 X 2 X 3 + + align:start position:0% + + + + align:start position:0% + +3 can be X 3 can be any number see from + + align:start position:0% +3 can be X 3 can be any number see from + + + align:start position:0% +3 can be X 3 can be any number see from +the second row we'll get the value of x + + align:start position:0% +the second row we'll get the value of x + + + align:start position:0% +the second row we'll get the value of x +2 it's 1 minus 2 times X 3 so 1 minus 2 + + align:start position:0% +2 it's 1 minus 2 times X 3 so 1 minus 2 + + + align:start position:0% +2 it's 1 minus 2 times X 3 so 1 minus 2 +times C and X 1 is 2 minus X it's 2 + + align:start position:0% +times C and X 1 is 2 minus X it's 2 + + + align:start position:0% +times C and X 1 is 2 minus X it's 2 +minus X 1 minus X sorry 2 times 2 minus + + align:start position:0% +minus X 1 minus X sorry 2 times 2 minus + + + align:start position:0% +minus X 1 minus X sorry 2 times 2 minus +X 2 minus X 3 so write this as 2 minus X + + align:start position:0% +X 2 minus X 3 so write this as 2 minus X + + + align:start position:0% +X 2 minus X 3 so write this as 2 minus X +2 is 1 minus joke to C minus C 1 minus 2 + + align:start position:0% +2 is 1 minus joke to C minus C 1 minus 2 + + + align:start position:0% +2 is 1 minus joke to C minus C 1 minus 2 +C C okay + + align:start position:0% +C C okay + + + align:start position:0% +C C okay +so will decompose this vector here into + + align:start position:0% +so will decompose this vector here into + + + align:start position:0% +so will decompose this vector here into +a component which is independent of C + + align:start position:0% +a component which is independent of C + + + align:start position:0% +a component which is independent of C +and a component which is a multiple + + align:start position:0% +and a component which is a multiple + + + align:start position:0% +and a component which is a multiple +let's see okay so this is 2 minus 1 + + align:start position:0% +let's see okay so this is 2 minus 1 + + + align:start position:0% +let's see okay so this is 2 minus 1 +should be 1 1 0 plus C times will have 2 + + align:start position:0% +should be 1 1 0 plus C times will have 2 + + + align:start position:0% +should be 1 1 0 plus C times will have 2 +C minus C C so C times 1 here will have + + align:start position:0% +C minus C C so C times 1 here will have + + + align:start position:0% +C minus C C so C times 1 here will have +minus 2 C so 2 and here we'll have 1 and + + align:start position:0% +minus 2 C so 2 and here we'll have 1 and + + + align:start position:0% +minus 2 C so 2 and here we'll have 1 and +thus we get the particular solution for + + align:start position:0% +thus we get the particular solution for + + + align:start position:0% +thus we get the particular solution for +the system and the special solution for + + align:start position:0% +the system and the special solution for + + + align:start position:0% +the system and the special solution for +the system ok we're kind of done here if + + align:start position:0% +the system ok we're kind of done here if + + + align:start position:0% +the system ok we're kind of done here if +you're at an exam you should immediately + + align:start position:0% +you're at an exam you should immediately + + + align:start position:0% +you're at an exam you should immediately +start the next problem good luck and + + align:start position:0% +start the next problem good luck and + + + align:start position:0% +start the next problem good luck and +I'll see you later \ No newline at end of file diff --git a/AivFineIBqA.txt b/AivFineIBqA.txt new file mode 100644 index 0000000000000000000000000000000000000000..0f25188599df33b1557c399d9d74624d2eba8ccd --- /dev/null +++ b/AivFineIBqA.txt @@ -0,0 +1,14152 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following content is provided by MIT +open courseware under a Creative Commons + + align:start position:0% +open courseware under a Creative Commons + + + align:start position:0% +open courseware under a Creative Commons +license additional information about our + + align:start position:0% +license additional information about our + + + align:start position:0% +license additional information about our +license and MIT open courseware in + + align:start position:0% +license and MIT open courseware in + + + align:start position:0% +license and MIT open courseware in +general is available at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu let's begin talking about + + align:start position:0% +ocw.mit.edu let's begin talking about + + + align:start position:0% +ocw.mit.edu let's begin talking about +the + + align:start position:0% +the + + + align:start position:0% +the +homework who have made + + align:start position:0% + + + + align:start position:0% + +it okay + + align:start position:0% + + + + align:start position:0% + +you can access here if you want + + align:start position:0% +you can access here if you want + + + align:start position:0% +you can access here if you want +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +okay yeah okay + + align:start position:0% + + + + align:start position:0% + +hi + + align:start position:0% +hi + + + align:start position:0% +hi +um you get minutes to + + align:start position:0% + + + + align:start position:0% + +get display + + align:start position:0% + + + + align:start position:0% + +uh we will wait she to + + align:start position:0% +uh we will wait she to + + + align:start position:0% +uh we will wait she to +finish her + + align:start position:0% +finish her + + + align:start position:0% +finish her +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +intented it's like movie + + align:start position:0% +intented it's like movie + + + align:start position:0% +intented it's like movie +know and we can all read after of this + + align:start position:0% + + + + align:start position:0% + +okay okay it's not + + align:start position:0% + + + + align:start position:0% + +required + + align:start position:0% +required + + + align:start position:0% +required +I printed the + + align:start position:0% +I printed the + + + align:start position:0% +I printed the +handouts okay but we we will begin + + align:start position:0% +handouts okay but we we will begin + + + align:start position:0% +handouts okay but we we will begin +talking + + align:start position:0% +talking + + + align:start position:0% +talking +about + + align:start position:0% +about + + + align:start position:0% +about +the the experience + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% +you + + + align:start position:0% +you +have doing your + + align:start position:0% +have doing your + + + align:start position:0% +have doing your +homework the F the first question + + align:start position:0% + + + + align:start position:0% + +is what what + + align:start position:0% + + + + align:start position:0% + +challenges have your experience of doing + + align:start position:0% +challenges have your experience of doing + + + align:start position:0% +challenges have your experience of doing +the + + align:start position:0% + + + + align:start position:0% + +homework how do you feel challenged by + + align:start position:0% +homework how do you feel challenged by + + + align:start position:0% +homework how do you feel challenged by +the by those questions + + align:start position:0% + + + + align:start position:0% + +of is here + + align:start position:0% +of is here + + + align:start position:0% +of is here +so just a + + align:start position:0% +so just a + + + align:start position:0% +so just a +brief uh descri where we are we + + align:start position:0% +brief uh descri where we are we + + + align:start position:0% +brief uh descri where we are we +we okay we had a specific problem in + + align:start position:0% +we okay we had a specific problem in + + + align:start position:0% +we okay we had a specific problem in +framing him that we Tred to frame and + + align:start position:0% +framing him that we Tred to frame and + + + align:start position:0% +framing him that we Tred to frame and +then they were given the two questions + + align:start position:0% +then they were given the two questions + + + align:start position:0% +then they were given the two questions +to work on at home one was like what + + align:start position:0% +to work on at home one was like what + + + align:start position:0% +to work on at home one was like what +um what were the you + + align:start position:0% +um what were the you + + + align:start position:0% +um what were the you +know + + align:start position:0% +know + + + align:start position:0% +know +values that would that they think are + + align:start position:0% +values that would that they think are + + + align:start position:0% +values that would that they think are +behind their framing of the problem and + + align:start position:0% +behind their framing of the problem and + + + align:start position:0% +behind their framing of the problem and +what what are the + + align:start position:0% +what what are the + + + align:start position:0% +what what are the +assumptions that they think are behind + + align:start position:0% + + + + align:start position:0% + +that yes you were thinking about values + + align:start position:0% +that yes you were thinking about values + + + align:start position:0% +that yes you were thinking about values +and assumptions of your framework + + align:start position:0% + + + + align:start position:0% + +what what kind of + + align:start position:0% +what what kind of + + + align:start position:0% +what what kind of +difficulties + + align:start position:0% +difficulties + + + align:start position:0% +difficulties +you have doing + + align:start position:0% +you have doing + + + align:start position:0% +you have doing +that or it was absolutely smooth is just + + align:start position:0% +that or it was absolutely smooth is just + + + align:start position:0% +that or it was absolutely smooth is just +to + + align:start position:0% +to + + + align:start position:0% +to +to to answer + + align:start position:0% + + + + align:start position:0% + +what were reasons and what were + + align:start position:0% +what were reasons and what were + + + align:start position:0% +what were reasons and what were +what and what were assumption just + + align:start position:0% +what and what were assumption just + + + align:start position:0% +what and what were assumption just +distinguishing between reasons and + + align:start position:0% +distinguishing between reasons and + + + align:start position:0% +distinguishing between reasons and +assumptions okay and and + + align:start position:0% +assumptions okay and and + + + align:start position:0% +assumptions okay and and +identifying that there had been reasons + + align:start position:0% +identifying that there had been reasons + + + align:start position:0% +identifying that there had been reasons +for okay just the very Act + + align:start position:0% +for okay just the very Act + + + align:start position:0% +for okay just the very Act +of analyzing + + align:start position:0% + + + + align:start position:0% + +reasons + + align:start position:0% +reasons + + + align:start position:0% +reasons +okay in some + + align:start position:0% +okay in some + + + align:start position:0% +okay in some +some in some cases is difficult to + + align:start position:0% +some in some cases is difficult to + + + align:start position:0% +some in some cases is difficult to +separate both no okay we will talk about + + align:start position:0% +separate both no okay we will talk about + + + align:start position:0% +separate both no okay we will talk about +this a bit + + align:start position:0% +this a bit + + + align:start position:0% +this a bit +later another difficulty you have we are + + align:start position:0% +later another difficulty you have we are + + + align:start position:0% +later another difficulty you have we are +talking about the exercise of + + align:start position:0% +talking about the exercise of + + + align:start position:0% +talking about the exercise of +yesterday and asking + + align:start position:0% +yesterday and asking + + + align:start position:0% +yesterday and asking +you + + align:start position:0% +you + + + align:start position:0% +you +some difficulties you may have experienc + + align:start position:0% +some difficulties you may have experienc + + + align:start position:0% +some difficulties you may have experienc +it as doing the work + + align:start position:0% + + + + align:start position:0% + +I don't + + align:start position:0% + + + + align:start position:0% + +know before + + align:start position:0% +know before + + + align:start position:0% +know before +beginning we call to work on + + align:start position:0% +beginning we call to work on + + + align:start position:0% +beginning we call to work on +cards I could give you three questions + + align:start position:0% +cards I could give you three questions + + + align:start position:0% +cards I could give you three questions +and you could try to answer these + + align:start position:0% +and you could try to answer these + + + align:start position:0% +and you could try to answer these +questions in + + align:start position:0% + + + + align:start position:0% + +cards so it's okay for + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% +you + + + align:start position:0% +you +yeah yeah yes it's enough okay thank you + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +okay let's let's let's make a + + align:start position:0% +okay let's let's let's make a + + + align:start position:0% +okay let's let's let's make a +change please one for each + + align:start position:0% + + + + align:start position:0% + +one one for each + + align:start position:0% + + + + align:start position:0% + +one and one for each + + align:start position:0% +one and one for each + + + align:start position:0% +one and one for each +one uh + + align:start position:0% + + + + align:start position:0% + +Austin you don't need to answer the + + align:start position:0% +Austin you don't need to answer the + + + align:start position:0% +Austin you don't need to answer the +question + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay thank + + align:start position:0% + + + + align:start position:0% + +you thank + + align:start position:0% + + + + align:start position:0% + +you thank you please write one one in + + align:start position:0% +you thank you please write one one in + + + align:start position:0% +you thank you please write one one in +the pale + + align:start position:0% +the pale + + + align:start position:0% +the pale +blue white one in a + + align:start position:0% +blue white one in a + + + align:start position:0% +blue white one in a +corner right two in the + + align:start position:0% +corner right two in the + + + align:start position:0% +corner right two in the +orange and right three in the violet + + align:start position:0% + + + + align:start position:0% + +CL we put + + align:start position:0% + + + + align:start position:0% + +the okay CL we will put the questions in + + align:start position:0% +the okay CL we will put the questions in + + + align:start position:0% +the okay CL we will put the questions in +the sheet of paper but for you begin to + + align:start position:0% +the sheet of paper but for you begin to + + + align:start position:0% +the sheet of paper but for you begin to +think about that is one the first one is + + align:start position:0% +think about that is one the first one is + + + align:start position:0% +think about that is one the first one is +as you were working on the framework + + align:start position:0% +as you were working on the framework + + + align:start position:0% +as you were working on the framework +assignment yesterday today what + + align:start position:0% +assignment yesterday today what + + + align:start position:0% +assignment yesterday today what +challenges did you + + align:start position:0% +challenges did you + + + align:start position:0% +challenges did you +experience okay the first one challenges + + align:start position:0% +experience okay the first one challenges + + + align:start position:0% +experience okay the first one challenges +you have + + align:start position:0% +you have + + + align:start position:0% +you have +experienced + + align:start position:0% + + + + align:start position:0% + +okay the second question is about + + align:start position:0% + + + + align:start position:0% + +surprises what + + align:start position:0% +surprises what + + + align:start position:0% +surprises what +surprises you + + align:start position:0% +surprises you + + + align:start position:0% +surprises you +have you have had in experience + + align:start position:0% + + + + align:start position:0% + +and the third is about + + align:start position:0% +and the third is about + + + align:start position:0% +and the third is about +lessons what you have learned in the + + align:start position:0% +lessons what you have learned in the + + + align:start position:0% +lessons what you have learned in the +process of identifying values and + + align:start position:0% +process of identifying values and + + + align:start position:0% +process of identifying values and +assumptions embedded in your framing of + + align:start position:0% +assumptions embedded in your framing of + + + align:start position:0% +assumptions embedded in your framing of +a + + align:start position:0% +a + + + align:start position:0% +a +situation first challenge two + + align:start position:0% +situation first challenge two + + + align:start position:0% +situation first challenge two +surprises + + align:start position:0% +surprises + + + align:start position:0% +surprises +three + + align:start position:0% + + + + align:start position:0% + +lessons Okay we you will write this and + + align:start position:0% +lessons Okay we you will write this and + + + align:start position:0% +lessons Okay we you will write this and +we will organize groups of + + align:start position:0% + + + + align:start position:0% + +this during that class exercise not + + align:start position:0% +this during that class exercise not + + + align:start position:0% +this during that class exercise not +during last Mon's homework during the + + align:start position:0% +during last Mon's homework during the + + + align:start position:0% +during last Mon's homework during the +exercise class no for the + + align:start position:0% +exercise class no for the + + + align:start position:0% +exercise class no for the +homework yes the questions are for the + + align:start position:0% +homework yes the questions are for the + + + align:start position:0% +homework yes the questions are for the +homework okay because it was the less + + align:start position:0% +homework okay because it was the less + + + align:start position:0% +homework okay because it was the less +thing you have done no the homework + + align:start position:0% + + + + align:start position:0% + +so here are the + + align:start position:0% + + + + align:start position:0% + +questions we have about 8 minutes + + align:start position:0% +questions we have about 8 minutes + + + align:start position:0% +questions we have about 8 minutes +pleas + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +next for + + align:start position:0% + + + + align:start position:0% + +just + + align:start position:0% + + + + align:start position:0% + +sh + + align:start position:0% + + + + align:start position:0% + +and try to be specific you know if you + + align:start position:0% +and try to be specific you know if you + + + align:start position:0% +and try to be specific you know if you +say the challenge was figuring the + + align:start position:0% +say the challenge was figuring the + + + align:start position:0% +say the challenge was figuring the +Assumption figuring out the Assumption I + + align:start position:0% +Assumption figuring out the Assumption I + + + align:start position:0% +Assumption figuring out the Assumption I +figure out what was challenging about + + align:start position:0% +figure out what was challenging about + + + align:start position:0% +figure out what was challenging about +that + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +I think this is comp + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +okay can you put + + align:start position:0% +okay can you put + + + align:start position:0% +okay can you put +your cards there please + + align:start position:0% + + + + align:start position:0% + +okay once you have finished take + + align:start position:0% + + + + align:start position:0% + +your okay + + align:start position:0% + + + + align:start position:0% + +yes okay + + align:start position:0% + + + + align:start position:0% + +can you say + + align:start position:0% +can you say + + + align:start position:0% +can you say +one say one oh one one no no no no can + + align:start position:0% +one say one oh one one no no no no can + + + align:start position:0% +one say one oh one one no no no no can +you say one okay two count up two three + + align:start position:0% +you say one okay two count up two three + + + align:start position:0% +you say one okay two count up two three +three one + + align:start position:0% + + + + align:start position:0% + +yes you want three three I got it yes + + align:start position:0% +yes you want three three I got it yes + + + align:start position:0% +yes you want three three I got it yes +people + + align:start position:0% +people + + + align:start position:0% +people +one + + align:start position:0% +one + + + align:start position:0% +one +will + + align:start position:0% +will + + + align:start position:0% +will +prepare a synthesis about the question + + align:start position:0% +prepare a synthesis about the question + + + align:start position:0% +prepare a synthesis about the question +one people who are two will write a syn + + align:start position:0% +one people who are two will write a syn + + + align:start position:0% +one people who are two will write a syn +about the question two and people who + + align:start position:0% +about the question two and people who + + + align:start position:0% +about the question two and people who +are three will write a syn about the + + align:start position:0% +are three will write a syn about the + + + align:start position:0% +are three will write a syn about the +question three + + align:start position:0% +question three + + + align:start position:0% +question three +okay let's + + align:start position:0% + + + + align:start position:0% + +go now all we can work because we will + + align:start position:0% +go now all we can work because we will + + + align:start position:0% +go now all we can work because we will +try to understand + + align:start position:0% +try to understand + + + align:start position:0% +try to understand +so I'm number three you are three I'm + + align:start position:0% +so I'm number three you are three I'm + + + align:start position:0% +so I'm number three you are three I'm +number three right yes three are lessons + + align:start position:0% +number three right yes three are lessons + + + align:start position:0% +number three right yes three are lessons +lessons Okay Okay + + align:start position:0% + + + + align:start position:0% + +you here + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% + + + + align:start position:0% + +worked really well + + align:start position:0% + + + + align:start position:0% + +with + + align:start position:0% + + + + align:start position:0% + +there but now it's + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +wa + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +let you two take the lead on this + + align:start position:0% +let you two take the lead on this + + + align:start position:0% +let you two take the lead on this +no is that you no this is me because I I + + align:start position:0% +no is that you no this is me because I I + + + align:start position:0% +no is that you no this is me because I I +don't did thisall no this is me this is + + align:start position:0% +don't did thisall no this is me this is + + + align:start position:0% +don't did thisall no this is me this is +because I thought we use it for the + + align:start position:0% +because I thought we use it for the + + + align:start position:0% +because I thought we use it for the +exercise it would be done I didn't + + align:start position:0% + + + + align:start position:0% + +realize no was suppos to be the + + align:start position:0% +realize no was suppos to be the + + + align:start position:0% +realize no was suppos to be the +group what the + + align:start position:0% +group what the + + + align:start position:0% +group what the +group I think is what they told + + align:start position:0% +group I think is what they told + + + align:start position:0% +group I think is what they told +me I don't know I have no idea what the + + align:start position:0% +me I don't know I have no idea what the + + + align:start position:0% +me I don't know I have no idea what the +homework assignment was here + + align:start position:0% + + + + align:start position:0% + +floundering in the sea of + + align:start position:0% + + + + align:start position:0% + +vag depends on how you approach that + + align:start position:0% + + + + align:start position:0% + +understand we didn't know any + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% +of + + + align:start position:0% +of +our different conscious i + + align:start position:0% +our different conscious i + + + align:start position:0% +our different conscious i +o c o n s c i o + + align:start position:0% + + + + align:start position:0% + +i i + + align:start position:0% +i i + + + align:start position:0% +i i +u + + align:start position:0% +u + + + align:start position:0% +u +i yeah we need ours and other + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +multiple values into + + align:start position:0% + + + + align:start position:0% + +single okay good job okay okay sorry + + align:start position:0% +single okay good job okay okay sorry + + + align:start position:0% +single okay good job okay okay sorry +great now + + align:start position:0% +great now + + + align:start position:0% +great now +who will present the first group for the + + align:start position:0% +who will present the first group for the + + + align:start position:0% +who will present the first group for the +first + + align:start position:0% +first + + + align:start position:0% +first +group who are the + + align:start position:0% +group who are the + + + align:start position:0% +group who are the +volunteer for the first + + align:start position:0% +volunteer for the first + + + align:start position:0% +volunteer for the first +group uh you you were design assigned as + + align:start position:0% +group uh you you were design assigned as + + + align:start position:0% +group uh you you were design assigned as +a volunteer okay summary what did we + + align:start position:0% +a volunteer okay summary what did we + + + align:start position:0% +a volunteer okay summary what did we +pick up from the cards some people did + + align:start position:0% +pick up from the cards some people did + + + align:start position:0% +pick up from the cards some people did +the um did the answer the cards + + align:start position:0% +the um did the answer the cards + + + align:start position:0% +the um did the answer the cards +considering the exercise and some people + + align:start position:0% +considering the exercise and some people + + + align:start position:0% +considering the exercise and some people +didn't considering the assignment first + + align:start position:0% +didn't considering the assignment first + + + align:start position:0% +didn't considering the assignment first +observation second observation there + + align:start position:0% +observation second observation there + + + align:start position:0% +observation second observation there +were challenges going from General to + + align:start position:0% +were challenges going from General to + + + align:start position:0% +were challenges going from General to +specific and the third one there were + + align:start position:0% +specific and the third one there were + + + align:start position:0% +specific and the third one there were +challenges going from tacit to + + align:start position:0% + + + + align:start position:0% + +explicit can you explain it a bit more + + align:start position:0% +explicit can you explain it a bit more + + + align:start position:0% +explicit can you explain it a bit more +because you were very + + align:start position:0% + + + + align:start position:0% + +sens what is about general what case + + align:start position:0% +sens what is about general what case + + + align:start position:0% +sens what is about general what case +about General to specific and what case + + align:start position:0% +about General to specific and what case + + + align:start position:0% +about General to specific and what case +about t it to explicit we have 10 + + align:start position:0% +about t it to explicit we have 10 + + + align:start position:0% +about t it to explicit we have 10 +minutes for for his presentation our + + align:start position:0% +minutes for for his presentation our + + + align:start position:0% +minutes for for his presentation our +conversation it's a discussion okay well + + align:start position:0% +conversation it's a discussion okay well + + + align:start position:0% +conversation it's a discussion okay well +you can ask me maybe they can ask me + + align:start position:0% +you can ask me maybe they can ask me + + + align:start position:0% +you can ask me maybe they can ask me +questions yes when I was a + + align:start position:0% +questions yes when I was a + + + align:start position:0% +questions yes when I was a +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +baby so this one was pretty obvious some + + align:start position:0% +baby so this one was pretty obvious some + + + align:start position:0% +baby so this one was pretty obvious some +people responded this um in terms of + + align:start position:0% +people responded this um in terms of + + + align:start position:0% +people responded this um in terms of +they referred to the exercise like + + align:start position:0% +they referred to the exercise like + + + align:start position:0% +they referred to the exercise like +during the discussion blah blah blah and + + align:start position:0% +during the discussion blah blah blah and + + + align:start position:0% +during the discussion blah blah blah and +then here it was trying to come up with + + align:start position:0% +then here it was trying to come up with + + + align:start position:0% +then here it was trying to come up with +reasons which was the + + align:start position:0% +reasons which was the + + + align:start position:0% +reasons which was the +assignment this was the difficulty so + + align:start position:0% +assignment this was the difficulty so + + + align:start position:0% +assignment this was the difficulty so +that was I think interesting to begin + + align:start position:0% +that was I think interesting to begin + + + align:start position:0% +that was I think interesting to begin +with + + align:start position:0% + + + + align:start position:0% + +what then these are the two the types + + align:start position:0% +what then these are the two the types + + + align:start position:0% +what then these are the two the types +the summaries mean specifically I can + + align:start position:0% +the summaries mean specifically I can + + + align:start position:0% +the summaries mean specifically I can +read these out to you but what was your + + align:start position:0% +read these out to you but what was your + + + align:start position:0% +read these out to you but what was your +question this was observations + + align:start position:0% +question this was observations + + + align:start position:0% +question this was observations +observations I just didn't quite sorry + + align:start position:0% +observations I just didn't quite sorry + + + align:start position:0% +observations I just didn't quite sorry +everyone feel + + align:start position:0% +everyone feel + + + align:start position:0% +everyone feel +that ER their comments are here do you + + align:start position:0% +that ER their comments are here do you + + + align:start position:0% +that ER their comments are here do you +feel that your comments are here + + align:start position:0% +feel that your comments are here + + + align:start position:0% +feel that your comments are here +sure um can I ask yes you can ask can I + + align:start position:0% +sure um can I ask yes you can ask can I + + + align:start position:0% +sure um can I ask yes you can ask can I +add something yeah okay one of the + + align:start position:0% +add something yeah okay one of the + + + align:start position:0% +add something yeah okay one of the +things that I identified as a challenge + + align:start position:0% +things that I identified as a challenge + + + align:start position:0% +things that I identified as a challenge +was to differentiate from values and + + align:start position:0% +was to differentiate from values and + + + align:start position:0% +was to differentiate from values and +assumptions I mean when I was writing + + align:start position:0% +assumptions I mean when I was writing + + + align:start position:0% +assumptions I mean when I was writing +about it I was thinking is this a values + + align:start position:0% +about it I was thinking is this a values + + + align:start position:0% +about it I was thinking is this a values +an assumption and I also think that they + + align:start position:0% +an assumption and I also think that they + + + align:start position:0% +an assumption and I also think that they +can be sometimes they can it's hard for + + align:start position:0% +can be sometimes they can it's hard for + + + align:start position:0% +can be sometimes they can it's hard for +to separate one tcid versus the tcid + + align:start position:0% +to separate one tcid versus the tcid + + + align:start position:0% +to separate one tcid versus the tcid +versus explicit making you know these + + align:start position:0% +versus explicit making you know these + + + align:start position:0% +versus explicit making you know these +values and assumptions that you have + + align:start position:0% +values and assumptions that you have + + + align:start position:0% +values and assumptions that you have +like in your head being able to + + align:start position:0% +like in your head being able to + + + align:start position:0% +like in your head being able to +verbalize them and draw them out this do + + align:start position:0% +verbalize them and draw them out this do + + + align:start position:0% +verbalize them and draw them out this do +you feel that that would fall into that + + align:start position:0% +you feel that that would fall into that + + + align:start position:0% +you feel that that would fall into that +c probably + + align:start position:0% +c probably + + + align:start position:0% +c probably +um I mean like what's what's the + + align:start position:0% +um I mean like what's what's the + + + align:start position:0% +um I mean like what's what's the +difficulty of differentiating like you + + align:start position:0% +difficulty of differentiating like you + + + align:start position:0% +difficulty of differentiating like you +know them but you just don't know which + + align:start position:0% +know them but you just don't know which + + + align:start position:0% +know them but you just don't know which +category they sometimes Val assumption + + align:start position:0% +category they sometimes Val assumption + + + align:start position:0% +category they sometimes Val assumption +so I don't know exactly the distinction + + align:start position:0% +so I don't know exactly the distinction + + + align:start position:0% +so I don't know exactly the distinction +the distinction between the two I mean + + align:start position:0% +the distinction between the two I mean + + + align:start position:0% +the distinction between the two I mean +it's my + + align:start position:0% +it's my + + + align:start position:0% +it's my +own um could be a fact assumption versus + + align:start position:0% +own um could be a fact assumption versus + + + align:start position:0% +own um could be a fact assumption versus +Assumption of what is good versus what + + align:start position:0% +Assumption of what is good versus what + + + align:start position:0% +Assumption of what is good versus what +is bad so I'd say i' say value is an + + align:start position:0% +is bad so I'd say i' say value is an + + + align:start position:0% +is bad so I'd say i' say value is an +assumption of what's good and what's bad + + align:start position:0% +assumption of what's good and what's bad + + + align:start position:0% +assumption of what's good and what's bad +or you know is did something happen but + + align:start position:0% +or you know is did something happen but + + + align:start position:0% +or you know is did something happen but +I can have an assumption that he a + + align:start position:0% +I can have an assumption that he a + + + align:start position:0% +I can have an assumption that he a +value well I'm trying to make a + + align:start position:0% +value well I'm trying to make a + + + align:start position:0% +value well I'm trying to make a +distinction in a a value is an + + align:start position:0% +distinction in a a value is an + + + align:start position:0% +distinction in a a value is an +assumption of good and bad whereas an + + align:start position:0% +assumption of good and bad whereas an + + + align:start position:0% +assumption of good and bad whereas an +assumption could be something is true + + align:start position:0% +assumption could be something is true + + + align:start position:0% +assumption could be something is true +you know more generally like this person + + align:start position:0% +you know more generally like this person + + + align:start position:0% +you know more generally like this person +did talk to that person these people did + + align:start position:0% +did talk to that person these people did + + + align:start position:0% +did talk to that person these people did +not do this it's not you're not you're + + align:start position:0% +not do this it's not you're not you're + + + align:start position:0% +not do this it's not you're not you're +not assigning good or bad to + + align:start position:0% + + + + align:start position:0% + +okay we can discuss later about + + align:start position:0% +okay we can discuss later about + + + align:start position:0% +okay we can discuss later about +difference + + align:start position:0% +difference + + + align:start position:0% +difference +between value and + + align:start position:0% +between value and + + + align:start position:0% +between value and +assumptions for going forward in the + + align:start position:0% +assumptions for going forward in the + + + align:start position:0% +assumptions for going forward in the +challenges okay + + align:start position:0% +challenges okay + + + align:start position:0% +challenges okay +but we will take note of that + + align:start position:0% + + + + align:start position:0% + +okay this one referred to tacit to + + align:start position:0% +okay this one referred to tacit to + + + align:start position:0% +okay this one referred to tacit to +explicit referred to um assumptions you + + align:start position:0% +explicit referred to um assumptions you + + + align:start position:0% +explicit referred to um assumptions you +know how do you make explicit some + + align:start position:0% +know how do you make explicit some + + + align:start position:0% +know how do you make explicit some +assumptions that maybe I have that are + + align:start position:0% +assumptions that maybe I have that are + + + align:start position:0% +assumptions that maybe I have that are +tested + + align:start position:0% +tested + + + align:start position:0% +tested +okay it's okay anybody have questions + + align:start position:0% +okay it's okay anybody have questions + + + align:start position:0% +okay it's okay anybody have questions +can anyone give an example of of this + + align:start position:0% +can anyone give an example of of this + + + align:start position:0% +can anyone give an example of of this +difficulty cuz it's kind of hard to know + + align:start position:0% +difficulty cuz it's kind of hard to know + + + align:start position:0% +difficulty cuz it's kind of hard to know +that you are having that difficulty if + + align:start position:0% +that you are having that difficulty if + + + align:start position:0% +that you are having that difficulty if +it's + + align:start position:0% + + + + align:start position:0% + +t I guess once you get to he you + + align:start position:0% +t I guess once you get to he you + + + align:start position:0% +t I guess once you get to he you +realized that it was Ted so give me an + + align:start position:0% +realized that it was Ted so give me an + + + align:start position:0% +realized that it was Ted so give me an +example of when you got there and you're + + align:start position:0% +example of when you got there and you're + + + align:start position:0% +example of when you got there and you're +like wow well I + + align:start position:0% + + + + align:start position:0% + +okay in this exercise in this + + align:start position:0% +okay in this exercise in this + + + align:start position:0% +okay in this exercise in this +homeworking + + align:start position:0% +homeworking + + + align:start position:0% +homeworking +yeah that was mine so I don't + + align:start position:0% +yeah that was mine so I don't + + + align:start position:0% +yeah that was mine so I don't +know anyone + + align:start position:0% + + + + align:start position:0% + +have anyone was able to do that and tell + + align:start position:0% +have anyone was able to do that and tell + + + align:start position:0% +have anyone was able to do that and tell +about how they did + + align:start position:0% + + + + align:start position:0% + +it yeah + + align:start position:0% +it yeah + + + align:start position:0% +it yeah +okay it's more question then is it when + + align:start position:0% +okay it's more question then is it when + + + align:start position:0% +okay it's more question then is it when +you when you try when you need to + + align:start position:0% +you when you try when you need to + + + align:start position:0% +you when you try when you need to +express or were your assumptions in your + + align:start position:0% +express or were your assumptions in your + + + align:start position:0% +express or were your assumptions in your +values behind the + + align:start position:0% +values behind the + + + align:start position:0% +values behind the +argument the effort you made to to + + align:start position:0% +argument the effort you made to to + + + align:start position:0% +argument the effort you made to to +express it or to write it down makes + + align:start position:0% +express it or to write it down makes + + + align:start position:0% +express it or to write it down makes +that knowledge about the situation + + align:start position:0% + + + + align:start position:0% + +explicit I mean that's what I felt when + + align:start position:0% +explicit I mean that's what I felt when + + + align:start position:0% +explicit I mean that's what I felt when +I was answering something that I had in + + align:start position:0% +I was answering something that I had in + + + align:start position:0% +I was answering something that I had in +my mind that I I mean I use it to build + + align:start position:0% +my mind that I I mean I use it to build + + + align:start position:0% +my mind that I I mean I use it to build +we use it in the group to build the the + + align:start position:0% +we use it in the group to build the the + + + align:start position:0% +we use it in the group to build the the +argument when you need to express + + align:start position:0% +argument when you need to express + + + align:start position:0% +argument when you need to express +it instead of just thinking about it and + + align:start position:0% +it instead of just thinking about it and + + + align:start position:0% +it instead of just thinking about it and +we need to express it it becomes + + align:start position:0% +we need to express it it becomes + + + align:start position:0% +we need to express it it becomes +explicit exactly so and that was the + + align:start position:0% +explicit exactly so and that was the + + + align:start position:0% +explicit exactly so and that was the +assignment which is make explicit your + + align:start position:0% +assignment which is make explicit your + + + align:start position:0% +assignment which is make explicit your +assumptions okay so in doing + + align:start position:0% +assumptions okay so in doing + + + align:start position:0% +assumptions okay so in doing +so people realized that they had some + + align:start position:0% +so people realized that they had some + + + align:start position:0% +so people realized that they had some +assumptions thank you very much let's go + + align:start position:0% +assumptions thank you very much let's go + + + align:start position:0% +assumptions thank you very much let's go +to the next one who will present the + + align:start position:0% +to the next one who will present the + + + align:start position:0% +to the next one who will present the +surprises of the group it's all + + align:start position:0% + + + + align:start position:0% + +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +you OB moment but um that the surprise + + align:start position:0% +you OB moment but um that the surprise + + + align:start position:0% +you OB moment but um that the surprise +was how difficult it was to define the + + align:start position:0% +was how difficult it was to define the + + + align:start position:0% +was how difficult it was to define the +assumptions which goes along with the + + align:start position:0% +assumptions which goes along with the + + + align:start position:0% +assumptions which goes along with the +challenge of going from okay um that it + + align:start position:0% +challenge of going from okay um that it + + + align:start position:0% +challenge of going from okay um that it +was easier than it was than expected to + + align:start position:0% +was easier than it was than expected to + + + align:start position:0% +was easier than it was than expected to +identify + + align:start position:0% +identify + + + align:start position:0% +identify +values and easier to work on this in a + + align:start position:0% +values and easier to work on this in a + + + align:start position:0% +values and easier to work on this in a +group than they than it was than was + + align:start position:0% + + + + align:start position:0% + +expected okay that's it's they're really + + align:start position:0% +expected okay that's it's they're really + + + align:start position:0% +expected okay that's it's they're really +uh brief so it was hard to + + align:start position:0% +uh brief so it was hard to + + + align:start position:0% +uh brief so it was hard to +okay okay all the surprises of each one + + align:start position:0% +okay okay all the surprises of each one + + + align:start position:0% +okay okay all the surprises of each one +you feel that are represented in this + + align:start position:0% + + + + align:start position:0% + +summary which + + align:start position:0% +summary which + + + align:start position:0% +summary which +of one is your surprise represented here + + align:start position:0% +of one is your surprise represented here + + + align:start position:0% +of one is your surprise represented here +you see your input represented on this + + align:start position:0% +you see your input represented on this + + + align:start position:0% +you see your input represented on this +summary or you have had a different + + align:start position:0% +summary or you have had a different + + + align:start position:0% +summary or you have had a different +surprise that's not here + + align:start position:0% +surprise that's not here + + + align:start position:0% +surprise that's not here +I have one that is completely the + + align:start position:0% +I have one that is completely the + + + align:start position:0% +I have one that is completely the +opposite of one that is is your C up + + align:start position:0% + + + + align:start position:0% + +here okay but + + align:start position:0% +here okay but + + + align:start position:0% +here okay but +CH okay for me it was not easy at all to + + align:start position:0% +CH okay for me it was not easy at all to + + + align:start position:0% +CH okay for me it was not easy at all to +identify + + align:start position:0% +identify + + + align:start position:0% +identify +Val I mean my most difficult thing was + + align:start position:0% +Val I mean my most difficult thing was + + + align:start position:0% +Val I mean my most difficult thing was +Finding to finding values so those of + + align:start position:0% +Finding to finding values so those of + + + align:start position:0% +Finding to finding values so those of +you who thought that it was easier to + + align:start position:0% +you who thought that it was easier to + + + align:start position:0% +you who thought that it was easier to +identify + + align:start position:0% +identify + + + align:start position:0% +identify +values than assumptions why why did you + + align:start position:0% +values than assumptions why why did you + + + align:start position:0% +values than assumptions why why did you +find that to be the + + align:start position:0% + + + + align:start position:0% + +case I mean like for me you know I am an + + align:start position:0% +case I mean like for me you know I am an + + + align:start position:0% +case I mean like for me you know I am an +urban planner therefore I value um you + + align:start position:0% +urban planner therefore I value um you + + + align:start position:0% +urban planner therefore I value um you +know I'm an hcd I value communities I + + align:start position:0% +know I'm an hcd I value communities I + + + align:start position:0% +know I'm an hcd I value communities I +value organizing I value bottom up + + align:start position:0% +value organizing I value bottom up + + + align:start position:0% +value organizing I value bottom up +planning like these are things + + align:start position:0% +planning like these are things + + + align:start position:0% +planning like these are things +that you know like I just I don't know + + align:start position:0% +that you know like I just I don't know + + + align:start position:0% +that you know like I just I don't know +for me it was just + + align:start position:0% + + + + align:start position:0% + +easier the whole reason that I'm here is + + align:start position:0% +easier the whole reason that I'm here is + + + align:start position:0% +easier the whole reason that I'm here is +because you know those are the things + + align:start position:0% +because you know those are the things + + + align:start position:0% +because you know those are the things +that I value + + align:start position:0% + + + + align:start position:0% + +so I put um my card there says level of + + align:start position:0% +so I put um my card there says level of + + + align:start position:0% +so I put um my card there says level of +compromise or something like that and I + + align:start position:0% +compromise or something like that and I + + + align:start position:0% +compromise or something like that and I +actually my surprise + + align:start position:0% +actually my surprise + + + align:start position:0% +actually my surprise +was I had a negative sensation around + + align:start position:0% +was I had a negative sensation around + + + align:start position:0% +was I had a negative sensation around +that how much we + + align:start position:0% +that how much we + + + align:start position:0% +that how much we +compromised uh how much you know like in + + align:start position:0% +compromised uh how much you know like in + + + align:start position:0% +compromised uh how much you know like in +during the exercise I was realizing + + align:start position:0% +during the exercise I was realizing + + + align:start position:0% +during the exercise I was realizing +during my homework assignment I was + + align:start position:0% +during my homework assignment I was + + + align:start position:0% +during my homework assignment I was +realizing how much we actually gave in + + align:start position:0% +realizing how much we actually gave in + + + align:start position:0% +realizing how much we actually gave in +to come to a common + + align:start position:0% +to come to a common + + + align:start position:0% +to come to a common +um uh that common description of the + + align:start position:0% + + + + align:start position:0% + +problem and Andia why was it so hard for + + align:start position:0% +problem and Andia why was it so hard for + + + align:start position:0% +problem and Andia why was it so hard for +you to think of your Val + + align:start position:0% + + + + align:start position:0% + +identify I think I had a problem in + + align:start position:0% +identify I think I had a problem in + + + align:start position:0% +identify I think I had a problem in +differentiating from values and + + align:start position:0% +differentiating from values and + + + align:start position:0% +differentiating from values and +assumptions so from that I had a problem + + align:start position:0% +assumptions so from that I had a problem + + + align:start position:0% +assumptions so from that I had a problem +identifying values too so that was a + + align:start position:0% +identifying values too so that was a + + + align:start position:0% +identifying values too so that was a +consequence from that too um and I think + + align:start position:0% +consequence from that too um and I think + + + align:start position:0% +consequence from that too um and I think +I think it's always hard for you to + + align:start position:0% +I think it's always hard for you to + + + align:start position:0% +I think it's always hard for you to +assume that you are committed with some + + align:start position:0% +assume that you are committed with some + + + align:start position:0% +assume that you are committed with some +values in some + + align:start position:0% +values in some + + + align:start position:0% +values in some +point because those I mean the value + + align:start position:0% +point because those I mean the value + + + align:start position:0% +point because those I mean the value +things is + + align:start position:0% +things is + + + align:start position:0% +things is +very it's personally your position + + align:start position:0% +very it's personally your position + + + align:start position:0% +very it's personally your position +towards something so it's like it's + + align:start position:0% +towards something so it's like it's + + + align:start position:0% +towards something so it's like it's +assuming that you have a way of seeing + + align:start position:0% +assuming that you have a way of seeing + + + align:start position:0% +assuming that you have a way of seeing +things that it's your way of seeing + + align:start position:0% +things that it's your way of seeing + + + align:start position:0% +things that it's your way of seeing +things so it's like a personal + + align:start position:0% +things so it's like a personal + + + align:start position:0% +things so it's like a personal +identification with a problem it's more + + align:start position:0% +identification with a problem it's more + + + align:start position:0% +identification with a problem it's more +it's more than just uh an abstract anal + + align:start position:0% +it's more than just uh an abstract anal + + + align:start position:0% +it's more than just uh an abstract anal +analysis it's your own values that + + align:start position:0% +analysis it's your own values that + + + align:start position:0% +analysis it's your own values that +influence that analysis and being aware + + align:start position:0% +influence that analysis and being aware + + + align:start position:0% +influence that analysis and being aware +of that for me it's it's kind of + + align:start position:0% +of that for me it's it's kind of + + + align:start position:0% +of that for me it's it's kind of +a and it's always Limited it's bed in + + align:start position:0% +a and it's always Limited it's bed in + + + align:start position:0% +a and it's always Limited it's bed in +specific + + align:start position:0% + + + + align:start position:0% + +values so these are questions that are + + align:start position:0% +values so these are questions that are + + + align:start position:0% +values so these are questions that are +interesting that are coming up to keep + + align:start position:0% +interesting that are coming up to keep + + + align:start position:0% +interesting that are coming up to keep +in mind when we start to talk about + + align:start position:0% +in mind when we start to talk about + + + align:start position:0% +in mind when we start to talk about +functions and values later on we will + + align:start position:0% +functions and values later on we will + + + align:start position:0% +functions and values later on we will +make an exercise later if it's being too + + align:start position:0% +make an exercise later if it's being too + + + align:start position:0% +make an exercise later if it's being too +difficult for you + + align:start position:0% +difficult for you + + + align:start position:0% +difficult for you +to to clarify more the ideas we we'll + + align:start position:0% +to to clarify more the ideas we we'll + + + align:start position:0% +to to clarify more the ideas we we'll +come back later to this discussion after + + align:start position:0% +come back later to this discussion after + + + align:start position:0% +come back later to this discussion after +the exercise that we will do in class in + + align:start position:0% +the exercise that we will do in class in + + + align:start position:0% +the exercise that we will do in class in +a few minutes more okay okay but let's + + align:start position:0% +a few minutes more okay okay but let's + + + align:start position:0% +a few minutes more okay okay but let's +listen people from + + align:start position:0% +listen people from + + + align:start position:0% +listen people from +lessons to rescue the + + align:start position:0% + + + + align:start position:0% + +lessons + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +uh so was we definitely thought it was + + align:start position:0% +uh so was we definitely thought it was + + + align:start position:0% +uh so was we definitely thought it was +it was really important to be conscious + + align:start position:0% +it was really important to be conscious + + + align:start position:0% +it was really important to be conscious +of what's going on underneath and uh the + + align:start position:0% +of what's going on underneath and uh the + + + align:start position:0% +of what's going on underneath and uh the +more the more you can do that or you + + align:start position:0% +more the more you can do that or you + + + align:start position:0% +more the more you can do that or you +could work with value systems um we + + align:start position:0% +could work with value systems um we + + + align:start position:0% +could work with value systems um we +thought we thought it was difficult to + + align:start position:0% +thought we thought it was difficult to + + + align:start position:0% +thought we thought it was difficult to +make the values + + align:start position:0% +make the values + + + align:start position:0% +make the values +explicit um but it was very important to + + align:start position:0% +explicit um but it was very important to + + + align:start position:0% +explicit um but it was very important to +make thinking very explicit and that + + align:start position:0% +make thinking very explicit and that + + + align:start position:0% +make thinking very explicit and that +really that really helps clarify the + + align:start position:0% +really that really helps clarify the + + + align:start position:0% +really that really helps clarify the +value system so at least once you get + + align:start position:0% +value system so at least once you get + + + align:start position:0% +value system so at least once you get +everything out in the open uh then it + + align:start position:0% +everything out in the open uh then it + + + align:start position:0% +everything out in the open uh then it +makes it more possible to integrate + + align:start position:0% +makes it more possible to integrate + + + align:start position:0% +makes it more possible to integrate +multiple values into a single frame + + align:start position:0% +multiple values into a single frame + + + align:start position:0% +multiple values into a single frame +which then sort of forms a shared basis + + align:start position:0% +which then sort of forms a shared basis + + + align:start position:0% +which then sort of forms a shared basis +fraction um and I didn't get a chance to + + align:start position:0% +fraction um and I didn't get a chance to + + + align:start position:0% +fraction um and I didn't get a chance to +add mine but that was work with people + + align:start position:0% +add mine but that was work with people + + + align:start position:0% +add mine but that was work with people +who really think pretty similarly to you + + align:start position:0% +who really think pretty similarly to you + + + align:start position:0% +who really think pretty similarly to you +so it makes life easier so but + + align:start position:0% +so it makes life easier so but + + + align:start position:0% +so it makes life easier so but +unfortunately that's not always possible + + align:start position:0% +unfortunately that's not always possible + + + align:start position:0% +unfortunately that's not always possible +but try to do it when you + + align:start position:0% +but try to do it when you + + + align:start position:0% +but try to do it when you +can comments or questions to + + align:start position:0% + + + + align:start position:0% + +him it's also I think it's also a + + align:start position:0% +him it's also I think it's also a + + + align:start position:0% +him it's also I think it's also a +process that helps you identify your + + align:start position:0% +process that helps you identify your + + + align:start position:0% +process that helps you identify your +weaknesses within your + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +argument one of the lessons is about + + align:start position:0% +argument one of the lessons is about + + + align:start position:0% +argument one of the lessons is about +identifying weaknesses within the whole + + align:start position:0% +identifying weaknesses within the whole + + + align:start position:0% +identifying weaknesses within the whole +scription of the argument what do you + + align:start position:0% +scription of the argument what do you + + + align:start position:0% +scription of the argument what do you +mean by Witnesses + + align:start position:0% +mean by Witnesses + + + align:start position:0% +mean by Witnesses +witness + + align:start position:0% +witness + + + align:start position:0% +witness +oh Witnesses what within your argument + + align:start position:0% +oh Witnesses what within your argument + + + align:start position:0% +oh Witnesses what within your argument +within your + + align:start position:0% + + + + align:start position:0% + +argument it was about that last question + + align:start position:0% +argument it was about that last question + + + align:start position:0% +argument it was about that last question +what is missing within all the argument + + align:start position:0% +what is missing within all the argument + + + align:start position:0% +what is missing within all the argument +question we had to answer + + align:start position:0% +question we had to answer + + + align:start position:0% +question we had to answer +do + + align:start position:0% + + + + align:start position:0% + +exercise I guess missing inconsistent or + + align:start position:0% +exercise I guess missing inconsistent or + + + align:start position:0% +exercise I guess missing inconsistent or +false be argument could be + + align:start position:0% + + + + align:start position:0% + +wrong anything + + align:start position:0% + + + + align:start position:0% + +okay okay thank you very + + align:start position:0% + + + + align:start position:0% + +much + + align:start position:0% + + + + align:start position:0% + +yeah there's a so we'll add um Claudia + + align:start position:0% +yeah there's a so we'll add um Claudia + + + align:start position:0% +yeah there's a so we'll add um Claudia +here she had + + align:start position:0% +here she had + + + align:start position:0% +here she had +a it's difficult to differentiate + + align:start position:0% +a it's difficult to differentiate + + + align:start position:0% +a it's difficult to differentiate +between values and assumptions yes we + + align:start position:0% +between values and assumptions yes we + + + align:start position:0% +between values and assumptions yes we +may have different surprises because + + align:start position:0% +may have different surprises because + + + align:start position:0% +may have different surprises because +people may have experience in different + + align:start position:0% +people may have experience in different + + + align:start position:0% +people may have experience in different +surprises okay we don't need to be + + align:start position:0% +surprises okay we don't need to be + + + align:start position:0% +surprises okay we don't need to be +consistent in these + + align:start position:0% + + + + align:start position:0% + +statements okay so we'll put these aside + + align:start position:0% +statements okay so we'll put these aside + + + align:start position:0% +statements okay so we'll put these aside +but we'll put them there so you can keep + + align:start position:0% +but we'll put them there so you can keep + + + align:start position:0% +but we'll put them there so you can keep +them in mind as you are hearing some Sal + + align:start position:0% +them in mind as you are hearing some Sal + + + align:start position:0% +them in mind as you are hearing some Sal +presentation and working through the + + align:start position:0% +presentation and working through the + + + align:start position:0% +presentation and working through the +exercises we do later okay and we will + + align:start position:0% +exercises we do later okay and we will + + + align:start position:0% +exercises we do later okay and we will +come back to the same kind of issues + + align:start position:0% +come back to the same kind of issues + + + align:start position:0% +come back to the same kind of issues +okay + + align:start position:0% + + + + align:start position:0% + +he + + align:start position:0% + + + + align:start position:0% + +no no no it's not this one + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +okay this it's really big + + align:start position:0% + + + + align:start position:0% + +okay we + + align:start position:0% + + + + align:start position:0% + +begin the first idea is that it's an art + + align:start position:0% +begin the first idea is that it's an art + + + align:start position:0% +begin the first idea is that it's an art +no it's a question of learning in + + align:start position:0% +no it's a question of learning in + + + align:start position:0% +no it's a question of learning in +practice how to do + + align:start position:0% + + + + align:start position:0% + +that these are some some examples of how + + align:start position:0% +that these are some some examples of how + + + align:start position:0% +that these are some some examples of how +people framed the same + + align:start position:0% + + + + align:start position:0% + +situation the issue of energy in the + + align:start position:0% +situation the issue of energy in the + + + align:start position:0% +situation the issue of energy in the +United + + align:start position:0% + + + + align:start position:0% + +States what's very interesting from in + + align:start position:0% +States what's very interesting from in + + + align:start position:0% +States what's very interesting from in +these examples is that + + align:start position:0% +these examples is that + + + align:start position:0% +these examples is that +they use two elements + + align:start position:0% +they use two elements + + + align:start position:0% +they use two elements +for naming the frame a short name and + + align:start position:0% +for naming the frame a short name and + + + align:start position:0% +for naming the frame a short name and +reliable + + align:start position:0% +reliable + + + align:start position:0% +reliable +sources and a name + + align:start position:0% +sources and a name + + + align:start position:0% +sources and a name +that is focused on the objective that + + align:start position:0% +that is focused on the objective that + + + align:start position:0% +that is focused on the objective that +they are proposing for the solution of + + align:start position:0% +they are proposing for the solution of + + + align:start position:0% +they are proposing for the solution of +the + + align:start position:0% +the + + + align:start position:0% +the +issue for the first one is reduce + + align:start position:0% +issue for the first one is reduce + + + align:start position:0% +issue for the first one is reduce +dependence for the second + + align:start position:0% + + + + align:start position:0% + +is reduce the use of f POS F and the + + align:start position:0% +is reduce the use of f POS F and the + + + align:start position:0% +is reduce the use of f POS F and the +third one is + + align:start position:0% +third one is + + + align:start position:0% +third one is +reducing + + align:start position:0% + + + + align:start position:0% + +demand can you + + align:start position:0% +demand can you + + + align:start position:0% +demand can you +go so one idea that I was thinking about + + align:start position:0% +go so one idea that I was thinking about + + + align:start position:0% +go so one idea that I was thinking about +is that perhaps should be good for us to + + align:start position:0% +is that perhaps should be good for us to + + + align:start position:0% +is that perhaps should be good for us to +put a name to our frames the work or + + align:start position:0% +put a name to our frames the work or + + + align:start position:0% +put a name to our frames the work or +framing that we made yesterday we should + + align:start position:0% +framing that we made yesterday we should + + + align:start position:0% +framing that we made yesterday we should +put name for it for each one okay + + align:start position:0% +put name for it for each one okay + + + align:start position:0% +put name for it for each one okay +assumptions there is two kind of + + align:start position:0% +assumptions there is two kind of + + + align:start position:0% +assumptions there is two kind of +assumptions + + align:start position:0% + + + + align:start position:0% + +some assumptions are about + + align:start position:0% + + + + align:start position:0% + +realities no X th000 people + + align:start position:0% + + + + align:start position:0% + +use uh open course whereare each year I + + align:start position:0% +use uh open course whereare each year I + + + align:start position:0% +use uh open course whereare each year I +can go to + + align:start position:0% + + + + align:start position:0% + +the reality I can apply a make a + + align:start position:0% +the reality I can apply a make a + + + align:start position:0% +the reality I can apply a make a +research and I can verify this + + align:start position:0% +research and I can verify this + + + align:start position:0% +research and I can verify this +assumption with just with number I have + + align:start position:0% +assumption with just with number I have + + + align:start position:0% +assumption with just with number I have +data and I may compare the data with the + + align:start position:0% +data and I may compare the data with the + + + align:start position:0% +data and I may compare the data with the +Assumption it's very simple this kind of + + align:start position:0% +Assumption it's very simple this kind of + + + align:start position:0% +Assumption it's very simple this kind of +assumptions + + align:start position:0% +assumptions + + + align:start position:0% +assumptions +okay the physician when he + + align:start position:0% +okay the physician when he + + + align:start position:0% +okay the physician when he +makes + + align:start position:0% +makes + + + align:start position:0% +makes +an diagnosis + + align:start position:0% +an diagnosis + + + align:start position:0% +an diagnosis +diagnostic he makes a lot of assumptions + + align:start position:0% +diagnostic he makes a lot of assumptions + + + align:start position:0% +diagnostic he makes a lot of assumptions +about how + + align:start position:0% +about how + + + align:start position:0% +about how +our temperature things like that and he + + align:start position:0% +our temperature things like that and he + + + align:start position:0% +our temperature things like that and he +put the thermometer and he is able to + + align:start position:0% +put the thermometer and he is able to + + + align:start position:0% +put the thermometer and he is able to +verify how high is the + + align:start position:0% +verify how high is the + + + align:start position:0% +verify how high is the +fever this kind of assumption is very + + align:start position:0% +fever this kind of assumption is very + + + align:start position:0% +fever this kind of assumption is very +easy it's more easy for identify the + + align:start position:0% +easy it's more easy for identify the + + + align:start position:0% +easy it's more easy for identify the +second kind of assumptions is assumpt + + align:start position:0% +second kind of assumptions is assumpt + + + align:start position:0% +second kind of assumptions is assumpt +assumptions about CA + + align:start position:0% +assumptions about CA + + + align:start position:0% +assumptions about CA +relations in this case is more difficult + + align:start position:0% +relations in this case is more difficult + + + align:start position:0% +relations in this case is more difficult +to separate from reasons + + align:start position:0% + + + + align:start position:0% + +the second kind is about how I think the + + align:start position:0% +the second kind is about how I think the + + + align:start position:0% +the second kind is about how I think the +word + + align:start position:0% +word + + + align:start position:0% +word +works like this statement democracy + + align:start position:0% +works like this statement democracy + + + align:start position:0% +works like this statement democracy +improves the quality of + + align:start position:0% +improves the quality of + + + align:start position:0% +improves the quality of +life okay it's a + + align:start position:0% +life okay it's a + + + align:start position:0% +life okay it's a +belief there's also + + align:start position:0% +belief there's also + + + align:start position:0% +belief there's also +behind this are values okay but the + + align:start position:0% +behind this are values okay but the + + + align:start position:0% +behind this are values okay but the +statement is not about + + align:start position:0% +statement is not about + + + align:start position:0% +statement is not about +value the + + align:start position:0% +value the + + + align:start position:0% +value the +statement contains value but not about + + align:start position:0% +statement contains value but not about + + + align:start position:0% +statement contains value but not about +values okay the statement is that this + + align:start position:0% +values okay the statement is that this + + + align:start position:0% +values okay the statement is that this +kind of political + + align:start position:0% +kind of political + + + align:start position:0% +kind of political +system has an impact in the quality of + + align:start position:0% +system has an impact in the quality of + + + align:start position:0% +system has an impact in the quality of +life I can make a research for verifying + + align:start position:0% +life I can make a research for verifying + + + align:start position:0% +life I can make a research for verifying +this but it's not only a question of + + align:start position:0% +this but it's not only a question of + + + align:start position:0% +this but it's not only a question of +compare ER raw data + + align:start position:0% + + + + align:start position:0% + +no for example people think + + align:start position:0% + + + + align:start position:0% + +that in Peru peasant thinks that it's + + align:start position:0% +that in Peru peasant thinks that it's + + + align:start position:0% +that in Peru peasant thinks that it's +impossible to reach the market of Lima + + align:start position:0% +impossible to reach the market of Lima + + + align:start position:0% +impossible to reach the market of Lima +for + + align:start position:0% +for + + + align:start position:0% +for +the whole Traders + + align:start position:0% + + + + align:start position:0% + +they have this idea in their mind it's + + align:start position:0% +they have this idea in their mind it's + + + align:start position:0% +they have this idea in their mind it's +impossible to reach directly the market + + align:start position:0% +impossible to reach directly the market + + + align:start position:0% +impossible to reach directly the market +of + + align:start position:0% + + + + align:start position:0% + +Lima uh it's not only a question of to + + align:start position:0% +Lima uh it's not only a question of to + + + align:start position:0% +Lima uh it's not only a question of to +get + + align:start position:0% +get + + + align:start position:0% +get +information also but for this case of + + align:start position:0% +information also but for this case of + + + align:start position:0% +information also but for this case of +assumption we can challenge the + + align:start position:0% +assumption we can challenge the + + + align:start position:0% +assumption we can challenge the +Assumption with examples how things work + + align:start position:0% +Assumption with examples how things work + + + align:start position:0% +Assumption with examples how things work +differently for be for helping them to + + align:start position:0% +differently for be for helping them to + + + align:start position:0% +differently for be for helping them to +understand + + align:start position:0% +understand + + + align:start position:0% +understand +that this cause relation is not so + + align:start position:0% +that this cause relation is not so + + + align:start position:0% +that this cause relation is not so +absolute + + align:start position:0% + + + + align:start position:0% + +yeah the Lessing is very + + align:start position:0% +yeah the Lessing is very + + + align:start position:0% +yeah the Lessing is very +simple we always are using the name + + align:start position:0% +simple we always are using the name + + + align:start position:0% +simple we always are using the name +assumption when it is tacit no it is + + align:start position:0% +assumption when it is tacit no it is + + + align:start position:0% +assumption when it is tacit no it is +implicit once we make it explicit we + + align:start position:0% +implicit once we make it explicit we + + + align:start position:0% +implicit once we make it explicit we +begin to work with as + + align:start position:0% + + + + align:start position:0% + +hypothesis okay + + align:start position:0% +hypothesis okay + + + align:start position:0% +hypothesis okay +what are + + align:start position:0% +what are + + + align:start position:0% +what are +value value are + + align:start position:0% + + + + align:start position:0% + +criterias it's impossible to verify if a + + align:start position:0% +criterias it's impossible to verify if a + + + align:start position:0% +criterias it's impossible to verify if a +value + + align:start position:0% +value + + + align:start position:0% +value +is true or + + align:start position:0% + + + + align:start position:0% + +false I have my + + align:start position:0% +false I have my + + + align:start position:0% +false I have my +values okay I for me my values are + + align:start position:0% +values okay I for me my values are + + + align:start position:0% +values okay I for me my values are +always truth + + align:start position:0% +always truth + + + align:start position:0% +always truth +I believe in them are something inent to + + align:start position:0% +I believe in them are something inent to + + + align:start position:0% +I believe in them are something inent to +to me the assumptions about the reality + + align:start position:0% +to me the assumptions about the reality + + + align:start position:0% +to me the assumptions about the reality +they are separa from me I may believe in + + align:start position:0% +they are separa from me I may believe in + + + align:start position:0% +they are separa from me I may believe in +them but if I see data I can just + + align:start position:0% +them but if I see data I can just + + + align:start position:0% +them but if I see data I can just +discard + + align:start position:0% +discard + + + align:start position:0% +discard +them okay the problem is when some + + align:start position:0% +them okay the problem is when some + + + align:start position:0% +them okay the problem is when some +people is unable to separate this kind + + align:start position:0% +people is unable to separate this kind + + + align:start position:0% +people is unable to separate this kind +of two + + align:start position:0% +of two + + + align:start position:0% +of two +things and begins to defend some + + align:start position:0% +things and begins to defend some + + + align:start position:0% +things and begins to defend some +statements about reality as if they were + + align:start position:0% +statements about reality as if they were + + + align:start position:0% +statements about reality as if they were +values it's very difficult for one to + + align:start position:0% +values it's very difficult for one to + + + align:start position:0% +values it's very difficult for one to +renew and for for reframe our thinking + + align:start position:0% +renew and for for reframe our thinking + + + align:start position:0% +renew and for for reframe our thinking +when we confuse these two + + align:start position:0% +when we confuse these two + + + align:start position:0% +when we confuse these two +categories okay so values are criteria I + + align:start position:0% +categories okay so values are criteria I + + + align:start position:0% +categories okay so values are criteria I +use to + + align:start position:0% + + + + align:start position:0% + +evaluate in the first example the value + + align:start position:0% +evaluate in the first example the value + + + align:start position:0% +evaluate in the first example the value +is Security in the second example is + + align:start position:0% +is Security in the second example is + + + align:start position:0% +is Security in the second example is +justice + + align:start position:0% + + + + align:start position:0% + +in the first example of + + align:start position:0% + + + + align:start position:0% + +the energy + + align:start position:0% +the energy + + + align:start position:0% +the energy +issue the value is the protection of the + + align:start position:0% + + + + align:start position:0% + +environment and the second example is + + align:start position:0% + + + + align:start position:0% + +Independence so when we have some values + + align:start position:0% +Independence so when we have some values + + + align:start position:0% +Independence so when we have some values +we frame the situation in different + + align:start position:0% +we frame the situation in different + + + align:start position:0% +we frame the situation in different +ways in most + + align:start position:0% +ways in most + + + align:start position:0% +ways in most +case the most important differences + + align:start position:0% +case the most important differences + + + align:start position:0% +case the most important differences +between frames are based in different + + align:start position:0% + + + + align:start position:0% + +values + + align:start position:0% +values + + + align:start position:0% +values +okay yeah + + align:start position:0% + + + + align:start position:0% + +two things from here one is that the box + + align:start position:0% +two things from here one is that the box + + + align:start position:0% +two things from here one is that the box +is + + align:start position:0% +is + + + align:start position:0% +is +invisible so it's very hard a conclusion + + align:start position:0% +invisible so it's very hard a conclusion + + + align:start position:0% +invisible so it's very hard a conclusion +you found it's very hard to to discover + + align:start position:0% +you found it's very hard to to discover + + + align:start position:0% +you found it's very hard to to discover +assumptions people who are outside from + + align:start position:0% +assumptions people who are outside from + + + align:start position:0% +assumptions people who are outside from +our mind are much more able to discover + + align:start position:0% +our mind are much more able to discover + + + align:start position:0% +our mind are much more able to discover +our + + align:start position:0% +our + + + align:start position:0% +our +assumptions people who disagree with us + + align:start position:0% +assumptions people who disagree with us + + + align:start position:0% +assumptions people who disagree with us +are much more acute in doing that so + + align:start position:0% +are much more acute in doing that so + + + align:start position:0% +are much more acute in doing that so +it's very + + align:start position:0% +it's very + + + align:start position:0% +it's very +good AR the + + align:start position:0% +good AR the + + + align:start position:0% +good AR the +goose teaching about how an organization + + align:start position:0% +goose teaching about how an organization + + + align:start position:0% +goose teaching about how an organization +can learn he explained he suggest that a + + align:start position:0% +can learn he explained he suggest that a + + + align:start position:0% +can learn he explained he suggest that a +good practice is to talk with people who + + align:start position:0% +good practice is to talk with people who + + + align:start position:0% +good practice is to talk with people who +disagree profoundly with + + align:start position:0% +disagree profoundly with + + + align:start position:0% +disagree profoundly with +us if you are a able to talk with him + + align:start position:0% + + + + align:start position:0% + +friendly because talking with this kind + + align:start position:0% +friendly because talking with this kind + + + align:start position:0% +friendly because talking with this kind +of people they will help us to discover + + align:start position:0% +of people they will help us to discover + + + align:start position:0% +of people they will help us to discover +our + + align:start position:0% +our + + + align:start position:0% +our +assumptions and they will also disturb + + align:start position:0% +assumptions and they will also disturb + + + align:start position:0% +assumptions and they will also disturb +disturb our framing so his conclusion is + + align:start position:0% +disturb our framing so his conclusion is + + + align:start position:0% +disturb our framing so his conclusion is +that it's highly useful to talk with + + align:start position:0% +that it's highly useful to talk with + + + align:start position:0% +that it's highly useful to talk with +this kind of people to look for these + + align:start position:0% +this kind of people to look for these + + + align:start position:0% +this kind of people to look for these +people and try to to establish a + + align:start position:0% +people and try to to establish a + + + align:start position:0% +people and try to to establish a +discussion + + align:start position:0% +discussion + + + align:start position:0% +discussion +about some + + align:start position:0% +about some + + + align:start position:0% +about some +issues + + align:start position:0% +issues + + + align:start position:0% +issues +okay the second idea is + + align:start position:0% +okay the second idea is + + + align:start position:0% +okay the second idea is +that to discover assumptions is like + + align:start position:0% +that to discover assumptions is like + + + align:start position:0% +that to discover assumptions is like +reverse + + align:start position:0% +reverse + + + align:start position:0% +reverse +engineering okay it's like to look at a + + align:start position:0% +engineering okay it's like to look at a + + + align:start position:0% +engineering okay it's like to look at a +computer and to dismantle the computer + + align:start position:0% +computer and to dismantle the computer + + + align:start position:0% +computer and to dismantle the computer +to discover how it + + align:start position:0% + + + + align:start position:0% + +works okay + + align:start position:0% + + + + align:start position:0% + +let's + + align:start position:0% + + + + align:start position:0% + +go the logic is if these assumptions are + + align:start position:0% +go the logic is if these assumptions are + + + align:start position:0% +go the logic is if these assumptions are +real the factor a produces the + + align:start position:0% +real the factor a produces the + + + align:start position:0% +real the factor a produces the +situation C or the factor B generate the + + align:start position:0% +situation C or the factor B generate the + + + align:start position:0% +situation C or the factor B generate the +situation C + + align:start position:0% + + + + align:start position:0% + +we + + align:start position:0% +we + + + align:start position:0% +we +normally don't include the group of + + align:start position:0% +normally don't include the group of + + + align:start position:0% +normally don't include the group of +assumptions we are using in our + + align:start position:0% + + + + align:start position:0% + +thinking the idea is to go back to the + + align:start position:0% +thinking the idea is to go back to the + + + align:start position:0% +thinking the idea is to go back to the +logical structure or to the cause of + + align:start position:0% +logical structure or to the cause of + + + align:start position:0% +logical structure or to the cause of +relations asking + + align:start position:0% +relations asking + + + align:start position:0% +relations asking +wise asking wise for the state M and + + align:start position:0% +wise asking wise for the state M and + + + align:start position:0% +wise asking wise for the state M and +asking why for the + + align:start position:0% +asking why for the + + + align:start position:0% +asking why for the +relations backyard no one one when we + + align:start position:0% +relations backyard no one one when we + + + align:start position:0% +relations backyard no one one when we +when we write an assumption we should + + align:start position:0% +when we write an assumption we should + + + align:start position:0% +when we write an assumption we should +make an + + align:start position:0% +make an + + + align:start position:0% +make an +effort to make + + align:start position:0% +effort to make + + + align:start position:0% +effort to make +it false + + align:start position:0% + + + + align:start position:0% + +feable okay to to write it to formulate + + align:start position:0% +feable okay to to write it to formulate + + + align:start position:0% +feable okay to to write it to formulate +it in a way that I can verify if it is + + align:start position:0% +it in a way that I can verify if it is + + + align:start position:0% +it in a way that I can verify if it is +true or not + + align:start position:0% + + + + align:start position:0% + +true + + align:start position:0% +true + + + align:start position:0% +true +okay yes thank + + align:start position:0% +okay yes thank + + + align:start position:0% +okay yes thank +you and this is the + + align:start position:0% +you and this is the + + + align:start position:0% +you and this is the +idea for the exercise we will do + + align:start position:0% +idea for the exercise we will do + + + align:start position:0% +idea for the exercise we will do +next we framed the + + align:start position:0% +next we framed the + + + align:start position:0% +next we framed the +situation with the instructions that you + + align:start position:0% +situation with the instructions that you + + + align:start position:0% +situation with the instructions that you +received with this + + align:start position:0% +received with this + + + align:start position:0% +received with this +schem + + align:start position:0% +schem + + + align:start position:0% +schem +okay you identify the problem you + + align:start position:0% +okay you identify the problem you + + + align:start position:0% +okay you identify the problem you +identified some factors that are + + align:start position:0% +identified some factors that are + + + align:start position:0% +identified some factors that are +generating the problem and you + + align:start position:0% +generating the problem and you + + + align:start position:0% +generating the problem and you +identified an impact of the + + align:start position:0% +identified an impact of the + + + align:start position:0% +identified an impact of the +problem no this was the way we organized + + align:start position:0% +problem no this was the way we organized + + + align:start position:0% +problem no this was the way we organized +our frame about the situation in + + align:start position:0% +our frame about the situation in + + + align:start position:0% +our frame about the situation in +Fram MH okay so the idea + + align:start position:0% +Fram MH okay so the idea + + + align:start position:0% +Fram MH okay so the idea +is first to be to begin from the + + align:start position:0% +is first to be to begin from the + + + align:start position:0% +is first to be to begin from the +scenario is why do you think that this + + align:start position:0% +scenario is why do you think that this + + + align:start position:0% +scenario is why do you think that this +problem will produce + + align:start position:0% +problem will produce + + + align:start position:0% +problem will produce +this + + align:start position:0% + + + + align:start position:0% + +impact we can make the question for the + + align:start position:0% +impact we can make the question for the + + + align:start position:0% +impact we can make the question for the +a scenario as a whole and we make + + align:start position:0% +a scenario as a whole and we make + + + align:start position:0% +a scenario as a whole and we make +questions about some components of the + + align:start position:0% +questions about some components of the + + + align:start position:0% +questions about some components of the +scenario + + align:start position:0% +scenario + + + align:start position:0% +scenario +for getting more detail about the + + align:start position:0% +for getting more detail about the + + + align:start position:0% +for getting more detail about the +assumptions after that we will try to do + + align:start position:0% +assumptions after that we will try to do + + + align:start position:0% +assumptions after that we will try to do +the same analysis to the factors that + + align:start position:0% +the same analysis to the factors that + + + align:start position:0% +the same analysis to the factors that +are generated the problem why do you + + align:start position:0% +are generated the problem why do you + + + align:start position:0% +are generated the problem why do you +think that these factors generate the + + align:start position:0% +think that these factors generate the + + + align:start position:0% +think that these factors generate the +problem + + align:start position:0% + + + + align:start position:0% + +okay yes why this scenario or one + + align:start position:0% +okay yes why this scenario or one + + + align:start position:0% +okay yes why this scenario or one +component of this scenario is generated + + align:start position:0% +component of this scenario is generated + + + align:start position:0% +component of this scenario is generated +by the problem why the factor a + + align:start position:0% +by the problem why the factor a + + + align:start position:0% +by the problem why the factor a +contributes to the + + align:start position:0% +contributes to the + + + align:start position:0% +contributes to the +problem and with conditions can you come + + align:start position:0% +problem and with conditions can you come + + + align:start position:0% +problem and with conditions can you come +back a bit okay we these are + + align:start position:0% +back a bit okay we these are + + + align:start position:0% +back a bit okay we these are +real under some conditions + + align:start position:0% +real under some conditions + + + align:start position:0% +real under some conditions +that we did not state + + align:start position:0% +that we did not state + + + align:start position:0% +that we did not state +yesterday now you should make the effort + + align:start position:0% +yesterday now you should make the effort + + + align:start position:0% +yesterday now you should make the effort +for identifying condition + + align:start position:0% +for identifying condition + + + align:start position:0% +for identifying condition +for the causes work in this + + align:start position:0% +for the causes work in this + + + align:start position:0% +for the causes work in this +way + + align:start position:0% +way + + + align:start position:0% +way +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yeah yes + + align:start position:0% +yeah yes + + + align:start position:0% +yeah yes +here for exploring + + align:start position:0% +here for exploring + + + align:start position:0% +here for exploring +values why do you think it's a + + align:start position:0% +values why do you think it's a + + + align:start position:0% +values why do you think it's a +problem okay + + align:start position:0% + + + + align:start position:0% + +or why are you concerned about this + + align:start position:0% +or why are you concerned about this + + + align:start position:0% +or why are you concerned about this +scenario why do you think this that this + + align:start position:0% +scenario why do you think this that this + + + align:start position:0% +scenario why do you think this that this +scenario is + + align:start position:0% + + + + align:start position:0% + +bad okay the reasons why the scenario is + + align:start position:0% +bad okay the reasons why the scenario is + + + align:start position:0% +bad okay the reasons why the scenario is +bad are values + + align:start position:0% +bad are values + + + align:start position:0% +bad are values +okay and the other thing are motivations + + align:start position:0% + + + + align:start position:0% + +we should try to + + align:start position:0% +we should try to + + + align:start position:0% +we should try to +discover at the in the process of our + + align:start position:0% +discover at the in the process of our + + + align:start position:0% +discover at the in the process of our +thinking what kind + + align:start position:0% + + + + align:start position:0% + +of values in this case or elements I was + + align:start position:0% +of values in this case or elements I was + + + align:start position:0% +of values in this case or elements I was +trying to protect in this process or to + + align:start position:0% + + + + align:start position:0% + +reinforce + + align:start position:0% +reinforce + + + align:start position:0% +reinforce +okay some values may be my interests + + align:start position:0% +okay some values may be my interests + + + align:start position:0% +okay some values may be my interests +I may be invested in some interests and + + align:start position:0% +I may be invested in some interests and + + + align:start position:0% +I may be invested in some interests and +I may be putting my + + align:start position:0% + + + + align:start position:0% + +interest under the form of a value as a + + align:start position:0% + + + + align:start position:0% + +value okay in in political discussion + + align:start position:0% +value okay in in political discussion + + + align:start position:0% +value okay in in political discussion +this is very + + align:start position:0% +this is very + + + align:start position:0% +this is very +frequent a group present their interests + + align:start position:0% +frequent a group present their interests + + + align:start position:0% +frequent a group present their interests +as + + align:start position:0% +as + + + align:start position:0% +as +values okay to make + + align:start position:0% +values okay to make + + + align:start position:0% +values okay to make +it invisible for the public no so we + + align:start position:0% +it invisible for the public no so we + + + align:start position:0% +it invisible for the public no so we +should take a look if we are being + + align:start position:0% +should take a look if we are being + + + align:start position:0% +should take a look if we are being +transparent in our analysis of if we are + + align:start position:0% +transparent in our analysis of if we are + + + align:start position:0% +transparent in our analysis of if we are +putting some interest we have as values + + align:start position:0% +putting some interest we have as values + + + align:start position:0% +putting some interest we have as values +so to look for interest and motivations + + align:start position:0% +so to look for interest and motivations + + + align:start position:0% +so to look for interest and motivations +is a way is a way to find + + align:start position:0% +is a way is a way to find + + + align:start position:0% +is a way is a way to find +values okay this is the + + align:start position:0% +values okay this is the + + + align:start position:0% +values okay this is the +idea now you will make the + + align:start position:0% +idea now you will make the + + + align:start position:0% +idea now you will make the +exercise as a group + + align:start position:0% + + + + align:start position:0% + +we will have a break no this moment + + align:start position:0% +we will have a break no this moment + + + align:start position:0% +we will have a break no this moment +first before the break if you want to + + align:start position:0% +first before the break if you want to + + + align:start position:0% +first before the break if you want to +talk about this for some minutes a few + + align:start position:0% +talk about this for some minutes a few + + + align:start position:0% +talk about this for some minutes a few +minutes okay after that we will have a + + align:start position:0% +minutes okay after that we will have a + + + align:start position:0% +minutes okay after that we will have a +break and we will come here to make the + + align:start position:0% +break and we will come here to make the + + + align:start position:0% +break and we will come here to make the +exercise in + + align:start position:0% +exercise in + + + align:start position:0% +exercise in +groups we perhaps we can the same groups + + align:start position:0% +groups we perhaps we can the same groups + + + align:start position:0% +groups we perhaps we can the same groups +of + + align:start position:0% +of + + + align:start position:0% +of +yesterday + + align:start position:0% +yesterday + + + align:start position:0% +yesterday +okay for the kind of frame for frame a B + + align:start position:0% +okay for the kind of frame for frame a B + + + align:start position:0% +okay for the kind of frame for frame a B +and + + align:start position:0% +and + + + align:start position:0% +and +C the same + + align:start position:0% +C the same + + + align:start position:0% +C the same +groups do you remember that + + align:start position:0% +groups do you remember that + + + align:start position:0% +groups do you remember that +we made the + + align:start position:0% +we made the + + + align:start position:0% +we made the +exercise + + align:start position:0% + + + + align:start position:0% + +of expressing our frames no B developing + + align:start position:0% +of expressing our frames no B developing + + + align:start position:0% +of expressing our frames no B developing +our frame based on the similarity of + + align:start position:0% +our frame based on the similarity of + + + align:start position:0% +our frame based on the similarity of +problem no and the format groups okay + + align:start position:0% +problem no and the format groups okay + + + align:start position:0% +problem no and the format groups okay +let's talk if you want to talk about + + align:start position:0% +let's talk if you want to talk about + + + align:start position:0% +let's talk if you want to talk about +some of these things before to go to the + + align:start position:0% +some of these things before to go to the + + + align:start position:0% +some of these things before to go to the +exercise do you think scenario planning + + align:start position:0% +exercise do you think scenario planning + + + align:start position:0% +exercise do you think scenario planning +is a good way to get assumptions and + + align:start position:0% +is a good way to get assumptions and + + + align:start position:0% +is a good way to get assumptions and +values + + align:start position:0% +values + + + align:start position:0% +values +H in a show how how do you could you go + + align:start position:0% +H in a show how how do you could you go + + + align:start position:0% +H in a show how how do you could you go +in yes it's the main reason why scenario + + align:start position:0% +in yes it's the main reason why scenario + + + align:start position:0% +in yes it's the main reason why scenario +planning emerged was for making + + align:start position:0% +planning emerged was for making + + + align:start position:0% +planning emerged was for making +assumptions + + align:start position:0% +assumptions + + + align:start position:0% +assumptions +explicit the big the most important + + align:start position:0% +explicit the big the most important + + + align:start position:0% +explicit the big the most important +example about that was the price of oil + + align:start position:0% +example about that was the price of oil + + + align:start position:0% +example about that was the price of oil +no because the creators of scenario + + align:start position:0% +no because the creators of scenario + + + align:start position:0% +no because the creators of scenario +planning or or the first big company + + align:start position:0% +planning or or the first big company + + + align:start position:0% +planning or or the first big company +that implemented it systematically was + + align:start position:0% +that implemented it systematically was + + + align:start position:0% +that implemented it systematically was +shell + + align:start position:0% +shell + + + align:start position:0% +shell +no + + align:start position:0% + + + + align:start position:0% + +and they got to go from sixth place in + + align:start position:0% +and they got to go from sixth place in + + + align:start position:0% +and they got to go from sixth place in +the world to the second place as uh + + align:start position:0% +the world to the second place as uh + + + align:start position:0% +the world to the second place as uh +company no and the the the + + align:start position:0% +company no and the the the + + + align:start position:0% +company no and the the the +main factor that enabled them + + align:start position:0% +main factor that enabled them + + + align:start position:0% +main factor that enabled them +to to achieve that is + + align:start position:0% +to to achieve that is + + + align:start position:0% +to to achieve that is +that all the other companies were + + align:start position:0% +that all the other companies were + + + align:start position:0% +that all the other companies were +assumed that the price + + align:start position:0% +assumed that the price + + + align:start position:0% +assumed that the price +should ER go up + + align:start position:0% +should ER go up + + + align:start position:0% +should ER go up +again + + align:start position:0% +again + + + align:start position:0% +again +and they sh assumed that it it would be + + align:start position:0% +and they sh assumed that it it would be + + + align:start position:0% +and they sh assumed that it it would be +stable + + align:start position:0% +stable + + + align:start position:0% +stable +for a long run so they invested in ref + + align:start position:0% +for a long run so they invested in ref + + + align:start position:0% +for a long run so they invested in ref +and the other companies invested in + + align:start position:0% +and the other companies invested in + + + align:start position:0% +and the other companies invested in +Exploration 10 years later there is a + + align:start position:0% +Exploration 10 years later there is a + + + align:start position:0% +Exploration 10 years later there is a +lot of people exploring + + align:start position:0% +lot of people exploring + + + align:start position:0% +lot of people exploring +producing oil and very very few + + align:start position:0% +producing oil and very very few + + + align:start position:0% +producing oil and very very few +refineries okay yes it's very it's a + + align:start position:0% +refineries okay yes it's very it's a + + + align:start position:0% +refineries okay yes it's very it's a +very poent to to make scenario planning + + align:start position:0% +very poent to to make scenario planning + + + align:start position:0% +very poent to to make scenario planning +and the main reason is because it makes + + align:start position:0% +and the main reason is because it makes + + + align:start position:0% +and the main reason is because it makes +the assumptions + + align:start position:0% +the assumptions + + + align:start position:0% +the assumptions +explicit can you use it to make values + + align:start position:0% +explicit can you use it to make values + + + align:start position:0% +explicit can you use it to make values +explicit or is there a way to what can + + align:start position:0% +explicit or is there a way to what can + + + align:start position:0% +explicit or is there a way to what can +you use it also to make values + + align:start position:0% + + + + align:start position:0% + +explicit no it's not it's not so + + align:start position:0% +explicit no it's not it's not so + + + align:start position:0% +explicit no it's not it's not so +effective for making values + + align:start position:0% + + + + align:start position:0% + +explicit + + align:start position:0% +explicit + + + align:start position:0% +explicit +and you can make the exercise of + + align:start position:0% +and you can make the exercise of + + + align:start position:0% +and you can make the exercise of +explicit values values in the analysis + + align:start position:0% +explicit values values in the analysis + + + align:start position:0% +explicit values values in the analysis +of the the scenario + + align:start position:0% +of the the scenario + + + align:start position:0% +of the the scenario +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but it's not a reason for doing scenario + + align:start position:0% +but it's not a reason for doing scenario + + + align:start position:0% +but it's not a reason for doing scenario +planning my understanding + + align:start position:0% + + + + align:start position:0% + +okay another + + align:start position:0% + + + + align:start position:0% + +question okay if we have no question + + align:start position:0% +question okay if we have no question + + + align:start position:0% +question okay if we have no question +let's go to the break and you come back + + align:start position:0% +let's go to the break and you come back + + + align:start position:0% +let's go to the break and you come back +here for the exercise please we have 10 + + align:start position:0% +here for the exercise please we have 10 + + + align:start position:0% +here for the exercise please we have 10 +minutes for the break okay we are not so + + align:start position:0% +minutes for the break okay we are not so + + + align:start position:0% +minutes for the break okay we are not so +far today from the coffee okay so we + + align:start position:0% +far today from the coffee okay so we + + + align:start position:0% +far today from the coffee okay so we +have no reason + + align:start position:0% +have no reason + + + align:start position:0% +have no reason +okay people + + align:start position:0% + + + + align:start position:0% + +please problem lack of let's begin + + align:start position:0% + + + + align:start position:0% + +in your case are two two sheets of paper + + align:start position:0% + + + + align:start position:0% + +no it's not + + align:start position:0% +no it's not + + + align:start position:0% +no it's not +yours ah okay + + align:start position:0% + + + + align:start position:0% + +I think that should be better to work + + align:start position:0% +I think that should be better to work + + + align:start position:0% +I think that should be better to work +here should be better to work + + align:start position:0% + + + + align:start position:0% + +here the same groups of yesterday is for + + align:start position:0% +here the same groups of yesterday is for + + + align:start position:0% +here the same groups of yesterday is for +him to to + + align:start position:0% + + + + align:start position:0% + +record + + align:start position:0% +record + + + align:start position:0% +record +or the three groups I will clean the the + + align:start position:0% +or the three groups I will clean the the + + + align:start position:0% +or the three groups I will clean the the +the wall okay do you + + align:start position:0% + + + + align:start position:0% + +this is your + + align:start position:0% + + + + align:start position:0% + +group what's your + + align:start position:0% +group what's your + + + align:start position:0% +group what's your +grp this + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% + + + + align:start position:0% + +I we are beginning the + + align:start position:0% + + + + align:start position:0% + +exercise 2 years one year since it's + + align:start position:0% +exercise 2 years one year since it's + + + align:start position:0% +exercise 2 years one year since it's +been out I + + align:start position:0% + + + + align:start position:0% + +mean in your group fre and determine a + + align:start position:0% +mean in your group fre and determine a + + + align:start position:0% +mean in your group fre and determine a +title for your + + align:start position:0% + + + + align:start position:0% + +C title for your frame what if you had + + align:start position:0% +C title for your frame what if you had + + + align:start position:0% +C title for your frame what if you had +to summarize your frame in a few with a + + align:start position:0% +to summarize your frame in a few with a + + + align:start position:0% +to summarize your frame in a few with a +few words three words like like we did + + align:start position:0% +few words three words like like we did + + + align:start position:0% +few words three words like like we did +with the frames of the energy the United + + align:start position:0% +with the frames of the energy the United + + + align:start position:0% +with the frames of the energy the United +the energy issue this is one group no + + align:start position:0% +the energy issue this is one group no + + + align:start position:0% +the energy issue this is one group no +how would you do that this we need to + + align:start position:0% +how would you do that this we need to + + + align:start position:0% +how would you do that this we need to +reorganize this + + align:start position:0% +reorganize this + + + align:start position:0% +reorganize this +this each group we work + + align:start position:0% +this each group we work + + + align:start position:0% +this each group we work +together okay just for the title and + + align:start position:0% +together okay just for the title and + + + align:start position:0% +together okay just for the title and +then we where where we're going to do is + + align:start position:0% +then we where where we're going to do is + + + align:start position:0% +then we where where we're going to do is +present each group will have 20 minutes + + align:start position:0% +present each group will have 20 minutes + + + align:start position:0% +present each group will have 20 minutes +to present the the responses to the five + + align:start position:0% +to present the the responses to the five + + + align:start position:0% +to present the the responses to the five +questions that we looked at + + align:start position:0% +questions that we looked at + + + align:start position:0% +questions that we looked at +yesterday um and we'll be we we'll be um + + align:start position:0% +yesterday um and we'll be we we'll be um + + + align:start position:0% +yesterday um and we'll be we we'll be um +the audience will be facilitating the + + align:start position:0% +the audience will be facilitating the + + + align:start position:0% +the audience will be facilitating the +conversation in the sense that they'll + + align:start position:0% +conversation in the sense that they'll + + + align:start position:0% +conversation in the sense that they'll +be asking questions will help the group + + align:start position:0% +be asking questions will help the group + + + align:start position:0% +be asking questions will help the group +identify more clearly the assumptions in + + align:start position:0% +identify more clearly the assumptions in + + + align:start position:0% +identify more clearly the assumptions in +the values + + align:start position:0% + + + + align:start position:0% + +so right now we just have name our frame + + align:start position:0% +so right now we just have name our frame + + + align:start position:0% +so right now we just have name our frame +right now it's a title for your frame + + align:start position:0% +right now it's a title for your frame + + + align:start position:0% +right now it's a title for your frame +and then we'll begin with the present + + align:start position:0% +and then we'll begin with the present + + + align:start position:0% +and then we'll begin with the present +but I I'd like to ask you to to organize + + align:start position:0% +but I I'd like to ask you to to organize + + + align:start position:0% +but I I'd like to ask you to to organize +as groups let's move the sheet of paper + + align:start position:0% +as groups let's move the sheet of paper + + + align:start position:0% +as groups let's move the sheet of paper +so so that one group may be here the + + align:start position:0% +so so that one group may be here the + + + align:start position:0% +so so that one group may be here the +other group will be here and the other + + align:start position:0% +other group will be here and the other + + + align:start position:0% +other group will be here and the other +one can be displaced okay let's move + + align:start position:0% +one can be displaced okay let's move + + + align:start position:0% +one can be displaced okay let's move +because for you not to + + align:start position:0% +because for you not to + + + align:start position:0% +because for you not to +listen Okay each other okay please let + + align:start position:0% +listen Okay each other okay please let + + + align:start position:0% +listen Okay each other okay please let +can we move this for + + align:start position:0% +can we move this for + + + align:start position:0% +can we move this for +here let's take this off and put this + + align:start position:0% +here let's take this off and put this + + + align:start position:0% +here let's take this off and put this +paper here okay and organize a youu + + align:start position:0% +paper here okay and organize a youu + + + align:start position:0% +paper here okay and organize a youu +around here I only do + + align:start position:0% + + + + align:start position:0% + +one okay + + align:start position:0% +one okay + + + align:start position:0% +one okay +[Applause] + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um can you come excuse me excuse me can + + align:start position:0% +um can you come excuse me excuse me can + + + align:start position:0% +um can you come excuse me excuse me can +you come move one meter here from + + align:start position:0% +you come move one meter here from + + + align:start position:0% +you come move one meter here from +here like that yes yes please please + + align:start position:0% +here like that yes yes please please + + + align:start position:0% +here like that yes yes please please +what is your this you joining us no so + + align:start position:0% +what is your this you joining us no so + + + align:start position:0% +what is your this you joining us no so +so move the is here please okay + + align:start position:0% + + + + align:start position:0% + +okay you can see + + align:start position:0% +okay you can see + + + align:start position:0% +okay you can see +that okay I will put here for + + align:start position:0% + + + + align:start position:0% + +okay okay + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +but I + + align:start position:0% + + + + align:start position:0% + +guess + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +it's process or something like + + align:start position:0% +it's process or something like + + + align:start position:0% +it's process or something like +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +that for + + align:start position:0% +that for + + + align:start position:0% +that for + + align:start position:0% + + + align:start position:0% +minutes something very easy okay you + + align:start position:0% +minutes something very easy okay you + + + align:start position:0% +minutes something very easy okay you +just decide what name + + align:start position:0% + + + + align:start position:0% + +you the third example on the sheet has + + align:start position:0% +you the third example on the sheet has + + + align:start position:0% +you the third example on the sheet has +three + + align:start position:0% +three + + + align:start position:0% +three +words yeah yeah no I mean I'm not tied + + align:start position:0% +words yeah yeah no I mean I'm not tied + + + align:start position:0% +words yeah yeah no I mean I'm not tied +to two or three or whatever just trying + + align:start position:0% +to two or three or whatever just trying + + + align:start position:0% +to two or three or whatever just trying +to be + + align:start position:0% +to be + + + align:start position:0% +to be +concise um + + align:start position:0% + + + + align:start position:0% + +got it done we need to get the no I + + align:start position:0% +got it done we need to get the no I + + + align:start position:0% +got it done we need to get the no I +think we only we got + + align:start position:0% + + + + align:start position:0% + +the that's my + + align:start position:0% + + + + align:start position:0% + +understanding this and that's why I was + + align:start position:0% +understanding this and that's why I was + + + align:start position:0% +understanding this and that's why I was +saying do we need to use the same word + + align:start position:0% +saying do we need to use the same word + + + align:start position:0% +saying do we need to use the same word +you know do we need to pull words out of + + align:start position:0% +you know do we need to pull words out of + + + align:start position:0% +you know do we need to pull words out of +that is there another way that we can + + align:start position:0% +that is there another way that we can + + + align:start position:0% +that is there another way that we can +name that without using we have to have + + align:start position:0% +name that without using we have to have + + + align:start position:0% +name that without using we have to have +the sub question + + align:start position:0% +the sub question + + + align:start position:0% +the sub question +like R start depending on energy that's + + align:start position:0% +like R start depending on energy that's + + + align:start position:0% +like R start depending on energy that's +why I'm saying what we have is the + + align:start position:0% +why I'm saying what we have is the + + + align:start position:0% +why I'm saying what we have is the +sub is the way I was thinking of it so + + align:start position:0% +sub is the way I was thinking of it so + + + align:start position:0% +sub is the way I was thinking of it so +that is a description + + align:start position:0% +that is a description + + + align:start position:0% +that is a description +of what I mean is structure they've got + + align:start position:0% +of what I mean is structure they've got + + + align:start position:0% +of what I mean is structure they've got +a and then a little subtitle + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +okay but we're supposed to organize an + + align:start position:0% +okay but we're supposed to organize an + + + align:start position:0% +okay but we're supposed to organize an +answer right we're supposed to summarize + + align:start position:0% +answer right we're supposed to summarize + + + align:start position:0% +answer right we're supposed to summarize +our + + align:start position:0% +our + + + align:start position:0% +our +frame our framing problem is the + + align:start position:0% +frame our framing problem is the + + + align:start position:0% +frame our framing problem is the +perception Visions held by + + align:start position:0% +perception Visions held by + + + align:start position:0% +perception Visions held by +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +stakeholders unreliable sour + + align:start position:0% +stakeholders unreliable sour + + + align:start position:0% +stakeholders unreliable sour +of get out of + + align:start position:0% + + + + align:start position:0% + +you said cause and effect I mean like + + align:start position:0% +you said cause and effect I mean like + + + align:start position:0% +you said cause and effect I mean like +one is one is we have unreliable sources + + align:start position:0% +one is one is we have unreliable sources + + + align:start position:0% +one is one is we have unreliable sources +therefore we need to reduce our + + align:start position:0% +therefore we need to reduce our + + + align:start position:0% +therefore we need to reduce our +dependence emissions + + align:start position:0% + + + + align:start position:0% + +warning therefore prog reduce our demain + + align:start position:0% +warning therefore prog reduce our demain + + + align:start position:0% +warning therefore prog reduce our demain +or vice versa + + align:start position:0% + + + + align:start position:0% + +so conflicting Visions + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +therefore perception of + + align:start position:0% +therefore perception of + + + align:start position:0% +therefore perception of +conf we don't really know that the + + align:start position:0% +conf we don't really know that the + + + align:start position:0% +conf we don't really know that the +Visions perception of conflicting + + align:start position:0% + + + + align:start position:0% + +Visions with the facilitated + + align:start position:0% +Visions with the facilitated + + + align:start position:0% +Visions with the facilitated +diog right maybe the the title would + + align:start position:0% +diog right maybe the the title would + + + align:start position:0% +diog right maybe the the title would +be um maybe the the + + align:start position:0% +be um maybe the the + + + align:start position:0% +be um maybe the the +summary of our FR would be facilitated + + align:start position:0% + + + + align:start position:0% + +di no that's not our problem + + align:start position:0% + + + + align:start position:0% + +problem our problem is that people think + + align:start position:0% +problem our problem is that people think + + + align:start position:0% +problem our problem is that people think +they're + + align:start position:0% + + + + align:start position:0% + +reconcile one solution to that is + + align:start position:0% +reconcile one solution to that is + + + align:start position:0% +reconcile one solution to that is +get all together + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and as the as the + + align:start position:0% +and as the as the + + + align:start position:0% +and as the as the +[Music] + + align:start position:0% + + + + align:start position:0% + +summer don't get crunch yes yep make so + + align:start position:0% +summer don't get crunch yes yep make so + + + align:start position:0% +summer don't get crunch yes yep make so +much more + + align:start position:0% + + + + align:start position:0% + +keep telling me if I + + align:start position:0% +keep telling me if I + + + align:start position:0% +keep telling me if I +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +EF I think it's a + + align:start position:0% + + + + align:start position:0% + +lot so + + align:start position:0% +lot so + + + align:start position:0% +lot so +what's + + align:start position:0% +what's + + + align:start position:0% +what's +conf facated + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +dial it isn't it isn't facilitated be + + align:start position:0% +dial it isn't it isn't facilitated be + + + align:start position:0% +dial it isn't it isn't facilitated be +facilitated + + align:start position:0% +facilitated + + + align:start position:0% +facilitated +[Music] + + align:start position:0% + + + + align:start position:0% + +you want to say facilitate dialogue or + + align:start position:0% +you want to say facilitate dialogue or + + + align:start position:0% +you want to say facilitate dialogue or +facilitate + + align:start position:0% + + + + align:start position:0% + +mediation mediation by nature is + + align:start position:0% + + + + align:start position:0% + +facilitate I'll go with whatever + + align:start position:0% + + + + align:start position:0% + +what do you think + + align:start position:0% +what do you think + + + align:start position:0% +what do you think +is + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +think therefore + + align:start position:0% +think therefore + + + align:start position:0% +think therefore +[Music] + + align:start position:0% + + + + align:start 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you + + + align:start position:0% +um whatever do you +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +think you know globally versus loc + + align:start position:0% +think you know globally versus loc + + + align:start position:0% +think you know globally versus loc +Global local is one that continues to be + + align:start position:0% +Global local is one that continues to be + + + align:start position:0% +Global local is one that continues to be +a a tension in our Poli all about + + align:start position:0% +a a tension in our Poli all about + + + align:start position:0% +a a tension in our Poli all about +when do you make you know you can't be + + align:start position:0% +when do you make you know you can't be + + + align:start position:0% +when do you make you know you can't be +all IGN the + + align:start position:0% +all IGN the + + + align:start position:0% +all IGN the +world you can't be + + align:start position:0% + + + + align:start 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+contribut you don't understand it's + + + align:start position:0% +contribut you don't understand it's +culturaly + + align:start position:0% +culturaly + + + align:start position:0% +culturaly +way dealing with you know and it's the + + align:start position:0% +way dealing with you know and it's the + + + align:start position:0% +way dealing with you know and it's the +subject you never want to say to anybody + + align:start position:0% +subject you never want to say to anybody + + + align:start position:0% +subject you never want to say to anybody +oh BL that this is not + + align:start position:0% + + + + align:start position:0% + +culturally here's the culture you got + + align:start position:0% +culturally here's the culture you got + + + align:start position:0% +culturally here's the culture you got +away with a lot of bad behavior as a + + align:start position:0% + + + + align:start position:0% + +child in the + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +metime these are V the examples are + + align:start position:0% +metime these are V the examples are + + + align:start position:0% +metime these are V the examples are +not + + align:start position:0% +not + + + align:start position:0% +not +explicit they're not explicit + + align:start position:0% + + + + align:start position:0% + +I I had plan the exercise in one way but + + align:start position:0% +I I had plan the exercise in one way but + + + align:start position:0% +I I had plan the exercise in one way but +I think that it can work better in a + + align:start position:0% +I think that it can work better in a + + + align:start position:0% +I think that it can work better in a +different + + align:start position:0% +different + + + align:start position:0% +different +way the exercise was planned originally + + align:start position:0% +way the exercise was planned originally + + + align:start position:0% +way the exercise was planned originally +that each group should make + + align:start position:0% +that each group should make + + + align:start position:0% +that each group should make +it and the other two group + + align:start position:0% +it and the other two group + + + align:start position:0% +it and the other two group +should look at the + + align:start position:0% +should look at the + + + align:start position:0% +should look at the +experiment but I think that perhaps + + align:start position:0% +experiment but I think that perhaps + + + align:start position:0% +experiment but I think that perhaps +it should be better that each group will + + align:start position:0% +it should be better that each group will + + + align:start position:0% +it should be better that each group will +make its uh their own exercise and after + + align:start position:0% +make its uh their own exercise and after + + + align:start position:0% +make its uh their own exercise and after +the end we will present it at the same + + align:start position:0% +the end we will present it at the same + + + align:start position:0% +the end we will present it at the same +in the same method that we worked all + + align:start position:0% +in the same method that we worked all + + + align:start position:0% +in the same method that we worked all +these days + + align:start position:0% +these days + + + align:start position:0% +these days +so the the exercise you need to do is + + align:start position:0% +so the the exercise you need to do is + + + align:start position:0% +so the the exercise you need to do is +now to + + align:start position:0% +now to + + + align:start position:0% +now to +identify your + + align:start position:0% +identify your + + + align:start position:0% +identify your +assumptions as group you made the the + + align:start position:0% +assumptions as group you made the the + + + align:start position:0% +assumptions as group you made the the +homework each person made the homework + + align:start position:0% +homework each person made the homework + + + align:start position:0% +homework each person made the homework +trying to ident ify the assumptions of + + align:start position:0% +trying to ident ify the assumptions of + + + align:start position:0% +trying to ident ify the assumptions of +the the frame no now the exercise should + + align:start position:0% +the the frame no now the exercise should + + + align:start position:0% +the the frame no now the exercise should +be to identify to to synthesize as a + + align:start position:0% +be to identify to to synthesize as a + + + align:start position:0% +be to identify to to synthesize as a +group these assumptions for each frame + + align:start position:0% +group these assumptions for each frame + + + align:start position:0% +group these assumptions for each frame +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and after that each group will present + + align:start position:0% +and after that each group will present + + + align:start position:0% +and after that each group will present +and we will + + align:start position:0% +and we will + + + align:start position:0% +and we will +discuss about it okay present only the + + align:start position:0% +discuss about it okay present only the + + + align:start position:0% +discuss about it okay present only the +assumptions or the whole the the + + align:start position:0% +assumptions or the whole the the + + + align:start position:0% +assumptions or the whole the the +assumptions and and the + + align:start position:0% +assumptions and and the + + + align:start position:0% +assumptions and and the +values you found in the + + align:start position:0% +values you found in the + + + align:start position:0% +values you found in the +frame are we supposed to di it's not + + align:start position:0% +frame are we supposed to di it's not + + + align:start position:0% +frame are we supposed to di it's not +necessary the diagram is only for + + align:start position:0% +necessary the diagram is only for + + + align:start position:0% +necessary the diagram is only for +remember the logic that I will make + + align:start position:0% +remember the logic that I will make + + + align:start position:0% +remember the logic that I will make +questions + + align:start position:0% +questions + + + align:start position:0% +questions +about why the problem generate the + + align:start position:0% +about why the problem generate the + + + align:start position:0% +about why the problem generate the +scenario and I will make the the + + align:start position:0% +scenario and I will make the the + + + align:start position:0% +scenario and I will make the the +question about why the causes or the + + align:start position:0% +question about why the causes or the + + + align:start position:0% +question about why the causes or the +factors influence + + align:start position:0% +factors influence + + + align:start position:0% +factors influence +the the problem and I will make + + align:start position:0% +the the problem and I will make + + + align:start position:0% +the the problem and I will make +questions + + align:start position:0% + + + + align:start position:0% + +about conditions required for this work + + align:start position:0% +about conditions required for this work + + + align:start position:0% +about conditions required for this work +in this + + align:start position:0% +in this + + + align:start position:0% +in this +way + + align:start position:0% +way + + + align:start position:0% +way +okay factors the + + align:start position:0% +okay factors the + + + align:start position:0% +okay factors the +same no the assumptions is why the + + align:start position:0% +same no the assumptions is why the + + + align:start position:0% +same no the assumptions is why the +factors are cause of the + + align:start position:0% +factors are cause of the + + + align:start position:0% 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make + + align:start position:0% +just make + + + align:start position:0% +just make +not uh my was the the final product I + + align:start position:0% +not uh my was the the final product I + + + align:start position:0% +not uh my was the the final product I +was waiting for is a list of + + align:start position:0% + + + + align:start position:0% + +assumptions + + align:start position:0% +assumptions + + + align:start position:0% +assumptions +that I have for + + align:start position:0% +that I have for + + + align:start position:0% +that I have for +example scenario + + align:start position:0% +example scenario + + + align:start position:0% +example scenario +problem + + align:start position:0% + + + + align:start position:0% + +assumptions you have a list of factors + + align:start position:0% +assumptions you have a list of factors + + + align:start position:0% +assumptions you have a list of factors +no for each factor you may have one or + + align:start position:0% +no for each factor you may have one or + + + align:start position:0% +no for each factor you may have one or +more assumption or you may have + + align:start position:0% +more assumption or you may have + + + align:start position:0% +more assumption or you may have +assumptions that are common to different + + align:start position:0% +assumptions that are common to different + + + align:start position:0% +assumptions that are common to different +factors I don't know yet how you + + align:start position:0% +factors I don't know yet how you + + + align:start position:0% +factors I don't know yet how you +will identify what you will identify + + align:start position:0% +will identify what you will identify + + + align:start position:0% +will identify what you will identify +so + + align:start position:0% +so + + + align:start position:0% +so +one one group of assumptions will will + + align:start position:0% +one one group of assumptions will will + + + align:start position:0% +one one group of assumptions will will +be + + align:start position:0% +be + + + align:start position:0% +be +about the relation scenario problem the + + align:start position:0% +about the relation scenario problem the + + + align:start position:0% +about the relation scenario problem the +other group of assumptions will be about + + align:start position:0% +other group of assumptions will be about + + + align:start position:0% +other group of assumptions will be about +the relation factors problem and the + + align:start position:0% +the relation factors problem and the + + + align:start position:0% +the relation factors problem and the +third group of assumptions will be about + + align:start position:0% + + + + align:start position:0% + +conditions okay three groups of of + + align:start position:0% +conditions okay three groups of of + + + align:start position:0% +conditions okay three groups of of +assumptions what do you mean by + + align:start position:0% +assumptions what do you mean by + + + align:start position:0% +assumptions what do you mean by +condition like just assumptions cont yes + + align:start position:0% +condition like just assumptions cont yes + + + align:start position:0% +condition like just assumptions cont yes +yes it's it's the exactly the conditions + + align:start position:0% +yes it's it's the exactly the conditions + + + align:start position:0% +yes it's it's the exactly the conditions +are not about + + align:start position:0% +are not about + + + align:start position:0% +are not about +the the problem in itself but about some + + align:start position:0% +the the problem in itself but about some + + + align:start position:0% +the the problem in itself but about some +requirements in a bigger + + align:start position:0% +requirements in a bigger + + + align:start position:0% +requirements in a bigger +context that I don't know how you frame + + align:start position:0% +context that I don't know how you frame + + + align:start position:0% +context that I don't know how you frame +the problem you may find + + align:start position:0% +the problem you may find + + + align:start position:0% +the problem you may find +that it's very important + + align:start position:0% + + + + align:start position:0% + +okay for + + align:start position:0% + + + + align:start position:0% + +example the different kind + + align:start position:0% +example the different kind + + + align:start position:0% +example the different kind +of policies that + + align:start position:0% +of policies that + + + align:start position:0% +of policies that +had Carter and + + align:start position:0% +had Carter and + + + align:start position:0% +had Carter and +Reagan generate different kind of + + align:start position:0% +Reagan generate different kind of + + + align:start position:0% +Reagan generate different kind of +problems + + align:start position:0% +problems + + + align:start position:0% +problems +in Evolutions in + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% + + + + align:start position:0% + +neighborhoods the dynamic of the + + align:start position:0% +neighborhoods the dynamic of the + + + align:start position:0% +neighborhoods the dynamic of the +neighborhoods Chang + + align:start position:0% +neighborhoods Chang + + + align:start position:0% +neighborhoods Chang +with these two + + align:start position:0% + + + + align:start position:0% + +governments don't try to be exhaustive + + align:start position:0% +governments don't try to be exhaustive + + + align:start position:0% +governments don't try to be exhaustive +in the conditions just if you remember + + align:start position:0% +in the conditions just if you remember + + + align:start position:0% +in the conditions just if you remember +some of them you put it okay because we + + align:start position:0% +some of them you put it okay because we + + + align:start position:0% +some of them you put it okay because we +we didn't make an analysis about that + + align:start position:0% +we didn't make an analysis about that + + + align:start position:0% +we didn't make an analysis about that +just for remember that + + align:start position:0% +just for remember that + + + align:start position:0% +just for remember that +maybe May there be assumptions that are + + align:start position:0% +maybe May there be assumptions that are + + + align:start position:0% +maybe May there be assumptions that are +not directly related to the problem in + + align:start position:0% +not directly related to the problem in + + + align:start position:0% +not directly related to the problem in +itself but to the the context where this + + align:start position:0% +itself but to the the context where this + + + align:start position:0% +itself but to the the context where this +problem is is + + align:start position:0% + + + + align:start position:0% + +happening it's it's now is it clear + + align:start position:0% +happening it's it's now is it clear + + + align:start position:0% +happening it's it's now is it clear +yes no this group is telling me that + + align:start position:0% +yes no this group is telling me that + + + align:start position:0% +yes no this group is telling me that +it's not + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +clear okay I can the product okay can I + + align:start position:0% +clear okay I can the product okay can I + + + align:start position:0% +clear okay I can the product okay can I +design the product the final product + + align:start position:0% +design the product the final product + + + align:start position:0% +design the product the final product +okay okay + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +my + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +I + + align:start position:0% + + + + align:start position:0% + +okay assumption + + align:start position:0% + + + + align:start position:0% + +one assumption two and so on + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +problem + + align:start position:0% +problem + + + align:start position:0% +problem +factors okay the same + + align:start position:0% +factors okay the same + + + align:start position:0% +factors okay the same +thing + + align:start position:0% + + + + align:start position:0% + +assumption one 2 Etc + + align:start position:0% +assumption one 2 Etc + + + align:start position:0% +assumption one 2 Etc +okay scenario scenario the next one next + + align:start position:0% +okay scenario scenario the next one next + + + align:start position:0% +okay scenario scenario the next one next +to + + align:start position:0% +to + + + align:start position:0% +to +scenario problem yeah assumption one + + align:start position:0% +scenario problem yeah assumption one + + + align:start position:0% +scenario problem yeah assumption one +assumption two assumption three okay + + align:start position:0% +assumption two assumption three okay + + + align:start position:0% +assumption two assumption three okay +okay what's the next word problem + + align:start position:0% +okay what's the next word problem + + + align:start position:0% +okay what's the next word problem +factors problem + + align:start position:0% + + + + align:start position:0% + +factors and you + + align:start position:0% +factors and you + + + align:start position:0% +factors and you +may you may find some assumptions about + + align:start position:0% +may you may find some assumptions about + + + align:start position:0% +may you may find some assumptions about +conditions I don't + + align:start position:0% +conditions I don't + + + align:start position:0% +conditions I don't +know okay now now it's clear yeah okay + + align:start position:0% +know okay now now it's clear yeah okay + + + align:start position:0% +know okay now now it's clear yeah okay +so take take your the result of your + + align:start position:0% +so take take your the result of your + + + align:start position:0% +so take take your the result of your +homework + + align:start position:0% +homework + + + align:start position:0% +homework +and this will the raw material you will + + align:start position:0% +and this will the raw material you will + + + align:start position:0% +and this will the raw material you will +work with + + align:start position:0% +work with + + + align:start position:0% +work with +Okay + + align:start position:0% +Okay + + + align:start position:0% +Okay +and try to go through this + + align:start position:0% +and try to go through this + + + align:start position:0% +and try to go through this +process + + align:start position:0% + + + + align:start position:0% + +okay my name made a suggestion yes yes + + align:start position:0% + + + + align:start position:0% + +they + + align:start position:0% + + + + align:start position:0% + +so the scenario is you know essentially + + align:start position:0% +so the scenario is you know essentially + + + align:start position:0% +so the scenario is you know essentially +Caesar's + + align:start position:0% +Caesar's + + + align:start position:0% +Caesar's +description well I wait it's C + + align:start position:0% +description well I wait it's C + + + align:start position:0% +description well I wait it's C +description our + + align:start position:0% +description our + + + align:start position:0% +description our +problem scenario problem problem and + + align:start position:0% +problem scenario problem problem and + + + align:start position:0% +problem scenario problem problem and +factors are ours scenario problem is + + align:start position:0% +factors are ours scenario problem is + + + align:start position:0% +factors are ours scenario problem is +what Cesar got the way I + + align:start position:0% +what Cesar got the way I + + + align:start position:0% +what Cesar got the way I +understood what's the + + align:start position:0% +understood what's the + + + align:start position:0% +understood what's the +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +scenario + + align:start position:0% + + + + align:start position:0% + +problem because all he did over there + + align:start position:0% +problem because all he did over there + + + align:start position:0% +problem because all he did over there +was repeat what he said over here which + + align:start position:0% +was repeat what he said over here which + + + align:start position:0% +was repeat what he said over here which +wasn't clear my impression was + + align:start position:0% +wasn't clear my impression was + + + align:start position:0% +wasn't clear my impression was +that the scenario and what we think the + + align:start position:0% +that the scenario and what we think the + + + align:start position:0% +that the scenario and what we think the +problem is and then our assumptions + + align:start position:0% +problem is and then our assumptions + + + align:start position:0% +problem is and then our assumptions +about that and then our assumptions and + + align:start position:0% +about that and then our assumptions and + + + align:start position:0% +about that and then our assumptions and +what about what we assume the factors of + + align:start position:0% +what about what we assume the factors of + + + align:start position:0% +what about what we assume the factors of +the problem to be but I might be so look + + align:start position:0% +the problem to be but I might be so look + + + align:start position:0% +the problem to be but I might be so look +at that thing up there that big arrow is + + align:start position:0% +at that thing up there that big arrow is + + + align:start position:0% +at that thing up there that big arrow is +our title or that number one is related + + align:start position:0% +our title or that number one is related + + + align:start position:0% +our title or that number one is related +to problem right and then number three + + align:start position:0% +to problem right and then number three + + + align:start position:0% +to problem right and then number three +are the little bubbles bubbles and then + + align:start position:0% +are the little bubbles bubbles and then + + + align:start position:0% +are the little bubbles bubbles and then +box is what + + align:start position:0% +box is what + + + align:start position:0% +box is what +said no I think the scenario in that + + align:start position:0% +said no I think the scenario in that + + + align:start position:0% +said no I think the scenario in that +case + + align:start position:0% +case + + + align:start position:0% +case +is what we + + align:start position:0% + + + + align:start position:0% + +pce this to me was a repeat of what you + + align:start position:0% +pce this to me was a repeat of what you + + + align:start position:0% +pce this to me was a repeat of what you +said over here so I'm still lost is the + + align:start position:0% +said over here so I'm still lost is the + + + align:start position:0% +said over here so I'm still lost is the +scenario what Cesar presented no + + align:start position:0% +scenario what Cesar presented no + + + align:start position:0% +scenario what Cesar presented no +scenario you the scenario uhuh the + + align:start position:0% +scenario you the scenario uhuh the + + + align:start position:0% +scenario you the scenario uhuh the +impact the impact of the development + + align:start position:0% +impact the impact of the development + + + align:start position:0% +impact the impact of the development +process if nothing happens yes the the + + align:start position:0% +process if nothing happens yes the the + + + align:start position:0% +process if nothing happens yes the the +bubbles there represent the answer to + + align:start position:0% +bubbles there represent the answer to + + + align:start position:0% +bubbles there represent the answer to +question three and the arrow is number + + align:start position:0% +question three and the arrow is number + + + align:start position:0% +question three and the arrow is number +one in the scenario is the development + + align:start position:0% +one in the scenario is the development + + + align:start position:0% +one in the scenario is the development +it's the impact of the problem impct the + + align:start position:0% +it's the impact of the problem impct the + + + align:start position:0% +it's the impact of the problem impct the +development happen the impact of the + + align:start position:0% +development happen the impact of the + + + align:start position:0% +development happen the impact of the +problem that's + + align:start position:0% +problem that's + + + align:start position:0% +problem that's +the the impact of the problem + + align:start position:0% +the the impact of the problem + + + align:start position:0% +the the impact of the problem +development + + align:start position:0% +development + + + align:start position:0% +development +so that is what Caesar described no what + + align:start position:0% +so that is what Caesar described no what + + + align:start position:0% +so that is what Caesar described no what +Caesar described is what's the current + + align:start position:0% +Caesar described is what's the current + + + align:start position:0% +Caesar described is what's the current +situation so that's a future + + align:start position:0% +situation so that's a future + + + align:start position:0% +situation so that's a future +situation yeah so you're making all + + align:start position:0% +situation yeah so you're making all + + + align:start position:0% +situation yeah so you're making all +these assumptions about what how your + + align:start position:0% +these assumptions about what how your + + + align:start position:0% +these assumptions about what how your +how your problem is going to play + + align:start position:0% +how your problem is going to play + + + align:start position:0% +how your problem is going to play +out if the development happens so it's + + align:start position:0% +out if the development happens so it's + + + align:start position:0% +out if the development happens so it's +that third fourth question like if + + align:start position:0% +that third fourth question like if + + + align:start position:0% +that third fourth question like if +happen how will your problem as you st + + align:start position:0% +happen how will your problem as you st + + + align:start position:0% +happen how will your problem as you st +it okay so it's basically like impa 3 + + align:start position:0% +it okay so it's basically like impa 3 + + + align:start position:0% +it okay so it's basically like impa 3 +4 as it go so the problem is the way we + + align:start position:0% +4 as it go so the problem is the way we + + + align:start position:0% +4 as it go so the problem is the way we +State yeah the problem + + align:start position:0% +State yeah the problem + + + align:start position:0% +State yeah the problem +you which is what I understand and the + + align:start position:0% +you which is what I understand and the + + + align:start position:0% +you which is what I understand and the +why why do you think that's a problem + + align:start position:0% +why why do you think that's a problem + + + align:start position:0% +why why do you think that's a problem +are the factors okay and then we're + + align:start position:0% +are the factors okay and then we're + + + align:start position:0% +are the factors okay and then we're +trying + + align:start position:0% +trying + + + align:start position:0% +trying +to no questions one and two are within + + align:start position:0% +to no questions one and two are within + + + align:start position:0% +to no questions one and two are within +that problem question three is the the + + align:start position:0% +that problem question three is the the + + + align:start position:0% +that problem question three is the the +little circles behind the problem the + + align:start position:0% +little circles behind the problem the + + + align:start position:0% +little circles behind the problem the +factors that are contributing to that + + align:start position:0% +factors that are contributing to that + + + align:start position:0% +factors that are contributing to that +problem which is condition and then + + align:start position:0% +problem which is condition and then + + + align:start position:0% +problem which is condition and then +question four is the impact of your + + align:start position:0% +question four is the impact of your + + + align:start position:0% +question four is the impact of your +problem and we want to figure out the + + align:start position:0% + + + + align:start position:0% + +assumption but there's only over + + align:start position:0% + + + + align:start position:0% + +there adding one more thing to this here + + align:start position:0% +there adding one more thing to this here + + + align:start position:0% +there adding one more thing to this here +which is context what are you seeing + + align:start position:0% +which is context what are you seeing + + + align:start position:0% +which is context what are you seeing +about the context the + + align:start position:0% +about the context the + + + align:start position:0% +about the context the +conditions there's one more thing over + + align:start position:0% +conditions there's one more thing over + + + align:start position:0% +conditions there's one more thing over +there exactly that's + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +problem let me let me see if I can + + align:start position:0% +problem let me let me see if I can + + + align:start position:0% +problem let me let me see if I can +combine problem and factors + + align:start position:0% +combine problem and factors + + + align:start position:0% +combine problem and factors +together let me see if I can restate it + + align:start position:0% +together let me see if I can restate it + + + align:start position:0% +together let me see if I can restate it +the impact scenario is + + align:start position:0% +the impact scenario is + + + align:start position:0% +the impact scenario is +if + + align:start position:0% +if + + + align:start position:0% +if +if the problem we see it that's over + + align:start position:0% +if the problem we see it that's over + + + align:start position:0% +if the problem we see it that's over +here is nothing's done that's what we + + align:start position:0% +here is nothing's done that's what we + + + align:start position:0% +here is nothing's done that's what we +see us happen + + align:start position:0% +see us happen + + + align:start position:0% +see us happen +right the framework of our + + align:start position:0% +right the framework of our + + + align:start position:0% +right the framework of our +problem the scenario the scenario is the + + align:start position:0% +problem the scenario the scenario is the + + + align:start position:0% +problem the scenario the scenario is the +impact of your problem if the + + align:start position:0% +impact of your problem if the + + + align:start position:0% +impact of your problem if the +development + + align:start position:0% +development + + + align:start position:0% +development +efforts all right that's that's question + + align:start position:0% +efforts all right that's that's question + + + align:start position:0% +efforts all right that's that's question +four that's not that's the first item on + + align:start position:0% +four that's not that's the first item on + + + align:start position:0% +four that's not that's the first item on +the list is the first item on the list + + align:start position:0% +the list is the first item on the list + + + align:start position:0% +the list is the first item on the list +so that's number four + + align:start position:0% +so that's number four + + + align:start position:0% +so that's number four +then problem factors problem factors is + + align:start position:0% +then problem factors problem factors is + + + align:start position:0% +then problem factors problem factors is +our problem way we stated it it's one + + align:start position:0% +our problem way we stated it it's one + + + align:start position:0% +our problem way we stated it it's one +and two and what led to what ass we made + + align:start position:0% +and two and what led to what ass we made + + + align:start position:0% +and two and what led to what ass we made +to get + + align:start position:0% +to get + + + align:start position:0% +to get +there the problem factors are what + + align:start position:0% +there the problem factors are what + + + align:start position:0% +there the problem factors are what +assumption + + align:start position:0% +assumption + + + align:start position:0% +assumption +like you're you're analyzing the problem + + align:start position:0% +like you're you're analyzing the problem + + + align:start position:0% +like you're you're analyzing the problem +itself + + align:start position:0% +itself + + + align:start position:0% +itself +like the problem as we State as you + + align:start position:0% +like the problem as we State as you + + + align:start position:0% +like the problem as we State as you +stated and the relationship between the + + align:start position:0% +stated and the relationship between the + + + align:start position:0% +stated and the relationship between the +factors and the + + align:start position:0% + + + + align:start position:0% + +problem so it's actually one two the + + align:start position:0% +problem so it's actually one two the + + + align:start position:0% +problem so it's actually one two the +factors that are contributing to the + + align:start position:0% +factors that are contributing to the + + + align:start position:0% +factors that are contributing to the +problem and your problem itself you're + + align:start position:0% +problem and your problem itself you're + + + align:start position:0% +problem and your problem itself you're +analyzing the relationship between + + align:start position:0% + + + + align:start position:0% + +so the relationship is why do you think + + align:start position:0% +so the relationship is why do you think + + + align:start position:0% +so the relationship is why do you think +those factors are + + align:start position:0% + + + + align:start position:0% + +contrib I I am + + align:start position:0% + + + + align:start position:0% + +lost the problem is the number one no + + align:start position:0% +lost the problem is the number one no + + + align:start position:0% +lost the problem is the number one no +you you state the problem this way no + + align:start position:0% +you you state the problem this way no + + + align:start position:0% +you you state the problem this way no +your + + align:start position:0% +your + + + align:start position:0% +your +group the perception that that Visions + + align:start position:0% +group the perception that that Visions + + + align:start position:0% +group the perception that that Visions +held by diverse + + align:start position:0% +held by diverse + + + align:start position:0% +held by diverse +stakehold are conflicted this is the + + align:start position:0% +stakehold are conflicted this is the + + + align:start position:0% +stakehold are conflicted this is the +problem you stated the factor the second + + align:start position:0% +problem you stated the factor the second + + + align:start position:0% +problem you stated the factor the second +question is about why you state the + + align:start position:0% +question is about why you state the + + + align:start position:0% +question is about why you state the +problem + + align:start position:0% +problem + + + align:start position:0% +problem +no if you remember the exercise + + align:start position:0% +no if you remember the exercise + + + align:start position:0% +no if you remember the exercise +yesterday the third question is about + + align:start position:0% +yesterday the third question is about + + + align:start position:0% +yesterday the third question is about +which + + align:start position:0% +which + + + align:start position:0% +which +factors are generating the + + align:start position:0% +factors are generating the + + + align:start position:0% +factors are generating the +problem for + + align:start position:0% +problem for + + + align:start position:0% +problem for +example the problem for you is + + align:start position:0% +example the problem for you is + + + align:start position:0% +example the problem for you is +that the of stakeholders are conflicting + + align:start position:0% +that the of stakeholders are conflicting + + + align:start position:0% +that the of stakeholders are conflicting +this is the + + align:start position:0% +this is the + + + align:start position:0% +this is the +problem no you State this way yes and + + align:start position:0% +problem no you State this way yes and + + + align:start position:0% +problem no you State this way yes and +you say that one factor is the power + + align:start position:0% +you say that one factor is the power + + + align:start position:0% +you say that one factor is the power +Dynamic the imbalance in the power + + align:start position:0% +Dynamic the imbalance in the power + + + align:start position:0% +Dynamic the imbalance in the power +dynamics 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position:0% +the assumption is about the relationship +between + + align:start position:0% +between + + + align:start position:0% +between +factors the + + align:start position:0% +factors the + + + align:start position:0% +factors the +relationship the first one the + + align:start position:0% +relationship the first one the + + + align:start position:0% +relationship the first one the +assumptions behind the + + align:start position:0% +assumptions behind the + + + align:start position:0% +assumptions behind the +relationship + + align:start position:0% +relationship + + + align:start position:0% +relationship +problem where it will be exactly okay + + align:start position:0% +problem where it will be exactly okay + + + align:start position:0% +problem where it will be exactly okay +not just one or the other what about + + align:start position:0% +not just one or the other what about + + + align:start position:0% +not just one or the other what about +conditions conditions is like context + + align:start position:0% +conditions conditions is like context + + + align:start position:0% +conditions conditions is like context +like what assumptions about the context + + align:start position:0% +like what assumptions about the context + + + align:start position:0% +like what assumptions about the context +are us + + align:start position:0% +are us + + + align:start position:0% +are us +for this + + align:start position:0% +for this + + + align:start position:0% +for this +whole thing to + + align:start position:0% + + + + align:start position:0% + +to to + + align:start position:0% +to to + + + align:start position:0% +to to +[Music] + + align:start position:0% + + + + align:start position:0% + +exist and two + + align:start position:0% + + + + align:start position:0% + +doesn't which + + align:start position:0% +doesn't which + + + align:start position:0% +doesn't which +was why is it a problem it's kind of + + align:start position:0% +was why is it a problem it's kind of + + + align:start position:0% +was why is it a problem it's kind of +embedded in one + + align:start position:0% +embedded in one + + + align:start position:0% +embedded in one +and then it's it's kind of + + align:start position:0% +and then it's it's kind of + + + align:start position:0% +and then it's it's kind of +like what's between the factors and the + + align:start position:0% + + + + align:start position:0% + +problem it's it's more but no I'm sorry + + align:start position:0% +problem it's it's more but no I'm sorry + + + align:start position:0% +problem it's it's more but no I'm sorry +number two is really about + + align:start position:0% +number two is really about + + + align:start position:0% +number two is really about +value like why do you think it's a + + align:start position:0% +value like why do you think it's a + + + align:start position:0% +value like why do you think it's a +problem that's that you ask the question + + align:start position:0% +problem that's that you ask the question + + + align:start position:0% +problem that's that you ask the question +why is problem why why is a problem that + + align:start position:0% +why is problem why why is a problem that + + + align:start position:0% +why is problem why why is a problem that +will get you at your thought okay right + + align:start position:0% +will get you at your thought okay right + + + align:start position:0% +will get you at your thought okay right +now we're looking + + align:start position:0% + + + + align:start position:0% + +at sorry about + + align:start position:0% + + + + align:start position:0% + +confusion what did + + align:start position:0% + + + + align:start position:0% + +you so what + + align:start position:0% +you so what + + + align:start position:0% +you so what +were don't look at me this class + + align:start position:0% + + + + align:start position:0% + +just + + align:start position:0% + + + + align:start position:0% + +all should have stayed home and den + + align:start position:0% +all should have stayed home and den + + + align:start position:0% +all should have stayed home and den +[Music] + + align:start position:0% + + + + align:start position:0% + +much's not a lot of + + align:start position:0% + + + + align:start position:0% + +are + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah yeah + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +that's right + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +this is this is a core problem I think + + align:start position:0% +this is this is a core problem I think + + + align:start position:0% +this is this is a core problem I think +we have assum that there may be others + + align:start position:0% +we have assum that there may be others + + + align:start position:0% +we have assum that there may be others +for sub problems that into this + + align:start position:0% +for sub problems that into this + + + align:start position:0% +for sub problems that into this +problem right so I'll put a not about + + align:start position:0% +problem right so I'll put a not about + + + align:start position:0% +problem right so I'll put a not about +that say ackn expit + + align:start position:0% + + + + align:start position:0% + +I'm saying I'm just trying to separate + + align:start position:0% +I'm saying I'm just trying to separate + + + align:start position:0% +I'm saying I'm just trying to separate +[Music] + + align:start position:0% + + + + align:start position:0% + +a like um identify all the that we have + + align:start position:0% +a like um identify all the that we have + + + align:start position:0% +a like um identify all the that we have +and then try to categorize them are like + + align:start position:0% +and then try to categorize them are like + + + align:start position:0% +and then try to categorize them are like +scenario + + align:start position:0% +scenario + + + align:start position:0% +scenario +something a conversation we can + + align:start position:0% +something a conversation we can + + + align:start position:0% +something a conversation we can +better sure about either what they are + + align:start position:0% +better sure about either what they are + + + align:start position:0% +better sure about either what they are +because I'm not really sure about that + + align:start position:0% +because I'm not really sure about that + + + align:start position:0% +because I'm not really sure about that +Vision that we make some of them are not + + align:start position:0% +Vision that we make some of them are not + + + align:start position:0% +Vision that we make some of them are not +like I mean I have some + + align:start position:0% +like I mean I have some + + + align:start position:0% +like I mean I have some +issu I mean I don't I as you I cannot + + align:start position:0% +issu I mean I don't I as you I cannot + + + align:start position:0% +issu I mean I don't I as you I cannot +distinguish if it is assumption based on + + align:start position:0% +distinguish if it is assumption based on + + + align:start position:0% +distinguish if it is assumption based on +the scenario + + align:start position:0% +the scenario + + + align:start position:0% +the scenario +B I + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +have because I mean here if we say + + align:start position:0% +have because I mean here if we say + + + align:start position:0% +have because I mean here if we say +Brazilian Community is not integrated + + align:start position:0% +Brazilian Community is not integrated + + + align:start position:0% +Brazilian Community is not integrated +into the whole + + align:start position:0% + + + + align:start position:0% + +Community not right is that why is not + + align:start position:0% +Community not right is that why is not + + + align:start position:0% +Community not right is that why is not +this scenario I I mean I + + align:start position:0% +this scenario I I mean I + + + align:start position:0% +this scenario I I mean I +don't + + align:start position:0% +don't + + + align:start position:0% +don't +condition cont cont is a + + align:start position:0% +condition cont cont is a + + + align:start position:0% +condition cont cont is a +scenario the scenario I think the + + align:start position:0% +scenario the scenario I think the + + + align:start position:0% +scenario the scenario I think the +thinking scenarios in the future it's + + align:start position:0% +thinking scenarios in the future it's + + + align:start position:0% +thinking scenarios in the future it's +like explicitly like something that's + + align:start position:0% +like explicitly like something that's + + + align:start position:0% +like explicitly like something that's +going to happen versus the present + + align:start position:0% +going to happen versus the present + + + align:start position:0% +going to happen versus the present +there's a difference between the present + + align:start position:0% +there's a difference between the present + + + align:start position:0% +there's a difference between the present +and the future scenario the present is + + align:start position:0% +and the future scenario the present is + + + align:start position:0% +and the future scenario the present is +the problem the present scenario is the + + align:start position:0% +the problem the present scenario is the + + + align:start position:0% +the problem the present scenario is the +problem the future scenario is impacts + + align:start position:0% +problem the future scenario is impacts + + + align:start position:0% +problem the future scenario is impacts +the stuff you're trying to avoid + + align:start position:0% +the stuff you're trying to avoid + + + align:start position:0% +the stuff you're trying to avoid +or right + + align:start position:0% + + + + align:start position:0% + +and factors are things that have been + + align:start position:0% +and factors are things that have been + + + align:start position:0% +and factors are things that have been +contributing to the present + + align:start position:0% +contributing to the present + + + align:start position:0% +contributing to the present +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +situation is it cold here inside here or + + align:start position:0% +situation is it cold here inside here or + + + align:start position:0% +situation is it cold here inside here or +is it I'm comfortable but I have on + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so we + + align:start position:0% +so we + + + align:start position:0% +so we +hope it's a it's an assumption you know + + align:start position:0% +hope it's a it's an assumption you know + + + align:start position:0% +hope it's a it's an assumption you know +they might they might be like no we + + align:start position:0% +they might they might be like no we + + + align:start position:0% +they might they might be like no we +don't want to do all + + align:start position:0% +don't want to do all + + + align:start position:0% +don't want to do all +that we're scared you know we're we + + align:start position:0% +that we're scared you know we're we + + + align:start position:0% +that we're scared you know we're we +don't want to do + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +that and then we assume that + + align:start position:0% +that and then we assume that + + + align:start position:0% +that and then we assume that +[Music] + + align:start position:0% + + + + align:start position:0% + +there's because for + + align:start position:0% +there's because for + + + align:start position:0% +there's because for +being seen everyone + + align:start position:0% + + + + align:start position:0% + +okay it's your + + align:start position:0% +okay it's your + + + align:start position:0% +okay it's your +group yeah please + + align:start position:0% +group yeah please + + + align:start position:0% +group yeah please +can come to the + + align:start position:0% +can come to the + + + align:start position:0% +can come to the +group + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +okay okay + + align:start position:0% + + + + align:start position:0% + +okay each group will + + align:start position:0% + + + + align:start position:0% + +have three minutes okay + + align:start position:0% + + + + align:start position:0% + +for presenting his + + align:start position:0% +for presenting his + + + align:start position:0% +for presenting his +experience we will discuss later are the + + align:start position:0% +experience we will discuss later are the + + + align:start position:0% +experience we will discuss later are the +assumptions you have + + align:start position:0% +assumptions you have + + + align:start position:0% +assumptions you have +found the the moment now is just for + + align:start position:0% +found the the moment now is just for + + + align:start position:0% +found the the moment now is just for +expressing The + + align:start position:0% +expressing The + + + align:start position:0% +expressing The +Experience okay the experience of the + + align:start position:0% +Experience okay the experience of the + + + align:start position:0% +Experience okay the experience of the +exercise what you + + align:start position:0% +exercise what you + + + align:start position:0% +exercise what you +found it's similar to the same + + align:start position:0% +found it's similar to the same + + + align:start position:0% +found it's similar to the same +conversation in the morning what + + align:start position:0% +conversation in the morning what + + + align:start position:0% +conversation in the morning what +challenge okay and what lessons I think + + align:start position:0% +challenge okay and what lessons I think + + + align:start position:0% +challenge okay and what lessons I think +that these two things are enough for now + + align:start position:0% + + + + align:start position:0% + +but I would ask you just to name things + + align:start position:0% +but I would ask you just to name things + + + align:start position:0% +but I would ask you just to name things +not to give + + align:start position:0% +not to give + + + align:start position:0% +not to give +explanations just say the difficulty was + + align:start position:0% +explanations just say the difficulty was + + + align:start position:0% +explanations just say the difficulty was +and five to 10 words the the lesson was + + align:start position:0% +and five to 10 words the the lesson was + + + align:start position:0% +and five to 10 words the the lesson was +5 to 10 words + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but I think that we can do it not by + + align:start position:0% +but I think that we can do it not by + + + align:start position:0% +but I think that we can do it not by +group but by people okay okay each + + align:start position:0% +group but by people okay okay each + + + align:start position:0% +group but by people okay okay each +person who once May begin to + + align:start position:0% +person who once May begin to + + + align:start position:0% +person who once May begin to +talk + + align:start position:0% +talk + + + align:start position:0% +talk +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh I you try to take + + align:start position:0% + + + + align:start position:0% + +note who wants to + + align:start position:0% +note who wants to + + + align:start position:0% +note who wants to +begin you okay um I think the biggest + + align:start position:0% +begin you okay um I think the biggest + + + align:start position:0% +begin you okay um I think the biggest +difficulty + + align:start position:0% +difficulty + + + align:start position:0% +difficulty +was really figuring + + align:start position:0% +was really figuring + + + align:start position:0% +was really figuring +out like where in this process + + align:start position:0% +out like where in this process + + + align:start position:0% +out like where in this process +the + + align:start position:0% +the + + + align:start position:0% +the +assumptions were + + align:start position:0% +assumptions were + + + align:start position:0% +assumptions were +yes um you know just figuring out okay + + align:start position:0% +yes um you know just figuring out okay + + + align:start position:0% +yes um you know just figuring out okay +well is this a part of the problem or + + align:start position:0% +well is this a part of the problem or + + + align:start position:0% +well is this a part of the problem or +does this come before the problem you + + align:start position:0% +does this come before the problem you + + + align:start position:0% +does this come before the problem you +know we kind of really it took us some + + align:start position:0% +know we kind of really it took us some + + + align:start position:0% +know we kind of really it took us some +time to kind of really get through that + + align:start position:0% +time to kind of really get through that + + + align:start position:0% +time to kind of really get through that +okay and really figure out where our + + align:start position:0% +okay and really figure out where our + + + align:start position:0% +okay and really figure out where our +assumptions okay thank you very + + align:start position:0% + + + + align:start position:0% + +much that was our + + align:start position:0% +much that was our + + + align:start position:0% +much that was our +experience that was our group's + + align:start position:0% +experience that was our group's + + + align:start position:0% +experience that was our group's +experience as well the same + + align:start position:0% +experience as well the same + + + align:start position:0% +experience as well the same +yeah for me it's a big surprise yeah + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +uh other + + align:start position:0% + + + + align:start position:0% + +difficulty try to put into words the + + align:start position:0% +difficulty try to put into words the + + + align:start position:0% +difficulty try to put into words the +Assumption in a in a positive state + + align:start position:0% +Assumption in a in a positive state + + + align:start position:0% +Assumption in a in a positive state +the if then kind of + + align:start position:0% +the if then kind of + + + align:start position:0% +the if then kind of +statement because what we had stated + + align:start position:0% +statement because what we had stated + + + align:start position:0% +statement because what we had stated +yesterday as factors were in a negative + + align:start position:0% +yesterday as factors were in a negative + + + align:start position:0% +yesterday as factors were in a negative +State we went from lack of dialogue M as + + align:start position:0% +State we went from lack of dialogue M as + + + align:start position:0% +State we went from lack of dialogue M as +a factor to an assumption that if there + + align:start position:0% +a factor to an assumption that if there + + + align:start position:0% +a factor to an assumption that if there +were better dialogue then something + + align:start position:0% +were better dialogue then something + + + align:start position:0% +were better dialogue then something +positive would occur great + + align:start position:0% +positive would occur great + + + align:start position:0% +positive would occur great +yes + + align:start position:0% +yes + + + align:start position:0% +yes +sh mhm + + align:start position:0% +sh mhm + + + align:start position:0% +sh mhm +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +it's a very interesting thing I + + align:start position:0% +it's a very interesting thing I + + + align:start position:0% +it's a very interesting thing I +will talk a little about this because + + align:start position:0% +will talk a little about this because + + + align:start position:0% +will talk a little about this because +when we State a factor as a lack + + align:start position:0% +when we State a factor as a lack + + + align:start position:0% +when we State a factor as a lack +of what we are stating is not a factor + + align:start position:0% +of what we are stating is not a factor + + + align:start position:0% +of what we are stating is not a factor +it's an + + align:start position:0% +it's an + + + align:start position:0% +it's an +assumption so it's a topology we we we + + align:start position:0% +assumption so it's a topology we we we + + + align:start position:0% +assumption so it's a topology we we we +are not increasing information in the + + align:start position:0% +are not increasing information in the + + + align:start position:0% +are not increasing information in the +system we are just expressing a belief + + align:start position:0% +system we are just expressing a belief + + + align:start position:0% +system we are just expressing a belief +we have + + align:start position:0% + + + + align:start position:0% + +so the exercise made it clear for you + + align:start position:0% +so the exercise made it clear for you + + + align:start position:0% +so the exercise made it clear for you +not for your group that you can just to + + align:start position:0% +not for your group that you can just to + + + align:start position:0% +not for your group that you can just to +to transform the lack of in some + + align:start position:0% +to transform the lack of in some + + + align:start position:0% +to transform the lack of in some +affirmative statement and this is the + + align:start position:0% +affirmative statement and this is the + + + align:start position:0% +affirmative statement and this is the +Assumption no yes + + align:start position:0% + + + + align:start position:0% + +great for people who + + align:start position:0% +great for people who + + + align:start position:0% +great for people who +construct three of problems + + align:start position:0% +construct three of problems + + + align:start position:0% +construct three of problems +this is a limitation in constructing + + align:start position:0% +this is a limitation in constructing + + + align:start position:0% +this is a limitation in constructing +three of problems because a lot of the + + align:start position:0% +three of problems because a lot of the + + + align:start position:0% +three of problems because a lot of the +the roots of the tree the causes of the + + align:start position:0% +the roots of the tree the causes of the + + + align:start position:0% +the roots of the tree the causes of the +problem are stated as lack + + align:start position:0% + + + + align:start position:0% + +off okay there is no the agnostic in + + align:start position:0% +off okay there is no the agnostic in + + + align:start position:0% +off okay there is no the agnostic in +that there are only assumptions about + + align:start position:0% +that there are only assumptions about + + + align:start position:0% +that there are only assumptions about +how the world + + align:start position:0% + + + + align:start position:0% + +Works + + align:start position:0% +Works + + + align:start position:0% +Works +yes well I'm realizing even the things + + align:start position:0% +yes well I'm realizing even the things + + + align:start position:0% +yes well I'm realizing even the things +that we had written down that weren't + + align:start position:0% +that we had written down that weren't + + + align:start position:0% +that we had written down that weren't +written as lack of could be restated as + + align:start position:0% +written as lack of could be restated as + + + align:start position:0% +written as lack of could be restated as +lack of so what is that just in the way + + align:start position:0% +lack of so what is that just in the way + + + align:start position:0% +lack of so what is that just in the way +that we printed or is that something + + align:start position:0% +that we printed or is that something + + + align:start position:0% +that we printed or is that something +that other people share in their framing + + align:start position:0% +that other people share in their framing + + + align:start position:0% +that other people share in their framing +of the factors and is possible to write + + align:start position:0% +of the factors and is possible to write + + + align:start position:0% +of the factors and is possible to write +any sort of factor in + + align:start position:0% +any sort of factor in + + + align:start position:0% +any sort of factor in +L then what is the + + align:start position:0% +L then what is the + + + align:start position:0% +L then what is the +factor when we State a factor is lack + + align:start position:0% +factor when we State a factor is lack + + + align:start position:0% +factor when we State a factor is lack +off it's clear that we we have not find + + align:start position:0% +off it's clear that we we have not find + + + align:start position:0% +off it's clear that we we have not find +the factor in + + align:start position:0% +the factor in + + + align:start position:0% +the factor in +itself we have two things that are + + align:start position:0% +itself we have two things that are + + + align:start position:0% +itself we have two things that are +stated there power dynamics stratified + + align:start position:0% +stated there power dynamics stratified + + + align:start position:0% +stated there power dynamics stratified +resan Community you can restate those as + + align:start position:0% +resan Community you can restate those as + + + align:start position:0% +resan Community you can restate those as +lack of Power Balance or lack of equity + + align:start position:0% +lack of Power Balance or lack of equity + + + align:start position:0% +lack of Power Balance or lack of equity +inan Community yes you can restate every + + align:start position:0% +inan Community yes you can restate every + + + align:start position:0% +inan Community yes you can restate every +Factor as lack of the problem yes so are + + align:start position:0% +Factor as lack of the problem yes so are + + + align:start position:0% +Factor as lack of the problem yes so are +there other can you give us example + + align:start position:0% +there other can you give us example + + + align:start position:0% +there other can you give us example +maybe other people's support here that + + align:start position:0% +maybe other people's support here that + + + align:start position:0% +maybe other people's support here that +would be not some sort of lack of that + + align:start position:0% +would be not some sort of lack of that + + + align:start position:0% +would be not some sort of lack of that +would be a verifyable + + align:start position:0% +would be a verifyable + + + align:start position:0% +would be a verifyable +[Music] + + align:start position:0% + + + + align:start position:0% + +real it's better to State a factor as + + align:start position:0% +real it's better to State a factor as + + + align:start position:0% +real it's better to State a factor as +something that + + align:start position:0% +something that + + + align:start position:0% +something that +exist to to try to to describe what + + align:start position:0% +exist to to try to to describe what + + + align:start position:0% +exist to to try to to describe what +exist and not to describe what doesn't + + align:start position:0% + + + + align:start position:0% + +exist sometimes it's not easy can you + + align:start position:0% +exist sometimes it's not easy can you + + + align:start position:0% +exist sometimes it's not easy can you +point to one of these things and read + + align:start position:0% +point to one of these things and read + + + align:start position:0% +point to one of these things and read +that + + align:start position:0% +that + + + align:start position:0% +that +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +is the first + + align:start position:0% +is the first + + + align:start position:0% +is the first +one the the the the dynamic of power is + + align:start position:0% + + + + align:start position:0% + +imbalanced it's verifiable it's possible + + align:start position:0% +imbalanced it's verifiable it's possible + + + align:start position:0% +imbalanced it's verifiable it's possible +to verify but it's you could say lack of + + align:start position:0% +to verify but it's you could say lack of + + + align:start position:0% +to verify but it's you could say lack of +balance in power you can say lack of + + align:start position:0% +balance in power you can say lack of + + + align:start position:0% +balance in power you can say lack of +balance of + + align:start position:0% +balance of + + + align:start position:0% +balance of +power + + align:start position:0% +power + + + align:start position:0% +power +and in this case you can verify if + + align:start position:0% +and in this case you can verify if + + + align:start position:0% +and in this case you can verify if +exist but you it's most difficult to + + align:start position:0% +exist but you it's most difficult to + + + align:start position:0% +exist but you it's most difficult to +understand what is + + align:start position:0% + + + + align:start position:0% + +happening if if I if I think about the + + align:start position:0% +happening if if I if I think about the + + + align:start position:0% +happening if if I if I think about the +imbalance of power I can look at what is + + align:start position:0% +imbalance of power I can look at what is + + + align:start position:0% +imbalance of power I can look at what is +happening if I talk about lack of + + align:start position:0% +happening if I talk about lack of + + + align:start position:0% +happening if I talk about lack of +balance + + align:start position:0% +balance + + + align:start position:0% +balance +I'm talking about what I think that + + align:start position:0% +I'm talking about what I think that + + + align:start position:0% +I'm talking about what I think that +should exist and I am not looking at the + + align:start position:0% +should exist and I am not looking at the + + + align:start position:0% +should exist and I am not looking at the +at the factor in itself it displays the + + align:start position:0% +at the factor in itself it displays the + + + align:start position:0% +at the factor in itself it displays the +the effort the focus of the mind so is + + align:start position:0% +the effort the focus of the mind so is + + + align:start position:0% +the effort the focus of the mind so is +it is it then possible to re phrase the + + align:start position:0% +it is it then possible to re phrase the + + + align:start position:0% +it is it then possible to re phrase the +two statements that are written as lack + + align:start position:0% +two statements that are written as lack + + + align:start position:0% +two statements that are written as lack +up in way that makes the real + + align:start position:0% +up in way that makes the real + + + align:start position:0% +up in way that makes the real +fact so the second one second and the + + align:start position:0% +fact so the second one second and the + + + align:start position:0% +fact so the second one second and the +third one like of dialog like lack of + + align:start position:0% +third one like of dialog like lack of + + + align:start position:0% +third one like of dialog like lack of +dialogue yes it's better to describe + + align:start position:0% +dialogue yes it's better to describe + + + align:start position:0% +dialogue yes it's better to describe +what is happening in the lack of + + align:start position:0% +what is happening in the lack of + + + align:start position:0% +what is happening in the lack of +dialogue okay what kind of relation + + align:start position:0% +dialogue okay what kind of relation + + + align:start position:0% +dialogue okay what kind of relation +exist in the lack of dialogue because + + align:start position:0% +exist in the lack of dialogue because + + + align:start position:0% +exist in the lack of dialogue because +there is something there is not there is + + align:start position:0% +there is something there is not there is + + + align:start position:0% +there is something there is not there is +not dialogue but something is happening + + align:start position:0% +not dialogue but something is happening + + + align:start position:0% +not dialogue but something is happening +this moment okay the description of what + + align:start position:0% +this moment okay the description of what + + + align:start position:0% +this moment okay the description of what +is happening this moment is much more + + align:start position:0% +is happening this moment is much more + + + align:start position:0% +is happening this moment is much more +precise okay + + align:start position:0% +precise okay + + + align:start position:0% +precise okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and indeed it's difficult to find + + align:start position:0% +and indeed it's difficult to find + + + align:start position:0% +and indeed it's difficult to find +to to go beyond if I like if I write as + + align:start position:0% +to to go beyond if I like if I write as + + + align:start position:0% +to to go beyond if I like if I write as +lack of dialogue the only assumption is + + align:start position:0% +lack of dialogue the only assumption is + + + align:start position:0% +lack of dialogue the only assumption is +that if there exist dialogue it should + + align:start position:0% +that if there exist dialogue it should + + + align:start position:0% +that if there exist dialogue it should +be + + align:start position:0% +be + + + align:start position:0% +be +better okay but I I I'm not + + align:start position:0% +better okay but I I I'm not + + + align:start position:0% +better okay but I I I'm not +understanding how is working this + + align:start position:0% +understanding how is working this + + + align:start position:0% +understanding how is working this +moment okay I have an assumption about + + align:start position:0% +moment okay I have an assumption about + + + align:start position:0% +moment okay I have an assumption about +the future not about the the + + align:start position:0% +the future not about the the + + + align:start position:0% +the future not about the the +present okay so my my the idea I have + + align:start position:0% +present okay so my my the idea I have + + + align:start position:0% +present okay so my my the idea I have +the + + align:start position:0% +the + + + align:start position:0% +the +level of knowledge that I have about the + + align:start position:0% +level of knowledge that I have about the + + + align:start position:0% +level of knowledge that I have about the +the problem is more limited when I + + align:start position:0% +the problem is more limited when I + + + align:start position:0% +the problem is more limited when I +express using lack of some things some + + align:start position:0% +express using lack of some things some + + + align:start position:0% +express using lack of some things some +desires lack of + + align:start position:0% + + + + align:start position:0% + +desires it's not concrete it's not + + align:start position:0% +desires it's not concrete it's not + + + align:start position:0% +desires it's not concrete it's not +concrete and it's a an assumption about + + align:start position:0% +concrete and it's a an assumption about + + + align:start position:0% +concrete and it's a an assumption about +the + + align:start position:0% +the + + + align:start position:0% +the +solution and not a description of the + + align:start position:0% +solution and not a description of the + + + align:start position:0% +solution and not a description of the +problem + + align:start position:0% +problem + + + align:start position:0% +problem +is I go to the physician and the + + align:start position:0% +is I go to the physician and the + + + align:start position:0% +is I go to the physician and the +physician says to me you need + + align:start position:0% +physician says to me you need + + + align:start position:0% +physician says to me you need +antibiotics okay but I like to know why + + align:start position:0% +antibiotics okay but I like to know why + + + align:start position:0% +antibiotics okay but I like to know why +I need antibiotics you you your sickness + + align:start position:0% +I need antibiotics you you your sickness + + + align:start position:0% +I need antibiotics you you your sickness +is because you are lacking + + align:start position:0% +is because you are lacking + + + align:start position:0% +is because you are lacking +antibiotics okay so he has the recite + + align:start position:0% +antibiotics okay so he has the recite + + + align:start position:0% +antibiotics okay so he has the recite +before to have the + + align:start position:0% +before to have the + + + align:start position:0% +before to have the +diagnostic this is the problem + + align:start position:0% +diagnostic this is the problem + + + align:start position:0% +diagnostic this is the problem +here so maybe like to reframe this or + + align:start position:0% +here so maybe like to reframe this or + + + align:start position:0% +here so maybe like to reframe this or +restate this is U lack of + + align:start position:0% +restate this is U lack of + + + align:start position:0% +restate this is U lack of +sorry um yes it's not + + align:start position:0% +sorry um yes it's not + + + align:start position:0% +sorry um yes it's not +easy don't don't worry about to to be + + align:start position:0% +easy don't don't worry about to to be + + + align:start position:0% +easy don't don't worry about to to be +able to have difficulties for state in + + align:start position:0% +able to have difficulties for state in + + + align:start position:0% +able to have difficulties for state in +this + + align:start position:0% +this + + + align:start position:0% +this +moment we we we need to go again to the + + align:start position:0% +moment we we we need to go again to the + + + align:start position:0% +moment we we we need to go again to the +object and to to + + align:start position:0% +object and to to + + + align:start position:0% +object and to to +observe so + + align:start position:0% +observe so + + + align:start position:0% +observe so +maybe better communication with reduced + + align:start position:0% +maybe better communication with reduced + + + align:start position:0% +maybe better communication with reduced +conflict between visions of + + align:start position:0% +conflict between visions of + + + align:start position:0% +conflict between visions of +stakeholders it it's very common that if + + align:start position:0% +stakeholders it it's very common that if + + + align:start position:0% +stakeholders it it's very common that if +you have not dialogue you may have that + + align:start position:0% +you have not dialogue you may have that + + + align:start position:0% +you have not dialogue you may have that +some kind of power is being ex applied + + align:start position:0% +some kind of power is being ex applied + + + align:start position:0% +some kind of power is being ex applied +in some + + align:start position:0% +in some + + + align:start position:0% +in some +way okay and you hope that if if existed + + align:start position:0% +way okay and you hope that if if existed + + + align:start position:0% +way okay and you hope that if if existed +dialogue this should should not be + + align:start position:0% +dialogue this should should not be + + + align:start position:0% +dialogue this should should not be +happen in this + + align:start position:0% +happen in this + + + align:start position:0% +happen in this +way + + align:start position:0% +way + + + align:start position:0% +way +okay okay let's come back to the + + align:start position:0% +okay okay let's come back to the + + + align:start position:0% +okay okay let's come back to the +exercise or I should talk about where + + align:start position:0% +exercise or I should talk about where + + + align:start position:0% +exercise or I should talk about where +the assumptions + + align:start position:0% +the assumptions + + + align:start position:0% +the assumptions +were because what was difficult for you + + align:start position:0% +were because what was difficult for you + + + align:start position:0% +were because what was difficult for you +no to to localize the + + align:start position:0% +no to to localize the + + + align:start position:0% +no to to localize the +assumptions + + align:start position:0% + + + + align:start position:0% + +the H would it help to do this part for + + align:start position:0% +the H would it help to do this part for + + + align:start position:0% +the H would it help to do this part for +that yes + + align:start position:0% +that yes + + + align:start position:0% +that yes +perhaps we should present again the + + align:start position:0% +perhaps we should present again the + + + align:start position:0% +perhaps we should present again the +cognitive logic we had in mind when we + + align:start position:0% +cognitive logic we had in mind when we + + + align:start position:0% +cognitive logic we had in mind when we +propose the exercise and we can continue + + align:start position:0% +propose the exercise and we can continue + + + align:start position:0% +propose the exercise and we can continue +to talk tomorrow okay + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% + + + + align:start position:0% + +what these are just the steps that you + + align:start position:0% +what these are just the steps that you + + + align:start position:0% +what these are just the steps that you +guys took to to try to identify the + + align:start position:0% +guys took to to try to identify the + + + align:start position:0% +guys took to to try to identify the +assumptions the first was to and the + + align:start position:0% +assumptions the first was to and the + + + align:start position:0% +assumptions the first was to and the +first step you try to do is is that you + + align:start position:0% +first step you try to do is is that you + + + align:start position:0% +first step you try to do is is that you +deconstruct your + + align:start position:0% +deconstruct your + + + align:start position:0% +deconstruct your +frame in order to identify the main + + align:start position:0% +frame in order to identify the main + + + align:start position:0% +frame in order to identify the main +components of your frame and yesterday + + align:start position:0% +components of your frame and yesterday + + + align:start position:0% +components of your frame and yesterday +you didn't deconstruct you actually + + align:start position:0% +you didn't deconstruct you actually + + + align:start position:0% +you didn't deconstruct you actually +constructed the the frame based on + + align:start position:0% +constructed the the frame based on + + + align:start position:0% +constructed the the frame based on +components but in general you you + + align:start position:0% +components but in general you you + + + align:start position:0% +components but in general you you +usually have the frame already and + + align:start position:0% +usually have the frame already and + + + align:start position:0% +usually have the frame already and +you've got a deconstructed in + + align:start position:0% +you've got a deconstructed in + + + align:start position:0% +you've got a deconstructed in +yesterday's example exercise the main + + align:start position:0% +yesterday's example exercise the main + + + align:start position:0% +yesterday's example exercise the main +components of the frame that you + + align:start position:0% +components of the frame that you + + + align:start position:0% +components of the frame that you +constructed were the problem the impact + + align:start position:0% +constructed were the problem the impact + + + align:start position:0% +constructed were the problem the impact +of the problem or the + + align:start position:0% +of the problem or the + + + align:start position:0% +of the problem or the +scenario the factors that you think are + + align:start position:0% +scenario the factors that you think are + + + align:start position:0% +scenario the factors that you think are +contributing to that + + align:start position:0% +contributing to that + + + align:start position:0% +contributing to that +problem and something that was tacit in + + align:start position:0% +problem and something that was tacit in + + + align:start position:0% +problem and something that was tacit in +your construction of the frame was the + + align:start position:0% +your construction of the frame was the + + + align:start position:0% +your construction of the frame was the +contextual conditions that you had in + + align:start position:0% +contextual conditions that you had in + + + align:start position:0% +contextual conditions that you had in +your mind as you were constructing that + + align:start position:0% +your mind as you were constructing that + + + align:start position:0% +your mind as you were constructing that +frame + + align:start position:0% +frame + + + align:start position:0% +frame +so so if you can go through the process + + align:start position:0% +so so if you can go through the process + + + align:start position:0% +so so if you can go through the process +of deconstructing your frame and + + align:start position:0% +of deconstructing your frame and + + + align:start position:0% +of deconstructing your frame and +identify those components something that + + align:start position:0% +identify those components something that + + + align:start position:0% +identify those components something that +really helps is to express that those + + align:start position:0% +really helps is to express that those + + + align:start position:0% +really helps is to express that those +components and their relationships to + + align:start position:0% +components and their relationships to + + + align:start position:0% +components and their relationships to +one another uh + + align:start position:0% +one another uh + + + align:start position:0% +one another uh +graphically um Shan uses matrices seasal + + align:start position:0% +graphically um Shan uses matrices seasal + + + align:start position:0% +graphically um Shan uses matrices seasal +today had represented it graphically in + + align:start position:0% +today had represented it graphically in + + + align:start position:0% +today had represented it graphically in +a map of Cal + + align:start position:0% +a map of Cal + + + align:start position:0% +a map of Cal +relations like this one you know but it + + align:start position:0% +relations like this one you know but it + + + align:start position:0% +relations like this one you know but it +usually helps organize your + + align:start position:0% +usually helps organize your + + + align:start position:0% +usually helps organize your +mind and then the last thing is to look + + align:start position:0% +mind and then the last thing is to look + + + align:start position:0% +mind and then the last thing is to look +to analyze the relationships between the + + align:start position:0% +to analyze the relationships between the + + + align:start position:0% +to analyze the relationships between the +components of your + + align:start position:0% +components of your + + + align:start position:0% +components of your +frame and in those in those + + align:start position:0% +frame and in those in those + + + align:start position:0% +frame and in those in those +relationships that's where you find the + + align:start position:0% +relationships that's where you find the + + + align:start position:0% +relationships that's where you find the +Assumption in this case you were + + align:start position:0% +Assumption in this case you were + + + align:start position:0% +Assumption in this case you were +analyzing the relationship between the + + align:start position:0% +analyzing the relationship between the + + + align:start position:0% +analyzing the relationship between the +scenario and the + + align:start position:0% +scenario and the + + + align:start position:0% +scenario and the +problem the impact and the + + align:start position:0% +problem the impact and the + + + align:start position:0% +problem the impact and the +problem the main question you were + + align:start position:0% +problem the main question you were + + + align:start position:0% +problem the main question you were +asking yourself in that + + align:start position:0% +asking yourself in that + + + align:start position:0% +asking yourself in that +analysis was why do you think that + + align:start position:0% +analysis was why do you think that + + + align:start position:0% +analysis was why do you think that +scenario will be generated by the + + align:start position:0% +scenario will be generated by the + + + align:start position:0% +scenario will be generated by the +problem that was a question that you + + align:start position:0% +problem that was a question that you + + + align:start position:0% +problem that was a question that you +were that you were using to help your + + align:start position:0% +were that you were using to help your + + + align:start position:0% +were that you were using to help your +thinking process in order to figure out + + align:start position:0% +thinking process in order to figure out + + + align:start position:0% +thinking process in order to figure out +the + + align:start position:0% +the + + + align:start position:0% +the +Assumption between those two components + + align:start position:0% +Assumption between those two components + + + align:start position:0% +Assumption between those two components +the other question that you were using + + align:start position:0% +the other question that you were using + + + align:start position:0% +the other question that you were using +was why do the factors contribute to the + + align:start position:0% +was why do the factors contribute to the + + + align:start position:0% +was why do the factors contribute to the +problem that you were using in order to + + align:start position:0% +problem that you were using in order to + + + align:start position:0% +problem that you were using in order to +ident to identify the assumptions behind + + align:start position:0% +ident to identify the assumptions behind + + + align:start position:0% +ident to identify the assumptions behind +that relationship between the factors + + align:start position:0% +that relationship between the factors + + + align:start position:0% +that relationship between the factors +that are contributing to the problem and + + align:start position:0% +that are contributing to the problem and + + + align:start position:0% +that are contributing to the problem and +the problem as you have defined + + align:start position:0% +the problem as you have defined + + + align:start position:0% +the problem as you have defined +it and lastly the question of which + + align:start position:0% +it and lastly the question of which + + + align:start position:0% +it and lastly the question of which +conditions are required for for like + + align:start position:0% +conditions are required for for like + + + align:start position:0% +conditions are required for for like +which contextual conditions are required + + align:start position:0% +which contextual conditions are required + + + align:start position:0% +which contextual conditions are required +for all of these casual relationships to + + align:start position:0% +for all of these casual relationships to + + + align:start position:0% +for all of these casual relationships to +exist as you have framed + + align:start position:0% +exist as you have framed + + + align:start position:0% +exist as you have framed +them so that's just a quick summary of + + align:start position:0% +them so that's just a quick summary of + + + align:start position:0% +them so that's just a quick summary of +this process that you went through and + + align:start position:0% +this process that you went through and + + + align:start position:0% +this process that you went through and +and pay attention just like we we were + + align:start position:0% +and pay attention just like we we were + + + align:start position:0% +and pay attention just like we we were +just talking about how important it is + + align:start position:0% +just talking about how important it is + + + align:start position:0% +just talking about how important it is +for for the mind for the for the + + align:start position:0% +for for the mind for the for the + + + align:start position:0% +for for the mind for the for the +thinking process for you to focus not on + + align:start position:0% +thinking process for you to focus not on + + + align:start position:0% +thinking process for you to focus not on +what doesn't exist but what exists same + + align:start position:0% +what doesn't exist but what exists same + + + align:start position:0% +what doesn't exist but what exists same +thing pay attention when we're asking + + align:start position:0% +thing pay attention when we're asking + + + align:start position:0% +thing pay attention when we're asking +about the relationship between scenario + + align:start position:0% +about the relationship between scenario + + + align:start position:0% +about the relationship between scenario +and problem you can think you can use + + align:start position:0% +and problem you can think you can use + + + align:start position:0% +and problem you can think you can use +the scenario and the characteristics of + + align:start position:0% +the scenario and the characteristics of + + + align:start position:0% +the scenario and the characteristics of +the scenario as your Point of + + align:start position:0% +the scenario as your Point of + + + align:start position:0% +the scenario as your Point of +Departure to think about how it relates + + align:start position:0% +Departure to think about how it relates + + + align:start position:0% +Departure to think about how it relates +to the problem or you can do it the + + align:start position:0% +to the problem or you can do it the + + + align:start position:0% +to the problem or you can do it the +other way around the problem think about + + align:start position:0% +other way around the problem think about + + + align:start position:0% +other way around the problem think about +how the problem actually gets creates + + align:start position:0% +how the problem actually gets creates + + + align:start position:0% +how the problem actually gets creates +the scenario but notice how seast is + + align:start position:0% +the scenario but notice how seast is + + + align:start position:0% +the scenario but notice how seast is +asking you to do the the opposite + + align:start position:0% +asking you to do the the opposite + + + align:start position:0% +asking you to do the the opposite +and it's all because of the Mind process + + align:start position:0% +and it's all because of the Mind process + + + align:start position:0% +and it's all because of the Mind process +this holds this keeps your mind focused + + align:start position:0% +this holds this keeps your mind focused + + + align:start position:0% +this holds this keeps your mind focused +on the scenario in order to think about + + align:start position:0% +on the scenario in order to think about + + + align:start position:0% +on the scenario in order to think about +the how the problem is causing that + + align:start position:0% +the how the problem is causing that + + + align:start position:0% +the how the problem is causing that +scenario if you do it the other way + + align:start position:0% +scenario if you do it the other way + + + align:start position:0% +scenario if you do it the other way +around your mind you doesn't have any + + align:start position:0% +around your mind you doesn't have any + + + align:start position:0% +around your mind you doesn't have any +discipline and you can go to all types + + align:start position:0% +discipline and you can go to all types + + + align:start position:0% +discipline and you can go to all types +of scenarios when you're trying to think + + align:start position:0% +of scenarios when you're trying to think + + + align:start position:0% +of scenarios when you're trying to think +how it relates to the scenario so those + + align:start position:0% +how it relates to the scenario so those + + + align:start position:0% +how it relates to the scenario so those +types of things I don't know if this + + align:start position:0% +types of things I don't know if this + + + align:start position:0% +types of things I don't know if this +helps + + align:start position:0% +helps + + + align:start position:0% +helps +but yes + + align:start position:0% +but yes + + + align:start position:0% +but yes +um we actually didn't do it that + + align:start position:0% +um we actually didn't do it that + + + align:start position:0% +um we actually didn't do it that +way in your group huh in your group in + + align:start position:0% +way in your group huh in your group in + + + align:start position:0% +way in your group huh in your group in +our + + align:start position:0% +our + + + align:start position:0% +our +grou we uh we captured the brainstorming + + align:start position:0% +grou we uh we captured the brainstorming + + + align:start position:0% +grou we uh we captured the brainstorming +we did last night and then tried to + + align:start position:0% +we did last night and then tried to + + + align:start position:0% +we did last night and then tried to +identify what kind of assumption it + + align:start position:0% +identify what kind of assumption it + + + align:start position:0% +identify what kind of assumption it +was and that was actually useful for us + + align:start position:0% +was and that was actually useful for us + + + align:start position:0% +was and that was actually useful for us +because it didn't force us to do the + + align:start position:0% +because it didn't force us to do the + + + align:start position:0% +because it didn't force us to do the +why um I think the doing the Y is useful + + align:start position:0% +why um I think the doing the Y is useful + + + align:start position:0% +why um I think the doing the Y is useful +but I think not doing the Y + + align:start position:0% +but I think not doing the Y + + + align:start position:0% +but I think not doing the Y +opened up a bag of assumptions and we + + align:start position:0% +opened up a bag of assumptions and we + + + align:start position:0% +opened up a bag of assumptions and we +like wow what kind of assumption is this + + align:start position:0% +like wow what kind of assumption is this + + + align:start position:0% +like wow what kind of assumption is this +and that was kind of fun too we + + align:start position:0% +and that was kind of fun too we + + + align:start position:0% +and that was kind of fun too we +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +actually all we try to see where they + + align:start position:0% +actually all we try to see where they + + + align:start position:0% +actually all we try to see where they +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +fit because otherwise we'll we be stuck + + align:start position:0% +fit because otherwise we'll we be stuck + + + align:start position:0% +fit because otherwise we'll we be stuck +in so is scenario is this we'll be stuck + + align:start position:0% +in so is scenario is this we'll be stuck + + + align:start position:0% +in so is scenario is this we'll be stuck +in one specific area and we will get + + align:start position:0% +in one specific area and we will get + + + align:start position:0% +in one specific area and we will get +assumptions to come + + align:start position:0% +assumptions to come + + + align:start position:0% +assumptions to come +out we assumed + + align:start position:0% +out we assumed + + + align:start position:0% +out we assumed +supposed to use + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +okay great okay tomorrow we we the + + align:start position:0% +okay great okay tomorrow we we the + + + align:start position:0% +okay great okay tomorrow we we the +exercise of tomorrow thank you the + + align:start position:0% +exercise of tomorrow thank you the + + + align:start position:0% +exercise of tomorrow thank you the +exercise of + + align:start position:0% + + + + align:start position:0% + +Tomorrow a homework + + align:start position:0% +Tomorrow a homework + + + align:start position:0% +Tomorrow a homework +okay tomorrow we will try to + + align:start position:0% +okay tomorrow we will try to + + + align:start position:0% +okay tomorrow we will try to +reframe the process of reframing will be + + align:start position:0% +reframe the process of reframing will be + + + align:start position:0% +reframe the process of reframing will be +basically one to evaluate how trustable + + align:start position:0% +basically one to evaluate how trustable + + + align:start position:0% +basically one to evaluate how trustable +are these + + align:start position:0% + + + + align:start position:0% + +assumptions if one + + align:start position:0% +assumptions if one + + + align:start position:0% +assumptions if one +assumption + + align:start position:0% +assumption + + + align:start position:0% +assumption +Falls the Assumption brings part of the + + align:start position:0% +Falls the Assumption brings part of the + + + align:start position:0% +Falls the Assumption brings part of the +frame with + + align:start position:0% + + + + align:start position:0% + +it each time one + + align:start position:0% +it each time one + + + align:start position:0% +it each time one +assumption lacks + + align:start position:0% +assumption lacks + + + align:start position:0% +assumption lacks +trustability we needs to revise the + + align:start position:0% +trustability we needs to revise the + + + align:start position:0% +trustability we needs to revise the +scenario in this area we we do this + + align:start position:0% +scenario in this area we we do this + + + align:start position:0% +scenario in this area we we do this +tomorrow the homework will + + align:start position:0% +tomorrow the homework will + + + align:start position:0% +tomorrow the homework will +be the homework will be if you can + + align:start position:0% +be the homework will be if you can + + + align:start position:0% +be the homework will be if you can +create an Excel + + align:start position:0% +create an Excel + + + align:start position:0% +create an Excel +sheet um with three + + align:start position:0% +sheet um with three + + + align:start position:0% +sheet um with three +columns the First Column is for + + align:start position:0% +columns the First Column is for + + + align:start position:0% +columns the First Column is for +assumptions so you list out the + + align:start position:0% +assumptions so you list out the + + + align:start position:0% +assumptions so you list out the +assumptions that you guys identified in + + align:start position:0% +assumptions that you guys identified in + + + align:start position:0% +assumptions that you guys identified in +your groups + + align:start position:0% +your groups + + + align:start position:0% +your groups +today and the second column is + + align:start position:0% +today and the second column is + + + align:start position:0% +today and the second column is +information if you can get information + + align:start position:0% +information if you can get information + + + align:start position:0% +information if you can get information +for verif verifying how trustable is the + + align:start position:0% +for verif verifying how trustable is the + + + align:start position:0% +for verif verifying how trustable is the +assumption + + align:start position:0% +assumption + + + align:start position:0% +assumption +like what kind of information would you + + align:start position:0% +like what kind of information would you + + + align:start position:0% +like what kind of information would you +need to + + align:start position:0% +need to + + + align:start position:0% +need to +verify yeah that would support it or + + align:start position:0% +verify yeah that would support it or + + + align:start position:0% +verify yeah that would support it or +actually challenge your + + align:start position:0% +actually challenge your + + + align:start position:0% +actually challenge your +assumption and the last uh column is + + align:start position:0% +assumption and the last uh column is + + + align:start position:0% +assumption and the last uh column is +what it's kind of like an evaluation of + + align:start position:0% +what it's kind of like an evaluation of + + + align:start position:0% +what it's kind of like an evaluation of +the Assumption based on the information + + align:start position:0% +the Assumption based on the information + + + align:start position:0% +the Assumption based on the information +you found like what parts of the + + align:start position:0% +you found like what parts of the + + + align:start position:0% +you found like what parts of the +Assumption were + + align:start position:0% +Assumption were + + + align:start position:0% +Assumption were +challenged or strengthened by the + + align:start position:0% +challenged or strengthened by the + + + align:start position:0% +challenged or strengthened by the +information by the + + align:start position:0% + + + + align:start position:0% + +information yes + + align:start position:0% +information yes + + + align:start position:0% +information yes +just as an exercise to tomorrow we from + + align:start position:0% +just as an exercise to tomorrow we from + + + align:start position:0% +just as an exercise to tomorrow we from +today for tomorrow I I'm not sure that + + align:start position:0% +today for tomorrow I I'm not sure that + + + align:start position:0% +today for tomorrow I I'm not sure that +we will be possible to get enough + + align:start position:0% +we will be possible to get enough + + + align:start position:0% +we will be possible to get enough +information for for verify all the + + align:start position:0% +information for for verify all the + + + align:start position:0% +information for for verify all the +assumptions whatever you can okay just + + align:start position:0% +assumptions whatever you can okay just + + + align:start position:0% +assumptions whatever you can okay just +for interet or talking to people who you + + align:start position:0% +for interet or talking to people who you + + + align:start position:0% +for interet or talking to people who you +know from framing him + + align:start position:0% + + + + align:start position:0% + +whatever + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah can + + align:start position:0% + + + + align:start position:0% + +please tomorrow will be here the class + + align:start position:0% +please tomorrow will be here the class + + + align:start position:0% +please tomorrow will be here the class +the class will be here tomorrow the + + align:start position:0% +the class will be here tomorrow the + + + align:start position:0% +the class will be here tomorrow the +class will be here tomorrow + + align:start position:0% +class will be here tomorrow + + + align:start position:0% +class will be here tomorrow +okay okay anything else we can send you + + align:start position:0% +okay okay anything else we can send you + + + align:start position:0% +okay okay anything else we can send you +an + + align:start position:0% + + + + align:start position:0% + +email as your list of assumptions and + + align:start position:0% +email as your list of assumptions and + + + align:start position:0% +email as your list of assumptions and +then look for information that will + + align:start position:0% +then look for information that will + + + align:start position:0% +then look for information that will +support or challenge or + + align:start position:0% +support or challenge or + + + align:start position:0% +support or challenge or +something okay and then evaluate your + + align:start position:0% +something okay and then evaluate your + + + align:start position:0% +something okay and then evaluate your +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +assumption thank you very much + + align:start position:0% +assumption thank you very much + + + align:start position:0% +assumption thank you very much +[Music] \ No newline at end of file diff --git a/B3_z1qTD2ZE.txt b/B3_z1qTD2ZE.txt new file mode 100644 index 0000000000000000000000000000000000000000..af0ea2b193e3f58b2ea7f43362843ad675feb5d9 --- /dev/null +++ b/B3_z1qTD2ZE.txt @@ -0,0 +1,1419 @@ +align:start position:0% + +so one of the big mantras in any kind of + + align:start position:0% +so one of the big mantras in any kind of + + + align:start position:0% +so one of the big mantras in any kind of +game development is uh testing we you + + align:start position:0% +game development is uh testing we you + + + align:start position:0% +game development is uh testing we you +have to keep testing your game uh + + align:start position:0% +have to keep testing your game uh + + + align:start position:0% +have to keep testing your game uh +because no plan meets first contact with + + align:start position:0% +because no plan meets first contact with + + + align:start position:0% +because no plan meets first contact with +the user uh you have to be able to see + + align:start position:0% +the user uh you have to be able to see + + + align:start position:0% +the user uh you have to be able to see +how real people are going to respond to + + align:start position:0% +how real people are going to respond to + + + align:start position:0% +how real people are going to respond to +the stuff that you're making as soon as + + align:start position:0% +the stuff that you're making as soon as + + + align:start position:0% +the stuff that you're making as soon as +possible because many of your + + align:start position:0% +possible because many of your + + + align:start position:0% +possible because many of your +assumptions going into a project are + + align:start position:0% +assumptions going into a project are + + + align:start position:0% +assumptions going into a project are +going to be wrong now uh we encourage + + align:start position:0% +going to be wrong now uh we encourage + + + align:start position:0% +going to be wrong now uh we encourage +students to uh to to go out and test + + align:start position:0% +students to uh to to go out and test + + + align:start position:0% +students to uh to to go out and test +their games with as many people as + + align:start position:0% +their games with as many people as + + + align:start position:0% +their games with as many people as +possible outside of class uh this is uh + + align:start position:0% +possible outside of class uh this is uh + + + align:start position:0% +possible outside of class uh this is uh +this is this is crucial for the + + align:start position:0% +this is this is crucial for the + + + align:start position:0% +this is this is crucial for the +development process and there are a + + align:start position:0% +development process and there are a + + + align:start position:0% +development process and there are a +couple of assignments where they + + align:start position:0% +couple of assignments where they + + + align:start position:0% +couple of assignments where they +actually have to show us that uh the the + + align:start position:0% +actually have to show us that uh the the + + + align:start position:0% +actually have to show us that uh the the +results of that testing and it's pretty + + align:start position:0% +results of that testing and it's pretty + + + align:start position:0% +results of that testing and it's pretty +much as simple as sitting somebody in + + align:start position:0% +much as simple as sitting somebody in + + + align:start position:0% +much as simple as sitting somebody in +front of a computer with the latest + + align:start position:0% +front of a computer with the latest + + + align:start position:0% +front of a computer with the latest +version of the game or maybe with the + + align:start position:0% +version of the game or maybe with the + + + align:start position:0% +version of the game or maybe with the +paper version of the game giving them a + + align:start position:0% +paper version of the game giving them a + + + align:start position:0% +paper version of the game giving them a +couple of instructions just so that they + + align:start position:0% +couple of instructions just so that they + + + align:start position:0% +couple of instructions just so that they +can get started and then step back + + align:start position:0% +can get started and then step back + + + align:start position:0% +can get started and then step back +watching and taking notes uh trying to + + align:start position:0% +watching and taking notes uh trying to + + + align:start position:0% +watching and taking notes uh trying to +provide as little guidance as possible + + align:start position:0% +provide as little guidance as possible + + + align:start position:0% +provide as little guidance as possible +so that they can actually see how a + + align:start position:0% +so that they can actually see how a + + + align:start position:0% +so that they can actually see how a +player who knows nothing about the Game + + align:start position:0% +player who knows nothing about the Game + + + align:start position:0% +player who knows nothing about the Game +responds to it for the first time + + align:start position:0% +responds to it for the first time + + + align:start position:0% +responds to it for the first time +however um sometimes it can be difficult + + align:start position:0% +however um sometimes it can be difficult + + + align:start position:0% +however um sometimes it can be difficult +to uh get a lot of testing done uh + + align:start position:0% +to uh get a lot of testing done uh + + + align:start position:0% +to uh get a lot of testing done uh +outside of class and uh students may be + + align:start position:0% +outside of class and uh students may be + + + align:start position:0% +outside of class and uh students may be +a little bit shy approaching strangers + + align:start position:0% +a little bit shy approaching strangers + + + align:start position:0% +a little bit shy approaching strangers +for instance even other MIT students so + + align:start position:0% +for instance even other MIT students so + + + align:start position:0% +for instance even other MIT students so +what we do also in class is we get uh + + align:start position:0% +what we do also in class is we get uh + + + align:start position:0% +what we do also in class is we get uh +different teams to play each other's + + align:start position:0% +different teams to play each other's + + + align:start position:0% +different teams to play each other's +games and give the Fe feedback the + + align:start position:0% +games and give the Fe feedback the + + + align:start position:0% +games and give the Fe feedback the +quality of that feedback is a little bit + + align:start position:0% +quality of that feedback is a little bit + + + align:start position:0% +quality of that feedback is a little bit +different because everybody in a room at + + align:start position:0% +different because everybody in a room at + + + align:start position:0% +different because everybody in a room at +that point is kind of in the same boat + + align:start position:0% +that point is kind of in the same boat + + + align:start position:0% +that point is kind of in the same boat +they're all making games and they're all + + align:start position:0% +they're all making games and they're all + + + align:start position:0% +they're all making games and they're all +trying to give feedback in the way that + + align:start position:0% +trying to give feedback in the way that + + + align:start position:0% +trying to give feedback in the way that +a game developer will give another game + + align:start position:0% +a game developer will give another game + + + align:start position:0% +a game developer will give another game +developer as opposed to say a naive + + align:start position:0% +developer as opposed to say a naive + + + align:start position:0% +developer as opposed to say a naive +player who's who who just wants to have + + align:start position:0% +player who's who who just wants to have + + + align:start position:0% +player who's who who just wants to have +a fun time playing this game uh we will + + align:start position:0% +a fun time playing this game uh we will + + + align:start position:0% +a fun time playing this game uh we will +also be giving feedback as instructors + + align:start position:0% +also be giving feedback as instructors + + + align:start position:0% +also be giving feedback as instructors +we give them uh uh our experience both + + align:start position:0% +we give them uh uh our experience both + + + align:start position:0% +we give them uh uh our experience both +as developers and as instructors and we + + align:start position:0% +as developers and as instructors and we + + + align:start position:0% +as developers and as instructors and we +can tell them that's a great idea but + + align:start position:0% +can tell them that's a great idea but + + + align:start position:0% +can tell them that's a great idea but +there's no way they going to get it done + + align:start position:0% +there's no way they going to get it done + + + align:start position:0% +there's no way they going to get it done +within the amount uh of time left in + + align:start position:0% +within the amount uh of time left in + + + align:start position:0% +within the amount uh of time left in +this semester because we've seen it + + align:start position:0% +this semester because we've seen it + + + align:start position:0% +this semester because we've seen it +we've seen how these projects tend to go + + align:start position:0% +we've seen how these projects tend to go + + + align:start position:0% +we've seen how these projects tend to go +during the the class no one in no one + + align:start position:0% +during the the class no one in no one + + + align:start position:0% +during the the class no one in no one +else in the class has gone through this + + align:start position:0% +else in the class has gone through this + + + align:start position:0% +else in the class has gone through this +class multiple times um so this is + + align:start position:0% +class multiple times um so this is + + + align:start position:0% +class multiple times um so this is +basically a way to give feedback about + + align:start position:0% +basically a way to give feedback about + + + align:start position:0% +basically a way to give feedback about +the game and uh we teach students + + align:start position:0% +the game and uh we teach students + + + align:start position:0% +the game and uh we teach students +various methods to get the information + + align:start position:0% +various methods to get the information + + + align:start position:0% +various methods to get the information +they want and to record it uh such as um + + align:start position:0% +they want and to record it uh such as um + + + align:start position:0% +they want and to record it uh such as um +questionnaires for instance + + align:start position:0% +questionnaires for instance + + + align:start position:0% +questionnaires for instance +uh different observational techniques + + align:start position:0% +uh different observational techniques + + + align:start position:0% +uh different observational techniques +different ways to script the process of + + align:start position:0% +different ways to script the process of + + + align:start position:0% +different ways to script the process of +getting a new user to actually get + + align:start position:0% +getting a new user to actually get + + + align:start position:0% +getting a new user to actually get +started um and um and most importantly + + align:start position:0% +started um and um and most importantly + + + align:start position:0% +started um and um and most importantly +the importance of just doing this a lot + + align:start position:0% +the importance of just doing this a lot + + + align:start position:0% +the importance of just doing this a lot +so there are a lot of different ways you + + align:start position:0% +so there are a lot of different ways you + + + align:start position:0% +so there are a lot of different ways you +can do project management um the one + + align:start position:0% +can do project management um the one + + + align:start position:0% +can do project management um the one +that we teach and we favor at in our + + align:start position:0% +that we teach and we favor at in our + + + align:start position:0% +that we teach and we favor at in our +course is um we look at agile project + + align:start position:0% +course is um we look at agile project + + + align:start position:0% +course is um we look at agile project +management techniques um most + + align:start position:0% +management techniques um most + + + align:start position:0% +management techniques um most +specifically we look at the one called + + align:start position:0% +specifically we look at the one called + + + align:start position:0% +specifically we look at the one called +scrum and by the nature of of + + align:start position:0% +scrum and by the nature of of + + + align:start position:0% +scrum and by the nature of of +agile agile project management really + + align:start position:0% +agile agile project management really + + + align:start position:0% +agile agile project management really +requires a team to work with itself a + + align:start position:0% +requires a team to work with itself a + + + align:start position:0% +requires a team to work with itself a +lot to understand how the team works + + align:start position:0% +lot to understand how the team works + + + align:start position:0% +lot to understand how the team works +together and to understand each of their + + align:start position:0% +together and to understand each of their + + + align:start position:0% +together and to understand each of their +team members strengths and weaknesses + + align:start position:0% +team members strengths and weaknesses + + + align:start position:0% +team members strengths and weaknesses +this is exactly not what we give our CH + + align:start position:0% +this is exactly not what we give our CH + + + align:start position:0% +this is exactly not what we give our CH +our students a chance to do in the + + align:start position:0% +our students a chance to do in the + + + align:start position:0% +our students a chance to do in the +course of the project unfortunate in the + + align:start position:0% +course of the project unfortunate in the + + + align:start position:0% +course of the project unfortunate in the +course of the course + + align:start position:0% +course of the course + + + align:start position:0% +course of the course +unfortunately because they're working on + + align:start position:0% +unfortunately because they're working on + + + align:start position:0% +unfortunately because they're working on +short projects each project tends to + + align:start position:0% +short projects each project tends to + + + align:start position:0% +short projects each project tends to +have slightly different goals and + + align:start position:0% +have slightly different goals and + + + align:start position:0% +have slightly different goals and +they're changing teams + + align:start position:0% +they're changing teams + + + align:start position:0% +they're changing teams +frequently um so what we do do is we + + align:start position:0% +frequently um so what we do do is we + + + align:start position:0% +frequently um so what we do do is we +give them a set of agile tools um we + + align:start position:0% +give them a set of agile tools um we + + + align:start position:0% +give them a set of agile tools um we +introduced them to the concept of + + align:start position:0% +introduced them to the concept of + + + align:start position:0% +introduced them to the concept of +backlogs project backlogs um + + align:start position:0% +backlogs project backlogs um + + + align:start position:0% +backlogs project backlogs um +creating very short vision statements to + + align:start position:0% +creating very short vision statements to + + + align:start position:0% +creating very short vision statements to +describe what the goal of their project + + align:start position:0% +describe what the goal of their project + + + align:start position:0% +describe what the goal of their project +is but not go into a whole lot of + + align:start position:0% +is but not go into a whole lot of + + + align:start position:0% +is but not go into a whole lot of +detail um we have them make project + + align:start position:0% +detail um we have them make project + + + align:start position:0% +detail um we have them make project +backlogs that list all the features they + + align:start position:0% +backlogs that list all the features they + + + align:start position:0% +backlogs that list all the features they +would like to have we have them take a + + align:start position:0% +would like to have we have them take a + + + align:start position:0% +would like to have we have them take a +look at how they break that + + align:start position:0% +look at how they break that + + + align:start position:0% +look at how they break that +that amount of work down into how much + + align:start position:0% +that amount of work down into how much + + + align:start position:0% +that amount of work down into how much +can we get done in a week um and + + align:start position:0% +can we get done in a week um and + + + align:start position:0% +can we get done in a week um and +realistically trying to figure out how + + align:start position:0% +realistically trying to figure out how + + + align:start position:0% +realistically trying to figure out how +much they can get down in a week at + + align:start position:0% +much they can get down in a week at + + + align:start position:0% +much they can get down in a week at +which point they realize their project + + align:start position:0% +which point they realize their project + + + align:start position:0% +which point they realize their project +backlog is about nine weeks long and + + align:start position:0% +backlog is about nine weeks long and + + + align:start position:0% +backlog is about nine weeks long and +they can trim down from there before + + align:start position:0% +they can trim down from there before + + + align:start position:0% +they can trim down from there before +they get started on some of the less + + align:start position:0% +they get started on some of the less + + + align:start position:0% +they get started on some of the less +important things um but we show them the + + align:start position:0% +important things um but we show them the + + + align:start position:0% +important things um but we show them the +tools we walk them through using the + + align:start position:0% +tools we walk them through using the + + + align:start position:0% +tools we walk them through using the +tools and then we encourage them to use + + align:start position:0% +tools and then we encourage them to use + + + align:start position:0% +tools and then we encourage them to use +the tools that work best for the group + + align:start position:0% +the tools that work best for the group + + + align:start position:0% +the tools that work best for the group +that they're with and the project + + align:start position:0% +that they're with and the project + + + align:start position:0% +that they're with and the project +they're working on so instead of saying + + align:start position:0% +they're working on so instead of saying + + + align:start position:0% +they're working on so instead of saying +this is how you do it shun we say here + + align:start position:0% +this is how you do it shun we say here + + + align:start position:0% +this is how you do it shun we say here +are a set of + + align:start position:0% +are a set of + + + align:start position:0% +are a set of +tools work with all of them use the ones + + align:start position:0% +tools work with all of them use the ones + + + align:start position:0% +tools work with all of them use the ones +that work best and try to iterate not + + align:start position:0% +that work best and try to iterate not + + + align:start position:0% +that work best and try to iterate not +just your project but also the way you + + align:start position:0% +just your project but also the way you + + + align:start position:0% +just your project but also the way you +are managing your project and the way + + align:start position:0% +are managing your project and the way + + + align:start position:0% +are managing your project and the way +you're working together with each other + + align:start position:0% +you're working together with each other + + + align:start position:0% +you're working together with each other +because that's the only way to get to a + + align:start position:0% +because that's the only way to get to a + + + align:start position:0% +because that's the only way to get to a +better working team is to find out what + + align:start position:0% +better working team is to find out what + + + align:start position:0% +better working team is to find out what +works accept that some of your + + align:start position:0% +works accept that some of your + + + align:start position:0% +works accept that some of your +techniques don't work and try something + + align:start position:0% +techniques don't work and try something + + + align:start position:0% +techniques don't work and try something +new and try something better until you + + align:start position:0% +new and try something better until you + + + align:start position:0% +new and try something better until you +do find what works with that particular + + align:start position:0% +do find what works with that particular + + + align:start position:0% +do find what works with that particular +group of people so we're not only only + + align:start position:0% +group of people so we're not only only + + + align:start position:0% +group of people so we're not only only +talking about the tools and processes um + + align:start position:0% +talking about the tools and processes um + + + align:start position:0% +talking about the tools and processes um +the hard skills when it comes to project + + align:start position:0% +the hard skills when it comes to project + + + align:start position:0% +the hard skills when it comes to project +management but we're also looking at + + align:start position:0% +management but we're also looking at + + + align:start position:0% +management but we're also looking at +iterating on their soft skills um which + + align:start position:0% +iterating on their soft skills um which + + + align:start position:0% +iterating on their soft skills um which +often comes down to just how do you talk + + align:start position:0% +often comes down to just how do you talk + + + align:start position:0% +often comes down to just how do you talk +to another person + + align:start position:0% +to another person + + + align:start position:0% +to another person +respectfully um we talk about Team + + align:start position:0% +respectfully um we talk about Team + + + align:start position:0% +respectfully um we talk about Team +Dynamics so teams tend to grow in a + + align:start position:0% +Dynamics so teams tend to grow in a + + + align:start position:0% +Dynamics so teams tend to grow in a +particular way and often there are um + + align:start position:0% +particular way and often there are um + + + align:start position:0% +particular way and often there are um +shared qualities that all teams form um + + align:start position:0% +shared qualities that all teams form um + + + align:start position:0% +shared qualities that all teams form um +have um when it comes from + + align:start position:0% +have um when it comes from + + + align:start position:0% +have um when it comes from +forming um from when they're getting + + align:start position:0% +forming um from when they're getting + + + align:start position:0% +forming um from when they're getting +their first conflict and trying to get + + align:start position:0% +their first conflict and trying to get + + + align:start position:0% +their first conflict and trying to get +over their first conflict to when + + align:start position:0% +over their first conflict to when + + + align:start position:0% +over their first conflict to when +they're actually performing Pretty + + align:start position:0% +they're actually performing Pretty + + + align:start position:0% +they're actually performing Pretty +efficiently and then when they feel like + + align:start position:0% +efficiently and then when they feel like + + + align:start position:0% +efficiently and then when they feel like +they're just really kicking butt and + + align:start position:0% +they're just really kicking butt and + + + align:start position:0% +they're just really kicking butt and +just really moving forward um we try to + + align:start position:0% +just really moving forward um we try to + + + align:start position:0% +just really moving forward um we try to +help them get through to that final + + align:start position:0% +help them get through to that final + + + align:start position:0% +help them get through to that final +stage at best they usually get to right + + align:start position:0% +stage at best they usually get to right + + + align:start position:0% +stage at best they usually get to right +to the point where they really start + + align:start position:0% +to the point where they really start + + + align:start position:0% +to the point where they really start +performing well and really start um + + align:start position:0% +performing well and really start um + + + align:start position:0% +performing well and really start um +being efficient in what they're doing + + align:start position:0% +being efficient in what they're doing + + + align:start position:0% +being efficient in what they're doing +but what we want to do is see have them + + align:start position:0% +but what we want to do is see have them + + + align:start position:0% +but what we want to do is see have them +see the whole process see how the stages + + align:start position:0% +see the whole process see how the stages + + + align:start position:0% +see the whole process see how the stages +differ and then come up with um ways and + + align:start position:0% +differ and then come up with um ways and + + + align:start position:0% +differ and then come up with um ways and +approaches to then + + align:start position:0% +approaches to then + + + align:start position:0% +approaches to then +uh get themselves through the process + + align:start position:0% +uh get themselves through the process + + + align:start position:0% +uh get themselves through the process +and get talk being able to talk to their + + align:start position:0% +and get talk being able to talk to their + + + align:start position:0% +and get talk being able to talk to their +other teammates + + align:start position:0% +other teammates + + + align:start position:0% +other teammates +about maybe a a problem happened U maybe + + align:start position:0% +about maybe a a problem happened U maybe + + + align:start position:0% +about maybe a a problem happened U maybe +somebody didn't check in some code and + + align:start position:0% +somebody didn't check in some code and + + + align:start position:0% +somebody didn't check in some code and +it caused two days of of work to go away + + align:start position:0% +it caused two days of of work to go away + + + align:start position:0% +it caused two days of of work to go away +um there are better things to do than + + align:start position:0% +um there are better things to do than + + + align:start position:0% +um there are better things to do than +just to rant and rail at this other + + align:start position:0% +just to rant and rail at this other + + + align:start position:0% +just to rant and rail at this other +person so what are the other things they + + align:start position:0% +person so what are the other things they + + + align:start position:0% +person so what are the other things they +can do to to get through that problem so + + align:start position:0% +can do to to get through that problem so + + + align:start position:0% +can do to to get through that problem so +we want them to talk about that we want + + align:start position:0% +we want them to talk about that we want + + + align:start position:0% +we want them to talk about that we want +them to think about that we talk about + + align:start position:0% +them to think about that we talk about + + + align:start position:0% +them to think about that we talk about +it a little bit in class um and we ask + + align:start position:0% +it a little bit in class um and we ask + + + align:start position:0% +it a little bit in class um and we ask +them to give us what would they do again + + align:start position:0% +them to give us what would they do again + + + align:start position:0% +them to give us what would they do again +in the like if they had to do this again + + align:start position:0% +in the like if they had to do this again + + + align:start position:0% +in the like if they had to do this again +in the future what would they change + + align:start position:0% +in the future what would they change + + + align:start position:0% +in the future what would they change +what would they do differently so we're + + align:start position:0% +what would they do differently so we're + + + align:start position:0% +what would they do differently so we're +asking them to do that through their + + align:start position:0% +asking them to do that through their + + + align:start position:0% +asking them to do that through their +individual writeups um we ask for a lot + + align:start position:0% +individual writeups um we ask for a lot + + + align:start position:0% +individual writeups um we ask for a lot +of reflection in the class on not just + + align:start position:0% +of reflection in the class on not just + + + align:start position:0% +of reflection in the class on not just +the game design process the game + + align:start position:0% +the game design process the game + + + align:start position:0% +the game design process the game +development process but also this + + align:start position:0% +development process but also this + + + align:start position:0% +development process but also this +project management process and the the + + align:start position:0% +project management process and the the + + + align:start position:0% +project management process and the the +communication between team members as + + align:start position:0% +communication between team members as + + + align:start position:0% +communication between team members as +well \ No newline at end of file diff --git a/B6wI0CE4GjM.txt b/B6wI0CE4GjM.txt new file mode 100644 index 0000000000000000000000000000000000000000..179bf214d790975019cd982d2144e7595983aad6 --- /dev/null +++ b/B6wI0CE4GjM.txt @@ -0,0 +1,9019 @@ +align:start position:0% + +today we're gonna catch our discussion + + align:start position:0% +today we're gonna catch our discussion + + + align:start position:0% +today we're gonna catch our discussion +of savings I continue my nagging on you + + align:start position:0% +of savings I continue my nagging on you + + + align:start position:0% +of savings I continue my nagging on you +guys about how you should be saving + + align:start position:0% +guys about how you should be saving + + + align:start position:0% +guys about how you should be saving +money and then we're gonna move on and + + align:start position:0% +money and then we're gonna move on and + + + align:start position:0% +money and then we're gonna move on and +talk about international trade so let's + + align:start position:0% +talk about international trade so let's + + + align:start position:0% +talk about international trade so let's +finish our discussion of savings + + align:start position:0% + + + + align:start position:0% + +now savings turns out to be a critically + + align:start position:0% +now savings turns out to be a critically + + + align:start position:0% +now savings turns out to be a critically +important element of growth in the + + align:start position:0% +important element of growth in the + + + align:start position:0% +important element of growth in the +economy and we've now traced through why + + align:start position:0% +economy and we've now traced through why + + + align:start position:0% +economy and we've now traced through why +that happens okay our basic story is + + align:start position:0% +that happens okay our basic story is + + + align:start position:0% +that happens okay our basic story is +that savings goes up as savings goes up + + align:start position:0% +that savings goes up as savings goes up + + + align:start position:0% +that savings goes up as savings goes up +that means that the capital supply + + align:start position:0% +that means that the capital supply + + + align:start position:0% +that means that the capital supply +shifts out so this habit of supply curve + + align:start position:0% +shifts out so this habit of supply curve + + + align:start position:0% +shifts out so this habit of supply curve +shift outward as people save more + + align:start position:0% +shift outward as people save more + + + align:start position:0% +shift outward as people save more +that's an increase in the capital supply + + align:start position:0% +that's an increase in the capital supply + + + align:start position:0% +that's an increase in the capital supply +curve in the capital markets that means + + align:start position:0% +curve in the capital markets that means + + + align:start position:0% +curve in the capital markets that means +that interest rates fall okay because + + align:start position:0% +that interest rates fall okay because + + + align:start position:0% +that interest rates fall okay because +there's more supply for a given demand + + align:start position:0% +there's more supply for a given demand + + + align:start position:0% +there's more supply for a given demand +the price is gonna fall the price of + + align:start position:0% +the price is gonna fall the price of + + + align:start position:0% +the price is gonna fall the price of +capital is the interest rate so as + + align:start position:0% +capital is the interest rate so as + + + align:start position:0% +capital is the interest rate so as +people save more that's more supplying + + align:start position:0% +people save more that's more supplying + + + align:start position:0% +people save more that's more supplying +to capital markets it's increasing the + + align:start position:0% +to capital markets it's increasing the + + + align:start position:0% +to capital markets it's increasing the +pool from which firms have to borrow for + + align:start position:0% +pool from which firms have to borrow for + + + align:start position:0% +pool from which firms have to borrow for +a given pool firms have to pay less + + align:start position:0% +a given pool firms have to pay less + + + align:start position:0% +a given pool firms have to pay less +money to borrow from that if the + + align:start position:0% +money to borrow from that if the + + + align:start position:0% +money to borrow from that if the +interest rate goes down that means the + + align:start position:0% +interest rate goes down that means the + + + align:start position:0% +interest rate goes down that means the +NPV of investment goes up because + + align:start position:0% +NPV of investment goes up because + + + align:start position:0% +NPV of investment goes up because +remember the net present value + + align:start position:0% +remember the net present value + + + align:start position:0% +remember the net present value +investment is a negative function of the + + align:start position:0% +investment is a negative function of the + + + align:start position:0% +investment is a negative function of the +interest rate the lower the interest + + align:start position:0% +interest rate the lower the interest + + + align:start position:0% +interest rate the lower the interest +rate the more firms will say I might as + + align:start position:0% +rate the more firms will say I might as + + + align:start position:0% +rate the more firms will say I might as +well buy a new machine because the + + align:start position:0% +well buy a new machine because the + + + align:start position:0% +well buy a new machine because the +bank's not paying me anything okay that + + align:start position:0% +bank's not paying me anything okay that + + + align:start position:0% +bank's not paying me anything okay that +means that NPV investment goes up which + + align:start position:0% +means that NPV investment goes up which + + + align:start position:0% +means that NPV investment goes up which +means the investment goes up so the + + align:start position:0% +means the investment goes up so the + + + align:start position:0% +means the investment goes up so the +bottom line is the way we get firms to + + align:start position:0% +bottom line is the way we get firms to + + + align:start position:0% +bottom line is the way we get firms to +invest more and grow the economy + + align:start position:0% +invest more and grow the economy + + + align:start position:0% +invest more and grow the economy +is by saving more we save more we + + align:start position:0% +is by saving more we save more we + + + align:start position:0% +is by saving more we save more we +increase capital supply that lowers the + + align:start position:0% +increase capital supply that lowers the + + + align:start position:0% +increase capital supply that lowers the +interest rate that raises the NPV of + + align:start position:0% +interest rate that raises the NPV of + + + align:start position:0% +interest rate that raises the NPV of +investment which leads to more + + align:start position:0% +investment which leads to more + + + align:start position:0% +investment which leads to more +investment so that's the link by which + + align:start position:0% +investment so that's the link by which + + + align:start position:0% +investment so that's the link by which +savings Leath economic growth is that + + align:start position:0% +savings Leath economic growth is that + + + align:start position:0% +savings Leath economic growth is that +savings leads firm to invest more okay + + align:start position:0% +savings leads firm to invest more okay + + + align:start position:0% +savings leads firm to invest more okay +is that clear from this sort of + + align:start position:0% +is that clear from this sort of + + + align:start position:0% +is that clear from this sort of +structure we built in the last couple + + align:start position:0% +structure we built in the last couple + + + align:start position:0% +structure we built in the last couple +lectures okay if it's not just go back + + align:start position:0% +lectures okay if it's not just go back + + + align:start position:0% +lectures okay if it's not just go back +through and work through the math but + + align:start position:0% +through and work through the math but + + + align:start position:0% +through and work through the math but +you'll see we talked about the + + align:start position:0% +you'll see we talked about the + + + align:start position:0% +you'll see we talked about the +capital market the interest rates the + + align:start position:0% +capital market the interest rates the + + + align:start position:0% +capital market the interest rates the +price in the capital market last time we + + align:start position:0% +price in the capital market last time we + + + align:start position:0% +price in the capital market last time we +talked about the interest rate this the + + align:start position:0% +talked about the interest rate this the + + + align:start position:0% +talked about the interest rate this the +lower the industry the higher than that + + align:start position:0% +lower the industry the higher than that + + + align:start position:0% +lower the industry the higher than that +present value of any given investment + + align:start position:0% +present value of any given investment + + + align:start position:0% +present value of any given investment +that means firms will invest more so + + align:start position:0% +that means firms will invest more so + + + align:start position:0% +that means firms will invest more so +that means a critical public policy + + align:start position:0% +that means a critical public policy + + + align:start position:0% +that means a critical public policy +concern is getting people to save enough + + align:start position:0% +concern is getting people to save enough + + + align:start position:0% +concern is getting people to save enough +now obviously that varies with economic + + align:start position:0% +now obviously that varies with economic + + + align:start position:0% +now obviously that varies with economic +conditions in a deep recession we don't + + align:start position:0% +conditions in a deep recession we don't + + + align:start position:0% +conditions in a deep recession we don't +actually want as much savings we're not + + align:start position:0% +actually want as much savings we're not + + + align:start position:0% +actually want as much savings we're not +in recession but in general in the long + + align:start position:0% +in recession but in general in the long + + + align:start position:0% +in recession but in general in the long +run we will grow more as an economy if + + align:start position:0% +run we will grow more as an economy if + + + align:start position:0% +run we will grow more as an economy if +we save more as a society and the u.s. + + align:start position:0% +we save more as a society and the u.s. + + + align:start position:0% +we save more as a society and the u.s. +is an incredible low savings rate our + + align:start position:0% +is an incredible low savings rate our + + + align:start position:0% +is an incredible low savings rate our +savings rate in the u.s. depending how + + align:start position:0% +savings rate in the u.s. depending how + + + align:start position:0% +savings rate in the u.s. depending how +you define in is maybe three to five + + align:start position:0% +you define in is maybe three to five + + + align:start position:0% +you define in is maybe three to five +percent in Europe in Japan it's like + + align:start position:0% +percent in Europe in Japan it's like + + + align:start position:0% +percent in Europe in Japan it's like +fifteen plus percent okay so we have a + + align:start position:0% +fifteen plus percent okay so we have a + + + align:start position:0% +fifteen plus percent okay so we have a +very low savings rate and as a result + + align:start position:0% +very low savings rate and as a result + + + align:start position:0% +very low savings rate and as a result +that has led public policymakers to try + + align:start position:0% +that has led public policymakers to try + + + align:start position:0% +that has led public policymakers to try +to think about tools they can use to + + align:start position:0% +to think about tools they can use to + + + align:start position:0% +to think about tools they can use to +encourage savings and the major tool we + + align:start position:0% +encourage savings and the major tool we + + + align:start position:0% +encourage savings and the major tool we +use in public policy to encourage + + align:start position:0% +use in public policy to encourage + + + align:start position:0% +use in public policy to encourage +savings is the tax subsidy to retirement + + align:start position:0% +savings is the tax subsidy to retirement + + + align:start position:0% +savings is the tax subsidy to retirement +savings the tax subsidy to retirement + + align:start position:0% +savings the tax subsidy to retirement + + + align:start position:0% +savings the tax subsidy to retirement +savings is the major tool that we use to + + align:start position:0% +savings is the major tool that we use to + + + align:start position:0% +savings is the major tool that we use to +increase savings in the US okay and how + + align:start position:0% +increase savings in the US okay and how + + + align:start position:0% +increase savings in the US okay and how +does this work okay the basic logic is + + align:start position:0% +does this work okay the basic logic is + + + align:start position:0% +does this work okay the basic logic is +the following when I put my money in the + + align:start position:0% +the following when I put my money in the + + + align:start position:0% +the following when I put my money in the +bank and I earn interest that interest + + align:start position:0% +bank and I earn interest that interest + + + align:start position:0% +bank and I earn interest that interest +gets taxed just like my labor supply + + align:start position:0% +gets taxed just like my labor supply + + + align:start position:0% +gets taxed just like my labor supply +gets taxed my capital income gets taxed + + align:start position:0% +gets taxed my capital income gets taxed + + + align:start position:0% +gets taxed my capital income gets taxed +okay so when I put money in the bank I + + align:start position:0% +okay so when I put money in the bank I + + + align:start position:0% +okay so when I put money in the bank I +don't just throw in the interest rate + + align:start position:0% +don't just throw in the interest rate + + + align:start position:0% +don't just throw in the interest rate +well make use art where we care about + + align:start position:0% +well make use art where we care about + + + align:start position:0% +well make use art where we care about +real and trade I don't use the learning + + align:start position:0% +real and trade I don't use the learning + + + align:start position:0% +real and trade I don't use the learning +in straight iron are times 1 minus taw + + align:start position:0% +in straight iron are times 1 minus taw + + + align:start position:0% +in straight iron are times 1 minus taw +we're tars the tax rate that's all I + + align:start position:0% +we're tars the tax rate that's all I + + + align:start position:0% +we're tars the tax rate that's all I +take home so the bank's takes me ten + + align:start position:0% +take home so the bank's takes me ten + + + align:start position:0% +take home so the bank's takes me ten +percent say inflation zero so nominal + + align:start position:0% +percent say inflation zero so nominal + + + align:start position:0% +percent say inflation zero so nominal +interest rates are the same to make + + align:start position:0% +interest rates are the same to make + + + align:start position:0% +interest rates are the same to make +pigmies ten percent and my tax rates 50 + + align:start position:0% +pigmies ten percent and my tax rates 50 + + + align:start position:0% +pigmies ten percent and my tax rates 50 +percent I only take home five percent on + + align:start position:0% +percent I only take home five percent on + + + align:start position:0% +percent I only take home five percent on +that okay if we assume substitution + + align:start position:0% +that okay if we assume substitution + + + align:start position:0% +that okay if we assume substitution +effects dominate which is the big + + align:start position:0% +effects dominate which is the big + + + align:start position:0% +effects dominate which is the big +assumption but a typically one we make + + align:start position:0% +assumption but a typically one we make + + + align:start position:0% +assumption but a typically one we make +this will lead this means the taxation + + align:start position:0% +this will lead this means the taxation + + + align:start position:0% +this will lead this means the taxation +by lowering the return to savings will + + align:start position:0% +by lowering the return to savings will + + + align:start position:0% +by lowering the return to savings will +lead to less savings so might + + align:start position:0% +lead to less savings so might + + + align:start position:0% +lead to less savings so might +acting's people's savings we lead to + + align:start position:0% +acting's people's savings we lead to + + + align:start position:0% +acting's people's savings we lead to +less of it because we sort of assumed + + align:start position:0% +less of it because we sort of assumed + + + align:start position:0% +less of it because we sort of assumed +substitution effects dominated + + align:start position:0% +substitution effects dominated + + + align:start position:0% +substitution effects dominated +okay to offset this we say well I'll + + align:start position:0% +okay to offset this we say well I'll + + + align:start position:0% +okay to offset this we say well I'll +tell you what if you save for retirement + + align:start position:0% +tell you what if you save for retirement + + + align:start position:0% +tell you what if you save for retirement +we won't tax it so if you save didn't + + align:start position:0% +we won't tax it so if you save didn't + + + align:start position:0% +we won't tax it so if you save didn't +you pull it out next year we're gonna + + align:start position:0% +you pull it out next year we're gonna + + + align:start position:0% +you pull it out next year we're gonna +tax it but if you put it in special + + align:start position:0% +tax it but if you put it in special + + + align:start position:0% +tax it but if you put it in special +accounts which we've labeled as + + align:start position:0% +accounts which we've labeled as + + + align:start position:0% +accounts which we've labeled as +retirement savings we won't tax it okay + + align:start position:0% +retirement savings we won't tax it okay + + + align:start position:0% +retirement savings we won't tax it okay +so these have a number of forms one form + + align:start position:0% +so these have a number of forms one form + + + align:start position:0% +so these have a number of forms one form +is employer sponsored pensions these are + + align:start position:0% +is employer sponsored pensions these are + + + align:start position:0% +is employer sponsored pensions these are +things where your employer takes some of + + align:start position:0% +things where your employer takes some of + + + align:start position:0% +things where your employer takes some of +your pay puts it aside in an account and + + align:start position:0% +your pay puts it aside in an account and + + + align:start position:0% +your pay puts it aside in an account and +when he does that + + align:start position:0% +when he does that + + + align:start position:0% +when he does that +you're not taxed on that pay so if MIT + + align:start position:0% +you're not taxed on that pay so if MIT + + + align:start position:0% +you're not taxed on that pay so if MIT +if MIT is gonna pay me a hundred + + align:start position:0% +if MIT is gonna pay me a hundred + + + align:start position:0% +if MIT is gonna pay me a hundred +thousand dollars and they pull ten + + align:start position:0% +thousand dollars and they pull ten + + + align:start position:0% +thousand dollars and they pull ten +thousand aside and put into pension I'm + + align:start position:0% +thousand aside and put into pension I'm + + + align:start position:0% +thousand aside and put into pension I'm +only taxed on ninety thousand that ten + + align:start position:0% +only taxed on ninety thousand that ten + + + align:start position:0% +only taxed on ninety thousand that ten +thousand isn't taxed and likewise the + + align:start position:0% +thousand isn't taxed and likewise the + + + align:start position:0% +thousand isn't taxed and likewise the +interest that's earned on that isn't + + align:start position:0% +interest that's earned on that isn't + + + align:start position:0% +interest that's earned on that isn't +texts okay there's also 401 k s-- a 401 + + align:start position:0% +texts okay there's also 401 k s-- a 401 + + + align:start position:0% +texts okay there's also 401 k s-- a 401 +k is like a pension but where you + + align:start position:0% +k is like a pension but where you + + + align:start position:0% +k is like a pension but where you +control the money so when you get a job + + align:start position:0% +control the money so when you get a job + + + align:start position:0% +control the money so when you get a job +you might get off with a 401 k that's + + align:start position:0% +you might get off with a 401 k that's + + + align:start position:0% +you might get off with a 401 k that's +something where some of your money gets + + align:start position:0% +something where some of your money gets + + + align:start position:0% +something where some of your money gets +pulled out of your salary it doesn't get + + align:start position:0% +pulled out of your salary it doesn't get + + + align:start position:0% +pulled out of your salary it doesn't get +taxed and it gets saved instead and you + + align:start position:0% +taxed and it gets saved instead and you + + + align:start position:0% +taxed and it gets saved instead and you +control where it goes okay and then we + + align:start position:0% +control where it goes okay and then we + + + align:start position:0% +control where it goes okay and then we +also have individual retirement accounts + + align:start position:0% +also have individual retirement accounts + + + align:start position:0% +also have individual retirement accounts +under the unfortunately IRA there's not + + align:start position:0% +under the unfortunately IRA there's not + + + align:start position:0% +under the unfortunately IRA there's not +the irish republican army but individual + + align:start position:0% +the irish republican army but individual + + + align:start position:0% +the irish republican army but individual +retirement accounts which are similar + + align:start position:0% +retirement accounts which are similar + + + align:start position:0% +retirement accounts which are similar +features where you could take their + + align:start position:0% +features where you could take their + + + align:start position:0% +features where you could take their +money and save it on a tax-free basis + + align:start position:0% +money and save it on a tax-free basis + + + align:start position:0% +money and save it on a tax-free basis +okay now here's the trick about how all + + align:start position:0% +okay now here's the trick about how all + + + align:start position:0% +okay now here's the trick about how all +these things work is they're not + + align:start position:0% +these things work is they're not + + + align:start position:0% +these things work is they're not +actually tax-free they are tax deferred + + align:start position:0% +actually tax-free they are tax deferred + + + align:start position:0% +actually tax-free they are tax deferred +and what do I mean by that what I mean + + align:start position:0% +and what do I mean by that what I mean + + + align:start position:0% +and what do I mean by that what I mean +by that is that when you take the money + + align:start position:0% +by that is that when you take the money + + + align:start position:0% +by that is that when you take the money +out eventually it does get taxed so the + + align:start position:0% +out eventually it does get taxed so the + + + align:start position:0% +out eventually it does get taxed so the +way say your 401 K would work you get a + + align:start position:0% +way say your 401 K would work you get a + + + align:start position:0% +way say your 401 K would work you get a +job at you know whatever some say you + + align:start position:0% +job at you know whatever some say you + + + align:start position:0% +job at you know whatever some say you +know at Google Google Offers your 401 K + + align:start position:0% +know at Google Google Offers your 401 K + + + align:start position:0% +know at Google Google Offers your 401 K +you put money in it that money that + + align:start position:0% +you put money in it that money that + + + align:start position:0% +you put money in it that money that +accumulates and when you take it out you + + align:start position:0% +accumulates and when you take it out you + + + align:start position:0% +accumulates and when you take it out you +put money in that money's not taxed when + + align:start position:0% +put money in that money's not taxed when + + + align:start position:0% +put money in that money's not taxed when +you put it in well you take it out it is + + align:start position:0% +you put it in well you take it out it is + + + align:start position:0% +you put it in well you take it out it is +taxed okay so it is eventually taxed + + align:start position:0% +taxed okay so it is eventually taxed + + + align:start position:0% +taxed okay so it is eventually taxed +so why would that what good is that do + + align:start position:0% +so why would that what good is that do + + + align:start position:0% +so why would that what good is that do +you what good does that do you it's + + align:start position:0% +you what good does that do you it's + + + align:start position:0% +you what good does that do you it's +gonna get taxed eventually anyway yeah + + align:start position:0% + + + + align:start position:0% + +right it takes advantage of present + + align:start position:0% +right it takes advantage of present + + + align:start position:0% +right it takes advantage of present +value more we talked about this last + + align:start position:0% +value more we talked about this last + + + align:start position:0% +value more we talked about this last +time with present value money in the + + align:start position:0% +time with present value money in the + + + align:start position:0% +time with present value money in the +future is worth less than money today by + + align:start position:0% +future is worth less than money today by + + + align:start position:0% +future is worth less than money today by +the same logic + + align:start position:0% +the same logic + + + align:start position:0% +the same logic +paying taxes in the future cost you less + + align:start position:0% +paying taxes in the future cost you less + + + align:start position:0% +paying taxes in the future cost you less +than paying taxes today because you have + + align:start position:0% +than paying taxes today because you have + + + align:start position:0% +than paying taxes today because you have +the money today you can earn all the + + align:start position:0% +the money today you can earn all the + + + align:start position:0% +the money today you can earn all the +same suristan it and you have to pay + + align:start position:0% +same suristan it and you have to pay + + + align:start position:0% +same suristan it and you have to pay +taxes on it off in the future so let's + + align:start position:0% +taxes on it off in the future so let's + + + align:start position:0% +taxes on it off in the future so let's +see an example of that let's look at + + align:start position:0% +see an example of that let's look at + + + align:start position:0% +see an example of that let's look at +figure eighteen one okay let's say you + + align:start position:0% +figure eighteen one okay let's say you + + + align:start position:0% +figure eighteen one okay let's say you +have two types of accounts a regular + + align:start position:0% +have two types of accounts a regular + + + align:start position:0% +have two types of accounts a regular +account or an IRA account which is a tax + + align:start position:0% +account or an IRA account which is a tax + + + align:start position:0% +account or an IRA account which is a tax +deferred account and let's say the tax + + align:start position:0% +deferred account and let's say the tax + + + align:start position:0% +deferred account and let's say the tax +rate is 25% and the interest rate is 10% + + align:start position:0% +rate is 25% and the interest rate is 10% + + + align:start position:0% +rate is 25% and the interest rate is 10% +and let's say you're just gonna put the + + align:start position:0% +and let's say you're just gonna put the + + + align:start position:0% +and let's say you're just gonna put the +money in to make life easy imagine you + + align:start position:0% +money in to make life easy imagine you + + + align:start position:0% +money in to make life easy imagine you +put the money for when your imagine + + align:start position:0% +put the money for when your imagine + + + align:start position:0% +put the money for when your imagine +retiring next year this is a super easy + + align:start position:0% +retiring next year this is a super easy + + + align:start position:0% +retiring next year this is a super easy +example you're retiring next year the + + align:start position:0% +example you're retiring next year the + + + align:start position:0% +example you're retiring next year the +questions for this last year of work + + align:start position:0% +questions for this last year of work + + + align:start position:0% +questions for this last year of work +should you put your money in a tax + + align:start position:0% +should you put your money in a tax + + + align:start position:0% +should you put your money in a tax +deferred account or in a regular account + + align:start position:0% +deferred account or in a regular account + + + align:start position:0% +deferred account or in a regular account +okay well if you put it in the regular + + align:start position:0% +okay well if you put it in the regular + + + align:start position:0% +okay well if you put it in the regular +account you will take your hundred + + align:start position:0% +account you will take your hundred + + + align:start position:0% +account you will take your hundred +dollars earnings to pay twenty five + + align:start position:0% +dollars earnings to pay twenty five + + + align:start position:0% +dollars earnings to pay twenty five +dollars of taxes right away so you only + + align:start position:0% +dollars of taxes right away so you only + + + align:start position:0% +dollars of taxes right away so you only +get to put 75 dollars in on that seventy + + align:start position:0% +get to put 75 dollars in on that seventy + + + align:start position:0% +get to put 75 dollars in on that seventy +five dollars drill earn 750 and when you + + align:start position:0% +five dollars drill earn 750 and when you + + + align:start position:0% +five dollars drill earn 750 and when you +take the 750 out you'll pay a dollar + + align:start position:0% +take the 750 out you'll pay a dollar + + + align:start position:0% +take the 750 out you'll pay a dollar +eighty eight in taxes okay so you paid + + align:start position:0% +eighty eight in taxes okay so you paid + + + align:start position:0% +eighty eight in taxes okay so you paid +$25 on your earnings you pay another + + align:start position:0% +$25 on your earnings you pay another + + + align:start position:0% +$25 on your earnings you pay another +dollar eighty eight on the interest you + + align:start position:0% +dollar eighty eight on the interest you + + + align:start position:0% +dollar eighty eight on the interest you +earn and you end up with eighty dollars + + align:start position:0% +earn and you end up with eighty dollars + + + align:start position:0% +earn and you end up with eighty dollars +and sixty-two cents now let's say + + align:start position:0% +and sixty-two cents now let's say + + + align:start position:0% +and sixty-two cents now let's say +instead you set up an IRA well there you + + align:start position:0% +instead you set up an IRA well there you + + + align:start position:0% +instead you set up an IRA well there you +get to put the whole hundred in that + + align:start position:0% +get to put the whole hundred in that + + + align:start position:0% +get to put the whole hundred in that +hundred dollars earns ten dollars and + + align:start position:0% +hundred dollars earns ten dollars and + + + align:start position:0% +hundred dollars earns ten dollars and +when you take out the hundred ten + + align:start position:0% +when you take out the hundred ten + + + align:start position:0% +when you take out the hundred ten +dollars then you pay tax on it so you + + align:start position:0% +dollars then you pay tax on it so you + + + align:start position:0% +dollars then you pay tax on it so you +pay twenty seven fifty then in the end + + align:start position:0% +pay twenty seven fifty then in the end + + + align:start position:0% +pay twenty seven fifty then in the end +but if you put it all together you end + + align:start position:0% +but if you put it all together you end + + + align:start position:0% +but if you put it all together you end +up with more money + + align:start position:0% +up with more money + + + align:start position:0% +up with more money +8250 rather than eighty sixty two why is + + align:start position:0% +8250 rather than eighty sixty two why is + + + align:start position:0% +8250 rather than eighty sixty two why is +that it's because you delayed paying + + align:start position:0% +that it's because you delayed paying + + + align:start position:0% +that it's because you delayed paying +taxes by a year by paying taxes one year + + align:start position:0% +taxes by a year by paying taxes one year + + + align:start position:0% +taxes by a year by paying taxes one year +later you got to earn the interest on + + align:start position:0% +later you got to earn the interest on + + + align:start position:0% +later you got to earn the interest on +that money during the year think of it + + align:start position:0% +that money during the year think of it + + + align:start position:0% +that money during the year think of it +this way if you pay taxes now the + + align:start position:0% +this way if you pay taxes now the + + + align:start position:0% +this way if you pay taxes now the +government gets the money and they get + + align:start position:0% +government gets the money and they get + + + align:start position:0% +government gets the money and they get +to earn interest on it if you pay taxes + + align:start position:0% +to earn interest on it if you pay taxes + + + align:start position:0% +to earn interest on it if you pay taxes +next year you keep the money in your + + align:start position:0% +next year you keep the money in your + + + align:start position:0% +next year you keep the money in your +interest on it so it's much better to + + align:start position:0% +interest on it so it's much better to + + + align:start position:0% +interest on it so it's much better to +pay taxes later and that's why the + + align:start position:0% +pay taxes later and that's why the + + + align:start position:0% +pay taxes later and that's why the +counts matter this is a simple example + + align:start position:0% +counts matter this is a simple example + + + align:start position:0% +counts matter this is a simple example +okay it's a simple example if you have a + + align:start position:0% +okay it's a simple example if you have a + + + align:start position:0% +okay it's a simple example if you have a +30 year account if we kept the interest + + align:start position:0% +30 year account if we kept the interest + + + align:start position:0% +30 year account if we kept the interest +rate of 10% and the tax rate of 25% and + + align:start position:0% +rate of 10% and the tax rate of 25% and + + + align:start position:0% +rate of 10% and the tax rate of 25% and +did a 30-year calculation you would have + + align:start position:0% +did a 30-year calculation you would have + + + align:start position:0% +did a 30-year calculation you would have +twice as much money + + align:start position:0% +twice as much money + + + align:start position:0% +twice as much money +after 30 years if you put an IRA rather + + align:start position:0% +after 30 years if you put an IRA rather + + + align:start position:0% +after 30 years if you put an IRA rather +than putting a regular bank account so + + align:start position:0% +than putting a regular bank account so + + + align:start position:0% +than putting a regular bank account so +even though it eventually gets taxed + + align:start position:0% +even though it eventually gets taxed + + + align:start position:0% +even though it eventually gets taxed +it's a big advantage it's a big + + align:start position:0% +it's a big advantage it's a big + + + align:start position:0% +it's a big advantage it's a big +advantage and that's why we think that's + + align:start position:0% +advantage and that's why we think that's + + + align:start position:0% +advantage and that's why we think that's +why public policy introduced these tools + + align:start position:0% +why public policy introduced these tools + + + align:start position:0% +why public policy introduced these tools +401ks pensions IRAs because they're + + align:start position:0% +401ks pensions IRAs because they're + + + align:start position:0% +401ks pensions IRAs because they're +trying to encourage saving by raising + + align:start position:0% +trying to encourage saving by raising + + + align:start position:0% +trying to encourage saving by raising +the return to saving okay and they hope + + align:start position:0% +the return to saving okay and they hope + + + align:start position:0% +the return to saving okay and they hope +that by encouraging saving they'll get + + align:start position:0% +that by encouraging saving they'll get + + + align:start position:0% +that by encouraging saving they'll get +all this good stuff coming out of it so + + align:start position:0% +all this good stuff coming out of it so + + + align:start position:0% +all this good stuff coming out of it so +that's why these things come up so the + + align:start position:0% +that's why these things come up so the + + + align:start position:0% +that's why these things come up so the +first lesson is 401 just like my + + align:start position:0% +first lesson is 401 just like my + + + align:start position:0% +first lesson is 401 just like my +continued nag on you it's savory and + + align:start position:0% +continued nag on you it's savory and + + + align:start position:0% +continued nag on you it's savory and +save often things like 401 KS by putting + + align:start position:0% +save often things like 401 KS by putting + + + align:start position:0% +save often things like 401 KS by putting +your money away not only did the + + align:start position:0% +your money away not only did the + + + align:start position:0% +your money away not only did the +compounding I talked about before but + + align:start position:0% +compounding I talked about before but + + + align:start position:0% +compounding I talked about before but +you also get the tax benefit of paying + + align:start position:0% +you also get the tax benefit of paying + + + align:start position:0% +you also get the tax benefit of paying +taxes later rather than sooner okay get + + align:start position:0% +taxes later rather than sooner okay get + + + align:start position:0% +taxes later rather than sooner okay get +the compounding on the money and the + + align:start position:0% +the compounding on the money and the + + + align:start position:0% +the compounding on the money and the +compounding on the taxes okay + + align:start position:0% +compounding on the taxes okay + + + align:start position:0% +compounding on the taxes okay +so these kinds of retirement accounts + + align:start position:0% +so these kinds of retirement accounts + + + align:start position:0% +so these kinds of retirement accounts +when you get your job and you're + + align:start position:0% +when you get your job and you're + + + align:start position:0% +when you get your job and you're +thinking about why would I worry about + + align:start position:0% +thinking about why would I worry about + + + align:start position:0% +thinking about why would I worry about +retirement worried about retirement + + align:start position:0% +retirement worried about retirement + + + align:start position:0% +retirement worried about retirement +there's a big there's a big advantage + + align:start position:0% +there's a big there's a big advantage + + + align:start position:0% +there's a big there's a big advantage +now then you ask me okay that's fine + + align:start position:0% +now then you ask me okay that's fine + + + align:start position:0% +now then you ask me okay that's fine +John but when I get my 401 K paperwork + + align:start position:0% +John but when I get my 401 K paperwork + + + align:start position:0% +John but when I get my 401 K paperwork +I've got like a million things I can + + align:start position:0% +I've got like a million things I can + + + align:start position:0% +I've got like a million things I can +invest in what do I do with the money so + + align:start position:0% +invest in what do I do with the money so + + + align:start position:0% +invest in what do I do with the money so +let's talk for a couple minutes about + + align:start position:0% +let's talk for a couple minutes about + + + align:start position:0% +let's talk for a couple minutes about +investment strategy about what you do + + align:start position:0% +investment strategy about what you do + + + align:start position:0% +investment strategy about what you do +with the money okay so let's think about + + align:start position:0% +with the money okay so let's think about + + + align:start position:0% +with the money okay so let's think about +three different ways you can invest your + + align:start position:0% +three different ways you can invest your + + + align:start position:0% +three different ways you can invest your +retirement money three class of options + + align:start position:0% +retirement money three class of options + + + align:start position:0% +retirement money three class of options +a 401 K will typically have they'll + + align:start position:0% +a 401 K will typically have they'll + + + align:start position:0% +a 401 K will typically have they'll +typically be a money market fund market + + align:start position:0% +typically be a money market fund market + + + align:start position:0% +typically be a money market fund market +fund a bond fund and a stock fund and + + align:start position:0% +fund a bond fund and a stock fund and + + + align:start position:0% +fund a bond fund and a stock fund and +then we various combinations of these + + align:start position:0% +then we various combinations of these + + + align:start position:0% +then we various combinations of these +but these are the categories what do + + align:start position:0% +but these are the categories what do + + + align:start position:0% +but these are the categories what do +these mean money market means the + + align:start position:0% +these mean money market means the + + + align:start position:0% +these mean money market means the +money's invested in government bonds + + align:start position:0% +money's invested in government bonds + + + align:start position:0% +money's invested in government bonds +okay the money's invested or what call + + align:start position:0% +okay the money's invested or what call + + + align:start position:0% +okay the money's invested or what call +Treasury security + + align:start position:0% +Treasury security + + + align:start position:0% +Treasury security +government bonds these are things which + + align:start position:0% +government bonds these are things which + + + align:start position:0% +government bonds these are things which +are ultra safe as long as the US doesn't + + align:start position:0% +are ultra safe as long as the US doesn't + + + align:start position:0% +are ultra safe as long as the US doesn't +default on its debt which we've never + + align:start position:0% +default on its debt which we've never + + + align:start position:0% +default on its debt which we've never +done in our history and the good Lord + + align:start position:0% +done in our history and the good Lord + + + align:start position:0% +done in our history and the good Lord +willing we won't do in the near term + + align:start position:0% +willing we won't do in the near term + + + align:start position:0% +willing we won't do in the near term +well if US doesn't default on its debt + + align:start position:0% +well if US doesn't default on its debt + + + align:start position:0% +well if US doesn't default on its debt +you get paid back + + align:start position:0% +you get paid back + + + align:start position:0% +you get paid back +these are super safe it's the safest + + align:start position:0% +these are super safe it's the safest + + + align:start position:0% +these are super safe it's the safest +place you can put your money but they + + align:start position:0% +place you can put your money but they + + + align:start position:0% +place you can put your money but they +pay a very low interest rate right now + + align:start position:0% +pay a very low interest rate right now + + + align:start position:0% +pay a very low interest rate right now +they're paying interest rates the + + align:start position:0% +they're paying interest rates the + + + align:start position:0% +they're paying interest rates the +typical government bond fund right now + + align:start position:0% +typical government bond fund right now + + + align:start position:0% +typical government bond fund right now +be paying interest at around sort of + + align:start position:0% +be paying interest at around sort of + + + align:start position:0% +be paying interest at around sort of +maybe 2% to 2/3 maybe 1 to 2% very low + + align:start position:0% +maybe 2% to 2/3 maybe 1 to 2% very low + + + align:start position:0% +maybe 2% to 2/3 maybe 1 to 2% very low +interest rate maybe up to 3 now but very + + align:start position:0% +interest rate maybe up to 3 now but very + + + align:start position:0% +interest rate maybe up to 3 now but very +very low single digits but totally safe + + align:start position:0% +very low single digits but totally safe + + + align:start position:0% +very low single digits but totally safe +a bond fund invests your money in + + align:start position:0% +a bond fund invests your money in + + + align:start position:0% +a bond fund invests your money in +corporate bonds these are basically this + + align:start position:0% +corporate bonds these are basically this + + + align:start position:0% +corporate bonds these are basically this +is making loans to corporations instead + + align:start position:0% +is making loans to corporations instead + + + align:start position:0% +is making loans to corporations instead +of flowing the mind of the government + + align:start position:0% +of flowing the mind of the government + + + align:start position:0% +of flowing the mind of the government +you loan them under corporation you're + + align:start position:0% +you loan them under corporation you're + + + align:start position:0% +you loan them under corporation you're +not actually buying a bond in GM that's + + align:start position:0% +not actually buying a bond in GM that's + + + align:start position:0% +not actually buying a bond in GM that's +too hard so what these 401k accounts do + + align:start position:0% +too hard so what these 401k accounts do + + + align:start position:0% +too hard so what these 401k accounts do +is they say we're gonna buy a bunch of + + align:start position:0% +is they say we're gonna buy a bunch of + + + align:start position:0% +is they say we're gonna buy a bunch of +bonds we're gonna put them together and + + align:start position:0% +bonds we're gonna put them together and + + + align:start position:0% +bonds we're gonna put them together and +let you own own a small piece of that + + align:start position:0% +let you own own a small piece of that + + + align:start position:0% +let you own own a small piece of that +entire set of bonds that's what a bond + + align:start position:0% +entire set of bonds that's what a bond + + + align:start position:0% +entire set of bonds that's what a bond +fund is ok so you're a small piece a + + align:start position:0% +fund is ok so you're a small piece a + + + align:start position:0% +fund is ok so you're a small piece a +bunch of corporate bonds the difference + + align:start position:0% +bunch of corporate bonds the difference + + + align:start position:0% +bunch of corporate bonds the difference +is unlike the government corporations do + + align:start position:0% +is unlike the government corporations do + + + align:start position:0% +is unlike the government corporations do +go out of business all the time so these + + align:start position:0% +go out of business all the time so these + + + align:start position:0% +go out of business all the time so these +are riskier + + align:start position:0% +are riskier + + + align:start position:0% +are riskier +okay these are riskier but they pay a + + align:start position:0% +okay these are riskier but they pay a + + + align:start position:0% +okay these are riskier but they pay a +higher interest rate bond funds + + align:start position:0% +higher interest rate bond funds + + + align:start position:0% +higher interest rate bond funds +typically are paying 4 to 5 percent + + align:start position:0% +typically are paying 4 to 5 percent + + + align:start position:0% +typically are paying 4 to 5 percent +right now okay then finally the last + + align:start position:0% +right now okay then finally the last + + + align:start position:0% +right now okay then finally the last +thing in your mind is you can put it in + + align:start position:0% +thing in your mind is you can put it in + + + align:start position:0% +thing in your mind is you can put it in +stocks you can literally own corporate + + align:start position:0% +stocks you can literally own corporate + + + align:start position:0% +stocks you can literally own corporate +equity you can own a piece of companies + + align:start position:0% +equity you can own a piece of companies + + + align:start position:0% +equity you can own a piece of companies +okay you can own a piece of the + + align:start position:0% +okay you can own a piece of the + + + align:start position:0% +okay you can own a piece of the +companies and then what you get is you + + align:start position:0% +companies and then what you get is you + + + align:start position:0% +companies and then what you get is you +get something it doesn't really matter + + align:start position:0% +get something it doesn't really matter + + + align:start position:0% +get something it doesn't really matter +with these two it only matters you get + + align:start position:0% +with these two it only matters you get + + + align:start position:0% +with these two it only matters you get +paid as long as the company or the + + align:start position:0% +paid as long as the company or the + + + align:start position:0% +paid as long as the company or the +government of the company don't go out + + align:start position:0% +government of the company don't go out + + + align:start position:0% +government of the company don't go out +of business here you get paid in + + align:start position:0% +of business here you get paid in + + + align:start position:0% +of business here you get paid in +proportion to how well the company does + + align:start position:0% +proportion to how well the company does + + + align:start position:0% +proportion to how well the company does +if it does really well you make a lot of + + align:start position:0% +if it does really well you make a lot of + + + align:start position:0% +if it does really well you make a lot of +money stock prices go up because badly + + align:start position:0% +money stock prices go up because badly + + + align:start position:0% +money stock prices go up because badly +you lose money if it goes bankrupt you + + align:start position:0% +you lose money if it goes bankrupt you + + + align:start position:0% +you lose money if it goes bankrupt you +lose everything okay so similarly these + + align:start position:0% +lose everything okay so similarly these + + + align:start position:0% +lose everything okay so similarly these +in the bankruptcy cost you everything + + align:start position:0% +in the bankruptcy cost you everything + + + align:start position:0% +in the bankruptcy cost you everything +the difference is these are either you + + align:start position:0% +the difference is these are either you + + + align:start position:0% +the difference is these are either you +get paid or you go bankrupt here and you + + align:start position:0% +get paid or you go bankrupt here and you + + + align:start position:0% +get paid or you go bankrupt here and you +get bet it's much more variable things + + align:start position:0% +get bet it's much more variable things + + + align:start position:0% +get bet it's much more variable things +do well you get more things go badly you + + align:start position:0% +do well you get more things go badly you + + + align:start position:0% +do well you get more things go badly you +get less so this is the riskiest option + + align:start position:0% +get less so this is the riskiest option + + + align:start position:0% +get less so this is the riskiest option +of all + + align:start position:0% +of all + + + align:start position:0% +of all +but it also pays the highest rate of + + align:start position:0% +but it also pays the highest rate of + + + align:start position:0% +but it also pays the highest rate of +return traditionally stock investments + + align:start position:0% +return traditionally stock investments + + + align:start position:0% +return traditionally stock investments +pay along where to retire about seven + + align:start position:0% +pay along where to retire about seven + + + align:start position:0% +pay along where to retire about seven +percent a year so what we see here we + + align:start position:0% +percent a year so what we see here we + + + align:start position:0% +percent a year so what we see here we +compare these is what economists call + + align:start position:0% +compare these is what economists call + + + align:start position:0% +compare these is what economists call +the risk return trade-off the risk + + align:start position:0% +the risk return trade-off the risk + + + align:start position:0% +the risk return trade-off the risk +return trade-off the riskier things are + + align:start position:0% +return trade-off the riskier things are + + + align:start position:0% +return trade-off the riskier things are +the higher you earn by investing in them + + align:start position:0% +the higher you earn by investing in them + + + align:start position:0% +the higher you earn by investing in them +but the riskier that earnings is the + + align:start position:0% +but the riskier that earnings is the + + + align:start position:0% +but the riskier that earnings is the +more you're investing them but the risk + + align:start position:0% +more you're investing them but the risk + + + align:start position:0% +more you're investing them but the risk +you that earnings is okay that in other + + align:start position:0% +you that earnings is okay that in other + + + align:start position:0% +you that earnings is okay that in other +words people are willing to accept a + + align:start position:0% +words people are willing to accept a + + + align:start position:0% +words people are willing to accept a +lower interest rate for a safe + + align:start position:0% +lower interest rate for a safe + + + align:start position:0% +lower interest rate for a safe +investment then they want for a risky + + align:start position:0% +investment then they want for a risky + + + align:start position:0% +investment then they want for a risky +investment and we'll talk about in the + + align:start position:0% +investment and we'll talk about in the + + + align:start position:0% +investment and we'll talk about in the +next lecture in two lectures from now + + align:start position:0% +next lecture in two lectures from now + + + align:start position:0% +next lecture in two lectures from now +why that is why people's preferences are + + align:start position:0% +why that is why people's preferences are + + + align:start position:0% +why that is why people's preferences are +that way it's because people are what we + + align:start position:0% +that way it's because people are what we + + + align:start position:0% +that way it's because people are what we +call risk averse people don't like risk + + align:start position:0% +call risk averse people don't like risk + + + align:start position:0% +call risk averse people don't like risk +and we'll talk about why that's a + + align:start position:0% +and we'll talk about why that's a + + + align:start position:0% +and we'll talk about why that's a +natural way to be okay so basically that + + align:start position:0% +natural way to be okay so basically that + + + align:start position:0% +natural way to be okay so basically that +is your set of choices and what + + align:start position:0% +is your set of choices and what + + + align:start position:0% +is your set of choices and what +economists recommend is that the key in + + align:start position:0% +economists recommend is that the key in + + + align:start position:0% +economists recommend is that the key in +all these investments is to diversify + + align:start position:0% +all these investments is to diversify + + + align:start position:0% +all these investments is to diversify +the key recommendation of economists is + + align:start position:0% +the key recommendation of economists is + + + align:start position:0% +the key recommendation of economists is +diversification that you put your money + + align:start position:0% +diversification that you put your money + + + align:start position:0% +diversification that you put your money +you spread your money across these + + align:start position:0% +you spread your money across these + + + align:start position:0% +you spread your money across these +options to get the right balance of risk + + align:start position:0% +options to get the right balance of risk + + + align:start position:0% +options to get the right balance of risk +and return okay so that basically if + + align:start position:0% +and return okay so that basically if + + + align:start position:0% +and return okay so that basically if +you're someone if if you're someone who + + align:start position:0% +you're someone if if you're someone who + + + align:start position:0% +you're someone if if you're someone who +now how you balance depends on your + + align:start position:0% +now how you balance depends on your + + + align:start position:0% +now how you balance depends on your +taste for rich there's no one who really + + align:start position:0% +taste for rich there's no one who really + + + align:start position:0% +taste for rich there's no one who really +hates risk you put most of your money + + align:start position:0% +hates risk you put most of your money + + + align:start position:0% +hates risk you put most of your money +here but it's silly to put all your + + align:start position:0% +here but it's silly to put all your + + + align:start position:0% +here but it's silly to put all your +money in money markets because you're + + align:start position:0% +money in money markets because you're + + + align:start position:0% +money in money markets because you're +losing out a lot of return if you're + + align:start position:0% +losing out a lot of return if you're + + + align:start position:0% +losing out a lot of return if you're +someone who's risk loving you might want + + align:start position:0% +someone who's risk loving you might want + + + align:start position:0% +someone who's risk loving you might want +to put most - money in stocks but still + + align:start position:0% +to put most - money in stocks but still + + + align:start position:0% +to put most - money in stocks but still +put all your money in stocks because + + align:start position:0% +put all your money in stocks because + + + align:start position:0% +put all your money in stocks because +you're you have a hot much higher risk + + align:start position:0% +you're you have a hot much higher risk + + + align:start position:0% +you're you have a hot much higher risk +you want some safety behind you as well + + align:start position:0% +you want some safety behind you as well + + + align:start position:0% +you want some safety behind you as well +so economists would say you should + + align:start position:0% +so economists would say you should + + + align:start position:0% +so economists would say you should +diversify now that's a general I can't + + align:start position:0% +diversify now that's a general I can't + + + align:start position:0% +diversify now that's a general I can't +tell you what percentage is the right + + align:start position:0% +tell you what percentage is the right + + + align:start position:0% +tell you what percentage is the right +percentages are you telling diversified + + align:start position:0% +percentages are you telling diversified + + + align:start position:0% +percentages are you telling diversified +but I can give you one specific piece of + + align:start position:0% +but I can give you one specific piece of + + + align:start position:0% +but I can give you one specific piece of +advice that when you go work for company + + align:start position:0% +advice that when you go work for company + + + align:start position:0% +advice that when you go work for company +X the one thing you do not want to do is + + align:start position:0% +X the one thing you do not want to do is + + + align:start position:0% +X the one thing you do not want to do is +put your money in the stock of company X + + align:start position:0% +put your money in the stock of company X + + + align:start position:0% +put your money in the stock of company X +why is that + + align:start position:0% +why is that + + + align:start position:0% +why is that +why is the last thing we wanted you when + + align:start position:0% +why is the last thing we wanted you when + + + align:start position:0% +why is the last thing we wanted you when +you go to work for company x2 put a + + align:start position:0% +you go to work for company x2 put a + + + align:start position:0% +you go to work for company x2 put a +bunch of your money in the stock of + + align:start position:0% +bunch of your money in the stock of + + + align:start position:0% +bunch of your money in the stock of +company X yeah no I know this would be + + align:start position:0% +company X yeah no I know this would be + + + align:start position:0% +company X yeah no I know this would be +through a 401k 401k account it wouldn't + + align:start position:0% +through a 401k 401k account it wouldn't + + + align:start position:0% +through a 401k 401k account it wouldn't +be like that yeah that is the maximally + + align:start position:0% +be like that yeah that is the maximally + + + align:start position:0% +be like that yeah that is the maximally +risky strategy because you are tying + + align:start position:0% +risky strategy because you are tying + + + align:start position:0% +risky strategy because you are tying +your risk of your investments to your + + align:start position:0% +your risk of your investments to your + + + align:start position:0% +your risk of your investments to your +risk of your salary okay that's the most + + align:start position:0% +risk of your salary okay that's the most + + + align:start position:0% +risk of your salary okay that's the most +risky thing you can do okay so + + align:start position:0% +risky thing you can do okay so + + + align:start position:0% +risky thing you can do okay so +absolutely what you would not want to do + + align:start position:0% +absolutely what you would not want to do + + + align:start position:0% +absolutely what you would not want to do +is go work for Google and say oh good + + align:start position:0% +is go work for Google and say oh good + + + align:start position:0% +is go work for Google and say oh good +I'm going all my retirement in Google + + align:start position:0% +I'm going all my retirement in Google + + + align:start position:0% +I'm going all my retirement in Google +stock you might think Google's safe but + + align:start position:0% +stock you might think Google's safe but + + + align:start position:0% +stock you might think Google's safe but +safer copies in Google at the Cubbies + + align:start position:0% +safer copies in Google at the Cubbies + + + align:start position:0% +safer copies in Google at the Cubbies +thought to be safely Google at some + + align:start position:0% +thought to be safely Google at some + + + align:start position:0% +thought to be safely Google at some +point I've gone bankrupt who else + + align:start position:0% +point I've gone bankrupt who else + + + align:start position:0% +point I've gone bankrupt who else +bankrupt you're totally screwed you've + + align:start position:0% +bankrupt you're totally screwed you've + + + align:start position:0% +bankrupt you're totally screwed you've +lost all your savings and your job so + + align:start position:0% +lost all your savings and your job so + + + align:start position:0% +lost all your savings and your job so +last thing you wanna do is that yeah + + align:start position:0% + + + + align:start position:0% + +well I mean certainly a lot of companies + + align:start position:0% +well I mean certainly a lot of companies + + + align:start position:0% +well I mean certainly a lot of companies +give you stock options where you're sort + + align:start position:0% +give you stock options where you're sort + + + align:start position:0% +give you stock options where you're sort +of stuck in the stock of that company + + align:start position:0% +of stuck in the stock of that company + + + align:start position:0% +of stuck in the stock of that company +and my little lesson there would be well + + align:start position:0% +and my little lesson there would be well + + + align:start position:0% +and my little lesson there would be well +that's part of conversation but as soon + + align:start position:0% +that's part of conversation but as soon + + + align:start position:0% +that's part of conversation but as soon +as it vest sell it and get out okay that + + align:start position:0% +as it vest sell it and get out okay that + + + align:start position:0% +as it vest sell it and get out okay that +doesn't mean you shouldn't you should + + align:start position:0% +doesn't mean you shouldn't you should + + + align:start position:0% +doesn't mean you shouldn't you should +you should values it's not saying stock + + align:start position:0% +you should values it's not saying stock + + + align:start position:0% +you should values it's not saying stock +options at a company are worthless + + align:start position:0% +options at a company are worthless + + + align:start position:0% +options at a company are worthless +they're worth something it's just + + align:start position:0% +they're worth something it's just + + + align:start position:0% +they're worth something it's just +they're worth less than if they just + + align:start position:0% +they're worth less than if they just + + + align:start position:0% +they're worth less than if they just +gave you the cash because you got the + + align:start position:0% +gave you the cash because you got the + + + align:start position:0% +gave you the cash because you got the +cash and go invest it in somewhere that + + align:start position:0% +cash and go invest it in somewhere that + + + align:start position:0% +cash and go invest it in somewhere that +wouldn't be tied to your job okay and + + align:start position:0% +wouldn't be tied to your job okay and + + + align:start position:0% +wouldn't be tied to your job okay and +this came to a head with the example of + + align:start position:0% +this came to a head with the example of + + + align:start position:0% +this came to a head with the example of +Enron which is sort of before your time + + align:start position:0% +Enron which is sort of before your time + + + align:start position:0% +Enron which is sort of before your time +okay that's sort of when you were young + + align:start position:0% +okay that's sort of when you were young + + + align:start position:0% +okay that's sort of when you were young +but basically Enron was an energy + + align:start position:0% +but basically Enron was an energy + + + align:start position:0% +but basically Enron was an energy +company that got into some really shady + + align:start position:0% +company that got into some really shady + + + align:start position:0% +company that got into some really shady +dealings to try to essentially prop up + + align:start position:0% +dealings to try to essentially prop up + + + align:start position:0% +dealings to try to essentially prop up +its stock price to make itself look + + align:start position:0% +its stock price to make itself look + + + align:start position:0% +its stock price to make itself look +valuable it essentially created shell + + align:start position:0% +valuable it essentially created shell + + + align:start position:0% +valuable it essentially created shell +companies that were the same company and + + align:start position:0% +companies that were the same company and + + + align:start position:0% +companies that were the same company and +sold to them so like it was generating a + + align:start position:0% +sold to them so like it was generating a + + + align:start position:0% +sold to them so like it was generating a +lot of sales was just selling to itself + + align:start position:0% +lot of sales was just selling to itself + + + align:start position:0% +lot of sales was just selling to itself +okay leaked it was a legal activity but + + align:start position:0% +okay leaked it was a legal activity but + + + align:start position:0% +okay leaked it was a legal activity but +it caused their stock price to go + + align:start position:0% +it caused their stock price to go + + + align:start position:0% +it caused their stock price to go +through the roof and Enron in order to + + align:start position:0% +through the roof and Enron in order to + + + align:start position:0% +through the roof and Enron in order to +have enough money in the company + + align:start position:0% +have enough money in the company + + + align:start position:0% +have enough money in the company +encourage their employees to invest all + + align:start position:0% +encourage their employees to invest all + + + align:start position:0% +encourage their employees to invest all +the retirement savings at Enron indeed + + align:start position:0% +the retirement savings at Enron indeed + + + align:start position:0% +the retirement savings at Enron indeed +the Enron 401k said we'll give you extra + + align:start position:0% +the Enron 401k said we'll give you extra + + + align:start position:0% +the Enron 401k said we'll give you extra +money in your account if you invest your + + align:start position:0% +money in your account if you invest your + + + align:start position:0% +money in your account if you invest your +money in Enron + + align:start position:0% +money in Enron + + + align:start position:0% +money in Enron +so most people Enron had their + + align:start position:0% +so most people Enron had their + + + align:start position:0% +so most people Enron had their +retirement saving invested at Enron when + + align:start position:0% +retirement saving invested at Enron when + + + align:start position:0% +retirement saving invested at Enron when +the whole thing and Enron was a very + + align:start position:0% +the whole thing and Enron was a very + + + align:start position:0% +the whole thing and Enron was a very +successful company very heating in the + + align:start position:0% +successful company very heating in the + + + align:start position:0% +successful company very heating in the +and 500 doing quite well when the whole + + align:start position:0% +and 500 doing quite well when the whole + + + align:start position:0% +and 500 doing quite well when the whole +thing collapsed diesel anomaly lost + + align:start position:0% +thing collapsed diesel anomaly lost + + + align:start position:0% +thing collapsed diesel anomaly lost +their jobs they lost their entire + + align:start position:0% +their jobs they lost their entire + + + align:start position:0% +their jobs they lost their entire +savings okay that's the problem not on + + align:start position:0% +savings okay that's the problem not on + + + align:start position:0% +savings okay that's the problem not on +diversification and the open for non + + align:start position:0% +diversification and the open for non + + + align:start position:0% +diversification and the open for non +diversification is to invest in the + + align:start position:0% +diversification is to invest in the + + + align:start position:0% +diversification is to invest in the +company you're working for okay have a + + align:start position:0% +company you're working for okay have a + + + align:start position:0% +company you're working for okay have a +scared us any questions about that okay + + align:start position:0% +scared us any questions about that okay + + + align:start position:0% +scared us any questions about that okay +now let's move on that finishes our + + align:start position:0% +now let's move on that finishes our + + + align:start position:0% +now let's move on that finishes our +discussion of savings let's move on to a + + align:start position:0% +discussion of savings let's move on to a + + + align:start position:0% +discussion of savings let's move on to a +totally new topic which we'll talk about + + align:start position:0% +totally new topic which we'll talk about + + + align:start position:0% +totally new topic which we'll talk about +this lecture in the rest of next lecture + + align:start position:0% +this lecture in the rest of next lecture + + + align:start position:0% +this lecture in the rest of next lecture +which is international trade and let's + + align:start position:0% +which is international trade and let's + + + align:start position:0% +which is international trade and let's +start with what is international trade + + align:start position:0% +start with what is international trade + + + align:start position:0% +start with what is international trade +and why the ruckus this is a great time + + align:start position:0% +and why the ruckus this is a great time + + + align:start position:0% +and why the ruckus this is a great time +to view an international trade probably + + align:start position:0% +to view an international trade probably + + + align:start position:0% +to view an international trade probably +the best most exciting time is the of + + align:start position:0% +the best most exciting time is the of + + + align:start position:0% +the best most exciting time is the of +any year I've ever taught this topic its + + align:start position:0% +any year I've ever taught this topic its + + + align:start position:0% +any year I've ever taught this topic its +front and center in a way it hasn't been + + align:start position:0% +front and center in a way it hasn't been + + + align:start position:0% +front and center in a way it hasn't been +probably in decades so what's the big + + align:start position:0% +probably in decades so what's the big + + + align:start position:0% +probably in decades so what's the big +deal + + align:start position:0% +deal + + + align:start position:0% +deal +well let's talk about a simple example + + align:start position:0% +well let's talk about a simple example + + + align:start position:0% +well let's talk about a simple example +how many people have ever given someone + + align:start position:0% +how many people have ever given someone + + + align:start position:0% +how many people have ever given someone +roses for Valentine's Day + + align:start position:0% +roses for Valentine's Day + + + align:start position:0% +roses for Valentine's Day +raise your hands a mighty man all right + + align:start position:0% +raise your hands a mighty man all right + + + align:start position:0% +raise your hands a mighty man all right +uh okay that's okay when I was your age + + align:start position:0% +uh okay that's okay when I was your age + + + align:start position:0% +uh okay that's okay when I was your age +I hadn't either + + align:start position:0% +I hadn't either + + + align:start position:0% +I hadn't either +um now here's an interesting problem + + align:start position:0% +um now here's an interesting problem + + + align:start position:0% +um now here's an interesting problem +with Valentine's Day Valentine's Day + + align:start position:0% +with Valentine's Day Valentine's Day + + + align:start position:0% +with Valentine's Day Valentine's Day +falls in the winter roses don't grow + + align:start position:0% +falls in the winter roses don't grow + + + align:start position:0% +falls in the winter roses don't grow +outside in the cold in the winter so + + align:start position:0% +outside in the cold in the winter so + + + align:start position:0% +outside in the cold in the winter so +what do you do well for many years what + + align:start position:0% +what do you do well for many years what + + + align:start position:0% +what do you do well for many years what +we did was we had hot houses where we + + align:start position:0% +we did was we had hot houses where we + + + align:start position:0% +we did was we had hot houses where we +grew basically were dedicated the very + + align:start position:0% +grew basically were dedicated the very + + + align:start position:0% +grew basically were dedicated the very +reason for existing was to essentially + + align:start position:0% +reason for existing was to essentially + + + align:start position:0% +reason for existing was to essentially +grow Valentine's Day roses such an + + align:start position:0% +grow Valentine's Day roses such an + + + align:start position:0% +grow Valentine's Day roses such an +industry around growing these indoor + + align:start position:0% +industry around growing these indoor + + + align:start position:0% +industry around growing these indoor +roses in the winter so that you could so + + align:start position:0% +roses in the winter so that you could so + + + align:start position:0% +roses in the winter so that you could so +you could have them available but what + + align:start position:0% +you could have them available but what + + + align:start position:0% +you could have them available but what +happened over time is we realize it was + + align:start position:0% +happened over time is we realize it was + + + align:start position:0% +happened over time is we realize it was +a lot cheaper tax just buy the roses in + + align:start position:0% +a lot cheaper tax just buy the roses in + + + align:start position:0% +a lot cheaper tax just buy the roses in +Colombia or countries like that and fly + + align:start position:0% +Colombia or countries like that and fly + + + align:start position:0% +Colombia or countries like that and fly +them up then to actually have them grown + + align:start position:0% +them up then to actually have them grown + + + align:start position:0% +them up then to actually have them grown +here so what happened was we all now get + + align:start position:0% +here so what happened was we all now get + + + align:start position:0% +here so what happened was we all now get +all the roses we get now in the winter + + align:start position:0% +all the roses we get now in the winter + + + align:start position:0% +all the roses we get now in the winter +come from South America okay and we + + align:start position:0% +come from South America okay and we + + + align:start position:0% +come from South America okay and we +don't grow roses in America anymore in + + align:start position:0% +don't grow roses in America anymore in + + + align:start position:0% +don't grow roses in America anymore in +the winter so is that a good thing or a + + align:start position:0% +the winter so is that a good thing or a + + + align:start position:0% +the winter so is that a good thing or a +bad thing well in the one end roses are + + align:start position:0% +bad thing well in the one end roses are + + + align:start position:0% +bad thing well in the one end roses are +a ton cheaper now than where when I was + + align:start position:0% +a ton cheaper now than where when I was + + + align:start position:0% +a ton cheaper now than where when I was +a kid okay so that's a good thing for + + align:start position:0% +a kid okay so that's a good thing for + + + align:start position:0% +a kid okay so that's a good thing for +the Romantics among us you can get a + + align:start position:0% +the Romantics among us you can get a + + + align:start position:0% +the Romantics among us you can get a +does he get a rope dozen roses for 25 + + align:start position:0% +does he get a rope dozen roses for 25 + + + align:start position:0% +does he get a rope dozen roses for 25 +bucks it was like 80 bucks another kid + + align:start position:0% +bucks it was like 80 bucks another kid + + + align:start position:0% +bucks it was like 80 bucks another kid +or something how's crazy okay on the + + align:start position:0% +or something how's crazy okay on the + + + align:start position:0% +or something how's crazy okay on the +other hand a bunch of guys used to grow + + align:start position:0% +other hand a bunch of guys used to grow + + + align:start position:0% +other hand a bunch of guys used to grow +these roses are added + + align:start position:0% +these roses are added + + + align:start position:0% +these roses are added +there was an industry devoted to growing + + align:start position:0% +there was an industry devoted to growing + + + align:start position:0% +there was an industry devoted to growing +these roses and these people now have no + + align:start position:0% +these roses and these people now have no + + + align:start position:0% +these roses and these people now have no +job because they're grown somewhere else + + align:start position:0% +job because they're grown somewhere else + + + align:start position:0% +job because they're grown somewhere else +so how do we think about this trade-off + + align:start position:0% +so how do we think about this trade-off + + + align:start position:0% +so how do we think about this trade-off +is sort of a microcosm of the larger + + align:start position:0% +is sort of a microcosm of the larger + + + align:start position:0% +is sort of a microcosm of the larger +debate around international trade the + + align:start position:0% +debate around international trade the + + + align:start position:0% +debate around international trade the +larger debate about whether trade is + + align:start position:0% +larger debate about whether trade is + + + align:start position:0% +larger debate about whether trade is +good or bad comes down to this roses + + align:start position:0% +good or bad comes down to this roses + + + align:start position:0% +good or bad comes down to this roses +example it sort of summarizes that issue + + align:start position:0% +example it sort of summarizes that issue + + + align:start position:0% +example it sort of summarizes that issue +so now we think about international + + align:start position:0% +so now we think about international + + + align:start position:0% +so now we think about international +trade we think about three concepts we + + align:start position:0% +trade we think about three concepts we + + + align:start position:0% +trade we think about three concepts we +think about exports which are the amount + + align:start position:0% +think about exports which are the amount + + + align:start position:0% +think about exports which are the amount +of goods that we sell to other countries + + align:start position:0% +of goods that we sell to other countries + + + align:start position:0% +of goods that we sell to other countries +okay and imports where - the amount of + + align:start position:0% +okay and imports where - the amount of + + + align:start position:0% +okay and imports where - the amount of +goods that we buy from other countries + + align:start position:0% +goods that we buy from other countries + + + align:start position:0% +goods that we buy from other countries +so a country exports to other countries + + align:start position:0% +so a country exports to other countries + + + align:start position:0% +so a country exports to other countries +it imports from other countries okay + + align:start position:0% +it imports from other countries okay + + + align:start position:0% +it imports from other countries okay +currently the u.s. exports about 1.6 + + align:start position:0% +currently the u.s. exports about 1.6 + + + align:start position:0% +currently the u.s. exports about 1.6 +trillion dollars of goods a year that's + + align:start position:0% +trillion dollars of goods a year that's + + + align:start position:0% +trillion dollars of goods a year that's +what that's trillion with the tea and + + align:start position:0% +what that's trillion with the tea and + + + align:start position:0% +what that's trillion with the tea and +imports about two point four trillion + + align:start position:0% +imports about two point four trillion + + + align:start position:0% +imports about two point four trillion +dollars of goods a year leaving us with + + align:start position:0% +dollars of goods a year leaving us with + + + align:start position:0% +dollars of goods a year leaving us with +an 800 billion trade deficit you may + + align:start position:0% +an 800 billion trade deficit you may + + + align:start position:0% +an 800 billion trade deficit you may +have heard the president mention this + + align:start position:0% +have heard the president mention this + + + align:start position:0% +have heard the president mention this +once or twice okay and I heard your + + align:start position:0% +once or twice okay and I heard your + + + align:start position:0% +once or twice okay and I heard your +billion dollar trade deficit so the + + align:start position:0% +billion dollar trade deficit so the + + + align:start position:0% +billion dollar trade deficit so the +question want to ask is how big a + + align:start position:0% +question want to ask is how big a + + + align:start position:0% +question want to ask is how big a +problem is this that we have a trade + + align:start position:0% +problem is this that we have a trade + + + align:start position:0% +problem is this that we have a trade +deficit and the answer economists give + + align:start position:0% +deficit and the answer economists give + + + align:start position:0% +deficit and the answer economists give +is none problem okay + + align:start position:0% +is none problem okay + + + align:start position:0% +is none problem okay +no no spinal tap fancier okay whatever + + align:start position:0% +no no spinal tap fancier okay whatever + + + align:start position:0% +no no spinal tap fancier okay whatever +okay so basically let's explain this at + + align:start position:0% +okay so basically let's explain this at + + + align:start position:0% +okay so basically let's explain this at +a simple example imagine that you have + + align:start position:0% +a simple example imagine that you have + + + align:start position:0% +a simple example imagine that you have +two Pikachu's and your friend has two + + align:start position:0% +two Pikachu's and your friend has two + + + align:start position:0% +two Pikachu's and your friend has two +Jigglypuff's okay and you want to have a + + align:start position:0% +Jigglypuff's okay and you want to have a + + + align:start position:0% +Jigglypuff's okay and you want to have a +more diverse set of Pokemon so you go to + + align:start position:0% +more diverse set of Pokemon so you go to + + + align:start position:0% +more diverse set of Pokemon so you go to +your friend and you say I will trade you + + align:start position:0% +your friend and you say I will trade you + + + align:start position:0% +your friend and you say I will trade you +one Pikachu for one Jigglypuff so you + + align:start position:0% +one Pikachu for one Jigglypuff so you + + + align:start position:0% +one Pikachu for one Jigglypuff so you +send your friend a Pikachu he sends you + + align:start position:0% +send your friend a Pikachu he sends you + + + align:start position:0% +send your friend a Pikachu he sends you +a Jigglypuff you've just created a + + align:start position:0% +a Jigglypuff you've just created a + + + align:start position:0% +a Jigglypuff you've just created a +massive Pikachu deficit think about it + + align:start position:0% +massive Pikachu deficit think about it + + + align:start position:0% +massive Pikachu deficit think about it +used to have - Pikachu's you sent one + + align:start position:0% +used to have - Pikachu's you sent one + + + align:start position:0% +used to have - Pikachu's you sent one +away you + + align:start position:0% +away you + + + align:start position:0% +away you +you said we didn't get any Pikachu's + + align:start position:0% +you said we didn't get any Pikachu's + + + align:start position:0% +you said we didn't get any Pikachu's +back did you so you've created a huge + + align:start position:0% +back did you so you've created a huge + + + align:start position:0% +back did you so you've created a huge +deficit of one Pikachu is that bad + + align:start position:0% +deficit of one Pikachu is that bad + + + align:start position:0% +deficit of one Pikachu is that bad +no you got a tickly puff you're happy + + align:start position:0% +no you got a tickly puff you're happy + + + align:start position:0% +no you got a tickly puff you're happy +you want to make the trade you made the + + align:start position:0% +you want to make the trade you made the + + + align:start position:0% +you want to make the trade you made the +trade calling the trade deficit define + + align:start position:0% +trade calling the trade deficit define + + + align:start position:0% +trade calling the trade deficit define +trade deficit in terms of if you define + + align:start position:0% +trade deficit in terms of if you define + + + align:start position:0% +trade deficit in terms of if you define +traitors instead of terms of + + align:start position:0% +traitors instead of terms of + + + align:start position:0% +traitors instead of terms of +Jigglypuff's you've got a huge trade + + align:start position:0% +Jigglypuff's you've got a huge trade + + + align:start position:0% +Jigglypuff's you've got a huge trade +surplus you used to get no G to the + + align:start position:0% +surplus you used to get no G to the + + + align:start position:0% +surplus you used to get no G to the +puffs now you get one so what basically + + align:start position:0% +puffs now you get one so what basically + + + align:start position:0% +puffs now you get one so what basically +a trade EV straight circle is all about + + align:start position:0% +a trade EV straight circle is all about + + + align:start position:0% +a trade EV straight circle is all about +an arbitrary definition the bottom line + + align:start position:0% +an arbitrary definition the bottom line + + + align:start position:0% +an arbitrary definition the bottom line +is America sin spends eight hundred + + align:start position:0% +is America sin spends eight hundred + + + align:start position:0% +is America sin spends eight hundred +billion dollars more you're sending + + align:start position:0% +billion dollars more you're sending + + + align:start position:0% +billion dollars more you're sending +money to other countries but we get 800 + + align:start position:0% +money to other countries but we get 800 + + + align:start position:0% +money to other countries but we get 800 +billion dollars a year more stuff for it + + align:start position:0% +billion dollars a year more stuff for it + + + align:start position:0% +billion dollars a year more stuff for it +there's no bad or good + + align:start position:0% +there's no bad or good + + + align:start position:0% +there's no bad or good +it's just the way trade works okay so + + align:start position:0% +it's just the way trade works okay so + + + align:start position:0% +it's just the way trade works okay so +anytime you've had a trade in your life + + align:start position:0% +anytime you've had a trade in your life + + + align:start position:0% +anytime you've had a trade in your life +of anything with a friend or whatever + + align:start position:0% +of anything with a friend or whatever + + + align:start position:0% +of anything with a friend or whatever +you've created a deficit and a surplus + + align:start position:0% +you've created a deficit and a surplus + + + align:start position:0% +you've created a deficit and a surplus +but that doesn't mean anyone's worse off + + align:start position:0% +but that doesn't mean anyone's worse off + + + align:start position:0% +but that doesn't mean anyone's worse off +or better off whether worse not better + + align:start position:0% +or better off whether worse not better + + + align:start position:0% +or better off whether worse not better +off depends on the indicators of the + + align:start position:0% +off depends on the indicators of the + + + align:start position:0% +off depends on the indicators of the +trade depends on how much each party + + align:start position:0% +trade depends on how much each party + + + align:start position:0% +trade depends on how much each party +values what's going on okay so basically + + align:start position:0% +values what's going on okay so basically + + + align:start position:0% +values what's going on okay so basically +if I said oh good lord + + align:start position:0% +if I said oh good lord + + + align:start position:0% +if I said oh good lord +find a headline good lord you know + + align:start position:0% +find a headline good lord you know + + + align:start position:0% +find a headline good lord you know +Gruber creates Pikachu deficit must end + + align:start position:0% +Gruber creates Pikachu deficit must end + + + align:start position:0% +Gruber creates Pikachu deficit must end +trade with Jigglypuff land okay and we + + align:start position:0% +trade with Jigglypuff land okay and we + + + align:start position:0% +trade with Jigglypuff land okay and we +must shut down trade because good lord + + align:start position:0% +must shut down trade because good lord + + + align:start position:0% +must shut down trade because good lord +where we're creating this huge Pikachu + + align:start position:0% +where we're creating this huge Pikachu + + + align:start position:0% +where we're creating this huge Pikachu +deficit that would be bad because I + + align:start position:0% +deficit that would be bad because I + + + align:start position:0% +deficit that would be bad because I +wanted to trade my ticket you for + + align:start position:0% +wanted to trade my ticket you for + + + align:start position:0% +wanted to trade my ticket you for +Jigglypuff I was happier okay that would + + align:start position:0% +Jigglypuff I was happier okay that would + + + align:start position:0% +Jigglypuff I was happier okay that would +be a bad thing to shut that off and that + + align:start position:0% +be a bad thing to shut that off and that + + + align:start position:0% +be a bad thing to shut that off and that +in stupid example is why economists like + + align:start position:0% +in stupid example is why economists like + + + align:start position:0% +in stupid example is why economists like +international trade okay it's the same + + align:start position:0% +international trade okay it's the same + + + align:start position:0% +international trade okay it's the same +reason we like trade in general think + + align:start position:0% +reason we like trade in general think + + + align:start position:0% +reason we like trade in general think +about this whole course so course about + + align:start position:0% +about this whole course so course about + + + align:start position:0% +about this whole course so course about +bit about trade it's about been training + + align:start position:0% +bit about trade it's about been training + + + align:start position:0% +bit about trade it's about been training +our money for cookies a pizza about + + align:start position:0% +our money for cookies a pizza about + + + align:start position:0% +our money for cookies a pizza about +trading a firm's money for workers and + + align:start position:0% +trading a firm's money for workers and + + + align:start position:0% +trading a firm's money for workers and +machines okay about trading my time for + + align:start position:0% +machines okay about trading my time for + + + align:start position:0% +machines okay about trading my time for +a wage life is all about trades + + align:start position:0% +a wage life is all about trades + + + align:start position:0% +a wage life is all about trades +international trades just another + + align:start position:0% +international trades just another + + + align:start position:0% +international trades just another +example of that Jessica's got this + + align:start position:0% +example of that Jessica's got this + + + align:start position:0% +example of that Jessica's got this +bizarre label of a trade deficit we + + align:start position:0% +bizarre label of a trade deficit we + + + align:start position:0% +bizarre label of a trade deficit we +think about it differently okay so + + align:start position:0% +think about it differently okay so + + + align:start position:0% +think about it differently okay so +that's sort of basically if you think + + align:start position:0% +that's sort of basically if you think + + + align:start position:0% +that's sort of basically if you think +think about now let's replace Pikachu + + align:start position:0% +think about now let's replace Pikachu + + + align:start position:0% +think about now let's replace Pikachu +and Jigglypuff with the US and a poor + + align:start position:0% +and Jigglypuff with the US and a poor + + + align:start position:0% +and Jigglypuff with the US and a poor +country instead of us having two + + align:start position:0% +country instead of us having two + + + align:start position:0% +country instead of us having two +Pikachu's do you + + align:start position:0% +Pikachu's do you + + + align:start position:0% +Pikachu's do you +has tons of money instead of the poor + + align:start position:0% +has tons of money instead of the poor + + + align:start position:0% +has tons of money instead of the poor +country having to Jigglypuff's the poor + + align:start position:0% +country having to Jigglypuff's the poor + + + align:start position:0% +country having to Jigglypuff's the poor +country has really underpaid workers who + + align:start position:0% +country has really underpaid workers who + + + align:start position:0% +country has really underpaid workers who +can make stuff really cheaply so I am + + align:start position:0% +can make stuff really cheaply so I am + + + align:start position:0% +can make stuff really cheaply so I am +USA wait I have a lot of money you got a + + align:start position:0% +USA wait I have a lot of money you got a + + + align:start position:0% +USA wait I have a lot of money you got a +lot of sweaters I'm gonna send you my + + align:start position:0% +lot of sweaters I'm gonna send you my + + + align:start position:0% +lot of sweaters I'm gonna send you my +money and get your sweaters I'm better + + align:start position:0% +money and get your sweaters I'm better + + + align:start position:0% +money and get your sweaters I'm better +off because I was happy to buy those + + align:start position:0% +off because I was happy to buy those + + + align:start position:0% +off because I was happy to buy those +sweaters cheaply + + align:start position:0% +sweaters cheaply + + + align:start position:0% +sweaters cheaply +you're better off because you can't eat + + align:start position:0% +you're better off because you can't eat + + + align:start position:0% +you're better off because you can't eat +sweaters you need money so you get some + + align:start position:0% +sweaters you need money so you get some + + + align:start position:0% +sweaters you need money so you get some +of my money + + align:start position:0% +of my money + + + align:start position:0% +of my money +we're both better off but I've created a + + align:start position:0% +we're both better off but I've created a + + + align:start position:0% +we're both better off but I've created a +trade deficit okay that is not + + align:start position:0% +trade deficit okay that is not + + + align:start position:0% +trade deficit okay that is not +inherently a problem now of course the + + align:start position:0% +inherently a problem now of course the + + + align:start position:0% +inherently a problem now of course the +reality is more complicated the reality + + align:start position:0% +reality is more complicated the reality + + + align:start position:0% +reality is more complicated the reality +is that when I send in the money to + + align:start position:0% +is that when I send in the money to + + + align:start position:0% +is that when I send in the money to +those countries to buy the sweaters and + + align:start position:0% +those countries to buy the sweaters and + + + align:start position:0% +those countries to buy the sweaters and +I bring the sweaters in my consumers of + + align:start position:0% +I bring the sweaters in my consumers of + + + align:start position:0% +I bring the sweaters in my consumers of +sweaters are much happier and I keep + + align:start position:0% +sweaters are much happier and I keep + + + align:start position:0% +sweaters are much happier and I keep +focusing on sweaters because it's just + + align:start position:0% +focusing on sweaters because it's just + + + align:start position:0% +focusing on sweaters because it's just +amazing okay this sweater I just got at + + align:start position:0% +amazing okay this sweater I just got at + + + align:start position:0% +amazing okay this sweater I just got at +Old Navy okay $15 pretty nice decent + + align:start position:0% +Old Navy okay $15 pretty nice decent + + + align:start position:0% +Old Navy okay $15 pretty nice decent +you know it's not cotton whatever $15 + + align:start position:0% +you know it's not cotton whatever $15 + + + align:start position:0% +you know it's not cotton whatever $15 +this would have been a fortune when I + + align:start position:0% +this would have been a fortune when I + + + align:start position:0% +this would have been a fortune when I +was your age okay it knows these dollars + + align:start position:0% +was your age okay it knows these dollars + + + align:start position:0% +was your age okay it knows these dollars +it would have been $30 and that would be + + align:start position:0% +it would have been $30 and that would be + + + align:start position:0% +it would have been $30 and that would be +like $70 today okay why China okay + + align:start position:0% +like $70 today okay why China okay + + + align:start position:0% +like $70 today okay why China okay +because we used to movies to make these + + align:start position:0% +because we used to movies to make these + + + align:start position:0% +because we used to movies to make these +in North Carolina now we make them in + + align:start position:0% +in North Carolina now we make them in + + + align:start position:0% +in North Carolina now we make them in +China okay so the good news is I went to + + align:start position:0% +China okay so the good news is I went to + + + align:start position:0% +China okay so the good news is I went to +Old Navy I got two pairs of pants and + + align:start position:0% +Old Navy I got two pairs of pants and + + + align:start position:0% +Old Navy I got two pairs of pants and +like four sweaters like a hundred bucks + + align:start position:0% +like four sweaters like a hundred bucks + + + align:start position:0% +like four sweaters like a hundred bucks +okay that's the good news okay the bad + + align:start position:0% +okay that's the good news okay the bad + + + align:start position:0% +okay that's the good news okay the bad +news is the guys North Carolina lost + + align:start position:0% +news is the guys North Carolina lost + + + align:start position:0% +news is the guys North Carolina lost +their jobs that's the bad news so + + align:start position:0% +their jobs that's the bad news so + + + align:start position:0% +their jobs that's the bad news so +there's a trade-off + + align:start position:0% +there's a trade-off + + + align:start position:0% +there's a trade-off +now I'm gonna argue over the next + + align:start position:0% +now I'm gonna argue over the next + + + align:start position:0% +now I'm gonna argue over the next +lecture and a half that that trade-off + + align:start position:0% +lecture and a half that that trade-off + + + align:start position:0% +lecture and a half that that trade-off +is worth it in aggregate but we can't + + align:start position:0% +is worth it in aggregate but we can't + + + align:start position:0% +is worth it in aggregate but we can't +ignore the fact there's a trade-off + + align:start position:0% +ignore the fact there's a trade-off + + + align:start position:0% +ignore the fact there's a trade-off +because that's what leads to the very + + align:start position:0% +because that's what leads to the very + + + align:start position:0% +because that's what leads to the very +intense debates around your national + + align:start position:0% +intense debates around your national + + + align:start position:0% +intense debates around your national +trade is the fundamental tension between + + align:start position:0% +trade is the fundamental tension between + + + align:start position:0% +trade is the fundamental tension between +the consumers of goods that are made + + align:start position:0% +the consumers of goods that are made + + + align:start position:0% +the consumers of goods that are made +cheaper by the international trade and + + align:start position:0% +cheaper by the international trade and + + + align:start position:0% +cheaper by the international trade and +the producers of goods that get wiped + + align:start position:0% +the producers of goods that get wiped + + + align:start position:0% +the producers of goods that get wiped +out by international trade okay so + + align:start position:0% +out by international trade okay so + + + align:start position:0% +out by international trade okay so +that's our setup that's our big picture + + align:start position:0% +that's our setup that's our big picture + + + align:start position:0% +that's our setup that's our big picture +now I'm gonna dive in and I'm gonna + + align:start position:0% +now I'm gonna dive in and I'm gonna + + + align:start position:0% +now I'm gonna dive in and I'm gonna +teach you the nitty-gritty of how we + + align:start position:0% +teach you the nitty-gritty of how we + + + align:start position:0% +teach you the nitty-gritty of how we +think about this with models but that's + + align:start position:0% +think about this with models but that's + + + align:start position:0% +think about this with models but that's +the big picture once you have in mind so + + align:start position:0% +the big picture once you have in mind so + + + align:start position:0% +the big picture once you have in mind so +let's dive into the models that you do + + align:start position:0% +let's dive into the models that you do + + + align:start position:0% +let's dive into the models that you do +the models I need introduced a new a new + + align:start position:0% +the models I need introduced a new a new + + + align:start position:0% +the models I need introduced a new a new +tool to you which is the production + + align:start position:0% +tool to you which is the production + + + align:start position:0% +tool to you which is the production +possibility frontier + + align:start position:0% +possibility frontier + + + align:start position:0% +possibility frontier +PPF the production possibility frontier + + align:start position:0% + + + + align:start position:0% + +what the PPF shows you is the maximum + + align:start position:0% +what the PPF shows you is the maximum + + + align:start position:0% +what the PPF shows you is the maximum +combination of outputs you can produce + + align:start position:0% +combination of outputs you can produce + + + align:start position:0% +combination of outputs you can produce +for any given set of inputs okay so + + align:start position:0% +for any given set of inputs okay so + + + align:start position:0% +for any given set of inputs okay so +basically let's think about that let's + + align:start position:0% +basically let's think about that let's + + + align:start position:0% +basically let's think about that let's +go to figure 18 - it's easier to see + + align:start position:0% +go to figure 18 - it's easier to see + + + align:start position:0% +go to figure 18 - it's easier to see +this graphically let's go to figure 18 - + + align:start position:0% + + + + align:start position:0% + +let's think of you as a firm and you as + + align:start position:0% +let's think of you as a firm and you as + + + align:start position:0% +let's think of you as a firm and you as +a firm produce two things problem set + + align:start position:0% +a firm produce two things problem set + + + align:start position:0% +a firm produce two things problem set +points and exam points sorry it's all + + align:start position:0% +points and exam points sorry it's all + + + align:start position:0% +points and exam points sorry it's all +you're good for at MIT here you produce + + align:start position:0% +you're good for at MIT here you produce + + + align:start position:0% +you're good for at MIT here you produce +problem set points and exam points but + + align:start position:0% +problem set points and exam points but + + + align:start position:0% +problem set points and exam points but +you can produce either those you two + + align:start position:0% +you can produce either those you two + + + align:start position:0% +you can produce either those you two +things you produce and to make life easy + + align:start position:0% +things you produce and to make life easy + + + align:start position:0% +things you produce and to make life easy +let's say given your innate intelligence + + align:start position:0% +let's say given your innate intelligence + + + align:start position:0% +let's say given your innate intelligence +the points are produced as a function of + + align:start position:0% +the points are produced as a function of + + + align:start position:0% +the points are produced as a function of +time + + align:start position:0% +time + + + align:start position:0% +time +literally the more time you put in + + align:start position:0% +literally the more time you put in + + + align:start position:0% +literally the more time you put in +studying for an exam the better you do + + align:start position:0% +studying for an exam the better you do + + + align:start position:0% +studying for an exam the better you do +the more time you're spending the + + align:start position:0% +the more time you're spending the + + + align:start position:0% +the more time you're spending the +problem sets they better you do and you + + align:start position:0% +problem sets they better you do and you + + + align:start position:0% +problem sets they better you do and you +have one scarce input which is time this + + align:start position:0% +have one scarce input which is time this + + + align:start position:0% +have one scarce input which is time this +production possibility frontier tells + + align:start position:0% +production possibility frontier tells + + + align:start position:0% +production possibility frontier tells +you if you devote your scarce input + + align:start position:0% +you if you devote your scarce input + + + align:start position:0% +you if you devote your scarce input +across different activities what will + + align:start position:0% +across different activities what will + + + align:start position:0% +across different activities what will +the result be in terms of what's + + align:start position:0% +the result be in terms of what's + + + align:start position:0% +the result be in terms of what's +produced so what's this line saying on + + align:start position:0% +produced so what's this line saying on + + + align:start position:0% +produced so what's this line saying on +the left-hand side is saying look if I + + align:start position:0% +the left-hand side is saying look if I + + + align:start position:0% +the left-hand side is saying look if I +put all my time into studying for exams + + align:start position:0% +put all my time into studying for exams + + + align:start position:0% +put all my time into studying for exams +I'll get 200 points at exams and zero on + + align:start position:0% +I'll get 200 points at exams and zero on + + + align:start position:0% +I'll get 200 points at exams and zero on +problem sets if I spend all my time + + align:start position:0% +problem sets if I spend all my time + + + align:start position:0% +problem sets if I spend all my time +doing problem sets I've got 200 points + + align:start position:0% +doing problem sets I've got 200 points + + + align:start position:0% +doing problem sets I've got 200 points +on problem sets and zero on exams and + + align:start position:0% +on problem sets and zero on exams and + + + align:start position:0% +on problem sets and zero on exams and +some combinations in between that is a + + align:start position:0% +some combinations in between that is a + + + align:start position:0% +some combinations in between that is a +production possibility frontier okay it + + align:start position:0% +production possibility frontier okay it + + + align:start position:0% +production possibility frontier okay it +shows the combination of outputs you get + + align:start position:0% +shows the combination of outputs you get + + + align:start position:0% +shows the combination of outputs you get +for any given fixed level of inputs now + + align:start position:0% +for any given fixed level of inputs now + + + align:start position:0% +for any given fixed level of inputs now +what is wrong with the graph on the left + + align:start position:0% +what is wrong with the graph on the left + + + align:start position:0% +what is wrong with the graph on the left +and why is the graph on the right + + align:start position:0% +and why is the graph on the right + + + align:start position:0% +and why is the graph on the right +probably more realistic description of + + align:start position:0% +probably more realistic description of + + + align:start position:0% +probably more realistic description of +what your actual production possibility + + align:start position:0% +what your actual production possibility + + + align:start position:0% +what your actual production possibility +frontier looks like + + align:start position:0% + + + + align:start position:0% + +yeah yeah it's wrong because in fact + + align:start position:0% +yeah yeah it's wrong because in fact + + + align:start position:0% +yeah yeah it's wrong because in fact +what this system features is something + + align:start position:0% +what this system features is something + + + align:start position:0% +what this system features is something +we call economies of scope we talked + + align:start position:0% +we call economies of scope we talked + + + align:start position:0% +we call economies of scope we talked +about economies of scale a number of + + align:start position:0% +about economies of scale a number of + + + align:start position:0% +about economies of scale a number of +lectures ago the notion that when if you + + align:start position:0% +lectures ago the notion that when if you + + + align:start position:0% +lectures ago the notion that when if you +double inputs do you double output this + + align:start position:0% +double inputs do you double output this + + + align:start position:0% +double inputs do you double output this +economies of scope which is that by + + align:start position:0% +economies of scope which is that by + + + align:start position:0% +economies of scope which is that by +producing more than one thing at once + + align:start position:0% +producing more than one thing at once + + + align:start position:0% +producing more than one thing at once +you may get better at both let by + + align:start position:0% +you may get better at both let by + + + align:start position:0% +you may get better at both let by +studying for an exam you get better at + + align:start position:0% +studying for an exam you get better at + + + align:start position:0% +studying for an exam you get better at +problem sets and by doing problem sets + + align:start position:0% +problem sets and by doing problem sets + + + align:start position:0% +problem sets and by doing problem sets +you do better on the exam so what that + + align:start position:0% +you do better on the exam so what that + + + align:start position:0% +you do better on the exam so what that +means is doing some of both leads to a + + align:start position:0% +means is doing some of both leads to a + + + align:start position:0% +means is doing some of both leads to a +better outcome than doing all of one or + + align:start position:0% +better outcome than doing all of one or + + + align:start position:0% +better outcome than doing all of one or +all the other okay you get a concave to + + align:start position:0% +all the other okay you get a concave to + + + align:start position:0% +all the other okay you get a concave to +the origin production possibility + + align:start position:0% +the origin production possibility + + + align:start position:0% +the origin production possibility +frontier a concave larger production + + align:start position:0% +frontier a concave larger production + + + align:start position:0% +frontier a concave larger production +possibility frontier demonstrates the + + align:start position:0% +possibility frontier demonstrates the + + + align:start position:0% +possibility frontier demonstrates the +economies of scope doing some of both is + + align:start position:0% +economies of scope doing some of both is + + + align:start position:0% +economies of scope doing some of both is +better than doing all of just one all + + align:start position:0% +better than doing all of just one all + + + align:start position:0% +better than doing all of just one all +the other and that makes sense for you + + align:start position:0% +the other and that makes sense for you + + + align:start position:0% +the other and that makes sense for you +and doing problem sets in exams it makes + + align:start position:0% +and doing problem sets in exams it makes + + + align:start position:0% +and doing problem sets in exams it makes +sense you'd be better off doing some of + + align:start position:0% +sense you'd be better off doing some of + + + align:start position:0% +sense you'd be better off doing some of +both than devoting all your attention to + + align:start position:0% +both than devoting all your attention to + + + align:start position:0% +both than devoting all your attention to +one and just just one in just the other + + align:start position:0% +one and just just one in just the other + + + align:start position:0% +one and just just one in just the other +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that is a production possibility + + align:start position:0% +so that is a production possibility + + + align:start position:0% +so that is a production possibility +frontier now there can also be dis + + align:start position:0% +frontier now there can also be dis + + + align:start position:0% +frontier now there can also be dis +economies of scope another great example + + align:start position:0% +economies of scope another great example + + + align:start position:0% +economies of scope another great example +for MIT is that when I was here as an + + align:start position:0% +for MIT is that when I was here as an + + + align:start position:0% +for MIT is that when I was here as an +undergrad I came in as a tennis player + + align:start position:0% +undergrad I came in as a tennis player + + + align:start position:0% +undergrad I came in as a tennis player +and I was on the tennis team now tennis + + align:start position:0% +and I was on the tennis team now tennis + + + align:start position:0% +and I was on the tennis team now tennis +was only in the fall and spring in the + + align:start position:0% +was only in the fall and spring in the + + + align:start position:0% +was only in the fall and spring in the +winter they had squash so I thought I'd + + align:start position:0% +winter they had squash so I thought I'd + + + align:start position:0% +winter they had squash so I thought I'd +play squash well it turns out that the + + align:start position:0% +play squash well it turns out that the + + + align:start position:0% +play squash well it turns out that the +key with tennis is keeping your wrist on + + align:start position:0% +key with tennis is keeping your wrist on + + + align:start position:0% +key with tennis is keeping your wrist on +the huge squash is keeping your wrist + + align:start position:0% +the huge squash is keeping your wrist + + + align:start position:0% +the huge squash is keeping your wrist +flexible and by playing squash I screwed + + align:start position:0% +flexible and by playing squash I screwed + + + align:start position:0% +flexible and by playing squash I screwed +up my tennis game am i playing tennis I + + align:start position:0% +up my tennis game am i playing tennis I + + + align:start position:0% +up my tennis game am i playing tennis I +screwed up my swashy a squash game so I + + align:start position:0% +screwed up my swashy a squash game so I + + + align:start position:0% +screwed up my swashy a squash game so I +had a diseconomy of scope + + align:start position:0% +had a diseconomy of scope + + + align:start position:0% +had a diseconomy of scope +I was worse off at both things by + + align:start position:0% +I was worse off at both things by + + + align:start position:0% +I was worse off at both things by +playing both the ribbon is just playing + + align:start position:0% +playing both the ribbon is just playing + + + align:start position:0% +playing both the ribbon is just playing +one or the other okay + + align:start position:0% +one or the other okay + + + align:start position:0% +one or the other okay +so it can be economies of scope which is + + align:start position:0% +so it can be economies of scope which is + + + align:start position:0% +so it can be economies of scope which is +when doing both things make you better + + align:start position:0% +when doing both things make you better + + + align:start position:0% +when doing both things make you better +at both and diseconomies a scoop when + + align:start position:0% +at both and diseconomies a scoop when + + + align:start position:0% +at both and diseconomies a scoop when +doing both things make you worse at both + + align:start position:0% +doing both things make you worse at both + + + align:start position:0% +doing both things make you worse at both +okay and that's the nature of the shape + + align:start position:0% +okay and that's the nature of the shape + + + align:start position:0% +okay and that's the nature of the shape +of production possibilities frontier and + + align:start position:0% +of production possibilities frontier and + + + align:start position:0% +of production possibilities frontier and +the economy of scope is when doing both + + align:start position:0% +the economy of scope is when doing both + + + align:start position:0% +the economy of scope is when doing both +makes you better off a dis economy of + + align:start position:0% +makes you better off a dis economy of + + + align:start position:0% +makes you better off a dis economy of +scope is when doing both makes you're + + align:start position:0% +scope is when doing both makes you're + + + align:start position:0% +scope is when doing both makes you're +worse off okay questions about that + + align:start position:0% +worse off okay questions about that + + + align:start position:0% +worse off okay questions about that +now it just ensures that tool because + + align:start position:0% +now it just ensures that tool because + + + align:start position:0% +now it just ensures that tool because +that tool it could be the fundamental + + align:start position:0% +that tool it could be the fundamental + + + align:start position:0% +that tool it could be the fundamental +modeling feature that allows us to + + align:start position:0% +modeling feature that allows us to + + + align:start position:0% +modeling feature that allows us to +demonstrate why international trade is + + align:start position:0% +demonstrate why international trade is + + + align:start position:0% +demonstrate why international trade is +beneficial okay so now we're gonna take + + align:start position:0% +beneficial okay so now we're gonna take + + + align:start position:0% +beneficial okay so now we're gonna take +that tool and we're gonna go and talk + + align:start position:0% +that tool and we're gonna go and talk + + + align:start position:0% +that tool and we're gonna go and talk +about the concept of comparative + + align:start position:0% +about the concept of comparative + + + align:start position:0% +about the concept of comparative +advantage which is the core concept in + + align:start position:0% +advantage which is the core concept in + + + align:start position:0% +advantage which is the core concept in +international trade economics this is + + align:start position:0% +international trade economics this is + + + align:start position:0% +international trade economics this is +the core of how it all works okay let's + + align:start position:0% +the core of how it all works okay let's + + + align:start position:0% +the core of how it all works okay let's +think of a particular example to + + align:start position:0% +think of a particular example to + + + align:start position:0% +think of a particular example to +understand this let's take the US and + + align:start position:0% +understand this let's take the US and + + + align:start position:0% +understand this let's take the US and +Colombia and the Rose market okay and as + + align:start position:0% +Colombia and the Rose market okay and as + + + align:start position:0% +Colombia and the Rose market okay and as +I said before let's say it's expensive + + align:start position:0% +I said before let's say it's expensive + + + align:start position:0% +I said before let's say it's expensive +for the u.s. in the Valentine's Day rose + + align:start position:0% +for the u.s. in the Valentine's Day rose + + + align:start position:0% +for the u.s. in the Valentine's Day rose +market it's expensive for the us to grow + + align:start position:0% +market it's expensive for the us to grow + + + align:start position:0% +market it's expensive for the us to grow +Valentine's Day roses it's cheap in + + align:start position:0% +Valentine's Day roses it's cheap in + + + align:start position:0% +Valentine's Day roses it's cheap in +Colombia okay on the other hand let's + + align:start position:0% +Colombia okay on the other hand let's + + + align:start position:0% +Colombia okay on the other hand let's +compare roses to computers roses are + + align:start position:0% +compare roses to computers roses are + + + align:start position:0% +compare roses to computers roses are +cheap to produce in Colombia and + + align:start position:0% +cheap to produce in Colombia and + + + align:start position:0% +cheap to produce in Colombia and +expensive in America computers are the + + align:start position:0% +expensive in America computers are the + + + align:start position:0% +expensive in America computers are the +opposite we have giant factories and + + align:start position:0% +opposite we have giant factories and + + + align:start position:0% +opposite we have giant factories and +skilled labor and giant machines that + + align:start position:0% +skilled labor and giant machines that + + + align:start position:0% +skilled labor and giant machines that +can quickly crank out computers in + + align:start position:0% +can quickly crank out computers in + + + align:start position:0% +can quickly crank out computers in +Colombia that have to like assemble the + + align:start position:0% +Colombia that have to like assemble the + + + align:start position:0% +Colombia that have to like assemble the +computer by hand okay so it's a lot + + align:start position:0% +computer by hand okay so it's a lot + + + align:start position:0% +computer by hand okay so it's a lot +cheaper to produce a computer in the US + + align:start position:0% +cheaper to produce a computer in the US + + + align:start position:0% +cheaper to produce a computer in the US +than it is in Colombia it's a lot + + align:start position:0% +than it is in Colombia it's a lot + + + align:start position:0% +than it is in Colombia it's a lot +cheaper to produce a rose in Colombia + + align:start position:0% +cheaper to produce a rose in Colombia + + + align:start position:0% +cheaper to produce a rose in Colombia +that is in the US the way to think about + + align:start position:0% +that is in the US the way to think about + + + align:start position:0% +that is in the US the way to think about +this is through the lens of opportunity + + align:start position:0% +this is through the lens of opportunity + + + align:start position:0% +this is through the lens of opportunity +cost what we're saying is the + + align:start position:0% +cost what we're saying is the + + + align:start position:0% +cost what we're saying is the +opportunity cost of making a rose in + + align:start position:0% +opportunity cost of making a rose in + + + align:start position:0% +opportunity cost of making a rose in +terms of computers is higher in the US + + align:start position:0% +terms of computers is higher in the US + + + align:start position:0% +terms of computers is higher in the US +you know though it's the amount of + + align:start position:0% +you know though it's the amount of + + + align:start position:0% +you know though it's the amount of +computers you have to give up to make a + + align:start position:0% +computers you have to give up to make a + + + align:start position:0% +computers you have to give up to make a +rose is high in u.s. because computers + + align:start position:0% +rose is high in u.s. because computers + + + align:start position:0% +rose is high in u.s. because computers +are cheap and roses are expensive the + + align:start position:0% +are cheap and roses are expensive the + + + align:start position:0% +are cheap and roses are expensive the +amount of computers you have to the + + align:start position:0% +amount of computers you have to the + + + align:start position:0% +amount of computers you have to the +command of roses you have to give up to + + align:start position:0% +command of roses you have to give up to + + + align:start position:0% +command of roses you have to give up to +make computer in Columbia's higher + + align:start position:0% +make computer in Columbia's higher + + + align:start position:0% +make computer in Columbia's higher +because roses are cheaper computers are + + align:start position:0% +because roses are cheaper computers are + + + align:start position:0% +because roses are cheaper computers are +expensive so we say that Colombia has a + + align:start position:0% +expensive so we say that Colombia has a + + + align:start position:0% +expensive so we say that Colombia has a +comparative advantage in roses is + + align:start position:0% +comparative advantage in roses is + + + align:start position:0% +comparative advantage in roses is +relatively cheap in a world of computers + + align:start position:0% +relatively cheap in a world of computers + + + align:start position:0% +relatively cheap in a world of computers +and roses + + align:start position:0% +and roses + + + align:start position:0% +and roses +is relatively cheap for them to produce + + align:start position:0% +is relatively cheap for them to produce + + + align:start position:0% +is relatively cheap for them to produce +roses compared to computers the + + align:start position:0% +roses compared to computers the + + + align:start position:0% +roses compared to computers the +opportunity cost entrance of argon + + align:start position:0% +opportunity cost entrance of argon + + + align:start position:0% +opportunity cost entrance of argon +computers is lower whereas the US has a + + align:start position:0% +computers is lower whereas the US has a + + + align:start position:0% +computers is lower whereas the US has a +comparative advantage in computers it is + + align:start position:0% +comparative advantage in computers it is + + + align:start position:0% +comparative advantage in computers it is +comparatively cheaper for us to produce + + align:start position:0% +comparatively cheaper for us to produce + + + align:start position:0% +comparatively cheaper for us to produce +computers so international trade is all + + align:start position:0% +computers so international trade is all + + + align:start position:0% +computers so international trade is all +about what you're relatively better at + + align:start position:0% +about what you're relatively better at + + + align:start position:0% +about what you're relatively better at +now let me emphasize relative for a + + align:start position:0% +now let me emphasize relative for a + + + align:start position:0% +now let me emphasize relative for a +second this is an important concept the + + align:start position:0% +second this is an important concept the + + + align:start position:0% +second this is an important concept the +reason we don't just say advantage and + + align:start position:0% +reason we don't just say advantage and + + + align:start position:0% +reason we don't just say advantage and +we say comparative advantage is it + + align:start position:0% +we say comparative advantage is it + + + align:start position:0% +we say comparative advantage is it +doesn't actually matter if you're better + + align:start position:0% +doesn't actually matter if you're better + + + align:start position:0% +doesn't actually matter if you're better +it matters you're relatively better let + + align:start position:0% +it matters you're relatively better let + + + align:start position:0% +it matters you're relatively better let +me explain this is hard this is I would + + align:start position:0% +me explain this is hard this is I would + + + align:start position:0% +me explain this is hard this is I would +say of the main economics constants in + + align:start position:0% +say of the main economics constants in + + + align:start position:0% +say of the main economics constants in +the world that we need people understand + + align:start position:0% +the world that we need people understand + + + align:start position:0% +the world that we need people understand +this is one of the top three least + + align:start position:0% +this is one of the top three least + + + align:start position:0% +this is one of the top three least +understood concepts in all the world + + align:start position:0% +understood concepts in all the world + + + align:start position:0% +understood concepts in all the world +okay in economics credit vanch like in + + align:start position:0% +okay in economics credit vanch like in + + + align:start position:0% +okay in economics credit vanch like in +our blood we can understand my regular + + align:start position:0% +our blood we can understand my regular + + + align:start position:0% +our blood we can understand my regular +people can understand it it's because + + align:start position:0% +people can understand it it's because + + + align:start position:0% +people can understand it it's because +it's hard ok let me give you let me give + + align:start position:0% +it's hard ok let me give you let me give + + + align:start position:0% +it's hard ok let me give you let me give +an example take me and LeBron James and + + align:start position:0% +an example take me and LeBron James and + + + align:start position:0% +an example take me and LeBron James and +imagine his two activities in life + + align:start position:0% +imagine his two activities in life + + + align:start position:0% +imagine his two activities in life +mowing a lawn and playing basketball + + align:start position:0% +mowing a lawn and playing basketball + + + align:start position:0% +mowing a lawn and playing basketball +that's all life consisteth ok now LeBron + + align:start position:0% +that's all life consisteth ok now LeBron + + + align:start position:0% +that's all life consisteth ok now LeBron +James is better than me at both playing + + align:start position:0% +James is better than me at both playing + + + align:start position:0% +James is better than me at both playing +basketball and mowing along but he's + + align:start position:0% +basketball and mowing along but he's + + + align:start position:0% +basketball and mowing along but he's +much much much much much better than me + + align:start position:0% +much much much much much better than me + + + align:start position:0% +much much much much much better than me +at basketball and only much better than + + align:start position:0% +at basketball and only much better than + + + align:start position:0% +at basketball and only much better than +me and rolling along + + align:start position:0% +me and rolling along + + + align:start position:0% +me and rolling along +so LeBron James has an advantage in + + align:start position:0% +so LeBron James has an advantage in + + + align:start position:0% +so LeBron James has an advantage in +everything both activities but he only + + align:start position:0% +everything both activities but he only + + + align:start position:0% +everything both activities but he only +has a comparative advantage in + + align:start position:0% +has a comparative advantage in + + + align:start position:0% +has a comparative advantage in +basketball he only is a comparative a + + align:start position:0% +basketball he only is a comparative a + + + align:start position:0% +basketball he only is a comparative a +ninja best the pair advantage is about + + align:start position:0% +ninja best the pair advantage is about + + + align:start position:0% +ninja best the pair advantage is about +opportunity costs in other words the + + align:start position:0% +opportunity costs in other words the + + + align:start position:0% +opportunity costs in other words the +amount it's LeBron James mows his lawn + + align:start position:0% +amount it's LeBron James mows his lawn + + + align:start position:0% +amount it's LeBron James mows his lawn +the amount of basketball he's giving up + + align:start position:0% +the amount of basketball he's giving up + + + align:start position:0% +the amount of basketball he's giving up +is ungodly it's crazy I mow his lawn + + align:start position:0% +is ungodly it's crazy I mow his lawn + + + align:start position:0% +is ungodly it's crazy I mow his lawn +give me my bachelor could have played if + + align:start position:0% +give me my bachelor could have played if + + + align:start position:0% +give me my bachelor could have played if +I mow my lawn I'm not giving orange + + align:start position:0% +I mow my lawn I'm not giving orange + + + align:start position:0% +I mow my lawn I'm not giving orange +basketballs I suck at basketball so I + + align:start position:0% +basketballs I suck at basketball so I + + + align:start position:0% +basketballs I suck at basketball so I +have a comparative advantage in lawn + + align:start position:0% +have a comparative advantage in lawn + + + align:start position:0% +have a comparative advantage in lawn +mowing might say how could your not + + align:start position:0% +mowing might say how could your not + + + align:start position:0% +mowing might say how could your not +better at lawn when LeBron James I'm not + + align:start position:0% +better at lawn when LeBron James I'm not + + + align:start position:0% +better at lawn when LeBron James I'm not +but I have a comparative antigen in lawn + + align:start position:0% +but I have a comparative antigen in lawn + + + align:start position:0% +but I have a comparative antigen in lawn +mowing because the opportunity cost to + + align:start position:0% +mowing because the opportunity cost to + + + align:start position:0% +mowing because the opportunity cost to +me is much lower the opportunity costs + + align:start position:0% +me is much lower the opportunity costs + + + align:start position:0% +me is much lower the opportunity costs +LeBron James of mowing his lawn is high + + align:start position:0% +LeBron James of mowing his lawn is high + + + align:start position:0% +LeBron James of mowing his lawn is high +because he could be playing basketball + + align:start position:0% +because he could be playing basketball + + + align:start position:0% +because he could be playing basketball +the opportunity cost to me is low + + align:start position:0% +the opportunity cost to me is low + + + align:start position:0% +the opportunity cost to me is low +because I can't play basketball yeah + + align:start position:0% + + + + align:start position:0% + +that's a weird educates I won't do that + + align:start position:0% +that's a weird educates I won't do that + + + align:start position:0% +that's a weird educates I won't do that +then there'd be no true then there'll be + + align:start position:0% +then there'd be no true then there'll be + + + align:start position:0% +then there'd be no true then there'll be +no reason for that makes trade things + + align:start position:0% +no reason for that makes trade things + + + align:start position:0% +no reason for that makes trade things +hard look we can come back to that now + + align:start position:0% +hard look we can come back to that now + + + align:start position:0% +hard look we can come back to that now +of course the example doesn't stop there + + align:start position:0% +of course the example doesn't stop there + + + align:start position:0% +of course the example doesn't stop there +should I mow my lawn no I should not mow + + align:start position:0% +should I mow my lawn no I should not mow + + + align:start position:0% +should I mow my lawn no I should not mow +my lawn because there is someone who's + + align:start position:0% +my lawn because there is someone who's + + + align:start position:0% +my lawn because there is someone who's +who as doesn't have as much education as + + align:start position:0% +who as doesn't have as much education as + + + align:start position:0% +who as doesn't have as much education as +I who canter as much money and I at work + + align:start position:0% +I who canter as much money and I at work + + + align:start position:0% +I who canter as much money and I at work +and they have a comparative Japan gin + + align:start position:0% +and they have a comparative Japan gin + + + align:start position:0% +and they have a comparative Japan gin +lawn mowing I care advantage in office + + align:start position:0% +lawn mowing I care advantage in office + + + align:start position:0% +lawn mowing I care advantage in office +work so in fact the only should I'm + + align:start position:0% +work so in fact the only should I'm + + + align:start position:0% +work so in fact the only should I'm +alive carriage over LeBron in lawn + + align:start position:0% +alive carriage over LeBron in lawn + + + align:start position:0% +alive carriage over LeBron in lawn +mowing but some less educated the guy is + + align:start position:0% +mowing but some less educated the guy is + + + align:start position:0% +mowing but some less educated the guy is +a comparative Ange over me in lawn + + align:start position:0% +a comparative Ange over me in lawn + + + align:start position:0% +a comparative Ange over me in lawn +mowing so just as LeBron be better off + + align:start position:0% +mowing so just as LeBron be better off + + + align:start position:0% +mowing so just as LeBron be better off +letting me mow his lawn and I've got + + align:start position:0% +letting me mow his lawn and I've got + + + align:start position:0% +letting me mow his lawn and I've got +after letting him play basketball I'm + + align:start position:0% +after letting him play basketball I'm + + + align:start position:0% +after letting him play basketball I'm +better off letting some less educated + + align:start position:0% +better off letting some less educated + + + align:start position:0% +better off letting some less educated +guy mow my lawn and letting me go sit in + + align:start position:0% +guy mow my lawn and letting me go sit in + + + align:start position:0% +guy mow my lawn and letting me go sit in +my cinema from my computer all day okay + + align:start position:0% +my cinema from my computer all day okay + + + align:start position:0% +my cinema from my computer all day okay +comparative image is all about what + + align:start position:0% +comparative image is all about what + + + align:start position:0% +comparative image is all about what +you're relatively better at and the key + + align:start position:0% +you're relatively better at and the key + + + align:start position:0% +you're relatively better at and the key +insight okay of international trade is + + align:start position:0% +insight okay of international trade is + + + align:start position:0% +insight okay of international trade is +that in a world of comparative advantage + + align:start position:0% +that in a world of comparative advantage + + + align:start position:0% +that in a world of comparative advantage +people should always specialize in a + + align:start position:0% +people should always specialize in a + + + align:start position:0% +people should always specialize in a +world of comparative advantage people + + align:start position:0% +world of comparative advantage people + + + align:start position:0% +world of comparative advantage people +should always specialize you should do + + align:start position:0% +should always specialize you should do + + + align:start position:0% +should always specialize you should do +what you're best at okay + + align:start position:0% +what you're best at okay + + + align:start position:0% +what you're best at okay +you should do what you're best at + + align:start position:0% +you should do what you're best at + + + align:start position:0% +you should do what you're best at +because otherwise it's simply silly for + + align:start position:0% +because otherwise it's simply silly for + + + align:start position:0% +because otherwise it's simply silly for +LeBron spent any time only as long as + + align:start position:0% +LeBron spent any time only as long as + + + align:start position:0% +LeBron spent any time only as long as +much as my wife thinks I'm just trying + + align:start position:0% +much as my wife thinks I'm just trying + + + align:start position:0% +much as my wife thinks I'm just trying +to get out of it it's simply silly for + + align:start position:0% +to get out of it it's simply silly for + + + align:start position:0% +to get out of it it's simply silly for +you to spend any time mowing my lawn + + align:start position:0% +you to spend any time mowing my lawn + + + align:start position:0% +you to spend any time mowing my lawn +okay I have a I have a compare advantage + + align:start position:0% +okay I have a I have a compare advantage + + + align:start position:0% +okay I have a I have a compare advantage +it's study in front of my computer and + + align:start position:0% +it's study in front of my computer and + + + align:start position:0% +it's study in front of my computer and +doing that stuff so I should hire + + align:start position:0% +doing that stuff so I should hire + + + align:start position:0% +doing that stuff so I should hire +someone else to mow my lawn so to + + align:start position:0% +someone else to mow my lawn so to + + + align:start position:0% +someone else to mow my lawn so to +actually see that let's go to figure + + align:start position:0% +actually see that let's go to figure + + + align:start position:0% +actually see that let's go to figure +eighteen three this is a confusing + + align:start position:0% +eighteen three this is a confusing + + + align:start position:0% +eighteen three this is a confusing +figure so I'm going to go through it + + align:start position:0% +figure so I'm going to go through it + + + align:start position:0% +figure so I'm going to go through it +slowly okay on the top we have the US + + align:start position:0% +slowly okay on the top we have the US + + + align:start position:0% +slowly okay on the top we have the US +production possibilities frontier and to + + align:start position:0% +production possibilities frontier and to + + + align:start position:0% +production possibilities frontier and to +make life easy let's assume that there's + + align:start position:0% +make life easy let's assume that there's + + + align:start position:0% +make life easy let's assume that there's +no economies of scope between roses and + + align:start position:0% +no economies of scope between roses and + + + align:start position:0% +no economies of scope between roses and +computers make sense there wouldn't be + + align:start position:0% +computers make sense there wouldn't be + + + align:start position:0% +computers make sense there wouldn't be +right let's assume there's no economies + + align:start position:0% +right let's assume there's no economies + + + align:start position:0% +right let's assume there's no economies +or diseconomies who knows the computers + + align:start position:0% +or diseconomies who knows the computers + + + align:start position:0% +or diseconomies who knows the computers +it's a linear production possibility + + align:start position:0% +it's a linear production possibility + + + align:start position:0% +it's a linear production possibility +frontier so we're showing each graph is + + align:start position:0% +frontier so we're showing each graph is + + + align:start position:0% +frontier so we're showing each graph is +production possibility frontier between + + align:start position:0% +production possibility frontier between + + + align:start position:0% +production possibility frontier between +roses and computers and we're assuming + + align:start position:0% +roses and computers and we're assuming + + + align:start position:0% +roses and computers and we're assuming +it's just linear which makes sense right + + align:start position:0% +it's just linear which makes sense right + + + align:start position:0% +it's just linear which makes sense right +you don't you don't make better + + align:start position:0% +you don't you don't make better + + + align:start position:0% +you don't you don't make better +computers by making Rosen and vice versa + + align:start position:0% +computers by making Rosen and vice versa + + + align:start position:0% +computers by making Rosen and vice versa +on the top we have the u.s. let's say + + align:start position:0% +on the top we have the u.s. let's say + + + align:start position:0% +on the top we have the u.s. let's say +that the u.s. is production production + + align:start position:0% +that the u.s. is production production + + + align:start position:0% +that the u.s. is production production +possibility frontiers the following + + align:start position:0% +possibility frontiers the following + + + align:start position:0% +possibility frontiers the following +given the resources we have in the US we + + align:start position:0% +given the resources we have in the US we + + + align:start position:0% +given the resources we have in the US we +could produce two thousand computers or + + align:start position:0% +could produce two thousand computers or + + + align:start position:0% +could produce two thousand computers or +one thousand boxes of roses given our + + align:start position:0% +one thousand boxes of roses given our + + + align:start position:0% +one thousand boxes of roses given our +resource our skill level our capital + + align:start position:0% +resource our skill level our capital + + + align:start position:0% +resource our skill level our capital +intensity etc now go to Columbia say + + align:start position:0% +intensity etc now go to Columbia say + + + align:start position:0% +intensity etc now go to Columbia say +that Columbia given their skill level + + align:start position:0% +that Columbia given their skill level + + + align:start position:0% +that Columbia given their skill level +resources the sunshine the beautiful + + align:start position:0% +resources the sunshine the beautiful + + + align:start position:0% +resources the sunshine the beautiful +weather any Colombians here sounds + + align:start position:0% +weather any Colombians here sounds + + + align:start position:0% +weather any Colombians here sounds +perfect it's like 75 all the time + + align:start position:0% +perfect it's like 75 all the time + + + align:start position:0% +perfect it's like 75 all the time +okay um you end up they can make two + + align:start position:0% +okay um you end up they can make two + + + align:start position:0% +okay um you end up they can make two +thousand roses and one thousand + + align:start position:0% +thousand roses and one thousand + + + align:start position:0% +thousand roses and one thousand +computers or one thousand compares or + + align:start position:0% +computers or one thousand compares or + + + align:start position:0% +computers or one thousand compares or +sub combination in between so the first + + align:start position:0% +sub combination in between so the first + + + align:start position:0% +sub combination in between so the first +things I want to make you hear is guys + + align:start position:0% +things I want to make you hear is guys + + + align:start position:0% +things I want to make you hear is guys +understand why these are sensible + + align:start position:0% +understand why these are sensible + + + align:start position:0% +understand why these are sensible +production possibility frontiers for + + align:start position:0% +production possibility frontiers for + + + align:start position:0% +production possibility frontiers for +each country the sense of production + + align:start position:0% +each country the sense of production + + + align:start position:0% +each country the sense of production +possibility frontiers because they + + align:start position:0% +possibility frontiers because they + + + align:start position:0% +possibility frontiers because they +basically show the US has a comparative + + align:start position:0% +basically show the US has a comparative + + + align:start position:0% +basically show the US has a comparative +advantage in computers that is the + + align:start position:0% +advantage in computers that is the + + + align:start position:0% +advantage in computers that is the +trade-off in terms of roses forgone to + + align:start position:0% +trade-off in terms of roses forgone to + + + align:start position:0% +trade-off in terms of roses forgone to +make a computer he's lower in the u.s. + + align:start position:0% +make a computer he's lower in the u.s. + + + align:start position:0% +make a computer he's lower in the u.s. +than Columbia okay and Columbia has a + + align:start position:0% +than Columbia okay and Columbia has a + + + align:start position:0% +than Columbia okay and Columbia has a +comparative advantage in roses okay the + + align:start position:0% +comparative advantage in roses okay the + + + align:start position:0% +comparative advantage in roses okay the +trade-off in terms of foregone computers + + align:start position:0% +trade-off in terms of foregone computers + + + align:start position:0% +trade-off in terms of foregone computers +to make a rose is much lower in Columbia + + align:start position:0% +to make a rose is much lower in Columbia + + + align:start position:0% +to make a rose is much lower in Columbia +than in the u.s. so comparative ang + + align:start position:0% +than in the u.s. so comparative ang + + + align:start position:0% +than in the u.s. so comparative ang +members about opportunity cost let me + + align:start position:0% +members about opportunity cost let me + + + align:start position:0% +members about opportunity cost let me +say it again the US has a comparative + + align:start position:0% +say it again the US has a comparative + + + align:start position:0% +say it again the US has a comparative +advantage of computers cuz to make a + + align:start position:0% +advantage of computers cuz to make a + + + align:start position:0% +advantage of computers cuz to make a +computer we have to give up less roses + + align:start position:0% +computer we have to give up less roses + + + align:start position:0% +computer we have to give up less roses +than Columbia does to make one computer + + align:start position:0% +than Columbia does to make one computer + + + align:start position:0% +than Columbia does to make one computer +we give up half a box of roses that's + + align:start position:0% +we give up half a box of roses that's + + + align:start position:0% +we give up half a box of roses that's +the slope of this line Columbia to make + + align:start position:0% +the slope of this line Columbia to make + + + align:start position:0% +the slope of this line Columbia to make +one computer has to give up two boxes of + + align:start position:0% +one computer has to give up two boxes of + + + align:start position:0% +one computer has to give up two boxes of +roses so we have a comparative advantage + + align:start position:0% +roses so we have a comparative advantage + + + align:start position:0% +roses so we have a comparative advantage +in computers yeah + + align:start position:0% + + + + align:start position:0% + +that's the term comparative you can have + + align:start position:0% +that's the term comparative you can have + + + align:start position:0% +that's the term comparative you can have +an absolute event in this simple 2x2 + + align:start position:0% +an absolute event in this simple 2x2 + + + align:start position:0% +an absolute event in this simple 2x2 +model you've ever ancient multiple + + align:start position:0% +model you've ever ancient multiple + + + align:start position:0% +model you've ever ancient multiple +things in life but the simple model you + + align:start position:0% +things in life but the simple model you + + + align:start position:0% +things in life but the simple model you +can have the absolute advantage of both + + align:start position:0% +can have the absolute advantage of both + + + align:start position:0% +can have the absolute advantage of both +but you can't have a comparative + + align:start position:0% +but you can't have a comparative + + + align:start position:0% +but you can't have a comparative +advantage of both that's absolutely + + align:start position:0% +advantage of both that's absolutely + + + align:start position:0% +advantage of both that's absolutely +right in this model with two goods in + + align:start position:0% +right in this model with two goods in + + + align:start position:0% +right in this model with two goods in +two countries each country has a + + align:start position:0% +two countries each country has a + + + align:start position:0% +two countries each country has a +comparative image of one thing or the + + align:start position:0% +comparative image of one thing or the + + + align:start position:0% +comparative image of one thing or the +other okay or there could be weird edge + + align:start position:0% +other okay or there could be weird edge + + + align:start position:0% +other okay or there could be weird edge +cases but generally that's right okay so + + align:start position:0% +cases but generally that's right okay so + + + align:start position:0% +cases but generally that's right okay so +so now I did compares now it's flip and + + align:start position:0% +so now I did compares now it's flip and + + + align:start position:0% +so now I did compares now it's flip and +do roses in roses for the u.s. to + + align:start position:0% +do roses in roses for the u.s. to + + + align:start position:0% +do roses in roses for the u.s. to +produce a box of roses they have to give + + align:start position:0% +produce a box of roses they have to give + + + align:start position:0% +produce a box of roses they have to give +up two computers for Columbia to proves + + align:start position:0% +up two computers for Columbia to proves + + + align:start position:0% +up two computers for Columbia to proves +a box of roses they only give up half a + + align:start position:0% +a box of roses they only give up half a + + + align:start position:0% +a box of roses they only give up half a +computer so they have a comparative + + align:start position:0% +computer so they have a comparative + + + align:start position:0% +computer so they have a comparative +advantage in roses okay + + align:start position:0% +advantage in roses okay + + + align:start position:0% +advantage in roses okay +people understand the setup here these + + align:start position:0% +people understand the setup here these + + + align:start position:0% +people understand the setup here these +graphs on the left yeah so for right now + + align:start position:0% +graphs on the left yeah so for right now + + + align:start position:0% +graphs on the left yeah so for right now +we're ignoring prices we'll come back to + + align:start position:0% +we're ignoring prices we'll come back to + + + align:start position:0% +we're ignoring prices we'll come back to +prices later but right now are doing the + + align:start position:0% +prices later but right now are doing the + + + align:start position:0% +prices later but right now are doing the +prices right now we're just sort of what + + align:start position:0% +prices right now we're just sort of what + + + align:start position:0% +prices right now we're just sort of what +we're gonna basically have prices coming + + align:start position:0% +we're gonna basically have prices coming + + + align:start position:0% +we're gonna basically have prices coming +in later but for right now we're doing + + align:start position:0% +in later but for right now we're doing + + + align:start position:0% +in later but for right now we're doing +prices okay so now let's imagine that + + align:start position:0% +prices okay so now let's imagine that + + + align:start position:0% +prices okay so now let's imagine that +tastes are such that consumers in the + + align:start position:0% +tastes are such that consumers in the + + + align:start position:0% +tastes are such that consumers in the +u.s. one a thousand appears in five + + align:start position:0% +u.s. one a thousand appears in five + + + align:start position:0% +u.s. one a thousand appears in five +hundred boxes of roses that's point seen + + align:start position:0% +hundred boxes of roses that's point seen + + + align:start position:0% +hundred boxes of roses that's point seen +us and consumers in Columbia what five + + align:start position:0% +us and consumers in Columbia what five + + + align:start position:0% +us and consumers in Columbia what five +hundred computers in a thousand box of + + align:start position:0% +hundred computers in a thousand box of + + + align:start position:0% +hundred computers in a thousand box of +roses I just made this up see see us and + + align:start position:0% +roses I just made this up see see us and + + + align:start position:0% +roses I just made this up see see us and +see oh I just made up tastes I just said + + align:start position:0% +see oh I just made up tastes I just said + + + align:start position:0% +see oh I just made up tastes I just said +let's just make up a case where people + + align:start position:0% +let's just make up a case where people + + + align:start position:0% +let's just make up a case where people +in Columbia like roses better people in + + align:start position:0% +in Columbia like roses better people in + + + align:start position:0% +in Columbia like roses better people in +America like computers better and + + align:start position:0% +America like computers better and + + + align:start position:0% +America like computers better and +imagine we do not allow international + + align:start position:0% +imagine we do not allow international + + + align:start position:0% +imagine we do not allow international +trade this is the best case actually the + + align:start position:0% +trade this is the best case actually the + + + align:start position:0% +trade this is the best case actually the +international trade would be even more + + align:start position:0% +international trade would be even more + + + align:start position:0% +international trade would be even more +valuable with different assumptions I've + + align:start position:0% +valuable with different assumptions I've + + + align:start position:0% +valuable with different assumptions I've +made assumptions which make trade less + + align:start position:0% +made assumptions which make trade less + + + align:start position:0% +made assumptions which make trade less +valuable than it would otherwise be I've + + align:start position:0% +valuable than it would otherwise be I've + + + align:start position:0% +valuable than it would otherwise be I've +said look look columbia produces roses + + align:start position:0% +said look look columbia produces roses + + + align:start position:0% +said look look columbia produces roses +and people there like roses american who + + align:start position:0% +and people there like roses american who + + + align:start position:0% +and people there like roses american who +produces computers and people there like + + align:start position:0% +produces computers and people there like + + + align:start position:0% +produces computers and people there like +computers but not totally some US if I + + align:start position:0% +computers but not totally some US if I + + + align:start position:0% +computers but not totally some US if I +still want some roses I'm home and guys + + align:start position:0% +still want some roses I'm home and guys + + + align:start position:0% +still want some roses I'm home and guys +don't want some computers now imagine we + + align:start position:0% +don't want some computers now imagine we + + + align:start position:0% +don't want some computers now imagine we +don't allow trait what's the outcome + + align:start position:0% +don't allow trait what's the outcome + + + align:start position:0% +don't allow trait what's the outcome +well in the US we will produce we want + + align:start position:0% +well in the US we will produce we want + + + align:start position:0% +well in the US we will produce we want +like I said we want a thousand computers + + align:start position:0% +like I said we want a thousand computers + + + align:start position:0% +like I said we want a thousand computers +and five hundred roses so will produce a + + align:start position:0% +and five hundred roses so will produce a + + + align:start position:0% +and five hundred roses so will produce a +thousand compete + + align:start position:0% +thousand compete + + + align:start position:0% +thousand compete +and will consume a thousand computers so + + align:start position:0% +and will consume a thousand computers so + + + align:start position:0% +and will consume a thousand computers so +on the chart on the right you've got + + align:start position:0% +on the chart on the right you've got + + + align:start position:0% +on the chart on the right you've got +production and consumption for the US + + align:start position:0% +production and consumption for the US + + + align:start position:0% +production and consumption for the US +will produce a thousand computers + + align:start position:0% +will produce a thousand computers + + + align:start position:0% +will produce a thousand computers +consume a thousand computers we have to + + align:start position:0% +consume a thousand computers we have to + + + align:start position:0% +consume a thousand computers we have to +consume we produce there's no trade and + + align:start position:0% +consume we produce there's no trade and + + + align:start position:0% +consume we produce there's no trade and +same with rose will produce 500 consume + + align:start position:0% +same with rose will produce 500 consume + + + align:start position:0% +same with rose will produce 500 consume +500 Colombia's the flip so you end up in + + align:start position:0% +500 Colombia's the flip so you end up in + + + align:start position:0% +500 Colombia's the flip so you end up in +the world with 1500 computers being + + align:start position:0% +the world with 1500 computers being + + + align:start position:0% +the world with 1500 computers being +produced and consumed and 1500 rose is + + align:start position:0% +produced and consumed and 1500 rose is + + + align:start position:0% +produced and consumed and 1500 rose is +being produced and consumed now you + + align:start position:0% +being produced and consumed now you + + + align:start position:0% +being produced and consumed now you +might say that silly computers cost more + + align:start position:0% +might say that silly computers cost more + + + align:start position:0% +might say that silly computers cost more +than roses we'll come back to prices for + + align:start position:0% +than roses we'll come back to prices for + + + align:start position:0% +than roses we'll come back to prices for +now this is just sort of we're leaving + + align:start position:0% +now this is just sort of we're leaving + + + align:start position:0% +now this is just sort of we're leaving +prices out of it okay the point is given + + align:start position:0% +prices out of it okay the point is given + + + align:start position:0% +prices out of it okay the point is given +the tastes I'd suggested with see us and + + align:start position:0% +the tastes I'd suggested with see us and + + + align:start position:0% +the tastes I'd suggested with see us and +see oh I just made those up given those + + align:start position:0% +see oh I just made those up given those + + + align:start position:0% +see oh I just made those up given those +tastes we'll end up in a situation where + + align:start position:0% +tastes we'll end up in a situation where + + + align:start position:0% +tastes we'll end up in a situation where +every country just consumes what they + + align:start position:0% +every country just consumes what they + + + align:start position:0% +every country just consumes what they +produce because there's no trade and the + + align:start position:0% +produce because there's no trade and the + + + align:start position:0% +produce because there's no trade and the +world's the whole will produce 1500 box + + align:start position:0% +world's the whole will produce 1500 box + + + align:start position:0% +world's the whole will produce 1500 box +the Rosa 1500 computers okay now let's + + align:start position:0% +the Rosa 1500 computers okay now let's + + + align:start position:0% +the Rosa 1500 computers okay now let's +say that we allow trade what trade does + + align:start position:0% +say that we allow trade what trade does + + + align:start position:0% +say that we allow trade what trade does +is introduce economies of scope why + + align:start position:0% +is introduce economies of scope why + + + align:start position:0% +is introduce economies of scope why +because trade allows specialization flip + + align:start position:0% +because trade allows specialization flip + + + align:start position:0% +because trade allows specialization flip +to the next figure + + align:start position:0% +to the next figure + + + align:start position:0% +to the next figure +the next figures are figure for the + + align:start position:0% +the next figures are figure for the + + + align:start position:0% +the next figures are figure for the +world imagine the world only wanted + + align:start position:0% +world imagine the world only wanted + + + align:start position:0% +world imagine the world only wanted +computers that's the point on the y-axis + + align:start position:0% +computers that's the point on the y-axis + + + align:start position:0% +computers that's the point on the y-axis +then us have produced 2,000 M Colombians + + align:start position:0% +then us have produced 2,000 M Colombians + + + align:start position:0% +then us have produced 2,000 M Colombians +a thousand would have 3000 I'm back to + + align:start position:0% +a thousand would have 3000 I'm back to + + + align:start position:0% +a thousand would have 3000 I'm back to +the world only wanted roses the flip + + align:start position:0% +the world only wanted roses the flip + + + align:start position:0% +the world only wanted roses the flip +side we have 3000 but if the world wants + + align:start position:0% +side we have 3000 but if the world wants + + + align:start position:0% +side we have 3000 but if the world wants +both you get more why why is it outward + + align:start position:0% +both you get more why why is it outward + + + align:start position:0% +both you get more why why is it outward +bending when you allow trade why does + + align:start position:0% +bending when you allow trade why does + + + align:start position:0% +bending when you allow trade why does +trade this is not a technological change + + align:start position:0% +trade this is not a technological change + + + align:start position:0% +trade this is not a technological change +I'm changing technologically all we've + + align:start position:0% +I'm changing technologically all we've + + + align:start position:0% +I'm changing technologically all we've +done is take these two PPF siga buying + + align:start position:0% +done is take these two PPF siga buying + + + align:start position:0% +done is take these two PPF siga buying +that allow trade why does that suddenly + + align:start position:0% +that allow trade why does that suddenly + + + align:start position:0% +that allow trade why does that suddenly +introduce economies of scope because + + align:start position:0% +introduce economies of scope because + + + align:start position:0% +introduce economies of scope because +what a country's get to do compared to + + align:start position:0% +what a country's get to do compared to + + + align:start position:0% +what a country's get to do compared to +what they were doing before when they + + align:start position:0% +what they were doing before when they + + + align:start position:0% +what they were doing before when they +couldn't trade what do they get to do + + align:start position:0% +couldn't trade what do they get to do + + + align:start position:0% +couldn't trade what do they get to do +now specialize the u.s. specializes in + + align:start position:0% +now specialize the u.s. specializes in + + + align:start position:0% +now specialize the u.s. specializes in +and Colombia specializes in roses by + + align:start position:0% +and Colombia specializes in roses by + + + align:start position:0% +and Colombia specializes in roses by +specializing we can make more because + + align:start position:0% +specializing we can make more because + + + align:start position:0% +specializing we can make more because +that's what we're good at + + align:start position:0% +that's what we're good at + + + align:start position:0% +that's what we're good at +so by training we allow specialization + + align:start position:0% +so by training we allow specialization + + + align:start position:0% +so by training we allow specialization +without training we can't specialize + + align:start position:0% +without training we can't specialize + + + align:start position:0% +without training we can't specialize +because some guys new + + align:start position:0% +because some guys new + + + align:start position:0% +because some guys new +Rosen's got to make some roses but + + align:start position:0% +Rosen's got to make some roses but + + + align:start position:0% +Rosen's got to make some roses but +that's stupid we shouldn't make roses + + align:start position:0% +that's stupid we shouldn't make roses + + + align:start position:0% +that's stupid we shouldn't make roses +which like Columbia make roses okay if + + align:start position:0% +which like Columbia make roses okay if + + + align:start position:0% +which like Columbia make roses okay if +LeBron can't hire anyone to mow his lawn + + align:start position:0% +LeBron can't hire anyone to mow his lawn + + + align:start position:0% +LeBron can't hire anyone to mow his lawn +he's gonna mow his lawn that's stupid + + align:start position:0% +he's gonna mow his lawn that's stupid + + + align:start position:0% +he's gonna mow his lawn that's stupid +LeBron should hire son mows along play + + align:start position:0% +LeBron should hire son mows along play + + + align:start position:0% +LeBron should hire son mows along play +basketball the time by allowing trade we + + align:start position:0% +basketball the time by allowing trade we + + + align:start position:0% +basketball the time by allowing trade we +allow people to specialize and take + + align:start position:0% +allow people to specialize and take + + + align:start position:0% +allow people to specialize and take +advantage of their comparative + + align:start position:0% +advantage of their comparative + + + align:start position:0% +advantage of their comparative +advantages without trade you can't take + + align:start position:0% +advantages without trade you can't take + + + align:start position:0% +advantages without trade you can't take +advantage of competitive advantage + + align:start position:0% +advantage of competitive advantage + + + align:start position:0% +advantage of competitive advantage +without trade it doesn't matter if the + + align:start position:0% +without trade it doesn't matter if the + + + align:start position:0% +without trade it doesn't matter if the +u.s. is better person computers or Rosas + + align:start position:0% +u.s. is better person computers or Rosas + + + align:start position:0% +u.s. is better person computers or Rosas +what's produced just to turn by people's + + align:start position:0% +what's produced just to turn by people's + + + align:start position:0% +what's produced just to turn by people's +tastes okay but with trade you can + + align:start position:0% +tastes okay but with trade you can + + + align:start position:0% +tastes okay but with trade you can +specialize and that yields the outcome + + align:start position:0% +specialize and that yields the outcome + + + align:start position:0% +specialize and that yields the outcome +we discuss and figure 18 five figure 18 + + align:start position:0% +we discuss and figure 18 five figure 18 + + + align:start position:0% +we discuss and figure 18 five figure 18 +five takes the previous figure eighteen + + align:start position:0% +five takes the previous figure eighteen + + + align:start position:0% +five takes the previous figure eighteen +three and adds trade so let me go + + align:start position:0% +three and adds trade so let me go + + + align:start position:0% +three and adds trade so let me go +through this the basic the blue the PPF + + align:start position:0% +through this the basic the blue the PPF + + + align:start position:0% +through this the basic the blue the PPF +SAR the same on the left okay same PBS's + + align:start position:0% +SAR the same on the left okay same PBS's + + + align:start position:0% +SAR the same on the left okay same PBS's +before and if you look at point c o and + + align:start position:0% +before and if you look at point c o and + + + align:start position:0% +before and if you look at point c o and +see us we could have a thousand + + align:start position:0% +see us we could have a thousand + + + align:start position:0% +see us we could have a thousand +computers of 500 rows in the US or a + + align:start position:0% +computers of 500 rows in the US or a + + + align:start position:0% +computers of 500 rows in the US or a +thousand rows and 500 computers in + + align:start position:0% +thousand rows and 500 computers in + + + align:start position:0% +thousand rows and 500 computers in +colombia but now suppose we allow trade + + align:start position:0% +colombia but now suppose we allow trade + + + align:start position:0% +colombia but now suppose we allow trade +what happens now what happens now is the + + align:start position:0% +what happens now what happens now is the + + + align:start position:0% +what happens now what happens now is the +u.s. goes to producing only computers + + align:start position:0% +u.s. goes to producing only computers + + + align:start position:0% +u.s. goes to producing only computers +and colombia goes to brew sing only + + align:start position:0% +and colombia goes to brew sing only + + + align:start position:0% +and colombia goes to brew sing only +roses now let's assume just to make life + + align:start position:0% +roses now let's assume just to make life + + + align:start position:0% +roses now let's assume just to make life +easy let's just assume that people + + align:start position:0% +easy let's just assume that people + + + align:start position:0% +easy let's just assume that people +states are proportional so if there's + + align:start position:0% +states are proportional so if there's + + + align:start position:0% +states are proportional so if there's +more computers more roses they just want + + align:start position:0% +more computers more roses they just want + + + align:start position:0% +more computers more roses they just want +proportionally more of each so the US as + + align:start position:0% +proportionally more of each so the US as + + + align:start position:0% +proportionally more of each so the US as +the more of both wants a you know two + + align:start position:0% +the more of both wants a you know two + + + align:start position:0% +the more of both wants a you know two +two computers for every rose and + + align:start position:0% +two computers for every rose and + + + align:start position:0% +two computers for every rose and +colombia wants two roses for every + + align:start position:0% +colombia wants two roses for every + + + align:start position:0% +colombia wants two roses for every +computer that's just their tastes what + + align:start position:0% +computer that's just their tastes what + + + align:start position:0% +computer that's just their tastes what +happens now is we shift out to these new + + align:start position:0% +happens now is we shift out to these new + + + align:start position:0% +happens now is we shift out to these new +levels c-prime us and c-prime colombia + + align:start position:0% +levels c-prime us and c-prime colombia + + + align:start position:0% +levels c-prime us and c-prime colombia +at the new levels the US produces two + + align:start position:0% +at the new levels the US produces two + + + align:start position:0% +at the new levels the US produces two +thousand computers all the newest + + align:start position:0% +thousand computers all the newest + + + align:start position:0% +thousand computers all the newest +computers colombia produces two thousand + + align:start position:0% +computers colombia produces two thousand + + + align:start position:0% +computers colombia produces two thousand +roses the world as a whole ends up with + + align:start position:0% +roses the world as a whole ends up with + + + align:start position:0% +roses the world as a whole ends up with +more flip back to pages and look at the + + align:start position:0% +more flip back to pages and look at the + + + align:start position:0% +more flip back to pages and look at the +table on the right the world's whole + + align:start position:0% +table on the right the world's whole + + + align:start position:0% +table on the right the world's whole +ended up with 1500 rows and 1,500 + + align:start position:0% +ended up with 1500 rows and 1,500 + + + align:start position:0% +ended up with 1500 rows and 1,500 +computers now the world's the whole ends + + align:start position:0% +computers now the world's the whole ends + + + align:start position:0% +computers now the world's the whole ends +up with two thousand roses and two + + align:start position:0% +up with two thousand roses and two + + + align:start position:0% +up with two thousand roses and two +thousand computers + + align:start position:0% +thousand computers + + + align:start position:0% +thousand computers +what happened nothing changed + + align:start position:0% +what happened nothing changed + + + align:start position:0% +what happened nothing changed +technologically st. PPS years before all + + align:start position:0% +technologically st. PPS years before all + + + align:start position:0% +technologically st. PPS years before all +the change is by training we allowed + + align:start position:0% +the change is by training we allowed + + + align:start position:0% +the change is by training we allowed +people to exploit their comparative + + align:start position:0% +people to exploit their comparative + + + align:start position:0% +people to exploit their comparative +advantage through specialization without + + align:start position:0% +advantage through specialization without + + + align:start position:0% +advantage through specialization without +trading the US was inefficiently + + align:start position:0% +trading the US was inefficiently + + + align:start position:0% +trading the US was inefficiently +producing roses and Colombia was + + align:start position:0% +producing roses and Colombia was + + + align:start position:0% +producing roses and Colombia was +inefficiently producing computers with + + align:start position:0% +inefficiently producing computers with + + + align:start position:0% +inefficiently producing computers with +trading we've now opened up the + + align:start position:0% +trading we've now opened up the + + + align:start position:0% +trading we've now opened up the +possibility that they've been + + align:start position:0% +possibility that they've been + + + align:start position:0% +possibility that they've been +specializing what they're good at and + + align:start position:0% +specializing what they're good at and + + + align:start position:0% +specializing what they're good at and +the world's the whole ends up better off + + align:start position:0% +the world's the whole ends up better off + + + align:start position:0% +the world's the whole ends up better off +okay so and look at both countries both + + align:start position:0% +okay so and look at both countries both + + + align:start position:0% +okay so and look at both countries both +countries end up with more consumption + + align:start position:0% +countries end up with more consumption + + + align:start position:0% +countries end up with more consumption +the they each get the u.s. gets more + + align:start position:0% +the they each get the u.s. gets more + + + align:start position:0% +the they each get the u.s. gets more +computers so flip back and forth in 1813 + + align:start position:0% +computers so flip back and forth in 1813 + + + align:start position:0% +computers so flip back and forth in 1813 +eighteen five the u.s. goes from five + + align:start position:0% +eighteen five the u.s. goes from five + + + align:start position:0% +eighteen five the u.s. goes from five +hundred rows and a thousand computers to + + align:start position:0% +hundred rows and a thousand computers to + + + align:start position:0% +hundred rows and a thousand computers to +750 rows and twelve fifty computers + + align:start position:0% +750 rows and twelve fifty computers + + + align:start position:0% +750 rows and twelve fifty computers +Columbia goes from 1250 roses goes from + + align:start position:0% +Columbia goes from 1250 roses goes from + + + align:start position:0% +Columbia goes from 1250 roses goes from +I'm sorry a thousand rows in five + + align:start position:0% +I'm sorry a thousand rows in five + + + align:start position:0% +I'm sorry a thousand rows in five +hundred computers to 1250 rows and 750 + + align:start position:0% +hundred computers to 1250 rows and 750 + + + align:start position:0% +hundred computers to 1250 rows and 750 +computer computers now the split between + + align:start position:0% +computer computers now the split between + + + align:start position:0% +computer computers now the split between +rows computers here is is not + + align:start position:0% +rows computers here is is not + + + align:start position:0% +rows computers here is is not +determinate that's just made up I made + + align:start position:0% +determinate that's just made up I made + + + align:start position:0% +determinate that's just made up I made +up what taste look like the point to see + + align:start position:0% +up what taste look like the point to see + + + align:start position:0% +up what taste look like the point to see +the point C and C prime that's just made + + align:start position:0% +the point C and C prime that's just made + + + align:start position:0% +the point C and C prime that's just made +up what you care about is the bottom + + align:start position:0% +up what you care about is the bottom + + + align:start position:0% +up what you care about is the bottom +panel we gave us the bottom panel well + + align:start position:0% +panel we gave us the bottom panel well + + + align:start position:0% +panel we gave us the bottom panel well +you care about is the fact that the + + align:start position:0% +you care about is the fact that the + + + align:start position:0% +you care about is the fact that the +world as a whole now has more rows and + + align:start position:0% +world as a whole now has more rows and + + + align:start position:0% +world as a whole now has more rows and +more computers in it and that is the + + align:start position:0% +more computers in it and that is the + + + align:start position:0% +more computers in it and that is the +mechanics of why international trade + + align:start position:0% +mechanics of why international trade + + + align:start position:0% +mechanics of why international trade +expands our production possibility + + align:start position:0% +expands our production possibility + + + align:start position:0% +expands our production possibility +frontier we have more goods in the world + + align:start position:0% +frontier we have more goods in the world + + + align:start position:0% +frontier we have more goods in the world +once we can trade not because I mean you + + align:start position:0% +once we can trade not because I mean you + + + align:start position:0% +once we can trade not because I mean you +still simmer Pikachu and when I + + align:start position:0% +still simmer Pikachu and when I + + + align:start position:0% +still simmer Pikachu and when I +allow trade between you and your friend + + align:start position:0% +allow trade between you and your friend + + + align:start position:0% +allow trade between you and your friend +that doesn't create any more goods each + + align:start position:0% +that doesn't create any more goods each + + + align:start position:0% +that doesn't create any more goods each +have two cards but in the real world + + align:start position:0% +have two cards but in the real world + + + align:start position:0% +have two cards but in the real world +that creates trade because of production + + align:start position:0% +that creates trade because of production + + + align:start position:0% +that creates trade because of production +allows people to specialize and that's + + align:start position:0% +allows people to specialize and that's + + + align:start position:0% +allows people to specialize and that's +the beauty of trade alright + + align:start position:0% +the beauty of trade alright + + + align:start position:0% +the beauty of trade alright +well come back next time and do a + + align:start position:0% +well come back next time and do a + + + align:start position:0% +well come back next time and do a +welfare analysis of why of talking about + + align:start position:0% +welfare analysis of why of talking about + + + align:start position:0% +welfare analysis of why of talking about +why international trade makes people + + align:start position:0% +why international trade makes people + + + align:start position:0% +why international trade makes people +better off \ No newline at end of file diff --git a/BOryXuUMjI0.txt b/BOryXuUMjI0.txt new file mode 100644 index 0000000000000000000000000000000000000000..e207adc591767e23f7c75b7dae372ac903a752cf --- /dev/null +++ b/BOryXuUMjI0.txt @@ -0,0 +1,9339 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +all right well good morning everyone I'm + + align:start position:0% +all right well good morning everyone I'm + + + align:start position:0% +all right well good morning everyone I'm +not Bob field but I'm Troy nice to see + + align:start position:0% +not Bob field but I'm Troy nice to see + + + align:start position:0% +not Bob field but I'm Troy nice to see +everyone so I'm here we're gonna spend + + align:start position:0% +everyone so I'm here we're gonna spend + + + align:start position:0% +everyone so I'm here we're gonna spend +the next couple of lectures talking + + align:start position:0% +the next couple of lectures talking + + + align:start position:0% +the next couple of lectures talking +about electronic structure theory and at + + align:start position:0% +about electronic structure theory and at + + + align:start position:0% +about electronic structure theory and at +this point I'll I'll give you the I'll + + align:start position:0% +this point I'll I'll give you the I'll + + + align:start position:0% +this point I'll I'll give you the I'll +give you the big reveal which is that at + + align:start position:0% +give you the big reveal which is that at + + + align:start position:0% +give you the big reveal which is that at +this point you if you you have already + + align:start position:0% +this point you if you you have already + + + align:start position:0% +this point you if you you have already +encountered virtually every problem that + + align:start position:0% +encountered virtually every problem that + + + align:start position:0% +encountered virtually every problem that +you can solve by hand in electronic + + align:start position:0% +you can solve by hand in electronic + + + align:start position:0% +you can solve by hand in electronic +structure theory so there's a handful of + + align:start position:0% +structure theory so there's a handful of + + + align:start position:0% +structure theory so there's a handful of +other things you could do if you really + + align:start position:0% +other things you could do if you really + + + align:start position:0% +other things you could do if you really +like knew your hypergeometric functions + + align:start position:0% +like knew your hypergeometric functions + + + align:start position:0% +like knew your hypergeometric functions +and some things like this but basically + + align:start position:0% +and some things like this but basically + + + align:start position:0% +and some things like this but basically +every electronic structure problem that + + align:start position:0% +every electronic structure problem that + + + align:start position:0% +every electronic structure problem that +you can solve by hand you've already + + align:start position:0% +you can solve by hand you've already + + + align:start position:0% +you can solve by hand you've already +encountered and so if chemistry relied + + align:start position:0% +encountered and so if chemistry relied + + + align:start position:0% +encountered and so if chemistry relied +on us being able to solve things by hand + + align:start position:0% +on us being able to solve things by hand + + + align:start position:0% +on us being able to solve things by hand +we wouldn't get very far be pretty + + align:start position:0% +we wouldn't get very far be pretty + + + align:start position:0% +we wouldn't get very far be pretty +limited in what we can do so we end up + + align:start position:0% +limited in what we can do so we end up + + + align:start position:0% +limited in what we can do so we end up +using the fact that we have computers + + align:start position:0% +using the fact that we have computers + + + align:start position:0% +using the fact that we have computers +and computers are far more good at doing + + align:start position:0% +and computers are far more good at doing + + + align:start position:0% +and computers are far more good at doing +tedious repetitive things than human + + align:start position:0% +tedious repetitive things than human + + + align:start position:0% +tedious repetitive things than human +beings are they don't complain at all + + align:start position:0% +beings are they don't complain at all + + + align:start position:0% +beings are they don't complain at all +and so we can use computers to do fairly + + align:start position:0% +and so we can use computers to do fairly + + + align:start position:0% +and so we can use computers to do fairly +neat things so I'll show you a couple of + + align:start position:0% +neat things so I'll show you a couple of + + + align:start position:0% +neat things so I'll show you a couple of +just a couple of quick pictures here of + + align:start position:0% +just a couple of quick pictures here of + + + align:start position:0% +just a couple of quick pictures here of +things that you can we can do so if you + + align:start position:0% +things that you can we can do so if you + + + align:start position:0% +things that you can we can do so if you +open up any research paper these days + + align:start position:0% +open up any research paper these days + + + align:start position:0% +open up any research paper these days +even if it's just in that synthesis you + + align:start position:0% +even if it's just in that synthesis you + + + align:start position:0% +even if it's just in that synthesis you +know we made this catalyst we did this + + align:start position:0% +know we made this catalyst we did this + + + align:start position:0% +know we made this catalyst we did this +thing whatever there's always some part + + align:start position:0% +thing whatever there's always some part + + + align:start position:0% +thing whatever there's always some part +of the part of it where they say well + + align:start position:0% +of the part of it where they say well + + + align:start position:0% +of the part of it where they say well +when we did a calculation and you know + + align:start position:0% +when we did a calculation and you know + + + align:start position:0% +when we did a calculation and you know +this is what the structure looks like or + + align:start position:0% +this is what the structure looks like or + + + align:start position:0% +this is what the structure looks like or +this is what the orbitals look like or + + align:start position:0% +this is what the orbitals look like or + + + align:start position:0% +this is what the orbitals look like or +something like this so this was actually + + align:start position:0% +something like this so this was actually + + + align:start position:0% +something like this so this was actually +a calculation we are computational + + align:start position:0% +a calculation we are computational + + + align:start position:0% +a calculation we are computational +chemists I guess I'll use this screen + + align:start position:0% +chemists I guess I'll use this screen + + + align:start position:0% +chemists I guess I'll use this screen +over here am i using is this the one + + align:start position:0% +over here am i using is this the one + + + align:start position:0% +over here am i using is this the one +that you're are you filming this one + + align:start position:0% +that you're are you filming this one + + + align:start position:0% +that you're are you filming this one +this one aren't so I'll film this one go + + align:start position:0% +this one aren't so I'll film this one go + + + align:start position:0% +this one aren't so I'll film this one go +this one breaking the fourth wall there + + align:start position:0% +this one breaking the fourth wall there + + + align:start position:0% +this one breaking the fourth wall there +so this is a picture of the homo the + + align:start position:0% +so this is a picture of the homo the + + + align:start position:0% +so this is a picture of the homo the +reactive orbital in a water splitting + + align:start position:0% +reactive orbital in a water splitting + + + align:start position:0% +reactive orbital in a water splitting +catalyst that we computed so you can see + + align:start position:0% +catalyst that we computed so you can see + + + align:start position:0% +catalyst that we computed so you can see +that there's you know 50 60 atoms here + + align:start position:0% +that there's you know 50 60 atoms here + + + align:start position:0% +that there's you know 50 60 atoms here +probably several hundred electrons we + + align:start position:0% +probably several hundred electrons we + + + align:start position:0% +probably several hundred electrons we +did not do this by hand we didn't draw + + align:start position:0% +did not do this by hand we didn't draw + + + align:start position:0% +did not do this by hand we didn't draw +the surfaces by hand the computer did + + align:start position:0% +the surfaces by hand the computer did + + + align:start position:0% +the surfaces by hand the computer did +all of this for us and you can also do + + align:start position:0% +all of this for us and you can also do + + + align:start position:0% +all of this for us and you can also do +things like look at chemical reactions + + align:start position:0% +things like look at chemical reactions + + + align:start position:0% +things like look at chemical reactions +and run dynamics so we can do there we + + align:start position:0% +and run dynamics so we can do there we + + + align:start position:0% +and run dynamics so we can do there we +go so you can run dynamics of molecules + + align:start position:0% +go so you can run dynamics of molecules + + + align:start position:0% +go so you can run dynamics of molecules +so this is a particular molecule in + + align:start position:0% +so this is a particular molecule in + + + align:start position:0% +so this is a particular molecule in +solution and we can use + + align:start position:0% +solution and we can use + + + align:start position:0% +solution and we can use +the electronic energy in order to govern + + align:start position:0% +the electronic energy in order to govern + + + align:start position:0% +the electronic energy in order to govern +the dynamics of the molecule and + + align:start position:0% +the dynamics of the molecule and + + + align:start position:0% +the dynamics of the molecule and +actually computer can actually predict + + align:start position:0% +actually computer can actually predict + + + align:start position:0% +actually computer can actually predict +for us whether this molecule is gonna + + align:start position:0% +for us whether this molecule is gonna + + + align:start position:0% +for us whether this molecule is gonna +react what it's going to do how it's + + align:start position:0% +react what it's going to do how it's + + + align:start position:0% +react what it's going to do how it's +gonna behave and so in one solution say + + align:start position:0% +gonna behave and so in one solution say + + + align:start position:0% +gonna behave and so in one solution say +versus another or at one particular + + align:start position:0% +versus another or at one particular + + + align:start position:0% +versus another or at one particular +temperature versus another are those + + align:start position:0% +temperature versus another are those + + + align:start position:0% +temperature versus another are those +kinds of things and all of these again + + align:start position:0% +kinds of things and all of these again + + + align:start position:0% +kinds of things and all of these again +are based off of the idea that we can + + align:start position:0% +are based off of the idea that we can + + + align:start position:0% +are based off of the idea that we can +use computers to solve problems in + + align:start position:0% +use computers to solve problems in + + + align:start position:0% +use computers to solve problems in +electronic structure or at least + + align:start position:0% +electronic structure or at least + + + align:start position:0% +electronic structure or at least +approximately solve problems that we + + align:start position:0% +approximately solve problems that we + + + align:start position:0% +approximately solve problems that we +couldn't do by hand and so what what the + + align:start position:0% +couldn't do by hand and so what what the + + + align:start position:0% +couldn't do by hand and so what what the +goal over the next couple lectures is is + + align:start position:0% +goal over the next couple lectures is is + + + align:start position:0% +goal over the next couple lectures is is +for us to learn enough of the basics so + + align:start position:0% +for us to learn enough of the basics so + + + align:start position:0% +for us to learn enough of the basics so +that you you can do some calculations + + align:start position:0% +that you you can do some calculations + + + align:start position:0% +that you you can do some calculations +like this yourselves and then see see + + align:start position:0% +like this yourselves and then see see + + + align:start position:0% +like this yourselves and then see see +what what you what you can do with that + + align:start position:0% +what what you what you can do with that + + + align:start position:0% +what what you what you can do with that +alright so now I will switch over the + + align:start position:0% +alright so now I will switch over the + + + align:start position:0% +alright so now I will switch over the +want to notice one of the other you'll + + align:start position:0% +want to notice one of the other you'll + + + align:start position:0% +want to notice one of the other you'll +find one the other differences which is + + align:start position:0% +find one the other differences which is + + + align:start position:0% +find one the other differences which is +that I don't and don't like the feeling + + align:start position:0% +that I don't and don't like the feeling + + + align:start position:0% +that I don't and don't like the feeling +of chalk on my fingers so I use my iPad + + align:start position:0% +of chalk on my fingers so I use my iPad + + + align:start position:0% +of chalk on my fingers so I use my iPad +as a chalk board so the rest of this + + align:start position:0% +as a chalk board so the rest of this + + + align:start position:0% +as a chalk board so the rest of this +will all be on the iPad there we go + + align:start position:0% +will all be on the iPad there we go + + + align:start position:0% +will all be on the iPad there we go +so for those of you who want to you may + + align:start position:0% +so for those of you who want to you may + + + align:start position:0% +so for those of you who want to you may +not have gotten that gotten them gotten + + align:start position:0% +not have gotten that gotten them gotten + + + align:start position:0% +not have gotten that gotten them gotten +them this time but I will add the idle + + align:start position:0% +them this time but I will add the idle + + + align:start position:0% +them this time but I will add the idle +I've literally posted the but what I'm + + align:start position:0% +I've literally posted the but what I'm + + + align:start position:0% +I've literally posted the but what I'm +gonna be writing on here these blank + + align:start position:0% +gonna be writing on here these blank + + + align:start position:0% +gonna be writing on here these blank +notes online you can download them and + + align:start position:0% +notes online you can download them and + + + align:start position:0% +notes online you can download them and +print them off if you want if you have + + align:start position:0% +print them off if you want if you have + + + align:start position:0% +print them off if you want if you have +an iPad and you like to take an or + + align:start position:0% +an iPad and you like to take an or + + + align:start position:0% +an iPad and you like to take an or +computer and you like to take notes on + + align:start position:0% +computer and you like to take notes on + + + align:start position:0% +computer and you like to take notes on +that you can download them to your iPad + + align:start position:0% +that you can download them to your iPad + + + align:start position:0% +that you can download them to your iPad +or computer and take notes that way but + + align:start position:0% +or computer and take notes that way but + + + align:start position:0% +or computer and take notes that way but +I find it's just it's good because there + + align:start position:0% +I find it's just it's good because there + + + align:start position:0% +I find it's just it's good because there +are some things that take a long time + + align:start position:0% +are some things that take a long time + + + align:start position:0% +are some things that take a long time +for me to write at the board and that it + + align:start position:0% +for me to write at the board and that it + + + align:start position:0% +for me to write at the board and that it +would take a long time for you to write + + align:start position:0% +would take a long time for you to write + + + align:start position:0% +would take a long time for you to write +in your notes and we can just sort of + + align:start position:0% +in your notes and we can just sort of + + + align:start position:0% +in your notes and we can just sort of +have them written down in advance so the + + align:start position:0% +have them written down in advance so the + + + align:start position:0% +have them written down in advance so the +starting point for all of these things + + align:start position:0% +starting point for all of these things + + + align:start position:0% +starting point for all of these things +that you can do on a computer for + + align:start position:0% +that you can do on a computer for + + + align:start position:0% +that you can do on a computer for +electronic structure theory we start + + align:start position:0% +electronic structure theory we start + + + align:start position:0% +electronic structure theory we start +with the born-oppenheimer approximation + + align:start position:0% +with the born-oppenheimer approximation + + + align:start position:0% +with the born-oppenheimer approximation +so the born-oppenheimer approximation + + align:start position:0% +so the born-oppenheimer approximation + + + align:start position:0% +so the born-oppenheimer approximation +was the idea that because the nuclei are + + align:start position:0% +was the idea that because the nuclei are + + + align:start position:0% +was the idea that because the nuclei are +very heavy you can clamp their positions + + align:start position:0% +very heavy you can clamp their positions + + + align:start position:0% +very heavy you can clamp their positions +down to some particular values so in + + align:start position:0% +down to some particular values so in + + + align:start position:0% +down to some particular values so in +this particular case here in this + + align:start position:0% +this particular case here in this + + + align:start position:0% +this particular case here in this +equation I have it such that big R here + + align:start position:0% +equation I have it such that big R here + + + align:start position:0% +equation I have it such that big R here +are the nuclear positions so there's + + align:start position:0% +are the nuclear positions so there's + + + align:start position:0% +are the nuclear positions so there's +going to be more than one nucleus + + align:start position:0% +going to be more than one nucleus + + + align:start position:0% +going to be more than one nucleus +generally so there's gonna be R 1 R 2 R + + align:start position:0% +generally so there's gonna be R 1 R 2 R + + + align:start position:0% +generally so there's gonna be R 1 R 2 R +3 all those crammed together I'm just + + align:start position:0% +3 all those crammed together I'm just + + + align:start position:0% +3 all those crammed together I'm just +going to denote big R and that's where + + align:start position:0% +going to denote big R and that's where + + + align:start position:0% +going to denote big R and that's where +the nuclei are and so + + align:start position:0% +the nuclei are and so + + + align:start position:0% +the nuclei are and so +in the born-oppenheimer approximation we + + align:start position:0% +in the born-oppenheimer approximation we + + + align:start position:0% +in the born-oppenheimer approximation we +clamp the nuclei down and then what + + align:start position:0% +clamp the nuclei down and then what + + + align:start position:0% +clamp the nuclei down and then what +we're left with is the electrons the + + align:start position:0% +we're left with is the electrons the + + + align:start position:0% +we're left with is the electrons the +electrons whiz around they move in the + + align:start position:0% +electrons whiz around they move in the + + + align:start position:0% +electrons whiz around they move in the +field dictated by those by those nuclei + + align:start position:0% +field dictated by those by those nuclei + + + align:start position:0% +field dictated by those by those nuclei +so we have a Schrodinger equation that + + align:start position:0% +so we have a Schrodinger equation that + + + align:start position:0% +so we have a Schrodinger equation that +describes the motion of the electrons in + + align:start position:0% +describes the motion of the electrons in + + + align:start position:0% +describes the motion of the electrons in +the presence of the nuclei and so here + + align:start position:0% +the presence of the nuclei and so here + + + align:start position:0% +the presence of the nuclei and so here +I'm using the lowercase letters + + align:start position:0% +I'm using the lowercase letters + + + align:start position:0% +I'm using the lowercase letters +lowercase R so again many electron so R + + align:start position:0% +lowercase R so again many electron so R + + + align:start position:0% +lowercase R so again many electron so R +1 R 2 R 3 so on and so forth and it's + + align:start position:0% +1 R 2 R 3 so on and so forth and it's + + + align:start position:0% +1 R 2 R 3 so on and so forth and it's +the electrons that are really doing all + + align:start position:0% +the electrons that are really doing all + + + align:start position:0% +the electrons that are really doing all +that all the dirty work in this equation + + align:start position:0% +that all the dirty work in this equation + + + align:start position:0% +that all the dirty work in this equation +they're the ones that are moving around + + align:start position:0% +they're the ones that are moving around + + + align:start position:0% +they're the ones that are moving around +I've clamped the nuclei down there just + + align:start position:0% +I've clamped the nuclei down there just + + + align:start position:0% +I've clamped the nuclei down there just +parameters in this equation and so what + + align:start position:0% +parameters in this equation and so what + + + align:start position:0% +parameters in this equation and so what +I have is I have an electronic wave + + align:start position:0% +I have is I have an electronic wave + + + align:start position:0% +I have is I have an electronic wave +function that describes the distribution + + align:start position:0% +function that describes the distribution + + + align:start position:0% +function that describes the distribution +in electrons I have an electronic + + align:start position:0% +in electrons I have an electronic + + + align:start position:0% +in electrons I have an electronic +Hamiltonian that governs the motion of + + align:start position:0% +Hamiltonian that governs the motion of + + + align:start position:0% +Hamiltonian that governs the motion of +the electrons I'm gonna have an + + align:start position:0% +the electrons I'm gonna have an + + + align:start position:0% +the electrons I'm gonna have an +electronic energy after I've solved this + + align:start position:0% +electronic energy after I've solved this + + + align:start position:0% +electronic energy after I've solved this +Schrodinger equation and the nice thing + + align:start position:0% +Schrodinger equation and the nice thing + + + align:start position:0% +Schrodinger equation and the nice thing +about this is that for an arbitrary + + align:start position:0% +about this is that for an arbitrary + + + align:start position:0% +about this is that for an arbitrary +number of electrons in an arbitrary + + align:start position:0% +number of electrons in an arbitrary + + + align:start position:0% +number of electrons in an arbitrary +number of nuclei I can in one line in + + align:start position:0% +number of nuclei I can in one line in + + + align:start position:0% +number of nuclei I can in one line in +about 10 seconds write down the + + align:start position:0% +about 10 seconds write down the + + + align:start position:0% +about 10 seconds write down the +Hamiltonian so the Hamiltonian is pretty + + align:start position:0% +Hamiltonian so the Hamiltonian is pretty + + + align:start position:0% +Hamiltonian so the Hamiltonian is pretty +easy to write down I've even written it + + align:start position:0% +easy to write down I've even written it + + + align:start position:0% +easy to write down I've even written it +right here + + align:start position:0% +right here + + + align:start position:0% +right here +so I did use the cheat of using atomic + + align:start position:0% +so I did use the cheat of using atomic + + + align:start position:0% +so I did use the cheat of using atomic +units so the reason there's no H bars or + + align:start position:0% +units so the reason there's no H bars or + + + align:start position:0% +units so the reason there's no H bars or +mass of the electrons or any of that + + align:start position:0% +mass of the electrons or any of that + + + align:start position:0% +mass of the electrons or any of that +appearing in here is because I chose + + align:start position:0% +appearing in here is because I chose + + + align:start position:0% +appearing in here is because I chose +atomic units but then the ingredients of + + align:start position:0% +atomic units but then the ingredients of + + + align:start position:0% +atomic units but then the ingredients of +my Hamiltonian are all pretty + + align:start position:0% +my Hamiltonian are all pretty + + + align:start position:0% +my Hamiltonian are all pretty +well-defined so I'll have some kinetic + + align:start position:0% +well-defined so I'll have some kinetic + + + align:start position:0% +well-defined so I'll have some kinetic +energy and that kinetic energy will just + + align:start position:0% +energy and that kinetic energy will just + + + align:start position:0% +energy and that kinetic energy will just +be for the electrons because the nuclei + + align:start position:0% +be for the electrons because the nuclei + + + align:start position:0% +be for the electrons because the nuclei +are fixed I'll have an electron electron + + align:start position:0% +are fixed I'll have an electron electron + + + align:start position:0% +are fixed I'll have an electron electron +repulsion term so of course the + + align:start position:0% +repulsion term so of course the + + + align:start position:0% +repulsion term so of course the +electrons repel each repel each other + + align:start position:0% +electrons repel each repel each other + + + align:start position:0% +electrons repel each repel each other +I'll have an electron nuclear attraction + + align:start position:0% +I'll have an electron nuclear attraction + + + align:start position:0% +I'll have an electron nuclear attraction +term because the nuclei are fixed in + + align:start position:0% +term because the nuclei are fixed in + + + align:start position:0% +term because the nuclei are fixed in +positions and the electrons feel a + + align:start position:0% +positions and the electrons feel a + + + align:start position:0% +positions and the electrons feel a +potential due to that and then I have a + + align:start position:0% +potential due to that and then I have a + + + align:start position:0% +potential due to that and then I have a +nuclear-nuclear repulsion term and in + + align:start position:0% +nuclear-nuclear repulsion term and in + + + align:start position:0% +nuclear-nuclear repulsion term and in +this case because the nuclei are fixed + + align:start position:0% +this case because the nuclei are fixed + + + align:start position:0% +this case because the nuclei are fixed +that nuclear-nuclear repulsion is just a + + align:start position:0% +that nuclear-nuclear repulsion is just a + + + align:start position:0% +that nuclear-nuclear repulsion is just a +number because I've know where all my + + align:start position:0% +number because I've know where all my + + + align:start position:0% +number because I've know where all my +nuclei are they have some particular + + align:start position:0% +nuclei are they have some particular + + + align:start position:0% +nuclei are they have some particular +repulsion energy that's just some number + + align:start position:0% +repulsion energy that's just some number + + + align:start position:0% +repulsion energy that's just some number +that I add onto my Hamiltonian there but + + align:start position:0% +that I add onto my Hamiltonian there but + + + align:start position:0% +that I add onto my Hamiltonian there but +if I put all those things together + + align:start position:0% +if I put all those things together + + + align:start position:0% +if I put all those things together +I get the Hamiltonian so I can write + + align:start position:0% +I get the Hamiltonian so I can write + + + align:start position:0% +I get the Hamiltonian so I can write +down the Hamiltonian without too much + + align:start position:0% +down the Hamiltonian without too much + + + align:start position:0% +down the Hamiltonian without too much +difficulty but of course the interesting + + align:start position:0% +difficulty but of course the interesting + + + align:start position:0% +difficulty but of course the interesting +thing here is this Hamiltonian depends + + align:start position:0% +thing here is this Hamiltonian depends + + + align:start position:0% +thing here is this Hamiltonian depends +on these nuclear positions so I have to + + align:start position:0% +on these nuclear positions so I have to + + + align:start position:0% +on these nuclear positions so I have to +know what we're depending on where the + + align:start position:0% +know what we're depending on where the + + + align:start position:0% +know what we're depending on where the +nuclei are I'm parametric parametrically + + align:start position:0% +nuclei are I'm parametric parametrically + + + align:start position:0% +nuclei are I'm parametric parametrically +changing this Hamiltonian that changes H + + align:start position:0% +changing this Hamiltonian that changes H + + + align:start position:0% +changing this Hamiltonian that changes H +and it also changes the eigen value the + + align:start position:0% +and it also changes the eigen value the + + + align:start position:0% +and it also changes the eigen value the +electronic eigen value E and so there's + + align:start position:0% +electronic eigen value E and so there's + + + align:start position:0% +electronic eigen value E and so there's +an obvious question well what is this + + align:start position:0% +an obvious question well what is this + + + align:start position:0% +an obvious question well what is this +electronic eigen value it turns out to + + align:start position:0% +electronic eigen value it turns out to + + + align:start position:0% +electronic eigen value it turns out to +be a very important thing we will + + align:start position:0% +be a very important thing we will + + + align:start position:0% +be a very important thing we will +typically call this thing a potential + + align:start position:0% + + + + align:start position:0% + +energy surface and it turns out it turns + + align:start position:0% +energy surface and it turns out it turns + + + align:start position:0% +energy surface and it turns out it turns +out to Jen to govern a whole host of + + align:start position:0% +out to Jen to govern a whole host of + + + align:start position:0% +out to Jen to govern a whole host of +chemical phenomena so the first thing + + align:start position:0% +chemical phenomena so the first thing + + + align:start position:0% +chemical phenomena so the first thing +that it could generate that it that + + align:start position:0% +that it could generate that it that + + + align:start position:0% +that it could generate that it that +we've we've actually we can look at + + align:start position:0% +we've we've actually we can look at + + + align:start position:0% +we've we've actually we can look at +we've already actually seen potential + + align:start position:0% +we've already actually seen potential + + + align:start position:0% +we've already actually seen potential +energy surfaces so on the left-hand side + + align:start position:0% +energy surfaces so on the left-hand side + + + align:start position:0% +energy surfaces so on the left-hand side +here I have the picture from the case of + + align:start position:0% +here I have the picture from the case of + + + align:start position:0% +here I have the picture from the case of +H 2 plus so here we had the energy of + + align:start position:0% +H 2 plus so here we had the energy of + + + align:start position:0% +H 2 plus so here we had the energy of +the Sigma orbital as a function of R it + + align:start position:0% +the Sigma orbital as a function of R it + + + align:start position:0% +the Sigma orbital as a function of R it +formed some bond so as we brought that + + align:start position:0% +formed some bond so as we brought that + + + align:start position:0% +formed some bond so as we brought that +Vadar shorter the Sigma orbital formed a + + align:start position:0% +Vadar shorter the Sigma orbital formed a + + + align:start position:0% +Vadar shorter the Sigma orbital formed a +bond and we had also this Sigma star + + align:start position:0% +bond and we had also this Sigma star + + + align:start position:0% +bond and we had also this Sigma star +orbital as a function of R when who + + align:start position:0% +orbital as a function of R when who + + + align:start position:0% +orbital as a function of R when who +brought the atoms together and that one + + align:start position:0% +brought the atoms together and that one + + + align:start position:0% +brought the atoms together and that one +there was no bond those Fermi energy + + align:start position:0% +there was no bond those Fermi energy + + + align:start position:0% +there was no bond those Fermi energy +just went straight up so we've got two + + align:start position:0% +just went straight up so we've got two + + + align:start position:0% +just went straight up so we've got two +of these things and I should label my + + align:start position:0% +of these things and I should label my + + + align:start position:0% +of these things and I should label my +axes so I'm plotting here is the energy + + align:start position:0% + + + + align:start position:0% + +as a function of the bond distance R so + + align:start position:0% +as a function of the bond distance R so + + + align:start position:0% +as a function of the bond distance R so +this was our first example of a + + align:start position:0% +this was our first example of a + + + align:start position:0% +this was our first example of a +potential energy surface electronic + + align:start position:0% +potential energy surface electronic + + + align:start position:0% +potential energy surface electronic +energy as a function of R and we see + + align:start position:0% +energy as a function of R and we see + + + align:start position:0% +energy as a function of R and we see +that it taught us about the bond the + + align:start position:0% +that it taught us about the bond the + + + align:start position:0% +that it taught us about the bond the +bond strength so forth there's one other + + align:start position:0% +bond strength so forth there's one other + + + align:start position:0% +bond strength so forth there's one other +thing that that this picture reminds me + + align:start position:0% +thing that that this picture reminds me + + + align:start position:0% +thing that that this picture reminds me +of is and that's that for the same + + align:start position:0% +of is and that's that for the same + + + align:start position:0% +of is and that's that for the same +problem here I actually had two + + align:start position:0% +problem here I actually had two + + + align:start position:0% +problem here I actually had two +different potential energy surfaces I + + align:start position:0% +different potential energy surfaces I + + + align:start position:0% +different potential energy surfaces I +have the Sigma's potential a new surface + + align:start position:0% +have the Sigma's potential a new surface + + + align:start position:0% +have the Sigma's potential a new surface +and Sigma star and that's because I left + + align:start position:0% +and Sigma star and that's because I left + + + align:start position:0% +and Sigma star and that's because I left +something out in my Schrodinger equation + + align:start position:0% +something out in my Schrodinger equation + + + align:start position:0% +something out in my Schrodinger equation +up here there's of course an index I + + align:start position:0% +up here there's of course an index I + + + align:start position:0% +up here there's of course an index I +have different eigenfunction + + align:start position:0% +have different eigenfunction + + + align:start position:0% +have different eigenfunction +of the Schrodinger equation so I have an + + align:start position:0% +of the Schrodinger equation so I have an + + + align:start position:0% +of the Schrodinger equation so I have an +electronic Hamiltonian you'll have many + + align:start position:0% +electronic Hamiltonian you'll have many + + + align:start position:0% +electronic Hamiltonian you'll have many +different eigenfunctions so I have an + + align:start position:0% +different eigenfunctions so I have an + + + align:start position:0% +different eigenfunctions so I have an +index n for those eigen functions and + + align:start position:0% +index n for those eigen functions and + + + align:start position:0% +index n for those eigen functions and +each of those eigen functions will have + + align:start position:0% +each of those eigen functions will have + + + align:start position:0% +each of those eigen functions will have +a different energy and each of those + + align:start position:0% +a different energy and each of those + + + align:start position:0% +a different energy and each of those +energies is a different potential energy + + align:start position:0% +energies is a different potential energy + + + align:start position:0% +energies is a different potential energy +surface so the Sigma state was the + + align:start position:0% +surface so the Sigma state was the + + + align:start position:0% +surface so the Sigma state was the +lowest solution the Sigma star state was + + align:start position:0% +lowest solution the Sigma star state was + + + align:start position:0% +lowest solution the Sigma star state was +the next lowest solution they had + + align:start position:0% +the next lowest solution they had + + + align:start position:0% +the next lowest solution they had +different potential surfaces but I will + + align:start position:0% +different potential surfaces but I will + + + align:start position:0% +different potential surfaces but I will +often not refer to potential energy + + align:start position:0% +often not refer to potential energy + + + align:start position:0% +often not refer to potential energy +surfaces plural but instead to potential + + align:start position:0% +surfaces plural but instead to potential + + + align:start position:0% +surfaces plural but instead to potential +energy surface singular because most + + align:start position:0% +energy surface singular because most + + + align:start position:0% +energy surface singular because most +chemistry occurs on the lowest potential + + align:start position:0% +chemistry occurs on the lowest potential + + + align:start position:0% +chemistry occurs on the lowest potential +energy surface so it involves just the + + align:start position:0% +energy surface so it involves just the + + + align:start position:0% +energy surface so it involves just the +lowest potential energy surface and the + + align:start position:0% +lowest potential energy surface and the + + + align:start position:0% +lowest potential energy surface and the +reason for that is because electronic + + align:start position:0% +reason for that is because electronic + + + align:start position:0% +reason for that is because electronic +energies tend to be very big in chemical + + align:start position:0% +energies tend to be very big in chemical + + + align:start position:0% +energies tend to be very big in chemical +terms so the interesting Sigma and Sigma + + align:start position:0% +terms so the interesting Sigma and Sigma + + + align:start position:0% +terms so the interesting Sigma and Sigma +star is several evie and typically and + + align:start position:0% +star is several evie and typically and + + + align:start position:0% +star is several evie and typically and +chemical reactions on that same scale + + align:start position:0% +chemical reactions on that same scale + + + align:start position:0% +chemical reactions on that same scale +are usually tenths or hundreds of an + + align:start position:0% +are usually tenths or hundreds of an + + + align:start position:0% +are usually tenths or hundreds of an +Eevee so the chemical reaction energy + + align:start position:0% +Eevee so the chemical reaction energy + + + align:start position:0% +Eevee so the chemical reaction energy +might be somewhere way down here way way + + align:start position:0% +might be somewhere way down here way way + + + align:start position:0% +might be somewhere way down here way way +way below the amount of energy you would + + align:start position:0% +way below the amount of energy you would + + + align:start position:0% +way below the amount of energy you would +need to get all the way up to Sigma star + + align:start position:0% +need to get all the way up to Sigma star + + + align:start position:0% +need to get all the way up to Sigma star +and so the Sigma star penetrative + + align:start position:0% +and so the Sigma star penetrative + + + align:start position:0% +and so the Sigma star penetrative +service is just irrelevant it's there + + align:start position:0% +service is just irrelevant it's there + + + align:start position:0% +service is just irrelevant it's there +but it doesn't participate in reactions + + align:start position:0% +but it doesn't participate in reactions + + + align:start position:0% +but it doesn't participate in reactions +at all so in most cases knowing about + + align:start position:0% +at all so in most cases knowing about + + + align:start position:0% +at all so in most cases knowing about +the lowest potential energy surface gets + + align:start position:0% +the lowest potential energy surface gets + + + align:start position:0% +the lowest potential energy surface gets +you most of chemistry and so then let's + + align:start position:0% +you most of chemistry and so then let's + + + align:start position:0% +you most of chemistry and so then let's +look at a but then we can also sort of + + align:start position:0% +look at a but then we can also sort of + + + align:start position:0% +look at a but then we can also sort of +schematically talk about how these + + align:start position:0% +schematically talk about how these + + + align:start position:0% +schematically talk about how these +potential energy surfaces will look for + + align:start position:0% +potential energy surfaces will look for + + + align:start position:0% +potential energy surfaces will look for +a more complicated example so let's say + + align:start position:0% +a more complicated example so let's say + + + align:start position:0% +a more complicated example so let's say +I had the water the water molecule H 0 H + + align:start position:0% +I had the water the water molecule H 0 H + + + align:start position:0% +I had the water the water molecule H 0 H +so this is a more general case we have + + align:start position:0% +so this is a more general case we have + + + align:start position:0% +so this is a more general case we have +at least two coordinates here R 1 and R + + align:start position:0% +at least two coordinates here R 1 and R + + + align:start position:0% +at least two coordinates here R 1 and R +2 there's also going to be an angle but + + align:start position:0% +2 there's also going to be an angle but + + + align:start position:0% +2 there's also going to be an angle but +I can't really plot 3 dimensional hyper + + align:start position:0% +I can't really plot 3 dimensional hyper + + + align:start position:0% +I can't really plot 3 dimensional hyper +surfaces even with my computer so I'll + + align:start position:0% +surfaces even with my computer so I'll + + + align:start position:0% +surfaces even with my computer so I'll +stick with two there's a third and third + + align:start position:0% +stick with two there's a third and third + + + align:start position:0% +stick with two there's a third and third +coordinate there which is theta which + + align:start position:0% +coordinate there which is theta which + + + align:start position:0% +coordinate there which is theta which +I'm not gonna play around with but we'll + + align:start position:0% +I'm not gonna play around with but we'll + + + align:start position:0% +I'm not gonna play around with but we'll +play it will play around with just R 1 + + align:start position:0% +play it will play around with just R 1 + + + align:start position:0% +play it will play around with just R 1 +and R 2 so I can change individually the + + align:start position:0% +and R 2 so I can change individually the + + + align:start position:0% +and R 2 so I can change individually the +O H bond lengths in this molecule so + + align:start position:0% +O H bond lengths in this molecule so + + + align:start position:0% +O H bond lengths in this molecule so +then this is going to give me an at the + + align:start position:0% +then this is going to give me an at the + + + align:start position:0% +then this is going to give me an at the +energy as a function of R 1 and R 2 so + + align:start position:0% +energy as a function of R 1 and R 2 so + + + align:start position:0% +energy as a function of R 1 and R 2 so +it'll be a surface + + align:start position:0% +it'll be a surface + + + align:start position:0% +it'll be a surface +so it's a function of two variables + + align:start position:0% +so it's a function of two variables + + + align:start position:0% +so it's a function of two variables +that's a surface and that surface might + + align:start position:0% +that's a surface and that surface might + + + align:start position:0% +that's a surface and that surface might +look like what I have plotted there + + align:start position:0% +look like what I have plotted there + + + align:start position:0% +look like what I have plotted there +where it would have you know various + + align:start position:0% +where it would have you know various + + + align:start position:0% +where it would have you know various +peaks and valleys on it the very very + + align:start position:0% +peaks and valleys on it the very very + + + align:start position:0% +peaks and valleys on it the very very +lowest Valley the very lowest minimum + + align:start position:0% +lowest Valley the very lowest minimum + + + align:start position:0% +lowest Valley the very lowest minimum +just like we found for h2 that lowest + + align:start position:0% +just like we found for h2 that lowest + + + align:start position:0% +just like we found for h2 that lowest +minimum was the equilibrium bond bonding + + align:start position:0% +minimum was the equilibrium bond bonding + + + align:start position:0% +minimum was the equilibrium bond bonding +configuration so for this + + align:start position:0% +configuration so for this + + + align:start position:0% +configuration so for this +two-dimensional potential surface that + + align:start position:0% +two-dimensional potential surface that + + + align:start position:0% +two-dimensional potential surface that +lowest minimum is going to be the + + align:start position:0% +lowest minimum is going to be the + + + align:start position:0% +lowest minimum is going to be the +equilibrium configuration but there's + + align:start position:0% +equilibrium configuration but there's + + + align:start position:0% +equilibrium configuration but there's +also the possibility of other minima on + + align:start position:0% +also the possibility of other minima on + + + align:start position:0% +also the possibility of other minima on +this potential energy surface those + + align:start position:0% +this potential energy surface those + + + align:start position:0% +this potential energy surface those +would be metastable intermediates things + + align:start position:0% +would be metastable intermediates things + + + align:start position:0% +would be metastable intermediates things +that you could get trapped in things + + align:start position:0% +that you could get trapped in things + + + align:start position:0% +that you could get trapped in things +that would live for a while but + + align:start position:0% +that would live for a while but + + + align:start position:0% +that would live for a while but +eventually go down towards the lowest + + align:start position:0% +eventually go down towards the lowest + + + align:start position:0% +eventually go down towards the lowest +minimum and there'd also be reaction + + align:start position:0% +minimum and there'd also be reaction + + + align:start position:0% +minimum and there'd also be reaction +barriers so these are the things that we + + align:start position:0% +barriers so these are the things that we + + + align:start position:0% +barriers so these are the things that we +learn about governing how fast they + + align:start position:0% +learn about governing how fast they + + + align:start position:0% +learn about governing how fast they +convert from these metastable States + + align:start position:0% +convert from these metastable States + + + align:start position:0% +convert from these metastable States +into the most stable States so that's + + align:start position:0% +into the most stable States so that's + + + align:start position:0% +into the most stable States so that's +what you would get if you had just two + + align:start position:0% +what you would get if you had just two + + + align:start position:0% +what you would get if you had just two +coordinates and so then you can sort of + + align:start position:0% +coordinates and so then you can sort of + + + align:start position:0% +coordinates and so then you can sort of +try to generalize in your head well what + + align:start position:0% +try to generalize in your head well what + + + align:start position:0% +try to generalize in your head well what +if we had 3 4 5 6 + + align:start position:0% +if we had 3 4 5 6 + + + align:start position:0% +if we had 3 4 5 6 +127 368 lots and lots of coordinates in + + align:start position:0% +127 368 lots and lots of coordinates in + + + align:start position:0% +127 368 lots and lots of coordinates in +some many dimensional space that would + + align:start position:0% +some many dimensional space that would + + + align:start position:0% +some many dimensional space that would +still have the same qualities there'd be + + align:start position:0% +still have the same qualities there'd be + + + align:start position:0% +still have the same qualities there'd be +minima and barriers and so forth and we + + align:start position:0% +minima and barriers and so forth and we + + + align:start position:0% +minima and barriers and so forth and we +would get those out of the Schrodinger + + align:start position:0% +would get those out of the Schrodinger + + + align:start position:0% +would get those out of the Schrodinger +equation the electronic show dagger + + align:start position:0% +equation the electronic show dagger + + + align:start position:0% +equation the electronic show dagger +equation and so that is the electronic + + align:start position:0% +equation and so that is the electronic + + + align:start position:0% +equation and so that is the electronic +structure problem how do we accurately + + align:start position:0% +structure problem how do we accurately + + + align:start position:0% +structure problem how do we accurately +solve we look for the electronic + + align:start position:0% +solve we look for the electronic + + + align:start position:0% +solve we look for the electronic +eigenvalue and the electronic wave + + align:start position:0% +eigenvalue and the electronic wave + + + align:start position:0% +eigenvalue and the electronic wave +function for an arbitrary molecule and + + align:start position:0% +function for an arbitrary molecule and + + + align:start position:0% +function for an arbitrary molecule and +the key word here is accurately I didn't + + align:start position:0% +the key word here is accurately I didn't + + + align:start position:0% +the key word here is accurately I didn't +just say how can we solve for electronic + + align:start position:0% +just say how can we solve for electronic + + + align:start position:0% +just say how can we solve for electronic +energy and the electronic wave function + + align:start position:0% +energy and the electronic wave function + + + align:start position:0% +energy and the electronic wave function +because in general here's exact and + + align:start position:0% +because in general here's exact and + + + align:start position:0% +because in general here's exact and +solutions are impossible and I don't + + align:start position:0% +solutions are impossible and I don't + + + align:start position:0% +solutions are impossible and I don't +mean impossible for 561 I mean + + align:start position:0% +mean impossible for 561 I mean + + + align:start position:0% +mean impossible for 561 I mean +impossible for humans or computers so in + + align:start position:0% +impossible for humans or computers so in + + + align:start position:0% +impossible for humans or computers so in +general electronic structure theorists + + align:start position:0% +general electronic structure theorists + + + align:start position:0% +general electronic structure theorists +love approximations we love to make + + align:start position:0% +love approximations we love to make + + + align:start position:0% +love approximations we love to make +approximations because that's the only + + align:start position:0% +approximations because that's the only + + + align:start position:0% +approximations because that's the only +way that you can make progress and so + + align:start position:0% +way that you can make progress and so + + + align:start position:0% +way that you can make progress and so +what we're gonna learn about today and + + align:start position:0% +what we're gonna learn about today and + + + align:start position:0% +what we're gonna learn about today and +next Monday are they're sort of + + align:start position:0% +next Monday are they're sort of + + + align:start position:0% +next Monday are they're sort of +different categories of approximations + + align:start position:0% +different categories of approximations + + + align:start position:0% +different categories of approximations +that we make and what the pluses and + + align:start position:0% +that we make and what the pluses and + + + align:start position:0% +that we make and what the pluses and +minuses of those are so I'll pause there + + align:start position:0% +minuses of those are so I'll pause there + + + align:start position:0% +minuses of those are so I'll pause there +and see if anybody has any questions + + align:start position:0% + + + + align:start position:0% + +all right so we'll move on then so we we + + align:start position:0% +all right so we'll move on then so we we + + + align:start position:0% +all right so we'll move on then so we we +have an out there's X so it there's + + align:start position:0% +have an out there's X so it there's + + + align:start position:0% +have an out there's X so it there's +actually an outline of how different + + align:start position:0% +actually an outline of how different + + + align:start position:0% +actually an outline of how different +electronic modern electronic structure + + align:start position:0% +electronic modern electronic structure + + + align:start position:0% +electronic modern electronic structure +methods make approximations and these + + align:start position:0% +methods make approximations and these + + + align:start position:0% +methods make approximations and these +follow the same kinds of steps that you + + align:start position:0% +follow the same kinds of steps that you + + + align:start position:0% +follow the same kinds of steps that you +would use in a molecular orbital + + align:start position:0% +would use in a molecular orbital + + + align:start position:0% +would use in a molecular orbital +calculation okay so the first thing that + + align:start position:0% +calculation okay so the first thing that + + + align:start position:0% +calculation okay so the first thing that +you typically had to do in these + + align:start position:0% +you typically had to do in these + + + align:start position:0% +you typically had to do in these +calculations it was to choose a set of + + align:start position:0% +calculations it was to choose a set of + + + align:start position:0% +calculations it was to choose a set of +basis functions so you had to choose + + align:start position:0% +basis functions so you had to choose + + + align:start position:0% +basis functions so you had to choose +like 1s function over here or 1s + + align:start position:0% +like 1s function over here or 1s + + + align:start position:0% +like 1s function over here or 1s +function over there 2's function to P + + align:start position:0% +function over there 2's function to P + + + align:start position:0% +function over there 2's function to P +and to choose some set of atomic + + align:start position:0% +and to choose some set of atomic + + + align:start position:0% +and to choose some set of atomic +orbitals that you're going to use as the + + align:start position:0% +orbitals that you're going to use as the + + + align:start position:0% +orbitals that you're going to use as the +starting point of your calculation then + + align:start position:0% +starting point of your calculation then + + + align:start position:0% +starting point of your calculation then +you've made linear combinations of those + + align:start position:0% +you've made linear combinations of those + + + align:start position:0% +you've made linear combinations of those +things to get better functions and so + + align:start position:0% +things to get better functions and so + + + align:start position:0% +things to get better functions and so +then after you'd chosen that that basis + + align:start position:0% +then after you'd chosen that that basis + + + align:start position:0% +then after you'd chosen that that basis +you had to build some matrices and then + + align:start position:0% +you had to build some matrices and then + + + align:start position:0% +you had to build some matrices and then +you had to solve the eigenvalue problem + + align:start position:0% +you had to solve the eigenvalue problem + + + align:start position:0% +you had to solve the eigenvalue problem +for that matrix then you had to pick out + + align:start position:0% +for that matrix then you had to pick out + + + align:start position:0% +for that matrix then you had to pick out +which orbitals you were actually gonna + + align:start position:0% +which orbitals you were actually gonna + + + align:start position:0% +which orbitals you were actually gonna +occupy those were the next few steps and + + align:start position:0% +occupy those were the next few steps and + + + align:start position:0% +occupy those were the next few steps and +then finally you had to compute the + + align:start position:0% +then finally you had to compute the + + + align:start position:0% +then finally you had to compute the +energy now that's already kind of a + + align:start position:0% +energy now that's already kind of a + + + align:start position:0% +energy now that's already kind of a +detailed outline if it seemed like we + + align:start position:0% +detailed outline if it seemed like we + + + align:start position:0% +detailed outline if it seemed like we +had to understand the nuances of every + + align:start position:0% +had to understand the nuances of every + + + align:start position:0% +had to understand the nuances of every +one of those five steps we'd be kind to + + align:start position:0% +one of those five steps we'd be kind to + + + align:start position:0% +one of those five steps we'd be kind to +beat well we could we can't you can do + + align:start position:0% +beat well we could we can't you can do + + + align:start position:0% +beat well we could we can't you can do +that it would be an entire course unto + + align:start position:0% +that it would be an entire course unto + + + align:start position:0% +that it would be an entire course unto +itself and that's not what we're gonna + + align:start position:0% +itself and that's not what we're gonna + + + align:start position:0% +itself and that's not what we're gonna +be doing the reason that we can avoid + + align:start position:0% +be doing the reason that we can avoid + + + align:start position:0% +be doing the reason that we can avoid +going over every single nuance is + + align:start position:0% +going over every single nuance is + + + align:start position:0% +going over every single nuance is +twofold so first we can do we can avoid + + align:start position:0% +twofold so first we can do we can avoid + + + align:start position:0% +twofold so first we can do we can avoid +more or less steps two through four + + align:start position:0% +more or less steps two through four + + + align:start position:0% +more or less steps two through four +because they're done automatically so + + align:start position:0% +because they're done automatically so + + + align:start position:0% +because they're done automatically so +once you have chosen your basis that you + + align:start position:0% +once you have chosen your basis that you + + + align:start position:0% +once you have chosen your basis that you +want to use the computer knows how to + + align:start position:0% +want to use the computer knows how to + + + align:start position:0% +want to use the computer knows how to +build matrices it knows how to + + align:start position:0% +build matrices it knows how to + + + align:start position:0% +build matrices it knows how to +diagonalize matrices and find + + align:start position:0% +diagonalize matrices and find + + + align:start position:0% +diagonalize matrices and find +eigenvalues it knows how to pick out + + align:start position:0% +eigenvalues it knows how to pick out + + + align:start position:0% +eigenvalues it knows how to pick out +which orbitals to occupy it knows how to + + align:start position:0% +which orbitals to occupy it knows how to + + + align:start position:0% +which orbitals to occupy it knows how to +do all those things without you telling + + align:start position:0% +do all those things without you telling + + + align:start position:0% +do all those things without you telling +anything telling it to do anything you + + align:start position:0% +anything telling it to do anything you + + + align:start position:0% +anything telling it to do anything you +don't really have to do you know to + + align:start position:0% +don't really have to do you know to + + + align:start position:0% +don't really have to do you know to +change anything so the only things you + + align:start position:0% +change anything so the only things you + + + align:start position:0% +change anything so the only things you +have to worry about our choosing a good + + align:start position:0% +have to worry about our choosing a good + + + align:start position:0% +have to worry about our choosing a good +basis and then also choosing telling the + + align:start position:0% +basis and then also choosing telling the + + + align:start position:0% +basis and then also choosing telling the +computer a good way to compute the + + align:start position:0% +computer a good way to compute the + + + align:start position:0% +computer a good way to compute the +energy the other reason that we can + + align:start position:0% +energy the other reason that we can + + + align:start position:0% +energy the other reason that we can +actually do something useful here is + + align:start position:0% +actually do something useful here is + + + align:start position:0% +actually do something useful here is +because using a computer to solve an + + align:start position:0% +because using a computer to solve an + + + align:start position:0% +because using a computer to solve an +electronic structure problem is much + + align:start position:0% +electronic structure problem is much + + + align:start position:0% +electronic structure problem is much +like using an NMR to get a spectrum of a + + align:start position:0% +like using an NMR to get a spectrum of a + + + align:start position:0% +like using an NMR to get a spectrum of a +compound I doubt that anybody in this + + align:start position:0% +compound I doubt that anybody in this + + + align:start position:0% +compound I doubt that anybody in this +room could build their own functioning + + align:start position:0% +room could build their own functioning + + + align:start position:0% +room could build their own functioning +NMR like we just I mean I know general + + align:start position:0% +NMR like we just I mean I know general + + + align:start position:0% +NMR like we just I mean I know general +the principles of how an NMR works but + + align:start position:0% +the principles of how an NMR works but + + + align:start position:0% +the principles of how an NMR works but +building from the ground up oh so we + + align:start position:0% +building from the ground up oh so we + + + align:start position:0% +building from the ground up oh so we +ever do have any takers anybody maybe + + align:start position:0% +ever do have any takers anybody maybe + + + align:start position:0% +ever do have any takers anybody maybe +we'll build an NMR huh from the ground + + align:start position:0% +we'll build an NMR huh from the ground + + + align:start position:0% +we'll build an NMR huh from the ground +up I'm betting you see yeah you got it + + align:start position:0% +up I'm betting you see yeah you got it + + + align:start position:0% +up I'm betting you see yeah you got it +like you know get your you have to + + align:start position:0% +like you know get your you have to + + + align:start position:0% +like you know get your you have to +actually like make your own + + align:start position:0% +actually like make your own + + + align:start position:0% +actually like make your own +superconducting magnet you've got it you + + align:start position:0% +superconducting magnet you've got it you + + + align:start position:0% +superconducting magnet you've got it you +know from the ground up actually + + align:start position:0% +know from the ground up actually + + + align:start position:0% +know from the ground up actually +building your own NMR will be very very + + align:start position:0% +building your own NMR will be very very + + + align:start position:0% +building your own NMR will be very very +difficult but that doesn't preclude you + + align:start position:0% +difficult but that doesn't preclude you + + + align:start position:0% +difficult but that doesn't preclude you +from knowing how to use in NMR because + + align:start position:0% +from knowing how to use in NMR because + + + align:start position:0% +from knowing how to use in NMR because +you know okay well this piece is right + + align:start position:0% +you know okay well this piece is right + + + align:start position:0% +you know okay well this piece is right +this dial is roughly doing this I change + + align:start position:0% +this dial is roughly doing this I change + + + align:start position:0% +this dial is roughly doing this I change +this over here i sim this that's how I + + align:start position:0% +this over here i sim this that's how I + + + align:start position:0% +this over here i sim this that's how I +make the NMR work it's the same thing + + align:start position:0% +make the NMR work it's the same thing + + + align:start position:0% +make the NMR work it's the same thing +with electronic structure codes you need + + align:start position:0% +with electronic structure codes you need + + + align:start position:0% +with electronic structure codes you need +to understand a little bit of how they + + align:start position:0% +to understand a little bit of how they + + + align:start position:0% +to understand a little bit of how they +work in order to use them effectively + + align:start position:0% +work in order to use them effectively + + + align:start position:0% +work in order to use them effectively +but you don't have to understand every + + align:start position:0% +but you don't have to understand every + + + align:start position:0% +but you don't have to understand every +single line of code that went into + + align:start position:0% +single line of code that went into + + + align:start position:0% +single line of code that went into +building it which is good because + + align:start position:0% +building it which is good because + + + align:start position:0% +building it which is good because +there's you know several hundred + + align:start position:0% +there's you know several hundred + + + align:start position:0% +there's you know several hundred +thousand lines of codes and many of + + align:start position:0% +thousand lines of codes and many of + + + align:start position:0% +thousand lines of codes and many of +these electronic structure packages so + + align:start position:0% +these electronic structure packages so + + + align:start position:0% +these electronic structure packages so +we're gonna try to understand the + + align:start position:0% +we're gonna try to understand the + + + align:start position:0% +we're gonna try to understand the +principles that go into this so that we + + align:start position:0% +principles that go into this so that we + + + align:start position:0% +principles that go into this so that we +know how to be good users of + + align:start position:0% +know how to be good users of + + + align:start position:0% +know how to be good users of +computational tools and we can actually + + align:start position:0% +computational tools and we can actually + + + align:start position:0% +computational tools and we can actually +then organize so roughly speaking we'll + + align:start position:0% +then organize so roughly speaking we'll + + + align:start position:0% +then organize so roughly speaking we'll +be focusing on step one today and step + + align:start position:0% +be focusing on step one today and step + + + align:start position:0% +be focusing on step one today and step +five next Monday but we can organize + + align:start position:0% +five next Monday but we can organize + + + align:start position:0% +five next Monday but we can organize +these approximations on a sort of two + + align:start position:0% +these approximations on a sort of two + + + align:start position:0% +these approximations on a sort of two +dimensional accent two-dimensional plot + + align:start position:0% +dimensional accent two-dimensional plot + + + align:start position:0% +dimensional accent two-dimensional plot +which is sort of summarizes the whole + + align:start position:0% +which is sort of summarizes the whole + + + align:start position:0% +which is sort of summarizes the whole +idea of what we're going to be getting + + align:start position:0% +idea of what we're going to be getting + + + align:start position:0% +idea of what we're going to be getting +at so the idea here is that on one axis + + align:start position:0% +at so the idea here is that on one axis + + + align:start position:0% +at so the idea here is that on one axis +we have the step one thing which is the + + align:start position:0% +we have the step one thing which is the + + + align:start position:0% +we have the step one thing which is the +basis the atomic orbital basis and we + + align:start position:0% +basis the atomic orbital basis and we + + + align:start position:0% +basis the atomic orbital basis and we +can organize those basis those choices + + align:start position:0% +can organize those basis those choices + + + align:start position:0% +can organize those basis those choices +of basis from roughly speaking on the + + align:start position:0% +of basis from roughly speaking on the + + + align:start position:0% +of basis from roughly speaking on the +left hand we have bad choices and then + + align:start position:0% +left hand we have bad choices and then + + + align:start position:0% +left hand we have bad choices and then +on the right hand we have good choices + + align:start position:0% +on the right hand we have good choices + + + align:start position:0% +on the right hand we have good choices +now you might say well why would you + + align:start position:0% +now you might say well why would you + + + align:start position:0% +now you might say well why would you +even include choices if we know they're + + align:start position:0% +even include choices if we know they're + + + align:start position:0% +even include choices if we know they're +bad because the bad ones also happen to + + align:start position:0% +bad because the bad ones also happen to + + + align:start position:0% +bad because the bad ones also happen to +be the fast basis and the good ones tend + + align:start position:0% +be the fast basis and the good ones tend + + + align:start position:0% +be the fast basis and the good ones tend +to be slow and so it's a time trade-off + + align:start position:0% +to be slow and so it's a time trade-off + + + align:start position:0% +to be slow and so it's a time trade-off +so you have a lot of time you might + + align:start position:0% +so you have a lot of time you might + + + align:start position:0% +so you have a lot of time you might +choose a really good basis set if you + + align:start position:0% +choose a really good basis set if you + + + align:start position:0% +choose a really good basis set if you +have basis if you have not a lot of time + + align:start position:0% +have basis if you have not a lot of time + + + align:start position:0% +have basis if you have not a lot of time +you might choose not a very good one and + + align:start position:0% +you might choose not a very good one and + + + align:start position:0% +you might choose not a very good one and +then we can do the same thing with the + + align:start position:0% +then we can do the same thing with the + + + align:start position:0% +then we can do the same thing with the +energy we have different choices of how + + align:start position:0% +energy we have different choices of how + + + align:start position:0% +energy we have different choices of how +we compute the energy and we can roughly + + align:start position:0% +we compute the energy and we can roughly + + + align:start position:0% +we compute the energy and we can roughly +arrange those from bad choices to good + + align:start position:0% +arrange those from bad choices to good + + + align:start position:0% +arrange those from bad choices to good +ones but again these bad choices are + + align:start position:0% +ones but again these bad choices are + + + align:start position:0% +ones but again these bad choices are +fast and the good ones are slow + + align:start position:0% + + + + align:start position:0% + +and so the general thing that we want is + + align:start position:0% +and so the general thing that we want is + + + align:start position:0% +and so the general thing that we want is +we want to get up here into the upper + + align:start position:0% +we want to get up here into the upper + + + align:start position:0% +we want to get up here into the upper +right hand corner where the exact answer + + align:start position:0% +right hand corner where the exact answer + + + align:start position:0% +right hand corner where the exact answer +is somewhere up there with a very good + + align:start position:0% +is somewhere up there with a very good + + + align:start position:0% +is somewhere up there with a very good +energy and a very good basis we're gonna + + align:start position:0% +energy and a very good basis we're gonna + + + align:start position:0% +energy and a very good basis we're gonna +get the exact or nearly the exact answer + + align:start position:0% +get the exact or nearly the exact answer + + + align:start position:0% +get the exact or nearly the exact answer +so that's where we want to get but + + align:start position:0% +so that's where we want to get but + + + align:start position:0% +so that's where we want to get but +moving from the lower left to the upper + + align:start position:0% +moving from the lower left to the upper + + + align:start position:0% +moving from the lower left to the upper +right every time we move in that + + align:start position:0% +right every time we move in that + + + align:start position:0% +right every time we move in that +direction we're making the calculation + + align:start position:0% +direction we're making the calculation + + + align:start position:0% +direction we're making the calculation +slower and slower and slower and slower + + align:start position:0% +slower and slower and slower and slower + + + align:start position:0% +slower and slower and slower and slower +and slower until eventually we just lose + + align:start position:0% +and slower until eventually we just lose + + + align:start position:0% +and slower until eventually we just lose +patience and so then we cut it off and + + align:start position:0% +patience and so then we cut it off and + + + align:start position:0% +patience and so then we cut it off and +say all right this is as far as I'm + + align:start position:0% +say all right this is as far as I'm + + + align:start position:0% +say all right this is as far as I'm +willing to go what's the best answer I + + align:start position:0% +willing to go what's the best answer I + + + align:start position:0% +willing to go what's the best answer I +can get what's the most best + + align:start position:0% +can get what's the most best + + + align:start position:0% +can get what's the most best +cost-benefit analysis I can do and so in + + align:start position:0% +cost-benefit analysis I can do and so in + + + align:start position:0% +cost-benefit analysis I can do and so in +terms of being good users of electronic + + align:start position:0% +terms of being good users of electronic + + + align:start position:0% +terms of being good users of electronic +computational chemistry it's about + + align:start position:0% +computational chemistry it's about + + + align:start position:0% +computational chemistry it's about +knowing okay well if I've only got you + + align:start position:0% +knowing okay well if I've only got you + + + align:start position:0% +knowing okay well if I've only got you +know three hours for this calculation to + + align:start position:0% +know three hours for this calculation to + + + align:start position:0% +know three hours for this calculation to +run or two days or however long I'm + + align:start position:0% +run or two days or however long I'm + + + align:start position:0% +run or two days or however long I'm +willing to let the computer run on this + + align:start position:0% +willing to let the computer run on this + + + align:start position:0% +willing to let the computer run on this +you know what's the best combination of + + align:start position:0% +you know what's the best combination of + + + align:start position:0% +you know what's the best combination of +a basis and an energy to get me a decent + + align:start position:0% +a basis and an energy to get me a decent + + + align:start position:0% +a basis and an energy to get me a decent +result in that kind of time + + align:start position:0% +result in that kind of time + + + align:start position:0% +result in that kind of time +okay so questions about that before I + + align:start position:0% +okay so questions about that before I + + + align:start position:0% +okay so questions about that before I +move on okay so we'll focus on choosing + + align:start position:0% +move on okay so we'll focus on choosing + + + align:start position:0% +move on okay so we'll focus on choosing +an atomic orbital basis so we already + + align:start position:0% +an atomic orbital basis so we already + + + align:start position:0% +an atomic orbital basis so we already +have chosen an atomic orbital basis + + align:start position:0% +have chosen an atomic orbital basis + + + align:start position:0% +have chosen an atomic orbital basis +before so when when we did h2 plus which + + align:start position:0% +before so when when we did h2 plus which + + + align:start position:0% +before so when when we did h2 plus which +is sort of standard Scituate standard + + align:start position:0% +is sort of standard Scituate standard + + + align:start position:0% +is sort of standard Scituate standard +problem that you can actually solve by + + align:start position:0% +problem that you can actually solve by + + + align:start position:0% +problem that you can actually solve by +hand if you choose the right basis when + + align:start position:0% +hand if you choose the right basis when + + + align:start position:0% +hand if you choose the right basis when +we did that calculation we chose to have + + align:start position:0% +we did that calculation we chose to have + + + align:start position:0% +we did that calculation we chose to have +an atomic orbital on a the 1s function + + align:start position:0% +an atomic orbital on a the 1s function + + + align:start position:0% +an atomic orbital on a the 1s function +on a and the atomic orbital on b1 s on B + + align:start position:0% +on a and the atomic orbital on b1 s on B + + + align:start position:0% +on a and the atomic orbital on b1 s on B +and those two things together formed our + + align:start position:0% +and those two things together formed our + + + align:start position:0% +and those two things together formed our +basis so we wrote our molecular orbitals + + align:start position:0% +basis so we wrote our molecular orbitals + + + align:start position:0% +basis so we wrote our molecular orbitals +as linear combinations of those two + + align:start position:0% +as linear combinations of those two + + + align:start position:0% +as linear combinations of those two +functions we got Sigma and Sigma star + + align:start position:0% +functions we got Sigma and Sigma star + + + align:start position:0% +functions we got Sigma and Sigma star +out and we were able to work out the + + align:start position:0% +out and we were able to work out the + + + align:start position:0% +out and we were able to work out the +energies now this type of basis is a + + align:start position:0% +energies now this type of basis is a + + + align:start position:0% +energies now this type of basis is a +useful basis and it has a name and is + + align:start position:0% +useful basis and it has a name and is + + + align:start position:0% +useful basis and it has a name and is +called a minimal basis and it's minimal + + align:start position:0% +called a minimal basis and it's minimal + + + align:start position:0% +called a minimal basis and it's minimal +because you could not possibly do less + + align:start position:0% +because you could not possibly do less + + + align:start position:0% +because you could not possibly do less +so if you want to form a bond between + + align:start position:0% +so if you want to form a bond between + + + align:start position:0% +so if you want to form a bond between +two atoms you need at least one bate one + + align:start position:0% +two atoms you need at least one bate one + + + align:start position:0% +two atoms you need at least one bate one +function on each atom + + align:start position:0% +function on each atom + + + align:start position:0% +function on each atom +if you had more you know if you had only + + align:start position:0% +if you had more you know if you had only + + + align:start position:0% +if you had more you know if you had only +one function period you couldn't really + + align:start position:0% +one function period you couldn't really + + + align:start position:0% +one function period you couldn't really +four move out so it's as low as you can + + align:start position:0% +four move out so it's as low as you can + + + align:start position:0% +four move out so it's as low as you can +go can't go lower than this now you + + align:start position:0% +go can't go lower than this now you + + + align:start position:0% +go can't go lower than this now you +could think about the possibility of + + align:start position:0% +could think about the possibility of + + + align:start position:0% +could think about the possibility of +adding additional functions so I could + + align:start position:0% +adding additional functions so I could + + + align:start position:0% +adding additional functions so I could +add in say the 2s function on a 2's + + align:start position:0% +add in say the 2s function on a 2's + + + align:start position:0% +add in say the 2s function on a 2's +function on B I can come up with various + + align:start position:0% +function on B I can come up with various + + + align:start position:0% +function on B I can come up with various +things now you might ask why would I + + align:start position:0% +things now you might ask why would I + + + align:start position:0% +things now you might ask why would I +want to do this and there's a very good + + align:start position:0% +want to do this and there's a very good + + + align:start position:0% +want to do this and there's a very good +reason for doing this which is one of + + align:start position:0% +reason for doing this which is one of + + + align:start position:0% +reason for doing this which is one of +the principles that we need to learn in + + align:start position:0% +the principles that we need to learn in + + + align:start position:0% +the principles that we need to learn in +constructing basis functions basis + + align:start position:0% +constructing basis functions basis + + + align:start position:0% +constructing basis functions basis +choosing our basis which is that adding + + align:start position:0% +choosing our basis which is that adding + + + align:start position:0% +choosing our basis which is that adding +basis functions always improves the + + align:start position:0% +basis functions always improves the + + + align:start position:0% +basis functions always improves the +calculation so even though I think that + + align:start position:0% +calculation so even though I think that + + + align:start position:0% +calculation so even though I think that +adding 2's a and 2's be why would those + + align:start position:0% +adding 2's a and 2's be why would those + + + align:start position:0% +adding 2's a and 2's be why would those +be important I can't really say adding + + align:start position:0% +be important I can't really say adding + + + align:start position:0% +be important I can't really say adding +basis functions always makes matters + + align:start position:0% +basis functions always makes matters + + + align:start position:0% +basis functions always makes matters +better makes things better and the + + align:start position:0% +better makes things better and the + + + align:start position:0% +better makes things better and the +reason for that is because we're doing a + + align:start position:0% +reason for that is because we're doing a + + + align:start position:0% +reason for that is because we're doing a +variational calculation we're trying to + + align:start position:0% +variational calculation we're trying to + + + align:start position:0% +variational calculation we're trying to +approximate the lowest energy of the + + align:start position:0% +approximate the lowest energy of the + + + align:start position:0% +approximate the lowest energy of the +system and just choosing the 1s a and + + align:start position:0% +system and just choosing the 1s a and + + + align:start position:0% +system and just choosing the 1s a and +1's B functions doesn't give you the + + align:start position:0% +1's B functions doesn't give you the + + + align:start position:0% +1's B functions doesn't give you the +lowest energy it may be close but it's + + align:start position:0% +lowest energy it may be close but it's + + + align:start position:0% +lowest energy it may be close but it's +not exact so then by adding the 2's + + align:start position:0% +not exact so then by adding the 2's + + + align:start position:0% +not exact so then by adding the 2's +functions the result could get better by + + align:start position:0% +functions the result could get better by + + + align:start position:0% +functions the result could get better by +adding a little you know by making c3 + + align:start position:0% +adding a little you know by making c3 + + + align:start position:0% +adding a little you know by making c3 +and c4 maybe you know a little bit + + align:start position:0% +and c4 maybe you know a little bit + + + align:start position:0% +and c4 maybe you know a little bit +adding making c3 and c4 not quite zero + + align:start position:0% +adding making c3 and c4 not quite zero + + + align:start position:0% +adding making c3 and c4 not quite zero +here maybe the answer gets a little bit + + align:start position:0% +here maybe the answer gets a little bit + + + align:start position:0% +here maybe the answer gets a little bit +better maybe it doesn't but it can't get + + align:start position:0% +better maybe it doesn't but it can't get + + + align:start position:0% +better maybe it doesn't but it can't get +worse because it could the calculation + + align:start position:0% +worse because it could the calculation + + + align:start position:0% +worse because it could the calculation +could always choose c3 and c4 to be 0 so + + align:start position:0% +could always choose c3 and c4 to be 0 so + + + align:start position:0% +could always choose c3 and c4 to be 0 so +adding basis functions always makes + + align:start position:0% +adding basis functions always makes + + + align:start position:0% +adding basis functions always makes +things either better or at least not + + align:start position:0% +things either better or at least not + + + align:start position:0% +things either better or at least not +worse than they were and so well you'll + + align:start position:0% +worse than they were and so well you'll + + + align:start position:0% +worse than they were and so well you'll +find is that when we're talking about a + + align:start position:0% +find is that when we're talking about a + + + align:start position:0% +find is that when we're talking about a +o basis choosing an a o basis we're + + align:start position:0% +o basis choosing an a o basis we're + + + align:start position:0% +o basis choosing an a o basis we're +gonna be choosing bases that are much + + align:start position:0% +gonna be choosing bases that are much + + + align:start position:0% +gonna be choosing bases that are much +bigger than your chemical intuition + + align:start position:0% +bigger than your chemical intuition + + + align:start position:0% +bigger than your chemical intuition +would suggest okay so for h2 I think o + + align:start position:0% +would suggest okay so for h2 I think o + + + align:start position:0% +would suggest okay so for h2 I think o +1sa 1sb that should more or less + + align:start position:0% +1sa 1sb that should more or less + + + align:start position:0% +1sa 1sb that should more or less +describe things and if I was doing + + align:start position:0% +describe things and if I was doing + + + align:start position:0% +describe things and if I was doing +things by hand that's what I would do + + align:start position:0% +things by hand that's what I would do + + + align:start position:0% +things by hand that's what I would do +but if the computers doing the work + + align:start position:0% +but if the computers doing the work + + + align:start position:0% +but if the computers doing the work +well it doesn't Renault skin off my nose + + align:start position:0% +well it doesn't Renault skin off my nose + + + align:start position:0% +well it doesn't Renault skin off my nose +at this computer waste some time doing + + align:start position:0% +at this computer waste some time doing + + + align:start position:0% +at this computer waste some time doing +some 2's or 3s or 4s integrals + + align:start position:0% +some 2's or 3s or 4s integrals + + + align:start position:0% +some 2's or 3s or 4s integrals +I'll let the computer do that as long as + + align:start position:0% +I'll let the computer do that as long as + + + align:start position:0% +I'll let the computer do that as long as +it gives me a better answer so the bases + + align:start position:0% +it gives me a better answer so the bases + + + align:start position:0% +it gives me a better answer so the bases +we have will be much bigger because of + + align:start position:0% +we have will be much bigger because of + + + align:start position:0% +we have will be much bigger because of +this but the other thing I want to note + + align:start position:0% +this but the other thing I want to note + + + align:start position:0% +this but the other thing I want to note +is that when I talk about these + + align:start position:0% +is that when I talk about these + + + align:start position:0% +is that when I talk about these +one s functions I probably you probably + + align:start position:0% +one s functions I probably you probably + + + align:start position:0% +one s functions I probably you probably +all have in your head you know you know + + align:start position:0% +all have in your head you know you know + + + align:start position:0% +all have in your head you know you know +what one s functions look like they look + + align:start position:0% +what one s functions look like they look + + + align:start position:0% +what one s functions look like they look +like e to the minus a times R so they + + align:start position:0% +like e to the minus a times R so they + + + align:start position:0% +like e to the minus a times R so they +just look like exponential decay decay + + align:start position:0% +just look like exponential decay decay + + + align:start position:0% +just look like exponential decay decay +functions it turns out that for for + + align:start position:0% +functions it turns out that for for + + + align:start position:0% +functions it turns out that for for +practical reasons these are inconvenient + + align:start position:0% +practical reasons these are inconvenient + + + align:start position:0% +practical reasons these are inconvenient +things to use on a computer and that is + + align:start position:0% +things to use on a computer and that is + + + align:start position:0% +things to use on a computer and that is +because integrals involving + + align:start position:0% +because integrals involving + + + align:start position:0% +because integrals involving +Exponential's are not analytic in three + + align:start position:0% +Exponential's are not analytic in three + + + align:start position:0% +Exponential's are not analytic in three +dimensions primarily because of the cusp + + align:start position:0% +dimensions primarily because of the cusp + + + align:start position:0% +dimensions primarily because of the cusp +that occurs at R equals zero + + align:start position:0% +that occurs at R equals zero + + + align:start position:0% +that occurs at R equals zero +so if you multiply two of these things + + align:start position:0% +so if you multiply two of these things + + + align:start position:0% +so if you multiply two of these things +times each other and try to do an + + align:start position:0% +times each other and try to do an + + + align:start position:0% +times each other and try to do an +integral you have a cusp over here and a + + align:start position:0% +integral you have a cusp over here and a + + + align:start position:0% +integral you have a cusp over here and a +cusp over here and the integral is just + + align:start position:0% +cusp over here and the integral is just + + + align:start position:0% +cusp over here and the integral is just +not something that can be worked out and + + align:start position:0% +not something that can be worked out and + + + align:start position:0% +not something that can be worked out and +so when the going gets tough the tough + + align:start position:0% +so when the going gets tough the tough + + + align:start position:0% +so when the going gets tough the tough +get empirical and so instead of using + + align:start position:0% +get empirical and so instead of using + + + align:start position:0% +get empirical and so instead of using +these exponential functions what we use + + align:start position:0% +these exponential functions what we use + + + align:start position:0% +these exponential functions what we use +in practice are gaussians so gaussians + + align:start position:0% +in practice are gaussians so gaussians + + + align:start position:0% +in practice are gaussians so gaussians +are things that instead of looking like + + align:start position:0% +are things that instead of looking like + + + align:start position:0% +are things that instead of looking like +e to the minus AR they look like e to + + align:start position:0% +e to the minus AR they look like e to + + + align:start position:0% +e to the minus AR they look like e to +the minus alpha r squared so if I was to + + align:start position:0% +the minus alpha r squared so if I was to + + + align:start position:0% +the minus alpha r squared so if I was to +plot a Gaussian here on the same axes + + align:start position:0% +plot a Gaussian here on the same axes + + + align:start position:0% +plot a Gaussian here on the same axes +and choose the Alpha value appropriately + + align:start position:0% +and choose the Alpha value appropriately + + + align:start position:0% +and choose the Alpha value appropriately +I could get a Gaussian that might look + + align:start position:0% +I could get a Gaussian that might look + + + align:start position:0% +I could get a Gaussian that might look +like that similar to that one s that + + align:start position:0% +like that similar to that one s that + + + align:start position:0% +like that similar to that one s that +actual 1s function but particularly near + + align:start position:0% +actual 1s function but particularly near + + + align:start position:0% +actual 1s function but particularly near +the origin where it doesn't have a cusp + + align:start position:0% +the origin where it doesn't have a cusp + + + align:start position:0% +the origin where it doesn't have a cusp +and and particularly in the tails where + + align:start position:0% +and and particularly in the tails where + + + align:start position:0% +and and particularly in the tails where +it where e to the minus alpha R squared + + align:start position:0% +it where e to the minus alpha R squared + + + align:start position:0% +it where e to the minus alpha R squared +decays very quickly they don't actually + + align:start position:0% +decays very quickly they don't actually + + + align:start position:0% +decays very quickly they don't actually +look that similar so the whole read the + + align:start position:0% +look that similar so the whole read the + + + align:start position:0% +look that similar so the whole read the +whole reason to do this is not that we + + align:start position:0% +whole reason to do this is not that we + + + align:start position:0% +whole reason to do this is not that we +have some physical reason to think that + + align:start position:0% +have some physical reason to think that + + + align:start position:0% +have some physical reason to think that +Gaussian described atoms better than + + align:start position:0% +Gaussian described atoms better than + + + align:start position:0% +Gaussian described atoms better than +hydrogenic functions they don't it's + + align:start position:0% +hydrogenic functions they don't it's + + + align:start position:0% +hydrogenic functions they don't it's +just that we can do the integrals so + + align:start position:0% +just that we can do the integrals so + + + align:start position:0% +just that we can do the integrals so +there's easy integrals here and if we + + align:start position:0% +there's easy integrals here and if we + + + align:start position:0% +there's easy integrals here and if we +want really do want a hydrogen like + + align:start position:0% +want really do want a hydrogen like + + + align:start position:0% +want really do want a hydrogen like +function we can get that by just + + align:start position:0% +function we can get that by just + + + align:start position:0% +function we can get that by just +including more than one Gaussian so one + + align:start position:0% +including more than one Gaussian so one + + + align:start position:0% +including more than one Gaussian so one +Gaussian doesn't look very much like an + + align:start position:0% +Gaussian doesn't look very much like an + + + align:start position:0% +Gaussian doesn't look very much like an +exponential but if I take two gaussians + + align:start position:0% +exponential but if I take two gaussians + + + align:start position:0% +exponential but if I take two gaussians +and choose their exponents and their + + align:start position:0% +and choose their exponents and their + + + align:start position:0% +and choose their exponents and their +coefficients appropriately I can make a + + align:start position:0% +coefficients appropriately I can make a + + + align:start position:0% +coefficients appropriately I can make a +linear combination of two gaussians so + + align:start position:0% +linear combination of two gaussians so + + + align:start position:0% +linear combination of two gaussians so +this was the one Gaussian result I could + + align:start position:0% +this was the one Gaussian result I could + + + align:start position:0% +this was the one Gaussian result I could +make I could make with two gaussians I + + align:start position:0% +make I could make with two gaussians I + + + align:start position:0% +make I could make with two gaussians I +could make something that might look + + align:start position:0% + + + + align:start position:0% + +and with three gaussians I might be able + + align:start position:0% +and with three gaussians I might be able + + + align:start position:0% +and with three gaussians I might be able +to do something that would look like and + + align:start position:0% +to do something that would look like and + + + align:start position:0% +to do something that would look like and +for gaussians in five gaussians six + + align:start position:0% +for gaussians in five gaussians six + + + align:start position:0% +for gaussians in five gaussians six +gaussians but it's clear then that by + + align:start position:0% +gaussians but it's clear then that by + + + align:start position:0% +gaussians but it's clear then that by +using a large number of gaussians i + + align:start position:0% +using a large number of gaussians i + + + align:start position:0% +using a large number of gaussians i +could get whatever i want just by Bruce + + align:start position:0% +could get whatever i want just by Bruce + + + align:start position:0% +could get whatever i want just by Bruce +brute-force and so those are the two + + align:start position:0% +brute-force and so those are the two + + + align:start position:0% +brute-force and so those are the two +things about building basis choosing + + align:start position:0% +things about building basis choosing + + + align:start position:0% +things about building basis choosing +basis beyo basis and at this point you + + align:start position:0% +basis beyo basis and at this point you + + + align:start position:0% +basis beyo basis and at this point you +should start to feel a little bit + + align:start position:0% +should start to feel a little bit + + + align:start position:0% +should start to feel a little bit +intimidated because I've said that for + + align:start position:0% +intimidated because I've said that for + + + align:start position:0% +intimidated because I've said that for +atoms you're going to need more basis + + align:start position:0% +atoms you're going to need more basis + + + align:start position:0% +atoms you're going to need more basis +functions than you thought just to try + + align:start position:0% +functions than you thought just to try + + + align:start position:0% +functions than you thought just to try +to get a variational a lower energy and + + align:start position:0% +to get a variational a lower energy and + + + align:start position:0% +to get a variational a lower energy and +those basis functions are likely to be + + align:start position:0% +those basis functions are likely to be + + + align:start position:0% +those basis functions are likely to be +constructed out of gaussians of which + + align:start position:0% +constructed out of gaussians of which + + + align:start position:0% +constructed out of gaussians of which +you'll need a bunch of gaussians to even + + align:start position:0% +you'll need a bunch of gaussians to even + + + align:start position:0% +you'll need a bunch of gaussians to even +really approximate one hydrogen like + + align:start position:0% +really approximate one hydrogen like + + + align:start position:0% +really approximate one hydrogen like +orbital so you're gonna have lots and + + align:start position:0% +orbital so you're gonna have lots and + + + align:start position:0% +orbital so you're gonna have lots and +lots and lots of gaussians for on every + + align:start position:0% +lots and lots of gaussians for on every + + + align:start position:0% +lots and lots of gaussians for on every +atom and you're gonna choose the + + align:start position:0% +atom and you're gonna choose the + + + align:start position:0% +atom and you're gonna choose the +exponents if every single one of those + + align:start position:0% +exponents if every single one of those + + + align:start position:0% +exponents if every single one of those +gaussians be yourself and that would be + + align:start position:0% +gaussians be yourself and that would be + + + align:start position:0% +gaussians be yourself and that would be +just horrible to have to do and the + + align:start position:0% +just horrible to have to do and the + + + align:start position:0% +just horrible to have to do and the +thing that comes to our rescue is a + + align:start position:0% +thing that comes to our rescue is a + + + align:start position:0% +thing that comes to our rescue is a +thing that's known as a basis set so a + + align:start position:0% +thing that's known as a basis set so a + + + align:start position:0% +thing that's known as a basis set so a +basis set is constructed in the + + align:start position:0% +basis set is constructed in the + + + align:start position:0% +basis set is constructed in the +following way a graduate student + + align:start position:0% +following way a graduate student + + + align:start position:0% +following way a graduate student +probably long before you were born + + align:start position:0% +probably long before you were born + + + align:start position:0% +probably long before you were born +spent years of their life going through + + align:start position:0% +spent years of their life going through + + + align:start position:0% +spent years of their life going through +and figuring out okay for carbon what is + + align:start position:0% +and figuring out okay for carbon what is + + + align:start position:0% +and figuring out okay for carbon what is +a good combination of gaussian exponents + + align:start position:0% +a good combination of gaussian exponents + + + align:start position:0% +a good combination of gaussian exponents +okay they're a hundred and thirteen + + align:start position:0% +okay they're a hundred and thirteen + + + align:start position:0% +okay they're a hundred and thirteen +point six seventy four point two eleven + + align:start position:0% +point six seventy four point two eleven + + + align:start position:0% +point six seventy four point two eleven +point three and one point six and they + + align:start position:0% +point three and one point six and they + + + align:start position:0% +point three and one point six and they +wrote that down they said okay now for + + align:start position:0% +wrote that down they said okay now for + + + align:start position:0% +wrote that down they said okay now for +nitrogen what are a good set of gaussian + + align:start position:0% +nitrogen what are a good set of gaussian + + + align:start position:0% +nitrogen what are a good set of gaussian +textbooks and then they went through and + + align:start position:0% +textbooks and then they went through and + + + align:start position:0% +textbooks and then they went through and +they did this for every element or at + + align:start position:0% +they did this for every element or at + + + align:start position:0% +they did this for every element or at +least many many many elements in the + + align:start position:0% +least many many many elements in the + + + align:start position:0% +least many many many elements in the +Parekh table and then they wrote a paper + + align:start position:0% +Parekh table and then they wrote a paper + + + align:start position:0% +Parekh table and then they wrote a paper +that said here is and i did it so i'm + + align:start position:0% +that said here is and i did it so i'm + + + align:start position:0% +that said here is and i did it so i'm +gonna say here is the troy basis set and + + align:start position:0% +gonna say here is the troy basis set and + + + align:start position:0% +gonna say here is the troy basis set and +it the troy basis that means when you + + align:start position:0% +it the troy basis that means when you + + + align:start position:0% +it the troy basis that means when you +say you're doing the troy basis that + + align:start position:0% +say you're doing the troy basis that + + + align:start position:0% +say you're doing the troy basis that +means you're using though those + + align:start position:0% +means you're using though those + + + align:start position:0% +means you're using though those +exponents that i wrote down for carbon + + align:start position:0% +exponents that i wrote down for carbon + + + align:start position:0% +exponents that i wrote down for carbon +or for nitrogen or for oxygen or for + + align:start position:0% +or for nitrogen or for oxygen or for + + + align:start position:0% +or for nitrogen or for oxygen or for +fluorine or for hydrogen and it's all + + align:start position:0% +fluorine or for hydrogen and it's all + + + align:start position:0% +fluorine or for hydrogen and it's all +predefined it's all laid out you know + + align:start position:0% +predefined it's all laid out you know + + + align:start position:0% +predefined it's all laid out you know +and if I was really diligent its laid + + align:start position:0% +and if I was really diligent its laid + + + align:start position:0% +and if I was really diligent its laid +out for every element in the periodic + + align:start position:0% +out for every element in the periodic + + + align:start position:0% +out for every element in the periodic +table if I was less diligent maybe it's + + align:start position:0% +table if I was less diligent maybe it's + + + align:start position:0% +table if I was less diligent maybe it's +only the first two rows or something + + align:start position:0% +only the first two rows or something + + + align:start position:0% +only the first two rows or something +like that but the result is that all you + + align:start position:0% +like that but the result is that all you + + + align:start position:0% +like that but the result is that all you +have to say is I want the Troy basis set + + align:start position:0% +have to say is I want the Troy basis set + + + align:start position:0% +have to say is I want the Troy basis set +because Troy makes really good base of + + align:start position:0% +because Troy makes really good base of + + + align:start position:0% +because Troy makes really good base of +sets and + + align:start position:0% +sets and + + + align:start position:0% +sets and +so I'm gonna use that and then the + + align:start position:0% +so I'm gonna use that and then the + + + align:start position:0% +so I'm gonna use that and then the +computer can go and just say okay well + + align:start position:0% +computer can go and just say okay well + + + align:start position:0% +computer can go and just say okay well +there's some file that has all those + + align:start position:0% +there's some file that has all those + + + align:start position:0% +there's some file that has all those +exponents and the computer looks up the + + align:start position:0% +exponents and the computer looks up the + + + align:start position:0% +exponents and the computer looks up the +numbers and says four-carbon you need + + align:start position:0% +numbers and says four-carbon you need + + + align:start position:0% +numbers and says four-carbon you need +this for oxygen this for nitrogenous and + + align:start position:0% +this for oxygen this for nitrogenous and + + + align:start position:0% +this for oxygen this for nitrogenous and +so the key idea here is that these are + + align:start position:0% +so the key idea here is that these are + + + align:start position:0% +so the key idea here is that these are +predefined sets of AO basis functions so + + align:start position:0% +predefined sets of AO basis functions so + + + align:start position:0% +predefined sets of AO basis functions so +somebody already defined these you don't + + align:start position:0% +somebody already defined these you don't + + + align:start position:0% +somebody already defined these you don't +have to make a choice other than + + align:start position:0% +have to make a choice other than + + + align:start position:0% +have to make a choice other than +choosing the set there's not other knobs + + align:start position:0% +choosing the set there's not other knobs + + + align:start position:0% +choosing the set there's not other knobs +that you have to turn so there's you can + + align:start position:0% +that you have to turn so there's you can + + + align:start position:0% +that you have to turn so there's you can +obviously see the benefit of this which + + align:start position:0% +obviously see the benefit of this which + + + align:start position:0% +obviously see the benefit of this which +is you don't have to put down hundreds + + align:start position:0% +is you don't have to put down hundreds + + + align:start position:0% +is you don't have to put down hundreds +and hundreds of numbers in order to get + + align:start position:0% +and hundreds of numbers in order to get + + + align:start position:0% +and hundreds of numbers in order to get +the calculation to run so that's a big + + align:start position:0% +the calculation to run so that's a big + + + align:start position:0% +the calculation to run so that's a big +win which hopefully you remember for the + + align:start position:0% +win which hopefully you remember for the + + + align:start position:0% +win which hopefully you remember for the +next 25 minutes because the the downside + + align:start position:0% +next 25 minutes because the the downside + + + align:start position:0% +next 25 minutes because the the downside +then is that you just noticed I called + + align:start position:0% +then is that you just noticed I called + + + align:start position:0% +then is that you just noticed I called +my basic set the Troi basis set which + + align:start position:0% +my basic set the Troi basis set which + + + align:start position:0% +my basic set the Troi basis set which +would give you absolutely no idea of + + align:start position:0% +would give you absolutely no idea of + + + align:start position:0% +would give you absolutely no idea of +what was in that basis and adjust that I + + align:start position:0% +what was in that basis and adjust that I + + + align:start position:0% +what was in that basis and adjust that I +made the base of set and then if + + align:start position:0% +made the base of set and then if + + + align:start position:0% +made the base of set and then if +somebody else might call it the the + + align:start position:0% +somebody else might call it the the + + + align:start position:0% +somebody else might call it the the +Cambridge basis set because they did it + + align:start position:0% +Cambridge basis set because they did it + + + align:start position:0% +Cambridge basis set because they did it +in Cambridge and somebody else might + + align:start position:0% +in Cambridge and somebody else might + + + align:start position:0% +in Cambridge and somebody else might +might number their basis sets you know + + align:start position:0% +might number their basis sets you know + + + align:start position:0% +might number their basis sets you know +this is this is basis set number 17 and + + align:start position:0% +this is this is basis set number 17 and + + + align:start position:0% +this is this is basis set number 17 and +none of those things actually tell you + + align:start position:0% +none of those things actually tell you + + + align:start position:0% +none of those things actually tell you +what's actually in the basis set and how + + align:start position:0% +what's actually in the basis set and how + + + align:start position:0% +what's actually in the basis set and how +they designed it they just give it a + + align:start position:0% +they designed it they just give it a + + + align:start position:0% +they designed it they just give it a +name but then that name is you have to + + align:start position:0% +name but then that name is you have to + + + align:start position:0% +name but then that name is you have to +know the name in order to be able to + + align:start position:0% +know the name in order to be able to + + + align:start position:0% +know the name in order to be able to +specify the basis set and you have to + + align:start position:0% +specify the basis set and you have to + + + align:start position:0% +specify the basis set and you have to +know what you know you have to have to + + align:start position:0% +know what you know you have to have to + + + align:start position:0% +know what you know you have to have to +sort of memorize oh well this basis that + + align:start position:0% +sort of memorize oh well this basis that + + + align:start position:0% +sort of memorize oh well this basis that +does this this basis set does this or at + + align:start position:0% +does this this basis set does this or at + + + align:start position:0% +does this this basis set does this or at +least remember where to look up what + + align:start position:0% +least remember where to look up what + + + align:start position:0% +least remember where to look up what +those basis sets do so for the next 20 + + align:start position:0% +those basis sets do so for the next 20 + + + align:start position:0% +those basis sets do so for the next 20 +minutes or so we're gonna talk about + + align:start position:0% +minutes or so we're gonna talk about + + + align:start position:0% +minutes or so we're gonna talk about +some of those things and you bit you'll + + align:start position:0% +some of those things and you bit you'll + + + align:start position:0% +some of those things and you bit you'll +be annoyed at the fact that these basis + + align:start position:0% +be annoyed at the fact that these basis + + + align:start position:0% +be annoyed at the fact that these basis +sets have these funky weird names and + + align:start position:0% +sets have these funky weird names and + + + align:start position:0% +sets have these funky weird names and +design principles I think but just + + align:start position:0% +design principles I think but just + + + align:start position:0% +design principles I think but just +remember I don't have to put in a + + align:start position:0% +remember I don't have to put in a + + + align:start position:0% +remember I don't have to put in a +hundred numbers this is the price you + + align:start position:0% +hundred numbers this is the price you + + + align:start position:0% +hundred numbers this is the price you +pay for not having to put in 100 numbers + + align:start position:0% +pay for not having to put in 100 numbers + + + align:start position:0% +pay for not having to put in 100 numbers +okay so the first thing that we talked + + align:start position:0% +okay so the first thing that we talked + + + align:start position:0% +okay so the first thing that we talked +about here so so I'll say that basis + + align:start position:0% +about here so so I'll say that basis + + + align:start position:0% +about here so so I'll say that basis +sets are typically grouped by by row of + + align:start position:0% +sets are typically grouped by by row of + + + align:start position:0% +sets are typically grouped by by row of +course the basis that's gonna be + + align:start position:0% +course the basis that's gonna be + + + align:start position:0% +course the basis that's gonna be +different so hydrogen is gonna have a + + align:start position:0% +different so hydrogen is gonna have a + + + align:start position:0% +different so hydrogen is gonna have a +different number of basis function need + + align:start position:0% +different number of basis function need + + + align:start position:0% +different number of basis function need +and different number of basis functions + + align:start position:0% +and different number of basis functions + + + align:start position:0% +and different number of basis functions +than carbon + + align:start position:0% +than carbon + + + align:start position:0% +than carbon +you know argon is gonna need a different + + align:start position:0% +you know argon is gonna need a different + + + align:start position:0% +you know argon is gonna need a different +number from carbon or hydrogen just + + align:start position:0% +number from carbon or hydrogen just + + + align:start position:0% +number from carbon or hydrogen just +because they have different numbers of + + align:start position:0% +because they have different numbers of + + + align:start position:0% +because they have different numbers of +valence functions and different numbers + + align:start position:0% +valence functions and different numbers + + + align:start position:0% +valence functions and different numbers +of core functions and I'm also going to + + align:start position:0% +of core functions and I'm also going to + + + align:start position:0% +of core functions and I'm also going to +introduce a shorthand oops so first of + + align:start position:0% +introduce a shorthand oops so first of + + + align:start position:0% +introduce a shorthand oops so first of +all I'll note that we already have + + align:start position:0% +all I'll note that we already have + + + align:start position:0% +all I'll note that we already have +okay so I shall just introduce the + + align:start position:0% +okay so I shall just introduce the + + + align:start position:0% +okay so I shall just introduce the +shorthand so for say for nitrogen and + + align:start position:0% +shorthand so for say for nitrogen and + + + align:start position:0% +shorthand so for say for nitrogen and +for the basis that we talked about + + align:start position:0% +for the basis that we talked about + + + align:start position:0% +for the basis that we talked about +before we've talked about so far the + + align:start position:0% +before we've talked about so far the + + + align:start position:0% +before we've talked about so far the +minimal basis of a set the smallest + + align:start position:0% +minimal basis of a set the smallest + + + align:start position:0% +minimal basis of a set the smallest +basis that I can come up with come up + + align:start position:0% +basis that I can come up with come up + + + align:start position:0% +basis that I can come up with come up +with four nitrogen would need to have + + align:start position:0% +with four nitrogen would need to have + + + align:start position:0% +with four nitrogen would need to have +the 1s function the 2's function and the + + align:start position:0% +the 1s function the 2's function and the + + + align:start position:0% +the 1s function the 2's function and the +2p function I need at least those + + align:start position:0% +2p function I need at least those + + + align:start position:0% +2p function I need at least those +functions to have places to put all of + + align:start position:0% +functions to have places to put all of + + + align:start position:0% +functions to have places to put all of +my nitrogen electrons now I get I'll get + + align:start position:0% +my nitrogen electrons now I get I'll get + + + align:start position:0% +my nitrogen electrons now I get I'll get +writers cramp if I have to write all of + + align:start position:0% +writers cramp if I have to write all of + + + align:start position:0% +writers cramp if I have to write all of +these things out so I'm going to develop + + align:start position:0% +these things out so I'm going to develop + + + align:start position:0% +these things out so I'm going to develop +a shorthand which is when I have 1s and + + align:start position:0% +a shorthand which is when I have 1s and + + + align:start position:0% +a shorthand which is when I have 1s and +2s I'm just going to denote that as 2's + + align:start position:0% +2s I'm just going to denote that as 2's + + + align:start position:0% +2s I'm just going to denote that as 2's +so that's not not indicating that 2's is + + align:start position:0% +so that's not not indicating that 2's is + + + align:start position:0% +so that's not not indicating that 2's is +the last function indicating that there + + align:start position:0% +the last function indicating that there + + + align:start position:0% +the last function indicating that there +are two of them so I have two s type + + align:start position:0% +are two of them so I have two s type + + + align:start position:0% +are two of them so I have two s type +functions one that sort of core like and + + align:start position:0% +functions one that sort of core like and + + + align:start position:0% +functions one that sort of core like and +one that sort of valence like but + + align:start position:0% +one that sort of valence like but + + + align:start position:0% +one that sort of valence like but +there's two of them and then I have one + + align:start position:0% +there's two of them and then I have one + + + align:start position:0% +there's two of them and then I have one +P like function so I'll put one piece so + + align:start position:0% +P like function so I'll put one piece so + + + align:start position:0% +P like function so I'll put one piece so +that's just telling me how many of each + + align:start position:0% +that's just telling me how many of each + + + align:start position:0% +that's just telling me how many of each +of these things I have so again this is + + align:start position:0% +of these things I have so again this is + + + align:start position:0% +of these things I have so again this is +the number S type functions this is the + + align:start position:0% +the number S type functions this is the + + + align:start position:0% +the number S type functions this is the +number of P type function and so then we + + align:start position:0% +number of P type function and so then we + + + align:start position:0% +number of P type function and so then we +can go and we can talk about the one + + align:start position:0% +can go and we can talk about the one + + + align:start position:0% +can go and we can talk about the one +basis set we've dealt with so far which + + align:start position:0% +basis set we've dealt with so far which + + + align:start position:0% +basis set we've dealt with so far which +is the minimal basis set so for hydrogen + + align:start position:0% +is the minimal basis set so for hydrogen + + + align:start position:0% +is the minimal basis set so for hydrogen +and helium there's just gonna be that 1s + + align:start position:0% +and helium there's just gonna be that 1s + + + align:start position:0% +and helium there's just gonna be that 1s +function on each of those and then when + + align:start position:0% +function on each of those and then when + + + align:start position:0% +function on each of those and then when +I go down to the next row it looks just + + align:start position:0% +I go down to the next row it looks just + + + align:start position:0% +I go down to the next row it looks just +like nitrogen they all gonna orginated + + align:start position:0% +like nitrogen they all gonna orginated + + + align:start position:0% +like nitrogen they all gonna orginated +in s core function and their + + align:start position:0% +in s core function and their + + + align:start position:0% +in s core function and their +surveillance function and a P valus + + align:start position:0% +surveillance function and a P valus + + + align:start position:0% +surveillance function and a P valus +function so they'll be 2 s 1 P like and + + align:start position:0% +function so they'll be 2 s 1 P like and + + + align:start position:0% +function so they'll be 2 s 1 P like and +then I go down one more row for sodium + + align:start position:0% +then I go down one more row for sodium + + + align:start position:0% +then I go down one more row for sodium +through argon and I'll need another s + + align:start position:0% +through argon and I'll need another s + + + align:start position:0% +through argon and I'll need another s +function so they'll be total of 3 s type + + align:start position:0% +function so they'll be total of 3 s type + + + align:start position:0% +function so they'll be total of 3 s type +functions and then I need two sets of P + + align:start position:0% +functions and then I need two sets of P + + + align:start position:0% +functions and then I need two sets of P +a core P and a valence P so there's 2 P + + align:start position:0% + + + + align:start position:0% + +so that's the the minimal basis set + + align:start position:0% +so that's the the minimal basis set + + + align:start position:0% +so that's the the minimal basis set +that's the smallest basis that I could + + align:start position:0% +that's the smallest basis that I could + + + align:start position:0% +that's the smallest basis that I could +conceive of for any atom and then we're + + align:start position:0% +conceive of for any atom and then we're + + + align:start position:0% +conceive of for any atom and then we're +going to have various ways of trying to + + align:start position:0% +going to have various ways of trying to + + + align:start position:0% +going to have various ways of trying to +make these things more elaborate more + + align:start position:0% +make these things more elaborate more + + + align:start position:0% +make these things more elaborate more +baroque and the most common way to do + + align:start position:0% +baroque and the most common way to do + + + align:start position:0% +baroque and the most common way to do +this is to note that well when I bring + + align:start position:0% +this is to note that well when I bring + + + align:start position:0% +this is to note that well when I bring +atoms together + + align:start position:0% +atoms together + + + align:start position:0% +atoms together +it's the valence functions that actually + + align:start position:0% +it's the valence functions that actually + + + align:start position:0% +it's the valence functions that actually +either contract or expand + + align:start position:0% +either contract or expand + + + align:start position:0% +either contract or expand +in order to describe those the electrons + + align:start position:0% +in order to describe those the electrons + + + align:start position:0% +in order to describe those the electrons +moving around the core functions don't + + align:start position:0% +moving around the core functions don't + + + align:start position:0% +moving around the core functions don't +really change very much and so in order + + align:start position:0% +really change very much and so in order + + + align:start position:0% +really change very much and so in order +to give the valence functions functions + + align:start position:0% +to give the valence functions functions + + + align:start position:0% +to give the valence functions functions +flexibility to change it makes sense to + + align:start position:0% +flexibility to change it makes sense to + + + align:start position:0% +flexibility to change it makes sense to +add more valence like functions so if + + align:start position:0% +add more valence like functions so if + + + align:start position:0% +add more valence like functions so if +the valence was s it makes sense to add + + align:start position:0% +the valence was s it makes sense to add + + + align:start position:0% +the valence was s it makes sense to add +another s function or if the valence was + + align:start position:0% +another s function or if the valence was + + + align:start position:0% +another s function or if the valence was +P it makes sense to add another P + + align:start position:0% +P it makes sense to add another P + + + align:start position:0% +P it makes sense to add another P +function and so we get a name here this + + align:start position:0% +function and so we get a name here this + + + align:start position:0% +function and so we get a name here this +concept which is a minimal basis is + + align:start position:0% +concept which is a minimal basis is + + + align:start position:0% +concept which is a minimal basis is +what's known as a single zeta basis set + + align:start position:0% +what's known as a single zeta basis set + + + align:start position:0% +what's known as a single zeta basis set +because it has just one set of valence + + align:start position:0% +because it has just one set of valence + + + align:start position:0% +because it has just one set of valence +functions it might make it might seem + + align:start position:0% +functions it might make it might seem + + + align:start position:0% +functions it might make it might seem +like would make better sense to call it + + align:start position:0% +like would make better sense to call it + + + align:start position:0% +like would make better sense to call it +a single valence basis set but history + + align:start position:0% +a single valence basis set but history + + + align:start position:0% +a single valence basis set but history +made a different choice it said that + + align:start position:0% +made a different choice it said that + + + align:start position:0% +made a different choice it said that +it's data I don't know why they chose + + align:start position:0% +it's data I don't know why they chose + + + align:start position:0% +it's data I don't know why they chose +the name Zeta but they did so the Zeta + + align:start position:0% +the name Zeta but they did so the Zeta + + + align:start position:0% +the name Zeta but they did so the Zeta +just means that there's one set of + + align:start position:0% +just means that there's one set of + + + align:start position:0% +just means that there's one set of +valence functions and then you could + + align:start position:0% +valence functions and then you could + + + align:start position:0% +valence functions and then you could +think about making a double Zeta so you + + align:start position:0% +think about making a double Zeta so you + + + align:start position:0% +think about making a double Zeta so you +take every valence function just add a + + align:start position:0% +take every valence function just add a + + + align:start position:0% +take every valence function just add a +another valence function that has a + + align:start position:0% +another valence function that has a + + + align:start position:0% +another valence function that has a +different exponent so it would allow + + align:start position:0% +different exponent so it would allow + + + align:start position:0% +different exponent so it would allow +more flexibility so that would be a + + align:start position:0% +more flexibility so that would be a + + + align:start position:0% +more flexibility so that would be a +double Zeta base to set DZ so for + + align:start position:0% +double Zeta base to set DZ so for + + + align:start position:0% +double Zeta base to set DZ so for +hydrogen and helium we would just dump + + align:start position:0% +hydrogen and helium we would just dump + + + align:start position:0% +hydrogen and helium we would just dump +it all valence so we just get two s + + align:start position:0% +it all valence so we just get two s + + + align:start position:0% +it all valence so we just get two s +functions for things in the in the same + + align:start position:0% +functions for things in the in the same + + + align:start position:0% +functions for things in the in the same +row as lithium and neon the valence + + align:start position:0% +row as lithium and neon the valence + + + align:start position:0% +row as lithium and neon the valence +function is functions are 1s and one are + + align:start position:0% +function is functions are 1s and one are + + + align:start position:0% +function is functions are 1s and one are +an S and a P and so when we double those + + align:start position:0% +an S and a P and so when we double those + + + align:start position:0% +an S and a P and so when we double those +where it's gonna add another S type + + align:start position:0% +where it's gonna add another S type + + + align:start position:0% +where it's gonna add another S type +function and another P type function so + + align:start position:0% +function and another P type function so + + + align:start position:0% +function and another P type function so +we would go three s to P here because + + align:start position:0% +we would go three s to P here because + + + align:start position:0% +we would go three s to P here because +we'd add one s function and one P + + align:start position:0% +we'd add one s function and one P + + + align:start position:0% +we'd add one s function and one P +function and then for sodium through + + align:start position:0% +function and then for sodium through + + + align:start position:0% +function and then for sodium through +argon we would have 4 s 3 P and then we + + align:start position:0% +argon we would have 4 s 3 P and then we + + + align:start position:0% +argon we would have 4 s 3 P and then we +could go on and talk about Oh what about + + align:start position:0% +could go on and talk about Oh what about + + + align:start position:0% +could go on and talk about Oh what about +a triple Zeta so triple Zeta would be 3 + + align:start position:0% +a triple Zeta so triple Zeta would be 3 + + + align:start position:0% +a triple Zeta so triple Zeta would be 3 +s for hydrogen helium and then we add an + + align:start position:0% +s for hydrogen helium and then we add an + + + align:start position:0% +s for hydrogen helium and then we add an +S and a P for the next row so it's 4 s 3 + + align:start position:0% +S and a P for the next row so it's 4 s 3 + + + align:start position:0% +S and a P for the next row so it's 4 s 3 +P and then we add s and P for this we + + align:start position:0% +P and then we add s and P for this we + + + align:start position:0% +P and then we add s and P for this we +end of 5 s 4 P + + align:start position:0% + + + + align:start position:0% + +and so again the idea here is that you + + align:start position:0% +and so again the idea here is that you + + + align:start position:0% +and so again the idea here is that you +know for carbon we might have 1s that's + + align:start position:0% +know for carbon we might have 1s that's + + + align:start position:0% +know for carbon we might have 1s that's +the core and then we'd have 2 s and 2 P + + align:start position:0% +the core and then we'd have 2 s and 2 P + + + align:start position:0% +the core and then we'd have 2 s and 2 P +as the first valence and then 3 P and + + align:start position:0% +as the first valence and then 3 P and + + + align:start position:0% +as the first valence and then 3 P and +these would respectively be so the + + align:start position:0% +these would respectively be so the + + + align:start position:0% +these would respectively be so the +single Zeta or and then you include the + + align:start position:0% +single Zeta or and then you include the + + + align:start position:0% +single Zeta or and then you include the +next shell and it becomes alright single + + align:start position:0% +next shell and it becomes alright single + + + align:start position:0% +next shell and it becomes alright single +data would be all of this sorry how was + + align:start position:0% +data would be all of this sorry how was + + + align:start position:0% +data would be all of this sorry how was +the core and then you could do say all + + align:start position:0% +the core and then you could do say all + + + align:start position:0% +the core and then you could do say all +right well but then I include another + + align:start position:0% +right well but then I include another + + + align:start position:0% +right well but then I include another +set and this gives me a double Zeta kind + + align:start position:0% +set and this gives me a double Zeta kind + + + align:start position:0% +set and this gives me a double Zeta kind +of basis set and then I could include + + align:start position:0% +of basis set and then I could include + + + align:start position:0% +of basis set and then I could include +yet another set and this would give me a + + align:start position:0% +yet another set and this would give me a + + + align:start position:0% +yet another set and this would give me a +triple theta kind of basis set and you + + align:start position:0% +triple theta kind of basis set and you + + + align:start position:0% +triple theta kind of basis set and you +can go on and on and on okay so you can + + align:start position:0% +can go on and on and on okay so you can + + + align:start position:0% +can go on and on and on okay so you can +just make a quadruple Zeta and quintuple + + align:start position:0% +just make a quadruple Zeta and quintuple + + + align:start position:0% +just make a quadruple Zeta and quintuple +Zeta basis set and then this is where + + align:start position:0% +Zeta basis set and then this is where + + + align:start position:0% +Zeta basis set and then this is where +the names get annoying so there the name + + align:start position:0% +the names get annoying so there the name + + + align:start position:0% +the names get annoying so there the name +of the most common minimal basis set is + + align:start position:0% +of the most common minimal basis set is + + + align:start position:0% +of the most common minimal basis set is +sto - 3 c g and that stands for slater + + align:start position:0% +sto - 3 c g and that stands for slater + + + align:start position:0% +sto - 3 c g and that stands for slater +type orbitals 3 gaussians just in case + + align:start position:0% +type orbitals 3 gaussians just in case + + + align:start position:0% +type orbitals 3 gaussians just in case +you're wondering why it's sto 3g and + + align:start position:0% +you're wondering why it's sto 3g and + + + align:start position:0% +you're wondering why it's sto 3g and +then for the double zeta basis set there + + align:start position:0% +then for the double zeta basis set there + + + align:start position:0% +then for the double zeta basis set there +are ones that are called 3 - 2 1 g 6 - 3 + + align:start position:0% +are ones that are called 3 - 2 1 g 6 - 3 + + + align:start position:0% +are ones that are called 3 - 2 1 g 6 - 3 +1 g another one that is somewhat + + align:start position:0% +1 g another one that is somewhat + + + align:start position:0% +1 g another one that is somewhat +confusingly just called easy double Zeta + + align:start position:0% +confusingly just called easy double Zeta + + + align:start position:0% +confusingly just called easy double Zeta +as if there was only one such basis set + + align:start position:0% +as if there was only one such basis set + + + align:start position:0% +as if there was only one such basis set +and then for triple Zeta you can do 6 - + + align:start position:0% +and then for triple Zeta you can do 6 - + + + align:start position:0% +and then for triple Zeta you can do 6 - +3 1 1 G triple Zeta valence others so + + align:start position:0% +3 1 1 G triple Zeta valence others so + + + align:start position:0% +3 1 1 G triple Zeta valence others so +there are other abbreviations out there + + align:start position:0% +there are other abbreviations out there + + + align:start position:0% +there are other abbreviations out there +as well but that's how you would do + + align:start position:0% +as well but that's how you would do + + + align:start position:0% +as well but that's how you would do +these kinds of how you change there's + + align:start position:0% +these kinds of how you change there's + + + align:start position:0% +these kinds of how you change there's +the Zeta the valence four questions + + align:start position:0% +the Zeta the valence four questions + + + align:start position:0% +the Zeta the valence four questions +about those + + align:start position:0% + + + + align:start position:0% + +yeah so is there lineups in the example + + align:start position:0% +yeah so is there lineups in the example + + + align:start position:0% +yeah so is there lineups in the example +you're including as your additional data + + align:start position:0% +you're including as your additional data + + + align:start position:0% +you're including as your additional data +it's like yes so there are occasionally + + align:start position:0% +it's like yes so there are occasionally + + + align:start position:0% +it's like yes so there are occasionally +times where people include basis + + align:start position:0% +times where people include basis + + + align:start position:0% +times where people include basis +functions that aren't don't look like + + align:start position:0% +functions that aren't don't look like + + + align:start position:0% +functions that aren't don't look like +atomic orbitals so the most common one + + align:start position:0% +atomic orbitals so the most common one + + + align:start position:0% +atomic orbitals so the most common one +is to make bond centered functions like + + align:start position:0% +is to make bond centered functions like + + + align:start position:0% +is to make bond centered functions like +you say oh I want a bond here I'm gonna + + align:start position:0% +you say oh I want a bond here I'm gonna + + + align:start position:0% +you say oh I want a bond here I'm gonna +put a put a basis functions there there + + align:start position:0% +put a put a basis functions there there + + + align:start position:0% +put a put a basis functions there there +are there's a couple of reasons that + + align:start position:0% +are there's a couple of reasons that + + + align:start position:0% +are there's a couple of reasons that +becomes just undesirable one one is that + + align:start position:0% +becomes just undesirable one one is that + + + align:start position:0% +becomes just undesirable one one is that +then you can't use a standard basis set + + align:start position:0% +then you can't use a standard basis set + + + align:start position:0% +then you can't use a standard basis set +because the basis sets have to be sort + + align:start position:0% +because the basis sets have to be sort + + + align:start position:0% +because the basis sets have to be sort +of anchored to the atoms that's how we + + align:start position:0% +of anchored to the atoms that's how we + + + align:start position:0% +of anchored to the atoms that's how we +catalog them if you're say oh I'm gonna + + align:start position:0% +catalog them if you're say oh I'm gonna + + + align:start position:0% +catalog them if you're say oh I'm gonna +put one in the middle of the bond you + + align:start position:0% +put one in the middle of the bond you + + + align:start position:0% +put one in the middle of the bond you +say well it would depend on both atoms + + align:start position:0% +say well it would depend on both atoms + + + align:start position:0% +say well it would depend on both atoms +involved in the bond and how long the + + align:start position:0% +involved in the bond and how long the + + + align:start position:0% +involved in the bond and how long the +bond was and things like that so that's + + align:start position:0% +bond was and things like that so that's + + + align:start position:0% +bond was and things like that so that's +a little bit undesirable the other one + + align:start position:0% +a little bit undesirable the other one + + + align:start position:0% +a little bit undesirable the other one +is that unless you pin that bond + + align:start position:0% +is that unless you pin that bond + + + align:start position:0% +is that unless you pin that bond +function down to a particular position + + align:start position:0% +function down to a particular position + + + align:start position:0% +function down to a particular position +if you let it let the center of that + + align:start position:0% +if you let it let the center of that + + + align:start position:0% +if you let it let the center of that +bond function move there's actually a + + align:start position:0% +bond function move there's actually a + + + align:start position:0% +bond function move there's actually a +numerical instability that happens when + + align:start position:0% +numerical instability that happens when + + + align:start position:0% +numerical instability that happens when +two gaussians come on top of each other + + align:start position:0% +two gaussians come on top of each other + + + align:start position:0% +two gaussians come on top of each other +and that can sometimes cause calculation + + align:start position:0% +and that can sometimes cause calculation + + + align:start position:0% +and that can sometimes cause calculation +that computer to choke so so that in + + align:start position:0% +that computer to choke so so that in + + + align:start position:0% +that computer to choke so so that in +practice we usually stick to in + + align:start position:0% +practice we usually stick to in + + + align:start position:0% +practice we usually stick to in +increasing the atomic basis sets but um + + align:start position:0% +increasing the atomic basis sets but um + + + align:start position:0% +increasing the atomic basis sets but um +oh but there is also one other case in + + align:start position:0% +oh but there is also one other case in + + + align:start position:0% +oh but there is also one other case in +physics they are much more fond of using + + align:start position:0% +physics they are much more fond of using + + + align:start position:0% +physics they are much more fond of using +solids that's sort of one of the things + + align:start position:0% +solids that's sort of one of the things + + + align:start position:0% +solids that's sort of one of the things +that chemists tend to think about + + align:start position:0% +that chemists tend to think about + + + align:start position:0% +that chemists tend to think about +molecules as the example physicists tend + + align:start position:0% +molecules as the example physicists tend + + + align:start position:0% +molecules as the example physicists tend +to think about solids and in solids + + align:start position:0% +to think about solids and in solids + + + align:start position:0% +to think about solids and in solids +they're much more fond of using plane + + align:start position:0% +they're much more fond of using plane + + + align:start position:0% +they're much more fond of using plane +waves as their basis basis set so they + + align:start position:0% +waves as their basis basis set so they + + + align:start position:0% +waves as their basis basis set so they +start off with the fruit they're free + + align:start position:0% +start off with the fruit they're free + + + align:start position:0% +start off with the fruit they're free +and so they're starting off with atoms + + align:start position:0% +and so they're starting off with atoms + + + align:start position:0% +and so they're starting off with atoms +is their reference they start off with + + align:start position:0% +is their reference they start off with + + + align:start position:0% +is their reference they start off with +free electrons as their reference and + + align:start position:0% +free electrons as their reference and + + + align:start position:0% +free electrons as their reference and +then say oh and then we introduce these + + align:start position:0% +then say oh and then we introduce these + + + align:start position:0% +then say oh and then we introduce these +potentials which are perturbations to + + align:start position:0% +potentials which are perturbations to + + + align:start position:0% +potentials which are perturbations to +the free electron so you get plane waves + + align:start position:0% +the free electron so you get plane waves + + + align:start position:0% +the free electron so you get plane waves +as your basis set you make linear + + align:start position:0% +as your basis set you make linear + + + align:start position:0% +as your basis set you make linear +combinations of plane waves instead of + + align:start position:0% +combinations of plane waves instead of + + + align:start position:0% +combinations of plane waves instead of +atomic + + align:start position:0% +atomic + + + align:start position:0% +atomic +functions yeah + + align:start position:0% + + + + align:start position:0% + +that's exactly the next next you hit on + + align:start position:0% +that's exactly the next next you hit on + + + align:start position:0% +that's exactly the next next you hit on +exactly the next thing which is that + + align:start position:0% +exactly the next thing which is that + + + align:start position:0% +exactly the next thing which is that +none of those include any D functions so + + align:start position:0% +none of those include any D functions so + + + align:start position:0% +none of those include any D functions so +on cart on a man I could go up to like a + + align:start position:0% +on cart on a man I could go up to like a + + + align:start position:0% +on cart on a man I could go up to like a +team Zeta and I would never have any D + + align:start position:0% +team Zeta and I would never have any D + + + align:start position:0% +team Zeta and I would never have any D +functions and on he hydrogen and helium + + align:start position:0% +functions and on he hydrogen and helium + + + align:start position:0% +functions and on he hydrogen and helium +I could go up takings and I wouldn't + + align:start position:0% +I could go up takings and I wouldn't + + + align:start position:0% +I could go up takings and I wouldn't +even have any P functions and certainly + + align:start position:0% +even have any P functions and certainly + + + align:start position:0% +even have any P functions and certainly +there are situations where you would + + align:start position:0% +there are situations where you would + + + align:start position:0% +there are situations where you would +want these higher angular momentum + + align:start position:0% +want these higher angular momentum + + + align:start position:0% +want these higher angular momentum +Mendte one of them is if you're in an + + align:start position:0% +Mendte one of them is if you're in an + + + align:start position:0% +Mendte one of them is if you're in an +electric field + + align:start position:0% +electric field + + + align:start position:0% +electric field +so that polarizes electrons intends to + + align:start position:0% +so that polarizes electrons intends to + + + align:start position:0% +so that polarizes electrons intends to +actually require slightly hiring + + align:start position:0% +actually require slightly hiring + + + align:start position:0% +actually require slightly hiring +Alimentum functions in order to describe + + align:start position:0% +Alimentum functions in order to describe + + + align:start position:0% +Alimentum functions in order to describe +that polarization and the other one is + + align:start position:0% +that polarization and the other one is + + + align:start position:0% +that polarization and the other one is +for just the directionality of bonding + + align:start position:0% +for just the directionality of bonding + + + align:start position:0% +for just the directionality of bonding +that you know if you had like an sn2 + + align:start position:0% +that you know if you had like an sn2 + + + align:start position:0% +that you know if you had like an sn2 +reaction or something like this where + + align:start position:0% +reaction or something like this where + + + align:start position:0% +reaction or something like this where +temporarily something was either + + align:start position:0% +temporarily something was either + + + align:start position:0% +temporarily something was either +actually hypervalent or you know sort of + + align:start position:0% +actually hypervalent or you know sort of + + + align:start position:0% +actually hypervalent or you know sort of +hypervalent you would need these higher + + align:start position:0% +hypervalent you would need these higher + + + align:start position:0% +hypervalent you would need these higher +angular momentum functions to describe + + align:start position:0% +angular momentum functions to describe + + + align:start position:0% +angular momentum functions to describe +the hyper valency and so those are + + align:start position:0% +the hyper valency and so those are + + + align:start position:0% +the hyper valency and so those are +called polarization functions so here + + align:start position:0% +called polarization functions so here + + + align:start position:0% +called polarization functions so here +polarization functions are things that + + align:start position:0% +polarization functions are things that + + + align:start position:0% +polarization functions are things that +add higher angular momentum and valence + + align:start position:0% +add higher angular momentum and valence + + + align:start position:0% +add higher angular momentum and valence +so yeah you need this for things like + + align:start position:0% +so yeah you need this for things like + + + align:start position:0% +so yeah you need this for things like +polarizability which is why they're + + align:start position:0% +polarizability which is why they're + + + align:start position:0% +polarizability which is why they're +called polarization functions but you + + align:start position:0% +called polarization functions but you + + + align:start position:0% +called polarization functions but you +also needed it for things like hyper + + align:start position:0% +also needed it for things like hyper + + + align:start position:0% +also needed it for things like hyper +valency and so that nomenclature for + + align:start position:0% +valency and so that nomenclature for + + + align:start position:0% +valency and so that nomenclature for +polarization functions is a little bit + + align:start position:0% +polarization functions is a little bit + + + align:start position:0% +polarization functions is a little bit +is is also a bit weird but the the + + align:start position:0% +is is also a bit weird but the the + + + align:start position:0% +is is also a bit weird but the the +simplest one is that you just add the + + align:start position:0% +simplest one is that you just add the + + + align:start position:0% +simplest one is that you just add the +letter P so P standing for polarization + + align:start position:0% +letter P so P standing for polarization + + + align:start position:0% +letter P so P standing for polarization +to the basis set and then the idea is + + align:start position:0% +to the basis set and then the idea is + + + align:start position:0% +to the basis set and then the idea is +that you're just gonna add one function + + align:start position:0% +that you're just gonna add one function + + + align:start position:0% +that you're just gonna add one function +with that P you at when you add the P + + align:start position:0% +with that P you at when you add the P + + + align:start position:0% +with that P you at when you add the P +that means you're adding one function + + align:start position:0% +that means you're adding one function + + + align:start position:0% +that means you're adding one function +that has one unit higher angular + + align:start position:0% +that has one unit higher angular + + + align:start position:0% +that has one unit higher angular +momentum so if P was your highest + + align:start position:0% +momentum so if P was your highest + + + align:start position:0% +momentum so if P was your highest +angular momentum you're gonna add a D + + align:start position:0% +angular momentum you're gonna add a D + + + align:start position:0% +angular momentum you're gonna add a D +function and if s was your highest anka + + align:start position:0% +function and if s was your highest anka + + + align:start position:0% +function and if s was your highest anka +Wrentham you're going to add a P + + align:start position:0% +Wrentham you're going to add a P + + + align:start position:0% +Wrentham you're going to add a P +function so hydrogen helium that's got a + + align:start position:0% +function so hydrogen helium that's got a + + + align:start position:0% +function so hydrogen helium that's got a +p2 lithium two argon it's gonna add a D + + align:start position:0% +p2 lithium two argon it's gonna add a D + + + align:start position:0% +p2 lithium two argon it's gonna add a D +if you did this also two transistors + + align:start position:0% +if you did this also two transistors + + + align:start position:0% +if you did this also two transistors +metal atoms you would note the + + align:start position:0% +metal atoms you would note the + + + align:start position:0% +metal atoms you would note the +transition line metal atoms have D + + align:start position:0% +transition line metal atoms have D + + + align:start position:0% +transition line metal atoms have D +functions already so the polarization + + align:start position:0% +functions already so the polarization + + + align:start position:0% +functions already so the polarization +would add in F function just adding one + + align:start position:0% +would add in F function just adding one + + + align:start position:0% +would add in F function just adding one +higher in go Wrentham so then going back + + align:start position:0% +higher in go Wrentham so then going back + + + align:start position:0% +higher in go Wrentham so then going back +to our table up here use my magic copy + + align:start position:0% +to our table up here use my magic copy + + + align:start position:0% +to our table up here use my magic copy +that double zeta basis results here copy + + align:start position:0% + + + + align:start position:0% + +there's my double zeta now I'm just + + align:start position:0% +there's my double zeta now I'm just + + + align:start position:0% +there's my double zeta now I'm just +gonna add the polarisation to this so + + align:start position:0% +gonna add the polarisation to this so + + + align:start position:0% +gonna add the polarisation to this so +double Zeta plus polarization now I add + + align:start position:0% +double Zeta plus polarization now I add + + + align:start position:0% +double Zeta plus polarization now I add +my polarization functions and so for + + align:start position:0% +my polarization functions and so for + + + align:start position:0% +my polarization functions and so for +hydrogen and helium I'm gonna add one P + + align:start position:0% +hydrogen and helium I'm gonna add one P + + + align:start position:0% +hydrogen and helium I'm gonna add one P +function to get a dzp basis set for + + align:start position:0% +function to get a dzp basis set for + + + align:start position:0% +function to get a dzp basis set for +lithium to neon I'm gonna add one D + + align:start position:0% +lithium to neon I'm gonna add one D + + + align:start position:0% +lithium to neon I'm gonna add one D +function for sodium to argon I'm gonna + + align:start position:0% +function for sodium to argon I'm gonna + + + align:start position:0% +function for sodium to argon I'm gonna +add one D function and then I can do the + + align:start position:0% +add one D function and then I can do the + + + align:start position:0% +add one D function and then I can do the +same thing with triple Zeta so if I make + + align:start position:0% +same thing with triple Zeta so if I make + + + align:start position:0% +same thing with triple Zeta so if I make +a tzp basis set and I'll add one p 1d + + align:start position:0% +a tzp basis set and I'll add one p 1d + + + align:start position:0% +a tzp basis set and I'll add one p 1d +and I'll note that you could also do a + + align:start position:0% +and I'll note that you could also do a + + + align:start position:0% +and I'll note that you could also do a +TZ to P basis set and then you're added + + align:start position:0% +TZ to P basis set and then you're added + + + align:start position:0% +TZ to P basis set and then you're added +the 2p just indicates that I'm adding + + align:start position:0% +the 2p just indicates that I'm adding + + + align:start position:0% +the 2p just indicates that I'm adding +even more polarization function so I'm + + align:start position:0% +even more polarization function so I'm + + + align:start position:0% +even more polarization function so I'm +adding two sets of D functions instead + + align:start position:0% +adding two sets of D functions instead + + + align:start position:0% +adding two sets of D functions instead +of just one or two sets of P functions + + align:start position:0% +of just one or two sets of P functions + + + align:start position:0% +of just one or two sets of P functions +instead of just one and then these + + align:start position:0% +instead of just one and then these + + + align:start position:0% +instead of just one and then these +things have names so there's a 6-3 one g + + align:start position:0% +things have names so there's a 6-3 one g + + + align:start position:0% +things have names so there's a 6-3 one g +star which is a very common dzp basis + + align:start position:0% +star which is a very common dzp basis + + + align:start position:0% +star which is a very common dzp basis +set or there's also DZ basis that i + + align:start position:0% +set or there's also DZ basis that i + + + align:start position:0% +set or there's also DZ basis that i +mentioned above has a DZ p + + align:start position:0% +mentioned above has a DZ p + + + align:start position:0% +mentioned above has a DZ p +generalization of it or you could have + + align:start position:0% +generalization of it or you could have + + + align:start position:0% +generalization of it or you could have +for the triple zeta the TZ VP basis or + + align:start position:0% +for the triple zeta the TZ VP basis or + + + align:start position:0% +for the triple zeta the TZ VP basis or +the longest basis set named 6-3 one 1g + + align:start position:0% +the longest basis set named 6-3 one 1g + + + align:start position:0% +the longest basis set named 6-3 one 1g +parentheses D comma P so these are these + + align:start position:0% +parentheses D comma P so these are these + + + align:start position:0% +parentheses D comma P so these are these +are via Noi this is this is where the + + align:start position:0% +are via Noi this is this is where the + + + align:start position:0% +are via Noi this is this is where the +annoyance starts to come in you're like + + align:start position:0% +annoyance starts to come in you're like + + + align:start position:0% +annoyance starts to come in you're like +this is annoying but it's less annoying + + align:start position:0% +this is annoying but it's less annoying + + + align:start position:0% +this is annoying but it's less annoying +than the alternative so we deal with it + + align:start position:0% +than the alternative so we deal with it + + + align:start position:0% +than the alternative so we deal with it +okay so questions about that + + align:start position:0% +okay so questions about that + + + align:start position:0% +okay so questions about that +yeah yep all right sorry like one D just + + align:start position:0% +yeah yep all right sorry like one D just + + + align:start position:0% +yeah yep all right sorry like one D just +like its which one set of D functions + + align:start position:0% +like its which one set of D functions + + + align:start position:0% +like its which one set of D functions +yes yeah yeah yep what oh we could but + + align:start position:0% +yes yeah yeah yep what oh we could but + + + align:start position:0% +yes yeah yeah yep what oh we could but +yeah we couldn't do that so this that + + align:start position:0% +yeah we couldn't do that so this that + + + align:start position:0% +yeah we couldn't do that so this that +part of this has to do with that and + + align:start position:0% +part of this has to do with that and + + + align:start position:0% +part of this has to do with that and +there are a couple of basis sets that do + + align:start position:0% +there are a couple of basis sets that do + + + align:start position:0% +there are a couple of basis sets that do +that this mainly represents the + + align:start position:0% +that this mainly represents the + + + align:start position:0% +that this mainly represents the +hierarchy of empirically what people + + align:start position:0% +hierarchy of empirically what people + + + align:start position:0% +hierarchy of empirically what people +have found is most important so if you + + align:start position:0% +have found is most important so if you + + + align:start position:0% +have found is most important so if you +just start with a minimal single zeta + + align:start position:0% +just start with a minimal single zeta + + + align:start position:0% +just start with a minimal single zeta +basis set you say well what's the next + + align:start position:0% +basis set you say well what's the next + + + align:start position:0% +basis set you say well what's the next +most important thing usually going + + align:start position:0% +most important thing usually going + + + align:start position:0% +most important thing usually going +almost always going to double zeta base + + align:start position:0% +almost always going to double zeta base + + + align:start position:0% +almost always going to double zeta base +double zeta is more important than the + + align:start position:0% +double zeta is more important than the + + + align:start position:0% +double zeta is more important than the +polarization functions so every no one + + align:start position:0% +polarization functions so every no one + + + align:start position:0% +polarization functions so every no one +bothers making very few people bother + + align:start position:0% +bothers making very few people bother + + + align:start position:0% +bothers making very few people bother +making single Zeta plus polarization + + align:start position:0% +making single Zeta plus polarization + + + align:start position:0% +making single Zeta plus polarization +they'll say okay well do double zeta and + + align:start position:0% +they'll say okay well do double zeta and + + + align:start position:0% +they'll say okay well do double zeta and +then after you double say - then maybe + + align:start position:0% +then after you double say - then maybe + + + align:start position:0% +then after you double say - then maybe +you want to go to polarization or maybe + + align:start position:0% +you want to go to polarization or maybe + + + align:start position:0% +you want to go to polarization or maybe +you want to go to triple zeta depending + + align:start position:0% +you want to go to triple zeta depending + + + align:start position:0% +you want to go to triple zeta depending +on what you're doing does that make + + align:start position:0% +on what you're doing does that make + + + align:start position:0% +on what you're doing does that make +sense + + align:start position:0% +sense + + + align:start position:0% +sense +it would be 1 s 1 P 4 hydrogen 2 s 1 P 1 + + align:start position:0% +it would be 1 s 1 P 4 hydrogen 2 s 1 P 1 + + + align:start position:0% +it would be 1 s 1 P 4 hydrogen 2 s 1 P 1 +D 4 carbon it would just be to add that + + align:start position:0% +D 4 carbon it would just be to add that + + + align:start position:0% +D 4 carbon it would just be to add that +extra polarization function on top of + + align:start position:0% +extra polarization function on top of + + + align:start position:0% +extra polarization function on top of +the existing set + + align:start position:0% + + + + align:start position:0% + +which you know what I mean it would be + + align:start position:0% +which you know what I mean it would be + + + align:start position:0% +which you know what I mean it would be +like adding that no so for hydrogen it + + align:start position:0% +like adding that no so for hydrogen it + + + align:start position:0% +like adding that no so for hydrogen it +would be like adding yeah hi drew be + + align:start position:0% +would be like adding yeah hi drew be + + + align:start position:0% +would be like adding yeah hi drew be +like the 2p function but again when we + + align:start position:0% +like the 2p function but again when we + + + align:start position:0% +like the 2p function but again when we +go back we remember that we're not + + align:start position:0% +go back we remember that we're not + + + align:start position:0% +go back we remember that we're not +actually using the hydrogenic functions + + align:start position:0% +actually using the hydrogenic functions + + + align:start position:0% +actually using the hydrogenic functions +we're using gaussians to approximate + + align:start position:0% +we're using gaussians to approximate + + + align:start position:0% +we're using gaussians to approximate +them and so all it really means is that + + align:start position:0% +them and so all it really means is that + + + align:start position:0% +them and so all it really means is that +it has the same angular distribution as + + align:start position:0% +it has the same angular distribution as + + + align:start position:0% +it has the same angular distribution as +a P function but the radial part is + + align:start position:0% +a P function but the radial part is + + + align:start position:0% +a P function but the radial part is +whatever the person who made the basis + + align:start position:0% +whatever the person who made the basis + + + align:start position:0% +whatever the person who made the basis +set decided to make it alright then I + + align:start position:0% +set decided to make it alright then I + + + align:start position:0% +set decided to make it alright then I +have a question so then when I teach + + align:start position:0% +have a question so then when I teach + + + align:start position:0% +have a question so then when I teach +this class I often have clicker + + align:start position:0% +this class I often have clicker + + + align:start position:0% +this class I often have clicker +questions so this would have been the + + align:start position:0% +questions so this would have been the + + + align:start position:0% +questions so this would have been the +clicker question so we'll do it by show + + align:start position:0% +clicker question so we'll do it by show + + + align:start position:0% +clicker question so we'll do it by show +of hands instead of by clicker since you + + align:start position:0% +of hands instead of by clicker since you + + + align:start position:0% +of hands instead of by clicker since you +know we're small enough so so here here + + align:start position:0% +know we're small enough so so here here + + + align:start position:0% +know we're small enough so so here here +here here's a test of whether we + + align:start position:0% +here here's a test of whether we + + + align:start position:0% +here here's a test of whether we +understand I can't show any way so I'll + + align:start position:0% +understand I can't show any way so I'll + + + align:start position:0% +understand I can't show any way so I'll +go back and put the put that put things + + align:start position:0% +go back and put the put that put things + + + align:start position:0% +go back and put the put that put things +up in just a second if you need them but + + align:start position:0% +up in just a second if you need them but + + + align:start position:0% +up in just a second if you need them but +my question is how many basis functions + + align:start position:0% +my question is how many basis functions + + + align:start position:0% +my question is how many basis functions +will there be for C 60 in AD Z P basis + + align:start position:0% +will there be for C 60 in AD Z P basis + + + align:start position:0% +will there be for C 60 in AD Z P basis +set I guess I should say about this so + + align:start position:0% +set I guess I should say about this so + + + align:start position:0% +set I guess I should say about this so +option a is there'll be 60 basis + + align:start position:0% +option a is there'll be 60 basis + + + align:start position:0% +option a is there'll be 60 basis +functions so that would be how many + + align:start position:0% +functions so that would be how many + + + align:start position:0% +functions so that would be how many +basis functions per carbon atom one all + + align:start position:0% +basis functions per carbon atom one all + + + align:start position:0% +basis functions per carbon atom one all +right + + align:start position:0% +right + + + align:start position:0% +right +or 180 that's three per carbon 360 + + align:start position:0% +or 180 that's three per carbon 360 + + + align:start position:0% +or 180 that's three per carbon 360 +that's six per carbon 840 is okay + + align:start position:0% +that's six per carbon 840 is okay + + + align:start position:0% +that's six per carbon 840 is okay +anybody do the math better than me is + + align:start position:0% +anybody do the math better than me is + + + align:start position:0% +anybody do the math better than me is +that fourteen no no wait yeah it's + + align:start position:0% +that fourteen no no wait yeah it's + + + align:start position:0% +that fourteen no no wait yeah it's +fourteen yeah fourteen fourteen per + + align:start position:0% +fourteen yeah fourteen fourteen per + + + align:start position:0% +fourteen yeah fourteen fourteen per +carbon this is huh eighteen and then + + align:start position:0% +carbon this is huh eighteen and then + + + align:start position:0% +carbon this is huh eighteen and then +this is twenty-one then right yes so so + + align:start position:0% +this is twenty-one then right yes so so + + + align:start position:0% +this is twenty-one then right yes so so +we've got one three six fourteen + + align:start position:0% +we've got one three six fourteen + + + align:start position:0% +we've got one three six fourteen +eighteen twenty-one as the number of + + align:start position:0% +eighteen twenty-one as the number of + + + align:start position:0% +eighteen twenty-one as the number of +basis functions per and I'll go back and + + align:start position:0% +basis functions per and I'll go back and + + + align:start position:0% +basis functions per and I'll go back and +throw this up for those who want the + + align:start position:0% +throw this up for those who want the + + + align:start position:0% +throw this up for those who want the +table up we didn't write all that down + + align:start position:0% +table up we didn't write all that down + + + align:start position:0% +table up we didn't write all that down +so here's our easy P basis vet carbons + + align:start position:0% +so here's our easy P basis vet carbons + + + align:start position:0% +so here's our easy P basis vet carbons +in this this group here + + align:start position:0% +in this this group here + + + align:start position:0% +in this this group here +so I'll give you a minute to think about + + align:start position:0% +so I'll give you a minute to think about + + + align:start position:0% +so I'll give you a minute to think about +it all right so then now I'll go back + + align:start position:0% +it all right so then now I'll go back + + + align:start position:0% +it all right so then now I'll go back +everybody feel like they got their + + align:start position:0% +everybody feel like they got their + + + align:start position:0% +everybody feel like they got their +answer okay so how so by show of hands + + align:start position:0% +answer okay so how so by show of hands + + + align:start position:0% +answer okay so how so by show of hands +how many people think the answer is a 60 + + align:start position:0% +how many people think the answer is a 60 + + + align:start position:0% +how many people think the answer is a 60 +nobody all right how about b/c we got + + align:start position:0% +nobody all right how about b/c we got + + + align:start position:0% +nobody all right how about b/c we got +most on C okay D I don't know what e F + + align:start position:0% +most on C okay D I don't know what e F + + + align:start position:0% +most on C okay D I don't know what e F +okay everybody every since C C is not + + align:start position:0% +okay everybody every since C C is not + + + align:start position:0% +okay everybody every since C C is not +the correct answer and every year every + + align:start position:0% +the correct answer and every year every + + + align:start position:0% +the correct answer and every year every +year but if you people miss this + + align:start position:0% +year but if you people miss this + + + align:start position:0% +year but if you people miss this +question so so the the the key thing to + + align:start position:0% +question so so the the the key thing to + + + align:start position:0% +question so so the the the key thing to +get that get this right them we're gonna + + align:start position:0% +get that get this right them we're gonna + + + align:start position:0% +get that get this right them we're gonna +repol in a minute here but the key thing + + align:start position:0% +repol in a minute here but the key thing + + + align:start position:0% +repol in a minute here but the key thing +to get this right was actually the + + align:start position:0% +to get this right was actually the + + + align:start position:0% +to get this right was actually the +question that you asked which is that + + align:start position:0% +question that you asked which is that + + + align:start position:0% +question that you asked which is that +you said when I add the defunct who do I + + align:start position:0% +you said when I add the defunct who do I + + + align:start position:0% +you said when I add the defunct who do I +add D when I add a DP folks do I had DZ + + align:start position:0% +add D when I add a DP folks do I had DZ + + + align:start position:0% +add D when I add a DP folks do I had DZ +squared or do I and I said no you add a + + align:start position:0% +squared or do I and I said no you add a + + + align:start position:0% +squared or do I and I said no you add a +set of D functions which is how many + + align:start position:0% +set of D functions which is how many + + + align:start position:0% +set of D functions which is how many +functions in d5 all right so now Han + + align:start position:0% +functions in d5 all right so now Han + + + align:start position:0% +functions in d5 all right so now Han +will go back and look all right but + + align:start position:0% +will go back and look all right but + + + align:start position:0% +will go back and look all right but +don't feel bad it happened every year + + align:start position:0% +don't feel bad it happened every year + + + align:start position:0% +don't feel bad it happened every year +the majority of people choose choose + + align:start position:0% +the majority of people choose choose + + + align:start position:0% +the majority of people choose choose +that same answer so now let's do that's + + align:start position:0% +that same answer so now let's do that's + + + align:start position:0% +that same answer so now let's do that's +redo our math never gotten it right okay + + align:start position:0% + + + + align:start position:0% + +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +all right so now now we'll go through + + align:start position:0% +all right so now now we'll go through + + + align:start position:0% +all right so now now we'll go through +okay how many people think a how many B + + align:start position:0% +okay how many people think a how many B + + + align:start position:0% +okay how many people think a how many B +okay nobody just AC because iron told + + align:start position:0% +okay nobody just AC because iron told + + + align:start position:0% +okay nobody just AC because iron told +Ron how many people say D alright good + + align:start position:0% +Ron how many people say D alright good + + + align:start position:0% +Ron how many people say D alright good +you're alright yes the answer is D and + + align:start position:0% +you're alright yes the answer is D and + + + align:start position:0% +you're alright yes the answer is D and +the dzp basis there are 14 basis + + align:start position:0% +the dzp basis there are 14 basis + + + align:start position:0% +the dzp basis there are 14 basis +functions per carbon atom now you can + + align:start position:0% +functions per carbon atom now you can + + + align:start position:0% +functions per carbon atom now you can +already start to see in for this D Z P + + align:start position:0% +already start to see in for this D Z P + + + align:start position:0% +already start to see in for this D Z P +basis which isn't the biggest basis + + align:start position:0% +basis which isn't the biggest basis + + + align:start position:0% +basis which isn't the biggest basis +we've talked about for C 60 you've got + + align:start position:0% +we've talked about for C 60 you've got + + + align:start position:0% +we've talked about for C 60 you've got +840 basis functions that's a lot of + + align:start position:0% +840 basis functions that's a lot of + + + align:start position:0% +840 basis functions that's a lot of +basis functions so that's why we're + + align:start position:0% +basis functions so that's why we're + + + align:start position:0% +basis functions so that's why we're +really glad that the computer is doing + + align:start position:0% +really glad that the computer is doing + + + align:start position:0% +really glad that the computer is doing +the work and not us because 840 + + align:start position:0% +the work and not us because 840 + + + align:start position:0% +the work and not us because 840 +integrals + + align:start position:0% +integrals + + + align:start position:0% +integrals +well 840 by 840 matrices are hard to + + align:start position:0% +well 840 by 840 matrices are hard to + + + align:start position:0% +well 840 by 840 matrices are hard to +diagonalize by hand doing all those + + align:start position:0% +diagonalize by hand doing all those + + + align:start position:0% +diagonalize by hand doing all those +integrals is really really a pain ok so + + align:start position:0% +integrals is really really a pain ok so + + + align:start position:0% +integrals is really really a pain ok so +then going beyond those basis so those + + align:start position:0% +then going beyond those basis so those + + + align:start position:0% +then going beyond those basis so those +two things are the key basis set ideas I + + align:start position:0% +two things are the key basis set ideas I + + + align:start position:0% +two things are the key basis set ideas I +will I'll just touch on a couple of + + align:start position:0% +will I'll just touch on a couple of + + + align:start position:0% +will I'll just touch on a couple of +other things before we before we finish + + align:start position:0% +other things before we before we finish + + + align:start position:0% +other things before we before we finish +up so the first thing is diffuse + + align:start position:0% +up so the first thing is diffuse + + + align:start position:0% +up so the first thing is diffuse +functions so occasionally if you have an + + align:start position:0% +functions so occasionally if you have an + + + align:start position:0% +functions so occasionally if you have an +anion so you have an extra electron that + + align:start position:0% +anion so you have an extra electron that + + + align:start position:0% +anion so you have an extra electron that +extra electron is not very well + + align:start position:0% +extra electron is not very well + + + align:start position:0% +extra electron is not very well +described by the valence because + + align:start position:0% +described by the valence because + + + align:start position:0% +described by the valence because +negative negative electrons tend to + + align:start position:0% +negative negative electrons tend to + + + align:start position:0% +negative negative electrons tend to +spread out a great deal if Bob is one of + + align:start position:0% +spread out a great deal if Bob is one of + + + align:start position:0% +spread out a great deal if Bob is one of +the world experts in in Rid Berg states + + align:start position:0% +the world experts in in Rid Berg states + + + align:start position:0% +the world experts in in Rid Berg states +which is where these electrons spread + + align:start position:0% +which is where these electrons spread + + + align:start position:0% +which is where these electrons spread +out a really really significant amount + + align:start position:0% +out a really really significant amount + + + align:start position:0% +out a really really significant amount +and so these Gaussian functions that + + align:start position:0% +and so these Gaussian functions that + + + align:start position:0% +and so these Gaussian functions that +decay quickly don't describe those well + + align:start position:0% +decay quickly don't describe those well + + + align:start position:0% +decay quickly don't describe those well +and so you have to add a Gaussian with a + + align:start position:0% +and so you have to add a Gaussian with a + + + align:start position:0% +and so you have to add a Gaussian with a +small value of alpha and it's mostly + + align:start position:0% +small value of alpha and it's mostly + + + align:start position:0% +small value of alpha and it's mostly +useful for anions and so you'll del you + + align:start position:0% +useful for anions and so you'll del you + + + align:start position:0% +useful for anions and so you'll del you +the so you add these in order to + + align:start position:0% +the so you add these in order to + + + align:start position:0% +the so you add these in order to +describe anions better and the notation + + align:start position:0% +describe anions better and the notation + + + align:start position:0% +describe anions better and the notation +here is either you use the phrase AAG or + + align:start position:0% +here is either you use the phrase AAG or + + + align:start position:0% +here is either you use the phrase AAG or +plus so the basis that has the word log + + align:start position:0% +plus so the basis that has the word log + + + align:start position:0% +plus so the basis that has the word log +in front of it that means it has some + + align:start position:0% +in front of it that means it has some + + + align:start position:0% +in front of it that means it has some +diffuse functions on it in order to + + align:start position:0% +diffuse functions on it in order to + + + align:start position:0% +diffuse functions on it in order to +describe those and weakly bound + + align:start position:0% +describe those and weakly bound + + + align:start position:0% +describe those and weakly bound +electrons or the plus indicates it has + + align:start position:0% +electrons or the plus indicates it has + + + align:start position:0% +electrons or the plus indicates it has +some of those functions in it and again + + align:start position:0% +some of those functions in it and again + + + align:start position:0% +some of those functions in it and again +that those are added with the same + + align:start position:0% +that those are added with the same + + + align:start position:0% +that those are added with the same +angular momentum is the valence they're + + align:start position:0% +angular momentum is the valence they're + + + align:start position:0% +angular momentum is the valence they're +not usually polarization and diffused at + + align:start position:0% +not usually polarization and diffused at + + + align:start position:0% +not usually polarization and diffused at +the same time + + align:start position:0% +the same time + + + align:start position:0% +the same time +and then the final thing is you can + + align:start position:0% +and then the final thing is you can + + + align:start position:0% +and then the final thing is you can +generalize these ideas to transition + + align:start position:0% +generalize these ideas to transition + + + align:start position:0% +generalize these ideas to transition +metals it's a little bit hazy because a + + align:start position:0% +metals it's a little bit hazy because a + + + align:start position:0% +metals it's a little bit hazy because a +lot of this is predicated on us knowing + + align:start position:0% +lot of this is predicated on us knowing + + + align:start position:0% +lot of this is predicated on us knowing +what the valence of the element is and + + align:start position:0% +what the valence of the element is and + + + align:start position:0% +what the valence of the element is and +for transition metals it's like well is + + align:start position:0% +for transition metals it's like well is + + + align:start position:0% +for transition metals it's like well is +s and the valence + + align:start position:0% +s and the valence + + + align:start position:0% +s and the valence +yeah probably is P in the valence well + + align:start position:0% +yeah probably is P in the valence well + + + align:start position:0% +yeah probably is P in the valence well +maybe I don't know D is definitely in + + align:start position:0% +maybe I don't know D is definitely in + + + align:start position:0% +maybe I don't know D is definitely in +the valence but depending on whether you + + align:start position:0% +the valence but depending on whether you + + + align:start position:0% +the valence but depending on whether you +think of what you think the valence is + + align:start position:0% +think of what you think the valence is + + + align:start position:0% +think of what you think the valence is +your definition of some of these things + + align:start position:0% +your definition of some of these things + + + align:start position:0% +your definition of some of these things +is a little bit fuzzier sometimes you + + align:start position:0% +is a little bit fuzzier sometimes you + + + align:start position:0% +is a little bit fuzzier sometimes you +add a P function sometimes you don't + + align:start position:0% +add a P function sometimes you don't + + + align:start position:0% +add a P function sometimes you don't +when you go from triple Zeta double Zeta + + align:start position:0% +when you go from triple Zeta double Zeta + + + align:start position:0% +when you go from triple Zeta double Zeta +to triple data for a transition metal + + align:start position:0% +to triple data for a transition metal + + + align:start position:0% +to triple data for a transition metal +and but the overall idea here is that + + align:start position:0% +and but the overall idea here is that + + + align:start position:0% +and but the overall idea here is that +we're trying to approach this this + + align:start position:0% +we're trying to approach this this + + + align:start position:0% +we're trying to approach this this +particular limit which is known as the + + align:start position:0% +particular limit which is known as the + + + align:start position:0% +particular limit which is known as the +complete basis set limit which is the + + align:start position:0% +complete basis set limit which is the + + + align:start position:0% +complete basis set limit which is the +result that you would hypothetically get + + align:start position:0% +result that you would hypothetically get + + + align:start position:0% +result that you would hypothetically get +with an infinite number of atomic + + align:start position:0% +with an infinite number of atomic + + + align:start position:0% +with an infinite number of atomic +orbitals so you just crank up conclude + + align:start position:0% +orbitals so you just crank up conclude + + + align:start position:0% +orbitals so you just crank up conclude +all the time the corbels the university + + align:start position:0% +all the time the corbels the university + + + align:start position:0% +all the time the corbels the university +would get to an answer that would be the + + align:start position:0% +would get to an answer that would be the + + + align:start position:0% +would get to an answer that would be the +right answer and we're just trying to + + align:start position:0% +right answer and we're just trying to + + + align:start position:0% +right answer and we're just trying to +asymptotically approach that by making + + align:start position:0% +asymptotically approach that by making + + + align:start position:0% +asymptotically approach that by making +our basis sets bigger and bigger until + + align:start position:0% +our basis sets bigger and bigger until + + + align:start position:0% +our basis sets bigger and bigger until +we run out of steam okay all right so + + align:start position:0% +we run out of steam okay all right so + + + align:start position:0% +we run out of steam okay all right so +that's everything about basis sets and + + align:start position:0% +that's everything about basis sets and + + + align:start position:0% +that's everything about basis sets and +tomorrow or not tomorrow next Monday we + + align:start position:0% +tomorrow or not tomorrow next Monday we + + + align:start position:0% +tomorrow or not tomorrow next Monday we +will talk about how you compute the + + align:start position:0% +will talk about how you compute the + + + align:start position:0% +will talk about how you compute the +energy all right + + align:start position:0% +energy all right + + + align:start position:0% +energy all right +Happy Thanksgiving \ No newline at end of file diff --git a/BVHwDed_X_w.txt b/BVHwDed_X_w.txt new file mode 100644 index 0000000000000000000000000000000000000000..5fc337c47a305fd74277e9baef942eb9a72182ee --- /dev/null +++ b/BVHwDed_X_w.txt @@ -0,0 +1,2579 @@ +align:start position:0% + +um this is a shumit + + align:start position:0% +um this is a shumit + + + align:start position:0% +um this is a shumit +pond uh to give you a perspective if you + + align:start position:0% +pond uh to give you a perspective if you + + + align:start position:0% +pond uh to give you a perspective if you +look at page + + align:start position:0% +look at page + + + align:start position:0% +look at page +12 that's page 12 see a shumit pond up + + align:start position:0% +12 that's page 12 see a shumit pond up + + + align:start position:0% +12 that's page 12 see a shumit pond up +here we're about 1,500 to 2,000 ft away + + align:start position:0% +here we're about 1,500 to 2,000 ft away + + + align:start position:0% +here we're about 1,500 to 2,000 ft away +from the SE disposal beds here which are + + align:start position:0% +from the SE disposal beds here which are + + + align:start position:0% +from the SE disposal beds here which are +obviously where we just came from all + + align:start position:0% +obviously where we just came from all + + + align:start position:0% +obviously where we just came from all +right um the water table Contour are + + align:start position:0% +right um the water table Contour are + + + align:start position:0% +right um the water table Contour are +shown uh in here that uh water tower you + + align:start position:0% +shown uh in here that uh water tower you + + + align:start position:0% +shown uh in here that uh water tower you +see over there is on the base uh but + + align:start position:0% +see over there is on the base uh but + + + align:start position:0% +see over there is on the base uh but +we're off the base now obviously um a + + align:start position:0% +we're off the base now obviously um a + + + align:start position:0% +we're off the base now obviously um a +Sho pond is um is typical of uh ponds on + + align:start position:0% +Sho pond is um is typical of uh ponds on + + + align:start position:0% +Sho pond is um is typical of uh ponds on +the cape it's a glacial kettle Pond and + + align:start position:0% +the cape it's a glacial kettle Pond and + + + align:start position:0% +the cape it's a glacial kettle Pond and +what that means is that you can imagine + + align:start position:0% +what that means is that you can imagine + + + align:start position:0% +what that means is that you can imagine +uh when the ice sheets were here and + + align:start position:0% +uh when the ice sheets were here and + + + align:start position:0% +uh when the ice sheets were here and +they they were Advanced all the way to + + align:start position:0% +they they were Advanced all the way to + + + align:start position:0% +they they were Advanced all the way to +marus Vineyard and Nantucket then they + + align:start position:0% +marus Vineyard and Nantucket then they + + + align:start position:0% +marus Vineyard and Nantucket then they +retreated and we use the word Retreat + + align:start position:0% +retreated and we use the word Retreat + + + align:start position:0% +retreated and we use the word Retreat +rather Loosely they don't actually the + + align:start position:0% +rather Loosely they don't actually the + + + align:start position:0% +rather Loosely they don't actually the +ice doesn't grind backwards you know + + align:start position:0% +ice doesn't grind backwards you know + + + align:start position:0% +ice doesn't grind backwards you know +what happens really happens is that the + + align:start position:0% +what happens really happens is that the + + + align:start position:0% +what happens really happens is that the +The Ice uh doesn't Advance as fast as + + align:start position:0% +The Ice uh doesn't Advance as fast as + + + align:start position:0% +The Ice uh doesn't Advance as fast as +it's melting away and eventually it sort + + align:start position:0% +it's melting away and eventually it sort + + + align:start position:0% +it's melting away and eventually it sort +of rots and gets you know melts away and + + align:start position:0% +of rots and gets you know melts away and + + + align:start position:0% +of rots and gets you know melts away and +leaves blocks temporarily and then the + + align:start position:0% +leaves blocks temporarily and then the + + + align:start position:0% +leaves blocks temporarily and then the +blocks eventually melt away and then + + align:start position:0% +blocks eventually melt away and then + + + align:start position:0% +blocks eventually melt away and then +there's a new front that's that occurs + + align:start position:0% +there's a new front that's that occurs + + + align:start position:0% +there's a new front that's that occurs +when the ice is advancing at the same + + align:start position:0% +when the ice is advancing at the same + + + align:start position:0% +when the ice is advancing at the same +rate it's melting so that's what + + align:start position:0% +rate it's melting so that's what + + + align:start position:0% +rate it's melting so that's what +happened is the ice began to advance + + align:start position:0% +happened is the ice began to advance + + + align:start position:0% +happened is the ice began to advance +more slowly than it was melting so it + + align:start position:0% +more slowly than it was melting so it + + + align:start position:0% +more slowly than it was melting so it +began to recede the front began to + + align:start position:0% +began to recede the front began to + + + align:start position:0% +began to recede the front began to +recede to about here and then for some + + align:start position:0% +recede to about here and then for some + + + align:start position:0% +recede to about here and then for some +period of time it stayed here and dumped + + align:start position:0% +period of time it stayed here and dumped + + + align:start position:0% +period of time it stayed here and dumped +some Sands and gravels well when it did + + align:start position:0% +some Sands and gravels well when it did + + + align:start position:0% +some Sands and gravels well when it did +that and those sand and gravel outwash + + align:start position:0% +that and those sand and gravel outwash + + + align:start position:0% +that and those sand and gravel outwash +is coming out ahead of it like you see + + align:start position:0% +is coming out ahead of it like you see + + + align:start position:0% +is coming out ahead of it like you see +in the pictures in Alaska or Greenland + + align:start position:0% +in the pictures in Alaska or Greenland + + + align:start position:0% +in the pictures in Alaska or Greenland +or New Zealand there were ice blocks + + align:start position:0% +or New Zealand there were ice blocks + + + align:start position:0% +or New Zealand there were ice blocks +left out ahead that hadn't melted yet + + align:start position:0% +left out ahead that hadn't melted yet + + + align:start position:0% +left out ahead that hadn't melted yet +and they got buried in the sand so what + + align:start position:0% +and they got buried in the sand so what + + + align:start position:0% +and they got buried in the sand so what +happens you have this beautiful plane of + + align:start position:0% +happens you have this beautiful plane of + + + align:start position:0% +happens you have this beautiful plane of +Sands and gravels with these braided + + align:start position:0% +Sands and gravels with these braided + + + align:start position:0% +Sands and gravels with these braided +streams but buried underne underneath + + align:start position:0% +streams but buried underne underneath + + + align:start position:0% +streams but buried underne underneath +our blocks of ice that hadn't had a + + align:start position:0% +our blocks of ice that hadn't had a + + + align:start position:0% +our blocks of ice that hadn't had a +chance to melt yet when they got buried + + align:start position:0% +chance to melt yet when they got buried + + + align:start position:0% +chance to melt yet when they got buried +and they gradually over the next couple + + align:start position:0% +and they gradually over the next couple + + + align:start position:0% +and they gradually over the next couple +thousand years melted out when they did + + align:start position:0% +thousand years melted out when they did + + + align:start position:0% +thousand years melted out when they did +they left the depression and if the + + align:start position:0% +they left the depression and if the + + + align:start position:0% +they left the depression and if the +depressions are deep enough the water + + align:start position:0% +depressions are deep enough the water + + + align:start position:0% +depressions are deep enough the water +table intersects them and they fill with + + align:start position:0% +table intersects them and they fill with + + + align:start position:0% +table intersects them and they fill with +water so these are actually locations of + + align:start position:0% +water so these are actually locations of + + + align:start position:0% +water so these are actually locations of +ice blocks that were left behind as the + + align:start position:0% +ice blocks that were left behind as the + + + align:start position:0% +ice blocks that were left behind as the +glacier melted that's later on collapsed + + align:start position:0% +glacier melted that's later on collapsed + + + align:start position:0% +glacier melted that's later on collapsed +in does that make sense everybody the + + align:start position:0% +in does that make sense everybody the + + + align:start position:0% +in does that make sense everybody the +other way I like to look at is if you go + + align:start position:0% +other way I like to look at is if you go + + + align:start position:0% +other way I like to look at is if you go +to the beach at low tide the ocean beach + + align:start position:0% +to the beach at low tide the ocean beach + + + align:start position:0% +to the beach at low tide the ocean beach +at low tide and you dig a little hole + + align:start position:0% +at low tide and you dig a little hole + + + align:start position:0% +at low tide and you dig a little hole +with your hand eventually it fills up + + align:start position:0% +with your hand eventually it fills up + + + align:start position:0% +with your hand eventually it fills up +with water you intersected the water + + align:start position:0% +with water you intersected the water + + + align:start position:0% +with water you intersected the water +table and you made yourself a little + + align:start position:0% +table and you made yourself a little + + + align:start position:0% +table and you made yourself a little +Kettle Pond okay so what's unique about + + align:start position:0% +Kettle Pond okay so what's unique about + + + align:start position:0% +Kettle Pond okay so what's unique about +these ponds is that although some of + + align:start position:0% +these ponds is that although some of + + + align:start position:0% +these ponds is that although some of +them have small streams coming out of + + align:start position:0% +them have small streams coming out of + + + align:start position:0% +them have small streams coming out of +them uh for the most part they're + + align:start position:0% +them uh for the most part they're + + + align:start position:0% +them uh for the most part they're +groundwater fed by direct discharge of + + align:start position:0% +groundwater fed by direct discharge of + + + align:start position:0% +groundwater fed by direct discharge of +groundwater and groundwater leaves them + + align:start position:0% +groundwater and groundwater leaves them + + + align:start position:0% +groundwater and groundwater leaves them +on the outflow side they're called + + align:start position:0% +on the outflow side they're called + + + align:start position:0% +on the outflow side they're called +groundwater flow through ponds right um + + align:start position:0% +groundwater flow through ponds right um + + + align:start position:0% +groundwater flow through ponds right um +and a shumit pond is one of those this + + align:start position:0% +and a shumit pond is one of those this + + + align:start position:0% +and a shumit pond is one of those this +really reflects the position of the + + align:start position:0% +really reflects the position of the + + + align:start position:0% +really reflects the position of the +water table in this area so the pond + + align:start position:0% +water table in this area so the pond + + + align:start position:0% +water table in this area so the pond +level right now is about 44 ft above sea + + align:start position:0% +level right now is about 44 ft above sea + + + align:start position:0% +level right now is about 44 ft above sea +level that's about the average water + + align:start position:0% +level that's about the average water + + + align:start position:0% +level that's about the average water +table around the lake right so it's + + align:start position:0% +table around the lake right so it's + + + align:start position:0% +table around the lake right so it's +really a I think of it as an outcrop of + + align:start position:0% +really a I think of it as an outcrop of + + + align:start position:0% +really a I think of it as an outcrop of +the water table right um the reason why + + align:start position:0% +the water table right um the reason why + + + align:start position:0% +the water table right um the reason why +we stopped here is uh that's the map of + + align:start position:0% +we stopped here is uh that's the map of + + + align:start position:0% +we stopped here is uh that's the map of +the sewage plume I showed you before and + + align:start position:0% +the sewage plume I showed you before and + + + align:start position:0% +the sewage plume I showed you before and +see this little sh shaded area up near + + align:start position:0% +see this little sh shaded area up near + + + align:start position:0% +see this little sh shaded area up near +the pond that this area of phosphorous + + align:start position:0% +the pond that this area of phosphorous + + + align:start position:0% +the pond that this area of phosphorous +contamination that's basically between + + align:start position:0% +contamination that's basically between + + + align:start position:0% +contamination that's basically between +us and the lake and the sewage plant um + + align:start position:0% +us and the lake and the sewage plant um + + + align:start position:0% +us and the lake and the sewage plant um +one of the contaminants of concern in + + align:start position:0% +one of the contaminants of concern in + + + align:start position:0% +one of the contaminants of concern in +sewage effluent is phosphorus uh a lot + + align:start position:0% +sewage effluent is phosphorus uh a lot + + + align:start position:0% +sewage effluent is phosphorus uh a lot +of surface water fresh waters um the + + align:start position:0% +of surface water fresh waters um the + + + align:start position:0% +of surface water fresh waters um the +ecosystems the productivity of the + + align:start position:0% +ecosystems the productivity of the + + + align:start position:0% +ecosystems the productivity of the +ecosystems are limited by the + + align:start position:0% +ecosystems are limited by the + + + align:start position:0% +ecosystems are limited by the +availability of phosphorus which of + + align:start position:0% +availability of phosphorus which of + + + align:start position:0% +availability of phosphorus which of +course is a a micronutrient that you + + align:start position:0% +course is a a micronutrient that you + + + align:start position:0% +course is a a micronutrient that you +know is essential to life so a lot of + + align:start position:0% +know is essential to life so a lot of + + + align:start position:0% +know is essential to life so a lot of +algae and macrofit plants uh would grow + + align:start position:0% +algae and macrofit plants uh would grow + + + align:start position:0% +algae and macrofit plants uh would grow +if there was enough phosphorus but they + + align:start position:0% +if there was enough phosphorus but they + + + align:start position:0% +if there was enough phosphorus but they +the growth is limited by the + + align:start position:0% +the growth is limited by the + + + align:start position:0% +the growth is limited by the +availability of phosphorus there isn't + + align:start position:0% +availability of phosphorus there isn't + + + align:start position:0% +availability of phosphorus there isn't +enough in the natural systems so the + + align:start position:0% +enough in the natural systems so the + + + align:start position:0% +enough in the natural systems so the +waters remain relatively clear which we + + align:start position:0% +waters remain relatively clear which we + + + align:start position:0% +waters remain relatively clear which we +consider good and clean which we + + align:start position:0% +consider good and clean which we + + + align:start position:0% +consider good and clean which we +consider good and there aren't a lot of + + align:start position:0% +consider good and there aren't a lot of + + + align:start position:0% +consider good and there aren't a lot of +weeds and algae which we consider good + + align:start position:0% +weeds and algae which we consider good + + + align:start position:0% +weeds and algae which we consider good +makes a nice for swimming fishing + + align:start position:0% +makes a nice for swimming fishing + + + align:start position:0% +makes a nice for swimming fishing +whatever else if you begin to add a + + align:start position:0% +whatever else if you begin to add a + + + align:start position:0% +whatever else if you begin to add a +phosphorus source to a typical + + align:start position:0% +phosphorus source to a typical + + + align:start position:0% +phosphorus source to a typical +freshwater lake in New England or in + + align:start position:0% +freshwater lake in New England or in + + + align:start position:0% +freshwater lake in New England or in +most places what happens is you sort of + + align:start position:0% +most places what happens is you sort of + + + align:start position:0% +most places what happens is you sort of +take the lid off of that limit and now + + align:start position:0% +take the lid off of that limit and now + + + align:start position:0% +take the lid off of that limit and now +the bacteria not the bacteria the algae + + align:start position:0% +the bacteria not the bacteria the algae + + + align:start position:0% +the bacteria not the bacteria the algae +can begin to bloom you guys have heard + + align:start position:0% +can begin to bloom you guys have heard + + + align:start position:0% +can begin to bloom you guys have heard +of Alo blooms okay so there's a real + + align:start position:0% +of Alo blooms okay so there's a real + + + align:start position:0% +of Alo blooms okay so there's a real +concern about the fade of the phosphorus + + align:start position:0% +concern about the fade of the phosphorus + + + align:start position:0% +concern about the fade of the phosphorus +coming out of the old sewage plant now + + align:start position:0% +coming out of the old sewage plant now + + + align:start position:0% +coming out of the old sewage plant now +phosphorus is unique as compared to say + + align:start position:0% +phosphorus is unique as compared to say + + + align:start position:0% +phosphorus is unique as compared to say +nitrate or chloride or boron in that it + + align:start position:0% +nitrate or chloride or boron in that it + + + align:start position:0% +nitrate or chloride or boron in that it +has a strong Affinity to stick to the + + align:start position:0% +has a strong Affinity to stick to the + + + align:start position:0% +has a strong Affinity to stick to the +iron oxides that coat the sediments and + + align:start position:0% +iron oxides that coat the sediments and + + + align:start position:0% +iron oxides that coat the sediments and +make them brown right so phosphorus + + align:start position:0% +make them brown right so phosphorus + + + align:start position:0% +make them brown right so phosphorus +likes to absorb to the iron oxides to + + align:start position:0% +likes to absorb to the iron oxides to + + + align:start position:0% +likes to absorb to the iron oxides to +the point where if I take a packet of + + align:start position:0% +the point where if I take a packet of + + + align:start position:0% +the point where if I take a packet of +water in the plume somewhere and I cut + + align:start position:0% +water in the plume somewhere and I cut + + + align:start position:0% +water in the plume somewhere and I cut +out a one cubic foot piece of acfer sand + + align:start position:0% +out a one cubic foot piece of acfer sand + + + align:start position:0% +out a one cubic foot piece of acfer sand +and water together and I look at all the + + align:start position:0% +and water together and I look at all the + + + align:start position:0% +and water together and I look at all the +phosphorus in that packet something like + + align:start position:0% +phosphorus in that packet something like + + + align:start position:0% +phosphorus in that packet something like +99% of it is absorbed to the sediments + + align:start position:0% +99% of it is absorbed to the sediments + + + align:start position:0% +99% of it is absorbed to the sediments +and only a little bit of it is in the + + align:start position:0% +and only a little bit of it is in the + + + align:start position:0% +and only a little bit of it is in the +water it's like the tip of the iceberg + + align:start position:0% +water it's like the tip of the iceberg + + + align:start position:0% +water it's like the tip of the iceberg +is what's in the water the phosphorus + + align:start position:0% +is what's in the water the phosphorus + + + align:start position:0% +is what's in the water the phosphorus +loves to stay on the sediments the + + align:start position:0% +loves to stay on the sediments the + + + align:start position:0% +loves to stay on the sediments the +result is that the phosphorus moves much + + align:start position:0% +result is that the phosphorus moves much + + + align:start position:0% +result is that the phosphorus moves much +more slowly than the other contaminants + + align:start position:0% +more slowly than the other contaminants + + + align:start position:0% +more slowly than the other contaminants +so even though the the water is moving + + align:start position:0% +so even though the the water is moving + + + align:start position:0% +so even though the the water is moving +at 1 to 2 ft per day the phosphorus is + + align:start position:0% +at 1 to 2 ft per day the phosphorus is + + + align:start position:0% +at 1 to 2 ft per day the phosphorus is +what we call greatly relative + + align:start position:0% +what we call greatly relative + + + align:start position:0% +what we call greatly relative +to other species it doesn't move very + + align:start position:0% +to other species it doesn't move very + + + align:start position:0% +to other species it doesn't move very +fast right the analogy I like to use if + + align:start position:0% +fast right the analogy I like to use if + + + align:start position:0% +fast right the analogy I like to use if +if you guys haven't you know haven't + + align:start position:0% +if you guys haven't you know haven't + + + align:start position:0% +if you guys haven't you know haven't +been exposed to this before and if you + + align:start position:0% +been exposed to this before and if you + + + align:start position:0% +been exposed to this before and if you +have you have to forgive me cuz it's + + align:start position:0% +have you have to forgive me cuz it's + + + align:start position:0% +have you have to forgive me cuz it's +kind of Mickey Mouse is um when you get + + align:start position:0% +kind of Mickey Mouse is um when you get + + + align:start position:0% +kind of Mickey Mouse is um when you get +in your car and you drive from Boston to + + align:start position:0% +in your car and you drive from Boston to + + + align:start position:0% +in your car and you drive from Boston to +New York it's 200 miles and you know you + + align:start position:0% +New York it's 200 miles and you know you + + + align:start position:0% +New York it's 200 miles and you know you +do the math in your head and you go I'm + + align:start position:0% +do the math in your head and you go I'm + + + align:start position:0% +do the math in your head and you go I'm +going to go I'm going to average 60 M an + + align:start position:0% +going to go I'm going to average 60 M an + + + align:start position:0% +going to go I'm going to average 60 M an +hour you know it's going to take me 3 + + align:start position:0% +hour you know it's going to take me 3 + + + align:start position:0% +hour you know it's going to take me 3 +hours and it always takes you 5 hours + + align:start position:0% +hours and it always takes you 5 hours + + + align:start position:0% +hours and it always takes you 5 hours +because you stop at the rest area for a + + align:start position:0% +because you stop at the rest area for a + + + align:start position:0% +because you stop at the rest area for a +while + + align:start position:0% +while + + + align:start position:0% +while +and so your average speed is lower even + + align:start position:0% +and so your average speed is lower even + + + align:start position:0% +and so your average speed is lower even +though when you're in the car you're + + align:start position:0% +though when you're in the car you're + + + align:start position:0% +though when you're in the car you're +moving 60 M an hour you know you have to + + align:start position:0% +moving 60 M an hour you know you have to + + + align:start position:0% +moving 60 M an hour you know you have to +average your speed for the trip while + + align:start position:0% +average your speed for the trip while + + + align:start position:0% +average your speed for the trip while +phosphorus is in the rest area 99% of + + align:start position:0% +phosphorus is in the rest area 99% of + + + align:start position:0% +phosphorus is in the rest area 99% of +the time so it takes a long time to make + + align:start position:0% +the time so it takes a long time to make + + + align:start position:0% +the time so it takes a long time to make +the trip okay so in the 60 years that + + align:start position:0% +the trip okay so in the 60 years that + + + align:start position:0% +the trip okay so in the 60 years that +disposal occurred the toe of the plume + + align:start position:0% +disposal occurred the toe of the plume + + + align:start position:0% +disposal occurred the toe of the plume +at a foot a day if you do a foot a day + + align:start position:0% +at a foot a day if you do a foot a day + + + align:start position:0% +at a foot a day if you do a foot a day +you know times 60 years it's made it all + + align:start position:0% +you know times 60 years it's made it all + + + align:start position:0% +you know times 60 years it's made it all +the way to the ocean we can track the + + align:start position:0% +the way to the ocean we can track the + + + align:start position:0% +the way to the ocean we can track the +the signature of the sewage plume all + + align:start position:0% +the signature of the sewage plume all + + + align:start position:0% +the signature of the sewage plume all +the way to the ocean but the phosphorus + + align:start position:0% +the way to the ocean but the phosphorus + + + align:start position:0% +the way to the ocean but the phosphorus +in 60 years only made it about to here + + align:start position:0% +in 60 years only made it about to here + + + align:start position:0% +in 60 years only made it about to here +in fact if we could drill wells in great + + align:start position:0% +in fact if we could drill wells in great + + + align:start position:0% +in fact if we could drill wells in great +detail along this beach and we've done + + align:start position:0% +detail along this beach and we've done + + + align:start position:0% +detail along this beach and we've done +that in some places the the tow of the + + align:start position:0% +that in some places the the tow of the + + + align:start position:0% +that in some places the the tow of the +phospherous Boom is right about where + + align:start position:0% +phospherous Boom is right about where + + + align:start position:0% +phospherous Boom is right about where +that ramp is literally I mean I'm not + + align:start position:0% +that ramp is literally I mean I'm not + + + align:start position:0% +that ramp is literally I mean I'm not +exaggerating so if you drill a well on + + align:start position:0% +exaggerating so if you drill a well on + + + align:start position:0% +exaggerating so if you drill a well on +this side of the ramp you're in + + align:start position:0% +this side of the ramp you're in + + + align:start position:0% +this side of the ramp you're in +phosphorus and you go to the other side + + align:start position:0% +phosphorus and you go to the other side + + + align:start position:0% +phosphorus and you go to the other side +of the ramp and you're out of the Foster + + align:start position:0% +of the ramp and you're out of the Foster + + + align:start position:0% +of the ramp and you're out of the Foster +P so it's only made it about 1,800 ft in + + align:start position:0% +P so it's only made it about 1,800 ft in + + + align:start position:0% +P so it's only made it about 1,800 ft in +60 years so it's greatly in its + + align:start position:0% +60 years so it's greatly in its + + + align:start position:0% +60 years so it's greatly in its +movement ahead the uh because it's + + align:start position:0% +movement ahead the uh because it's + + + align:start position:0% +movement ahead the uh because it's +moving so + + align:start position:0% +moving so + + + align:start position:0% +moving so +slowly being liting alra giv giv up a + + align:start position:0% +slowly being liting alra giv giv up a + + + align:start position:0% +slowly being liting alra giv giv up a +little bit of phosphorus over time is it + + align:start position:0% +little bit of phosphorus over time is it + + + align:start position:0% +little bit of phosphorus over time is it +really that much of an issue well that's + + align:start position:0% +really that much of an issue well that's + + + align:start position:0% +really that much of an issue well that's +where the rub comes in it's in the + + align:start position:0% +where the rub comes in it's in the + + + align:start position:0% +where the rub comes in it's in the +groundwater the concentrations of + + align:start position:0% +groundwater the concentrations of + + + align:start position:0% +groundwater the concentrations of +phosphorus are pretty elevated and even + + align:start position:0% +phosphorus are pretty elevated and even + + + align:start position:0% +phosphorus are pretty elevated and even +though that's only at the tip of the + + align:start position:0% +though that's only at the tip of the + + + align:start position:0% +though that's only at the tip of the +iceberg it's still milligrams per liter + + align:start position:0% +iceberg it's still milligrams per liter + + + align:start position:0% +iceberg it's still milligrams per liter +in the water so it doesn't sound like + + align:start position:0% +in the water so it doesn't sound like + + + align:start position:0% +in the water so it doesn't sound like +much but those are huge numbers when it + + align:start position:0% +much but those are huge numbers when it + + + align:start position:0% +much but those are huge numbers when it +comes to fertilization of a lake so + + align:start position:0% +comes to fertilization of a lake so + + + align:start position:0% +comes to fertilization of a lake so +they're standing by forication for well + + align:start position:0% +they're standing by forication for well + + + align:start position:0% +they're standing by forication for well +we'll get to that in a second okay + + align:start position:0% +we'll get to that in a second okay + + + align:start position:0% +we'll get to that in a second okay +that's we'll show you what they've done + + align:start position:0% +that's we'll show you what they've done + + + align:start position:0% +that's we'll show you what they've done +all right so um on page 13 I just I just + + align:start position:0% +all right so um on page 13 I just I just + + + align:start position:0% +all right so um on page 13 I just I just +want to reemphasize this this whole + + align:start position:0% +want to reemphasize this this whole + + + align:start position:0% +want to reemphasize this this whole +notion of these ground water flow + + align:start position:0% +notion of these ground water flow + + + align:start position:0% +notion of these ground water flow +through ponds uh this is just a cartoon + + align:start position:0% +through ponds uh this is just a cartoon + + + align:start position:0% +through ponds uh this is just a cartoon +obviously here's our Kettle hole where + + align:start position:0% +obviously here's our Kettle hole where + + + align:start position:0% +obviously here's our Kettle hole where +the ice block was underneath here melted + + align:start position:0% +the ice block was underneath here melted + + + align:start position:0% +the ice block was underneath here melted +out we have a water table on both sides + + align:start position:0% +out we have a water table on both sides + + + align:start position:0% +out we have a water table on both sides +if you're on the Upstream side of the + + align:start position:0% +if you're on the Upstream side of the + + + align:start position:0% +if you're on the Upstream side of the +pond the water level is actually higher + + align:start position:0% +pond the water level is actually higher + + + align:start position:0% +pond the water level is actually higher +than the lake level groundwater's + + align:start position:0% +than the lake level groundwater's + + + align:start position:0% +than the lake level groundwater's +flowing up into the pond bottom + + align:start position:0% +flowing up into the pond bottom + + + align:start position:0% +flowing up into the pond bottom +discharging into the pond and on the + + align:start position:0% +discharging into the pond and on the + + + align:start position:0% +discharging into the pond and on the +downstream side of the lake groundwater + + align:start position:0% +downstream side of the lake groundwater + + + align:start position:0% +downstream side of the lake groundwater +is actually being fed by the pond water + + align:start position:0% +is actually being fed by the pond water + + + align:start position:0% +is actually being fed by the pond water +going into the beach so there's actually + + align:start position:0% +going into the beach so there's actually + + + align:start position:0% +going into the beach so there's actually +a Passage through and of course if you + + align:start position:0% +a Passage through and of course if you + + + align:start position:0% +a Passage through and of course if you +get deep enough this Pond's only about + + align:start position:0% +get deep enough this Pond's only about + + + align:start position:0% +get deep enough this Pond's only about +60 ft deep the a is 300 ft deep there's + + align:start position:0% +60 ft deep the a is 300 ft deep there's + + + align:start position:0% +60 ft deep the a is 300 ft deep there's +some water that doesn't quite get in the + + align:start position:0% +some water that doesn't quite get in the + + + align:start position:0% +some water that doesn't quite get in the +lake passes beneath it all right so + + align:start position:0% +lake passes beneath it all right so + + + align:start position:0% +lake passes beneath it all right so +there's there's an aspect of flow like + + align:start position:0% +there's there's an aspect of flow like + + + align:start position:0% +there's there's an aspect of flow like +that right now you're standing on the + + align:start position:0% +that right now you're standing on the + + + align:start position:0% +that right now you're standing on the +groundwater inflow + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +side + + align:start position:0% + + + + align:start position:0% + +sand yeah but we're going to bring that + + align:start position:0% +sand yeah but we're going to bring that + + + align:start position:0% +sand yeah but we're going to bring that +stuff with + + align:start position:0% +stuff with + + + align:start position:0% +stuff with +us so probably the sand the sand and the + + align:start position:0% +us so probably the sand the sand and the + + + align:start position:0% +us so probably the sand the sand and the +uh the little Henry sampler that's in + + align:start position:0% +uh the little Henry sampler that's in + + + align:start position:0% +uh the little Henry sampler that's in +there there's a little the little I + + align:start position:0% +there there's a little the little I + + + align:start position:0% +there there's a little the little I +think I have one over here we'll just + + align:start position:0% +think I have one over here we'll just + + + align:start position:0% +think I have one over here we'll just +take this one just the + + align:start position:0% +take this one just the + + + align:start position:0% +take this one just the +sand I didn't get by with everything + + align:start position:0% + + + + align:start position:0% + +else + + align:start position:0% +else + + + align:start position:0% +else +um so what you have is you're on the + + align:start position:0% +um so what you have is you're on the + + + align:start position:0% +um so what you have is you're on the +groundwater inflow side of the lake here + + align:start position:0% +groundwater inflow side of the lake here + + + align:start position:0% +groundwater inflow side of the lake here +if you could uh take off your shoes and + + align:start position:0% +if you could uh take off your shoes and + + + align:start position:0% +if you could uh take off your shoes and +I don't recommend it right now and dig + + align:start position:0% +I don't recommend it right now and dig + + + align:start position:0% +I don't recommend it right now and dig +your feet into the sand right here 2 3 + + align:start position:0% +your feet into the sand right here 2 3 + + + align:start position:0% +your feet into the sand right here 2 3 +in it' be really cold about 50° fah it's + + align:start position:0% +in it' be really cold about 50° fah it's + + + align:start position:0% +in it' be really cold about 50° fah it's +the average temperature of the + + align:start position:0% +the average temperature of the + + + align:start position:0% +the average temperature of the +groundwater on the cape cuz you're in + + align:start position:0% +groundwater on the cape cuz you're in + + + align:start position:0% +groundwater on the cape cuz you're in +groundwater discharge area you go on the + + align:start position:0% +groundwater discharge area you go on the + + + align:start position:0% +groundwater discharge area you go on the +south side of the lake over there that's + + align:start position:0% +south side of the lake over there that's + + + align:start position:0% +south side of the lake over there that's +the outlow side the water is actually + + align:start position:0% +the outlow side the water is actually + + + align:start position:0% +the outlow side the water is actually +going infiltrating their Beach over + + align:start position:0% +going infiltrating their Beach over + + + align:start position:0% +going infiltrating their Beach over +there and going on so the water isn't + + align:start position:0% +there and going on so the water isn't + + + align:start position:0% +there and going on so the water isn't +the sand isn't cold over there in fact + + align:start position:0% +the sand isn't cold over there in fact + + + align:start position:0% +the sand isn't cold over there in fact +in the winter time there's an area here + + align:start position:0% +in the winter time there's an area here + + + align:start position:0% +in the winter time there's an area here +about 10 ft from the shore that never + + align:start position:0% +about 10 ft from the shore that never + + + align:start position:0% +about 10 ft from the shore that never +freezes because you have heated + + align:start position:0% +freezes because you have heated + + + align:start position:0% +freezes because you have heated +groundwater coming in and discharging + + align:start position:0% +groundwater coming in and discharging + + + align:start position:0% +groundwater coming in and discharging +whereas it freezes right up onto the + + align:start position:0% +whereas it freezes right up onto the + + + align:start position:0% +whereas it freezes right up onto the +beach on the southide so really good + + align:start position:0% +beach on the southide so really good + + + align:start position:0% +beach on the southide so really good +evidence of groundwater inflow all right + + align:start position:0% +evidence of groundwater inflow all right + + + align:start position:0% +evidence of groundwater inflow all right +right so if you look at page 14 this is + + align:start position:0% +right so if you look at page 14 this is + + + align:start position:0% +right so if you look at page 14 this is +a map of phosphorus in the + + align:start position:0% +a map of phosphorus in the + + + align:start position:0% +a map of phosphorus in the +aquifer and concentrations in the + + align:start position:0% +aquifer and concentrations in the + + + align:start position:0% +aquifer and concentrations in the +groundwater get up around 5 or 6 Mill + + align:start position:0% +groundwater get up around 5 or 6 Mill + + + align:start position:0% +groundwater get up around 5 or 6 Mill +per liter and with that kind of + + align:start position:0% +per liter and with that kind of + + + align:start position:0% +per liter and with that kind of +groundwater + + align:start position:0% +groundwater + + + align:start position:0% +groundwater +discharge coming into the lake the + + align:start position:0% +discharge coming into the lake the + + + align:start position:0% +discharge coming into the lake the +numbers of kilograms per year when you + + align:start position:0% +numbers of kilograms per year when you + + + align:start position:0% +numbers of kilograms per year when you +add it up it's like putting in about um + + align:start position:0% +add it up it's like putting in about um + + + align:start position:0% +add it up it's like putting in about um +170 kg per year of phosphorus into the + + align:start position:0% +170 kg per year of phosphorus into the + + + align:start position:0% +170 kg per year of phosphorus into the +lake so it's about uh almost 340 lbs it + + align:start position:0% +lake so it's about uh almost 340 lbs it + + + align:start position:0% +lake so it's about uh almost 340 lbs it +was it would be like you going to Home + + align:start position:0% +was it would be like you going to Home + + + align:start position:0% +was it would be like you going to Home +Depot or Ace Hardware and buying + + align:start position:0% +Depot or Ace Hardware and buying + + + align:start position:0% +Depot or Ace Hardware and buying +fertilizer for your lawn and coming over + + align:start position:0% +fertilizer for your lawn and coming over + + + align:start position:0% +fertilizer for your lawn and coming over +here and dumping in 3 or 400 lb of + + align:start position:0% +here and dumping in 3 or 400 lb of + + + align:start position:0% +here and dumping in 3 or 400 lb of +fertilizer in the lake every year so + + align:start position:0% +fertilizer in the lake every year so + + + align:start position:0% +fertilizer in the lake every year so +even though it's only a few few + + align:start position:0% +even though it's only a few few + + + align:start position:0% +even though it's only a few few +milligrams per liter added up over many + + align:start position:0% +milligrams per liter added up over many + + + align:start position:0% +milligrams per liter added up over many +liters it's a it's a very large load in + + align:start position:0% +liters it's a it's a very large load in + + + align:start position:0% +liters it's a it's a very large load in +fact I think that about 80% of the + + align:start position:0% +fact I think that about 80% of the + + + align:start position:0% +fact I think that about 80% of the +phosphorous load to this lake is from + + align:start position:0% +phosphorous load to this lake is from + + + align:start position:0% +phosphorous load to this lake is from +the sewage Plum and this lake is among + + align:start position:0% +the sewage Plum and this lake is among + + + align:start position:0% +the sewage Plum and this lake is among +the more utopic lakes on the cape + + align:start position:0% +the more utopic lakes on the cape + + + align:start position:0% +the more utopic lakes on the cape +they've had algo broom problems and they + + align:start position:0% +they've had algo broom problems and they + + + align:start position:0% +they've had algo broom problems and they +attribute it to the basis Wastewater + + align:start position:0% +attribute it to the basis Wastewater + + + align:start position:0% +attribute it to the basis Wastewater +Plant so that even though the + + align:start position:0% +Plant so that even though the + + + align:start position:0% +Plant so that even though the +phospherous has hardly moved at all + + align:start position:0% +phospherous has hardly moved at all + + + align:start position:0% +phospherous has hardly moved at all +relative to the whole length of the + + align:start position:0% +relative to the whole length of the + + + align:start position:0% +relative to the whole length of the +plume they put the plant in about the + + align:start position:0% +plume they put the plant in about the + + + align:start position:0% +plume they put the plant in about the +worst place they could have from a + + align:start position:0% +worst place they could have from a + + + align:start position:0% +worst place they could have from a +phospherous point of view a direct shots + + align:start position:0% +phospherous point of view a direct shots + + + align:start position:0% +phospherous point of view a direct shots +to the lake only 1500 ft and so + + align:start position:0% +to the lake only 1500 ft and so + + + align:start position:0% +to the lake only 1500 ft and so +unfortunately you know there was enough + + align:start position:0% +unfortunately you know there was enough + + + align:start position:0% +unfortunately you know there was enough +time for it to get here if they disposed + + align:start position:0% +time for it to get here if they disposed + + + align:start position:0% +time for it to get here if they disposed +of it a little bit further to the West + + align:start position:0% +of it a little bit further to the West + + + align:start position:0% +of it a little bit further to the West +it would have missed the lake but that + + align:start position:0% +it would have missed the lake but that + + + align:start position:0% +it would have missed the lake but that +you know you can't blame it for what + + align:start position:0% +you know you can't blame it for what + + + align:start position:0% +you know you can't blame it for what +they did in the 40s all right so let's + + align:start position:0% +they did in the 40s all right so let's + + + align:start position:0% +they did in the 40s all right so let's +uh what we're going to do right now is + + align:start position:0% +uh what we're going to do right now is + + + align:start position:0% +uh what we're going to do right now is +we're going to walk up along the shore + + align:start position:0% +we're going to walk up along the shore + + + align:start position:0% +we're going to walk up along the shore +to where the phospherous is coming in + + align:start position:0% +to where the phospherous is coming in + + + align:start position:0% +to where the phospherous is coming in +it's not that exciting but I got a few + + align:start position:0% +it's not that exciting but I got a few + + + align:start position:0% +it's not that exciting but I got a few +things to show you there gu why in + + align:start position:0% +things to show you there gu why in + + + align:start position:0% +things to show you there gu why in +general do the not divert and go through + + align:start position:0% +general do the not divert and go through + + + align:start position:0% +general do the not divert and go through +the pond it seems like this would be a + + align:start position:0% +the pond it seems like this would be a + + + align:start position:0% +the pond it seems like this would be a +low conductivity area high conductivity + + align:start position:0% +low conductivity area high conductivity + + + align:start position:0% +low conductivity area high conductivity +area right High yes and that's exactly + + align:start position:0% +area right High yes and that's exactly + + + align:start position:0% +area right High yes and that's exactly +what happens the pond is a lot like the + + align:start position:0% +what happens the pond is a lot like the + + + align:start position:0% +what happens the pond is a lot like the +well I was talking to you about it's + + align:start position:0% +well I was talking to you about it's + + + align:start position:0% +well I was talking to you about it's +like a huge well so it actually captures + + align:start position:0% +like a huge well so it actually captures + + + align:start position:0% +like a huge well so it actually captures +a lot of water it actually pulls water + + align:start position:0% +a lot of water it actually pulls water + + + align:start position:0% +a lot of water it actually pulls water +into itself but when I look at say this + + align:start position:0% +into itself but when I look at say this + + + align:start position:0% +into itself but when I look at say this +picture it looks like the plume is just + + align:start position:0% +picture it looks like the plume is just + + + align:start position:0% +picture it looks like the plume is just +raising the side and not really going + + align:start position:0% +raising the side and not really going + + + align:start position:0% +raising the side and not really going +through it well but it does a + + align:start position:0% +through it well but it does a + + + align:start position:0% +through it well but it does a +significant part of it discharges the + + align:start position:0% +significant part of it discharges the + + + align:start position:0% +significant part of it discharges the +Fisherman's Cove right here but this + + align:start position:0% +Fisherman's Cove right here but this + + + align:start position:0% +Fisherman's Cove right here but this +this the if you if you uh looked at the + + align:start position:0% +this the if you if you uh looked at the + + + align:start position:0% +this the if you if you uh looked at the +water table map in detail and did + + align:start position:0% +water table map in detail and did + + + align:start position:0% +water table map in detail and did +groundwater flow simulation the the + + align:start position:0% +groundwater flow simulation the the + + + align:start position:0% +groundwater flow simulation the the +sewage beds extended about, 1500 ft to + + align:start position:0% +sewage beds extended about, 1500 ft to + + + align:start position:0% +sewage beds extended about, 1500 ft to +the West when the plant was really + + align:start position:0% +the West when the plant was really + + + align:start position:0% +the West when the plant was really +operating at its Max and there are flow + + align:start position:0% +operating at its Max and there are flow + + + align:start position:0% +operating at its Max and there are flow +lines when they were disposing it as far + + align:start position:0% +lines when they were disposing it as far + + + align:start position:0% +lines when they were disposing it as far +away from the pwn as you can that graze + + align:start position:0% +away from the pwn as you can that graze + + + align:start position:0% +away from the pwn as you can that graze +the pond and keep going so they they + + align:start position:0% +the pond and keep going so they they + + + align:start position:0% +the pond and keep going so they they +sort of had the if they if they dispos + + align:start position:0% +sort of had the if they if they dispos + + + align:start position:0% +sort of had the if they if they dispos +of all the sewage to the east it would + + align:start position:0% +of all the sewage to the east it would + + + align:start position:0% +of all the sewage to the east it would +have all gone in the lake it would be no + + align:start position:0% +have all gone in the lake it would be no + + + align:start position:0% +have all gone in the lake it would be no +plume to the South if they dispose of it + + align:start position:0% +plume to the South if they dispose of it + + + align:start position:0% +plume to the South if they dispose of it +all further to the West in the beds that + + align:start position:0% +all further to the West in the beds that + + + align:start position:0% +all further to the West in the beds that +they had available to them none of it + + align:start position:0% +they had available to them none of it + + + align:start position:0% +they had available to them none of it +would have gone in the lake it would + + align:start position:0% +would have gone in the lake it would + + + align:start position:0% +would have gone in the lake it would +have just come by the lake and and + + align:start position:0% +have just come by the lake and and + + + align:start position:0% +have just come by the lake and and +missed the lake just because of the + + align:start position:0% +missed the lake just because of the + + + align:start position:0% +missed the lake just because of the +nature of the flow pan there's got to be + + align:start position:0% +nature of the flow pan there's got to be + + + align:start position:0% +nature of the flow pan there's got to be +a divide somewhere but they happen to + + align:start position:0% +a divide somewhere but they happen to + + + align:start position:0% +a divide somewhere but they happen to +put it on both places so they created a + + align:start position:0% +put it on both places so they created a + + + align:start position:0% +put it on both places so they created a +plume and polluted the lake at the same + + align:start position:0% +plume and polluted the lake at the same + + + align:start position:0% +plume and polluted the lake at the same +time which is great for + + align:start position:0% +time which is great for + + + align:start position:0% +time which is great for +me so let's walk up the sh bit \ No newline at end of file diff --git a/BmjKER_e7-s.txt b/BmjKER_e7-s.txt new file mode 100644 index 0000000000000000000000000000000000000000..0c20400692557fc46303d75f8c530bde679a4f9d --- /dev/null +++ b/BmjKER_e7-s.txt @@ -0,0 +1,10627 @@ +align:start position:0% + +all right so just a couple of + + align:start position:0% +all right so just a couple of + + + align:start position:0% +all right so just a couple of +announcements real quick um can you guys + + align:start position:0% +announcements real quick um can you guys + + + align:start position:0% +announcements real quick um can you guys +turn this down a little + + align:start position:0% +turn this down a little + + + align:start position:0% +turn this down a little +bit + + align:start position:0% + + + + align:start position:0% + +um so next time uh on for tomorrow you + + align:start position:0% +um so next time uh on for tomorrow you + + + align:start position:0% +um so next time uh on for tomorrow you +guys should all be ready to give these + + align:start position:0% +guys should all be ready to give these + + + align:start position:0% +guys should all be ready to give these +short presentations on your design + + align:start position:0% +short presentations on your design + + + align:start position:0% +short presentations on your design +projects in recitation uh we posted a + + align:start position:0% +projects in recitation uh we posted a + + + align:start position:0% +projects in recitation uh we posted a +sort of one-page uh guide talking about + + align:start position:0% +sort of one-page uh guide talking about + + + align:start position:0% +sort of one-page uh guide talking about +what it is that you should prepare for + + align:start position:0% +what it is that you should prepare for + + + align:start position:0% +what it is that you should prepare for +next time in class um these are short + + align:start position:0% +next time in class um these are short + + + align:start position:0% +next time in class um these are short +presentations I shouldn't take you + + align:start position:0% +presentations I shouldn't take you + + + align:start position:0% +presentations I shouldn't take you +shouldn't need to put too much time into + + align:start position:0% +shouldn't need to put too much time into + + + align:start position:0% +shouldn't need to put too much time into +getting them together but um please look + + align:start position:0% +getting them together but um please look + + + align:start position:0% +getting them together but um please look +at the web page and just uh if you're + + align:start position:0% +at the web page and just uh if you're + + + align:start position:0% +at the web page and just uh if you're +not sure what it is that you're supposed + + align:start position:0% +not sure what it is that you're supposed + + + align:start position:0% +not sure what it is that you're supposed +to be doing in class so today what we're + + align:start position:0% +to be doing in class so today what we're + + + align:start position:0% +to be doing in class so today what we're +going to do is we're going to um wrap up + + align:start position:0% +going to do is we're going to um wrap up + + + align:start position:0% +going to do is we're going to um wrap up +our discussion of + + align:start position:0% +our discussion of + + + align:start position:0% +our discussion of +security and what I want to do is I want + + align:start position:0% +security and what I want to do is I want + + + align:start position:0% +security and what I want to do is I want +to start off with sort of a fun little + + align:start position:0% +to start off with sort of a fun little + + + align:start position:0% +to start off with sort of a fun little +um diversion which is we over the past + + align:start position:0% +um diversion which is we over the past + + + align:start position:0% +um diversion which is we over the past +couple of times that you guys were in + + align:start position:0% +couple of times that you guys were in + + + align:start position:0% +couple of times that you guys were in +class we captured a log of all of the + + align:start position:0% +class we captured a log of all of the + + + align:start position:0% +class we captured a log of all of the +networ traffic that was going on while + + align:start position:0% +networ traffic that was going on while + + + align:start position:0% +networ traffic that was going on while +people were in class uh on their laptops + + align:start position:0% +people were in class uh on their laptops + + + align:start position:0% +people were in class uh on their laptops +and for the most part it turned out that + + align:start position:0% +and for the most part it turned out that + + + align:start position:0% +and for the most part it turned out that +you guys were pretty boring you didn't + + align:start position:0% +you guys were pretty boring you didn't + + + align:start position:0% +you guys were pretty boring you didn't +no nobody nobody was actually doing + + align:start position:0% +no nobody nobody was actually doing + + + align:start position:0% +no nobody nobody was actually doing +anything very exciting but there were a + + align:start position:0% +anything very exciting but there were a + + + align:start position:0% +anything very exciting but there were a +couple of interesting lessons so in case + + align:start position:0% +couple of interesting lessons so in case + + + align:start position:0% +couple of interesting lessons so in case +you're curious as to what we actually + + align:start position:0% +you're curious as to what we actually + + + align:start position:0% +you're curious as to what we actually +did + + align:start position:0% +did + + + align:start position:0% +did +um this thing is almost cutting off the + + align:start position:0% +um this thing is almost cutting off the + + + align:start position:0% +um this thing is almost cutting off the +bottom of this but um so we ran this uh + + align:start position:0% +bottom of this but um so we ran this uh + + + align:start position:0% +bottom of this but um so we ran this uh +TCP dump command so the pseudo command + + align:start position:0% +TCP dump command so the pseudo command + + + align:start position:0% +TCP dump command so the pseudo command +just says run this command as you as + + align:start position:0% +just says run this command as you as + + + align:start position:0% +just says run this command as you as +though you are super user as though you + + align:start position:0% +though you are super user as though you + + + align:start position:0% +though you are super user as though you +are SU and then TCP dump just says uh + + align:start position:0% +are SU and then TCP dump just says uh + + + align:start position:0% +are SU and then TCP dump just says uh +dump out all the traffic on the + + align:start position:0% +dump out all the traffic on the + + + align:start position:0% +dump out all the traffic on the +specified network interface so in this + + align:start position:0% +specified network interface so in this + + + align:start position:0% +specified network interface so in this +case it's dumping out all the traffic on + + align:start position:0% +case it's dumping out all the traffic on + + + align:start position:0% +case it's dumping out all the traffic on +en1 which on this computer is the + + align:start position:0% +en1 which on this computer is the + + + align:start position:0% +en1 which on this computer is the +wireless network so we're just dumping + + align:start position:0% +wireless network so we're just dumping + + + align:start position:0% +wireless network so we're just dumping +out all the packets that were sent out + + align:start position:0% +out all the packets that were sent out + + + align:start position:0% +out all the packets that were sent out +over en1 and what you see here is uh + + align:start position:0% +over en1 and what you see here is uh + + + align:start position:0% +over en1 and what you see here is uh +this the the the yellow part is the sort + + align:start position:0% +this the the the yellow part is the sort + + + align:start position:0% +this the the the yellow part is the sort +of header of the packet showing you what + + align:start position:0% +of header of the packet showing you what + + + align:start position:0% +of header of the packet showing you what +the uh saying this is an IP packet and + + align:start position:0% +the uh saying this is an IP packet and + + + align:start position:0% +the uh saying this is an IP packet and +specifying who the sender the the + + align:start position:0% +specifying who the sender the the + + + align:start position:0% +specifying who the sender the the +destination and recipient of this packet + + align:start position:0% +destination and recipient of this packet + + + align:start position:0% +destination and recipient of this packet +are and then there's some body text the + + align:start position:0% +are and then there's some body text the + + + align:start position:0% +are and then there's some body text the +some sort of payload associated with + + align:start position:0% +some sort of payload associated with + + + align:start position:0% +some sort of payload associated with +this packet so in this case this first + + align:start position:0% +this packet so in this case this first + + + align:start position:0% +this packet so in this case this first +packet is it's some binary data we can't + + align:start position:0% +packet is it's some binary data we can't + + + align:start position:0% +packet is it's some binary data we can't +make any sense of it but if you look at + + align:start position:0% +make any sense of it but if you look at + + + align:start position:0% +make any sense of it but if you look at +um some of these other packets for + + align:start position:0% +um some of these other packets for + + + align:start position:0% +um some of these other packets for +example this is a packet that is a HTTP + + align:start position:0% +example this is a packet that is a HTTP + + + align:start position:0% +example this is a packet that is a HTTP +uh HTTP request packet and what you see + + align:start position:0% +uh HTTP request packet and what you see + + + align:start position:0% +uh HTTP request packet and what you see +is that there in fact is English text so + + align:start position:0% +is that there in fact is English text so + + + align:start position:0% +is that there in fact is English text so +the HTTP protocol uses English text to + + align:start position:0% +the HTTP protocol uses English text to + + + align:start position:0% +the HTTP protocol uses English text to +transmit information and so this is + + align:start position:0% +transmit information and so this is + + + align:start position:0% +transmit information and so this is +specifying some information about the + + align:start position:0% +specifying some information about the + + + align:start position:0% +specifying some information about the +this is the actual HTTP uh request going + + align:start position:0% +this is the actual HTTP uh request going + + + align:start position:0% +this is the actual HTTP uh request going +out in this case it was going out from + + align:start position:0% +out in this case it was going out from + + + align:start position:0% +out in this case it was going out from +this laptop I just set this up as to + + align:start position:0% +this laptop I just set this up as to + + + align:start position:0% +this laptop I just set this up as to +illustrate what TCP dump does so we ran + + align:start position:0% +illustrate what TCP dump does so we ran + + + align:start position:0% +illustrate what TCP dump does so we ran +a command like this while you guys were + + align:start position:0% +a command like this while you guys were + + + align:start position:0% +a command like this while you guys were +in class and captured a trace of what + + align:start position:0% +in class and captured a trace of what + + + align:start position:0% +in class and captured a trace of what +you're doing then we ran a little Pearl + + align:start position:0% +you're doing then we ran a little Pearl + + + align:start position:0% +you're doing then we ran a little Pearl +script that went through this trace and + + align:start position:0% +script that went through this trace and + + + align:start position:0% +script that went through this trace and +sucked out we wrote a little Pearl + + align:start position:0% +sucked out we wrote a little Pearl + + + align:start position:0% +sucked out we wrote a little Pearl +script that went through this trace of + + align:start position:0% +script that went through this trace of + + + align:start position:0% +script that went through this trace of +packets and sucked out all the web pages + + align:start position:0% +packets and sucked out all the web pages + + + align:start position:0% +packets and sucked out all the web pages +that you guys had been looking at and we + + align:start position:0% +that you guys had been looking at and we + + + align:start position:0% +that you guys had been looking at and we +made pictures of some of the web pages + + align:start position:0% +made pictures of some of the web pages + + + align:start position:0% +made pictures of some of the web pages +so uh a lot of it as I said is pretty + + align:start position:0% +so uh a lot of it as I said is pretty + + + align:start position:0% +so uh a lot of it as I said is pretty +boring so there's somebody who was + + align:start position:0% +boring so there's somebody who was + + + align:start position:0% +boring so there's somebody who was +looking for a looking to buy a Micro + + align:start position:0% +looking for a looking to buy a Micro + + + align:start position:0% +looking for a looking to buy a Micro +Drive uh so they searched for Micro + + align:start position:0% +Drive uh so they searched for Micro + + + align:start position:0% +Drive uh so they searched for Micro +Center uh Cruiser USB highspeed uh on + + align:start position:0% +Center uh Cruiser USB highspeed uh on + + + align:start position:0% +Center uh Cruiser USB highspeed uh on +the on Google so we got we we saw this + + align:start position:0% +the on Google so we got we we saw this + + + align:start position:0% +the on Google so we got we we saw this +page being coming back from Google which + + align:start position:0% +page being coming back from Google which + + + align:start position:0% +page being coming back from Google which +was the search request um and in fact + + align:start position:0% +was the search request um and in fact + + + align:start position:0% +was the search request um and in fact +you sort of poke around some more and + + align:start position:0% +you sort of poke around some more and + + + align:start position:0% +you sort of poke around some more and +you see this person actually found the + + align:start position:0% +you see this person actually found the + + + align:start position:0% +you see this person actually found the +Microcenter website and went to + + align:start position:0% +Microcenter website and went to + + + align:start position:0% +Microcenter website and went to +Microcenter and uh apparently was trying + + align:start position:0% +Microcenter and uh apparently was trying + + + align:start position:0% +Microcenter and uh apparently was trying +to purchase this thing so um I also + + align:start position:0% +to purchase this thing so um I also + + + align:start position:0% +to purchase this thing so um I also +there were a couple people who were + + align:start position:0% +there were a couple people who were + + + align:start position:0% +there were a couple people who were +looking for movies so people who are + + align:start position:0% +looking for movies so people who are + + + align:start position:0% +looking for movies so people who are +looking to see uh you know look looking + + align:start position:0% +looking to see uh you know look looking + + + align:start position:0% +looking to see uh you know look looking +for a movie to see in fact we actually + + align:start position:0% +for a movie to see in fact we actually + + + align:start position:0% +for a movie to see in fact we actually +saw this on both days so it wasn't just + + align:start position:0% +saw this on both days so it wasn't just + + + align:start position:0% +saw this on both days so it wasn't just +one day that somebody was looking for + + align:start position:0% +one day that somebody was looking for + + + align:start position:0% +one day that somebody was looking for +movies but some keeps coming to class + + align:start position:0% +movies but some keeps coming to class + + + align:start position:0% +movies but some keeps coming to class +and looking for + + align:start position:0% +and looking for + + + align:start position:0% +and looking for +movies so the next one though is much + + align:start position:0% +movies so the next one though is much + + + align:start position:0% +movies so the next one though is much +more interesting so this is we saw + + align:start position:0% +more interesting so this is we saw + + + align:start position:0% +more interesting so this is we saw +there's a couple of web pages that are + + align:start position:0% +there's a couple of web pages that are + + + align:start position:0% +there's a couple of web pages that are +somebody is looking at a tool called + + align:start position:0% +somebody is looking at a tool called + + + align:start position:0% +somebody is looking at a tool called +game uh encryption uh and so gam + + align:start position:0% +game uh encryption uh and so gam + + + align:start position:0% +game uh encryption uh and so gam +encryption game is a is the is the The + + align:start position:0% +encryption game is a is the is the The + + + align:start position:0% +encryption game is a is the is the The +open- Source uh AOL Instant Messenger + + align:start position:0% +open- Source uh AOL Instant Messenger + + + align:start position:0% +open- Source uh AOL Instant Messenger +client okay so and gam encryption is a + + align:start position:0% +client okay so and gam encryption is a + + + align:start position:0% +client okay so and gam encryption is a +version of the The open- Source uh gam + + align:start position:0% +version of the The open- Source uh gam + + + align:start position:0% +version of the The open- Source uh gam +client that encrypts data that gets + + align:start position:0% +client that encrypts data that gets + + + align:start position:0% +client that encrypts data that gets +transmitted over the over the network + + align:start position:0% +transmitted over the over the network + + + align:start position:0% +transmitted over the over the network +the way it works is that it uh generate + + align:start position:0% +the way it works is that it uh generate + + + align:start position:0% +the way it works is that it uh generate +when you when you install this tool it + + align:start position:0% +when you when you install this tool it + + + align:start position:0% +when you when you install this tool it +generates you a public private key pair + + align:start position:0% +generates you a public private key pair + + + align:start position:0% +generates you a public private key pair +and then when you have a chat session + + align:start position:0% +and then when you have a chat session + + + align:start position:0% +and then when you have a chat session +with somebody else who's using this uh + + align:start position:0% +with somebody else who's using this uh + + + align:start position:0% +with somebody else who's using this uh +also using this gam encryption tool it + + align:start position:0% +also using this gam encryption tool it + + + align:start position:0% +also using this gam encryption tool it +sends that person your public key and + + align:start position:0% +sends that person your public key and + + + align:start position:0% +sends that person your public key and +then it uses the uh uses public private + + align:start position:0% +then it uses the uh uses public private + + + align:start position:0% +then it uses the uh uses public private +key encryption and signing in order to + + align:start position:0% +key encryption and signing in order to + + + align:start position:0% +key encryption and signing in order to +protect information that gets + + align:start position:0% +protect information that gets + + + align:start position:0% +protect information that gets +transmitted over the network so there + + align:start position:0% +transmitted over the network so there + + + align:start position:0% +transmitted over the network so there +was somebody who during class was + + align:start position:0% +was somebody who during class was + + + align:start position:0% +was somebody who during class was +looking at this tool so we see they go + + align:start position:0% +looking at this tool so we see they go + + + align:start position:0% +looking at this tool so we see they go +to the project page on Source Forge + + align:start position:0% +to the project page on Source Forge + + + align:start position:0% +to the project page on Source Forge +where this tool is hosted and they're + + align:start position:0% +where this tool is hosted and they're + + + align:start position:0% +where this tool is hosted and they're +clicking around looking at what the tool + + align:start position:0% +clicking around looking at what the tool + + + align:start position:0% +clicking around looking at what the tool +does reading about it and they see that + + align:start position:0% +does reading about it and they see that + + + align:start position:0% +does reading about it and they see that +they download this tool and in fact + + align:start position:0% +they download this tool and in fact + + + align:start position:0% +they download this tool and in fact +after that at some point there's a whole + + align:start position:0% +after that at some point there's a whole + + + align:start position:0% +after that at some point there's a whole +lot of AOL Instant Messenger traffic + + align:start position:0% +lot of AOL Instant Messenger traffic + + + align:start position:0% +lot of AOL Instant Messenger traffic +that is going out over the network um so + + align:start position:0% +that is going out over the network um so + + + align:start position:0% +that is going out over the network um so +I'm just surmising that this traffic + + align:start position:0% +I'm just surmising that this traffic + + + align:start position:0% +I'm just surmising that this traffic +actually belongs to this person who + + align:start position:0% +actually belongs to this person who + + + align:start position:0% +actually belongs to this person who +downloaded this tool um and you can see + + align:start position:0% +downloaded this tool um and you can see + + + align:start position:0% +downloaded this tool um and you can see +that in fact the tool appears to be + + align:start position:0% +that in fact the tool appears to be + + + align:start position:0% +that in fact the tool appears to be +working so that this just traffic is not + + align:start position:0% +working so that this just traffic is not + + + align:start position:0% +working so that this just traffic is not +intelligible and in other cases when you + + align:start position:0% +intelligible and in other cases when you + + + align:start position:0% +intelligible and in other cases when you +see the the this tool actually goes + + align:start position:0% +see the the this tool actually goes + + + align:start position:0% +see the the this tool actually goes +across the network in plain text uh the + + align:start position:0% +across the network in plain text uh the + + + align:start position:0% +across the network in plain text uh the +the gam normally runs in plain text and + + align:start position:0% +the gam normally runs in plain text and + + + align:start position:0% +the gam normally runs in plain text and +you can just see the entire transcript + + align:start position:0% +you can just see the entire transcript + + + align:start position:0% +you can just see the entire transcript +of the chat happening if you run this + + align:start position:0% +of the chat happening if you run this + + + align:start position:0% +of the chat happening if you run this +tool so the kind of nice the interesting + + align:start position:0% +tool so the kind of nice the interesting + + + align:start position:0% +tool so the kind of nice the interesting +this say there's a very interesting + + align:start position:0% +this say there's a very interesting + + + align:start position:0% +this say there's a very interesting +security lesson here which is that + + align:start position:0% +security lesson here which is that + + + align:start position:0% +security lesson here which is that +sometime later in this particular trace + + align:start position:0% +sometime later in this particular trace + + + align:start position:0% +sometime later in this particular trace +of a chat we see this same person so + + align:start position:0% +of a chat we see this same person so + + + align:start position:0% +of a chat we see this same person so +this person one their name is + + align:start position:0% +this person one their name is + + + align:start position:0% +this person one their name is +transmitted in in plain text so you see + + align:start position:0% +transmitted in in plain text so you see + + + align:start position:0% +transmitted in in plain text so you see +this same person even when when using + + align:start position:0% +this same person even when when using + + + align:start position:0% +this same person even when when using +the g a tool um but you don't see their + + align:start position:0% +the g a tool um but you don't see their + + + align:start position:0% +the g a tool um but you don't see their +messages in plain text but you see this + + align:start position:0% +messages in plain text but you see this + + + align:start position:0% +messages in plain text but you see this +same person now uh actually is talking + + align:start position:0% +same person now uh actually is talking + + + align:start position:0% +same person now uh actually is talking +having Aver ation and they think they + + align:start position:0% +having Aver ation and they think they + + + align:start position:0% +having Aver ation and they think they +they they sort of say oh I downloaded + + align:start position:0% +they they sort of say oh I downloaded + + + align:start position:0% +they they sort of say oh I downloaded +this G tool now I can talk encrypted to + + align:start position:0% +this G tool now I can talk encrypted to + + + align:start position:0% +this G tool now I can talk encrypted to +other people and yet there's this + + align:start position:0% +other people and yet there's this + + + align:start position:0% +other people and yet there's this +conversation where it's not encrypted + + align:start position:0% +conversation where it's not encrypted + + + align:start position:0% +conversation where it's not encrypted +and they're talking this sort of + + align:start position:0% +and they're talking this sort of + + + align:start position:0% +and they're talking this sort of +dialogue goes on they're talking about + + align:start position:0% +dialogue goes on they're talking about + + + align:start position:0% +dialogue goes on they're talking about +uh somebody who's in class they say why + + align:start position:0% +uh somebody who's in class they say why + + + align:start position:0% +uh somebody who's in class they say why +doesn't this person go to class anymore + + align:start position:0% +doesn't this person go to class anymore + + + align:start position:0% +doesn't this person go to class anymore +and they're having this little chat + + align:start position:0% +and they're having this little chat + + + align:start position:0% +and they're having this little chat +session back and forth about uh why this + + align:start position:0% +session back and forth about uh why this + + + align:start position:0% +session back and forth about uh why this +person isn't isn't in class and so this + + align:start position:0% +person isn't isn't in class and so this + + + align:start position:0% +person isn't isn't in class and so this +is this sort of very and the the + + align:start position:0% +is this sort of very and the the + + + align:start position:0% +is this sort of very and the the +dialogue goes on talking about how uh + + align:start position:0% +dialogue goes on talking about how uh + + + align:start position:0% +dialogue goes on talking about how uh +you know talking about their design + + align:start position:0% +you know talking about their design + + + align:start position:0% +you know talking about their design +project and how they're worried about it + + align:start position:0% +project and how they're worried about it + + + align:start position:0% +project and how they're worried about it +it's sort of a a nice example of a um a + + align:start position:0% +it's sort of a a nice example of a um a + + + align:start position:0% +it's sort of a a nice example of a um a +nice example of a security problem which + + align:start position:0% +nice example of a security problem which + + + align:start position:0% +nice example of a security problem which +is or a potential security problem right + + align:start position:0% +is or a potential security problem right + + + align:start position:0% +is or a potential security problem right +which is that this person actually did + + align:start position:0% +which is that this person actually did + + + align:start position:0% +which is that this person actually did +something that's sort of nice they you + + align:start position:0% +something that's sort of nice they you + + + align:start position:0% +something that's sort of nice they you +know came to security class they're + + align:start position:0% +know came to security class they're + + + align:start position:0% +know came to security class they're +learning about Security in class they go + + align:start position:0% +learning about Security in class they go + + + align:start position:0% +learning about Security in class they go +download this tool and they think okay + + align:start position:0% +download this tool and they think okay + + + align:start position:0% +download this tool and they think okay +I've got this tool installed now my + + align:start position:0% +I've got this tool installed now my + + + align:start position:0% +I've got this tool installed now my +conversations are protected and then as + + align:start position:0% +conversations are protected and then as + + + align:start position:0% +conversations are protected and then as +soon as they try and talk to somebody + + align:start position:0% +soon as they try and talk to somebody + + + align:start position:0% +soon as they try and talk to somebody +who doesn't isn't also running this + + align:start position:0% +who doesn't isn't also running this + + + align:start position:0% +who doesn't isn't also running this +version of tool their conversations are + + align:start position:0% +version of tool their conversations are + + + align:start position:0% +version of tool their conversations are +no longer protected anymore so this is + + align:start position:0% +no longer protected anymore so this is + + + align:start position:0% +no longer protected anymore so this is +sort of a nice example of why security + + align:start position:0% +sort of a nice example of why security + + + align:start position:0% +sort of a nice example of why security +is actually a really hard thing to get + + align:start position:0% +is actually a really hard thing to get + + + align:start position:0% +is actually a really hard thing to get +right because this person may have even + + align:start position:0% +right because this person may have even + + + align:start position:0% +right because this person may have even +believed that this person they were + + align:start position:0% +believed that this person they were + + + align:start position:0% +believed that this person they were +talking to had this had this tool + + align:start position:0% +talking to had this had this tool + + + align:start position:0% +talking to had this had this tool +installed as well but they just they you + + align:start position:0% +installed as well but they just they you + + + align:start position:0% +installed as well but they just they you +don't you sort of don't know that it's + + align:start position:0% +don't you sort of don't know that it's + + + align:start position:0% +don't you sort of don't know that it's +not working until somebody points out + + align:start position:0% +not working until somebody points out + + + align:start position:0% +not working until somebody points out +that it's not working somebody violates + + align:start position:0% +that it's not working somebody violates + + + align:start position:0% +that it's not working somebody violates +your you know goes in and + + align:start position:0% +your you know goes in and + + + align:start position:0% +your you know goes in and +uh is able to access this un unprotected + + align:start position:0% +uh is able to access this un unprotected + + + align:start position:0% +uh is able to access this un unprotected +data so this is a nice example of why + + align:start position:0% +data so this is a nice example of why + + + align:start position:0% +data so this is a nice example of why +security is hard and why uh sort of + + align:start position:0% +security is hard and why uh sort of + + + align:start position:0% +security is hard and why uh sort of +providing protection is essentially a + + align:start position:0% +providing protection is essentially a + + + align:start position:0% +providing protection is essentially a +negative goal right you never really + + align:start position:0% +negative goal right you never really + + + align:start position:0% +negative goal right you never really +know that you're protected until + + align:start position:0% +know that you're protected until + + + align:start position:0% +know that you're protected until +somebody points out that you're not + + align:start position:0% +somebody points out that you're not + + + align:start position:0% +somebody points out that you're not +protected okay so um that just sort of a + + align:start position:0% +protected okay so um that just sort of a + + + align:start position:0% +protected okay so um that just sort of a +little a little lesson about security + + align:start position:0% +little a little lesson about security + + + align:start position:0% +little a little lesson about security +and I hope that it sort of pointed out a + + align:start position:0% +and I hope that it sort of pointed out a + + + align:start position:0% +and I hope that it sort of pointed out a +way a reason in which know why it is + + align:start position:0% +way a reason in which know why it is + + + align:start position:0% +way a reason in which know why it is +that security is something that's both + + align:start position:0% +that security is something that's both + + + align:start position:0% +that security is something that's both +difficult and something that you might + + align:start position:0% +difficult and something that you might + + + align:start position:0% +difficult and something that you might +want to be conscious of you know when + + align:start position:0% +want to be conscious of you know when + + + align:start position:0% +want to be conscious of you know when +you're sitting there often times when + + align:start position:0% +you're sitting there often times when + + + align:start position:0% +you're sitting there often times when +you're sitting there using your laptop + + align:start position:0% +you're sitting there using your laptop + + + align:start position:0% +you're sitting there using your laptop +you have this perception that is you + + align:start position:0% +you have this perception that is you + + + align:start position:0% +you have this perception that is you +know my La my information I'm sending + + align:start position:0% +know my La my information I'm sending + + + align:start position:0% +know my La my information I'm sending +nobody's going to be able to overhear + + align:start position:0% +nobody's going to be able to overhear + + + align:start position:0% +nobody's going to be able to overhear +this information it's going so fast and + + align:start position:0% +this information it's going so fast and + + + align:start position:0% +this information it's going so fast and +being transmitted so instantly that you + + align:start position:0% +being transmitted so instantly that you + + + align:start position:0% +being transmitted so instantly that you +know of course I'm private you feel very + + align:start position:0% +know of course I'm private you feel very + + + align:start position:0% +know of course I'm private you feel very +sort of isolated when you're having this + + align:start position:0% +sort of isolated when you're having this + + + align:start position:0% +sort of isolated when you're having this +communication until somebody points out + + align:start position:0% +communication until somebody points out + + + align:start position:0% +communication until somebody points out +that they it's actually very easy I mean + + align:start position:0% +that they it's actually very easy I mean + + + align:start position:0% +that they it's actually very easy I mean +this is a tool that standard on all + + align:start position:0% +this is a tool that standard on all + + + align:start position:0% +this is a tool that standard on all +Linux distributions and you know it's + + align:start position:0% +Linux distributions and you know it's + + + align:start position:0% +Linux distributions and you know it's +one line that we type into the into our + + align:start position:0% +one line that we type into the into our + + + align:start position:0% +one line that we type into the into our +computer to get this information it's + + align:start position:0% +computer to get this information it's + + + align:start position:0% +computer to get this information it's +actually very easy to do this and so + + align:start position:0% +actually very easy to do this and so + + + align:start position:0% +actually very easy to do this and so +it's something that when you're + + align:start position:0% +it's something that when you're + + + align:start position:0% +it's something that when you're +transmitting sensitive information out + + align:start position:0% +transmitting sensitive information out + + + align:start position:0% +transmitting sensitive information out +over the network over an email or in in + + align:start position:0% +over the network over an email or in in + + + align:start position:0% +over the network over an email or in in +an instant messenger you might want to + + align:start position:0% +an instant messenger you might want to + + + align:start position:0% +an instant messenger you might want to +actually think about whether or not + + align:start position:0% +actually think about whether or not + + + align:start position:0% +actually think about whether or not +there you know you you want to be + + align:start position:0% +there you know you you want to be + + + align:start position:0% +there you know you you want to be +sending this information out in the way + + align:start position:0% +sending this information out in the way + + + align:start position:0% +sending this information out in the way +that you're sending it out + + align:start position:0% +that you're sending it out + + + align:start position:0% +that you're sending it out +okay so what I want to do now is + + align:start position:0% +okay so what I want to do now is + + + align:start position:0% +okay so what I want to do now is +um come back to a little uh something we + + align:start position:0% +um come back to a little uh something we + + + align:start position:0% +um come back to a little uh something we +were talking about last time um finish + + align:start position:0% +were talking about last time um finish + + + align:start position:0% +were talking about last time um finish +up our discussion a little bit of + + align:start position:0% +up our discussion a little bit of + + + align:start position:0% +up our discussion a little bit of +authorization and then talk about uh + + align:start position:0% +authorization and then talk about uh + + + align:start position:0% +authorization and then talk about uh +sort of how we can start thinking about + + align:start position:0% +sort of how we can start thinking about + + + align:start position:0% +sort of how we can start thinking about +designing protocols that are actually um + + align:start position:0% +designing protocols that are actually um + + + align:start position:0% +designing protocols that are actually um +provide how we can reason about the + + align:start position:0% +provide how we can reason about the + + + align:start position:0% +provide how we can reason about the +security protocols that we are using + + align:start position:0% +security protocols that we are using + + + align:start position:0% +security protocols that we are using +particularly how we can reason about + + align:start position:0% +particularly how we can reason about + + + align:start position:0% +particularly how we can reason about +authentication protocols uh within + + align:start position:0% +authentication protocols uh within + + + align:start position:0% +authentication protocols uh within +within within networks so um if you + + align:start position:0% +within within networks so um if you + + + align:start position:0% +within within networks so um if you +remember last + + align:start position:0% + + + + align:start position:0% + +time we talked about uh this idea of + + align:start position:0% +time we talked about uh this idea of + + + align:start position:0% +time we talked about uh this idea of +building up a secure communication + + align:start position:0% + + + + align:start position:0% + +Channel then we talked about building + + align:start position:0% +Channel then we talked about building + + + align:start position:0% +Channel then we talked about building +doing authorization on top of that + + align:start position:0% +doing authorization on top of that + + + align:start position:0% +doing authorization on top of that +channel + + align:start position:0% +channel + + + align:start position:0% +channel +okay remember authorization is this + + align:start position:0% +okay remember authorization is this + + + align:start position:0% +okay remember authorization is this +process of deter determining whether a + + align:start position:0% +process of deter determining whether a + + + align:start position:0% +process of deter determining whether a +given user uh should have access to a + + align:start position:0% +given user uh should have access to a + + + align:start position:0% +given user uh should have access to a +particular resource that they want + + align:start position:0% +particular resource that they want + + + align:start position:0% +particular resource that they want +access to we talked about two main + + align:start position:0% +access to we talked about two main + + + align:start position:0% +access to we talked about two main +techniques for doing this uh ACLS and uh + + align:start position:0% +techniques for doing this uh ACLS and uh + + + align:start position:0% +techniques for doing this uh ACLS and uh +tickets so an ACL is an access control + + align:start position:0% +tickets so an ACL is an access control + + + align:start position:0% +tickets so an ACL is an access control +list an access Access Control list is + + align:start position:0% +list an access Access Control list is + + + align:start position:0% +list an access Access Control list is +just a list of users who are uh who are + + align:start position:0% +just a list of users who are uh who are + + + align:start position:0% +just a list of users who are uh who are +authorized to access a particular + + align:start position:0% +authorized to access a particular + + + align:start position:0% +authorized to access a particular +resource and so the way typically an + + align:start position:0% +resource and so the way typically an + + + align:start position:0% +resource and so the way typically an +access control list works is that the + + align:start position:0% +access control list works is that the + + + align:start position:0% +access control list works is that the +system first authenticates the user to + + align:start position:0% +system first authenticates the user to + + + align:start position:0% +system first authenticates the user to +determine what their identity is and + + align:start position:0% +determine what their identity is and + + + align:start position:0% +determine what their identity is and +then it checks to see whether that + + align:start position:0% +then it checks to see whether that + + + align:start position:0% +then it checks to see whether that +identity is uh is authorized that that + + align:start position:0% +identity is uh is authorized that that + + + align:start position:0% +identity is uh is authorized that that +identity is actually on this Access + + align:start position:0% +identity is actually on this Access + + + align:start position:0% +identity is actually on this Access +Control list and the user is authorized + + align:start position:0% +Control list and the user is authorized + + + align:start position:0% +Control list and the user is authorized +to access this particular resource they + + align:start position:0% +to access this particular resource they + + + align:start position:0% +to access this particular resource they +want access to a ticket has a slightly + + align:start position:0% +want access to a ticket has a slightly + + + align:start position:0% +want access to a ticket has a slightly +different flavor which is that typically + + align:start position:0% +different flavor which is that typically + + + align:start position:0% +different flavor which is that typically +you're a ticket if a user presents a + + align:start position:0% +you're a ticket if a user presents a + + + align:start position:0% +you're a ticket if a user presents a +ticket there you don't you don't need to + + align:start position:0% +ticket there you don't you don't need to + + + align:start position:0% +ticket there you don't you don't need to +actually check and see what their + + align:start position:0% +actually check and see what their + + + align:start position:0% +actually check and see what their +identity is Simply Having the ticket is + + align:start position:0% +identity is Simply Having the ticket is + + + align:start position:0% +identity is Simply Having the ticket is +sufficient to allow somebody to have + + align:start position:0% +sufficient to allow somebody to have + + + align:start position:0% +sufficient to allow somebody to have +access to a resource the analogy here is + + align:start position:0% +access to a resource the analogy here is + + + align:start position:0% +access to a resource the analogy here is +very similar to uh you know a physical + + align:start position:0% +very similar to uh you know a physical + + + align:start position:0% +very similar to uh you know a physical +ticket in the real world you go to a + + align:start position:0% +ticket in the real world you go to a + + + align:start position:0% +ticket in the real world you go to a +concert you hand them a ticket they let + + align:start position:0% +concert you hand them a ticket they let + + + align:start position:0% +concert you hand them a ticket they let +you into the concert without checking + + align:start position:0% +you into the concert without checking + + + align:start position:0% +you into the concert without checking +your ID um tickets have the so tickets a + + align:start position:0% +your ID um tickets have the so tickets a + + + align:start position:0% +your ID um tickets have the so tickets a +common example of a ticket in the real + + align:start position:0% +common example of a ticket in the real + + + align:start position:0% +common example of a ticket in the real +world is say is in the web on the web + + align:start position:0% +world is say is in the web on the web + + + align:start position:0% +world is say is in the web on the web +you get these cookies which are like + + align:start position:0% +you get these cookies which are like + + + align:start position:0% +you get these cookies which are like +tickets and the reason that you want to + + align:start position:0% +tickets and the reason that you want to + + + align:start position:0% +tickets and the reason that you want to +you use cookies instead of checking + + align:start position:0% +you use cookies instead of checking + + + align:start position:0% +you use cookies instead of checking +Access Control list every time is that + + align:start position:0% +Access Control list every time is that + + + align:start position:0% +Access Control list every time is that +when you have a particular cookie the + + align:start position:0% +when you have a particular cookie the + + + align:start position:0% +when you have a particular cookie the +system doesn't have to reauthenticate + + align:start position:0% +system doesn't have to reauthenticate + + + align:start position:0% +system doesn't have to reauthenticate +you in order to allow you to have access + + align:start position:0% +you in order to allow you to have access + + + align:start position:0% +you in order to allow you to have access +to the system every time you say revisit + + align:start position:0% +to the system every time you say revisit + + + align:start position:0% +to the system every time you say revisit +a page so I have a cookie for you know + + align:start position:0% +a page so I have a cookie for you know + + + align:start position:0% +a page so I have a cookie for you know +amazon.com on my computer when I'm uh + + align:start position:0% +amazon.com on my computer when I'm uh + + + align:start position:0% +amazon.com on my computer when I'm uh +visiting the uh you know when I'm in the + + align:start position:0% +visiting the uh you know when I'm in the + + + align:start position:0% +visiting the uh you know when I'm in the +process of purchasing some item from + + align:start position:0% +process of purchasing some item from + + + align:start position:0% +process of purchasing some item from +Amazon.com that identifies my identity + + align:start position:0% +Amazon.com that identifies my identity + + + align:start position:0% +Amazon.com that identifies my identity +and my shopping cart and I don't have to + + align:start position:0% +and my shopping cart and I don't have to + + + align:start position:0% +and my shopping cart and I don't have to +sort of relog in every time I request a + + align:start position:0% +sort of relog in every time I request a + + + align:start position:0% +sort of relog in every time I request a +new page from a new secure page from + + align:start position:0% + + + + align:start position:0% + +Amazon okay so this model the so the the + + align:start position:0% +Amazon okay so this model the so the the + + + align:start position:0% +Amazon okay so this model the so the the +example we specifically were talking + + align:start position:0% +example we specifically were talking + + + align:start position:0% +example we specifically were talking +about was the web and we had this notion + + align:start position:0% +about was the web and we had this notion + + + align:start position:0% +about was the web and we had this notion +of a we had a + + align:start position:0% +of a we had a + + + align:start position:0% +of a we had a +browser and a uh web server okay and the + + align:start position:0% +browser and a uh web server okay and the + + + align:start position:0% +browser and a uh web server okay and the +browser and the web + + align:start position:0% +browser and the web + + + align:start position:0% +browser and the web +server we talking over one of these + + align:start position:0% +server we talking over one of these + + + align:start position:0% +server we talking over one of these +secure communication + + align:start position:0% + + + + align:start position:0% + +channels we said this channel is uh both + + align:start position:0% +channels we said this channel is uh both + + + align:start position:0% +channels we said this channel is uh both +authenticated uh is both has been + + align:start position:0% +authenticated uh is both has been + + + align:start position:0% +authenticated uh is both has been +authenticated and is is + + align:start position:0% + + + + align:start position:0% + +confidential okay and authorization we + + align:start position:0% +confidential okay and authorization we + + + align:start position:0% +confidential okay and authorization we +said is uh authorization happens there's + + align:start position:0% +said is uh authorization happens there's + + + align:start position:0% +said is uh authorization happens there's +some guard process that's in charge of + + align:start position:0% +some guard process that's in charge of + + + align:start position:0% +some guard process that's in charge of +authorization this is our + + align:start position:0% +authorization this is our + + + align:start position:0% +authorization this is our +guard and it sits in front of the + + align:start position:0% +guard and it sits in front of the + + + align:start position:0% +guard and it sits in front of the +services on the + + align:start position:0% +services on the + + + align:start position:0% +services on the +system okay so when the when a request + + align:start position:0% +system okay so when the when a request + + + align:start position:0% +system okay so when the when a request +comes in to access a service the web + + align:start position:0% +comes in to access a service the web + + + align:start position:0% +comes in to access a service the web +server passes that request on to the + + align:start position:0% +server passes that request on to the + + + align:start position:0% +server passes that request on to the +guard module which does the + + align:start position:0% +guard module which does the + + + align:start position:0% +guard module which does the +authorization and then if the request is + + align:start position:0% +authorization and then if the request is + + + align:start position:0% +authorization and then if the request is +authorized it goes ahead and passes it + + align:start position:0% +authorized it goes ahead and passes it + + + align:start position:0% +authorized it goes ahead and passes it +on to the service + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so what we've talked about so with this + + align:start position:0% +so what we've talked about so with this + + + align:start position:0% +so what we've talked about so with this +this is this sort of we we and we we + + align:start position:0% +this is this sort of we we and we we + + + align:start position:0% +this is this sort of we we and we we +talked about remember this we have this + + align:start position:0% +talked about remember this we have this + + + align:start position:0% +talked about remember this we have this +notion of how we establish a secure + + align:start position:0% +notion of how we establish a secure + + + align:start position:0% +notion of how we establish a secure +Communication channel typically we do + + align:start position:0% +Communication channel typically we do + + + align:start position:0% +Communication channel typically we do +that by exchanging you know we we the + + align:start position:0% +that by exchanging you know we we the + + + align:start position:0% +that by exchanging you know we we the +one way that we talk about doing this is + + align:start position:0% +one way that we talk about doing this is + + + align:start position:0% +one way that we talk about doing this is +where B for example would discover W's + + align:start position:0% +where B for example would discover W's + + + align:start position:0% +where B for example would discover W's +public key somehow and then use that + + align:start position:0% +public key somehow and then use that + + + align:start position:0% +public key somehow and then use that +public key in order to uh exchange with + + align:start position:0% +public key in order to uh exchange with + + + align:start position:0% +public key in order to uh exchange with +w a uh shared secret key that they could + + align:start position:0% +w a uh shared secret key that they could + + + align:start position:0% +w a uh shared secret key that they could +use to encrypt all their communication + + align:start position:0% +use to encrypt all their communication + + + align:start position:0% +use to encrypt all their communication +so I'll show that protocol again in a + + align:start position:0% +so I'll show that protocol again in a + + + align:start position:0% +so I'll show that protocol again in a +minute but um the question and the + + align:start position:0% +minute but um the question and the + + + align:start position:0% +minute but um the question and the +question that we're really going to get + + align:start position:0% +question that we're really going to get + + + align:start position:0% +question that we're really going to get +at today is how it is that we want to + + align:start position:0% +at today is how it is that we want to + + + align:start position:0% +at today is how it is that we want to +focus in more on this this question of + + align:start position:0% +focus in more on this this question of + + + align:start position:0% +focus in more on this this question of +how it is that b actually discovers uh + + align:start position:0% +how it is that b actually discovers uh + + + align:start position:0% +how it is that b actually discovers uh +W's sh say uh public key um in a in a + + align:start position:0% +W's sh say uh public key um in a in a + + + align:start position:0% +W's sh say uh public key um in a in a +public key system and how it is that B + + align:start position:0% +public key system and how it is that B + + + align:start position:0% +public key system and how it is that B +can it can sort of convince itself that + + align:start position:0% +can it can sort of convince itself that + + + align:start position:0% +can it can sort of convince itself that +or Vin itself that in fact uh it's + + align:start position:0% +or Vin itself that in fact uh it's + + + align:start position:0% +or Vin itself that in fact uh it's +actually talking with a service that is + + align:start position:0% +actually talking with a service that is + + + align:start position:0% +actually talking with a service that is +it's actually talking with this service + + align:start position:0% +it's actually talking with this service + + + align:start position:0% +it's actually talking with this service +W so if B wants to have a conversation + + align:start position:0% +W so if B wants to have a conversation + + + align:start position:0% +W so if B wants to have a conversation +with amazon.com how does it actually + + align:start position:0% +with amazon.com how does it actually + + + align:start position:0% +with amazon.com how does it actually +convince itself that this public key + + align:start position:0% +convince itself that this public key + + + align:start position:0% +convince itself that this public key +that it has in fact belongs to + + align:start position:0% +that it has in fact belongs to + + + align:start position:0% +that it has in fact belongs to +amazon.com and that Amazon and that it's + + align:start position:0% +amazon.com and that Amazon and that it's + + + align:start position:0% +amazon.com and that Amazon and that it's +actually having a conversation with + + align:start position:0% +actually having a conversation with + + + align:start position:0% +actually having a conversation with +amazon.com instead of with somebody else + + align:start position:0% +amazon.com instead of with somebody else + + + align:start position:0% +amazon.com instead of with somebody else +who's pretending to be Amazon.com or who + + align:start position:0% +who's pretending to be Amazon.com or who + + + align:start position:0% +who's pretending to be Amazon.com or who +has lied about amazon.com's public key + + align:start position:0% +has lied about amazon.com's public key + + + align:start position:0% +has lied about amazon.com's public key +so that it can overhear amazon.com's + + align:start position:0% +so that it can overhear amazon.com's + + + align:start position:0% +so that it can overhear amazon.com's +traffic so we're going to focus in more + + align:start position:0% +traffic so we're going to focus in more + + + align:start position:0% +traffic so we're going to focus in more +on that now um so let's look at + + align:start position:0% + + + + align:start position:0% + +this a simplified version of an + + align:start position:0% +this a simplified version of an + + + align:start position:0% +this a simplified version of an +Authentication + + align:start position:0% +Authentication + + + align:start position:0% +Authentication +Protocol so this is going to be like + + align:start position:0% +Protocol so this is going to be like + + + align:start position:0% +Protocol so this is going to be like +that that Denning sacko protocol that I + + align:start position:0% +that that Denning sacko protocol that I + + + align:start position:0% +that that Denning sacko protocol that I +showed with the broken example or like + + align:start position:0% +showed with the broken example or like + + + align:start position:0% +showed with the broken example or like +SSL for example on the internet also + + align:start position:0% +SSL for example on the internet also + + + align:start position:0% +SSL for example on the internet also +sort of works in in roughly this way so + + align:start position:0% +sort of works in in roughly this way so + + + align:start position:0% +sort of works in in roughly this way so +we've got our browser got our web server + + align:start position:0% +we've got our browser got our web server + + + align:start position:0% +we've got our browser got our web server +and say we have some certificate + + align:start position:0% +and say we have some certificate + + + align:start position:0% +and say we have some certificate +Authority so this is the kind of picture + + align:start position:0% +Authority so this is the kind of picture + + + align:start position:0% +Authority so this is the kind of picture +we drew before we said the browser sends + + align:start position:0% +we drew before we said the browser sends + + + align:start position:0% +we drew before we said the browser sends +to the certificate Authority a request + + align:start position:0% +to the certificate Authority a request + + + align:start position:0% +to the certificate Authority a request +for a uh say the public key of w + + align:start position:0% +for a uh say the public key of w + + + align:start position:0% +for a uh say the public key of w +certificate Authority sends a message + + align:start position:0% +certificate Authority sends a message + + + align:start position:0% +certificate Authority sends a message +back which has say the certificates for + + align:start position:0% +back which has say the certificates for + + + align:start position:0% +back which has say the certificates for +B and the certificate for w and these + + align:start position:0% +B and the certificate for w and these + + + align:start position:0% +B and the certificate for w and these +are just simply signed uh things that + + align:start position:0% +are just simply signed uh things that + + + align:start position:0% +are just simply signed uh things that +the certificate Authority has has signed + + align:start position:0% +the certificate Authority has has signed + + + align:start position:0% +the certificate Authority has has signed +that include the public key for B and W + + align:start position:0% +that include the public key for B and W + + + align:start position:0% +that include the public key for B and W +in them so all certificates are and then + + align:start position:0% +in them so all certificates are and then + + + align:start position:0% +in them so all certificates are and then +B sends a message to W and there's some + + align:start position:0% +B sends a message to W and there's some + + + align:start position:0% +B sends a message to W and there's some +trickiness in getting this message right + + align:start position:0% +trickiness in getting this message right + + + align:start position:0% +trickiness in getting this message right +but this message basically is a signed + + align:start position:0% +but this message basically is a signed + + + align:start position:0% +but this message basically is a signed +and encrypted message that tells W that + + align:start position:0% +and encrypted message that tells W that + + + align:start position:0% +and encrypted message that tells W that +it would like to initiate a conversation + + align:start position:0% +it would like to initiate a conversation + + + align:start position:0% +it would like to initiate a conversation +with it and perhaps it pro proposes a + + align:start position:0% +with it and perhaps it pro proposes a + + + align:start position:0% +with it and perhaps it pro proposes a +shared key that it can use in that + + align:start position:0% +shared key that it can use in that + + + align:start position:0% +shared key that it can use in that +conversation right um so it's a little + + align:start position:0% +conversation right um so it's a little + + + align:start position:0% +conversation right um so it's a little +bit tricky to actually get figure out + + align:start position:0% +bit tricky to actually get figure out + + + align:start position:0% +bit tricky to actually get figure out +get make sure we get the format of that + + align:start position:0% +get make sure we get the format of that + + + align:start position:0% +get make sure we get the format of that +message right and that was there's this + + align:start position:0% +message right and that was there's this + + + align:start position:0% +message right and that was there's this +bug with the Denning SEO protocol but + + align:start position:0% +bug with the Denning SEO protocol but + + + align:start position:0% +bug with the Denning SEO protocol but +you get the idea so w then sends a + + align:start position:0% +you get the idea so w then sends a + + + align:start position:0% +you get the idea so w then sends a +message back saying perhaps asking the + + align:start position:0% +message back saying perhaps asking the + + + align:start position:0% +message back saying perhaps asking the +user to go ahead and uh trying to + + align:start position:0% +user to go ahead and uh trying to + + + align:start position:0% +user to go ahead and uh trying to +authorize the user saying okay you know + + align:start position:0% +authorize the user saying okay you know + + + align:start position:0% +authorize the user saying okay you know +I agree that that's the key now what's + + align:start position:0% +I agree that that's the key now what's + + + align:start position:0% +I agree that that's the key now what's +your you know what's your name and uh + + align:start position:0% +your you know what's your name and uh + + + align:start position:0% +your you know what's your name and uh +you know what's your password for + + align:start position:0% +you know what's your password for + + + align:start position:0% +you know what's your password for +example and then once it's exchanged + + align:start position:0% +example and then once it's exchanged + + + align:start position:0% +example and then once it's exchanged +that name and password then B is allowed + + align:start position:0% +that name and password then B is allowed + + + align:start position:0% +that name and password then B is allowed +to log into the system and access you + + align:start position:0% +to log into the system and access you + + + align:start position:0% +to log into the system and access you +know whatever B's resources B should + + align:start position:0% +know whatever B's resources B should + + + align:start position:0% +know whatever B's resources B should +have access to on the on the + + align:start position:0% + + + + align:start position:0% + +server so the question that I I want to + + align:start position:0% +server so the question that I I want to + + + align:start position:0% +server so the question that I I want to +focus on is this question about how B + + align:start position:0% +focus on is this question about how B + + + align:start position:0% +focus on is this question about how B +actually decides that the certificate + + align:start position:0% +actually decides that the certificate + + + align:start position:0% +actually decides that the certificate +Authority is a certificate Authority + + align:start position:0% +Authority is a certificate Authority + + + align:start position:0% +Authority is a certificate Authority +that it should trust how does B + + align:start position:0% +that it should trust how does B + + + align:start position:0% +that it should trust how does B +initially establish uh the sort of + + align:start position:0% +initially establish uh the sort of + + + align:start position:0% +initially establish uh the sort of +authenticity of this certificate + + align:start position:0% +authenticity of this certificate + + + align:start position:0% +authenticity of this certificate +Authority so when we talk about + + align:start position:0% +Authority so when we talk about + + + align:start position:0% +Authority so when we talk about +authentication before we presented this + + align:start position:0% +authentication before we presented this + + + align:start position:0% +authentication before we presented this +model that was sort of well you know + + align:start position:0% +model that was sort of well you know + + + align:start position:0% +model that was sort of well you know +you're going to learn you're going to + + align:start position:0% +you're going to learn you're going to + + + align:start position:0% +you're going to learn you're going to +you're going to authentic you're going + + align:start position:0% +you're going to authentic you're going + + + align:start position:0% +you're going to authentic you're going +to decide that you trust somebody by for + + align:start position:0% +to decide that you trust somebody by for + + + align:start position:0% +to decide that you trust somebody by for +example having a conversation with them + + align:start position:0% +example having a conversation with them + + + align:start position:0% +example having a conversation with them +right you're gonna you know I'm going to + + align:start position:0% +right you're gonna you know I'm going to + + + align:start position:0% +right you're gonna you know I'm going to +talk to you I'm G to run into you in the + + align:start position:0% +talk to you I'm G to run into you in the + + + align:start position:0% +talk to you I'm G to run into you in the +hall and you're going to say my public + + align:start position:0% +hall and you're going to say my public + + + align:start position:0% +hall and you're going to say my public +key is X and then I'm going to be able + + align:start position:0% +key is X and then I'm going to be able + + + align:start position:0% +key is X and then I'm going to be able +to have a a conversation with you but + + align:start position:0% +to have a a conversation with you but + + + align:start position:0% +to have a a conversation with you but +clearly that's not what happens in the + + align:start position:0% +clearly that's not what happens in the + + + align:start position:0% +clearly that's not what happens in the +case of the internet right like for + + align:start position:0% +case of the internet right like for + + + align:start position:0% +case of the internet right like for +example I don't go in on on the internet + + align:start position:0% +example I don't go in on on the internet + + + align:start position:0% +example I don't go in on on the internet +I don't um have to call up amazon.com or + + align:start position:0% +I don't um have to call up amazon.com or + + + align:start position:0% +I don't um have to call up amazon.com or +call up my certificate Authority and get + + align:start position:0% +call up my certificate Authority and get + + + align:start position:0% +call up my certificate Authority and get +the ceric get authorities public key + + align:start position:0% +the ceric get authorities public key + + + align:start position:0% +the ceric get authorities public key +from them right somehow I've already + + align:start position:0% +from them right somehow I've already + + + align:start position:0% +from them right somehow I've already +gotten this thing and so uh we sort of + + align:start position:0% +gotten this thing and so uh we sort of + + + align:start position:0% +gotten this thing and so uh we sort of +want to think about how it is that we + + align:start position:0% +want to think about how it is that we + + + align:start position:0% +want to think about how it is that we +can actually exchange these keys and how + + align:start position:0% +can actually exchange these keys and how + + + align:start position:0% +can actually exchange these keys and how +it is that uh we can think about these H + + align:start position:0% +it is that uh we can think about these H + + + align:start position:0% +it is that uh we can think about these H +how how it is that these systems can + + align:start position:0% +how how it is that these systems can + + + align:start position:0% +how how it is that these systems can +actually decide that they trust each + + align:start position:0% +actually decide that they trust each + + + align:start position:0% +actually decide that they trust each +other and that they are willing to + + align:start position:0% +other and that they are willing to + + + align:start position:0% +other and that they are willing to +authenticate each + + align:start position:0% +authenticate each + + + align:start position:0% +authenticate each +other so to do that what we're going to + + align:start position:0% +other so to do that what we're going to + + + align:start position:0% +other so to do that what we're going to +do is look at something called + + align:start position:0% +do is look at something called + + + align:start position:0% +do is look at something called +authentication logic + + align:start position:0% + + + + align:start position:0% + +this is also some the the specific + + align:start position:0% +this is also some the the specific + + + align:start position:0% +this is also some the the specific +version of authentication logic we're + + align:start position:0% +version of authentication logic we're + + + align:start position:0% +version of authentication logic we're +going to talk about is something called + + align:start position:0% +going to talk about is something called + + + align:start position:0% +going to talk about is something called +ban ban logic ba and N just stand for + + align:start position:0% +ban ban logic ba and N just stand for + + + align:start position:0% +ban ban logic ba and N just stand for +the the names of the three people who + + align:start position:0% +the the names of the three people who + + + align:start position:0% +the the names of the three people who +proposed this thing so it's not not a + + align:start position:0% +proposed this thing so it's not not a + + + align:start position:0% +proposed this thing so it's not not a +specific acronym you need to know um and + + align:start position:0% +specific acronym you need to know um and + + + align:start position:0% +specific acronym you need to know um and +so what authentication logic is going to + + align:start position:0% +so what authentication logic is going to + + + align:start position:0% +so what authentication logic is going to +do is it's going to allow us to reason + + align:start position:0% +do is it's going to allow us to reason + + + align:start position:0% +do is it's going to allow us to reason +about these uh protocols for exchanging + + align:start position:0% +about these uh protocols for exchanging + + + align:start position:0% +about these uh protocols for exchanging +for deciding whether or not we should + + align:start position:0% +for deciding whether or not we should + + + align:start position:0% +for deciding whether or not we should +authorize somebody to uh we we we + + align:start position:0% +authorize somebody to uh we we we + + + align:start position:0% +authorize somebody to uh we we we +actually trust something like a a given + + align:start position:0% +actually trust something like a a given + + + align:start position:0% +actually trust something like a a given +certificate Authority okay so let me + + align:start position:0% +certificate Authority okay so let me + + + align:start position:0% +certificate Authority okay so let me +just give you to to think about this a + + align:start position:0% +just give you to to think about this a + + + align:start position:0% +just give you to to think about this a +little bit more let's look at a specific + + align:start position:0% +little bit more let's look at a specific + + + align:start position:0% +little bit more let's look at a specific +example so + + align:start position:0% +example so + + + align:start position:0% +example so +suppose that you receive a message over + + align:start position:0% +suppose that you receive a message over + + + align:start position:0% +suppose that you receive a message over +the + + align:start position:0% +the + + + align:start position:0% +the +Internet okay suppose this message says + + align:start position:0% +Internet okay suppose this message says + + + align:start position:0% +Internet okay suppose this message says +now it's some message M and the message + + align:start position:0% +now it's some message M and the message + + + align:start position:0% +now it's some message M and the message +says sign is signed M with some key K + + align:start position:0% +says sign is signed M with some key K + + + align:start position:0% +says sign is signed M with some key K +call it case sub a + + align:start position:0% +call it case sub a + + + align:start position:0% +call it case sub a +okay um and suppose that the contents of + + align:start position:0% +okay um and suppose that the contents of + + + align:start position:0% +okay um and suppose that the contents of +message M are m + + align:start position:0% +message M are m + + + align:start position:0% +message M are m +equals uh give a your credit card + + align:start position:0% +equals uh give a your credit card + + + align:start position:0% +equals uh give a your credit card +number + + align:start position:0% + + + + align:start position:0% + +okay so this might be a valid request + + align:start position:0% +okay so this might be a valid request + + + align:start position:0% +okay so this might be a valid request +right we might + + align:start position:0% +right we might + + + align:start position:0% +right we might +be purchasing something from amazon.com + + align:start position:0% +be purchasing something from amazon.com + + + align:start position:0% +be purchasing something from amazon.com +right so that in that case you might + + align:start position:0% +right so that in that case you might + + + align:start position:0% +right so that in that case you might +think uh it might be it might might be + + align:start position:0% +think uh it might be it might might be + + + align:start position:0% +think uh it might be it might might be +okay for uh we might expect to receive a + + align:start position:0% +okay for uh we might expect to receive a + + + align:start position:0% +okay for uh we might expect to receive a +request like this right but the question + + align:start position:0% +request like this right but the question + + + align:start position:0% +request like this right but the question +is so this thing was signed with Ka and + + align:start position:0% +is so this thing was signed with Ka and + + + align:start position:0% +is so this thing was signed with Ka and +the message said give a your credit card + + align:start position:0% +the message said give a your credit card + + + align:start position:0% +the message said give a your credit card +number but how do we actually know how + + align:start position:0% +number but how do we actually know how + + + align:start position:0% +number but how do we actually know how +do we actually and you know maybe a in + + align:start position:0% +do we actually and you know maybe a in + + + align:start position:0% +do we actually and you know maybe a in +this case is give it to amazon.com and + + align:start position:0% +this case is give it to amazon.com and + + + align:start position:0% +this case is give it to amazon.com and +we know that we're talking to amazon.com + + align:start position:0% +we know that we're talking to amazon.com + + + align:start position:0% +we know that we're talking to amazon.com +and so if this in fact were an authentic + + align:start position:0% +and so if this in fact were an authentic + + + align:start position:0% +and so if this in fact were an authentic +message we would be you know we might + + align:start position:0% +message we would be you know we might + + + align:start position:0% +message we would be you know we might +not be that uh we might we we might be + + align:start position:0% +not be that uh we might we we might be + + + align:start position:0% +not be that uh we might we we might be +actually willing to give amazon.com + + align:start position:0% +actually willing to give amazon.com + + + align:start position:0% +actually willing to give amazon.com +Amazon our credit card number but so how + + align:start position:0% +Amazon our credit card number but so how + + + align:start position:0% +Amazon our credit card number but so how +do we actually know though that uh this + + align:start position:0% +do we actually know though that uh this + + + align:start position:0% +do we actually know though that uh this +message that that Ka is a message is is + + align:start position:0% +message that that Ka is a message is is + + + align:start position:0% +message that that Ka is a message is is +the key that belongs to amazon.com right + + align:start position:0% +the key that belongs to amazon.com right + + + align:start position:0% +the key that belongs to amazon.com right +so we want to answer the question how do + + align:start position:0% +so we want to answer the question how do + + + align:start position:0% +so we want to answer the question how do +we know that or trust + + align:start position:0% + + + + align:start position:0% + +that uh Ka we're going to say speaks + + align:start position:0% + + + + align:start position:0% + +for a okay so this notation speaks for + + align:start position:0% +for a okay so this notation speaks for + + + align:start position:0% +for a okay so this notation speaks for +just means that K if we see something uh + + align:start position:0% +just means that K if we see something uh + + + align:start position:0% +just means that K if we see something uh +that where that for example ass signed + + align:start position:0% +that where that for example ass signed + + + align:start position:0% +that where that for example ass signed +with Ka uh that we might that that + + align:start position:0% +with Ka uh that we might that that + + + align:start position:0% +with Ka uh that we might that that +claims to be from from a we might + + align:start position:0% +claims to be from from a we might + + + align:start position:0% +claims to be from from a we might +actually trust in fact that this thing + + align:start position:0% +actually trust in fact that this thing + + + align:start position:0% +actually trust in fact that this thing +came from a okay we want to know we want + + align:start position:0% +came from a okay we want to know we want + + + align:start position:0% +came from a okay we want to know we want +to sort of deter we're going to try and + + align:start position:0% +to sort of deter we're going to try and + + + align:start position:0% +to sort of deter we're going to try and +answer the question of how do we how do + + align:start position:0% +answer the question of how do we how do + + + align:start position:0% +answer the question of how do we how do +we how do we trust this okay so one way + + align:start position:0% +we how do we trust this okay so one way + + + align:start position:0% +we how do we trust this okay so one way +that we might trust that this is true is + + align:start position:0% +that we might trust that this is true is + + + align:start position:0% +that we might trust that this is true is +if we had heard for example that + + align:start position:0% +if we had heard for example that + + + align:start position:0% +if we had heard for example that +b we we had heard some + + align:start position:0% +b we we had heard some + + + align:start position:0% +b we we had heard some +message let's call it M2 um + + align:start position:0% + + + + align:start position:0% + +from somebody B um that had said + + align:start position:0% + + + + align:start position:0% + +that where that this message said Ka is + + align:start position:0% +that where that this message said Ka is + + + align:start position:0% +that where that this message said Ka is +A's key okay so one way that we might + + align:start position:0% +A's key okay so one way that we might + + + align:start position:0% +A's key okay so one way that we might +start thinking about why one way that we + + align:start position:0% +start thinking about why one way that we + + + align:start position:0% +start thinking about why one way that we +might trust a is if we'd heard from + + align:start position:0% +might trust a is if we'd heard from + + + align:start position:0% +might trust a is if we'd heard from +somebody else or heard from from some + + align:start position:0% +somebody else or heard from from some + + + align:start position:0% +somebody else or heard from from some +other place that uh K that Ka was A's + + align:start position:0% +other place that uh K that Ka was A's + + + align:start position:0% +other place that uh K that Ka was A's +key okay um but now we're sort of this + + align:start position:0% +key okay um but now we're sort of this + + + align:start position:0% +key okay um but now we're sort of this +this is kind of a slippery slope right + + align:start position:0% +this is kind of a slippery slope right + + + align:start position:0% +this is kind of a slippery slope right +because now you say the question well + + align:start position:0% +because now you say the question well + + + align:start position:0% +because now you say the question well +how did you determine that you trust B's + + align:start position:0% +how did you determine that you trust B's + + + align:start position:0% +how did you determine that you trust B's +key right so there's sort of this + + align:start position:0% +key right so there's sort of this + + + align:start position:0% +key right so there's sort of this +infinite process that you could end up + + align:start position:0% +infinite process that you could end up + + + align:start position:0% +infinite process that you could end up +going through that doesn't doesn't sound + + align:start position:0% +going through that doesn't doesn't sound + + + align:start position:0% +going through that doesn't doesn't sound +like a very good idea okay um + + align:start position:0% + + + + align:start position:0% + +so one but so one one way in which this + + align:start position:0% +so one but so one one way in which this + + + align:start position:0% +so one but so one one way in which this +sort of we might bottom out this + + align:start position:0% +sort of we might bottom out this + + + align:start position:0% +sort of we might bottom out this +recursion we might end this this sort of + + align:start position:0% +recursion we might end this this sort of + + + align:start position:0% +recursion we might end this this sort of +infinite process of collecting Keys is + + align:start position:0% +infinite process of collecting Keys is + + + align:start position:0% +infinite process of collecting Keys is +if we actually sort of in the example I + + align:start position:0% +if we actually sort of in the example I + + + align:start position:0% +if we actually sort of in the example I +gave you we'd heard from one person at + + align:start position:0% +gave you we'd heard from one person at + + + align:start position:0% +gave you we'd heard from one person at +some point you know suppose there's a b + + align:start position:0% +some point you know suppose there's a b + + + align:start position:0% +some point you know suppose there's a b +and a c and a d and an e and an f and + + align:start position:0% +and a c and a d and an e and an f and + + + align:start position:0% +and a c and a d and an e and an f and +then eventually get to F and F is our + + align:start position:0% +then eventually get to F and F is our + + + align:start position:0% +then eventually get to F and F is our +friend who we had talked to and F had + + align:start position:0% +friend who we had talked to and F had + + + align:start position:0% +friend who we had talked to and F had +said my public key is this um and here's + + align:start position:0% +said my public key is this um and here's + + + align:start position:0% +said my public key is this um and here's +the public keys for a few people that I + + align:start position:0% +the public keys for a few people that I + + + align:start position:0% +the public keys for a few people that I +know right so you might F you might + + align:start position:0% +know right so you might F you might + + + align:start position:0% +know right so you might F you might +trust F and you might believe that F + + align:start position:0% +trust F and you might believe that F + + + align:start position:0% +trust F and you might believe that F +knows a few other people and then uh + + align:start position:0% +knows a few other people and then uh + + + align:start position:0% +knows a few other people and then uh +those those people who F knows might in + + align:start position:0% +those those people who F knows might in + + + align:start position:0% +those those people who F knows might in +turn know a few other people and + + align:start position:0% +turn know a few other people and + + + align:start position:0% +turn know a few other people and +eventually we might be able to sort of + + align:start position:0% +eventually we might be able to sort of + + + align:start position:0% +eventually we might be able to sort of +have this web of interconnected people + + align:start position:0% +have this web of interconnected people + + + align:start position:0% +have this web of interconnected people +who all of whom we trust okay so one + + align:start position:0% +who all of whom we trust okay so one + + + align:start position:0% +who all of whom we trust okay so one +thing we might end up so this would be + + align:start position:0% +thing we might end up so this would be + + + align:start position:0% +thing we might end up so this would be +sort of a web of + + align:start position:0% + + + + align:start position:0% + +trust okay so we might be able to build + + align:start position:0% +trust okay so we might be able to build + + + align:start position:0% +trust okay so we might be able to build +up a web of trust like this but you + + align:start position:0% +up a web of trust like this but you + + + align:start position:0% +up a web of trust like this but you +could imagine that these relationships + + align:start position:0% +could imagine that these relationships + + + align:start position:0% +could imagine that these relationships +are pretty complicated right that you + + align:start position:0% +are pretty complicated right that you + + + align:start position:0% +are pretty complicated right that you +know each person for example a might you + + align:start position:0% +know each person for example a might you + + + align:start position:0% +know each person for example a might you +know B might trust a few people and C + + align:start position:0% +know B might trust a few people and C + + + align:start position:0% +know B might trust a few people and C +might trust a few people and D might + + align:start position:0% +might trust a few people and D might + + + align:start position:0% +might trust a few people and D might +trust a few people and every time we're + + align:start position:0% +trust a few people and every time we're + + + align:start position:0% +trust a few people and every time we're +presented with uh some message we need + + align:start position:0% +presented with uh some message we need + + + align:start position:0% +presented with uh some message we need +to have some sort of principled way of + + align:start position:0% +to have some sort of principled way of + + + align:start position:0% +to have some sort of principled way of +thinking about whether we have a set of + + align:start position:0% +thinking about whether we have a set of + + + align:start position:0% +thinking about whether we have a set of +these signatures + + align:start position:0% +these signatures + + + align:start position:0% +these signatures +or a set of these keys for example that + + align:start position:0% +or a set of these keys for example that + + + align:start position:0% +or a set of these keys for example that +actually allow us to decide whether we + + align:start position:0% +actually allow us to decide whether we + + + align:start position:0% +actually allow us to decide whether we +should accept this message or believe + + align:start position:0% +should accept this message or believe + + + align:start position:0% +should accept this message or believe +this message or not right so if we had a + + align:start position:0% +this message or not right so if we had a + + + align:start position:0% +this message or not right so if we had a +web of trust like this we would sort of + + align:start position:0% +web of trust like this we would sort of + + + align:start position:0% +web of trust like this we would sort of +need some way of going about VA + + align:start position:0% +need some way of going about VA + + + align:start position:0% +need some way of going about VA +validating or verifying that in fact uh + + align:start position:0% +validating or verifying that in fact uh + + + align:start position:0% +validating or verifying that in fact uh +these messages were were messages we + + align:start position:0% +these messages were were messages we + + + align:start position:0% +these messages were were messages we +should trust so that's what + + align:start position:0% +should trust so that's what + + + align:start position:0% +should trust so that's what +authentication logic is really all about + + align:start position:0% +authentication logic is really all about + + + align:start position:0% +authentication logic is really all about +um so this is the simplified ban logic + + align:start position:0% +um so this is the simplified ban logic + + + align:start position:0% +um so this is the simplified ban logic +that's presented in the text it's on + + align:start position:0% +that's presented in the text it's on + + + align:start position:0% +that's presented in the text it's on +page 1185 um if you want to copy it down + + align:start position:0% +page 1185 um if you want to copy it down + + + align:start position:0% +page 1185 um if you want to copy it down +I'll try and leave time for you but in + + align:start position:0% +I'll try and leave time for you but in + + + align:start position:0% +I'll try and leave time for you but in +case you want to just copy it out of the + + align:start position:0% +case you want to just copy it out of the + + + align:start position:0% +case you want to just copy it out of the +text you might not need to worry about + + align:start position:0% +text you might not need to worry about + + + align:start position:0% +text you might not need to worry about +copying down the exact logic here so + + align:start position:0% +copying down the exact logic here so + + + align:start position:0% +copying down the exact logic here so +there are three rules in this simplified + + align:start position:0% +there are three rules in this simplified + + + align:start position:0% +there are three rules in this simplified +authentication logic and they correspond + + align:start position:0% +authentication logic and they correspond + + + align:start position:0% +authentication logic and they correspond +to this they use this notation this + + align:start position:0% +to this they use this notation this + + + align:start position:0% +to this they use this notation this +speaks for notation and they're also + + align:start position:0% +speaks for notation and they're also + + + align:start position:0% +speaks for notation and they're also +going to use some notation that we call + + align:start position:0% +going to use some notation that we call + + + align:start position:0% +going to use some notation that we call +that says this says notation okay + + align:start position:0% +that says this says notation okay + + + align:start position:0% +that says this says notation okay +so what this rule says so this says if a + + align:start position:0% +so what this rule says so this says if a + + + align:start position:0% +so what this rule says so this says if a +says b speaks for a then B speaks for a + + align:start position:0% +says b speaks for a then B speaks for a + + + align:start position:0% +says b speaks for a then B speaks for a +okay so this sounds like sort of an + + align:start position:0% +okay so this sounds like sort of an + + + align:start position:0% +okay so this sounds like sort of an +obvious statement right um what this + + align:start position:0% +obvious statement right um what this + + + align:start position:0% +obvious statement right um what this +depends on so what saying saying that a + + align:start position:0% +depends on so what saying saying that a + + + align:start position:0% +depends on so what saying saying that a +says something means + + align:start position:0% +says something means + + + align:start position:0% +says something means +that in if if we hear a say something + + align:start position:0% +that in if if we hear a say something + + + align:start position:0% +that in if if we hear a say something +that means that we actually uh sort of a + + align:start position:0% +that means that we actually uh sort of a + + + align:start position:0% +that means that we actually uh sort of a +a told us and we believe that this in + + align:start position:0% +a told us and we believe that this in + + + align:start position:0% +a told us and we believe that this in +fact was a who told us this thing right + + align:start position:0% +fact was a who told us this thing right + + + align:start position:0% +fact was a who told us this thing right +so in order for a to say something we + + align:start position:0% +so in order for a to say something we + + + align:start position:0% +so in order for a to say something we +have to actually believe that it was we + + align:start position:0% +have to actually believe that it was we + + + align:start position:0% +have to actually believe that it was we +we this can't be a message for example + + align:start position:0% +we this can't be a message for example + + + align:start position:0% +we this can't be a message for example +that rece we received over an untrusted + + align:start position:0% +that rece we received over an untrusted + + + align:start position:0% +that rece we received over an untrusted +Network right this has to be you know I + + align:start position:0% +Network right this has to be you know I + + + align:start position:0% +Network right this has to be you know I +sat next to a in the hall and a actually + + align:start position:0% +sat next to a in the hall and a actually + + + align:start position:0% +sat next to a in the hall and a actually +said B speaks for me right right so in + + align:start position:0% +said B speaks for me right right so in + + + align:start position:0% +said B speaks for me right right so in +this case b might be um for example uh + + align:start position:0% +this case b might be um for example uh + + + align:start position:0% +this case b might be um for example uh +some key right so B so a might say my + + align:start position:0% +some key right so B so a might say my + + + align:start position:0% +some key right so B so a might say my +public key is Ka okay + + align:start position:0% +public key is Ka okay + + + align:start position:0% +public key is Ka okay +um if that is true and in fact we + + align:start position:0% +um if that is true and in fact we + + + align:start position:0% +um if that is true and in fact we +believe that a is the person who said + + align:start position:0% +believe that a is the person who said + + + align:start position:0% +believe that a is the person who said +this to us then we might have we might + + align:start position:0% +this to us then we might have we might + + + align:start position:0% +this to us then we might have we might +be able to infer from that that this key + + align:start position:0% +be able to infer from that that this key + + + align:start position:0% +be able to infer from that that this key +this k key Ka actually speaks for a okay + + align:start position:0% +this k key Ka actually speaks for a okay + + + align:start position:0% +this k key Ka actually speaks for a okay +so this is what the first rule is and + + align:start position:0% +so this is what the first rule is and + + + align:start position:0% +so this is what the first rule is and +this just gives us a way of uh sort of + + align:start position:0% +this just gives us a way of uh sort of + + + align:start position:0% +this just gives us a way of uh sort of +this is the the base case of you have + + align:start position:0% +this is the the base case of you have + + + align:start position:0% +this is the the base case of you have +something that you you sort of have a + + align:start position:0% +something that you you sort of have a + + + align:start position:0% +something that you you sort of have a +trusted Communication channel with + + align:start position:0% +trusted Communication channel with + + + align:start position:0% +trusted Communication channel with +communicating with a and you can use + + align:start position:0% +communicating with a and you can use + + + align:start position:0% +communicating with a and you can use +that trusted Communication channel to + + align:start position:0% +that trusted Communication channel to + + + align:start position:0% +that trusted Communication channel to +actually build up uh some belief about + + align:start position:0% +actually build up uh some belief about + + + align:start position:0% +actually build up uh some belief about +say for example a a key representing + + align:start position:0% +say for example a a key representing + + + align:start position:0% +say for example a a key representing +somebody okay so now the next rule is + + align:start position:0% +somebody okay so now the next rule is + + + align:start position:0% +somebody okay so now the next rule is +one that sort of says given that we have + + align:start position:0% +one that sort of says given that we have + + + align:start position:0% +one that sort of says given that we have +uh some belief about uh somebody uh you + + align:start position:0% +uh some belief about uh somebody uh you + + + align:start position:0% +uh some belief about uh somebody uh you +know one of these things like um for + + align:start position:0% +know one of these things like um for + + + align:start position:0% +know one of these things like um for +example if we know that b speaks for a + + align:start position:0% +example if we know that b speaks for a + + + align:start position:0% +example if we know that b speaks for a +we know what A's public key is um and we + + align:start position:0% +we know what A's public key is um and we + + + align:start position:0% +we know what A's public key is um and we +overhear uh B saying that a says X um + + align:start position:0% +overhear uh B saying that a says X um + + + align:start position:0% +overhear uh B saying that a says X um +then we might believe in fact that a + + align:start position:0% +then we might believe in fact that a + + + align:start position:0% +then we might believe in fact that a +says X so a simple example of this is + + align:start position:0% +says X so a simple example of this is + + + align:start position:0% +says X so a simple example of this is +suppose we get a message that's been + + align:start position:0% +suppose we get a message that's been + + + align:start position:0% +suppose we get a message that's been +signed um by this key Ka okay so we said + + align:start position:0% +signed um by this key Ka okay so we said + + + align:start position:0% +signed um by this key Ka okay so we said +uh and that this uh so if if we see that + + align:start position:0% +uh and that this uh so if if we see that + + + align:start position:0% +uh and that this uh so if if we see that +then we might in fact have a have a rule + + align:start position:0% +then we might in fact have a have a rule + + + align:start position:0% +then we might in fact have a have a rule +that says we might believe that Ka + + align:start position:0% +that says we might believe that Ka + + + align:start position:0% +that says we might believe that Ka +actually says this thing the KA says + + align:start position:0% +actually says this thing the KA says + + + align:start position:0% +actually says this thing the KA says +that a say a says M and we might believe + + align:start position:0% +that a say a says M and we might believe + + + align:start position:0% +that a say a says M and we might believe +that Ka says this because we believe + + align:start position:0% +that Ka says this because we believe + + + align:start position:0% +that Ka says this because we believe +that this sign uh this sort of + + align:start position:0% +that this sign uh this sort of + + + align:start position:0% +that this sign uh this sort of +sign primitive actually means that if we + + align:start position:0% +sign primitive actually means that if we + + + align:start position:0% +sign primitive actually means that if we +see something that was signed with ka's + + align:start position:0% +see something that was signed with ka's + + + align:start position:0% +see something that was signed with ka's +key that in fact that thing was + + align:start position:0% +key that in fact that thing was + + + align:start position:0% +key that in fact that thing was +generated by Ka right that nobody else + + align:start position:0% +generated by Ka right that nobody else + + + align:start position:0% +generated by Ka right that nobody else +could have generated a signed message + + align:start position:0% +could have generated a signed message + + + align:start position:0% +could have generated a signed message +that worked with Ka okay so uh we can + + align:start position:0% +that worked with Ka okay so uh we can + + + align:start position:0% +that worked with Ka okay so uh we can +use this now to for example build up a a + + align:start position:0% +use this now to for example build up a a + + + align:start position:0% +use this now to for example build up a a +we can actually now we can receive a + + align:start position:0% +we can actually now we can receive a + + + align:start position:0% +we can actually now we can receive a +message from a um that's been signed + + align:start position:0% +message from a um that's been signed + + + align:start position:0% +message from a um that's been signed +using Ka and we can in fact believe that + + align:start position:0% +using Ka and we can in fact believe that + + + align:start position:0% +using Ka and we can in fact believe that +you know a said something okay now the + + align:start position:0% +you know a said something okay now the + + + align:start position:0% +you know a said something okay now the +final rule that we have is sort of a + + align:start position:0% +final rule that we have is sort of a + + + align:start position:0% +final rule that we have is sort of a +transitivity rule which is a way of + + align:start position:0% +transitivity rule which is a way of + + + align:start position:0% +transitivity rule which is a way of +uh sort + + align:start position:0% +uh sort + + + align:start position:0% +uh sort +of learning which is a way of sort of + + align:start position:0% +of learning which is a way of sort of + + + align:start position:0% +of learning which is a way of sort of +expanding this web of who's related to + + align:start position:0% +expanding this web of who's related to + + + align:start position:0% +expanding this web of who's related to +whom so this says if B speaks for a okay + + align:start position:0% +whom so this says if B speaks for a okay + + + align:start position:0% +whom so this says if B speaks for a okay +and a speaks for C then what we're going + + align:start position:0% +and a speaks for C then what we're going + + + align:start position:0% +and a speaks for C then what we're going +to believe is that b speaks for C okay + + align:start position:0% +to believe is that b speaks for C okay + + + align:start position:0% +to believe is that b speaks for C okay +so this is just a transitive + + align:start position:0% +so this is just a transitive + + + align:start position:0% +so this is just a transitive +relationship so for example um if we + + align:start position:0% +relationship so for example um if we + + + align:start position:0% +relationship so for example um if we +know that Ka speaks for a um and we + + align:start position:0% +know that Ka speaks for a um and we + + + align:start position:0% +know that Ka speaks for a um and we +definitely overhear B saying a speaks + + align:start position:0% +definitely overhear B saying a speaks + + + align:start position:0% +definitely overhear B saying a speaks +for B right if B delegates it says a + + align:start position:0% +for B right if B delegates it says a + + + align:start position:0% +for B right if B delegates it says a +everything you know that a can a can + + align:start position:0% +everything you know that a can a can + + + align:start position:0% +everything you know that a can a can +speak for me then we might believe that + + align:start position:0% +speak for me then we might believe that + + + align:start position:0% +speak for me then we might believe that +k k key Ka also speaks for B okay so + + align:start position:0% +k k key Ka also speaks for B okay so + + + align:start position:0% +k k key Ka also speaks for B okay so +this is a simple transitivity + + align:start position:0% +this is a simple transitivity + + + align:start position:0% +this is a simple transitivity +relationship so um the idea with these + + align:start position:0% +relationship so um the idea with these + + + align:start position:0% +relationship so um the idea with these +rules is that we're going to be able to + + align:start position:0% +rules is that we're going to be able to + + + align:start position:0% +rules is that we're going to be able to +use them to actually think about uh + + align:start position:0% +use them to actually think about uh + + + align:start position:0% +use them to actually think about uh +whether or not we we so so we can we can + + align:start position:0% +whether or not we we so so we can we can + + + align:start position:0% +whether or not we we so so we can we can +sort of anytime we have a Sor this thing + + align:start position:0% +sort of anytime we have a Sor this thing + + + align:start position:0% +sort of anytime we have a Sor this thing +isn't quite far enough down this there's + + align:start position:0% +isn't quite far enough down this there's + + + align:start position:0% +isn't quite far enough down this there's +a then here that should say then B + + align:start position:0% +a then here that should say then B + + + align:start position:0% +a then here that should say then B +speaks for C sorry that got cut off + + align:start position:0% +speaks for C sorry that got cut off + + + align:start position:0% +speaks for C sorry that got cut off +um so if we have this if we have a set + + align:start position:0% +um so if we have this if we have a set + + + align:start position:0% +um so if we have this if we have a set +of rules like this then we're going to + + align:start position:0% +of rules like this then we're going to + + + align:start position:0% +of rules like this then we're going to +going to be able to apply these rules + + align:start position:0% +going to be able to apply these rules + + + align:start position:0% +going to be able to apply these rules +sort of anytime we have a conversation + + align:start position:0% +sort of anytime we have a conversation + + + align:start position:0% +sort of anytime we have a conversation +to decide again whether we actually + + align:start position:0% +to decide again whether we actually + + + align:start position:0% +to decide again whether we actually +trust uh trust the people who we're + + align:start position:0% +trust uh trust the people who we're + + + align:start position:0% +trust uh trust the people who we're +communicating with um and you may have + + align:start position:0% +communicating with um and you may have + + + align:start position:0% +communicating with um and you may have +noticed when I was talking about this + + align:start position:0% +noticed when I was talking about this + + + align:start position:0% +noticed when I was talking about this +that I had a lot of there was sort of a + + align:start position:0% +that I had a lot of there was sort of a + + + align:start position:0% +that I had a lot of there was sort of a +lot of statements like if we believe + + align:start position:0% +lot of statements like if we believe + + + align:start position:0% +lot of statements like if we believe +that s of X you know that sin x uh no + + align:start position:0% +that s of X you know that sin x uh no + + + align:start position:0% +that s of X you know that sin x uh no +nobody can actually fake this this + + align:start position:0% +nobody can actually fake this this + + + align:start position:0% +nobody can actually fake this this +protocol sin x right we believe that Ka + + align:start position:0% +protocol sin x right we believe that Ka + + + align:start position:0% +protocol sin x right we believe that Ka +that that signing a message with Ka is + + align:start position:0% +that that signing a message with Ka is + + + align:start position:0% +that that signing a message with Ka is +uh as good as um actually the signing + + align:start position:0% +uh as good as um actually the signing + + + align:start position:0% +uh as good as um actually the signing +that nobody could Forge this message + + align:start position:0% +that nobody could Forge this message + + + align:start position:0% +that nobody could Forge this message +that was signed with KA for example + + align:start position:0% +that was signed with KA for example + + + align:start position:0% +that was signed with KA for example +right if we believe that that's true + + align:start position:0% +right if we believe that that's true + + + align:start position:0% +right if we believe that that's true +then we can say Ka says this thing so + + align:start position:0% +then we can say Ka says this thing so + + + align:start position:0% +then we can say Ka says this thing so +this authentication logic is full of a + + align:start position:0% +this authentication logic is full of a + + + align:start position:0% +this authentication logic is full of a +lot of these sort of like if we believe + + align:start position:0% +lot of these sort of like if we believe + + + align:start position:0% +lot of these sort of like if we believe +this thing is true uh kinds of + + align:start position:0% +this thing is true uh kinds of + + + align:start position:0% +this thing is true uh kinds of +assumptions that we're going to be + + align:start position:0% +assumptions that we're going to be + + + align:start position:0% +assumptions that we're going to be +making okay is there a + + align:start position:0% + + + + align:start position:0% + +question the third rule what part Sor + + align:start position:0% +question the third rule what part Sor + + + align:start position:0% +question the third rule what part Sor +this I can see the bottom part on the + + align:start position:0% +this I can see the bottom part on the + + + align:start position:0% +this I can see the bottom part on the +left okay I just mean I don't know like + + align:start position:0% +left okay I just mean I don't know like + + + align:start position:0% +left okay I just mean I don't know like +in the example which part is C oh okay + + align:start position:0% +in the example which part is C oh okay + + + align:start position:0% +in the example which part is C oh okay +so in this case sorry sorry you're right + + align:start position:0% +so in this case sorry sorry you're right + + + align:start position:0% +so in this case sorry sorry you're right +my example is kind of confusing the the + + align:start position:0% +my example is kind of confusing the the + + + align:start position:0% +my example is kind of confusing the the +uh so my this example uh in this example + + align:start position:0% +uh so my this example uh in this example + + + align:start position:0% +uh so my this example uh in this example +B is actually C + + align:start position:0% +B is actually C + + + align:start position:0% +B is actually C +so sorry uh no no no it's it's uh K + + align:start position:0% +so sorry uh no no no it's it's uh K + + + align:start position:0% +so sorry uh no no no it's it's uh K +speaks for a right so Ka a is b a right + + align:start position:0% +speaks for a right so Ka a is b a right + + + align:start position:0% +speaks for a right so Ka a is b a right +so it's sort of so it says if if um if B + + align:start position:0% +so it's sort of so it says if if um if B + + + align:start position:0% +so it's sort of so it says if if um if B +says that if we know that b speaks for C + + align:start position:0% +says that if we know that b speaks for C + + + align:start position:0% +says that if we know that b speaks for C +if we if we know that a speaks for B + + align:start position:0% +if we if we know that a speaks for B + + + align:start position:0% +if we if we know that a speaks for B +right then we might be willing to + + align:start position:0% +right then we might be willing to + + + align:start position:0% +right then we might be willing to +believe that Ka actually speaks for B + + align:start position:0% +believe that Ka actually speaks for B + + + align:start position:0% +believe that Ka actually speaks for B +given that uh Ka speaks for a right so + + align:start position:0% +given that uh Ka speaks for a right so + + + align:start position:0% +given that uh Ka speaks for a right so +we have this transitivity kind of a + + align:start position:0% +we have this transitivity kind of a + + + align:start position:0% +we have this transitivity kind of a +relationship sorry that I that that + + align:start position:0% +relationship sorry that I that that + + + align:start position:0% +relationship sorry that I that that +notation is a little bit confusing I + + align:start position:0% +notation is a little bit confusing I + + + align:start position:0% +notation is a little bit confusing I +agree + + align:start position:0% +agree + + + align:start position:0% +agree +so okay so + + align:start position:0% +so okay so + + + align:start position:0% +so okay so +um so the the the challenge here is uh + + align:start position:0% +um so the the the challenge here is uh + + + align:start position:0% +um so the the the challenge here is uh +that we want to try and make so we're + + align:start position:0% +that we want to try and make so we're + + + align:start position:0% +that we want to try and make so we're +going to be making anytime we're using + + align:start position:0% +going to be making anytime we're using + + + align:start position:0% +going to be making anytime we're using +this authentication logic in order to + + align:start position:0% +this authentication logic in order to + + + align:start position:0% +this authentication logic in order to +actually determine that somebody + + align:start position:0% +actually determine that somebody + + + align:start position:0% +actually determine that somebody +definitely said something we're going to + + align:start position:0% +definitely said something we're going to + + + align:start position:0% +definitely said something we're going to +have to make some sort of set of + + align:start position:0% +have to make some sort of set of + + + align:start position:0% +have to make some sort of set of +assumptions about what we trust and what + + align:start position:0% +assumptions about what we trust and what + + + align:start position:0% +assumptions about what we trust and what +we believe so um and one of the things + + align:start position:0% +we believe so um and one of the things + + + align:start position:0% +we believe so um and one of the things +that's important anytime using this + + align:start position:0% +that's important anytime using this + + + align:start position:0% +that's important anytime using this +authentication logic is to actually make + + align:start position:0% +authentication logic is to actually make + + + align:start position:0% +authentication logic is to actually make +these assumptions as explicit as you can + + align:start position:0% + + + + align:start position:0% + +okay so let's look at a set of + + align:start position:0% +okay so let's look at a set of + + + align:start position:0% +okay so let's look at a set of +assumptions that we're making here so I + + align:start position:0% +assumptions that we're making here so I + + + align:start position:0% +assumptions that we're making here so I +said something like s when I see a + + align:start position:0% +said something like s when I see a + + + align:start position:0% +said something like s when I see a +message that says s uh M comma + + align:start position:0% +message that says s uh M comma + + + align:start position:0% +message that says s uh M comma +Ka right um + + align:start position:0% + + + + align:start position:0% + +and then I infer from that that a says + + align:start position:0% +and then I infer from that that a says + + + align:start position:0% +and then I infer from that that a says +M right assuming that I already know + + align:start position:0% +M right assuming that I already know + + + align:start position:0% +M right assuming that I already know +that K and I know already that + + align:start position:0% +that K and I know already that + + + align:start position:0% +that K and I know already that +Ka + + align:start position:0% +Ka + + + align:start position:0% +Ka +speaks for a okay so if I have something + + align:start position:0% +speaks for a okay so if I have something + + + align:start position:0% +speaks for a okay so if I have something +like this and I make this inference that + + align:start position:0% +like this and I make this inference that + + + align:start position:0% +like this and I make this inference that +a says M given that that a says M given + + align:start position:0% +a says M given that that a says M given + + + align:start position:0% +a says M given that that a says M given +K I Saw the Sign thing right um I'm + + align:start position:0% +K I Saw the Sign thing right um I'm + + + align:start position:0% +K I Saw the Sign thing right um I'm +making a set of assumptions when I do + + align:start position:0% +making a set of assumptions when I do + + + align:start position:0% +making a set of assumptions when I do +this I'm making making a set of + + align:start position:0% +this I'm making making a set of + + + align:start position:0% +this I'm making making a set of +assumptions in particular about what uh + + align:start position:0% +assumptions in particular about what uh + + + align:start position:0% +assumptions in particular about what uh +this this sign protocol does so I'm + + align:start position:0% +this this sign protocol does so I'm + + + align:start position:0% +this this sign protocol does so I'm +assuming for example that the sign + + align:start position:0% +assuming for example that the sign + + + align:start position:0% +assuming for example that the sign +protocol is actually that that sign is + + align:start position:0% +protocol is actually that that sign is + + + align:start position:0% +protocol is actually that that sign is +actually secure in some way right so I'm + + align:start position:0% + + + + align:start position:0% + +assuming that this + + align:start position:0% +assuming that this + + + align:start position:0% +assuming that this +signature is not forgeable right that I + + align:start position:0% +signature is not forgeable right that I + + + align:start position:0% +signature is not forgeable right that I +couldn't have that somebody else + + align:start position:0% +couldn't have that somebody else + + + align:start position:0% +couldn't have that somebody else +couldn't have generated a signature + + align:start position:0% +couldn't have generated a signature + + + align:start position:0% +couldn't have generated a signature +unless they actually had access for + + align:start position:0% +unless they actually had access for + + + align:start position:0% +unless they actually had access for +example to the private key or or to to + + align:start position:0% +example to the private key or or to to + + + align:start position:0% +example to the private key or or to to +to the private key of a right right so + + align:start position:0% +to the private key of a right right so + + + align:start position:0% +to the private key of a right right so +they wouldn't this this signature is not + + align:start position:0% +they wouldn't this this signature is not + + + align:start position:0% +they wouldn't this this signature is not +fortunate I'm also assuming um for + + align:start position:0% +fortunate I'm also assuming um for + + + align:start position:0% +fortunate I'm also assuming um for +example that uh if this is if if this is + + align:start position:0% +example that uh if this is if if this is + + + align:start position:0% +example that uh if this is if if this is +a uh + + align:start position:0% +a uh + + + align:start position:0% +a uh +that I'm also + + align:start position:0% +that I'm also + + + align:start position:0% +that I'm also +assuming + + align:start position:0% +assuming + + + align:start position:0% +assuming +that um any that any private + + align:start position:0% +that um any that any private + + + align:start position:0% +that um any that any private +keys are actually private right so I'm + + align:start position:0% +keys are actually private right so I'm + + + align:start position:0% +keys are actually private right so I'm +assuming that for + + align:start position:0% +assuming that for + + + align:start position:0% +assuming that for +example a hasn't gone out and + + align:start position:0% +example a hasn't gone out and + + + align:start position:0% +example a hasn't gone out and +broadcasted key out to everybody else in + + align:start position:0% +broadcasted key out to everybody else in + + + align:start position:0% +broadcasted key out to everybody else in +the world right because if a had done + + align:start position:0% +the world right because if a had done + + + align:start position:0% +the world right because if a had done +that then I wouldn't actually know that + + align:start position:0% +that then I wouldn't actually know that + + + align:start position:0% +that then I wouldn't actually know that +this message that a actually said M it + + align:start position:0% +this message that a actually said M it + + + align:start position:0% +this message that a actually said M it +could have been anybody who said am + + align:start position:0% +could have been anybody who said am + + + align:start position:0% +could have been anybody who said am +right so I would be in trouble if that + + align:start position:0% +right so I would be in trouble if that + + + align:start position:0% +right so I would be in trouble if that +were the case so anytime that I sort of + + align:start position:0% +were the case so anytime that I sort of + + + align:start position:0% +were the case so anytime that I sort of +take this make this inference from + + align:start position:0% +take this make this inference from + + + align:start position:0% +take this make this inference from +seeing a sign like this then that + + align:start position:0% +seeing a sign like this then that + + + align:start position:0% +seeing a sign like this then that +suggests that I'm sort of making these + + align:start position:0% +suggests that I'm sort of making these + + + align:start position:0% +suggests that I'm sort of making these +two assumptions and you know it's not + + align:start position:0% +two assumptions and you know it's not + + + align:start position:0% +two assumptions and you know it's not +that these assumptions are wrong or bad + + align:start position:0% +that these assumptions are wrong or bad + + + align:start position:0% +that these assumptions are wrong or bad +it's just that it's good to think about + + align:start position:0% +it's just that it's good to think about + + + align:start position:0% +it's just that it's good to think about +explicitly what they are right so + + align:start position:0% +explicitly what they are right so + + + align:start position:0% +explicitly what they are right so +assuming that the signature is not forg + + align:start position:0% +assuming that the signature is not forg + + + align:start position:0% +assuming that the signature is not forg +well we all know that cryptograph can + + align:start position:0% +well we all know that cryptograph can + + + align:start position:0% +well we all know that cryptograph can +sometimes be broken right it's not that + + align:start position:0% +sometimes be broken right it's not that + + + align:start position:0% +sometimes be broken right it's not that +cryptography is totally foolproof but we + + align:start position:0% +cryptography is totally foolproof but we + + + align:start position:0% +cryptography is totally foolproof but we +may have a relatively high confidence + + align:start position:0% +may have a relatively high confidence + + + align:start position:0% +may have a relatively high confidence +that this this cryptography is is going + + align:start position:0% +that this this cryptography is is going + + + align:start position:0% +that this this cryptography is is going +to be difficult for somebody to break + + align:start position:0% +to be difficult for somebody to break + + + align:start position:0% +to be difficult for somebody to break +right um and well assuming that private + + align:start position:0% +right um and well assuming that private + + + align:start position:0% +right um and well assuming that private +keys are actually private um you know we + + align:start position:0% +keys are actually private um you know we + + + align:start position:0% +keys are actually private um you know we +might be willing to assume that a we we + + align:start position:0% +might be willing to assume that a we we + + + align:start position:0% +might be willing to assume that a we we +might sort of know a personally and + + align:start position:0% +might sort of know a personally and + + + align:start position:0% +might sort of know a personally and +believe that well you know a is an + + align:start position:0% +believe that well you know a is an + + + align:start position:0% +believe that well you know a is an +upstanding an up an upright upstanding + + align:start position:0% +upstanding an up an upright upstanding + + + align:start position:0% +upstanding an up an upright upstanding +individual you know we're going to trust + + align:start position:0% +individual you know we're going to trust + + + align:start position:0% +individual you know we're going to trust +that she hasn't gone and disseminated + + align:start position:0% +that she hasn't gone and disseminated + + + align:start position:0% +that she hasn't gone and disseminated +her key around everywhere around the + + align:start position:0% +her key around everywhere around the + + + align:start position:0% +her key around everywhere around the +world because that wouldn't really in + + align:start position:0% +world because that wouldn't really in + + + align:start position:0% +world because that wouldn't really in +her interest and we take her to be a + + align:start position:0% +her interest and we take her to be a + + + align:start position:0% +her interest and we take her to be a +trustworthy person so this is a bit of a + + align:start position:0% +trustworthy person so this is a bit of a + + + align:start position:0% +trustworthy person so this is a bit of a +leap of faith that we're making about + + align:start position:0% +leap of faith that we're making about + + + align:start position:0% +leap of faith that we're making about +this right but if we believe those two + + align:start position:0% +this right but if we believe those two + + + align:start position:0% +this right but if we believe those two +things then we can in fact infer that a + + align:start position:0% +things then we can in fact infer that a + + + align:start position:0% +things then we can in fact infer that a +says M when we see a message that's + + align:start position:0% +says M when we see a message that's + + + align:start position:0% +says M when we see a message that's +signed with K + + align:start position:0% +signed with K + + + align:start position:0% +signed with K +okay all right so let's look at this and + + align:start position:0% +okay all right so let's look at this and + + + align:start position:0% +okay all right so let's look at this and +let's look at a little bit more uh + + align:start position:0% +let's look at a little bit more uh + + + align:start position:0% +let's look at a little bit more uh +another example um that works with with + + align:start position:0% +another example um that works with with + + + align:start position:0% +another example um that works with with +this sort of public key cryptography + + align:start position:0% +this sort of public key cryptography + + + align:start position:0% +this sort of public key cryptography +that we talked about uh say in this + + align:start position:0% +that we talked about uh say in this + + + align:start position:0% +that we talked about uh say in this +example of this Authentication Protocol + + align:start position:0% +example of this Authentication Protocol + + + align:start position:0% +example of this Authentication Protocol +here um + + align:start position:0% +here um + + + align:start position:0% +here um +okay so suppose I see some suppose that + + align:start position:0% +okay so suppose I see some suppose that + + + align:start position:0% +okay so suppose I see some suppose that +a tells me my public key is kaap Pub and + + align:start position:0% +a tells me my public key is kaap Pub and + + + align:start position:0% +a tells me my public key is kaap Pub and +I this is done over a secure + + align:start position:0% +I this is done over a secure + + + align:start position:0% +I this is done over a secure +Communication channel like in personal + + align:start position:0% +Communication channel like in personal + + + align:start position:0% +Communication channel like in personal +in person communication I might then + + align:start position:0% +in person communication I might then + + + align:start position:0% +in person communication I might then +infer that kaap Pub actually speaks for + + align:start position:0% +infer that kaap Pub actually speaks for + + + align:start position:0% +infer that kaap Pub actually speaks for +a okay now suppose I see a message + + align:start position:0% +a okay now suppose I see a message + + + align:start position:0% +a okay now suppose I see a message +that's been signed with Ka private + + align:start position:0% +that's been signed with Ka private + + + align:start position:0% +that's been signed with Ka private +um this message uh so I might say that + + align:start position:0% +um this message uh so I might say that + + + align:start position:0% +um this message uh so I might say that +then Ka private says so this is this is + + align:start position:0% +then Ka private says so this is this is + + + align:start position:0% +then Ka private says so this is this is +an inference I might say Ka private says + + align:start position:0% +an inference I might say Ka private says + + + align:start position:0% +an inference I might say Ka private says +that a says M okay um the question now + + align:start position:0% +that a says M okay um the question now + + + align:start position:0% +that a says M okay um the question now +is then what we want to ask now is okay + + align:start position:0% +is then what we want to ask now is okay + + + align:start position:0% +is then what we want to ask now is okay +so should we given this should we + + align:start position:0% +so should we given this should we + + + align:start position:0% +so should we given this should we +actually believe that a said M so I saw + + align:start position:0% +actually believe that a said M so I saw + + + align:start position:0% +actually believe that a said M so I saw +a message I know what A's public key is + + align:start position:0% +a message I know what A's public key is + + + align:start position:0% +a message I know what A's public key is +and I trust A's public key maybe and I + + align:start position:0% +and I trust A's public key maybe and I + + + align:start position:0% +and I trust A's public key maybe and I +saw this sign thing and now I need to + + align:start position:0% +saw this sign thing and now I need to + + + align:start position:0% +saw this sign thing and now I need to +think about you know okay does is this + + align:start position:0% +think about you know okay does is this + + + align:start position:0% +think about you know okay does is this +do I believe now that a actually said M + + align:start position:0% +do I believe now that a actually said M + + + align:start position:0% +do I believe now that a actually said M +given that I saw a message that was + + align:start position:0% +given that I saw a message that was + + + align:start position:0% +given that I saw a message that was +signed with Ka a priv that was signed + + align:start position:0% +signed with Ka a priv that was signed + + + align:start position:0% +signed with Ka a priv that was signed +with Ka private okay well so there's + + align:start position:0% +with Ka private okay well so there's + + + align:start position:0% +with Ka private okay well so there's +something obviously that we need to do + + align:start position:0% +something obviously that we need to do + + + align:start position:0% +something obviously that we need to do +which is that we need to verify this + + align:start position:0% +which is that we need to verify this + + + align:start position:0% +which is that we need to verify this +message so suppose we go and we run this + + align:start position:0% +message so suppose we go and we run this + + + align:start position:0% +message so suppose we go and we run this +verify step on this message and this + + align:start position:0% +verify step on this message and this + + + align:start position:0% +verify step on this message and this +verify comes out to be true right so + + align:start position:0% +verify comes out to be true right so + + + align:start position:0% +verify comes out to be true right so +what verify so I verify using kaap Pub + + align:start position:0% +what verify so I verify using kaap Pub + + + align:start position:0% +what verify so I verify using kaap Pub +then in fact this message was + + align:start position:0% +then in fact this message was + + + align:start position:0% +then in fact this message was +appropriately signed um the verify says + + align:start position:0% +appropriately signed um the verify says + + + align:start position:0% +appropriately signed um the verify says +yes this this message is the the + + align:start position:0% +yes this this message is the the + + + align:start position:0% +yes this this message is the the +signature on this message checks so now + + align:start position:0% +signature on this message checks so now + + + align:start position:0% +signature on this message checks so now +should I believe that this message + + align:start position:0% +should I believe that this message + + + align:start position:0% +should I believe that this message +actually came from that that a actually + + align:start position:0% +actually came from that that a actually + + + align:start position:0% +actually came from that that a actually +said + + align:start position:0% +said + + + align:start position:0% +said +M so that depends right there's a couple + + align:start position:0% +M so that depends right there's a couple + + + align:start position:0% +M so that depends right there's a couple +of conditions which we might again + + align:start position:0% +of conditions which we might again + + + align:start position:0% +of conditions which we might again +there's this sort of set of assumptions + + align:start position:0% +there's this sort of set of assumptions + + + align:start position:0% +there's this sort of set of assumptions +that we're making so one thing we're + + align:start position:0% +that we're making so one thing we're + + + align:start position:0% +that we're making so one thing we're +clearly doing is assuming that this + + align:start position:0% +clearly doing is assuming that this + + + align:start position:0% +clearly doing is assuming that this +crypto system is secure um we're also + + align:start position:0% +crypto system is secure um we're also + + + align:start position:0% +crypto system is secure um we're also +believing that this verification step + + align:start position:0% +believing that this verification step + + + align:start position:0% +believing that this verification step +actually uh sort of that this ver that + + align:start position:0% +actually uh sort of that this ver that + + + align:start position:0% +actually uh sort of that this ver that +this verification step actually uh gives + + align:start position:0% +this verification step actually uh gives + + + align:start position:0% +this verification step actually uh gives +us + + align:start position:0% +us + + + align:start position:0% +us +a that by by taking something that has + + align:start position:0% +a that by by taking something that has + + + align:start position:0% +a that by by taking something that has +been signed with the private key and + + align:start position:0% +been signed with the private key and + + + align:start position:0% +been signed with the private key and +then verifying it with the public key + + align:start position:0% +then verifying it with the public key + + + align:start position:0% +then verifying it with the public key +that that is as good as uh a actually + + align:start position:0% +that that is as good as uh a actually + + + align:start position:0% +that that is as good as uh a actually +saying something so one thing clearly + + align:start position:0% +saying something so one thing clearly + + + align:start position:0% +saying something so one thing clearly +that depends on as well is that the + + align:start position:0% +that depends on as well is that the + + + align:start position:0% +that depends on as well is that the +crypto system is secure sorry my I'm + + align:start position:0% +crypto system is secure sorry my I'm + + + align:start position:0% +crypto system is secure sorry my I'm +just going to erase some text here + + align:start position:0% +just going to erase some text here + + + align:start position:0% +just going to erase some text here +because the bottom got cut off so so you + + align:start position:0% +because the bottom got cut off so so you + + + align:start position:0% +because the bottom got cut off so so you +guys can read + + align:start position:0% + + + + align:start position:0% + +um okay so uh there are a couple of + + align:start position:0% +um okay so uh there are a couple of + + + align:start position:0% +um okay so uh there are a couple of +other assumptions though that + + align:start position:0% + + + + align:start position:0% + +we're making + + align:start position:0% +we're making + + + align:start position:0% +we're making +so so one thing is that it definitely + + align:start position:0% +so so one thing is that it definitely + + + align:start position:0% +so so one thing is that it definitely +again requires that Ka private has + + align:start position:0% +again requires that Ka private has + + + align:start position:0% +again requires that Ka private has +actually been kept secret um and + + align:start position:0% +actually been kept secret um and + + + align:start position:0% +actually been kept secret um and +furthermore uh it requires that a didn't + + align:start position:0% +furthermore uh it requires that a didn't + + + align:start position:0% +furthermore uh it requires that a didn't +lie to us about what Ka public was right + + align:start position:0% +lie to us about what Ka public was right + + + align:start position:0% +lie to us about what Ka public was right +because if a had given us a wrong Ka + + align:start position:0% +because if a had given us a wrong Ka + + + align:start position:0% +because if a had given us a wrong Ka +public um then she somebody else could + + align:start position:0% +public um then she somebody else could + + + align:start position:0% +public um then she somebody else could +have signed this message and then we + + align:start position:0% +have signed this message and then we + + + align:start position:0% +have signed this message and then we +might verify we might try and verify the + + align:start position:0% +might verify we might try and verify the + + + align:start position:0% +might verify we might try and verify the +message using the the lied about Ka + + align:start position:0% +message using the the lied about Ka + + + align:start position:0% +message using the the lied about Ka +public and then we might be in trouble + + align:start position:0% +public and then we might be in trouble + + + align:start position:0% +public and then we might be in trouble +okay so again this is similar to this + + align:start position:0% +okay so again this is similar to this + + + align:start position:0% +okay so again this is similar to this +example with just a single with just say + + align:start position:0% +example with just a single with just say + + + align:start position:0% +example with just a single with just say +just Ka but just showing how it works + + align:start position:0% +just Ka but just showing how it works + + + align:start position:0% +just Ka but just showing how it works +with uh with public and private key + + align:start position:0% +with uh with public and private key + + + align:start position:0% +with uh with public and private key +encryption okay so the case it's this + + align:start position:0% +encryption okay so the case it's this + + + align:start position:0% +encryption okay so the case it's this +case that uh again we sort of need to + + align:start position:0% +case that uh again we sort of need to + + + align:start position:0% +case that uh again we sort of need to +always think about making our + + align:start position:0% +always think about making our + + + align:start position:0% +always think about making our +assumptions as as explicit as possible + + align:start position:0% +assumptions as as explicit as possible + + + align:start position:0% +assumptions as as explicit as possible +okay that's really what it's about + + align:start position:0% +okay that's really what it's about + + + align:start position:0% +okay that's really what it's about +deciding that we trust for example the + + align:start position:0% +deciding that we trust for example the + + + align:start position:0% +deciding that we trust for example the +signature is true is is analogist to + + align:start position:0% +signature is true is is analogist to + + + align:start position:0% +signature is true is is analogist to +deciding that we uh we have to sort of + + align:start position:0% +deciding that we uh we have to sort of + + + align:start position:0% +deciding that we uh we have to sort of +trust that we trust the cryptography um + + align:start position:0% +trust that we trust the cryptography um + + + align:start position:0% +trust that we trust the cryptography um +it's possible to apply this + + align:start position:0% +it's possible to apply this + + + align:start position:0% +it's possible to apply this +authentication logic in other + + align:start position:0% +authentication logic in other + + + align:start position:0% +authentication logic in other +environments well as well that aren't + + align:start position:0% +environments well as well that aren't + + + align:start position:0% +environments well as well that aren't +necessarily based on on cryptography + + align:start position:0% +necessarily based on on cryptography + + + align:start position:0% +necessarily based on on cryptography +right so I might for example instead of + + align:start position:0% +right so I might for example instead of + + + align:start position:0% +right so I might for example instead of +trusting that the cryptographic system + + align:start position:0% +trusting that the cryptographic system + + + align:start position:0% +trusting that the cryptographic system +works I might trust that a particular + + align:start position:0% +works I might trust that a particular + + + align:start position:0% +works I might trust that a particular +Communication channel is secure right so + + align:start position:0% +Communication channel is secure right so + + + align:start position:0% +Communication channel is secure right so +for example um if I pick up the + + align:start position:0% +for example um if I pick up the + + + align:start position:0% +for example um if I pick up the +telephone and call you and I say you + + align:start position:0% +telephone and call you and I say you + + + align:start position:0% +telephone and call you and I say you +know I I get say some me give you some + + align:start position:0% +know I I get say some me give you some + + + align:start position:0% +know I I get say some me give you some +message you might trust that it's me + + align:start position:0% +message you might trust that it's me + + + align:start position:0% +message you might trust that it's me +because say for example you believe that + + align:start position:0% +because say for example you believe that + + + align:start position:0% +because say for example you believe that +it wouldn't be possible for somebody to + + align:start position:0% +it wouldn't be possible for somebody to + + + align:start position:0% +it wouldn't be possible for somebody to +fake my voice and you recognize my voice + + align:start position:0% +fake my voice and you recognize my voice + + + align:start position:0% +fake my voice and you recognize my voice +because you've come to lecture so many + + align:start position:0% +because you've come to lecture so many + + + align:start position:0% +because you've come to lecture so many +times right um so that would be an + + align:start position:0% +times right um so that would be an + + + align:start position:0% +times right um so that would be an +example of a way in which you might uh + + align:start position:0% +example of a way in which you might uh + + + align:start position:0% +example of a way in which you might uh +sort of decide that you trust that + + align:start position:0% +sort of decide that you trust that + + + align:start position:0% +sort of decide that you trust that +something is actually true and uh that + + align:start position:0% +something is actually true and uh that + + + align:start position:0% +something is actually true and uh that +would be an assumption that you're + + align:start position:0% +would be an assumption that you're + + + align:start position:0% +would be an assumption that you're +making about somebody not being able to + + align:start position:0% +making about somebody not being able to + + + align:start position:0% +making about somebody not being able to +validate my voice so the point of + + align:start position:0% +validate my voice so the point of + + + align:start position:0% +validate my voice so the point of +authentication fake my voice so the + + align:start position:0% +authentication fake my voice so the + + + align:start position:0% +authentication fake my voice so the +point of authentication logic is that it + + align:start position:0% +point of authentication logic is that it + + + align:start position:0% +point of authentication logic is that it +gives us a way to kind of Reason about + + align:start position:0% +gives us a way to kind of Reason about + + + align:start position:0% +gives us a way to kind of Reason about +these uh it gives us a way to reason + + align:start position:0% +these uh it gives us a way to reason + + + align:start position:0% +these uh it gives us a way to reason +about these kinds of deductions about + + align:start position:0% +about these kinds of deductions about + + + align:start position:0% +about these kinds of deductions about +whether or not we actually believe that + + align:start position:0% +whether or not we actually believe that + + + align:start position:0% +whether or not we actually believe that +somebody said something was true or + + align:start position:0% + + + + align:start position:0% + +not okay so that's that's fine um we + + align:start position:0% +not okay so that's that's fine um we + + + align:start position:0% +not okay so that's that's fine um we +still though at least when we're using + + align:start position:0% +still though at least when we're using + + + align:start position:0% +still though at least when we're using +public and private key cryptography we + + align:start position:0% +public and private key cryptography we + + + align:start position:0% +public and private key cryptography we +still don't haven't exactly answer the + + align:start position:0% +still don't haven't exactly answer the + + + align:start position:0% +still don't haven't exactly answer the +question of how we go about establishing + + align:start position:0% +question of how we go about establishing + + + align:start position:0% +question of how we go about establishing +this initial trust step right so we said + + align:start position:0% +this initial trust step right so we said + + + align:start position:0% +this initial trust step right so we said +we might establish initial trust by uh + + align:start position:0% +we might establish initial trust by uh + + + align:start position:0% +we might establish initial trust by uh +so so there there's always sort of at + + align:start position:0% +so so there there's always sort of at + + + align:start position:0% +so so there there's always sort of at +the bottom of this is we have to + + align:start position:0% +the bottom of this is we have to + + + align:start position:0% +the bottom of this is we have to +actually physically over here somebody + + align:start position:0% +actually physically over here somebody + + + align:start position:0% +actually physically over here somebody +say something over a secure + + align:start position:0% +say something over a secure + + + align:start position:0% +say something over a secure +Communication channel we think right we + + align:start position:0% +Communication channel we think right we + + + align:start position:0% +Communication channel we think right we +have to have some way of to getting this + + align:start position:0% +have to have some way of to getting this + + + align:start position:0% +have to have some way of to getting this +first step that says you know getting + + align:start position:0% +first step that says you know getting + + + align:start position:0% +first step that says you know getting +this first rule where a says m in order + + align:start position:0% +this first rule where a says m in order + + + align:start position:0% +this first rule where a says m in order +a a a says that my for example public + + align:start position:0% +a a a says that my for example public + + + align:start position:0% +a a a says that my for example public +key is something so we can learn A's + + align:start position:0% +key is something so we can learn A's + + + align:start position:0% +key is something so we can learn A's +public key so that then we can bootstrap + + align:start position:0% +public key so that then we can bootstrap + + + align:start position:0% +public key so that then we can bootstrap +communication with a they haven't yet + + align:start position:0% +communication with a they haven't yet + + + align:start position:0% +communication with a they haven't yet +answer the question of how we actually + + align:start position:0% +answer the question of how we actually + + + align:start position:0% +answer the question of how we actually +uh exchange these keys + + align:start position:0% +uh exchange these keys + + + align:start position:0% +uh exchange these keys +except for by this one method that we + + align:start position:0% +except for by this one method that we + + + align:start position:0% +except for by this one method that we +talked about this web of trust method + + align:start position:0% +talked about this web of trust method + + + align:start position:0% +talked about this web of trust method +okay so there's this question about + + align:start position:0% + + + + align:start position:0% + +establishing some + + align:start position:0% + + + + align:start position:0% + +initial trust okay so one way we might + + align:start position:0% +initial trust okay so one way we might + + + align:start position:0% +initial trust okay so one way we might +do this is using this web of trust + + align:start position:0% +do this is using this web of trust + + + align:start position:0% +do this is using this web of trust +approach where I get a little bit of TR + + align:start position:0% +approach where I get a little bit of TR + + + align:start position:0% +approach where I get a little bit of TR +I I I meet a friend that friend gives me + + align:start position:0% +I I I meet a friend that friend gives me + + + align:start position:0% +I I I meet a friend that friend gives me +some information tells me about some + + align:start position:0% +some information tells me about some + + + align:start position:0% +some information tells me about some +other people some people who he she + + align:start position:0% +other people some people who he she + + + align:start position:0% +other people some people who he she +trusts and then his th those friends + + align:start position:0% +trusts and then his th those friends + + + align:start position:0% +trusts and then his th those friends +those friends friends in turn know a few + + align:start position:0% +those friends friends in turn know a few + + + align:start position:0% +those friends friends in turn know a few +people and eventually we establish + + align:start position:0% +people and eventually we establish + + + align:start position:0% +people and eventually we establish +communication with everybody so there + + align:start position:0% +communication with everybody so there + + + align:start position:0% +communication with everybody so there +are some computer systems that work this + + align:start position:0% +are some computer systems that work this + + + align:start position:0% +are some computer systems that work this +way in particular there's a system + + align:start position:0% +way in particular there's a system + + + align:start position:0% +way in particular there's a system +called pgp for pretty good privacy which + + align:start position:0% +called pgp for pretty good privacy which + + + align:start position:0% +called pgp for pretty good privacy which +is an email based privacy privacy and + + align:start position:0% +is an email based privacy privacy and + + + align:start position:0% +is an email based privacy privacy and +encryption system that works this way + + align:start position:0% +encryption system that works this way + + + align:start position:0% +encryption system that works this way +and there are in fact websites that are + + align:start position:0% +and there are in fact websites that are + + + align:start position:0% +and there are in fact websites that are +dedicated that you sort of the idea is + + align:start position:0% +dedicated that you sort of the idea is + + + align:start position:0% +dedicated that you sort of the idea is +you find somebody else who you has used + + align:start position:0% +you find somebody else who you has used + + + align:start position:0% +you find somebody else who you has used +this system you share you exchange uh + + align:start position:0% +this system you share you exchange uh + + + align:start position:0% +this system you share you exchange uh +public keys with them and then once you + + align:start position:0% +public keys with them and then once you + + + align:start position:0% +public keys with them and then once you +have a few public Keys you can sort of + + align:start position:0% +have a few public Keys you can sort of + + + align:start position:0% +have a few public Keys you can sort of +build out this web of trust to everybody + + align:start position:0% +build out this web of trust to everybody + + + align:start position:0% +build out this web of trust to everybody +else by trusting people who your friends + + align:start position:0% +else by trusting people who your friends + + + align:start position:0% +else by trusting people who your friends +trust okay um the problem is that one + + align:start position:0% +trust okay um the problem is that one + + + align:start position:0% +trust okay um the problem is that one +clearly the internet doesn't work this + + align:start position:0% +clearly the internet doesn't work this + + + align:start position:0% +clearly the internet doesn't work this +way right so we don't you don't have + + align:start position:0% +way right so we don't you don't have + + + align:start position:0% +way right so we don't you don't have +this kind of a system that you're using + + align:start position:0% +this kind of a system that you're using + + + align:start position:0% +this kind of a system that you're using +on the internet and two these kinds of + + align:start position:0% +on the internet and two these kinds of + + + align:start position:0% +on the internet and two these kinds of +systems are very difficult to set up and + + align:start position:0% +systems are very difficult to set up and + + + align:start position:0% +systems are very difficult to set up and +maintain and there ends up being some + + align:start position:0% +maintain and there ends up being some + + + align:start position:0% +maintain and there ends up being some +centralized Administration that's sort + + align:start position:0% +centralized Administration that's sort + + + align:start position:0% +centralized Administration that's sort +of you end up with having to have some + + align:start position:0% +of you end up with having to have some + + + align:start position:0% +of you end up with having to have some +uh sort of way it becomes very difficult + + align:start position:0% +uh sort of way it becomes very difficult + + + align:start position:0% +uh sort of way it becomes very difficult +to actually disseminate these kinds of + + align:start position:0% +to actually disseminate these kinds of + + + align:start position:0% +to actually disseminate these kinds of +uh public keys in in these kinds of + + align:start position:0% +uh public keys in in these kinds of + + + align:start position:0% +uh public keys in in these kinds of +systems so the way this works is there's + + align:start position:0% +systems so the way this works is there's + + + align:start position:0% +systems so the way this works is there's +some there's a centralized website for + + align:start position:0% +some there's a centralized website for + + + align:start position:0% +some there's a centralized website for +there's a website for pgp that's a giant + + align:start position:0% +there's a website for pgp that's a giant + + + align:start position:0% +there's a website for pgp that's a giant +database of keys and you sort of uh try + + align:start position:0% +database of keys and you sort of uh try + + + align:start position:0% +database of keys and you sort of uh try +and discover people's keys by walking as + + align:start position:0% +and discover people's keys by walking as + + + align:start position:0% +and discover people's keys by walking as +web of trust but tends to be difficult + + align:start position:0% +web of trust but tends to be difficult + + + align:start position:0% +web of trust but tends to be difficult +to + + align:start position:0% +to + + + align:start position:0% +to +use okay so let's talk a little bit + + align:start position:0% +use okay so let's talk a little bit + + + align:start position:0% +use okay so let's talk a little bit +about how this actually works in the + + align:start position:0% +about how this actually works in the + + + align:start position:0% +about how this actually works in the +context of the + + align:start position:0% +context of the + + + align:start position:0% +context of the +internet um so suppose that this browser + + align:start position:0% +internet um so suppose that this browser + + + align:start position:0% +internet um so suppose that this browser +here there's actually some person P + + align:start position:0% +here there's actually some person P + + + align:start position:0% +here there's actually some person P +who's sitting in front of this + + align:start position:0% +who's sitting in front of this + + + align:start position:0% +who's sitting in front of this +browser and there's some questions that + + align:start position:0% +browser and there's some questions that + + + align:start position:0% +browser and there's some questions that +we might want to ask when we're thinking + + align:start position:0% +we might want to ask when we're thinking + + + align:start position:0% +we might want to ask when we're thinking +about deciding whether or not we trust + + align:start position:0% +about deciding whether or not we trust + + + align:start position:0% +about deciding whether or not we trust +this person P okay so one question that + + align:start position:0% +this person P okay so one question that + + + align:start position:0% +this person P okay so one question that +the web server might ask + + align:start position:0% +the web server might ask + + + align:start position:0% +the web server might ask +is does + + align:start position:0% +is does + + + align:start position:0% +is does +w know or trust person P okay um or how + + align:start position:0% +w know or trust person P okay um or how + + + align:start position:0% +w know or trust person P okay um or how +does + + align:start position:0% + + + + align:start position:0% + +it okay so if this is a commercial + + align:start position:0% +it okay so if this is a commercial + + + align:start position:0% +it okay so if this is a commercial +website like amazon.com actually the + + align:start position:0% +website like amazon.com actually the + + + align:start position:0% +website like amazon.com actually the +trust story turns out to not be that + + align:start position:0% +trust story turns out to not be that + + + align:start position:0% +trust story turns out to not be that +complicated right amazon.com doesn't + + align:start position:0% +complicated right amazon.com doesn't + + + align:start position:0% +complicated right amazon.com doesn't +really care that you're who you claim to + + align:start position:0% +really care that you're who you claim to + + + align:start position:0% +really care that you're who you claim to +be as long as you give them the money + + align:start position:0% +be as long as you give them the money + + + align:start position:0% +be as long as you give them the money +that they want right so you can go on + + align:start position:0% +that they want right so you can go on + + + align:start position:0% +that they want right so you can go on +and tell them that you you're Oscar of + + align:start position:0% +and tell them that you you're Oscar of + + + align:start position:0% +and tell them that you you're Oscar of +the Grouch they don't care as long as + + align:start position:0% +the Grouch they don't care as long as + + + align:start position:0% +the Grouch they don't care as long as +you give them the money that they want + + align:start position:0% +you give them the money that they want + + + align:start position:0% +you give them the money that they want +for whatever it is that you order right + + align:start position:0% +for whatever it is that you order right + + + align:start position:0% +for whatever it is that you order right +that's all that matters to them so in + + align:start position:0% +that's all that matters to them so in + + + align:start position:0% +that's all that matters to them so in +fact what Amazon does is they they don't + + align:start position:0% +fact what Amazon does is they they don't + + + align:start position:0% +fact what Amazon does is they they don't +actually know whether who you are + + align:start position:0% +actually know whether who you are + + + align:start position:0% +actually know whether who you are +exactly but they might decide that they + + align:start position:0% +exactly but they might decide that they + + + align:start position:0% +exactly but they might decide that they +trust you because the credit card + + align:start position:0% +trust you because the credit card + + + align:start position:0% +trust you because the credit card +company the the credit card number is + + align:start position:0% +company the the credit card number is + + + align:start position:0% +company the the credit card number is +good um and is verified by the by + + align:start position:0% +good um and is verified by the by + + + align:start position:0% +good um and is verified by the by +verified by the say credit card company + + align:start position:0% +verified by the say credit card company + + + align:start position:0% +verified by the say credit card company +so when they try and charge your credit + + align:start position:0% +so when they try and charge your credit + + + align:start position:0% +so when they try and charge your credit +card they get the money they're happy + + align:start position:0% +card they get the money they're happy + + + align:start position:0% +card they get the money they're happy +there's this other question though which + + align:start position:0% +there's this other question though which + + + align:start position:0% +there's this other question though which +is that about how + + align:start position:0% +is that about how + + + align:start position:0% +is that about how +does + + align:start position:0% +does + + + align:start position:0% +does +p trust W + + align:start position:0% +p trust W + + + align:start position:0% +p trust W +okay um and the way that this works on + + align:start position:0% +okay um and the way that this works on + + + align:start position:0% +okay um and the way that this works on +the Internet + + align:start position:0% +the Internet + + + align:start position:0% +the Internet +is basically the same it's basically + + align:start position:0% +is basically the same it's basically + + + align:start position:0% +is basically the same it's basically +like the way that this Authentication + + align:start position:0% +like the way that this Authentication + + + align:start position:0% +like the way that this Authentication +Protocol that I've shown you here works + + align:start position:0% +Protocol that I've shown you here works + + + align:start position:0% +Protocol that I've shown you here works +this is how SSL Works + + align:start position:0% +this is how SSL Works + + + align:start position:0% +this is how SSL Works +um and it turns out that it's the sort + + align:start position:0% +um and it turns out that it's the sort + + + align:start position:0% +um and it turns out that it's the sort +of whether whether or not you should it + + align:start position:0% +of whether whether or not you should it + + + align:start position:0% +of whether whether or not you should it +the it it turns out to be very subtle or + + align:start position:0% +the it it turns out to be very subtle or + + + align:start position:0% +the it it turns out to be very subtle or +very sort of uh it can be quite hard to + + align:start position:0% +very sort of uh it can be quite hard to + + + align:start position:0% +very sort of uh it can be quite hard to +actually convince yourself that you + + align:start position:0% +actually convince yourself that you + + + align:start position:0% +actually convince yourself that you +should trust a given website if you + + align:start position:0% +should trust a given website if you + + + align:start position:0% +should trust a given website if you +actually start dring down on it so um + + align:start position:0% +actually start dring down on it so um + + + align:start position:0% +actually start dring down on it so um +there's some issues so the way that it's + + align:start position:0% +there's some issues so the way that it's + + + align:start position:0% +there's some issues so the way that it's +going to decide that it trusts W is by + + align:start position:0% +going to decide that it trusts W is by + + + align:start position:0% +going to decide that it trusts W is by +checking with some certificate Authority + + align:start position:0% +checking with some certificate Authority + + + align:start position:0% +checking with some certificate Authority +that's how it works on the internet and + + align:start position:0% +that's how it works on the internet and + + + align:start position:0% +that's how it works on the internet and +there's some issues with this okay which + + align:start position:0% +there's some issues with this okay which + + + align:start position:0% +there's some issues with this okay which +is how does the certificate + + align:start position:0% +is how does the certificate + + + align:start position:0% +is how does the certificate +Authority + + align:start position:0% +Authority + + + align:start position:0% +Authority +um + + align:start position:0% +um + + + align:start position:0% +um +authenticate W okay how does the + + align:start position:0% +authenticate W okay how does the + + + align:start position:0% +authenticate W okay how does the +certificate Authority decide what W's + + align:start position:0% +certificate Authority decide what W's + + + align:start position:0% +certificate Authority decide what W's +key was and how did they securely + + align:start position:0% +key was and how did they securely + + + align:start position:0% +key was and how did they securely +exchange key for w + + align:start position:0% +exchange key for w + + + align:start position:0% +exchange key for w +um how did the user get the ca's public + + align:start position:0% + + + + align:start position:0% + +key um and then what happens + + align:start position:0% +key um and then what happens + + + align:start position:0% +key um and then what happens +say what if somebody's private keys are + + align:start position:0% +say what if somebody's private keys are + + + align:start position:0% +say what if somebody's private keys are +stolen for example + + align:start position:0% + + + + align:start position:0% + +W or their certificate authorties + + align:start position:0% +W or their certificate authorties + + + align:start position:0% +W or their certificate authorties +private keys are still so what I want to + + align:start position:0% +private keys are still so what I want to + + + align:start position:0% +private keys are still so what I want to +do is um just sort of show you at a high + + align:start position:0% +do is um just sort of show you at a high + + + align:start position:0% +do is um just sort of show you at a high +level how this actually works on the + + align:start position:0% +level how this actually works on the + + + align:start position:0% +level how this actually works on the +internet I thought it might be + + align:start position:0% +internet I thought it might be + + + align:start position:0% +internet I thought it might be +instructive just to see an example of + + align:start position:0% +instructive just to see an example of + + + align:start position:0% +instructive just to see an example of +what what is actually going on on the + + align:start position:0% +what what is actually going on on the + + + align:start position:0% +what what is actually going on on the +internet and uh to kind of illustrate + + align:start position:0% +internet and uh to kind of illustrate + + + align:start position:0% +internet and uh to kind of illustrate +how some of these issues are and are not + + align:start position:0% +how some of these issues are and are not + + + align:start position:0% +how some of these issues are and are not +properly addressed by the current uh + + align:start position:0% +properly addressed by the current uh + + + align:start position:0% +properly addressed by the current uh +sort of ssl-based Internet architecture + + align:start position:0% +sort of ssl-based Internet architecture + + + align:start position:0% +sort of ssl-based Internet architecture +so um I have a couple of websites open + + align:start position:0% +so um I have a couple of websites open + + + align:start position:0% +so um I have a couple of websites open +here I have an amazon.com website and I + + align:start position:0% +here I have an amazon.com website and I + + + align:start position:0% +here I have an amazon.com website and I +have a in this case it's an apple + + align:start position:0% +have a in this case it's an apple + + + align:start position:0% +have a in this case it's an apple +developer website both of which you'll + + align:start position:0% +developer website both of which you'll + + + align:start position:0% +developer website both of which you'll +notice are have https URLs associated + + align:start position:0% +notice are have https URLs associated + + + align:start position:0% +notice are have https URLs associated +with them so in this browser if I click + + align:start position:0% +with them so in this browser if I click + + + align:start position:0% +with them so in this browser if I click +on the this little secure icon here + + align:start position:0% +on the this little secure icon here + + + align:start position:0% +on the this little secure icon here +almost any browser would have a similar + + align:start position:0% +almost any browser would have a similar + + + align:start position:0% +almost any browser would have a similar +sort of a feature uh a little lock + + align:start position:0% +sort of a feature uh a little lock + + + align:start position:0% +sort of a feature uh a little lock +somewhere that's when you're viewing an + + align:start position:0% +somewhere that's when you're viewing an + + + align:start position:0% +somewhere that's when you're viewing an +https page what I see is something that + + align:start position:0% +https page what I see is something that + + + align:start position:0% +https page what I see is something that +it lists all the certificates that are + + align:start position:0% +it lists all the certificates that are + + + align:start position:0% +it lists all the certificates that are +associated with this uh with the lists + + align:start position:0% +associated with this uh with the lists + + + align:start position:0% +associated with this uh with the lists +how it was that this site actually uh + + align:start position:0% +how it was that this site actually uh + + + align:start position:0% +how it was that this site actually uh +decided that this was a secure site that + + align:start position:0% +decided that this was a secure site that + + + align:start position:0% +decided that this was a secure site that +it should communicate with so when that + + align:start position:0% +it should communicate with so when that + + + align:start position:0% +it should communicate with so when that +little lock appears it means that my + + align:start position:0% +little lock appears it means that my + + + align:start position:0% +little lock appears it means that my +browser has actually decided that it + + align:start position:0% +browser has actually decided that it + + + align:start position:0% +browser has actually decided that it +trusts this site okay we're at the point + + align:start position:0% +trusts this site okay we're at the point + + + align:start position:0% +trusts this site okay we're at the point +we've already said we trust this site um + + align:start position:0% +we've already said we trust this site um + + + align:start position:0% +we've already said we trust this site um +and the reason that we trust this site + + align:start position:0% +and the reason that we trust this site + + + align:start position:0% +and the reason that we trust this site +it says is because well we have a this + + align:start position:0% +it says is because well we have a this + + + align:start position:0% +it says is because well we have a this +site uh is + + align:start position:0% +site uh is + + + align:start position:0% +site uh is +www.amazon.com and we have a signature + + align:start position:0% +www.amazon.com and we have a signature + + + align:start position:0% +www.amazon.com and we have a signature +that's we have this uh certificate for + + align:start position:0% +that's we have this uh certificate for + + + align:start position:0% +that's we have this uh certificate for +this site that was issued by uh RSA data + + align:start position:0% +this site that was issued by uh RSA data + + + align:start position:0% +this site that was issued by uh RSA data +security Incorporated okay so you might + + align:start position:0% +security Incorporated okay so you might + + + align:start position:0% +security Incorporated okay so you might +say who who is RSA data security + + align:start position:0% +say who who is RSA data security + + + align:start position:0% +say who who is RSA data security +Incorporated I've never heard of these + + align:start position:0% +Incorporated I've never heard of these + + + align:start position:0% +Incorporated I've never heard of these +people I've never exchanged any + + align:start position:0% +people I've never exchanged any + + + align:start position:0% +people I've never exchanged any +information with them I've never you + + align:start position:0% +information with them I've never you + + + align:start position:0% +information with them I've never you +know but they're the certificate + + align:start position:0% +know but they're the certificate + + + align:start position:0% +know but they're the certificate +Authority okay so that's the person who + + align:start position:0% +Authority okay so that's the person who + + + align:start position:0% +Authority okay so that's the person who +signed this thing I can look at this I + + align:start position:0% +signed this thing I can look at this I + + + align:start position:0% +signed this thing I can look at this I +can sort of drill down on this and what + + align:start position:0% +can sort of drill down on this and what + + + align:start position:0% +can sort of drill down on this and what +you'll see is well some information + + align:start position:0% +you'll see is well some information + + + align:start position:0% +you'll see is well some information +about amazon.com so this is the actual + + align:start position:0% +about amazon.com so this is the actual + + + align:start position:0% +about amazon.com so this is the actual +certificate itself um this is some + + align:start position:0% +certificate itself um this is some + + + align:start position:0% +certificate itself um this is some +information about the certificate the + + align:start position:0% +information about the certificate the + + + align:start position:0% +information about the certificate the +the certificate Authority including + + align:start position:0% +the certificate Authority including + + + align:start position:0% +the certificate Authority including +information about what algorithm the + + align:start position:0% +information about what algorithm the + + + align:start position:0% +information about what algorithm the +certificate Authority has used to sign + + align:start position:0% +certificate Authority has used to sign + + + align:start position:0% +certificate Authority has used to sign +uh has used to generate this certificate + + align:start position:0% +uh has used to generate this certificate + + + align:start position:0% +uh has used to generate this certificate +um and then now what we have is this + + align:start position:0% +um and then now what we have is this + + + align:start position:0% +um and then now what we have is this +public key information is the actual + + align:start position:0% +public key information is the actual + + + align:start position:0% +public key information is the actual +public key that corresponds to + + align:start position:0% +public key that corresponds to + + + align:start position:0% +public key that corresponds to +amazon.com okay so this certificate + + align:start position:0% +amazon.com okay so this certificate + + + align:start position:0% +amazon.com okay so this certificate +contains amazon.com's public key that + + align:start position:0% +contains amazon.com's public key that + + + align:start position:0% +contains amazon.com's public key that +was encrypted using the RSA algorithm um + + align:start position:0% +was encrypted using the RSA algorithm um + + + align:start position:0% +was encrypted using the RSA algorithm um +and then there also is some information + + align:start position:0% +and then there also is some information + + + align:start position:0% +and then there also is some information +uh this signature that goes with this + + align:start position:0% +uh this signature that goes with this + + + align:start position:0% +uh this signature that goes with this +public key so this is the signature that + + align:start position:0% +public key so this is the signature that + + + align:start position:0% +public key so this is the signature that +was signed by this RSA this this RSA uh + + align:start position:0% +was signed by this RSA this this RSA uh + + + align:start position:0% +was signed by this RSA this this RSA uh +Corporation okay um if I go to a + + align:start position:0% +Corporation okay um if I go to a + + + align:start position:0% +Corporation okay um if I go to a +different site like for example this + + align:start position:0% +different site like for example this + + + align:start position:0% +different site like for example this +apple site over here we see that this c + + align:start position:0% +apple site over here we see that this c + + + align:start position:0% +apple site over here we see that this c +key this thing was actually signed by + + align:start position:0% +key this thing was actually signed by + + + align:start position:0% +key this thing was actually signed by +somebody else okay so this certificate + + align:start position:0% +somebody else okay so this certificate + + + align:start position:0% +somebody else okay so this certificate +is signed by somebody called Vera sign + + align:start position:0% +is signed by somebody called Vera sign + + + align:start position:0% +is signed by somebody called Vera sign +Incorporated and again you have no idea + + align:start position:0% +Incorporated and again you have no idea + + + align:start position:0% +Incorporated and again you have no idea +who verisign Incorporated is but you'll + + align:start position:0% +who verisign Incorporated is but you'll + + + align:start position:0% +who verisign Incorporated is but you'll +notice that these are two different + + align:start position:0% +notice that these are two different + + + align:start position:0% +notice that these are two different +secur certificate authorities so it's + + align:start position:0% +secur certificate authorities so it's + + + align:start position:0% +secur certificate authorities so it's +not the case that there's one master + + align:start position:0% +not the case that there's one master + + + align:start position:0% +not the case that there's one master +certificate Authority out there on the + + align:start position:0% +certificate Authority out there on the + + + align:start position:0% +certificate Authority out there on the +internet that's in charge of everything + + align:start position:0% +internet that's in charge of everything + + + align:start position:0% +internet that's in charge of everything +okay so on a Mac anyway and the same is + + align:start position:0% +okay so on a Mac anyway and the same is + + + align:start position:0% +okay so on a Mac anyway and the same is +true of most other operating systems + + align:start position:0% +true of most other operating systems + + + align:start position:0% +true of most other operating systems +there's some way to go and look at + + align:start position:0% +there's some way to go and look at + + + align:start position:0% +there's some way to go and look at +there's a way that we can go and look at + + align:start position:0% +there's a way that we can go and look at + + + align:start position:0% +there's a way that we can go and look at +the actual uh list of all the people who + + align:start position:0% +the actual uh list of all the people who + + + align:start position:0% +the actual uh list of all the people who +we trust are so sort of this is sort of + + align:start position:0% +we trust are so sort of this is sort of + + + align:start position:0% +we trust are so sort of this is sort of +an instructive thing to do to go and see + + align:start position:0% +an instructive thing to do to go and see + + + align:start position:0% +an instructive thing to do to go and see +who it is that you actually trust that's + + align:start position:0% +who it is that you actually trust that's + + + align:start position:0% +who it is that you actually trust that's +on this computer um so what this list is + + align:start position:0% +on this computer um so what this list is + + + align:start position:0% +on this computer um so what this list is +I can look click on this if you can see + + align:start position:0% +I can look click on this if you can see + + + align:start position:0% +I can look click on this if you can see +that yeah this certificates over here + + align:start position:0% +that yeah this certificates over here + + + align:start position:0% +that yeah this certificates over here +this is a list of all the certificates + + align:start position:0% +this is a list of all the certificates + + + align:start position:0% +this is a list of all the certificates +um that on this machine that are uh I I + + align:start position:0% +um that on this machine that are uh I I + + + align:start position:0% +um that on this machine that are uh I I +have and where I would accept things + + align:start position:0% +have and where I would accept things + + + align:start position:0% +have and where I would accept things +from okay so you can see that there is a + + align:start position:0% +from okay so you can see that there is a + + + align:start position:0% +from okay so you can see that there is a +very large number of certificates that + + align:start position:0% +very large number of certificates that + + + align:start position:0% +very large number of certificates that +this machine has installed these are not + + align:start position:0% +this machine has installed these are not + + + align:start position:0% +this machine has installed these are not +just certificates but actual certificate + + align:start position:0% +just certificates but actual certificate + + + align:start position:0% +just certificates but actual certificate +authorities people who I would actually + + align:start position:0% +authorities people who I would actually + + + align:start position:0% +authorities people who I would actually +trust to uh sign a given a given a + + align:start position:0% +trust to uh sign a given a given a + + + align:start position:0% +trust to uh sign a given a given a +website from a different a given a given + + align:start position:0% +website from a different a given a given + + + align:start position:0% +website from a different a given a given +a certificate to sign a uh communication + + align:start position:0% +a certificate to sign a uh communication + + + align:start position:0% +a certificate to sign a uh communication +with a given site to provide me with a + + align:start position:0% +with a given site to provide me with a + + + align:start position:0% +with a given site to provide me with a +certificate for uh say some web server + + align:start position:0% +certificate for uh say some web server + + + align:start position:0% +certificate for uh say some web server +that I want to communicate with okay um + + align:start position:0% +that I want to communicate with okay um + + + align:start position:0% +that I want to communicate with okay um +and so what's going on here is so for + + align:start position:0% +and so what's going on here is so for + + + align:start position:0% +and so what's going on here is so for +example one of the things and these + + align:start position:0% +example one of the things and these + + + align:start position:0% +example one of the things and these +things now the qu now the question is + + align:start position:0% +things now the qu now the question is + + + align:start position:0% +things now the qu now the question is +okay so where did these things come from + + align:start position:0% +okay so where did these things come from + + + align:start position:0% +okay so where did these things come from +they came from one or two places either + + align:start position:0% +they came from one or two places either + + + align:start position:0% +they came from one or two places either +added them to the system myself so in + + align:start position:0% +added them to the system myself so in + + + align:start position:0% +added them to the system myself so in +this case I have for example an MIT + + align:start position:0% +this case I have for example an MIT + + + align:start position:0% +this case I have for example an MIT +certification Authority right so if any + + align:start position:0% +certification Authority right so if any + + + align:start position:0% +certification Authority right so if any +of you have ever used MIT certificates + + align:start position:0% +of you have ever used MIT certificates + + + align:start position:0% +of you have ever used MIT certificates +like when you're logging on to webis um + + align:start position:0% +like when you're logging on to webis um + + + align:start position:0% +like when you're logging on to webis um +those you in order to be able to access + + align:start position:0% +those you in order to be able to access + + + align:start position:0% +those you in order to be able to access +that system you had to add support for a + + align:start position:0% +that system you had to add support for a + + + align:start position:0% +that system you had to add support for a +given certificate to the to to your + + align:start position:0% +given certificate to the to to your + + + align:start position:0% +given certificate to the to to your +browser okay so this MIT certification + + align:start position:0% +browser okay so this MIT certification + + + align:start position:0% +browser okay so this MIT certification +certification Authority is a certificate + + align:start position:0% +certification Authority is a certificate + + + align:start position:0% +certification Authority is a certificate +that came from MIT um and this web + + align:start position:0% +that came from MIT um and this web + + + align:start position:0% +that came from MIT um and this web +browser and this this uh keychain thing + + align:start position:0% +browser and this this uh keychain thing + + + align:start position:0% +browser and this this uh keychain thing +which shows me all my certificates has + + align:start position:0% +which shows me all my certificates has + + + align:start position:0% +which shows me all my certificates has +this funny sort of message that says + + align:start position:0% +this funny sort of message that says + + + align:start position:0% +this funny sort of message that says +this certificate is not in the trusted + + align:start position:0% +this certificate is not in the trusted + + + align:start position:0% +this certificate is not in the trusted +root database the reason it says that is + + align:start position:0% +root database the reason it says that is + + + align:start position:0% +root database the reason it says that is +because I just got this certificate off + + align:start position:0% +because I just got this certificate off + + + align:start position:0% +because I just got this certificate off +the way this I got this uh so this is a + + align:start position:0% +the way this I got this uh so this is a + + + align:start position:0% +the way this I got this uh so this is a +certificate for the MIT certification + + align:start position:0% +certificate for the MIT certification + + + align:start position:0% +certificate for the MIT certification +Authority I just got this certificate + + align:start position:0% +Authority I just got this certificate + + + align:start position:0% +Authority I just got this certificate +for the certification Authority off the + + align:start position:0% +for the certification Authority off the + + + align:start position:0% +for the certification Authority off the +web somewhere right and I didn't do + + align:start position:0% +web somewhere right and I didn't do + + + align:start position:0% +web somewhere right and I didn't do +something that it wanted me to do to + + align:start position:0% +something that it wanted me to do to + + + align:start position:0% +something that it wanted me to do to +actually verify that this in fact was a + + align:start position:0% +actually verify that this in fact was a + + + align:start position:0% +actually verify that this in fact was a +legitimate certificate from this + + align:start position:0% +legitimate certificate from this + + + align:start position:0% +legitimate certificate from this +certificate Authority right so somebody + + align:start position:0% +certificate Authority right so somebody + + + align:start position:0% +certificate Authority right so somebody +could have put this thing on the web and + + align:start position:0% +could have put this thing on the web and + + + align:start position:0% +could have put this thing on the web and +said this is a certificate for the MIT + + align:start position:0% +said this is a certificate for the MIT + + + align:start position:0% +said this is a certificate for the MIT +certificate Authority and you know you + + align:start position:0% +certificate Authority and you know you + + + align:start position:0% +certificate Authority and you know you +should use it to uh discover + + align:start position:0% +should use it to uh discover + + + align:start position:0% +should use it to uh discover +certificates for anybody who claims to + + align:start position:0% +certificates for anybody who claims to + + + align:start position:0% +certificates for anybody who claims to +be coming from mit.edu they could have + + align:start position:0% +be coming from mit.edu they could have + + + align:start position:0% +be coming from mit.edu they could have +lied about it and then I would have been + + align:start position:0% +lied about it and then I would have been + + + align:start position:0% +lied about it and then I would have been +in I would be in trouble uh if so it's + + align:start position:0% +in I would be in trouble uh if so it's + + + align:start position:0% +in I would be in trouble uh if so it's +possible that this is a fake certificate + + align:start position:0% +possible that this is a fake certificate + + + align:start position:0% +possible that this is a fake certificate +for the MIT certificate Authority but + + align:start position:0% +for the MIT certificate Authority but + + + align:start position:0% +for the MIT certificate Authority but +um I I sort of have made this trust this + + align:start position:0% +um I I sort of have made this trust this + + + align:start position:0% +um I I sort of have made this trust this +assumption that it's not because I + + align:start position:0% +assumption that it's not because I + + + align:start position:0% +assumption that it's not because I +downloaded it from a website and I + + align:start position:0% +downloaded it from a website and I + + + align:start position:0% +downloaded it from a website and I +believe that in fact this is a valid + + align:start position:0% +believe that in fact this is a valid + + + align:start position:0% +believe that in fact this is a valid +certificate the other case the other + + align:start position:0% +certificate the other case the other + + + align:start position:0% +certificate the other case the other +things you see here see this large + + align:start position:0% +things you see here see this large + + + align:start position:0% +things you see here see this large +number of certificates um for example + + align:start position:0% +number of certificates um for example + + + align:start position:0% +number of certificates um for example +one of the ones that we see is the uh + + align:start position:0% +one of the ones that we see is the uh + + + align:start position:0% +one of the ones that we see is the uh +see if we can find RSA here uh the r + + align:start position:0% +see if we can find RSA here uh the r + + + align:start position:0% +see if we can find RSA here uh the r +this RSA security right so here I see + + align:start position:0% +this RSA security right so here I see + + + align:start position:0% +this RSA security right so here I see +RSA security um and this thing it + + align:start position:0% +RSA security um and this thing it + + + align:start position:0% +RSA security um and this thing it +actually says this certificate is valid + + align:start position:0% +actually says this certificate is valid + + + align:start position:0% +actually says this certificate is valid +so now there's this question about okay + + align:start position:0% +so now there's this question about okay + + + align:start position:0% +so now there's this question about okay +where did where did RSA security come + + align:start position:0% +where did where did RSA security come + + + align:start position:0% +where did where did RSA security come +from and the way that this works is that + + align:start position:0% +from and the way that this works is that + + + align:start position:0% +from and the way that this works is that +this browser and this oper in this case + + align:start position:0% +this browser and this oper in this case + + + align:start position:0% +this browser and this oper in this case +the operating system itself has actually + + align:start position:0% +the operating system itself has actually + + + align:start position:0% +the operating system itself has actually +been shipped with a bunch of + + align:start position:0% +been shipped with a bunch of + + + align:start position:0% +been shipped with a bunch of +certificates from a bunch of different + + align:start position:0% +certificates from a bunch of different + + + align:start position:0% +certificates from a bunch of different +certificate authorities okay um and so + + align:start position:0% +certificate authorities okay um and so + + + align:start position:0% +certificate authorities okay um and so +these have been installed by the + + align:start position:0% +these have been installed by the + + + align:start position:0% +these have been installed by the +operating system manufacturer and I'm + + align:start position:0% +operating system manufacturer and I'm + + + align:start position:0% +operating system manufacturer and I'm +saying okay I trust Apple to have gotten + + align:start position:0% +saying okay I trust Apple to have gotten + + + align:start position:0% +saying okay I trust Apple to have gotten +the appropriate certificates and loaded + + align:start position:0% +the appropriate certificates and loaded + + + align:start position:0% +the appropriate certificates and loaded +them appropriately into the computer and + + align:start position:0% +them appropriately into the computer and + + + align:start position:0% +them appropriately into the computer and +anytime you download a browser basically + + align:start position:0% +anytime you download a browser basically + + + align:start position:0% +anytime you download a browser basically +that browser already has these + + align:start position:0% +that browser already has these + + + align:start position:0% +that browser already has these +certificates sort of it has a set of + + align:start position:0% +certificates sort of it has a set of + + + align:start position:0% +certificates sort of it has a set of +certificates for a set of certificate + + align:start position:0% +certificates for a set of certificate + + + align:start position:0% +certificates for a set of certificate +authorities already installed in it and + + align:start position:0% +authorities already installed in it and + + + align:start position:0% +authorities already installed in it and +that's where all these base certificate + + align:start position:0% +that's where all these base certificate + + + align:start position:0% +that's where all these base certificate +authorities come from so you can see + + align:start position:0% +authorities come from so you can see + + + align:start position:0% +authorities come from so you can see +that when you're using one of these + + align:start position:0% +that when you're using one of these + + + align:start position:0% +that when you're using one of these +things you've already placed quite a bit + + align:start position:0% +things you've already placed quite a bit + + + align:start position:0% +things you've already placed quite a bit +of trust you've made a number of + + align:start position:0% +of trust you've made a number of + + + align:start position:0% +of trust you've made a number of +assumptions about sort of who you trust + + align:start position:0% +assumptions about sort of who you trust + + + align:start position:0% +assumptions about sort of who you trust +and what you should trust just by using + + align:start position:0% +and what you should trust just by using + + + align:start position:0% +and what you should trust just by using +this + + align:start position:0% +this + + + align:start position:0% +this +system um okay so this we've answered + + align:start position:0% +system um okay so this we've answered + + + align:start position:0% +system um okay so this we've answered +this question now about okay where did + + align:start position:0% +this question now about okay where did + + + align:start position:0% +this question now about okay where did +the user get the public key for their + + align:start position:0% +the user get the public key for their + + + align:start position:0% +the user get the public key for their +ific Authority well either they + + align:start position:0% +ific Authority well either they + + + align:start position:0% +ific Authority well either they +explicitly added it by downloading it + + align:start position:0% +explicitly added it by downloading it + + + align:start position:0% +explicitly added it by downloading it +from a website say for example or it + + align:start position:0% +from a website say for example or it + + + align:start position:0% +from a website say for example or it +came with their browser so what about + + align:start position:0% +came with their browser so what about + + + align:start position:0% +came with their browser so what about +this question how does the certificate + + align:start position:0% +this question how does the certificate + + + align:start position:0% +this question how does the certificate +Authority ident authenticate an actual + + align:start position:0% +Authority ident authenticate an actual + + + align:start position:0% +Authority ident authenticate an actual +website so how does amazon.com get a + + align:start position:0% +website so how does amazon.com get a + + + align:start position:0% +website so how does amazon.com get a +certificate from say + + align:start position:0% +certificate from say + + + align:start position:0% +certificate from say +verisign so the answer this turns out to + + align:start position:0% +verisign so the answer this turns out to + + + align:start position:0% +verisign so the answer this turns out to +be that well amazon.com probably paid + + align:start position:0% +be that well amazon.com probably paid + + + align:start position:0% +be that well amazon.com probably paid +veras sign some money um and it's not + + align:start position:0% +veras sign some money um and it's not + + + align:start position:0% +veras sign some money um and it's not +clear what else you you probably it's + + align:start position:0% +clear what else you you probably it's + + + align:start position:0% +clear what else you you probably it's +not even clear you could say that but in + + align:start position:0% +not even clear you could say that but in + + + align:start position:0% +not even clear you could say that but in +the case of verason you're probably + + align:start position:0% +the case of verason you're probably + + + align:start position:0% +the case of verason you're probably +pretty sure that amazon.com paid them + + align:start position:0% +pretty sure that amazon.com paid them + + + align:start position:0% +pretty sure that amazon.com paid them +some money and verisign you could + + align:start position:0% +some money and verisign you could + + + align:start position:0% +some money and verisign you could +probably go to the verisign website and + + align:start position:0% +probably go to the verisign website and + + + align:start position:0% +probably go to the verisign website and +see a list of things that they claim to + + align:start position:0% +see a list of things that they claim to + + + align:start position:0% +see a list of things that they claim to +have done in sort of authenticating + + align:start position:0% +have done in sort of authenticating + + + align:start position:0% +have done in sort of authenticating +amazon.com right so they may have forced + + align:start position:0% +amazon.com right so they may have forced + + + align:start position:0% +amazon.com right so they may have forced +amazon.com to present them with some + + align:start position:0% +amazon.com to present them with some + + + align:start position:0% +amazon.com to present them with some +information that actually suggests that + + align:start position:0% +information that actually suggests that + + + align:start position:0% +information that actually suggests that +they're the company Amazon.com or they + + align:start position:0% +they're the company Amazon.com or they + + + align:start position:0% +they're the company Amazon.com or they +own some right to the name Amazon.com or + + align:start position:0% +own some right to the name Amazon.com or + + + align:start position:0% +own some right to the name Amazon.com or +that they're Incorporated under the name + + align:start position:0% +that they're Incorporated under the name + + + align:start position:0% +that they're Incorporated under the name +amazon.com so basically the certificate + + align:start position:0% +amazon.com so basically the certificate + + + align:start position:0% +amazon.com so basically the certificate +Authority uh has some protocol that it + + align:start position:0% +Authority uh has some protocol that it + + + align:start position:0% +Authority uh has some protocol that it +uses to authenticate W and that protocol + + align:start position:0% +uses to authenticate W and that protocol + + + align:start position:0% +uses to authenticate W and that protocol +we don't know what that protocol is but + + align:start position:0% +we don't know what that protocol is but + + + align:start position:0% +we don't know what that protocol is but +you're sort of implicitly trusting that + + align:start position:0% +you're sort of implicitly trusting that + + + align:start position:0% +you're sort of implicitly trusting that +all these certificate authorities that + + align:start position:0% +all these certificate authorities that + + + align:start position:0% +all these certificate authorities that +Apple has already approved for you in + + align:start position:0% +Apple has already approved for you in + + + align:start position:0% +Apple has already approved for you in +fact use some process that will be + + align:start position:0% +fact use some process that will be + + + align:start position:0% +fact use some process that will be +reasonably assured of guaranteeing your + + align:start position:0% +reasonably assured of guaranteeing your + + + align:start position:0% +reasonably assured of guaranteeing your +privacy or guaranteeing that these + + align:start position:0% +privacy or guaranteeing that these + + + align:start position:0% +privacy or guaranteeing that these +certific that the websites that you're + + align:start position:0% +certific that the websites that you're + + + align:start position:0% +certific that the websites that you're +connecting to are in fact valid websites + + align:start position:0% +connecting to are in fact valid websites + + + align:start position:0% +connecting to are in fact valid websites +that you should feel comfortable giving + + align:start position:0% +that you should feel comfortable giving + + + align:start position:0% +that you should feel comfortable giving +your credit card number two okay so you + + align:start position:0% +your credit card number two okay so you + + + align:start position:0% +your credit card number two okay so you +can see that this is a little bit dicey + + align:start position:0% +can see that this is a little bit dicey + + + align:start position:0% +can see that this is a little bit dicey +right it feels a little bit like it's + + align:start position:0% +right it feels a little bit like it's + + + align:start position:0% +right it feels a little bit like it's +not incredibly it's not clear that this + + align:start position:0% +not incredibly it's not clear that this + + + align:start position:0% +not incredibly it's not clear that this +is incredibly secure um and then the + + align:start position:0% +is incredibly secure um and then the + + + align:start position:0% +is incredibly secure um and then the +last question is well what if your + + align:start position:0% +last question is well what if your + + + align:start position:0% +last question is well what if your +private keys are stolen if your private + + align:start position:0% +private keys are stolen if your private + + + align:start position:0% +private keys are stolen if your private +keys are stolen uh this particular + + align:start position:0% +keys are stolen uh this particular + + + align:start position:0% +keys are stolen uh this particular +example the certificates that you have + + align:start position:0% +example the certificates that you have + + + align:start position:0% +example the certificates that you have +from say Amazon.com or from one of the + + align:start position:0% +from say Amazon.com or from one of the + + + align:start position:0% +from say Amazon.com or from one of the +so if amazon.com's private keys are + + align:start position:0% +so if amazon.com's private keys are + + + align:start position:0% +so if amazon.com's private keys are +stolen or you one of the certificate + + align:start position:0% +stolen or you one of the certificate + + + align:start position:0% +stolen or you one of the certificate +authorities private keys are stolen then + + align:start position:0% +authorities private keys are stolen then + + + align:start position:0% +authorities private keys are stolen then +you're in trouble these certificates + + align:start position:0% +you're in trouble these certificates + + + align:start position:0% +you're in trouble these certificates +typically have expiration dates + + align:start position:0% +typically have expiration dates + + + align:start position:0% +typically have expiration dates +associated with them but these + + align:start position:0% +associated with them but these + + + align:start position:0% +associated with them but these +expiration dates are often years or more + + align:start position:0% +expiration dates are often years or more + + + align:start position:0% +expiration dates are often years or more +into you know a year or more into the + + align:start position:0% +into you know a year or more into the + + + align:start position:0% +into you know a year or more into the +future right and so you're going to + + align:start position:0% +future right and so you're going to + + + align:start position:0% +future right and so you're going to +continue to trust that certificate until + + align:start position:0% +continue to trust that certificate until + + + align:start position:0% +continue to trust that certificate until +the certificate expires in the future + + align:start position:0% +the certificate expires in the future + + + align:start position:0% +the certificate expires in the future +when you'll go try and get a new one for + + align:start position:0% +when you'll go try and get a new one for + + + align:start position:0% +when you'll go try and get a new one for +that whole time that you trust that + + align:start position:0% +that whole time that you trust that + + + align:start position:0% +that whole time that you trust that +certificate somebody who had access to + + align:start position:0% +certificate somebody who had access to + + + align:start position:0% +certificate somebody who had access to +the private keys from that certificate + + align:start position:0% +the private keys from that certificate + + + align:start position:0% +the private keys from that certificate +Authority or from that website would be + + align:start position:0% +Authority or from that website would be + + + align:start position:0% +Authority or from that website would be +able to pretend to be that certificate + + align:start position:0% +able to pretend to be that certificate + + + align:start position:0% +able to pretend to be that certificate +Authority or that website so that might + + align:start position:0% +Authority or that website so that might + + + align:start position:0% +Authority or that website so that might +be + + align:start position:0% +be + + + align:start position:0% +be +problematic okay um so that's sort of + + align:start position:0% +problematic okay um so that's sort of + + + align:start position:0% +problematic okay um so that's sort of +the end of the this little discussion + + align:start position:0% +the end of the this little discussion + + + align:start position:0% +the end of the this little discussion +about how certificate authorities work I + + align:start position:0% +about how certificate authorities work I + + + align:start position:0% +about how certificate authorities work I +hope you can see that this + + align:start position:0% +hope you can see that this + + + align:start position:0% +hope you can see that this +authentication logic is sort of a way + + align:start position:0% +authentication logic is sort of a way + + + align:start position:0% +authentication logic is sort of a way +that we can start to get it thinking + + align:start position:0% +that we can start to get it thinking + + + align:start position:0% +that we can start to get it thinking +about what the trust assumptions that + + align:start position:0% +about what the trust assumptions that + + + align:start position:0% +about what the trust assumptions that +we're making are when we're using these + + align:start position:0% +we're making are when we're using these + + + align:start position:0% +we're making are when we're using these +systems um so this wraps up our + + align:start position:0% +systems um so this wraps up our + + + align:start position:0% +systems um so this wraps up our +discussion of security uh and what we're + + align:start position:0% +discussion of security uh and what we're + + + align:start position:0% +discussion of security uh and what we're +going to start to what we're going to do + + align:start position:0% +going to start to what we're going to do + + + align:start position:0% +going to start to what we're going to do +and we have one one class session left + + align:start position:0% +and we have one one class session left + + + align:start position:0% +and we have one one class session left +and the last class session is actually + + align:start position:0% +and the last class session is actually + + + align:start position:0% +and the last class session is actually +going to be a guest lecture and it's + + align:start position:0% +going to be a guest lecture and it's + + + align:start position:0% +going to be a guest lecture and it's +going to be somebody talking about um + + align:start position:0% +going to be somebody talking about um + + + align:start position:0% +going to be somebody talking about um +sort of how law and computers and + + align:start position:0% +sort of how law and computers and + + + align:start position:0% +sort of how law and computers and +Technology interact with each other so + + align:start position:0% +Technology interact with each other so + + + align:start position:0% +Technology interact with each other so +we're going to kind of step back and + + align:start position:0% +we're going to kind of step back and + + + align:start position:0% +we're going to kind of step back and +talk much more about high level pictures + + align:start position:0% +talk much more about high level pictures + + + align:start position:0% +talk much more about high level pictures +like policy and law next time and + + align:start position:0% +like policy and law next time and + + + align:start position:0% +like policy and law next time and +hopefully it'll give you a good picture + + align:start position:0% +hopefully it'll give you a good picture + + + align:start position:0% +hopefully it'll give you a good picture +of sort of uh a good wrapup for the + + align:start position:0% +of sort of uh a good wrapup for the + + + align:start position:0% +of sort of uh a good wrapup for the +whole class of 63 so um we'll see you + + align:start position:0% +whole class of 63 so um we'll see you + + + align:start position:0% +whole class of 63 so um we'll see you +next time please come to class because + + align:start position:0% +next time please come to class because + + + align:start position:0% +next time please come to class because +there will be questions on the guest + + align:start position:0% +there will be questions on the guest + + + align:start position:0% +there will be questions on the guest +lecture on the exam so you want to make + + align:start position:0% +lecture on the exam so you want to make + + + align:start position:0% +lecture on the exam so you want to make +sure you don't miss them okay \ No newline at end of file diff --git a/CB9I4mwpQ5E.txt b/CB9I4mwpQ5E.txt new file mode 100644 index 0000000000000000000000000000000000000000..085457c7c2d3185e113b94fa21946db055378108 --- /dev/null +++ b/CB9I4mwpQ5E.txt @@ -0,0 +1,1819 @@ +align:start position:0% + +okay uh we're still talking about first + + align:start position:0% +okay uh we're still talking about first + + + align:start position:0% +okay uh we're still talking about first +order differential equations with a + + align:start position:0% +order differential equations with a + + + align:start position:0% +order differential equations with a +dydt and there is still a growth term + + align:start position:0% +dydt and there is still a growth term + + + align:start position:0% +dydt and there is still a growth term +proportional to the to the balance if + + align:start position:0% +proportional to the to the balance if + + + align:start position:0% +proportional to the to the balance if +this is this might be the interest + + align:start position:0% +this is this might be the interest + + + align:start position:0% +this is this might be the interest +that's added on to + + align:start position:0% +that's added on to + + + align:start position:0% +that's added on to +Y and then there is input a source + + align:start position:0% +Y and then there is input a source + + + align:start position:0% +Y and then there is input a source +term uh deposits being made all the time + + align:start position:0% +term uh deposits being made all the time + + + align:start position:0% +term uh deposits being made all the time +so I'm looking to solve that + + align:start position:0% +so I'm looking to solve that + + + align:start position:0% +so I'm looking to solve that +differential equation and this is the + + align:start position:0% +differential equation and this is the + + + align:start position:0% +differential equation and this is the +best possible function for differential + + align:start position:0% +best possible function for differential + + + align:start position:0% +best possible function for differential +equations exponentials because the + + align:start position:0% +equations exponentials because the + + + align:start position:0% +equations exponentials because the +derivative of exponential is exponential + + align:start position:0% +derivative of exponential is exponential + + + align:start position:0% +derivative of exponential is exponential +it just it's just easy easiest to work + + align:start position:0% +it just it's just easy easiest to work + + + align:start position:0% +it just it's just easy easiest to work +with so and uh the output the solution + + align:start position:0% +with so and uh the output the solution + + + align:start position:0% +with so and uh the output the solution +is called the exponential response that + + align:start position:0% +is called the exponential response that + + + align:start position:0% +is called the exponential response that +word response says what comes out when e + + align:start position:0% +word response says what comes out when e + + + align:start position:0% +word response says what comes out when e +to the St goes in and as before we have + + align:start position:0% +to the St goes in and as before we have + + + align:start position:0% +to the St goes in and as before we have +some starting deposit y of 0 initial + + align:start position:0% +some starting deposit y of 0 initial + + + align:start position:0% +some starting deposit y of 0 initial +condition at time Z okay here's the key + + align:start position:0% +condition at time Z okay here's the key + + + align:start position:0% +condition at time Z okay here's the key +point that with this nice Source + + align:start position:0% +point that with this nice Source + + + align:start position:0% +point that with this nice Source +function the solution or one solution a + + align:start position:0% +function the solution or one solution a + + + align:start position:0% +function the solution or one solution a +particular solution will be just a + + align:start position:0% +particular solution will be just a + + + align:start position:0% +particular solution will be just a +multiple of e to the St so all I have to + + align:start position:0% +multiple of e to the St so all I have to + + + align:start position:0% +multiple of e to the St so all I have to +do is find that number capital Y and + + align:start position:0% +do is find that number capital Y and + + + align:start position:0% +do is find that number capital Y and +I've got a solution to that equation how + + align:start position:0% +I've got a solution to that equation how + + + align:start position:0% +I've got a solution to that equation how +do I do it + + align:start position:0% +do I do it + + + align:start position:0% +do I do it +substitute this into the equation and + + align:start position:0% +substitute this into the equation and + + + align:start position:0% +substitute this into the equation and +solve for y so let's do that uh the + + align:start position:0% +solve for y so let's do that uh the + + + align:start position:0% +solve for y so let's do that uh the +derivative of this the derivative of + + align:start position:0% +derivative of this the derivative of + + + align:start position:0% +derivative of this the derivative of +exponential will bring down a Factor s + + align:start position:0% +exponential will bring down a Factor s + + + align:start position:0% +exponential will bring down a Factor s +so there'll be a y s e to the St from + + align:start position:0% +so there'll be a y s e to the St from + + + align:start position:0% +so there'll be a y s e to the St from +the derivative and that will have to + + align:start position:0% +the derivative and that will have to + + + align:start position:0% +the derivative and that will have to +equal a * y e to the St plus the source + + align:start position:0% +equal a * y e to the St plus the source + + + align:start position:0% +equal a * y e to the St plus the source +term e to the + + align:start position:0% +term e to the + + + align:start position:0% +term e to the +St good I just sub substituted it in now + + align:start position:0% +St good I just sub substituted it in now + + + align:start position:0% +St good I just sub substituted it in now +the nice thing I cancel or I divide by e + + align:start position:0% +the nice thing I cancel or I divide by e + + + align:start position:0% +the nice thing I cancel or I divide by e +to the St which is never zero so I + + align:start position:0% +to the St which is never zero so I + + + align:start position:0% +to the St which is never zero so I +divide by factor out e to the St factor + + align:start position:0% +divide by factor out e to the St factor + + + align:start position:0% +divide by factor out e to the St factor +that out it just leaves me with a one so + + align:start position:0% +that out it just leaves me with a one so + + + align:start position:0% +that out it just leaves me with a one so +I have y * s y * a + 1 so let me write + + align:start position:0% +I have y * s y * a + 1 so let me write + + + align:start position:0% +I have y * s y * a + 1 so let me write +that equation so you see it that's just + + align:start position:0% +that equation so you see it that's just + + + align:start position:0% +that equation so you see it that's just +s - A * Y is 1 right took a * Y and put + + align:start position:0% +s - A * Y is 1 right took a * Y and put + + + align:start position:0% +s - A * Y is 1 right took a * Y and put +it on the left side of the equation so + + align:start position:0% +it on the left side of the equation so + + + align:start position:0% +it on the left side of the equation so +I've discovered the exponential response + + align:start position:0% +I've discovered the exponential response + + + align:start position:0% +I've discovered the exponential response +1 over s- + + align:start position:0% +1 over s- + + + align:start position:0% +1 over s- +a okay so I have a solution to the + + align:start position:0% +a okay so I have a solution to the + + + align:start position:0% +a okay so I have a solution to the +equation that's not the end because that + + align:start position:0% +equation that's not the end because that + + + align:start position:0% +equation that's not the end because that +solution won't match the initial + + align:start position:0% +solution won't match the initial + + + align:start position:0% +solution won't match the initial +condition so how do I match an initial + + align:start position:0% +condition so how do I match an initial + + + align:start position:0% +condition so how do I match an initial +condition what I have found is a + + align:start position:0% +condition what I have found is a + + + align:start position:0% +condition what I have found is a +particular solution and I need also the + + align:start position:0% +particular solution and I need also the + + + align:start position:0% +particular solution and I need also the +null solution the homogeneous solution + + align:start position:0% +null solution the homogeneous solution + + + align:start position:0% +null solution the homogeneous solution +so the the the full solution y of + + align:start position:0% +so the the the full solution y of + + + align:start position:0% +so the the the full solution y of +T is it is this y + + align:start position:0% +T is it is this y + + + align:start position:0% +T is it is this y +particular this so capital Y I now know + + align:start position:0% +particular this so capital Y I now know + + + align:start position:0% +particular this so capital Y I now know +is that so I have an e to the s t over + + align:start position:0% +is that so I have an e to the s t over + + + align:start position:0% +is that so I have an e to the s t over +I'm putting in y the right value of + + align:start position:0% +I'm putting in y the right value of + + + align:start position:0% +I'm putting in y the right value of +y so that's the particular solution that + + align:start position:0% +y so that's the particular solution that + + + align:start position:0% +y so that's the particular solution that +I + + align:start position:0% +I + + + align:start position:0% +I +found plus any null solution so the + + align:start position:0% +found plus any null solution so the + + + align:start position:0% +found plus any null solution so the +remember the null solutions that term is + + align:start position:0% +remember the null solutions that term is + + + align:start position:0% +remember the null solutions that term is +gone so the source is zero that's why + + align:start position:0% +gone so the source is zero that's why + + + align:start position:0% +gone so the source is zero that's why +the word null so I'm looking for the + + align:start position:0% +the word null so I'm looking for the + + + align:start position:0% +the word null so I'm looking for the +solution to Dy dtal a y and the + + align:start position:0% +solution to Dy dtal a y and the + + + align:start position:0% +solution to Dy dtal a y and the +solutions to dydt equal a y r e to the a + + align:start position:0% +solutions to dydt equal a y r e to the a + + + align:start position:0% +solutions to dydt equal a y r e to the a +t times any + + align:start position:0% +t times any + + + align:start position:0% +t times any +number because the right hand side is + + align:start position:0% +number because the right hand side is + + + align:start position:0% +number because the right hand side is +zero now for this is this is y + + align:start position:0% +zero now for this is this is y + + + align:start position:0% +zero now for this is this is y +particular and let me write that this is + + align:start position:0% +particular and let me write that this is + + + align:start position:0% +particular and let me write that this is +y particular and this is + + align:start position:0% +y particular and this is + + + align:start position:0% +y particular and this is +y null or Y homogeneous so that's the + + align:start position:0% +y null or Y homogeneous so that's the + + + align:start position:0% +y null or Y homogeneous so that's the +general solution the complete solution + + align:start position:0% +general solution the complete solution + + + align:start position:0% +general solution the complete solution +is has that form and now I can match yal + + align:start position:0% +is has that form and now I can match yal + + + align:start position:0% +is has that form and now I can match yal +y of 0 at tal 0 I put in tal 0 I get y + + align:start position:0% +y of 0 at tal 0 I put in tal 0 I get y + + + align:start position:0% +y of 0 at tal 0 I put in tal 0 I get y +of + + align:start position:0% +of + + + align:start position:0% +of +0 equal tal 0 this is 1 so 1 / s - A and + + align:start position:0% +0 equal tal 0 this is 1 so 1 / s - A and + + + align:start position:0% +0 equal tal 0 this is 1 so 1 / s - A and +when t is0 this is one so plus + + align:start position:0% +when t is0 this is one so plus + + + align:start position:0% +when t is0 this is one so plus +C so and now I know what c is and notice + + align:start position:0% +C so and now I know what c is and notice + + + align:start position:0% +C so and now I know what c is and notice +C is not just y of0 as we saw in the + + align:start position:0% +C is not just y of0 as we saw in the + + + align:start position:0% +C is not just y of0 as we saw in the +sometimes in the past C is y of 0 minus + + align:start position:0% +sometimes in the past C is y of 0 minus + + + align:start position:0% +sometimes in the past C is y of 0 minus +this are you ready now for the complete + + align:start position:0% +this are you ready now for the complete + + + align:start position:0% +this are you ready now for the complete +solution with satisfying the initial + + align:start position:0% +solution with satisfying the initial + + + align:start position:0% +solution with satisfying the initial +conditions so now I'm I'm going to this + + align:start position:0% +conditions so now I'm I'm going to this + + + align:start position:0% +conditions so now I'm I'm going to this +is the correct form this tells me what C + + align:start position:0% +is the correct form this tells me what C + + + align:start position:0% +is the correct form this tells me what C +has to be so I put it in and I have the + + align:start position:0% +has to be so I put it in and I have the + + + align:start position:0% +has to be so I put it in and I have the +solution y of T is e to the s t over s - + + align:start position:0% +solution y of T is e to the s t over s - + + + align:start position:0% +solution y of T is e to the s t over s - +A the easy one plus C now C is y + + align:start position:0% +A the easy one plus C now C is y + + + align:start position:0% +A the easy one plus C now C is y +of0 - 1 / s - A that's what we needed + + align:start position:0% +of0 - 1 / s - A that's what we needed + + + align:start position:0% +of0 - 1 / s - A that's what we needed +times e to the + + align:start position:0% +times e to the + + + align:start position:0% +times e to the +a that's our + + align:start position:0% +a that's our + + + align:start position:0% +a that's our +answer that's our answer I I can make it + + align:start position:0% +answer that's our answer I I can make it + + + align:start position:0% +answer that's our answer I I can make it +look a little nicer I want to I want to + + align:start position:0% +look a little nicer I want to I want to + + + align:start position:0% +look a little nicer I want to I want to +separate out the Y of Zero part the part + + align:start position:0% +separate out the Y of Zero part the part + + + align:start position:0% +separate out the Y of Zero part the part +that's just growing from the initial + + align:start position:0% +that's just growing from the initial + + + align:start position:0% +that's just growing from the initial +condition from the part that is coming + + align:start position:0% +condition from the part that is coming + + + align:start position:0% +condition from the part that is coming +from the source term so I just want to + + align:start position:0% +from the source term so I just want to + + + align:start position:0% +from the source term so I just want to +put that together with this so I have + + align:start position:0% +put that together with this so I have + + + align:start position:0% +put that together with this so I have +the same s minus a below here is an e to + + align:start position:0% +the same s minus a below here is an e to + + + align:start position:0% +the same s minus a below here is an e to +the St above and I have a minus that 1 / + + align:start position:0% +the St above and I have a minus that 1 / + + + align:start position:0% +the St above and I have a minus that 1 / +s - A Time e to the + + align:start position:0% +s - A Time e to the + + + align:start position:0% +s - A Time e to the +A and then I have this + + align:start position:0% +A and then I have this + + + align:start position:0% +A and then I have this +term which + + align:start position:0% +term which + + + align:start position:0% +term which +is + + align:start position:0% + + + + align:start position:0% + +growing oh this is really good this is + + align:start position:0% +growing oh this is really good this is + + + align:start position:0% +growing oh this is really good this is +the part growing out of the initial + + align:start position:0% +the part growing out of the initial + + + align:start position:0% +the part growing out of the initial +deposit I'm using again money in a bank + + align:start position:0% +deposit I'm using again money in a bank + + + align:start position:0% +deposit I'm using again money in a bank +with with uh additional deposits e to + + align:start position:0% +with with uh additional deposits e to + + + align:start position:0% +with with uh additional deposits e to +the St and this is the part coming from + + align:start position:0% +the St and this is the part coming from + + + align:start position:0% +the St and this is the part coming from +those later deposits initial part and + + align:start position:0% +those later deposits initial part and + + + align:start position:0% +those later deposits initial part and +the part coming from there so this is + + align:start position:0% +the part coming from there so this is + + + align:start position:0% +the part coming from there so this is +again a null solution a multiple of e to + + align:start position:0% +again a null solution a multiple of e to + + + align:start position:0% +again a null solution a multiple of e to +the a t this is another particular + + align:start position:0% +the a t this is another particular + + + align:start position:0% +the a t this is another particular +solution remember there isn't just one + + align:start position:0% +solution remember there isn't just one + + + align:start position:0% +solution remember there isn't just one +particular solution any solution is a + + align:start position:0% +particular solution any solution is a + + + align:start position:0% +particular solution any solution is a +particular solution and this is a I call + + align:start position:0% +particular solution and this is a I call + + + align:start position:0% +particular solution and this is a I call +that the very particular solution + + align:start position:0% +that the very particular solution + + + align:start position:0% +that the very particular solution +because it has the nice property that it + + align:start position:0% +because it has the nice property that it + + + align:start position:0% +because it has the nice property that it +starts from zero so a t equals 0 that's + + align:start position:0% +starts from zero so a t equals 0 that's + + + align:start position:0% +starts from zero so a t equals 0 that's +1 - 1 I'm getting zero so this is so I + + align:start position:0% +1 - 1 I'm getting zero so this is so I + + + align:start position:0% +1 - 1 I'm getting zero so this is so I +would call that y VP I'll introduce + + align:start position:0% +would call that y VP I'll introduce + + + align:start position:0% +would call that y VP I'll introduce +those letters not standard for the that + + align:start position:0% +those letters not standard for the that + + + align:start position:0% +those letters not standard for the that +part and then y homogeneous or Y null is + + align:start position:0% +part and then y homogeneous or Y null is + + + align:start position:0% +part and then y homogeneous or Y null is +this part okay problem + + align:start position:0% +this part okay problem + + + align:start position:0% +this part okay problem +solved the exponential + + align:start position:0% +solved the exponential + + + align:start position:0% +solved the exponential +grows uh + + align:start position:0% +grows uh + + + align:start position:0% +grows uh +in this way and the starting initial + + align:start position:0% +in this way and the starting initial + + + align:start position:0% +in this way and the starting initial +condition grows directly that way + + align:start position:0% +condition grows directly that way + + + align:start position:0% +condition grows directly that way +okay the problem is solved with one + + align:start position:0% +okay the problem is solved with one + + + align:start position:0% +okay the problem is solved with one +exception and now I have to take a + + align:start position:0% +exception and now I have to take a + + + align:start position:0% +exception and now I have to take a +minute with that exception the exception + + align:start position:0% +minute with that exception the exception + + + align:start position:0% +minute with that exception the exception +is the formula breaks + + align:start position:0% +is the formula breaks + + + align:start position:0% +is the formula breaks +down if s equals a if s equals a I'm + + align:start position:0% +down if s equals a if s equals a I'm + + + align:start position:0% +down if s equals a if s equals a I'm +dividing by zero my formula is falling + + align:start position:0% +dividing by zero my formula is falling + + + align:start position:0% +dividing by zero my formula is falling +apart and that's the case of resonance + + align:start position:0% +apart and that's the case of resonance + + + align:start position:0% +apart and that's the case of resonance +so let me put over here we + + align:start position:0% + + + + align:start position:0% + +always s equal + + align:start position:0% +always s equal + + + align:start position:0% +always s equal +a that's that's + + align:start position:0% +a that's that's + + + align:start position:0% +a that's that's +resonance and uh we always have to + + align:start position:0% +resonance and uh we always have to + + + align:start position:0% +resonance and uh we always have to +expect that that's a possibility that + + align:start position:0% +expect that that's a possibility that + + + align:start position:0% +expect that that's a possibility that +we're putting money in at the same with + + align:start position:0% +we're putting money in at the same with + + + align:start position:0% +we're putting money in at the same with +the same exponential as the natural + + align:start position:0% +the same exponential as the natural + + + align:start position:0% +the same exponential as the natural +growth of the money or whatever we're + + align:start position:0% +growth of the money or whatever we're + + + align:start position:0% +growth of the money or whatever we're +growing uh and uh our formula has to + + align:start position:0% +growing uh and uh our formula has to + + + align:start position:0% +growing uh and uh our formula has to +change well you might say it's infinite + + align:start position:0% +change well you might say it's infinite + + + align:start position:0% +change well you might say it's infinite +because I'm dividing by zero but notice + + align:start position:0% +because I'm dividing by zero but notice + + + align:start position:0% +because I'm dividing by zero but notice +the part above is also zero if s equals + + align:start position:0% +the part above is also zero if s equals + + + align:start position:0% +the part above is also zero if s equals +a this is one this is this is e to the + + align:start position:0% +a this is one this is this is e to the + + + align:start position:0% +a this is one this is this is e to the +St minus E to the a t those are the same + + align:start position:0% +St minus E to the a t those are the same + + + align:start position:0% +St minus E to the a t those are the same +so I have a 0 over Z situation my + + align:start position:0% +so I have a 0 over Z situation my + + + align:start position:0% +so I have a 0 over Z situation my +formula is breaking down but it isn't + + align:start position:0% +formula is breaking down but it isn't + + + align:start position:0% +formula is breaking down but it isn't +dying it's just it needs more thinking + + align:start position:0% +dying it's just it needs more thinking + + + align:start position:0% +dying it's just it needs more thinking +the reson the case of resonance needs to + + align:start position:0% +the reson the case of resonance needs to + + + align:start position:0% +the reson the case of resonance needs to +I have to understand what this + + align:start position:0% +I have to understand what this + + + align:start position:0% +I have to understand what this +is when s equals a let me tell you what + + align:start position:0% +is when s equals a let me tell you what + + + align:start position:0% +is when s equals a let me tell you what +it is and then show you why so this is + + align:start position:0% +it is and then show you why so this is + + + align:start position:0% +it is and then show you why so this is +the case s equal a so + + align:start position:0% +the case s equal a so + + + align:start position:0% +the case s equal a so +if s equal a + + align:start position:0% +if s equal a + + + align:start position:0% +if s equal a +then y very particular plus y null + + align:start position:0% +then y very particular plus y null + + + align:start position:0% +then y very particular plus y null +space so it's this very particular + + align:start position:0% +space so it's this very particular + + + align:start position:0% +space so it's this very particular +solution that I have to has to have a + + align:start position:0% +solution that I have to has to have a + + + align:start position:0% +solution that I have to has to have a +different form and here's the form it + + align:start position:0% +different form and here's the form it + + + align:start position:0% +different form and here's the form it +gets a factor T appears you just learn + + align:start position:0% +gets a factor T appears you just learn + + + align:start position:0% +gets a factor T appears you just learn +to recognize resonance by that factor T + + align:start position:0% +to recognize resonance by that factor T + + + align:start position:0% +to recognize resonance by that factor T +so it'll be a t e to the a t a is the + + align:start position:0% +so it'll be a t e to the a t a is the + + + align:start position:0% +so it'll be a t e to the a t a is the +same as s now so s doesn't appear so + + align:start position:0% +same as s now so s doesn't appear so + + + align:start position:0% +same as s now so s doesn't appear so +that's the solution which starts from + + align:start position:0% +that's the solution which starts from + + + align:start position:0% +that's the solution which starts from +zero + + align:start position:0% +zero + + + align:start position:0% +zero +and it comes from the + + align:start position:0% +and it comes from the + + + align:start position:0% +and it comes from the +input + + align:start position:0% +input + + + align:start position:0% +input +and uh this is the part that starts from + + align:start position:0% +and uh this is the part that starts from + + + align:start position:0% +and uh this is the part that starts from +y of Z + + align:start position:0% +y of Z + + + align:start position:0% +y of Z +and grows so you see eventually this is + + align:start position:0% +and grows so you see eventually this is + + + align:start position:0% +and grows so you see eventually this is +going to be the bigger one uh the + + align:start position:0% +going to be the bigger one uh the + + + align:start position:0% +going to be the bigger one uh the +resonant case it grows uh like e to the + + align:start position:0% +resonant case it grows uh like e to the + + + align:start position:0% +resonant case it grows uh like e to the +a t with that little bit extra growth of + + align:start position:0% +a t with that little bit extra growth of + + + align:start position:0% +a t with that little bit extra growth of +T okay so now I have the solution in + + align:start position:0% +T okay so now I have the solution in + + + align:start position:0% +T okay so now I have the solution in +that special case also when when s + + align:start position:0% +that special case also when when s + + + align:start position:0% +that special case also when when s +equals a all right do you want to know + + align:start position:0% +equals a all right do you want to know + + + align:start position:0% +equals a all right do you want to know +how this comes out of this as s + + align:start position:0% +how this comes out of this as s + + + align:start position:0% +how this comes out of this as s +approaches + + align:start position:0% +approaches + + + align:start position:0% +approaches +a let me take three minutes to tell you + + align:start position:0% +a let me take three minutes to tell you + + + align:start position:0% +a let me take three minutes to tell you +about that it's lal's rule do you + + align:start position:0% +about that it's lal's rule do you + + + align:start position:0% +about that it's lal's rule do you +remember from calculus 0 over Z the way + + align:start position:0% +remember from calculus 0 over Z the way + + + align:start position:0% +remember from calculus 0 over Z the way +to deal with that was called This by + + align:start position:0% +to deal with that was called This by + + + align:start position:0% +to deal with that was called This by +this guy's name + + align:start position:0% + + + + align:start position:0% + +lital H hospital I guess probably + + align:start position:0% +lital H hospital I guess probably + + + align:start position:0% +lital H hospital I guess probably +Hospital in + + align:start position:0% +Hospital in + + + align:start position:0% +Hospital in +French and and it's you take this Z over + + align:start position:0% +French and and it's you take this Z over + + + align:start position:0% +French and and it's you take this Z over +zero + + align:start position:0% +zero + + + align:start position:0% +zero +expression it's a ratio of two things + + align:start position:0% +expression it's a ratio of two things + + + align:start position:0% +expression it's a ratio of two things +the + + align:start position:0% +the + + + align:start position:0% +the +top going to Zer when s goes to a + + align:start position:0% +top going to Zer when s goes to a + + + align:start position:0% +top going to Zer when s goes to a +because these become the same the bottom + + align:start position:0% +because these become the same the bottom + + + align:start position:0% +because these become the same the bottom +going to zero when s goes to a and the + + align:start position:0% +going to zero when s goes to a and the + + + align:start position:0% +going to zero when s goes to a and the +right lal's cool idea was you you get + + align:start position:0% +right lal's cool idea was you you get + + + align:start position:0% +right lal's cool idea was you you get +the same answer if you take the r + + align:start position:0% +the same answer if you take the r + + + align:start position:0% +the same answer if you take the r +IO of the derivatives so Lal says take + + align:start position:0% +IO of the derivatives so Lal says take + + + align:start position:0% +IO of the derivatives so Lal says take +the ratio of the + + align:start position:0% +the ratio of the + + + align:start position:0% +the ratio of the +derivatives of the + + align:start position:0% + + + + align:start position:0% + +top minus the derivative oh divided by + + align:start position:0% +top minus the derivative oh divided by + + + align:start position:0% +top minus the derivative oh divided by +the derivative of the + + align:start position:0% +the derivative of the + + + align:start position:0% +the derivative of the +bottom and then let s go to a in the end + + align:start position:0% +bottom and then let s go to a in the end + + + align:start position:0% +bottom and then let s go to a in the end +okay so I have to take this derivative I + + align:start position:0% +okay so I have to take this derivative I + + + align:start position:0% +okay so I have to take this derivative I +have to take that derivative with + + align:start position:0% +have to take that derivative with + + + align:start position:0% +have to take that derivative with +respect to to S often in calculus it was + + align:start position:0% +respect to to S often in calculus it was + + + align:start position:0% +respect to to S often in calculus it was +a it was an X here it's an S no big deal + + align:start position:0% +a it was an X here it's an S no big deal + + + align:start position:0% +a it was an X here it's an S no big deal +so that derivative is I can you take the + + align:start position:0% +so that derivative is I can you take the + + + align:start position:0% +so that derivative is I can you take the +derivative with respect to S we'll bring + + align:start position:0% +derivative with respect to S we'll bring + + + align:start position:0% +derivative with respect to S we'll bring +down ah here comes the T the derivative + + align:start position:0% +down ah here comes the T the derivative + + + align:start position:0% +down ah here comes the T the derivative +of s is t e to the + + align:start position:0% + + + + align:start position:0% + +St and the derivative of this thing is + + align:start position:0% +St and the derivative of this thing is + + + align:start position:0% +St and the derivative of this thing is +one and now I let s go to a well it's + + align:start position:0% +one and now I let s go to a well it's + + + align:start position:0% +one and now I let s go to a well it's +easy to let s go away now this + + align:start position:0% +easy to let s go away now this + + + align:start position:0% +easy to let s go away now this +thing + + align:start position:0% +thing + + + align:start position:0% +thing +approaches that I have the t e to the a + + align:start position:0% +approaches that I have the t e to the a + + + align:start position:0% +approaches that I have the t e to the a +t in the limit so lal's rule was the the + + align:start position:0% +t in the limit so lal's rule was the the + + + align:start position:0% +t in the limit so lal's rule was the the +reason behind this uh formula for + + align:start position:0% +reason behind this uh formula for + + + align:start position:0% +reason behind this uh formula for +resonance but again I emphasize + + align:start position:0% +resonance but again I emphasize + + + align:start position:0% +resonance but again I emphasize +that expect a factor T when you have + + align:start position:0% +that expect a factor T when you have + + + align:start position:0% +that expect a factor T when you have +this + + align:start position:0% +this + + + align:start position:0% +this +resonance okay so that's the solution + + align:start position:0% +resonance okay so that's the solution + + + align:start position:0% +resonance okay so that's the solution +for the best Poss possible right hand + + align:start position:0% +for the best Poss possible right hand + + + align:start position:0% +for the best Poss possible right hand +side e to the St well maybe the best is + + align:start position:0% +side e to the St well maybe the best is + + + align:start position:0% +side e to the St well maybe the best is +a constant second simplest is an + + align:start position:0% +a constant second simplest is an + + + align:start position:0% +a constant second simplest is an +exponential next will come signs and + + align:start position:0% +exponential next will come signs and + + + align:start position:0% +exponential next will come signs and +cosiness uh that's the next lecture + + align:start position:0% +cosiness uh that's the next lecture + + + align:start position:0% +cosiness uh that's the next lecture +thanks \ No newline at end of file diff --git a/CfBeCHrQj_U.txt b/CfBeCHrQj_U.txt new file mode 100644 index 0000000000000000000000000000000000000000..ae70b6ea93c2ead103bf323589422a90ece6089e --- /dev/null +++ b/CfBeCHrQj_U.txt @@ -0,0 +1,715 @@ +align:start position:0% + +today we'd like to discuss tension in a + + align:start position:0% +today we'd like to discuss tension in a + + + align:start position:0% +today we'd like to discuss tension in a +rope under what conditions is the + + align:start position:0% +rope under what conditions is the + + + align:start position:0% +rope under what conditions is the +tension uniform recall that if we had a + + align:start position:0% +tension uniform recall that if we had a + + + align:start position:0% +tension uniform recall that if we had a +rope and say we were pulling here's our + + align:start position:0% +rope and say we were pulling here's our + + + align:start position:0% +rope and say we were pulling here's our +one end we'll call that + + align:start position:0% +one end we'll call that + + + align:start position:0% +one end we'll call that +we're pulling at this end with the force + + align:start position:0% +we're pulling at this end with the force + + + align:start position:0% +we're pulling at this end with the force +a and we pull on this end B with a force + + align:start position:0% +a and we pull on this end B with a force + + + align:start position:0% +a and we pull on this end B with a force +B that what we meant by tension at any + + align:start position:0% +B that what we meant by tension at any + + + align:start position:0% +B that what we meant by tension at any +point in the rope + + align:start position:0% +point in the rope + + + align:start position:0% +point in the rope +was that we took an imaginary slice of + + align:start position:0% +was that we took an imaginary slice of + + + align:start position:0% +was that we took an imaginary slice of +the Rope P and we looked at the two + + align:start position:0% +the Rope P and we looked at the two + + + align:start position:0% +the Rope P and we looked at the two +sides and here if we call this the left + + align:start position:0% +sides and here if we call this the left + + + align:start position:0% +sides and here if we call this the left +side and this the right side then on the + + align:start position:0% +side and this the right side then on the + + + align:start position:0% +side and this the right side then on the +left side we have that the right side of + + align:start position:0% +left side we have that the right side of + + + align:start position:0% +left side we have that the right side of +the Rope is pulling the left side of the + + align:start position:0% +the Rope is pulling the left side of the + + + align:start position:0% +the Rope is pulling the left side of the +rope by some force F and this is the + + align:start position:0% +rope by some force F and this is the + + + align:start position:0% +rope by some force F and this is the +left side and the right side is being + + align:start position:0% +left side and the right side is being + + + align:start position:0% +left side and the right side is being +pulled by the left side so that's the + + align:start position:0% +pulled by the left side so that's the + + + align:start position:0% +pulled by the left side so that's the +right side being pulled by the left side + + align:start position:0% +right side being pulled by the left side + + + align:start position:0% +right side being pulled by the left side +and what we define the tension at the + + align:start position:0% +and what we define the tension at the + + + align:start position:0% +and what we define the tension at the +point P was to be the magnitude of this + + align:start position:0% +point P was to be the magnitude of this + + + align:start position:0% +point P was to be the magnitude of this +action-reaction pair and that's how we + + align:start position:0% +action-reaction pair and that's how we + + + align:start position:0% +action-reaction pair and that's how we +define tension at a point inside a rope + + align:start position:0% +define tension at a point inside a rope + + + align:start position:0% +define tension at a point inside a rope +now we'd like to address the question is + + align:start position:0% +now we'd like to address the question is + + + align:start position:0% +now we'd like to address the question is +when is the tension under what + + align:start position:0% +when is the tension under what + + + align:start position:0% +when is the tension under what +conditions can we say that the tension + + align:start position:0% +conditions can we say that the tension + + + align:start position:0% +conditions can we say that the tension +is uniform which means that at all + + align:start position:0% +is uniform which means that at all + + + align:start position:0% +is uniform which means that at all +points P the tension is the same and in + + align:start position:0% +points P the tension is the same and in + + + align:start position:0% +points P the tension is the same and in +order to analyze this we'll apply + + align:start position:0% +order to analyze this we'll apply + + + align:start position:0% +order to analyze this we'll apply +Newton's second law so let's begin with + + align:start position:0% +Newton's second law so let's begin with + + + align:start position:0% +Newton's second law so let's begin with +the same situation as before let's + + align:start position:0% +the same situation as before let's + + + align:start position:0% +the same situation as before let's +consider a rope where we're pulling this + + align:start position:0% +consider a rope where we're pulling this + + + align:start position:0% +consider a rope where we're pulling this +side with a force at the end by the way + + align:start position:0% +side with a force at the end by the way + + + align:start position:0% +side with a force at the end by the way +we can call this the tension at that end + + align:start position:0% +we can call this the tension at that end + + + align:start position:0% +we can call this the tension at that end +T of a and on this side we can refer to + + align:start position:0% +T of a and on this side we can refer to + + + align:start position:0% +T of a and on this side we can refer to +this as the tension on side B now + + align:start position:0% +this as the tension on side B now + + + align:start position:0% +this as the tension on side B now +suppose that our mass of the Rope is + + align:start position:0% +suppose that our mass of the Rope is + + + align:start position:0% +suppose that our mass of the Rope is +nonzero and we now want to apply + + align:start position:0% +nonzero and we now want to apply + + + align:start position:0% +nonzero and we now want to apply +Newton's second law but let's also apply + + align:start position:0% +Newton's second law but let's also apply + + + align:start position:0% +Newton's second law but let's also apply +the condition that the acceleration of + + align:start position:0% +the condition that the acceleration of + + + align:start position:0% +the condition that the acceleration of +the rope is nonzero so you're holding + + align:start position:0% +the rope is nonzero so you're holding + + + align:start position:0% +the rope is nonzero so you're holding +the rope under some tension by pulling + + align:start position:0% +the rope under some tension by pulling + + + align:start position:0% +the rope under some tension by pulling +both sides but the rope is not + + align:start position:0% +both sides but the rope is not + + + align:start position:0% +both sides but the rope is not +accelerating + + align:start position:0% +accelerating + + + align:start position:0% +accelerating +and so what does that mean when we apply + + align:start position:0% +and so what does that mean when we apply + + + align:start position:0% +and so what does that mean when we apply +Newton's second law to the rope well + + align:start position:0% +Newton's second law to the rope well + + + align:start position:0% +Newton's second law to the rope well +let's just arbitrarily call that our + + align:start position:0% +let's just arbitrarily call that our + + + align:start position:0% +let's just arbitrarily call that our +positive direction we see by vector + + align:start position:0% +positive direction we see by vector + + + align:start position:0% +positive direction we see by vector +decomposition that we have TB minus ta + + align:start position:0% +decomposition that we have TB minus ta + + + align:start position:0% +decomposition that we have TB minus ta +equals mass of the rope but because the + + align:start position:0% +equals mass of the rope but because the + + + align:start position:0% +equals mass of the rope but because the +acceleration of the rope is zero this + + align:start position:0% +acceleration of the rope is zero this + + + align:start position:0% +acceleration of the rope is zero this +side is zero and we can use Newton's + + align:start position:0% +side is zero and we can use Newton's + + + align:start position:0% +side is zero and we can use Newton's +second law to conclude that the tension + + align:start position:0% +second law to conclude that the tension + + + align:start position:0% +second law to conclude that the tension +in the rope is uniform when the rope is + + align:start position:0% +in the rope is uniform when the rope is + + + align:start position:0% +in the rope is uniform when the rope is +not accelerating and this is what we'll + + align:start position:0% +not accelerating and this is what we'll + + + align:start position:0% +not accelerating and this is what we'll +call our case one a zero tension in the + + align:start position:0% +call our case one a zero tension in the + + + align:start position:0% +call our case one a zero tension in the +rope is uniform now let's suppose case + + align:start position:0% +rope is uniform now let's suppose case + + + align:start position:0% +rope is uniform now let's suppose case +two that a is not zero and so now we + + align:start position:0% +two that a is not zero and so now we + + + align:start position:0% +two that a is not zero and so now we +have the rope this is point B here's + + align:start position:0% +have the rope this is point B here's + + + align:start position:0% +have the rope this is point B here's +point a will choose a uniform direction + + align:start position:0% +point a will choose a uniform direction + + + align:start position:0% +point a will choose a uniform direction +a and now we can see when we apply F + + align:start position:0% +a and now we can see when we apply F + + + align:start position:0% +a and now we can see when we apply F +equals MA that TB minus ta equals mass + + align:start position:0% +equals MA that TB minus ta equals mass + + + align:start position:0% +equals MA that TB minus ta equals mass +of the Rope times the acceleration of + + align:start position:0% +of the Rope times the acceleration of + + + align:start position:0% +of the Rope times the acceleration of +the rope so you're pulling such that TB + + align:start position:0% +the rope so you're pulling such that TB + + + align:start position:0% +the rope so you're pulling such that TB +is greater than TA by precisely the + + align:start position:0% +is greater than TA by precisely the + + + align:start position:0% +is greater than TA by precisely the +quantity M R times a and so the tension + + align:start position:0% +quantity M R times a and so the tension + + + align:start position:0% +quantity M R times a and so the tension +at the ends are not the same and + + align:start position:0% +at the ends are not the same and + + + align:start position:0% +at the ends are not the same and +therefore the tension in the rope is not + + align:start position:0% +therefore the tension in the rope is not + + + align:start position:0% +therefore the tension in the rope is not +uniform now there's a special case here + + align:start position:0% +uniform now there's a special case here + + + align:start position:0% +uniform now there's a special case here +that we want to consider so even though + + align:start position:0% +that we want to consider so even though + + + align:start position:0% +that we want to consider so even though +a is nonzero let's assume that the mass + + align:start position:0% +a is nonzero let's assume that the mass + + + align:start position:0% +a is nonzero let's assume that the mass +of the Rope is very small and this is + + align:start position:0% +of the Rope is very small and this is + + + align:start position:0% +of the Rope is very small and this is +often people call this assume the rope + + align:start position:0% +often people call this assume the rope + + + align:start position:0% +often people call this assume the rope +is massless well that's a little strange + + align:start position:0% +is massless well that's a little strange + + + align:start position:0% +is massless well that's a little strange +we can say the Matt the very very light + + align:start position:0% +we can say the Matt the very very light + + + align:start position:0% +we can say the Matt the very very light +string is often the same type of + + align:start position:0% +string is often the same type of + + + align:start position:0% +string is often the same type of +modeling and under those circumstances + + align:start position:0% +modeling and under those circumstances + + + align:start position:0% +modeling and under those circumstances +with that assumption you see that there + + align:start position:0% +with that assumption you see that there + + + align:start position:0% +with that assumption you see that there +is no contribution here and with that + + align:start position:0% +is no contribution here and with that + + + align:start position:0% +is no contribution here and with that +assumption that the tension is + + align:start position:0% +assumption that the tension is + + + align:start position:0% +assumption that the tension is +approximately uniform ropes are not + + align:start position:0% +approximately uniform ropes are not + + + align:start position:0% +approximately uniform ropes are not +massless there's a small difference but + + align:start position:0% +massless there's a small difference but + + + align:start position:0% +massless there's a small difference but +under those circumstances when we say a + + align:start position:0% +under those circumstances when we say a + + + align:start position:0% +under those circumstances when we say a +very light rope that even if it is + + align:start position:0% +very light rope that even if it is + + + align:start position:0% +very light rope that even if it is +accelerating implies that T is uniform + + align:start position:0% +accelerating implies that T is uniform + + + align:start position:0% +accelerating implies that T is uniform +in the rope and we can say the rope is + + align:start position:0% +in the rope and we can say the rope is + + + align:start position:0% +in the rope and we can say the rope is +under uniform tension and we will often + + align:start position:0% +under uniform tension and we will often + + + align:start position:0% +under uniform tension and we will often +refer to this case when we analyze + + align:start position:0% +refer to this case when we analyze + + + align:start position:0% +refer to this case when we analyze +problems where we're pulling objects for + + align:start position:0% +problems where we're pulling objects for + + + align:start position:0% +problems where we're pulling objects for +instance in a typical pulley problem \ No newline at end of file diff --git a/CxUEyN4exSg.txt b/CxUEyN4exSg.txt new file mode 100644 index 0000000000000000000000000000000000000000..973a9e9383a4aca60df787cc0ff0b54496ab8bce --- /dev/null +++ b/CxUEyN4exSg.txt @@ -0,0 +1,5339 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% +of MIT courses visit mitop courseware at + + + align:start position:0% +of MIT courses visit mitop courseware at +ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +hi today we in a manner of speaking + + align:start position:0% +hi today we in a manner of speaking + + + align:start position:0% +hi today we in a manner of speaking +start the second part of this part of + + align:start position:0% +start the second part of this part of + + + align:start position:0% +start the second part of this part of +our course that what we have done up to + + align:start position:0% +our course that what we have done up to + + + align:start position:0% +our course that what we have done up to +now is hopefully to have presented the + + align:start position:0% +now is hopefully to have presented the + + + align:start position:0% +now is hopefully to have presented the +concept of partial derivatives in with + + align:start position:0% +concept of partial derivatives in with + + + align:start position:0% +concept of partial derivatives in with +all the trimmings and now what we would + + align:start position:0% +all the trimmings and now what we would + + + align:start position:0% +all the trimmings and now what we would +like to do is devote the remainder of + + align:start position:0% +like to do is devote the remainder of + + + align:start position:0% +like to do is devote the remainder of +the course to what we could call + + align:start position:0% +the course to what we could call + + + align:start position:0% +the course to what we could call +selected topics in which the partial + + align:start position:0% +selected topics in which the partial + + + align:start position:0% +selected topics in which the partial +derivative plays a fundamental + + align:start position:0% +derivative plays a fundamental + + + align:start position:0% +derivative plays a fundamental +underlying thread uh in in other words a + + align:start position:0% +underlying thread uh in in other words a + + + align:start position:0% +underlying thread uh in in other words a +situation in which we will now pick + + align:start position:0% +situation in which we will now pick + + + align:start position:0% +situation in which we will now pick +specific areas of calculus and show how + + align:start position:0% +specific areas of calculus and show how + + + align:start position:0% +specific areas of calculus and show how +what we've learned about partial + + align:start position:0% +what we've learned about partial + + + align:start position:0% +what we've learned about partial +derivatives can be applied to these + + align:start position:0% +derivatives can be applied to these + + + align:start position:0% +derivatives can be applied to these +particular areas now the First Natural + + align:start position:0% +particular areas now the First Natural + + + align:start position:0% +particular areas now the First Natural +Area which would suggest itself it seems + + align:start position:0% +Area which would suggest itself it seems + + + align:start position:0% +Area which would suggest itself it seems +to me would be the concept of + + align:start position:0% +to me would be the concept of + + + align:start position:0% +to me would be the concept of +integrating a function of several + + align:start position:0% +integrating a function of several + + + align:start position:0% +integrating a function of several +variables since after we study + + align:start position:0% +variables since after we study + + + align:start position:0% +variables since after we study +derivatives we next Associated the + + align:start position:0% +derivatives we next Associated the + + + align:start position:0% +derivatives we next Associated the +definite integral with an anti + + align:start position:0% +definite integral with an anti + + + align:start position:0% +definite integral with an anti +anti-derivative it might seem that a + + align:start position:0% +anti-derivative it might seem that a + + + align:start position:0% +anti-derivative it might seem that a +very natural inquiry now is to discuss + + align:start position:0% +very natural inquiry now is to discuss + + + align:start position:0% +very natural inquiry now is to discuss +the concept of infinite multiple sums as + + align:start position:0% +the concept of infinite multiple sums as + + + align:start position:0% +the concept of infinite multiple sums as +being the analog of the definite + + align:start position:0% +being the analog of the definite + + + align:start position:0% +being the analog of the definite +integral in our study of calculus of a + + align:start position:0% +integral in our study of calculus of a + + + align:start position:0% +integral in our study of calculus of a +single variable now because these topics + + align:start position:0% +single variable now because these topics + + + align:start position:0% +single variable now because these topics +that we're picking have great + + align:start position:0% +that we're picking have great + + + align:start position:0% +that we're picking have great +application and have been studied in + + align:start position:0% +application and have been studied in + + + align:start position:0% +application and have been studied in +great depth we by necessity will sort of + + align:start position:0% +great depth we by necessity will sort of + + + align:start position:0% +great depth we by necessity will sort of +skim the surface of many of these topics + + align:start position:0% +skim the surface of many of these topics + + + align:start position:0% +skim the surface of many of these topics +so that we can present as many of the + + align:start position:0% +so that we can present as many of the + + + align:start position:0% +so that we can present as many of the +key points as we can in the time + + align:start position:0% +key points as we can in the time + + + align:start position:0% +key points as we can in the time +allotted for for the course we will make + + align:start position:0% +allotted for for the course we will make + + + align:start position:0% +allotted for for the course we will make +the lectures hopefully as short as + + align:start position:0% +the lectures hopefully as short as + + + align:start position:0% +the lectures hopefully as short as +possible as pungent as possible and + + align:start position:0% +possible as pungent as possible and + + + align:start position:0% +possible as pungent as possible and +leave most of the details to the + + align:start position:0% +leave most of the details to the + + + align:start position:0% +leave most of the details to the +learning exercises and to the uh + + align:start position:0% +learning exercises and to the uh + + + align:start position:0% +learning exercises and to the uh +supplementary notes at any rate what our + + align:start position:0% +supplementary notes at any rate what our + + + align:start position:0% +supplementary notes at any rate what our +lecture today is called is double sums + + align:start position:0% +lecture today is called is double sums + + + align:start position:0% +lecture today is called is double sums +or perhaps a better word would be + + align:start position:0% +or perhaps a better word would be + + + align:start position:0% +or perhaps a better word would be +multiple sums but we will concentrate on + + align:start position:0% +multiple sums but we will concentrate on + + + align:start position:0% +multiple sums but we will concentrate on +the case of double sums for the usual + + align:start position:0% +the case of double sums for the usual + + + align:start position:0% +the case of double sums for the usual +reason that namely in the case of two + + align:start position:0% +reason that namely in the case of two + + + align:start position:0% +reason that namely in the case of two +independent variables we have convenient + + align:start position:0% +independent variables we have convenient + + + align:start position:0% +independent variables we have convenient +pictures still left at our conv V now + + align:start position:0% +pictures still left at our conv V now + + + align:start position:0% +pictures still left at our conv V now +the idea is let's consider a region R + + align:start position:0% +the idea is let's consider a region R + + + align:start position:0% +the idea is let's consider a region R +say the re the square the unit Square on + + align:start position:0% +say the re the square the unit Square on + + + align:start position:0% +say the re the square the unit Square on +the coordinate axes with vertices 0 0 1 + + align:start position:0% +the coordinate axes with vertices 0 0 1 + + + align:start position:0% +the coordinate axes with vertices 0 0 1 +0 1 1 and 0 1 now what we're going to do + + align:start position:0% +0 1 1 and 0 1 now what we're going to do + + + align:start position:0% +0 1 1 and 0 1 now what we're going to do +now is Imagine That R is a thin plate + + align:start position:0% +now is Imagine That R is a thin plate + + + align:start position:0% +now is Imagine That R is a thin plate +and what we would like to do is to find + + align:start position:0% +and what we would like to do is to find + + + align:start position:0% +and what we would like to do is to find +the mass of this plate are assuming that + + align:start position:0% +the mass of this plate are assuming that + + + align:start position:0% +the mass of this plate are assuming that +the plate has a variable density in + + align:start position:0% +the plate has a variable density in + + + align:start position:0% +the plate has a variable density in +other words what we want to do is find + + align:start position:0% +other words what we want to do is find + + + align:start position:0% +other words what we want to do is find +the mass of the plate R if its density + + align:start position:0% +the mass of the plate R if its density + + + align:start position:0% +the mass of the plate R if its density +row at the point x comma Y and R is + + align:start position:0% +row at the point x comma Y and R is + + + align:start position:0% +row at the point x comma Y and R is +given by row of XY = x^2 + y^2 you see + + align:start position:0% +given by row of XY = x^2 + y^2 you see + + + align:start position:0% +given by row of XY = x^2 + y^2 you see +by the way the reason I picked this + + align:start position:0% +by the way the reason I picked this + + + align:start position:0% +by the way the reason I picked this +particular density of distribution is + + align:start position:0% +particular density of distribution is + + + align:start position:0% +particular density of distribution is +you may notice that x^2 + y^2 quite + + align:start position:0% +you may notice that x^2 + y^2 quite + + + align:start position:0% +you may notice that x^2 + y^2 quite +simply is the square of the distance + + align:start position:0% +simply is the square of the distance + + + align:start position:0% +simply is the square of the distance +from the of the point x comma y from the + + align:start position:0% +from the of the point x comma y from the + + + align:start position:0% +from the of the point x comma y from the +origin and this will make it very easy + + align:start position:0% +origin and this will make it very easy + + + align:start position:0% +origin and this will make it very easy +later for me to find where lowest + + align:start position:0% +later for me to find where lowest + + + align:start position:0% +later for me to find where lowest +densities occur where greatest densities + + align:start position:0% +densities occur where greatest densities + + + align:start position:0% +densities occur where greatest densities +occur whereas this may not seem like a + + align:start position:0% +occur whereas this may not seem like a + + + align:start position:0% +occur whereas this may not seem like a +very applied problem notice that if you + + align:start position:0% +very applied problem notice that if you + + + align:start position:0% +very applied problem notice that if you +want a geometric picture of what's going + + align:start position:0% +want a geometric picture of what's going + + + align:start position:0% +want a geometric picture of what's going +on here the idea is is that the density + + align:start position:0% +on here the idea is is that the density + + + align:start position:0% +on here the idea is is that the density +is varying radially as we move away from + + align:start position:0% +is varying radially as we move away from + + + align:start position:0% +is varying radially as we move away from +the origin in other words the density is + + align:start position:0% +the origin in other words the density is + + + align:start position:0% +the origin in other words the density is +the square of the distance of the point + + align:start position:0% +the square of the distance of the point + + + align:start position:0% +the square of the distance of the point +from the origin which means that the + + align:start position:0% +from the origin which means that the + + + align:start position:0% +from the origin which means that the +density is constant on any Circle + + align:start position:0% +density is constant on any Circle + + + align:start position:0% +density is constant on any Circle +centered at the origin again the key + + align:start position:0% +centered at the origin again the key + + + align:start position:0% +centered at the origin again the key +building block that we're going to use + + align:start position:0% +building block that we're going to use + + + align:start position:0% +building block that we're going to use +is again analogous to what we used in + + align:start position:0% +is again analogous to what we used in + + + align:start position:0% +is again analogous to what we used in +calculus of a single variable for + + align:start position:0% +calculus of a single variable for + + + align:start position:0% +calculus of a single variable for +example in calculus of a single variable + + align:start position:0% +example in calculus of a single variable + + + align:start position:0% +example in calculus of a single variable +when we said that distance was equal to + + align:start position:0% +when we said that distance was equal to + + + align:start position:0% +when we said that distance was equal to +rate time time it was assumed that the + + align:start position:0% +rate time time it was assumed that the + + + align:start position:0% +rate time time it was assumed that the +rate was constant in a similar way + + align:start position:0% +rate was constant in a similar way + + + align:start position:0% +rate was constant in a similar way +notice that if we assumed that the + + align:start position:0% +notice that if we assumed that the + + + align:start position:0% +notice that if we assumed that the +density were constant if the density + + align:start position:0% +density were constant if the density + + + align:start position:0% +density were constant if the density +were constant then the mass would just + + align:start position:0% +were constant then the mass would just + + + align:start position:0% +were constant then the mass would just +be the density times the area again most + + align:start position:0% +be the density times the area again most + + + align:start position:0% +be the density times the area again most +of us are used to thinking of density in + + align:start position:0% +of us are used to thinking of density in + + + align:start position:0% +of us are used to thinking of density in +terms of three dimensions that the mass + + align:start position:0% +terms of three dimensions that the mass + + + align:start position:0% +terms of three dimensions that the mass +is the dens it times the volume I prefer + + align:start position:0% +is the dens it times the volume I prefer + + + align:start position:0% +is the dens it times the volume I prefer +to pick a thin plate here simply to + + align:start position:0% +to pick a thin plate here simply to + + + align:start position:0% +to pick a thin plate here simply to +utilize a simple diagram that I did not + + align:start position:0% +utilize a simple diagram that I did not + + + align:start position:0% +utilize a simple diagram that I did not +want to get involved with + + align:start position:0% +want to get involved with + + + align:start position:0% +want to get involved with +three-dimensional diagrams another + + align:start position:0% +three-dimensional diagrams another + + + align:start position:0% +three-dimensional diagrams another +drawback perhaps to this system is that + + align:start position:0% +drawback perhaps to this system is that + + + align:start position:0% +drawback perhaps to this system is that +you may be wondering why we're not using + + align:start position:0% +you may be wondering why we're not using + + + align:start position:0% +you may be wondering why we're not using +the counterpart of what area was in + + align:start position:0% +the counterpart of what area was in + + + align:start position:0% +the counterpart of what area was in +calculus of a single variable why aren't + + align:start position:0% +calculus of a single variable why aren't + + + align:start position:0% +calculus of a single variable why aren't +we talking about Cal uh the volume in + + align:start position:0% +we talking about Cal uh the volume in + + + align:start position:0% +we talking about Cal uh the volume in +two Dimensions why couldn't we somehow + + align:start position:0% +two Dimensions why couldn't we somehow + + + align:start position:0% +two Dimensions why couldn't we somehow +visualize a volume problem here again if + + align:start position:0% +visualize a volume problem here again if + + + align:start position:0% +visualize a volume problem here again if +that's what you'd like to do notice that + + align:start position:0% +that's what you'd like to do notice that + + + align:start position:0% +that's what you'd like to do notice that +we could graph the density as a function + + align:start position:0% +we could graph the density as a function + + + align:start position:0% +we could graph the density as a function +of the point x comma y in the region R + + align:start position:0% +of the point x comma y in the region R + + + align:start position:0% +of the point x comma y in the region R +plot the density in the direction of the + + align:start position:0% +plot the density in the direction of the + + + align:start position:0% +plot the density in the direction of the +positive z-axis in which case the + + align:start position:0% +positive z-axis in which case the + + + align:start position:0% +positive z-axis in which case the +problem that we would then be trying to + + align:start position:0% +problem that we would then be trying to + + + align:start position:0% +problem that we would then be trying to +solve would be to find the volume of a + + align:start position:0% +solve would be to find the volume of a + + + align:start position:0% +solve would be to find the volume of a +solid that you get by taking the + + align:start position:0% +solid that you get by taking the + + + align:start position:0% +solid that you get by taking the +parallelopiped whose base is the region + + align:start position:0% +parallelopiped whose base is the region + + + align:start position:0% +parallelopiped whose base is the region +R and intersect that with the surface Z + + align:start position:0% +R and intersect that with the surface Z + + + align:start position:0% +R and intersect that with the surface Z += x^2 + y^2 again we will leave these + + align:start position:0% += x^2 + y^2 again we will leave these + + + align:start position:0% += x^2 + y^2 again we will leave these +details for the exercises but the + + align:start position:0% +details for the exercises but the + + + align:start position:0% +details for the exercises but the +surface Z = x^2 + y^2 as you look in + + align:start position:0% +surface Z = x^2 + y^2 as you look in + + + align:start position:0% +surface Z = x^2 + y^2 as you look in +along the z-axis here is a parabolic + + align:start position:0% +along the z-axis here is a parabolic + + + align:start position:0% +along the z-axis here is a parabolic +ball opening up in other words Z = x^2 + + + align:start position:0% +ball opening up in other words Z = x^2 + + + + align:start position:0% +ball opening up in other words Z = x^2 + +y^2 if you take Z equals a positive + + align:start position:0% +y^2 if you take Z equals a positive + + + align:start position:0% +y^2 if you take Z equals a positive +constant in other words slice this + + align:start position:0% +constant in other words slice this + + + align:start position:0% +constant in other words slice this +parallel to the XY plane if Z is a + + align:start position:0% +parallel to the XY plane if Z is a + + + align:start position:0% +parallel to the XY plane if Z is a +positive constant x^2 + y^2 equal a + + align:start position:0% +positive constant x^2 + y^2 equal a + + + align:start position:0% +positive constant x^2 + y^2 equal a +positive constant is a circle and any + + align:start position:0% +positive constant is a circle and any + + + align:start position:0% +positive constant is a circle and any +rate just to summarize that the + + align:start position:0% +rate just to summarize that the + + + align:start position:0% +rate just to summarize that the +geometric equivalent to our problem is + + align:start position:0% +geometric equivalent to our problem is + + + align:start position:0% +geometric equivalent to our problem is +find the volume of the solid s if s is + + align:start position:0% +find the volume of the solid s if s is + + + align:start position:0% +find the volume of the solid s if s is +the parallelopiped with the base R where + + align:start position:0% +the parallelopiped with the base R where + + + align:start position:0% +the parallelopiped with the base R where +R is just as given and the top meaning + + align:start position:0% +R is just as given and the top meaning + + + align:start position:0% +R is just as given and the top meaning +it's intersected with the surface Z = + + align:start position:0% +it's intersected with the surface Z = + + + align:start position:0% +it's intersected with the surface Z = +x^2 + y^2 and again let me mention as an + + align:start position:0% +x^2 + y^2 and again let me mention as an + + + align:start position:0% +x^2 + y^2 and again let me mention as an +aside that the same analogy occurs in + + align:start position:0% +aside that the same analogy occurs in + + + align:start position:0% +aside that the same analogy occurs in +calculus of a single variable namely if + + align:start position:0% +calculus of a single variable namely if + + + align:start position:0% +calculus of a single variable namely if +I write down the definite integral from + + align:start position:0% +I write down the definite integral from + + + align:start position:0% +I write down the definite integral from +0 to 1 x^2 DX I may view this well in + + align:start position:0% +0 to 1 x^2 DX I may view this well in + + + align:start position:0% +0 to 1 x^2 DX I may view this well in +many ways but two of the major ways in + + align:start position:0% +many ways but two of the major ways in + + + align:start position:0% +many ways but two of the major ways in +which I may view this the major one that + + align:start position:0% +which I may view this the major one that + + + align:start position:0% +which I may view this the major one that +we emphasized in our course was as an + + align:start position:0% +we emphasized in our course was as an + + + align:start position:0% +we emphasized in our course was as an +area I can also view this as a mass more + + align:start position:0% +area I can also view this as a mass more + + + align:start position:0% +area I can also view this as a mass more +specifically let me take the Cur the + + align:start position:0% +specifically let me take the Cur the + + + align:start position:0% +specifically let me take the Cur the +region r as shown here then you see one + + align:start position:0% +region r as shown here then you see one + + + align:start position:0% +region r as shown here then you see one +interpretation of the integral from 0 to + + align:start position:0% +interpretation of the integral from 0 to + + + align:start position:0% +interpretation of the integral from 0 to +1 X2 DX is that it's the area of the + + align:start position:0% +1 X2 DX is that it's the area of the + + + align:start position:0% +1 X2 DX is that it's the area of the +region R another interpretation is + + align:start position:0% +region R another interpretation is + + + align:start position:0% +region R another interpretation is +imagine that you have a very thin rod + + align:start position:0% +imagine that you have a very thin rod + + + align:start position:0% +imagine that you have a very thin rod +geometrically of uniform shape in other + + align:start position:0% +geometrically of uniform shape in other + + + align:start position:0% +geometrically of uniform shape in other +words it's essentially a segment of the + + align:start position:0% +words it's essentially a segment of the + + + align:start position:0% +words it's essentially a segment of the +xaxis from 0 to 1 and that the density + + align:start position:0% +xaxis from 0 to 1 and that the density + + + align:start position:0% +xaxis from 0 to 1 and that the density +of this Rod is a function of position X + + align:start position:0% +of this Rod is a function of position X + + + align:start position:0% +of this Rod is a function of position X +say row of X is X2 then notice in a + + align:start position:0% +say row of X is X2 then notice in a + + + align:start position:0% +say row of X is X2 then notice in a +manner analogous to what we were just + + align:start position:0% +manner analogous to what we were just + + + align:start position:0% +manner analogous to what we were just +talking about the mass of this Rod would + + align:start position:0% +talking about the mass of this Rod would + + + align:start position:0% +talking about the mass of this Rod would +be found by integrating X2 from 0 to 1 + + align:start position:0% +be found by integrating X2 from 0 to 1 + + + align:start position:0% +be found by integrating X2 from 0 to 1 +by the way notice again a very important + + align:start position:0% +by the way notice again a very important + + + align:start position:0% +by the way notice again a very important +thing that comes up here and that is + + align:start position:0% +thing that comes up here and that is + + + align:start position:0% +thing that comes up here and that is +that these two diagrams may be used for + + align:start position:0% +that these two diagrams may be used for + + + align:start position:0% +that these two diagrams may be used for +the same problem you see in many cases + + align:start position:0% +the same problem you see in many cases + + + align:start position:0% +the same problem you see in many cases +when one has a density distribution like + + align:start position:0% +when one has a density distribution like + + + align:start position:0% +when one has a density distribution like +this one one visualizes the density + + align:start position:0% +this one one visualizes the density + + + align:start position:0% +this one one visualizes the density +being plotted in in other words the + + align:start position:0% +being plotted in in other words the + + + align:start position:0% +being plotted in in other words the +density row of X = x^2 is plotted as the + + align:start position:0% +density row of X = x^2 is plotted as the + + + align:start position:0% +density row of X = x^2 is plotted as the +curve yal row of X in this case y = x^2 + + align:start position:0% +curve yal row of X in this case y = x^2 + + + align:start position:0% +curve yal row of X in this case y = x^2 +and we then think of a way of being able + + align:start position:0% +and we then think of a way of being able + + + align:start position:0% +and we then think of a way of being able +to visualize what the density is doing + + align:start position:0% +to visualize what the density is doing + + + align:start position:0% +to visualize what the density is doing +here in terms of the shape of the curve + + align:start position:0% +here in terms of the shape of the curve + + + align:start position:0% +here in terms of the shape of the curve +here that's exactly what we were doing + + align:start position:0% +here that's exactly what we were doing + + + align:start position:0% +here that's exactly what we were doing +uh earlier in the lecture when we said + + align:start position:0% +uh earlier in the lecture when we said + + + align:start position:0% +uh earlier in the lecture when we said +that we could visualize the density row + + align:start position:0% +that we could visualize the density row + + + align:start position:0% +that we could visualize the density row +of XY as a function Z equals row of XY + + align:start position:0% +of XY as a function Z equals row of XY + + + align:start position:0% +of XY as a function Z equals row of XY +the analogy being that with two + + align:start position:0% +the analogy being that with two + + + align:start position:0% +the analogy being that with two +independent variables we wouldn't have a + + align:start position:0% +independent variables we wouldn't have a + + + align:start position:0% +independent variables we wouldn't have a +curve but rather we would have a Surface + + align:start position:0% +curve but rather we would have a Surface + + + align:start position:0% +curve but rather we would have a Surface +by the way again notice how this + + align:start position:0% +by the way again notice how this + + + align:start position:0% +by the way again notice how this +emphasizes the fact that the definite + + align:start position:0% +emphasizes the fact that the definite + + + align:start position:0% +emphasizes the fact that the definite +integral is in reality the an infinite + + align:start position:0% +integral is in reality the an infinite + + + align:start position:0% +integral is in reality the an infinite +sum that it is convenient in many cases + + align:start position:0% +sum that it is convenient in many cases + + + align:start position:0% +sum that it is convenient in many cases +to view this limit of a sum in terms of + + align:start position:0% +to view this limit of a sum in terms of + + + align:start position:0% +to view this limit of a sum in terms of +an area under a curve but that the + + align:start position:0% +an area under a curve but that the + + + align:start position:0% +an area under a curve but that the +definite integr itself exists for more + + align:start position:0% +definite integr itself exists for more + + + align:start position:0% +definite integr itself exists for more +problems than just for computing areas + + align:start position:0% +problems than just for computing areas + + + align:start position:0% +problems than just for computing areas +now at any rate all we're trying to + + align:start position:0% +now at any rate all we're trying to + + + align:start position:0% +now at any rate all we're trying to +point point out here is that the same + + align:start position:0% +point point out here is that the same + + + align:start position:0% +point point out here is that the same +analogy will exist when we go to + + align:start position:0% +analogy will exist when we go to + + + align:start position:0% +analogy will exist when we go to +functions of several variables if in + + align:start position:0% +functions of several variables if in + + + align:start position:0% +functions of several variables if in +fact we now return to the problem stated + + align:start position:0% +fact we now return to the problem stated + + + align:start position:0% +fact we now return to the problem stated +at the beginning of the lecture we take + + align:start position:0% +at the beginning of the lecture we take + + + align:start position:0% +at the beginning of the lecture we take +our region R remember what this is now + + align:start position:0% +our region R remember what this is now + + + align:start position:0% +our region R remember what this is now +it has it's the square with vertices at + + align:start position:0% +it has it's the square with vertices at + + + align:start position:0% +it has it's the square with vertices at +these + + align:start position:0% +these + + + align:start position:0% +these +points we know that the density is given + + align:start position:0% +points we know that the density is given + + + align:start position:0% +points we know that the density is given +at any point x comma y by x^2 + y^2 and + + align:start position:0% +at any point x comma y by x^2 + y^2 and + + + align:start position:0% +at any point x comma y by x^2 + y^2 and +what we'd like to do now is find the + + align:start position:0% +what we'd like to do now is find the + + + align:start position:0% +what we'd like to do now is find the +mass of this particular plate now just + + align:start position:0% +mass of this particular plate now just + + + align:start position:0% +mass of this particular plate now just +as in C calcus of a single variable the + + align:start position:0% +as in C calcus of a single variable the + + + align:start position:0% +as in C calcus of a single variable the +argument that we use now is nothing more + + align:start position:0% +argument that we use now is nothing more + + + align:start position:0% +argument that we use now is nothing more +than if we took a small enough region + + align:start position:0% +than if we took a small enough region + + + align:start position:0% +than if we took a small enough region +here we could assume that the variable + + align:start position:0% +here we could assume that the variable + + + align:start position:0% +here we could assume that the variable +density was essentially constant in + + align:start position:0% +density was essentially constant in + + + align:start position:0% +density was essentially constant in +other words this is how one makes + + align:start position:0% +other words this is how one makes + + + align:start position:0% +other words this is how one makes +physical approximations we break this + + align:start position:0% +physical approximations we break this + + + align:start position:0% +physical approximations we break this +thing up into small pieces somehow + + align:start position:0% +thing up into small pieces somehow + + + align:start position:0% +thing up into small pieces somehow +rather find the mass of each small piece + + align:start position:0% +rather find the mass of each small piece + + + align:start position:0% +rather find the mass of each small piece +and add those all up the key point being + + align:start position:0% +and add those all up the key point being + + + align:start position:0% +and add those all up the key point being +if the pieces are small enough for an + + align:start position:0% +if the pieces are small enough for an + + + align:start position:0% +if the pieces are small enough for an +approximation we can say that the + + align:start position:0% +approximation we can say that the + + + align:start position:0% +approximation we can say that the +density is essentially constant by the + + align:start position:0% +density is essentially constant by the + + + align:start position:0% +density is essentially constant by the +way in the the same way that we had to + + align:start position:0% +way in the the same way that we had to + + + align:start position:0% +way in the the same way that we had to +learn the sigma notation back in part + + align:start position:0% +learn the sigma notation back in part + + + align:start position:0% +learn the sigma notation back in part +one of our course we will now have to + + align:start position:0% +one of our course we will now have to + + + align:start position:0% +one of our course we will now have to +somehow or other learn to master the + + align:start position:0% +somehow or other learn to master the + + + align:start position:0% +somehow or other learn to master the +notation for double sums the idea again + + align:start position:0% +notation for double sums the idea again + + + align:start position:0% +notation for double sums the idea again +being this if I partition this into n + + align:start position:0% +being this if I partition this into n + + + align:start position:0% +being this if I partition this into n +equal parts and this segment into m + + align:start position:0% +equal parts and this segment into m + + + align:start position:0% +equal parts and this segment into m +equal parts and if I call a typical X + + align:start position:0% +equal parts and if I call a typical X + + + align:start position:0% +equal parts and if I call a typical X +segment Delta x sub I and a typical y + + align:start position:0% +segment Delta x sub I and a typical y + + + align:start position:0% +segment Delta x sub I and a typical y +segment Delta YJ then to match up in + + align:start position:0% +segment Delta YJ then to match up in + + + align:start position:0% +segment Delta YJ then to match up in +coordinate fashion what the mass of this + + align:start position:0% +coordinate fashion what the mass of this + + + align:start position:0% +coordinate fashion what the mass of this +little piece would be I would call that + + align:start position:0% +little piece would be I would call that + + + align:start position:0% +little piece would be I would call that +the the i j Mass corresponding to the if + + align:start position:0% +the the i j Mass corresponding to the if + + + align:start position:0% +the the i j Mass corresponding to the if +x partition and the j y partition and + + align:start position:0% +x partition and the j y partition and + + + align:start position:0% +x partition and the j y partition and +the idea is I'm going to add all of + + align:start position:0% +the idea is I'm going to add all of + + + align:start position:0% +the idea is I'm going to add all of +these up that would motivate the + + align:start position:0% +these up that would motivate the + + + align:start position:0% +these up that would motivate the +notation called the double sum namely + + align:start position:0% +notation called the double sum namely + + + align:start position:0% +notation called the double sum namely +the way you read this is you say let me + + align:start position:0% +the way you read this is you say let me + + + align:start position:0% +the way you read this is you say let me +first pick a fixed value of J and for + + align:start position:0% +first pick a fixed value of J and for + + + align:start position:0% +first pick a fixed value of J and for +that fixed value of J I will sum up all + + align:start position:0% +that fixed value of J I will sum up all + + + align:start position:0% +that fixed value of J I will sum up all +these pieces as I goes from 1 to n what + + align:start position:0% +these pieces as I goes from 1 to n what + + + align:start position:0% +these pieces as I goes from 1 to n what +that means pictorially is this I will + + align:start position:0% +that means pictorially is this I will + + + align:start position:0% +that means pictorially is this I will +pick a fixed value of J well since J + + align:start position:0% +pick a fixed value of J well since J + + + align:start position:0% +pick a fixed value of J well since J +controls the y coordinate a fixed value + + align:start position:0% +controls the y coordinate a fixed value + + + align:start position:0% +controls the y coordinate a fixed value +of J fixes your horizontal strip and + + align:start position:0% +of J fixes your horizontal strip and + + + align:start position:0% +of J fixes your horizontal strip and +what you're saying is I will now add up + + align:start position:0% +what you're saying is I will now add up + + + align:start position:0% +what you're saying is I will now add up +all the masses along that strip then + + align:start position:0% +all the masses along that strip then + + + align:start position:0% +all the masses along that strip then +what you say is and then as I do that + + align:start position:0% +what you say is and then as I do that + + + align:start position:0% +what you say is and then as I do that +let me perform that for each J as J goes + + align:start position:0% +let me perform that for each J as J goes + + + align:start position:0% +let me perform that for each J as J goes +from 1 to m in other words what this + + align:start position:0% +from 1 to m in other words what this + + + align:start position:0% +from 1 to m in other words what this +would say is add up all of the Delta M's + + align:start position:0% +would say is add up all of the Delta M's + + + align:start position:0% +would say is add up all of the Delta M's +along each row and then take the sum of + + align:start position:0% +along each row and then take the sum of + + + align:start position:0% +along each row and then take the sum of +the all the possible values that the + + align:start position:0% +the all the possible values that the + + + align:start position:0% +the all the possible values that the +rows can take on in other words I'll + + align:start position:0% +rows can take on in other words I'll + + + align:start position:0% +rows can take on in other words I'll +take add up these pieces these pieces + + align:start position:0% +take add up these pieces these pieces + + + align:start position:0% +take add up these pieces these pieces +these pieces these pieces then add those + + align:start position:0% +these pieces these pieces then add those + + + align:start position:0% +these pieces these pieces then add those +sums together notice of course I could + + align:start position:0% +sums together notice of course I could + + + align:start position:0% +sums together notice of course I could +have written this in the reverse + + align:start position:0% + + + + align:start position:0% + +order namely this would say what first + + align:start position:0% +order namely this would say what first + + + align:start position:0% +order namely this would say what first +hold I constant and for a fixed I sum + + align:start position:0% +hold I constant and for a fixed I sum + + + align:start position:0% +hold I constant and for a fixed I sum +these as J goes from 1 to m in other + + align:start position:0% +these as J goes from 1 to m in other + + + align:start position:0% +these as J goes from 1 to m in other +words for a fixed I sum these + + align:start position:0% +words for a fixed I sum these + + + align:start position:0% +words for a fixed I sum these +J goes from 1 to M and then sum over all + + align:start position:0% +J goes from 1 to M and then sum over all + + + align:start position:0% +J goes from 1 to M and then sum over all +the J's over all the I's at any rate the + + align:start position:0% +the J's over all the I's at any rate the + + + align:start position:0% +the J's over all the I's at any rate the +learning exercises will take care of + + align:start position:0% +learning exercises will take care of + + + align:start position:0% +learning exercises will take care of +making sure that you learn to manipulate + + align:start position:0% +making sure that you learn to manipulate + + + align:start position:0% +making sure that you learn to manipulate +this particular notation the theory + + align:start position:0% +this particular notation the theory + + + align:start position:0% +this particular notation the theory +works as follows what we do is assuming + + align:start position:0% +works as follows what we do is assuming + + + align:start position:0% +works as follows what we do is assuming +that the density function is continuous + + align:start position:0% +that the density function is continuous + + + align:start position:0% +that the density function is continuous +at each particular little rectangle that + + align:start position:0% +at each particular little rectangle that + + + align:start position:0% +at each particular little rectangle that +we have here we pick the point which has + + align:start position:0% +we have here we pick the point which has + + + align:start position:0% +we have here we pick the point which has +the smallest density we pick the point + + align:start position:0% +the smallest density we pick the point + + + align:start position:0% +the smallest density we pick the point +which has the largest density we then + + align:start position:0% +which has the largest density we then + + + align:start position:0% +which has the largest density we then +imagine that we had replaced this little + + align:start position:0% +imagine that we had replaced this little + + + align:start position:0% +imagine that we had replaced this little +segment by the same area but with a + + align:start position:0% +segment by the same area but with a + + + align:start position:0% +segment by the same area but with a +material which had this a constant + + align:start position:0% +material which had this a constant + + + align:start position:0% +material which had this a constant +smallest density so that the true Mass + + align:start position:0% +smallest density so that the true Mass + + + align:start position:0% +smallest density so that the true Mass +must be greater than the mass of that + + align:start position:0% +must be greater than the mass of that + + + align:start position:0% +must be greater than the mass of that +piece and then we assume that this + + align:start position:0% +piece and then we assume that this + + + align:start position:0% +piece and then we assume that this +little piece was replaced by a new piece + + align:start position:0% +little piece was replaced by a new piece + + + align:start position:0% +little piece was replaced by a new piece +with the same shape but whose density + + align:start position:0% +with the same shape but whose density + + + align:start position:0% +with the same shape but whose density +was constantly equal to the greatest + + align:start position:0% +was constantly equal to the greatest + + + align:start position:0% +was constantly equal to the greatest +density on this so this particular Mass + + align:start position:0% +density on this so this particular Mass + + + align:start position:0% +density on this so this particular Mass +must be less than the mass of the new + + align:start position:0% +must be less than the mass of the new + + + align:start position:0% +must be less than the mass of the new +piece and in that way we we squeeze the + + align:start position:0% +piece and in that way we we squeeze the + + + align:start position:0% +piece and in that way we we squeeze the +true the true Mass between two extremes + + align:start position:0% +true the true Mass between two extremes + + + align:start position:0% +true the true Mass between two extremes +again just as we did in calculus of a + + align:start position:0% +again just as we did in calculus of a + + + align:start position:0% +again just as we did in calculus of a +single variable and again to keep the + + align:start position:0% +single variable and again to keep the + + + align:start position:0% +single variable and again to keep the +notation going the same way I let Delta + + align:start position:0% +notation going the same way I let Delta + + + align:start position:0% +notation going the same way I let Delta +M sub J lower bar denote the mass of the + + align:start position:0% +M sub J lower bar denote the mass of the + + + align:start position:0% +M sub J lower bar denote the mass of the +piece that I get by replacing the + + align:start position:0% +piece that I get by replacing the + + + align:start position:0% +piece that I get by replacing the +density by the constant density equal to + + align:start position:0% +density by the constant density equal to + + + align:start position:0% +density by the constant density equal to +the smallest density row sub i j lower + + align:start position:0% +the smallest density row sub i j lower + + + align:start position:0% +the smallest density row sub i j lower +bar treating that as a constant + + align:start position:0% +bar treating that as a constant + + + align:start position:0% +bar treating that as a constant +multiplying that by the cross-sectional + + align:start position:0% +multiplying that by the cross-sectional + + + align:start position:0% +multiplying that by the cross-sectional +area Delta x i * Delta y j I prefer to + + align:start position:0% +area Delta x i * Delta y j I prefer to + + + align:start position:0% +area Delta x i * Delta y j I prefer to +call that Delta a sub i j so we don't + + align:start position:0% +call that Delta a sub i j so we don't + + + align:start position:0% +call that Delta a sub i j so we don't +Prejudice either the order in which we + + align:start position:0% +Prejudice either the order in which we + + + align:start position:0% +Prejudice either the order in which we +write these factors or the particular + + align:start position:0% +write these factors or the particular + + + align:start position:0% +write these factors or the particular +coordinate system that one wants to use + + align:start position:0% +coordinate system that one wants to use + + + align:start position:0% +coordinate system that one wants to use +but because I think you're more familiar + + align:start position:0% +but because I think you're more familiar + + + align:start position:0% +but because I think you're more familiar +with cartisian coordinates I will + + align:start position:0% +with cartisian coordinates I will + + + align:start position:0% +with cartisian coordinates I will +continue to write this but the idea is I + + align:start position:0% +continue to write this but the idea is I + + + align:start position:0% +continue to write this but the idea is I +compute the lowest the + + align:start position:0% +compute the lowest the + + + align:start position:0% +compute the lowest the +smallest mass in other words an + + align:start position:0% +smallest mass in other words an + + + align:start position:0% +smallest mass in other words an +underestimate in a similar way I compute + + align:start position:0% +underestimate in a similar way I compute + + + align:start position:0% +underestimate in a similar way I compute +and + + align:start position:0% +and + + + align:start position:0% +and +overestimate I then know that the true + + align:start position:0% +overestimate I then know that the true + + + align:start position:0% +overestimate I then know that the true +mass of my J piece is caught between + + align:start position:0% +mass of my J piece is caught between + + + align:start position:0% +mass of my J piece is caught between +these two therefore my total mass which + + align:start position:0% +these two therefore my total mass which + + + align:start position:0% +these two therefore my total mass which +is the double sum of these over I and J + + align:start position:0% +is the double sum of these over I and J + + + align:start position:0% +is the double sum of these over I and J +must be be must be in turn cut between + + align:start position:0% +must be be must be in turn cut between + + + align:start position:0% +must be be must be in turn cut between +these two double sums in other words + + align:start position:0% +these two double sums in other words + + + align:start position:0% +these two double sums in other words +what I have now done is caught the true + + align:start position:0% +what I have now done is caught the true + + + align:start position:0% +what I have now done is caught the true +Mass between a lower bound and an upper + + align:start position:0% +Mass between a lower bound and an upper + + + align:start position:0% +Mass between a lower bound and an upper +bound and again to write this thing more + + align:start position:0% +bound and again to write this thing more + + + align:start position:0% +bound and again to write this thing more +symbolically so you can look at it here + + align:start position:0% +symbolically so you can look at it here + + + align:start position:0% +symbolically so you can look at it here +what I'm saying is on the one hand my + + align:start position:0% +what I'm saying is on the one hand my + + + align:start position:0% +what I'm saying is on the one hand my +mass must be at least as the great as + + align:start position:0% +mass must be at least as the great as + + + align:start position:0% +mass must be at least as the great as +great as the value of this double sum on + + align:start position:0% +great as the value of this double sum on + + + align:start position:0% +great as the value of this double sum on +the other hand it can be no greater than + + align:start position:0% +the other hand it can be no greater than + + + align:start position:0% +the other hand it can be no greater than +the value of this double sum somehow or + + align:start position:0% +the value of this double sum somehow or + + + align:start position:0% +the value of this double sum somehow or +other the same as I did in calculus of a + + align:start position:0% +other the same as I did in calculus of a + + + align:start position:0% +other the same as I did in calculus of a +single variable I would now like to put + + align:start position:0% +single variable I would now like to put + + + align:start position:0% +single variable I would now like to put +the squeeze on this as the sizes of the + + align:start position:0% +the squeeze on this as the sizes of the + + + align:start position:0% +the squeeze on this as the sizes of the +pieces Delta XI and Delta YJ are allowed + + align:start position:0% +pieces Delta XI and Delta YJ are allowed + + + align:start position:0% +pieces Delta XI and Delta YJ are allowed +to go get arbitrarily close to zero in + + align:start position:0% +to go get arbitrarily close to zero in + + + align:start position:0% +to go get arbitrarily close to zero in +size what I hope happens is that in that + + align:start position:0% +size what I hope happens is that in that + + + align:start position:0% +size what I hope happens is that in that +limit + + align:start position:0% +limit + + + align:start position:0% +limit +this difference goes to zero so that m + + align:start position:0% +this difference goes to zero so that m + + + align:start position:0% +this difference goes to zero so that m +is caught between two equal things and + + align:start position:0% +is caught between two equal things and + + + align:start position:0% +is caught between two equal things and +hence the the true value of M must be + + align:start position:0% +hence the the true value of M must be + + + align:start position:0% +hence the the true value of M must be +that common value you see in a manner of + + align:start position:0% +that common value you see in a manner of + + + align:start position:0% +that common value you see in a manner of +speaking theoretically nothing new is + + align:start position:0% +speaking theoretically nothing new is + + + align:start position:0% +speaking theoretically nothing new is +happening that didn't already happen in + + align:start position:0% +happening that didn't already happen in + + + align:start position:0% +happening that didn't already happen in +calculus of a single variable but from a + + align:start position:0% +calculus of a single variable but from a + + + align:start position:0% +calculus of a single variable but from a +computational point of view limits of + + align:start position:0% +computational point of view limits of + + + align:start position:0% +computational point of view limits of +single sums have now been replaced by + + align:start position:0% +single sums have now been replaced by + + + align:start position:0% +single sums have now been replaced by +limits of double sums so that + + align:start position:0% +limits of double sums so that + + + align:start position:0% +limits of double sums so that +computationally there is a degree of + + align:start position:0% +computationally there is a degree of + + + align:start position:0% +computationally there is a degree of +difficulty more present in our present + + align:start position:0% +difficulty more present in our present + + + align:start position:0% +difficulty more present in our present +study than there was in our study of + + align:start position:0% +study than there was in our study of + + + align:start position:0% +study than there was in our study of +calculus of a single variable the + + align:start position:0% +calculus of a single variable the + + + align:start position:0% +calculus of a single variable the +computation becomes more difficult the + + align:start position:0% +computation becomes more difficult the + + + align:start position:0% +computation becomes more difficult the +theory stays the same now before we + + align:start position:0% +theory stays the same now before we + + + align:start position:0% +theory stays the same now before we +start getting into the idea of what + + align:start position:0% +start getting into the idea of what + + + align:start position:0% +start getting into the idea of what +limits mean let me just summarize this + + align:start position:0% +limits mean let me just summarize this + + + align:start position:0% +limits mean let me just summarize this +for you in terms of a more concrete + + align:start position:0% +for you in terms of a more concrete + + + align:start position:0% +for you in terms of a more concrete +interpretation let me again take that + + align:start position:0% +interpretation let me again take that + + + align:start position:0% +interpretation let me again take that +rect that square r with its vertices you + + align:start position:0% +rect that square r with its vertices you + + + align:start position:0% +rect that square r with its vertices you +know the same one we dealt with 0 0 1 0 + + align:start position:0% +know the same one we dealt with 0 0 1 0 + + + align:start position:0% +know the same one we dealt with 0 0 1 0 +1 1 0 1 and let me now take as a special + + align:start position:0% +1 1 0 1 and let me now take as a special + + + align:start position:0% +1 1 0 1 and let me now take as a special +case the case in which I divide both the + + align:start position:0% +case the case in which I divide both the + + + align:start position:0% +case the case in which I divide both the +X region and the Y region into two equal + + align:start position:0% +X region and the Y region into two equal + + + align:start position:0% +X region and the Y region into two equal +parts so that my points of + + align:start position:0% +parts so that my points of + + + align:start position:0% +parts so that my points of +partition you see look like + + align:start position:0% +partition you see look like + + + align:start position:0% +partition you see look like +this now you see the advantage of + + align:start position:0% +this now you see the advantage of + + + align:start position:0% +this now you see the advantage of +picking my density to be x^2 + y^2 is + + align:start position:0% +picking my density to be x^2 + y^2 is + + + align:start position:0% +picking my density to be x^2 + y^2 is +that since the density is radial what + + align:start position:0% +that since the density is radial what + + + align:start position:0% +that since the density is radial what +this means is that in each of my + + align:start position:0% +this means is that in each of my + + + align:start position:0% +this means is that in each of my +partitioned rectangles in this case each + + align:start position:0% +partitioned rectangles in this case each + + + align:start position:0% +partitioned rectangles in this case each +of my rectangles is a square you see + + align:start position:0% +of my rectangles is a square you see + + + align:start position:0% +of my rectangles is a square you see +keep in mind that first of all I don't + + align:start position:0% +keep in mind that first of all I don't + + + align:start position:0% +keep in mind that first of all I don't +have to divide these two dimens ions + + align:start position:0% +have to divide these two dimens ions + + + align:start position:0% +have to divide these two dimens ions +into the same number of equal parts + + align:start position:0% +into the same number of equal parts + + + align:start position:0% +into the same number of equal parts +secondly they don't even have to be + + align:start position:0% +secondly they don't even have to be + + + align:start position:0% +secondly they don't even have to be +equal parts but I've just for symmetry + + align:start position:0% +equal parts but I've just for symmetry + + + align:start position:0% +equal parts but I've just for symmetry +here elected to do this just so we get + + align:start position:0% +here elected to do this just so we get + + + align:start position:0% +here elected to do this just so we get +an idea of what's happening + + align:start position:0% +an idea of what's happening + + + align:start position:0% +an idea of what's happening +computationally and the more difficult + + align:start position:0% +computationally and the more difficult + + + align:start position:0% +computationally and the more difficult +cases will be taken care of in the + + align:start position:0% +cases will be taken care of in the + + + align:start position:0% +cases will be taken care of in the +exercises the idea now is what that for + + align:start position:0% +exercises the idea now is what that for + + + align:start position:0% +exercises the idea now is what that for +each of these particular squares the + + align:start position:0% +each of these particular squares the + + + align:start position:0% +each of these particular squares the +lowest density occurs at the point which + + align:start position:0% +lowest density occurs at the point which + + + align:start position:0% +lowest density occurs at the point which +makes up the lower leftand corner + + align:start position:0% +makes up the lower leftand corner + + + align:start position:0% +makes up the lower leftand corner +because that will be the closest point + + align:start position:0% +because that will be the closest point + + + align:start position:0% +because that will be the closest point +to the origin in each of these squares + + align:start position:0% +to the origin in each of these squares + + + align:start position:0% +to the origin in each of these squares +and the furthest point from the origin + + align:start position:0% +and the furthest point from the origin + + + align:start position:0% +and the furthest point from the origin +in each of these squares will be the + + align:start position:0% +in each of these squares will be the + + + align:start position:0% +in each of these squares will be the +point in the upper right hand corner so + + align:start position:0% +point in the upper right hand corner so + + + align:start position:0% +point in the upper right hand corner so +you see in this particular case let me + + align:start position:0% +you see in this particular case let me + + + align:start position:0% +you see in this particular case let me +do both of these at once to find the + + align:start position:0% +do both of these at once to find the + + + align:start position:0% +do both of these at once to find the +smallest density in each of these + + align:start position:0% +smallest density in each of these + + + align:start position:0% +smallest density in each of these +regions let me have the smallest one + + align:start position:0% +regions let me have the smallest one + + + align:start position:0% +regions let me have the smallest one +written in the black chalk on the lower + + align:start position:0% +written in the black chalk on the lower + + + align:start position:0% +written in the black chalk on the lower +part of this diagonal you see the point0 + + align:start position:0% +part of this diagonal you see the point0 + + + align:start position:0% +part of this diagonal you see the point0 +corresponds to a density of zero so the + + align:start position:0% +corresponds to a density of zero so the + + + align:start position:0% +corresponds to a density of zero so the +lowest possible density is zero in this + + align:start position:0% +lowest possible density is zero in this + + + align:start position:0% +lowest possible density is zero in this +block the2 comma 0 is the closest point + + align:start position:0% +block the2 comma 0 is the closest point + + + align:start position:0% +block the2 comma 0 is the closest point +to the origin in this little square so + + align:start position:0% +to the origin in this little square so + + + align:start position:0% +to the origin in this little square so +x^2 + y^2 in that case is simply 1 122 + + + align:start position:0% +x^2 + y^2 in that case is simply 1 122 + + + + align:start position:0% +x^2 + y^2 in that case is simply 1 122 + +0 squ which is a quarter the closest + + align:start position:0% +0 squ which is a quarter the closest + + + align:start position:0% +0 squ which is a quarter the closest +point here is 1 12 comma 1/2 so if we + + align:start position:0% +point here is 1 12 comma 1/2 so if we + + + align:start position:0% +point here is 1 12 comma 1/2 so if we +Square the coordinates and add we get a + + align:start position:0% +Square the coordinates and add we get a + + + align:start position:0% +Square the coordinates and add we get a +quarter plus a quarter which is a half + + align:start position:0% +quarter plus a quarter which is a half + + + align:start position:0% +quarter plus a quarter which is a half +and in a similar way the lowest density + + align:start position:0% +and in a similar way the lowest density + + + align:start position:0% +and in a similar way the lowest density +in this block is also + + align:start position:0% +in this block is also + + + align:start position:0% +in this block is also +one4 now again using the same argument + + align:start position:0% +one4 now again using the same argument + + + align:start position:0% +one4 now again using the same argument +the point in the first block which is + + align:start position:0% +the point in the first block which is + + + align:start position:0% +the point in the first block which is +further from the origin is 1/2 comma 1/2 + + align:start position:0% +further from the origin is 1/2 comma 1/2 + + + align:start position:0% +further from the origin is 1/2 comma 1/2 +that density corresponds to 1/2 in other + + align:start position:0% +that density corresponds to 1/2 in other + + + align:start position:0% +that density corresponds to 1/2 in other +words a half squ plus a half squar so + + align:start position:0% +words a half squ plus a half squar so + + + align:start position:0% +words a half squ plus a half squar so +now putting in the biggest densities in + + align:start position:0% +now putting in the biggest densities in + + + align:start position:0% +now putting in the biggest densities in +each block and carrying out the + + align:start position:0% +each block and carrying out the + + + align:start position:0% +each block and carrying out the +computations in a very trivial way we + + align:start position:0% +computations in a very trivial way we + + + align:start position:0% +computations in a very trivial way we +see that the maximum densities are 1/2 + + align:start position:0% +see that the maximum densities are 1/2 + + + align:start position:0% +see that the maximum densities are 1/2 +here 54s here two here and 54s here okay + + align:start position:0% +here 54s here two here and 54s here okay + + + align:start position:0% +here 54s here two here and 54s here okay +the idea is going to be now that what we + + align:start position:0% +the idea is going to be now that what we + + + align:start position:0% +the idea is going to be now that what we +can now do is we know that the area of + + align:start position:0% +can now do is we know that the area of + + + align:start position:0% +can now do is we know that the area of +each of these pieces is a half by a half + + align:start position:0% +each of these pieces is a half by a half + + + align:start position:0% +each of these pieces is a half by a half +which is is a quarter I will now assume + + align:start position:0% +which is is a quarter I will now assume + + + align:start position:0% +which is is a quarter I will now assume +two different plates one will be the + + align:start position:0% +two different plates one will be the + + + align:start position:0% +two different plates one will be the +plate which has the same shape as this + + align:start position:0% +plate which has the same shape as this + + + align:start position:0% +plate which has the same shape as this +but in this quadrant here has a constant + + align:start position:0% +but in this quadrant here has a constant + + + align:start position:0% +but in this quadrant here has a constant +density of zero in this quadrant here + + align:start position:0% +density of zero in this quadrant here + + + align:start position:0% +density of zero in this quadrant here +has a constant density of a quarter in + + align:start position:0% +has a constant density of a quarter in + + + align:start position:0% +has a constant density of a quarter in +this quadrant here constant density of a + + align:start position:0% +this quadrant here constant density of a + + + align:start position:0% +this quadrant here constant density of a +half and this quadrant a constant + + align:start position:0% +half and this quadrant a constant + + + align:start position:0% +half and this quadrant a constant +density of one qu I can now compute that + + align:start position:0% +density of one qu I can now compute that + + + align:start position:0% +density of one qu I can now compute that +mass and I know that that mass must be + + align:start position:0% +mass and I know that that mass must be + + + align:start position:0% +mass and I know that that mass must be +less than the mass than I'm looking for + + align:start position:0% +less than the mass than I'm looking for + + + align:start position:0% +less than the mass than I'm looking for +because I have picked the lowest + + align:start position:0% +because I have picked the lowest + + + align:start position:0% +because I have picked the lowest +possible density in each quadrant + + align:start position:0% +possible density in each quadrant + + + align:start position:0% +possible density in each quadrant +correspondingly if I now compute the + + align:start position:0% +correspondingly if I now compute the + + + align:start position:0% +correspondingly if I now compute the +mass of another plate which has the same + + align:start position:0% +mass of another plate which has the same + + + align:start position:0% +mass of another plate which has the same +shape but in which each quadrant has the + + align:start position:0% +shape but in which each quadrant has the + + + align:start position:0% +shape but in which each quadrant has the +density of the greatest value of the + + align:start position:0% +density of the greatest value of the + + + align:start position:0% +density of the greatest value of the +density in each quadrant that must give + + align:start position:0% +density in each quadrant that must give + + + align:start position:0% +density in each quadrant that must give +me an over approximation and so my Mass + + align:start position:0% +me an over approximation and so my Mass + + + align:start position:0% +me an over approximation and so my Mass +is cut between these two and just so you + + align:start position:0% +is cut between these two and just so you + + + align:start position:0% +is cut between these two and just so you +get an idea of what this notation means + + align:start position:0% +get an idea of what this notation means + + + align:start position:0% +get an idea of what this notation means +notice that Delta a sub i j in this case + + align:start position:0% +notice that Delta a sub i j in this case + + + align:start position:0% +notice that Delta a sub i j in this case +is 1 qu for I = 1 2 and Jal 1 and 2 in + + align:start position:0% +is 1 qu for I = 1 2 and Jal 1 and 2 in + + + align:start position:0% +is 1 qu for I = 1 2 and Jal 1 and 2 in +other words our four elements of area + + align:start position:0% +other words our four elements of area + + + align:start position:0% +other words our four elements of area +are a sub1 one a sub12 a sub uh 21 a sub + + align:start position:0% +are a sub1 one a sub12 a sub uh 21 a sub + + + align:start position:0% +are a sub1 one a sub12 a sub uh 21 a sub +22 where if you want to do these in + + align:start position:0% +22 where if you want to do these in + + + align:start position:0% +22 where if you want to do these in +order just let I be one and two here J + + align:start position:0% +order just let I be one and two here J + + + align:start position:0% +order just let I be one and two here J +be one and two here for example the den + + align:start position:0% +be one and two here for example the den + + + align:start position:0% +be one and two here for example the den +the maximum density in the first row + + align:start position:0% +the maximum density in the first row + + + align:start position:0% +the maximum density in the first row +second column well I'm I'm reading these + + align:start position:0% +second column well I'm I'm reading these + + + align:start position:0% +second column well I'm I'm reading these +the wrong way here the J first row + + align:start position:0% +the wrong way here the J first row + + + align:start position:0% +the wrong way here the J first row +second column up this way is 54s the + + align:start position:0% +second column up this way is 54s the + + + align:start position:0% +second column up this way is 54s the +minimum density in that same column in + + align:start position:0% +minimum density in that same column in + + + align:start position:0% +minimum density in that same column in +that same quadrant is 1/4 Etc at any + + align:start position:0% +that same quadrant is 1/4 Etc at any + + + align:start position:0% +that same quadrant is 1/4 Etc at any +rate what I'm saying is if I now take + + align:start position:0% +rate what I'm saying is if I now take + + + align:start position:0% +rate what I'm saying is if I now take +the fact that for constant density the + + align:start position:0% +the fact that for constant density the + + + align:start position:0% +the fact that for constant density the +mass is the density times the area a + + align:start position:0% +mass is the density times the area a + + + align:start position:0% +mass is the density times the area a +lower approximation to my Mass is + + align:start position:0% +lower approximation to my Mass is + + + align:start position:0% +lower approximation to my Mass is +obtained by adding up all of my constant + + align:start position:0% +obtained by adding up all of my constant + + + align:start position:0% +obtained by adding up all of my constant +densities and multiplying by the area in + + align:start position:0% +densities and multiplying by the area in + + + align:start position:0% +densities and multiplying by the area in +other words 0 * a quarter plus a quar + + align:start position:0% +other words 0 * a quarter plus a quar + + + align:start position:0% +other words 0 * a quarter plus a quar +time a quar plus a half time a quarter + + align:start position:0% +time a quar plus a half time a quarter + + + align:start position:0% +time a quar plus a half time a quarter +plus a quar times a quarter that sum + + align:start position:0% +plus a quar times a quarter that sum + + + align:start position:0% +plus a quar times a quarter that sum +comes out to be one quarter + + align:start position:0% +comes out to be one quarter + + + align:start position:0% +comes out to be one quarter +correspondingly the upper sum is what I + + align:start position:0% +correspondingly the upper sum is what I + + + align:start position:0% +correspondingly the upper sum is what I +get by taking each of the constant + + align:start position:0% +get by taking each of the constant + + + align:start position:0% +get by taking each of the constant +densities and multiplying it by the + + align:start position:0% +densities and multiplying it by the + + + align:start position:0% +densities and multiplying it by the +constant area one quarter that leads to + + align:start position:0% +constant area one quarter that leads to + + + align:start position:0% +constant area one quarter that leads to +a sum of 54s and therefore no matter + + align:start position:0% +a sum of 54s and therefore no matter + + + align:start position:0% +a sum of 54s and therefore no matter +what else I know about the mass of my + + align:start position:0% +what else I know about the mass of my + + + align:start position:0% +what else I know about the mass of my +region R I know that it must be more + + align:start position:0% +region R I know that it must be more + + + align:start position:0% +region R I know that it must be more +than a quarter but less than five + + align:start position:0% +than a quarter but less than five + + + align:start position:0% +than a quarter but less than five +quarters and the idea is that by putting + + align:start position:0% +quarters and the idea is that by putting + + + align:start position:0% +quarters and the idea is that by putting +on the squeeze by making more and more + + align:start position:0% +on the squeeze by making more and more + + + align:start position:0% +on the squeeze by making more and more +subdivisions I can hopefully find the + + align:start position:0% +subdivisions I can hopefully find the + + + align:start position:0% +subdivisions I can hopefully find the +exact value of M subr but finding this + + align:start position:0% +exact value of M subr but finding this + + + align:start position:0% +exact value of M subr but finding this +exact value involves a very very + + align:start position:0% +exact value involves a very very + + + align:start position:0% +exact value involves a very very +difficult computation namely I divide + + align:start position:0% +difficult computation namely I divide + + + align:start position:0% +difficult computation namely I divide +this up into M * n little elements of + + align:start position:0% +this up into M * n little elements of + + + align:start position:0% +this up into M * n little elements of +area I pick a point in each region the + + align:start position:0% +area I pick a point in each region the + + + align:start position:0% +area I pick a point in each region the +density the + + align:start position:0% +density the + + + align:start position:0% +density the +density at a particular point that I've + + align:start position:0% +density at a particular point that I've + + + align:start position:0% +density at a particular point that I've +picked out in that region which I'll + + align:start position:0% +picked out in that region which I'll + + + align:start position:0% +picked out in that region which I'll +call + + align:start position:0% +call + + + align:start position:0% +call +CI comma D J is CI j^ 2 plus d j 2 this + + align:start position:0% +CI comma D J is CI j^ 2 plus d j 2 this + + + align:start position:0% +CI comma D J is CI j^ 2 plus d j 2 this +would give give me + + align:start position:0% +would give give me + + + align:start position:0% +would give give me +the mass of a particular piece and I add + + align:start position:0% +the mass of a particular piece and I add + + + align:start position:0% +the mass of a particular piece and I add +these up as I goes from 1 to n as J goes + + align:start position:0% +these up as I goes from 1 to n as J goes + + + align:start position:0% +these up as I goes from 1 to n as J goes +from 1 to n and take the limit as the + + align:start position:0% +from 1 to n and take the limit as the + + + align:start position:0% +from 1 to n and take the limit as the +maximum Delta x sub I and the maximum + + align:start position:0% +maximum Delta x sub I and the maximum + + + align:start position:0% +maximum Delta x sub I and the maximum +Delta y subj approach zero and this in + + align:start position:0% +Delta y subj approach zero and this in + + + align:start position:0% +Delta y subj approach zero and this in +most cases is very very difficult and in + + align:start position:0% +most cases is very very difficult and in + + + align:start position:0% +most cases is very very difficult and in +fact even in this relatively simple case + + align:start position:0% +fact even in this relatively simple case + + + align:start position:0% +fact even in this relatively simple case +what do I mean by a relatively simple + + align:start position:0% +what do I mean by a relatively simple + + + align:start position:0% +what do I mean by a relatively simple +case in terms of a region what could be + + align:start position:0% +case in terms of a region what could be + + + align:start position:0% +case in terms of a region what could be +more straightforward than our little + + align:start position:0% +more straightforward than our little + + + align:start position:0% +more straightforward than our little +square r that we chose in general uh + + align:start position:0% +square r that we chose in general uh + + + align:start position:0% +square r that we chose in general uh +will have more complicated regions let + + align:start position:0% +will have more complicated regions let + + + align:start position:0% +will have more complicated regions let +me summarize today's lesson essentially + + align:start position:0% +me summarize today's lesson essentially + + + align:start position:0% +me summarize today's lesson essentially +by showing you in particular what we it + + align:start position:0% +by showing you in particular what we it + + + align:start position:0% +by showing you in particular what we it +is that we're talking about in terms of + + align:start position:0% +is that we're talking about in terms of + + + align:start position:0% +is that we're talking about in terms of +double sums namely what we're going to + + align:start position:0% +double sums namely what we're going to + + + align:start position:0% +double sums namely what we're going to +do is we'll assume that R is a + + align:start position:0% +do is we'll assume that R is a + + + align:start position:0% +do is we'll assume that R is a +reasonable subset of two-dimensional + + align:start position:0% +reasonable subset of two-dimensional + + + align:start position:0% +reasonable subset of two-dimensional +space and by reasonable I mean that it's + + align:start position:0% +space and by reasonable I mean that it's + + + align:start position:0% +space and by reasonable I mean that it's +not a kinky type of thing that leads to + + align:start position:0% +not a kinky type of thing that leads to + + + align:start position:0% +not a kinky type of thing that leads to +pathological problems the technical + + align:start position:0% +pathological problems the technical + + + align:start position:0% +pathological problems the technical +words are things like R is Simply + + align:start position:0% +words are things like R is Simply + + + align:start position:0% +words are things like R is Simply +Connected and things like this we'll + + align:start position:0% +Connected and things like this we'll + + + align:start position:0% +Connected and things like this we'll +talk about that more detail what I'm + + align:start position:0% +talk about that more detail what I'm + + + align:start position:0% +talk about that more detail what I'm +saying is let me imagine that R is a + + align:start position:0% +saying is let me imagine that R is a + + + align:start position:0% +saying is let me imagine that R is a +fairly welldefined region in the XY + + align:start position:0% +fairly welldefined region in the XY + + + align:start position:0% +fairly welldefined region in the XY +plane let me assume that I have a + + align:start position:0% +plane let me assume that I have a + + + align:start position:0% +plane let me assume that I have a +mapping F that carries R into e what + + align:start position:0% +mapping F that carries R into e what + + + align:start position:0% +mapping F that carries R into e what +does that mean f is a function a real + + align:start position:0% +does that mean f is a function a real + + + align:start position:0% +does that mean f is a function a real +valued function of two independent + + align:start position:0% +valued function of two independent + + + align:start position:0% +valued function of two independent +variables namely R is a two-dimensional + + align:start position:0% +variables namely R is a two-dimensional + + + align:start position:0% +variables namely R is a two-dimensional +space so a typical element in R is a + + align:start position:0% +space so a typical element in R is a + + + align:start position:0% +space so a typical element in R is a +point is a twole x comma Y and we're + + align:start position:0% +point is a twole x comma Y and we're + + + align:start position:0% +point is a twole x comma Y and we're +saying is that F Maps X comma Y into + + align:start position:0% +saying is that F Maps X comma Y into + + + align:start position:0% +saying is that F Maps X comma Y into +some number remember e E1 if you want to + + align:start position:0% +some number remember e E1 if you want to + + + align:start position:0% +some number remember e E1 if you want to +call it that is the set of real numbers + + align:start position:0% +call it that is the set of real numbers + + + align:start position:0% +call it that is the set of real numbers +so the idea is let's what we can say now + + align:start position:0% +so the idea is let's what we can say now + + + align:start position:0% +so the idea is let's what we can say now +is this let's take this region R let's + + align:start position:0% +is this let's take this region R let's + + + align:start position:0% +is this let's take this region R let's +partition it into a mesh not mesh mesh + + align:start position:0% +partition it into a mesh not mesh mesh + + + align:start position:0% +partition it into a mesh not mesh mesh +of little rectangles here let's in the + + align:start position:0% +of little rectangles here let's in the + + + align:start position:0% +of little rectangles here let's in the +IJ rectangle namely the rectangle whose + + align:start position:0% +IJ rectangle namely the rectangle whose + + + align:start position:0% +IJ rectangle namely the rectangle whose +dimensions are Delta XI by Delta y j + + align:start position:0% +dimensions are Delta XI by Delta y j + + + align:start position:0% +dimensions are Delta XI by Delta y j +let's pick a particular Point see and to + + align:start position:0% +let's pick a particular Point see and to + + + align:start position:0% +let's pick a particular Point see and to +identify it call it cbig J comma d sub J + + align:start position:0% +identify it call it cbig J comma d sub J + + + align:start position:0% +identify it call it cbig J comma d sub J +let's compute F at that point all right + + align:start position:0% +let's compute F at that point all right + + + align:start position:0% +let's compute F at that point all right +then we'll compute ftimes this area and + + align:start position:0% +then we'll compute ftimes this area and + + + align:start position:0% +then we'll compute ftimes this area and +we'll sum this thing up as I goes from 1 + + align:start position:0% +we'll sum this thing up as I goes from 1 + + + align:start position:0% +we'll sum this thing up as I goes from 1 +to n and J goes from 1 to n m and we're + + align:start position:0% +to n and J goes from 1 to n m and we're + + + align:start position:0% +to n and J goes from 1 to n m and we're +going to take a limit as this partition + + align:start position:0% +going to take a limit as this partition + + + align:start position:0% +going to take a limit as this partition +gets as fine as we wish meaning the size + + align:start position:0% +gets as fine as we wish meaning the size + + + align:start position:0% +gets as fine as we wish meaning the size +of the pieces get arbitrarily close to + + align:start position:0% +of the pieces get arbitrarily close to + + + align:start position:0% +of the pieces get arbitrarily close to +zero in area both in the X and in the y + + align:start position:0% +zero in area both in the X and in the y + + + align:start position:0% +zero in area both in the X and in the y +direction notice by the way that because + + align:start position:0% +direction notice by the way that because + + + align:start position:0% +direction notice by the way that because +this is not a rectangular region pieces + + align:start position:0% +this is not a rectangular region pieces + + + align:start position:0% +this is not a rectangular region pieces +of rectangles are left out and that from + + align:start position:0% +of rectangles are left out and that from + + + align:start position:0% +of rectangles are left out and that from +a computational point of view as you + + align:start position:0% +a computational point of view as you + + + align:start position:0% +a computational point of view as you +make this refinement greater and greater + + align:start position:0% +make this refinement greater and greater + + + align:start position:0% +make this refinement greater and greater +this is why the theory is so voluminous + + align:start position:0% +this is why the theory is so voluminous + + + align:start position:0% +this is why the theory is so voluminous +on this particular type of topic you + + align:start position:0% +on this particular type of topic you + + + align:start position:0% +on this particular type of topic you +must show that you squeezing out all the + + align:start position:0% +must show that you squeezing out all the + + + align:start position:0% +must show that you squeezing out all the +error and things like this but + + align:start position:0% +error and things like this but + + + align:start position:0% +error and things like this but +conceptually all that we're really doing + + align:start position:0% +conceptually all that we're really doing + + + align:start position:0% +conceptually all that we're really doing +here is the following what we do is is + + align:start position:0% +here is the following what we do is is + + + align:start position:0% +here is the following what we do is is +we pick a particular point in a + + align:start position:0% +we pick a particular point in a + + + align:start position:0% +we pick a particular point in a +particular one of these rectangles we + + align:start position:0% +particular one of these rectangles we + + + align:start position:0% +particular one of these rectangles we +evaluate F at that particular point + + align:start position:0% +evaluate F at that particular point + + + align:start position:0% +evaluate F at that particular point +which exists because we're assuming that + + align:start position:0% +which exists because we're assuming that + + + align:start position:0% +which exists because we're assuming that +f is defined on this and if you're + + align:start position:0% +f is defined on this and if you're + + + align:start position:0% +f is defined on this and if you're +having trouble visualizing this F has + + align:start position:0% +having trouble visualizing this F has + + + align:start position:0% +having trouble visualizing this F has +nothing to do with this boundary f is a + + align:start position:0% +nothing to do with this boundary f is a + + + align:start position:0% +nothing to do with this boundary f is a +function which Maps each point into a + + align:start position:0% +function which Maps each point into a + + + align:start position:0% +function which Maps each point into a +number so graphically you can think of f + + align:start position:0% +number so graphically you can think of f + + + align:start position:0% +number so graphically you can think of f +as being a surface here namely if we map + + align:start position:0% +as being a surface here namely if we map + + + align:start position:0% +as being a surface here namely if we map +if we visualize F ofx comma y as being + + align:start position:0% +if we visualize F ofx comma y as being + + + align:start position:0% +if we visualize F ofx comma y as being +mapped with respect to the z-axis we + + align:start position:0% +mapped with respect to the z-axis we + + + align:start position:0% +mapped with respect to the z-axis we +have a surface coming out here and in a + + align:start position:0% +have a surface coming out here and in a + + + align:start position:0% +have a surface coming out here and in a +sense what we're really trying to do is + + align:start position:0% +sense what we're really trying to do is + + + align:start position:0% +sense what we're really trying to do is +to find an approximation for the volume + + align:start position:0% +to find an approximation for the volume + + + align:start position:0% +to find an approximation for the volume +of the region cut off by this cylinder + + align:start position:0% +of the region cut off by this cylinder + + + align:start position:0% +of the region cut off by this cylinder +and whose top is the particular surface + + align:start position:0% +and whose top is the particular surface + + + align:start position:0% +and whose top is the particular surface +zal f ofx y but forgetting about that + + align:start position:0% +zal f ofx y but forgetting about that + + + align:start position:0% +zal f ofx y but forgetting about that +for the time being mechanically all we + + align:start position:0% +for the time being mechanically all we + + + align:start position:0% +for the time being mechanically all we +do is we form this particular double sum + + align:start position:0% +do is we form this particular double sum + + + align:start position:0% +do is we form this particular double sum +we form this double sum and now I've put + + align:start position:0% +we form this double sum and now I've put + + + align:start position:0% +we form this double sum and now I've put +the brackets in here to emphasize that + + align:start position:0% +the brackets in here to emphasize that + + + align:start position:0% +the brackets in here to emphasize that +what this says is you first pick a fixed + + align:start position:0% +what this says is you first pick a fixed + + + align:start position:0% +what this says is you first pick a fixed +value of J and sum this over all I from + + align:start position:0% +value of J and sum this over all I from + + + align:start position:0% +value of J and sum this over all I from +1 to n and when you're all through with + + align:start position:0% +1 to n and when you're all through with + + + align:start position:0% +1 to n and when you're all through with +that the I know longer appears you have + + align:start position:0% +that the I know longer appears you have + + + align:start position:0% +that the I know longer appears you have +a something that depends only on J and + + align:start position:0% +a something that depends only on J and + + + align:start position:0% +a something that depends only on J and +you now do what sum this result up over + + align:start position:0% +you now do what sum this result up over + + + align:start position:0% +you now do what sum this result up over +all values of J as J goes from 1 to M + + align:start position:0% +all values of J as J goes from 1 to M + + + align:start position:0% +all values of J as J goes from 1 to M +and you then compute the limit as the + + align:start position:0% +and you then compute the limit as the + + + align:start position:0% +and you then compute the limit as the +maximum Delta XI and maximum Delta YJ + + align:start position:0% +maximum Delta XI and maximum Delta YJ + + + align:start position:0% +maximum Delta XI and maximum Delta YJ +both approach zero now first of all this + + align:start position:0% +both approach zero now first of all this + + + align:start position:0% +both approach zero now first of all this +limit may not exist secondly the limit + + align:start position:0% +limit may not exist secondly the limit + + + align:start position:0% +limit may not exist secondly the limit +may exist but it depends on the order in + + align:start position:0% +may exist but it depends on the order in + + + align:start position:0% +may exist but it depends on the order in +which you're adding these terms if after + + align:start position:0% +which you're adding these terms if after + + + align:start position:0% +which you're adding these terms if after +all we saw that we could change the sum + + align:start position:0% +all we saw that we could change the sum + + + align:start position:0% +all we saw that we could change the sum +of a simple infinite series by changing + + align:start position:0% +of a simple infinite series by changing + + + align:start position:0% +of a simple infinite series by changing +the order of the term terms certainly it + + align:start position:0% +the order of the term terms certainly it + + + align:start position:0% +the order of the term terms certainly it +shouldn't be surprising that an infinite + + align:start position:0% +shouldn't be surprising that an infinite + + + align:start position:0% +shouldn't be surprising that an infinite +double double sum isn't affected or is + + align:start position:0% +double double sum isn't affected or is + + + align:start position:0% +double double sum isn't affected or is +affected it shouldn't be surprising that + + align:start position:0% +affected it shouldn't be surprising that + + + align:start position:0% +affected it shouldn't be surprising that +it is affected if we change the order of + + align:start position:0% +it is affected if we change the order of + + + align:start position:0% +it is affected if we change the order of +the terms so we have one of two ways of + + align:start position:0% +the terms so we have one of two ways of + + + align:start position:0% +the terms so we have one of two ways of +doing this in terms of being + + align:start position:0% +doing this in terms of being + + + align:start position:0% +doing this in terms of being +systematized do we first summon terms of + + align:start position:0% +systematized do we first summon terms of + + + align:start position:0% +systematized do we first summon terms of +the x's and then add up the the Y + + align:start position:0% +the x's and then add up the the Y + + + align:start position:0% +the x's and then add up the the Y +increments or the other way around the + + align:start position:0% +increments or the other way around the + + + align:start position:0% +increments or the other way around the +key result is this though it's that this + + align:start position:0% +key result is this though it's that this + + + align:start position:0% +key result is this though it's that this +particular limit will exist and it will + + align:start position:0% +particular limit will exist and it will + + + align:start position:0% +particular limit will exist and it will +be independent of what order you add + + align:start position:0% +be independent of what order you add + + + align:start position:0% +be independent of what order you add +these in provided only that the function + + align:start position:0% +these in provided only that the function + + + align:start position:0% +these in provided only that the function +f is at least piecewise continuous it + + align:start position:0% +f is at least piecewise continuous it + + + align:start position:0% +f is at least piecewise continuous it +can in other words that f is a + + align:start position:0% +can in other words that f is a + + + align:start position:0% +can in other words that f is a +continuous function and if it's not + + align:start position:0% +continuous function and if it's not + + + align:start position:0% +continuous function and if it's not +continuous it has breaks at only a + + align:start position:0% +continuous it has breaks at only a + + + align:start position:0% +continuous it has breaks at only a +finite number of places and the idea is + + align:start position:0% +finite number of places and the idea is + + + align:start position:0% +finite number of places and the idea is +that not only will this limit exist but + + align:start position:0% +that not only will this limit exist but + + + align:start position:0% +that not only will this limit exist but +in a manner analogous to the definite + + align:start position:0% +in a manner analogous to the definite + + + align:start position:0% +in a manner analogous to the definite +integral when this limit exists we + + align:start position:0% +integral when this limit exists we + + + align:start position:0% +integral when this limit exists we +denote it by what we replace this by X + + align:start position:0% +denote it by what we replace this by X + + + align:start position:0% +denote it by what we replace this by X +and Y this gets replaced by DX and Dy + + align:start position:0% +and Y this gets replaced by DX and Dy + + + align:start position:0% +and Y this gets replaced by DX and Dy +and the double sum gets replaced by a + + align:start position:0% +and the double sum gets replaced by a + + + align:start position:0% +and the double sum gets replaced by a +double integral and what we now do is + + align:start position:0% +double integral and what we now do is + + + align:start position:0% +double integral and what we now do is +indicate what the region R is over here + + align:start position:0% +indicate what the region R is over here + + + align:start position:0% +indicate what the region R is over here +in other words in terms of a summary + + align:start position:0% +in other words in terms of a summary + + + align:start position:0% +in other words in terms of a summary +whenever I write + + align:start position:0% +whenever I write + + + align:start position:0% +whenever I write +down this + + align:start position:0% +down this + + + align:start position:0% +down this +expression it's an abbreviation for a + + align:start position:0% +expression it's an abbreviation for a + + + align:start position:0% +expression it's an abbreviation for a +limit of a double sum and what limit of + + align:start position:0% +limit of a double sum and what limit of + + + align:start position:0% +limit of a double sum and what limit of +a double sum is it it's the particular + + align:start position:0% +a double sum is it it's the particular + + + align:start position:0% +a double sum is it it's the particular +limit of this double sum if it exists + + align:start position:0% +limit of this double sum if it exists + + + align:start position:0% +limit of this double sum if it exists +and that limit will exist if f is pie y + + align:start position:0% +and that limit will exist if f is pie y + + + align:start position:0% +and that limit will exist if f is pie y +continuous now the key point that I want + + align:start position:0% +continuous now the key point that I want + + + align:start position:0% +continuous now the key point that I want +to bring out here and in fact this will + + align:start position:0% +to bring out here and in fact this will + + + align:start position:0% +to bring out here and in fact this will +lead into the lecture of next time also + + align:start position:0% +lead into the lecture of next time also + + + align:start position:0% +lead into the lecture of next time also +is that if I had never heard of partial + + align:start position:0% +is that if I had never heard of partial + + + align:start position:0% +is that if I had never heard of partial +derivatives it makes sense to talk about + + align:start position:0% +derivatives it makes sense to talk about + + + align:start position:0% +derivatives it makes sense to talk about +this kind of a sum in other words note + + align:start position:0% +this kind of a sum in other words note + + + align:start position:0% +this kind of a sum in other words note +that forming this limit does not require + + align:start position:0% +that forming this limit does not require + + + align:start position:0% +that forming this limit does not require +any knowledge of partial derivatives in + + align:start position:0% +any knowledge of partial derivatives in + + + align:start position:0% +any knowledge of partial derivatives in +the same way that finding infinite sums + + align:start position:0% +the same way that finding infinite sums + + + align:start position:0% +the same way that finding infinite sums +in calculus one could be done + + align:start position:0% +in calculus one could be done + + + align:start position:0% +in calculus one could be done +independently of any knowledge of the + + align:start position:0% +independently of any knowledge of the + + + align:start position:0% +independently of any knowledge of the +derivative this particular concept this + + align:start position:0% +derivative this particular concept this + + + align:start position:0% +derivative this particular concept this +particular limit makes sense even if + + align:start position:0% +particular limit makes sense even if + + + align:start position:0% +particular limit makes sense even if +we've never heard of partial derivatives + + align:start position:0% +we've never heard of partial derivatives + + + align:start position:0% +we've never heard of partial derivatives +and what what does this double sum + + align:start position:0% +and what what does this double sum + + + align:start position:0% +and what what does this double sum +represent just by way of a of a quick + + align:start position:0% +represent just by way of a of a quick + + + align:start position:0% +represent just by way of a of a quick +summary again there are two very + + align:start position:0% +summary again there are two very + + + align:start position:0% +summary again there are two very +specific physical interpretations we can + + align:start position:0% +specific physical interpretations we can + + + align:start position:0% +specific physical interpretations we can +give this one is that this double sum + + align:start position:0% +give this one is that this double sum + + + align:start position:0% +give this one is that this double sum +represents the density of the plate + + align:start position:0% +represents the density of the plate + + + align:start position:0% +represents the density of the plate +whose shape is the region I the mass of + + align:start position:0% +whose shape is the region I the mass of + + + align:start position:0% +whose shape is the region I the mass of +the plate whose shape is the region R + + align:start position:0% +the plate whose shape is the region R + + + align:start position:0% +the plate whose shape is the region R +and whose density at the point x comma Y + + align:start position:0% +and whose density at the point x comma Y + + + align:start position:0% +and whose density at the point x comma Y +and R is given by F of XY in other words + + align:start position:0% +and R is given by F of XY in other words + + + align:start position:0% +and R is given by F of XY in other words +this part here controls the density and + + align:start position:0% +this part here controls the density and + + + align:start position:0% +this part here controls the density and +this part here controls the shape of the + + align:start position:0% +this part here controls the shape of the + + + align:start position:0% +this part here controls the shape of the +region a second interpretation is that + + align:start position:0% +region a second interpretation is that + + + align:start position:0% +region a second interpretation is that +this limit when it exists represents the + + align:start position:0% +this limit when it exists represents the + + + align:start position:0% +this limit when it exists represents the +volume of the right cylinder that means + + align:start position:0% +volume of the right cylinder that means + + + align:start position:0% +volume of the right cylinder that means +a cylinder that's obtained by tracing + + align:start position:0% +a cylinder that's obtained by tracing + + + align:start position:0% +a cylinder that's obtained by tracing +over the region r with a line + + align:start position:0% +over the region r with a line + + + align:start position:0% +over the region r with a line +perpendicular to the XY plane that + + align:start position:0% +perpendicular to the XY plane that + + + align:start position:0% +perpendicular to the XY plane that +particular cylinder whose top is the + + align:start position:0% +particular cylinder whose top is the + + + align:start position:0% +particular cylinder whose top is the +surface zal f of XY other words here are + + align:start position:0% +surface zal f of XY other words here are + + + align:start position:0% +surface zal f of XY other words here are +then the two interpretations that we + + align:start position:0% +then the two interpretations that we + + + align:start position:0% +then the two interpretations that we +give this one is it can be a mass the + + align:start position:0% +give this one is it can be a mass the + + + align:start position:0% +give this one is it can be a mass the +other is it can be a volume the key + + align:start position:0% +other is it can be a volume the key + + + align:start position:0% +other is it can be a volume the key +point is that to evaluate these double + + align:start position:0% +point is that to evaluate these double + + + align:start position:0% +point is that to evaluate these double +sums these limits of double sums or if + + align:start position:0% +sums these limits of double sums or if + + + align:start position:0% +sums these limits of double sums or if +you want to call them infinite double + + align:start position:0% +you want to call them infinite double + + + align:start position:0% +you want to call them infinite double +sums there is no necessity for knowing + + align:start position:0% +sums there is no necessity for knowing + + + align:start position:0% +sums there is no necessity for knowing +partial derivatives however one might + + align:start position:0% +partial derivatives however one might + + + align:start position:0% +partial derivatives however one might +expect that in the same way that there + + align:start position:0% +expect that in the same way that there + + + align:start position:0% +expect that in the same way that there +was a connection between single infinite + + align:start position:0% +was a connection between single infinite + + + align:start position:0% +was a connection between single infinite +sums and ordinary anti-derivatives there + + align:start position:0% +sums and ordinary anti-derivatives there + + + align:start position:0% +sums and ordinary anti-derivatives there +should be a connection between double or + + align:start position:0% +should be a connection between double or + + + align:start position:0% +should be a connection between double or +multiple sums and anti-derivatives of + + align:start position:0% +multiple sums and anti-derivatives of + + + align:start position:0% +multiple sums and anti-derivatives of +partial well well the anti-derivative + + align:start position:0% +partial well well the anti-derivative + + + align:start position:0% +partial well well the anti-derivative +involving partial derivatives it turns + + align:start position:0% +involving partial derivatives it turns + + + align:start position:0% +involving partial derivatives it turns +out that this is indeed the case we will + + align:start position:0% +out that this is indeed the case we will + + + align:start position:0% +out that this is indeed the case we will +talk about this in more detail next time + + align:start position:0% +talk about this in more detail next time + + + align:start position:0% +talk about this in more detail next time +but between now and next time what I + + align:start position:0% +but between now and next time what I + + + align:start position:0% +but between now and next time what I +would like you to do is to drill + + align:start position:0% +would like you to do is to drill + + + align:start position:0% +would like you to do is to drill +particularly hard on these exercises and + + align:start position:0% +particularly hard on these exercises and + + + align:start position:0% +particularly hard on these exercises and +make sure that you become familiar and + + align:start position:0% +make sure that you become familiar and + + + align:start position:0% +make sure that you become familiar and +feel at home with the notation that's + + align:start position:0% +feel at home with the notation that's + + + align:start position:0% +feel at home with the notation that's +used in denoting double and other + + align:start position:0% +used in denoting double and other + + + align:start position:0% +used in denoting double and other +multiple sums at any rate then until + + align:start position:0% +multiple sums at any rate then until + + + align:start position:0% +multiple sums at any rate then until +next time + + align:start position:0% + + + + align:start position:0% + +goodbye funding for the publication of + + align:start position:0% +goodbye funding for the publication of + + + align:start position:0% +goodbye funding for the publication of +this video was provided by the Gabriella + + align:start position:0% +this video was provided by the Gabriella + + + align:start position:0% +this video was provided by the Gabriella +and Paul rosenbom + + align:start position:0% +and Paul rosenbom + + + align:start position:0% +and Paul rosenbom +foundation help ocw continue to provide + + align:start position:0% +foundation help ocw continue to provide + + + align:start position:0% +foundation help ocw continue to provide +free and open access to MIT courses by + + align:start position:0% +free and open access to MIT courses by + + + align:start position:0% +free and open access to MIT courses by +making a donation at ocw.mit.edu/donate \ No newline at end of file diff --git a/DCcPG4aS5I0.txt b/DCcPG4aS5I0.txt new file mode 100644 index 0000000000000000000000000000000000000000..788ea8db257f77d7357fd322335038f0e0897351 --- /dev/null +++ b/DCcPG4aS5I0.txt @@ -0,0 +1,1323 @@ +align:start position:0% + +so far we've only considered optimizing + + align:start position:0% +so far we've only considered optimizing + + + align:start position:0% +so far we've only considered optimizing +the fares for a single route in this + + align:start position:0% +the fares for a single route in this + + + align:start position:0% +the fares for a single route in this +video we'll change our optimization + + align:start position:0% +video we'll change our optimization + + + align:start position:0% +video we'll change our optimization +formulation to include connecting + + align:start position:0% +formulation to include connecting + + + align:start position:0% +formulation to include connecting +flights now instead of just being able + + align:start position:0% +flights now instead of just being able + + + align:start position:0% +flights now instead of just being able +to go from JFK and New York to LAX in + + align:start position:0% +to go from JFK and New York to LAX in + + + align:start position:0% +to go from JFK and New York to LAX in +Los Angeles let's suppose that the plane + + align:start position:0% +Los Angeles let's suppose that the plane + + + align:start position:0% +Los Angeles let's suppose that the plane +stops in Dallas at the Dallas Fort Worth + + align:start position:0% +stops in Dallas at the Dallas Fort Worth + + + align:start position:0% +stops in Dallas at the Dallas Fort Worth +Airport we still are just using one + + align:start position:0% +Airport we still are just using one + + + align:start position:0% +Airport we still are just using one +plane but the passengers can now fly + + align:start position:0% +plane but the passengers can now fly + + + align:start position:0% +plane but the passengers can now fly +from New York to Dallas Dallas to Los + + align:start position:0% +from New York to Dallas Dallas to Los + + + align:start position:0% +from New York to Dallas Dallas to Los +Angeles or from New York to Los Angeles + + align:start position:0% +Angeles or from New York to Los Angeles + + + align:start position:0% +Angeles or from New York to Los Angeles +by just staying on the plane in Dallas + + align:start position:0% +by just staying on the plane in Dallas + + + align:start position:0% +by just staying on the plane in Dallas +so how does our optimization problem + + align:start position:0% +so how does our optimization problem + + + align:start position:0% +so how does our optimization problem +change we now have six types of seats + + align:start position:0% +change we now have six types of seats + + + align:start position:0% +change we now have six types of seats +that we can offer the original two types + + align:start position:0% +that we can offer the original two types + + + align:start position:0% +that we can offer the original two types +regular and discount from New York to LA + + align:start position:0% +regular and discount from New York to LA + + + align:start position:0% +regular and discount from New York to LA +and four new types we can sell both + + align:start position:0% +and four new types we can sell both + + + align:start position:0% +and four new types we can sell both +regular and discount seats from New York + + align:start position:0% +regular and discount seats from New York + + + align:start position:0% +regular and discount seats from New York +to Dallas and regular and discount seats + + align:start position:0% +to Dallas and regular and discount seats + + + align:start position:0% +to Dallas and regular and discount seats +from Dallas to Los Angeles we know the + + align:start position:0% +from Dallas to Los Angeles we know the + + + align:start position:0% +from Dallas to Los Angeles we know the +price of each type of ticket as well as + + align:start position:0% +price of each type of ticket as well as + + + align:start position:0% +price of each type of ticket as well as +the forecasted demand for each type of + + align:start position:0% +the forecasted demand for each type of + + + align:start position:0% +the forecasted demand for each type of +ticket we also know that we have a + + align:start position:0% +ticket we also know that we have a + + + align:start position:0% +ticket we also know that we have a +capacity of 166 seats on our plane for + + align:start position:0% +capacity of 166 seats on our plane for + + + align:start position:0% +capacity of 166 seats on our plane for +each leg of the trip there's room for + + align:start position:0% +each leg of the trip there's room for + + + align:start position:0% +each leg of the trip there's room for +166 passengers on the plane from New + + align:start position:0% +166 passengers on the plane from New + + + align:start position:0% +166 passengers on the plane from New +York to Dallas or the first leg of the + + align:start position:0% +York to Dallas or the first leg of the + + + align:start position:0% +York to Dallas or the first leg of the +trip then the passengers with a final + + align:start position:0% +trip then the passengers with a final + + + align:start position:0% +trip then the passengers with a final +destination of Dallas will get off the + + align:start position:0% +destination of Dallas will get off the + + + align:start position:0% +destination of Dallas will get off the +plane and the passengers flying from + + align:start position:0% +plane and the passengers flying from + + + align:start position:0% +plane and the passengers flying from +Dallas to LA will get on the plane on + + align:start position:0% +Dallas to LA will get on the plane on + + + align:start position:0% +Dallas to LA will get on the plane on +the second leg of the trip flying from + + align:start position:0% +the second leg of the trip flying from + + + align:start position:0% +the second leg of the trip flying from +Dallas to LA we also have a capacity of + + align:start position:0% +Dallas to LA we also have a capacity of + + + align:start position:0% +Dallas to LA we also have a capacity of +166 seats so we need to remember that + + align:start position:0% +166 seats so we need to remember that + + + align:start position:0% +166 seats so we need to remember that +the passengers flying from New York to + + align:start position:0% +the passengers flying from New York to + + + align:start position:0% +the passengers flying from New York to +LA will take up capacity on both legs of + + align:start position:0% +LA will take up capacity on both legs of + + + align:start position:0% +LA will take up capacity on both legs of +the trip while the other types of + + align:start position:0% +the trip while the other types of + + + align:start position:0% +the trip while the other types of +passengers will only take up capacity on + + align:start position:0% +passengers will only take up capacity on + + + align:start position:0% +passengers will only take up capacity on +one leg of the trip so what are our + + align:start position:0% +one leg of the trip so what are our + + + align:start position:0% +one leg of the trip so what are our +decisions now there the number of + + align:start position:0% +decisions now there the number of + + + align:start position:0% +decisions now there the number of +regular tickets to sell for each type + + align:start position:0% +regular tickets to sell for each type + + + align:start position:0% +regular tickets to sell for each type +and the number of discount tickets to + + align:start position:0% +and the number of discount tickets to + + + align:start position:0% +and the number of discount tickets to +sell for each type so in total we have + + align:start position:0% +sell for each type so in total we have + + + align:start position:0% +sell for each type so in total we have +six + + align:start position:0% +six + + + align:start position:0% +six +decisions to make now let's define our + + align:start position:0% +decisions to make now let's define our + + + align:start position:0% +decisions to make now let's define our +objective like before it's to maximize + + align:start position:0% +objective like before it's to maximize + + + align:start position:0% +objective like before it's to maximize +the total revenue this is the sum of the + + align:start position:0% +the total revenue this is the sum of the + + + align:start position:0% +the total revenue this is the sum of the +price of the ticket times the number of + + align:start position:0% +price of the ticket times the number of + + + align:start position:0% +price of the ticket times the number of +seats of that type we sell for each type + + align:start position:0% +seats of that type we sell for each type + + + align:start position:0% +seats of that type we sell for each type +of ticket and like before we have two + + align:start position:0% +of ticket and like before we have two + + + align:start position:0% +of ticket and like before we have two +types of constraints capacity + + align:start position:0% +types of constraints capacity + + + align:start position:0% +types of constraints capacity +constraints and demand constraints for + + align:start position:0% +constraints and demand constraints for + + + align:start position:0% +constraints and demand constraints for +the capacity constraints the airline + + align:start position:0% +the capacity constraints the airline + + + align:start position:0% +the capacity constraints the airline +shouldn't sell more seats than the + + align:start position:0% +shouldn't sell more seats than the + + + align:start position:0% +shouldn't sell more seats than the +capacity of the plane for each leg of + + align:start position:0% +capacity of the plane for each leg of + + + align:start position:0% +capacity of the plane for each leg of +the trip so we need two capacity + + align:start position:0% +the trip so we need two capacity + + + align:start position:0% +the trip so we need two capacity +constraints here one for the New York to + + align:start position:0% +constraints here one for the New York to + + + align:start position:0% +constraints here one for the New York to +Dallas leg and one for the Dallas to LA + + align:start position:0% +Dallas leg and one for the Dallas to LA + + + align:start position:0% +Dallas leg and one for the Dallas to LA +leg note that the New York to LA + + align:start position:0% +leg note that the New York to LA + + + align:start position:0% +leg note that the New York to LA +passengers have to be counted on both + + align:start position:0% +passengers have to be counted on both + + + align:start position:0% +passengers have to be counted on both +legs of the trip so the first constraint + + align:start position:0% +legs of the trip so the first constraint + + + align:start position:0% +legs of the trip so the first constraint +accounts for all passengers that need to + + align:start position:0% +accounts for all passengers that need to + + + align:start position:0% +accounts for all passengers that need to +be on the plane when it flies from New + + align:start position:0% +be on the plane when it flies from New + + + align:start position:0% +be on the plane when it flies from New +York to Dallas and the second constraint + + align:start position:0% +York to Dallas and the second constraint + + + align:start position:0% +York to Dallas and the second constraint +accounts for all passengers that need to + + align:start position:0% +accounts for all passengers that need to + + + align:start position:0% +accounts for all passengers that need to +be on the plane when it flies from + + align:start position:0% +be on the plane when it flies from + + + align:start position:0% +be on the plane when it flies from +Dallas to LA we also need six demand + + align:start position:0% +Dallas to LA we also need six demand + + + align:start position:0% +Dallas to LA we also need six demand +constraints one for each type of ticket + + align:start position:0% +constraints one for each type of ticket + + + align:start position:0% +constraints one for each type of ticket +the number of seats sold should not + + align:start position:0% +the number of seats sold should not + + + align:start position:0% +the number of seats sold should not +exceed the forecasted demand for each + + align:start position:0% +exceed the forecasted demand for each + + + align:start position:0% +exceed the forecasted demand for each +type and lastly we can't sell a negative + + align:start position:0% +type and lastly we can't sell a negative + + + align:start position:0% +type and lastly we can't sell a negative +number of seats so we have our non + + align:start position:0% +number of seats so we have our non + + + align:start position:0% +number of seats so we have our non +negativity constraints to prevent the + + align:start position:0% +negativity constraints to prevent the + + + align:start position:0% +negativity constraints to prevent the +variables from being negative let's now + + align:start position:0% +variables from being negative let's now + + + align:start position:0% +variables from being negative let's now +go to Libre Office and adjust our + + align:start position:0% +go to Libre Office and adjust our + + + align:start position:0% +go to Libre Office and adjust our +formulation to solve this bigger problem + + align:start position:0% +formulation to solve this bigger problem + + + align:start position:0% +formulation to solve this bigger problem +in libreoffice go ahead and open the + + align:start position:0% +in libreoffice go ahead and open the + + + align:start position:0% +in libreoffice go ahead and open the +file week 9 airline RM connecting ODS in + + align:start position:0% +file week 9 airline RM connecting ODS in + + + align:start position:0% +file week 9 airline RM connecting ODS in +this file i've set up our data our + + align:start position:0% +this file i've set up our data our + + + align:start position:0% +this file i've set up our data our +decisions our objective and our + + align:start position:0% +decisions our objective and our + + + align:start position:0% +decisions our objective and our +constraints our decisions again are + + align:start position:0% +constraints our decisions again are + + + align:start position:0% +constraints our decisions again are +highlighted in yellow we have a decision + + align:start position:0% +highlighted in yellow we have a decision + + + align:start position:0% +highlighted in yellow we have a decision +for each type of seat on each flight our + + align:start position:0% +for each type of seat on each flight our + + + align:start position:0% +for each type of seat on each flight our +objective here is the spot in blue to + + align:start position:0% +objective here is the spot in blue to + + + align:start position:0% +objective here is the spot in blue to +build our objective will use the + + align:start position:0% +build our objective will use the + + + align:start position:0% +build our objective will use the +sum-product function so type equals and + + align:start position:0% +sum-product function so type equals and + + + align:start position:0% +sum-product function so type equals and +then sum product and in parentheses + + align:start position:0% +then sum product and in parentheses + + + align:start position:0% +then sum product and in parentheses +select all six prices type a semicolon + + align:start position:0% +select all six prices type a semicolon + + + align:start position:0% +select all six prices type a semicolon +and then select all six decisions close + + align:start position:0% +and then select all six decisions close + + + align:start position:0% +and then select all six decisions close +the parentheses and hit enter we see + + align:start position:0% +the parentheses and hit enter we see + + + align:start position:0% +the parentheses and hit enter we see +here like we did before that we have + + align:start position:0% +here like we did before that we have + + + align:start position:0% +here like we did before that we have +zero and our objective because right now + + align:start position:0% +zero and our objective because right now + + + align:start position:0% +zero and our objective because right now +we're not selling any seats now let's + + align:start position:0% +we're not selling any seats now let's + + + align:start position:0% +we're not selling any seats now let's +create our constraints the first + + align:start position:0% +create our constraints the first + + + align:start position:0% +create our constraints the first +constraints our capacity constraints the + + align:start position:0% +constraints our capacity constraints the + + + align:start position:0% +constraints our capacity constraints the +first is the capacity on the lake from + + align:start position:0% +first is the capacity on the lake from + + + align:start position:0% +first is the capacity on the lake from +New York to Dallas the left hand side + + align:start position:0% +New York to Dallas the left hand side + + + align:start position:0% +New York to Dallas the left hand side +should be equal to the seats from New + + align:start position:0% +should be equal to the seats from New + + + align:start position:0% +should be equal to the seats from New +York to LA plus the seats from New York + + align:start position:0% +York to LA plus the seats from New York + + + align:start position:0% +York to LA plus the seats from New York +to Dallas the sign is less than or + + align:start position:0% +to Dallas the sign is less than or + + + align:start position:0% +to Dallas the sign is less than or +equals and the right hand side is 166 + + align:start position:0% +equals and the right hand side is 166 + + + align:start position:0% +equals and the right hand side is 166 +the capacity of our aircraft now we need + + align:start position:0% +the capacity of our aircraft now we need + + + align:start position:0% +the capacity of our aircraft now we need +to build the capacity constraint from + + align:start position:0% +to build the capacity constraint from + + + align:start position:0% +to build the capacity constraint from +Dallas to LA the left hand side is equal + + align:start position:0% +Dallas to LA the left hand side is equal + + + align:start position:0% +Dallas to LA the left hand side is equal +to the seats from New York to LA plus + + align:start position:0% +to the seats from New York to LA plus + + + align:start position:0% +to the seats from New York to LA plus +the seats from Dallas to LA our sign is + + align:start position:0% +the seats from Dallas to LA our sign is + + + align:start position:0% +the seats from Dallas to LA our sign is +again less than or equals and our right + + align:start position:0% +again less than or equals and our right + + + align:start position:0% +again less than or equals and our right +hand side is 166 for the demand + + align:start position:0% +hand side is 166 for the demand + + + align:start position:0% +hand side is 166 for the demand +constraints and the non negativity + + align:start position:0% +constraints and the non negativity + + + align:start position:0% +constraints and the non negativity +constraints because we have six of each + + align:start position:0% +constraints because we have six of each + + + align:start position:0% +constraints because we have six of each +this time will actually make them in a + + align:start position:0% +this time will actually make them in a + + + align:start position:0% +this time will actually make them in a +more efficient way than before so we + + align:start position:0% +more efficient way than before so we + + + align:start position:0% +more efficient way than before so we +just have a note down there that we need + + align:start position:0% +just have a note down there that we need + + + align:start position:0% +just have a note down there that we need +to remember to add these constraints so + + align:start position:0% +to remember to add these constraints so + + + align:start position:0% +to remember to add these constraints so +now go ahead and in the Tools menu + + align:start position:0% +now go ahead and in the Tools menu + + + align:start position:0% +now go ahead and in the Tools menu +select solver we need to first fill in + + align:start position:0% +select solver we need to first fill in + + + align:start position:0% +select solver we need to first fill in +the target cell which should be the + + align:start position:0% +the target cell which should be the + + + align:start position:0% +the target cell which should be the +objective make sure that maximum is + + align:start position:0% +objective make sure that maximum is + + + align:start position:0% +objective make sure that maximum is +selected then in the changing cells box + + align:start position:0% +selected then in the changing cells box + + + align:start position:0% +selected then in the changing cells box +select all six decisions down in the + + align:start position:0% +select all six decisions down in the + + + align:start position:0% +select all six decisions down in the +limiting conditions let's now build our + + align:start position:0% +limiting conditions let's now build our + + + align:start position:0% +limiting conditions let's now build our +constraints for the cell reference + + align:start position:0% +constraints for the cell reference + + + align:start position:0% +constraints for the cell reference +column let's start by selecting the left + + align:start position:0% +column let's start by selecting the left + + + align:start position:0% +column let's start by selecting the left +hand side of the two capacity + + align:start position:0% +hand side of the two capacity + + + align:start position:0% +hand side of the two capacity +constraints the operator should be less + + align:start position:0% +constraints the operator should be less + + + align:start position:0% +constraints the operator should be less +than or equals and the value should be + + align:start position:0% +than or equals and the value should be + + + align:start position:0% +than or equals and the value should be +the right-hand side of these two + + align:start position:0% +the right-hand side of these two + + + align:start position:0% +the right-hand side of these two +capacity constraints now let's make the + + align:start position:0% +capacity constraints now let's make the + + + align:start position:0% +capacity constraints now let's make the +demand constraints in cell reference + + align:start position:0% +demand constraints in cell reference + + + align:start position:0% +demand constraints in cell reference +just directly select the six decision + + align:start position:0% +just directly select the six decision + + + align:start position:0% +just directly select the six decision +variables make sure the operators less + + align:start position:0% +variables make sure the operators less + + + align:start position:0% +variables make sure the operators less +than or equals and for the value select + + align:start position:0% +than or equals and for the value select + + + align:start position:0% +than or equals and for the value select +the six demand constraints this was a + + align:start position:0% +the six demand constraints this was a + + + align:start position:0% +the six demand constraints this was a +bit easier + + align:start position:0% +bit easier + + + align:start position:0% +bit easier +than what we did before because we + + align:start position:0% +than what we did before because we + + + align:start position:0% +than what we did before because we +didn't have to type them all out in our + + align:start position:0% +didn't have to type them all out in our + + + align:start position:0% +didn't have to type them all out in our +spreadsheet now let's do a similar thing + + align:start position:0% +spreadsheet now let's do a similar thing + + + align:start position:0% +spreadsheet now let's do a similar thing +for the non negativity constraints we're + + align:start position:0% +for the non negativity constraints we're + + + align:start position:0% +for the non negativity constraints we're +in cell reference we select the six + + align:start position:0% +in cell reference we select the six + + + align:start position:0% +in cell reference we select the six +decisions the operator this time should + + align:start position:0% +decisions the operator this time should + + + align:start position:0% +decisions the operator this time should +be greater than or equals and for the + + align:start position:0% +be greater than or equals and for the + + + align:start position:0% +be greater than or equals and for the +value just type zero make sure in + + align:start position:0% +value just type zero make sure in + + + align:start position:0% +value just type zero make sure in +options that the linear solver is + + align:start position:0% +options that the linear solver is + + + align:start position:0% +options that the linear solver is +selected and go ahead and hit solve the + + align:start position:0% +selected and go ahead and hit solve the + + + align:start position:0% +selected and go ahead and hit solve the +solving result should say solving + + align:start position:0% +solving result should say solving + + + align:start position:0% +solving result should say solving +successfully finished result a hundred + + align:start position:0% +successfully finished result a hundred + + + align:start position:0% +successfully finished result a hundred +and twenty thousand five hundred and + + align:start position:0% +and twenty thousand five hundred and + + + align:start position:0% +and twenty thousand five hundred and +fourteen this is our total revenue go + + align:start position:0% +fourteen this is our total revenue go + + + align:start position:0% +fourteen this is our total revenue go +ahead and click keep result and let's + + align:start position:0% +ahead and click keep result and let's + + + align:start position:0% +ahead and click keep result and let's +take a look at our solution so we see + + align:start position:0% +take a look at our solution so we see + + + align:start position:0% +take a look at our solution so we see +here that the optimal solution is to + + align:start position:0% +here that the optimal solution is to + + + align:start position:0% +here that the optimal solution is to +sell eighty tickets for the regular + + align:start position:0% +sell eighty tickets for the regular + + + align:start position:0% +sell eighty tickets for the regular +price from New York to LA zero of the + + align:start position:0% +price from New York to LA zero of the + + + align:start position:0% +price from New York to LA zero of the +discount price from New York to LA + + align:start position:0% +discount price from New York to LA + + + align:start position:0% +discount price from New York to LA +seventy five of the regular price from + + align:start position:0% +seventy five of the regular price from + + + align:start position:0% +seventy five of the regular price from +New York to Dallas eleven of the + + align:start position:0% +New York to Dallas eleven of the + + + align:start position:0% +New York to Dallas eleven of the +discount price from New York to Dallas + + align:start position:0% +discount price from New York to Dallas + + + align:start position:0% +discount price from New York to Dallas +sixty of the regular price from Dallas + + align:start position:0% +sixty of the regular price from Dallas + + + align:start position:0% +sixty of the regular price from Dallas +to LA and lastly twenty six of the + + align:start position:0% +to LA and lastly twenty six of the + + + align:start position:0% +to LA and lastly twenty six of the +discount price from Dallas to LA we saw + + align:start position:0% +discount price from Dallas to LA we saw + + + align:start position:0% +discount price from Dallas to LA we saw +here that we could pretty easily solve a + + align:start position:0% +here that we could pretty easily solve a + + + align:start position:0% +here that we could pretty easily solve a +more complicated problem in libreoffice + + align:start position:0% +more complicated problem in libreoffice + + + align:start position:0% +more complicated problem in libreoffice +that we probably couldn't have solved + + align:start position:0% +that we probably couldn't have solved + + + align:start position:0% +that we probably couldn't have solved +this easily by inspection + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/DUA6lk7X2VY.txt b/DUA6lk7X2VY.txt new file mode 100644 index 0000000000000000000000000000000000000000..eefb34ca73c77bfb7a973082a40c6f5c29911e4b --- /dev/null +++ b/DUA6lk7X2VY.txt @@ -0,0 +1,9051 @@ +align:start position:0% + +for the past couple lectures we've been + + align:start position:0% +for the past couple lectures we've been + + + align:start position:0% +for the past couple lectures we've been +talking about Ross theorem and we showed + + align:start position:0% +talking about Ross theorem and we showed + + + align:start position:0% +talking about Ross theorem and we showed +so we saw a proof of glass theorem using + + align:start position:0% +so we saw a proof of glass theorem using + + + align:start position:0% +so we saw a proof of glass theorem using +Fourier analytic methods and we saw + + align:start position:0% +Fourier analytic methods and we saw + + + align:start position:0% +Fourier analytic methods and we saw +basically the same proof but in two + + align:start position:0% +basically the same proof but in two + + + align:start position:0% +basically the same proof but in two +different settings all right so two + + align:start position:0% +different settings all right so two + + + align:start position:0% +different settings all right so two +lectures ago we saw a proof in F 3 to + + align:start position:0% +lectures ago we saw a proof in F 3 to + + + align:start position:0% +lectures ago we saw a proof in F 3 to +the M and basically the same strategy + + align:start position:0% +the M and basically the same strategy + + + align:start position:0% +the M and basically the same strategy +but with a bit more work we were able to + + align:start position:0% +but with a bit more work we were able to + + + align:start position:0% +but with a bit more work we were able to +show Ross theorem with roughly + + align:start position:0% +show Ross theorem with roughly + + + align:start position:0% +show Ross theorem with roughly +comparable bounds in over the integers + + align:start position:0% +comparable bounds in over the integers + + + align:start position:0% +comparable bounds in over the integers +today I want to show you a very + + align:start position:0% +today I want to show you a very + + + align:start position:0% +today I want to show you a very +different kind of proof of Ross theorem + + align:start position:0% +different kind of proof of Ross theorem + + + align:start position:0% +different kind of proof of Ross theorem +in the finite field setting so first let + + align:start position:0% +in the finite field setting so first let + + + align:start position:0% +in the finite field setting so first let +me remind you the parent that we saw + + align:start position:0% +me remind you the parent that we saw + + + align:start position:0% +me remind you the parent that we saw +last time for roster in F 3 to the M + + align:start position:0% +last time for roster in F 3 to the M + + + align:start position:0% +last time for roster in F 3 to the M +gave an upper bound on the maximum + + align:start position:0% +gave an upper bound on the maximum + + + align:start position:0% +gave an upper bound on the maximum +number of elements in the 3 P free set + + align:start position:0% +number of elements in the 3 P free set + + + align:start position:0% +number of elements in the 3 P free set +that were of the form 3 to the N over N + + align:start position:0% + + + + align:start position:0% + +and so this proof up wasn't too bad + + align:start position:0% +and so this proof up wasn't too bad + + + align:start position:0% +and so this proof up wasn't too bad +right so we did it in one lecture and + + align:start position:0% +right so we did it in one lecture and + + + align:start position:0% +right so we did it in one lecture and +then with a lot more work and people + + align:start position:0% +then with a lot more work and people + + + align:start position:0% +then with a lot more work and people +willing to try very very hard to improve + + align:start position:0% +willing to try very very hard to improve + + + align:start position:0% +willing to try very very hard to improve +this and there was a paper that got it + + align:start position:0% +this and there was a paper that got it + + + align:start position:0% +this and there was a paper that got it +just a little bit more and this was a + + align:start position:0% +just a little bit more and this was a + + + align:start position:0% +just a little bit more and this was a +lot of work and this was something that + + align:start position:0% +lot of work and this was something that + + + align:start position:0% +lot of work and this was something that +people thought was very exciting at the + + align:start position:0% +people thought was very exciting at the + + + align:start position:0% +people thought was very exciting at the +time and then just a few years ago there + + align:start position:0% +time and then just a few years ago there + + + align:start position:0% +time and then just a few years ago there +was a major breakthrough a very + + align:start position:0% +was a major breakthrough a very + + + align:start position:0% +was a major breakthrough a very +surprising breakthrough where you know + + align:start position:0% +surprising breakthrough where you know + + + align:start position:0% +surprising breakthrough where you know +at this point it wasn't even clear + + align:start position:0% +at this point it wasn't even clear + + + align:start position:0% +at this point it wasn't even clear +whether 3 should be the right base for + + align:start position:0% +whether 3 should be the right base for + + + align:start position:0% +whether 3 should be the right base for +this exponent and that was a big open + + align:start position:0% +this exponent and that was a big open + + + align:start position:0% +this exponent and that was a big open +problem and then it was a big + + align:start position:0% +problem and then it was a big + + + align:start position:0% +problem and then it was a big +breakthrough where the following bound + + align:start position:0% +breakthrough where the following bound + + + align:start position:0% +breakthrough where the following bound +was proved that it was exponentially + + align:start position:0% +was proved that it was exponentially + + + align:start position:0% +was proved that it was exponentially +less than the previous bound so this is + + align:start position:0% +less than the previous bound so this is + + + align:start position:0% +less than the previous bound so this is +the one that I want to talk about in the + + align:start position:0% +the one that I want to talk about in the + + + align:start position:0% +the one that I want to talk about in the +first part of today's lecture and so + + align:start position:0% +first part of today's lecture and so + + + align:start position:0% +first part of today's lecture and so +this development came first the + + align:start position:0% +this development came first the + + + align:start position:0% +this development came first the +histories have been interesting so crude + + align:start position:0% +histories have been interesting so crude + + + align:start position:0% +histories have been interesting so crude +leaven Park uploaded the people to the + + align:start position:0% +leaven Park uploaded the people to the + + + align:start position:0% +leaven Park uploaded the people to the +archive May 5th 2016 where they showed + + align:start position:0% +archive May 5th 2016 where they showed + + + align:start position:0% +archive May 5th 2016 where they showed +not exactly this theorem but in a + + align:start position:0% +not exactly this theorem but in a + + + align:start position:0% +not exactly this theorem but in a +slightly different setting in this group + + align:start position:0% +slightly different setting in this group + + + align:start position:0% +slightly different setting in this group +so in Z mod 4 instead of Z mod 3 + + align:start position:0% +so in Z mod 4 instead of Z mod 3 + + + align:start position:0% +so in Z mod 4 instead of Z mod 3 +and and this was already quite exciting + + align:start position:0% +and and this was already quite exciting + + + align:start position:0% +and and this was already quite exciting +getting exponential improvement in this + + align:start position:0% +getting exponential improvement in this + + + align:start position:0% +getting exponential improvement in this +setting but it wasn't exactly obvious + + align:start position:0% +setting but it wasn't exactly obvious + + + align:start position:0% +setting but it wasn't exactly obvious +how to use their method to get f3 but + + align:start position:0% +how to use their method to get f3 but + + + align:start position:0% +how to use their method to get f3 but +that was done about a week later so + + align:start position:0% +that was done about a week later so + + + align:start position:0% +that was done about a week later so +elenberg and hash wit they managed to + + align:start position:0% +elenberg and hash wit they managed to + + + align:start position:0% +elenberg and hash wit they managed to +improve use this technique modify the + + align:start position:0% +improve use this technique modify the + + + align:start position:0% +improve use this technique modify the +crude left part technique to the f2 to + + align:start position:0% +crude left part technique to the f2 to + + + align:start position:0% +crude left part technique to the f2 to +the air setting which is the one that + + align:start position:0% +the air setting which is the one that + + + align:start position:0% +the air setting which is the one that +that we've been interested in so there's + + align:start position:0% +that we've been interested in so there's + + + align:start position:0% +that we've been interested in so there's +a small difference between these two + + align:start position:0% +a small difference between these two + + + align:start position:0% +a small difference between these two +namely this group has elements of water + + align:start position:0% +namely this group has elements of water + + + align:start position:0% +namely this group has elements of water +too which makes things a bit easier to + + align:start position:0% +too which makes things a bit easier to + + + align:start position:0% +too which makes things a bit easier to +do it here with so this is the crude + + align:start position:0% +do it here with so this is the crude + + + align:start position:0% +do it here with so this is the crude +left Park method is often called in + + align:start position:0% +left Park method is often called in + + + align:start position:0% +left Park method is often called in +literature and we'll see that it's a + + align:start position:0% +literature and we'll see that it's a + + + align:start position:0% +literature and we'll see that it's a +very ingenious use of this so-called + + align:start position:0% +very ingenious use of this so-called + + + align:start position:0% +very ingenious use of this so-called +linear algebraic method in common it + + align:start position:0% +linear algebraic method in common it + + + align:start position:0% +linear algebraic method in common it +works in this case the polynomial method + + align:start position:0% +works in this case the polynomial method + + + align:start position:0% +works in this case the polynomial method +and it works specifically in the finite + + align:start position:0% +and it works specifically in the finite + + + align:start position:0% +and it works specifically in the finite +field vector space setting so what we're + + align:start position:0% +field vector space setting so what we're + + + align:start position:0% +field vector space setting so what we're +talking about this part of the lecture + + align:start position:0% +talking about this part of the lecture + + + align:start position:0% +talking about this part of the lecture +does not translate whatsoever it is with + + align:start position:0% +does not translate whatsoever it is with + + + align:start position:0% +does not translate whatsoever it is with +nobody knows how to translate this + + align:start position:0% +nobody knows how to translate this + + + align:start position:0% +nobody knows how to translate this +technique to the integer setting okay so + + align:start position:0% +technique to the integer setting okay so + + + align:start position:0% +technique to the integer setting okay so +how does it work the presentation I'm + + align:start position:0% +how does it work the presentation I'm + + + align:start position:0% +how does it work the presentation I'm +going to give follows not the original + + align:start position:0% +going to give follows not the original + + + align:start position:0% +going to give follows not the original +paper which is quite nice to read by the + + align:start position:0% +paper which is quite nice to read by the + + + align:start position:0% +paper which is quite nice to read by the +way it's only about four pages long it's + + align:start position:0% +way it's only about four pages long it's + + + align:start position:0% +way it's only about four pages long it's +a pleasant to read but there's a + + align:start position:0% +a pleasant to read but there's a + + + align:start position:0% +a pleasant to read but there's a +slightly even nicer formulation on + + align:start position:0% +slightly even nicer formulation on + + + align:start position:0% +slightly even nicer formulation on +Carrick house block and that's the one + + align:start position:0% +Carrick house block and that's the one + + + align:start position:0% +Carrick house block and that's the one +that I'm presenting so the idea is that + + align:start position:0% +that I'm presenting so the idea is that + + + align:start position:0% +that I'm presenting so the idea is that +if you have a subset of F 3 to the n + + align:start position:0% +if you have a subset of F 3 to the n + + + align:start position:0% +if you have a subset of F 3 to the n +that is 383 and such a set also has a + + align:start position:0% +that is 383 and such a set also has a + + + align:start position:0% +that is 383 and such a set also has a +name cap set which is also used in + + align:start position:0% +name cap set which is also used in + + + align:start position:0% +name cap set which is also used in +literature for in this specific setting + + align:start position:0% +literature for in this specific setting + + + align:start position:0% +literature for in this specific setting +where you have no three points on the + + align:start position:0% +where you have no three points on the + + + align:start position:0% +where you have no three points on the +line in this case then we have the + + align:start position:0% +line in this case then we have the + + + align:start position:0% +line in this case then we have the +following identity so here Delta is the + + align:start position:0% +following identity so here Delta is the + + + align:start position:0% +following identity so here Delta is the +Dirac Delta let me write that down in a + + align:start position:0% +Dirac Delta let me write that down in a + + + align:start position:0% +Dirac Delta let me write that down in a +second + + align:start position:0% + + + + align:start position:0% + +so the delta of a is the Dirac Delta is + + align:start position:0% +so the delta of a is the Dirac Delta is + + + align:start position:0% +so the delta of a is the Dirac Delta is +either one if x equals to a and zero if + + align:start position:0% +either one if x equals to a and zero if + + + align:start position:0% +either one if x equals to a and zero if +X does not equal to it so this is simply + + align:start position:0% +X does not equal to it so this is simply + + + align:start position:0% +X does not equal to it so this is simply +rewriting the fact that XYZ from a + + align:start position:0% +rewriting the fact that XYZ from a + + + align:start position:0% +rewriting the fact that XYZ from a +through a P if and only if their sum is + + align:start position:0% +through a P if and only if their sum is + + + align:start position:0% +through a P if and only if their sum is +equal to zero and because you're 383 the + + align:start position:0% +equal to zero and because you're 383 the + + + align:start position:0% +equal to zero and because you're 383 the +only three ApS are the trivial ones + + align:start position:0% +only three ApS are the trivial ones + + + align:start position:0% +only three ApS are the trivial ones +recorded on the right hand side so this + + align:start position:0% +recorded on the right hand side so this + + + align:start position:0% +recorded on the right hand side so this +is simply a recording of the statement + + align:start position:0% +is simply a recording of the statement + + + align:start position:0% +is simply a recording of the statement +that a is 3 P 3 and the idea now is that + + align:start position:0% +that a is 3 P 3 and the idea now is that + + + align:start position:0% +that a is 3 P 3 and the idea now is that +you have this expression up there and I + + align:start position:0% +you have this expression up there and I + + + align:start position:0% +you have this expression up there and I +want to show that if a is very very + + align:start position:0% +want to show that if a is very very + + + align:start position:0% +want to show that if a is very very +large then I could get a contradiction + + align:start position:0% +large then I could get a contradiction + + + align:start position:0% +large then I could get a contradiction +by considering some notion of rank so we + + align:start position:0% +by considering some notion of rank so we + + + align:start position:0% +by considering some notion of rank so we +will show that the left hand side is in + + align:start position:0% +will show that the left hand side is in + + + align:start position:0% +will show that the left hand side is in +some sense wrong rank I haven't told you + + align:start position:0% +some sense wrong rank I haven't told you + + + align:start position:0% +some sense wrong rank I haven't told you +what rank means yet but the left-hand + + align:start position:0% +what rank means yet but the left-hand + + + align:start position:0% +what rank means yet but the left-hand +side somewhat no rank and the right-hand + + align:start position:0% +side somewhat no rank and the right-hand + + + align:start position:0% +side somewhat no rank and the right-hand +side is a high rank object so what has + + align:start position:0% +side is a high rank object so what has + + + align:start position:0% +side is a high rank object so what has +ranked me so recall from linear algebra + + align:start position:0% + + + + align:start position:0% + +so the classical notion of rank + + align:start position:0% +so the classical notion of rank + + + align:start position:0% +so the classical notion of rank +correspond to two variable functions so + + align:start position:0% +correspond to two variable functions so + + + align:start position:0% +correspond to two variable functions so +you should think of f as a matrix over + + align:start position:0% +you should think of f as a matrix over + + + align:start position:0% +you should think of f as a matrix over +an arbitrary field F so such a function + + align:start position:0% +an arbitrary field F so such a function + + + align:start position:0% +an arbitrary field F so such a function +or a corresponding matrix is called rank + + align:start position:0% +or a corresponding matrix is called rank + + + align:start position:0% +or a corresponding matrix is called rank +1 if it is nonzero and it can be written + + align:start position:0% +1 if it is nonzero and it can be written + + + align:start position:0% +1 if it is nonzero and it can be written +in the following form f of XY is f of X + + align:start position:0% +in the following form f of XY is f of X + + + align:start position:0% +in the following form f of XY is f of X +G Y for some functions that are one + + align:start position:0% +G Y for some functions that are one + + + align:start position:0% +G Y for some functions that are one +variable each so in matrix language so + + align:start position:0% +variable each so in matrix language so + + + align:start position:0% +variable each so in matrix language so +this is a column vector times a row + + align:start position:0% +this is a column vector times a row + + + align:start position:0% +this is a column vector times a row +vector + + align:start position:0% +vector + + + align:start position:0% +vector +so that's the meaning of rank one and to + + align:start position:0% +so that's the meaning of rank one and to + + + align:start position:0% +so that's the meaning of rank one and to +say that something is of high rank of a + + align:start position:0% +say that something is of high rank of a + + + align:start position:0% +say that something is of high rank of a +specific rank rather the rank of F is + + align:start position:0% +specific rank rather the rank of F is + + + align:start position:0% +specific rank rather the rank of F is +defined to be the minimum number of rank + + align:start position:0% +defined to be the minimum number of rank + + + align:start position:0% +defined to be the minimum number of rank +one functions needed to write F as a sum + + align:start position:0% +one functions needed to write F as a sum + + + align:start position:0% +one functions needed to write F as a sum +or linear combination so this is rank 1 + + align:start position:0% +or linear combination so this is rank 1 + + + align:start position:0% +or linear combination so this is rank 1 +and if you add up our rank when + + align:start position:0% +and if you add up our rank when + + + align:start position:0% +and if you add up our rank when +functions then you get something that's + + align:start position:0% +functions then you get something that's + + + align:start position:0% +functions then you get something that's +most rank R so that's the basic + + align:start position:0% +most rank R so that's the basic + + + align:start position:0% +most rank R so that's the basic +definition of rank from linear algebra + + align:start position:0% +definition of rank from linear algebra + + + align:start position:0% +definition of rank from linear algebra +for three variable functions you can + + align:start position:0% +for three variable functions you can + + + align:start position:0% +for three variable functions you can +come up with other notions of rank okay + + align:start position:0% +come up with other notions of rank okay + + + align:start position:0% +come up with other notions of rank okay +so what about three variable functions + + align:start position:0% + + + + align:start position:0% + +so what how do we define the rank of + + align:start position:0% +so what how do we define the rank of + + + align:start position:0% +so what how do we define the rank of +such a function so you might have seen + + align:start position:0% +such a function so you might have seen + + + align:start position:0% +such a function so you might have seen +such objects as generalizations of + + align:start position:0% +such objects as generalizations of + + + align:start position:0% +such objects as generalizations of +matrices called tensors and tensors have + + align:start position:0% +matrices called tensors and tensors have + + + align:start position:0% +matrices called tensors and tensors have +already a natural notion of rank and + + align:start position:0% +already a natural notion of rank and + + + align:start position:0% +already a natural notion of rank and +this is called tensor rank just like how + + align:start position:0% +this is called tensor rank just like how + + + align:start position:0% +this is called tensor rank just like how +here F is we say rank one if it's + + align:start position:0% +here F is we say rank one if it's + + + align:start position:0% +here F is we say rank one if it's +decomposable like that we say F has + + align:start position:0% +decomposable like that we say F has + + + align:start position:0% +decomposable like that we say F has +tensor rank one if the three variable + + align:start position:0% +tensor rank one if the three variable + + + align:start position:0% +tensor rank one if the three variable +function is decomposable as a product of + + align:start position:0% +function is decomposable as a product of + + + align:start position:0% +function is decomposable as a product of +one variable functions as a potential + + align:start position:0% +one variable functions as a potential + + + align:start position:0% +one variable functions as a potential +rank it turns out okay so this is an + + align:start position:0% +rank it turns out okay so this is an + + + align:start position:0% +rank it turns out okay so this is an +important notion which is actually quite + + align:start position:0% +important notion which is actually quite + + + align:start position:0% +important notion which is actually quite +mysterious there's a lot of important + + align:start position:0% +mysterious there's a lot of important + + + align:start position:0% +mysterious there's a lot of important +problems that boil down to us not really + + align:start position:0% +problems that boil down to us not really + + + align:start position:0% +problems that boil down to us not really +understanding what tensor rank how it + + align:start position:0% +understanding what tensor rank how it + + + align:start position:0% +understanding what tensor rank how it +behaves and it turns out this is not the + + align:start position:0% +behaves and it turns out this is not the + + + align:start position:0% +behaves and it turns out this is not the +right notion to use for our problem so + + align:start position:0% +right notion to use for our problem so + + + align:start position:0% +right notion to use for our problem so +we're going to use a different notion of + + align:start position:0% +we're going to use a different notion of + + + align:start position:0% +we're going to use a different notion of +rank here rank one is decomposing this + + align:start position:0% +rank here rank one is decomposing this + + + align:start position:0% +rank here rank one is decomposing this +three variable function into a product + + align:start position:0% +three variable function into a product + + + align:start position:0% +three variable function into a product +of three one variable functions but + + align:start position:0% +of three one variable functions but + + + align:start position:0% +of three one variable functions but +instead I can define a different notion + + align:start position:0% +instead I can define a different notion + + + align:start position:0% +instead I can define a different notion +we say that f has sliced rank one so + + align:start position:0% +we say that f has sliced rank one so + + + align:start position:0% +we say that f has sliced rank one so +this is definition that's introduced in + + align:start position:0% +this is definition that's introduced in + + + align:start position:0% +this is definition that's introduced in +the context of this problem although + + align:start position:0% +the context of this problem although + + + align:start position:0% +the context of this problem although +it's also quite a natural definition if + + align:start position:0% +it's also quite a natural definition if + + + align:start position:0% +it's also quite a natural definition if +it has + + align:start position:0% +it has + + + align:start position:0% +it has +one of the following forms so I can + + align:start position:0% +one of the following forms so I can + + + align:start position:0% +one of the following forms so I can +write it as a product of a one variable + + align:start position:0% +write it as a product of a one variable + + + align:start position:0% +write it as a product of a one variable +function and a two variable function + + align:start position:0% +function and a two variable function + + + align:start position:0% +function and a two variable function +it's one variable and the remaining two + + align:start position:0% +it's one variable and the remaining two + + + align:start position:0% +it's one variable and the remaining two +variables but this definition should + + align:start position:0% +variables but this definition should + + + align:start position:0% +variables but this definition should +also be symmetric in the variables so + + align:start position:0% +also be symmetric in the variables so + + + align:start position:0% +also be symmetric in the variables so +the other combinations are okay as well + + align:start position:0% + + + + align:start position:0% + +so this is the definition of a rank one + + align:start position:0% +so this is the definition of a rank one + + + align:start position:0% +so this is the definition of a rank one +function a slice rank one and also non + + align:start position:0% +function a slice rank one and also non + + + align:start position:0% +function a slice rank one and also non +zero if it's nonzero and can be written + + align:start position:0% +zero if it's nonzero and can be written + + + align:start position:0% +zero if it's nonzero and can be written +in one of these forms and just like + + align:start position:0% +in one of these forms and just like + + + align:start position:0% +in one of these forms and just like +earlier we define the slice rank + + align:start position:0% +earlier we define the slice rank + + + align:start position:0% +earlier we define the slice rank +of F to be the minimum number of slice + + align:start position:0% +of F to be the minimum number of slice + + + align:start position:0% +of F to be the minimum number of slice +rank one functions right same as before + + align:start position:0% +rank one functions right same as before + + + align:start position:0% +rank one functions right same as before +that you need to write I say some I can + + align:start position:0% +that you need to write I say some I can + + + align:start position:0% +that you need to write I say some I can +decompose this F into a sum of slice + + align:start position:0% +decompose this F into a sum of slice + + + align:start position:0% +decompose this F into a sum of slice +rank one functions what's the most + + align:start position:0% +rank one functions what's the most + + + align:start position:0% +rank one functions what's the most +efficient way to do so so that's the + + align:start position:0% +efficient way to do so so that's the + + + align:start position:0% +efficient way to do so so that's the +definition of slice rank and you see you + + align:start position:0% +definition of slice rank and you see you + + + align:start position:0% +definition of slice rank and you see you +can come up with this definition for any + + align:start position:0% +can come up with this definition for any + + + align:start position:0% +can come up with this definition for any +number of variables where slice rank 1 + + align:start position:0% +number of variables where slice rank 1 + + + align:start position:0% +number of variables where slice rank 1 +means decompose into two functions where + + align:start position:0% +means decompose into two functions where + + + align:start position:0% +means decompose into two functions where +one function takes one variable and the + + align:start position:0% +one function takes one variable and the + + + align:start position:0% +one function takes one variable and the +other function takes all the remaining + + align:start position:0% +other function takes all the remaining + + + align:start position:0% +other function takes all the remaining +variables and then for two variables + + align:start position:0% +variables and then for two variables + + + align:start position:0% +variables and then for two variables +slice rank and rank correspond to the + + align:start position:0% +slice rank and rank correspond to the + + + align:start position:0% +slice rank and rank correspond to the +same notion okay any questions so far + + align:start position:0% + + + + align:start position:0% + +all right so let's look at the function + + align:start position:0% +all right so let's look at the function + + + align:start position:0% +all right so let's look at the function +on the right so think of it as a matrix + + align:start position:0% +on the right so think of it as a matrix + + + align:start position:0% +on the right so think of it as a matrix +or tensor so what is it well it's kind + + align:start position:0% +or tensor so what is it well it's kind + + + align:start position:0% +or tensor so what is it well it's kind +of like a diagonal matrix so that's what + + align:start position:0% +of like a diagonal matrix so that's what + + + align:start position:0% +of like a diagonal matrix so that's what +it is it's a diagonal matrix so what is + + align:start position:0% +it is it's a diagonal matrix so what is + + + align:start position:0% +it is it's a diagonal matrix so what is +the rank of a diagonal matrix in this + + align:start position:0% +the rank of a diagonal matrix in this + + + align:start position:0% +the rank of a diagonal matrix in this +case diagonal function well you know + + align:start position:0% +case diagonal function well you know + + + align:start position:0% +case diagonal function well you know +from linear algebra that if you have a + + align:start position:0% +from linear algebra that if you have a + + + align:start position:0% +from linear algebra that if you have a +matrix then the rank of a diagonal + + align:start position:0% +matrix then the rank of a diagonal + + + align:start position:0% +matrix then the rank of a diagonal +matrix is the number of nonzero entries + + align:start position:0% +matrix is the number of nonzero entries + + + align:start position:0% +matrix is the number of nonzero entries +so something similar is true for slice + + align:start position:0% +so something similar is true for slice + + + align:start position:0% +so something similar is true for slice +rank although it's less obvious + + align:start position:0% +rank although it's less obvious + + + align:start position:0% +rank although it's less obvious +you will require a proof so if I have + + align:start position:0% +you will require a proof so if I have + + + align:start position:0% +you will require a proof so if I have +this three variable function defined by + + align:start position:0% + + + + align:start position:0% + +the following formula so in other words + + align:start position:0% +the following formula so in other words + + + align:start position:0% +the following formula so in other words +it's a diagonal function where the + + align:start position:0% +it's a diagonal function where the + + + align:start position:0% +it's a diagonal function where the +entries on the diagonals are the CAS + + align:start position:0% +entries on the diagonals are the CAS + + + align:start position:0% +entries on the diagonals are the CAS +okay so what is the rank of this + + align:start position:0% +okay so what is the rank of this + + + align:start position:0% +okay so what is the rank of this +function that's sort of slice rank in + + align:start position:0% +function that's sort of slice rank in + + + align:start position:0% +function that's sort of slice rank in +the matrix case it will be the number of + + align:start position:0% +the matrix case it will be the number of + + + align:start position:0% +the matrix case it will be the number of +nonzero entries it's exactly the same + + align:start position:0% +nonzero entries it's exactly the same + + + align:start position:0% +nonzero entries it's exactly the same +here none number of nonzero diagonal + + align:start position:0% +here none number of nonzero diagonal + + + align:start position:0% +here none number of nonzero diagonal +entries that turns out to be the slice + + align:start position:0% +entries that turns out to be the slice + + + align:start position:0% +entries that turns out to be the slice +rank let's see a proof so we go back to + + align:start position:0% +rank let's see a proof so we go back to + + + align:start position:0% +rank let's see a proof so we go back to +the definition of slice rank and we see + + align:start position:0% +the definition of slice rank and we see + + + align:start position:0% +the definition of slice rank and we see +that one of the directions is easy okay + + align:start position:0% +that one of the directions is easy okay + + + align:start position:0% +that one of the directions is easy okay +so this less than or equal to greater + + align:start position:0% +so this less than or equal to greater + + + align:start position:0% +so this less than or equal to greater +than you caught you okay so which one is + + align:start position:0% +than you caught you okay so which one is + + + align:start position:0% +than you caught you okay so which one is +easy + + align:start position:0% + + + + align:start position:0% + +see the right hand side is a some of our + + align:start position:0% +see the right hand side is a some of our + + + align:start position:0% +see the right hand side is a some of our +of a this menu rank one functions so + + align:start position:0% +of a this menu rank one functions so + + + align:start position:0% +of a this menu rank one functions so +this direction is okay so this direction + + align:start position:0% +this direction is okay so this direction + + + align:start position:0% +this direction is okay so this direction +is clear I'm just looking at the + + align:start position:0% +is clear I'm just looking at the + + + align:start position:0% +is clear I'm just looking at the +definition I can write F explicitly as + + align:start position:0% +definition I can write F explicitly as + + + align:start position:0% +definition I can write F explicitly as +that many rank one slice prank one + + align:start position:0% +that many rank one slice prank one + + + align:start position:0% +that many rank one slice prank one +functions okay so the tricky part is + + align:start position:0% +functions okay so the tricky part is + + + align:start position:0% +functions okay so the tricky part is +greater than or equal to and for the + + align:start position:0% +greater than or equal to and for the + + + align:start position:0% +greater than or equal to and for the +greater than or equal to let's assume + + align:start position:0% +greater than or equal to let's assume + + + align:start position:0% +greater than or equal to let's assume +that all the Bagnall entries are nonzero + + align:start position:0% +that all the Bagnall entries are nonzero + + + align:start position:0% +that all the Bagnall entries are nonzero +okay so why can we do this if it's not + + align:start position:0% +okay so why can we do this if it's not + + + align:start position:0% +okay so why can we do this if it's not +nonzero I claim that we can remove this + + align:start position:0% +nonzero I claim that we can remove this + + + align:start position:0% +nonzero I claim that we can remove this +element from a okay if the CA is not + + align:start position:0% +element from a okay if the CA is not + + + align:start position:0% +element from a okay if the CA is not +zero then I remove a from the set and + + align:start position:0% +zero then I remove a from the set and + + + align:start position:0% +zero then I remove a from the set and +doing so cannot increase the rack know a + + align:start position:0% +doing so cannot increase the rack know a + + + align:start position:0% +doing so cannot increase the rack know a +probably the rank might go down if you + + align:start position:0% +probably the rank might go down if you + + + align:start position:0% +probably the rank might go down if you +get rid of an entry right because if you + + align:start position:0% +get rid of an entry right because if you + + + align:start position:0% +get rid of an entry right because if you +add an entry even though the function + + align:start position:0% +add an entry even though the function + + + align:start position:0% +add an entry even though the function +doesn't change on the original set if + + align:start position:0% +doesn't change on the original set if + + + align:start position:0% +doesn't change on the original set if +you increase your set maybe you have + + align:start position:0% +you increase your set maybe you have + + + align:start position:0% +you increase your set maybe you have +more space maybe you have more + + align:start position:0% +more space maybe you have more + + + align:start position:0% +more space maybe you have more +flexibility to work with especially if + + align:start position:0% +flexibility to work with especially if + + + align:start position:0% +flexibility to work with especially if +you remove an element so the rank cannot + + align:start position:0% +you remove an element so the rank cannot + + + align:start position:0% +you remove an element so the rank cannot +go up + + align:start position:0% + + + + align:start position:0% + +No so suppose the slice rank of F is + + align:start position:0% +No so suppose the slice rank of F is + + + align:start position:0% +No so suppose the slice rank of F is +strictly less than the size of a so all + + align:start position:0% +strictly less than the size of a so all + + + align:start position:0% +strictly less than the size of a so all +piece CAS are nonzero so suppose for + + align:start position:0% +piece CAS are nonzero so suppose for + + + align:start position:0% +piece CAS are nonzero so suppose for +contradiction that there's some + + align:start position:0% +contradiction that there's some + + + align:start position:0% +contradiction that there's some +different way to write function f that + + align:start position:0% +different way to write function f that + + + align:start position:0% +different way to write function f that +uses fewer terms so what would such a + + align:start position:0% +uses fewer terms so what would such a + + + align:start position:0% +uses fewer terms so what would such a +sum look like so I would be able to + + align:start position:0% +sum look like so I would be able to + + + align:start position:0% +sum look like so I would be able to +write this function f in a different way + + align:start position:0% +write this function f in a different way + + + align:start position:0% +write this function f in a different way +like that and then now I look at these + + align:start position:0% +like that and then now I look at these + + + align:start position:0% +like that and then now I look at these +other types of functions using different + + align:start position:0% +other types of functions using different + + + align:start position:0% +other types of functions using different +combinations of the variables + + align:start position:0% + + + + align:start position:0% + +okay so suppose there were a different + + align:start position:0% +okay so suppose there were a different + + + align:start position:0% +okay so suppose there were a different +way to write this function f that uses + + align:start position:0% +way to write this function f that uses + + + align:start position:0% +way to write this function f that uses +fewer terms + + align:start position:0% +fewer terms + + + align:start position:0% +fewer terms +okay so I assume uses exactly the size + + align:start position:0% +okay so I assume uses exactly the size + + + align:start position:0% +okay so I assume uses exactly the size +of a minus 1 terms and always putting 0 + + align:start position:0% +of a minus 1 terms and always putting 0 + + + align:start position:0% +of a minus 1 terms and always putting 0 +functions if you like ok so now I claim + + align:start position:0% +functions if you like ok so now I claim + + + align:start position:0% +functions if you like ok so now I claim +that there exists a function H on the + + align:start position:0% +that there exists a function H on the + + + align:start position:0% +that there exists a function H on the +set a whose support so the support is a + + align:start position:0% +set a whose support so the support is a + + + align:start position:0% +set a whose support so the support is a +number of entries that give nonzero + + align:start position:0% +number of entries that give nonzero + + + align:start position:0% +number of entries that give nonzero +values the support of f is bigger than M + + align:start position:0% +values the support of f is bigger than M + + + align:start position:0% +values the support of f is bigger than M +such that the following sum is 0 + + align:start position:0% + + + + align:start position:0% + +okay so I claim that okay so we can find + + align:start position:0% +okay so I claim that okay so we can find + + + align:start position:0% +okay so I claim that okay so we can find +a function f H such that think of it as + + align:start position:0% +a function f H such that think of it as + + + align:start position:0% +a function f H such that think of it as +in the kernel of some of these F so this + + align:start position:0% +in the kernel of some of these F so this + + + align:start position:0% +in the kernel of some of these F so this +is a linear algebraic statement okay yes + + align:start position:0% + + + + align:start position:0% + +sir it's just H it's a single function H + + align:start position:0% +sir it's just H it's a single function H + + + align:start position:0% +sir it's just H it's a single function H +such that this equation is true for all + + align:start position:0% +such that this equation is true for all + + + align:start position:0% +such that this equation is true for all +X's + + align:start position:0% + + + + align:start position:0% + +you are right so okay so what do I want + + align:start position:0% +you are right so okay so what do I want + + + align:start position:0% +you are right so okay so what do I want +to say here + + align:start position:0% + + + + align:start position:0% + +so we want to find a function H such + + align:start position:0% +so we want to find a function H such + + + align:start position:0% +so we want to find a function H such +that the support of H is at least + + align:start position:0% + + + + align:start position:0% + +okay so right so what do we want to say + + align:start position:0% +okay so right so what do we want to say + + + align:start position:0% +okay so right so what do we want to say +I want to say that yeah so your right + + align:start position:0% +I want to say that yeah so your right + + + align:start position:0% +I want to say that yeah so your right +side this is not what I want to say and + + align:start position:0% +side this is not what I want to say and + + + align:start position:0% +side this is not what I want to say and +instead it's something + + align:start position:0% + + + + align:start position:0% + +okay so let's accept so here we have + + align:start position:0% +okay so let's accept so here we have + + + align:start position:0% +okay so let's accept so here we have +some number of functions guys who have + + align:start position:0% +some number of functions guys who have + + + align:start position:0% +some number of functions guys who have +some number of functions and for each a + + align:start position:0% +some number of functions and for each a + + + align:start position:0% +some number of functions and for each a +I have four each + + align:start position:0% + + + + align:start position:0% + +I'm sure know so I do want to show no + + align:start position:0% +I'm sure know so I do want to show no + + + align:start position:0% +I'm sure know so I do want to show no +there's no induction because I'm in + + align:start position:0% +there's no induction because I'm in + + + align:start position:0% +there's no induction because I'm in +three variables and I want to get rid of + + align:start position:0% +three variables and I want to get rid of + + + align:start position:0% +three variables and I want to get rid of +so the point is okay so let's see where + + align:start position:0% +so the point is okay so let's see where + + + align:start position:0% +so the point is okay so let's see where +we're going thankfully and then we'll + + align:start position:0% +we're going thankfully and then we'll + + + align:start position:0% +we're going thankfully and then we'll +figure out what happened up there + + align:start position:0% +figure out what happened up there + + + align:start position:0% +figure out what happened up there +so we want to consider okay so I would + + align:start position:0% +so we want to consider okay so I would + + + align:start position:0% +so we want to consider okay so I would +like to eventually consider the + + align:start position:0% +like to eventually consider the + + + align:start position:0% +like to eventually consider the +following some so I wouldn't consider + + align:start position:0% +following some so I wouldn't consider + + + align:start position:0% +following some so I wouldn't consider +this sum which comes from okay so you + + align:start position:0% +this sum which comes from okay so you + + + align:start position:0% +this sum which comes from okay so you +look at so let's look at this f of X Y Z + + align:start position:0% +look at so let's look at this f of X Y Z + + + align:start position:0% +look at so let's look at this f of X Y Z +ok so f being that sum + + align:start position:0% + + + + align:start position:0% + +so take that F up there and let me + + align:start position:0% +so take that F up there and let me + + + align:start position:0% +so take that F up there and let me +consider basically taking the inner + + align:start position:0% +consider basically taking the inner + + + align:start position:0% +consider basically taking the inner +product of this function viewed as a + + align:start position:0% +product of this function viewed as a + + + align:start position:0% +product of this function viewed as a +function in Z okay so consider this in a + + align:start position:0% +function in Z okay so consider this in a + + + align:start position:0% +function in Z okay so consider this in a +product and if I so what I want to say + + align:start position:0% +product and if I so what I want to say + + + align:start position:0% +product and if I so what I want to say +is not this so what I want to say is if + + align:start position:0% +is not this so what I want to say is if + + + align:start position:0% +is not this so what I want to say is if +I look at in the product of H with so + + align:start position:0% +I look at in the product of H with so + + + align:start position:0% +I look at in the product of H with so +take one of these halves okay take one + + align:start position:0% +take one of these halves okay take one + + + align:start position:0% +take one of these halves okay take one +of these apps and look at the look at + + align:start position:0% +of these apps and look at the look at + + + align:start position:0% +of these apps and look at the look at +the bilinear form relating H and F so + + align:start position:0% +the bilinear form relating H and F so + + + align:start position:0% +the bilinear form relating H and F so +that this sum vanishes for all I between + + align:start position:0% +that this sum vanishes for all I between + + + align:start position:0% +that this sum vanishes for all I between +n plus 1 and the size of a minus 1 okay + + align:start position:0% +n plus 1 and the size of a minus 1 okay + + + align:start position:0% +n plus 1 and the size of a minus 1 okay +so this role I want to vanish when being + + align:start position:0% +so this role I want to vanish when being + + + align:start position:0% +so this role I want to vanish when being +taken bilinear form with h so that makes + + align:start position:0% +taken bilinear form with h so that makes + + + align:start position:0% +taken bilinear form with h so that makes +sense now okay + + align:start position:0% + + + + align:start position:0% + +all right so the fact that such a non + + align:start position:0% +all right so the fact that such a non + + + align:start position:0% +all right so the fact that such a non +zero H exists simply as a matter of + + align:start position:0% +zero H exists simply as a matter of + + + align:start position:0% +zero H exists simply as a matter of +counting parameters it's a linear + + align:start position:0% +counting parameters it's a linear + + + align:start position:0% +counting parameters it's a linear +algebraic statement you have some number + + align:start position:0% +algebraic statement you have some number + + + align:start position:0% +algebraic statement you have some number +of freedoms you have some number of + + align:start position:0% +of freedoms you have some number of + + + align:start position:0% +of freedoms you have some number of +constraints so it's a set of such H ok + + align:start position:0% +constraints so it's a set of such H ok + + + align:start position:0% +constraints so it's a set of such H ok +satisfying all of these constraints so + + align:start position:0% +satisfying all of these constraints so + + + align:start position:0% +satisfying all of these constraints so +there are this many constraints well + + align:start position:0% +there are this many constraints well + + + align:start position:0% +there are this many constraints well +each one of them could cut you down to + + align:start position:0% +each one of them could cut you down to + + + align:start position:0% +each one of them could cut you down to +one dimension s but the set of such H is + + align:start position:0% +one dimension s but the set of such H is + + + align:start position:0% +one dimension s but the set of such H is +a linear subspace dimension bigger than + + align:start position:0% +a linear subspace dimension bigger than + + + align:start position:0% +a linear subspace dimension bigger than +M yes I have eight dimensions and I have + + align:start position:0% +M yes I have eight dimensions and I have + + + align:start position:0% +M yes I have eight dimensions and I have +these many constraints so the set of + + align:start position:0% +these many constraints so the set of + + + align:start position:0% +these many constraints so the set of +such H is there are lots of + + align:start position:0% +such H is there are lots of + + + align:start position:0% +such H is there are lots of +possibilities and furthermore it is also + + align:start position:0% +possibilities and furthermore it is also + + + align:start position:0% +possibilities and furthermore it is also +true that and this is a linear algebraic + + align:start position:0% +true that and this is a linear algebraic + + + align:start position:0% +true that and this is a linear algebraic +statement that every subspace of + + align:start position:0% +statement that every subspace of + + + align:start position:0% +statement that every subspace of +dimension M plus 1 has a vector whose + + align:start position:0% +dimension M plus 1 has a vector whose + + + align:start position:0% +dimension M plus 1 has a vector whose +support has size at least n plus 1 ok + + align:start position:0% +support has size at least n plus 1 ok + + + align:start position:0% +support has size at least n plus 1 ok +I'll leave this as a linear algebraic + + align:start position:0% +I'll leave this as a linear algebraic + + + align:start position:0% +I'll leave this as a linear algebraic +exercise it's not entirely obvious but + + align:start position:0% +exercise it's not entirely obvious but + + + align:start position:0% +exercise it's not entirely obvious but +it is true now you put these two things + + align:start position:0% +it is true now you put these two things + + + align:start position:0% +it is true now you put these two things +together you find that there is some + + align:start position:0% +together you find that there is some + + + align:start position:0% +together you find that there is some +vector so I think of the coordinates of + + align:start position:0% +vector so I think of the coordinates of + + + align:start position:0% +vector so I think of the coordinates of +the vectors has index by the set a there + + align:start position:0% +the vectors has index by the set a there + + + align:start position:0% +the vectors has index by the set a there +is some vector whose support is large + + align:start position:0% +is some vector whose support is large + + + align:start position:0% +is some vector whose support is large +enough okay + + align:start position:0% + + + + align:start position:0% + +yeah so we prove the claim let's go back + + align:start position:0% +yeah so we prove the claim let's go back + + + align:start position:0% +yeah so we prove the claim let's go back +to this this lemma about this diagonal + + align:start position:0% +to this this lemma about this diagonal + + + align:start position:0% +to this this lemma about this diagonal +function having high rank take H from + + align:start position:0% +function having high rank take H from + + + align:start position:0% +function having high rank take H from +the claim ok so let's take H from the + + align:start position:0% +the claim ok so let's take H from the + + + align:start position:0% +the claim ok so let's take H from the +claim then let's consider this sum over + + align:start position:0% +claim then let's consider this sum over + + + align:start position:0% +claim then let's consider this sum over +here on one hand what the sum is is you + + align:start position:0% +here on one hand what the sum is is you + + + align:start position:0% +here on one hand what the sum is is you +know you can do the sum on the on the + + align:start position:0% +know you can do the sum on the on the + + + align:start position:0% +know you can do the sum on the on the +right hand side we see that it's like + + align:start position:0% +right hand side we see that it's like + + + align:start position:0% +right hand side we see that it's like +multiplying a diagonal matrix by a + + align:start position:0% +multiplying a diagonal matrix by a + + + align:start position:0% +multiplying a diagonal matrix by a +vector so what you get following the + + align:start position:0% +vector so what you get following the + + + align:start position:0% +vector so what you get following the +formula on the right hand side it's the + + align:start position:0% +formula on the right hand side it's the + + + align:start position:0% +formula on the right hand side it's the +following we write this part sum over a + + align:start position:0% +following we write this part sum over a + + + align:start position:0% +following we write this part sum over a +C sub a H of a delta sub a X Delta sub a + + align:start position:0% +C sub a H of a delta sub a X Delta sub a + + + align:start position:0% +C sub a H of a delta sub a X Delta sub a +of Y just looking at a formula from the + + align:start position:0% +of Y just looking at a formula from the + + + align:start position:0% +of Y just looking at a formula from the +right hand side on the other hand if you + + align:start position:0% +right hand side on the other hand if you + + + align:start position:0% +right hand side on the other hand if you +had a decomposition up there doing this + + align:start position:0% +had a decomposition up there doing this + + + align:start position:0% +had a decomposition up there doing this +sum and noting the claim we see that the + + align:start position:0% +sum and noting the claim we see that the + + + align:start position:0% +sum and noting the claim we see that the +third row is gone so what you would have + + align:start position:0% +third row is gone so what you would have + + + align:start position:0% +third row is gone so what you would have +is sum over this this + + align:start position:0% + + + + align:start position:0% + +like this so you would have a some + + align:start position:0% +like this so you would have a some + + + align:start position:0% +like this so you would have a some +values of the form F 1 of X and G tilde + + align:start position:0% +values of the form F 1 of X and G tilde + + + align:start position:0% +values of the form F 1 of X and G tilde +1 of Y where G tilde is basically the + + align:start position:0% +1 of Y where G tilde is basically the + + + align:start position:0% +1 of Y where G tilde is basically the +inner product of G 1 as a function of Z + + align:start position:0% +inner product of G 1 as a function of Z + + + align:start position:0% +inner product of G 1 as a function of Z +with H X G and then also so there exist + + align:start position:0% +with H X G and then also so there exist + + + align:start position:0% +with H X G and then also so there exist +some functions G which come from G + + align:start position:0% +some functions G which come from G + + + align:start position:0% +some functions G which come from G +thought that would come from the cheese + + align:start position:0% +thought that would come from the cheese + + + align:start position:0% +thought that would come from the cheese +up there such that this is true ok but + + align:start position:0% +up there such that this is true ok but + + + align:start position:0% +up there such that this is true ok but +now we're in the world of two variable + + align:start position:0% +now we're in the world of two variable + + + align:start position:0% +now we're in the world of two variable +functions so left hand left and right + + align:start position:0% +functions so left hand left and right + + + align:start position:0% +functions so left hand left and right +hand side are two variable functions and + + align:start position:0% +hand side are two variable functions and + + + align:start position:0% +hand side are two variable functions and +for two variable functions you + + align:start position:0% +for two variable functions you + + + align:start position:0% +for two variable functions you +understand what is the rank of a + + align:start position:0% +understand what is the rank of a + + + align:start position:0% +understand what is the rank of a +diagonal function so the left hand side + + align:start position:0% +diagonal function so the left hand side + + + align:start position:0% +diagonal function so the left hand side +has more than M diagonal entries because + + align:start position:0% +has more than M diagonal entries because + + + align:start position:0% +has more than M diagonal entries because +H has support so the number of diagonal + + align:start position:0% +H has support so the number of diagonal + + + align:start position:0% +H has support so the number of diagonal +entries is just the support of H whereas + + align:start position:0% +entries is just the support of H whereas + + + align:start position:0% +entries is just the support of H whereas +the right hand side has rank so now + + align:start position:0% +the right hand side has rank so now + + + align:start position:0% +the right hand side has rank so now +linear algebraic matrix rank at most M + + align:start position:0% + + + + align:start position:0% + +and that's a contradiction okay so we + + align:start position:0% +and that's a contradiction okay so we + + + align:start position:0% +and that's a contradiction okay so we +can show a similar statement for + + align:start position:0% +can show a similar statement for + + + align:start position:0% +can show a similar statement for +arbitrary number of variables by + + align:start position:0% +arbitrary number of variables by + + + align:start position:0% +arbitrary number of variables by +generalizing this proof and using + + align:start position:0% +generalizing this proof and using + + + align:start position:0% +generalizing this proof and using +induction on the number of variables but + + align:start position:0% +induction on the number of variables but + + + align:start position:0% +induction on the number of variables but +we only need three variables for now any + + align:start position:0% +we only need three variables for now any + + + align:start position:0% +we only need three variables for now any +questions it's just a recap what we + + align:start position:0% +questions it's just a recap what we + + + align:start position:0% +questions it's just a recap what we +proved is the generalization of the + + align:start position:0% +proved is the generalization of the + + + align:start position:0% +proved is the generalization of the +statement that a diagonal matrix has + + align:start position:0% +statement that a diagonal matrix has + + + align:start position:0% +statement that a diagonal matrix has +rank equal to the number of nonzero + + align:start position:0% +rank equal to the number of nonzero + + + align:start position:0% +rank equal to the number of nonzero +diagonal entries but the same fact is + + align:start position:0% +diagonal entries but the same fact is + + + align:start position:0% +diagonal entries but the same fact is +true for these three variable functions + + align:start position:0% +true for these three variable functions + + + align:start position:0% +true for these three variable functions +with respect to slice rank so this is + + align:start position:0% +with respect to slice rank so this is + + + align:start position:0% +with respect to slice rank so this is +intuitively obvious but the execution is + + align:start position:0% +intuitively obvious but the execution is + + + align:start position:0% +intuitively obvious but the execution is +slightly tricky all right so now we have + + align:start position:0% +slightly tricky all right so now we have + + + align:start position:0% +slightly tricky all right so now we have +this statement here let's proceed to + + align:start position:0% +this statement here let's proceed to + + + align:start position:0% +this statement here let's proceed to +analyze this function which comes from + + align:start position:0% +analyze this function which comes from + + + align:start position:0% +analyze this function which comes from +so this relationship here coming from a + + align:start position:0% +so this relationship here coming from a + + + align:start position:0% +so this relationship here coming from a +set a that is 383 so suppose now I'm in + + align:start position:0% +set a that is 383 so suppose now I'm in + + + align:start position:0% +set a that is 383 so suppose now I'm in +so many so everything so far + + align:start position:0% +so many so everything so far + + + align:start position:0% +so many so everything so far +works generally with any eight but now + + align:start position:0% +works generally with any eight but now + + + align:start position:0% +works generally with any eight but now +let me think about specifically + + align:start position:0% +let me think about specifically + + + align:start position:0% +let me think about specifically +functions finite field vector space F 3 + + align:start position:0% +functions finite field vector space F 3 + + + align:start position:0% +functions finite field vector space F 3 +to the N function taking value F 3 and + + align:start position:0% +to the N function taking value F 3 and + + + align:start position:0% +to the N function taking value F 3 and +this function is defined to be the + + align:start position:0% +this function is defined to be the + + + align:start position:0% +this function is defined to be the +left-hand side of that equation over + + align:start position:0% +left-hand side of that equation over + + + align:start position:0% +left-hand side of that equation over +there so the claim is that + + align:start position:0% +there so the claim is that + + + align:start position:0% +there so the claim is that +okay so the left-hand-side claim that + + align:start position:0% +okay so the left-hand-side claim that + + + align:start position:0% +okay so the left-hand-side claim that +this function has low rank so we claim + + align:start position:0% +this function has low rank so we claim + + + align:start position:0% +this function has low rank so we claim +that a slice rank of this function is + + align:start position:0% +that a slice rank of this function is + + + align:start position:0% +that a slice rank of this function is +that most three M where m is the sum + + align:start position:0% + + + + align:start position:0% + +essentially this multinomial coefficient + + align:start position:0% + + + + align:start position:0% + +okay we'll analyze this number in a + + align:start position:0% +okay we'll analyze this number in a + + + align:start position:0% +okay we'll analyze this number in a +second but this number is supposed to be + + align:start position:0% +second but this number is supposed to be + + + align:start position:0% +second but this number is supposed to be +small all right so we want to show that + + align:start position:0% +small all right so we want to show that + + + align:start position:0% +small all right so we want to show that +this function here has small rank so + + align:start position:0% +this function here has small rank so + + + align:start position:0% +this function here has small rank so +let's rewrite this function in a form + + align:start position:0% +let's rewrite this function in a form + + + align:start position:0% +let's rewrite this function in a form +explicitly as a sum of products by + + align:start position:0% +explicitly as a sum of products by + + + align:start position:0% +explicitly as a sum of products by +expanding this function after writing it + + align:start position:0% +expanding this function after writing it + + + align:start position:0% +expanding this function after writing it +in a slightly different form so in F 3 + + align:start position:0% +in a slightly different form so in F 3 + + + align:start position:0% +in a slightly different form so in F 3 +and the three variable in characteristic + + align:start position:0% +and the three variable in characteristic + + + align:start position:0% +and the three variable in characteristic +so in F 3 you have this equation you can + + align:start position:0% +so in F 3 you have this equation you can + + + align:start position:0% +so in F 3 you have this equation you can +check that it's true for X equal to 0 1 + + align:start position:0% +check that it's true for X equal to 0 1 + + + align:start position:0% +check that it's true for X equal to 0 1 +or 2 so take that and plug it in over + + align:start position:0% +or 2 so take that and plug it in over + + + align:start position:0% +or 2 so take that and plug it in over +here so we find so now XYZ are in F 6 + + align:start position:0% +here so we find so now XYZ are in F 6 + + + align:start position:0% +here so we find so now XYZ are in F 6 +p.m. so we find that applying this guy + + align:start position:0% +p.m. so we find that applying this guy + + + align:start position:0% +p.m. so we find that applying this guy +here coordinate wise + + align:start position:0% + + + + align:start position:0% + +so you have this product great now let's + + align:start position:0% +so you have this product great now let's + + + align:start position:0% +so you have this product great now let's +pretend we're expanding everything this + + align:start position:0% +pretend we're expanding everything this + + + align:start position:0% +pretend we're expanding everything this +is a polynomial in three and variables 3 + + align:start position:0% +is a polynomial in three and variables 3 + + + align:start position:0% +is a polynomial in three and variables 3 +n variables its degree as qm so if we + + align:start position:0% +n variables its degree as qm so if we + + + align:start position:0% +n variables its degree as qm so if we +expand we get a bunch of monomials and + + align:start position:0% +expand we get a bunch of monomials and + + + align:start position:0% +expand we get a bunch of monomials and +the monomials they all have the + + align:start position:0% +the monomials they all have the + + + align:start position:0% +the monomials they all have the +following form so the axis which whose + + align:start position:0% +following form so the axis which whose + + + align:start position:0% +following form so the axis which whose +exponents I call I the Y's whose + + align:start position:0% +exponents I call I the Y's whose + + + align:start position:0% +exponents I call I the Y's whose +exponents I call J and disease whose + + align:start position:0% +exponents I call J and disease whose + + + align:start position:0% +exponents I call J and disease whose +exponents I call okay where so get a sum + + align:start position:0% +exponents I call okay where so get a sum + + + align:start position:0% +exponents I call okay where so get a sum +of monomials that where all of these IJ + + align:start position:0% +of monomials that where all of these IJ + + + align:start position:0% +of monomials that where all of these IJ +is in case are either 0 1 or 2 + + align:start position:0% + + + + align:start position:0% + +all right so I get this big sum of + + align:start position:0% +all right so I get this big sum of + + + align:start position:0% +all right so I get this big sum of +monomials and I want to show that it is + + align:start position:0% +monomials and I want to show that it is + + + align:start position:0% +monomials and I want to show that it is +possible to write this sum as a small + + align:start position:0% +possible to write this sum as a small + + + align:start position:0% +possible to write this sum as a small +number of functions that can be written + + align:start position:0% +number of functions that can be written + + + align:start position:0% +number of functions that can be written +as a product where one of the factors + + align:start position:0% +as a product where one of the factors + + + align:start position:0% +as a product where one of the factors +only involves one of XYZ so what we can + + align:start position:0% +only involves one of XYZ so what we can + + + align:start position:0% +only involves one of XYZ so what we can +do is to group them ok so group these + + align:start position:0% +do is to group them ok so group these + + + align:start position:0% +do is to group them ok so group these +monomials + + align:start position:0% + + + + align:start position:0% + +by the so for example okay so I'm going + + align:start position:0% +by the so for example okay so I'm going + + + align:start position:0% +by the so for example okay so I'm going +to group these monomials by using the + + align:start position:0% +to group these monomials by using the + + + align:start position:0% +to group these monomials by using the +following observation so by pigeonhole + + align:start position:0% + + + + align:start position:0% + +at least one-half of the exponents of X + + align:start position:0% +at least one-half of the exponents of X + + + align:start position:0% +at least one-half of the exponents of X +or the exponents of Y or the exponents + + align:start position:0% +or the exponents of Y or the exponents + + + align:start position:0% +or the exponents of Y or the exponents +of Z at least one of these guys is at + + align:start position:0% +of Z at least one of these guys is at + + + align:start position:0% +of Z at least one of these guys is at +most two n over three so I group these + + align:start position:0% +most two n over three so I group these + + + align:start position:0% +most two n over three so I group these +monomials by one of X Y Z that has a + + align:start position:0% +monomials by one of X Y Z that has a + + + align:start position:0% +monomials by one of X Y Z that has a +smallest exponent so the contributions + + align:start position:0% +smallest exponent so the contributions + + + align:start position:0% +smallest exponent so the contributions +to the rank or the slice rank from + + align:start position:0% +to the rank or the slice rank from + + + align:start position:0% +to the rank or the slice rank from +monomials with the degree of X being at + + align:start position:0% +monomials with the degree of X being at + + + align:start position:0% +monomials with the degree of X being at +most 2 and over 3 well I can write such + + align:start position:0% +most 2 and over 3 well I can write such + + + align:start position:0% +most 2 and over 3 well I can write such +contributions in the form like that + + align:start position:0% +contributions in the form like that + + + align:start position:0% +contributions in the form like that +where this f of X is a monomial and the + + align:start position:0% +where this f of X is a monomial and the + + + align:start position:0% +where this f of X is a monomial and the +G is a sum of whatever that could come + + align:start position:0% +G is a sum of whatever that could come + + + align:start position:0% +G is a sum of whatever that could come +up this is a sum but this this is a + + align:start position:0% +up this is a sum but this this is a + + + align:start position:0% +up this is a sum but this this is a +monomial so the number of such terms ok + + align:start position:0% +monomial so the number of such terms ok + + + align:start position:0% +monomial so the number of such terms ok +so the number of such terms is the + + align:start position:0% +so the number of such terms is the + + + align:start position:0% +so the number of such terms is the +number of monomials corresponding to + + align:start position:0% +number of monomials corresponding to + + + align:start position:0% +number of monomials corresponding to +choices of ice that sum to 2 n over 3 an + + align:start position:0% +choices of ice that sum to 2 n over 3 an + + + align:start position:0% +choices of ice that sum to 2 n over 3 an +individualised coming from 0 + + align:start position:0% +individualised coming from 0 + + + align:start position:0% +individualised coming from 0 +one or two and that number is precisely + + align:start position:0% +one or two and that number is precisely + + + align:start position:0% +one or two and that number is precisely +M so M counts the number of choices of + + align:start position:0% +M so M counts the number of choices of + + + align:start position:0% +M so M counts the number of choices of +zero one tooth there are n of them and + + align:start position:0% +zero one tooth there are n of them and + + + align:start position:0% +zero one tooth there are n of them and +the sums of the Isis at most 2 n over 3 + + align:start position:0% + + + + align:start position:0% + +okay so these are contributions coming + + align:start position:0% +okay so these are contributions coming + + + align:start position:0% +okay so these are contributions coming +from + + align:start position:0% +from + + + align:start position:0% +from +Gnomeo square the degree of X is at most + + align:start position:0% +Gnomeo square the degree of X is at most + + + align:start position:0% +Gnomeo square the degree of X is at most +2 and over 3 and similarly with degree + + align:start position:0% +2 and over 3 and similarly with degree + + + align:start position:0% +2 and over 3 and similarly with degree +of y being 2 and over 3 and also the + + align:start position:0% +of y being 2 and over 3 and also the + + + align:start position:0% +of y being 2 and over 3 and also the +degree of Z being at most 2 n over 3 but + + align:start position:0% +degree of Z being at most 2 n over 3 but + + + align:start position:0% +degree of Z being at most 2 n over 3 but +so all the monomials can be grouped in + + align:start position:0% +so all the monomials can be grouped in + + + align:start position:0% +so all the monomials can be grouped in +one of these three groups and I count + + align:start position:0% +one of these three groups and I count + + + align:start position:0% +one of these three groups and I count +the contribution to the to the slice + + align:start position:0% +the contribution to the to the slice + + + align:start position:0% +the contribution to the to the slice +rank okay the question is do we have a + + align:start position:0% +rank okay the question is do we have a + + + align:start position:0% +rank okay the question is do we have a +good idea as to how sharp this bound + + align:start position:0% +good idea as to how sharp this bound + + + align:start position:0% +good idea as to how sharp this bound +this that's a really good question + + align:start position:0% +this that's a really good question + + + align:start position:0% +this that's a really good question +I don't know so that finishes the proof + + align:start position:0% +I don't know so that finishes the proof + + + align:start position:0% +I don't know so that finishes the proof +of this lemma ok so now we have this + + align:start position:0% +of this lemma ok so now we have this + + + align:start position:0% +of this lemma ok so now we have this +lemma I can compare ok so we have these + + align:start position:0% +lemma I can compare ok so we have these + + + align:start position:0% +lemma I can compare ok so we have these +two lemmas one of them tells me the rank + + align:start position:0% +two lemmas one of them tells me the rank + + + align:start position:0% +two lemmas one of them tells me the rank +of the right hand side which is a let's + + align:start position:0% +of the right hand side which is a let's + + + align:start position:0% +of the right hand side which is a let's +compare ranks the slice rank + + align:start position:0% + + + + align:start position:0% + +so the left hand side we know it has at + + align:start position:0% +so the left hand side we know it has at + + + align:start position:0% +so the left hand side we know it has at +most this quantity and the right hand + + align:start position:0% +most this quantity and the right hand + + + align:start position:0% +most this quantity and the right hand +side is equal to 8 so we automatically + + align:start position:0% +side is equal to 8 so we automatically + + + align:start position:0% +side is equal to 8 so we automatically +find this bound because now we want to + + align:start position:0% +find this bound because now we want to + + + align:start position:0% +find this bound because now we want to +know how big this number M is + + align:start position:0% +know how big this number M is + + + align:start position:0% +know how big this number M is +so there's actually this is a fairly + + align:start position:0% +so there's actually this is a fairly + + + align:start position:0% +so there's actually this is a fairly +standard prom to solve to estimate the + + align:start position:0% +standard prom to solve to estimate the + + + align:start position:0% +standard prom to solve to estimate the +growth of this function M so let me show + + align:start position:0% +growth of this function M so let me show + + + align:start position:0% +growth of this function M so let me show +you how to do it and this is basically + + align:start position:0% +you how to do it and this is basically + + + align:start position:0% +you how to do it and this is basically +the universal methods notice that I can + + align:start position:0% +the universal methods notice that I can + + + align:start position:0% +the universal methods notice that I can +if I look at this number here where if + + align:start position:0% +if I look at this number here where if + + + align:start position:0% +if I look at this number here where if +okay so now X is some real number + + align:start position:0% +okay so now X is some real number + + + align:start position:0% +okay so now X is some real number +between 0 & 1 then I claim the following + + align:start position:0% +between 0 & 1 then I claim the following + + + align:start position:0% +between 0 & 1 then I claim the following +is true and this is because if you + + align:start position:0% +is true and this is because if you + + + align:start position:0% +is true and this is because if you +expand the right hand side and count + + align:start position:0% +expand the right hand side and count + + + align:start position:0% +expand the right hand side and count +your monomials so just keep track of + + align:start position:0% +your monomials so just keep track of + + + align:start position:0% +your monomials so just keep track of +which monomials occur and there n of + + align:start position:0% +which monomials occur and there n of + + + align:start position:0% +which monomials occur and there n of +them where you can lower bound by this + + align:start position:0% +them where you can lower bound by this + + + align:start position:0% +them where you can lower bound by this +quantity here so this is related to + + align:start position:0% +quantity here so this is related to + + + align:start position:0% +quantity here so this is related to +things in probability theory on large + + align:start position:0% +things in probability theory on large + + + align:start position:0% +things in probability theory on large +deviations for the premier theorem but + + align:start position:0% +deviations for the premier theorem but + + + align:start position:0% +deviations for the premier theorem but +but that's that's what you can do so + + align:start position:0% +but that's that's what you can do so + + + align:start position:0% +but that's that's what you can do so +this is true for every value of x so you + + align:start position:0% +this is true for every value of x so you + + + align:start position:0% +this is true for every value of x so you +pick one that gives you the best pound + + align:start position:0% +pick one that gives you the best pound + + + align:start position:0% +pick one that gives you the best pound +so M is at most + + align:start position:0% + + + + align:start position:0% + +of this quantity here okay and and you + + align:start position:0% +of this quantity here okay and and you + + + align:start position:0% +of this quantity here okay and and you +know to show you any banner I just have + + align:start position:0% +know to show you any banner I just have + + + align:start position:0% +know to show you any banner I just have +to plug in some value so if I plug in + + align:start position:0% +to plug in some value so if I plug in + + + align:start position:0% +to plug in some value so if I plug in +for example X being 0.6 I already get a + + align:start position:0% +for example X being 0.6 I already get a + + + align:start position:0% +for example X being 0.6 I already get a +bound which is the one that claimed okay + + align:start position:0% +bound which is the one that claimed okay + + + align:start position:0% +bound which is the one that claimed okay +and and it turns out you know this this + + align:start position:0% +and and it turns out you know this this + + + align:start position:0% +and and it turns out you know this this +step here is not lossy that's an + + align:start position:0% +step here is not lossy that's an + + + align:start position:0% +step here is not lossy that's an +basically up to one plus not align the + + align:start position:0% +basically up to one plus not align the + + + align:start position:0% +basically up to one plus not align the +exponent this is the correct bound and + + align:start position:0% +exponent this is the correct bound and + + + align:start position:0% +exponent this is the correct bound and +that follows from general results in + + align:start position:0% +that follows from general results in + + + align:start position:0% +that follows from general results in +large deviation theory and not finish + + align:start position:0% +large deviation theory and not finish + + + align:start position:0% +large deviation theory and not finish +the proof alternatively you can also + + align:start position:0% +the proof alternatively you can also + + + align:start position:0% +the proof alternatively you can also +estimate am using Sterling's formula its + + align:start position:0% +estimate am using Sterling's formula its + + + align:start position:0% +estimate am using Sterling's formula its +but this I think is cleaner great any + + align:start position:0% +but this I think is cleaner great any + + + align:start position:0% +but this I think is cleaner great any +questions + + align:start position:0% + + + + align:start position:0% + +okay so why is this step true so if you + + align:start position:0% +okay so why is this step true so if you + + + align:start position:0% +okay so why is this step true so if you +expand the right hand side you see that + + align:start position:0% +expand the right hand side you see that + + + align:start position:0% +expand the right hand side you see that +the right hand side is upper bounded by + + align:start position:0% +the right hand side is upper bounded by + + + align:start position:0% +the right hand side is upper bounded by +all these ABC s in same as over here X + + align:start position:0% +all these ABC s in same as over here X + + + align:start position:0% +all these ABC s in same as over here X +to the B plus 2c right and because how + + align:start position:0% +to the B plus 2c right and because how + + + align:start position:0% +to the B plus 2c right and because how +many terms and also there's a binomial + + align:start position:0% +many terms and also there's a binomial + + + align:start position:0% +many terms and also there's a binomial +coefficient so basically I'm doing the + + align:start position:0% +coefficient so basically I'm doing the + + + align:start position:0% +coefficient so basically I'm doing the +multinomial expansion except I hustled + + align:start position:0% +multinomial expansion except I hustled + + + align:start position:0% +multinomial expansion except I hustled +everything which is not part of the + + align:start position:0% +everything which is not part of the + + + align:start position:0% +everything which is not part of the +index and because B plus 2c is at most + + align:start position:0% +index and because B plus 2c is at most + + + align:start position:0% +index and because B plus 2c is at most +two n over three I get M times X to the + + align:start position:0% + + + + align:start position:0% + +alright you know I want you convey a + + align:start position:0% +alright you know I want you convey a + + + align:start position:0% +alright you know I want you convey a +sense of mystique about this proof this + + align:start position:0% +sense of mystique about this proof this + + + align:start position:0% +sense of mystique about this proof this +is this is a really cool proof okay so + + align:start position:0% +is this is a really cool proof okay so + + + align:start position:0% +is this is a really cool proof okay so +because you're seeing lecture maybe when + + align:start position:0% +because you're seeing lecture maybe when + + + align:start position:0% +because you're seeing lecture maybe when +we buy very quickly but you know when + + align:start position:0% +we buy very quickly but you know when + + + align:start position:0% +we buy very quickly but you know when +this proof came out people were very + + align:start position:0% +this proof came out people were very + + + align:start position:0% +this proof came out people were very +shocked they didn't expect that this + + align:start position:0% +shocked they didn't expect that this + + + align:start position:0% +shocked they didn't expect that this +palm would be tackled would be solved + + align:start position:0% +palm would be tackled would be solved + + + align:start position:0% +palm would be tackled would be solved +using a method that is so unexpected and + + align:start position:0% +using a method that is so unexpected and + + + align:start position:0% +using a method that is so unexpected and +this is part of this power of the + + align:start position:0% +this is part of this power of the + + + align:start position:0% +this is part of this power of the +algebraic method in combinatorics where + + align:start position:0% +algebraic method in combinatorics where + + + align:start position:0% +algebraic method in combinatorics where +we often end up with these short + + align:start position:0% +we often end up with these short + + + align:start position:0% +we often end up with these short +surprising proofs that take very long + + align:start position:0% +surprising proofs that take very long + + + align:start position:0% +surprising proofs that take very long +time to find but they turn out to be + + align:start position:0% +time to find but they turn out to be + + + align:start position:0% +time to find but they turn out to be +very short so this is very short this + + align:start position:0% +very short so this is very short this + + + align:start position:0% +very short so this is very short this +was basically a four-page paper but when + + align:start position:0% +was basically a four-page paper but when + + + align:start position:0% +was basically a four-page paper but when +they work they work beautifully they + + align:start position:0% +they work they work beautifully they + + + align:start position:0% +they work they work beautifully they +work like magic but it's hard to predict + + align:start position:0% +work like magic but it's hard to predict + + + align:start position:0% +work like magic but it's hard to predict +when they work and also these methods + + align:start position:0% +when they work and also these methods + + + align:start position:0% +when they work and also these methods +are somewhat fragile so unlike the + + align:start position:0% +are somewhat fragile so unlike the + + + align:start position:0% +are somewhat fragile so unlike the +Fourier analytic methods that we saw + + align:start position:0% +Fourier analytic methods that we saw + + + align:start position:0% +Fourier analytic methods that we saw +last time where that method you know + + align:start position:0% +last time where that method you know + + + align:start position:0% +last time where that method you know +it's very analytic work works in one + + align:start position:0% +it's very analytic work works in one + + + align:start position:0% +it's very analytic work works in one +situation you can play with the massager + + align:start position:0% +situation you can play with the massager + + + align:start position:0% +situation you can play with the massager +work make it work in a different + + align:start position:0% +work make it work in a different + + + align:start position:0% +work make it work in a different +situation + + align:start position:0% +situation + + + align:start position:0% +situation +here you know we're using something very + + align:start position:0% +here you know we're using something very + + + align:start position:0% +here you know we're using something very +implicit very + + align:start position:0% +implicit very + + + align:start position:0% +implicit very +special about these many variables and + + align:start position:0% +special about these many variables and + + + align:start position:0% +special about these many variables and +if you try to tweak the problem just a + + align:start position:0% +if you try to tweak the problem just a + + + align:start position:0% +if you try to tweak the problem just a +little bit the method seems to break + + align:start position:0% +little bit the method seems to break + + + align:start position:0% +little bit the method seems to break +down all right so in particular it is + + align:start position:0% +down all right so in particular it is + + + align:start position:0% +down all right so in particular it is +open how to extend this method to other + + align:start position:0% +open how to extend this method to other + + + align:start position:0% +open how to extend this method to other +settings it's not very clear what the + + align:start position:0% +settings it's not very clear what the + + + align:start position:0% +settings it's not very clear what the +results should be right so it's open to + + align:start position:0% +results should be right so it's open to + + + align:start position:0% +results should be right so it's open to +extend it to for example for a piece I + + align:start position:0% + + + + align:start position:0% + +said we do not know if the maximum size + + align:start position:0% +said we do not know if the maximum size + + + align:start position:0% +said we do not know if the maximum size +of 483 subset of F 5 to the N is less + + align:start position:0% +of 483 subset of F 5 to the N is less + + + align:start position:0% +of 483 subset of F 5 to the N is less +than some constant 4.99 to D okay so + + align:start position:0% +than some constant 4.99 to D okay so + + + align:start position:0% +than some constant 4.99 to D okay so +that's that's very much open by the way + + align:start position:0% +that's that's very much open by the way + + + align:start position:0% +that's that's very much open by the way +all of this 3 AP stuff right now I've + + align:start position:0% +all of this 3 AP stuff right now I've + + + align:start position:0% +all of this 3 AP stuff right now I've +only done it in F 3 but works for 3 AP + + align:start position:0% +only done it in F 3 but works for 3 AP + + + align:start position:0% +only done it in F 3 but works for 3 AP +in any finite field it also is open to + + align:start position:0% +in any finite field it also is open to + + + align:start position:0% +in any finite field it also is open to +extend it to corners ok so you can + + align:start position:0% +extend it to corners ok so you can + + + align:start position:0% +extend it to corners ok so you can +define a notion of corners so previously + + align:start position:0% +define a notion of corners so previously + + + align:start position:0% +define a notion of corners so previously +we saw a corners integer grid but + + align:start position:0% +we saw a corners integer grid but + + + align:start position:0% +we saw a corners integer grid but +replace integer by some other group so + + align:start position:0% +replace integer by some other group so + + + align:start position:0% +replace integer by some other group so +you can define a notion of corner step + + align:start position:0% +you can define a notion of corner step + + + align:start position:0% +you can define a notion of corner step +so not clear how to extend this method + + align:start position:0% +so not clear how to extend this method + + + align:start position:0% +so not clear how to extend this method +the corners and also is there some way + + align:start position:0% +the corners and also is there some way + + + align:start position:0% +the corners and also is there some way +to extend you know some ideas from this + + align:start position:0% +to extend you know some ideas from this + + + align:start position:0% +to extend you know some ideas from this +method to the integers there's + + align:start position:0% +method to the integers there's + + + align:start position:0% +method to the integers there's +completely fails right so this methods + + align:start position:0% +completely fails right so this methods + + + align:start position:0% +completely fails right so this methods +not clear at all how you might have a + + align:start position:0% +not clear at all how you might have a + + + align:start position:0% +not clear at all how you might have a +work in a setting where you don't have + + align:start position:0% +work in a setting where you don't have + + + align:start position:0% +work in a setting where you don't have +this high dimensionality I mean the + + align:start position:0% +this high dimensionality I mean the + + + align:start position:0% +this high dimensionality I mean the +result will be different because the + + align:start position:0% +result will be different because the + + + align:start position:0% +result will be different because the +integers we know that there's no power + + align:start position:0% +integers we know that there's no power + + + align:start position:0% +integers we know that there's no power +saving but maybe you can get some other + + align:start position:0% +saving but maybe you can get some other + + + align:start position:0% +saving but maybe you can get some other +bounds any questions + + align:start position:0% + + + + align:start position:0% + +okay great let's take a break so in the + + align:start position:0% +okay great let's take a break so in the + + + align:start position:0% +okay great let's take a break so in the +first part of today's lecture I showed + + align:start position:0% +first part of today's lecture I showed + + + align:start position:0% +first part of today's lecture I showed +you a proof of roster F 3 to the end + + align:start position:0% +you a proof of roster F 3 to the end + + + align:start position:0% +you a proof of roster F 3 to the end +that gave you a much better bound and + + align:start position:0% +that gave you a much better bound and + + + align:start position:0% +that gave you a much better bound and +what we did with for a second part I + + align:start position:0% +what we did with for a second part I + + + align:start position:0% +what we did with for a second part I +want to show you another proof ok so yet + + align:start position:0% +want to show you another proof ok so yet + + + align:start position:0% +want to show you another proof ok so yet +another proof of Ross in F 2 to the N + + align:start position:0% +another proof of Ross in F 2 to the N + + + align:start position:0% +another proof of Ross in F 2 to the N +and this time giving you much worse + + align:start position:0% +and this time giving you much worse + + + align:start position:0% +and this time giving you much worse +bound of course I do this for a reason + + align:start position:0% +bound of course I do this for a reason + + + align:start position:0% +bound of course I do this for a reason +ok so we'll give you us and the new + + align:start position:0% +ok so we'll give you us and the new + + + align:start position:0% +ok so we'll give you us and the new +result so we'll give you some more + + align:start position:0% +result so we'll give you some more + + + align:start position:0% +result so we'll give you some more +information about 3/8 piece and F 3 to + + align:start position:0% +information about 3/8 piece and F 3 to + + + align:start position:0% +information about 3/8 piece and F 3 to +the N but the more important reason is + + align:start position:0% +the N but the more important reason is + + + align:start position:0% +the N but the more important reason is +that you know I in this course I tried + + align:start position:0% +that you know I in this course I tried + + + align:start position:0% +that you know I in this course I tried +to make some connections between graph + + align:start position:0% +to make some connections between graph + + + align:start position:0% +to make some connections between graph +theory and one kind and additive common + + align:start position:0% +theory and one kind and additive common + + + align:start position:0% +theory and one kind and additive common +networks on the other hand and so far + + align:start position:0% +networks on the other hand and so far + + + align:start position:0% +networks on the other hand and so far +we've seen some analogies in the proof + + align:start position:0% +we've seen some analogies in the proof + + + align:start position:0% +we've seen some analogies in the proof +of similarities graph regularity lemma + + align:start position:0% +of similarities graph regularity lemma + + + align:start position:0% +of similarities graph regularity lemma +versus the proof the Fourier analytic + + align:start position:0% +versus the proof the Fourier analytic + + + align:start position:0% +versus the proof the Fourier analytic +proof of Rosse theorem there was this + + align:start position:0% +proof of Rosse theorem there was this + + + align:start position:0% +proof of Rosse theorem there was this +common thing of structure versus pseudo + + align:start position:0% +common thing of structure versus pseudo + + + align:start position:0% +common thing of structure versus pseudo +randomness but the actual execution of + + align:start position:0% +randomness but the actual execution of + + + align:start position:0% +randomness but the actual execution of +the proofs are somewhat different + + align:start position:0% +the proofs are somewhat different + + + align:start position:0% +the proofs are somewhat different +because on one hand in regularity lemma + + align:start position:0% +because on one hand in regularity lemma + + + align:start position:0% +because on one hand in regularity lemma +you have energy increment you have + + align:start position:0% +you have energy increment you have + + + align:start position:0% +you have energy increment you have +partitioning and energy increment and on + + align:start position:0% +partitioning and energy increment and on + + + align:start position:0% +partitioning and energy increment and on +the other hand with Roth you have + + align:start position:0% +the other hand with Roth you have + + + align:start position:0% +the other hand with Roth you have +density increment or you're not + + align:start position:0% +density increment or you're not + + + align:start position:0% +density increment or you're not +partitioning you're zooming in take a + + align:start position:0% +partitioning you're zooming in take a + + + align:start position:0% +partitioning you're zooming in take a +set find some structure zoom in find + + align:start position:0% +set find some structure zoom in find + + + align:start position:0% +set find some structure zoom in find +some structure zoom in you've kept + + align:start position:0% +some structure zoom in you've kept + + + align:start position:0% +some structure zoom in you've kept +density increment so it's similar but + + align:start position:0% +density increment so it's similar but + + + align:start position:0% +density increment so it's similar but +differently executed so today I mean + + align:start position:0% +differently executed so today I mean + + + align:start position:0% +differently executed so today I mean +this second half I want to show you how + + align:start position:0% +this second half I want to show you how + + + align:start position:0% +this second half I want to show you how +to do a different proof of Rosse theorem + + align:start position:0% +to do a different proof of Rosse theorem + + + align:start position:0% +to do a different proof of Rosse theorem +that is much more closely related to the + + align:start position:0% +that is much more closely related to the + + + align:start position:0% +that is much more closely related to the +regularity proof right so that has this + + align:start position:0% +regularity proof right so that has this + + + align:start position:0% +regularity proof right so that has this +energy increment element to it and I + + align:start position:0% +energy increment element to it and I + + + align:start position:0% +energy increment element to it and I +show you this proof because it also + + align:start position:0% +show you this proof because it also + + + align:start position:0% +show you this proof because it also +gives you a stronger consequence and + + align:start position:0% +gives you a stronger consequence and + + + align:start position:0% +gives you a stronger consequence and +namely we'll get that there is also not + + align:start position:0% +namely we'll get that there is also not + + + align:start position:0% +namely we'll get that there is also not +just three atps but three a piece with + + align:start position:0% +just three atps but three a piece with + + + align:start position:0% +just three atps but three a piece with +popular difference so here's the result + + align:start position:0% +popular difference so here's the result + + + align:start position:0% +popular difference so here's the result +that we'll see today + + align:start position:0% +that we'll see today + + + align:start position:0% +that we'll see today +so it's proved by penguin now for every + + align:start position:0% +so it's proved by penguin now for every + + + align:start position:0% +so it's proved by penguin now for every +epsilon there exists some and not + + align:start position:0% + + + + align:start position:0% + +such that every a being subset of F 3 to + + align:start position:0% +such that every a being subset of F 3 to + + + align:start position:0% +such that every a being subset of F 3 to +the N worth density + + align:start position:0% +the N worth density + + + align:start position:0% +the N worth density +alpha there exists some nonzero Y such + + align:start position:0% +alpha there exists some nonzero Y such + + + align:start position:0% +alpha there exists some nonzero Y such +that the number of three a piece with + + align:start position:0% +that the number of three a piece with + + + align:start position:0% +that the number of three a piece with +common difference Y okay so so let's + + align:start position:0% +common difference Y okay so so let's + + + align:start position:0% +common difference Y okay so so let's +think about what's going on here so if I + + align:start position:0% +think about what's going on here so if I + + + align:start position:0% +think about what's going on here so if I +just give you a set a and ask you how + + align:start position:0% +just give you a set a and ask you how + + + align:start position:0% +just give you a set a and ask you how +many three ApS are there and compared to + + align:start position:0% +many three ApS are there and compared to + + + align:start position:0% +many three ApS are there and compared to +what you get from random random meaning + + align:start position:0% +what you get from random random meaning + + + align:start position:0% +what you get from random random meaning +if a were random set of the same density + + align:start position:0% +if a were random set of the same density + + + align:start position:0% +if a were random set of the same density +so questions can the number of three a + + align:start position:0% +so questions can the number of three a + + + align:start position:0% +so questions can the number of three a +piece be less than the random count okay + + align:start position:0% +piece be less than the random count okay + + + align:start position:0% +piece be less than the random count okay +and the answer is yes so for example you + + align:start position:0% +and the answer is yes so for example you + + + align:start position:0% +and the answer is yes so for example you +could have in the integers you can have + + align:start position:0% +could have in the integers you can have + + + align:start position:0% +could have in the integers you can have +aberrant type a construction there's no + + align:start position:0% +aberrant type a construction there's no + + + align:start position:0% +aberrant type a construction there's no +three a piece so certainly it has fewer + + align:start position:0% +three a piece so certainly it has fewer + + + align:start position:0% +three a piece so certainly it has fewer +three piece than random and you can do + + align:start position:0% +three piece than random and you can do + + + align:start position:0% +three piece than random and you can do +similar things here but what greens + + align:start position:0% +similar things here but what greens + + + align:start position:0% +similar things here but what greens +theorem says is that there exists on + + align:start position:0% +theorem says is that there exists on + + + align:start position:0% +theorem says is that there exists on +popular common difference so this is a + + align:start position:0% +popular common difference so this is a + + + align:start position:0% +popular common difference so this is a +popular common difference such that the + + align:start position:0% +popular common difference such that the + + + align:start position:0% +popular common difference such that the +number of three a piece in a with this + + align:start position:0% +number of three a piece in a with this + + + align:start position:0% +number of three a piece in a with this +common difference is at least as much as + + align:start position:0% +common difference is at least as much as + + + align:start position:0% +common difference is at least as much as +what you should expect in a random + + align:start position:0% +what you should expect in a random + + + align:start position:0% +what you should expect in a random +setting up to a minus epsilon so this is + + align:start position:0% +setting up to a minus epsilon so this is + + + align:start position:0% +setting up to a minus epsilon so this is +this is a theorem okay so let me say the + + align:start position:0% +this is a theorem okay so let me say the + + + align:start position:0% +this is a theorem okay so let me say the +intuition again says that given an + + align:start position:0% +intuition again says that given an + + + align:start position:0% +intuition again says that given an +arbitrary set a provided a space + + align:start position:0% +arbitrary set a provided a space + + + align:start position:0% +arbitrary set a provided a space +dimensions large enough there exists + + align:start position:0% +dimensions large enough there exists + + + align:start position:0% +dimensions large enough there exists +some popular common difference where + + align:start position:0% +some popular common difference where + + + align:start position:0% +some popular common difference where +popular means that the number of three a + + align:start position:0% +popular means that the number of three a + + + align:start position:0% +popular means that the number of three a +piece with that common difference is at + + align:start position:0% +piece with that common difference is at + + + align:start position:0% +piece with that common difference is at +least roughly as men + + align:start position:0% +least roughly as men + + + align:start position:0% +least roughly as men +yes random in particular this proofs + + align:start position:0% +yes random in particular this proofs + + + align:start position:0% +yes random in particular this proofs +roth's theorem right because you have at + + align:start position:0% +roth's theorem right because you have at + + + align:start position:0% +roth's theorem right because you have at +least sound 3 a piece but it tells you + + align:start position:0% +least sound 3 a piece but it tells you + + + align:start position:0% +least sound 3 a piece but it tells you +more it tells you there there's some + + align:start position:0% +more it tells you there there's some + + + align:start position:0% +more it tells you there there's some +common difference that has lots of three + + align:start position:0% +common difference that has lots of three + + + align:start position:0% +common difference that has lots of three +APs + + align:start position:0% +APs + + + align:start position:0% +APs +even though on average if you just take + + align:start position:0% +even though on average if you just take + + + align:start position:0% +even though on average if you just take +an average if you take a random wire + + align:start position:0% +an average if you take a random wire + + + align:start position:0% +an average if you take a random wire +this is false any questions about the + + align:start position:0% +this is false any questions about the + + + align:start position:0% +this is false any questions about the +statement all right + + align:start position:0% +statement all right + + + align:start position:0% +statement all right +so green developed an arithmetic analog + + align:start position:0% +so green developed an arithmetic analog + + + align:start position:0% +so green developed an arithmetic analog +of similarities graph regularity in + + align:start position:0% +of similarities graph regularity in + + + align:start position:0% +of similarities graph regularity in +order to prove this theorem + + align:start position:0% + + + + align:start position:0% + +ok so starting with similarities graph + + align:start position:0% +ok so starting with similarities graph + + + align:start position:0% +ok so starting with similarities graph +regularity lemma he found a way to + + align:start position:0% +regularity lemma he found a way to + + + align:start position:0% +regularity lemma he found a way to +import that technique into the earth + + align:start position:0% +import that technique into the earth + + + align:start position:0% +import that technique into the earth +metric setting in F 3 to the M ok so I + + align:start position:0% +metric setting in F 3 to the M ok so I + + + align:start position:0% +metric setting in F 3 to the M ok so I +want to show you how roughly how this is + + align:start position:0% +want to show you how roughly how this is + + + align:start position:0% +want to show you how roughly how this is +done and just like in some rarities + + align:start position:0% +done and just like in some rarities + + + align:start position:0% +done and just like in some rarities +graph regularity lemma there the world + + align:start position:0% +graph regularity lemma there the world + + + align:start position:0% +graph regularity lemma there the world +on the voidable bounce which are of + + align:start position:0% +on the voidable bounce which are of + + + align:start position:0% +on the voidable bounce which are of +tower type the same thing is true in the + + align:start position:0% +tower type the same thing is true in the + + + align:start position:0% +tower type the same thing is true in the +arithmetic setting so greens proof shows + + align:start position:0% +arithmetic setting so greens proof shows + + + align:start position:0% +arithmetic setting so greens proof shows +that the theorem is true worth and not + + align:start position:0% +that the theorem is true worth and not + + + align:start position:0% +that the theorem is true worth and not +being something like tower in a tower of + + align:start position:0% +being something like tower in a tower of + + + align:start position:0% +being something like tower in a tower of +two's the height of the tower is + + align:start position:0% +two's the height of the tower is + + + align:start position:0% +two's the height of the tower is +polynomial in 1 over Epsilon okay so + + align:start position:0% +polynomial in 1 over Epsilon okay so + + + align:start position:0% +polynomial in 1 over Epsilon okay so +just like in regularity lemma for graphs + + align:start position:0% +just like in regularity lemma for graphs + + + align:start position:0% +just like in regularity lemma for graphs +so this was recently improved in a paper + + align:start position:0% +so this was recently improved in a paper + + + align:start position:0% +so this was recently improved in a paper +by fox and fan but just a couple years + + align:start position:0% +by fox and fan but just a couple years + + + align:start position:0% +by fox and fan but just a couple years +ago where and this is the this is a + + align:start position:0% +ago where and this is the this is a + + + align:start position:0% +ago where and this is the this is a +proof that I'll show you today where you + + align:start position:0% +proof that I'll show you today where you + + + align:start position:0% +proof that I'll show you today where you +can take and not to be slightly better + + align:start position:0% +can take and not to be slightly better + + + align:start position:0% +can take and not to be slightly better +but still a tower but powernow height + + align:start position:0% +but still a tower but powernow height + + + align:start position:0% +but still a tower but powernow height +log in 1 over Epsilon really really big + + align:start position:0% +log in 1 over Epsilon really really big + + + align:start position:0% +log in 1 over Epsilon really really big +tower to just slightly less big Tower + + align:start position:0% + + + + align:start position:0% + +but more importantly it turns out so + + align:start position:0% +but more importantly it turns out so + + + align:start position:0% +but more importantly it turns out so +they also showed that this is tight you + + align:start position:0% +they also showed that this is tight you + + + align:start position:0% +they also showed that this is tight you +cannot do better + + align:start position:0% +cannot do better + + + align:start position:0% +cannot do better +there exists constructions there exists + + align:start position:0% +there exists constructions there exists + + + align:start position:0% +there exists constructions there exists +sets a from which you this theorem is + + align:start position:0% +sets a from which you this theorem is + + + align:start position:0% +sets a from which you this theorem is +false if you replace the big ol by less + + align:start position:0% +false if you replace the big ol by less + + + align:start position:0% +false if you replace the big ol by less +than some very small constant so many + + align:start position:0% +than some very small constant so many + + + align:start position:0% +than some very small constant so many +applications are the regularity lemma + + align:start position:0% +applications are the regularity lemma + + + align:start position:0% +applications are the regularity lemma +you know the first proof may be using + + align:start position:0% +you know the first proof may be using + + + align:start position:0% +you know the first proof may be using +regularity in the difficult gives you a + + align:start position:0% +regularity in the difficult gives you a + + + align:start position:0% +regularity in the difficult gives you a +very poor bound but subsequently there + + align:start position:0% +very poor bound but subsequently there + + + align:start position:0% +very poor bound but subsequently there +were other proofs better proofs that + + align:start position:0% +were other proofs better proofs that + + + align:start position:0% +were other proofs better proofs that +give you non power tight bounds but this + + align:start position:0% +give you non power tight bounds but this + + + align:start position:0% +give you non power tight bounds but this +is the first application that we've seen + + align:start position:0% +is the first application that we've seen + + + align:start position:0% +is the first application that we've seen +where it turns out the regularity lemma + + align:start position:0% +where it turns out the regularity lemma + + + align:start position:0% +where it turns out the regularity lemma +gives you the correct bound so it's + + align:start position:0% +gives you the correct bound so it's + + + align:start position:0% +gives you the correct bound so it's +really you need a tower type I mean we + + align:start position:0% +really you need a tower type I mean we + + + align:start position:0% +really you need a tower type I mean we +know the regularity lemma itself means + + align:start position:0% +know the regularity lemma itself means + + + align:start position:0% +know the regularity lemma itself means +tower type bounds but turns out this + + align:start position:0% +tower type bounds but turns out this + + + align:start position:0% +tower type bounds but turns out this +application also needs tower type bounds + + align:start position:0% +application also needs tower type bounds + + + align:start position:0% +application also needs tower type bounds +that's quite interesting + + align:start position:0% +that's quite interesting + + + align:start position:0% +that's quite interesting +so here the use of regularity is really + + align:start position:0% +so here the use of regularity is really + + + align:start position:0% +so here the use of regularity is really +necessary in this quantitative sense ok + + align:start position:0% +necessary in this quantitative sense ok + + + align:start position:0% +necessary in this quantitative sense ok +so let's see the proof so let me first + + align:start position:0% +so let's see the proof so let me first + + + align:start position:0% +so let's see the proof so let me first +prove a slightly technical lemma about + + align:start position:0% +prove a slightly technical lemma about + + + align:start position:0% +prove a slightly technical lemma about +bounded increments so this is + + align:start position:0% +bounded increments so this is + + + align:start position:0% +bounded increments so this is +corresponds to the statement that if you + + align:start position:0% +corresponds to the statement that if you + + + align:start position:0% +corresponds to the statement that if you +have energy increments you cannot + + align:start position:0% +have energy increments you cannot + + + align:start position:0% +have energy increments you cannot +increase too many times but in a + + align:start position:0% +increase too many times but in a + + + align:start position:0% +increase too many times but in a +slightly different form so suppose you + + align:start position:0% +slightly different form so suppose you + + + align:start position:0% +slightly different form so suppose you +have numbers alpha and epsilon bigger + + align:start position:0% +have numbers alpha and epsilon bigger + + + align:start position:0% +have numbers alpha and epsilon bigger +than zero and if you have this sequence + + align:start position:0% +than zero and if you have this sequence + + + align:start position:0% +than zero and if you have this sequence +of ACE between zero and one and such + + align:start position:0% +of ACE between zero and one and such + + + align:start position:0% +of ACE between zero and one and such +that a naught is at least alpha then + + align:start position:0% +that a naught is at least alpha then + + + align:start position:0% +that a naught is at least alpha then +there exists some K at most log base 2 + + align:start position:0% +there exists some K at most log base 2 + + + align:start position:0% +there exists some K at most log base 2 +of 1 over epsilon such that 2 a sub K + + align:start position:0% +of 1 over epsilon such that 2 a sub K + + + align:start position:0% +of 1 over epsilon such that 2 a sub K +minus a sub K plus 1 is at least + + align:start position:0% +minus a sub K plus 1 is at least + + + align:start position:0% +minus a sub K plus 1 is at least +alpha cubed minus Epsilon okay so don't + + align:start position:0% +alpha cubed minus Epsilon okay so don't + + + align:start position:0% +alpha cubed minus Epsilon okay so don't +worry about this form will see shortly + + align:start position:0% +worry about this form will see shortly + + + align:start position:0% +worry about this form will see shortly +why we want something like that but the + + align:start position:0% +why we want something like that but the + + + align:start position:0% +why we want something like that but the +proof itself is very straightforward + + align:start position:0% +proof itself is very straightforward + + + align:start position:0% +proof itself is very straightforward +because otherwise so you start with a + + align:start position:0% +because otherwise so you start with a + + + align:start position:0% +because otherwise so you start with a +knot now then if this is not true for K + + align:start position:0% +knot now then if this is not true for K + + + align:start position:0% +knot now then if this is not true for K +equals to 0 then a 1 is at least to a + + align:start position:0% +equals to 0 then a 1 is at least to a + + + align:start position:0% +equals to 0 then a 1 is at least to a +naught minus epsilon cube plus epsilon + + align:start position:0% +naught minus epsilon cube plus epsilon + + + align:start position:0% +naught minus epsilon cube plus epsilon +naught is at least of a cube so if + + align:start position:0% +naught is at least of a cube so if + + + align:start position:0% +naught is at least of a cube so if +otherwise you have some lower bound down + + align:start position:0% +otherwise you have some lower bound down + + + align:start position:0% +otherwise you have some lower bound down +alpha 1 so which is at least of a Q plus + + align:start position:0% +alpha 1 so which is at least of a Q plus + + + align:start position:0% +alpha 1 so which is at least of a Q plus +Epsilon and likewise you have some lower + + align:start position:0% +Epsilon and likewise you have some lower + + + align:start position:0% +Epsilon and likewise you have some lower +bound of alpha 2 you have some lower + + align:start position:0% +bound of alpha 2 you have some lower + + + align:start position:0% +bound of alpha 2 you have some lower +bound down alpha 2 and this lower bound + + align:start position:0% +bound down alpha 2 and this lower bound + + + align:start position:0% +bound down alpha 2 and this lower bound +is plus 2 Epsilon okay so you keep + + align:start position:0% +is plus 2 Epsilon okay so you keep + + + align:start position:0% +is plus 2 Epsilon okay so you keep +iterating you see the next thing is for + + align:start position:0% +iterating you see the next thing is for + + + align:start position:0% +iterating you see the next thing is for +epsilon and so on so if you get to more + + align:start position:0% +epsilon and so on so if you get to more + + + align:start position:0% +epsilon and so on so if you get to more +than this many iterations you go more + + align:start position:0% +than this many iterations you go more + + + align:start position:0% +than this many iterations you go more +than one okay it's bigger than 1 if K + + align:start position:0% +than one okay it's bigger than 1 if K + + + align:start position:0% +than one okay it's bigger than 1 if K +yes ceiling of log base 2 of 1 over + + align:start position:0% +yes ceiling of log base 2 of 1 over + + + align:start position:0% +yes ceiling of log base 2 of 1 over +Epsilon and that will be a contradiction + + align:start position:0% +Epsilon and that will be a contradiction + + + align:start position:0% +Epsilon and that will be a contradiction +to the hypothesis ok so this is a small + + align:start position:0% +to the hypothesis ok so this is a small + + + align:start position:0% +to the hypothesis ok so this is a small +variation on this fact that you cannot + + align:start position:0% +variation on this fact that you cannot + + + align:start position:0% +variation on this fact that you cannot +increment too many times each time you + + align:start position:0% +increment too many times each time you + + + align:start position:0% +increment too many times each time you +go up by bit + + align:start position:0% +go up by bit + + + align:start position:0% +go up by bit +whereas we save a little bit because the + + align:start position:0% +whereas we save a little bit because the + + + align:start position:0% +whereas we save a little bit because the +number of iterations is now logarithmic + + align:start position:0% +number of iterations is now logarithmic + + + align:start position:0% +number of iterations is now logarithmic +because you double in epsilon each time + + align:start position:0% + + + + align:start position:0% + +what + + align:start position:0% + + + + align:start position:0% + +if I give you a function f f3 to the M + + align:start position:0% +if I give you a function f f3 to the M + + + align:start position:0% +if I give you a function f f3 to the M +and you it's a subspace so this notation + + align:start position:0% +and you it's a subspace so this notation + + + align:start position:0% +and you it's a subspace so this notation +means subspace let me write f sub u to + + align:start position:0% +means subspace let me write f sub u to + + + align:start position:0% +means subspace let me write f sub u to +be the function obtained by averaging f + + align:start position:0% +be the function obtained by averaging f + + + align:start position:0% +be the function obtained by averaging f +on each you Cosette so you have some + + align:start position:0% +on each you Cosette so you have some + + + align:start position:0% +on each you Cosette so you have some +subspace you partition your space into + + align:start position:0% +subspace you partition your space into + + + align:start position:0% +subspace you partition your space into +translate of that subspace and you + + align:start position:0% +translate of that subspace and you + + + align:start position:0% +translate of that subspace and you +replace the value of F on each co set by + + align:start position:0% +replace the value of F on each co set by + + + align:start position:0% +replace the value of F on each co set by +its average on that Co set so this is + + align:start position:0% +its average on that Co set so this is + + + align:start position:0% +its average on that Co set so this is +similar to what we did with graphics + + align:start position:0% +similar to what we did with graphics + + + align:start position:0% +similar to what we did with graphics +you're stepping + + align:start position:0% +you're stepping + + + align:start position:0% +you're stepping +so you're averaging each block so now + + align:start position:0% +so you're averaging each block so now + + + align:start position:0% +so you're averaging each block so now +let me prove something which is kind of + + align:start position:0% +let me prove something which is kind of + + + align:start position:0% +let me prove something which is kind of +like an arithmetic regularity lemma and + + align:start position:0% +like an arithmetic regularity lemma and + + + align:start position:0% +like an arithmetic regularity lemma and +I mean this statement will be will be + + align:start position:0% +I mean this statement will be will be + + + align:start position:0% +I mean this statement will be will be +new to you but it should look similar to + + align:start position:0% +new to you but it should look similar to + + + align:start position:0% +new to you but it should look similar to +some of the statements we've seen before + + align:start position:0% +some of the statements we've seen before + + + align:start position:0% +some of the statements we've seen before +in the course and the statement is that + + align:start position:0% +in the course and the statement is that + + + align:start position:0% +in the course and the statement is that +for every epsilon there exists some M + + align:start position:0% +for every epsilon there exists some M + + + align:start position:0% +for every epsilon there exists some M +which is a function of Epsilon and in + + align:start position:0% +which is a function of Epsilon and in + + + align:start position:0% +which is a function of Epsilon and in +fact it will be bounded in terms of + + align:start position:0% +fact it will be bounded in terms of + + + align:start position:0% +fact it will be bounded in terms of +power of height and most waterlog with + + align:start position:0% +power of height and most waterlog with + + + align:start position:0% +power of height and most waterlog with +making one over epsilon such that for + + align:start position:0% +making one over epsilon such that for + + + align:start position:0% +making one over epsilon such that for +every function f on f 3 to the n that + + align:start position:0% +every function f on f 3 to the n that + + + align:start position:0% +every function f on f 3 to the n that +our value is bounded between 0 and 1 + + align:start position:0% +our value is bounded between 0 and 1 + + + align:start position:0% +our value is bounded between 0 and 1 +there exist subspaces W and you + + align:start position:0% + + + + align:start position:0% + +we're the co dimension of W is at most M + + align:start position:0% +we're the co dimension of W is at most M + + + align:start position:0% +we're the co dimension of W is at most M +so you should think of this as the + + align:start position:0% +so you should think of this as the + + + align:start position:0% +so you should think of this as the +course partition in the fine partition + + align:start position:0% +course partition in the fine partition + + + align:start position:0% +course partition in the fine partition +in the partition regularity lemma and + + align:start position:0% +in the partition regularity lemma and + + + align:start position:0% +in the partition regularity lemma and +the co dimension is corresponds to the + + align:start position:0% +the co dimension is corresponds to the + + + align:start position:0% +the co dimension is corresponds to the +number of pieces right so three ways to + + align:start position:0% +number of pieces right so three ways to + + + align:start position:0% +number of pieces right so three ways to +call dimension is the number of cosets + + align:start position:0% +call dimension is the number of cosets + + + align:start position:0% +call dimension is the number of cosets +so you have bound in many parts and have + + align:start position:0% +so you have bound in many parts and have + + + align:start position:0% +so you have bound in many parts and have +two partitions and what I would like is + + align:start position:0% +two partitions and what I would like is + + + align:start position:0% +two partitions and what I would like is +that the number okay so if I I want F to + + align:start position:0% +that the number okay so if I I want F to + + + align:start position:0% +that the number okay so if I I want F to +be pseudo-random after doing this + + align:start position:0% +be pseudo-random after doing this + + + align:start position:0% +be pseudo-random after doing this +partitioning so to speak + + align:start position:0% +partitioning so to speak + + + align:start position:0% +partitioning so to speak +and this corresponds to the statement + + align:start position:0% +and this corresponds to the statement + + + align:start position:0% +and this corresponds to the statement +that if I look at F minus FW then the + + align:start position:0% +that if I look at F minus FW then the + + + align:start position:0% +that if I look at F minus FW then the +maximum Fourier coefficient yes quite + + align:start position:0% +maximum Fourier coefficient yes quite + + + align:start position:0% +maximum Fourier coefficient yes quite +small we're quite small means that most + + align:start position:0% +small we're quite small means that most + + + align:start position:0% +small we're quite small means that most +epsilon over the size of you complement + + align:start position:0% +epsilon over the size of you complement + + + align:start position:0% +epsilon over the size of you complement +size of U perp and also there is this + + align:start position:0% +size of U perp and also there is this + + + align:start position:0% +size of U perp and also there is this +other condition which tells you that the + + align:start position:0% +other condition which tells you that the + + + align:start position:0% +other condition which tells you that the +l-3 norms between F sub U and F sub W + + align:start position:0% +l-3 norms between F sub U and F sub W + + + align:start position:0% +l-3 norms between F sub U and F sub W +are related in this way so we haven't + + align:start position:0% +are related in this way so we haven't + + + align:start position:0% +are related in this way so we haven't +seen this before in fact specifically + + align:start position:0% +seen this before in fact specifically + + + align:start position:0% +seen this before in fact specifically +this inequality is very ad hoc to the + + align:start position:0% +this inequality is very ad hoc to the + + + align:start position:0% +this inequality is very ad hoc to the +application of popular difference in + + align:start position:0% +application of popular difference in + + + align:start position:0% +application of popular difference in +three APs + + align:start position:0% +three APs + + + align:start position:0% +three APs +but we have seen something similar where + + align:start position:0% +but we have seen something similar where + + + align:start position:0% +but we have seen something similar where +this relationship is replaced by + + align:start position:0% +this relationship is replaced by + + + align:start position:0% +this relationship is replaced by +something that accounts for the + + align:start position:0% +something that accounts for the + + + align:start position:0% +something that accounts for the +difference between our two norms so if + + align:start position:0% +difference between our two norms so if + + + align:start position:0% +difference between our two norms so if +you go back to your notes when we + + align:start position:0% +you go back to your notes when we + + + align:start position:0% +you go back to your notes when we +discussed regularity lemma in a more + + align:start position:0% +discussed regularity lemma in a more + + + align:start position:0% +discussed regularity lemma in a more +analytic fashion we have that and you + + align:start position:0% +analytic fashion we have that and you + + + align:start position:0% +analytic fashion we have that and you +should think of this you know when we + + align:start position:0% +should think of this you know when we + + + align:start position:0% +should think of this you know when we +discussed strong regularity lemma this + + align:start position:0% +discussed strong regularity lemma this + + + align:start position:0% +discussed strong regularity lemma this +definition here is roughly corresponds + + align:start position:0% +definition here is roughly corresponds + + + align:start position:0% +definition here is roughly corresponds +to the definition in the fine partition + + align:start position:0% +to the definition in the fine partition + + + align:start position:0% +to the definition in the fine partition +versus the coarse partition the edge + + align:start position:0% +versus the coarse partition the edge + + + align:start position:0% +versus the coarse partition the edge +densities are roughly the similar when + + align:start position:0% +densities are roughly the similar when + + + align:start position:0% +densities are roughly the similar when +you do the further partitioning we're + + align:start position:0% +you do the further partitioning we're + + + align:start position:0% +you do the further partitioning we're +not changing densities up by very much + + align:start position:0% + + + + align:start position:0% + +okay so that's arithmetic regularity + + align:start position:0% +okay so that's arithmetic regularity + + + align:start position:0% +okay so that's arithmetic regularity +lemma and once you have the statement I + + align:start position:0% +lemma and once you have the statement I + + + align:start position:0% +lemma and once you have the statement I +mean I think the hardest part is writing + + align:start position:0% +mean I think the hardest part is writing + + + align:start position:0% +mean I think the hardest part is writing +down this statement once you have the + + align:start position:0% +down this statement once you have the + + + align:start position:0% +down this statement once you have the +statement I mean the proof is office + + align:start position:0% +statement I mean the proof is office + + + align:start position:0% +statement I mean the proof is office +kind of this follow your nose approach + + align:start position:0% +kind of this follow your nose approach + + + align:start position:0% +kind of this follow your nose approach +where you first define the sequence of + + align:start position:0% +where you first define the sequence of + + + align:start position:0% +where you first define the sequence of +epsilon epsilon naught is 1 epsilon + + align:start position:0% +epsilon epsilon naught is 1 epsilon + + + align:start position:0% +epsilon epsilon naught is 1 epsilon +sub-k plus 1 and okay so don't worry + + align:start position:0% +sub-k plus 1 and okay so don't worry + + + align:start position:0% +sub-k plus 1 and okay so don't worry +about this for now you will see in a + + align:start position:0% +about this for now you will see in a + + + align:start position:0% +about this for now you will see in a +second why these numbers are chosen let + + align:start position:0% +second why these numbers are chosen let + + + align:start position:0% +second why these numbers are chosen let +me write R sub K to be the set of ours + + align:start position:0% +me write R sub K to be the set of ours + + + align:start position:0% +me write R sub K to be the set of ours +so there will be characters such that + + align:start position:0% +so there will be characters such that + + + align:start position:0% +so there will be characters such that +before a coefficient and R is at least + + align:start position:0% +before a coefficient and R is at least + + + align:start position:0% +before a coefficient and R is at least +epsilon sub K okay so the ours are + + align:start position:0% +epsilon sub K okay so the ours are + + + align:start position:0% +epsilon sub K okay so the ours are +supposed to identify how we're going to + + align:start position:0% +supposed to identify how we're going to + + + align:start position:0% +supposed to identify how we're going to +do the partitioning now the size of this + + align:start position:0% +do the partitioning now the size of this + + + align:start position:0% +do the partitioning now the size of this +R is bounded so we claim that the size + + align:start position:0% +R is bounded so we claim that the size + + + align:start position:0% +R is bounded so we claim that the size +of R is at most one over epsilon sub K + + align:start position:0% +of R is at most one over epsilon sub K + + + align:start position:0% +of R is at most one over epsilon sub K +squared and that's because there is this + + align:start position:0% +squared and that's because there is this + + + align:start position:0% +squared and that's because there is this +possible identity which tells you that + + align:start position:0% +possible identity which tells you that + + + align:start position:0% +possible identity which tells you that +the l2 sum of the Fourier coefficients + + align:start position:0% +the l2 sum of the Fourier coefficients + + + align:start position:0% +the l2 sum of the Fourier coefficients +is equal to the l2 of the function which + + align:start position:0% +is equal to the l2 of the function which + + + align:start position:0% +is equal to the l2 of the function which +is at most 1 so the number of Fourier + + align:start position:0% +is at most 1 so the number of Fourier + + + align:start position:0% +is at most 1 so the number of Fourier +coefficients that exceed a certain + + align:start position:0% +coefficients that exceed a certain + + + align:start position:0% +coefficients that exceed a certain +quantity cannot be too many + + align:start position:0% + + + + align:start position:0% + +okay so let you now be the subspace + + align:start position:0% +okay so let you now be the subspace + + + align:start position:0% +okay so let you now be the subspace +defined by taking the orthogonal + + align:start position:0% +defined by taking the orthogonal + + + align:start position:0% +defined by taking the orthogonal +complement of these R's and let's note + + align:start position:0% +complement of these R's and let's note + + + align:start position:0% +complement of these R's and let's note +that if we take alpha sub K to be the if + + align:start position:0% +that if we take alpha sub K to be the if + + + align:start position:0% +that if we take alpha sub K to be the if +we take alpha sub K to be the l3 norm + + align:start position:0% +we take alpha sub K to be the l3 norm + + + align:start position:0% +we take alpha sub K to be the l3 norm +cube or the function derived from + + align:start position:0% +cube or the function derived from + + + align:start position:0% +cube or the function derived from +averaging F along the use and then + + align:start position:0% +averaging F along the use and then + + + align:start position:0% +averaging F along the use and then +looking at the third moment of these + + align:start position:0% +looking at the third moment of these + + + align:start position:0% +looking at the third moment of these +densities so these alphas we can apply + + align:start position:0% +densities so these alphas we can apply + + + align:start position:0% +densities so these alphas we can apply +the increment lemma initially to deduce + + align:start position:0% +the increment lemma initially to deduce + + + align:start position:0% +the increment lemma initially to deduce +that there exists okay so in particular + + align:start position:0% +that there exists okay so in particular + + + align:start position:0% +that there exists okay so in particular +this number here is at least alpha cubed + + align:start position:0% +this number here is at least alpha cubed + + + align:start position:0% +this number here is at least alpha cubed +by convexity so by the previous lemma + + align:start position:0% +by convexity so by the previous lemma + + + align:start position:0% +by convexity so by the previous lemma +there exists some K no more than on the + + align:start position:0% +there exists some K no more than on the + + + align:start position:0% +there exists some K no more than on the +order of 1 over a log 1 over epsilon + + align:start position:0% +order of 1 over a log 1 over epsilon + + + align:start position:0% +order of 1 over a log 1 over epsilon +such that 2 alpha sub K minus alpha sub + + align:start position:0% +such that 2 alpha sub K minus alpha sub + + + align:start position:0% +such that 2 alpha sub K minus alpha sub +K plus 1 is at least the density of F + + align:start position:0% +K plus 1 is at least the density of F + + + align:start position:0% +K plus 1 is at least the density of F +cubed minus Epsilon okay so this alpha + + align:start position:0% +cubed minus Epsilon okay so this alpha + + + align:start position:0% +cubed minus Epsilon okay so this alpha +is supposed to be the density of F + + align:start position:0% + + + + align:start position:0% + +all right so we find this K and we have + + align:start position:0% +all right so we find this K and we have + + + align:start position:0% +all right so we find this K and we have +this bound over here from satisfying + + align:start position:0% +this bound over here from satisfying + + + align:start position:0% +this bound over here from satisfying +that inequality so this is a density + + align:start position:0% +that inequality so this is a density + + + align:start position:0% +that inequality so this is a density +increment argument the energy increment + + align:start position:0% +increment argument the energy increment + + + align:start position:0% +increment argument the energy increment +argument doing the energy in chrome + + align:start position:0% +argument doing the energy in chrome + + + align:start position:0% +argument doing the energy in chrome +argument basically the same argument as + + align:start position:0% +argument basically the same argument as + + + align:start position:0% +argument basically the same argument as +the one that we did when we discussed + + align:start position:0% +the one that we did when we discussed + + + align:start position:0% +the one that we did when we discussed +graph regularity lemma + + align:start position:0% +graph regularity lemma + + + align:start position:0% +graph regularity lemma +but now presented in a slightly + + align:start position:0% +but now presented in a slightly + + + align:start position:0% +but now presented in a slightly +different form in the different water of + + align:start position:0% +different form in the different water of + + + align:start position:0% +different form in the different water of +logic but it's the same argument and + + align:start position:0% +logic but it's the same argument and + + + align:start position:0% +logic but it's the same argument and +what we would like to show is that you + + align:start position:0% +what we would like to show is that you + + + align:start position:0% +what we would like to show is that you +also have this pseudo randomness + + align:start position:0% +also have this pseudo randomness + + + align:start position:0% +also have this pseudo randomness +condition about having small Fourier + + align:start position:0% +condition about having small Fourier + + + align:start position:0% +condition about having small Fourier +coefficients so what's happening here + + align:start position:0% +coefficients so what's happening here + + + align:start position:0% +coefficients so what's happening here +was the Fourier coefficients you know + + align:start position:0% +was the Fourier coefficients you know + + + align:start position:0% +was the Fourier coefficients you know +how is the Fourier coefficient of an + + align:start position:0% +how is the Fourier coefficient of an + + + align:start position:0% +how is the Fourier coefficient of an +average death related to the original f + + align:start position:0% +average death related to the original f + + + align:start position:0% +average death related to the original f +so that's something we want to + + align:start position:0% +so that's something we want to + + + align:start position:0% +so that's something we want to +understand up there and that's something + + align:start position:0% +understand up there and that's something + + + align:start position:0% +understand up there and that's something +that's not hard to analyze because if + + align:start position:0% +that's not hard to analyze because if + + + align:start position:0% +that's not hard to analyze because if +you have a function U or W 1 then the + + align:start position:0% +you have a function U or W 1 then the + + + align:start position:0% +you have a function U or W 1 then the +Fourier coefficients of this averaged + + align:start position:0% +Fourier coefficients of this averaged + + + align:start position:0% +Fourier coefficients of this averaged +version it's very much related to the + + align:start position:0% +version it's very much related to the + + + align:start position:0% +version it's very much related to the +original function it turns out that if + + align:start position:0% +original function it turns out that if + + + align:start position:0% +original function it turns out that if +you take an R which is in the orthogonal + + align:start position:0% +you take an R which is in the orthogonal + + + align:start position:0% +you take an R which is in the orthogonal +complement then the Fourier coefficient + + align:start position:0% +complement then the Fourier coefficient + + + align:start position:0% +complement then the Fourier coefficient +doesn't change and if you are not in the + + align:start position:0% +doesn't change and if you are not in the + + + align:start position:0% +doesn't change and if you are not in the +orthogonal complement and before your + + align:start position:0% +orthogonal complement and before your + + + align:start position:0% +orthogonal complement and before your +coefficient gets zeroed out + + align:start position:0% + + + + align:start position:0% + +okay so that's that's something that's + + align:start position:0% +okay so that's that's something that's + + + align:start position:0% +okay so that's that's something that's +not too hard to check no urge you to + + align:start position:0% +not too hard to check no urge you to + + + align:start position:0% +not too hard to check no urge you to +think about it + + align:start position:0% +think about it + + + align:start position:0% +think about it +so with that in mind let's go back to + + align:start position:0% +so with that in mind let's go back to + + + align:start position:0% +so with that in mind let's go back to +verifying this over here so what we have + + align:start position:0% +verifying this over here so what we have + + + align:start position:0% +verifying this over here so what we have +now is that the so this quantity which + + align:start position:0% +now is that the so this quantity which + + + align:start position:0% +now is that the so this quantity which +measures largest for your coefficient + + align:start position:0% +measures largest for your coefficient + + + align:start position:0% +measures largest for your coefficient +the difference between F and u sub k + + align:start position:0% +the difference between F and u sub k + + + align:start position:0% +the difference between F and u sub k +plus 1 is at most and what u sub k plus + + align:start position:0% +plus 1 is at most and what u sub k plus + + + align:start position:0% +plus 1 is at most and what u sub k plus +1 is doing is we're looking at possible + + align:start position:0% +1 is doing is we're looking at possible + + + align:start position:0% +1 is doing is we're looking at possible +large Fourier coefficients and we are + + align:start position:0% +large Fourier coefficients and we are + + + align:start position:0% +large Fourier coefficients and we are +getting rid of them right so we're + + align:start position:0% +getting rid of them right so we're + + + align:start position:0% +getting rid of them right so we're +zeroing out these large for your + + align:start position:0% +zeroing out these large for your + + + align:start position:0% +zeroing out these large for your +coefficients so that the remaining for + + align:start position:0% +coefficients so that the remaining for + + + align:start position:0% +coefficients so that the remaining for +your coefficients are all quite small + + align:start position:0% + + + + align:start position:0% + +but we chose our R so that if so this + + align:start position:0% +but we chose our R so that if so this + + + align:start position:0% +but we chose our R so that if so this +big R so that if your little ARS not in + + align:start position:0% +big R so that if your little ARS not in + + + align:start position:0% +big R so that if your little ARS not in +a big R then the Fourier coefficient + + align:start position:0% +a big R then the Fourier coefficient + + + align:start position:0% +a big R then the Fourier coefficient +must be small that's how we chose the + + align:start position:0% +must be small that's how we chose the + + + align:start position:0% +must be small that's how we chose the +big R so so we have this bound over here + + align:start position:0% +big R so so we have this bound over here + + + align:start position:0% +big R so so we have this bound over here +and by the definition of the epsilon we + + align:start position:0% +and by the definition of the epsilon we + + + align:start position:0% +and by the definition of the epsilon we +have that bound so we're combining with + + align:start position:0% +have that bound so we're combining with + + + align:start position:0% +have that bound so we're combining with +this estimate upper bound estimate on + + align:start position:0% +this estimate upper bound estimate on + + + align:start position:0% +this estimate upper bound estimate on +the size of our sub K ok so point being + + align:start position:0% + + + + align:start position:0% + +so now take W to be u sub K + 1 + u to + + align:start position:0% +so now take W to be u sub K + 1 + u to + + + align:start position:0% +so now take W to be u sub K + 1 + u to +be u sub K and then we have everything + + align:start position:0% +be u sub K and then we have everything + + + align:start position:0% +be u sub K and then we have everything +that we want + + align:start position:0% + + + + align:start position:0% + +great questions why is the co dimension + + align:start position:0% +great questions why is the co dimension + + + align:start position:0% +great questions why is the co dimension +of W is small so what is the co + + align:start position:0% +of W is small so what is the co + + + align:start position:0% +of W is small so what is the co +dimension of W so we won't know that the + + align:start position:0% +dimension of W so we won't know that the + + + align:start position:0% +dimension of W so we won't know that the +co dimension of W is bounded right so + + align:start position:0% +co dimension of W is bounded right so + + + align:start position:0% +co dimension of W is bounded right so +the co dimension of W is hoping the co + + align:start position:0% +the co dimension of W is hoping the co + + + align:start position:0% +the co dimension of W is hoping the co +dimension of any of this u sub case is + + align:start position:0% +dimension of any of this u sub case is + + + align:start position:0% +dimension of any of this u sub case is +at most three raised to the number of + + align:start position:0% +at most three raised to the number of + + + align:start position:0% +at most three raised to the number of +ours that produce it and the size of our + + align:start position:0% +ours that produce it and the size of our + + + align:start position:0% +ours that produce it and the size of our +is bounded so if we pick M to that so + + align:start position:0% +is bounded so if we pick M to that so + + + align:start position:0% +is bounded so if we pick M to that so +that uniformly bounds the size of our + + align:start position:0% +that uniformly bounds the size of our + + + align:start position:0% +that uniformly bounds the size of our +then we have a bound on the cult + + align:start position:0% +then we have a bound on the cult + + + align:start position:0% +then we have a bound on the cult +dimension okay so that's that's + + align:start position:0% +dimension okay so that's that's + + + align:start position:0% +dimension okay so that's that's +important right so we need to know that + + align:start position:0% +important right so we need to know that + + + align:start position:0% +important right so we need to know that +we call dimension is small otherwise you + + align:start position:0% +we call dimension is small otherwise you + + + align:start position:0% +we call dimension is small otherwise you +know if you do have the ban on all + + align:start position:0% +know if you do have the ban on all + + + align:start position:0% +know if you do have the ban on all +dimensions you can just take the zero + + align:start position:0% +dimensions you can just take the zero + + + align:start position:0% +dimensions you can just take the zero +subspace trivially everything is true + + align:start position:0% + + + + align:start position:0% + +you have a regularity lemma and what + + align:start position:0% +you have a regularity lemma and what + + + align:start position:0% +you have a regularity lemma and what +comes with the regularity lemma is a + + align:start position:0% +comes with the regularity lemma is a + + + align:start position:0% +comes with the regularity lemma is a +counting lemma so let me write down the + + align:start position:0% +counting lemma so let me write down the + + + align:start position:0% +counting lemma so let me write down the +county mama and I'll skip the proof so + + align:start position:0% +county mama and I'll skip the proof so + + + align:start position:0% +county mama and I'll skip the proof so +the county level tells you that if you + + align:start position:0% +the county level tells you that if you + + + align:start position:0% +the county level tells you that if you +have F and G both functions on F 3 p.m. + + align:start position:0% +have F and G both functions on F 3 p.m. + + + align:start position:0% +have F and G both functions on F 3 p.m. +and you it's a subspace then ok so let + + align:start position:0% +and you it's a subspace then ok so let + + + align:start position:0% +and you it's a subspace then ok so let +me define so the quantity that I'm + + align:start position:0% +me define so the quantity that I'm + + + align:start position:0% +me define so the quantity that I'm +interested in is so I'm interested in + + align:start position:0% +interested in is so I'm interested in + + + align:start position:0% +interested in is so I'm interested in +understanding 3 a piece where the common + + align:start position:0% +understanding 3 a piece where the common + + + align:start position:0% +understanding 3 a piece where the common +difference is in a particular subspace + + align:start position:0% + + + + align:start position:0% + +okay so we claim that the three AP count + + align:start position:0% +okay so we claim that the three AP count + + + align:start position:0% +okay so we claim that the three AP count +of F with common difference restricted + + align:start position:0% +of F with common difference restricted + + + align:start position:0% +of F with common difference restricted +to the subspace you so it's similar + + align:start position:0% +to the subspace you so it's similar + + + align:start position:0% +to the subspace you so it's similar +between F and G if F and G are close to + + align:start position:0% +between F and G if F and G are close to + + + align:start position:0% +between F and G if F and G are close to +each other in for you + + align:start position:0% + + + + align:start position:0% + +not quite because okay so something like + + align:start position:0% +not quite because okay so something like + + + align:start position:0% +not quite because okay so something like +this we saw earlier in a proof of Ross + + align:start position:0% +this we saw earlier in a proof of Ross + + + align:start position:0% +this we saw earlier in a proof of Ross +theorem if we don't restrict the common + + align:start position:0% +theorem if we don't restrict the common + + + align:start position:0% +theorem if we don't restrict the common +difference turns out if you restrict the + + align:start position:0% +difference turns out if you restrict the + + + align:start position:0% +difference turns out if you restrict the +common difference you lose a little bit + + align:start position:0% +common difference you lose a little bit + + + align:start position:0% +common difference you lose a little bit +okay so you lose a factor which is + + align:start position:0% +okay so you lose a factor which is + + + align:start position:0% +okay so you lose a factor which is +basically the size of the complement of + + align:start position:0% +basically the size of the complement of + + + align:start position:0% +basically the size of the complement of +you so I won't prove that but now let me + + align:start position:0% +you so I won't prove that but now let me + + + align:start position:0% +you so I won't prove that but now let me +go on to the punchline so if we start + + align:start position:0% +go on to the punchline so if we start + + + align:start position:0% +go on to the punchline so if we start +with again F function in your space + + align:start position:0% +with again F function in your space + + + align:start position:0% +with again F function in your space +taking values between 0 & 1 and I have + + align:start position:0% +taking values between 0 & 1 and I have + + + align:start position:0% +taking values between 0 & 1 and I have +subspaces U and W I claim that P if I + + align:start position:0% +subspaces U and W I claim that P if I + + + align:start position:0% +subspaces U and W I claim that P if I +look at f average through W and I + + align:start position:0% +look at f average through W and I + + + align:start position:0% +look at f average through W and I +consider 3 AP counts with common + + align:start position:0% +consider 3 AP counts with common + + + align:start position:0% +consider 3 AP counts with common +difference restricted to you then this + + align:start position:0% +difference restricted to you then this + + + align:start position:0% +difference restricted to you then this +quantity here is lower bounded by this + + align:start position:0% +quantity here is lower bounded by this + + + align:start position:0% +quantity here is lower bounded by this +difference between L 3 norms + + align:start position:0% + + + + align:start position:0% + +okay so I claim this is true so this is + + align:start position:0% +okay so I claim this is true so this is + + + align:start position:0% +okay so I claim this is true so this is +just some inequality right there's some + + align:start position:0% +just some inequality right there's some + + + align:start position:0% +just some inequality right there's some +inequality and you know so I for all the + + align:start position:0% +inequality and you know so I for all the + + + align:start position:0% +inequality and you know so I for all the +things that I did back in high school + + align:start position:0% +things that I did back in high school + + + align:start position:0% +things that I did back in high school +doing math competitions I think the one + + align:start position:0% +doing math competitions I think the one + + + align:start position:0% +doing math competitions I think the one +skill which I think I find most helpful + + align:start position:0% +skill which I think I find most helpful + + + align:start position:0% +skill which I think I find most helpful +now is being able to do inequalities and + + align:start position:0% +now is being able to do inequalities and + + + align:start position:0% +now is being able to do inequalities and +you know I thought I would never see the + + align:start position:0% +you know I thought I would never see the + + + align:start position:0% +you know I thought I would never see the +three variable inequalities again but + + align:start position:0% +three variable inequalities again but + + + align:start position:0% +three variable inequalities again but +when I saw this one so you know Fox and + + align:start position:0% +when I saw this one so you know Fox and + + + align:start position:0% +when I saw this one so you know Fox and +famine when they first showed me a + + align:start position:0% +famine when they first showed me a + + + align:start position:0% +famine when they first showed me a +somewhat different proof of an approach + + align:start position:0% +somewhat different proof of an approach + + + align:start position:0% +somewhat different proof of an approach +that didn't go through this specific + + align:start position:0% +that didn't go through this specific + + + align:start position:0% +that didn't go through this specific +inequality I told them hey you know + + align:start position:0% +inequality I told them hey you know + + + align:start position:0% +inequality I told them hey you know +there's this thing I remember from high + + align:start position:0% +there's this thing I remember from high + + + align:start position:0% +there's this thing I remember from high +school it's called sure sin equality and + + align:start position:0% +school it's called sure sin equality and + + + align:start position:0% +school it's called sure sin equality and +I thought I would never see it again + + align:start position:0% +I thought I would never see it again + + + align:start position:0% +I thought I would never see it again +after high school but apparently it's + + align:start position:0% +after high school but apparently it's + + + align:start position:0% +after high school but apparently it's +still useful so okay so what shirt's + + align:start position:0% +still useful so okay so what shirt's + + + align:start position:0% +still useful so okay so what shirt's +inequality says this is one of those + + align:start position:0% +inequality says this is one of those + + + align:start position:0% +inequality says this is one of those +three variable inequalities that you + + align:start position:0% +three variable inequalities that you + + + align:start position:0% +three variable inequalities that you +would know if you did Math Olympiad okay + + align:start position:0% +would know if you did Math Olympiad okay + + + align:start position:0% +would know if you did Math Olympiad okay +so it's inequality between non-negative + + align:start position:0% +so it's inequality between non-negative + + + align:start position:0% +so it's inequality between non-negative +actually it's true for real numbers as + + align:start position:0% +actually it's true for real numbers as + + + align:start position:0% +actually it's true for real numbers as +well but let's say it's non-negative + + align:start position:0% +well but let's say it's non-negative + + + align:start position:0% +well but let's say it's non-negative +real numbers so that's your sanity so if + + align:start position:0% +real numbers so that's your sanity so if + + + align:start position:0% +real numbers so that's your sanity so if +you look at the left hand side + + align:start position:0% + + + + align:start position:0% + +the left-hand side is it can be written + + align:start position:0% +the left-hand side is it can be written + + + align:start position:0% +the left-hand side is it can be written +as a sum in the following way I mean it + + align:start position:0% +as a sum in the following way I mean it + + + align:start position:0% +as a sum in the following way I mean it +can be written in the following way + + align:start position:0% +can be written in the following way + + + align:start position:0% +can be written in the following way +so it's expectation over XYZ that are + + align:start position:0% +so it's expectation over XYZ that are + + + align:start position:0% +so it's expectation over XYZ that are +three APs + + align:start position:0% +three APs + + + align:start position:0% +three APs +in the same you Cosette there's I'm + + align:start position:0% +in the same you Cosette there's I'm + + + align:start position:0% +in the same you Cosette there's I'm +counting three a piece with common + + align:start position:0% +counting three a piece with common + + + align:start position:0% +counting three a piece with common +difference restricted to you so common + + align:start position:0% +difference restricted to you so common + + + align:start position:0% +difference restricted to you so common +three a piece in the same new Cosette + + align:start position:0% +three a piece in the same new Cosette + + + align:start position:0% +three a piece in the same new Cosette +and I am looking at the product of F sub + + align:start position:0% +and I am looking at the product of F sub + + + align:start position:0% +and I am looking at the product of F sub +W evaluated on this three AP so what I + + align:start position:0% +W evaluated on this three AP so what I + + + align:start position:0% +W evaluated on this three AP so what I +would like to do now is apply shirts + + align:start position:0% +would like to do now is apply shirts + + + align:start position:0% +would like to do now is apply shirts +inequality to a B and C being these + + align:start position:0% +inequality to a B and C being these + + + align:start position:0% +inequality to a B and C being these +three numbers the point is you have this + + align:start position:0% +three numbers the point is you have this + + + align:start position:0% +three numbers the point is you have this +ABC on the left and then everything on + + align:start position:0% +ABC on the left and then everything on + + + align:start position:0% +ABC on the left and then everything on +the right involves only a subset of ABC + + align:start position:0% +the right involves only a subset of ABC + + + align:start position:0% +the right involves only a subset of ABC +and they simplify so if I do this then I + + align:start position:0% +and they simplify so if I do this then I + + + align:start position:0% +and they simplify so if I do this then I +lower bound this quantity by twice the + + align:start position:0% +lower bound this quantity by twice the + + + align:start position:0% +lower bound this quantity by twice the +expectation of x and y in same coset + + align:start position:0% + + + + align:start position:0% + +same you co set F sub W of x squared and + + align:start position:0% +same you co set F sub W of x squared and + + + align:start position:0% +same you co set F sub W of x squared and +F sub W of what maybe I've took two + + align:start position:0% +F sub W of what maybe I've took two + + + align:start position:0% +F sub W of what maybe I've took two +other things but they're all symmetric + + align:start position:0% +other things but they're all symmetric + + + align:start position:0% +other things but they're all symmetric +with respect to each other and minus the + + align:start position:0% +with respect to each other and minus the + + + align:start position:0% +with respect to each other and minus the +term that corresponds to this sum of + + align:start position:0% +term that corresponds to this sum of + + + align:start position:0% +term that corresponds to this sum of +cubes like that okay so this is a + + align:start position:0% +cubes like that okay so this is a + + + align:start position:0% +cubes like that okay so this is a +consequence of shirts inequality applied + + align:start position:0% +consequence of shirts inequality applied + + + align:start position:0% +consequence of shirts inequality applied +with ABC like this + + align:start position:0% + + + + align:start position:0% + +but now you see over here I can analyze + + align:start position:0% +but now you see over here I can analyze + + + align:start position:0% +but now you see over here I can analyze +this expression even further because if + + align:start position:0% +this expression even further because if + + + align:start position:0% +this expression even further because if +I let Y vary within the same you Cosette + + align:start position:0% +I let Y vary within the same you Cosette + + + align:start position:0% +I let Y vary within the same you Cosette +then over here averages out to you + + align:start position:0% +then over here averages out to you + + + align:start position:0% +then over here averages out to you +cosets right so U is bigger than W so + + align:start position:0% +cosets right so U is bigger than W so + + + align:start position:0% +cosets right so U is bigger than W so +what we have is so what we have over + + align:start position:0% +what we have is so what we have over + + + align:start position:0% +what we have is so what we have over +here is that it is at least twice of F F + + align:start position:0% +here is that it is at least twice of F F + + + align:start position:0% +here is that it is at least twice of F F +okay + + align:start position:0% +okay + + + align:start position:0% +okay +half of you f w squared fu minus + + align:start position:0% +half of you f w squared fu minus + + + align:start position:0% +half of you f w squared fu minus +expectation of F W squared F W cubed + + align:start position:0% +expectation of F W squared F W cubed + + + align:start position:0% +expectation of F W squared F W cubed +and I can use complexity F sub W to cat + + align:start position:0% + + + + align:start position:0% + +which is what we're looking for + + align:start position:0% + + + + align:start position:0% + +I'm learning through a little bit + + align:start position:0% +I'm learning through a little bit + + + align:start position:0% +I'm learning through a little bit +quicker because we're running out of + + align:start position:0% +quicker because we're running out of + + + align:start position:0% +quicker because we're running out of +time but all of these steps are fairly + + align:start position:0% +time but all of these steps are fairly + + + align:start position:0% +time but all of these steps are fairly +simple once you observe the first thing + + align:start position:0% +simple once you observe the first thing + + + align:start position:0% +simple once you observe the first thing +you can do is search in equality and + + align:start position:0% + + + + align:start position:0% + +we're almost there it's a work we're + + align:start position:0% +we're almost there it's a work we're + + + align:start position:0% +we're almost there it's a work we're +almost done we're almost done so from + + align:start position:0% +almost done we're almost done so from + + + align:start position:0% +almost done we're almost done so from +that lemma up there + + align:start position:0% +that lemma up there + + + align:start position:0% +that lemma up there +I claim now that for every epsilon there + + align:start position:0% +I claim now that for every epsilon there + + + align:start position:0% +I claim now that for every epsilon there +exists some M which is power log in one + + align:start position:0% +exists some M which is power log in one + + + align:start position:0% +exists some M which is power log in one +over epsilon such that if + + align:start position:0% +over epsilon such that if + + + align:start position:0% +over epsilon such that if +f is a function on f3 to the end + + align:start position:0% +f is a function on f3 to the end + + + align:start position:0% +f is a function on f3 to the end +taking values between 0 and 1 then there + + align:start position:0% +taking values between 0 and 1 then there + + + align:start position:0% +taking values between 0 and 1 then there +exists a subspace you of codimension at + + align:start position:0% +exists a subspace you of codimension at + + + align:start position:0% +exists a subspace you of codimension at +most M such that the 3p count 3 AP + + align:start position:0% +most M such that the 3p count 3 AP + + + align:start position:0% +most M such that the 3p count 3 AP +density with common difference + + align:start position:0% +density with common difference + + + align:start position:0% +density with common difference +restricted to you is at least the random + + align:start position:0% +restricted to you is at least the random + + + align:start position:0% +restricted to you is at least the random +bound minus epsilon okay why is this + + align:start position:0% +bound minus epsilon okay why is this + + + align:start position:0% +bound minus epsilon okay why is this +true well we put everything together + + align:start position:0% +true well we put everything together + + + align:start position:0% +true well we put everything together +choose U and W send regularity lemma and + + align:start position:0% + + + + align:start position:0% + +by counting lemma we have that the 3 AP + + align:start position:0% +by counting lemma we have that the 3 AP + + + align:start position:0% +by counting lemma we have that the 3 AP +density of F so it is at least so we're + + align:start position:0% +density of F so it is at least so we're + + + align:start position:0% +density of F so it is at least so we're +using counting lemma over here it has at + + align:start position:0% +using counting lemma over here it has at + + + align:start position:0% +using counting lemma over here it has at +least three AP density of F sub W view- + + align:start position:0% +least three AP density of F sub W view- + + + align:start position:0% +least three AP density of F sub W view- +a small error which we could control so + + align:start position:0% +a small error which we could control so + + + align:start position:0% +a small error which we could control so +this step is counting and now we apply + + align:start position:0% +this step is counting and now we apply + + + align:start position:0% +this step is counting and now we apply +the inequality up there + + align:start position:0% + + + + align:start position:0% + +and finally we chose our U and W in the + + align:start position:0% +and finally we chose our U and W in the + + + align:start position:0% +and finally we chose our U and W in the +regularity lemma so that this difference + + align:start position:0% +regularity lemma so that this difference + + + align:start position:0% +regularity lemma so that this difference +here is controlled so it is controlled + + align:start position:0% +here is controlled so it is controlled + + + align:start position:0% +here is controlled so it is controlled +by the random bound minus Epsilon + + align:start position:0% + + + + align:start position:0% + +and that's it so you change epsilon to + + align:start position:0% +and that's it so you change epsilon to + + + align:start position:0% +and that's it so you change epsilon to +for epsilon but you change it back and + + align:start position:0% +for epsilon but you change it back and + + + align:start position:0% +for epsilon but you change it back and +that's it so we have the statement that + + align:start position:0% +that's it so we have the statement that + + + align:start position:0% +that's it so we have the statement that +you have this subspace of bounded + + align:start position:0% +you have this subspace of bounded + + + align:start position:0% +you have this subspace of bounded +codimension + + align:start position:0% +codimension + + + align:start position:0% +codimension +where you have this popular difference + + align:start position:0% +where you have this popular difference + + + align:start position:0% +where you have this popular difference +result it doesn't quite guarantee you a + + align:start position:0% +result it doesn't quite guarantee you a + + + align:start position:0% +result it doesn't quite guarantee you a +single common difference because well + + align:start position:0% +single common difference because well + + + align:start position:0% +single common difference because well +you don't really want it to be the case + + align:start position:0% +you don't really want it to be the case + + + align:start position:0% +you don't really want it to be the case +where u is just a single point because I + + align:start position:0% +where u is just a single point because I + + + align:start position:0% +where u is just a single point because I +want a nonzero common difference but if + + align:start position:0% +want a nonzero common difference but if + + + align:start position:0% +want a nonzero common difference but if +u is large enough and it's large enough + + align:start position:0% +u is large enough and it's large enough + + + align:start position:0% +u is large enough and it's large enough +I found that codimension + + align:start position:0% +I found that codimension + + + align:start position:0% +I found that codimension +so that the size of U is large enough so + + align:start position:0% +so that the size of U is large enough so + + + align:start position:0% +so that the size of U is large enough so +then there exists some nouns your own + + align:start position:0% +then there exists some nouns your own + + + align:start position:0% +then there exists some nouns your own +common difference you pick some nonzero + + align:start position:0% +common difference you pick some nonzero + + + align:start position:0% +common difference you pick some nonzero +element of you on average it should work + + align:start position:0% +element of you on average it should work + + + align:start position:0% +element of you on average it should work +out just fine so I'll leave that to you + + align:start position:0% +out just fine so I'll leave that to you + + + align:start position:0% +out just fine so I'll leave that to you +one more thing I want to mention is that + + align:start position:0% +one more thing I want to mention is that + + + align:start position:0% +one more thing I want to mention is that +all of this machinery involving + + align:start position:0% +all of this machinery involving + + + align:start position:0% +all of this machinery involving +regularity in Fourier as were things + + align:start position:0% +regularity in Fourier as were things + + + align:start position:0% +regularity in Fourier as were things +we've done before carries over to other + + align:start position:0% +we've done before carries over to other + + + align:start position:0% +we've done before carries over to other +settings general abelian groups and also + + align:start position:0% +settings general abelian groups and also + + + align:start position:0% +settings general abelian groups and also +the integers and you may ask well we + + align:start position:0% +the integers and you may ask well we + + + align:start position:0% +the integers and you may ask well we +have this for 380s what about longer + + align:start position:0% +have this for 380s what about longer + + + align:start position:0% +have this for 380s what about longer +arithmetic progressions in the integers + + align:start position:0% +arithmetic progressions in the integers + + + align:start position:0% +arithmetic progressions in the integers +it turns out it is also true you know + + align:start position:0% +it turns out it is also true you know + + + align:start position:0% +it turns out it is also true you know +that green statement in the integers if + + align:start position:0% +that green statement in the integers if + + + align:start position:0% +that green statement in the integers if +you replace 3 AP by 4 AP that's a term + + align:start position:0% +you replace 3 AP by 4 AP that's a term + + + align:start position:0% +you replace 3 AP by 4 AP that's a term +of green and how involving higher-order + + align:start position:0% +of green and how involving higher-order + + + align:start position:0% +of green and how involving higher-order +quadratic analysis of quadratic for your + + align:start position:0% +quadratic analysis of quadratic for your + + + align:start position:0% +quadratic analysis of quadratic for your +analysis however and rather surprisingly + + align:start position:0% + + + + align:start position:0% + +for AP it's okay but five AP and longer + + align:start position:0% +for AP it's okay but five AP and longer + + + align:start position:0% +for AP it's okay but five AP and longer +it is false the corresponding statement + + align:start position:0% +it is false the corresponding statement + + + align:start position:0% +it is false the corresponding statement +about popular differences for five AP in + + align:start position:0% +about popular differences for five AP in + + + align:start position:0% +about popular differences for five AP in +integers is false there are counter + + align:start position:0% +integers is false there are counter + + + align:start position:0% +integers is false there are counter +examples so it's really a statement + + align:start position:0% +examples so it's really a statement + + + align:start position:0% +examples so it's really a statement +about three pieces for a piece and + + align:start position:0% +about three pieces for a piece and + + + align:start position:0% +about three pieces for a piece and +there's some magic cancellations that + + align:start position:0% +there's some magic cancellations that + + + align:start position:0% +there's some magic cancellations that +happen for a piece that make it true + + align:start position:0% + + + + align:start position:0% + +okay okay so that's all for today \ No newline at end of file diff --git a/DUyOjsFTOgQ.txt b/DUyOjsFTOgQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..eee7e7a92e25526441860e274a4aac86331758fd --- /dev/null +++ b/DUyOjsFTOgQ.txt @@ -0,0 +1,5443 @@ +ANNOUNCER: The following content +is provided under a + +Creative Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or to view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Great, hi everyone. + +It's great to be here, and +I hope you guys are + +having fun so far. + +It's great to meet +all of you too. + +So this is the day where we talk +about how to randomize. + +A few other topics will come +up here and there, and + +hopefully you will stop me +whenever you have questions, + +and let me know. + +So don't hesitate to stop even +if it's just a clarifying + +point or a deeper, more +substantive question about + +what I'm saying. + +The three basic components of +this morning's lecture will be + +first about methods of +randomization, and that'll + +be-- the majority of what we'll +talk about is going + +through a few different ways +that we talk about + +randomization when we +talk randomization. + +One of the common misperceptions +that I've seen + +in the world when I am meeting +with organizations or + +governments for the first time, +and they've heard of a + +randomized trial as a concept, +they often have a very well + +defined and narrowly defined +concept of what that means. + +And the fact is, there's a lot +of creative ways that we go + +about doing randomized trials +that adapt to different + +settings, because there's a lot +of situations in which you + +can't do what might be +considered the most standard + +prescription drug type +randomized trial. + +And so we have to be a little +bit creative in settings and + +understanding, what are the +constraints we're facing, and + +how can we adapt the methodology +to fit in this + +particular setting? + +Or maybe not, right? + +So that's going to be methods +of randomization, we'll go + +through a few of the key +approaches that we use. + +The second, and this is +a topic which really-- + +to say this is topic one, topic +two, topic three isn't + +quite exactly right. + +And by the time we finish one, +we're going to have talked a + +lot about number two and number +three, a lot of the + +number two being gathering +support for evaluation. + +And the point here is that one +of the reasons why we choose + +one method over another when +we're thinking about how to go + +about setting up the design is +because some methods are going + +to be easier for gathering +support for evaluation, and so + +that's part of a back and +forth process with + +organizations and situations. + +And then we're going to try to +walk through a typical plan, + +so to speak. + +Perhaps in my mind, one of the +single most important things + +to remember about doing an +evaluation is to remember that + +we're not trying to just +ask, how did we do? + +There's nothing wrong with +asking that, but it's very + +short-sighted. + +What we should be asking +is, what should we do? + +And that's the point of a good +evaluation, is to guide us in + +future decisions. + +If you're a donor, and you're +running a huge initiative, and + +you're spending $20 million +or something-- + +I'm just picking a number-- + +and you want to do an +evaluation of this. + +But because of whatever the +nature of your program is, + +this is it, this is the only +time you're ever going to do + +it, and it's a weird program +that you believe in, but it's + +weird, and no one else is +ever going to do it. + +I realize it's kind of a weird +example, just go with me. + +And so that's a situation +in which, I think, most + +reasonable people would say, +why are you doing an + +evaluation? + +What's the point? + +Is it just to pat yourself +on the back? + +Is that really the goal? + +Because if there's not future +money that's at stake, future + +money that we have to decide +how are we going to spend, + +what's the point of doing all +this, other than just to see + +whether I made a good decision +in the past or not? + +But that's not really useful, +that's not why we're here. + +We're here because we realize +that there are tons of future + +decisions being made, and we +need better information in + +order to make those decisions. + +And we need those as donors, +but we also need those as + +organizations. + +And that's one of the key things +going back to point + +number two in the outline. + +How do you get organizations +on board and excited and + +involved in evaluation? + +It's when the evaluation is +actually able to speak to + +questions that they have. + +And so good evaluations often +help to identify the key + +implementer's questions +and answer them. + +And I know I'm making that sound +really simple, like oh, + +that's all we have to do. + +But the key really is to taking +that type of approach + +when working with +organizations. + +How do you turn these things +into win win for operations? + +If you're a leader in an +organization, and you're not a + +researcher, so you kind of +understand the value of + +research, and it sounds like a +good thing, but you're hired + +because you need to go and +deliver these services, and + +you need to be efficient in +delivering your services. + +You want to know that the +research is nice and good and + +needs to be done, but isn't +going to get in your way. + +Or if it is going to get in your +way, you're going to get + +something for it. + +And that's a very common +attitude, and I can respect + +that attitude, if someone is +just really focused on + +operations. + +And so the question is, how can +we design research, how + +can we listen to what the +operations people are saying + +about what their challenges are, +what their struggles are, + +the choices that they're +making that are tough? + +And actually build into the +research ways of helping them + +answer those questions. + +So that's something that +we often aim to do. + +Methods of randomization. + +I'm going to walk through four +different methods that we will + +often use: basic lottery, a +phase in, a rotation, and + +encouragement. + +And we'll talk about +each of these. + +These are not all mutually +exclusive + +methods, to be clear. + +So I'm just going to point out +there's different ways and + +levers for doing things. + +Is that readable? + +OK. + +Sorry, let me skip that slide, +and we'll come back to it at + +the end to recap. + +So let's start with the +simplest, which is a lottery. + +A lottery is like a clinical +trial, where if we were + +running a test for prescription +drugs, it would + +be a very standard, regimented +process. + +We'd be perhaps in +some hospital. + +We'd have some sort of intake +process with people who are in + +the hospital and have certain +criteria, and then we'd + +approach them and say, +there's a new drug. + +It's experimental. + +There's risks, there's +potential + +rewards, it's up to you. + +You have the following disease, +these are the issues + +you're facing. + +What do you want to do? + +But that's a situation +where we would take + +1,000 of the people. + +They would all get informed +consent being told about what + +the risks were. + +There would be parameters set +up so that if the outcomes + +were proving very decisive +one way or another, + +the study would end. + +But it's fairly straightforward +from a + +statistical standpoint and +from a research design + +standpoint. + +You bring them in, 1,000 are +entered into the study, 500 of + +them are randomly chosen to get +a pill, 500 are randomly + +chosen to get a placebo, and +you measure the outcomes, + +whatever they may be, +from getting the + +pill versus the placebo. + +And so the question is, can we +apply this in social science, + +outside the laboratory +type setting? + +So some of the constraints that +we face when we try to + +take that really simplistic +way of doing things. + +So the first is that +we often can't-- + +when you're doing a randomized +trial on a prescription drug, + +the whole point is the +research study. + +That is what it is. + +There is no program +around this. + +It's a study to see what +the effectiveness of a + +particular pill is. + +If we're working with an +organization that is trying to + +do teacher training in schools, +trying to issue + +loans, trying to promote +savings, trying to teach + +agricultural practices, +there's a program + +there that's involved. + +And you can't just go in and +change things around in the + +program without paying attention +to what this + +actually means for the goals +of the program has. + +So the second really important +element is that it must be + +perceived as fair. + +Now the thing that's the single +most common situation + +that I find myself in is when +I'm dealing with organizations + +that are capacity constrained. + +They only have enough money +to go to 200 schools. + +They only have enough money +to make 1,000 loans. + +They only have enough marketing +people to visit + +5,000 households and promote +savings, or whatever the + +activity is they're doing, +there's some capacity + +constraint. + +And so one principle that I've +actually taught my children, + +very young, they all know-- + +so like last week, we had to +fly, and I hadn't seen them + +for the weekend. + +So the kids all wanted +to sit next to me. + +I have three kids. + +And it was resolved +very simply, + +no whining, no nothing. + +We just randomly chose one. + +And they all knew immediately. + +Now in fairness, I've +done this before. + +But they knew instinctfully just +that this is-- there's no + +complaining here. + +There's no favoritism. + +We took each of their +boarding passes, we + +flipped them upside down. + +We chose one. + +Actually I said it backwards. + +It was one that couldn't +sit with me. + +It was two with me and one +without, so we chose the one + +who didn't. + +Now ironically, the two that did +win ended up both falling + +asleep immediately, and so I +switched seats in the end. + +But that's a different issue. + +But the point hopefully is +clear, that there's really, in + +some respect, nothing more fair +than a random process. + +It is giving everybody who is +eligible, who's aware or not + +aware, depending on how the set +up is, but everybody who + +is within a setting of-- + +who has access to a program, and +giving them all the same + +chance of participating. + +Now in a lot of settings, we +would actually suggest that + +this is actually more fair than, +for instance, letting + +politics and letting nepotism +and letting any sort of other + +favoritism play in to +deciding who gets + +things and who doesn't. + +Which we all know, in many +places are serious issues for + +the allocation of any sort of +resource, that depending on + +how it happens, then that could +actually be the worst + +possible outcome that we +would want to see as + +philanthropists, as utilitarian +individuals + +interested first and foremost +in alleviating poverty. + +But you could tell other stories +in which there is + +processes where you really want +to reach the very poorest + +of the poor. + +And so you have to-- + +let's come back to that +issue towards the end. + +I'll use that as an example +later in the lecture. + +So it must be politically +feasible. + +Now, it might not be politically +feasible if people + +who have the power in the local +settings are not willing + +to do it, because they want to +be able to choose the people + +in their networks to provide +the services to them. + +So the politically feasible +could be for the exact reason + +that we want to do +it randomly. + +It also can just be politically +infeasible for + +other interpersonal reasons. + +The right people who need to be +part of the decision making + +process just haven't really +brought into the value of an + +evaluation. + +And there are situations we face +all the time like that, + +where there's nothing +we can do. + +There's just someone who is the +decision maker who needs + +to be on board with something, +and is simply not on board + +with doing a rigorous +evaluation, and perhaps + +concerned about the results that +are going to come out of + +the project, in terms of is +suspicious of external + +evaluators. + +They feel like we know what +works and what doesn't, and + +they don't want to relax +control to an outsider. + +There's also obviously +situations where people just + +feel like what do +I have to lose-- + +I'm sorry, what do +I have to gain? + +Where organizations will be of +the ilk that, look, we have + +lots of media, lots +of attention + +for what we're doing. + +Everybody tells us it's +a great idea. + +We're executing, we're +implementing. + +What do I have to gain from +doing an evaluation. + +If we absorbed more money right +now, I wouldn't know how + +to spend it. + +And there are organizations that +I've interacted with that + +are more or less of that ilk. + +And so there's clearly +situations like that. + +Must be ethical. + +So this is something we're +always very concerned about + +and cautious about. + +And there are many situations +we find ourselves for the + +reasons I mentioned above, in +terms of fairness, that the + +random process is arguably +the more ethical process. + +But they're clearly situations +that someone could put forward + +where you could say, +well, wait a + +second, that's not good. + +That's not right. + +So these are issues that one +has to be sensitive to. + +I think one of the things that's +most important here is + +not necessarily whether +something's-- we might all be + +able to analytically agree on +the ethics, but that doesn't + +mean that everybody else will +agree and perceive things the + +way we perceive them. + +And so even if we can +analytically understand that a + +random process is fair, if +someone is just bringing a + +certain bias to the table in +terms of the way they think + +about a random processes, then +this can be a problem. + +And again, this is one of +persuasion and personality + +more so than logic +and philosophy. + +So, why resource constraints are +an evaluators best friend. + +I think I've actually now said +most of this, but basically, + +most programs have limited +resources. + +And so examples of where this +has been done is training + +programs for entrepreneurs +or farmers. + +School vouchers is perhaps one +of the single most common + +examples we've seen this done, +where there's a government + +program to provide school +vouchers for private school or + +secondary school, or even +college, and they just can't + +educate the entire population +of people who want to go to + +private school. + +And so there's a voucher +program, there's an enrollment + +process, you apply. + +There's a public lottery +literally done openly through + +the newspapers or on TV. + +And that type of transparency +is done in order to make it + +politically feasible, so +that everybody can see. + +If it's not done that way, then +the concerns become about + +whether is really truly random, +it was done behind + +closed doors. + +Was the politician really just +kind of pulling out his + +favorite people? + +So lotteries become, in the +simplest of case, it's often + +the starting point. + +If we can pull off a public +lottery in this way, or + +private, either way, then it +really does become the + +simplest approach. + +So when it's possible, +it's nice. + +But there are clearly situations +that come up where + +this is not going +to be possible. + +So there's also flexible ways +of doing the lottery. + +So let's go through a few +different scenarios here. + +So first of all, there's often a +question about the unit over + +which you randomize. + +What we mean by this is, if +you're going to do a lottery, + +do you do a lottery at +the individual level? + +Or do you do a lottery, for +instance, at the village, by + +offering an entire village +a package of services? + +Or if you're building wells, for +instance, this is actually + +a treatment that's really being +done at the village, not + +the individual. + +There might be some individuals +who live closer to + +the well than others further, +but you're really choosing a + +village and building wells. + +And so the lottery system +is flexible in this way. + +The general concept +is the same. + +We've done interventions in +Ghana, for instance, where the + +randomization was done at the +village level for receiving a + +community driven development +type program. + +And so different geographic +clusters were all put into a + +public lottery, and half of +them randomly chosen to + +receive financial resources +in order to help build an + +epicenter, and lots of labor +in terms of helping and + +guiding and facilitating the +process for building these + +quote, epicenters. + +So the second point is that +sometimes when we do + +lotteries, sometimes it's kind +of a full versus partial. + +What we mean by this is whether +it's done all at once + +in one kind of public way, or +whether it's done through an + +ongoing process. + +And depending on how things +are set up, sometimes it's + +done one way or the other. + +So the school vouchers is an +example where we would do it + +all at the very same time. + +There's a whole bunch of people +who apply for a school + +voucher program. + +There's 5,000 applicants, +there's 2,000 school vouchers, + +we randomly choose 2,000, they +get the school vouchers. + +In a situation that we've done +in South Africa and also the + +Philippines, when we build it +into a credit scoring process. + +And so every day, there's 10 +applications for a loan. + +The bank is not going to +issue all the loans. + +They take those 10, they +put them in three + +piles, yes, no and maybe. + +And then what happens is they +take the maybes and they say, + +we only want to make +half of these. + +And then we randomize which half +of those get credit and + +which do not. + +And this is something we've done +now a few times in order + +to measure the impact +of credit. + +From the bank's perspective, +this is exactly one of the + +cases I was talking about before +where there's a win win + +from an operations standpoint. + +This is a bank who says, these +are genuine maybes. + +We don't know if we should be +lending to them or not. + +We're not sure if +it's profitable + +for us, we're a bank. + +So this is a method for them +that helps mitigate their + +risks in deciding what their +portfolio should + +look like as a whole. + +And from our perspective, +provides this nice lottery + +system where some people are +randomly assigned to get + +credit and others not. + +So let's go back, and now let's +think about some of the + +things that will often happen +when you do a lottery design. + +Suppose you have 500 +applicants and + +you have 500 slots. + +At first glance, you might think +you're kind of screwed. + +You set up this nice, big +process, and lo and behold, it + +turns out you didn't have +over-subscription. + +You thought you did. + +You thought you were going to +use this over-subscription to + +randomize who gets in +and who does not. + +So what can you do in this +type of situation? + +So there's some low hanging +fruit type answers, and + +there's also a possibility +that this wouldn't work. + +But the first is, could you +increase the outreach + +activities? + +That a lot of times in this +situation, what this really + +means is that whatever was done +to market this program + +was not effective in getting in +the right number of people. + +Because the intent was to get +1,000 or 2,000 people + +applying, and only +500 applied. + +So now think about, from an +operations standpoint, what + +does that tell you +about applying? + +And that might be one of those +cases where there's actually + +useful, interesting research +for the organization. + +If the organization was saying, +we're going to get + +2,000 people applying for this, +and then only get 500, + +well, it tells you that maybe +you could do something to help + +them learn how they can get +their marketing up. + +And so then you can test out +different approaches for + +marketing that helps the +operations learn more about + +what is it that brings in people +to apply for these + +scholarships, or whatever it is +that's being done, and at + +the same time, benefits the +program from increasing-- + +I'm sorry, benefits the +evaluation from getting a + +larger intake. + +The risk with this is that you +end up bringing people into + +the program who weren't really +part of the target program. + +So if that's the answer, then +this is actually a really bad + +idea to go out and do more +extensive marketing. + +If you have to go through extra +leaps and bounds in + +order to bring people in, so +much so that it changes the + +nature of what the program is, +that's a situation where you + +might want to go back to the +drawing board and think again + +about what the right +answer is. + +Suppose there's 2,000 +applicants, and suppose in the + +process of doing this that the +organization that's doing + +things says, you know what? + +There's 500 worthy candidates +and there's 500 slots. + +So a simple lottery +would not work. + +So we have some sort of +screening process, and we + +ranked them. + +And we can rank them, and we +put numbers by everyone. + +So why should we do anything +other than just + +taking the top 500? + +So when that type of thing +happens, a lot of times the + +questions that we want to ask +then are about what was the + +screening process that +was being used here? + +So let's go back to the credit +scoring study that I was + +referring to. + +The thing that we're struck by +when we've done this credit + +scoring is really how wide that +maybe category is, when + +you really get into the nuts and +bolts in talking with the + +lenders about where their data +are coming from, and the + +quality of the data, and how +they're individual judgment + +weighs in to influence where +people fall within those three + +buckets, the yes, no, maybe. + +And the fact is that the +profitability of the person at + +the high end of the maybe is +really not much different, if + +at all, from the low +end of the maybe. + +And so the point is that when +you get inside and figure out, + +what is it that's really going +on that made them say, well, + +we had 2,000 applicants +and we had 500 + +eligible, so we're done. + +If you got inside the box a +little bit more and talked + +with them about how they got +to those 500, things would + +start coming out of that process +that might be the + +exact areas were you can +say, why is that + +necessary as a criteria? + +Is that really something you +want to filter on to bring + +people in or out? + +Yeah? + +AUDIENCE: Let's say your +criteria are, one is gender + +and one is educational level +for the purpose here. + +And let's say that, for whatever +reason, you can't be + +sure that the educational +level is really + +what they say it is. + +So you could go ahead and +select on the basis of + +educational level, knowing +that maybe people are not + +telling the truth and +that would be OK. + +You could remove that as a +criteria entirely, or you + +could find some other +kind of proxy. + +That might work, right? + +PROFESSOR: Right. + +AUDIENCE: OK. + +Kind of random. + +PROFESSOR: But that's exactly +kind of one of the key things + +that would come out. + +So the point is, let's just go +with the middle example. + +If you really think that the +education was what you wanted + +to screen on, but you don't have +confidence in what you're + +looking at as actually being a +reliable measure of education. + +But yet that's causing +a filter to draw + +you down to the 500. + +But then when you get inside +and you realize this is a + +really bad measure +of education, why + +are we using this? + +And then all of the sudden you +relax that one rule and you're + +up to 900 people, it tells you +that maybe this isn't such a + +good way to be filtering, and +I should be doing the 900. + +And while I'm at it, maybe I +should try to think about how + +to measure education better +or something. + +So let's take another kind of +example, which is-- and this + +actually mimics the story I have +up here about training, + +but the credit scoring +example is another + +example exactly of this. + +Where you end up-- + +and I said that right +here, sorry-- + +you can think about having two +different piles of people + +that, when you say there's 500 +that are eligible, really + +maybe what you have is not 500 +that are eligible, but you had + +200 that are really eligible. + +You really want them in the +program, they must be there. + +And then the next 300, you're a +little more questionable on. + +And the next 300 really weren't +so different from the + +300 after those. + +And so what you can do in that +type of situation is set up a + +process where you say look, if +you have certain eligibility + +requirements, you're in. + +And then you're also not +part of the evaluation. + +And it's the next 300 that we're +going to combine with + +the following 300 after that, +we're going to put together a + +pool of 600, and we're going +to randomize those. + +Now this has a clear benefit +and a clear cost. + +The benefit is that you can +now get a very nice, clean + +estimate on the impact +of those 600. + +The cost is we've changed the +research question here. + +We've changed the evaluation +question. + +We're no longer answering the +question, what is the impact + +on everyone who receives +this service? + +And that's not a good thing. + +We don't want to lead +with methodology and + +then force fit questions. + +We want to set the research +questions. + +We have to ask ourselves, how +much are we losing by only + +studying those individuals? + +And in some settings, those are +the exact individuals you + +want to study. + +But in some, maybe that's +not so the case. + +So in the credit scoring, I +think of those as the exact + +people we want to study. + +Because when we think about +programs that expand access to + +credit, what we're doing is +we're talking about those + +people on the bubble, and we're +talking about ways of + +getting them access that they +didn't have otherwise. + +And the people who have really, +really good credit + +scores and are very credit +worthy, they're not the ones + +we're thinking about +when we think about + +expanding access to credit. + +So let me give you another +example of one where this + +would be bad. + +So we are doing these programs +about targeting the + +ultra-poor, where we +go into countries-- + +I'm sorry, we do go +into countries, + +but we go into villages-- + +and we first identify the 20 +poorest people in the village. + +And then of those 20, we hold +a lottery, and 10 receive + +services and 10 do not. + +And then we do this in +about 30 villages. + +And the organizations we're +working with, it's exactly the + +setting I'm describing here. + +The organizations we're +working with + +have a fixed budget. + +They can provide services in +each situation to 1,200 + +people, and that's it. + +And if we went into +120 villages, they + +can do 10 per village. + +If we went into 60 villages, +they could do 20. + +But either way they look at it, +they got 1,200 people that + +they're going to be able to +provide these services to. + +It's going to be an asset +transfer, they're going be on + +goats and training and +consumption bundles. + +Now, if in some these villages +people said, + +well, wait a second. + +We have the 20 poorest people +in the village, yes. + +But four of these people are +really just standout poor. + +They're much, much poorer +than everybody else. + +So we want to exclude the four +very, very, very poorest and + +make sure that they get it with +certainty, and then only + +evaluate the other 16. + +So this would actually be a bad +thing from the evaluation + +perspective. + +It might be the right thing to +do, and we can talk about what + +the trade offs are. + +We're not actually doing that, +and I'll explain why. + +But from an evaluation +perspective, that would be now + +changing the research question +in a bad way, as compared to + +the credit scoring, where +I was arguing + +that it's a good change. + +So why? + +Well, because this is a problem +where we really do + +actually want to know the impact +on those bottom four as + +well as the next 16. + +And so if we did something where +we just allowed the very + +bottom four to get the program +with certainty, and then only + +evaluated the next 16, we're +missing an important part of + +the sample frame. + +Now, the reason why, in these +settings, we've done it as the + +full 20 is because +realistically, when we've + +actually gone into these +villages and done this type of + +exercise, it's difficult, if +not impossible, to get + +consensus that there's really +four people that stand out. + +And the fact is, even when +you're measuring poverty-- + +and we do have some objective +things, we all know that + +there's lots of components +to poverty. + +There's lots of ways +of measuring it. + +It's not even just consumption +this month, its vulnerability + +in general as a concept, which +could be about the variation + +over time, and how vulnerable +you are, and how your social + +networks are for helping +you absorb shocks. + +There's just many different ways +of measuring it, and it's + +unrealistic to think then we +can go into a village and + +really draw these amazingly fine +lines to say these people + +are standout different +than the rest. + +When you're going into a village +of this size and + +you're finding the 20 poorest, +those 20 are statistically + +indistinguishable from each +other, more or less. + +So that's the philosophy +of the organizations. + +And that's the reason +for doing it the + +way we're doing it. + +So sometimes, exclusion +is not desirable. + +Sometimes there's no way, +whatever the context is, of + +excluding individuals. + +So other points that we will +often use is the expansion of + +a program, or any sort of +program where there's some + +sort of initial stage, and +then what you're doing is + +you're simply randomizing where +that initial stage is, + +or where the program +expands into. + +A program is only going to go to +so many villages, and they + +can't exclude, but they can +control where their + +individuals, where their credit +officers, where their + +program officers, education +trainers, whatever it is that + +they're doing, they obviously +can control what villages they + +go to and what they do not. + +So when there is a process +like this, where there's + +gradual expansion, we often +will think about doing a + +program evaluation using +a phase in approach. + +A phase in approach basically +says, look, we're going to go + +to all 1,200 of these villages +over the next three years, but + +we can randomize which ones +we go to in each year. + +So everybody's going to get +services in the long run. + +Now one thing that's nice about +that is, particularly + +when there's community led +interventions, there's + +oftentimes a desire to have +some involvement from + +everybody in the program +at some point + +in time in the program. + +And this is often something that +organizations do ask for. + +So phase in approaches allow +for that more naturally, + +because everybody's going +to be receiving a + +service at some point. + +Similarly, the rotation-- + +which I'll mention in a second-- +is a very similar + +twist on the phase in. + +Where the rotation, instead of +having it be where you slowly + +phase in a process, it's a +process where everybody's + +actually receiving a service +at all points in time, and + +we're just randomizing +who gets what. + +So we'll talk about some +examples in a moment about + +when that can work. + +So some key advantages is that +everyone gets something + +eventually, and this provides +incentives to maintain contact + +as well with control villages. + +They're not just participating +in surveys, although we do do + +a lot of surveys sometimes where +there is no intervention + +related, and people are +often more than-- + +at least in our experience-- +more than happy to participate + +in this interesting, weird +thing, with these people + +coming and asking us all +these questions. + +But having said that, there are +situations where you want + +that continuous support and +continuous buy in to what + +we're doing, and so the +advantage is that it provides + +them some incentive to +maintain contact. + +Some of the concerns is that it +does complicate estimating + +long line effects. + +If the goal was to study +something over 10 years, but + +everybody got phased in at the +end of three, well, you can't + +study the 10 year effects. + +You can study the effect of +getting something for two more + +years 10 years later, but +that's not nearly as + +interesting as asking what the +10 year effect is from getting + +a particular service. + +So let me give you an example of +a situation where the first + +is actually perfectly +interesting. + +Take neonatal care. + +If you want to study the effect +of neonatal care, doing + +a phase in across villages is +perfectly fine, because this + +is something that is going +to be affecting infants. + +And so when you provide that +neonatal care, and you do this + +as a phase in, you're now +studying those children, and + +this is perfectly fine. + +You can study now the effect +of the neonatal care over a + +10, 15 year horizon, +even though it was + +phased in to everybody. + +Because once it's phased in, the +control area of those kids + +are three, four, five years old, +and so it doesn't apply. + +So I think the main thing to +talk about in terms of phase + +ins that does become an issue +about expectations. + +So let me give you the +simplest example. + +In the world of credit, this +is usually something that + +concerns me a lot when we're +talking about doing studies. + +And in fact, I've personally +been involved in studies where + +there was a proposal to do a +phased in credit program and + +we said no. + +We didn't do it, because we were +very concerned about what + +happens to a control group +individual who was told, + +you're going to get a loan, +but just please wait six + +months, or year, or year and a +half, or two years, whatever + +the amount is. + +Now the longer you have to wait, +the less it's an issue. + +But if it's a relatively short +period of time, like a year, + +then the question is, well, +what were they going to do + +with that money? + +And is it something they're +willing to wait a year for? + +And if the answer is yes, well +then this is a real problem + +for thinking that this is a +valid control group, because + +what it says is, we're going to +see a delay in an activity + +specifically because of +getting access to + +this loan in one year. + +So what it says is they did +have other options. + +They were a little bit more +expensive perhaps, a little + +more costly either in +time or interest. + +And they said, you know what? + +I don't need to build +that new roof now. + +I don't need to buy that new +sewing machine for my + +enterprise. + +I'll go ahead and just put it +off, and I'll do it in a year. + +And what it would do is it would +lead us to overestimate + +the impact of getting access +to credit, whereas if they + +weren't promised this good +loan in the year, they + +would've just borrowed at +a little bit of a higher + +interest rate right now. + +And they still would have made +the investment in their + +business, they just would have +had a higher interest cost + +that would cause us to +overestimate the impact of our + +program, because +we would only-- + +the true impact is just really +a savings in interest, not + +about access to credit in +a binary sense, but + +just about the price. + +But yet what we would then find +ourselves measuring is + +seeing a treatment group of +people who fix their homes and + +bought sewing machines for +their businesses, and a + +control that didn't, and we +would think that aha, there + +was a real binary constraint +here where people were + +actually held back from getting +access to credit. + +And this program didn't have +that positive effect. + +So a rotation design. + +So a rotation design is +basically groups getting + +treatment in turns. + +Group A gets treatment in the +first period, group B gets + +treatment in the second. + +The main advantage is it's +perceived as fair and easier + +to get accepted. + +Everybody's getting something, +we're just randomizing what + +you get in a given round. + +So we have the same anticipation +issue that we + +just mentioned with phase +in as one concern here. + +It depends on what the two +treatments are, but if you + +really want that other treatment +that other people + +are getting, and you're told +you're going to get it in a + +year, this could affect +your behavior now + +for the same reason. + +Also it does have the same long +term problem of the phase + +in, in that everybody-- + +if we're just rotating-- +everybody + +is getting the treatment. + +Now, another twist on rotation +is not rotating just-- + +call it like a placebo +design, so to speak. + +Suppose that you just have two +different treatments doing two + +totally different things, +everybody gets something. + +And you use one to measure +the impact of the + +other and vice versa. + +So it's similar to rotation, +except not going full circle. + +It just means everybody +gets something. + +So in something like that, you +don't have this long term + +impact issue, or this issue. + +But you do have a problem where +it's not so clear what + +you're comparing anymore. + +So you'd have to be really +careful and think about what + +it is you're trying to do. + +We tend to think that a lot of +interventions have indirect + +effects in many facets +of our life. + +So if you're providing +training about + +entrepreneurship to one group, +and another group you're + +providing some health service, +and you think, well, this is + +great, because what does +entrepreneurship training have + +to do with health? + +And what does health +have to do with + +entrepreneurship training? + +So I can provide my health +services over here and measure + +the health outcomes for my other +group and compare them. + +And the same thing with +business activity. + +But it's not too hard to tell +stories where these are going + +to interact with each other. + +So you're healthier, and this +makes you more able to work, + +and your business does better. + +Your business does better, this +makes you richer, and you + +spend more money on health. + +It's not hard to tell stories +across two seemingly unrelated + +sectors where you will have that +type of effect on each. + +You have to think about +those types of issues. + +Yeah? + +AUDIENCE: Can a rotation work +well in agriculture? + +A given country would have-- + +so you'd like to give +the farmers-- + +everybody gets something. + +Some people get credit, some +people get seeds, some people + +get a variety of things. + +But obviously some places have +good soil, some places the + +farmers are near a road, and the +data that you need to look + +at your sampling design is kind +of tricky, because you + +may not know that much about all +the variables that would + +impact a farmer's success. + +Rotation seems a nice way to-- + +because there are so many +different treatments that + +people can get, that it would +seem pretty tricky to + +implement if there were--? + +PROFESSOR: So I think, in that +type of setting what you're + +describing, we'll come +to one in the end. + +But let me just say an example +here, which is the question + +you're proposing about +agriculture is about how + +different treatments will +interact with other + +treatments, and with +underlying context. + +So there's two things going +on in your question. + +One is how does soil quality +affect whether a certain + +treatment is effective or not? + +And the second is maybe credit +alone is bad, and maybe seeds + +alone is bad, but the two +together is good, and things + +of this nature. + +So that's not a setting where +we would think instinctively + +about a rotation design. + +That's a study where we would +think about two things. + +One is making sure that our +study is being done in a wide + +enough variety of soil, to use +that example, so that we can + +actually study the effect on one +soil quality and another. + +And then the second thing is we +were thinking about having + +multiple treatments, but not in +a rotation style, but in a + +way that you have some people, +they get seed. + +Some people, they +get training. + +Some people, they get +seed plus training. + +Some people, they get nothing. + +So we'll get to an example like +that hopefully towards + +the end, but that's +that design. + +A rotation design is really more +about when you're doing + +something that realistically +will not have an indirect + +effect on the other group. + +So the example I'm going to give +you is a rotation study + +that was done, the Balsakhi Case +that's done, I think it's + +one of the cases in +your reading. + +It's what what you do +this morning, right? + +So that's a classic rotation +example, because what we're + +doing is, some schools got third +grade, and some schools + +got fourth grade, and +then they rotate. + +And the idea is as long as the +third graders don't affect the + +fourth, and the fourth graders +don't affect the third, then + +this is good, and every +school got something. + +And then we just rotate around +what they're getting. + +And that's what we mean more +by rotation design. + +The key here is that this is a +great example of where the + +rotation design was a useful way +of getting the support of + +the schools. + +It's going to the schools and +get them to agree to do all + +these tests with the children. + +And it would have been hard to +just go in and get them to do + +tests without being offered some +service along with that. + +Now they're willing to accept +that the service only went to + +one grade, not both. + +They understood it was a phase +in within their school, one + +gets it one year, that +other, the next. + +But that was the way of +getting the schools to + +cooperate was by offering +it through this + +type of rotation design. + +So next is encouragement +design. + +Now encouragement +designs are-- + +first of all, this is orthogonal +to everything else + +I've been saying. + +Encouragement design can be done +on top of a phase in, on + +top of a rotation, on +top of a lottery. + +This is not mutually +exclusive with the + +others that I've discussed. + +Yeah? + +AUDIENCE: I just had +a question on + +the phase in approach. + +PROFESSOR: Yeah? + +AUDIENCE: So suppose you wanted +to roll out packaging + +group one, and then you'll roll +out packaging group two. + +When you roll out packaging, you +notice that something is + +not working that well, and then +you wanted to tweak it a + +little bit, you wanted +to change the spec. + +And for the sake of the +experiment, are you not + +supposed to tweak it when you +roll it out to the second + +group, you just keep +it the same? + +Because [UNINTELLIGIBLE PHRASE]? + +PROFESSOR: Right. + +So great question. + +I think the key here is to +think about the timeline. + +I don't really have +a chalkboard. + +The key is to remember that with +the phase in-- so let's + +go with a really simple +phase in, two waves. + +So in that setting, the second +group, when you do the + +treatment with them, that's +actually after + +the study is over. + +So the idea is that they're +really your control group, but + +they're participating with you +because they know they're + +going to get it in the future, +or whatever the + +circumstance is. + +So that's a situation in which +the answer is yeah, you can do + +whatever you want with them. + +But if you did know from +operational observations that + +the treatment itself wasn't +working so well, then just + +remember that when you're +evaluating something, what + +you're evaluating was a program +which you already + +think from operational reasons +was less than effective. + +And so that should perhaps +inform you a little bit about + +things like what to measure in +terms of what you want to put + +in the followup surveys. + +I suppose we could complicate +your question a little bit and + +add a third wave. + +So you have three waves, +one for each year. + +And after the first year you +learn, oh, turns out we + +shouldn't have done +it like this. + +We should have done it +differently, and so you want + +to change things for +the second wave. + +And that's perfectly fine. + +It does mean now when you're +doing your analysis, you + +should think about this +as two studies. + +You have your first wave, and +you can compare that to your + +wave three, that is control +for the entire study. + +And then you have your second +wave, and you can look at them + +for one year and compare them to +wave three, and you really + +have two different studies +in that setting. + +So encouragement designs, like +I said, this is not mutually + +exclusive to the others. + +And encouragement design, +just think about + +what the word means. + +It means we're encouraging +people to do something. + +We're not forcing, we're +not mandating. + +That means the control group +does not necessarily have + +nobody getting services, and +a treatment group does not + +necessarily have everybody +getting the service. + +There's simply something done +to encourage people to do + +something, to participate. + +Now the key here is to think +about what we're really + +saying, is the control in the +phrase randomized control + +trial, the reason for the word +control is this idea that the + +researcher has some control over +the process in deciding + +who gets a service +and who doesn't. + +So now we're just moving the +control, and it's no longer + +over who gets the service +and who doesn't. + +It's over who's offered the +service and who's not, or who + +has some encouragement to +get the service or not. + +And we still have perfect +control if it's executed + +properly over that offer, over +that suggestion, that + +encouragement. + +But we don't have perfect +control over who actually gets + +the service. + +So a very simple example of this +is suppose that I gave + +each of you a marketing brochure +to go to Au Bon Pain + +during lunch and go because of +their delicious scones, and I + +only gave it to half of you. + +I am now encouraging half of you +to go, the other half not. + +Anybody can go to Au Bon Pain, +I'm not controlling that. + +And if I wanted to then, for +some reason, study the effect + +of going to Au Bon Pain, +I could do that. + +I'm not sure what the point +of that would be. + +But the point is, I'm only +controlling who receives this + +offer and who doesn't. + +I'm not controlling who actually +goes to Au Bon Pain + +and who does not. + +And so this is often the easiest +thing to control in + +the process. + +And the entire key here from +a statistical perspective-- + +not the entire, we'll go into +some other issues-- is about + +what that differential usage +rate will be among those who + +were encouraged and those +who were not. + +And when you get into power +calculations later in this + +week, that's going to be a +very important element to + +think about. + +Because if that encouragement +is really, really weak and + +just barely changes people's +behavior, it means you need a + +huge sample. + +In an extreme, an encouragement +design is + +exactly a perfectly controlled +randomized controlled trial. + +An encouragement that gets +people who get the marketing, + +every single one of you goes +to Au Bon Pain, and if you + +didn't receive the marketing, +nobody goes. + +Statistically it's +the same now as a + +perfect lottery system. + +But usually when we're doing +encouragement design is when + +we have some expectation for it +not to be perfect, and so + +we're using that. + +So what makes something +a good encouragement? + +So I think there's two +things to think + +about that are important. + +One is that it's not +itself a treatment. + +The minute the encouragement +design itself becomes a + +treatment, then we have to think +about what is it that + +you're actually evaluating +here. + +Your goal is for your +encouragement to be totally + +innocuous, to just by chance, +by randomness, some people + +will be more likely to use +a service than others. + +So you want it to be as +innocuous as possible. + +So a good idea is typically +marketing. + +We typically think of marketing +as a good approach, + +just making people aware of +a service makes them more + +likely to use it. + +So we've done marketing +experiments, for instance, in + +the Philippines a lot where +we're doing some sort of door + +to door marketing of +a savings product + +offering people savings. + +Anybody in the village could +walk into the bank and open a + +bank account. + +But realistically, only those +who get a knock on their door + +become aware enough of +it to actually go and + +open up a bank account. + +Here's a bad idea. + +Let's provide training to people +that encourages them to + +use credit. + +So let's bring them in, let's +give them a big course about + +business management and how to +use credit in order to take + +out a loan. + +And let's use that as an +encouragement tool for + +measuring the effect of credit, +because after doing + +this course, they'll be +more likely to borrow. + +So the problem with this, if +we want to look at business + +outcomes, is we just gave them +a month long course in + +management of an enterprise. + +And that alone is going to +have an impact on their + +enterprise, we think, we hope. + +And so if it does, well +then, what are you + +measuring the impact on? + +Was it an impact of the +training program? + +Or was it an impact of getting +access to credit? + +And you can't separate +these out at all. + +So this first thing to think +about is just making sure that + +treatment is really innocuous. + +In econometrics, we refer +to this as the exclusion + +restriction, in that what it's +saying is that we want to make + +sure that the only-- + +if we're going to draw a link +from the encouragement to the + +take up decision to the outcome +measure we care about, + +that the only path through +which the encouragement + +affects the outcome is as it +generates higher take up. + +If it has its own effect outside +of the decision to + +take up, now it's a problem +econometrically, and we can't + +really claim that we're +measuring the impact of using + +the service. + +We could only measure the net +effect of the two together. + +So the second issue +is for whom are we + +estimating the treatment. + +So here's my favorite tongue +in cheek example for this. + +Suppose we went into a village +and we offered free alcohol to + +anybody who takes out a loan. + +Might be great in the first +stage in the sense that it + +generates lots of higher +borrowing. + +But what are we measuring +here in terms + +of who we're studying? + +We're studying people who +respond to this particular + +incentive of free alcohol. + +That's certainly not the program +that we're typically + +trying to evaluate when we're +trying to do an evaluation of + +microcredit. + +And we want to make sure that +we're getting the people in + +the study who are the right +people, who are the types of + +people that are thought about +as the target audience for a + +microcredit program. + +That means not drunkards. + +And so you want to make sure, +you do want whatever that + +approach is to be something that +is sensible, that seems + +somewhat in the scope +of normal. + +Or at least doesn't create a +sample selection bias in the + +sense that it doesn't make the +people who take up the program + +be particularly different in +a way that is not useful. + +Yeah? + +AUDIENCE: So an example that I'm +thinking about is access + +or information about a +microcredit program to + +participants who are +typically very + +uninformed about these things. + +So the information +is out there. + +Theoretically, it's +really accessible. + +But we know that unless we tell +them that this program is + +out there for them, chances are +very good that they would + +never think of it +on their own. + +So that would not then be a good +situation for this kind + +of a thing, because we know that +we are in effect offering + +them a sort of special in by +the very effect of offering + +it, even though theoretically +it's accessible. + +PROFESSOR: I would actually +says that's + +actually a perfect setting. + +To do this, let me rephrase the +question, which is suppose + +you have a program, and only the +highly informed normally + +are going to come in. + +And so in order to do an +encouragement design, what + +you're doing is you're going out +and you're only going to + +move the people who are +not highly informed. + +The highly informed already +know about you. + +They're either coming +in or they're not. + +You give them information, it +doesn't matter, I already knew + +about this. + +So what you're doing is you're +moving the less informed + +people, you're informing them +about the service you're + +offering, and now they're coming +in or not as they wish. + +But they're more likely to come +in now than the people + +who are not informed. + +So this is a perfectly relevant +approach if it's the + +case that this is an +organization that does aspire + +to grow, and they're going to +grow through informing people. + +In most of the settings I've +been involved in, at least the + +type of information we're +dealing with is usually not + +much different than what +they do normally. + +It's just marketing. + +It's just targeted and +controlled marketing, where we + +control what villages they go +to do the marketing, or what + +household's doors +they knock on. + +But in a lot of situations, +the encouragement design + +literally has them doing exactly +the same operation's + +that they normally would do. + +But it's just recognizing +that it's + +still a voluntary decision. + +They can't make someone +borrow. + +They're going to a village, +they're holding meetings, + +they're presenting what +they do, and some + +borrow and some don't. + +AUDIENCE: I think I'm saying +something slightly different, + +but that might +[UNINTELLIGIBLE PHRASE]. + +So among the group who would not +normally know about this, + +it's not that I'm going to-- + +I'm not saying the group who +knows, forget about them. + +I don't know, I'm confusing +myself. + +We're assuming that the group of +people that we work with to + +provide our program, we would +provide a precursor program, + +and we would say among people +that we work with, half of + +them we would tell, and half +of them we won't tell. + +Is that what you're +saying too? + +PROFESSOR: You would go out +of your way to give them + +information about the program. + +Everyone can get in, but you go +out of your way to approach + +half and tell them about +the services. + +AUDIENCE: Understanding that +chances are that if we don't + +tell them, they won't go, +because they're just + +uninformed? + +OK. + +PROFESSOR: Right. + +Yeah? + +AUDIENCE: I don't want to +interrupt if there was more to + +this exchange. + +My question is about +distiguishing thing between + +marketing and training. + +If the treatment is something +like a financial product or + +service that's poorly +understood, and you don't want + +to-- do you think that maybe +financial literacy is an + +important determinant, but you +want to isolate just access to + +the product or service and keep + +financial liberty separate? + +How do you draw the distinction +between marketing + +and training? + +PROFESSOR: I can tell you in +one setting, here's what we + +did to try to understand +this better. + +Let me restate the question, +which is how do you + +distinguish between marketing +and training? + +This is really a spectrum. + +So an example I gave that was +bad was a month long training + +program, and I said it's fine +to just knock on a door. + +Why am I drawing +the line there? + +And it's a perfect question, +and I can tell you that the + +first time I actually ever did +this type of design, we + +actually had an entire treatment +group that was just + +knocking on doors, but +with no product. + +It was just to test out whether +the knocking on the + +door had an effect on savings. + +So we had two treatment +groups. + +We had a treatment +group that got a + +commitment savings account. + +A bank officer went to the door, +knocked on it, gave them + +a pitch about why they need to +save, and savings is good, and + +here's a goal. + +You should have a goal +for savings. + +And here's an account that we'll +offer you to help you + +reach your goal. + +It wasn't a very long pitch, but +it was a marketing visit. + +And we had a pure control that +got no contact from the bank. + +And then we had a second +treatment group that we called + +the marketing treatment group. + +And this group got the knock +on the door, got the same + +pitch for about 5, 10 minutes +about why it's important to + +save, and how the bank is there +to help them save, but + +didn't get offered that special +savings account that + +had special rules to it. + +And that's done exactly to +try to understand where + +to draw that line. + +So if it's a situation where +you're particularly concerned, + +then you could actually think +about having treatments + +designed specifically to test +whether there is a direct + +effect without the treatment +you really care about. + +Yeah? + +AUDIENCE: I'm kind of jumping +onto the last point as well. + +But the one encouragement design +that I'm familiar with + +is one where a subsidy was +actually utilized, but then it + +was a random distribution of who +was offered the subsidy. + +And, for that matter, because +they're trying to determine a + +demand curve, the +subsidy varied. + +So maybe you'd be offered +35% off, maybe you'd + +be offered 75% off. + +Still random in who was given +the offer, but then they had + +the encouragement to take +off based on how + +big the subsidy was. + +But it seem my initial-- not +knowing enough about the + +details of the program-- + +is that there would be a problem +based on the economic + +status of those who were offered +a program in the first + +thing if they were not +very, very similar. + +If I am marginally wealthy and +I'm offered a 35% discount, + +I'm more likely to take out than +someone who is broke and + +is offered a 35% discount. + +Then that would affect +your sample. + +PROFESSOR: With one twist. + +So it's not the levels that +matter, but it's actually the + +slope that would +have to matter. + +It has to be not that the +wealthy is more likely to take + +up with any given level. + +It's that they have to be more +elastic or less elastic than + +the poor in order for +that to be an issue. + +And then you're absolutely +right, that is an issue. + +And then what you're studying +is when you do that subsidy, + +you're studying your treatment +effect on those people who are + +going to be more responsive +to that subsidy. + +Is there another hand? + +No. + +Wendy, now we're to your +question, multiple treatments. + +So let me just say +one more thing on + +encouragement designs. + +So one of the key things to +remember with encouragement + +designs is that in a lot of +situations, the encouragement + +design is-- + +in some situations, it is set +up where the control group + +does get into a program. + +So where you're dealing with a +10% take up rate in control, + +and a 30% take up rate in the +treatment, In a lot of the + +setting, though, it's really +more that you just have + +incomplete take up in the +treatment group, that + +participation is voluntary. + +And so by encouragement, all we +really mean here is that a + +treatment is being offered +to people. + +They can say yes or no, and +they're not being offered to + +the control group. + +And so we end up with take +up of some percent in the + +treatment group, and +zero in control. + +Like the savings experiment +that I just referred to a + +moment ago, we had a 28% take up +in the treatment group, we + +can't make people open +a savings account. + +All we can do is offer it to +them, and we had a 0% take up + +rate in the control. + +We did a similar thing in the +same place in the Philippines + +on a commitment account +to stop smoking. + +Again, 11% take up rate in +the treatment group. + +We can't make people want to +stop smoking and sign accounts + +and contracts to do this. + +But we can prevent the +control group. + +So there was perfect control in +the control, in the sense + +that they were not offered the + +opportunity to open the account. + +But the treatment group +has to be voluntary. + +That is what it is. + +And so it's an encouragement +design, with 11% percent take + +up rate in the treatment +and 0% in the control. + +So sometimes you do have control +on one half but not + +the other for who uses. + +Yeah? + +AUDIENCE: And so just the main +point is that what constraint + +are you going around by an +encouragement design? + +Just an ethical problem +if you can't afford + +treatment to everybody? + +PROFESSOR: In that situation, +I don't know that I'd pose + +that as an ethical issue. + +But the point to be made is +just that you can't force + +people into a program. + +It's a voluntary participation, +and that's OK. + +So one of the things that I've +often read or heard is when + +someone says, well, +wait a second. + +This is voluntary + +participation, so how can you-- + +doesn't that introduce +selection bias? + +And the answer is no, because +what we're going to do when we + +do the analysis of that, is +we're going to compare + +everybody who was offered the +account, everybody who was not + +offered the account. + +And so there's no selection +bias there. + +There would be a selection +bias if what we did is we + +analyzed everybody who took up +in the treatment group, and + +compared them to everybody +in control. + +And that would be a +flawed analysis. + +But that's not what we do. + +So if you ever hear someone say, +ah, encouragement design, + +doesn't that introduce a +selection bias, because + +participation is voluntary? + +The answer is no. + +That only introduces selection +bias if you do + +the analysis wrong. + +What you want to do is compare +what's refereed to as the + +intent to treat analysis, and +it means comparing everybody + +who's offered to everybody +who's not offered. + +Multiple treatments. + +So this goes back to +Wendy's question. + +This is one of the areas where +I tend to think is most ripe + +for helping-- + +going back to one of the first +points I was making about + +making sure that the evaluation +speaks nicely and + +informatively to needs of the +implementers, needs of the + +organization. + +That a lot of times, there's +very specific operational + +questions that they have. + +Should we really +do it this way? + +Or should we do it this way? + +I really made some tough choices +here, and I just went + +with what I thought was best. + +But gosh, if the research can +actually help guide me and + +tell me whether this particular +component is + +necessary or not, that +would be great. + +So imagine you're doing-- + +let's go with Wendy's example +of an agricultural program. + +And suppose that you're trying +to decide, how important is + +this training component? + +I'm going to provide seeds, +and introduce people to + +marketplaces. + +I'm just making something up. + +Let's not get into the details +too much, but let's just say + +there's a training component +alongside of it. + +And that training component is +really expensive, it takes a + +lot of time. + +And I'm thinking to myself, OK, +I can help twice as many + +people and drop the training, or +keep it my current program + +size and have training. + +What's better? + +Well, the research can help +answer that question by having + +an evaluation which evaluates +the overall program, but then + +also randomizes whether or not +there's training involved. + +And so this is one of those key +areas where it's a win win + +for operations. + +Where you can help answer +questions for them beyond the + +simple impact question. + +There are situations in multiple +treatments that we've + +been in where there's +no pure control. + +And there's nothing invalid +about doing that. + +It does validate the study, but +we just have to remember + +that you're no longer saying, +what is the impact of the + +program compared to not +doing the program? + +You're now comparing it one +option relative to another + +option relative to +another option. + +And hopefully in the design +there, you have one option + +which is kind of like a placebo, +so that you have some + +group that you really don't-- + +it was in a very extensive way, +but you have some method + +of being able to say what +the overall effect is. + +But there's many situations +we're in where that's actually + +just not part of what +the study's about. + +So we've done savings product +designs are a perfect example + +of this, where we're dealing +with people who opened a + +savings account. + +There's no control group of +people who were not offered a + +savings account. + +We're just dealing with a bank +and they take people in. + +And the question to us was, +well, how can you help our + +existing savings people +save more? + +So we tested something out in +three different countries + +where we sent people +reminders to save. + +So half the people basically +got a little text message + +saying, hey, don't forget +to save this month, + +and half did not. + +So we have no control group +here of people who got no + +savings account. + +So we're not measuring the +impact of savings on things. + +We're just measuring the +impact of getting this + +reminder on how much you save. + +And we've done similar things +with loan repayments. + +There's no study on the impact +of the credit, we're just + +testing out operational +questions about how to run the + +program better. + +And in those types of designs, +we'll often test out five + +different messages all +at the same time. + +I think I said that slide. + +Oh, maybe not. + +Yeah, we talked about +randomization in the bubble. + +So this is the list of +the various things + +that we've now described. + +And just remember that these +are not mutually exclusive. + +Multiple treatments and +encouragement design in + +particular kind of fit within +almost any of these other + +things going on here. + +Any questions so far? + +OK, part two, gathering +support. + +So here are some things +that we commonly hear. + +So this part of the lecture is +really all about how we deal + +with this kind of introductory +conversations, exploratory + +conversations where we're trying +to work with partners + +to figure out how to go about +doing a randomized trial. + +So one answer which is always +a tough one to get, but I + +already know the answer. + +And I don't want to risk +learning that we + +do not have an impact. + +There are situations that we'll +be in-- and I don't mean + +to sound like a pessimist-- but +there are situations we'll + +be in where you just realize +this is not a + +good setting for it. + +You have to work with +people who actually + +want to know the answer. + +And you can recognize that +merely observing that their + +program has grown is not +necessarily a sufficient + +measure to say whether they've +had an impact. + +And it's certainly not a +sufficient measure to say + +whether their program is a good +allocation of resources + +compared to other programs that +have also had similar + +operational success. + +And so when we have to make +the tough choices, this is + +where we need the evidence. + +Listening is probably the +single most trite but + +important thing I have to say on +how to have these types of + +conversations. + +Trying to understand the +perspectives and the + +objectives of the people +in the table. + +What is it that's making +them tick? + +What is it that's making them +have this conversation in the + +first place? + +And finding ways to make the +research operationally useful + +is perhaps the single most +useful and important thing to + +do when working in the field. + +One thing that I've often found +too is that often in + +practice, there's a caution. + +There's almost a mistrust that +some might have if they're not + +familiar with what is +that's going on. + +And it's one of the most +important things that the + +field staff can do in working +with the organization is to + +just gain the trust of the +people in the field who are + +working for that organization. + +And some of this comes about in +getting their feedback and + +input into things like +survey design. + +Having it so they feel part of +the process, and their input + +is received and incorporated +into what we're doing. + +And that's good for the +program, good for the + +evaluation to get +their feedback. + +It's also good in a purely +interpersonal way, in terms of + +helping to have a relationship +that's good by making sure + +that people feel that they +are part of that process. + +So some other specific +things that come up. + +The first, one of the most +common things is gossip. + +People will talk. + +So what do we do if the control +group finds out about + +the program? + +So I think the thing to think +about is to try to separate + +out these types of issues. + +Let's just put this into a more +general category called + +spillovers. + +So spillovers meaning there's +any sort of indirect effects + +that are going to occur, from +those who were treated to + +those who are untreated. + +I think it's really important +to separate these into two + +categories. + +There's natural spillovers, and +let's call them research + +spillovers. + +Now, by a natural spillover, +what do I mean here? + +I mean a spillover that is +naturally occurring. + +That is, if you go and you +provide a service to 100 + +people, the fact is this is +going to affect those 100 + +people and 200 more. + +And that's the nature +of the intervention. + +It has nothing to do +with the research. + +The example that you have +a case on is deworming. + +We're going to deworm +half of you. + +The other half will benefit +from that, because you're + +going to be less likely +to catch the worms + +from the first half. + +Let's say I took half of you +right now, and I went into the + +other room, and I gave you a +whole big lesson in power + +calculations, and I ignored the +other half, and I didn't + +give that to you. + +Well, there'd be a spillover. + +You'd come back, you're in +a group, you'd talk. + +Oh no, no, I just learned about +power calculations, let + +me show you. + +Hopefully it'd be +a positive one. + +So these are all natural +spillovers though. + +There's learning that +takes place. + +You teach some people, +they teach others. + +You deworm schoolchildren, other +schoolchildren benefit + +because they're less likely +to catch the worms. + +There could be negative +spillovers. + +We go and we offered really, +really cheap credit to some + +people, or we only offer it +to some because we're + +constrained. + +That's the organization. + +That's just how many +loans we make. + +It gives them a competitive +advantage-- + +I'm not saying this is right. + +But this is an argument that +people will make when they are + +arguing against subsidized +microcredit. + +And what does this do to the +people who don't get access to + +the microcredit loans? + +It shuts them out of business. + +It makes it so they can't +operate their enterprise + +because they're competing +against someone who's getting + +subsidized credit. + +So that has a negative +spillover. + +These are natural, though. + +So a good study is one that +helps to measure these things. + +And there are ways that we can +design experiments to measure + +those types of spillovers. + +So a very simple example of +one that measures this is + +suppose we have villages. + +And what we're going to do is +take 90 villages, and instead + +of just dividing them up +treatment, control, what we're + +going to do is we're going to +divide them into three piles. + +We're going to divide +them first into two, + +treatment and control. + +So we'll have 60 of those +villages being treatment and + +30 being control. + +And then within the 60 that +are treatment, we're only + +going to go and deliver services +to half the people in + +those villages. + +So what do we have? + +We have a treatment village +that's half treated, half + +untreated, and we have +control villages. + +Now throw away the people +that got treated. + +Just ignore them. + +What's an interesting analysis +to do here is to compare the + +untreated children or people, +or whatever the intervention + +is in the treatment +villages, and + +compare them to the control. + +These are two people that +didn't get services. + +Neither one got treated. + +But some of them live near +people who got treated and + +some of them do not. + +So that measures the +indirect effect. + +That measures the natural +spillover. + +So if a natural spillover is +something that one was + +concerned with, this is exactly +the way you would + +think ahead of time about +setting up the research design + +to measure that. + +But then there's unnatural +spillover, what I was + +referring to as research +spillovers. + +Yeah? + +AUDIENCE: Just a +quick question. + +Does the fact that now the +treatment is half the size + +compared to the entire control +group, does it matter? + +PROFESSOR: Yes, it matters. + +And that's a question of +power calculations. + +And so you have to trade off +your measurement of the + +spillover versus your +measurement + +of the direct effect. + +But that's a mathematical +problem that can be solved + +analytically. + +So research spillovers, those +are the bad ones. + +These are the ones we don't +like, because it's not + +interesting, it's not useful. + +It's not representative of what +happens in the real world + +when you do an intervention. + +It's just an artifact of +the research process. + +The simplest example is the +control group person who says, + +I don't like the fact that I +am in the control group. + +Maybe they don't believe it was +truly random, or they just + +don't like the fact that they +didn't win the lottery. + +And so they actually change +their behavior + +now because of this. + +Let's use a very simple example +of being in a bank, + +and let's say you're doing +a lottery across existing + +borrowers, and half of them +got an extra service to go + +along with their loan, +and others did not. + +The ones who didn't +get the extra + +service, they're now upset. + +I didn't get the extra service, +I'm not happy. + +Why did they get it? + +I didn't get it. + +And you can explain, well, +it was random. + +They don't accept that that. + +And now what do they do? + +Maybe they don't pay +back their loan. + +Maybe they leave the +program altogether + +because they're mad. + +Now in studies we've had, I can +honestly tell you we've + +not had this happen yet in a +microcredit setting, but + +there's certainly things +that we will do to try + +to avoid the problem. + +So for instance, one of the +studies we had where this was + +a bigger concern than others was +we were testing out group + +versus individual liability. + +Now most borrowers really like +the idea of individual + +liability if they're +given a choice. + +They don't want to be on the +hook with other people in + +their community, they much +prefer to have a loan that's + +just to them and them alone. + +So when we were randomizing +whether people got offered + +group or individual +liability-- + +and it was existing borrowers +who were already borrowing + +from a bank-- + +what we had to do is take +villages that were really + +right next to each other +and put them together. + +Because we couldn't have it +that we had these little + +sister villages where there +was lots of interaction + +across, and one got switched +and the other did not. + +So we put them together and +treated them like one. + +And so basically, it's another +way of saying this is when you + +think this is an issue, you +just need to think about + +making sure that you have some +sort of boundaries separating + +out your treatment and +your control areas. + +Now in an urban setting, it +could be a little bit harder + +if you don't have clearly +defined boundaries. + +But it's still feasible to +do this type of process. + +You just have to think a little +bit about how to do the + +boundary, and also what to do +if you have control group + +people who do come in. + +And so this is an area where +encouragement designs might + +actually be a useful way of +dealing with it, is to allow + +some control group people in, +for instance, if they come in. + +But otherwise not unless they +actually come on their own. + +So this is another way of saying +take an urban area, and + +you just encourage some blocks +to borrow and not others. + +Encourage some blocks to go to +school and get some extra + +service, and not others, +whatever the program is. + +And that's a way of trying to +make sure that if the groups + +talk to each other, it's OK. + +It's not going to ruin the +study, and there's no + +jealousy, it's just a matter +of some receiving + +encouragement and others not. + +So fairness, hopefully this is-- +the one point, if I had + +to leave you with one simple +thought of this lecture, it's + +the fairness point. + +It's perhaps the single most +commonly raised issue, and + +it's the easiest of the issues +to explain in 99.9% of the + +settings we're in. + +And it's this fairness issue of, +oh, but gosh, I don't want + +to do it by lottery, I want to +do it by some other process. + +And the answer-- + +or gosh, I can't imagine +restricting access to people. + +And the answer is always just +about the same, which is how + +many people can you deliver +in this program? + +What's your budget? + +Now let's divide by the +cost per person. + +And so you can do this for +1,000 people, or 2,000, + +10,000, whatever your constraint +is, you have a + +constraint. + +Now all we're going to do is +use that constraint to then + +find a way to do this +randomization, and that's it. + +So we're not restricting +access to anyone. + +The only sense in which we're +restricting access is perhaps + +a bigger picture or thought, +which is if half a million + +dollars is being spent on the +evaluation, that's half a + +million dollars that's not +being spent on services. + +That's the only sense in which +the randomization is costly in + +terms of delivering services. + +But this is a different +calculation all together. + +This is now asking the question +of whether it's worth + +half a million dollars to +find out the impact of + +this program or not. + +And that's just a very +different question. + +It's not about the resources +and the fairness to those + +individuals, it's about the +question of whether this + +program will be done enough +times in the future, and will + +the marginal value in terms of +our knowledge about what's + +being learned from this study +be high enough to warrant + +spending the money on +the research period. + +It's a different question. + +So on ethics, some of the things +that we'll often hear + +are statements like, well, it's +wrong to use people as + +guinea pigs. + +Or if it works, then it's wrong +not to treat everyone. + +So the first thing to think +about is that first + +of all, it's not-- + +I think it's a very leading +question first of all. + +One thing to often +ask yourself-- + +or ask people in this type +of conversation-- + +is why is this different than +prescription drugs? + +Why should we be more willing +to proceed and deliver + +interventions and deliver +services to people without + +knowing their impact then we +are to prescribe drugs? + +We ourselves, for instance, +would never take a + +prescription drug if it hadn't +gone through a randomized + +trial, or more than one. + +And so why should we be using +a different set of standards + +in terms of the ethics of the +two, in terms of the bar, the + +rigor that we want to use in +order to decide how to + +allocate our resources. + +The second thing to think +about in terms of, if it + +works, then it's wrong not to +treat everyone, I think + +there's an important point to +note, that there's lots of + +ideas that-- + +there's two issues that often +come up in this setting. + +First of all, there's lots of +ideas that sound good, but + +then when evaluated, turn +out to not work. + +And even when something works, +the question is how + +well does it work? + +We have other ideas that work. + +So even if something is good, +even if everyone around the + +table is totally confident that +it's going to work in + +some respect, we don't know how +well it's going to work. + +And when we're allocating +resources, we're not just + +trying to beat zero, although +that's always good. + +We're actually trying to +do the best we can. + +And so we're choosing across +five ideas, and + +they all sound good. + +No one's throwing out ideas +that-- well, I shouldn't say + +that, that's probably +not true. + +We can probably think of some +that don't sound good. + +But for the most part, we like +to think that we're sitting + +around the table thinking across +choices that sound + +good, and we have to choose. + +And so that's the most important +thing to remember in + +that type of conversation. + +Cost. + +So there is two things that +often come up when people talk + +about cost. + +And there is a common perception +and argument that + +randomized trials are much +more expensive than other + +approaches. + +So I think there's two things to +think about when this type + +of conversation or +point is made. + +The first is thinking about +what the cost-- + +it's about doing a cost +benefit analysis. + +So let's assume for a +second randomized + +trials are more expensive. + +And I'll point out some +examples in a + +moment where it's not. + +But let's say it is in +a given setting. + +Well, that's only part +of the equation. + +You have to say, well, what's +the cost and the benefit? + +The whole point of doing +randomized trial is to think + +about costs and benefits too. + +There's no reason why we should +think any differently + +when we think about +how to evaluate. + +So what's the benefit we're +going to get them from doing a + +randomized trial versus a +non-randonized trial, and + +what's the cost difference? + +And if the benefit that we're +going to get in terms of the + +reliability in results is high +enough to then make more + +impact on our ability to make +future decisions, well then, + +it's probably worth spending a +little bit more money on the + +evaluation itself. + +Now obviously, that's relative +to our existing + +knowledge in the space. + +If something's already been +tested 15, 20 times, then this + +might become a situation in +which you would argue that no, + +the benefits don't outweigh +it, because the marginal + +impact from the research on one +more study is not going to + +be that high. + +And so the costs are +not worth it. + +I'm not aware of situations +I would say fit that, but + +hopefully we will be +there someday. + +The second is that the cost of +doing randomized trials is + +often not actually more +expensive than + +non-randomized methods. + +But it's really key to state +clearly what the + +counter-factual is here. + +What's the alternative method +one's describing? + +So it's clearly cheaper +than doing nothing. + +And there are situations that +I've been in where my best + +advice is don't evaluate. + +For whatever reason, +the setting is-- + +you're not going to get a +reliable result, and the best + +thing one can do is to not +do the evaluation. + +Let's compare now to the most +common comparison one makes, + +which is to a non-experimental +quantitative method. + +So suppose the alternative +approach is to survey a bunch + +of people who received a +service, and to survey a bunch + +of people who didn't +receive a service. + +It wasn't done randomly. + +It was some people chose +to be borrowers from + +a microcredit program. + +For those of you who know me +know I do a lot of work in + +microcredit, this is why I keep + +using microcredit examples. + +So I'm going to survey a whole +bunch of people in microcredit + +that are part of a program. + +And then I'm going to go into +the same community so I can + +find people who seem very +similar, have the same + +macroeconomic conditions, but +are not participating in the + +program and going +to survey them. + +I'm going to follow everybody +before and after. + +So this is actually a more +expensive study. + +Why? + +Well, I need a larger +sample size here. + +I need a larger sample size +because I actually have to + +really understand something +deeper now about who's opting + +in and who's not. + +And I have to try to use my +econometric tools to correct + +for selection biases. + +And this costs me sample size. + +And so this study would actually +cost more money, + +because I would want a larger +number of observations in the + +analysis in order to try +to get it right. + +Now it's clearly going +to be more expensive. + +Now let's flip to another one. + +If our counter-factual approach +is to not even do any + +surveys, like there's no big +econometrics, but instead to + +do a simple before after. + +I'm just going to compare +before after. + +So you've studied yesterday, you +talked about before after, + +you went through some of the +issues that you have that you + +don't know what else is changing +the environment. + +But if that's the comparison +you're going to be using, well + +then yeah, this is the more +expensive, because yopu've got + +to survey control group +people too. + +That's an example where it's +hard to come up with settings + +in which there aren't +outside factors-- + +economic, social, environmental, +health-- + +that cause changes over time in +outcomes for people, such + +that a simple before after +analysis is in anyway + +informative at all about the +impact of a program. + +Timing, OK. + +I'm going to try to +wrap up quickly. + +The one thing to say about +timing is it's very common to + +have a constraint where the +organization is like, but we + +need the answers now. + +Randomized trials are no +different than non-randomized + +trials that follow people before +after, but they're + +certainly going to be a lot +longer than things that simply + +look retrospectively at people +that have already received + +services and hold focus groups +and discussions to try to + +assess impact. + +And there's no way +around that. + +So this is a question of just +being patient, and working + +with organizations that are able +to be patient in order to + +have those answers. + +I'm just going to run through +this initial slide so you can + +have the basic key points of +the overall plan when we're + +doing an evaluation. + +So the three steps we have +listed here are plan, pilot, + +and implement. + +I think it is important to note +that there are situations + +where we don't actually +do a pilot. + +Depending on the circumstances, +the situations + +in which we do pilots are +typically when there's a lot + +of uncertainty about what the +intervention is in the first + +place, and so we're actually +working with the organization + +to figure that out. + +Or if there's some uncertainty +about the way the process is + +going to play out. + +Maybe we're uncertain about +the encouragement design. + +We're not sure if it's +going to work. + +We're not really sure, will this +actually encourage people + +to come in and use +a service more so + +than they would otherwise? + +So we need a pilot to test out +whether that approach will + +have an effect or not. + +We just need a smaller sample +just to gauge whether we're + +dealing with 60% take up rate +in our treatment group as a + +result of encouragement and 10 +in the control, or are we + +dealing with 12 and 10. + +What's our range? + +So the five steps we've laid +out here is identify the + +problem and proposed solution. + +So I think one of the things +that should never escape us is + +that you don't take a +randomized trial. + +You don't start off saying we +have a tool, now what research + +questions can we ask? + +You go the other way around. + +You want to think, well, what's +the research question + +we're asking here? + +What is the problem that we see +in the market we're in, in + +the society we're in? + +What's the market failure that +this intervention is trying to + +solve or measure or test, +and then what's + +the proposed solution? + +Think totally abstractly, don't +even get into what the + +randomized trial is and how +it will be designed. + +Just think first order about +what the market failure is, + +and what the logic is behind +the proposed solution. + +Second, and this goes back +somewhat when we're talking + +about in terms of identifying +the key players. + +There's nothing more frustrating +than a really good + +project, where you just don't +have the right players on + +board participating and +collaborating in a cooperative + +way to make the project work. + +Identify the key operations +questions to + +include in the study. + +This goes back to hopefully the +other theme of my lecture + +this morning, is about making +the research into win win + +opportunities, finding those +operation questions and trying + +to build them into the +research as well. + +Then design the randomization +strategy, and define the data + +collection plan. + +Data collection can be done +continuously lots of waves, + +one wave at the end. + +There's lots of other tools +that we can use in data + +collection, both qualitative and +quantitative approaches. + +One of the other common +misperceptions that I've heard + +is people saying that there's a +spectrum between qualitative + +and randomized trials. + +That's kind of mixing +apples and oranges. + +Qualitative versus quantitative +is about how you + +go about measuring things +and what you measure. + +A randomized trial is just about +identification of the + +effect of an intervention. + +It's about random assignments of +treatment and control, but + +it has nothing to do with +whether the measurement is + +going to be done through +a qualitative or + +quantitative process. + +And there's a lot of examples +of studies that we have that + +use mixed methods and creative +approaches for measuring + +things, and there's a lot of +studies we have where it's + +very cut and dry, normal +quantitative, how many + +potatoes did you eat +type questions. + +So pilots vary in +size and rigor. + +The pilots and the qualitative +steps that often go into them + +are very important for helping +to understand the intervention + +and design it, particularly when +we get into designs that + +are doing sub-treatments. + +A lot of times those come out of +the qualitative process in + +the design of a study. + +And then for the actual +implementation-- + +oh, I skipped something. + +Identifying the actual target +population is going to be + +covered later in the day, +in the second lecture. + +And then collecting the +baseline data will be + +discussed later on. + +When we do it, we usually +do it, but not always. + +The actual randomization, there +is various times and + +points in which you do it. + +This is what we were talking +about in the beginning of the + +class, real time randomization +like the credit scoring all at + +once, villages known up front, +and you randomize them in or + +not to a program. + +Then the next phase is +implementation intervention to + +the treatment groups, and this +is where internal controls can + +be really critical. + +There's nothing worse than doing +all of this work, doing + +all these surveys, and then not +having the right control + +in the field to be working with +the individuals from the + +organizations that are +delivering services to make + +sure that things happen +the way they're + +actually supposed to happen. + +And I've had projects go bust, +where we're working with + +organizations that thought they +had the right internal + +controls in place. + +And when we go in to do spot +checks to see, and we go to + +some villages to see, are they +getting services or not? + +And lo and behold, +they were not. + +Or they were when they +shouldn't be. + +And we go back and we try +to work with them. + +I've had at least one project I +can point to that literally + +we just canceled after +a year and a half. + +It was very unfortunate, but +this is what happens when + +there wasn't the right level of +internal controls in place. + +And I learned. + +And then measuring +the questions. + +One of the most common +questions we get with + +measuring is, how long +should we wait? + +And there's really no +one answer to this. + +There's often a trade +off with operations. + +If there is any sort of holding +back of a control + +area, then this is going to be +something that has to be + +negotiated and discussed +with operations. + +In a lot of situations we're in +though, it's not that the + +two sides are actually +differing-- + +I mean, the operations maybe-- +but the head of the + +organization might have +incentives that are perfectly + +aligned with the researchers. + +They want to wait long enough +in order to make sure that + +they've given their +program a full + +chance to have its impact. + +And so usually when I am posed +with this question by an + +organization, I usually just ask +right back to them, well, + +you tell me. + +What do you think you need in +order to see the impact of + +your program? + +If you're telling me a story +about it being a 5, 10 year + +program in order to see +everything flourish, well then + +that's your answer. + +If you're telling me that this +is like an amazing thing that + +just transforms people's lives +within six months, well then + +we can go in six months +and see that amazing + +transformation. + +We might also want to see the +two year impacts, but that + +would be something that could +happen with the organization, + +and they could say, yes, we +think it's transformation in + +six months. + +And two years is just beyond-- + +I mean, I don't know what the +word is to say beyond + +transferring. + +Lastly, analyse and +assess results. + +And obviously, there's a lot +more in the class that will be + +discussing that. \ No newline at end of file diff --git a/D_lVfCfGVao.txt b/D_lVfCfGVao.txt new file mode 100644 index 0000000000000000000000000000000000000000..8b49c7239d0637f2c56ebd1f1bf24311870723d5 --- /dev/null +++ b/D_lVfCfGVao.txt @@ -0,0 +1,3754 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Ladies and gentlemen, +welcome to this + +lecture on non-linear finite +element analysis of solids and + +structures. + +In this lecture, I'd like to +continue with our discussion + +of the methods of solution for +the finite element equations + +that we are encountering in +non-linear dynamic analysis. + +In the previous lecture, +I pointed out that the + +techniques used for the solution +of these finite + +element equations in non-linear +dynamic analysis + +can be classified as data +integration techniques, + +methods of multiple position, +and substructuring. + +We talked in the previous +lecture about these types of + +methods, and in particular, +we discussed in detail an + +explicit integration method, +namely the central difference + +method, and an implicit +integration method, namely the + +trapezoidal rule. + +We talked about how these +methods are applied, how time + +steps might be selected, what +the restrictions of these + +methods are, and so on. + +I'd like to now in this lecture +discuss with you the + +method of multiple position, +and also + +substructuring technique. + +After the discussion off these +two techniques, I'd like to + +talk with you about +some examples. + +As a first example, we want +to consider the wave + +propagation in a rod. + +As a second example, I'd like to +share with you experiences + +regarding the response of a 3 +degree of freedom system. + +As a third example, then, we +want to consider the analysis + +of a 10-story tapered tower. + +Example 3 and example 1 are +really solutions of a linear + +system, but we learn quite a +bit, even regarding non-linear + +analysis, from these examples. + +As the fourth example, then, +I'd like to share with you + +experiences obtained in the +analysis of a pendulum that + +goes through very large +displacement. + +As a fifth example, then, we +consider the pipe whip + +response solution. + +This is of much practical +interest. + +And after these examples, +which I've prepared view + +graphs for, I'd like to consider +with you some slides. + +On these slides, we will have +the analysis of a control rod + +drive housing with the response +of a spherical cap, a + +highly non-linear problem, +large displacement, + +elastoplastic response, and then +the analysis of a fluid + +structure interaction problem, +a pipe test in which we are + +comparing our computer's +results with + +experimental results. + +I should point out right now +that the details regarding + +these example solutions are +given in some papers that I + +had also earlier. + +And please look at the study +guide, where the references to + +these papers are given. + +Let me now walk over here to +the view graph that we have + +prepared regarding +this lecture. + +And the first method of solution +that I wanted to + +discuss with you is the method +of multiple position. + +Quite a number of you probably +have used this technique + +already in linear analysis. + +In fact, the word +"superposition" somehow + +implies that you are dealing +with a linear analysis. + +However, we can extend that +method directly to non-linear + +analysis if we recognize that +the mode shape vectors of the + +system at a particular time +can be used as generalized + +displacements, or basis vectors, +to express the + +response to any other +time, as well. + +The method is effective when, +in non-linear analysis, the + +response lies in only a few +vibration modes, just the same + +way as we are applying multiple +position also in + +linear analysis, namely, it's +only effective really when a + +few vibration modes capture the +total dynamic response. + +The same holds here, of course, + +in non-linear analysis. + +And when the system has +possibly only local + +non-linearities. + +Let's look at is equations +that we're using in this + +multiple position technique. + +The basic starting point are +the equations that we have + +seen before regarding +dynamic analysis. + +But notice in this particular +equation, I have assumed now + +that the damping matrix is not +present, so we have no damping + +in the system coming from +the damping matrix. + +There could, of course, be +damping due to the material + +non-linearities, which +are captured in + +the K and the F matrix. + +Well, this is the +set of equations + +that we want to solve. + +And usually, we just iterate on +these equations until the + +right-hand side is 0, where of +course we also would bring + +this one here onto the +right-hand side. + +So think of this one here as a +minus on the right-hand side, + +and if, then, this right-hand +side, with M on that + +right-hand side is 0, meaning +the data UK is 0, no more + +updating to the incremental +displacements, then we have + +established equilibrium +configuration corresponding to + +time t, of course, including +inertia effects. + +In multiple position, we don't +want to directly to deal with + +these equations in this form. + +Instead, we want to transform +them into a new form, and into + +a form such that we obtain less +unknowns to deal with. + +Let's assume for the moment that +tau is equal to 0 so that + +we are dealing with the solution +of the equations + +using the initial +stress method. + +We talked about initial stress +method in an earlier lecture. + +Then using this transformation +here, where phi R are the + +eigenvectors of this problem +down here, And the xi are the + +generalized displacements +corresponding to these + +eigenvectors. + +Notice this equation is exactly +the same that we're + +used to seeing in +linear analysis. + +Of course, in linear analysis, +we are usually not putting + +this t plus delta t up there. + +It's understood that the time +dependency is in xi, but the + +space dependency is in phi i. + +And notice we are summing +here from r to s. + +r would have to be selected +by the analyst, + +and s the same way. + +Having introduced this +transformation with this + +eigenvalue problem here, and +substituting for the U + +displacements in the general +equilibrium equation, and + +using the same approach as +we are used to in linear + +analysis, we directly obtain +this set of equations. + +Now, notice here that in this +vector x double dot, and in + +this vector x, delta meaning +increment, we have only the + +components corresponding to the +r mode up to the s mode. + +These are the generalized +displacements corresponding to + +phi r up to phi s. + +Here we have phi r to +phi s listed in this + +matrix, capital phi. + +Lower-case phi for these here. + +These are the columns in this +matrix that is denoted as a + +capital phi. + +Notice here we define an omega +squared matrix, 0 elements in + +the off-diagonals. + +And on the diagonal, we have the +frequencies of the system, + +of the actually linear system, +because we use 0K in the + +eigenvalue solution. + +These are the entries for +this equation up here. + +And notice that we have now here +much less equations than + +the total number of finite +element degrees of freedom. + +Typically, r might be 1, s might +be 20, and then we would + +have 20 equations here, +20 equations only. + +Of course, r could also be 25, +and s 30, in which case we + +have here a multiple position +corresponding to the 25th up + +to the 30th mode. + +In any case, in general, we will +have much less equations + +then finite element degrees of +freedom that are listed, for + +example, in this vector +here, R, I should say. + +The externally applied load +corresponding to these degrees + +of freedom are listed in here. + +Of course, the F vector is the +vector of nodal point forces + +corresponding to the element +stresses at time t plus delta + +t, and at the end of iteration, +k minus 1. + +This matrix times that vector +gives us a vector which has + +the same length as this vector +has and that vector has. + +So we are not dealing anymore +with all the degrees of + +freedom that are listed for +which we have the forces here + +in the solution of the equation, +but with much less + +degrees of freedom, the degrees +of freedom being equal + +to the number of mode shapes +that are being employed. + +An interesting and most +important point is that in + +non-linear analysis, we have a +coupling, due to this vector + +appearing in here, between +the different mode shape + +equations, or modal equations. + +We cannot solve, as we usually +do in linear analysis, one + +equation of the modes of a +position after the other. + +In linear analysis, you would +typically solve the dynamic + +response equation in mode 1, +then the one in mode 2, then + +the one in mode 3, and like +that, you'd sweep over all the + +generalized degrees of freedom, +one after the other, + +for the total response from +time 0 to the end of the + +response time that you're +interested in. + +In non-linear analysis, we have +to go step by step still + +forward in time, solving all +equations, all modal equations + +at time t, then all modal +equations at time t plus delta + +t, then at time t plus 2 delta +t, and so on, because there is + +this coupling, and because we +don't know f unless we have + +all the information coming +from all the mode shapes. + +Well, a typical problem that you +might want to solve with + +this approach is the +pipe whip problem. + +Here we have a very long, +slender pipe. + +There is here a restraint +that has a gap. + +And suddenly, this end of the +pipe is subjected to a very + +large force. + +The pipe undergoes dynamic +motion, a wave travels along + +here, goes plastic, hits +this stop, et cetera. + +It's a very complicated problem, +and this approach of + +multiple position is it cheap +way of obtaining a solution to + +this problem. + +Of course, the accuracy of the +solution depends on how many + +mode shapes you include. + +If you only include a few mode +shapes, the solution is quite + +inexpensive, but the accuracy +is not very high. + +If you include as many mode +shapes as there are finite + +element degrees of freedom, +then of course you get the + +exact response. + +All you have done is transformed +from one basis, + +the finite element degrees of +freedom basis, to the mode + +shape basis. + +But then, of course, the +solution is very expensive, + +and you don't want to +ever do is that. + +The point is that you want to +perform such analysis if you + +only need to include +a few modes in + +the response solution. + +We would actually look at this +problem, or such a problem, a + +little later, when we discuss +example analyses. + +As a second technique that can +also be very useful in + +non-linear dynamic analysis, I'd +like to discuss with you + +the substructuring technique. + +This procedure is used is +implicit time integration, and + +the important aspect is that +prior to the analysis, we are + +setting u this effective +stiffness matrix corresponding + +to the linear degrees of freedom +only, and we are + +statically condensing out all +the degrees of freedom that + +will remain linear throughout +the response solution. + +It is quite effective for +local non-linearities. + +Here, for example, we have a +tower structure, and the only + +non-linearity that this +structure sees, say, is the + +slip down here. + +This typically would mean that +we have a large number of + +linear degrees of freedom that +we can deal with very + +effectively, using the +substructuring approach. + +The non-linear degrees of +freedom here, of course, + +require iteration and updating +of matrices, and those we deal + +with in the usual way. + +Let me show you in more detail +what I mean here. + +Let's look schematically +at an example. + +Here we have a 10-story +building, and that 10-story + +building is discretized, +idealized, as shown here. + +We also want to include the +elasticity of the foundation, + +and that is modeled very simply +here as an assemblage + +of springs. + +We deal here with two +substructures, shown in red + +for the substructure degrees +of freedom and in black for + +the master degrees of freedom. + +This is also part of the master +degrees of freedom. + +Notice that here we have +one substructure-- + +in other words, this part here +is nothing else than that part + +right here. + +That's what is one +substructure. + +And of course, you see here +another substructure. + +But we have a repetition here-- +in other words, this + +substructure here is identically +equal to that + +substructure. + +This, of course, is the fact +because of the particular + +design of this building. + +The upper stories look the same +way as the lower stories. + +That's the reason why we can +say, this is one substructure + +model which can model this part +of the structure and that + +part of the structure, +as well. + +If we look at the stiffness +matrix, or the effective + +stiffness matrix of this +structure that he would + +encounter in a direct +integration solution using + +implicit time integration, + +schematically, we see the following. + +Notice here we have the entries +coming from the + +substructures, and here +we have entries + +from the master structure. + +This coupling here corresponds +also to master degrees of + +freedom, and similarly, this +coupling corresponds to master + +degrees of freedom. + +Here we have the displacement +vector, the incremental + +displacement vector. + +And let's see here that these +master degrees of freedom of + +course correspond to these +element entries here. + +These master degrees of freedom +correspond to these + +entries, and these master +degrees of freedom correspond + +to these entries. + +Now what we can do is condense +out all the linear degrees of + +freedom effects. + +And that is achieved +as follows. + +We recognize that the total +effective stiffness matrix + +corresponding to time t is made +up of this part here, + +which is the linear stiffness +matrix plus + +the total mass matrix. + +I should point out here that +this K matrix contains all the + +linear contributions, where that +M matrix here corresponds + +to all the contributions from +the masses at the master + +degrees of freedom and the + +substructure degrees of freedom. + +Because we're assuming here that +the total mass matrix is + +linear, we can put all the mass +effects right in there. + +And then since this is not the +total effect of stiffness, we + +add the effect of the +non-linear element + +stiffnesses, right here. + +And in this particular analysis, +this might be, for + +example, the non-linear +springs down there. + +The non-linear springs modelling +the foundation on + +the structure. + +Well, this can be written +in this form. + +And if we perform static +condensation on this combined + +matrix, we arrive at +this matrix here. + +Notice here we have a condensed +degree of freedom + +vector carrying only the master +degrees of freedom, and + +here we have the entries +corresponding to the master + +degrees of freedom in +the tK hat matrix. + +We put a c on there, +meaning condensed. + +After static condensation, +this is a matrix + +that has been reached. + +These black squares here +correspond to as the black + +squares that you saw earlier. + +Of course, they have now been +changed a bit because of the + +static condensation, because +the effect of the linear + +degrees of freedom have +been carried into + +these entries here. + +The major steps in the solution +are as follows. + +Prior to the step-by-step +solution, we establish the K + +hat, the linear effective +stiffness matrix containing K + +plus 4 over delta t squared m. + +And this K hat matrix is then +used to statically condense + +out all internal substructure +degrees of freedom to obtain + +this K hat c, c standing +for condensed matrix. + +We note that the actual +effective stiffness matrix + +including the non-linear effects +is then obtained by + +taking the linear effective +stiffness matrix and adding + +the non-linear stiffness +effects to it. + +Notice, once again, this matrix +is obtained from this + +matrix here, as I mentioned +earlier. + +We use this matrix to statically +condense out all + +the linear degrees of freedom. + +The solution is then obtained in +each time step as follows. + +We update the condensed +matrix K hat c-- + +there should be no t here-- + +K hat c for non-linearities. + +That means we're adding the tK +matrix to it, corresponding to + +the non-linearities that have +occurred in the system. + +We establish the complete load +vector for all degrees of + +freedom, and condense out the +substructure internal degrees + +of freedom. + +This is important +to recognize. + +We have to calculate the +complete load vector because + +of the intertia effects on the +internal substructure degrees + +of freedom. + +The intertia forces on the +internal substructure degrees + +of freedom carry forces to the +master degrees of freedom that + +we have to take into account in +each time step and in each + +equilibrium iteration. + +We then solve for the master +degrees of freedom, using the + +small system size, the tK +hat c, the velocities, + +accelerations, and calculate all +the substructural degrees + +of freedom-- + +velocities, displacements, +and accelerations. + +These are required here to +calculate the load vector + +corresponding to all +degrees of freedom. + +Schematically, the solution +procedure, therefore, proceeds + +as follows. + +For each time step and each +iteration, we start with the + +displacement velocities and +accelerations at time t. + +We calculate the effective load +vector, corresponding to + +time t plus delta t, +the way I've been + +talking about it earlier. + +And then we condense that load +vector, as shown here, to the + +condensed load vector, c +meaning condensation. + +We then, from this load vector, +calculate with the + +effective tension stiffness +matrix, the t plus delta t Uc + +vector, and this vector is +used to calculate the + +displacement, velocity, and +accelerations of all the + +degrees of freedom at +time t plus delta t. + +Of course here I'm showing +only the process for a + +typical time step. + +If you iterate, as we usually do +in non-linear analysis, of + +course, then you would have to +also introduce the iteration + +counter here in these vectors. + +Notice that using this solution +procedure, we get the + +same results as if we had not +performed the substructuring. + +In other words, there is no +additional assumption that + +we're introducing into +the solution. + +You get the same results. + +However, the solution cost is +reduced, because we are + +dealing with one substructure, +a typical substructure, only + +once regarding the +factorization-- + +the LDL transpose factorization +and static + +condensation that has +to be performed. + +Let us now look at some +example solutions. + +And the first example that I'd +like to consider with you is + +the solution of the wave +propagation in a rod. + +Here we have a uniform freely +floating rod, and we apply to + +the left end of that rod a force +that varies as shown + +here as step load +of 1000 newtons. + +The material data for the +rod are given here. + +We want to perform a linear +elastic analysis, but although + +this is a linear analysis, we +still will learn quite a bit + +from it regarding non-linear +analysis. + +We want to consider the +compressive force at a point + +at the center of the +rod, right there. + +And the exact solution for this +force at that point is + +plotted here. + +You have, once again, apply 1000 +newtons, and here we have + +the time scale. + +Notice up to 1/2 t star, there's +no force at point a, + +because the applied force +in fact has to + +propagate through the rod. + +Then we have the full force up +to 3/2 t star, and then no + +force again, where t star is the +time for the stress waves + +to travel through the +complete rod. + +This is the analytical +solution, well-known, + +well-established, and we want to +compare with this solution + +when we perform our finite +element analysis. + +For the finite element analysis, +we use a mesh off + +2-noded truss elements, as shown +here, and we measure the + +force at the midpoint of the +total structure by the + +compressive force +in this element. + +We use in this analysis first +essential difference method, + +and recognize that the time +step that we use has to be + +small or equal to the critical +time step, as we discussed in + +the previous lecture. + +And that critical time step +is given by Le/c. + +Please refer to as the previous +lecture notes, and + +you would see this formula +there, which is nothing else + +than t star divided by the +number of elements. + +We recall that if delta t is +greater than delta t critical, + +we would produce an +unstable solution. + +We also need to deal +with the initial + +conditions for this problem. + +And we recognize that if the +initial displacements are 0 + +and R is given, then we can +calculate the initial + +acceleration, as shown here. + +Using now a time step equal to +the critical time step, we + +obtain the correct result, and +I pointed that out in the + +earlier lecture already, that +we in fact obtain the exact + +solution for any number +of finite elements + +to model the rod. + +And here is a finite element +solution, compared with the + +exact solution. + +A wonderful solution, right +on the exact solution. + +Using, however, now a +smaller time step-- + +and this is frequently +of surprise-- + +using a smaller time step, we +get a much worse result. + +Here we use a time step of +1/2 delta t critical. + +Half the time step that +we used before. + +And just solution looks actually +very bad right here. + +Frequently one sort of +intuitively thinks, well, if I + +use a smaller time step, I +should get better results. + +My costs go up, and surely I +should get better results. + +Well, it turns out that using +the explicit time integration + +scheme for this type of problem, +this wave propagation + +problem, with a smaller time +step, more cost, higher cost, + +you get worse results. + +That is really something +to keep in mind. + +Now let us consider the +trapezoidal rule. + +The trapezoidal rule-- we +discussed this method in the + +earlier lecture. + +And I'd like to refer you +once again to the notes + +corresponding to that lecture, +where we have identified that + +a stable solution would +be obtained with any + +choice of delta t. + +Remember, this is a linear +analysis, and the trapezoidal + +rule is unconditionally +stable. + +We could use a consistent +or lumped mass matrix. + +And in this particular case, we +use a lumped mass matrix, + +because we also like to compare +our results with those + +that we obtained using the +central difference method. + +If we use the trapezoidal rule +with the time step that we + +employ in the central +difference method-- + +in fact, the critical time +step that we used there-- + +and we also use the initial +conditions computed as shown + +here, the way we did it for the +central difference method + +solution, we find that the +solution is very inaccurate + +when compared to the +exact solution. + +Here, of course, we also use +the 10-element mesh. + +If we use 0 initial conditions +for the trapezoidal rule, we + +get this solution. + +Not much different, really, from +the solution that I just + +showed you. + +So whether we use 0 initial +conditions or the initial + +conditions corresponding to the +equation MU double dot is + +equal to R, which we have seen +on the previous view graph, + +makes very little difference +when using + +the trapezoidal rule. + +It makes a lot of difference +using the explicit central + +difference method. + +And for that reason, in fact, +we have to use the proper + +initial conditions obtained from +MU double dot equals R at + +time 0 when we use the central +difference method. + +Using now twice the time step of +what we just used, namely, + +delta t equal to 2 times delta +t, critical of the central + +difference method, this solution +is stable, but very + +inaccurate. + +It is stable because we're +using an unconditionally + +stable operator. + +We discussed it in the +previous lectures. + +Note that this is the solution +we're obtaining when compared + +to the exact solution. + +Now we look at the solution +where we have half the time + +step off the critical size, +corresponding to the central + +difference method. + +And you see here, the solution, +again, very + +inaccurate when compared to +the exact solution, but of + +course stable, because the +method is always stable for + +any time step delta t. + +The question now could, of +course, be, and should be, + +what happens if we take more +elements to discretize the + +whole structure? + +Here we use the 10-element +model. + +Why not use more elements? + +And here we now look at the +solution obtained with the + +essential difference method when +we use 100 elements to + +model the total bar. + +Here the exact solution in red, +and that exact solution + +is reached if you integrate the +equilibrium equations with + +this time step. + +We discussed that earlier. + +That exact solution is always +obtained for any number of + +elements that you use to +discretize a structure, + +provided you use delta t equals +delta t critical. + +If you then use a smaller time +step, in fact, delta t equals + +1/2 delta t critical was used +here, we obtain a solution + +that is not the exact solution, +but as you can see + +here, it oscillates for this +time step this amount about + +the exact solution. + +So we have much the same +observations that we have seen + +already earlier, namely, when +the time step is decreased in + +the central difference +method solution-- + +from the critical time step, +here we see a decrease-- + +the solution that one might +expect to be better actually + +deteriorates. + +Of course, it couldn't +be better + +than the exact solution. + +But we see here a deterioration, +and a quite + +significant one. + +If you use the trapezoidal rule, +this is the solution + +that you obtain with the time +step equal to the critical + +time step of the central +difference method. + +Again, here, we're using +the 100-element mesh. + +The solution is certainly better +than what we have seen + +for the 10-element mesh, +but it does not give + +us the exact solution-- + +in other words, a +[UNINTELLIGIBLE] wavefront as + +we would like to obtain. + +Of course, this is a very +difficult problem to solve, + +because we have infinitely steep +wave fronts here and + +there, basically, to model. + +And an overshoot would obviously +obtain it, but we + +would like to have said +overshoot and undershoot, with + +this oscillation here as small +as possible, of course, with + +the solution scheme +that we employ. + +There is one more important +consideration that I'd like to + +bring to your attention. + +Here we use a 2-dimensional +element mesh to model the bar. + +Notice these are 4-node +elements, plane stress + +elements here to +model the bar. + +And in this particular +case, we use the + +central difference methods. + +The thickness is given +here, the material + +data are given here. + +For this solution, notice that +this distance here is half the + +distance that we have here. + +And that is something that leads +to a phenomenon that one + +has to be aware of. + +Notice our the critical time +step that we identified for + +the one-dimensional wave +propagation here would, of + +course, be calculated depending +on this length. + +However, we have to allow for +the fact that there is also a + +possibility of wave propagation +this way, and the + +actual critical time step that +we have to use in this problem + +is given by this length, by the +shortest element distance. + +Please refer to the previous +lecture, in which I discussed + +this already. + +You have to use the shortest +distance between nodal points + +within an element to determine +the critical time step. + +So this relationship here does +not hold anymore, because this + +distance is less than that. + +And if you were to use delta +t equal to t star over 10 + +elements, which was a critical +time step that we used when we + +solved the truss element model, +then we would find that + +the solution diverges. + +In fact, in element 5, which was +the element that we always + +used to measure our stress, we +find that tau zz, the absolute + +value of tau zz, is greater than +1000 newtons divided by + +the area at this time. + +Notice that it was 1000 newton +that we applied. + +So a stress that should be 0, +really, because tau zz should + +really be 0, it's the stress in +the transverse direction, + +the wave travels this way, and +tau zz is acting that way. + +This stress should be 0. + +We find, actually, that it +grows, and it grows because we + +are using a time step that is +larger than the critical time + +step that should be used +for this problem. + +Let us now look at another +example, a second example from + +which we can also learn +quite a bit. + +Here we have a very simple 3 +degree of freedom system. + +These are the degrees of +freedom, x1, x2, x3. + +Notice we have masses m here, +and we have a linear spring + +connecting these masses, a +non-linear spring connecting + +these masses, and a linear +spring connecting this mass to + +the rigid support. + +For this problem, the linear +spring has is distance here, + +and the non-linear spring is +characterized by this force + +displacement relationship. + +Notice there's a kink +going from 1 to 100. + +So the spring gets suddenly, at +a particular distance, or + +rather deformations, +I should say-- + +displacement x2 minus x3-- + +at a particular deformation, the +spring becomes 100 times + +as stiff as prior +to that point. + +Well, we can calculate a +critical time step based on + +this spring stiffness here, the +linear part, or rather, + +this spring stiffness for +small displacements. + +And that critical time step for +this problem is given as + +1.11 seconds. + +As long as the response of this +system is such that we + +would, in this non-linear +spring, never go around this + +kink, we would deal with a +linear system, and this would + +be the proper critical +time step to use. + +However, as soon as we are going +around this kink here, + +due to the fact that the forces +that I applied, or the + +initial conditions that we are +applying to these degrees of + +freedom, are large enough, as +soon as we go around this + +kink, our new critical time step +is based on this spring + +stiffness, and if this given +right down here. + +This is a new critical +time step. + +So if we now perform essential +difference method solutions of + +this problem, and if the +solution brings us into this + +regime, it is very important +to use, as a critical time + +step, 0.14 seconds. + +It is very important, even if +we're only in this regime for + +just a few steps. + +You see, what might happen in +the response is that most of + +the time, you're +in this regime. + +But then all of a sudden, for +just a few steps, you're + +getting into this regime, +and because of this high + +stiffness, you're thrown +back into this regime. + +If your time step that you use +in the time integration is + +then larger than that value, you +are having an instability + +for just these few time steps, +and that introduces an error + +in the solution which, if you +don't have a comparison with + +an exact analytical solution, +will of course be an error + +that you not necessarily +will see, directly. + +And that's one of the +important points. + +You see, in linear analysis, +when you use the essential + +difference method in linear +analysis with a time step that + +is larger than the critical time +step, you will, after a + +few time step integrations, see +that the response becomes + +very large, and the instability +is obvious. + +The instability is really +obvious when you apply the + +central difference method with +a time step that is larger + +than the critical time step to +the solution of the system. + +However, in non-linear analysis, +as I mentioned in + +the earlier lectures, and you +are now well aware of it, in + +non-linear analysis, the +frequencies change. + +The critical frequency being the +largest frequency in the + +system changes. + +The smallest period of the +system changes, as we are + +seeing here in this +view graph, also. + +And it is important that your +time step is always smaller + +than the critical time step +based on the highest frequency + +that you can ever encounter +in the solution. + +If that is not the case, then +you might have only an + +instability for a few time +steps, and the solution may + +not have time to blow up, +or give you very large + +displacements. + +So the instability will +not be obvious. + +Instead, the instability over +these few time steps only + +introduces an error in the +solution, an error of which + +you really don't know +the magnitude. + +And after these few steps have +been completed, you're using + +now a time step that +is again stable, + +giving a stable solution. + +That error which we have +accumulated, of course, is + +carried forward, but +you have not seen a + +blow-up of the solution. + +And that's one important +consideration when you apply + +the central difference method +in non-linear analysis. + +Of course, the important point, +the sort of ground rule + +that you have to observe, is +that delta t must always be + +smaller than the critical time +step of the mesh where that + +critical time step changes +throughout the solution. + +Let's look at this +example here. + +What happens if we violate +that condition? + +I show you here the solution +with delta t equals 0.15 + +seconds, compared to +the solution with + +delta t 0.05 seconds. + +Notice that the response of the +right math here for both + +of these time steps is slightly +different, but we can + +say that for this time step, +we don't get displacements + +that are very much different +than we obtain + +with this time step. + +If we look at the response of +the center mass, there are + +more differences in +displacements. + +And if we look at the response +of the left mass, in fact, we + +have even larger differences. + +But the important point is that +if you only have this + +solution here corresponding to +the time step 0.15 seconds, + +which is larger than the +critical time step, you would + +certainly not expect that this +solution was unstable. + +It in fact was only unstable +for a very few time steps. + +There is an error accumulation, + +fairly large here. + +In fact, very large. + +You can see that these +displacements are only about + +50% of those displacements. + +But you cannot see directly an +instability here if you don't + +know this solution. + +Let's look at the force +in the center truss. + +Here we list the time, here we +list the solution for delta t, + +0.05 seconds. + +And here we list the solution +for delta t 0.15 seconds. + +And you can see here that at +the beginning, the forces + +compare quite well, +and then the error + +becomes larger and larger. + +In fact, here we have an +opposite sign in the force. + +This being here, say, the +accurate solution with a small + +enough time step, and this +being, of course, a grossly + +inaccurate solution. + +But it is not evident that this +is a grossly inaccurate + +solution if you don't +know this solution. + +And that's the point I wanted +to make with this example. + +The next example that I like +to discuss with you Is the + +analysis of a tower. + +The tower is shown here, +subjected to a pressure that + +is induced by a blast. + +Here we have some geometric +and material data + +regarding the tower. + +The applied load on the +tower is shown here. + +Notice it's a load that we +assume to be instantaneously + +there, and then to decay, +as shown here, over 200 + +milliseconds. + +The purpose of the analysis is +to determine the displacement + +and velocities at the top off +the tower, to determine the + +moments at the base +of the tower. + +And in this particular +analysis, we use the + +trapezoidal rule and the lumped +mass matrix to solve + +the problem. + +We must make a number of +decisions here, and two + +decisions are most important. + +We must choose a mesh that is, +in other words, we have to + +establish an appropriate finite +element discretization + +for the tower, and we have to +choose a time step for the + +time integration. + +The choice of mesh and the +choice of the time step are + +two very closely related items, +and that's what I would + +like to discuss with you in this +example in more depth. + +Of course, the time step and the +mesh must both depend on + +the loading that is supplied. + +Let's look at some +observations. + +The point is that the choice +of mesh will determines the + +highest natural frequency, and +of course, the corresponding + +mode shape, that is properly, +accurately represented in the + +finite element analysis. + +The more elements you use, just +as a rule of thumb, the + +higher the frequency that can be +properly represented, that + +can be accurately picked +up, with the choice + +of mesh we're using. + +The time step that you're using +will of course determine + +how high a frequency you're +integrating accurately. + +In other words, you want to use +really enough elements to + +have a mesh that is accurate, +and you want to use is small + +enough time step to integrate +the frequency of the mesh that + +you need to integrate in order +to have an accurate response + +prediction. + +I used the word "accurate," and +we have to now of course + +look closely at what +I mean by that. + +It is most effective, really, +to choose the mesh and the + +time step such that the highest +frequency, accurately + +integrated, is equal to the +highest frequency accurately + +represented by the mesh. + +To choose the mesh and the +time step, we look at the + +applied loading, in other words, +the physics of the + +problem, and we represent +this applied loading + +as a Fourier series. + +If we do so, that Fourier +series will display the + +important frequencies that are +to be accurately represented + +by the mesh. + +Here for this particular loading +that we're looking at, + +we did a Fourier analysis, and +you can see that with this + +Fourier analysis, we include +terms now in our first + +analysis, in case one, up to fn +17 hertz, and in case two, + +in our second analysis, up +fn equal to 30 hertz. + +If we truncate our Fourier +representation of the loading + +at 17 hertz, we obtain this +approximation here to the + +actual applied noting. + +If we truncate our Fourier +representation at 30 hertz, we + +obtain this Fourier +approximation + +to the actual loading. + +As you can see, surely, as +expected, if you include more + +terms in the Fourier +approximation, your + +approximation to the actual +loading becomes better. + +Now having identified that we +want to perform the analysis + +with two meshes, first there's +a mesh that gives us + +frequencies accurate up to 17 +hertz, and then with a mesh + +that is accurate up to 30 hertz, +we have to look for + +those meshes. + +And we do so by establishing +three meshes + +that are shown here. + +Here we have a 30-element +mesh. + +Notice that one element spans +from the bottom of a floor to + +the top off the floor, +and across from one + +column to the other. + +A 60-element mesh, in which we +simply have subdivided each + +element here in this more coarse +mesh into two elements, + +and a 120-element mesh, in which +we again have taken one + +element here and represent +it as two elements. + +We use these meshes here to +calculate frequencies. + +And on this view graph here, +you see the frequencies + +calculated for the 30-element +mesh and the 60-element mesh. + +Notice mode numbers +in this column. + +30-element mesh results here, +60-element mesh results here, + +in each case, hertz. + +We notice that up to this red +line, the difference between + +the frequencies is less +than 1 hertz. + +In other words, the difference +between the frequencies + +obtained from the 30-element +mesh and the 60-element mesh + +is less than 1 hertz, and +that is also right at + +the 17 hertz level. + +So we can say that the +30-element mesh really + +represents the frequencies up to +17 hertz quite accurately. + +You should also remember, +please, that since we are + +using a lumped mass matrix in +the analysis, there's no + +bounding theorem saying that +the frequencies of the + +60-element mesh must always be +below the frequencies of the + +30-element mesh. + +For a larger mesh, we can +actually have frequencies that + +are smaller or larger than +for the more coarse mesh. + +That of course also applies +for when we compare the + +60-element mesh result with +the 120-element mesh + +result later on. + +So we say that for the +30-element mesh, we have + +accurately represented now the +frequencies up to 17 hertz, + +and therefore, there +is the mesh to use. + +We calculate the time step via +is this relationship here as + +being 0.033 seconds, being the +cutoff frequency, and delta t + +then is given here as +0.0017 seconds. + +This mesh now should be +integrated with this time + +step, and then we can say is +that the mesh up to 17 hertz + +represents the frequencies quite +accurately, and we have + +integrated the frequencies up to +17 hertz quite accurately, + +and therefore, we have an +accurate solution of the + +problem up to 17 hertz-- + +and what I mean by this "up to +17 hertz" is that also in the + +Fourier representation, we in +effect only have represented + +the load by the Fourier +representation up to + +17 hertz, in effect. + +Of course, in the actual +step-by-step solution, we also + +will carry terms +above 17 hertz. + +But these terms are assumed not +to contribute to very much + +to the response, because we are +not picking them up very + +well in the mesh and in the +time step selection. + +If we proceed now with the same +ideas to also look at the + +60-element mesh, then we +perform there also the + +frequency analysis for the +60-element mesh and the + +120-element mesh, and we find +that up to 30 hertz in the + +60-element mesh, we gain +represent all the frequencies + +accurately. + +Notice that above the red line, +below these frequencies + +here, the difference between +these frequencies + +is less than 1 hertz. + +Above this line, the difference +between the + +frequencies is larger than +1 hertz, and that + +is our cutoff line. + +Well, if we want to perform +now the direct time + +integration of the 60-element +mesh, we proceed as for the + +30-element mesh. + +We calculate our cut-off +frequency, our delta t, the + +proper time step, 20 steps for +the highest frequency or the + +smallest period that we want +to integrate accurately. + +That's the rule of thumb +we're using. + +And with this time step, we +perform the analysis. + +Notice a smaller time step would +be accurately integrate + +frequencies which are +not accurately + +represented by the mesh. + +Therefore, there is no point +choosing a smaller time step. + +A larger time step would not +accurately integrate all + +frequencies which +are accurately + +represented by the mesh. + +It is not good to choose a +larger time step, because your + +mesh is chosen to represent the +frequencies up to 30 hertz + +quite accurately, and to get all +of what you can get out of + +the mesh, so to say, you want to +take a time step that is in + +accordance selected +with the mesh. + +And that times step selection +gives you this result here, + +0.003 seconds. + +Let's look now at the actual +response that is calculated. + +Considering the horizontal +displacement at the top of the + +tower, denoted as u, here, +we find that in fact the + +30-element mesh and the +60-element mesh give virtually + +the same response. + +If we look at the horizontal +velocity at the top off the + +tower, we find that there are +some small differences between + +the 30-element and +60-element mesh. + +If we were to look at the +accelerations, these + +differences would of course +be even larger. + +But the purpose of this analysis +was to calculate the + +displacement and velocities +at the top of the tower. + +Let's look at the moment, which +was also one requirement + +for our analysis, the moment +right down here at the bottom + +off the tower. + +And here we see that the +30-element mesh gives the + +smooth result. + +The 60-element mesh gives +the zig-zagged result. + +But overall, really, basically +a good response prediction + +already with the 30-element +mesh. + +If we look at the displacements +of the tower, we + +have amplified these +displacements here. + +The 30-element mesh at 200 +millisecond looks like that. + +The 60-element mesh. + +looks like that. + +At 400 milliseconds, +the 30-element mesh + +looks as shown here. + +The 60-element mesh looks +as shown there. + +Regarding these analyses, +we now can + +summarize some comments. + +We saw some high-frequency +oscillations when we looked at + +the moment reaction response +of the 60-element mesh. + +However, this high-frequency +response, which actually can + +be identified to be 110 hertz, +is probably inaccurate, + +because our mesh did not +represent frequencies + +accurately up to that level. + +The obtained solutions for the +horizontal displacement and + +the velocity at the top off the +tower are really virtually + +identical for the 30- and +60- element mesh. + +Let us now look at +another example. + +This is the example +of a pendulum. + +A large displacement analysis of +this pendulum is performed, + +and basically what we're looking +at here is, if I can + +just have your attention here, +is at the pendulum that + +originally is horizontal, +it's pinned right here. + +And we let this pendulum go +through very large motions, + +and pendle around +as shown here. + +If always should come back to +the horizontal position, + +unless we have damping +in the system. + +Since we don't have damping in +the system, the pendulum + +should just keep on +going forever. + +We have a frictionless hinge +right here, and this is + +pictorially represented here +on the view graph, a + +frictionless hinge +right there. + +The pendulum is modelled by a +truss element of stiffness EA. + +The length is given here. + +The mass is concentrated +right there. + +So there's no distributed +mass here. + +All of the mass of the pendulum +is concentrated here, + +half of it here, and +half of it there. + +The initial conditions of the +pendulum are listed here. + +The initial angle is 90 degrees +theta, so the pendulum + +is up here, as I explained +already. + +And initially, it +has 0 velocity. + +And now we let the pendulum go, +and as I said, it should + +spring up and down +here, of course, + +under the gravity loading. + +The dynamic response that we +want to calculate is obtained + +using the trapezoidal rule. + +And we are using full Newton +iterations to establish the + +equilibrium during +every time step. + +The convergence tolerance that +we use, and that I have to + +refer you now to our earlier +view graph regarding + +convergence tolerances. + +The tolerance that we're using +here is ETOL equal to 10 to + +the minus seventh. + +We talked about what ETOL is +in an earlier lecture. + +In our first analysis, we chose +the time step to be + +equal to 0.1 seconds. + +And in that case, the following + +response is obtained here. + +We expect that solution is shown +as a solid line, and + +these circles here show +the calculated + +finite element solution. + +Notice 90 degrees theta here +minus 90 degrees here, and + +then we return to 90 degrees. + +The solution looks quite +fine, looks stable. + +And in fact, if you look at the +textbook, you would find + +that there I'm giving the +solution up to here. + +Everything looks good. + +However, if we plot the strain +in the truss, we find that at + +larger times, the strain +oscillates very much, and in + +fact, this oscillation grows. + +This clearly signifies +an instability in + +the solution process. + +The instability is unchanged +when we tighten our + +convergence tolerance or when we +use the BFGS method instead + +of the full Newton method. + +We should recall here that the +trapezoidal rule is only + +unconditionally stable +in a linear analysis. + +Here we are talking about a +non-linear analysis, and you + +cannot select any time step +magnitude delta t and expect a + +stable solution. + +So what we have to do now is +to use a smaller time step, + +and we choose delta t equal +to 0.025 seconds, + +and repeat the analysis. + +Theta degrees here as +a function of time. + +And once again, a very nice, +smooth response solution, + +starting with 90 degrees, going +to minus 90 degrees, + +coming back to 90 degrees, +and so on. + +Of course, even with a larger +time step, you got a smooth + +solution for theta. + +What really told us about the +instability in the solution + +was our look at the strain +in the truss. + +So we look now also at this +strain, and in this particular + +case, with this time step, +we see a smooth + +solution for the strain. + +You should please observe that +the scale on the strain is + +here different from the strain +scale that we had in the + +earlier view graph. + +If you refer back to the earlier +view graph, you see + +that we had a different +scale there. + +But we have a smooth solution +here, in fact, a solution the + +way we would expect it. + +If we don't iterate, then we +obtain a solution that looks + +as shown here. + +In other words, instead of +getting this oscillatory + +response that we would like to +obtain, we obtain really a + +highly damped solution +response. + +This, of course, shows the +importance of iteration. + +We have to iterate in the +solution of a dynamic problem. + +It's very important to +integrate in order to + +establish equilibrium for every +time step, for every + +discrete time that we're +considering. + +In this particular case, we see +that we obtained a highly + +damped solution. + +In other cases, the solution +might blow up. + +So it is important to iterate +in the nonlinear dynamic + +solutions when you +use an implicit + +time integration scheme. + +Although the solution obtained +with the equilibrium iteration + +is highly inaccurate, +the solution + +is, of course, stable. + +And that is also seen when one +looks at the strain plot. + +Notice here we're plotting +strains in the truss element + +as a function of time. + +No blow-up of that strain, +no violent oscillation. + +It is, in fact, going up here, +and then becoming this rather + +small oscillating, +as shown here. + +So we don't have an unstable +solution, but a highly + +inaccurate solution. + +Let's look at the next example +now, the analysis of a pipe + +whip problem. + +Here we have a long pipe, +dimension given here and here, + +that is subjected suddenly to a + +concentrated load at its end. + +There is also, below the +pipe, a restraint. + +That restraint is only active +once this gap is closed. + +Notice there is a 3-inch +gap here between the + +pipe and the restraint. + +Of course, this restraint, in +an engineering design, is + +installed to prevent violent +emotions of the + +pipe at this point. + +What our objective here is, +to determine the transient + +response of this pipe. + +Notice that under this very +large load, the pipe very + +rapidly becomes plastic. + +And the difficulty of this +problem really lies in that + +the pipe going plastic becomes +very flexible here, but the + +restraint suddenly hitting the +pipe, or the pipe hitting the + +restraint, rather, means that +a very large difference is + +suddenly introduced +at this end. + +The finite element model +we used is shown here. + +6 summation beam elements that +of course can go plastic. + +There's more of the +elastoplasticity + +in the system properly. + +And a truss element from +this node to that node. + +This truss element contains +a 3-inch gap. + +The material properties for +the pipes are listed here. + +Notice the material property +corresponding to the + +elastoplasticity. + +We assume no strain hardening +and for the restraint. + +Again, the restraint also +is modeled as an + +elastoplastic material. + +The analysis performed, in this +particular case, using + +multiple position with two +modes and direct time + +integration. + +We want to compare the response +that we predict using + +the multiple position procedure, +which I discussed + +earlier in this lecture, with +the response that we obtain + +using a time integration +analysis. + +For the time integration +analysis, we use the + +trapezoidal rule. + +And in fact, even in the +multiple position, we also use + +the trapezoidal rule. + +And for the mass representation, +we have chosen + +a consistent mass matrix. + +In this particular case of +convergence tolerance, ETOL + +was used with this +value down here. + +If we perform the eigenvalue +solution of the initial + +system, in other words, of the +elastic pipe in the initial + +state, we obtain these natural +frequencies, 8.5 + +hertz and 53 hertz. + +These are also the +mode shapes. + +And of course, these frequencies +will change as + +time progresses in the +elastoplastic response, and + +also the mode shapes will +change, particularly once + +their restraint is hit. + +However, what we are saying is +that we believe we can capture + +the elastoplastic response of +the pipe, approximately, by + +using this mode shape and that +mode shape as generalized + +displacement patterns +to represent + +the total pipe response. + +Of course, there are the heavy +approximations that we reduce + +all of the pipe degrees +of freedom to adjust 2 + +generalized degrees +of freedom. + +To integrate a response, we have +to choose a time step. + +And here we have delta t 1/20 +of the cutoff period that we + +want to use here. + +Notice that we have only two +modes in this problem that we + +want to consider, with the +frequencies that I + +showed you just now. + +And this equation gives +us, as a time + +step, 1/1000 of a second. + +Of course, once again, this +estimate, or this choice of + +time step, is based solely on +looking at the linear response + +of the pipe. + +In other words, assuming that +the pipe remains elastic and + +that the restraint is +not there either. + +If we look at the results +obtained from these two + +analyses, we find that the +multiple position response for + +the displacements looks as shown +here, the direct time + +integration response looks +as shown here. + +Notice that this is here the +distance of the gap, so at + +this particular time, the gap +is closed and the restraint + +comes into action. + +We note from this graph that the +multiple position solution + +is really very close to the +direct integration solution + +for the displacement at +the tip off the pipe. + +Now let us look at +the moment at the + +built-in end of the pipe. + +And here we have the moment +response plotted as a function + +of time for the direct +integration solution, as shown + +here, and for the multiple +position + +solution, as shown here. + +We notice that the maximum +moment occurring at the + +built-in end in the pipe is +almost the same when predicted + +by the multiple position +solution and the direct + +integration solution. + +There's some small difference, +but the difference is + +certainly not very large. + +However, if we look at what +happened at earlier times, we + +see that there is a large +difference between the results + +obtained using the multiple +position solution and the + +direct integration solution. + +The reason is that the response +here at earlier times + +is very complex, and the +multiple position solution + +cannot pick that complex +response up very well. + +However, it's one important +point you should keep in mind. + +And that is, if we had used +more modes in the multiple + +position solution, we would come +closer to the response + +obtained, predicted with the +direct integration solution. + +In fact, if the number of modes +used in the multiple + +position solution is equal to +the number of degrees of + +freedom in the finite element +mesh, then the multiple + +position solution gives you +the same response as you + +calculate with the direct +integration solution. + +I mentioned that earlier in the +lecture already, and the + +reason, of course, is that in +that case, all you would have + +done is a change of bases +from the finite element + +displacements to the +mode shape bases. + +So if you use, even with this +initial stiffness matrix that + +you have used to calculate the +mode shapes, even with that + +initial stiffness matrix, if +use all the modes, as many + +modes as there are degrees of +freedom, in this multiple + +position solution, you would +get the same response + +prediction with the multiple +position solution as we're + +seeing here, with the direct +integration solution. + +And that means we can be quite +assured that as we increase + +the number of modes in the +multiple position solution, we + +will get closer and closer to +this complex response that is + +predicted using the direct +integration solution. + +In general, one, of course, does +not know the error when + +you use the multiple position +solution, and there must + +always be a question of how +large is the error, for + +example, that we're +seeing here. + +And that can only be assessed +by a more accurate solution. + +However, I believe that's the +multiple position solution is + +of much value in the initial +design analysis stages when + +you want to obtain fairly +inexpensive solutions for the + +response, and you want to just +understand how the system acts + +that you are analyzing +and designing. + +The multiple position solution +really yields relatively + +inexpensive response solutions +of the system which may be + +very helpful in the initial +design stages of that + +structural system. + +This completes, then, the +discussion of our examples for + +which I have prepared +view graphs. + +I'd like to now share with you +some further experiences that + +are summarized on this slide. + +And let me go over here, +where I have + +the first slide projected. + +I should point out, before we +discuss the information on + +these slides once more, that +we will go fairly rapidly + +through these slides, and that +not all details pertaining to + +the solutions that we are +looking at here are given on + +these slides. + +Please refer to the papers-- + +the references are given in the +study guide-- in order to + +find all of the details +pertaining to the solutions + +that I'm now discussing +with the slides. + +Here we consider now the +analysis of a control rod + +drive housing, which is modelled +using four beam + +elements and point masses. + +Notice that the structure is +subjected to motion up here. + +The non-linearity in the system +lies in the fact that + +there's a gap between the tip +of that beam here and the + +spring on the right-hand side +and on the left-hand side. + +On the next slide, we see now +the solutions obtained. + +We obtain a solution using +direct integration, and using + +a multiple position analysis, +including two modes. + +These two solutions are compared +with a solution that + +was reported at some earlier +time by Peterson and myself. + +Here you see the comparison +of the results obtained. + +Notice there is a difference +here between the solution that + +we reported earlier, that +Peterson and myself reported + +earlier, and the solution +that we generated now. + +But that difference is due to +the fact that Peterson and + +myself used, at that time, a +different solution scheme. + +The response solution that we +obtained with the multiple + +position analysis is very close +to the response solution + +that we calculated using +direct integration. + +Now the next analysis that I'd +like to discuss this you + +involves the analysis of a +spherical shell subjected to a + +uniform pressure. + +And that pressure is suddenly +applied as shown down here. + +Notice this is a step pressure +constant in time. + +The material data of the +shell are given here. + +We want to calculate the +elastoplastic response. + +And some geometric data +are given here. + +Notice the shell was idealized +using 10 8-node + +axis-symmetric elements. + +It's a spherical shell, so we +use an axis-symmetric model to + +model the shell. + +We use Newmark integration +with delta and + +alpha as given here. + +We chose these values because +Nagarajan and Popov had chosen + +these same values, +and we wanted to + +compare with their solution. + +We used 2-by-2 Gauss integration +and a consistent + +mass matrix for the problem. + +The time step was 10 +microseconds, and we used the + +total Lagrangian formulation +in the analysis. + +The next slide now shows the +response that we predicted. + +Here we see the ADINA solution, +a dashed line, + +compared with the solution by +Nagarajan and Popov given by + +the solid line. + +Notice we are plotting here the +apex displacement of the + +shell as a function of time. + +Now in this particular case, +we use the consistent mass + +matrix, 2-by-2 integration, +and specific solution + +parameter, and we want to do now +change these parameters in + +order to see the effect of +these parameters on the + +solution that is predicted. + +The next slide now shows again +the apex displacement of the + +shell as a function of time, +but using once a consistent + +mass matrix, and once using +a lumped mass matrix. + +And in this particular case, we +use the trapezoidal rule, + +which corresponds to the Newmark +integration with delta + +equals 0.5 and alpha +equals 1/4. + +Notice that there are only slide +differences between the + +lumped mass solution results +and the consistent mass + +solution results. + +Another parameter that one +might want to vary is the + +integration order. + +Here we have the response, +using 2-by-2 integration, + +which we saw already earlier. + +Actually, we didn't quite see +this response earlier, because + +earlier we used different delta +and alpha parameters. + +Very close to these parameters, +however. + +Anyway, here we have the 2-by-2 +integration results, + +and then we have the 3-by-3 +integration results and the + +4-by-4 integration +results here. + +Very small differences between +these solutions, but it's + +interesting to perform these +solutions, and really assure + +oneself that there are +small differences. + +We know that shells are rather +sensitive structures, and we + +want to make sure about the +modeling that we're using for + +the representation of these +types of structures. + +The next slide now shows the +analysis of a problem for + +which we had experimental +results to compare with. + +Here we have a pipe, a very +rigid pipe, and a flexible + +pipe, a nickel pipe here. + +And these pipes, both being +straight, are totally filled + +with water. + +At the end off this pipe here, +a pulse gun sets off a pulse, + +and that pulse travels through +the water, all the way along. + +And of course, there's an +interaction between the pipe + +and the water. + +In other words, it's a fluid +structure interaction problem. + +This pipe here is very rigid, +so that we model it as + +infinitely rigid. + +You will see that just now +on the next slide. + +Notice here we have pressure +gauges indicated. + +The pressures and the strains +in the pipe, in this nickel + +pipe, the flexible pipe, were +measured by the Stanford + +Research Institute. + +Here we have the nickel +properties, we assume an + +elastoplastic material, and +the water properties. + +On the next slide now, we see +the pressure pulse as a + +function of time. + +Of course, this was given +to us for our analysis. + +And this slide now shows +the finite element + +model that we use. + +We used an axis-symmetric +model. + +The center line is right here. + +And notice that the water here +in the rigid pipe was + +represented by 81 elements. + +Notice the rigid pipe was +modelled as infinitely rigid, + +because these are rollers +on an infinitely rigid + +surface, so to say. + +Notice here is a nickel pipe +representation, and here we + +have water elements again, +and a thin layer of + +water elements here. + +On the next slide now, we see +the response predicted by + +ADINA and the experimental +results, the ADINA response + +shown as a solid line and the +experimental result shown as a + +dashed line. + +Of course, the experimental +results reported by the + +Stanford Research Institute. + +Notice we are plotting here the +pressure as a function of + +time for one of the +pressure stations. + +And here you'll see the same +information for another + +pressure station, and for +another pressure station, and + +one more pressure station-- + +the pressure stations that I +pointed out to you earlier. + +Notice that here finally we +compare the hoop stress + +predicted by ADINA with the +experimentally observed hoop + +stress as a function of +time at one of the + +stations within the pipe. + +Notice that for the hoop stress +here, we have four + +experimental results +corresponding to the + +measurements that were taken at +the north pole, the south + +pole, east pole, and west +pole on the pipe. + +In the ADINA solution, +of course, we use an + +axis-symmetric model, and that +axis-symmetric model only + +gives one hoop strain. + +And that hoop strain, as you +can see here, lies quite + +nicely within the experimental +results obtained by the + +Stanford Research Institute. + +I should also point out that +the comparison of the ADINA + +results with the experimental +results is really very good, + +except that we don't pick +up these high-frequency + +oscillations that have been +observed in the experiment. + +Well, the ADINA finite element +mesh that we used in this + +analysis is not able, really, +to represent these + +high-frequency oscillations, +and of course, that is + +certainly one of the reasons why +we could not hope to pick + +these frequency oscillations +up. + +This, then, brings me to the +last slide that I wanted to + +share with you in this lecture, +and also to the end + +of this lecture. + +Thank you very much for +your attention. \ No newline at end of file diff --git a/DrFkf-T-6Co.txt b/DrFkf-T-6Co.txt new file mode 100644 index 0000000000000000000000000000000000000000..868e8b8ca82083a0f0fe53e2ba17024de1b29f7c --- /dev/null +++ b/DrFkf-T-6Co.txt @@ -0,0 +1,3600 @@ +[MUSIC PLAYING] + +PROFESSOR: Well, so +far in this course + +we've been talking +about procedures, + +and then just to remind +you of this framework + +that we introduced for +talking about languages, + +we talked about the +primitive things that + +are built into the system. + +We mentioned some +means of combination + +by which you take +the primitive things + +and you make more +complicated things. + +And then we talked about +the means of abstraction, + +how you can take those +complicated things + +and name them so you can use +them as simple building blocks. + +And then last time you saw +we went even beyond that. + +We saw that by using +higher order procedures, + +you can actually express general +methods for computing things. + +Like the method +of doing something + +by fixed points, or +Newton's method, and so + +the incredible +expressive power you + +can get just by combining +these means of abstraction. + +And the crucial +idea in all of this + +is the one that we +build a layered system. + +So for instance, if we're +writing the square root + +procedure, somewhere the +square root procedure + +uses a procedure +called good-enough, + +and between those there is some +sort of abstraction boundary. + +It's almost as if we go out +and in writing square root, + +we go and make a +contract with George, + +and tell George that his +job is to write good-enough, + +and so long as +good-enough works, + +we don't care what it does. + +We don't care exactly +how it's implemented. + +There are levels of +detail here that are + +George's concern and not ours. + +So for instance, George might +use an absolute value procedure + +that's written by Harry, and +we don't much care about that + +or even know that, +maybe, Harry exists. + +So the crucial idea is that +when we're building things, + +we divorce the task +of building things + +from the task of +implementing the parts. + +And in a large +system, of course, + +we have abstraction barriers +like this at lots, and lots, + +and lots of levels. + +And that's the idea that we've +been using so far over and over + +in implementing procedures. + +Well, now what we're +going to do is look + +at the same issues for data. + +We're going to see that the +system has primitive data. + +In fact, we've +already seen that. + +We've talked about +numbers as primitive data. + +And then we're going to see +their means of combination + +for data. + +There's glue that allows you +to put primitive data together + +to make more complicated, +kind of compound data. + +And then we're going to see +a methodology for abstraction + +that's a very good thing to use +when you start building up data + +in terms of simpler data. + +And again, the key +idea is that you're + +going to build the +system in layers + +and set up abstraction +barriers that + +isolate the details +at the lower layers + +from the thing that's going +on at the upper layers. + +The details at the lower layers, +the ideas, they won't matter. + +They're going to +be George's concern + +because he signed this +contract with us for how + +the stuff that he +implements behaves, + +and how he implements +the thing is his problem. + +All right, well let's +look at an example. + +And the example I'm +going to talk about + +is a system that does +arithmetic on rational numbers. + +And what I have in mind is +that we should have something + +in the computer that +allows us to ask it, like, + +what's the sum of 1/2 and +1/4, and somehow the system + +should say, yeah, that's 3/4. + +Or we should be able to +say what's 3/4 times 2/3, + +and the system should be able +to say, yeah, that's 1/2. + +Right? + +And you know what +I have in mind. + +And you also know how to +do this from, I don't know, + +fifth grade or sixth grade. + +There are these +formulas that say + +if I have some fraction which is +a numerator over a denominator, + +and I want to add that to +some other fraction which + +is another numerator +over another denominator, + +then the answer is the +numerator of the first times + +the denominator of the +second, plus the numerator + +of the second times the +denominator of the first. + +That's the numerator +of the answer, + +and the denominator +is the product + +of the two denominators. + +Right? + +So there's something from +fifth or sixth grade fraction + +arithmetic. + +And then similarly, if I +want to multiply two things, + +n1 over d1 multiplied +by n2 over d2 + +is the product of the +numerators over the product + +of the denominators. + +So it's no problem at all, +but it's absolutely no problem + +to think about what +computation you + +want to make in adding and +multiplying these fractions. + +But as soon as we +go to implement it, + +we run up across something. + +We don't have what a +rational number is. + +So we said that the system +gives us individual numbers, + +so we can have 5 and +3, but somehow we + +don't have a way +of saying there's + +a thing that has both a 3 and +a 4 in it, or both a 2 and a 3. + +It's almost as if we'd like +to imagine that somehow there + +are these clouds, +and a cloud somehow + +has both a numerator +and a denominator in it, + +and that's what we'd +like to work in terms of. + +Well, how are we going +to solve that problem? + +We're going to +solve that problem + +by using this incredibly +powerful design + +strategy that you've already +seen us use over and over. + +And that's the strategy +of wishful thinking. + +Just like before when we didn't +have a procedure, we said, + +well, let's imagine that that +procedure already exists. + +We'll say, well, let's imagine +that we have these clouds. + +Now more precisely +what I mean is + +let's imagine that we +have three procedures, + +one called make-RAT. + +make-RAT is going to take +as arguments two numbers, + +so I'll call them +numerator and denominator, + +and it'll return for us a +cloud-- one of these clouds. + +I don't really know +what a cloud is. + +It's whatever make-RAT +returns, that's its business. + +And then we're going +to say, suppose + +we've got one of these clouds, +we have a procedure called + +numer, which takes in a cloud +that has an n and a d in it, + +whatever a cloud is, and I don't +know what it is, and returns + +for us the numerator part. + +And then we'll assume we +have a procedure denom, + +which again takes +in a cloud, whatever + +a cloud is, and returns for us +the denominator [? required. ?] + +This is just like +before, when if we're + +building a square +root, we assume + +that we have good enough. + +Right? + +And what we'll say is, +we'll go find George, + +and we'll say to George, +well, it's your business + +to make us these procedures. + +And how you choose to +implement these clouds, + +that's your problem. + +We don't want to know. + +Well, having pushed this +task off onto George, + +then it's pretty easy +to do the other part. + +Once we've got the +clouds, it's pretty easy + +to write the thing that does say +addition of rational numbers. + +You can just say define, +well, let's say +RAT. + +Define +RAT, which will take in +two rational numbers, x and y. + +x and y are each these clouds. + +And what does it do? + +Well, it's going to return +for us a rational number. + +What rational number is it? + +Well, we've got +the formulas there. + +The numerator of it is the sum +of the product of the numerator + +of x and the denominator of y. + +It's one thing in the sum. + +And the other thing +in the numerator + +is the product of the numerator +of y and the denominator of x. + +The star, close the plus. + +Right, that's the first +argument to make-RAT, + +which is the numerator of +the thing I'm constructing. + +And then the rest +of the thing goes + +into make-RAT is the +denominator of the answer, which + +is the product of +the denominator of x + +and the denominator of y. + +Like that. + +OK? + +So there is the analog of +doing rational number addition. + +And it's no problem +at all, assuming + +that we have these clouds. + +And of course, we can do +multiplication in the same way. + +Define how to get the product +of two rational numbers, + +call it *RAT. + +Takes in two of these +clouds, x and y, it returns + +a rational number, +make-RAT, whose numerator + +is the product of the +numerators-- numerator of x + +times the numerator of y. + +And the denominator of the +thing it's going to return + +is the product of +the denominators. + +Well, except that I haven't +told you what these clouds are, + +that's all there is to it. + +See, what did I do? + +I assumed by wishful +thinking that I + +had a new kind of data object. + +And in particular, +I assumed I had ways + +of creating these data objects. + +Make-RAT creates +one of these things. + +This is called a constructor. + +All right, I have a thing that +constructs such data objects. + +And then I assume I have things +that, having made these things, + +I have ways of +getting the parts out. + +Those are called selectors. + +And so formally, what +I said is I assumed + +I had procedures +that are constructors + +and selectors for +these data objects, + +and then I went +off and used them. + +That's no different +in kind from saying + +I assume I have a +procedure good-enough, + +and I go use it to +implement square root. + +OK, well before we +go on, let's ask + +the question of why do we want +to do this in the first place? + +See, why do we want a procedure +like +RAT that takes in two + +rational numbers and +returns a rational number? + +See, another way to think +about this is, well, + +here's this formula. + +And I've also got to +implement something + +that adds rational numbers. + +One other way to think about +is, well, there's this thing, + +and I type in four +numbers, an n1, and a d1, + +and an n2, and a d2. + +And it sets some +registers in the machine + +to this numerator +and this denominator. + +So I might say, +well, why don't I + +just add rational +numbers by I type in four + +numbers, numerators +and denominators, + +and get out two +numbers, which is + +a numerator and a denominator. + +Why are we worrying +about building things + +like this anyway? + +Well, the answer +is, suppose you want + +to think about expressing +something like this, + +suppose I'd like to +express the idea of taking + +two rational numbers, +x plus y, say, + +and multiplying that by the sum +of two other rational numbers. + +Well, the way I do it, having +things like +RAT and *RAT, + +is I'd say, oh yeah, what +that is is just the product. + +That's *RAT of the sum of x +and y and the sum of s and t. + +So except for syntax, +I get an expression + +that looks like the +way I want to think + +about it mathematically. + +I want to say there +are two numbers. + +There's a thing which +is the sum of them, + +and there's a thing which +is the sum of these two. + +That's this and this. + +And then I multiply them. + +So I get an expression that +matches this expression. + +If I did the other +thing, if I said, + +well, the way I want +to think about this + +is I type into my machine +four numbers, which + +are the numerators and the +denominators of x and y, + +and then four more numbers, +which are the numerators + +and denominators of s and t. + +And then what I'd be sitting +with is, well, what would I do? + +I'd add these, and +somehow I'd have + +to have two temporary variables, +which are the numerators + +and denominators of +this sum, and I'd + +go off and store them someplace. + +And then I'd go over here, +I'd type in four more numbers, + +I'd get two more +temporary variables, + +which are the numerators +and denominators of s and t. + +And then finally, I put those +together by multiplying them. + +You see, what's +starting to happen, + +there are all these +temporary variables, which + +are sort of the guts +of the internals + +of these rational numbers +that start hanging + +out all over the system. + +And of course, if I had more and +more complicated expressions, + +there'd be more and +more guts hanging out + +that confuse my programming. + +And those of you who +sort of programmed things + +like that, where you're just +adding numbers in assembly + +language, you sort +of see you have + +to suddenly be concerned with +these temporary variables. + +But more importantly than +confusing my programming, + +they're going to +confuse my mind. + +Because the whole +name of this game + +is that we'd like the +programming language to express + +the concepts that we +have in our heads, + +like rational numbers are things +that you can add and then take + +that result and multiply them. + +Let's break for questions. + +Yeah? + +AUDIENCE: I don't +quite see the need- + +when we had make-RAT with the +numerator and denominator, + +we had to have the numerator +and denominator to pass + +as parameters to +create the cloud, + +and then we extracted to +get back what we had to have + +originally. + +PROFESSOR: That's right. + +So the question +is, I sort of have + +the numerator and +the denominator, + +why am I worrying about +having the cloud given that I + +have to get the pieces out? + +That's sort of what I +tried to say at the end, + +but let me try and say it +again, because that's really + +the crucial question. + +The point is, I want to carry +this numerator and denominator + +around together all the time. + +And it's almost as +if I want to know, + +yeah, there's a numerator +and denominator in there, + +but also, I would like to say, +fine, but from another point + +of view, that's x. + +And I carry x around, and I +name it as x, and I hold it. + +And I can say things +like, the sum of x and y, + +rather than just have-- see, +it's not so bad when I only + +think about x, but if +I have a system with 10 + +rational numbers, suddenly +I have 20 numerators + +and denominators, which +are not necessarily-- + +if I don't link +them, then it's just + +20 arbitrary +numbers that are not + +linked in any particular way. + +It's a lot like saying, well, +I have these instructions + +that are the body +of the procedures, + +why do I want to package them +and say it's the procedure? + +It's exactly the same idea. + +No? + +OK. + +Let's break, let's just stretch +and get somebody-- [INAUDIBLE] + +[MUSIC PLAYING] + +OK, well, we've been working on +this rational number arithmetic + +system, and then what we +did, the important thing + +about what we did, is we +thought about the problem + +by breaking it into two pieces. + +We said, assume there is +this contract with George, + +and George has +figured out the way + +to how to construct +these clouds, + +provided us procedures +make-RAT, which + +was a constructor, +and selectors, which + +are numerator and denominator. + +And then in terms +of that, we went off + +and implemented addition +and multiplication + +of rational numbers. + +Well, now let's go look +at George's problem. + +How can we go and +package together + +a numerator and a +denominator and actually make + +one of these clouds? + +See, what we need is a kind of +glue, a glue for data objects + +that allows us to +put things together. + +And Lisp provides such +a glue, and that glue + +is called list structure. + +List structure is a +way of gluing things + +together, and more +precisely, Lisp + +provides a way of constructing +things called pairs. + +There's a primitive operator +in Lisp called cons. + +We can take a look at it. + +There's a thing called cons. + +Cons is an operator which +takes in two arguments called + +x and y, and it returns for +us a thing called a pair. + +All right, so a thing called +a pair that has a first part + +a second part. + +So cons takes two objects. + +There's a thing called a pair. + +The first part of the cons is x, +and the second part of the cons + +is y. + +And that's what it builds. + +And then we also assume we have +ways of getting things out. + +If you're given a pair, +there's a thing called car, + +and car of a pair, +p, gives you out + +the first part of the pair, p. + +And there's a thing called +cdr, and cdr of the pair, p, + +gives you the second +part of the pair, p. + +OK, so that's how +we construct things. + +There's also a conventional +way of drawing pictures + +of these things. + +Just like we write down that as +the conventional way of writing + +Plato's idea of two, +the way we could + +draw a diagram to represent cons +of two and three is like this. + +We draw a little box. + +And so here's the box +we're talking about, + +and this box has two +arrows coming out of it. + +And say the first part +of this pair is 2, + +and the second part +of this pair is 3. + +And this notation +has a name, it's + +called box and pointer notation. + +By the way, let me say right +now that a lot of people + +get confused that +there's some significance + +to the geometric way I drew +these pointers, the directions. + +Like some people think +it'd be different + +if I took this pointer +and turned it up here, + +and put the 3 out here. + +That has no significance. + +All right? + +It's merely you have +a bunch of arrows, + +these pointers, and the boxes. + +The only issue is how +they're connected, + +not the geometric +arrangement of whether I + +write the pointer +across, or up, or down. + +Now it's completely +un-obvious, probably, + +why that's called +list structure. + +We're not actually going +to talk about that today. + +We'll see that next time. + +So those are pairs, there's +cons that constructs them. + +And what I'm going to know +about cons, and car, and cdr, + +is precisely that if I have +any x and y, all right, + +if I have any things x and y, +and I use cons to construct + +a pair, then the +car of that pair + +is going to be x, +the thing I put in, + +and the cdr of that +pair is going to be y. + +That's the behavior of these +operators, cons, car, and cdr. + +Given them, it's +pretty clear how + +George can go off and +construct his rational numbers. + +After all, all he +has to do-- remember + +George's problem was to +implement make-RAT, numerator, + +and denom. + +So all George has +to do is say define + +make-RAT of some n and a d-- so +all I have to do is cons them. + +That's cons of n and d. + +And then if I want +to get the numerator + +out, I would say define +the numerator, numer, + +of some rational number, x. + +If the rational number's +implemented as a pair, + +then all I have to do +is get out the car of x. + +And then similarly, define the +denom is going to be the cdr, + +the other thing I +put into the pair. + +Well, now we're in business. + +That's a complete implementation +of rational numbers. + +Let's use it. + +Suppose I want to say, +so I want to think + +about how to add 1/2 plus 1/4 +and watch the system work. + +Well, the way I'd use that is +I'd say, well, maybe define a. + +I have to make a 1/2. + +Well, that's a rational +number with numerator 1 + +and denominator 2, so a +will be make-RAT of 1 and 2. + +And then I'll construct the 1/4. + +I'll say define d to +be make-RAT of 1 and 4. + +And if I'd like to look +at the answer-- well, + +assuming I don't have a special +thing that prints rational + +numbers, or I could make one-- +I could say, for instance, + +define the answer to be +RAT +of a and b, and now I can say, + +what's the answer? + +What are the numerators and +denominators of the answer? + +So if I'm adding +1/2 and 1/4, I'll + +say, what is the +numerator of the answer? + +And the system is going +to type out, well, 6. + +Bad news. + +And if I say what's the +denominator of the answer, + +the system's going +to type out 8. + +So instead of what +I would really like, + +which is for it to say +that 1/2 and 1/4 is 3/4, + +this foolish machine is +going to say, no, it's 6/8. + +Well, that's sort of bad news. + +Where's the bug? + +Why does it do that, after all? + +Well, it's the way +that we just had +RAT. + ++RAT just took the-- it said +you add the numerator times + +the denominator, you add +that to the numerator times + +the denominator, and put that +over the product of the two + +denominators, and +that's why you get 6/8. + +So what was wrong with our +implementation of +RAT? + +What's wrong with that rational +number arithmetic stuff + +that we did before the break? + +Well, the answer is +one way to look at it + +is absolutely nothing's wrong. + +That's perfectly +good implementation. + +It follows the sixth grade, +fifth grade mathematic + +for adding fractions. + +One thing we can say is, +well, that's George's problem. + +Like, boy, wasn't +George dumb to say + +that he can make a +rational number simply + +by sticking together the +numerator and the denominator? + +Wouldn't it be +better for George, + +when he made a rational +number, to reduce + +the stuff to lowest terms? + +And what I mean is, wouldn't +it be better for George, + +instead of using this +version of make-RAT, + +to use this one on the slide? + +Or instead of just saying cons +together n and d, what you do + +is compute the greatest +common divisor of n and d, + +and gcd is the procedure +which, well, for all we + +care is a primitive, which +computes the greatest + +common divisor of two numbers. + +So the way I can construct +a rational number is + +get the greatest common +divisor of the two numbers, + +and I'm going to +call that g, and then + +instead of consing +together n and d, + +I'll divide them through. + +I'll cons together +the quotient of n + +by the the gcd and the +quotient of d by the gcd. + +And that will reduce +the rational number + +to lowest terms. + +So when I do this addition, +when +RAT calls make-RAT-- + +and for the definition of +RAT +it had a make-RAT in there-- + +just by the fact that +it's constructing that, + +the thing will get reduced to +lowest terms automatically. + +OK, that is a complete system. + +For rational number arithmetic, +let's look at what we've done. + +All right, we said we want +to build rational number + +arithmetic, and we had +a thing called +RAT. + +We implemented that. + +And I showed you multiplying +rational numbers, + +and although I didn't +put them up there, + +presumably we'd like +to have something + +that subtracts rational +numbers, and I don't know, + +all sorts of things. + +Things that test equality in +division, and maybe things that + +print rational numbers +in some particular way. + +And we implemented +those in terms of pairs. + +These pairs, cons, car, and +cdr that are built into Lisp. + +But the important thing is +that between these and these, + +we set up an +abstraction barrier. + +We set up a layer +of abstraction. + +And what was that +layer of abstraction? + +That layer of abstraction +was precisely the constructor + +and the selectors. + +This layer was make-RAT, +and numer, and denom. + +This methodology, another +way to say what it's doing, + +is that we are separating +the way something is used, + +separating the use +of data objects, + +from the representation +of data objects. + +So up here, we have the way +that rational numbers are used, + +do arithmetic on them. + +Down here, we have the way +that they're represented, + +and they're separated +by this boundary. + +The boundary is the +constructors and selectors. + +And this methodology has a name. + +This is called data abstraction. + +Data abstraction is sort of +the programming methodology + +of setting up data objects +by postulating constructors + +and selectors to isolate +use from representation. + +Well, so why? + +I mean, after all, we didn't +have to do it this way. + +It's perfectly possible to +do rational number addition + +without having any compound data +objects, and here on the slide + +is one example. + +We certainly could +have defined +RAT, + +which takes in things +x and y, and we'll say, + +well what are these +rational numbers really? + +So really, they're just +pairs, and the numerator's + +the car and the denominator's +the cdr. So what we'll do + +is we'll take the car of x times +the cdr of y, multiply them. + +Take the car of y times the +cdr of x, multiply them. + +Add them. + +Take the cdr of x +and the cdr of y, + +multiply them, and then +constitute together. + +Well, that sort of +does the same thing. + +But this ignores the +problem of reducing things + +to lowest terms, but let's not +worry about that for a minute. + +But so what? + +Why don't we do it that way? + +Right? + +After all, there are sort of +fewer procedures to define, + +and it's a lot more +straightforward. + +It saves all this +self-righteous BS + +about talking about +data abstraction. + +We just sort of do it. + +I mean, who knows, maybe it's +even marginally more efficient + +depending on whatever +compiler were using for this. + +What's the point of +isolating the use + +from the representation? + +Well, it goes back to +this notion of naming. + +Remember, one of the +most important principles + +in programming is +the same as one + +of the most important principles +in sorcery, all right? + +That's if you have the +name of the spirit, + +you get control over it. + +And if you go back +and look at the slide, + +you see what's in there is +we have this thing +RAT, + +but nowhere in the system, +if I have a +RAT and a -RAT + +and a *RAT, and things +that look like that, + +nowhere in the system do I +have a thing that I can point + +at which is a rational number. + +I don't have, in a +system like that, + +the idea of rational number +as a conceptual entity. + +Well, what's the +advantage of that? + +What's the advantage +of isolating + +the idea of rational numbers +as a conceptual entity, + +and really naming it +with make-RAT, numerator, + +and denominator. + +Well, one advantage is +you might want to have + +alternative representations. + +See, before I showed you +that one way George can solve + +this things not reduced +to lowest terms problem, + +is when you build +a rational number, + +you divide up by the +greatest common denominator. + +Another way to do that +is shown over here. + +I can have an alternative +representation + +for rational numbers where when +you make a rational number, + +you just cons them. + +However, when you +go to select out + +the numerator, at that point +you compute the gcd of the stuff + +that's sitting in that pair, +and divide out by the gcd. + +And similarly, when I +get the denominator, + +at that point when I go +to get the denominator, + +I'll divide out by the gcd. + +So the difference would be in +the old representation, when + +ans was constructed +here, say what's 6 and 8, + +in the first way, +the 6 and 8 would + +have got reduced when they +got stuck into that pair, + +numerator would select out 3. + +And in the way I +just showed you, + +well, ans would +get 6 and 8 put in, + +and then at the point +where I said numerator, + +some computation would get +done to put out 3 instead of 6. + +So those are two different +ways I might do it. + +Which one's better? + +Well, it depends, right? + +If I'm making a system +where I am mostly + +constructing rational numbers +and hardly ever looking + +at them, then it's +probably better + +not to do that gcd computation +when I construct them. + +If I'm doing a system where +I look at things a lot more + +than I construct them, +then it's probably better + +to do the work when +I construct them. + +So there's a choice there. + +But the real issue +is that you might not + +be able to decide at the +moment you're worrying + +about these rational numbers. + +See, in general, as +systems designers, + +you're forced with the +necessity to make decisions + +about how you're +going to do things, + +and in general, the way you'd +like to retain flexibility + +is to never make up +your mind about anything + +until you're forced to do it. + +The problem is, there's +a very, very narrow line + +between deferring decisions +and outright procrastination. + +So you'd like to make progress, +but also at the same time, + +never be bound by the +consequences of your decisions. + +Data abstraction's +one way of doing this. + +What we did is we +used wishful thinking. + +See, we gave a name +to the decision. + +We said, make-RAT, +numerator, and denominator + +will stand for however +it's going to be done, + +and however it's going to +be done is George's problem. + +But really, what that was +doing is giving a name + +to the decision of how +we're going to do it, + +and then continuing as +if we made the decision. + +And then eventually, when +we really wanted it to work, + +coming back and facing +what we really had to do. + +And in fact, we'll see +a couple times from now + +that you may never +have to choose + +any particular +representation, ever, ever. + +Anyway, that's a very +powerful design technique. + +It's the key to the reason +people use data abstraction. + +And we're going to see +that idea again and again. + +Let's stop for questions. + +AUDIENCE: What does +this decision making + +through abstraction layers do to +the axiom of do all your design + +before any of your code? + +PROFESSOR: Well, +that's someone's axiom, + +and I bet that's the +axiom of someone who + +hasn't implemented very large +computer systems very much. + +I said that computer +science is a lot like magic, + +and it's sort of good +that it's like magic. + +There's a bad part +of computer science + +that's a lot like religion. + +And in general, I +think people who + +really believe that you design +everything before you implement + +it basically are people +who haven't designed + +very many things. + +The real power is +that you can pretend + +that you've made the +decision and then later + +on figure out which one is +right, which decision you ought + +to have made. + +And when you can do that, you +have the best of both worlds. + +AUDIENCE: Can you +explain the difference + +between let and define? + +PROFESSOR: Oh, OK. + +Let is a way to +establish local names. + +Let me give you sort +of the half answer. + +And I'll say, later on we +can talk about the whole very + +complicated thing. + +But the big difference +for now is that, see, + +when you're typing +at Lisp, you're + +typing in this environment +where you're making definitions. + +And when you say define a to be +5, if I say define a to be 5, + +then from then on the thing +will remember that a is 5. + +Let is a way to set up +a local context where + +there's a definition. + +So if I type something +like, saying let a-- no, + +I shouldn't say +a-- if I said let z + +be 10, and within that context, +tell me what the sum of z and z + +is. + +So if I typed in this expression +to Lisp, and then this + +would put out 20. + +However, then if +I said what's z, + +the computer would say +that's an unbound variable. + +So let is a way of +setting up a context where + +you can make definitions. + +But those definitions are +local to this context. + +And of course, if I'd said +a in here, I'd still get 20. + +But this a would not interfere +at all with this one. + +So if I type this, and then type +this, and then say what's a? + +a will still be 5. + +So there's some other +subtle differences + +between let and define, but +that's the most important one. + +All right, well, we've looked at +implementing this little system + +for doing arithmetic +on rational numbers + +as an example of this +methodology of data + +abstraction. + +And that's a way of controlling +complexity in large systems. + +But, see, like +procedure definition, + +and like all the +ways we're going + +to talk about for +controlling complexity, + +the real power of these things +show up not when you sort of do + +these things in themselves, +like it's not such a great thing + +that we've done rational +number arithmetic, + +it's that you can use +these as building blocks + +for making more +complicated things. + +So it's no wonderful idea that +you can just put two numbers + +together to form a pair. + +If that's all you +ever wanted to do, + +there are tons of ways +that you can do that. + +The real issue is can +you do that in such a way + +so that the things +that you build + +become building blocks for doing +something even more complex? + +So whenever someone +shows you a method + +for controlling complexity, you +should say, yeah, that's great, + +but what can I build with it? + +So for example, let me just run +through another thing that's + +a lot like the +rational number one. + +Suppose we would like to +represent points in the plane. + +You sort of say, +well, there's a point, + +and we're going to +call that point p. + +And that point might +have coordinates, + +like this might be +the point 1 comma 2. + +The x-coordinate might be 1, and +it's y-coordinate might be 2. + +And we'll make a little +system for manipulating points + +in the plane. + +And again, we can +do that-- here's + +a little example of that. + +It can represent vectors, the +same as points in the plane, + +and we'll say, yep, there's a +constructor called make-vector, + +make-vector's going to +take two coordinates, + +and here we can implement +them if we like as pairs, + +but the important thing is +that there's a constructor. + +And then given some vector, p, +we can find its x-coordinate, + +or we can get its y-coordinate. + +So there's a constructor +and selectors + +for points in the plane. + +Well, given points +in the plane, we + +might want to use them +to build something. + +So for instance, we +might want to talk + +about, we might have a +point, p, and a point, q, + +and p might be the point 1, 2, +and q might be the point 2, 3. + +And we might want to talk +about the line segment that + +starts at p and ends at q. + +And that might be the segment s. + +So we might want to +build points for vectors + +in terms of numbers, and +segments in terms of vectors. + +So we can represent +line segments + +in exactly the same way. + +All right, so the line +segment from p to q, + +we'll say there's a +constructor, make-segment. + +And make up names +for the selectors, + +the starting point +of the segment + +and the ending point +of the segment. + +And again, we can implement +a segment using cons + +as a pair of points, and car +and cdr get out the two points + +that we put together +to get the segment. + +Well, now having +done that, we can + +have some operations on them. + +Like we could say, what's the +midpoint of a line segment? + +So here's the midpoint +of a line segment, + +that's going to be the +points whose coordinates are + +the averages of the +coordinates of the endpoints. + +OK, there's the midpoint. + +So to get the midpoint +of a line segment, + +s, we'll just say grab the +starting point to the segment, + +grab the ending +point of the segment, + +and now make a vector-- make +a point whose coordinates are + +the average of the +x-coordinate of the first point + +and the x-coordinate +of the second point, + +and whose y-coordinate is the +average of the y-coordinates. + +So there's an +implementation of midpoint. + +And then similarly, +we can build something + +like the length of the segment. + +The length of the +segment is a thing + +whose-- use Pythagoras's rule, +the length of the segment + +is the square root of the d +x squared plus d y squared. + +We'll say to get the +length of a line segment, + +we'll let dx be the difference +of the x-coordinate of one + +endpoint and the x-coordinate +of the other endpoint, + +and we'll let dy +be the difference + +of the y-coordinates. + +And then we'll take +the square root + +of the sum of the squares of dx +and dy, that's what this says. + +All right, so there's an +implementation of length. + +And again, what we built +is a layered system. + +We built a system which +has, well, say up here + +there's segments. + +And then there's an +abstraction barrier. + +The abstraction barrier +separates the implementation + +of segments from the +implementation of vectors + +and points, and what that +abstraction barrier is + +are the constructors +and selectors. + +It's make-segment, and +segment-start, and segment-end. + +And then there are vectors. + +And vectors in turn are built +on top of pairs and numbers. + +So I'll say pairs and numbers. + +And that has its own +abstraction barrier, + +which is make-vector, and +x-coordinate, and y-coordinate. + +So we have, again, +a layered system. + +You're starting to see +that there are layers here. + +I ought to mention, there +is a very important thing + +that I kind of took for granted. + +And it's sort of so natural, +but on the other hand + +it's a very important thing. + +Notice that in order to +represent this segment + +s, I said this segment +is a pair of points. + +And a point is a +pair of numbers. + +And if I were going to +draw the box and pointers + +structure for that, I +would say, oh, the segment + +is, given those particular +representations that I showed + +you, I'd say this +segment s is a pair, + +and the first thing in +the pair is a vector, + +and the vector is +a pair of numbers. + +And that's this, that's p. + +And the other thing +in the segment + +is q, which is itself +a pair of numbers. + +So I almost took +it for granted when + +I said that cons allows +you to put things together. + +But it's very easy +to not appreciate + +that, because notice, some of +the things I can put together + +can themselves be pairs. + +And let me introduce a word that +I'll talk about more next time, + +it's one of my favorite +words, called closure. + +And by closure I mean that +the means of combination + +in your system are such that +when you put things together + +using them, like we make a pair, +you can then put those together + +with the same means +of combination. + +So I can have not only +a pair of numbers, + +but I can have a pair of pairs. + +So for instance, making arrays +in a language like Fortran + +is not a closed +means of combination, + +because I can make +an array of numbers, + +but I can't make +an array of arrays. + +And one of the things that you +should ask, one of your tests + +of quality for a +means of combination + +that someone shows +you, is gee, are + +the things you make closed +under that means of combination? + +So pairs would not be nearly so +interesting if all I could do + +was make a pair of numbers. + +I couldn't build very +much structure at all. + +OK, well, we'll +come back to that. + +I just wanted to mention it now. + +You'll hear a lot +about closure later on. + +You can also see the +potential for losing control + +of complexity as you have +a layered system if you + +don't use data abstraction. + +Let's go back and look +at this slide for length. + +Length works and is a simple +thing because I can say, + +when I want to get this +value, I can say, oh, + +that is the x-coordinate of the +first endpoint of the segment. + +And each of these things, +each of these selectors, + +x-coordinate and endpoint, +stand for a decision choice + +whose details I don't +have to look at. + +So I could perfectly +well, again, just + +like rational numbers +I did before, I + +could say, oh well, +gee, a segment really + +is a pair of pairs. + +And the x-coordinate of the +first endpoint or the segment + +really is the-- +well, what is it? + +It's the car of the +car of the segment. + +So I could perfectly well +go and redefine length. + +I could say, define the +length of some segment s. + +And I could start +off writing something + +like, well, we'll let dx be-- +well, what's it have to be? + +It's got to be the difference +of the two coordinates, + +so that's the difference +of, the first one is + +the car of the car +of s, subtracted + +from the first one, the car +of the other half of it, + +the cdr of s. + +All right, and then +dy would be-- well, + +let's see, I'd get +the y-coordinate, + +so it'd be the difference +of the cdr of the car of s, + +and the cdr of the cdr +of s, sort of go on. + +You can see that's +much harder to read + +than the program I had before. + +But worse than that, suppose +you'd gone and implemented + +length? + +And then the next day, +George comes to you and says, + +I'm sorry, I changed my mind. + +I want to write points with +the x-coordinate first. + +So you come back you +stare at this code + +and say, oh gee, what was that? + +That was the car, so I +have to change this to cdr, + +and this is cdr, and +this now has to be car. + +And this has to be car. + +And you sort of +do that, and then + +the next day George +comes back and says, + +sorry, the guys +designing the display + +would like lines to be painted +in the opposite direction, + +so I have to write the +endpoint first in the order. + +And then you come back and you +stare at this code, and say, + +gee, what was it talking about? + +Oh yeah, well I've got to +change this one to cdr, + +and this one becomes +car, this one comes car, + +and this becomes cdr. + +And you go up and do that, +and then the next day, George + +comes back and says, +I'm sorry, what I really + +meant is that the +segments always + +have to be painted from +left to right on the screen. + +And then you sort +of, it's clear, + +you just go and punch George +in the mouth at that point. + +But you see, as soon as +we have a 10 layer system, + +you see how that complexity +immediately builds up + +to the point where even +something like this + +gets out of control. + +So again, the way we've +gotten out of that + +is we've named that spirit. + +We built a system where +there is a thing, which + +is the representation +choice for how you're + +going to talk about vectors. + +And choices about +that representation + +are localized right there. + +They don't have +their guts spilling + +over into things like how +you compute the length + +and how you compute +the midpoint. + +And that's the real +power of this system. + +OK, we're explicit +about them, so + +that we have control over them. + +All right, questions? + +AUDIENCE: What happens +in the case where + +you don't want to be treating +objects in terms of pairs? + +For instance, in +three-dimensional space, + +you'd have three coordinates. + +Or even in the case where you +have n-dimensional space, what + +happens? + +PROFESSOR: Right, OK. + +Well, this is a preview +of what I'll say tomorrow. + +But the point is, once +you have two things, + +you have as many +things as you want. + +All right? + +Because if I want to +make three things, + +I could start making things +like a pair whose first thing is + +1, and whose second thing +is another pair that, + +say, has 2 and 3 in it. + +And so on, a hundred things. + +I can nest them out of pairs. + +I made a pretty arbitrary +decision about how to do it, + +and you can +immediately see there + +are lots of ways to do that. + +What we'll start +talking about next time + +are conventions for how +to do things like that. + +But notice that what this +really depends on is I + +can make pairs of pairs. + +If all I could do was make +pairs of numbers, I'd be stuck. + +OK. + +Let's break. + +[MUSIC PLAYING] + +All right, well, +we've just gone off + +and done a couple of simple +examples of data abstraction. + +Now I want to do something +more complicated. + +We're going to talk +about what it means. + +And this will be harder, +because it's always + +much harder in +computer programming + +to talk about what something +means than to go off and do it. + +But let's go back to +almost the very beginning. + +Let's go back to the +point where I said, + +we just assumed that there +were procedures, make-RAT, + +and numer, and denom. + +Let's go back to where we had +this, at the very beginning, + +constructors and +selectors, and went off + +and defined the rational +number arithmetic. + +And remember, I +said at that point + +we were sort of done, +except for George. + +Well, what is it that we'd +actually done at that point? + +What was it that was done? + +Well, what I want +to say is, what + +was done after we'd +implemented the operations + +and terms of these, was that we +had defined a rational number + +representation in +terms of abstract data. + +What do I mean by abstract data? + +Well, the idea is +that at that point, + +when we had our ++RAT and our *RAT, + +that any implementation of +make-RAT, and numerator, + +and denominator that +George supplied us with, + +could be the basis for a +rational number representation. + +Like, it wasn't our concern +where you divided through + +to get the greatest common +denominator, or any of that. + +So the idea is +that what we built + +is a rational arithmetic +system that would sit + +on top of any representation. + +What do I mean by +any representation? + +I mean, certainly it can't +be the case that all I mean + +is George can reach +in a bag and pull out + +three arbitrary procedures +and say, well, fine, + +now that's the implementation. + +That can't be what I mean. + +What I've got to +mean is that there's + +some way of saying whether +three procedures are + +going to be suitable as a +basis for rational number + +representation. + +If we think about +it, what suitable + +might mean is if I have to +assume something like this, + +I have to say that if +x is the result of say, + +doing make-RAT of n and d, +then the numerator of x divided + +by the denominator of +x is equal to n over d. + +See, what that is is +that's George's contract. + +What we mean by writing a +contract for rational numbers, + +if you think about it, +this is the right thing. + +And the two ones we +showed do the right thing. + +See, if I'm taking out +greatest common divisors, + +it doesn't matter whether +I take them out or not, + +or the place where I take +them, because the idea is I'm + +going to divide through. + +But see, this is +George's contract. + +So what we really +say to George is + +your business is to +go off and find us + +three procedures, +make-RAT, and numerator, + +and denominator, that +fulfill this contract + +for any choice of n and d. + +And that's what we +mean by we can use that + +as the basis for a rational +number representation. + +And other than that, it +fulfills this contract. + +We don't care how he does it. + +It's not our business. + +It's below the layer +of abstraction. + +In fact, if we want to say, what +is a rational number really? + +See, what's it +really, without having + +to talk about going below the +layer of abstraction, what + +we're forced into saying +is a rational number + +really is sort of this +axiom, is three procedures, + +make-RAT, numerator, +and denominator, + +that satisfy this axiom. + +In some sense, +abstractly, that's + +what a rational +number is really. + +That's sort of easy +words to listen to, + +because what you have +in your head, of course, + +is well, for all this +thing about saying + +that's what a rational +number is really, + +you actually just saw that +we built rational numbers. + +See, what we really did is +we built rational numbers + +on top of pairs. + +So for all I'm +saying abstractly, + +we can say a rational number +really is just this axiom. + +You can listen to +that comfortably, + +because you're +saying, well, yeah, + +but really it's actually pairs, +and I'm just annoying you + +by trying to be abstract. + +Well, let me, as an +antidote for that, + +let me do something that I think +is really going to terrify you. + +I mean, it's really +going to bring + +you face to face with the +sort of existential reality + +of this abstraction that +we're talking about. + +And what I'm going to talk +about is, what are pairs really? + +See, what did I tell +you about pairs? + +I tricked you, right? + +I said that Lisp has +this primitive called + +cons that builds pairs. + +But what did I really +tell you about? + +If you go back and said, +let's look on this slide, + +all I really told +you about pairs + +is that there happens to be +this property, these properties + +of cons, car, and +cdr. And all I really + +said about pairs is that +there's a thing called cons, + +and a thing called car, +and a thing called cdr. + +And it is the case that +if I build cons of x, y + +and take car of it, I get x. + +And if I build cons of x, y +and get cdr of it, I get y. + +And even though I lulled you +into thinking that there's + +something in Lisp that does +that, so you pretended you knew + +what it was, in fact, I +didn't tell you any more + +about pairs than this tells +you about rational numbers. + +It's just some axiom for pairs. + +Well, to drive that +home, let me really + +scare you, and show you what we +might build pairs in terms of. + +And what you're going +to see is that we + +can build rational +numbers, and line segments, + +and vectors, and all of this +stuff in terms of pairs, + +and we're going to see +below here that pairs can + +be built out of nothing at all. + +Pure abstraction. + +So let me show you on this +slide an implementation + +of cons, car, and cdr. And we'll +look at it again in a second, + +but notice that their procedure +definitions of cons, car, + +and cdr, you don't see any +data in there, what you see + +is a lambda. + +So cons here is +going to return-- + +is a procedure that +returns a procedure, just + +like AVERAGE DAMP. + +Cons of a and b returns a +procedure of an argument + +called pick, and it says, +if pick is equal to 1, + +I'm going to return a, +and if pick is equal to 2, + +I'm going to return +b, and that's + +what cons is going to be. + +Car of a thing x, +car of a pair x, + +is going to be x applied to 1. + +And notice that makes sense. + +You might not understand why +or how I'm doing such a thing, + +but at least it makes sense, +because the thing constructed + +by cons is a procedure, +and car applies that to 1. + +And similarly, cdr +applies that thing to 2. + +OK, now I claimed that this is +a representation of cons, car, + +and cdr, and notice +there's no data in it. + +All right, it's +built out of air. + +It's just procedures. + +There's no data objects at +all in that representation. + +Well, what could +that possibly mean? + +Well, if you really +believe this stuff, + +then you have to +believe that in order + +to show that that's a +representation for cons, car, + +and cdr, all I +have to do is show + +that it satisfies the axiom. + +See, all I should have +to convince you of + +is, for example, that gee, +that car of cons of 37 and 49 + +is 37 for arbitrary +values of 37 and 49. + +And cdr the same way. + +See, if I really can +demonstrate to you + +that that weird procedure +definition, in terms + +of [? air ?], has the property +that it satisfies this, + +then you just have +to grant me that that + +is a possible implementation of +cons, car, and cdr, on which I + +can build everything else. + +Well, let's look at that. + +And this will be practice +in the substitution model. + +How could we check this? + +We sort of know how to do that. + +It's just the same +substitution model. + +Let's look. + +We start out, and we say, +what's car of cons of 37 and 49? + +What do we do? + +Cons is some procedure. + +Its value is cons was +a procedure of a and b. + +The thing returned by +cons is its procedure body + +with 37 and 49 substituted +for the parameters. + +It'll be 37 substituted for +a and 49 substituted for b. + +So this expression has the same +meaning as this expression. + +Its car of, and the body +of cons was this thing + +that started with lambda. + +And it says, so if +pick is equal to 1, + +where pick is this +other argument, + +if pick is equal to 1, it's +37, that's where a was, + +and if pick is +equal to 2, it's 49. + +So that's the first step. + +I'm just going through +mechanical substitution. + +And remember, at this +point in the course, + +if you're confused +about what things mean, + +go mechanically through +the substitution model. + +Well, what is this reduced to? + +Car said, take your argument, +which in this case is this, + +and apply it to 1. + +That was the definition of car. + +So if I look at car, if +I do that, the answer is, + +well, it's that argument, +this was the argument to car, + +applied to 1. + +Well, what does that mean? + +I take 1, and I +substitute it in the body + +here for this value +of pick, which + +is the name of the +argument, what do I get? + +Well, I get the thing that +says if 1 equals 1 it's 37, + +and if 1 equals 2 it's +49, so the answer's 37. + +And similarly, if I'd taken +cdr, that would apply it to 2, + +and I'd get 49. + +So you see, what +I've demonstrated + +is that that completely weird +implementation of cons, car, + +and cdr, satisfies the axioms. + +So it's a perfectly +valid way of building, + +in fact, all of the data objects +we're going to see in Lisp. + +So they all, if you +like, can be built + +on sort of existential nothing. + +And as far as you know, +that's how it works. + +You couldn't tell. + +If all you're ever +going to do with pairs + +is construct them with cons and +look at them with car and cdr, + +you couldn't possibly +tell how this thing works. + +Now, it might give you a sort +of warm feeling inside if I say, + +well, yeah, in fact, for +various reasons there happens + +to be a primitive called +cons, car, and cdr, + +and if it's too scary, if this +kind of stuff is too scary, + +you don't have to +look inside of it. + +So that might make +you feel better, + +but the point is, it +really could work this way, + +and it wouldn't +make any difference + +to the system at all. + +So in some sense, we +don't need data at all + +to build these +data abstractions. + +We can do everything +in terms of procedures. + +OK, well, why did I +terrify you in this way? + +First, I really +want to reinforce + +this idea of abstraction, +that you really + +can do these things abstractly. + +Secondly, I want to +introduce an idea + +we're going to see more and +more of in this course, which + +is we're going to blur the +line between what's data + +and what's a procedure. + +See, in this funny +implementation + +it turned out that +cons of something + +happened to be represented +in terms of a procedure, + +even though we +think of it as data. + +While here that's sort +of a mathematical trick, + +but one of the +things we'll see is + +that a lot of the very +important programming + +techniques that we're +going to get to sort of + +depend very +crucially on blurring + +this traditional line between +what you consider a procedure + +and what you consider data. + +We're going to see more and more +of that, especially next time. + +OK, questions? + +AUDIENCE: If you +asked the system + +to print a, what would happen? + +PROFESSOR: The question +is, what would happen if I + +asked the system to print a. + +Given this representation, +you already know the answer. + +The answer is compound procedure +a, just like last time. + +It'd say compound procedure. + +It might say a little bit more. + +It might say compound procedure +lambda or something or other, + +depending on details +of how I named it. + +But it's a procedure. + +And the only reason +for that is I + +haven't told the +system anything special + +about how to print such things. + +Now, it's in fact true that +with the actual implementation + +of cons that to be +built in the system, + +it would print something else. + +It would print, +say, this is a pair. + +AUDIENCE: When you +define cons, and then you + +pass it into values, +how does it know + +where to look for the cons, +because you can use cons + +over and over again? + +How does it know where to +look to know which a and b + +it's supposed to pull back out? + +I don't know if I'm +expressing that quite right. + +Where is it stored? + +PROFESSOR: OK, the +question is, I sort of have + +a cons with a 37 and a 49, +and I might make another cons + +with a 1 and a 2, and I +might have one called a, + +and I might have one called b. + +And the question is, +how does it know? + +And why don't they get confused? + +And that's a very good question. + +See, you have to really +believe that the procedures are + +objects. + +It's sort of like saying-- let's +try another simpler example. + +Suppose I ask for +the square root of 3. + +So I asked for the +square root of 5, + +and then I ask for +the square of 20. + +You're probably +not the least bit + +bothered that I can take +square root and apply it to 5, + +and then I can take square +root and apply it to 20. + +And there's sort +of no issue, gee, + +doesn't it get confused +about whether it's + +working on 5 or 20? + +There's no issue about +that because you're + +thinking of a procedure which +goes off and does something. + +Now, in some sense you're +asking me the same question. + +But it's really bothering +you, and it's bothering you + +for a really good reason. + +Because when I write that, +you're saying gee, this is, + +I know, sort of a procedure. + +But it's not a procedure +that's just running. + +It's just sort of a +procedure sitting there. + +And how can it be that sometimes +this procedure has 37 and 49, + +and there might be another one +which has 5 and 6 in there, + +and why don't they get confused? + +So there's something very, very +important that's bothering you. + +And it's really crucial +to what's going on. + +We're suddenly saying that +procedures are not just the act + +of doing something. + +Procedures are conceptual +entities, objects, + +and if I built +cons of 37 and 49, + +that's a particular +procedure that sits there. + +And it's different +from cons of 3 and 4. + +That's another procedure +that sits there. + +AUDIENCE: Both of them +exist independently. + +PROFESSOR: And +exists independently. + +AUDIENCE: And they both can +be referenced by car and cdr. + +PROFESSOR: And they both would +be referenced by car and cdr. + +Just like I could +increment this, + +and I could increment that. + +They're objects. + +And that's sort of +where we're going. + +See, the fact that you're +asking the question + +shows that you're +really starting + +to think about the implications +of what's going on. + +It's the difference between +saying a procedure is just + +the act of doing something. + +And a procedure is a real +object that has existence. + +AUDIENCE: So when the +procedure gets built, + +the actual values are now +substituted for a and b-- + +PROFESSOR: That's right. + +AUDIENCE: And then that +procedure exists as lambda, + +and pick is what's +actually passed in. + +PROFESSOR: Yes, when cons gets +called, and the result of cons + +is a new procedure +that's constructed, + +that new procedure has an +argument that's called pick. + +AUDIENCE: But it no +longer has an a and b. + +The a and b are the actual +values that are passed through. + +PROFESSOR: And it has-- right, +according to the substitution + +model, what it now has is not +those arbitrary names a and b, + +it somehow has that +37 and 49 in there. + +But you're right, that's a +hard thing to think about it, + +and it's different +from the way you've + +been thinking about procedures. + +AUDIENCE: And if I have +again cons of 37 and 49, + +it's a different object? + +PROFESSOR: And if you make +another cons of 37 and 49, + +you're into a wonderful +philosophical problem, which + +is going to be what the +lecture about halfway + +through this course is about. + +Which is, if I cons 37 +and 49, and I do it again, + +is that the same thing, or +is it a different thing? + +And how could you tell? + +And when could it +possibly matter? + +And that's sort of like saying, +is that the same thing as this? + +Or is this the +same thing as that? + +It's the same kind of question. + +And that's a very, +very deep question. + +And I can't answer +in less than an hour. + +But we will. \ No newline at end of file diff --git a/EWFGkZ64ng4.txt b/EWFGkZ64ng4.txt new file mode 100644 index 0000000000000000000000000000000000000000..8e69a3e31eb52021a3900c5b2153c2d29f260b94 --- /dev/null +++ b/EWFGkZ64ng4.txt @@ -0,0 +1,10395 @@ +align:start position:0% + +hi everyone welcome back to the MIT + + align:start position:0% +hi everyone welcome back to the MIT + + + align:start position:0% +hi everyone welcome back to the MIT +lecture series on Urban Energy Systems + + align:start position:0% +lecture series on Urban Energy Systems + + + align:start position:0% +lecture series on Urban Energy Systems +and policy today we're going to be + + align:start position:0% +and policy today we're going to be + + + align:start position:0% +and policy today we're going to be +talking about cities and personal + + align:start position:0% +talking about cities and personal + + + align:start position:0% +talking about cities and personal +Transportation the first of a number of + + align:start position:0% +Transportation the first of a number of + + + align:start position:0% +Transportation the first of a number of +lectures on transportation and energy + + align:start position:0% +lectures on transportation and energy + + + align:start position:0% +lectures on transportation and energy +systems in cities again if you've been + + align:start position:0% +systems in cities again if you've been + + + align:start position:0% +systems in cities again if you've been +watching these lectures my name is David + + align:start position:0% +watching these lectures my name is David + + + align:start position:0% +watching these lectures my name is David +Sue I'm associate professor of urban + + align:start position:0% +Sue I'm associate professor of urban + + + align:start position:0% +Sue I'm associate professor of urban +studies and planning at MIT today we're + + align:start position:0% +studies and planning at MIT today we're + + + align:start position:0% +studies and planning at MIT today we're +going to talk about energy and personal + + align:start position:0% +going to talk about energy and personal + + + align:start position:0% +going to talk about energy and personal +transport again the materials assigned + + align:start position:0% +transport again the materials assigned + + + align:start position:0% +transport again the materials assigned +for the lecture today a lot of them are + + align:start position:0% +for the lecture today a lot of them are + + + align:start position:0% +for the lecture today a lot of them are +available online if you search + + align:start position:0% +available online if you search + + + align:start position:0% +available online if you search +around and the main questions I want to + + align:start position:0% +around and the main questions I want to + + + align:start position:0% +around and the main questions I want to +talk about today are why is personal + + align:start position:0% +talk about today are why is personal + + + align:start position:0% +talk about today are why is personal +Mobility important in terms of energy + + align:start position:0% +Mobility important in terms of energy + + + align:start position:0% +Mobility important in terms of energy +we're going to talk about why or whether + + align:start position:0% +we're going to talk about why or whether + + + align:start position:0% +we're going to talk about why or whether +or not electric vehicles are more + + align:start position:0% +or not electric vehicles are more + + + align:start position:0% +or not electric vehicles are more +efficient than internal combustion + + align:start position:0% +efficient than internal combustion + + + align:start position:0% +efficient than internal combustion +engine cars we're going to ask by how + + align:start position:0% +engine cars we're going to ask by how + + + align:start position:0% +engine cars we're going to ask by how +much and is this the same in all places + + align:start position:0% +much and is this the same in all places + + + align:start position:0% +much and is this the same in all places +we're going to talk about other kinds of + + align:start position:0% +we're going to talk about other kinds of + + + align:start position:0% +we're going to talk about other kinds of +vehicles such as bicycles electric + + align:start position:0% +vehicles such as bicycles electric + + + align:start position:0% +vehicles such as bicycles electric +bicycles and + + align:start position:0% +bicycles and + + + align:start position:0% +bicycles and +scooters and one little chapter of our + + align:start position:0% +scooters and one little chapter of our + + + align:start position:0% +scooters and one little chapter of our +talk today will be on what policies can + + align:start position:0% +talk today will be on what policies can + + + align:start position:0% +talk today will be on what policies can +be used to move the international + + align:start position:0% +be used to move the international + + + align:start position:0% +be used to move the international +vehicle market and to sway International + + align:start position:0% +vehicle market and to sway International + + + align:start position:0% +vehicle market and to sway International +automakers one answer is what Mary + + align:start position:0% +automakers one answer is what Mary + + + align:start position:0% +automakers one answer is what Mary +Nichols and the California air resources + + align:start position:0% +Nichols and the California air resources + + + align:start position:0% +Nichols and the California air resources +board have done in California I we'll + + align:start position:0% +board have done in California I we'll + + + align:start position:0% +board have done in California I we'll +talk a little bit about what the + + align:start position:0% +talk a little bit about what the + + + align:start position:0% +talk a little bit about what the +inflation reduction act does to + + align:start position:0% +inflation reduction act does to + + + align:start position:0% +inflation reduction act does to +encourage electric vehicles and how its + + align:start position:0% +encourage electric vehicles and how its + + + align:start position:0% +encourage electric vehicles and how its +policy incentives work and next week + + align:start position:0% +policy incentives work and next week + + + align:start position:0% +policy incentives work and next week +we'll start talking about what about + + align:start position:0% +we'll start talking about what about + + + align:start position:0% +we'll start talking about what about +larger infrastructure how do roads + + align:start position:0% +larger infrastructure how do roads + + + align:start position:0% +larger infrastructure how do roads +fueling infrastructure such as oil and + + align:start position:0% +fueling infrastructure such as oil and + + + align:start position:0% +fueling infrastructure such as oil and +electric grid uh play into the energy + + align:start position:0% +electric grid uh play into the energy + + + align:start position:0% +electric grid uh play into the energy +use of + + align:start position:0% +use of + + + align:start position:0% +use of +transportation and so we'll just start + + align:start position:0% +transportation and so we'll just start + + + align:start position:0% +transportation and so we'll just start +by talking about why Mobility is so + + align:start position:0% +by talking about why Mobility is so + + + align:start position:0% +by talking about why Mobility is so +important Mobility is essentially a + + align:start position:0% +important Mobility is essentially a + + + align:start position:0% +important Mobility is essentially a +superpower Mobility gives us the ability + + align:start position:0% +superpower Mobility gives us the ability + + + align:start position:0% +superpower Mobility gives us the ability +to access jobs Housing Services and + + align:start position:0% +to access jobs Housing Services and + + + align:start position:0% +to access jobs Housing Services and +Leisure the more Mobility we have the + + align:start position:0% +Leisure the more Mobility we have the + + + align:start position:0% +Leisure the more Mobility we have the +more ability we have to disaggregate all + + align:start position:0% +more ability we have to disaggregate all + + + align:start position:0% +more ability we have to disaggregate all +of these things we want to access if you + + align:start position:0% +of these things we want to access if you + + + align:start position:0% +of these things we want to access if you +live in a dense compact neighborhood + + align:start position:0% +live in a dense compact neighborhood + + + align:start position:0% +live in a dense compact neighborhood +your job housing and services could be + + align:start position:0% +your job housing and services could be + + + align:start position:0% +your job housing and services could be +the same place but you may want to + + align:start position:0% +the same place but you may want to + + + align:start position:0% +the same place but you may want to +travel around the city hopefully by + + align:start position:0% +travel around the city hopefully by + + + align:start position:0% +travel around the city hopefully by +easily accessible modes of + + align:start position:0% +easily accessible modes of + + + align:start position:0% +easily accessible modes of +transportation or if you live in a place + + align:start position:0% +transportation or if you live in a place + + + align:start position:0% +transportation or if you live in a place +that has very low population density + + align:start position:0% +that has very low population density + + + align:start position:0% +that has very low population density +your job your housing your services your + + align:start position:0% +your job your housing your services your + + + align:start position:0% +your job your housing your services your +leisure opportunities may be farflung + + align:start position:0% +leisure opportunities may be farflung + + + align:start position:0% +leisure opportunities may be farflung +like in many US cities + + align:start position:0% +like in many US cities + + + align:start position:0% +like in many US cities +but it's also particularly important to + + align:start position:0% +but it's also particularly important to + + + align:start position:0% +but it's also particularly important to +note that enabling mobility in cities is + + align:start position:0% +note that enabling mobility in cities is + + + align:start position:0% +note that enabling mobility in cities is +particularly hard due to population + + align:start position:0% +particularly hard due to population + + + align:start position:0% +particularly hard due to population +density if you want to build good + + align:start position:0% +density if you want to build good + + + align:start position:0% +density if you want to build good +infrastructure to enable Mobility you + + align:start position:0% +infrastructure to enable Mobility you + + + align:start position:0% +infrastructure to enable Mobility you +have to plan that if you are trying to + + align:start position:0% +have to plan that if you are trying to + + + align:start position:0% +have to plan that if you are trying to +retrofit cities with new infrastructure + + align:start position:0% +retrofit cities with new infrastructure + + + align:start position:0% +retrofit cities with new infrastructure +that enable Mobility without inducing + + align:start position:0% +that enable Mobility without inducing + + + align:start position:0% +that enable Mobility without inducing +let's say more traffic or more + + align:start position:0% +let's say more traffic or more + + + align:start position:0% +let's say more traffic or more +congestion you also have to think very + + align:start position:0% +congestion you also have to think very + + + align:start position:0% +congestion you also have to think very +hard about how to retrofit cities that + + align:start position:0% +hard about how to retrofit cities that + + + align:start position:0% +hard about how to retrofit cities that +already have a certain level of + + align:start position:0% +already have a certain level of + + + align:start position:0% +already have a certain level of +population + + align:start position:0% +population + + + align:start position:0% +population +and so there's a nice way to think about + + align:start position:0% +and so there's a nice way to think about + + + align:start position:0% +and so there's a nice way to think about +the carbon emissions from personal + + align:start position:0% +the carbon emissions from personal + + + align:start position:0% +the carbon emissions from personal +Transportation are Daniel Sperling at UC + + align:start position:0% +Transportation are Daniel Sperling at UC + + + align:start position:0% +Transportation are Daniel Sperling at UC +Davis also a member of the California + + align:start position:0% +Davis also a member of the California + + + align:start position:0% +Davis also a member of the California +air resources board has a nice little + + align:start position:0% +air resources board has a nice little + + + align:start position:0% +air resources board has a nice little +Identity or nice way to think about this + + align:start position:0% +Identity or nice way to think about this + + + align:start position:0% +Identity or nice way to think about this +it's an identity that goes like this you + + align:start position:0% +it's an identity that goes like this you + + + align:start position:0% +it's an identity that goes like this you +measure mobility in terms of vehicle + + align:start position:0% +measure mobility in terms of vehicle + + + align:start position:0% +measure mobility in terms of vehicle +miles travel that's essentially an + + align:start position:0% +miles travel that's essentially an + + + align:start position:0% +miles travel that's essentially an +indication of demand you multiply times + + align:start position:0% +indication of demand you multiply times + + + align:start position:0% +indication of demand you multiply times +vehicle Energy Efficiency which is + + align:start position:0% +vehicle Energy Efficiency which is + + + align:start position:0% +vehicle Energy Efficiency which is +measur in terms of energy use per + + align:start position:0% +measur in terms of energy use per + + + align:start position:0% +measur in terms of energy use per +vehicle mile that's a measure of how the + + align:start position:0% +vehicle mile that's a measure of how the + + + align:start position:0% +vehicle mile that's a measure of how the +technology is and you multiply times the + + align:start position:0% +technology is and you multiply times the + + + align:start position:0% +technology is and you multiply times the +carbon intensity of the energy going in + + align:start position:0% +carbon intensity of the energy going in + + + align:start position:0% +carbon intensity of the energy going in +measuring essentially the carbon + + align:start position:0% +measuring essentially the carbon + + + align:start position:0% +measuring essentially the carbon +intensity of the fuel going in which is + + align:start position:0% +intensity of the fuel going in which is + + + align:start position:0% +intensity of the fuel going in which is +measured in terms of greenhouse gases + + align:start position:0% +measured in terms of greenhouse gases + + + align:start position:0% +measured in terms of greenhouse gases +per unit of energy if you multiply all + + align:start position:0% +per unit of energy if you multiply all + + + align:start position:0% +per unit of energy if you multiply all +these three things together you get + + align:start position:0% +these three things together you get + + + align:start position:0% +these three things together you get +greenhouse gas emissions but this is a + + align:start position:0% +greenhouse gas emissions but this is a + + + align:start position:0% +greenhouse gas emissions but this is a +way of decomposing greenhouse gas + + align:start position:0% +way of decomposing greenhouse gas + + + align:start position:0% +way of decomposing greenhouse gas +emissions to say that it matters how + + align:start position:0% +emissions to say that it matters how + + + align:start position:0% +emissions to say that it matters how +much we demand in the first place in + + align:start position:0% +much we demand in the first place in + + + align:start position:0% +much we demand in the first place in +terms of Mobility it matters how + + align:start position:0% +terms of Mobility it matters how + + + align:start position:0% +terms of Mobility it matters how +efficient our technology is in terms of + + align:start position:0% +efficient our technology is in terms of + + + align:start position:0% +efficient our technology is in terms of +turning energy into + + align:start position:0% +turning energy into + + + align:start position:0% +turning energy into +transportation and then it matters how + + align:start position:0% +transportation and then it matters how + + + align:start position:0% +transportation and then it matters how +much what the fuel intensity of our + + align:start position:0% +much what the fuel intensity of our + + + align:start position:0% +much what the fuel intensity of our +energy going in is in other words how + + align:start position:0% +energy going in is in other words how + + + align:start position:0% +energy going in is in other words how +much emissions do we incur to create the + + align:start position:0% +much emissions do we incur to create the + + + align:start position:0% +much emissions do we incur to create the +fuels for the technology to satisfy our + + align:start position:0% +fuels for the technology to satisfy our + + + align:start position:0% +fuels for the technology to satisfy our +demand and so another way to answer what + + align:start position:0% +demand and so another way to answer what + + + align:start position:0% +demand and so another way to answer what +the importance of energy is or why + + align:start position:0% +the importance of energy is or why + + + align:start position:0% +the importance of energy is or why +energy and transportation are linked is + + align:start position:0% +energy and transportation are linked is + + + align:start position:0% +energy and transportation are linked is +to go back to our helpful sanki diagram + + align:start position:0% +to go back to our helpful sanki diagram + + + align:start position:0% +to go back to our helpful sanki diagram +I think I showed you this in a few + + align:start position:0% +I think I showed you this in a few + + + align:start position:0% +I think I showed you this in a few +lectures past this is the estimated us + + align:start position:0% +lectures past this is the estimated us + + + align:start position:0% +lectures past this is the estimated us +energy consumption in + + align:start position:0% +energy consumption in + + + align:start position:0% +energy consumption in +2021 roughly + + align:start position:0% +2021 roughly + + + align:start position:0% +2021 roughly +97 quads which are quadrillion BTUs it's + + align:start position:0% +97 quads which are quadrillion BTUs it's + + + align:start position:0% +97 quads which are quadrillion BTUs it's +a helpful number because the US economy + + align:start position:0% +a helpful number because the US economy + + + align:start position:0% +a helpful number because the US economy +has roughly been at around 100 quads so + + align:start position:0% +has roughly been at around 100 quads so + + + align:start position:0% +has roughly been at around 100 quads so +when you look at the source energy use + + align:start position:0% +when you look at the source energy use + + + align:start position:0% +when you look at the source energy use +on the + + align:start position:0% +on the + + + align:start position:0% +on the +left over here you can think of most of + + align:start position:0% +left over here you can think of most of + + + align:start position:0% +left over here you can think of most of +these numbers as roughly within about 3% + + align:start position:0% +these numbers as roughly within about 3% + + + align:start position:0% +these numbers as roughly within about 3% +of the percentage of the total source + + align:start position:0% +of the percentage of the total source + + + align:start position:0% +of the percentage of the total source +energy or primary energy for the US + + align:start position:0% +energy or primary energy for the US + + + align:start position:0% +energy or primary energy for the US +economy when you look at these final + + align:start position:0% +economy when you look at these final + + + align:start position:0% +economy when you look at these final +sectors of use you can get a sense of + + align:start position:0% +sectors of use you can get a sense of + + + align:start position:0% +sectors of use you can get a sense of +how much uh energy is converted from the + + align:start position:0% +how much uh energy is converted from the + + + align:start position:0% +how much uh energy is converted from the +primary sources into final consumption + + align:start position:0% +primary sources into final consumption + + + align:start position:0% +primary sources into final consumption +and of course we have intermediate steps + + align:start position:0% +and of course we have intermediate steps + + + align:start position:0% +and of course we have intermediate steps +like generating electricity for lighting + + align:start position:0% +like generating electricity for lighting + + + align:start position:0% +like generating electricity for lighting +at the same time we also have this kind + + align:start position:0% +at the same time we also have this kind + + + align:start position:0% +at the same time we also have this kind +of gray bar which breaks down the total + + align:start position:0% +of gray bar which breaks down the total + + + align:start position:0% +of gray bar which breaks down the total +amount of energy that's rejected through + + align:start position:0% +amount of energy that's rejected through + + + align:start position:0% +amount of energy that's rejected through +heat loss versus how much is actually + + align:start position:0% +heat loss versus how much is actually + + + align:start position:0% +heat loss versus how much is actually +converted into the services we want so + + align:start position:0% +converted into the services we want so + + + align:start position:0% +converted into the services we want so +Energy Services are the services or + + align:start position:0% +Energy Services are the services or + + + align:start position:0% +Energy Services are the services or +final consumption we want or order to do + + align:start position:0% +final consumption we want or order to do + + + align:start position:0% +final consumption we want or order to do +that we actually have some rejected + + align:start position:0% +that we actually have some rejected + + + align:start position:0% +that we actually have some rejected +energy mostly energy that's lost as heat + + align:start position:0% +energy mostly energy that's lost as heat + + + align:start position:0% +energy mostly energy that's lost as heat +as we combust fossil fuels and so just + + align:start position:0% +as we combust fossil fuels and so just + + + align:start position:0% +as we combust fossil fuels and so just +to understand again to break down the + + align:start position:0% +to understand again to break down the + + + align:start position:0% +to understand again to break down the +numbers on the sanky diagram and + + align:start position:0% +numbers on the sanky diagram and + + + align:start position:0% +numbers on the sanky diagram and +understand why energy is so important + + align:start position:0% +understand why energy is so important + + + align:start position:0% +understand why energy is so important +for transportation you can see that the + + align:start position:0% +for transportation you can see that the + + + align:start position:0% +for transportation you can see that the +vast majority of petroleum here goes + + align:start position:0% +vast majority of petroleum here goes + + + align:start position:0% +vast majority of petroleum here goes +towards about maybe twoth thirds of it + + align:start position:0% +towards about maybe twoth thirds of it + + + align:start position:0% +towards about maybe twoth thirds of it +or 34s of it goes to Transportation 1/4 + + align:start position:0% +or 34s of it goes to Transportation 1/4 + + + align:start position:0% +or 34s of it goes to Transportation 1/4 +of it goes to Industrial uses and then + + align:start position:0% +of it goes to Industrial uses and then + + + align:start position:0% +of it goes to Industrial uses and then +you can see that of the energy that went + + align:start position:0% +you can see that of the energy that went + + + align:start position:0% +you can see that of the energy that went +to Transportation a lot of it gets + + align:start position:0% +to Transportation a lot of it gets + + + align:start position:0% +to Transportation a lot of it gets +rejected as heat basically out of the + + align:start position:0% +rejected as heat basically out of the + + + align:start position:0% +rejected as heat basically out of the +tailpipe of the car or out of the Smoke + + align:start position:0% +tailpipe of the car or out of the Smoke + + + align:start position:0% +tailpipe of the car or out of the Smoke +Stack of a power plant if we're + + align:start position:0% +Stack of a power plant if we're + + + align:start position:0% +Stack of a power plant if we're +generating electricity and so actually a + + align:start position:0% +generating electricity and so actually a + + + align:start position:0% +generating electricity and so actually a +very small fraction of the energy + + align:start position:0% +very small fraction of the energy + + + align:start position:0% +very small fraction of the energy +transportation is actually the service + + align:start position:0% +transportation is actually the service + + + align:start position:0% +transportation is actually the service +we want of moving people and goods so if + + align:start position:0% +we want of moving people and goods so if + + + align:start position:0% +we want of moving people and goods so if +we want to look at the + + align:start position:0% +we want to look at the + + + align:start position:0% +we want to look at the +percentages of how this plays out in + + align:start position:0% +percentages of how this plays out in + + + align:start position:0% +percentages of how this plays out in +terms of Transportation you can see the + + align:start position:0% +terms of Transportation you can see the + + + align:start position:0% +terms of Transportation you can see the +percentages for transportation are + + align:start position:0% +percentages for transportation are + + + align:start position:0% +percentages for transportation are +relatively unique and we'll calculate + + align:start position:0% +relatively unique and we'll calculate + + + align:start position:0% +relatively unique and we'll calculate +some of those directly using the numbers + + align:start position:0% +some of those directly using the numbers + + + align:start position:0% +some of those directly using the numbers +off the sanki diagram + + align:start position:0% +off the sanki diagram + + + align:start position:0% +off the sanki diagram +and so if you are seeing this for the + + align:start position:0% +and so if you are seeing this for the + + + align:start position:0% +and so if you are seeing this for the +first time I encourage you to flip back + + align:start position:0% +first time I encourage you to flip back + + + align:start position:0% +first time I encourage you to flip back +and forth between these two slides and + + align:start position:0% +and forth between these two slides and + + + align:start position:0% +and forth between these two slides and +spend some time figuring out what the + + align:start position:0% +spend some time figuring out what the + + + align:start position:0% +spend some time figuring out what the +blue numbers come from and how we do + + align:start position:0% +blue numbers come from and how we do + + + align:start position:0% +blue numbers come from and how we do +these + + align:start position:0% +these + + + align:start position:0% +these +calculations if you want to see how much + + align:start position:0% +calculations if you want to see how much + + + align:start position:0% +calculations if you want to see how much +petroleum is of the total amount of + + align:start position:0% +petroleum is of the total amount of + + + align:start position:0% +petroleum is of the total amount of +energy in the economy it's + + align:start position:0% +energy in the economy it's + + + align:start position:0% +energy in the economy it's +35.1 quads divided by 97.3 quads total + + align:start position:0% +35.1 quads divided by 97.3 quads total + + + align:start position:0% +35.1 quads divided by 97.3 quads total +means that petroleum is 30 36% of all us + + align:start position:0% +means that petroleum is 30 36% of all us + + + align:start position:0% +means that petroleum is 30 36% of all us +primary + + align:start position:0% +primary + + + align:start position:0% +primary +energy if you want to understand the + + align:start position:0% +energy if you want to understand the + + + align:start position:0% +energy if you want to understand the +percentage of petroleum used in + + align:start position:0% +percentage of petroleum used in + + + align:start position:0% +percentage of petroleum used in +transportation it's about 24.3 quads out + + align:start position:0% +transportation it's about 24.3 quads out + + + align:start position:0% +transportation it's about 24.3 quads out +of 35.1 quads of petroleum total meaning + + align:start position:0% +of 35.1 quads of petroleum total meaning + + + align:start position:0% +of 35.1 quads of petroleum total meaning +that 70% essentially about 70% of all + + align:start position:0% +that 70% essentially about 70% of all + + + align:start position:0% +that 70% essentially about 70% of all +petroleum is used for transportation as + + align:start position:0% +petroleum is used for transportation as + + + align:start position:0% +petroleum is used for transportation as +you can see from our sanki diagram I'll + + align:start position:0% +you can see from our sanki diagram I'll + + + align:start position:0% +you can see from our sanki diagram I'll +flip back here you can see that's fairly + + align:start position:0% +flip back here you can see that's fairly + + + align:start position:0% +flip back here you can see that's fairly +unique among all the energy sources here + + align:start position:0% +unique among all the energy sources here + + + align:start position:0% +unique among all the energy sources here +on the left and we know that we've been + + align:start position:0% +on the left and we know that we've been + + + align:start position:0% +on the left and we know that we've been +talking about the energy implications of + + align:start position:0% +talking about the energy implications of + + + align:start position:0% +talking about the energy implications of +petroleum for many years not only in ter + + align:start position:0% +petroleum for many years not only in ter + + + align:start position:0% +petroleum for many years not only in ter +terms of um our Reliance on overseas + + align:start position:0% +terms of um our Reliance on overseas + + + align:start position:0% +terms of um our Reliance on overseas +Imports but more recently in terms of + + align:start position:0% +Imports but more recently in terms of + + + align:start position:0% +Imports but more recently in terms of +the greenhouse gas emissions + + align:start position:0% +the greenhouse gas emissions + + + align:start position:0% +the greenhouse gas emissions +implications and also in terms of energy + + align:start position:0% +implications and also in terms of energy + + + align:start position:0% +implications and also in terms of energy +security where do we get this energy + + align:start position:0% +security where do we get this energy + + + align:start position:0% +security where do we get this energy +from and of course more recent story is + + align:start position:0% +from and of course more recent story is + + + align:start position:0% +from and of course more recent story is +that the US has become one of the + + align:start position:0% +that the US has become one of the + + + align:start position:0% +that the US has become one of the +largest petroleum producers in the world + + align:start position:0% +largest petroleum producers in the world + + + align:start position:0% +largest petroleum producers in the world +also so we are also contributing + + align:start position:0% +also so we are also contributing + + + align:start position:0% +also so we are also contributing +petroleum to the world uh which has + + align:start position:0% +petroleum to the world uh which has + + + align:start position:0% +petroleum to the world uh which has +definite implications for our production + + align:start position:0% +definite implications for our production + + + align:start position:0% +definite implications for our production +and how much greenhouse gas emissions + + align:start position:0% +and how much greenhouse gas emissions + + + align:start position:0% +and how much greenhouse gas emissions +we're exporting to the rest of the world + + align:start position:0% +we're exporting to the rest of the world + + + align:start position:0% +we're exporting to the rest of the world +if you look at the total amount of + + align:start position:0% +if you look at the total amount of + + + align:start position:0% +if you look at the total amount of +energy in transportation you can see + + align:start position:0% +energy in transportation you can see + + + align:start position:0% +energy in transportation you can see +that we use about 26.9 quads of energy + + align:start position:0% +that we use about 26.9 quads of energy + + + align:start position:0% +that we use about 26.9 quads of energy +divided by + + align:start position:0% +divided by + + + align:start position:0% +divided by +73.7 quads of all sector energy use mean + + align:start position:0% +73.7 quads of all sector energy use mean + + + align:start position:0% +73.7 quads of all sector energy use mean +that transportation is one of the + + align:start position:0% +that transportation is one of the + + + align:start position:0% +that transportation is one of the +largest energy using sectors it + + align:start position:0% +largest energy using sectors it + + + align:start position:0% +largest energy using sectors it +represents 36% of all energy + + align:start position:0% +represents 36% of all energy + + + align:start position:0% +represents 36% of all energy +use and in terms of Energy Services we + + align:start position:0% +use and in terms of Energy Services we + + + align:start position:0% +use and in terms of Energy Services we +only get 5.65 quads out of 26.9 quads in + + align:start position:0% +only get 5.65 quads out of 26.9 quads in + + + align:start position:0% +only get 5.65 quads out of 26.9 quads in +put energy meaning that only 21% of the + + align:start position:0% +put energy meaning that only 21% of the + + + align:start position:0% +put energy meaning that only 21% of the +energy that we put into Transportation + + align:start position:0% +energy that we put into Transportation + + + align:start position:0% +energy that we put into Transportation +becomes the final service we want the + + align:start position:0% +becomes the final service we want the + + + align:start position:0% +becomes the final service we want the +actual mobility of the actual movement + + align:start position:0% +actual mobility of the actual movement + + + align:start position:0% +actual mobility of the actual movement +of goods and services and so as I + + align:start position:0% +of goods and services and so as I + + + align:start position:0% +of goods and services and so as I +pointed out before the rejected energy + + align:start position:0% +pointed out before the rejected energy + + + align:start position:0% +pointed out before the rejected energy +that's all mostly heat energy that goes + + align:start position:0% +that's all mostly heat energy that goes + + + align:start position:0% +that's all mostly heat energy that goes +out of the tailpipe of internal + + align:start position:0% +out of the tailpipe of internal + + + align:start position:0% +out of the tailpipe of internal +combustion engines 21.2 quads divid by + + align:start position:0% +combustion engines 21.2 quads divid by + + + align:start position:0% +combustion engines 21.2 quads divid by +26.9 quads means that we' basically + + align:start position:0% +26.9 quads means that we' basically + + + align:start position:0% +26.9 quads means that we' basically +wasted 78% of our energy inputs into + + align:start position:0% +wasted 78% of our energy inputs into + + + align:start position:0% +wasted 78% of our energy inputs into +transportation and so thinking back to + + align:start position:0% +transportation and so thinking back to + + + align:start position:0% +transportation and so thinking back to +the uh spings identity weighing demand + + align:start position:0% +the uh spings identity weighing demand + + + align:start position:0% +the uh spings identity weighing demand +and efficiency of vehicles versus the + + align:start position:0% +and efficiency of vehicles versus the + + + align:start position:0% +and efficiency of vehicles versus the +carbon intensity of the energy we can + + align:start position:0% +carbon intensity of the energy we can + + + align:start position:0% +carbon intensity of the energy we can +use all these percentages to think about + + align:start position:0% +use all these percentages to think about + + + align:start position:0% +use all these percentages to think about +how do we perhaps reduce our demand how + + align:start position:0% +how do we perhaps reduce our demand how + + + align:start position:0% +how do we perhaps reduce our demand how +do we perhaps increase the efficiency of + + align:start position:0% +do we perhaps increase the efficiency of + + + align:start position:0% +do we perhaps increase the efficiency of +our vehicles and how do we reduce the + + align:start position:0% +our vehicles and how do we reduce the + + + align:start position:0% +our vehicles and how do we reduce the +carbonate intensity of our + + align:start position:0% +carbonate intensity of our + + + align:start position:0% +carbonate intensity of our +fuels so this is why it's exciting to + + align:start position:0% +fuels so this is why it's exciting to + + + align:start position:0% +fuels so this is why it's exciting to +talk about electrification and this is + + align:start position:0% +talk about electrification and this is + + + align:start position:0% +talk about electrification and this is +why I start with electrification or + + align:start position:0% +why I start with electrification or + + + align:start position:0% +why I start with electrification or +building the energy system from the + + align:start position:0% +building the energy system from the + + + align:start position:0% +building the energy system from the +bottom up when I started teaching this + + align:start position:0% +bottom up when I started teaching this + + + align:start position:0% +bottom up when I started teaching this +class around7 + + align:start position:0% +class around7 + + + align:start position:0% +class around7 +The Economist had this cover on the left + + align:start position:0% +The Economist had this cover on the left + + + align:start position:0% +The Economist had this cover on the left +declaring the internal combustion engine + + align:start position:0% +declaring the internal combustion engine + + + align:start position:0% +declaring the internal combustion engine +roadkill and one of the figures they + + align:start position:0% +roadkill and one of the figures they + + + align:start position:0% +roadkill and one of the figures they +used to support this were the estimates + + align:start position:0% +used to support this were the estimates + + + align:start position:0% +used to support this were the estimates +showing that all of these major + + align:start position:0% +showing that all of these major + + + align:start position:0% +showing that all of these major +forecasting organizations blomberg new + + align:start position:0% +forecasting organizations blomberg new + + + align:start position:0% +forecasting organizations blomberg new +energy Finance OPEC the organization of + + align:start position:0% +energy Finance OPEC the organization of + + + align:start position:0% +energy Finance OPEC the organization of +petroleum exporting uh countries and + + align:start position:0% +petroleum exporting uh countries and + + + align:start position:0% +petroleum exporting uh countries and +Exxon Mobile had all increased their V + + align:start position:0% +Exxon Mobile had all increased their V + + + align:start position:0% +Exxon Mobile had all increased their V +electric vehicle sales forecasts of + + align:start position:0% +electric vehicle sales forecasts of + + + align:start position:0% +electric vehicle sales forecasts of +course Bloomberg new energy Finance has + + align:start position:0% +course Bloomberg new energy Finance has + + + align:start position:0% +course Bloomberg new energy Finance has +been perhaps the most aggressive + + align:start position:0% +been perhaps the most aggressive + + + align:start position:0% +been perhaps the most aggressive +forecast our most aggressive forecast + + align:start position:0% +forecast our most aggressive forecast + + + align:start position:0% +forecast our most aggressive forecast +for the number of electric vehicles but + + align:start position:0% +for the number of electric vehicles but + + + align:start position:0% +for the number of electric vehicles but +you can see between between 2016 and + + align:start position:0% +you can see between between 2016 and + + + align:start position:0% +you can see between between 2016 and +2017 both OPEC and Exxon Mobile two + + align:start position:0% +2017 both OPEC and Exxon Mobile two + + + align:start position:0% +2017 both OPEC and Exxon Mobile two +entities that uh probably are not + + align:start position:0% +entities that uh probably are not + + + align:start position:0% +entities that uh probably are not +welcoming the adoption electric vehicles + + align:start position:0% +welcoming the adoption electric vehicles + + + align:start position:0% +welcoming the adoption electric vehicles +also increase their sales + + align:start position:0% +also increase their sales + + + align:start position:0% +also increase their sales +forecast if we look more recently at + + align:start position:0% +forecast if we look more recently at + + + align:start position:0% +forecast if we look more recently at +Bloomberg new energy finances electric + + align:start position:0% +Bloomberg new energy finances electric + + + align:start position:0% +Bloomberg new energy finances electric +vehicle Outlook in 2022 you can see + + align:start position:0% +vehicle Outlook in 2022 you can see + + + align:start position:0% +vehicle Outlook in 2022 you can see +they've further increased their economic + + align:start position:0% +they've further increased their economic + + + align:start position:0% +they've further increased their economic +transition scenario or their estimates + + align:start position:0% +transition scenario or their estimates + + + align:start position:0% +transition scenario or their estimates +of the global long-term passenger EV + + align:start position:0% +of the global long-term passenger EV + + + align:start position:0% +of the global long-term passenger EV +Fleet by market and you can see that + + align:start position:0% +Fleet by market and you can see that + + + align:start position:0% +Fleet by market and you can see that +their estimates are now up to around 700 + + align:start position:0% +their estimates are now up to around 700 + + + align:start position:0% +their estimates are now up to around 700 +million electric vehicles when a few + + align:start position:0% +million electric vehicles when a few + + + align:start position:0% +million electric vehicles when a few +years ago they're at 500 million and if + + align:start position:0% +years ago they're at 500 million and if + + + align:start position:0% +years ago they're at 500 million and if +you look at their forecast of what the + + align:start position:0% +you look at their forecast of what the + + + align:start position:0% +you look at their forecast of what the +global passenger vehicle Fleet by drive + + align:start position:0% +global passenger vehicle Fleet by drive + + + align:start position:0% +global passenger vehicle Fleet by drive +train will look like on the right hand + + align:start position:0% +train will look like on the right hand + + + align:start position:0% +train will look like on the right hand +side they show that internal combustion + + align:start position:0% +side they show that internal combustion + + + align:start position:0% +side they show that internal combustion +engines this gray block will decrease + + align:start position:0% +engines this gray block will decrease + + + align:start position:0% +engines this gray block will decrease +slow increase slowly to 2020 or so and + + align:start position:0% +slow increase slowly to 2020 or so and + + + align:start position:0% +slow increase slowly to 2020 or so and +then start decreasing pretty much around + + align:start position:0% +then start decreasing pretty much around + + + align:start position:0% +then start decreasing pretty much around +now they show that hybrid uh Vehicles + + align:start position:0% +now they show that hybrid uh Vehicles + + + align:start position:0% +now they show that hybrid uh Vehicles +will increase but be a relatively small + + align:start position:0% +will increase but be a relatively small + + + align:start position:0% +will increase but be a relatively small +share of our future drivetrain Fleet uh + + align:start position:0% +share of our future drivetrain Fleet uh + + + align:start position:0% +share of our future drivetrain Fleet uh +battery uh plugin hybrids and Fuel Cell + + align:start position:0% +battery uh plugin hybrids and Fuel Cell + + + align:start position:0% +battery uh plugin hybrids and Fuel Cell +Vehicles barely you can see them here + + align:start position:0% +Vehicles barely you can see them here + + + align:start position:0% +Vehicles barely you can see them here +but the more majority of vehicle growth + + align:start position:0% +but the more majority of vehicle growth + + + align:start position:0% +but the more majority of vehicle growth +will be in battery electric until by + + align:start position:0% +will be in battery electric until by + + + align:start position:0% +will be in battery electric until by +2040 there will be as many battery + + align:start position:0% +2040 there will be as many battery + + + align:start position:0% +2040 there will be as many battery +electric vehicles as there there are + + align:start position:0% +electric vehicles as there there are + + + align:start position:0% +electric vehicles as there there are +internal combustion engine vehicles and + + align:start position:0% +internal combustion engine vehicles and + + + align:start position:0% +internal combustion engine vehicles and +this of course depends on Bloomberg new + + align:start position:0% +this of course depends on Bloomberg new + + + align:start position:0% +this of course depends on Bloomberg new +energy finances forecast and some of + + align:start position:0% +energy finances forecast and some of + + + align:start position:0% +energy finances forecast and some of +their + + align:start position:0% +their + + + align:start position:0% +their +modeling but it's also worth pointing + + align:start position:0% +modeling but it's also worth pointing + + + align:start position:0% +modeling but it's also worth pointing +out and I like to point this out every + + align:start position:0% +out and I like to point this out every + + + align:start position:0% +out and I like to point this out every +year since 2016 or 2017 that electric + + align:start position:0% +year since 2016 or 2017 that electric + + + align:start position:0% +year since 2016 or 2017 that electric +vehicles are still very new technologies + + align:start position:0% +vehicles are still very new technologies + + + align:start position:0% +vehicles are still very new technologies +they're still very new products in a + + align:start position:0% +they're still very new products in a + + + align:start position:0% +they're still very new products in a +consumer Marketplace the bolt electric + + align:start position:0% +consumer Marketplace the bolt electric + + + align:start position:0% +consumer Marketplace the bolt electric +vehicle one of the first lowcost + + align:start position:0% +vehicle one of the first lowcost + + + align:start position:0% +vehicle one of the first lowcost +electric vehicles was long range was + + align:start position:0% +electric vehicles was long range was + + + align:start position:0% +electric vehicles was long range was +only introduced in + + align:start position:0% +only introduced in + + + align:start position:0% +only introduced in +2016 they beat Tesla to the market by + + align:start position:0% +2016 they beat Tesla to the market by + + + align:start position:0% +2016 they beat Tesla to the market by +one year when Tesla introduced their + + align:start position:0% +one year when Tesla introduced their + + + align:start position:0% +one year when Tesla introduced their +first I think sub35 + + align:start position:0% +first I think sub35 + + + align:start position:0% +first I think sub35 +$40,000 model the model 3 in + + align:start position:0% +$40,000 model the model 3 in + + + align:start position:0% +$40,000 model the model 3 in +2017 it is worth pointing that most + + align:start position:0% +2017 it is worth pointing that most + + + align:start position:0% +2017 it is worth pointing that most +automakers have yet to introduce + + align:start position:0% +automakers have yet to introduce + + + align:start position:0% +automakers have yet to introduce +electric vehicle + + align:start position:0% +electric vehicle + + + align:start position:0% +electric vehicle +models even though if you look at Car + + align:start position:0% +models even though if you look at Car + + + align:start position:0% +models even though if you look at Car +and Driver magazine you'll see that you + + align:start position:0% +and Driver magazine you'll see that you + + + align:start position:0% +and Driver magazine you'll see that you +know 50 or 100 new electric vehicle + + align:start position:0% +know 50 or 100 new electric vehicle + + + align:start position:0% +know 50 or 100 new electric vehicle +models are expected to come out in the + + align:start position:0% +models are expected to come out in the + + + align:start position:0% +models are expected to come out in the +next few years but it's worth looking at + + align:start position:0% +next few years but it's worth looking at + + + align:start position:0% +next few years but it's worth looking at +how quickly electric vehicle sales are + + align:start position:0% +how quickly electric vehicle sales are + + + align:start position:0% +how quickly electric vehicle sales are +growing as a share of new cars if we + + align:start position:0% +growing as a share of new cars if we + + + align:start position:0% +growing as a share of new cars if we +compare the first half of 2021 numbers + + align:start position:0% +compare the first half of 2021 numbers + + + align:start position:0% +compare the first half of 2021 numbers +the first half of 2022 numbers + + align:start position:0% +the first half of 2022 numbers + + + align:start position:0% +the first half of 2022 numbers +uh globally electric vehicles went from + + align:start position:0% +uh globally electric vehicles went from + + + align:start position:0% +uh globally electric vehicles went from +last year to this year from four to 5% + + align:start position:0% +last year to this year from four to 5% + + + align:start position:0% +last year to this year from four to 5% +of new car sales to + + align:start position:0% +of new car sales to + + + align:start position:0% +of new car sales to +12% in Germany they went slightly from + + align:start position:0% +12% in Germany they went slightly from + + + align:start position:0% +12% in Germany they went slightly from +up from 12% to almost + + align:start position:0% +up from 12% to almost + + + align:start position:0% +up from 12% to almost +14% in China they went from 12 to 20% of + + align:start position:0% +14% in China they went from 12 to 20% of + + + align:start position:0% +14% in China they went from 12 to 20% of +new car sales and the US they almost + + align:start position:0% +new car sales and the US they almost + + + align:start position:0% +new car sales and the US they almost +doubled from 3.6 to + + align:start position:0% +doubled from 3.6 to + + + align:start position:0% +doubled from 3.6 to +6.2% despite declines in the sales of + + align:start position:0% +6.2% despite declines in the sales of + + + align:start position:0% +6.2% despite declines in the sales of +other vehicles partly due to price + + align:start position:0% +other vehicles partly due to price + + + align:start position:0% +other vehicles partly due to price +inflation and Rises and vehicle + + align:start position:0% +inflation and Rises and vehicle + + + align:start position:0% +inflation and Rises and vehicle +shortages but despite all these problems + + align:start position:0% +shortages but despite all these problems + + + align:start position:0% +shortages but despite all these problems +electric vehicles have increased their + + align:start position:0% +electric vehicles have increased their + + + align:start position:0% +electric vehicles have increased their +market share of new car + + align:start position:0% +market share of new car + + + align:start position:0% +market share of new car +sales so this is what we'll start by + + align:start position:0% +sales so this is what we'll start by + + + align:start position:0% +sales so this is what we'll start by +analyzing private Vehicles AKA personal + + align:start position:0% +analyzing private Vehicles AKA personal + + + align:start position:0% +analyzing private Vehicles AKA personal +transport and understand them in terms + + align:start position:0% +transport and understand them in terms + + + align:start position:0% +transport and understand them in terms +of their energy consumption in terms of + + align:start position:0% +of their energy consumption in terms of + + + align:start position:0% +of their energy consumption in terms of +energy per person per kilometer or per + + align:start position:0% +energy per person per kilometer or per + + + align:start position:0% +energy per person per kilometer or per +100 kilometers so this is a figure from + + align:start position:0% +100 kilometers so this is a figure from + + + align:start position:0% +100 kilometers so this is a figure from +aai + + align:start position:0% + + + + align:start position:0% + +20.23% axis is the speed in terms of + + align:start position:0% +20.23% axis is the speed in terms of + + + align:start position:0% +20.23% axis is the speed in terms of +kilometers per hour and you can see if + + align:start position:0% +kilometers per hour and you can see if + + + align:start position:0% +kilometers per hour and you can see if +we were to compare let's say two of the + + align:start position:0% +we were to compare let's say two of the + + + align:start position:0% +we were to compare let's say two of the +waterborne uh Transportation modes uh + + align:start position:0% +waterborne uh Transportation modes uh + + + align:start position:0% +waterborne uh Transportation modes uh +the Vancouver SE bus a c bus that I've + + align:start position:0% +the Vancouver SE bus a c bus that I've + + + align:start position:0% +the Vancouver SE bus a c bus that I've +ridden quite a bit is compared to a + + align:start position:0% +ridden quite a bit is compared to a + + + align:start position:0% +ridden quite a bit is compared to a +catamaran and you can see that the + + align:start position:0% +catamaran and you can see that the + + + align:start position:0% +catamaran and you can see that the +energy consumption of the catamaran is + + align:start position:0% +energy consumption of the catamaran is + + + align:start position:0% +energy consumption of the catamaran is +actually higher though the speed is + + align:start position:0% +actually higher though the speed is + + + align:start position:0% +actually higher though the speed is +higher I assume that this is a motorized + + align:start position:0% +higher I assume that this is a motorized + + + align:start position:0% +higher I assume that this is a motorized +or a fueled catamaran rather than a + + align:start position:0% +or a fueled catamaran rather than a + + + align:start position:0% +or a fueled catamaran rather than a +sailing catamaran and you can see that + + align:start position:0% +sailing catamaran and you can see that + + + align:start position:0% +sailing catamaran and you can see that +the energy consumption for the C bus is + + align:start position:0% +the energy consumption for the C bus is + + + align:start position:0% +the energy consumption for the C bus is +relatively lower because it's lower on + + align:start position:0% +relatively lower because it's lower on + + + align:start position:0% +relatively lower because it's lower on +the vertical axis of course it could be + + align:start position:0% +the vertical axis of course it could be + + + align:start position:0% +the vertical axis of course it could be +because the cab bus has a limited range + + align:start position:0% +because the cab bus has a limited range + + + align:start position:0% +because the cab bus has a limited range +and moves about 400 people at a time if + + align:start position:0% +and moves about 400 people at a time if + + + align:start position:0% +and moves about 400 people at a time if +we look in terms of the Airborne modes + + align:start position:0% +we look in terms of the Airborne modes + + + align:start position:0% +we look in terms of the Airborne modes +of transportation you see that a turbo + + align:start position:0% +of transportation you see that a turbo + + + align:start position:0% +of transportation you see that a turbo +prop plane has much lower fuel + + align:start position:0% +prop plane has much lower fuel + + + align:start position:0% +prop plane has much lower fuel +consumption than a Boeing 747 even if + + align:start position:0% +consumption than a Boeing 747 even if + + + align:start position:0% +consumption than a Boeing 747 even if +the Boeing 747 is full and of course + + align:start position:0% +the Boeing 747 is full and of course + + + align:start position:0% +the Boeing 747 is full and of course +lower than a b Boeing 747 if the Boeing + + align:start position:0% +lower than a b Boeing 747 if the Boeing + + + align:start position:0% +lower than a b Boeing 747 if the Boeing +747 is not entirely full + + align:start position:0% +747 is not entirely full + + + align:start position:0% +747 is not entirely full +of course the most useful part of this + + align:start position:0% +of course the most useful part of this + + + align:start position:0% +of course the most useful part of this +graph I think is comparing the different + + align:start position:0% +graph I think is comparing the different + + + align:start position:0% +graph I think is comparing the different +modes of transportation for example + + align:start position:0% +modes of transportation for example + + + align:start position:0% +modes of transportation for example +whether or not what the energy + + align:start position:0% +whether or not what the energy + + + align:start position:0% +whether or not what the energy +consumption of a car is versus public + + align:start position:0% +consumption of a car is versus public + + + align:start position:0% +consumption of a car is versus public +transportation so if you look at a car + + align:start position:0% +transportation so if you look at a car + + + align:start position:0% +transportation so if you look at a car +that is full it has roughly about 20 + + align:start position:0% +that is full it has roughly about 20 + + + align:start position:0% +that is full it has roughly about 20 +kilowatt hours per 100 kilometers per + + align:start position:0% +kilowatt hours per 100 kilometers per + + + align:start position:0% +kilowatt hours per 100 kilometers per +person the underground system looks like + + align:start position:0% +person the underground system looks like + + + align:start position:0% +person the underground system looks like +it's about i''s say 15 or 16 kilowatt + + align:start position:0% +it's about i''s say 15 or 16 kilowatt + + + align:start position:0% +it's about i''s say 15 or 16 kilowatt +hours per 100 kilometers per per person + + align:start position:0% +hours per 100 kilometers per per person + + + align:start position:0% +hours per 100 kilometers per per person +of course if the underground train is + + align:start position:0% +of course if the underground train is + + + align:start position:0% +of course if the underground train is +full that drives it very low to about + + align:start position:0% +full that drives it very low to about + + + align:start position:0% +full that drives it very low to about +four kilowatt hours per person um per + + align:start position:0% +four kilowatt hours per person um per + + + align:start position:0% +four kilowatt hours per person um per +100 kilometers and of course walking and + + align:start position:0% +100 kilometers and of course walking and + + + align:start position:0% +100 kilometers and of course walking and +cycling is still lower but the speeds + + align:start position:0% +cycling is still lower but the speeds + + + align:start position:0% +cycling is still lower but the speeds +are lower and so you can start to see + + align:start position:0% +are lower and so you can start to see + + + align:start position:0% +are lower and so you can start to see +this tradeoff between the speeds we + + align:start position:0% +this tradeoff between the speeds we + + + align:start position:0% +this tradeoff between the speeds we +would like to attain either for short + + align:start position:0% +would like to attain either for short + + + align:start position:0% +would like to attain either for short +distances in terms of walking or cycling + + align:start position:0% +distances in terms of walking or cycling + + + align:start position:0% +distances in terms of walking or cycling +or long distances like highspeed trains + + align:start position:0% +or long distances like highspeed trains + + + align:start position:0% +or long distances like highspeed trains +and of course you can see why in many + + align:start position:0% +and of course you can see why in many + + + align:start position:0% +and of course you can see why in many +cases highp speed trains are out + + align:start position:0% +cases highp speed trains are out + + + align:start position:0% +cases highp speed trains are out +competing short Hall aviation in North + + align:start position:0% +competing short Hall aviation in North + + + align:start position:0% +competing short Hall aviation in North +America we tend to use turbo prop planes + + align:start position:0% +America we tend to use turbo prop planes + + + align:start position:0% +America we tend to use turbo prop planes +for short Hall Aviation uh instead of + + align:start position:0% +for short Hall Aviation uh instead of + + + align:start position:0% +for short Hall Aviation uh instead of +large Jets like a Boeing + + align:start position:0% +large Jets like a Boeing + + + align:start position:0% +large Jets like a Boeing +747 but also if you look at compare that + + align:start position:0% +747 but also if you look at compare that + + + align:start position:0% +747 but also if you look at compare that +to an electric highspeed train electric + + align:start position:0% +to an electric highspeed train electric + + + align:start position:0% +to an electric highspeed train electric +highspeed train has much lower energy + + align:start position:0% +highspeed train has much lower energy + + + align:start position:0% +highspeed train has much lower energy +consumption than a turbo plane this is + + align:start position:0% +consumption than a turbo plane this is + + + align:start position:0% +consumption than a turbo plane this is +essentially why China building a large + + align:start position:0% +essentially why China building a large + + + align:start position:0% +essentially why China building a large +highspeed rail network has apparently + + align:start position:0% +highspeed rail network has apparently + + + align:start position:0% +highspeed rail network has apparently +wiped out the entire short Hall Aviation + + align:start position:0% +wiped out the entire short Hall Aviation + + + align:start position:0% +wiped out the entire short Hall Aviation +Market of course you can make do with + + align:start position:0% +Market of course you can make do with + + + align:start position:0% +Market of course you can make do with +things like a bus or a coach that is + + align:start position:0% +things like a bus or a coach that is + + + align:start position:0% +things like a bus or a coach that is +full also has much lower energy + + align:start position:0% +full also has much lower energy + + + align:start position:0% +full also has much lower energy +consumption than individual cars but you + + align:start position:0% +consumption than individual cars but you + + + align:start position:0% +consumption than individual cars but you +can see that trains can largely out + + align:start position:0% +can see that trains can largely out + + + align:start position:0% +can see that trains can largely out +compete a trains electric trains or + + align:start position:0% +compete a trains electric trains or + + + align:start position:0% +compete a trains electric trains or +high-speed trains can out compete buses + + align:start position:0% +high-speed trains can out compete buses + + + align:start position:0% +high-speed trains can out compete buses +quite easily of course they have a + + align:start position:0% +quite easily of course they have a + + + align:start position:0% +quite easily of course they have a +larger upfront cost in terms of land and + + align:start position:0% +larger upfront cost in terms of land and + + + align:start position:0% +larger upfront cost in terms of land and +building the rails and the electrical + + align:start position:0% +building the rails and the electrical + + + align:start position:0% +building the rails and the electrical +grid required to support those + + align:start position:0% +grid required to support those + + + align:start position:0% +grid required to support those +trains so if we use graphs like this you + + align:start position:0% +trains so if we use graphs like this you + + + align:start position:0% +trains so if we use graphs like this you +can compare not only the energy + + align:start position:0% +can compare not only the energy + + + align:start position:0% +can compare not only the energy +consumption but the speed that we would + + align:start position:0% +consumption but the speed that we would + + + align:start position:0% +consumption but the speed that we would +like in terms of to achieve + + align:start position:0% +like in terms of to achieve + + + align:start position:0% +like in terms of to achieve +mobility and so here's a kind of a bit + + align:start position:0% +mobility and so here's a kind of a bit + + + align:start position:0% +mobility and so here's a kind of a bit +of a teaser that I put in the problem + + align:start position:0% +of a teaser that I put in the problem + + + align:start position:0% +of a teaser that I put in the problem +set let's ask a simple policy question + + align:start position:0% +set let's ask a simple policy question + + + align:start position:0% +set let's ask a simple policy question +which vehicles should we focus on focus + + align:start position:0% +which vehicles should we focus on focus + + + align:start position:0% +which vehicles should we focus on focus +on making more efficient in terms of + + align:start position:0% +on making more efficient in terms of + + + align:start position:0% +on making more efficient in terms of +policy we want to Target our policies + + align:start position:0% +policy we want to Target our policies + + + align:start position:0% +policy we want to Target our policies +well we want to spend our time as + + align:start position:0% +well we want to spend our time as + + + align:start position:0% +well we want to spend our time as +government officials having the most + + align:start position:0% +government officials having the most + + + align:start position:0% +government officials having the most +impact for the time we spend so should + + align:start position:0% +impact for the time we spend so should + + + align:start position:0% +impact for the time we spend so should +we make SUVs slightly less gross maybe + + align:start position:0% +we make SUVs slightly less gross maybe + + + align:start position:0% +we make SUVs slightly less gross maybe +increasing their average 11 miles per + + align:start position:0% +increasing their average 11 miles per + + + align:start position:0% +increasing their average 11 miles per +gallon to a whopping 13 miles per gallon + + align:start position:0% +gallon to a whopping 13 miles per gallon + + + align:start position:0% +gallon to a whopping 13 miles per gallon +or should we make Passenger cars super + + align:start position:0% +or should we make Passenger cars super + + + align:start position:0% +or should we make Passenger cars super +efficient let's say going from the fleet + + align:start position:0% +efficient let's say going from the fleet + + + align:start position:0% +efficient let's say going from the fleet +average for passenger cars from 29 miles + + align:start position:0% +average for passenger cars from 29 miles + + + align:start position:0% +average for passenger cars from 29 miles +per gallon maybe changing them to hybrid + + align:start position:0% +per gallon maybe changing them to hybrid + + + align:start position:0% +per gallon maybe changing them to hybrid +drivetrains that get 49 miles per gallon + + align:start position:0% +drivetrains that get 49 miles per gallon + + + align:start position:0% +drivetrains that get 49 miles per gallon +so if we use some of the calculations uh + + align:start position:0% +so if we use some of the calculations uh + + + align:start position:0% +so if we use some of the calculations uh +we you learned in maai chapters 3 and 20 + + align:start position:0% +we you learned in maai chapters 3 and 20 + + + align:start position:0% +we you learned in maai chapters 3 and 20 +you can see that actually going from if + + align:start position:0% +you can see that actually going from if + + + align:start position:0% +you can see that actually going from if +we flip this over in terms of 11 miles + + align:start position:0% +we flip this over in terms of 11 miles + + + align:start position:0% +we flip this over in terms of 11 miles +per gallon that has roughly + + align:start position:0% +per gallon that has roughly + + + align:start position:0% +per gallon that has roughly +0.091 gallons to go per mile and if we + + align:start position:0% +0.091 gallons to go per mile and if we + + + align:start position:0% +0.091 gallons to go per mile and if we +flip over 13 miles per gallon that + + align:start position:0% +flip over 13 miles per gallon that + + + align:start position:0% +flip over 13 miles per gallon that +basically implies + + align:start position:0% +basically implies + + + align:start position:0% +basically implies +0.077 gallons per mile and so this is + + align:start position:0% +0.077 gallons per mile and so this is + + + align:start position:0% +0.077 gallons per mile and so this is +the point from the kai reading we want + + align:start position:0% +the point from the kai reading we want + + + align:start position:0% +the point from the kai reading we want +to look less at miles per gallon which + + align:start position:0% +to look less at miles per gallon which + + + align:start position:0% +to look less at miles per gallon which +is indication how many miles you can go + + align:start position:0% +is indication how many miles you can go + + + align:start position:0% +is indication how many miles you can go +on a given amount of fuel instead look + + align:start position:0% +on a given amount of fuel instead look + + + align:start position:0% +on a given amount of fuel instead look +at how much energy are we spending to to + + align:start position:0% +at how much energy are we spending to to + + + align:start position:0% +at how much energy are we spending to to +go a certain distance this emphasizes + + align:start position:0% +go a certain distance this emphasizes + + + align:start position:0% +go a certain distance this emphasizes +the service we want to get which is + + align:start position:0% +the service we want to get which is + + + align:start position:0% +the service we want to get which is +mobility so we take this number flip it + + align:start position:0% +mobility so we take this number flip it + + + align:start position:0% +mobility so we take this number flip it +over and we measure how much energy we + + align:start position:0% +over and we measure how much energy we + + + align:start position:0% +over and we measure how much energy we +need to go a certain Mile and so if we + + align:start position:0% +need to go a certain Mile and so if we + + + align:start position:0% +need to go a certain Mile and so if we +go from a gross SUV from + + align:start position:0% +go from a gross SUV from + + + align:start position:0% +go from a gross SUV from +0.91 gallons per mile and make it more + + align:start position:0% +0.91 gallons per mile and make it more + + + align:start position:0% +0.91 gallons per mile and make it more +efficient we go to + + align:start position:0% +efficient we go to + + + align:start position:0% +efficient we go to +0.77 gallons per mile if we do the same + + align:start position:0% +0.77 gallons per mile if we do the same + + + align:start position:0% +0.77 gallons per mile if we do the same +thing for high for passenger cars we go + + align:start position:0% +thing for high for passenger cars we go + + + align:start position:0% +thing for high for passenger cars we go +from 29 miles per gallon to 0.3 4 Gall + + align:start position:0% +from 29 miles per gallon to 0.3 4 Gall + + + align:start position:0% +from 29 miles per gallon to 0.3 4 Gall +per mile and we go from 49 miles per + + align:start position:0% +per mile and we go from 49 miles per + + + align:start position:0% +per mile and we go from 49 miles per +gallon to + + align:start position:0% +gallon to + + + align:start position:0% +gallon to +0.20 Gall per mile but this is a bit of + + align:start position:0% +0.20 Gall per mile but this is a bit of + + + align:start position:0% +0.20 Gall per mile but this is a bit of +a brain teaser or I guess a trick + + align:start position:0% +a brain teaser or I guess a trick + + + align:start position:0% +a brain teaser or I guess a trick +question because the difference between + + align:start position:0% +question because the difference between + + + align:start position:0% +question because the difference between +both pairs of vehicles is the same we're + + align:start position:0% +both pairs of vehicles is the same we're + + + align:start position:0% +both pairs of vehicles is the same we're +actually going improving them by 0.14 + + align:start position:0% +actually going improving them by 0.14 + + + align:start position:0% +actually going improving them by 0.14 +gallons per + + align:start position:0% +gallons per + + + align:start position:0% +gallons per +mile this is just a kind of a trick + + align:start position:0% +mile this is just a kind of a trick + + + align:start position:0% +mile this is just a kind of a trick +question I want to use to illustrate a + + align:start position:0% +question I want to use to illustrate a + + + align:start position:0% +question I want to use to illustrate a +point about consumer perceptions and + + align:start position:0% +point about consumer perceptions and + + + align:start position:0% +point about consumer perceptions and +misperceptions of energy costs this is a + + align:start position:0% +misperceptions of energy costs this is a + + + align:start position:0% +misperceptions of energy costs this is a +paper by hunt cut in the American + + align:start position:0% +paper by hunt cut in the American + + + align:start position:0% +paper by hunt cut in the American +Economic Review and what this is called + + align:start position:0% +Economic Review and what this is called + + + align:start position:0% +Economic Review and what this is called +is the mpg illusion which most people + + align:start position:0% +is the mpg illusion which most people + + + align:start position:0% +is the mpg illusion which most people +think intuitively the automobile fuel + + align:start position:0% +think intuitively the automobile fuel + + + align:start position:0% +think intuitively the automobile fuel +costs scale linearly in miles per gallon + + align:start position:0% +costs scale linearly in miles per gallon + + + align:start position:0% +costs scale linearly in miles per gallon +where in fact what we care about is the + + align:start position:0% +where in fact what we care about is the + + + align:start position:0% +where in fact what we care about is the +amount of energy we spend on service + + align:start position:0% +amount of energy we spend on service + + + align:start position:0% +amount of energy we spend on service +which is going G how many how many + + align:start position:0% +which is going G how many how many + + + align:start position:0% +which is going G how many how many +gallons of gasoline do we need to go per + + align:start position:0% +gallons of gasoline do we need to go per + + + align:start position:0% +gallons of gasoline do we need to go per +mile or how much fuel do we need to go + + align:start position:0% +mile or how much fuel do we need to go + + + align:start position:0% +mile or how much fuel do we need to go +per mile of service and so this is just + + align:start position:0% +per mile of service and so this is just + + + align:start position:0% +per mile of service and so this is just +an indication that this is a systemic + + align:start position:0% +an indication that this is a systemic + + + align:start position:0% +an indication that this is a systemic +bias that or systemic misperception that + + align:start position:0% +bias that or systemic misperception that + + + align:start position:0% +bias that or systemic misperception that +people have about energy + + align:start position:0% +people have about energy + + + align:start position:0% +people have about energy +costs so let's focus on the powert train + + align:start position:0% +costs so let's focus on the powert train + + + align:start position:0% +costs so let's focus on the powert train +options we have to achieve the service + + align:start position:0% +options we have to achieve the service + + + align:start position:0% +options we have to achieve the service +we want which is mobility internal + + align:start position:0% +we want which is mobility internal + + + align:start position:0% +we want which is mobility internal +combustion engines this essentially is + + align:start position:0% +combustion engines this essentially is + + + align:start position:0% +combustion engines this essentially is +where we burn fossil fuels to move the + + align:start position:0% +where we burn fossil fuels to move the + + + align:start position:0% +where we burn fossil fuels to move the +car we have hybrid uh drivetrains which + + align:start position:0% +car we have hybrid uh drivetrains which + + + align:start position:0% +car we have hybrid uh drivetrains which +have been around for I think almost 15 + + align:start position:0% +have been around for I think almost 15 + + + align:start position:0% +have been around for I think almost 15 +or 20 years now where fossil fuels move + + align:start position:0% +or 20 years now where fossil fuels move + + + align:start position:0% +or 20 years now where fossil fuels move +the car but we integrate a small battery + + align:start position:0% +the car but we integrate a small battery + + + align:start position:0% +the car but we integrate a small battery +to store the power from braking or to + + align:start position:0% +to store the power from braking or to + + + align:start position:0% +to store the power from braking or to +move the car this is the well-known + + align:start position:0% +move the car this is the well-known + + + align:start position:0% +move the car this is the well-known +Prius that's been around for many + + align:start position:0% +Prius that's been around for many + + + align:start position:0% +Prius that's been around for many +years we have plug-in hybrid electric + + align:start position:0% +years we have plug-in hybrid electric + + + align:start position:0% +years we have plug-in hybrid electric +vehicles or phvs for short where we have + + align:start position:0% +vehicles or phvs for short where we have + + + align:start position:0% +vehicles or phvs for short where we have +a larger battery that moves the car up + + align:start position:0% +a larger battery that moves the car up + + + align:start position:0% +a larger battery that moves the car up +to 20 or 40 miles and then we have a + + align:start position:0% +to 20 or 40 miles and then we have a + + + align:start position:0% +to 20 or 40 miles and then we have a +fossil fuel engine still in the car + + align:start position:0% +fossil fuel engine still in the car + + + align:start position:0% +fossil fuel engine still in the car +that's used to extend the range of the + + align:start position:0% +that's used to extend the range of the + + + align:start position:0% +that's used to extend the range of the +battery and you can charge the battery + + align:start position:0% +battery and you can charge the battery + + + align:start position:0% +battery and you can charge the battery +off gas if you run off run out of + + align:start position:0% +off gas if you run off run out of + + + align:start position:0% +off gas if you run off run out of +electricity and of course we have fully + + align:start position:0% +electricity and of course we have fully + + + align:start position:0% +electricity and of course we have fully +battery electric vehicles where the + + align:start position:0% +battery electric vehicles where the + + + align:start position:0% +battery electric vehicles where the +battery moves the car 200 to 400 miles + + align:start position:0% +battery moves the car 200 to 400 miles + + + align:start position:0% +battery moves the car 200 to 400 miles +these electric vehicles have drastically + + align:start position:0% +these electric vehicles have drastically + + + align:start position:0% +these electric vehicles have drastically +less maintenance because an electric + + align:start position:0% +less maintenance because an electric + + + align:start position:0% +less maintenance because an electric +motor is easier to maintain than + + align:start position:0% +motor is easier to maintain than + + + align:start position:0% +motor is easier to maintain than +internal combustion engine they're less + + align:start position:0% +internal combustion engine they're less + + + align:start position:0% +internal combustion engine they're less +mechanically complex but they also as we + + align:start position:0% +mechanically complex but they also as we + + + align:start position:0% +mechanically complex but they also as we +saw in the readings from Mi ATL paper or + + align:start position:0% +saw in the readings from Mi ATL paper or + + + align:start position:0% +saw in the readings from Mi ATL paper or +the ker article ker chapter the cost + + align:start position:0% +the ker article ker chapter the cost + + + align:start position:0% +the ker article ker chapter the cost +electric vehicle largely depends on + + align:start position:0% +electric vehicle largely depends on + + + align:start position:0% +electric vehicle largely depends on +battery costs almost 35 or 40% I think + + align:start position:0% +battery costs almost 35 or 40% I think + + + align:start position:0% +battery costs almost 35 or 40% I think +of the entire cost of the vehicle is + + align:start position:0% +of the entire cost of the vehicle is + + + align:start position:0% +of the entire cost of the vehicle is +simply the battery this is also why + + align:start position:0% +simply the battery this is also why + + + align:start position:0% +simply the battery this is also why +Tesla has built a gigafactory to turn + + align:start position:0% +Tesla has built a gigafactory to turn + + + align:start position:0% +Tesla has built a gigafactory to turn +out batteries at lower cost at at higher + + align:start position:0% +out batteries at lower cost at at higher + + + align:start position:0% +out batteries at lower cost at at higher +volumes Tesla believes and I think + + align:start position:0% +volumes Tesla believes and I think + + + align:start position:0% +volumes Tesla believes and I think +they're being proven correctly being + + align:start position:0% +they're being proven correctly being + + + align:start position:0% +they're being proven correctly being +being proven right that if they produce + + align:start position:0% +being proven right that if they produce + + + align:start position:0% +being proven right that if they produce +batteries and very large volumes they'll + + align:start position:0% +batteries and very large volumes they'll + + + align:start position:0% +batteries and very large volumes they'll +learn about how to make the batteries + + align:start position:0% +learn about how to make the batteries + + + align:start position:0% +learn about how to make the batteries +more efficient they'll produce a lot + + align:start position:0% +more efficient they'll produce a lot + + + align:start position:0% +more efficient they'll produce a lot +more batteries and drive the cost per + + align:start position:0% +more batteries and drive the cost per + + + align:start position:0% +more batteries and drive the cost per +unit down therefore that will lower the + + align:start position:0% +unit down therefore that will lower the + + + align:start position:0% +unit down therefore that will lower the +cost of the cars are selling because + + align:start position:0% +cost of the cars are selling because + + + align:start position:0% +cost of the cars are selling because +most of the cost of the car is the cost + + align:start position:0% +most of the cost of the car is the cost + + + align:start position:0% +most of the cost of the car is the cost +of the battery or much of the cost of + + align:start position:0% +of the battery or much of the cost of + + + align:start position:0% +of the battery or much of the cost of +the car is the cost of the + + align:start position:0% +the car is the cost of the + + + align:start position:0% +the car is the cost of the +battery just to show you what these + + align:start position:0% +battery just to show you what these + + + align:start position:0% +battery just to show you what these +different powertrain options look like + + align:start position:0% +different powertrain options look like + + + align:start position:0% +different powertrain options look like +this is a diagram from the kitner + + align:start position:0% +this is a diagram from the kitner + + + align:start position:0% +this is a diagram from the kitner +chapter that I assed and referenced at + + align:start position:0% +chapter that I assed and referenced at + + + align:start position:0% +chapter that I assed and referenced at +the beginning of the lecture you can see + + align:start position:0% +the beginning of the lecture you can see + + + align:start position:0% +the beginning of the lecture you can see +a battery electric vehicle has a fairly + + align:start position:0% +a battery electric vehicle has a fairly + + + align:start position:0% +a battery electric vehicle has a fairly +simple drivetrain it has a charger going + + align:start position:0% +simple drivetrain it has a charger going + + + align:start position:0% +simple drivetrain it has a charger going +to a battery to a power converter to + + align:start position:0% +to a battery to a power converter to + + + align:start position:0% +to a battery to a power converter to +electric motor to the + + align:start position:0% +electric motor to the + + + align:start position:0% +electric motor to the +transmission a series uh electric + + align:start position:0% +transmission a series uh electric + + + align:start position:0% +transmission a series uh electric +vehicle has not only a battery a power + + align:start position:0% +vehicle has not only a battery a power + + + align:start position:0% +vehicle has not only a battery a power +converter you can generate P power from + + align:start position:0% +converter you can generate P power from + + + align:start position:0% +converter you can generate P power from +the fuel tank the internal combustion + + align:start position:0% +the fuel tank the internal combustion + + + align:start position:0% +the fuel tank the internal combustion +and convert power into electric motor + + align:start position:0% +and convert power into electric motor + + + align:start position:0% +and convert power into electric motor +which goes in transmission + + align:start position:0% +which goes in transmission + + + align:start position:0% +which goes in transmission +a series plugin hybrid electric vehicle + + align:start position:0% +a series plugin hybrid electric vehicle + + + align:start position:0% +a series plugin hybrid electric vehicle +has the ability to plug in to the wall + + align:start position:0% +has the ability to plug in to the wall + + + align:start position:0% +has the ability to plug in to the wall +power the battery power the converter or + + align:start position:0% +power the battery power the converter or + + + align:start position:0% +power the battery power the converter or +you can also put gas into a fuel tank + + align:start position:0% +you can also put gas into a fuel tank + + + align:start position:0% +you can also put gas into a fuel tank +that drives the contr combustion engine + + align:start position:0% +that drives the contr combustion engine + + + align:start position:0% +that drives the contr combustion engine +that runs a generator that creates + + align:start position:0% +that runs a generator that creates + + + align:start position:0% +that runs a generator that creates +electricity that goes into a + + align:start position:0% +electricity that goes into a + + + align:start position:0% +electricity that goes into a +transmission and then you have a fuel + + align:start position:0% +transmission and then you have a fuel + + + align:start position:0% +transmission and then you have a fuel +cell electric vehicle where the fuel + + align:start position:0% +cell electric vehicle where the fuel + + + align:start position:0% +cell electric vehicle where the fuel +cell essentially is another way of + + align:start position:0% +cell essentially is another way of + + + align:start position:0% +cell essentially is another way of +storing electricity whether from + + align:start position:0% +storing electricity whether from + + + align:start position:0% +storing electricity whether from +gasoline or from natural gas or whether + + align:start position:0% +gasoline or from natural gas or whether + + + align:start position:0% +gasoline or from natural gas or whether +not from hydrogen there's a fuel cell + + align:start position:0% +not from hydrogen there's a fuel cell + + + align:start position:0% +not from hydrogen there's a fuel cell +stack the fuel cell stack use to run a + + align:start position:0% +stack the fuel cell stack use to run a + + + align:start position:0% +stack the fuel cell stack use to run a +generator which creates electricity the + + align:start position:0% +generator which creates electricity the + + + align:start position:0% +generator which creates electricity the +battery can also be charged from outside + + align:start position:0% +battery can also be charged from outside + + + align:start position:0% +battery can also be charged from outside +the vehicle which all Drive the + + align:start position:0% +the vehicle which all Drive the + + + align:start position:0% +the vehicle which all Drive the +transmission again so this is to say + + align:start position:0% +transmission again so this is to say + + + align:start position:0% +transmission again so this is to say +that there's many different possible + + align:start position:0% +that there's many different possible + + + align:start position:0% +that there's many different possible +drivetrains uh for the kind of Mobility + + align:start position:0% +drivetrains uh for the kind of Mobility + + + align:start position:0% +drivetrains uh for the kind of Mobility +Services you want in passenger + + align:start position:0% +Services you want in passenger + + + align:start position:0% +Services you want in passenger +vehicles just to do a few simple + + align:start position:0% +vehicles just to do a few simple + + + align:start position:0% +vehicles just to do a few simple +calculations to illustrate the amount of + + align:start position:0% +calculations to illustrate the amount of + + + align:start position:0% +calculations to illustrate the amount of +energy we need per service or per + + align:start position:0% +energy we need per service or per + + + align:start position:0% +energy we need per service or per +distance we want to go for an internal + + align:start position:0% +distance we want to go for an internal + + + align:start position:0% +distance we want to go for an internal +combustion engine that gets SUV that + + align:start position:0% +combustion engine that gets SUV that + + + align:start position:0% +combustion engine that gets SUV that +gets let's say 22 miles per gallon kind + + align:start position:0% +gets let's say 22 miles per gallon kind + + + align:start position:0% +gets let's say 22 miles per gallon kind +of generous for most SUVs to be honest + + align:start position:0% +of generous for most SUVs to be honest + + + align:start position:0% +of generous for most SUVs to be honest +uh we have the energy density of the + + align:start position:0% +uh we have the energy density of the + + + align:start position:0% +uh we have the energy density of the +fuel which is 10 kilowatt hours per + + align:start position:0% +fuel which is 10 kilowatt hours per + + + align:start position:0% +fuel which is 10 kilowatt hours per +liter that's the that's the figure from + + align:start position:0% +liter that's the that's the figure from + + + align:start position:0% +liter that's the that's the figure from +maai we multiply times the inverse of + + align:start position:0% +maai we multiply times the inverse of + + + align:start position:0% +maai we multiply times the inverse of +gallons per 22 miles we convert liters + + align:start position:0% +gallons per 22 miles we convert liters + + + align:start position:0% +gallons per 22 miles we convert liters +to gallon we convert miles to kilometers + + align:start position:0% +to gallon we convert miles to kilometers + + + align:start position:0% +to gallon we convert miles to kilometers +and we multiply times 100 so we get 100 + + align:start position:0% +and we multiply times 100 so we get 100 + + + align:start position:0% +and we multiply times 100 so we get 100 +kilowatt hours per 100 kilomet this is + + align:start position:0% +kilowatt hours per 100 kilomet this is + + + align:start position:0% +kilowatt hours per 100 kilomet this is +simply dimensional analysis so you cross + + align:start position:0% +simply dimensional analysis so you cross + + + align:start position:0% +simply dimensional analysis so you cross +cross out liters top and bottom cross + + align:start position:0% +cross out liters top and bottom cross + + + align:start position:0% +cross out liters top and bottom cross +out gallons top and bottom cross out + + align:start position:0% +out gallons top and bottom cross out + + + align:start position:0% +out gallons top and bottom cross out +miles top top and bottom I just want to + + align:start position:0% +miles top top and bottom I just want to + + + align:start position:0% +miles top top and bottom I just want to +show you how to convert some of these + + align:start position:0% +show you how to convert some of these + + + align:start position:0% +show you how to convert some of these +metric or SI units to Imperial numbers + + align:start position:0% +metric or SI units to Imperial numbers + + + align:start position:0% +metric or SI units to Imperial numbers +that we might be more familiar with or + + align:start position:0% +that we might be more familiar with or + + + align:start position:0% +that we might be more familiar with or +imperial or us system measurement if we + + align:start position:0% +imperial or us system measurement if we + + + align:start position:0% +imperial or us system measurement if we +take the same calculation for Toyota + + align:start position:0% +take the same calculation for Toyota + + + align:start position:0% +take the same calculation for Toyota +Prius which is a hybrid vehicle we put + + align:start position:0% +Prius which is a hybrid vehicle we put + + + align:start position:0% +Prius which is a hybrid vehicle we put +in the energy + + align:start position:0% +in the energy + + + align:start position:0% +in the energy +density per volume of the gasoline that + + align:start position:0% +density per volume of the gasoline that + + + align:start position:0% +density per volume of the gasoline that +goes in but as we know Priuses are + + align:start position:0% +goes in but as we know Priuses are + + + align:start position:0% +goes in but as we know Priuses are +drastically more efficient because they + + align:start position:0% +drastically more efficient because they + + + align:start position:0% +drastically more efficient because they +have the Hybrid battery to help them + + align:start position:0% +have the Hybrid battery to help them + + + align:start position:0% +have the Hybrid battery to help them +store energy from breaking so you take + + align:start position:0% +store energy from breaking so you take + + + align:start position:0% +store energy from breaking so you take +the 10 kilowatt hours per liter divided + + align:start position:0% +the 10 kilowatt hours per liter divided + + + align:start position:0% +the 10 kilowatt hours per liter divided +by 56 miles per gallon so this 56 + + align:start position:0% +by 56 miles per gallon so this 56 + + + align:start position:0% +by 56 miles per gallon so this 56 +decreases the energy consumption by + + align:start position:0% +decreases the energy consumption by + + + align:start position:0% +decreases the energy consumption by +factor of two all the other factors are + + align:start position:0% +factor of two all the other factors are + + + align:start position:0% +factor of two all the other factors are +the same and you can see that we get to + + align:start position:0% +the same and you can see that we get to + + + align:start position:0% +the same and you can see that we get to +43 kilowatt hours per 100 K kilometers + + align:start position:0% +43 kilowatt hours per 100 K kilometers + + + align:start position:0% +43 kilowatt hours per 100 K kilometers +traveled for our Prius and of course EES + + align:start position:0% +traveled for our Prius and of course EES + + + align:start position:0% +traveled for our Prius and of course EES +according to makai's research assumption + + align:start position:0% +according to makai's research assumption + + + align:start position:0% +according to makai's research assumption +in 2009 get about 100 km for every 15 or + + align:start position:0% +in 2009 get about 100 km for every 15 or + + + align:start position:0% +in 2009 get about 100 km for every 15 or +20 kilowatt hours of energy going in so + + align:start position:0% +20 kilowatt hours of energy going in so + + + align:start position:0% +20 kilowatt hours of energy going in so +if you want to kind of do a simple + + align:start position:0% +if you want to kind of do a simple + + + align:start position:0% +if you want to kind of do a simple +summary of what this means you can see + + align:start position:0% +summary of what this means you can see + + + align:start position:0% +summary of what this means you can see +that there's multiples between these + + align:start position:0% +that there's multiples between these + + + align:start position:0% +that there's multiples between these +different vehicle types you can see that + + align:start position:0% +different vehicle types you can see that + + + align:start position:0% +different vehicle types you can see that +the difference between SUV versus an + + align:start position:0% +the difference between SUV versus an + + + align:start position:0% +the difference between SUV versus an +electric vehicle is five to seven times + + align:start position:0% +electric vehicle is five to seven times + + + align:start position:0% +electric vehicle is five to seven times +more efficient in electric vehicle even + + align:start position:0% +more efficient in electric vehicle even + + + align:start position:0% +more efficient in electric vehicle even +between a hybrid vehicle and electric + + align:start position:0% +between a hybrid vehicle and electric + + + align:start position:0% +between a hybrid vehicle and electric +vehicle it's two to three times more + + align:start position:0% +vehicle it's two to three times more + + + align:start position:0% +vehicle it's two to three times more +efficient so this is our argument for + + align:start position:0% +efficient so this is our argument for + + + align:start position:0% +efficient so this is our argument for +electrification this is why electric + + align:start position:0% +electrification this is why electric + + + align:start position:0% +electrification this is why electric +vehicle + + align:start position:0% +vehicle + + + align:start position:0% +vehicle +are so efficient and why we're trying to + + align:start position:0% +are so efficient and why we're trying to + + + align:start position:0% +are so efficient and why we're trying to +pursue electric + + align:start position:0% +pursue electric + + + align:start position:0% +pursue electric +vehicles if we look at the Mi at all + + align:start position:0% +vehicles if we look at the Mi at all + + + align:start position:0% +vehicles if we look at the Mi at all +paper in figure one you can see that + + align:start position:0% +paper in figure one you can see that + + + align:start position:0% +paper in figure one you can see that +basically every single battery electric + + align:start position:0% +basically every single battery electric + + + align:start position:0% +basically every single battery electric +vehicle symbolized here in the yellow uh + + align:start position:0% +vehicle symbolized here in the yellow uh + + + align:start position:0% +vehicle symbolized here in the yellow uh +area envelope is lower energy + + align:start position:0% +area envelope is lower energy + + + align:start position:0% +area envelope is lower energy +consumption than pretty much every + + align:start position:0% +consumption than pretty much every + + + align:start position:0% +consumption than pretty much every +hybrid vehicle uh lower sorry vehicle + + align:start position:0% +hybrid vehicle uh lower sorry vehicle + + + align:start position:0% +hybrid vehicle uh lower sorry vehicle +and fuel life cycle greenhouse gas + + align:start position:0% +and fuel life cycle greenhouse gas + + + align:start position:0% +and fuel life cycle greenhouse gas +emissions which are very closely + + align:start position:0% +emissions which are very closely + + + align:start position:0% +emissions which are very closely +associated with how much energy they + + align:start position:0% +associated with how much energy they + + + align:start position:0% +associated with how much energy they +consume and you can see that there's + + align:start position:0% +consume and you can see that there's + + + align:start position:0% +consume and you can see that there's +envelope es stretching along the + + align:start position:0% +envelope es stretching along the + + + align:start position:0% +envelope es stretching along the +horizontal axis because we know that + + align:start position:0% +horizontal axis because we know that + + + align:start position:0% +horizontal axis because we know that +some of these cars are more expensive + + align:start position:0% +some of these cars are more expensive + + + align:start position:0% +some of these cars are more expensive +than others a electric Chevrolet Spark + + align:start position:0% +than others a electric Chevrolet Spark + + + align:start position:0% +than others a electric Chevrolet Spark +is much cheaper in terms of vehicle fuel + + align:start position:0% +is much cheaper in terms of vehicle fuel + + + align:start position:0% +is much cheaper in terms of vehicle fuel +and maintenance cost than a Tesla Model + + align:start position:0% +and maintenance cost than a Tesla Model + + + align:start position:0% +and maintenance cost than a Tesla Model +S of course the Tesla Model S is more + + align:start position:0% +S of course the Tesla Model S is more + + + align:start position:0% +S of course the Tesla Model S is more +expensive but much lower life cycle + + align:start position:0% +expensive but much lower life cycle + + + align:start position:0% +expensive but much lower life cycle +greous gas emissions than pretty much + + align:start position:0% +greous gas emissions than pretty much + + + align:start position:0% +greous gas emissions than pretty much +all the fuel or hybrid vehicles out + + align:start position:0% +all the fuel or hybrid vehicles out + + + align:start position:0% +all the fuel or hybrid vehicles out +here you also might notice that all of + + align:start position:0% +here you also might notice that all of + + + align:start position:0% +here you also might notice that all of +the uh gasoline combustion engine + + align:start position:0% +the uh gasoline combustion engine + + + align:start position:0% +the uh gasoline combustion engine +Vehicles here with the black dots do not + + align:start position:0% +Vehicles here with the black dots do not + + + align:start position:0% +Vehicles here with the black dots do not +meet our 2030 targets for the Paris + + align:start position:0% +meet our 2030 targets for the Paris + + + align:start position:0% +meet our 2030 targets for the Paris +climate agreement some of our hybrid + + align:start position:0% +climate agreement some of our hybrid + + + align:start position:0% +climate agreement some of our hybrid +vehicles do get under the 2030 Target + + align:start position:0% +vehicles do get under the 2030 Target + + + align:start position:0% +vehicles do get under the 2030 Target +and all pretty much all battery electric + + align:start position:0% +and all pretty much all battery electric + + + align:start position:0% +and all pretty much all battery electric +vehicles meet our 2030 targets but do + + align:start position:0% +vehicles meet our 2030 targets but do + + + align:start position:0% +vehicles meet our 2030 targets but do +not meet our 2040 Targets in fact if you + + align:start position:0% +not meet our 2040 Targets in fact if you + + + align:start position:0% +not meet our 2040 Targets in fact if you +look at all the vehicles on this chart + + align:start position:0% +look at all the vehicles on this chart + + + align:start position:0% +look at all the vehicles on this chart +there are no vehicles that meet our 2040 + + align:start position:0% +there are no vehicles that meet our 2040 + + + align:start position:0% +there are no vehicles that meet our 2040 +or 2050 targets we still have some time + + align:start position:0% +or 2050 targets we still have some time + + + align:start position:0% +or 2050 targets we still have some time +before those years we have 18 years + + align:start position:0% +before those years we have 18 years + + + align:start position:0% +before those years we have 18 years +until 2040 so we can still develop new + + align:start position:0% +until 2040 so we can still develop new + + + align:start position:0% +until 2040 so we can still develop new +vehicles that hopefully meet those + + align:start position:0% +vehicles that hopefully meet those + + + align:start position:0% +vehicles that hopefully meet those +requirements but right now it's worth + + align:start position:0% +requirements but right now it's worth + + + align:start position:0% +requirements but right now it's worth +saying that none of our vehicles today + + align:start position:0% +saying that none of our vehicles today + + + align:start position:0% +saying that none of our vehicles today +that are commercially available meet our + + align:start position:0% +that are commercially available meet our + + + align:start position:0% +that are commercially available meet our +2040 or 2050 Paris climate agreement + + align:start position:0% +2040 or 2050 Paris climate agreement + + + align:start position:0% +2040 or 2050 Paris climate agreement +targets that is also uh those are + + align:start position:0% +targets that is also uh those are + + + align:start position:0% +targets that is also uh those are +capital assets that individual consumers + + align:start position:0% +capital assets that individual consumers + + + align:start position:0% +capital assets that individual consumers +and uh countries will have to invest in + + align:start position:0% +and uh countries will have to invest in + + + align:start position:0% +and uh countries will have to invest in +so we can meet our Paris climate + + align:start position:0% +so we can meet our Paris climate + + + align:start position:0% +so we can meet our Paris climate +agreement + + align:start position:0% +agreement + + + align:start position:0% +agreement +targets if you look at all the ways that + + align:start position:0% +targets if you look at all the ways that + + + align:start position:0% +targets if you look at all the ways that +we can try to improve our existing + + align:start position:0% +we can try to improve our existing + + + align:start position:0% +we can try to improve our existing +powertrain or drivet train Technologies + + align:start position:0% +powertrain or drivet train Technologies + + + align:start position:0% +powertrain or drivet train Technologies +on the graph here figure four from Mi at + + align:start position:0% +on the graph here figure four from Mi at + + + align:start position:0% +on the graph here figure four from Mi at +all paper you can look the average + + align:start position:0% +all paper you can look the average + + + align:start position:0% +all paper you can look the average +emissions based on 2014 models in terms + + align:start position:0% +emissions based on 2014 models in terms + + + align:start position:0% +emissions based on 2014 models in terms +of grams of CO2 equivalent per kilometer + + align:start position:0% +of grams of CO2 equivalent per kilometer + + + align:start position:0% +of grams of CO2 equivalent per kilometer +and you can see all the different + + align:start position:0% +and you can see all the different + + + align:start position:0% +and you can see all the different +vertical bars represent different drivve + + align:start position:0% +vertical bars represent different drivve + + + align:start position:0% +vertical bars represent different drivve +Trin or powertrain + + align:start position:0% +Trin or powertrain + + + align:start position:0% +Trin or powertrain +Technologies and what we can do what + + align:start position:0% +Technologies and what we can do what + + + align:start position:0% +Technologies and what we can do what +this graph tells us is that if we do a + + align:start position:0% +this graph tells us is that if we do a + + + align:start position:0% +this graph tells us is that if we do a +series of things to try to improve each + + align:start position:0% +series of things to try to improve each + + + align:start position:0% +series of things to try to improve each +technology how far can we put these + + align:start position:0% +technology how far can we put these + + + align:start position:0% +technology how far can we put these +Technologies so we could try to uh start + + align:start position:0% +Technologies so we could try to uh start + + + align:start position:0% +Technologies so we could try to uh start +with the sales weighted average of 2014 + + align:start position:0% +with the sales weighted average of 2014 + + + align:start position:0% +with the sales weighted average of 2014 +models these are new cars or basic trims + + align:start position:0% +models these are new cars or basic trims + + + align:start position:0% +models these are new cars or basic trims +we can for each of these Technologies + + align:start position:0% +we can for each of these Technologies + + + align:start position:0% +we can for each of these Technologies +try to downsize two compact cars uh in + + align:start position:0% +try to downsize two compact cars uh in + + + align:start position:0% +try to downsize two compact cars uh in +the electric using Technologies like + + align:start position:0% +the electric using Technologies like + + + align:start position:0% +the electric using Technologies like +electric vehicles or Plugin hybrids we + + align:start position:0% +electric vehicles or Plugin hybrids we + + + align:start position:0% +electric vehicles or Plugin hybrids we +can increase the amount of low carbon + + align:start position:0% +can increase the amount of low carbon + + + align:start position:0% +can increase the amount of low carbon +electricity available we can make the + + align:start position:0% +electricity available we can make the + + + align:start position:0% +electricity available we can make the +maximum efficiency improvements and in + + align:start position:0% +maximum efficiency improvements and in + + + align:start position:0% +maximum efficiency improvements and in +some cases we could try to use best case + + align:start position:0% +some cases we could try to use best case + + + align:start position:0% +some cases we could try to use best case +biofuels and of course in the best case + + align:start position:0% +biofuels and of course in the best case + + + align:start position:0% +biofuels and of course in the best case +for all these Technologies we do all the + + align:start position:0% +for all these Technologies we do all the + + + align:start position:0% +for all these Technologies we do all the +above things and you can see that + + align:start position:0% +above things and you can see that + + + align:start position:0% +above things and you can see that +there's fundamental limitations to + + align:start position:0% +there's fundamental limitations to + + + align:start position:0% +there's fundamental limitations to +different powertrain Technologies for + + align:start position:0% +different powertrain Technologies for + + + align:start position:0% +different powertrain Technologies for +internal + + align:start position:0% +internal + + + align:start position:0% +internal +combustion uh Vehicles internal + + align:start position:0% +combustion uh Vehicles internal + + + align:start position:0% +combustion uh Vehicles internal +combustion vehicles that use gasoline we + + align:start position:0% +combustion vehicles that use gasoline we + + + align:start position:0% +combustion vehicles that use gasoline we +can only better get better than our 2030 + + align:start position:0% +can only better get better than our 2030 + + + align:start position:0% +can only better get better than our 2030 +targets but we can't get to our 2040 + + align:start position:0% +targets but we can't get to our 2040 + + + align:start position:0% +targets but we can't get to our 2040 +targets for internal combustion engine + + align:start position:0% +targets for internal combustion engine + + + align:start position:0% +targets for internal combustion engine +vehicles that use E85 that's ethanol + + align:start position:0% +vehicles that use E85 that's ethanol + + + align:start position:0% +vehicles that use E85 that's ethanol +fuel uh 15% ethanol fuel I think I think + + align:start position:0% +fuel uh 15% ethanol fuel I think I think + + + align:start position:0% +fuel uh 15% ethanol fuel I think I think +uh you can see that we can barely meet + + align:start position:0% +uh you can see that we can barely meet + + + align:start position:0% +uh you can see that we can barely meet +our 2040 T 2030 targets but sorry 2040 + + align:start position:0% +our 2040 T 2030 targets but sorry 2040 + + + align:start position:0% +our 2040 T 2030 targets but sorry 2040 +targets but we can't meet our 2050 + + align:start position:0% +targets but we can't meet our 2050 + + + align:start position:0% +targets but we can't meet our 2050 +targets it is possible with internal + + align:start position:0% +targets it is possible with internal + + + align:start position:0% +targets it is possible with internal +combustion engine Vehicles such as + + align:start position:0% +combustion engine Vehicles such as + + + align:start position:0% +combustion engine Vehicles such as +diesel to get below our 2050 targets if + + align:start position:0% +diesel to get below our 2050 targets if + + + align:start position:0% +diesel to get below our 2050 targets if +we pull out all the stops of course that + + align:start position:0% +we pull out all the stops of course that + + + align:start position:0% +we pull out all the stops of course that +ignores the fact that diesel had severe + + align:start position:0% +ignores the fact that diesel had severe + + + align:start position:0% +ignores the fact that diesel had severe +air pollution impacts also something + + align:start position:0% +air pollution impacts also something + + + align:start position:0% +air pollution impacts also something +seen in many European cities uh the + + align:start position:0% +seen in many European cities uh the + + + align:start position:0% +seen in many European cities uh the +reason why we see let's say a lot of old + + align:start position:0% +reason why we see let's say a lot of old + + + align:start position:0% +reason why we see let's say a lot of old +statues um degraded um or their features + + align:start position:0% +statues um degraded um or their features + + + align:start position:0% +statues um degraded um or their features +are starting to be worn away is from + + align:start position:0% +are starting to be worn away is from + + + align:start position:0% +are starting to be worn away is from +diesel fumes they also have severe + + align:start position:0% +diesel fumes they also have severe + + + align:start position:0% +diesel fumes they also have severe +Health impacts if you look at hybri + + align:start position:0% +Health impacts if you look at hybri + + + align:start position:0% +Health impacts if you look at hybri +electric vehicles and plugin Hy electric + + align:start position:0% +electric vehicles and plugin Hy electric + + + align:start position:0% +electric vehicles and plugin Hy electric +vehicles they are much better but barely + + align:start position:0% +vehicles they are much better but barely + + + align:start position:0% +vehicles they are much better but barely +barely get to our uh within range of our + + align:start position:0% +barely get to our uh within range of our + + + align:start position:0% +barely get to our uh within range of our +2040 targets the only technology here + + align:start position:0% +2040 targets the only technology here + + + align:start position:0% +2040 targets the only technology here +that can exceed our 2050 targets our + + align:start position:0% +that can exceed our 2050 targets our + + + align:start position:0% +that can exceed our 2050 targets our +battery electric vehicles or fuel cell + + align:start position:0% +battery electric vehicles or fuel cell + + + align:start position:0% +battery electric vehicles or fuel cell +Vehicles where the uh vehicle where the + + align:start position:0% +Vehicles where the uh vehicle where the + + + align:start position:0% +Vehicles where the uh vehicle where the +energy is from + + align:start position:0% +energy is from + + + align:start position:0% +energy is from +electrolysis uh where in other words we + + align:start position:0% +electrolysis uh where in other words we + + + align:start position:0% +electrolysis uh where in other words we +use renewable resources to create + + align:start position:0% +use renewable resources to create + + + align:start position:0% +use renewable resources to create +hydrogen and the hydrogen used is used + + align:start position:0% +hydrogen and the hydrogen used is used + + + align:start position:0% +hydrogen and the hydrogen used is used +to Power Fuel Cell Vehicles fuel cell + + align:start position:0% +to Power Fuel Cell Vehicles fuel cell + + + align:start position:0% +to Power Fuel Cell Vehicles fuel cell +vehicles are a technology that's being + + align:start position:0% +vehicles are a technology that's being + + + align:start position:0% +vehicles are a technology that's being +uh tested in the Toyota marai and pilot + + align:start position:0% +uh tested in the Toyota marai and pilot + + + align:start position:0% +uh tested in the Toyota marai and pilot +uh Sals of the marai in places like + + align:start position:0% +uh Sals of the marai in places like + + + align:start position:0% +uh Sals of the marai in places like +California they have not been terribly + + align:start position:0% +California they have not been terribly + + + align:start position:0% +California they have not been terribly +popular yet and there's a real question + + align:start position:0% +popular yet and there's a real question + + + align:start position:0% +popular yet and there's a real question +they'll ever become as popular as + + align:start position:0% +they'll ever become as popular as + + + align:start position:0% +they'll ever become as popular as +battery electric vehicles which are + + align:start position:0% +battery electric vehicles which are + + + align:start position:0% +battery electric vehicles which are +taking off very quickly as I showed you + + align:start position:0% +taking off very quickly as I showed you + + + align:start position:0% +taking off very quickly as I showed you +on previous slides + + align:start position:0% +on previous slides + + + align:start position:0% +on previous slides +so here's a fundamental question you + + align:start position:0% +so here's a fundamental question you + + + align:start position:0% +so here's a fundamental question you +know if we're looking at Mai's book + + align:start position:0% +know if we're looking at Mai's book + + + align:start position:0% +know if we're looking at Mai's book +which was written in 2009 let's ask + + align:start position:0% +which was written in 2009 let's ask + + + align:start position:0% +which was written in 2009 let's ask +ourselves have electric vehicles changed + + align:start position:0% +ourselves have electric vehicles changed + + + align:start position:0% +ourselves have electric vehicles changed +since Mai's book and we can do figure + + align:start position:0% +since Mai's book and we can do figure + + + align:start position:0% +since Mai's book and we can do figure +this out by looking at a fairly simple + + align:start position:0% +this out by looking at a fairly simple + + + align:start position:0% +this out by looking at a fairly simple +set of numbers that you can look up from + + align:start position:0% +set of numbers that you can look up from + + + align:start position:0% +set of numbers that you can look up from +any manufacturer or Car and Driver + + align:start position:0% +any manufacturer or Car and Driver + + + align:start position:0% +any manufacturer or Car and Driver +magazine or Consumer Reports what have + + align:start position:0% +magazine or Consumer Reports what have + + + align:start position:0% +magazine or Consumer Reports what have +you let's look at makai's assumptions in + + align:start position:0% +you let's look at makai's assumptions in + + + align:start position:0% +you let's look at makai's assumptions in +2009 he assumes that we get we have + + align:start position:0% +2009 he assumes that we get we have + + + align:start position:0% +2009 he assumes that we get we have +about 15 kilowatt hours of energy to get + + align:start position:0% +about 15 kilowatt hours of energy to get + + + align:start position:0% +about 15 kilowatt hours of energy to get +about 100 kilm of range that's his + + align:start position:0% +about 100 kilm of range that's his + + + align:start position:0% +about 100 kilm of range that's his +estimate about 15 kilowatt hours per 100 + + align:start position:0% +estimate about 15 kilowatt hours per 100 + + + align:start position:0% +estimate about 15 kilowatt hours per 100 +kilm his conservative estimate is a + + align:start position:0% +kilm his conservative estimate is a + + + align:start position:0% +kilm his conservative estimate is a +higher amount of energy per 100 kilm 20 + + align:start position:0% +higher amount of energy per 100 kilm 20 + + + align:start position:0% +higher amount of energy per 100 kilm 20 +kilowatt hours per 100 kilometers and + + align:start position:0% +kilowatt hours per 100 kilometers and + + + align:start position:0% +kilowatt hours per 100 kilometers and +let's compare this to the Tesla roader + + align:start position:0% +let's compare this to the Tesla roader + + + align:start position:0% +let's compare this to the Tesla roader +which was first sold in 2008 it got + + align:start position:0% +which was first sold in 2008 it got + + + align:start position:0% +which was first sold in 2008 it got +about has about a capacity of 53 kilow + + align:start position:0% +about has about a capacity of 53 kilow + + + align:start position:0% +about has about a capacity of 53 kilow +hours in its battery this is one of the + + align:start position:0% +hours in its battery this is one of the + + + align:start position:0% +hours in its battery this is one of the +small roadsters that Tesla first built + + align:start position:0% +small roadsters that Tesla first built + + + align:start position:0% +small roadsters that Tesla first built +it had a fairly limited range of 220 mil + + align:start position:0% +it had a fairly limited range of 220 mil + + + align:start position:0% +it had a fairly limited range of 220 mil +or 354 km + + align:start position:0% +or 354 km + + + align:start position:0% +or 354 km +and that means it calculates almost + + align:start position:0% +and that means it calculates almost + + + align:start position:0% +and that means it calculates almost +exactly to Mai's estimate in 2009 15 + + align:start position:0% +exactly to Mai's estimate in 2009 15 + + + align:start position:0% +exactly to Mai's estimate in 2009 15 +kilowatt hours per 100 + + align:start position:0% +kilowatt hours per 100 + + + align:start position:0% +kilowatt hours per 100 +kilometers of course makai's numbers + + align:start position:0% +kilometers of course makai's numbers + + + align:start position:0% +kilometers of course makai's numbers +were based on just a few electric + + align:start position:0% +were based on just a few electric + + + align:start position:0% +were based on just a few electric +vehicles available at the time very + + align:start position:0% +vehicles available at the time very + + + align:start position:0% +vehicles available at the time very +famously the Tesla Roser was relatively + + align:start position:0% +famously the Tesla Roser was relatively + + + align:start position:0% +famously the Tesla Roser was relatively +expensive uh Elon Musk was very clear + + align:start position:0% +expensive uh Elon Musk was very clear + + + align:start position:0% +expensive uh Elon Musk was very clear +about using high cost almost bespoke + + align:start position:0% +about using high cost almost bespoke + + + align:start position:0% +about using high cost almost bespoke +built electric vehicles to subsidize + + align:start position:0% +built electric vehicles to subsidize + + + align:start position:0% +built electric vehicles to subsidize +building of manufacturing of more + + align:start position:0% +building of manufacturing of more + + + align:start position:0% +building of manufacturing of more +electric vehicles + + align:start position:0% +electric vehicles + + + align:start position:0% +electric vehicles +so uh that is exactly what Tesla did + + align:start position:0% +so uh that is exactly what Tesla did + + + align:start position:0% +so uh that is exactly what Tesla did +they built the Tesla S which is a much + + align:start position:0% +they built the Tesla S which is a much + + + align:start position:0% +they built the Tesla S which is a much +larger passenger vehicle the Tesla X + + align:start position:0% +larger passenger vehicle the Tesla X + + + align:start position:0% +larger passenger vehicle the Tesla X +which was their uh SUV version they had + + align:start position:0% +which was their uh SUV version they had + + + align:start position:0% +which was their uh SUV version they had +much higher capacities or much larger + + align:start position:0% +much higher capacities or much larger + + + align:start position:0% +much higher capacities or much larger +batteries they had increased ranges but + + align:start position:0% +batteries they had increased ranges but + + + align:start position:0% +batteries they had increased ranges but +you can see that actually of all things + + align:start position:0% +you can see that actually of all things + + + align:start position:0% +you can see that actually of all things +they go more towards makai's + + align:start position:0% +they go more towards makai's + + + align:start position:0% +they go more towards makai's +conservative estimate for vehicles + + align:start position:0% +conservative estimate for vehicles + + + align:start position:0% +conservative estimate for vehicles +because they had much larger form + + align:start position:0% +because they had much larger form + + + align:start position:0% +because they had much larger form +factors and much larger weight they + + align:start position:0% +factors and much larger weight they + + + align:start position:0% +factors and much larger weight they +actually required more energy to go the + + align:start position:0% +actually required more energy to go the + + + align:start position:0% +actually required more energy to go the +same amount of distance and you can see + + align:start position:0% +same amount of distance and you can see + + + align:start position:0% +same amount of distance and you can see +their costs were very high $80,000 for a + + align:start position:0% +their costs were very high $80,000 for a + + + align:start position:0% +their costs were very high $80,000 for a +Tesla S $83,000 I think for the base + + align:start position:0% +Tesla S $83,000 I think for the base + + + align:start position:0% +Tesla S $83,000 I think for the base +model the Tesla X and you can start to + + align:start position:0% +model the Tesla X and you can start to + + + align:start position:0% +model the Tesla X and you can start to +calculate their energy per distance per + + align:start position:0% +calculate their energy per distance per + + + align:start position:0% +calculate their energy per distance per +cost this is just to show you how you + + align:start position:0% +cost this is just to show you how you + + + align:start position:0% +cost this is just to show you how you +can take very simple numbers and start + + align:start position:0% +can take very simple numbers and start + + + align:start position:0% +can take very simple numbers and start +to calculate a basic metric to compare + + align:start position:0% +to calculate a basic metric to compare + + + align:start position:0% +to calculate a basic metric to compare +different models of course the Chevy + + align:start position:0% +different models of course the Chevy + + + align:start position:0% +different models of course the Chevy +Bolt the GM model that I mentioned that + + align:start position:0% +Bolt the GM model that I mentioned that + + + align:start position:0% +Bolt the GM model that I mentioned that +was introduced in 2016 had a smaller + + align:start position:0% +was introduced in 2016 had a smaller + + + align:start position:0% +was introduced in 2016 had a smaller +battery pack it had a lower range but + + align:start position:0% +battery pack it had a lower range but + + + align:start position:0% +battery pack it had a lower range but +started to get closer again to the uh + + align:start position:0% +started to get closer again to the uh + + + align:start position:0% +started to get closer again to the uh +estimate from aai in 2009 16 kilowatt + + align:start position:0% +estimate from aai in 2009 16 kilowatt + + + align:start position:0% +estimate from aai in 2009 16 kilowatt +hours per 100 kilometers but the DraStic + + align:start position:0% +hours per 100 kilometers but the DraStic + + + align:start position:0% +hours per 100 kilometers but the DraStic +change from the Teslas was that they + + align:start position:0% +change from the Teslas was that they + + + align:start position:0% +change from the Teslas was that they +only charged + + align:start position:0% +only charged + + + align:start position:0% +only charged +$337,000 for the initial model driving + + align:start position:0% +$337,000 for the initial model driving + + + align:start position:0% +$337,000 for the initial model driving +the energy per distance per cost way + + align:start position:0% +the energy per distance per cost way + + + align:start position:0% +the energy per distance per cost way +down if you look at the Tesla 3 which + + align:start position:0% +down if you look at the Tesla 3 which + + + align:start position:0% +down if you look at the Tesla 3 which +was introduced in 2017 you can see that + + align:start position:0% +was introduced in 2017 you can see that + + + align:start position:0% +was introduced in 2017 you can see that +they have a comparable B battery packs + + align:start position:0% +they have a comparable B battery packs + + + align:start position:0% +they have a comparable B battery packs +for both the standard and the the long + + align:start position:0% +for both the standard and the the long + + + align:start position:0% +for both the standard and the the long +range versions they have slightly longer + + align:start position:0% +range versions they have slightly longer + + + align:start position:0% +range versions they have slightly longer +ranges because um or they have + + align:start position:0% +ranges because um or they have + + + align:start position:0% +ranges because um or they have +comparable ranges to the Tesla Roadster + + align:start position:0% +comparable ranges to the Tesla Roadster + + + align:start position:0% +comparable ranges to the Tesla Roadster +or the long range model which has a + + align:start position:0% +or the long range model which has a + + + align:start position:0% +or the long range model which has a +larger battery pack but you can see that + + align:start position:0% +larger battery pack but you can see that + + + align:start position:0% +larger battery pack but you can see that +fundamentally the amount of energy used + + align:start position:0% +fundamentally the amount of energy used + + + align:start position:0% +fundamentally the amount of energy used +per distance has not changed again what + + align:start position:0% +per distance has not changed again what + + + align:start position:0% +per distance has not changed again what +they're doing is competing in terms of + + align:start position:0% +they're doing is competing in terms of + + + align:start position:0% +they're doing is competing in terms of +price now because we're trying to reach + + align:start position:0% +price now because we're trying to reach + + + align:start position:0% +price now because we're trying to reach +the broader part of the market that can + + align:start position:0% +the broader part of the market that can + + + align:start position:0% +the broader part of the market that can +afford $40,000 cars rather $80,000 cars + + align:start position:0% +afford $40,000 cars rather $80,000 cars + + + align:start position:0% +afford $40,000 cars rather $80,000 cars +and you can see that the Tesla basically + + align:start position:0% +and you can see that the Tesla basically + + + align:start position:0% +and you can see that the Tesla basically +comes in roughly in the same ballpark as + + align:start position:0% +comes in roughly in the same ballpark as + + + align:start position:0% +comes in roughly in the same ballpark as +the Chevy bolts they are directly + + align:start position:0% +the Chevy bolts they are directly + + + align:start position:0% +the Chevy bolts they are directly +competing the Tesla long range is more + + align:start position:0% +competing the Tesla long range is more + + + align:start position:0% +competing the Tesla long range is more +expensive simply because you're paying + + align:start position:0% +expensive simply because you're paying + + + align:start position:0% +expensive simply because you're paying +for that range even if the fundamental + + align:start position:0% +for that range even if the fundamental + + + align:start position:0% +for that range even if the fundamental +technology in terms of energy per + + align:start position:0% +technology in terms of energy per + + + align:start position:0% +technology in terms of energy per +distance is not more efficient and of + + align:start position:0% +distance is not more efficient and of + + + align:start position:0% +distance is not more efficient and of +course what we're seeing now is a + + align:start position:0% +course what we're seeing now is a + + + align:start position:0% +course what we're seeing now is a +manufacturers like Hyundai and Kia large + + align:start position:0% +manufacturers like Hyundai and Kia large + + + align:start position:0% +manufacturers like Hyundai and Kia large +Korean automakers starting to crowd into + + align:start position:0% +Korean automakers starting to crowd into + + + align:start position:0% +Korean automakers starting to crowd into +the same Market you can see that they've + + align:start position:0% +the same Market you can see that they've + + + align:start position:0% +the same Market you can see that they've +almost standardized their models on a 64 + + align:start position:0% +almost standardized their models on a 64 + + + align:start position:0% +almost standardized their models on a 64 +KW hour battery pack they're starting to + + align:start position:0% +KW hour battery pack they're starting to + + + align:start position:0% +KW hour battery pack they're starting to +get long longer ranges with the same + + align:start position:0% +get long longer ranges with the same + + + align:start position:0% +get long longer ranges with the same +size battery pack because battery + + align:start position:0% +size battery pack because battery + + + align:start position:0% +size battery pack because battery +technologies have advanced but + + align:start position:0% +technologies have advanced but + + + align:start position:0% +technologies have advanced but +fundamentally the efficiency of these + + align:start position:0% +fundamentally the efficiency of these + + + align:start position:0% +fundamentally the efficiency of these +vehicles hasn't changed that much it's + + align:start position:0% +vehicles hasn't changed that much it's + + + align:start position:0% +vehicles hasn't changed that much it's +17 14 16 kilowatt hours per 100 + + align:start position:0% +17 14 16 kilowatt hours per 100 + + + align:start position:0% +17 14 16 kilowatt hours per 100 +kilometer what's fundamentally changed + + align:start position:0% +kilometer what's fundamentally changed + + + align:start position:0% +kilometer what's fundamentally changed +is the cost of these vehicles these + + align:start position:0% +is the cost of these vehicles these + + + align:start position:0% +is the cost of these vehicles these +vehicles are all meant to be sold around + + align:start position:0% +vehicles are all meant to be sold around + + + align:start position:0% +vehicles are all meant to be sold around +$40,000 and you can see in terms of the + + align:start position:0% +$40,000 and you can see in terms of the + + + align:start position:0% +$40,000 and you can see in terms of the +energy times cost divided by distance + + align:start position:0% +energy times cost divided by distance + + + align:start position:0% +energy times cost divided by distance +you can see that their cost is going + + align:start position:0% +you can see that their cost is going + + + align:start position:0% +you can see that their cost is going +down driving this metric + + align:start position:0% +down driving this metric + + + align:start position:0% +down driving this metric +lower this is we most compet tion is + + align:start position:0% +lower this is we most compet tion is + + + align:start position:0% +lower this is we most compet tion is +occurring but my point is the + + align:start position:0% +occurring but my point is the + + + align:start position:0% +occurring but my point is the +fundamental technology under battery + + align:start position:0% +fundamental technology under battery + + + align:start position:0% +fundamental technology under battery +electric vehicles has not changed that + + align:start position:0% +electric vehicles has not changed that + + + align:start position:0% +electric vehicles has not changed that +much over the last 12 or 13 years simply + + align:start position:0% +much over the last 12 or 13 years simply + + + align:start position:0% +much over the last 12 or 13 years simply +because they're pretty simple they have + + align:start position:0% +because they're pretty simple they have + + + align:start position:0% +because they're pretty simple they have +a battery they have electric motor + + align:start position:0% +a battery they have electric motor + + + align:start position:0% +a battery they have electric motor +depending on how many luxury items or + + align:start position:0% +depending on how many luxury items or + + + align:start position:0% +depending on how many luxury items or +how big the form factor is that might + + align:start position:0% +how big the form factor is that might + + + align:start position:0% +how big the form factor is that might +affect the efficiency but the + + align:start position:0% +affect the efficiency but the + + + align:start position:0% +affect the efficiency but the +fundamental technology is fairly simple + + align:start position:0% +fundamental technology is fairly simple + + + align:start position:0% +fundamental technology is fairly simple +a battery uh based mostly on lithium + + align:start position:0% +a battery uh based mostly on lithium + + + align:start position:0% +a battery uh based mostly on lithium +cells driving electric motor some cars + + align:start position:0% +cells driving electric motor some cars + + + align:start position:0% +cells driving electric motor some cars +might have all-wheel drive with multiple + + align:start position:0% +might have all-wheel drive with multiple + + + align:start position:0% +might have all-wheel drive with multiple +electric motors they're all roughly the + + align:start position:0% +electric motors they're all roughly the + + + align:start position:0% +electric motors they're all roughly the +same efficiency but the cost is going + + align:start position:0% +same efficiency but the cost is going + + + align:start position:0% +same efficiency but the cost is going +down as we adopt more electric vehicles + + align:start position:0% +down as we adopt more electric vehicles + + + align:start position:0% +down as we adopt more electric vehicles +and as more manufacturers compete in the + + align:start position:0% +and as more manufacturers compete in the + + + align:start position:0% +and as more manufacturers compete in the +market so one question you might have is + + align:start position:0% +market so one question you might have is + + + align:start position:0% +market so one question you might have is +what about the carbon of the electricity + + align:start position:0% +what about the carbon of the electricity + + + align:start position:0% +what about the carbon of the electricity +that's going to electric vehicles itself + + align:start position:0% +that's going to electric vehicles itself + + + align:start position:0% +that's going to electric vehicles itself +and this is worth pointing out it's a + + align:start position:0% +and this is worth pointing out it's a + + + align:start position:0% +and this is worth pointing out it's a +question that maai answers in his book + + align:start position:0% +question that maai answers in his book + + + align:start position:0% +question that maai answers in his book +his question is you've shown the + + align:start position:0% +his question is you've shown the + + + align:start position:0% +his question is you've shown the +electric cars are more energy efficient + + align:start position:0% +electric cars are more energy efficient + + + align:start position:0% +electric cars are more energy efficient +than fossil cars but are they better if + + align:start position:0% +than fossil cars but are they better if + + + align:start position:0% +than fossil cars but are they better if +our objective is to reduce the CO2 + + align:start position:0% +our objective is to reduce the CO2 + + + align:start position:0% +our objective is to reduce the CO2 +emissions and the electricity is still + + align:start position:0% +emissions and the electricity is still + + + align:start position:0% +emissions and the electricity is still +generated by f fuel power stations using + + align:start position:0% +generated by f fuel power stations using + + + align:start position:0% +generated by f fuel power stations using +Ma's reasoning I again encourage you to + + align:start position:0% +Ma's reasoning I again encourage you to + + + align:start position:0% +Ma's reasoning I again encourage you to +go back to the book If you haven't read + + align:start position:0% +go back to the book If you haven't read + + + align:start position:0% +go back to the book If you haven't read +this part this is a quite easy + + align:start position:0% +this part this is a quite easy + + + align:start position:0% +this part this is a quite easy +calculation to do assume the electric + + align:start position:0% +calculation to do assume the electric + + + align:start position:0% +calculation to do assume the electric +vehicle's energy cost is 20 kilowatt + + align:start position:0% +vehicle's energy cost is 20 kilowatt + + + align:start position:0% +vehicle's energy cost is 20 kilowatt +hours of electricity for 100 kilometers + + align:start position:0% +hours of electricity for 100 kilometers + + + align:start position:0% +hours of electricity for 100 kilometers +that's his conservative estimate if the + + align:start position:0% +that's his conservative estimate if the + + + align:start position:0% +that's his conservative estimate if the +Grid electricity has a carbon foit of + + align:start position:0% +Grid electricity has a carbon foit of + + + align:start position:0% +Grid electricity has a carbon foit of +500 grams of CO2 per kilowatt hour of + + align:start position:0% +500 grams of CO2 per kilowatt hour of + + + align:start position:0% +500 grams of CO2 per kilowatt hour of +electricity then the effective emissions + + align:start position:0% +electricity then the effective emissions + + + align:start position:0% +electricity then the effective emissions +of this car are 100 gr CO2 perometer + + align:start position:0% +of this car are 100 gr CO2 perometer + + + align:start position:0% +of this car are 100 gr CO2 perometer +which is as good as the best fossil cars + + align:start position:0% +which is as good as the best fossil cars + + + align:start position:0% +which is as good as the best fossil cars +2009 fossil cars have unfortunately not + + align:start position:0% +2009 fossil cars have unfortunately not + + + align:start position:0% +2009 fossil cars have unfortunately not +gotten that much better since 2009 so + + align:start position:0% +gotten that much better since 2009 so + + + align:start position:0% +gotten that much better since 2009 so +maai could conclude in 2009 that + + align:start position:0% +maai could conclude in 2009 that + + + align:start position:0% +maai could conclude in 2009 that +electric cars are already a good idea + + align:start position:0% +electric cars are already a good idea + + + align:start position:0% +electric cars are already a good idea +even before we green our electricity + + align:start position:0% +even before we green our electricity + + + align:start position:0% +even before we green our electricity +Supply if we look at more recent + + align:start position:0% +Supply if we look at more recent + + + align:start position:0% +Supply if we look at more recent +calculations from the union of concerned + + align:start position:0% +calculations from the union of concerned + + + align:start position:0% +calculations from the union of concerned +scientists they do a miles per gallon + + align:start position:0% +scientists they do a miles per gallon + + + align:start position:0% +scientists they do a miles per gallon +calculation equivalent comparing what + + align:start position:0% +calculation equivalent comparing what + + + align:start position:0% +calculation equivalent comparing what +the grid energy is and what the + + align:start position:0% +the grid energy is and what the + + + align:start position:0% +the grid energy is and what the +emissions are of the grid energy as a + + align:start position:0% +emissions are of the grid energy as a + + + align:start position:0% +emissions are of the grid energy as a +gas miles per gon equivalent this is why + + align:start position:0% +gas miles per gon equivalent this is why + + + align:start position:0% +gas miles per gon equivalent this is why +if you buy a new car you'll see + + align:start position:0% +if you buy a new car you'll see + + + align:start position:0% +if you buy a new car you'll see +mpge or the miles per gallon equivalent + + align:start position:0% +mpge or the miles per gallon equivalent + + + align:start position:0% +mpge or the miles per gallon equivalent +for electric cars but if you calculate + + align:start position:0% +for electric cars but if you calculate + + + align:start position:0% +for electric cars but if you calculate +backwards and show the gasoline miles + + align:start position:0% +backwards and show the gasoline miles + + + align:start position:0% +backwards and show the gasoline miles +per gallon equivalent is of the Grid + + align:start position:0% +per gallon equivalent is of the Grid + + + align:start position:0% +per gallon equivalent is of the Grid +electricity you'll see that places like + + align:start position:0% +electricity you'll see that places like + + + align:start position:0% +electricity you'll see that places like +California or the Northwest that have + + align:start position:0% +California or the Northwest that have + + + align:start position:0% +California or the Northwest that have +relatively low Bon gas emissions in + + align:start position:0% +relatively low Bon gas emissions in + + + align:start position:0% +relatively low Bon gas emissions in +their electricity mix have amazingly + + align:start position:0% +their electricity mix have amazingly + + + align:start position:0% +their electricity mix have amazingly +high miles per gallon in miles per + + align:start position:0% +high miles per gallon in miles per + + + align:start position:0% +high miles per gallon in miles per +gallon equivalent gasoline in other + + align:start position:0% +gallon equivalent gasoline in other + + + align:start position:0% +gallon equivalent gasoline in other +words grid electricity in California is + + align:start position:0% +words grid electricity in California is + + + align:start position:0% +words grid electricity in California is +relative clean that's the equivalent + + align:start position:0% +relative clean that's the equivalent + + + align:start position:0% +relative clean that's the equivalent +terms of greenhouse gas emissions of + + align:start position:0% +terms of greenhouse gas emissions of + + + align:start position:0% +terms of greenhouse gas emissions of +getting 134 miles per gallon so you can + + align:start position:0% +getting 134 miles per gallon so you can + + + align:start position:0% +getting 134 miles per gallon so you can +basically completely out compete by a + + align:start position:0% +basically completely out compete by a + + + align:start position:0% +basically completely out compete by a +factor for any fossil fuel cars uh here + + align:start position:0% +factor for any fossil fuel cars uh here + + + align:start position:0% +factor for any fossil fuel cars uh here +in New England we have uh an Upstate New + + align:start position:0% +in New England we have uh an Upstate New + + + align:start position:0% +in New England we have uh an Upstate New +York because of hydrop power they have + + align:start position:0% +York because of hydrop power they have + + + align:start position:0% +York because of hydrop power they have +amazingly clean energy 255 miles per + + align:start position:0% +amazingly clean energy 255 miles per + + + align:start position:0% +amazingly clean energy 255 miles per +gallon gasoline equivalent uh here in + + align:start position:0% +gallon gasoline equivalent uh here in + + + align:start position:0% +gallon gasoline equivalent uh here in +New England we have 122 miles per gallon + + align:start position:0% +New England we have 122 miles per gallon + + + align:start position:0% +New England we have 122 miles per gallon +equivalent but the key thing is even in + + align:start position:0% +equivalent but the key thing is even in + + + align:start position:0% +equivalent but the key thing is even in +places like the Midwest that relies + + align:start position:0% +places like the Midwest that relies + + + align:start position:0% +places like the Midwest that relies +heavily on relatively dirty sources of + + align:start position:0% +heavily on relatively dirty sources of + + + align:start position:0% +heavily on relatively dirty sources of +electricity like Coal fire power plants + + align:start position:0% +electricity like Coal fire power plants + + + align:start position:0% +electricity like Coal fire power plants +you can see that most places in the + + align:start position:0% +you can see that most places in the + + + align:start position:0% +you can see that most places in the +midwest get about 60 miles per gallon + + align:start position:0% +midwest get about 60 miles per gallon + + + align:start position:0% +midwest get about 60 miles per gallon +equivalent in other words if you get an + + align:start position:0% +equivalent in other words if you get an + + + align:start position:0% +equivalent in other words if you get an +electric vehicle you're getting the + + align:start position:0% +electric vehicle you're getting the + + + align:start position:0% +electric vehicle you're getting the +equivalent of 60 miles per gallon + + align:start position:0% +equivalent of 60 miles per gallon + + + align:start position:0% +equivalent of 60 miles per gallon +electricity in terms of greous gas + + align:start position:0% +electricity in terms of greous gas + + + align:start position:0% +electricity in terms of greous gas +emissions only two places in the US uh + + align:start position:0% +emissions only two places in the US uh + + + align:start position:0% +emissions only two places in the US uh +looks like Minnesota and parts of the + + align:start position:0% +looks like Minnesota and parts of the + + + align:start position:0% +looks like Minnesota and parts of the +Midwest get relatively low greenhouse + + align:start position:0% +Midwest get relatively low greenhouse + + + align:start position:0% +Midwest get relatively low greenhouse +gas gas efficiencies from electricity 41 + + align:start position:0% +gas gas efficiencies from electricity 41 + + + align:start position:0% +gas gas efficiencies from electricity 41 +miles per gallon 43 miles per gallon + + align:start position:0% +miles per gallon 43 miles per gallon + + + align:start position:0% +miles per gallon 43 miles per gallon +that's lower than you could get with a + + align:start position:0% +that's lower than you could get with a + + + align:start position:0% +that's lower than you could get with a +comparable hybrid in those places if you + + align:start position:0% +comparable hybrid in those places if you + + + align:start position:0% +comparable hybrid in those places if you +simply powered a hybrid from gasoline + + align:start position:0% +simply powered a hybrid from gasoline + + + align:start position:0% +simply powered a hybrid from gasoline +but most cars are not hybrids and the + + align:start position:0% +but most cars are not hybrids and the + + + align:start position:0% +but most cars are not hybrids and the +average US efficiency is something like + + align:start position:0% +average US efficiency is something like + + + align:start position:0% +average US efficiency is something like +20 25 miles per gallon so even in these + + align:start position:0% +20 25 miles per gallon so even in these + + + align:start position:0% +20 25 miles per gallon so even in these +places an electric vehicle can out + + align:start position:0% +places an electric vehicle can out + + + align:start position:0% +places an electric vehicle can out +compete your typical fossil fuel car if + + align:start position:0% +compete your typical fossil fuel car if + + + align:start position:0% +compete your typical fossil fuel car if +not your typical hybrid the average for + + align:start position:0% +not your typical hybrid the average for + + + align:start position:0% +not your typical hybrid the average for +all us electric vehicles is around 93 + + align:start position:0% +all us electric vehicles is around 93 + + + align:start position:0% +all us electric vehicles is around 93 +miles per gallon + + align:start position:0% +miles per gallon + + + align:start position:0% +miles per gallon +equivalent so this is to say that um in + + align:start position:0% +equivalent so this is to say that um in + + + align:start position:0% +equivalent so this is to say that um in +almost all cases from a on a just fuel + + align:start position:0% +almost all cases from a on a just fuel + + + align:start position:0% +almost all cases from a on a just fuel +basis uh we have much lower greenhouse + + align:start position:0% +basis uh we have much lower greenhouse + + + align:start position:0% +basis uh we have much lower greenhouse +gas emissions from electric vehicles uh + + align:start position:0% +gas emissions from electric vehicles uh + + + align:start position:0% +gas emissions from electric vehicles uh +the miat paper counted the vehicle and + + align:start position:0% +the miat paper counted the vehicle and + + + align:start position:0% +the miat paper counted the vehicle and +the fuel lifetime carbon emissions and + + align:start position:0% +the fuel lifetime carbon emissions and + + + align:start position:0% +the fuel lifetime carbon emissions and +all caves is there you also saw electric + + align:start position:0% +all caves is there you also saw electric + + + align:start position:0% +all caves is there you also saw electric +vehicles were lower emissions than + + align:start position:0% +vehicles were lower emissions than + + + align:start position:0% +vehicles were lower emissions than +hybrid vehicles or gasoline + + align:start position:0% +hybrid vehicles or gasoline + + + align:start position:0% +hybrid vehicles or gasoline +vehicles so this brings me to an article + + align:start position:0% +vehicles so this brings me to an article + + + align:start position:0% +vehicles so this brings me to an article +that I wish I included in the syllabus + + align:start position:0% +that I wish I included in the syllabus + + + align:start position:0% +that I wish I included in the syllabus +but didn't have time to because it only + + align:start position:0% +but didn't have time to because it only + + + align:start position:0% +but didn't have time to because it only +came out last week or so uh actually + + align:start position:0% +came out last week or so uh actually + + + align:start position:0% +came out last week or so uh actually +came from outside magazine and the + + align:start position:0% +came from outside magazine and the + + + align:start position:0% +came from outside magazine and the +headline is why you should buy an ebike + + align:start position:0% +headline is why you should buy an ebike + + + align:start position:0% +headline is why you should buy an ebike +instead of of an electric vehicle I have + + align:start position:0% +instead of of an electric vehicle I have + + + align:start position:0% +instead of of an electric vehicle I have +an electric bicycle I love it so I guess + + align:start position:0% +an electric bicycle I love it so I guess + + + align:start position:0% +an electric bicycle I love it so I guess +I'm encouraging you to read this article + + align:start position:0% +I'm encouraging you to read this article + + + align:start position:0% +I'm encouraging you to read this article +for that reason but also because the + + align:start position:0% +for that reason but also because the + + + align:start position:0% +for that reason but also because the +article is actually full of calculations + + align:start position:0% +article is actually full of calculations + + + align:start position:0% +article is actually full of calculations +for what the cost of ownership is for + + align:start position:0% +for what the cost of ownership is for + + + align:start position:0% +for what the cost of ownership is for +electric vehicle for a lot of people who + + align:start position:0% +electric vehicle for a lot of people who + + + align:start position:0% +electric vehicle for a lot of people who +are considering replacing their current + + align:start position:0% +are considering replacing their current + + + align:start position:0% +are considering replacing their current +fossil fuel cars the author Joe Lindsay + + align:start position:0% +fossil fuel cars the author Joe Lindsay + + + align:start position:0% +fossil fuel cars the author Joe Lindsay +argues that it's much better to actually + + align:start position:0% +argues that it's much better to actually + + + align:start position:0% +argues that it's much better to actually +add an ebike to your household rather + + align:start position:0% +add an ebike to your household rather + + + align:start position:0% +add an ebike to your household rather +than replacing your current car you + + align:start position:0% +than replacing your current car you + + + align:start position:0% +than replacing your current car you +might keep your fossil fuel car but if + + align:start position:0% +might keep your fossil fuel car but if + + + align:start position:0% +might keep your fossil fuel car but if +you try an ebike you might like it uh so + + align:start position:0% +you try an ebike you might like it uh so + + + align:start position:0% +you try an ebike you might like it uh so +much that you simply leave the car in + + align:start position:0% +much that you simply leave the car in + + + align:start position:0% +much that you simply leave the car in +the garage and only reserve it for long + + align:start position:0% +the garage and only reserve it for long + + + align:start position:0% +the garage and only reserve it for long +distance camping trips occasionally like + + align:start position:0% +distance camping trips occasionally like + + + align:start position:0% +distance camping trips occasionally like +the typical reader of an outside + + align:start position:0% +the typical reader of an outside + + + align:start position:0% +the typical reader of an outside +magazine might go on I'd also argue to + + align:start position:0% +magazine might go on I'd also argue to + + + align:start position:0% +magazine might go on I'd also argue to +you that electric bikes have a lot of + + align:start position:0% +you that electric bikes have a lot of + + + align:start position:0% +you that electric bikes have a lot of +advantages over electric cars or + + align:start position:0% +advantages over electric cars or + + + align:start position:0% +advantages over electric cars or +internal commuion cars for example I do + + align:start position:0% +internal commuion cars for example I do + + + align:start position:0% +internal commuion cars for example I do +a lot of errands on my electric bike I + + align:start position:0% +a lot of errands on my electric bike I + + + align:start position:0% +a lot of errands on my electric bike I +never have to park it I just pull up in + + align:start position:0% +never have to park it I just pull up in + + + align:start position:0% +never have to park it I just pull up in +front of a store or the library and I + + align:start position:0% +front of a store or the library and I + + + align:start position:0% +front of a store or the library and I +knock out six errands in my relatively + + align:start position:0% +knock out six errands in my relatively + + + align:start position:0% +knock out six errands in my relatively +dense suburb and under an hour so I can + + align:start position:0% +dense suburb and under an hour so I can + + + align:start position:0% +dense suburb and under an hour so I can +just cruise around avoid traffic parking + + align:start position:0% +just cruise around avoid traffic parking + + + align:start position:0% +just cruise around avoid traffic parking +that time savings is worth a lot for me + + align:start position:0% +that time savings is worth a lot for me + + + align:start position:0% +that time savings is worth a lot for me +as an for to buy an ebike and so this + + align:start position:0% +as an for to buy an ebike and so this + + + align:start position:0% +as an for to buy an ebike and so this +brings me to the idea of two and 3wh + + align:start position:0% +brings me to the idea of two and 3wh + + + align:start position:0% +brings me to the idea of two and 3wh +vehicles uh if you don't know what this + + align:start position:0% +vehicles uh if you don't know what this + + + align:start position:0% +vehicles uh if you don't know what this +is this is a Tuk tok a three-wheel + + align:start position:0% +is this is a Tuk tok a three-wheel + + + align:start position:0% +is this is a Tuk tok a three-wheel +vehicle also called a Rick Shaw + + align:start position:0% +vehicle also called a Rick Shaw + + + align:start position:0% +vehicle also called a Rick Shaw +sometimes and you can see this + + align:start position:0% +sometimes and you can see this + + + align:start position:0% +sometimes and you can see this +particular case it looks basically like + + align:start position:0% +particular case it looks basically like + + + align:start position:0% +particular case it looks basically like +a motorcycle up front it's got a cargo + + align:start position:0% +a motorcycle up front it's got a cargo + + + align:start position:0% +a motorcycle up front it's got a cargo +bed here in back where it looks like + + align:start position:0% +bed here in back where it looks like + + + align:start position:0% +bed here in back where it looks like +maybe five or six people could ride or + + align:start position:0% +maybe five or six people could ride or + + + align:start position:0% +maybe five or six people could ride or +cargo could be carried uh if you've ever + + align:start position:0% +cargo could be carried uh if you've ever + + + align:start position:0% +cargo could be carried uh if you've ever +been to uh very I countries in + + align:start position:0% +been to uh very I countries in + + + align:start position:0% +been to uh very I countries in +developing world like India or Thailand + + align:start position:0% +developing world like India or Thailand + + + align:start position:0% +developing world like India or Thailand +or um Subs Africa or parts of Latin + + align:start position:0% +or um Subs Africa or parts of Latin + + + align:start position:0% +or um Subs Africa or parts of Latin +America you'll see a lot of these two + + align:start position:0% +America you'll see a lot of these two + + + align:start position:0% +America you'll see a lot of these two +and three-wheel Vehicles they're called + + align:start position:0% +and three-wheel Vehicles they're called + + + align:start position:0% +and three-wheel Vehicles they're called +Tuk Tuk in Southeast Asia here's a + + align:start position:0% +Tuk Tuk in Southeast Asia here's a + + + align:start position:0% +Tuk Tuk in Southeast Asia here's a +picture of a Tuk Tuk traffic jam in + + align:start position:0% +picture of a Tuk Tuk traffic jam in + + + align:start position:0% +picture of a Tuk Tuk traffic jam in +Nigeria you can see that these are the + + align:start position:0% +Nigeria you can see that these are the + + + align:start position:0% +Nigeria you can see that these are the +prevalent form of vehicles you can see + + align:start position:0% +prevalent form of vehicles you can see + + + align:start position:0% +prevalent form of vehicles you can see +this uh relatively low density pickup + + align:start position:0% +this uh relatively low density pickup + + + align:start position:0% +this uh relatively low density pickup +truck in this traffic jam you can see + + align:start position:0% +truck in this traffic jam you can see + + + align:start position:0% +truck in this traffic jam you can see +one car going the opposite direction in + + align:start position:0% +one car going the opposite direction in + + + align:start position:0% +one car going the opposite direction in +this traffic jam + + align:start position:0% +this traffic jam + + + align:start position:0% +this traffic jam +but the vast majority of vehicles are + + align:start position:0% +but the vast majority of vehicles are + + + align:start position:0% +but the vast majority of vehicles are +Tuk toes and the reason why this is + + align:start position:0% +Tuk toes and the reason why this is + + + align:start position:0% +Tuk toes and the reason why this is +important we go back to the Bloomberg + + align:start position:0% +important we go back to the Bloomberg + + + align:start position:0% +important we go back to the Bloomberg +new energy U electric vehicle Outlook + + align:start position:0% +new energy U electric vehicle Outlook + + + align:start position:0% +new energy U electric vehicle Outlook +again and you can see that two and three + + align:start position:0% +again and you can see that two and three + + + align:start position:0% +again and you can see that two and three +wheel vehicles and Municipal buses this + + align:start position:0% +wheel vehicles and Municipal buses this + + + align:start position:0% +wheel vehicles and Municipal buses this +is their actual U breakdown of Road + + align:start position:0% +is their actual U breakdown of Road + + + align:start position:0% +is their actual U breakdown of Road +Transport segment progress towards Net + + align:start position:0% +Transport segment progress towards Net + + + align:start position:0% +Transport segment progress towards Net +Zero from what they forecast you can see + + align:start position:0% +Zero from what they forecast you can see + + + align:start position:0% +Zero from what they forecast you can see +that two and three wheel vehicles and + + align:start position:0% +that two and three wheel vehicles and + + + align:start position:0% +that two and three wheel vehicles and +Municipal buses are actually almost on + + align:start position:0% +Municipal buses are actually almost on + + + align:start position:0% +Municipal buses are actually almost on +track to head hit a n zero scenario 100% + + align:start position:0% +track to head hit a n zero scenario 100% + + + align:start position:0% +track to head hit a n zero scenario 100% +zero electric vehicle share by + + align:start position:0% +zero electric vehicle share by + + + align:start position:0% +zero electric vehicle share by +2050 uh you can see that 74% of two + + align:start position:0% +2050 uh you can see that 74% of two + + + align:start position:0% +2050 uh you can see that 74% of two +wheelers will be zero Mission vehicles + + align:start position:0% +wheelers will be zero Mission vehicles + + + align:start position:0% +wheelers will be zero Mission vehicles +94% of three-wheelers will be electric + + align:start position:0% +94% of three-wheelers will be electric + + + align:start position:0% +94% of three-wheelers will be electric +vehicles and essentially with 1.1 + + align:start position:0% +vehicles and essentially with 1.1 + + + align:start position:0% +vehicles and essentially with 1.1 +billion of these vehicles already on the + + align:start position:0% +billion of these vehicles already on the + + + align:start position:0% +billion of these vehicles already on the +road 3.8 million Municipal buses on the + + align:start position:0% +road 3.8 million Municipal buses on the + + + align:start position:0% +road 3.8 million Municipal buses on the +road we are almost on track to hit our + + align:start position:0% +road we are almost on track to hit our + + + align:start position:0% +road we are almost on track to hit our +Net Zero scenarios where we need to do + + align:start position:0% +Net Zero scenarios where we need to do + + + align:start position:0% +Net Zero scenarios where we need to do +more work is in terms of passenger + + align:start position:0% +more work is in terms of passenger + + + align:start position:0% +more work is in terms of passenger +vehicles and Light commercial vehicles + + align:start position:0% +vehicles and Light commercial vehicles + + + align:start position:0% +vehicles and Light commercial vehicles +the kind of vehicles that Americans + + align:start position:0% +the kind of vehicles that Americans + + + align:start position:0% +the kind of vehicles that Americans +typically tend to drive and we need to + + align:start position:0% +typically tend to drive and we need to + + + align:start position:0% +typically tend to drive and we need to +make a lot of effort in terms of getting + + align:start position:0% +make a lot of effort in terms of getting + + + align:start position:0% +make a lot of effort in terms of getting +to net zero emissions from medium and + + align:start position:0% +to net zero emissions from medium and + + + align:start position:0% +to net zero emissions from medium and +heavy commercial vehicles as we know + + align:start position:0% +heavy commercial vehicles as we know + + + align:start position:0% +heavy commercial vehicles as we know +from planning cities that if we want to + + align:start position:0% +from planning cities that if we want to + + + align:start position:0% +from planning cities that if we want to +have more two and three wheel vehicles + + align:start position:0% +have more two and three wheel vehicles + + + align:start position:0% +have more two and three wheel vehicles +in developed countries like the us or + + align:start position:0% +in developed countries like the us or + + + align:start position:0% +in developed countries like the us or +low density countries like the us we + + align:start position:0% +low density countries like the us we + + + align:start position:0% +low density countries like the us we +need to improve our biking + + align:start position:0% +need to improve our biking + + + align:start position:0% +need to improve our biking +infrastructure or infrastructure in + + align:start position:0% +infrastructure or infrastructure in + + + align:start position:0% +infrastructure or infrastructure in +terms of allowing these two and + + align:start position:0% +terms of allowing these two and + + + align:start position:0% +terms of allowing these two and +three-wheel + + align:start position:0% +three-wheel + + + align:start position:0% +three-wheel +Vehicles mical buses are a uh + + align:start position:0% +Vehicles mical buses are a uh + + + align:start position:0% +Vehicles mical buses are a uh +already a costeffective alternative for + + align:start position:0% +already a costeffective alternative for + + + align:start position:0% +already a costeffective alternative for +transportation relatively convenient to + + align:start position:0% +transportation relatively convenient to + + + align:start position:0% +transportation relatively convenient to +charge because they go on the same route + + align:start position:0% +charge because they go on the same route + + + align:start position:0% +charge because they go on the same route +every day but we know that Municipal + + align:start position:0% +every day but we know that Municipal + + + align:start position:0% +every day but we know that Municipal +buses already still cost more upfront + + align:start position:0% +buses already still cost more upfront + + + align:start position:0% +buses already still cost more upfront +and so we're going to need incentives to + + align:start position:0% +and so we're going to need incentives to + + + align:start position:0% +and so we're going to need incentives to +get people over The Upfront cost even if + + align:start position:0% +get people over The Upfront cost even if + + + align:start position:0% +get people over The Upfront cost even if +their lifetime is comparable in terms of + + align:start position:0% +their lifetime is comparable in terms of + + + align:start position:0% +their lifetime is comparable in terms of +fuel + + align:start position:0% +fuel + + + align:start position:0% +fuel +cost and so this brings me to this + + align:start position:0% +cost and so this brings me to this + + + align:start position:0% +cost and so this brings me to this +headline which you probably saw a few + + align:start position:0% +headline which you probably saw a few + + + align:start position:0% +headline which you probably saw a few +weeks ago what to know about + + align:start position:0% +weeks ago what to know about + + + align:start position:0% +weeks ago what to know about +California's ban on new gasoline powered + + align:start position:0% +California's ban on new gasoline powered + + + align:start position:0% +California's ban on new gasoline powered +cars by 2035 California Shoppers looking + + align:start position:0% +cars by 2035 California Shoppers looking + + + align:start position:0% +cars by 2035 California Shoppers looking +for new vehicles will have to buy + + align:start position:0% +for new vehicles will have to buy + + + align:start position:0% +for new vehicles will have to buy +electric + + align:start position:0% +electric + + + align:start position:0% +electric +vehicles there won't be a ban on the + + align:start position:0% +vehicles there won't be a ban on the + + + align:start position:0% +vehicles there won't be a ban on the +internal combustion engine vehicles that + + align:start position:0% +internal combustion engine vehicles that + + + align:start position:0% +internal combustion engine vehicles that +already exist in California but if + + align:start position:0% +already exist in California but if + + + align:start position:0% +already exist in California but if +you're a shopper buying a new car or + + align:start position:0% +you're a shopper buying a new car or + + + align:start position:0% +you're a shopper buying a new car or +licensing a new vehicle in California + + align:start position:0% +licensing a new vehicle in California + + + align:start position:0% +licensing a new vehicle in California +you're probably going to have to license + + align:start position:0% +you're probably going to have to license + + + align:start position:0% +you're probably going to have to license +an electric car if it's a new vehicle + + align:start position:0% +an electric car if it's a new vehicle + + + align:start position:0% +an electric car if it's a new vehicle +and why is this important what I want to + + align:start position:0% +and why is this important what I want to + + + align:start position:0% +and why is this important what I want to +talk about is some of the policies that + + align:start position:0% +talk about is some of the policies that + + + align:start position:0% +talk about is some of the policies that +could be used to basically shape the + + align:start position:0% +could be used to basically shape the + + + align:start position:0% +could be used to basically shape the +international auto market how California + + align:start position:0% +international auto market how California + + + align:start position:0% +international auto market how California +has played a key role and I also like to + + align:start position:0% +has played a key role and I also like to + + + align:start position:0% +has played a key role and I also like to +tell the story about Mary Nichols Mary + + align:start position:0% +tell the story about Mary Nichols Mary + + + align:start position:0% +tell the story about Mary Nichols Mary +Nichols is um a 28-year-old law Yale law + + align:start position:0% +Nichols is um a 28-year-old law Yale law + + + align:start position:0% +Nichols is um a 28-year-old law Yale law +law graduate she successfully helps to + + align:start position:0% +law graduate she successfully helps to + + + align:start position:0% +law graduate she successfully helps to +sue EPA for not enforcing a Clean Air + + align:start position:0% +sue EPA for not enforcing a Clean Air + + + align:start position:0% +sue EPA for not enforcing a Clean Air +Act in + + align:start position:0% +Act in + + + align:start position:0% +Act in +1970 and this is building on efforts in + + align:start position:0% +1970 and this is building on efforts in + + + align:start position:0% +1970 and this is building on efforts in +the state of California to intervene in + + align:start position:0% +the state of California to intervene in + + + align:start position:0% +the state of California to intervene in +local Air Pollution issues that led to + + align:start position:0% +local Air Pollution issues that led to + + + align:start position:0% +local Air Pollution issues that led to +the design of air quality management + + align:start position:0% +the design of air quality management + + + align:start position:0% +the design of air quality management +districts and the California air + + align:start position:0% +districts and the California air + + + align:start position:0% +districts and the California air +resources board before the Us Clean Air + + align:start position:0% +resources board before the Us Clean Air + + + align:start position:0% +resources board before the Us Clean Air +Act was passed in 1970 + + align:start position:0% +Act was passed in 1970 + + + align:start position:0% +Act was passed in 1970 +so from these efforts both from the + + align:start position:0% +so from these efforts both from the + + + align:start position:0% +so from these efforts both from the +state of California and from these + + align:start position:0% +state of California and from these + + + align:start position:0% +state of California and from these +efforts by environmental groups to sue + + align:start position:0% +efforts by environmental groups to sue + + + align:start position:0% +efforts by environmental groups to sue +the EPA for not enforcing the Clean Air + + align:start position:0% +the EPA for not enforcing the Clean Air + + + align:start position:0% +the EPA for not enforcing the Clean Air +Act which was passed by Congress in 1970 + + align:start position:0% +Act which was passed by Congress in 1970 + + + align:start position:0% +Act which was passed by Congress in 1970 +they essentially push uh California's um + + align:start position:0% +they essentially push uh California's um + + + align:start position:0% +they essentially push uh California's um +California's regulations for vehicles + + align:start position:0% +California's regulations for vehicles + + + align:start position:0% +California's regulations for vehicles +and air pollution are essentially + + align:start position:0% +and air pollution are essentially + + + align:start position:0% +and air pollution are essentially +grandfathered into the Clean Air Act uh + + align:start position:0% +grandfathered into the Clean Air Act uh + + + align:start position:0% +grandfathered into the Clean Air Act uh +Mary Nichols joins the California a res + + align:start position:0% +Mary Nichols joins the California a res + + + align:start position:0% +Mary Nichols joins the California a res +resources board in 1975 becomes the + + align:start position:0% +resources board in 1975 becomes the + + + align:start position:0% +resources board in 1975 becomes the +chairman in 1979 + + align:start position:0% +chairman in 1979 + + + align:start position:0% +chairman in 1979 +and this is a picture of Mary Nichols + + align:start position:0% +and this is a picture of Mary Nichols + + + align:start position:0% +and this is a picture of Mary Nichols +more recently in the last decade she + + align:start position:0% +more recently in the last decade she + + + align:start position:0% +more recently in the last decade she +goes on to work at Bill Clinton's EPA + + align:start position:0% +goes on to work at Bill Clinton's EPA + + + align:start position:0% +goes on to work at Bill Clinton's EPA +1993 works on sulfur dioxide and acid + + align:start position:0% +1993 works on sulfur dioxide and acid + + + align:start position:0% +1993 works on sulfur dioxide and acid +rain she works on the first national + + align:start position:0% +rain she works on the first national + + + align:start position:0% +rain she works on the first national +limit for fine particulates and then + + align:start position:0% +limit for fine particulates and then + + + align:start position:0% +limit for fine particulates and then +rejoins the California air resources + + align:start position:0% +rejoins the California air resources + + + align:start position:0% +rejoins the California air resources +board in 2003 under Governor Arnold + + align:start position:0% +board in 2003 under Governor Arnold + + + align:start position:0% +board in 2003 under Governor Arnold +schweger and Governor Jerry Brown and + + align:start position:0% +schweger and Governor Jerry Brown and + + + align:start position:0% +schweger and Governor Jerry Brown and +this is to say that you know California + + align:start position:0% +this is to say that you know California + + + align:start position:0% +this is to say that you know California +always had a focus on air pollution + + align:start position:0% +always had a focus on air pollution + + + align:start position:0% +always had a focus on air pollution +before National efforts uh Mary Nichols + + align:start position:0% +before National efforts uh Mary Nichols + + + align:start position:0% +before National efforts uh Mary Nichols +is i' just like to use as an example of + + align:start position:0% +is i' just like to use as an example of + + + align:start position:0% +is i' just like to use as an example of +a young successful University graduate + + align:start position:0% +a young successful University graduate + + + align:start position:0% +a young successful University graduate +like many of you will be and how she + + align:start position:0% +like many of you will be and how she + + + align:start position:0% +like many of you will be and how she +gets involved in air pollution issues + + align:start position:0% +gets involved in air pollution issues + + + align:start position:0% +gets involved in air pollution issues +and how California's regulations which + + align:start position:0% +and how California's regulations which + + + align:start position:0% +and how California's regulations which +proceed the cleaner act enable + + align:start position:0% +proceed the cleaner act enable + + + align:start position:0% +proceed the cleaner act enable +California to pass successively more + + align:start position:0% +California to pass successively more + + + align:start position:0% +California to pass successively more +aggressive air pollution legislation or + + align:start position:0% +aggressive air pollution legislation or + + + align:start position:0% +aggressive air pollution legislation or +regulations and so to bring us back to + + align:start position:0% +regulations and so to bring us back to + + + align:start position:0% +regulations and so to bring us back to +how can you use these standards uh the + + align:start position:0% +how can you use these standards uh the + + + align:start position:0% +how can you use these standards uh the +California air resources aboard + + align:start position:0% +California air resources aboard + + + align:start position:0% +California air resources aboard +standards or Z zero emission V mandates + + align:start position:0% +standards or Z zero emission V mandates + + + align:start position:0% +standards or Z zero emission V mandates +how do you force large national + + align:start position:0% +how do you force large national + + + align:start position:0% +how do you force large national +International automakers to perform to + + align:start position:0% +International automakers to perform to + + + align:start position:0% +International automakers to perform to +your regulations well California is a + + align:start position:0% +your regulations well California is a + + + align:start position:0% +your regulations well California is a +large part of the US vehicle Market they + + align:start position:0% +large part of the US vehicle Market they + + + align:start position:0% +large part of the US vehicle Market they +decide their goal is going to be 22% of + + align:start position:0% +decide their goal is going to be 22% of + + + align:start position:0% +decide their goal is going to be 22% of +zero emission vehicles in 2025 just a + + align:start position:0% +zero emission vehicles in 2025 just a + + + align:start position:0% +zero emission vehicles in 2025 just a +few years from now and what they do + + align:start position:0% +few years from now and what they do + + + align:start position:0% +few years from now and what they do +quite effectively is join with other + + align:start position:0% +quite effectively is join with other + + + align:start position:0% +quite effectively is join with other +states they basically essentially form a + + align:start position:0% +states they basically essentially form a + + + align:start position:0% +states they basically essentially form a +coalition of zero zero emission vehicle + + align:start position:0% +coalition of zero zero emission vehicle + + + align:start position:0% +coalition of zero zero emission vehicle +States this is California plus 13 States + + align:start position:0% +States this is California plus 13 States + + + align:start position:0% +States this is California plus 13 States +including Massachusetts that adds about + + align:start position:0% +including Massachusetts that adds about + + + align:start position:0% +including Massachusetts that adds about +800,000 Vehicles as of course at this um + + align:start position:0% +800,000 Vehicles as of course at this um + + + align:start position:0% +800,000 Vehicles as of course at this um +when the Trump Administration tried to + + align:start position:0% +when the Trump Administration tried to + + + align:start position:0% +when the Trump Administration tried to +roll back emission standards that + + align:start position:0% +roll back emission standards that + + + align:start position:0% +roll back emission standards that +California these 13 states had basically + + align:start position:0% +California these 13 states had basically + + + align:start position:0% +California these 13 states had basically +passed 23 States actually sued to stop + + align:start position:0% +passed 23 States actually sued to stop + + + align:start position:0% +passed 23 States actually sued to stop +the roll backs of these um of these EPA + + align:start position:0% +the roll backs of these um of these EPA + + + align:start position:0% +the roll backs of these um of these EPA +standards in the fall of + + align:start position:0% +standards in the fall of + + + align:start position:0% +standards in the fall of +2019 even more States sued to stop the + + align:start position:0% +2019 even more States sued to stop the + + + align:start position:0% +2019 even more States sued to stop the +roll backs because once one large State + + align:start position:0% +roll backs because once one large State + + + align:start position:0% +roll backs because once one large State +like California has passed certain + + align:start position:0% +like California has passed certain + + + align:start position:0% +like California has passed certain +regulations automakers want to supply + + align:start position:0% +regulations automakers want to supply + + + align:start position:0% +regulations automakers want to supply +vehicles to that state once California + + align:start position:0% +vehicles to that state once California + + + align:start position:0% +vehicles to that state once California +joins with 13 other states that's a + + align:start position:0% +joins with 13 other states that's a + + + align:start position:0% +joins with 13 other states that's a +large fraction of the total Auto Sales + + align:start position:0% +large fraction of the total Auto Sales + + + align:start position:0% +large fraction of the total Auto Sales +in the United States which is itself a + + align:start position:0% +in the United States which is itself a + + + align:start position:0% +in the United States which is itself a +large Auto consuming country and 23 + + align:start position:0% +large Auto consuming country and 23 + + + align:start position:0% +large Auto consuming country and 23 +States Sue to stop these roll backs in + + align:start position:0% +States Sue to stop these roll backs in + + + align:start position:0% +States Sue to stop these roll backs in +Fall 2019 because States and automakers + + align:start position:0% +Fall 2019 because States and automakers + + + align:start position:0% +Fall 2019 because States and automakers +both like having some regulatory + + align:start position:0% +both like having some regulatory + + + align:start position:0% +both like having some regulatory +certainty and the industry and the + + align:start position:0% +certainty and the industry and the + + + align:start position:0% +certainty and the industry and the +states had already agreed on what the + + align:start position:0% +states had already agreed on what the + + + align:start position:0% +states had already agreed on what the +zero emission mandates or standards + + align:start position:0% +zero emission mandates or standards + + + align:start position:0% +zero emission mandates or standards +would + + align:start position:0% +would + + + align:start position:0% +would +be and one of the aspects of the zero + + align:start position:0% +be and one of the aspects of the zero + + + align:start position:0% +be and one of the aspects of the zero +emission standards or mandates from + + align:start position:0% +emission standards or mandates from + + + align:start position:0% +emission standards or mandates from +California is that manufact + + align:start position:0% +California is that manufact + + + align:start position:0% +California is that manufact +manufacturers have to make enough + + align:start position:0% +manufacturers have to make enough + + + align:start position:0% +manufacturers have to make enough +vehicles uh + + align:start position:0% +vehicles uh + + + align:start position:0% +vehicles uh +15.4% of all sales are in + + align:start position:0% +15.4% of all sales are in + + + align:start position:0% +15.4% of all sales are in +California and so this is basically + + align:start position:0% +California and so this is basically + + + align:start position:0% +California and so this is basically +essentially getting um entities like + + align:start position:0% +essentially getting um entities like + + + align:start position:0% +essentially getting um entities like +Volkswagen or Hyundai or kia if they are + + align:start position:0% +Volkswagen or Hyundai or kia if they are + + + align:start position:0% +Volkswagen or Hyundai or kia if they are +want to sell vehicles in California they + + align:start position:0% +want to sell vehicles in California they + + + align:start position:0% +want to sell vehicles in California they +have to uh formed to California + + align:start position:0% +have to uh formed to California + + + align:start position:0% +have to uh formed to California +standards and so some of the analysis + + align:start position:0% +standards and so some of the analysis + + + align:start position:0% +standards and so some of the analysis +that California air resources board does + + align:start position:0% +that California air resources board does + + + align:start position:0% +that California air resources board does +is that this is going to add about $1900 + + align:start position:0% +is that this is going to add about $1900 + + + align:start position:0% +is that this is going to add about $1900 +to the cost of a new vehicle but this + + align:start position:0% +to the cost of a new vehicle but this + + + align:start position:0% +to the cost of a new vehicle but this +efficiency or these fuel standards will + + align:start position:0% +efficiency or these fuel standards will + + + align:start position:0% +efficiency or these fuel standards will +pay for themselves in about 3 years we + + align:start position:0% +pay for themselves in about 3 years we + + + align:start position:0% +pay for themselves in about 3 years we +get a 47% reduction in greenhouse gas + + align:start position:0% +get a 47% reduction in greenhouse gas + + + align:start position:0% +get a 47% reduction in greenhouse gas +emissions compared to today and a 75% + + align:start position:0% +emissions compared to today and a 75% + + + align:start position:0% +emissions compared to today and a 75% +reduction in air pollution compared to + + align:start position:0% +reduction in air pollution compared to + + + align:start position:0% +reduction in air pollution compared to +today a summon one point worth noticing + + align:start position:0% +today a summon one point worth noticing + + + align:start position:0% +today a summon one point worth noticing +is that you know people in California + + align:start position:0% +is that you know people in California + + + align:start position:0% +is that you know people in California +care about greenhouse gas missions but + + align:start position:0% +care about greenhouse gas missions but + + + align:start position:0% +care about greenhouse gas missions but +these standards or these mandates + + align:start position:0% +these standards or these mandates + + + align:start position:0% +these standards or these mandates +started with local air pollution and + + align:start position:0% +started with local air pollution and + + + align:start position:0% +started with local air pollution and +smog when I was growing up Los Angeles + + align:start position:0% +smog when I was growing up Los Angeles + + + align:start position:0% +smog when I was growing up Los Angeles +was known as a quite smoggy Place air + + align:start position:0% +was known as a quite smoggy Place air + + + align:start position:0% +was known as a quite smoggy Place air +pollution has vastly improved in + + align:start position:0% +pollution has vastly improved in + + + align:start position:0% +pollution has vastly improved in +California leading to much better health + + align:start position:0% +California leading to much better health + + + align:start position:0% +California leading to much better health +outcomes and leading to these arguments + + align:start position:0% +outcomes and leading to these arguments + + + align:start position:0% +outcomes and leading to these arguments +that not only is it cost efficient it's + + align:start position:0% +that not only is it cost efficient it's + + + align:start position:0% +that not only is it cost efficient it's +also efficient in terms of what we spend + + align:start position:0% +also efficient in terms of what we spend + + + align:start position:0% +also efficient in terms of what we spend +on health care for chronic pulmonary + + align:start position:0% +on health care for chronic pulmonary + + + align:start position:0% +on health care for chronic pulmonary +heart disease or + + align:start position:0% +heart disease or + + + align:start position:0% +heart disease or +asthma and so California has led to + + align:start position:0% +asthma and so California has led to + + + align:start position:0% +asthma and so California has led to +successively more uh has passed + + align:start position:0% +successively more uh has passed + + + align:start position:0% +successively more uh has passed +successively more stringent standards + + align:start position:0% +successively more stringent standards + + + align:start position:0% +successively more stringent standards +and regulations as I said 2035 the goal + + align:start position:0% +and regulations as I said 2035 the goal + + + align:start position:0% +and regulations as I said 2035 the goal +is 100% of new Vehicles will be sold as + + align:start position:0% +is 100% of new Vehicles will be sold as + + + align:start position:0% +is 100% of new Vehicles will be sold as +zero emissions Vehicles there also be + + align:start position:0% +zero emissions Vehicles there also be + + + align:start position:0% +zero emissions Vehicles there also be +greater use of low carbon fuels being + + align:start position:0% +greater use of low carbon fuels being + + + align:start position:0% +greater use of low carbon fuels being +promoted such as hydrogen such as fuel + + align:start position:0% +promoted such as hydrogen such as fuel + + + align:start position:0% +promoted such as hydrogen such as fuel +sale vehicles by 2050 they'll be trying + + align:start position:0% +sale vehicles by 2050 they'll be trying + + + align:start position:0% +sale vehicles by 2050 they'll be trying +to phase out all the internal combustion + + align:start position:0% +to phase out all the internal combustion + + + align:start position:0% +to phase out all the internal combustion +engine cars so you won't be able to + + align:start position:0% +engine cars so you won't be able to + + + align:start position:0% +engine cars so you won't be able to +drive old gas cars uh still so currently + + align:start position:0% +drive old gas cars uh still so currently + + + align:start position:0% +drive old gas cars uh still so currently +we have almost 100% of all cars in + + align:start position:0% +we have almost 100% of all cars in + + + align:start position:0% +we have almost 100% of all cars in +California run on gas they're Target by + + align:start position:0% +California run on gas they're Target by + + + align:start position:0% +California run on gas they're Target by +250 is to have about 53% run on fuel + + align:start position:0% +250 is to have about 53% run on fuel + + + align:start position:0% +250 is to have about 53% run on fuel +cells because fuel cells and hydrogen + + align:start position:0% +cells because fuel cells and hydrogen + + + align:start position:0% +cells because fuel cells and hydrogen +are even more effici ient than battery + + align:start position:0% +are even more effici ient than battery + + + align:start position:0% +are even more effici ient than battery +electric vehicles are perspectively more + + align:start position:0% +electric vehicles are perspectively more + + + align:start position:0% +electric vehicles are perspectively more +efficient only 17% of cars in 2050 will + + align:start position:0% +efficient only 17% of cars in 2050 will + + + align:start position:0% +efficient only 17% of cars in 2050 will +still be running on battery electric + + align:start position:0% +still be running on battery electric + + + align:start position:0% +still be running on battery electric +vehicles 99.7% will be plug in and 21% + + align:start position:0% +vehicles 99.7% will be plug in and 21% + + + align:start position:0% +vehicles 99.7% will be plug in and 21% +will still be using gasoline that's + + align:start position:0% +will still be using gasoline that's + + + align:start position:0% +will still be using gasoline that's +their Target in 2050 but what you can + + align:start position:0% +their Target in 2050 but what you can + + + align:start position:0% +their Target in 2050 but what you can +see is also a very deliberate clear + + align:start position:0% +see is also a very deliberate clear + + + align:start position:0% +see is also a very deliberate clear +regulatory road map for automakers to + + align:start position:0% +regulatory road map for automakers to + + + align:start position:0% +regulatory road map for automakers to +follow the reason why a lot of + + align:start position:0% +follow the reason why a lot of + + + align:start position:0% +follow the reason why a lot of +automakers want to keep these standards + + align:start position:0% +automakers want to keep these standards + + + align:start position:0% +automakers want to keep these standards +is because they've already developed + + align:start position:0% +is because they've already developed + + + align:start position:0% +is because they've already developed +their technology Pathways or they've + + align:start position:0% +their technology Pathways or they've + + + align:start position:0% +their technology Pathways or they've +already designed their product for the + + align:start position:0% +already designed their product for the + + + align:start position:0% +already designed their product for the +future to meet these standards they + + align:start position:0% +future to meet these standards they + + + align:start position:0% +future to meet these standards they +don't want to see these standards + + align:start position:0% +don't want to see these standards + + + align:start position:0% +don't want to see these standards +fluctuating every four years depending + + align:start position:0% +fluctuating every four years depending + + + align:start position:0% +fluctuating every four years depending +on the occupant of the white + + align:start position:0% +on the occupant of the white + + + align:start position:0% +on the occupant of the white +house so let's talk a little bit about + + align:start position:0% +house so let's talk a little bit about + + + align:start position:0% +house so let's talk a little bit about +the inflation reduction act I just + + align:start position:0% +the inflation reduction act I just + + + align:start position:0% +the inflation reduction act I just +assigned these Hawkins and MJ Bradley + + align:start position:0% +assigned these Hawkins and MJ Bradley + + + align:start position:0% +assigned these Hawkins and MJ Bradley +articles to highlight some of the policy + + align:start position:0% +articles to highlight some of the policy + + + align:start position:0% +articles to highlight some of the policy +design of how the uh federal government + + align:start position:0% +design of how the uh federal government + + + align:start position:0% +design of how the uh federal government +is going to try to incentivize people to + + align:start position:0% +is going to try to incentivize people to + + + align:start position:0% +is going to try to incentivize people to +buy electric vehicles by getting over + + align:start position:0% +buy electric vehicles by getting over + + + align:start position:0% +buy electric vehicles by getting over +the higher upfront cost even if the + + align:start position:0% +the higher upfront cost even if the + + + align:start position:0% +the higher upfront cost even if the +future fuel cost is lower they've + + align:start position:0% +future fuel cost is lower they've + + + align:start position:0% +future fuel cost is lower they've +extended incentives for manufacturers + + align:start position:0% +extended incentives for manufacturers + + + align:start position:0% +extended incentives for manufacturers +over 200,000 Vehicles the California a + + align:start position:0% +over 200,000 Vehicles the California a + + + align:start position:0% +over 200,000 Vehicles the California a +res resources board uh was taking away + + align:start position:0% +res resources board uh was taking away + + + align:start position:0% +res resources board uh was taking away +incentives over 200,000 Vehicles because + + align:start position:0% +incentives over 200,000 Vehicles because + + + align:start position:0% +incentives over 200,000 Vehicles because +the idea with that incentives would + + align:start position:0% +the idea with that incentives would + + + align:start position:0% +the idea with that incentives would +simply get manufacturers to start + + align:start position:0% +simply get manufacturers to start + + + align:start position:0% +simply get manufacturers to start +building electric vehicles and they + + align:start position:0% +building electric vehicles and they + + + align:start position:0% +building electric vehicles and they +would need additional incentives of + + align:start position:0% +would need additional incentives of + + + align:start position:0% +would need additional incentives of +course three manufacturers passed over + + align:start position:0% +course three manufacturers passed over + + + align:start position:0% +course three manufacturers passed over +the 200,000 vehicle limit GM Tesla and + + align:start position:0% +the 200,000 vehicle limit GM Tesla and + + + align:start position:0% +the 200,000 vehicle limit GM Tesla and +Toyota and so they no longer got + + align:start position:0% +Toyota and so they no longer got + + + align:start position:0% +Toyota and so they no longer got +incentives meaning their cars were no + + align:start position:0% +incentives meaning their cars were no + + + align:start position:0% +incentives meaning their cars were no +longer cost competitive based on tax + + align:start position:0% +longer cost competitive based on tax + + + align:start position:0% +longer cost competitive based on tax +incentives even though the idea is that + + align:start position:0% +incentives even though the idea is that + + + align:start position:0% +incentives even though the idea is that +they start making up vehicles that they + + align:start position:0% +they start making up vehicles that they + + + align:start position:0% +they start making up vehicles that they +can learn enough and get to enough + + align:start position:0% +can learn enough and get to enough + + + align:start position:0% +can learn enough and get to enough +economies of scale that they can compete + + align:start position:0% +economies of scale that they can compete + + + align:start position:0% +economies of scale that they can compete +without tax incentives one difference in + + align:start position:0% +without tax incentives one difference in + + + align:start position:0% +without tax incentives one difference in +the inflation reduction Act is that it + + align:start position:0% +the inflation reduction Act is that it + + + align:start position:0% +the inflation reduction Act is that it +gives point of sale tax rebates for EVS + + align:start position:0% +gives point of sale tax rebates for EVS + + + align:start position:0% +gives point of sale tax rebates for EVS +to overcome those higher UPR costs uh + + align:start position:0% +to overcome those higher UPR costs uh + + + align:start position:0% +to overcome those higher UPR costs uh +the point of sale tax rebate means that + + align:start position:0% +the point of sale tax rebate means that + + + align:start position:0% +the point of sale tax rebate means that +the consumer immediately sees the lower + + align:start position:0% +the consumer immediately sees the lower + + + align:start position:0% +the consumer immediately sees the lower +cost of the vehicle rather than waiting + + align:start position:0% +cost of the vehicle rather than waiting + + + align:start position:0% +cost of the vehicle rather than waiting +for a tax return credit when they file + + align:start position:0% +for a tax return credit when they file + + + align:start position:0% +for a tax return credit when they file +their taxes uh the inflation reduction + + align:start position:0% +their taxes uh the inflation reduction + + + align:start position:0% +their taxes uh the inflation reduction +act also as a firsttime tax fee bait for + + align:start position:0% +act also as a firsttime tax fee bait for + + + align:start position:0% +act also as a firsttime tax fee bait for +used electric vehicles I think $4,000 to + + align:start position:0% +used electric vehicles I think $4,000 to + + + align:start position:0% +used electric vehicles I think $4,000 to +create a secondary market for electric + + align:start position:0% +create a secondary market for electric + + + align:start position:0% +create a secondary market for electric +vehicles to encourage people to buy + + align:start position:0% +vehicles to encourage people to buy + + + align:start position:0% +vehicles to encourage people to buy +electric vehicles knowing that the the + + align:start position:0% +electric vehicles knowing that the the + + + align:start position:0% +electric vehicles knowing that the the +subse person buying the vehicle from + + align:start position:0% +subse person buying the vehicle from + + + align:start position:0% +subse person buying the vehicle from +them will be subsidized so that it + + align:start position:0% +them will be subsidized so that it + + + align:start position:0% +them will be subsidized so that it +maintain resale value uh funny thing is + + align:start position:0% +maintain resale value uh funny thing is + + + align:start position:0% +maintain resale value uh funny thing is +if you look for a used electric vehicle + + align:start position:0% +if you look for a used electric vehicle + + + align:start position:0% +if you look for a used electric vehicle +you'll quite often see electric vehicles + + align:start position:0% +you'll quite often see electric vehicles + + + align:start position:0% +you'll quite often see electric vehicles +that are actually relatively high in + + align:start position:0% +that are actually relatively high in + + + align:start position:0% +that are actually relatively high in +price as you used vehicles but because + + align:start position:0% +price as you used vehicles but because + + + align:start position:0% +price as you used vehicles but because +the first owner got a tax incentive uh + + align:start position:0% +the first owner got a tax incentive uh + + + align:start position:0% +the first owner got a tax incentive uh +the subsequent owner even with a low + + align:start position:0% +the subsequent owner even with a low + + + align:start position:0% +the subsequent owner even with a low +mileage vehicle will pay much more than + + align:start position:0% +mileage vehicle will pay much more than + + + align:start position:0% +mileage vehicle will pay much more than +for a new vehic so this fortime tax + + align:start position:0% +for a new vehic so this fortime tax + + + align:start position:0% +for a new vehic so this fortime tax +rebate for used EVS is meant to overcome + + align:start position:0% +rebate for used EVS is meant to overcome + + + align:start position:0% +rebate for used EVS is meant to overcome +this problem of the one-time tax rebate + + align:start position:0% +this problem of the one-time tax rebate + + + align:start position:0% +this problem of the one-time tax rebate +for the first owner and of course uh the + + align:start position:0% +for the first owner and of course uh the + + + align:start position:0% +for the first owner and of course uh the +part the Hawkins article focuses on the + + align:start position:0% +part the Hawkins article focuses on the + + + align:start position:0% +part the Hawkins article focuses on the +most is that there's new domestic + + align:start position:0% +most is that there's new domestic + + + align:start position:0% +most is that there's new domestic +manufacturing requirements for vehicles + + align:start position:0% +manufacturing requirements for vehicles + + + align:start position:0% +manufacturing requirements for vehicles +and batteries meaning that for the next + + align:start position:0% +and batteries meaning that for the next + + + align:start position:0% +and batteries meaning that for the next +couple years it actually may be + + align:start position:0% +couple years it actually may be + + + align:start position:0% +couple years it actually may be +relatively hard to buy electric vehicle + + align:start position:0% +relatively hard to buy electric vehicle + + + align:start position:0% +relatively hard to buy electric vehicle +because of Supply supply chain issues + + align:start position:0% +because of Supply supply chain issues + + + align:start position:0% +because of Supply supply chain issues +but simply because most electric + + align:start position:0% +but simply because most electric + + + align:start position:0% +but simply because most electric +vehicles aren't manufactured in the US + + align:start position:0% +vehicles aren't manufactured in the US + + + align:start position:0% +vehicles aren't manufactured in the US +the idea is we're going to increase the + + align:start position:0% +the idea is we're going to increase the + + + align:start position:0% +the idea is we're going to increase the +manufacturing in the us and we're giving + + align:start position:0% +manufacturing in the us and we're giving + + + align:start position:0% +manufacturing in the us and we're giving +people in incentives to manufacture + + align:start position:0% +people in incentives to manufacture + + + align:start position:0% +people in incentives to manufacture +vehicles and batteries in the US and + + align:start position:0% +vehicles and batteries in the US and + + + align:start position:0% +vehicles and batteries in the US and +that's what's going to get incentives + + align:start position:0% +that's what's going to get incentives + + + align:start position:0% +that's what's going to get incentives +going down the road there's probably + + align:start position:0% +going down the road there's probably + + + align:start position:0% +going down the road there's probably +more aspects of the inflation reduction + + align:start position:0% +more aspects of the inflation reduction + + + align:start position:0% +more aspects of the inflation reduction +act but I want to focus on the + + align:start position:0% +act but I want to focus on the + + + align:start position:0% +act but I want to focus on the +implications for your personal + + align:start position:0% +implications for your personal + + + align:start position:0% +implications for your personal +Transportation especially between the + + align:start position:0% +Transportation especially between the + + + align:start position:0% +Transportation especially between the +market for electric vehicle and the near + + align:start position:0% +market for electric vehicle and the near + + + align:start position:0% +market for electric vehicle and the near +future so that concludes our lecture for + + align:start position:0% +future so that concludes our lecture for + + + align:start position:0% +future so that concludes our lecture for +today I'll see you in class or the next + + align:start position:0% +today I'll see you in class or the next + + + align:start position:0% +today I'll see you in class or the next +lecture uh have a great + + align:start position:0% + + + + align:start position:0% + +day for \ No newline at end of file diff --git a/EmwHY7Ibu9k.txt b/EmwHY7Ibu9k.txt new file mode 100644 index 0000000000000000000000000000000000000000..470ed12a1e660c94051492ff31dbf9e9a97bcf8f --- /dev/null +++ b/EmwHY7Ibu9k.txt @@ -0,0 +1,1243 @@ +align:start position:0% + +so I will say that one of the things + + align:start position:0% +so I will say that one of the things + + + align:start position:0% +so I will say that one of the things +that I used to be pretty insecure about + + align:start position:0% +that I used to be pretty insecure about + + + align:start position:0% +that I used to be pretty insecure about +as an educator um so to put this in + + align:start position:0% +as an educator um so to put this in + + + align:start position:0% +as an educator um so to put this in +context I just graduated with my PhD um + + align:start position:0% +context I just graduated with my PhD um + + + align:start position:0% +context I just graduated with my PhD um +over the summer and after spending five + + align:start position:0% +over the summer and after spending five + + + align:start position:0% +over the summer and after spending five +years working on one Niche problem + + align:start position:0% +years working on one Niche problem + + + align:start position:0% +years working on one Niche problem +you're like all right well I don't have + + align:start position:0% +you're like all right well I don't have + + + align:start position:0% +you're like all right well I don't have +a lot of usable skills I just have a lot + + align:start position:0% +a lot of usable skills I just have a lot + + + align:start position:0% +a lot of usable skills I just have a lot +of knowledge about this one tiny problem + + align:start position:0% +of knowledge about this one tiny problem + + + align:start position:0% +of knowledge about this one tiny problem +one am I what can I possibly + + align:start position:0% +one am I what can I possibly + + + align:start position:0% +one am I what can I possibly +teach um and so I used to think about + + align:start position:0% +teach um and so I used to think about + + + align:start position:0% +teach um and so I used to think about +that a lot + + align:start position:0% +that a lot + + + align:start position:0% +that a lot +um but something this class showed me + + align:start position:0% +um but something this class showed me + + + align:start position:0% +um but something this class showed me +was that actually just the ability to + + align:start position:0% +was that actually just the ability to + + + align:start position:0% +was that actually just the ability to +be + + align:start position:0% +be + + + align:start position:0% +be +entrepreneurial the ability to be + + align:start position:0% +entrepreneurial the ability to be + + + align:start position:0% +entrepreneurial the ability to be +adaptable the ability to be a + + align:start position:0% +adaptable the ability to be a + + + align:start position:0% +adaptable the ability to be a +facilitator a communicator a mediator + + align:start position:0% +facilitator a communicator a mediator + + + align:start position:0% +facilitator a communicator a mediator +between people which I think were all + + align:start position:0% +between people which I think were all + + + align:start position:0% +between people which I think were all +huge parts of this class um was the most + + align:start position:0% +huge parts of this class um was the most + + + align:start position:0% +huge parts of this class um was the most +important thing in being an educator + + align:start position:0% +important thing in being an educator + + + align:start position:0% +important thing in being an educator +here so it wasn't + + align:start position:0% +here so it wasn't + + + align:start position:0% +here so it wasn't +so much about knowledge of subject + + align:start position:0% +so much about knowledge of subject + + + align:start position:0% +so much about knowledge of subject +material or knowledge of a specific + + align:start position:0% +material or knowledge of a specific + + + align:start position:0% +material or knowledge of a specific +skill but just a ability to facilitate + + align:start position:0% +skill but just a ability to facilitate + + + align:start position:0% +skill but just a ability to facilitate +learning which a lot of the times just + + align:start position:0% +learning which a lot of the times just + + + align:start position:0% +learning which a lot of the times just +comes down to knowing how to ask the + + align:start position:0% +comes down to knowing how to ask the + + + align:start position:0% +comes down to knowing how to ask the +right + + align:start position:0% +right + + + align:start position:0% +right +questions + + align:start position:0% +questions + + + align:start position:0% +questions +um of what is needed at this moment to + + align:start position:0% +um of what is needed at this moment to + + + align:start position:0% +um of what is needed at this moment to +help my student learn and succeed and + + align:start position:0% +help my student learn and succeed and + + + align:start position:0% +help my student learn and succeed and +being able to answer that + + align:start position:0% +being able to answer that + + + align:start position:0% +being able to answer that +questions um yeah so I didn't need to + + align:start position:0% +questions um yeah so I didn't need to + + + align:start position:0% +questions um yeah so I didn't need to +know the knowledge I didn't need to have + + align:start position:0% +know the knowledge I didn't need to have + + + align:start position:0% +know the knowledge I didn't need to have +the skills but I just needed to know + + align:start position:0% +the skills but I just needed to know + + + align:start position:0% +the skills but I just needed to know +where to find that Knowledge and Skills + + align:start position:0% +where to find that Knowledge and Skills + + + align:start position:0% +where to find that Knowledge and Skills +and be able to bring my student to that + + align:start position:0% +and be able to bring my student to that + + + align:start position:0% +and be able to bring my student to that +place + + align:start position:0% + + + + align:start position:0% + +yeah yeah wow um sorry no no no + + align:start position:0% + + + + align:start position:0% + +uh so I I think it's a this is a you + + align:start position:0% +uh so I I think it's a this is a you + + + align:start position:0% +uh so I I think it's a this is a you +know a challenging question to answer + + align:start position:0% +know a challenging question to answer + + + align:start position:0% +know a challenging question to answer +sort of uh kind of what I learned in + + align:start position:0% +sort of uh kind of what I learned in + + + align:start position:0% +sort of uh kind of what I learned in +terms of teaching or being uh an + + align:start position:0% +terms of teaching or being uh an + + + align:start position:0% +terms of teaching or being uh an +educator + + align:start position:0% + + + + align:start position:0% + +um one thing I'd say so I I'm a current + + align:start position:0% +um one thing I'd say so I I'm a current + + + align:start position:0% +um one thing I'd say so I I'm a current +I'm currently a PhD student and so uh + + align:start position:0% +I'm currently a PhD student and so uh + + + align:start position:0% +I'm currently a PhD student and so uh +this semester I was a graduate + + align:start position:0% +this semester I was a graduate + + + align:start position:0% +this semester I was a graduate +instructor and uh it was a little bit + + align:start position:0% +instructor and uh it was a little bit + + + align:start position:0% +instructor and uh it was a little bit +unexpected certainly to be involved in + + align:start position:0% +unexpected certainly to be involved in + + + align:start position:0% +unexpected certainly to be involved in +teaching the course um this uh semester + + align:start position:0% +teaching the course um this uh semester + + + align:start position:0% +teaching the course um this uh semester +and uh to uh try to carry on and extend + + align:start position:0% +and uh to uh try to carry on and extend + + + align:start position:0% +and uh to uh try to carry on and extend +the work that Seth teller had done um in + + align:start position:0% +the work that Seth teller had done um in + + + align:start position:0% +the work that Seth teller had done um in +this class was to me sort of personally + + align:start position:0% +this class was to me sort of personally + + + align:start position:0% +this class was to me sort of personally +a very um + + align:start position:0% +a very um + + + align:start position:0% +a very um +Monumental um undertaking so + + align:start position:0% +Monumental um undertaking so + + + align:start position:0% +Monumental um undertaking so +um uh yeah I mean Seth was my Master's + + align:start position:0% +um uh yeah I mean Seth was my Master's + + + align:start position:0% +um uh yeah I mean Seth was my Master's +thesis adviser and I worked on assistive + + align:start position:0% +thesis adviser and I worked on assistive + + + align:start position:0% +thesis adviser and I worked on assistive +technology um with him and and saw him + + align:start position:0% +technology um with him and and saw him + + + align:start position:0% +technology um with him and and saw him +teach the class the first time and gone + + align:start position:0% +teach the class the first time and gone + + + align:start position:0% +teach the class the first time and gone +to the some of the classes and and + + align:start position:0% +to the some of the classes and and + + + align:start position:0% +to the some of the classes and and +helped out in a little bit in the last + + align:start position:0% +helped out in a little bit in the last + + + align:start position:0% +helped out in a little bit in the last +uh two years or 3 years um as well um so + + align:start position:0% +uh two years or 3 years um as well um so + + + align:start position:0% +uh two years or 3 years um as well um so +to sort of suddenly be + + align:start position:0% +to sort of suddenly be + + + align:start position:0% +to sort of suddenly be +um uh a co-instructor um of the class uh + + align:start position:0% +um uh a co-instructor um of the class uh + + + align:start position:0% +um uh a co-instructor um of the class uh +with Grace was um kind of a a sudden + + align:start position:0% +with Grace was um kind of a a sudden + + + align:start position:0% +with Grace was um kind of a a sudden +almost kind of jarring kind of + + align:start position:0% +almost kind of jarring kind of + + + align:start position:0% +almost kind of jarring kind of +experience a baptism of fire um perhaps + + align:start position:0% +experience a baptism of fire um perhaps + + + align:start position:0% +experience a baptism of fire um perhaps +so um maybe there's there's there's + + align:start position:0% +so um maybe there's there's there's + + + align:start position:0% +so um maybe there's there's there's +three things to say one is it was you + + align:start position:0% +three things to say one is it was you + + + align:start position:0% +three things to say one is it was you +know immensely challenging it is + + align:start position:0% +know immensely challenging it is + + + align:start position:0% +know immensely challenging it is +different from doing um research which + + align:start position:0% +different from doing um research which + + + align:start position:0% +different from doing um research which +is mostly what I'm doing as a PhD uh + + align:start position:0% +is mostly what I'm doing as a PhD uh + + + align:start position:0% +is mostly what I'm doing as a PhD uh +student even you know working on + + align:start position:0% +student even you know working on + + + align:start position:0% +student even you know working on +projects with different people you sort + + align:start position:0% +projects with different people you sort + + + align:start position:0% +projects with different people you sort +of have this kind of um one level remove + + align:start position:0% +of have this kind of um one level remove + + + align:start position:0% +of have this kind of um one level remove +where suddenly as Grace is talking about + + align:start position:0% +where suddenly as Grace is talking about + + + align:start position:0% +where suddenly as Grace is talking about +you know working with students and + + align:start position:0% +you know working with students and + + + align:start position:0% +you know working with students and +trying to um encourage them in certain + + align:start position:0% +trying to um encourage them in certain + + + align:start position:0% +trying to um encourage them in certain +directions and there's certainly some + + align:start position:0% +directions and there's certainly some + + + align:start position:0% +directions and there's certainly some +uncertainty Associated um with that or + + align:start position:0% +uncertainty Associated um with that or + + + align:start position:0% +uncertainty Associated um with that or +whether they will um take your advice I + + align:start position:0% +whether they will um take your advice I + + + align:start position:0% +whether they will um take your advice I +guess or whether you should nudge them + + align:start position:0% +guess or whether you should nudge them + + + align:start position:0% +guess or whether you should nudge them +further in this direction or sometimes + + align:start position:0% +further in this direction or sometimes + + + align:start position:0% +further in this direction or sometimes +they surprise you or you know very often + + align:start position:0% +they surprise you or you know very often + + + align:start position:0% +they surprise you or you know very often +frankly they surprise you very + + align:start position:0% +frankly they surprise you very + + + align:start position:0% +frankly they surprise you very +pleasantly in terms of what they're able + + align:start position:0% +pleasantly in terms of what they're able + + + align:start position:0% +pleasantly in terms of what they're able +to accomplish um over the semester so + + align:start position:0% +to accomplish um over the semester so + + + align:start position:0% +to accomplish um over the semester so +how to kind of inspire or Mentor um + + align:start position:0% +how to kind of inspire or Mentor um + + + align:start position:0% +how to kind of inspire or Mentor um +students is really uh something that uh + + align:start position:0% +students is really uh something that uh + + + align:start position:0% +students is really uh something that uh +that that I learned over the uh semester + + align:start position:0% +that that I learned over the uh semester + + + align:start position:0% +that that I learned over the uh semester +um I think a part of this is that it was + + align:start position:0% +um I think a part of this is that it was + + + align:start position:0% +um I think a part of this is that it was +um it was pretty emotional I guess I + + align:start position:0% +um it was pretty emotional I guess I + + + align:start position:0% +um it was pretty emotional I guess I +think maybe that's the right uh word in + + align:start position:0% +think maybe that's the right uh word in + + + align:start position:0% +think maybe that's the right uh word in +terms of the the kind of the history um + + align:start position:0% +terms of the the kind of the history um + + + align:start position:0% +terms of the the kind of the history um +of this class the very personal nature + + align:start position:0% +of this class the very personal nature + + + align:start position:0% +of this class the very personal nature +um of it I think we got to know you know + + align:start position:0% +um of it I think we got to know you know + + + align:start position:0% +um of it I think we got to know you know +our 35 students very well over the + + align:start position:0% +our 35 students very well over the + + + align:start position:0% +our 35 students very well over the +semester and certainly um uh the clients + + align:start position:0% +semester and certainly um uh the clients + + + align:start position:0% +semester and certainly um uh the clients +as well the 11 clients that we uh worked + + align:start position:0% +as well the 11 clients that we uh worked + + + align:start position:0% +as well the 11 clients that we uh worked +with and so you really kind of + + align:start position:0% +with and so you really kind of + + + align:start position:0% +with and so you really kind of +experience the ups and downs with um + + align:start position:0% +experience the ups and downs with um + + + align:start position:0% +experience the ups and downs with um +with the students over the course of the + + align:start position:0% +with the students over the course of the + + + align:start position:0% +with the students over the course of the +projects and um that's you know I think + + align:start position:0% +projects and um that's you know I think + + + align:start position:0% +projects and um that's you know I think +challenging sometimes or you know + + align:start position:0% +challenging sometimes or you know + + + align:start position:0% +challenging sometimes or you know +interesting to uh + + align:start position:0% +interesting to uh + + + align:start position:0% +interesting to uh +experience + + align:start position:0% +experience + + + align:start position:0% +experience +um I think the third thing I'd say is + + align:start position:0% +um I think the third thing I'd say is + + + align:start position:0% +um I think the third thing I'd say is +that it was it was it was in the end + + align:start position:0% +that it was it was it was in the end + + + align:start position:0% +that it was it was it was in the end +very rewarding I mean to uh see the + + align:start position:0% +very rewarding I mean to uh see the + + + align:start position:0% +very rewarding I mean to uh see the +results and see students excited about + + align:start position:0% +results and see students excited about + + + align:start position:0% +results and see students excited about +what they had + + align:start position:0% +what they had + + + align:start position:0% +what they had +done um to be able to um work with a + + align:start position:0% +done um to be able to um work with a + + + align:start position:0% +done um to be able to um work with a +really um great team of people all + + align:start position:0% +really um great team of people all + + + align:start position:0% +really um great team of people all +passionate about um uh the course so the + + align:start position:0% +passionate about um uh the course so the + + + align:start position:0% +passionate about um uh the course so the +co-instructors and and you know our + + align:start position:0% +co-instructors and and you know our + + + align:start position:0% +co-instructors and and you know our +teaching and lab assistants who had + + align:start position:0% +teaching and lab assistants who had + + + align:start position:0% +teaching and lab assistants who had +taken the class before and really wanted + + align:start position:0% +taken the class before and really wanted + + + align:start position:0% +taken the class before and really wanted +to um make this a positive experience um + + align:start position:0% +to um make this a positive experience um + + + align:start position:0% +to um make this a positive experience um +for students I think in a lot of sense + + align:start position:0% +for students I think in a lot of sense + + + align:start position:0% +for students I think in a lot of sense +it's pretty unprecedented I don't know + + align:start position:0% +it's pretty unprecedented I don't know + + + align:start position:0% +it's pretty unprecedented I don't know +if I will ever do anything like this + + align:start position:0% +if I will ever do anything like this + + + align:start position:0% +if I will ever do anything like this +again for + + align:start position:0% +again for + + + align:start position:0% +again for +um a fairly long time I guess in terms + + align:start position:0% +um a fairly long time I guess in terms + + + align:start position:0% +um a fairly long time I guess in terms +of sort of the meaningfulness and the uh + + align:start position:0% +of sort of the meaningfulness and the uh + + + align:start position:0% +of sort of the meaningfulness and the uh +the challenge and the kind of the you + + align:start position:0% +the challenge and the kind of the you + + + align:start position:0% +the challenge and the kind of the you +know personal side of it um I think I I + + align:start position:0% +know personal side of it um I think I I + + + align:start position:0% +know personal side of it um I think I I +I might beack in Poetic I guess but I + + align:start position:0% +I might beack in Poetic I guess but I + + + align:start position:0% +I might beack in Poetic I guess but I +think um you know it was really exciting + + align:start position:0% +think um you know it was really exciting + + + align:start position:0% +think um you know it was really exciting +to be able to put something uh like this + + align:start position:0% +to be able to put something uh like this + + + align:start position:0% +to be able to put something uh like this +um together and for that matter I think + + align:start position:0% +um together and for that matter I think + + + align:start position:0% +um together and for that matter I think +it's one reason uh to you know try to + + align:start position:0% +it's one reason uh to you know try to + + + align:start position:0% +it's one reason uh to you know try to +share you know kind of our experience + + align:start position:0% +share you know kind of our experience + + + align:start position:0% +share you know kind of our experience +our Full Experience really it's the + + align:start position:0% +our Full Experience really it's the + + + align:start position:0% +our Full Experience really it's the +things that worked and things that maybe + + align:start position:0% +things that worked and things that maybe + + + align:start position:0% +things that worked and things that maybe +didn't work as well on something like + + align:start position:0% +didn't work as well on something like + + + align:start position:0% +didn't work as well on something like +ocw almost you know warts and all I + + align:start position:0% +ocw almost you know warts and all I + + + align:start position:0% +ocw almost you know warts and all I +suppose in terms of what we tried and + + align:start position:0% +suppose in terms of what we tried and + + + align:start position:0% +suppose in terms of what we tried and +what was + + align:start position:0% +what was + + + align:start position:0% +what was +successful what guidelines um we might + + align:start position:0% +successful what guidelines um we might + + + align:start position:0% +successful what guidelines um we might +have to other Educators so I think + + align:start position:0% +have to other Educators so I think + + + align:start position:0% +have to other Educators so I think +really the focus of our class or if + + align:start position:0% +really the focus of our class or if + + + align:start position:0% +really the focus of our class or if +we've delivered a good class this + + align:start position:0% +we've delivered a good class this + + + align:start position:0% +we've delivered a good class this +semester and and provided a good + + align:start position:0% +semester and and provided a good + + + align:start position:0% +semester and and provided a good +learning experience for our students and + + align:start position:0% +learning experience for our students and + + + align:start position:0% +learning experience for our students and +our students have learned and taken away + + align:start position:0% +our students have learned and taken away + + + align:start position:0% +our students have learned and taken away +something from principles and practice + + align:start position:0% +something from principles and practice + + + align:start position:0% +something from principles and practice +of assistive technology this semester + + align:start position:0% +of assistive technology this semester + + + align:start position:0% +of assistive technology this semester +then I think that's what we set out to + + align:start position:0% +then I think that's what we set out to + + + align:start position:0% +then I think that's what we set out to +do if we can Inspire Educators and uh + + align:start position:0% +do if we can Inspire Educators and uh + + + align:start position:0% +do if we can Inspire Educators and uh +students uh elsewhere who who might be + + align:start position:0% +students uh elsewhere who who might be + + + align:start position:0% +students uh elsewhere who who might be +interested in assistive technology or + + align:start position:0% +interested in assistive technology or + + + align:start position:0% +interested in assistive technology or +working in this space if we can kind of + + align:start position:0% +working in this space if we can kind of + + + align:start position:0% +working in this space if we can kind of +let a thousand flowers bloom when it + + align:start position:0% +let a thousand flowers bloom when it + + + align:start position:0% +let a thousand flowers bloom when it +comes to um assistive technology or the + + align:start position:0% +comes to um assistive technology or the + + + align:start position:0% +comes to um assistive technology or the +work that we're doing then then maybe + + align:start position:0% +work that we're doing then then maybe + + + align:start position:0% +work that we're doing then then maybe +we've done our job this semester \ No newline at end of file diff --git a/FKp-6sojt9A.txt b/FKp-6sojt9A.txt new file mode 100644 index 0000000000000000000000000000000000000000..286387711628f13aff8af12ec5080de0bef5cd1c --- /dev/null +++ b/FKp-6sojt9A.txt @@ -0,0 +1,323 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right so let's + + align:start position:0% + + + + align:start position:0% + +see so first we have L1 is equal to + + align:start position:0% +see so first we have L1 is equal to + + + align:start position:0% +see so first we have L1 is equal to +bacon eggs I'm going to short for Shand + + align:start position:0% +bacon eggs I'm going to short for Shand + + + align:start position:0% +bacon eggs I'm going to short for Shand +this L2 is equal to toast and + + align:start position:0% +this L2 is equal to toast and + + + align:start position:0% +this L2 is equal to toast and +jam + + align:start position:0% +jam + + + align:start position:0% +jam +brunch I should actually make these + + align:start position:0% +brunch I should actually make these + + + align:start position:0% +brunch I should actually make these +arrows brunch is equal to L1 so this is + + align:start position:0% +arrows brunch is equal to L1 so this is + + + align:start position:0% +arrows brunch is equal to L1 so this is +just aliasing which means brunch is + + align:start position:0% +just aliasing which means brunch is + + + align:start position:0% +just aliasing which means brunch is +going to point to whatever L1 object + + align:start position:0% +going to point to whatever L1 object + + + align:start position:0% +going to point to whatever L1 object +points + + align:start position:0% +points + + + align:start position:0% +points +to and if I do L1 do aen juice L1 is now + + align:start position:0% +to and if I do L1 do aen juice L1 is now + + + align:start position:0% +to and if I do L1 do aen juice L1 is now +going to be bacon eggs and juice + + align:start position:0% + + + + align:start position:0% + +okay this L1 has been mutated to be that + + align:start position:0% +okay this L1 has been mutated to be that + + + align:start position:0% +okay this L1 has been mutated to be that +and since brunch still points to the + + align:start position:0% +and since brunch still points to the + + + align:start position:0% +and since brunch still points to the +same object that L1 points to brunch is + + align:start position:0% +same object that L1 points to brunch is + + + align:start position:0% +same object that L1 points to brunch is +now going to point to + + align:start position:0% +now going to point to + + + align:start position:0% +now going to point to +there + + align:start position:0% +there + + + align:start position:0% +there +okay so when I do brunch. extend L2 I'm + + align:start position:0% +okay so when I do brunch. extend L2 I'm + + + align:start position:0% +okay so when I do brunch. extend L2 I'm +going to take whatever brunch is which + + align:start position:0% +going to take whatever brunch is which + + + align:start position:0% +going to take whatever brunch is which +is this part + + align:start position:0% +is this part + + + align:start position:0% +is this part +here + + align:start position:0% +here + + + align:start position:0% +here +and I'm going to extend it by L2 which + + align:start position:0% +and I'm going to extend it by L2 which + + + align:start position:0% +and I'm going to extend it by L2 which +is toast and + + align:start position:0% +is toast and + + + align:start position:0% +is toast and +Jam okay so it's just going to contain a + + align:start position:0% +Jam okay so it's just going to contain a + + + align:start position:0% +Jam okay so it's just going to contain a +large list of those five + + align:start position:0% +large list of those five + + + align:start position:0% +large list of those five +elements + + align:start position:0% +elements + + + align:start position:0% +elements +because because of this side effect + + align:start position:0% +because because of this side effect + + + align:start position:0% +because because of this side effect +issue where brunch was was this pointing + + align:start position:0% +issue where brunch was was this pointing + + + align:start position:0% +issue where brunch was was this pointing +to the same thing that L1 was pointing + + align:start position:0% +to the same thing that L1 was pointing + + + align:start position:0% +to the same thing that L1 was pointing +it + + align:start position:0% +it + + + align:start position:0% +it +to okay so it's close but I think + + align:start position:0% +to okay so it's close but I think + + + align:start position:0% +to okay so it's close but I think +perfect yes that's that's the right + + align:start position:0% +perfect yes that's that's the right + + + align:start position:0% +perfect yes that's that's the right +answer \ No newline at end of file diff --git a/FQZN92nEC0Q.txt b/FQZN92nEC0Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..bd8eae72ba3856950d3556811d5ed8884f514b24 --- /dev/null +++ b/FQZN92nEC0Q.txt @@ -0,0 +1,4013 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: So today, we're +going to be talking about + +today and on Thursday, we're +going to be trying to answer + +this question. + +We're going to give a slightly +different answer + +today than on Thursday. + +Just to give you a road map of +where we are going, today is + +more going to be about the +poverty trap in the sense that + +Pak Solhin described +it to us in-- + +I think it was our first +lecture together. + +We started from Pak Solhin +description of a poverty trap, + +which was really based on the +immediate impact of the + +calories on your productivity +that very day. + +And then that's what we're going +to look at today, which + +is try to answer +[? Daiquiri's ?] + +question which I've been putting +off until now, which + +is to say well, can we really +believe his story? + +And then on Thursday, we are +going to further our inquiry + +into nutrition based poverty +trap by looking at things a + +little bit more subtle than the +impact of calories on your + +productivity the very next day +by looking at things like + +micro nutrients and by looking +at things like feeding your + +children or feeding pregnant +mother so that the kids that + +they bear grow up as different +people, et cetera. + +So that's kind of the road +map for our work + +today and on Thursday. + +At the end of last lecture, +we discussed the important + +observation by Amartya Sen +that maybe there are no + +famines in today's democracies, +that the large + +big famines are gone or at least +that when we observe + +them, they are due to some +really extraordinary + +circumstances like a +war or a civil war. + +So there is a paper that I +didn't ask you to read because + +it's a little long. + +But the title is Is +Famine History? + +And it sort of concludes that +it might be outside of + +specific circumstances. + +I should say that it's history +that might come back because + +we have no idea what global +warming is going to do to the + +productivity of agriculture, +and it may or may not be + +sufficiently bad that +it might come back. + +But in the short term, we may be +in a situation where people + +are not starving to death in +very large number like they + +did in West Mongol outside +of some big + +serious political crisis. + +However, malnutrition and +under nutrition is not. + +You can see the food and +agriculture organization + +that's based in Rome is in +charge of trying to monitor + +people's situation. + +They try to estimate how many +people are, they call, hungry. + +So they give periodically a +number of the number of hungry + +people in the world. + +And not long ago, they came +up with one billion. + +And that number, if you've seen, +has been all about the + +newspaper, one billion hungry +people in the world. + +To be completely honest, I am +not fully understood how they + +compute the number of hungry +people in the world, because I + +suppose you could ask them. + +But I don't think this is +what they are doing. + +I think they are trying to +estimate the calorie + +requirement that people +might need to fit. + +And the question is do we really +know what's a calorie + +requirement? + +And the answer to that is no. + +We don't really exactly know +what's a calorie requirement. + +So maybe this notion of what's +a hungry person is a little + +bit more hazy than we'd +like it to be. + +But there is not really +a lot of people + +who look very skinny. + +So do you know what the +bodymass index? + +The bodymass index is your-- + +sorry, go ahead. + +AUDIENCE: 730 times your +height divided + +by your weight squared. + +PROFESSOR: 730? + +I didn't know that that's 730. + +I think it's your weight +divided by your + +height squared in meter. + +That's maybe the 730 +coming from. + +It's your weight in kilograms +divided by your height in + +meter squared. + +So sometimes I'm trying to think +that this means that + +we're trying to elongate the +person over a square meter and + +see how fat that rectangle +would be. + +So that's the BMI. + +Do you know what the threshold +for the BMI is. + +AUDIENCE: 18.5. + +PROFESSOR: 18.5. + +So 18.5 is undernourished. + +And there is a large number +of people we know who are + +undernourished by +this standard. + +Also there is about 2 billion +people in the + +world who are anemic. + +That means they don't +have enough + +hemoglobin in their blood. + +Now all of anemia is due to +poor nutrition, but it's + +estimated that maybe half +of this is due to + +iron deficiency anemia. + +So it's a deficiency +in one particular + +micronutrient which is iron. + +So that's about one billion +people who are anemic due to + +some deficiency in iron +in their diet. + +Is there deficiency in +iron or difficulty in + +absorbing the iron? + +A lot of these anemic +people is in India. + +And sadly, Indians combine the +fact that many of them are + +vegetarian and their diet is +rich in rice which is rich in + +phytates, which is an inhibitant +for the absorption + +of iron, which is one reason +why the rate of anemia is + +particularly high in India, is +that on the one hand, they get + +less iron in their diet than +other people at comparable + +level of calorie intake +just because those + +come less from meat. + +Then on the other hand, they +are less good at absorbing + +them due to the rice. + +There was a large increase +in food prices in 2006. + +And then again, they collapsed +during the crisis. + +And they increased again +in 2010 to be + +almost at 2008 level. + +And there are two consequences +of an increase in food prices + +on those of the poor who are net +consumer of food, that is + +those who produce less +than they consume. + +Those are, for example, +the urban poor. + +And those are on the one hand, +a large proportion of the + +budget of the poor. + +A larger proportion of the +budget of the poor is spent on + +food, so an increase in the +price of food affect the + +poorest more than +proportionally, compared to + +any other source of inflation. + +So if the source of inflation is +sort of a general increase + +in priced or it's driven by +the price of housing, then + +that affects everybody the +same or that might + +affect the rich more. + +But if the inflation is as +it is today, driven by an + +increase in the price of food, +then it affects more the + +people who are relying the +most, of course, on food. + +And that's the first story. + +That's one reason why +organizations like the World + +Bank, the UN, they FAO are +practically worried about an + +increase in food prices, +because that's + +disproportionately affecting +the poor. + +And it's also disproportionately +affecting + +the urban poor, which may be one +of the many reasons that + +have led to the unrest that +you observe today in the + +Middle East. + +The reason why I'm mentioning +that is that in 2008, at the + +height of the previous increase +in food prices, there + +were food riots in Egypt that +never had achieved the kind of + +intensity of what we saw in the +last few weeks, but were + +clearly and very directly +prompted by the price of food. + +And here, the whole rhetoric +of the revolt was framed + +around political reform, but it +is not impossible that part + +of the reason why so many +people, in particular in urban + +centers, were willing to +spending so much time outside + +protesting is because they were +profoundly unhappy with + +the increase in the +price of food. + +The second reason why we might +be worried about an increase + +in the price of food is if we +take Pak Solhin's story + +seriously and we are wondering +that this increase in hunger + +is going to lead to some +vicious circle. + +So If you read the World +Bank document about-- + +the World Bank's job, in a +sense, is to raise money for + +developing countries. + +So part of the World Bank's +communication department job + +is to be slightly alarmist, so +we need to take everything + +they say with a pinch of salt. + +But one of the thing that they +would very frequently say is + +the price of food increase-- + +that makes the poor poorer. + +That makes them more difficult +for them to get enough + +calories, which means they +can't work as hard, which + +means they will be plunged +back into poverty. + +And so this is the story that +Pak Solhin told us in our + +first lecture. + +And that's what I want to +investigate with you today, + +whether we have reasons to be +worried about this kind of + +immediate vicious circle. + +So I want to give us a quick +refresher of what's Pak + +Solhin's story. + +So with your daily wage, it's +a short term nutrition, a + +nutrition based poverty trap. + +With your wage, you buy food. + +That gives you strength, and +allows you to get some more + +wages at the end. + +So you buy more food, and +that gives you strength. + +And you have more wages, +et cetera. + +And that's how you survive +maybe on a daily basis. + +So that means that it creates +a relationship between how + +much you start from one fine +evening and what is your + +income tomorrow. + +And that also means that it +creates a relationship with + +the wage level and your ability +to do any work at all. + +So Pak Solhin's story was that +the wage had dropped because + +of the increase in input prices +and the uncertainty + +that the farmer had about +whether they were going to be + +able to raise their output +prices corresponding. + +That had led to a decrease in +the wage at the same time as + +there was an increase in the +food prices, so big decrease + +in the real wage in term of the +food entitlement of a day + +of work as Amartya Sen would +say, which means that if you + +took this food entitlement and +you had nothing else to + +supplement it with, this just +was not enough to give you the + +strength to do the work +to earn that wage. + +So that means that someone like +Pak Solhin that had no + +extra resources was not +able to work at all. + +So that creates an inequality +among people. + +Take Pak Solhin and imagine +that, in fact, he also had a + +little piece of land. + +Then what could he have done +with this little piece of land + +once the wages had gone down? + +Ben? + +AUDIENCE: Sell some of it. + +PROFESSOR: So he could have sold +some of it to get money. + +Or he could have rented some +of it and get money. + +So suppose he rents some +of it and gets money? + +So he starts the morning with +1000 rupee he has from the + +rent of his field. + +And that can be complimented +with whatever wage he's earned + +yesterday for his work. + +And that might be enough to give +him the strength to do a + +day of work. + +So if you compare Pak Solhin to +his brother, for example-- + +he has a brother in +the story, right? + +If you compare Pak Solhin with +his brother, who had a piece + +of land, they might be exactly +similar in term of their + +underlying body and their +strength, et cetera. + +But the fact that one of them +has a piece of land allow them + +to work, and therefore they +start with a little bit more + +non-labor income, which gives +them much more labor income. + +So the existing inequality +in non-labor income is + +strengthened by the inequality +in labor income, which is very + +different from what we would +see in our standard models + +where the richer people would be +less likely to work because + +they already have the non +labor income money. + +So the labor market would serve +to make people more + +similar rather than +less similar. + +So that's the story +he told us. + +And as we saw last time, the +necessary condition for such a + +poverty trap is that the +capacity curve, which relates + +your income to that, your +income tomorrow via the + +biology of the body, has this +S shape curve that we + +discussed that intersects below +the 45 degree line, then + +at some point crosses it +and then comes back. + +So we are not going to go back +to that, because we saw it in + +detail last time. + +That was supposed to +be the shape again. + +It doesn't want to come back. + +So the S shape is made +of two relations. + +The S shape is the relationship +between income + +today and income tomorrow, +midrow since I can't have it + +on the slide. + +So this is income today +and income tomorrow. + +And so the S shape is actually +not one function, it's the + +product of two functions. + +One is given how much income you +have, how much calories do + +you decide to eat? + +And then the calorie +that you eat-- + +how much productive +do that make you? + +So if we write it in math, it's +like there is income, + +nutrition is equal to g, +function g of income today. + +Because you get your wages and +then you eat some good meal. + +And then income tomorrow is +a function f of nutrition. + +That means that income +tomorrow is f + +of g of income today. + +So this is what makes +this S shape. + +So what we can do today is to +look separately at these two + +relationships. + +What's the strength of the +relationship between income + +tomorrow and nutrition today? + +And what's the relationship +between nutrition today and + +income today? + +And here, when I mean today and +tomorrow, I really mean + +today and tomorrow. + +This is a short run phenomenon +that we are talking about. + +Maybe next week, but +not a matter of + +generations or years. + +So suppose that there is indeed +that this particular + +relationship, income tomorrow +and nutrition, is indeed S + +shape, and suppose that you were +a very poor person, so + +you are in a low part of the S, +and suppose that you happen + +onto a bit of money, what would +you do with this money? + +If this relationship between +income and nutrition was S + +shape and you were a very poor +person, but you find a pile of + +money on the ground, what would +you do with the money? + +AUDIENCE: Well, if that +holds true, then you + +would want to eat more. + +PROFESSOR: If that holds +true, then I know you + +would want to eat more. + +So that means that if there is +indeed an S shape between + +income tomorrow and nutrition, +then we should see a very + +strong relationship between +nutrition and income for the + +very poor, because it is like +for an excellent investment. + +If you find yourself here, there +is no better investment + +you can do than eating +some more. + +So a first thing you can do is +we can see whether poor people + +are really trying to +put all of the + +possible money into food. + +Now the question is the possible +money, so that means + +that we would find the share of +food in the budget should + +be very high for the poor. + +And the second thing it would +mean is that it would increase + +quite fast with income. + +And possibly, it would again +have a form of S shape for the + +following reason. + +Suppose that you have some +unavoidable expense to solve. + +For example, you need a house +and you need some clothes. + +So unless you live in a very +hot country where you don't + +really need much clothes, you +need a house, you need a piece + +of land to put the house on, +and you need some clothes. + +So someone who was a budget of +20 rupees will spend, say, + +five rupees on clothing +and house. + +They can't do anything +more than that. + +And 15 rupees on food. + +So that's the poorest person. + +And then if there is really this +S shape here, this person + +would be somewhere here. + +So they would remain +quite poor. + +And now another person, +comparable in other aspect, + +but has a total budget of 30 +rupees, let's say because they + +have some non labor income or +because they have a bit more + +weight, than they would still +spend unavoidable expenses on + +clothing and houses, but they +would not do any more. + +They will still do +just the minimum. + +And they would spend all +the rest on food. + +That means that by how much did +I increase the income of + +this person? + +Sorry? + +AUDIENCE: By 10. + +PROFESSOR: Yeah, 10 out of +20, and [INAUDIBLE]. + +AUDIENCE: 50% + +PROFESSOR: 50%, and this is +how much of [INAUDIBLE]? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: It's 25 out of 15. + +An increase from 15 to 25. + +It's 10 on the basis of 15. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: I trust you. + +You are the MA student. + +So whatever it is, that's +going to be on video. + +66? + +Let's go with 66. + +That means that when I increase +your income by 50%, + +your expenditure on food +increases by 66%. + +So if I divide by one +of the other, what + +concept is it called? + +An elasticity. + +So this means the elasticity +of food expenditure with + +respect to overall expenditure +is more than one for the + +extremely poor. + +Because you start by +taking care of + +your essentially needs. + +And after that you're putting +all of the money into food + +because you think this +is highly valuable. + +So this is one thing. + +And the second thing is now you +go from someone who gets + +30 rupees to someone +who gets 45 rupees. + +So I've rigged this so +that it's nicely + +another increase of 50%. + +And now this person who +makes 45 rupees-- + +they're already kind of over +here somewhere, so the + +marginal value of one +more rupees into + +food is not that high. + +So they are still going to spend +a bit more on food, but + +only five rupees more. + +Going to spend a bit more +to have a nicer + +clothing and some houses. + +And now they can bring in +entertainment, because now + +they are basically just +taken care of. + +The marginal value of extra +is not that high. + +So they can get into +doing other things. + +So now the elasticity is +going to be 0.25 to 30. + +That's out of 25. + +Sorry? + +AUDIENCE: 20% + +PROFESSOR: 20%, is that? + +Yes, 20%. + +20% out of an increase in 50%. + +Now the elasticity is +much less than 1. + +So what we would see is a group +of people, the poorest + +people, where we have very +high elasticity. + +And then for anybody who +is somewhat richer, the + +elasticity of food consumption +with overall budget would be + +less than 1, which is what +people refer to as the Engel + +curve, which is the share of +food of the budget increases + +less than proportionately. + +So the Engel curve refers to +this phenomenon, which is the + +share of food increases less +than proportionately as you + +become richer, but it's worth +pointing out that in an S + +shaped world, we would probably +have and reverse + +Engel curve phenomenon, where +the share of food of the + +budget first increases +and then decreases. + +So the question is, do we see +this, that the poor spend as + +much money as they +can on food? + +And the second question is, do +we see this, which is do we + +see anybody who's elasticity +of food consumption with + +respect to budget +is more than 1? + +So that's kind of where +I want to go next. + +So first, let's look at the +food share in the budget + +around the world. + +And this comes from +a data set that-- + +the World Bank collect data set +in many countries called + +the Living Standard Measurement +Surveys. + +And they very nicely put +them on the website-- + +not all of their surveys, +because in some case, they + +have agreement with governments +that doesn't allow + +them to do that. + +But a lot of their surveys +are on the web. + +You can actually download +them and play with them. + +You're welcome to do that. + +And we did that. + +So we took the overall +expenditure to compute + +people's budget transferred +into PPP dollars. + +So this is people who live +under a dollar a day, at + +pressures in power poverty, +so in US prices. + +And look at the share +of their budget. + +So this is what we find for a +bunch of people living in the + +rural areas. + +And this is food, alcohol, +tobacco, education and health. + +So what are your remarks when +you see these numbers? + +AUDIENCE: I have a question +about the education + +percentages. + +Do those mean that we'd be +paying for tuition or + +educational [INAUDIBLE]? + +PROFESSOR: So this is only +education expenditure. + +So this is tuition if the child +is in a private school + +or if they get extra tuition, +which a lot of people in + +developing countries do. + +They get extra help at home. + +This could be school uniform, +school books, boarding school + +for kids who are in +boarding school. + +Any education related +expenditure would be in there. + +Yeah, Ben. + +AUDIENCE: I guess a couple +confusions, [INAUDIBLE]. + +PROFESSOR: So in 2.1, Mexico +is spending more on alcohol + +and tobacco than on education. + +Spends very, very little +on health. + +That doesn't mean people +are totally unhealthy. + +But actually, Mexico has an +excellent health care system, + +but basically is free +for most people. + +And in all of the countries, +the share on alcohol and + +tobacco tends to be at least +comparable to what we see for + +education and health. + +Yeah. + +AUDIENCE: Why don't the numbers +add up to 100%? + +PROFESSOR: Because there are +other things you do with your + +money other than food, alcohol, +education or health. + +AUDIENCE: Got it. + +PROFESSOR: Going to the movies, +putting some cloth on + +your back, that kind of stuff. + +If it adds up to more than 100, +we're in trouble, which + +is quite possible. + +But I hope not, I hope not. + +I don't guarantee it, but +I hope that that kind of + +mistakes would not always +send scrutiny. + +Any other observation +on this table? + +Let me ask one question then. + +Do you think the share of the +budget on food is high or low? + +AUDIENCE: High. + +PROFESSOR: High, you think the +share of food is high? + +Yes. + +[INAUDIBLE]. + +Ben? + +AUDIENCE: I mean, [INAUDIBLE], +I don't think you'd have much + +wiggle room to spend your money +on other [INAUDIBLE]. + +PROFESSOR: It's about right. + +Yeah, so the question is whether +it's high or low. + +So one thing I should say is +that it's kind of viability. + +It goes from pretty low in +India, 56%, to pretty high in + +Timor, 77%. + +Remember, this is all people who +are equally poor in term + +of their ability to consume +things, because they're all + +below a dollar a day at PPP. + +They make very different +choices. + +They are quite viable. + +Whether it's high or low, +I think it's in + +the eye of the beholder. + +On the one hand, it's certainly +a high part of the + +budget, compared to what +people spend, for + +example, in the US. + +On the other hand, if you +compare it with, for example, + +what they spent on tobacco, even +on education, given that + +a lot of these countries have +a free education system, the + +education expenditure they are +making are extras, I'm sure + +surely value extras. + +But that means that there seems +to be actually some + +wiggle room, that you could do +something about your food + +budget and increase it without +sacrificing anything else + +that's vital for the house. + +Yes. + +AUDIENCE: I just +have a question + +about what you presented. + +The people who spend +more on food, is + +their nutrition better? + +Or is it [INAUDIBLE]? + +PROFESSOR: So that's an +excellent question. + +We're going to look into that, +which is when you spend more + +money on food, it could +be on more nutritious + +food or more calories. + +It could be on not so much +more nutritious food. + +It could be on better +tasting food. + +And the short answer is that +the two are happening. + +I don't know whether it's true +at the country level. + +For example, India is a country +that spends very + +little on food and which has +probably the worst nutritional + +stages for this group of people +within the world. + +But at the individual level, +we're going to see that very + +soon when people increase how +much money they spend on food, + +they both get more food and +they get better food, more + +expensive food for the calories +and the nutrition + +they are getting. + +So both things happen +together. + +AUDIENCE: What is the +requirement for the + +[INAUDIBLE] + +children and [INAUDIBLE]? + +PROFESSOR: No, this +is everyone. + +This is everyone who lives +on less than a + +dollar a day per capita. + +So if there are five of +them, they are entire + +budget divided by 5. + +And if no one has any children, +then they won't + +spend anything on education. + +AUDIENCE: They migh have spent +quite a bit more on education. + +PROFESSOR: This means that per +child, they spend a fair + +amount on education. + +AUDIENCE: [INAUDIBLE] + +is more expensive in South +Africa or Timor, so + +[INAUDIBLE] basically be buying +the same quantity of + +food to be spending more. + +PROFESSOR: Right, so that's +an excellent point. + +The point is in answer to the +unstated question, which is + +what explains this variation +across countries, our first + +possible explanation +is the relative + +price of food is different. + +So food could be relatively more +expensive in Timor Leste, + +which is why people are spending +more money to get the + +same thing. + +What is interesting is that the +opposite seems to be true, + +which is because India is a +very large economy that is + +able to produce very many things +in India, the relative + +price of things like toothbrush, +even DVDs, + +cellphones-- + +that kind of things +relative to food-- + +is lower in India. + +So one of the reasons why people +seem to be spending, or + +one possible reason-- + +I'm not saying this +is a tirant. + +But this is a conjecture, let's +say-- is one of the + +reasons why people in India +spend much less on food and + +more on other things compared to +people in Papua New Guinea, + +is that there is nothing +to get in Papua New + +Guinea except food. + +So if you are poor, like +what can you buy? + +Well, in India, you can buy +shampoo of this kind, and + +everything is produced locally, +hence the relative + +prices are lower. + +So that's a possible explanation +for this pattern. + +Yeah. + +AUDIENCE: In terms of the +different prices across + +countries for food, I thought +that the one dollar a day + +standard was in terms of +purchasing power, so + +[INAUDIBLE]. + +PROFESSOR: For your +entire budget. + +So the one dollar a day standard +takes a basket of + +consumption good. + +Of course, food is an important +part o it, but there + +is also other things that +people consume. + +So one dollar a day takes +the basket of goods. + +In fact, the way it's computed +here, it's 16 + +rupees a day, actually-- + +takes the basket of good that is +consumed by the poor rather + +than your basket of good or my +basket of good, and price it + +in the different places +and adjust with that. + +So good plays an +important part. + +But other things play as well. + +And then within a single dollar +a day, it could be + +that, say in India, for example, +food is relatively + +expensive relative to other +things just because the other + +things are so cheap +and available. + +Yes, Eve. + +AUDIENCE: Could it be that it's +hotter in India than the + +other places, so in other places +people need to eat more + +food to have more fat to +preserve heat, whereas in + +India, they don't need to eat as +much food because it's hot + +all the time? + +PROFESSOR: So it could be. + +It's a very interesting point, +and we are going + +to make this point. + +We are going to see this +point coming up in + +another guide very soon. + +The point is that we don't +know what's the calorie + +requirement for a human being, +partly because it depends on + +the climate and it depends +on what you are doing. + +And it depends on how much +calories you are losing to + +illnesses and other +things like that. + +One piece of evidence that +suggests it's not the entire + +story is that if it were the +case, if I looked at the size + +of the Indian people compared +to the size of anyone else, + +what should I see? + +Sorry? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Well, in your +hypothesis where the + +difference is due to the fact +that they need less calories + +because it's warm, if everything +was explained here + +by the fact that Indian people +don't need that much calorie + +compare to-- + +see, all these countries +are warm. + +But compared to South Africa, +South Africa is a bit more + +temperate, so poor people in +South Africa need to eat a lot + +because it's cold when it's +the winter there. + +Then if all the differences in +calorie consumption were to be + +explained by these needs, we +would find people whose + +nutrition status would +be comparable. + +So their height would be the +same and their weight + +would be the same. + +And in fact, Indian people are +very, very short and they are + +very, very skinny. + +Now you might say, yes, +but that's genetic. + +It's just, like, Indian +people are short. + +But that's actually not true, +because the children, when + +Indian migrants come to the US, +they start eating US food, + +their children are +still smaller. + +But the children of +their children-- + +some of you might be that-- + +are exactly as tall +as anybody else. + +So it suggests that the genetic +potential of Indian + +people in term of height and +body size is no different than + +that of anybody else. + +But it's their nutritional +status that is different. + +And that affects them directly, +and that affects + +their children just because +of when you're in utero in + +someone who doesn't eat enough, + +you'll also be smaller. + +For the longest time, +people said + +Japanese people were short. + +But it turns out that the height +in Japan are converging + +to the height of everybody +else in the world. + +So this is more of a nutrition +thing than all this cereal and + +maize that we are consuming, +than a + +genetic potential probably. + +So going back to sort of the +two punch lines here-- + +one is that this is moving a +lot, which suggests that there + +is some margin of choices, at +least in India, for example. + +Second is we have this alcohol +and tobacco that we could, in + +principle, get rid of. + +And then all of that would +be extra calories. + +So that suggests that this is +high, this is important. + +But there seems to be some +amount of wiggle room take + +Ben's word. + +There is some amount of +wiggle room here. + +And to look at other form of +wiggle room, so another way to + +look at it is to look at this +question, which is what is the + +elasticity of calorie +consumption with respect to + +your income? + +So this log per capita outlay +is some fancy way of saying + +log per capita expenditure, +which is a good measure of + +your wealth. + +And what you can see +is that this is the + +log per capita calorie. + +This is looking at Maharashtra +in 1993. + +India has grown a lot since +1993, but Maharashtra in 1993 + +was a pretty poor place. + +And what you find is that as +people become richer, they do + +consume more. + +The slope of this line +is about 0.3. + +And the slope of this line when +I run a regression of log + +per capita calorie on log per +capita outlay, what is the + +slope giving me? + +The elasticity. + +So whenever I go log log +regression, I get the + +elasticity. + +Interestingly, this is +not a regression. + +I mean, this is a regression, +but not a linear regression. + +This is a non parametric +regression, which means that + +if the shape had been what I +told you it could be, which is + +very high elasticity early on, +and then a lower one, so + +something we would expect if we +were in the S shape world + +of the elasticity being above +one for the poor and then + +less, the way they have +estimated this regression + +allows for this to +be the case. + +But that's not what they find. + +They find the elasticity of +1.5 pretty much constant + +across the range in the data. + +Now no one here is very rich, so +it's quite possible that it + +starts going down here. + +But the point is that even for +the very poorest, that + +elasticity is not above one, so +even the very poorest have + +an Engel curve phenomenon, +which is as they become + +richer, they don't start eating +as much as possible, + +eating the extra calories up. + +They're eating, in terms of +calories, if I increase your + +income by 10%, you increase +your calorie + +consumption by 30%. + +So these two first things +suggest that maybe this is + +somewhat unlikely that there +would be this very strong S + +shape, because otherwise people +would be behaving in a + +very bizarre way. + +So we've seen that. + +So I think we've covered this. + +So the calories increased with +overall consumption, but not + +one for one. + +When total expenditure +increased by 10%, the + +consumption of calorie +increased by 3.5%. + +So we have an Engel curve. + +That is true for everyone. + +So why is the slope of the Engel +curve less than one? + +So what happens is what was +suggested earlier, which is + +when people get a bit more +money, they do increase the + +share of the budget going +to other things. + +So the elasticity of overall +food expenditure + +is less than one. + +It's about 0.7. + +So if I increase your budget by +10%, you increase your food + +consumption by 7%. + +And then it means you increase +something else more than + +proportionally. + +So maybe you start spending +money on the movies, which you + +were not doing before. + +So that's the first thing. + +So 7% is not 3, though. + +So what is the difference +between 7 and 3? + +When I increase your budget by +10%, you increase your food + +budget by 7%. + +But your calories only +increase by 3.5. + +So what happened in +the meantime? + +[INAUDIBLE]. + +AUDIENCE: Maybe all your food +wasn't as high in calories. + +PROFESSOR: They bought more +expensive food anyway. + +Maybe because that food was +yummier, maybe because it was + +more nutritious, but certainly +more expensive food. + +So what happens is that when +you spend more on food, you + +start buying more expensive +calories and you do that in + +various ways. + +You start eating meat instead +of eating cereals, and you + +start eating more expensive +cereals instead of the course + +cereals you were +eating before. + +And even within the more +expensive cereals, rice for + +example, you buy more +expensive rice. + +So all of this margin happens. + +And we can see it here +in the table. + +We can see this is Maharashtra, +1983. + +These are the poorest +10% and the top 10%. + +We can see that the poorest 10% +spent 46% of their budget + +on cereals, and the +top 10%, 31%. + +And if we look at meat, meat +is 8.5% for the poorest and + +12% for the richest. + +Things like are constant, +however, in terms of fraction + +of the budget is sugar. + +And the sugar actually goes +down 7.425%, and oil. + +That remains about the same. + +The fraction of the budget spent +on oil is 9% for both. + +But you get cereal going down, +and you get meat going up. + +And the price per calorie of +cereal is much cheaper + +compared to the price +per calorie of meat. + +And now within cereal, people +who are poor spend 9% of their + +budget on the rice. + +And the rich are spending +almost 11% of + +their budget on rice. + +And then the price of rice is +also cheaper than the price of + +other things. + +Price is more expensive, sorry, +than other things like + +the course cereal. + +And even within rice, the +poor are buying cheaper + +rice than the rich. + +The poor are spending 18 paise +per calorie for the rice, and + +one rupee per calorie for +the richer people. + +So all of this margin happen, +which again suggests that + +there is some amount +of flexibility. + +Because otherwise, what you +would do is to, within the + +same budget, continue to eat +the same thing, but more of + +the same thing. + +So if you were at subsistence +level, the share of your + +calories that comes from +the staple food + +would remain constant. + +And it's only after you've +reached some level of + +subsistence that you would +say, now I can + +start eating more meat. + +It's more expensive, +but it's yummier. + +And so the fact that even for +these relatively poor people + +who see that the share of +calories that comes from rice + +declines is an indication that +they probably see themselves + +having some margin of choice. + +So even among the very poor +people, an increase in + +economic well being has +positive, but not a huge, + +impact on calories consumed. + +So you take the poorest person +here and you increase their + +budget by 10%, they will +increase their calories by + +3.5%, partly because there are +other things they like to do, + +partly because within +food, they also like + +to eat better food. + +So that brings us to this Jensen +and Miller idea, which + +is the idea of a Giffen good. + +So what's a Giffen good? + +AUDIENCE: It's a good that +when the price increases, + +there's an increase in demand. + +PROFESSOR: When the price +increase, there is + +an increase in demand. + +That's right. + +Why is that surprising? + +AUDIENCE: Because generally +the demand curves-- + +PROFESSOR: Yeah, go ahead. + +AUDIENCE: Generally as the price +increases, there's a + +decrease in the demand +for the quantity. + +PROFESSOR: Generally, we +think of the demand + +curve as looking down. + +So if there is an increase +in the price, you + +decrease your demand. + +So why is it not a violation +of everything + +we know about economics? + +AUDIENCE: Because if the price +of some good increases, then + +you wouldn't be able to +substitute out [INAUDIBLE] + +pretty easily. + +So the example of rice and +meat-- if the price of rice + +increases, then in order to get +the calories you need, you + +might have to buy more rice +and just stop buying meat. + +PROFESSOR: Right, Mr. Giffen is +referred to by who for the + +first time? + +Are there some writings +by Mr. Giffen? + +AUDIENCE: Indiana Jones. + +PROFESSOR: Indiana Jones-- + +but before that. + +So Mr. Giffen-- we have no +writing from him directly, but + +he was referred to +by Adam Smith. + +And Adam Smith gives +the example + +of potatoes in Ireland. + +The price of potatoes goes up, +but potatoes is such an + +important part of the budget +that when the price of + +potatoes goes up, it does an +income effect, so that is + +always true. + +When the price of a good goes +up, it has an income effect + +and it has a substitution +effect. + +What do we know about the +substitution effect? + +Yeah. + +AUDIENCE: Generally when the +price of one good goes up, + +[INAUDIBLE]. + +PROFESSOR: Right, so when the +price of a good goes up, you + +substitute to another good. + +So the substitution effect +is always negative. + +But the income effect can be +either positive or negative. + +So the income effect-- + +in what case is it positive? + +So for example, if you look at +iPod consumption, would that + +tend to have a positive +income effect or a + +negative income effect? + +So the goods that are more like +luxury goods, that are a + +bit expensive, will have +positive income effect, + +meaning as you become richer, +you will consume more of them. + +The goods that are cheaper and +that are not particularly + +desirable will have negative +income effect. + +For example, think about +your own budget. + +As you become richer, maybe +you are going to buy more + +orange juice. + +That is a positive +income effect. + +Maybe you are going to get +fewer macaroni and cheese + +pre-packed. + +That has a negative +income effect. + +So the income effect could be +positive or could be negative. + +It's positive if it's +a normal good. + +It's negative if it's +an inferior good. + +So now something like potato is + +presumably an inferior good. + +That's not something +people love. + +It's something that as they +become richer, they will try + +and substitute to +another thing. + +So the question is whether the +income effect of an inferior + +good like potato is so large-- + +not only it's negative, but it +is so large that it out does + +the substitution effect. + +So if the income effect is so +large that it more than + +compensates for the substitution +effect, then you + +might be getting a +different good. + +So that is the story of the +potato famine, which is + +possibly apocryphal, +the story being the + +price of potato increases. + +But that makes people poorer, +so that actually increases + +their consumption of potatoes, +because they stop eating meat, + +and they eat only potatoes +because they have no money + +left to buy any meat. + +So this is a different good. + +So until this paper, I think +there was a strong suspicion + +among economists that +different goods-- + +actually, they didn't exist, +but they were a nice + +theoretical possibility, but +that in practice, you don't + +see a good where the income +effect is so large that it + +outdoes the substitution effect, +so that if you become + +richer, you eat fewer +potatoes. + +But if the price of +potatoes declines, + +you eat more potatoes. + +So this is the story. + +So a staple food that +constitutes a large part of + +the budget, like potatoes for +Irish famine or the example + +they have in China are what? + +AUDIENCE: These were two +provinces in the North + +[INAUDIBLE]. + +PROFESSOR: Wheat and rice. + +So these are foods which are a +fairly large part of the food + +budget and a fairly large part +of the overall budget. + +So this is a good confident +for a different good. + +Because for the income effect to +have any chance to be large + +enough, it has to be something +that takes a large part of + +your budget. + +So that's why they decided +on this thing. + +So the first thing they've done +is they looked at these + +two provinces and they observed +that, for example, in + +a rice consuming region, they +observed that in cities where + +the price of rice is higher, +people consume more rice. + +And first, they are very happy, +and they said oh, we + +have found our Giffen good. + +But then they get depressed and +they realize maybe it is + +not a Giffen good. + +So why do they conclude +that it doesn't give + +them a Giffen good? + +AUDIENCE: [INAUDIBLE] + +is it because the price is +higher that people consume + +more rice, which would make it +an incident? or is it that + +people consume more rice, so +the price becomes higher? + +PROFESSOR: Right, +we don't know. + +We are trying to trace +a demand curve. + +But if we only observe prices +and quantity, we might be + +tracing the supply curve. + +So we don't know whether we have +traced the demand curve + +or the supply curve. + +And this would be the normal +shape for a supply curve. + +So this is exactly the same type +of problems that we were + +facing when we were trying to +look at the effect of malaria + +prices on bednets, which is if +we just look at the variation + +in the world, there is the +effect that we are trying to + +identify, and there is a +possible of a reverse + +causality, in this case, very +clear, which is we also have a + +supply curve that we are +trying to trace. + +So that's why they decided +that's not working. + +So what did they decide to do? + +AUDIENCE: They subsidized +rice and wheat. + +[INAUDIBLE]. + +PROFESSOR: Exactly, what they +decided to do is to run the + +maize experiment where they +subsidized the price of rice + +in the rice consuming region +and wheat in the wheat + +consuming region at +various levels. + +I think there are three +levels of subsidies. + +So they take a sample +of households. + +They distribute a voucher for +the reduced price of rice in + +Hunan and reduced price of wheat +in Gangsu to a random + +sub sample for more than a +month's supply every month. + +They made sure that +the household + +wouldn't extend them. + +Otherwise, what would be a +problem if households started + +trading them? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Exactly, in +particular you try + +to reduce the price. + +But if you give voucher and +people start exchanging them, + +think of food stamps when people +sell their food stamps. + +When they sell their food +stamps, they are getting + +money, which is-- + +I mean, it's not bad. + +But why do we think +it's an issue? + +And why would there +be a theoretical + +issue in their cases? + +AUDIENCE: Essentially, the price +of the rice would need + +to be changed. + +PROFESSOR: It wouldn't +be changing. + +So the people would get their +voucher, and then they would + +sell it to someone. + +So they would get +money instead. + +And then they would, with that +many, perhaps buy some rice + +and wheat and buy some +other things as well. + +So their experiment where they +tried to change the price of + +rice or wheat would end up just +changing their income + +without changing the price. + +Because the marginal price that +they are facing once they + +have sold their voucher is the +same, except they now have + +more money. + +So now all they would identify +is the income effect. + +And of course, the income +effect would be negative + +because that's an +inferior good. + +So they would be finding +a Giffen good. + +But that would not +be a real one. + +That would be a fake one due to +the fact that their price + +experiment would be transformed +into an income + +experiment. + +So it's very important for +them to keep the price + +experiment in tact. + +So they tried to do that and +they tried to argue in the + +paper and in the post that you +read in Freakonomics that + +they've done this properly. + +And after six months, they came +back, and then they asked + +detailed questions about the +consumption of rice, wheat and + +other things. + +So what do they find? + +So I'm going to show you the +regression table which gives + +us the results directly and +explain to you what's in the + +regression table. + +So it's a long table. + +But for now, focus on +the first column. + +So what they regress is the +percent increase in rice + +consumption over the +percent subsidy. + +There are three groups +of subsidies. + +I was looking everywhere in the +paper for you to have the + +three prices and the three +reductions so that I could + +plot them, but they +were not there. + +So this is the overall result. + +So basically, the way you +read this graph-- + +it's saying that your +consumption of rice reduces by + +23.5% when the subsidy +increases by 100%. + +It's directly a percentage +of a percentage. + +So your consumption of rice +reduces in percentage about a + +quarter of the reduction +in price. + +So the important thing +here is, of + +course, that it's negative. + +And below the coefficient +here, you get + +the standard error. + +So the coefficient is 0.235. + +The standard error 0.14. + +If you divide by one the other, +you get the familiar T + +statistics. + +This one is above 1.7, so this +means this is significant at + +10% level, which tells +you that this is not + +entirely due to chance. + +This negative is +not some fluke. + +It is something which is +indeed significantly + +different from 0. + +So that's what they +find for Hunan. + +And then they find the opposite +for seafood, where + +the elasticity of seafood +consumption with respect to + +the price of rice is +very positive. + +So what happened in +their experiment-- + +this is your typical Giffen +good behavior-- + +is the price of rice increases, +but increases + +because rice is such an +important part of your budget. + +It amounts to increasing +your income. + +And because of this increase in +your income, you feel that + +you can now get more of your +calories from shrimps and + +fewer from food. + +So that's for Hunan. + +So this is the explanation. + +And for Gansu, we have a +positive elasticity. + +So it means that wheat doesn't +appear to be a + +Giffen good in Gansu. + +It appears to be an +inferior good. + +It increased less than one for +one, but in fact, it's not + +significantly positive. + +But it's certainly +not negative. + +And they explain why they find +a different result in a + +different place. + +[INAUDIBLE]. + +AUDIENCE: What prevented then +from just [INAUDIBLE] rice + +they got to give more money +by substituting goods? + +PROFESSOR: Right, so they +tried to stop that. + +But we don't know for sure +that they succeeded. + +What they were very worried +about is the + +resale of the voucher. + +And their view then is once you +had resold the voucher, + +then you wouldn't have +resold the rice. + +And what they did after that +is they did a survey. + +So the data here doesn't come +from the administrative data + +of what was sold in the shop. + +The survey comes from what +people consumed at + +the end of the day. + +So to the extent that people +didn't lie to them, this is + +the actually consumption. + +So it could still be the case +that they bought the rice. + +They sold the rice. + +They bought the rice with the +voucher because they couldn't + +exchange the voucher. + +But then, they went to the +trouble of selling the rice. + +And that's why it's just an +income effect that we are + +estimating, which is +why it's negative. + +They tried to argue that it +didn't happen, but that's, of + +course, a key concept. + +So what do they say about wheat, +that why did the wheat + +show them a different good for +the wheat, but they have one + +for the rice? + +AUDIENCE: Because people aren't +eating wheat itself. + +They're eating wheat products, +like noodles. + +PROFESSOR: Exactly, you are +saying that it's not their own + +group, that people rice. + +They don't buy big packets of +wheat, so that it was kind of + +the wrong idea. + +This, of course, has implication +for nutrition, and + +in particular for a very +frequent policy that we find + +in developing world, which is +food price's subsidy for + +greater nutrition. + +So for example, in Indonesia, +we have the ration program. + +If you remember, in Pak Solhin's +stories, he got some + +free rice from the +ration program. + +In India, India just introduced +the Right to Food + +Act and a subsidy scheme +for rice in + +rice consuming regions. + +So India has something called +a public distribution system + +where they distribute food to +households at reduced prices, + +to poor households at +reduced prices. + +Egypt spent something like 3% of +its GDP on food subsidies. + +So food subsidies is a very +important part of help to the + +poor in developing countries. + +It's also a very important +part of our-- + +our meaning the US-- + +aid to poor countries is in the +form of food aid, directly + +food which we send to +poor countries. + +Why are we spending a lot of our +aid in terms of food aid? + +AUDIENCE: [INAUDIBLE] + +lot of food [INAUDIBLE]. + +It's easier for us to just +take that [INAUDIBLE]. + +PROFESSOR: Yes, so part of the +reason why a lot of our aid is + +in the form of food aid +is that it's also + +aid for our own farmers. + +And it's a way of kind of +buying the [INAUDIBLE] + +and sending them out. + +So when the weather has been +good in the US and the harvest + +is very big, a lot more food +aid is being spent + +all over the world. + +But with that aside, this is a +policy that many countries + +have to try to subsidize +the price of food. + +But if we have something like +the Giffen good, what may + +happen if you make the price +of the staple less high, if + +you make the price of +the staple lower? + +Yes. + +AUDIENCE: Then they'll spend +their income on other sorts of + +stuff, not on the [INAUDIBLE]. + +PROFESSOR: Yes, we might find +that something like this + +happens, which is the price +of rice has now gone down. + +Instead of eating more rice, +you ate less rice and more + +shrimps and maybe also +more cellphones. + +So if rice is indeed a Giffen +good, the increase in the + +calories you are getting from a +decline in the price of rice + +might actually not +be very high. + +In fact, it might even +be negative. + +Because if the income effect is +sufficiently large, it made + +outdo, again, the +price effect. + +And we might find that as we +make food cheaper, people eat + +less instead of eating more. + +And that's exactly what they +found in Hunan where rice was + +a Giffen good. + +They find that as you decrease +the price of rice, people eat + +fewer calories, not more. + +So this would be the very +standard poor price policy in + +your average developing +countries, to try to subsidize + +the staple. + +And the justification of this +policy will typically be in + +the form of we need to +increase the calorie + +consumption because people are +trapped in poverty trap like + +our friend, Pak Solhin. + +But in fact, if you look at this +for this urban household + +in China, you find the opposite, +which is subsidizing + +the price of rice actually +leads to + +fewer calories consumed. + +And it's not because people gain +in terms of other micro + +nutrients, though we +don't have all + +the other micro nutrient. + +But we get fewer portions +being consumed as well. + +So this is what they find +in Hunan, but they + +don't have it in Gansu. + +So it's not to say that +it happens necessarily + +everywhere, but it is something +that might happen. + +So it is not a total given that +a reduction in the price + +of food will lead to an +increase in nutrition. + +On the bright side, it also +means that it's not + +necessarily a given that the +current increase in the food + +prices that we are observing +will lead to people eating + +fewer calories. + +Because it might have this +progress effect of making them + +poorer and therefore leading +them to eat more of calories. + +AUDIENCE: Yeah, I think +one way [INAUDIBLE] + +food [INAUDIBLE]. + +Because, for example, if you eat +shrimps, shrimps may not + +be very calorie rich. + +In India, people eat +a lot of lentils. + +And the next thing that they eat +to rice is durum, which is + +actually full of protein. + +So eating less rice, and if they +spend more on protein, + +[INAUDIBLE]. + +PROFESSOR: Right, so this is, +of course, completely + +dependent on what you +substitute with. + +If you substitute rice with +lentils, actually it might be + +more nutrition, and more iron, +more nutrition, et cetera. + +So we might find an increase in +nutrition due to subsidy in + +the price the rice. + +So the only point here was +not to say that it + +has to be the case. + +It was to say that it doesn't +have to be the case that + +subsidizing the price the rice +will lead to more rice and + +more calories being consumed. + +Now let's look at India, +precisely. + +So before that, there is +something that should surprise + +you in when you put together +this Jenson and Miller result + +and what we had before +in India. + +We found that a household that +are 10% richer eat about 3.5 + +more calories. + +But the Jenson and +Miller result-- + +what does it suggest about +the income effect? + +We are finding that when the +price of rice decreases, you + +eat less, not more. + +What the income effect +has to be? + +AUDIENCE: It's negative. + +PROFESSOR: It has +to be negative. + +So on the one hand, I showed you +positive income effect-- + +maybe not very large, but +certainly positive for India. + +On the other hand, I'm showing +you price effect in China + +which suggest that the income +effect has to be negative, and + +in fact, very negative. + +So how can this be? + +How can we have the two +things together? + +So the first thing is that in +India, we were comparing + +different households. + +We were not comparing the +same household to + +which I give more money. + +And different households +are different. + +Maybe they're households +that are a bit richer. + +They are also more educated and +they understand the value + +of nutrition, and that's +why they eat more. + +So the idea in experiment would +be to give people a + +little bit more money, really +literally do that and see + +whether they spend this +money on food or not. + +And that would allow us to +estimate the income effect. + +To my knowledge, no +one has done that. + +It's a little bit difficult +to parachute [INAUDIBLE] + +drops of money on people-- + +not impossible, but it's not +been done, I don't think. + +So what we have when we looked +at the India curve, we find + +that people who have more +money eat more. + +But it may be because they have +different tastes or it + +might be because they eat more, +and therefore they're + +more productive, therefore they +have more money, so the + +opposite relationship. + +So that may be an +underestimate. + +That positive estimate, which +was already not that high of + +the income effect, might have +been an over estimate. + +And one thing that's +suggested-- + +and it goes back to +[? Swati's ?] point earlier-- + +is when we plug the Engel curve +over time in India, we + +see two interesting things. + +Number one, all of the Engel +curve for the rural areas are + +above the Engel curve +for the urban areas. + +Why do you think that +would be the case? + +AUDIENCE: The work in the rural +area is much more labor + +intensive, so you need +to eat more to + +have physical strength. + +PROFESSOR: Exactly, the work +in rural area is more + +intensive, and so they +need more calories. + +So this is interesting that +you are making this point, + +because this is the point you +were making earlier about + +maybe the needs of calorie in +South Africa are bigger + +because it's colder. + +So that's the first +things we notice. + +So this we can explain. + +And what's the other interesting +trend in this + +picture is that over time, the +Engel curves are falling down. + +People are eating less, and +less, and less for the same + +level of income. + +So what happened in India over +time is that, of course, + +people got richer. + +So if the Engel curves had been +stable, they would have + +eaten more. + +But because the Engel curves are +also falling down at the + +same time, what happened over +time is that people are moving + +first across to another Engel +curve and then up along an + +Engel curve. + +So take someone who would +be at a log income of 5. + +15 years later, they have a log +income maybe of 5.5, but + +the Engel curve have +also moved. + +Take someone who is at 5, and +then 15 years later, they + +would be, let's say, at 6. + +But now we need to find the 6 on +the much lower Engel curve. + +So instead of eating more, as +they would have if the Engel + +curve had become stable, we find +that people in India eat + +less and less. + +So over time, the poor in India +are eating less and less + +instead of eating more and more, +which does suggest some + +negative income elasticity for +the country as a whole. + +The country is becoming richer +and those people are becoming + +richer, but they are eating +less and less. + +So this now starts to make sense +with the two results, + +where maybe the income +elasticity of food + +consumption-- + +not only it's not above one, +which is what we would have in + +a poverty trap kind of a +world, but it might be + +negative, which is as people +become richer, they-- a funny + +thing-- eat fewer calories. + +So if we look at nutrition in +India, we have a pretty + +interesting phenomenon, which is +this is the share of people + +who are eating below 2,100 +in urban areas and + +2,400 in rural areas. + +This is the number of calories +they consume per head. + +Why are these interesting +thresholds? + +Yeah. + +You had a question or you +were just moving? + +AUDIENCE: Yeah, I was going +to ask [INAUDIBLE]. + +PROFESSOR: Go ahead, go ahead. + +AUDIENCE: I was wondering +if that couldn't just be + +explained because of inflation +and not necessarily for a + +negative effect. + +PROFESSOR: Very good, +I could be that the + +price of food has changed. + +People have become richer, but +food is now more expensive. + +Remember, it has to be relative +prices, because + +people have become richer +in real term. + +Even corrected for inflation, +India is richer now. + +And there are also fewer +poor people. + +But it could be that food prices +increase relative to + +other things. + +And that's actually not +the case until 2005. + +And then it became very much +the case after 2005. + +But these results are until +2005, where the relative price + +of food were relatively +stable. + +That's a very good point. + +2,100, 2,400. + +Yeah. + +AUDIENCE: So I was just +wondering the calculation that + +was done for people who are +doing sort of intensive labor, + +how many calories they would +need as a bare minimum to be + +able to succeed in that? + +PROFESSOR: Again, we don't +really know how many calories + +we need, but this is +what the Indian + +government says you need. + +And maybe they get it a bit +wrong, because this is the + +fraction of people in rural +area who are getting + +less than they need. + +So it's very high. + +Yet these people are +still all alive. + +But what is striking is that +this is increasing both in + +rural area and in urban area, +but even more in rural area. + +So one first explanation was +yours, is maybe it's the + +relative price of food. + +That would be true after 2005, +but not until 2005. + +What could be other +explanation? + +AUDIENCE: Maybe a lot of poor +people have come from rural + +areas, and very poor +[INAUDIBLE] + +rural areas and then sort of +broke up into rural areas + +[INAUDIBLE]. + +PROFESSOR: So that's a +very good suggestion. + +Maybe that the people who are +in rural area now are the + +very, very poor, so they are +relatively poorer, so we get + +more of them who are +eating less. + +And the urban area also getting +poorer, because the + +people from the rural +area move to them. + +That's a very good suggestion, +a composition effect. + +That probably doesn't explain +it, because if you look at + +that overall consumption per +capita of these people, are + +the function of people who live +below a dollar a day, + +that is going down here +and down here. + +So that's probably not-- + +AUDIENCE: There has been +more technology. + +They're going to spend other +money on other stuff. + +PROFESSOR: Right, so this would +be another explanation, + +which is the similar explanation +from what we are + +seeing on the wall, which +is there are more + +and more things available. + +In particular, one thing that +has clearly happened is the + +advent of cell phone. + +And so now cell phones weren't +there, and now they are there. + +In India, you can get a cell +phone and airtime everywhere. + +And so that's one thing. + +So more things become available, +very good. + +Yeah. + +AUDIENCE: I think this might +be what you meant, but + +technology that might make the +work easier, so you require + +fewer calories because the +work is not as difficult. + +PROFESSOR: Right, this is not +what she meant just now, but + +that's what she meant earlier. + +So I was surprised she is not +making this point again. + +But that's exactly a very good +point, which is maybe these + +are what the Indian government +says, but who + +knows what they know. + +And maybe the calorie +requirements have changed. + +One of the reasons would be that +you're less likely to do + +back breaking work, or maybe +because there is more + +irrigation, there is more +mechanisation of agriculture. + +People are less likely +to be in agriculture, + +even in rural areas. + +What would be another reason +why the calorie requirement + +would have gone down? + +So one is clearly, you are +less likely to work. + +What competes with calories +with you? + +AUDIENCE: Are you talking +about worms and health? + +PROFESSOR: Worms, and health and +diarrhea, and other nice + +things like that. + +Generally being sick consumes +a lot of calories. + +And so one thing that has +happened in India is drinking + +water has become more available +and cleaner, so + +people are much less +likely to be sick. + +Another thing that uses a lot of +calories is being pregnant, + +and you have many fewer +children being born. + +So that's also compete +less for calories. + +So one possible reason for all +of these, for these changes, + +is that the calorie requirements +have just changed + +and people are staying at the +same level as before. + +They spend less. + +And they are used to a +particular level, so they just + +stay there, and it costs them +less money than before. + +So this leads us to a +possibility for why people are + +not easy more generally. + +Maybe they're not eating because +that's not such a + +great investment. + +And so when we went through +out little theory section + +here, we said that if you happen +to be right here in the + +capacity curve, it's very +valuable for you to eat. + +But if, in the real world, +the effect of calories on + +productivity is not that loud, +then you might as well do + +something else with +your money. + +And in fact, what we find when +we look at the effect is that + +this is the effect of calories +consumed on your productivity + +if you're a farmer +in Sierra Leone. + +And it's hard to find a job that +requires less strength + +than being a farmer +in Sierra Leone. + +And what you find is that +while it is increasing, + +certainly, people +who eat more-- + +this is your calorie +consumption, and this is how + +productive you are-- + +people are more productive +when they eat more. + +But what's the shape +of the curve? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: It's our inverted +L shape, and it's not + +greater than one. + +So now we finally can answer +the question that + +you asked ages ago. + +There is no real sign. + +This is probably the most +favorable case, which is why I + +put it on the board. + +There is no real sign that this +phenomenon that you need + +to eat enough calories, +otherwise you can't be + +productive enough to do anything +is really there. + +So in the very short run, +everything starts to fit, + +which is people don't really +need the extra calories that + +much, because the extra +calories makes them + +productive, but not that +much more productive. + +Hence, they are not +eating them. + +And in fact, we see over time +that they are eating less and + +less of the calories +because they need + +less and less of them. + +And they have a level of +strength that allows them to + +do their day to day work, and +with the rest of their money, + +they do other things, and that +makes now perfect sense. + +So in terms of policies, +what does it mean? + +Well in term of policies, it +means that policies that are + +going to insist that the big +problem is starvation in terms + +of not eating enough grain +are probably going to be + +misleading, and are probably +going to lead to a + +fair amount of waste. + +So in summary, at the maximum +when your income today + +increases by 10%, your calorie +consumption increase by 3.5%. + +That's what we saw in India, +and that's almost surely a + +wild over estimate. + +But let's say that it's +a maximum possible. + +And then your productivity-- + +you multiply that by another +4%, so when your income + +increases by 10%, your income +increases by 1.4% tomorrow. + +That would be the S shape, +except it's not S, because + +there is no point where it would +cause the 45 degree line + +from below, because the +elasticity is much, much less + +than one instead of +being above one. + +So we don't have a place where +the curve is crossing the 45 + +degree line from below. + +The curve is just not steep +enough to create a poverty + +trap from this phenomenon. + +Just to be sure that you don't +go away thinking everything is + +well, this may be very different +from other things + +than calories, for +example iron. + +And this may be very different +for children, because the + +investment in a child, the +investment you're making at + +one specific time is going to +help them for their entire + +life instead of just +for tomorrow. + +So what we are going to do on +Thursday is look at what I + +call the hidden trap, which +is that there might be a + +nutrition productivity poverty +trap, but it's not in the + +usual sense where we +were looking for. + +It's in these more subtle +things, nutrients, + +micronutrients, children's +nutrition, + +pregnant women's nutrition. \ No newline at end of file diff --git a/G8o7WcoW2Ms.txt b/G8o7WcoW2Ms.txt new file mode 100644 index 0000000000000000000000000000000000000000..50f0e56af348f428c629e992fac70af0182496ee --- /dev/null +++ b/G8o7WcoW2Ms.txt @@ -0,0 +1,8955 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license 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ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay so no quiz today and no quiz Friday + + align:start position:0% +okay so no quiz today and no quiz Friday + + + align:start position:0% +okay so no quiz today and no quiz Friday +uh + + align:start position:0% +uh + + + align:start position:0% +uh +but I am posting a homework that will be + + align:start position:0% +but I am posting a homework that will be + + + align:start position:0% +but I am posting a homework that will be +due Friday + + align:start position:0% + + + + align:start position:0% + +very late on Friday + + align:start position:0% + + + + align:start position:0% + +we can't officially have them do + + align:start position:0% +we can't officially have them do + + + align:start position:0% +we can't officially have them do +after + + align:start position:0% +after + + + align:start position:0% +after +Friday so + + align:start position:0% +Friday so + + + align:start position:0% +Friday so +but I felt the homework would be more + + align:start position:0% +but I felt the homework would be more + + + align:start position:0% +but I felt the homework would be more +useful to you and getting ready for the + + align:start position:0% +useful to you and getting ready for the + + + align:start position:0% +useful to you and getting ready for the +final + + align:start position:0% +final + + + align:start position:0% +final +and uh + + align:start position:0% + + + + align:start position:0% + +I wrote eight questions we want you to + + align:start position:0% +I wrote eight questions we want you to + + + align:start position:0% +I wrote eight questions we want you to +write on six of them at least if you + + align:start position:0% +write on six of them at least if you + + + align:start position:0% +write on six of them at least if you +want to write on the extra ones if you + + align:start position:0% +want to write on the extra ones if you + + + align:start position:0% +want to write on the extra ones if you +have time that's fine we'll give you + + align:start position:0% +have time that's fine we'll give you + + + align:start position:0% +have time that's fine we'll give you +extra credit for that + + align:start position:0% +extra credit for that + + + align:start position:0% +extra credit for that +all right now from the last session what + + align:start position:0% +all right now from the last session what + + + align:start position:0% +all right now from the last session what +we didn't finish + + align:start position:0% +we didn't finish + + + align:start position:0% +we didn't finish +was uh + + align:start position:0% +was uh + + + align:start position:0% +was uh +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +we talked about stem cells put in the + + align:start position:0% +we talked about stem cells put in the + + + align:start position:0% +we talked about stem cells put in the +brain as a treatment + + align:start position:0% + + + + align:start position:0% + +for Parkinson's and uh + + align:start position:0% + + + + align:start position:0% + +I want to talk about the cells that are + + align:start position:0% +I want to talk about the cells that are + + + align:start position:0% +I want to talk about the cells that are +being generated normally in the adult + + align:start position:0% +being generated normally in the adult + + + align:start position:0% +being generated normally in the adult +brain + + align:start position:0% +brain + + + align:start position:0% +brain +this was first discovered here at MIT + + align:start position:0% +this was first discovered here at MIT + + + align:start position:0% +this was first discovered here at MIT +when Joseph aldman was in the department + + align:start position:0% +when Joseph aldman was in the department + + + align:start position:0% +when Joseph aldman was in the department +before he took up a position at Purdue + + align:start position:0% +before he took up a position at Purdue + + + align:start position:0% +before he took up a position at Purdue +University where he's been ever since + + align:start position:0% + + + + align:start position:0% + +he discovered them in two places we + + align:start position:0% +he discovered them in two places we + + + align:start position:0% +he discovered them in two places we +talked about + + align:start position:0% +talked about + + + align:start position:0% +talked about +one of those already the new neurons + + align:start position:0% +one of those already the new neurons + + + align:start position:0% +one of those already the new neurons +that are generated in the olfactory bulb + + align:start position:0% +that are generated in the olfactory bulb + + + align:start position:0% +that are generated in the olfactory bulb +but he also discovered that they were + + align:start position:0% +but he also discovered that they were + + + align:start position:0% +but he also discovered that they were +generated in adult rats in the + + align:start position:0% +generated in adult rats in the + + + align:start position:0% +generated in adult rats in the +hippocampus + + align:start position:0% +hippocampus + + + align:start position:0% +hippocampus +specifically in the dentate gyrus the + + align:start position:0% +specifically in the dentate gyrus the + + + align:start position:0% +specifically in the dentate gyrus the +granule cells of the dentate Yards + + align:start position:0% +granule cells of the dentate Yards + + + align:start position:0% +granule cells of the dentate Yards +similarly in the olfactory bulbs they + + align:start position:0% +similarly in the olfactory bulbs they + + + align:start position:0% +similarly in the olfactory bulbs they +were the granule cells that have + + align:start position:0% +were the granule cells that have + + + align:start position:0% +were the granule cells that have +turnover + + align:start position:0% +turnover + + + align:start position:0% +turnover +about a 40-day turnover in res + + align:start position:0% + + + + align:start position:0% + +and they migrate from the lateral + + align:start position:0% +and they migrate from the lateral + + + align:start position:0% +and they migrate from the lateral +ventricles to the olfactory bulbs and in + + align:start position:0% +ventricles to the olfactory bulbs and in + + + align:start position:0% +ventricles to the olfactory bulbs and in +the hippocampus + + align:start position:0% +the hippocampus + + + align:start position:0% +the hippocampus +similarly they're generated in the + + align:start position:0% +similarly they're generated in the + + + align:start position:0% +similarly they're generated in the +ventricular layer and they migrate + + align:start position:0% +ventricular layer and they migrate + + + align:start position:0% +ventricular layer and they migrate +to their the adult position + + align:start position:0% +to their the adult position + + + align:start position:0% +to their the adult position +turnover of those cells it's not that + + align:start position:0% +turnover of those cells it's not that + + + align:start position:0% +turnover of those cells it's not that +we're getting a bigger and bigger + + align:start position:0% +we're getting a bigger and bigger + + + align:start position:0% +we're getting a bigger and bigger +vintage errors because we learn more and + + align:start position:0% +vintage errors because we learn more and + + + align:start position:0% +vintage errors because we learn more and +more + + align:start position:0% +more + + + align:start position:0% +more +there's actually turnover + + align:start position:0% + + + + align:start position:0% + +there is there are data obtained by some + + align:start position:0% +there is there are data obtained by some + + + align:start position:0% +there is there are data obtained by some +Labs that indicate that there's a much + + align:start position:0% +Labs that indicate that there's a much + + + align:start position:0% +Labs that indicate that there's a much +lower level of + + align:start position:0% +lower level of + + + align:start position:0% +lower level of +a generation of new cells in other + + align:start position:0% +a generation of new cells in other + + + align:start position:0% +a generation of new cells in other +places as well + + align:start position:0% +places as well + + + align:start position:0% +places as well +including neocortex but it's been a lot + + align:start position:0% +including neocortex but it's been a lot + + + align:start position:0% +including neocortex but it's been a lot +more controversial when you're just + + align:start position:0% +more controversial when you're just + + + align:start position:0% +more controversial when you're just +looking at missile stains it can be very + + align:start position:0% +looking at missile stains it can be very + + + align:start position:0% +looking at missile stains it can be very +difficult + + align:start position:0% +difficult + + + align:start position:0% +difficult +to discriminate uh + + align:start position:0% +to discriminate uh + + + align:start position:0% +to discriminate uh +some glial cells + + align:start position:0% +some glial cells + + + align:start position:0% +some glial cells +some astrocytes from neurons and + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +with all the reports that have appeared + + align:start position:0% +with all the reports that have appeared + + + align:start position:0% +with all the reports that have appeared +and the studies have been done there are + + align:start position:0% +and the studies have been done there are + + + align:start position:0% +and the studies have been done there are +antibodies that allow them to + + align:start position:0% +antibodies that allow them to + + + align:start position:0% +antibodies that allow them to +discriminate there appears to be some + + align:start position:0% +discriminate there appears to be some + + + align:start position:0% +discriminate there appears to be some +new neurons generated + + align:start position:0% +new neurons generated + + + align:start position:0% +new neurons generated +in the adult brain + + align:start position:0% +in the adult brain + + + align:start position:0% +in the adult brain +but we know we really don't know + + align:start position:0% +but we know we really don't know + + + align:start position:0% +but we know we really don't know +anything about them and their function + + align:start position:0% +anything about them and their function + + + align:start position:0% +anything about them and their function +except in the + + align:start position:0% +except in the + + + align:start position:0% +except in the +in the hippocampus where they've been + + align:start position:0% +in the hippocampus where they've been + + + align:start position:0% +in the hippocampus where they've been +studied + + align:start position:0% + + + + align:start position:0% + +these are just pictures to remind you + + align:start position:0% +these are just pictures to remind you + + + align:start position:0% +these are just pictures to remind you +about I noticed here looking at these + + align:start position:0% +about I noticed here looking at these + + + align:start position:0% +about I noticed here looking at these +old Scientific American figures + + align:start position:0% +old Scientific American figures + + + align:start position:0% +old Scientific American figures +by temperament engage where they were + + align:start position:0% +by temperament engage where they were + + + align:start position:0% +by temperament engage where they were +talking about the new cell generation + + align:start position:0% +talking about the new cell generation + + + align:start position:0% +talking about the new cell generation +hippocampus + + align:start position:0% +hippocampus + + + align:start position:0% +hippocampus +they have this picture and they they + + align:start position:0% +they have this picture and they they + + + align:start position:0% +they have this picture and they they +show this box here + + align:start position:0% +show this box here + + + align:start position:0% +show this box here +and then here's the blow up and the blow + + align:start position:0% +and then here's the blow up and the blow + + + align:start position:0% +and then here's the blow up and the blow +up is from down here + + align:start position:0% +up is from down here + + + align:start position:0% +up is from down here +is notice down here the dendrites the + + align:start position:0% +is notice down here the dendrites the + + + align:start position:0% +is notice down here the dendrites the +cells would be here and the dendrites + + align:start position:0% +cells would be here and the dendrites + + + align:start position:0% +cells would be here and the dendrites +would be going up like this + + align:start position:0% +would be going up like this + + + align:start position:0% +would be going up like this +well there the dendrites are going down + + align:start position:0% +well there the dendrites are going down + + + align:start position:0% +well there the dendrites are going down +okay but these are the way those + + align:start position:0% +okay but these are the way those + + + align:start position:0% +okay but these are the way those +little cells in the dentate gyrus look + + align:start position:0% +little cells in the dentate gyrus look + + + align:start position:0% +little cells in the dentate gyrus look +and this is a study I did put in the + + align:start position:0% +and this is a study I did put in the + + + align:start position:0% +and this is a study I did put in the +book because it it gave a demonstration + + align:start position:0% +book because it it gave a demonstration + + + align:start position:0% +book because it it gave a demonstration +that these new cells are being generated + + align:start position:0% +that these new cells are being generated + + + align:start position:0% +that these new cells are being generated +in humans as well these were people that + + align:start position:0% +in humans as well these were people that + + + align:start position:0% +in humans as well these were people that +were being + + align:start position:0% +were being + + + align:start position:0% +were being +uh treated for cancer + + align:start position:0% +uh treated for cancer + + + align:start position:0% +uh treated for cancer +and in taking tissue from the cancer + + align:start position:0% +and in taking tissue from the cancer + + + align:start position:0% +and in taking tissue from the cancer +they needed to know you know how much + + align:start position:0% +they needed to know you know how much + + + align:start position:0% +they needed to know you know how much +new cell generation was there you know + + align:start position:0% +new cell generation was there you know + + + align:start position:0% +new cell generation was there you know +in a cancer there's proliferation + + align:start position:0% +in a cancer there's proliferation + + + align:start position:0% +in a cancer there's proliferation +abnormal proliferation of cells + + align:start position:0% +abnormal proliferation of cells + + + align:start position:0% +abnormal proliferation of cells +so they they give them + + align:start position:0% +so they they give them + + + align:start position:0% +so they they give them +bromodeoxyridine which labels the newly + + align:start position:0% +bromodeoxyridine which labels the newly + + + align:start position:0% +bromodeoxyridine which labels the newly +generated cells + + align:start position:0% +generated cells + + + align:start position:0% +generated cells +so in + + align:start position:0% +so in + + + align:start position:0% +so in +patients who died they were able to get + + align:start position:0% +patients who died they were able to get + + + align:start position:0% +patients who died they were able to get +some tissue + + align:start position:0% +some tissue + + + align:start position:0% +some tissue +and this is just an example of that + + align:start position:0% +and this is just an example of that + + + align:start position:0% +and this is just an example of that +where they show a BRD brdu labels + + align:start position:0% +where they show a BRD brdu labels + + + align:start position:0% +where they show a BRD brdu labels +granule cell indicating that it was + + align:start position:0% +granule cell indicating that it was + + + align:start position:0% +granule cell indicating that it was +generated + + align:start position:0% +generated + + + align:start position:0% +generated +around the time that brdu was injected + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +now the studies of this cell generation + + align:start position:0% +now the studies of this cell generation + + + align:start position:0% +now the studies of this cell generation +in rats have they not only look at the + + align:start position:0% +in rats have they not only look at the + + + align:start position:0% +in rats have they not only look at the +cell generation they look at its rate + + align:start position:0% +cell generation they look at its rate + + + align:start position:0% +cell generation they look at its rate +how and what conditions are affecting it + + align:start position:0% +how and what conditions are affecting it + + + align:start position:0% +how and what conditions are affecting it +and + + align:start position:0% +and + + + align:start position:0% +and +this is from an earlier study where they + + align:start position:0% +this is from an earlier study where they + + + align:start position:0% +this is from an earlier study where they +had shown that if you enrich the + + align:start position:0% +had shown that if you enrich the + + + align:start position:0% +had shown that if you enrich the +environment this is an enriched + + align:start position:0% +environment this is an enriched + + + align:start position:0% +environment this is an enriched +environment + + align:start position:0% +environment + + + align:start position:0% +environment +uh these + + align:start position:0% + + + + align:start position:0% + +are these mice are rats + + align:start position:0% + + + + align:start position:0% + +well it happens in both of them + + align:start position:0% +well it happens in both of them + + + align:start position:0% +well it happens in both of them +I think these are rats and that shows + + align:start position:0% +I think these are rats and that shows + + + align:start position:0% +I think these are rats and that shows +they're small rats and they show + + align:start position:0% +they're small rats and they show + + + align:start position:0% +they're small rats and they show +and you know all kinds of toys places to + + align:start position:0% +and you know all kinds of toys places to + + + align:start position:0% +and you know all kinds of toys places to +run around they're changing these toys a + + align:start position:0% +run around they're changing these toys a + + + align:start position:0% +run around they're changing these toys a +lot so they keep some novelty there so + + align:start position:0% +lot so they keep some novelty there so + + + align:start position:0% +lot so they keep some novelty there so +the rats are always exploring + + align:start position:0% +the rats are always exploring + + + align:start position:0% +the rats are always exploring +and when they have an environment like + + align:start position:0% +and when they have an environment like + + + align:start position:0% +and when they have an environment like +that instead of just putting the same + + align:start position:0% +that instead of just putting the same + + + align:start position:0% +that instead of just putting the same +number in a small plastic cage where + + align:start position:0% +number in a small plastic cage where + + + align:start position:0% +number in a small plastic cage where +there's + + align:start position:0% +there's + + + align:start position:0% +there's +not much to do + + align:start position:0% +not much to do + + + align:start position:0% +not much to do +these animals these animals show a lot + + align:start position:0% +these animals these animals show a lot + + + align:start position:0% +these animals these animals show a lot +more neurogenesis in the dentate gyrus + + align:start position:0% +more neurogenesis in the dentate gyrus + + + align:start position:0% +more neurogenesis in the dentate gyrus +and there's a picture showing different + + align:start position:0% +and there's a picture showing different + + + align:start position:0% +and there's a picture showing different +rate of neurogenesis + + align:start position:0% +rate of neurogenesis + + + align:start position:0% +rate of neurogenesis +now if you look online you'll see that + + align:start position:0% +now if you look online you'll see that + + + align:start position:0% +now if you look online you'll see that +the more recent Studies have extended + + align:start position:0% +the more recent Studies have extended + + + align:start position:0% +the more recent Studies have extended +this kind of work they found + + align:start position:0% +this kind of work they found + + + align:start position:0% +this kind of work they found +that + + align:start position:0% +that + + + align:start position:0% +that +animals that are under a lot of stress + + align:start position:0% +animals that are under a lot of stress + + + align:start position:0% +animals that are under a lot of stress +I mean if you give them learning to do + + align:start position:0% +I mean if you give them learning to do + + + align:start position:0% +I mean if you give them learning to do +but it's very stressful and they're + + align:start position:0% +but it's very stressful and they're + + + align:start position:0% +but it's very stressful and they're +being shocked or this or that + + align:start position:0% +being shocked or this or that + + + align:start position:0% +being shocked or this or that +you know + + align:start position:0% +you know + + + align:start position:0% +you know +animals under stress produce fewer new + + align:start position:0% +animals under stress produce fewer new + + + align:start position:0% +animals under stress produce fewer new +cells in in the dentate jars + + align:start position:0% +cells in in the dentate jars + + + align:start position:0% +cells in in the dentate jars +so the cell turnover is much less or + + align:start position:0% +so the cell turnover is much less or + + + align:start position:0% +so the cell turnover is much less or +slower + + align:start position:0% +slower + + + align:start position:0% +slower +whereas the happy animals the animals + + align:start position:0% +whereas the happy animals the animals + + + align:start position:0% +whereas the happy animals the animals +that are getting reward and it's not + + align:start position:0% +that are getting reward and it's not + + + align:start position:0% +that are getting reward and it's not +stressful they are generating more cells + + align:start position:0% +stressful they are generating more cells + + + align:start position:0% +stressful they are generating more cells +and so people with these are fairly new + + align:start position:0% +and so people with these are fairly new + + + align:start position:0% +and so people with these are fairly new +findings but it should apply to humans + + align:start position:0% +findings but it should apply to humans + + + align:start position:0% +findings but it should apply to humans +as well + + align:start position:0% +as well + + + align:start position:0% +as well +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +it's a good incentive to to get married + + align:start position:0% +it's a good incentive to to get married + + + align:start position:0% +it's a good incentive to to get married +and be happy because you'll be happier + + align:start position:0% +and be happy because you'll be happier + + + align:start position:0% +and be happy because you'll be happier +and you'll generate more you'll you'll + + align:start position:0% +and you'll generate more you'll you'll + + + align:start position:0% +and you'll generate more you'll you'll +remember things better + + align:start position:0% +remember things better + + + align:start position:0% +remember things better +okay uh is there any + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% + + + + align:start position:0% + +them yeah can you what what would be the + + align:start position:0% +them yeah can you what what would be the + + + align:start position:0% +them yeah can you what what would be the +function of that + + align:start position:0% + + + + align:start position:0% + +it's a good question you know + + align:start position:0% +it's a good question you know + + + align:start position:0% +it's a good question you know +that's what we have to think about and + + align:start position:0% +that's what we have to think about and + + + align:start position:0% +that's what we have to think about and +we need the research but if you look + + align:start position:0% +we need the research but if you look + + + align:start position:0% +we need the research but if you look +online you will see there is some recent + + align:start position:0% +online you will see there is some recent + + + align:start position:0% +online you will see there is some recent +work in this area + + align:start position:0% + + + + align:start position:0% + +I suggest in the book that we know that + + align:start position:0% +I suggest in the book that we know that + + + align:start position:0% +I suggest in the book that we know that +young young neurons in the brains with a + + align:start position:0% +young young neurons in the brains with a + + + align:start position:0% +young young neurons in the brains with a +lot of young neurons in other words that + + align:start position:0% +lot of young neurons in other words that + + + align:start position:0% +lot of young neurons in other words that +are developing + + align:start position:0% +are developing + + + align:start position:0% +are developing +animals and people + + align:start position:0% +animals and people + + + align:start position:0% +animals and people +the amount of learning they do is much + + align:start position:0% +the amount of learning they do is much + + + align:start position:0% +the amount of learning they do is much +much greater than in adults think of + + align:start position:0% +much greater than in adults think of + + + align:start position:0% +much greater than in adults think of +acquiring language and kids are learning + + align:start position:0% +acquiring language and kids are learning + + + align:start position:0% +acquiring language and kids are learning +many new words every day and that's a + + align:start position:0% +many new words every day and that's a + + + align:start position:0% +many new words every day and that's a +lot of learning they're learning many + + align:start position:0% +lot of learning they're learning many + + + align:start position:0% +lot of learning they're learning many +other things as well + + align:start position:0% + + + + align:start position:0% + +so it just could be that young neurons + + align:start position:0% +so it just could be that young neurons + + + align:start position:0% +so it just could be that young neurons +are going to be more plastic and the + + align:start position:0% +are going to be more plastic and the + + + align:start position:0% +are going to be more plastic and the +data indicate that that's true + + align:start position:0% + + + + align:start position:0% + +in stress + + align:start position:0% +in stress + + + align:start position:0% +in stress +yes + + align:start position:0% + + + + align:start position:0% + +in other words the growth itself is for + + align:start position:0% +in other words the growth itself is for + + + align:start position:0% +in other words the growth itself is for +taking up energy yeah + + align:start position:0% +taking up energy yeah + + + align:start position:0% +taking up energy yeah +interesting + + align:start position:0% + + + + align:start position:0% + +oh very good okay this is in key + + align:start position:0% +oh very good okay this is in key + + + align:start position:0% +oh very good okay this is in key +gruesome's lab you've been studying + + align:start position:0% +gruesome's lab you've been studying + + + align:start position:0% +gruesome's lab you've been studying +stress effects + + align:start position:0% +stress effects + + + align:start position:0% +stress effects +since she's come to MIT and joined the + + align:start position:0% +since she's come to MIT and joined the + + + align:start position:0% +since she's come to MIT and joined the +faculty here + + align:start position:0% + + + + align:start position:0% + +all right uh + + align:start position:0% +all right uh + + + align:start position:0% +all right uh +I just want to show you briefly this + + align:start position:0% +I just want to show you briefly this + + + align:start position:0% +I just want to show you briefly this +experiment with implantation of stem + + align:start position:0% +experiment with implantation of stem + + + align:start position:0% +experiment with implantation of stem +cells I thought I had done this last + + align:start position:0% +cells I thought I had done this last + + + align:start position:0% +cells I thought I had done this last +time but it's here + + align:start position:0% +time but it's here + + + align:start position:0% +time but it's here +this was an earlier earlier work and + + align:start position:0% +this was an earlier earlier work and + + + align:start position:0% +this was an earlier earlier work and +this has been going on it had started to + + align:start position:0% +this has been going on it had started to + + + align:start position:0% +this has been going on it had started to +be just a little before this and then + + align:start position:0% +be just a little before this and then + + + align:start position:0% +be just a little before this and then +but you will see this kind of work going + + align:start position:0% +but you will see this kind of work going + + + align:start position:0% +but you will see this kind of work going +on right up till + + align:start position:0% +on right up till + + + align:start position:0% +on right up till +the current year and there's a lot of it + + align:start position:0% +the current year and there's a lot of it + + + align:start position:0% +the current year and there's a lot of it +and a lot of competition in the area you + + align:start position:0% +and a lot of competition in the area you + + + align:start position:0% +and a lot of competition in the area you +know to find sources of stem cells + + align:start position:0% +know to find sources of stem cells + + + align:start position:0% +know to find sources of stem cells +that can be used in treating human + + align:start position:0% +that can be used in treating human + + + align:start position:0% +that can be used in treating human +patients + + align:start position:0% +patients + + + align:start position:0% +patients +including Parkinson's but other things + + align:start position:0% +including Parkinson's but other things + + + align:start position:0% +including Parkinson's but other things +as well + + align:start position:0% + + + + align:start position:0% + +this was an experiment just to prove + + align:start position:0% +this was an experiment just to prove + + + align:start position:0% +this was an experiment just to prove +that in rats you can get these cells to + + align:start position:0% +that in rats you can get these cells to + + + align:start position:0% +that in rats you can get these cells to +survive + + align:start position:0% +survive + + + align:start position:0% +survive +so in this + + align:start position:0% +so in this + + + align:start position:0% +so in this +SEC this picture of a brain from the + + align:start position:0% +SEC this picture of a brain from the + + + align:start position:0% +SEC this picture of a brain from the +medial side that you've seen before I I + + align:start position:0% +medial side that you've seen before I I + + + align:start position:0% +medial side that you've seen before I I +show the level of a frontal section that + + align:start position:0% +show the level of a frontal section that + + + align:start position:0% +show the level of a frontal section that +goes right through the basal forebrain + + align:start position:0% +goes right through the basal forebrain + + + align:start position:0% +goes right through the basal forebrain +and septum + + align:start position:0% +and septum + + + align:start position:0% +and septum +with some neocortex at the top and + + align:start position:0% +with some neocortex at the top and + + + align:start position:0% +with some neocortex at the top and +here's the picture from the rat + + align:start position:0% +here's the picture from the rat + + + align:start position:0% +here's the picture from the rat +and they what they've done is they've + + align:start position:0% +and they what they've done is they've + + + align:start position:0% +and they what they've done is they've +injected a cannula + + align:start position:0% +injected a cannula + + + align:start position:0% +injected a cannula +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that goes down like this + + align:start position:0% +that goes down like this + + + align:start position:0% +that goes down like this +they're injecting into the basal + + align:start position:0% +they're injecting into the basal + + + align:start position:0% +they're injecting into the basal +forebrain here here's the septal area up + + align:start position:0% +forebrain here here's the septal area up + + + align:start position:0% +forebrain here here's the septal area up +here + + align:start position:0% + + + + align:start position:0% + +and these are the basal form brain + + align:start position:0% +and these are the basal form brain + + + align:start position:0% +and these are the basal form brain +structures olfactor tubercle there at + + align:start position:0% +structures olfactor tubercle there at + + + align:start position:0% +structures olfactor tubercle there at +the bottom and they've taken the + + align:start position:0% +the bottom and they've taken the + + + align:start position:0% +the bottom and they've taken the +pictures uh + + align:start position:0% +pictures uh + + + align:start position:0% +pictures uh +of histological results where they made + + align:start position:0% +of histological results where they made + + + align:start position:0% +of histological results where they made +the section right through the where the + + align:start position:0% +the section right through the where the + + + align:start position:0% +the section right through the where the +cannula went through the tissue + + align:start position:0% +cannula went through the tissue + + + align:start position:0% +cannula went through the tissue +and + + align:start position:0% +and + + + align:start position:0% +and +as they put it in some cells of course + + align:start position:0% +as they put it in some cells of course + + + align:start position:0% +as they put it in some cells of course +leaked out of the canyon even though the + + align:start position:0% +leaked out of the canyon even though the + + + align:start position:0% +leaked out of the canyon even though the +main injection is down here in the + + align:start position:0% +main injection is down here in the + + + align:start position:0% +main injection is down here in the +basophobic and there you see label cells + + align:start position:0% +basophobic and there you see label cells + + + align:start position:0% +basophobic and there you see label cells +four to nine months they got results + + align:start position:0% +four to nine months they got results + + + align:start position:0% +four to nine months they got results +four to nine months after these were put + + align:start position:0% +four to nine months after these were put + + + align:start position:0% +four to nine months after these were put +in they got these results indicating + + align:start position:0% +in they got these results indicating + + + align:start position:0% +in they got these results indicating +these cells are surviving + + align:start position:0% +these cells are surviving + + + align:start position:0% +these cells are surviving +over a long period of time + + align:start position:0% +over a long period of time + + + align:start position:0% +over a long period of time +and in the area of the injection you can + + align:start position:0% +and in the area of the injection you can + + + align:start position:0% +and in the area of the injection you can +see many + + align:start position:0% +see many + + + align:start position:0% +see many +living cells that + + align:start position:0% +living cells that + + + align:start position:0% +living cells that +weren't native to this brain they were + + align:start position:0% +weren't native to this brain they were + + + align:start position:0% +weren't native to this brain they were +put in + + align:start position:0% +put in + + + align:start position:0% +put in +so they know it but what do they become + + align:start position:0% +so they know it but what do they become + + + align:start position:0% +so they know it but what do they become +do we even know that they're neurons + + align:start position:0% +do we even know that they're neurons + + + align:start position:0% +do we even know that they're neurons +and + + align:start position:0% +and + + + align:start position:0% +and +so they tried staining for neurofilament + + align:start position:0% +so they tried staining for neurofilament + + + align:start position:0% +so they tried staining for neurofilament +protein for staining with glial + + align:start position:0% +protein for staining with glial + + + align:start position:0% +protein for staining with glial +fibrillary acidic protein to label + + align:start position:0% +fibrillary acidic protein to label + + + align:start position:0% +fibrillary acidic protein to label +astrocytes + + align:start position:0% +astrocytes + + + align:start position:0% +astrocytes +and they saw that they got both + + align:start position:0% +and they saw that they got both + + + align:start position:0% +and they saw that they got both +astrocytes and neurons + + align:start position:0% +astrocytes and neurons + + + align:start position:0% +astrocytes and neurons +after these implantations and then by + + align:start position:0% +after these implantations and then by + + + align:start position:0% +after these implantations and then by +looking + + align:start position:0% +looking + + + align:start position:0% +looking +at uh + + align:start position:0% +at uh + + + align:start position:0% +at uh +other proteins they showed that some of + + align:start position:0% +other proteins they showed that some of + + + align:start position:0% +other proteins they showed that some of +these cells are chlorinergic + + align:start position:0% +these cells are chlorinergic + + + align:start position:0% +these cells are chlorinergic +okay like the basal nucleus medial + + align:start position:0% +okay like the basal nucleus medial + + + align:start position:0% +okay like the basal nucleus medial +septal cells various cells in the basal + + align:start position:0% +septal cells various cells in the basal + + + align:start position:0% +septal cells various cells in the basal +forebrain from the basal nucleus on up + + align:start position:0% +forebrain from the basal nucleus on up + + + align:start position:0% +forebrain from the basal nucleus on up +into the septum use acetylcholine as a + + align:start position:0% +into the septum use acetylcholine as a + + + align:start position:0% +into the septum use acetylcholine as a +transmitter and they some of these stem + + align:start position:0% +transmitter and they some of these stem + + + align:start position:0% +transmitter and they some of these stem +cells are differentiating + + align:start position:0% +cells are differentiating + + + align:start position:0% +cells are differentiating +not only + + align:start position:0% +not only + + + align:start position:0% +not only +acetylcholine cells but they seem to + + align:start position:0% +acetylcholine cells but they seem to + + + align:start position:0% +acetylcholine cells but they seem to +diff they're picking up signals from the + + align:start position:0% +diff they're picking up signals from the + + + align:start position:0% +diff they're picking up signals from the +local environment that affects their + + align:start position:0% +local environment that affects their + + + align:start position:0% +local environment that affects their +differentiation remember their stem + + align:start position:0% +differentiation remember their stem + + + align:start position:0% +differentiation remember their stem +cells when they put them in totally + + align:start position:0% +cells when they put them in totally + + + align:start position:0% +cells when they put them in totally +undifferentiated + + align:start position:0% +undifferentiated + + + align:start position:0% +undifferentiated +okay and then they they are maturing in + + align:start position:0% +okay and then they they are maturing in + + + align:start position:0% +okay and then they they are maturing in +the brain and their friendships + + align:start position:0% + + + + align:start position:0% + +here I just mentioned that it's being + + align:start position:0% +here I just mentioned that it's being + + + align:start position:0% +here I just mentioned that it's being +done here at MIT Rudy yenish + + align:start position:0% +done here at MIT Rudy yenish + + + align:start position:0% +done here at MIT Rudy yenish +in rudyanish's lab and he had various + + align:start position:0% +in rudyanish's lab and he had various + + + align:start position:0% +in rudyanish's lab and he had various +collaborators and + + align:start position:0% +collaborators and + + + align:start position:0% +collaborators and +they + + align:start position:0% +they + + + align:start position:0% +they +this is the reference to a paper they + + align:start position:0% +this is the reference to a paper they + + + align:start position:0% +this is the reference to a paper they +published + + align:start position:0% +published + + + align:start position:0% +published +in the proceedings of the National + + align:start position:0% +in the proceedings of the National + + + align:start position:0% +in the proceedings of the National +Academy of Sciences in 2008 and noticed + + align:start position:0% +Academy of Sciences in 2008 and noticed + + + align:start position:0% +Academy of Sciences in 2008 and noticed +that it involved Marta Constantine + + align:start position:0% +that it involved Marta Constantine + + + align:start position:0% +that it involved Marta Constantine +Patton + + align:start position:0% +Patton + + + align:start position:0% +Patton +and this is uh + + align:start position:0% +and this is uh + + + align:start position:0% +and this is uh +in yanish's lab in various people that + + align:start position:0% +in yanish's lab in various people that + + + align:start position:0% +in yanish's lab in various people that +helped with that research and uh you'll + + align:start position:0% +helped with that research and uh you'll + + + align:start position:0% +helped with that research and uh you'll +see other Publications in that year and + + align:start position:0% +see other Publications in that year and + + + align:start position:0% +see other Publications in that year and +there's been a number since + + align:start position:0% +there's been a number since + + + align:start position:0% +there's been a number since +means of methodology for large-scale + + align:start position:0% +means of methodology for large-scale + + + align:start position:0% +means of methodology for large-scale +generation + + align:start position:0% +generation + + + align:start position:0% +generation +dopamine producing sound cells will + + align:start position:0% +dopamine producing sound cells will + + + align:start position:0% +dopamine producing sound cells will +differentiate into six cells + + align:start position:0% + + + + align:start position:0% + +from stem cells they have various + + align:start position:0% +from stem cells they have various + + + align:start position:0% +from stem cells they have various +sources of these stem cells + + align:start position:0% +sources of these stem cells + + + align:start position:0% +sources of these stem cells +ideally when you if you can get stem + + align:start position:0% +ideally when you if you can get stem + + + align:start position:0% +ideally when you if you can get stem +cells that you can generate from the + + align:start position:0% +cells that you can generate from the + + + align:start position:0% +cells that you can generate from the +patient themselves it's + + align:start position:0% +patient themselves it's + + + align:start position:0% +patient themselves it's +it's the best + + align:start position:0% +it's the best + + + align:start position:0% +it's the best +all right uh + + align:start position:0% +all right uh + + + align:start position:0% +all right uh +let's talk about neocortex now for the + + align:start position:0% +let's talk about neocortex now for the + + + align:start position:0% +let's talk about neocortex now for the +rest of the class + + align:start position:0% + + + + align:start position:0% + +in this first class I just want to talk + + align:start position:0% +in this first class I just want to talk + + + align:start position:0% +in this first class I just want to talk +about Evolution and functions of end + + align:start position:0% +about Evolution and functions of end + + + align:start position:0% +about Evolution and functions of end +brain structures + + align:start position:0% + + + + align:start position:0% + +and uh so some of this will be reviewed + + align:start position:0% +and uh so some of this will be reviewed + + + align:start position:0% +and uh so some of this will be reviewed +because I want to bring things together + + align:start position:0% +because I want to bring things together + + + align:start position:0% +because I want to bring things together +and make sure you're understanding major + + align:start position:0% +and make sure you're understanding major + + + align:start position:0% +and make sure you're understanding major +points about the end brain many a number + + align:start position:0% +points about the end brain many a number + + + align:start position:0% +points about the end brain many a number +of which I've been talking about at + + align:start position:0% +of which I've been talking about at + + + align:start position:0% +of which I've been talking about at +various times in class + + align:start position:0% +various times in class + + + align:start position:0% +various times in class +so in this first class we'll talk about + + align:start position:0% +so in this first class we'll talk about + + + align:start position:0% +so in this first class we'll talk about +Evolution functions + + align:start position:0% +Evolution functions + + + align:start position:0% +Evolution functions +and next time we'll talk about cell + + align:start position:0% +and next time we'll talk about cell + + + align:start position:0% +and next time we'll talk about cell +types and uh + + align:start position:0% +types and uh + + + align:start position:0% +types and uh +how they're connected different regions + + align:start position:0% +how they're connected different regions + + + align:start position:0% +how they're connected different regions +of the neocortex major fiber roots and + + align:start position:0% +of the neocortex major fiber roots and + + + align:start position:0% +of the neocortex major fiber roots and +not of the in brain + + align:start position:0% +not of the in brain + + + align:start position:0% +not of the in brain +and then we'll talk about the particle + + align:start position:0% +and then we'll talk about the particle + + + align:start position:0% +and then we'll talk about the particle +system + + align:start position:0% +system + + + align:start position:0% +system +and about Association cortex where + + align:start position:0% +and about Association cortex where + + + align:start position:0% +and about Association cortex where +they're getting their thalamic input the + + align:start position:0% +they're getting their thalamic input the + + + align:start position:0% +they're getting their thalamic input the +transcortical connections that + + align:start position:0% +transcortical connections that + + + align:start position:0% +transcortical connections that +interconnect these association areas + + align:start position:0% +interconnect these association areas + + + align:start position:0% +interconnect these association areas +and I'll say a little bit about + + align:start position:0% +and I'll say a little bit about + + + align:start position:0% +and I'll say a little bit about +evolution of that about the Islamic + + align:start position:0% +evolution of that about the Islamic + + + align:start position:0% +evolution of that about the Islamic +structures + + align:start position:0% +structures + + + align:start position:0% +structures +and then finally this is the last + + align:start position:0% +and then finally this is the last + + + align:start position:0% +and then finally this is the last +chapter of the book + + align:start position:0% +chapter of the book + + + align:start position:0% +chapter of the book +chapter 34 we'll talk go back to + + align:start position:0% +chapter 34 we'll talk go back to + + + align:start position:0% +chapter 34 we'll talk go back to +development to talk specifically about + + align:start position:0% +development to talk specifically about + + + align:start position:0% +development to talk specifically about +neocortical development because some of + + align:start position:0% +neocortical development because some of + + + align:start position:0% +neocortical development because some of +it is a little different from it the + + align:start position:0% +it is a little different from it the + + + align:start position:0% +it is a little different from it the +spinal development that we focused on + + align:start position:0% +spinal development that we focused on + + + align:start position:0% +spinal development that we focused on +initially + + align:start position:0% +initially + + + align:start position:0% +initially +uh + + align:start position:0% +uh + + + align:start position:0% +uh +we also talked a bit about it + + align:start position:0% +we also talked a bit about it + + + align:start position:0% +we also talked a bit about it +development of the tectum + + align:start position:0% +development of the tectum + + + align:start position:0% +development of the tectum +and then cortical plasticity especially + + align:start position:0% +and then cortical plasticity especially + + + align:start position:0% +and then cortical plasticity especially +with an interest in adult plasticity and + + align:start position:0% +with an interest in adult plasticity and + + + align:start position:0% +with an interest in adult plasticity and +structural changes that have been found + + align:start position:0% +structural changes that have been found + + + align:start position:0% +structural changes that have been found +all right so this is a picture we've + + align:start position:0% +all right so this is a picture we've + + + align:start position:0% +all right so this is a picture we've +seen a few times + + align:start position:0% +seen a few times + + + align:start position:0% +seen a few times +it was one of the early studies using + + align:start position:0% +it was one of the early studies using + + + align:start position:0% +it was one of the early studies using +gene expression patterns + + align:start position:0% +gene expression patterns + + + align:start position:0% +gene expression patterns +to show how gene expression patterns for + + align:start position:0% +to show how gene expression patterns for + + + align:start position:0% +to show how gene expression patterns for +certain genes here they this is uh these + + align:start position:0% +certain genes here they this is uh these + + + align:start position:0% +certain genes here they this is uh these +two genes + + align:start position:0% +two genes + + + align:start position:0% +two genes +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it looks like I + + align:start position:0% +it looks like I + + + align:start position:0% +it looks like I +I screwed this up I didn't take the + + align:start position:0% +I screwed this up I didn't take the + + + align:start position:0% +I screwed this up I didn't take the +right one because what they actually did + + align:start position:0% +right one because what they actually did + + + align:start position:0% +right one because what they actually did +is I remember is emx1 and then + + align:start position:0% +is I remember is emx1 and then + + + align:start position:0% +is I remember is emx1 and then +the gene that's expressed in the green + + align:start position:0% +the gene that's expressed in the green + + + align:start position:0% +the gene that's expressed in the green +areas here + + align:start position:0% +areas here + + + align:start position:0% +areas here +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +sorry about that it's correct in the + + align:start position:0% +sorry about that it's correct in the + + + align:start position:0% +sorry about that it's correct in the +book I checked that and double checked + + align:start position:0% +book I checked that and double checked + + + align:start position:0% +book I checked that and double checked +it + + align:start position:0% +it + + + align:start position:0% +it +but anyway it regardless it always shows + + align:start position:0% +but anyway it regardless it always shows + + + align:start position:0% +but anyway it regardless it always shows +this kind of pattern where you + + align:start position:0% +this kind of pattern where you + + + align:start position:0% +this kind of pattern where you +the cortex + + align:start position:0% +the cortex + + + align:start position:0% +the cortex +in mammals + + align:start position:0% +in mammals + + + align:start position:0% +in mammals +expresses + + align:start position:0% +expresses + + + align:start position:0% +expresses +emx1 + + align:start position:0% + + + + align:start position:0% + +the same gene is expressed in the frog + + align:start position:0% +the same gene is expressed in the frog + + + align:start position:0% +the same gene is expressed in the frog +in the dorsal cortex + + align:start position:0% +in the dorsal cortex + + + align:start position:0% +in the dorsal cortex +and dorsal cortex there includes they're + + align:start position:0% +and dorsal cortex there includes they're + + + align:start position:0% +and dorsal cortex there includes they're +including the medial pallium which + + align:start position:0% +including the medial pallium which + + + align:start position:0% +including the medial pallium which +becomes hippocampus + + align:start position:0% +becomes hippocampus + + + align:start position:0% +becomes hippocampus +so that would be way over here in the + + align:start position:0% +so that would be way over here in the + + + align:start position:0% +so that would be way over here in the +mammal and it also includes + + align:start position:0% +mammal and it also includes + + + align:start position:0% +mammal and it also includes +uh a large part of the olfactory cortex + + align:start position:0% + + + + align:start position:0% + +and then this is the striatal area which + + align:start position:0% +and then this is the striatal area which + + + align:start position:0% +and then this is the striatal area which +expresses different genes + + align:start position:0% +expresses different genes + + + align:start position:0% +expresses different genes +and these intermediate areas + + align:start position:0% +and these intermediate areas + + + align:start position:0% +and these intermediate areas +Express other genes that they didn't + + align:start position:0% +Express other genes that they didn't + + + align:start position:0% +Express other genes that they didn't +study in this initial work but + + align:start position:0% +study in this initial work but + + + align:start position:0% +study in this initial work but +that corresponds in the mammal mainly to + + align:start position:0% +that corresponds in the mammal mainly to + + + align:start position:0% +that corresponds in the mammal mainly to +the amygdala area in the clostrum + + align:start position:0% +the amygdala area in the clostrum + + + align:start position:0% +the amygdala area in the clostrum +the amygdala region + + align:start position:0% +the amygdala region + + + align:start position:0% +the amygdala region +and they find that that Gene is + + align:start position:0% +and they find that that Gene is + + + align:start position:0% +and they find that that Gene is +expressed in reversal ventricular Ridge + + align:start position:0% +expressed in reversal ventricular Ridge + + + align:start position:0% +expressed in reversal ventricular Ridge +area the reptiles and the birds + + align:start position:0% +area the reptiles and the birds + + + align:start position:0% +area the reptiles and the birds +we don't call it dorsal ventricular + + align:start position:0% +we don't call it dorsal ventricular + + + align:start position:0% +we don't call it dorsal ventricular +Ridge in the adult bread we call it + + align:start position:0% +Ridge in the adult bread we call it + + + align:start position:0% +Ridge in the adult bread we call it +the night opallium + + align:start position:0% +the night opallium + + + align:start position:0% +the night opallium +and + + align:start position:0% +and + + + align:start position:0% +and +sub-complements of the night of + + align:start position:0% +sub-complements of the night of + + + align:start position:0% +sub-complements of the night of +Talladega we keep calling it dorsal + + align:start position:0% +Talladega we keep calling it dorsal + + + align:start position:0% +Talladega we keep calling it dorsal +ventricular Ridge and the reptiles and + + align:start position:0% +ventricular Ridge and the reptiles and + + + align:start position:0% +ventricular Ridge and the reptiles and +turtles + + align:start position:0% +turtles + + + align:start position:0% +turtles +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +you see it's there in fraud also + + align:start position:0% +you see it's there in fraud also + + + align:start position:0% +you see it's there in fraud also +but not in the same configuration + + align:start position:0% +but not in the same configuration + + + align:start position:0% +but not in the same configuration +all right + + align:start position:0% + + + + align:start position:0% + +so we think + + align:start position:0% +so we think + + + align:start position:0% +so we think +it's not just gene expression patterns + + align:start position:0% +it's not just gene expression patterns + + + align:start position:0% +it's not just gene expression patterns +that indicate this we think the + + align:start position:0% +that indicate this we think the + + + align:start position:0% +that indicate this we think the +neocortex of mammals + + align:start position:0% +neocortex of mammals + + + align:start position:0% +neocortex of mammals +evolved from the doors that dorsal + + align:start position:0% +evolved from the doors that dorsal + + + align:start position:0% +evolved from the doors that dorsal +palium or dorsal cortex of the ancestral + + align:start position:0% +palium or dorsal cortex of the ancestral + + + align:start position:0% +palium or dorsal cortex of the ancestral +vertebrates + + align:start position:0% +vertebrates + + + align:start position:0% +vertebrates +and the dorsal cortex of amphibians and + + align:start position:0% +and the dorsal cortex of amphibians and + + + align:start position:0% +and the dorsal cortex of amphibians and +reptiles evolve from that same area and + + align:start position:0% +reptiles evolve from that same area and + + + align:start position:0% +reptiles evolve from that same area and +the hyperpalium of birds evolved from + + align:start position:0% +the hyperpalium of birds evolved from + + + align:start position:0% +the hyperpalium of birds evolved from +that region in words + + align:start position:0% +that region in words + + + align:start position:0% +that region in words +so we'll show pictures of that part of + + align:start position:0% +so we'll show pictures of that part of + + + align:start position:0% +so we'll show pictures of that part of +the hyperpalian we call the wolst + + align:start position:0% +the hyperpalian we call the wolst + + + align:start position:0% +the hyperpalian we call the wolst +can be compared to + + align:start position:0% +can be compared to + + + align:start position:0% +can be compared to +neocortex quite specifically in terms of + + align:start position:0% +neocortex quite specifically in terms of + + + align:start position:0% +neocortex quite specifically in terms of +its connections + + align:start position:0% + + + + align:start position:0% + +okay and this + + align:start position:0% + + + + align:start position:0% + +refers to the amygdala which + + align:start position:0% +refers to the amygdala which + + + align:start position:0% +refers to the amygdala which +now the gene expression data I should + + align:start position:0% +now the gene expression data I should + + + align:start position:0% +now the gene expression data I should +point out is actually much more complex + + align:start position:0% +point out is actually much more complex + + + align:start position:0% +point out is actually much more complex +than this indicates + + align:start position:0% +than this indicates + + + align:start position:0% +than this indicates +and it's there's been a lot of it and + + align:start position:0% +and it's there's been a lot of it and + + + align:start position:0% +and it's there's been a lot of it and +there's multiple genes and sometimes the + + align:start position:0% +there's multiple genes and sometimes the + + + align:start position:0% +there's multiple genes and sometimes the +expression patterns don't lead to as + + align:start position:0% +expression patterns don't lead to as + + + align:start position:0% +expression patterns don't lead to as +clear-cut a conclusion as others + + align:start position:0% +clear-cut a conclusion as others + + + align:start position:0% +clear-cut a conclusion as others +so in the book facing that kind of + + align:start position:0% +so in the book facing that kind of + + + align:start position:0% +so in the book facing that kind of +complexity I did I do cite that kind of + + align:start position:0% +complexity I did I do cite that kind of + + + align:start position:0% +complexity I did I do cite that kind of +data but I've + + align:start position:0% +data but I've + + + align:start position:0% +data but I've +I've stressed + + align:start position:0% +I've stressed + + + align:start position:0% +I've stressed +function and connections because I know + + align:start position:0% +function and connections because I know + + + align:start position:0% +function and connections because I know +it's the connections that ultimately are + + align:start position:0% +it's the connections that ultimately are + + + align:start position:0% +it's the connections that ultimately are +determining Behavior it's not those Gene + + align:start position:0% +determining Behavior it's not those Gene + + + align:start position:0% +determining Behavior it's not those Gene +expressions + + align:start position:0% +expressions + + + align:start position:0% +expressions +that determines the function it's the + + align:start position:0% +that determines the function it's the + + + align:start position:0% +that determines the function it's the +connections what they become + + align:start position:0% +connections what they become + + + align:start position:0% +connections what they become +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and we'll see that neocortex is actually + + align:start position:0% +and we'll see that neocortex is actually + + + align:start position:0% +and we'll see that neocortex is actually +made up we've already seen that you get + + align:start position:0% +made up we've already seen that you get + + + align:start position:0% +made up we've already seen that you get +contributions from various structures + + align:start position:0% +contributions from various structures + + + align:start position:0% +contributions from various structures +not just that + + align:start position:0% +not just that + + + align:start position:0% +not just that +ventricular layer of the neocortex they + + align:start position:0% +ventricular layer of the neocortex they + + + align:start position:0% +ventricular layer of the neocortex they +come from subcritical regions too + + align:start position:0% +come from subcritical regions too + + + align:start position:0% +come from subcritical regions too +and the same actually is true for these + + align:start position:0% +and the same actually is true for these + + + align:start position:0% +and the same actually is true for these +ventral structures like the amygdala and + + align:start position:0% +ventral structures like the amygdala and + + + align:start position:0% +ventral structures like the amygdala and +the the anterior olfactory nucleus which + + align:start position:0% +the the anterior olfactory nucleus which + + + align:start position:0% +the the anterior olfactory nucleus which +is part of the amygdala again is it's + + align:start position:0% +is part of the amygdala again is it's + + + align:start position:0% +is part of the amygdala again is it's +partly paleo partly striatal okay and + + align:start position:0% +partly paleo partly striatal okay and + + + align:start position:0% +partly paleo partly striatal okay and +the neocortex itself is like that + + align:start position:0% +the neocortex itself is like that + + + align:start position:0% +the neocortex itself is like that +so that's one of the complexities we're + + align:start position:0% +so that's one of the complexities we're + + + align:start position:0% +so that's one of the complexities we're +faced with so + + align:start position:0% +faced with so + + + align:start position:0% +faced with so +I look at the amygdala and I study the + + align:start position:0% +I look at the amygdala and I study the + + + align:start position:0% +I look at the amygdala and I study the +connections + + align:start position:0% +connections + + + align:start position:0% +connections +its inputs and its outputs and its + + align:start position:0% +its inputs and its outputs and its + + + align:start position:0% +its inputs and its outputs and its +connections with itself different + + align:start position:0% +connections with itself different + + + align:start position:0% +connections with itself different +components of that structure and I see + + align:start position:0% +components of that structure and I see + + + align:start position:0% +components of that structure and I see +that it is a single structure in terms + + align:start position:0% +that it is a single structure in terms + + + align:start position:0% +that it is a single structure in terms +of function + + align:start position:0% +of function + + + align:start position:0% +of function +so that's the way that's the approach I + + align:start position:0% +so that's the way that's the approach I + + + align:start position:0% +so that's the way that's the approach I +take because I'm interested in function + + align:start position:0% +take because I'm interested in function + + + align:start position:0% +take because I'm interested in function +primarily + + align:start position:0% +primarily + + + align:start position:0% +primarily +all right because I know that that's + + align:start position:0% +all right because I know that that's + + + align:start position:0% +all right because I know that that's +what drives evolution + + align:start position:0% + + + + align:start position:0% + +it's a functional adaptations + + align:start position:0% + + + + align:start position:0% + +so what sensory modality and what + + align:start position:0% +so what sensory modality and what + + + align:start position:0% +so what sensory modality and what +projections in that modality underlie + + align:start position:0% +projections in that modality underlie + + + align:start position:0% +projections in that modality underlie +the two major types of learning that + + align:start position:0% +the two major types of learning that + + + align:start position:0% +the two major types of learning that +I've been talking about in this class + + align:start position:0% +I've been talking about in this class + + + align:start position:0% +I've been talking about in this class +they're so important in evolution to + + align:start position:0% +they're so important in evolution to + + + align:start position:0% +they're so important in evolution to +forebrain + + align:start position:0% +forebrain + + + align:start position:0% +forebrain +so what are those two types + + align:start position:0% + + + + align:start position:0% + +and what are the structures they Center + + align:start position:0% +and what are the structures they Center + + + align:start position:0% +and what are the structures they Center +on + + align:start position:0% +on + + + align:start position:0% +on +one of them + + align:start position:0% +one of them + + + align:start position:0% +one of them +sensory motor habits the other + + align:start position:0% + + + + align:start position:0% + +spatial learning + + align:start position:0% +spatial learning + + + align:start position:0% +spatial learning +knowledge place in the things in those + + align:start position:0% +knowledge place in the things in those + + + align:start position:0% +knowledge place in the things in those +places so that's what we usually talk + + align:start position:0% +places so that's what we usually talk + + + align:start position:0% +places so that's what we usually talk +about when we talk about long-term + + align:start position:0% +about when we talk about long-term + + + align:start position:0% +about when we talk about long-term +memory + + align:start position:0% +memory + + + align:start position:0% +memory +but it is separate from habit formation + + align:start position:0% +but it is separate from habit formation + + + align:start position:0% +but it is separate from habit formation +this triadal learning + + align:start position:0% +this triadal learning + + + align:start position:0% +this triadal learning +so what was the modality + + align:start position:0% +so what was the modality + + + align:start position:0% +so what was the modality +the initial one that dominated + + align:start position:0% +the initial one that dominated + + + align:start position:0% +the initial one that dominated +the end brain the Primitive membrane + + align:start position:0% +the end brain the Primitive membrane + + + align:start position:0% +the end brain the Primitive membrane +which was olfaction + + align:start position:0% +which was olfaction + + + align:start position:0% +which was olfaction +olfaction + + align:start position:0% +olfaction + + + align:start position:0% +olfaction +initially totally dominated the membrane + + align:start position:0% +initially totally dominated the membrane + + + align:start position:0% +initially totally dominated the membrane +I mean the end brain is basically an + + align:start position:0% +I mean the end brain is basically an + + + align:start position:0% +I mean the end brain is basically an +outgrowth of the olfactory system + + align:start position:0% +outgrowth of the olfactory system + + + align:start position:0% +outgrowth of the olfactory system +which developed up there in the nostril + + align:start position:0% +which developed up there in the nostril + + + align:start position:0% +which developed up there in the nostril +across the land of the brain in front of + + align:start position:0% +across the land of the brain in front of + + + align:start position:0% +across the land of the brain in front of +the + + align:start position:0% +the + + + align:start position:0% +the +primitive diencephalon + + align:start position:0% +primitive diencephalon + + + align:start position:0% +primitive diencephalon +so these are the two kinds of learning + + align:start position:0% +so these are the two kinds of learning + + + align:start position:0% +so these are the two kinds of learning +so we talk about object identification + + align:start position:0% +so we talk about object identification + + + align:start position:0% +so we talk about object identification +of objects in places + + align:start position:0% +of objects in places + + + align:start position:0% +of objects in places +uh + + align:start position:0% +uh + + + align:start position:0% +uh +very different kind of learning from the + + align:start position:0% +very different kind of learning from the + + + align:start position:0% +very different kind of learning from the +midbrain because the midbrain remember + + align:start position:0% +midbrain because the midbrain remember + + + align:start position:0% +midbrain because the midbrain remember +when this was happening in the forebrain + + align:start position:0% +when this was happening in the forebrain + + + align:start position:0% +when this was happening in the forebrain +animals already had this huge they + + align:start position:0% +animals already had this huge they + + + align:start position:0% +animals already had this huge they +haven't had a membrane a midbrain that + + align:start position:0% +haven't had a membrane a midbrain that + + + align:start position:0% +haven't had a membrane a midbrain that +in some animals became very very large + + align:start position:0% +in some animals became very very large + + + align:start position:0% +in some animals became very very large +remember the predatory fish the enormous + + align:start position:0% +remember the predatory fish the enormous + + + align:start position:0% +remember the predatory fish the enormous +of detective and the little end brain + + align:start position:0% +of detective and the little end brain + + + align:start position:0% +of detective and the little end brain +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but what kind of learning goes on in the + + align:start position:0% +but what kind of learning goes on in the + + + align:start position:0% +but what kind of learning goes on in the +midbrain + + align:start position:0% +midbrain + + + align:start position:0% +midbrain +not these kinds of learning you don't + + align:start position:0% +not these kinds of learning you don't + + + align:start position:0% +not these kinds of learning you don't +have reinforcement learning habit + + align:start position:0% +have reinforcement learning habit + + + align:start position:0% +have reinforcement learning habit +formation + + align:start position:0% +formation + + + align:start position:0% +formation +you don't have a long-term memory for + + align:start position:0% +you don't have a long-term memory for + + + align:start position:0% +you don't have a long-term memory for +places + + align:start position:0% +places + + + align:start position:0% +places +what you have is innate recognition + + align:start position:0% +what you have is innate recognition + + + align:start position:0% +what you have is innate recognition +triggering of innate responses think of + + align:start position:0% +triggering of innate responses think of + + + align:start position:0% +triggering of innate responses think of +the Frog and his feeding + + align:start position:0% + + + + align:start position:0% + +so we talk about I think the ethologists + + align:start position:0% +so we talk about I think the ethologists + + + align:start position:0% +so we talk about I think the ethologists +give the best descriptions of That + + align:start position:0% +give the best descriptions of That + + + align:start position:0% +give the best descriptions of That +Behavior when they talk about + + align:start position:0% +Behavior when they talk about + + + align:start position:0% +Behavior when they talk about +visually Illustrated fixed action + + align:start position:0% +visually Illustrated fixed action + + + align:start position:0% +visually Illustrated fixed action +patterns + + align:start position:0% +patterns + + + align:start position:0% +patterns +where the key stimuli for eliciting them + + align:start position:0% +where the key stimuli for eliciting them + + + align:start position:0% +where the key stimuli for eliciting them +are visual + + align:start position:0% + + + + align:start position:0% + +many of them dealing with optic tectum + + align:start position:0% +many of them dealing with optic tectum + + + align:start position:0% +many of them dealing with optic tectum +the plasticity is just sensitization and + + align:start position:0% +the plasticity is just sensitization and + + + align:start position:0% +the plasticity is just sensitization and +habituation + + align:start position:0% +habituation + + + align:start position:0% +habituation +but in the end brain you've got you got + + align:start position:0% +but in the end brain you've got you got + + + align:start position:0% +but in the end brain you've got you got +a lot more than just old-fashioned you + + align:start position:0% +a lot more than just old-fashioned you + + + align:start position:0% +a lot more than just old-fashioned you +have these new forms of plasticity two + + align:start position:0% +have these new forms of plasticity two + + + align:start position:0% +have these new forms of plasticity two +types of I just mentioned + + align:start position:0% +types of I just mentioned + + + align:start position:0% +types of I just mentioned +I just spelled it out + + align:start position:0% +I just spelled it out + + + align:start position:0% +I just spelled it out +you can read any of this and here I just + + align:start position:0% +you can read any of this and here I just + + + align:start position:0% +you can read any of this and here I just +fill out some details about the ancient + + align:start position:0% +fill out some details about the ancient + + + align:start position:0% +fill out some details about the ancient +inputs to the object Learning System and + + align:start position:0% +inputs to the object Learning System and + + + align:start position:0% +inputs to the object Learning System and +the original outputs + + align:start position:0% +the original outputs + + + align:start position:0% +the original outputs +they're very much like the connections + + align:start position:0% +they're very much like the connections + + + align:start position:0% +they're very much like the connections +to the amygdala invention okay we've + + align:start position:0% +to the amygdala invention okay we've + + + align:start position:0% +to the amygdala invention okay we've +already gone over + + align:start position:0% +already gone over + + + align:start position:0% +already gone over +and then the learning of Place Learning + + align:start position:0% +and then the learning of Place Learning + + + align:start position:0% +and then the learning of Place Learning +allowed anticipation of odors reaching + + align:start position:0% +allowed anticipation of odors reaching + + + align:start position:0% +allowed anticipation of odors reaching +the nostrils and the possible action + + align:start position:0% +the nostrils and the possible action + + + align:start position:0% +the nostrils and the possible action +they could anticipate the actions needed + + align:start position:0% +they could anticipate the actions needed + + + align:start position:0% +they could anticipate the actions needed +again + + align:start position:0% +again + + + align:start position:0% +again +evolved largely out of the olfactory + + align:start position:0% +evolved largely out of the olfactory + + + align:start position:0% +evolved largely out of the olfactory +system + + align:start position:0% +system + + + align:start position:0% +system +and of course later the non olfactory + + align:start position:0% +and of course later the non olfactory + + + align:start position:0% +and of course later the non olfactory +inputs became more and more important + + align:start position:0% +inputs became more and more important + + + align:start position:0% +inputs became more and more important +and certainly in the primates that + + align:start position:0% +and certainly in the primates that + + + align:start position:0% +and certainly in the primates that +become dominant + + align:start position:0% +become dominant + + + align:start position:0% +become dominant +in most Prime primates though in some + + align:start position:0% +in most Prime primates though in some + + + align:start position:0% +in most Prime primates though in some +primates of faction is still very + + align:start position:0% +primates of faction is still very + + + align:start position:0% +primates of faction is still very +important + + align:start position:0% + + + + align:start position:0% + +and we know that the medial pallium is + + align:start position:0% +and we know that the medial pallium is + + + align:start position:0% +and we know that the medial pallium is +the + + align:start position:0% +the + + + align:start position:0% +the +most critical structure important for + + align:start position:0% +most critical structure important for + + + align:start position:0% +most critical structure important for +those functions that evolved into the + + align:start position:0% +those functions that evolved into the + + + align:start position:0% +those functions that evolved into the +hippocampus + + align:start position:0% + + + + align:start position:0% + +so then I talk about that Invasion model + + align:start position:0% +so then I talk about that Invasion model + + + align:start position:0% +so then I talk about that Invasion model +Factory inputs + + align:start position:0% +Factory inputs + + + align:start position:0% +Factory inputs +you can read through this just to remind + + align:start position:0% +you can read through this just to remind + + + align:start position:0% +you can read through this just to remind +yourself of that when you read these + + align:start position:0% +yourself of that when you read these + + + align:start position:0% +yourself of that when you read these +slides and what that did + + align:start position:0% +slides and what that did + + + align:start position:0% +slides and what that did +uh + + align:start position:0% +uh + + + align:start position:0% +uh +these are the questions I put in + + align:start position:0% +these are the questions I put in + + + align:start position:0% +these are the questions I put in +so + + align:start position:0% +so + + + align:start position:0% +so +from what part of the Primitive power in + + align:start position:0% +from what part of the Primitive power in + + + align:start position:0% +from what part of the Primitive power in +the premammalian reptiles in the cortex + + align:start position:0% +the premammalian reptiles in the cortex + + + align:start position:0% +the premammalian reptiles in the cortex +signal what did I say earlier in the + + align:start position:0% +signal what did I say earlier in the + + + align:start position:0% +signal what did I say earlier in the +class + + align:start position:0% +class + + + align:start position:0% +class +what is it called + + align:start position:0% + + + + align:start position:0% + +dorsal palium or dorsal cortex + + align:start position:0% +dorsal palium or dorsal cortex + + + align:start position:0% +dorsal palium or dorsal cortex +and uh + + align:start position:0% + + + + align:start position:0% + +what part of the mammalian karsticks + + align:start position:0% +what part of the mammalian karsticks + + + align:start position:0% +what part of the mammalian karsticks +does this paleo region in modern + + align:start position:0% +does this paleo region in modern + + + align:start position:0% +does this paleo region in modern +reptiles most closely resemble well how + + align:start position:0% +reptiles most closely resemble well how + + + align:start position:0% +reptiles most closely resemble well how +do you study that + + align:start position:0% +do you study that + + + align:start position:0% +do you study that +look at connections so why I ask this + + align:start position:0% +look at connections so why I ask this + + + align:start position:0% +look at connections so why I ask this +question + + align:start position:0% +question + + + align:start position:0% +question +I was surprised that anatomy books never + + align:start position:0% +I was surprised that anatomy books never + + + align:start position:0% +I was surprised that anatomy books never +do that I just looked to see + + align:start position:0% +do that I just looked to see + + + align:start position:0% +do that I just looked to see +studies of dorsal cortex in reptiles and + + align:start position:0% +studies of dorsal cortex in reptiles and + + + align:start position:0% +studies of dorsal cortex in reptiles and +I found some + + align:start position:0% +I found some + + + align:start position:0% +I found some +and I looked at the projections they're + + align:start position:0% +and I looked at the projections they're + + + align:start position:0% +and I looked at the projections they're +all like connections of the Campbell + + align:start position:0% +all like connections of the Campbell + + + align:start position:0% +all like connections of the Campbell +areas in the mammal + + align:start position:0% +areas in the mammal + + + align:start position:0% +areas in the mammal +they're not connections like neocortex + + align:start position:0% +they're not connections like neocortex + + + align:start position:0% +they're not connections like neocortex +at all although there are connections + + align:start position:0% +at all although there are connections + + + align:start position:0% +at all although there are connections +from non-of-factory modalities come in + + align:start position:0% +from non-of-factory modalities come in + + + align:start position:0% +from non-of-factory modalities come in +there + + align:start position:0% +there + + + align:start position:0% +there +part of it does get directional Factory + + align:start position:0% +part of it does get directional Factory + + + align:start position:0% +part of it does get directional Factory +input but much of it doesn't most of + + align:start position:0% +input but much of it doesn't most of + + + align:start position:0% +input but much of it doesn't most of +it's multimodal but sometimes you even + + align:start position:0% +it's multimodal but sometimes you even + + + align:start position:0% +it's multimodal but sometimes you even +have unimodal areas developing but the + + align:start position:0% +have unimodal areas developing but the + + + align:start position:0% +have unimodal areas developing but the +outputs are going into the medial palium + + align:start position:0% +outputs are going into the medial palium + + + align:start position:0% +outputs are going into the medial palium +which is the major thickest part + + align:start position:0% +which is the major thickest part + + + align:start position:0% +which is the major thickest part +of the pallium in these animals + + align:start position:0% +of the pallium in these animals + + + align:start position:0% +of the pallium in these animals +remember that very thick medial palium + + align:start position:0% +remember that very thick medial palium + + + align:start position:0% +remember that very thick medial palium +of the Frog for example + + align:start position:0% + + + + align:start position:0% + +and yet that area is that dorsal cortex + + align:start position:0% +and yet that area is that dorsal cortex + + + align:start position:0% +and yet that area is that dorsal cortex +is the part that + + align:start position:0% +is the part that + + + align:start position:0% +is the part that +changed in the mammals in neocortex + + align:start position:0% +changed in the mammals in neocortex + + + align:start position:0% +changed in the mammals in neocortex +evolved + + align:start position:0% +evolved + + + align:start position:0% +evolved +and what structure in the burden brain + + align:start position:0% +and what structure in the burden brain + + + align:start position:0% +and what structure in the burden brain +evolved in a way that resembles the way + + align:start position:0% +evolved in a way that resembles the way + + + align:start position:0% +evolved in a way that resembles the way +neocortex evolved in mammals + + align:start position:0% + + + + align:start position:0% + +remember what it's got a couple of + + align:start position:0% +remember what it's got a couple of + + + align:start position:0% +remember what it's got a couple of +different names + + align:start position:0% +different names + + + align:start position:0% +different names +any of you remember + + align:start position:0% +any of you remember + + + align:start position:0% +any of you remember +it's just + + align:start position:0% + + + + align:start position:0% + +the wolf is one name we use for it and + + align:start position:0% +the wolf is one name we use for it and + + + align:start position:0% +the wolf is one name we use for it and +I'll show pictures of that + + align:start position:0% +I'll show pictures of that + + + align:start position:0% +I'll show pictures of that +um + + align:start position:0% +um + + + align:start position:0% +um +we also call it the hyperpalium + + align:start position:0% +we also call it the hyperpalium + + + align:start position:0% +we also call it the hyperpalium +now they call all those structures paleo + + align:start position:0% +now they call all those structures paleo + + + align:start position:0% +now they call all those structures paleo +partly because of the homologies with + + align:start position:0% +partly because of the homologies with + + + align:start position:0% +partly because of the homologies with +mammals and also because of how they + + align:start position:0% +mammals and also because of how they + + + align:start position:0% +mammals and also because of how they +evolved in how they develop in the + + align:start position:0% +evolved in how they develop in the + + + align:start position:0% +evolved in how they develop in the +embryo okay they are originally paleo + + align:start position:0% +embryo okay they are originally paleo + + + align:start position:0% +embryo okay they are originally paleo +okay + + align:start position:0% + + + + align:start position:0% + +so this is just about what I just said + + align:start position:0% +so this is just about what I just said + + + align:start position:0% +so this is just about what I just said +so why + + align:start position:0% +so why + + + align:start position:0% +so why +the mammals evolve the neocortex and + + align:start position:0% +the mammals evolve the neocortex and + + + align:start position:0% +the mammals evolve the neocortex and +birds evolve a wolf + + align:start position:0% + + + + align:start position:0% + +you know it's a very good question that + + align:start position:0% +you know it's a very good question that + + + align:start position:0% +you know it's a very good question that +almond takes up in his little book and + + align:start position:0% +almond takes up in his little book and + + + align:start position:0% +almond takes up in his little book and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +he describes the + + align:start position:0% +he describes the + + + align:start position:0% +he describes the +the avian wolves is much more efficient + + align:start position:0% +the avian wolves is much more efficient + + + align:start position:0% +the avian wolves is much more efficient +what does he mean by that + + align:start position:0% +what does he mean by that + + + align:start position:0% +what does he mean by that +his this is a picture where I show these + + align:start position:0% +his this is a picture where I show these + + + align:start position:0% +his this is a picture where I show these +structures + + align:start position:0% +structures + + + align:start position:0% +structures +when we talked about the visual system + + align:start position:0% +when we talked about the visual system + + + align:start position:0% +when we talked about the visual system +I'm showing the geniculate pathway + + align:start position:0% +I'm showing the geniculate pathway + + + align:start position:0% +I'm showing the geniculate pathway +carrying visual information to neocortex + + align:start position:0% +carrying visual information to neocortex + + + align:start position:0% +carrying visual information to neocortex +and a pathway through the tectum the + + align:start position:0% +and a pathway through the tectum the + + + align:start position:0% +and a pathway through the tectum the +spirit colliculus it goes to the lateral + + align:start position:0% +spirit colliculus it goes to the lateral + + + align:start position:0% +spirit colliculus it goes to the lateral +felons + + align:start position:0% +felons + + + align:start position:0% +felons +a part of the pulpin art + + align:start position:0% +a part of the pulpin art + + + align:start position:0% +a part of the pulpin art +usually we call it LP and the lab animal + + align:start position:0% +usually we call it LP and the lab animal + + + align:start position:0% +usually we call it LP and the lab animal +the little lab animals we use the rats + + align:start position:0% +the little lab animals we use the rats + + + align:start position:0% +the little lab animals we use the rats +hamsters and mice + + align:start position:0% +hamsters and mice + + + align:start position:0% +hamsters and mice +and IT projects primarily to the extra + + align:start position:0% +and IT projects primarily to the extra + + + align:start position:0% +and IT projects primarily to the extra +strike visual areas by primarily I mean + + align:start position:0% +strike visual areas by primarily I mean + + + align:start position:0% +strike visual areas by primarily I mean +where the densest projections are they + + align:start position:0% +where the densest projections are they + + + align:start position:0% +where the densest projections are they +do project more broadly as well but + + align:start position:0% +do project more broadly as well but + + + align:start position:0% +do project more broadly as well but +these are the main projections but if + + align:start position:0% +these are the main projections but if + + + align:start position:0% +these are the main projections but if +you look at reptiles and birds + + align:start position:0% +you look at reptiles and birds + + + align:start position:0% +you look at reptiles and birds +they also contain these two pathways + + align:start position:0% +they also contain these two pathways + + + align:start position:0% +they also contain these two pathways +one homologist to the geniculostrite + + align:start position:0% +one homologist to the geniculostrite + + + align:start position:0% +one homologist to the geniculostrite +system + + align:start position:0% +system + + + align:start position:0% +system +and that one goes to this dorsolateral + + align:start position:0% +and that one goes to this dorsolateral + + + align:start position:0% +and that one goes to this dorsolateral +cortex in reptiles + + align:start position:0% + + + + align:start position:0% + +and it goes to the wolves + + align:start position:0% +and it goes to the wolves + + + align:start position:0% +and it goes to the wolves +or hyper paleo area in the boots + + align:start position:0% +or hyper paleo area in the boots + + + align:start position:0% +or hyper paleo area in the boots +and in very visual Birds + + align:start position:0% +and in very visual Birds + + + align:start position:0% +and in very visual Birds +that have a large end brain like the owl + + align:start position:0% +that have a large end brain like the owl + + + align:start position:0% +that have a large end brain like the owl +the wolf is quite large + + align:start position:0% +the wolf is quite large + + + align:start position:0% +the wolf is quite large +and in fact much thicker than the + + align:start position:0% +and in fact much thicker than the + + + align:start position:0% +and in fact much thicker than the +neocortex here + + align:start position:0% +neocortex here + + + align:start position:0% +neocortex here +this other pathway doesn't go to the + + align:start position:0% +this other pathway doesn't go to the + + + align:start position:0% +this other pathway doesn't go to the +wolves + + align:start position:0% +wolves + + + align:start position:0% +wolves +the other pathway here in the reptiles + + align:start position:0% +the other pathway here in the reptiles + + + align:start position:0% +the other pathway here in the reptiles +goes to that north of ventricular Ridge + + align:start position:0% +goes to that north of ventricular Ridge + + + align:start position:0% +goes to that north of ventricular Ridge +area that stays subordical + + align:start position:0% +area that stays subordical + + + align:start position:0% +area that stays subordical +subcortical structure + + align:start position:0% +subcortical structure + + + align:start position:0% +subcortical structure +but it's not it used to be called + + align:start position:0% +but it's not it used to be called + + + align:start position:0% +but it's not it used to be called +striatum or neostriatum but we don't + + align:start position:0% +striatum or neostriatum but we don't + + + align:start position:0% +striatum or neostriatum but we don't +call it that anymore because it's not + + align:start position:0% +call it that anymore because it's not + + + align:start position:0% +call it that anymore because it's not +homologous in its connections for its + + align:start position:0% +homologous in its connections for its + + + align:start position:0% +homologous in its connections for its +development to the striatum and that's + + align:start position:0% +development to the striatum and that's + + + align:start position:0% +development to the striatum and that's +been supported by those gene expression + + align:start position:0% +been supported by those gene expression + + + align:start position:0% +been supported by those gene expression +studies + + align:start position:0% +studies + + + align:start position:0% +studies +okay this triatum is down here + + align:start position:0% +okay this triatum is down here + + + align:start position:0% +okay this triatum is down here +striatum is done here in Birds + + align:start position:0% +striatum is done here in Birds + + + align:start position:0% +striatum is done here in Birds +but this whole area in between the real + + align:start position:0% +but this whole area in between the real + + + align:start position:0% +but this whole area in between the real +striatum and the wolves + + align:start position:0% +striatum and the wolves + + + align:start position:0% +striatum and the wolves +is called the nested palette the Nido + + align:start position:0% +is called the nested palette the Nido + + + align:start position:0% +is called the nested palette the Nido +pallium and we subdivided the part that + + align:start position:0% +pallium and we subdivided the part that + + + align:start position:0% +pallium and we subdivided the part that +gets the visual projection here from + + align:start position:0% +gets the visual projection here from + + + align:start position:0% +gets the visual projection here from +tecton to nucleus rotundus + + align:start position:0% +tecton to nucleus rotundus + + + align:start position:0% +tecton to nucleus rotundus +which is much larger than this area that + + align:start position:0% +which is much larger than this area that + + + align:start position:0% +which is much larger than this area that +gets the direct input from the retina + + align:start position:0% +gets the direct input from the retina + + + align:start position:0% +gets the direct input from the retina +goes to this area called the undertale + + align:start position:0% +goes to this area called the undertale + + + align:start position:0% +goes to this area called the undertale +those that were that was one of the + + align:start position:0% +those that were that was one of the + + + align:start position:0% +those that were that was one of the +discoveries made here at MIT by Harvey + + align:start position:0% +discoveries made here at MIT by Harvey + + + align:start position:0% +discoveries made here at MIT by Harvey +carton + + align:start position:0% +carton + + + align:start position:0% +carton +quite a bit and been in touch with + + align:start position:0% +quite a bit and been in touch with + + + align:start position:0% +quite a bit and been in touch with +recently by the way he's + + align:start position:0% + + + + align:start position:0% + +interacting with me with with me a bit + + align:start position:0% +interacting with me with with me a bit + + + align:start position:0% +interacting with me with with me a bit +about the book I sent him a copy of it + + align:start position:0% +about the book I sent him a copy of it + + + align:start position:0% +about the book I sent him a copy of it +because + + align:start position:0% +because + + + align:start position:0% +because +he's been such an important player in + + align:start position:0% +he's been such an important player in + + + align:start position:0% +he's been such an important player in +this field + + align:start position:0% +this field + + + align:start position:0% +this field +and he's still quite active in Southern + + align:start position:0% +and he's still quite active in Southern + + + align:start position:0% +and he's still quite active in Southern +Cal in San Diego area he's in La Jolla + + align:start position:0% +Cal in San Diego area he's in La Jolla + + + align:start position:0% +Cal in San Diego area he's in La Jolla +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +this is uh almond simplified picture of + + align:start position:0% +this is uh almond simplified picture of + + + align:start position:0% +this is uh almond simplified picture of +neocortex and that much thicker + + align:start position:0% +neocortex and that much thicker + + + align:start position:0% +neocortex and that much thicker +wolf area + + align:start position:0% +wolf area + + + align:start position:0% +wolf area +wolves means bulge and you can see how + + align:start position:0% +wolves means bulge and you can see how + + + align:start position:0% +wolves means bulge and you can see how +in this section + + align:start position:0% +in this section + + + align:start position:0% +in this section +it bulges out from the rest of the end + + align:start position:0% +it bulges out from the rest of the end + + + align:start position:0% +it bulges out from the rest of the end +brain in the how + + align:start position:0% + + + + align:start position:0% + +it's a little bit + + align:start position:0% +it's a little bit + + + align:start position:0% +it's a little bit +uh we picked an owl and an owl monkey + + align:start position:0% +uh we picked an owl and an owl monkey + + + align:start position:0% +uh we picked an owl and an owl monkey +okay but any monkey would do + + align:start position:0% +okay but any monkey would do + + + align:start position:0% +okay but any monkey would do +to make such a comparison + + align:start position:0% +to make such a comparison + + + align:start position:0% +to make such a comparison +but we're going to talk about this + + align:start position:0% +but we're going to talk about this + + + align:start position:0% +but we're going to talk about this +simple lamination of the neocortex the + + align:start position:0% +simple lamination of the neocortex the + + + align:start position:0% +simple lamination of the neocortex the +wolf's lamination is much there are many + + align:start position:0% +wolf's lamination is much there are many + + + align:start position:0% +wolf's lamination is much there are many +more layers okay and the cells are + + align:start position:0% +more layers okay and the cells are + + + align:start position:0% +more layers okay and the cells are +different we have the pyramidal cell in + + align:start position:0% +different we have the pyramidal cell in + + + align:start position:0% +different we have the pyramidal cell in +cortex + + align:start position:0% +cortex + + + align:start position:0% +cortex +these neurons in the walls are generally + + align:start position:0% +these neurons in the walls are generally + + + align:start position:0% +these neurons in the walls are generally +stellated shape + + align:start position:0% +stellated shape + + + align:start position:0% +stellated shape +okay so to get the same processing power + + align:start position:0% +okay so to get the same processing power + + + align:start position:0% +okay so to get the same processing power +that you have in the wolves mammals have + + align:start position:0% +that you have in the wolves mammals have + + + align:start position:0% +that you have in the wolves mammals have +evolved multiple visual areas that are + + align:start position:0% +evolved multiple visual areas that are + + + align:start position:0% +evolved multiple visual areas that are +interconnected + + align:start position:0% +interconnected + + + align:start position:0% +interconnected +it seems to work extremely well but with + + align:start position:0% +it seems to work extremely well but with + + + align:start position:0% +it seems to work extremely well but with +two disadvantages you've got + + align:start position:0% +two disadvantages you've got + + + align:start position:0% +two disadvantages you've got +a lot more Axon + + align:start position:0% +a lot more Axon + + + align:start position:0% +a lot more Axon +here the axons are shorter + + align:start position:0% +here the axons are shorter + + + align:start position:0% +here the axons are shorter +interconnecting the different parts of + + align:start position:0% +interconnecting the different parts of + + + align:start position:0% +interconnecting the different parts of +the Wolf + + align:start position:0% +the Wolf + + + align:start position:0% +the Wolf +because it's a thicker + + align:start position:0% +because it's a thicker + + + align:start position:0% +because it's a thicker +structure + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +so we have to ask you know well what are + + align:start position:0% +so we have to ask you know well what are + + + align:start position:0% +so we have to ask you know well what are +the advantages just look at neocortex + + align:start position:0% +the advantages just look at neocortex + + + align:start position:0% +the advantages just look at neocortex +first this is a well-known type of + + align:start position:0% +first this is a well-known type of + + + align:start position:0% +first this is a well-known type of +illustration illustrating cortex in + + align:start position:0% +illustration illustrating cortex in + + + align:start position:0% +illustration illustrating cortex in +three different histological uh stains + + align:start position:0% +three different histological uh stains + + + align:start position:0% +three different histological uh stains +at the far right is the missile stain + + align:start position:0% +at the far right is the missile stain + + + align:start position:0% +at the far right is the missile stain +where you see the shape of the cell body + + align:start position:0% +where you see the shape of the cell body + + + align:start position:0% +where you see the shape of the cell body +and the densities the cells and their + + align:start position:0% +and the densities the cells and their + + + align:start position:0% +and the densities the cells and their +size in the different layers + + align:start position:0% +size in the different layers + + + align:start position:0% +size in the different layers +which are numbered here layer one is + + align:start position:0% +which are numbered here layer one is + + + align:start position:0% +which are numbered here layer one is +always a layer of very few cells at the + + align:start position:0% +always a layer of very few cells at the + + + align:start position:0% +always a layer of very few cells at the +top and you see here in the Golgi + + align:start position:0% +top and you see here in the Golgi + + + align:start position:0% +top and you see here in the Golgi +picture + + align:start position:0% +picture + + + align:start position:0% +picture +that that's mainly a layer of dendrites + + align:start position:0% +that that's mainly a layer of dendrites + + + align:start position:0% +that that's mainly a layer of dendrites +and accents here in an axon stain you + + align:start position:0% +and accents here in an axon stain you + + + align:start position:0% +and accents here in an axon stain you +see that a lot of axons are including + + align:start position:0% +see that a lot of axons are including + + + align:start position:0% +see that a lot of axons are including +many transversely running Accents in + + align:start position:0% +many transversely running Accents in + + + align:start position:0% +many transversely running Accents in +layer one + + align:start position:0% +layer one + + + align:start position:0% +layer one +and layer two and three are the smaller + + align:start position:0% +and layer two and three are the smaller + + + align:start position:0% +and layer two and three are the smaller +pyramidal cells of the cortex + + align:start position:0% +pyramidal cells of the cortex + + + align:start position:0% +pyramidal cells of the cortex +and you see them here in missile where + + align:start position:0% +and you see them here in missile where + + + align:start position:0% +and you see them here in missile where +it's a really big pyramidal cells are + + align:start position:0% +it's a really big pyramidal cells are + + + align:start position:0% +it's a really big pyramidal cells are +down here in layer five and that's where + + align:start position:0% +down here in layer five and that's where + + + align:start position:0% +down here in layer five and that's where +you find the cells that give rise to the + + align:start position:0% +you find the cells that give rise to the + + + align:start position:0% +you find the cells that give rise to the +long outputs to subcortical Regions + + align:start position:0% + + + + align:start position:0% + +some of the pyramidal cells in layer + + align:start position:0% +some of the pyramidal cells in layer + + + align:start position:0% +some of the pyramidal cells in layer +three or three B here are are pretty + + align:start position:0% +three or three B here are are pretty + + + align:start position:0% +three or three B here are are pretty +large also they're the ones with long + + align:start position:0% +large also they're the ones with long + + + align:start position:0% +large also they're the ones with long +transportical connections okay and then + + align:start position:0% +transportical connections okay and then + + + align:start position:0% +transportical connections okay and then +in layer four this varies a little bit + + align:start position:0% +in layer four this varies a little bit + + + align:start position:0% +in layer four this varies a little bit +with the species and uh and the stain + + align:start position:0% +with the species and uh and the stain + + + align:start position:0% +with the species and uh and the stain +you're using you can see here in in a + + align:start position:0% +you're using you can see here in in a + + + align:start position:0% +you're using you can see here in in a +good missile stain they're always these + + align:start position:0% +good missile stain they're always these + + + align:start position:0% +good missile stain they're always these +small + + align:start position:0% +small + + + align:start position:0% +small +cells and if we look in the Golgi we see + + align:start position:0% +cells and if we look in the Golgi we see + + + align:start position:0% +cells and if we look in the Golgi we see +that there are the stellate cells + + align:start position:0% +that there are the stellate cells + + + align:start position:0% +that there are the stellate cells +they're generally not pyramidal cells + + align:start position:0% +they're generally not pyramidal cells + + + align:start position:0% +they're generally not pyramidal cells +and there are other non-pyramidal cells + + align:start position:0% +and there are other non-pyramidal cells + + + align:start position:0% +and there are other non-pyramidal cells +scattered through the cortex + + align:start position:0% +scattered through the cortex + + + align:start position:0% +scattered through the cortex +here in the fiber stain + + align:start position:0% +here in the fiber stain + + + align:start position:0% +here in the fiber stain +you see a couple of additional things + + align:start position:0% +you see a couple of additional things + + + align:start position:0% +you see a couple of additional things +for one thing you see that there's more + + align:start position:0% +for one thing you see that there's more + + + align:start position:0% +for one thing you see that there's more +than just six layers + + align:start position:0% +than just six layers + + + align:start position:0% +than just six layers +even in the initial stain it would be + + align:start position:0% +even in the initial stain it would be + + + align:start position:0% +even in the initial stain it would be +easy to name more than six layers a + + align:start position:0% +easy to name more than six layers a + + + align:start position:0% +easy to name more than six layers a +layer six is always can be divided into + + align:start position:0% +layer six is always can be divided into + + + align:start position:0% +layer six is always can be divided into +usually at least three layers + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +to make sense out of all cortex using + + align:start position:0% +to make sense out of all cortex using + + + align:start position:0% +to make sense out of all cortex using +the same kind of + + align:start position:0% +the same kind of + + + align:start position:0% +the same kind of +terms we name just six layers and then + + align:start position:0% +terms we name just six layers and then + + + align:start position:0% +terms we name just six layers and then +we talk about sublamination + + align:start position:0% +we talk about sublamination + + + align:start position:0% +we talk about sublamination +fiber stain shows some additional layers + + align:start position:0% +fiber stain shows some additional layers + + + align:start position:0% +fiber stain shows some additional layers +because of these layers of transverse + + align:start position:0% +because of these layers of transverse + + + align:start position:0% +because of these layers of transverse +fibers + + align:start position:0% +fibers + + + align:start position:0% +fibers +and then we see these + + align:start position:0% +and then we see these + + + align:start position:0% +and then we see these +fibers that travel uh + + align:start position:0% +fibers that travel uh + + + align:start position:0% +fibers that travel uh +perpendicular to the surface of the + + align:start position:0% +perpendicular to the surface of the + + + align:start position:0% +perpendicular to the surface of the +cortex + + align:start position:0% +cortex + + + align:start position:0% +cortex +that divide the cortex up into these + + align:start position:0% +that divide the cortex up into these + + + align:start position:0% +that divide the cortex up into these +different + + align:start position:0% +different + + + align:start position:0% +different +columns + + align:start position:0% + + + + align:start position:0% + +and we want to know what those axons are + + align:start position:0% +and we want to know what those axons are + + + align:start position:0% +and we want to know what those axons are +okay what are the transverse fibers what + + align:start position:0% +okay what are the transverse fibers what + + + align:start position:0% +okay what are the transverse fibers what +are these + + align:start position:0% +are these + + + align:start position:0% +are these +vertically traveling fibers + + align:start position:0% +vertically traveling fibers + + + align:start position:0% +vertically traveling fibers +okay and this is just a Mark if you just + + align:start position:0% +okay and this is just a Mark if you just + + + align:start position:0% +okay and this is just a Mark if you just +look at the Golgi stain I took one here + + align:start position:0% +look at the Golgi stain I took one here + + + align:start position:0% +look at the Golgi stain I took one here +from poliocox the Russian great Russian + + align:start position:0% +from poliocox the Russian great Russian + + + align:start position:0% +from poliocox the Russian great Russian +and adamant + + align:start position:0% +and adamant + + + align:start position:0% +and adamant +in some of his pictures of the cortex + + align:start position:0% +in some of his pictures of the cortex + + + align:start position:0% +in some of his pictures of the cortex +which are quite elaborate and nice and + + align:start position:0% +which are quite elaborate and nice and + + + align:start position:0% +which are quite elaborate and nice and +you see more of the cell types here you + + align:start position:0% +you see more of the cell types here you + + + align:start position:0% +you see more of the cell types here you +see some of the cellulite cells in very + + align:start position:0% +see some of the cellulite cells in very + + + align:start position:0% +see some of the cellulite cells in very +dense dendritic Arbors and axonal arbors + + align:start position:0% +dense dendritic Arbors and axonal arbors + + + align:start position:0% +dense dendritic Arbors and axonal arbors +we'll see some of them are well you'll + + align:start position:0% +we'll see some of them are well you'll + + + align:start position:0% +we'll see some of them are well you'll +you'll see in the book there's a picture + + align:start position:0% +you'll see in the book there's a picture + + + align:start position:0% +you'll see in the book there's a picture +there + + align:start position:0% +there + + + align:start position:0% +there +showing different cell types in the + + align:start position:0% +showing different cell types in the + + + align:start position:0% +showing different cell types in the +cortex + + align:start position:0% +cortex + + + align:start position:0% +cortex +it's actually in chapter 33 which you + + align:start position:0% +it's actually in chapter 33 which you + + + align:start position:0% +it's actually in chapter 33 which you +may not have looked at but the first two + + align:start position:0% +may not have looked at but the first two + + + align:start position:0% +may not have looked at but the first two +pictures in chapter 33 show + + align:start position:0% +pictures in chapter 33 show + + + align:start position:0% +pictures in chapter 33 show +some interesting things about these cell + + align:start position:0% +some interesting things about these cell + + + align:start position:0% +some interesting things about these cell +types and cortex + + align:start position:0% + + + + align:start position:0% + +the 33 1 shows two major types of cells + + align:start position:0% +the 33 1 shows two major types of cells + + + align:start position:0% +the 33 1 shows two major types of cells +the excitatory uh get a glutamatergic + + align:start position:0% +the excitatory uh get a glutamatergic + + + align:start position:0% +the excitatory uh get a glutamatergic +cells and then the other type are all + + align:start position:0% +cells and then the other type are all + + + align:start position:0% +cells and then the other type are all +the inhibitory + + align:start position:0% +the inhibitory + + + align:start position:0% +the inhibitory +they also want the first type is finally + + align:start position:0% +they also want the first type is finally + + + align:start position:0% +they also want the first type is finally +the second is non-spiny so it'll be + + align:start position:0% +the second is non-spiny so it'll be + + + align:start position:0% +the second is non-spiny so it'll be +different in their morphology + + align:start position:0% +different in their morphology + + + align:start position:0% +different in their morphology +both groups include some Stellar cells + + align:start position:0% +both groups include some Stellar cells + + + align:start position:0% +both groups include some Stellar cells +but especially + + align:start position:0% +but especially + + + align:start position:0% +but especially +the cells used in Gaba the inhibitory + + align:start position:0% +the cells used in Gaba the inhibitory + + + align:start position:0% +the cells used in Gaba the inhibitory +interneurons + + align:start position:0% +interneurons + + + align:start position:0% +interneurons +okay in the Golgi stain you can't see + + align:start position:0% +okay in the Golgi stain you can't see + + + align:start position:0% +okay in the Golgi stain you can't see +which of these + + align:start position:0% +which of these + + + align:start position:0% +which of these +most of these are in fact inhibitory + + align:start position:0% +most of these are in fact inhibitory + + + align:start position:0% +most of these are in fact inhibitory +intramurals okay the main excitatory + + align:start position:0% +intramurals okay the main excitatory + + + align:start position:0% +intramurals okay the main excitatory +interneurons are the neurons in layer + + align:start position:0% +interneurons are the neurons in layer + + + align:start position:0% +interneurons are the neurons in layer +four + + align:start position:0% +four + + + align:start position:0% +four +okay + + align:start position:0% + + + + align:start position:0% + +in this chapter and in this particular + + align:start position:0% +in this chapter and in this particular + + + align:start position:0% +in this chapter and in this particular +question I'm asking + + align:start position:0% +question I'm asking + + + align:start position:0% +question I'm asking +for descriptions of different types of + + align:start position:0% +for descriptions of different types of + + + align:start position:0% +for descriptions of different types of +axon projections + + align:start position:0% +axon projections + + + align:start position:0% +axon projections +axons that start in the cortex and end + + align:start position:0% +axons that start in the cortex and end + + + align:start position:0% +axons that start in the cortex and end +in the cortex + + align:start position:0% +in the cortex + + + align:start position:0% +in the cortex +remember we talked about proprio spinal + + align:start position:0% +remember we talked about proprio spinal + + + align:start position:0% +remember we talked about proprio spinal +connections where these are proprio + + align:start position:0% +connections where these are proprio + + + align:start position:0% +connections where these are proprio +cortical connections okay and some of + + align:start position:0% +cortical connections okay and some of + + + align:start position:0% +cortical connections okay and some of +them are just connections within a + + align:start position:0% +them are just connections within a + + + align:start position:0% +them are just connections within a +column others are cross columns and + + align:start position:0% +column others are cross columns and + + + align:start position:0% +column others are cross columns and +other the other the others are long + + align:start position:0% +other the other the others are long + + + align:start position:0% +other the other the others are long +transcordical connections and those + + align:start position:0% +transcordical connections and those + + + align:start position:0% +transcordical connections and those +generally + + align:start position:0% +generally + + + align:start position:0% +generally +go into the white matter they go down + + align:start position:0% +go into the white matter they go down + + + align:start position:0% +go into the white matter they go down +into the white matter and then they + + align:start position:0% +into the white matter and then they + + + align:start position:0% +into the white matter and then they +travel over a long distance to another + + align:start position:0% +travel over a long distance to another + + + align:start position:0% +travel over a long distance to another +cortical area where then they go back up + + align:start position:0% +cortical area where then they go back up + + + align:start position:0% +cortical area where then they go back up +into the layers of cells so this is my + + align:start position:0% +into the layers of cells so this is my + + + align:start position:0% +into the layers of cells so this is my +picture of a of a single column where + + align:start position:0% +picture of a of a single column where + + + align:start position:0% +picture of a of a single column where +I've taken the cells and x and so I've + + align:start position:0% +I've taken the cells and x and so I've + + + align:start position:0% +I've taken the cells and x and so I've +pulled them apart a little bit to make + + align:start position:0% +pulled them apart a little bit to make + + + align:start position:0% +pulled them apart a little bit to make +it broader than it really would be + + align:start position:0% +it broader than it really would be + + + align:start position:0% +it broader than it really would be +so you can see the different types and + + align:start position:0% +so you can see the different types and + + + align:start position:0% +so you can see the different types and +how they're connected I show one of the + + align:start position:0% +how they're connected I show one of the + + + align:start position:0% +how they're connected I show one of the +large pyramidal cells in the Deep part + + align:start position:0% +large pyramidal cells in the Deep part + + + align:start position:0% +large pyramidal cells in the Deep part +of layer five it has an axon that goes + + align:start position:0% +of layer five it has an axon that goes + + + align:start position:0% +of layer five it has an axon that goes +out generally to subcortical areas + + align:start position:0% +out generally to subcortical areas + + + align:start position:0% +out generally to subcortical areas +and I simplify the dendrites because if + + align:start position:0% +and I simplify the dendrites because if + + + align:start position:0% +and I simplify the dendrites because if +I drew all of them then you wouldn't see + + align:start position:0% +I drew all of them then you wouldn't see + + + align:start position:0% +I drew all of them then you wouldn't see +the rest of the things the rest of the + + align:start position:0% +the rest of the things the rest of the + + + align:start position:0% +the rest of the things the rest of the +cells + + align:start position:0% +cells + + + align:start position:0% +cells +so I'm just giving examples of their + + align:start position:0% +so I'm just giving examples of their + + + align:start position:0% +so I'm just giving examples of their +major dendrites the basal dendrites and + + align:start position:0% +major dendrites the basal dendrites and + + + align:start position:0% +major dendrites the basal dendrites and +the apical dendrite and I'm showing that + + align:start position:0% +the apical dendrite and I'm showing that + + + align:start position:0% +the apical dendrite and I'm showing that +they arborize these dendrites arborize + + align:start position:0% +they arborize these dendrites arborize + + + align:start position:0% +they arborize these dendrites arborize +up in layer one + + align:start position:0% +up in layer one + + + align:start position:0% +up in layer one +I show a few cells in layer one + + align:start position:0% +I show a few cells in layer one + + + align:start position:0% +I show a few cells in layer one +with a dendritic spread and then a + + align:start position:0% +with a dendritic spread and then a + + + align:start position:0% +with a dendritic spread and then a +longer axon distribution that's mostly + + align:start position:0% +longer axon distribution that's mostly + + + align:start position:0% +longer axon distribution that's mostly +interconnecting + + align:start position:0% + + + + align:start position:0% + +adjacent areas of Cortex + + align:start position:0% +adjacent areas of Cortex + + + align:start position:0% +adjacent areas of Cortex +then I show the pyramidal smaller + + align:start position:0% +then I show the pyramidal smaller + + + align:start position:0% +then I show the pyramidal smaller +pyramidal cells here I show the small + + align:start position:0% +pyramidal cells here I show the small + + + align:start position:0% +pyramidal cells here I show the small +granule cells in layer four that are + + align:start position:0% +granule cells in layer four that are + + + align:start position:0% +granule cells in layer four that are +receiving input from the white matter as + + align:start position:0% +receiving input from the white matter as + + + align:start position:0% +receiving input from the white matter as +these are this would be an axon coming + + align:start position:0% +these are this would be an axon coming + + + align:start position:0% +these are this would be an axon coming +from the thalamus I show you here its + + align:start position:0% +from the thalamus I show you here its + + + align:start position:0% +from the thalamus I show you here its +main connections are in therefore there + + align:start position:0% +main connections are in therefore there + + + align:start position:0% +main connections are in therefore there +are other connections + + align:start position:0% +are other connections + + + align:start position:0% +are other connections +they also go to layer one + + align:start position:0% + + + + align:start position:0% + +and layer five and six in fact they + + align:start position:0% +and layer five and six in fact they + + + align:start position:0% +and layer five and six in fact they +really go to all the layers but they're + + align:start position:0% +really go to all the layers but they're + + + align:start position:0% +really go to all the layers but they're +much denser in layer four so we often + + align:start position:0% +much denser in layer four so we often + + + align:start position:0% +much denser in layer four so we often +picture them as just terminating in + + align:start position:0% +picture them as just terminating in + + + align:start position:0% +picture them as just terminating in +layer four and they're terminating on + + align:start position:0% +layer four and they're terminating on + + + align:start position:0% +layer four and they're terminating on +these excitatory interneurons which then + + align:start position:0% +these excitatory interneurons which then + + + align:start position:0% +these excitatory interneurons which then +have axons that connect to the overlying + + align:start position:0% +have axons that connect to the overlying + + + align:start position:0% +have axons that connect to the overlying +layers primarily + + align:start position:0% +layers primarily + + + align:start position:0% +layers primarily +and then I'm showing connections from + + align:start position:0% +and then I'm showing connections from + + + align:start position:0% +and then I'm showing connections from +the these layer six neurons some of + + align:start position:0% +the these layer six neurons some of + + + align:start position:0% +the these layer six neurons some of +which go out they go to the thalamus + + align:start position:0% +which go out they go to the thalamus + + + align:start position:0% +which go out they go to the thalamus +and others + + align:start position:0% +and others + + + align:start position:0% +and others +go to the other other layers so these + + align:start position:0% +go to the other other layers so these + + + align:start position:0% +go to the other other layers so these +are intercolluminum axons + + align:start position:0% +are intercolluminum axons + + + align:start position:0% +are intercolluminum axons +several types + + align:start position:0% +several types + + + align:start position:0% +several types +in layer four from layer six + + align:start position:0% +in layer four from layer six + + + align:start position:0% +in layer four from layer six +and also + + align:start position:0% +and also + + + align:start position:0% +and also +from these upper layers where you see + + align:start position:0% +from these upper layers where you see + + + align:start position:0% +from these upper layers where you see +this is axons + + align:start position:0% +this is axons + + + align:start position:0% +this is axons +they almost always have collaterals even + + align:start position:0% +they almost always have collaterals even + + + align:start position:0% +they almost always have collaterals even +if they're going to another area and + + align:start position:0% +if they're going to another area and + + + align:start position:0% +if they're going to another area and +this what do we call this type + + align:start position:0% +this what do we call this type + + + align:start position:0% +this what do we call this type +it goes down into the white matter + + align:start position:0% +it goes down into the white matter + + + align:start position:0% +it goes down into the white matter +goes to another area then goes back up + + align:start position:0% +goes to another area then goes back up + + + align:start position:0% +goes to another area then goes back up +and call it a u fiber because it's going + + align:start position:0% +and call it a u fiber because it's going + + + align:start position:0% +and call it a u fiber because it's going +down over and up okay + + align:start position:0% +down over and up okay + + + align:start position:0% +down over and up okay +those are the you Fighters these others + + align:start position:0% +those are the you Fighters these others + + + align:start position:0% +those are the you Fighters these others +are intercortical axons that are not you + + align:start position:0% +are intercortical axons that are not you + + + align:start position:0% +are intercortical axons that are not you +Fighters they're all just they never go + + align:start position:0% +Fighters they're all just they never go + + + align:start position:0% +Fighters they're all just they never go +into the white manner all right + + align:start position:0% +into the white manner all right + + + align:start position:0% +into the white manner all right +this is very typical of a + + align:start position:0% +this is very typical of a + + + align:start position:0% +this is very typical of a +very simplified picture the column + + align:start position:0% +very simplified picture the column + + + align:start position:0% +very simplified picture the column +columnar Arrangement that's repeated + + align:start position:0% +columnar Arrangement that's repeated + + + align:start position:0% +columnar Arrangement that's repeated +throughout the cortex right + + align:start position:0% +throughout the cortex right + + + align:start position:0% +throughout the cortex right +this just shows some + + align:start position:0% +this just shows some + + + align:start position:0% +this just shows some +this these aren't from Golgi they're in + + align:start position:0% +this these aren't from Golgi they're in + + + align:start position:0% +this these aren't from Golgi they're in +injected cells in more recent studies + + align:start position:0% +injected cells in more recent studies + + + align:start position:0% +injected cells in more recent studies +this is the work of Charlie Gilbert I + + align:start position:0% +this is the work of Charlie Gilbert I + + + align:start position:0% +this is the work of Charlie Gilbert I +believe who worked a lot with hubel and + + align:start position:0% +believe who worked a lot with hubel and + + + align:start position:0% +believe who worked a lot with hubel and +weasel and has published a lot on these + + align:start position:0% +weasel and has published a lot on these + + + align:start position:0% +weasel and has published a lot on these +neuron types in the visual areas + + align:start position:0% +neuron types in the visual areas + + + align:start position:0% +neuron types in the visual areas +and the cat and the monkey there's + + align:start position:0% +and the cat and the monkey there's + + + align:start position:0% +and the cat and the monkey there's +another one where he shows the steli + + align:start position:0% +another one where he shows the steli + + + align:start position:0% +another one where he shows the steli +player two and three with elaborate + + align:start position:0% +player two and three with elaborate + + + align:start position:0% +player two and three with elaborate +dendrites and Axon + + align:start position:0% + + + + align:start position:0% + +so just talk briefly about the basic + + align:start position:0% +so just talk briefly about the basic + + + align:start position:0% +so just talk briefly about the basic +sensory motor functions of the cortex + + align:start position:0% + + + + align:start position:0% + +we know + + align:start position:0% +we know + + + align:start position:0% +we know +in the sensory cortex + + align:start position:0% +in the sensory cortex + + + align:start position:0% +in the sensory cortex +the when you have more cortex devoted to + + align:start position:0% +the when you have more cortex devoted to + + + align:start position:0% +the when you have more cortex devoted to +a given area of receptors you have more + + align:start position:0% +a given area of receptors you have more + + + align:start position:0% +a given area of receptors you have more +Acuity so if you look at the foveal + + align:start position:0% +Acuity so if you look at the foveal + + + align:start position:0% +Acuity so if you look at the foveal +representation the visual cortex it's + + align:start position:0% +representation the visual cortex it's + + + align:start position:0% +representation the visual cortex it's +much greater than the representation of + + align:start position:0% +much greater than the representation of + + + align:start position:0% +much greater than the representation of +the lower Acuity regions of our visual + + align:start position:0% +the lower Acuity regions of our visual + + + align:start position:0% +the lower Acuity regions of our visual +field the same is true for its meta + + align:start position:0% +field the same is true for its meta + + + align:start position:0% +field the same is true for its meta +sensory cortex so what are the big big + + align:start position:0% +sensory cortex so what are the big big + + + align:start position:0% +sensory cortex so what are the big big +parts of medicine's three cortex + + align:start position:0% +parts of medicine's three cortex + + + align:start position:0% +parts of medicine's three cortex +representing the fingertips the tongue + + align:start position:0% +representing the fingertips the tongue + + + align:start position:0% +representing the fingertips the tongue +the lips you know the parts where our + + align:start position:0% +the lips you know the parts where our + + + align:start position:0% +the lips you know the parts where our +Acuity is the most + + align:start position:0% +Acuity is the most + + + align:start position:0% +Acuity is the most +the same is true of animals remember we + + align:start position:0% +the same is true of animals remember we + + + align:start position:0% +the same is true of animals remember we +showed the picture of the raccoon we + + align:start position:0% +showed the picture of the raccoon we + + + align:start position:0% +showed the picture of the raccoon we +actually got a different gyrus for each + + align:start position:0% +actually got a different gyrus for each + + + align:start position:0% +actually got a different gyrus for each +digit very high Acuity in their front + + align:start position:0% +digit very high Acuity in their front + + + align:start position:0% +digit very high Acuity in their front +pause + + align:start position:0% +pause + + + align:start position:0% +pause +and the same thing is true in the motor + + align:start position:0% +and the same thing is true in the motor + + + align:start position:0% +and the same thing is true in the motor +system where we can we can talk about + + align:start position:0% +system where we can we can talk about + + + align:start position:0% +system where we can we can talk about +motor Acuity or dexterity if we're + + align:start position:0% +motor Acuity or dexterity if we're + + + align:start position:0% +motor Acuity or dexterity if we're +talking about the hands but it's true + + align:start position:0% +talking about the hands but it's true + + + align:start position:0% +talking about the hands but it's true +for other parts too + + align:start position:0% +for other parts too + + + align:start position:0% +for other parts too +the spider monkey has high + + align:start position:0% +the spider monkey has high + + + align:start position:0% +the spider monkey has high +motor acuities in his tail + + align:start position:0% +motor acuities in his tail + + + align:start position:0% +motor acuities in his tail +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so he's got a lot more cortex + + align:start position:0% +so he's got a lot more cortex + + + align:start position:0% +so he's got a lot more cortex +representing + + align:start position:0% +representing + + + align:start position:0% +representing +the movement of that tail + + align:start position:0% + + + + align:start position:0% + +and of course that's true for the tongue + + align:start position:0% +and of course that's true for the tongue + + + align:start position:0% +and of course that's true for the tongue +we don't just have high sensory acuity + + align:start position:0% +we don't just have high sensory acuity + + + align:start position:0% +we don't just have high sensory acuity +in the trunk we have high motor Acuity + + align:start position:0% +in the trunk we have high motor Acuity + + + align:start position:0% +in the trunk we have high motor Acuity +we need it not only for speaking but for + + align:start position:0% +we need it not only for speaking but for + + + align:start position:0% +we need it not only for speaking but for +manipulating food for + + align:start position:0% +manipulating food for + + + align:start position:0% +manipulating food for +oh + + align:start position:0% +oh + + + align:start position:0% +oh +all the various things we do at our time + + align:start position:0% +all the various things we do at our time + + + align:start position:0% +all the various things we do at our time +we're probably the best kissers in the + + align:start position:0% +we're probably the best kissers in the + + + align:start position:0% +we're probably the best kissers in the +animal kingdom because of that + + align:start position:0% +animal kingdom because of that + + + align:start position:0% +animal kingdom because of that +tremendous control of our tongues + + align:start position:0% +tremendous control of our tongues + + + align:start position:0% +tremendous control of our tongues +all right so + + align:start position:0% + + + + align:start position:0% + +then I bring up this I I talk about + + align:start position:0% +then I bring up this I I talk about + + + align:start position:0% +then I bring up this I I talk about +I like to refer to messlein because he + + align:start position:0% +I like to refer to messlein because he + + + align:start position:0% +I like to refer to messlein because he +made this so clear in his recent + + align:start position:0% +made this so clear in his recent + + + align:start position:0% +made this so clear in his recent +writings he pictured the paralympic + + align:start position:0% +writings he pictured the paralympic + + + align:start position:0% +writings he pictured the paralympic +cortical areas + + align:start position:0% +cortical areas + + + align:start position:0% +cortical areas +has divided into two main regions now + + align:start position:0% +has divided into two main regions now + + + align:start position:0% +has divided into two main regions now +these are the the paralympic cortical + + align:start position:0% +these are the the paralympic cortical + + + align:start position:0% +these are the the paralympic cortical +areas are sort of in between the + + align:start position:0% +areas are sort of in between the + + + align:start position:0% +areas are sort of in between the +neocortex and the limbic areas okay some + + align:start position:0% +neocortex and the limbic areas okay some + + + align:start position:0% +neocortex and the limbic areas okay some +people will say well there really are + + align:start position:0% +people will say well there really are + + + align:start position:0% +people will say well there really are +neocortex but + + align:start position:0% +neocortex but + + + align:start position:0% +neocortex but +if you take a strict structural + + align:start position:0% +if you take a strict structural + + + align:start position:0% +if you take a strict structural +definition of neocortex they don't + + align:start position:0% +definition of neocortex they don't + + + align:start position:0% +definition of neocortex they don't +really have the same kind of six layers + + align:start position:0% +really have the same kind of six layers + + + align:start position:0% +really have the same kind of six layers +okay you could easily Name six layers + + align:start position:0% +okay you could easily Name six layers + + + align:start position:0% +okay you could easily Name six layers +there but they're a little bit simpler + + align:start position:0% +there but they're a little bit simpler + + + align:start position:0% +there but they're a little bit simpler +cortex but they're always in between + + align:start position:0% + + + + align:start position:0% + +neocortex and limbic areas in fact a lot + + align:start position:0% +neocortex and limbic areas in fact a lot + + + align:start position:0% +neocortex and limbic areas in fact a lot +of the connections go in both ways from + + align:start position:0% +of the connections go in both ways from + + + align:start position:0% +of the connections go in both ways from +from paralympic years + + align:start position:0% +from paralympic years + + + align:start position:0% +from paralympic years +but + + align:start position:0% +but + + + align:start position:0% +but +the two regions correspond to what we've + + align:start position:0% +the two regions correspond to what we've + + + align:start position:0% +the two regions correspond to what we've +been talking about Place sense and + + align:start position:0% +been talking about Place sense and + + + align:start position:0% +been talking about Place sense and +object sense + + align:start position:0% +object sense + + + align:start position:0% +object sense +so let's just look at his picture here + + align:start position:0% +so let's just look at his picture here + + + align:start position:0% +so let's just look at his picture here +here I I put this in the book + + align:start position:0% +here I I put this in the book + + + align:start position:0% +here I I put this in the book +I think we redrw it but not very much + + align:start position:0% +I think we redrw it but not very much + + + align:start position:0% +I think we redrw it but not very much +and it shows the singular all the way + + align:start position:0% +and it shows the singular all the way + + + align:start position:0% +and it shows the singular all the way +from Peril Factory + + align:start position:0% +from Peril Factory + + + align:start position:0% +from Peril Factory +just beyond the anterior cingulate here + + align:start position:0% +just beyond the anterior cingulate here + + + align:start position:0% +just beyond the anterior cingulate here +through the entire singular gyrus and + + align:start position:0% +through the entire singular gyrus and + + + align:start position:0% +through the entire singular gyrus and +retrospelenial cortex + + align:start position:0% +retrospelenial cortex + + + align:start position:0% +retrospelenial cortex +and then continuous with the whole para + + align:start position:0% +and then continuous with the whole para + + + align:start position:0% +and then continuous with the whole para +hippocampal area so the para hippocampal + + align:start position:0% +hippocampal area so the para hippocampal + + + align:start position:0% +hippocampal area so the para hippocampal +gyrus in humans is part of that + + align:start position:0% +gyrus in humans is part of that + + + align:start position:0% +gyrus in humans is part of that +so that's hippocampocentric + + align:start position:0% +so that's hippocampocentric + + + align:start position:0% +so that's hippocampocentric +these areas all connect with para + + align:start position:0% +these areas all connect with para + + + align:start position:0% +these areas all connect with para +hippocampal areas which connect to the + + align:start position:0% +hippocampal areas which connect to the + + + align:start position:0% +hippocampal areas which connect to the +hippocampus they connect to enter + + align:start position:0% +hippocampus they connect to enter + + + align:start position:0% +hippocampus they connect to enter +rhinocortex for example + + align:start position:0% +rhinocortex for example + + + align:start position:0% +rhinocortex for example +all right + + align:start position:0% +all right + + + align:start position:0% +all right +these other areas + + align:start position:0% +these other areas + + + align:start position:0% +these other areas +he called olfactocentric + + align:start position:0% +he called olfactocentric + + + align:start position:0% +he called olfactocentric +and this is interesting because the + + align:start position:0% +and this is interesting because the + + + align:start position:0% +and this is interesting because the +connections of all these regions are + + align:start position:0% +connections of all these regions are + + + align:start position:0% +connections of all these regions are +different + + align:start position:0% +different + + + align:start position:0% +different +than the ones than the hippocampus + + align:start position:0% +than the ones than the hippocampus + + + align:start position:0% +than the ones than the hippocampus +Centric areas they go for example + + align:start position:0% +Centric areas they go for example + + + align:start position:0% +Centric areas they go for example +they're heavily connected to the + + align:start position:0% +they're heavily connected to the + + + align:start position:0% +they're heavily connected to the +amygdala and basal former okay + + align:start position:0% +amygdala and basal former okay + + + align:start position:0% +amygdala and basal former okay +the areas that are evolved + + align:start position:0% +the areas that are evolved + + + align:start position:0% +the areas that are evolved +they're closely connected to the old + + align:start position:0% +they're closely connected to the old + + + align:start position:0% +they're closely connected to the old +factory system + + align:start position:0% +factory system + + + align:start position:0% +factory system +and their to these systems that evolve + + align:start position:0% +and their to these systems that evolve + + + align:start position:0% +and their to these systems that evolve +or object discrimination or we are + + align:start position:0% +or object discrimination or we are + + + align:start position:0% +or object discrimination or we are +affective responses to objects + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% +and then + + + align:start position:0% +and then +I go through one other thing that played + + align:start position:0% +I go through one other thing that played + + + align:start position:0% +I go through one other thing that played +a critical role in Evolutions meta + + align:start position:0% +a critical role in Evolutions meta + + + align:start position:0% +a critical role in Evolutions meta +sensory system that where one of the + + align:start position:0% +sensory system that where one of the + + + align:start position:0% +sensory system that where one of the +medicine tree areas specialized for + + align:start position:0% +medicine tree areas specialized for + + + align:start position:0% +medicine tree areas specialized for +controlling fine movement and that's + + align:start position:0% +controlling fine movement and that's + + + align:start position:0% +controlling fine movement and that's +what we call primary motor cortex + + align:start position:0% +what we call primary motor cortex + + + align:start position:0% +what we call primary motor cortex +what's the evidence that + + align:start position:0% +what's the evidence that + + + align:start position:0% +what's the evidence that +it actually the motor cortex evolved out + + align:start position:0% +it actually the motor cortex evolved out + + + align:start position:0% +it actually the motor cortex evolved out +of a cementosensory area + + align:start position:0% +of a cementosensory area + + + align:start position:0% +of a cementosensory area +but one thing it does get some tomato + + align:start position:0% +but one thing it does get some tomato + + + align:start position:0% +but one thing it does get some tomato +sensory input + + align:start position:0% +sensory input + + + align:start position:0% +sensory input +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it's adjacent to just rostral to what we + + align:start position:0% +it's adjacent to just rostral to what we + + + align:start position:0% +it's adjacent to just rostral to what we +call center sensory area one + + align:start position:0% +call center sensory area one + + + align:start position:0% +call center sensory area one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but in some animals it's actually not + + align:start position:0% +but in some animals it's actually not + + + align:start position:0% +but in some animals it's actually not +separate + + align:start position:0% +separate + + + align:start position:0% +separate +like the Virginia apostle + + align:start position:0% +like the Virginia apostle + + + align:start position:0% +like the Virginia apostle +remember this + + align:start position:0% +remember this + + + align:start position:0% +remember this +do I have the picture here + + align:start position:0% + + + + align:start position:0% + +I guess I didn't put it here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but that motor cortex was so critical + + align:start position:0% +but that motor cortex was so critical + + + align:start position:0% +but that motor cortex was so critical +except we we can tell which area it is + + align:start position:0% +except we we can tell which area it is + + + align:start position:0% +except we we can tell which area it is +because + + align:start position:0% +because + + + align:start position:0% +because +the ventral anterior nucleus and the + + align:start position:0% +the ventral anterior nucleus and the + + + align:start position:0% +the ventral anterior nucleus and the +ventral lateral nucleus the parts + + align:start position:0% +ventral lateral nucleus the parts + + + align:start position:0% +ventral lateral nucleus the parts +anterior to the system at a sensory part + + align:start position:0% +anterior to the system at a sensory part + + + align:start position:0% +anterior to the system at a sensory part +of the thalamus okay project + + align:start position:0% +of the thalamus okay project + + + align:start position:0% +of the thalamus okay project +to the motor areas the VL and the VA + + align:start position:0% +to the motor areas the VL and the VA + + + align:start position:0% +to the motor areas the VL and the VA +okay + + align:start position:0% +okay + + + align:start position:0% +okay +we usually can separate them even in the + + align:start position:0% +we usually can separate them even in the + + + align:start position:0% +we usually can separate them even in the +apostle + + align:start position:0% +apostle + + + align:start position:0% +apostle +the vielgus or belarian puts primarily + + align:start position:0% +the vielgus or belarian puts primarily + + + align:start position:0% +the vielgus or belarian puts primarily +the VA gets + + align:start position:0% +the VA gets + + + align:start position:0% +the VA gets +Creator outputs primarily and IT + + align:start position:0% +Creator outputs primarily and IT + + + align:start position:0% +Creator outputs primarily and IT +projects to the pre-order areas VL + + align:start position:0% +projects to the pre-order areas VL + + + align:start position:0% +projects to the pre-order areas VL +projects to the motor strip motor cortex + + align:start position:0% +projects to the motor strip motor cortex + + + align:start position:0% +projects to the motor strip motor cortex +but in the opossum + + align:start position:0% + + + + align:start position:0% + +these these nuclei projected the very + + align:start position:0% +these these nuclei projected the very + + + align:start position:0% +these these nuclei projected the very +same cortex that the posterior nucleus + + align:start position:0% +same cortex that the posterior nucleus + + + align:start position:0% +same cortex that the posterior nucleus +projects so it's the meta sensory + + align:start position:0% + + + + align:start position:0% + +all right so + + align:start position:0% +all right so + + + align:start position:0% +all right so +and what evolved as associationary is + + align:start position:0% +and what evolved as associationary is + + + align:start position:0% +and what evolved as associationary is +right in front of these motor areas + + align:start position:0% +right in front of these motor areas + + + align:start position:0% +right in front of these motor areas +are the areas involved in + + align:start position:0% +are the areas involved in + + + align:start position:0% +are the areas involved in +anticipating in planning + + align:start position:0% +anticipating in planning + + + align:start position:0% +anticipating in planning +became the + + align:start position:0% +became the + + + align:start position:0% +became the +locus of the executive functions of the + + align:start position:0% +locus of the executive functions of the + + + align:start position:0% +locus of the executive functions of the +prefrontal cortex + + align:start position:0% +prefrontal cortex + + + align:start position:0% +prefrontal cortex +which is so critical for human behavior + + align:start position:0% +which is so critical for human behavior + + + align:start position:0% +which is so critical for human behavior +but it's very important in animals too + + align:start position:0% +but it's very important in animals too + + + align:start position:0% +but it's very important in animals too +this ability to anticipate + + align:start position:0% +this ability to anticipate + + + align:start position:0% +this ability to anticipate +to hold the get inputs from the + + align:start position:0% +to hold the get inputs from the + + + align:start position:0% +to hold the get inputs from the +posterior areas like from the visual + + align:start position:0% +posterior areas like from the visual + + + align:start position:0% +posterior areas like from the visual +system tell them where the + + align:start position:0% +system tell them where the + + + align:start position:0% +system tell them where the +locations of things right that were just + + align:start position:0% +locations of things right that were just + + + align:start position:0% +locations of things right that were just +in the environment scanning that we're + + align:start position:0% +in the environment scanning that we're + + + align:start position:0% +in the environment scanning that we're +scanning + + align:start position:0% +scanning + + + align:start position:0% +scanning +we retain that information briefly and + + align:start position:0% +we retain that information briefly and + + + align:start position:0% +we retain that information briefly and +working memory and that's affecting + + align:start position:0% +working memory and that's affecting + + + align:start position:0% +working memory and that's affecting +where we move our eyes where we choose + + align:start position:0% +where we move our eyes where we choose + + + align:start position:0% +where we move our eyes where we choose +to memorize + + align:start position:0% +to memorize + + + align:start position:0% +to memorize +all right we'll come back here + + align:start position:0% + + + + align:start position:0% + +with this slide + + align:start position:0% +with this slide + + + align:start position:0% +with this slide +and then we'll go on and talk a little + + align:start position:0% +and then we'll go on and talk a little + + + align:start position:0% +and then we'll go on and talk a little +bit more about structural details of the + + align:start position:0% +bit more about structural details of the + + + align:start position:0% +bit more about structural details of the +hippocampus next time but please read + + align:start position:0% +hippocampus next time but please read + + + align:start position:0% +hippocampus next time but please read +through all these + + align:start position:0% +through all these + + + align:start position:0% +through all these +all of these they're all online + + align:start position:0% +all of these they're all online + + + align:start position:0% +all of these they're all online +so we won't have to spend so much time + + align:start position:0% +so we won't have to spend so much time + + + align:start position:0% +so we won't have to spend so much time +with the rest of this particular group + + align:start position:0% +with the rest of this particular group + + + align:start position:0% +with the rest of this particular group +of + + align:start position:0% +of + + + align:start position:0% +of +the chapter 32 things \ No newline at end of file diff --git a/GJpt_3ie4WU.txt b/GJpt_3ie4WU.txt new file mode 100644 index 0000000000000000000000000000000000000000..90b0ab90a5c9dfe7ed672f5c749b10ca001aa3fc --- /dev/null +++ b/GJpt_3ie4WU.txt @@ -0,0 +1,11975 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer high quality educational + + align:start position:0% +to offer high quality educational + + + align:start position:0% +to offer high quality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so welcome to this week uh + + align:start position:0% +ocw.mit.edu so welcome to this week uh + + + align:start position:0% +ocw.mit.edu so welcome to this week uh +we're going to talk about uh trees + + align:start position:0% +we're going to talk about uh trees + + + align:start position:0% +we're going to talk about uh trees +mainly we're going to talk talk about + + align:start position:0% +mainly we're going to talk talk about + + + align:start position:0% +mainly we're going to talk talk about +some very special ones spanning trees uh + + align:start position:0% +some very special ones spanning trees uh + + + align:start position:0% +some very special ones spanning trees uh +but before we do this we will go through + + align:start position:0% +but before we do this we will go through + + + align:start position:0% +but before we do this we will go through +a whole bunch of definitions and I will + + align:start position:0% +a whole bunch of definitions and I will + + + align:start position:0% +a whole bunch of definitions and I will +give examples um to explain how it + + align:start position:0% +give examples um to explain how it + + + align:start position:0% +give examples um to explain how it +works + + align:start position:0% + + + + align:start position:0% + +um so let's talk about uh walks and + + align:start position:0% + + + + align:start position:0% + +paths + + align:start position:0% +paths + + + align:start position:0% +paths +um so you've already seen uh a bit of + + align:start position:0% +um so you've already seen uh a bit of + + + align:start position:0% +um so you've already seen uh a bit of +graph Theory we talked about uh uh craft + + align:start position:0% +graph Theory we talked about uh uh craft + + + align:start position:0% +graph Theory we talked about uh uh craft +colorings and so on uh but now we're + + align:start position:0% +colorings and so on uh but now we're + + + align:start position:0% +colorings and so on uh but now we're +going to talk about special types of + + align:start position:0% +going to talk about special types of + + + align:start position:0% +going to talk about special types of +graphs and special structures within + + align:start position:0% +graphs and special structures within + + + align:start position:0% +graphs and special structures within +such + + align:start position:0% +such + + + align:start position:0% +such +graphs + + align:start position:0% +graphs + + + align:start position:0% +graphs +um well let's start with the first + + align:start position:0% +um well let's start with the first + + + align:start position:0% +um well let's start with the first +definition uh how do we Define a walk + + align:start position:0% +definition uh how do we Define a walk + + + align:start position:0% +definition uh how do we Define a walk +well a walk is something very simple you + + align:start position:0% +well a walk is something very simple you + + + align:start position:0% +well a walk is something very simple you +walk from one vertic in the graph over + + align:start position:0% +walk from one vertic in the graph over + + + align:start position:0% +walk from one vertic in the graph over +an edge to the next vertex to a next + + align:start position:0% +an edge to the next vertex to a next + + + align:start position:0% +an edge to the next vertex to a next +vertex and so on so how do we Define + + align:start position:0% +vertex and so on so how do we Define + + + align:start position:0% +vertex and so on so how do we Define +this uh a walk + + align:start position:0% +this uh a walk + + + align:start position:0% +this uh a walk +is uh a + + align:start position:0% + + + + align:start position:0% + +sequence of uh vertices that are + + align:start position:0% + + + + align:start position:0% + +connected uh by + + align:start position:0% +connected uh by + + + align:start position:0% +connected uh by +edges so for example we may have + + align:start position:0% +edges so for example we may have + + + align:start position:0% +edges so for example we may have +something that looks like a first verx + + align:start position:0% +something that looks like a first verx + + + align:start position:0% +something that looks like a first verx +that we call a start and an edge that + + align:start position:0% +that we call a start and an edge that + + + align:start position:0% +that we call a start and an edge that +goes to a second vertex and and we + + align:start position:0% +goes to a second vertex and and we + + + align:start position:0% +goes to a second vertex and and we +continue like this till we end say at VK + + align:start position:0% +continue like this till we end say at VK + + + align:start position:0% +continue like this till we end say at VK +which we call the end of the walk and uh + + align:start position:0% +which we call the end of the walk and uh + + + align:start position:0% +which we call the end of the walk and uh +if you look at this we say this is a + + align:start position:0% +if you look at this we say this is a + + + align:start position:0% +if you look at this we say this is a +walk from v0 all the way to VK it has + + align:start position:0% +walk from v0 all the way to VK it has + + + align:start position:0% +walk from v0 all the way to VK it has +exactly K edges and we say that the + + align:start position:0% +exactly K edges and we say that the + + + align:start position:0% +exactly K edges and we say that the +length is actually equal to + + align:start position:0% +length is actually equal to + + + align:start position:0% +length is actually equal to +K so this is uh uh a very basic notion + + align:start position:0% +K so this is uh uh a very basic notion + + + align:start position:0% +K so this is uh uh a very basic notion +and what we are really interested in is + + align:start position:0% +and what we are really interested in is + + + align:start position:0% +and what we are really interested in is +actually uh + + align:start position:0% +actually uh + + + align:start position:0% +actually uh +paths and paths are special types of + + align:start position:0% +paths and paths are special types of + + + align:start position:0% +paths and paths are special types of +walks in which all those vertices are + + align:start position:0% +walks in which all those vertices are + + + align:start position:0% +walks in which all those vertices are +actually different from one another but + + align:start position:0% +actually different from one another but + + + align:start position:0% +actually different from one another but +let's uh first uh give an example of a + + align:start position:0% +let's uh first uh give an example of a + + + align:start position:0% +let's uh first uh give an example of a +graph that we will study throughout the + + align:start position:0% +graph that we will study throughout the + + + align:start position:0% +graph that we will study throughout the +whole leure especially when we come to + + align:start position:0% +whole leure especially when we come to + + + align:start position:0% +whole leure especially when we come to +spanning + + align:start position:0% +spanning + + + align:start position:0% +spanning +trees um so let's have a look at the + + align:start position:0% +trees um so let's have a look at the + + + align:start position:0% +trees um so let's have a look at the +following graph + + align:start position:0% + + + + align:start position:0% + +uh actually let me + + align:start position:0% +uh actually let me + + + align:start position:0% +uh actually let me +just + + align:start position:0% + + + + align:start position:0% + +this so let this be a graph then for + + align:start position:0% +this so let this be a graph then for + + + align:start position:0% +this so let this be a graph then for +example we can have a walk that goes + + align:start position:0% +example we can have a walk that goes + + + align:start position:0% +example we can have a walk that goes +from + + align:start position:0% +from + + + align:start position:0% +from +um this particular Edge say we call this + + align:start position:0% +um this particular Edge say we call this + + + align:start position:0% +um this particular Edge say we call this +v0 it goes over this Edge over here so + + align:start position:0% +v0 it goes over this Edge over here so + + + align:start position:0% +v0 it goes over this Edge over here so +supp I want to end over here um well I + + align:start position:0% +supp I want to end over here um well I + + + align:start position:0% +supp I want to end over here um well I +can go many ways in this particular one + + align:start position:0% +can go many ways in this particular one + + + align:start position:0% +can go many ways in this particular one +I can go over this Edge I may go over + + align:start position:0% +I can go over this Edge I may go over + + + align:start position:0% +I can go over this Edge I may go over +here I may go all the way to this part + + align:start position:0% +here I may go all the way to this part + + + align:start position:0% +here I may go all the way to this part +over here and may return if I want to + + align:start position:0% +over here and may return if I want to + + + align:start position:0% +over here and may return if I want to +and then finally I take this Edge for + + align:start position:0% +and then finally I take this Edge for + + + align:start position:0% +and then finally I take this Edge for +example back to um over this Edge I will + + align:start position:0% +example back to um over this Edge I will + + + align:start position:0% +example back to um over this Edge I will +end in the last vertx + + align:start position:0% +end in the last vertx + + + align:start position:0% +end in the last vertx +VK so what we notice here is that we + + align:start position:0% +VK so what we notice here is that we + + + align:start position:0% +VK so what we notice here is that we +have a walk that actually uh gets to + + align:start position:0% +have a walk that actually uh gets to + + + align:start position:0% +have a walk that actually uh gets to +this particular vertex and then returns + + align:start position:0% +this particular vertex and then returns + + + align:start position:0% +this particular vertex and then returns +to this vertex over a few other edges + + align:start position:0% +to this vertex over a few other edges + + + align:start position:0% +to this vertex over a few other edges +and goes all the way to + + align:start position:0% +and goes all the way to + + + align:start position:0% +and goes all the way to +VK so if you talk about the path then we + + align:start position:0% +VK so if you talk about the path then we + + + align:start position:0% +VK so if you talk about the path then we +really want all the different vertices + + align:start position:0% +really want all the different vertices + + + align:start position:0% +really want all the different vertices +not to occur + + align:start position:0% +not to occur + + + align:start position:0% +not to occur +twice so let's define this so a + + align:start position:0% +twice so let's define this so a + + + align:start position:0% +twice so let's define this so a +definition + + align:start position:0% +definition + + + align:start position:0% +definition +is that a path is actually a + + align:start position:0% + + + + align:start position:0% + +walk is a + + align:start position:0% +walk is a + + + align:start position:0% +walk is a +walk uh where all edges where all + + align:start position:0% +walk uh where all edges where all + + + align:start position:0% +walk uh where all edges where all +FES f + + align:start position:0% +FES f + + + align:start position:0% +FES f +i are + + align:start position:0% + + + + align:start position:0% + +different + + align:start position:0% +different + + + align:start position:0% +different +and in this particular case uh well for + + align:start position:0% +and in this particular case uh well for + + + align:start position:0% +and in this particular case uh well for +example if we strip off this part over + + align:start position:0% +example if we strip off this part over + + + align:start position:0% +example if we strip off this part over +here you will get a path from v0 to here + + align:start position:0% +here you will get a path from v0 to here + + + align:start position:0% +here you will get a path from v0 to here +to here to here and all these vertices + + align:start position:0% +to here to here and all these vertices + + + align:start position:0% +to here to here and all these vertices +on the path on this walk are different + + align:start position:0% +on the path on this walk are different + + + align:start position:0% +on the path on this walk are different +and therefore it is a + + align:start position:0% +and therefore it is a + + + align:start position:0% +and therefore it is a +path um this also shows us something + + align:start position:0% +path um this also shows us something + + + align:start position:0% +path um this also shows us something +um it is possible to construct from a + + align:start position:0% +um it is possible to construct from a + + + align:start position:0% +um it is possible to construct from a +walk a path as you can see we started + + align:start position:0% +walk a path as you can see we started + + + align:start position:0% +walk a path as you can see we started +off with this particular walk and uh we + + align:start position:0% +off with this particular walk and uh we + + + align:start position:0% +off with this particular walk and uh we +just uh deleted essentially a part where + + align:start position:0% +just uh deleted essentially a part where + + + align:start position:0% +just uh deleted essentially a part where +we sort of came back to the same fex + + align:start position:0% +we sort of came back to the same fex + + + align:start position:0% +we sort of came back to the same fex +again and when we delete all those kinds + + align:start position:0% +again and when we delete all those kinds + + + align:start position:0% +again and when we delete all those kinds +of parts we will end up with a path so + + align:start position:0% +of parts we will end up with a path so + + + align:start position:0% +of parts we will end up with a path so +can we formalize this a little bit + + align:start position:0% +can we formalize this a little bit + + + align:start position:0% +can we formalize this a little bit +better um then we get the next + + align:start position:0% +better um then we get the next + + + align:start position:0% +better um then we get the next +LMA so let's uh + + align:start position:0% +LMA so let's uh + + + align:start position:0% +LMA so let's uh +uh call this LMA + + align:start position:0% +uh call this LMA + + + align:start position:0% +uh call this LMA +one and let's see whether we can prove + + align:start position:0% +one and let's see whether we can prove + + + align:start position:0% +one and let's see whether we can prove +this uh so we want to show that if there + + align:start position:0% +this uh so we want to show that if there + + + align:start position:0% +this uh so we want to show that if there +exists a + + align:start position:0% +exists a + + + align:start position:0% +exists a +walk uh from say a fex u to uh well + + align:start position:0% +walk uh from say a fex u to uh well + + + align:start position:0% +walk uh from say a fex u to uh well +maybe I should not use + + align:start position:0% +maybe I should not use + + + align:start position:0% +maybe I should not use +arrows that's + + align:start position:0% +arrows that's + + + align:start position:0% +arrows that's +confusing from U to + + align:start position:0% +confusing from U to + + + align:start position:0% +confusing from U to +V uh + + align:start position:0% +V uh + + + align:start position:0% +V uh +then there also exists a path + + align:start position:0% +then there also exists a path + + + align:start position:0% +then there also exists a path +from + + align:start position:0% +from + + + align:start position:0% +from +U to + + align:start position:0% +U to + + + align:start position:0% +U to +V so how can we prove this do you have + + align:start position:0% +V so how can we prove this do you have + + + align:start position:0% +V so how can we prove this do you have +any + + align:start position:0% +any + + + align:start position:0% +any +ideas + + align:start position:0% +ideas + + + align:start position:0% +ideas +so what kind of proof techniques can we + + align:start position:0% +so what kind of proof techniques can we + + + align:start position:0% +so what kind of proof techniques can we +use + + align:start position:0% +use + + + align:start position:0% +use +here um maybe uh one of the principles + + align:start position:0% +here um maybe uh one of the principles + + + align:start position:0% +here um maybe uh one of the principles +that we have + + align:start position:0% + + + + align:start position:0% + +seen have idea how you could show this + + align:start position:0% +seen have idea how you could show this + + + align:start position:0% +seen have idea how you could show this +basically if you visit one vertex T + + align:start position:0% +basically if you visit one vertex T + + + align:start position:0% +basically if you visit one vertex T +let's say you + + align:start position:0% +let's say you + + + align:start position:0% +let's say you +go 1 2 3 4 5 3 six and walk from one to + + align:start position:0% +go 1 2 3 4 5 3 six and walk from one to + + + align:start position:0% +go 1 2 3 4 5 3 six and walk from one to +six then you just take out the four five + + align:start position:0% +six then you just take out the four five + + + align:start position:0% +six then you just take out the four five +so you just go one two 3 six right so + + align:start position:0% +so you just go one two 3 six right so + + + align:start position:0% +so you just go one two 3 six right so +what did we do there we essentially had + + align:start position:0% +what did we do there we essentially had + + + align:start position:0% +what did we do there we essentially had +a walk and then we cut out a smaller + + align:start position:0% +a walk and then we cut out a smaller + + + align:start position:0% +a walk and then we cut out a smaller +part here that recurs in a sense and uh + + align:start position:0% +part here that recurs in a sense and uh + + + align:start position:0% +part here that recurs in a sense and uh +we have shortened the path uh we have + + align:start position:0% +we have shortened the path uh we have + + + align:start position:0% +we have shortened the path uh we have +shortened the walk to a small + + align:start position:0% +shortened the walk to a small + + + align:start position:0% +shortened the walk to a small +path so what we have used here that we + + align:start position:0% +path so what we have used here that we + + + align:start position:0% +path so what we have used here that we +can sort of uh take out uh parts of the + + align:start position:0% +can sort of uh take out uh parts of the + + + align:start position:0% +can sort of uh take out uh parts of the +walk just like what we did over here + + align:start position:0% +walk just like what we did over here + + + align:start position:0% +walk just like what we did over here +until it's the walk gets shorter and + + align:start position:0% +until it's the walk gets shorter and + + + align:start position:0% +until it's the walk gets shorter and +shorter and shorter so maybe one of the + + align:start position:0% +shorter and shorter so maybe one of the + + + align:start position:0% +shorter and shorter so maybe one of the +things that we may consider is uh a walk + + align:start position:0% +things that we may consider is uh a walk + + + align:start position:0% +things that we may consider is uh a walk +of shortest + + align:start position:0% +of shortest + + + align:start position:0% +of shortest +length so uh and we know that this uh + + align:start position:0% +length so uh and we know that this uh + + + align:start position:0% +length so uh and we know that this uh +this is + + align:start position:0% +this is + + + align:start position:0% +this is +possible um oops sorry about that + + align:start position:0% + + + + align:start position:0% + +um so let's prove this so for example uh + + align:start position:0% +um so let's prove this so for example uh + + + align:start position:0% +um so let's prove this so for example uh +there exists supposed to exist such a + + align:start position:0% +there exists supposed to exist such a + + + align:start position:0% +there exists supposed to exist such a +walk from U to V then we know by the + + align:start position:0% +walk from U to V then we know by the + + + align:start position:0% +walk from U to V then we know by the +well ordering principle that there + + align:start position:0% +well ordering principle that there + + + align:start position:0% +well ordering principle that there +exists a walk of minimal length so + + align:start position:0% +exists a walk of minimal length so + + + align:start position:0% +exists a walk of minimal length so +that's what we're going to use here and + + align:start position:0% +that's what we're going to use here and + + + align:start position:0% +that's what we're going to use here and +then we're going to uh essentially go in + + align:start position:0% +then we're going to uh essentially go in + + + align:start position:0% +then we're going to uh essentially go in +the same direction as what you were + + align:start position:0% +the same direction as what you were + + + align:start position:0% +the same direction as what you were +talking about because you're going to + + align:start position:0% +talking about because you're going to + + + align:start position:0% +talking about because you're going to +show + + align:start position:0% +show + + + align:start position:0% +show +that it's not possible to delete any + + align:start position:0% +that it's not possible to delete any + + + align:start position:0% +that it's not possible to delete any +more because otherwise if you could do + + align:start position:0% +more because otherwise if you could do + + + align:start position:0% +more because otherwise if you could do +that the walk would get shorter and + + align:start position:0% +that the walk would get shorter and + + + align:start position:0% +that the walk would get shorter and +that's not possible because by the well + + align:start position:0% +that's not possible because by the well + + + align:start position:0% +that's not possible because by the well +ordering + + align:start position:0% +ordering + + + align:start position:0% +ordering +principle + + align:start position:0% +principle + + + align:start position:0% +principle +uh + + align:start position:0% +uh + + + align:start position:0% +uh +we simply + + align:start position:0% +we simply + + + align:start position:0% +we simply +consider + + align:start position:0% +consider + + + align:start position:0% +consider +uh that there exists a walk of minimal + + align:start position:0% +uh that there exists a walk of minimal + + + align:start position:0% +uh that there exists a walk of minimal +length that we are interested + + align:start position:0% + + + + align:start position:0% + +in and + + align:start position:0% + + + + align:start position:0% + +we will show that this particular walk + + align:start position:0% +we will show that this particular walk + + + align:start position:0% +we will show that this particular walk +is actually going to be a path so let's + + align:start position:0% +is actually going to be a path so let's + + + align:start position:0% +is actually going to be a path so let's +see how we can do this so so let's uh + + align:start position:0% +see how we can do this so so let's uh + + + align:start position:0% +see how we can do this so so let's uh +the walk be equal to well starts in v0 + + align:start position:0% +the walk be equal to well starts in v0 + + + align:start position:0% +the walk be equal to well starts in v0 +is equal to U there's an edge to say V1 + + align:start position:0% +is equal to U there's an edge to say V1 + + + align:start position:0% +is equal to U there's an edge to say V1 +goes all the way up to + + align:start position:0% +goes all the way up to + + + align:start position:0% +goes all the way up to +VK which is the last vertex + + align:start position:0% +VK which is the last vertex + + + align:start position:0% +VK which is the last vertex +V so what are we going to prove we're + + align:start position:0% +V so what are we going to prove we're + + + align:start position:0% +V so what are we going to prove we're +going to prove that this is actually a + + align:start position:0% +going to prove that this is actually a + + + align:start position:0% +going to prove that this is actually a +path and uh since this is a walk of + + align:start position:0% +path and uh since this is a walk of + + + align:start position:0% +path and uh since this is a walk of +minimal length well suppose it is not a + + align:start position:0% +minimal length well suppose it is not a + + + align:start position:0% +minimal length well suppose it is not a +path so we are going to use + + align:start position:0% + + + + align:start position:0% + +contradiction well if it's not a path + + align:start position:0% +contradiction well if it's not a path + + + align:start position:0% +contradiction well if it's not a path +then by our definitions over here there + + align:start position:0% +then by our definitions over here there + + + align:start position:0% +then by our definitions over here there +must be two vertices that are actually + + align:start position:0% +must be two vertices that are actually + + + align:start position:0% +must be two vertices that are actually +the same just like in here so we go from + + align:start position:0% +the same just like in here so we go from + + + align:start position:0% +the same just like in here so we go from +v0 to say this particular vertex to this + + align:start position:0% +v0 to say this particular vertex to this + + + align:start position:0% +v0 to say this particular vertex to this +one and then we come back to this one + + align:start position:0% +one and then we come back to this one + + + align:start position:0% +one and then we come back to this one +and then all the way to VK so if it is + + align:start position:0% +and then all the way to VK so if it is + + + align:start position:0% +and then all the way to VK so if it is +not a + + align:start position:0% +not a + + + align:start position:0% +not a +path then two two of those must be equal + + align:start position:0% +path then two two of those must be equal + + + align:start position:0% +path then two two of those must be equal +to one another and then we're going to + + align:start position:0% +to one another and then we're going to + + + align:start position:0% +to one another and then we're going to +use this trick we're going to take out + + align:start position:0% +use this trick we're going to take out + + + align:start position:0% +use this trick we're going to take out +this part we get a shorter walk but that + + align:start position:0% +this part we get a shorter walk but that + + + align:start position:0% +this part we get a shorter walk but that +contradicts that our walk is minimal + + align:start position:0% +contradicts that our walk is minimal + + + align:start position:0% +contradicts that our walk is minimal +length so that's sort of the proof + + align:start position:0% +length so that's sort of the proof + + + align:start position:0% +length so that's sort of the proof +technique that we are doing okay let's + + align:start position:0% +technique that we are doing okay let's + + + align:start position:0% +technique that we are doing okay let's +uh do + + align:start position:0% + + + + align:start position:0% + +this so um well first uh let's consider + + align:start position:0% +this so um well first uh let's consider + + + align:start position:0% +this so um well first uh let's consider +a few cases if k equals z then that's + + align:start position:0% +a few cases if k equals z then that's + + + align:start position:0% +a few cases if k equals z then that's +pretty obvious we have only a single + + align:start position:0% +pretty obvious we have only a single + + + align:start position:0% +pretty obvious we have only a single +vertex U that is connected by a zero + + align:start position:0% +vertex U that is connected by a zero + + + align:start position:0% +vertex U that is connected by a zero +length path to itself so this is fine + + align:start position:0% +length path to itself so this is fine + + + align:start position:0% +length path to itself so this is fine +for k equals 1 we have just a single + + align:start position:0% +for k equals 1 we have just a single + + + align:start position:0% +for k equals 1 we have just a single +edge and then we're done two that's a + + align:start position:0% +edge and then we're done two that's a + + + align:start position:0% +edge and then we're done two that's a +path as well so let's uh consider the + + align:start position:0% +path as well so let's uh consider the + + + align:start position:0% +path as well so let's uh consider the +case where K is at least + + align:start position:0% +case where K is at least + + + align:start position:0% +case where K is at least +two well suppose that the walk is not a + + align:start position:0% +two well suppose that the walk is not a + + + align:start position:0% +two well suppose that the walk is not a +path so we are going to uh assume the + + align:start position:0% +path so we are going to uh assume the + + + align:start position:0% +path so we are going to uh assume the +opposite + + align:start position:0% + + + + align:start position:0% + +if it's not a + + align:start position:0% +if it's not a + + + align:start position:0% +if it's not a +path then we concluded that two of those + + align:start position:0% +path then we concluded that two of those + + + align:start position:0% +path then we concluded that two of those +V I must be equal to one another so + + align:start position:0% +V I must be equal to one another so + + + align:start position:0% +V I must be equal to one another so +there exists an i une equal to J such + + align:start position:0% +there exists an i une equal to J such + + + align:start position:0% +there exists an i une equal to J such +that verx V equals + + align:start position:0% +that verx V equals + + + align:start position:0% +that verx V equals +VJ ah but now we have a walk + + align:start position:0% +VJ ah but now we have a walk + + + align:start position:0% +VJ ah but now we have a walk +that goes from + + align:start position:0% +that goes from + + + align:start position:0% +that goes from +v0 all the way to say V I which is equal + + align:start position:0% +v0 all the way to say V I which is equal + + + align:start position:0% +v0 all the way to say V I which is equal +to VJ and then we go all the way up to + + align:start position:0% +to VJ and then we go all the way up to + + + align:start position:0% +to VJ and then we go all the way up to +VK which is equal to V so essentially we + + align:start position:0% +VK which is equal to V so essentially we + + + align:start position:0% +VK which is equal to V so essentially we +have created a shorter walk we have + + align:start position:0% +have created a shorter walk we have + + + align:start position:0% +have created a shorter walk we have +taken out this little triangle over + + align:start position:0% + + + + align:start position:0% + +here now this is a shorter + + align:start position:0% +here now this is a shorter + + + align:start position:0% +here now this is a shorter +walk + + align:start position:0% +walk + + + align:start position:0% +walk +and this + + align:start position:0% +and this + + + align:start position:0% +and this +contradicts our Assumption of minimality + + align:start position:0% + + + + align:start position:0% + +so that means that our assumption over + + align:start position:0% +so that means that our assumption over + + + align:start position:0% +so that means that our assumption over +here is not + + align:start position:0% +here is not + + + align:start position:0% +here is not +true so the walk is actually a path so + + align:start position:0% +true so the walk is actually a path so + + + align:start position:0% +true so the walk is actually a path so +this concludes the + + align:start position:0% + + + + align:start position:0% + +proof so even though this LMA is pretty + + align:start position:0% +proof so even though this LMA is pretty + + + align:start position:0% +proof so even though this LMA is pretty +straightforward in the sense that we all + + align:start position:0% +straightforward in the sense that we all + + + align:start position:0% +straightforward in the sense that we all +feel that if you have a walk then you + + align:start position:0% +feel that if you have a walk then you + + + align:start position:0% +feel that if you have a walk then you +can create a path if you really want to + + align:start position:0% +can create a path if you really want to + + + align:start position:0% +can create a path if you really want to +write it down with all the principles + + align:start position:0% +write it down with all the principles + + + align:start position:0% +write it down with all the principles +that we have been taught uh you can see + + align:start position:0% +that we have been taught uh you can see + + + align:start position:0% +that we have been taught uh you can see +a few things appearing here so we first + + align:start position:0% +a few things appearing here so we first + + + align:start position:0% +a few things appearing here so we first +started with well ordering principle and + + align:start position:0% +started with well ordering principle and + + + align:start position:0% +started with well ordering principle and +also we + + align:start position:0% +also we + + + align:start position:0% +also we +use the method of contradiction in our + + align:start position:0% +use the method of contradiction in our + + + align:start position:0% +use the method of contradiction in our +proof okay so let's uh talk about the + + align:start position:0% +proof okay so let's uh talk about the + + + align:start position:0% +proof okay so let's uh talk about the +next definition so we talked about walks + + align:start position:0% +next definition so we talked about walks + + + align:start position:0% +next definition so we talked about walks +and paths uh let's talk about + + align:start position:0% + + + + align:start position:0% + +connectivity + + align:start position:0% + + + + align:start position:0% + +and we actually + + align:start position:0% +and we actually + + + align:start position:0% +and we actually +Define two vertices u and v to be + + align:start position:0% +Define two vertices u and v to be + + + align:start position:0% +Define two vertices u and v to be +connected if there is a path that + + align:start position:0% +connected if there is a path that + + + align:start position:0% +connected if there is a path that +connects U to V so u and v are + + align:start position:0% + + + + align:start position:0% + +connected if there is a + + align:start position:0% + + + + align:start position:0% + +path + + align:start position:0% +path + + + align:start position:0% +path +from U to + + align:start position:0% +from U to + + + align:start position:0% +from U to +V and uh now we can talk about graphs + + align:start position:0% +V and uh now we can talk about graphs + + + align:start position:0% +V and uh now we can talk about graphs +that are connected that's a very + + align:start position:0% +that are connected that's a very + + + align:start position:0% +that are connected that's a very +important + + align:start position:0% +important + + + align:start position:0% +important +concept a graph is connected + + align:start position:0% + + + + align:start position:0% + +if if every pair of + + align:start position:0% +if if every pair of + + + align:start position:0% +if if every pair of +vertices is + + align:start position:0% +vertices is + + + align:start position:0% +vertices is +connected so when every + + align:start position:0% +connected so when every + + + align:start position:0% +connected so when every +pair of vertices in the + + align:start position:0% + + + + align:start position:0% + +graph are connected so an example is + + align:start position:0% +graph are connected so an example is + + + align:start position:0% +graph are connected so an example is +that particular graph + + align:start position:0% +that particular graph + + + align:start position:0% +that particular graph +on the + + align:start position:0% +on the + + + align:start position:0% +on the +Blackboard and you can see here that + + align:start position:0% +Blackboard and you can see here that + + + align:start position:0% +Blackboard and you can see here that +there's always a path to be found from + + align:start position:0% +there's always a path to be found from + + + align:start position:0% +there's always a path to be found from +this verx to this one or to that one to + + align:start position:0% +this verx to this one or to that one to + + + align:start position:0% +this verx to this one or to that one to +this to that to this or that um you can + + align:start position:0% +this to that to this or that um you can + + + align:start position:0% +this to that to this or that um you can +uh do this for any two vertices so this + + align:start position:0% +uh do this for any two vertices so this + + + align:start position:0% +uh do this for any two vertices so this +is a connected graph a graph that is not + + align:start position:0% +is a connected graph a graph that is not + + + align:start position:0% +is a connected graph a graph that is not +connected uh looks something like + + align:start position:0% +connected uh looks something like + + + align:start position:0% +connected uh looks something like +uh like this for example you may have a + + align:start position:0% +uh like this for example you may have a + + + align:start position:0% +uh like this for example you may have a +single + + align:start position:0% +single + + + align:start position:0% +single +edge plus say you + + align:start position:0% +edge plus say you + + + align:start position:0% +edge plus say you +triangle and maybe with another Edge or + + align:start position:0% +triangle and maybe with another Edge or + + + align:start position:0% +triangle and maybe with another Edge or +something like that so they are + + align:start position:0% +something like that so they are + + + align:start position:0% +something like that so they are +disconnected from this vertex I do not + + align:start position:0% +disconnected from this vertex I do not + + + align:start position:0% +disconnected from this vertex I do not +have a graph that connects to a Vertex + + align:start position:0% +have a graph that connects to a Vertex + + + align:start position:0% +have a graph that connects to a Vertex +over + + align:start position:0% +over + + + align:start position:0% +over +here okay so this is uh about + + align:start position:0% +here okay so this is uh about + + + align:start position:0% +here okay so this is uh about +connectivity and uh now we can start + + align:start position:0% +connectivity and uh now we can start + + + align:start position:0% +connectivity and uh now we can start +talking about uh cycles and closed + + align:start position:0% +talking about uh cycles and closed + + + align:start position:0% +talking about uh cycles and closed +walks and + + align:start position:0% + + + + align:start position:0% + +together these the the + + align:start position:0% +together these the the + + + align:start position:0% +together these the the +uh get these Concepts will uh will will + + align:start position:0% +uh get these Concepts will uh will will + + + align:start position:0% +uh get these Concepts will uh will will +help us to Define trees and then we can + + align:start position:0% +help us to Define trees and then we can + + + align:start position:0% +help us to Define trees and then we can +start talking about this very special + + align:start position:0% +start talking about this very special + + + align:start position:0% +start talking about this very special +concept spanning + + align:start position:0% +concept spanning + + + align:start position:0% +concept spanning +trees okay so let's see how that + + align:start position:0% + + + + align:start position:0% + +works so cycles and uh closed + + align:start position:0% + + + + align:start position:0% + +walks you first Define uh a closed + + align:start position:0% +walks you first Define uh a closed + + + align:start position:0% +walks you first Define uh a closed +walk and and uh once we have done this + + align:start position:0% +walk and and uh once we have done this + + + align:start position:0% +walk and and uh once we have done this +we are able to get into Cycles so what's + + align:start position:0% +we are able to get into Cycles so what's + + + align:start position:0% +we are able to get into Cycles so what's +a closed walk well it's uh it's actually + + align:start position:0% +a closed walk well it's uh it's actually + + + align:start position:0% +a closed walk well it's uh it's actually +a walk for which the start and the end + + align:start position:0% +a walk for which the start and the end + + + align:start position:0% +a walk for which the start and the end +vertex are the + + align:start position:0% + + + + align:start position:0% + +same so it + + align:start position:0% +same so it + + + align:start position:0% +same so it +starts and + + align:start position:0% + + + + align:start position:0% + +ends at exactly the same vertex + + align:start position:0% + + + + align:start position:0% + +so this is all pretty straightforward so + + align:start position:0% +so this is all pretty straightforward so + + + align:start position:0% +so this is all pretty straightforward so +we have v0 connected to say V1 all the + + align:start position:0% +we have v0 connected to say V1 all the + + + align:start position:0% +we have v0 connected to say V1 all the +way up to + + align:start position:0% +way up to + + + align:start position:0% +way up to +VK and VK itself is equal to v0 so you + + align:start position:0% +VK and VK itself is equal to v0 so you + + + align:start position:0% +VK and VK itself is equal to v0 so you +have a walk that goes all the way from + + align:start position:0% +have a walk that goes all the way from + + + align:start position:0% +have a walk that goes all the way from +v0 all the way back to VK for example in + + align:start position:0% +v0 all the way back to VK for example in + + + align:start position:0% +v0 all the way back to VK for example in +this graph you could have uh walked all + + align:start position:0% +this graph you could have uh walked all + + + align:start position:0% +this graph you could have uh walked all +the way back to v0 and you would have a + + align:start position:0% +the way back to v0 and you would have a + + + align:start position:0% +the way back to v0 and you would have a +closed walk so what's a cycle a cycle is + + align:start position:0% +closed walk so what's a cycle a cycle is + + + align:start position:0% +closed walk so what's a cycle a cycle is +a little bit more special uh in which + + align:start position:0% +a little bit more special uh in which + + + align:start position:0% +a little bit more special uh in which +all these fuses over here are actually + + align:start position:0% +all these fuses over here are actually + + + align:start position:0% +all these fuses over here are actually +different from one + + align:start position:0% +different from one + + + align:start position:0% +different from one +another so if K is at least three so + + align:start position:0% +another so if K is at least three so + + + align:start position:0% +another so if K is at least three so +it's so the walk is not just a simple + + align:start position:0% +it's so the walk is not just a simple + + + align:start position:0% +it's so the walk is not just a simple +Edge or just a single + + align:start position:0% + + + + align:start position:0% + +vertex and if all v0 V1 all the way up + + align:start position:0% +vertex and if all v0 V1 all the way up + + + align:start position:0% +vertex and if all v0 V1 all the way up +to FK minus one are uh different + + align:start position:0% + + + + align:start position:0% + +then we + + align:start position:0% +then we + + + align:start position:0% +then we +are + + align:start position:0% +are + + + align:start position:0% +are +saying uh that we have a cycle then it + + align:start position:0% +saying uh that we have a cycle then it + + + align:start position:0% +saying uh that we have a cycle then it +is called a + + align:start position:0% + + + + align:start position:0% + +cycle + + align:start position:0% + + + + align:start position:0% + +okay so these two concept connectivity + + align:start position:0% +okay so these two concept connectivity + + + align:start position:0% +okay so these two concept connectivity +and Cycles will help us to Define + + align:start position:0% + + + + align:start position:0% + +trees so what are + + align:start position:0% +trees so what are + + + align:start position:0% +trees so what are +trees uh a simple example is some + + align:start position:0% +trees uh a simple example is some + + + align:start position:0% +trees uh a simple example is some +something that looks like uh this for + + align:start position:0% + + + + align:start position:0% + +example um the idea is that a tree is + + align:start position:0% +example um the idea is that a tree is + + + align:start position:0% +example um the idea is that a tree is +both + + align:start position:0% +both + + + align:start position:0% +both +connected and it has no Cycles so in + + align:start position:0% +connected and it has no Cycles so in + + + align:start position:0% +connected and it has no Cycles so in +this case we can see that uh you know + + align:start position:0% +this case we can see that uh you know + + + align:start position:0% +this case we can see that uh you know +every fex is connected to every other + + align:start position:0% +every fex is connected to every other + + + align:start position:0% +every fex is connected to every other +fex but there is no cycle like a + + align:start position:0% +fex but there is no cycle like a + + + align:start position:0% +fex but there is no cycle like a +triangle or something that is connected + + align:start position:0% +triangle or something that is connected + + + align:start position:0% +triangle or something that is connected +all around so let's define this + + align:start position:0% +all around so let's define this + + + align:start position:0% +all around so let's define this +properly uh a definition is that a + + align:start position:0% + + + + align:start position:0% + +connected and a cyclic + + align:start position:0% + + + + align:start position:0% + +graph is called a + + align:start position:0% + + + + align:start position:0% + +tree all + + align:start position:0% +tree all + + + align:start position:0% +tree all +right and within trees we also have + + align:start position:0% +right and within trees we also have + + + align:start position:0% +right and within trees we also have +something very special that we call + + align:start position:0% +something very special that we call + + + align:start position:0% +something very special that we call +leaves leaves are exactly those nodes + + align:start position:0% +leaves leaves are exactly those nodes + + + align:start position:0% +leaves leaves are exactly those nodes +that have a degree one so for example + + align:start position:0% +that have a degree one so for example + + + align:start position:0% +that have a degree one so for example +this node has degree one right it has + + align:start position:0% +this node has degree one right it has + + + align:start position:0% +this node has degree one right it has +only this Edge connected to it so this + + align:start position:0% +only this Edge connected to it so this + + + align:start position:0% +only this Edge connected to it so this +is called a leaf this one also is a leaf + + align:start position:0% +is called a leaf this one also is a leaf + + + align:start position:0% +is called a leaf this one also is a leaf +because it has just uh one uh Edge + + align:start position:0% +because it has just uh one uh Edge + + + align:start position:0% +because it has just uh one uh Edge +connected to it but this Leaf over here + + align:start position:0% +connected to it but this Leaf over here + + + align:start position:0% +connected to it but this Leaf over here +has three edges so it has the grie three + + align:start position:0% +has three edges so it has the grie three + + + align:start position:0% +has three edges so it has the grie three +this one has the grie four this is a + + align:start position:0% +this one has the grie four this is a + + + align:start position:0% +this one has the grie four this is a +leaf again this one is a leaf this one + + align:start position:0% +leaf again this one is a leaf this one + + + align:start position:0% +leaf again this one is a leaf this one +and this + + align:start position:0% +and this + + + align:start position:0% +and this +one so this is a very important concept + + align:start position:0% +one so this is a very important concept + + + align:start position:0% +one so this is a very important concept +we often use leaves in our proofs and we + + align:start position:0% +we often use leaves in our proofs and we + + + align:start position:0% +we often use leaves in our proofs and we +will get to one + + align:start position:0% +will get to one + + + align:start position:0% +will get to one +so a + + align:start position:0% + + + + align:start position:0% + +leaf is a + + align:start position:0% + + + + align:start position:0% + +note with degree + + align:start position:0% + + + + align:start position:0% + +one in a + + align:start position:0% + + + + align:start position:0% + +tree okay + + align:start position:0% + + + + align:start position:0% + +great so now let's have a look at the + + align:start position:0% +great so now let's have a look at the + + + align:start position:0% +great so now let's have a look at the +trees uh suppose I'm looking at a + + align:start position:0% +trees uh suppose I'm looking at a + + + align:start position:0% +trees uh suppose I'm looking at a +subgraph + + align:start position:0% +subgraph + + + align:start position:0% +subgraph +of a tree what can we say about a + + align:start position:0% +of a tree what can we say about a + + + align:start position:0% +of a tree what can we say about a +subgraph what kind of structure does + + align:start position:0% +subgraph what kind of structure does + + + align:start position:0% +subgraph what kind of structure does +this have so suppose for example I would + + align:start position:0% +this have so suppose for example I would + + + align:start position:0% +this have so suppose for example I would +to take uh some uh connected subgraph so + + align:start position:0% +to take uh some uh connected subgraph so + + + align:start position:0% +to take uh some uh connected subgraph so +that's what I'm actually interested in + + align:start position:0% +that's what I'm actually interested in + + + align:start position:0% +that's what I'm actually interested in +so for example I take this uh well + + align:start position:0% +so for example I take this uh well + + + align:start position:0% +so for example I take this uh well +suppose to take this connected + + align:start position:0% +suppose to take this connected + + + align:start position:0% +suppose to take this connected +subgraph then uh what does it look like + + align:start position:0% +subgraph then uh what does it look like + + + align:start position:0% +subgraph then uh what does it look like +do we see some uh structure in + + align:start position:0% + + + + align:start position:0% + +this it's a no it's a tree yeah it's a + + align:start position:0% +this it's a no it's a tree yeah it's a + + + align:start position:0% +this it's a no it's a tree yeah it's a +tree so uh are we able to prove this + + align:start position:0% +tree so uh are we able to prove this + + + align:start position:0% +tree so uh are we able to prove this +also so let's uh so this LMA we'll + + align:start position:0% +also so let's uh so this LMA we'll + + + align:start position:0% +also so let's uh so this LMA we'll +actually lose later + + align:start position:0% +actually lose later + + + align:start position:0% +actually lose later +on um so any + + align:start position:0% +on um so any + + + align:start position:0% +on um so any +connected + + align:start position:0% + + + + align:start position:0% + +subgraph of a + + align:start position:0% +subgraph of a + + + align:start position:0% +subgraph of a +tree is a + + align:start position:0% + + + + align:start position:0% + +tree and the proof Pro well how can we + + align:start position:0% +tree and the proof Pro well how can we + + + align:start position:0% +tree and the proof Pro well how can we +start out a proof any + + align:start position:0% +start out a proof any + + + align:start position:0% +start out a proof any +suggestions so let's have a look here um + + align:start position:0% +suggestions so let's have a look here um + + + align:start position:0% +suggestions so let's have a look here um +so how may I think about this well I may + + align:start position:0% +so how may I think about this well I may + + + align:start position:0% +so how may I think about this well I may +take a connected subgraph and I want to + + align:start position:0% +take a connected subgraph and I want to + + + align:start position:0% +take a connected subgraph and I want to +show of of a tree and I want to show + + align:start position:0% +show of of a tree and I want to show + + + align:start position:0% +show of of a tree and I want to show +that it is a tree u a general method + + align:start position:0% +that it is a tree u a general method + + + align:start position:0% +that it is a tree u a general method +could be for example + + align:start position:0% + + + + align:start position:0% + +to you know one of the things one of the + + align:start position:0% +to you know one of the things one of the + + + align:start position:0% +to you know one of the things one of the +conditions is it has to + + align:start position:0% +conditions is it has to + + + align:start position:0% +conditions is it has to +be so since since you're not adding + + align:start position:0% +be so since since you're not adding + + + align:start position:0% +be so since since you're not adding +nodes and you're not starting with any + + align:start position:0% +nodes and you're not starting with any + + + align:start position:0% +nodes and you're not starting with any +uh Cycles you can't create a new cycle + + align:start position:0% +uh Cycles you can't create a new cycle + + + align:start position:0% +uh Cycles you can't create a new cycle +yeah I think you're saying something + + align:start position:0% +yeah I think you're saying something + + + align:start position:0% +yeah I think you're saying something +like um if I have a connected subgraph + + align:start position:0% +like um if I have a connected subgraph + + + align:start position:0% +like um if I have a connected subgraph +which is like uh a smaller part of the + + align:start position:0% +which is like uh a smaller part of the + + + align:start position:0% +which is like uh a smaller part of the +tree now suppose that would not be a + + align:start position:0% +tree now suppose that would not be a + + + align:start position:0% +tree now suppose that would not be a +tree say it would have a cycle then that + + align:start position:0% +tree say it would have a cycle then that + + + align:start position:0% +tree say it would have a cycle then that +cycle would also be present in the tree + + align:start position:0% +cycle would also be present in the tree + + + align:start position:0% +cycle would also be present in the tree +itself and that is not really possible + + align:start position:0% +itself and that is not really possible + + + align:start position:0% +itself and that is not really possible +because a tree has no + + align:start position:0% +because a tree has no + + + align:start position:0% +because a tree has no +Cycles so that's sort of indeed how the + + align:start position:0% +Cycles so that's sort of indeed how the + + + align:start position:0% +Cycles so that's sort of indeed how the +proof goes and um so we essentially use + + align:start position:0% +proof goes and um so we essentially use + + + align:start position:0% +proof goes and um so we essentially use +uh + + align:start position:0% + + + + align:start position:0% + +contradiction and uh so let's + + align:start position:0% + + + + align:start position:0% + +suppose that this connected subgraph is + + align:start position:0% +suppose that this connected subgraph is + + + align:start position:0% +suppose that this connected subgraph is +actually not a + + align:start position:0% + + + + align:start position:0% + +tree so suppose that the connected sub + + align:start position:0% +tree so suppose that the connected sub + + + align:start position:0% +tree so suppose that the connected sub +graph is not a + + align:start position:0% +graph is not a + + + align:start position:0% +graph is not a +threee well then in that case it must + + align:start position:0% +threee well then in that case it must + + + align:start position:0% +threee well then in that case it must +have a cycle right because a tree is + + align:start position:0% +have a cycle right because a tree is + + + align:start position:0% +have a cycle right because a tree is +something that is both connected and has + + align:start position:0% +something that is both connected and has + + + align:start position:0% +something that is both connected and has +a cycle and and and is a cyclic um we + + align:start position:0% +a cycle and and and is a cyclic um we + + + align:start position:0% +a cycle and and and is a cyclic um we +have a connected subgraph which is not a + + align:start position:0% +have a connected subgraph which is not a + + + align:start position:0% +have a connected subgraph which is not a +threee so must have a + + align:start position:0% +threee so must have a + + + align:start position:0% +threee so must have a +cycle okay so it has a + + align:start position:0% +cycle okay so it has a + + + align:start position:0% +cycle okay so it has a +cycle but now since it is a subgraph of + + align:start position:0% +cycle but now since it is a subgraph of + + + align:start position:0% +cycle but now since it is a subgraph of +the bigger + + align:start position:0% +the bigger + + + align:start position:0% +the bigger +graph we know that the cycle must also + + align:start position:0% +graph we know that the cycle must also + + + align:start position:0% +graph we know that the cycle must also +be in the whole graph so the whole graph + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +has this particular + + align:start position:0% +has this particular + + + align:start position:0% +has this particular +cycle but wait a + + align:start position:0% +cycle but wait a + + + align:start position:0% +cycle but wait a +minute uh the whole graph is the + + align:start position:0% +minute uh the whole graph is the + + + align:start position:0% +minute uh the whole graph is the +tree and a tree is a cyclic so we get a + + align:start position:0% +tree and a tree is a cyclic so we get a + + + align:start position:0% +tree and a tree is a cyclic so we get a +contradiction so that means that our + + align:start position:0% +contradiction so that means that our + + + align:start position:0% +contradiction so that means that our +original assumption that it is not a + + align:start position:0% +original assumption that it is not a + + + align:start position:0% +original assumption that it is not a +tree is is is is wrong so it is a tree + + align:start position:0% +tree is is is is wrong so it is a tree + + + align:start position:0% +tree is is is is wrong so it is a tree +so this is the again uh such a general + + align:start position:0% +so this is the again uh such a general + + + align:start position:0% +so this is the again uh such a general +kind of proof method that we repeatedly + + align:start position:0% +kind of proof method that we repeatedly + + + align:start position:0% +kind of proof method that we repeatedly +use here okay so this Lemma which we + + align:start position:0% +use here okay so this Lemma which we + + + align:start position:0% +use here okay so this Lemma which we +will call + + align:start position:0% +will call + + + align:start position:0% +will call +two we will use in the next proof where + + align:start position:0% +two we will use in the next proof where + + + align:start position:0% +two we will use in the next proof where +we're going to talk about uh the + + align:start position:0% +we're going to talk about uh the + + + align:start position:0% +we're going to talk about uh the +relationship between feres and edges + + align:start position:0% +relationship between feres and edges + + + align:start position:0% +relationship between feres and edges +within uh + + align:start position:0% +within uh + + + align:start position:0% +within uh +trees + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +and it's a very a beautiful relationship + + align:start position:0% +and it's a very a beautiful relationship + + + align:start position:0% +and it's a very a beautiful relationship +sh uh the LMA + + align:start position:0% +sh uh the LMA + + + align:start position:0% +sh uh the LMA +states that if you have a tree that has + + align:start position:0% +states that if you have a tree that has + + + align:start position:0% +states that if you have a tree that has +n vertices then it must have n minus one + + align:start position:0% +n vertices then it must have n minus one + + + align:start position:0% +n vertices then it must have n minus one +edges so there a very tight relationship + + align:start position:0% +edges so there a very tight relationship + + + align:start position:0% +edges so there a very tight relationship +here so a + + align:start position:0% +here so a + + + align:start position:0% +here so a +tree + + align:start position:0% +tree + + + align:start position:0% +tree +with n + + align:start position:0% + + + + align:start position:0% + +feres has n minus one + + align:start position:0% +feres has n minus one + + + align:start position:0% +feres has n minus one +edges so let's see how can we prove this + + align:start position:0% +edges so let's see how can we prove this + + + align:start position:0% +edges so let's see how can we prove this +one any suggestion so what what what did + + align:start position:0% +one any suggestion so what what what did + + + align:start position:0% +one any suggestion so what what what did +did we use at the beginning of the + + align:start position:0% +did we use at the beginning of the + + + align:start position:0% +did we use at the beginning of the +course here so we have nvertices + + align:start position:0% +course here so we have nvertices + + + align:start position:0% +course here so we have nvertices +um and we want to show that it has n + + align:start position:0% +um and we want to show that it has n + + + align:start position:0% +um and we want to show that it has n +minus one + + align:start position:0% + + + + align:start position:0% + +edges we can use induction right so + + align:start position:0% +edges we can use induction right so + + + align:start position:0% +edges we can use induction right so +let's uh use + + align:start position:0% +let's uh use + + + align:start position:0% +let's uh use +induction on N so how do we proceed if + + align:start position:0% +induction on N so how do we proceed if + + + align:start position:0% +induction on N so how do we proceed if +you do this well we always start out + + align:start position:0% +you do this well we always start out + + + align:start position:0% +you do this well we always start out +with uh an induction hypothesis so the + + align:start position:0% +with uh an induction hypothesis so the + + + align:start position:0% +with uh an induction hypothesis so the +statement here would be something like + + align:start position:0% +statement here would be something like + + + align:start position:0% +statement here would be something like +uh + + align:start position:0% +uh + + + align:start position:0% +uh +well there + + align:start position:0% +well there + + + align:start position:0% +well there +are n minus one + + align:start position:0% +are n minus one + + + align:start position:0% +are n minus one +edges in + + align:start position:0% +edges in + + + align:start position:0% +edges in +any n + + align:start position:0% +any n + + + align:start position:0% +any n +ferx + + align:start position:0% + + + + align:start position:0% + +tree and if we start with induction we + + align:start position:0% +tree and if we start with induction we + + + align:start position:0% +tree and if we start with induction we +always start with the base case right so + + align:start position:0% +always start with the base case right so + + + align:start position:0% +always start with the base case right so +we have the base + + align:start position:0% +we have the base + + + align:start position:0% +we have the base +case so how does this work + + align:start position:0% +case so how does this work + + + align:start position:0% +case so how does this work +so for example we have you want to + + align:start position:0% +so for example we have you want to + + + align:start position:0% +so for example we have you want to +consider + + align:start position:0% +consider + + + align:start position:0% +consider +P1 so there are zero edges in any one + + align:start position:0% +P1 so there are zero edges in any one + + + align:start position:0% +P1 so there are zero edges in any one +fex 3 well that's true right I have just + + align:start position:0% +fex 3 well that's true right I have just + + + align:start position:0% +fex 3 well that's true right I have just +one fex there's no Edge so this is + + align:start position:0% +one fex there's no Edge so this is + + + align:start position:0% +one fex there's no Edge so this is +definitely + + align:start position:0% +definitely + + + align:start position:0% +definitely +correct so that's easy so let's prove uh + + align:start position:0% +correct so that's easy so let's prove uh + + + align:start position:0% +correct so that's easy so let's prove uh +the other part which is the induction uh + + align:start position:0% +the other part which is the induction uh + + + align:start position:0% +the other part which is the induction uh +the inductive + + align:start position:0% +the inductive + + + align:start position:0% +the inductive +step an inductive step um + + align:start position:0% + + + + align:start position:0% + +is so to do the inductive step um we're + + align:start position:0% +is so to do the inductive step um we're + + + align:start position:0% +is so to do the inductive step um we're +going to always assume right uh PN and + + align:start position:0% +going to always assume right uh PN and + + + align:start position:0% +going to always assume right uh PN and +then you want to prove PN + + + align:start position:0% +then you want to prove PN + + + + align:start position:0% +then you want to prove PN + +one so let's do this so we have the + + align:start position:0% +one so let's do this so we have the + + + align:start position:0% +one so let's do this so we have the +inductive + + align:start position:0% + + + + align:start position:0% + +step and we always start out the same + + align:start position:0% +step and we always start out the same + + + align:start position:0% +step and we always start out the same +way so we suppose + + align:start position:0% + + + + align:start position:0% + +P of + + align:start position:0% +P of + + + align:start position:0% +P of +N and now we want to prove p n + one so + + align:start position:0% +N and now we want to prove p n + one so + + + align:start position:0% +N and now we want to prove p n + one so +how do we do this well take a tree that + + align:start position:0% +how do we do this well take a tree that + + + align:start position:0% +how do we do this well take a tree that +has n plus1 feses and we want to show + + align:start position:0% +has n plus1 feses and we want to show + + + align:start position:0% +has n plus1 feses and we want to show +that it has n edges so take any such + + align:start position:0% +that it has n edges so take any such + + + align:start position:0% +that it has n edges so take any such +tree so let + + align:start position:0% +tree so let + + + align:start position:0% +tree so let +T be a + + align:start position:0% +T be a + + + align:start position:0% +T be a +tree that + + align:start position:0% +tree that + + + align:start position:0% +tree that +has n + one feses + + align:start position:0% + + + + align:start position:0% + +so how can we use the induction + + align:start position:0% +so how can we use the induction + + + align:start position:0% +so how can we use the induction +hypothesis + + align:start position:0% +hypothesis + + + align:start position:0% +hypothesis +here so do you have any ideas over here + + align:start position:0% +here so do you have any ideas over here + + + align:start position:0% +here so do you have any ideas over here +so I have a tree with n plus1 + + align:start position:0% +so I have a tree with n plus1 + + + align:start position:0% +so I have a tree with n plus1 +vertices and if I want to be able to use + + align:start position:0% +vertices and if I want to be able to use + + + align:start position:0% +vertices and if I want to be able to use +this induction uh had this induction + + align:start position:0% +this induction uh had this induction + + + align:start position:0% +this induction uh had this induction +hypothesis then I can only apply it on + + align:start position:0% +hypothesis then I can only apply it on + + + align:start position:0% +hypothesis then I can only apply it on +trees of uh that have nvertices so + + align:start position:0% +trees of uh that have nvertices so + + + align:start position:0% +trees of uh that have nvertices so +somehow I have to delete one fex right + + align:start position:0% +somehow I have to delete one fex right + + + align:start position:0% +somehow I have to delete one fex right +so what kind of fex can I delete in such + + align:start position:0% +so what kind of fex can I delete in such + + + align:start position:0% +so what kind of fex can I delete in such +a way that we still have a + + align:start position:0% +a way that we still have a + + + align:start position:0% +a way that we still have a +tree um + + align:start position:0% +tree um + + + align:start position:0% +tree um +well and I need that because this uh + + align:start position:0% +well and I need that because this uh + + + align:start position:0% +well and I need that because this uh +induction step can only be applied to + + align:start position:0% +induction step can only be applied to + + + align:start position:0% +induction step can only be applied to +trees so what type of fex can I remove + + align:start position:0% +trees so what type of fex can I remove + + + align:start position:0% +trees so what type of fex can I remove +from a tree and it still stays and still + + align:start position:0% +from a tree and it still stays and still + + + align:start position:0% +from a tree and it still stays and still +stays a tree so for example if you look + + align:start position:0% +stays a tree so for example if you look + + + align:start position:0% +stays a tree so for example if you look +at this example up here uh um what kind + + align:start position:0% +at this example up here uh um what kind + + + align:start position:0% +at this example up here uh um what kind +of fex can I remove + + align:start position:0% +of fex can I remove + + + align:start position:0% +of fex can I remove +here yeah exactly I can remove a leaf + + align:start position:0% +here yeah exactly I can remove a leaf + + + align:start position:0% +here yeah exactly I can remove a leaf +for example this one and why is that + + align:start position:0% +for example this one and why is that + + + align:start position:0% +for example this one and why is that +because it has only one Edge connected + + align:start position:0% +because it has only one Edge connected + + + align:start position:0% +because it has only one Edge connected +to the rest of the tree so if I leave it + + align:start position:0% +to the rest of the tree so if I leave it + + + align:start position:0% +to the rest of the tree so if I leave it +if if I if I delete it I will actually + + align:start position:0% +if if I if I delete it I will actually + + + align:start position:0% +if if I if I delete it I will actually +keep a tree so that's how the proof will + + align:start position:0% +keep a tree so that's how the proof will + + + align:start position:0% +keep a tree so that's how the proof will +continue so we take out one + + align:start position:0% +continue so we take out one + + + align:start position:0% +continue so we take out one +fex so let Fe be a leaf of the tree + + align:start position:0% + + + + align:start position:0% + +and uh let's remove this particular + + align:start position:0% + + + + align:start position:0% + +fex so what do we get well we again have + + align:start position:0% +fex so what do we get well we again have + + + align:start position:0% +fex so what do we get well we again have +a uh connected + + align:start position:0% +a uh connected + + + align:start position:0% +a uh connected +subgraph so this + + align:start position:0% +subgraph so this + + + align:start position:0% +subgraph so this +creates a + + align:start position:0% + + + + align:start position:0% + +connected + + align:start position:0% +connected + + + align:start position:0% +connected +subgraph and uh + + align:start position:0% +subgraph and uh + + + align:start position:0% +subgraph and uh +we also know that this is a tree so how + + align:start position:0% +we also know that this is a tree so how + + + align:start position:0% +we also know that this is a tree so how +can we conclude that well we had another + + align:start position:0% +can we conclude that well we had another + + + align:start position:0% +can we conclude that well we had another +LMA somewhere that's behind this + + align:start position:0% +LMA somewhere that's behind this + + + align:start position:0% +LMA somewhere that's behind this +Blackboard that says that if we have a + + align:start position:0% +Blackboard that says that if we have a + + + align:start position:0% +Blackboard that says that if we have a +connected subgraph then we still have a + + align:start position:0% +connected subgraph then we still have a + + + align:start position:0% +connected subgraph then we still have a +tree so that's great so this is also + + align:start position:0% +tree so that's great so this is also + + + align:start position:0% +tree so that's great so this is also +uh a + + align:start position:0% + + + + align:start position:0% + +tree so now we can + + align:start position:0% +tree so now we can + + + align:start position:0% +tree so now we can +apply PN because we have n vertices + + align:start position:0% +apply PN because we have n vertices + + + align:start position:0% +apply PN because we have n vertices +because we deleted one so by + + align:start position:0% +because we deleted one so by + + + align:start position:0% +because we deleted one so by +PN we can conclude that this particular + + align:start position:0% +PN we can conclude that this particular + + + align:start position:0% +PN we can conclude that this particular +subgraph has n minus one + + align:start position:0% +subgraph has n minus one + + + align:start position:0% +subgraph has n minus one +edges you simply apply our statement + + align:start position:0% +edges you simply apply our statement + + + align:start position:0% +edges you simply apply our statement +over + + align:start position:0% +over + + + align:start position:0% +over +here so but we want to say something + + align:start position:0% +here so but we want to say something + + + align:start position:0% +here so but we want to say something +about the original tree so how do we do + + align:start position:0% +about the original tree so how do we do + + + align:start position:0% +about the original tree so how do we do +this well we have to somehow reconstruct + + align:start position:0% +this well we have to somehow reconstruct + + + align:start position:0% +this well we have to somehow reconstruct +this tree well we have deleted fee so we + + align:start position:0% +this tree well we have deleted fee so we + + + align:start position:0% +this tree well we have deleted fee so we +have to reattach fee again + + align:start position:0% +have to reattach fee again + + + align:start position:0% +have to reattach fee again +so let's do + + align:start position:0% +so let's do + + + align:start position:0% +so let's do +this so we + + align:start position:0% +this so we + + + align:start position:0% +this so we +reattach V and if I do this well let's + + align:start position:0% +reattach V and if I do this well let's + + + align:start position:0% +reattach V and if I do this well let's +look at this example over here I + + align:start position:0% +look at this example over here I + + + align:start position:0% +look at this example over here I +reattach the leaf I will add one more + + align:start position:0% +reattach the leaf I will add one more + + + align:start position:0% +reattach the leaf I will add one more +Edge so if I reattach this particular + + align:start position:0% +Edge so if I reattach this particular + + + align:start position:0% +Edge so if I reattach this particular +Leaf um I will get back the original uh + + align:start position:0% +Leaf um I will get back the original uh + + + align:start position:0% +Leaf um I will get back the original uh +uh T over here and + + align:start position:0% +uh T over here and + + + align:start position:0% +uh T over here and +how many edges does it have well it has + + align:start position:0% +how many edges does it have well it has + + + align:start position:0% +how many edges does it have well it has +these n minus one + + align:start position:0% + + + + align:start position:0% + +edges plus the one Edge that is needed + + align:start position:0% +edges plus the one Edge that is needed + + + align:start position:0% +edges plus the one Edge that is needed +to reattach the + + align:start position:0% +to reattach the + + + align:start position:0% +to reattach the +leaf so that's Al together exactly n + + align:start position:0% +leaf so that's Al together exactly n + + + align:start position:0% +leaf so that's Al together exactly n +edges ah so now we have shown that for + + align:start position:0% +edges ah so now we have shown that for + + + align:start position:0% +edges ah so now we have shown that for +every n+1 fex + + align:start position:0% +every n+1 fex + + + align:start position:0% +every n+1 fex + + align:start position:0% + + + align:start position:0% +um every such tree has n + + align:start position:0% +um every such tree has n + + + align:start position:0% +um every such tree has n +edges so now done because this shows uh + + align:start position:0% +edges so now done because this shows uh + + + align:start position:0% +edges so now done because this shows uh +p n + one so this is how the Lemma uh is + + align:start position:0% +p n + one so this is how the Lemma uh is + + + align:start position:0% +p n + one so this is how the Lemma uh is +proved and in the homework you actually + + align:start position:0% +proved and in the homework you actually + + + align:start position:0% +proved and in the homework you actually +uh use + + align:start position:0% + + + + align:start position:0% + +this okay so um let's now talk about + + align:start position:0% +this okay so um let's now talk about + + + align:start position:0% +this okay so um let's now talk about +very special uh uh trees spanning trees + + align:start position:0% +very special uh uh trees spanning trees + + + align:start position:0% +very special uh uh trees spanning trees +now + + align:start position:0% +now + + + align:start position:0% +now +it's I think this is a very exciting + + align:start position:0% +it's I think this is a very exciting + + + align:start position:0% +it's I think this is a very exciting +topic so uh let's uh look at this + + align:start position:0% +topic so uh let's uh look at this + + + align:start position:0% +topic so uh let's uh look at this +particular graph over here and and + + align:start position:0% + + + + align:start position:0% + +um let's define spinning trees so what's + + align:start position:0% +um let's define spinning trees so what's + + + align:start position:0% +um let's define spinning trees so what's +a spinning tree a spanning tree is a + + align:start position:0% +a spinning tree a spanning tree is a + + + align:start position:0% +a spinning tree a spanning tree is a +subgraph of a graph that somehow spans + + align:start position:0% +subgraph of a graph that somehow spans + + + align:start position:0% +subgraph of a graph that somehow spans +all the vertices within this graph so + + align:start position:0% +all the vertices within this graph so + + + align:start position:0% +all the vertices within this graph so +it's a + + align:start position:0% +it's a + + + align:start position:0% +it's a +tree that touches every single vertic so + + align:start position:0% +tree that touches every single vertic so + + + align:start position:0% +tree that touches every single vertic so +for + + align:start position:0% +for + + + align:start position:0% +for +example uh we may have + + align:start position:0% +example uh we may have + + + align:start position:0% +example uh we may have +uh maybe this is not such a bright color + + align:start position:0% + + + + align:start position:0% + +maybe this + + align:start position:0% +maybe this + + + align:start position:0% +maybe this +one so for + + align:start position:0% +one so for + + + align:start position:0% +one so for +example we may have a tree that looks + + align:start position:0% +example we may have a tree that looks + + + align:start position:0% +example we may have a tree that looks +like + + align:start position:0% + + + + align:start position:0% + +this so in this in this particular graph + + align:start position:0% +this so in this in this particular graph + + + align:start position:0% +this so in this in this particular graph +we can create a + + align:start position:0% +we can create a + + + align:start position:0% +we can create a +subgraph with the thickened green edges + + align:start position:0% +subgraph with the thickened green edges + + + align:start position:0% +subgraph with the thickened green edges +over here which is a tree and also CS + + align:start position:0% +over here which is a tree and also CS + + + align:start position:0% +over here which is a tree and also CS +all the different vertices of the + + align:start position:0% +all the different vertices of the + + + align:start position:0% +all the different vertices of the +original + + align:start position:0% +original + + + align:start position:0% +original +graph um this is actually pretty amazing + + align:start position:0% +graph um this is actually pretty amazing + + + align:start position:0% +graph um this is actually pretty amazing +that you can do this you can actually + + align:start position:0% +that you can do this you can actually + + + align:start position:0% +that you can do this you can actually +create such uh a kind of uh a tree and + + align:start position:0% +create such uh a kind of uh a tree and + + + align:start position:0% +create such uh a kind of uh a tree and +what we want to prove first of all is + + align:start position:0% +what we want to prove first of all is + + + align:start position:0% +what we want to prove first of all is +that for every connected graph we can + + align:start position:0% +that for every connected graph we can + + + align:start position:0% +that for every connected graph we can +construct such a spanning tree so let's + + align:start position:0% +construct such a spanning tree so let's + + + align:start position:0% +construct such a spanning tree so let's +first Define this and then uh we will + + align:start position:0% +first Define this and then uh we will + + + align:start position:0% +first Define this and then uh we will +prove this + + align:start position:0% + + + + align:start position:0% + +theorem and then after this we're going + + align:start position:0% +theorem and then after this we're going + + + align:start position:0% +theorem and then after this we're going +to talk about uh weighted graphs that + + align:start position:0% +to talk about uh weighted graphs that + + + align:start position:0% +to talk about uh weighted graphs that +will lead to uh minimum weight spanning + + align:start position:0% +will lead to uh minimum weight spanning + + + align:start position:0% +will lead to uh minimum weight spanning +trees and then it gets really + + align:start position:0% +trees and then it gets really + + + align:start position:0% +trees and then it gets really +interesting because we want to figure + + align:start position:0% +interesting because we want to figure + + + align:start position:0% +interesting because we want to figure +out how we can actually construct those + + align:start position:0% +out how we can actually construct those + + + align:start position:0% +out how we can actually construct those +for any + + align:start position:0% +for any + + + align:start position:0% +for any +graph + + align:start position:0% +graph + + + align:start position:0% +graph +okay so let's uh Define a spanning + + align:start position:0% +okay so let's uh Define a spanning + + + align:start position:0% +okay so let's uh Define a spanning +tree a spanning + + align:start position:0% + + + + align:start position:0% + +tree and we abbreviate this as + + align:start position:0% +tree and we abbreviate this as + + + align:start position:0% +tree and we abbreviate this as +SD of + + align:start position:0% +SD of + + + align:start position:0% +SD of +a connected + + align:start position:0% + + + + align:start position:0% + +graph is actually a + + align:start position:0% + + + + align:start position:0% + +subgraph that is a + + align:start position:0% +subgraph that is a + + + align:start position:0% +subgraph that is a +tree so that's the first condition and + + align:start position:0% +tree so that's the first condition and + + + align:start position:0% +tree so that's the first condition and +it also covers all the other fices so it + + align:start position:0% +it also covers all the other fices so it + + + align:start position:0% +it also covers all the other fices so it +has the same + + align:start position:0% + + + + align:start position:0% + +feres as the + + align:start position:0% + + + + align:start position:0% + +graph + + align:start position:0% + + + + align:start position:0% + +okay and over here we have this + + align:start position:0% +okay and over here we have this + + + align:start position:0% +okay and over here we have this +example so now what we want to show is + + align:start position:0% +example so now what we want to show is + + + align:start position:0% +example so now what we want to show is +is the following theorem that any + + align:start position:0% +is the following theorem that any + + + align:start position:0% +is the following theorem that any +connected graph actually has such a + + align:start position:0% +connected graph actually has such a + + + align:start position:0% +connected graph actually has such a +spanning + + align:start position:0% +spanning + + + align:start position:0% +spanning +tree so the theorem is + + align:start position:0% + + + + align:start position:0% + +every + + align:start position:0% + + + + align:start position:0% + +connected + + align:start position:0% + + + + align:start position:0% + +oh every connected + + align:start position:0% + + + + align:start position:0% + +graph has a spanning + + align:start position:0% +graph has a spanning + + + align:start position:0% +graph has a spanning +tree and uh let's uh think about a proof + + align:start position:0% +tree and uh let's uh think about a proof + + + align:start position:0% +tree and uh let's uh think about a proof +together so for example uh you know we + + align:start position:0% +together so for example uh you know we + + + align:start position:0% +together so for example uh you know we +may uh start with + + align:start position:0% +may uh start with + + + align:start position:0% +may uh start with +uh the IDE to use + + align:start position:0% +uh the IDE to use + + + align:start position:0% +uh the IDE to use +contradiction Suppose there exists a + + align:start position:0% +contradiction Suppose there exists a + + + align:start position:0% +contradiction Suppose there exists a +connected graph that has no spanning + + align:start position:0% +connected graph that has no spanning + + + align:start position:0% +connected graph that has no spanning +tree so how would we go + + align:start position:0% + + + + align:start position:0% + +ahead so how can we prove that there is + + align:start position:0% +ahead so how can we prove that there is + + + align:start position:0% +ahead so how can we prove that there is +uh that we have a contradiction here so + + align:start position:0% +uh that we have a contradiction here so + + + align:start position:0% +uh that we have a contradiction here so +the proof that we're going to propose + + align:start position:0% +the proof that we're going to propose + + + align:start position:0% +the proof that we're going to propose +here is by contradiction + + align:start position:0% + + + + align:start position:0% + +and uh that means that we're going to + + align:start position:0% +and uh that means that we're going to + + + align:start position:0% +and uh that means that we're going to +assume the opposite so + + align:start position:0% +assume the opposite so + + + align:start position:0% +assume the opposite so +assume that we have a connected graph + + align:start position:0% +assume that we have a connected graph + + + align:start position:0% +assume that we have a connected graph +oops connected graph a + + align:start position:0% + + + + align:start position:0% + +g um that has no spanning tree + + align:start position:0% +g um that has no spanning tree + + + align:start position:0% +g um that has no spanning tree +H so how can we uh use this how could + + align:start position:0% +H so how can we uh use this how could + + + align:start position:0% +H so how can we uh use this how could +this be strange or uh what can we do + + align:start position:0% +this be strange or uh what can we do + + + align:start position:0% +this be strange or uh what can we do +here + + align:start position:0% + + + + align:start position:0% + +well yeah so one of the nice things + + align:start position:0% +well yeah so one of the nice things + + + align:start position:0% +well yeah so one of the nice things +about about trees over here is so that's + + align:start position:0% +about about trees over here is so that's + + + align:start position:0% +about about trees over here is so that's +that maybe gives us some insight is that + + align:start position:0% +that maybe gives us some insight is that + + + align:start position:0% +that maybe gives us some insight is that +um if we have a + + align:start position:0% +um if we have a + + + align:start position:0% +um if we have a +tree um well it seems like such kind of + + align:start position:0% +tree um well it seems like such kind of + + + align:start position:0% +tree um well it seems like such kind of +spanning trees like the the + + align:start position:0% +spanning trees like the the + + + align:start position:0% +spanning trees like the the +the it's a solution to a subgraph that + + align:start position:0% +the it's a solution to a subgraph that + + + align:start position:0% +the it's a solution to a subgraph that +is connected with a minimum number of + + align:start position:0% +is connected with a minimum number of + + + align:start position:0% +is connected with a minimum number of +edges um like if I have any other type + + align:start position:0% +edges um like if I have any other type + + + align:start position:0% +edges um like if I have any other type +of of of of subgraph for example if it + + align:start position:0% +of of of of subgraph for example if it + + + align:start position:0% +of of of of subgraph for example if it +has Cycles I can always remove an edge + + align:start position:0% +has Cycles I can always remove an edge + + + align:start position:0% +has Cycles I can always remove an edge +of course so um we know that a a + + align:start position:0% +of course so um we know that a a + + + align:start position:0% +of course so um we know that a a +subgraph of G that had had it that + + align:start position:0% +subgraph of G that had had it that + + + align:start position:0% +subgraph of G that had had it that +touches all the different edges and it + + align:start position:0% +touches all the different edges and it + + + align:start position:0% +touches all the different edges and it +and has and has a cycle can get uh + + align:start position:0% +and has and has a cycle can get uh + + + align:start position:0% +and has and has a cycle can get uh +shortened by eliminating one edge of a + + align:start position:0% +shortened by eliminating one edge of a + + + align:start position:0% +shortened by eliminating one edge of a +cycle that's within such a subgraph so + + align:start position:0% +cycle that's within such a subgraph so + + + align:start position:0% +cycle that's within such a subgraph so +maybe we have an idea here and maybe we + + align:start position:0% +maybe we have an idea here and maybe we + + + align:start position:0% +maybe we have an idea here and maybe we +can uh use this so maybe we can say + + align:start position:0% +can uh use this so maybe we can say + + + align:start position:0% +can uh use this so maybe we can say +let's + + align:start position:0% +let's + + + align:start position:0% +let's +consider um a uh graph + + align:start position:0% +consider um a uh graph + + + align:start position:0% +consider um a uh graph +T so let T be a connected subgraph of G + + align:start position:0% +T so let T be a connected subgraph of G + + + align:start position:0% +T so let T be a connected subgraph of G +but with the property that it has a + + align:start position:0% +but with the property that it has a + + + align:start position:0% +but with the property that it has a +minimum number of + + align:start position:0% +minimum number of + + + align:start position:0% +minimum number of +edges so let this be a connected + + align:start position:0% + + + + align:start position:0% + +subgraph of G and we + + align:start position:0% +subgraph of G and we + + + align:start position:0% +subgraph of G and we +assume that it has the same vertices as + + align:start position:0% +assume that it has the same vertices as + + + align:start position:0% +assume that it has the same vertices as +G of + + align:start position:0% +G of + + + align:start position:0% +G of +course + + align:start position:0% + + + + align:start position:0% + +and in + + align:start position:0% +and in + + + align:start position:0% +and in +addition it has + + align:start position:0% +addition it has + + + align:start position:0% +addition it has +the smallest number of edges + + align:start position:0% + + + + align:start position:0% + +possible + + align:start position:0% +possible + + + align:start position:0% +possible +okay so what do we know well let's uh + + align:start position:0% +okay so what do we know well let's uh + + + align:start position:0% +okay so what do we know well let's uh +look at our assumption here uh we said + + align:start position:0% +look at our assumption here uh we said + + + align:start position:0% +look at our assumption here uh we said +that a connected graph uh G that's what + + align:start position:0% +that a connected graph uh G that's what + + + align:start position:0% +that a connected graph uh G that's what +we consider here for which uh well there + + align:start position:0% +we consider here for which uh well there + + + align:start position:0% +we consider here for which uh well there +is no spanning tree so what do we know + + align:start position:0% +is no spanning tree so what do we know + + + align:start position:0% +is no spanning tree so what do we know +we know that this particular T over here + + align:start position:0% +we know that this particular T over here + + + align:start position:0% +we know that this particular T over here +can definitely not be a spanning tree + + align:start position:0% +can definitely not be a spanning tree + + + align:start position:0% +can definitely not be a spanning tree +because that's what we assume + + align:start position:0% +because that's what we assume + + + align:start position:0% +because that's what we assume +here so um can we use + + align:start position:0% +here so um can we use + + + align:start position:0% +here so um can we use +this so let's think about + + align:start position:0% + + + + align:start position:0% + +this so if it is not um uh a spanning + + align:start position:0% +this so if it is not um uh a spanning + + + align:start position:0% +this so if it is not um uh a spanning +tree then what must it have so we all + + align:start position:0% +tree then what must it have so we all + + + align:start position:0% +tree then what must it have so we all +have we already know + + align:start position:0% +have we already know + + + align:start position:0% +have we already know +that uh T is a connected subgraph of G + + align:start position:0% +that uh T is a connected subgraph of G + + + align:start position:0% +that uh T is a connected subgraph of G +with the same vertices of uh G so the + + align:start position:0% +with the same vertices of uh G so the + + + align:start position:0% +with the same vertices of uh G so the +only difference between uh a spanning + + align:start position:0% +only difference between uh a spanning + + + align:start position:0% +only difference between uh a spanning +tree and T is that a spanning tree is a + + align:start position:0% +tree and T is that a spanning tree is a + + + align:start position:0% +tree and T is that a spanning tree is a +tree and uh and and and T is not a tree + + align:start position:0% +tree and uh and and and T is not a tree + + + align:start position:0% +tree and uh and and and T is not a tree +so therefore T must have a cycle + + align:start position:0% +so therefore T must have a cycle + + + align:start position:0% +so therefore T must have a cycle +so we use our assumption over here we + + align:start position:0% +so we use our assumption over here we + + + align:start position:0% +so we use our assumption over here we +know that t is + + align:start position:0% +know that t is + + + align:start position:0% +know that t is +not a spanning tree + + align:start position:0% +not a spanning tree + + + align:start position:0% +not a spanning tree +and now we can conclude we can conclude + + align:start position:0% +and now we can conclude we can conclude + + + align:start position:0% +and now we can conclude we can conclude +that it must have a + + align:start position:0% + + + + align:start position:0% + +cycle so now we can uh start uh thinking + + align:start position:0% +cycle so now we can uh start uh thinking + + + align:start position:0% +cycle so now we can uh start uh thinking +about this uh cycle and let's feel + + align:start position:0% +about this uh cycle and let's feel + + + align:start position:0% +about this uh cycle and let's feel +what what can we do here + + align:start position:0% +what what can we do here + + + align:start position:0% +what what can we do here +so we constructed t as the subgraph that + + align:start position:0% +so we constructed t as the subgraph that + + + align:start position:0% +so we constructed t as the subgraph that +has the smallest the minimum number of + + align:start position:0% +has the smallest the minimum number of + + + align:start position:0% +has the smallest the minimum number of +edges possible so now if we have a cycle + + align:start position:0% +edges possible so now if we have a cycle + + + align:start position:0% +edges possible so now if we have a cycle +the whole IDE is that we're going to + + align:start position:0% +the whole IDE is that we're going to + + + align:start position:0% +the whole IDE is that we're going to +delete one of the edges of the cycle and + + align:start position:0% +delete one of the edges of the cycle and + + + align:start position:0% +delete one of the edges of the cycle and +if you do that we will be able to + + align:start position:0% +if you do that we will be able to + + + align:start position:0% +if you do that we will be able to +construct a smaller uh subgraph T + + align:start position:0% +construct a smaller uh subgraph T + + + align:start position:0% +construct a smaller uh subgraph T +essentially uh with a with a smaller + + align:start position:0% +essentially uh with a with a smaller + + + align:start position:0% +essentially uh with a with a smaller +number of edges and that + + align:start position:0% +number of edges and that + + + align:start position:0% +number of edges and that +contradicts this particular statement + + align:start position:0% +contradicts this particular statement + + + align:start position:0% +contradicts this particular statement +over here so that's sort of how we go + + align:start position:0% +over here so that's sort of how we go + + + align:start position:0% +over here so that's sort of how we go +ahead so if it has a cycle let's write + + align:start position:0% +ahead so if it has a cycle let's write + + + align:start position:0% +ahead so if it has a cycle let's write +it out for example here we have a + + align:start position:0% +it out for example here we have a + + + align:start position:0% +it out for example here we have a +cycle um like this + + align:start position:0% +cycle um like this + + + align:start position:0% +cycle um like this +um well let's uh uh prove that uh if we + + align:start position:0% +um well let's uh uh prove that uh if we + + + align:start position:0% +um well let's uh uh prove that uh if we +remove one edge of the cycle that we + + align:start position:0% +remove one edge of the cycle that we + + + align:start position:0% +remove one edge of the cycle that we +still have a uh connected subgraph so + + align:start position:0% +still have a uh connected subgraph so + + + align:start position:0% +still have a uh connected subgraph so +the whole graph T is much bigger right + + align:start position:0% +the whole graph T is much bigger right + + + align:start position:0% +the whole graph T is much bigger right +it has lots of uh connections and so on + + align:start position:0% +it has lots of uh connections and so on + + + align:start position:0% +it has lots of uh connections and so on +um suppose he will remove this + + align:start position:0% +um suppose he will remove this + + + align:start position:0% +um suppose he will remove this +particular Edge over here so we remove + + align:start position:0% +particular Edge over here so we remove + + + align:start position:0% +particular Edge over here so we remove +this + + align:start position:0% +this + + + align:start position:0% +this +one um do we still have a connected + + align:start position:0% +one um do we still have a connected + + + align:start position:0% +one um do we still have a connected +subgraph of G that covers all the + + align:start position:0% +subgraph of G that covers all the + + + align:start position:0% +subgraph of G that covers all the +vertices of G well of course it covers + + align:start position:0% +vertices of G well of course it covers + + + align:start position:0% +vertices of G well of course it covers +all the feres of G because you only + + align:start position:0% +all the feres of G because you only + + + align:start position:0% +all the feres of G because you only +remove an edge over here so that's + + align:start position:0% +remove an edge over here so that's + + + align:start position:0% +remove an edge over here so that's +that's fine all these parts are still + + align:start position:0% +that's fine all these parts are still + + + align:start position:0% +that's fine all these parts are still +connected to the rest + + align:start position:0% +connected to the rest + + + align:start position:0% +connected to the rest +um if it if it can show that it is + + align:start position:0% +um if it if it can show that it is + + + align:start position:0% +um if it if it can show that it is +connected well then we + + align:start position:0% +connected well then we + + + align:start position:0% +connected well then we +just uh well we removed one Edge so we + + align:start position:0% +just uh well we removed one Edge so we + + + align:start position:0% +just uh well we removed one Edge so we +actually created a smaller uh graph and + + align:start position:0% +actually created a smaller uh graph and + + + align:start position:0% +actually created a smaller uh graph and +then then we get contradiction and then + + align:start position:0% +then then we get contradiction and then + + + align:start position:0% +then then we get contradiction and then +we're done with our our proof so let's + + align:start position:0% +we're done with our our proof so let's + + + align:start position:0% +we're done with our our proof so let's +see whether we can prove that if we + + align:start position:0% +see whether we can prove that if we + + + align:start position:0% +see whether we can prove that if we +remove this particular Edge over here + + align:start position:0% +remove this particular Edge over here + + + align:start position:0% +remove this particular Edge over here +that we still have a connected subgraph + + align:start position:0% +that we still have a connected subgraph + + + align:start position:0% +that we still have a connected subgraph +so how can we do + + align:start position:0% +so how can we do + + + align:start position:0% +so how can we do +this um well let's take um uh so the + + align:start position:0% +this um well let's take um uh so the + + + align:start position:0% +this um well let's take um uh so the +first case would be uh if uh a fex x is + + align:start position:0% +first case would be uh if uh a fex x is + + + align:start position:0% +first case would be uh if uh a fex x is +connected to Y so I want to take any + + align:start position:0% +connected to Y so I want to take any + + + align:start position:0% +connected to Y so I want to take any +pair X Y or + + align:start position:0% +pair X Y or + + + align:start position:0% +pair X Y or +vertices and suppose that the path that + + align:start position:0% +vertices and suppose that the path that + + + align:start position:0% +vertices and suppose that the path that +connects X and Y does not contain this + + align:start position:0% +connects X and Y does not contain this + + + align:start position:0% +connects X and Y does not contain this +particular Edge e that I remove here so + + align:start position:0% +particular Edge e that I remove here so + + + align:start position:0% +particular Edge e that I remove here so +suppose this does + + align:start position:0% + + + + align:start position:0% + +not + + align:start position:0% +not + + + align:start position:0% +not +contain + + align:start position:0% +contain + + + align:start position:0% +contain +e uh so I look at at the graph T I know + + align:start position:0% +e uh so I look at at the graph T I know + + + align:start position:0% +e uh so I look at at the graph T I know +T is connected so I take a pair of + + align:start position:0% +T is connected so I take a pair of + + + align:start position:0% +T is connected so I take a pair of +vertices X and Y I know there is a path + + align:start position:0% +vertices X and Y I know there is a path + + + align:start position:0% +vertices X and Y I know there is a path +between X and Y in + + align:start position:0% +between X and Y in + + + align:start position:0% +between X and Y in +t if this path does not contain the edge + + align:start position:0% +t if this path does not contain the edge + + + align:start position:0% +t if this path does not contain the edge +e then I know that the same path still + + align:start position:0% +e then I know that the same path still + + + align:start position:0% +e then I know that the same path still +exists in the same graph where I have + + align:start position:0% +exists in the same graph where I have + + + align:start position:0% +exists in the same graph where I have +removed this particular Edge so that's + + align:start position:0% +removed this particular Edge so that's + + + align:start position:0% +removed this particular Edge so that's +great right so then I have shown that X + + align:start position:0% +great right so then I have shown that X + + + align:start position:0% +great right so then I have shown that X +and Y are still connected in the new + + align:start position:0% +and Y are still connected in the new + + + align:start position:0% +and Y are still connected in the new +graph where I've removed this + + align:start position:0% +graph where I've removed this + + + align:start position:0% +graph where I've removed this +e so now let's look at another case for + + align:start position:0% +e so now let's look at another case for + + + align:start position:0% +e so now let's look at another case for +example X is over here and it is + + align:start position:0% +example X is over here and it is + + + align:start position:0% +example X is over here and it is +connected it um all the way through here + + align:start position:0% +connected it um all the way through here + + + align:start position:0% +connected it um all the way through here +over this particular + + align:start position:0% +over this particular + + + align:start position:0% +over this particular +Edge all the way to say why over here so + + align:start position:0% +Edge all the way to say why over here so + + + align:start position:0% +Edge all the way to say why over here so +this is case number + + align:start position:0% + + + + align:start position:0% + +two um well are X and Y still connected + + align:start position:0% +two um well are X and Y still connected + + + align:start position:0% +two um well are X and Y still connected +yes they are right because I have + + align:start position:0% +yes they are right because I have + + + align:start position:0% +yes they are right because I have +removed + + align:start position:0% +removed + + + align:start position:0% +removed +E from a cycle so I can still call + + align:start position:0% +E from a cycle so I can still call + + + align:start position:0% +E from a cycle so I can still call +into the other direction of the cycle + + align:start position:0% +into the other direction of the cycle + + + align:start position:0% +into the other direction of the cycle +and connect back towards y so what we + + align:start position:0% +and connect back towards y so what we + + + align:start position:0% +and connect back towards y so what we +see here is that X can go all the way to + + align:start position:0% +see here is that X can go all the way to + + + align:start position:0% +see here is that X can go all the way to +here but it can still go of the cycle + + align:start position:0% +here but it can still go of the cycle + + + align:start position:0% +here but it can still go of the cycle +back to here and then to + + align:start position:0% +back to here and then to + + + align:start position:0% +back to here and then to +Y so we are still + + align:start position:0% +Y so we are still + + + align:start position:0% +Y so we are still +connected so this shows that in both of + + align:start position:0% +connected so this shows that in both of + + + align:start position:0% +connected so this shows that in both of +the cases for any pair of vertices even + + align:start position:0% +the cases for any pair of vertices even + + + align:start position:0% +the cases for any pair of vertices even +after removal of e the graph T minus + + align:start position:0% +after removal of e the graph T minus + + + align:start position:0% +after removal of e the graph T minus +this h e is still + + align:start position:0% +this h e is still + + + align:start position:0% +this h e is still +connected so let's write this out so all + + align:start position:0% + + + + align:start position:0% + +vertices uh in + + align:start position:0% + + + + align:start position:0% + +G are still + + align:start position:0% + + + + align:start position:0% + +connected um after removing + + align:start position:0% + + + + align:start position:0% + +E from + + align:start position:0% +E from + + + align:start position:0% +E from +T so now we're done so why was that + + align:start position:0% +T so now we're done so why was that + + + align:start position:0% +T so now we're done so why was that +again um we now constructed a smaller + + align:start position:0% +again um we now constructed a smaller + + + align:start position:0% +again um we now constructed a smaller +graph smaller in the sense that it has a + + align:start position:0% +graph smaller in the sense that it has a + + + align:start position:0% +graph smaller in the sense that it has a +one less Edge that is still + + align:start position:0% +one less Edge that is still + + + align:start position:0% +one less Edge that is still +connected and with the same vertices as + + align:start position:0% +connected and with the same vertices as + + + align:start position:0% +connected and with the same vertices as +G but I assume that t was already the + + align:start position:0% +G but I assume that t was already the + + + align:start position:0% +G but I assume that t was already the +smallest such graph such subgraph so we + + align:start position:0% +smallest such graph such subgraph so we + + + align:start position:0% +smallest such graph such subgraph so we +have a + + align:start position:0% +have a + + + align:start position:0% +have a +contradiction so what does this mean + + align:start position:0% +contradiction so what does this mean + + + align:start position:0% +contradiction so what does this mean +this means that our or origal assumption + + align:start position:0% +this means that our or origal assumption + + + align:start position:0% +this means that our or origal assumption +that we have over here cannot be true + + align:start position:0% +that we have over here cannot be true + + + align:start position:0% +that we have over here cannot be true +because we started off with this + + align:start position:0% +because we started off with this + + + align:start position:0% +because we started off with this +assumption because of this we could + + align:start position:0% +assumption because of this we could + + + align:start position:0% +assumption because of this we could +start to construct this and then we + + align:start position:0% +start to construct this and then we + + + align:start position:0% +start to construct this and then we +could derive this + + align:start position:0% +could derive this + + + align:start position:0% +could derive this +whole uh argumentation and in the end we + + align:start position:0% +whole uh argumentation and in the end we + + + align:start position:0% +whole uh argumentation and in the end we +get a contradiction so our original + + align:start position:0% +get a contradiction so our original + + + align:start position:0% +get a contradiction so our original +assumption is wrong so actually + + align:start position:0% +assumption is wrong so actually + + + align:start position:0% +assumption is wrong so actually +uh this is not possible there does not + + align:start position:0% +uh this is not possible there does not + + + align:start position:0% +uh this is not possible there does not +exist a connected graph G that has no ST + + align:start position:0% +exist a connected graph G that has no ST + + + align:start position:0% +exist a connected graph G that has no ST +so the theorem is + + align:start position:0% +so the theorem is + + + align:start position:0% +so the theorem is +true okay so this is uh uh an important + + align:start position:0% +true okay so this is uh uh an important + + + align:start position:0% +true okay so this is uh uh an important +theorem so now we can uh start talking + + align:start position:0% +theorem so now we can uh start talking + + + align:start position:0% +theorem so now we can uh start talking +about weighted minimum spanning + + align:start position:0% +about weighted minimum spanning + + + align:start position:0% +about weighted minimum spanning +trees + + align:start position:0% + + + + align:start position:0% + +um so let's uh use this picture over + + align:start position:0% +um so let's uh use this picture over + + + align:start position:0% +um so let's uh use this picture over +here and uh assign some weights to this + + align:start position:0% +here and uh assign some weights to this + + + align:start position:0% +here and uh assign some weights to this +graph um so for example uh we have uh + + align:start position:0% +graph um so for example uh we have uh + + + align:start position:0% +graph um so for example uh we have uh +one uh + + align:start position:0% +one uh + + + align:start position:0% +one uh +two + + align:start position:0% +two + + + align:start position:0% +two +uh + + align:start position:0% +uh + + + align:start position:0% +uh +two + + align:start position:0% +two + + + align:start position:0% +two +three three three one over here another + + align:start position:0% +three three three one over here another + + + align:start position:0% +three three three one over here another +one + + align:start position:0% +one + + + align:start position:0% +one +one four and + + align:start position:0% +one four and + + + align:start position:0% +one four and +seven and let's + + align:start position:0% +seven and let's + + + align:start position:0% +seven and let's +um construct uh a spanning tree so let + + align:start position:0% +um construct uh a spanning tree so let + + + align:start position:0% +um construct uh a spanning tree so let +me give an example over here oh actually + + align:start position:0% +me give an example over here oh actually + + + align:start position:0% +me give an example over here oh actually +this is an example that we have right + + align:start position:0% +this is an example that we have right + + + align:start position:0% +this is an example that we have right +here in in the thick line l in + + align:start position:0% +here in in the thick line l in + + + align:start position:0% +here in in the thick line l in +green um so what is the weight of this + + align:start position:0% +green um so what is the weight of this + + + align:start position:0% +green um so what is the weight of this +spanning tree that we have here well we + + align:start position:0% +spanning tree that we have here well we + + + align:start position:0% +spanning tree that we have here well we +simply add the weights of all the edges + + align:start position:0% +simply add the weights of all the edges + + + align:start position:0% +simply add the weights of all the edges +so we have seven three that makes 10 11 + + align:start position:0% +so we have seven three that makes 10 11 + + + align:start position:0% +so we have seven three that makes 10 11 +14 another 2 16 17 18 19 so the weight + + align:start position:0% +14 another 2 16 17 18 19 so the weight + + + align:start position:0% +14 another 2 16 17 18 19 so the weight +of this + + align:start position:0% +of this + + + align:start position:0% +of this +particular uh spanning + + align:start position:0% +particular uh spanning + + + align:start position:0% +particular uh spanning +tree is 19 so now the problem is and + + align:start position:0% +tree is 19 so now the problem is and + + + align:start position:0% +tree is 19 so now the problem is and +that's the rest of the lecture + + align:start position:0% +that's the rest of the lecture + + + align:start position:0% +that's the rest of the lecture +how can we construct a minimum weight + + align:start position:0% +how can we construct a minimum weight + + + align:start position:0% +how can we construct a minimum weight +spanning tree one that has uh the + + align:start position:0% +spanning tree one that has uh the + + + align:start position:0% +spanning tree one that has uh the +minimum weight uh um possible so do you + + align:start position:0% +minimum weight uh um possible so do you + + + align:start position:0% +minimum weight uh um possible so do you +see another example so could I swap some + + align:start position:0% +see another example so could I swap some + + + align:start position:0% +see another example so could I swap some +edges around or something like that such + + align:start position:0% +edges around or something like that such + + + align:start position:0% +edges around or something like that such +that I can get a less + + align:start position:0% +that I can get a less + + + align:start position:0% +that I can get a less +weight so for example over here I have + + align:start position:0% +weight so for example over here I have + + + align:start position:0% +weight so for example over here I have +uh for example this node over here right + + align:start position:0% +uh for example this node over here right + + + align:start position:0% +uh for example this node over here right +is connected by an edge that's that has + + align:start position:0% +is connected by an edge that's that has + + + align:start position:0% +is connected by an edge that's that has +weight three but I could also have + + align:start position:0% +weight three but I could also have + + + align:start position:0% +weight three but I could also have +connected it to this particular one over + + align:start position:0% +connected it to this particular one over + + + align:start position:0% +connected it to this particular one over +here which is only weight one if I do + + align:start position:0% +here which is only weight one if I do + + + align:start position:0% +here which is only weight one if I do +this I actually improve uh the spanning + + align:start position:0% +this I actually improve uh the spanning + + + align:start position:0% +this I actually improve uh the spanning +tree + + align:start position:0% +tree + + + align:start position:0% +tree +construction so I will get something + + align:start position:0% +construction so I will get something + + + align:start position:0% +construction so I will get something +that looks like + + align:start position:0% + + + + align:start position:0% + +um let + + align:start position:0% +um let + + + align:start position:0% +um let +see that looks like + + align:start position:0% + + + + align:start position:0% + +this and uh now we have have replaced + + align:start position:0% +this and uh now we have have replaced + + + align:start position:0% +this and uh now we have have replaced +three by one so we get uh + + align:start position:0% +three by one so we get uh + + + align:start position:0% +three by one so we get uh +17 so can we do anything less than + + align:start position:0% +17 so can we do anything less than + + + align:start position:0% +17 so can we do anything less than +this uh that's maybe and it's still a + + align:start position:0% +this uh that's maybe and it's still a + + + align:start position:0% +this uh that's maybe and it's still a +tree right because there's no cycle here + + align:start position:0% +tree right because there's no cycle here + + + align:start position:0% +tree right because there's no cycle here +we have this this this this part over + + align:start position:0% +we have this this this this part over + + + align:start position:0% +we have this this this this part over +here um if you want to have a connected + + align:start position:0% +here um if you want to have a connected + + + align:start position:0% +here um if you want to have a connected +subgraph I always need the seven in + + align:start position:0% +subgraph I always need the seven in + + + align:start position:0% +subgraph I always need the seven in +here + + align:start position:0% +here + + + align:start position:0% +here +um well it seems like cannot really + + align:start position:0% +um well it seems like cannot really + + + align:start position:0% +um well it seems like cannot really +replace anything by something cheaper + + align:start position:0% +replace anything by something cheaper + + + align:start position:0% +replace anything by something cheaper +like any Edge in + + align:start position:0% +like any Edge in + + + align:start position:0% +like any Edge in +here seems to be pretty uh um necessary + + align:start position:0% +here seems to be pretty uh um necessary + + + align:start position:0% +here seems to be pretty uh um necessary +of course what I could do is I could + + align:start position:0% +of course what I could do is I could + + + align:start position:0% +of course what I could do is I could +create other minimum spanning trees so + + align:start position:0% +create other minimum spanning trees so + + + align:start position:0% +create other minimum spanning trees so +actually it turns out that 17 is the + + align:start position:0% +actually it turns out that 17 is the + + + align:start position:0% +actually it turns out that 17 is the +minimum weight for example I could + + align:start position:0% +minimum weight for example I could + + + align:start position:0% +minimum weight for example I could +instead of this Edge I could use this + + align:start position:0% +instead of this Edge I could use this + + + align:start position:0% +instead of this Edge I could use this +Edge that's another solution or instead + + align:start position:0% +Edge that's another solution or instead + + + align:start position:0% +Edge that's another solution or instead +of this Edge I can use this + + align:start position:0% +of this Edge I can use this + + + align:start position:0% +of this Edge I can use this +Edge um so let's uh um + + align:start position:0% + + + + align:start position:0% + +yeah so how do we construct such a + + align:start position:0% +yeah so how do we construct such a + + + align:start position:0% +yeah so how do we construct such a +minimum weight uh spanning tree can we + + align:start position:0% +minimum weight uh spanning tree can we + + + align:start position:0% +minimum weight uh spanning tree can we +uh somehow find an algorithm that + + align:start position:0% +uh somehow find an algorithm that + + + align:start position:0% +uh somehow find an algorithm that +creates this and that's uh the big + + align:start position:0% +creates this and that's uh the big + + + align:start position:0% +creates this and that's uh the big +problem of + + align:start position:0% +problem of + + + align:start position:0% +problem of +today so let me uh write out one + + align:start position:0% +today so let me uh write out one + + + align:start position:0% +today so let me uh write out one +spanning tree that I will use uh for the + + align:start position:0% +spanning tree that I will use uh for the + + + align:start position:0% +spanning tree that I will use uh for the +rest uh of of of of this class and maybe + + align:start position:0% +rest uh of of of of this class and maybe + + + align:start position:0% +rest uh of of of of this class and maybe +I will use um a little bit different uh + + align:start position:0% +I will use um a little bit different uh + + + align:start position:0% +I will use um a little bit different uh +color + + align:start position:0% + + + + align:start position:0% + +so let's use uh red over + + align:start position:0% + + + + align:start position:0% + +here I hope this is + + align:start position:0% +here I hope this is + + + align:start position:0% +here I hope this is +visible so we have + + align:start position:0% +visible so we have + + + align:start position:0% +visible so we have +red this one and this + + align:start position:0% +red this one and this + + + align:start position:0% +red this one and this +one and this one and this one and this + + align:start position:0% +one and this one and this one and this + + + align:start position:0% +one and this one and this one and this +one that's going to be this is going to + + align:start position:0% +one that's going to be this is going to + + + align:start position:0% +one that's going to be this is going to +be the spinning tree that I'm going to + + align:start position:0% +be the spinning tree that I'm going to + + + align:start position:0% +be the spinning tree that I'm going to +look at this is also weight + + align:start position:0% +look at this is also weight + + + align:start position:0% +look at this is also weight + + align:start position:0% + + + + align:start position:0% + +oops so let's first Define what a + + align:start position:0% +oops so let's first Define what a + + + align:start position:0% +oops so let's first Define what a +minimum weage spending tree is just to + + align:start position:0% +minimum weage spending tree is just to + + + align:start position:0% +minimum weage spending tree is just to +be very precise and then let's uh have + + align:start position:0% +be very precise and then let's uh have + + + align:start position:0% +be very precise and then let's uh have +an algorithm maybe you have already + + align:start position:0% +an algorithm maybe you have already + + + align:start position:0% +an algorithm maybe you have already +ideas how this could be + + align:start position:0% +ideas how this could be + + + align:start position:0% +ideas how this could be +done uh it turns out actually that if + + align:start position:0% +done uh it turns out actually that if + + + align:start position:0% +done uh it turns out actually that if +you just start with a greedy approach + + align:start position:0% +you just start with a greedy approach + + + align:start position:0% +you just start with a greedy approach +you just start to add sort of the F the + + align:start position:0% +you just start to add sort of the F the + + + align:start position:0% +you just start to add sort of the F the +the edges of minimum weight that you can + + align:start position:0% +the edges of minimum weight that you can + + + align:start position:0% +the edges of minimum weight that you can +still add without creating any Cycles + + align:start position:0% +still add without creating any Cycles + + + align:start position:0% +still add without creating any Cycles +you will get an algorithm that is going + + align:start position:0% +you will get an algorithm that is going + + + align:start position:0% +you will get an algorithm that is going +to do the trick for + + align:start position:0% +to do the trick for + + + align:start position:0% +to do the trick for +you so that's kind of + + align:start position:0% +you so that's kind of + + + align:start position:0% +you so that's kind of +surprising so let's uh talk about the + + align:start position:0% + + + + align:start position:0% + +definition so the minimum spanning + + align:start position:0% + + + + align:start position:0% + +tree um + + align:start position:0% +tree um + + + align:start position:0% +tree um +of an edge weighted + + align:start position:0% + + + + align:start position:0% + +graph is defined as + + align:start position:0% + + + + align:start position:0% + +um it's a find as a spanning tree of + + align:start position:0% +um it's a find as a spanning tree of + + + align:start position:0% +um it's a find as a spanning tree of +G such that it + + align:start position:0% +G such that it + + + align:start position:0% +G such that it +has the + + align:start position:0% + + + + align:start position:0% + +smallest possible sum + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% + + + + align:start position:0% + +ights + + align:start position:0% +ights + + + align:start position:0% +ights +so well the algorithm that I'm thinking + + align:start position:0% +so well the algorithm that I'm thinking + + + align:start position:0% +so well the algorithm that I'm thinking +about here is very + + align:start position:0% +about here is very + + + align:start position:0% +about here is very +straightforward actually I use uh this + + align:start position:0% +straightforward actually I use uh this + + + align:start position:0% +straightforward actually I use uh this +Blackboard because this algorithm will + + align:start position:0% +Blackboard because this algorithm will + + + align:start position:0% +Blackboard because this algorithm will +be the focus of the rest of the + + align:start position:0% +be the focus of the rest of the + + + align:start position:0% +be the focus of the rest of the +lecture um + + align:start position:0% + + + + align:start position:0% + +okay so what's the + + align:start position:0% + + + + align:start position:0% + +algorithm we actually + + align:start position:0% +algorithm we actually + + + align:start position:0% +algorithm we actually +grow a subgraph step by + + align:start position:0% +grow a subgraph step by + + + align:start position:0% +grow a subgraph step by +step so one Edge at a time + + align:start position:0% + + + + align:start position:0% + +such that at each + + align:start position:0% + + + + align:start position:0% + +step we want to + + align:start position:0% + + + + align:start position:0% + +add the minimum weight + + align:start position:0% + + + + align:start position:0% + +H um that keeps a sub gra a + + align:start position:0% + + + + align:start position:0% + +cyclic so this is our algorithm let's + + align:start position:0% +cyclic so this is our algorithm let's + + + align:start position:0% +cyclic so this is our algorithm let's +have a look how this works in this + + align:start position:0% +have a look how this works in this + + + align:start position:0% +have a look how this works in this +particular graph over + + align:start position:0% + + + + align:start position:0% + +here so suppose I would start start off + + align:start position:0% +here so suppose I would start start off + + + align:start position:0% +here so suppose I would start start off +uh with uh well if if if if I start with + + align:start position:0% +uh with uh well if if if if I start with + + + align:start position:0% +uh with uh well if if if if I start with +this algorithm I take say uh any minimum + + align:start position:0% +this algorithm I take say uh any minimum + + + align:start position:0% +this algorithm I take say uh any minimum +weight Edge say I take this particular + + align:start position:0% +weight Edge say I take this particular + + + align:start position:0% +weight Edge say I take this particular +one so this could be my first Edge that + + align:start position:0% +one so this could be my first Edge that + + + align:start position:0% +one so this could be my first Edge that +I + + align:start position:0% +I + + + align:start position:0% +I +choose um then I may want to choose + + align:start position:0% +choose um then I may want to choose + + + align:start position:0% +choose um then I may want to choose +another minimum weight Edge such that I + + align:start position:0% +another minimum weight Edge such that I + + + align:start position:0% +another minimum weight Edge such that I +do not create a cycle well which one + + align:start position:0% +do not create a cycle well which one + + + align:start position:0% +do not create a cycle well which one +could I choose I could choose this one I + + align:start position:0% +could I choose I could choose this one I + + + align:start position:0% +could I choose I could choose this one I +could also choose this one with this one + + align:start position:0% +could also choose this one with this one + + + align:start position:0% +could also choose this one with this one +I could choose this part with this one I + + align:start position:0% +I could choose this part with this one I + + + align:start position:0% +I could choose this part with this one I +could choose that part I could also + + align:start position:0% +could choose that part I could also + + + align:start position:0% +could choose that part I could also +choose this one so let's choose this one + + align:start position:0% +choose this one so let's choose this one + + + align:start position:0% +choose this one so let's choose this one +actually um that would be our second uh + + align:start position:0% +actually um that would be our second uh + + + align:start position:0% +actually um that would be our second uh +step in our our second Edge that we + + align:start position:0% +step in our our second Edge that we + + + align:start position:0% +step in our our second Edge that we +select in our algorithm these are two + + align:start position:0% +select in our algorithm these are two + + + align:start position:0% +select in our algorithm these are two +disjointed edges so there's definitely + + align:start position:0% +disjointed edges so there's definitely + + + align:start position:0% +disjointed edges so there's definitely +no + + align:start position:0% +no + + + align:start position:0% +no +graph um well maybe in our third step um + + align:start position:0% +graph um well maybe in our third step um + + + align:start position:0% +graph um well maybe in our third step um +I can choose one of these uh + + align:start position:0% +I can choose one of these uh + + + align:start position:0% +I can choose one of these uh +edges uh which also has just weight one + + align:start position:0% +edges uh which also has just weight one + + + align:start position:0% +edges uh which also has just weight one +which is minimum weight so this could be + + align:start position:0% +which is minimum weight so this could be + + + align:start position:0% +which is minimum weight so this could be +my third uh possibility + + align:start position:0% +my third uh possibility + + + align:start position:0% +my third uh possibility +then what's the fourth possibility well + + align:start position:0% +then what's the fourth possibility well + + + align:start position:0% +then what's the fourth possibility well +I have uh uh well I have to choose one + + align:start position:0% +I have uh uh well I have to choose one + + + align:start position:0% +I have uh uh well I have to choose one +of those actually um I cannot choose uh + + align:start position:0% +of those actually um I cannot choose uh + + + align:start position:0% +of those actually um I cannot choose uh +the Min the the uh this weight one Edge + + align:start position:0% +the Min the the uh this weight one Edge + + + align:start position:0% +the Min the the uh this weight one Edge +why not because that would create a + + align:start position:0% +why not because that would create a + + + align:start position:0% +why not because that would create a +cycle so I'm not allowed to choose this + + align:start position:0% +cycle so I'm not allowed to choose this + + + align:start position:0% +cycle so I'm not allowed to choose this +one anymore so I choose one of these two + + align:start position:0% +one anymore so I choose one of these two + + + align:start position:0% +one anymore so I choose one of these two +so for example I choose uh this one over + + align:start position:0% +so for example I choose uh this one over + + + align:start position:0% +so for example I choose uh this one over +here this the fourth Edge that I add to + + align:start position:0% +here this the fourth Edge that I add to + + + align:start position:0% +here this the fourth Edge that I add to +the whole picture so notice that in in + + align:start position:0% +the whole picture so notice that in in + + + align:start position:0% +the whole picture so notice that in in +the meantime I have two disconnected + + align:start position:0% +the meantime I have two disconnected + + + align:start position:0% +the meantime I have two disconnected +components right one over here which is + + align:start position:0% +components right one over here which is + + + align:start position:0% +components right one over here which is +this Arc and another Arc over + + align:start position:0% +this Arc and another Arc over + + + align:start position:0% +this Arc and another Arc over +here okay so which Edge do I attach now + + align:start position:0% +here okay so which Edge do I attach now + + + align:start position:0% +here okay so which Edge do I attach now +in the algorithm well I can still add + + align:start position:0% +in the algorithm well I can still add + + + align:start position:0% +in the algorithm well I can still add +this minimum weight Edge over here of of + + align:start position:0% +this minimum weight Edge over here of of + + + align:start position:0% +this minimum weight Edge over here of of +of weight two because it does not create + + align:start position:0% +of weight two because it does not create + + + align:start position:0% +of weight two because it does not create +any cycle so this would be the fifth one + + align:start position:0% +any cycle so this would be the fifth one + + + align:start position:0% +any cycle so this would be the fifth one +that I add to the whole + + align:start position:0% +that I add to the whole + + + align:start position:0% +that I add to the whole +picture well now I can + + align:start position:0% +picture well now I can + + + align:start position:0% +picture well now I can +choose either one of those so for + + align:start position:0% +choose either one of those so for + + + align:start position:0% +choose either one of those so for +example this would be my six step and + + align:start position:0% +example this would be my six step and + + + align:start position:0% +example this would be my six step and +then finally I can choose none of these + + align:start position:0% +then finally I can choose none of these + + + align:start position:0% +then finally I can choose none of these +because those would create Cycles but I + + align:start position:0% +because those would create Cycles but I + + + align:start position:0% +because those would create Cycles but I +can choose this one so this is going to + + align:start position:0% +can choose this one so this is going to + + + align:start position:0% +can choose this one so this is going to +be the seventh one that I add to the + + align:start position:0% +be the seventh one that I add to the + + + align:start position:0% +be the seventh one that I add to the +whole uh uh graph that I construct here + + align:start position:0% +whole uh uh graph that I construct here + + + align:start position:0% +whole uh uh graph that I construct here +and grow in this algorithm it turns out + + align:start position:0% +and grow in this algorithm it turns out + + + align:start position:0% +and grow in this algorithm it turns out +this algorithm actually creates for you + + align:start position:0% +this algorithm actually creates for you + + + align:start position:0% +this algorithm actually creates for you +a minimum spanning tree and the proof is + + align:start position:0% +a minimum spanning tree and the proof is + + + align:start position:0% +a minimum spanning tree and the proof is +uh much more complex than what we have + + align:start position:0% +uh much more complex than what we have + + + align:start position:0% +uh much more complex than what we have +seen + + align:start position:0% +seen + + + align:start position:0% +seen +before uh so that's uh what we're going + + align:start position:0% +before uh so that's uh what we're going + + + align:start position:0% +before uh so that's uh what we're going +to do right + + align:start position:0% +to do right + + + align:start position:0% +to do right +now um so when we think about this + + align:start position:0% +now um so when we think about this + + + align:start position:0% +now um so when we think about this +algorithm then somehow I want to + + align:start position:0% +algorithm then somehow I want to + + + align:start position:0% +algorithm then somehow I want to +guarantee that at every single step I + + align:start position:0% +guarantee that at every single step I + + + align:start position:0% +guarantee that at every single step I +will be able to grow into a minimum + + align:start position:0% +will be able to grow into a minimum + + + align:start position:0% +will be able to grow into a minimum +spanning tree and that's the basic uh + + align:start position:0% +spanning tree and that's the basic uh + + + align:start position:0% +spanning tree and that's the basic uh +intuition that we have and that's the + + align:start position:0% +intuition that we have and that's the + + + align:start position:0% +intuition that we have and that's the +Lemma that we want to prove + + align:start position:0% +Lemma that we want to prove + + + align:start position:0% +Lemma that we want to prove +first so + + align:start position:0% +first so + + + align:start position:0% +first so +formalizing uh we get + + align:start position:0% +formalizing uh we get + + + align:start position:0% +formalizing uh we get +the following we want to prove the + + align:start position:0% +the following we want to prove the + + + align:start position:0% +the following we want to prove the +following + + align:start position:0% +following + + + align:start position:0% +following +statement + + align:start position:0% + + + + align:start position:0% + +um so the LMA that will help + + align:start position:0% +um so the LMA that will help + + + align:start position:0% +um so the LMA that will help +us is let s be the set of edges that I + + align:start position:0% +us is let s be the set of edges that I + + + align:start position:0% +us is let s be the set of edges that I +have been selecting uh up to uh up to + + align:start position:0% +have been selecting uh up to uh up to + + + align:start position:0% +have been selecting uh up to uh up to +now in the algorithm so let s consist + + align:start position:0% +now in the algorithm so let s consist + + + align:start position:0% +now in the algorithm so let s consist +for example of the first M + + align:start position:0% + + + + align:start position:0% + +edges + + align:start position:0% + + + + align:start position:0% + +and what they want to show + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +that we can still extend this set of + + align:start position:0% +that we can still extend this set of + + + align:start position:0% +that we can still extend this set of +edges into a minimum spanning tree we + + align:start position:0% +edges into a minimum spanning tree we + + + align:start position:0% +edges into a minimum spanning tree we +can still grow within the algorithm into + + align:start position:0% +can still grow within the algorithm into + + + align:start position:0% +can still grow within the algorithm into +a minimum spanning tree that's what we + + align:start position:0% +a minimum spanning tree that's what we + + + align:start position:0% +a minimum spanning tree that's what we +want to show + + align:start position:0% +want to show + + + align:start position:0% +want to show +so I want to show that there exists a uh + + align:start position:0% +so I want to show that there exists a uh + + + align:start position:0% +so I want to show that there exists a uh +minimum spanning + + align:start position:0% +minimum spanning + + + align:start position:0% +minimum spanning +tree T that has the vertic set V and an + + align:start position:0% +tree T that has the vertic set V and an + + + align:start position:0% +tree T that has the vertic set V and an +edge set + + align:start position:0% +edge set + + + align:start position:0% +edge set +e + + align:start position:0% +e + + + align:start position:0% +e +uh so this is a minimum spanning tree + + align:start position:0% +uh so this is a minimum spanning tree + + + align:start position:0% +uh so this is a minimum spanning tree +for the graph G such + + align:start position:0% + + + + align:start position:0% + +that s is actually a a subset of the + + align:start position:0% +that s is actually a a subset of the + + + align:start position:0% +that s is actually a a subset of the +edges in this minimum spanning tree so + + align:start position:0% +edges in this minimum spanning tree so + + + align:start position:0% +edges in this minimum spanning tree so +this is a nice mathematical formulation + + align:start position:0% +this is a nice mathematical formulation + + + align:start position:0% +this is a nice mathematical formulation +that uh really uh precisely states that + + align:start position:0% +that uh really uh precisely states that + + + align:start position:0% +that uh really uh precisely states that +we can still keep on growing into IM + + align:start position:0% +we can still keep on growing into IM + + + align:start position:0% +we can still keep on growing into IM +spanic tree so how would this LMA help + + align:start position:0% +spanic tree so how would this LMA help + + + align:start position:0% +spanic tree so how would this LMA help +us improving the theorem that we want to + + align:start position:0% +us improving the theorem that we want to + + + align:start position:0% +us improving the theorem that we want to +show uh actually where is the + + align:start position:0% +show uh actually where is the + + + align:start position:0% +show uh actually where is the +theorem I did not write down the theorem + + align:start position:0% +theorem I did not write down the theorem + + + align:start position:0% +theorem I did not write down the theorem +so far so let me put it over here so the + + align:start position:0% +so far so let me put it over here so the + + + align:start position:0% +so far so let me put it over here so the +theorem that want to show + + align:start position:0% +theorem that want to show + + + align:start position:0% +theorem that want to show +is that uh for + + align:start position:0% + + + + align:start position:0% + +any + + align:start position:0% + + + + align:start position:0% + +connected weighted graph + + align:start position:0% + + + + align:start position:0% + +G the algorithm creates a minimum + + align:start position:0% +G the algorithm creates a minimum + + + align:start position:0% +G the algorithm creates a minimum +spending + + align:start position:0% + + + + align:start position:0% + +tree the algorithm produces + + align:start position:0% + + + + align:start position:0% + +a minimum spanning + + align:start position:0% +a minimum spanning + + + align:start position:0% +a minimum spanning +tree so how can we prove this + + align:start position:0% +tree so how can we prove this + + + align:start position:0% +tree so how can we prove this +theorem suppose we know that this LMA is + + align:start position:0% +theorem suppose we know that this LMA is + + + align:start position:0% +theorem suppose we know that this LMA is +true which we will prove later then um + + align:start position:0% +true which we will prove later then um + + + align:start position:0% +true which we will prove later then um +how do we know that this theorem + + align:start position:0% + + + + align:start position:0% + +holds actually I'm wiping out this + + align:start position:0% +holds actually I'm wiping out this + + + align:start position:0% +holds actually I'm wiping out this +particular theorem over here we will use + + align:start position:0% +particular theorem over here we will use + + + align:start position:0% +particular theorem over here we will use +this in a moment so we know that every + + align:start position:0% +this in a moment so we know that every + + + align:start position:0% +this in a moment so we know that every +connected graph has a spinning tree we + + align:start position:0% +connected graph has a spinning tree we + + + align:start position:0% +connected graph has a spinning tree we +already know that + + align:start position:0% +already know that + + + align:start position:0% +already know that +but now we want to show that we can even + + align:start position:0% +but now we want to show that we can even + + + align:start position:0% +but now we want to show that we can even +construct the minimum bending tree for a + + align:start position:0% +construct the minimum bending tree for a + + + align:start position:0% +construct the minimum bending tree for a +weighted + + align:start position:0% +weighted + + + align:start position:0% +weighted +graph okay so how are we going + + align:start position:0% +graph okay so how are we going + + + align:start position:0% +graph okay so how are we going +ahead um the proof of the + + align:start position:0% + + + + align:start position:0% + +theorem is as follows well suppose that + + align:start position:0% +theorem is as follows well suppose that + + + align:start position:0% +theorem is as follows well suppose that +the number of edges uh the number of + + align:start position:0% +the number of edges uh the number of + + + align:start position:0% +the number of edges uh the number of +vertices is actually equal to + + align:start position:0% +vertices is actually equal to + + + align:start position:0% +vertices is actually equal to +n + + align:start position:0% +n + + + align:start position:0% +n +and if we want to show that we get to a + + align:start position:0% +and if we want to show that we get to a + + + align:start position:0% +and if we want to show that we get to a +minimum spanning tree you want to first + + align:start position:0% +minimum spanning tree you want to first + + + align:start position:0% +minimum spanning tree you want to first +of all show that the algorithm is able + + align:start position:0% +of all show that the algorithm is able + + + align:start position:0% +of all show that the algorithm is able +to choose uh at least n minus one edges + + align:start position:0% +to choose uh at least n minus one edges + + + align:start position:0% +to choose uh at least n minus one edges +right because a tree has n minus one + + align:start position:0% +right because a tree has n minus one + + + align:start position:0% +right because a tree has n minus one +edges we have shown this before um so uh + + align:start position:0% +edges we have shown this before um so uh + + + align:start position:0% +edges we have shown this before um so uh +the algorithm should not get stuck so + + align:start position:0% +the algorithm should not get stuck so + + + align:start position:0% +the algorithm should not get stuck so +let's first prove that so suppose I have + + align:start position:0% +let's first prove that so suppose I have + + + align:start position:0% +let's first prove that so suppose I have +chosen less than n minus one + + align:start position:0% + + + + align:start position:0% + +edges uh so + + align:start position:0% + + + + align:start position:0% + +suppose we have less than n minus one as + + align:start position:0% +suppose we have less than n minus one as + + + align:start position:0% +suppose we have less than n minus one as +just picked well then what do we + + align:start position:0% +just picked well then what do we + + + align:start position:0% +just picked well then what do we +know well there exists an + + align:start position:0% + + + + align:start position:0% + +edge in E minus s so let's uh well let + + align:start position:0% +edge in E minus s so let's uh well let + + + align:start position:0% +edge in E minus s so let's uh well let +me first write it out uh that can be + + align:start position:0% + + + + align:start position:0% + +added without + + align:start position:0% +added without + + + align:start position:0% +added without +creating a + + align:start position:0% + + + + align:start position:0% + +cycle so why is this uh well uh I know + + align:start position:0% +cycle so why is this uh well uh I know + + + align:start position:0% +cycle so why is this uh well uh I know +that e is the EDG set of my minimum + + align:start position:0% +that e is the EDG set of my minimum + + + align:start position:0% +that e is the EDG set of my minimum +spanning tree I know that s is a part + + align:start position:0% +spanning tree I know that s is a part + + + align:start position:0% +spanning tree I know that s is a part +of uh uh is a subset of all the edges I + + align:start position:0% +of uh uh is a subset of all the edges I + + + align:start position:0% +of uh uh is a subset of all the edges I +know that the minimum spanning tree is a + + align:start position:0% +know that the minimum spanning tree is a + + + align:start position:0% +know that the minimum spanning tree is a +tree it's a tree on nvertices + + align:start position:0% +tree it's a tree on nvertices + + + align:start position:0% +tree it's a tree on nvertices +we know that a tree on n feses has n + + align:start position:0% +we know that a tree on n feses has n + + + align:start position:0% +we know that a tree on n feses has n +minus one + + align:start position:0% +minus one + + + align:start position:0% +minus one +edges I know that less than n minus one + + align:start position:0% +edges I know that less than n minus one + + + align:start position:0% +edges I know that less than n minus one +edges have been chosen so far so that + + align:start position:0% +edges have been chosen so far so that + + + align:start position:0% +edges have been chosen so far so that +means that s has less than n minus one + + align:start position:0% +means that s has less than n minus one + + + align:start position:0% +means that s has less than n minus one +uh edges e has exactly n minus one edges + + align:start position:0% +uh edges e has exactly n minus one edges + + + align:start position:0% +uh edges e has exactly n minus one edges +so there's at least one Edge that is + + align:start position:0% +so there's at least one Edge that is + + + align:start position:0% +so there's at least one Edge that is +contained that is an element in e but + + align:start position:0% +contained that is an element in e but + + + align:start position:0% +contained that is an element in e but +not in + + align:start position:0% +not in + + + align:start position:0% +not in +s and uh for that particular Edge uh + + align:start position:0% +s and uh for that particular Edge uh + + + align:start position:0% +s and uh for that particular Edge uh +well since it's part of this tree + + align:start position:0% +well since it's part of this tree + + + align:start position:0% +well since it's part of this tree +together with uh with with s which is + + align:start position:0% +together with uh with with s which is + + + align:start position:0% +together with uh with with s which is +also part of uh of of of all the edges + + align:start position:0% +also part of uh of of of all the edges + + + align:start position:0% +also part of uh of of of all the edges +within the tree well we know that that + + align:start position:0% +within the tree well we know that that + + + align:start position:0% +within the tree well we know that that +edge for that reason will not create a + + align:start position:0% +edge for that reason will not create a + + + align:start position:0% +edge for that reason will not create a +cycle right because otherwise the + + align:start position:0% +cycle right because otherwise the + + + align:start position:0% +cycle right because otherwise the +original tree would have a + + align:start position:0% +original tree would have a + + + align:start position:0% +original tree would have a +cycle okay so we know that the algorithm + + align:start position:0% +cycle okay so we know that the algorithm + + + align:start position:0% +cycle okay so we know that the algorithm +can always select an edge such that no + + align:start position:0% +can always select an edge such that no + + + align:start position:0% +can always select an edge such that no +cycle is created and that means that + + align:start position:0% +cycle is created and that means that + + + align:start position:0% +cycle is created and that means that +that we can keep on going in the + + align:start position:0% +that we can keep on going in the + + + align:start position:0% +that we can keep on going in the +algorithm until at least n minus one + + align:start position:0% +algorithm until at least n minus one + + + align:start position:0% +algorithm until at least n minus one +edges are selected so what happens if we + + align:start position:0% +edges are selected so what happens if we + + + align:start position:0% +edges are selected so what happens if we +have n minus one + + align:start position:0% + + + + align:start position:0% + +edges so once + + align:start position:0% +edges so once + + + align:start position:0% +edges so once +um n minus one uh edges have been + + align:start position:0% +um n minus one uh edges have been + + + align:start position:0% +um n minus one uh edges have been +chosen well then s has exactly n minus + + align:start position:0% +chosen well then s has exactly n minus + + + align:start position:0% +chosen well then s has exactly n minus +one edes e has exactly nus one edges + + align:start position:0% +one edes e has exactly nus one edges + + + align:start position:0% +one edes e has exactly nus one edges +because it's a tree they are subsets of + + align:start position:0% +because it's a tree they are subsets of + + + align:start position:0% +because it's a tree they are subsets of +one another so they must be equal to one + + align:start position:0% +one another so they must be equal to one + + + align:start position:0% +one another so they must be equal to one +another so essentially what we have here + + align:start position:0% +another so essentially what we have here + + + align:start position:0% +another so essentially what we have here +is that s exactly defines the minimum + + align:start position:0% +is that s exactly defines the minimum + + + align:start position:0% +is that s exactly defines the minimum +spanning + + align:start position:0% +spanning + + + align:start position:0% +spanning +tree that we are looking for so the + + align:start position:0% +tree that we are looking for so the + + + align:start position:0% +tree that we are looking for so the +algorithm at the very end when it has + + align:start position:0% +algorithm at the very end when it has + + + align:start position:0% +algorithm at the very end when it has +chosen n minus one edges produces a + + align:start position:0% +chosen n minus one edges produces a + + + align:start position:0% +chosen n minus one edges produces a +minimum spanning + + align:start position:0% +minimum spanning + + + align:start position:0% +minimum spanning +tree so we + + align:start position:0% + + + + align:start position:0% + +know that s + + align:start position:0% +know that s + + + align:start position:0% +know that s +uh defines the edges + + align:start position:0% + + + + align:start position:0% + +of a minimum weight spanning + + align:start position:0% +of a minimum weight spanning + + + align:start position:0% +of a minimum weight spanning +tree so if this LMA really holds through + + align:start position:0% +tree so if this LMA really holds through + + + align:start position:0% +tree so if this LMA really holds through +then this theorem can be shown so now + + align:start position:0% +then this theorem can be shown so now + + + align:start position:0% +then this theorem can be shown so now +let's have a look at this LMA and we + + align:start position:0% +let's have a look at this LMA and we + + + align:start position:0% +let's have a look at this LMA and we +going to use that picture over there to + + align:start position:0% +going to use that picture over there to + + + align:start position:0% +going to use that picture over there to +see how we can prove this so this is a + + align:start position:0% +see how we can prove this so this is a + + + align:start position:0% +see how we can prove this so this is a +little bit um + + align:start position:0% +little bit um + + + align:start position:0% +little bit um +tricky and uh the way to go about this + + align:start position:0% +tricky and uh the way to go about this + + + align:start position:0% +tricky and uh the way to go about this +is uh + + align:start position:0% +is uh + + + align:start position:0% +is uh +actually to use + + align:start position:0% +actually to use + + + align:start position:0% +actually to use +induction so let's uh let's see whether + + align:start position:0% +induction so let's uh let's see whether + + + align:start position:0% +induction so let's uh let's see whether +we can do this + + align:start position:0% +we can do this + + + align:start position:0% +we can do this +together + + align:start position:0% + + + + align:start position:0% + +um so the proof of the Lemma is as + + align:start position:0% + + + + align:start position:0% + +follows um you want to use + + align:start position:0% +follows um you want to use + + + align:start position:0% +follows um you want to use +induction on what do you think we going + + align:start position:0% +induction on what do you think we going + + + align:start position:0% +induction on what do you think we going +to induct here well we want to prove + + align:start position:0% +to induct here well we want to prove + + + align:start position:0% +to induct here well we want to prove +this particular LMA and we have this + + align:start position:0% +this particular LMA and we have this + + + align:start position:0% +this particular LMA and we have this +particular variable M so that seems to + + align:start position:0% +particular variable M so that seems to + + + align:start position:0% +particular variable M so that seems to +be a good method to to continue so we + + align:start position:0% +be a good method to to continue so we + + + align:start position:0% +be a good method to to continue so we +use induction on + + align:start position:0% +use induction on + + + align:start position:0% +use induction on +M and + + align:start position:0% +M and + + + align:start position:0% +M and +um let's State the inductive uh the + + align:start position:0% +um let's State the inductive uh the + + + align:start position:0% +um let's State the inductive uh the +induction hypothesis well it's exactly + + align:start position:0% +induction hypothesis well it's exactly + + + align:start position:0% +induction hypothesis well it's exactly +the same as in the LMA so we say for all + + align:start position:0% +the same as in the LMA so we say for all + + + align:start position:0% +the same as in the LMA so we say for all +G and for all sets s that + + align:start position:0% +G and for all sets s that + + + align:start position:0% +G and for all sets s that +consist + + align:start position:0% +consist + + + align:start position:0% +consist +of the first + + align:start position:0% +of the first + + + align:start position:0% +of the first +M selected + + align:start position:0% + + + + align:start position:0% + +edges there exists a minimum spanning + + align:start position:0% + + + + align:start position:0% + +tree uh of + + align:start position:0% +tree uh of + + + align:start position:0% +tree uh of +G such that + + align:start position:0% + + + + align:start position:0% + +s is a subset of e so this is our + + align:start position:0% +s is a subset of e so this is our + + + align:start position:0% +s is a subset of e so this is our +induction hypothesis and as always we + + align:start position:0% +induction hypothesis and as always we + + + align:start position:0% +induction hypothesis and as always we +start with the base case and the base + + align:start position:0% +start with the base case and the base + + + align:start position:0% +start with the base case and the base +case is going to be pretty + + align:start position:0% +case is going to be pretty + + + align:start position:0% +case is going to be pretty +straightforward in this particular case + + align:start position:0% +straightforward in this particular case + + + align:start position:0% +straightforward in this particular case +at least + + align:start position:0% +at least + + + align:start position:0% +at least +um well we have to do a little bit of + + align:start position:0% +um well we have to do a little bit of + + + align:start position:0% +um well we have to do a little bit of +work for it so let's see how that works + + align:start position:0% +work for it so let's see how that works + + + align:start position:0% +work for it so let's see how that works +so the base case is m equals z so let's + + align:start position:0% +so the base case is m equals z so let's + + + align:start position:0% +so the base case is m equals z so let's +reread this statement where m is equal + + align:start position:0% +reread this statement where m is equal + + + align:start position:0% +reread this statement where m is equal +to zero well + + align:start position:0% +to zero well + + + align:start position:0% +to zero well +if we have zero selected edges then s is + + align:start position:0% +if we have zero selected edges then s is + + + align:start position:0% +if we have zero selected edges then s is +the empty + + align:start position:0% +the empty + + + align:start position:0% +the empty +set so I have to prove that for all G + + align:start position:0% +set so I have to prove that for all G + + + align:start position:0% +set so I have to prove that for all G +there exists a minimum spanning tree + + align:start position:0% +there exists a minimum spanning tree + + + align:start position:0% +there exists a minimum spanning tree +such that the empty set is a subset of e + + align:start position:0% +such that the empty set is a subset of e + + + align:start position:0% +such that the empty set is a subset of e +well the empty set is always a subset of + + align:start position:0% +well the empty set is always a subset of + + + align:start position:0% +well the empty set is always a subset of +e right so that's no + + align:start position:0% +e right so that's no + + + align:start position:0% +e right so that's no +problem um so what I need to prove is + + align:start position:0% +problem um so what I need to prove is + + + align:start position:0% +problem um so what I need to prove is +that for all G there exists a minimum + + align:start position:0% +that for all G there exists a minimum + + + align:start position:0% +that for all G there exists a minimum +spanning tree of G + + align:start position:0% +spanning tree of G + + + align:start position:0% +spanning tree of G +and this is where our previous theorem + + align:start position:0% +and this is where our previous theorem + + + align:start position:0% +and this is where our previous theorem +comes in because we showed that for all + + align:start position:0% +comes in because we showed that for all + + + align:start position:0% +comes in because we showed that for all +graphs G there exists a spanning tree + + align:start position:0% +graphs G there exists a spanning tree + + + align:start position:0% +graphs G there exists a spanning tree +and if there exists a spanning tree + + align:start position:0% +and if there exists a spanning tree + + + align:start position:0% +and if there exists a spanning tree +there also exists a minimum weight + + align:start position:0% +there also exists a minimum weight + + + align:start position:0% +there also exists a minimum weight +spanning + + align:start position:0% +spanning + + + align:start position:0% +spanning +tree so that's the base case so m equals + + align:start position:0% +tree so that's the base case so m equals + + + align:start position:0% +tree so that's the base case so m equals +z implies that s is equal to the empty + + align:start position:0% +z implies that s is equal to the empty + + + align:start position:0% +z implies that s is equal to the empty +set so that means that s is definitely a + + align:start position:0% +set so that means that s is definitely a + + + align:start position:0% +set so that means that s is definitely a +subset for + + align:start position:0% +subset for + + + align:start position:0% +subset for +any + + align:start position:0% +any + + + align:start position:0% +any +um uh set of edges of a uh minimum + + align:start position:0% +um uh set of edges of a uh minimum + + + align:start position:0% +um uh set of edges of a uh minimum +weight spanning + + align:start position:0% + + + + align:start position:0% + +tree and now we're going to use our + + align:start position:0% +tree and now we're going to use our + + + align:start position:0% +tree and now we're going to use our +theorem to show that there also exists a + + align:start position:0% +theorem to show that there also exists a + + + align:start position:0% +theorem to show that there also exists a +minimum spanic Tre so this in itself is + + align:start position:0% +minimum spanic Tre so this in itself is + + + align:start position:0% +minimum spanic Tre so this in itself is +not yet sufficient right do you see that + + align:start position:0% +not yet sufficient right do you see that + + + align:start position:0% +not yet sufficient right do you see that +um yeah I know that for if s is the + + align:start position:0% +um yeah I know that for if s is the + + + align:start position:0% +um yeah I know that for if s is the +empty set then I know that this always + + align:start position:0% +empty set then I know that this always + + + align:start position:0% +empty set then I know that this always +holds but the statement is a little bit + + align:start position:0% +holds but the statement is a little bit + + + align:start position:0% +holds but the statement is a little bit +bigger for all G I still need to prove + + align:start position:0% +bigger for all G I still need to prove + + + align:start position:0% +bigger for all G I still need to prove +that there exists a minimum spending + + align:start position:0% +that there exists a minimum spending + + + align:start position:0% +that there exists a minimum spending +tree and that's why our previous theorem + + align:start position:0% +tree and that's why our previous theorem + + + align:start position:0% +tree and that's why our previous theorem +told us so we'll not write that part out + + align:start position:0% +told us so we'll not write that part out + + + align:start position:0% +told us so we'll not write that part out +so we have the base + + align:start position:0% +so we have the base + + + align:start position:0% +so we have the base +case + + align:start position:0% +case + + + align:start position:0% +case +um let's + + align:start position:0% + + + + align:start position:0% + +see I think I will go and prove this + + align:start position:0% +see I think I will go and prove this + + + align:start position:0% +see I think I will go and prove this +over + + align:start position:0% +over + + + align:start position:0% +over +here so let's look at the + + align:start position:0% +here so let's look at the + + + align:start position:0% +here so let's look at the +uh at the inductive step and then + + align:start position:0% +uh at the inductive step and then + + + align:start position:0% +uh at the inductive step and then +hopefully we can uh play a little bit + + align:start position:0% +hopefully we can uh play a little bit + + + align:start position:0% +hopefully we can uh play a little bit +with this picture up here to get some + + align:start position:0% + + + + align:start position:0% + +inside so how do we do this um well with + + align:start position:0% +inside so how do we do this um well with + + + align:start position:0% +inside so how do we do this um well with +an inductive + + align:start position:0% +an inductive + + + align:start position:0% +an inductive +step we start as + + align:start position:0% + + + + align:start position:0% + +usual right we + + align:start position:0% + + + + align:start position:0% + +assume that P of M HS + + align:start position:0% +assume that P of M HS + + + align:start position:0% +assume that P of M HS +now how do we go ahead so I want to + + align:start position:0% +now how do we go ahead so I want to + + + align:start position:0% +now how do we go ahead so I want to +prove p m + one which is uh stated over + + align:start position:0% +prove p m + one which is uh stated over + + + align:start position:0% +prove p m + one which is uh stated over +here so um I want to consider the set s + + align:start position:0% +here so um I want to consider the set s + + + align:start position:0% +here so um I want to consider the set s +that consists of the first n plus one + + align:start position:0% +that consists of the first n plus one + + + align:start position:0% +that consists of the first n plus one +selected edges so well essentially what + + align:start position:0% +selected edges so well essentially what + + + align:start position:0% +selected edges so well essentially what +I am interested in is what happens in + + align:start position:0% +I am interested in is what happens in + + + align:start position:0% +I am interested in is what happens in +the N plus one + + align:start position:0% +the N plus one + + + align:start position:0% +the N plus one +step so um let e denote + + align:start position:0% +step so um let e denote + + + align:start position:0% +step so um let e denote +The Edge um that I added in the m + one + + align:start position:0% + + + + align:start position:0% + +step and let s uh + + align:start position:0% +step and let s uh + + + align:start position:0% +step and let s uh +be uh the first M selected edges and we + + align:start position:0% +be uh the first M selected edges and we + + + align:start position:0% +be uh the first M selected edges and we +know that we can apply P of M for S + + align:start position:0% +know that we can apply P of M for S + + + align:start position:0% +know that we can apply P of M for S +right because we we assume this is this + + align:start position:0% +right because we we assume this is this + + + align:start position:0% +right because we we assume this is this +is our inductive step so we can apply + + align:start position:0% +is our inductive step so we can apply + + + align:start position:0% +is our inductive step so we can apply +something for S we would like to show PN + + align:start position:0% +something for S we would like to show PN + + + align:start position:0% +something for S we would like to show PN ++ one so we would like to show something + + align:start position:0% ++ one so we would like to show something + + + align:start position:0% ++ one so we would like to show something +for the union of those two so let me + + align:start position:0% +for the union of those two so let me + + + align:start position:0% +for the union of those two so let me +repeat that so um let s + + align:start position:0% +repeat that so um let s + + + align:start position:0% +repeat that so um let s +denote the + + align:start position:0% +denote the + + + align:start position:0% +denote the +first M selected + + align:start position:0% +first M selected + + + align:start position:0% +first M selected +edges um + + align:start position:0% +edges um + + + align:start position:0% +edges um +so by our induction + + align:start position:0% +so by our induction + + + align:start position:0% +so by our induction +hypothesis we + + align:start position:0% +hypothesis we + + + align:start position:0% +hypothesis we +can uh well let's apply it uh we know + + align:start position:0% +can uh well let's apply it uh we know + + + align:start position:0% +can uh well let's apply it uh we know +that there exists a minimum spanning + + align:start position:0% +that there exists a minimum spanning + + + align:start position:0% +that there exists a minimum spanning +tree such that s is a subset of the + + align:start position:0% +tree such that s is a subset of the + + + align:start position:0% +tree such that s is a subset of the +edges so let's just pick one such + + align:start position:0% +edges so let's just pick one such + + + align:start position:0% +edges so let's just pick one such +minimum spanning + + align:start position:0% +minimum spanning + + + align:start position:0% +minimum spanning +tree um so let T star be such a minimum + + align:start position:0% +tree um so let T star be such a minimum + + + align:start position:0% +tree um so let T star be such a minimum +spanning + + align:start position:0% +spanning + + + align:start position:0% +spanning +tree it has edes e + + align:start position:0% +tree it has edes e + + + align:start position:0% +tree it has edes e +star + + align:start position:0% +star + + + align:start position:0% +star +and + + align:start position:0% + + + + align:start position:0% + +uh and we know that s is actually a + + align:start position:0% +uh and we know that s is actually a + + + align:start position:0% +uh and we know that s is actually a +subset of + + align:start position:0% + + + + align:start position:0% + +e + + align:start position:0% +e + + + align:start position:0% +e +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so let's uh look at the very first case + + align:start position:0% +so let's uh look at the very first case + + + align:start position:0% +so let's uh look at the very first case +so what are the kind of cases that we + + align:start position:0% +so what are the kind of cases that we + + + align:start position:0% +so what are the kind of cases that we +are interested in so so let's think + + align:start position:0% +are interested in so so let's think + + + align:start position:0% +are interested in so so let's think +again what do we need to prove we need + + align:start position:0% +again what do we need to prove we need + + + align:start position:0% +again what do we need to prove we need +to prove p m + one so we need to prove + + align:start position:0% +to prove p m + one so we need to prove + + + align:start position:0% +to prove p m + one so we need to prove +something about the union of S and E we + + align:start position:0% +something about the union of S and E we + + + align:start position:0% +something about the union of S and E we +want to show that there is a minimum + + align:start position:0% +want to show that there is a minimum + + + align:start position:0% +want to show that there is a minimum +spanning tree such that the edge set of + + align:start position:0% +spanning tree such that the edge set of + + + align:start position:0% +spanning tree such that the edge set of +this spanning Tre contains both s and + + align:start position:0% +this spanning Tre contains both s and + + + align:start position:0% +this spanning Tre contains both s and +also + + align:start position:0% +also + + + align:start position:0% +also +e um so what kind of cases can we handle + + align:start position:0% +e um so what kind of cases can we handle + + + align:start position:0% +e um so what kind of cases can we handle +here well what would be a really good + + align:start position:0% +here well what would be a really good + + + align:start position:0% +here well what would be a really good +first case uh the first case could be + + align:start position:0% +first case uh the first case could be + + + align:start position:0% +first case uh the first case could be +that e is actually already part of e + + align:start position:0% +that e is actually already part of e + + + align:start position:0% +that e is actually already part of e +star well if that's true then of course + + align:start position:0% +star well if that's true then of course + + + align:start position:0% +star well if that's true then of course +s together with e is also a subset of e + + align:start position:0% +s together with e is also a subset of e + + + align:start position:0% +s together with e is also a subset of e +star and that + + align:start position:0% +star and that + + + align:start position:0% +star and that +means that we done in this particular + + align:start position:0% +means that we done in this particular + + + align:start position:0% +means that we done in this particular +case and why is this because uh this is + + align:start position:0% +case and why is this because uh this is + + + align:start position:0% +case and why is this because uh this is +an example of a Minimus Banning tree + + align:start position:0% +an example of a Minimus Banning tree + + + align:start position:0% +an example of a Minimus Banning tree +that contains both S and E so it + + align:start position:0% +that contains both S and E so it + + + align:start position:0% +that contains both S and E so it +contains the N plus one first selected + + align:start position:0% +contains the N plus one first selected + + + align:start position:0% +contains the N plus one first selected +edges and so this is pn+ one now the + + align:start position:0% +edges and so this is pn+ one now the + + + align:start position:0% +edges and so this is pn+ one now the +next case is the difficult + + align:start position:0% +next case is the difficult + + + align:start position:0% +next case is the difficult +part + + align:start position:0% + + + + align:start position:0% + +um okay let's uh + + align:start position:0% +um okay let's uh + + + align:start position:0% +um okay let's uh +wipe out uh actually we do not really + + align:start position:0% +wipe out uh actually we do not really + + + align:start position:0% +wipe out uh actually we do not really +need the proof of the theorem + + align:start position:0% +need the proof of the theorem + + + align:start position:0% +need the proof of the theorem +anymore so let's take this off the + + align:start position:0% +anymore so let's take this off the + + + align:start position:0% +anymore so let's take this off the +Blackboard + + align:start position:0% + + + + align:start position:0% + +um so the way to do this is to + + align:start position:0% +um so the way to do this is to + + + align:start position:0% +um so the way to do this is to +um sort of see how we can uh use the uh + + align:start position:0% +um sort of see how we can uh use the uh + + + align:start position:0% +um sort of see how we can uh use the uh +three T star and somehow transform it + + align:start position:0% +three T star and somehow transform it + + + align:start position:0% +three T star and somehow transform it +into another tree for this particular + + align:start position:0% +into another tree for this particular + + + align:start position:0% +into another tree for this particular +case where we assume that e is not in E + + align:start position:0% +case where we assume that e is not in E + + + align:start position:0% +case where we assume that e is not in E +star + + align:start position:0% +star + + + align:start position:0% +star +so + + align:start position:0% +so + + + align:start position:0% +so +um so let's have a look at that graph up + + align:start position:0% +um so let's have a look at that graph up + + + align:start position:0% +um so let's have a look at that graph up +up there let me rewrite it a little bit + + align:start position:0% +up there let me rewrite it a little bit + + + align:start position:0% +up there let me rewrite it a little bit +and let's uh look at what happens in the + + align:start position:0% +and let's uh look at what happens in the + + + align:start position:0% +and let's uh look at what happens in the +algorithm after two steps so will redraw + + align:start position:0% +algorithm after two steps so will redraw + + + align:start position:0% +algorithm after two steps so will redraw +the + + align:start position:0% +the + + + align:start position:0% +the +graph um so so we have + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +say these + + align:start position:0% +say these + + + align:start position:0% +say these +edges + + align:start position:0% + + + + align:start position:0% + +um this + + align:start position:0% +um this + + + align:start position:0% +um this +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +one let me + + align:start position:0% +one let me + + + align:start position:0% +one let me +see I want to use some different + + align:start position:0% +see I want to use some different + + + align:start position:0% +see I want to use some different +colors to make this as clear as possible + + align:start position:0% +colors to make this as clear as possible + + + align:start position:0% +colors to make this as clear as possible +and we have this + + align:start position:0% +and we have this + + + align:start position:0% +and we have this +one we have this one we have this + + align:start position:0% +one we have this one we have this + + + align:start position:0% +one we have this one we have this +one and we also have this one actually + + align:start position:0% +one and we also have this one actually + + + align:start position:0% +one and we also have this one actually +sorry all right so uh let's define the + + align:start position:0% +sorry all right so uh let's define the + + + align:start position:0% +sorry all right so uh let's define the +different uh edges uh the straight + + align:start position:0% +different uh edges uh the straight + + + align:start position:0% +different uh edges uh the straight +ones form the set s so after two steps + + align:start position:0% +ones form the set s so after two steps + + + align:start position:0% +ones form the set s so after two steps +over there we have selected this Edge + + align:start position:0% +over there we have selected this Edge + + + align:start position:0% +over there we have selected this Edge +first and then this Edge was the second + + align:start position:0% +first and then this Edge was the second + + + align:start position:0% +first and then this Edge was the second +Edge that we selected in our algorithm + + align:start position:0% +Edge that we selected in our algorithm + + + align:start position:0% +Edge that we selected in our algorithm +so these two together can form the set + + align:start position:0% +so these two together can form the set + + + align:start position:0% +so these two together can form the set +s so what is T star T star could be for + + align:start position:0% +s so what is T star T star could be for + + + align:start position:0% +s so what is T star T star could be for +example the spanning tree that contains + + align:start position:0% +example the spanning tree that contains + + + align:start position:0% +example the spanning tree that contains +both these + + align:start position:0% + + + + align:start position:0% + +edges plus uh the dotted + + align:start position:0% +edges plus uh the dotted + + + align:start position:0% +edges plus uh the dotted +ones so let's have a look here this is + + align:start position:0% +ones so let's have a look here this is + + + align:start position:0% +ones so let's have a look here this is +indeed a tree + + align:start position:0% +indeed a tree + + + align:start position:0% +indeed a tree +right and if we uh look into this uh + + align:start position:0% +right and if we uh look into this uh + + + align:start position:0% +right and if we uh look into this uh +picture over here you can see that the + + align:start position:0% +picture over here you can see that the + + + align:start position:0% +picture over here you can see that the +weight of this particular tree is 17 + + align:start position:0% +weight of this particular tree is 17 + + + align:start position:0% +weight of this particular tree is 17 +it's also a minimum weight spinning + + align:start position:0% +it's also a minimum weight spinning + + + align:start position:0% +it's also a minimum weight spinning +tree okay what is g g is the complete + + align:start position:0% +tree okay what is g g is the complete + + + align:start position:0% +tree okay what is g g is the complete +graph and contains not only these two + + align:start position:0% +graph and contains not only these two + + + align:start position:0% +graph and contains not only these two +types of + + align:start position:0% +types of + + + align:start position:0% +types of +edges but also these sort of more orange + + align:start position:0% +edges but also these sort of more orange + + + align:start position:0% +edges but also these sort of more orange +colored + + align:start position:0% + + + + align:start position:0% + +ones so this is the situation that we + + align:start position:0% +ones so this is the situation that we + + + align:start position:0% +ones so this is the situation that we +are + + align:start position:0% +are + + + align:start position:0% +are +in now in our algorithm we want to + + align:start position:0% +in now in our algorithm we want to + + + align:start position:0% +in now in our algorithm we want to +choose uh this particular third + + align:start position:0% +choose uh this particular third + + + align:start position:0% +choose uh this particular third +Edge so this is uh going to be our + + align:start position:0% +Edge so this is uh going to be our + + + align:start position:0% +Edge so this is uh going to be our +e this particular Edge and as you can + + align:start position:0% +e this particular Edge and as you can + + + align:start position:0% +e this particular Edge and as you can +see e is not part of T star it's not one + + align:start position:0% +see e is not part of T star it's not one + + + align:start position:0% +see e is not part of T star it's not one +of those two kinds of edges It's + + align:start position:0% +of those two kinds of edges It's + + + align:start position:0% +of those two kinds of edges It's +actually an one of the orange + + align:start position:0% +actually an one of the orange + + + align:start position:0% +actually an one of the orange +edges so what can we do here uh well the + + align:start position:0% +edges so what can we do here uh well the + + + align:start position:0% +edges so what can we do here uh well the +idea is is that we want to recreate like + + align:start position:0% +idea is is that we want to recreate like + + + align:start position:0% +idea is is that we want to recreate like +a new uh uh Tree in which we somehow + + align:start position:0% +a new uh uh Tree in which we somehow + + + align:start position:0% +a new uh uh Tree in which we somehow +exchange e um exchange one of the edges + + align:start position:0% +exchange e um exchange one of the edges + + + align:start position:0% +exchange e um exchange one of the edges +in t star with E and still sort of + + align:start position:0% +in t star with E and still sort of + + + align:start position:0% +in t star with E and still sort of +maintaining the minimum spanning tree + + align:start position:0% +maintaining the minimum spanning tree + + + align:start position:0% +maintaining the minimum spanning tree +property so how can we prove + + align:start position:0% +property so how can we prove + + + align:start position:0% +property so how can we prove +this + + align:start position:0% +this + + + align:start position:0% +this +um + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the way to do this is to uh + + align:start position:0% +so the way to do this is to uh + + + align:start position:0% +so the way to do this is to uh +figure out what the algorithm teaches us + + align:start position:0% +figure out what the algorithm teaches us + + + align:start position:0% +figure out what the algorithm teaches us +about e and also what the tree property + + align:start position:0% +about e and also what the tree property + + + align:start position:0% +about e and also what the tree property +tells + + align:start position:0% + + + + align:start position:0% + +us so let's combine all our knowledge so + + align:start position:0% +us so let's combine all our knowledge so + + + align:start position:0% +us so let's combine all our knowledge so +first of all we know that the + + align:start position:0% +first of all we know that the + + + align:start position:0% +first of all we know that the +algorithm from its definition implies + + align:start position:0% +algorithm from its definition implies + + + align:start position:0% +algorithm from its definition implies +that s together with e + + align:start position:0% +that s together with e + + + align:start position:0% +that s together with e +actually has no + + align:start position:0% +actually has no + + + align:start position:0% +actually has no +cycle that's how we + + align:start position:0% +cycle that's how we + + + align:start position:0% +cycle that's how we +select the N plus one Edge there's no it + + align:start position:0% +select the N plus one Edge there's no it + + + align:start position:0% +select the N plus one Edge there's no it +it the all the selected edges together + + align:start position:0% +it the all the selected edges together + + + align:start position:0% +it the all the selected edges together +should not contain a cycle that's the + + align:start position:0% +should not contain a cycle that's the + + + align:start position:0% +should not contain a cycle that's the +definition of the algorithm we know that + + align:start position:0% +definition of the algorithm we know that + + + align:start position:0% +definition of the algorithm we know that +t star is a + + align:start position:0% +t star is a + + + align:start position:0% +t star is a +tree and this + + align:start position:0% +tree and this + + + align:start position:0% +tree and this +implies that um if you look at the graph + + align:start position:0% +implies that um if you look at the graph + + + align:start position:0% +implies that um if you look at the graph +that has the uh edges has the vertices V + + align:start position:0% +that has the uh edges has the vertices V + + + align:start position:0% +that has the uh edges has the vertices V +together with e star with Edge e then + + align:start position:0% +together with e star with Edge e then + + + align:start position:0% +together with e star with Edge e then +this must contain a + + align:start position:0% + + + + align:start position:0% + +cycle now this property I will not prove + + align:start position:0% +cycle now this property I will not prove + + + align:start position:0% +cycle now this property I will not prove +right now but it is pretty + + align:start position:0% +right now but it is pretty + + + align:start position:0% +right now but it is pretty +straightforward it's a on line proof + + align:start position:0% +straightforward it's a on line proof + + + align:start position:0% +straightforward it's a on line proof +actually in the book so you can look it + + align:start position:0% +actually in the book so you can look it + + + align:start position:0% +actually in the book so you can look it +up so it simply states that if you have + + align:start position:0% +up so it simply states that if you have + + + align:start position:0% +up so it simply states that if you have +a tree if we add another Edge an edge + + align:start position:0% +a tree if we add another Edge an edge + + + align:start position:0% +a tree if we add another Edge an edge +that is not contained in E then we will + + align:start position:0% +that is not contained in E then we will + + + align:start position:0% +that is not contained in E then we will +create a + + align:start position:0% +create a + + + align:start position:0% +create a +cycle ah so now we can combine these two + + align:start position:0% +cycle ah so now we can combine these two + + + align:start position:0% +cycle ah so now we can combine these two +statements together and conclude that + + align:start position:0% +statements together and conclude that + + + align:start position:0% +statements together and conclude that +um well if s with e has no cycle but e + + align:start position:0% +um well if s with e has no cycle but e + + + align:start position:0% +um well if s with e has no cycle but e +star with e has a cycle and S is + + align:start position:0% +star with e has a cycle and S is + + + align:start position:0% +star with e has a cycle and S is +contained in E star well there's only + + align:start position:0% +contained in E star well there's only + + + align:start position:0% +contained in E star well there's only +one possibility and that is that uh this + + align:start position:0% +one possibility and that is that uh this + + + align:start position:0% +one possibility and that is that uh this +cycle uh must have an + + align:start position:0% + + + + align:start position:0% + +edge e Prime that is in e starus + + align:start position:0% +edge e Prime that is in e starus + + + align:start position:0% +edge e Prime that is in e starus +s because if it would not have such an + + align:start position:0% +s because if it would not have such an + + + align:start position:0% +s because if it would not have such an +edge then all the edges of the cycle + + align:start position:0% +edge then all the edges of the cycle + + + align:start position:0% +edge then all the edges of the cycle +must be located in s but uh in in s + + align:start position:0% +must be located in s but uh in in s + + + align:start position:0% +must be located in s but uh in in s +together with e but s together with e + + align:start position:0% +together with e but s together with e + + + align:start position:0% +together with e but s together with e +has no cycle so that's not possible so + + align:start position:0% +has no cycle so that's not possible so + + + align:start position:0% +has no cycle so that's not possible so +this cycle must have an hge e Prime that + + align:start position:0% +this cycle must have an hge e Prime that + + + align:start position:0% +this cycle must have an hge e Prime that +is outside s but still in E star so we + + align:start position:0% +is outside s but still in E star so we + + + align:start position:0% +is outside s but still in E star so we +can find one over + + align:start position:0% +can find one over + + + align:start position:0% +can find one over +here e Prime can be this particular Edge + + align:start position:0% +here e Prime can be this particular Edge + + + align:start position:0% +here e Prime can be this particular Edge +so so e Prime is in + + align:start position:0% +so so e Prime is in + + + align:start position:0% +so so e Prime is in +e but it is not already selected in + + align:start position:0% +e but it is not already selected in + + + align:start position:0% +e but it is not already selected in +s okay so now we are going to do a + + align:start position:0% +s okay so now we are going to do a + + + align:start position:0% +s okay so now we are going to do a +trick um the idea is to uh swap e and e + + align:start position:0% +trick um the idea is to uh swap e and e + + + align:start position:0% +trick um the idea is to uh swap e and e +Prime so that's the main ID so let's uh + + align:start position:0% +Prime so that's the main ID so let's uh + + + align:start position:0% +Prime so that's the main ID so let's uh +first write down what we know about the + + align:start position:0% +first write down what we know about the + + + align:start position:0% +first write down what we know about the +weight of e Prime and + + align:start position:0% +weight of e Prime and + + + align:start position:0% +weight of e Prime and +E so since the algorithm + + align:start position:0% + + + + align:start position:0% + +uh well could have + + align:start position:0% + + + + align:start position:0% + +selected uh e or E prime it did select e + + align:start position:0% +selected uh e or E prime it did select e + + + align:start position:0% +selected uh e or E prime it did select e +right but it could have also selected e + + align:start position:0% +right but it could have also selected e + + + align:start position:0% +right but it could have also selected e +Prime because e Prime um you know does + + align:start position:0% +Prime because e Prime um you know does + + + align:start position:0% +Prime because e Prime um you know does +not create a cycle with s that's what we + + align:start position:0% +not create a cycle with s that's what we + + + align:start position:0% +not create a cycle with s that's what we +uh have seen here + + align:start position:0% +uh have seen here + + + align:start position:0% +uh have seen here +so this really implies therefore that + + align:start position:0% +so this really implies therefore that + + + align:start position:0% +so this really implies therefore that +the weight + + align:start position:0% +the weight + + + align:start position:0% +the weight +of E is at + + align:start position:0% +of E is at + + + align:start position:0% +of E is at +most the + + align:start position:0% +most the + + + align:start position:0% +most the +weight of e + + align:start position:0% +weight of e + + + align:start position:0% +weight of e +Prime so why is this because the + + align:start position:0% +Prime so why is this because the + + + align:start position:0% +Prime so why is this because the +algorithm always chooses the minimum + + align:start position:0% +algorithm always chooses the minimum + + + align:start position:0% +algorithm always chooses the minimum +weight and it can choose between e or E + + align:start position:0% +weight and it can choose between e or E + + + align:start position:0% +weight and it can choose between e or E +Prime but it CHS e so the weight of e + + align:start position:0% +Prime but it CHS e so the weight of e + + + align:start position:0% +Prime but it CHS e so the weight of e +must be less than the weight of e Prime + + align:start position:0% +must be less than the weight of e Prime + + + align:start position:0% +must be less than the weight of e Prime +so that's what we know also so now let's + + align:start position:0% +so that's what we know also so now let's + + + align:start position:0% +so that's what we know also so now let's +swap uh e and e Prime in T and then + + align:start position:0% +swap uh e and e Prime in T and then + + + align:start position:0% +swap uh e and e Prime in T and then +we're almost done with this proof + + align:start position:0% +we're almost done with this proof + + + align:start position:0% +we're almost done with this proof +because + + align:start position:0% +because + + + align:start position:0% +because +um that will be the tree of which we + + align:start position:0% +um that will be the tree of which we + + + align:start position:0% +um that will be the tree of which we +will prove that it is a minimum spanning + + align:start position:0% + + + + align:start position:0% + +tree okay so the key idea is to + + align:start position:0% +tree okay so the key idea is to + + + align:start position:0% +tree okay so the key idea is to +swap e and e + + align:start position:0% +swap e and e + + + align:start position:0% +swap e and e +Prime in + + align:start position:0% +Prime in + + + align:start position:0% +Prime in +t how do we do it so well let t dou star + + align:start position:0% +t how do we do it so well let t dou star + + + align:start position:0% +t how do we do it so well let t dou star +be equal to V with the edge + + align:start position:0% +be equal to V with the edge + + + align:start position:0% +be equal to V with the edge +set e double star where e double star is + + align:start position:0% +set e double star where e double star is + + + align:start position:0% +set e double star where e double star is +really equal to well the original set e + + align:start position:0% +really equal to well the original set e + + + align:start position:0% +really equal to well the original set e +star but we take out of this e Prime so + + align:start position:0% +star but we take out of this e Prime so + + + align:start position:0% +star but we take out of this e Prime so +this one is taken out of the minimum + + align:start position:0% +this one is taken out of the minimum + + + align:start position:0% +this one is taken out of the minimum +spanning tree and we add e in here in + + align:start position:0% + + + + align:start position:0% + +here now we want to prove that this + + align:start position:0% +here now we want to prove that this + + + align:start position:0% +here now we want to prove that this +particular t double star is a minimum + + align:start position:0% +particular t double star is a minimum + + + align:start position:0% +particular t double star is a minimum +spanning tree that fits our + + align:start position:0% +spanning tree that fits our + + + align:start position:0% +spanning tree that fits our +Lama so uh what do we know we know that + + align:start position:0% +Lama so uh what do we know we know that + + + align:start position:0% +Lama so uh what do we know we know that +t double star is a + + align:start position:0% + + + + align:start position:0% + +cyclic uh and why is this well we + + align:start position:0% +cyclic uh and why is this well we + + + align:start position:0% +cyclic uh and why is this well we +actually + + align:start position:0% +actually + + + align:start position:0% +actually +uh we actually removed e Prime + + align:start position:0% +uh we actually removed e Prime + + + align:start position:0% +uh we actually removed e Prime +from the only cycle so so look up here + + align:start position:0% +from the only cycle so so look up here + + + align:start position:0% +from the only cycle so so look up here +also the only + + align:start position:0% +also the only + + + align:start position:0% +also the only +cycle in uh e star together with + + align:start position:0% +cycle in uh e star together with + + + align:start position:0% +cycle in uh e star together with +e so it's ay it's a + + align:start position:0% +e so it's ay it's a + + + align:start position:0% +e so it's ay it's a +cyclic t double star is also + + align:start position:0% +cyclic t double star is also + + + align:start position:0% +cyclic t double star is also +connected and why is that + + align:start position:0% +connected and why is that + + + align:start position:0% +connected and why is that +well since e Prime is removed but it was + + align:start position:0% +well since e Prime is removed but it was + + + align:start position:0% +well since e Prime is removed but it was +on a cycle so it remains connected + + align:start position:0% + + + + align:start position:0% + +and finally we also know that t double + + align:start position:0% +and finally we also know that t double + + + align:start position:0% +and finally we also know that t double +star actually + + align:start position:0% +star actually + + + align:start position:0% +star actually +contains + + align:start position:0% +contains + + + align:start position:0% +contains +all the + + align:start position:0% + + + + align:start position:0% + +feres in G so all these three together + + align:start position:0% +feres in G so all these three together + + + align:start position:0% +feres in G so all these three together +will prove us that t double star is a + + align:start position:0% +will prove us that t double star is a + + + align:start position:0% +will prove us that t double star is a +spinning + + align:start position:0% +spinning + + + align:start position:0% +spinning +tree of G because it's a cyclic + + align:start position:0% +tree of G because it's a cyclic + + + align:start position:0% +tree of G because it's a cyclic +connected contains all the vertices is + + align:start position:0% +connected contains all the vertices is + + + align:start position:0% +connected contains all the vertices is +it the minimum weight spanning + + align:start position:0% +it the minimum weight spanning + + + align:start position:0% +it the minimum weight spanning +tree now we are really almost done + + align:start position:0% +tree now we are really almost done + + + align:start position:0% +tree now we are really almost done +because uh let me write it out here we + + align:start position:0% +because uh let me write it out here we + + + align:start position:0% +because uh let me write it out here we +know that the + + align:start position:0% +know that the + + + align:start position:0% +know that the +weight of t double star is at most the + + align:start position:0% +weight of t double star is at most the + + + align:start position:0% +weight of t double star is at most the +weight of T star why is this well we + + align:start position:0% +weight of T star why is this well we + + + align:start position:0% +weight of T star why is this well we +showed just now uh that the weight of E + + align:start position:0% +showed just now uh that the weight of E + + + align:start position:0% +showed just now uh that the weight of E +is at most the weight of e Prime so we + + align:start position:0% +is at most the weight of e Prime so we + + + align:start position:0% +is at most the weight of e Prime so we +have exchanged e and e Prime so that + + align:start position:0% +have exchanged e and e Prime so that + + + align:start position:0% +have exchanged e and e Prime so that +means that the weight of t double star + + align:start position:0% +means that the weight of t double star + + + align:start position:0% +means that the weight of t double star +is at most that of the weight of T star + + align:start position:0% +is at most that of the weight of T star + + + align:start position:0% +is at most that of the weight of T star +we also know that t double the T + + align:start position:0% +we also know that t double the T + + + align:start position:0% +we also know that t double the T +star is a minimum spanning tree so if we + + align:start position:0% +star is a minimum spanning tree so if we + + + align:start position:0% +star is a minimum spanning tree so if we +combine these two + + align:start position:0% +combine these two + + + align:start position:0% +combine these two +together uh then we know that the weight + + align:start position:0% +together uh then we know that the weight + + + align:start position:0% +together uh then we know that the weight +of tar cannot get less than the minimum + + align:start position:0% +of tar cannot get less than the minimum + + + align:start position:0% +of tar cannot get less than the minimum +weight possibility so it is it it also + + align:start position:0% +weight possibility so it is it it also + + + align:start position:0% +weight possibility so it is it it also +has minimum weight right so t double + + align:start position:0% +has minimum weight right so t double + + + align:start position:0% +has minimum weight right so t double +star is a minimum spanning tree ah so + + align:start position:0% +star is a minimum spanning tree ah so + + + align:start position:0% +star is a minimum spanning tree ah so +now we're done because in this case we + + align:start position:0% +now we're done because in this case we + + + align:start position:0% +now we're done because in this case we +have constructed a t uh double star such + + align:start position:0% +have constructed a t uh double star such + + + align:start position:0% +have constructed a t uh double star such +that s together with e is a subset of e + + align:start position:0% +that s together with e is a subset of e + + + align:start position:0% +that s together with e is a subset of e +double star and that means that we have + + align:start position:0% +double star and that means that we have + + + align:start position:0% +double star and that means that we have +shown that + + align:start position:0% +shown that + + + align:start position:0% +shown that +our um induction step is is true we have + + align:start position:0% +our um induction step is is true we have + + + align:start position:0% +our um induction step is is true we have +shown that PN plus one holds so now we + + align:start position:0% +shown that PN plus one holds so now we + + + align:start position:0% +shown that PN plus one holds so now we +finally have figured out that the LMA is + + align:start position:0% +finally have figured out that the LMA is + + + align:start position:0% +finally have figured out that the LMA is +true and now we can and and we showed + + align:start position:0% +true and now we can and and we showed + + + align:start position:0% +true and now we can and and we showed +already that how to use this LMA in our + + align:start position:0% +already that how to use this LMA in our + + + align:start position:0% +already that how to use this LMA in our +proof uh in our proof for for this + + align:start position:0% +proof uh in our proof for for this + + + align:start position:0% +proof uh in our proof for for this +particular + + align:start position:0% +particular + + + align:start position:0% +particular +theorem so this is uh uh the end of this + + align:start position:0% +theorem so this is uh uh the end of this + + + align:start position:0% +theorem so this is uh uh the end of this +lecture and to and tomorrow you will + + align:start position:0% +lecture and to and tomorrow you will + + + align:start position:0% +lecture and to and tomorrow you will +actually go again over this proof + + align:start position:0% +actually go again over this proof + + + align:start position:0% +actually go again over this proof +because it's rather complex and then uh + + align:start position:0% +because it's rather complex and then uh + + + align:start position:0% +because it's rather complex and then uh +hopefully you really get into all the + + align:start position:0% +hopefully you really get into all the + + + align:start position:0% +hopefully you really get into all the +different proof techniques okay thank + + align:start position:0% +different proof techniques okay thank + + + align:start position:0% +different proof techniques okay thank +you \ No newline at end of file diff --git a/Gxefx9BDCq0.txt b/Gxefx9BDCq0.txt new file mode 100644 index 0000000000000000000000000000000000000000..14f8b8f615e80bc14fdb46e522458bc358d7a9cd --- /dev/null +++ b/Gxefx9BDCq0.txt @@ -0,0 +1,3315 @@ +align:start position:0% + +so now let's add to our theory + + align:start position:0% +so now let's add to our theory + + + align:start position:0% +so now let's add to our theory +ways in which droplets can be removed or + + align:start position:0% +ways in which droplets can be removed or + + + align:start position:0% +ways in which droplets can be removed or +infectious virions can be removed within + + align:start position:0% +infectious virions can be removed within + + + align:start position:0% +infectious virions can be removed within +the room + + align:start position:0% +the room + + + align:start position:0% +the room +in addition to ventilation and + + align:start position:0% +in addition to ventilation and + + + align:start position:0% +in addition to ventilation and +filtration effects that we've already + + align:start position:0% +filtration effects that we've already + + + align:start position:0% +filtration effects that we've already +described + + align:start position:0% +described + + + align:start position:0% +described +so the primary way that can occur is + + align:start position:0% +so the primary way that can occur is + + + align:start position:0% +so the primary way that can occur is +simply by settling of the droplets so + + align:start position:0% +simply by settling of the droplets so + + + align:start position:0% +simply by settling of the droplets so +we've already talked about the stoke's + + align:start position:0% +we've already talked about the stoke's + + + align:start position:0% +we've already talked about the stoke's +settling speed which scales as the + + align:start position:0% +settling speed which scales as the + + + align:start position:0% +settling speed which scales as the +radius of the droplets squared so + + align:start position:0% +radius of the droplets squared so + + + align:start position:0% +radius of the droplets squared so +basically larger droplets fall + + align:start position:0% +basically larger droplets fall + + + align:start position:0% +basically larger droplets fall +fairly quickly and in fact we've already + + align:start position:0% +fairly quickly and in fact we've already + + + align:start position:0% +fairly quickly and in fact we've already +discussed how they can + + align:start position:0% +discussed how they can + + + align:start position:0% +discussed how they can +fall to the ground in a fairly short + + align:start position:0% +fall to the ground in a fairly short + + + align:start position:0% +fall to the ground in a fairly short +time it could be on the order of + + align:start position:0% +time it could be on the order of + + + align:start position:0% +time it could be on the order of +minutes or less for large droplets + + align:start position:0% +minutes or less for large droplets + + + align:start position:0% +minutes or less for large droplets +such as those which are spewing out of + + align:start position:0% +such as those which are spewing out of + + + align:start position:0% +such as those which are spewing out of +your + + align:start position:0% +your + + + align:start position:0% +your +throat when you cough or when you sneeze + + align:start position:0% +throat when you cough or when you sneeze + + + align:start position:0% +throat when you cough or when you sneeze +out of your nose + + align:start position:0% +out of your nose + + + align:start position:0% +out of your nose +but also the smaller aerosol droplets + + align:start position:0% +but also the smaller aerosol droplets + + + align:start position:0% +but also the smaller aerosol droplets +that we've already calculated + + align:start position:0% +that we've already calculated + + + align:start position:0% +that we've already calculated +can stay in the air for a very long time + + align:start position:0% +can stay in the air for a very long time + + + align:start position:0% +can stay in the air for a very long time +so they settle much more solely but they + + align:start position:0% +so they settle much more solely but they + + + align:start position:0% +so they settle much more solely but they +do still settle + + align:start position:0% +do still settle + + + align:start position:0% +do still settle +so we can try to see how this enters in + + align:start position:0% +so we can try to see how this enters in + + + align:start position:0% +so we can try to see how this enters in +and the second topic is also + + align:start position:0% +and the second topic is also + + + align:start position:0% +and the second topic is also +deactivation we've mentioned that the + + align:start position:0% +deactivation we've mentioned that the + + + align:start position:0% +deactivation we've mentioned that the +virus doesn't live forever so the + + align:start position:0% +virus doesn't live forever so the + + + align:start position:0% +virus doesn't live forever so the +virions in these droplets + + align:start position:0% +virions in these droplets + + + align:start position:0% +virions in these droplets +do need to find a target and + + align:start position:0% +do need to find a target and + + + align:start position:0% +do need to find a target and +get out of those droplets and into the + + align:start position:0% +get out of those droplets and into the + + + align:start position:0% +get out of those droplets and into the +into some healthy tissue to infect it + + align:start position:0% +into some healthy tissue to infect it + + + align:start position:0% +into some healthy tissue to infect it +uh within a certain period of time so + + align:start position:0% +uh within a certain period of time so + + + align:start position:0% +uh within a certain period of time so +there's a notion of a viral + + align:start position:0% +there's a notion of a viral + + + align:start position:0% +there's a notion of a viral +deactivation rate which can also be a + + align:start position:0% +deactivation rate which can also be a + + + align:start position:0% +deactivation rate which can also be a +parameter in our models + + align:start position:0% +parameter in our models + + + align:start position:0% +parameter in our models +so if we now add those two effects to + + align:start position:0% +so if we now add those two effects to + + + align:start position:0% +so if we now add those two effects to +our existing model i'll just keep + + align:start position:0% +our existing model i'll just keep + + + align:start position:0% +our existing model i'll just keep +rewriting our mass balance equation + + align:start position:0% +rewriting our mass balance equation + + + align:start position:0% +rewriting our mass balance equation +uh and this is uh the mass balance for + + align:start position:0% +uh and this is uh the mass balance for + + + align:start position:0% +uh and this is uh the mass balance for +the concentration of virions in the air + + align:start position:0% +the concentration of virions in the air + + + align:start position:0% +the concentration of virions in the air +i've also used the terminology in + + align:start position:0% +i've also used the terminology in + + + align:start position:0% +i've also used the terminology in +chemical engineering we're going to call + + align:start position:0% +chemical engineering we're going to call + + + align:start position:0% +chemical engineering we're going to call +this kind of approximation the cstr + + align:start position:0% +this kind of approximation the cstr + + + align:start position:0% +this kind of approximation the cstr +or the continuously stirred tank reactor + + align:start position:0% +or the continuously stirred tank reactor + + + align:start position:0% +or the continuously stirred tank reactor +approximation and now with all the + + align:start position:0% +approximation and now with all the + + + align:start position:0% +approximation and now with all the +effects we're including it's starting to + + align:start position:0% +effects we're including it's starting to + + + align:start position:0% +effects we're including it's starting to +look more like actual modeling of + + align:start position:0% +look more like actual modeling of + + + align:start position:0% +look more like actual modeling of +chemical reactors in chemical plants + + align:start position:0% +chemical reactors in chemical plants + + + align:start position:0% +chemical reactors in chemical plants +by this method so the mass balance tells + + align:start position:0% +by this method so the mass balance tells + + + align:start position:0% +by this method so the mass balance tells +me that the volume of the room + + align:start position:0% +me that the volume of the room + + + align:start position:0% +me that the volume of the room +times dc dt where again c is the vary on + + align:start position:0% +times dc dt where again c is the vary on + + + align:start position:0% +times dc dt where again c is the vary on +concentration per volume in the air + + align:start position:0% +concentration per volume in the air + + + align:start position:0% +concentration per volume in the air +is the production rate p minus and then + + align:start position:0% +is the production rate p minus and then + + + align:start position:0% +is the production rate p minus and then +we have a flux which is a flow rate + + align:start position:0% +we have a flux which is a flow rate + + + align:start position:0% +we have a flux which is a flow rate +times a concentration + + align:start position:0% +times a concentration + + + align:start position:0% +times a concentration +and there are several flow rates here + + align:start position:0% +and there are several flow rates here + + + align:start position:0% +and there are several flow rates here +there's q there's the + + align:start position:0% +there's q there's the + + + align:start position:0% +there's q there's the +which is ventilation there is filtration + + align:start position:0% +which is ventilation there is filtration + + + align:start position:0% +which is ventilation there is filtration +which is p + + align:start position:0% +which is p + + + align:start position:0% +which is p +f q f and then we have now + + align:start position:0% +f q f and then we have now + + + align:start position:0% +f q f and then we have now +a new term which i'll write in another + + align:start position:0% +a new term which i'll write in another + + + align:start position:0% +a new term which i'll write in another +color + + align:start position:0% +color + + + align:start position:0% +color +plus vs + + align:start position:0% +plus vs + + + align:start position:0% +plus vs +a so that's the settling here + + align:start position:0% +a so that's the settling here + + + align:start position:0% +a so that's the settling here +so that is in a well-mixed room there's + + align:start position:0% +so that is in a well-mixed room there's + + + align:start position:0% +so that is in a well-mixed room there's +a complex flow profile which is leading + + align:start position:0% +a complex flow profile which is leading + + + align:start position:0% +a complex flow profile which is leading +to the mixing by by convection of the + + align:start position:0% +to the mixing by by convection of the + + + align:start position:0% +to the mixing by by convection of the +air + + align:start position:0% +air + + + align:start position:0% +air +and you might say well okay that flow is + + align:start position:0% +and you might say well okay that flow is + + + align:start position:0% +and you might say well okay that flow is +sort of very quickly carrying the + + align:start position:0% +sort of very quickly carrying the + + + align:start position:0% +sort of very quickly carrying the +particles up + + align:start position:0% +particles up + + + align:start position:0% +particles up +carrying them down but on average the + + align:start position:0% +carrying them down but on average the + + + align:start position:0% +carrying them down but on average the +particles go down just as much as they + + align:start position:0% +particles go down just as much as they + + + align:start position:0% +particles go down just as much as they +go up + + align:start position:0% +go up + + + align:start position:0% +go up +and if it's well mixed then the + + align:start position:0% +and if it's well mixed then the + + + align:start position:0% +and if it's well mixed then the +particles essentially are sampling the + + align:start position:0% +particles essentially are sampling the + + + align:start position:0% +particles essentially are sampling the +whole space + + align:start position:0% +whole space + + + align:start position:0% +whole space +and relative to that well-mixed flow + + align:start position:0% +and relative to that well-mixed flow + + + align:start position:0% +and relative to that well-mixed flow +which kind of averages to zero + + align:start position:0% +which kind of averages to zero + + + align:start position:0% +which kind of averages to zero +they are slowly settling and so a + + align:start position:0% +they are slowly settling and so a + + + align:start position:0% +they are slowly settling and so a +reasonable approximation is to say well + + align:start position:0% +reasonable approximation is to say well + + + align:start position:0% +reasonable approximation is to say well +the removal is basically + + align:start position:0% +the removal is basically + + + align:start position:0% +the removal is basically +happening with a flux rate which is that + + align:start position:0% +happening with a flux rate which is that + + + align:start position:0% +happening with a flux rate which is that +velocity of falling + + align:start position:0% +velocity of falling + + + align:start position:0% +velocity of falling +times the area that's how quickly sort + + align:start position:0% +times the area that's how quickly sort + + + align:start position:0% +times the area that's how quickly sort +of those particles are kind of falling + + align:start position:0% +of those particles are kind of falling + + + align:start position:0% +of those particles are kind of falling +through any horizontal surface you make + + align:start position:0% +through any horizontal surface you make + + + align:start position:0% +through any horizontal surface you make +relative to their kind of average zero + + align:start position:0% +relative to their kind of average zero + + + align:start position:0% +relative to their kind of average zero +motion + + align:start position:0% +motion + + + align:start position:0% +motion +from convective mixing okay so that's + + align:start position:0% +from convective mixing okay so that's + + + align:start position:0% +from convective mixing okay so that's +this is the new effect of sedimentation + + align:start position:0% + + + + align:start position:0% + +and then actually i will also add to + + align:start position:0% +and then actually i will also add to + + + align:start position:0% +and then actually i will also add to +that + + align:start position:0% +that + + + align:start position:0% +that +another new term which is the + + align:start position:0% +another new term which is the + + + align:start position:0% +another new term which is the +deactivation and so here we will also + + align:start position:0% +deactivation and so here we will also + + + align:start position:0% +deactivation and so here we will also +add + + align:start position:0% +add + + + align:start position:0% +add +lambda v times the volume so this is + + align:start position:0% +lambda v times the volume so this is + + + align:start position:0% +lambda v times the volume so this is +just saying that + + align:start position:0% +just saying that + + + align:start position:0% +just saying that +throughout the whole volume of the room + + align:start position:0% +throughout the whole volume of the room + + + align:start position:0% +throughout the whole volume of the room +there is a rate at which every virion is + + align:start position:0% +there is a rate at which every virion is + + + align:start position:0% +there is a rate at which every virion is +just slowly deactivating + + align:start position:0% +just slowly deactivating + + + align:start position:0% +just slowly deactivating +that'll be lambda v also if you have any + + align:start position:0% +that'll be lambda v also if you have any + + + align:start position:0% +that'll be lambda v also if you have any +volumetric + + align:start position:0% +volumetric + + + align:start position:0% +volumetric +treatments of the error such as chemical + + align:start position:0% +treatments of the error such as chemical + + + align:start position:0% +treatments of the error such as chemical +disinfectants + + align:start position:0% +disinfectants + + + align:start position:0% +disinfectants +or even uv light that may also + + align:start position:0% +or even uv light that may also + + + align:start position:0% +or even uv light that may also +slowly kill the bacteria or us excuse me + + align:start position:0% +slowly kill the bacteria or us excuse me + + + align:start position:0% +slowly kill the bacteria or us excuse me +deactivate the virus or the virions + + align:start position:0% +deactivate the virus or the virions + + + align:start position:0% +deactivate the virus or the virions +in the air with a term that goes like + + align:start position:0% +in the air with a term that goes like + + + align:start position:0% +in the air with a term that goes like +this so i'll just mention + + align:start position:0% +this so i'll just mention + + + align:start position:0% +this so i'll just mention +that maybe briefly here so lambda v + + align:start position:0% +that maybe briefly here so lambda v + + + align:start position:0% +that maybe briefly here so lambda v +is the virion deactivation rate + + align:start position:0% + + + + align:start position:0% + +and well if we look at + + align:start position:0% +and well if we look at + + + align:start position:0% +and well if we look at +tv which we've talked about before which + + align:start position:0% +tv which we've talked about before which + + + align:start position:0% +tv which we've talked about before which +is lambda v inverse + + align:start position:0% +is lambda v inverse + + + align:start position:0% +is lambda v inverse +this is the deactivation time + + align:start position:0% + + + + align:start position:0% + +this thing has been measured to be of + + align:start position:0% +this thing has been measured to be of + + + align:start position:0% +this thing has been measured to be of +order one hour + + align:start position:0% +order one hour + + + align:start position:0% +order one hour +in some studies but also even greater + + align:start position:0% +in some studies but also even greater + + + align:start position:0% +in some studies but also even greater +than 16 hours in aerosol form + + align:start position:0% +than 16 hours in aerosol form + + + align:start position:0% +than 16 hours in aerosol form +in other studies for sars cove 2. so + + align:start position:0% +in other studies for sars cove 2. so + + + align:start position:0% +in other studies for sars cove 2. so +it could be potentially long + + align:start position:0% + + + + align:start position:0% + +also what this could include + + align:start position:0% +also what this could include + + + align:start position:0% +also what this could include +effects such as i mentioned uv light + + align:start position:0% +effects such as i mentioned uv light + + + align:start position:0% +effects such as i mentioned uv light +treatments which might be sort of + + align:start position:0% +treatments which might be sort of + + + align:start position:0% +treatments which might be sort of +operating in a certain part of the room + + align:start position:0% +operating in a certain part of the room + + + align:start position:0% +operating in a certain part of the room +but then the air kind of circulates and + + align:start position:0% +but then the air kind of circulates and + + + align:start position:0% +but then the air kind of circulates and +we're essentially + + align:start position:0% +we're essentially + + + align:start position:0% +we're essentially +treating treating a significant part of + + align:start position:0% +treating treating a significant part of + + + align:start position:0% +treating treating a significant part of +the volume + + align:start position:0% +the volume + + + align:start position:0% +the volume +it could also be chemical disinfectants + + align:start position:0% + + + + align:start position:0% + +so there are various chemicals that can + + align:start position:0% +so there are various chemicals that can + + + align:start position:0% +so there are various chemicals that can +be sprayed in the air which are believed + + align:start position:0% +be sprayed in the air which are believed + + + align:start position:0% +be sprayed in the air which are believed +to + + align:start position:0% +to + + + align:start position:0% +to +essentially kill the virus or deactivate + + align:start position:0% +essentially kill the virus or deactivate + + + align:start position:0% +essentially kill the virus or deactivate +the virions although they may cause + + align:start position:0% +the virions although they may cause + + + align:start position:0% +the virions although they may cause +other harmful + + align:start position:0% +other harmful + + + align:start position:0% +other harmful +effects and so it's not so widely used + + align:start position:0% +effects and so it's not so widely used + + + align:start position:0% +effects and so it's not so widely used +but in principle that would also appear + + align:start position:0% +but in principle that would also appear + + + align:start position:0% +but in principle that would also appear +in our simple model + + align:start position:0% +in our simple model + + + align:start position:0% +in our simple model +lumped into land of e so let's put all + + align:start position:0% +lumped into land of e so let's put all + + + align:start position:0% +lumped into land of e so let's put all +these effects together now so again we + + align:start position:0% +these effects together now so again we + + + align:start position:0% +these effects together now so again we +haven't really changed the calculation + + align:start position:0% +haven't really changed the calculation + + + align:start position:0% +haven't really changed the calculation +much we're just building it up and + + align:start position:0% +much we're just building it up and + + + align:start position:0% +much we're just building it up and +making it a little more complicated each + + align:start position:0% +making it a little more complicated each + + + align:start position:0% +making it a little more complicated each +time + + align:start position:0% +time + + + align:start position:0% +time +okay so let's see here so one thing we + + align:start position:0% +okay so let's see here so one thing we + + + align:start position:0% +okay so let's see here so one thing we +did with this equation we divided both + + align:start position:0% +did with this equation we divided both + + + align:start position:0% +did with this equation we divided both +sides by + + align:start position:0% +sides by + + + align:start position:0% +sides by +v and so let me write this equation + + align:start position:0% +v and so let me write this equation + + + align:start position:0% +v and so let me write this equation +again + + align:start position:0% +again + + + align:start position:0% +again +after such a division that would be dc + + align:start position:0% +after such a division that would be dc + + + align:start position:0% +after such a division that would be dc +dt + + align:start position:0% +dt + + + align:start position:0% +dt +is equal to well there's a p + + align:start position:0% +is equal to well there's a p + + + align:start position:0% +is equal to well there's a p +over v + + align:start position:0% + + + + align:start position:0% + +but then we have over here uh what we ha + + align:start position:0% +but then we have over here uh what we ha + + + align:start position:0% +but then we have over here uh what we ha +a q over v + + align:start position:0% +a q over v + + + align:start position:0% +a q over v +is is our is our lambda but notice all + + align:start position:0% +is is our is our lambda but notice all + + + align:start position:0% +is is our is our lambda but notice all +these things are essentially giving us a + + align:start position:0% +these things are essentially giving us a + + + align:start position:0% +these things are essentially giving us a +correction + + align:start position:0% +correction + + + align:start position:0% +correction +to lambda the relaxation time and + + align:start position:0% +to lambda the relaxation time and + + + align:start position:0% +to lambda the relaxation time and +actually i should say this is a minus + + align:start position:0% +actually i should say this is a minus + + + align:start position:0% +actually i should say this is a minus +sign + + align:start position:0% +sign + + + align:start position:0% +sign +so we get minus lambda and i'll say + + align:start position:0% +so we get minus lambda and i'll say + + + align:start position:0% +so we get minus lambda and i'll say +lambda c + + align:start position:0% +lambda c + + + align:start position:0% +lambda c +just for the relaxation rate of the + + align:start position:0% +just for the relaxation rate of the + + + align:start position:0% +just for the relaxation rate of the +concentration field + + align:start position:0% +concentration field + + + align:start position:0% +concentration field +so we can lump all these parameters and + + align:start position:0% +so we can lump all these parameters and + + + align:start position:0% +so we can lump all these parameters and +we can write + + align:start position:0% +we can write + + + align:start position:0% +we can write +lambda c is + + align:start position:0% +lambda c is + + + align:start position:0% +lambda c is +well from the first one q or v is lambda + + align:start position:0% +well from the first one q or v is lambda + + + align:start position:0% +well from the first one q or v is lambda +a that's the air change rate of outdoor + + align:start position:0% +a that's the air change rate of outdoor + + + align:start position:0% +a that's the air change rate of outdoor +fresh air + + align:start position:0% +fresh air + + + align:start position:0% +fresh air +there is p f lambda f which is the + + align:start position:0% +there is p f lambda f which is the + + + align:start position:0% +there is p f lambda f which is the +rate of filtration times the mass + + align:start position:0% +rate of filtration times the mass + + + align:start position:0% +rate of filtration times the mass +filtration or the + + align:start position:0% +filtration or the + + + align:start position:0% +filtration or the +filter filtration efficiency pf + + align:start position:0% +filter filtration efficiency pf + + + align:start position:0% +filter filtration efficiency pf +and then we have another term which we + + align:start position:0% +and then we have another term which we + + + align:start position:0% +and then we have another term which we +can write as + + align:start position:0% +can write as + + + align:start position:0% +can write as +we have lambda v that's an easy one and + + align:start position:0% +we have lambda v that's an easy one and + + + align:start position:0% +we have lambda v that's an easy one and +then the sedimentation term is the one i + + align:start position:0% +then the sedimentation term is the one i + + + align:start position:0% +then the sedimentation term is the one i +want to focus on right now + + align:start position:0% +want to focus on right now + + + align:start position:0% +want to focus on right now +that is vs we can write as vs + + align:start position:0% +that is vs we can write as vs + + + align:start position:0% +that is vs we can write as vs +over h where i've divided by v + + align:start position:0% +over h where i've divided by v + + + align:start position:0% +over h where i've divided by v +and i'm writing v over a as h so i'm + + align:start position:0% +and i'm writing v over a as h so i'm + + + align:start position:0% +and i'm writing v over a as h so i'm +writing + + align:start position:0% +writing + + + align:start position:0% +writing +h equals v over a so if we have a + + align:start position:0% +h equals v over a so if we have a + + + align:start position:0% +h equals v over a so if we have a +rectangular box of a room + + align:start position:0% +rectangular box of a room + + + align:start position:0% +rectangular box of a room +then h is the ceiling height but this is + + align:start position:0% +then h is the ceiling height but this is + + + align:start position:0% +then h is the ceiling height but this is +some kind of effective + + align:start position:0% +some kind of effective + + + align:start position:0% +some kind of effective +ceiling height if it's not a perfect + + align:start position:0% +ceiling height if it's not a perfect + + + align:start position:0% +ceiling height if it's not a perfect +box shape + + align:start position:0% + + + + align:start position:0% + +but if you take the volume and divide by + + align:start position:0% +but if you take the volume and divide by + + + align:start position:0% +but if you take the volume and divide by +sort of the projected area + + align:start position:0% +sort of the projected area + + + align:start position:0% +sort of the projected area +of horizontal surfaces then that's + + align:start position:0% +of horizontal surfaces then that's + + + align:start position:0% +of horizontal surfaces then that's +giving you a sense of the typical height + + align:start position:0% +giving you a sense of the typical height + + + align:start position:0% +giving you a sense of the typical height +and that's the typical distance by which + + align:start position:0% +and that's the typical distance by which + + + align:start position:0% +and that's the typical distance by which +particles have to fall + + align:start position:0% +particles have to fall + + + align:start position:0% +particles have to fall +okay and notice velocity is distance per + + align:start position:0% +okay and notice velocity is distance per + + + align:start position:0% +okay and notice velocity is distance per +time so when i do vs and divide by h i + + align:start position:0% +time so when i do vs and divide by h i + + + align:start position:0% +time so when i do vs and divide by h i +am getting something with units of + + align:start position:0% +am getting something with units of + + + align:start position:0% +am getting something with units of +inverse time so it's just like all the + + align:start position:0% +inverse time so it's just like all the + + + align:start position:0% +inverse time so it's just like all the +other lamb does it is basically a rate + + align:start position:0% +other lamb does it is basically a rate + + + align:start position:0% +other lamb does it is basically a rate +per something per time okay + + align:start position:0% + + + + align:start position:0% + +so this is the concentration relaxation + + align:start position:0% +so this is the concentration relaxation + + + align:start position:0% +so this is the concentration relaxation +rate + + align:start position:0% + + + + align:start position:0% + +i guess would be the virion + + align:start position:0% +i guess would be the virion + + + align:start position:0% +i guess would be the virion +concentration in the air + + align:start position:0% +concentration in the air + + + align:start position:0% +concentration in the air +which is relaxing at this rate lambda c + + align:start position:0% +which is relaxing at this rate lambda c + + + align:start position:0% +which is relaxing at this rate lambda c +and then we come back to solving the + + align:start position:0% +and then we come back to solving the + + + align:start position:0% +and then we come back to solving the +same simple order differential equation + + align:start position:0% +same simple order differential equation + + + align:start position:0% +same simple order differential equation +that we've done all along + + align:start position:0% +that we've done all along + + + align:start position:0% +that we've done all along +and the solution is just c of t + + align:start position:0% +and the solution is just c of t + + + align:start position:0% +and the solution is just c of t +is a steady state value times 1 minus + + align:start position:0% +is a steady state value times 1 minus + + + align:start position:0% +is a steady state value times 1 minus +e to the minus lambda c t + + align:start position:0% +e to the minus lambda c t + + + align:start position:0% +e to the minus lambda c t +assuming uh that you know these are this + + align:start position:0% +assuming uh that you know these are this + + + align:start position:0% +assuming uh that you know these are this +this thing is a constant for the moment + + align:start position:0% +this thing is a constant for the moment + + + align:start position:0% +this thing is a constant for the moment +and also we know that the cs is + + align:start position:0% +and also we know that the cs is + + + align:start position:0% +and also we know that the cs is +p over v lambda c + + align:start position:0% +p over v lambda c + + + align:start position:0% +p over v lambda c +so basically if lambda c is high if all + + align:start position:0% +so basically if lambda c is high if all + + + align:start position:0% +so basically if lambda c is high if all +these removal rates are high + + align:start position:0% +these removal rates are high + + + align:start position:0% +these removal rates are high +then that makes cs low so the + + align:start position:0% +then that makes cs low so the + + + align:start position:0% +then that makes cs low so the +background concentration in the room is + + align:start position:0% +background concentration in the room is + + + align:start position:0% +background concentration in the room is +much smaller + + align:start position:0% +much smaller + + + align:start position:0% +much smaller +if these lambda rates are all high + + align:start position:0% +if these lambda rates are all high + + + align:start position:0% +if these lambda rates are all high +also if the lambda rates are high then + + align:start position:0% +also if the lambda rates are high then + + + align:start position:0% +also if the lambda rates are high then +the relaxation is very fast so you very + + align:start position:0% +the relaxation is very fast so you very + + + align:start position:0% +the relaxation is very fast so you very +quickly get to the final + + align:start position:0% +quickly get to the final + + + align:start position:0% +quickly get to the final +value and so that's actually worth + + align:start position:0% +value and so that's actually worth + + + align:start position:0% +value and so that's actually worth +sketching what that looks like + + align:start position:0% +sketching what that looks like + + + align:start position:0% +sketching what that looks like +so if i plot what + + align:start position:0% +so if i plot what + + + align:start position:0% +so if i plot what +is the concentration c + + align:start position:0% + + + + align:start position:0% + +as a function of time we have here this + + align:start position:0% +as a function of time we have here this + + + align:start position:0% +as a function of time we have here this +kind of lambda c inverse + + align:start position:0% +kind of lambda c inverse + + + align:start position:0% +kind of lambda c inverse +is the kind of overall concentration + + align:start position:0% +is the kind of overall concentration + + + align:start position:0% +is the kind of overall concentration +relaxation time + + align:start position:0% +relaxation time + + + align:start position:0% +relaxation time +so it looks like an exponential + + align:start position:0% +so it looks like an exponential + + + align:start position:0% +so it looks like an exponential +relaxation to a value cs + + align:start position:0% +relaxation to a value cs + + + align:start position:0% +relaxation to a value cs +but i just want to emphasize what i just + + align:start position:0% +but i just want to emphasize what i just + + + align:start position:0% +but i just want to emphasize what i just +said kind of verbally looking at these + + align:start position:0% +said kind of verbally looking at these + + + align:start position:0% +said kind of verbally looking at these +equations + + align:start position:0% +equations + + + align:start position:0% +equations +is that as i vary lambda c so if i have + + align:start position:0% +is that as i vary lambda c so if i have + + + align:start position:0% +is that as i vary lambda c so if i have +like a fast relaxation let's say lambda + + align:start position:0% +like a fast relaxation let's say lambda + + + align:start position:0% +like a fast relaxation let's say lambda +c is a large value + + align:start position:0% +c is a large value + + + align:start position:0% +c is a large value +then i start out kind of at the same + + align:start position:0% +then i start out kind of at the same + + + align:start position:0% +then i start out kind of at the same +rate but i kind of saturate a lot faster + + align:start position:0% +rate but i kind of saturate a lot faster + + + align:start position:0% +rate but i kind of saturate a lot faster +and at a lower value so if it's here + + align:start position:0% +and at a lower value so if it's here + + + align:start position:0% +and at a lower value so if it's here +this is sort of fast lambda c + + align:start position:0% +this is sort of fast lambda c + + + align:start position:0% +this is sort of fast lambda c +so if i increase lambda c relative to + + align:start position:0% +so if i increase lambda c relative to + + + align:start position:0% +so if i increase lambda c relative to +the blue curve the whole thing comes + + align:start position:0% +the blue curve the whole thing comes + + + align:start position:0% +the blue curve the whole thing comes +down + + align:start position:0% +down + + + align:start position:0% +down +but also relaxes more quickly on the + + align:start position:0% +but also relaxes more quickly on the + + + align:start position:0% +but also relaxes more quickly on the +other hand if i have + + align:start position:0% +other hand if i have + + + align:start position:0% +other hand if i have +slow relaxation because any of these + + align:start position:0% +slow relaxation because any of these + + + align:start position:0% +slow relaxation because any of these +processes here are slow + + align:start position:0% +processes here are slow + + + align:start position:0% +processes here are slow +then i get something which kind of + + align:start position:0% +then i get something which kind of + + + align:start position:0% +then i get something which kind of +relaxes much more slowly and ends up at + + align:start position:0% +relaxes much more slowly and ends up at + + + align:start position:0% +relaxes much more slowly and ends up at +a higher value + + align:start position:0% +a higher value + + + align:start position:0% +a higher value +so if i'm if someone is breathing + + align:start position:0% +so if i'm if someone is breathing + + + align:start position:0% +so if i'm if someone is breathing +infectious air out + + align:start position:0% +infectious air out + + + align:start position:0% +infectious air out +exhaling the infected person and + + align:start position:0% +exhaling the infected person and + + + align:start position:0% +exhaling the infected person and +there's only very slow processes in the + + align:start position:0% +there's only very slow processes in the + + + align:start position:0% +there's only very slow processes in the +room which are removing + + align:start position:0% +room which are removing + + + align:start position:0% +room which are removing +that infectious air then it's slow to + + align:start position:0% +that infectious air then it's slow to + + + align:start position:0% +that infectious air then it's slow to +build up + + align:start position:0% +build up + + + align:start position:0% +build up +but it keeps building and building and + + align:start position:0% +but it keeps building and building and + + + align:start position:0% +but it keeps building and building and +building until it finally saturates so + + align:start position:0% +building until it finally saturates so + + + align:start position:0% +building until it finally saturates so +this is basically + + align:start position:0% +this is basically + + + align:start position:0% +this is basically +whenever lambda c is not a large value + + align:start position:0% +whenever lambda c is not a large value + + + align:start position:0% +whenever lambda c is not a large value +or slower you have a slow process + + align:start position:0% +or slower you have a slow process + + + align:start position:0% +or slower you have a slow process +but it also builds up a lot higher okay + + align:start position:0% +but it also builds up a lot higher okay + + + align:start position:0% +but it also builds up a lot higher okay +so this + + align:start position:0% +so this + + + align:start position:0% +so this +effect of lambda c is very important to + + align:start position:0% +effect of lambda c is very important to + + + align:start position:0% +effect of lambda c is very important to +keep in mind + + align:start position:0% +keep in mind + + + align:start position:0% +keep in mind +especially because these parameters here + + align:start position:0% +especially because these parameters here + + + align:start position:0% +especially because these parameters here +are not necessarily constants in + + align:start position:0% +are not necessarily constants in + + + align:start position:0% +are not necessarily constants in +particular vs has a very strong + + align:start position:0% +particular vs has a very strong + + + align:start position:0% +particular vs has a very strong +dependence on size + + align:start position:0% +dependence on size + + + align:start position:0% +dependence on size +so these different kind of saturation + + align:start position:0% +so these different kind of saturation + + + align:start position:0% +so these different kind of saturation +curves are + + align:start position:0% +curves are + + + align:start position:0% +curves are +at the very least dependent on the size + + align:start position:0% +at the very least dependent on the size + + + align:start position:0% +at the very least dependent on the size +of the droplets that we're talking about + + align:start position:0% +of the droplets that we're talking about + + + align:start position:0% +of the droplets that we're talking about +and there's not just one size so we will + + align:start position:0% +and there's not just one size so we will + + + align:start position:0% +and there's not just one size so we will +come to that point + + align:start position:0% +come to that point + + + align:start position:0% +come to that point +but why don't we um still just think a + + align:start position:0% +but why don't we um still just think a + + + align:start position:0% +but why don't we um still just think a +little bit more about the calculation + + align:start position:0% +little bit more about the calculation + + + align:start position:0% +little bit more about the calculation +that we've done here + + align:start position:0% +that we've done here + + + align:start position:0% +that we've done here +with regard to the sedimenting droplets + + align:start position:0% +with regard to the sedimenting droplets + + + align:start position:0% +with regard to the sedimenting droplets +so + + align:start position:0% +so + + + align:start position:0% +so +let me plug some numbers here into this + + align:start position:0% +let me plug some numbers here into this + + + align:start position:0% +let me plug some numbers here into this +i've already done this earlier and i'll + + align:start position:0% +i've already done this earlier and i'll + + + align:start position:0% +i've already done this earlier and i'll +just remind you + + align:start position:0% +just remind you + + + align:start position:0% +just remind you +that the sedimentation velocity + + align:start position:0% +that the sedimentation velocity + + + align:start position:0% +that the sedimentation velocity +is one millimeter a second for a three m + + align:start position:0% +is one millimeter a second for a three m + + + align:start position:0% +is one millimeter a second for a three m +three micron radius so that kind of + + align:start position:0% +three micron radius so that kind of + + + align:start position:0% +three micron radius so that kind of +gives you a sense + + align:start position:0% +gives you a sense + + + align:start position:0% +gives you a sense +of what these numbers are and the radius + + align:start position:0% +of what these numbers are and the radius + + + align:start position:0% +of what these numbers are and the radius +comes in squared + + align:start position:0% +comes in squared + + + align:start position:0% +comes in squared +so if i take a given radius r if i want + + align:start position:0% +so if i take a given radius r if i want + + + align:start position:0% +so if i take a given radius r if i want +to know how it depends on r + + align:start position:0% +to know how it depends on r + + + align:start position:0% +to know how it depends on r +it's r divided by um about + + align:start position:0% +it's r divided by um about + + + align:start position:0% +it's r divided by um about +uh three microns squared so if you give + + align:start position:0% +uh three microns squared so if you give + + + align:start position:0% +uh three microns squared so if you give +me a different radius then basically the + + align:start position:0% +me a different radius then basically the + + + align:start position:0% +me a different radius then basically the +the sedimentation velocity + + align:start position:0% +the sedimentation velocity + + + align:start position:0% +the sedimentation velocity +you know depends on r that way so it'll + + align:start position:0% +you know depends on r that way so it'll + + + align:start position:0% +you know depends on r that way so it'll +look + + align:start position:0% +look + + + align:start position:0% +look +something like this where at + + align:start position:0% +something like this where at + + + align:start position:0% +something like this where at +three microns the value is one + + align:start position:0% +three microns the value is one + + + align:start position:0% +three microns the value is one +millimeter second okay so that's the + + align:start position:0% +millimeter second okay so that's the + + + align:start position:0% +millimeter second okay so that's the +scale we're talking about + + align:start position:0% +scale we're talking about + + + align:start position:0% +scale we're talking about +um and so uh + + align:start position:0% +um and so uh + + + align:start position:0% +um and so uh +an interesting question to ask is how + + align:start position:0% +an interesting question to ask is how + + + align:start position:0% +an interesting question to ask is how +does the settling compare to the other + + align:start position:0% +does the settling compare to the other + + + align:start position:0% +does the settling compare to the other +values here so basically how big is this + + align:start position:0% +values here so basically how big is this + + + align:start position:0% +values here so basically how big is this +term + + align:start position:0% +term + + + align:start position:0% +term +relative to the others now + + align:start position:0% +relative to the others now + + + align:start position:0% +relative to the others now +the most important one here really is + + align:start position:0% +the most important one here really is + + + align:start position:0% +the most important one here really is +the lambda a because that's the overall + + align:start position:0% +the lambda a because that's the overall + + + align:start position:0% +the lambda a because that's the overall +ventilation in the system we know that's + + align:start position:0% +ventilation in the system we know that's + + + align:start position:0% +ventilation in the system we know that's +a really important parameter that was + + align:start position:0% +a really important parameter that was + + + align:start position:0% +a really important parameter that was +the first one that i presented to you + + align:start position:0% +the first one that i presented to you + + + align:start position:0% +the first one that i presented to you +the other ones are kind of corrections + + align:start position:0% +the other ones are kind of corrections + + + align:start position:0% +the other ones are kind of corrections +that can be important + + align:start position:0% +that can be important + + + align:start position:0% +that can be important +but only if you know maybe the virion is + + align:start position:0% +but only if you know maybe the virion is + + + align:start position:0% +but only if you know maybe the virion is +deactivating very quickly or if you have + + align:start position:0% +deactivating very quickly or if you have + + + align:start position:0% +deactivating very quickly or if you have +a very aggressive filtration system but + + align:start position:0% +a very aggressive filtration system but + + + align:start position:0% +a very aggressive filtration system but +the thing you really want to think about + + align:start position:0% +the thing you really want to think about + + + align:start position:0% +the thing you really want to think about +is this lambda a + + align:start position:0% +is this lambda a + + + align:start position:0% +is this lambda a +so in particular if + + align:start position:0% +so in particular if + + + align:start position:0% +so in particular if +v s is bigger than + + align:start position:0% +v s is bigger than + + + align:start position:0% +v s is bigger than +lambda a times h + + align:start position:0% +lambda a times h + + + align:start position:0% +lambda a times h +then those droplets will settle + + align:start position:0% +then those droplets will settle + + + align:start position:0% +then those droplets will settle +to the ground or to the flat maybe to + + align:start position:0% +to the ground or to the flat maybe to + + + align:start position:0% +to the ground or to the flat maybe to +tables or other flat surfaces + + align:start position:0% +tables or other flat surfaces + + + align:start position:0% +tables or other flat surfaces +faster than removal + + align:start position:0% +faster than removal + + + align:start position:0% +faster than removal +by ventilation + + align:start position:0% + + + + align:start position:0% + +so those are really the particles that + + align:start position:0% +so those are really the particles that + + + align:start position:0% +so those are really the particles that +will those are the droplets that will + + align:start position:0% +will those are the droplets that will + + + align:start position:0% +will those are the droplets that will +sediment + + align:start position:0% +sediment + + + align:start position:0% +sediment +out actually okay um + + align:start position:0% +out actually okay um + + + align:start position:0% +out actually okay um +and so if we and if we just want to + + align:start position:0% +and so if we and if we just want to + + + align:start position:0% +and so if we and if we just want to +estimate sort of what kind of size are + + align:start position:0% +estimate sort of what kind of size are + + + align:start position:0% +estimate sort of what kind of size are +we talking about here + + align:start position:0% +we talking about here + + + align:start position:0% +we talking about here +well if we uh pick a lambda a which is + + align:start position:0% +well if we uh pick a lambda a which is + + + align:start position:0% +well if we uh pick a lambda a which is +three + + align:start position:0% +three + + + align:start position:0% +three +inverse hours so three achs that's sort + + align:start position:0% +inverse hours so three achs that's sort + + + align:start position:0% +inverse hours so three achs that's sort +of a typical + + align:start position:0% +of a typical + + + align:start position:0% +of a typical +kind of moderate ventilation rate um + + align:start position:0% +kind of moderate ventilation rate um + + + align:start position:0% +kind of moderate ventilation rate um +and we take a typical room size which + + align:start position:0% +and we take a typical room size which + + + align:start position:0% +and we take a typical room size which +may be something like maybe three meters + + align:start position:0% +may be something like maybe three meters + + + align:start position:0% +may be something like maybe three meters +um it's maybe not quite that high but + + align:start position:0% +um it's maybe not quite that high but + + + align:start position:0% +um it's maybe not quite that high but +maybe it's only one or two meters but + + align:start position:0% +maybe it's only one or two meters but + + + align:start position:0% +maybe it's only one or two meters but +i'm just trying to get an overall sense + + align:start position:0% +i'm just trying to get an overall sense + + + align:start position:0% +i'm just trying to get an overall sense +here when i plug that in + + align:start position:0% +here when i plug that in + + + align:start position:0% +here when i plug that in +you can see this was three microns and + + align:start position:0% +you can see this was three microns and + + + align:start position:0% +you can see this was three microns and +so when i kind of work out the units + + align:start position:0% +so when i kind of work out the units + + + align:start position:0% +so when i kind of work out the units +here + + align:start position:0% +here + + + align:start position:0% +here +i'm left with 0.03 + + align:start position:0% +i'm left with 0.03 + + + align:start position:0% +i'm left with 0.03 +millimeters per second which can also be + + align:start position:0% +millimeters per second which can also be + + + align:start position:0% +millimeters per second which can also be +written as + + align:start position:0% +written as + + + align:start position:0% +written as +30 microns per second + + align:start position:0% +30 microns per second + + + align:start position:0% +30 microns per second +so that's a typical speed + + align:start position:0% +so that's a typical speed + + + align:start position:0% +so that's a typical speed +above which uh you know particles will + + align:start position:0% +above which uh you know particles will + + + align:start position:0% +above which uh you know particles will +be sedimenting + + align:start position:0% +be sedimenting + + + align:start position:0% +be sedimenting +to the ground if i now convert that back + + align:start position:0% +to the ground if i now convert that back + + + align:start position:0% +to the ground if i now convert that back +to a radius + + align:start position:0% +to a radius + + + align:start position:0% +to a radius +then i'm finding that the um + + align:start position:0% +then i'm finding that the um + + + align:start position:0% +then i'm finding that the um +in order for this condition to hold that + + align:start position:0% +in order for this condition to hold that + + + align:start position:0% +in order for this condition to hold that +the rate because v goes like r squared i + + align:start position:0% +the rate because v goes like r squared i + + + align:start position:0% +the rate because v goes like r squared i +basically take a square root + + align:start position:0% +basically take a square root + + + align:start position:0% +basically take a square root +so the r will be bigger than sort of 3 + + align:start position:0% +so the r will be bigger than sort of 3 + + + align:start position:0% +so the r will be bigger than sort of 3 +microns + + align:start position:0% +microns + + + align:start position:0% +microns +times the square root of 0.03 + + align:start position:0% +times the square root of 0.03 + + + align:start position:0% +times the square root of 0.03 +because that was already in microns here + + align:start position:0% +because that was already in microns here + + + align:start position:0% +because that was already in microns here +and that's going to give me 0.5 + + align:start position:0% +and that's going to give me 0.5 + + + align:start position:0% +and that's going to give me 0.5 +microns so basically + + align:start position:0% +microns so basically + + + align:start position:0% +microns so basically +at this ventilation rate the particles + + align:start position:0% +at this ventilation rate the particles + + + align:start position:0% +at this ventilation rate the particles +that + + align:start position:0% +that + + + align:start position:0% +that +fall to the ground faster than the + + align:start position:0% +fall to the ground faster than the + + + align:start position:0% +fall to the ground faster than the +removed by ventilation are those that + + align:start position:0% +removed by ventilation are those that + + + align:start position:0% +removed by ventilation are those that +are + + align:start position:0% +are + + + align:start position:0% +are +larger than 0.5 micron radius or 1 + + align:start position:0% +larger than 0.5 micron radius or 1 + + + align:start position:0% +larger than 0.5 micron radius or 1 +micron diameter + + align:start position:0% +micron diameter + + + align:start position:0% +micron diameter +so this is telling us that the submicron + + align:start position:0% +so this is telling us that the submicron + + + align:start position:0% +so this is telling us that the submicron +particles are truly aerosols and that + + align:start position:0% +particles are truly aerosols and that + + + align:start position:0% +particles are truly aerosols and that +they're really not going to make it to + + align:start position:0% +they're really not going to make it to + + + align:start position:0% +they're really not going to make it to +the ground + + align:start position:0% +the ground + + + align:start position:0% +the ground +before they even get swept away by the + + align:start position:0% +before they even get swept away by the + + + align:start position:0% +before they even get swept away by the +ventilation + + align:start position:0% +ventilation + + + align:start position:0% +ventilation +and the rest of the time they're all + + align:start position:0% +and the rest of the time they're all + + + align:start position:0% +and the rest of the time they're all +just floating around and even the + + align:start position:0% +just floating around and even the + + + align:start position:0% +just floating around and even the +particles that are a bit bigger than + + align:start position:0% +particles that are a bit bigger than + + + align:start position:0% +particles that are a bit bigger than +this maybe that are several microns + + align:start position:0% +this maybe that are several microns + + + align:start position:0% +this maybe that are several microns +are still spending a significant amount + + align:start position:0% +are still spending a significant amount + + + align:start position:0% +are still spending a significant amount +of time swirling around the entire room + + align:start position:0% +of time swirling around the entire room + + + align:start position:0% +of time swirling around the entire room +and they're not really reaching surfaces + + align:start position:0% +and they're not really reaching surfaces + + + align:start position:0% +and they're not really reaching surfaces +that quickly + + align:start position:0% +that quickly + + + align:start position:0% +that quickly +and the typical lifetime of such + + align:start position:0% +and the typical lifetime of such + + + align:start position:0% +and the typical lifetime of such +droplets is they're emitted from the + + align:start position:0% +droplets is they're emitted from the + + + align:start position:0% +droplets is they're emitted from the +mouth + + align:start position:0% +mouth + + + align:start position:0% +mouth +they swirl all around the room reaching + + align:start position:0% +they swirl all around the room reaching + + + align:start position:0% +they swirl all around the room reaching +oftentimes every corner and then + + align:start position:0% +oftentimes every corner and then + + + align:start position:0% +oftentimes every corner and then +eventually they leave through the + + align:start position:0% +eventually they leave through the + + + align:start position:0% +eventually they leave through the +ventilation system + + align:start position:0% +ventilation system + + + align:start position:0% +ventilation system +or in some cases they sediment if + + align:start position:0% +or in some cases they sediment if + + + align:start position:0% +or in some cases they sediment if +they're a little bit larger than this + + align:start position:0% +they're a little bit larger than this + + + align:start position:0% +they're a little bit larger than this +number + + align:start position:0% +number + + + align:start position:0% +number +so that's just important to keep in mind + + align:start position:0% +so that's just important to keep in mind + + + align:start position:0% +so that's just important to keep in mind +the the fate of the different droplets + + align:start position:0% +the the fate of the different droplets + + + align:start position:0% +the the fate of the different droplets +that are emitted by an infected person + + align:start position:0% + + + + align:start position:0% + +indoors \ No newline at end of file diff --git a/GyC3gl6weYo.txt b/GyC3gl6weYo.txt new file mode 100644 index 0000000000000000000000000000000000000000..9ed72dfeb72ae4974e1f8b4f8d62b0e2a6027f0a --- /dev/null +++ b/GyC3gl6weYo.txt @@ -0,0 +1,2027 @@ +align:start position:0% + +I'm moving now to the second half of + + align:start position:0% +I'm moving now to the second half of + + + align:start position:0% +I'm moving now to the second half of +linear algebra + + align:start position:0% +linear algebra + + + align:start position:0% +linear algebra +it's about eigenvalues and eigenvectors + + align:start position:0% +it's about eigenvalues and eigenvectors + + + align:start position:0% +it's about eigenvalues and eigenvectors +the first half I just had a matrix I + + align:start position:0% +the first half I just had a matrix I + + + align:start position:0% +the first half I just had a matrix I +solved equations the second half you'll + + align:start position:0% +solved equations the second half you'll + + + align:start position:0% +solved equations the second half you'll +see the point of eigenvalues and + + align:start position:0% +see the point of eigenvalues and + + + align:start position:0% +see the point of eigenvalues and +eigenvectors as a new way to look deeper + + align:start position:0% +eigenvectors as a new way to look deeper + + + align:start position:0% +eigenvectors as a new way to look deeper +into the matrix to see what's important + + align:start position:0% +into the matrix to see what's important + + + align:start position:0% +into the matrix to see what's important +there okay so what are they this is a + + align:start position:0% +there okay so what are they this is a + + + align:start position:0% +there okay so what are they this is a +big equation s times X so s is our + + align:start position:0% +big equation s times X so s is our + + + align:start position:0% +big equation s times X so s is our +matrix and I've called it s because I'm + + align:start position:0% +matrix and I've called it s because I'm + + + align:start position:0% +matrix and I've called it s because I'm +taking it to be a symmetric matrix + + align:start position:0% +taking it to be a symmetric matrix + + + align:start position:0% +taking it to be a symmetric matrix +what's what's on one side of the + + align:start position:0% +what's what's on one side of the + + + align:start position:0% +what's what's on one side of the +diagonal is also on the other side of + + align:start position:0% +diagonal is also on the other side of + + + align:start position:0% +diagonal is also on the other side of +the diagonal so those have the beautiful + + align:start position:0% +the diagonal so those have the beautiful + + + align:start position:0% +the diagonal so those have the beautiful +properties those are the kings of linear + + align:start position:0% +properties those are the kings of linear + + + align:start position:0% +properties those are the kings of linear +algebra now about eigen vectors X and + + align:start position:0% +algebra now about eigen vectors X and + + + align:start position:0% +algebra now about eigen vectors X and +eigen values lambda so what does that + + align:start position:0% +eigen values lambda so what does that + + + align:start position:0% +eigen values lambda so what does that +equation SX equal lambda X tell me that + + align:start position:0% +equation SX equal lambda X tell me that + + + align:start position:0% +equation SX equal lambda X tell me that +says that I have a special vector X when + + align:start position:0% +says that I have a special vector X when + + + align:start position:0% +says that I have a special vector X when +I multiply it by s my matrix + + align:start position:0% +I multiply it by s my matrix + + + align:start position:0% +I multiply it by s my matrix +I'm stay in the same direction as the + + align:start position:0% +I'm stay in the same direction as the + + + align:start position:0% +I'm stay in the same direction as the +original X it might get multiplied by 2 + + align:start position:0% +original X it might get multiplied by 2 + + + align:start position:0% +original X it might get multiplied by 2 +lambda could be 2 + + align:start position:0% +lambda could be 2 + + + align:start position:0% +lambda could be 2 +it might get multiplied by 0 lambda + + align:start position:0% +it might get multiplied by 0 lambda + + + align:start position:0% +it might get multiplied by 0 lambda +could even be 0 + + align:start position:0% +could even be 0 + + + align:start position:0% +could even be 0 +it might get multiplied by minus 2 + + align:start position:0% +it might get multiplied by minus 2 + + + align:start position:0% +it might get multiplied by minus 2 +whatever but it's along the same line so + + align:start position:0% +whatever but it's along the same line so + + + align:start position:0% +whatever but it's along the same line so +that's like taking a matrix and turning + + align:start position:0% +that's like taking a matrix and turning + + + align:start position:0% +that's like taking a matrix and turning +discovering inside it something that's + + align:start position:0% +discovering inside it something that's + + + align:start position:0% +discovering inside it something that's +all that stays on a line that means that + + align:start position:0% +all that stays on a line that means that + + + align:start position:0% +all that stays on a line that means that +it's really a sort of one dimensional + + align:start position:0% +it's really a sort of one dimensional + + + align:start position:0% +it's really a sort of one dimensional +problem if we're looking at along that + + align:start position:0% +problem if we're looking at along that + + + align:start position:0% +problem if we're looking at along that +eigen vector and that makes computations + + align:start position:0% +eigen vector and that makes computations + + + align:start position:0% +eigen vector and that makes computations +infinitely easier so the hard part of a + + align:start position:0% +infinitely easier so the hard part of a + + + align:start position:0% +infinitely easier so the hard part of a +matrix is all the all the connections + + align:start position:0% +matrix is all the all the connections + + + align:start position:0% +matrix is all the all the connections +between different rows and columns so + + align:start position:0% +between different rows and columns so + + + align:start position:0% +between different rows and columns so +eigenvectors are the guys that stay in + + align:start position:0% +eigenvectors are the guys that stay in + + + align:start position:0% +eigenvectors are the guys that stay in +that same direction so and and there's y + + align:start position:0% +that same direction so and and there's y + + + align:start position:0% +that same direction so and and there's y +is another eigenvector it has its own + + align:start position:0% +is another eigenvector it has its own + + + align:start position:0% +is another eigenvector it has its own +eigenvalue it got multiplied by alpha + + align:start position:0% +eigenvalue it got multiplied by alpha + + + align:start position:0% +eigenvalue it got multiplied by alpha +where SX multiplied the x by some other + + align:start position:0% +where SX multiplied the x by some other + + + align:start position:0% +where SX multiplied the x by some other +number lambda so those are a couple of + + align:start position:0% +number lambda so those are a couple of + + + align:start position:0% +number lambda so those are a couple of +eigenvectors and the beautiful fact is + + align:start position:0% +eigenvectors and the beautiful fact is + + + align:start position:0% +eigenvectors and the beautiful fact is +because s is symmetric those two eigen + + align:start position:0% +because s is symmetric those two eigen + + + align:start position:0% +because s is symmetric those two eigen +vectors are perpendicular there + + align:start position:0% +vectors are perpendicular there + + + align:start position:0% +vectors are perpendicular there +orthogonal as it says up there so + + align:start position:0% +orthogonal as it says up there so + + + align:start position:0% +orthogonal as it says up there so +symmetric matrices are really the best + + align:start position:0% +symmetric matrices are really the best + + + align:start position:0% +symmetric matrices are really the best +because they're eigen vectors are + + align:start position:0% +because they're eigen vectors are + + + align:start position:0% +because they're eigen vectors are +perpendicular and we have a bunch of + + align:start position:0% +perpendicular and we have a bunch of + + + align:start position:0% +perpendicular and we have a bunch of +one-dimensional problems and here I've + + align:start position:0% +one-dimensional problems and here I've + + + align:start position:0% +one-dimensional problems and here I've +included a proof do you want to proof + + align:start position:0% +included a proof do you want to proof + + + align:start position:0% +included a proof do you want to proof +that the eigen vectors are perpendicular + + align:start position:0% +that the eigen vectors are perpendicular + + + align:start position:0% +that the eigen vectors are perpendicular +so what does perpendicular mean it means + + align:start position:0% +so what does perpendicular mean it means + + + align:start position:0% +so what does perpendicular mean it means +that X transpose times y that dot + + align:start position:0% +that X transpose times y that dot + + + align:start position:0% +that X transpose times y that dot +product is 0 the angle is 90 degrees the + + align:start position:0% +product is 0 the angle is 90 degrees the + + + align:start position:0% +product is 0 the angle is 90 degrees the +cosine is 1 okay how to show well of + + align:start position:0% +cosine is 1 okay how to show well of + + + align:start position:0% +cosine is 1 okay how to show well of +course I might be 0 how to how to show + + align:start position:0% +course I might be 0 how to how to show + + + align:start position:0% +course I might be 0 how to how to show +that ya proof this is like just you can + + align:start position:0% +that ya proof this is like just you can + + + align:start position:0% +that ya proof this is like just you can +tune out for 2 minutes if you hate + + align:start position:0% +tune out for 2 minutes if you hate + + + align:start position:0% +tune out for 2 minutes if you hate +proofs ok I start with what I know and + + align:start position:0% +proofs ok I start with what I know and + + + align:start position:0% +proofs ok I start with what I know and +what I know is in that box SX is lambda + + align:start position:0% +what I know is in that box SX is lambda + + + align:start position:0% +what I know is in that box SX is lambda +X as one eigenvector that tells me the + + align:start position:0% +X as one eigenvector that tells me the + + + align:start position:0% +X as one eigenvector that tells me the +eigenvector Y this tells me the eigen + + align:start position:0% +eigenvector Y this tells me the eigen + + + align:start position:0% +eigenvector Y this tells me the eigen +values are different and that tells me + + align:start position:0% +values are different and that tells me + + + align:start position:0% +values are different and that tells me +the matrix is symmetric I'm just gonna + + align:start position:0% +the matrix is symmetric I'm just gonna + + + align:start position:0% +the matrix is symmetric I'm just gonna +juggle those four facts and I'll end up + + align:start position:0% +juggle those four facts and I'll end up + + + align:start position:0% +juggle those four facts and I'll end up +with X transpose y equals 0 that's + + align:start position:0% +with X transpose y equals 0 that's + + + align:start position:0% +with X transpose y equals 0 that's +orthogonal T okay so just I'll just do + + align:start position:0% +orthogonal T okay so just I'll just do + + + align:start position:0% +orthogonal T okay so just I'll just do +it quickly - quickly so I take this + + align:start position:0% +it quickly - quickly so I take this + + + align:start position:0% +it quickly - quickly so I take this +first thing and I transpose it turn it + + align:start position:0% +first thing and I transpose it turn it + + + align:start position:0% +first thing and I transpose it turn it +into row vectors and then when I + + align:start position:0% +into row vectors and then when I + + + align:start position:0% +into row vectors and then when I +transpose it that transposes transpose + + align:start position:0% +transpose it that transposes transpose + + + align:start position:0% +transpose it that transposes transpose +means I flip rows and columns but for a + + align:start position:0% +means I flip rows and columns but for a + + + align:start position:0% +means I flip rows and columns but for a +symmetric matrix no difference so s + + align:start position:0% +symmetric matrix no difference so s + + + align:start position:0% +symmetric matrix no difference so s +transpose is the same as s and then I + + align:start position:0% +transpose is the same as s and then I + + + align:start position:0% +transpose is the same as s and then I +look at this one and I multiply that by + + align:start position:0% +look at this one and I multiply that by + + + align:start position:0% +look at this one and I multiply that by +X transpose both both sides by X + + align:start position:0% +X transpose both both sides by X + + + align:start position:0% +X transpose both both sides by X +transpose what I end up with is + + align:start position:0% +transpose what I end up with is + + + align:start position:0% +transpose what I end up with is +recognizing that lambda times that dot + + align:start position:0% +recognizing that lambda times that dot + + + align:start position:0% +recognizing that lambda times that dot +product equals alpha times that dot + + align:start position:0% +product equals alpha times that dot + + + align:start position:0% +product equals alpha times that dot +product but lambda is different from + + align:start position:0% +product but lambda is different from + + + align:start position:0% +product but lambda is different from +alpha so the only way lambda times that + + align:start position:0% +alpha so the only way lambda times that + + + align:start position:0% +alpha so the only way lambda times that +number can equal alpha times that number + + align:start position:0% +number can equal alpha times that number + + + align:start position:0% +number can equal alpha times that number +is that number has to be 0 and that's + + align:start position:0% +is that number has to be 0 and that's + + + align:start position:0% +is that number has to be 0 and that's +the answer ok so that's the proof that + + align:start position:0% +the answer ok so that's the proof that + + + align:start position:0% +the answer ok so that's the proof that +used exactly every fact we knew end of + + align:start position:0% +used exactly every fact we knew end of + + + align:start position:0% +used exactly every fact we knew end of +proof + + align:start position:0% +proof + + + align:start position:0% +proof +main point to remember I convector czar + + align:start position:0% +main point to remember I convector czar + + + align:start position:0% +main point to remember I convector czar +perpendicular when the matrix is + + align:start position:0% +perpendicular when the matrix is + + + align:start position:0% +perpendicular when the matrix is +symmetric okay in that case now you + + align:start position:0% +symmetric okay in that case now you + + + align:start position:0% +symmetric okay in that case now you +always want to express these facts as + + align:start position:0% +always want to express these facts as + + + align:start position:0% +always want to express these facts as +from multiplying matrices that that's so + + align:start position:0% +from multiplying matrices that that's so + + + align:start position:0% +from multiplying matrices that that's so +that says everything in a few symbols + + align:start position:0% +that says everything in a few symbols + + + align:start position:0% +that says everything in a few symbols +where I had to use all those words on + + align:start position:0% +where I had to use all those words on + + + align:start position:0% +where I had to use all those words on +the previous slide so this is that + + align:start position:0% +the previous slide so this is that + + + align:start position:0% +the previous slide so this is that +that's the result that I'm shooting for + + align:start position:0% +that's the result that I'm shooting for + + + align:start position:0% +that's the result that I'm shooting for +that symmetric matrix + + align:start position:0% +that symmetric matrix + + + align:start position:0% +that symmetric matrix +yeah it just focus on that it's that box + + align:start position:0% +yeah it just focus on that it's that box + + + align:start position:0% +yeah it just focus on that it's that box +a symmetric matrix can be broken up into + + align:start position:0% +a symmetric matrix can be broken up into + + + align:start position:0% +a symmetric matrix can be broken up into +its eigenvectors those are in q its + + align:start position:0% +its eigenvectors those are in q its + + + align:start position:0% +its eigenvectors those are in q its +eigenvalues those are the lambdas those + + align:start position:0% +eigenvalues those are the lambdas those + + + align:start position:0% +eigenvalues those are the lambdas those +are the or the numbers lambda 1 to + + align:start position:0% +are the or the numbers lambda 1 to + + + align:start position:0% +are the or the numbers lambda 1 to +lambda n on the diagonal lambda and then + + align:start position:0% +lambda n on the diagonal lambda and then + + + align:start position:0% +lambda n on the diagonal lambda and then +the transpose so the eigenvectors are + + align:start position:0% +the transpose so the eigenvectors are + + + align:start position:0% +the transpose so the eigenvectors are +now rows in q transpose that's just + + align:start position:0% +now rows in q transpose that's just + + + align:start position:0% +now rows in q transpose that's just +perfect perfect every symmetric matrix + + align:start position:0% +perfect perfect every symmetric matrix + + + align:start position:0% +perfect perfect every symmetric matrix +is an orthogonal matrix times a diagonal + + align:start position:0% +is an orthogonal matrix times a diagonal + + + align:start position:0% +is an orthogonal matrix times a diagonal +matrix times the transpose of the + + align:start position:0% +matrix times the transpose of the + + + align:start position:0% +matrix times the transpose of the +orthogonal matrix yeah that's called the + + align:start position:0% +orthogonal matrix yeah that's called the + + + align:start position:0% +orthogonal matrix yeah that's called the +spectral theorem in it you could say + + align:start position:0% +spectral theorem in it you could say + + + align:start position:0% +spectral theorem in it you could say +it's it's up there with the most + + align:start position:0% +it's it's up there with the most + + + align:start position:0% +it's it's up there with the most +important facts in linear algebra and in + + align:start position:0% +important facts in linear algebra and in + + + align:start position:0% +important facts in linear algebra and in +wider mathematics yeah so that's the + + align:start position:0% +wider mathematics yeah so that's the + + + align:start position:0% +wider mathematics yeah so that's the +fact that that controls what we do yeah + + align:start position:0% +fact that that controls what we do yeah + + + align:start position:0% +fact that that controls what we do yeah +what we do here oh now I have to say + + align:start position:0% +what we do here oh now I have to say + + + align:start position:0% +what we do here oh now I have to say +what's the situation if the matrix is + + align:start position:0% +what's the situation if the matrix is + + + align:start position:0% +what's the situation if the matrix is +not symmetric now I am NOT going to get + + align:start position:0% +not symmetric now I am NOT going to get + + + align:start position:0% +not symmetric now I am NOT going to get +perpendicular eigenvectors that was a + + align:start position:0% +perpendicular eigenvectors that was a + + + align:start position:0% +perpendicular eigenvectors that was a +symmetric thing mostly but I'll get on + + align:start position:0% +symmetric thing mostly but I'll get on + + + align:start position:0% +symmetric thing mostly but I'll get on +vectors so I'll get ax equal lambda X + + align:start position:0% +vectors so I'll get ax equal lambda X + + + align:start position:0% +vectors so I'll get ax equal lambda X +they just the first one won't be + + align:start position:0% +they just the first one won't be + + + align:start position:0% +they just the first one won't be +perpendicular to the second one the + + align:start position:0% +perpendicular to the second one the + + + align:start position:0% +perpendicular to the second one the +matrix a it has to be square or this + + align:start position:0% +matrix a it has to be square or this + + + align:start position:0% +matrix a it has to be square or this +doesn't make sense so so eigenvalues and + + align:start position:0% +doesn't make sense so so eigenvalues and + + + align:start position:0% +doesn't make sense so so eigenvalues and +eigenvectors are the way to break up a + + align:start position:0% +eigenvectors are the way to break up a + + + align:start position:0% +eigenvectors are the way to break up a +square matrix into and and find this + + align:start position:0% +square matrix into and and find this + + + align:start position:0% +square matrix into and and find this +diagonal matrix lambda with the + + align:start position:0% +diagonal matrix lambda with the + + + align:start position:0% +diagonal matrix lambda with the +eigenvalues + + align:start position:0% +eigenvalues + + + align:start position:0% +eigenvalues +- 1 lambda 2 2 lambda n that's that's + + align:start position:0% +- 1 lambda 2 2 lambda n that's that's + + + align:start position:0% +- 1 lambda 2 2 lambda n that's that's +the purpose is an eigen vectors are + + align:start position:0% +the purpose is an eigen vectors are + + + align:start position:0% +the purpose is an eigen vectors are +perpendicular when it's a symmetric + + align:start position:0% +perpendicular when it's a symmetric + + + align:start position:0% +perpendicular when it's a symmetric +matrix otherwise I just have X n its + + align:start position:0% +matrix otherwise I just have X n its + + + align:start position:0% +matrix otherwise I just have X n its +inverse matrix but none no symmetry ok + + align:start position:0% +inverse matrix but none no symmetry ok + + + align:start position:0% +inverse matrix but none no symmetry ok +so that's the that's the quick + + align:start position:0% +so that's the that's the quick + + + align:start position:0% +so that's the that's the quick +expression another factorization of + + align:start position:0% +expression another factorization of + + + align:start position:0% +expression another factorization of +eigenvalues in lambda diagonal just + + align:start position:0% +eigenvalues in lambda diagonal just + + + align:start position:0% +eigenvalues in lambda diagonal just +numbers and eigenvectors in the columns + + align:start position:0% +numbers and eigenvectors in the columns + + + align:start position:0% +numbers and eigenvectors in the columns +of X ok and now I'm not going to oh I + + align:start position:0% +of X ok and now I'm not going to oh I + + + align:start position:0% +of X ok and now I'm not going to oh I +was going to say I'm not going to solve + + align:start position:0% +was going to say I'm not going to solve + + + align:start position:0% +was going to say I'm not going to solve +all the problems of applied math but + + align:start position:0% +all the problems of applied math but + + + align:start position:0% +all the problems of applied math but +that's what these are for + + align:start position:0% +that's what these are for + + + align:start position:0% +that's what these are for +let's just see what special hear about + + align:start position:0% +let's just see what special hear about + + + align:start position:0% +let's just see what special hear about +these eigenvectors suppose I multiply + + align:start position:0% +these eigenvectors suppose I multiply + + + align:start position:0% +these eigenvectors suppose I multiply +again by a I start with ax equal lambda + + align:start position:0% +again by a I start with ax equal lambda + + + align:start position:0% +again by a I start with ax equal lambda +X now I'm gonna multiply both sides by a + + align:start position:0% +X now I'm gonna multiply both sides by a + + + align:start position:0% +X now I'm gonna multiply both sides by a +that'll tell me something about eigen + + align:start position:0% +that'll tell me something about eigen + + + align:start position:0% +that'll tell me something about eigen +values of a squared because when I + + align:start position:0% +values of a squared because when I + + + align:start position:0% +values of a squared because when I +multiply by a so let me start with a + + align:start position:0% +multiply by a so let me start with a + + + align:start position:0% +multiply by a so let me start with a +squared now times X which means a times + + align:start position:0% +squared now times X which means a times + + + align:start position:0% +squared now times X which means a times +ax a times ax but ax is lambda X so I + + align:start position:0% +ax a times ax but ax is lambda X so I + + + align:start position:0% +ax a times ax but ax is lambda X so I +have a times lambda X and I pull out + + align:start position:0% +have a times lambda X and I pull out + + + align:start position:0% +have a times lambda X and I pull out +that number lambda so I said I still + + align:start position:0% +that number lambda so I said I still + + + align:start position:0% +that number lambda so I said I still +have a 1 ax and that's also still lambda + + align:start position:0% +have a 1 ax and that's also still lambda + + + align:start position:0% +have a 1 ax and that's also still lambda +X you see I'm just talking around in a + + align:start position:0% +X you see I'm just talking around in a + + + align:start position:0% +X you see I'm just talking around in a +little circle here just using ax equal + + align:start position:0% +little circle here just using ax equal + + + align:start position:0% +little circle here just using ax equal +lambda X a couple of times and the + + align:start position:0% +lambda X a couple of times and the + + + align:start position:0% +lambda X a couple of times and the +result is do you see what that means + + align:start position:0% +result is do you see what that means + + + align:start position:0% +result is do you see what that means +that result that means that the eigen + + align:start position:0% +that result that means that the eigen + + + align:start position:0% +that result that means that the eigen +value for a squared same eigen vector X + + align:start position:0% +value for a squared same eigen vector X + + + align:start position:0% +value for a squared same eigen vector X +the eigen value is lambda squared and if + + align:start position:0% +the eigen value is lambda squared and if + + + align:start position:0% +the eigen value is lambda squared and if +I had a cubed the eigen value would come + + align:start position:0% +I had a cubed the eigen value would come + + + align:start position:0% +I had a cubed the eigen value would come +out lambda cubed and if I have a to the + + align:start position:0% +out lambda cubed and if I have a to the + + + align:start position:0% +out lambda cubed and if I have a to the +yeah yeah it's so if I had a 10 x + n + + align:start position:0% +yeah yeah it's so if I had a 10 x + n + + + align:start position:0% +yeah yeah it's so if I had a 10 x + n +multiple so when would you have a to a + + align:start position:0% +multiple so when would you have a to a + + + align:start position:0% +multiple so when would you have a to a +high power that's a interesting matrix + + align:start position:0% +high power that's a interesting matrix + + + align:start position:0% +high power that's a interesting matrix +take a matrix and square it cubit take + + align:start position:0% +take a matrix and square it cubit take + + + align:start position:0% +take a matrix and square it cubit take +high powers of it the eigen values the + + align:start position:0% +high powers of it the eigen values the + + + align:start position:0% +high powers of it the eigen values the +eigen vectors don't change that's the + + align:start position:0% +eigen vectors don't change that's the + + + align:start position:0% +eigen vectors don't change that's the +great thing that's the whole point of + + align:start position:0% +great thing that's the whole point of + + + align:start position:0% +great thing that's the whole point of +in vectors they don't change and the + + align:start position:0% +in vectors they don't change and the + + + align:start position:0% +in vectors they don't change and the +eigenvalues just get taken to the high + + align:start position:0% +eigenvalues just get taken to the high + + + align:start position:0% +eigenvalues just get taken to the high +power so for example we could ask the + + align:start position:0% +power so for example we could ask the + + + align:start position:0% +power so for example we could ask the +question when if I multiply a matrix by + + align:start position:0% +question when if I multiply a matrix by + + + align:start position:0% +question when if I multiply a matrix by +itself over and over and over again when + + align:start position:0% +itself over and over and over again when + + + align:start position:0% +itself over and over and over again when +do I approach zero well if these numbers + + align:start position:0% +do I approach zero well if these numbers + + + align:start position:0% +do I approach zero well if these numbers +are below one so eigenvectors + + align:start position:0% +are below one so eigenvectors + + + align:start position:0% +are below one so eigenvectors +eigenvalues gives you something that you + + align:start position:0% +eigenvalues gives you something that you + + + align:start position:0% +eigenvalues gives you something that you +just could not see by those column + + align:start position:0% +just could not see by those column + + + align:start position:0% +just could not see by those column +operations or l times you this is + + align:start position:0% +operations or l times you this is + + + align:start position:0% +operations or l times you this is +looking deeper okay and okay + + align:start position:0% +looking deeper okay and okay + + + align:start position:0% +looking deeper okay and okay +and then you'll see we have almost + + align:start position:0% +and then you'll see we have almost + + + align:start position:0% +and then you'll see we have almost +already seen with least squares this + + align:start position:0% +already seen with least squares this + + + align:start position:0% +already seen with least squares this +combination a transpose a so remember a + + align:start position:0% +combination a transpose a so remember a + + + align:start position:0% +combination a transpose a so remember a +is is a rectangular matrix and by n i + + align:start position:0% +is is a rectangular matrix and by n i + + + align:start position:0% +is is a rectangular matrix and by n i +multiply it by its transpose when i + + align:start position:0% +multiply it by its transpose when i + + + align:start position:0% +multiply it by its transpose when i +transpose it i have n by m and when I + + align:start position:0% +transpose it i have n by m and when I + + + align:start position:0% +transpose it i have n by m and when I +multiply them together I get n by n so a + + align:start position:0% +multiply them together I get n by n so a + + + align:start position:0% +multiply them together I get n by n so a +transpose a is a is a four theory is a + + align:start position:0% +transpose a is a is a four theory is a + + + align:start position:0% +transpose a is a is a four theory is a +great matrix a transpose times a it's + + align:start position:0% +great matrix a transpose times a it's + + + align:start position:0% +great matrix a transpose times a it's +symmetric yeah let's just see what we + + align:start position:0% +symmetric yeah let's just see what we + + + align:start position:0% +symmetric yeah let's just see what we +have about eight its square for sure oh + + align:start position:0% +have about eight its square for sure oh + + + align:start position:0% +have about eight its square for sure oh +yeah this tells me that it's symmetric + + align:start position:0% +yeah this tells me that it's symmetric + + + align:start position:0% +yeah this tells me that it's symmetric +and you remember why I'm always looking + + align:start position:0% +and you remember why I'm always looking + + + align:start position:0% +and you remember why I'm always looking +for symmetric matrices because they have + + align:start position:0% +for symmetric matrices because they have + + + align:start position:0% +for symmetric matrices because they have +those orthogonal eigenvectors they + + align:start position:0% +those orthogonal eigenvectors they + + + align:start position:0% +those orthogonal eigenvectors they +they're the beauty beautiful ones for + + align:start position:0% +they're the beauty beautiful ones for + + + align:start position:0% +they're the beauty beautiful ones for +eigenvectors and a transpose a + + align:start position:0% +eigenvectors and a transpose a + + + align:start position:0% +eigenvectors and a transpose a +automatically symmetric you just you + + align:start position:0% +automatically symmetric you just you + + + align:start position:0% +automatically symmetric you just you +know you just you you're multiplying + + align:start position:0% +know you just you you're multiplying + + + align:start position:0% +know you just you you're multiplying +something by its its adjoint it's its + + align:start position:0% +something by its its adjoint it's its + + + align:start position:0% +something by its its adjoint it's its +transpose and the result is that you you + + align:start position:0% +transpose and the result is that you you + + + align:start position:0% +transpose and the result is that you you +know this matrix is symmetric and maybe + + align:start position:0% +know this matrix is symmetric and maybe + + + align:start position:0% +know this matrix is symmetric and maybe +there's even more about they transpose a + + align:start position:0% +there's even more about they transpose a + + + align:start position:0% +there's even more about they transpose a +yes + + align:start position:0% +yes + + + align:start position:0% +yes +what is that here's a final i always + + align:start position:0% +what is that here's a final i always + + + align:start position:0% +what is that here's a final i always +saying matrix certain matrices are + + align:start position:0% +saying matrix certain matrices are + + + align:start position:0% +saying matrix certain matrices are +important but these are the winners + + align:start position:0% +important but these are the winners + + + align:start position:0% +important but these are the winners +they're symmetric matrices if i want + + align:start position:0% +they're symmetric matrices if i want + + + align:start position:0% +they're symmetric matrices if i want +beautiful matrices make them symmetric + + align:start position:0% +beautiful matrices make them symmetric + + + align:start position:0% +beautiful matrices make them symmetric +and make the eigenvalues positive so + + align:start position:0% +and make the eigenvalues positive so + + + align:start position:0% +and make the eigenvalues positive so +or rather than a nonnegative allows zero + + align:start position:0% +or rather than a nonnegative allows zero + + + align:start position:0% +or rather than a nonnegative allows zero +so I can either say positive definite + + align:start position:0% +so I can either say positive definite + + + align:start position:0% +so I can either say positive definite +when the eigenvalues are positive or I + + align:start position:0% +when the eigenvalues are positive or I + + + align:start position:0% +when the eigenvalues are positive or I +can say non-negative which allows zero + + align:start position:0% +can say non-negative which allows zero + + + align:start position:0% +can say non-negative which allows zero +and that and that so I have greater than + + align:start position:0% +and that and that so I have greater than + + + align:start position:0% +and that and that so I have greater than +or equal to zero I just want to say that + + align:start position:0% +or equal to zero I just want to say that + + + align:start position:0% +or equal to zero I just want to say that +that bringing all the pieces of linear + + align:start position:0% +that bringing all the pieces of linear + + + align:start position:0% +that bringing all the pieces of linear +algebra come together in these matrices + + align:start position:0% +algebra come together in these matrices + + + align:start position:0% +algebra come together in these matrices +and we're seeing the eigenvalue part of + + align:start position:0% +and we're seeing the eigenvalue part of + + + align:start position:0% +and we're seeing the eigenvalue part of +it and here I've mentioned something + + align:start position:0% +it and here I've mentioned something + + + align:start position:0% +it and here I've mentioned something +called the energy so that's a physical + + align:start position:0% +called the energy so that's a physical + + + align:start position:0% +called the energy so that's a physical +quantity that also is greater or equal + + align:start position:0% +quantity that also is greater or equal + + + align:start position:0% +quantity that also is greater or equal +to zero so that's a transpose a is the + + align:start position:0% +to zero so that's a transpose a is the + + + align:start position:0% +to zero so that's a transpose a is the +matrix that I'm going to use in the + + align:start position:0% +matrix that I'm going to use in the + + + align:start position:0% +matrix that I'm going to use in the +final part of this video to achieve + + align:start position:0% +final part of this video to achieve + + + align:start position:0% +final part of this video to achieve +great the greatest factorization Q + + align:start position:0% +great the greatest factorization Q + + + align:start position:0% +great the greatest factorization Q +lambda Q transpose was fantastic but for + + align:start position:0% +lambda Q transpose was fantastic but for + + + align:start position:0% +lambda Q transpose was fantastic but for +our non square matrix it's not for a non + + align:start position:0% +our non square matrix it's not for a non + + + align:start position:0% +our non square matrix it's not for a non +square matrix + + align:start position:0% +square matrix + + + align:start position:0% +square matrix +they don't even have eigenvalues and + + align:start position:0% +they don't even have eigenvalues and + + + align:start position:0% +they don't even have eigenvalues and +eigenvectors but data comes in non + + align:start position:0% +eigenvectors but data comes in non + + + align:start position:0% +eigenvectors but data comes in non +square matrices data is about like we + + align:start position:0% +square matrices data is about like we + + + align:start position:0% +square matrices data is about like we +have a bunch of diseases and a bunch of + + align:start position:0% +have a bunch of diseases and a bunch of + + + align:start position:0% +have a bunch of diseases and a bunch of +patients or a bunch of medicines and the + + align:start position:0% +patients or a bunch of medicines and the + + + align:start position:0% +patients or a bunch of medicines and the +number of medicines is not equal the + + align:start position:0% +number of medicines is not equal the + + + align:start position:0% +number of medicines is not equal the +number of patients or diseases those are + + align:start position:0% +number of patients or diseases those are + + + align:start position:0% +number of patients or diseases those are +different numbers so the matrices that + + align:start position:0% +different numbers so the matrices that + + + align:start position:0% +different numbers so the matrices that +we see in data are rectangular and they + + align:start position:0% +we see in data are rectangular and they + + + align:start position:0% +we see in data are rectangular and they +don't I can values don't make sense for + + align:start position:0% +don't I can values don't make sense for + + + align:start position:0% +don't I can values don't make sense for +those and singular values take their + + align:start position:0% +those and singular values take their + + + align:start position:0% +those and singular values take their +place of eigen values so singular values + + align:start position:0% +place of eigen values so singular values + + + align:start position:0% +place of eigen values so singular values +and my hope is that linear algebra + + align:start position:0% +and my hope is that linear algebra + + + align:start position:0% +and my hope is that linear algebra +courses 1806 for sure will always reach + + align:start position:0% +courses 1806 for sure will always reach + + + align:start position:0% +courses 1806 for sure will always reach +after you to explain eigen values that + + align:start position:0% +after you to explain eigen values that + + + align:start position:0% +after you to explain eigen values that +everybody agrees is important yet + + align:start position:0% +everybody agrees is important yet + + + align:start position:0% +everybody agrees is important yet +singular values into the course because + + align:start position:0% +singular values into the course because + + + align:start position:0% +singular values into the course because +they really have come on as the big + + align:start position:0% +they really have come on as the big + + + align:start position:0% +they really have come on as the big +things to do in data so that would be + + align:start position:0% +things to do in data so that would be + + + align:start position:0% +things to do in data so that would be +the last part of this summary video for + + align:start position:0% +the last part of this summary video for + + + align:start position:0% +the last part of this summary video for +20/20 vision of linear algebra as they + + align:start position:0% +20/20 vision of linear algebra as they + + + align:start position:0% +20/20 vision of linear algebra as they +get singular values in there okay that's + + align:start position:0% +get singular values in there okay that's + + + align:start position:0% +get singular values in there okay that's +kind + + align:start position:0% +kind + + + align:start position:0% +kind +next \ No newline at end of file diff --git a/H9gipVkw6tY.txt b/H9gipVkw6tY.txt new file mode 100644 index 0000000000000000000000000000000000000000..2f1eaeb433d55dcf86c06463d607f307aebfeee9 --- /dev/null +++ b/H9gipVkw6tY.txt @@ -0,0 +1,315 @@ +align:start position:0% + +open education here means open resources + + align:start position:0% +open education here means open resources + + + align:start position:0% +open education here means open resources +in and outside of the classroom for our + + align:start position:0% +in and outside of the classroom for our + + + align:start position:0% +in and outside of the classroom for our +students we're inventing a more open + + align:start position:0% +students we're inventing a more open + + + align:start position:0% +students we're inventing a more open +Future for all curious minds by sharing + + align:start position:0% +Future for all curious minds by sharing + + + align:start position:0% +Future for all curious minds by sharing +a treasure of knowledge for you to + + align:start position:0% +a treasure of knowledge for you to + + + align:start position:0% +a treasure of knowledge for you to +discover anywhere + + align:start position:0% +discover anywhere + + + align:start position:0% +discover anywhere +anytime we're rethinking open by + + align:start position:0% +anytime we're rethinking open by + + + align:start position:0% +anytime we're rethinking open by +recognizing voices and expertise from + + align:start position:0% +recognizing voices and expertise from + + + align:start position:0% +recognizing voices and expertise from +people of diverse backgrounds are + + align:start position:0% +people of diverse backgrounds are + + + align:start position:0% +people of diverse backgrounds are +absolutely necessary for expanding and + + align:start position:0% +absolutely necessary for expanding and + + + align:start position:0% +absolutely necessary for expanding and +growing open educational + + align:start position:0% +growing open educational + + + align:start position:0% +growing open educational +resources 20% of our faculty have + + align:start position:0% +resources 20% of our faculty have + + + align:start position:0% +resources 20% of our faculty have +adapted adopted and are created OE we + + align:start position:0% +adapted adopted and are created OE we + + + align:start position:0% +adapted adopted and are created OE we +are inventing a more open Future for all + + align:start position:0% +are inventing a more open Future for all + + + align:start position:0% +are inventing a more open Future for all +consumers and producers of knowledge by + + align:start position:0% +consumers and producers of knowledge by + + + align:start position:0% +consumers and producers of knowledge by +leading in the development of + + align:start position:0% +leading in the development of + + + align:start position:0% +leading in the development of +sustainable open publishing models and + + align:start position:0% +sustainable open publishing models and + + + align:start position:0% +sustainable open publishing models and +open source publishing Technologies we + + align:start position:0% +open source publishing Technologies we + + + align:start position:0% +open source publishing Technologies we +are Relentless in our pursuit of a more + + align:start position:0% +are Relentless in our pursuit of a more + + + align:start position:0% +are Relentless in our pursuit of a more +open and Equitable scholarly landscape + + align:start position:0% +open and Equitable scholarly landscape + + + align:start position:0% +open and Equitable scholarly landscape +open is democratizing learning and + + align:start position:0% +open is democratizing learning and + + + align:start position:0% +open is democratizing learning and +knowledge to the + + align:start position:0% +knowledge to the + + + align:start position:0% +knowledge to the +[Music] + + align:start position:0% + + + + align:start position:0% + +world here open is in our DNA it + + align:start position:0% +world here open is in our DNA it + + + align:start position:0% +world here open is in our DNA it +captures our commitment to sharing our + + align:start position:0% +captures our commitment to sharing our + + + align:start position:0% +captures our commitment to sharing our +best educational contributions in a way + + align:start position:0% +best educational contributions in a way + + + align:start position:0% +best educational contributions in a way +that everyone can build on them and make + + align:start position:0% +that everyone can build on them and make + + + align:start position:0% +that everyone can build on them and make +them even better here openness is a core + + align:start position:0% +them even better here openness is a core + + + align:start position:0% +them even better here openness is a core +value we share information Innovations + + align:start position:0% +value we share information Innovations + + + align:start position:0% +value we share information Innovations +and ideas with enthusiasm we Champion + + align:start position:0% +and ideas with enthusiasm we Champion + + + align:start position:0% +and ideas with enthusiasm we Champion +open courseware Open Access and open + + align:start position:0% +open courseware Open Access and open + + + align:start position:0% +open courseware Open Access and open +science all crucial to our mission our + + align:start position:0% +science all crucial to our mission our + + + align:start position:0% +science all crucial to our mission our +doors are open too so come join us come + + align:start position:0% +doors are open too so come join us come + + + align:start position:0% +doors are open too so come join us come +join us come join us come invent with us + + align:start position:0% +join us come join us come invent with us + + + align:start position:0% +join us come join us come invent with us +come invent with us we can't wait to + + align:start position:0% +come invent with us we can't wait to + + + align:start position:0% +come invent with us we can't wait to +welcome you I think you would enjoy + + align:start position:0% +welcome you I think you would enjoy + + + align:start position:0% +welcome you I think you would enjoy +seeing Cambridge and I certainly look + + align:start position:0% +seeing Cambridge and I certainly look + + + align:start position:0% +seeing Cambridge and I certainly look +forward to meeting you so let's do it + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] \ No newline at end of file diff --git a/HXwdm2DM18M.txt b/HXwdm2DM18M.txt new file mode 100644 index 0000000000000000000000000000000000000000..3d981b2dc9324730e74e78999df1e04906195b09 --- /dev/null +++ b/HXwdm2DM18M.txt @@ -0,0 +1,795 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +is a respiratory disease caused by the + + align:start position:0% +is a respiratory disease caused by the + + + align:start position:0% +is a respiratory disease caused by the +transmission of the virus SARS cov2 + + align:start position:0% +transmission of the virus SARS cov2 + + + align:start position:0% +transmission of the virus SARS cov2 +the primary mechanism of transmission is + + align:start position:0% +the primary mechanism of transmission is + + + align:start position:0% +the primary mechanism of transmission is +through aerosol particulates from mucous + + align:start position:0% +through aerosol particulates from mucous + + + align:start position:0% +through aerosol particulates from mucous +or saliva that contain the virus and are + + align:start position:0% +or saliva that contain the virus and are + + + align:start position:0% +or saliva that contain the virus and are +emitted during breathing talking singing + + align:start position:0% +emitted during breathing talking singing + + + align:start position:0% +emitted during breathing talking singing +coughing or sneezing + + align:start position:0% +coughing or sneezing + + + align:start position:0% +coughing or sneezing +MIT Lincoln laboratory conducted a study + + align:start position:0% +MIT Lincoln laboratory conducted a study + + + align:start position:0% +MIT Lincoln laboratory conducted a study +to investigate how aerosols are + + align:start position:0% +to investigate how aerosols are + + + align:start position:0% +to investigate how aerosols are +dispersed and potential mitigation + + align:start position:0% +dispersed and potential mitigation + + + align:start position:0% +dispersed and potential mitigation +techniques in mass transit vehicles + + align:start position:0% +techniques in mass transit vehicles + + + align:start position:0% +techniques in mass transit vehicles +the objective was to determine how + + align:start position:0% +the objective was to determine how + + + align:start position:0% +the objective was to determine how +changes in the operating conditions of + + align:start position:0% +changes in the operating conditions of + + + align:start position:0% +changes in the operating conditions of +the vehicle affected how aerosols are + + align:start position:0% +the vehicle affected how aerosols are + + + align:start position:0% +the vehicle affected how aerosols are +dispersed inside the vehicle so the + + align:start position:0% +dispersed inside the vehicle so the + + + align:start position:0% +dispersed inside the vehicle so the +transit operators could determine + + align:start position:0% +transit operators could determine + + + align:start position:0% +transit operators could determine +actions to lower the risk of infection + + align:start position:0% +actions to lower the risk of infection + + + align:start position:0% +actions to lower the risk of infection +to occupants + + align:start position:0% +to occupants + + + align:start position:0% +to occupants +we aerosolized a safe liquid in a way + + align:start position:0% +we aerosolized a safe liquid in a way + + + align:start position:0% +we aerosolized a safe liquid in a way +that mimicked a person copying and a + + align:start position:0% +that mimicked a person copying and a + + + align:start position:0% +that mimicked a person copying and a +variety of sensors were distributed + + align:start position:0% +variety of sensors were distributed + + + align:start position:0% +variety of sensors were distributed +throughout the vehicle to measure the + + align:start position:0% +throughout the vehicle to measure the + + + align:start position:0% +throughout the vehicle to measure the +size and the number of aerosols detected + + align:start position:0% +size and the number of aerosols detected + + + align:start position:0% +size and the number of aerosols detected +at each location over time + + align:start position:0% +at each location over time + + + align:start position:0% +at each location over time +a critical operating condition + + align:start position:0% +a critical operating condition + + + align:start position:0% +a critical operating condition +investigated was how a vehicle's air + + align:start position:0% +investigated was how a vehicle's air + + + align:start position:0% +investigated was how a vehicle's air +filtration system affected the aerosol + + align:start position:0% +filtration system affected the aerosol + + + align:start position:0% +filtration system affected the aerosol +dispersion + + align:start position:0% +dispersion + + + align:start position:0% +dispersion +not all air filters are created equal + + align:start position:0% +not all air filters are created equal + + + align:start position:0% +not all air filters are created equal +they're categorized by filtration + + align:start position:0% +they're categorized by filtration + + + align:start position:0% +they're categorized by filtration +efficiency ratings also known as Merv + + align:start position:0% +efficiency ratings also known as Merv + + + align:start position:0% +efficiency ratings also known as Merv +ratings depending on what size aerosols + + align:start position:0% +ratings depending on what size aerosols + + + align:start position:0% +ratings depending on what size aerosols +they can filter effectively from the air + + align:start position:0% +they can filter effectively from the air + + + align:start position:0% +they can filter effectively from the air +for example common Merv AIDS or nine + + align:start position:0% +for example common Merv AIDS or nine + + + align:start position:0% +for example common Merv AIDS or nine +filters can efficiently remove most + + align:start position:0% +filters can efficiently remove most + + + align:start position:0% +filters can efficiently remove most +pollen and other very large particles + + align:start position:0% +pollen and other very large particles + + + align:start position:0% +pollen and other very large particles +unfortunately an infected person can + + align:start position:0% +unfortunately an infected person can + + + align:start position:0% +unfortunately an infected person can +emit aerosols containing SARS Kobe 2 in + + align:start position:0% +emit aerosols containing SARS Kobe 2 in + + + align:start position:0% +emit aerosols containing SARS Kobe 2 in +a wide range of sizes from hundreds of + + align:start position:0% +a wide range of sizes from hundreds of + + + align:start position:0% +a wide range of sizes from hundreds of +microns which is the width of a human + + align:start position:0% +microns which is the width of a human + + + align:start position:0% +microns which is the width of a human +hair down to tens of nanometers or 10 + + align:start position:0% +hair down to tens of nanometers or 10 + + + align:start position:0% +hair down to tens of nanometers or 10 +times smaller than a single red blood + + align:start position:0% +times smaller than a single red blood + + + align:start position:0% +times smaller than a single red blood +cell + + align:start position:0% +cell + + + align:start position:0% +cell +these smaller respiratory aerosols + + align:start position:0% +these smaller respiratory aerosols + + + align:start position:0% +these smaller respiratory aerosols +require higher efficiency Merv ratings + + align:start position:0% +require higher efficiency Merv ratings + + + align:start position:0% +require higher efficiency Merv ratings +such as Murph 13 or higher in order to + + align:start position:0% +such as Murph 13 or higher in order to + + + align:start position:0% +such as Murph 13 or higher in order to +increase the likelihood of removing the + + align:start position:0% +increase the likelihood of removing the + + + align:start position:0% +increase the likelihood of removing the +SARS cov2 Laden aerosols the trade-off + + align:start position:0% +SARS cov2 Laden aerosols the trade-off + + + align:start position:0% +SARS cov2 Laden aerosols the trade-off +is that these higher efficiency filters + + align:start position:0% +is that these higher efficiency filters + + + align:start position:0% +is that these higher efficiency filters +are also costlier and typically slow + + align:start position:0% +are also costlier and typically slow + + + align:start position:0% +are also costlier and typically slow +down air movement + + align:start position:0% +down air movement + + + align:start position:0% +down air movement +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +we can apply several aspects of this + + align:start position:0% +we can apply several aspects of this + + + align:start position:0% +we can apply several aspects of this +study to help solve another related + + align:start position:0% +study to help solve another related + + + align:start position:0% +study to help solve another related +problem + + align:start position:0% +problem + + + align:start position:0% +problem +how to obtain Clean Water by creating a + + align:start position:0% +how to obtain Clean Water by creating a + + + align:start position:0% +how to obtain Clean Water by creating a +water filtration system + + align:start position:0% +water filtration system + + + align:start position:0% +water filtration system +one of the most important things to + + align:start position:0% +one of the most important things to + + + align:start position:0% +one of the most important things to +understand before creating a solution to + + align:start position:0% +understand before creating a solution to + + + align:start position:0% +understand before creating a solution to +any problem is the requirements what + + align:start position:0% +any problem is the requirements what + + + align:start position:0% +any problem is the requirements what +problem are we trying to solve how + + align:start position:0% +problem are we trying to solve how + + + align:start position:0% +problem are we trying to solve how +efficient does this filtration system + + align:start position:0% +efficient does this filtration system + + + align:start position:0% +efficient does this filtration system +need to be + + align:start position:0% +need to be + + + align:start position:0% +need to be +how large or small must it be + + align:start position:0% +how large or small must it be + + + align:start position:0% +how large or small must it be +what is the budget how much time do we + + align:start position:0% +what is the budget how much time do we + + + align:start position:0% +what is the budget how much time do we +have to complete this project + + align:start position:0% +have to complete this project + + + align:start position:0% +have to complete this project +after determining the requirements we + + align:start position:0% +after determining the requirements we + + + align:start position:0% +after determining the requirements we +can start to build a team and Define + + align:start position:0% +can start to build a team and Define + + + align:start position:0% +can start to build a team and Define +tasks to have a successful team it is + + align:start position:0% +tasks to have a successful team it is + + + align:start position:0% +tasks to have a successful team it is +important to have team members with the + + align:start position:0% +important to have team members with the + + + align:start position:0% +important to have team members with the +correct types of expertise and a clear + + align:start position:0% +correct types of expertise and a clear + + + align:start position:0% +correct types of expertise and a clear +road map to fulfill these requirements + + align:start position:0% +road map to fulfill these requirements + + + align:start position:0% +road map to fulfill these requirements +accompanied by well-defined tasks and + + align:start position:0% +accompanied by well-defined tasks and + + + align:start position:0% +accompanied by well-defined tasks and +role + + align:start position:0% +role + + + align:start position:0% +role +when thinking about how to build a water + + align:start position:0% +when thinking about how to build a water + + + align:start position:0% +when thinking about how to build a water +filtration system consider the + + align:start position:0% +filtration system consider the + + + align:start position:0% +filtration system consider the +trade-offs that each material or + + align:start position:0% +trade-offs that each material or + + + align:start position:0% +trade-offs that each material or +component may have + + align:start position:0% +component may have + + + align:start position:0% +component may have +for our study one key trade-off was + + align:start position:0% +for our study one key trade-off was + + + align:start position:0% +for our study one key trade-off was +between filtration efficiency and + + align:start position:0% +between filtration efficiency and + + + align:start position:0% +between filtration efficiency and +airflow + + align:start position:0% +airflow + + + align:start position:0% +airflow +when trying to remove sediments from + + align:start position:0% +when trying to remove sediments from + + + align:start position:0% +when trying to remove sediments from +water with your filtration system a wire + + align:start position:0% +water with your filtration system a wire + + + align:start position:0% +water with your filtration system a wire +mesh may allow water to exit the filter + + align:start position:0% +mesh may allow water to exit the filter + + + align:start position:0% +mesh may allow water to exit the filter +at a higher flow rate but may only + + align:start position:0% +at a higher flow rate but may only + + + align:start position:0% +at a higher flow rate but may only +capture the larger granular particles + + align:start position:0% +capture the larger granular particles + + + align:start position:0% +capture the larger granular particles +on the other hand + + align:start position:0% +on the other hand + + + align:start position:0% +on the other hand +a cotton ball May remove finer sediments + + align:start position:0% +a cotton ball May remove finer sediments + + + align:start position:0% +a cotton ball May remove finer sediments +but may have a slower flow rate + + align:start position:0% +but may have a slower flow rate + + + align:start position:0% +but may have a slower flow rate +as you can imagine there may be several + + align:start position:0% +as you can imagine there may be several + + + align:start position:0% +as you can imagine there may be several +options or combinations of options that + + align:start position:0% +options or combinations of options that + + + align:start position:0% +options or combinations of options that +can solve the same problem + + align:start position:0% +can solve the same problem + + + align:start position:0% +can solve the same problem +determining which options would create a + + align:start position:0% +determining which options would create a + + + align:start position:0% +determining which options would create a +water filtration system that meets all + + align:start position:0% +water filtration system that meets all + + + align:start position:0% +water filtration system that meets all +of the requirements considering the + + align:start position:0% +of the requirements considering the + + + align:start position:0% +of the requirements considering the +constraints and trade-offs of size time + + align:start position:0% +constraints and trade-offs of size time + + + align:start position:0% +constraints and trade-offs of size time +and budget are all part of the fun in + + align:start position:0% +and budget are all part of the fun in + + + align:start position:0% +and budget are all part of the fun in +engineering \ No newline at end of file diff --git a/HaySEpWEsdU.txt b/HaySEpWEsdU.txt new file mode 100644 index 0000000000000000000000000000000000000000..5a619452e91d21b6c4d50335cae8cb7eab2d3b3d --- /dev/null +++ b/HaySEpWEsdU.txt @@ -0,0 +1,3291 @@ +align:start position:0% + +I've been teaching at MIT since 2001 and + + align:start position:0% +I've been teaching at MIT since 2001 and + + + align:start position:0% +I've been teaching at MIT since 2001 and +I've taught all kinds of classes but the + + align:start position:0% +I've taught all kinds of classes but the + + + align:start position:0% +I've taught all kinds of classes but the +innovation I'm excited to be torn out + + align:start position:0% +innovation I'm excited to be torn out + + + align:start position:0% +innovation I'm excited to be torn out +today is a new set of linked projects + + align:start position:0% +today is a new set of linked projects + + + align:start position:0% +today is a new set of linked projects +that I helped our mid-career Executive + + align:start position:0% +that I helped our mid-career Executive + + + align:start position:0% +that I helped our mid-career Executive +students the Sloan fellow MBAs on this + + align:start position:0% +students the Sloan fellow MBAs on this + + + align:start position:0% +students the Sloan fellow MBAs on this +past year so I hung up my shingle and + + align:start position:0% +past year so I hung up my shingle and + + + align:start position:0% +past year so I hung up my shingle and +asked students who had a passion for + + align:start position:0% +asked students who had a passion for + + + align:start position:0% +asked students who had a passion for +linking technology with social impact in + + align:start position:0% +linking technology with social impact in + + + align:start position:0% +linking technology with social impact in +some way to come and talk to me and I + + align:start position:0% +some way to come and talk to me and I + + + align:start position:0% +some way to come and talk to me and I +created with them a set of projects + + align:start position:0% +created with them a set of projects + + + align:start position:0% +created with them a set of projects +which allowed the students to really dig + + align:start position:0% +which allowed the students to really dig + + + align:start position:0% +which allowed the students to really dig +into areas that they came to MIT + + align:start position:0% +into areas that they came to MIT + + + align:start position:0% +into areas that they came to MIT +passionate about but also to link it to + + align:start position:0% +passionate about but also to link it to + + + align:start position:0% +passionate about but also to link it to +their coursework and their degree + + align:start position:0% +their coursework and their degree + + + align:start position:0% +their coursework and their degree +program could you talk a little bit + + align:start position:0% +program could you talk a little bit + + + align:start position:0% +program could you talk a little bit +about some of the specific projects that + + align:start position:0% +about some of the specific projects that + + + align:start position:0% +about some of the specific projects that +students did the project students did + + align:start position:0% +students did the project students did + + + align:start position:0% +students did the project students did +ranged greatly but all had as a theme + + align:start position:0% +ranged greatly but all had as a theme + + + align:start position:0% +ranged greatly but all had as a theme +using what they were learning here and + + align:start position:0% +using what they were learning here and + + + align:start position:0% +using what they were learning here and +tapping into emerging or existing + + align:start position:0% +tapping into emerging or existing + + + align:start position:0% +tapping into emerging or existing +technology in new ways to find solutions + + align:start position:0% +technology in new ways to find solutions + + + align:start position:0% +technology in new ways to find solutions +to problems that face many that's the + + align:start position:0% +to problems that face many that's the + + + align:start position:0% +to problems that face many that's the +social impact aspect of it and it took + + align:start position:0% +social impact aspect of it and it took + + + align:start position:0% +social impact aspect of it and it took +with each student some effort to really + + align:start position:0% +with each student some effort to really + + + align:start position:0% +with each student some effort to really +map out a good enough and focused enough + + align:start position:0% +map out a good enough and focused enough + + + align:start position:0% +map out a good enough and focused enough +question that was doable as an + + align:start position:0% +question that was doable as an + + + align:start position:0% +question that was doable as an +independent study project and that was + + align:start position:0% +independent study project and that was + + + align:start position:0% +independent study project and that was +deep enough to allow me to really bring + + align:start position:0% +deep enough to allow me to really bring + + + align:start position:0% +deep enough to allow me to really bring +to bear the educational goals that I had + + align:start position:0% +to bear the educational goals that I had + + + align:start position:0% +to bear the educational goals that I had +for the projects so one student Doreen + + align:start position:0% +for the projects so one student Doreen + + + align:start position:0% +for the projects so one student Doreen +was really interested in the problem of + + align:start position:0% +was really interested in the problem of + + + align:start position:0% +was really interested in the problem of +creating agricultural products in Africa + + align:start position:0% +creating agricultural products in Africa + + + align:start position:0% +creating agricultural products in Africa +using crops and products that are grown + + align:start position:0% +using crops and products that are grown + + + align:start position:0% +using crops and products that are grown +right there in Africa why is Africa + + align:start position:0% +right there in Africa why is Africa + + + align:start position:0% +right there in Africa why is Africa +importing a lot of consumer products + + align:start position:0% +importing a lot of consumer products + + + align:start position:0% +importing a lot of consumer products +when the continent has a lot of + + align:start position:0% +when the continent has a lot of + + + align:start position:0% +when the continent has a lot of +agricultural assets so she was really + + align:start position:0% +agricultural assets so she was really + + + align:start position:0% +agricultural assets so she was really +interested in understanding what are the + + align:start position:0% +interested in understanding what are the + + + align:start position:0% +interested in understanding what are the +business models what are the constraints + + align:start position:0% +business models what are the constraints + + + align:start position:0% +business models what are the constraints +what are the opportunities when it comes + + align:start position:0% +what are the opportunities when it comes + + + align:start position:0% +what are the opportunities when it comes +to finding new ways to create locally + + align:start position:0% +to finding new ways to create locally + + + align:start position:0% +to finding new ways to create locally +sourced products that could actually + + align:start position:0% +sourced products that could actually + + + align:start position:0% +sourced products that could actually +serve beauty nutrition or other needs + + align:start position:0% +serve beauty nutrition or other needs + + + align:start position:0% +serve beauty nutrition or other needs +in her native Zimbabwe or elsewhere in + + align:start position:0% +in her native Zimbabwe or elsewhere in + + + align:start position:0% +in her native Zimbabwe or elsewhere in +Africa I'll tell you about another + + align:start position:0% +Africa I'll tell you about another + + + align:start position:0% +Africa I'll tell you about another +project + + align:start position:0% +project + + + align:start position:0% +project +Eloy a student who came to me after deep + + align:start position:0% +Eloy a student who came to me after deep + + + align:start position:0% +Eloy a student who came to me after deep +experience at the World Bank was really + + align:start position:0% +experience at the World Bank was really + + + align:start position:0% +experience at the World Bank was really +interested in a challenge that + + align:start position:0% +interested in a challenge that + + + align:start position:0% +interested in a challenge that +traditional governmental organizations + + align:start position:0% +traditional governmental organizations + + + align:start position:0% +traditional governmental organizations +really wrestle with how do we tap into + + align:start position:0% +really wrestle with how do we tap into + + + align:start position:0% +really wrestle with how do we tap into +entrepreneurship when we're trying to + + align:start position:0% +entrepreneurship when we're trying to + + + align:start position:0% +entrepreneurship when we're trying to +serve the public good there seems to be + + align:start position:0% +serve the public good there seems to be + + + align:start position:0% +serve the public good there seems to be +a challenge in linking the entrepreneur + + align:start position:0% +a challenge in linking the entrepreneur + + + align:start position:0% +a challenge in linking the entrepreneur +and the public sector and we know that + + align:start position:0% +and the public sector and we know that + + + align:start position:0% +and the public sector and we know that +there are all kinds of innovations that + + align:start position:0% +there are all kinds of innovations that + + + align:start position:0% +there are all kinds of innovations that +kind of play in this sphere from ride + + align:start position:0% +kind of play in this sphere from ride + + + align:start position:0% +kind of play in this sphere from ride +sharing and other had and regulated + + align:start position:0% +sharing and other had and regulated + + + align:start position:0% +sharing and other had and regulated +industries all the way through to + + align:start position:0% +industries all the way through to + + + align:start position:0% +industries all the way through to +providing in a better way the services + + align:start position:0% +providing in a better way the services + + + align:start position:0% +providing in a better way the services +that governments are already on the hook + + align:start position:0% +that governments are already on the hook + + + align:start position:0% +that governments are already on the hook +for so they're either regulated or they + + align:start position:0% +for so they're either regulated or they + + + align:start position:0% +for so they're either regulated or they +are substitutes for improvements of + + align:start position:0% +are substitutes for improvements of + + + align:start position:0% +are substitutes for improvements of +services that governments provide and + + align:start position:0% +services that governments provide and + + + align:start position:0% +services that governments provide and +sometimes they're also missing services + + align:start position:0% +sometimes they're also missing services + + + align:start position:0% +sometimes they're also missing services +how do you find that what are the + + align:start position:0% +how do you find that what are the + + + align:start position:0% +how do you find that what are the +barriers to this where the opportunities + + align:start position:0% +barriers to this where the opportunities + + + align:start position:0% +barriers to this where the opportunities +what are the trends and can we actually + + align:start position:0% +what are the trends and can we actually + + + align:start position:0% +what are the trends and can we actually +map out where we think this field could + + align:start position:0% +map out where we think this field could + + + align:start position:0% +map out where we think this field could +go of mixing entrepreneurship and the + + align:start position:0% +go of mixing entrepreneurship and the + + + align:start position:0% +go of mixing entrepreneurship and the +public sector one of my students aleni + + align:start position:0% +public sector one of my students aleni + + + align:start position:0% +public sector one of my students aleni +came to MIT with completely on fire with + + align:start position:0% +came to MIT with completely on fire with + + + align:start position:0% +came to MIT with completely on fire with +this idea of tapping into analytics and + + align:start position:0% +this idea of tapping into analytics and + + + align:start position:0% +this idea of tapping into analytics and +AI to solve what she saw as a major + + align:start position:0% +AI to solve what she saw as a major + + + align:start position:0% +AI to solve what she saw as a major +challenge when it came to bringing + + align:start position:0% +challenge when it came to bringing + + + align:start position:0% +challenge when it came to bringing +finance to small holder and small-scale + + align:start position:0% +finance to small holder and small-scale + + + align:start position:0% +finance to small holder and small-scale +farmers she's an expert on agricultural + + align:start position:0% +farmers she's an expert on agricultural + + + align:start position:0% +farmers she's an expert on agricultural +finance and she realized that in her + + align:start position:0% +finance and she realized that in her + + + align:start position:0% +finance and she realized that in her +native Brazil and elsewhere people who + + align:start position:0% +native Brazil and elsewhere people who + + + align:start position:0% +native Brazil and elsewhere people who +didn't have good credit standing and + + align:start position:0% +didn't have good credit standing and + + + align:start position:0% +didn't have good credit standing and +good credit records farmers who didn't + + align:start position:0% +good credit records farmers who didn't + + + align:start position:0% +good credit records farmers who didn't +have those assets couldn't get loans and + + align:start position:0% +have those assets couldn't get loans and + + + align:start position:0% +have those assets couldn't get loans and +were forever locked out so there's a big + + align:start position:0% +were forever locked out so there's a big + + + align:start position:0% +were forever locked out so there's a big +dichotomy between the people of access + + align:start position:0% +dichotomy between the people of access + + + align:start position:0% +dichotomy between the people of access +to finance and those who don't + + align:start position:0% +to finance and those who don't + + + align:start position:0% +to finance and those who don't +could she break down that barrier in + + align:start position:0% +could she break down that barrier in + + + align:start position:0% +could she break down that barrier in +some way could new forms of data and + + align:start position:0% +some way could new forms of data and + + + align:start position:0% +some way could new forms of data and +technology help do that so instead of + + align:start position:0% +technology help do that so instead of + + + align:start position:0% +technology help do that so instead of +relying only on somebody's credit record + + align:start position:0% +relying only on somebody's credit record + + + align:start position:0% +relying only on somebody's credit record +could you look at the whether they're + + align:start position:0% +could you look at the whether they're + + + align:start position:0% +could you look at the whether they're +farming choices they + + align:start position:0% +farming choices they + + + align:start position:0% +farming choices they +behaviors and physical data and use it + + align:start position:0% +behaviors and physical data and use it + + + align:start position:0% +behaviors and physical data and use it +to come up with a better assessment of + + align:start position:0% +to come up with a better assessment of + + + align:start position:0% +to come up with a better assessment of +the riskiness of a given farmer from a + + align:start position:0% +the riskiness of a given farmer from a + + + align:start position:0% +the riskiness of a given farmer from a +lender's point of view slightly + + align:start position:0% +lender's point of view slightly + + + align:start position:0% +lender's point of view slightly +technical area but it actually has huge + + align:start position:0% +technical area but it actually has huge + + + align:start position:0% +technical area but it actually has huge +implications because it could open the + + align:start position:0% +implications because it could open the + + + align:start position:0% +implications because it could open the +door to all kinds of folks who are + + align:start position:0% +door to all kinds of folks who are + + + align:start position:0% +door to all kinds of folks who are +excluded from traditional finance by + + align:start position:0% +excluded from traditional finance by + + + align:start position:0% +excluded from traditional finance by +providing other methods of sorting out + + align:start position:0% +providing other methods of sorting out + + + align:start position:0% +providing other methods of sorting out +their riskiness and their + + align:start position:0% +their riskiness and their + + + align:start position:0% +their riskiness and their +creditworthiness so how did it all work + + align:start position:0% +creditworthiness so how did it all work + + + align:start position:0% +creditworthiness so how did it all work +logistically how did you manage to + + align:start position:0% +logistically how did you manage to + + + align:start position:0% +logistically how did you manage to +create all these different individual + + align:start position:0% +create all these different individual + + + align:start position:0% +create all these different individual +projects so that's the downside of this + + align:start position:0% +projects so that's the downside of this + + + align:start position:0% +projects so that's the downside of this +approach each project was customized + + align:start position:0% +approach each project was customized + + + align:start position:0% +approach each project was customized +it's kind of a boutique learning + + align:start position:0% +it's kind of a boutique learning + + + align:start position:0% +it's kind of a boutique learning +experience in a sense and one of the + + align:start position:0% +experience in a sense and one of the + + + align:start position:0% +experience in a sense and one of the +things I've learned about trying to + + align:start position:0% +things I've learned about trying to + + + align:start position:0% +things I've learned about trying to +innovate when it comes to teaching is + + align:start position:0% +innovate when it comes to teaching is + + + align:start position:0% +innovate when it comes to teaching is +you have to be willing to invest a lot + + align:start position:0% +you have to be willing to invest a lot + + + align:start position:0% +you have to be willing to invest a lot +the first few rounds the first few years + + align:start position:0% +the first few rounds the first few years + + + align:start position:0% +the first few rounds the first few years +you do something and then over time you + + align:start position:0% +you do something and then over time you + + + align:start position:0% +you do something and then over time you +learn how to make it a little more + + align:start position:0% +learn how to make it a little more + + + align:start position:0% +learn how to make it a little more +efficient streamlined maybe scalable and + + align:start position:0% +efficient streamlined maybe scalable and + + + align:start position:0% +efficient streamlined maybe scalable and +more cost effective but this year was + + align:start position:0% +more cost effective but this year was + + + align:start position:0% +more cost effective but this year was +definitely a labor of love + + align:start position:0% +definitely a labor of love + + + align:start position:0% +definitely a labor of love +so students came to me with all kinds of + + align:start position:0% +so students came to me with all kinds of + + + align:start position:0% +so students came to me with all kinds of +ideas and I had open office hours I have + + align:start position:0% +ideas and I had open office hours I have + + + align:start position:0% +ideas and I had open office hours I have +a wiki page where students can sign up + + align:start position:0% +a wiki page where students can sign up + + + align:start position:0% +a wiki page where students can sign up +to meet with me in 20 minute increments + + align:start position:0% +to meet with me in 20 minute increments + + + align:start position:0% +to meet with me in 20 minute increments +and I would just set up hours of these + + align:start position:0% +and I would just set up hours of these + + + align:start position:0% +and I would just set up hours of these +meetings every week and sit and talk to + + align:start position:0% +meetings every week and sit and talk to + + + align:start position:0% +meetings every week and sit and talk to +students about their ideas try to + + align:start position:0% +students about their ideas try to + + + align:start position:0% +students about their ideas try to +formulate some reasonable next steps + + align:start position:0% +formulate some reasonable next steps + + + align:start position:0% +formulate some reasonable next steps +really push them to think about how + + align:start position:0% +really push them to think about how + + + align:start position:0% +really push them to think about how +they're using their coursework here and + + align:start position:0% +they're using their coursework here and + + + align:start position:0% +they're using their coursework here and +their presence on campus to craft + + align:start position:0% +their presence on campus to craft + + + align:start position:0% +their presence on campus to craft +something they couldn't do anywhere else + + align:start position:0% +something they couldn't do anywhere else + + + align:start position:0% +something they couldn't do anywhere else +and that spoke to everything else they + + align:start position:0% +and that spoke to everything else they + + + align:start position:0% +and that spoke to everything else they +had access to while they were here so + + align:start position:0% +had access to while they were here so + + + align:start position:0% +had access to while they were here so +that process took a lot of + + align:start position:0% +that process took a lot of + + + align:start position:0% +that process took a lot of +back-and-forth usually I would meet with + + align:start position:0% +back-and-forth usually I would meet with + + + align:start position:0% +back-and-forth usually I would meet with +students once a week I opened a shared + + align:start position:0% +students once a week I opened a shared + + + align:start position:0% +students once a week I opened a shared +folder with each of them and would shoot + + align:start position:0% +folder with each of them and would shoot + + + align:start position:0% +folder with each of them and would shoot +materials that I found into the folder + + align:start position:0% +materials that I found into the folder + + + align:start position:0% +materials that I found into the folder +and have them load their drafts work + + align:start position:0% +and have them load their drafts work + + + align:start position:0% +and have them load their drafts work +plans and other work in progress there + + align:start position:0% +plans and other work in progress there + + + align:start position:0% +plans and other work in progress there +and then I also would got into a very + + align:start position:0% +and then I also would got into a very + + + align:start position:0% +and then I also would got into a very +quick habit of sending any interesting + + align:start position:0% +quick habit of sending any interesting + + + align:start position:0% +quick habit of sending any interesting +reading news article conference notice + + align:start position:0% +reading news article conference notice + + + align:start position:0% +reading news article conference notice +directly to the students so some of them + + align:start position:0% +directly to the students so some of them + + + align:start position:0% +directly to the students so some of them +would be getting 10 emails from me but + + align:start position:0% +would be getting 10 emails from me but + + + align:start position:0% +would be getting 10 emails from me but +that really got us going because they + + align:start position:0% +that really got us going because they + + + align:start position:0% +that really got us going because they +could see I was thinking about it all + + align:start position:0% +could see I was thinking about it all + + + align:start position:0% +could see I was thinking about it all +week and they were too I learned I had + + align:start position:0% +week and they were too I learned I had + + + align:start position:0% +week and they were too I learned I had +to keep a whiteboard up in my office + + align:start position:0% +to keep a whiteboard up in my office + + + align:start position:0% +to keep a whiteboard up in my office +with each project in each person because + + align:start position:0% +with each project in each person because + + + align:start position:0% +with each project in each person because +I had a over a dozen running to keep + + align:start position:0% +I had a over a dozen running to keep + + + align:start position:0% +I had a over a dozen running to keep +them straight and try to remember who's + + align:start position:0% +them straight and try to remember who's + + + align:start position:0% +them straight and try to remember who's +doing what so that when I saw it when I + + align:start position:0% +doing what so that when I saw it when I + + + align:start position:0% +doing what so that when I saw it when I +came into the office I had that person + + align:start position:0% +came into the office I had that person + + + align:start position:0% +came into the office I had that person +would be on my mind or that project + + align:start position:0% +would be on my mind or that project + + + align:start position:0% +would be on my mind or that project +would be on my mind + + align:start position:0% +would be on my mind + + + align:start position:0% +would be on my mind +Wow do you see this as something that is + + align:start position:0% +Wow do you see this as something that is + + + align:start position:0% +Wow do you see this as something that is +potentially scalable in the future I do + + align:start position:0% +potentially scalable in the future I do + + + align:start position:0% +potentially scalable in the future I do +one question I've been thinking about a + + align:start position:0% +one question I've been thinking about a + + + align:start position:0% +one question I've been thinking about a +lot is how you could also use peers + + align:start position:0% +lot is how you could also use peers + + + align:start position:0% +lot is how you could also use peers +could we craft project kind of clusters + + align:start position:0% +could we craft project kind of clusters + + + align:start position:0% +could we craft project kind of clusters +so could we link the themes but we could + + align:start position:0% +so could we link the themes but we could + + + align:start position:0% +so could we link the themes but we could +we also have students helping each other + + align:start position:0% +we also have students helping each other + + + align:start position:0% +we also have students helping each other +coaching each other a little bit could + + align:start position:0% +coaching each other a little bit could + + + align:start position:0% +coaching each other a little bit could +we use group meetings as a way to + + align:start position:0% +we use group meetings as a way to + + + align:start position:0% +we use group meetings as a way to +surface a helpful discussion about + + align:start position:0% +surface a helpful discussion about + + + align:start position:0% +surface a helpful discussion about +what's working and what isn't I think + + align:start position:0% +what's working and what isn't I think + + + align:start position:0% +what's working and what isn't I think +that that's the next step so that I + + align:start position:0% +that that's the next step so that I + + + align:start position:0% +that that's the next step so that I +think that we'll get to some scalability + + align:start position:0% +think that we'll get to some scalability + + + align:start position:0% +think that we'll get to some scalability +I do think mundane as it sounds I think + + align:start position:0% +I do think mundane as it sounds I think + + + align:start position:0% +I do think mundane as it sounds I think +it's also important to have good like + + align:start position:0% +it's also important to have good like + + + align:start position:0% +it's also important to have good like +forms and people work having people + + align:start position:0% +forms and people work having people + + + align:start position:0% +forms and people work having people +really articulate in writing briefly + + align:start position:0% +really articulate in writing briefly + + + align:start position:0% +really articulate in writing briefly +what they want to do and having a + + align:start position:0% +what they want to do and having a + + + align:start position:0% +what they want to do and having a +structured kind of update process really + + align:start position:0% +structured kind of update process really + + + align:start position:0% +structured kind of update process really +helps keep the momentum and build the + + align:start position:0% +helps keep the momentum and build the + + + align:start position:0% +helps keep the momentum and build the +focus how do you measure success in + + align:start position:0% +focus how do you measure success in + + + align:start position:0% +focus how do you measure success in +projects like this it's a great question + + align:start position:0% +projects like this it's a great question + + + align:start position:0% +projects like this it's a great question +because students who are following their + + align:start position:0% +because students who are following their + + + align:start position:0% +because students who are following their +passions really get into it you give + + align:start position:0% +passions really get into it you give + + + align:start position:0% +passions really get into it you give +them enough freedom they will have a + + align:start position:0% +them enough freedom they will have a + + + align:start position:0% +them enough freedom they will have a +good time but part of our challenge as + + align:start position:0% +good time but part of our challenge as + + + align:start position:0% +good time but part of our challenge as +as their teachers is to help make sure + + align:start position:0% +as their teachers is to help make sure + + + align:start position:0% +as their teachers is to help make sure +that we're embedding into their approach + + align:start position:0% +that we're embedding into their approach + + + align:start position:0% +that we're embedding into their approach +enough rigor that we're looking at the + + align:start position:0% +enough rigor that we're looking at the + + + align:start position:0% +enough rigor that we're looking at the +data and the evidence and that it's been + + align:start position:0% +data and the evidence and that it's been + + + align:start position:0% +data and the evidence and that it's been +linked to the content we're teaching + + align:start position:0% +linked to the content we're teaching + + + align:start position:0% +linked to the content we're teaching +here so a passion project by itself may + + align:start position:0% +here so a passion project by itself may + + + align:start position:0% +here so a passion project by itself may +or may not be academic so there there's + + align:start position:0% +or may not be academic so there there's + + + align:start position:0% +or may not be academic so there there's +a bit of tension + + align:start position:0% +a bit of tension + + + align:start position:0% +a bit of tension +they're of us having to remind students + + align:start position:0% +they're of us having to remind students + + + align:start position:0% +they're of us having to remind students +of the need to keep making all of these + + align:start position:0% +of the need to keep making all of these + + + align:start position:0% +of the need to keep making all of these +connections so I would really view + + align:start position:0% +connections so I would really view + + + align:start position:0% +connections so I would really view +success as when we're able to get the + + align:start position:0% +success as when we're able to get the + + + align:start position:0% +success as when we're able to get the +students to not only pull out develop + + align:start position:0% +students to not only pull out develop + + + align:start position:0% +students to not only pull out develop +polish a great new idea but also to link + + align:start position:0% +polish a great new idea but also to link + + + align:start position:0% +polish a great new idea but also to link +it to what they've been learning here + + align:start position:0% +it to what they've been learning here + + + align:start position:0% +it to what they've been learning here +and test their ideas with a level of + + align:start position:0% +and test their ideas with a level of + + + align:start position:0% +and test their ideas with a level of +attention to that data even if it's + + align:start position:0% +attention to that data even if it's + + + align:start position:0% +attention to that data even if it's +qualitative that really we can all stand + + align:start position:0% +qualitative that really we can all stand + + + align:start position:0% +qualitative that really we can all stand +behind and how did you do that in in + + align:start position:0% +behind and how did you do that in in + + + align:start position:0% +behind and how did you do that in in +these projects so part of the + + align:start position:0% +these projects so part of the + + + align:start position:0% +these projects so part of the +requirement is to really make sure that + + align:start position:0% +requirement is to really make sure that + + + align:start position:0% +requirement is to really make sure that +if a student there's actually quite a + + align:start position:0% +if a student there's actually quite a + + + align:start position:0% +if a student there's actually quite a +lot of work in trying to unpack the + + align:start position:0% +lot of work in trying to unpack the + + + align:start position:0% +lot of work in trying to unpack the +logic the thinking behind a new idea and + + align:start position:0% +logic the thinking behind a new idea and + + + align:start position:0% +logic the thinking behind a new idea and +I would spend a lot of time trying to + + align:start position:0% +I would spend a lot of time trying to + + + align:start position:0% +I would spend a lot of time trying to +help figure out where is it we need to + + align:start position:0% +help figure out where is it we need to + + + align:start position:0% +help figure out where is it we need to +drill down to back up this idea where is + + align:start position:0% +drill down to back up this idea where is + + + align:start position:0% +drill down to back up this idea where is +it that we use the literature and the + + align:start position:0% +it that we use the literature and the + + + align:start position:0% +it that we use the literature and the +research where you're going to do desk + + align:start position:0% +research where you're going to do desk + + + align:start position:0% +research where you're going to do desk +research to sort of shore up one leg of + + align:start position:0% +research to sort of shore up one leg of + + + align:start position:0% +research to sort of shore up one leg of +what you're doing and where is it that + + align:start position:0% +what you're doing and where is it that + + + align:start position:0% +what you're doing and where is it that +you're gonna gather new information + + align:start position:0% +you're gonna gather new information + + + align:start position:0% +you're gonna gather new information +whether it's by observation by + + align:start position:0% +whether it's by observation by + + + align:start position:0% +whether it's by observation by +interviews by other methods that you can + + align:start position:0% +interviews by other methods that you can + + + align:start position:0% +interviews by other methods that you can +bring to bear so you I really want it + + align:start position:0% +bring to bear so you I really want it + + + align:start position:0% +bring to bear so you I really want it +was looking for both where's the link to + + align:start position:0% +was looking for both where's the link to + + + align:start position:0% +was looking for both where's the link to +other people's work to the research in + + align:start position:0% +other people's work to the research in + + + align:start position:0% +other people's work to the research in +the literature where's the link to + + align:start position:0% +the literature where's the link to + + + align:start position:0% +the literature where's the link to +something new that you've uncovered and + + align:start position:0% +something new that you've uncovered and + + + align:start position:0% +something new that you've uncovered and +then using methods that you were going + + align:start position:0% +then using methods that you were going + + + align:start position:0% +then using methods that you were going +to describe systematically I see the + + align:start position:0% +to describe systematically I see the + + + align:start position:0% +to describe systematically I see the +great thing about this is that it helps + + align:start position:0% +great thing about this is that it helps + + + align:start position:0% +great thing about this is that it helps +me to learn so part of what I think the + + align:start position:0% +me to learn so part of what I think the + + + align:start position:0% +me to learn so part of what I think the +huge value in teaching this way is that + + align:start position:0% +huge value in teaching this way is that + + + align:start position:0% +huge value in teaching this way is that +you as the instructor have this like + + align:start position:0% +you as the instructor have this like + + + align:start position:0% +you as the instructor have this like +gift of hearing new ideas that aren't + + align:start position:0% +gift of hearing new ideas that aren't + + + align:start position:0% +gift of hearing new ideas that aren't +necessarily embedded into the academic + + align:start position:0% +necessarily embedded into the academic + + + align:start position:0% +necessarily embedded into the academic +structure yet so I discovered there + + align:start position:0% +structure yet so I discovered there + + + align:start position:0% +structure yet so I discovered there +really is a need to build a better + + align:start position:0% +really is a need to build a better + + + align:start position:0% +really is a need to build a better +theory and framework around public + + align:start position:0% +theory and framework around public + + + align:start position:0% +theory and framework around public +entrepreneurship that's that's really + + align:start position:0% +entrepreneurship that's that's really + + + align:start position:0% +entrepreneurship that's that's really +interesting that helps me think about my + + align:start position:0% +interesting that helps me think about my + + + align:start position:0% +interesting that helps me think about my +own research goals and where I might + + align:start position:0% +own research goals and where I might + + + align:start position:0% +own research goals and where I might +build new collaborations here on campus + + align:start position:0% +build new collaborations here on campus + + + align:start position:0% +build new collaborations here on campus +other faculty and researchers in + + align:start position:0% +other faculty and researchers in + + + align:start position:0% +other faculty and researchers in +speaking of collaborations what was the + + align:start position:0% +speaking of collaborations what was the + + + align:start position:0% +speaking of collaborations what was the +role of networking in this experience + + align:start position:0% +role of networking in this experience + + + align:start position:0% +role of networking in this experience +for our fellows so students coming here + + align:start position:0% +for our fellows so students coming here + + + align:start position:0% +for our fellows so students coming here +have varying predilections for + + align:start position:0% +have varying predilections for + + + align:start position:0% +have varying predilections for +networking and connecting with others + + align:start position:0% +networking and connecting with others + + + align:start position:0% +networking and connecting with others +and many of them really benefit from + + align:start position:0% +and many of them really benefit from + + + align:start position:0% +and many of them really benefit from +having a focus to that so very often we + + align:start position:0% +having a focus to that so very often we + + + align:start position:0% +having a focus to that so very often we +tell students you have this gift of + + align:start position:0% +tell students you have this gift of + + + align:start position:0% +tell students you have this gift of +being here on campus for a while make + + align:start position:0% +being here on campus for a while make + + + align:start position:0% +being here on campus for a while make +the most of it + + align:start position:0% +the most of it + + + align:start position:0% +the most of it +but if you're just trying to meet people + + align:start position:0% +but if you're just trying to meet people + + + align:start position:0% +but if you're just trying to meet people +to fill up your rolodex + + align:start position:0% +to fill up your rolodex + + + align:start position:0% +to fill up your rolodex +it's rather self-serving and it's + + align:start position:0% +it's rather self-serving and it's + + + align:start position:0% +it's rather self-serving and it's +awkward and there's no reason to meet + + align:start position:0% +awkward and there's no reason to meet + + + align:start position:0% +awkward and there's no reason to meet +but if you can articulate a really + + align:start position:0% +but if you can articulate a really + + + align:start position:0% +but if you can articulate a really +interesting question this gives students + + align:start position:0% +interesting question this gives students + + + align:start position:0% +interesting question this gives students +a reason to contact people so I really + + align:start position:0% +a reason to contact people so I really + + + align:start position:0% +a reason to contact people so I really +view the two is linked develop a great + + align:start position:0% +view the two is linked develop a great + + + align:start position:0% +view the two is linked develop a great +problem statement or research question + + align:start position:0% +problem statement or research question + + + align:start position:0% +problem statement or research question +use that to look at what you have access + + align:start position:0% +use that to look at what you have access + + + align:start position:0% +use that to look at what you have access +to on campus that might include faculty + + align:start position:0% +to on campus that might include faculty + + + align:start position:0% +to on campus that might include faculty +postdocs research teams that might + + align:start position:0% +postdocs research teams that might + + + align:start position:0% +postdocs research teams that might +include alumni it it includes folks + + align:start position:0% +include alumni it it includes folks + + + align:start position:0% +include alumni it it includes folks +within the MIT sort of ecosystems you + + align:start position:0% +within the MIT sort of ecosystems you + + + align:start position:0% +within the MIT sort of ecosystems you +might head over to an incubator or some + + align:start position:0% +might head over to an incubator or some + + + align:start position:0% +might head over to an incubator or some +other a venue an event where people are + + align:start position:0% +other a venue an event where people are + + + align:start position:0% +other a venue an event where people are +and then because we get a lot of people + + align:start position:0% +and then because we get a lot of people + + + align:start position:0% +and then because we get a lot of people +passing through as well as invitations + + align:start position:0% +passing through as well as invitations + + + align:start position:0% +passing through as well as invitations +to meetings conferences and events + + align:start position:0% +to meetings conferences and events + + + align:start position:0% +to meetings conferences and events +globally I would shoot those to my + + align:start position:0% +globally I would shoot those to my + + + align:start position:0% +globally I would shoot those to my +students so say so-and-so is coming to + + align:start position:0% +students so say so-and-so is coming to + + + align:start position:0% +students so say so-and-so is coming to +campus next week you know see if you can + + align:start position:0% +campus next week you know see if you can + + + align:start position:0% +campus next week you know see if you can +get on their agenda and that would often + + align:start position:0% +get on their agenda and that would often + + + align:start position:0% +get on their agenda and that would often +work yeah how are you looking to tweak + + align:start position:0% +work yeah how are you looking to tweak + + + align:start position:0% +work yeah how are you looking to tweak +this experience the next time you teach + + align:start position:0% +this experience the next time you teach + + + align:start position:0% +this experience the next time you teach +it so I think having the steps in the + + align:start position:0% +it so I think having the steps in the + + + align:start position:0% +it so I think having the steps in the +process a little bit clearer and having + + align:start position:0% +process a little bit clearer and having + + + align:start position:0% +process a little bit clearer and having +the motivating question of each step in + + align:start position:0% +the motivating question of each step in + + + align:start position:0% +the motivating question of each step in +a project like this really central so + + align:start position:0% +a project like this really central so + + + align:start position:0% +a project like this really central so +early stages here's what you should be + + align:start position:0% +early stages here's what you should be + + + align:start position:0% +early stages here's what you should be +thinking about here's the questions you + + align:start position:0% +thinking about here's the questions you + + + align:start position:0% +thinking about here's the questions you +need to answer middle stages late so if + + align:start position:0% +need to answer middle stages late so if + + + align:start position:0% +need to answer middle stages late so if +I have a better framework for the steps + + align:start position:0% +I have a better framework for the steps + + + align:start position:0% +I have a better framework for the steps +in the work I think that's a that would + + align:start position:0% +in the work I think that's a that would + + + align:start position:0% +in the work I think that's a that would +be a big benefit + + align:start position:0% +be a big benefit + + + align:start position:0% +be a big benefit +and others to realize not every student + + align:start position:0% +and others to realize not every student + + + align:start position:0% +and others to realize not every student +who comes in with their passion project + + align:start position:0% +who comes in with their passion project + + + align:start position:0% +who comes in with their passion project +is necessarily gonna want to or should + + align:start position:0% +is necessarily gonna want to or should + + + align:start position:0% +is necessarily gonna want to or should +turn it into an in-depth study so I've + + align:start position:0% +turn it into an in-depth study so I've + + + align:start position:0% +turn it into an in-depth study so I've +learned that you can't convert everyone + + align:start position:0% +learned that you can't convert everyone + + + align:start position:0% +learned that you can't convert everyone +and that's okay mm-hmm + + align:start position:0% +and that's okay mm-hmm + + + align:start position:0% +and that's okay mm-hmm +it's it's it's because we're offering it + + align:start position:0% +it's it's it's because we're offering it + + + align:start position:0% +it's it's it's because we're offering it +this is an offering of a new learning + + align:start position:0% +this is an offering of a new learning + + + align:start position:0% +this is an offering of a new learning +experience it's very much driven by the + + align:start position:0% +experience it's very much driven by the + + + align:start position:0% +experience it's very much driven by the +students interest you need to really be + + align:start position:0% +students interest you need to really be + + + align:start position:0% +students interest you need to really be +able to allow the students to + + align:start position:0% +able to allow the students to + + + align:start position:0% +able to allow the students to +self-select + + align:start position:0% +self-select + + + align:start position:0% +self-select +in it's hard to offer something like + + align:start position:0% +in it's hard to offer something like + + + align:start position:0% +in it's hard to offer something like +this as a requirement so that's another + + align:start position:0% +this as a requirement so that's another + + + align:start position:0% +this as a requirement so that's another +piece is striking the right balance + + align:start position:0% +piece is striking the right balance + + + align:start position:0% +piece is striking the right balance +between kind of opening the door and + + align:start position:0% +between kind of opening the door and + + + align:start position:0% +between kind of opening the door and +inviting people in this is cracking the + + align:start position:0% +inviting people in this is cracking the + + + align:start position:0% +inviting people in this is cracking the +whip and following up on them students + + align:start position:0% +whip and following up on them students + + + align:start position:0% +whip and following up on them students +get really busy so one downside of an + + align:start position:0% +get really busy so one downside of an + + + align:start position:0% +get really busy so one downside of an +unstructured course is that it can fall + + align:start position:0% +unstructured course is that it can fall + + + align:start position:0% +unstructured course is that it can fall +by the wayside because they have their + + align:start position:0% +by the wayside because they have their + + + align:start position:0% +by the wayside because they have their +structured requirements and course + + align:start position:0% +structured requirements and course + + + align:start position:0% +structured requirements and course +meetings for all their other classes and + + align:start position:0% +meetings for all their other classes and + + + align:start position:0% +meetings for all their other classes and +this begins to feel like something on + + align:start position:0% +this begins to feel like something on + + + align:start position:0% +this begins to feel like something on +the side so how you kind of maintain the + + align:start position:0% +the side so how you kind of maintain the + + + align:start position:0% +the side so how you kind of maintain the +momentum and make sure that enough + + align:start position:0% +momentum and make sure that enough + + + align:start position:0% +momentum and make sure that enough +investment is going in is really + + align:start position:0% +investment is going in is really + + + align:start position:0% +investment is going in is really +important so better sort of sourcing and + + align:start position:0% +important so better sort of sourcing and + + + align:start position:0% +important so better sort of sourcing and +screening better process and having kind + + align:start position:0% +screening better process and having kind + + + align:start position:0% +screening better process and having kind +of regular meetings are all really + + align:start position:0% +of regular meetings are all really + + + align:start position:0% +of regular meetings are all really +important ingredients is there anything + + align:start position:0% +important ingredients is there anything + + + align:start position:0% +important ingredients is there anything +else you'd like to share about + + align:start position:0% +else you'd like to share about + + + align:start position:0% +else you'd like to share about +facilitating an experience like this + + align:start position:0% +facilitating an experience like this + + + align:start position:0% +facilitating an experience like this +that we haven't touched on yet I think + + align:start position:0% +that we haven't touched on yet I think + + + align:start position:0% +that we haven't touched on yet I think +one of the challenges that an instructor + + align:start position:0% +one of the challenges that an instructor + + + align:start position:0% +one of the challenges that an instructor +has to balance is how far am I willing + + align:start position:0% +has to balance is how far am I willing + + + align:start position:0% +has to balance is how far am I willing +to go outside of my domain of expertise + + align:start position:0% +to go outside of my domain of expertise + + + align:start position:0% +to go outside of my domain of expertise +how much do I know about the blockchain + + align:start position:0% +how much do I know about the blockchain + + + align:start position:0% +how much do I know about the blockchain +that's not an area of my research so how + + align:start position:0% +that's not an area of my research so how + + + align:start position:0% +that's not an area of my research so how +far do I want to go down a set of + + align:start position:0% +far do I want to go down a set of + + + align:start position:0% +far do I want to go down a set of +projects that take that on I need to be + + align:start position:0% +projects that take that on I need to be + + + align:start position:0% +projects that take that on I need to be +able to figure it out for myself and + + align:start position:0% +able to figure it out for myself and + + + align:start position:0% +able to figure it out for myself and +then also be very clear with the + + align:start position:0% +then also be very clear with the + + + align:start position:0% +then also be very clear with the +students I'm interested in this topic + + align:start position:0% +students I'm interested in this topic + + + align:start position:0% +students I'm interested in this topic +I'll learn with you but my domain of + + align:start position:0% +I'll learn with you but my domain of + + + align:start position:0% +I'll learn with you but my domain of +expertise relates to these areas we can + + align:start position:0% +expertise relates to these areas we can + + + align:start position:0% +expertise relates to these areas we can +apply it to your questions we can apply + + align:start position:0% +apply it to your questions we can apply + + + align:start position:0% +apply it to your questions we can apply +systems thinking or organizational + + align:start position:0% +systems thinking or organizational + + + align:start position:0% +systems thinking or organizational +change or business models + + align:start position:0% +change or business models + + + align:start position:0% +change or business models +to the questions you're articulating but + + align:start position:0% +to the questions you're articulating but + + + align:start position:0% +to the questions you're articulating but +I am not the technical expert on this + + align:start position:0% +I am not the technical expert on this + + + align:start position:0% +I am not the technical expert on this +domain so you'll need to work with + + align:start position:0% +domain so you'll need to work with + + + align:start position:0% +domain so you'll need to work with +someone else on that and different + + align:start position:0% +someone else on that and different + + + align:start position:0% +someone else on that and different +instructors have different interests and + + align:start position:0% +instructors have different interests and + + + align:start position:0% +instructors have different interests and +stepping out of their comfort zone so + + align:start position:0% +stepping out of their comfort zone so + + + align:start position:0% +stepping out of their comfort zone so +that I think that's really important + + align:start position:0% +that I think that's really important + + + align:start position:0% +that I think that's really important +another big question is how willing are + + align:start position:0% +another big question is how willing are + + + align:start position:0% +another big question is how willing are +you as an instructor to have a mishmash + + align:start position:0% +you as an instructor to have a mishmash + + + align:start position:0% +you as an instructor to have a mishmash +of projects that take on very different + + align:start position:0% +of projects that take on very different + + + align:start position:0% +of projects that take on very different +domains or would you like them to be + + align:start position:0% +domains or would you like them to be + + + align:start position:0% +domains or would you like them to be +geographically or thematically linked + + align:start position:0% +geographically or thematically linked + + + align:start position:0% +geographically or thematically linked +hmm + + align:start position:0% +hmm + + + align:start position:0% +hmm +I suspect that I'm gonna evolve a little + + align:start position:0% +I suspect that I'm gonna evolve a little + + + align:start position:0% +I suspect that I'm gonna evolve a little +more towards clustered projects and I've + + align:start position:0% +more towards clustered projects and I've + + + align:start position:0% +more towards clustered projects and I've +seen some of my colleagues use such + + align:start position:0% +seen some of my colleagues use such + + + align:start position:0% +seen some of my colleagues use such +clusters of projects over time to build + + align:start position:0% +clusters of projects over time to build + + + align:start position:0% +clusters of projects over time to build +their own research insights so I think + + align:start position:0% +their own research insights so I think + + + align:start position:0% +their own research insights so I think +that's really exciting the idea of + + align:start position:0% +that's really exciting the idea of + + + align:start position:0% +that's really exciting the idea of +encouraging students to take on projects + + align:start position:0% +encouraging students to take on projects + + + align:start position:0% +encouraging students to take on projects +that motivate them but that also speak + + align:start position:0% +that motivate them but that also speak + + + align:start position:0% +that motivate them but that also speak +to an ongoing research program and on + + align:start position:0% +to an ongoing research program and on + + + align:start position:0% +to an ongoing research program and on +which you can start to build more + + align:start position:0% +which you can start to build more + + + align:start position:0% +which you can start to build more +knowledge and evidence do you have any + + align:start position:0% +knowledge and evidence do you have any + + + align:start position:0% +knowledge and evidence do you have any +words of advice to your colleagues out + + align:start position:0% +words of advice to your colleagues out + + + align:start position:0% +words of advice to your colleagues out +in the world who might want to try + + align:start position:0% +in the world who might want to try + + + align:start position:0% +in the world who might want to try +something similar teaching this way is + + align:start position:0% +something similar teaching this way is + + + align:start position:0% +something similar teaching this way is +incredibly rewarding and also really + + align:start position:0% +incredibly rewarding and also really + + + align:start position:0% +incredibly rewarding and also really +scary you often be invited into domains + + align:start position:0% +scary you often be invited into domains + + + align:start position:0% +scary you often be invited into domains +we don't have the expertise and it's + + align:start position:0% +we don't have the expertise and it's + + + align:start position:0% +we don't have the expertise and it's +quite hard to predict how a given + + align:start position:0% +quite hard to predict how a given + + + align:start position:0% +quite hard to predict how a given +session or a conversation will go it's + + align:start position:0% +session or a conversation will go it's + + + align:start position:0% +session or a conversation will go it's +not like running a case where you know + + align:start position:0% +not like running a case where you know + + + align:start position:0% +not like running a case where you know +the story and you know what you're gonna + + align:start position:0% +the story and you know what you're gonna + + + align:start position:0% +the story and you know what you're gonna +say at each moment in class or you're at + + align:start position:0% +say at each moment in class or you're at + + + align:start position:0% +say at each moment in class or you're at +least got a sense of what that might + + align:start position:0% +least got a sense of what that might + + + align:start position:0% +least got a sense of what that might +look like because very often students + + align:start position:0% +look like because very often students + + + align:start position:0% +look like because very often students +will come in and say I've totally + + align:start position:0% +will come in and say I've totally + + + align:start position:0% +will come in and say I've totally +changed my mind and you have to deal + + align:start position:0% +changed my mind and you have to deal + + + align:start position:0% +changed my mind and you have to deal +with that so there's both the kind of + + align:start position:0% +with that so there's both the kind of + + + align:start position:0% +with that so there's both the kind of +personal journey of learning that's less + + align:start position:0% +personal journey of learning that's less + + + align:start position:0% +personal journey of learning that's less +predictable and the domaine part that's + + align:start position:0% +predictable and the domaine part that's + + + align:start position:0% +predictable and the domaine part that's +less predictable but you as the + + align:start position:0% +less predictable but you as the + + + align:start position:0% +less predictable but you as the +instructor get to set some of those + + align:start position:0% +instructor get to set some of those + + + align:start position:0% +instructor get to set some of those +parameters by for instance requiring a + + align:start position:0% +parameters by for instance requiring a + + + align:start position:0% +parameters by for instance requiring a +written update before a meeting you can + + align:start position:0% +written update before a meeting you can + + + align:start position:0% +written update before a meeting you can +manage the conversation better and by + + align:start position:0% +manage the conversation better and by + + + align:start position:0% +manage the conversation better and by +specifying the specific the types of + + align:start position:0% +specifying the specific the types of + + + align:start position:0% +specifying the specific the types of +projects that you would really want to + + align:start position:0% +projects that you would really want to + + + align:start position:0% +projects that you would really want to +take on + + align:start position:0% +take on + + + align:start position:0% +take on +you can also ensure that they're + + align:start position:0% +you can also ensure that they're + + + align:start position:0% +you can also ensure that they're +clustered in + + align:start position:0% +clustered in + + + align:start position:0% +clustered in +that are relevant to your own expertise + + align:start position:0% +that are relevant to your own expertise + + + align:start position:0% +that are relevant to your own expertise +for me one of the challenges I have to + + align:start position:0% +for me one of the challenges I have to + + + align:start position:0% +for me one of the challenges I have to +tell you is branding + + align:start position:0% +tell you is branding + + + align:start position:0% +tell you is branding +what do I call this is it something + + align:start position:0% +what do I call this is it something + + + align:start position:0% +what do I call this is it something +different than just doing a bunch of + + align:start position:0% +different than just doing a bunch of + + + align:start position:0% +different than just doing a bunch of +independent studies I think it's a work + + align:start position:0% +independent studies I think it's a work + + + align:start position:0% +independent studies I think it's a work +in progress so I think the first few + + align:start position:0% +in progress so I think the first few + + + align:start position:0% +in progress so I think the first few +times you try out something like this it + + align:start position:0% +times you try out something like this it + + + align:start position:0% +times you try out something like this it +doesn't yet have a fully distinct + + align:start position:0% +doesn't yet have a fully distinct + + + align:start position:0% +doesn't yet have a fully distinct +identity and then as I hone it I'm gonna + + align:start position:0% +identity and then as I hone it I'm gonna + + + align:start position:0% +identity and then as I hone it I'm gonna +give it a clearer name but I've been + + align:start position:0% +give it a clearer name but I've been + + + align:start position:0% +give it a clearer name but I've been +using terms that link to social impact + + align:start position:0% +using terms that link to social impact + + + align:start position:0% +using terms that link to social impact +that link to technology and that also + + align:start position:0% +that link to technology and that also + + + align:start position:0% +that link to technology and that also +frame perhaps because it's focusing on + + align:start position:0% +frame perhaps because it's focusing on + + + align:start position:0% +frame perhaps because it's focusing on +the students I'm teaching but the idea + + align:start position:0% +the students I'm teaching but the idea + + + align:start position:0% +the students I'm teaching but the idea +of thinking strategically thinking as a + + align:start position:0% +of thinking strategically thinking as a + + + align:start position:0% +of thinking strategically thinking as a +leader and really kind of putting + + align:start position:0% +leader and really kind of putting + + + align:start position:0% +leader and really kind of putting +yourselves in the shoes of the of an + + align:start position:0% +yourselves in the shoes of the of an + + + align:start position:0% +yourselves in the shoes of the of an +entrepreneur or an executive so I want + + align:start position:0% +entrepreneur or an executive so I want + + + align:start position:0% +entrepreneur or an executive so I want +them to not simply kind of make general + + align:start position:0% +them to not simply kind of make general + + + align:start position:0% +them to not simply kind of make general +arguments about what should happen but + + align:start position:0% +arguments about what should happen but + + + align:start position:0% +arguments about what should happen but +to think about what they could do as a + + align:start position:0% +to think about what they could do as a + + + align:start position:0% +to think about what they could do as a +leader and entrepreneur and executive so + + align:start position:0% +leader and entrepreneur and executive so + + + align:start position:0% +leader and entrepreneur and executive so +ya come up with a great name I'm still + + align:start position:0% +ya come up with a great name I'm still + + + align:start position:0% +ya come up with a great name I'm still +working on mine all suggestions are + + align:start position:0% +working on mine all suggestions are + + + align:start position:0% +working on mine all suggestions are +welcome I put in their terms like new + + align:start position:0% +welcome I put in their terms like new + + + align:start position:0% +welcome I put in their terms like new +executive thinking the social impact or + + align:start position:0% +executive thinking the social impact or + + + align:start position:0% +executive thinking the social impact or +for it so technology for social impact + + align:start position:0% +for it so technology for social impact + + + align:start position:0% +for it so technology for social impact +so we'll see how that plays out check + + align:start position:0% +so we'll see how that plays out check + + + align:start position:0% +so we'll see how that plays out check +back later thank you so much sure \ No newline at end of file diff --git a/IdG07-Ga4BM.txt b/IdG07-Ga4BM.txt new file mode 100644 index 0000000000000000000000000000000000000000..3a7c3df8bde390454a46e50311166b0db8403530 --- /dev/null +++ b/IdG07-Ga4BM.txt @@ -0,0 +1,7384 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +I'd like to welcome you to another + + align:start position:0% +I'd like to welcome you to another + + + align:start position:0% +I'd like to welcome you to another +installment or another lecture in my MIT + + align:start position:0% +installment or another lecture in my MIT + + + align:start position:0% +installment or another lecture in my MIT +class on Urban Energy Systems + + align:start position:0% +class on Urban Energy Systems + + + align:start position:0% +class on Urban Energy Systems +my name is David Sue I'm an associate + + align:start position:0% +my name is David Sue I'm an associate + + + align:start position:0% +my name is David Sue I'm an associate +professor of urban studies and planning + + align:start position:0% +professor of urban studies and planning + + + align:start position:0% +professor of urban studies and planning +at MIT and this week we're going to talk + + align:start position:0% +at MIT and this week we're going to talk + + + align:start position:0% +at MIT and this week we're going to talk +about cities and transportation systems + + align:start position:0% +about cities and transportation systems + + + align:start position:0% +about cities and transportation systems +in our last lecture we talked about + + align:start position:0% +in our last lecture we talked about + + + align:start position:0% +in our last lecture we talked about +electric vehicles and why certain new + + align:start position:0% +electric vehicles and why certain new + + + align:start position:0% +electric vehicles and why certain new +technologies are much more efficient + + align:start position:0% +technologies are much more efficient + + + align:start position:0% +technologies are much more efficient +than our previous internal combustion + + align:start position:0% +than our previous internal combustion + + + align:start position:0% +than our previous internal combustion +engine or fossil fuel using Technologies + + align:start position:0% +engine or fossil fuel using Technologies + + + align:start position:0% +engine or fossil fuel using Technologies +and how we need to achieve + + align:start position:0% +and how we need to achieve + + + align:start position:0% +and how we need to achieve +electrification to achieve lower + + align:start position:0% +electrification to achieve lower + + + align:start position:0% +electrification to achieve lower +greenhouse gas emissions + + align:start position:0% +greenhouse gas emissions + + + align:start position:0% +greenhouse gas emissions +today I want to talk about + + align:start position:0% +today I want to talk about + + + align:start position:0% +today I want to talk about +transportation systems + + align:start position:0% +transportation systems + + + align:start position:0% +transportation systems +and I want to take a different attack + + align:start position:0% +and I want to take a different attack + + + align:start position:0% +and I want to take a different attack +our different tact on the subject + + align:start position:0% +our different tact on the subject + + + align:start position:0% +our different tact on the subject +presentation systems we'll start with + + align:start position:0% +presentation systems we'll start with + + + align:start position:0% +presentation systems we'll start with +Paul's analysis + + align:start position:0% +Paul's analysis + + + align:start position:0% +Paul's analysis +here's the materials for today they're + + align:start position:0% +here's the materials for today they're + + + align:start position:0% +here's the materials for today they're +all in the syllabus + + align:start position:0% +all in the syllabus + + + align:start position:0% +all in the syllabus +and + + align:start position:0% +and + + + align:start position:0% +and +I want to talk about say policy analysis + + align:start position:0% +I want to talk about say policy analysis + + + align:start position:0% +I want to talk about say policy analysis +quite often when we teach in public + + align:start position:0% +quite often when we teach in public + + + align:start position:0% +quite often when we teach in public +policy schools or urban planning schools + + align:start position:0% +policy schools or urban planning schools + + + align:start position:0% +policy schools or urban planning schools +this fundamentally an economic perennial + + align:start position:0% +this fundamentally an economic perennial + + + align:start position:0% +this fundamentally an economic perennial +policy analysis it's a cost benefit + + align:start position:0% +policy analysis it's a cost benefit + + + align:start position:0% +policy analysis it's a cost benefit +analysis or as one of my previous + + align:start position:0% +analysis or as one of my previous + + + align:start position:0% +analysis or as one of my previous +advisors say a benefit cost analysis + + align:start position:0% +advisors say a benefit cost analysis + + + align:start position:0% +advisors say a benefit cost analysis +because you would want to emphasize the + + align:start position:0% +because you would want to emphasize the + + + align:start position:0% +because you would want to emphasize the +benefits over the costs if we take + + align:start position:0% +benefits over the costs if we take + + + align:start position:0% +benefits over the costs if we take +certain public policy actions and so the + + align:start position:0% +certain public policy actions and so the + + + align:start position:0% +certain public policy actions and so the +two main concerns we typically teach in + + align:start position:0% +two main concerns we typically teach in + + + align:start position:0% +two main concerns we typically teach in +economic styles of policy analysis our + + align:start position:0% +economic styles of policy analysis our + + + align:start position:0% +economic styles of policy analysis our +efficiency what are the highest priority + + align:start position:0% +efficiency what are the highest priority + + + align:start position:0% +efficiency what are the highest priority +items this assumed that resources in the + + align:start position:0% +items this assumed that resources in the + + + align:start position:0% +items this assumed that resources in the +public sphere are scarce and we can only + + align:start position:0% +public sphere are scarce and we can only + + + align:start position:0% +public sphere are scarce and we can only +basically deploy certain level resources + + align:start position:0% +basically deploy certain level resources + + + align:start position:0% +basically deploy certain level resources +to address social problems of course we + + align:start position:0% +to address social problems of course we + + + align:start position:0% +to address social problems of course we +could also question whether or not + + align:start position:0% +could also question whether or not + + + align:start position:0% +could also question whether or not +resources are scarce or what kinds of + + align:start position:0% +resources are scarce or what kinds of + + + align:start position:0% +resources are scarce or what kinds of +political economy let's say leads to the + + align:start position:0% +political economy let's say leads to the + + + align:start position:0% +political economy let's say leads to the +scarcity but if you have scarce + + align:start position:0% +scarcity but if you have scarce + + + align:start position:0% +scarcity but if you have scarce +resources you would want to establish + + align:start position:0% +resources you would want to establish + + + align:start position:0% +resources you would want to establish +what the highest priority items are + + align:start position:0% +what the highest priority items are + + + align:start position:0% +what the highest priority items are +and the second main concern that is + + align:start position:0% +and the second main concern that is + + + align:start position:0% +and the second main concern that is +usually given I'd argue a slightly less + + align:start position:0% +usually given I'd argue a slightly less + + + align:start position:0% +usually given I'd argue a slightly less +emphasis in public policy analysis is + + align:start position:0% +emphasis in public policy analysis is + + + align:start position:0% +emphasis in public policy analysis is +equity is the distribution of benefits + + align:start position:0% +equity is the distribution of benefits + + + align:start position:0% +equity is the distribution of benefits +and costs there + + align:start position:0% +and costs there + + + align:start position:0% +and costs there +and of course we want to emphasize that + + align:start position:0% +and of course we want to emphasize that + + + align:start position:0% +and of course we want to emphasize that +this economic style policy analysis + + align:start position:0% +this economic style policy analysis + + + align:start position:0% +this economic style policy analysis +hasn't always included broader concerns + + align:start position:0% +hasn't always included broader concerns + + + align:start position:0% +hasn't always included broader concerns +for example risks we know from recent + + align:start position:0% +for example risks we know from recent + + + align:start position:0% +for example risks we know from recent +disasters like wildfires in California + + align:start position:0% +disasters like wildfires in California + + + align:start position:0% +disasters like wildfires in California +of course the covid-19 + + align:start position:0% +of course the covid-19 + + + align:start position:0% +of course the covid-19 +endemic that we can have unexpected or + + align:start position:0% +endemic that we can have unexpected or + + + align:start position:0% +endemic that we can have unexpected or +low probability disasters we could argue + + align:start position:0% +low probability disasters we could argue + + + align:start position:0% +low probability disasters we could argue +that their low probability or fairly + + align:start position:0% +that their low probability or fairly + + + align:start position:0% +that their low probability or fairly +rare but of course they can also be + + align:start position:0% +rare but of course they can also be + + + align:start position:0% +rare but of course they can also be +potentially out of sprocketing so + + align:start position:0% +potentially out of sprocketing so + + + align:start position:0% +potentially out of sprocketing so +there's increased interest in how do you + + align:start position:0% +there's increased interest in how do you + + + align:start position:0% +there's increased interest in how do you +achieve resilience to disasters like + + align:start position:0% +achieve resilience to disasters like + + + align:start position:0% +achieve resilience to disasters like +wildfires or covet 19. + + align:start position:0% +wildfires or covet 19. + + + align:start position:0% +wildfires or covet 19. +of course if we talk about Equity we can + + align:start position:0% +of course if we talk about Equity we can + + + align:start position:0% +of course if we talk about Equity we can +also talk about definitions of fairness + + align:start position:0% +also talk about definitions of fairness + + + align:start position:0% +also talk about definitions of fairness +or Justice uh we could talk on terms of + + align:start position:0% +or Justice uh we could talk on terms of + + + align:start position:0% +or Justice uh we could talk on terms of +Rights or opportunities or capabilities + + align:start position:0% +Rights or opportunities or capabilities + + + align:start position:0% +Rights or opportunities or capabilities +those are all differently distributed or + + align:start position:0% +those are all differently distributed or + + + align:start position:0% +those are all differently distributed or +considered or conceived of by different + + align:start position:0% +considered or conceived of by different + + + align:start position:0% +considered or conceived of by different +groups and of course this leads us to + + align:start position:0% +groups and of course this leads us to + + + align:start position:0% +groups and of course this leads us to +the overall question of what is justice + + align:start position:0% +the overall question of what is justice + + + align:start position:0% +the overall question of what is justice +it's also uh perhaps fair to say that + + align:start position:0% +it's also uh perhaps fair to say that + + + align:start position:0% +it's also uh perhaps fair to say that +public policy analysis doesn't always + + align:start position:0% +public policy analysis doesn't always + + + align:start position:0% +public policy analysis doesn't always +include Behavior we know behaviors can + + align:start position:0% +include Behavior we know behaviors can + + + align:start position:0% +include Behavior we know behaviors can +rapidly change that may be a result of + + align:start position:0% +rapidly change that may be a result of + + + align:start position:0% +rapidly change that may be a result of +signaling or culture or incentives but + + align:start position:0% +signaling or culture or incentives but + + + align:start position:0% +signaling or culture or incentives but +essentially I would take the approach + + align:start position:0% +essentially I would take the approach + + + align:start position:0% +essentially I would take the approach +that our economic framing is within a + + align:start position:0% +that our economic framing is within a + + + align:start position:0% +that our economic framing is within a +certain context we quite often draw on + + align:start position:0% +certain context we quite often draw on + + + align:start position:0% +certain context we quite often draw on +evidence in a similar context but we + + align:start position:0% +evidence in a similar context but we + + + align:start position:0% +evidence in a similar context but we +also know that behaviors and cultures do + + align:start position:0% +also know that behaviors and cultures do + + + align:start position:0% +also know that behaviors and cultures do +change and those behaviors and cultures + + align:start position:0% +change and those behaviors and cultures + + + align:start position:0% +change and those behaviors and cultures +actually establish what should be valued + + align:start position:0% +actually establish what should be valued + + + align:start position:0% +actually establish what should be valued +in economic systems or markets of course + + align:start position:0% +in economic systems or markets of course + + + align:start position:0% +in economic systems or markets of course +there's non-monetary values + + align:start position:0% +there's non-monetary values + + + align:start position:0% +there's non-monetary values +environmental economists have spent a + + align:start position:0% +environmental economists have spent a + + + align:start position:0% +environmental economists have spent a +lot of time trying to establish the + + align:start position:0% +lot of time trying to establish the + + + align:start position:0% +lot of time trying to establish the +non-monetary value of things things that + + align:start position:0% +non-monetary value of things things that + + + align:start position:0% +non-monetary value of things things that +simply exist but may not necessarily be + + align:start position:0% +simply exist but may not necessarily be + + + align:start position:0% +simply exist but may not necessarily be +traded in a market economy examples + + align:start position:0% +traded in a market economy examples + + + align:start position:0% +traded in a market economy examples +include a particular species like let's + + align:start position:0% +include a particular species like let's + + + align:start position:0% +include a particular species like let's +say the desert tortoise or the Grand + + align:start position:0% +say the desert tortoise or the Grand + + + align:start position:0% +say the desert tortoise or the Grand +Canyon how do you put an existence value + + align:start position:0% +Canyon how do you put an existence value + + + align:start position:0% +Canyon how do you put an existence value +on the desert Portis or the Grand Canyon + + align:start position:0% +on the desert Portis or the Grand Canyon + + + align:start position:0% +on the desert Portis or the Grand Canyon +Grand Canyon people have tried to do it + + align:start position:0% +Grand Canyon people have tried to do it + + + align:start position:0% +Grand Canyon people have tried to do it +we can discuss or debate whether or not + + align:start position:0% +we can discuss or debate whether or not + + + align:start position:0% +we can discuss or debate whether or not +we think those non-modern values are in + + align:start position:0% +we think those non-modern values are in + + + align:start position:0% +we think those non-modern values are in +fact things that we believe are accurate + + align:start position:0% +fact things that we believe are accurate + + + align:start position:0% +fact things that we believe are accurate +and of course as I alluded to before the + + align:start position:0% +and of course as I alluded to before the + + + align:start position:0% +and of course as I alluded to before the +total budget or resources we have to + + align:start position:0% +total budget or resources we have to + + + align:start position:0% +total budget or resources we have to +address social problems are we actually + + align:start position:0% +address social problems are we actually + + + align:start position:0% +address social problems are we actually +taking into account let's say future + + align:start position:0% +taking into account let's say future + + + align:start position:0% +taking into account let's say future +chaos foreign investments or even the + + align:start position:0% +chaos foreign investments or even the + + + align:start position:0% +chaos foreign investments or even the +sustainability of our public policy + + align:start position:0% +sustainability of our public policy + + + align:start position:0% +sustainability of our public policy +actions + + align:start position:0% +actions + + + align:start position:0% +actions +this brings into question also + + align:start position:0% +this brings into question also + + + align:start position:0% +this brings into question also +implementation we can analyze whether or + + align:start position:0% +implementation we can analyze whether or + + + align:start position:0% +implementation we can analyze whether or +not things have certain benefits or + + align:start position:0% +not things have certain benefits or + + + align:start position:0% +not things have certain benefits or +costs but of course if we have a public + + align:start position:0% +costs but of course if we have a public + + + align:start position:0% +costs but of course if we have a public +policy that cannot be implemented then + + align:start position:0% +policy that cannot be implemented then + + + align:start position:0% +policy that cannot be implemented then +it may not have any effects that leads + + align:start position:0% +it may not have any effects that leads + + + align:start position:0% +it may not have any effects that leads +us to questions of who how and where our + + align:start position:0% +us to questions of who how and where our + + + align:start position:0% +us to questions of who how and where our +policy is going to be implemented and of + + align:start position:0% +policy is going to be implemented and of + + + align:start position:0% +policy is going to be implemented and of +course of course growth and speed we + + align:start position:0% +course of course growth and speed we + + + align:start position:0% +course of course growth and speed we +often do our policy analysis based on + + align:start position:0% +often do our policy analysis based on + + + align:start position:0% +often do our policy analysis based on +existing data we may not capture large + + align:start position:0% +existing data we may not capture large + + + align:start position:0% +existing data we may not capture large +shifts in systems or situations and of + + align:start position:0% +shifts in systems or situations and of + + + align:start position:0% +shifts in systems or situations and of +course we know that certain Technologies + + align:start position:0% +course we know that certain Technologies + + + align:start position:0% +course we know that certain Technologies +are growing faster than others so are we + + align:start position:0% +are growing faster than others so are we + + + align:start position:0% +are growing faster than others so are we +understanding is our public policy + + align:start position:0% +understanding is our public policy + + + align:start position:0% +understanding is our public policy +analysis durable or in a technical + + align:start position:0% +analysis durable or in a technical + + + align:start position:0% +analysis durable or in a technical +phrase stationary and we assume that our + + align:start position:0% +phrase stationary and we assume that our + + + align:start position:0% +phrase stationary and we assume that our +results from one period of time are + + align:start position:0% +results from one period of time are + + + align:start position:0% +results from one period of time are +General liable to another + + align:start position:0% +General liable to another + + + align:start position:0% +General liable to another +and finally geography similarly can we + + align:start position:0% +and finally geography similarly can we + + + align:start position:0% +and finally geography similarly can we +assume that our public policy analysis + + align:start position:0% +assume that our public policy analysis + + + align:start position:0% +assume that our public policy analysis +and our public policies work the same in + + align:start position:0% +and our public policies work the same in + + + align:start position:0% +and our public policies work the same in +all places again can we generalize the + + align:start position:0% +all places again can we generalize the + + + align:start position:0% +all places again can we generalize the +effects of our public policy analyzes + + align:start position:0% +effects of our public policy analyzes + + + align:start position:0% +effects of our public policy analyzes +from one place to another + + align:start position:0% +from one place to another + + + align:start position:0% +from one place to another +and so in terms of policy analysis today + + align:start position:0% +and so in terms of policy analysis today + + + align:start position:0% +and so in terms of policy analysis today +and for transportation systems I want to + + align:start position:0% +and for transportation systems I want to + + + align:start position:0% +and for transportation systems I want to +talk about three case studies and those + + align:start position:0% +talk about three case studies and those + + + align:start position:0% +talk about three case studies and those +three case studies we'll use as just + + align:start position:0% +three case studies we'll use as just + + + align:start position:0% +three case studies we'll use as just +examples of different kinds of policies + + align:start position:0% +examples of different kinds of policies + + + align:start position:0% +examples of different kinds of policies +and different kind of analyzes uh the + + align:start position:0% +and different kind of analyzes uh the + + + align:start position:0% +and different kind of analyzes uh the +first one is global Aviation which we've + + align:start position:0% +first one is global Aviation which we've + + + align:start position:0% +first one is global Aviation which we've +talked about in this class more I think + + align:start position:0% +talked about in this class more I think + + + align:start position:0% +talked about in this class more I think +it's an exciting topic for us to talk + + align:start position:0% +it's an exciting topic for us to talk + + + align:start position:0% +it's an exciting topic for us to talk +about because as I argued to you before + + align:start position:0% +about because as I argued to you before + + + align:start position:0% +about because as I argued to you before +I think it's a cultural blind spot for + + align:start position:0% +I think it's a cultural blind spot for + + + align:start position:0% +I think it's a cultural blind spot for +many committed environmentalists who are + + align:start position:0% +many committed environmentalists who are + + + align:start position:0% +many committed environmentalists who are +relatively High income and educated + + align:start position:0% +relatively High income and educated + + + align:start position:0% +relatively High income and educated +we'll talk about the case study from the + + align:start position:0% +we'll talk about the case study from the + + + align:start position:0% +we'll talk about the case study from the +Mimi sheller paper on walking bicycling + + align:start position:0% +Mimi sheller paper on walking bicycling + + + align:start position:0% +Mimi sheller paper on walking bicycling +and transit in Philadelphia and we'll + + align:start position:0% +and transit in Philadelphia and we'll + + + align:start position:0% +and transit in Philadelphia and we'll +just touch briefly I have Los Angeles's + + align:start position:0% +just touch briefly I have Los Angeles's + + + align:start position:0% +just touch briefly I have Los Angeles's +efforts towards clean air which led to + + align:start position:0% +efforts towards clean air which led to + + + align:start position:0% +efforts towards clean air which led to +the California air resources board that + + align:start position:0% +the California air resources board that + + + align:start position:0% +the California air resources board that +chapter is a great chapter just to kind + + align:start position:0% +chapter is a great chapter just to kind + + + align:start position:0% +chapter is a great chapter just to kind +of reinforce uh questions about how long + + align:start position:0% +of reinforce uh questions about how long + + + align:start position:0% +of reinforce uh questions about how long +does it take or how do we achieve public + + align:start position:0% +does it take or how do we achieve public + + + align:start position:0% +does it take or how do we achieve public +policy over time + + align:start position:0% +policy over time + + + align:start position:0% +policy over time +and so just talk talk about global + + align:start position:0% +and so just talk talk about global + + + align:start position:0% +and so just talk talk about global +Aviation for a moment we look at the + + align:start position:0% +Aviation for a moment we look at the + + + align:start position:0% +Aviation for a moment we look at the +growth of Air transport over the last 50 + + align:start position:0% +growth of Air transport over the last 50 + + + align:start position:0% +growth of Air transport over the last 50 +or 60 years this is from the + + align:start position:0% +or 60 years this is from the + + + align:start position:0% +or 60 years this is from the +international civil aviation + + align:start position:0% +international civil aviation + + + align:start position:0% +international civil aviation +organization you can see that they've + + align:start position:0% +organization you can see that they've + + + align:start position:0% +organization you can see that they've +basically charted a fairly constant + + align:start position:0% +basically charted a fairly constant + + + align:start position:0% +basically charted a fairly constant +upwork trajectory do you see minor blips + + align:start position:0% +upwork trajectory do you see minor blips + + + align:start position:0% +upwork trajectory do you see minor blips +in the upward growth for the 1970s oil + + align:start position:0% +in the upward growth for the 1970s oil + + + align:start position:0% +in the upward growth for the 1970s oil +crisis later on Iraq war the Gulf War + + align:start position:0% +crisis later on Iraq war the Gulf War + + + align:start position:0% +crisis later on Iraq war the Gulf War +the Asian monetary crisis the 1990s the + + align:start position:0% +the Asian monetary crisis the 1990s the + + + align:start position:0% +the Asian monetary crisis the 1990s the +911 terrorist attack in 2001 SARS and + + align:start position:0% +911 terrorist attack in 2001 SARS and + + + align:start position:0% +911 terrorist attack in 2001 SARS and +the world Obsession those all have some + + align:start position:0% +the world Obsession those all have some + + + align:start position:0% +the world Obsession those all have some +effect on the growth in Air transport + + align:start position:0% +effect on the growth in Air transport + + + align:start position:0% +effect on the growth in Air transport +but if you had to summarize over the + + align:start position:0% +but if you had to summarize over the + + + align:start position:0% +but if you had to summarize over the +last seven years so years you could + + align:start position:0% +last seven years so years you could + + + align:start position:0% +last seven years so years you could +basically say that it's been an + + align:start position:0% +basically say that it's been an + + + align:start position:0% +basically say that it's been an +uninterrupted growth of + + align:start position:0% +uninterrupted growth of + + + align:start position:0% +uninterrupted growth of +um + + align:start position:0% +um + + + align:start position:0% +um +of Air transport here I think it said + + align:start position:0% +of Air transport here I think it said + + + align:start position:0% +of Air transport here I think it said +it's a 7.1 percent growth rate versus + + align:start position:0% +it's a 7.1 percent growth rate versus + + + align:start position:0% +it's a 7.1 percent growth rate versus + + align:start position:0% + + + align:start position:0% +um that is in terms of Revenue passenger + + align:start position:0% +um that is in terms of Revenue passenger + + + align:start position:0% +um that is in terms of Revenue passenger +kilometers and Freight ton law burners + + align:start position:0% +kilometers and Freight ton law burners + + + align:start position:0% +kilometers and Freight ton law burners +both have grown fairly relentlessly + + align:start position:0% +both have grown fairly relentlessly + + + align:start position:0% +both have grown fairly relentlessly +of course we're talking about this in + + align:start position:0% +of course we're talking about this in + + + align:start position:0% +of course we're talking about this in +2022 this is one year after be perhaps + + align:start position:0% +2022 this is one year after be perhaps + + + align:start position:0% +2022 this is one year after be perhaps +greatest decline in world history in + + align:start position:0% +greatest decline in world history in + + + align:start position:0% +greatest decline in world history in +world air traffic air passenger traffic + + align:start position:0% +world air traffic air passenger traffic + + + align:start position:0% +world air traffic air passenger traffic +you can see the effect of the covid-19 + + align:start position:0% +you can see the effect of the covid-19 + + + align:start position:0% +you can see the effect of the covid-19 +pandemic + + align:start position:0% +pandemic + + + align:start position:0% +pandemic +has had an effect that all those + + align:start position:0% +has had an effect that all those + + + align:start position:0% +has had an effect that all those +previous crises did not have on air + + align:start position:0% +previous crises did not have on air + + + align:start position:0% +previous crises did not have on air +travel + + align:start position:0% +travel + + + align:start position:0% +travel +we can discuss or we will discuss in + + align:start position:0% +we can discuss or we will discuss in + + + align:start position:0% +we can discuss or we will discuss in +class whether or not this is a good + + align:start position:0% +class whether or not this is a good + + + align:start position:0% +class whether or not this is a good +thing + + align:start position:0% +thing + + + align:start position:0% +thing +I'm sure we can agree that over 19 was + + align:start position:0% +I'm sure we can agree that over 19 was + + + align:start position:0% +I'm sure we can agree that over 19 was +not a good thing but the question is + + align:start position:0% +not a good thing but the question is + + + align:start position:0% +not a good thing but the question is +after covid-19 is air travel going to + + align:start position:0% +after covid-19 is air travel going to + + + align:start position:0% +after covid-19 is air travel going to +Simply resume and go back to the level + + align:start position:0% +Simply resume and go back to the level + + + align:start position:0% +Simply resume and go back to the level +that it was in 2019 and we'll continue + + align:start position:0% +that it was in 2019 and we'll continue + + + align:start position:0% +that it was in 2019 and we'll continue +to resume its upward growth some + + align:start position:0% +to resume its upward growth some + + + align:start position:0% +to resume its upward growth some +forecasts estimate that Aviation and + + align:start position:0% +forecasts estimate that Aviation and + + + align:start position:0% +forecasts estimate that Aviation and +transportation will be 30 percent of our + + align:start position:0% +transportation will be 30 percent of our + + + align:start position:0% +transportation will be 30 percent of our +total greenhouse gas emissions in 2050 + + align:start position:0% +total greenhouse gas emissions in 2050 + + + align:start position:0% +total greenhouse gas emissions in 2050 +we obviously cannot sustain that growth + + align:start position:0% +we obviously cannot sustain that growth + + + align:start position:0% +we obviously cannot sustain that growth +if we also want to try to achieve + + align:start position:0% +if we also want to try to achieve + + + align:start position:0% +if we also want to try to achieve +decarbonization + + align:start position:0% +decarbonization + + + align:start position:0% +decarbonization +and of course just to talk about + + align:start position:0% +and of course just to talk about + + + align:start position:0% +and of course just to talk about +behavior and culture change over the + + align:start position:0% +behavior and culture change over the + + + align:start position:0% +behavior and culture change over the +last five years the economists I think + + align:start position:0% +last five years the economists I think + + + align:start position:0% +last five years the economists I think +up to 2019 or 2020 had a graph of + + align:start position:0% +up to 2019 or 2020 had a graph of + + + align:start position:0% +up to 2019 or 2020 had a graph of +airline passengers and speed in and they + + align:start position:0% +airline passengers and speed in and they + + + align:start position:0% +airline passengers and speed in and they +call it flig scum which I think is uh + + align:start position:0% +call it flig scum which I think is uh + + + align:start position:0% +call it flig scum which I think is uh +not quite the right pronunciation but it + + align:start position:0% +not quite the right pronunciation but it + + + align:start position:0% +not quite the right pronunciation but it +basically translates as flying shame and + + align:start position:0% +basically translates as flying shame and + + + align:start position:0% +basically translates as flying shame and +you can see that the number of + + align:start position:0% +you can see that the number of + + + align:start position:0% +you can see that the number of +passengers at seateds 10 business + + align:start position:0% +passengers at seateds 10 business + + + align:start position:0% +passengers at seateds 10 business +airports had declined for a number of + + align:start position:0% +airports had declined for a number of + + + align:start position:0% +airports had declined for a number of +years you could also attribute this + + align:start position:0% +years you could also attribute this + + + align:start position:0% +years you could also attribute this +perhaps to Greta bunburg making great + + align:start position:0% +perhaps to Greta bunburg making great + + + align:start position:0% +perhaps to Greta bunburg making great +efforts to publicize the hypocrisy + + align:start position:0% +efforts to publicize the hypocrisy + + + align:start position:0% +efforts to publicize the hypocrisy +perhaps of flying and choosing to take a + + align:start position:0% +perhaps of flying and choosing to take a + + + align:start position:0% +perhaps of flying and choosing to take a +boat to the conference the climate + + align:start position:0% +boat to the conference the climate + + + align:start position:0% +boat to the conference the climate +conference in New York to avoid being + + align:start position:0% +conference in New York to avoid being + + + align:start position:0% +conference in New York to avoid being +charged as a hypocrite + + align:start position:0% +charged as a hypocrite + + + align:start position:0% +charged as a hypocrite +lying shame is been translated to number + + align:start position:0% +lying shame is been translated to number + + + align:start position:0% +lying shame is been translated to number +of languages I think this is actually a + + align:start position:0% +of languages I think this is actually a + + + align:start position:0% +of languages I think this is actually a +cultural ship that we may be seeing + + align:start position:0% +cultural ship that we may be seeing + + + align:start position:0% +cultural ship that we may be seeing +just to talk about why Global Aviation + + align:start position:0% +just to talk about why Global Aviation + + + align:start position:0% +just to talk about why Global Aviation +is an important factor in climate action + + align:start position:0% +is an important factor in climate action + + + align:start position:0% +is an important factor in climate action +or climate change uh this lead at all + + align:start position:0% +or climate change uh this lead at all + + + align:start position:0% +or climate change uh this lead at all +2021 paper is not one that I assigned in + + align:start position:0% +2021 paper is not one that I assigned in + + + align:start position:0% +2021 paper is not one that I assigned in +the syllabus but if you have the PDF + + align:start position:0% +the syllabus but if you have the PDF + + + align:start position:0% +the syllabus but if you have the PDF +slides I encourage you to click on the + + align:start position:0% +slides I encourage you to click on the + + + align:start position:0% +slides I encourage you to click on the +link and it's important to note what + + align:start position:0% +link and it's important to note what + + + align:start position:0% +link and it's important to note what +this paper says this paper basically + + align:start position:0% +this paper says this paper basically + + + align:start position:0% +this paper says this paper basically +argues that the greenhouse gas emissions + + align:start position:0% +argues that the greenhouse gas emissions + + + align:start position:0% +argues that the greenhouse gas emissions +from plane engines themselves are not + + align:start position:0% +from plane engines themselves are not + + + align:start position:0% +from plane engines themselves are not +their only contribution to radiative + + align:start position:0% +their only contribution to radiative + + + align:start position:0% +their only contribution to radiative +forcing or through the greenhouse effect + + align:start position:0% +forcing or through the greenhouse effect + + + align:start position:0% +forcing or through the greenhouse effect +the contrails created a high atmosphere + + align:start position:0% +the contrails created a high atmosphere + + + align:start position:0% +the contrails created a high atmosphere +also results in additional greenhouse + + align:start position:0% +also results in additional greenhouse + + + align:start position:0% +also results in additional greenhouse +gas warming in fact Aviation is about + + align:start position:0% +gas warming in fact Aviation is about + + + align:start position:0% +gas warming in fact Aviation is about +3.5 total of the total radiative forcing + + align:start position:0% +3.5 total of the total radiative forcing + + + align:start position:0% +3.5 total of the total radiative forcing +estimated as paper you might see the + + align:start position:0% +estimated as paper you might see the + + + align:start position:0% +estimated as paper you might see the +off-pot number of two percent Aviation + + align:start position:0% +off-pot number of two percent Aviation + + + align:start position:0% +off-pot number of two percent Aviation +of only two percent of global emissions + + align:start position:0% +of only two percent of global emissions + + + align:start position:0% +of only two percent of global emissions +first I would press you to find out + + align:start position:0% +first I would press you to find out + + + align:start position:0% +first I would press you to find out +where that number actually comes from I + + align:start position:0% +where that number actually comes from I + + + align:start position:0% +where that number actually comes from I +know industry has circulated number at + + align:start position:0% +know industry has circulated number at + + + align:start position:0% +know industry has circulated number at +various times but also that number has I + + align:start position:0% +various times but also that number has I + + + align:start position:0% +various times but also that number has I +think is relatively old but also to + + align:start position:0% +think is relatively old but also to + + + align:start position:0% +think is relatively old but also to +point out it doesn't include this + + align:start position:0% +point out it doesn't include this + + + align:start position:0% +point out it doesn't include this +relatively large non-co2 effect it'd be + + align:start position:0% +relatively large non-co2 effect it'd be + + + align:start position:0% +relatively large non-co2 effect it'd be +considered Aviation to be a country it'd + + align:start position:0% +considered Aviation to be a country it'd + + + align:start position:0% +considered Aviation to be a country it'd +be the fifth or sixth biggest + + align:start position:0% +be the fifth or sixth biggest + + + align:start position:0% +be the fifth or sixth biggest +contributor to Global Mass gas missions + + align:start position:0% +contributor to Global Mass gas missions + + + align:start position:0% +contributor to Global Mass gas missions +and of course that country would be a + + align:start position:0% +and of course that country would be a + + + align:start position:0% +and of course that country would be a +pariah if it didn't take efforts to try + + align:start position:0% +pariah if it didn't take efforts to try + + + align:start position:0% +pariah if it didn't take efforts to try +to reduce its emissions + + align:start position:0% +to reduce its emissions + + + align:start position:0% +to reduce its emissions +and so just to kind of reinforce this + + align:start position:0% +and so just to kind of reinforce this + + + align:start position:0% +and so just to kind of reinforce this +point a little bit about how Global + + align:start position:0% +point a little bit about how Global + + + align:start position:0% +point a little bit about how Global +Aviation is an equitably distributed + + align:start position:0% +Aviation is an equitably distributed + + + align:start position:0% +Aviation is an equitably distributed +among the flying population this is from + + align:start position:0% +among the flying population this is from + + + align:start position:0% +among the flying population this is from +the Gosling and humpy 2020 paper and it + + align:start position:0% +the Gosling and humpy 2020 paper and it + + + align:start position:0% +the Gosling and humpy 2020 paper and it +basically divides the world population + + align:start position:0% +basically divides the world population + + + align:start position:0% +basically divides the world population +into four income brackets the low-income + + align:start position:0% +into four income brackets the low-income + + + align:start position:0% +into four income brackets the low-income +countries about 700 million people lower + + align:start position:0% +countries about 700 million people lower + + + align:start position:0% +countries about 700 million people lower +middle income countries about three + + align:start position:0% +middle income countries about three + + + align:start position:0% +middle income countries about three +billion people upper middle income + + align:start position:0% +billion people upper middle income + + + align:start position:0% +billion people upper middle income +countries about 2.7 billion people and + + align:start position:0% +countries about 2.7 billion people and + + + align:start position:0% +countries about 2.7 billion people and +1.2 billion High income people + + align:start position:0% +1.2 billion High income people + + + align:start position:0% +1.2 billion High income people +all they do is simply take numbers from + + align:start position:0% +all they do is simply take numbers from + + + align:start position:0% +all they do is simply take numbers from +the World Bank + + align:start position:0% +the World Bank + + + align:start position:0% +the World Bank +actually the number of flight passengers + + align:start position:0% +actually the number of flight passengers + + + align:start position:0% +actually the number of flight passengers +per country they calculate how many + + align:start position:0% +per country they calculate how many + + + align:start position:0% +per country they calculate how many +passengers there are per capita and they + + align:start position:0% +passengers there are per capita and they + + + align:start position:0% +passengers there are per capita and they +assume that if you know every single + + align:start position:0% +assume that if you know every single + + + align:start position:0% +assume that if you know every single +person who could fly + + align:start position:0% +person who could fly + + + align:start position:0% +person who could fly +blue and they can calculate theoretical + + align:start position:0% +blue and they can calculate theoretical + + + align:start position:0% +blue and they can calculate theoretical +maximum fine automation so if you take + + align:start position:0% +maximum fine automation so if you take + + + align:start position:0% +maximum fine automation so if you take +0.03 passage of per capita assume only + + align:start position:0% +0.03 passage of per capita assume only + + + align:start position:0% +0.03 passage of per capita assume only +people take one flight you should get to + + align:start position:0% +people take one flight you should get to + + + align:start position:0% +people take one flight you should get to +a maximum only 1.63 of the population + + align:start position:0% +a maximum only 1.63 of the population + + + align:start position:0% +a maximum only 1.63 of the population +has flown + + align:start position:0% +has flown + + + align:start position:0% +has flown +of course in high income countries since + + align:start position:0% +of course in high income countries since + + + align:start position:0% +of course in high income countries since +we average about two flights per capita + + align:start position:0% +we average about two flights per capita + + + align:start position:0% +we average about two flights per capita +in high income countries they assume + + align:start position:0% +in high income countries they assume + + + align:start position:0% +in high income countries they assume +that the total maximum fine population + + align:start position:0% +that the total maximum fine population + + + align:start position:0% +that the total maximum fine population +is 100 percent + + align:start position:0% +is 100 percent + + + align:start position:0% +is 100 percent +obviously that doesn't actually reflect + + align:start position:0% +obviously that doesn't actually reflect + + + align:start position:0% +obviously that doesn't actually reflect +the number of people who flew we'll talk + + align:start position:0% +the number of people who flew we'll talk + + + align:start position:0% +the number of people who flew we'll talk +about that in a second but this is just + + align:start position:0% +about that in a second but this is just + + + align:start position:0% +about that in a second but this is just +getting to a maximum buying population + + align:start position:0% +getting to a maximum buying population + + + align:start position:0% +getting to a maximum buying population +and already can see that there's a + + align:start position:0% +and already can see that there's a + + + align:start position:0% +and already can see that there's a +global inequity between who flies or who + + align:start position:0% +global inequity between who flies or who + + + align:start position:0% +global inequity between who flies or who +even could possibly apply of the 2.1 + + align:start position:0% +even could possibly apply of the 2.1 + + + align:start position:0% +even could possibly apply of the 2.1 +billion people who have flown the + + align:start position:0% +billion people who have flown the + + + align:start position:0% +billion people who have flown the +maximum or 2.1 billion perhaps flights + + align:start position:0% +maximum or 2.1 billion perhaps flights + + + align:start position:0% +maximum or 2.1 billion perhaps flights +the maximum flying population includes + + align:start position:0% +the maximum flying population includes + + + align:start position:0% +the maximum flying population includes +all these high countries and that's + + align:start position:0% +all these high countries and that's + + + align:start position:0% +all these high countries and that's +approximately 100 times what the Maxwell + + align:start position:0% +approximately 100 times what the Maxwell + + + align:start position:0% +approximately 100 times what the Maxwell +flying population in the below in some + + align:start position:0% +flying population in the below in some + + + align:start position:0% +flying population in the below in some +countries + + align:start position:0% +countries + + + align:start position:0% +countries +similarly if you adjust it for the + + align:start position:0% +similarly if you adjust it for the + + + align:start position:0% +similarly if you adjust it for the +non-flying share of the population + + align:start position:0% +non-flying share of the population + + + align:start position:0% +non-flying share of the population +because some people in many countries or + + align:start position:0% +because some people in many countries or + + + align:start position:0% +because some people in many countries or +even higher countries do not fly you can + + align:start position:0% +even higher countries do not fly you can + + + align:start position:0% +even higher countries do not fly you can +calculate this through again and you can + + align:start position:0% +calculate this through again and you can + + + align:start position:0% +calculate this through again and you can +find out that roughly 40 percent of the + + align:start position:0% +find out that roughly 40 percent of the + + + align:start position:0% +find out that roughly 40 percent of the +flying population in high income + + align:start position:0% +flying population in high income + + + align:start position:0% +flying population in high income +countries flies 0.7 percent of the + + align:start position:0% +countries flies 0.7 percent of the + + + align:start position:0% +countries flies 0.7 percent of the +flying population and low income + + align:start position:0% +flying population and low income + + + align:start position:0% +flying population and low income +countries I'm sorry 0.7 of the + + align:start position:0% +countries I'm sorry 0.7 of the + + + align:start position:0% +countries I'm sorry 0.7 of the +population at low-income countries could + + align:start position:0% +population at low-income countries could + + + align:start position:0% +population at low-income countries could +be flying and of course you also get to + + align:start position:0% +be flying and of course you also get to + + + align:start position:0% +be flying and of course you also get to +these drastic inequities where High + + align:start position:0% +these drastic inequities where High + + + align:start position:0% +these drastic inequities where High +income countries approximately have a + + align:start position:0% +income countries approximately have a + + + align:start position:0% +income countries approximately have a +hundred times more blank population than + + align:start position:0% +hundred times more blank population than + + + align:start position:0% +hundred times more blank population than +low income countries regardless of the + + align:start position:0% +low income countries regardless of the + + + align:start position:0% +low income countries regardless of the +total population in these income + + align:start position:0% +total population in these income + + + align:start position:0% +total population in these income +brackets + + align:start position:0% +brackets + + + align:start position:0% +brackets +and so just to reinforce this point + + align:start position:0% +and so just to reinforce this point + + + align:start position:0% +and so just to reinforce this point +again it is not just rich countries + + align:start position:0% +again it is not just rich countries + + + align:start position:0% +again it is not just rich countries +versus poor countries and it's actually + + align:start position:0% +versus poor countries and it's actually + + + align:start position:0% +versus poor countries and it's actually +people who are flying more in all these + + align:start position:0% +people who are flying more in all these + + + align:start position:0% +people who are flying more in all these +countries the distributions in table one + + align:start position:0% +countries the distributions in table one + + + align:start position:0% +countries the distributions in table one +do not consider that there's a + + align:start position:0% +do not consider that there's a + + + align:start position:0% +do not consider that there's a +significant share of the population in + + align:start position:0% +significant share of the population in + + + align:start position:0% +significant share of the population in +every country that does not fly while + + align:start position:0% +every country that does not fly while + + + align:start position:0% +every country that does not fly while +some of our Travelers participate in one + + align:start position:0% +some of our Travelers participate in one + + + align:start position:0% +some of our Travelers participate in one +two or multiple trips if you can look at + + align:start position:0% +two or multiple trips if you can look at + + + align:start position:0% +two or multiple trips if you can look at +look at all these countries in this + + align:start position:0% +look at all these countries in this + + + align:start position:0% +look at all these countries in this +quote in the paper + + align:start position:0% +quote in the paper + + + align:start position:0% +quote in the paper +you can see that the national surveys + + align:start position:0% +you can see that the national surveys + + + align:start position:0% +you can see that the national surveys +indicate that high income countries + + align:start position:0% +indicate that high income countries + + + align:start position:0% +indicate that high income countries +between 53 and 65 percent of the + + align:start position:0% +between 53 and 65 percent of the + + + align:start position:0% +between 53 and 65 percent of the +population will not fly in a given year + + align:start position:0% +population will not fly in a given year + + + align:start position:0% +population will not fly in a given year +this actually the case that a majority + + align:start position:0% +this actually the case that a majority + + + align:start position:0% +this actually the case that a majority +and actually a fairly large proportion + + align:start position:0% +and actually a fairly large proportion + + + align:start position:0% +and actually a fairly large proportion +population almost two-thirds of the + + align:start position:0% +population almost two-thirds of the + + + align:start position:0% +population almost two-thirds of the +population doesn't apply in a given year + + align:start position:0% +population doesn't apply in a given year + + + align:start position:0% +population doesn't apply in a given year +I want to reinforce this point because I + + align:start position:0% +I want to reinforce this point because I + + + align:start position:0% +I want to reinforce this point because I +think in academic settings and + + align:start position:0% +think in academic settings and + + + align:start position:0% +think in academic settings and +educational settings we tend to assume + + align:start position:0% +educational settings we tend to assume + + + align:start position:0% +educational settings we tend to assume +that most people are like us they fly + + align:start position:0% +that most people are like us they fly + + + align:start position:0% +that most people are like us they fly +all the time + + align:start position:0% +all the time + + + align:start position:0% +all the time +that's actually not the case in many + + align:start position:0% +that's actually not the case in many + + + align:start position:0% +that's actually not the case in many +high income countries also I want to + + align:start position:0% +high income countries also I want to + + + align:start position:0% +high income countries also I want to +show this again for the United States + + align:start position:0% +show this again for the United States + + + align:start position:0% +show this again for the United States +this is uh from the internet I think the + + align:start position:0% +this is uh from the internet I think the + + + align:start position:0% +this is uh from the internet I think the +um + + align:start position:0% +um + + + align:start position:0% +um +the air for America or the airline + + align:start position:0% +the air for America or the airline + + + align:start position:0% +the air for America or the airline +industry trade Association did a similar + + align:start position:0% +industry trade Association did a similar + + + align:start position:0% +industry trade Association did a similar +survey and they finally in a given year + + align:start position:0% +survey and they finally in a given year + + + align:start position:0% +survey and they finally in a given year +53 of adults do not fly + + align:start position:0% +53 of adults do not fly + + + align:start position:0% +53 of adults do not fly +either 35 of adults in a given year take + + align:start position:0% +either 35 of adults in a given year take + + + align:start position:0% +either 35 of adults in a given year take +one to five trips and twelve percent of + + align:start position:0% +one to five trips and twelve percent of + + + align:start position:0% +one to five trips and twelve percent of +adults or one-eighth of the population + + align:start position:0% +adults or one-eighth of the population + + + align:start position:0% +adults or one-eighth of the population +take about six trips or more I'll let + + align:start position:0% +take about six trips or more I'll let + + + align:start position:0% +take about six trips or more I'll let +you think back on your last few years + + align:start position:0% +you think back on your last few years + + + align:start position:0% +you think back on your last few years +before covid and think about what you're + + align:start position:0% +before covid and think about what you're + + + align:start position:0% +before covid and think about what you're +finding here's them this is something + + align:start position:0% +finding here's them this is something + + + align:start position:0% +finding here's them this is something +I've certainly considered as I've been + + align:start position:0% +I've certainly considered as I've been + + + align:start position:0% +I've certainly considered as I've been +trying to increase my efforts towards + + align:start position:0% +trying to increase my efforts towards + + + align:start position:0% +trying to increase my efforts towards +reducing my gas emissions + + align:start position:0% +reducing my gas emissions + + + align:start position:0% +reducing my gas emissions +and most importantly if you look at the + + align:start position:0% +and most importantly if you look at the + + + align:start position:0% +and most importantly if you look at the +forecast from here to 2050 this is a + + align:start position:0% +forecast from here to 2050 this is a + + + align:start position:0% +forecast from here to 2050 this is a +2020 paper where they look at 2018 + + align:start position:0% +2020 paper where they look at 2018 + + + align:start position:0% +2020 paper where they look at 2018 +numbers and 20 50 20 50 numbers + + align:start position:0% +numbers and 20 50 20 50 numbers + + + align:start position:0% +numbers and 20 50 20 50 numbers +and you can see that this is also quite + + align:start position:0% +and you can see that this is also quite + + + align:start position:0% +and you can see that this is also quite +inactively distributed across regions of + + align:start position:0% +inactively distributed across regions of + + + align:start position:0% +inactively distributed across regions of +the world North America is the Lion's + + align:start position:0% +the world North America is the Lion's + + + align:start position:0% +the world North America is the Lion's +Share of the emissions now from + + align:start position:0% +Share of the emissions now from + + + align:start position:0% +Share of the emissions now from +commercial air passenger transport along + + align:start position:0% +commercial air passenger transport along + + + align:start position:0% +commercial air passenger transport along +with Europe it's much lower in I guess + + align:start position:0% +with Europe it's much lower in I guess + + + align:start position:0% +with Europe it's much lower in I guess +Asia Pacific it's also quite high but on + + align:start position:0% +Asia Pacific it's also quite high but on + + + align:start position:0% +Asia Pacific it's also quite high but on +a per capita basis overwhelmingly flying + + align:start position:0% +a per capita basis overwhelmingly flying + + + align:start position:0% +a per capita basis overwhelmingly flying +a person North America and Europe to a + + align:start position:0% +a person North America and Europe to a + + + align:start position:0% +a person North America and Europe to a +lesser extent in the Middle East with + + align:start position:0% +lesser extent in the Middle East with + + + align:start position:0% +lesser extent in the Middle East with +perhaps much lower populations and the + + align:start position:0% +perhaps much lower populations and the + + + align:start position:0% +perhaps much lower populations and the +population on a per capita basis even + + align:start position:0% +population on a per capita basis even + + + align:start position:0% +population on a per capita basis even +though Asia does have a lot of air + + align:start position:0% +though Asia does have a lot of air + + + align:start position:0% +though Asia does have a lot of air +passenger transport as expected to + + align:start position:0% +passenger transport as expected to + + + align:start position:0% +passenger transport as expected to +apparently a lot of people in this + + align:start position:0% +apparently a lot of people in this + + + align:start position:0% +apparently a lot of people in this +forecast it is still much lower than + + align:start position:0% +forecast it is still much lower than + + + align:start position:0% +forecast it is still much lower than +North America and Europe + + align:start position:0% +North America and Europe + + + align:start position:0% +North America and Europe +and so this completes the homework + + align:start position:0% +and so this completes the homework + + + align:start position:0% +and so this completes the homework +problem just to give you a sense of how + + align:start position:0% +problem just to give you a sense of how + + + align:start position:0% +problem just to give you a sense of how +we might achieve different + + align:start position:0% +we might achieve different + + + align:start position:0% +we might achieve different +Transportation modes this is a figure + + align:start position:0% +Transportation modes this is a figure + + + align:start position:0% +Transportation modes this is a figure +from Makai an iBook figure 2023 chapter + + align:start position:0% +from Makai an iBook figure 2023 chapter + + + align:start position:0% +from Makai an iBook figure 2023 chapter +20. the vertical axis is in kilowatt + + align:start position:0% +20. the vertical axis is in kilowatt + + + align:start position:0% +20. the vertical axis is in kilowatt +hours per passenger per 100 kilometers + + align:start position:0% +hours per passenger per 100 kilometers + + + align:start position:0% +hours per passenger per 100 kilometers +and a horizontal axis you can see the + + align:start position:0% +and a horizontal axis you can see the + + + align:start position:0% +and a horizontal axis you can see the +speed in kilometers per hour as I said + + align:start position:0% +speed in kilometers per hour as I said + + + align:start position:0% +speed in kilometers per hour as I said +to you in the last lecture Mobility is a + + align:start position:0% +to you in the last lecture Mobility is a + + + align:start position:0% +to you in the last lecture Mobility is a +superpower it gives us the ability to + + align:start position:0% +superpower it gives us the ability to + + + align:start position:0% +superpower it gives us the ability to +access jobs Leisure housing travel and + + align:start position:0% +access jobs Leisure housing travel and + + + align:start position:0% +access jobs Leisure housing travel and +so as you think about our transportation + + align:start position:0% +so as you think about our transportation + + + align:start position:0% +so as you think about our transportation +modes you can see that all of these + + align:start position:0% +modes you can see that all of these + + + align:start position:0% +modes you can see that all of these +different modes of transportation the + + align:start position:0% +different modes of transportation the + + + align:start position:0% +different modes of transportation the +red ones I think all being ground + + align:start position:0% +red ones I think all being ground + + + align:start position:0% +red ones I think all being ground +transport the green ones being ocean + + align:start position:0% +transport the green ones being ocean + + + align:start position:0% +transport the green ones being ocean +transport or water-based transport and + + align:start position:0% +transport or water-based transport and + + + align:start position:0% +transport or water-based transport and +the blue ones being Air transport they + + align:start position:0% +the blue ones being Air transport they + + + align:start position:0% +the blue ones being Air transport they +all have different energetic + + align:start position:0% +all have different energetic + + + align:start position:0% +all have different energetic +implications along with vertical axis + + align:start position:0% +implications along with vertical axis + + + align:start position:0% +implications along with vertical axis +and different speed implications along + + align:start position:0% +and different speed implications along + + + align:start position:0% +and different speed implications along +the horizontal axis so what I wanted to + + align:start position:0% +the horizontal axis so what I wanted to + + + align:start position:0% +the horizontal axis so what I wanted to +do the homework was to calculate simply + + align:start position:0% +do the homework was to calculate simply + + + align:start position:0% +do the homework was to calculate simply +if you had a choice + + align:start position:0% +if you had a choice + + + align:start position:0% +if you had a choice +between traveling let's say by train or + + align:start position:0% +between traveling let's say by train or + + + align:start position:0% +between traveling let's say by train or +by a turboprop plane which one you + + align:start position:0% +by a turboprop plane which one you + + + align:start position:0% +by a turboprop plane which one you +should take and what the energy + + align:start position:0% +should take and what the energy + + + align:start position:0% +should take and what the energy +implications of that are because energy + + align:start position:0% +implications of that are because energy + + + align:start position:0% +implications of that are because energy +is closely linked to the greenhouse gas + + align:start position:0% +is closely linked to the greenhouse gas + + + align:start position:0% +is closely linked to the greenhouse gas +emissions + + align:start position:0% +emissions + + + align:start position:0% +emissions +so after the homework to compare taking + + align:start position:0% +so after the homework to compare taking + + + align:start position:0% +so after the homework to compare taking +a turbo crop plane versus a high speed + + align:start position:0% +a turbo crop plane versus a high speed + + + align:start position:0% +a turbo crop plane versus a high speed +train + + align:start position:0% +train + + + align:start position:0% +train +assuming that in the United States if + + align:start position:0% +assuming that in the United States if + + + align:start position:0% +assuming that in the United States if +you want to take a turbo prop plane you + + align:start position:0% +you want to take a turbo prop plane you + + + align:start position:0% +you want to take a turbo prop plane you +have to go to the airport and check into + + align:start position:0% +have to go to the airport and check into + + + align:start position:0% +have to go to the airport and check into +security I think it's the reasonable + + align:start position:0% +security I think it's the reasonable + + + align:start position:0% +security I think it's the reasonable +assumption that it would take three more + + align:start position:0% +assumption that it would take three more + + + align:start position:0% +assumption that it would take three more +hours to travel so the key to this + + align:start position:0% +hours to travel so the key to this + + + align:start position:0% +hours to travel so the key to this +problem is setting it up so that they + + align:start position:0% +problem is setting it up so that they + + + align:start position:0% +problem is setting it up so that they +travel the same distance + + align:start position:0% +travel the same distance + + + align:start position:0% +travel the same distance +and you can see you take from the trains + + align:start position:0% +and you can see you take from the trains + + + align:start position:0% +and you can see you take from the trains +perspective the plane has a higher speed + + align:start position:0% +perspective the plane has a higher speed + + + align:start position:0% +perspective the plane has a higher speed +but gets let's say x number of hours + + align:start position:0% +but gets let's say x number of hours + + + align:start position:0% +but gets let's say x number of hours +minus three hours to travel and that is + + align:start position:0% +minus three hours to travel and that is + + + align:start position:0% +minus three hours to travel and that is +probably the equivalent distance because + + align:start position:0% +probably the equivalent distance because + + + align:start position:0% +probably the equivalent distance because +you crossed out the hours as a train + + align:start position:0% +you crossed out the hours as a train + + + align:start position:0% +you crossed out the hours as a train +going 200 kilometers per hour traveling + + align:start position:0% +going 200 kilometers per hour traveling + + + align:start position:0% +going 200 kilometers per hour traveling +for X hours and you simply solve for x + + align:start position:0% +for X hours and you simply solve for x + + + align:start position:0% +for X hours and you simply solve for x +and you do the algebra and you can see + + align:start position:0% +and you do the algebra and you can see + + + align:start position:0% +and you do the algebra and you can see +that the train from the trains + + align:start position:0% +that the train from the trains + + + align:start position:0% +that the train from the trains +perspective it takes 4.27 hours by train + + align:start position:0% +perspective it takes 4.27 hours by train + + + align:start position:0% +perspective it takes 4.27 hours by train +and you go 855 kilometers if you set it + + align:start position:0% +and you go 855 kilometers if you set it + + + align:start position:0% +and you go 855 kilometers if you set it +up on the planes perspective you simply + + align:start position:0% +up on the planes perspective you simply + + + align:start position:0% +up on the planes perspective you simply +put the three hour difference on the + + align:start position:0% +put the three hour difference on the + + + align:start position:0% +put the three hour difference on the +other side you can see that we're + + align:start position:0% +other side you can see that we're + + + align:start position:0% +other side you can see that we're +traveling X hours by plane the train + + align:start position:0% +traveling X hours by plane the train + + + align:start position:0% +traveling X hours by plane the train +gets a three hour Head Start we + + align:start position:0% +gets a three hour Head Start we + + + align:start position:0% +gets a three hour Head Start we +calculated through the plane only takes + + align:start position:0% +calculated through the plane only takes + + + align:start position:0% +calculated through the plane only takes +1.27 hours but only goes the same + + align:start position:0% +1.27 hours but only goes the same + + + align:start position:0% +1.27 hours but only goes the same +distance of 855 kilometers + + align:start position:0% +distance of 855 kilometers + + + align:start position:0% +distance of 855 kilometers +so go on a coach and then calculate the + + align:start position:0% +so go on a coach and then calculate the + + + align:start position:0% +so go on a coach and then calculate the +energy you can look back at that graph + + align:start position:0% +energy you can look back at that graph + + + align:start position:0% +energy you can look back at that graph +from Makai 2023 and look at how much + + align:start position:0% +from Makai 2023 and look at how much + + + align:start position:0% +from Makai 2023 and look at how much +energy is required to go a certain + + align:start position:0% +energy is required to go a certain + + + align:start position:0% +energy is required to go a certain +distance so if 38 kilowatt hours per + + align:start position:0% +distance so if 38 kilowatt hours per + + + align:start position:0% +distance so if 38 kilowatt hours per +passenger per 100 kilometers to go 670 + + align:start position:0% +passenger per 100 kilometers to go 670 + + + align:start position:0% +passenger per 100 kilometers to go 670 +kilometers per hour or per volt plane + + align:start position:0% +kilometers per hour or per volt plane + + + align:start position:0% +kilometers per hour or per volt plane +and for a high-speed train they take it + + align:start position:0% +and for a high-speed train they take it + + + align:start position:0% +and for a high-speed train they take it +requires four kilowatt hours per + + align:start position:0% +requires four kilowatt hours per + + + align:start position:0% +requires four kilowatt hours per +passenger for 100 kilometers to go 200 + + align:start position:0% +passenger for 100 kilometers to go 200 + + + align:start position:0% +passenger for 100 kilometers to go 200 +kilometers per hour + + align:start position:0% +kilometers per hour + + + align:start position:0% +kilometers per hour +and so if you multiply it through you + + align:start position:0% +and so if you multiply it through you + + + align:start position:0% +and so if you multiply it through you +simply take the 38 times the 856 + + align:start position:0% +simply take the 38 times the 856 + + + align:start position:0% +simply take the 38 times the 856 +kilometers you get to 325 kilowatt hours + + align:start position:0% +kilometers you get to 325 kilowatt hours + + + align:start position:0% +kilometers you get to 325 kilowatt hours +per passenger + + align:start position:0% +per passenger + + + align:start position:0% +per passenger +or high-speed train it is 4 times 856 or + + align:start position:0% +or high-speed train it is 4 times 856 or + + + align:start position:0% +or high-speed train it is 4 times 856 or +34 kilowatt hours per passenger + + align:start position:0% +34 kilowatt hours per passenger + + + align:start position:0% +34 kilowatt hours per passenger +because you cross out the 100 kilometers + + align:start position:0% +because you cross out the 100 kilometers + + + align:start position:0% +because you cross out the 100 kilometers +from the bottom + + align:start position:0% +from the bottom + + + align:start position:0% +from the bottom +you can see that it's roughly a 10x or + + align:start position:0% +you can see that it's roughly a 10x or + + + align:start position:0% +you can see that it's roughly a 10x or +exactly a 9.5 x difference between the + + align:start position:0% +exactly a 9.5 x difference between the + + + align:start position:0% +exactly a 9.5 x difference between the +two and you can see it because they use + + align:start position:0% +two and you can see it because they use + + + align:start position:0% +two and you can see it because they use +the exact same distance the key numbers + + align:start position:0% +the exact same distance the key numbers + + + align:start position:0% +the exact same distance the key numbers +here are the 38 and the four + + align:start position:0% +here are the 38 and the four + + + align:start position:0% +here are the 38 and the four +so this brings us to makai's question in + + align:start position:0% +so this brings us to makai's question in + + + align:start position:0% +so this brings us to makai's question in +appendix C which is can we improve + + align:start position:0% +appendix C which is can we improve + + + align:start position:0% +appendix C which is can we improve +planes + + align:start position:0% +planes + + + align:start position:0% +planes +and he argues in this chapter that + + align:start position:0% +and he argues in this chapter that + + + align:start position:0% +and he argues in this chapter that +engine efficiency can only be boosted a + + align:start position:0% +engine efficiency can only be boosted a + + + align:start position:0% +engine efficiency can only be boosted a +tiny bit by technological progress the + + align:start position:0% +tiny bit by technological progress the + + + align:start position:0% +tiny bit by technological progress the +shape of the plane is already highly + + align:start position:0% +shape of the plane is already highly + + + align:start position:0% +shape of the plane is already highly +efficient and argues that there's little + + align:start position:0% +efficient and argues that there's little + + + align:start position:0% +efficient and argues that there's little +that can be done to improve the + + align:start position:0% +that can be done to improve the + + + align:start position:0% +that can be done to improve the +transportation efficiency of planes I + + align:start position:0% +transportation efficiency of planes I + + + align:start position:0% +transportation efficiency of planes I +will uh defer to my colleagues in Arrow + + align:start position:0% +will uh defer to my colleagues in Arrow + + + align:start position:0% +will uh defer to my colleagues in Arrow +Astro or students in that area it looks + + align:start position:0% +Astro or students in that area it looks + + + align:start position:0% +Astro or students in that area it looks +like there are some possible ways to try + + align:start position:0% +like there are some possible ways to try + + + align:start position:0% +like there are some possible ways to try +to improve the efficiency of planes and + + align:start position:0% +to improve the efficiency of planes and + + + align:start position:0% +to improve the efficiency of planes and +so this reminds me of this headline I + + align:start position:0% +so this reminds me of this headline I + + + align:start position:0% +so this reminds me of this headline I +saw last year on CNN this is the + + align:start position:0% +saw last year on CNN this is the + + + align:start position:0% +saw last year on CNN this is the +long-awaited celera 500L bullet plane + + align:start position:0% +long-awaited celera 500L bullet plane + + + align:start position:0% +long-awaited celera 500L bullet plane +you can see that it's taken a number of + + align:start position:0% +you can see that it's taken a number of + + + align:start position:0% +you can see that it's taken a number of +measures the bullet shape these small + + align:start position:0% +measures the bullet shape these small + + + align:start position:0% +measures the bullet shape these small +stubby Wings the places where the + + align:start position:0% +stubby Wings the places where the + + + align:start position:0% +stubby Wings the places where the +engines are all designed to increase its + + align:start position:0% +engines are all designed to increase its + + + align:start position:0% +engines are all designed to increase its +efficiency got this turbo prop and back + + align:start position:0% +efficiency got this turbo prop and back + + + align:start position:0% +efficiency got this turbo prop and back +and this article says that it gets 18 to + + align:start position:0% +and this article says that it gets 18 to + + + align:start position:0% +and this article says that it gets 18 to +25 miles per gallon compared to two to + + align:start position:0% +25 miles per gallon compared to two to + + + align:start position:0% +25 miles per gallon compared to two to +three miles per a comparable small and + + align:start position:0% +three miles per a comparable small and + + + align:start position:0% +three miles per a comparable small and +presumably private jet + + align:start position:0% +presumably private jet + + + align:start position:0% +presumably private jet +so just to calculate these in a rough + + align:start position:0% +so just to calculate these in a rough + + + align:start position:0% +so just to calculate these in a rough +way assuming it uses gasoline our least + + align:start position:0% +way assuming it uses gasoline our least + + + align:start position:0% +way assuming it uses gasoline our least +energy the density of gasoline though + + align:start position:0% +energy the density of gasoline though + + + align:start position:0% +energy the density of gasoline though +it's probably uses a particular fuel for + + align:start position:0% +it's probably uses a particular fuel for + + + align:start position:0% +it's probably uses a particular fuel for +a private jet we have the 10 kilowatt + + align:start position:0% +a private jet we have the 10 kilowatt + + + align:start position:0% +a private jet we have the 10 kilowatt +hours per liter we used for gas engines + + align:start position:0% +hours per liter we used for gas engines + + + align:start position:0% +hours per liter we used for gas engines +in the previous lecture we divided by + + align:start position:0% +in the previous lecture we divided by + + + align:start position:0% +in the previous lecture we divided by +2.5 miles per gallon inverting the miles + + align:start position:0% +2.5 miles per gallon inverting the miles + + + align:start position:0% +2.5 miles per gallon inverting the miles +per gallon factor and we get to a figure + + align:start position:0% +per gallon factor and we get to a figure + + + align:start position:0% +per gallon factor and we get to a figure +of 961 961 kilowatt hours per 100 + + align:start position:0% +of 961 961 kilowatt hours per 100 + + + align:start position:0% +of 961 961 kilowatt hours per 100 +kilometers uh if you let's calculate + + align:start position:0% +kilometers uh if you let's calculate + + + align:start position:0% +kilometers uh if you let's calculate +that like we did last week for the + + align:start position:0% +that like we did last week for the + + + align:start position:0% +that like we did last week for the +internal combustion engine of an SUV the + + align:start position:0% +internal combustion engine of an SUV the + + + align:start position:0% +internal combustion engine of an SUV the +only change we've made here is we give + + align:start position:0% +only change we've made here is we give + + + align:start position:0% +only change we've made here is we give +you the same energy density of the fuel + + align:start position:0% +you the same energy density of the fuel + + + align:start position:0% +you the same energy density of the fuel +but we've made this SUV 22 miles per + + align:start position:0% +but we've made this SUV 22 miles per + + + align:start position:0% +but we've made this SUV 22 miles per +gallon that seems relatively generous + + align:start position:0% +gallon that seems relatively generous + + + align:start position:0% +gallon that seems relatively generous +and you get to almost a factor of nine + + align:start position:0% +and you get to almost a factor of nine + + + align:start position:0% +and you get to almost a factor of nine +less 109 kilowatt hours per 100 + + align:start position:0% +less 109 kilowatt hours per 100 + + + align:start position:0% +less 109 kilowatt hours per 100 +kilometers + + align:start position:0% +kilometers + + + align:start position:0% +kilometers +and for the seller of 500 which is + + align:start position:0% +and for the seller of 500 which is + + + align:start position:0% +and for the seller of 500 which is +quoted to get 18 to 25 miles per gallon + + align:start position:0% +quoted to get 18 to 25 miles per gallon + + + align:start position:0% +quoted to get 18 to 25 miles per gallon +you can do the exact same calculation + + align:start position:0% +you can do the exact same calculation + + + align:start position:0% +you can do the exact same calculation +because we know that 18 25 miles per + + align:start position:0% +because we know that 18 25 miles per + + + align:start position:0% +because we know that 18 25 miles per +gallon encompasses are 22 miles per + + align:start position:0% +gallon encompasses are 22 miles per + + + align:start position:0% +gallon encompasses are 22 miles per +gallon for SUV so give the exact same + + align:start position:0% +gallon for SUV so give the exact same + + + align:start position:0% +gallon for SUV so give the exact same +number these are rough estimates the + + align:start position:0% +number these are rough estimates the + + + align:start position:0% +number these are rough estimates the +reason why we do these is simply to try + + align:start position:0% +reason why we do these is simply to try + + + align:start position:0% +reason why we do these is simply to try +to prepare the modes + + align:start position:0% +to prepare the modes + + + align:start position:0% +to prepare the modes +and if we assume they all care about six + + align:start position:0% +and if we assume they all care about six + + + align:start position:0% +and if we assume they all care about six +people you could divide this energy used + + align:start position:0% +people you could divide this energy used + + + align:start position:0% +people you could divide this energy used +by six to get kilowatt hours per person + + align:start position:0% +by six to get kilowatt hours per person + + + align:start position:0% +by six to get kilowatt hours per person +per kilometer + + align:start position:0% +per kilometer + + + align:start position:0% +per kilometer +if you want to compare this new + + align:start position:0% +if you want to compare this new + + + align:start position:0% +if you want to compare this new +calculation to our previous calculation + + align:start position:0% +calculation to our previous calculation + + + align:start position:0% +calculation to our previous calculation +for the turbo prop plane and the high + + align:start position:0% +for the turbo prop plane and the high + + + align:start position:0% +for the turbo prop plane and the high +speed train you can see that the private + + align:start position:0% +speed train you can see that the private + + + align:start position:0% +speed train you can see that the private +jet is a very high number for an energy + + align:start position:0% +jet is a very high number for an energy + + + align:start position:0% +jet is a very high number for an energy +per person to go this 856 kilometer trip + + align:start position:0% +per person to go this 856 kilometer trip + + + align:start position:0% +per person to go this 856 kilometer trip +the turbo prop plane is roughly + + align:start position:0% +the turbo prop plane is roughly + + + align:start position:0% +the turbo prop plane is roughly +one-fourth of what the private jet is + + align:start position:0% +one-fourth of what the private jet is + + + align:start position:0% +one-fourth of what the private jet is +the accelera or a six-person SUV is + + align:start position:0% +the accelera or a six-person SUV is + + + align:start position:0% +the accelera or a six-person SUV is +about a half of what a turbo prop plane + + align:start position:0% +about a half of what a turbo prop plane + + + align:start position:0% +about a half of what a turbo prop plane +is and of course the high-speed train is + + align:start position:0% +is and of course the high-speed train is + + + align:start position:0% +is and of course the high-speed train is +still much lower than all the other + + align:start position:0% +still much lower than all the other + + + align:start position:0% +still much lower than all the other +modes so this is to say that you know we + + align:start position:0% +modes so this is to say that you know we + + + align:start position:0% +modes so this is to say that you know we +have different passenger capacity + + align:start position:0% +have different passenger capacity + + + align:start position:0% +have different passenger capacity +we have different speeds certainly for + + align:start position:0% +we have different speeds certainly for + + + align:start position:0% +we have different speeds certainly for +all these modes but this also causes the + + align:start position:0% +all these modes but this also causes the + + + align:start position:0% +all these modes but this also causes the +question what kind of infrastructure you + + align:start position:0% +question what kind of infrastructure you + + + align:start position:0% +question what kind of infrastructure you +want to build to achieve these different + + align:start position:0% +want to build to achieve these different + + + align:start position:0% +want to build to achieve these different +modes if you want to decarbonize and + + align:start position:0% +modes if you want to decarbonize and + + + align:start position:0% +modes if you want to decarbonize and +reduce our greenhouse gas emissions we + + align:start position:0% +reduce our greenhouse gas emissions we + + + align:start position:0% +reduce our greenhouse gas emissions we +are going to have to change how we take + + align:start position:0% +are going to have to change how we take + + + align:start position:0% +are going to have to change how we take +some trips and you can see some + + align:start position:0% +some trips and you can see some + + + align:start position:0% +some trips and you can see some +countries like China have essentially + + align:start position:0% +countries like China have essentially + + + align:start position:0% +countries like China have essentially +tried to eliminate their short haul + + align:start position:0% +tried to eliminate their short haul + + + align:start position:0% +tried to eliminate their short haul +Aviation Market by building high-speed + + align:start position:0% +Aviation Market by building high-speed + + + align:start position:0% +Aviation Market by building high-speed +train networks their high speed train + + align:start position:0% +train networks their high speed train + + + align:start position:0% +train networks their high speed train +networks are out competing many of their + + align:start position:0% +networks are out competing many of their + + + align:start position:0% +networks are out competing many of their +historical aircraft and so apparently + + align:start position:0% +historical aircraft and so apparently + + + align:start position:0% +historical aircraft and so apparently +the short haul aviation industry had + + align:start position:0% +the short haul aviation industry had + + + align:start position:0% +the short haul aviation industry had +gone away in China and parts of Europe + + align:start position:0% +gone away in China and parts of Europe + + + align:start position:0% +gone away in China and parts of Europe +some universities now say that you can't + + align:start position:0% +some universities now say that you can't + + + align:start position:0% +some universities now say that you can't +take a plane to a conference if it's + + align:start position:0% +take a plane to a conference if it's + + + align:start position:0% +take a plane to a conference if it's +within I think 500 kilometers because + + align:start position:0% +within I think 500 kilometers because + + + align:start position:0% +within I think 500 kilometers because +the argument is you can get to that + + align:start position:0% +the argument is you can get to that + + + align:start position:0% +the argument is you can get to that +conference just as quickly by train and + + align:start position:0% +conference just as quickly by train and + + + align:start position:0% +conference just as quickly by train and +you know we are seeing a growth as one + + align:start position:0% +you know we are seeing a growth as one + + + align:start position:0% +you know we are seeing a growth as one +of our students sent in an article of + + align:start position:0% +of our students sent in an article of + + + align:start position:0% +of our students sent in an article of +short-haul aviation in Europe but + + align:start position:0% +short-haul aviation in Europe but + + + align:start position:0% +short-haul aviation in Europe but +obviously I would argue that Europe + + align:start position:0% +obviously I would argue that Europe + + + align:start position:0% +obviously I would argue that Europe +especially has actually a lot of + + align:start position:0% +especially has actually a lot of + + + align:start position:0% +especially has actually a lot of +opportunities to try to eliminate short + + align:start position:0% +opportunities to try to eliminate short + + + align:start position:0% +opportunities to try to eliminate short +haul Aviation flights + + align:start position:0% +haul Aviation flights + + + align:start position:0% +haul Aviation flights +so this brings me to the O'Leary chapter + + align:start position:0% +so this brings me to the O'Leary chapter + + + align:start position:0% +so this brings me to the O'Leary chapter +on Aviation and it's just worth noting + + align:start position:0% +on Aviation and it's just worth noting + + + align:start position:0% +on Aviation and it's just worth noting +what the history of policy actions are + + align:start position:0% +what the history of policy actions are + + + align:start position:0% +what the history of policy actions are +on Aviation in 1997 the KIRO protocol + + align:start position:0% +on Aviation in 1997 the KIRO protocol + + + align:start position:0% +on Aviation in 1997 the KIRO protocol +asked all countries to reduce their + + align:start position:0% +asked all countries to reduce their + + + align:start position:0% +asked all countries to reduce their +greenhouse gas emissions by five percent + + align:start position:0% +greenhouse gas emissions by five percent + + + align:start position:0% +greenhouse gas emissions by five percent +from 1990 to 2012. the cuter protocol is + + align:start position:0% +from 1990 to 2012. the cuter protocol is + + + align:start position:0% +from 1990 to 2012. the cuter protocol is +never brought for a vote to the Senate + + align:start position:0% +never brought for a vote to the Senate + + + align:start position:0% +never brought for a vote to the Senate +by the Clinton Administration United + + align:start position:0% +by the Clinton Administration United + + + align:start position:0% +by the Clinton Administration United +States because they thought our view + + align:start position:0% +States because they thought our view + + + align:start position:0% +States because they thought our view +that it would fail in the Senate when + + align:start position:0% +that it would fail in the Senate when + + + align:start position:0% +that it would fail in the Senate when +President Obama became president in 2008 + + align:start position:0% +President Obama became president in 2008 + + + align:start position:0% +President Obama became president in 2008 +one of the initiatives you proud Olympic + + align:start position:0% +one of the initiatives you proud Olympic + + + align:start position:0% +one of the initiatives you proud Olympic +greenhouse gas emissions with the wax + + align:start position:0% +greenhouse gas emissions with the wax + + + align:start position:0% +greenhouse gas emissions with the wax +and Marquee bill which apparently + + align:start position:0% +and Marquee bill which apparently + + + align:start position:0% +and Marquee bill which apparently +included Provisions for Aviation but + + align:start position:0% +included Provisions for Aviation but + + + align:start position:0% +included Provisions for Aviation but +that actually did fail in the Senate + + align:start position:0% +that actually did fail in the Senate + + + align:start position:0% +that actually did fail in the Senate +even though it passed the house + + align:start position:0% +even though it passed the house + + + align:start position:0% +even though it passed the house +in 2012 European introduced animations + + align:start position:0% +in 2012 European introduced animations + + + align:start position:0% +in 2012 European introduced animations +trading scheme but preemptively in 2011 + + align:start position:0% +trading scheme but preemptively in 2011 + + + align:start position:0% +trading scheme but preemptively in 2011 +the US Congress passed a Prohibition act + + align:start position:0% +the US Congress passed a Prohibition act + + + align:start position:0% +the US Congress passed a Prohibition act +where the United States is never to join + + align:start position:0% +where the United States is never to join + + + align:start position:0% +where the United States is never to join +into the same trading scheme as the + + align:start position:0% +into the same trading scheme as the + + + align:start position:0% +into the same trading scheme as the +European Union + + align:start position:0% +European Union + + + align:start position:0% +European Union +and in 2016 the EPA found that under the + + align:start position:0% +and in 2016 the EPA found that under the + + + align:start position:0% +and in 2016 the EPA found that under the +Clean Air Act greenhouse gas emissions + + align:start position:0% +Clean Air Act greenhouse gas emissions + + + align:start position:0% +Clean Air Act greenhouse gas emissions +did endanger human health which is what + + align:start position:0% +did endanger human health which is what + + + align:start position:0% +did endanger human health which is what +the Clean Air Act tax regards against at + + align:start position:0% +the Clean Air Act tax regards against at + + + align:start position:0% +the Clean Air Act tax regards against at +the same time in the international civil + + align:start position:0% +the same time in the international civil + + + align:start position:0% +the same time in the international civil +aviation organization developed course + + align:start position:0% +aviation organization developed course + + + align:start position:0% +aviation organization developed course +you have a carbon cap and offsetting + + align:start position:0% +you have a carbon cap and offsetting + + + align:start position:0% +you have a carbon cap and offsetting +scheme for 2020 and 2017 they adopted a + + align:start position:0% +scheme for 2020 and 2017 they adopted a + + + align:start position:0% +scheme for 2020 and 2017 they adopted a +CO2 standard for aircraft essentially + + align:start position:0% +CO2 standard for aircraft essentially + + + align:start position:0% +CO2 standard for aircraft essentially +kind of a greenhouse gas emissions limit + + align:start position:0% +kind of a greenhouse gas emissions limit + + + align:start position:0% +kind of a greenhouse gas emissions limit +for planes and in 2017 the EU decided + + align:start position:0% +for planes and in 2017 the EU decided + + + align:start position:0% +for planes and in 2017 the EU decided +was only applied to intra-eu flights the + + align:start position:0% +was only applied to intra-eu flights the + + + align:start position:0% +was only applied to intra-eu flights the +reason also why I want to focus on + + align:start position:0% +reason also why I want to focus on + + + align:start position:0% +reason also why I want to focus on +global Aviation as a policy issue is + + align:start position:0% +global Aviation as a policy issue is + + + align:start position:0% +global Aviation as a policy issue is +that Aviation and shipping are not + + align:start position:0% +that Aviation and shipping are not + + + align:start position:0% +that Aviation and shipping are not +included in Paris climate agreements in + + align:start position:0% +included in Paris climate agreements in + + + align:start position:0% +included in Paris climate agreements in +2016. which is to say it's one of our + + align:start position:0% +2016. which is to say it's one of our + + + align:start position:0% +2016. which is to say it's one of our +fastest growing sectors of Beyond gas + + align:start position:0% +fastest growing sectors of Beyond gas + + + align:start position:0% +fastest growing sectors of Beyond gas +missions but we actually don't have an + + align:start position:0% +missions but we actually don't have an + + + align:start position:0% +missions but we actually don't have an +international policy to try to limit + + align:start position:0% +international policy to try to limit + + + align:start position:0% +international policy to try to limit +these emissions this perhaps brings into + + align:start position:0% +these emissions this perhaps brings into + + + align:start position:0% +these emissions this perhaps brings into +a question is international policy the + + align:start position:0% +a question is international policy the + + + align:start position:0% +a question is international policy the +right way to tackle this problem + + align:start position:0% +right way to tackle this problem + + + align:start position:0% +right way to tackle this problem +the O'Leary chapter I think provides + + align:start position:0% +the O'Leary chapter I think provides + + + align:start position:0% +the O'Leary chapter I think provides +some really interesting ideas for policy + + align:start position:0% +some really interesting ideas for policy + + + align:start position:0% +some really interesting ideas for policy +options the options include improving + + align:start position:0% +options the options include improving + + + align:start position:0% +options the options include improving +the efficiency of the vehicles + + align:start position:0% +the efficiency of the vehicles + + + align:start position:0% +the efficiency of the vehicles +themselves trying to use biofuels + + align:start position:0% +themselves trying to use biofuels + + + align:start position:0% +themselves trying to use biofuels +presumably where those have carbon + + align:start position:0% +presumably where those have carbon + + + align:start position:0% +presumably where those have carbon +capture a carbonates after are utilized + + align:start position:0% +capture a carbonates after are utilized + + + align:start position:0% +capture a carbonates after are utilized +or stored we could try to change our + + align:start position:0% +or stored we could try to change our + + + align:start position:0% +or stored we could try to change our +operational measures increase the + + align:start position:0% +operational measures increase the + + + align:start position:0% +operational measures increase the +efficiency of the system itself to + + align:start position:0% +efficiency of the system itself to + + + align:start position:0% +efficiency of the system itself to +reduce its gas emissions or we could + + align:start position:0% +reduce its gas emissions or we could + + + align:start position:0% +reduce its gas emissions or we could +simply try to reduce our demand + + align:start position:0% +simply try to reduce our demand + + + align:start position:0% +simply try to reduce our demand +and so we translate the adverse options + + align:start position:0% +and so we translate the adverse options + + + align:start position:0% +and so we translate the adverse options +into U.S policy options that could + + align:start position:0% +into U.S policy options that could + + + align:start position:0% +into U.S policy options that could +include a cover tax including Aviation + + align:start position:0% +include a cover tax including Aviation + + + align:start position:0% +include a cover tax including Aviation +missions we could specifically increase + + align:start position:0% +missions we could specifically increase + + + align:start position:0% +missions we could specifically increase +taxes on Aviation just like we tax other + + align:start position:0% +taxes on Aviation just like we tax other + + + align:start position:0% +taxes on Aviation just like we tax other +things that have high social impacts + + align:start position:0% +things that have high social impacts + + + align:start position:0% +things that have high social impacts +Like Liquor guns and cigarettes or we + + align:start position:0% +Like Liquor guns and cigarettes or we + + + align:start position:0% +Like Liquor guns and cigarettes or we +could introduce an emission standard for + + align:start position:0% +could introduce an emission standard for + + + align:start position:0% +could introduce an emission standard for +planes to say that only planes of a + + align:start position:0% +planes to say that only planes of a + + + align:start position:0% +planes to say that only planes of a +certain efficiency are allowed to pick + + align:start position:0% +certain efficiency are allowed to pick + + + align:start position:0% +certain efficiency are allowed to pick +flights to the U.S we could require or + + align:start position:0% +flights to the U.S we could require or + + + align:start position:0% +flights to the U.S we could require or +encourage the use of biofuels for planes + + align:start position:0% +encourage the use of biofuels for planes + + + align:start position:0% +encourage the use of biofuels for planes +we try to reduce emissions at airports + + align:start position:0% +we try to reduce emissions at airports + + + align:start position:0% +we try to reduce emissions at airports +such as the airport operations + + align:start position:0% +such as the airport operations + + + align:start position:0% +such as the airport operations +themselves or reducing acting time that + + align:start position:0% +themselves or reducing acting time that + + + align:start position:0% +themselves or reducing acting time that +it's like idling for trucks we could ask + + align:start position:0% +it's like idling for trucks we could ask + + + align:start position:0% +it's like idling for trucks we could ask +Airlines to engage in volunteer + + align:start position:0% +Airlines to engage in volunteer + + + align:start position:0% +Airlines to engage in volunteer +Innovations reduction measures we could + + align:start position:0% +Innovations reduction measures we could + + + align:start position:0% +Innovations reduction measures we could +enable or encourage less flying as a + + align:start position:0% +enable or encourage less flying as a + + + align:start position:0% +enable or encourage less flying as a +demand reduction measure individuals + + align:start position:0% +demand reduction measure individuals + + + align:start position:0% +demand reduction measure individuals +could have purchased high quality + + align:start position:0% +could have purchased high quality + + + align:start position:0% +could have purchased high quality +offsets this is what MIT is pursuing as + + align:start position:0% +offsets this is what MIT is pursuing as + + + align:start position:0% +offsets this is what MIT is pursuing as +a net zero strategy or we could try to + + align:start position:0% +a net zero strategy or we could try to + + + align:start position:0% +a net zero strategy or we could try to +reduce our freight emissions + + align:start position:0% +reduce our freight emissions + + + align:start position:0% +reduce our freight emissions +and so this is something I want to + + align:start position:0% +and so this is something I want to + + + align:start position:0% +and so this is something I want to +discuss in the class when we meet which + + align:start position:0% +discuss in the class when we meet which + + + align:start position:0% +discuss in the class when we meet which +is is Aviation a moral or individual + + align:start position:0% +is is Aviation a moral or individual + + + align:start position:0% +is is Aviation a moral or individual +issue and does that actually translate + + align:start position:0% +issue and does that actually translate + + + align:start position:0% +issue and does that actually translate +into a policy issue I would argue there + + align:start position:0% +into a policy issue I would argue there + + + align:start position:0% +into a policy issue I would argue there +are two schools of thought the first one + + align:start position:0% +are two schools of thought the first one + + + align:start position:0% +are two schools of thought the first one +argues that Aviation is a red herring + + align:start position:0% +argues that Aviation is a red herring + + + align:start position:0% +argues that Aviation is a red herring +and a Canard or a waste of time of our + + align:start position:0% +and a Canard or a waste of time of our + + + align:start position:0% +and a Canard or a waste of time of our +policy analysts to talk about and some + + align:start position:0% +policy analysts to talk about and some + + + align:start position:0% +policy analysts to talk about and some +of their arguments are these different + + align:start position:0% +of their arguments are these different + + + align:start position:0% +of their arguments are these different +lines first they argue that our + + align:start position:0% +lines first they argue that our + + + align:start position:0% +lines first they argue that our +individual missions are concerned about + + align:start position:0% +individual missions are concerned about + + + align:start position:0% +individual missions are concerned about +our individual missions our individual + + align:start position:0% +our individual missions our individual + + + align:start position:0% +our individual missions our individual +carbon Footprints is essentially the + + align:start position:0% +carbon Footprints is essentially the + + + align:start position:0% +carbon Footprints is essentially the +product of a corporate marketing + + align:start position:0% +product of a corporate marketing + + + align:start position:0% +product of a corporate marketing +campaign from BP or exploring in the + + align:start position:0% +campaign from BP or exploring in the + + + align:start position:0% +campaign from BP or exploring in the +1970s and 80s that's been well + + align:start position:0% +1970s and 80s that's been well + + + align:start position:0% +1970s and 80s that's been well +documented and of course not a line of + + align:start position:0% +documented and of course not a line of + + + align:start position:0% +documented and of course not a line of +thought is that 70 of fossil fuels have + + align:start position:0% +thought is that 70 of fossil fuels have + + + align:start position:0% +thought is that 70 of fossil fuels have +been sold by 30 or so companies you can + + align:start position:0% +been sold by 30 or so companies you can + + + align:start position:0% +been sold by 30 or so companies you can +see that news headline in the guardian + + align:start position:0% +see that news headline in the guardian + + + align:start position:0% +see that news headline in the guardian +and so they blame corporations for these + + align:start position:0% +and so they blame corporations for these + + + align:start position:0% +and so they blame corporations for these +emissions from Aviation or other + + align:start position:0% +emissions from Aviation or other + + + align:start position:0% +emissions from Aviation or other +activities rather than the consumers + + align:start position:0% +activities rather than the consumers + + + align:start position:0% +activities rather than the consumers +and of course there's one more line of + + align:start position:0% +and of course there's one more line of + + + align:start position:0% +and of course there's one more line of +thought that individual actions can + + align:start position:0% +thought that individual actions can + + + align:start position:0% +thought that individual actions can +demotivate people toward larger + + align:start position:0% +demotivate people toward larger + + + align:start position:0% +demotivate people toward larger +Collective actions you spend all your + + align:start position:0% +Collective actions you spend all your + + + align:start position:0% +Collective actions you spend all your +time thinking about recycling or + + align:start position:0% +time thinking about recycling or + + + align:start position:0% +time thinking about recycling or +bicycling or vegetarianism you may have + + align:start position:0% +bicycling or vegetarianism you may have + + + align:start position:0% +bicycling or vegetarianism you may have +less time to participate in larger + + align:start position:0% +less time to participate in larger + + + align:start position:0% +less time to participate in larger +policy or social organizing I would + + align:start position:0% +policy or social organizing I would + + + align:start position:0% +policy or social organizing I would +actually disagree with that but some + + align:start position:0% +actually disagree with that but some + + + align:start position:0% +actually disagree with that but some +people also have well done well + + align:start position:0% +people also have well done well + + + align:start position:0% +people also have well done well +documented Atari Atari at Indiana + + align:start position:0% +documented Atari Atari at Indiana + + + align:start position:0% +documented Atari Atari at Indiana +University has documented how people are + + align:start position:0% +University has documented how people are + + + align:start position:0% +University has documented how people are +very bad at judging the effects of their + + align:start position:0% +very bad at judging the effects of their + + + align:start position:0% +very bad at judging the effects of their +actions whether or not they are changing + + align:start position:0% +actions whether or not they are changing + + + align:start position:0% +actions whether or not they are changing +light bulbs or engaging Energy + + align:start position:0% +light bulbs or engaging Energy + + + align:start position:0% +light bulbs or engaging Energy +Efficiency or buying energy efficient + + align:start position:0% +Efficiency or buying energy efficient + + + align:start position:0% +Efficiency or buying energy efficient +laptop people just don't really + + align:start position:0% +laptop people just don't really + + + align:start position:0% +laptop people just don't really +understand necessarily how much + + align:start position:0% +understand necessarily how much + + + align:start position:0% +understand necessarily how much +implications or how much effect their + + align:start position:0% +implications or how much effect their + + + align:start position:0% +implications or how much effect their +actions have I would argue that we spent + + align:start position:0% +actions have I would argue that we spent + + + align:start position:0% +actions have I would argue that we spent +a lot of time talking about let's say + + align:start position:0% +a lot of time talking about let's say + + + align:start position:0% +a lot of time talking about let's say +bicycling or vegetarianism or consuming + + align:start position:0% +bicycling or vegetarianism or consuming + + + align:start position:0% +bicycling or vegetarianism or consuming +less + + align:start position:0% +less + + + align:start position:0% +less +but then we completely offset that by + + align:start position:0% +but then we completely offset that by + + + align:start position:0% +but then we completely offset that by +taking a long flight to another + + align:start position:0% +taking a long flight to another + + + align:start position:0% +taking a long flight to another +continent + + align:start position:0% +continent + + + align:start position:0% +continent +and finally there's one school thought + + align:start position:0% +and finally there's one school thought + + + align:start position:0% +and finally there's one school thought +that alumin has shown us that individual + + align:start position:0% +that alumin has shown us that individual + + + align:start position:0% +that alumin has shown us that individual +actions aren't that effective we did + + align:start position:0% +actions aren't that effective we did + + + align:start position:0% +actions aren't that effective we did +reduce pronounced gas emissions that + + align:start position:0% +reduce pronounced gas emissions that + + + align:start position:0% +reduce pronounced gas emissions that +much during covet even though he didn't + + align:start position:0% +much during covet even though he didn't + + + align:start position:0% +much during covet even though he didn't +fly + + align:start position:0% +fly + + + align:start position:0% +fly +and that we need larger policy change so + + align:start position:0% +and that we need larger policy change so + + + align:start position:0% +and that we need larger policy change so +these are all arguments why policy + + align:start position:0% +these are all arguments why policy + + + align:start position:0% +these are all arguments why policy +changes are more important than + + align:start position:0% +changes are more important than + + + align:start position:0% +changes are more important than +individual action + + align:start position:0% +individual action + + + align:start position:0% +individual action +another school thought you may have + + align:start position:0% +another school thought you may have + + + align:start position:0% +another school thought you may have +heard my skepticism about some of the + + align:start position:0% +heard my skepticism about some of the + + + align:start position:0% +heard my skepticism about some of the +arguments is that + + align:start position:0% +arguments is that + + + align:start position:0% +arguments is that +addressing Aviation or taking individual + + align:start position:0% +addressing Aviation or taking individual + + + align:start position:0% +addressing Aviation or taking individual +action is necessary and essential we can + + align:start position:0% +action is necessary and essential we can + + + align:start position:0% +action is necessary and essential we can +blame fossil fuel companies for selling + + align:start position:0% +blame fossil fuel companies for selling + + + align:start position:0% +blame fossil fuel companies for selling +products to Consumers but we are + + align:start position:0% +products to Consumers but we are + + + align:start position:0% +products to Consumers but we are +consumers every single day everything we + + align:start position:0% +consumers every single day everything we + + + align:start position:0% +consumers every single day everything we +buy eat travel and essentially use with + + align:start position:0% +buy eat travel and essentially use with + + + align:start position:0% +buy eat travel and essentially use with +fossil fuels I would argue that there's + + align:start position:0% +fossil fuels I would argue that there's + + + align:start position:0% +fossil fuels I would argue that there's +a strong Equity component especially for + + align:start position:0% +a strong Equity component especially for + + + align:start position:0% +a strong Equity component especially for +people watching this in North America or + + align:start position:0% +people watching this in North America or + + + align:start position:0% +people watching this in North America or +Europe where we are relatively Rich + + align:start position:0% +Europe where we are relatively Rich + + + align:start position:0% +Europe where we are relatively Rich +developed and + + align:start position:0% +developed and + + + align:start position:0% +developed and +prosperous rich countries consume much + + align:start position:0% +prosperous rich countries consume much + + + align:start position:0% +prosperous rich countries consume much +more than four ones rich people consume + + align:start position:0% +more than four ones rich people consume + + + align:start position:0% +more than four ones rich people consume +much more than four people even in four + + align:start position:0% +much more than four people even in four + + + align:start position:0% +much more than four people even in four +countries so there's an equity issue + + align:start position:0% +countries so there's an equity issue + + + align:start position:0% +countries so there's an equity issue +between you know we're arguing that we + + align:start position:0% +between you know we're arguing that we + + + align:start position:0% +between you know we're arguing that we +don't have to take action is that a + + align:start position:0% +don't have to take action is that a + + + align:start position:0% +don't have to take action is that a +privilege for us field to be able to + + align:start position:0% +privilege for us field to be able to + + + align:start position:0% +privilege for us field to be able to +argue that + + align:start position:0% +argue that + + + align:start position:0% +argue that +another problem is that Aviation is + + align:start position:0% +another problem is that Aviation is + + + align:start position:0% +another problem is that Aviation is +going to be very hard to decarbonized + + align:start position:0% +going to be very hard to decarbonized + + + align:start position:0% +going to be very hard to decarbonized +we don't currently have a lot of + + align:start position:0% +we don't currently have a lot of + + + align:start position:0% +we don't currently have a lot of +technological options to reduce the + + align:start position:0% +technological options to reduce the + + + align:start position:0% +technological options to reduce the +emissions from Aviation there has been + + align:start position:0% +emissions from Aviation there has been + + + align:start position:0% +emissions from Aviation there has been +some discussion of electric slave + + align:start position:0% +some discussion of electric slave + + + align:start position:0% +some discussion of electric slave +electric planes those will only be able + + align:start position:0% +electric planes those will only be able + + + align:start position:0% +electric planes those will only be able +to go short all distances I'll talk + + align:start position:0% +to go short all distances I'll talk + + + align:start position:0% +to go short all distances I'll talk +about that more in the next lecture + + align:start position:0% +about that more in the next lecture + + + align:start position:0% +about that more in the next lecture +but also and a more important uh social + + align:start position:0% +but also and a more important uh social + + + align:start position:0% +but also and a more important uh social +level I would argue that most people + + align:start position:0% +level I would argue that most people + + + align:start position:0% +level I would argue that most people +want to participate most people want to + + align:start position:0% +want to participate most people want to + + + align:start position:0% +want to participate most people want to +try to do the right thing if they know + + align:start position:0% +try to do the right thing if they know + + + align:start position:0% +try to do the right thing if they know +what that is but another thing is that + + align:start position:0% +what that is but another thing is that + + + align:start position:0% +what that is but another thing is that +as advocates if we're trying to Advocate + + align:start position:0% +as advocates if we're trying to Advocate + + + align:start position:0% +as advocates if we're trying to Advocate +taking action on climate change there + + align:start position:0% +taking action on climate change there + + + align:start position:0% +taking action on climate change there +are research respondings again from + + align:start position:0% +are research respondings again from + + + align:start position:0% +are research respondings again from +shazina Target group and Indiana + + align:start position:0% +shazina Target group and Indiana + + + align:start position:0% +shazina Target group and Indiana +University The Advocates are not taken + + align:start position:0% +University The Advocates are not taken + + + align:start position:0% +University The Advocates are not taken +seriously unless they abide by their + + align:start position:0% +seriously unless they abide by their + + + align:start position:0% +seriously unless they abide by their +advocacy in other words we can say that + + align:start position:0% +advocacy in other words we can say that + + + align:start position:0% +advocacy in other words we can say that +you know we try to reduce greenhouse gas + + align:start position:0% +you know we try to reduce greenhouse gas + + + align:start position:0% +you know we try to reduce greenhouse gas +missions but if we are not demonstrating + + align:start position:0% +missions but if we are not demonstrating + + + align:start position:0% +missions but if we are not demonstrating +that we are willing to do it ourselves + + align:start position:0% +that we are willing to do it ourselves + + + align:start position:0% +that we are willing to do it ourselves +people will actually take our advocacy + + align:start position:0% +people will actually take our advocacy + + + align:start position:0% +people will actually take our advocacy +less seriously to give you an example I + + align:start position:0% +less seriously to give you an example I + + + align:start position:0% +less seriously to give you an example I +think every time Prince Harry applies to + + align:start position:0% +think every time Prince Harry applies to + + + align:start position:0% +think every time Prince Harry applies to +a climate change conference and a + + align:start position:0% +a climate change conference and a + + + align:start position:0% +a climate change conference and a +private jet the first thing newspapers + + align:start position:0% +private jet the first thing newspapers + + + align:start position:0% +private jet the first thing newspapers +and some people will say is oh look he's + + align:start position:0% +and some people will say is oh look he's + + + align:start position:0% +and some people will say is oh look he's +buying a private jet he doesn't even + + align:start position:0% +buying a private jet he doesn't even + + + align:start position:0% +buying a private jet he doesn't even +understand what his actions are that are + + align:start position:0% +understand what his actions are that are + + + align:start position:0% +understand what his actions are that are +resulting to be honest gas emissions why + + align:start position:0% +resulting to be honest gas emissions why + + + align:start position:0% +resulting to be honest gas emissions why +should we listen to him talking about + + align:start position:0% +should we listen to him talking about + + + align:start position:0% +should we listen to him talking about +reducing greenhouse gas emissions or + + align:start position:0% +reducing greenhouse gas emissions or + + + align:start position:0% +reducing greenhouse gas emissions or +saving the environment + + align:start position:0% +saving the environment + + + align:start position:0% +saving the environment +and of course from an ecological or + + align:start position:0% +and of course from an ecological or + + + align:start position:0% +and of course from an ecological or +physical basis our consumption + + align:start position:0% +physical basis our consumption + + + align:start position:0% +physical basis our consumption +expectations can outgrow infinitely + + align:start position:0% +expectations can outgrow infinitely + + + align:start position:0% +expectations can outgrow infinitely +unless you believe that human Ingenuity + + align:start position:0% +unless you believe that human Ingenuity + + + align:start position:0% +unless you believe that human Ingenuity +will engineer our way out of any + + align:start position:0% +will engineer our way out of any + + + align:start position:0% +will engineer our way out of any +environmental problem that we create + + align:start position:0% +environmental problem that we create + + + align:start position:0% +environmental problem that we create +so I would summarize these arguments as + + align:start position:0% +so I would summarize these arguments as + + + align:start position:0% +so I would summarize these arguments as +arguing for individual action not over + + align:start position:0% +arguing for individual action not over + + + align:start position:0% +arguing for individual action not over +policy action but to complement policy + + align:start position:0% +policy action but to complement policy + + + align:start position:0% +policy action but to complement policy +action I think you know we could have + + align:start position:0% +action I think you know we could have + + + align:start position:0% +action I think you know we could have +this debate but it's also quite possible + + align:start position:0% +this debate but it's also quite possible + + + align:start position:0% +this debate but it's also quite possible +that would be individual and policy + + align:start position:0% +that would be individual and policy + + + align:start position:0% +that would be individual and policy +action together + + align:start position:0% +action together + + + align:start position:0% +action together +well this brings me to this shallow + + align:start position:0% +well this brings me to this shallow + + + align:start position:0% +well this brings me to this shallow +paper and the reason why I was signed + + align:start position:0% +paper and the reason why I was signed + + + align:start position:0% +paper and the reason why I was signed +this paper the title is racialized + + align:start position:0% +this paper the title is racialized + + + align:start position:0% +this paper the title is racialized +mobility transitions in Philadelphia + + align:start position:0% +mobility transitions in Philadelphia + + + align:start position:0% +mobility transitions in Philadelphia +connecting Urban sustainability and + + align:start position:0% +connecting Urban sustainability and + + + align:start position:0% +connecting Urban sustainability and +transport Justice it's a 2015 paper it + + align:start position:0% +transport Justice it's a 2015 paper it + + + align:start position:0% +transport Justice it's a 2015 paper it +describes Philadelphia a city I know + + align:start position:0% +describes Philadelphia a city I know + + + align:start position:0% +describes Philadelphia a city I know +well where I used to live but it's also + + align:start position:0% +well where I used to live but it's also + + + align:start position:0% +well where I used to live but it's also +important to notice that some of the + + align:start position:0% +important to notice that some of the + + + align:start position:0% +important to notice that some of the +things that they talk on the paper are + + align:start position:0% +things that they talk on the paper are + + + align:start position:0% +things that they talk on the paper are +shell or talks on this paper you could + + align:start position:0% +shell or talks on this paper you could + + + align:start position:0% +shell or talks on this paper you could +simply substitute transport Justice for + + align:start position:0% +simply substitute transport Justice for + + + align:start position:0% +simply substitute transport Justice for +energy and it would tie back to a lot of + + align:start position:0% +energy and it would tie back to a lot of + + + align:start position:0% +energy and it would tie back to a lot of +the Justice concerns we talked about a + + align:start position:0% +the Justice concerns we talked about a + + + align:start position:0% +the Justice concerns we talked about a +few classes ago and so I want us just to + + align:start position:0% +few classes ago and so I want us just to + + + align:start position:0% +few classes ago and so I want us just to +put these analogous question out there + + align:start position:0% +put these analogous question out there + + + align:start position:0% +put these analogous question out there +for discussion in class how do we think + + align:start position:0% +for discussion in class how do we think + + + align:start position:0% +for discussion in class how do we think +about our transition to lower emitting + + align:start position:0% +about our transition to lower emitting + + + align:start position:0% +about our transition to lower emitting +hyper taking Technologies what would we + + align:start position:0% +hyper taking Technologies what would we + + + align:start position:0% +hyper taking Technologies what would we +have to do to make these Technologies + + align:start position:0% +have to do to make these Technologies + + + align:start position:0% +have to do to make these Technologies +Equitable fair and just Schiller does I + + align:start position:0% +Equitable fair and just Schiller does I + + + align:start position:0% +Equitable fair and just Schiller does I +think is a really good job of arguing + + align:start position:0% +think is a really good job of arguing + + + align:start position:0% +think is a really good job of arguing +that for transportation transitions + + align:start position:0% +that for transportation transitions + + + align:start position:0% +that for transportation transitions +already occurring in Philadelphia like + + align:start position:0% +already occurring in Philadelphia like + + + align:start position:0% +already occurring in Philadelphia like +from Cars to electric vehicles or from + + align:start position:0% +from Cars to electric vehicles or from + + + align:start position:0% +from Cars to electric vehicles or from +Cars to bicycling and walking they are + + align:start position:0% +Cars to bicycling and walking they are + + + align:start position:0% +Cars to bicycling and walking they are +not Equity distributed among the + + align:start position:0% +not Equity distributed among the + + + align:start position:0% +not Equity distributed among the +population you have gentrification + + align:start position:0% +population you have gentrification + + + align:start position:0% +population you have gentrification +happening in the center city you have + + align:start position:0% +happening in the center city you have + + + align:start position:0% +happening in the center city you have +young white people accessing bicycling + + align:start position:0% +young white people accessing bicycling + + + align:start position:0% +young white people accessing bicycling +and walking and Subway modes more and + + align:start position:0% +and walking and Subway modes more and + + + align:start position:0% +and walking and Subway modes more and +the bus system being relatively ignored + + align:start position:0% +the bus system being relatively ignored + + + align:start position:0% +the bus system being relatively ignored +and also people of color or blacks not + + align:start position:0% +and also people of color or blacks not + + + align:start position:0% +and also people of color or blacks not +necessarily being seen as bicyclists or + + align:start position:0% +necessarily being seen as bicyclists or + + + align:start position:0% +necessarily being seen as bicyclists or +perhaps their bicycling is seen as + + align:start position:0% +perhaps their bicycling is seen as + + + align:start position:0% +perhaps their bicycling is seen as +something necessary or because they + + align:start position:0% +something necessary or because they + + + align:start position:0% +something necessary or because they +cannot afford a car this is to say that + + align:start position:0% +cannot afford a car this is to say that + + + align:start position:0% +cannot afford a car this is to say that +how people use cars electric bikes or + + align:start position:0% +how people use cars electric bikes or + + + align:start position:0% +how people use cars electric bikes or +bicycles Subway Light Rail walking about + + align:start position:0% +bicycles Subway Light Rail walking about + + + align:start position:0% +bicycles Subway Light Rail walking about +buses are all quite heterogeneously + + align:start position:0% +buses are all quite heterogeneously + + + align:start position:0% +buses are all quite heterogeneously +distributed people don't use the same + + align:start position:0% +distributed people don't use the same + + + align:start position:0% +distributed people don't use the same +modes and some time in some many cases + + align:start position:0% +modes and some time in some many cases + + + align:start position:0% +modes and some time in some many cases +their use of different modes is not + + align:start position:0% +their use of different modes is not + + + align:start position:0% +their use of different modes is not +necessarily Fair Equitable or just so + + align:start position:0% +necessarily Fair Equitable or just so + + + align:start position:0% +necessarily Fair Equitable or just so +the last thing this brings into question + + align:start position:0% +the last thing this brings into question + + + align:start position:0% +the last thing this brings into question +tying us back to cities is our land use + + align:start position:0% +tying us back to cities is our land use + + + align:start position:0% +tying us back to cities is our land use +and living patterns implicated in this + + align:start position:0% +and living patterns implicated in this + + + align:start position:0% +and living patterns implicated in this +the reason why + + align:start position:0% +the reason why + + + align:start position:0% +the reason why +transportation and Mobility as a + + align:start position:0% +transportation and Mobility as a + + + align:start position:0% +transportation and Mobility as a +superpower is that enables to live in + + align:start position:0% +superpower is that enables to live in + + + align:start position:0% +superpower is that enables to live in +different places and allows us to have + + align:start position:0% +different places and allows us to have + + + align:start position:0% +different places and allows us to have +different patterns of living but as we + + align:start position:0% +different patterns of living but as we + + + align:start position:0% +different patterns of living but as we +know cities like Philadelphia and Boston + + align:start position:0% +know cities like Philadelphia and Boston + + + align:start position:0% +know cities like Philadelphia and Boston +are highly segregated so if we're + + align:start position:0% +are highly segregated so if we're + + + align:start position:0% +are highly segregated so if we're +talking about transportation and trying + + align:start position:0% +talking about transportation and trying + + + align:start position:0% +talking about transportation and trying +to decarbonate Transportation are we + + align:start position:0% +to decarbonate Transportation are we + + + align:start position:0% +to decarbonate Transportation are we +willing to tackle our implications for + + align:start position:0% +willing to tackle our implications for + + + align:start position:0% +willing to tackle our implications for +our land use and living patterns if we + + align:start position:0% +our land use and living patterns if we + + + align:start position:0% +our land use and living patterns if we +want to give people equal access to the + + align:start position:0% +want to give people equal access to the + + + align:start position:0% +want to give people equal access to the +superpower of ability + + align:start position:0% +superpower of ability + + + align:start position:0% +superpower of ability +maybe a chapter again something we'll + + align:start position:0% +maybe a chapter again something we'll + + + align:start position:0% +maybe a chapter again something we'll +discuss in class this article + + align:start position:0% +discuss in class this article + + + align:start position:0% +discuss in class this article +art reply because it simply describes + + align:start position:0% +art reply because it simply describes + + + align:start position:0% +art reply because it simply describes +how Los Angeles has been pursuing clean + + align:start position:0% +how Los Angeles has been pursuing clean + + + align:start position:0% +how Los Angeles has been pursuing clean +air over a 50 or 60 year period and it + + align:start position:0% +air over a 50 or 60 year period and it + + + align:start position:0% +air over a 50 or 60 year period and it +says that the clean the staga to achieve + + align:start position:0% +says that the clean the staga to achieve + + + align:start position:0% +says that the clean the staga to achieve +pain air has spent three different + + align:start position:0% +pain air has spent three different + + + align:start position:0% +pain air has spent three different +epochs + + align:start position:0% +epochs + + + align:start position:0% +epochs +and The Saga of making long-term changes + + align:start position:0% +and The Saga of making long-term changes + + + align:start position:0% +and The Saga of making long-term changes +in the automobile system or land use or + + align:start position:0% +in the automobile system or land use or + + + align:start position:0% +in the automobile system or land use or +Regional governments are all important + + align:start position:0% +Regional governments are all important + + + align:start position:0% +Regional governments are all important +questions first to think about them as + + align:start position:0% +questions first to think about them as + + + align:start position:0% +questions first to think about them as +we think about the city's Appling + + align:start position:0% +we think about the city's Appling + + + align:start position:0% +we think about the city's Appling +climate change we need to ask yourself + + align:start position:0% +climate change we need to ask yourself + + + align:start position:0% +climate change we need to ask yourself +what changes do we have to start making + + align:start position:0% +what changes do we have to start making + + + align:start position:0% +what changes do we have to start making +now + + align:start position:0% +now + + + align:start position:0% +now +but the effects also show you that some + + align:start position:0% +but the effects also show you that some + + + align:start position:0% +but the effects also show you that some +of those efforts haven't been sustained + + align:start position:0% +of those efforts haven't been sustained + + + align:start position:0% +of those efforts haven't been sustained +over time because some weren't + + align:start position:0% +over time because some weren't + + + align:start position:0% +over time because some weren't +particularly popular the question is how + + align:start position:0% +particularly popular the question is how + + + align:start position:0% +particularly popular the question is how +do we sustain the changes in efforts + + align:start position:0% +do we sustain the changes in efforts + + + align:start position:0% +do we sustain the changes in efforts +over a long period of time as I said in + + align:start position:0% +over a long period of time as I said in + + + align:start position:0% +over a long period of time as I said in +the last lecture the California + + align:start position:0% +the last lecture the California + + + align:start position:0% +the last lecture the California +resources board is one of the most + + align:start position:0% +resources board is one of the most + + + align:start position:0% +resources board is one of the most +aggressive agencies in the world helping + + align:start position:0% +aggressive agencies in the world helping + + + align:start position:0% +aggressive agencies in the world helping +to shape vehicle efficiency standards + + align:start position:0% +to shape vehicle efficiency standards + + + align:start position:0% +to shape vehicle efficiency standards +across the world and for Global + + align:start position:0% +across the world and for Global + + + align:start position:0% +across the world and for Global +automakers as far along as Korea or + + align:start position:0% +automakers as far along as Korea or + + + align:start position:0% +automakers as far along as Korea or +Germany but even in this chapter you can + + align:start position:0% +Germany but even in this chapter you can + + + align:start position:0% +Germany but even in this chapter you can +see that the city of Los Angeles the + + align:start position:0% +see that the city of Los Angeles the + + + align:start position:0% +see that the city of Los Angeles the +Regional Air Quality Management District + + align:start position:0% +Regional Air Quality Management District + + + align:start position:0% +Regional Air Quality Management District +the California areas of support have not + + align:start position:0% +the California areas of support have not + + + align:start position:0% +the California areas of support have not +always been able to achieve all the + + align:start position:0% +always been able to achieve all the + + + align:start position:0% +always been able to achieve all the +things they wanted to especially in + + align:start position:0% +things they wanted to especially in + + + align:start position:0% +things they wanted to especially in +terms of land use + + align:start position:0% +terms of land use + + + align:start position:0% +terms of land use +and so on Tuesday we're going to talk + + align:start position:0% +and so on Tuesday we're going to talk + + + align:start position:0% +and so on Tuesday we're going to talk +about how to achieve Justice fairness + + align:start position:0% +about how to achieve Justice fairness + + + align:start position:0% +about how to achieve Justice fairness +and equity in different Urban modes of + + align:start position:0% +and equity in different Urban modes of + + + align:start position:0% +and equity in different Urban modes of +transport and I'll argue that it'll help + + align:start position:0% +transport and I'll argue that it'll help + + + align:start position:0% +transport and I'll argue that it'll help +it would help you to think of other + + align:start position:0% +it would help you to think of other + + + align:start position:0% +it would help you to think of other +various readings from previous classes + + align:start position:0% +various readings from previous classes + + + align:start position:0% +various readings from previous classes +to do this exercise + + align:start position:0% +to do this exercise + + + align:start position:0% +to do this exercise +for all the modes uh in the slide on the + + align:start position:0% +for all the modes uh in the slide on the + + + align:start position:0% +for all the modes uh in the slide on the +sheller article you should be able to + + align:start position:0% +sheller article you should be able to + + + align:start position:0% +sheller article you should be able to +argue for the existing status quo or + + align:start position:0% +argue for the existing status quo or + + + align:start position:0% +argue for the existing status quo or +trajectory of the system we have + + align:start position:0% +trajectory of the system we have + + + align:start position:0% +trajectory of the system we have +or argue for radical changes to achieve + + align:start position:0% +or argue for radical changes to achieve + + + align:start position:0% +or argue for radical changes to achieve +a lower emitting modes of transportation + + align:start position:0% +a lower emitting modes of transportation + + + align:start position:0% +a lower emitting modes of transportation +I'll let you decide which one did the + + align:start position:0% +I'll let you decide which one did the + + + align:start position:0% +I'll let you decide which one did the +status quo and what you consider radical + + align:start position:0% +status quo and what you consider radical + + + align:start position:0% +status quo and what you consider radical +changes + + align:start position:0% +changes + + + align:start position:0% +changes +but the point of this exercise is to + + align:start position:0% +but the point of this exercise is to + + + align:start position:0% +but the point of this exercise is to +kind of do you may have heard this quote + + align:start position:0% +kind of do you may have heard this quote + + + align:start position:0% +kind of do you may have heard this quote +the test of appropriate intelligence is + + align:start position:0% +the test of appropriate intelligence is + + + align:start position:0% +the test of appropriate intelligence is +the ability to hold two opposed ideas in + + align:start position:0% +the ability to hold two opposed ideas in + + + align:start position:0% +the ability to hold two opposed ideas in +the mind at the same time and still + + align:start position:0% +the mind at the same time and still + + + align:start position:0% +the mind at the same time and still +retain the ability to function this is a + + align:start position:0% +retain the ability to function this is a + + + align:start position:0% +retain the ability to function this is a +quote attribute to F Scott Fitzgerald + + align:start position:0% +quote attribute to F Scott Fitzgerald + + + align:start position:0% +quote attribute to F Scott Fitzgerald +though there's many other similar quotes + + align:start position:0% +though there's many other similar quotes + + + align:start position:0% +though there's many other similar quotes +what I liked about this quote I never + + align:start position:0% +what I liked about this quote I never + + + align:start position:0% +what I liked about this quote I never +read the second part which is one should + + align:start position:0% +read the second part which is one should + + + align:start position:0% +read the second part which is one should +for example be able to see that things + + align:start position:0% +for example be able to see that things + + + align:start position:0% +for example be able to see that things +are hopeless and you have to be + + align:start position:0% +are hopeless and you have to be + + + align:start position:0% +are hopeless and you have to be +determined that you have to be + + align:start position:0% +determined that you have to be + + + align:start position:0% +determined that you have to be +determined to make them otherwise and so + + align:start position:0% +determined to make them otherwise and so + + + align:start position:0% +determined to make them otherwise and so +this is the Crux of the problem for land + + align:start position:0% +this is the Crux of the problem for land + + + align:start position:0% +this is the Crux of the problem for land +use and cities we know cities are big + + align:start position:0% +use and cities we know cities are big + + + align:start position:0% +use and cities we know cities are big +and hard to change but we can also see + + align:start position:0% +and hard to change but we can also see + + + align:start position:0% +and hard to change but we can also see +the transportation system is clearly + + align:start position:0% +the transportation system is clearly + + + align:start position:0% +the transportation system is clearly +linked to the entire built environment + + align:start position:0% +linked to the entire built environment + + + align:start position:0% +linked to the entire built environment +and it seems like a hard system change + + align:start position:0% +and it seems like a hard system change + + + align:start position:0% +and it seems like a hard system change +but we should be determined to make the + + align:start position:0% +but we should be determined to make the + + + align:start position:0% +but we should be determined to make the +system change because it dictates so + + align:start position:0% +system change because it dictates so + + + align:start position:0% +system change because it dictates so +many of the aspects of city of life + + align:start position:0% +many of the aspects of city of life + + + align:start position:0% +many of the aspects of city of life +thank you very much + + align:start position:0% +thank you very much + + + align:start position:0% +thank you very much +I look forward to seeing the next + + align:start position:0% +I look forward to seeing the next + + + align:start position:0% +I look forward to seeing the next +lecture \ No newline at end of file diff --git a/ImKFBTqLqdE.txt b/ImKFBTqLqdE.txt new file mode 100644 index 0000000000000000000000000000000000000000..f10f8c9200e1ac79c31bba026b1f1d54f4880273 --- /dev/null +++ b/ImKFBTqLqdE.txt @@ -0,0 +1,3729 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK. + +I guess we might as +well get started. + +We talked a little bit about +Markov processes last week. + +I want to review a little bit of +what we did then, and then + +move on pretty quickly. + +This is a rather strange +chapter, because + +it's full of notation. + +When I first started reviewing +it myself after not having + +looked at it for about a year, +I was horrified by the amount + +of notation. + +And then I realized, what we're +doing in this chapter is + +putting together all the +stuff we've learned + +from Poisson processes. + +There are Poisson processes +all through this + +Markov chains renewals. + +And all three of these, with +all their notation, are all + +sitting here. + +And then we get into new things, +also, so I apologize + +for the notation. + +I'm going to try to keep +it down to the + +minimal amount this time. + +And see if we can sort of get +to the bottom line as easily + +as we can, so that when you do +the exercises and read the + +notes, you can go back in +fill in some of the + +things that are missing. + +OK. + +So accountable state +Markov process. + +The easiest way to define it, +and the way we're defining it + +is as an extension +of accountable + +state Markov chain. + +So you start out with +accountable state Markov + +chain, and then along with each +step, say from state x + +sub n to x sub n plus 1, there +is an exponential holding + +time, u sub n plus 1. + +We said that it was a little +strange associating the + +holding time of the +final state rather + +than the initial state. + +But you almost had to do that, +because of many things that + +would get very confusing +otherwise. + +So we're just doing that. + +We start out in state x0, +which is usually given. + +If it's not given, +it can be random. + +And then we go to state x1 after +a waiting time, u sub 1. + +Go from x1 to x2 with a +waiting time u sub 2. + +The waiting time u sub i is a +function of the state we're + +coming from, in the sense that +it's an exponential random + +variable who's rate is +given by the state + +we're coming from. + +So this diagram here gives +you, really, what the + +dependence of this set of +random variables is. + +You have a sequence of random +variables here. + +A sequence of random +variables here. + +Each random variable here +conditional on the initial + +state that it's coming +from, is independent + +of everything else. + +And that's what this dependence +diagram means. + +It's a generalization of what +we talked about before. + +When we talked about Markov +chains before, we just had a + +string of states. + +And each state x sub n is +dependent only on the prior + +state x sub n minus 1. + +And given the prior state +x sub n minus 1, it's + +statistically independent of +all states before that. + +Here we have this more general +situation of a tree. + +I thought I'd better illustrate +this a little more. + +If you have a directed tree, the +dependencies, each random + +variable conditional as parent +is statistically independent + +of all earlier random +variables. + +In other words, this random +variable here conditional on + +this random variable is +statistically independent of + +this, this, this, and this. + +And so you can move forward in +this way, defining each random + +variable as being statistically +independent of + +everything in the past, +conditional on just one + +previous random variable. + +As an example of this, if you +look at the probability of x0, + +x1, x2, and u2, these five +random variables here. + +Probability of x0, probability +of x1 given x0. + +Probability of x2 given x1. + +Probability of u2 given x1. + +You can write that +out in that way. + +From this, you can rewrite this +in any way you want to. + +You take these two equations, +and you can rewrite them as a + +probability of x1 times the +probability of x0 given x1, + +times the probability of +x2 given x1, times the + +probability u2 given x1. + +In other words, what's happening +here is if you + +condition everything on x1, +this random variable here, + +this stuff is statistically +independent of this. + +Is statistically independent +of all of this. + +Given any one node in this +three, given the value of that + +node, everything on every set of +branches coming out from it + +is statistically independent. + +This is a remarkably +useful property. + +This is the Markov property +in general. + +I mean, Markov chains, +we only use the fact + +that it's on a chain. + +In general you use the fact +that it's on a tree. + +And all of this stuff can be +used in remarkable ways. + +I didn't know this until +probably five years ago. + +And suddenly when I realized it, +I think because somebody + +was pointing it out +in a research + +paper they were writing. + +Suddenly all sorts of things +became much, much easier. + +Because everything like the fact +we pointed out before, + +that the past is independent +of the future, given the + +present, that's one +example of this. + +But this is far more +general than that. + +It says that anything on this +tree, if you can start at any + +point on the tree, and +everything going out from + +there is statistically +independent, given this node + +on the tree. + +So that's a valuable thing. + +And so you get your condition +on any node, breaks a tree + +into independent sub trees. + +You can then go on from there +and break it down further and + +further and further, until you +get out to the leaves. + +So this independence property +is really the general thing + +that we refer to when we +say a set of random + +variables are Markov. + +OK. + +The evolution in time with a +Markov process, this diagram I + +find very helpful to +see what's going + +on in a Markov process. + +You have a set of states. + +Initially, you're in a state +x0, the state at time 0 is + +some given value i. + +This is a sample path here. + +The next state we'll say is +j, the next state is a k. + +When you're in state i, there's +some holding time, + +which has rate new +1, new sub i. + +It's an exponential random +variable which tells you how + +long it takes until +this transition. + +This transition occurs +at time s1, which is + +u1 is equal to s1. + +The next transition is at s2. + +Equals u1 plus u2. + +The next transition is at x3, +which is u1 plus u2 plus u3. + +Now you start to see why we've +numbered these holding times + +the way we have, so we can talk +about the times that each + +of these transitions +take place. + +We usually assume that the +embedded Markov chain for a + +Markov process, remember, the +embedded Markov chain now is + +just the Markov chain +itself without these + +holding times on it. + +We assume it has no self +transitions because if you're + +sitting in a state x of t equals +i, and suddenly there's + +a transition back to i again, +and you look at the process in + +terms of x of t, t greater +than or equal to 0. + +The state that you're in at +each time t, what happens? + +You don't see it. + +It's a totally invisible +transition, because you're + +sitting in state i. + +You suddenly have a transition +back to i that takes 0 time. + +So you stay in state i. + +You can put that transition +in or you can take it out. + +It doesn't make any +difference. + +It won't affect the +process at all. + +OK. + +Aside from that issue of these +self transitions, a sample + +path of both x sub n, each of +these x sub 0 equals i, x sub + +1 equals j. + +x sub 2 equals k. + +A sample path as those plus the +holding times specifies + +what x of t is at each +instant of time. + +And if you know what x of t is +at each unit of time, that + +tells you when the transitions +are occurring. + +When you know when the +transitions are occurring, you + +know what the these u's are. + +And when you see what the +transition is into, you know + +what the state is. + +So the description of a Markov +process in terms of the + +process, what we call a process +x sub t for all t + +greater than or equal to 0, +and the set of random + +variables, the embedded Markov +chain, and the holding times + +are both equivalent +to each other. + +This shouldn't be any surprise +to you by now, because every + +process we've talked to, +we've talked about. + +We've described in +the same way. + +We described the Poisson process +in multiple ways. + +We described Markov chains +in multiple ways. + +We described renewal processes +in multiple ways. + +And this is just another +example of that. + +You use whatever description you +want to after you've shown + +they're all equivalent. + +So there's really nothing +new here. + +Or is there? + +Who can see what there is about +this relationship, which + +is different from what we've +just been talking about? + +It's using one extra property. + +This is not just a consequence +of this, it also uses + +something else. + +And what else does it use? + +What I'm doing is saying x of +t at this instance of time + +here is dependent on given +x of t is some + +previous time here. + +The state here, given the state +here is independent of + +everything in the past. + +So what else am I using there? + +I'm using the memory looseness +of the Poisson process. + +I'm using the memory +looseness of the + +exponential random variable. + +If I'm given the state here, +and I'm conditioning on the + +state here, this is +an exponential + +random variable in here. + +The time the next transition +is exponential + +given this time here. + +And it doesn't matter +when the previous + +transition took place. + +So if I'm given the state at +this time here, the time to + +the next transition is an +exponential random variable, + +the same distribution as u2. + +So what this says is I'm using +the initial description in + +terms of an embedded Markov +chain plus holding times, and + +I'm adding to that the fact +that the holding times are + +exponential, and therefore +they're memory less. + +OK, that clear to everybody? + +It's vitally important +for all of this. + +Because it's hard to do anything +with Markov processes + +without realizing explicitly +that you're using the fact + +that these random variables +are memory less. + +At the end of this chapter, +there's something called semi + +Markov processes. + +The description is that +semi Markov processes + +are exactly the same. + +Semi Markov chains are exactly +the same as markup processes + +except, these holding times +are not exponential. + +They can be anything. + +And as soon as the holding times +can be anything, the + +process gets so complicated that +you hardly want to talk + +about it anymore. + +So the fact that we have these +exponential holding times is + +really important in terms of +getting this condition here, + +which lets you talk directly +about the process, instead of + +the embedded Markov chain. + +You're going to represent a +Markov process by a graph for + +the embedded Markov chain, and +then you give the rates on top + +of the nodes. + +So if you're in state 0, the +holding time until you enter + +the next state is given as +some, the rate of that + +exponential is given as new 0. + +The rate here is given +as new 1, so forth. + +Ultimately, we're usually +interested in this process, x + +of t, t greater than or equal +to 0, which is the Markov + +process itself. + +x of t is equal to xn for t in +sub n, between sub n and + +s sub n plus 1. + +What does that mean? + +Well, it means at this point, +we're taking the Markov + +process as the fundamental +thing, and we're describing it + +in terms of the nth +state transition. + +But we know that the nth state +transition takes place at time + +s sub n, namely it takes place +at the sum of all of these + +exponential holding times +up until that point. + +And that state stays there until +the next exponential + +holding time. + +So this really gives you the +linkage between the Markov + +process in this expression, +and the markup process in + +terms of this graphical +expression here with the + +embedded chain, and the +exponential holding times. + +OK. + +You can visualize a transition +from one state to another in + +tree very convenient ways. + +And these are ways that we've, I +hope we've really learned to + +think about from looking +at Poisson processes. + +You can visualize this +transition by first using the + +next state by these transition +probabilities in the embedded + +Markov chain. + +And then you choose a transition +time, which is + +exponential with +rate new sub i. + +Equivalently, because it's a +Poisson process, you can + +choose the-- + +well, no, because these are +independent given the state. + +You can choose the transition +time first, and then you can + +choose the state, because these +are independent of each + +other conditional on the +state that you're in. + +And finally, equivalently, which +is where the Poisson + +process comes in, a really neat +way to think of Poisson + +processes is to have an +enormously large number of + +Poisson processes running +all the time. + +There's one Poisson process for +every transition in this + +Markov chain. + +So you have accountably infinite +number of Poisson + +processes, which sounds a little +complicated at first. + +But you visualize a Poisson +process for each state pair i + +to j, which has a rate q sub ij, +which is the rate at which + +transitions occur out of +state i times p sub ij. + +This is the rate which, when +you're in state i, you will go + +to state j. + +And this makes use of all this +stuff about splitting and + +combining Poisson processes. + +If you have a Poisson process +which has rate new sub i and + +you split it into a number of +Poisson processes, for each + +next state you might go to, +you're splitting it into + +Poisson processes of rate new +sub i times p sub ij. + +And what's happening there is +there's a little switch. + +The little switch has +probabilities p sub ij, and + +that switch is telling you which +state to go to next. + +All of this is totally +artificial. + +And I hope by this time, you are +comfortable about looking + +at physical things in a totally +artificial way, + +because that's the magic +of mathematics. + +If you didn't have mathematics, +you couldn't look + +at real things in +artificial ways. + +And all the science would +suddenly disappear. + +So what we're doing here is +defining this Markov process + +in this artificial way of all +of these little Poisson + +processes, and we now know +how they all work. + +When the entry to state i, the +next state is the j with an x + +Poisson arrival, according +to q sub ij. + +So all these Poisson processes +are waiting to have an + +arrival come out. + +To have a race, one of +them wins, and you + +go off to that state. + +OK, question. + +What's the conditional +distribution of u1 given that + +x0 i, and x1 equals j? + +And to imagine this, suppose +that there are only two places + +you can go from state 0. + +You can go into state 1 +with some very large + +probability, say 0.999. + +Or you can go into state 2 with +some very, very small + +probability. + +And what that means is this +exponential random variable + +going from state 0 into state +2 is a very, very + +slow, random variable. + +It has a very small rate. + +And the exponential random +variable going into state 1 is + +a very, very large +random variable. + +So you would think that if you +go from state 0 the state x2, + +it means it must take a very +long time to get there. + +Well, that's absolutely wrong. + +The time that it takes to go +from x0 to x2 is this random + +variable, u sub i. + +Where u sub i is the state you +happen to be in at this point + +when you're in-- + +x0 is the state that +we start in. + +x0 is a random variable. + +It has some value i. + +With this value i, there's an +exponential random variable + +that determines how long +it takes you to + +get to the next state. + +This random variable conditional +on x0 equals i is + +independent of which state +you happen to go to. + +And what that means is that the +conditional distribution + +of u1, given x sub 0 is equal +to i, and x sub 1 equals j. + +If you've had your ears at all +open for the last 10 minutes, + +it is exponential with rate i. + +With rate new sub i. + +These holding times and the +next states you go to are + +independent of each other, +conditional on where you + +happen to be. + +It's the same thing we saw back +in Poisson processes. + +It was confusing as +hell back then. + +It is still confusing as hell. + +If you didn't get it sorted out +in your mind then, go back + +and think about it again now, +and try to get your common + +sense, which tells you when +you go to state 2, it must + +take a long time to get there, +because that exponential + +random variable has a very +long holding time. + +And that just isn't true. + +And it wasn't true when we were +dealing with a Poisson + +process, which got +split either. + +These two things are independent +of each other. + +Intuitively, why that is, I +almost hesitate to try to say + +why it is, because it's such +a tricky statement. + +If you happen to go to state 2 +instead of to state 1, what's + +happening is that all of this +time that you're waiting to + +have a state transition, when +you finally have this state + +transition, you then flip a +switch to see which state + +you're going to go to. + +And the fact that it's taken you +a long time to get there + +says nothing whatsoever about +what this switch is doing, + +because that switch is +independent of how long it + +takes you for the switch +to operate. + +And I know. + +It's not entirely intuitive, +and you just have to beat + +yourself on the head until +it becomes intuitive. + +I've beaten myself on +the head until I can + +hardly think straight. + +It still isn't intuitive to me, +but maybe it will become + +intuitive to you. + +I hope so. + +So anyway, this gives the +conditional distribution of u1 + +given that x0 is equal to i, +and x1 is equal to-- no. + +This says that the exponential +rate out of state i is equal + +to the sum of the exponential +rates to each of the states we + +might be going to. + +We have to go to some +other state. + +We have no self transitions as +far as we're concerned here. + +Even if we had self transitions, +this formula + +would still be correct, but +it's easier to think of it + +without self transitions. + +p sub ij, this is the +switch probability. + +It's q sub ij divided +by new sub i. + +This is the probability you're +going to go to j given that + +you were in state i. + +The matrix of all of these cues +specifies the matrix of + +all of these p's, and +it specifies new. + +That's what this formula says. + +If I know what q is, I know what +new is, I know what p is. + +And we've already said that if +you know what p is and you + +know what new is, you know +what q sub ij is. + +So these are completely +equivalent representations of + +the same thing. + +You can work with either +one you want to. + +Sometimes one is useful, +sometimes the other is useful. + +If you look at an mm1q, +mm1q, you remember, + +is exponential arrivals. + +Exponential service time. + +The time of the service is +independent of when it + +happens, or who it happens to. + +These service times are just +individual exponential random + +variables of some rate mu. + +The arrivals are the +inter-arrival intervals are + +exponential random variables +of rate lambda. + +So when you're sitting in state +0, the only place you + +can is to state one. + +You're sitting there, and +if you're in state 0, + +the server is idle. + +You're waiting for the first +arrival to occur. + +The next thing that happens has +to be an arrival because + +it can't be a service. + +So the transition here is +with probability 1. + +All these other transitions are +with probability lambda + +divided by lambda plus mu, +because in all of these other + +states, you can get an arrival +or a departure. + +Each of them are exponential +random variables. + +The switch probability that +we're talking about is in + +lambda over lambda +plus mu to go up. + +Mu over lambda plus mu +to go down for all + +states other than 0. + +If you write this, this +is in terms of the + +embedded Markov chain. + +And if you write this in +terms of the transition + +probabilities, it +looks like this. + +Which is simpler? + +Which is more transparent? + +Well this, really, is +what the mm1q is. + +That's where we started +when we started + +talking about mm1q's. + +This in this situation is +certainly far simpler. + +You're giving these transition +probabilities. + +But don't forget that we still +have this embedded Markov + +chain in the background. + +Both these graphs have +the same information. + +Both these graphs have the same +information for every + +Markov process you want + +to talk about OK. + +Let's look at sample time + +approximations to Markov processes. + +And we already did it +in the last chapter. + +We just didn't talk about +it quite so much. + +We quantized time to increments +of delta. + +We viewed all Poisson processes +in a Markov process. + +Remember, we can view all +of these transitions as + +independent Poisson processes +all running + +away at the same time. + +We can view all of these Poisson +processes as Bernoulli + +processes with probability of +a transition from i to j in + +the increment delta, given as +a delta times qij, to first + +order in delta. + +So we can take this Markov +process, turn it into a rather + +strange kind of Bernoulli +process. + +For the M/M/1 queue, all that's +doing is turning into a + +sample time, M/M/1 process. + +And we can sort of think +the same way about + +general Markov processes. + +We'll see when we can +and when we can't. + +Since shrinking Bernoulli goes +to Poisson, we would + +conjecture the limiting Markov +chain as delta goes to 0 goes + +through a Markov process. + +In a sense that X of t is + +approximately equal to X prime. + +This is X prime as in +the Bernoulli domain + +at delta times n. + +You have to put self-transition +into a sample + +time approximation. + +Because if you have a very small +delta, there aren't big + +enough transition probabilities +going out of the + +chain to fill up the +probability space. + +So in most transition, you're +going to just have a + +self-transition. + +So you need a self-transition, +which is 1 minus delta times + +nu sub i, and these transitions +to other states, + +which are delta times +q sub ij. + +This has the advantage that if +you believe this, you can + +ignore everything we're saying +about Poisson processes + +because you already +know all of it. + +We already talked about +sample time processes. + +You can do this for any +old process almost. + +And when you do this for any old +process, you're turning it + +into a Markov change instead +of a Markov process. + +This is the same argument you +tried to use when you were a + +senior in high school or +freshman in college when you + +said, I don't have to learn +calculus, because all it is is + +just taking increments +to be very small and + +looking at a limit. + +So I will just ignore +all that stuff. + +It didn't work there. + +It doesn't work here. + +But it's a good thing to go +every time you get confused, + +because this you can sort +out for yourself. + +There is one problem here. + +When you start making shrieking +delta more and more, + +if you want to get a sample time +approximation, delta has + +to be smaller than 1 over the +maximum of the nu sub i's. + +If it's not smaller than the +maximum of the nu sub i's, the + +self-transition probability +here is + +unfortunately negative. + +And we don't like negative +probabilities. + +So you can't do that. + +If you have a Markov process, +has a countably infinite + +number of states, each of these +nu sub i's are positive. + +But they can approach +0 as a limit. + +As if they approach 0 as a +limit, you cannot describe a + +sample time Markov chain to go +with the Markov process. + +All you can do is truncate +the chain also and + +then see what happens. + +And that's often a good +way to do it. + +OK, so we can always do this +sample time approximation. + +What is nice about the sample +time approximation is that we + +will find it in general, if you +could use the sample time + +approximation, it always gives +you the exact steady state + +probabilities. + +No matter how crude you are in +this approximation, you always + +wind up with the exact rate +values when you're all done. + +I don't know why. + +We will essentially prove +today that that happens. + +But that's a nice thing. + +But it doesn't work with the nu +sub i's approach 0, because + +then you can't get +a sample time + +approximation to start with. + +OK, let's look at the embedded +chain model in the sample time + +model of M/M/1 queue. + +I hate to keep coming back +to the M/M/1 queue. + +But for Markov processes, +they're all so similar to each + +other that you might as well +get very familiar with one + +particular model of them, +because that one particular + +model tells you most of the +distinctions that you have to + +be careful about. + +Let's see. + +What is this? + +This is the embedded chain +model that we've + +talked about before. + +When you're in state 0, +the only place you can + +go is to state 1. + +When you're in state 1, you +can go down with some + +probability. + +You can go up with +some probability. + +And since these probabilities +have to add up to 1, it's mu + +over lambda plus mu and lambda +over lambda plus mu, and the + +same thing forever after. + +If we're dealing with the sample +time model, what we + +wind up with is we start +out with qij, + +which is lambda here. + +The time it takes to get from +state 0 to make a transition, + +the only place you can make a +transition to is state 1. + +You make those transitions +at rate lambda. + +So the sample time model has +this transition and discrete + +time with probability lambda +delta, this transition with + +probability mu delta +and so forth up. + +You need these self-transitions +in order to + +make things add up correctly. + +The steady state for the +embedded chain is pi sub 0 + +equals 1 minus rho over 2. + +How do I know that? + +You just have to use +algebra for that. + +But it's very easy. + +I'm going to have to get +three of these things. + +OK, any time you have a +birth-death chain, you can + +find the steady state +probabilities. + +The probability of going this +way is equal to the + +probability of going this way. + +If you add in the probability +of the steady state that + +you're concerned with, steady +state transition this way, the + +same as the probability +of a steady state + +transition this way. + +And you remember, the reason for +this is in a birth-death + +chain, the total number of +transitions from here to here + +has to be within 1 of the number +of transitions from + +here to there. + +So that if steady state +means anything-- + +and if these of long-term sample +space probabilities + +with probability 1 +mean anything-- + +this has to be true. + +So when you do that, this +is what you get here. + +This is a strange 1 +minus rho over 2. + +It's strange because of this +strange probability one here, + +and this strange probability mu +over lambda plus mu here. + +And otherwise, everything is +symmetric, so it looks the + +same as this one here. + +For this one, the steady state +for the sample time doesn't + +depend on delta. + +And it's pi sub i prime equals 1 +minus rho times rho to the i + +where rho equals +lambda over mu. + +This is what we did before. + +And what we found is since +transitions this way have to + +equal transitions this way, +these self-transitions don't + +make any difference here. + +And you get the same answer +no matter what delta is. + +And therefore you have pretty +much a conviction, which can't + +totally rely on, that you can go +to the limit as delta goes + +to 0 and find out what is going +on in the actual Markov + +process itself. + +You'll be very surprised with +this result if this were not + +the result for steady state +probabilities in some sense + +for the Markov process. + +However, the embedded chain +probabilities and these + +probabilities down here +are not the same. + +What's the difference +between them? + +For the embedded chain, what +you're talking about is the + +ratio of transitions +that go from one + +state to another state. + +When you're dealing with the +process, what you're talking + +about is the probability that +you will be in one state. + +If when you get in one state +you stay there for a long + +time, because the rate of +transitions out of that state + +is very small, so you're going +to stay there for a long time. + +That enhances the probability +of being in that state. + +You see that right here, +because pi 0 is 1 + +minus rho over 2. + +And pi 0 prime is 1 minus rho. + +It's bigger. + +And it's bigger because you're +going to stay there longer, + +because the rate of getting out +of there is not as big as + +it was before. + +So the steady state +probabilities in the embedded + +chain and the steady state +probabilities and the sample + +time approximation +are different. + +And the steady state +probabilities and the sample + +time approximation are the same, +when you go to the limit + +of infinitely fine +sample time. + +Now what we have to do is go +back and look at renewal + +theory and all those that and +actually convince ourselves + +that this works. + +OK, so here we have renewals +for Markov processes. + +And what have we done so far? + +We've been looking at +the Poisson process. + +We've been looking +at Markov chains. + +And we've been trying to refer +to this new kind of process. + +Now we bring in the last +actor, renewal theory. + +And as usual, Poisson processes +gives you the easy + +way to look at a problem. + +Markov chains gives you a way +to look at the problem, when + +you'd rather write equations +and think about it. + +And we renewal theory gives +you the way to look at the + +problem when you really are a +glutton for punishment, and + +you want to spend a lot of +time thinking about it. + +And you don't want to write any +equations, or you don't + +want to write many equation. + +OK, an irreducible Markov +process is a Markov process + +for which the embedded Markov +chain is irreducible. + +Remember that an irreducible a +Markov chain is one where all + +states are in the same class. + +We saw that irreducible Markov +chains when we had a countably + +infinite number of states, that +they could be transient, + +the state simply wanders +off with high + +probability, never to return. + +If you have an M/M/1 queue, +and the expect the service + +time is bigger than the +expected time between + +arrivals, then gradually +the queue builds up. + +The queue keeps getting longer +and longer as time goes on. + +There isn't any steady state. + +Looked at another way, the +steady state probabilities are + +always 0, if you want to +just calculate them. + +So we're going to see the +irreducible Markov processes + +can have even more bizarre +behavior than these Markov + +chains can. + +And part of that more bizarre +behavior is infinitely many + +transitions in a finite time. + +I mean, how do you talk about +steady state when you have an + +infinite number of transitions +and a finite time? + +I mean, essentially, the +Markov process is + +blowing up on you. + +Transitions get more +and more frequent. + +They go off to infinity. + +What do you do after that? + +I don't know. + +I can write these equations. + +I can solve these equations. + +But they don't mean anything. + +In other words sometimes, +talking about steady state, we + +usually write equations +for steady state. + +But as we saw with countable +state Markov chains, steady + +state doesn't always +exist there. + +There it evidenced itself with +steady state probabilities + +that were equal to 0, which +said that as time went on, + +things just got very diffused +or things wandered off to + +infinity or something +like that. + +Here it's this much worse thing, +where in fact you get + +an infinite number of +transitions very fast. + +And we'll see how that happens +a little later. + +You might have a transition +rate which goes down to 0. + +The process is chugging along +and gets slower, and slower, + +and slower, and pretty soon +nothing happens anymore. + +Well, always something happens +if you wait long enough, but + +as you wait longer and +longer, things happen + +more and more slowly. + +So we'll see all of these +things, and we'll see + +how this comes out. + +OK, let's review briefly +accountable + +state Markov chains-- + +an irreducible, that means +everything can talk to + +everything else; is positive +recurrent if and only if the + +steady state equations, pi sub +j equals the sum of pi + +sub i, p sub ij. + +Remember what this is. + +If you're in steady state, the +probability of being in a + +state j is supposed +to be pi sub j. + +The probability of being in a +state is supposed to be equal + +then to the sum of the +probabilities of being in + +another state and going +to that state. + +That's the way it has to +be if you're going to + +have a steady state. + +So this is necessary. + +The pi sub j's have to be +greater than or equal to 0. + +And the sum of the pi sub +j's is equal to 1. + +It has a solution. + +If this has a solution, it's +unique, and if pi sub i is + +greater than 0 for all i, if +it's positive recurrent. + +We saw that if it wasn't +positive recurrent, other + +things could happen. + +Also the number of visits, n +sub ij of n, remember in a + +Markov chain, what we talked +about when we used renewal + +theory was the number of visits +over a particular + +number transitions +from i to j. + +n sub ij of n is the number +of times we hit j's + +in the first n trials. + +I always do this. + +Please take that n sub ij of n +and write 1 over n times n sub + +ij of n is equal to pi j. + +You all know that. + +I know it too. + +I don't know why it always gets +left off of my slides. + +Now, we guessed for a Markov +process the fraction of time + +in state j should be p sub j +equals pi sub j over a nu sub + +j divided by the sum over i +of pi sub i over nu sub i. + +Perhaps I should say I guessed +that because I + +already know it. + +I want to indicate to you why +if you didn't know anything + +and if you weren't suspicious +by this time, you would make + +that guess, OK? + +We had this embedded +Markov chain. + +Over a very long period +of time, the number of + +transitions into state i is +going to be the number of + +transitions into state i +divided by n is going + +to be pi sub i. + +That's what this equation here +says, or what it would say if + +I had written it correctly. + +Now, each time we get to pi +sub i, we're going to stay + +there for a while. + +The holding time in state +i is proportional to + +1 over nu sub i. + +The rate of the next transition +is nu sub i. + +So the expected holding time is +going to be 1 over nu sub + +i, which says that the fraction +of time that we're + +actually in state i should be +proportional to the number of + +times we go into state j times +the expected holding + +time in state j. + +Now when you write p sub j +equals pi sub j over nu sub j, + +you have a constant there +which is missing. + +Because what we're doing is +we're amortizing this over + +some long period of time. + +And we don't know what the +constant of amortization is. + +But these probability +should add up to 1. + +If life is at all fair to us, +the fraction of time that we + +spent in each state j should be +some number which adds up + +to 1 as we sum over j. + +So this is just a normalization +factor that you + +need to make the p sub +j's sum up to 1. + +Now what this means physically, +and why it appears + +here, is something we have to go +through some more analysis. + +But this is what we +would guess if we + +didn't know any better. + +And in fact, it's pretty +much true. + +It's not always true, but +it's pretty much true. + +So now let's use renewal +theory to actually see + +what's going on. + +And here's where we need a +little more notation even. + +Let n sub i of t be the number +of transitions between 0 and t + +for a Markov process starting +in state i. + +I can't talk about the number of +transitions if I don't say + +what state we start in, because +then I don't really + +have a random variable. + +I could say let's start and +steady state, and that seems + +very, very appealing. + +I've tried to do that many +times, because it would + +simplify all these theorems. + +And it just doesn't +work, believe me. + +So let's take the extra pain +of saying let's start + +in some state i. + +We don't know what it is, but +we'll just assume there is + +some state. + +And the theorem says that the +limit of M sub i of t is equal + +to infinity. + +Here I don't have a 1 over +t in front of it. + +I've written incorrectly. + +And this is a very technical +theorem. + +We proved the same kind of +technical theorem when we were + +talking about Markov chains, +if you remember. + +We were talking about +Markov chains. + +We said that in some sense, an +infinite number of transitions + +into each one of the states +had to occur. + +The same kind of proof +is the proof here. + +It had the same kind of proof +when we were talking about + +renewal theory. + +What is going on is given any +state, given the state the + +transition has to occur within +finite time, because there + +some exponential holding +time there. + +So the expected amount of time +for the next transition is 1 + +over nu sub i. + +And that's finite for every +i in the chain. + +And therefore, as you go from +one state to another, as the + +frog those jumping from one lily +pad to another, and each + +lily pad that it jumps on +there's some expected time + +before it moves, and therefore +assuming that it keeps moving + +forever and doesn't die, which +is what we assume with these + +Markov chains, it will +eventually go through an + +infinite number of steps. + +And the proof of that +is in the text. + +But it's exactly the same proof +as you've seen several + +times before for renewal process +in countable state + +Markov chains. + +Next theorem is to say let M sub +ij of t be the number of + +transitions to j, starting +in state i. + +We can't get rid of the +starting state. + +Somehow we have to +keep it in there. + +We have some confidence that +it's not important, that it + +shouldn't be there. + +And we're going to see it +disappear very shortly. + +But we have to keep it there +for the time being. + +So if the embedded chain is +recurrent, then n sub ij of t + +is a delayed renewal process. + +And we sort of know that. + +Essentially, transitions +keep occurring. + +So renewals in the state +j must keep occurring. + +And therefore, any time you go +to state j, the amount of time + +that it takes until you get +there again, is finite. + +We're not selling it to expect +at time is finite. + +Expect time might be infinite. + +We'll see lots of cases +where it is. + +But you've got to get +there eventually. + +That's the same kind of thing we +saw for renewal theory when + +we had renewals and the things +that could happen eventually + +they did happen. + +I don't know whether any of +you are old enough to have + +heard about Murphy's Law. + +Murphy was an Irish +American to whom + +awful things kept happening. + +And Murphy's Law says that +if something awful + +can happen, it will. + +This says if this can happen, +eventually it will happen. + +It doesn't say it will +happen immediately. + +But it says it will +happen eventually. + +You can think of this as +Murphy's Law, if you want to, + +if you're familiar with that. + +So we want to talk about steady +state for irreducible + +Markov processes. + +Now, let p sub j of i be the +time average fraction of time + +in state j for the delayed +renewal process. + +Remember we talked about p sub +j in terms of these sample + +time Markov change. + +And we talked about them a +little bit in terms of + +imagining how long you would +stay in state j if you were in + +some kind of steady state. + +Here we want to talk +about p sub j of i. + +In terms of strong law of +large numbers kinds of + +results, we want to look at the +sample path average and + +see the convergence with +probability one. + +OK, so p sub j of i is a time +average fraction of time in + +state j for the delayed +renewal process. + +Remember we said that delay +renewal processes were really + +the same as renewal processes. + +You just had this first renewal, +which really didn't + +make any difference. + +And so p sub j of i is going +to be the limit as t + +approaches infinity of the +reward that we pick up forever + +of being in state j. + +You get one unit of reward +whenever you're in state j, 0 + +units when you're +anywhere else. + +So this is the time average +fraction of time + +you're in state j. + +This is divided by t. + +And the assumption is +you start in time i. + +So that affects this +a little bit. + +The picture here says whenever +you go to state j, you're + +going to stay in state j for +some holding time U sub n. + +Then you go back to 0 reward +until the next time you went + +to state j. + +Then you jump up +to reward of 1. + +You stay there for your holding +time until you get + +into some other state, a +and that keeps going + +on forever and ever. + +What does the delayed renewal +reward theorem say? + +It says that the expected reward +over time is going to + +be the expect to reward in one +renewal divided by the + +expected length of +the renewal path. + +It says it's going to be +expected value of U sub n + +divided by the expected time +that you stay in state j. + +So it's 1 over nu sub j times +the expected time + +you're in a state j. + +That's a really neat result +that connects this steady + +state probability. + +Excuse my impolite computer. + +This relates to fraction of time +you're in state i to the + +expected delay in state j. + +It's one of those maddening +things where you say that's + +great, but I don't know how to +find either of those things. + +So we go on. + +We will find them. + +And what we will find +is W sub j. + +If we can find W sub j, we'll +also know p sub j. + +M sub ij of t is delayed +renewal process. + +The strong law for renewal says +the limit as t approaches + +infinity of Mi j of t over t is +1 over this waiting time. + +This is the number of +renewals you have + +as t goes to infinity. + +This is equal to 1 over the +expected length of that + +renewal period. + +Great. + +So we take the limit as +t goes to infinity. + +Of mij of t over mi of t. + +This is the number of +transitions overall up to time + +t starting in state i. + +This is the number of those +transitions which + +go into state j. + +How do I talk about that? + +Well, this quantity up here is +the number of transitions into + +state j over the number of +transition that take place. + +n sub ij of t is the number of +transitions out of total + +transitions. + +mi of t is the total number +of transitions. + +mi of t goes to infinity. + +So this limit here goes to the +limit of n sub ij of n over n. + +Remember, we even proved this +very carefully in class for + +the last application of it. + +This is something we've done +many times already in + +different situations. + +And this particular time we're +doing it, we won't go through + +any fuss about it. + +It's just a limit of n +sub ij of n over n. + +And what is that? + +That's the fraction, long term +fraction of transitions that + +go into state j. + +We know that for accountable +state Markov chain, which is + +recurrent, which is positive +recurrent, this is + +equal to pi sub j. + +So we have that as equal +to pi sub j. + +We then have one over w sub j, +that's what we're trying to + +find is equal to the limit of +mij, of t over t, which is the + +limit of mij of t over mi of +t times mi of t over t. + +We break this into a limit of +two terms, which we've done + +very carefully before. + +And this limit here +is pi sub j. + +This limit here is the limit +of m sub i of t. + +And we have already shown that +the limit of n sub i + +of t is equal to-- + +Somewhere we showed that. + +Yeah. + +1 over w sub j is equal +to pj times new sub j. + +That's what we proved right +down here. p sub j of i is + +equal to 1 over new sub +j times w sub j. + +Except now we're just calling +it p sub j because we've + +already seen it. + +Doesn't depend on i at all. + +So one over w sub j is equal +to p sub j times new sub j. + +This says if we know what +w sub j is, we know + +what p sub j is. + +So it looks like we're not +making any progress. + +So what's going on? + +OK, well let's look at this +a little more carefully. + +This quantity here is a +function only of i. + +1 over w sub j, over p sub +j and new sub j is a + +function only of j. + +Everything else in this +equation is a + +function only of j. + +That says that this quantity +here is independent of i, and + +it's also independent of j. + +And what is it? + +It's the rate at which +transitions occur. + +Overall transitions. + +If you're in steady state, this +says that looking at any + +state j, the total number of +transitions that occur is + +equal to, well, I do it +on the next page. + +So let's goes there. + +It says that p sub j is equal +to 1 over new sub j. + +w sub j is equal to pi j over +new j times this limit here. + +OK. + +So in fact, we now have a way +of finding p sub j for all j + +if we can just find this +one number here. + +This is independent of i, so +this is just one number, which + +we now know is something that +approaches some limit with + +probability one. + +So we only have one unknown +instead of this countably + +infinite number of unknowns. + +Seems like we haven't really +made any progress, because + +before, what we did was to +normalize these p sub js. + +We said they have to add up to +1, and let's normalize them. + +And here we're doing +the same thing. + +We're saying p sub j is equal +to pi sub j over new sub j + +with this normalization +factor in. + +And we're saying here that this +normalization factor has + +to be equal to 1 over the +sum of pi k over new k. + +In other words, if the p sub +j's add to 1, then the only + +value this didn't have is +1 over the sum of pi k + +times new sub k. + +Unfortunately, there are +examples where the sum of pi + +sub k over new sub k is +equal to infinity. + +That's very awkward. + +I'm going to give you an example +of that in just a + +minute, and you'll see +what's going on. + +But if pi sub k over new sub k +is equal to infinity, and the + +theorem is true, it says that +the limit of mi of t over t is + +equal to 1 over infinity, +which says it's zero. + +So what this is telling us is +what we sort of visualize + +before, but we couldn't +quite visualize it. + +It was saying that either these +probabilities add up to + +1, or if they don't add up to 1, +this quantity here doesn't + +make any sense. + +This is not approaching +a limit. + +The only way this can approach, +well, this can + +approach a limit where +the limit is 0. + +Because this theorem holds +whether it approaches the + +limit or not. + +So it is possible for +this limit to the 0. + +In this case, these p +sub js are all 0. + +And we've seen this kind +of thing before. + +We've seen that on a Markov +chain, all the steady state + +probabilities can be equal to +zero, and that's a sign that + +we're either in a transient +condition, or in a null + +recurrent position. + +Namely, the state just wonders +away, and over the long term, + +each state has 0 probability. + +And that looks like the same +kind of thing which is + +happening here. + +This looks trivial. + +There's a fairly long proof +in the notes doing this. + +The only way I can find to do +this is to truncate the chain, + +and then go to the limit as +the number of states gets + +larger and larger. + +And when you do that, this +theorem becomes clear. + +OK, let's look at an example +where the sum of pi k over new + +k is equal to infinity, and +see what's going on. + +Visualize something +like an mm1 queue. + +We have arrivals, and +we have a server. + +But as soon as the queue starts +building up, the server + +starts to get very rattled. + +And as the server gets more and +more rattled, it starts to + +make more and more mistakes. + +And as the queue builds up also, +customers come in and + +look at the queue, and say I'll +come back tomorrow when + +the queue isn't so long. + +So we both have this situation +where as the queue is building + +up, service is getting slower +and the arrival rate is + +getting slower. + +And we're assuming here to make +a nice example that the + +two of them build up in +exactly the same way. + +So that's what's +happening here. + +The service rate when there's +one customer being served is 2 + +to the minus 1. + +The service right rate when +there are two customers in the + +system is 2 to the minus 2. + +The service rate when there +are three customers in the + +system is 2 to the minus 3. + +For each of these states, we +still have these transition + +probabilities for the +embedded chain. + +And the embedded chain, the only +way to get from here to + +here is with probability 1, +because that's the only + +transition possible here. + +We assume that from state 1, +you go to states 0 with + +probability 0.6. + +You go to state two with +probability 0.4. + +With state 1, from state 2, +you go up with probability + +0.4, you go down with +probability 0.6. + +The embedded chain +looks great. + +There's nothing wrong +with that. + +That's a perfectly stable mm1 +queue type of situation. + +It's these damned holding +times which become very + +disturbing. + +Because if you look at pi sub +j, which is supposed to be 1 + +minus rho times rho to the j. + +Rho is 2/3, it's +lambda over mu. + +So it's lambda over lambda +plus mu over rho + +plus lambda plus mu. + +It's 0.4 divided by +0.6, which is 2/3. + +If we look at pi sub j over new +sub j, it's equal to 2 to + +the j times 1 minus rho, +times rho to the j. + +It's 1 minus rho times +4/3 to the j. + +This quantity gets bigger and +bigger as j increases. + +So when you try to +sum pi i over new + +sub j, you get infinity. + +So what's going on? + +None of the states here have +an infinite holding time + +associated with them. + +It's just that the expected +holding time + +is going to be infinite. + +The expected number of +transitions over a long period + +of time, according to this +equation here, expected + +transitions per unit +time is going to 0. + +As time goes on, you keep +floating back to state 0, as + +far as the embedded chain +is concerned. + +But you're eventually going to +a steady state distribution, + +which is laid out over +all the states. + +That steady state distribution +looks very nice. + +That's 1 minus rho times +rho to the j. + +Rho is 2/3, so the probability +of being in state j is going + +down exponentially +as j gets big. + +But the time that you spend +there is going up + +exponentially even faster. + +And therefore, when we sum all +of these things up, the + +overall expected rate is equal +to zero, because the sum of + +the pi j over new j is +equal to infinity. + +OK. + +So this is one of the awful +things that are going to + +happen with Markov processes. + +We still have an +embedded chain. + +The embedded chain +can be stable. + +It can have a steady state, but +we've already found that + +the fraction of time in a state +is not equal to the + +fraction of transitions that go +into that state. pi sub j + +is not in general equal +to p sub j. + +And for this example here with +the rattled server and the + +discouraged customers, the +amount of time that it takes, + +the expected amount of time that +it takes for customers to + +get served is going to zero. + +Even though the queue +was saying stable. + +Does mathematics lie? + +I don't know. + +I don't think so. + +I've looked at this often enough +with great frustration, + +but I believe it +at this point. + +If you don't believe it, take +this chain here and truncate + +it, and solve the problem for +the truncated chain, and then + +look at what happens +as you start adding + +states on one by one. + +What happens as you start adding +states on one by one is + +that the rate at which this +Markov process is serving + +things is going to zero. + +So the dilemma as the number +of states becomes infinite, + +the rate at which things +happen is equal to 0. + +It's not pleasant. + +It's not intuitive. + +But that's what it is. + +And that can happen. + +Again, let's go back to the +typical case of a positive + +recurrent embedded chain, where +this funny sum here is + +less than infinity. + +If the sum here is less than +infinity, then you can + +certainly express p sub j as +pi sub j over new sub j + +divided by the sum over k of +p sub k over new sub k. + +Why can I do that? + +Because that's what +the formula says. + +I don't like to live with +formulas, but sometimes things + +get so dirty, the mathematics +play such awful tricks with + +you that you have to live with +the formulas, and just try to + +explain what they're doing. + +p sub j is equal to this. + +Limit of the service rate, if +this quantity is non infinite, + +then things get churned +out of this queueing + +system at some rate. + +And the p sub js can +be solved for. + +And this is the way +to solve for them. + +OK, so that's pretty neat. + +It says that if you can solve +the embedded chain, then you + +have a nice formula for finding +the steady state + +probabilities. + +And you have a theorem which +says that so long as this + +quantity is less than infinity +with probability one, the + +fraction of time that you +stay in state j is + +equal to this quantity. + +Well, that's not good enough. + +Because for the mm1 queue, we +saw that it was really a pain + +in the neck to solve for the +steady state equations for the + +embedded chain. + +Things looked simpler for +the process itself. + +So let's see if we can get those +equations back also. + +What we would like to do is +to solve for the p sub j's + +directly by using the steady +state embedded equation. + +Embedded equations say that pi +sub j is equal to the sum over + +i, pi sub i times p sub ij. + +The probability of going into +a state is equal to the + +probability of going +out of a state. + +If I use this formula here, pi +sub j over new sub j divided + +by some constant is +what p sub j is. + +So pi sub j is equal to +p sub j times new sub + +j times that constant. + +Here we have the p sub +j times the new sub j + +divided by that constant. + +And that's equal to this sum +here over all i divided by the + +same constant. + +So the constant cancels out. + +Namely, we left out that term +here, but that term is on this + +side, and it's on this side. + +So we have this equation here. + +If you remember, I can't +remember, but you being + +younger can perhaps remember. + +But when we were dealing with +a sample time approximation, + +if you leave the deltas out, +this is exactly the equation + +that you got. + +It's a nice equation. + +It says that the rate at which +transitions occur out of state + +i, the rate at which transitions +occur out of state + +i, out of state j, excuse me, +is p sub j times new sub j. + +Here's the holding time, and +there's also the probability + +of being there. + +Excuse me. + +Let's be more clear +about that. + +I'm not talking about given +you're in state j, the rate at + +which you get out of state j. + +I'm talking about the rate at +which you're in state j and + +you're getting out of state j. + +If you could make sense +out of that. + +That's what this is. + +This quantity here is the +overall rate at which you're + +entering state j. + +So these equations sort of +have the same intuitive + +meaning as these equations +here do. + +And then if you solve this +equation in the same way, + +what's that doing? + +Oh. + +This gets you pi sub j in +terms of the p sub j's. + +So there's a very nice symmetry + +about this set of equations. + +The p sub j's are found for the +pi sub j's in this way. + +The pi sub j's are found from +the p sub j's by this same + +sort of expression. + +The theorem then says if the +embedded chain is positive + +recurrent, and the sum of pi +i over new i is less than + +infinity, then this equation +has a unique solution. + +In other words, there is a +solution to the steady state + +process equations. + +And pi sub j and p sub j are +related by this, and by this. + +If you know the pi sub j's, you +can find the p sub j's. + +If you know the p sub j's, you +can find the pi sub j's. + +There's a fudge factor, and the +sum of pi sub i over new + +sub i is equal to sum of +p sub j times new sub j + +to the minus 1. + +This equation just falls out +of looking at this equation + +and this equation. + +I'm not going to do that here, +but if you just fiddle with + +these equations a little bit, +that's what you find. + +I think graduate students +love to push equations. + +And if you push these equations, +you will rapidly + +find that out. + +So there's no point +to doing it here. + +OK. + +You can do the opposite +thing, also. + +If the steady state process +equations are satisfied, and + +the p sub j's are all greater +than zero, and the sum of the + +p sub j's are equal to 1. + +And if these equations are less +than infinity, this is + +just by symmetry with +what we already did. + +Then pi sub j has to be equal +to p sub j times new sub j + +divided by this sum. + +And this gives the steady +state equations for the + +embedded chain. + +And this shows that the embedded +chain has to be + +positive recurrent, and says +that you have to be + +able to go both ways. + +So we already know that if you +can solve the steady state + +equations for the embedded +chain, they have to be unique, + +the probabilities all +have to be positive. + +All those neat things for +accountable state and Markov + +chains hold true. + +This says that if you can solve +that virtually identical + +set of equations for the +process, and you get a + +solution, and the sum here is +finite, then in fact you can + +go back the other way. + +And going back the other way, +you know from what we know + +about embedded chains that +there's a unique solution. + +So there has to be a unique +solution both ways. + +There has to be positive +recurrence both ways. + +So we have a complete +story at this point. + +I mean, you'll have to spend a +little more time putting it + +together, but it really +is there. + +If new sub j is bounded over +j, then the sum over j of p + +sub j, new sub j is less +than infinity. + +Also, the sample time +chain exists + +because this is bounded. + +It has the same steady +state solution as the + +Markov process solution. + +In other words, go back and look +at the solution for the + +sample time chain. + +Drop out the delta, and what +you will get is this set of + +equations here. + +If you have a birth death +process, it's a birth death + +process for both the Markov +process, and also for the + +embedded chain. + +For the embedded chain, +you know that what you + +have to do to get-- + +for a birth death chain, you +know an easy way to solve the + +steady state equations for the +chain are to say transitions + +this way equal transitions +this way. + +It's the same for the process. + +The amount of time that you +spend going this way is equal + +to the average amount of time +you spent going this way. + +So it says for a birth death +process, p sub i times q sub + +i, i plus one. + +That's an i there, is equal to +p sub i plus 1 times the + +transition probability from +i plus 1 back to i. + +So this symmetry exists +almost everywhere. + +And then if the sum of p sub +j, new sub j is equal to + +infinity, that's the bad case. + +These equations say that +pi sub j is equal to 0 + +everywhere. + +This is sort of the dual +of the situation we + +already looked at. + +In the case we already looked +at of the lazy or rattled + +server and the discouraged +customers, eventually the rate + +at which service occurred +went to 0. + +This situation is a situation +where as far as the embedded + +chain is concerned, it thinks +it's transient. + +As far as the process is +concerned, the process thinks + +it's just fine. + +But then you look at the +process, and you find out that + +what's happening is that an +infinite number of transitions + +are taking place in +a finite time. + +Markov process people call these +irregular processes. + +Here's a picture of it +on the next slide. + +Essentially, the embedded chain +for a hyperactive birth + +death chain. + +As you go to higher states, the +rate at which transitions + +take place gets higher +and higher. + +And for this particular example +here, you can solve + +those process equations. + +The process equations +look just fine. + +This is where you have to be +careful with Markov processes. + +Because you can solve these +Markov process equations, and + +you get things that look fine, +when actually there isn't any + +steady state behavior at all. + +It's even worse than the +rate going to zero. + +When the rate goes to infinity, +you can have an + +infinite number of transitions +taking place in a finite time. + +And then nothing happens. + +Well, I don't know whether +something happens or not. + +I can't visualize what happens +after the thing has exploded. + +Except essentially, at +that point, there's + +nothing nice going on. + +And you have to say that even +though the process equations + +have a steady state solution, +there is no steady state in + +terms of over the long period of +time, this is the fraction + +of time you spend in state j. + +Because that's not the +way it's behaving. + +OK. + +I mean, you can see this +when you look at + +the embedded chain. + +The embedded chain +is transient. + +You're moving up with +probability 0.6. + +You're moving down with +probability 0.4. + +So you keep moving up. + +When you look at the process in +terms of the process with + +the transition rates q sub ij, +the rates going up are always + +less than the rates +going down. + +This is because as you +move up in state, + +you act so much faster. + +The transition rates are higher +in higher states, and + +therefore the transition rates +down are higher, and the + +transition rate down from state +2 to state 1 is bigger + +than the transition right +up from i to i plus 1. + +And it looks stable, as far as +the process is concerned. + +This is one example where you +can't look at the process and + +find out anything from it +without also looking at the + +embedded chain, and looking at +how many transitions you're + +getting per unit time. + +OK, so that's it. + +Thank you. \ No newline at end of file diff --git a/JS4JD2MpFN8.txt b/JS4JD2MpFN8.txt new file mode 100644 index 0000000000000000000000000000000000000000..73bb3790adfc7c7d88e7720e5c3823074cd17974 --- /dev/null +++ b/JS4JD2MpFN8.txt @@ -0,0 +1,11547 @@ +align:start position:0% + +that we have at this point and some the + + align:start position:0% +that we have at this point and some the + + + align:start position:0% +that we have at this point and some the +suggestions that come out of that that + + align:start position:0% +suggestions that come out of that that + + + align:start position:0% +suggestions that come out of that that +we think make sense uh in terms of + + align:start position:0% +we think make sense uh in terms of + + + align:start position:0% +we think make sense uh in terms of +viable Economic Development strategies + + align:start position:0% +viable Economic Development strategies + + + align:start position:0% +viable Economic Development strategies +for this group and for this particular + + align:start position:0% +for this group and for this particular + + + align:start position:0% +for this group and for this particular +neighborhood um towards the end of our + + align:start position:0% +neighborhood um towards the end of our + + + align:start position:0% +neighborhood um towards the end of our +presentation this afternoon we're going + + align:start position:0% +presentation this afternoon we're going + + + align:start position:0% +presentation this afternoon we're going +to suggest a few of the next steps that + + align:start position:0% +to suggest a few of the next steps that + + + align:start position:0% +to suggest a few of the next steps that +we would like to move forward on based + + align:start position:0% +we would like to move forward on based + + + align:start position:0% +we would like to move forward on based +on your reactions to what we talk about + + align:start position:0% +on your reactions to what we talk about + + + align:start position:0% +on your reactions to what we talk about +today and what that part of the + + align:start position:0% +today and what that part of the + + + align:start position:0% +today and what that part of the +presentation would really involve is + + align:start position:0% +presentation would really involve is + + + align:start position:0% +presentation would really involve is +something much more interactive in the + + align:start position:0% +something much more interactive in the + + + align:start position:0% +something much more interactive in the +first 20 minutes or so where we're + + align:start position:0% +first 20 minutes or so where we're + + + align:start position:0% +first 20 minutes or so where we're +actually going to talk about what we've + + align:start position:0% +actually going to talk about what we've + + + align:start position:0% +actually going to talk about what we've +learned after that we really want to + + align:start position:0% +learned after that we really want to + + + align:start position:0% +learned after that we really want to +engage in a substantive dialogue with + + align:start position:0% +engage in a substantive dialogue with + + + align:start position:0% +engage in a substantive dialogue with +each of you and get as candid feedback + + align:start position:0% +each of you and get as candid feedback + + + align:start position:0% +each of you and get as candid feedback +as possible to everything that we just + + align:start position:0% +as possible to everything that we just + + + align:start position:0% +as possible to everything that we just +did so um + + align:start position:0% +did so um + + + align:start position:0% +did so um +as Dr scav said in many ways this + + align:start position:0% +as Dr scav said in many ways this + + + align:start position:0% +as Dr scav said in many ways this +particular class exercise for this year + + align:start position:0% +particular class exercise for this year + + + align:start position:0% +particular class exercise for this year +was trying to build on the Strategic + + align:start position:0% +was trying to build on the Strategic + + + align:start position:0% +was trying to build on the Strategic +plan for neon and when we look back on + + align:start position:0% +plan for neon and when we look back on + + + align:start position:0% +plan for neon and when we look back on +what that document outlined there were + + align:start position:0% +what that document outlined there were + + + align:start position:0% +what that document outlined there were +sort of four very powerful goals that + + align:start position:0% +sort of four very powerful goals that + + + align:start position:0% +sort of four very powerful goals that +were enumerated and that we took as + + align:start position:0% +were enumerated and that we took as + + + align:start position:0% +were enumerated and that we took as +really indicative of our mandate and our + + align:start position:0% +really indicative of our mandate and our + + + align:start position:0% +really indicative of our mandate and our +charge Economic Development referring to + + align:start position:0% +charge Economic Development referring to + + + align:start position:0% +charge Economic Development referring to +the creation of jobs and businesses + + align:start position:0% +the creation of jobs and businesses + + + align:start position:0% +the creation of jobs and businesses +Education and + + align:start position:0% +Education and + + + align:start position:0% +Education and +Training U addressing perception of the + + align:start position:0% +Training U addressing perception of the + + + align:start position:0% +Training U addressing perception of the +neighborhood and creating a sense of + + align:start position:0% +neighborhood and creating a sense of + + + align:start position:0% +neighborhood and creating a sense of +safety within it as being key functions + + align:start position:0% +safety within it as being key functions + + + align:start position:0% +safety within it as being key functions +of creating these other goals and health + + align:start position:0% +of creating these other goals and health + + + align:start position:0% +of creating these other goals and health +U it it for us as as students of + + align:start position:0% +U it it for us as as students of + + + align:start position:0% +U it it for us as as students of +planning um it's really an excellent + + align:start position:0% +planning um it's really an excellent + + + align:start position:0% +planning um it's really an excellent +opportunity to interact with people from + + align:start position:0% +opportunity to interact with people from + + + align:start position:0% +opportunity to interact with people from +uh human and social service agencies and + + align:start position:0% +uh human and social service agencies and + + + align:start position:0% +uh human and social service agencies and +to think of Health as a real Cornerstone + + align:start position:0% +to think of Health as a real Cornerstone + + + align:start position:0% +to think of Health as a real Cornerstone +or as a real lens of describing economic + + align:start position:0% +or as a real lens of describing economic + + + align:start position:0% +or as a real lens of describing economic +and social + + align:start position:0% +and social + + + align:start position:0% +and social +wellbeing and even aside from that + + align:start position:0% +wellbeing and even aside from that + + + align:start position:0% +wellbeing and even aside from that +thinking of the tremendous success that + + align:start position:0% +thinking of the tremendous success that + + + align:start position:0% +thinking of the tremendous success that +Brightwood and other agencies in the uh + + align:start position:0% +Brightwood and other agencies in the uh + + + align:start position:0% +Brightwood and other agencies in the uh +Northend have had in the ways in which + + align:start position:0% +Northend have had in the ways in which + + + align:start position:0% +Northend have had in the ways in which +they've created lasting Partnerships + + align:start position:0% +they've created lasting Partnerships + + + align:start position:0% +they've created lasting Partnerships +with other organizations in the ways in + + align:start position:0% +with other organizations in the ways in + + + align:start position:0% +with other organizations in the ways in +which they've been able to raise funds + + align:start position:0% +which they've been able to raise funds + + + align:start position:0% +which they've been able to raise funds +and really make a difference for the + + align:start position:0% +and really make a difference for the + + + align:start position:0% +and really make a difference for the +residents of the north end so we wanted + + align:start position:0% +residents of the north end so we wanted + + + align:start position:0% +residents of the north end so we wanted +to use the experience of the past the + + align:start position:0% +to use the experience of the past the + + + align:start position:0% +to use the experience of the past the +knowledge base built up jointly by Neon + + align:start position:0% +knowledge base built up jointly by Neon + + + align:start position:0% +knowledge base built up jointly by Neon +and mit's uh Center + + align:start position:0% +and mit's uh Center + + + align:start position:0% +and mit's uh Center +and really begin to think about what + + align:start position:0% +and really begin to think about what + + + align:start position:0% +and really begin to think about what +does a populationbased approach to + + align:start position:0% +does a populationbased approach to + + + align:start position:0% +does a populationbased approach to +Economic Development look like what + + align:start position:0% +Economic Development look like what + + + align:start position:0% +Economic Development look like what +would it look like in this community in + + align:start position:0% +would it look like in this community in + + + align:start position:0% +would it look like in this community in +the North End in the City of Springfield + + align:start position:0% +the North End in the City of Springfield + + + align:start position:0% +the North End in the City of Springfield +in the B Springfield + + align:start position:0% +in the B Springfield + + + align:start position:0% +in the B Springfield +region and so really beginning after + + align:start position:0% +region and so really beginning after + + + align:start position:0% +region and so really beginning after +Labor Day with the start of the semester + + align:start position:0% +Labor Day with the start of the semester + + + align:start position:0% +Labor Day with the start of the semester +we've taken as far a plunge as we + + align:start position:0% +we've taken as far a plunge as we + + + align:start position:0% +we've taken as far a plunge as we +possibly could looking at data looking + + align:start position:0% +possibly could looking at data looking + + + align:start position:0% +possibly could looking at data looking +at qualitative information looking at + + align:start position:0% +at qualitative information looking at + + + align:start position:0% +at qualitative information looking at +mapping looking at the work product + + align:start position:0% +mapping looking at the work product + + + align:start position:0% +mapping looking at the work product +of our colleagues who've gone through + + align:start position:0% +of our colleagues who've gone through + + + align:start position:0% +of our colleagues who've gone through +this class in years + + align:start position:0% +this class in years + + + align:start position:0% +this class in years +previously and try to come up with some + + align:start position:0% +previously and try to come up with some + + + align:start position:0% +previously and try to come up with some +kind of an analysis even if it's just a + + align:start position:0% +kind of an analysis even if it's just a + + + align:start position:0% +kind of an analysis even if it's just a +first rough cut of what the + + align:start position:0% +first rough cut of what the + + + align:start position:0% +first rough cut of what the +opportunities and constraints for + + align:start position:0% +opportunities and constraints for + + + align:start position:0% +opportunities and constraints for +economic development are in this + + align:start position:0% +economic development are in this + + + align:start position:0% +economic development are in this +community and where we are today sort of + + align:start position:0% +community and where we are today sort of + + + align:start position:0% +community and where we are today sort of +signified by the purple oval there is + + align:start position:0% +signified by the purple oval there is + + + align:start position:0% +signified by the purple oval there is +really sort of an term review and + + align:start position:0% +really sort of an term review and + + + align:start position:0% +really sort of an term review and +presentation to you and on the basis of + + align:start position:0% +presentation to you and on the basis of + + + align:start position:0% +presentation to you and on the basis of +that talking about the next steps and + + align:start position:0% +that talking about the next steps and + + + align:start position:0% +that talking about the next steps and +then actually crafting some kind of + + align:start position:0% +then actually crafting some kind of + + + align:start position:0% +then actually crafting some kind of +action plan figuring out what the + + align:start position:0% +action plan figuring out what the + + + align:start position:0% +action plan figuring out what the +sequence of tasks that need to be uh + + align:start position:0% +sequence of tasks that need to be uh + + + align:start position:0% +sequence of tasks that need to be uh +realized over the next year and beyond + + align:start position:0% +realized over the next year and beyond + + + align:start position:0% +realized over the next year and beyond +that for the community to actually begin + + align:start position:0% +that for the community to actually begin + + + align:start position:0% +that for the community to actually begin +to um get onto some kind of path of + + align:start position:0% +to um get onto some kind of path of + + + align:start position:0% +to um get onto some kind of path of +economic + + align:start position:0% +economic + + + align:start position:0% +economic +progress + + align:start position:0% +progress + + + align:start position:0% +progress +um so I I want to sort of hand over now + + align:start position:0% +um so I I want to sort of hand over now + + + align:start position:0% +um so I I want to sort of hand over now +to Alice who's actually also I should + + align:start position:0% +to Alice who's actually also I should + + + align:start position:0% +to Alice who's actually also I should +mentioned the project manager for our + + align:start position:0% +mentioned the project manager for our + + + align:start position:0% +mentioned the project manager for our +team and uh so if you have complaints + + align:start position:0% +team and uh so if you have complaints + + + align:start position:0% +team and uh so if you have complaints +about any of us individually you should + + align:start position:0% +about any of us individually you should + + + align:start position:0% +about any of us individually you should +take it to her and uh she's going to + + align:start position:0% +take it to her and uh she's going to + + + align:start position:0% +take it to her and uh she's going to +talk about some of the findings that uh + + align:start position:0% +talk about some of the findings that uh + + + align:start position:0% +talk about some of the findings that uh +I let me back up a second actually we + + align:start position:0% +I let me back up a second actually we + + + align:start position:0% +I let me back up a second actually we +sort of divided ourselves into three + + align:start position:0% +sort of divided ourselves into three + + + align:start position:0% +sort of divided ourselves into three +groups around three major components of + + align:start position:0% +groups around three major components of + + + align:start position:0% +groups around three major components of +Economic Development employment and + + align:start position:0% +Economic Development employment and + + + align:start position:0% +Economic Development employment and +Workforce training business development + + align:start position:0% +Workforce training business development + + + align:start position:0% +Workforce training business development +around small businesses and + + align:start position:0% +around small businesses and + + + align:start position:0% +around small businesses and +microenterprises and real estate + + align:start position:0% +microenterprises and real estate + + + align:start position:0% +microenterprises and real estate +development trying to turn around the + + align:start position:0% +development trying to turn around the + + + align:start position:0% +development trying to turn around the +physical resources and assets of the + + align:start position:0% +physical resources and assets of the + + + align:start position:0% +physical resources and assets of the +neighborhood and um what each of us is + + align:start position:0% +neighborhood and um what each of us is + + + align:start position:0% +neighborhood and um what each of us is +going to do is just sort of go over what + + align:start position:0% +going to do is just sort of go over what + + + align:start position:0% +going to do is just sort of go over what +we have found under each of these + + align:start position:0% +we have found under each of these + + + align:start position:0% +we have found under each of these +sections and then make some + + align:start position:0% +sections and then make some + + + align:start position:0% +sections and then make some +recommendations of how we can move + + align:start position:0% +recommendations of how we can move + + + align:start position:0% +recommendations of how we can move +forward using that information and + + align:start position:0% +forward using that information and + + + align:start position:0% +forward using that information and +making the most of the opportunity that + + align:start position:0% +making the most of the opportunity that + + + align:start position:0% +making the most of the opportunity that +exist so where Alice is going to start + + align:start position:0% +exist so where Alice is going to start + + + align:start position:0% +exist so where Alice is going to start +off with is talking about the employment + + align:start position:0% +off with is talking about the employment + + + align:start position:0% +off with is talking about the employment +situation in the North End in the + + align:start position:0% +situation in the North End in the + + + align:start position:0% +situation in the North End in the +Greater Springfield region and what some + + align:start position:0% +Greater Springfield region and what some + + + align:start position:0% +Greater Springfield region and what some +of the opportunities there might be and + + align:start position:0% +of the opportunities there might be and + + + align:start position:0% +of the opportunities there might be and +the ways in which it links to broader + + align:start position:0% +the ways in which it links to broader + + + align:start position:0% +the ways in which it links to broader +Economic Development + + align:start position:0% + + + + align:start position:0% + +outcomes okay so um I'm going to talk + + align:start position:0% +outcomes okay so um I'm going to talk + + + align:start position:0% +outcomes okay so um I'm going to talk +about about uh an employment I'm not + + align:start position:0% +about about uh an employment I'm not + + + align:start position:0% +about about uh an employment I'm not +sure that you totally explained but we + + align:start position:0% +sure that you totally explained but we + + + align:start position:0% +sure that you totally explained but we +kind of thought of three strategies to + + align:start position:0% +kind of thought of three strategies to + + + align:start position:0% +kind of thought of three strategies to +look into and first one that I think is + + align:start position:0% +look into and first one that I think is + + + align:start position:0% +look into and first one that I think is +uh very commonly associated with + + align:start position:0% +uh very commonly associated with + + + align:start position:0% +uh very commonly associated with +economic development is an employment + + align:start position:0% +economic development is an employment + + + align:start position:0% +economic development is an employment +strategy and this means both um + + align:start position:0% +strategy and this means both um + + + align:start position:0% +strategy and this means both um +identifying and connecting people to + + align:start position:0% +identifying and connecting people to + + + align:start position:0% +identifying and connecting people to +jobs so job search counseling that kind + + align:start position:0% +jobs so job search counseling that kind + + + align:start position:0% +jobs so job search counseling that kind +of thing as well as + + align:start position:0% +of thing as well as + + + align:start position:0% +of thing as well as +um training and education Workforce + + align:start position:0% +um training and education Workforce + + + align:start position:0% +um training and education Workforce +Development programs so so the goals of + + align:start position:0% +Development programs so so the goals of + + + align:start position:0% +Development programs so so the goals of +an employment strategy are to both + + align:start position:0% +an employment strategy are to both + + + align:start position:0% +an employment strategy are to both +connect people to existing jobs to + + align:start position:0% +connect people to existing jobs to + + + align:start position:0% +connect people to existing jobs to +increase connectivity of the labor + + align:start position:0% +increase connectivity of the labor + + + align:start position:0% +increase connectivity of the labor +market to connect people to the existing + + align:start position:0% +market to connect people to the existing + + + align:start position:0% +market to connect people to the existing +job Force Workforce Development programs + + align:start position:0% +job Force Workforce Development programs + + + align:start position:0% +job Force Workforce Development programs +that are out there and to identify and + + align:start position:0% +that are out there and to identify and + + + align:start position:0% +that are out there and to identify and +fill gaps in those um existing services + + align:start position:0% +fill gaps in those um existing services + + + align:start position:0% +fill gaps in those um existing services +so for example there are um significant + + align:start position:0% +so for example there are um significant + + + align:start position:0% +so for example there are um significant +gaps between maybe some training + + align:start position:0% +gaps between maybe some training + + + align:start position:0% +gaps between maybe some training +programs and the level of skills that + + align:start position:0% +programs and the level of skills that + + + align:start position:0% +programs and the level of skills that +residents currently have gaps in uh + + align:start position:0% +residents currently have gaps in uh + + + align:start position:0% +residents currently have gaps in uh +literacy English basic math + + align:start position:0% +literacy English basic math + + + align:start position:0% +literacy English basic math +skills so addressing some of those + + align:start position:0% +skills so addressing some of those + + + align:start position:0% +skills so addressing some of those +skills both makes people more ready to + + align:start position:0% +skills both makes people more ready to + + + align:start position:0% +skills both makes people more ready to +take advantage of jobs and and take + + align:start position:0% +take advantage of jobs and and take + + + align:start position:0% +take advantage of jobs and and take +advantage of more advanced training + + align:start position:0% + + + + align:start position:0% + +programs uh employment + + align:start position:0% +programs uh employment + + + align:start position:0% +programs uh employment +opportunity we've actually done some + + align:start position:0% +opportunity we've actually done some + + + align:start position:0% +opportunity we've actually done some +analysis of the Census Data out there + + align:start position:0% +analysis of the Census Data out there + + + align:start position:0% +analysis of the Census Data out there +and the job market that's out there and + + align:start position:0% +and the job market that's out there and + + + align:start position:0% +and the job market that's out there and +found that there are actually + + align:start position:0% +found that there are actually + + + align:start position:0% +found that there are actually +significant numbers of jobs in + + align:start position:0% +significant numbers of jobs in + + + align:start position:0% +significant numbers of jobs in +Springfield both that are career + + align:start position:0% +Springfield both that are career + + + align:start position:0% +Springfield both that are career +oriented meaning that they have a job + + align:start position:0% +oriented meaning that they have a job + + + align:start position:0% +oriented meaning that they have a job +ladder that are good paying meaning that + + align:start position:0% +ladder that are good paying meaning that + + + align:start position:0% +ladder that are good paying meaning that +they're at least $12 an hour and that + + align:start position:0% +they're at least $12 an hour and that + + + align:start position:0% +they're at least $12 an hour and that +are accessible to people without college + + align:start position:0% +are accessible to people without college + + + align:start position:0% +are accessible to people without college +degree so just looking over at some of + + align:start position:0% +degree so just looking over at some of + + + align:start position:0% +degree so just looking over at some of +these industries the main industries in + + align:start position:0% +these industries the main industries in + + + align:start position:0% +these industries the main industries in +Springfield being Insurance education + + align:start position:0% +Springfield being Insurance education + + + align:start position:0% +Springfield being Insurance education +and Healthcare you can see that there + + align:start position:0% +and Healthcare you can see that there + + + align:start position:0% +and Healthcare you can see that there +are a thousand jobs in the Springfield + + align:start position:0% +are a thousand jobs in the Springfield + + + align:start position:0% +are a thousand jobs in the Springfield +area right now every year that come open + + align:start position:0% +area right now every year that come open + + + align:start position:0% +area right now every year that come open +that you don't need a college education + + align:start position:0% +that you don't need a college education + + + align:start position:0% +that you don't need a college education +to get that you can step in on that + + align:start position:0% +to get that you can step in on that + + + align:start position:0% +to get that you can step in on that +Bottom Rung and move up making more + + align:start position:0% +Bottom Rung and move up making more + + + align:start position:0% +Bottom Rung and move up making more +money every year and increasing your + + align:start position:0% +money every year and increasing your + + + align:start position:0% +money every year and increasing your +benefits and + + align:start position:0% +benefits and + + + align:start position:0% +benefits and +um employeers are actually having a + + align:start position:0% +um employeers are actually having a + + + align:start position:0% +um employeers are actually having a +tough time filling these jobs which to + + align:start position:0% +tough time filling these jobs which to + + + align:start position:0% +tough time filling these jobs which to +me says that this is + + align:start position:0% +me says that this is + + + align:start position:0% +me says that this is +a potentially really impactful way to go + + align:start position:0% +a potentially really impactful way to go + + + align:start position:0% +a potentially really impactful way to go +um another advantage of the + + align:start position:0% +um another advantage of the + + + align:start position:0% +um another advantage of the +employment take is that it can directly + + align:start position:0% +employment take is that it can directly + + + align:start position:0% +employment take is that it can directly +and immediately impact the broadest + + align:start position:0% +and immediately impact the broadest + + + align:start position:0% +and immediately impact the broadest +number of people which goes back to the + + align:start position:0% +number of people which goes back to the + + + align:start position:0% +number of people which goes back to the +population based strategy that sh Ben + + align:start position:0% +population based strategy that sh Ben + + + align:start position:0% +population based strategy that sh Ben +mentioned earlier + + align:start position:0% + + + + align:start position:0% + +um talking about challenges and + + align:start position:0% +um talking about challenges and + + + align:start position:0% +um talking about challenges and +resources there are an abundance of + + align:start position:0% +resources there are an abundance of + + + align:start position:0% +resources there are an abundance of +resources in the employment in um I want + + align:start position:0% +resources in the employment in um I want + + + align:start position:0% +resources in the employment in um I want +to say industry but there there are a + + align:start position:0% +to say industry but there there are a + + + align:start position:0% +to say industry but there there are a +lot of Workforce Development programs + + align:start position:0% +lot of Workforce Development programs + + + align:start position:0% +lot of Workforce Development programs +out there right now a lot of them are + + align:start position:0% +out there right now a lot of them are + + + align:start position:0% +out there right now a lot of them are +very successful but they're they're + + align:start position:0% +very successful but they're they're + + + align:start position:0% +very successful but they're they're +they're almost too small and maybe + + align:start position:0% +they're almost too small and maybe + + + align:start position:0% +they're almost too small and maybe +people don't always know how to get into + + align:start position:0% +people don't always know how to get into + + + align:start position:0% +people don't always know how to get into +them they don't always know where they + + align:start position:0% +them they don't always know where they + + + align:start position:0% +them they don't always know where they +are and this is where neon can really + + align:start position:0% +are and this is where neon can really + + + align:start position:0% +are and this is where neon can really +come in because it's already connected + + align:start position:0% +come in because it's already connected + + + align:start position:0% +come in because it's already connected +to so many people that if it could also + + align:start position:0% +to so many people that if it could also + + + align:start position:0% +to so many people that if it could also +connect on the other end to employment + + align:start position:0% +connect on the other end to employment + + + align:start position:0% +connect on the other end to employment +training programs there could be a lot + + align:start position:0% +training programs there could be a lot + + + align:start position:0% +training programs there could be a lot +of blow through to connect to productive + + align:start position:0% +of blow through to connect to productive + + + align:start position:0% +of blow through to connect to productive +and already existing + + align:start position:0% +and already existing + + + align:start position:0% +and already existing +infrastructure um there also this is a + + align:start position:0% +infrastructure um there also this is a + + + align:start position:0% +infrastructure um there also this is a +lot of potential to use the campus + + align:start position:0% +lot of potential to use the campus + + + align:start position:0% +lot of potential to use the campus +facilities there already classrooms + + align:start position:0% +facilities there already classrooms + + + align:start position:0% +facilities there already classrooms +there's computer + + align:start position:0% +there's computer + + + align:start position:0% +there's computer +facilities and there are some + + align:start position:0% +facilities and there are some + + + align:start position:0% +facilities and there are some +investing funding streams now challenges + + align:start position:0% +investing funding streams now challenges + + + align:start position:0% +investing funding streams now challenges +one is of course that there's limited + + align:start position:0% +one is of course that there's limited + + + align:start position:0% +one is of course that there's limited +Works participation now so if people + + align:start position:0% +Works participation now so if people + + + align:start position:0% +Works participation now so if people +aren't working it may seem like it's + + align:start position:0% +aren't working it may seem like it's + + + align:start position:0% +aren't working it may seem like it's +difficult to get them to work um also + + align:start position:0% +difficult to get them to work um also + + + align:start position:0% +difficult to get them to work um also +when you talk about employment you don't + + align:start position:0% +when you talk about employment you don't + + + align:start position:0% +when you talk about employment you don't +you don't see a building going up you're + + align:start position:0% +you don't see a building going up you're + + + align:start position:0% +you don't see a building going up you're +not seeing something physical so it can + + align:start position:0% +not seeing something physical so it can + + + align:start position:0% +not seeing something physical so it can +be difficult to Rally around that and + + align:start position:0% +be difficult to Rally around that and + + + align:start position:0% +be difficult to Rally around that and +it's also kind of maybe a limited payoff + + align:start position:0% +it's also kind of maybe a limited payoff + + + align:start position:0% +it's also kind of maybe a limited payoff +maybe people don't think that they're + + align:start position:0% +maybe people don't think that they're + + + align:start position:0% +maybe people don't think that they're +going to get a job in the end maybe + + align:start position:0% +going to get a job in the end maybe + + + align:start position:0% +going to get a job in the end maybe +people think that it's not going to go + + align:start position:0% +people think that it's not going to go + + + align:start position:0% +people think that it's not going to go +with them anymore so that that's + + align:start position:0% +with them anymore so that that's + + + align:start position:0% +with them anymore so that that's +definitely a challenge and there is + + align:start position:0% +definitely a challenge and there is + + + align:start position:0% +definitely a challenge and there is +talking to people a lot of + + align:start position:0% +talking to people a lot of + + + align:start position:0% +talking to people a lot of +pessimism about community members abil + + align:start position:0% +pessimism about community members abil + + + align:start position:0% +pessimism about community members abil +motivations maybe and um but talking to + + align:start position:0% +motivations maybe and um but talking to + + + align:start position:0% +motivations maybe and um but talking to +some other people there's there's also a + + align:start position:0% +some other people there's there's also a + + + align:start position:0% +some other people there's there's also a +lot of optimism that that these programs + + align:start position:0% +lot of optimism that that these programs + + + align:start position:0% +lot of optimism that that these programs +do work that they can work and that + + align:start position:0% +do work that they can work and that + + + align:start position:0% +do work that they can work and that +really there's just not enough of them + + align:start position:0% +really there's just not enough of them + + + align:start position:0% +really there's just not enough of them +to go + + align:start position:0% + + + + align:start position:0% + +around all right um I'm going talk a + + align:start position:0% +around all right um I'm going talk a + + + align:start position:0% +around all right um I'm going talk a +little bit about business development um + + align:start position:0% +little bit about business development um + + + align:start position:0% +little bit about business development um +what we've researched what we found out + + align:start position:0% +what we've researched what we found out + + + align:start position:0% +what we've researched what we found out +thus far um and talk to you about goals + + align:start position:0% +thus far um and talk to you about goals + + + align:start position:0% +thus far um and talk to you about goals +opportunities resources challenges same + + align:start position:0% +opportunities resources challenges same + + + align:start position:0% +opportunities resources challenges same +types of things but in this Dimension so + + align:start position:0% +types of things but in this Dimension so + + + align:start position:0% +types of things but in this Dimension so +first I want to talk about the goals + + align:start position:0% +first I want to talk about the goals + + + align:start position:0% +first I want to talk about the goals +when I say business development as sh + + align:start position:0% +when I say business development as sh + + + align:start position:0% +when I say business development as sh +said earlier um we are in this case + + align:start position:0% +said earlier um we are in this case + + + align:start position:0% +said earlier um we are in this case +speaking specifically about small + + align:start position:0% +speaking specifically about small + + + align:start position:0% +speaking specifically about small +business micro Enterprise uh growing + + align:start position:0% +business micro Enterprise uh growing + + + align:start position:0% +business micro Enterprise uh growing +increasing uh quality quantity and + + align:start position:0% +increasing uh quality quantity and + + + align:start position:0% +increasing uh quality quantity and +strengthening providing support for um + + align:start position:0% +strengthening providing support for um + + + align:start position:0% +strengthening providing support for um +four goals we called out uh the first is + + align:start position:0% +four goals we called out uh the first is + + + align:start position:0% +four goals we called out uh the first is +to promote local entrepreneurial + + align:start position:0% +to promote local entrepreneurial + + + align:start position:0% +to promote local entrepreneurial +Dynamics and that is the strengthening + + align:start position:0% +Dynamics and that is the strengthening + + + align:start position:0% +Dynamics and that is the strengthening +um and supporting increasing local + + align:start position:0% +um and supporting increasing local + + + align:start position:0% +um and supporting increasing local +ownership local ownership of businesses + + align:start position:0% +ownership local ownership of businesses + + + align:start position:0% +ownership local ownership of businesses +and minimizing a supply and demand gap + + align:start position:0% +and minimizing a supply and demand gap + + + align:start position:0% +and minimizing a supply and demand gap +which I'll talk a little bit more about + + align:start position:0% +which I'll talk a little bit more about + + + align:start position:0% +which I'll talk a little bit more about +in a second and then of course creating + + align:start position:0% +in a second and then of course creating + + + align:start position:0% +in a second and then of course creating +jobs for local residents again the local + + align:start position:0% +jobs for local residents again the local + + + align:start position:0% +jobs for local residents again the local +and + + align:start position:0% +and + + + align:start position:0% +and +all three of these together helping to + + align:start position:0% +all three of these together helping to + + + align:start position:0% +all three of these together helping to +raise the resident income + + align:start position:0% +raise the resident income + + + align:start position:0% +raise the resident income +level want to talk a little bit about + + align:start position:0% +level want to talk a little bit about + + + align:start position:0% +level want to talk a little bit about +the um type of information uh and that + + align:start position:0% +the um type of information uh and that + + + align:start position:0% +the um type of information uh and that +was gathered and looked at and the + + align:start position:0% +was gathered and looked at and the + + + align:start position:0% +was gathered and looked at and the +opportunities that came out of that + + align:start position:0% +opportunities that came out of that + + + align:start position:0% +opportunities that came out of that +information um you see numbers and + + align:start position:0% +information um you see numbers and + + + align:start position:0% +information um you see numbers and +tables in front of my team so of course + + align:start position:0% +tables in front of my team so of course + + + align:start position:0% +tables in front of my team so of course +that's an obligation of ours to have + + align:start position:0% +that's an obligation of ours to have + + + align:start position:0% +that's an obligation of ours to have +those in our presentation but what I + + align:start position:0% +those in our presentation but what I + + + align:start position:0% +those in our presentation but what I +want you to see from this is that + + align:start position:0% +want you to see from this is that + + + align:start position:0% +want you to see from this is that +essentially one of the things that the + + align:start position:0% +essentially one of the things that the + + + align:start position:0% +essentially one of the things that the +team did was to look at different uh + + align:start position:0% +team did was to look at different uh + + + align:start position:0% +team did was to look at different uh +retail categories or sectors and through + + align:start position:0% +retail categories or sectors and through + + + align:start position:0% +retail categories or sectors and through +a series of calculations flowcharts + + align:start position:0% +a series of calculations flowcharts + + + align:start position:0% +a series of calculations flowcharts +Excel spreadsheets determine what in the + + align:start position:0% +Excel spreadsheets determine what in the + + + align:start position:0% +Excel spreadsheets determine what in the +North End what types what quantity of + + align:start position:0% +North End what types what quantity of + + + align:start position:0% +North End what types what quantity of +retail in that category could be + + align:start position:0% +retail in that category could be + + + align:start position:0% +retail in that category could be +supported and then what was actually on + + align:start position:0% +supported and then what was actually on + + + align:start position:0% +supported and then what was actually on +the ground now so what you see in this + + align:start position:0% +the ground now so what you see in this + + + align:start position:0% +the ground now so what you see in this +table is that I will call out two + + align:start position:0% +table is that I will call out two + + + align:start position:0% +table is that I will call out two +categories I want you to look at the + + align:start position:0% +categories I want you to look at the + + + align:start position:0% +categories I want you to look at the +restaurants and the apparel and services + + align:start position:0% +restaurants and the apparel and services + + + align:start position:0% +restaurants and the apparel and services +and what you'll see is that according to + + align:start position:0% +and what you'll see is that according to + + + align:start position:0% +and what you'll see is that according to +our calculations um the square footage + + align:start position:0% +our calculations um the square footage + + + align:start position:0% +our calculations um the square footage +of is considerably higher than what is + + align:start position:0% +of is considerably higher than what is + + + align:start position:0% +of is considerably higher than what is +actually on the ground now meaning that + + align:start position:0% +actually on the ground now meaning that + + + align:start position:0% +actually on the ground now meaning that +the internal demand the money flowing + + align:start position:0% +the internal demand the money flowing + + + align:start position:0% +the internal demand the money flowing +around in the North End could + + align:start position:0% +around in the North End could + + + align:start position:0% +around in the North End could +support more than what is actually there + + align:start position:0% +support more than what is actually there + + + align:start position:0% +support more than what is actually there +okay and the same is true for parall + + align:start position:0% +okay and the same is true for parall + + + align:start position:0% +okay and the same is true for parall +inserm that there we didn't find any + + align:start position:0% +inserm that there we didn't find any + + + align:start position:0% +inserm that there we didn't find any +evidence of square footage of that + + align:start position:0% +evidence of square footage of that + + + align:start position:0% +evidence of square footage of that +informal business sector in the North + + align:start position:0% +informal business sector in the North + + + align:start position:0% +informal business sector in the North +End right now so the key opportunities I + + align:start position:0% +End right now so the key opportunities I + + + align:start position:0% +End right now so the key opportunities I +want you to take away from this are that + + align:start position:0% +want you to take away from this are that + + + align:start position:0% +want you to take away from this are that +in these two sectors um there are + + align:start position:0% +in these two sectors um there are + + + align:start position:0% +in these two sectors um there are +relatively low barriers to starting + + align:start position:0% +relatively low barriers to starting + + + align:start position:0% +relatively low barriers to starting +small businesses in these sectors that's + + align:start position:0% +small businesses in these sectors that's + + + align:start position:0% +small businesses in these sectors that's +a positive that's a great opportunity um + + align:start position:0% +a positive that's a great opportunity um + + + align:start position:0% +a positive that's a great opportunity um +and I call out restaurants because + + align:start position:0% +and I call out restaurants because + + + align:start position:0% +and I call out restaurants because +that's something that we've sort of + + align:start position:0% +that's something that we've sort of + + + align:start position:0% +that's something that we've sort of +heard in our discussions and our + + align:start position:0% +heard in our discussions and our + + + align:start position:0% +heard in our discussions and our +interviews with a number of people and + + align:start position:0% +interviews with a number of people and + + + align:start position:0% +interviews with a number of people and +because there already is some support + + align:start position:0% +because there already is some support + + + align:start position:0% +because there already is some support +for this increasing it might be more + + align:start position:0% +for this increasing it might be more + + + align:start position:0% +for this increasing it might be more +viable than trying to start up + + align:start position:0% +viable than trying to start up + + + align:start position:0% +viable than trying to start up +something finally let's take a look at + + align:start position:0% +something finally let's take a look at + + + align:start position:0% +something finally let's take a look at +uh challenges and resources that we + + align:start position:0% +uh challenges and resources that we + + + align:start position:0% +uh challenges and resources that we +found in our analysis first I'm going to + + align:start position:0% +found in our analysis first I'm going to + + + align:start position:0% +found in our analysis first I'm going to +go through the challenges um there is + + align:start position:0% +go through the challenges um there is + + + align:start position:0% +go through the challenges um there is +this has been mentioned before there's a + + align:start position:0% +this has been mentioned before there's a + + + align:start position:0% +this has been mentioned before there's a +perception a negative perception of the + + align:start position:0% +perception a negative perception of the + + + align:start position:0% +perception a negative perception of the +neighborhood which means it would be a + + align:start position:0% +neighborhood which means it would be a + + + align:start position:0% +neighborhood which means it would be a +little more difficult perhaps initially + + align:start position:0% +little more difficult perhaps initially + + + align:start position:0% +little more difficult perhaps initially +to draw uh both people to buy the + + align:start position:0% +to draw uh both people to buy the + + + align:start position:0% +to draw uh both people to buy the +products well people who are interested + + align:start position:0% +products well people who are interested + + + align:start position:0% +products well people who are interested +in selling the products from the North + + align:start position:0% +in selling the products from the North + + + align:start position:0% +in selling the products from the North +End there's a possibility of crowding + + align:start position:0% +End there's a possibility of crowding + + + align:start position:0% +End there's a possibility of crowding +out once you call the attention of + + align:start position:0% +out once you call the attention of + + + align:start position:0% +out once you call the attention of +Greater Springfield area North End is + + align:start position:0% +Greater Springfield area North End is + + + align:start position:0% +Greater Springfield area North End is +here and it's about developing small + + align:start position:0% +here and it's about developing small + + + align:start position:0% +here and it's about developing small +businesses and small business owners you + + align:start position:0% +businesses and small business owners you + + + align:start position:0% +businesses and small business owners you +have the the uh challenge of making sure + + align:start position:0% +have the the uh challenge of making sure + + + align:start position:0% +have the the uh challenge of making sure +that those incoming persons that want to + + align:start position:0% +that those incoming persons that want to + + + align:start position:0% +that those incoming persons that want to +start businesses are not crowding out or + + align:start position:0% +start businesses are not crowding out or + + + align:start position:0% +start businesses are not crowding out or +closing down the businesses that are + + align:start position:0% +closing down the businesses that are + + + align:start position:0% +closing down the businesses that are +already here and that are owned by local + + align:start position:0% +already here and that are owned by local + + + align:start position:0% +already here and that are owned by local +North End + + align:start position:0% +North End + + + align:start position:0% +North End +residents there's also insufficient + + align:start position:0% +residents there's also insufficient + + + align:start position:0% +residents there's also insufficient +education and information or disconnect + + align:start position:0% +education and information or disconnect + + + align:start position:0% +education and information or disconnect +I'm going to talk about some of the + + align:start position:0% +I'm going to talk about some of the + + + align:start position:0% +I'm going to talk about some of the +programs that are available right now in + + align:start position:0% +programs that are available right now in + + + align:start position:0% +programs that are available right now in +a second but just know that there are + + align:start position:0% +a second but just know that there are + + + align:start position:0% +a second but just know that there are +some and that the information is not + + align:start position:0% +some and that the information is not + + + align:start position:0% +some and that the information is not +really meeting the people that it needs + + align:start position:0% +really meeting the people that it needs + + + align:start position:0% +really meeting the people that it needs +to get to um this could be of Comm + + align:start position:0% +to get to um this could be of Comm + + + align:start position:0% +to get to um this could be of Comm +communication could be language barriers + + align:start position:0% +communication could be language barriers + + + align:start position:0% +communication could be language barriers +or a number of factors that's something + + align:start position:0% +or a number of factors that's something + + + align:start position:0% +or a number of factors that's something +that is a challenge that have you + + align:start position:0% +that is a challenge that have you + + + align:start position:0% +that is a challenge that have you +there's also need for models and + + align:start position:0% +there's also need for models and + + + align:start position:0% +there's also need for models and +incentives meaning there are very few + + align:start position:0% +incentives meaning there are very few + + + align:start position:0% +incentives meaning there are very few +strong + + align:start position:0% +strong + + + align:start position:0% +strong +and uh publicized role models of small + + align:start position:0% +and uh publicized role models of small + + + align:start position:0% +and uh publicized role models of small +successful thriving businesses owned by + + align:start position:0% +successful thriving businesses owned by + + + align:start position:0% +successful thriving businesses owned by +local residents and the incentives for + + align:start position:0% +local residents and the incentives for + + + align:start position:0% +local residents and the incentives for +starting that type of Enterprise is not + + align:start position:0% +starting that type of Enterprise is not + + + align:start position:0% +starting that type of Enterprise is not +readily available readily seen so that's + + align:start position:0% +readily available readily seen so that's + + + align:start position:0% +readily available readily seen so that's +something that we would have to work on + + align:start position:0% +something that we would have to work on + + + align:start position:0% +something that we would have to work on +in order to make this viable strategy + + align:start position:0% +in order to make this viable strategy + + + align:start position:0% +in order to make this viable strategy +and finally it's a high Capital + + align:start position:0% +and finally it's a high Capital + + + align:start position:0% +and finally it's a high Capital +high-risk type of venture uh it takes a + + align:start position:0% +high-risk type of venture uh it takes a + + + align:start position:0% +high-risk type of venture uh it takes a +lot of money to start up a business some + + align:start position:0% +lot of money to start up a business some + + + align:start position:0% +lot of money to start up a business some +of you I know know um and then the risk + + align:start position:0% +of you I know know um and then the risk + + + align:start position:0% +of you I know know um and then the risk +is that you may or may not succeed and + + align:start position:0% +is that you may or may not succeed and + + + align:start position:0% +is that you may or may not succeed and +you've already put a lot of money + + align:start position:0% +you've already put a lot of money + + + align:start position:0% +you've already put a lot of money +a210 please the a210 okay I'll just to + + align:start position:0% +a210 please the a210 okay I'll just to + + + align:start position:0% +a210 please the a210 okay I'll just to +talk quickly about the resources the + + align:start position:0% +talk quickly about the resources the + + + align:start position:0% +talk quickly about the resources the +positives um there are a lot of programs + + align:start position:0% +positives um there are a lot of programs + + + align:start position:0% +positives um there are a lot of programs +and information as I mentioned before + + align:start position:0% +and information as I mentioned before + + + align:start position:0% +and information as I mentioned before +great Springfield Chamber of Commerce + + align:start position:0% +great Springfield Chamber of Commerce + + + align:start position:0% +great Springfield Chamber of Commerce +there loan programs uh there's + + align:start position:0% +there loan programs uh there's + + + align:start position:0% +there loan programs uh there's +infrastructure support programs um and + + align:start position:0% +infrastructure support programs um and + + + align:start position:0% +infrastructure support programs um and +then there's also money uh an Enterprise + + align:start position:0% +then there's also money uh an Enterprise + + + align:start position:0% +then there's also money uh an Enterprise +fund so there are some things available + + align:start position:0% +fund so there are some things available + + + align:start position:0% +fund so there are some things available +I think the next thing um we're going to + + align:start position:0% +I think the next thing um we're going to + + + align:start position:0% +I think the next thing um we're going to +go through are real estate + + align:start position:0% + + + + align:start position:0% + +options see the area of analysis that we + + align:start position:0% +options see the area of analysis that we + + + align:start position:0% +options see the area of analysis that we +looked at is real estate and so by real + + align:start position:0% +looked at is real estate and so by real + + + align:start position:0% +looked at is real estate and so by real +estate we mean the fiscal assets of the + + align:start position:0% +estate we mean the fiscal assets of the + + + align:start position:0% +estate we mean the fiscal assets of the +North End and we looked at both + + align:start position:0% +North End and we looked at both + + + align:start position:0% +North End and we looked at both +commercial and residential properties um + + align:start position:0% +commercial and residential properties um + + + align:start position:0% +commercial and residential properties um +as we'll see we we tended to focus on un + + align:start position:0% +as we'll see we we tended to focus on un + + + align:start position:0% +as we'll see we we tended to focus on un +residential given the opportunities that + + align:start position:0% +residential given the opportunities that + + + align:start position:0% +residential given the opportunities that +we saw um but we did look at both sides + + align:start position:0% +we saw um but we did look at both sides + + + align:start position:0% +we saw um but we did look at both sides +uh and also just a word about our our + + align:start position:0% +uh and also just a word about our our + + + align:start position:0% +uh and also just a word about our our +approach we um looked at different + + align:start position:0% +approach we um looked at different + + + align:start position:0% +approach we um looked at different +landlords in the neighborhood we looked + + align:start position:0% +landlords in the neighborhood we looked + + + align:start position:0% +landlords in the neighborhood we looked +at um housing data from the Census with + + align:start position:0% +at um housing data from the Census with + + + align:start position:0% +at um housing data from the Census with +the zoning codes uh of course talking to + + align:start position:0% +the zoning codes uh of course talking to + + + align:start position:0% +the zoning codes uh of course talking to +all of you so try to take a holistic + + align:start position:0% +all of you so try to take a holistic + + + align:start position:0% +all of you so try to take a holistic +approach to looking at at real + + align:start position:0% +approach to looking at at real + + + align:start position:0% +approach to looking at at real +estate the goals as we saw them from + + align:start position:0% +estate the goals as we saw them from + + + align:start position:0% +estate the goals as we saw them from +talking to people in the neighborhood um + + align:start position:0% +talking to people in the neighborhood um + + + align:start position:0% +talking to people in the neighborhood um +one strengthen community control and + + align:start position:0% +one strengthen community control and + + + align:start position:0% +one strengthen community control and +stability uh this is really a major + + align:start position:0% +stability uh this is really a major + + + align:start position:0% +stability uh this is really a major +thing but uh I I think throughout our + + align:start position:0% +thing but uh I I think throughout our + + + align:start position:0% +thing but uh I I think throughout our +whole presentation you will see that a + + align:start position:0% +whole presentation you will see that a + + + align:start position:0% +whole presentation you will see that a +common a common goal is to strengthen + + align:start position:0% +common a common goal is to strengthen + + + align:start position:0% +common a common goal is to strengthen +community control and real estate in + + align:start position:0% +community control and real estate in + + + align:start position:0% +community control and real estate in +control of real estate is really a major + + align:start position:0% +control of real estate is really a major + + + align:start position:0% +control of real estate is really a major +major mechanism through which to do that + + align:start position:0% +major mechanism through which to do that + + + align:start position:0% +major mechanism through which to do that +uh to develop Blended properties and + + align:start position:0% +uh to develop Blended properties and + + + align:start position:0% +uh to develop Blended properties and +improv neighborhood image uh uh 6% of + + align:start position:0% +improv neighborhood image uh uh 6% of + + + align:start position:0% +improv neighborhood image uh uh 6% of +property in the North End is is vacant + + align:start position:0% +property in the North End is is vacant + + + align:start position:0% +property in the North End is is vacant +State average is + + align:start position:0% +State average is + + + align:start position:0% +State average is +1.4% uh there's a lot of vacant property + + align:start position:0% +1.4% uh there's a lot of vacant property + + + align:start position:0% +1.4% uh there's a lot of vacant property +in the North End and as we'll talk about + + align:start position:0% +in the North End and as we'll talk about + + + align:start position:0% +in the North End and as we'll talk about +a bit more I mean that can be a + + align:start position:0% +a bit more I mean that can be a + + + align:start position:0% +a bit more I mean that can be a +hindrance to the neighborhood but it's + + align:start position:0% +hindrance to the neighborhood but it's + + + align:start position:0% +hindrance to the neighborhood but it's +also a major opportunity um you know + + align:start position:0% +also a major opportunity um you know + + + align:start position:0% +also a major opportunity um you know +there's always two sides to the + + align:start position:0% +there's always two sides to the + + + align:start position:0% +there's always two sides to the +coin three is increased afford + + align:start position:0% +coin three is increased afford + + + align:start position:0% +coin three is increased afford +affordable home + + align:start position:0% +affordable home + + + align:start position:0% +affordable home +ownership uh another figure home + + align:start position:0% +ownership uh another figure home + + + align:start position:0% +ownership uh another figure home +ownership rates in the North End um are + + align:start position:0% +ownership rates in the North End um are + + + align:start position:0% +ownership rates in the North End um are +about + + align:start position:0% +about + + + align:start position:0% +about +133% stay Aver is + + align:start position:0% +133% stay Aver is + + + align:start position:0% +133% stay Aver is +64% um that I mean to us that's just + + align:start position:0% +64% um that I mean to us that's just + + + align:start position:0% +64% um that I mean to us that's just +striking that's really incredibly low + + align:start position:0% +striking that's really incredibly low + + + align:start position:0% +striking that's really incredibly low +home ownership and it gets back to LA of + + align:start position:0% +home ownership and it gets back to LA of + + + align:start position:0% +home ownership and it gets back to LA of +community + + align:start position:0% +community + + + align:start position:0% +community +control fin determined balance and + + align:start position:0% +control fin determined balance and + + + align:start position:0% +control fin determined balance and +affordable market rate housing several + + align:start position:0% +affordable market rate housing several + + + align:start position:0% +affordable market rate housing several +people have mentioned that uh there is + + align:start position:0% +people have mentioned that uh there is + + + align:start position:0% +people have mentioned that uh there is +clearly unmet demand for for housing and + + align:start position:0% +clearly unmet demand for for housing and + + + align:start position:0% +clearly unmet demand for for housing and +I think additional analysis needs to be + + align:start position:0% +I think additional analysis needs to be + + + align:start position:0% +I think additional analysis needs to be +done on how much of that is market rate + + align:start position:0% +done on how much of that is market rate + + + align:start position:0% +done on how much of that is market rate +how much is that affordable um I I think + + align:start position:0% +how much is that affordable um I I think + + + align:start position:0% +how much is that affordable um I I think +you know there is a good amount of total + + align:start position:0% +you know there is a good amount of total + + + align:start position:0% +you know there is a good amount of total +housing in the North End doesn't mean + + align:start position:0% +housing in the North End doesn't mean + + + align:start position:0% +housing in the North End doesn't mean +that there there can't be and shouldn't + + align:start position:0% +that there there can't be and shouldn't + + + align:start position:0% +that there there can't be and shouldn't +be more um but I think that's just + + align:start position:0% +be more um but I think that's just + + + align:start position:0% +be more um but I think that's just +something that kind of collectively we + + align:start position:0% +something that kind of collectively we + + + align:start position:0% +something that kind of collectively we +need to look + + align:start position:0% +need to look + + + align:start position:0% +need to look +at so means the opportunities that we + + align:start position:0% +at so means the opportunities that we + + + align:start position:0% +at so means the opportunities that we +see in real estate uh number one + + align:start position:0% +see in real estate uh number one + + + align:start position:0% +see in real estate uh number one +developable developable land is in + + align:start position:0% +developable developable land is in + + + align:start position:0% +developable developable land is in +Supply um as I mentioned 131 Parcels um + + align:start position:0% +Supply um as I mentioned 131 Parcels um + + + align:start position:0% +Supply um as I mentioned 131 Parcels um +about 2/3 of which are zoned for + + align:start position:0% +about 2/3 of which are zoned for + + + align:start position:0% +about 2/3 of which are zoned for +residential use uh which really led us + + align:start position:0% +residential use uh which really led us + + + align:start position:0% +residential use uh which really led us +to focusing on residential real estate + + align:start position:0% +to focusing on residential real estate + + + align:start position:0% +to focusing on residential real estate +development you can kind of see um in + + align:start position:0% +development you can kind of see um in + + + align:start position:0% +development you can kind of see um in +this map I hope you might be able to see + + align:start position:0% +this map I hope you might be able to see + + + align:start position:0% +this map I hope you might be able to see +but these areas in blue actually + + align:start position:0% +but these areas in blue actually + + + align:start position:0% +but these areas in blue actually +highlight where the Bing Residential + + align:start position:0% +highlight where the Bing Residential + + + align:start position:0% +highlight where the Bing Residential +Properties + + align:start position:0% +Properties + + + align:start position:0% +Properties +Li as I mentioned unmet is demand for + + align:start position:0% +Li as I mentioned unmet is demand for + + + align:start position:0% +Li as I mentioned unmet is demand for +residential space you know tons of + + align:start position:0% +residential space you know tons of + + + align:start position:0% +residential space you know tons of +people have told us uh just anecdotally + + align:start position:0% +people have told us uh just anecdotally + + + align:start position:0% +people have told us uh just anecdotally +that especially in the Brightwood + + align:start position:0% +that especially in the Brightwood + + + align:start position:0% +that especially in the Brightwood +section they're looking for housing + + align:start position:0% +section they're looking for housing + + + align:start position:0% +section they're looking for housing +people are looking to buy and you know + + align:start position:0% +people are looking to buy and you know + + + align:start position:0% +people are looking to buy and you know +the opportunities don't really exist uh + + align:start position:0% +the opportunities don't really exist uh + + + align:start position:0% +the opportunities don't really exist uh +so that really that really says that + + align:start position:0% +so that really that really says that + + + align:start position:0% +so that really that really says that +there is um you know that there there + + align:start position:0% +there is um you know that there there + + + align:start position:0% +there is um you know that there there +are opportunities there is a demand for + + align:start position:0% +are opportunities there is a demand for + + + align:start position:0% +are opportunities there is a demand for +distri + + align:start position:0% +distri + + + align:start position:0% +distri +housing as the map shows that uh these + + align:start position:0% +housing as the map shows that uh these + + + align:start position:0% +housing as the map shows that uh these +Residential Properties that that are and + + align:start position:0% +Residential Properties that that are and + + + align:start position:0% +Residential Properties that that are and +are spread throughout the neighborhood + + align:start position:0% +are spread throughout the neighborhood + + + align:start position:0% +are spread throughout the neighborhood +uh you know if you're doing commercial + + align:start position:0% +uh you know if you're doing commercial + + + align:start position:0% +uh you know if you're doing commercial +space maybe that might be a hindrance + + align:start position:0% +space maybe that might be a hindrance + + + align:start position:0% +space maybe that might be a hindrance +because it doesn't allow consolidation + + align:start position:0% +because it doesn't allow consolidation + + + align:start position:0% +because it doesn't allow consolidation +perhaps and creating larger spaces but + + align:start position:0% +perhaps and creating larger spaces but + + + align:start position:0% +perhaps and creating larger spaces but +for if we're looking to develop + + align:start position:0% +for if we're looking to develop + + + align:start position:0% +for if we're looking to develop +additional affordable um home ownership + + align:start position:0% +additional affordable um home ownership + + + align:start position:0% +additional affordable um home ownership +having having residential vacancies + + align:start position:0% +having having residential vacancies + + + align:start position:0% +having having residential vacancies +spread throughout the neighborhood + + align:start position:0% +spread throughout the neighborhood + + + align:start position:0% +spread throughout the neighborhood +especially small lot sizes can be a real + + align:start position:0% +especially small lot sizes can be a real + + + align:start position:0% +especially small lot sizes can be a real +Advantage City's a major property owner + + align:start position:0% +Advantage City's a major property owner + + + align:start position:0% +Advantage City's a major property owner +uh that it's the the city including with + + align:start position:0% +uh that it's the the city including with + + + align:start position:0% +uh that it's the the city including with +the Springfield development authorities + + align:start position:0% +the Springfield development authorities + + + align:start position:0% +the Springfield development authorities +is the major property owner including + + align:start position:0% +is the major property owner including + + + align:start position:0% +is the major property owner including +the major proper being owner of vacant + + align:start position:0% +the major proper being owner of vacant + + + align:start position:0% +the major proper being owner of vacant +lands in the North End um that offers a + + align:start position:0% +lands in the North End um that offers a + + + align:start position:0% +lands in the North End um that offers a +real opportunity for partnership with + + align:start position:0% +real opportunity for partnership with + + + align:start position:0% +real opportunity for partnership with +the city um I think there there have + + align:start position:0% +the city um I think there there have + + + align:start position:0% +the city um I think there there have +been some mve in that direction but + + align:start position:0% +been some mve in that direction but + + + align:start position:0% +been some mve in that direction but +really solidifying partnership uh with + + align:start position:0% +really solidifying partnership uh with + + + align:start position:0% +really solidifying partnership uh with +the city would um we really see as a + + align:start position:0% +the city would um we really see as a + + + align:start position:0% +the city would um we really see as a +major + + align:start position:0% +major + + + align:start position:0% +major +opportunity public subsidies for + + align:start position:0% +opportunity public subsidies for + + + align:start position:0% +opportunity public subsidies for +affordable housing uh Section 8 there's + + align:start position:0% +affordable housing uh Section 8 there's + + + align:start position:0% +affordable housing uh Section 8 there's +about I think 3,400 Section 8 vouchers + + align:start position:0% +about I think 3,400 Section 8 vouchers + + + align:start position:0% +about I think 3,400 Section 8 vouchers +in Springfield large majority of them + + align:start position:0% +in Springfield large majority of them + + + align:start position:0% +in Springfield large majority of them +are in the North End that was a great + + align:start position:0% +are in the North End that was a great + + + align:start position:0% +are in the North End that was a great +investment by the city um by by a real + + align:start position:0% +investment by the city um by by a real + + + align:start position:0% +investment by the city um by by a real +Financial investment + + align:start position:0% +Financial investment + + + align:start position:0% +Financial investment +and that's something that we certainly + + align:start position:0% +and that's something that we certainly + + + align:start position:0% +and that's something that we certainly +need to take advantage of we understand + + align:start position:0% +need to take advantage of we understand + + + align:start position:0% +need to take advantage of we understand +that you know Financial subsidies that's + + align:start position:0% +that you know Financial subsidies that's + + + align:start position:0% +that you know Financial subsidies that's +a difficult tricky issue but you know + + align:start position:0% +a difficult tricky issue but you know + + + align:start position:0% +a difficult tricky issue but you know +there is there is a commitment there and + + align:start position:0% +there is there is a commitment there and + + + align:start position:0% +there is there is a commitment there and +it's something that can be built upon + + align:start position:0% +it's something that can be built upon + + + align:start position:0% +it's something that can be built upon +and finally increase the tax spase for + + align:start position:0% +and finally increase the tax spase for + + + align:start position:0% +and finally increase the tax spase for +the city uh this is somewhat of a long a + + align:start position:0% +the city uh this is somewhat of a long a + + + align:start position:0% +the city uh this is somewhat of a long a +longterm uh long-term opportunity but by + + align:start position:0% +longterm uh long-term opportunity but by + + + align:start position:0% +longterm uh long-term opportunity but by +you know raising property values by + + align:start position:0% +you know raising property values by + + + align:start position:0% +you know raising property values by +doing by implementing some of the + + align:start position:0% +doing by implementing some of the + + + align:start position:0% +doing by implementing some of the +recommendations we're going to talk + + align:start position:0% +recommendations we're going to talk + + + align:start position:0% +recommendations we're going to talk +about in the long term that does + + align:start position:0% +about in the long term that does + + + align:start position:0% +about in the long term that does +increase revenues for the + + align:start position:0% +increase revenues for the + + + align:start position:0% +increase revenues for the +city and finally just moving into our + + align:start position:0% +city and finally just moving into our + + + align:start position:0% +city and finally just moving into our +the challenges and resources that that + + align:start position:0% +the challenges and resources that that + + + align:start position:0% +the challenges and resources that that +we found uh number one challenge + + align:start position:0% +we found uh number one challenge + + + align:start position:0% +we found uh number one challenge +absentee landlords I think every single + + align:start position:0% +absentee landlords I think every single + + + align:start position:0% +absentee landlords I think every single +person we spoke to um noted that absente + + align:start position:0% +person we spoke to um noted that absente + + + align:start position:0% +person we spoke to um noted that absente +landlords just a major problem obviously + + align:start position:0% +landlords just a major problem obviously + + + align:start position:0% +landlords just a major problem obviously +you know low home ownership lots of + + align:start position:0% +you know low home ownership lots of + + + align:start position:0% +you know low home ownership lots of +absente landlords and I think that that + + align:start position:0% +absente landlords and I think that that + + + align:start position:0% +absente landlords and I think that that +signifies different things um on on the + + align:start position:0% +signifies different things um on on the + + + align:start position:0% +signifies different things um on on the +one hand it's this idea of of lack of + + align:start position:0% +one hand it's this idea of of lack of + + + align:start position:0% +one hand it's this idea of of lack of +community control and people not being + + align:start position:0% +community control and people not being + + + align:start position:0% +community control and people not being +invested in their own neighborhood which + + align:start position:0% +invested in their own neighborhood which + + + align:start position:0% +invested in their own neighborhood which +which is is incredibly important and I + + align:start position:0% +which is is incredibly important and I + + + align:start position:0% +which is is incredibly important and I +think one of the one of the outcomes of + + align:start position:0% +think one of the one of the outcomes of + + + align:start position:0% +think one of the one of the outcomes of +that is that it's really hard to plan if + + align:start position:0% +that is that it's really hard to plan if + + + align:start position:0% +that is that it's really hard to plan if +you don't have people who are invest in + + align:start position:0% +you don't have people who are invest in + + + align:start position:0% +you don't have people who are invest in +your neighor who homeowners uh who + + align:start position:0% +your neighor who homeowners uh who + + + align:start position:0% +your neighor who homeowners uh who +really are are looking at um the + + align:start position:0% +really are are looking at um the + + + align:start position:0% +really are are looking at um the +community's interest it's it's not only + + align:start position:0% +community's interest it's it's not only + + + align:start position:0% +community's interest it's it's not only +results in kind of blighted properties + + align:start position:0% +results in kind of blighted properties + + + align:start position:0% +results in kind of blighted properties +but it also makes it really difficult to + + align:start position:0% +but it also makes it really difficult to + + + align:start position:0% +but it also makes it really difficult to +plan in a coordinated + + align:start position:0% +plan in a coordinated + + + align:start position:0% +plan in a coordinated +manner Second Challenge is a lack of a + + align:start position:0% +manner Second Challenge is a lack of a + + + align:start position:0% +manner Second Challenge is a lack of a +strong development entity uh there there + + align:start position:0% +strong development entity uh there there + + + align:start position:0% +strong development entity uh there there +are organizations doing work in the + + align:start position:0% +are organizations doing work in the + + + align:start position:0% +are organizations doing work in the +north end but it really seems like Creer + + align:start position:0% +north end but it really seems like Creer + + + align:start position:0% +north end but it really seems like Creer +cooperation is needed and really whether + + align:start position:0% +cooperation is needed and really whether + + + align:start position:0% +cooperation is needed and really whether +it's an existing organization or perhaps + + align:start position:0% +it's an existing organization or perhaps + + + align:start position:0% +it's an existing organization or perhaps +a new collaboration among uh different + + align:start position:0% +a new collaboration among uh different + + + align:start position:0% +a new collaboration among uh different +people maybe people in this room um + + align:start position:0% +people maybe people in this room um + + + align:start position:0% +people maybe people in this room um +there needs to to be me a stronger + + align:start position:0% +there needs to to be me a stronger + + + align:start position:0% +there needs to to be me a stronger +development organizational presence in + + align:start position:0% +development organizational presence in + + + align:start position:0% +development organizational presence in +the north and that really has the + + align:start position:0% +the north and that really has the + + + align:start position:0% +the north and that really has the +community's interests um as its main + + align:start position:0% +community's interests um as its main + + + align:start position:0% +community's interests um as its main +focus and finally low resident income + + align:start position:0% +focus and finally low resident income + + + align:start position:0% +focus and finally low resident income +levels is a CH I mean I said this horest + + align:start position:0% +levels is a CH I mean I said this horest + + + align:start position:0% +levels is a CH I mean I said this horest +you know por sens tracks in the state + + align:start position:0% +you know por sens tracks in the state + + + align:start position:0% +you know por sens tracks in the state +and that can be difficult to promote + + align:start position:0% +and that can be difficult to promote + + + align:start position:0% +and that can be difficult to promote +home ownership when people just don't + + align:start position:0% +home ownership when people just don't + + + align:start position:0% +home ownership when people just don't +have the supposable income to spend um + + align:start position:0% +have the supposable income to spend um + + + align:start position:0% +have the supposable income to spend um +on on homes uh however there is funding + + align:start position:0% +on on homes uh however there is funding + + + align:start position:0% +on on homes uh however there is funding +available and um there are different + + align:start position:0% +available and um there are different + + + align:start position:0% +available and um there are different +levels of affordable home ownership and + + align:start position:0% +levels of affordable home ownership and + + + align:start position:0% +levels of affordable home ownership and +I think I I think to be honest that's + + align:start position:0% +I think I I think to be honest that's + + + align:start position:0% +I think I I think to be honest that's +something we need to do some more + + align:start position:0% +something we need to do some more + + + align:start position:0% +something we need to do some more +analysis on + + align:start position:0% +analysis on + + + align:start position:0% +analysis on +that certainly is a challenge but it's + + align:start position:0% +that certainly is a challenge but it's + + + align:start position:0% +that certainly is a challenge but it's +something that we are ready to + + align:start position:0% +something that we are ready to + + + align:start position:0% +something that we are ready to +address on the other side of our of our + + align:start position:0% +address on the other side of our of our + + + align:start position:0% +address on the other side of our of our +en scale is a the resources I mention + + align:start position:0% +en scale is a the resources I mention + + + align:start position:0% +en scale is a the resources I mention +funding programs uh Community + + align:start position:0% +funding programs uh Community + + + align:start position:0% +funding programs uh Community +Development block grants loow income + + align:start position:0% +Development block grants loow income + + + align:start position:0% +Development block grants loow income +housing tax credits uh spring + + align:start position:0% +housing tax credits uh spring + + + align:start position:0% +housing tax credits uh spring +Redevelopment Authority there there + + align:start position:0% +Redevelopment Authority there there + + + align:start position:0% +Redevelopment Authority there there +there are funding mechanisms out there + + align:start position:0% +there are funding mechanisms out there + + + align:start position:0% +there are funding mechanisms out there +uh you know the city and they yor + + align:start position:0% +uh you know the city and they yor + + + align:start position:0% +uh you know the city and they yor +already take advantage of of many of + + align:start position:0% +already take advantage of of many of + + + align:start position:0% +already take advantage of of many of +them and I think that's something that + + align:start position:0% +them and I think that's something that + + + align:start position:0% +them and I think that's something that +we can build upon Edgewater and pinent + + align:start position:0% +we can build upon Edgewater and pinent + + + align:start position:0% +we can build upon Edgewater and pinent +Terrace they are really you know there + + align:start position:0% +Terrace they are really you know there + + + align:start position:0% +Terrace they are really you know there +are strong affordable housing + + align:start position:0% +are strong affordable housing + + + align:start position:0% +are strong affordable housing +developments already in the North End uh + + align:start position:0% +developments already in the North End uh + + + align:start position:0% +developments already in the North End uh +not only do they receive a lot of + + align:start position:0% +not only do they receive a lot of + + + align:start position:0% +not only do they receive a lot of +financial support but they're undergoing + + align:start position:0% +financial support but they're undergoing + + + align:start position:0% +financial support but they're undergoing +Rehabilitation and that really does show + + align:start position:0% +Rehabilitation and that really does show + + + align:start position:0% +Rehabilitation and that really does show +commitment by the neighborhood and by + + align:start position:0% +commitment by the neighborhood and by + + + align:start position:0% +commitment by the neighborhood and by +the city um to to Really build a fund + + align:start position:0% +the city um to to Really build a fund + + + align:start position:0% +the city um to to Really build a fund +for home + + align:start position:0% +for home + + + align:start position:0% +for home +ownership mentioned a lot developable + + align:start position:0% +ownership mentioned a lot developable + + + align:start position:0% +ownership mentioned a lot developable +land I think that'll be a theme that's + + align:start position:0% +land I think that'll be a theme that's + + + align:start position:0% +land I think that'll be a theme that's +just a major asset and I think we can't + + align:start position:0% +just a major asset and I think we can't + + + align:start position:0% +just a major asset and I think we can't +say that enough it can it can be a + + align:start position:0% +say that enough it can it can be a + + + align:start position:0% +say that enough it can it can be a +hindrance it can you know they can be + + align:start position:0% +hindrance it can you know they can be + + + align:start position:0% +hindrance it can you know they can be +bled properties but it can also be a + + align:start position:0% +bled properties but it can also be a + + + align:start position:0% +bled properties but it can also be a +real + + align:start position:0% +real + + + align:start position:0% +real +opportunity and and finally um we have + + align:start position:0% +opportunity and and finally um we have + + + align:start position:0% +opportunity and and finally um we have +mobilized Community actors I think I + + align:start position:0% +mobilized Community actors I think I + + + align:start position:0% +mobilized Community actors I think I +can't stress this enough is that you + + align:start position:0% +can't stress this enough is that you + + + align:start position:0% +can't stress this enough is that you +know you can have all the opportunity + + align:start position:0% +know you can have all the opportunity + + + align:start position:0% +know you can have all the opportunity +you can have all the money in the world + + align:start position:0% +you can have all the money in the world + + + align:start position:0% +you can have all the money in the world +but if you don't have Community will + + align:start position:0% +but if you don't have Community will + + + align:start position:0% +but if you don't have Community will +then you know nothing's going to happen + + align:start position:0% +then you know nothing's going to happen + + + align:start position:0% +then you know nothing's going to happen +I think just you know seeing everyone in + + align:start position:0% +I think just you know seeing everyone in + + + align:start position:0% +I think just you know seeing everyone in +this room and listening to all the + + align:start position:0% +this room and listening to all the + + + align:start position:0% +this room and listening to all the +people that we've spoken to there's + + align:start position:0% +people that we've spoken to there's + + + align:start position:0% +people that we've spoken to there's +really real you know strong interest and + + align:start position:0% +really real you know strong interest and + + + align:start position:0% +really real you know strong interest and +commitment and and will to really um + + align:start position:0% +commitment and and will to really um + + + align:start position:0% +commitment and and will to really um +improve the real estate improve the + + align:start position:0% +improve the real estate improve the + + + align:start position:0% +improve the real estate improve the +physical assets of the north end I think + + align:start position:0% +physical assets of the north end I think + + + align:start position:0% +physical assets of the north end I think +that's something that we should all keep + + align:start position:0% +that's something that we should all keep + + + align:start position:0% +that's something that we should all keep +in mind is is cannot be undervalued so + + align:start position:0% +in mind is is cannot be undervalued so + + + align:start position:0% +in mind is is cannot be undervalued so +that kind of sums up our analysis um and + + align:start position:0% +that kind of sums up our analysis um and + + + align:start position:0% +that kind of sums up our analysis um and +some of our findings we're going to + + align:start position:0% +some of our findings we're going to + + + align:start position:0% +some of our findings we're going to +transition now into how we turn that how + + align:start position:0% +transition now into how we turn that how + + + align:start position:0% +transition now into how we turn that how +we see that move into our + + align:start position:0% + + + + align:start position:0% + +recommendations so uh it's my job to now + + align:start position:0% +recommendations so uh it's my job to now + + + align:start position:0% +recommendations so uh it's my job to now +boil down all this information that's + + align:start position:0% +boil down all this information that's + + + align:start position:0% +boil down all this information that's +been thrown at you to a a rationale and + + align:start position:0% +been thrown at you to a a rationale and + + + align:start position:0% +been thrown at you to a a rationale and +a proposed action plan and I'll be using + + align:start position:0% +a proposed action plan and I'll be using + + + align:start position:0% +a proposed action plan and I'll be using +this Hightech presentation as I do that + + align:start position:0% +this Hightech presentation as I do that + + + align:start position:0% +this Hightech presentation as I do that +um first I want to just before I dive + + align:start position:0% +um first I want to just before I dive + + + align:start position:0% +um first I want to just before I dive +right into this I want to say what went + + align:start position:0% +right into this I want to say what went + + + align:start position:0% +right into this I want to say what went +into our considerations when we talked + + align:start position:0% +into our considerations when we talked + + + align:start position:0% +into our considerations when we talked +about what we want to propose to you and + + align:start position:0% +about what we want to propose to you and + + + align:start position:0% +about what we want to propose to you and +a lot of this was very difficult because + + align:start position:0% +a lot of this was very difficult because + + + align:start position:0% +a lot of this was very difficult because +we wanted to recommend how to work on + + align:start position:0% +we wanted to recommend how to work on + + + align:start position:0% +we wanted to recommend how to work on +everything that everyone wants to do in + + align:start position:0% +everything that everyone wants to do in + + + align:start position:0% +everything that everyone wants to do in +economic development in the north end + + align:start position:0% +economic development in the north end + + + align:start position:0% +economic development in the north end +but uh there are problems with that in + + align:start position:0% +but uh there are problems with that in + + + align:start position:0% +but uh there are problems with that in +so far as we need to be able to produce + + align:start position:0% +so far as we need to be able to produce + + + align:start position:0% +so far as we need to be able to produce +a concrete product for you that is + + align:start position:0% +a concrete product for you that is + + + align:start position:0% +a concrete product for you that is +actionable and um it would just be too + + align:start position:0% +actionable and um it would just be too + + + align:start position:0% +actionable and um it would just be too +diffuse uh for to be acted upon if we + + align:start position:0% +diffuse uh for to be acted upon if we + + + align:start position:0% +diffuse uh for to be acted upon if we +just said we'll do everything so the way + + align:start position:0% +just said we'll do everything so the way + + + align:start position:0% +just said we'll do everything so the way +we tried to narrow this down was through + + align:start position:0% +we tried to narrow this down was through + + + align:start position:0% +we tried to narrow this down was through +considerations of what activities are in + + align:start position:0% +considerations of what activities are in + + + align:start position:0% +considerations of what activities are in +and of themselves easy and + + align:start position:0% +and of themselves easy and + + + align:start position:0% +and of themselves easy and +difficult uh with a special eye towards + + align:start position:0% +difficult uh with a special eye towards + + + align:start position:0% +difficult uh with a special eye towards +are the payoffs shortterm or longterm to + + align:start position:0% +are the payoffs shortterm or longterm to + + + align:start position:0% +are the payoffs shortterm or longterm to +this Initiative for this project another + + align:start position:0% +this Initiative for this project another + + + align:start position:0% +this Initiative for this project another +consideration was of course is the + + align:start position:0% +consideration was of course is the + + + align:start position:0% +consideration was of course is the +capacity existing in the area high or + + align:start position:0% +capacity existing in the area high or + + + align:start position:0% +capacity existing in the area high or +low to actually produce results on a + + align:start position:0% +low to actually produce results on a + + + align:start position:0% +low to actually produce results on a +given project and finally another issue + + align:start position:0% +given project and finally another issue + + + align:start position:0% +given project and finally another issue +was what kind of sequencing issues exist + + align:start position:0% +was what kind of sequencing issues exist + + + align:start position:0% +was what kind of sequencing issues exist +where certain projects lead logically + + align:start position:0% +where certain projects lead logically + + + align:start position:0% +where certain projects lead logically +into others and build momentum towards + + align:start position:0% +into others and build momentum towards + + + align:start position:0% +into others and build momentum towards +those others so given that and given the + + align:start position:0% +those others so given that and given the + + + align:start position:0% +those others so given that and given the +strengths and weaknesses that have + + align:start position:0% +strengths and weaknesses that have + + + align:start position:0% +strengths and weaknesses that have +already been described um this is a very + + align:start position:0% +already been described um this is a very + + + align:start position:0% +already been described um this is a very +you know theistic way of looking at uh + + align:start position:0% +you know theistic way of looking at uh + + + align:start position:0% +you know theistic way of looking at uh +the strength the respective strengths + + align:start position:0% +the strength the respective strengths + + + align:start position:0% +the strength the respective strengths +and weaknesses of the different projects + + align:start position:0% +and weaknesses of the different projects + + + align:start position:0% +and weaknesses of the different projects +but it's just to give that overall um + + align:start position:0% +but it's just to give that overall um + + + align:start position:0% +but it's just to give that overall um +view that we took that there are greater + + align:start position:0% +view that we took that there are greater + + + align:start position:0% +view that we took that there are greater +strengths and weak uh greater strengths + + align:start position:0% +strengths and weak uh greater strengths + + + align:start position:0% +strengths and weak uh greater strengths +and less weaknesses on the employment + + align:start position:0% +and less weaknesses on the employment + + + align:start position:0% +and less weaknesses on the employment +and real + + align:start position:0% +and real + + + align:start position:0% +and real +estate areas than in business + + align:start position:0% +estate areas than in business + + + align:start position:0% +estate areas than in business +development and just to sum up the + + align:start position:0% +development and just to sum up the + + + align:start position:0% +development and just to sum up the +reasons for this are that employment has + + align:start position:0% +reasons for this are that employment has + + + align:start position:0% +reasons for this are that employment has +programs that are in effect that + + align:start position:0% +programs that are in effect that + + + align:start position:0% +programs that are in effect that +apparently work that place people in + + align:start position:0% +apparently work that place people in + + + align:start position:0% +apparently work that place people in +jobs uh and the main challenges to + + align:start position:0% +jobs uh and the main challenges to + + + align:start position:0% +jobs uh and the main challenges to +expanding on that are resources but we + + align:start position:0% +expanding on that are resources but we + + + align:start position:0% +expanding on that are resources but we +think that given the + + align:start position:0% +think that given the + + + align:start position:0% +think that given the +capacity of this group those resources + + align:start position:0% +capacity of this group those resources + + + align:start position:0% +capacity of this group those resources +can be effectively expand expanded as + + align:start position:0% +can be effectively expand expanded as + + + align:start position:0% +can be effectively expand expanded as +well as Outreach issues addressed in + + align:start position:0% +well as Outreach issues addressed in + + + align:start position:0% +well as Outreach issues addressed in +business development there is a lot of + + align:start position:0% +business development there is a lot of + + + align:start position:0% +business development there is a lot of +small business activity but the + + align:start position:0% +small business activity but the + + + align:start position:0% +small business activity but the +overriding constraints to this were the + + align:start position:0% +overriding constraints to this were the + + + align:start position:0% +overriding constraints to this were the +uh public safety issues uh long-term the + + align:start position:0% +uh public safety issues uh long-term the + + + align:start position:0% +uh public safety issues uh long-term the +issue of it being kind of a long-term + + align:start position:0% +issue of it being kind of a long-term + + + align:start position:0% +issue of it being kind of a long-term +project building these types of + + align:start position:0% +project building these types of + + + align:start position:0% +project building these types of +businesses and also the issue of capture + + align:start position:0% +businesses and also the issue of capture + + + align:start position:0% +businesses and also the issue of capture +of the capital and potential crowding + + align:start position:0% +of the capital and potential crowding + + + align:start position:0% +of the capital and potential crowding +out effects also an important note is + + align:start position:0% +out effects also an important note is + + + align:start position:0% +out effects also an important note is +that a lot of what can happen in + + align:start position:0% +that a lot of what can happen in + + + align:start position:0% +that a lot of what can happen in +employment Workforce Development can + + align:start position:0% +employment Workforce Development can + + + align:start position:0% +employment Workforce Development can +sequence well into business development + + align:start position:0% +sequence well into business development + + + align:start position:0% +sequence well into business development +finally on the real estate there's a lot + + align:start position:0% +finally on the real estate there's a lot + + + align:start position:0% +finally on the real estate there's a lot +of demonstrated enthusiasm and people + + align:start position:0% +of demonstrated enthusiasm and people + + + align:start position:0% +of demonstrated enthusiasm and people +are taking action on this issue right + + align:start position:0% +are taking action on this issue right + + + align:start position:0% +are taking action on this issue right +now which is a major strength and on the + + align:start position:0% +now which is a major strength and on the + + + align:start position:0% +now which is a major strength and on the +negative side the low Community + + align:start position:0% +negative side the low Community + + + align:start position:0% +negative side the low Community +stability was a concern but it's also + + align:start position:0% +stability was a concern but it's also + + + align:start position:0% +stability was a concern but it's also +the concern that creates the need to + + align:start position:0% +the concern that creates the need to + + + align:start position:0% +the concern that creates the need to +work on this so in the end what we found + + align:start position:0% +work on this so in the end what we found + + + align:start position:0% +work on this so in the end what we found +that these two areas were the ones that + + align:start position:0% +that these two areas were the ones that + + + align:start position:0% +that these two areas were the ones that +we thought would be best for us to + + align:start position:0% +we thought would be best for us to + + + align:start position:0% +we thought would be best for us to +develop further and look with you + + align:start position:0% +develop further and look with you + + + align:start position:0% +develop further and look with you +want that's a visual + + align:start position:0% +want that's a visual + + + align:start position:0% +want that's a visual +representation so + + align:start position:0% +representation so + + + align:start position:0% +representation so +uh generally speaking uh honing in on + + align:start position:0% +uh generally speaking uh honing in on + + + align:start position:0% +uh generally speaking uh honing in on +the Workforce Development + + align:start position:0% +the Workforce Development + + + align:start position:0% +the Workforce Development +and real estate + + align:start position:0% +and real estate + + + align:start position:0% +and real estate +areas you all can read this I won't I + + align:start position:0% +areas you all can read this I won't I + + + align:start position:0% +areas you all can read this I won't I +won't go down and read every piece of + + align:start position:0% +won't go down and read every piece of + + + align:start position:0% +won't go down and read every piece of +text but what I just want to highlight + + align:start position:0% +text but what I just want to highlight + + + align:start position:0% +text but what I just want to highlight +with these Concepts is that focusing on + + align:start position:0% +with these Concepts is that focusing on + + + align:start position:0% +with these Concepts is that focusing on +Workforce Development is essentially + + align:start position:0% +Workforce Development is essentially + + + align:start position:0% +Workforce Development is essentially +starting on a path of building a + + align:start position:0% +starting on a path of building a + + + align:start position:0% +starting on a path of building a +comprehensive human capital + + align:start position:0% +comprehensive human capital + + + align:start position:0% +comprehensive human capital +strategy and that just seems to be an + + align:start position:0% +strategy and that just seems to be an + + + align:start position:0% +strategy and that just seems to be an +overriding concern for this area and + + align:start position:0% +overriding concern for this area and + + + align:start position:0% +overriding concern for this area and +issue number one for getting people + + align:start position:0% +issue number one for getting people + + + align:start position:0% +issue number one for getting people +increasing people's income and their + + align:start position:0% +increasing people's income and their + + + align:start position:0% +increasing people's income and their +wealth and their ability to compete on + + align:start position:0% +wealth and their ability to compete on + + + align:start position:0% +wealth and their ability to compete on +the job market and to establish + + align:start position:0% +the job market and to establish + + + align:start position:0% +the job market and to establish +businesses is language and so that's + + align:start position:0% +businesses is language and so that's + + + align:start position:0% +businesses is language and so that's +that would probably be at the very start + + align:start position:0% +that would probably be at the very start + + + align:start position:0% +that would probably be at the very start +of any path toward Workforce Development + + align:start position:0% +of any path toward Workforce Development + + + align:start position:0% +of any path toward Workforce Development +strategy uh also important to note on + + align:start position:0% +strategy uh also important to note on + + + align:start position:0% +strategy uh also important to note on +Workforce + + align:start position:0% +Workforce + + + align:start position:0% +Workforce +Development is that it's just the local + + align:start position:0% +Development is that it's just the local + + + align:start position:0% +Development is that it's just the local +assets aspect of it is immediate + + align:start position:0% +assets aspect of it is immediate + + + align:start position:0% +assets aspect of it is immediate +people's incomes are increased that is + + align:start position:0% +people's incomes are increased that is + + + align:start position:0% +people's incomes are increased that is +the first outcome you have when you + + align:start position:0% +the first outcome you have when you + + + align:start position:0% +the first outcome you have when you +place people on + + align:start position:0% +place people on + + + align:start position:0% +place people on +jobs then moving along to uh real estate + + align:start position:0% +jobs then moving along to uh real estate + + + align:start position:0% +jobs then moving along to uh real estate +conceptual that as a strategy that the + + align:start position:0% +conceptual that as a strategy that the + + + align:start position:0% +conceptual that as a strategy that the +anchor to this is that as a it works as + + align:start position:0% +anchor to this is that as a it works as + + + align:start position:0% +anchor to this is that as a it works as +a good compliment to the human capital + + align:start position:0% +a good compliment to the human capital + + + align:start position:0% +a good compliment to the human capital +side because this is about stabilizing + + align:start position:0% +side because this is about stabilizing + + + align:start position:0% +side because this is about stabilizing +the physical assets of the + + align:start position:0% +the physical assets of the + + + align:start position:0% +the physical assets of the +community so what this does is it + + align:start position:0% +community so what this does is it + + + align:start position:0% +community so what this does is it +creates a good Counterpoint to the human + + align:start position:0% +creates a good Counterpoint to the human + + + align:start position:0% +creates a good Counterpoint to the human +capital strategy that can create a + + align:start position:0% +capital strategy that can create a + + + align:start position:0% +capital strategy that can create a +Synergy that we're both in concert can + + align:start position:0% +Synergy that we're both in concert can + + + align:start position:0% +Synergy that we're both in concert can +lead toward a lot of the goals that + + align:start position:0% +lead toward a lot of the goals that + + + align:start position:0% +lead toward a lot of the goals that +aren't the immediate primary objectives + + align:start position:0% +aren't the immediate primary objectives + + + align:start position:0% +aren't the immediate primary objectives +of these plans as we hope to develop + + align:start position:0% +of these plans as we hope to develop + + + align:start position:0% +of these plans as we hope to develop +come for you by the end of the + + align:start position:0% +come for you by the end of the + + + align:start position:0% +come for you by the end of the +semester and I think moving + + align:start position:0% + + + + align:start position:0% + +along how are we conceptualizing these + + align:start position:0% +along how are we conceptualizing these + + + align:start position:0% +along how are we conceptualizing these +as action + + align:start position:0% +as action + + + align:start position:0% +as action +plans Workforce + + align:start position:0% +plans Workforce + + + align:start position:0% +plans Workforce +Development as an action plan requires + + align:start position:0% +Development as an action plan requires + + + align:start position:0% +Development as an action plan requires +needs assessment of where the barriers + + align:start position:0% +needs assessment of where the barriers + + + align:start position:0% +needs assessment of where the barriers +are Community level organization that's + + align:start position:0% +are Community level organization that's + + + align:start position:0% +are Community level organization that's +tied to people on the Grassroots level + + align:start position:0% +tied to people on the Grassroots level + + + align:start position:0% +tied to people on the Grassroots level +that can take a systematic view and say + + align:start position:0% +that can take a systematic view and say + + + align:start position:0% +that can take a systematic view and say +where are the barriers between people + + align:start position:0% +where are the barriers between people + + + align:start position:0% +where are the barriers between people +and the Workforce Development programs + + align:start position:0% +and the Workforce Development programs + + + align:start position:0% +and the Workforce Development programs +and between people who have gone through + + align:start position:0% +and between people who have gone through + + + align:start position:0% +and between people who have gone through +the Workforce Development programs and + + align:start position:0% +the Workforce Development programs and + + + align:start position:0% +the Workforce Development programs and +getting + + align:start position:0% +getting + + + align:start position:0% +getting +emplo a lot of what will happen in the + + align:start position:0% +emplo a lot of what will happen in the + + + align:start position:0% +emplo a lot of what will happen in the +short term is improving on the Outreach + + align:start position:0% +short term is improving on the Outreach + + + align:start position:0% +short term is improving on the Outreach +and building a coalition that can gain + + align:start position:0% +and building a coalition that can gain + + + align:start position:0% +and building a coalition that can gain +enough steam to increase the local + + align:start position:0% +enough steam to increase the local + + + align:start position:0% +enough steam to increase the local +resources for Workforce Development and + + align:start position:0% +resources for Workforce Development and + + + align:start position:0% +resources for Workforce Development and +deep in how Workforce Development is + + align:start position:0% +deep in how Workforce Development is + + + align:start position:0% +deep in how Workforce Development is +conceptualized and practiced in this + + align:start position:0% +conceptualized and practiced in this + + + align:start position:0% +conceptualized and practiced in this +area so that means in the long + + align:start position:0% +area so that means in the long + + + align:start position:0% +area so that means in the long +term funds will be sought in partnership + + align:start position:0% +term funds will be sought in partnership + + + align:start position:0% +term funds will be sought in partnership +with Cooperative groups that will be + + align:start position:0% +with Cooperative groups that will be + + + align:start position:0% +with Cooperative groups that will be +stronger on Grant applications because + + align:start position:0% +stronger on Grant applications because + + + align:start position:0% +stronger on Grant applications because +they represent various + + align:start position:0% +they represent various + + + align:start position:0% +they represent various +sectors curricula will be expanded and + + align:start position:0% +sectors curricula will be expanded and + + + align:start position:0% +sectors curricula will be expanded and +customized to the neighborhood specific + + align:start position:0% +customized to the neighborhood specific + + + align:start position:0% +customized to the neighborhood specific +issues collaboration with employers can + + align:start position:0% +issues collaboration with employers can + + + align:start position:0% +issues collaboration with employers can +build job + + align:start position:0% +build job + + + align:start position:0% +build job +ladders and eventually perhaps the plan + + align:start position:0% +ladders and eventually perhaps the plan + + + align:start position:0% +ladders and eventually perhaps the plan +as it matures can build towards + + align:start position:0% +as it matures can build towards + + + align:start position:0% +as it matures can build towards +something where the local Coalition can + + align:start position:0% +something where the local Coalition can + + + align:start position:0% +something where the local Coalition can +plan effectively to compete for desired + + align:start position:0% +plan effectively to compete for desired + + + align:start position:0% +plan effectively to compete for desired +employers to expand the type of + + align:start position:0% +employers to expand the type of + + + align:start position:0% +employers to expand the type of +employment that exists here in a + + align:start position:0% +employment that exists here in a + + + align:start position:0% +employment that exists here in a +pre-planned + + align:start position:0% +pre-planned + + + align:start position:0% +pre-planned +way then in real + + align:start position:0% +way then in real + + + align:start position:0% +way then in real +estate what we are suggesting is that in + + align:start position:0% +estate what we are suggesting is that in + + + align:start position:0% +estate what we are suggesting is that in +the short term there need to be local + + align:start position:0% +the short term there need to be local + + + align:start position:0% +the short term there need to be local +discussions of what it means to + + align:start position:0% +discussions of what it means to + + + align:start position:0% +discussions of what it means to +stabilize our physical Assets in this + + align:start position:0% +stabilize our physical Assets in this + + + align:start position:0% +stabilize our physical Assets in this +community and that will + + align:start position:0% +community and that will + + + align:start position:0% +community and that will +involve a lot of getting everyone around + + align:start position:0% +involve a lot of getting everyone around + + + align:start position:0% +involve a lot of getting everyone around +the table about this thinking about the + + align:start position:0% +the table about this thinking about the + + + align:start position:0% +the table about this thinking about the +home ownership issues how they TI to + + align:start position:0% +home ownership issues how they TI to + + + align:start position:0% +home ownership issues how they TI to +financing + + align:start position:0% +financing + + + align:start position:0% +financing +issues and then in the long term not + + align:start position:0% +issues and then in the long term not + + + align:start position:0% +issues and then in the long term not +only acting on that stabilization plan + + align:start position:0% +only acting on that stabilization plan + + + align:start position:0% +only acting on that stabilization plan +but thinking about how that expands + + align:start position:0% +but thinking about how that expands + + + align:start position:0% +but thinking about how that expands +outwards how that stabilization plan + + align:start position:0% +outwards how that stabilization plan + + + align:start position:0% +outwards how that stabilization plan +leads to a better environment for + + align:start position:0% +leads to a better environment for + + + align:start position:0% +leads to a better environment for +business and I believe that is all I was + + align:start position:0% +business and I believe that is all I was + + + align:start position:0% +business and I believe that is all I was +supposed to speak about so I will pass + + align:start position:0% +supposed to speak about so I will pass + + + align:start position:0% +supposed to speak about so I will pass +it along to a wrap + + align:start position:0% +it along to a wrap + + + align:start position:0% +it along to a wrap +up so just reiterate what Seth and + + align:start position:0% +up so just reiterate what Seth and + + + align:start position:0% +up so just reiterate what Seth and +everyone before him said is that the + + align:start position:0% +everyone before him said is that the + + + align:start position:0% +everyone before him said is that the +advantages of pursuing two tracks + + align:start position:0% +advantages of pursuing two tracks + + + align:start position:0% +advantages of pursuing two tracks +employment Workforce Development on one + + align:start position:0% +employment Workforce Development on one + + + align:start position:0% +employment Workforce Development on one +hand real estate development on the + + align:start position:0% +hand real estate development on the + + + align:start position:0% +hand real estate development on the +other hand is to really create a sense + + align:start position:0% +other hand is to really create a sense + + + align:start position:0% +other hand is to really create a sense +of Hope in the community really begin to + + align:start position:0% +of Hope in the community really begin to + + + align:start position:0% +of Hope in the community really begin to +turn it around make people feel like + + align:start position:0% +turn it around make people feel like + + + align:start position:0% +turn it around make people feel like +there + + align:start position:0% +there + + + align:start position:0% +there +is there are resources and there is good + + align:start position:0% +is there are resources and there is good + + + align:start position:0% +is there are resources and there is good +reason to believe that they can get + + align:start position:0% +reason to believe that they can get + + + align:start position:0% +reason to believe that they can get +access to jobs and even were they so + + align:start position:0% +access to jobs and even were they so + + + align:start position:0% +access to jobs and even were they so +inclined into small businesses + + align:start position:0% +inclined into small businesses + + + align:start position:0% +inclined into small businesses +on one hand on the other hand just + + align:start position:0% +on one hand on the other hand just + + + align:start position:0% +on one hand on the other hand just +changing the way the neighborhood looks + + align:start position:0% +changing the way the neighborhood looks + + + align:start position:0% +changing the way the neighborhood looks +and feels making people believe that + + align:start position:0% +and feels making people believe that + + + align:start position:0% +and feels making people believe that +they can own their own homes that they + + align:start position:0% +they can own their own homes that they + + + align:start position:0% +they can own their own homes that they +don't have to rent from a landlord who + + align:start position:0% +don't have to rent from a landlord who + + + align:start position:0% +don't have to rent from a landlord who +lives in Boston or New York or nowhere + + align:start position:0% +lives in Boston or New York or nowhere + + + align:start position:0% +lives in Boston or New York or nowhere +and I think that what we're really + + align:start position:0% +and I think that what we're really + + + align:start position:0% +and I think that what we're really +suggesting to you here today is if this + + align:start position:0% +suggesting to you here today is if this + + + align:start position:0% +suggesting to you here today is if this +is acceptable then we need to come up + + align:start position:0% +is acceptable then we need to come up + + + align:start position:0% +is acceptable then we need to come up +very quickly with a set of ideas and + + align:start position:0% +very quickly with a set of ideas and + + + align:start position:0% +very quickly with a set of ideas and +steps that we need to take as a way of + + align:start position:0% +steps that we need to take as a way of + + + align:start position:0% +steps that we need to take as a way of +Flesh fling out concrete ideas and plans + + align:start position:0% +Flesh fling out concrete ideas and plans + + + align:start position:0% +Flesh fling out concrete ideas and plans +that then can be implemented by this + + align:start position:0% +that then can be implemented by this + + + align:start position:0% +that then can be implemented by this +group and potentially other + + align:start position:0% +group and potentially other + + + align:start position:0% +group and potentially other +institutional partners that you wish to + + align:start position:0% +institutional partners that you wish to + + + align:start position:0% +institutional partners that you wish to +invite to the table to begin to create + + align:start position:0% +invite to the table to begin to create + + + align:start position:0% +invite to the table to begin to create +Workforce um and employment programs + + align:start position:0% +Workforce um and employment programs + + + align:start position:0% +Workforce um and employment programs +that actually get people into jobs that + + align:start position:0% +that actually get people into jobs that + + + align:start position:0% +that actually get people into jobs that +are more than just jobs they really are + + align:start position:0% +are more than just jobs they really are + + + align:start position:0% +are more than just jobs they really are +long-term careers on one hand and get + + align:start position:0% +long-term careers on one hand and get + + + align:start position:0% +long-term careers on one hand and get +people into not just their own homes but + + align:start position:0% +people into not just their own homes but + + + align:start position:0% +people into not just their own homes but +into good quality housing stock into + + align:start position:0% +into good quality housing stock into + + + align:start position:0% +into good quality housing stock into +homes that will be wellmaintained on + + align:start position:0% +homes that will be wellmaintained on + + + align:start position:0% +homes that will be wellmaintained on +streets people want to live and so some + + align:start position:0% +streets people want to live and so some + + + align:start position:0% +streets people want to live and so some +of the ideas that we've had I'm just + + align:start position:0% +of the ideas that we've had I'm just + + + align:start position:0% +of the ideas that we've had I'm just +going to look at the laundry list here + + align:start position:0% +going to look at the laundry list here + + + align:start position:0% +going to look at the laundry list here +on my notepad for ways in which we might + + align:start position:0% +on my notepad for ways in which we might + + + align:start position:0% +on my notepad for ways in which we might +move forward if this basic two track + + align:start position:0% +move forward if this basic two track + + + align:start position:0% +move forward if this basic two track +approach is acceptable to you is we need + + align:start position:0% +approach is acceptable to you is we need + + + align:start position:0% +approach is acceptable to you is we need +to do more survey work there is more + + align:start position:0% +to do more survey work there is more + + + align:start position:0% +to do more survey work there is more +research that we need to do both in + + align:start position:0% +research that we need to do both in + + + align:start position:0% +research that we need to do both in +terms of inventorying employers and + + align:start position:0% +terms of inventorying employers and + + + align:start position:0% +terms of inventorying employers and +businesses with a much finer grain of + + align:start position:0% +businesses with a much finer grain of + + + align:start position:0% +businesses with a much finer grain of +detail and uh also on the real estate + + align:start position:0% +detail and uh also on the real estate + + + align:start position:0% +detail and uh also on the real estate +side actually beginning to understand + + align:start position:0% +side actually beginning to understand + + + align:start position:0% +side actually beginning to understand +individual pieces of land and some of + + align:start position:0% +individual pieces of land and some of + + + align:start position:0% +individual pieces of land and some of +the land assembly requirements with + + align:start position:0% +the land assembly requirements with + + + align:start position:0% +the land assembly requirements with +again much greater attention to detail + + align:start position:0% +again much greater attention to detail + + + align:start position:0% +again much greater attention to detail +and on this score there's a lot of this + + align:start position:0% +and on this score there's a lot of this + + + align:start position:0% +and on this score there's a lot of this +work that we would want to work with the + + align:start position:0% +work that we would want to work with the + + + align:start position:0% +work that we would want to work with the +Northend uh campus committee as well as + + align:start position:0% +Northend uh campus committee as well as + + + align:start position:0% +Northend uh campus committee as well as +with neon on for two reasons one it's + + align:start position:0% +with neon on for two reasons one it's + + + align:start position:0% +with neon on for two reasons one it's +just obviously efficient to work with + + align:start position:0% +just obviously efficient to work with + + + align:start position:0% +just obviously efficient to work with +you you're in the community every day of + + align:start position:0% +you you're in the community every day of + + + align:start position:0% +you you're in the community every day of +the week you have very strong + + align:start position:0% +the week you have very strong + + + align:start position:0% +the week you have very strong +relationships with employers and + + align:start position:0% +relationships with employers and + + + align:start position:0% +relationships with employers and +residents in the area + + align:start position:0% +residents in the area + + + align:start position:0% +residents in the area +and it makes our work obviously much + + align:start position:0% +and it makes our work obviously much + + + align:start position:0% +and it makes our work obviously much +easier there's another aspect to it of + + align:start position:0% +easier there's another aspect to it of + + + align:start position:0% +easier there's another aspect to it of +course is that if we do Hit Upon a set + + align:start position:0% +course is that if we do Hit Upon a set + + + align:start position:0% +course is that if we do Hit Upon a set +of strategies that do work then it + + align:start position:0% +of strategies that do work then it + + + align:start position:0% +of strategies that do work then it +really makes sense to get people from + + align:start position:0% +really makes sense to get people from + + + align:start position:0% +really makes sense to get people from +this room and from your agencies + + align:start position:0% +this room and from your agencies + + + align:start position:0% +this room and from your agencies +involved in the process right from the + + align:start position:0% +involved in the process right from the + + + align:start position:0% +involved in the process right from the +get go have you as a part of the + + align:start position:0% +get go have you as a part of the + + + align:start position:0% +get go have you as a part of the +planning team not just a part of the + + align:start position:0% +planning team not just a part of the + + + align:start position:0% +planning team not just a part of the +implementation team so the idea there + + align:start position:0% +implementation team so the idea there + + + align:start position:0% +implementation team so the idea there +was not just doing the surveying work + + align:start position:0% +was not just doing the surveying work + + + align:start position:0% +was not just doing the surveying work +and the interviewing work that we need + + align:start position:0% +and the interviewing work that we need + + + align:start position:0% +and the interviewing work that we need +to do but really kind of involving in + + align:start position:0% +to do but really kind of involving in + + + align:start position:0% +to do but really kind of involving in +neon and the campus Committee in that + + align:start position:0% +neon and the campus Committee in that + + + align:start position:0% +neon and the campus Committee in that +possibly one of the ideas that we've + + align:start position:0% +possibly one of the ideas that we've + + + align:start position:0% +possibly one of the ideas that we've +thought about for + + align:start position:0% +thought about for + + + align:start position:0% +thought about for +creating working groups or some kind of + + align:start position:0% +creating working groups or some kind of + + + align:start position:0% +creating working groups or some kind of +advisory committee on these two themes + + align:start position:0% +advisory committee on these two themes + + + align:start position:0% +advisory committee on these two themes +uh based on people's experience based on + + align:start position:0% +uh based on people's experience based on + + + align:start position:0% +uh based on people's experience based on +their own interests and and uh where + + align:start position:0% +their own interests and and uh where + + + align:start position:0% +their own interests and and uh where +they think they might be able to most + + align:start position:0% +they think they might be able to most + + + align:start position:0% +they think they might be able to most +effectively or their institutions might + + align:start position:0% +effectively or their institutions might + + + align:start position:0% +effectively or their institutions might +be most able to uh effectively + + align:start position:0% +be most able to uh effectively + + + align:start position:0% +be most able to uh effectively +contribute to forward + + align:start position:0% +contribute to forward + + + align:start position:0% +contribute to forward +movement and um one of the other things + + align:start position:0% +movement and um one of the other things + + + align:start position:0% +movement and um one of the other things +that we think we should probably really + + align:start position:0% +that we think we should probably really + + + align:start position:0% +that we think we should probably really +get focused on very quickly are uh + + align:start position:0% +get focused on very quickly are uh + + + align:start position:0% +get focused on very quickly are uh +funding opportunities just doing a bit + + align:start position:0% +funding opportunities just doing a bit + + + align:start position:0% +funding opportunities just doing a bit +of basic uh Grant research trying to + + align:start position:0% +of basic uh Grant research trying to + + + align:start position:0% +of basic uh Grant research trying to +think about well even during the + + align:start position:0% +think about well even during the + + + align:start position:0% +think about well even during the +planning stage how is this process going + + align:start position:0% +planning stage how is this process going + + + align:start position:0% +planning stage how is this process going +to pay for itself and uh are there ways + + align:start position:0% +to pay for itself and uh are there ways + + + align:start position:0% +to pay for itself and uh are there ways +in which we can flag resources for you + + align:start position:0% +in which we can flag resources for you + + + align:start position:0% +in which we can flag resources for you +right now that would be easily + + align:start position:0% +right now that would be easily + + + align:start position:0% +right now that would be easily +accessible to you were you to apply for + + align:start position:0% +accessible to you were you to apply for + + + align:start position:0% +accessible to you were you to apply for +them so I don't really want to say much + + align:start position:0% +them so I don't really want to say much + + + align:start position:0% +them so I don't really want to say much +more like I said this is just sort of + + align:start position:0% +more like I said this is just sort of + + + align:start position:0% +more like I said this is just sort of +suggestions for next steps for us to + + align:start position:0% +suggestions for next steps for us to + + + align:start position:0% +suggestions for next steps for us to +take what I wanted to do right now is to + + align:start position:0% +take what I wanted to do right now is to + + + align:start position:0% +take what I wanted to do right now is to +open it up uh to a broad + + align:start position:0% +open it up uh to a broad + + + align:start position:0% +open it up uh to a broad +discussion um it's just coming on 1:00 + + align:start position:0% +discussion um it's just coming on 1:00 + + + align:start position:0% +discussion um it's just coming on 1:00 +so we I think definitely have plenty of + + align:start position:0% +so we I think definitely have plenty of + + + align:start position:0% +so we I think definitely have plenty of +time we don't have anything else to + + align:start position:0% +time we don't have anything else to + + + align:start position:0% +time we don't have anything else to +formally present but we're very happy to + + align:start position:0% +formally present but we're very happy to + + + align:start position:0% +formally present but we're very happy to +clarify anything that we have spoken + + align:start position:0% +clarify anything that we have spoken + + + align:start position:0% +clarify anything that we have spoken +about + + align:start position:0% + + + + align:start position:0% + +today do you have a list of the people + + align:start position:0% +today do you have a list of the people + + + align:start position:0% +today do you have a list of the people +you've interviewed and are they from + + align:start position:0% +you've interviewed and are they from + + + align:start position:0% +you've interviewed and are they from +this area or did you interview some + + align:start position:0% +this area or did you interview some + + + align:start position:0% +this area or did you interview some +people from City you know City in + + align:start position:0% +people from City you know City in + + + align:start position:0% +people from City you know City in +general we do have a list and I think uh + + align:start position:0% +general we do have a list and I think uh + + + align:start position:0% +general we do have a list and I think uh +Andre off the top what the number is um + + align:start position:0% +Andre off the top what the number is um + + + align:start position:0% +Andre off the top what the number is um +yes it's about 15 people actually let me + + align:start position:0% +yes it's about 15 people actually let me + + + align:start position:0% +yes it's about 15 people actually let me +take something when you make a comment + + align:start position:0% +take something when you make a comment + + + align:start position:0% +take something when you make a comment +or question if you could please say your + + align:start position:0% +or question if you could please say your + + + align:start position:0% +or question if you could please say your +name first just so I can make sure to + + align:start position:0% +name first just so I can make sure to + + + align:start position:0% +name first just so I can make sure to +get back to people if necessary okay Tim + + align:start position:0% +get back to people if necessary okay Tim + + + align:start position:0% +get back to people if necessary okay Tim +Allen theing okay thanks yeah so it's + + align:start position:0% +Allen theing okay thanks yeah so it's + + + align:start position:0% +Allen theing okay thanks yeah so it's +about um successful interviews meaning + + align:start position:0% +about um successful interviews meaning + + + align:start position:0% +about um successful interviews meaning +we actually have caught up with people + + align:start position:0% +we actually have caught up with people + + + align:start position:0% +we actually have caught up with people +um they're about 15 uh we've tried a + + align:start position:0% +um they're about 15 uh we've tried a + + + align:start position:0% +um they're about 15 uh we've tried a +number of others um and and it's a it's + + align:start position:0% +number of others um and and it's a it's + + + align:start position:0% +number of others um and and it's a it's +a to respond to your question it's a + + align:start position:0% +a to respond to your question it's a + + + align:start position:0% +a to respond to your question it's a +fairly good mix a lot of residents and a + + align:start position:0% +fairly good mix a lot of residents and a + + + align:start position:0% +fairly good mix a lot of residents and a +lot of workers uh from the community + + align:start position:0% +lot of workers uh from the community + + + align:start position:0% +lot of workers uh from the community +itself but we've also reached out to + + align:start position:0% +itself but we've also reached out to + + + align:start position:0% +itself but we've also reached out to +people in city government as well as + + align:start position:0% +people in city government as well as + + + align:start position:0% +people in city government as well as +people in P Valley Planning Commission + + align:start position:0% +people in P Valley Planning Commission + + + align:start position:0% +people in P Valley Planning Commission +and Regional and state level um and + + align:start position:0% +and Regional and state level um and + + + align:start position:0% +and Regional and state level um and +there are obviously more conversations + + align:start position:0% +there are obviously more conversations + + + align:start position:0% +there are obviously more conversations +around that to be had and if there were + + align:start position:0% +around that to be had and if there were + + + align:start position:0% +around that to be had and if there were +specific people who felt that we should + + align:start position:0% +specific people who felt that we should + + + align:start position:0% +specific people who felt that we should +speak to uh we may have well missed them + + align:start position:0% +speak to uh we may have well missed them + + + align:start position:0% +speak to uh we may have well missed them +on our r on we definitely want to know + + align:start position:0% +on our r on we definitely want to know + + + align:start position:0% +on our r on we definitely want to know +about + + align:start position:0% +about + + + align:start position:0% +about +that one of the uh my name is Rari + + align:start position:0% +that one of the uh my name is Rari + + + align:start position:0% +that one of the uh my name is Rari +principal one of the bu show there's a + + align:start position:0% +principal one of the bu show there's a + + + align:start position:0% +principal one of the bu show there's a +negative perception of the + + align:start position:0% +negative perception of the + + + align:start position:0% +negative perception of the +area one board in that area was the that + + align:start position:0% +area one board in that area was the that + + + align:start position:0% +area one board in that area was the that +people have + + align:start position:0% +people have + + + align:start position:0% +people have +nor that I think + + align:start position:0% +nor that I think + + + align:start position:0% +nor that I think +that is the negative perception is under + + align:start position:0% +that is the negative perception is under + + + align:start position:0% +that is the negative perception is under +that umbrella is essentially safety + + align:start position:0% +that umbrella is essentially safety + + + align:start position:0% +that umbrella is essentially safety +issues um the people that we talked to + + align:start position:0% +issues um the people that we talked to + + + align:start position:0% +issues um the people that we talked to +both who some who live here um others + + align:start position:0% +both who some who live here um others + + + align:start position:0% +both who some who live here um others +who + + align:start position:0% +who + + + align:start position:0% +who +don't and talking about why they perhaps + + align:start position:0% +don't and talking about why they perhaps + + + align:start position:0% +don't and talking about why they perhaps +did did not live here the types of + + align:start position:0% +did did not live here the types of + + + align:start position:0% +did did not live here the types of +activities they pursued here the issue + + align:start position:0% +activities they pursued here the issue + + + align:start position:0% +activities they pursued here the issue +of safety came up a lot and I say + + align:start position:0% +of safety came up a lot and I say + + + align:start position:0% +of safety came up a lot and I say +perception because of you know I can't + + align:start position:0% +perception because of you know I can't + + + align:start position:0% +perception because of you know I can't +judge how real that is I don't you know + + align:start position:0% +judge how real that is I don't you know + + + align:start position:0% +judge how real that is I don't you know +say la of + + align:start position:0% +say la of + + + align:start position:0% +say la of +police the comments were not as specific + + align:start position:0% +police the comments were not as specific + + + align:start position:0% +police the comments were not as specific +as that but certainly that could lead to + + align:start position:0% +as that but certainly that could lead to + + + align:start position:0% +as that but certainly that could lead to +it but crime uh drugs drugs yeah + + align:start position:0% +it but crime uh drugs drugs yeah + + + align:start position:0% +it but crime uh drugs drugs yeah +actually we we heard a couple comments + + align:start position:0% +actually we we heard a couple comments + + + align:start position:0% +actually we we heard a couple comments +that said specifically need more + + align:start position:0% +that said specifically need more + + + align:start position:0% +that said specifically need more +police I how people feel about that but + + align:start position:0% +police I how people feel about that but + + + align:start position:0% +police I how people feel about that but +people did mention that I think there's + + align:start position:0% +people did mention that I think there's + + + align:start position:0% +people did mention that I think there's +also a real sort of mix in uh the + + align:start position:0% +also a real sort of mix in uh the + + + align:start position:0% +also a real sort of mix in uh the +responses that we received some people + + align:start position:0% +responses that we received some people + + + align:start position:0% +responses that we received some people +talked about Springfield and general + + align:start position:0% +talked about Springfield and general + + + align:start position:0% +talked about Springfield and general +having public safety concerns others yet + + align:start position:0% +having public safety concerns others yet + + + align:start position:0% +having public safety concerns others yet +singled out the North End a lot of + + align:start position:0% +singled out the North End a lot of + + + align:start position:0% +singled out the North End a lot of +people qualified at saying we don't know + + align:start position:0% +people qualified at saying we don't know + + + align:start position:0% +people qualified at saying we don't know +if it's true or not it's just a sense + + align:start position:0% +if it's true or not it's just a sense + + + align:start position:0% +if it's true or not it's just a sense +that we have it's a sense that other + + align:start position:0% +that we have it's a sense that other + + + align:start position:0% +that we have it's a sense that other +people we spoken to have and I think + + align:start position:0% +people we spoken to have and I think + + + align:start position:0% +people we spoken to have and I think +aside from Public Safety there's also + + align:start position:0% +aside from Public Safety there's also + + + align:start position:0% +aside from Public Safety there's also +just a negative perception of the + + align:start position:0% +just a negative perception of the + + + align:start position:0% +just a negative perception of the +neighborhood as being + + align:start position:0% +neighborhood as being + + + align:start position:0% +neighborhood as being +uh unable to really stand on its on its + + align:start position:0% +uh unable to really stand on its on its + + + align:start position:0% +uh unable to really stand on its on its +own feet and I think that from our + + align:start position:0% +own feet and I think that from our + + + align:start position:0% +own feet and I think that from our +perspective having actually come in and + + align:start position:0% +perspective having actually come in and + + + align:start position:0% +perspective having actually come in and +spent a day at at the uh on the campus + + align:start position:0% +spent a day at at the uh on the campus + + + align:start position:0% +spent a day at at the uh on the campus +literally that was really hard to + + align:start position:0% +literally that was really hard to + + + align:start position:0% +literally that was really hard to +believe didn't really seem + + align:start position:0% + + + + align:start position:0% + +qualified oh + + align:start position:0% +qualified oh + + + align:start position:0% +qualified oh +sorry I just want to say that I was I + + align:start position:0% +sorry I just want to say that I was I + + + align:start position:0% +sorry I just want to say that I was I +was struck in that it it's it surprised + + align:start position:0% +was struck in that it it's it surprised + + + align:start position:0% +was struck in that it it's it surprised +me a little bit that you got the two + + align:start position:0% +me a little bit that you got the two + + + align:start position:0% +me a little bit that you got the two +things you pulled out the real estate + + align:start position:0% +things you pulled out the real estate + + + align:start position:0% +things you pulled out the real estate +and the Workforce Development they're + + align:start position:0% +and the Workforce Development they're + + + align:start position:0% +and the Workforce Development they're +obvious but at the same time I think + + align:start position:0% +obvious but at the same time I think + + + align:start position:0% +obvious but at the same time I think +it's interesting those the two you + + align:start position:0% +it's interesting those the two you + + + align:start position:0% +it's interesting those the two you +pulled out as immediate needs being for + + align:start position:0% +pulled out as immediate needs being for + + + align:start position:0% +pulled out as immediate needs being for +the City of Springfield um and certainly + + align:start position:0% +the City of Springfield um and certainly + + + align:start position:0% +the City of Springfield um and certainly +the the land that you were showing there + + align:start position:0% +the the land that you were showing there + + + align:start position:0% +the the land that you were showing there +under the ownership is something that's + + align:start position:0% +under the ownership is something that's + + + align:start position:0% +under the ownership is something that's +under my guys especially the Springfield + + align:start position:0% +under my guys especially the Springfield + + + align:start position:0% +under my guys especially the Springfield +Redevelopment Authority land and um a + + align:start position:0% +Redevelopment Authority land and um a + + + align:start position:0% +Redevelopment Authority land and um a +lot of the tax title property something + + align:start position:0% +lot of the tax title property something + + + align:start position:0% +lot of the tax title property something +I said to Shand presentation was that + + align:start position:0% +I said to Shand presentation was that + + + align:start position:0% +I said to Shand presentation was that +you know this is one of the few + + align:start position:0% +you know this is one of the few + + + align:start position:0% +you know this is one of the few +neighborhoods we don't really have a + + align:start position:0% +neighborhoods we don't really have a + + + align:start position:0% +neighborhoods we don't really have a +housing CDC that's doing a lot of + + align:start position:0% +housing CDC that's doing a lot of + + + align:start position:0% +housing CDC that's doing a lot of +housing Redevelopment in other + + align:start position:0% +housing Redevelopment in other + + + align:start position:0% +housing Redevelopment in other +neighborhoods like in hung hill we have + + align:start position:0% +neighborhoods like in hung hill we have + + + align:start position:0% +neighborhoods like in hung hill we have +someone who is you know building houses + + align:start position:0% +someone who is you know building houses + + + align:start position:0% +someone who is you know building houses +and going doing this thing we have some + + align:start position:0% +and going doing this thing we have some + + + align:start position:0% +and going doing this thing we have some +organizations in the area that will buy + + align:start position:0% +organizations in the area that will buy + + + align:start position:0% +organizations in the area that will buy +buy the land and then it's a year to + + align:start position:0% +buy the land and then it's a year to + + + align:start position:0% +buy the land and then it's a year to +twoyear process to get the tax credits + + align:start position:0% +twoyear process to get the tax credits + + + align:start position:0% +twoyear process to get the tax credits +and then do the house so it's not an + + align:start position:0% +and then do the house so it's not an + + + align:start position:0% +and then do the house so it's not an +immediate construction so that there's a + + align:start position:0% +immediate construction so that there's a + + + align:start position:0% +immediate construction so that there's a +lot of impatience around that and I want + + align:start position:0% +lot of impatience around that and I want + + + align:start position:0% +lot of impatience around that and I want +to emphasize that I think that's a + + align:start position:0% +to emphasize that I think that's a + + + align:start position:0% +to emphasize that I think that's a +really important one and I think if + + align:start position:0% +really important one and I think if + + + align:start position:0% +really important one and I think if +because we can really do can increase + + align:start position:0% +because we can really do can increase + + + align:start position:0% +because we can really do can increase +the economy's a scale because there's so + + align:start position:0% +the economy's a scale because there's so + + + align:start position:0% +the economy's a scale because there's so +many pieces of land and I'm struck how + + align:start position:0% +many pieces of land and I'm struck how + + + align:start position:0% +many pieces of land and I'm struck how +you may be able to think about pulling + + align:start position:0% +you may be able to think about pulling + + + align:start position:0% +you may be able to think about pulling +in a developer to do a large scale you + + align:start position:0% +in a developer to do a large scale you + + + align:start position:0% +in a developer to do a large scale you +know single family housing + + align:start position:0% +know single family housing + + + align:start position:0% +know single family housing +drive just because there is so much to + + align:start position:0% +drive just because there is so much to + + + align:start position:0% +drive just because there is so much to +build on we have an RFP right out right + + align:start position:0% +build on we have an RFP right out right + + + align:start position:0% +build on we have an RFP right out right +now for about 11 parcels and I know that + + align:start position:0% +now for about 11 parcels and I know that + + + align:start position:0% +now for about 11 parcels and I know that +they're being bid on peac meal um you + + align:start position:0% +they're being bid on peac meal um you + + + align:start position:0% +they're being bid on peac meal um you +know we let the neighborhood councils + + align:start position:0% +know we let the neighborhood councils + + + align:start position:0% +know we let the neighborhood councils +know that they're available we let + + align:start position:0% +know that they're available we let + + + align:start position:0% +know that they're available we let +everyone that we possibly know they're + + align:start position:0% +everyone that we possibly know they're + + + align:start position:0% +everyone that we possibly know they're +available but I know we're not going to + + align:start position:0% +available but I know we're not going to + + + align:start position:0% +available but I know we're not going to +get a developer coming in and developing + + align:start position:0% +get a developer coming in and developing + + + align:start position:0% +get a developer coming in and developing +all of those pieces of land but in + + align:start position:0% +all of those pieces of land but in + + + align:start position:0% +all of those pieces of land but in +reality it'd be kind of nice if someone + + align:start position:0% +reality it'd be kind of nice if someone + + + align:start position:0% +reality it'd be kind of nice if someone +came in and had a few models of houses + + align:start position:0% +came in and had a few models of houses + + + align:start position:0% +came in and had a few models of houses +were really like and started just Blitz + + align:start position:0% +were really like and started just Blitz + + + align:start position:0% +were really like and started just Blitz +building a lot of stuff at once so I + + align:start position:0% +building a lot of stuff at once so I + + + align:start position:0% +building a lot of stuff at once so I +think we need to rethink our strategy + + align:start position:0% +think we need to rethink our strategy + + + align:start position:0% +think we need to rethink our strategy +how we infill these lots and I'm + + align:start position:0% +how we infill these lots and I'm + + + align:start position:0% +how we infill these lots and I'm +certainly at the table and need help + + align:start position:0% +certainly at the table and need help + + + align:start position:0% +certainly at the table and need help +with others to come up with some good + + align:start position:0% +with others to come up with some good + + + align:start position:0% +with others to come up with some good +solutions for that it's not like it + + align:start position:0% +solutions for that it's not like it + + + align:start position:0% +solutions for that it's not like it +hasn't been done in other places and um + + align:start position:0% +hasn't been done in other places and um + + + align:start position:0% +hasn't been done in other places and um +the question I have on Workforce + + align:start position:0% +the question I have on Workforce + + + align:start position:0% +the question I have on Workforce +Development was really to Neon I know + + align:start position:0% +Development was really to Neon I know + + + align:start position:0% +Development was really to Neon I know +that you guys go door too and in your + + align:start position:0% +that you guys go door too and in your + + + align:start position:0% +that you guys go door too and in your +neighborhood and know the needs of every + + align:start position:0% +neighborhood and know the needs of every + + + align:start position:0% +neighborhood and know the needs of every +resident basically in this neighborhood + + align:start position:0% +resident basically in this neighborhood + + + align:start position:0% +resident basically in this neighborhood +do you have any sense of your Workforce + + align:start position:0% +do you have any sense of your Workforce + + + align:start position:0% +do you have any sense of your Workforce +a split between how many people are + + align:start position:0% +a split between how many people are + + + align:start position:0% +a split between how many people are +there who really are not working but + + align:start position:0% +there who really are not working but + + + align:start position:0% +there who really are not working but +really want to work and really want to + + align:start position:0% +really want to work and really want to + + + align:start position:0% +really want to work and really want to +get those skills and how many people I + + align:start position:0% +get those skills and how many people I + + + align:start position:0% +get those skills and how many people I +don't know how to phrase politely but + + align:start position:0% +don't know how to phrase politely but + + + align:start position:0% +don't know how to phrase politely but +really aren't interested in entering the + + align:start position:0% +really aren't interested in entering the + + + align:start position:0% +really aren't interested in entering the +workforce and do you get a sense of what + + align:start position:0% +workforce and do you get a sense of what + + + align:start position:0% +workforce and do you get a sense of what +that split is and and and what that + + align:start position:0% +that split is and and and what that + + + align:start position:0% +that split is and and and what that +looks like I can say that a lot of the + + align:start position:0% +looks like I can say that a lot of the + + + align:start position:0% +looks like I can say that a lot of the +information we' gaed that we have a lot + + align:start position:0% +information we' gaed that we have a lot + + + align:start position:0% +information we' gaed that we have a lot +of folks that are not working a large + + align:start position:0% +of folks that are not working a large + + + align:start position:0% +of folks that are not working a large +statistics wise um and it some of them + + align:start position:0% +statistics wise um and it some of them + + + align:start position:0% +statistics wise um and it some of them +are not not and they do their own um + + align:start position:0% +are not not and they do their own um + + + align:start position:0% +are not not and they do their own um +hair at home their own cooking at home + + align:start position:0% +hair at home their own cooking at home + + + align:start position:0% +hair at home their own cooking at home +that they did this um survey last year + + align:start position:0% +that they did this um survey last year + + + align:start position:0% +that they did this um survey last year +with + + align:start position:0% +with + + + align:start position:0% +with +tell you is that they're very interested + + align:start position:0% +tell you is that they're very interested + + + align:start position:0% +tell you is that they're very interested +in obtaining GED and getting skills and + + align:start position:0% +in obtaining GED and getting skills and + + + align:start position:0% +in obtaining GED and getting skills and +because of the language + + align:start position:0% +because of the language + + + align:start position:0% +because of the language +barrier it's hard to do the things that + + align:start position:0% +barrier it's hard to do the things that + + + align:start position:0% +barrier it's hard to do the things that +they want to do but that's a big need + + align:start position:0% +they want to do but that's a big need + + + align:start position:0% +they want to do but that's a big need +and address + + align:start position:0% +and address + + + align:start position:0% +and address +it yeah I think when you proceed to + + align:start position:0% +it yeah I think when you proceed to + + + align:start position:0% +it yeah I think when you proceed to +collect more data I think that's the + + align:start position:0% +collect more data I think that's the + + + align:start position:0% +collect more data I think that's the +real question is it the language barrier + + align:start position:0% +real question is it the language barrier + + + align:start position:0% +real question is it the language barrier +and the lack + + align:start position:0% +and the lack + + + align:start position:0% +and the lack +OFA that that that affects the + + align:start position:0% +OFA that that that affects the + + + align:start position:0% +OFA that that that affects the +employability + + align:start position:0% +employability + + + align:start position:0% +employability +and how many folks like that do we have + + align:start position:0% +and how many folks like that do we have + + + align:start position:0% +and how many folks like that do we have +is there needs to establish a vibrant + + align:start position:0% +is there needs to establish a vibrant + + + align:start position:0% +is there needs to establish a vibrant +Adult Educational ly piece in the North + + align:start position:0% +Adult Educational ly piece in the North + + + align:start position:0% +Adult Educational ly piece in the North +End and what what do we have to do to do + + align:start position:0% +End and what what do we have to do to do + + + align:start position:0% +End and what what do we have to do to do +that to get people on the RS so we + + align:start position:0% +that to get people on the RS so we + + + align:start position:0% +that to get people on the RS so we +really need to flush that out this a + + align:start position:0% +really need to flush that out this a + + + align:start position:0% +really need to flush that out this a +reality is a fact what what does the + + align:start position:0% +reality is a fact what what does the + + + align:start position:0% +reality is a fact what what does the +data show us and not and not to be + + align:start position:0% +data show us and not and not to be + + + align:start position:0% +data show us and not and not to be +passive about it I mean people might be + + align:start position:0% +passive about it I mean people might be + + + align:start position:0% +passive about it I mean people might be +discouraged this could be and say I + + align:start position:0% +discouraged this could be and say I + + + align:start position:0% +discouraged this could be and say I +don't want to work but really there + + align:start position:0% +don't want to work but really there + + + align:start position:0% +don't want to work but really there +there's there's lots reasons for people + + align:start position:0% +there's there's lots reasons for people + + + align:start position:0% +there's there's lots reasons for people +to want to and if we're not passive + + align:start position:0% +to want to and if we're not passive + + + align:start position:0% +to want to and if we're not passive +about it that that will take + + align:start position:0% +about it that that will take + + + align:start position:0% +about it that that will take +hold also just to tou + + align:start position:0% +hold also just to tou + + + align:start position:0% +hold also just to tou +on an example isia from this + + align:start position:0% +on an example isia from this + + + align:start position:0% +on an example isia from this +school got + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +together on now um we ran the the + + align:start position:0% +together on now um we ran the the + + + align:start position:0% +together on now um we ran the the +classes last year and we had we just had + + align:start position:0% +classes last year and we had we just had + + + align:start position:0% +classes last year and we had we just had +5 months to run the program out of that + + align:start position:0% +5 months to run the program out of that + + + align:start position:0% +5 months to run the program out of that +fun um five month we ended up having + + align:start position:0% +fun um five month we ended up having + + + align:start position:0% +fun um five month we ended up having +another 30 assigned you know that came + + align:start position:0% +another 30 assigned you know that came + + + align:start position:0% +another 30 assigned you know that came +in and registered this year when we did + + align:start position:0% +in and registered this year when we did + + + align:start position:0% +in and registered this year when we did +the information night we ended up with + + align:start position:0% +the information night we ended up with + + + align:start position:0% +the information night we ended up with +50 but we have another 60 that from last + + align:start position:0% +50 but we have another 60 that from last + + + align:start position:0% +50 but we have another 60 that from last +week up to now that came in and + + align:start position:0% +week up to now that came in and + + + align:start position:0% +week up to now that came in and +registered for the ES cost so that is a + + align:start position:0% +registered for the ES cost so that is a + + + align:start position:0% +registered for the ES cost so that is a +big need another thing is that we're + + align:start position:0% +big need another thing is that we're + + + align:start position:0% +big need another thing is that we're +working on getting the GED and classes + + align:start position:0% +working on getting the GED and classes + + + align:start position:0% +working on getting the GED and classes +we we're working for the process of it + + align:start position:0% +we we're working for the process of it + + + align:start position:0% +we we're working for the process of it +now we're going to have the GED the + + align:start position:0% +now we're going to have the GED the + + + align:start position:0% +now we're going to have the GED the +classes given in Spanish and take the + + align:start position:0% +classes given in Spanish and take the + + + align:start position:0% +classes given in Spanish and take the +test in Spanish and this way it'll bring + + align:start position:0% +test in Spanish and this way it'll bring + + + align:start position:0% +test in Spanish and this way it'll bring +up your self-esteem they'll feel more + + align:start position:0% +up your self-esteem they'll feel more + + + align:start position:0% +up your self-esteem they'll feel more +confident then they will come to the eso + + align:start position:0% +confident then they will come to the eso + + + align:start position:0% +confident then they will come to the eso +classes and then this way we can help + + align:start position:0% +classes and then this way we can help + + + align:start position:0% +classes and then this way we can help +them a job placement assisting them on + + align:start position:0% +them a job placement assisting them on + + + align:start position:0% +them a job placement assisting them on +other other needs that they have + + align:start position:0% +other other needs that they have + + + align:start position:0% +other other needs that they have +alen Blair from The Economic Council I + + align:start position:0% +alen Blair from The Economic Council I + + + align:start position:0% +alen Blair from The Economic Council I +I'm just curious about the uh work + + align:start position:0% +I'm just curious about the uh work + + + align:start position:0% +I'm just curious about the uh work +capacity comments that you made about + + align:start position:0% +capacity comments that you made about + + + align:start position:0% +capacity comments that you made about +organizations that are put in place to + + align:start position:0% +organizations that are put in place to + + + align:start position:0% +organizations that are put in place to +assist with Workforce Development um and + + align:start position:0% +assist with Workforce Development um and + + + align:start position:0% +assist with Workforce Development um and +what your assessment is of U of + + align:start position:0% +what your assessment is of U of + + + align:start position:0% +what your assessment is of U of +organizations that have been in place a + + align:start position:0% +organizations that have been in place a + + + align:start position:0% +organizations that have been in place a +long time and seem to be uh well funded + + align:start position:0% +long time and seem to be uh well funded + + + align:start position:0% +long time and seem to be uh well funded +and with a lot of capacity and I'm + + align:start position:0% +and with a lot of capacity and I'm + + + align:start position:0% +and with a lot of capacity and I'm +thinking about mcdi for example as a + + align:start position:0% +thinking about mcdi for example as a + + + align:start position:0% +thinking about mcdi for example as a +place that does a lot of eso and there + + align:start position:0% +place that does a lot of eso and there + + + align:start position:0% +place that does a lot of eso and there +long history of that is is a capacity + + align:start position:0% +long history of that is is a capacity + + + align:start position:0% +long history of that is is a capacity +issue there or is it that it's not + + align:start position:0% +issue there or is it that it's not + + + align:start position:0% +issue there or is it that it's not +there's a disconnect between this + + align:start position:0% +there's a disconnect between this + + + align:start position:0% +there's a disconnect between this +neighborhood and that facility why isn't + + align:start position:0% +neighborhood and that facility why isn't + + + align:start position:0% +neighborhood and that facility why isn't +that being used more frequently more + + align:start position:0% +that being used more frequently more + + + align:start position:0% +that being used more frequently more +often I I think that uh what what I he + + align:start position:0% +often I I think that uh what what I he + + + align:start position:0% +often I I think that uh what what I he +appearance it's local it's it's in + + align:start position:0% +appearance it's local it's it's in + + + align:start position:0% +appearance it's local it's it's in +walking distance um we also have the + + align:start position:0% +walking distance um we also have the + + + align:start position:0% +walking distance um we also have the +child care provider um they can come + + align:start position:0% +child care provider um they can come + + + align:start position:0% +child care provider um they can come +they can bring their child they don't + + align:start position:0% +they can bring their child they don't + + + align:start position:0% +they can bring their child they don't +have to worry about doing their child at + + align:start position:0% +have to worry about doing their child at + + + align:start position:0% +have to worry about doing their child at +home um they can come in the other thing + + align:start position:0% +home um they can come in the other thing + + + align:start position:0% +home um they can come in the other thing +is um you you kind of give them a more + + align:start position:0% +is um you you kind of give them a more + + + align:start position:0% +is um you you kind of give them a more +likely friendly welcome so that they can + + align:start position:0% +likely friendly welcome so that they can + + + align:start position:0% +likely friendly welcome so that they can +come that they can feel that this is the + + align:start position:0% +come that they can feel that this is the + + + align:start position:0% +come that they can feel that this is the +neighborhood schol you're welcome to + + align:start position:0% +neighborhood schol you're welcome to + + + align:start position:0% +neighborhood schol you're welcome to +come here so not only that we have this + + align:start position:0% +come here so not only that we have this + + + align:start position:0% +come here so not only that we have this +area but you know like the parents from + + align:start position:0% +area but you know like the parents from + + + align:start position:0% +area but you know like the parents from +herena and bright we all connect so this + + align:start position:0% +herena and bright we all connect so this + + + align:start position:0% +herena and bright we all connect so this +has become a place where they feel that + + align:start position:0% +has become a place where they feel that + + + align:start position:0% +has become a place where they feel that +moreable and just uh then kind of lead + + align:start position:0% +moreable and just uh then kind of lead + + + align:start position:0% +moreable and just uh then kind of lead +you + + align:start position:0% +you + + + align:start position:0% +you +to ask how can you decentralize some of + + align:start position:0% +to ask how can you decentralize some of + + + align:start position:0% +to ask how can you decentralize some of +these services that have been pulled + + align:start position:0% +these services that have been pulled + + + align:start position:0% +these services that have been pulled +together for efficiency purposes in one + + align:start position:0% +together for efficiency purposes in one + + + align:start position:0% +together for efficiency purposes in one +central location so that they are more + + align:start position:0% +central location so that they are more + + + align:start position:0% +central location so that they are more +accessible and what are the + + align:start position:0% +accessible and what are the + + + align:start position:0% +accessible and what are the +corresponding costs of doing that + + align:start position:0% +corresponding costs of doing that + + + align:start position:0% +corresponding costs of doing that +because there is obviously going to be a + + align:start position:0% +because there is obviously going to be a + + + align:start position:0% +because there is obviously going to be a +cost of doing that to + + align:start position:0% +cost of doing that to + + + align:start position:0% +cost of doing that to +facilitate so work for Workforce + + align:start position:0% +facilitate so work for Workforce + + + align:start position:0% +facilitate so work for Workforce +Development there is um always something + + align:start position:0% +Development there is um always something + + + align:start position:0% +Development there is um always something +that I um is near and dear to me number + + align:start position:0% +that I um is near and dear to me number + + + align:start position:0% +that I um is near and dear to me number +one Healthcare + + align:start position:0% +one Healthcare + + + align:start position:0% +one Healthcare +um we have have uh we've discussed we + + align:start position:0% +um we have have uh we've discussed we + + + align:start position:0% +um we have have uh we've discussed we +have so many people in this community + + align:start position:0% +have so many people in this community + + + align:start position:0% +have so many people in this community +who actually know how to who know how to + + align:start position:0% +who actually know how to who know how to + + + align:start position:0% +who actually know how to who know how to +be caregivers and we have a tremendous + + align:start position:0% +be caregivers and we have a tremendous + + + align:start position:0% +be caregivers and we have a tremendous +need for caregivers that's in medical + + align:start position:0% +need for caregivers that's in medical + + + align:start position:0% +need for caregivers that's in medical +health care that's in home health care + + align:start position:0% +health care that's in home health care + + + align:start position:0% +health care that's in home health care +that's in actually daycare as well and + + align:start position:0% +that's in actually daycare as well and + + + align:start position:0% +that's in actually daycare as well and +uh that is a resource in this community + + align:start position:0% +uh that is a resource in this community + + + align:start position:0% +uh that is a resource in this community +people who have spent their lives and + + align:start position:0% +people who have spent their lives and + + + align:start position:0% +people who have spent their lives and +have become incredibly wonderful + + align:start position:0% +have become incredibly wonderful + + + align:start position:0% +have become incredibly wonderful +caregivers but there's a part of that + + align:start position:0% +caregivers but there's a part of that + + + align:start position:0% +caregivers but there's a part of that +that we've not done and that's the + + align:start position:0% +that we've not done and that's the + + + align:start position:0% +that we've not done and that's the +development of that and the uh the + + align:start position:0% +development of that and the uh the + + + align:start position:0% +development of that and the uh the +training in that and the focusing in + + align:start position:0% +training in that and the focusing in + + + align:start position:0% +training in that and the focusing in +that and the the view of that as entry + + align:start position:0% +that and the the view of that as entry + + + align:start position:0% +that and the the view of that as entry +into other things we haven't done it I I + + align:start position:0% +into other things we haven't done it I I + + + align:start position:0% +into other things we haven't done it I I +I know that as far as um Personal Care + + align:start position:0% +I know that as far as um Personal Care + + + align:start position:0% +I know that as far as um Personal Care +attendance several million dollars a + + align:start position:0% +attendance several million dollars a + + + align:start position:0% +attendance several million dollars a +year are paid to people in this + + align:start position:0% +year are paid to people in this + + + align:start position:0% +year are paid to people in this +community who are personal care + + align:start position:0% +community who are personal care + + + align:start position:0% +community who are personal care +attenders for others it's quite + + align:start position:0% +attenders for others it's quite + + + align:start position:0% +attenders for others it's quite +extensive it's very important we have to + + align:start position:0% +extensive it's very important we have to + + + align:start position:0% +extensive it's very important we have to +capture + + align:start position:0% +capture + + + align:start position:0% +capture +understand it build on it and and use it + + align:start position:0% +understand it build on it and and use it + + + align:start position:0% +understand it build on it and and use it +as a jumping off point for for things I + + align:start position:0% +as a jumping off point for for things I + + + align:start position:0% +as a jumping off point for for things I +mean that's the particular thing I know + + align:start position:0% +mean that's the particular thing I know + + + align:start position:0% +mean that's the particular thing I know +about but how about in education I mean + + align:start position:0% +about but how about in education I mean + + + align:start position:0% +about but how about in education I mean +if we don't have you know if you can't + + align:start position:0% +if we don't have you know if you can't + + + align:start position:0% +if we don't have you know if you can't +look at our schools and say hey why + + align:start position:0% +look at our schools and say hey why + + + align:start position:0% +look at our schools and say hey why +aren't there more people in the + + align:start position:0% +aren't there more people in the + + + align:start position:0% +aren't there more people in the +classroom that's another thing that + + align:start position:0% +classroom that's another thing that + + + align:start position:0% +classroom that's another thing that +really needs to happen more people in + + align:start position:0% +really needs to happen more people in + + + align:start position:0% +really needs to happen more people in +the classroom and and it doesn't have to + + align:start position:0% +the classroom and and it doesn't have to + + + align:start position:0% +the classroom and and it doesn't have to +be uh everybody with master's degrees I + + align:start position:0% +be uh everybody with master's degrees I + + + align:start position:0% +be uh everybody with master's degrees I +mean there's plenty of room for other + + align:start position:0% +mean there's plenty of room for other + + + align:start position:0% +mean there's plenty of room for other +people from the community Who start + + align:start position:0% +people from the community Who start + + + align:start position:0% +people from the community Who start +getting skills and then look at at that + + align:start position:0% +getting skills and then look at at that + + + align:start position:0% +getting skills and then look at at that +as a as a way to move forward same with + + align:start position:0% +as a as a way to move forward same with + + + align:start position:0% +as a as a way to move forward same with +daycare we have home daycare providers + + align:start position:0% +daycare we have home daycare providers + + + align:start position:0% +daycare we have home daycare providers +we have institutional daycare + + align:start position:0% +we have institutional daycare + + + align:start position:0% +we have institutional daycare +providers people can come they can learn + + align:start position:0% +providers people can come they can learn + + + align:start position:0% +providers people can come they can learn +they can they can learn how to do well + + align:start position:0% +they can they can learn how to do well + + + align:start position:0% +they can they can learn how to do well +and learn Child Development and then + + align:start position:0% +and learn Child Development and then + + + align:start position:0% +and learn Child Development and then +that leads to the next step as well we + + align:start position:0% +that leads to the next step as well we + + + align:start position:0% +that leads to the next step as well we +need to focus + + align:start position:0% +need to focus + + + align:start position:0% +need to focus +and um th those are just the examples + + align:start position:0% +and um th those are just the examples + + + align:start position:0% +and um th those are just the examples +that come to me because I can see them + + align:start position:0% +that come to me because I can see them + + + align:start position:0% +that come to me because I can see them +every day one of the points that was put + + align:start position:0% +every day one of the points that was put + + + align:start position:0% +every day one of the points that was put +up under Workforce Development that I + + align:start position:0% +up under Workforce Development that I + + + align:start position:0% +up under Workforce Development that I +found pry was the the notion that that + + align:start position:0% +found pry was the the notion that that + + + align:start position:0% +found pry was the the notion that that +by uh creating a a skilled + + align:start position:0% +by uh creating a a skilled + + + align:start position:0% +by uh creating a a skilled +Workforce you would be a competitive + + align:start position:0% +Workforce you would be a competitive + + + align:start position:0% +Workforce you would be a competitive +place to attract companies who need that + + align:start position:0% +place to attract companies who need that + + + align:start position:0% +place to attract companies who need that +kind of Workforce and uh that's kind of + + align:start position:0% +kind of Workforce and uh that's kind of + + + align:start position:0% +kind of Workforce and uh that's kind of +an interesting strategy to have uh for + + align:start position:0% +an interesting strategy to have uh for + + + align:start position:0% +an interesting strategy to have uh for +one thing but but in terms of today's + + align:start position:0% +one thing but but in terms of today's + + + align:start position:0% +one thing but but in terms of today's +reality you already have a demand in the + + align:start position:0% +reality you already have a demand in the + + + align:start position:0% +reality you already have a demand in the +market which is in healthare and um to a + + align:start position:0% +market which is in healthare and um to a + + + align:start position:0% +market which is in healthare and um to a +large degree was in healthare so just + + align:start position:0% +large degree was in healthare so just + + + align:start position:0% +large degree was in healthare so just +reversing that process a little bit and + + align:start position:0% +reversing that process a little bit and + + + align:start position:0% +reversing that process a little bit and +designing program that prepare people + + align:start position:0% +designing program that prepare people + + + align:start position:0% +designing program that prepare people +for those for those jobs and uh and + + align:start position:0% +for those for those jobs and uh and + + + align:start position:0% +for those for those jobs and uh and +increasing the the awareness around the + + align:start position:0% +increasing the the awareness around the + + + align:start position:0% +increasing the the awareness around the +value of those jobs might be the + + align:start position:0% +value of those jobs might be the + + + align:start position:0% +value of those jobs might be the +incentive that people need to get + + align:start position:0% +incentive that people need to get + + + align:start position:0% +incentive that people need to get +engaged in the training I know a lot of + + align:start position:0% +engaged in the training I know a lot of + + + align:start position:0% +engaged in the training I know a lot of +the training sometimes without the + + align:start position:0% +the training sometimes without the + + + align:start position:0% +the training sometimes without the +immediacy of a job at the end of the + + align:start position:0% +immediacy of a job at the end of the + + + align:start position:0% +immediacy of a job at the end of the +training + + align:start position:0% +training + + + align:start position:0% +training +program uh is discouraging for people to + + align:start position:0% +program uh is discouraging for people to + + + align:start position:0% +program uh is discouraging for people to +enter because they're not sure of the + + align:start position:0% +enter because they're not sure of the + + + align:start position:0% +enter because they're not sure of the +pay payback for the effort and here you + + align:start position:0% +pay payback for the effort and here you + + + align:start position:0% +pay payback for the effort and here you +almost have assured Payback + + align:start position:0% + + + + align:start position:0% + +a couple questions Tim Allen again um we + + align:start position:0% +a couple questions Tim Allen again um we + + + align:start position:0% +a couple questions Tim Allen again um we +worked with Rosa a couple years ago on + + align:start position:0% +worked with Rosa a couple years ago on + + + align:start position:0% +worked with Rosa a couple years ago on +putting that adult basic Ed program + + align:start position:0% +putting that adult basic Ed program + + + align:start position:0% +putting that adult basic Ed program +together and it was an eye opener to me + + align:start position:0% +together and it was an eye opener to me + + + align:start position:0% +together and it was an eye opener to me +uh that the need for adult basic Ed and + + align:start position:0% +uh that the need for adult basic Ed and + + + align:start position:0% +uh that the need for adult basic Ed and +the the amount the percentage of the + + align:start position:0% +the the amount the percentage of the + + + align:start position:0% +the the amount the percentage of the +need that is met is about the lowest + + align:start position:0% +need that is met is about the lowest + + + align:start position:0% +need that is met is about the lowest +thing I've ever heard in this Society + + align:start position:0% +thing I've ever heard in this Society + + + align:start position:0% +thing I've ever heard in this Society +it's about 4% + + align:start position:0% +it's about 4% + + + align:start position:0% +it's about 4% +so to talk about employment + + align:start position:0% +so to talk about employment + + + align:start position:0% +so to talk about employment +possibilities for people without + + align:start position:0% +possibilities for people without + + + align:start position:0% +possibilities for people without +focusing on adult base again and + + align:start position:0% +focusing on adult base again and + + + align:start position:0% +focusing on adult base again and +increasing those services at an alarming + + align:start position:0% +increasing those services at an alarming + + + align:start position:0% +increasing those services at an alarming +rate um is so I hope you include that + + align:start position:0% +rate um is so I hope you include that + + + align:start position:0% +rate um is so I hope you include that +some some discussion of that in your + + align:start position:0% +some some discussion of that in your + + + align:start position:0% +some some discussion of that in your +study that's definitely if that didn't + + align:start position:0% +study that's definitely if that didn't + + + align:start position:0% +study that's definitely if that didn't +come through in the presentation that + + align:start position:0% +come through in the presentation that + + + align:start position:0% +come through in the presentation that +was definitely something we've been + + align:start position:0% +was definitely something we've been + + + align:start position:0% +was definitely something we've been +discussing previous to presenting for of + + align:start position:0% +discussing previous to presenting for of + + + align:start position:0% +discussing previous to presenting for of +VI is that a lot of this has to do with + + align:start position:0% +VI is that a lot of this has to do with + + + align:start position:0% +VI is that a lot of this has to do with +just that so that's on our mindes okay + + align:start position:0% +just that so that's on our mindes okay + + + align:start position:0% +just that so that's on our mindes okay +and and the second part is one thing + + align:start position:0% +and and the second part is one thing + + + align:start position:0% +and and the second part is one thing +that I've learned in the last couple + + align:start position:0% +that I've learned in the last couple + + + align:start position:0% +that I've learned in the last couple +years in step of Springfield and working + + align:start position:0% +years in step of Springfield and working + + + align:start position:0% +years in step of Springfield and working +with the Latino community and something + + align:start position:0% +with the Latino community and something + + + align:start position:0% +with the Latino community and something +you didn't speak of because you're + + align:start position:0% +you didn't speak of because you're + + + align:start position:0% +you didn't speak of because you're +speaking of the North End of geographic + + align:start position:0% +speaking of the North End of geographic + + + align:start position:0% +speaking of the North End of geographic +area but which is largely Latino is that + + align:start position:0% +area but which is largely Latino is that + + + align:start position:0% +area but which is largely Latino is that +the cultural issues you didn't really + + align:start position:0% +the cultural issues you didn't really + + + align:start position:0% +the cultural issues you didn't really +discuss and I'm not sure how much you + + align:start position:0% +discuss and I'm not sure how much you + + + align:start position:0% +discuss and I'm not sure how much you +should discuss them or how much you + + align:start position:0% +should discuss them or how much you + + + align:start position:0% +should discuss them or how much you +shouldn't but it's a very relationship + + align:start position:0% +shouldn't but it's a very relationship + + + align:start position:0% +shouldn't but it's a very relationship +based culture which doesn't respond very + + align:start position:0% +based culture which doesn't respond very + + + align:start position:0% +based culture which doesn't respond very +well to typical institutional Solutions + + align:start position:0% +well to typical institutional Solutions + + + align:start position:0% +well to typical institutional Solutions +that's my those are my words and I hope + + align:start position:0% +that's my those are my words and I hope + + + align:start position:0% +that's my those are my words and I hope +I'm not offending anyone but I I think + + align:start position:0% +I'm not offending anyone but I I think + + + align:start position:0% +I'm not offending anyone but I I think +those those kind of things need to be in + + align:start position:0% +those those kind of things need to be in + + + align:start position:0% +those those kind of things need to be in +your report and maybe maybe you should + + align:start position:0% +your report and maybe maybe you should + + + align:start position:0% +your report and maybe maybe you should +talk to some people in the North End + + align:start position:0% +talk to some people in the North End + + + align:start position:0% +talk to some people in the North End +specifically about that because we found + + align:start position:0% +specifically about that because we found + + + align:start position:0% +specifically about that because we found +it that there are certain + + align:start position:0% +it that there are certain + + + align:start position:0% +it that there are certain +characteristics in the in the Puerto + + align:start position:0% +characteristics in the in the Puerto + + + align:start position:0% +characteristics in the in the Puerto +Rican culture that are different in than + + align:start position:0% +Rican culture that are different in than + + + align:start position:0% +Rican culture that are different in than +in other cultures and how Society + + align:start position:0% +in other cultures and how Society + + + align:start position:0% +in other cultures and how Society +response to that is important if we're + + align:start position:0% +response to that is important if we're + + + align:start position:0% +response to that is important if we're +going to try to raise the level of water + + align:start position:0% +going to try to raise the level of water + + + align:start position:0% +going to try to raise the level of water +har I just wanted a comment and then I + + align:start position:0% +har I just wanted a comment and then I + + + align:start position:0% +har I just wanted a comment and then I +wanted to ask you followup question call + + align:start position:0% +wanted to ask you followup question call + + + align:start position:0% +wanted to ask you followup question call +just want to add to what Tim was just + + align:start position:0% +just want to add to what Tim was just + + + align:start position:0% +just want to add to what Tim was just +saying I think one of the concerns we + + align:start position:0% +saying I think one of the concerns we + + + align:start position:0% +saying I think one of the concerns we +have is very clearly based on the + + align:start position:0% +have is very clearly based on the + + + align:start position:0% +have is very clearly based on the +message the distribution of the message + + align:start position:0% +message the distribution of the message + + + align:start position:0% +message the distribution of the message +and who is the + + align:start position:0% +and who is the + + + align:start position:0% +and who is the +recipient of that message that is really + + align:start position:0% +recipient of that message that is really + + + align:start position:0% +recipient of that message that is really +I think at the heart of a little bit of + + align:start position:0% +I think at the heart of a little bit of + + + align:start position:0% +I think at the heart of a little bit of +what Tim was talking about I can presume + + align:start position:0% +what Tim was talking about I can presume + + + align:start position:0% +what Tim was talking about I can presume +to interpret but that I think that's + + align:start position:0% +to interpret but that I think that's + + + align:start position:0% +to interpret but that I think that's +also very very CRI for us to be + + align:start position:0% +also very very CRI for us to be + + + align:start position:0% +also very very CRI for us to be +effective and helping to be part of the + + align:start position:0% +effective and helping to be part of the + + + align:start position:0% +effective and helping to be part of the +solution + + align:start position:0% + + + + align:start position:0% + +I wonder if you could speak to your + + align:start position:0% +I wonder if you could speak to your + + + align:start position:0% +I wonder if you could speak to your +experience little detail what are the + + align:start position:0% +experience little detail what are the + + + align:start position:0% +experience little detail what are the +ways in which you've been able to + + align:start position:0% +ways in which you've been able to + + + align:start position:0% +ways in which you've been able to +overcome that sense that the traditional + + align:start position:0% +overcome that sense that the traditional + + + align:start position:0% +overcome that sense that the traditional +institutional setups don't work for this + + align:start position:0% +institutional setups don't work for this + + + align:start position:0% +institutional setups don't work for this +neighborhood well I'm on a big learning + + align:start position:0% +neighborhood well I'm on a big learning + + + align:start position:0% +neighborhood well I'm on a big learning +curve and some people could tell could + + align:start position:0% +curve and some people could tell could + + + align:start position:0% +curve and some people could tell could +you know could certainly validate that + + align:start position:0% +you know could certainly validate that + + + align:start position:0% +you know could certainly validate that +in here because I work with some people + + align:start position:0% +in here because I work with some people + + + align:start position:0% +in here because I work with some people +in here and I don't profess to have + + align:start position:0% +in here and I don't profess to have + + + align:start position:0% +in here and I don't profess to have +Solutions but I I do feel that + + align:start position:0% +Solutions but I I do feel that + + + align:start position:0% +Solutions but I I do feel that +um you know Allan offered the mcdi + + align:start position:0% +um you know Allan offered the mcdi + + + align:start position:0% +um you know Allan offered the mcdi +solution and Rose's response was it's + + align:start position:0% +solution and Rose's response was it's + + + align:start position:0% +solution and Rose's response was it's +not close and that I can't I can't + + align:start position:0% +not close and that I can't I can't + + + align:start position:0% +not close and that I can't I can't +magnify that answer enough um that uh + + align:start position:0% +magnify that answer enough um that uh + + + align:start position:0% +magnify that answer enough um that uh +that's a wonderful mcdi and Regional + + align:start position:0% +that's a wonderful mcdi and Regional + + + align:start position:0% +that's a wonderful mcdi and Regional +employment board they're all wonderful + + align:start position:0% +employment board they're all wonderful + + + align:start position:0% +employment board they're all wonderful +Solutions but if people don't feel like + + align:start position:0% +Solutions but if people don't feel like + + + align:start position:0% +Solutions but if people don't feel like +they know what they are or that they can + + align:start position:0% +they know what they are or that they can + + + align:start position:0% +they know what they are or that they can +personally relate or that there aren't + + align:start position:0% +personally relate or that there aren't + + + align:start position:0% +personally relate or that there aren't +steps that somehow show that if I do + + align:start position:0% +steps that somehow show that if I do + + + align:start position:0% +steps that somehow show that if I do +this then I do this then I do this then + + align:start position:0% +this then I do this then I do this then + + + align:start position:0% +this then I do this then I do this then +I do this and then that opportunity + + align:start position:0% +I do this and then that opportunity + + + align:start position:0% +I do this and then that opportunity +might be available to + + align:start position:0% +might be available to + + + align:start position:0% +might be available to +without that type of coaching and + + align:start position:0% +without that type of coaching and + + + align:start position:0% +without that type of coaching and +mentoring and understanding of where + + align:start position:0% +mentoring and understanding of where + + + align:start position:0% +mentoring and understanding of where +people are we're going to still have a + + align:start position:0% +people are we're going to still have a + + + align:start position:0% +people are we're going to still have a +gap and um I I'm not probably not giving + + align:start position:0% +gap and um I I'm not probably not giving + + + align:start position:0% +gap and um I I'm not probably not giving +you good examples Peter Jeff other + + align:start position:0% +you good examples Peter Jeff other + + + align:start position:0% +you good examples Peter Jeff other +people who lived in this community work + + align:start position:0% +people who lived in this community work + + + align:start position:0% +people who lived in this community work +in this community could certainly do a + + align:start position:0% +in this community could certainly do a + + + align:start position:0% +in this community could certainly do a +better job than me Rosa Mila but those + + align:start position:0% +better job than me Rosa Mila but those + + + align:start position:0% +better job than me Rosa Mila but those +are my + + align:start position:0% +are my + + + align:start position:0% +are my +perceptions that I think are worth + + align:start position:0% +perceptions that I think are worth + + + align:start position:0% +perceptions that I think are worth +probably a little more + + align:start position:0% +probably a little more + + + align:start position:0% +probably a little more +investigation I think you you need to + + align:start position:0% +investigation I think you you need to + + + align:start position:0% +investigation I think you you need to +also investigate how the + + align:start position:0% +also investigate how the + + + align:start position:0% +also investigate how the +state um did be out the money about + + align:start position:0% +state um did be out the money about + + + align:start position:0% +state um did be out the money about +education this time and what happened to + + align:start position:0% +education this time and what happened to + + + align:start position:0% +education this time and what happened to +the institutions that applied for that + + align:start position:0% +the institutions that applied for that + + + align:start position:0% +the institutions that applied for that +money uh this time and mcdi clearly + + align:start position:0% +money uh this time and mcdi clearly + + + align:start position:0% +money uh this time and mcdi clearly +guarded The major portion of the funding + + align:start position:0% +guarded The major portion of the funding + + + align:start position:0% +guarded The major portion of the funding +for spr and so some who traditional + + align:start position:0% +for spr and so some who traditional + + + align:start position:0% +for spr and so some who traditional +adult education providers who were + + align:start position:0% +adult education providers who were + + + align:start position:0% +adult education providers who were +culturally connected to the community + + align:start position:0% +culturally connected to the community + + + align:start position:0% +culturally connected to the community +were left + + align:start position:0% +were left + + + align:start position:0% +were left +out and that's a + + align:start position:0% +out and that's a + + + align:start position:0% +out and that's a +significant institution that was left + + align:start position:0% +significant institution that was left + + + align:start position:0% +significant institution that was left +out this time and there's been no result + + align:start position:0% +out this time and there's been no result + + + align:start position:0% +out this time and there's been no result +them how to get them back in and that's + + align:start position:0% +them how to get them back in and that's + + + align:start position:0% +them how to get them back in and that's +that's + + align:start position:0% + + + + align:start position:0% + +important can we um I'd like to pick up + + align:start position:0% +important can we um I'd like to pick up + + + align:start position:0% +important can we um I'd like to pick up +on something that Katie said um and to + + align:start position:0% +on something that Katie said um and to + + + align:start position:0% +on something that Katie said um and to +and and go over to the um real estate + + align:start position:0% +and and go over to the um real estate + + + align:start position:0% +and and go over to the um real estate +aspect which I think we would leave + + align:start position:0% +aspect which I think we would leave + + + align:start position:0% +aspect which I think we would leave +alone if we could um there's a lot of + + align:start position:0% +alone if we could um there's a lot of + + + align:start position:0% +alone if we could um there's a lot of +property um was saying something about + + align:start position:0% +property um was saying something about + + + align:start position:0% +property um was saying something about +uh Blitz developing or getting uh large + + align:start position:0% +uh Blitz developing or getting uh large + + + align:start position:0% +uh Blitz developing or getting uh large +groups develop but really what + + align:start position:0% + + + + align:start position:0% + +about + + align:start position:0% +about + + + align:start position:0% +about +Community uh based planning for that + + align:start position:0% +Community uh based planning for that + + + align:start position:0% +Community uh based planning for that +property communitybased control over + + align:start position:0% +property communitybased control over + + + align:start position:0% +property communitybased control over +that property it's a tremendous problem + + align:start position:0% +that property it's a tremendous problem + + + align:start position:0% +that property it's a tremendous problem +for us you you know you can't really + + align:start position:0% +for us you you know you can't really + + + align:start position:0% +for us you you know you can't really +move ahead it if things were going + + align:start position:0% +move ahead it if things were going + + + align:start position:0% +move ahead it if things were going +better halfhazard community development + + align:start position:0% +better halfhazard community development + + + align:start position:0% +better halfhazard community development +would would be okay because the the the + + align:start position:0% +would would be okay because the the the + + + align:start position:0% +would would be okay because the the the +environment around that haphazard + + align:start position:0% +environment around that haphazard + + + align:start position:0% +environment around that haphazard +development would dictate what's + + align:start position:0% +development would dictate what's + + + align:start position:0% +development would dictate what's +happening we need to we need to figure + + align:start position:0% +happening we need to we need to figure + + + align:start position:0% +happening we need to we need to figure +out how to get control over those + + align:start position:0% +out how to get control over those + + + align:start position:0% +out how to get control over those +properties or how to get control over + + align:start position:0% +properties or how to get control over + + + align:start position:0% +properties or how to get control over +what kind of developments H H + + align:start position:0% +what kind of developments H H + + + align:start position:0% +what kind of developments H H +development happens in those properties + + align:start position:0% +development happens in those properties + + + align:start position:0% +development happens in those properties +and sort of instead of the first thing + + align:start position:0% +and sort of instead of the first thing + + + align:start position:0% +and sort of instead of the first thing +being Blitz development how about H + + align:start position:0% +being Blitz development how about H + + + align:start position:0% +being Blitz development how about H +helping us figure out how to get control + + align:start position:0% +helping us figure out how to get control + + + align:start position:0% +helping us figure out how to get control +control over it I know that other places + + align:start position:0% +control over it I know that other places + + + align:start position:0% +control over it I know that other places +have done it in Dudley Street they + + align:start position:0% +have done it in Dudley Street they + + + align:start position:0% +have done it in Dudley Street they +actually figured out a way to do it and + + align:start position:0% +actually figured out a way to do it and + + + align:start position:0% +actually figured out a way to do it and +implemented it and it is a success for + + align:start position:0% +implemented it and it is a success for + + + align:start position:0% +implemented it and it is a success for +all of us to look at today um there are + + align:start position:0% +all of us to look at today um there are + + + align:start position:0% +all of us to look at today um there are +uh Community Development corporations + + align:start position:0% +uh Community Development corporations + + + align:start position:0% +uh Community Development corporations +that could take the lead on that new + + align:start position:0% +that could take the lead on that new + + + align:start position:0% +that could take the lead on that new +ones or established ones but anyone that + + align:start position:0% +ones or established ones but anyone that + + + align:start position:0% +ones or established ones but anyone that +is who has the North End development in + + align:start position:0% +is who has the North End development in + + + align:start position:0% +is who has the North End development in +in as their first priority and there are + + align:start position:0% +in as their first priority and there are + + + align:start position:0% +in as their first priority and there are +other things I mean we talked to um + + align:start position:0% +other things I mean we talked to um + + + align:start position:0% +other things I mean we talked to um +we've talked with Gus newort about and + + align:start position:0% +we've talked with Gus newort about and + + + align:start position:0% +we've talked with Gus newort about and +and with and SAU was uh working on + + align:start position:0% +and with and SAU was uh working on + + + align:start position:0% +and with and SAU was uh working on +Community Land trusts I don't know Co I + + align:start position:0% +Community Land trusts I don't know Co I + + + align:start position:0% +Community Land trusts I don't know Co I +don't know what the best way to do that + + align:start position:0% +don't know what the best way to do that + + + align:start position:0% +don't know what the best way to do that +is but if we could get started with a + + align:start position:0% +is but if we could get started with a + + + align:start position:0% +is but if we could get started with a +strategy of how to capture that land + + align:start position:0% +strategy of how to capture that land + + + align:start position:0% +strategy of how to capture that land +that needs to be developed and then + + align:start position:0% +that needs to be developed and then + + + align:start position:0% +that needs to be developed and then +start developing it as a um with a plan + + align:start position:0% +start developing it as a um with a plan + + + align:start position:0% +start developing it as a um with a plan +I mean I think that's where we need to + + align:start position:0% +I mean I think that's where we need to + + + align:start position:0% +I mean I think that's where we need to +start this is not so different than than + + align:start position:0% +start this is not so different than than + + + align:start position:0% +start this is not so different than than +happened 30 years I agree with you I + + align:start position:0% +happened 30 years I agree with you I + + + align:start position:0% +happened 30 years I agree with you I +guess my my original point was I don't + + align:start position:0% +guess my my original point was I don't + + + align:start position:0% +guess my my original point was I don't +think we have a local CDC or something + + align:start position:0% +think we have a local CDC or something + + + align:start position:0% +think we have a local CDC or something +set up right now that can do that but I + + align:start position:0% +set up right now that can do that but I + + + align:start position:0% +set up right now that can do that but I +guess one yeah exactly but we need one + + align:start position:0% +guess one yeah exactly but we need one + + + align:start position:0% +guess one yeah exactly but we need one +because that is the first step we have + + align:start position:0% +because that is the first step we have + + + align:start position:0% +because that is the first step we have +to take so that we do have the local + + align:start position:0% +to take so that we do have the local + + + align:start position:0% +to take so that we do have the local +control I meant a big Builder would + + align:start position:0% +control I meant a big Builder would + + + align:start position:0% +control I meant a big Builder would +implement it but that we do need to CDC + + align:start position:0% +implement it but that we do need to CDC + + + align:start position:0% +implement it but that we do need to CDC +and we need to and actually that in this + + align:start position:0% +and we need to and actually that in this + + + align:start position:0% +and we need to and actually that in this +neighborhood those scattered properties + + align:start position:0% +neighborhood those scattered properties + + + align:start position:0% +neighborhood those scattered properties +and and the history of what Dudley + + align:start position:0% +and and the history of what Dudley + + + align:start position:0% +and and the history of what Dudley +Street did might give us some good some + + align:start position:0% +Street did might give us some good some + + + align:start position:0% +Street did might give us some good some +good lessons I I don't know if they all + + align:start position:0% +good lessons I I don't know if they all + + + align:start position:0% +good lessons I I don't know if they all +apply but just a couple of other things + + align:start position:0% +apply but just a couple of other things + + + align:start position:0% +apply but just a couple of other things +that have been discussed in this regard + + align:start position:0% +that have been discussed in this regard + + + align:start position:0% +that have been discussed in this regard +this the housing issue has been + + align:start position:0% +this the housing issue has been + + + align:start position:0% +this the housing issue has been +discussed that very recently over the + + align:start position:0% +discussed that very recently over the + + + align:start position:0% +discussed that very recently over the +past few or four months and in several + + align:start position:0% +past few or four months and in several + + + align:start position:0% +past few or four months and in several +neighborhoods in the city not just the + + align:start position:0% +neighborhoods in the city not just the + + + align:start position:0% +neighborhoods in the city not just the +north end but applies obviously here um + + align:start position:0% +north end but applies obviously here um + + + align:start position:0% +north end but applies obviously here um +very well and and one of the one of the + + align:start position:0% +very well and and one of the one of the + + + align:start position:0% +very well and and one of the one of the +issues discussed often is the need for + + align:start position:0% +issues discussed often is the need for + + + align:start position:0% +issues discussed often is the need for +code enforcement so the properties that + + align:start position:0% +code enforcement so the properties that + + + align:start position:0% +code enforcement so the properties that +do exist today are up to code and that + + align:start position:0% +do exist today are up to code and that + + + align:start position:0% +do exist today are up to code and that +that has a way of putting pressure on + + align:start position:0% +that has a way of putting pressure on + + + align:start position:0% +that has a way of putting pressure on +lands to make sure that they forced to + + align:start position:0% +lands to make sure that they forced to + + + align:start position:0% +lands to make sure that they forced to +be up to C and rents and other things + + align:start position:0% +be up to C and rents and other things + + + align:start position:0% +be up to C and rents and other things +kind of uh rise to the levels they + + align:start position:0% +kind of uh rise to the levels they + + + align:start position:0% +kind of uh rise to the levels they +should be in order for them to support + + align:start position:0% +should be in order for them to support + + + align:start position:0% +should be in order for them to support +the the structure that encourages other + + align:start position:0% +the the structure that encourages other + + + align:start position:0% +the the structure that encourages other +development because it increases land + + align:start position:0% +development because it increases land + + + align:start position:0% +development because it increases land +values and encourages those others to + + align:start position:0% +values and encourages those others to + + + align:start position:0% +values and encourages those others to +make investments that's one point + + align:start position:0% +make investments that's one point + + + align:start position:0% +make investments that's one point +another point to just keep in mind as + + align:start position:0% +another point to just keep in mind as + + + align:start position:0% +another point to just keep in mind as +you look at this is that the city has + + align:start position:0% +you look at this is that the city has + + + align:start position:0% +you look at this is that the city has +this + + align:start position:0% +this + + + align:start position:0% +this +overarching imperative to raise revenue + + align:start position:0% +overarching imperative to raise revenue + + + align:start position:0% +overarching imperative to raise revenue +and and the disposition of these vacant + + align:start position:0% +and and the disposition of these vacant + + + align:start position:0% +and and the disposition of these vacant +Parcels is U is being viewed I think + + align:start position:0% +Parcels is U is being viewed I think + + + align:start position:0% +Parcels is U is being viewed I think +both as a means of regenerating the + + align:start position:0% +both as a means of regenerating the + + + align:start position:0% +both as a means of regenerating the +neighborhood but also recapturing some + + align:start position:0% +neighborhood but also recapturing some + + + align:start position:0% +neighborhood but also recapturing some +Revenue lost through the tax title + + align:start position:0% +Revenue lost through the tax title + + + align:start position:0% +Revenue lost through the tax title +procedures and otherwise so that the + + align:start position:0% +procedures and otherwise so that the + + + align:start position:0% +procedures and otherwise so that the +effect of a of a of a Community + + align:start position:0% +effect of a of a of a Community + + + align:start position:0% +effect of a of a of a Community +Development organization to be created + + align:start position:0% +Development organization to be created + + + align:start position:0% +Development organization to be created +to acquire control plan so on would have + + align:start position:0% +to acquire control plan so on would have + + + align:start position:0% +to acquire control plan so on would have +to be done in this in this environment + + align:start position:0% +to be done in this in this environment + + + align:start position:0% +to be done in this in this environment +of acute pressure on Revenue which is + + align:start position:0% +of acute pressure on Revenue which is + + + align:start position:0% +of acute pressure on Revenue which is +one of the reasons why you go out to bid + + align:start position:0% +one of the reasons why you go out to bid + + + align:start position:0% +one of the reasons why you go out to bid +and hope the market will increase the + + align:start position:0% +and hope the market will increase the + + + align:start position:0% +and hope the market will increase the +values and you maximize the revenue so + + align:start position:0% +values and you maximize the revenue so + + + align:start position:0% +values and you maximize the revenue so +that's the backdrop for the current + + align:start position:0% +that's the backdrop for the current + + + align:start position:0% +that's the backdrop for the current +environment that we're in in the city + + align:start position:0% +environment that we're in in the city + + + align:start position:0% +environment that we're in in the city +and that affects a lot of the decisions + + align:start position:0% +and that affects a lot of the decisions + + + align:start position:0% +and that affects a lot of the decisions +being we have to we have to keep in mind + + align:start position:0% +being we have to we have to keep in mind + + + align:start position:0% +being we have to we have to keep in mind +the other thing that you've told us is + + align:start position:0% +the other thing that you've told us is + + + align:start position:0% +the other thing that you've told us is +that if we have 133% home + + align:start position:0% +that if we have 133% home + + + align:start position:0% +that if we have 133% home +ownership and then you throw everything + + align:start position:0% +ownership and then you throw everything + + + align:start position:0% +ownership and then you throw everything +out to bid we'll wind up with 5% home + + align:start position:0% +out to bid we'll wind up with 5% home + + + align:start position:0% +out to bid we'll wind up with 5% home +ownership so that and we're no we're + + align:start position:0% +ownership so that and we're no we're + + + align:start position:0% +ownership so that and we're no we're +going nowhere that way we go nowhere + + align:start position:0% +going nowhere that way we go nowhere + + + align:start position:0% +going nowhere that way we go nowhere +without home ownership we go nowhere + + align:start position:0% +without home ownership we go nowhere + + + align:start position:0% +without home ownership we go nowhere +without Safe Streets and we go nowhere + + align:start position:0% +without Safe Streets and we go nowhere + + + align:start position:0% +without Safe Streets and we go nowhere +without our kids being educated nowhere + + align:start position:0% +without our kids being educated nowhere + + + align:start position:0% +without our kids being educated nowhere +and if if Economic Development doesn't + + align:start position:0% +and if if Economic Development doesn't + + + align:start position:0% +and if if Economic Development doesn't +have a basis in those things you know we + + align:start position:0% +have a basis in those things you know we + + + align:start position:0% +have a basis in those things you know we +but Jeff let me say all the properties + + align:start position:0% +but Jeff let me say all the properties + + + align:start position:0% +but Jeff let me say all the properties +we put out for bid for the SRA and for + + align:start position:0% +we put out for bid for the SRA and for + + + align:start position:0% +we put out for bid for the SRA and for +tax title are required to be home + + align:start position:0% +tax title are required to be home + + + align:start position:0% +tax title are required to be home +ownership units and everything we got + + align:start position:0% +ownership units and everything we got + + + align:start position:0% +ownership units and everything we got +out right now we're requiring single + + align:start position:0% +out right now we're requiring single + + + align:start position:0% +out right now we're requiring single +family homes requiring home ownership + + align:start position:0% +family homes requiring home ownership + + + align:start position:0% +family homes requiring home ownership +and we require to improve of all designs + + align:start position:0% +and we require to improve of all designs + + + align:start position:0% +and we require to improve of all designs +site plans Etc of every unit so that you + + align:start position:0% +site plans Etc of every unit so that you + + + align:start position:0% +site plans Etc of every unit so that you +know they're building attractive housing + + align:start position:0% +know they're building attractive housing + + + align:start position:0% +know they're building attractive housing +so at least there is a level of control + + align:start position:0% +so at least there is a level of control + + + align:start position:0% +so at least there is a level of control +now it's through City Hall but certainly + + align:start position:0% +now it's through City Hall but certainly + + + align:start position:0% +now it's through City Hall but certainly +the planning department is making sure + + align:start position:0% +the planning department is making sure + + + align:start position:0% +the planning department is making sure +that it is it is increasing home + + align:start position:0% +that it is it is increasing home + + + align:start position:0% +that it is it is increasing home +ownership and ownership over the + + align:start position:0% +ownership and ownership over the + + + align:start position:0% +ownership and ownership over the +neighborhood be grateful for the work + + align:start position:0% +neighborhood be grateful for the work + + + align:start position:0% +neighborhood be grateful for the work +that the planning department has done + + align:start position:0% +that the planning department has done + + + align:start position:0% +that the planning department has done +for us in this there's no question about + + align:start position:0% +for us in this there's no question about + + + align:start position:0% +for us in this there's no question about +it but we can do on a small scale we + + align:start position:0% +it but we can do on a small scale we + + + align:start position:0% +it but we can do on a small scale we +just need to think about the future and + + align:start position:0% +just need to think about the future and + + + align:start position:0% +just need to think about the future and +taking this neighborhood from where it + + align:start position:0% +taking this neighborhood from where it + + + align:start position:0% +taking this neighborhood from where it +is to one that has um more of the things + + align:start position:0% +is to one that has um more of the things + + + align:start position:0% +is to one that has um more of the things +that will allow our our folks to to live + + align:start position:0% +that will allow our our folks to to live + + + align:start position:0% +that will allow our our folks to to live +better lives we have to do that I think + + align:start position:0% +better lives we have to do that I think + + + align:start position:0% +better lives we have to do that I think +from our perspective as a class this + + align:start position:0% +from our perspective as a class this + + + align:start position:0% +from our perspective as a class this +conversation is really exciting and it + + align:start position:0% +conversation is really exciting and it + + + align:start position:0% +conversation is really exciting and it +sort of reinforces or underscores the + + align:start position:0% +sort of reinforces or underscores the + + + align:start position:0% +sort of reinforces or underscores the +need to create some kind of Advisory + + align:start position:0% +need to create some kind of Advisory + + + align:start position:0% +need to create some kind of Advisory +Group just on real estate I think that + + align:start position:0% +Group just on real estate I think that + + + align:start position:0% +Group just on real estate I think that +there was much less of a diversity of + + align:start position:0% +there was much less of a diversity of + + + align:start position:0% +there was much less of a diversity of +opinion I think there was much more + + align:start position:0% +opinion I think there was much more + + + align:start position:0% +opinion I think there was much more +convergence on what to do on education + + align:start position:0% +convergence on what to do on education + + + align:start position:0% +convergence on what to do on education +and Workforce Development but I think + + align:start position:0% +and Workforce Development but I think + + + align:start position:0% +and Workforce Development but I think +creating community control as well as a + + align:start position:0% +creating community control as well as a + + + align:start position:0% +creating community control as well as a +solid asset base for the community is + + align:start position:0% +solid asset base for the community is + + + align:start position:0% +solid asset base for the community is +much more complex in some senses what + + align:start position:0% +much more complex in some senses what + + + align:start position:0% +much more complex in some senses what +the right balance of political and + + align:start position:0% +the right balance of political and + + + align:start position:0% +the right balance of political and +economic strategies might be where there + + align:start position:0% +economic strategies might be where there + + + align:start position:0% +economic strategies might be where there +might exist stary opportunities um + + align:start position:0% +might exist stary opportunities um + + + align:start position:0% +might exist stary opportunities um +really would require us to have a little + + align:start position:0% +really would require us to have a little + + + align:start position:0% +really would require us to have a little +more guidance so again I just want to + + align:start position:0% +more guidance so again I just want to + + + align:start position:0% +more guidance so again I just want to +suggest that from our perspective this + + align:start position:0% +suggest that from our perspective this + + + align:start position:0% +suggest that from our perspective this +is one way to move forward is to really + + align:start position:0% +is one way to move forward is to really + + + align:start position:0% +is one way to move forward is to really +begin to bring together people from at + + align:start position:0% +begin to bring together people from at + + + align:start position:0% +begin to bring together people from at +least this room on this one question we + + align:start position:0% +least this room on this one question we + + + align:start position:0% +least this room on this one question we +will will work with you as effectively + + align:start position:0% +will will work with you as effectively + + + align:start position:0% +will will work with you as effectively +as we can \ No newline at end of file diff --git a/K0_VieRmuq4.txt b/K0_VieRmuq4.txt new file mode 100644 index 0000000000000000000000000000000000000000..06d22518a2ad2fff71de028464f0c238f420df7e --- /dev/null +++ b/K0_VieRmuq4.txt @@ -0,0 +1,1395 @@ +align:start position:0% + +we think about conventional activities + + align:start position:0% +we think about conventional activities + + + align:start position:0% +we think about conventional activities +to expand thematic and conceptual + + align:start position:0% +to expand thematic and conceptual + + + align:start position:0% +to expand thematic and conceptual +exploration so the traditional ways or + + align:start position:0% +exploration so the traditional ways or + + + align:start position:0% +exploration so the traditional ways or +maybe more conventional agent might + + align:start position:0% +maybe more conventional agent might + + + align:start position:0% +maybe more conventional agent might +think about art education or learning + + align:start position:0% +think about art education or learning + + + align:start position:0% +think about art education or learning +studio practices sculpture working with + + align:start position:0% +studio practices sculpture working with + + + align:start position:0% +studio practices sculpture working with +clay working with wood working with + + align:start position:0% +clay working with wood working with + + + align:start position:0% +clay working with wood working with +paint or drawing practices those are + + align:start position:0% +paint or drawing practices those are + + + align:start position:0% +paint or drawing practices those are +fine if we want to develop a set of + + align:start position:0% +fine if we want to develop a set of + + + align:start position:0% +fine if we want to develop a set of +skills but what about thinking about + + align:start position:0% +skills but what about thinking about + + + align:start position:0% +skills but what about thinking about +concepts and themes and issues well you + + align:start position:0% +concepts and themes and issues well you + + + align:start position:0% +concepts and themes and issues well you +might as well get started and do some of + + align:start position:0% +might as well get started and do some of + + + align:start position:0% +might as well get started and do some of +that now so we're gonna make a little + + align:start position:0% +that now so we're gonna make a little + + + align:start position:0% +that now so we're gonna make a little +transition I'm gonna set up a still-life + + align:start position:0% +transition I'm gonna set up a still-life + + + align:start position:0% +transition I'm gonna set up a still-life +over here and we're going to do some + + align:start position:0% +over here and we're going to do some + + + align:start position:0% +over here and we're going to do some +drawing I don't the range of ways in + + align:start position:0% +drawing I don't the range of ways in + + + align:start position:0% +drawing I don't the range of ways in +which people draw is perfectly + + align:start position:0% +which people draw is perfectly + + + align:start position:0% +which people draw is perfectly +acceptable perfectly acceptable so if + + align:start position:0% +acceptable perfectly acceptable so if + + + align:start position:0% +acceptable perfectly acceptable so if +you're a concern that you it's tough for + + align:start position:0% +you're a concern that you it's tough for + + + align:start position:0% +you're a concern that you it's tough for +you to draw a conclusion or draw a + + align:start position:0% +you to draw a conclusion or draw a + + + align:start position:0% +you to draw a conclusion or draw a +straight line don't be concerned by that + + align:start position:0% +straight line don't be concerned by that + + + align:start position:0% +straight line don't be concerned by that +it's the process that we're interested + + align:start position:0% +it's the process that we're interested + + + align:start position:0% +it's the process that we're interested +in not the visual representation we have + + align:start position:0% +in not the visual representation we have + + + align:start position:0% +in not the visual representation we have +the three chairs in the center with your + + align:start position:0% +the three chairs in the center with your + + + align:start position:0% +the three chairs in the center with your +marker I would like you to to draw what + + align:start position:0% +marker I would like you to to draw what + + + align:start position:0% +marker I would like you to to draw what +you see and you can draw it on this + + align:start position:0% +you see and you can draw it on this + + + align:start position:0% +you see and you can draw it on this +paper the way that it makes sense to you + + align:start position:0% +paper the way that it makes sense to you + + + align:start position:0% +paper the way that it makes sense to you +if you want to draw it as large as you + + align:start position:0% +if you want to draw it as large as you + + + align:start position:0% +if you want to draw it as large as you +can that's great if you want to draw it + + align:start position:0% +can that's great if you want to draw it + + + align:start position:0% +can that's great if you want to draw it +smaller that's fine but here's our still + + align:start position:0% +smaller that's fine but here's our still + + + align:start position:0% +smaller that's fine but here's our still +if these three chairs kind of sitting in + + align:start position:0% +if these three chairs kind of sitting in + + + align:start position:0% +if these three chairs kind of sitting in +relationship to each other will take + + align:start position:0% +relationship to each other will take + + + align:start position:0% +relationship to each other will take +about eight to ten minutes to draw this + + align:start position:0% +about eight to ten minutes to draw this + + + align:start position:0% +about eight to ten minutes to draw this +oh but there's one thing this is my is + + align:start position:0% +oh but there's one thing this is my is + + + align:start position:0% +oh but there's one thing this is my is +one more thing you'll draw for thirty + + align:start position:0% +one more thing you'll draw for thirty + + + align:start position:0% +one more thing you'll draw for thirty +seconds at a time and then after your 30 + + align:start position:0% +seconds at a time and then after your 30 + + + align:start position:0% +seconds at a time and then after your 30 +seconds is over I have another task for + + align:start position:0% +seconds is over I have another task for + + + align:start position:0% +seconds is over I have another task for +you okay so you're gonna draw the chairs + + align:start position:0% +you okay so you're gonna draw the chairs + + + align:start position:0% +you okay so you're gonna draw the chairs +for 30 seconds and then I'll give you + + align:start position:0% +for 30 seconds and then I'll give you + + + align:start position:0% +for 30 seconds and then I'll give you +another step to continue your drawing + + align:start position:0% +another step to continue your drawing + + + align:start position:0% +another step to continue your drawing +got it alright so when you ready set go + + align:start position:0% +got it alright so when you ready set go + + + align:start position:0% +got it alright so when you ready set go +it's not a race I you just go time + + align:start position:0% +it's not a race I you just go time + + + align:start position:0% +it's not a race I you just go time +starts now + + align:start position:0% +starts now + + + align:start position:0% +starts now +[Applause] + + align:start position:0% + + + + align:start position:0% + +try to put in as much information as you + + align:start position:0% +try to put in as much information as you + + + align:start position:0% +try to put in as much information as you +can all right stop stop now what you're + + align:start position:0% +can all right stop stop now what you're + + + align:start position:0% +can all right stop stop now what you're +gonna have to do is slide back and your + + align:start position:0% +gonna have to do is slide back and your + + + align:start position:0% +gonna have to do is slide back and your +chair slide back a little bit and then + + align:start position:0% +chair slide back a little bit and then + + + align:start position:0% +chair slide back a little bit and then +stand up and then move one drawing to + + align:start position:0% +stand up and then move one drawing to + + + align:start position:0% +stand up and then move one drawing to +the left so now you're standing in front + + align:start position:0% +the left so now you're standing in front + + + align:start position:0% +the left so now you're standing in front +of somebody else's drawing to the left + + align:start position:0% +of somebody else's drawing to the left + + + align:start position:0% +of somebody else's drawing to the left +okay standing prints the next pert near + + align:start position:0% +okay standing prints the next pert near + + + align:start position:0% +okay standing prints the next pert near +that next drawing all right now keep + + align:start position:0% +that next drawing all right now keep + + + align:start position:0% +that next drawing all right now keep +drawing continue the drawing that this + + align:start position:0% +drawing continue the drawing that this + + + align:start position:0% +drawing continue the drawing that this +other person has started go + + align:start position:0% + + + + align:start position:0% + +all right stop move did you learn + + align:start position:0% +all right stop move did you learn + + + align:start position:0% +all right stop move did you learn +something about drawing from other + + align:start position:0% +something about drawing from other + + + align:start position:0% +something about drawing from other +people's drawings like as you went + + align:start position:0% +people's drawings like as you went + + + align:start position:0% +people's drawings like as you went +through it nice at times oh there was + + align:start position:0% +through it nice at times oh there was + + + align:start position:0% +through it nice at times oh there was +some things happening at this new + + align:start position:0% +some things happening at this new + + + align:start position:0% +some things happening at this new +drawing that you're sitting at that you + + align:start position:0% +drawing that you're sitting at that you + + + align:start position:0% +drawing that you're sitting at that you +hadn't thought about that maybe he tried + + align:start position:0% +hadn't thought about that maybe he tried + + + align:start position:0% +hadn't thought about that maybe he tried +to replicate or he tried to avoid my + + align:start position:0% +to replicate or he tried to avoid my + + + align:start position:0% +to replicate or he tried to avoid my +attitude toward what I was doing changed + + align:start position:0% +attitude toward what I was doing changed + + + align:start position:0% +attitude toward what I was doing changed +rather markedly in different parts of + + align:start position:0% +rather markedly in different parts of + + + align:start position:0% +rather markedly in different parts of +the circle so I started out with trying + + align:start position:0% +the circle so I started out with trying + + + align:start position:0% +the circle so I started out with trying +to take the assignment literally and I + + align:start position:0% +to take the assignment literally and I + + + align:start position:0% +to take the assignment literally and I +assumed that somebody else that's their + + align:start position:0% +assumed that somebody else that's their + + + align:start position:0% +assumed that somebody else that's their +representation of that it's my job to + + align:start position:0% +representation of that it's my job to + + + align:start position:0% +representation of that it's my job to +come to Edie to complete their + + align:start position:0% +come to Edie to complete their + + + align:start position:0% +come to Edie to complete their +representation but about over there by + + align:start position:0% +representation but about over there by + + + align:start position:0% +representation but about over there by +that time since I couldn't figure their + + align:start position:0% +that time since I couldn't figure their + + + align:start position:0% +that time since I couldn't figure their +representation relative to what I was + + align:start position:0% +representation relative to what I was + + + align:start position:0% +representation relative to what I was +looking at that I finally decided well I + + align:start position:0% +looking at that I finally decided well I + + + align:start position:0% +looking at that I finally decided well I +could contribute something to this but + + align:start position:0% +could contribute something to this but + + + align:start position:0% +could contribute something to this but +it isn't their representation that I'm + + align:start position:0% +it isn't their representation that I'm + + + align:start position:0% +it isn't their representation that I'm +helping to finish I'll just focus on + + align:start position:0% +helping to finish I'll just focus on + + + align:start position:0% +helping to finish I'll just focus on +adding solid services to ones that don't + + align:start position:0% +adding solid services to ones that don't + + + align:start position:0% +adding solid services to ones that don't +have solid services because clearly + + align:start position:0% +have solid services because clearly + + + align:start position:0% +have solid services because clearly +there's some solid services so as I + + align:start position:0% +there's some solid services so as I + + + align:start position:0% +there's some solid services so as I +moved along I was making sure I added + + align:start position:0% +moved along I was making sure I added + + + align:start position:0% +moved along I was making sure I added +something but I wasn't any longer trying + + align:start position:0% +something but I wasn't any longer trying + + + align:start position:0% +something but I wasn't any longer trying +to complete what the message was that + + align:start position:0% +to complete what the message was that + + + align:start position:0% +to complete what the message was that +the previous person that the original + + align:start position:0% +the previous person that the original + + + align:start position:0% +the previous person that the original +person had left but the time I got + + align:start position:0% +person had left but the time I got + + + align:start position:0% +person had left but the time I got +thought of over there I realized people + + align:start position:0% +thought of over there I realized people + + + align:start position:0% +thought of over there I realized people +were adding things that were extraneous + + align:start position:0% +were adding things that were extraneous + + + align:start position:0% +were adding things that were extraneous +to the literal assignment and that's + + align:start position:0% +to the literal assignment and that's + + + align:start position:0% +to the literal assignment and that's +sort of oh I see this is just a picture + + align:start position:0% +sort of oh I see this is just a picture + + + align:start position:0% +sort of oh I see this is just a picture +now this is no longer a still life that + + align:start position:0% +now this is no longer a still life that + + + align:start position:0% +now this is no longer a still life that +has to be represented now there's people + + align:start position:0% +has to be represented now there's people + + + align:start position:0% +has to be represented now there's people +just making it into a picture they're + + align:start position:0% +just making it into a picture they're + + + align:start position:0% +just making it into a picture they're +putting things that are not there in the + + align:start position:0% +putting things that are not there in the + + + align:start position:0% +putting things that are not there in the +picture oh okay that's fun and so now I + + align:start position:0% +picture oh okay that's fun and so now I + + + align:start position:0% +picture oh okay that's fun and so now I +realized that the assignment had changed + + align:start position:0% +realized that the assignment had changed + + + align:start position:0% +realized that the assignment had changed +or I had my conception of it had + + align:start position:0% +or I had my conception of it had + + + align:start position:0% +or I had my conception of it had +radically altered and then by the time I + + align:start position:0% +radically altered and then by the time I + + + align:start position:0% +radically altered and then by the time I +get back to my own I recognize nothing + + align:start position:0% +get back to my own I recognize nothing + + + align:start position:0% +get back to my own I recognize nothing +and I said okay well I can barely find + + align:start position:0% +and I said okay well I can barely find + + + align:start position:0% +and I said okay well I can barely find +what I started with there's layers of + + align:start position:0% +what I started with there's layers of + + + align:start position:0% +what I started with there's layers of +what other people produce but my sense + + align:start position:0% +what other people produce but my sense + + + align:start position:0% +what other people produce but my sense +of what I was doing changed as there + + align:start position:0% +of what I was doing changed as there + + + align:start position:0% +of what I was doing changed as there +were + + align:start position:0% +were + + + align:start position:0% +were +Changez imposed by many people before me + + align:start position:0% +Changez imposed by many people before me + + + align:start position:0% +Changez imposed by many people before me +getting to the picture mad that's a + + align:start position:0% +getting to the picture mad that's a + + + align:start position:0% +getting to the picture mad that's a +wonderful what I want to transition to + + align:start position:0% +wonderful what I want to transition to + + + align:start position:0% +wonderful what I want to transition to +the next drawing task but inherent in + + align:start position:0% +the next drawing task but inherent in + + + align:start position:0% +the next drawing task but inherent in +what everyone was saying could be + + align:start position:0% +what everyone was saying could be + + + align:start position:0% +what everyone was saying could be +applied to other tasks other subjects + + align:start position:0% +applied to other tasks other subjects + + + align:start position:0% +applied to other tasks other subjects +imagine if we didn't have a set of + + align:start position:0% +imagine if we didn't have a set of + + + align:start position:0% +imagine if we didn't have a set of +chairs there well imagine if there was a + + align:start position:0% +chairs there well imagine if there was a + + + align:start position:0% +chairs there well imagine if there was a +person there instead of drawing with + + align:start position:0% +person there instead of drawing with + + + align:start position:0% +person there instead of drawing with +lines we were drawing with the questions + + align:start position:0% +lines we were drawing with the questions + + + align:start position:0% +lines we were drawing with the questions +we were asking this person who had never + + align:start position:0% +we were asking this person who had never + + + align:start position:0% +we were asking this person who had never +met before or maybe we passed this + + align:start position:0% +met before or maybe we passed this + + + align:start position:0% +met before or maybe we passed this +person numerous times like we passed + + align:start position:0% +person numerous times like we passed + + + align:start position:0% +person numerous times like we passed +these chairs all the time these chairs + + align:start position:0% +these chairs all the time these chairs + + + align:start position:0% +these chairs all the time these chairs +are just in the room but now we put them + + align:start position:0% +are just in the room but now we put them + + + align:start position:0% +are just in the room but now we put them +in a space of of inquiry oh now I have + + align:start position:0% +in a space of of inquiry oh now I have + + + align:start position:0% +in a space of of inquiry oh now I have +to look I've learned some things about + + align:start position:0% +to look I've learned some things about + + + align:start position:0% +to look I've learned some things about +these chairs in this circle that I + + align:start position:0% +these chairs in this circle that I + + + align:start position:0% +these chairs in this circle that I +didn't realize about the chairs before + + align:start position:0% +didn't realize about the chairs before + + + align:start position:0% +didn't realize about the chairs before +just by the act of mark-making so what + + align:start position:0% +just by the act of mark-making so what + + + align:start position:0% +just by the act of mark-making so what +if we put a person there someone we may + + align:start position:0% +if we put a person there someone we may + + + align:start position:0% +if we put a person there someone we may +pass on the street every day and we just + + align:start position:0% +pass on the street every day and we just + + + align:start position:0% +pass on the street every day and we just +we stopped instead of drawing them we + + align:start position:0% +we stopped instead of drawing them we + + + align:start position:0% +we stopped instead of drawing them we +could draw them what if we asked + + align:start position:0% +could draw them what if we asked + + + align:start position:0% +could draw them what if we asked +questions of them what if each mark that + + align:start position:0% +questions of them what if each mark that + + + align:start position:0% +questions of them what if each mark that +we're making is some form of a question + + align:start position:0% +we're making is some form of a question + + + align:start position:0% +we're making is some form of a question +that we're asking how much more would we + + align:start position:0% +that we're asking how much more would we + + + align:start position:0% +that we're asking how much more would we +learn about that person just by talking + + align:start position:0% +learn about that person just by talking + + + align:start position:0% +learn about that person just by talking +to that the idea here will be that we'll + + align:start position:0% +to that the idea here will be that we'll + + + align:start position:0% +to that the idea here will be that we'll +still use the chairs and we're still + + align:start position:0% +still use the chairs and we're still + + + align:start position:0% +still use the chairs and we're still +building on this premise of learning + + align:start position:0% +building on this premise of learning + + + align:start position:0% +building on this premise of learning +from each other's drawings but now + + align:start position:0% +from each other's drawings but now + + + align:start position:0% +from each other's drawings but now +instead of us all drawing and moving to + + align:start position:0% +instead of us all drawing and moving to + + + align:start position:0% +instead of us all drawing and moving to +each other's drawings one person will + + align:start position:0% +each other's drawings one person will + + + align:start position:0% +each other's drawings one person will +take the drawing implement and you will + + align:start position:0% +take the drawing implement and you will + + + align:start position:0% +take the drawing implement and you will +be connected fixed to that drawing + + align:start position:0% +be connected fixed to that drawing + + + align:start position:0% +be connected fixed to that drawing +implement in other words you're an + + align:start position:0% +implement in other words you're an + + + align:start position:0% +implement in other words you're an +extension of that drawing implement and + + align:start position:0% +extension of that drawing implement and + + + align:start position:0% +extension of that drawing implement and +your partner has to find a way to use + + align:start position:0% +your partner has to find a way to use + + + align:start position:0% +your partner has to find a way to use +you the drawing implement to draw the + + align:start position:0% +you the drawing implement to draw the + + + align:start position:0% +you the drawing implement to draw the +chairs all you're doing drawing + + align:start position:0% +chairs all you're doing drawing + + + align:start position:0% +chairs all you're doing drawing +implement is holding the marker the + + align:start position:0% +implement is holding the marker the + + + align:start position:0% +implement is holding the marker the +person who is your partner is using they + + align:start position:0% +person who is your partner is using they + + + align:start position:0% +person who is your partner is using they +might have to hold your hand or your + + align:start position:0% +might have to hold your hand or your + + + align:start position:0% +might have to hold your hand or your +elbow or your shoulder or shoulder and + + align:start position:0% +elbow or your shoulder or shoulder and + + + align:start position:0% +elbow or your shoulder or shoulder and +wrist that's what I'm saying you need to + + align:start position:0% +wrist that's what I'm saying you need to + + + align:start position:0% +wrist that's what I'm saying you need to +have the permission of the other person + + align:start position:0% +have the permission of the other person + + + align:start position:0% +have the permission of the other person +and then they're going to draw what they + + align:start position:0% +and then they're going to draw what they + + + align:start position:0% +and then they're going to draw what they +see they're going to draw the chairs + + align:start position:0% +see they're going to draw the chairs + + + align:start position:0% +see they're going to draw the chairs +using you and the marker as the + + align:start position:0% +using you and the marker as the + + + align:start position:0% +using you and the marker as the +implement and you're they implement + + align:start position:0% +implement and you're they implement + + + align:start position:0% +implement and you're they implement +you're kind of in it to see + + align:start position:0% +you're kind of in it to see + + + align:start position:0% +you're kind of in it to see +how this drawing turns out so some of + + align:start position:0% +how this drawing turns out so some of + + + align:start position:0% +how this drawing turns out so some of +the words I'm hearing that to me work in + + align:start position:0% +the words I'm hearing that to me work in + + + align:start position:0% +the words I'm hearing that to me work in +tandem with this notion of themes or + + align:start position:0% +tandem with this notion of themes or + + + align:start position:0% +tandem with this notion of themes or +concepts responsibilities influence + + align:start position:0% +concepts responsibilities influence + + + align:start position:0% +concepts responsibilities influence +there's some notion of liberation in + + align:start position:0% +there's some notion of liberation in + + + align:start position:0% +there's some notion of liberation in +what you said over there right + + align:start position:0% +what you said over there right + + + align:start position:0% +what you said over there right +cooperation so these are themes or + + align:start position:0% +cooperation so these are themes or + + + align:start position:0% +cooperation so these are themes or +concepts that might be important to many + + align:start position:0% +concepts that might be important to many + + + align:start position:0% +concepts that might be important to many +disciplines or many discourses but one + + align:start position:0% +disciplines or many discourses but one + + + align:start position:0% +disciplines or many discourses but one +way we might get to it could be doing an + + align:start position:0% +way we might get to it could be doing an + + + align:start position:0% +way we might get to it could be doing an +activity like this even though this + + align:start position:0% +activity like this even though this + + + align:start position:0% +activity like this even though this +activity is could also be taken very + + align:start position:0% +activity is could also be taken very + + + align:start position:0% +activity is could also be taken very +literally in terms of formal approach + + align:start position:0% +literally in terms of formal approach + + + align:start position:0% +literally in terms of formal approach +--is to revise and enhance the way + + align:start position:0% +--is to revise and enhance the way + + + align:start position:0% +--is to revise and enhance the way +people render in through drawings to + + align:start position:0% +people render in through drawings to + + + align:start position:0% +people render in through drawings to +render realistically the objects that + + align:start position:0% +render realistically the objects that + + + align:start position:0% +render realistically the objects that +they're seeing but there's also + + align:start position:0% +they're seeing but there's also + + + align:start position:0% +they're seeing but there's also +conceptual piece here that we don't want + + align:start position:0% +conceptual piece here that we don't want + + + align:start position:0% +conceptual piece here that we don't want +to miss + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/K7gCCLUBSA8.txt b/K7gCCLUBSA8.txt new file mode 100644 index 0000000000000000000000000000000000000000..19d3aa7889da7897bb36f34d22546105f3e39d36 --- /dev/null +++ b/K7gCCLUBSA8.txt @@ -0,0 +1,13219 @@ +align:start position:0% + +okay so good + + align:start position:0% + + + + align:start position:0% + +morning but we finally got to the heat + + align:start position:0% + + + + align:start position:0% + +interaction so we're almost uh + + align:start position:0% +interaction so we're almost uh + + + align:start position:0% +interaction so we're almost uh +comfortable with the old ideas of uh + + align:start position:0% +comfortable with the old ideas of uh + + + align:start position:0% +comfortable with the old ideas of uh +thermodynamics being the the theory of + + align:start position:0% +thermodynamics being the the theory of + + + align:start position:0% +thermodynamics being the the theory of +uh heat and + + align:start position:0% +uh heat and + + + align:start position:0% +uh heat and +work we did + + align:start position:0% + + + + align:start position:0% + +temperature um usually there is also + + align:start position:0% +temperature um usually there is also + + + align:start position:0% +temperature um usually there is also +another thing that maybe I didn't stress + + align:start position:0% +another thing that maybe I didn't stress + + + align:start position:0% +another thing that maybe I didn't stress +enough + + align:start position:0% +enough + + + align:start position:0% +enough +uh + + align:start position:0% +uh + + + align:start position:0% +uh +usually you taught that thermodynamics + + align:start position:0% +usually you taught that thermodynamics + + + align:start position:0% +usually you taught that thermodynamics +deals with large amounts of uh + + align:start position:0% +deals with large amounts of uh + + + align:start position:0% +deals with large amounts of uh +substances many particle systems + + align:start position:0% + + + + align:start position:0% + +but you see that um if you went to the + + align:start position:0% +but you see that um if you went to the + + + align:start position:0% +but you see that um if you went to the +seminar yesterday suggested if you're + + align:start position:0% +seminar yesterday suggested if you're + + + align:start position:0% +seminar yesterday suggested if you're +going to the seminar by Professor Howard + + align:start position:0% +going to the seminar by Professor Howard + + + align:start position:0% +going to the seminar by Professor Howard +Stone uh who is a very important name in + + align:start position:0% +Stone uh who is a very important name in + + + align:start position:0% +Stone uh who is a very important name in +in fluid mechanics and uh you'll see + + align:start position:0% +in fluid mechanics and uh you'll see + + + align:start position:0% +in fluid mechanics and uh you'll see +today that uh much of current interest + + align:start position:0% +today that uh much of current interest + + + align:start position:0% +today that uh much of current interest +is in small devices + + align:start position:0% +is in small devices + + + align:start position:0% +is in small devices +microfluidics uh + + align:start position:0% +microfluidics uh + + + align:start position:0% +microfluidics uh +bacteria floating on uh + + align:start position:0% +bacteria floating on uh + + + align:start position:0% +bacteria floating on uh +um Solutions trying to find food or + + align:start position:0% +um Solutions trying to find food or + + + align:start position:0% +um Solutions trying to find food or +other + + align:start position:0% + + + + align:start position:0% + +things few + + align:start position:0% +things few + + + align:start position:0% +things few +particles in some extremes like in the + + align:start position:0% +particles in some extremes like in the + + + align:start position:0% +particles in some extremes like in the +quantum thermodynamics only very few + + align:start position:0% +quantum thermodynamics only very few + + + align:start position:0% +quantum thermodynamics only very few +particles maybe + + align:start position:0% +particles maybe + + + align:start position:0% +particles maybe +one whereas in the fluid mechanics of of + + align:start position:0% +one whereas in the fluid mechanics of of + + + align:start position:0% +one whereas in the fluid mechanics of of +small systems it's it's few but not so + + align:start position:0% +small systems it's it's few but not so + + + align:start position:0% +small systems it's it's few but not so +few nevertheless it's not many so these + + align:start position:0% +few nevertheless it's not many so these + + + align:start position:0% +few nevertheless it's not many so these +are not macroscopic systems so you would + + align:start position:0% +are not macroscopic systems so you would + + + align:start position:0% +are not macroscopic systems so you would +Wonder well H does thermodynamics + + align:start position:0% +Wonder well H does thermodynamics + + + align:start position:0% +Wonder well H does thermodynamics +apply okay this is precisely the reason + + align:start position:0% +apply okay this is precisely the reason + + + align:start position:0% +apply okay this is precisely the reason +why I'm postponing the part that deals + + align:start position:0% +why I'm postponing the part that deals + + + align:start position:0% +why I'm postponing the part that deals +with many particles in other words all + + align:start position:0% +with many particles in other words all + + + align:start position:0% +with many particles in other words all +that we have done so far if you noticed + + align:start position:0% +that we have done so far if you noticed + + + align:start position:0% +that we have done so far if you noticed +didn't require require any assumption + + align:start position:0% +didn't require require any assumption + + + align:start position:0% +didn't require require any assumption +about the number of particles so all the + + align:start position:0% +about the number of particles so all the + + + align:start position:0% +about the number of particles so all the +things that we do also today until uh + + align:start position:0% +things that we do also today until uh + + + align:start position:0% +things that we do also today until uh +maybe the next or the next uh + + align:start position:0% +maybe the next or the next uh + + + align:start position:0% +maybe the next or the next uh +other uh lecture does + + align:start position:0% +other uh lecture does + + + align:start position:0% +other uh lecture does +apply to microscopic and mesoscopic + + align:start position:0% +apply to microscopic and mesoscopic + + + align:start position:0% +apply to microscopic and mesoscopic +systems right so this is important + + align:start position:0% +systems right so this is important + + + align:start position:0% +systems right so this is important +because if you do if you if you work + + align:start position:0% +because if you do if you if you work + + + align:start position:0% +because if you do if you if you work +downstairs in the atopos microfluidics + + align:start position:0% +downstairs in the atopos microfluidics + + + align:start position:0% +downstairs in the atopos microfluidics +lab or if you do research in + + align:start position:0% +lab or if you do research in + + + align:start position:0% +lab or if you do research in +biology at some point you're going to + + align:start position:0% +biology at some point you're going to + + + align:start position:0% +biology at some point you're going to +have to uh even if you are an + + align:start position:0% +have to uh even if you are an + + + align:start position:0% +have to uh even if you are an +experimentalist you're going to have to + + align:start position:0% +experimentalist you're going to have to + + + align:start position:0% +experimentalist you're going to have to +make a model of your experiments if you + + align:start position:0% +make a model of your experiments if you + + + align:start position:0% +make a model of your experiments if you +are a theorist you start from the model + + align:start position:0% +are a theorist you start from the model + + + align:start position:0% +are a theorist you start from the model +if you're an experiment theist you want + + align:start position:0% +if you're an experiment theist you want + + + align:start position:0% +if you're an experiment theist you want +to uh correlate your data and you need a + + align:start position:0% +to uh correlate your data and you need a + + + align:start position:0% +to uh correlate your data and you need a +model usually to do + + align:start position:0% +model usually to do + + + align:start position:0% +model usually to do +that and therefore what we are doing + + align:start position:0% +that and therefore what we are doing + + + align:start position:0% +that and therefore what we are doing +which is of course a lot of theory a lot + + align:start position:0% +which is of course a lot of theory a lot + + + align:start position:0% +which is of course a lot of theory a lot +of + + align:start position:0% +of + + + align:start position:0% +of +equations + + align:start position:0% +equations + + + align:start position:0% +equations +but is exactly what you need to do this + + align:start position:0% +but is exactly what you need to do this + + + align:start position:0% +but is exactly what you need to do this +modeling so that's the motivation for + + align:start position:0% +modeling so that's the motivation for + + + align:start position:0% +modeling so that's the motivation for +this course + + align:start position:0% +this course + + + align:start position:0% +this course +it's it's timely also because uh + + align:start position:0% +it's it's timely also because uh + + + align:start position:0% +it's it's timely also because uh +it's it's one of the few ways of + + align:start position:0% +it's it's one of the few ways of + + + align:start position:0% +it's it's one of the few ways of +presenting thermodynamics in such a way + + align:start position:0% +presenting thermodynamics in such a way + + + align:start position:0% +presenting thermodynamics in such a way +that in it starts from generalities that + + align:start position:0% +that in it starts from generalities that + + + align:start position:0% +that in it starts from generalities that +hold not only for macroscopic + + align:start position:0% + + + + align:start position:0% + +systems okay me just uh review quickly + + align:start position:0% +systems okay me just uh review quickly + + + align:start position:0% +systems okay me just uh review quickly +what we did last time we defined heat + + align:start position:0% +what we did last time we defined heat + + + align:start position:0% +what we did last time we defined heat +interactions + + align:start position:0% +interactions + + + align:start position:0% +interactions +so a heat + + align:start position:0% +so a heat + + + align:start position:0% +so a heat +interaction was defined as one in which + + align:start position:0% +interaction was defined as one in which + + + align:start position:0% +interaction was defined as one in which +a + + align:start position:0% +a + + + align:start position:0% +a +system two systems A and B initially at + + align:start position:0% +system two systems A and B initially at + + + align:start position:0% +system two systems A and B initially at +uh stable equilibrium + + align:start position:0% +uh stable equilibrium + + + align:start position:0% +uh stable equilibrium +States exchange energy and + + align:start position:0% +States exchange energy and + + + align:start position:0% +States exchange energy and +entropy but they do so in such a way + + align:start position:0% +entropy but they do so in such a way + + + align:start position:0% +entropy but they do so in such a way +that even if you + + align:start position:0% + + + + align:start position:0% + +put uh in between them some Machinery + + align:start position:0% +put uh in between them some Machinery + + + align:start position:0% +put uh in between them some Machinery +that tries to separate the the energy + + align:start position:0% +that tries to separate the the energy + + + align:start position:0% +that tries to separate the the energy +transferred into + + align:start position:0% +transferred into + + + align:start position:0% +transferred into +uh into two streams one of which is pure + + align:start position:0% +uh into two streams one of which is pure + + + align:start position:0% +uh into two streams one of which is pure +is work so it's just pure energy and no + + align:start position:0% +is work so it's just pure energy and no + + + align:start position:0% +is work so it's just pure energy and no +entropy that machine will not succeed so + + align:start position:0% +entropy that machine will not succeed so + + + align:start position:0% +entropy that machine will not succeed so +no no fraction of the energy exchanged + + align:start position:0% +no no fraction of the energy exchanged + + + align:start position:0% +no no fraction of the energy exchanged +can be recognized as + + align:start position:0% +can be recognized as + + + align:start position:0% +can be recognized as +work so + + align:start position:0% +work so + + + align:start position:0% +work so +heat + + align:start position:0% +heat + + + align:start position:0% +heat +is the extreme the the farthest non-w + + align:start position:0% +is the extreme the the farthest non-w + + + align:start position:0% +is the extreme the the farthest non-w +work interaction hardest from work most + + align:start position:0% +work interaction hardest from work most + + + align:start position:0% +work interaction hardest from work most +distinguishable from work and that + + align:start position:0% +distinguishable from work and that + + + align:start position:0% +distinguishable from work and that +definition uh leads to the condition + + align:start position:0% +definition uh leads to the condition + + + align:start position:0% +definition uh leads to the condition +that the two systems to have a heat + + align:start position:0% +that the two systems to have a heat + + + align:start position:0% +that the two systems to have a heat +interaction must be at almost the same + + align:start position:0% +interaction must be at almost the same + + + align:start position:0% +interaction must be at almost the same +temperature if not the same + + align:start position:0% +temperature if not the same + + + align:start position:0% +temperature if not the same +temperature because only in that limit + + align:start position:0% +temperature because only in that limit + + + align:start position:0% +temperature because only in that limit +the carau ratio between the two + + align:start position:0% +the carau ratio between the two + + + align:start position:0% +the carau ratio between the two +temperatures which represents the + + align:start position:0% +temperatures which represents the + + + align:start position:0% +temperatures which represents the +fraction of the energy that could be uh + + align:start position:0% +fraction of the energy that could be uh + + + align:start position:0% +fraction of the energy that could be uh +uh identified as + + align:start position:0% +uh identified as + + + align:start position:0% +uh identified as +work goes to + + align:start position:0% +work goes to + + + align:start position:0% +work goes to +zero okay we also mentioned + + align:start position:0% +zero okay we also mentioned + + + align:start position:0% +zero okay we also mentioned +that in spite of the usual understanding + + align:start position:0% +that in spite of the usual understanding + + + align:start position:0% +that in spite of the usual understanding +that uh heat is uh the energy transfer + + align:start position:0% +that uh heat is uh the energy transfer + + + align:start position:0% +that uh heat is uh the energy transfer +between bodies at different + + align:start position:0% +between bodies at different + + + align:start position:0% +between bodies at different +temperature uh and therefore seems to + + align:start position:0% +temperature uh and therefore seems to + + + align:start position:0% +temperature uh and therefore seems to +contradict what our + + align:start position:0% +contradict what our + + + align:start position:0% +contradict what our +definition we notice that if uh the + + align:start position:0% +definition we notice that if uh the + + + align:start position:0% +definition we notice that if uh the +standard model that we adopt in a heat + + align:start position:0% +standard model that we adopt in a heat + + + align:start position:0% +standard model that we adopt in a heat +transfer is a local uh equilibrium or + + align:start position:0% +transfer is a local uh equilibrium or + + + align:start position:0% +transfer is a local uh equilibrium or +quas equilibrium + + align:start position:0% +quas equilibrium + + + align:start position:0% +quas equilibrium +model whereby the + + align:start position:0% +model whereby the + + + align:start position:0% +model whereby the +system is divided in in smaller + + align:start position:0% +system is divided in in smaller + + + align:start position:0% +system is divided in in smaller +systems that are modeled as being near + + align:start position:0% +systems that are modeled as being near + + + align:start position:0% +systems that are modeled as being near +equilibrium not at equilibrium + + align:start position:0% +equilibrium not at equilibrium + + + align:start position:0% +equilibrium not at equilibrium +like highlighted + + align:start position:0% +like highlighted + + + align:start position:0% +like highlighted +here uh near near equilibrium and + + align:start position:0% +here uh near near equilibrium and + + + align:start position:0% +here uh near near equilibrium and +therefore in that way + + align:start position:0% + + + + align:start position:0% + +first of all you could assign the + + align:start position:0% +first of all you could assign the + + + align:start position:0% +first of all you could assign the +temperature of the of the equilibrium + + align:start position:0% +temperature of the of the equilibrium + + + align:start position:0% +temperature of the of the equilibrium +state that they these elements would + + align:start position:0% +state that they these elements would + + + align:start position:0% +state that they these elements would +reach if you isolate them from the rest + + align:start position:0% +reach if you isolate them from the rest + + + align:start position:0% +reach if you isolate them from the rest +and just let them relax to + + align:start position:0% +and just let them relax to + + + align:start position:0% +and just let them relax to +equilibrium and uh and second um + + align:start position:0% +equilibrium and uh and second um + + + align:start position:0% +equilibrium and uh and second um +the on the eever Suess + + align:start position:0% +the on the eever Suess + + + align:start position:0% +the on the eever Suess +diagram we notice also this is important + + align:start position:0% +diagram we notice also this is important + + + align:start position:0% +diagram we notice also this is important +and we'll return to this uh the heat + + align:start position:0% +and we'll return to this uh the heat + + + align:start position:0% +and we'll return to this uh the heat +interaction + + align:start position:0% +interaction + + + align:start position:0% +interaction +on one + + align:start position:0% +on one + + + align:start position:0% +on one +side um pulls the pulls the system in a + + align:start position:0% +side um pulls the pulls the system in a + + + align:start position:0% +side um pulls the pulls the system in a +in a direction that uh so on the eers + + align:start position:0% +in a direction that uh so on the eers + + + align:start position:0% +in a direction that uh so on the eers +sucess + + align:start position:0% +sucess + + + align:start position:0% +sucess +diagram if I'm here and I'm going to + + align:start position:0% +diagram if I'm here and I'm going to + + + align:start position:0% +diagram if I'm here and I'm going to +inject uh both energy and + + align:start position:0% +inject uh both energy and + + + align:start position:0% +inject uh both energy and +entropy that's the direction in which my + + align:start position:0% +entropy that's the direction in which my + + + align:start position:0% +entropy that's the direction in which my +state will + + align:start position:0% +state will + + + align:start position:0% +state will +move and if another interaction + + align:start position:0% +move and if another interaction + + + align:start position:0% +move and if another interaction +injects uh the same energy + + align:start position:0% +injects uh the same energy + + + align:start position:0% +injects uh the same energy +uh but takes away I'm sorry takes away + + align:start position:0% +uh but takes away I'm sorry takes away + + + align:start position:0% +uh but takes away I'm sorry takes away +energy same energy but takes away more + + align:start position:0% +energy same energy but takes away more + + + align:start position:0% +energy same energy but takes away more +entropy then it goes that way and the + + align:start position:0% +entropy then it goes that way and the + + + align:start position:0% +entropy then it goes that way and the +two are not aligned so in order to align + + align:start position:0% +two are not aligned so in order to align + + + align:start position:0% +two are not aligned so in order to align +them to to keep the state at steady + + align:start position:0% +them to to keep the state at steady + + + align:start position:0% +them to to keep the state at steady +state so so that the state doesn't move + + align:start position:0% +state so so that the state doesn't move + + + align:start position:0% +state so so that the state doesn't move +you need also something and that + + align:start position:0% +you need also something and that + + + align:start position:0% +you need also something and that +something is + + align:start position:0% +something is + + + align:start position:0% +something is +uh is another Vector which which is uh + + align:start position:0% +uh is another Vector which which is uh + + + align:start position:0% +uh is another Vector which which is uh +representing the entropy produced by + + align:start position:0% + + + + align:start position:0% + +irreversibility so you need a + + align:start position:0% +irreversibility so you need a + + + align:start position:0% +irreversibility so you need a +irreversibility to + + align:start position:0% +irreversibility to + + + align:start position:0% +irreversibility to +keep fluid element or a solid element in + + align:start position:0% +keep fluid element or a solid element in + + + align:start position:0% +keep fluid element or a solid element in +a uh steady state when subjected to a + + align:start position:0% +a uh steady state when subjected to a + + + align:start position:0% +a uh steady state when subjected to a +gradient in temperature so that means a + + align:start position:0% +gradient in temperature so that means a + + + align:start position:0% +gradient in temperature so that means a +temperature difference between one side + + align:start position:0% +temperature difference between one side + + + align:start position:0% +temperature difference between one side +and the other + + align:start position:0% +and the other + + + align:start position:0% +and the other +side + + align:start position:0% +side + + + align:start position:0% +side +okay so let's do something new + + align:start position:0% +okay so let's do something new + + + align:start position:0% +okay so let's do something new +now not very new but it's another + + align:start position:0% +now not very new but it's another + + + align:start position:0% +now not very new but it's another +another it's + + align:start position:0% +another it's + + + align:start position:0% +another it's +similar um to what we have done when we + + align:start position:0% +similar um to what we have done when we + + + align:start position:0% +similar um to what we have done when we +proved the conditions for Mutual + + align:start position:0% +proved the conditions for Mutual + + + align:start position:0% +proved the conditions for Mutual +equilibrium between + + align:start position:0% +equilibrium between + + + align:start position:0% +equilibrium between +systems this time + + align:start position:0% +systems this time + + + align:start position:0% +systems this time +though we are not applying the maximum + + align:start position:0% +though we are not applying the maximum + + + align:start position:0% +though we are not applying the maximum +entropy principle but we apply are + + align:start position:0% +entropy principle but we apply are + + + align:start position:0% +entropy principle but we apply are +applying the principle of entropy non + + align:start position:0% +applying the principle of entropy non + + + align:start position:0% +applying the principle of entropy non +decrease in weight processes + + align:start position:0% + + + + align:start position:0% + +and let me say it again the principle of + + align:start position:0% +and let me say it again the principle of + + + align:start position:0% +and let me say it again the principle of +entropy non + + align:start position:0% +entropy non + + + align:start position:0% +entropy non +decrease is for weight processes or for + + align:start position:0% +decrease is for weight processes or for + + + align:start position:0% +decrease is for weight processes or for +systems that are isolated in other words + + align:start position:0% +systems that are isolated in other words + + + align:start position:0% +systems that are isolated in other words +it's impossible to decrease the entropy + + align:start position:0% +it's impossible to decrease the entropy + + + align:start position:0% +it's impossible to decrease the entropy +of an is of an isolated system or a + + align:start position:0% +of an is of an isolated system or a + + + align:start position:0% +of an is of an isolated system or a +system that under goes only a weight + + align:start position:0% +system that under goes only a weight + + + align:start position:0% +system that under goes only a weight +process otherwise it is possible to + + align:start position:0% +process otherwise it is possible to + + + align:start position:0% +process otherwise it is possible to +decrease the entropy like we do here + + align:start position:0% +decrease the entropy like we do here + + + align:start position:0% +decrease the entropy like we do here +like heat interaction is precisely the + + align:start position:0% +like heat interaction is precisely the + + + align:start position:0% +like heat interaction is precisely the +kind of interaction that allows to + + align:start position:0% +kind of interaction that allows to + + + align:start position:0% +kind of interaction that allows to +extract entropy from a system + + align:start position:0% +extract entropy from a system + + + align:start position:0% +extract entropy from a system +right all + + align:start position:0% +right all + + + align:start position:0% +right all +right so here the idea is that we start + + align:start position:0% +right so here the idea is that we start + + + align:start position:0% +right so here the idea is that we start +from a composite system of two systems A + + align:start position:0% +from a composite system of two systems A + + + align:start position:0% +from a composite system of two systems A +and + + align:start position:0% + + + + align:start position:0% + +B at different + + align:start position:0% +B at different + + + align:start position:0% +B at different +temperatures this time they're different + + align:start position:0% + + + + align:start position:0% + +and we uh ask ourselves is it possible + + align:start position:0% +and we uh ask ourselves is it possible + + + align:start position:0% +and we uh ask ourselves is it possible +when is it + + align:start position:0% +when is it + + + align:start position:0% +when is it +possible for them to exchange energy and + + align:start position:0% +possible for them to exchange energy and + + + align:start position:0% +possible for them to exchange energy and +volume so through + + align:start position:0% +volume so through + + + align:start position:0% +volume so through +a movable + + align:start position:0% + + + + align:start position:0% + +partition so here is the initial State + + align:start position:0% +partition so here is the initial State + + + align:start position:0% +partition so here is the initial State +and on the E sucess diagram for the + + align:start position:0% +and on the E sucess diagram for the + + + align:start position:0% +and on the E sucess diagram for the +composite system I denoted by this point + + align:start position:0% +composite system I denoted by this point + + + align:start position:0% +composite system I denoted by this point +here + + align:start position:0% +here + + + align:start position:0% +here +and here's the final State same energy + + align:start position:0% +and here's the final State same energy + + + align:start position:0% +and here's the final State same energy +and same volume so it's on on the same + + align:start position:0% +and same volume so it's on on the same + + + align:start position:0% +and same volume so it's on on the same +energy line for the composite system but + + align:start position:0% +energy line for the composite system but + + + align:start position:0% +energy line for the composite system but +internally some energy has gone from a + + align:start position:0% +internally some energy has gone from a + + + align:start position:0% +internally some energy has gone from a +from A to B so for example if de is + + align:start position:0% +from A to B so for example if de is + + + align:start position:0% +from A to B so for example if de is +greater than + + align:start position:0% +greater than + + + align:start position:0% +greater than +zero uh the energy of a is increased so + + align:start position:0% +zero uh the energy of a is increased so + + + align:start position:0% +zero uh the energy of a is increased so +the energy has flown from uh B to + + align:start position:0% +the energy has flown from uh B to + + + align:start position:0% +the energy has flown from uh B to +a or if DV is greater than zero + + align:start position:0% +a or if DV is greater than zero + + + align:start position:0% +a or if DV is greater than zero +uh the volume has increased so that + + align:start position:0% +uh the volume has increased so that + + + align:start position:0% +uh the volume has increased so that +again system B has Lo lost volume for + + align:start position:0% +again system B has Lo lost volume for + + + align:start position:0% +again system B has Lo lost volume for +the gain of volume of system + + align:start position:0% + + + + align:start position:0% + +a what we apply here is a condition that + + align:start position:0% +a what we apply here is a condition that + + + align:start position:0% +a what we apply here is a condition that +since this is a system is isolated so a + + align:start position:0% +since this is a system is isolated so a + + + align:start position:0% +since this is a system is isolated so a +particular case of a weight process with + + align:start position:0% +particular case of a weight process with + + + align:start position:0% +particular case of a weight process with +no external effects + + align:start position:0% +no external effects + + + align:start position:0% +no external effects +uh the the entropy can only + + align:start position:0% +uh the the entropy can only + + + align:start position:0% +uh the the entropy can only +or remain zero if the if the process is + + align:start position:0% +or remain zero if the if the process is + + + align:start position:0% +or remain zero if the if the process is +reversing + + align:start position:0% +reversing + + + align:start position:0% +reversing +so the final + + align:start position:0% +so the final + + + align:start position:0% +so the final +entropy of the composite must be greater + + align:start position:0% +entropy of the composite must be greater + + + align:start position:0% +entropy of the composite must be greater +than the initial and so we have this + + align:start position:0% +than the initial and so we have this + + + align:start position:0% +than the initial and so we have this +inequality here S2 greater than S1 which + + align:start position:0% +inequality here S2 greater than S1 which + + + align:start position:0% +inequality here S2 greater than S1 which +we write this way which we write this + + align:start position:0% +we write this way which we write this + + + align:start position:0% +we write this way which we write this +way then the tools are the same that we + + align:start position:0% +way then the tools are the same that we + + + align:start position:0% +way then the tools are the same that we +already used we use + + align:start position:0% +already used we use + + + align:start position:0% +already used we use +additivity we use + + align:start position:0% +additivity we use + + + align:start position:0% +additivity we use +the + + align:start position:0% +the + + + align:start position:0% +the +fundamental + + align:start position:0% + + + + align:start position:0% + +relation remember now here your system + + align:start position:0% +relation remember now here your system + + + align:start position:0% +relation remember now here your system +system a starts from a stable + + align:start position:0% +system a starts from a stable + + + align:start position:0% +system a starts from a stable +equilibrium State we want to extract or + + align:start position:0% +equilibrium State we want to extract or + + + align:start position:0% +equilibrium State we want to extract or +to uh let's + + align:start position:0% +to uh let's + + + align:start position:0% +to uh let's +say change with a negative + + align:start position:0% +say change with a negative + + + align:start position:0% +say change with a negative +de the the + + align:start position:0% +de the the + + + align:start position:0% +de the the +energy and so at the new level of energy + + align:start position:0% +energy and so at the new level of energy + + + align:start position:0% +energy and so at the new level of energy +there are many states that can be + + align:start position:0% +there are many states that can be + + + align:start position:0% +there are many states that can be +obtained so I'm trying to explain the + + align:start position:0% +obtained so I'm trying to explain the + + + align:start position:0% +obtained so I'm trying to explain the +reason for this less than or equal to + + align:start position:0% +reason for this less than or equal to + + + align:start position:0% +reason for this less than or equal to +the change in entropy for system a + + align:start position:0% + + + + align:start position:0% + +is either this one but it can also be + + align:start position:0% +is either this one but it can also be + + + align:start position:0% +is either this one but it can also be +less I mean I'm sorry + + align:start position:0% + + + + align:start position:0% + +more + + align:start position:0% + + + + align:start position:0% + +okay and the same for B + + align:start position:0% +okay and the same for B + + + align:start position:0% +okay and the same for B +so we end up with this relation + + align:start position:0% +so we end up with this relation + + + align:start position:0% +so we end up with this relation +here and so these things must be greater + + align:start position:0% +here and so these things must be greater + + + align:start position:0% +here and so these things must be greater +than + + align:start position:0% +than + + + align:start position:0% +than +zero because these are all + + align:start position:0% + + + + align:start position:0% + +connected so now we can still uh choose + + align:start position:0% +connected so now we can still uh choose + + + align:start position:0% +connected so now we can still uh choose +some special + + align:start position:0% +some special + + + align:start position:0% +some special +cases for + + align:start position:0% + + + + align:start position:0% + +example uh suppose we don't change the + + align:start position:0% +example uh suppose we don't change the + + + align:start position:0% +example uh suppose we don't change the +volume so the Piston is uh + + align:start position:0% +volume so the Piston is uh + + + align:start position:0% +volume so the Piston is uh +it's it's blocked by a + + align:start position:0% +it's it's blocked by a + + + align:start position:0% +it's it's blocked by a +stop uh or there is no Pistons this is + + align:start position:0% +stop uh or there is no Pistons this is + + + align:start position:0% +stop uh or there is no Pistons this is +just a + + align:start position:0% +just a + + + align:start position:0% +just a +wall then DV is equal to zero so this + + align:start position:0% +wall then DV is equal to zero so this + + + align:start position:0% +wall then DV is equal to zero so this +contribution isn't + + align:start position:0% +contribution isn't + + + align:start position:0% +contribution isn't +there and suppose we want to transfer + + align:start position:0% +there and suppose we want to transfer + + + align:start position:0% +there and suppose we want to transfer +energy from B to a so that de is greater + + align:start position:0% +energy from B to a so that de is greater + + + align:start position:0% +energy from B to a so that de is greater +than zero here it + + align:start position:0% +than zero here it + + + align:start position:0% +than zero here it +is so if this is greater than zero then + + align:start position:0% +is so if this is greater than zero then + + + align:start position:0% +is so if this is greater than zero then +this term in parenthesis must be greater + + align:start position:0% +this term in parenthesis must be greater + + + align:start position:0% +this term in parenthesis must be greater +than + + align:start position:0% + + + + align:start position:0% + +Zer and that hopefully will say that t1b + + align:start position:0% +Zer and that hopefully will say that t1b + + + align:start position:0% +Zer and that hopefully will say that t1b +must be greater than T1 a + + align:start position:0% +must be greater than T1 a + + + align:start position:0% +must be greater than T1 a +if in a process without external effects + + align:start position:0% +if in a process without external effects + + + align:start position:0% +if in a process without external effects +some energy is transferred in the + + align:start position:0% +some energy is transferred in the + + + align:start position:0% +some energy is transferred in the +direction from B to + + align:start position:0% +direction from B to + + + align:start position:0% +direction from B to +a we we we we say this in words by + + align:start position:0% +a we we we we say this in words by + + + align:start position:0% +a we we we we say this in words by +saying + + align:start position:0% +saying + + + align:start position:0% +saying +that uh the + + align:start position:0% +that uh the + + + align:start position:0% +that uh the +temperature or + + align:start position:0% +temperature or + + + align:start position:0% +temperature or +better somehow or equivalently the minus + + align:start position:0% +better somehow or equivalently the minus + + + align:start position:0% +better somehow or equivalently the minus +the in the negative of the inverse of + + align:start position:0% +the in the negative of the inverse of + + + align:start position:0% +the in the negative of the inverse of +the + + align:start position:0% +the + + + align:start position:0% +the +temperature can be understood as an + + align:start position:0% +temperature can be understood as an + + + align:start position:0% +temperature can be understood as an +escaping tendency for + + align:start position:0% +escaping tendency for + + + align:start position:0% +escaping tendency for +energy so if you have two systems that + + align:start position:0% +energy so if you have two systems that + + + align:start position:0% +energy so if you have two systems that +have the different escaping energies the + + align:start position:0% +have the different escaping energies the + + + align:start position:0% +have the different escaping energies the +one who manages to give energy to the + + align:start position:0% +one who manages to give energy to the + + + align:start position:0% +one who manages to give energy to the +other is the hotter one the one that has + + align:start position:0% +other is the hotter one the one that has + + + align:start position:0% +other is the hotter one the one that has +a higher escaping + + align:start position:0% + + + + align:start position:0% + +tendency all or we could + + align:start position:0% + + + + align:start position:0% + +choose suppose we choose that the two + + align:start position:0% +choose suppose we choose that the two + + + align:start position:0% +choose suppose we choose that the two +systems A and B are initially at the + + align:start position:0% +systems A and B are initially at the + + + align:start position:0% +systems A and B are initially at the +same + + align:start position:0% +same + + + align:start position:0% +same +temperature so this term in parenthesis + + align:start position:0% +temperature so this term in parenthesis + + + align:start position:0% +temperature so this term in parenthesis +isn't + + align:start position:0% + + + + align:start position:0% + +there and we want system a to acquire + + align:start position:0% +there and we want system a to acquire + + + align:start position:0% +there and we want system a to acquire +volume at the expense of system B all + + align:start position:0% +volume at the expense of system B all + + + align:start position:0% +volume at the expense of system B all +right so T the denominators here are + + align:start position:0% +right so T the denominators here are + + + align:start position:0% +right so T the denominators here are +equal uh and so we find that P1 a must + + align:start position:0% +equal uh and so we find that P1 a must + + + align:start position:0% +equal uh and so we find that P1 a must +be greater than P1 2 B me sorry this + + align:start position:0% +be greater than P1 2 B me sorry this + + + align:start position:0% +be greater than P1 2 B me sorry this +should be also one + + align:start position:0% +should be also one + + + align:start position:0% +should be also one +one this should be ones I have to + + align:start position:0% +one this should be ones I have to + + + align:start position:0% +one this should be ones I have to +correct + + align:start position:0% + + + + align:start position:0% + +that so + + align:start position:0% +that so + + + align:start position:0% +that so +that's so you can interpret + + align:start position:0% +that's so you can interpret + + + align:start position:0% +that's so you can interpret +pressure as we all have the typical idea + + align:start position:0% +pressure as we all have the typical idea + + + align:start position:0% +pressure as we all have the typical idea +as a capturing tendency for volume + + align:start position:0% + + + + align:start position:0% + +okay now we can do the + + align:start position:0% +okay now we can do the + + + align:start position:0% +okay now we can do the +same when instead of exchanging energy + + align:start position:0% +same when instead of exchanging energy + + + align:start position:0% +same when instead of exchanging energy +and volume these two systems exchange + + align:start position:0% +and volume these two systems exchange + + + align:start position:0% +and volume these two systems exchange +energy and + + align:start position:0% +energy and + + + align:start position:0% +energy and +particles and let's say + + align:start position:0% +particles and let's say + + + align:start position:0% +particles and let's say +particles of one type I see here again + + align:start position:0% +particles of one type I see here again + + + align:start position:0% +particles of one type I see here again +another two that slipped fine I to + + align:start position:0% +another two that slipped fine I to + + + align:start position:0% +another two that slipped fine I to +remember to correct that + + align:start position:0% + + + + align:start position:0% + +so it's the same story only that instead + + align:start position:0% +so it's the same story only that instead + + + align:start position:0% +so it's the same story only that instead +of energy and volume it's now energy and + + align:start position:0% +of energy and volume it's now energy and + + + align:start position:0% +of energy and volume it's now energy and +amount of constituent + + align:start position:0% +amount of constituent + + + align:start position:0% +amount of constituent +I still the system is isolated the + + align:start position:0% +I still the system is isolated the + + + align:start position:0% +I still the system is isolated the +entropy can only increase and we end up + + align:start position:0% +entropy can only increase and we end up + + + align:start position:0% +entropy can only increase and we end up +with these uh + + align:start position:0% +with these uh + + + align:start position:0% +with these uh +inequalities the first one still + + align:start position:0% +inequalities the first one still + + + align:start position:0% +inequalities the first one still +confirms that uh uh the minus one /t is + + align:start position:0% +confirms that uh uh the minus one /t is + + + align:start position:0% +confirms that uh uh the minus one /t is +escaping tendency for + + align:start position:0% +escaping tendency for + + + align:start position:0% +escaping tendency for +energy regarding chemical potentials + + align:start position:0% +energy regarding chemical potentials + + + align:start position:0% +energy regarding chemical potentials +again suppose + + align:start position:0% +again suppose + + + align:start position:0% +again suppose +that you choose the initial temperatures + + align:start position:0% +that you choose the initial temperatures + + + align:start position:0% +that you choose the initial temperatures +T1 and ta and TB to be + + align:start position:0% +T1 and ta and TB to be + + + align:start position:0% +T1 and ta and TB to be +equal so the denominators here become + + align:start position:0% +equal so the denominators here become + + + align:start position:0% +equal so the denominators here become +equal and this is going to be zero so + + align:start position:0% +equal and this is going to be zero so + + + align:start position:0% +equal and this is going to be zero so +the only term is is this must be greater + + align:start position:0% +the only term is is this must be greater + + + align:start position:0% +the only term is is this must be greater +than zero so if I want and also this DV + + align:start position:0% +than zero so if I want and also this DV + + + align:start position:0% +than zero so if I want and also this DV +sorry for the uh the slide is was a cut + + align:start position:0% +sorry for the uh the slide is was a cut + + + align:start position:0% +sorry for the uh the slide is was a cut +and + + align:start position:0% +and + + + align:start position:0% +and +paste this should be at D + + align:start position:0% + + + + align:start position:0% + +end and also this + + align:start position:0% +end and also this + + + align:start position:0% +end and also this +one I want to see if you + + align:start position:0% + + + + align:start position:0% + +are uh if you're + + align:start position:0% +are uh if you're + + + align:start position:0% +are uh if you're +attentive well + + align:start position:0% +attentive well + + + align:start position:0% +attentive well +anyway the result is that + + align:start position:0% +anyway the result is that + + + align:start position:0% +anyway the result is that +U if dni must be greater than zero if + + align:start position:0% +U if dni must be greater than zero if + + + align:start position:0% +U if dni must be greater than zero if +you want want therefore that system a + + align:start position:0% +you want want therefore that system a + + + align:start position:0% +you want want therefore that system a +acquires uh particles of type I through + + align:start position:0% +acquires uh particles of type I through + + + align:start position:0% +acquires uh particles of type I through +this semi perable membrane that allows + + align:start position:0% +this semi perable membrane that allows + + + align:start position:0% +this semi perable membrane that allows +it to get it from system + + align:start position:0% +it to get it from system + + + align:start position:0% +it to get it from system +B you need the chemical + + align:start position:0% +B you need the chemical + + + align:start position:0% +B you need the chemical +potential of uh a to be greater than the + + align:start position:0% +potential of uh a to be greater than the + + + align:start position:0% +potential of uh a to be greater than the +chemical potential of + + align:start position:0% + + + + align:start position:0% + +B is that + + align:start position:0% + + + + align:start position:0% + +correct I'm not so sure anymore because + + align:start position:0% +correct I'm not so sure anymore because + + + align:start position:0% +correct I'm not so sure anymore because +of all these + + align:start position:0% +of all these + + + align:start position:0% +of all these +mistakes and in fact it + + align:start position:0% + + + + align:start position:0% + +shouldn't it should be uh because + + align:start position:0% +shouldn't it should be uh because + + + align:start position:0% +shouldn't it should be uh because +there's a minor sign here and so I + + align:start position:0% +there's a minor sign here and so I + + + align:start position:0% +there's a minor sign here and so I +either put a minus sign there or I + + align:start position:0% +either put a minus sign there or I + + + align:start position:0% +either put a minus sign there or I +invert the and the positions of andb + + align:start position:0% +invert the and the positions of andb + + + align:start position:0% +invert the and the positions of andb +okay + + align:start position:0% +okay + + + align:start position:0% +okay +because in order for constituent I to + + align:start position:0% +because in order for constituent I to + + + align:start position:0% +because in order for constituent I to +flow from D to to a I need that the + + align:start position:0% +flow from D to to a I need that the + + + align:start position:0% +flow from D to to a I need that the +chemical + + align:start position:0% +chemical + + + align:start position:0% +chemical +potential of constituent I in system B + + align:start position:0% +potential of constituent I in system B + + + align:start position:0% +potential of constituent I in system B +be higher than that in a because + + align:start position:0% +be higher than that in a because + + + align:start position:0% +be higher than that in a because +chemical potential at least the title I + + align:start position:0% +chemical potential at least the title I + + + align:start position:0% +chemical potential at least the title I +got wrong right and it's an escaping + + align:start position:0% +got wrong right and it's an escaping + + + align:start position:0% +got wrong right and it's an escaping +tendency for + + align:start position:0% + + + + align:start position:0% + +constituents so this gets a feel of what + + align:start position:0% +constituents so this gets a feel of what + + + align:start position:0% +constituents so this gets a feel of what +the chemical potentials are if you have + + align:start position:0% +the chemical potentials are if you have + + + align:start position:0% +the chemical potentials are if you have +a feel of what the temperature is you + + align:start position:0% +a feel of what the temperature is you + + + align:start position:0% +a feel of what the temperature is you +also have a feel of what chemical + + align:start position:0% +also have a feel of what chemical + + + align:start position:0% +also have a feel of what chemical +potentials are temperature works for + + align:start position:0% +potentials are temperature works for + + + align:start position:0% +potentials are temperature works for +energy chemical potentials work works + + align:start position:0% +energy chemical potentials work works + + + align:start position:0% +energy chemical potentials work works +for uh molecules and atoms and so + + align:start position:0% + + + + align:start position:0% + +on and in + + align:start position:0% +on and in + + + align:start position:0% +on and in +fact again if you visit the talk today + + align:start position:0% +fact again if you visit the talk today + + + align:start position:0% +fact again if you visit the talk today +by Professor Stone you'll see a lot of + + align:start position:0% +by Professor Stone you'll see a lot of + + + align:start position:0% +by Professor Stone you'll see a lot of +uh chemical potentials + + align:start position:0% +uh chemical potentials + + + align:start position:0% +uh chemical potentials +they the chemical gradients they call + + align:start position:0% +they the chemical gradients they call + + + align:start position:0% +they the chemical gradients they call +them they don't to for short instead of + + align:start position:0% +them they don't to for short instead of + + + align:start position:0% +them they don't to for short instead of +saying chemical potential gradient or + + align:start position:0% +saying chemical potential gradient or + + + align:start position:0% +saying chemical potential gradient or +gradient in chemical potential I simply + + align:start position:0% +gradient in chemical potential I simply + + + align:start position:0% +gradient in chemical potential I simply +say chemical gradient and since the + + align:start position:0% +say chemical gradient and since the + + + align:start position:0% +say chemical gradient and since the +chemical + + align:start position:0% +chemical + + + align:start position:0% +chemical +potential goes with the logarithm of the + + align:start position:0% +potential goes with the logarithm of the + + + align:start position:0% +potential goes with the logarithm of the +concentration we'll + + align:start position:0% +concentration we'll + + + align:start position:0% +concentration we'll +see so a gradient in the chemical + + align:start position:0% +see so a gradient in the chemical + + + align:start position:0% +see so a gradient in the chemical +potential goes with the gradient of the + + align:start position:0% +potential goes with the gradient of the + + + align:start position:0% +potential goes with the gradient of the +log of C + + align:start position:0% + + + + align:start position:0% + +and that's 1 / C gradient of + + align:start position:0% + + + + align:start position:0% + +C + + align:start position:0% +C + + + align:start position:0% +C +usually people don't talk a lot about + + align:start position:0% +usually people don't talk a lot about + + + align:start position:0% +usually people don't talk a lot about +this one / C in + + align:start position:0% +this one / C in + + + align:start position:0% +this one / C in +front uh and they simply say well for + + align:start position:0% +front uh and they simply say well for + + + align:start position:0% +front uh and they simply say well for +example diffusion processes + + align:start position:0% +example diffusion processes + + + align:start position:0% +example diffusion processes +uh depend on the gradient in + + align:start position:0% +uh depend on the gradient in + + + align:start position:0% +uh depend on the gradient in +concentrations + + align:start position:0% +concentrations + + + align:start position:0% +concentrations +true they also also depend on on the + + align:start position:0% +true they also also depend on on the + + + align:start position:0% +true they also also depend on on the +gradi in concentration but there is this + + align:start position:0% +gradi in concentration but there is this + + + align:start position:0% +gradi in concentration but there is this +C at the + + align:start position:0% + + + + align:start position:0% + +denominator and when you have a number + + align:start position:0% +denominator and when you have a number + + + align:start position:0% +denominator and when you have a number +at denominator and it is small this + + align:start position:0% +at denominator and it is small this + + + align:start position:0% +at denominator and it is small this +enhances things so the gradient in + + align:start position:0% +enhances things so the gradient in + + + align:start position:0% +enhances things so the gradient in +chemical + + align:start position:0% +chemical + + + align:start position:0% +chemical +potential uh is has two contributions + + align:start position:0% +potential uh is has two contributions + + + align:start position:0% +potential uh is has two contributions +one is also this C at the + + align:start position:0% + + + + align:start position:0% + +denominator so for dilute systems the uh + + align:start position:0% +denominator so for dilute systems the uh + + + align:start position:0% +denominator so for dilute systems the uh +this gets + + align:start position:0% + + + + align:start position:0% + +Amplified and uh it's very nice to see + + align:start position:0% +Amplified and uh it's very nice to see + + + align:start position:0% +Amplified and uh it's very nice to see +how many + + align:start position:0% +how many + + + align:start position:0% +how many +experiments uh they are able to do in + + align:start position:0% +experiments uh they are able to do in + + + align:start position:0% +experiments uh they are able to do in +which this is the driving + + align:start position:0% + + + + align:start position:0% + +force but it's also very nice to see + + align:start position:0% +force but it's also very nice to see + + + align:start position:0% +force but it's also very nice to see +how the modeling + + align:start position:0% +how the modeling + + + align:start position:0% +how the modeling +part is still a bit uh I would say + + align:start position:0% +part is still a bit uh I would say + + + align:start position:0% +part is still a bit uh I would say +primordial uh and uh + + align:start position:0% +primordial uh and uh + + + align:start position:0% +primordial uh and uh +uh very few people really care about uh + + align:start position:0% +uh very few people really care about uh + + + align:start position:0% +uh very few people really care about uh +checking uh if some of the non- + + align:start position:0% +checking uh if some of the non- + + + align:start position:0% +checking uh if some of the non- +equilibrium phenomena that we will talk + + align:start position:0% +equilibrium phenomena that we will talk + + + align:start position:0% +equilibrium phenomena that we will talk +in particular on Sager reciprocity cross + + align:start position:0% +in particular on Sager reciprocity cross + + + align:start position:0% +in particular on Sager reciprocity cross +coupling effects that we will discuss in + + align:start position:0% +coupling effects that we will discuss in + + + align:start position:0% +coupling effects that we will discuss in +the third part of the course whether + + align:start position:0% +the third part of the course whether + + + align:start position:0% +the third part of the course whether +they do play a role or not whether they + + align:start position:0% +they do play a role or not whether they + + + align:start position:0% +they do play a role or not whether they +are small or not + + align:start position:0% +are small or not + + + align:start position:0% +are small or not +usually they are neglected but just + + align:start position:0% +usually they are neglected but just + + + align:start position:0% +usually they are neglected but just +neglected because you want a simple + + align:start position:0% +neglected because you want a simple + + + align:start position:0% +neglected because you want a simple +model not because you know that the + + align:start position:0% +model not because you know that the + + + align:start position:0% +model not because you know that the +effect isn't + + align:start position:0% + + + + align:start position:0% + +there so that's why there is a still a + + align:start position:0% +there so that's why there is a still a + + + align:start position:0% +there so that's why there is a still a +lot of research and you find lots of uh + + align:start position:0% +lot of research and you find lots of uh + + + align:start position:0% +lot of research and you find lots of uh +very interesting papers on these + + align:start position:0% +very interesting papers on these + + + align:start position:0% +very interesting papers on these +subjects okay so talking about + + align:start position:0% +subjects okay so talking about + + + align:start position:0% +subjects okay so talking about +experiments uh last time we also talked + + align:start position:0% +experiments uh last time we also talked + + + align:start position:0% +experiments uh last time we also talked +about we made a quick uh survey of + + align:start position:0% +about we made a quick uh survey of + + + align:start position:0% +about we made a quick uh survey of +the + + align:start position:0% +the + + + align:start position:0% +the +methods that we have in order to measure + + align:start position:0% +methods that we have in order to measure + + + align:start position:0% +methods that we have in order to measure +properties of substances or properties + + align:start position:0% +properties of substances or properties + + + align:start position:0% +properties of substances or properties +of + + align:start position:0% +of + + + align:start position:0% +of +systems so one is the measuring the + + align:start position:0% +systems so one is the measuring the + + + align:start position:0% +systems so one is the measuring the +temperature with the thermometer + + align:start position:0% +temperature with the thermometer + + + align:start position:0% +temperature with the thermometer +measuring the pressure with the + + align:start position:0% + + + + align:start position:0% + +monometer measuring the chemical Pro + + align:start position:0% +monometer measuring the chemical Pro + + + align:start position:0% +monometer measuring the chemical Pro +potentials through a measurement of the + + align:start position:0% +potentials through a measurement of the + + + align:start position:0% +potentials through a measurement of the +partial pressure of a + + align:start position:0% + + + + align:start position:0% + +constituent when this constituent is in + + align:start position:0% +constituent when this constituent is in + + + align:start position:0% +constituent when this constituent is in +mutual equilibrium with the system of + + align:start position:0% +mutual equilibrium with the system of + + + align:start position:0% +mutual equilibrium with the system of +Interest through a semi-permeable + + align:start position:0% +Interest through a semi-permeable + + + align:start position:0% +Interest through a semi-permeable +membrane permeable only to that + + align:start position:0% +membrane permeable only to that + + + align:start position:0% +membrane permeable only to that +constituent When You Reach chemical + + align:start position:0% +constituent When You Reach chemical + + + align:start position:0% +constituent When You Reach chemical +equilibrium that defines the partial + + align:start position:0% +equilibrium that defines the partial + + + align:start position:0% +equilibrium that defines the partial +pressure of the constituent in the + + align:start position:0% +pressure of the constituent in the + + + align:start position:0% +pressure of the constituent in the +mixture and that's how you measure that + + align:start position:0% + + + + align:start position:0% + +and I skip uh the other slides but just + + align:start position:0% +and I skip uh the other slides but just + + + align:start position:0% +and I skip uh the other slides but just +uh uh remind you that we we we said that + + align:start position:0% +uh uh remind you that we we we said that + + + align:start position:0% +uh uh remind you that we we we said that +eventually if you are an experimentalist + + align:start position:0% +eventually if you are an experimentalist + + + align:start position:0% +eventually if you are an experimentalist +and you like to characterize properties + + align:start position:0% +and you like to characterize properties + + + align:start position:0% +and you like to characterize properties +of substances or maybe you discover a + + align:start position:0% +of substances or maybe you discover a + + + align:start position:0% +of substances or maybe you discover a +new substance and you want to + + align:start position:0% +new substance and you want to + + + align:start position:0% +new substance and you want to +characterize it what you have to measure + + align:start position:0% +characterize it what you have to measure + + + align:start position:0% +characterize it what you have to measure +in the + + align:start position:0% +in the + + + align:start position:0% +in the +lab and what you have to publish and + + align:start position:0% +lab and what you have to publish and + + + align:start position:0% +lab and what you have to publish and +eventually gets listed in a um like the + + align:start position:0% +eventually gets listed in a um like the + + + align:start position:0% +eventually gets listed in a um like the +handbook of a chemical + + align:start position:0% +handbook of a chemical + + + align:start position:0% +handbook of a chemical +physics or the nist uh website where you + + align:start position:0% +physics or the nist uh website where you + + + align:start position:0% +physics or the nist uh website where you +can find properties of substances as in + + align:start position:0% +can find properties of substances as in + + + align:start position:0% +can find properties of substances as in +the old times you you would buy the book + + align:start position:0% +the old times you you would buy the book + + + align:start position:0% +the old times you you would buy the book +The CRC Handbook of chemical physics now + + align:start position:0% +The CRC Handbook of chemical physics now + + + align:start position:0% +The CRC Handbook of chemical physics now +uh books are like uh + + align:start position:0% +uh books are like uh + + + align:start position:0% +uh books are like uh +in + + align:start position:0% +in + + + align:start position:0% +in +disappearing uh so you're all virtual + + align:start position:0% +disappearing uh so you're all virtual + + + align:start position:0% +disappearing uh so you're all virtual +and so you go to the uh websites and + + align:start position:0% +and so you go to the uh websites and + + + align:start position:0% +and so you go to the uh websites and +look for these properties or you buy + + align:start position:0% +look for these properties or you buy + + + align:start position:0% +look for these properties or you buy +softwares + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +I you probably use some software uh that + + align:start position:0% +I you probably use some software uh that + + + align:start position:0% +I you probably use some software uh that +has + + align:start position:0% +has + + + align:start position:0% +has +builtin uh correlations for many + + align:start position:0% +builtin uh correlations for many + + + align:start position:0% +builtin uh correlations for many +substances and these + + align:start position:0% +substances and these + + + align:start position:0% +substances and these +correlations give you + + align:start position:0% +correlations give you + + + align:start position:0% +correlations give you +values for these quantities the specific + + align:start position:0% +values for these quantities the specific + + + align:start position:0% +values for these quantities the specific +I'm sorry the yeah the heat capacities + + align:start position:0% +I'm sorry the yeah the heat capacities + + + align:start position:0% +I'm sorry the yeah the heat capacities +of your + + align:start position:0% +of your + + + align:start position:0% +of your +substance um + + align:start position:0% +substance um + + + align:start position:0% +substance um +the + + align:start position:0% +the + + + align:start position:0% +the +compressibility + + align:start position:0% +compressibility + + + align:start position:0% +compressibility +Kappa + + align:start position:0% +Kappa + + + align:start position:0% +Kappa +isothermal or sometimes also another + + align:start position:0% +isothermal or sometimes also another + + + align:start position:0% +isothermal or sometimes also another +kind + + align:start position:0% +kind + + + align:start position:0% +kind +of the isentropic + + align:start position:0% +of the isentropic + + + align:start position:0% +of the isentropic +compressibility which is equivalent or + + align:start position:0% +compressibility which is equivalent or + + + align:start position:0% +compressibility which is equivalent or +connected to this one and also here it's + + align:start position:0% +connected to this one and also here it's + + + align:start position:0% +connected to this one and also here it's +either the heat capacity at constant + + align:start position:0% +either the heat capacity at constant + + + align:start position:0% +either the heat capacity at constant +pressure or the heat capacity at + + align:start position:0% +pressure or the heat capacity at + + + align:start position:0% +pressure or the heat capacity at +constant volume because through the + + align:start position:0% +constant volume because through the + + + align:start position:0% +constant volume because through the +Mayer relation they are + + align:start position:0% +Mayer relation they are + + + align:start position:0% +Mayer relation they are +related and the coefficient of expansion + + align:start position:0% +related and the coefficient of expansion + + + align:start position:0% +related and the coefficient of expansion +of your + + align:start position:0% +of your + + + align:start position:0% +of your +substance for + + align:start position:0% +substance for + + + align:start position:0% +substance for +example the + + align:start position:0% +example the + + + align:start position:0% +example the +compressibility uh if you are in solid + + align:start position:0% +compressibility uh if you are in solid + + + align:start position:0% +compressibility uh if you are in solid +mechanics you remember the young modulus + + align:start position:0% +mechanics you remember the young modulus + + + align:start position:0% +mechanics you remember the young modulus +of uh some + + align:start position:0% +of uh some + + + align:start position:0% +of uh some +elasticity well uh this is a sort of + + align:start position:0% +elasticity well uh this is a sort of + + + align:start position:0% +elasticity well uh this is a sort of +young modulus in the bulk so in + + align:start position:0% +young modulus in the bulk so in + + + align:start position:0% +young modulus in the bulk so in +elasticity you do the stretching in one + + align:start position:0% +elasticity you do the stretching in one + + + align:start position:0% +elasticity you do the stretching in one +direction if you do it in all three + + align:start position:0% +direction if you do it in all three + + + align:start position:0% +direction if you do it in all three +directions you get uh the + + align:start position:0% +directions you get uh the + + + align:start position:0% +directions you get uh the +compressibility + + align:start position:0% + + + + align:start position:0% + +coefficient + + align:start position:0% +coefficient + + + align:start position:0% +coefficient +no that's because uh uh that's because V + + align:start position:0% +no that's because uh uh that's because V + + + align:start position:0% +no that's because uh uh that's because V +you for a specimen of + + align:start position:0% +you for a specimen of + + + align:start position:0% +you for a specimen of +like parallel + + align:start position:0% +like parallel + + + align:start position:0% +like parallel +ID uh is given by that and uh if you + + align:start position:0% +ID uh is given by that and uh if you + + + align:start position:0% +ID uh is given by that and uh if you +have one + + align:start position:0% +have one + + + align:start position:0% +have one +over V + + align:start position:0% +over V + + + align:start position:0% +over V +times the partial of V with respect to + + align:start position:0% +times the partial of V with respect to + + + align:start position:0% +times the partial of V with respect to +um P at constant T time minus that's + + align:start position:0% +um P at constant T time minus that's + + + align:start position:0% +um P at constant T time minus that's +Capa + + align:start position:0% +Capa + + + align:start position:0% +Capa +T that's the isothermal + + align:start position:0% + + + + align:start position:0% + +compressibility so you could you could + + align:start position:0% +compressibility so you could you could + + + align:start position:0% +compressibility so you could you could +write that as + + align:start position:0% +write that as + + + align:start position:0% +write that as +minus the partial of the log of V with + + align:start position:0% +minus the partial of the log of V with + + + align:start position:0% +minus the partial of the log of V with +respect to + + align:start position:0% + + + + align:start position:0% + +p and because of the additivity of + + align:start position:0% +p and because of the additivity of + + + align:start position:0% +p and because of the additivity of +logarithm this is uh you could write it + + align:start position:0% +logarithm this is uh you could write it + + + align:start position:0% +logarithm this is uh you could write it +as the partial of + + align:start position:0% +as the partial of + + + align:start position:0% +as the partial of +L1 respect to P + + align:start position:0% +L1 respect to P + + + align:start position:0% +L1 respect to P +so times partial of + + align:start position:0% + + + + align:start position:0% + +L2 is that + + align:start position:0% + + + + align:start position:0% + +correct yeah no uh plus not minus + + align:start position:0% +correct yeah no uh plus not minus + + + align:start position:0% +correct yeah no uh plus not minus +not minus okay minus uh + + align:start position:0% + + + + align:start position:0% + +L3 okay so + + align:start position:0% +L3 okay so + + + align:start position:0% +L3 okay so +this and that's also sorry uh oh + + align:start position:0% +this and that's also sorry uh oh + + + align:start position:0% +this and that's also sorry uh oh +boy that's more than a senior uh moment + + align:start position:0% +boy that's more than a senior uh moment + + + align:start position:0% +boy that's more than a senior uh moment +let's do it + + align:start position:0% +let's do it + + + align:start position:0% +let's do it +again log L1 + + align:start position:0% + + + + align:start position:0% + +partial PT minus log + + align:start position:0% +partial PT minus log + + + align:start position:0% +partial PT minus log +L2 and so + + align:start position:0% +L2 and so + + + align:start position:0% +L2 and so +on and each one of + + align:start position:0% +on and each one of + + + align:start position:0% +on and each one of +these is the young module it's one over + + align:start position:0% +these is the young module it's one over + + + align:start position:0% +these is the young module it's one over +LDL over P so it's the the percentage + + align:start position:0% +LDL over P so it's the the percentage + + + align:start position:0% +LDL over P so it's the the percentage +stretching changing in in + + align:start position:0% +stretching changing in in + + + align:start position:0% +stretching changing in in +distance uh for an increase in uh in in + + align:start position:0% +distance uh for an increase in uh in in + + + align:start position:0% +distance uh for an increase in uh in in +pressure uh + + align:start position:0% +pressure uh + + + align:start position:0% +pressure uh +uh and that's the thing that you measure + + align:start position:0% +uh and that's the thing that you measure + + + align:start position:0% +uh and that's the thing that you measure +with the compression compression machine + + align:start position:0% +with the compression compression machine + + + align:start position:0% +with the compression compression machine +it's the young mod modulus in that + + align:start position:0% +it's the young mod modulus in that + + + align:start position:0% +it's the young mod modulus in that +direction all right once what we + + align:start position:0% +direction all right once what we + + + align:start position:0% +direction all right once what we +proved is that once you have U + + align:start position:0% +proved is that once you have U + + + align:start position:0% +proved is that once you have U +this functions + + align:start position:0% +this functions + + + align:start position:0% +this functions +here you don't just need the one point + + align:start position:0% +here you don't just need the one point + + + align:start position:0% +here you don't just need the one point +you need the entire function so how they + + align:start position:0% +you need the entire function so how they + + + align:start position:0% +you need the entire function so how they +vary in temperature and pressure at + + align:start position:0% +vary in temperature and pressure at + + + align:start position:0% +vary in temperature and pressure at +given + + align:start position:0% +given + + + align:start position:0% +given +composition then using these formulas + + align:start position:0% +composition then using these formulas + + + align:start position:0% +composition then using these formulas +you can integrate these + + align:start position:0% +you can integrate these + + + align:start position:0% +you can integrate these +formulas and obtain the values for + + align:start position:0% +formulas and obtain the values for + + + align:start position:0% +formulas and obtain the values for +energy and entropy and therefore you can + + align:start position:0% +energy and entropy and therefore you can + + + align:start position:0% +energy and entropy and therefore you can +reconstruct the fundamental relation so + + align:start position:0% +reconstruct the fundamental relation so + + + align:start position:0% +reconstruct the fundamental relation so +that's how you measure the fundamental + + align:start position:0% +that's how you measure the fundamental + + + align:start position:0% +that's how you measure the fundamental +relation somewhat indirectly through its + + align:start position:0% +relation somewhat indirectly through its + + + align:start position:0% +relation somewhat indirectly through its +derivatives temperature pressure and + + align:start position:0% +derivatives temperature pressure and + + + align:start position:0% +derivatives temperature pressure and +derivatives of derivatives like the + + align:start position:0% +derivatives of derivatives like the + + + align:start position:0% +derivatives of derivatives like the +specific heat or the heat + + align:start position:0% +specific heat or the heat + + + align:start position:0% +specific heat or the heat +capacities Okay so that introduces to + + align:start position:0% +capacities Okay so that introduces to + + + align:start position:0% +capacities Okay so that introduces to +the subject that I started uh I just + + align:start position:0% +the subject that I started uh I just + + + align:start position:0% +the subject that I started uh I just +barely started last + + align:start position:0% +barely started last + + + align:start position:0% +barely started last +time which is a + + align:start position:0% + + + + align:start position:0% + +again uh a bit boring because it's like + + align:start position:0% +again uh a bit boring because it's like + + + align:start position:0% +again uh a bit boring because it's like +a mathematical game played on the + + align:start position:0% +a mathematical game played on the + + + align:start position:0% +a mathematical game played on the +fundamental + + align:start position:0% +fundamental + + + align:start position:0% +fundamental +relation but it is part of the + + align:start position:0% +relation but it is part of the + + + align:start position:0% +relation but it is part of the +traditional um topics that we do in + + align:start position:0% +traditional um topics that we do in + + + align:start position:0% +traditional um topics that we do in +thermodynamics I certainly think that + + align:start position:0% +thermodynamics I certainly think that + + + align:start position:0% +thermodynamics I certainly think that +are needed when you do measurements and + + align:start position:0% +are needed when you do measurements and + + + align:start position:0% +are needed when you do measurements and +you want to correlate the data you want + + align:start position:0% +you want to correlate the data you want + + + align:start position:0% +you want to correlate the data you want +to make sure that this relations are are + + align:start position:0% +to make sure that this relations are are + + + align:start position:0% +to make sure that this relations are are +are + + align:start position:0% +are + + + align:start position:0% +are +satisfied so let's just let's do it I'll + + align:start position:0% +satisfied so let's just let's do it I'll + + + align:start position:0% +satisfied so let's just let's do it I'll +do it as quickly as + + align:start position:0% +do it as quickly as + + + align:start position:0% +do it as quickly as +possible + + align:start position:0% +possible + + + align:start position:0% +possible +um so the idea of Leandra + + align:start position:0% +um so the idea of Leandra + + + align:start position:0% +um so the idea of Leandra +transform is to describe a a curve this + + align:start position:0% + + + + align:start position:0% + +curve instead as the the the the direct + + align:start position:0% +curve instead as the the the the direct + + + align:start position:0% +curve instead as the the the the direct +description f equals F of Y so this is f + + align:start position:0% +description f equals F of Y so this is f + + + align:start position:0% +description f equals F of Y so this is f +and + + align:start position:0% +and + + + align:start position:0% +and +Y in a more indirect + + align:start position:0% +Y in a more indirect + + + align:start position:0% +Y in a more indirect +description in terms of the + + align:start position:0% +description in terms of the + + + align:start position:0% +description in terms of the +family of it the tangent lines to the + + align:start position:0% +family of it the tangent lines to the + + + align:start position:0% +family of it the tangent lines to the +curve so that the curve becomes the + + align:start position:0% +curve so that the curve becomes the + + + align:start position:0% +curve so that the curve becomes the +envelope of this family of + + align:start position:0% + + + + align:start position:0% + +lines and this family of lines is + + align:start position:0% +lines and this family of lines is + + + align:start position:0% +lines and this family of lines is +described by uh in such a way that you + + align:start position:0% +described by uh in such a way that you + + + align:start position:0% +described by uh in such a way that you +choose a value + + align:start position:0% +choose a value + + + align:start position:0% +choose a value +for the slope of the line and then you + + align:start position:0% +for the slope of the line and then you + + + align:start position:0% +for the slope of the line and then you +shift the line until you make you find + + align:start position:0% +shift the line until you make you find + + + align:start position:0% +shift the line until you make you find +the point in which your curve is tangent + + align:start position:0% +the point in which your curve is tangent + + + align:start position:0% +the point in which your curve is tangent +to that line with that slope and then + + align:start position:0% +to that line with that slope and then + + + align:start position:0% +to that line with that slope and then +you mark the value of the intercept at y + + align:start position:0% +you mark the value of the intercept at y + + + align:start position:0% +you mark the value of the intercept at y +equal 0 here we call it l of L of Lambda + + align:start position:0% +equal 0 here we call it l of L of Lambda + + + align:start position:0% +equal 0 here we call it l of L of Lambda +so this L of + + align:start position:0% +so this L of + + + align:start position:0% +so this L of +Lambda is the legender transform of your + + align:start position:0% +Lambda is the legender transform of your + + + align:start position:0% +Lambda is the legender transform of your +original + + align:start position:0% + + + + align:start position:0% + +function when I have more time but I + + align:start position:0% +function when I have more time but I + + + align:start position:0% +function when I have more time but I +don't uh + + align:start position:0% +don't uh + + + align:start position:0% +don't uh +hear I like to play this game this is a + + align:start position:0% +hear I like to play this game this is a + + + align:start position:0% +hear I like to play this game this is a +game in which you can this is + + align:start position:0% +game in which you can this is + + + align:start position:0% +game in which you can this is +the the Lan Transformer has applications + + align:start position:0% +the the Lan Transformer has applications + + + align:start position:0% +the the Lan Transformer has applications +also + + align:start position:0% +also + + + align:start position:0% +also +in mechanics for example it allows you + + align:start position:0% +in mechanics for example it allows you + + + align:start position:0% +in mechanics for example it allows you +to + + align:start position:0% +to + + + align:start position:0% +to +design uh in a bridge you know those + + align:start position:0% +design uh in a bridge you know those + + + align:start position:0% +design uh in a bridge you know those +bridges with lots of wires you want to + + align:start position:0% +bridges with lots of wires you want to + + + align:start position:0% +bridges with lots of wires you want to +have the wires be distributed in such a + + align:start position:0% +have the wires be distributed in such a + + + align:start position:0% +have the wires be distributed in such a +way that they make this envelope and you + + align:start position:0% +way that they make this envelope and you + + + align:start position:0% +way that they make this envelope and you +want to decide which shape of envelope + + align:start position:0% +want to decide which shape of envelope + + + align:start position:0% +want to decide which shape of envelope +you want okay for example so here's my + + align:start position:0% + + + + align:start position:0% + +bridge and suppose I want my + + align:start position:0% + + + + align:start position:0% + +uh the the envelope of these uh things + + align:start position:0% +uh the the envelope of these uh things + + + align:start position:0% +uh the the envelope of these uh things +that sustain the + + align:start position:0% + + + + align:start position:0% + +bridge from a distant distance you want + + align:start position:0% +bridge from a distant distance you want + + + align:start position:0% +bridge from a distant distance you want +it to have a certain shape maybe a + + align:start position:0% +it to have a certain shape maybe a + + + align:start position:0% +it to have a certain shape maybe a +circle or maybe an ellipse or whatever + + align:start position:0% +circle or maybe an ellipse or whatever + + + align:start position:0% +circle or maybe an ellipse or whatever +so you fix that shape and then by doing + + align:start position:0% +so you fix that shape and then by doing + + + align:start position:0% +so you fix that shape and then by doing +the Leandra transform you find the um uh + + align:start position:0% +the Leandra transform you find the um uh + + + align:start position:0% +the Leandra transform you find the um uh +the the points where you have to U Pull + + align:start position:0% +the the points where you have to U Pull + + + align:start position:0% +the the points where you have to U Pull +or or attach your + + align:start position:0% + + + + align:start position:0% + +wires + + align:start position:0% + + + + align:start position:0% + +okay so by construction + + align:start position:0% +okay so by construction + + + align:start position:0% +okay so by construction +here essentially L you see if you look + + align:start position:0% +here essentially L you see if you look + + + align:start position:0% +here essentially L you see if you look +at this triangle you realize that L is + + align:start position:0% +at this triangle you realize that L is + + + align:start position:0% +at this triangle you realize that L is +simply + + align:start position:0% +simply + + + align:start position:0% +simply +F minus y times the tangent of this Ang + + align:start position:0% +F minus y times the tangent of this Ang + + + align:start position:0% +F minus y times the tangent of this Ang +angle which is + + align:start position:0% +angle which is + + + align:start position:0% +angle which is +Lambda so L is f minus Lambda + + align:start position:0% +Lambda so L is f minus Lambda + + + align:start position:0% +Lambda so L is f minus Lambda +y f f minus Lambda + + align:start position:0% +y f f minus Lambda + + + align:start position:0% +y f f minus Lambda +y so that's how you construct + + align:start position:0% +y so that's how you construct + + + align:start position:0% +y so that's how you construct +it h you can play these are some + + align:start position:0% +it h you can play these are some + + + align:start position:0% +it h you can play these are some +examples for example e to the + + align:start position:0% +examples for example e to the + + + align:start position:0% +examples for example e to the +Y the Lan transform is Lambda minus + + align:start position:0% +Y the Lan transform is Lambda minus + + + align:start position:0% +Y the Lan transform is Lambda minus +Lambda log + + align:start position:0% + + + + align:start position:0% + +Lambda or thean form of of half of Y 2 + + align:start position:0% +Lambda or thean form of of half of Y 2 + + + align:start position:0% +Lambda or thean form of of half of Y 2 +like + + align:start position:0% +like + + + align:start position:0% +like +Parabola uh is + + align:start position:0% +Parabola uh is + + + align:start position:0% +Parabola uh is +exactly uh the same + + align:start position:0% + + + + align:start position:0% + +function and so for quadratic + + align:start position:0% +function and so for quadratic + + + align:start position:0% +function and so for quadratic +forms if you put the half the half is + + align:start position:0% +forms if you put the half the half is + + + align:start position:0% +forms if you put the half the half is +important what is also interesting is if + + align:start position:0% +important what is also interesting is if + + + align:start position:0% +important what is also interesting is if +you like this game I'm not going to to + + align:start position:0% +you like this game I'm not going to to + + + align:start position:0% +you like this game I'm not going to to +the details but here is the proof that + + align:start position:0% +the details but here is the proof that + + + align:start position:0% +the details but here is the proof that +uh when you do this kind of + + align:start position:0% +uh when you do this kind of + + + align:start position:0% +uh when you do this kind of +transformation and this is why Leander + + align:start position:0% +transformation and this is why Leander + + + align:start position:0% +transformation and this is why Leander +does it you don't lose information about + + align:start position:0% +does it you don't lose information about + + + align:start position:0% +does it you don't lose information about +the original + + align:start position:0% + + + + align:start position:0% + +function uh and so if you do + + align:start position:0% +function uh and so if you do + + + align:start position:0% +function uh and so if you do +again the lender transform of the of the + + align:start position:0% +again the lender transform of the of the + + + align:start position:0% +again the lender transform of the of the +lender transform you get back your + + align:start position:0% +lender transform you get back your + + + align:start position:0% +lender transform you get back your +original + + align:start position:0% + + + + align:start position:0% + +function this is similar to what we've + + align:start position:0% +function this is similar to what we've + + + align:start position:0% +function this is similar to what we've +done + + align:start position:0% +done + + + align:start position:0% +done +here because we describe + + align:start position:0% +here because we describe + + + align:start position:0% +here because we describe +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh this function + + align:start position:0% +uh this function + + + align:start position:0% +uh this function +here + + align:start position:0% +here + + + align:start position:0% +here +in in a smart way which was devised by + + align:start position:0% +in in a smart way which was devised by + + + align:start position:0% +in in a smart way which was devised by +Gibbs uh in the late 19 uh 18 + + align:start position:0% +Gibbs uh in the late 19 uh 18 + + + align:start position:0% +Gibbs uh in the late 19 uh 18 +1800s + + align:start position:0% +1800s + + + align:start position:0% +1800s +um by descri by tangents by you you + + align:start position:0% +um by descri by tangents by you you + + + align:start position:0% +um by descri by tangents by you you +describe this function by its partial + + align:start position:0% +describe this function by its partial + + + align:start position:0% +describe this function by its partial +derivatives the temperature is is the + + align:start position:0% +derivatives the temperature is is the + + + align:start position:0% +derivatives the temperature is is the +slope in One Direction and pressure is + + align:start position:0% +slope in One Direction and pressure is + + + align:start position:0% +slope in One Direction and pressure is +the slope in the other direction so this + + align:start position:0% +the slope in the other direction so this + + + align:start position:0% +the slope in the other direction so this +is why this transformation + + align:start position:0% +is why this transformation + + + align:start position:0% +is why this transformation +matters and uh here in fact is that + + align:start position:0% +matters and uh here in fact is that + + + align:start position:0% +matters and uh here in fact is that +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +done starting for example on the + + align:start position:0% +done starting for example on the + + + align:start position:0% +done starting for example on the +fundamental relation based on energy in + + align:start position:0% +fundamental relation based on energy in + + + align:start position:0% +fundamental relation based on energy in +energy + + align:start position:0% +energy + + + align:start position:0% +energy +form for for which you + + align:start position:0% +form for for which you + + + align:start position:0% +form for for which you +remember this is the form of the + + align:start position:0% +remember this is the form of the + + + align:start position:0% +remember this is the form of the +differential so D is TDS minus + + align:start position:0% +differential so D is TDS minus + + + align:start position:0% +differential so D is TDS minus +pdv plus chemical + + align:start position:0% +pdv plus chemical + + + align:start position:0% +pdv plus chemical +potentials times the + + align:start position:0% + + + + align:start position:0% + +end and this line reminds you of what we + + align:start position:0% +end and this line reminds you of what we + + + align:start position:0% +end and this line reminds you of what we +just saw so it's the definition of the + + align:start position:0% +just saw so it's the definition of the + + + align:start position:0% +just saw so it's the definition of the +generic definition of Lan transform for + + align:start position:0% +generic definition of Lan transform for + + + align:start position:0% +generic definition of Lan transform for +for a function f of + + align:start position:0% +for a function f of + + + align:start position:0% +for a function f of +Y so L IS F Lambda + + align:start position:0% +Y so L IS F Lambda + + + align:start position:0% +Y so L IS F Lambda +Y and here is the application so if I + + align:start position:0% +Y and here is the application so if I + + + align:start position:0% +Y and here is the application so if I +take that + + align:start position:0% + + + + align:start position:0% + +function now it is a function of many + + align:start position:0% +function now it is a function of many + + + align:start position:0% +function now it is a function of many +variables so I have to choose one at a + + align:start position:0% +variables so I have to choose one at a + + + align:start position:0% +variables so I have to choose one at a +time and do a lan transform of one for + + align:start position:0% +time and do a lan transform of one for + + + align:start position:0% +time and do a lan transform of one for +example I want to substitute + + align:start position:0% + + + + align:start position:0% + +s with + + align:start position:0% + + + + align:start position:0% + +T so I want to find an equivalent a + + align:start position:0% +T so I want to find an equivalent a + + + align:start position:0% +T so I want to find an equivalent a +function that contains the same + + align:start position:0% +function that contains the same + + + align:start position:0% +function that contains the same +information + + align:start position:0% +information + + + align:start position:0% +information +of the fundamental + + align:start position:0% +of the fundamental + + + align:start position:0% +of the fundamental +relation but in which the independent I + + align:start position:0% +relation but in which the independent I + + + align:start position:0% +relation but in which the independent I +change the independent variable s to the + + align:start position:0% +change the independent variable s to the + + + align:start position:0% +change the independent variable s to the +uh to its + + align:start position:0% +uh to its + + + align:start position:0% +uh to its +slope + + align:start position:0% +slope + + + align:start position:0% +slope +T all + + align:start position:0% +T all + + + align:start position:0% +T all +right so it's f f the new function the + + align:start position:0% +right so it's f f the new function the + + + align:start position:0% +right so it's f f the new function the +Lan transform is the original function + + align:start position:0% +Lan transform is the original function + + + align:start position:0% +Lan transform is the original function +minus the product of Lambda time y so + + align:start position:0% +minus the product of Lambda time y so + + + align:start position:0% +minus the product of Lambda time y so +Lambda in this case is T and Y is s + + align:start position:0% +Lambda in this case is T and Y is s + + + align:start position:0% +Lambda in this case is T and Y is s +this function is called the hel mol free + + align:start position:0% + + + + align:start position:0% + +energy and you can uh uh also write very + + align:start position:0% +energy and you can uh uh also write very + + + align:start position:0% +energy and you can uh uh also write very +easily uh + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +uh let's do it um + + align:start position:0% + + + + align:start position:0% + +only forget about the amounts so + + align:start position:0% + + + + align:start position:0% + +okay so we have this one up + + align:start position:0% +okay so we have this one up + + + align:start position:0% +okay so we have this one up +there now we have defined the function + + align:start position:0% +there now we have defined the function + + + align:start position:0% +there now we have defined the function +fals e minus + + align:start position:0% +fals e minus + + + align:start position:0% +fals e minus +TS we want to compute + + align:start position:0% + + + + align:start position:0% + +DF all right so this is like + + align:start position:0% +DF all right so this is like + + + align:start position:0% +DF all right so this is like +D minus D of + + align:start position:0% +D minus D of + + + align:start position:0% +D minus D of +TS and then we can use the I think it's + + align:start position:0% +TS and then we can use the I think it's + + + align:start position:0% +TS and then we can use the I think it's +called lightness Rule that this is equal + + align:start position:0% +called lightness Rule that this is equal + + + align:start position:0% +called lightness Rule that this is equal +to uh so D for de we have it up there + + align:start position:0% +to uh so D for de we have it up there + + + align:start position:0% +to uh so D for de we have it up there +it's t d s minus P + + align:start position:0% +it's t d s minus P + + + align:start position:0% +it's t d s minus P +DV and here this is minus t d s minus s + + align:start position:0% + + + + align:start position:0% + +DT so one of these will cancel + + align:start position:0% +DT so one of these will cancel + + + align:start position:0% +DT so one of these will cancel +that and we are left with minus sdt + + align:start position:0% +that and we are left with minus sdt + + + align:start position:0% +that and we are left with minus sdt +minus P DV which I hope is what is + + align:start position:0% +minus P DV which I hope is what is + + + align:start position:0% +minus P DV which I hope is what is +written there + + align:start position:0% +written there + + + align:start position:0% +written there +yeah + + align:start position:0% + + + + align:start position:0% + +okay okay now so in a sense from the + + align:start position:0% +okay okay now so in a sense from the + + + align:start position:0% +okay okay now so in a sense from the +Practical point of view what have we + + align:start position:0% +Practical point of view what have we + + + align:start position:0% +Practical point of view what have we +done here we gained the fact that we we + + align:start position:0% +done here we gained the fact that we we + + + align:start position:0% +done here we gained the fact that we we +we we have a new function that contains + + align:start position:0% +we we have a new function that contains + + + align:start position:0% +we we have a new function that contains +the same information and it is in terms + + align:start position:0% +the same information and it is in terms + + + align:start position:0% +the same information and it is in terms +of properties easily measurable + + align:start position:0% +of properties easily measurable + + + align:start position:0% +of properties easily measurable +temperature volume + + align:start position:0% + + + + align:start position:0% + +I could have done it + + align:start position:0% +I could have done it + + + align:start position:0% +I could have done it +also with respect to the second variable + + align:start position:0% +also with respect to the second variable + + + align:start position:0% +also with respect to the second variable +so change the volume with pressure it's + + align:start position:0% +so change the volume with pressure it's + + + align:start position:0% +so change the volume with pressure it's +the conjugate variable so the the temp + + align:start position:0% +the conjugate variable so the the temp + + + align:start position:0% +the conjugate variable so the the temp +the the doope in that direction is the + + align:start position:0% +the the doope in that direction is the + + + align:start position:0% +the the doope in that direction is the +conjugate value uh to the volume is the + + align:start position:0% +conjugate value uh to the volume is the + + + align:start position:0% +conjugate value uh to the volume is the +pressure is minus the + + align:start position:0% +pressure is minus the + + + align:start position:0% +pressure is minus the +pressure all right then the L transform + + align:start position:0% +pressure all right then the L transform + + + align:start position:0% +pressure all right then the L transform +is u e the original function minus the + + align:start position:0% +is u e the original function minus the + + + align:start position:0% +is u e the original function minus the +slope which is minus P * V so that's e + + align:start position:0% +slope which is minus P * V so that's e + + + align:start position:0% +slope which is minus P * V so that's e +plus + + align:start position:0% +plus + + + align:start position:0% +plus +PV that's called the + + align:start position:0% +PV that's called the + + + align:start position:0% +PV that's called the +enthalpy and you have used it for bulk + + align:start position:0% +enthalpy and you have used it for bulk + + + align:start position:0% +enthalpy and you have used it for bulk +flow interactions we'll review that + + align:start position:0% +flow interactions we'll review that + + + align:start position:0% +flow interactions we'll review that +extremely quickly uh probably next + + align:start position:0% +extremely quickly uh probably next + + + align:start position:0% +extremely quickly uh probably next +time no later because it needs uh uh to + + align:start position:0% +time no later because it needs uh uh to + + + align:start position:0% +time no later because it needs uh uh to +it needs the the microscopic the simple + + align:start position:0% +it needs the the microscopic the simple + + + align:start position:0% +it needs the the microscopic the simple +system + + align:start position:0% +system + + + align:start position:0% +system +model all right so you take + + align:start position:0% +model all right so you take + + + align:start position:0% +model all right so you take +uh you take this one it still as the + + align:start position:0% +uh you take this one it still as the + + + align:start position:0% +uh you take this one it still as the +uh see this is now a fun becomes a + + align:start position:0% +uh see this is now a fun becomes a + + + align:start position:0% +uh see this is now a fun becomes a +function of spnn you can compute as we + + align:start position:0% +function of spnn you can compute as we + + + align:start position:0% +function of spnn you can compute as we +did the + + align:start position:0% + + + + align:start position:0% + +differential and uh it's it still has + + align:start position:0% +differential and uh it's it still has + + + align:start position:0% +differential and uh it's it still has +entropy so now we can take the Lan trans + + align:start position:0% +entropy so now we can take the Lan trans + + + align:start position:0% +entropy so now we can take the Lan trans +form of this + + align:start position:0% +form of this + + + align:start position:0% +form of this +one with respect to entropy so + + align:start position:0% +one with respect to entropy so + + + align:start position:0% +one with respect to entropy so +substitute s with its conjugate which is + + align:start position:0% + + + + align:start position:0% + +T not it's not at always entropy that t + + align:start position:0% +T not it's not at always entropy that t + + + align:start position:0% +T not it's not at always entropy that t +is the conjugate of s because previously + + align:start position:0% +is the conjugate of s because previously + + + align:start position:0% +is the conjugate of s because previously +here you prove by looking at the + + align:start position:0% +here you prove by looking at the + + + align:start position:0% +here you prove by looking at the +differential that t is also the partial + + align:start position:0% +differential that t is also the partial + + + align:start position:0% +differential that t is also the partial +of H with respect to + + align:start position:0% +of H with respect to + + + align:start position:0% +of H with respect to +S so by doing that differential we we + + align:start position:0% +S so by doing that differential we we + + + align:start position:0% +S so by doing that differential we we +have found that + + align:start position:0% +have found that + + + align:start position:0% +have found that +t which is from the fundamental relation + + align:start position:0% +t which is from the fundamental relation + + + align:start position:0% +t which is from the fundamental relation +up there is the partial of e with + + align:start position:0% +up there is the partial of e with + + + align:start position:0% +up there is the partial of e with +respect to S when the other variable is + + align:start position:0% +respect to S when the other variable is + + + align:start position:0% +respect to S when the other variable is +V I forget the N for the + + align:start position:0% +V I forget the N for the + + + align:start position:0% +V I forget the N for the +moment now we also + + align:start position:0% +moment now we also + + + align:start position:0% +moment now we also +proved well we didn't prove it but that + + align:start position:0% +proved well we didn't prove it but that + + + align:start position:0% +proved well we didn't prove it but that +lines that form of differential says + + align:start position:0% +lines that form of differential says + + + align:start position:0% +lines that form of differential says +that this is the partial of + + align:start position:0% +that this is the partial of + + + align:start position:0% +that this is the partial of +H what is it partial of H with respect + + align:start position:0% +H what is it partial of H with respect + + + align:start position:0% +H what is it partial of H with respect +to + + align:start position:0% +to + + + align:start position:0% +to +S when the other variable + + align:start position:0% +S when the other variable + + + align:start position:0% +S when the other variable +is + + align:start position:0% +is + + + align:start position:0% +is +p + + align:start position:0% +p + + + align:start position:0% +p +okay so I do the Lan transform of this + + align:start position:0% +okay so I do the Lan transform of this + + + align:start position:0% +okay so I do the Lan transform of this +one so H minus the slope which is T + + align:start position:0% +one so H minus the slope which is T + + + align:start position:0% +one so H minus the slope which is T +times the the the original variable + + align:start position:0% +times the the the original variable + + + align:start position:0% +times the the the original variable +independent variable so that's H minus + + align:start position:0% +independent variable so that's H minus + + + align:start position:0% +independent variable so that's H minus +TS that's e minus TS plus PV that's the + + align:start position:0% +TS that's e minus TS plus PV that's the + + + align:start position:0% +TS that's e minus TS plus PV that's the +Gibs free energy very + + align:start position:0% + + + + align:start position:0% + +important and you + + align:start position:0% +important and you + + + align:start position:0% +important and you +to compute this uh uh + + align:start position:0% + + + + align:start position:0% + +differential yeah because you see by + + align:start position:0% +differential yeah because you see by + + + align:start position:0% +differential yeah because you see by +looking at + + align:start position:0% +looking at + + + align:start position:0% +looking at +U by looking at the form of the + + align:start position:0% +U by looking at the form of the + + + align:start position:0% +U by looking at the form of the +differential like this + + align:start position:0% +differential like this + + + align:start position:0% +differential like this +one I look at the + + align:start position:0% + + + + align:start position:0% + +coefficients uh it is clear + + align:start position:0% + + + + align:start position:0% + +that this that I circled is the partial + + align:start position:0% +that this that I circled is the partial + + + align:start position:0% +that this that I circled is the partial +derivative of x with respect to T when V + + align:start position:0% +derivative of x with respect to T when V + + + align:start position:0% +derivative of x with respect to T when V +is the other + + align:start position:0% +is the other + + + align:start position:0% +is the other +variable so from this one I immediately + + align:start position:0% +variable so from this one I immediately + + + align:start position:0% +variable so from this one I immediately +can see that minus s is the partial of f + + align:start position:0% +can see that minus s is the partial of f + + + align:start position:0% +can see that minus s is the partial of f +with respect to + + align:start position:0% + + + + align:start position:0% + +T when V is the other + + align:start position:0% +T when V is the other + + + align:start position:0% +T when V is the other +variable and the other it says that + + align:start position:0% +variable and the other it says that + + + align:start position:0% +variable and the other it says that +minus p is the partial of f with respect + + align:start position:0% +minus p is the partial of f with respect + + + align:start position:0% +minus p is the partial of f with respect +to + + align:start position:0% +to + + + align:start position:0% +to +V when T is the other variable + + align:start position:0% + + + + align:start position:0% + +okay we could also go + + align:start position:0% +okay we could also go + + + align:start position:0% +okay we could also go +on usually Nobody Does this + + align:start position:0% +on usually Nobody Does this + + + align:start position:0% +on usually Nobody Does this +because uh you're not interested in + + align:start position:0% +because uh you're not interested in + + + align:start position:0% +because uh you're not interested in +small + + align:start position:0% +small + + + align:start position:0% +small +systems but we do it because we + + align:start position:0% +systems but we do it because we + + + align:start position:0% +systems but we do it because we +are so if I take the Gibs free energy + + align:start position:0% +are so if I take the Gibs free energy + + + align:start position:0% +are so if I take the Gibs free energy +and transform with respect to one uh of + + align:start position:0% +and transform with respect to one uh of + + + align:start position:0% +and transform with respect to one uh of +the amount ounts so I want to substitute + + align:start position:0% +the amount ounts so I want to substitute + + + align:start position:0% +the amount ounts so I want to substitute +now amounts ni I with its conjugate + + align:start position:0% +now amounts ni I with its conjugate + + + align:start position:0% +now amounts ni I with its conjugate +which is the chemical + + align:start position:0% +which is the chemical + + + align:start position:0% +which is the chemical +potential the + + align:start position:0% + + + + align:start position:0% + +slope because the chemical potential is + + align:start position:0% +slope because the chemical potential is + + + align:start position:0% +slope because the chemical potential is +the partial of G with respect to Mu at + + align:start position:0% +the partial of G with respect to Mu at + + + align:start position:0% +the partial of G with respect to Mu at +constant + + align:start position:0% +constant + + + align:start position:0% +constant +10 or + + align:start position:0% +10 or + + + align:start position:0% +10 or +when all right so I have G minus uh n * + + align:start position:0% +when all right so I have G minus uh n * + + + align:start position:0% +when all right so I have G minus uh n * +mu and I + + align:start position:0% +mu and I + + + align:start position:0% +mu and I +mui + + align:start position:0% +mui + + + align:start position:0% +mui +okay + + align:start position:0% + + + + align:start position:0% + +um I was short of letters for this uh + + align:start position:0% +um I was short of letters for this uh + + + align:start position:0% +um I was short of letters for this uh +game + + align:start position:0% +game + + + align:start position:0% +game +so since eventually the last one I want + + align:start position:0% +so since eventually the last one I want + + + align:start position:0% +so since eventually the last one I want +to call Oiler free + + align:start position:0% +to call Oiler free + + + align:start position:0% +to call Oiler free +energy and this + + align:start position:0% +energy and this + + + align:start position:0% +energy and this +one maybe could be called osmotic free + + align:start position:0% +one maybe could be called osmotic free + + + align:start position:0% +one maybe could be called osmotic free +energy because it plays a role and but + + align:start position:0% +energy because it plays a role and but + + + align:start position:0% +energy because it plays a role and but +because uh + + align:start position:0% +because uh + + + align:start position:0% +because uh +some colleagues uh who are working on + + align:start position:0% +some colleagues uh who are working on + + + align:start position:0% +some colleagues uh who are working on +Nano + + align:start position:0% +Nano + + + align:start position:0% +Nano +thermodynamics uh are using introd are + + align:start position:0% +thermodynamics uh are using introd are + + + align:start position:0% +thermodynamics uh are using introd are +introduc beginning to introduce these + + align:start position:0% +introduc beginning to introduce these + + + align:start position:0% +introduc beginning to introduce these +names uh so I just call it EU + + align:start position:0% + + + + align:start position:0% + +Sabi and if I do this not just for one + + align:start position:0% +Sabi and if I do this not just for one + + + align:start position:0% +Sabi and if I do this not just for one +but for all so I keep going until I + + align:start position:0% +but for all so I keep going until I + + + align:start position:0% +but for all so I keep going until I +exhausted all uh the um the constituents + + align:start position:0% + + + + align:start position:0% + +I have this function that I call the + + align:start position:0% +I have this function that I call the + + + align:start position:0% +I have this function that I call the +oiler + + align:start position:0% +oiler + + + align:start position:0% +oiler +relation Oiler free energy it's G the + + align:start position:0% +relation Oiler free energy it's G the + + + align:start position:0% +relation Oiler free energy it's G the +Gibs free energy minus mu * + + align:start position:0% +Gibs free energy minus mu * + + + align:start position:0% +Gibs free energy minus mu * +n okay + + align:start position:0% + + + + align:start position:0% + +if you remember + + align:start position:0% +if you remember + + + align:start position:0% +if you remember +yeah + + align:start position:0% + + + + align:start position:0% + +Sor the f + + align:start position:0% + + + + align:start position:0% + +ah yeah this is also probably a cut and + + align:start position:0% +ah yeah this is also probably a cut and + + + align:start position:0% +ah yeah this is also probably a cut and +paste problem I guess oh no no + + align:start position:0% +paste problem I guess oh no no + + + align:start position:0% +paste problem I guess oh no no +no no no this is still okay because if + + align:start position:0% +no no no this is still okay because if + + + align:start position:0% +no no no this is still okay because if +you if you start from um + + align:start position:0% +you if you start from um + + + align:start position:0% +you if you start from um +the Elmos free + + align:start position:0% +the Elmos free + + + align:start position:0% +the Elmos free +energy and you + + align:start position:0% +energy and you + + + align:start position:0% +energy and you +transform you get rid of the volume to + + align:start position:0% +transform you get rid of the volume to + + + align:start position:0% +transform you get rid of the volume to +get + + align:start position:0% +get + + + align:start position:0% +get +pressure then you you also get the G + + align:start position:0% +pressure then you you also get the G + + + align:start position:0% +pressure then you you also get the G +three energy because the G three for the + + align:start position:0% +three energy because the G three for the + + + align:start position:0% +three energy because the G three for the +GB you get G Gib three energy when you + + align:start position:0% +GB you get G Gib three energy when you + + + align:start position:0% +GB you get G Gib three energy when you +transform with respect to S and V and + + align:start position:0% +transform with respect to S and V and + + + align:start position:0% +transform with respect to S and V and +you can do it you can do it doing first + + align:start position:0% +you can do it you can do it doing first + + + align:start position:0% +you can do it you can do it doing first +the S and then the V or first the V and + + align:start position:0% +the S and then the V or first the V and + + + align:start position:0% +the S and then the V or first the V and +then the S and you get the same result + + align:start position:0% +then the S and you get the same result + + + align:start position:0% +then the S and you get the same result +sorry I think I was so f is comp energy + + align:start position:0% +sorry I think I was so f is comp energy + + + align:start position:0% +sorry I think I was so f is comp energy +f is the letter for the El free + + align:start position:0% + + + + align:start position:0% + +energy ah ah the F up there you're right + + align:start position:0% +energy ah ah the F up there you're right + + + align:start position:0% +energy ah ah the F up there you're right +yeah yeah yeah it's it's difficult to + + align:start position:0% +yeah yeah yeah it's it's difficult to + + + align:start position:0% +yeah yeah yeah it's it's difficult to +find + + align:start position:0% +find + + + align:start position:0% +find +letters uh even if you use the Greek + + align:start position:0% +letters uh even if you use the Greek + + + align:start position:0% +letters uh even if you use the Greek +alphabet and so on there's still not + + align:start position:0% +alphabet and so on there's still not + + + align:start position:0% +alphabet and so on there's still not +enough okay um I wanted to emphasize + + align:start position:0% +enough okay um I wanted to emphasize + + + align:start position:0% +enough okay um I wanted to emphasize +that this one will will go back to this + + align:start position:0% +that this one will will go back to this + + + align:start position:0% +that this one will will go back to this +one and I call it Oiler + + align:start position:0% +one and I call it Oiler + + + align:start position:0% +one and I call it Oiler +because some of you might object well + + align:start position:0% +because some of you might object well + + + align:start position:0% +because some of you might object well +but this is + + align:start position:0% + + + + align:start position:0% + +zero and and the answer is yes this will + + align:start position:0% +zero and and the answer is yes this will + + + align:start position:0% +zero and and the answer is yes this will +be zero for the macroscopic + + align:start position:0% +be zero for the macroscopic + + + align:start position:0% +be zero for the macroscopic +systems but for microscopic systems it + + align:start position:0% +systems but for microscopic systems it + + + align:start position:0% +systems but for microscopic systems it +is + + align:start position:0% +is + + + align:start position:0% +is +not and that's why I I want to uh uh + + align:start position:0% +not and that's why I I want to uh uh + + + align:start position:0% +not and that's why I I want to uh uh +give it a name and uh and uh let it play + + align:start position:0% +give it a name and uh and uh let it play + + + align:start position:0% +give it a name and uh and uh let it play +some role until we introduced the idea + + align:start position:0% +some role until we introduced the idea + + + align:start position:0% +some role until we introduced the idea +of many + + align:start position:0% +of many + + + align:start position:0% +of many +particles because um because you this so + + align:start position:0% +particles because um because you this so + + + align:start position:0% +particles because um because you this so +in a sense you we could write we will + + align:start position:0% +in a sense you we could write we will + + + align:start position:0% +in a sense you we could write we will +see that in the limit of many + + align:start position:0% + + + + align:start position:0% + +particles which means uh + + align:start position:0% + + + + align:start position:0% + +negligible wall raction + + align:start position:0% +negligible wall raction + + + align:start position:0% +negligible wall raction +effects because the key will be the the + + align:start position:0% +effects because the key will be the the + + + align:start position:0% +effects because the key will be the the +this will tend to + + align:start position:0% +this will tend to + + + align:start position:0% +this will tend to +zero + + align:start position:0% + + + + align:start position:0% + +yeah that this one is not + + align:start position:0% +yeah that this one is not + + + align:start position:0% +yeah that this one is not +zero and therefore it's something that + + align:start position:0% +zero and therefore it's something that + + + align:start position:0% +zero and therefore it's something that +you can measure it will depend on the on + + align:start position:0% +you can measure it will depend on the on + + + align:start position:0% +you can measure it will depend on the on +on how many particles you have um I just + + align:start position:0% +on how many particles you have um I just + + + align:start position:0% +on how many particles you have um I just +like for + + align:start position:0% + + + + align:start position:0% + +GBS + + align:start position:0% + + + + align:start position:0% + +do is in this realm it it starts from + + align:start position:0% +do is in this realm it it starts from + + + align:start position:0% +do is in this realm it it starts from +the oiler relation the oil requires uh + + align:start position:0% +the oiler relation the oil requires uh + + + align:start position:0% +the oiler relation the oil requires uh +the condition that EU equals + + align:start position:0% +the condition that EU equals + + + align:start position:0% +the condition that EU equals +zero and so you get all those like the + + align:start position:0% +zero and so you get all those like the + + + align:start position:0% +zero and so you get all those like the +phase rule that comes out of the GS do + + align:start position:0% +phase rule that comes out of the GS do + + + align:start position:0% +phase rule that comes out of the GS do +relation that + + align:start position:0% +relation that + + + align:start position:0% +relation that +applies in this domain of microscopic + + align:start position:0% +applies in this domain of microscopic + + + align:start position:0% +applies in this domain of microscopic +systems but + + align:start position:0% +systems but + + + align:start position:0% +systems but +here uh let's say that it's + + align:start position:0% +here uh let's say that it's + + + align:start position:0% +here uh let's say that it's +still a bit open no there is there is a + + align:start position:0% +still a bit open no there is there is a + + + align:start position:0% +still a bit open no there is there is a +book which by + + align:start position:0% +book which by + + + align:start position:0% +book which by +Terell maybe one are teral + + align:start position:0% +Terell maybe one are teral + + + align:start position:0% +Terell maybe one are teral +teral + + align:start position:0% +teral + + + align:start position:0% +teral +kill thod + + align:start position:0% +kill thod + + + align:start position:0% +kill thod +dynamics of uh small + + align:start position:0% +dynamics of uh small + + + align:start position:0% +dynamics of uh small +systems long ago forget now the exact + + align:start position:0% +systems long ago forget now the exact + + + align:start position:0% +systems long ago forget now the exact +date + + align:start position:0% +date + + + align:start position:0% +date +uh who did care about uh this + + align:start position:0% + + + + align:start position:0% + +thing but I'm not sure that he + + align:start position:0% +thing but I'm not sure that he + + + align:start position:0% +thing but I'm not sure that he +went uh far enough to talk about phase + + align:start position:0% +went uh far enough to talk about phase + + + align:start position:0% +went uh far enough to talk about phase +uh phase transitions in in that + + align:start position:0% +uh phase transitions in in that + + + align:start position:0% +uh phase transitions in in that +domain so this is still pretty + + align:start position:0% +domain so this is still pretty + + + align:start position:0% +domain so this is still pretty +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +open subject but it's becoming important + + align:start position:0% +open subject but it's becoming important + + + align:start position:0% +open subject but it's becoming important +because of the enormous advances in the + + align:start position:0% +because of the enormous advances in the + + + align:start position:0% +because of the enormous advances in the +in in + + align:start position:0% +in in + + + align:start position:0% +in in +in I would say experimental technologies + + align:start position:0% +in I would say experimental technologies + + + align:start position:0% +in I would say experimental technologies +that allow you with microfluidics or uh + + align:start position:0% +that allow you with microfluidics or uh + + + align:start position:0% +that allow you with microfluidics or uh +um Quantum dots and all that stuff to + + align:start position:0% +um Quantum dots and all that stuff to + + + align:start position:0% +um Quantum dots and all that stuff to +deal with very small uh systems a few + + align:start position:0% + + + + align:start position:0% + +particles okay + + align:start position:0% + + + + align:start position:0% + +well math and math and math all + + align:start position:0% +well math and math and math all + + + align:start position:0% +well math and math and math all +right I told you when we have a function + + align:start position:0% +right I told you when we have a function + + + align:start position:0% +right I told you when we have a function +we can play as as as much math as we + + align:start position:0% +we can play as as as much math as we + + + align:start position:0% +we can play as as as much math as we +want forever and + + align:start position:0% +want forever and + + + align:start position:0% +want forever and +ever there are so I'm I'm concerned here + + align:start position:0% +ever there are so I'm I'm concerned here + + + align:start position:0% +ever there are so I'm I'm concerned here +to tell you only about the useful + + align:start position:0% +to tell you only about the useful + + + align:start position:0% +to tell you only about the useful +math and apparently also the second + + align:start position:0% +math and apparently also the second + + + align:start position:0% +math and apparently also the second +derivatives are useful + + align:start position:0% +derivatives are useful + + + align:start position:0% +derivatives are useful +at least if our project is that of uh + + align:start position:0% +at least if our project is that of uh + + + align:start position:0% +at least if our project is that of uh +measuring + + align:start position:0% + + + + align:start position:0% + +properties because again we don't have + + align:start position:0% +properties because again we don't have + + + align:start position:0% +properties because again we don't have +the entropy meter and we don't have the + + align:start position:0% +the entropy meter and we don't have the + + + align:start position:0% +the entropy meter and we don't have the +energy + + align:start position:0% +energy + + + align:start position:0% +energy +meter so you have to rely on these + + align:start position:0% +meter so you have to rely on these + + + align:start position:0% +meter so you have to rely on these +tangents to measure + + align:start position:0% +tangents to measure + + + align:start position:0% +tangents to measure +properties so each one of the functions + + align:start position:0% +properties so each one of the functions + + + align:start position:0% +properties so each one of the functions +that we have defined through the Leandra + + align:start position:0% +that we have defined through the Leandra + + + align:start position:0% +that we have defined through the Leandra +transform + + align:start position:0% +transform + + + align:start position:0% +transform +has first uh order derivatives but also + + align:start position:0% +has first uh order derivatives but also + + + align:start position:0% +has first uh order derivatives but also +second order derivatives for which we + + align:start position:0% +second order derivatives for which we + + + align:start position:0% +second order derivatives for which we +have the Schwarz theorem of + + align:start position:0% +have the Schwarz theorem of + + + align:start position:0% +have the Schwarz theorem of +uh symmetry that says that the order of + + align:start position:0% +uh symmetry that says that the order of + + + align:start position:0% +uh symmetry that says that the order of +derivation doesn't + + align:start position:0% + + + + align:start position:0% + +matter so for example if I take the + + align:start position:0% +matter so for example if I take the + + + align:start position:0% +matter so for example if I take the +second derivative of the just the + + align:start position:0% +second derivative of the just the + + + align:start position:0% +second derivative of the just the +fundamental relation in energy + + align:start position:0% +fundamental relation in energy + + + align:start position:0% +fundamental relation in energy +form with respect to snv + + align:start position:0% +form with respect to snv + + + align:start position:0% +form with respect to snv +that's + + align:start position:0% +that's + + + align:start position:0% +that's +equal if I do first s and after V and + + align:start position:0% +equal if I do first s and after V and + + + align:start position:0% +equal if I do first s and after V and +and vice versa okay so since the partial + + align:start position:0% +and vice versa okay so since the partial + + + align:start position:0% +and vice versa okay so since the partial +of e with respect to V is minus the + + align:start position:0% +of e with respect to V is minus the + + + align:start position:0% +of e with respect to V is minus the +pressure this one can also be viewed as + + align:start position:0% +pressure this one can also be viewed as + + + align:start position:0% +pressure this one can also be viewed as +minus the derivative of minus the + + align:start position:0% +minus the derivative of minus the + + + align:start position:0% +minus the derivative of minus the +pressure with respect to the entropy + + align:start position:0% +pressure with respect to the entropy + + + align:start position:0% +pressure with respect to the entropy +when the other variables are V and + + align:start position:0% +when the other variables are V and + + + align:start position:0% +when the other variables are V and +N the right hand side can be viewed as + + align:start position:0% +N the right hand side can be viewed as + + + align:start position:0% +N the right hand side can be viewed as +the partial of e with respect to S + + align:start position:0% +the partial of e with respect to S + + + align:start position:0% +the partial of e with respect to S +that's T the temperature + + align:start position:0% +that's T the temperature + + + align:start position:0% +that's T the temperature +so it's a partial of the temperature we + + align:start position:0% +so it's a partial of the temperature we + + + align:start position:0% +so it's a partial of the temperature we +expect to be at constant I mean at when + + align:start position:0% +expect to be at constant I mean at when + + + align:start position:0% +expect to be at constant I mean at when +when s and n are the other variables so + + align:start position:0% +when s and n are the other variables so + + + align:start position:0% +when s and n are the other variables so +we get a relation + + align:start position:0% + + + + align:start position:0% + +here is the relation is still + + align:start position:0% +here is the relation is still + + + align:start position:0% +here is the relation is still +not fully practical because yes it does + + align:start position:0% +not fully practical because yes it does + + + align:start position:0% +not fully practical because yes it does +have measurable properties almost all + + align:start position:0% +have measurable properties almost all + + + align:start position:0% +have measurable properties almost all +all the all places except entropy here + + align:start position:0% +all the all places except entropy here + + + align:start position:0% +all the all places except entropy here +and entropy there + + align:start position:0% + + + + align:start position:0% + +let's do the the same game these are + + align:start position:0% +let's do the the same game these are + + + align:start position:0% +let's do the the same game these are +called Maxwell relations by the way + + align:start position:0% +called Maxwell relations by the way + + + align:start position:0% +called Maxwell relations by the way +uh and there are many anything that + + align:start position:0% +uh and there are many anything that + + + align:start position:0% +uh and there are many anything that +derives from this Force theorem becomes + + align:start position:0% +derives from this Force theorem becomes + + + align:start position:0% +derives from this Force theorem becomes +a Max + + align:start position:0% +a Max + + + align:start position:0% +a Max +relation if you play that with on the + + align:start position:0% +relation if you play that with on the + + + align:start position:0% +relation if you play that with on the +elol free + + align:start position:0% + + + + align:start position:0% + +energy here is what we + + align:start position:0% +energy here is what we + + + align:start position:0% +energy here is what we +get this is a bit more practical because + + align:start position:0% +get this is a bit more practical because + + + align:start position:0% +get this is a bit more practical because +you see we have just the entropy here + + align:start position:0% +you see we have just the entropy here + + + align:start position:0% +you see we have just the entropy here +and the rest is easy easy measurable + + align:start position:0% +and the rest is easy easy measurable + + + align:start position:0% +and the rest is easy easy measurable +stuff pressure volume + + align:start position:0% +stuff pressure volume + + + align:start position:0% +stuff pressure volume +temperature so that means that if you + + align:start position:0% +temperature so that means that if you + + + align:start position:0% +temperature so that means that if you +take your + + align:start position:0% +take your + + + align:start position:0% +take your +substance and want to know how much the + + align:start position:0% +substance and want to know how much the + + + align:start position:0% +substance and want to know how much the +entropy varies with volume at a constant + + align:start position:0% +entropy varies with volume at a constant + + + align:start position:0% +entropy varies with volume at a constant +temperature you could measure it + + align:start position:0% +temperature you could measure it + + + align:start position:0% +temperature you could measure it +indirectly using this relation by + + align:start position:0% +indirectly using this relation by + + + align:start position:0% +indirectly using this relation by +measuring how + + align:start position:0% +measuring how + + + align:start position:0% +measuring how +much by taking the substance increasing + + align:start position:0% +much by taking the substance increasing + + + align:start position:0% +much by taking the substance increasing +the temperature a little bit seeing how + + align:start position:0% +the temperature a little bit seeing how + + + align:start position:0% +the temperature a little bit seeing how +the pressure increases at constant + + align:start position:0% +the pressure increases at constant + + + align:start position:0% +the pressure increases at constant +volume and and once you've measured that + + align:start position:0% +volume and and once you've measured that + + + align:start position:0% +volume and and once you've measured that +you've measured that indirectly so this + + align:start position:0% +you've measured that indirectly so this + + + align:start position:0% +you've measured that indirectly so this +is one way to it's like an entropy + + align:start position:0% +is one way to it's like an entropy + + + align:start position:0% +is one way to it's like an entropy +meter it's an indirect measurement of + + align:start position:0% +meter it's an indirect measurement of + + + align:start position:0% +meter it's an indirect measurement of +entropy you could build an entropy meter + + align:start position:0% +entropy you could build an entropy meter + + + align:start position:0% +entropy you could build an entropy meter +based on this + + align:start position:0% + + + + align:start position:0% + +relation if you do the same with the + + align:start position:0% +relation if you do the same with the + + + align:start position:0% +relation if you do the same with the +enthalpy you get this one not very + + align:start position:0% +enthalpy you get this one not very + + + align:start position:0% +enthalpy you get this one not very +useful because it has s on both sides + + align:start position:0% +useful because it has s on both sides + + + align:start position:0% +useful because it has s on both sides +it's not easy to keep s constant because + + align:start position:0% +it's not easy to keep s constant because + + + align:start position:0% +it's not easy to keep s constant because +keep s + + align:start position:0% +keep s + + + align:start position:0% +keep s +constant + + align:start position:0% +constant + + + align:start position:0% +constant +uh yes you could + + align:start position:0% +uh yes you could + + + align:start position:0% +uh yes you could +do a a weight + + align:start position:0% +do a a weight + + + align:start position:0% +do a a weight +process and uh you could make sure that + + align:start position:0% +process and uh you could make sure that + + + align:start position:0% +process and uh you could make sure that +it is + + align:start position:0% +it is + + + align:start position:0% +it is +reversible but usually reversible + + align:start position:0% +reversible but usually reversible + + + align:start position:0% +reversible but usually reversible +processes are not easy to do and often + + align:start position:0% +processes are not easy to do and often + + + align:start position:0% +processes are not easy to do and often +you have to + + align:start position:0% +you have to + + + align:start position:0% +you have to +extrapolate to some zero velocities or + + align:start position:0% +extrapolate to some zero velocities or + + + align:start position:0% +extrapolate to some zero velocities or +some very high velocities so not easy to + + align:start position:0% +some very high velocities so not easy to + + + align:start position:0% +some very high velocities so not easy to +make a to make sure that the to be sure + + align:start position:0% +make a to make sure that the to be sure + + + align:start position:0% +make a to make sure that the to be sure +in the lab that your process is + + align:start position:0% + + + + align:start position:0% + +reversible the last one if you play the + + align:start position:0% +reversible the last one if you play the + + + align:start position:0% +reversible the last one if you play the +Maxwell relations game on the G free + + align:start position:0% +Maxwell relations game on the G free + + + align:start position:0% +Maxwell relations game on the G free +energy is also useful it could also be a + + align:start position:0% +energy is also useful it could also be a + + + align:start position:0% +energy is also useful it could also be a +basis for an entropy meter because it + + align:start position:0% +basis for an entropy meter because it + + + align:start position:0% +basis for an entropy meter because it +has entropy only on one + + align:start position:0% +has entropy only on one + + + align:start position:0% +has entropy only on one +side so you can see how the entropy + + align:start position:0% +side so you can see how the entropy + + + align:start position:0% +side so you can see how the entropy +changes the function of + + align:start position:0% +changes the function of + + + align:start position:0% +changes the function of +pressure at constant temperature by + + align:start position:0% +pressure at constant temperature by + + + align:start position:0% +pressure at constant temperature by +measuring how the volume + + align:start position:0% +measuring how the volume + + + align:start position:0% +measuring how the volume +changes if you change the temperature at + + align:start position:0% +changes if you change the temperature at + + + align:start position:0% +changes if you change the temperature at +constant + + align:start position:0% + + + + align:start position:0% + +pressure + + align:start position:0% + + + + align:start position:0% + +okay you can also have Max will + + align:start position:0% +okay you can also have Max will + + + align:start position:0% +okay you can also have Max will +relations when you take some derivatives + + align:start position:0% +relations when you take some derivatives + + + align:start position:0% +relations when you take some derivatives +second order I mean second yeah second + + align:start position:0% +second order I mean second yeah second + + + align:start position:0% +second order I mean second yeah second +order + + align:start position:0% + + + + align:start position:0% + +derivatives with + + align:start position:0% +derivatives with + + + align:start position:0% +derivatives with +respect + + align:start position:0% +respect + + + align:start position:0% +respect +to pair of variables of which one is the + + align:start position:0% +to pair of variables of which one is the + + + align:start position:0% +to pair of variables of which one is the +the uh the amount of one + + align:start position:0% + + + + align:start position:0% + +constituent okay so if I do + + align:start position:0% +constituent okay so if I do + + + align:start position:0% +constituent okay so if I do +that temperature and one constituent + + align:start position:0% +that temperature and one constituent + + + align:start position:0% +that temperature and one constituent +here's the + + align:start position:0% + + + + align:start position:0% + +relation the derivative of G with + + align:start position:0% +relation the derivative of G with + + + align:start position:0% +relation the derivative of G with +respect to + + align:start position:0% +respect to + + + align:start position:0% +respect to +n is the chemical + + align:start position:0% + + + + align:start position:0% + +potential so this is the derivative is + + align:start position:0% +potential so this is the derivative is + + + align:start position:0% +potential so this is the derivative is +minus the chemical potential + + align:start position:0% +minus the chemical potential + + + align:start position:0% +minus the chemical potential +uh no + + align:start position:0% + + + + align:start position:0% + +sorry no it's is the chemical potential + + align:start position:0% +sorry no it's is the chemical potential + + + align:start position:0% +sorry no it's is the chemical potential +then I I I I move the minus sign on the + + align:start position:0% +then I I I I move the minus sign on the + + + align:start position:0% +then I I I I move the minus sign on the +other + + align:start position:0% +other + + + align:start position:0% +other +side so the so this one is the + + align:start position:0% +side so the so this one is the + + + align:start position:0% +side so the so this one is the +derivative of mu with respect to + + align:start position:0% +derivative of mu with respect to + + + align:start position:0% +derivative of mu with respect to +T whereas the derivative of G with + + align:start position:0% +T whereas the derivative of G with + + + align:start position:0% +T whereas the derivative of G with +respect to T is minus + + align:start position:0% +respect to T is minus + + + align:start position:0% +respect to T is minus +s and so this is the derivative of s + + align:start position:0% +s and so this is the derivative of s + + + align:start position:0% +s and so this is the derivative of s +with respect to + + align:start position:0% +with respect to + + + align:start position:0% +with respect to +n when the other variables are TP and + + align:start position:0% +n when the other variables are TP and + + + align:start position:0% +n when the other variables are TP and +the other amounts of + + align:start position:0% + + + + align:start position:0% + +constituents this is important because + + align:start position:0% +constituents this is important because + + + align:start position:0% +constituents this is important because +as we do um mixtures uh + + align:start position:0% +as we do um mixtures uh + + + align:start position:0% +as we do um mixtures uh +starting + + align:start position:0% +starting + + + align:start position:0% +starting +soon the second part of the course uh we + + align:start position:0% +soon the second part of the course uh we + + + align:start position:0% +soon the second part of the course uh we +will call this the + + align:start position:0% +will call this the + + + align:start position:0% +will call this the +partial entropy of + + align:start position:0% +partial entropy of + + + align:start position:0% +partial entropy of +constituent uh constituent I in the + + align:start position:0% +constituent uh constituent I in the + + + align:start position:0% +constituent uh constituent I in the +mixture + + align:start position:0% + + + + align:start position:0% + +in the limit of large amounts the + + align:start position:0% +in the limit of large amounts the + + + align:start position:0% +in the limit of large amounts the +partial entropy contributes to the + + align:start position:0% +partial entropy contributes to the + + + align:start position:0% +partial entropy contributes to the +properties of the mixture in proportion + + align:start position:0% +properties of the mixture in proportion + + + align:start position:0% +properties of the mixture in proportion +to the amount so you multiply the + + align:start position:0% +to the amount so you multiply the + + + align:start position:0% +to the amount so you multiply the +amount times the partial entropy sum up + + align:start position:0% +amount times the partial entropy sum up + + + align:start position:0% +amount times the partial entropy sum up +and you get the entropy for your mixture + + align:start position:0% +and you get the entropy for your mixture + + + align:start position:0% +and you get the entropy for your mixture +that's why it's called partial + + align:start position:0% +that's why it's called partial + + + align:start position:0% +that's why it's called partial +entropy this is true only in the limit + + align:start position:0% +entropy this is true only in the limit + + + align:start position:0% +entropy this is true only in the limit +of Oiler going to + + align:start position:0% +of Oiler going to + + + align:start position:0% +of Oiler going to +zero you do this same instead of T you + + align:start position:0% +zero you do this same instead of T you + + + align:start position:0% +zero you do this same instead of T you +do for the pressure and you get this + + align:start position:0% +do for the pressure and you get this + + + align:start position:0% +do for the pressure and you get this +other derivative of the chemical + + align:start position:0% +other derivative of the chemical + + + align:start position:0% +other derivative of the chemical +potential with respect to + + align:start position:0% +potential with respect to + + + align:start position:0% +potential with respect to +p and this is what we will call the + + align:start position:0% +p and this is what we will call the + + + align:start position:0% +p and this is what we will call the +partial volume of the constituent in the + + align:start position:0% +partial volume of the constituent in the + + + align:start position:0% +partial volume of the constituent in the +mixture again if you take this one + + align:start position:0% +mixture again if you take this one + + + align:start position:0% +mixture again if you take this one +multiply by the amount sum over all + + align:start position:0% +multiply by the amount sum over all + + + align:start position:0% +multiply by the amount sum over all +constituents that gives you the volume + + align:start position:0% + + + + align:start position:0% + +with in + + align:start position:0% +with in + + + align:start position:0% +with in +general as long as Oiler is equal to + + align:start position:0% + + + + align:start position:0% + +zero you could also take the the the + + align:start position:0% +zero you could also take the the the + + + align:start position:0% +zero you could also take the the the +double derivative with respect to two + + align:start position:0% +double derivative with respect to two + + + align:start position:0% +double derivative with respect to two +different amounts of + + align:start position:0% + + + + align:start position:0% + +constituents and you have this sort of + + align:start position:0% +constituents and you have this sort of + + + align:start position:0% +constituents and you have this sort of +reciprocal uh relation says that uh the + + align:start position:0% +reciprocal uh relation says that uh the + + + align:start position:0% +reciprocal uh relation says that uh the +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +of potential of constituent one + + align:start position:0% +of potential of constituent one + + + align:start position:0% +of potential of constituent one +with respect to the amounts of + + align:start position:0% +with respect to the amounts of + + + align:start position:0% +with respect to the amounts of +constituent two is equal to the + + align:start position:0% +constituent two is equal to the + + + align:start position:0% +constituent two is equal to the +derivative of potential of two with + + align:start position:0% +derivative of potential of two with + + + align:start position:0% +derivative of potential of two with +respect to the amount of constituent + + align:start position:0% + + + + align:start position:0% + +one we will uh use + + align:start position:0% +one we will uh use + + + align:start position:0% +one we will uh use +this in one of the proofs related to the + + align:start position:0% +this in one of the proofs related to the + + + align:start position:0% +this in one of the proofs related to the +DM + + align:start position:0% +DM + + + align:start position:0% +DM +margules + + align:start position:0% + + + + align:start position:0% + +relation yeah you could + + align:start position:0% + + + + align:start position:0% + +also play the same + + align:start position:0% + + + + align:start position:0% + +game starting with + + align:start position:0% +game starting with + + + align:start position:0% +game starting with +the + + align:start position:0% +the + + + align:start position:0% +the +relation + + align:start position:0% +relation + + + align:start position:0% +relation +uh I don't have well starting not with + + align:start position:0% +uh I don't have well starting not with + + + align:start position:0% +uh I don't have well starting not with +the fundamental relation in energy form + + align:start position:0% +the fundamental relation in energy form + + + align:start position:0% +the fundamental relation in energy form +but in entropy + + align:start position:0% +but in entropy + + + align:start position:0% +but in entropy +form and here is the result of the game + + align:start position:0% +form and here is the result of the game + + + align:start position:0% +form and here is the result of the game +let me skip the details + + align:start position:0% +let me skip the details + + + align:start position:0% +let me skip the details +one of the functions is called the mure + + align:start position:0% +one of the functions is called the mure + + + align:start position:0% +one of the functions is called the mure +free + + align:start position:0% + + + + align:start position:0% + +energy It's s minus E over + + align:start position:0% + + + + align:start position:0% + +T is + + align:start position:0% +T is + + + align:start position:0% +T is +entropy or say entropic + + align:start position:0% +entropy or say entropic + + + align:start position:0% +entropy or say entropic +formulation uh becomes more and more + + align:start position:0% +formulation uh becomes more and more + + + align:start position:0% +formulation uh becomes more and more +important and so you will + + align:start position:0% +important and so you will + + + align:start position:0% +important and so you will +find in the literature + + align:start position:0% +find in the literature + + + align:start position:0% +find in the literature +often uh if you go + + align:start position:0% +often uh if you go + + + align:start position:0% +often uh if you go +um yeah people that + + align:start position:0% +um yeah people that + + + align:start position:0% +um yeah people that +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +do small systems or Quantum + + align:start position:0% +do small systems or Quantum + + + align:start position:0% +do small systems or Quantum +thermodynamics uh s minus U over T you + + align:start position:0% +thermodynamics uh s minus U over T you + + + align:start position:0% +thermodynamics uh s minus U over T you +find it a + + align:start position:0% +find it a + + + align:start position:0% +find it a +lot some of them recognize that this is + + align:start position:0% +lot some of them recognize that this is + + + align:start position:0% +lot some of them recognize that this is +due to M some just call it free + + align:start position:0% +due to M some just call it free + + + align:start position:0% +due to M some just call it free +something or free + + align:start position:0% +something or free + + + align:start position:0% +something or free +entropy so this + + align:start position:0% +entropy so this + + + align:start position:0% +entropy so this +um following them I'll call it massure + + align:start position:0% +um following them I'll call it massure + + + align:start position:0% +um following them I'll call it massure +free entropy although the + + align:start position:0% +free entropy although the + + + align:start position:0% +free entropy although the +I I think the term may be a bit + + align:start position:0% +I I think the term may be a bit + + + align:start position:0% +I I think the term may be a bit +confusing because um um I'm not sure I'm + + align:start position:0% +confusing because um um I'm not sure I'm + + + align:start position:0% +confusing because um um I'm not sure I'm +not sure what free entropy + + align:start position:0% + + + + align:start position:0% + +means sometimes the words the wrong + + align:start position:0% +means sometimes the words the wrong + + + align:start position:0% +means sometimes the words the wrong +words are are confusing and cause uh a + + align:start position:0% +words are are confusing and cause uh a + + + align:start position:0% +words are are confusing and cause uh a +lot of damage so if I do that I'm sorry + + align:start position:0% +lot of damage so if I do that I'm sorry + + + align:start position:0% +lot of damage so if I do that I'm sorry +about + + align:start position:0% +about + + + align:start position:0% +about +this but I needed a + + align:start position:0% + + + + align:start position:0% + +name this is also because instead of um + + align:start position:0% +name this is also because instead of um + + + align:start position:0% +name this is also because instead of um +the G giving it this kind of name for + + align:start position:0% +the G giving it this kind of name for + + + align:start position:0% +the G giving it this kind of name for +example in the book with u uh Professor + + align:start position:0% +example in the book with u uh Professor + + + align:start position:0% +example in the book with u uh Professor +giftos we were very careful not to use + + align:start position:0% +giftos we were very careful not to use + + + align:start position:0% +giftos we were very careful not to use +names that were sort of misleading and + + align:start position:0% +names that were sort of misleading and + + + align:start position:0% +names that were sort of misleading and +so we used we call them characteristic + + align:start position:0% +so we used we call them characteristic + + + align:start position:0% +so we used we call them characteristic +functions characteristic stable + + align:start position:0% +functions characteristic stable + + + align:start position:0% +functions characteristic stable +equilibrium State functions it's a more + + align:start position:0% +equilibrium State functions it's a more + + + align:start position:0% +equilibrium State functions it's a more +a septic uh uh way of + + align:start position:0% + + + + align:start position:0% + +U defining the same thing plank also has + + align:start position:0% +U defining the same thing plank also has + + + align:start position:0% +U defining the same thing plank also has +its own + + align:start position:0% +its own + + + align:start position:0% +its own +and uh + + align:start position:0% + + + + align:start position:0% + +again if I do the transform with respect + + align:start position:0% +again if I do the transform with respect + + + align:start position:0% +again if I do the transform with respect +to all the variables includ + + align:start position:0% + + + + align:start position:0% + +uh should I includ yeah including also + + align:start position:0% +uh should I includ yeah including also + + + align:start position:0% +uh should I includ yeah including also +the yeah including also the all the + + align:start position:0% +the yeah including also the all the + + + align:start position:0% +the yeah including also the all the +amounts I end + + align:start position:0% + + + + align:start position:0% + +up with the equivalent of the oil + + align:start position:0% +up with the equivalent of the oil + + + align:start position:0% +up with the equivalent of the oil +uh relation + + align:start position:0% +uh relation + + + align:start position:0% +uh relation +here uh I'm call uh how did I call it + + align:start position:0% + + + + align:start position:0% + +Su which is equal to minus EU over + + align:start position:0% +Su which is equal to minus EU over + + + align:start position:0% +Su which is equal to minus EU over +T notice that also the + + align:start position:0% +T notice that also the + + + align:start position:0% +T notice that also the +others are very for example + + align:start position:0% +others are very for example + + + align:start position:0% +others are very for example +plank is minus G over T so it's like a + + align:start position:0% +plank is minus G over T so it's like a + + + align:start position:0% +plank is minus G over T so it's like a +GS free energy divided by the + + align:start position:0% +GS free energy divided by the + + + align:start position:0% +GS free energy divided by the +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +and M is L M over t so they are + + align:start position:0% +and M is L M over t so they are + + + align:start position:0% +and M is L M over t so they are +related and of course you can play also + + align:start position:0% +related and of course you can play also + + + align:start position:0% +related and of course you can play also +the game of uh double derivatives + + align:start position:0% +the game of uh double derivatives + + + align:start position:0% +the game of uh double derivatives +here + + align:start position:0% +here + + + align:start position:0% +here +well by the same token these derivatives + + align:start position:0% +well by the same token these derivatives + + + align:start position:0% +well by the same token these derivatives +are useful if you want to construct an + + align:start position:0% +are useful if you want to construct an + + + align:start position:0% +are useful if you want to construct an +energy + + align:start position:0% +energy + + + align:start position:0% +energy +meter okay the the first one not so much + + align:start position:0% +meter okay the the first one not so much + + + align:start position:0% +meter okay the the first one not so much +because you have energy on both sides + + align:start position:0% +because you have energy on both sides + + + align:start position:0% +because you have energy on both sides +but this one + + align:start position:0% +but this one + + + align:start position:0% +but this one +yes I can measure as how the energy + + align:start position:0% +yes I can measure as how the energy + + + align:start position:0% +yes I can measure as how the energy +varies with ECT to volume at constant + + align:start position:0% +varies with ECT to volume at constant + + + align:start position:0% +varies with ECT to volume at constant +temperature by measuring pressure + + align:start position:0% +temperature by measuring pressure + + + align:start position:0% +temperature by measuring pressure +temperature and how the pressure varies + + align:start position:0% +temperature and how the pressure varies + + + align:start position:0% +temperature and how the pressure varies +is a function of temperature constant + + align:start position:0% +is a function of temperature constant + + + align:start position:0% +is a function of temperature constant +volume so you could build an energy + + align:start position:0% +volume so you could build an energy + + + align:start position:0% +volume so you could build an energy +meter based on this + + align:start position:0% +meter based on this + + + align:start position:0% +meter based on this +equation this one no because it has uh + + align:start position:0% +equation this one no because it has uh + + + align:start position:0% +equation this one no because it has uh +both sides but the last one + + align:start position:0% +both sides but the last one + + + align:start position:0% +both sides but the last one +yes although it's not so + + align:start position:0% +yes although it's not so + + + align:start position:0% +yes although it's not so +simple you have to realize that uh + + align:start position:0% +simple you have to realize that uh + + + align:start position:0% +simple you have to realize that uh +you have to here change the + + align:start position:0% +you have to here change the + + + align:start position:0% +you have to here change the +temperature of your + + align:start position:0% +temperature of your + + + align:start position:0% +temperature of your +system and see how the volume will + + align:start position:0% +system and see how the volume will + + + align:start position:0% +system and see how the volume will +change while you + + align:start position:0% +change while you + + + align:start position:0% +change while you +keep p/ T constant so if you double the + + align:start position:0% +keep p/ T constant so if you double the + + + align:start position:0% +keep p/ T constant so if you double the +temperature you also have to double the + + align:start position:0% +temperature you also have to double the + + + align:start position:0% +temperature you also have to double the +pressure in order to keep that ratio + + align:start position:0% +pressure in order to keep that ratio + + + align:start position:0% +pressure in order to keep that ratio +constant and then you measure the energy + + align:start position:0% +constant and then you measure the energy + + + align:start position:0% +constant and then you measure the energy +how the energy varies with the function + + align:start position:0% +how the energy varies with the function + + + align:start position:0% +how the energy varies with the function +of + + align:start position:0% +of + + + align:start position:0% +of +P all right so we have ways to measure + + align:start position:0% +P all right so we have ways to measure + + + align:start position:0% +P all right so we have ways to measure +stuff and + + align:start position:0% + + + + align:start position:0% + +uh and therefore to characterize the + + align:start position:0% +uh and therefore to characterize the + + + align:start position:0% +uh and therefore to characterize the +stable equilibrium St states + + align:start position:0% +stable equilibrium St states + + + align:start position:0% +stable equilibrium St states +of + + align:start position:0% + + + + align:start position:0% + +substances all right so now we go + + align:start position:0% +substances all right so now we go + + + align:start position:0% +substances all right so now we go +back + + align:start position:0% +back + + + align:start position:0% +back +to one of the + + align:start position:0% +to one of the + + + align:start position:0% +to one of the +uh characteristic questions of + + align:start position:0% +uh characteristic questions of + + + align:start position:0% +uh characteristic questions of +that we for which thermodynamics was + + align:start position:0% +that we for which thermodynamics was + + + align:start position:0% +that we for which thermodynamics was +born how much useful things or how much + + align:start position:0% +born how much useful things or how much + + + align:start position:0% +born how much useful things or how much +work now that we've defined it can we + + align:start position:0% +work now that we've defined it can we + + + align:start position:0% +work now that we've defined it can we +do by uh exploiting a + + align:start position:0% +do by uh exploiting a + + + align:start position:0% +do by uh exploiting a +change of some system from one state to + + align:start position:0% +change of some system from one state to + + + align:start position:0% +change of some system from one state to +another for example by cooling a hot + + align:start position:0% +another for example by cooling a hot + + + align:start position:0% +another for example by cooling a hot +object or also what is the minimum + + align:start position:0% +object or also what is the minimum + + + align:start position:0% +object or also what is the minimum +amount of work that is necessary in + + align:start position:0% +amount of work that is necessary in + + + align:start position:0% +amount of work that is necessary in +order to obtain a certain change in + + align:start position:0% +order to obtain a certain change in + + + align:start position:0% +order to obtain a certain change in +state of some my system for example in + + align:start position:0% +state of some my system for example in + + + align:start position:0% +state of some my system for example in +material processing uh I + + align:start position:0% +material processing uh I + + + align:start position:0% +material processing uh I +transform uh I got bunch of raw + + align:start position:0% +transform uh I got bunch of raw + + + align:start position:0% +transform uh I got bunch of raw +materials coming in and I want to + + align:start position:0% +materials coming in and I want to + + + align:start position:0% +materials coming in and I want to +produce my uh product like steel no + + align:start position:0% +produce my uh product like steel no + + + align:start position:0% +produce my uh product like steel no +steel is product you have put you have + + align:start position:0% +steel is product you have put you have + + + align:start position:0% +steel is product you have put you have +to put in uh iron ore and carbon and + + align:start position:0% +to put in uh iron ore and carbon and + + + align:start position:0% +to put in uh iron ore and carbon and +lots of other stuff energy so what's the + + align:start position:0% +lots of other stuff energy so what's the + + + align:start position:0% +lots of other stuff energy so what's the +minimum + + align:start position:0% +minimum + + + align:start position:0% +minimum +requirement to uh produce a unit of your + + align:start position:0% +requirement to uh produce a unit of your + + + align:start position:0% +requirement to uh produce a unit of your +product that is + + align:start position:0% +product that is + + + align:start position:0% +product that is +also + + align:start position:0% + + + + align:start position:0% + +um the typical + + align:start position:0% +um the typical + + + align:start position:0% +um the typical +question we have already seen the + + align:start position:0% +question we have already seen the + + + align:start position:0% +question we have already seen the +answer for or uh the case of a + + align:start position:0% + + + + align:start position:0% + +system that varies in uh you want to you + + align:start position:0% +system that varies in uh you want to you + + + align:start position:0% +system that varies in uh you want to you +fix now select your system you want to + + align:start position:0% +fix now select your system you want to + + + align:start position:0% +fix now select your system you want to +have a change from A1 to + + align:start position:0% +have a change from A1 to + + + align:start position:0% +have a change from A1 to +A2 which could be heating or + + align:start position:0% +A2 which could be heating or + + + align:start position:0% +A2 which could be heating or +cooling if it is cooling it means that + + align:start position:0% +cooling if it is cooling it means that + + + align:start position:0% +cooling if it is cooling it means that +you are extracting energy out of your + + align:start position:0% +you are extracting energy out of your + + + align:start position:0% +you are extracting energy out of your +system and then maybe you want to know + + align:start position:0% +system and then maybe you want to know + + + align:start position:0% +system and then maybe you want to know +how much of that energy can be used in + + align:start position:0% +how much of that energy can be used in + + + align:start position:0% +how much of that energy can be used in +order to lift a weight so how much is it + + align:start position:0% +order to lift a weight so how much is it + + + align:start position:0% +order to lift a weight so how much is it +useful or it could be + + align:start position:0% +useful or it could be + + + align:start position:0% +useful or it could be +instead a an increase in energy you want + + align:start position:0% +instead a an increase in energy you want + + + align:start position:0% +instead a an increase in energy you want +to heat up your + + align:start position:0% +to heat up your + + + align:start position:0% +to heat up your +system and then maybe you want to + + align:start position:0% + + + + align:start position:0% + +know uh how much do I need to lower my + + align:start position:0% +know uh how much do I need to lower my + + + align:start position:0% +know uh how much do I need to lower my +weight so what's the minimum lowering so + + align:start position:0% +weight so what's the minimum lowering so + + + align:start position:0% +weight so what's the minimum lowering so +what's the minimum work I need to spend + + align:start position:0% +what's the minimum work I need to spend + + + align:start position:0% +what's the minimum work I need to spend +in order to heat up + + align:start position:0% +in order to heat up + + + align:start position:0% +in order to heat up +something and here we do it with a + + align:start position:0% +something and here we do it with a + + + align:start position:0% +something and here we do it with a +reservoir if we have a reservoir + + align:start position:0% +reservoir if we have a reservoir + + + align:start position:0% +reservoir if we have a reservoir +available we can do a lot of stuff that + + align:start position:0% +available we can do a lot of stuff that + + + align:start position:0% +available we can do a lot of stuff that +we cannot do in an adiabatic or a weight + + align:start position:0% +we cannot do in an adiabatic or a weight + + + align:start position:0% +we cannot do in an adiabatic or a weight +process without the reservoir so the + + align:start position:0% +process without the reservoir so the + + + align:start position:0% +process without the reservoir so the +reservoir plays a + + align:start position:0% +reservoir plays a + + + align:start position:0% +reservoir plays a +role as we + + align:start position:0% + + + + align:start position:0% + +know so all these questions about + + align:start position:0% +know so all these questions about + + + align:start position:0% +know so all these questions about +maximum minimum work that can be done or + + align:start position:0% +maximum minimum work that can be done or + + + align:start position:0% +maximum minimum work that can be done or +useful stuff that can be + + align:start position:0% +useful stuff that can be + + + align:start position:0% +useful stuff that can be +done get solved and this is the basis of + + align:start position:0% +done get solved and this is the basis of + + + align:start position:0% +done get solved and this is the basis of +all the homework problems that you have + + align:start position:0% +all the homework problems that you have + + + align:start position:0% +all the homework problems that you have +in our book but also uh any course in + + align:start position:0% +in our book but also uh any course in + + + align:start position:0% +in our book but also uh any course in +thermodynamics you solve this Problems + + align:start position:0% +thermodynamics you solve this Problems + + + align:start position:0% +thermodynamics you solve this Problems +by one defining the + + align:start position:0% +by one defining the + + + align:start position:0% +by one defining the +system uh choosing a system for which to + + align:start position:0% +system uh choosing a system for which to + + + align:start position:0% +system uh choosing a system for which to +make an energy balance and an entropy + + align:start position:0% +make an energy balance and an entropy + + + align:start position:0% +make an energy balance and an entropy +balance and the choice of your system + + align:start position:0% +balance and the choice of your system + + + align:start position:0% +balance and the choice of your system +depends on the question of the + + align:start position:0% + + + + align:start position:0% + +problem the energy balance + + align:start position:0% +problem the energy balance + + + align:start position:0% +problem the energy balance +here is easy and uh so + + align:start position:0% +here is easy and uh so + + + align:start position:0% +here is easy and uh so +it's the difference between the final + + align:start position:0% +it's the difference between the final + + + align:start position:0% +it's the difference between the final +and initial energy on the left hand side + + align:start position:0% +and initial energy on the left hand side + + + align:start position:0% +and initial energy on the left hand side +must be equal to the net energy + + align:start position:0% +must be equal to the net energy + + + align:start position:0% +must be equal to the net energy +input of your system so here since I'm + + align:start position:0% +input of your system so here since I'm + + + align:start position:0% +input of your system so here since I'm +interested in uh uh the the + + align:start position:0% +interested in uh uh the the + + + align:start position:0% +interested in uh uh the the +work done in order to lift the weight or + + align:start position:0% +work done in order to lift the weight or + + + align:start position:0% +work done in order to lift the weight or +maybe the work re received if the weight + + align:start position:0% +maybe the work re received if the weight + + + align:start position:0% +maybe the work re received if the weight +goes instead + + align:start position:0% +goes instead + + + align:start position:0% +goes instead +down um the system I I'm doing the + + align:start position:0% +down um the system I I'm doing the + + + align:start position:0% +down um the system I I'm doing the +energy for is the composite system a + + align:start position:0% +energy for is the composite system a + + + align:start position:0% +energy for is the composite system a +andr so the entropy + + align:start position:0% +andr so the entropy + + + align:start position:0% +andr so the entropy +balance + + align:start position:0% +balance + + + align:start position:0% +balance +says the final entropy which is the sum + + align:start position:0% +says the final entropy which is the sum + + + align:start position:0% +says the final entropy which is the sum +of the uh entropies of the two systems + + align:start position:0% +of the uh entropies of the two systems + + + align:start position:0% +of the uh entropies of the two systems +minus the initial + + align:start position:0% + + + + align:start position:0% + +entropy must be equal to the entropy + + align:start position:0% +entropy must be equal to the entropy + + + align:start position:0% +entropy must be equal to the entropy +exchanged plus the entropy generated + + align:start position:0% +exchanged plus the entropy generated + + + align:start position:0% +exchanged plus the entropy generated +within the system but since this is a + + align:start position:0% +within the system but since this is a + + + align:start position:0% +within the system but since this is a +work interaction only there is no + + align:start position:0% +work interaction only there is no + + + align:start position:0% +work interaction only there is no +entropy exchange so there is zero here + + align:start position:0% +entropy exchange so there is zero here + + + align:start position:0% +entropy exchange so there is zero here +and then there is uh entropy + + align:start position:0% + + + + align:start position:0% + +generation and then I also have to + + align:start position:0% +generation and then I also have to + + + align:start position:0% +generation and then I also have to +remember that at least for the reservoir + + align:start position:0% +remember that at least for the reservoir + + + align:start position:0% +remember that at least for the reservoir +I know uh + + align:start position:0% +I know uh + + + align:start position:0% +I know uh +it's I know an easy I mean the the the + + align:start position:0% +it's I know an easy I mean the the the + + + align:start position:0% +it's I know an easy I mean the the the +fundamental relation is easy enough that + + align:start position:0% +fundamental relation is easy enough that + + + align:start position:0% +fundamental relation is easy enough that +I can write it it's the equation of a + + align:start position:0% +I can write it it's the equation of a + + + align:start position:0% +I can write it it's the equation of a +straight line so a linear relation + + align:start position:0% +straight line so a linear relation + + + align:start position:0% +straight line so a linear relation +between change in energy and change in + + align:start position:0% +between change in energy and change in + + + align:start position:0% +between change in energy and change in +entropy the slope being the temperature + + align:start position:0% +entropy the slope being the temperature + + + align:start position:0% +entropy the slope being the temperature +of the + + align:start position:0% +of the + + + align:start position:0% +of the +reservoir + + align:start position:0% + + + + align:start position:0% + +okay all + + align:start position:0% +okay all + + + align:start position:0% +okay all +right so now you solve that so we have + + align:start position:0% +right so now you solve that so we have + + + align:start position:0% +right so now you solve that so we have +three equations you can use them to + + align:start position:0% +three equations you can use them to + + + align:start position:0% +three equations you can use them to +eliminate two variables so let's + + align:start position:0% +eliminate two variables so let's + + + align:start position:0% +eliminate two variables so let's +eliminate the change in energy for the + + align:start position:0% +eliminate the change in energy for the + + + align:start position:0% +eliminate the change in energy for the +reservoir and the change in entropy for + + align:start position:0% +reservoir and the change in entropy for + + + align:start position:0% +reservoir and the change in entropy for +the um for the + + align:start position:0% + + + + align:start position:0% + +res you combine and this is what you + + align:start position:0% +res you combine and this is what you + + + align:start position:0% +res you combine and this is what you +obtain you you're left with one + + align:start position:0% + + + + align:start position:0% + +equation E1 initial energy of a minus + + align:start position:0% +equation E1 initial energy of a minus + + + align:start position:0% +equation E1 initial energy of a minus +final energy of a minus the temperature + + align:start position:0% +final energy of a minus the temperature + + + align:start position:0% +final energy of a minus the temperature +of the res times initial entropy of a + + align:start position:0% +of the res times initial entropy of a + + + align:start position:0% +of the res times initial entropy of a +minus entropy of final entropy of a + + align:start position:0% +minus entropy of final entropy of a + + + align:start position:0% +minus entropy of final entropy of a +minus s generated multiplied by + + align:start position:0% +minus s generated multiplied by + + + align:start position:0% +minus s generated multiplied by +TR so you could write this as uh W + + align:start position:0% +TR so you could write this as uh W + + + align:start position:0% +TR so you could write this as uh W +rev minus TRS generated + + align:start position:0% + + + + align:start position:0% + +because when s generator is equal to + + align:start position:0% +because when s generator is equal to + + + align:start position:0% +because when s generator is equal to +zero the work is is corresponds to the + + align:start position:0% +zero the work is is corresponds to the + + + align:start position:0% +zero the work is is corresponds to the +reversible + + align:start position:0% + + + + align:start position:0% + +process you could also write this in + + align:start position:0% +process you could also write this in + + + align:start position:0% +process you could also write this in +terms of what we already defined as + + align:start position:0% +terms of what we already defined as + + + align:start position:0% +terms of what we already defined as +available + + align:start position:0% +available + + + align:start position:0% +available +energy so the work done in the + + align:start position:0% +energy so the work done in the + + + align:start position:0% +energy so the work done in the +reversible case so + + align:start position:0% +reversible case so + + + align:start position:0% +reversible case so +this uh first part of the right hand + + align:start position:0% +this uh first part of the right hand + + + align:start position:0% +this uh first part of the right hand +side is equal to the + + align:start position:0% +side is equal to the + + + align:start position:0% +side is equal to the +difference of the available energy of + + align:start position:0% +difference of the available energy of + + + align:start position:0% +difference of the available energy of +system a in the initial + + align:start position:0% +system a in the initial + + + align:start position:0% +system a in the initial +State and that in the final + + align:start position:0% +State and that in the final + + + align:start position:0% +State and that in the final +State and this is the formula for the + + align:start position:0% +State and this is the formula for the + + + align:start position:0% +State and this is the formula for the +available energy that we have seen when + + align:start position:0% +available energy that we have seen when + + + align:start position:0% +available energy that we have seen when +we just after the definition of entropy + + align:start position:0% +we just after the definition of entropy + + + align:start position:0% +we just after the definition of entropy +if you go back you can find that okay + + align:start position:0% +if you go back you can find that okay + + + align:start position:0% +if you go back you can find that okay +there is still another interesting way + + align:start position:0% +there is still another interesting way + + + align:start position:0% +there is still another interesting way +of writing + + align:start position:0% + + + + align:start position:0% + +this by defining + + align:start position:0% +this by defining + + + align:start position:0% +this by defining +a um we can call it an availability + + align:start position:0% +a um we can call it an availability + + + align:start position:0% +a um we can call it an availability +function another + + align:start position:0% +function another + + + align:start position:0% +function another +function uh um I'll call it canonical + + align:start position:0% +function uh um I'll call it canonical + + + align:start position:0% +function uh um I'll call it canonical +availability + + align:start position:0% +availability + + + align:start position:0% +availability +function just because + + align:start position:0% +function just because + + + align:start position:0% +function just because +later uh we need to Define other similar + + align:start position:0% +later uh we need to Define other similar + + + align:start position:0% +later uh we need to Define other similar +things and we need the names but soon we + + align:start position:0% +things and we need the names but soon we + + + align:start position:0% +things and we need the names but soon we +will get short of of letters and names + + align:start position:0% +will get short of of letters and names + + + align:start position:0% +will get short of of letters and names +also in this business here in any case + + align:start position:0% +also in this business here in any case + + + align:start position:0% +also in this business here in any case +we call gamma e minus + + align:start position:0% + + + + align:start position:0% + +TRS and notice therefore that the + + align:start position:0% +TRS and notice therefore that the + + + align:start position:0% +TRS and notice therefore that the +available + + align:start position:0% +available + + + align:start position:0% +available +energy is equal to gamma minus gamma + + align:start position:0% +energy is equal to gamma minus gamma + + + align:start position:0% +energy is equal to gamma minus gamma +R gamma + + align:start position:0% +R gamma + + + align:start position:0% +R gamma +R is the + + align:start position:0% +R is the + + + align:start position:0% +R is the +evaluation of this function at the state + + align:start position:0% +evaluation of this function at the state + + + align:start position:0% +evaluation of this function at the state +a r where the system a is in neutral + + align:start position:0% +a r where the system a is in neutral + + + align:start position:0% +a r where the system a is in neutral +stable equilibrium with the + + align:start position:0% + + + + align:start position:0% + +res + + align:start position:0% +res + + + align:start position:0% +res +okay so the available energy is the + + align:start position:0% +okay so the available energy is the + + + align:start position:0% +okay so the available energy is the +difference + + align:start position:0% +difference + + + align:start position:0% +difference +between the availability function at the + + align:start position:0% +between the availability function at the + + + align:start position:0% +between the availability function at the +generic state of your system and and the + + align:start position:0% +generic state of your system and and the + + + align:start position:0% +generic state of your system and and the +value of that availability function at + + align:start position:0% +value of that availability function at + + + align:start position:0% +value of that availability function at +the mutual equili state with the + + align:start position:0% + + + + align:start position:0% + +reservoir notice + + align:start position:0% +reservoir notice + + + align:start position:0% +reservoir notice +that when I am at in equilibrium with + + align:start position:0% +that when I am at in equilibrium with + + + align:start position:0% +that when I am at in equilibrium with +the reservoir the temperature of um by + + align:start position:0% +the reservoir the temperature of um by + + + align:start position:0% +the reservoir the temperature of um by +by the conditions for Mutual equilibrium + + align:start position:0% +by the conditions for Mutual equilibrium + + + align:start position:0% +by the conditions for Mutual equilibrium +the temperature of my system a is equal + + align:start position:0% +the temperature of my system a is equal + + + align:start position:0% +the temperature of my system a is equal +to the temperature of the + + align:start position:0% +to the temperature of the + + + align:start position:0% +to the temperature of the +reservoir and so this t R in that state + + align:start position:0% +reservoir and so this t R in that state + + + align:start position:0% +reservoir and so this t R in that state +is also the temperature of your + + align:start position:0% +is also the temperature of your + + + align:start position:0% +is also the temperature of your +system so in that stable M Mutual stable + + align:start position:0% +system so in that stable M Mutual stable + + + align:start position:0% +system so in that stable M Mutual stable +equilibrium State gamma + + align:start position:0% +equilibrium State gamma + + + align:start position:0% +equilibrium State gamma +R takes up the value of one of those + + align:start position:0% +R takes up the value of one of those + + + align:start position:0% +R takes up the value of one of those +Leander transform that we called the + + align:start position:0% +Leander transform that we called the + + + align:start position:0% +Leander transform that we called the +helal free energy we called it + + align:start position:0% +helal free energy we called it + + + align:start position:0% +helal free energy we called it +f e minus + + align:start position:0% +f e minus + + + align:start position:0% +f e minus +TS but this function is not e us Ts for + + align:start position:0% +TS but this function is not e us Ts for + + + align:start position:0% +TS but this function is not e us Ts for +other states it's e minus TR r s so it's + + align:start position:0% + + + + align:start position:0% + +different we can do the representation + + align:start position:0% +different we can do the representation + + + align:start position:0% +different we can do the representation +on the E sucess + + align:start position:0% + + + + align:start position:0% + +diagram so + + align:start position:0% +diagram so + + + align:start position:0% +diagram so +gamma is e minus TR + + align:start position:0% +gamma is e minus TR + + + align:start position:0% +gamma is e minus TR +RS okay so let's see uh + + align:start position:0% +RS okay so let's see uh + + + align:start position:0% +RS okay so let's see uh +e is this + + align:start position:0% +e is this + + + align:start position:0% +e is this +much from here to here + + align:start position:0% +much from here to here + + + align:start position:0% +much from here to here +to + + align:start position:0% + + + + align:start position:0% + +yeah no sorry let's say that we set this + + align:start position:0% +yeah no sorry let's say that we set this + + + align:start position:0% +yeah no sorry let's say that we set this +equal e is equal to zero is here the + + align:start position:0% +equal e is equal to zero is here the + + + align:start position:0% +equal e is equal to zero is here the +origin so E1 is this + + align:start position:0% +origin so E1 is this + + + align:start position:0% +origin so E1 is this +length Okay and then I need to to + + align:start position:0% +length Okay and then I need to to + + + align:start position:0% +length Okay and then I need to to +subtract TR * S1 so TR is the slope of + + align:start position:0% +subtract TR * S1 so TR is the slope of + + + align:start position:0% +subtract TR * S1 so TR is the slope of +this line so I take it as a line with a + + align:start position:0% +this line so I take it as a line with a + + + align:start position:0% +this line so I take it as a line with a +slope equal to tr starting from the + + align:start position:0% +slope equal to tr starting from the + + + align:start position:0% +slope equal to tr starting from the +origin so TR * S1 is this segment + + align:start position:0% +origin so TR * S1 is this segment + + + align:start position:0% +origin so TR * S1 is this segment +dashed so gamma is represented by + + align:start position:0% +dashed so gamma is represented by + + + align:start position:0% +dashed so gamma is represented by +this distance between this and that + + align:start position:0% +this distance between this and that + + + align:start position:0% +this distance between this and that +because it's this L length minus this + + align:start position:0% +because it's this L length minus this + + + align:start position:0% +because it's this L length minus this +length + + align:start position:0% +length + + + align:start position:0% +length +Okay this is for the generic State a A1 + + align:start position:0% +Okay this is for the generic State a A1 + + + align:start position:0% +Okay this is for the generic State a A1 +for the state in which the system is in + + align:start position:0% +for the state in which the system is in + + + align:start position:0% +for the state in which the system is in +mutual equilibrium with the reservoir + + align:start position:0% +mutual equilibrium with the reservoir + + + align:start position:0% +mutual equilibrium with the reservoir +its temperature + + align:start position:0% +its temperature + + + align:start position:0% +its temperature +TR we are + + align:start position:0% +TR we are + + + align:start position:0% +TR we are +here and that same construction so the + + align:start position:0% +here and that same construction so the + + + align:start position:0% +here and that same construction so the +distance from the line with lope TR + + align:start position:0% +distance from the line with lope TR + + + align:start position:0% +distance from the line with lope TR +originating at the origin + + align:start position:0% +originating at the origin + + + align:start position:0% +originating at the origin +uh is this + + align:start position:0% +uh is this + + + align:start position:0% +uh is this +much so so this is gamma + + align:start position:0% + + + + align:start position:0% + +R and now you may you may see that this + + align:start position:0% +R and now you may you may see that this + + + align:start position:0% +R and now you may you may see that this +gamma + + align:start position:0% +gamma + + + align:start position:0% +gamma +R is the minimum value that that + + align:start position:0% +R is the minimum value that that + + + align:start position:0% +R is the minimum value that that +characteristic function can + + align:start position:0% +characteristic function can + + + align:start position:0% +characteristic function can +take I'm sorry that availability + + align:start position:0% +take I'm sorry that availability + + + align:start position:0% +take I'm sorry that availability +function can + + align:start position:0% +function can + + + align:start position:0% +function can +take any other state whether it is + + align:start position:0% +take any other state whether it is + + + align:start position:0% +take any other state whether it is +stable equilibrium so if you go along + + align:start position:0% +stable equilibrium so if you go along + + + align:start position:0% +stable equilibrium so if you go along +this curve + + align:start position:0% +this curve + + + align:start position:0% +this curve +either side of AR or if you go inside + + align:start position:0% +either side of AR or if you go inside + + + align:start position:0% +either side of AR or if you go inside +the region of non + + align:start position:0% +the region of non + + + align:start position:0% +the region of non +equilibrium of course here we are + + align:start position:0% +equilibrium of course here we are + + + align:start position:0% +equilibrium of course here we are +talking about fixed values of N and + + align:start position:0% +talking about fixed values of N and + + + align:start position:0% +talking about fixed values of N and +V the function the the the values of + + align:start position:0% +V the function the the the values of + + + align:start position:0% +V the function the the the values of +gamma are greater than gamma R so gamma + + align:start position:0% +gamma are greater than gamma R so gamma + + + align:start position:0% +gamma are greater than gamma R so gamma +R is + + align:start position:0% + + + + align:start position:0% + +minimum so that means that if I start + + align:start position:0% +minimum so that means that if I start + + + align:start position:0% +minimum so that means that if I start +from here and go any where + + align:start position:0% +from here and go any where + + + align:start position:0% +from here and go any where +else I must decrease gamma I'm sorry I + + align:start position:0% +else I must decrease gamma I'm sorry I + + + align:start position:0% +else I must decrease gamma I'm sorry I +must increase + + align:start position:0% +must increase + + + align:start position:0% +must increase +gamma all + + align:start position:0% +gamma all + + + align:start position:0% +gamma all +right so I start from State a r go to + + align:start position:0% +right so I start from State a r go to + + + align:start position:0% +right so I start from State a r go to +any other + + align:start position:0% + + + + align:start position:0% + +state then the Delta so the change in + + align:start position:0% +state then the Delta so the change in + + + align:start position:0% +state then the Delta so the change in +gamma is + + align:start position:0% + + + + align:start position:0% + +positive that condition + + align:start position:0% + + + + align:start position:0% + +gives + + align:start position:0% +gives + + + align:start position:0% +gives +uh rules + + align:start position:0% + + + + align:start position:0% + +about + + align:start position:0% +about + + + align:start position:0% +about +um it it's the + + align:start position:0% +um it it's the + + + align:start position:0% +um it it's the +generating uh + + align:start position:0% +generating uh + + + align:start position:0% +generating uh +inequality for inequalities regarding + + align:start position:0% +inequality for inequalities regarding + + + align:start position:0% +inequality for inequalities regarding +the second order derivatives and + + align:start position:0% +the second order derivatives and + + + align:start position:0% +the second order derivatives and +therefore they have to go do with + + align:start position:0% +therefore they have to go do with + + + align:start position:0% +therefore they have to go do with +stability and the uh the concavity or + + align:start position:0% +stability and the uh the concavity or + + + align:start position:0% +stability and the uh the concavity or +convexity of Curves + + align:start position:0% + + + + align:start position:0% + +in particular this is in a sense a + + align:start position:0% +in particular this is in a sense a + + + align:start position:0% +in particular this is in a sense a +review because we already encountered + + align:start position:0% +review because we already encountered + + + align:start position:0% +review because we already encountered +these particular + + align:start position:0% +these particular + + + align:start position:0% +these particular +ones but this is just to give the idea + + align:start position:0% +ones but this is just to give the idea + + + align:start position:0% +ones but this is just to give the idea +so I'm I I apply this principle that is + + align:start position:0% +so I'm I I apply this principle that is + + + align:start position:0% +so I'm I I apply this principle that is +I move away from this state no matter + + align:start position:0% +I move away from this state no matter + + + align:start position:0% +I move away from this state no matter +where I go I Al I always increase + + align:start position:0% + + + + align:start position:0% + +gamma + + align:start position:0% +gamma + + + align:start position:0% +gamma +uh so let me apply it to one particular + + align:start position:0% +uh so let me apply it to one particular + + + align:start position:0% +uh so let me apply it to one particular +change so I decide to go + + align:start position:0% +change so I decide to go + + + align:start position:0% +change so I decide to go +to just a small change so with a small + + align:start position:0% +to just a small change so with a small + + + align:start position:0% +to just a small change so with a small +amount of u entropy change DS D for + + align:start position:0% +amount of u entropy change DS D for + + + align:start position:0% +amount of u entropy change DS D for +infinitesimal and also I choose to + + align:start position:0% +infinitesimal and also I choose to + + + align:start position:0% +infinitesimal and also I choose to +move along the stable equilibrium State + + align:start position:0% +move along the stable equilibrium State + + + align:start position:0% +move along the stable equilibrium State +curve so I'm going this side but the S + + align:start position:0% +curve so I'm going this side but the S + + + align:start position:0% +curve so I'm going this side but the S +could also be negative so I can go the + + align:start position:0% +could also be negative so I can go the + + + align:start position:0% +could also be negative so I can go the +other side but along the stable + + align:start position:0% +other side but along the stable + + + align:start position:0% +other side but along the stable +equilibrium State curve + + align:start position:0% + + + + align:start position:0% + +okay so if I change the entropy and I + + align:start position:0% +okay so if I change the entropy and I + + + align:start position:0% +okay so if I change the entropy and I +move along the uh stable equilibrium + + align:start position:0% +move along the uh stable equilibrium + + + align:start position:0% +move along the uh stable equilibrium +State curve the energy changes according + + align:start position:0% +State curve the energy changes according + + + align:start position:0% +State curve the energy changes according +to the fundamental + + align:start position:0% + + + + align:start position:0% + +relation so I + + align:start position:0% +relation so I + + + align:start position:0% +relation so I +move from + + align:start position:0% + + + + align:start position:0% + +ER to another energy which is given by + + align:start position:0% +ER to another energy which is given by + + + align:start position:0% +ER to another energy which is given by +the foundamental relation it's given by + + align:start position:0% +the foundamental relation it's given by + + + align:start position:0% +the foundamental relation it's given by +this + + align:start position:0% +this + + + align:start position:0% +this +one and I can use a tailor series + + align:start position:0% +one and I can use a tailor series + + + align:start position:0% +one and I can use a tailor series +expansion around uh the original + + align:start position:0% + + + + align:start position:0% + +point and + + align:start position:0% + + + + align:start position:0% + +uh there yeah okay so the taor series + + align:start position:0% +uh there yeah okay so the taor series + + + align:start position:0% +uh there yeah okay so the taor series +expansion has a value which is equal to + + align:start position:0% +expansion has a value which is equal to + + + align:start position:0% +expansion has a value which is equal to +a which cancels with that and I have + + align:start position:0% +a which cancels with that and I have + + + align:start position:0% +a which cancels with that and I have +first order term which is the derivative + + align:start position:0% +first order term which is the derivative + + + align:start position:0% +first order term which is the derivative +of e with respect to s which is the + + align:start position:0% +of e with respect to s which is the + + + align:start position:0% +of e with respect to s which is the +temperature which at the + + align:start position:0% +temperature which at the + + + align:start position:0% +temperature which at the +uh point where I stting uh is the + + align:start position:0% +uh point where I stting uh is the + + + align:start position:0% +uh point where I stting uh is the +temperature TR time the S Plus the + + align:start position:0% +temperature TR time the S Plus the + + + align:start position:0% +temperature TR time the S Plus the +second order terms in the tailor + + align:start position:0% +second order terms in the tailor + + + align:start position:0% +second order terms in the tailor +expansion and remember that here V and N + + align:start position:0% +expansion and remember that here V and N + + + align:start position:0% +expansion and remember that here V and N +are fixed so this we could call it the + + align:start position:0% +are fixed so this we could call it the + + + align:start position:0% +are fixed so this we could call it the +second differential of a at fixed n andv + + align:start position:0% + + + + align:start position:0% + +okay so that's Delta + + align:start position:0% +okay so that's Delta + + + align:start position:0% +okay so that's Delta +e now I substitute into Delta + + align:start position:0% +e now I substitute into Delta + + + align:start position:0% +e now I substitute into Delta +gamma to compute so Delta gamma is going + + align:start position:0% +gamma to compute so Delta gamma is going + + + align:start position:0% +gamma to compute so Delta gamma is going +to be uh since gamma is e minus TRS + + align:start position:0% +to be uh since gamma is e minus TRS + + + align:start position:0% +to be uh since gamma is e minus TRS +Delta gamma is Delta e minus TR Delta s + + align:start position:0% +Delta gamma is Delta e minus TR Delta s + + + align:start position:0% +Delta gamma is Delta e minus TR Delta s +so I + + align:start position:0% +so I + + + align:start position:0% +so I +substitute and this TR Delta + + align:start position:0% +substitute and this TR Delta + + + align:start position:0% +substitute and this TR Delta +s cancels with that one so I'm left with + + align:start position:0% +s cancels with that one so I'm left with + + + align:start position:0% +s cancels with that one so I'm left with +the second order differential only + + align:start position:0% + + + + align:start position:0% + +and since these plus the dots dots dots + + align:start position:0% +and since these plus the dots dots dots + + + align:start position:0% +and since these plus the dots dots dots +must be strictly greater than + + align:start position:0% +must be strictly greater than + + + align:start position:0% +must be strictly greater than +zero it + + align:start position:0% +zero it + + + align:start position:0% +zero it +requires that this term must be greater + + align:start position:0% +requires that this term must be greater + + + align:start position:0% +requires that this term must be greater +than or equal to zero so that gives + + align:start position:0% +than or equal to zero so that gives + + + align:start position:0% +than or equal to zero so that gives +us one + + align:start position:0% + + + + align:start position:0% + +condition I could also have chosen to + + align:start position:0% +condition I could also have chosen to + + + align:start position:0% +condition I could also have chosen to +move to a state + + align:start position:0% + + + + align:start position:0% + +in which instead I change I decide how + + align:start position:0% +in which instead I change I decide how + + + align:start position:0% +in which instead I change I decide how +much uh I change energy I still move + + align:start position:0% +much uh I change energy I still move + + + align:start position:0% +much uh I change energy I still move +along a stable equilibrium State curve + + align:start position:0% +along a stable equilibrium State curve + + + align:start position:0% +along a stable equilibrium State curve +but now I decide the value of the + + align:start position:0% + + + + align:start position:0% + +E well then the Taylor series expansion + + align:start position:0% +E well then the Taylor series expansion + + + align:start position:0% +E well then the Taylor series expansion +gives me this and the Delta gamma + + align:start position:0% +gives me this and the Delta gamma + + + align:start position:0% +gives me this and the Delta gamma +becomes + + align:start position:0% +becomes + + + align:start position:0% +becomes +minus the + + align:start position:0% +minus the + + + align:start position:0% +minus the +second lots of things cancel as before + + align:start position:0% +second lots of things cancel as before + + + align:start position:0% +second lots of things cancel as before +and so I'm left with Delta gamma is + + align:start position:0% +and so I'm left with Delta gamma is + + + align:start position:0% +and so I'm left with Delta gamma is +minus uh the second differential of + + align:start position:0% +minus uh the second differential of + + + align:start position:0% +minus uh the second differential of +s and for this to be greater than zero + + align:start position:0% +s and for this to be greater than zero + + + align:start position:0% +s and for this to be greater than zero +it + + align:start position:0% +it + + + align:start position:0% +it +requires that to be uh whoops this is + + align:start position:0% +requires that to be uh whoops this is + + + align:start position:0% +requires that to be uh whoops this is +wrong this should be I have to correct + + align:start position:0% +wrong this should be I have to correct + + + align:start position:0% +wrong this should be I have to correct +that too this should be less than or + + align:start position:0% +that too this should be less than or + + + align:start position:0% +that too this should be less than or +equal to + + align:start position:0% + + + + align:start position:0% + +zero okay I'll correct it in the slides + + align:start position:0% + + + + align:start position:0% + +okay so remember when we talked about + + align:start position:0% +okay so remember when we talked about + + + align:start position:0% +okay so remember when we talked about +concavity we had quickly passed this U + + align:start position:0% +concavity we had quickly passed this U + + + align:start position:0% +concavity we had quickly passed this U +uh slide where we took the fundamental + + align:start position:0% +uh slide where we took the fundamental + + + align:start position:0% +uh slide where we took the fundamental +relation and took in full Glory the uh + + align:start position:0% +relation and took in full Glory the uh + + + align:start position:0% +relation and took in full Glory the uh +Matrix of second order + + align:start position:0% +Matrix of second order + + + align:start position:0% +Matrix of second order +derivatives uh which is the asan of + + align:start position:0% +derivatives uh which is the asan of + + + align:start position:0% +derivatives uh which is the asan of +Matrix of the relation + + align:start position:0% + + + + align:start position:0% + +if some of + + align:start position:0% + + + + align:start position:0% + +these if you for if you keep fixed some + + align:start position:0% +these if you for if you keep fixed some + + + align:start position:0% +these if you for if you keep fixed some +of these variables it becomes a function + + align:start position:0% +of these variables it becomes a function + + + align:start position:0% +of these variables it becomes a function +of fewer variables so the the as becomes + + align:start position:0% +of fewer variables so the the as becomes + + + align:start position:0% +of fewer variables so the the as becomes +smaller and if I keep if I keep n and v + + align:start position:0% +smaller and if I keep if I keep n and v + + + align:start position:0% +smaller and if I keep if I keep n and v +as we did in the previous thing uh uh + + align:start position:0% +as we did in the previous thing uh uh + + + align:start position:0% +as we did in the previous thing uh uh +fixed this becomes just the as becomes + + align:start position:0% +fixed this becomes just the as becomes + + + align:start position:0% +fixed this becomes just the as becomes +just the second order + + align:start position:0% + + + + align:start position:0% + +derivative all right so let's we may + + align:start position:0% +derivative all right so let's we may + + + align:start position:0% +derivative all right so let's we may +call it the partial + + align:start position:0% + + + + align:start position:0% + +s and + + align:start position:0% +s and + + + align:start position:0% +s and +uh what we + + align:start position:0% + + + + align:start position:0% + +proved is that d s + + align:start position:0% +proved is that d s + + + align:start position:0% +proved is that d s +d2s should be and here it is correct + + align:start position:0% +d2s should be and here it is correct + + + align:start position:0% +d2s should be and here it is correct +less than or equal to zero + + align:start position:0% + + + + align:start position:0% + +okay so d2s is equal to uh the second + + align:start position:0% +okay so d2s is equal to uh the second + + + align:start position:0% +okay so d2s is equal to uh the second +derivative + + align:start position:0% + + + + align:start position:0% + +times D + + align:start position:0% + + + + align:start position:0% + +Squared because here the 2s in general + + align:start position:0% +Squared because here the 2s in general + + + align:start position:0% +Squared because here the 2s in general +is the asan Matrix that you gets + + align:start position:0% +is the asan Matrix that you gets + + + align:start position:0% +is the asan Matrix that you gets +Multiplied on left and also on the right + + align:start position:0% +Multiplied on left and also on the right + + + align:start position:0% +Multiplied on left and also on the right +by the de so you get the de squared and + + align:start position:0% +by the de so you get the de squared and + + + align:start position:0% +by the de so you get the de squared and +all the combinations this is in general + + align:start position:0% +all the combinations this is in general + + + align:start position:0% +all the combinations this is in general +in the particular case this is just de + + align:start position:0% +in the particular case this is just de + + + align:start position:0% +in the particular case this is just de +squared and since it is squared that + + align:start position:0% +squared and since it is squared that + + + align:start position:0% +squared and since it is squared that +simply + + align:start position:0% +simply + + + align:start position:0% +simply +requires that this + + align:start position:0% +requires that this + + + align:start position:0% +requires that this +derivative uh be negative and therefore + + align:start position:0% +derivative uh be negative and therefore + + + align:start position:0% +derivative uh be negative and therefore +we get the + + align:start position:0% +we get the + + + align:start position:0% +we get the +uh + + align:start position:0% + + + + align:start position:0% + +concavity of the S versus e relation + + align:start position:0% +concavity of the S versus e relation + + + align:start position:0% +concavity of the S versus e relation +which justifies + + align:start position:0% +which justifies + + + align:start position:0% +which justifies +uh our drawing the eers + + align:start position:0% +uh our drawing the eers + + + align:start position:0% +uh our drawing the eers +Suess diagram that + + align:start position:0% + + + + align:start position:0% + +way but for + + align:start position:0% +way but for + + + align:start position:0% +way but for +example recalling that the partial of s + + align:start position:0% +example recalling that the partial of s + + + align:start position:0% +example recalling that the partial of s +with respect to e is one over the + + align:start position:0% +with respect to e is one over the + + + align:start position:0% +with respect to e is one over the +temperature this + + align:start position:0% +temperature this + + + align:start position:0% +temperature this +derivative can be written this + + align:start position:0% +derivative can be written this + + + align:start position:0% +derivative can be written this +way because it's derivative with respect + + align:start position:0% +way because it's derivative with respect + + + align:start position:0% +way because it's derivative with respect +to e + + align:start position:0% +to e + + + align:start position:0% +to e +of one/ the temperature so it's minus 1 + + align:start position:0% +of one/ the temperature so it's minus 1 + + + align:start position:0% +of one/ the temperature so it's minus 1 +/ t t s * derivative of t with respect + + align:start position:0% +/ t t s * derivative of t with respect + + + align:start position:0% +/ t t s * derivative of t with respect +to e and if you go back to what we + + align:start position:0% +to e and if you go back to what we + + + align:start position:0% +to e and if you go back to what we +defined we called heat capacity at + + align:start position:0% +defined we called heat capacity at + + + align:start position:0% +defined we called heat capacity at +constant volume this is just the + + align:start position:0% +constant volume this is just the + + + align:start position:0% +constant volume this is just the +inverse of + + align:start position:0% + + + + align:start position:0% + +CD so this second derivative is equal to + + align:start position:0% +CD so this second derivative is equal to + + + align:start position:0% +CD so this second derivative is equal to +-1 / T ^2 over + + align:start position:0% +-1 / T ^2 over + + + align:start position:0% +-1 / T ^2 over +CV and that requires therefore that CV + + align:start position:0% +CV and that requires therefore that CV + + + align:start position:0% +CV and that requires therefore that CV +since it has to be negative it requires + + align:start position:0% +since it has to be negative it requires + + + align:start position:0% +since it has to be negative it requires +that CV is greater than equal to + + align:start position:0% + + + + align:start position:0% + +zero so for your models if you have a + + align:start position:0% +zero so for your models if you have a + + + align:start position:0% +zero so for your models if you have a +substance with a negative CV you are in + + align:start position:0% +substance with a negative CV you are in + + + align:start position:0% +substance with a negative CV you are in +trouble you have no substance you made a + + align:start position:0% + + + + align:start position:0% + +mistake + + align:start position:0% + + + + align:start position:0% + +um also from the other um equation that + + align:start position:0% +um also from the other um equation that + + + align:start position:0% +um also from the other um equation that +we have oops condition that we have here + + align:start position:0% +we have oops condition that we have here + + + align:start position:0% +we have oops condition that we have here +d2e greater than equal to zero we + + align:start position:0% +d2e greater than equal to zero we + + + align:start position:0% +d2e greater than equal to zero we +can uh remember that the partial of e + + align:start position:0% +can uh remember that the partial of e + + + align:start position:0% +can uh remember that the partial of e +with respect to S is the temperature see + + align:start position:0% +with respect to S is the temperature see + + + align:start position:0% +with respect to S is the temperature see +this is also written is also equal to + + align:start position:0% +this is also written is also equal to + + + align:start position:0% +this is also written is also equal to +the partial of t with respect to + + align:start position:0% +the partial of t with respect to + + + align:start position:0% +the partial of t with respect to +S + + align:start position:0% +S + + + align:start position:0% +S +okay which is greater than + + align:start position:0% +okay which is greater than + + + align:start position:0% +okay which is greater than +zero and this + + align:start position:0% +zero and this + + + align:start position:0% +zero and this +also uh is related to to the one above + + align:start position:0% +also uh is related to to the one above + + + align:start position:0% +also uh is related to to the one above +gives the same practical + + align:start position:0% + + + + align:start position:0% + +result these + + align:start position:0% + + + + align:start position:0% + +inequalities + + align:start position:0% +inequalities + + + align:start position:0% +inequalities +um give a an interesting uh give rise or + + align:start position:0% +um give a an interesting uh give rise or + + + align:start position:0% +um give a an interesting uh give rise or +are manifestations of a a general + + align:start position:0% +are manifestations of a a general + + + align:start position:0% +are manifestations of a a general +principle that it's chatelier or + + align:start position:0% +principle that it's chatelier or + + + align:start position:0% +principle that it's chatelier or +chatelier brown theorem or + + align:start position:0% + + + + align:start position:0% + +principle that uh if we combine it with + + align:start position:0% +principle that uh if we combine it with + + + align:start position:0% +principle that uh if we combine it with +the idea that we have seen today uh that + + align:start position:0% +the idea that we have seen today uh that + + + align:start position:0% +the idea that we have seen today uh that +temperature is an escaping tendency for + + align:start position:0% + + + + align:start position:0% + +energy you see what this + + align:start position:0% +energy you see what this + + + align:start position:0% +energy you see what this +says if uh at fixed N andv I give some + + align:start position:0% +says if uh at fixed N andv I give some + + + align:start position:0% +says if uh at fixed N andv I give some +energy to my system + + align:start position:0% + + + + align:start position:0% + +it increases its + + align:start position:0% +it increases its + + + align:start position:0% +it increases its +temperature well we all know that did we + + align:start position:0% +temperature well we all know that did we + + + align:start position:0% +temperature well we all know that did we +need so many lectures to get to this + + align:start position:0% +need so many lectures to get to this + + + align:start position:0% +need so many lectures to get to this +result all right this also says that if + + align:start position:0% +result all right this also says that if + + + align:start position:0% +result all right this also says that if +you give some + + align:start position:0% +you give some + + + align:start position:0% +you give some +entropy the temperature will + + align:start position:0% +entropy the temperature will + + + align:start position:0% +entropy the temperature will +increase but the + + align:start position:0% +increase but the + + + align:start position:0% +increase but the +temperature is the escaping tendency for + + align:start position:0% +temperature is the escaping tendency for + + + align:start position:0% +temperature is the escaping tendency for +energy so that means that if I give + + align:start position:0% +energy so that means that if I give + + + align:start position:0% +energy so that means that if I give +energy to my system + + align:start position:0% + + + + align:start position:0% + +in a sense it + + align:start position:0% +in a sense it + + + align:start position:0% +in a sense it +reacts by + + align:start position:0% +reacts by + + + align:start position:0% +reacts by +hiring its willingness to give away + + align:start position:0% +hiring its willingness to give away + + + align:start position:0% +hiring its willingness to give away +energy so it it is as if it counteracts + + align:start position:0% +energy so it it is as if it counteracts + + + align:start position:0% +energy so it it is as if it counteracts +it wants to counteract what you're doing + + align:start position:0% +it wants to counteract what you're doing + + + align:start position:0% +it wants to counteract what you're doing +so if you externally uh heat up the + + align:start position:0% +so if you externally uh heat up the + + + align:start position:0% +so if you externally uh heat up the +system uh you give energy and then it + + align:start position:0% +system uh you give energy and then it + + + align:start position:0% +system uh you give energy and then it +reacts + + align:start position:0% +reacts + + + align:start position:0% +reacts +by uh shaping things so it as as soon as + + align:start position:0% +by uh shaping things so it as as soon as + + + align:start position:0% +by uh shaping things so it as as soon as +it can it gives that energy away + + align:start position:0% +it can it gives that energy away + + + align:start position:0% +it can it gives that energy away +so for example if you start with your + + align:start position:0% +so for example if you start with your + + + align:start position:0% +so for example if you start with your +system in mutual equilibrium with your + + align:start position:0% +system in mutual equilibrium with your + + + align:start position:0% +system in mutual equilibrium with your +thermal Reservoir and externally give + + align:start position:0% +thermal Reservoir and externally give + + + align:start position:0% +thermal Reservoir and externally give +some energy to your system it will get + + align:start position:0% +some energy to your system it will get + + + align:start position:0% +some energy to your system it will get +off equilibrium off Mutual + + align:start position:0% +off equilibrium off Mutual + + + align:start position:0% +off equilibrium off Mutual +equilibrium higher temperature than the + + align:start position:0% +equilibrium higher temperature than the + + + align:start position:0% +equilibrium higher temperature than the +reservoir that higher temperature will + + align:start position:0% +reservoir that higher temperature will + + + align:start position:0% +reservoir that higher temperature will +so that will make will make up a + + align:start position:0% +so that will make will make up a + + + align:start position:0% +so that will make will make up a +difference in temperature that will + + align:start position:0% +difference in temperature that will + + + align:start position:0% +difference in temperature that will +drive an energy exchange back to the res + + align:start position:0% + + + + align:start position:0% + +thereby your system will try to + + align:start position:0% +thereby your system will try to + + + align:start position:0% +thereby your system will try to +reestablish + + align:start position:0% +reestablish + + + align:start position:0% +reestablish +equilibrium so you can see this natural + + align:start position:0% +equilibrium so you can see this natural + + + align:start position:0% +equilibrium so you can see this natural +tendency + + align:start position:0% +tendency + + + align:start position:0% +tendency +of uh reestablishing equilibrium here as + + align:start position:0% +of uh reestablishing equilibrium here as + + + align:start position:0% +of uh reestablishing equilibrium here as +a + + align:start position:0% +a + + + align:start position:0% +a +uh as a theorem + + align:start position:0% +uh as a theorem + + + align:start position:0% +uh as a theorem +that also emerges from the uh stability + + align:start position:0% +that also emerges from the uh stability + + + align:start position:0% +that also emerges from the uh stability +condition + + align:start position:0% +condition + + + align:start position:0% +condition +and the concavity of the fundamental + + align:start position:0% + + + + align:start position:0% + +relation chatelier Brown theorem of + + align:start position:0% +relation chatelier Brown theorem of + + + align:start position:0% +relation chatelier Brown theorem of +course is more General and we'll we'll + + align:start position:0% +course is more General and we'll we'll + + + align:start position:0% +course is more General and we'll we'll +see a little more the next time about + + align:start position:0% +see a little more the next time about + + + align:start position:0% +see a little more the next time about +this it's not just when you do this with + + align:start position:0% +this it's not just when you do this with + + + align:start position:0% +this it's not just when you do this with +respect to these variables but also when + + align:start position:0% +respect to these variables but also when + + + align:start position:0% +respect to these variables but also when +you do it with respect to many other + + align:start position:0% +you do it with respect to many other + + + align:start position:0% +you do it with respect to many other +variables and also it has an additional + + align:start position:0% +variables and also it has an additional + + + align:start position:0% +variables and also it has an additional +little um other twist that uh um we we + + align:start position:0% +little um other twist that uh um we we + + + align:start position:0% +little um other twist that uh um we we +will see when we do two + + align:start position:0% +will see when we do two + + + align:start position:0% +will see when we do two +variables okay but for today I think + + align:start position:0% +variables okay but for today I think + + + align:start position:0% +variables okay but for today I think +that yeah we are + + align:start position:0% +that yeah we are + + + align:start position:0% +that yeah we are +done and we are just in time okay so + + align:start position:0% +done and we are just in time okay so + + + align:start position:0% +done and we are just in time okay so +I'll see you next time \ No newline at end of file diff --git a/KXFF8m4uGDc.txt b/KXFF8m4uGDc.txt new file mode 100644 index 0000000000000000000000000000000000000000..999e80967dc0514f61c3ce3839f84dfe90811029 --- /dev/null +++ b/KXFF8m4uGDc.txt @@ -0,0 +1,3895 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educatiohal +resources for free. + +To make a donation or to view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: As this says, and +all the handouts say + +that this is 6.450. + +It's a first year graduate +course in the principles of + +digital communication. + +It's sort of the major first +course that you take as a + +graduate student in the +communication area. + +The information theory course +uses this as a prerequisite, + +uses it in a rather +strong way. + +6.432, the stochastic process +course uses it as a + +prerequisite. + +6.451, which is the companion +course which follows after + +this uses it as a +prerequisite. + +It's sort of material that you +have to know if you're going + +to go into the communication +area. + +It deals with this huge +industry, which is the + +communication industry. + +You look at the faculty here in +the department and you're a + +little surprised to see that +there are so few faculty + +members in digital +communication, so many faculty + +members in the computer area. + +You wonder why this is. + +It's sort of this historical +accident, because somehow or + +other the department didn't +realize as these two fields + +were growing, the one that +looked more glamorous for a + +long time was the +computer field. + +Nobody in retrospect understands +why that is. + +But at the same time +that's how it is. + +You will not see as much +excitement here. + +You also will see that because +of the big bust in the year + +2000, there's much less +commercial activity in the + +communications field now. + +As students, you ought +to relish this. + +You ought to really be happy +about this if you want to go + +into the communication field, +because at some point in the + +future, all of the failure to +start new investments, and all + +of the large communication +companies means a very + +explosive growth is +about to start. + +So I don't think this is a +dead field by any means. + +Looking back historically, every +time the communication + +field has seemed dead, and I +can think of three or four + +such times in history, those +have been the exact times + +where it was great to +get into the field. + +There was a time in the early +'70s when all the + +theoreticians who worked in +communication theory all were + +going around with long faces +saying everything that we can + +do has been done, the field is +dead, nothing more to do, + +might as well give up and +go into another field. + +This was really exactly the time +that a number of small + +communication companies were +really starting to grow very + +fast because they were using +some of the modern ideas of + +communication theory and they +were using these modern ideas + +to do new things. + +You now see companies like +Qualcomm that were started + +then, Motorola of whom +major divisions were + +started back then. + +An enormous amount of activity +was starting just then, partly + +because the field seemed to be +moribund and the theoreticians + +were turning and deciding well, +I guess we have to do + +something practical now. + +If you want to find a good +practical engineer, if you + +wind up in industry, if you wind +up as an entrepreneur or + +if you wind up climbing the +ladder and being a chief + +executive, if you want to find +somebody who will really do + +important things, find somebody +who understands + +theory who has decided that they +suddenly want to start to + +do practical things. + +Because if you point to the +people who have really done + +exciting things in this field, +those are the ones who have + +done most of it. + +OK, so anyway, the big field, +it's an important field. + +What we want to do is to study +the aspects of communication + +systems that are unique to +communication systems. + +In other words, we don't want +to study hardware here, we + +don't want to study software +here, because hardware is + +pretty much the same for any +problem you want to look at. + +It's not that highly +specialized, and software is + +not either. + +So we're not going to study +either of those things, we're + +going to study much more the +architectural principles of + +communication. + +We're going to study a lot of +the theory of communication, + +and I want to explain why it is +that we're going to do that + +as we move on. + +Because it's not at all clear at +first why we want to study + +the silly things that we'll be +studying in the course, and I + +want to give you some idea today +of why we're pushed into + +doing that. + +As we start doing these +things, I'll give + +you more of an idea. + +I know when I was a student I +couldn't figure out why I was + +learning the things that +I was learning. + +I just found that some things +were much more interesting + +than others, and the things that +tended to be interesting + +were the more theoretical +things, so I started looking + +at them harder and thought +gee, this is neat stuff. + +But I had no idea that it was +ever going to be important. + +So I'm going to try to explain +to you why this is important, + +and something today about what +the proper inter-relationship + +is of engineering and theory. + +As another example of my own +life, for a long time I + +thought -- this is rather +embarrassing to say -- + +but I was a theoretician and not +much of an engineer for a + +very long time. + +And I kept worrying about this +and saying well the stuff I'm + +doing is fun and I enjoy doing +it, but why should + +anybody pay me for it? + +Of course, I was being paid by +MIT, I was being paid as a + +consultant, but I felt I was +robbing all these people. + +And finally, I decided a +rationale for all of this. + +Most people felt that theory was +silly, and therefore, they + +would keep asking me well, +if you're so smart + +why aren't you rich? + +I didn't have any very good +answer to that because I felt + +I was smart because I understood +all this theory, + +but I wasn't rich. + +So I thought gee, what I've +gotta do is do enough + +engineering to get rich, and +then when people ask me that + +question I can say I am. + +I would suggest to all you, if +you have theoretical leadings, + +to focus on some engineering +also so you can become rich, + +not because there's anything to +do with the money, but just + +because it lets you hold your +head up high in a society that + +values money a lot more +than values intellect. + +So it's important. + +OK. + +This is a part of this +two-term sequence. + +One comment here is I'm not sure +that whether 6.451, which + +is the second part of this +sequence, is going to be + +taught in the spring or not. + +It might not be taught until +spring of the following year. + +If a large number of you decide +that you really want to + +do this and do it now, make +yourselves heard a little bit + +because the idea of a lot of +people want this course will + +have something to do on whether +somebody manages to + +teach it or not. + +As I was starting to say, theory +has had a very large + +impact on almost every field +we can think of. + +I mean you think of +electromagnetism, you think of + +all these other fields +and theory is very + +important in them. + +But in communication systems it +is particularly important. + +It's partly important because +back in 1948, Claude Shannon + +who was the inventor of +information theory -- you + +usually don't invent theories, +but he really did. + +This came whole cloth out +of this one mind. + +He had these ideas turning +around in his head for about + +eight years while the second +World War was going on. + +He was working on other things, +which were, in fact, + +very important things, and he +was doing those things for the + +government. + +He was working on aircraft +control and things like that. + +He was working on +cryptography. + +But he was just fascinated by +these communication problems + +and he couldn't get +his mind off them. + +He took up cryptography because +it happened to use all + +the ideas that he was really +interested in. + +He wrote something about +cryptography during the middle + +of the war, which made many +people believe that he had + +done his cryptography work +before he did his + +communication work. + +But in fact, it was the +other way around. + +This was purely the fact that +he could write about + +cryptography, and he never liked +to write, so he didn't + +want to write about +communication because it was a + +more complicated field +and he didn't + +understand the whole thing. + +So for 25 years it was a +theory floating around. + +You will learn a good deal +of what this theory is. + +Most graduate courses on +communication don't spend much + +time on information theory. + +This was not a mistake many, +many years ago, but it is a + +mistake now, because +communication theory at its + +core is information theory. + +Most people realize this. + +Most kids recognize it, +most people in the + +street recognize it. + +When they start to use a system +to communicate with the + +internet, what do +they talk about? + +Do they talk about +the bandwidth? + +No. + +They might call it bandwidth but +what they're talking about + +is the number of bits per second +they can communicate. + +This is a distinctly information +theoretic idea, + +because communication used to +be involved with studying + +different kinds of wave forms. + +Suddenly, at this point, people +are studying all these + +other things and are based on +Claude Shannon's ideas, + +therefore, we will teach some +of those ideas as we go. + +As a matter of fact, I was +talking a little bit about the + +fact that there's been a sort of +a love-hate relationship by + +communication engineers for +information theory. + +Back in 1960, a long, long time +ago when I got my PhD + +degree, the people at MIT, the +people who started this field, + +many of them told me that +information theory was dead at + +that point. + +There'd been an enormous amount +of research done on it + +in the ten years before 1960. + +They told me I should go into +vacuum tubes, which was the + +coming field at that time. + +Two points to that story. + +If people tell you that +information theory isn't + +important, please remember that +story or else tell them + +to start to study +vacuum tubes. + +The other point of it -- well, +I forgot what the other point + +of it is so let's go on. + +Anyway, information theory is +very much based on a bunch of + +very abstract ideas. + +I will start to say what that +means as we go on, but + +basically it means that +it's based on very + +simple-minded models. + +It's based on ignoring all +the complexities of the + +communication systems and +starting to play with toy + +models and trying to +understand those. + +That's part of what we have to +understand to understand why + +we're doing what we're doing. + +A very complex relationship +between modeling, theory, + +exercises and engineering +design. + +Maybe I shouldn't be talking +about that now and maybe the + +notes shouldn't talk about it, +but I want to open the subject + +because I want you to be +thinking about that + +throughout the term. + +Because it's something that +most people really don't + +understand. + +Something that most teachers +don't understand. + +It's something that most +students don't understand. + +When you're a student, you do +the exercises you do because + +you know you have to do them. + +There was a sort of apocryphal +story awhile ago that somebody + +told me about a graduate +student, not at MIT, thank + +God, who went into see the +person teaching a course on + +wireless and saying, I don't +want to know all that theory, + +I don't want to have to think +about these things, just tell + +me how to do the problems. + +Now, we will explain the +enormous stupidity of that as + +we move on. + +Part of the stupidity is that +the problems that you work on + +as a graduate student, even in +your thesis, the problems that + +you work on are not +real problems. + +The problems that we work on +everywhere in engineering are + +toy problems. + +We work on them because we want +to understand some aspect + +of the real problem. + +We can never understand the +whole problem, so we study one + +aspect, then we study +another aspect. + +The reason for all these +equations that we have, it's + +not a way to understand +reality. + +It really isn't. + +It's a way to understand little +pieces of reality. + +You take all of those and after +you have all of these in + +your mind, you then start to +study the real engineering + +problem and you say I put +together this and this and + +this and this and this -- this +is important, this is not so + +important, here, this +is more important. + +And then finally, if you're a +really good engineer, instead + +of writing down an equation, you +take an envelope, as the + +story goes, and you scribble +down a few numbers, and you + +say the way this system ought to +be built is the following. + +That's the way all important +systems get built, I claim. + +Important systems are not +designed by the kinds of + +things you do in homework +exercises. + +The things you do in homework +exercises are designed to help + +you understand small +pieces of problems. + +You have to understand those +small pieces of problems in + +order to understand the whole +engineering problems, but you + +don't do simulations to build +a communications system. + +You understand what the whole +system is, you can see it in + +your mind after you think about +it long enough, and + +that's where good system +design comes from. + +Simulations are a big part of +all of this, writing down + +equations are a big +part of it. + +But when you're all done, if +you design an engineering + +system and you don't see in your +mind why the whole thing + +works, you will wind up with +something like Microsoft Word. + +That's the truth. + +So the exercises that we're +going to be doing are really + +aimed at understanding +these simple models. + +The point of the exercises is +not to get the right answer. + +The answer is totally irrelevant +to everything. + +What's important is you start to +understand what assumptions + +in the problem lead to +what conclusions. + +How if you change something +it changes something else. + +That's when you're using system +design, because in + +system design you can never +understand the whole thing. + +You have to look at what parts +of it are important, what + +parts of it aren't important, +and the only way you can do + +that is having a catalog of the +simple-minded things in + +the back of your mind. + +Practical engineers get that by +dealing with real systems + +day-to-day all their lives. + +They see catastrophes occur. + +Those things tell them what to +avoid and what not to avoid. + +Students can do this in a +much more efficient way. + +Obviously, in the practical +experience also, but the + +experience that you get from +looking at these exercises and + +looking at this analytical +material in the right way, + +mainly looking at it is how do +you analyze these simple toy + +models, how do you make +conclusions from them is what + +let's you start being +a good engineer. + +I'm stressing this because at +some point this term, all of + +you, all of you at different +times are going to start + +saying why the hell +am I doing this? + +Why am I dealing with this +stupid little problem? + +Stupid little problems can get +incredibly frustrating at + +times, because you see something +that's so simple and + +you can't understand it. + +Then you say well, this +simple thing can't + +be important anyway. + +What I really want to do is +understand what this overall + +system is, and you give +up at that point. + +Don't do that. + +Sometimes there's a very +difficult question about what + +you mean by something +being simple. + +I will sometimes say that +something is very simple, and + +I will offend many you to +whom it's not simple. + +The point is something +becomes simple after + +you understand it. + +Nothing is simple before +you understand it. + +So there's that point at which +the light goes off in your + +head at which it +becomes simple. + +When I say that something is +simple, what I mean is that if + +you think about it long enough +a light will go off in your + +head and it will +become simple. + +It's not simple to start with. + +Other things are just messy. + +You've all heard of mathematical +problems which + +are just ugly. + +There are these things of +extraordinary complexity. + +There are things where there +just isn't any structure. + +You see a lot of these things +in computer science. + +I talked about Microsoft Word. + +Part of the reason it's such a +lousy language is because the + +problem is incredibly +difficult. + +It's incredibly unstructured. + +So people come up with things +that don't make any sense, + +because that inherently +is not simple. + +OK, these other things that +we'll be studying here are + +inherently simple and the only +problem is how do you get to + +the point of seeing these +simple ideas. + +OK, so that's enough +philosophy. + +No, not quite enough, a +little more of that. + +All the everyday communication +systems that we deal with are + +incredibly complex in terms of +the amount of hardware, the + +amount of software in them. + +If you look at the whole +system and you try to + +understand it as a whole, +you don't have prayer. + +There's no way to do it. + +These things work and they can +be understood because they're + +very highly structured. + +They have simple architectural +principles. + +What do I mean by architectural +principles? + +It's a word that engineers +use more and more. + +It started off with computer +systems because it became + +essential there to start +thinking in terms of + +architecture. + +It's exactly the same thing +that you mean when you're + +talking about a house +or a building. + +Mainly the architecture +is the overall design. + +It's the way the different +pieces fit together. + +In engineering, architecture +is the same thing. + +It's the thing that happens +when your eyes fuzz over a + +little bit and you can't see +any of the details anymore, + +and suddenly what you're doing +is you're looking at the whole + +thing as an entity +and saying how do + +the pieces fit together. + +Well, what we're going to +be focusing on here. + +One of the major keys to making +these things simpler is + +to have standardized + +interfaces and to have layering. + +And we'll talk a little bit +about each of these because + +our entire study of this subject +is based on studying + +the different layers that +we'll wind up with. + +OK, the most important and most +critical interface in a + +communication system +is between the + +source and the channel. + +Today, that standard interface +is almost always + +a binary data stream. + +You all know this. + +When you talk about +your modab, how do + +you talk about it? + +48 kilobits per second +if you're an + +old-fashioned kind of guy. + +1.2 megabits if you're a medium +technology person, or + +several gigabits if you're one +of these persons who likes to + +gobble up huge amounts +of stuff. + +That's the way you describe +channels -- how many bits per + +second can you send? + +The way you describe sources is +how many bits per second do + +you need as a way of viewing +that source. + +When you store a picture, how +do you talk about it? + +You don't talk about in terms of +the colors or any of these + +other things, picture +is a bunch of bits. + +That, at the fundamental +level, is + +what we're doing here. + +When you deal with source +coding, you're talking + +fundamentally about the problem +of taking whatever the + +source is, and it can be any +sort of thing at all -- it can + +be voice, it can be text, it can +be emails, the emails with + +viruses in it, whatever -- and +the problem is you want to + +turn it into a bit stream. + +Then this bit stream gets +presented to the channel. + +Channels and the channel +encoding equipment don't have + +any idea of what those +bits mean. + +They don't want to have any idea +of what those bits mean. + +That's what an interface +means. + +It means the problem of +interpreting the bits, the + +problem of going from something +which you view as + +having intelligence down to +a sequence of bits is the + +problem of the source coder. + +The problem of taking those bits +and moving them from one + +place to another is the function +of the channel + +designer, the network designer +and all of those things. + +When you talk about information +theory, it's a + +total misnomer from +the beginning. + +Information theory does not deal +with information at all, + +it deals with data. + +We will understand what that +distinction is as we go on. + +When you talk about a bit +stream, what you're talking + +about is a sequence of data. + +It doesn't mean anything. + +It's just that a one is +different from a zero, and you + +don't care how it's different, +it just is. + +So the channel input +is a binary stream. + +It doesn't have any +meaning as far as + +the channel is concerned. + +The bit stream does have a +meaning as far as the source + +is concerned. + +So the problem is the source +encoder takes these bits, + +takes the source, whatever it +is, with its meaning and + +everything else, turns it +into a stream of bits -- + +you would like to turn it into +as few bits as possible. + +Then you take those bits, you +transmit them on the channel, + +the channel designer understands +what the physical + +medium is all about, understands +what the network + +is all about, and doesn't +have a clue as to what + +all those bits mean. + +So the picture is +the following. + +That's the major layering of +all communication systems. + +Here's the input, which is +whatever it happens to be. + +Here's the source encoder. + +The source encoder has to +know a great deal about + +what that input is. + +You have to know the structure +of the input. + +You have a source encoder for +voice and you use it to try to + +encode a video stream it's not +going to work, obviously. + +If you try to use a source +encoder for English and try to + +use it on Chinese, it probably +won't work very well either. + +It won't work for anything +other than what + +it's intended for. + +So the source encoder has to +understand the source. + +When I say understand the +source, what do I mean? + +It means to understand +the probabilistic + +structure of the source. + +This is another of the things +that Shannon recognized + +clearly that hadn't been +recognized at all before this. + +You have to somehow understand +how to view what's coming out + +of the source, this picture, +say, as one of a possible set + +of pictures. + +If you know ahead of time that +a communication system is + +going to be sending the +Gettysburg Address or one of + +50 other highly-inspiring +texts, what do you do? + +Do you try to encode +these things, all + +these different texts? + +Of course not. + +You just assign number one to +the Gettysburg Address, number + +two to the second thing that +you might be interested in. + +You send a number and then at +the output out comes the + +Gettysburg Address because +you've stored that there. + +So that's the idea +of source coding. + +What is important is not the +complexity of the individual + +messages, it's the probabilistic +structure that + +tells you what are the different +possibilities. + +That's what happens when +you try to turn + +things into binary digits. + +You have one sequence of binary +digits for each of the + +possible things that you +want to represent. + +Then in the channel you have +the same sort of thing. + +You have noise, you have all +sorts of other crazy things on + +the channel. + +You have a sequence of bits +coming in, you have a sequence + +of bits coming out. + +The fundamental problem of the +channel is very, very simple. + +You want to spit out the +same bits that came in. + +You can take a certain amount +of delay doing that, but + +that's what you have to do. + +In order to do that, you have to +understand something about + +the probabilistic structure +of the noise. + +So both ways you have +probabilistic structure. + +It's why you have to understand +probability at the + +level of 6.041, which is the +undergraduate course here + +studying probability. + +If you don't have that +background, please don't take + +the course because you're +going to be crucified. + +If you think you can learn +it on the fly, don't. + +You can't learn it on the fly. + +As a matter of fact, if you've +taken the course, you still + +don't understand it, and you +will need to scramble a little + +bit to understand it at a +deeper level in order to + +understand what's +going on here. + +6.041 is a particularly good +undergraduate course. + +I think it's probably taught +here better than it's taught + +at most places. + +But you still don't understand +it the first time through. + +It's a tricky, subtle subject +you really need to understand + +enough of it, If you have +no exposure to it. + +If you've taken a course +called statistics and + +probability, which first teaches +you statistics and + +then tucks in a little bit of +probability at the end, go + +learn probability first because +you don't have enough + +of it to take this subject. + +The other part of dealing with +these channels is that + +suddenly we have to deal with +4AA analysis and all of these + +things, if you don't have +some kind of subject + +in signals and systems. + +Some computer scientists +don't learn that + +kind of material anymore. + +Again, you can't learn it on +the fly because you need a + +little bit of background +for it. + +Those two prerequisites +are really essential. + +Nothing else is essential. + +The more mathematics you know +the better off you are, but we + +will develop what we +need as we go. + +Now, we talked about this +fundamental layer in all + +communication systems, which is +between source coding and + +channel coding. + +You first turn the source into +bits, and then you turn the + +bits into something you can +transmit on the channel. + +Source coding breaks down into +three pieces itself. + +It doesn't have to break down +into those three pieces, but + +it usually does. + +Most source coding you start out +with a wave form, such as + +with voice, or with pictures you +start out with what's more + +complicated than a wave form, +some kind of mapping from + +x-coordinate and y-coordinate +and time, and you map all of + +those things into something. + +Our problem here is we want to +take these analog wave forms + +or generalizations of. + +It turns out that all we have +to deal with here is the + +analog wave forms because +everything else + +follows easily from that. + +So there's one question. + +How do you turn an analog +wave form into + +a sequence of numbers? + +This is the common way of +doing source coding. + +Many of you who have been +exposed to the sampling + +theorem, you think that's the +way to do it, this is + +one way to do it. + +We will talk a great +deal about this. + +You will find out that the +sampling theorem really isn't + +the way to do it. + +Although again, it's a simple +model, it's the way to start + +dealing with it. + +Then you learn the various +other parts of + +that as you go along. + +After you wind up with +sequences, sequences of + +numbers, we worry about how +to quantize those numbers, + +because fundamentally we're +trying to get from + +wave forms into bits. + +So the three stages in that +process are first go to + +sequences, go from sequences to +symbols -- namely, you have + +a finite number of symbols, +which are quantized versions + +of those analog numbers +which can be anything. + +Then finally, you encode +the symbols into bits. + +The coding goes in the +opposite order. + +Here's a picture which shows it +better than the words do. + +From the input wave form, you +sample it or something more + +generalized than sampling it. + +That gives you a sequence +of numbers. + +You quantize those numbers, +that gives + +you a symbol sequence. + +You have a discrete coder, which +turns those symbols into + +a sequence of bits +in some nice way. + +Then you have this reliable +binary channel. + +Notice what I've done here. + +This thing is that entire +system we were + +talking about before. + +This has a channel encoder in +it, a channel, a channel + +decoder and all of that. + +But what we've been saying in +this layering idea is when + +you're dealing with source +coding you ignore all of that. + +You say OK, it's Tom's job who +was designing the channel + +encoder to make sure that +my bits come out + +here as the same bits. + +If the bits are wrong +it's his fault. + +If the bits are right, and this +output wave form doesn't + +look like the input wave +form, it's my fault. + +So part of the layering idea is +we just recreate this whole + +thing here as the same bits and +we don't worry about what + +happens when the bits +are different. + +The other part of this is +that all of this breaks + +down in the same way. + +Namely, at this interface +between here and here, the + +idea is the same. + +Namely, there's an input wave +form that comes in, there's a + +sequence of numbers here. + +The job of this analog filter, +as we call it, and you'll see + +why we call it that later, is +to take numbers here, turn + +them back into wave forms. + +These numbers are supposed to +resemble these numbers in some + +way or other. + +I can deal with this part of the +problem totally separately + +from dealing with the other +parts of the problem. + +Namely, the only problem here is +how do I take numbers, turn + +them into wave forms. + +There are a bunch of other +problems hidden here, like + +these numbers are not going to +be exactly the same as these + +wave forms because I have +quantization involved here. + +Since the numbers are not +exactly the same, we have to + +deal with questions +of approximation. + +How to approximations in numbers +come out in terms of + +approximations in terms +of wave forms? + +That's where you need things +like the sampling theorem and + +the generalizations of it that +we're going to spend + +a lot of time with. + +Then you go down +to this point. + +At this point the quantizer +produces a string of symbols. + +Whatever those symbols happen +to be, but those symbols + +might, in fact, just be integers +whereas the things + +here were real valued numbers, +and in quantizing we turn real + +numbers into intergers by saying +-- well, it's the same + +way you approximate things +all the time. + +You round off the pennies +in your checkbook. + +It's the same idea. + +So the problem here is the +quantizer produces these + +symbols here. + +The job of all of this stuff +is to recreate those same + +symbols here. + +So the symbols now go into +something that does the + +reverse of a quantizer -- + +we'll call it a table look-up +because that's + +sort of what it is. + +So we can study this part of the +problem separately, also. + +You don't have to understand +anything about this problem to + +understand this problem. + +Finally, we have symbols here +going into a discrete encoder. + +We have an interesting problem +which says how do we take + +these symbols which have some +kind of probabilistic + +structure to them and turn them +into binary digits in an + +efficient way. + +If the symbols here, for +example, are binary symbols + +and the symbols happen to be 1 +with probability 999 out of + +1,000, and zero with probability +1 in 1,000, you + +don't really just want to take +these symbols and map them in + +a straightforward way, 1 into +1 and zero into zero. + +You want to look at whole +sequences of them. + +You want to do run length +coding, for example. + +You want to count how long it +is between these zero's, and + +then what you do is send those +counts and you encode them. + +So there are all kinds of tricks +that you can use here. + +But the point is, this problem +is separate, and this problem + +is separate from this problem. + +Now what we're going to do in +this course is start out with + +this problem, because this is +the cleanest and the neatest + +of the three problems. + +It's the one you can +say the most about. + +It's the one which has the +nicest results about it. + +In fact, a lot of source coding +problems just deal with + +this one part of it. + +Whenever you're encoding text, +you're starting out with + +symbols which are the letters +of whatever language you're + +dealing with and perhaps a bunch +of other things -- ask a + +code, you've generated 256 +different things, including + +all the letters, all the capital +letters, all of the + +junk that used to be on +typewriters, and some of the + +junk that's now in word +processing languages, and you + +have a way of mapping those +into binary digits. + +We want to look at better +ways of doing that. + +So this, in fact, covers the +whole problem of source coding + +when you're dealing with +text rather than + +dealing with wave forms. + +This problem here combined with +this problem deals with + +all of these many problems where +what you're interested + +in is taking a sequence of +numbers or a sequence of + +whatjamacallits and +quantitizing + +them and then coding. + +Finally, when you get to the +input wave forms and output + +wave forms, you've solved both +of these problems and you can + +then focus on what's +important here. + +This is a good case study of why +the information theoretic + +approach works and +why theory works. + +Because if you started out with +the problem of saying I + +want to build something to +encode voice, and you try to + +do all of these together, and +you look up all the things you + +can find about voice encoding on +the web and you read all of + +them, what you will wind up +with, I can guarantee you, is + +you will know an enormous amount +of jargon, you will + +know an enormous number of +different systems, which each + +half work, you will not have the +slightest clue as to how + +to build a better system. + +So you have to take the +structured viewpoint, which is + +really the only way to do things +to find new and better + +ways of doing things. + +Now there are some +extra things. + +I have over-simplified it. + +I want to over-simplify +things in this course. + +What I will always do is I'll +try to cheat you into thinking + +the problem is simpler than it +is, and then I will talk about + +all of the added little nasties +that come in as soon + +as you try to use any +of this stuff. + +There are always nasties. + +What I hope you will all do by +the end of the term is find + +those little nasties on your +own before I start to talk + +about them. + +Namely, when we start to talk +about a simple model, be + +interested in the simple model, +study it, find out what + +it's all about, but at the same +time, for Pete's sake, + +ask yourself the question. + +What does this have to do with +the price of rice in China or + +with anything else? + +And ask those questions. + +Don't let those questions +interfere with understanding + +the simple model, but you've got +to always be focusing on + +how that simple model relates +to what you visualize as a + +communication system problem. + +It usually will have +some relation but + +not a complete relation. + +Here the problems are in +this binary interface. + +The source might produce packets +or the source might + +produce a stream of data. + +In other words, if what you're +dealing with is the kind of + +situation where you're an +amateur photographer, you go + +around taking all sorts of +pictures, and then you encode + +these pictures -- + +what do I mean by encoding +the pictures? + +You turn them into +binary digits. + +Then you want to send your +pictures to somebody else, but + +what you're really doing is +sending these packets to + +someone else. + +You're not sending a stream of +data -- you have 10 pictures, + +you want to send those +10 pictures. + +At the output of the whole +system, you hope you see 10 + +separate pictures. + +You hope there's something in +there which can recognize that + +out of the stream of binary +digits that come across the + +channel, there's some packet +structure there. + +Well we're not going to talk +about that really. + +Whenever you start dealing with +this problem of source + +encoding, you also need to worry +a little bit about the + +packet structure. + +What are the protocols for +knowing when something new + +starts, when something +new ends. + +Those kinds of problems are +dealt with mostly in a network + +course here, and you can find +out all sorts of things about + +them there. + +But there are these two general +types of things -- + +packets and streams of data. + +In terms of understanding voice +encoding, you can study + +them both together. + +Why can you study them +both together? + +Because the packets are long +and because the packets are + +long because they include a lot +of data, you have a little + +bit of end effect about how to +start it, a little bit of end + +effect about how to end it, +but the main structural + +problem you'll be dealing +with is what to do + +with the whole thing. + +It's an added piece that comes +at the end to worry about how + +do you denote the beginning +and the end. + +That's a problem you have with +stream data also, because + +stream data does not start +at time minus infinity. + +Whatever the stream data is +coming from, what it's coming + +from did not at time, +t equals infinity. + +You just think of it that way +because you recognize you can + +postpone the problem of how do +you start it and how do you + +end it, and hopefully you can +postpone it until somebody + +else has taken over the job. + +What the channel accepts is +either of these binary streams + +or packets, but then +queueing exists. + +In other words, you have stuff +coming into a channel -- + +sometimes I'm sitting at home +and I want to send long files, + +I want to send this +whole textbook + +I'm writing to somebody. + +It queues up, it takes a long +time to get it out of my + +computer and into this other +person's computer. + +It would be nice if I could +send it at optical speeds. + +But I don't care much. + +I don't care much whether it +takes a second or a minute or + +an hour to get to this +other person. + +He won't read it for a week +anyway, if he reads it at all, + +so what difference +does it make? + +But anyway, we have these +queueing problems, which are, + +again, separable. + +They're dealt with mostly +in the network course. + +What we're mostly interested in +is how to reduce bit rate + +for sources. + +How do you encode things +more efficiently? + +Data compression is the word +usually given to this. + +How do you compress things into +a smaller number of bits + +using the statistical +structure of it? + +Then how do you increase the +number of bits you can send + +over a channel? + +That's the problem +with channels. + +If you have a channel that'll +send 4,800 bits per second, + +which is what telephone +lines used to do. + +If you build a new product +that sends 9,600 bits per + +second, which was a major +technological achievement back + +in the '70s and '80s, suddenly +your company becomes a very + +important communication +player. + +If you then take the same +channel and learn how to + +communicate at megabits over it, +that's a major thing also. + +How did people learn +to do that? + +Mostly by using all the ideas +that the people used in going + +from 4,800 bits per second +to 9,600 bits per second. + +It was the people who did that +first job who were the primary + +people involved in +the second job. + +The point of that is it doesn't +really make any + +difference as an engineer +whether you're going from + +4,800 to 9,600 or from 9,600 to +19.2 or from 19.9 to 38.4 + +or whatever it is, +or so forth up. + +Each one of these is just +putting in a few new goodies, + +recognizing a few new things, +making the system + +a little bit better. + +Let's talk about the +channel now. + +The channel is given -- + +in other words, it's not under +the control of the designer. + +This is something we haven't +talked about yet. + +In all of these communication +system design problems, one of + +the things that gets straight is +when you're worrying about + +the engineering of something, +what parts of the system can + +you control and what parts +of it can't you control. + +Even more when you get into +layering -- what parts can you + +control and what parts can +other people control. + +Namely, if I have some source +and I'm trying to transmit it + +over some physical channel and I +have two engineers -- one of + +them is a data compressor, and +the other is a channel guy. + +What the channel guy is trying +to do is to find a way of + +sending more bits over +this channel than + +could be done before. + +What the data compressor is +trying to do is to find a way + +to encode the source +into fewer bits. + +If the two come together, +the whole thing works. + +If the two don't come together, +then you have to + +fire the engineers, hire some +new engineers or do something + +else or you get fired. + +So that's the story. + +The things you can't change +here, you can't change the + +structure of the source usually, +and you can't change + +the structure of the channel. + +There's some very interesting +new problems coming into + +existence these days by +information theorists who are + +trying to study biological +systems. + +One of the peculiar things in +trying to understand how + +biological organisms, which have +remarkable systems for + +communicating information from +one place to another, how they + +manage to do it. + +One of the things you find is +that this separation that we + +use in studying electronic +communication does not exist + +in the body at all. + +In other words, what we +call a source gets + +blended with the channel. + +What we call the statistics of +the source get very much + +blended in with what this +organism is trying to do. + +If the organism cannot send such +refined data, it figures + +out ways to get the data that +it needs which is essential + +for its survival or it +dies and some other + +organism takes over. + +So you find the system which has +no constraints in it, and + +it evolves with all +of these things + +changing at the same time. + +The channels are changing, +the source statistics are + +changing, and the way the source +data is encoded is + +changing, and the way the data +is transmitted is changing. + +So it's a whole new +generalization of this whole + +problem of how do +you communicate. + +Here though, the problem we're +dealing with is these fixed + +channels, which you can think +of, depending on what your + +interests are, you can view the +canonical channel as being + +a piece of wire in a telephone +network, or even view it as + +being a cable in a cable TV +system, or you can view it as + +being a wireless channel. + +We will talk about all of +these in the course. + +The last three weeks of the +course is primarily talking + +about wireless because that's +where the problems are most + +interesting. + +But in any situation we look +at, the channel is fixed. + +It's given to us and +we can't change it. + +All we can do fiddle around with +the channel encoding and + +the channel decoding. + +The channels that we're most +interested in usually send + +wave forms. + +That brings up another +interesting question. + +We call this digital +communication, and what I've + +been telling you is that the +sources that we're interested + +in are most often wave +form sources. + +The channels that we're +interested in are most often + +channels that send wave forms, +receive wave forms and add + +noise, which is wave forms. + +Why do we call it digital +communication? + +Anybody have a clue as to why +we might call all of this + +digital communication? + +Yeah? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Because the analog +gets represented in binary + +digits, because we have chosen +essentially, because of having + +studied Shannon at some point, +to turn all the analog sources + +into binary bit streams. + +Namely, when you talk about +digital communication, what + +you're really doing is saying I +have decided there will be a + +digital interface between +source and channel. + +That's what digital +communication is. + +That's what most communication +today is. + +There's very little +communication today that + +starts out with an analog wave +form and finds a way to + +transmit it without first going +into a binary sequence. + +So here's a picture of one +of the noises that + +we're going to study. + +We have an input which +is now a wave form. + +We have noise, which +is a wave form. + +And we have an output, +which is a wave form. + +This input here is going to be +created somehow in a process + +of modulation from this binary +stream that's coming into the + +channel encoder. + +So somehow or other we're +taking a binary stream, + +turning it into a wave form. + +Now, think a little bit about +what might be essential in + +that process. + +If you know something about +practical engineering systems + +for communication, you know that +there's an organization + +in the U.S. called the FCC, and +every other country has + +its companion set of initials, +which says what part of the + +radio spectrum you can use and +what part of the radio + +spectrum you can't use. + +You suddenly realize that +somehow it's going to be + +important to turn these binary +streams into wave forms, which + +are more or less compressed +into some frequency bands. + +That's one of the problems +we're going to + +have to worry about. + +But at some level if I take +a whole bunch of different + +binary sequences, one thing I +can do, for example, I could + +take a binary sequence +of length 100. + +How many such binary sequences +are there? + +Has length 100, the first bit +can be 1 or zero, second bit + +can be 1 or zero -- that's +four combinations. + +Third bit can be 1 or zero +also -- that makes eight + +combinations of three bits. + +There are 2 to the 100th +combinations + +of 100 binary digits. + +So a theoretician says fine, +I'm at those 2 to the 100th + +different combinations of binary +digits into evenly + +spaced numbers between +zero and 1. + +Then I will take those evenly +spaced numbers between zero + +and 1 and I'll modulate some +wave form, whatever wave form + +I happen to choose, and I will +send that wave form. + +In the absence of noise, I pick +up that wave form and + +turn it back into my binary +sequence again. + +What's the conclusion +from this? + +The conclusion is if you don't +have noise there's no + +constraint on how much +data you can send. + +I can send as much data as I +want to, and there's nothing + +to stop me from doing it, +if I don't have noise. + +Yeah. + +AUDIENCE: So, is that +where something that + +[UNINTELLIGIBLE] basically +comes in. + +Like a difference between one +signal and the next signal. + +PROFESSOR: Somehow I have to +keep these things seperate. + +I don't necessarily have to +separate one binary digit from + +the next binary digit in time. + +I could, in fact, do something +like creating 2 to the 100th + +different wave forms or I could +do anything in between. + +I could take each sequence of +eight bits, turn them into 1 + +of 256 wave forms, transmit one +wave form, then a little + +bit later transmit another +wave form and so forth. + +So I can split up the pie in any +way I want to, and we'll + +talk about that a +lot as we go on. + +Now, I split them up into +different wave forms, which I + +send at spaced times. + +I somehow have to worry about +the fact that if I send them + +over a finite bandwidth, there +is no way in hell that you can + +take finite bandwidth +wave forms and send + +them in finite time. + +Anything which lasts for a +finite amount of time spreads + +out in bandwidth. + +Anything which is in a finite +amount of bandwidth spreads + +out in time. + +That's what you ought +to know from 6.003. + +So we're dealing with an +unsoluble problem here. + +Well, Nyquist back in 1928 +solved that problem. + +He said well no, you can't make +the wave form separate, + +but you can make the +sample separate. + +People earlier had figured out +they could do that with the + +sampling theorem, but the +sampling theorem wasn't very + +practical, but Nyquist's way +of doing it was practical. + +So, in fact, you can separate +these wave forms. + +But you still have the +problem how do you + +deal with the noise. + +Well, one of the favorite ways +of dealing with noise is to + +assume that it's something +called white Gaussian noise. + +What is white Gaussian noise? + +White Gaussian noise is noise +which no matter where you look + +it's sitting there. + +You can't get away from it. + +You move around to different +frequencies, the noise is + +still there. + +You move around to different +times, it's still there. + +It is somehow uniformed +throughout time + +and throughout frequency. + +Kind of an awkward thing because +if I developed a + +receiver which didn't have any +bandwidth constraint on it, + +and I looked at this noise +coming in, which was spread + +out over all frequencies, +the noise would + +burn out the receiver. + +In other words, this white +Gaussian noise + +has infinite power. + +That shouldn't bother +you too much. + +You deal with unit impulses +all the time. + +A unit impulse has infinite +energy also. + +You probably never thought +about it because most + +undergraduate courses try very +hard to conceal that fact from + +you because they like to use +impulses for everything, but + +impulses have infinite energy +associated with them, and + +that's kind of a nasty thing. + +But anyway, we will deal with +the fact that impulses have + +infinite energy, and therefore, +not use them to + +transmit data. + +And we will deal with the fact +that this noise has infinite + +power, and find out how +to deal with that. + +And we will learn how to +understand the statistical + +structure of that noise. + +So we'll deal with all of these +things when we start + +studying these channels. + +As we do that we will find out +that no matter what you do on + +a channel like this, there are +some fundamental constraints + +on how much data can +be transmitted. + +I can take you through a +little bit of a thought + +experiment which will sort +of explain that, I think. + +It's partly what we were just +starting to say over here. + +A simple-minded way to look at +this problem is I have binary + +digits coming in. + +I take these binary digits and +I separate them into shorts + +sequences of m binary +digits each. + +So, I take the first m binary +digits, then I take the next m + +binary digits, and the next m +binary digits and so forth. + +A sequence of m binary digits, +there are 2 to the m + +combinations of this. + +So I map these 2 to the m +combinations into one of 2 to + +the m different numbers. + +Now, you look at this noise +and you say I have to keep + +some separation between +these numbers. + +So, with a separation between +the numbers, say the + +separation is 1, let this +define the number 1. + +That's something we +theoreticians do all the time. + +So I have 2 to the m +different levels. + +I have to send this in +a certain bandwidth. + +The sampling theorem says I +can't send things that are + +more than twice the bandwidth +of this system, so I have a + +bandwidth of 2w. + +I can send m binary digits +in this bandwidth, w. + +Therefore, I can send bits +at a certain rate. + +This is all very crude but it's +going to lead us to an + +interesting trade-off. + +I can increase m and by +increasing m I can get by with + +a smaller bandwidth, because I +have these symbols, these m + +bit symbols coming along +at a slower rate. + +So by increasing m, I can +decrease the bandwidth, by + +increasing m, I can reduce the +bandwidth, but by reducing the + +bandwidth, the power +is going up. + +You can see that as I change +m, the power is going up + +exponentially with m. + +In other words, the trade-off +between bandwidth and power is + +kind of nasty in this +simple-minded picture. + +Let me jump ahead. + +For this added of white +Gaussian noise with a + +bandwidth constraint, Shannon +showed that the capacity was w + +times log of 1 plus the power in +the system times the noise + +power times w. + +Now, I don't expect you to +understand this formula now, + +and there's a lot of very tricky +and somewhat confusing + +things about it. + +One thing is that the power and +the noise is going up with + +the bandwidth that you're +looking at. + +Because I said the bandwidth is +everywhere, you can't avoid + +it, and therefore, if you use a +wider bandwidth system, you + +get more noise coming into it. + +If you have a certain amount of +power that you're willing + +to transmit and a certain +amount of noise, and the + +number of bits per second +you can transmit is + +going up with w. + +But look at this affect with p +here, the effect with p is + +logarithmic, which says as I +increase this parameter m and + +I put more and more bits into +one symbol, this quantity is + +going up exponentially, which +means the logarithm of this is + +going up just linearly with m. + +This gives you, if you look +at it carefully, the same + +trade-off as the simple-minded +example I was talking about. + +That simple-minded example +does not explain + +this formula at all. + +This formula's rather deep. + +We probably won't +even completely + +have proven this term. + +What Shannon's results says is +that no matter what you do, no + +matter how clever you are with +this noise that exists + +everywhere, the fastest you +can transmit with the most + +sophisticated coding schemes you +can think of is this rate + +right here, which is what you +would think it might be just + +from the scaling in terms of w +and m, where when you increase + +m the power goes up +exponentially. + +It's the same kind of answer +you get with that simple + +thought experiment. + +The fact that you have a 1 in +here is a little bit strange, + +and we'll find out where +that comes from. + +The idea here is that +this noise is + +something you can't beat. + +The noise is fundamental. + +It's a fundamental part of every +communication system. + +As I always like to say, noise +is like death and taxes, you + +can't avoid them, they're there, +and there's nothing you + +can do about them. + +Like death and taxes, you can +take care of yourself and live + +longer, and with taxes, well, +you can become wealthy and + +support the government and make +all sorts of payments and + +reduce your taxes that way. + +Or you can hire a +good accountant. + +So you can do things +there also. + +But those things are +still always there. + +So you're always stuck +with this. + +One of the major parts of the +course will be to understand + +what this noise is in a +much deeper context + +than we would otherwise. + +So, I'll save that and come +back to it later. + +We have the same kind of +layering in channel encoding. + +When I talk about channeling +encoding, I'm not talking + +about any kind of complicated +coding technique. + +6.451 talks about +all of those. + +What I'm talking about is simply +the question of how do + +you take a sequence of bits, +turn it into a sequence of + +wave forms in such a way that +at the receiver we can take + +that sequence of wave forms and +match them reliabily back + +into the original bits. + +There's a standard way of doing +this, which is to take + +the sequence of bits, +first send them + +through a discrete decoder. + +What the discrete encoder +code will do is + +something like this. + +And match bits at one rate into +bits at a higher rate, + +and this let's you correct +channel errors. + +A simple example of this is +you match zero into zero, + +zero, zero. + +1 into 1, 1, 1. + +If the rest of your system, +namely, if this part of the + +system makes a single error at +some point, this part of the + +system escapes from it. + +I sort of put these on one +slide but I couldn't. + +This takes a single zero, turns +it into three zeros. + +These three zeros go into this +modulator, which maps this + +into some wave from responsive +to these three zeros. + +Wave form goes through here, +noise gets added, the + +modulator, the text, those +binary digits, comes out with + +some approximation to +these three zeros. + +Every once in awhile because +of the noise, one of these + +bits comes out wrong, and +because they come out wrong + +this discrete decoder says +ah-ha, I know that what was + +sent/put in was either zero, +zero, zero or 1, 1, 1. + +It's more likely to have one +error than to have two errors, + +and therefore, any time +one error occurs I + +can decode it correctly. + +Now, that is a miserable code. + +A guy by the name of Hamming +became very famous for + +generalizing this just a little +bit into another single + +error correcting code, which +came through at a slightly + +higher rate but still corrected +single errors. + +He became inordinately famous +because he was a tireless + +self-promoter and people think +that he was the person who + +invented error correction +coding. + +He really wasn't. + +And his heirs will probably -- + +I don't know. + +Anyway, coding of this type, +namely mapping binary digits + +into longer strings of binary +digits in such a way that you + +can correct binary errors, has +always been a major part of + +communication system research. + +A large number of communication +systems work in + +exactly this way. + +In fact, the older systems which +use coding tended to + +work this way. + +This was a very popular way of +trying to design system. + +You would put a total layering +across here. + +Namely, this part of the system +didn't know that there + +was any coding going on here. + +At this point where you're doing +discrete decoding, you + +don't know anything about what +the detector is doing here. + +It doesn't take a lot of +imagination to say if you have + +a detector here and there's this +symbol that comes through + +here, noise gets added to it, +you're trying to decode this + +symbol, and there's this +Gaussian noise, which is just + +sort of spread around, +it's concentrated. + +Usually when errors occur, +errors occur just barely. + +What you see at this point is +you almost flip a coin to + +decide whether a zero or a 1 was +transmitted at this point. + +If this poor guy had that +information, this poor guy + +could work much, much better. + +Namely, this guy could correct +double errors instead of + +single errors, because if one +bit came through with a clear + +indication that that's what it +was, and the other two bits + +came through saying well, I +can't really tell what these + +are, then this guy could +correct two errors + +instead of one error. + +So this is a good example where +this layering in here is + +really a rotten idea. + +Most modern systems don't +do that strict layering. + +But a whole lot of modern +systems do, in fact, do this + +binary encoding here and they +use the principles that came + +out of the binary encoding +from a long time ago. + +The only extra thing they do +here is they use this extra + +information from the +demodulator. + +This is something called +soft decoding + +instead of hard decoding. + +In other words, what comes out +of the demodulator is soft + +decisions, and soft decisions +say well, I think it was this + +but I'm not sure or I am +sure and so forth. + +There's a whole range +of graduations. + +We will study detection theory +and we'll understand how that + +works and we'll understand how +you use those soft decisions + +and all of that stuff and +it's kind of neat. + +The modulation part of this is +what maps bit sequences into + +wave forms. + +When we map bit sequences into +wave form, there's this very + +simple idea. + +If I take a single bit that's +either zero or 1, I map a zero + +into one wave form, I map a 1 +into another wave form, I send + +either wave form a +or wave form b. + +I somehow want to make those +wave forms as different from + +each other as I can. + +Now, what do you mean by making +wave forms different? + +I know what it means to make +numbers different. + +I know that zero and 3 +are more different + +than zero and 2 are. + +Namely, I have a good measure +of distance for + +a sequence of numbers. + +One of the things that we have +to deal with is how do you + +find an appropriate measure of +distance for wave forms. + +When I find the measure of +distance for wave forms, what + +do I want to make it +responsive to? + +What I'm trying to do is to +overcome this noise, and + +therefore, I have to find the +measure of distance which is + +appropriate for what the +noise is doing to me. + +Well that's why we have to study +wave forms as much as we + +do in this course. + +What we will find is that you +can treat wave forms in the + +same way as you can treat +sequences of numbers. + +We will find that there's a +vector space associated with + +wave forms, which is exactly +the same as a vector space + +associated with infinite +sequences of numbers. + +It's almost the same as the +vector space associated with + +finite sequences of wave form, +and that vector space + +associated with a finite +sequence of numbers is exactly + +the vector space that you've +been looking at all of your + +lives, and which you use +primarily as a notational + +convenience to talk about +a sequence of numbers. + +What's the distance that +you use there? + +Well, you take the difference +between each number in the + +sequence, you square it, you +add it up and you take the + +square root of it. + +Namely, you look at the +energy difference + +between these sequences. + +What we will find remarkably +is when we do things right, + +the appropriate distance to talk +about on wave forms, is + +exactly what comes from the + +appropriate looking at sequences. + +In fact, we'll take wave forms +and break them into sequences. + +That's a major part of this +modulation process. + +You think of that in terms +of the sampling theorem. + +Namely, you take a bunch of +numbers, you take each number + +in the sampling theorem and you +put a little sin x over x + +hat around it and you transmit +that, and then you add up all + +of these different samples, +which is a sequence of + +numbers, each of them with these +little sin x over x caps + +around them. + +The neat thing about the sin x +over x caps around them is + +they all go to zero +with these sample + +points and it all works. + +Therefore, the sequences +look almost the + +same as a wave form. + +We'll find out that that +works in general, so we + +will do most of that. + +Modern practice often combines +all these layers into what's + +called coding modulation. + +In other words, they go further +than just this idea of + +soft decisions, and actually +treat the problem in general + +of what do you do with bits +coming into a sequence, into a + +system, how do you turn those +into wave forms that can be + +dealt with an appropriate way. + +And we'll talk just a little +bit about that and mostly + +6.451 talks about that. + +I want to talk a little bit +right at the end, I'm almost + +finished, about computational +complexity in these + +communication systems that we're +trying to worry about. + +One of the things that you will +become curious about as + +we move along is that we are +sometimes suggesting doing + +things in ways that +look very complex. + +The word complex is an +extraordinarily complex word. + +None of us know what it means +because it means so many + +different things. + +I was saying that these +telephone systems are + +inordinately complex. + +In a sense they aren't because +they have an incredible number + +of pieces, all of which +are the same. + +So you can understand a +telephone system in terms of + +understanding a relatively small +number of principles. + +You can understand these +Gaussian channels in terms of + +understanding a small number +of principles. + +So they're complex if you don't +know how to look at + +them, they're simple if you do +know how to look at them. + +Here what I'm talking about is +how many chips do you need to + +build something? + +How complicated are +those chips? + +Fundamentally, how much does it +cost to build the system? + +Well, one of the curious things +and one of the things + +that has made information theory +so popular in designing + +communication systems is that +we're almost at the point + +where chips are free. + +Now, what does that mean? + +It means if you want to do +something more complicated it + +hardly costs anything. + +This is sort of Moore's law. + +Moore's law says every year +you can put more and more + +stuff on a single chip. + +You can do this cheaply and +the chips work faster and + +faster so you can do more and +more complicated things very, + +very easily. + +There are some caveats. + +Low cost with high complexity +requires large volume. + +In other words, it takes a very +long time to design a + +chip, it takes an enormous +amount of lead time -- + +I mean we're not going to study +these details in the + +course, but I want you to be +aware of why it is that in a + +sense complexity doesn't +matter anymore. + +If you spend a long enough time +designing it and you can + +produce enough of them, you can +do extraordinarily complex + +things very, very cheaply. + +I mean you see this with +all the cellular + +phones that you buy. + +I mean cellular phones now are +actually give-away devices. + +You look at them to see what's +in them and they're + +inordinately complicated. + +You buy a personal computer +today and it's 1,000 times + +more powerful than the biggest +computers in the + +world 30 years ago. + +You can do everything +more cheaply now + +than you could before. + +What's the hitch? + +Well, you see the hitch when +you program a computer, + +namely, if you look at word +processing languages, yes, + +they become bigger and bigger +every year, they become more + +and more complex, they will +do more and more things. + +As far as their function of word +processing, some of us + +think there have been advances +in the last 30 years. + +Others, like myself, feel that +there have not been advances + +and, in fact, we're +going backwards. + +The problem is we have so much +complexity we don't know how + +to deal with it anymore. + +Most of us have become +blinking 12's. + +You know what a blinking +12 is. + +It's all of the electronic +equipment you have in your + +home, whenever you don't program +it right you see a 12 + +blinking on and off, which is +where the clock is and the + +clock hasn't been set, +and therefore, + +it's blinking at you. + +Most people who have complicated +devices, whether + +they're audio devices or what +have you, are using less than + +one percent of the fancy +features in them. + +You spend hours and hours trying +to bring that from one + +percent up to two percent. + +So that the cost of complexity +is not in what you can build, + +but it's in this conceptual +complexity. + +If you design an algorithm and +you understand the algorithm, + +it hardly makes any difference +how complicated it is, unless + +the complexity is going up +exponentially with something. + +That's the first caveat. + +It's actually the second +caveat, too. + +Complex systems are often not +well thought through. + +They often don't work +or are not robust. + +The non-robustness is the +worst part of it. + +The third caveat is when you +have special applications. + +Since they involve small +numbers, you're not going to + +build a lot of them, it takes +a long time to design them. + +The only way you can build +special applications is to + +make them minor modifications of +other things that have been + +done before. + +So this question of how +complicated the systems we can + +build are, if you can +make enough of + +them they become cheap. + +If you have enough lead time +they become cheap. + +Which says that this layering +of communication system that + +we're talking about really +ultimately makes sense. + +Starting next time, we're going +to start talking about + +this first part of source +coding, which is the discrete + +part of source coding. + +We will have those notes +on the web shortly. + +You can look ahead at +them, if you would + +like to, before Monday. + +Please review the probability +that you are supposed to know + +because you will need +it very shortly. + +Thanks. \ No newline at end of file diff --git a/KdN2mQ594t0.txt b/KdN2mQ594t0.txt new file mode 100644 index 0000000000000000000000000000000000000000..8f238aa5d7a6d9a3ec6683f772ee09d694d66dbf --- /dev/null +++ b/KdN2mQ594t0.txt @@ -0,0 +1,1187 @@ +align:start position:0% + +so with with every sort of advanced uh + + align:start position:0% +so with with every sort of advanced uh + + + align:start position:0% +so with with every sort of advanced uh +class that I teach there's a final + + align:start position:0% +class that I teach there's a final + + + align:start position:0% +class that I teach there's a final +project um and the goal of the final + + align:start position:0% +project um and the goal of the final + + + align:start position:0% +project um and the goal of the final +project is for students to somehow get + + align:start position:0% +project is for students to somehow get + + + align:start position:0% +project is for students to somehow get +their feet wet with the material and + + align:start position:0% +their feet wet with the material and + + + align:start position:0% +their feet wet with the material and +sort of experience it at a more + + align:start position:0% +sort of experience it at a more + + + align:start position:0% +sort of experience it at a more +researchy level um in general this can + + align:start position:0% +researchy level um in general this can + + + align:start position:0% +researchy level um in general this can +be things like surveying papers that I + + align:start position:0% +be things like surveying papers that I + + + align:start position:0% +be things like surveying papers that I +didn't cover in the class because + + align:start position:0% +didn't cover in the class because + + + align:start position:0% +didn't cover in the class because +there's only so much you can fit in one + + align:start position:0% +there's only so much you can fit in one + + + align:start position:0% +there's only so much you can fit in one +semester so they'll go and read other + + align:start position:0% +semester so they'll go and read other + + + align:start position:0% +semester so they'll go and read other +material and kind of aim to teach that + + align:start position:0% +material and kind of aim to teach that + + + align:start position:0% +material and kind of aim to teach that +to the students um so there's a written + + align:start position:0% +to the students um so there's a written + + + align:start position:0% +to the students um so there's a written +project part and then there's also a + + align:start position:0% +project part and then there's also a + + + align:start position:0% +project part and then there's also a +presentation in class so this is an + + align:start position:0% +presentation in class so this is an + + + align:start position:0% +presentation in class so this is an +opportunity for students to learn more + + align:start position:0% +opportunity for students to learn more + + + align:start position:0% +opportunity for students to learn more +but actually most students in this class + + align:start position:0% +but actually most students in this class + + + align:start position:0% +but actually most students in this class +uh aim for a particular type of project + + align:start position:0% +uh aim for a particular type of project + + + align:start position:0% +uh aim for a particular type of project +which is to solve an open problem um so + + align:start position:0% +which is to solve an open problem um so + + + align:start position:0% +which is to solve an open problem um so +actually Advance the field and then + + align:start position:0% +actually Advance the field and then + + + align:start position:0% +actually Advance the field and then +present their solution now of course not + + align:start position:0% +present their solution now of course not + + + align:start position:0% +present their solution now of course not +everyone succeeded but um and that's + + align:start position:0% +everyone succeeded but um and that's + + + align:start position:0% +everyone succeeded but um and that's +fine for a project you don't have to + + align:start position:0% +fine for a project you don't have to + + + align:start position:0% +fine for a project you don't have to +solve the problem that you set out to + + align:start position:0% +solve the problem that you set out to + + + align:start position:0% +solve the problem that you set out to +solve but at least you try different + + align:start position:0% +solve but at least you try different + + + align:start position:0% +solve but at least you try different +approaches and see what doesn't work um + + align:start position:0% +approaches and see what doesn't work um + + + align:start position:0% +approaches and see what doesn't work um +but actually most students actually + + align:start position:0% +but actually most students actually + + + align:start position:0% +but actually most students actually +solve their problem often in groups so + + align:start position:0% +solve their problem often in groups so + + + align:start position:0% +solve their problem often in groups so +the groups group size was unlimited so + + align:start position:0% +the groups group size was unlimited so + + + align:start position:0% +the groups group size was unlimited so +sometimes two or three or maybe more I + + align:start position:0% +sometimes two or three or maybe more I + + + align:start position:0% +sometimes two or three or maybe more I +think maximum four students um got + + align:start position:0% +think maximum four students um got + + + align:start position:0% +think maximum four students um got +together solved the problem jointly and + + align:start position:0% +together solved the problem jointly and + + + align:start position:0% +together solved the problem jointly and +then presented their solution uh so this + + align:start position:0% +then presented their solution uh so this + + + align:start position:0% +then presented their solution uh so this +I think was I think I mean it's really + + align:start position:0% +I think was I think I mean it's really + + + align:start position:0% +I think was I think I mean it's really +exciting for me to show that they engage + + align:start position:0% +exciting for me to show that they engage + + + align:start position:0% +exciting for me to show that they engage +with the material so much they can + + align:start position:0% +with the material so much they can + + + align:start position:0% +with the material so much they can +actually add new material um but it's + + align:start position:0% +actually add new material um but it's + + + align:start position:0% +actually add new material um but it's +also I think really uh exciting for the + + align:start position:0% +also I think really uh exciting for the + + + align:start position:0% +also I think really uh exciting for the +students to show hey I can actually + + align:start position:0% +students to show hey I can actually + + + align:start position:0% +students to show hey I can actually +solve these problems many of the + + align:start position:0% +solve these problems many of the + + + align:start position:0% +solve these problems many of the +students were not theoretical computer + + align:start position:0% +students were not theoretical computer + + + align:start position:0% +students were not theoretical computer +science students this is not their kind + + align:start position:0% +science students this is not their kind + + + align:start position:0% +science students this is not their kind +of main area but they were able to + + align:start position:0% +of main area but they were able to + + + align:start position:0% +of main area but they were able to +conquer it anyway and have fun doing it + + align:start position:0% +conquer it anyway and have fun doing it + + + align:start position:0% +conquer it anyway and have fun doing it +so I think uh it's a nice confidence + + align:start position:0% +so I think uh it's a nice confidence + + + align:start position:0% +so I think uh it's a nice confidence +Builder that actually you know it sounds + + align:start position:0% +Builder that actually you know it sounds + + + align:start position:0% +Builder that actually you know it sounds +hard the the field is called hardness + + align:start position:0% +hard the the field is called hardness + + + align:start position:0% +hard the the field is called hardness +but actually it's uh pretty accessible + + align:start position:0% +but actually it's uh pretty accessible + + + align:start position:0% +but actually it's uh pretty accessible +and uh I think it it gives them the + + align:start position:0% +and uh I think it it gives them the + + + align:start position:0% +and uh I think it it gives them the +confidence that they can go back to + + align:start position:0% +confidence that they can go back to + + + align:start position:0% +confidence that they can go back to +their research fields and say hey how + + align:start position:0% +their research fields and say hey how + + + align:start position:0% +their research fields and say hey how +can we prove that our problems are hard + + align:start position:0% +can we prove that our problems are hard + + + align:start position:0% +can we prove that our problems are hard +and justify why we're using her istics + + align:start position:0% +and justify why we're using her istics + + + align:start position:0% +and justify why we're using her istics +or uh why we're using exhaustive search + + align:start position:0% +or uh why we're using exhaustive search + + + align:start position:0% +or uh why we're using exhaustive search +maybe there's something better actually + + align:start position:0% +maybe there's something better actually + + + align:start position:0% +maybe there's something better actually +no we can show that's the limit we + + align:start position:0% +no we can show that's the limit we + + + align:start position:0% +no we can show that's the limit we +encouraged for all the projects not only + + align:start position:0% +encouraged for all the projects not only + + + align:start position:0% +encouraged for all the projects not only +to collaborate with other students but + + align:start position:0% +to collaborate with other students but + + + align:start position:0% +to collaborate with other students but +to collaborate with us uh the teaching + + align:start position:0% +to collaborate with us uh the teaching + + + align:start position:0% +to collaborate with us uh the teaching +staff the Tas and myself um so we would + + align:start position:0% +staff the Tas and myself um so we would + + + align:start position:0% +staff the Tas and myself um so we would +uh give them advice especially in the + + align:start position:0% +uh give them advice especially in the + + + align:start position:0% +uh give them advice especially in the +beginning so there's like a project + + align:start position:0% +beginning so there's like a project + + + align:start position:0% +beginning so there's like a project +proposal stage we would confirm that to + + align:start position:0% +proposal stage we would confirm that to + + + align:start position:0% +proposal stage we would confirm that to +our knowledge this problem hadn't been + + align:start position:0% +our knowledge this problem hadn't been + + + align:start position:0% +our knowledge this problem hadn't been +solved before um and then we would give + + align:start position:0% +solved before um and then we would give + + + align:start position:0% +solved before um and then we would give +them lots of pointers for you know you + + align:start position:0% +them lots of pointers for you know you + + + align:start position:0% +them lots of pointers for you know you +might try this technique you should + + align:start position:0% +might try this technique you should + + + align:start position:0% +might try this technique you should +rewatch lecture 7 video and see how + + align:start position:0% +rewatch lecture 7 video and see how + + + align:start position:0% +rewatch lecture 7 video and see how +those techniques apply or maybe you + + align:start position:0% +those techniques apply or maybe you + + + align:start position:0% +those techniques apply or maybe you +could reduce from this or reduce from + + align:start position:0% +could reduce from this or reduce from + + + align:start position:0% +could reduce from this or reduce from +that lots of different ideas for how to + + align:start position:0% +that lots of different ideas for how to + + + align:start position:0% +that lots of different ideas for how to +uh how they might solve their problem + + align:start position:0% +uh how they might solve their problem + + + align:start position:0% +uh how they might solve their problem +and then uh some of them came to us + + align:start position:0% +and then uh some of them came to us + + + align:start position:0% +and then uh some of them came to us +afterwards like well you know I've + + align:start position:0% +afterwards like well you know I've + + + align:start position:0% +afterwards like well you know I've +gotten this far but I'm stuck again any + + align:start position:0% +gotten this far but I'm stuck again any + + + align:start position:0% +gotten this far but I'm stuck again any +ideas and so I think the more you can + + align:start position:0% +ideas and so I think the more you can + + + align:start position:0% +ideas and so I think the more you can +talk to people about uh where you're + + align:start position:0% +talk to people about uh where you're + + + align:start position:0% +talk to people about uh where you're +stuck the the less stuck you will get + + align:start position:0% +stuck the the less stuck you will get + + + align:start position:0% +stuck the the less stuck you will get +and so that that helped a lot I thinking + + align:start position:0% +and so that that helped a lot I thinking + + + align:start position:0% +and so that that helped a lot I thinking +people generally found their solution U + + align:start position:0% +people generally found their solution U + + + align:start position:0% +people generally found their solution U +some people brought their problems to + + align:start position:0% +some people brought their problems to + + + align:start position:0% +some people brought their problems to +the open problem session and had all the + + align:start position:0% +the open problem session and had all the + + + align:start position:0% +the open problem session and had all the +students look at it um so there were + + align:start position:0% +students look at it um so there were + + + align:start position:0% +students look at it um so there were +lots of ways to do it but generally + + align:start position:0% +lots of ways to do it but generally + + + align:start position:0% +lots of ways to do it but generally +collaboration was the + + align:start position:0% +collaboration was the + + + align:start position:0% +collaboration was the +answer um so the last part of the + + align:start position:0% +answer um so the last part of the + + + align:start position:0% +answer um so the last part of the +project is for students to present their + + align:start position:0% +project is for students to present their + + + align:start position:0% +project is for students to present their +work in class um usually it's like a + + align:start position:0% +work in class um usually it's like a + + + align:start position:0% +work in class um usually it's like a +whole bunch of student presentations one + + align:start position:0% +whole bunch of student presentations one + + + align:start position:0% +whole bunch of student presentations one +after the other so each presentation is + + align:start position:0% +after the other so each presentation is + + + align:start position:0% +after the other so each presentation is +relatively short uh I forget if it was + + align:start position:0% +relatively short uh I forget if it was + + + align:start position:0% +relatively short uh I forget if it was +like 10 or 15 minutes um but I think + + align:start position:0% +like 10 or 15 minutes um but I think + + + align:start position:0% +like 10 or 15 minutes um but I think +it's really valuable experience + + align:start position:0% +it's really valuable experience + + + align:start position:0% +it's really valuable experience +presenting is also hard and uh the only + + align:start position:0% +presenting is also hard and uh the only + + + align:start position:0% +presenting is also hard and uh the only +way to get good at presenting your work + + align:start position:0% +way to get good at presenting your work + + + align:start position:0% +way to get good at presenting your work +is to do it a lot and so um generally I + + align:start position:0% +is to do it a lot and so um generally I + + + align:start position:0% +is to do it a lot and so um generally I +find MIT students are quite good at this + + align:start position:0% +find MIT students are quite good at this + + + align:start position:0% +find MIT students are quite good at this +they've had I think a lot of experience + + align:start position:0% +they've had I think a lot of experience + + + align:start position:0% +they've had I think a lot of experience +presenting their work uh but one of the + + align:start position:0% +presenting their work uh but one of the + + + align:start position:0% +presenting their work uh but one of the +things I like to stress in my classes is + + align:start position:0% +things I like to stress in my classes is + + + align:start position:0% +things I like to stress in my classes is +uh because most of the students most of + + align:start position:0% +uh because most of the students most of + + + align:start position:0% +uh because most of the students most of +the projects or joint with multiple + + align:start position:0% +the projects or joint with multiple + + + align:start position:0% +the projects or joint with multiple +students how to navigate a joint talk + + align:start position:0% +students how to navigate a joint talk + + + align:start position:0% +students how to navigate a joint talk +where one person talks for a few minutes + + align:start position:0% +where one person talks for a few minutes + + + align:start position:0% +where one person talks for a few minutes +or one slide and then they switch back + + align:start position:0% +or one slide and then they switch back + + + align:start position:0% +or one slide and then they switch back +and forth um and I give general advice + + align:start position:0% +and forth um and I give general advice + + + align:start position:0% +and forth um and I give general advice +about how to do this but for the most + + align:start position:0% +about how to do this but for the most + + + align:start position:0% +about how to do this but for the most +part the students just kind of figure it + + align:start position:0% +part the students just kind of figure it + + + align:start position:0% +part the students just kind of figure it +out and by practicing they find uh a + + align:start position:0% +out and by practicing they find uh a + + + align:start position:0% +out and by practicing they find uh a +good way to do it so uh there are no + + align:start position:0% +good way to do it so uh there are no + + + align:start position:0% +good way to do it so uh there are no +videos of the student presentations + + align:start position:0% +videos of the student presentations + + + align:start position:0% +videos of the student presentations +because I I think that would be a little + + align:start position:0% +because I I think that would be a little + + + align:start position:0% +because I I think that would be a little +bit too intimidating it takes a lot of + + align:start position:0% +bit too intimidating it takes a lot of + + + align:start position:0% +bit too intimidating it takes a lot of +practice before you're comfortable being + + align:start position:0% +practice before you're comfortable being + + + align:start position:0% +practice before you're comfortable being +video recorded like + + align:start position:0% +video recorded like + + + align:start position:0% +video recorded like +this um and in your lecture pictures but + + align:start position:0% +this um and in your lecture pictures but + + + align:start position:0% +this um and in your lecture pictures but +uh they were they are totally video + + align:start position:0% +uh they were they are totally video + + + align:start position:0% +uh they were they are totally video +quality um so it's a shame we can't + + align:start position:0% +quality um so it's a shame we can't + + + align:start position:0% +quality um so it's a shame we can't +share them but it's a chicken and egg + + align:start position:0% +share them but it's a chicken and egg + + + align:start position:0% +share them but it's a chicken and egg +problem I guess and so at the end of the + + align:start position:0% +problem I guess and so at the end of the + + + align:start position:0% +problem I guess and so at the end of the +class um the Tas and I each write a + + align:start position:0% +class um the Tas and I each write a + + + align:start position:0% +class um the Tas and I each write a +bunch of bullet points about their + + align:start position:0% +bunch of bullet points about their + + + align:start position:0% +bunch of bullet points about their +written project and the work that they + + align:start position:0% +written project and the work that they + + + align:start position:0% +written project and the work that they +did and their uh presentation I I pay + + align:start position:0% +did and their uh presentation I I pay + + + align:start position:0% +did and their uh presentation I I pay +particular attention to like how strong + + align:start position:0% +particular attention to like how strong + + + align:start position:0% +particular attention to like how strong +their voice is do they do they have good + + align:start position:0% +their voice is do they do they have good + + + align:start position:0% +their voice is do they do they have good +presence and that kind of thing and try + + align:start position:0% +presence and that kind of thing and try + + + align:start position:0% +presence and that kind of thing and try +to give them that feedback so they know + + align:start position:0% +to give them that feedback so they know + + + align:start position:0% +to give them that feedback so they know +where they need to improve um or where + + align:start position:0% +where they need to improve um or where + + + align:start position:0% +where they need to improve um or where +they're especially good uh whether the + + align:start position:0% +they're especially good uh whether the + + + align:start position:0% +they're especially good uh whether the +slides needed more figures that's my + + align:start position:0% +slides needed more figures that's my + + + align:start position:0% +slides needed more figures that's my +number one comment usually the answer is + + align:start position:0% +number one comment usually the answer is + + + align:start position:0% +number one comment usually the answer is +yes uh can never hurt to have more + + align:start position:0% +yes uh can never hurt to have more + + + align:start position:0% +yes uh can never hurt to have more +figures um and uh also on the research + + align:start position:0% +figures um and uh also on the research + + + align:start position:0% +figures um and uh also on the research +side we think we look at their results + + align:start position:0% +side we think we look at their results + + + align:start position:0% +side we think we look at their results +tell them whether we found any bugs but + + align:start position:0% +tell them whether we found any bugs but + + + align:start position:0% +tell them whether we found any bugs but +for the most part we're thinking how + + align:start position:0% +for the most part we're thinking how + + + align:start position:0% +for the most part we're thinking how +what would be the next step like oh + + align:start position:0% +what would be the next step like oh + + + align:start position:0% +what would be the next step like oh +here's another open problem that would + + align:start position:0% +here's another open problem that would + + + align:start position:0% +here's another open problem that would +Advance your problem a little farther uh + + align:start position:0% +Advance your problem a little farther uh + + + align:start position:0% +Advance your problem a little farther uh +and here are some ideas for solving it + + align:start position:0% +and here are some ideas for solving it + + + align:start position:0% +and here are some ideas for solving it +and that often leads to papers that we + + align:start position:0% +and that often leads to papers that we + + + align:start position:0% +and that often leads to papers that we +publish um and for f some final projects + + align:start position:0% +publish um and for f some final projects + + + align:start position:0% +publish um and for f some final projects +are basically done their papers ready to + + align:start position:0% +are basically done their papers ready to + + + align:start position:0% +are basically done their papers ready to +submit and then we give them feedback on + + align:start position:0% +submit and then we give them feedback on + + + align:start position:0% +submit and then we give them feedback on +where they should submit it what would + + align:start position:0% +where they should submit it what would + + + align:start position:0% +where they should submit it what would +be a good conference a good Journal uh + + align:start position:0% +be a good conference a good Journal uh + + + align:start position:0% +be a good conference a good Journal uh +we can basically help them publish it so + + align:start position:0% +we can basically help them publish it so + + + align:start position:0% +we can basically help them publish it so +that's part of the the full service \ No newline at end of file diff --git a/KnVNFj53Eq4.txt b/KnVNFj53Eq4.txt new file mode 100644 index 0000000000000000000000000000000000000000..0ba8d2b5462388f3ba345915039d921e1beece6e --- /dev/null +++ b/KnVNFj53Eq4.txt @@ -0,0 +1,907 @@ +align:start position:0% + +hello and welcome back to recitation the + + align:start position:0% +hello and welcome back to recitation the + + + align:start position:0% +hello and welcome back to recitation the +problem I'd like to work with you now is + + align:start position:0% +problem I'd like to work with you now is + + + align:start position:0% +problem I'd like to work with you now is +uh simply to compute some partial + + align:start position:0% +uh simply to compute some partial + + + align:start position:0% +uh simply to compute some partial +derivatives using the definitions we + + align:start position:0% +derivatives using the definitions we + + + align:start position:0% +derivatives using the definitions we +learned today in lecture uh so first + + align:start position:0% +learned today in lecture uh so first + + + align:start position:0% +learned today in lecture uh so first +we're going to compute the uh partial + + align:start position:0% +we're going to compute the uh partial + + + align:start position:0% +we're going to compute the uh partial +derivative in the X direction of this + + align:start position:0% +derivative in the X direction of this + + + align:start position:0% +derivative in the X direction of this +function x y^2 + x^2 y then we're going + + align:start position:0% +function x y^2 + x^2 y then we're going + + + align:start position:0% +function x y^2 + x^2 y then we're going +to compute its derivative in the y + + align:start position:0% +to compute its derivative in the y + + + align:start position:0% +to compute its derivative in the y +direction and then finally we're going + + align:start position:0% +direction and then finally we're going + + + align:start position:0% +direction and then finally we're going +to evaluate the partial derivative in + + align:start position:0% +to evaluate the partial derivative in + + + align:start position:0% +to evaluate the partial derivative in +the X Direction at a particular point + + align:start position:0% +the X Direction at a particular point + + + align:start position:0% +the X Direction at a particular point +one two it's the first problem and in + + align:start position:0% +one two it's the first problem and in + + + align:start position:0% +one two it's the first problem and in +the second problem we're going to + + align:start position:0% +the second problem we're going to + + + align:start position:0% +the second problem we're going to +compute uh second partial derivatives + + align:start position:0% +compute uh second partial derivatives + + + align:start position:0% +compute uh second partial derivatives +now these we just compute by taking the + + align:start position:0% +now these we just compute by taking the + + + align:start position:0% +now these we just compute by taking the +derivative of the derivative just as we + + align:start position:0% +derivative of the derivative just as we + + + align:start position:0% +derivative of the derivative just as we +do in one variable calculus so um why + + align:start position:0% +do in one variable calculus so um why + + + align:start position:0% +do in one variable calculus so um why +don't you work on these pause the tape + + align:start position:0% +don't you work on these pause the tape + + + align:start position:0% +don't you work on these pause the tape +and I'll check back in a moment and + + align:start position:0% +and I'll check back in a moment and + + + align:start position:0% +and I'll check back in a moment and +we'll see how I solve + + align:start position:0% + + + + align:start position:0% + +these okay welcome back let's get + + align:start position:0% +these okay welcome back let's get + + + align:start position:0% +these okay welcome back let's get +started so we have + + align:start position:0% +started so we have + + + align:start position:0% +started so we have +x^2 + + align:start position:0% +x^2 + + + align:start position:0% +x^2 +y excuse me X + + align:start position:0% +y excuse me X + + + align:start position:0% +y excuse me X +y^2 Plus x^2 y That's our + + align:start position:0% +y^2 Plus x^2 y That's our + + + align:start position:0% +y^2 Plus x^2 y That's our +F so when we take the partial + + align:start position:0% +F so when we take the partial + + + align:start position:0% +F so when we take the partial +derivative in the X Direction remember + + align:start position:0% +derivative in the X Direction remember + + + align:start position:0% +derivative in the X Direction remember +this just means that we uh treat y as if + + align:start position:0% +this just means that we uh treat y as if + + + align:start position:0% +this just means that we uh treat y as if +it were a constant and we just take an + + align:start position:0% +it were a constant and we just take an + + + align:start position:0% +it were a constant and we just take an +ordinary derivative in the X direction + + align:start position:0% +ordinary derivative in the X direction + + + align:start position:0% +ordinary derivative in the X direction +as we would do in one variable calculus + + align:start position:0% +as we would do in one variable calculus + + + align:start position:0% +as we would do in one variable calculus +so the derivative of this in the X dire + + align:start position:0% +so the derivative of this in the X dire + + + align:start position:0% +so the derivative of this in the X dire +direction is just y^2 because we only + + align:start position:0% +direction is just y^2 because we only + + + align:start position:0% +direction is just y^2 because we only +differentiate the X + + align:start position:0% +differentiate the X + + + align:start position:0% +differentiate the X +here similarly here the derivative of + + align:start position:0% +here similarly here the derivative of + + + align:start position:0% +here similarly here the derivative of +x^2 is + + align:start position:0% +x^2 is + + + align:start position:0% +x^2 is +2X and Y just comes along for the right + + align:start position:0% +2X and Y just comes along for the right + + + align:start position:0% +2X and Y just comes along for the right +as if it were a + + align:start position:0% + + + + align:start position:0% + +constant for the partial derivative in + + align:start position:0% +constant for the partial derivative in + + + align:start position:0% +constant for the partial derivative in +the y direction we do the same thing + + align:start position:0% +the y direction we do the same thing + + + align:start position:0% +the y direction we do the same thing +except now um X is a constant and we're + + align:start position:0% +except now um X is a constant and we're + + + align:start position:0% +except now um X is a constant and we're +taking a ordinary derivative in the y + + align:start position:0% +taking a ordinary derivative in the y + + + align:start position:0% +taking a ordinary derivative in the y +direction so we have 2X y y + + align:start position:0% +direction so we have 2X y y + + + align:start position:0% +direction so we have 2X y y ++ + + align:start position:0% + + + + align:start position:0% + +x^2 and then the final thing that we + + align:start position:0% +x^2 and then the final thing that we + + + align:start position:0% +x^2 and then the final thing that we +need to do is we want to evaluate + + align:start position:0% +need to do is we want to evaluate + + + align:start position:0% +need to do is we want to evaluate +partial F partial + + align:start position:0% +partial F partial + + + align:start position:0% +partial F partial +X in at the point one + + align:start position:0% +X in at the point one + + + align:start position:0% +X in at the point one +2 and so all that means is that we have + + align:start position:0% +2 and so all that means is that we have + + + align:start position:0% +2 and so all that means is that we have +to plug in uh x = 1 and y = 2 into our + + align:start position:0% +to plug in uh x = 1 and y = 2 into our + + + align:start position:0% +to plug in uh x = 1 and y = 2 into our +previous computation and so we get 2^ 2 + + align:start position:0% +previous computation and so we get 2^ 2 + + + align:start position:0% +previous computation and so we get 2^ 2 ++ 2 * 1 * 2 so all + + align:start position:0% ++ 2 * 1 * 2 so all + + + align:start position:0% ++ 2 * 1 * 2 so all +together we get + + align:start position:0% +together we get + + + align:start position:0% +together we get +eight so that's uh Computing uh partial + + align:start position:0% +eight so that's uh Computing uh partial + + + align:start position:0% +eight so that's uh Computing uh partial +derivatives now let's move on and + + align:start position:0% +derivatives now let's move on and + + + align:start position:0% +derivatives now let's move on and +compute the second partial + + align:start position:0% +compute the second partial + + + align:start position:0% +compute the second partial +derivatives so for instance if we want + + align:start position:0% +derivatives so for instance if we want + + + align:start position:0% +derivatives so for instance if we want +to compute + + align:start position:0% +to compute + + + align:start position:0% +to compute +partial the second partial + + align:start position:0% +partial the second partial + + + align:start position:0% +partial the second partial +derivative uh both times in the X + + align:start position:0% +derivative uh both times in the X + + + align:start position:0% +derivative uh both times in the X +Direction so all this means is that we + + align:start position:0% +Direction so all this means is that we + + + align:start position:0% +Direction so all this means is that we +when we took the first partial we we got + + align:start position:0% +when we took the first partial we we got + + + align:start position:0% +when we took the first partial we we got +a function of X and Y and now we just + + align:start position:0% +a function of X and Y and now we just + + + align:start position:0% +a function of X and Y and now we just +need to take its partial so uh we just + + align:start position:0% +need to take its partial so uh we just + + + align:start position:0% +need to take its partial so uh we just +need to take the derivative of this + + align:start position:0% +need to take the derivative of this + + + align:start position:0% +need to take the derivative of this +again in the X Direction so now the + + align:start position:0% +again in the X Direction so now the + + + align:start position:0% +again in the X Direction so now the +derivative of y^2 be careful the + + align:start position:0% +derivative of y^2 be careful the + + + align:start position:0% +derivative of y^2 be careful the +derivative of y^2 in the X direction is + + align:start position:0% +derivative of y^2 in the X direction is + + + align:start position:0% +derivative of y^2 in the X direction is +just zero because Y is a constant + + align:start position:0% +just zero because Y is a constant + + + align:start position:0% +just zero because Y is a constant +relative to X and so then alog together + + align:start position:0% +relative to X and so then alog together + + + align:start position:0% +relative to X and so then alog together +we just get 2 y when we take the + + align:start position:0% +we just get 2 y when we take the + + + align:start position:0% +we just get 2 y when we take the +derivative of this x we just get one so + + align:start position:0% +derivative of this x we just get one so + + + align:start position:0% +derivative of this x we just get one so +that's our partial derivative that's our + + align:start position:0% +that's our partial derivative that's our + + + align:start position:0% +that's our partial derivative that's our +second partial derivative in the X + + align:start position:0% +second partial derivative in the X + + + align:start position:0% +second partial derivative in the X +Direction and and + + align:start position:0% + + + + align:start position:0% + +now we can also take mixed + + align:start position:0% + + + + align:start position:0% + +partials so here we take uh a derivative + + align:start position:0% +partials so here we take uh a derivative + + + align:start position:0% +partials so here we take uh a derivative +in of f uh First We Take the derivative + + align:start position:0% +in of f uh First We Take the derivative + + + align:start position:0% +in of f uh First We Take the derivative +in the y direction and then we take a + + align:start position:0% +in the y direction and then we take a + + + align:start position:0% +in the y direction and then we take a +derivative of that in the X Direction so + + align:start position:0% +derivative of that in the X Direction so + + + align:start position:0% +derivative of that in the X Direction so +we can look at our derivative here + + align:start position:0% +we can look at our derivative here + + + align:start position:0% +we can look at our derivative here +partial F partial Y and we need to take + + align:start position:0% +partial F partial Y and we need to take + + + align:start position:0% +partial F partial Y and we need to take +its partial in the X Direction and so we + + align:start position:0% +its partial in the X Direction and so we + + + align:start position:0% +its partial in the X Direction and so we +get uh two + + align:start position:0% +get uh two + + + align:start position:0% +get uh two +y + 2 + + align:start position:0% + + + + align:start position:0% + +x now let's see what happens if we + + align:start position:0% +x now let's see what happens if we + + + align:start position:0% +x now let's see what happens if we +switch the order here and we take uh + + align:start position:0% +switch the order here and we take uh + + + align:start position:0% +switch the order here and we take uh +instead the partial + + align:start position:0% + + + + align:start position:0% + +derivative in the opposite order so now + + align:start position:0% +derivative in the opposite order so now + + + align:start position:0% +derivative in the opposite order so now +let's uh go back to our partial + + align:start position:0% +let's uh go back to our partial + + + align:start position:0% +let's uh go back to our partial +derivative of f in the X Direction and + + align:start position:0% +derivative of f in the X Direction and + + + align:start position:0% +derivative of f in the X Direction and +let's take its uh derivative now in the + + align:start position:0% +let's take its uh derivative now in the + + + align:start position:0% +let's take its uh derivative now in the +y direction + + align:start position:0% +y direction + + + align:start position:0% +y direction +so the first term there y^2 gives us a 2 + + align:start position:0% +so the first term there y^2 gives us a 2 + + + align:start position:0% +so the first term there y^2 gives us a 2 +Y and the second term gives us a + + align:start position:0% +Y and the second term gives us a + + + align:start position:0% +Y and the second term gives us a +2X and I want to just note that these + + align:start position:0% +2X and I want to just note that these + + + align:start position:0% +2X and I want to just note that these +are + + align:start position:0% +are + + + align:start position:0% +are +equal in fact the uh mixed partial + + align:start position:0% +equal in fact the uh mixed partial + + + align:start position:0% +equal in fact the uh mixed partial +derivatives uh whether you take them in + + align:start position:0% +derivatives uh whether you take them in + + + align:start position:0% +derivatives uh whether you take them in +the XY order or the YX order uh for for + + align:start position:0% +the XY order or the YX order uh for for + + + align:start position:0% +the XY order or the YX order uh for for +the sorts of functions that we're going + + align:start position:0% +the sorts of functions that we're going + + + align:start position:0% +the sorts of functions that we're going +to be considering in this class uh for + + align:start position:0% +to be considering in this class uh for + + + align:start position:0% +to be considering in this class uh for +instance all polinomial functions and + + align:start position:0% +instance all polinomial functions and + + + align:start position:0% +instance all polinomial functions and +all um + + align:start position:0% +all um + + + align:start position:0% +all um +differentiable functions of several + + align:start position:0% +differentiable functions of several + + + align:start position:0% +differentiable functions of several +variables these mixed partials are going + + align:start position:0% +variables these mixed partials are going + + + align:start position:0% +variables these mixed partials are going +to be equal in in your textbook there + + align:start position:0% +to be equal in in your textbook there + + + align:start position:0% +to be equal in in your textbook there +are some examples of uh sort of + + align:start position:0% +are some examples of uh sort of + + + align:start position:0% +are some examples of uh sort of +pathological functions where these are + + align:start position:0% +pathological functions where these are + + + align:start position:0% +pathological functions where these are +not equal but uh for certainly for any + + align:start position:0% +not equal but uh for certainly for any + + + align:start position:0% +not equal but uh for certainly for any +polinomial functions these are always + + align:start position:0% +polinomial functions these are always + + + align:start position:0% +polinomial functions these are always +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +equal and I think I'll leave it at that \ No newline at end of file diff --git a/LKNuAQWzWDE.txt b/LKNuAQWzWDE.txt new file mode 100644 index 0000000000000000000000000000000000000000..f273c43f786f48a5e9d938d6930777c986e7f160 --- /dev/null +++ b/LKNuAQWzWDE.txt @@ -0,0 +1,11656 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay so let's uh get started + + align:start position:0% +ocw.mit.edu okay so let's uh get started + + + align:start position:0% +ocw.mit.edu okay so let's uh get started +uh a + + align:start position:0% +uh a + + + align:start position:0% +uh a +recap you should be all pleased you have + + align:start position:0% +recap you should be all pleased you have + + + align:start position:0% +recap you should be all pleased you have +learned a lot uh we covered uh the + + align:start position:0% +learned a lot uh we covered uh the + + + align:start position:0% +learned a lot uh we covered uh the +quantum solid state and the statistical + + align:start position:0% +quantum solid state and the statistical + + + align:start position:0% +quantum solid state and the statistical +physics uh + + align:start position:0% +physics uh + + + align:start position:0% +physics uh +in this my lecture 11 okay and so what + + align:start position:0% +in this my lecture 11 okay and so what + + + align:start position:0% +in this my lecture 11 okay and so what +we + + align:start position:0% +we + + + align:start position:0% +we +learn uh first the quantum and S State + + align:start position:0% +learn uh first the quantum and S State + + + align:start position:0% +learn uh first the quantum and S State +gives us the energy levels and the + + align:start position:0% +gives us the energy levels and the + + + align:start position:0% +gives us the energy levels and the +energy State what is the Quantum state + + align:start position:0% +energy State what is the Quantum state + + + align:start position:0% +energy State what is the Quantum state +and statistics give us at the + + align:start position:0% +and statistics give us at the + + + align:start position:0% +and statistics give us at the +equilibrium each Quantum State how many + + align:start position:0% +equilibrium each Quantum State how many + + + align:start position:0% +equilibrium each Quantum State how many +particles uh Fons electrons + + align:start position:0% +particles uh Fons electrons + + + align:start position:0% +particles uh Fons electrons +photons and going back to counting the + + align:start position:0% +photons and going back to counting the + + + align:start position:0% +photons and going back to counting the +state degenerately we get the dens of + + align:start position:0% +state degenerately we get the dens of + + + align:start position:0% +state degenerately we get the dens of +States so at a certain energy level per + + align:start position:0% +States so at a certain energy level per + + + align:start position:0% +States so at a certain energy level per +unit energy interval or per unit we + + align:start position:0% +unit energy interval or per unit we + + + align:start position:0% +unit energy interval or per unit we +Vector how many uh Quantum States we + + align:start position:0% +Vector how many uh Quantum States we + + + align:start position:0% +Vector how many uh Quantum States we +have so with that that we you can do the + + align:start position:0% +have so with that that we you can do the + + + align:start position:0% +have so with that that we you can do the +counting and uh uh this this is a f * D + + align:start position:0% +counting and uh uh this this is a f * D + + + align:start position:0% +counting and uh uh this this is a f * D +gives me L of particles near that energy + + align:start position:0% +gives me L of particles near that energy + + + align:start position:0% +gives me L of particles near that energy +per energy interval if you integrate + + align:start position:0% +per energy interval if you integrate + + + align:start position:0% +per energy interval if you integrate +that should give you the total number of + + align:start position:0% +that should give you the total number of + + + align:start position:0% +that should give you the total number of +particles electrons Fons photons or if + + align:start position:0% +particles electrons Fons photons or if + + + align:start position:0% +particles electrons Fons photons or if +you multiply by the energy of a particle + + align:start position:0% +you multiply by the energy of a particle + + + align:start position:0% +you multiply by the energy of a particle +that gives you the energy if you + + align:start position:0% +that gives you the energy if you + + + align:start position:0% +that gives you the energy if you +multiply by charge give you the charge + + align:start position:0% +multiply by charge give you the charge + + + align:start position:0% +multiply by charge give you the charge +density if you uh multiply by momentum + + align:start position:0% +density if you uh multiply by momentum + + + align:start position:0% +density if you uh multiply by momentum +gives you momentum right so with that + + align:start position:0% +gives you momentum right so with that + + + align:start position:0% +gives you momentum right so with that +you can start doing uh the uh for + + align:start position:0% +you can start doing uh the uh for + + + align:start position:0% +you can start doing uh the uh for +example the energy stored specific heat + + align:start position:0% +example the energy stored specific heat + + + align:start position:0% +example the energy stored specific heat +Etc and then uh we said at the end of + + align:start position:0% +Etc and then uh we said at the end of + + + align:start position:0% +Etc and then uh we said at the end of +last lecture we're moving on to look at + + align:start position:0% +last lecture we're moving on to look at + + + align:start position:0% +last lecture we're moving on to look at +the + + align:start position:0% +the + + + align:start position:0% +the +transport and the first idea we we look + + align:start position:0% +transport and the first idea we we look + + + align:start position:0% +transport and the first idea we we look +at is if I want to find out how much + + align:start position:0% +at is if I want to find out how much + + + align:start position:0% +at is if I want to find out how much +energy is going from 0.1 to point2 in + + align:start position:0% +energy is going from 0.1 to point2 in + + + align:start position:0% +energy is going from 0.1 to point2 in +two different + + align:start position:0% +two different + + + align:start position:0% +two different +space and what I'm going to find out is + + align:start position:0% +space and what I'm going to find out is + + + align:start position:0% +space and what I'm going to find out is +what's the transmittance + + align:start position:0% +what's the transmittance + + + align:start position:0% +what's the transmittance +so if I have a particle or wave now I + + align:start position:0% +so if I have a particle or wave now I + + + align:start position:0% +so if I have a particle or wave now I +don't know how to call them right it's + + align:start position:0% +don't know how to call them right it's + + + align:start position:0% +don't know how to call them right it's +particle wave + + align:start position:0% +particle wave + + + align:start position:0% +particle wave +Duality and uh so if I have a a carrier + + align:start position:0% +Duality and uh so if I have a a carrier + + + align:start position:0% +Duality and uh so if I have a a carrier +right electron phon Photon launch from + + align:start position:0% +right electron phon Photon launch from + + + align:start position:0% +right electron phon Photon launch from +01 and the transmittance is how much how + + align:start position:0% +01 and the transmittance is how much how + + + align:start position:0% +01 and the transmittance is how much how +many of them will reach point2 right + + align:start position:0% +many of them will reach point2 right + + + align:start position:0% +many of them will reach point2 right +that's give me the uh fraction right and + + align:start position:0% +that's give me the uh fraction right and + + + align:start position:0% +that's give me the uh fraction right and +then say uh if I know the + + align:start position:0% +then say uh if I know the + + + align:start position:0% +then say uh if I know the +velocity then I know the flux from 0.1 + + align:start position:0% +velocity then I know the flux from 0.1 + + + align:start position:0% +velocity then I know the flux from 0.1 +to0 2 which is a velocity in that + + align:start position:0% +to0 2 which is a velocity in that + + + align:start position:0% +to0 2 which is a velocity in that +direction transmittance and if I want to + + align:start position:0% +direction transmittance and if I want to + + + align:start position:0% +direction transmittance and if I want to +find the energy flux that's per uh say + + align:start position:0% +find the energy flux that's per uh say + + + align:start position:0% +find the energy flux that's per uh say +um this is how much energy I have + + align:start position:0% +um this is how much energy I have + + + align:start position:0% +um this is how much energy I have +starting from that point right so uh + + align:start position:0% +starting from that point right so uh + + + align:start position:0% +starting from that point right so uh +this is where we're going uh in the uh + + align:start position:0% +this is where we're going uh in the uh + + + align:start position:0% +this is where we're going uh in the uh +coming chapter we're going to focus on + + align:start position:0% +coming chapter we're going to focus on + + + align:start position:0% +coming chapter we're going to focus on +using the wave picture to deal with this + + align:start position:0% +using the wave picture to deal with this + + + align:start position:0% +using the wave picture to deal with this +transmittance and then if I want to find + + align:start position:0% +transmittance and then if I want to find + + + align:start position:0% +transmittance and then if I want to find +the Le flux if you recall in chapter one + + align:start position:0% +the Le flux if you recall in chapter one + + + align:start position:0% +the Le flux if you recall in chapter one +when we derive FAL law we say it's from + + align:start position:0% +when we derive FAL law we say it's from + + + align:start position:0% +when we derive FAL law we say it's from +1 to two and minus 2 to one the + + align:start position:0% +1 to two and minus 2 to one the + + + align:start position:0% +1 to two and minus 2 to one the +difference give me the left + + align:start position:0% +difference give me the left + + + align:start position:0% +difference give me the left +flux right so uh What uh we're + + align:start position:0% +flux right so uh What uh we're + + + align:start position:0% +flux right so uh What uh we're +emphasizing so far is you know how to do + + align:start position:0% +emphasizing so far is you know how to do + + + align:start position:0% +emphasizing so far is you know how to do +the + + align:start position:0% +the + + + align:start position:0% +the +counting and + + align:start position:0% +counting and + + + align:start position:0% +counting and +uh our focus in this chapter is talking + + align:start position:0% +uh our focus in this chapter is talking + + + align:start position:0% +uh our focus in this chapter is talking +about the wave picture right we've been + + align:start position:0% +about the wave picture right we've been + + + align:start position:0% +about the wave picture right we've been +uh using the wave shinger equation for + + align:start position:0% +uh using the wave shinger equation for + + + align:start position:0% +uh using the wave shinger equation for +atoms electrons and all wave + + align:start position:0% +atoms electrons and all wave + + + align:start position:0% +atoms electrons and all wave +picture and uh uh if why we have to look + + align:start position:0% +picture and uh uh if why we have to look + + + align:start position:0% +picture and uh uh if why we have to look +at a wave and this is important if I + + align:start position:0% +at a wave and this is important if I + + + align:start position:0% +at a wave and this is important if I +deal with the + + align:start position:0% +deal with the + + + align:start position:0% +deal with the +interface because I mentioned before um + + align:start position:0% +interface because I mentioned before um + + + align:start position:0% +interface because I mentioned before um +ideal interface is zero + + align:start position:0% +ideal interface is zero + + + align:start position:0% +ideal interface is zero +thickness right is compared to wave + + align:start position:0% +thickness right is compared to wave + + + align:start position:0% +thickness right is compared to wave +length if that say very small compared + + align:start position:0% +length if that say very small compared + + + align:start position:0% +length if that say very small compared +to wave length then I should use the + + align:start position:0% +to wave length then I should use the + + + align:start position:0% +to wave length then I should use the +wave picture and so here is magnitude + + align:start position:0% +wave picture and so here is magnitude + + + align:start position:0% +wave picture and so here is magnitude +order magnitude of this wavelength right + + align:start position:0% +order magnitude of this wavelength right + + + align:start position:0% +order magnitude of this wavelength right +black body radiation wind dis + + align:start position:0% +black body radiation wind dis + + + align:start position:0% +black body radiation wind dis +displacement nor say wavelength times + + align:start position:0% +displacement nor say wavelength times + + + align:start position:0% +displacement nor say wavelength times +temperature is about 3,000 Micron K so + + align:start position:0% +temperature is about 3,000 Micron K so + + + align:start position:0% +temperature is about 3,000 Micron K so +at room temperature that's 10 Micron + + align:start position:0% +at room temperature that's 10 Micron + + + align:start position:0% +at room temperature that's 10 Micron +it's a very large distance uh 10 Micron + + align:start position:0% +it's a very large distance uh 10 Micron + + + align:start position:0% +it's a very large distance uh 10 Micron +uh uh compared to a zero thickness + + align:start position:0% +uh uh compared to a zero thickness + + + align:start position:0% +uh uh compared to a zero thickness +interface right so if I have a flat + + align:start position:0% +interface right so if I have a flat + + + align:start position:0% +interface right so if I have a flat +interface I need to consider the wave + + align:start position:0% +interface I need to consider the wave + + + align:start position:0% +interface I need to consider the wave +Optics so for uh for for even for Server + + align:start position:0% +Optics so for uh for for even for Server + + + align:start position:0% +Optics so for uh for for even for Server +radiation and uh + + align:start position:0% +radiation and uh + + + align:start position:0% +radiation and uh +electrons uh here are two different + + align:start position:0% +electrons uh here are two different + + + align:start position:0% +electrons uh here are two different +picture if I look at the electron in + + align:start position:0% +picture if I look at the electron in + + + align:start position:0% +picture if I look at the electron in +metal the formula will is within the + + align:start position:0% +metal the formula will is within the + + + align:start position:0% +metal the formula will is within the +band and the corresponding to this + + align:start position:0% +band and the corresponding to this + + + align:start position:0% +band and the corresponding to this +formula W those are the electron that + + align:start position:0% +formula W those are the electron that + + + align:start position:0% +formula W those are the electron that +mes near formula W are the electron that + + align:start position:0% +mes near formula W are the electron that + + + align:start position:0% +mes near formula W are the electron that +mes right and the corresponding wence is + + align:start position:0% +mes right and the corresponding wence is + + + align:start position:0% +mes right and the corresponding wence is +with in the bands right this is zero + + align:start position:0% +with in the bands right this is zero + + + align:start position:0% +with in the bands right this is zero +this is pi over a br on so if it's half + + align:start position:0% +this is pi over a br on so if it's half + + + align:start position:0% +this is pi over a br on so if it's half +that's a wence is about 2 + + align:start position:0% +that's a wence is about 2 + + + align:start position:0% +that's a wence is about 2 +a okay uh see of the order of fuel lce + + align:start position:0% +a okay uh see of the order of fuel lce + + + align:start position:0% +a okay uh see of the order of fuel lce +constant that's the electron wavelength + + align:start position:0% +constant that's the electron wavelength + + + align:start position:0% +constant that's the electron wavelength +in metal + + align:start position:0% +in metal + + + align:start position:0% +in metal +there and if I look at the + + align:start position:0% +there and if I look at the + + + align:start position:0% +there and if I look at the +semiconductors right uh if I say this is + + align:start position:0% +semiconductors right uh if I say this is + + + align:start position:0% +semiconductors right uh if I say this is +the valence band and most of the + + align:start position:0% +the valence band and most of the + + + align:start position:0% +the valence band and most of the +electron is at bottom of the valance B + + align:start position:0% +electron is at bottom of the valance B + + + align:start position:0% +electron is at bottom of the valance B +so that's ler k equal + + align:start position:0% +so that's ler k equal + + + align:start position:0% +so that's ler k equal +zero and those wave electron could have + + align:start position:0% +zero and those wave electron could have + + + align:start position:0% +zero and those wave electron could have +very long + + align:start position:0% +very long + + + align:start position:0% +very long +wavelength and uh uh in fact as say in + + align:start position:0% +wavelength and uh uh in fact as say in + + + align:start position:0% +wavelength and uh uh in fact as say in +the last lecture we talked about the bro + + align:start position:0% +the last lecture we talked about the bro + + + align:start position:0% +the last lecture we talked about the bro +so that's the thermal if I have a + + align:start position:0% +so that's the thermal if I have a + + + align:start position:0% +so that's the thermal if I have a +thermal energy KT of the say average + + align:start position:0% +thermal energy KT of the say average + + + align:start position:0% +thermal energy KT of the say average +energy is KT of the electron kinetic + + align:start position:0% +energy is KT of the electron kinetic + + + align:start position:0% +energy is KT of the electron kinetic +energy what's the corresponding + + align:start position:0% +energy what's the corresponding + + + align:start position:0% +energy what's the corresponding +wavelength that's the B wavelength right + + align:start position:0% +wavelength that's the B wavelength right + + + align:start position:0% +wavelength that's the B wavelength right +so the last lecture we get + + align:start position:0% +so the last lecture we get + + + align:start position:0% +so the last lecture we get +h² and 2 pi M + + align:start position:0% +h² and 2 pi M + + + align:start position:0% +h² and 2 pi M +KBT so if I substitute my Lumbers this + + align:start position:0% +KBT so if I substitute my Lumbers this + + + align:start position:0% +KBT so if I substitute my Lumbers this +is H is 6.6 10us 34 jar second right + + align:start position:0% +is H is 6.6 10us 34 jar second right + + + align:start position:0% +is H is 6.6 10us 34 jar second right +this H and in the denominator I have 2 + + align:start position:0% +this H and in the denominator I have 2 + + + align:start position:0% +this H and in the denominator I have 2 +pi if I think about + + align:start position:0% +pi if I think about + + + align:start position:0% +pi if I think about +electron electron Mass right 9.1 10us + + align:start position:0% +electron electron Mass right 9.1 10us + + + align:start position:0% +electron electron Mass right 9.1 10us +31 and KB is 1.38 10us + + align:start position:0% +31 and KB is 1.38 10us + + + align:start position:0% +31 and KB is 1.38 10us +23 and 300 kin square root you go to do + + align:start position:0% +23 and 300 kin square root you go to do + + + align:start position:0% +23 and 300 kin square root you go to do +that you get this l i get about 40 + + align:start position:0% +that you get this l i get about 40 + + + align:start position:0% +that you get this l i get about 40 +amstrong so it gives you the sort of + + align:start position:0% +amstrong so it gives you the sort of + + + align:start position:0% +amstrong so it gives you the sort of +average wence of this electrons with + + align:start position:0% +average wence of this electrons with + + + align:start position:0% +average wence of this electrons with +their energy KT near the bottom of the + + align:start position:0% +their energy KT near the bottom of the + + + align:start position:0% +their energy KT near the bottom of the +conduction + + align:start position:0% +conduction + + + align:start position:0% +conduction +band right so again uh uh this 40 40 uh + + align:start position:0% +band right so again uh uh this 40 40 uh + + + align:start position:0% +band right so again uh uh this 40 40 uh +Anon seems awfully small but we said + + align:start position:0% +Anon seems awfully small but we said + + + align:start position:0% +Anon seems awfully small but we said +before the uh sharp interface zero + + align:start position:0% +before the uh sharp interface zero + + + align:start position:0% +before the uh sharp interface zero +thickness and in fact you can deposit + + align:start position:0% +thickness and in fact you can deposit + + + align:start position:0% +thickness and in fact you can deposit +the layers almost atomically + + align:start position:0% +the layers almost atomically + + + align:start position:0% +the layers almost atomically +flat right so again say uh if in those + + align:start position:0% +flat right so again say uh if in those + + + align:start position:0% +flat right so again say uh if in those +cases you should consider uh the wave + + align:start position:0% +cases you should consider uh the wave + + + align:start position:0% +cases you should consider uh the wave +reflection transmission just as Optical + + align:start position:0% +reflection transmission just as Optical + + + align:start position:0% +reflection transmission just as Optical +waves and Fons this is the dispersion we + + align:start position:0% +waves and Fons this is the dispersion we + + + align:start position:0% +waves and Fons this is the dispersion we +uh learned before typical one and uh of + + align:start position:0% +uh learned before typical one and uh of + + + align:start position:0% +uh learned before typical one and uh of +course at the Zone boundary the wave + + align:start position:0% +course at the Zone boundary the wave + + + align:start position:0% +course at the Zone boundary the wave +length is 2 + + align:start position:0% +length is 2 + + + align:start position:0% +length is 2 +a right and it go goes for very long + + align:start position:0% +a right and it go goes for very long + + + align:start position:0% +a right and it go goes for very long +wavelength this is a uh the sound waves + + align:start position:0% +wavelength this is a uh the sound waves + + + align:start position:0% +wavelength this is a uh the sound waves +if you have a solid you lock it you hear + + align:start position:0% +if you have a solid you lock it you hear + + + align:start position:0% +if you have a solid you lock it you hear +it it's a very long wavelength at the + + align:start position:0% +it it's a very long wavelength at the + + + align:start position:0% +it it's a very long wavelength at the +zone Center to the whole just 2 a in + + align:start position:0% +zone Center to the whole just 2 a in + + + align:start position:0% +zone Center to the whole just 2 a in +between the LI constant right and if you + + align:start position:0% +between the LI constant right and if you + + + align:start position:0% +between the LI constant right and if you +do your uh uh like a black body for Fong + + align:start position:0% +do your uh uh like a black body for Fong + + + align:start position:0% +do your uh uh like a black body for Fong +uh you do your den of States uh uh you + + align:start position:0% +uh you do your den of States uh uh you + + + align:start position:0% +uh you do your den of States uh uh you +remember when we do black body radiation + + align:start position:0% +remember when we do black body radiation + + + align:start position:0% +remember when we do black body radiation +we do energy of photon times d sub + + align:start position:0% +we do energy of photon times d sub + + + align:start position:0% +we do energy of photon times d sub +States times the bste distribution + + align:start position:0% +States times the bste distribution + + + align:start position:0% +States times the bste distribution +that's how we get black body radiation + + align:start position:0% +that's how we get black body radiation + + + align:start position:0% +that's how we get black body radiation +and you do the same for Fon you'll say + + align:start position:0% +and you do the same for Fon you'll say + + + align:start position:0% +and you do the same for Fon you'll say +it's similar to black body this spectrum + + align:start position:0% +it's similar to black body this spectrum + + + align:start position:0% +it's similar to black body this spectrum +except you cut off you have a cut off + + align:start position:0% +except you cut off you have a cut off + + + align:start position:0% +except you cut off you have a cut off +wavelength because it's unlike + + align:start position:0% +wavelength because it's unlike + + + align:start position:0% +wavelength because it's unlike +electromagnetic wave in free space uh uh + + align:start position:0% +electromagnetic wave in free space uh uh + + + align:start position:0% +electromagnetic wave in free space uh uh +that that one goes very small right so + + align:start position:0% +that that one goes very small right so + + + align:start position:0% +that that one goes very small right so +the lce constant 2 a lce constant so + + align:start position:0% +the lce constant 2 a lce constant so + + + align:start position:0% +the lce constant 2 a lce constant so +overall uh it's good if we start with + + align:start position:0% +overall uh it's good if we start with + + + align:start position:0% +overall uh it's good if we start with +thinking uh when I calculate the + + align:start position:0% +thinking uh when I calculate the + + + align:start position:0% +thinking uh when I calculate the +transmission Le that I will consider one + + align:start position:0% +transmission Le that I will consider one + + + align:start position:0% +transmission Le that I will consider one +single interface if I have one to and I + + align:start position:0% +single interface if I have one to and I + + + align:start position:0% +single interface if I have one to and I +have this waves this could be uh + + align:start position:0% +have this waves this could be uh + + + align:start position:0% +have this waves this could be uh +electron wave could be Photon wave and + + align:start position:0% +electron wave could be Photon wave and + + + align:start position:0% +electron wave could be Photon wave and +could be Fong way comes to the interface + + align:start position:0% +could be Fong way comes to the interface + + + align:start position:0% +could be Fong way comes to the interface +and they will be + + align:start position:0% +and they will be + + + align:start position:0% +and they will be +reflected and they will also be could be + + align:start position:0% +reflected and they will also be could be + + + align:start position:0% +reflected and they will also be could be +transmitting across the interface how + + align:start position:0% +transmitting across the interface how + + + align:start position:0% +transmitting across the interface how +much how I can calculate how much is + + align:start position:0% +much how I can calculate how much is + + + align:start position:0% +much how I can calculate how much is +reflected how much + + align:start position:0% +reflected how much + + + align:start position:0% +reflected how much +transmitted right so that's a uh my + + align:start position:0% +transmitted right so that's a uh my + + + align:start position:0% +transmitted right so that's a uh my +first order of business and that will + + align:start position:0% +first order of business and that will + + + align:start position:0% +first order of business and that will +give me the transmission from one side + + align:start position:0% +give me the transmission from one side + + + align:start position:0% +give me the transmission from one side +of interface to the other side of + + align:start position:0% +of interface to the other side of + + + align:start position:0% +of interface to the other side of +interface right and of course I could + + align:start position:0% +interface right and of course I could + + + align:start position:0% +interface right and of course I could +have + + align:start position:0% +have + + + align:start position:0% +have +uh layers or I could have uh many layers + + align:start position:0% +uh layers or I could have uh many layers + + + align:start position:0% +uh layers or I could have uh many layers +right this is I'm I'm considering really + + align:start position:0% +right this is I'm I'm considering really + + + align:start position:0% +right this is I'm I'm considering really +a planner geometry make a 1D problem + + align:start position:0% +a planner geometry make a 1D problem + + + align:start position:0% +a planner geometry make a 1D problem +simpler right so in this case one and + + align:start position:0% +simpler right so in this case one and + + + align:start position:0% +simpler right so in this case one and +two and three will have mul layers + + align:start position:0% +two and three will have mul layers + + + align:start position:0% +two and three will have mul layers +coding when I use Optical + + align:start position:0% +coding when I use Optical + + + align:start position:0% +coding when I use Optical +codings right how I will calculate the + + align:start position:0% +codings right how I will calculate the + + + align:start position:0% +codings right how I will calculate the +transmission and reflection and turns + + align:start position:0% +transmission and reflection and turns + + + align:start position:0% +transmission and reflection and turns +out the waves are very similar whether + + align:start position:0% +out the waves are very similar whether + + + align:start position:0% +out the waves are very similar whether +it's a electron wave or Fon wave or + + align:start position:0% +it's a electron wave or Fon wave or + + + align:start position:0% +it's a electron wave or Fon wave or +electromagnetic wave you'll see the + + align:start position:0% +electromagnetic wave you'll see the + + + align:start position:0% +electromagnetic wave you'll see the +behavior are very similar although at + + align:start position:0% +behavior are very similar although at + + + align:start position:0% +behavior are very similar although at +the quantum level we know that electron + + align:start position:0% +the quantum level we know that electron + + + align:start position:0% +the quantum level we know that electron +Fon photons are different right but the + + align:start position:0% +Fon photons are different right but the + + + align:start position:0% +Fon photons are different right but the +general W behavior in terms of + + align:start position:0% +general W behavior in terms of + + + align:start position:0% +general W behavior in terms of +interference in terms of defraction in + + align:start position:0% +interference in terms of defraction in + + + align:start position:0% +interference in terms of defraction in +terms of teling all those exist for all + + align:start position:0% +terms of teling all those exist for all + + + align:start position:0% +terms of teling all those exist for all +waves and there are different technology + + align:start position:0% +waves and there are different technology + + + align:start position:0% +waves and there are different technology +develop based on this + + align:start position:0% +develop based on this + + + align:start position:0% +develop based on this +phenomenon so let's uh uh look + + align:start position:0% +phenomenon so let's uh uh look + + + align:start position:0% +phenomenon so let's uh uh look +at start with a plan wave at a one + + align:start position:0% +at start with a plan wave at a one + + + align:start position:0% +at start with a plan wave at a one +interface right let's just consider the + + align:start position:0% +interface right let's just consider the + + + align:start position:0% +interface right let's just consider the +simplest plan + + align:start position:0% + + + + align:start position:0% + +wave and the reflection reflection at + + align:start position:0% +wave and the reflection reflection at + + + align:start position:0% +wave and the reflection reflection at +the interface + + align:start position:0% + + + + align:start position:0% + +you can see here I'm not even + + align:start position:0% +you can see here I'm not even + + + align:start position:0% +you can see here I'm not even +distinguishing whether it's electron + + align:start position:0% +distinguishing whether it's electron + + + align:start position:0% +distinguishing whether it's electron +electromagnetic although my detailed + + align:start position:0% +electromagnetic although my detailed + + + align:start position:0% +electromagnetic although my detailed +derivation or have to WR start with + + align:start position:0% +derivation or have to WR start with + + + align:start position:0% +derivation or have to WR start with +different wave equations right and in + + align:start position:0% +different wave equations right and in + + + align:start position:0% +different wave equations right and in +this case I want to actually start with + + align:start position:0% +this case I want to actually start with + + + align:start position:0% +this case I want to actually start with +the quantum wave a electron and that's + + align:start position:0% +the quantum wave a electron and that's + + + align:start position:0% +the quantum wave a electron and that's +because that's + + align:start position:0% +because that's + + + align:start position:0% +because that's +simplest electron if you think about + + align:start position:0% +simplest electron if you think about + + + align:start position:0% +simplest electron if you think about +shinger equation in certain sense it's + + align:start position:0% +shinger equation in certain sense it's + + + align:start position:0% +shinger equation in certain sense it's +simple because it's scalar the wave + + align:start position:0% +simple because it's scalar the wave + + + align:start position:0% +simple because it's scalar the wave +function is scalar lot of vector when I + + align:start position:0% +function is scalar lot of vector when I + + + align:start position:0% +function is scalar lot of vector when I +go to acoustic + + align:start position:0% +go to acoustic + + + align:start position:0% +go to acoustic +waves right the latest vibration there + + align:start position:0% +waves right the latest vibration there + + + align:start position:0% +waves right the latest vibration there +three polarizes in two transverse one + + align:start position:0% +three polarizes in two transverse one + + + align:start position:0% +three polarizes in two transverse one +longitudal electromagnetic wave is a + + align:start position:0% +longitudal electromagnetic wave is a + + + align:start position:0% +longitudal electromagnetic wave is a +vector wave the electric field is + + align:start position:0% +vector wave the electric field is + + + align:start position:0% +vector wave the electric field is +perpendicular to the direction of + + align:start position:0% +perpendicular to the direction of + + + align:start position:0% +perpendicular to the direction of +propagation the two + + align:start position:0% +propagation the two + + + align:start position:0% +propagation the two +polarization so uh I will start with the + + align:start position:0% +polarization so uh I will start with the + + + align:start position:0% +polarization so uh I will start with the +simplest uh electron + + align:start position:0% +simplest uh electron + + + align:start position:0% +simplest uh electron +wave to the scalar + + align:start position:0% + + + + align:start position:0% + +right and we uh have done uh the + + align:start position:0% +right and we uh have done uh the + + + align:start position:0% +right and we uh have done uh the +electron wave Stringer equation before 2 + + align:start position:0% +electron wave Stringer equation before 2 + + + align:start position:0% +electron wave Stringer equation before 2 +m d side I let me think about the one + + align:start position:0% +m d side I let me think about the one + + + align:start position:0% +m d side I let me think about the one +electron 1 D DX S Plus u e this is the + + align:start position:0% +electron 1 D DX S Plus u e this is the + + + align:start position:0% +electron 1 D DX S Plus u e this is the +stady state part right you m e EO is the + + align:start position:0% +stady state part right you m e EO is the + + + align:start position:0% +stady state part right you m e EO is the +potential e is the electron + + align:start position:0% +potential e is the electron + + + align:start position:0% +potential e is the electron +energy and and of course there is a Time + + align:start position:0% +energy and and of course there is a Time + + + align:start position:0% +energy and and of course there is a Time +dependent part uh that's the uh Remember + + align:start position:0% +dependent part uh that's the uh Remember + + + align:start position:0% +dependent part uh that's the uh Remember +the Time dependent part is just + + align:start position:0% +the Time dependent part is just + + + align:start position:0% +the Time dependent part is just +exponential Mass I Omega t or this Omega + + align:start position:0% +exponential Mass I Omega t or this Omega + + + align:start position:0% +exponential Mass I Omega t or this Omega +equal e over H bar that's the prod + + align:start position:0% +equal e over H bar that's the prod + + + align:start position:0% +equal e over H bar that's the prod +relation + + align:start position:0% +relation + + + align:start position:0% +relation +right and uh for this + + align:start position:0% +right and uh for this + + + align:start position:0% +right and uh for this +way we solved the + + align:start position:0% +way we solved the + + + align:start position:0% +way we solved the +before it's a simple second order + + align:start position:0% +before it's a simple second order + + + align:start position:0% +before it's a simple second order +differential equation with constant + + align:start position:0% +differential equation with constant + + + align:start position:0% +differential equation with constant +coefficient so we solve this before and + + align:start position:0% +coefficient so we solve this before and + + + align:start position:0% +coefficient so we solve this before and +then let me write it down the general + + align:start position:0% +then let me write it down the general + + + align:start position:0% +then let me write it down the general +wave form as a if I combine the time and + + align:start position:0% +wave form as a if I combine the time and + + + align:start position:0% +wave form as a if I combine the time and +the space dependent all together that + + align:start position:0% +the space dependent all together that + + + align:start position:0% +the space dependent all together that +looks more like a wave plan wave I Omega + + align:start position:0% +looks more like a wave plan wave I Omega + + + align:start position:0% +looks more like a wave plan wave I Omega +tus k um + + align:start position:0% +tus k um + + + align:start position:0% +tus k um +X plus b e my I Omega t plus KX I have + + align:start position:0% +X plus b e my I Omega t plus KX I have + + + align:start position:0% +X plus b e my I Omega t plus KX I have +two Sol + + align:start position:0% +two Sol + + + align:start position:0% +two Sol +Solutions right that's what we written + + align:start position:0% +Solutions right that's what we written + + + align:start position:0% +Solutions right that's what we written +down + + align:start position:0% +down + + + align:start position:0% +down +before now you can tell me the first + + align:start position:0% +before now you can tell me the first + + + align:start position:0% +before now you can tell me the first +solution is a wave properly in which + + align:start position:0% +solution is a wave properly in which + + + align:start position:0% +solution is a wave properly in which +direction positive X second wave is leg + + align:start position:0% +direction positive X second wave is leg + + + align:start position:0% +direction positive X second wave is leg +X direction right that's are the two + + align:start position:0% +X direction right that's are the two + + + align:start position:0% +X direction right that's are the two +counterpropagating + + align:start position:0% +counterpropagating + + + align:start position:0% +counterpropagating +waves and it's a superposition of two + + align:start position:0% +waves and it's a superposition of two + + + align:start position:0% +waves and it's a superposition of two +waves now I'm going to look at the uh if + + align:start position:0% +waves now I'm going to look at the uh if + + + align:start position:0% +waves now I'm going to look at the uh if +I deposit the film with the interface + + align:start position:0% +I deposit the film with the interface + + + align:start position:0% +I deposit the film with the interface +right so this interface I look at the 1D + + align:start position:0% +right so this interface I look at the 1D + + + align:start position:0% +right so this interface I look at the 1D +uh so forget about the say YZ + + align:start position:0% +uh so forget about the say YZ + + + align:start position:0% +uh so forget about the say YZ +Direction and so 1D interface this is + + align:start position:0% +Direction and so 1D interface this is + + + align:start position:0% +Direction and so 1D interface this is +the one side of the film this is the + + align:start position:0% +the one side of the film this is the + + + align:start position:0% +the one side of the film this is the +other side of the + + align:start position:0% +other side of the + + + align:start position:0% +other side of the +film and uh uh this is a typically if + + align:start position:0% +film and uh uh this is a typically if + + + align:start position:0% +film and uh uh this is a typically if +you put a two different semiconductor + + align:start position:0% +you put a two different semiconductor + + + align:start position:0% +you put a two different semiconductor +together right and here is a conduction + + align:start position:0% +together right and here is a conduction + + + align:start position:0% +together right and here is a conduction +band + + align:start position:0% +band + + + align:start position:0% +band +ec1 here is a conduction band e + + align:start position:0% +ec1 here is a conduction band e + + + align:start position:0% +ec1 here is a conduction band e +C2 right so ec1 + + align:start position:0% + + + + align:start position:0% + +ec2 and at the interface there's a a + + align:start position:0% +ec2 and at the interface there's a a + + + align:start position:0% +ec2 and at the interface there's a a +discontinuity of the energy of the + + align:start position:0% +discontinuity of the energy of the + + + align:start position:0% +discontinuity of the energy of the +electrons right and the difference + + align:start position:0% + + + + align:start position:0% + +here is + + align:start position:0% +here is + + + align:start position:0% +here is +U or Delta the different place have + + align:start position:0% +U or Delta the different place have + + + align:start position:0% +U or Delta the different place have +different symbols and this is typically + + align:start position:0% +different symbols and this is typically + + + align:start position:0% +different symbols and this is typically +called a hro junction when I put a two + + align:start position:0% +called a hro junction when I put a two + + + align:start position:0% +called a hro junction when I put a two +different conductors together + + align:start position:0% +different conductors together + + + align:start position:0% +different conductors together +semiconductor together at the interface + + align:start position:0% +semiconductor together at the interface + + + align:start position:0% +semiconductor together at the interface +there's a potential barrier electrical + + align:start position:0% +there's a potential barrier electrical + + + align:start position:0% +there's a potential barrier electrical +potential barrier and the detail is more + + align:start position:0% +potential barrier and the detail is more + + + align:start position:0% +potential barrier and the detail is more +complic than I draw I draw a sharp one + + align:start position:0% +complic than I draw I draw a sharp one + + + align:start position:0% +complic than I draw I draw a sharp one +and in fact the electron here is not + + align:start position:0% +and in fact the electron here is not + + + align:start position:0% +and in fact the electron here is not +stable is going to fall into here so + + align:start position:0% +stable is going to fall into here so + + + align:start position:0% +stable is going to fall into here so +it's not going to be a flat as a flat as + + align:start position:0% +it's not going to be a flat as a flat as + + + align:start position:0% +it's not going to be a flat as a flat as +I'm drawing here here's a very simple + + align:start position:0% +I'm drawing here here's a very simple + + + align:start position:0% +I'm drawing here here's a very simple +approximation okay and now I have a + + align:start position:0% +approximation okay and now I have a + + + align:start position:0% +approximation okay and now I have a +electron wave comes in + + align:start position:0% + + + + align:start position:0% + +so I can take a form of the incident + + align:start position:0% +so I can take a form of the incident + + + align:start position:0% +so I can take a form of the incident +wave and if this is my X + + align:start position:0% +wave and if this is my X + + + align:start position:0% +wave and if this is my X +Direction and then at the + + align:start position:0% +Direction and then at the + + + align:start position:0% +Direction and then at the +interface there will be reflection the + + align:start position:0% +interface there will be reflection the + + + align:start position:0% +interface there will be reflection the +wave will go back + + align:start position:0% +wave will go back + + + align:start position:0% +wave will go back +right on the other side there could be + + align:start position:0% +right on the other side there could be + + + align:start position:0% +right on the other side there could be +transmission the wave can go over the + + align:start position:0% +transmission the wave can go over the + + + align:start position:0% +transmission the wave can go over the +barrier continue right so I have reflect + + align:start position:0% +barrier continue right so I have reflect + + + align:start position:0% +barrier continue right so I have reflect +I have transmission I want to find how + + align:start position:0% +I have transmission I want to find how + + + align:start position:0% +I have transmission I want to find how +much reflected how much + + align:start position:0% +much reflected how much + + + align:start position:0% +much reflected how much +transmitted okay + + align:start position:0% +transmitted okay + + + align:start position:0% +transmitted okay +so here you can use the plan wave + + align:start position:0% +so here you can use the plan wave + + + align:start position:0% +so here you can use the plan wave +solution for median one let me take this + + align:start position:0% +solution for median one let me take this + + + align:start position:0% +solution for median one let me take this +uh uh y as a reference this is zero here + + align:start position:0% +uh uh y as a reference this is zero here + + + align:start position:0% +uh uh y as a reference this is zero here +is a uh so electron here experience a + + align:start position:0% +is a uh so electron here experience a + + + align:start position:0% +is a uh so electron here experience a +difference between zero and magnitude + + align:start position:0% +difference between zero and magnitude + + + align:start position:0% +difference between zero and magnitude +U right so because of this my K in each + + align:start position:0% +U right so because of this my K in each + + + align:start position:0% +U right so because of this my K in each +each region in say in region let's say + + align:start position:0% +each region in say in region let's say + + + align:start position:0% +each region in say in region let's say +here is my zero or region of my + + align:start position:0% +here is my zero or region of my + + + align:start position:0% +here is my zero or region of my +coordinate and you can always take your + + align:start position:0% +coordinate and you can always take your + + + align:start position:0% +coordinate and you can always take your +origin but typically it's much easier if + + align:start position:0% +origin but typically it's much easier if + + + align:start position:0% +origin but typically it's much easier if +you set the origin at the interface at + + align:start position:0% +you set the origin at the interface at + + + align:start position:0% +you set the origin at the interface at +least at the first interface if you have + + align:start position:0% +least at the first interface if you have + + + align:start position:0% +least at the first interface if you have +multi layers you have to continue + + align:start position:0% +multi layers you have to continue + + + align:start position:0% +multi layers you have to continue +because there's distance from zero so + + align:start position:0% +because there's distance from zero so + + + align:start position:0% +because there's distance from zero so +you count that distance right so if I + + align:start position:0% +you count that distance right so if I + + + align:start position:0% +you count that distance right so if I +put this one at zero I have a incident + + align:start position:0% +put this one at zero I have a incident + + + align:start position:0% +put this one at zero I have a incident +wave side I + + align:start position:0% +wave side I + + + align:start position:0% +wave side I +right this is the incident and has a + + align:start position:0% +right this is the incident and has a + + + align:start position:0% +right this is the incident and has a +amplitude a and going to the right hand + + align:start position:0% +amplitude a and going to the right hand + + + align:start position:0% +amplitude a and going to the right hand +side so exponential Min I Omega tus k1x + + align:start position:0% +side so exponential Min I Omega tus k1x + + + align:start position:0% +side so exponential Min I Omega tus k1x +because this is region one and this is + + align:start position:0% +because this is region one and this is + + + align:start position:0% +because this is region one and this is +region + + align:start position:0% +region + + + align:start position:0% +region +two right my K is different because here + + align:start position:0% +two right my K is different because here + + + align:start position:0% +two right my K is different because here +K my + + align:start position:0% +K my + + + align:start position:0% +K my +K if you look at this is 2 + + align:start position:0% +K if you look at this is 2 + + + align:start position:0% +K if you look at this is 2 +m eus u IDE by uh H bar Square you + + align:start position:0% +m eus u IDE by uh H bar Square you + + + align:start position:0% +m eus u IDE by uh H bar Square you +combine this together and reverse the + + align:start position:0% +combine this together and reverse the + + + align:start position:0% +combine this together and reverse the +sign e u not u + + align:start position:0% +sign e u not u + + + align:start position:0% +sign e u not u +e okay so in this region U equal zero so + + align:start position:0% +e okay so in this region U equal zero so + + + align:start position:0% +e okay so in this region U equal zero so +whatever energy e of the electron minass + + align:start position:0% +whatever energy e of the electron minass + + + align:start position:0% +whatever energy e of the electron minass +potential zero so that's the wave form + + align:start position:0% +potential zero so that's the wave form + + + align:start position:0% +potential zero so that's the wave form +the wave Vector of + + align:start position:0% +the wave Vector of + + + align:start position:0% +the wave Vector of +K1 right and uh they reflect it here + + align:start position:0% +K1 right and uh they reflect it here + + + align:start position:0% +K1 right and uh they reflect it here +pign this one this is reflective wave + + align:start position:0% +pign this one this is reflective wave + + + align:start position:0% +pign this one this is reflective wave +you can see the reflective wave is going + + align:start position:0% +you can see the reflective wave is going + + + align:start position:0% +you can see the reflective wave is going +backward right my coefficient is UN long + + align:start position:0% +backward right my coefficient is UN long + + + align:start position:0% +backward right my coefficient is UN long +B I say I want to find out the the + + align:start position:0% +B I say I want to find out the the + + + align:start position:0% +B I say I want to find out the the +reflection a and the B + + align:start position:0% +reflection a and the B + + + align:start position:0% +reflection a and the B +relation my transmitted + + align:start position:0% +relation my transmitted + + + align:start position:0% +relation my transmitted +wave in region two so if I write down + + align:start position:0% +wave in region two so if I write down + + + align:start position:0% +wave in region two so if I write down +the transmitted wave is say exponential + + align:start position:0% +the transmitted wave is say exponential + + + align:start position:0% +the transmitted wave is say exponential +again it's forward propagating into X + + align:start position:0% +again it's forward propagating into X + + + align:start position:0% +again it's forward propagating into X +Direction positive X + + align:start position:0% +Direction positive X + + + align:start position:0% +Direction positive X +direction right so it's the say m i + + align:start position:0% +direction right so it's the say m i + + + align:start position:0% +direction right so it's the say m i +Omega T k2x not k1x and this + + align:start position:0% +Omega T k2x not k1x and this + + + align:start position:0% +Omega T k2x not k1x and this +K2 you can say is 2 um m eus u now h² + + align:start position:0% +K2 you can say is 2 um m eus u now h² + + + align:start position:0% +K2 you can say is 2 um m eus u now h² +and K1 is just yo is zero so it's 2 2 m + + align:start position:0% +and K1 is just yo is zero so it's 2 2 m + + + align:start position:0% +and K1 is just yo is zero so it's 2 2 m +e is the energy of the + + align:start position:0% +e is the energy of the + + + align:start position:0% +e is the energy of the +electron 2 m over e uh 2 m e over + + align:start position:0% +electron 2 m over e uh 2 m e over + + + align:start position:0% +electron 2 m over e uh 2 m e over +h² right so this is the difference of + + align:start position:0% +h² right so this is the difference of + + + align:start position:0% +h² right so this is the difference of +this + + align:start position:0% +this + + + align:start position:0% +this +waves here in region one the reflect + + align:start position:0% +waves here in region one the reflect + + + align:start position:0% +waves here in region one the reflect +incident reflected the differ only by + + align:start position:0% +incident reflected the differ only by + + + align:start position:0% +incident reflected the differ only by +here is a plus here is minus + + align:start position:0% +here is a plus here is minus + + + align:start position:0% +here is a plus here is minus +coefficients of the course are different + + align:start position:0% +coefficients of the course are different + + + align:start position:0% +coefficients of the course are different +and transmitted wave in region two the + + align:start position:0% +and transmitted wave in region two the + + + align:start position:0% +and transmitted wave in region two the +coefficient is different V Vector is + + align:start position:0% +coefficient is different V Vector is + + + align:start position:0% +coefficient is different V Vector is +different two difference + + align:start position:0% +different two difference + + + align:start position:0% +different two difference +right so I want to find out relation + + align:start position:0% +right so I want to find out relation + + + align:start position:0% +right so I want to find out relation +between one and + + align:start position:0% +between one and + + + align:start position:0% +between one and +[Applause] + + align:start position:0% + + + + align:start position:0% + +two and uh my to find this relation I + + align:start position:0% +two and uh my to find this relation I + + + align:start position:0% +two and uh my to find this relation I +have to use Contin the interface + + align:start position:0% +have to use Contin the interface + + + align:start position:0% +have to use Contin the interface +condition right at the interface the + + align:start position:0% +condition right at the interface the + + + align:start position:0% +condition right at the interface the +wave function is continuous the + + align:start position:0% +wave function is continuous the + + + align:start position:0% +wave function is continuous the +derivative of the wave function is + + align:start position:0% +derivative of the wave function is + + + align:start position:0% +derivative of the wave function is +continuous so uh the wave function so + + align:start position:0% +continuous so uh the wave function so + + + align:start position:0% +continuous so uh the wave function so +it's not just one wave function when I + + align:start position:0% +it's not just one wave function when I + + + align:start position:0% +it's not just one wave function when I +say wave function is all the waves all + + align:start position:0% +say wave function is all the waves all + + + align:start position:0% +say wave function is all the waves all +the you add them all together right you + + align:start position:0% +the you add them all together right you + + + align:start position:0% +the you add them all together right you +add the waves + + align:start position:0% +add the waves + + + align:start position:0% +add the waves +together and so at the X + + align:start position:0% +together and so at the X + + + align:start position:0% +together and so at the X +s0 what I have is a POS sign I plus + + align:start position:0% +s0 what I have is a POS sign I plus + + + align:start position:0% +s0 what I have is a POS sign I plus +cosine + + align:start position:0% +cosine + + + align:start position:0% +cosine +r on the left hand side I have two waves + + align:start position:0% +r on the left hand side I have two waves + + + align:start position:0% +r on the left hand side I have two waves +incident + + align:start position:0% +incident + + + align:start position:0% +incident +reflected + + align:start position:0% +reflected + + + align:start position:0% +reflected +right X to 0 = cosine t x to + + align:start position:0% + + + + align:start position:0% + +Z what I get so the incident is a uh X + + align:start position:0% +Z what I get so the incident is a uh X + + + align:start position:0% +Z what I get so the incident is a uh X +zero so K1 X that's + + align:start position:0% +zero so K1 X that's + + + align:start position:0% +zero so K1 X that's +zero U Min Omega T is Shar the same + + align:start position:0% +zero U Min Omega T is Shar the same + + + align:start position:0% +zero U Min Omega T is Shar the same +Omega is the + + align:start position:0% +Omega is the + + + align:start position:0% +Omega is the +energy of the of the particle right Eide + + align:start position:0% +energy of the of the particle right Eide + + + align:start position:0% +energy of the of the particle right Eide +by H is the same on both Sid so when you + + align:start position:0% +by H is the same on both Sid so when you + + + align:start position:0% +by H is the same on both Sid so when you +you go the wave go from one media into + + align:start position:0% +you go the wave go from one media into + + + align:start position:0% +you go the wave go from one media into +the other media the frequency doesn't + + align:start position:0% +the other media the frequency doesn't + + + align:start position:0% +the other media the frequency doesn't +change okay and so what I have here is + + align:start position:0% +change okay and so what I have here is + + + align:start position:0% +change okay and so what I have here is +really a + b equal + + align:start position:0% + + + + align:start position:0% + +C because eus I Omega t eus i Oma t + + align:start position:0% +C because eus I Omega t eus i Oma t + + + align:start position:0% +C because eus I Omega t eus i Oma t +andine t is eus I Omega T that all + + align:start position:0% +andine t is eus I Omega T that all + + + align:start position:0% +andine t is eus I Omega T that all +cancel right x equal Z so I have that my + + align:start position:0% +cancel right x equal Z so I have that my + + + align:start position:0% +cancel right x equal Z so I have that my +second condition is a + + align:start position:0% + + + + align:start position:0% + +derivative so it's a total derivative of + + align:start position:0% +derivative so it's a total derivative of + + + align:start position:0% +derivative so it's a total derivative of +all the waves and because the summation + + align:start position:0% +all the waves and because the summation + + + align:start position:0% +all the waves and because the summation +so I put the each one so I first take + + align:start position:0% +so I put the each one so I first take + + + align:start position:0% +so I put the each one so I first take +derivative you have to be careful First + + align:start position:0% +derivative you have to be careful First + + + align:start position:0% +derivative you have to be careful First +Take derivative you set to equal to + + align:start position:0% +Take derivative you set to equal to + + + align:start position:0% +Take derivative you set to equal to +Z and this + + align:start position:0% +Z and this + + + align:start position:0% +Z and this +equals derivative X = to 0 so if you + + align:start position:0% +equals derivative X = to 0 so if you + + + align:start position:0% +equals derivative X = to 0 so if you +take a deriva here so you say with + + align:start position:0% +take a deriva here so you say with + + + align:start position:0% +take a deriva here so you say with +respect to X so this is a ik k + + align:start position:0% +respect to X so this is a ik k + + + align:start position:0% +respect to X so this is a ik k +right negative negative so I have + + align:start position:0% +right negative negative so I have + + + align:start position:0% +right negative negative so I have +positive I + + align:start position:0% +positive I + + + align:start position:0% +positive I +K1 a that's the first term that's a + + align:start position:0% +K1 a that's the first term that's a + + + align:start position:0% +K1 a that's the first term that's a +incident reflected is B and here is min + + align:start position:0% +incident reflected is B and here is min + + + align:start position:0% +incident reflected is B and here is min +I * plus K so I have a sign change after + + align:start position:0% +I * plus K so I have a sign change after + + + align:start position:0% +I * plus K so I have a sign change after +I take + + align:start position:0% +I take + + + align:start position:0% +I take +derivative right so a must b equals I K2 + + align:start position:0% +derivative right so a must b equals I K2 + + + align:start position:0% +derivative right so a must b equals I K2 +* C so that's the + + align:start position:0% +* C so that's the + + + align:start position:0% +* C so that's the +application of the two boundary + + align:start position:0% +application of the two boundary + + + align:start position:0% +application of the two boundary +condition that's + + align:start position:0% + + + + align:start position:0% + +wres with the frequency change the W + + align:start position:0% +wres with the frequency change the W + + + align:start position:0% +wres with the frequency change the W +goes through or just no the frequency + + align:start position:0% +goes through or just no the frequency + + + align:start position:0% +goes through or just no the frequency +doesn't change right when you your light + + align:start position:0% +doesn't change right when you your light + + + align:start position:0% +doesn't change right when you your light +goes from one media into another media + + align:start position:0% +goes from one media into another media + + + align:start position:0% +goes from one media into another media +the frequency does not change the + + align:start position:0% +the frequency does not change the + + + align:start position:0% +the frequency does not change the +wavelength + + align:start position:0% +wavelength + + + align:start position:0% +wavelength +change okay so this is a k is my you + + align:start position:0% +change okay so this is a k is my you + + + align:start position:0% +change okay so this is a k is my you +remember HK gives me momentum P equals + + align:start position:0% +remember HK gives me momentum P equals + + + align:start position:0% +remember HK gives me momentum P equals +HK over + + align:start position:0% +HK over + + + align:start position:0% +HK over +say h bar or Lambda give me the momentum + + align:start position:0% +say h bar or Lambda give me the momentum + + + align:start position:0% +say h bar or Lambda give me the momentum +right so uh here is my uh two conditions + + align:start position:0% +right so uh here is my uh two conditions + + + align:start position:0% +right so uh here is my uh two conditions +and I want to find the ratio because I + + align:start position:0% +and I want to find the ratio because I + + + align:start position:0% +and I want to find the ratio because I +want to find transmission is C over a + + align:start position:0% +want to find transmission is C over a + + + align:start position:0% +want to find transmission is C over a +reflection is B already so I have two + + align:start position:0% +reflection is B already so I have two + + + align:start position:0% +reflection is B already so I have two +equation I want to find ratio I can find + + align:start position:0% +equation I want to find ratio I can find + + + align:start position:0% +equation I want to find ratio I can find +those + + align:start position:0% +those + + + align:start position:0% +those +ratios and the ratio I have is so based + + align:start position:0% +ratios and the ratio I have is so based + + + align:start position:0% +ratios and the ratio I have is so based +on this I have C over a is uh 2 + + align:start position:0% +on this I have C over a is uh 2 + + + align:start position:0% +on this I have C over a is uh 2 +K1 K1 + + + align:start position:0% +K1 K1 + + + + align:start position:0% +K1 K1 + +K2 and b/ a is k1 + + align:start position:0% +K2 and b/ a is k1 + + + align:start position:0% +K2 and b/ a is k1 +K2 uh K1 + + + align:start position:0% + + + + align:start position:0% + +K2 so those are my uh solutions for the + + align:start position:0% +K2 so those are my uh solutions for the + + + align:start position:0% +K2 so those are my uh solutions for the +coefficients are for the transmitted + + align:start position:0% +coefficients are for the transmitted + + + align:start position:0% +coefficients are for the transmitted +wave and reflective wave relative to the + + align:start position:0% +wave and reflective wave relative to the + + + align:start position:0% +wave and reflective wave relative to the +incident + + align:start position:0% +incident + + + align:start position:0% +incident +wave right + + align:start position:0% +wave right + + + align:start position:0% +wave right +but what does this coefficient really + + align:start position:0% +but what does this coefficient really + + + align:start position:0% +but what does this coefficient really +doesn't mean anything yet because we + + align:start position:0% +doesn't mean anything yet because we + + + align:start position:0% +doesn't mean anything yet because we +said before the wave function is not a + + align:start position:0% +said before the wave function is not a + + + align:start position:0% +said before the wave function is not a +measurable + + align:start position:0% +measurable + + + align:start position:0% +measurable +quantity + + align:start position:0% +quantity + + + align:start position:0% +quantity +right in Quantum is the P times complex + + align:start position:0% +right in Quantum is the P times complex + + + align:start position:0% +right in Quantum is the P times complex +conjugate that gives the particles right + + align:start position:0% +conjugate that gives the particles right + + + align:start position:0% +conjugate that gives the particles right +and uh the particle flux in quantum + + align:start position:0% + + + + align:start position:0% + +right the flux of the particle uh we + + align:start position:0% +right the flux of the particle uh we + + + align:start position:0% +right the flux of the particle uh we +give this expression before is a uh in + + align:start position:0% +give this expression before is a uh in + + + align:start position:0% +give this expression before is a uh in +the vector form is i h bar 2 m and Pai + + align:start position:0% +the vector form is i h bar 2 m and Pai + + + align:start position:0% +the vector form is i h bar 2 m and Pai +complex conjugate of gradient of + + align:start position:0% +complex conjugate of gradient of + + + align:start position:0% +complex conjugate of gradient of +Pai + + align:start position:0% +Pai + + + align:start position:0% +Pai +and Pai complex conjugate times gradient + + align:start position:0% +and Pai complex conjugate times gradient + + + align:start position:0% +and Pai complex conjugate times gradient +of Pai so that's the + + align:start position:0% +of Pai so that's the + + + align:start position:0% +of Pai so that's the +partical + + align:start position:0% +partical + + + align:start position:0% +partical +flux and uh another way to write this if + + align:start position:0% +flux and uh another way to write this if + + + align:start position:0% +flux and uh another way to write this if +you if you uh use a short hand this is + + align:start position:0% +you if you uh use a short hand this is + + + align:start position:0% +you if you uh use a short hand this is +real part of i h bar and + + align:start position:0% +real part of i h bar and + + + align:start position:0% +real part of i h bar and +mide complex conjugate of gradient + + align:start position:0% +mide complex conjugate of gradient + + + align:start position:0% +mide complex conjugate of gradient +because this one is complex conjugate of + + align:start position:0% +because this one is complex conjugate of + + + align:start position:0% +because this one is complex conjugate of +this one so the + + align:start position:0% +this one so the + + + align:start position:0% +this one so the +difference gives overall is is real part + + align:start position:0% +difference gives overall is is real part + + + align:start position:0% +difference gives overall is is real part +of this okay + + align:start position:0% +of this okay + + + align:start position:0% +of this okay +and now I'm going to plug in because I + + align:start position:0% +and now I'm going to plug in because I + + + align:start position:0% +and now I'm going to plug in because I +want to say what's my for example if I + + align:start position:0% +want to say what's my for example if I + + + align:start position:0% +want to say what's my for example if I +my incident if Pai is + + align:start position:0% +my incident if Pai is + + + align:start position:0% +my incident if Pai is +my Pai I + + align:start position:0% +my Pai I + + + align:start position:0% +my Pai I +right you see p i is a exponential Min I + + align:start position:0% +right you see p i is a exponential Min I + + + align:start position:0% +right you see p i is a exponential Min I +Omega tus + + align:start position:0% +Omega tus + + + align:start position:0% +Omega tus +KX okay so let's substitute the in so in + + align:start position:0% +KX okay so let's substitute the in so in + + + align:start position:0% +KX okay so let's substitute the in so in +this case the incident flux is + + align:start position:0% +this case the incident flux is + + + align:start position:0% +this case the incident flux is +part of i h bar to M pze A exponential I + + align:start position:0% +part of i h bar to M pze A exponential I + + + align:start position:0% +part of i h bar to M pze A exponential I +Omega T + + align:start position:0% +Omega T + + + align:start position:0% +Omega T +k1x that's incident so the derivative is + + align:start position:0% +k1x that's incident so the derivative is + + + align:start position:0% +k1x that's incident so the derivative is +deep side I first take complex + + align:start position:0% +deep side I first take complex + + + align:start position:0% +deep side I first take complex +conjugate and then I take the + + align:start position:0% +conjugate and then I take the + + + align:start position:0% +conjugate and then I take the +derivative and complex conjugate this + + align:start position:0% +derivative and complex conjugate this + + + align:start position:0% +derivative and complex conjugate this +one becomes plus because I right minus I + + align:start position:0% +one becomes plus because I right minus I + + + align:start position:0% +one becomes plus because I right minus I +becomes Plus I and + + align:start position:0% +becomes Plus I and + + + align:start position:0% +becomes Plus I and +K1 I'm going to take a more uniform I + + align:start position:0% +K1 I'm going to take a more uniform I + + + align:start position:0% +K1 I'm going to take a more uniform I +say it's complex cuz the Oma is a + + align:start position:0% +say it's complex cuz the Oma is a + + + align:start position:0% +say it's complex cuz the Oma is a +frequency we Vector I'm going to also + + align:start position:0% +frequency we Vector I'm going to also + + + align:start position:0% +frequency we Vector I'm going to also +say could be real and imaginary or + + align:start position:0% +say could be real and imaginary or + + + align:start position:0% +say could be real and imaginary or +complex number I TR it so in that case I + + align:start position:0% +complex number I TR it so in that case I + + + align:start position:0% +complex number I TR it so in that case I +have if I take a derivative I should + + align:start position:0% +have if I take a derivative I should + + + align:start position:0% +have if I take a derivative I should +have plus that's I and this uh is uh + + align:start position:0% +have plus that's I and this uh is uh + + + align:start position:0% +have plus that's I and this uh is uh +times mass complex conjugate K1 + + align:start position:0% +times mass complex conjugate K1 + + + align:start position:0% +times mass complex conjugate K1 +and exponential plus Omega tus K1 + + align:start position:0% +and exponential plus Omega tus K1 + + + align:start position:0% +and exponential plus Omega tus K1 +X and + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +right so or I have a a I should have a a + + align:start position:0% +right so or I have a a I should have a a + + + align:start position:0% +right so or I have a a I should have a a +here a complex + + align:start position:0% + + + + align:start position:0% + +conjugate + + align:start position:0% +conjugate + + + align:start position:0% +conjugate +okay and uh Min I Omega t plus I Omega t + + align:start position:0% +okay and uh Min I Omega t plus I Omega t + + + align:start position:0% +okay and uh Min I Omega t plus I Omega t +cancel time is not + + align:start position:0% +cancel time is not + + + align:start position:0% +cancel time is not +there right and I K + + align:start position:0% +there right and I K + + + align:start position:0% +there right and I K +k1x uh plus I + + align:start position:0% +k1x uh plus I + + + align:start position:0% +k1x uh plus I +k1x uh oh here I should be complex + + align:start position:0% +k1x uh oh here I should be complex + + + align:start position:0% +k1x uh oh here I should be complex +conjugate in + + align:start position:0% +conjugate in + + + align:start position:0% +conjugate in +general right because I first take a + + align:start position:0% +general right because I first take a + + + align:start position:0% +general right because I first take a +complex conjugator of this + + align:start position:0% +complex conjugator of this + + + align:start position:0% +complex conjugator of this +function and uh uh so in general this + + align:start position:0% +function and uh uh so in general this + + + align:start position:0% +function and uh uh so in general this +one may not be zero because this K1 and + + align:start position:0% +one may not be zero because this K1 and + + + align:start position:0% +one may not be zero because this K1 and +plus complex + + align:start position:0% +plus complex + + + align:start position:0% +plus complex +they may not cancel if it's a imager + + align:start position:0% +they may not cancel if it's a imager + + + align:start position:0% +they may not cancel if it's a imager +number right for my case here because uh + + align:start position:0% +number right for my case here because uh + + + align:start position:0% +number right for my case here because uh +in region + + align:start position:0% + + + + align:start position:0% + +one yo is zero so this one is + + align:start position:0% +one yo is zero so this one is + + + align:start position:0% +one yo is zero so this one is +real doesn't + + align:start position:0% +real doesn't + + + align:start position:0% +real doesn't +matter and also either xal + + align:start position:0% +matter and also either xal + + + align:start position:0% +matter and also either xal +Z right this also goes out so at the end + + align:start position:0% +Z right this also goes out so at the end + + + align:start position:0% +Z right this also goes out so at the end +is J at least I can say at The X zero + + align:start position:0% +is J at least I can say at The X zero + + + align:start position:0% +is J at least I can say at The X zero +you can say this is a a squ a * a + + align:start position:0% +you can say this is a a squ a * a + + + align:start position:0% +you can say this is a a squ a * a +complex conjugate I * I is netive 1 + + align:start position:0% +complex conjugate I * I is netive 1 + + + align:start position:0% +complex conjugate I * I is netive 1 +another + + align:start position:0% +another + + + align:start position:0% +another +negative right so that's a positive so I + + align:start position:0% +negative right so that's a positive so I + + + align:start position:0% +negative right so that's a positive so I +really have this I this I cancel I have + + align:start position:0% +really have this I this I cancel I have + + + align:start position:0% +really have this I this I cancel I have +a MH and K1 so G1 equals h m and + + align:start position:0% +a MH and K1 so G1 equals h m and + + + align:start position:0% +a MH and K1 so G1 equals h m and +K1 a squ + + align:start position:0% + + + + align:start position:0% + +okay so this is my partical flux + + align:start position:0% +okay so this is my partical flux + + + align:start position:0% +okay so this is my partical flux +incident + + align:start position:0% +incident + + + align:start position:0% +incident +flux and uh similarly the reflective + + align:start position:0% +flux and uh similarly the reflective + + + align:start position:0% +flux and uh similarly the reflective +flux is also if you substitute the in + + align:start position:0% +flux is also if you substitute the in + + + align:start position:0% +flux is also if you substitute the in +it's a same is a h K1 m b + + align:start position:0% +it's a same is a h K1 m b + + + align:start position:0% +it's a same is a h K1 m b +square right but the transmitted flux I + + align:start position:0% +square right but the transmitted flux I + + + align:start position:0% +square right but the transmitted flux I +have to be + + align:start position:0% +have to be + + + align:start position:0% +have to be +careful okay the reason I have to be + + align:start position:0% +careful okay the reason I have to be + + + align:start position:0% +careful okay the reason I have to be +careful is you can say my solution If + + align:start position:0% +careful is you can say my solution If + + + align:start position:0% +careful is you can say my solution If +energy is less than y K2 is + + align:start position:0% + + + + align:start position:0% + +imaginary + + align:start position:0% +imaginary + + + align:start position:0% +imaginary +okay so in that case I have to be really + + align:start position:0% +okay so in that case I have to be really + + + align:start position:0% +okay so in that case I have to be really +carrying that real part of + + align:start position:0% +carrying that real part of + + + align:start position:0% +carrying that real part of +K uh two complex conjugate because this + + align:start position:0% +K uh two complex conjugate because this + + + align:start position:0% +K uh two complex conjugate because this +is a complex conjugate K2 and the real + + align:start position:0% +is a complex conjugate K2 and the real + + + align:start position:0% +is a complex conjugate K2 and the real +part of + + align:start position:0% +part of + + + align:start position:0% +part of +that that's where I have to be careful + + align:start position:0% +that that's where I have to be careful + + + align:start position:0% +that that's where I have to be careful +okay so based on this I will Define the + + align:start position:0% +okay so based on this I will Define the + + + align:start position:0% +okay so based on this I will Define the +uh reflectance and + + align:start position:0% + + + + align:start position:0% + +transmittance sometimes I use + + align:start position:0% +transmittance sometimes I use + + + align:start position:0% +transmittance sometimes I use +reflectivity sometimes I use + + align:start position:0% +reflectivity sometimes I use + + + align:start position:0% +reflectivity sometimes I use +reflectance and the difference + + align:start position:0% +reflectance and the difference + + + align:start position:0% +reflectance and the difference +is uh some people most people don't + + align:start position:0% +is uh some people most people don't + + + align:start position:0% +is uh some people most people don't +distinguish + + align:start position:0% +distinguish + + + align:start position:0% +distinguish +it uh reflectivity is is more intrinsic + + align:start position:0% +it uh reflectivity is is more intrinsic + + + align:start position:0% +it uh reflectivity is is more intrinsic +so if you have a most ideal case that's + + align:start position:0% +so if you have a most ideal case that's + + + align:start position:0% +so if you have a most ideal case that's +a intrinsic surface property and + + align:start position:0% +a intrinsic surface property and + + + align:start position:0% +a intrinsic surface property and +reflectance is a extrinsic if your + + align:start position:0% +reflectance is a extrinsic if your + + + align:start position:0% +reflectance is a extrinsic if your +surface become changed or rough then + + align:start position:0% +surface become changed or rough then + + + align:start position:0% +surface become changed or rough then +there's a different value so this is a + + align:start position:0% +there's a different value so this is a + + + align:start position:0% +there's a different value so this is a +uh more rigorous uh way of calling it + + align:start position:0% +uh more rigorous uh way of calling it + + + align:start position:0% +uh more rigorous uh way of calling it +but uh you can most of the time people + + align:start position:0% +but uh you can most of the time people + + + align:start position:0% +but uh you can most of the time people +don't care so + + align:start position:0% +don't care so + + + align:start position:0% +don't care so +reflectivity for here might have a idea + + align:start position:0% +reflectivity for here might have a idea + + + align:start position:0% +reflectivity for here might have a idea +is Jr / Jr + + align:start position:0% +is Jr / Jr + + + align:start position:0% +is Jr / Jr +and because K1 cancel in the same media + + align:start position:0% +and because K1 cancel in the same media + + + align:start position:0% +and because K1 cancel in the same media +so reflected transmitted so it really + + align:start position:0% +so reflected transmitted so it really + + + align:start position:0% +so reflected transmitted so it really +just has is b square over a square and B + + align:start position:0% +just has is b square over a square and B + + + align:start position:0% +just has is b square over a square and B +Square over a square if you say B over a + + align:start position:0% +Square over a square if you say B over a + + + align:start position:0% +Square over a square if you say B over a +so I have K1 - + + align:start position:0% +so I have K1 - + + + align:start position:0% +so I have K1 - +K2 and K1 + K2 + + align:start position:0% + + + + align:start position:0% + +squar so that's the reflectance at the + + align:start position:0% +squar so that's the reflectance at the + + + align:start position:0% +squar so that's the reflectance at the +interface for a part partical wave due + + align:start position:0% +interface for a part partical wave due + + + align:start position:0% +interface for a part partical wave due +to Quantum + + align:start position:0% +to Quantum + + + align:start position:0% +to Quantum +reflection + + align:start position:0% +reflection + + + align:start position:0% +reflection +right and + + align:start position:0% + + + + align:start position:0% + +transmittance or transmittivity + + align:start position:0% + + + + align:start position:0% + +and it's also + + align:start position:0% + + + + align:start position:0% + +transmittance and uh in the transmission + + align:start position:0% +transmittance and uh in the transmission + + + align:start position:0% +transmittance and uh in the transmission +I use uh T equals j t/ j + + align:start position:0% +I use uh T equals j t/ j + + + align:start position:0% +I use uh T equals j t/ j +i and uh here it's different because J + + align:start position:0% +i and uh here it's different because J + + + align:start position:0% +i and uh here it's different because J +transmitted is real part of K2 complex + + align:start position:0% +transmitted is real part of K2 complex + + + align:start position:0% +transmitted is real part of K2 complex +conjugate or K1 is real anyway and uh uh + + align:start position:0% +conjugate or K1 is real anyway and uh uh + + + align:start position:0% +conjugate or K1 is real anyway and uh uh +uh here I have uh + + align:start position:0% +uh here I have uh + + + align:start position:0% +uh here I have uh +C squar over a + + align:start position:0% +C squar over a + + + align:start position:0% +C squar over a +square and this is a real part of + + align:start position:0% +square and this is a real part of + + + align:start position:0% +square and this is a real part of +K2 uh complex conjugate K1 and C square + + align:start position:0% +K2 uh complex conjugate K1 and C square + + + align:start position:0% +K2 uh complex conjugate K1 and C square +or a square uh you can say it is k1 + K2 + + align:start position:0% +or a square uh you can say it is k1 + K2 + + + align:start position:0% +or a square uh you can say it is k1 + K2 +and 2 + + align:start position:0% +and 2 + + + align:start position:0% +and 2 +K1 + + align:start position:0% +K1 + + + align:start position:0% +K1 +squar + + align:start position:0% +squar + + + align:start position:0% +squar +right that's my transmittance + + align:start position:0% + + + + align:start position:0% + +okay now because I carry this real + + align:start position:0% +okay now because I carry this real + + + align:start position:0% +okay now because I carry this real +part right I should really look at the + + align:start position:0% +part right I should really look at the + + + align:start position:0% +part right I should really look at the +scenario different scenario when energy + + align:start position:0% +scenario different scenario when energy + + + align:start position:0% +scenario different scenario when energy +is larger than + + align:start position:0% +is larger than + + + align:start position:0% +is larger than +U If energy is larger than y K2 is comp + + align:start position:0% +U If energy is larger than y K2 is comp + + + align:start position:0% +U If energy is larger than y K2 is comp +uh K2 if you look at the + + align:start position:0% +uh K2 if you look at the + + + align:start position:0% +uh K2 if you look at the +K2 is 2 m e o that's + + align:start position:0% +K2 is 2 m e o that's + + + align:start position:0% +K2 is 2 m e o that's +real right the energy of the electron is + + align:start position:0% +real right the energy of the electron is + + + align:start position:0% +real right the energy of the electron is +is larger than the barrier height that's + + align:start position:0% +is larger than the barrier height that's + + + align:start position:0% +is larger than the barrier height that's +real okay and in that case real so it's + + align:start position:0% +real okay and in that case real so it's + + + align:start position:0% +real okay and in that case real so it's +I can forget about this you can see this + + align:start position:0% +I can forget about this you can see this + + + align:start position:0% +I can forget about this you can see this +becomes a 4 K1 * K2 / K1 + K2 + + align:start position:0% +becomes a 4 K1 * K2 / K1 + K2 + + + align:start position:0% +becomes a 4 K1 * K2 / K1 + K2 +squ okay so in this case I have t uh is + + align:start position:0% +squ okay so in this case I have t uh is + + + align:start position:0% +squ okay so in this case I have t uh is +not zero but it's say R is not + + align:start position:0% +not zero but it's say R is not + + + align:start position:0% +not zero but it's say R is not +one right + + align:start position:0% +one right + + + align:start position:0% +one right +I have quer reflection even I through a + + align:start position:0% +I have quer reflection even I through a + + + align:start position:0% +I have quer reflection even I through a +electron even even you normally thinkle + + align:start position:0% +electron even even you normally thinkle + + + align:start position:0% +electron even even you normally thinkle +electron as a particle when it comes to + + align:start position:0% +electron as a particle when it comes to + + + align:start position:0% +electron as a particle when it comes to +a interface it has + + align:start position:0% +a interface it has + + + align:start position:0% +a interface it has +reflection right even if the energy is + + align:start position:0% +reflection right even if the energy is + + + align:start position:0% +reflection right even if the energy is +higher than the barrier height so now + + align:start position:0% +higher than the barrier height so now + + + align:start position:0% +higher than the barrier height so now +just say next time you through a wall + + align:start position:0% +just say next time you through a wall + + + align:start position:0% +just say next time you through a wall +through a ball over the wall there's a + + align:start position:0% +through a ball over the wall there's a + + + align:start position:0% +through a ball over the wall there's a +final probability bounce back even you + + align:start position:0% +final probability bounce back even you + + + align:start position:0% +final probability bounce back even you +through the higher than the W it's + + align:start position:0% +through the higher than the W it's + + + align:start position:0% +through the higher than the W it's +Quantum word + + align:start position:0% +Quantum word + + + align:start position:0% +Quantum word +right okay + + align:start position:0% +right okay + + + align:start position:0% +right okay +and uh uh so that's your first uh uh uh + + align:start position:0% +and uh uh so that's your first uh uh uh + + + align:start position:0% +and uh uh so that's your first uh uh uh +case and your second + + align:start position:0% +case and your second + + + align:start position:0% +case and your second +case is e less than + + align:start position:0% + + + + align:start position:0% + +o right is less than y if you look at + + align:start position:0% +o right is less than y if you look at + + + align:start position:0% +o right is less than y if you look at +the here your K2 is + + align:start position:0% +the here your K2 is + + + align:start position:0% +the here your K2 is +imaginary right K2 is + + align:start position:0% +imaginary right K2 is + + + align:start position:0% +imaginary right K2 is +imaginary and the real part that's zero + + align:start position:0% +imaginary and the real part that's zero + + + align:start position:0% +imaginary and the real part that's zero +so if the energy of the electron is less + + align:start position:0% +so if the energy of the electron is less + + + align:start position:0% +so if the energy of the electron is less +than the barrial height U your + + align:start position:0% +than the barrial height U your + + + align:start position:0% +than the barrial height U your +transmittance is + + align:start position:0% +transmittance is + + + align:start position:0% +transmittance is +zero and your reflectance if you plug in + + align:start position:0% +zero and your reflectance if you plug in + + + align:start position:0% +zero and your reflectance if you plug in +here this is real this is imagin this is + + align:start position:0% +here this is real this is imagin this is + + + align:start position:0% +here this is real this is imagin this is +real this imagin the modulus is + + align:start position:0% +real this imagin the modulus is + + + align:start position:0% +real this imagin the modulus is +one right so reflectance is + + align:start position:0% +one right so reflectance is + + + align:start position:0% +one right so reflectance is +one so the particle is all reflected + + align:start position:0% +one so the particle is all reflected + + + align:start position:0% +one so the particle is all reflected +it's expected right you through a ball + + align:start position:0% +it's expected right you through a ball + + + align:start position:0% +it's expected right you through a ball +on below the wall + + align:start position:0% +on below the wall + + + align:start position:0% +on below the wall +the parer the the the B bounce + + align:start position:0% +the parer the the the B bounce + + + align:start position:0% +the parer the the the B bounce +back but there are still something + + align:start position:0% +back but there are still something + + + align:start position:0% +back but there are still something +special okay you look at the other side + + align:start position:0% +special okay you look at the other side + + + align:start position:0% +special okay you look at the other side +of wall the ball the + + align:start position:0% +of wall the ball the + + + align:start position:0% +of wall the ball the +wall there is a finet wave of the wall + + align:start position:0% +wall there is a finet wave of the wall + + + align:start position:0% +wall there is a finet wave of the wall +of the + + align:start position:0% +of the + + + align:start position:0% +of the +ball right that's because if you look at + + align:start position:0% +ball right that's because if you look at + + + align:start position:0% +ball right that's because if you look at +the transmitt so also the transmitt + + align:start position:0% +the transmitt so also the transmitt + + + align:start position:0% +the transmitt so also the transmitt +there's no real particle go through the + + align:start position:0% +there's no real particle go through the + + + align:start position:0% +there's no real particle go through the +wall the barrier right but the wave is + + align:start position:0% +wall the barrier right but the wave is + + + align:start position:0% +wall the barrier right but the wave is +not zero because here this my wave 5 t m + + align:start position:0% +not zero because here this my wave 5 t m + + + align:start position:0% +not zero because here this my wave 5 t m +Omega T K2 is imaginary + + align:start position:0% +Omega T K2 is imaginary + + + align:start position:0% +Omega T K2 is imaginary +right K2 is imaginary so imagin times + + align:start position:0% +right K2 is imaginary so imagin times + + + align:start position:0% +right K2 is imaginary so imagin times +imaginary + + align:start position:0% +imaginary + + + align:start position:0% +imaginary +real it's a negative real so it's + + align:start position:0% +real it's a negative real so it's + + + align:start position:0% +real it's a negative real so it's +negative exponential decay + + align:start position:0% +negative exponential decay + + + align:start position:0% +negative exponential decay +function so in this case what I have is + + align:start position:0% +function so in this case what I have is + + + align:start position:0% +function so in this case what I have is +this is the + + align:start position:0% +this is the + + + align:start position:0% +this is the +uh a ball coming the particle comes in + + align:start position:0% +uh a ball coming the particle comes in + + + align:start position:0% +uh a ball coming the particle comes in +and there is a fin of the wave on the + + align:start position:0% +and there is a fin of the wave on the + + + align:start position:0% +and there is a fin of the wave on the +other side of the + + align:start position:0% + + + + align:start position:0% + +interface the time the average speed can + + align:start position:0% +interface the time the average speed can + + + align:start position:0% +interface the time the average speed can +there's no particle going to the other + + align:start position:0% +there's no particle going to the other + + + align:start position:0% +there's no particle going to the other +side but way function is not zero on the + + align:start position:0% +side but way function is not zero on the + + + align:start position:0% +side but way function is not zero on the +other + + align:start position:0% +other + + + align:start position:0% +other +side right and this wave is called + + align:start position:0% +side right and this wave is called + + + align:start position:0% +side right and this wave is called +evesson + + align:start position:0% + + + + align:start position:0% + +wave even Lent + + align:start position:0% + + + + align:start position:0% + +okay and + + align:start position:0% + + + + align:start position:0% + +uh now What's the + + align:start position:0% + + + + align:start position:0% + +magnitude of + + align:start position:0% + + + + align:start position:0% + +this right so if you look at your decay + + align:start position:0% +this right so if you look at your decay + + + align:start position:0% +this right so if you look at your decay +of this eveson + + align:start position:0% + + + + align:start position:0% + +wave if you look at decay of Evol wave + + align:start position:0% +wave if you look at decay of Evol wave + + + align:start position:0% +wave if you look at decay of Evol wave +is really the magnitude of the e u 2 MH + + align:start position:0% +is really the magnitude of the e u 2 MH + + + align:start position:0% +is really the magnitude of the e u 2 MH +Square that's the square root this is + + align:start position:0% +Square that's the square root this is + + + align:start position:0% +Square that's the square root this is +really the magnitude so what I have here + + align:start position:0% +really the magnitude so what I have here + + + align:start position:0% +really the magnitude so what I have here +the ma the magnitude of K is 2 m uh + + align:start position:0% +the ma the magnitude of K is 2 m uh + + + align:start position:0% +the ma the magnitude of K is 2 m uh +really e minus + + align:start position:0% +really e minus + + + align:start position:0% +really e minus +U and H bar squar that's by we uh the K2 + + align:start position:0% +U and H bar squar that's by we uh the K2 + + + align:start position:0% +U and H bar squar that's by we uh the K2 +that's the + + align:start position:0% +that's the + + + align:start position:0% +that's the +Decay right or U must + + align:start position:0% +Decay right or U must + + + align:start position:0% +Decay right or U must +e right so if I look at the electron U + + align:start position:0% +e right so if I look at the electron U + + + align:start position:0% +e right so if I look at the electron U +Mass E let's say take one one electron + + align:start position:0% +Mass E let's say take one one electron + + + align:start position:0% +Mass E let's say take one one electron +volt so the energy so what's the order + + align:start position:0% +volt so the energy so what's the order + + + align:start position:0% +volt so the energy so what's the order +magnitude is 2 * 9.1 10us + + align:start position:0% +magnitude is 2 * 9.1 10us + + + align:start position:0% +magnitude is 2 * 9.1 10us +31 and uh electron volts one electron + + align:start position:0% +31 and uh electron volts one electron + + + align:start position:0% +31 and uh electron volts one electron +volt is uh uh + + align:start position:0% +volt is uh uh + + + align:start position:0% +volt is uh uh +1.6 10 to the + + align:start position:0% +1.6 10 to the + + + align:start position:0% +1.6 10 to the +19 and uh H bar Square H bar is a uh 1 + + align:start position:0% +19 and uh H bar Square H bar is a uh 1 + + + align:start position:0% +19 and uh H bar Square H bar is a uh 1 +10 the 34 so + + align:start position:0% +10 the 34 so + + + align:start position:0% +10 the 34 so +68 right so this one 31 19 gives me + + align:start position:0% +68 right so this one 31 19 gives me + + + align:start position:0% +68 right so this one 31 19 gives me + + align:start position:0% + + + align:start position:0% +right and uh uh this gives me 68 so + + align:start position:0% +right and uh uh this gives me 68 so + + + align:start position:0% +right and uh uh this gives me 68 so +that's + + align:start position:0% +that's + + + align:start position:0% +that's +18 18 square root is of the order of + + align:start position:0% +18 18 square root is of the order of + + + align:start position:0% +18 18 square root is of the order of +line right and the rest is okay here + + align:start position:0% +line right and the rest is okay here + + + align:start position:0% +line right and the rest is okay here +maybe I have five order of line inverse + + align:start position:0% +maybe I have five order of line inverse + + + align:start position:0% +maybe I have five order of line inverse +meter + + align:start position:0% + + + + align:start position:0% + +okay so that's the magnitude of this + + align:start position:0% +okay so that's the magnitude of this + + + align:start position:0% +okay so that's the magnitude of this +wave extend if it's electron into the + + align:start position:0% +wave extend if it's electron into the + + + align:start position:0% +wave extend if it's electron into the +other side is of the order inverse of + + align:start position:0% +other side is of the order inverse of + + + align:start position:0% +other side is of the order inverse of +that gives me what two UNR + + align:start position:0% +that gives me what two UNR + + + align:start position:0% +that gives me what two UNR +strongs + + align:start position:0% +strongs + + + align:start position:0% +strongs +right so it's a Eves rapidly Decay + + align:start position:0% +right so it's a Eves rapidly Decay + + + align:start position:0% +right so it's a Eves rapidly Decay +exponential rapid Decay wave on the + + align:start position:0% +exponential rapid Decay wave on the + + + align:start position:0% +exponential rapid Decay wave on the +other side say who cares to + + align:start position:0% +other side say who cares to + + + align:start position:0% +other side say who cares to +unon right + + align:start position:0% +unon right + + + align:start position:0% +unon right +but let me tell the + + align:start position:0% +but let me tell the + + + align:start position:0% +but let me tell the +story so um there was this guy um he + + align:start position:0% +story so um there was this guy um he + + + align:start position:0% +story so um there was this guy um he +just finished his PhD and uh went to job + + align:start position:0% +just finished his PhD and uh went to job + + + align:start position:0% +just finished his PhD and uh went to job +interview at IBM + + align:start position:0% +interview at IBM + + + align:start position:0% +interview at IBM +Zurich and uh uh his name is + + align:start position:0% +Zurich and uh uh his name is + + + align:start position:0% +Zurich and uh uh his name is +Benish and the interviewer um uh asked + + align:start position:0% +Benish and the interviewer um uh asked + + + align:start position:0% +Benish and the interviewer um uh asked +him say they want to measure the surface + + align:start position:0% +him say they want to measure the surface + + + align:start position:0% +him say they want to measure the surface +roughness of say uh uh to very High + + align:start position:0% +roughness of say uh uh to very High + + + align:start position:0% +roughness of say uh uh to very High +Precision asking him whether he had + + align:start position:0% +Precision asking him whether he had + + + align:start position:0% +Precision asking him whether he had +ideas or + + align:start position:0% +ideas or + + + align:start position:0% +ideas or +not and uh he thought about this and + + align:start position:0% +not and uh he thought about this and + + + align:start position:0% +not and uh he thought about this and +came up with the idea that's using uh + + align:start position:0% +came up with the idea that's using uh + + + align:start position:0% +came up with the idea that's using uh +metal + + align:start position:0% +metal + + + align:start position:0% +metal +tip and this is a metal + + align:start position:0% +tip and this is a metal + + + align:start position:0% +tip and this is a metal +surface + + align:start position:0% +surface + + + align:start position:0% +surface +right and he put a bias so vacuum here + + align:start position:0% +right and he put a bias so vacuum here + + + align:start position:0% +right and he put a bias so vacuum here +there's the energy level that's you read + + align:start position:0% +there's the energy level that's you read + + + align:start position:0% +there's the energy level that's you read +the Einstein work + + align:start position:0% +the Einstein work + + + align:start position:0% +the Einstein work +function oh maybe you didn't read the + + align:start position:0% +function oh maybe you didn't read the + + + align:start position:0% +function oh maybe you didn't read the +you read the the leure the wave leure + + align:start position:0% +you read the the leure the wave leure + + + align:start position:0% +you read the the leure the wave leure +the particle L of light but say there is + + align:start position:0% +the particle L of light but say there is + + + align:start position:0% +the particle L of light but say there is +a few electron volts Gap here the + + align:start position:0% +a few electron volts Gap here the + + + align:start position:0% +a few electron volts Gap here the +barrier vacuum right work function of + + align:start position:0% +barrier vacuum right work function of + + + align:start position:0% +barrier vacuum right work function of +metal so here is a few electron + + align:start position:0% +metal so here is a few electron + + + align:start position:0% +metal so here is a few electron +volts and he say if you bias it with the + + align:start position:0% +volts and he say if you bias it with the + + + align:start position:0% +volts and he say if you bias it with the +voltage right the electron exponential + + align:start position:0% +voltage right the electron exponential + + + align:start position:0% +voltage right the electron exponential +decay but once they me the other metal + + align:start position:0% +decay but once they me the other metal + + + align:start position:0% +decay but once they me the other metal +become alive again we we'll talk about + + align:start position:0% +become alive again we we'll talk about + + + align:start position:0% +become alive again we we'll talk about +that that's a tunneling of this evolent + + align:start position:0% +that that's a tunneling of this evolent + + + align:start position:0% +that that's a tunneling of this evolent +wave and it's a very sensitive to atomic + + align:start position:0% +wave and it's a very sensitive to atomic + + + align:start position:0% +wave and it's a very sensitive to atomic +scale bumpy bumpless right because this + + align:start position:0% +scale bumpy bumpless right because this + + + align:start position:0% +scale bumpy bumpless right because this +unstr strong level + + align:start position:0% +unstr strong level + + + align:start position:0% +unstr strong level +exponential so with that you can + + align:start position:0% +exponential so with that you can + + + align:start position:0% +exponential so with that you can +measure to this the principle of + + align:start position:0% +measure to this the principle of + + + align:start position:0% +measure to this the principle of +scanning T microscope you really can + + align:start position:0% +scanning T microscope you really can + + + align:start position:0% +scanning T microscope you really can +measure the electron wave function on + + align:start position:0% +measure the electron wave function on + + + align:start position:0% +measure the electron wave function on +the + + align:start position:0% +the + + + align:start position:0% +the +surface so you can actually image + + align:start position:0% +surface so you can actually image + + + align:start position:0% +surface so you can actually image +atoms so he got a lber price for + + align:start position:0% +atoms so he got a lber price for + + + align:start position:0% +atoms so he got a lber price for +that okay hopefully you'll get a chance + + align:start position:0% +that okay hopefully you'll get a chance + + + align:start position:0% +that okay hopefully you'll get a chance +when you have an interview like that + + align:start position:0% +when you have an interview like that + + + align:start position:0% +when you have an interview like that +you have to think have to be able to + + align:start position:0% +you have to think have to be able to + + + align:start position:0% +you have to think have to be able to +come up with the idea right so uh that's + + align:start position:0% +come up with the idea right so uh that's + + + align:start position:0% +come up with the idea right so uh that's +the the quantum word it's going uper + + align:start position:0% +the the quantum word it's going uper + + + align:start position:0% +the the quantum word it's going uper +here now you reverse + + align:start position:0% +here now you reverse + + + align:start position:0% +here now you reverse +it you say what if my electron is going + + align:start position:0% +it you say what if my electron is going + + + align:start position:0% +it you say what if my electron is going +backwards from here to + + align:start position:0% +backwards from here to + + + align:start position:0% +backwards from here to +here is there + + align:start position:0% + + + + align:start position:0% + +reflection you look at the derivation + + align:start position:0% +reflection you look at the derivation + + + align:start position:0% +reflection you look at the derivation +there's no + + align:start position:0% +there's no + + + align:start position:0% +there's no +difference even you go downhill even if + + align:start position:0% +difference even you go downhill even if + + + align:start position:0% +difference even you go downhill even if +you not go barrier you go a step down + + align:start position:0% +you not go barrier you go a step down + + + align:start position:0% +you not go barrier you go a step down +you still have + + align:start position:0% +you still have + + + align:start position:0% +you still have +reflection right you have + + align:start position:0% +reflection right you have + + + align:start position:0% +reflection right you have +discontinuity in potential you have + + align:start position:0% +discontinuity in potential you have + + + align:start position:0% +discontinuity in potential you have +reflection + + align:start position:0% +reflection + + + align:start position:0% +reflection +there + + align:start position:0% +there + + + align:start position:0% +there +okay so uh this is the in fact this is L + + align:start position:0% +okay so uh this is the in fact this is L + + + align:start position:0% +okay so uh this is the in fact this is L +incidence right + + align:start position:0% +incidence right + + + align:start position:0% +incidence right +and uh when you consider actually + + align:start position:0% +and uh when you consider actually + + + align:start position:0% +and uh when you consider actually +electrical interface resistance for + + align:start position:0% +electrical interface resistance for + + + align:start position:0% +electrical interface resistance for +example right electron can actually come + + align:start position:0% +example right electron can actually come + + + align:start position:0% +example right electron can actually come +to interface lar as a normal it can come + + align:start position:0% +to interface lar as a normal it can come + + + align:start position:0% +to interface lar as a normal it can come +all + + align:start position:0% + + + + align:start position:0% + +directions and uh you should be able to + + align:start position:0% +directions and uh you should be able to + + + align:start position:0% +directions and uh you should be able to +sit there and do any angle in + + align:start position:0% +sit there and do any angle in + + + align:start position:0% +sit there and do any angle in +incidence right in fact I check a lot of + + align:start position:0% +incidence right in fact I check a lot of + + + align:start position:0% +incidence right in fact I check a lot of +electrical engineer book nobody even did + + align:start position:0% +electrical engineer book nobody even did + + + align:start position:0% +electrical engineer book nobody even did +that I was + + align:start position:0% +that I was + + + align:start position:0% +that I was +surprised okay if you're electric + + align:start position:0% +surprised okay if you're electric + + + align:start position:0% +surprised okay if you're electric +engineer you should do + + align:start position:0% +engineer you should do + + + align:start position:0% +engineer you should do +this + + align:start position:0% +this + + + align:start position:0% +this +okay so this is a uh for electron wave + + align:start position:0% +okay so this is a uh for electron wave + + + align:start position:0% +okay so this is a uh for electron wave +and uh now let's go we say this is + + align:start position:0% +and uh now let's go we say this is + + + align:start position:0% +and uh now let's go we say this is +scalar uh uh Wave It's easiest and let's + + align:start position:0% +scalar uh uh Wave It's easiest and let's + + + align:start position:0% +scalar uh uh Wave It's easiest and let's +go to more + + align:start position:0% +go to more + + + align:start position:0% +go to more +complicated and uh let's look at the + + align:start position:0% +complicated and uh let's look at the + + + align:start position:0% +complicated and uh let's look at the +vector + + align:start position:0% + + + + align:start position:0% + +wave and + + align:start position:0% +wave and + + + align:start position:0% +wave and +uh and Vector wave the less complicated + + align:start position:0% +uh and Vector wave the less complicated + + + align:start position:0% +uh and Vector wave the less complicated +Vector waves is electromagnetic + + align:start position:0% +Vector waves is electromagnetic + + + align:start position:0% +Vector waves is electromagnetic +wave right EM + + align:start position:0% +wave right EM + + + align:start position:0% +wave right EM +waves it's a quite big leap from a + + align:start position:0% +waves it's a quite big leap from a + + + align:start position:0% +waves it's a quite big leap from a +shinger equation which is scalar + + align:start position:0% +shinger equation which is scalar + + + align:start position:0% +shinger equation which is scalar +equation which is a by no means easy to + + align:start position:0% +equation which is a by no means easy to + + + align:start position:0% +equation which is a by no means easy to +solve you got a mulle electrons you + + align:start position:0% +solve you got a mulle electrons you + + + align:start position:0% +solve you got a mulle electrons you +there actually no good tool to solve + + align:start position:0% +there actually no good tool to solve + + + align:start position:0% +there actually no good tool to solve +that right now if you even if you have + + align:start position:0% +that right now if you even if you have + + + align:start position:0% +that right now if you even if you have +two or three electrons their Mutual + + align:start position:0% +two or three electrons their Mutual + + + align:start position:0% +two or three electrons their Mutual +interaction becomes very difficult to + + align:start position:0% +interaction becomes very difficult to + + + align:start position:0% +interaction becomes very difficult to +solve and that's man in body problem but + + align:start position:0% +solve and that's man in body problem but + + + align:start position:0% +solve and that's man in body problem but +say uh let's go to do EM waves and for + + align:start position:0% +say uh let's go to do EM waves and for + + + align:start position:0% +say uh let's go to do EM waves and for +that you have to go to Max + + align:start position:0% +that you have to go to Max + + + align:start position:0% +that you have to go to Max +equations right and uh uh even you + + align:start position:0% +equations right and uh uh even you + + + align:start position:0% +equations right and uh uh even you +forgot it but you heard about it so + + align:start position:0% +forgot it but you heard about it so + + + align:start position:0% +forgot it but you heard about it so +let's uh write rewrite the max + + align:start position:0% + + + + align:start position:0% + +equations and uh uh we have four + + align:start position:0% +equations and uh uh we have four + + + align:start position:0% +equations and uh uh we have four +equations e h min + + align:start position:0% +equations e h min + + + align:start position:0% +equations e h min +time + + align:start position:0% + + + + align:start position:0% + +derivative say the cross e and cross H + + align:start position:0% +derivative say the cross e and cross H + + + align:start position:0% +derivative say the cross e and cross H +is + + align:start position:0% +is + + + align:start position:0% +is +D DT plus the + + align:start position:0% +D DT plus the + + + align:start position:0% +D DT plus the +current and we have then + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% + + + + align:start position:0% + +um Divergence of the displacement field + + align:start position:0% +um Divergence of the displacement field + + + align:start position:0% +um Divergence of the displacement field +equals the charge density + + align:start position:0% +equals the charge density + + + align:start position:0% +equals the charge density +and magnetic diver magnetic induction is + + align:start position:0% +and magnetic diver magnetic induction is + + + align:start position:0% +and magnetic diver magnetic induction is +zero and uh uh just uh to review this is + + align:start position:0% +zero and uh uh just uh to review this is + + + align:start position:0% +zero and uh uh just uh to review this is +a uh essentially what the first equation + + align:start position:0% +a uh essentially what the first equation + + + align:start position:0% +a uh essentially what the first equation +say if you're changing magnetic field + + align:start position:0% +say if you're changing magnetic field + + + align:start position:0% +say if you're changing magnetic field +you have a generate electric field the + + align:start position:0% +you have a generate electric field the + + + align:start position:0% +you have a generate electric field the +second if you pass current through a + + align:start position:0% +second if you pass current through a + + + align:start position:0% +second if you pass current through a +coil right you generate magnetic + + align:start position:0% +coil right you generate magnetic + + + align:start position:0% +coil right you generate magnetic +field and uh this is the FR law this is + + align:start position:0% +field and uh this is the FR law this is + + + align:start position:0% +field and uh this is the FR law this is +more like and + + align:start position:0% +more like and + + + align:start position:0% +more like and +personal right some of the high school + + align:start position:0% +personal right some of the high school + + + align:start position:0% +personal right some of the high school +experiment and Maxwell only added one + + align:start position:0% + + + + align:start position:0% + +term and he got all the + + align:start position:0% +term and he got all the + + + align:start position:0% +term and he got all the +credit okay so uh uh what we have here + + align:start position:0% +credit okay so uh uh what we have here + + + align:start position:0% +credit okay so uh uh what we have here +e is the electrical + + align:start position:0% +e is the electrical + + + align:start position:0% +e is the electrical +field right the electric field uh is the + + align:start position:0% +field right the electric field uh is the + + + align:start position:0% +field right the electric field uh is the +gradient + + align:start position:0% +gradient + + + align:start position:0% +gradient +of electrostatic + + align:start position:0% +of electrostatic + + + align:start position:0% +of electrostatic +potential and so the unit is volt + + align:start position:0% + + + + align:start position:0% + +meter right and uh uh um uh H is a + + align:start position:0% +meter right and uh uh um uh H is a + + + align:start position:0% +meter right and uh uh um uh H is a +magnetic + + align:start position:0% +magnetic + + + align:start position:0% +magnetic +field and sometimes I don't remember the + + align:start position:0% +field and sometimes I don't remember the + + + align:start position:0% +field and sometimes I don't remember the +unit so I go back to think of this + + align:start position:0% +unit so I go back to think of this + + + align:start position:0% +unit so I go back to think of this +current density I + + align:start position:0% +current density I + + + align:start position:0% +current density I +know right current density is here is m + + align:start position:0% +know right current density is here is m + + + align:start position:0% +know right current density is here is m +per met + + align:start position:0% +per met + + + align:start position:0% +per met +Square so here is say times 1 meter that + + align:start position:0% +Square so here is say times 1 meter that + + + align:start position:0% +Square so here is say times 1 meter that +gives me magnetic field is M + + align:start position:0% +gives me magnetic field is M + + + align:start position:0% +gives me magnetic field is M +meter right so magnetic field is m per + + align:start position:0% + + + + align:start position:0% + +meter and uh + + align:start position:0% +meter and uh + + + align:start position:0% +meter and uh +D is the electrical + + align:start position:0% + + + + align:start position:0% + +displacement displacement + + align:start position:0% + + + + align:start position:0% + +and uh uh what it what it means is uh if + + align:start position:0% +and uh uh what it what it means is uh if + + + align:start position:0% +and uh uh what it what it means is uh if +you have a + + align:start position:0% +you have a + + + align:start position:0% +you have a +material right you have atoms atoms as + + align:start position:0% +material right you have atoms atoms as + + + align:start position:0% +material right you have atoms atoms as +electrons ions right if you have a + + align:start position:0% +electrons ions right if you have a + + + align:start position:0% +electrons ions right if you have a +electric field comes in you know that + + align:start position:0% +electric field comes in you know that + + + align:start position:0% +electric field comes in you know that +they will get + + align:start position:0% +they will get + + + align:start position:0% +they will get +polarized right positive charge has a + + align:start position:0% +polarized right positive charge has a + + + align:start position:0% +polarized right positive charge has a +force along the field Direction negative + + align:start position:0% +force along the field Direction negative + + + align:start position:0% +force along the field Direction negative +charge opposite field direction right so + + align:start position:0% +charge opposite field direction right so + + + align:start position:0% +charge opposite field direction right so +that means they will have a dipole so + + align:start position:0% +that means they will have a dipole so + + + align:start position:0% +that means they will have a dipole so +you'll have in this case you have more + + align:start position:0% +you'll have in this case you have more + + + align:start position:0% +you'll have in this case you have more +like a dipole here is positive here is + + align:start position:0% +like a dipole here is positive here is + + + align:start position:0% +like a dipole here is positive here is +negative okay right so + + align:start position:0% +negative okay right so + + + align:start position:0% +negative okay right so +D is the uh polarization per unit + + align:start position:0% +D is the uh polarization per unit + + + align:start position:0% +D is the uh polarization per unit +volume dipole moment per unit + + align:start position:0% +volume dipole moment per unit + + + align:start position:0% +volume dipole moment per unit +volume and plus the if you + + align:start position:0% +volume and plus the if you + + + align:start position:0% +volume and plus the if you +have uh + + align:start position:0% +have uh + + + align:start position:0% +have uh +original field comes in converted into + + align:start position:0% +original field comes in converted into + + + align:start position:0% +original field comes in converted into +the same + + align:start position:0% +the same + + + align:start position:0% +the same +unit right so that's a epsilon0 that's a + + align:start position:0% +unit right so that's a epsilon0 that's a + + + align:start position:0% +unit right so that's a epsilon0 that's a +vacuum plus uh the uh polarization per + + align:start position:0% +vacuum plus uh the uh polarization per + + + align:start position:0% +vacuum plus uh the uh polarization per +unit uh the the dipole moment per unit + + align:start position:0% +unit uh the the dipole moment per unit + + + align:start position:0% +unit uh the the dipole moment per unit +volume so dipole moment is uh the dipole + + align:start position:0% +volume so dipole moment is uh the dipole + + + align:start position:0% +volume so dipole moment is uh the dipole +moment is the charge times meter and per + + align:start position:0% +moment is the charge times meter and per + + + align:start position:0% +moment is the charge times meter and per +unit volume is cubic right so the unit + + align:start position:0% +unit volume is cubic right so the unit + + + align:start position:0% +unit volume is cubic right so the unit +here is Kon per meter Square + + align:start position:0% + + + + align:start position:0% + +okay and from colum per meter Square + + align:start position:0% +okay and from colum per meter Square + + + align:start position:0% +okay and from colum per meter Square +this isum per meter Square you find the + + align:start position:0% +this isum per meter Square you find the + + + align:start position:0% +this isum per meter Square you find the +Epsilon Z that's the vacuum uh per + + align:start position:0% +Epsilon Z that's the vacuum uh per + + + align:start position:0% +Epsilon Z that's the vacuum uh per +permitivity I will say permeability + + align:start position:0% +permitivity I will say permeability + + + align:start position:0% +permitivity I will say permeability +permitivity + + align:start position:0% +permitivity + + + align:start position:0% +permitivity +uh per uh permitivity + + align:start position:0% +uh per uh permitivity + + + align:start position:0% +uh per uh permitivity +epsilon0 is 8.8 10us 12 and uh uh here + + align:start position:0% +epsilon0 is 8.8 10us 12 and uh uh here + + + align:start position:0% +epsilon0 is 8.8 10us 12 and uh uh here +is a should be Kum Epsilon here uh is a + + align:start position:0% +is a should be Kum Epsilon here uh is a + + + align:start position:0% +is a should be Kum Epsilon here uh is a +far per + + align:start position:0% +far per + + + align:start position:0% +far per +meter + + align:start position:0% +meter + + + align:start position:0% +meter +okay so I have this one is a far per + + align:start position:0% +okay so I have this one is a far per + + + align:start position:0% +okay so I have this one is a far per +meter okay so I have the uh this is a uh + + align:start position:0% +meter okay so I have the uh this is a uh + + + align:start position:0% +meter okay so I have the uh this is a uh +D here the dis displacement + + align:start position:0% +D here the dis displacement + + + align:start position:0% +D here the dis displacement +field I said that this is the one uh uh + + align:start position:0% +field I said that this is the one uh uh + + + align:start position:0% +field I said that this is the one uh uh +external field create a dipole right in + + align:start position:0% +external field create a dipole right in + + + align:start position:0% +external field create a dipole right in +a real solid it's not that simple + + align:start position:0% +a real solid it's not that simple + + + align:start position:0% +a real solid it's not that simple +because you have atom here you have + + align:start position:0% +because you have atom here you have + + + align:start position:0% +because you have atom here you have +another atom here right you have + + align:start position:0% +another atom here right you have + + + align:start position:0% +another atom here right you have +adjacent + + align:start position:0% +adjacent + + + align:start position:0% +adjacent +atoms and not only the outside field but + + align:start position:0% +atoms and not only the outside field but + + + align:start position:0% +atoms and not only the outside field but +also the Le labor the dipole itself will + + align:start position:0% +also the Le labor the dipole itself will + + + align:start position:0% +also the Le labor the dipole itself will +affect my the atom itself so it's + + align:start position:0% +affect my the atom itself so it's + + + align:start position:0% +affect my the atom itself so it's +actually a summation of all this + + align:start position:0% +actually a summation of all this + + + align:start position:0% +actually a summation of all this +effect okay and this one for this is a + + align:start position:0% +effect okay and this one for this is a + + + align:start position:0% +effect okay and this one for this is a +nonmovable charge + + align:start position:0% +nonmovable charge + + + align:start position:0% +nonmovable charge +this is the charge attached to the + + align:start position:0% +this is the charge attached to the + + + align:start position:0% +this is the charge attached to the +atom okay that's dialectric right so uh + + align:start position:0% +atom okay that's dialectric right so uh + + + align:start position:0% +atom okay that's dialectric right so uh +we sometimes write Epsilon Epsilon R and + + align:start position:0% +we sometimes write Epsilon Epsilon R and + + + align:start position:0% +we sometimes write Epsilon Epsilon R and +time e or this combined together gives + + align:start position:0% +time e or this combined together gives + + + align:start position:0% +time e or this combined together gives +me another Epsilon that's dialectric + + align:start position:0% +me another Epsilon that's dialectric + + + align:start position:0% +me another Epsilon that's dialectric +function of the + + align:start position:0% +function of the + + + align:start position:0% +function of the +material it's not a constant sometimes + + align:start position:0% +material it's not a constant sometimes + + + align:start position:0% +material it's not a constant sometimes +we call dialectric constant it's not a + + align:start position:0% +we call dialectric constant it's not a + + + align:start position:0% +we call dialectric constant it's not a +constant it's a function of walence it's + + align:start position:0% +constant it's a function of walence it's + + + align:start position:0% +constant it's a function of walence it's +a function of + + align:start position:0% + + + + align:start position:0% + +frequency + + align:start position:0% +frequency + + + align:start position:0% +frequency +okay so uh that's the + + align:start position:0% +okay so uh that's the + + + align:start position:0% +okay so uh that's the +displacement and similarly magnetic + + align:start position:0% +displacement and similarly magnetic + + + align:start position:0% +displacement and similarly magnetic +induction B you can write as a Epsilon + + align:start position:0% +induction B you can write as a Epsilon + + + align:start position:0% +induction B you can write as a Epsilon +vacuum vacuum mu R and uh times + + align:start position:0% +vacuum vacuum mu R and uh times + + + align:start position:0% +vacuum vacuum mu R and uh times +H right this is just like we write into + + align:start position:0% +H right this is just like we write into + + + align:start position:0% +H right this is just like we write into +the displacement field is electric field + + align:start position:0% +the displacement field is electric field + + + align:start position:0% +the displacement field is electric field +times the dialectric constant and here + + align:start position:0% +times the dialectric constant and here + + + align:start position:0% +times the dialectric constant and here +is the vect vacuum permitivity the + + align:start position:0% +is the vect vacuum permitivity the + + + align:start position:0% +is the vect vacuum permitivity the +relative to vacuum most materials at a + + align:start position:0% +relative to vacuum most materials at a + + + align:start position:0% +relative to vacuum most materials at a +high V visible vivence or high frequency + + align:start position:0% +high V visible vivence or high frequency + + + align:start position:0% +high V visible vivence or high frequency +this one is about one it doesn't have + + align:start position:0% +this one is about one it doesn't have + + + align:start position:0% +this one is about one it doesn't have +magnetic response most + + align:start position:0% +magnetic response most + + + align:start position:0% +magnetic response most +materials right at a low frequency you + + align:start position:0% +materials right at a low frequency you + + + align:start position:0% +materials right at a low frequency you +have magnet but say high frequency most + + align:start position:0% +have magnet but say high frequency most + + + align:start position:0% +have magnet but say high frequency most +material don't don't have the magnetic + + align:start position:0% +material don't don't have the magnetic + + + align:start position:0% +material don't don't have the magnetic +response and in fact that was the basis + + align:start position:0% +response and in fact that was the basis + + + align:start position:0% +response and in fact that was the basis +of invention made by uh Professor Marin + + align:start position:0% +of invention made by uh Professor Marin + + + align:start position:0% +of invention made by uh Professor Marin +so say right + + align:start position:0% +so say right + + + align:start position:0% +so say right +he was trying to think about the how to + + align:start position:0% +he was trying to think about the how to + + + align:start position:0% +he was trying to think about the how to +you how do you get a + + align:start position:0% +you how do you get a + + + align:start position:0% +you how do you get a +powerless Wireless coreless power + + align:start position:0% +powerless Wireless coreless power + + + align:start position:0% +powerless Wireless coreless power +transfer and uh uh the problem is if you + + align:start position:0% +transfer and uh uh the problem is if you + + + align:start position:0% +transfer and uh uh the problem is if you +want to beam a lot of power through the + + align:start position:0% +want to beam a lot of power through the + + + align:start position:0% +want to beam a lot of power through the +space will will all be cooked we have + + align:start position:0% +space will will all be cooked we have + + + align:start position:0% +space will will all be cooked we have +dialectric response right + + align:start position:0% +dialectric response right + + + align:start position:0% +dialectric response right +microwave you heat it + + align:start position:0% +microwave you heat it + + + align:start position:0% +microwave you heat it +up but see because materials at high + + align:start position:0% +up but see because materials at high + + + align:start position:0% +up but see because materials at high +frequency don't have magnetic response + + align:start position:0% +frequency don't have magnetic response + + + align:start position:0% +frequency don't have magnetic response +so it's all about using magnetic field + + align:start position:0% +so it's all about using magnetic field + + + align:start position:0% +so it's all about using magnetic field +to deliver the + + align:start position:0% +to deliver the + + + align:start position:0% +to deliver the +power so we have the start + + align:start position:0% +power so we have the start + + + align:start position:0% +power so we have the start +up trying to commercialize that okay so + + align:start position:0% +up trying to commercialize that okay so + + + align:start position:0% +up trying to commercialize that okay so +that's the uh uh basic + + align:start position:0% +that's the uh uh basic + + + align:start position:0% +that's the uh uh basic +equations and uh uh few more + + align:start position:0% +equations and uh uh few more + + + align:start position:0% +equations and uh uh few more +comments the relation between current + + align:start position:0% +comments the relation between current + + + align:start position:0% +comments the relation between current +that's the when that's a real current a + + align:start position:0% +that's the when that's a real current a + + + align:start position:0% +that's the when that's a real current a +free electron the current flow right and + + align:start position:0% +free electron the current flow right and + + + align:start position:0% +free electron the current flow right and +current of course is related to electric + + align:start position:0% +current of course is related to electric + + + align:start position:0% +current of course is related to electric +field through the if you have a + + align:start position:0% +field through the if you have a + + + align:start position:0% +field through the if you have a +conductor or + + align:start position:0% +conductor or + + + align:start position:0% +conductor or +semiconductor that's the ohm + + align:start position:0% + + + + align:start position:0% + +SN so uh J equals electric conductivity + + align:start position:0% +SN so uh J equals electric conductivity + + + align:start position:0% +SN so uh J equals electric conductivity +that's oh no right electric conductivity + + align:start position:0% +that's oh no right electric conductivity + + + align:start position:0% +that's oh no right electric conductivity +Sigma and here the unit is inverse + + align:start position:0% +Sigma and here the unit is inverse + + + align:start position:0% +Sigma and here the unit is inverse +oh uh uh same + + align:start position:0% +oh uh uh same + + + align:start position:0% +oh uh uh same +meter + + align:start position:0% +meter + + + align:start position:0% +meter +right uh ohm centimeter yeah + + align:start position:0% +right uh ohm centimeter yeah + + + align:start position:0% +right uh ohm centimeter yeah +inverse + + align:start position:0% +inverse + + + align:start position:0% +inverse +no should be + + align:start position:0% + + + + align:start position:0% + +inverse or say inverse oh is also same m + + align:start position:0% +inverse or say inverse oh is also same m + + + align:start position:0% +inverse or say inverse oh is also same m +per meter different + + align:start position:0% +per meter different + + + align:start position:0% +per meter different +units if you don't use it often it's + + align:start position:0% +units if you don't use it often it's + + + align:start position:0% +units if you don't use it often it's +very + + align:start position:0% +very + + + align:start position:0% +very +confusing okay so we have all these + + align:start position:0% +confusing okay so we have all these + + + align:start position:0% +confusing okay so we have all these +quantities + + align:start position:0% +quantities + + + align:start position:0% +quantities +and uh further what is the Epsilon I say + + align:start position:0% +and uh further what is the Epsilon I say + + + align:start position:0% +and uh further what is the Epsilon I say +the charge + + align:start position:0% +the charge + + + align:start position:0% +the charge +density right and this charge density is + + align:start position:0% +density right and this charge density is + + + align:start position:0% +density right and this charge density is +the lad + + align:start position:0% +the lad + + + align:start position:0% +the lad +charge per unit volume in the + + align:start position:0% +charge per unit volume in the + + + align:start position:0% +charge per unit volume in the +material okay so if you have a + + align:start position:0% +material okay so if you have a + + + align:start position:0% +material okay so if you have a +semiconductor right in a semiconductor + + align:start position:0% +semiconductor right in a semiconductor + + + align:start position:0% +semiconductor right in a semiconductor +you can have positive + + align:start position:0% +you can have positive + + + align:start position:0% +you can have positive +donor right when uh say if you put a + + align:start position:0% +donor right when uh say if you put a + + + align:start position:0% +donor right when uh say if you put a +phosphor there okay so so let's say put + + align:start position:0% +phosphor there okay so so let's say put + + + align:start position:0% +phosphor there okay so so let's say put +a phosphor atom in Silicon and phosphor + + align:start position:0% +a phosphor atom in Silicon and phosphor + + + align:start position:0% +a phosphor atom in Silicon and phosphor +atom lose the + + align:start position:0% +atom lose the + + + align:start position:0% +atom lose the +electron so the atom itself is mobile + + align:start position:0% +electron so the atom itself is mobile + + + align:start position:0% +electron so the atom itself is mobile +electron becomes mobile right so what + + align:start position:0% +electron becomes mobile right so what + + + align:start position:0% +electron becomes mobile right so what +you need is the this is positive charge + + align:start position:0% +you need is the this is positive charge + + + align:start position:0% +you need is the this is positive charge +you also have electron negative charge + + align:start position:0% +you also have electron negative charge + + + align:start position:0% +you also have electron negative charge +you add them all together that's per + + align:start position:0% +you add them all together that's per + + + align:start position:0% +you add them all together that's per +unit unit volume how much charge you + + align:start position:0% +unit unit volume how much charge you + + + align:start position:0% +unit unit volume how much charge you +have so this are the uh set of equations + + align:start position:0% +have so this are the uh set of equations + + + align:start position:0% +have so this are the uh set of equations +describing the uh Max the + + align:start position:0% +describing the uh Max the + + + align:start position:0% +describing the uh Max the +electromagnetic + + align:start position:0% +electromagnetic + + + align:start position:0% +electromagnetic +waves and uh + + align:start position:0% +waves and uh + + + align:start position:0% +waves and uh +uh now we can see why uh let's do a few + + align:start position:0% +uh now we can see why uh let's do a few + + + align:start position:0% +uh now we can see why uh let's do a few +math operation just get familiar with it + + align:start position:0% +math operation just get familiar with it + + + align:start position:0% +math operation just get familiar with it +I uh you have seen them so uh if I look + + align:start position:0% +I uh you have seen them so uh if I look + + + align:start position:0% +I uh you have seen them so uh if I look +at this I can + + align:start position:0% +at this I can + + + align:start position:0% +at this I can +eliminate uh I will first + + align:start position:0% +eliminate uh I will first + + + align:start position:0% +eliminate uh I will first +eliminate because + + align:start position:0% +eliminate because + + + align:start position:0% +eliminate because +B right here I can write as a mu H mu0 * + + align:start position:0% +B right here I can write as a mu H mu0 * + + + align:start position:0% +B right here I can write as a mu H mu0 * +mu R Is mu and pertivity and so b equals + + align:start position:0% +mu R Is mu and pertivity and so b equals + + + align:start position:0% +mu R Is mu and pertivity and so b equals +mu H so I use the first one I get the uh + + align:start position:0% +mu H so I use the first one I get the uh + + + align:start position:0% +mu H so I use the first one I get the uh +um the first + + align:start position:0% +um the first + + + align:start position:0% +um the first +equation Delta cross E equals m d mu H + + align:start position:0% +equation Delta cross E equals m d mu H + + + align:start position:0% +equation Delta cross E equals m d mu H +DT that's the first equation and the + + align:start position:0% +DT that's the first equation and the + + + align:start position:0% +DT that's the first equation and the +second equation I have Delta cross + + align:start position:0% +second equation I have Delta cross + + + align:start position:0% +second equation I have Delta cross +H equals uh D + + align:start position:0% +H equals uh D + + + align:start position:0% +H equals uh D +DT and Epsilon times uh + + align:start position:0% +DT and Epsilon times uh + + + align:start position:0% +DT and Epsilon times uh +e this is + + align:start position:0% +e this is + + + align:start position:0% +e this is +the dialectric function which is + + align:start position:0% +the dialectric function which is + + + align:start position:0% +the dialectric function which is +epsilon0 * Epsilon R right the + + align:start position:0% +epsilon0 * Epsilon R right the + + + align:start position:0% +epsilon0 * Epsilon R right the +displacement field and plus uh Sigma * + + align:start position:0% + + + + align:start position:0% + +e those are the if I use consider + + align:start position:0% +e those are the if I use consider + + + align:start position:0% +e those are the if I use consider +relations + + align:start position:0% +relations + + + align:start position:0% +relations +and I eliminate uh B and D I got the + + align:start position:0% +and I eliminate uh B and D I got the + + + align:start position:0% +and I eliminate uh B and D I got the +equation here + + align:start position:0% +equation here + + + align:start position:0% +equation here +right and let me first drop this + + align:start position:0% +right and let me first drop this + + + align:start position:0% +right and let me first drop this +term okay let's consider uh D Electric + + align:start position:0% +term okay let's consider uh D Electric + + + align:start position:0% +term okay let's consider uh D Electric +there's no free + + align:start position:0% +there's no free + + + align:start position:0% +there's no free +charge in the material so electric + + align:start position:0% +charge in the material so electric + + + align:start position:0% +charge in the material so electric +conductivity is zero okay with that I + + align:start position:0% +conductivity is zero okay with that I + + + align:start position:0% +conductivity is zero okay with that I +can I can uh plug this H into here right + + align:start position:0% +can I can uh plug this H into here right + + + align:start position:0% +can I can uh plug this H into here right +and I take a Time derivative on both + + align:start position:0% +and I take a Time derivative on both + + + align:start position:0% +and I take a Time derivative on both +sides on both sides and then I get a DH + + align:start position:0% +sides on both sides and then I get a DH + + + align:start position:0% +sides on both sides and then I get a DH +so this is assuming mu and Epsilon are + + align:start position:0% +so this is assuming mu and Epsilon are + + + align:start position:0% +so this is assuming mu and Epsilon are +independent of + + align:start position:0% +independent of + + + align:start position:0% +independent of +time right and if it depends on time you + + align:start position:0% +time right and if it depends on time you + + + align:start position:0% +time right and if it depends on time you +have to be + + align:start position:0% +have to be + + + align:start position:0% +have to be +careful it's not mine right sorry oh + + align:start position:0% +careful it's not mine right sorry oh + + + align:start position:0% +careful it's not mine right sorry oh +okay uh so uh if I if I have the uh so + + align:start position:0% +okay uh so uh if I if I have the uh so + + + align:start position:0% +okay uh so uh if I if I have the uh so +if I + + align:start position:0% +if I + + + align:start position:0% +if I +uh eliminate uh uh if I take this + + align:start position:0% +uh eliminate uh uh if I take this + + + align:start position:0% +uh eliminate uh uh if I take this +Epsilon mu + + align:start position:0% +Epsilon mu + + + align:start position:0% +Epsilon mu +out I'll be independent of time and uh + + align:start position:0% +out I'll be independent of time and uh + + + align:start position:0% +out I'll be independent of time and uh +sometimes you have to be careful because + + align:start position:0% +sometimes you have to be careful because + + + align:start position:0% +sometimes you have to be careful because +when you do this kind of mathematical + + align:start position:0% +when you do this kind of mathematical + + + align:start position:0% +when you do this kind of mathematical +operation you make assumptions you may + + align:start position:0% +operation you make assumptions you may + + + align:start position:0% +operation you make assumptions you may +lose big + + align:start position:0% +lose big + + + align:start position:0% +lose big +opportunities + + align:start position:0% +opportunities + + + align:start position:0% +opportunities +okay and uh uh uh this electromagnetic + + align:start position:0% +okay and uh uh uh this electromagnetic + + + align:start position:0% +okay and uh uh uh this electromagnetic +field is uh uh uh there are lot of New + + align:start position:0% +field is uh uh uh there are lot of New + + + align:start position:0% +field is uh uh uh there are lot of New +Concept that is all based on going back + + align:start position:0% +Concept that is all based on going back + + + align:start position:0% +Concept that is all based on going back +to the original + + align:start position:0% +to the original + + + align:start position:0% +to the original +equation and uh uh relook at them and + + align:start position:0% +equation and uh uh relook at them and + + + align:start position:0% +equation and uh uh relook at them and +see where are they uh say if you say + + align:start position:0% +see where are they uh say if you say + + + align:start position:0% +see where are they uh say if you say +under where are the approximations made + + align:start position:0% +under where are the approximations made + + + align:start position:0% +under where are the approximations made +okay you were reading yovich chapter I + + align:start position:0% +okay you were reading yovich chapter I + + + align:start position:0% +okay you were reading yovich chapter I +say paper on photonic Crystal + + align:start position:0% +say paper on photonic Crystal + + + align:start position:0% +say paper on photonic Crystal +right and uh one of say uh his photonic + + align:start position:0% +right and uh one of say uh his photonic + + + align:start position:0% +right and uh one of say uh his photonic +crystal is uh really that the concept in + + align:start position:0% +crystal is uh really that the concept in + + + align:start position:0% +crystal is uh really that the concept in +that case the Epsilon which we typically + + align:start position:0% +that case the Epsilon which we typically + + + align:start position:0% +that case the Epsilon which we typically +take a + + align:start position:0% +take a + + + align:start position:0% +take a +uniform right but see he was really + + align:start position:0% +uniform right but see he was really + + + align:start position:0% +uniform right but see he was really +taking this un Epsilon as a periodic + + align:start position:0% +taking this un Epsilon as a periodic + + + align:start position:0% +taking this un Epsilon as a periodic +function so he put the ioniz periodic + + align:start position:0% +function so he put the ioniz periodic + + + align:start position:0% +function so he put the ioniz periodic +function and that's like a periodic + + align:start position:0% +function and that's like a periodic + + + align:start position:0% +function and that's like a periodic +potential for + + align:start position:0% +potential for + + + align:start position:0% +potential for +atoms right if you think about when we + + align:start position:0% +atoms right if you think about when we + + + align:start position:0% +atoms right if you think about when we +solve the band gap of electrons for + + align:start position:0% +solve the band gap of electrons for + + + align:start position:0% +solve the band gap of electrons for +sting equation that come from from the + + align:start position:0% +sting equation that come from from the + + + align:start position:0% +sting equation that come from from the +fact that the potential for electrons is + + align:start position:0% +fact that the potential for electrons is + + + align:start position:0% +fact that the potential for electrons is +a periodic right Max equation + + align:start position:0% +a periodic right Max equation + + + align:start position:0% +a periodic right Max equation +itself there's say no potential here + + align:start position:0% +itself there's say no potential here + + + align:start position:0% +itself there's say no potential here +right it's really he put this one + + align:start position:0% +right it's really he put this one + + + align:start position:0% +right it's really he put this one +Epsilon as constant and he was really + + align:start position:0% +Epsilon as constant and he was really + + + align:start position:0% +Epsilon as constant and he was really +using the analogy and U um in fact say + + align:start position:0% +using the analogy and U um in fact say + + + align:start position:0% +using the analogy and U um in fact say +uh I I SP one day I was in Berlin we + + align:start position:0% +uh I I SP one day I was in Berlin we + + + align:start position:0% +uh I I SP one day I was in Berlin we +both of us were R in the city so I was + + align:start position:0% +both of us were R in the city so I was + + + align:start position:0% +both of us were R in the city so I was +talking to him he said uh when he + + align:start position:0% +talking to him he said uh when he + + + align:start position:0% +talking to him he said uh when he +conserve the concept photonic + + align:start position:0% +conserve the concept photonic + + + align:start position:0% +conserve the concept photonic +Crystal uh he he wrote a paper so + + align:start position:0% +Crystal uh he he wrote a paper so + + + align:start position:0% +Crystal uh he he wrote a paper so +photonic Crystal what is photonic + + align:start position:0% +photonic Crystal what is photonic + + + align:start position:0% +photonic Crystal what is photonic +crystal is basically periodic + + align:start position:0% +crystal is basically periodic + + + align:start position:0% +crystal is basically periodic +arrangement of whatever glass bits you + + align:start position:0% +arrangement of whatever glass bits you + + + align:start position:0% +arrangement of whatever glass bits you +can think about that right and uh uh + + align:start position:0% +can think about that right and uh uh + + + align:start position:0% +can think about that right and uh uh +it's uh uh if you look at the evolution + + align:start position:0% +it's uh uh if you look at the evolution + + + align:start position:0% +it's uh uh if you look at the evolution +uh in electron in ball Crystal we have + + align:start position:0% +uh in electron in ball Crystal we have + + + align:start position:0% +uh in electron in ball Crystal we have +Bank + + align:start position:0% +Bank + + + align:start position:0% +Bank +Gap and uh uh in the' + + align:start position:0% +Gap and uh uh in the' + + + align:start position:0% +Gap and uh uh in the' +70s + + align:start position:0% +70s + + + align:start position:0% +70s +uh there is this concept of uh super + + align:start position:0% +uh there is this concept of uh super + + + align:start position:0% +uh there is this concept of uh super +lies Quantum Wells right you read again + + align:start position:0% +lies Quantum Wells right you read again + + + align:start position:0% +lies Quantum Wells right you read again +isake and two paper and that's put in + + align:start position:0% +isake and two paper and that's put in + + + align:start position:0% +isake and two paper and that's put in +multi layers of th films right that + + align:start position:0% +multi layers of th films right that + + + align:start position:0% +multi layers of th films right that +makes the one dimension you got the + + align:start position:0% +makes the one dimension you got the + + + align:start position:0% +makes the one dimension you got the +artificial this what we draw the + + align:start position:0% +artificial this what we draw the + + + align:start position:0% +artificial this what we draw the +potential per periodical potential + + align:start position:0% +potential per periodical potential + + + align:start position:0% +potential per periodical potential +That's The Chronic Panic model we talked + + align:start position:0% +That's The Chronic Panic model we talked + + + align:start position:0% +That's The Chronic Panic model we talked +before it's but it's artificial material + + align:start position:0% +before it's but it's artificial material + + + align:start position:0% +before it's but it's artificial material +right so you go from a threedimensional + + align:start position:0% +right so you go from a threedimensional + + + align:start position:0% +right so you go from a threedimensional +crystal periodical potential to + + align:start position:0% +crystal periodical potential to + + + align:start position:0% +crystal periodical potential to +1D and that's a big jump in concept + + align:start position:0% +1D and that's a big jump in concept + + + align:start position:0% +1D and that's a big jump in concept +because artificial Quantum + + align:start position:0% +because artificial Quantum + + + align:start position:0% +because artificial Quantum +structures right and uh on the other + + align:start position:0% +structures right and uh on the other + + + align:start position:0% +structures right and uh on the other +hand in Optics you have the form that + + align:start position:0% +hand in Optics you have the form that + + + align:start position:0% +hand in Optics you have the form that +the + + align:start position:0% +the + + + align:start position:0% +the +letter over 100 years people know how to + + align:start position:0% +letter over 100 years people know how to + + + align:start position:0% +letter over 100 years people know how to +do coding people have been doing + + align:start position:0% +do coding people have been doing + + + align:start position:0% +do coding people have been doing +refining Optics that Cod multi-layer + + align:start position:0% +refining Optics that Cod multi-layer + + + align:start position:0% +refining Optics that Cod multi-layer +films right some of this is a purely say + + align:start position:0% +films right some of this is a purely say + + + align:start position:0% +films right some of this is a purely say +anti-reflection or purely reflecting the + + align:start position:0% +anti-reflection or purely reflecting the + + + align:start position:0% +anti-reflection or purely reflecting the +purpose and uh so the Reas so you have + + align:start position:0% +purpose and uh so the Reas so you have + + + align:start position:0% +purpose and uh so the Reas so you have +those multi-layer SYM + + align:start position:0% +those multi-layer SYM + + + align:start position:0% +those multi-layer SYM +codings which is typically of the order + + align:start position:0% +codings which is typically of the order + + + align:start position:0% +codings which is typically of the order +like quarter wav + + align:start position:0% +like quarter wav + + + align:start position:0% +like quarter wav +length and you can code it so that it's + + align:start position:0% +length and you can code it so that it's + + + align:start position:0% +length and you can code it so that it's +complete + + align:start position:0% +complete + + + align:start position:0% +complete +reflecting what does complete reflection + + align:start position:0% +reflecting what does complete reflection + + + align:start position:0% +reflecting what does complete reflection +is the wave function of electromagnetic + + align:start position:0% +is the wave function of electromagnetic + + + align:start position:0% +is the wave function of electromagnetic +wave zero inside that's forbidden it's + + align:start position:0% +wave zero inside that's forbidden it's + + + align:start position:0% +wave zero inside that's forbidden it's +Bang Gap in + + align:start position:0% +Bang Gap in + + + align:start position:0% +Bang Gap in +1D right so what y propos photonic cryst + + align:start position:0% +1D right so what y propos photonic cryst + + + align:start position:0% +1D right so what y propos photonic cryst +is how to make this back into + + align:start position:0% +is how to make this back into + + + align:start position:0% +is how to make this back into +3D what ler has is electron Fons in + + align:start position:0% +3D what ler has is electron Fons in + + + align:start position:0% +3D what ler has is electron Fons in +3D and uh see uh researchers we have + + align:start position:0% +3D and uh see uh researchers we have + + + align:start position:0% +3D and uh see uh researchers we have +created this one D structure right so + + align:start position:0% +created this one D structure right so + + + align:start position:0% +created this one D structure right so +that's you see it's opposite direction + + align:start position:0% +that's you see it's opposite direction + + + align:start position:0% +that's you see it's opposite direction +going and here is trying to make + + align:start position:0% +going and here is trying to make + + + align:start position:0% +going and here is trying to make +photonic analogy of sinf to + + align:start position:0% +photonic analogy of sinf to + + + align:start position:0% +photonic analogy of sinf to +3D okay so he said that when he wrote + + align:start position:0% +3D okay so he said that when he wrote + + + align:start position:0% +3D okay so he said that when he wrote +the paper you go to read his + + align:start position:0% +the paper you go to read his + + + align:start position:0% +the paper you go to read his +paper and uh there's no math Insight + + align:start position:0% +paper and uh there's no math Insight + + + align:start position:0% +paper and uh there's no math Insight +right he was just a + + align:start position:0% +right he was just a + + + align:start position:0% +right he was just a +concept and uh uh he submitted the + + align:start position:0% +concept and uh uh he submitted the + + + align:start position:0% +concept and uh uh he submitted the +paper and uh uh he know who he wants to + + align:start position:0% +paper and uh uh he know who he wants to + + + align:start position:0% +paper and uh uh he know who he wants to +be + + align:start position:0% +be + + + align:start position:0% +be +reviewer and his friend said do you + + align:start position:0% +reviewer and his friend said do you + + + align:start position:0% +reviewer and his friend said do you +really want to Pure this + + align:start position:0% +really want to Pure this + + + align:start position:0% +really want to Pure this +paper uh this is this is a really + + align:start position:0% +paper uh this is this is a really + + + align:start position:0% +paper uh this is this is a really +doesn't look like a + + align:start position:0% +doesn't look like a + + + align:start position:0% +doesn't look like a +paper doesn't matter just publish it so + + align:start position:0% +paper doesn't matter just publish it so + + + align:start position:0% +paper doesn't matter just publish it so +that's what you read okay it's a it's + + align:start position:0% +that's what you read okay it's a it's + + + align:start position:0% +that's what you read okay it's a it's +the it's the beginning of a new field + + align:start position:0% +the it's the beginning of a new field + + + align:start position:0% +the it's the beginning of a new field +for T Crystal okay uh so that's Epsilon + + align:start position:0% +for T Crystal okay uh so that's Epsilon + + + align:start position:0% +for T Crystal okay uh so that's Epsilon +is a function of r periodic right and + + align:start position:0% +is a function of r periodic right and + + + align:start position:0% +is a function of r periodic right and +your Epsilon could also be a function of + + align:start position:0% +your Epsilon could also be a function of + + + align:start position:0% +your Epsilon could also be a function of +time in fact I was doing some uh uh when + + align:start position:0% +time in fact I was doing some uh uh when + + + align:start position:0% +time in fact I was doing some uh uh when +I did my graduate school study right I + + align:start position:0% +I did my graduate school study right I + + + align:start position:0% +I did my graduate school study right I +never came up with big ideas but the uh + + align:start position:0% +never came up with big ideas but the uh + + + align:start position:0% +never came up with big ideas but the uh +once I was writing down the loads I said + + align:start position:0% +once I was writing down the loads I said + + + align:start position:0% +once I was writing down the loads I said +okay because I was doing some uh uh + + align:start position:0% +okay because I was doing some uh uh + + + align:start position:0% +okay because I was doing some uh uh +stuff during the optical say fast laser + + align:start position:0% +stuff during the optical say fast laser + + + align:start position:0% +stuff during the optical say fast laser +material interaction I see during that + + align:start position:0% +material interaction I see during that + + + align:start position:0% +material interaction I see during that +process yon will change as function of + + align:start position:0% +process yon will change as function of + + + align:start position:0% +process yon will change as function of +temperature and temperature change the + + align:start position:0% +temperature and temperature change the + + + align:start position:0% +temperature and temperature change the +function of time so I have to keep the + + align:start position:0% +function of time so I have to keep the + + + align:start position:0% +function of time so I have to keep the +there I wrote all this equations and + + align:start position:0% +there I wrote all this equations and + + + align:start position:0% +there I wrote all this equations and +years say a few years later my friend + + align:start position:0% +years say a few years later my friend + + + align:start position:0% +years say a few years later my friend +asked me I said actually it's in my + + align:start position:0% +asked me I said actually it's in my + + + align:start position:0% +asked me I said actually it's in my +notes but uh it never got anywhere + + align:start position:0% +notes but uh it never got anywhere + + + align:start position:0% +notes but uh it never got anywhere +so one story but anyway let's continue + + align:start position:0% +so one story but anyway let's continue + + + align:start position:0% +so one story but anyway let's continue +here I have two equation I drop this I'm + + align:start position:0% +here I have two equation I drop this I'm + + + align:start position:0% +here I have two equation I drop this I'm +going to eliminate I say mu Epsilon + + align:start position:0% +going to eliminate I say mu Epsilon + + + align:start position:0% +going to eliminate I say mu Epsilon +constant and uh I'm going to then put it + + align:start position:0% +constant and uh I'm going to then put it + + + align:start position:0% +constant and uh I'm going to then put it +out and I can eliminate H and what I + + align:start position:0% +out and I can eliminate H and what I + + + align:start position:0% +out and I can eliminate H and what I +have here then is the equation uh so if + + align:start position:0% +have here then is the equation uh so if + + + align:start position:0% +have here then is the equation uh so if +I eliminate + + align:start position:0% +I eliminate + + + align:start position:0% +I eliminate +H I have Delta cross e + + align:start position:0% +H I have Delta cross e + + + align:start position:0% +H I have Delta cross e +over + + align:start position:0% +over + + + align:start position:0% +over +mu + + align:start position:0% +mu + + + align:start position:0% +mu +and uh here I have a uh + + align:start position:0% + + + + align:start position:0% + +Epsilon I start to get a wave + + align:start position:0% +Epsilon I start to get a wave + + + align:start position:0% +Epsilon I start to get a wave +equation + + align:start position:0% +equation + + + align:start position:0% +equation +okay and uh uh you can use the vector + + align:start position:0% +okay and uh uh you can use the vector + + + align:start position:0% +okay and uh uh you can use the vector +operation to write rewrite + + align:start position:0% +operation to write rewrite + + + align:start position:0% +operation to write rewrite +this into + + align:start position:0% + + + + align:start position:0% + +if you use a vector relation you will + + align:start position:0% +if you use a vector relation you will + + + align:start position:0% +if you use a vector relation you will +get uh actually sure there is a negative + + align:start position:0% +get uh actually sure there is a negative + + + align:start position:0% +get uh actually sure there is a negative +sign in the front and Delta Epsilon + + align:start position:0% +sign in the front and Delta Epsilon + + + align:start position:0% +sign in the front and Delta Epsilon +Square mu Epsilon d + + align:start position:0% +Square mu Epsilon d + + + align:start position:0% +Square mu Epsilon d +e DT + + align:start position:0% +e DT + + + align:start position:0% +e DT +s and uh uh if I continue carry that it + + align:start position:0% +s and uh uh if I continue carry that it + + + align:start position:0% +s and uh uh if I continue carry that it +will be mu Sigma d e + + align:start position:0% +will be mu Sigma d e + + + align:start position:0% +will be mu Sigma d e +DT okay this is the when I carry the uh + + align:start position:0% +DT okay this is the when I carry the uh + + + align:start position:0% +DT okay this is the when I carry the uh +uh metal term the conductivity term if I + + align:start position:0% +uh metal term the conductivity term if I + + + align:start position:0% +uh metal term the conductivity term if I +don't I have a pure wave equation if I + + align:start position:0% +don't I have a pure wave equation if I + + + align:start position:0% +don't I have a pure wave equation if I +drop this you can see this is a uh wave + + align:start position:0% +drop this you can see this is a uh wave + + + align:start position:0% +drop this you can see this is a uh wave +equation second order in space second + + align:start position:0% +equation second order in space second + + + align:start position:0% +equation second order in space second +order in time unlike the shortener + + align:start position:0% +order in time unlike the shortener + + + align:start position:0% +order in time unlike the shortener +equation which is the first order in + + align:start position:0% +equation which is the first order in + + + align:start position:0% +equation which is the first order in +time but has a imagin l in the front now + + align:start position:0% +time but has a imagin l in the front now + + + align:start position:0% +time but has a imagin l in the front now +I have a real wave equation is the + + align:start position:0% +I have a real wave equation is the + + + align:start position:0% +I have a real wave equation is the +second order in both space and + + align:start position:0% +second order in both space and + + + align:start position:0% +second order in both space and +time + + align:start position:0% +time + + + align:start position:0% +time +right so this is the uh maxal + + align:start position:0% +right so this is the uh maxal + + + align:start position:0% +right so this is the uh maxal +equation and uh uh if you look at the + + align:start position:0% +equation and uh uh if you look at the + + + align:start position:0% +equation and uh uh if you look at the +typical wave solution plan wave Epsilon + + align:start position:0% +typical wave solution plan wave Epsilon + + + align:start position:0% +typical wave solution plan wave Epsilon +is a function of R and + + align:start position:0% +is a function of R and + + + align:start position:0% +is a function of R and +T and uh this is a vector so that's the + + align:start position:0% +T and uh this is a vector so that's the + + + align:start position:0% +T and uh this is a vector so that's the +polarization Direction uh the uh + + align:start position:0% +polarization Direction uh the uh + + + align:start position:0% +polarization Direction uh the uh +electric field Direction + + align:start position:0% +electric field Direction + + + align:start position:0% +electric field Direction +and this is the propagation Direction + + align:start position:0% +and this is the propagation Direction + + + align:start position:0% +and this is the propagation Direction +Omega T minus k. + + align:start position:0% + + + + align:start position:0% + +R so this is a plan + + align:start position:0% +R so this is a plan + + + align:start position:0% +R so this is a plan +wave uh plan wave expression we talked + + align:start position:0% +wave uh plan wave expression we talked + + + align:start position:0% +wave uh plan wave expression we talked +before and you substitute back into here + + align:start position:0% +before and you substitute back into here + + + align:start position:0% +before and you substitute back into here +you will say it's satisfi the wave + + align:start position:0% +you will say it's satisfi the wave + + + align:start position:0% +you will say it's satisfi the wave +equation + + align:start position:0% +equation + + + align:start position:0% +equation +right and uh in fact if you do it if you + + align:start position:0% +right and uh in fact if you do it if you + + + align:start position:0% +right and uh in fact if you do it if you +substitute it back see this left hand + + align:start position:0% +substitute it back see this left hand + + + align:start position:0% +substitute it back see this left hand +side is the second order derivative in + + align:start position:0% +side is the second order derivative in + + + align:start position:0% +side is the second order derivative in +space so I'll get a k Square so I will + + align:start position:0% +space so I'll get a k Square so I will + + + align:start position:0% +space so I'll get a k Square so I will +get a + + align:start position:0% + + + + align:start position:0% + +k do K right and the right hand side I + + align:start position:0% +k do K right and the right hand side I + + + align:start position:0% +k do K right and the right hand side I +will get mu Omega Square this is + + align:start position:0% +will get mu Omega Square this is + + + align:start position:0% +will get mu Omega Square this is +time and uh Epsilon plus I Sigma and + + align:start position:0% +time and uh Epsilon plus I Sigma and + + + align:start position:0% +time and uh Epsilon plus I Sigma and +Omega this is the this term combine with + + align:start position:0% +Omega this is the this term combine with + + + align:start position:0% +Omega this is the this term combine with +the first term and the rest I Omega T + + align:start position:0% +the first term and the rest I Omega T + + + align:start position:0% +the first term and the rest I Omega T +that this term cancel the F Factor all + + align:start position:0% +that this term cancel the F Factor all + + + align:start position:0% +that this term cancel the F Factor all +cancel okay and uh this way I can write + + align:start position:0% +cancel okay and uh this way I can write + + + align:start position:0% +cancel okay and uh this way I can write +uh uh the expression as because Omega + + align:start position:0% +uh uh the expression as because Omega + + + align:start position:0% +uh uh the expression as because Omega +Square so I have M Epsilon T Omega + + align:start position:0% +Square so I have M Epsilon T Omega + + + align:start position:0% +Square so I have M Epsilon T Omega +Square the wave + + align:start position:0% +Square the wave + + + align:start position:0% +Square the wave +Vector is proportional to + + align:start position:0% +Vector is proportional to + + + align:start position:0% +Vector is proportional to +Omega for wave in free space this is + + align:start position:0% +Omega for wave in free space this is + + + align:start position:0% +Omega for wave in free space this is +epsilon0 mu0 free space + + align:start position:0% +epsilon0 mu0 free space + + + align:start position:0% +epsilon0 mu0 free space +right and this is what the TR of + + align:start position:0% +right and this is what the TR of + + + align:start position:0% +right and this is what the TR of +electromagnetic wave because we predict + + align:start position:0% +electromagnetic wave because we predict + + + align:start position:0% +electromagnetic wave because we predict +Max equation + + align:start position:0% +Max equation + + + align:start position:0% +Max equation +predicted the uh speed of + + align:start position:0% + + + + align:start position:0% + +light okay because when you do this uh + + align:start position:0% +light okay because when you do this uh + + + align:start position:0% +light okay because when you do this uh +you get the uh the + + align:start position:0% +you get the uh the + + + align:start position:0% +you get the uh the +magnitude K square equals uh Omega IDE + + align:start position:0% +magnitude K square equals uh Omega IDE + + + align:start position:0% +magnitude K square equals uh Omega IDE +by uh here I do the square root + + align:start position:0% +by uh here I do the square root + + + align:start position:0% +by uh here I do the square root +of uh Epsilon t + + align:start position:0% +of uh Epsilon t + + + align:start position:0% +of uh Epsilon t +m and U this one we can write + + align:start position:0% +m and U this one we can write + + + align:start position:0% +m and U this one we can write +it + + align:start position:0% + + + + align:start position:0% + +into so I can write it K the + + align:start position:0% +into so I can write it K the + + + align:start position:0% +into so I can write it K the +magnitude oh this is a not Square the + + align:start position:0% +magnitude oh this is a not Square the + + + align:start position:0% +magnitude oh this is a not Square the +magnitude so the magnitude of k + + align:start position:0% +magnitude so the magnitude of k + + + align:start position:0% +magnitude so the magnitude of k +equals uh + + align:start position:0% +equals uh + + + align:start position:0% +equals uh +uh Omega time C right c k Omega equal c + + align:start position:0% +uh Omega time C right c k Omega equal c + + + align:start position:0% +uh Omega time C right c k Omega equal c +k that's the + + align:start position:0% +k that's the + + + align:start position:0% +k that's the +dispersion and + + align:start position:0% +dispersion and + + + align:start position:0% +dispersion and +say is square root ofon K and mu and + + align:start position:0% +say is square root ofon K and mu and + + + align:start position:0% +say is square root ofon K and mu and +typically we Define refractive + + align:start position:0% +typically we Define refractive + + + align:start position:0% +typically we Define refractive +index as the speed of light in vacuum + + align:start position:0% +index as the speed of light in vacuum + + + align:start position:0% +index as the speed of light in vacuum +divided by speed of light in the + + align:start position:0% +divided by speed of light in the + + + align:start position:0% +divided by speed of light in the +medium right and the speed of light in + + align:start position:0% +medium right and the speed of light in + + + align:start position:0% +medium right and the speed of light in +vacuum this isilon 0 + + align:start position:0% +vacuum this isilon 0 + + + align:start position:0% +vacuum this isilon 0 +mu0 and uh it's approximate because I + + align:start position:0% +mu0 and uh it's approximate because I + + + align:start position:0% +mu0 and uh it's approximate because I +say most high frequency magnetic + + align:start position:0% +say most high frequency magnetic + + + align:start position:0% +say most high frequency magnetic +response is one so this is Epsilon 12 + + align:start position:0% +response is one so this is Epsilon 12 + + + align:start position:0% +response is one so this is Epsilon 12 +over + + align:start position:0% +over + + + align:start position:0% +over +epsilon0 and this one is Epsilon + + align:start position:0% +epsilon0 and this one is Epsilon + + + align:start position:0% +epsilon0 and this one is Epsilon +r so even for + + align:start position:0% +r so even for + + + align:start position:0% +r so even for +Metals + + align:start position:0% +Metals + + + align:start position:0% +Metals +right uh very often we tabulate we don't + + align:start position:0% +right uh very often we tabulate we don't + + + align:start position:0% +right uh very often we tabulate we don't +tabulate these two separately we just + + align:start position:0% +tabulate these two separately we just + + + align:start position:0% +tabulate these two separately we just +tabulate them together into Epsilon R + + align:start position:0% +tabulate them together into Epsilon R + + + align:start position:0% +tabulate them together into Epsilon R +the relative dialectric + + align:start position:0% +the relative dialectric + + + align:start position:0% +the relative dialectric +constant + + align:start position:0% +constant + + + align:start position:0% +constant +okay + + align:start position:0% + + + + align:start position:0% + +so there are few interesting story here + + align:start position:0% +so there are few interesting story here + + + align:start position:0% +so there are few interesting story here +again okay you take a positive uh square + + align:start position:0% +again okay you take a positive uh square + + + align:start position:0% +again okay you take a positive uh square +root going from here to here you take a + + align:start position:0% +root going from here to here you take a + + + align:start position:0% +root going from here to here you take a +square + + align:start position:0% +square + + + align:start position:0% +square +root and you see that's a leral + + align:start position:0% +root and you see that's a leral + + + align:start position:0% +root and you see that's a leral +solution right and if you go to look at + + align:start position:0% +solution right and if you go to look at + + + align:start position:0% +solution right and if you go to look at +your uh Max equation turns out this Wave + + align:start position:0% +your uh Max equation turns out this Wave + + + align:start position:0% +your uh Max equation turns out this Wave +It's a right hand wave so you go say + + align:start position:0% +It's a right hand wave so you go say + + + align:start position:0% +It's a right hand wave so you go say +this is Epsilon e Direction electric + + align:start position:0% +this is Epsilon e Direction electric + + + align:start position:0% +this is Epsilon e Direction electric +field + + align:start position:0% +field + + + align:start position:0% +field +direction right it's transverse wave you + + align:start position:0% +direction right it's transverse wave you + + + align:start position:0% +direction right it's transverse wave you +this is the what the equation tells you + + align:start position:0% +this is the what the equation tells you + + + align:start position:0% +this is the what the equation tells you +go you check right it's a transfer wave + + align:start position:0% +go you check right it's a transfer wave + + + align:start position:0% +go you check right it's a transfer wave +so electrical field + + align:start position:0% +so electrical field + + + align:start position:0% +so electrical field +will be perpendicular to magnetic field + + align:start position:0% +will be perpendicular to magnetic field + + + align:start position:0% +will be perpendicular to magnetic field +will be perpendicular to K the wave + + align:start position:0% +will be perpendicular to K the wave + + + align:start position:0% +will be perpendicular to K the wave +Vector the K the wave propagation they + + align:start position:0% +Vector the K the wave propagation they + + + align:start position:0% +Vector the K the wave propagation they +write that's why it's a transverse + + align:start position:0% +write that's why it's a transverse + + + align:start position:0% +write that's why it's a transverse +wave right it's not only transverse wave + + align:start position:0% +wave right it's not only transverse wave + + + align:start position:0% +wave right it's not only transverse wave +it's also right hand + + align:start position:0% +it's also right hand + + + align:start position:0% +it's also right hand +wave what the right hand mean is if you + + align:start position:0% +wave what the right hand mean is if you + + + align:start position:0% +wave what the right hand mean is if you +recall when you learn let's say is the E + + align:start position:0% +recall when you learn let's say is the E + + + align:start position:0% +recall when you learn let's say is the E +cross H goes to the wave propagation + + align:start position:0% +cross H goes to the wave propagation + + + align:start position:0% +cross H goes to the wave propagation +direction right + + align:start position:0% +direction right + + + align:start position:0% +direction right +so is right hand side your e Direction + + align:start position:0% +so is right hand side your e Direction + + + align:start position:0% +so is right hand side your e Direction +you grab to the H Direction the some + + align:start position:0% +you grab to the H Direction the some + + + align:start position:0% +you grab to the H Direction the some +point to do the K + + align:start position:0% +point to do the K + + + align:start position:0% +point to do the K +Direction + + align:start position:0% +Direction + + + align:start position:0% +Direction +okay so it's a right hand wave it's a + + align:start position:0% +okay so it's a right hand wave it's a + + + align:start position:0% +okay so it's a right hand wave it's a +transverse wave except I say we ignore + + align:start position:0% +transverse wave except I say we ignore + + + align:start position:0% +transverse wave except I say we ignore +the + + align:start position:0% +the + + + align:start position:0% +the +possibility of when you + + align:start position:0% +possibility of when you + + + align:start position:0% +possibility of when you +take uh this K square + + align:start position:0% +take uh this K square + + + align:start position:0% +take uh this K square +root it could be negative also root + + align:start position:0% +root it could be negative also root + + + align:start position:0% +root it could be negative also root +solution + + align:start position:0% +solution + + + align:start position:0% +solution +right leg solution uh typically are + + align:start position:0% +right leg solution uh typically are + + + align:start position:0% +right leg solution uh typically are +ruled + + align:start position:0% +ruled + + + align:start position:0% +ruled +out but if when Epsilon and mu could be + + align:start position:0% +out but if when Epsilon and mu could be + + + align:start position:0% +out but if when Epsilon and mu could be +negative right when both of them could + + align:start position:0% +negative right when both of them could + + + align:start position:0% +negative right when both of them could +be negative it turns out you go back to + + align:start position:0% +be negative it turns out you go back to + + + align:start position:0% +be negative it turns out you go back to +check the equation again you have to + + align:start position:0% +check the equation again you have to + + + align:start position:0% +check the equation again you have to +take a negative + + align:start position:0% +take a negative + + + align:start position:0% +take a negative +root so this effect was predicted in + + align:start position:0% +root so this effect was predicted in + + + align:start position:0% +root so this effect was predicted in +1950s by Russian scientist version + + align:start position:0% +1950s by Russian scientist version + + + align:start position:0% +1950s by Russian scientist version +nle and uh uh uh it paper was s + + align:start position:0% +nle and uh uh uh it paper was s + + + align:start position:0% +nle and uh uh uh it paper was s +forgotten okay but in '90s people start + + align:start position:0% +forgotten okay but in '90s people start + + + align:start position:0% +forgotten okay but in '90s people start +to pay attention to it first there are + + align:start position:0% +to pay attention to it first there are + + + align:start position:0% +to pay attention to it first there are +later Lal + + align:start position:0% +later Lal + + + align:start position:0% +later Lal +materials withon negative it just + + align:start position:0% +materials withon negative it just + + + align:start position:0% +materials withon negative it just +doesn't have natural material with mual + + align:start position:0% +doesn't have natural material with mual + + + align:start position:0% +doesn't have natural material with mual +negative why the natural material could + + align:start position:0% +negative why the natural material could + + + align:start position:0% +negative why the natural material could +have epon negative Epsilon remember is a + + align:start position:0% +have epon negative Epsilon remember is a + + + align:start position:0% +have epon negative Epsilon remember is a +response of the material I think I + + align:start position:0% +response of the material I think I + + + align:start position:0% +response of the material I think I +erased it when you have electric field + + align:start position:0% +erased it when you have electric field + + + align:start position:0% +erased it when you have electric field +the material will polarize right if it's + + align:start position:0% +the material will polarize right if it's + + + align:start position:0% +the material will polarize right if it's +a electron for example and then when you + + align:start position:0% +a electron for example and then when you + + + align:start position:0% +a electron for example and then when you +have a external wave comes in + + align:start position:0% +have a external wave comes in + + + align:start position:0% +have a external wave comes in +oscillating the electron create a + + align:start position:0% +oscillating the electron create a + + + align:start position:0% +oscillating the electron create a +resisting say Direction field and if + + align:start position:0% +resisting say Direction field and if + + + align:start position:0% +resisting say Direction field and if +that field is larger than the incident + + align:start position:0% +that field is larger than the incident + + + align:start position:0% +that field is larger than the incident +you get the negative + + align:start position:0% +you get the negative + + + align:start position:0% +you get the negative +Direction displacement so the epon + + align:start position:0% +Direction displacement so the epon + + + align:start position:0% +Direction displacement so the epon +become negative but there's no material + + align:start position:0% +become negative but there's no material + + + align:start position:0% +become negative but there's no material +with mu + + align:start position:0% +with mu + + + align:start position:0% +with mu +negative then say in 90 uh say '90s + + align:start position:0% +negative then say in 90 uh say '90s + + + align:start position:0% +negative then say in 90 uh say '90s +people dis designed this artificial + + align:start position:0% +people dis designed this artificial + + + align:start position:0% +people dis designed this artificial +resonator structure that create a + + align:start position:0% +resonator structure that create a + + + align:start position:0% +resonator structure that create a +generate uh say artificial magnetic so + + align:start position:0% +generate uh say artificial magnetic so + + + align:start position:0% +generate uh say artificial magnetic so +you basically create a + + align:start position:0% +you basically create a + + + align:start position:0% +you basically create a +loop with a gap and then when the + + align:start position:0% +loop with a gap and then when the + + + align:start position:0% +loop with a gap and then when the +electric current oscillate in this Loop + + align:start position:0% +electric current oscillate in this Loop + + + align:start position:0% +electric current oscillate in this Loop +they generate magnetic field and we make + + align:start position:0% +they generate magnetic field and we make + + + align:start position:0% +they generate magnetic field and we make +the very small the magnetic field could + + align:start position:0% +the very small the magnetic field could + + + align:start position:0% +the very small the magnetic field could +be very very fast make it smaller + + align:start position:0% +be very very fast make it smaller + + + align:start position:0% +be very very fast make it smaller +right and if you bring both Epsilon and + + align:start position:0% +right and if you bring both Epsilon and + + + align:start position:0% +right and if you bring both Epsilon and +M negative in the same frequency R you + + align:start position:0% +M negative in the same frequency R you + + + align:start position:0% +M negative in the same frequency R you +have to go to take that negative + + align:start position:0% +have to go to take that negative + + + align:start position:0% +have to go to take that negative +root so become a left hand material so e + + align:start position:0% +root so become a left hand material so e + + + align:start position:0% +root so become a left hand material so e +cross h k goes the other way so uh this + + align:start position:0% +cross h k goes the other way so uh this + + + align:start position:0% +cross h k goes the other way so uh this +is a k go this way by energy go this + + align:start position:0% +is a k go this way by energy go this + + + align:start position:0% +is a k go this way by energy go this +way not of confusion at the + + align:start position:0% +way not of confusion at the + + + align:start position:0% +way not of confusion at the +beginning because whether there is this + + align:start position:0% +beginning because whether there is this + + + align:start position:0% +beginning because whether there is this +possible or not and + + align:start position:0% +possible or not and + + + align:start position:0% +possible or not and +if you check the literature this is + + align:start position:0% +if you check the literature this is + + + align:start position:0% +if you check the literature this is +called meta + + align:start position:0% + + + + align:start position:0% + +material okay it's not a metal + + align:start position:0% +material okay it's not a metal + + + align:start position:0% +material okay it's not a metal +materials ma not the me okay and uh was + + align:start position:0% +materials ma not the me okay and uh was + + + align:start position:0% +materials ma not the me okay and uh was +interesting story many interesting + + align:start position:0% +interesting story many interesting + + + align:start position:0% +interesting story many interesting +stories but some people say metal + + align:start position:0% +stories but some people say metal + + + align:start position:0% +stories but some people say metal +material that's so we we study Metals + + align:start position:0% +material that's so we we study Metals + + + align:start position:0% +material that's so we we study Metals +but uh it's it's not a metal material + + align:start position:0% +but uh it's it's not a metal material + + + align:start position:0% +but uh it's it's not a metal material +it's a metal and the uh it's really + + align:start position:0% +it's a metal and the uh it's really + + + align:start position:0% +it's a metal and the uh it's really +artificially designed material so it has + + align:start position:0% +artificially designed material so it has + + + align:start position:0% +artificially designed material so it has +strange + + align:start position:0% +strange + + + align:start position:0% +strange +properties and one of this first + + align:start position:0% +properties and one of this first + + + align:start position:0% +properties and one of this first +achievement is design material in + + align:start position:0% +achievement is design material in + + + align:start position:0% +achievement is design material in +microwave range so that to prove that + + align:start position:0% +microwave range so that to prove that + + + align:start position:0% +microwave range so that to prove that +the refractive index really should be + + align:start position:0% +the refractive index really should be + + + align:start position:0% +the refractive index really should be +taken a negative value so that's really + + align:start position:0% +taken a negative value so that's really + + + align:start position:0% +taken a negative value so that's really +later on you'll say it's pretty strange + + align:start position:0% +later on you'll say it's pretty strange + + + align:start position:0% +later on you'll say it's pretty strange +because when we think about Optical + + align:start position:0% +because when we think about Optical + + + align:start position:0% +because when we think about Optical +light + + align:start position:0% +light + + + align:start position:0% +light +refraction right this is the ref + + align:start position:0% +refraction right this is the ref + + + align:start position:0% +refraction right this is the ref +fraction snail LW we'll talk Le snail LW + + align:start position:0% +fraction snail LW we'll talk Le snail LW + + + align:start position:0% +fraction snail LW we'll talk Le snail LW +right but when the N is negative the + + align:start position:0% +right but when the N is negative the + + + align:start position:0% +right but when the N is negative the +refraction actually happen this + + align:start position:0% +refraction actually happen this + + + align:start position:0% +refraction actually happen this +way and uh it's pretty weird so it's + + align:start position:0% +way and uh it's pretty weird so it's + + + align:start position:0% +way and uh it's pretty weird so it's +still a very active field and you heard + + align:start position:0% +still a very active field and you heard + + + align:start position:0% +still a very active field and you heard +Harry Potter + + align:start position:0% +Harry Potter + + + align:start position:0% +Harry Potter +story The + + align:start position:0% +story The + + + align:start position:0% +story The +clocking huh right the uh so in that + + align:start position:0% +clocking huh right the uh so in that + + + align:start position:0% +clocking huh right the uh so in that +case what happens is it could be + + align:start position:0% +case what happens is it could be + + + align:start position:0% +case what happens is it could be +solution of Maxwell equation + + align:start position:0% +solution of Maxwell equation + + + align:start position:0% +solution of Maxwell equation +come in here you have object and you + + align:start position:0% +come in here you have object and you + + + align:start position:0% +come in here you have object and you +this is actually will be easy for flu + + align:start position:0% +this is actually will be easy for flu + + + align:start position:0% +this is actually will be easy for flu +mechanics if you look at flu mechanics + + align:start position:0% +mechanics if you look at flu mechanics + + + align:start position:0% +mechanics if you look at flu mechanics +right and in small reload L flow go this + + align:start position:0% + + + + align:start position:0% + +way right so what it means the the maxim + + align:start position:0% +way right so what it means the the maxim + + + align:start position:0% +way right so what it means the the maxim +solution like this means is even you + + align:start position:0% +solution like this means is even you + + + align:start position:0% +solution like this means is even you +have a object here if you're away you + + align:start position:0% +have a object here if you're away you + + + align:start position:0% +have a object here if you're away you +don't see far away the the there's no + + align:start position:0% +don't see far away the the there's no + + + align:start position:0% +don't see far away the the there's no +scatter light right so what you see you + + align:start position:0% +scatter light right so what you see you + + + align:start position:0% +scatter light right so what you see you +the light goes WR but say you look at it + + align:start position:0% +the light goes WR but say you look at it + + + align:start position:0% +the light goes WR but say you look at it +it's just like the object doesn't exist + + align:start position:0% +it's just like the object doesn't exist + + + align:start position:0% +it's just like the object doesn't exist +that's what the say some of the strange + + align:start position:0% +that's what the say some of the strange + + + align:start position:0% +that's what the say some of the strange +effect of this m + + align:start position:0% +effect of this m + + + align:start position:0% +effect of this m +materials + + align:start position:0% +materials + + + align:start position:0% +materials +okay and uh I think uh say I'll stop + + align:start position:0% +okay and uh I think uh say I'll stop + + + align:start position:0% +okay and uh I think uh say I'll stop +here but let's look at the now you can + + align:start position:0% +here but let's look at the now you can + + + align:start position:0% +here but let's look at the now you can +see a lot of interesting stuff it's SL + + align:start position:0% +see a lot of interesting stuff it's SL + + + align:start position:0% +see a lot of interesting stuff it's SL +longer + + align:start position:0% + + + + align:start position:0% + +so if you go to check say this at the + + align:start position:0% +so if you go to check say this at the + + + align:start position:0% +so if you go to check say this at the +beginning there there there a lot of + + align:start position:0% +beginning there there there a lot of + + + align:start position:0% +beginning there there there a lot of +people there Pap say there's notive + + align:start position:0% +people there Pap say there's notive + + + align:start position:0% +people there Pap say there's notive +refraction uh there say uh basically uh + + align:start position:0% +refraction uh there say uh basically uh + + + align:start position:0% +refraction uh there say uh basically uh +this is a a little bit confusing because + + align:start position:0% +this is a a little bit confusing because + + + align:start position:0% +this is a a little bit confusing because +energy propag Mo forward and information + + align:start position:0% +energy propag Mo forward and information + + + align:start position:0% +energy propag Mo forward and information +is propagating backwards typically + + align:start position:0% +is propagating backwards typically + + + align:start position:0% +is propagating backwards typically +people like to associate V Vector to + + align:start position:0% +people like to associate V Vector to + + + align:start position:0% +people like to associate V Vector to +information and uh this a lot of uh + + align:start position:0% +information and uh this a lot of uh + + + align:start position:0% +information and uh this a lot of uh +debate in + + align:start position:0% +debate in + + + align:start position:0% +debate in +literature but now I think the debate is + + align:start position:0% +literature but now I think the debate is + + + align:start position:0% +literature but now I think the debate is +all gone and U uh it's a very + + align:start position:0% +all gone and U uh it's a very + + + align:start position:0% +all gone and U uh it's a very +uh active in fact + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +uh I just mentioned that Epsilon could + + align:start position:0% +uh I just mentioned that Epsilon could + + + align:start position:0% +uh I just mentioned that Epsilon could +be negative when negative there is also + + align:start position:0% +be negative when negative there is also + + + align:start position:0% +be negative when negative there is also +uh it turns out that they uh again all + + align:start position:0% +uh it turns out that they uh again all + + + align:start position:0% +uh it turns out that they uh again all +this is we're going to talk more next + + align:start position:0% +this is we're going to talk more next + + + align:start position:0% +this is we're going to talk more next +lecture uh the uh there is a surface + + align:start position:0% +lecture uh the uh there is a surface + + + align:start position:0% +lecture uh the uh there is a surface +wave we just said the evalent wave is + + align:start position:0% +wave we just said the evalent wave is + + + align:start position:0% +wave we just said the evalent wave is +exponentially Decay on one side right we + + align:start position:0% +exponentially Decay on one side right we + + + align:start position:0% +exponentially Decay on one side right we +just say the electron evalent wave you + + align:start position:0% +just say the electron evalent wave you + + + align:start position:0% +just say the electron evalent wave you +have Photon evalent wave but say this + + align:start position:0% +have Photon evalent wave but say this + + + align:start position:0% +have Photon evalent wave but say this +when ion is negative you could have a + + align:start position:0% +when ion is negative you could have a + + + align:start position:0% +when ion is negative you could have a +surface wave that decays on both sides + + align:start position:0% +surface wave that decays on both sides + + + align:start position:0% +surface wave that decays on both sides +doesn't exist far away from interface so + + align:start position:0% +doesn't exist far away from interface so + + + align:start position:0% +doesn't exist far away from interface so +is only confined to the surface and + + align:start position:0% +is only confined to the surface and + + + align:start position:0% +is only confined to the surface and +that's a surface plasmas so when the + + align:start position:0% +that's a surface plasmas so when the + + + align:start position:0% +that's a surface plasmas so when the +these are the electron so uh let's + + align:start position:0% +these are the electron so uh let's + + + align:start position:0% +these are the electron so uh let's +say let me just uh do a few phon + + align:start position:0% + + + + align:start position:0% + +um no now go to + + align:start position:0% +um no now go to + + + align:start position:0% +um no now go to +this uh + + align:start position:0% + + + + align:start position:0% + +image okay so uh though you can say that + + align:start position:0% +image okay so uh though you can say that + + + align:start position:0% +image okay so uh though you can say that +uh this is a + + align:start position:0% +uh this is a + + + align:start position:0% +uh this is a +uh um really periodic structure in 3D or + + align:start position:0% +uh um really periodic structure in 3D or + + + align:start position:0% +uh um really periodic structure in 3D or +2D originally is like films as I said + + align:start position:0% +2D originally is like films as I said + + + align:start position:0% +2D originally is like films as I said +right in fact I was at the UCA y UCA I + + align:start position:0% +right in fact I was at the UCA y UCA I + + + align:start position:0% +right in fact I was at the UCA y UCA I +remember once I attend a uh a student + + align:start position:0% +remember once I attend a uh a student + + + align:start position:0% +remember once I attend a uh a student +thesis meeting there was another + + align:start position:0% +thesis meeting there was another + + + align:start position:0% +thesis meeting there was another +professor just say there's no BR uh + + align:start position:0% +professor just say there's no BR uh + + + align:start position:0% +professor just say there's no BR uh +fonic Crystal it's just a br reflector + + align:start position:0% +fonic Crystal it's just a br reflector + + + align:start position:0% +fonic Crystal it's just a br reflector +brog reflector is the 1D structure + + align:start position:0% +brog reflector is the 1D structure + + + align:start position:0% +brog reflector is the 1D structure +people called Brock reflector right 3D + + align:start position:0% +people called Brock reflector right 3D + + + align:start position:0% +people called Brock reflector right 3D +gives you a different name and sudden + + align:start position:0% +gives you a different name and sudden + + + align:start position:0% +gives you a different name and sudden +open up your imagination and uh you so + + align:start position:0% +open up your imagination and uh you so + + + align:start position:0% +open up your imagination and uh you so +people start look at a a photonic + + align:start position:0% +people start look at a a photonic + + + align:start position:0% +people start look at a a photonic +semiconductor where you have a gap right + + align:start position:0% +semiconductor where you have a gap right + + + align:start position:0% +semiconductor where you have a gap right +and uh you can dope your Photon photonic + + align:start position:0% +and uh you can dope your Photon photonic + + + align:start position:0% +and uh you can dope your Photon photonic +Crystal and uh uh what does that mean + + align:start position:0% +Crystal and uh uh what does that mean + + + align:start position:0% +Crystal and uh uh what does that mean +right and uh so you can see some of this + + align:start position:0% +right and uh so you can see some of this + + + align:start position:0% +right and uh so you can see some of this +uh is uh you you can guid light in the + + align:start position:0% +uh is uh you you can guid light in the + + + align:start position:0% +uh is uh you you can guid light in the +structures and bending 90 degree and + + align:start position:0% +structures and bending 90 degree and + + + align:start position:0% +structures and bending 90 degree and +normally in optical fiber you can't do + + align:start position:0% +normally in optical fiber you can't do + + + align:start position:0% +normally in optical fiber you can't do +that and you have to make a slow turn if + + align:start position:0% +that and you have to make a slow turn if + + + align:start position:0% +that and you have to make a slow turn if +you use Optical fibers but if you use + + align:start position:0% +you use Optical fibers but if you use + + + align:start position:0% +you use Optical fibers but if you use +this kind of structure you can have more + + align:start position:0% +this kind of structure you can have more + + + align:start position:0% +this kind of structure you can have more +complicated uh say uh light + + align:start position:0% +complicated uh say uh light + + + align:start position:0% +complicated uh say uh light +path and + + align:start position:0% +path and + + + align:start position:0% +path and +uh me + + align:start position:0% +uh me + + + align:start position:0% +uh me +materials right and this was + + align:start position:0% +materials right and this was + + + align:start position:0% +materials right and this was +the first uh uh expr expent where they + + align:start position:0% +the first uh uh expr expent where they + + + align:start position:0% +the first uh uh expr expent where they +use the split R in fact it's a 2d uh so + + align:start position:0% +use the split R in fact it's a 2d uh so + + + align:start position:0% +use the split R in fact it's a 2d uh so +they show that + + align:start position:0% +they show that + + + align:start position:0% +they show that +uh um the this kind of structure and it + + align:start position:0% +uh um the this kind of structure and it + + + align:start position:0% +uh um the this kind of structure and it +could have say negative Epsilon and + + align:start position:0% +could have say negative Epsilon and + + + align:start position:0% +could have say negative Epsilon and +negative mu at the same frequency range + + align:start position:0% +negative mu at the same frequency range + + + align:start position:0% +negative mu at the same frequency range +and uh it was a pretty large structure + + align:start position:0% +and uh it was a pretty large structure + + + align:start position:0% +and uh it was a pretty large structure +and they did a microwave experiment show + + align:start position:0% +and they did a microwave experiment show + + + align:start position:0% +and they did a microwave experiment show +light can indeed go the wrong way that's + + align:start position:0% +light can indeed go the wrong way that's + + + align:start position:0% +light can indeed go the wrong way that's +what people say like bend the wrong way + + align:start position:0% +what people say like bend the wrong way + + + align:start position:0% +what people say like bend the wrong way +and normally against intu + + align:start position:0% +and normally against intu + + + align:start position:0% +and normally against intu +and after that there are lot + + align:start position:0% +and after that there are lot + + + align:start position:0% +and after that there are lot +of lot of structures right and let's + + align:start position:0% +of lot of structures right and let's + + + align:start position:0% +of lot of structures right and let's +look at the + + align:start position:0% + + + + align:start position:0% + +clocking well this is not people are not + + align:start position:0% +clocking well this is not people are not + + + align:start position:0% +clocking well this is not people are not +able to do that yet uh it's a different + + align:start position:0% +able to do that yet uh it's a different + + + align:start position:0% +able to do that yet uh it's a different +uh different way of doing it but that's + + align:start position:0% +uh different way of doing it but that's + + + align:start position:0% +uh different way of doing it but that's +the sort of what I was explaining right + + align:start position:0% +the sort of what I was explaining right + + + align:start position:0% +the sort of what I was explaining right +if your light doesn't get scatter into + + align:start position:0% +if your light doesn't get scatter into + + + align:start position:0% +if your light doesn't get scatter into +other directions essenti + + align:start position:0% +other directions essenti + + + align:start position:0% +other directions essenti +if you're way from way from if you're + + align:start position:0% +if you're way from way from if you're + + + align:start position:0% +if you're way from way from if you're +away from it is you don't look at + + align:start position:0% +away from it is you don't look at + + + align:start position:0% +away from it is you don't look at +there's no reflection signal you can + + align:start position:0% +there's no reflection signal you can + + + align:start position:0% +there's no reflection signal you can +detect okay and uh so story is don't Lo + + align:start position:0% +detect okay and uh so story is don't Lo + + + align:start position:0% +detect okay and uh so story is don't Lo +don't miss the + + align:start position:0% +don't miss the + + + align:start position:0% +don't miss the +details + + align:start position:0% +details + + + align:start position:0% +details +okay some of the tiny effect but it + + align:start position:0% +okay some of the tiny effect but it + + + align:start position:0% +okay some of the tiny effect but it +could be big + + align:start position:0% + + + + align:start position:0% + +story e \ No newline at end of file diff --git a/Lco0Jh892iA.txt b/Lco0Jh892iA.txt new file mode 100644 index 0000000000000000000000000000000000000000..909bd245769c5c116afce83baabeca199186c71c --- /dev/null +++ b/Lco0Jh892iA.txt @@ -0,0 +1,10627 @@ +align:start position:0% + +okay so today we're just going to go + + align:start position:0% +okay so today we're just going to go + + + align:start position:0% +okay so today we're just going to go +through some topics and um we stop me + + align:start position:0% +through some topics and um we stop me + + + align:start position:0% +through some topics and um we stop me +when you when you are I want to um first + + align:start position:0% +when you when you are I want to um first + + + align:start position:0% +when you when you are I want to um first +thing I'll do is just talk a little bit + + align:start position:0% +thing I'll do is just talk a little bit + + + align:start position:0% +thing I'll do is just talk a little bit +about some of the things in my research + + align:start position:0% +about some of the things in my research + + + align:start position:0% +about some of the things in my research +and some of them are connected with a + + align:start position:0% +and some of them are connected with a + + + align:start position:0% +and some of them are connected with a +topic that's lingering in the back of + + align:start position:0% +topic that's lingering in the back of + + + align:start position:0% +topic that's lingering in the back of +this class that um but that's not + + align:start position:0% +this class that um but that's not + + + align:start position:0% +this class that um but that's not +explicit and that is this the second + + align:start position:0% +explicit and that is this the second + + + align:start position:0% +explicit and that is this the second +adjacent field of statistical and pure + + align:start position:0% +adjacent field of statistical and pure + + + align:start position:0% +adjacent field of statistical and pure +math um sort of computational or + + align:start position:0% +math um sort of computational or + + + align:start position:0% +math um sort of computational or +musicology research that is not directly + + align:start position:0% +musicology research that is not directly + + + align:start position:0% +musicology research that is not directly +computational so we'll do a little bit + + align:start position:0% +computational so we'll do a little bit + + + align:start position:0% +computational so we'll do a little bit +with that um you'll find on the on the + + align:start position:0% +with that um you'll find on the on the + + + align:start position:0% +with that um you'll find on the on the +canvas site there's a very cool uh I + + align:start position:0% +canvas site there's a very cool uh I + + + align:start position:0% +canvas site there's a very cool uh I +think it's like nine page it's really + + align:start position:0% +think it's like nine page it's really + + + align:start position:0% +think it's like nine page it's really +short it has lots of pictures uh article + + align:start position:0% +short it has lots of pictures uh article + + + align:start position:0% +short it has lots of pictures uh article +that I'd like you to take some time to + + align:start position:0% +that I'd like you to take some time to + + + align:start position:0% +that I'd like you to take some time to +read by Leon H uh hackford who um wrote + + align:start position:0% +read by Leon H uh hackford who um wrote + + + align:start position:0% +read by Leon H uh hackford who um wrote +a whole book on mathematics and music + + align:start position:0% +a whole book on mathematics and music + + + align:start position:0% +a whole book on mathematics and music +which is very cool but I find the most + + align:start position:0% +which is very cool but I find the most + + + align:start position:0% +which is very cool but I find the most +cool thing about that is the Final + + align:start position:0% +cool thing about that is the Final + + + align:start position:0% +cool thing about that is the Final +Chapter how not to mix math and music + + align:start position:0% +Chapter how not to mix math and music + + + align:start position:0% +Chapter how not to mix math and music +and the ways people have mixed math and + + align:start position:0% +and the ways people have mixed math and + + + align:start position:0% +and the ways people have mixed math and +music and got things really um wrong so + + align:start position:0% +music and got things really um wrong so + + + align:start position:0% +music and got things really um wrong so +uh might bring that up a little bit more + + align:start position:0% +uh might bring that up a little bit more + + + align:start position:0% +uh might bring that up a little bit more +so we'll do a little bit with some + + align:start position:0% +so we'll do a little bit with some + + + align:start position:0% +so we'll do a little bit with some +statistical and math things uh that + + align:start position:0% +statistical and math things uh that + + + align:start position:0% +statistical and math things uh that +relate to my own research too okay so I + + align:start position:0% +relate to my own research too okay so I + + + align:start position:0% +relate to my own research too okay so I +um I'm trained as a um actually let me + + align:start position:0% +um I'm trained as a um actually let me + + + align:start position:0% +um I'm trained as a um actually let me +turn off this light somehow yep is that + + align:start position:0% +turn off this light somehow yep is that + + + align:start position:0% +turn off this light somehow yep is that +good I'm trained as a medieval music + + align:start position:0% +good I'm trained as a medieval music + + + align:start position:0% +good I'm trained as a medieval music +historian so uh I really really got into + + align:start position:0% +historian so uh I really really got into + + + align:start position:0% +historian so uh I really really got into +Medieval music you'll hear little clips + + align:start position:0% +Medieval music you'll hear little clips + + + align:start position:0% +Medieval music you'll hear little clips +of it here and there and + + align:start position:0% +of it here and there and + + + align:start position:0% +of it here and there and +um and that was you know really what I + + align:start position:0% +um and that was you know really what I + + + align:start position:0% +um and that was you know really what I +wanted to do when I programmed on the + + align:start position:0% +wanted to do when I programmed on the + + + align:start position:0% +wanted to do when I programmed on the +side uh to make some spending money and + + align:start position:0% +side uh to make some spending money and + + + align:start position:0% +side uh to make some spending money and +things like that when I got into + + align:start position:0% +things like that when I got into + + + align:start position:0% +things like that when I got into +Medieval music I thought I'd be looking + + align:start position:0% +Medieval music I thought I'd be looking + + + align:start position:0% +Medieval music I thought I'd be looking +at things that are really beautiful like + + align:start position:0% +at things that are really beautiful like + + + align:start position:0% +at things that are really beautiful like +this all the time these are uh people + + align:start position:0% +this all the time these are uh people + + + align:start position:0% +this all the time these are uh people +playing a little crank or her Gertie + + align:start position:0% +playing a little crank or her Gertie + + + align:start position:0% +playing a little crank or her Gertie +type thing and stuff and there are these + + align:start position:0% +type thing and stuff and there are these + + + align:start position:0% +type thing and stuff and there are these +beautiful beautiful music manuscripts + + align:start position:0% +beautiful beautiful music manuscripts + + + align:start position:0% +beautiful beautiful music manuscripts +this is from the early 14th C Century + + align:start position:0% +this is from the early 14th C Century + + + align:start position:0% +this is from the early 14th C Century +called the um the novel of Fel the horse + + align:start position:0% +called the um the novel of Fel the horse + + + align:start position:0% +called the um the novel of Fel the horse +named Fel the Randa Fel and you know + + align:start position:0% +named Fel the Randa Fel and you know + + + align:start position:0% +named Fel the Randa Fel and you know +they're all really really gorgeous or + + align:start position:0% +they're all really really gorgeous or + + + align:start position:0% +they're all really really gorgeous or +there's the the original Carmin Brana + + align:start position:0% +there's the the original Carmin Brana + + + align:start position:0% +there's the the original Carmin Brana +that um that Carl ORF based his uh music + + align:start position:0% +that um that Carl ORF based his uh music + + + align:start position:0% +that um that Carl ORF based his uh music +off of yes this is what music notation + + align:start position:0% +off of yes this is what music notation + + + align:start position:0% +off of yes this is what music notation +once looked like um and then you know + + align:start position:0% +once looked like um and then you know + + + align:start position:0% +once looked like um and then you know +gorgeous books in the shape of a heart + + align:start position:0% +gorgeous books in the shape of a heart + + + align:start position:0% +gorgeous books in the shape of a heart +or um so I started focusing on the 14th + + align:start position:0% +or um so I started focusing on the 14th + + + align:start position:0% +or um so I started focusing on the 14th +century in Italy where we have this one + + align:start position:0% +century in Italy where we have this one + + + align:start position:0% +century in Italy where we have this one +really amazing book this called the + + align:start position:0% +really amazing book this called the + + + align:start position:0% +really amazing book this called the +squatchy aupi codex has these beautiful + + align:start position:0% +squatchy aupi codex has these beautiful + + + align:start position:0% +squatchy aupi codex has these beautiful +pictures of all the musicians who are um + + align:start position:0% +pictures of all the musicians who are um + + + align:start position:0% +pictures of all the musicians who are um +who are in there and it's great I think + + align:start position:0% +who are in there and it's great I think + + + align:start position:0% +who are in there and it's great I think +it's valued around $35 million or + + align:start position:0% +it's valued around $35 million or + + + align:start position:0% +it's valued around $35 million or +something like that so I thought I'd be + + align:start position:0% +something like that so I thought I'd be + + + align:start position:0% +something like that so I thought I'd be +working on this well it turns out people + + align:start position:0% +working on this well it turns out people + + + align:start position:0% +working on this well it turns out people +have been doing Medieval music research + + align:start position:0% +have been doing Medieval music research + + + align:start position:0% +have been doing Medieval music research +for I know hundreds of years and guess + + align:start position:0% +for I know hundreds of years and guess + + + align:start position:0% +for I know hundreds of years and guess +what they've all studied the really + + align:start position:0% +what they've all studied the really + + + align:start position:0% +what they've all studied the really +pretty books so if you wanted to go into + + align:start position:0% +pretty books so if you wanted to go into + + + align:start position:0% +pretty books so if you wanted to go into +this in the you know around 1998 2000 + + align:start position:0% +this in the you know around 1998 2000 + + + align:start position:0% +this in the you know around 1998 2000 +whenever I really got it started about + + align:start position:0% +whenever I really got it started about + + + align:start position:0% +whenever I really got it started about +25 years ago uh here's what's left for + + align:start position:0% +25 years ago uh here's what's left for + + + align:start position:0% +25 years ago uh here's what's left for +us to + + align:start position:0% +us to + + + align:start position:0% +us to +study little things like that you can + + align:start position:0% +study little things like that you can + + + align:start position:0% +study little things like that you can +kind of see the the music here here and + + align:start position:0% +kind of see the the music here here and + + + align:start position:0% +kind of see the the music here here and +stuff like that or um this is one of the + + align:start position:0% +stuff like that or um this is one of the + + + align:start position:0% +stuff like that or um this is one of the +ones I've been looking at uh worms eat + + align:start position:0% +ones I've been looking at uh worms eat + + + align:start position:0% +ones I've been looking at uh worms eat +them ravages of time or other little + + align:start position:0% +them ravages of time or other little + + + align:start position:0% +them ravages of time or other little +indignities um that the music is wrapped + + align:start position:0% +indignities um that the music is wrapped + + + align:start position:0% +indignities um that the music is wrapped +up to keep people's um sewage payment + + align:start position:0% +up to keep people's um sewage payment + + + align:start position:0% +up to keep people's um sewage payment +records you have to pay somebody to + + align:start position:0% +records you have to pay somebody to + + + align:start position:0% +records you have to pay somebody to +clean out your chamber pots and you want + + align:start position:0% +clean out your chamber pots and you want + + + align:start position:0% +clean out your chamber pots and you want +to make sure that somebody's paid their + + align:start position:0% +to make sure that somebody's paid their + + + align:start position:0% +to make sure that somebody's paid their +bill and so you know you wrap it in a + + align:start position:0% +bill and so you know you wrap it in a + + + align:start position:0% +bill and so you know you wrap it in a +piece of worthless music and you do that + + align:start position:0% +piece of worthless music and you do that + + + align:start position:0% +piece of worthless music and you do that +um well when you're wrapping music on + + align:start position:0% +um well when you're wrapping music on + + + align:start position:0% +um well when you're wrapping music on +top of other documents sometimes the + + align:start position:0% +top of other documents sometimes the + + + align:start position:0% +top of other documents sometimes the +document smaller than the music so no + + align:start position:0% +document smaller than the music so no + + + align:start position:0% +document smaller than the music so no +problem you trim the music and uh then + + align:start position:0% +problem you trim the music and uh then + + + align:start position:0% +problem you trim the music and uh then +it fits there and some people um you + + align:start position:0% +it fits there and some people um you + + + align:start position:0% +it fits there and some people um you +know there's there's nothing important + + align:start position:0% +know there's there's nothing important + + + align:start position:0% +know there's there's nothing important +on the left side of a score right I mean + + align:start position:0% +on the left side of a score right I mean + + + align:start position:0% +on the left side of a score right I mean +just clefts time signatures key + + align:start position:0% +just clefts time signatures key + + + align:start position:0% +just clefts time signatures key +signatures you know you know nothing + + align:start position:0% +signatures you know you know nothing + + + align:start position:0% +signatures you know you know nothing +like that they used a lot of cffs back + + align:start position:0% +like that they used a lot of cffs back + + + align:start position:0% +like that they used a lot of cffs back +then um and then sometimes you wanted + + align:start position:0% +then um and then sometimes you wanted + + + align:start position:0% +then um and then sometimes you wanted +things to look really nice so you would + + align:start position:0% +things to look really nice so you would + + + align:start position:0% +things to look really nice so you would +uh wipe off wash off or scrape off all + + align:start position:0% +uh wipe off wash off or scrape off all + + + align:start position:0% +uh wipe off wash off or scrape off all +the music that was there so that you + + align:start position:0% +the music that was there so that you + + + align:start position:0% +the music that was there so that you +know your cover looked a little nicer + + align:start position:0% +know your cover looked a little nicer + + + align:start position:0% +know your cover looked a little nicer +and then once you've scraped everything + + align:start position:0% +and then once you've scraped everything + + + align:start position:0% +and then once you've scraped everything +off it's all parchment and Vellum and + + align:start position:0% +off it's all parchment and Vellum and + + + align:start position:0% +off it's all parchment and Vellum and +stuff uh then you can reuse it for in + + align:start position:0% +stuff uh then you can reuse it for in + + + align:start position:0% +stuff uh then you can reuse it for in +this case Church landold Holdings in + + align:start position:0% +this case Church landold Holdings in + + + align:start position:0% +this case Church landold Holdings in +Florence + + align:start position:0% +Florence + + + align:start position:0% +Florence +um and then there's these little streps + + align:start position:0% +um and then there's these little streps + + + align:start position:0% +um and then there's these little streps +that you find sometimes that you weren't + + align:start position:0% +that you find sometimes that you weren't + + + align:start position:0% +that you find sometimes that you weren't +even sure are music but oh th those kind + + align:start position:0% +even sure are music but oh th those kind + + + align:start position:0% +even sure are music but oh th those kind +of look like quarter note stems quarter + + align:start position:0% +of look like quarter note stems quarter + + + align:start position:0% +of look like quarter note stems quarter +note stems and stuff like that so uh and + + align:start position:0% +note stems and stuff like that so uh and + + + align:start position:0% +note stems and stuff like that so uh and +this is what was left for me so I became + + align:start position:0% +this is what was left for me so I became + + + align:start position:0% +this is what was left for me so I became +sort of a music fragment scholar and um + + align:start position:0% +sort of a music fragment scholar and um + + + align:start position:0% +sort of a music fragment scholar and um +my things are all on fragments of + + align:start position:0% +my things are all on fragments of + + + align:start position:0% +my things are all on fragments of +polyphonic music from The 14th Century + + align:start position:0% +polyphonic music from The 14th Century + + + align:start position:0% +polyphonic music from The 14th Century +so I wanted to look at these things and + + align:start position:0% +so I wanted to look at these things and + + + align:start position:0% +so I wanted to look at these things and +you know how to move forward uh one of + + align:start position:0% +you know how to move forward uh one of + + + align:start position:0% +you know how to move forward uh one of +the things back then you with no + + align:start position:0% +the things back then you with no + + + align:start position:0% +the things back then you with no +computers is just spend a lot of time so + + align:start position:0% +computers is just spend a lot of time so + + + align:start position:0% +computers is just spend a lot of time so +one of the things they were really good + + align:start position:0% +one of the things they were really good + + + align:start position:0% +one of the things they were really good +about then is that they like who was + + align:start position:0% +about then is that they like who was + + + align:start position:0% +about then is that they like who was +told that in a music class when you + + align:start position:0% +told that in a music class when you + + + align:start position:0% +told that in a music class when you +write a quarter + + align:start position:0% +write a quarter + + + align:start position:0% +write a quarter +note that's a very bad one when you + + align:start position:0% +note that's a very bad one when you + + + align:start position:0% +note that's a very bad one when you +write a quarter note its stem should be + + align:start position:0% +write a quarter note its stem should be + + + align:start position:0% +write a quarter note its stem should be +exactly an octave long and so therefore + + align:start position:0% +exactly an octave long and so therefore + + + align:start position:0% +exactly an octave long and so therefore +it's kind of exactly like this I don't + + align:start position:0% +it's kind of exactly like this I don't + + + align:start position:0% +it's kind of exactly like this I don't +know if people are still taught that + + align:start position:0% +know if people are still taught that + + + align:start position:0% +know if people are still taught that +well they were very good at that so you + + align:start position:0% +well they were very good at that so you + + + align:start position:0% +well they were very good at that so you +can kind of figure out based on the + + align:start position:0% +can kind of figure out based on the + + + align:start position:0% +can kind of figure out based on the +heights the stems What notes must have + + align:start position:0% +heights the stems What notes must have + + + align:start position:0% +heights the stems What notes must have +been cut off there and where they are + + align:start position:0% +been cut off there and where they are + + + align:start position:0% +been cut off there and where they are +and you just stare for hours and hours + + align:start position:0% +and you just stare for hours and hours + + + align:start position:0% +and you just stare for hours and hours +and hours of other books until + + align:start position:0% +and hours of other books until + + + align:start position:0% +and hours of other books until +eventually you find one where every one + + align:start position:0% +eventually you find one where every one + + + align:start position:0% +eventually you find one where every one +of the stems lines up I had to squish + + align:start position:0% +of the stems lines up I had to squish + + + align:start position:0% +of the stems lines up I had to squish +this by about 10% to get it but things + + align:start position:0% +this by about 10% to get it but things + + + align:start position:0% +this by about 10% to get it but things +like that or for something like this you + + align:start position:0% +like that or for something like this you + + + align:start position:0% +like that or for something like this you +just uh there's three parts they wrote + + align:start position:0% +just uh there's three parts they wrote + + + align:start position:0% +just uh there's three parts they wrote +the parts separately back then kind of + + align:start position:0% +the parts separately back then kind of + + + align:start position:0% +the parts separately back then kind of +like I don't know iterating through the + + align:start position:0% +like I don't know iterating through the + + + align:start position:0% +like I don't know iterating through the +recurse method and not the flatten + + align:start position:0% +recurse method and not the flatten + + + align:start position:0% +recurse method and not the flatten +method and so um part one part two part + + align:start position:0% +method and so um part one part two part + + + align:start position:0% +method and so um part one part two part +three and so you TR try every + + align:start position:0% +three and so you TR try every + + + align:start position:0% +three and so you TR try every +combination of clef and time signature + + align:start position:0% +combination of clef and time signature + + + align:start position:0% +combination of clef and time signature +and key signature until you finally find + + align:start position:0% +and key signature until you finally find + + + align:start position:0% +and key signature until you finally find +where things um line up then use your + + align:start position:0% +where things um line up then use your + + + align:start position:0% +where things um line up then use your +knowledge of Music Theory from The 14th + + align:start position:0% +knowledge of Music Theory from The 14th + + + align:start position:0% +knowledge of Music Theory from The 14th +Century to fill in the missing parts and + + align:start position:0% +Century to fill in the missing parts and + + + align:start position:0% +Century to fill in the missing parts and +eventually your friends record the piece + + align:start position:0% +eventually your friends record the piece + + + align:start position:0% +eventually your friends record the piece +for you + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +um then when the notes get big it's what + + align:start position:0% +um then when the notes get big it's what + + + align:start position:0% +um then when the notes get big it's what +we actually know + + align:start position:0% + + + + align:start position:0% + +so anyhow those was some of the things + + align:start position:0% +so anyhow those was some of the things + + + align:start position:0% +so anyhow those was some of the things +and and um then first place where + + align:start position:0% +and and um then first place where + + + align:start position:0% +and and um then first place where +computers really started coming in uh + + align:start position:0% +computers really started coming in uh + + + align:start position:0% +computers really started coming in uh +was about when we started getting nice + + align:start position:0% +was about when we started getting nice + + + align:start position:0% +was about when we started getting nice +color photographs before everything was + + align:start position:0% +color photographs before everything was + + + align:start position:0% +color photographs before everything was +black and white photoc copies and stuff + + align:start position:0% +black and white photoc copies and stuff + + + align:start position:0% +black and white photoc copies and stuff +and um I with some other people and some + + align:start position:0% +and um I with some other people and some + + + align:start position:0% +and um I with some other people and some +other people independent of me all came + + align:start position:0% +other people independent of me all came + + + align:start position:0% +other people independent of me all came +up about the same time with a technique + + align:start position:0% +up about the same time with a technique + + + align:start position:0% +up about the same time with a technique +that um that if you measured the colors + + align:start position:0% +that um that if you measured the colors + + + align:start position:0% +that um that if you measured the colors +of the overwriting and the colors of the + + align:start position:0% +of the overwriting and the colors of the + + + align:start position:0% +of the overwriting and the colors of the +under writing the ink would probably be + + align:start position:0% +under writing the ink would probably be + + + align:start position:0% +under writing the ink would probably be +different so you could remove one and + + align:start position:0% +different so you could remove one and + + + align:start position:0% +different so you could remove one and +bring the other up and so we had these + + align:start position:0% +bring the other up and so we had these + + + align:start position:0% +bring the other up and so we had these +various computer uh techniques for + + align:start position:0% +various computer uh techniques for + + + align:start position:0% +various computer uh techniques for +getting rid of the overwriting and + + align:start position:0% +getting rid of the overwriting and + + + align:start position:0% +getting rid of the overwriting and +getting to the music + + align:start position:0% + + + + align:start position:0% + +underneath but um everything after this + + align:start position:0% +underneath but um everything after this + + + align:start position:0% +underneath but um everything after this +was still going to be done by hand so I + + align:start position:0% +was still going to be done by hand so I + + + align:start position:0% +was still going to be done by hand so I +started thinking about ways to use + + align:start position:0% +started thinking about ways to use + + + align:start position:0% +started thinking about ways to use +statistics and computers to do various + + align:start position:0% +statistics and computers to do various + + + align:start position:0% +statistics and computers to do various +things so about this time started + + align:start position:0% +things so about this time started + + + align:start position:0% +things so about this time started +creating music 21 and if you ever wonder + + align:start position:0% +creating music 21 and if you ever wonder + + + align:start position:0% +creating music 21 and if you ever wonder +why there's some things that are obscure + + align:start position:0% +why there's some things that are obscure + + + align:start position:0% +why there's some things that are obscure +music 21's sole purpose was to try to + + align:start position:0% +music 21's sole purpose was to try to + + + align:start position:0% +music 21's sole purpose was to try to +identify music fragments like that and + + align:start position:0% +identify music fragments like that and + + + align:start position:0% +identify music fragments like that and +everything else that this class has uh + + align:start position:0% +everything else that this class has uh + + + align:start position:0% +everything else that this class has uh +sort of come about has just been sort of + + align:start position:0% +sort of come about has just been sort of + + + align:start position:0% +sort of come about has just been sort of +a side uh side project um + + align:start position:0% +a side uh side project um + + + align:start position:0% +a side uh side project um +so while I was building that I switched + + align:start position:0% +so while I was building that I switched + + + align:start position:0% +so while I was building that I switched +into sort of a statistical mode so we'll + + align:start position:0% +into sort of a statistical mode so we'll + + + align:start position:0% +into sort of a statistical mode so we'll +get back to music 21 in a bit but first + + align:start position:0% +get back to music 21 in a bit but first + + + align:start position:0% +get back to music 21 in a bit but first +want to think about some of the things + + align:start position:0% +want to think about some of the things + + + align:start position:0% +want to think about some of the things +that that were coming up with all these + + align:start position:0% +that that were coming up with all these + + + align:start position:0% +that that were coming up with all these +fragments and I was trying trying to + + align:start position:0% +fragments and I was trying trying to + + + align:start position:0% +fragments and I was trying trying to +figure out what they were and that meant + + align:start position:0% +figure out what they were and that meant + + + align:start position:0% +figure out what they were and that meant +I would need to find another piece that + + align:start position:0% +I would need to find another piece that + + + align:start position:0% +I would need to find another piece that +was like that but the odds that another + + align:start position:0% +was like that but the odds that another + + + align:start position:0% +was like that but the odds that another +piece would exist that matched up with + + align:start position:0% +piece would exist that matched up with + + + align:start position:0% +piece would exist that matched up with +the music I was told were really really + + align:start position:0% +the music I was told were really really + + + align:start position:0% +the music I was told were really really +low uh in fact uh a very famous uh + + align:start position:0% +low uh in fact uh a very famous uh + + + align:start position:0% +low uh in fact uh a very famous uh +article by uh somebody who's very famous + + align:start position:0% +article by uh somebody who's very famous + + + align:start position:0% +article by uh somebody who's very famous +in my field Nino Pera um the oral and + + align:start position:0% +in my field Nino Pera um the oral and + + + align:start position:0% +in my field Nino Pera um the oral and +written traditions of Music said that um + + align:start position:0% +written traditions of Music said that um + + + align:start position:0% +written traditions of Music said that um +the surviving music from the Middle Ages + + align:start position:0% +the surviving music from the Middle Ages + + + align:start position:0% +the surviving music from the Middle Ages +is the tip of the iceberg and that + + align:start position:0% +is the tip of the iceberg and that + + + align:start position:0% +is the tip of the iceberg and that +metaphor ended up being uh quoted and + + align:start position:0% +metaphor ended up being uh quoted and + + + align:start position:0% +metaphor ended up being uh quoted and +reused in whole bunch of other articles + + align:start position:0% +reused in whole bunch of other articles + + + align:start position:0% +reused in whole bunch of other articles +that you don't need to see here but um + + align:start position:0% +that you don't need to see here but um + + + align:start position:0% +that you don't need to see here but um +so th this became sort of what everybody + + align:start position:0% +so th this became sort of what everybody + + + align:start position:0% +so th this became sort of what everybody +knew so if you're thinking about music + + align:start position:0% +knew so if you're thinking about music + + + align:start position:0% +knew so if you're thinking about music +from you know 600 years ago and you + + align:start position:0% +from you know 600 years ago and you + + + align:start position:0% +from you know 600 years ago and you +think about all the things you've lost + + align:start position:0% +think about all the things you've lost + + + align:start position:0% +think about all the things you've lost +in your 20 years of life for however + + align:start position:0% +in your 20 years of life for however + + + align:start position:0% +in your 20 years of life for however +long um what percentage of things would + + align:start position:0% +long um what percentage of things would + + + align:start position:0% +long um what percentage of things would +have survived from 600 years + + align:start position:0% +have survived from 600 years + + + align:start position:0% +have survived from 600 years +ago or would be lost would be lost about + + align:start position:0% +ago or would be lost would be lost about + + + align:start position:0% +ago or would be lost would be lost about +90% + + align:start position:0% +90% + + + align:start position:0% +90% +99% + + align:start position:0% +99% + + + align:start position:0% +99% +99.9% these are all numbers that I found + + align:start position:0% +99.9% these are all numbers that I found + + + align:start position:0% +99.9% these are all numbers that I found +people said and then somebody said + + align:start position:0% +people said and then somebody said + + + align:start position:0% +people said and then somebody said +basically everything so I I have to + + align:start position:0% +basically everything so I I have to + + + align:start position:0% +basically everything so I I have to +convert everything to a number that's + + align:start position:0% +convert everything to a number that's + + + align:start position:0% +convert everything to a number that's +pretty close to basically everything for + + align:start position:0% +pretty close to basically everything for + + + align:start position:0% +pretty close to basically everything for +me + + align:start position:0% +me + + + align:start position:0% +me +um I'm going to skip over that we don't + + align:start position:0% +um I'm going to skip over that we don't + + + align:start position:0% +um I'm going to skip over that we don't +have all the time in the world um so I + + align:start position:0% +have all the time in the world um so I + + + align:start position:0% +have all the time in the world um so I +started to think about some statistical + + align:start position:0% +started to think about some statistical + + + align:start position:0% +started to think about some statistical +methodologies that could um that could + + align:start position:0% +methodologies that could um that could + + + align:start position:0% +methodologies that could um that could +help in this and one of the things that + + align:start position:0% +help in this and one of the things that + + + align:start position:0% +help in this and one of the things that +we have in some cases is uh this is a + + align:start position:0% +we have in some cases is uh this is a + + + align:start position:0% +we have in some cases is uh this is a +table of contents for a book of music + + align:start position:0% +table of contents for a book of music + + + align:start position:0% +table of contents for a book of music +from The 14th Century where the book + + align:start position:0% +from The 14th Century where the book + + + align:start position:0% +from The 14th Century where the book +doesn't exist but the table of contents + + align:start position:0% +doesn't exist but the table of contents + + + align:start position:0% +doesn't exist but the table of contents +does so I started looking at okay here's + + align:start position:0% +does so I started looking at okay here's + + + align:start position:0% +does so I started looking at okay here's +all the pieces that do not + + align:start position:0% +all the pieces that do not + + + align:start position:0% +all the pieces that do not +exist and then here's all the pieces + + align:start position:0% +exist and then here's all the pieces + + + align:start position:0% +exist and then here's all the pieces +that do + + align:start position:0% +that do + + + align:start position:0% +that do +exist and stting to look at the + + align:start position:0% +exist and stting to look at the + + + align:start position:0% +exist and stting to look at the +ratios and in this particular manuscript + + align:start position:0% +ratios and in this particular manuscript + + + align:start position:0% +ratios and in this particular manuscript +it looks like about 68% of them survive + + align:start position:0% +it looks like about 68% of them survive + + + align:start position:0% +it looks like about 68% of them survive +so that was that was the first thing + + align:start position:0% +so that was that was the first thing + + + align:start position:0% +so that was that was the first thing +that maybe the + + align:start position:0% +that maybe the + + + align:start position:0% +that maybe the +99.9999 number didn't exist and then I + + align:start position:0% +99.9999 number didn't exist and then I + + + align:start position:0% +99.9999 number didn't exist and then I +looked at there's a poet bunch of poetry + + align:start position:0% +looked at there's a poet bunch of poetry + + + align:start position:0% +looked at there's a poet bunch of poetry +manuscripts so this is um one from about + + align:start position:0% +manuscripts so this is um one from about + + + align:start position:0% +manuscripts so this is um one from about +the time of Dante or chasser um by a not + + align:start position:0% +the time of Dante or chasser um by a not + + + align:start position:0% +the time of Dante or chasser um by a not +very good poet named kenani but one of + + align:start position:0% +very good poet named kenani but one of + + + align:start position:0% +very good poet named kenani but one of +the things that makes him a bad poet + + align:start position:0% +the things that makes him a bad poet + + + align:start position:0% +the things that makes him a bad poet +that's really good is that when he gets + + align:start position:0% +that's really good is that when he gets + + + align:start position:0% +that's really good is that when he gets +into something when he's talking about a + + align:start position:0% +into something when he's talking about a + + + align:start position:0% +into something when he's talking about a +feast he will list for the next 50 lines + + align:start position:0% +feast he will list for the next 50 lines + + + align:start position:0% +feast he will list for the next 50 lines +everything they possibly ate and when it + + align:start position:0% +everything they possibly ate and when it + + + align:start position:0% +everything they possibly ate and when it +gets to a concert he lists um with the + + align:start position:0% +gets to a concert he lists um with the + + + align:start position:0% +gets to a concert he lists um with the +viola + + align:start position:0% + + + + align:start position:0% + +we played our Mayday songs we just had + + align:start position:0% +we played our Mayday songs we just had + + + align:start position:0% +we played our Mayday songs we just had +Mayday uh so these are the MayDay songs + + align:start position:0% +Mayday uh so these are the MayDay songs + + + align:start position:0% +Mayday uh so these are the MayDay songs +like the rose that never changes its + + align:start position:0% +like the rose that never changes its + + + align:start position:0% +like the rose that never changes its +color sweet um sweet taste and so on and + + align:start position:0% +color sweet um sweet taste and so on and + + + align:start position:0% +color sweet um sweet taste and so on and +these all look like names of songs and + + align:start position:0% +these all look like names of songs and + + + align:start position:0% +these all look like names of songs and +so we can look at for each one of them + + align:start position:0% +so we can look at for each one of them + + + align:start position:0% +so we can look at for each one of them +do we have a song by that name or do we + + align:start position:0% +do we have a song by that name or do we + + + align:start position:0% +do we have a song by that name or do we +not and so we have how many are known + + align:start position:0% +not and so we have how many are known + + + align:start position:0% +not and so we have how many are known +how many are unknown and we + + align:start position:0% +how many are unknown and we + + + align:start position:0% +how many are unknown and we +eventually get to a number that looks a + + align:start position:0% +eventually get to a number that looks a + + + align:start position:0% +eventually get to a number that looks a +little bit similar to the last one about + + align:start position:0% +little bit similar to the last one about + + + align:start position:0% +little bit similar to the last one about +71% + + align:start position:0% +71% + + + align:start position:0% +71% +survive so I was kind of going through + + align:start position:0% +survive so I was kind of going through + + + align:start position:0% +survive so I was kind of going through +this the chronology is a little bit + + align:start position:0% +this the chronology is a little bit + + + align:start position:0% +this the chronology is a little bit +wrong I had to justify this later but + + align:start position:0% +wrong I had to justify this later but + + + align:start position:0% +wrong I had to justify this later but +first I was thinking about how animal + + align:start position:0% +first I was thinking about how animal + + + align:start position:0% +first I was thinking about how animal +biologist uh ecologists count animals um + + align:start position:0% +biologist uh ecologists count animals um + + + align:start position:0% +biologist uh ecologists count animals um +has anyone taken a biology class or + + align:start position:0% +has anyone taken a biology class or + + + align:start position:0% +has anyone taken a biology class or +something where you do population + + align:start position:0% +something where you do population + + + align:start position:0% +something where you do population +estimates yeah what so one of the ways + + align:start position:0% +estimates yeah what so one of the ways + + + align:start position:0% +estimates yeah what so one of the ways +that you can do it is you um C you want + + align:start position:0% +that you can do it is you um C you want + + + align:start position:0% +that you can do it is you um C you want +to know how many deer are in the forest + + align:start position:0% +to know how many deer are in the forest + + + align:start position:0% +to know how many deer are in the forest +right so you go and you capture as many + + align:start position:0% +right so you go and you capture as many + + + align:start position:0% +right so you go and you capture as many +deer as you can in a month and a half + + align:start position:0% +deer as you can in a month and a half + + + align:start position:0% +deer as you can in a month and a half +you you come back smelling pretty bad + + align:start position:0% +you you come back smelling pretty bad + + + align:start position:0% +you you come back smelling pretty bad +and stuff but every time you find a deer + + align:start position:0% +and stuff but every time you find a deer + + + align:start position:0% +and stuff but every time you find a deer +you tag its uh ear or some way in some + + align:start position:0% +you tag its uh ear or some way in some + + + align:start position:0% +you tag its uh ear or some way in some +way that you can identify this is a deer + + align:start position:0% +way that you can identify this is a deer + + + align:start position:0% +way that you can identify this is a deer +that I saw and you come back several + + align:start position:0% +that I saw and you come back several + + + align:start position:0% +that I saw and you come back several +months later or whatever and then you + + align:start position:0% +months later or whatever and then you + + + align:start position:0% +months later or whatever and then you +count deer again and the percentage of + + align:start position:0% +count deer again and the percentage of + + + align:start position:0% +count deer again and the percentage of +deer that um that we're tagging the + + align:start position:0% +deer that um that we're tagging the + + + align:start position:0% +deer that um that we're tagging the +first time give you some sense of or the + + align:start position:0% +first time give you some sense of or the + + + align:start position:0% +first time give you some sense of or the +inverse of it gives you some sense sense + + align:start position:0% +inverse of it gives you some sense sense + + + align:start position:0% +inverse of it gives you some sense sense +of how big the population is if you + + align:start position:0% +of how big the population is if you + + + align:start position:0% +of how big the population is if you +tagged 100 deer the first time and you + + align:start position:0% +tagged 100 deer the first time and you + + + align:start position:0% +tagged 100 deer the first time and you +come back later and you only find then + + align:start position:0% +come back later and you only find then + + + align:start position:0% +come back later and you only find then +you capture 100 more deer and you only + + align:start position:0% +you capture 100 more deer and you only + + + align:start position:0% +you capture 100 more deer and you only +Capt see two of them are tagged you know + + align:start position:0% +Capt see two of them are tagged you know + + + align:start position:0% +Capt see two of them are tagged you know +there's a huge population of deer out + + align:start position:0% +there's a huge population of deer out + + + align:start position:0% +there's a huge population of deer out +there similarly if you captured 100 deer + + align:start position:0% +there similarly if you captured 100 deer + + + align:start position:0% +there similarly if you captured 100 deer +and next time you capture 100 deer 98 of + + align:start position:0% +and next time you capture 100 deer 98 of + + + align:start position:0% +and next time you capture 100 deer 98 of +them are tagged you probably saw most of + + align:start position:0% +them are tagged you probably saw most of + + + align:start position:0% +them are tagged you probably saw most of +them so started thinking about well if a + + align:start position:0% +them so started thinking about well if a + + + align:start position:0% +them so started thinking about well if a +piece appears in one manuscript we'll + + align:start position:0% +piece appears in one manuscript we'll + + + align:start position:0% +piece appears in one manuscript we'll +tag that piece and then we'll see how + + align:start position:0% +tag that piece and then we'll see how + + + align:start position:0% +tag that piece and then we'll see how +often it appears in another + + align:start position:0% +often it appears in another + + + align:start position:0% +often it appears in another +manuscript so I started coming up with + + align:start position:0% +manuscript so I started coming up with + + + align:start position:0% +manuscript so I started coming up with +formulas uh to do this type of thing and + + align:start position:0% +formulas uh to do this type of thing and + + + align:start position:0% +formulas uh to do this type of thing and +I realized that that there's an equation + + align:start position:0% +I realized that that there's an equation + + + align:start position:0% +I realized that that there's an equation +that tells us the number of missing + + align:start position:0% +that tells us the number of missing + + + align:start position:0% +that tells us the number of missing +pieces all you have to do is you take + + align:start position:0% +pieces all you have to do is you take + + + align:start position:0% +pieces all you have to do is you take +the number of pieces you originally had + + align:start position:0% +the number of pieces you originally had + + + align:start position:0% +the number of pieces you originally had +and you multiply by the probability that + + align:start position:0% +and you multiply by the probability that + + + align:start position:0% +and you multiply by the probability that +any piece would be missing tell me if + + align:start position:0% +any piece would be missing tell me if + + + align:start position:0% +any piece would be missing tell me if +I'm wrong you're the MIT students uh it + + align:start position:0% +I'm wrong you're the MIT students uh it + + + align:start position:0% +I'm wrong you're the MIT students uh it +equals the total number of missing + + align:start position:0% +equals the total number of missing + + + align:start position:0% +equals the total number of missing +pieces and it's a super great super + + align:start position:0% +pieces and it's a super great super + + + align:start position:0% +pieces and it's a super great super +simple formula except that it's a + + align:start position:0% +simple formula except that it's a + + + align:start position:0% +simple formula except that it's a +formula with three unknowns we don't + + align:start position:0% +formula with three unknowns we don't + + + align:start position:0% +formula with three unknowns we don't +know any of these three numbers + + align:start position:0% + + + + align:start position:0% + +but we can kind of figure out um some of + + align:start position:0% +but we can kind of figure out um some of + + + align:start position:0% +but we can kind of figure out um some of +these things so we can look at um well + + align:start position:0% +these things so we can look at um well + + + align:start position:0% +these things so we can look at um well +what's the probability that a given + + align:start position:0% +what's the probability that a given + + + align:start position:0% +what's the probability that a given +piece would be in a manuscript now we'll + + align:start position:0% +piece would be in a manuscript now we'll + + + align:start position:0% +piece would be in a manuscript now we'll +start with the assumption that every + + align:start position:0% +start with the assumption that every + + + align:start position:0% +start with the assumption that every +piece is sort of selected randomly so we + + align:start position:0% +piece is sort of selected randomly so we + + + align:start position:0% +piece is sort of selected randomly so we +start with how many pieces are there in + + align:start position:0% +start with how many pieces are there in + + + align:start position:0% +start with how many pieces are there in +a manuscript is just like a collection + + align:start position:0% +a manuscript is just like a collection + + + align:start position:0% +a manuscript is just like a collection +you know like a box set of of lots of + + align:start position:0% +you know like a box set of of lots of + + + align:start position:0% +you know like a box set of of lots of +tunes how many pieces are there in that + + align:start position:0% +tunes how many pieces are there in that + + + align:start position:0% +tunes how many pieces are there in that +manuscript we'll call that R subi and + + align:start position:0% +manuscript we'll call that R subi and + + + align:start position:0% +manuscript we'll call that R subi and +you divide it by the total number of + + align:start position:0% +you divide it by the total number of + + + align:start position:0% +you divide it by the total number of +pieces that were originally copied so we + + align:start position:0% +pieces that were originally copied so we + + + align:start position:0% +pieces that were originally copied so we +know how many pieces are in a manuscript + + align:start position:0% +know how many pieces are in a manuscript + + + align:start position:0% +know how many pieces are in a manuscript +because we can count that that survives + + align:start position:0% +because we can count that that survives + + + align:start position:0% +because we can count that that survives +but we don't know that so we just move + + align:start position:0% +but we don't know that so we just move + + + align:start position:0% +but we don't know that so we just move +our unknown to another + + align:start position:0% +our unknown to another + + + align:start position:0% +our unknown to another +place so we can also figure out what's + + align:start position:0% +place so we can also figure out what's + + + align:start position:0% +place so we can also figure out what's +the probability a piece is not in a + + align:start position:0% +the probability a piece is not in a + + + align:start position:0% +the probability a piece is not in a +given manuscript what's the what's the + + align:start position:0% +given manuscript what's the what's the + + + align:start position:0% +given manuscript what's the what's the +formula just see if you're awake if this + + align:start position:0% +formula just see if you're awake if this + + + align:start position:0% +formula just see if you're awake if this +is the F Formula it's in the manuscript + + align:start position:0% +is the F Formula it's in the manuscript + + + align:start position:0% +is the F Formula it's in the manuscript +what do we do one minus good good we're + + align:start position:0% +what do we do one minus good good we're + + + align:start position:0% +what do we do one minus good good we're +all on same page there great so what's + + align:start position:0% +all on same page there great so what's + + + align:start position:0% +all on same page there great so what's +the probability that it's not in too + + align:start position:0% +the probability that it's not in too + + + align:start position:0% +the probability that it's not in too +many + + align:start position:0% + + + + align:start position:0% + +scripts you just take the first + + align:start position:0% +scripts you just take the first + + + align:start position:0% +scripts you just take the first +probability and you multiply by the + + align:start position:0% +probability and you multiply by the + + + align:start position:0% +probability and you multiply by the +second one in the assumption that these + + align:start position:0% +second one in the assumption that these + + + align:start position:0% +second one in the assumption that these +are independent and so try to keep ones + + align:start position:0% +are independent and so try to keep ones + + + align:start position:0% +are independent and so try to keep ones +from different places whatever so + + align:start position:0% +from different places whatever so + + + align:start position:0% +from different places whatever so +then what's the probability that any + + align:start position:0% +then what's the probability that any + + + align:start position:0% +then what's the probability that any +given piece is not in any of there were + + align:start position:0% +given piece is not in any of there were + + + align:start position:0% +given piece is not in any of there were +at that point 85 surviving + + align:start position:0% +at that point 85 surviving + + + align:start position:0% +at that point 85 surviving +manuscripts well you just have something + + align:start position:0% +manuscripts well you just have something + + + align:start position:0% +manuscripts well you just have something +like + + align:start position:0% +like + + + align:start position:0% +like +this and that gives us takes uh but are + + align:start position:0% +this and that gives us takes uh but are + + + align:start position:0% +this and that gives us takes uh but are +two unknowns that gives us the + + align:start position:0% +two unknowns that gives us the + + + align:start position:0% +two unknowns that gives us the +probability that a piece is + + align:start position:0% +probability that a piece is + + + align:start position:0% +probability that a piece is +missing so we can go back to our + + align:start position:0% +missing so we can go back to our + + + align:start position:0% +missing so we can go back to our +original + + align:start position:0% +original + + + align:start position:0% +original +equation + + align:start position:0% +equation + + + align:start position:0% +equation +and plug that + + align:start position:0% +and plug that + + + align:start position:0% +and plug that +in and all of these have n as a + + align:start position:0% +in and all of these have n as a + + + align:start position:0% +in and all of these have n as a +denominator so now we've at least + + align:start position:0% +denominator so now we've at least + + + align:start position:0% +denominator so now we've at least +reduced our U giant we've reduced our of + + align:start position:0% +reduced our U giant we've reduced our of + + + align:start position:0% +reduced our U giant we've reduced our of +our Master our main equation into two + + align:start position:0% +our Master our main equation into two + + + align:start position:0% +our Master our main equation into two +unknowns so we're getting a little bit + + align:start position:0% +unknowns so we're getting a little bit + + + align:start position:0% +unknowns so we're getting a little bit +better then we + + align:start position:0% +better then we + + + align:start position:0% +better then we +thought what how many pieces were + + align:start position:0% +thought what how many pieces were + + + align:start position:0% +thought what how many pieces were +missing well the number of pieces that + + align:start position:0% +missing well the number of pieces that + + + align:start position:0% +missing well the number of pieces that +were missing is the number of pieces + + align:start position:0% +were missing is the number of pieces + + + align:start position:0% +were missing is the number of pieces +that originally were minus the number of + + align:start position:0% +that originally were minus the number of + + + align:start position:0% +that originally were minus the number of +pieces that + + align:start position:0% +pieces that + + + align:start position:0% +pieces that +survive + + align:start position:0% +survive + + + align:start position:0% +survive +so we can count the number of pieces + + align:start position:0% +so we can count the number of pieces + + + align:start position:0% +so we can count the number of pieces +that survive it takes a long time + + align:start position:0% +that survive it takes a long time + + + align:start position:0% +that survive it takes a long time +actually to to figure out every single + + align:start position:0% +actually to to figure out every single + + + align:start position:0% +actually to to figure out every single +thing because people count differently + + align:start position:0% +thing because people count differently + + + align:start position:0% +thing because people count differently +but we can kind of reduce this entire + + align:start position:0% +but we can kind of reduce this entire + + + align:start position:0% +but we can kind of reduce this entire +equation + + align:start position:0% +equation + + + align:start position:0% +equation +to one equation one unknown and at this + + align:start position:0% +to one equation one unknown and at this + + + align:start position:0% +to one equation one unknown and at this +point I was thinking I must have screwed + + align:start position:0% +point I was thinking I must have screwed + + + align:start position:0% +point I was thinking I must have screwed +up something really really bad I have a + + align:start position:0% +up something really really bad I have a + + + align:start position:0% +up something really really bad I have a +music degree I don't have a stats degree + + align:start position:0% +music degree I don't have a stats degree + + + align:start position:0% +music degree I don't have a stats degree +this seems like a pretty fundamental + + align:start position:0% +this seems like a pretty fundamental + + + align:start position:0% +this seems like a pretty fundamental +equation to have and it turns out people + + align:start position:0% +equation to have and it turns out people + + + align:start position:0% +equation to have and it turns out people +had been talking about equations like + + align:start position:0% +had been talking about equations like + + + align:start position:0% +had been talking about equations like +this a lot in the 60s or so but um back + + align:start position:0% +this a lot in the 60s or so but um back + + + align:start position:0% +this a lot in the 60s or so but um back +then it was all about what's the way + + align:start position:0% +then it was all about what's the way + + + align:start position:0% +then it was all about what's the way +that you solve an equation like this + + align:start position:0% +that you solve an equation like this + + + align:start position:0% +that you solve an equation like this +with 85 you know it's a what it's a 85th + + align:start position:0% +with 85 you know it's a what it's a 85th + + + align:start position:0% +with 85 you know it's a what it's a 85th +power equation or something like that um + + align:start position:0% +power equation or something like that um + + + align:start position:0% +power equation or something like that um +you know and so all of it was on the + + align:start position:0% +you know and so all of it was on the + + + align:start position:0% +you know and so all of it was on the +high math that I don't understand that + + align:start position:0% +high math that I don't understand that + + + align:start position:0% +high math that I don't understand that +can get you um something to this this + + align:start position:0% +can get you um something to this this + + + align:start position:0% +can get you um something to this this +answer but um this is my first uh + + align:start position:0% +answer but um this is my first uh + + + align:start position:0% +answer but um this is my first uh +computational thing it's in a language + + align:start position:0% +computational thing it's in a language + + + align:start position:0% +computational thing it's in a language +called Pearl where if you know it you're + + align:start position:0% +called Pearl where if you know it you're + + + align:start position:0% +called Pearl where if you know it you're +lying about your age uh it was the the + + align:start position:0% +lying about your age uh it was the the + + + align:start position:0% +lying about your age uh it was the the +big uh it was the language that built + + align:start position:0% +big uh it was the language that built + + + align:start position:0% +big uh it was the language that built +the internet in the 9s um things and the + + align:start position:0% +the internet in the 9s um things and the + + + align:start position:0% +the internet in the 9s um things and the +one of the things you can do is you can + + align:start position:0% +one of the things you can do is you can + + + align:start position:0% +one of the things you can do is you can +look at at um guess various numbers and + + align:start position:0% +look at at um guess various numbers and + + + align:start position:0% +look at at um guess various numbers and +look at the error between the left side + + align:start position:0% +look at the error between the left side + + + align:start position:0% +look at the error between the left side +of the equation and the right side of + + align:start position:0% +of the equation and the right side of + + + align:start position:0% +of the equation and the right side of +the equation until you find the number + + align:start position:0% +the equation until you find the number + + + align:start position:0% +the equation until you find the number +that comes closest to balancing it so + + align:start position:0% +that comes closest to balancing it so + + + align:start position:0% +that comes closest to balancing it so +you just kind of try everything and you + + align:start position:0% +you just kind of try everything and you + + + align:start position:0% +you just kind of try everything and you +multiply everything + + align:start position:0% +multiply everything + + + align:start position:0% +multiply everything +out and since this isn't really a class + + align:start position:0% +out and since this isn't really a class + + + align:start position:0% +out and since this isn't really a class +about that but it turned into um saying + + align:start position:0% +about that but it turned into um saying + + + align:start position:0% +about that but it turned into um saying +that the percentage of missing pieces + + align:start position:0% +that the percentage of missing pieces + + + align:start position:0% +that the percentage of missing pieces +varied by genre by type of piece it was + + align:start position:0% +varied by genre by type of piece it was + + + align:start position:0% +varied by genre by type of piece it was +interesting part is that the ma the mass + + align:start position:0% +interesting part is that the ma the mass + + + align:start position:0% +interesting part is that the ma the mass +the music written for sacred Services + + align:start position:0% +the music written for sacred Services + + + align:start position:0% +the music written for sacred Services +survives uh has more missing than the + + align:start position:0% +survives uh has more missing than the + + + align:start position:0% +survives uh has more missing than the +ones for everyday sort of dancing and + + align:start position:0% +ones for everyday sort of dancing and + + + align:start position:0% +ones for everyday sort of dancing and +love making and all that stuff and I + + align:start position:0% +love making and all that stuff and I + + + align:start position:0% +love making and all that stuff and I +think that's because uh over time nobody + + align:start position:0% +think that's because uh over time nobody + + + align:start position:0% +think that's because uh over time nobody +could read this music um so the only + + align:start position:0% +could read this music um so the only + + + align:start position:0% +could read this music um so the only +reason somebody would keep it around is + + align:start position:0% +reason somebody would keep it around is + + + align:start position:0% +reason somebody would keep it around is +for the text and you if you're um + + align:start position:0% +for the text and you if you're um + + + align:start position:0% +for the text and you if you're um +running a church you already have lots + + align:start position:0% +running a church you already have lots + + + align:start position:0% +running a church you already have lots +of copies of the text of the mass but + + align:start position:0% +of copies of the text of the mass but + + + align:start position:0% +of copies of the text of the mass but +the song about you know we all went off + + align:start position:0% +the song about you know we all went off + + + align:start position:0% +the song about you know we all went off +into the woods uh each one is a pair and + + align:start position:0% +into the woods uh each one is a pair and + + + align:start position:0% +into the woods uh each one is a pair and +we all came back as three um they you + + align:start position:0% +we all came back as three um they you + + + align:start position:0% +we all came back as three um they you +know that that's people still keep + + align:start position:0% +know that that's people still keep + + + align:start position:0% +know that that's people still keep +around so those sort of body songs uh + + align:start position:0% +around so those sort of body songs uh + + + align:start position:0% +around so those sort of body songs uh +have the least + + align:start position:0% +have the least + + + align:start position:0% +have the least +missing so it turns out that our best + + align:start position:0% +missing so it turns out that our best + + + align:start position:0% +missing so it turns out that our best +estimates now are that about + + align:start position:0% +estimates now are that about + + + align:start position:0% +estimates now are that about +25% of the pieces maybe 50% I don't know + + align:start position:0% +25% of the pieces maybe 50% I don't know + + + align:start position:0% +25% of the pieces maybe 50% I don't know +maybe 60 maybe I'm off by a little bit + + align:start position:0% +maybe 60 maybe I'm off by a little bit + + + align:start position:0% +maybe 60 maybe I'm off by a little bit +you know by a logarithm order of + + align:start position:0% +you know by a logarithm order of + + + align:start position:0% +you know by a logarithm order of +magnitude or something but we can + + align:start position:0% +magnitude or something but we can + + + align:start position:0% +magnitude or something but we can +actually really say something about + + align:start position:0% +actually really say something about + + + align:start position:0% +actually really say something about +Medieval music based on the fact that + + align:start position:0% +Medieval music based on the fact that + + + align:start position:0% +Medieval music based on the fact that +much of it + + align:start position:0% +much of it + + + align:start position:0% +much of it +survives and I was very very scared that + + align:start position:0% +survives and I was very very scared that + + + align:start position:0% +survives and I was very very scared that +somehow I had made a math error and + + align:start position:0% +somehow I had made a math error and + + + align:start position:0% +somehow I had made a math error and +stuff until there was just a math + + align:start position:0% +stuff until there was just a math + + + align:start position:0% +stuff until there was just a math +disertation at Yale that uh verified all + + align:start position:0% +disertation at Yale that uh verified all + + + align:start position:0% +disertation at Yale that uh verified all +the work and stuff so I'm finally + + align:start position:0% +the work and stuff so I'm finally + + + align:start position:0% +the work and stuff so I'm finally +finally not worried I'm going to have to + + align:start position:0% +finally not worried I'm going to have to + + + align:start position:0% +finally not worried I'm going to have to +do a retraction of one of my biggest + + align:start position:0% +do a retraction of one of my biggest + + + align:start position:0% +do a retraction of one of my biggest +papers okay so now we're going to get + + align:start position:0% +papers okay so now we're going to get + + + align:start position:0% +papers okay so now we're going to get +back to these + + align:start position:0% +back to these + + + align:start position:0% +back to these +little uh scores and once I had sort of + + align:start position:0% +little uh scores and once I had sort of + + + align:start position:0% +little uh scores and once I had sort of +convinced myself that a good chunk of + + align:start position:0% +convinced myself that a good chunk of + + + align:start position:0% +convinced myself that a good chunk of +the time three4 of the time was saying + + align:start position:0% +the time three4 of the time was saying + + + align:start position:0% +the time three4 of the time was saying +we're going to be able to figure out + + align:start position:0% +we're going to be able to figure out + + + align:start position:0% +we're going to be able to figure out +what music is on here because it's going + + align:start position:0% +what music is on here because it's going + + + align:start position:0% +what music is on here because it's going +to be in some other piece we already + + align:start position:0% + + + + align:start position:0% + +have so there's this collection that I + + align:start position:0% +have so there's this collection that I + + + align:start position:0% +have so there's this collection that I +mostly use it's called polyic music The + + align:start position:0% +mostly use it's called polyic music The + + + align:start position:0% +mostly use it's called polyic music The +14th Century we have it over in the + + align:start position:0% +14th Century we have it over in the + + + align:start position:0% +14th Century we have it over in the +Lewis music library it's beautiful it's + + align:start position:0% +Lewis music library it's beautiful it's + + + align:start position:0% +Lewis music library it's beautiful it's +expensive and things comes in these + + align:start position:0% +expensive and things comes in these + + + align:start position:0% +expensive and things comes in these +gorgeous green volumes and there's a lot + + align:start position:0% +gorgeous green volumes and there's a lot + + + align:start position:0% +gorgeous green volumes and there's a lot +of them all the music from The 14th + + align:start position:0% +of them all the music from The 14th + + + align:start position:0% +of them all the music from The 14th +Century uh it's about 20 it's 25 volumes + + align:start position:0% +Century uh it's about 20 it's 25 volumes + + + align:start position:0% +Century uh it's about 20 it's 25 volumes +in this series and then there's been + + align:start position:0% +in this series and then there's been + + + align:start position:0% +in this series and then there's been +some others since there so this gives + + align:start position:0% +some others since there so this gives + + + align:start position:0% +some others since there so this gives +you a sense of uh what it is and + + align:start position:0% +you a sense of uh what it is and + + + align:start position:0% +you a sense of uh what it is and +um now MIT was able I'm going to skip + + align:start position:0% +um now MIT was able I'm going to skip + + + align:start position:0% +um now MIT was able I'm going to skip +some of these MIT was able to help me um + + align:start position:0% +some of these MIT was able to help me um + + + align:start position:0% +some of these MIT was able to help me um +get some of this into um into a computer + + align:start position:0% +get some of this into um into a computer + + + align:start position:0% +get some of this into um into a computer +so we'll get on to that in a little bit + + align:start position:0% +so we'll get on to that in a little bit + + + align:start position:0% +so we'll get on to that in a little bit +but what what if you want to do if if + + align:start position:0% +but what what if you want to do if if + + + align:start position:0% +but what what if you want to do if if +you want to find if any of these pieces + + align:start position:0% +you want to find if any of these pieces + + + align:start position:0% +you want to find if any of these pieces +has a match in another thing because + + align:start position:0% +has a match in another thing because + + + align:start position:0% +has a match in another thing because +somebody's written down a lot of these + + align:start position:0% +somebody's written down a lot of these + + + align:start position:0% +somebody's written down a lot of these +little fragments or they've put all the + + align:start position:0% +little fragments or they've put all the + + + align:start position:0% +little fragments or they've put all the +pieces in and I wanted to see not just + + align:start position:0% +pieces in and I wanted to see not just + + + align:start position:0% +pieces in and I wanted to see not just +were any of these little fragments there + + align:start position:0% +were any of these little fragments there + + + align:start position:0% +were any of these little fragments there +but at this point are any pieces quoting + + align:start position:0% +but at this point are any pieces quoting + + + align:start position:0% +but at this point are any pieces quoting +or copying from or plagiarizing from + + align:start position:0% +or copying from or plagiarizing from + + + align:start position:0% +or copying from or plagiarizing from +anybody else's music so what you have to + + align:start position:0% +anybody else's music so what you have to + + + align:start position:0% +anybody else's music so what you have to +do is you take all the songs and you + + align:start position:0% +do is you take all the songs and you + + + align:start position:0% +do is you take all the songs and you +compare each one of them n by n right um + + align:start position:0% +compare each one of them n by n right um + + + align:start position:0% +compare each one of them n by n right um +sorry that's not enough we got to zoom + + align:start position:0% +sorry that's not enough we got to zoom + + + align:start position:0% +sorry that's not enough we got to zoom +out a little bit + + align:start position:0% + + + + align:start position:0% + +and there we go yeah so it's something + + align:start position:0% +and there we go yeah so it's something + + + align:start position:0% +and there we go yeah so it's something +like that that's actually just comparing + + align:start position:0% +like that that's actually just comparing + + + align:start position:0% +like that that's actually just comparing +each of the volumes we actually want to + + align:start position:0% +each of the volumes we actually want to + + + align:start position:0% +each of the volumes we actually want to +compare each of these volumes has about + + align:start position:0% +compare each of these volumes has about + + + align:start position:0% +compare each of these volumes has about +150 pieces so you have to do the square + + align:start position:0% +150 pieces so you have to do the square + + + align:start position:0% +150 pieces so you have to do the square +of the number of pieces divide by two + + align:start position:0% +of the number of pieces divide by two + + + align:start position:0% +of the number of pieces divide by two +because it's symmetrical and so you have + + align:start position:0% +because it's symmetrical and so you have + + + align:start position:0% +because it's symmetrical and so you have +about 3.1 million comparisons and that's + + align:start position:0% +about 3.1 million comparisons and that's + + + align:start position:0% +about 3.1 million comparisons and that's +the reason why nobody had done this + + align:start position:0% +the reason why nobody had done this + + + align:start position:0% +the reason why nobody had done this +before um I'm actually really lucky our + + align:start position:0% +before um I'm actually really lucky our + + + align:start position:0% +before um I'm actually really lucky our +best estimates which I don't know is + + align:start position:0% +best estimates which I don't know is + + + align:start position:0% +best estimates which I don't know is +that 14th century music is about + + align:start position:0% +that 14th century music is about + + + align:start position:0% +that 14th century music is about +10% of the size of 15th century music + + align:start position:0% +10% of the size of 15th century music + + + align:start position:0% +10% of the size of 15th century music +and every successive century is about + + align:start position:0% +and every successive century is about + + + align:start position:0% +and every successive century is about +tenfold more music so I have algorithms + + align:start position:0% +tenfold more music so I have algorithms + + + align:start position:0% +tenfold more music so I have algorithms +that I've devised that I think will also + + align:start position:0% +that I've devised that I think will also + + + align:start position:0% +that I've devised that I think will also +work for the 15th century and maybe if I + + align:start position:0% +work for the 15th century and maybe if I + + + align:start position:0% +work for the 15th century and maybe if I +ever had a huge research budget I could + + align:start position:0% +ever had a huge research budget I could + + + align:start position:0% +ever had a huge research budget I could +do the 16th but it's going to be up to + + align:start position:0% +do the 16th but it's going to be up to + + + align:start position:0% +do the 16th but it's going to be up to +you all to figure out what's the + + align:start position:0% +you all to figure out what's the + + + align:start position:0% +you all to figure out what's the +algorithm that can compare every piece + + align:start position:0% +algorithm that can compare every piece + + + align:start position:0% +algorithm that can compare every piece +of known music to every other piece and + + align:start position:0% +of known music to every other piece and + + + align:start position:0% +of known music to every other piece and +get that and that's why I care a lot + + align:start position:0% +get that and that's why I care a lot + + + align:start position:0% +get that and that's why I care a lot +about simil similar it so sorry I got + + align:start position:0% +about simil similar it so sorry I got + + + align:start position:0% +about simil similar it so sorry I got +ahead of myself so with um with great + + align:start position:0% +ahead of myself so with um with great + + + align:start position:0% +ahead of myself so with um with great +scholar Anna Katherine grow uh created + + align:start position:0% +scholar Anna Katherine grow uh created + + + align:start position:0% +scholar Anna Katherine grow uh created +the electronic Medieval music score + + align:start position:0% +the electronic Medieval music score + + + align:start position:0% +the electronic Medieval music score +archive project or msap uh which slides + + align:start position:0% +archive project or msap uh which slides + + + align:start position:0% +archive project or msap uh which slides +a little bit out of date but back then + + align:start position:0% +a little bit out of date but back then + + + align:start position:0% +a little bit out of date but back then +it had about 1.3 million notes now we're + + align:start position:0% +it had about 1.3 million notes now we're + + + align:start position:0% +it had about 1.3 million notes now we're +close to like 1.8 million and of course + + align:start position:0% +close to like 1.8 million and of course + + + align:start position:0% +close to like 1.8 million and of course +you know this this one right so what you + + align:start position:0% +you know this this one right so what you + + + align:start position:0% +you know this this one right so what you +do is you take all the take all the + + align:start position:0% +do is you take all the take all the + + + align:start position:0% +do is you take all the take all the +music and you take music 21 and then it + + align:start position:0% +music and you take music 21 and then it + + + align:start position:0% +music and you take music 21 and then it +does something like this and you know + + align:start position:0% +does something like this and you know + + + align:start position:0% +does something like this and you know +that's how that's how it looks when you + + align:start position:0% +that's how that's how it looks when you + + + align:start position:0% +that's how that's how it looks when you +do run the + + align:start position:0% +do run the + + + align:start position:0% +do run the +matches now you all know that this is + + align:start position:0% +matches now you all know that this is + + + align:start position:0% +matches now you all know that this is +what you do to uh to get funding for + + align:start position:0% +what you do to uh to get funding for + + + align:start position:0% +what you do to uh to get funding for +your project and that's not actually how + + align:start position:0% +your project and that's not actually how + + + align:start position:0% +your project and that's not actually how +it works right only in CSI uh no the way + + align:start position:0% +it works right only in CSI uh no the way + + + align:start position:0% +it works right only in CSI uh no the way +it actually works is you go and you take + + align:start position:0% +it actually works is you go and you take + + + align:start position:0% +it actually works is you go and you take +your scans that you've done and how do + + align:start position:0% +your scans that you've done and how do + + + align:start position:0% +your scans that you've done and how do +you get them scanned you spend all day + + align:start position:0% +you get them scanned you spend all day + + + align:start position:0% +you get them scanned you spend all day +putting them on a scanner um and + + align:start position:0% +putting them on a scanner um and + + + align:start position:0% +putting them on a scanner um and +then enter every one of these pieces + + align:start position:0% +then enter every one of these pieces + + + align:start position:0% +then enter every one of these pieces +into um mostly Muse Corell finale + + align:start position:0% +into um mostly Muse Corell finale + + + align:start position:0% +into um mostly Muse Corell finale +whatever it is and then we exported + + align:start position:0% +whatever it is and then we exported + + + align:start position:0% +whatever it is and then we exported +everything as music XML some people uh + + align:start position:0% +everything as music XML some people uh + + + align:start position:0% +everything as music XML some people uh +like there's a specific output for music + + align:start position:0% +like there's a specific output for music + + + align:start position:0% +like there's a specific output for music +uh musicology called Mei which is pretty + + align:start position:0% +uh musicology called Mei which is pretty + + + align:start position:0% +uh musicology called Mei which is pretty +similar uh but I use Music XML and so + + align:start position:0% +similar uh but I use Music XML and so + + + align:start position:0% +similar uh but I use Music XML and so +then we have here's the music XML for + + align:start position:0% +then we have here's the music XML for + + + align:start position:0% +then we have here's the music XML for +the first three first four notes of this + + align:start position:0% +the first three first four notes of this + + + align:start position:0% +the first three first four notes of this +one piece called sorry I'll just jump + + align:start position:0% +one piece called sorry I'll just jump + + + align:start position:0% +one piece called sorry I'll just jump +back called an Neu which is um + + align:start position:0% +back called an Neu which is um + + + align:start position:0% +back called an Neu which is um +completely only one copy of it in the + + align:start position:0% +completely only one copy of it in the + + + align:start position:0% +completely only one copy of it in the +world then uh wrote some programs python + + align:start position:0% +world then uh wrote some programs python + + + align:start position:0% +world then uh wrote some programs python +music 21 um things just to take every 31 + + align:start position:0% +music 21 um things just to take every 31 + + + align:start position:0% +music 21 um things just to take every 31 +note little segment I don't know why I + + align:start position:0% +note little segment I don't know why I + + + align:start position:0% +note little segment I don't know why I +ended up with 31 um and just + + align:start position:0% +ended up with 31 um and just + + + align:start position:0% +ended up with 31 um and just +automatically chop it up so that there's + + align:start position:0% +automatically chop it up so that there's + + + align:start position:0% +automatically chop it up so that there's +these um little segments things and + + align:start position:0% +these um little segments things and + + + align:start position:0% +these um little segments things and +ideally you would chop it up you would + + align:start position:0% +ideally you would chop it up you would + + + align:start position:0% +ideally you would chop it up you would +slide your window over one note at a + + align:start position:0% +slide your window over one note at a + + + align:start position:0% +slide your window over one note at a +time but there's a trade-off between + + align:start position:0% +time but there's a trade-off between + + + align:start position:0% +time but there's a trade-off between +getting the best um similarity and then + + align:start position:0% +getting the best um similarity and then + + + align:start position:0% +getting the best um similarity and then +um and also not having your database EXP + + align:start position:0% +um and also not having your database EXP + + + align:start position:0% +um and also not having your database EXP +explode with internal quotations so we + + align:start position:0% +explode with internal quotations so we + + + align:start position:0% +explode with internal quotations so we +did this and had it go through + + align:start position:0% +did this and had it go through + + + align:start position:0% +did this and had it go through +everything here and then once we had + + align:start position:0% +everything here and then once we had + + + align:start position:0% +everything here and then once we had +chopped up the pieces into these little + + align:start position:0% +chopped up the pieces into these little + + + align:start position:0% +chopped up the pieces into these little +31 note segments uh then we did uh what + + align:start position:0% +31 note segments uh then we did uh what + + + align:start position:0% +31 note segments uh then we did uh what +keep was talking about a a Viewpoint or + + align:start position:0% +keep was talking about a a Viewpoint or + + + align:start position:0% +keep was talking about a a Viewpoint or +a hash or an encoding system to try to + + align:start position:0% +a hash or an encoding system to try to + + + align:start position:0% +a hash or an encoding system to try to +reduce the complexity of it so the + + align:start position:0% +reduce the complexity of it so the + + + align:start position:0% +reduce the complexity of it so the +complexity the system that I used you're + + align:start position:0% +complexity the system that I used you're + + + align:start position:0% +complexity the system that I used you're +going to kind of laugh at um if a note + + align:start position:0% +going to kind of laugh at um if a note + + + align:start position:0% +going to kind of laugh at um if a note +was the same duration as the previous it + + align:start position:0% +was the same duration as the previous it + + + align:start position:0% +was the same duration as the previous it +got the asky letter A B CDE e f g I + + align:start position:0% +got the asky letter A B CDE e f g I + + + align:start position:0% +got the asky letter A B CDE e f g I +dropped Sharps and flats because + + align:start position:0% +dropped Sharps and flats because + + + align:start position:0% +dropped Sharps and flats because +different copies of the same piece in + + align:start position:0% +different copies of the same piece in + + + align:start position:0% +different copies of the same piece in +the middle ages sometimes write it as B + + align:start position:0% +the middle ages sometimes write it as B + + + align:start position:0% +the middle ages sometimes write it as B +flat sometimes they don't write a flat + + align:start position:0% +flat sometimes they don't write a flat + + + align:start position:0% +flat sometimes they don't write a flat +you're just supposed to hear that well + + align:start position:0% +you're just supposed to hear that well + + + align:start position:0% +you're just supposed to hear that well +obviously there was a augmented fourth + + align:start position:0% +obviously there was a augmented fourth + + + align:start position:0% +obviously there was a augmented fourth +I'm going to sing that flat so they + + align:start position:0% +I'm going to sing that flat so they + + + align:start position:0% +I'm going to sing that flat so they +don't always put that in so we get rid + + align:start position:0% +don't always put that in so we get rid + + + align:start position:0% +don't always put that in so we get rid +of accidentals and then if the note's + + align:start position:0% +of accidentals and then if the note's + + + align:start position:0% +of accidentals and then if the note's +longer than the previous note um then we + + align:start position:0% +longer than the previous note um then we + + + align:start position:0% +longer than the previous note um then we +use H through n and if it's shorter then + + align:start position:0% +use H through n and if it's shorter then + + + align:start position:0% +use H through n and if it's shorter then +it's O through U so um p is a b that is + + align:start position:0% +it's O through U so um p is a b that is + + + align:start position:0% +it's O through U so um p is a b that is +shorter than the previous note you just + + align:start position:0% +shorter than the previous note you just + + + align:start position:0% +shorter than the previous note you just +go through and put everything in like + + align:start position:0% +go through and put everything in like + + + align:start position:0% +go through and put everything in like +that and the first note I always just + + align:start position:0% +that and the first note I always just + + + align:start position:0% +that and the first note I always just +assume it's the same so we take all of + + align:start position:0% +assume it's the same so we take all of + + + align:start position:0% +assume it's the same so we take all of +these things and put it into a giant + + align:start position:0% +these things and put it into a giant + + + align:start position:0% +these things and put it into a giant +database um it's not that big it's about + + align:start position:0% +database um it's not that big it's about + + + align:start position:0% +database um it's not that big it's about +188,000 of these little segments at that + + align:start position:0% + + + + align:start position:0% + +time and so this is the segment for the + + align:start position:0% +time and so this is the segment for the + + + align:start position:0% +time and so this is the segment for the +opening of Ana it's kind of I always + + align:start position:0% +opening of Ana it's kind of I always + + + align:start position:0% +opening of Ana it's kind of I always +think it's kind of unceremoniously + + align:start position:0% +think it's kind of unceremoniously + + + align:start position:0% +think it's kind of unceremoniously +stored there like the arc at the end of + + align:start position:0% +stored there like the arc at the end of + + + align:start position:0% +stored there like the arc at the end of +the Indiana Jones film if you've ever + + align:start position:0% +the Indiana Jones film if you've ever + + + align:start position:0% +the Indiana Jones film if you've ever +seen it just can't really tell where it + + align:start position:0% +seen it just can't really tell where it + + + align:start position:0% +seen it just can't really tell where it +is so then we have to compare every one + + align:start position:0% +is so then we have to compare every one + + + align:start position:0% +is so then we have to compare every one +of these + + align:start position:0% +of these + + + align:start position:0% +of these +188,000 sequences against every other + + align:start position:0% +188,000 sequences against every other + + + align:start position:0% +188,000 sequences against every other +one so we take the first one the Anan + + align:start position:0% +one so we take the first one the Anan + + + align:start position:0% +one so we take the first one the Anan +Neu Melody and just some random other + + align:start position:0% +Neu Melody and just some random other + + + align:start position:0% +Neu Melody and just some random other +one and we can figure out what are all + + align:start position:0% +one and we can figure out what are all + + + align:start position:0% +one and we can figure out what are all +the things we have to do in um earth + + align:start position:0% +the things we have to do in um earth + + + align:start position:0% +the things we have to do in um earth +mover leein or some other distance thing + + align:start position:0% +mover leein or some other distance thing + + + align:start position:0% +mover leein or some other distance thing +in order to transform the first one to + + align:start position:0% +in order to transform the first one to + + + align:start position:0% +in order to transform the first one to +the second one so you have to well you + + align:start position:0% +the second one so you have to well you + + + align:start position:0% +the second one so you have to well you +insert a whole bunch of things and then + + align:start position:0% +insert a whole bunch of things and then + + + align:start position:0% +insert a whole bunch of things and then +some things the same delete whatever and + + align:start position:0% +some things the same delete whatever and + + + align:start position:0% +some things the same delete whatever and +the end you get a ratio from 0o to one + + align:start position:0% +the end you get a ratio from 0o to one + + + align:start position:0% +the end you get a ratio from 0o to one +of how similar they are I always like to + + align:start position:0% +of how similar they are I always like to + + + align:start position:0% +of how similar they are I always like to +store float uh store integers um in + + align:start position:0% +store float uh store integers um in + + + align:start position:0% +store float uh store integers um in +databases it saves a lot of space so I + + align:start position:0% +databases it saves a lot of space so I + + + align:start position:0% +databases it saves a lot of space so I +just multiply by 10,000 so I get a + + align:start position:0% +just multiply by 10,000 so I get a + + + align:start position:0% +just multiply by 10,000 so I get a +number between 0 and 10,000 to store + + align:start position:0% +number between 0 and 10,000 to store + + + align:start position:0% +number between 0 and 10,000 to store +these ones are 177% similar these are + + align:start position:0% +these ones are 177% similar these are + + + align:start position:0% +these ones are 177% similar these are +actually a + + align:start position:0% +actually a + + + align:start position:0% +actually a +surprisingly bad amount of similarity + + align:start position:0% +surprisingly bad amount of similarity + + + align:start position:0% +surprisingly bad amount of similarity +random pieces tend to be uh more similar + + align:start position:0% +random pieces tend to be uh more similar + + + align:start position:0% +random pieces tend to be uh more similar +but so this this is not a match right + + align:start position:0% +but so this this is not a match right + + + align:start position:0% +but so this this is not a match right +nobody's going to say that those that + + align:start position:0% +nobody's going to say that those that + + + align:start position:0% +nobody's going to say that those that +those two lines are the same piece + + align:start position:0% +those two lines are the same piece + + + align:start position:0% +those two lines are the same piece +slightly different + + align:start position:0% +slightly different + + + align:start position:0% +slightly different +no um but that's okay because we do it + + align:start position:0% +no um but that's okay because we do it + + + align:start position:0% +no um but that's okay because we do it +188,000 by 188,000 times or 35 billion + + align:start position:0% +188,000 by 188,000 times or 35 billion + + + align:start position:0% +188,000 by 188,000 times or 35 billion +divide by two since it's symmetrical 16 + + align:start position:0% +divide by two since it's symmetrical 16 + + + align:start position:0% +divide by two since it's symmetrical 16 +billion 18 billion right um + + align:start position:0% +billion 18 billion right um + + + align:start position:0% +billion 18 billion right um +yeah but then I went through and stored + + align:start position:0% +yeah but then I went through and stored + + + align:start position:0% +yeah but then I went through and stored +every single time there was something + + align:start position:0% +every single time there was something + + + align:start position:0% +every single time there was something +that was more than 50% similar so + + align:start position:0% +that was more than 50% similar so + + + align:start position:0% +that was more than 50% similar so +there's two IDs and the ratio of how + + align:start position:0% +there's two IDs and the ratio of how + + + align:start position:0% +there's two IDs and the ratio of how +similar they are and over 50% similar + + align:start position:0% +similar they are and over 50% similar + + + align:start position:0% +similar they are and over 50% similar +ended up with 814,000 things I'm never + + align:start position:0% +ended up with 814,000 things I'm never + + + align:start position:0% +ended up with 814,000 things I'm never +going to look at those that's just way + + align:start position:0% +going to look at those that's just way + + + align:start position:0% +going to look at those that's just way +too many so I started going to at around + + align:start position:0% +too many so I started going to at around + + + align:start position:0% +too many so I started going to at around +65% similar I started to suspect these + + align:start position:0% +65% similar I started to suspect these + + + align:start position:0% +65% similar I started to suspect these +tended to be pieces um by the same + + align:start position:0% +tended to be pieces um by the same + + + align:start position:0% +tended to be pieces um by the same +composer or uh quite often if we knew or + + align:start position:0% +composer or uh quite often if we knew or + + + align:start position:0% +composer or uh quite often if we knew or +I suspected they would be or something + + align:start position:0% +I suspected they would be or something + + + align:start position:0% +I suspected they would be or something +like that at 70% similar you're like wow + + align:start position:0% +like that at 70% similar you're like wow + + + align:start position:0% +like that at 70% similar you're like wow +these aren't the same piece but they're + + align:start position:0% +these aren't the same piece but they're + + + align:start position:0% +these aren't the same piece but they're +they're a lot like it but at definitely + + align:start position:0% +they're a lot like it but at definitely + + + align:start position:0% +they're a lot like it but at definitely +at over 80% similar um they're always + + align:start position:0% +at over 80% similar um they're always + + + align:start position:0% +at over 80% similar um they're always +the same piece and how can something be + + align:start position:0% +the same piece and how can something be + + + align:start position:0% +the same piece and how can something be +the same piece and be 20% off it could + + align:start position:0% +the same piece and be 20% off it could + + + align:start position:0% +the same piece and be 20% off it could +just be that they were sliced at + + align:start position:0% +just be that they were sliced at + + + align:start position:0% +just be that they were sliced at +different points so they're the exact + + align:start position:0% +different points so they're the exact + + + align:start position:0% +different points so they're the exact +same thing but the but the first third + + align:start position:0% +same thing but the but the first third + + + align:start position:0% +same thing but the but the first third +of one segment is in some other one okay + + align:start position:0% +of one segment is in some other one okay + + + align:start position:0% +of one segment is in some other one okay +okay so this is what the actual um + + align:start position:0% +okay so this is what the actual um + + + align:start position:0% +okay so this is what the actual um +workflow looks like I used to use + + align:start position:0% +workflow looks like I used to use + + + align:start position:0% +workflow looks like I used to use +Eclipse um and just running through all + + align:start position:0% +Eclipse um and just running through all + + + align:start position:0% +Eclipse um and just running through all +these pieces and occasionally it finds a + + align:start position:0% +these pieces and occasionally it finds a + + + align:start position:0% +these pieces and occasionally it finds a +match and it puts it up and I get to see + + align:start position:0% +match and it puts it up and I get to see + + + align:start position:0% +match and it puts it up and I get to see +okay does that look like that or yeah + + align:start position:0% +okay does that look like that or yeah + + + align:start position:0% +okay does that look like that or yeah +that one kind of looks like that one um + + align:start position:0% +that one kind of looks like that one um + + + align:start position:0% +that one kind of looks like that one um +and sometimes we already knew them the + + align:start position:0% +and sometimes we already knew them the + + + align:start position:0% +and sometimes we already knew them the +computer does not read uh what pieces we + + align:start position:0% +computer does not read uh what pieces we + + + align:start position:0% +computer does not read uh what pieces we +already knew were quoted but we ended up + + align:start position:0% +already knew were quoted but we ended up + + + align:start position:0% +already knew were quoted but we ended up +with some interesting things this is a + + align:start position:0% +with some interesting things this is a + + + align:start position:0% +with some interesting things this is a +piece by a guy named johanes this is + + align:start position:0% +piece by a guy named johanes this is + + + align:start position:0% +piece by a guy named johanes this is +unpublished yet don't don't put it all + + align:start position:0% +unpublished yet don't don't put it all + + + align:start position:0% +unpublished yet don't don't put it all +over everywhere um a guy the name of um + + align:start position:0% +over everywhere um a guy the name of um + + + align:start position:0% +over everywhere um a guy the name of um +johanes jonia one of the most important + + align:start position:0% +johanes jonia one of the most important + + + align:start position:0% +johanes jonia one of the most important +composes around 1400 and one of his + + align:start position:0% +composes around 1400 and one of his + + + align:start position:0% +composes around 1400 and one of his +pieces it's a part of the mass p poent + + align:start position:0% +pieces it's a part of the mass p poent + + + align:start position:0% +pieces it's a part of the mass p poent +and it turns out that a big chunk of it + + align:start position:0% +and it turns out that a big chunk of it + + + align:start position:0% +and it turns out that a big chunk of it +was taken from an unknown uh sort of uh + + align:start position:0% +was taken from an unknown uh sort of uh + + + align:start position:0% +was taken from an unknown uh sort of uh +an anonymous never recorded by anybody + + align:start position:0% +an anonymous never recorded by anybody + + + align:start position:0% +an anonymous never recorded by anybody +German + + align:start position:0% +German + + + align:start position:0% +German +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +song Let me see if I can do the + + align:start position:0% + + + + align:start position:0% + +here we are if you've never + + align:start position:0% + + + + align:start position:0% + +read so we can find that there was a lot + + align:start position:0% +read so we can find that there was a lot + + + align:start position:0% +read so we can find that there was a lot +more copying than we ever expected um + + align:start position:0% +more copying than we ever expected um + + + align:start position:0% +more copying than we ever expected um +this one of my favorites here's a a + + align:start position:0% +this one of my favorites here's a a + + + align:start position:0% +this one of my favorites here's a a +French piece and Italian piece nobody + + align:start position:0% +French piece and Italian piece nobody + + + align:start position:0% +French piece and Italian piece nobody +ever suspected they had anything in + + align:start position:0% +ever suspected they had anything in + + + align:start position:0% +ever suspected they had anything in +common because whoever and I don't know + + align:start position:0% +common because whoever and I don't know + + + align:start position:0% +common because whoever and I don't know +which direction the coping happened + + align:start position:0% +which direction the coping happened + + + align:start position:0% +which direction the coping happened +whoever did the coping did a good chance + + align:start position:0% +whoever did the coping did a good chance + + + align:start position:0% +whoever did the coping did a good chance +of covering their tracks the colored + + align:start position:0% +of covering their tracks the colored + + + align:start position:0% +of covering their tracks the colored +Parts represent the same music okay and + + align:start position:0% +Parts represent the same music okay and + + + align:start position:0% +Parts represent the same music okay and +then down here stole something from up + + align:start position:0% +then down here stole something from up + + + align:start position:0% +then down here stole something from up +there and then up here we stole + + align:start position:0% +there and then up here we stole + + + align:start position:0% +there and then up here we stole +something from over there and so on so + + align:start position:0% +something from over there and so on so + + + align:start position:0% +something from over there and so on so +it's just two that are pastiches of each + + align:start position:0% +it's just two that are pastiches of each + + + align:start position:0% +it's just two that are pastiches of each +other and then if this were a musicology + + align:start position:0% +other and then if this were a musicology + + + align:start position:0% +other and then if this were a musicology +class people would actually care about + + align:start position:0% +class people would actually care about + + + align:start position:0% +class people would actually care about +which one this um what all these other + + align:start position:0% +which one this um what all these other + + + align:start position:0% +which one this um what all these other +things but eventually we got to start + + align:start position:0% +things but eventually we got to start + + + align:start position:0% +things but eventually we got to start +reading these erased pieces and figuring + + align:start position:0% +reading these erased pieces and figuring + + + align:start position:0% +reading these erased pieces and figuring +out where they came from + + align:start position:0% +out where they came from + + + align:start position:0% +out where they came from +so that's the big reason why I created + + align:start position:0% +so that's the big reason why I created + + + align:start position:0% +so that's the big reason why I created +Music 21 and why you will find that + + align:start position:0% +Music 21 and why you will find that + + + align:start position:0% +Music 21 and why you will find that +there are lots of weird little things uh + + align:start position:0% +there are lots of weird little things uh + + + align:start position:0% +there are lots of weird little things uh +that are only useful for music uh for + + align:start position:0% +that are only useful for music uh for + + + align:start position:0% +that are only useful for music uh for +Medieval music hidden around deep inside + + align:start position:0% +Medieval music hidden around deep inside + + + align:start position:0% +Medieval music hidden around deep inside +the various um libraries and stuff so + + align:start position:0% +the various um libraries and stuff so + + + align:start position:0% +the various um libraries and stuff so +that's what I do when I'm not um + + align:start position:0% +that's what I do when I'm not um + + + align:start position:0% +that's what I do when I'm not um +enjoying in being in your company any + + align:start position:0% +enjoying in being in your company any + + + align:start position:0% +enjoying in being in your company any +questions or anything you want to see + + align:start position:0% + + + + align:start position:0% + +again there are by the way U lots of + + align:start position:0% +again there are by the way U lots of + + + align:start position:0% +again there are by the way U lots of +places do want um historians who can do + + align:start position:0% +places do want um historians who can do + + + align:start position:0% +places do want um historians who can do +this type of work so if you're all + + align:start position:0% +this type of work so if you're all + + + align:start position:0% +this type of work so if you're all +interested Humanities in general but + + align:start position:0% +interested Humanities in general but + + + align:start position:0% +interested Humanities in general but +you're like but you know I also want to + + align:start position:0% +you're like but you know I also want to + + + align:start position:0% +you're like but you know I also want to +program and stuff people are are dying + + align:start position:0% +program and stuff people are are dying + + + align:start position:0% +program and stuff people are are dying +for things like that yeah question so + + align:start position:0% +for things like that yeah question so + + + align:start position:0% +for things like that yeah question so +like what made you want to expand + + align:start position:0% +like what made you want to expand + + + align:start position:0% +like what made you want to expand +music uh you all uh your predecessors + + align:start position:0% +music uh you all uh your predecessors + + + align:start position:0% +music uh you all uh your predecessors +people for about 10 15 years before you + + align:start position:0% +people for about 10 15 years before you + + + align:start position:0% +people for about 10 15 years before you +from here at MIT it just felt like you + + align:start position:0% +from here at MIT it just felt like you + + + align:start position:0% +from here at MIT it just felt like you +know people wanted to uh do interesting + + align:start position:0% +know people wanted to uh do interesting + + + align:start position:0% +know people wanted to uh do interesting +things with composition with analysis uh + + align:start position:0% +things with composition with analysis uh + + + align:start position:0% +things with composition with analysis uh +everybody wanted to uh solve their first + + align:start position:0% +everybody wanted to uh solve their first + + + align:start position:0% +everybody wanted to uh solve their first +year Theory uh homework by computer um + + align:start position:0% +year Theory uh homework by computer um + + + align:start position:0% +year Theory uh homework by computer um +and why not if you can program the + + align:start position:0% +and why not if you can program the + + + align:start position:0% +and why not if you can program the +computer to do it and it's not uh you + + align:start position:0% +computer to do it and it's not uh you + + + align:start position:0% +computer to do it and it's not uh you +know complete Black AI you're probably + + align:start position:0% +know complete Black AI you're probably + + + align:start position:0% +know complete Black AI you're probably +teaching yourself how to do it better + + align:start position:0% +teaching yourself how to do it better + + + align:start position:0% +teaching yourself how to do it better +also so it was it was things things like + + align:start position:0% +also so it was it was things things like + + + align:start position:0% +also so it was it was things things like +that and of over time I've taken out a + + align:start position:0% +that and of over time I've taken out a + + + align:start position:0% +that and of over time I've taken out a +lot of the most egregious that only a + + align:start position:0% +lot of the most egregious that only a + + + align:start position:0% +lot of the most egregious that only a +person working on 14th century Italy + + align:start position:0% +person working on 14th century Italy + + + align:start position:0% +person working on 14th century Italy +would um would want to do this and put + + align:start position:0% +would um would want to do this and put + + + align:start position:0% +would um would want to do this and put +this in a separate project so there's no + + align:start position:0% +this in a separate project so there's no + + + align:start position:0% +this in a separate project so there's no +longer an automatic U change medieval + + align:start position:0% +longer an automatic U change medieval + + + align:start position:0% +longer an automatic U change medieval +notation into modern notation tool you + + align:start position:0% +notation into modern notation tool you + + + align:start position:0% +notation into modern notation tool you +have to install that separately but yeah + + align:start position:0% +have to install that separately but yeah + + + align:start position:0% +have to install that separately but yeah +um I just just felt like I was having + + align:start position:0% +um I just just felt like I was having + + + align:start position:0% +um I just just felt like I was having +too much fun and other people wanted to + + align:start position:0% +too much fun and other people wanted to + + + align:start position:0% +too much fun and other people wanted to +share in it and that meant eventually + + align:start position:0% +share in it and that meant eventually + + + align:start position:0% +share in it and that meant eventually +docs would have to happen and uh then a + + align:start position:0% +docs would have to happen and uh then a + + + align:start position:0% +docs would have to happen and uh then a +very generous uh funding organization + + align:start position:0% +very generous uh funding organization + + + align:start position:0% +very generous uh funding organization +called The sver Institute selected music + + align:start position:0% +called The sver Institute selected music + + + align:start position:0% +called The sver Institute selected music +21 to be uh one of MIT mit's + + align:start position:0% +21 to be uh one of MIT mit's + + + align:start position:0% +21 to be uh one of MIT mit's +representative project for their funding + + align:start position:0% +representative project for their funding + + + align:start position:0% +representative project for their funding +Organization for three years and that + + align:start position:0% +Organization for three years and that + + + align:start position:0% +Organization for three years and that +allowed me to do a little bit more than + + align:start position:0% +allowed me to do a little bit more than + + + align:start position:0% +allowed me to do a little bit more than +one person can do at their desk and now + + align:start position:0% +one person can do at their desk and now + + + align:start position:0% +one person can do at their desk and now +the thing that helps me do more than one + + align:start position:0% +the thing that helps me do more than one + + + align:start position:0% +the thing that helps me do more than one +person can do at the desk is community + + align:start position:0% +person can do at the desk is community + + + align:start position:0% +person can do at the desk is community +of a lot of people who keep adding to it + + align:start position:0% +of a lot of people who keep adding to it + + + align:start position:0% +of a lot of people who keep adding to it +um and doing cool things with it so + + align:start position:0% +um and doing cool things with it so + + + align:start position:0% +um and doing cool things with it so +thanks other + + align:start position:0% +thanks other + + + align:start position:0% +thanks other +cues why is it called music 21 uh course + + align:start position:0% +cues why is it called music 21 uh course + + + align:start position:0% +cues why is it called music 21 uh course +21 M I wanted something that um that + + align:start position:0% +21 M I wanted something that um that + + + align:start position:0% +21 M I wanted something that um that +would connected itself to MIT in some + + align:start position:0% +would connected itself to MIT in some + + + align:start position:0% +would connected itself to MIT in some +way but wasn't uh MIT music because your + + align:start position:0% +way but wasn't uh MIT music because your + + + align:start position:0% +way but wasn't uh MIT music because your +trademark office would probably uh get + + align:start position:0% +trademark office would probably uh get + + + align:start position:0% +trademark office would probably uh get +against me and also I was a second-year + + align:start position:0% +against me and also I was a second-year + + + align:start position:0% +against me and also I was a second-year +professor without tenure so I might have + + align:start position:0% +professor without tenure so I might have + + + align:start position:0% +professor without tenure so I might have +been denied tenure and needed to able to + + align:start position:0% +been denied tenure and needed to able to + + + align:start position:0% +been denied tenure and needed to able to +take it with me if I went someplace else + + align:start position:0% +take it with me if I went someplace else + + + align:start position:0% +take it with me if I went someplace else +but yeah so and then somebody later was + + align:start position:0% +but yeah so and then somebody later was + + + align:start position:0% +but yeah so and then somebody later was +like oh it's the thing for the 21st + + align:start position:0% +like oh it's the thing for the 21st + + + align:start position:0% +like oh it's the thing for the 21st +century I said I I actually never + + align:start position:0% +century I said I I actually never + + + align:start position:0% +century I said I I actually never +thought of that connotation if I had + + align:start position:0% +thought of that connotation if I had + + + align:start position:0% +thought of that connotation if I had +there's no way I would have called it 21 + + align:start position:0% +there's no way I would have called it 21 + + + align:start position:0% +there's no way I would have called it 21 +because that sounds very a arrogant and + + align:start position:0% +because that sounds very a arrogant and + + + align:start position:0% +because that sounds very a arrogant and +be um a little obsolete in 2006 when + + align:start position:0% +be um a little obsolete in 2006 when + + + align:start position:0% +be um a little obsolete in 2006 when +you're already in the 21st century it's + + align:start position:0% +you're already in the 21st century it's + + + align:start position:0% +you're already in the 21st century it's +perfect for 1980 or something + + align:start position:0% +perfect for 1980 or something + + + align:start position:0% +perfect for 1980 or something +yeah what was it called before music uh + + align:start position:0% +yeah what was it called before music uh + + + align:start position:0% +yeah what was it called before music uh +it was called um uh P music first for + + align:start position:0% +it was called um uh P music first for + + + align:start position:0% +it was called um uh P music first for +Pearl music when I was writing it in + + align:start position:0% +Pearl music when I was writing it in + + + align:start position:0% +Pearl music when I was writing it in +Pearl and then uh the fact then as soon + + align:start position:0% +Pearl and then uh the fact then as soon + + + align:start position:0% +Pearl and then uh the fact then as soon +as um the intro to CS class switched + + align:start position:0% +as um the intro to CS class switched + + + align:start position:0% +as um the intro to CS class switched +from your older language scheme to + + align:start position:0% +from your older language scheme to + + + align:start position:0% +from your older language scheme to +python I was like well if if all of MIT + + align:start position:0% +python I was like well if if all of MIT + + + align:start position:0% +python I was like well if if all of MIT +is going to move to a new language at + + align:start position:0% +is going to move to a new language at + + + align:start position:0% +is going to move to a new language at +the same time then um you know it it'll + + align:start position:0% +the same time then um you know it it'll + + + align:start position:0% +the same time then um you know it it'll +be easier for me to learn a new language + + align:start position:0% +be easier for me to learn a new language + + + align:start position:0% +be easier for me to learn a new language +than to have uh the rest of my life + + align:start position:0% +than to have uh the rest of my life + + + align:start position:0% +than to have uh the rest of my life +teach my students how to program in + + align:start position:0% +teach my students how to program in + + + align:start position:0% +teach my students how to program in +Pearl and I'm very glad I + + align:start position:0% +Pearl and I'm very glad I + + + align:start position:0% +Pearl and I'm very glad I +did uh the other thing is the work on it + + align:start position:0% +did uh the other thing is the work on it + + + align:start position:0% +did uh the other thing is the work on it +I sort of began in 2004 but work really + + align:start position:0% +I sort of began in 2004 but work really + + + align:start position:0% +I sort of began in 2004 but work really +began around + + align:start position:0% +began around + + + align:start position:0% +began around +2006 and at the time I predicted that it + + align:start position:0% +2006 and at the time I predicted that it + + + align:start position:0% +2006 and at the time I predicted that it +would have a 20year lifespan that it + + align:start position:0% +would have a 20year lifespan that it + + + align:start position:0% +would have a 20year lifespan that it +would be sort + + align:start position:0% +would be sort + + + align:start position:0% +would be sort +of five or six years of um of getting + + align:start position:0% +of five or six years of um of getting + + + align:start position:0% +of five or six years of um of getting +people to notice it and start using it + + align:start position:0% +people to notice it and start using it + + + align:start position:0% +people to notice it and start using it +seven or eight years of it being the + + align:start position:0% +seven or eight years of it being the + + + align:start position:0% +seven or eight years of it being the +main thing out there and um five to + + align:start position:0% +main thing out there and um five to + + + align:start position:0% +main thing out there and um five to +seven years of you know the decline + + align:start position:0% +seven years of you know the decline + + + align:start position:0% +seven years of you know the decline +while something else better came out and + + align:start position:0% +while something else better came out and + + + align:start position:0% +while something else better came out and +I'm still looking for that say better + + align:start position:0% +I'm still looking for that say better + + + align:start position:0% +I'm still looking for that say better +you guys can do that it's about there's + + align:start position:0% +you guys can do that it's about there's + + + align:start position:0% +you guys can do that it's about there's +there are things we've learned from + + align:start position:0% +there are things we've learned from + + + align:start position:0% +there are things we've learned from +using it that um I think are have have + + align:start position:0% +using it that um I think are have have + + + align:start position:0% +using it that um I think are have have +made realize that there's some pretty + + align:start position:0% +made realize that there's some pretty + + + align:start position:0% +made realize that there's some pretty +poor design decisions such as having to + + align:start position:0% +poor design decisions such as having to + + + align:start position:0% +poor design decisions such as having to +copy everything all the time and things + + align:start position:0% +copy everything all the time and things + + + align:start position:0% +copy everything all the time and things +like that and so um I would you know I'd + + align:start position:0% +like that and so um I would you know I'd + + + align:start position:0% +like that and so um I would you know I'd +really love it if somebody else would um + + align:start position:0% +really love it if somebody else would um + + + align:start position:0% +really love it if somebody else would um +would create something new and better so + + align:start position:0% +would create something new and better so + + + align:start position:0% +would create something new and better so +whoever's here or watching it uh you + + align:start position:0% +whoever's here or watching it uh you + + + align:start position:0% +whoever's here or watching it uh you +have my blessing to try to try to knock + + align:start position:0% +have my blessing to try to try to knock + + + align:start position:0% +have my blessing to try to try to knock +this off its shelf and maybe the new + + align:start position:0% +this off its shelf and maybe the new + + + align:start position:0% +this off its shelf and maybe the new +thing will have a lot of uh machine + + align:start position:0% +thing will have a lot of uh machine + + + align:start position:0% +thing will have a lot of uh machine +learning built in or something to be + + align:start position:0% +learning built in or something to be + + + align:start position:0% +learning built in or something to be +able to do better analysis yeah but + + align:start position:0% +able to do better analysis yeah but + + + align:start position:0% +able to do better analysis yeah but +Python's been enduring a lot longer than + + align:start position:0% +Python's been enduring a lot longer than + + + align:start position:0% +Python's been enduring a lot longer than +I thought it would be I mean it's sort + + align:start position:0% +I thought it would be I mean it's sort + + + align:start position:0% +I thought it would be I mean it's sort +of been 15 years as as a major language + + align:start position:0% +of been 15 years as as a major language + + + align:start position:0% +of been 15 years as as a major language +and it seems to be still growing so that + + align:start position:0% +and it seems to be still growing so that + + + align:start position:0% +and it seems to be still growing so that +probably will stop Julia's next Julia's + + align:start position:0% +probably will stop Julia's next Julia's + + + align:start position:0% +probably will stop Julia's next Julia's +next that's people have been saying that + + align:start position:0% +next that's people have been saying that + + + align:start position:0% +next that's people have been saying that +about Julia and R for there is a Julia + + align:start position:0% +about Julia and R for there is a Julia + + + align:start position:0% +about Julia and R for there is a Julia +Port of Music 21 if you like that I + + align:start position:0% +Port of Music 21 if you like that I + + + align:start position:0% +Port of Music 21 if you like that I +don't know how how good it works so + + align:start position:0% +don't know how how good it works so + + + align:start position:0% +don't know how how good it works so +that's a perfect transition oh we can we + + align:start position:0% +that's a perfect transition oh we can we + + + align:start position:0% +that's a perfect transition oh we can we +uh we can keep going more to a second + + align:start position:0% +uh we can keep going more to a second + + + align:start position:0% +uh we can keep going more to a second +topic so for this one get out your + + align:start position:0% +topic so for this one get out your + + + align:start position:0% +topic so for this one get out your +laptops we're going to have um because I + + align:start position:0% +laptops we're going to have um because I + + + align:start position:0% +laptops we're going to have um because I +couldn't have scripted a better + + align:start position:0% +couldn't have scripted a better + + + align:start position:0% +couldn't have scripted a better +transition to um okay so now more grab + + align:start position:0% +transition to um okay so now more grab + + + align:start position:0% +transition to um okay so now more grab +bag and these are more requested from + + align:start position:0% +bag and these are more requested from + + + align:start position:0% +bag and these are more requested from +previous years than anything sorry I + + align:start position:0% +previous years than anything sorry I + + + align:start position:0% +previous years than anything sorry I +can't stand all that dust + + align:start position:0% +can't stand all that dust + + + align:start position:0% +can't stand all that dust +um oops did pushing all this shut it + + align:start position:0% +um oops did pushing all this shut it + + + align:start position:0% +um oops did pushing all this shut it +down no here we + + align:start position:0% +down no here we + + + align:start position:0% +down no here we +go okay so here are some of the things + + align:start position:0% +go okay so here are some of the things + + + align:start position:0% +go okay so here are some of the things +go ahead and um go to this website M21 + + align:start position:0% +go ahead and um go to this website M21 + + + align:start position:0% +go ahead and um go to this website M21 +sand 2 if you leave off the two you get + + align:start position:0% +sand 2 if you leave off the two you get + + + align:start position:0% +sand 2 if you leave off the two you get +to use uh a three-year-old version of + + align:start position:0% +to use uh a three-year-old version of + + + align:start position:0% +to use uh a three-year-old version of +this you should be seeing something that + + align:start position:0% +this you should be seeing something that + + + align:start position:0% +this you should be seeing something that +looks a bit like this when you get + + align:start position:0% +looks a bit like this when you get + + + align:start position:0% +looks a bit like this when you get +there 21m + + align:start position:0% +there 21m + + + align:start position:0% +there 21m +21 M21 sand 2 + + align:start position:0% +21 M21 sand 2 + + + align:start position:0% +21 M21 sand 2 +M21 + + align:start position:0% +M21 + + + align:start position:0% +M21 +sand 2 sandbox the place where you play + + align:start position:0% + + + + align:start position:0% + +around so the thing I've always hated + + align:start position:0% +around so the thing I've always hated + + + align:start position:0% +around so the thing I've always hated +most about music 21 is that um you can't + + align:start position:0% +most about music 21 is that um you can't + + + align:start position:0% +most about music 21 is that um you can't +see anything uh that's two things you + + align:start position:0% +see anything uh that's two things you + + + align:start position:0% +see anything uh that's two things you +can't see anything you can't hear + + align:start position:0% +can't see anything you can't hear + + + align:start position:0% +can't see anything you can't hear +anything unless you you know we didn't + + align:start position:0% +anything unless you you know we didn't + + + align:start position:0% +anything unless you you know we didn't +even even have uh Jupiter notebooks or + + align:start position:0% +even even have uh Jupiter notebooks or + + + align:start position:0% +even even have uh Jupiter notebooks or +something back then so we didn't have + + align:start position:0% +something back then so we didn't have + + + align:start position:0% +something back then so we didn't have +that and number three it's so hard to + + align:start position:0% +that and number three it's so hard to + + + align:start position:0% +that and number three it's so hard to +install um that's getting easier but + + align:start position:0% +install um that's getting easier but + + + align:start position:0% +install um that's getting easier but +still so I thought that something where + + align:start position:0% +still so I thought that something where + + + align:start position:0% +still so I thought that something where +people can start playing with it + + align:start position:0% +people can start playing with it + + + align:start position:0% +people can start playing with it +immediately online would work and so + + align:start position:0% +immediately online would work and so + + + align:start position:0% +immediately online would work and so +I've been working on um sort of in + + align:start position:0% +I've been working on um sort of in + + + align:start position:0% +I've been working on um sort of in +parallel for the past six years um + + align:start position:0% +parallel for the past six years um + + + align:start position:0% +parallel for the past six years um +there's a typescript or JavaScript Port + + align:start position:0% +there's a typescript or JavaScript Port + + + align:start position:0% +there's a typescript or JavaScript Port +who who has done JavaScript here in some + + align:start position:0% +who who has done JavaScript here in some + + + align:start position:0% +who who has done JavaScript here in some +ways about about okay a little bit more + + align:start position:0% +ways about about okay a little bit more + + + align:start position:0% +ways about about okay a little bit more +than half things so the big difference + + align:start position:0% +than half things so the big difference + + + align:start position:0% +than half things so the big difference +in uh if you're new to JavaScript is + + align:start position:0% +in uh if you're new to JavaScript is + + + align:start position:0% +in uh if you're new to JavaScript is +that you're going to put new in front of + + align:start position:0% +that you're going to put new in front of + + + align:start position:0% +that you're going to put new in front of +anytime you want to instantiate + + align:start position:0% +anytime you want to instantiate + + + align:start position:0% +anytime you want to instantiate +something and I've imported music 21 + + align:start position:0% +something and I've imported music 21 + + + align:start position:0% +something and I've imported music 21 +without importing all of the things so + + align:start position:0% +without importing all of the things so + + + align:start position:0% +without importing all of the things so +you're going to have to type that quite + + align:start position:0% +you're going to have to type that quite + + + align:start position:0% +you're going to have to type that quite +a bit um but what's kind of nice is you + + align:start position:0% +a bit um but what's kind of nice is you + + + align:start position:0% +a bit um but what's kind of nice is you +can go through and change a note and + + align:start position:0% +can go through and change a note and + + + align:start position:0% +can go through and change a note and +immediately see the stream there or um + + align:start position:0% +immediately see the stream there or um + + + align:start position:0% +immediately see the stream there or um +octave things like that or put + + align:start position:0% +octave things like that or put + + + align:start position:0% +octave things like that or put +everything down what happens if we put + + align:start position:0% +everything down what happens if we put + + + align:start position:0% +everything down what happens if we put +everything down here doesn't it + + align:start position:0% +everything down here doesn't it + + + align:start position:0% +everything down here doesn't it +automatically giv me a good cluff no + + align:start position:0% +automatically giv me a good cluff no + + + align:start position:0% +automatically giv me a good cluff no +it's did I put it in okay well we can + + align:start position:0% +it's did I put it in okay well we can + + + align:start position:0% +it's did I put it in okay well we can +put in a proper cluff s so we'll pend to + + align:start position:0% +put in a proper cluff s so we'll pend to + + + align:start position:0% +put in a proper cluff s so we'll pend to +the stream a new music21 docf dobas + + align:start position:0% + + + + align:start position:0% + +cff and now we can see our notes again + + align:start position:0% +cff and now we can see our notes again + + + align:start position:0% +cff and now we can see our notes again +and uh by default if you click the + + align:start position:0% +and uh by default if you click the + + + align:start position:0% +and uh by default if you click the +thing by default + + align:start position:0% + + + + align:start position:0% + +there we go okay well I've lost all my + + align:start position:0% +there we go okay well I've lost all my + + + align:start position:0% +there we go okay well I've lost all my +changes but you can kind of see and so + + align:start position:0% +changes but you can kind of see and so + + + align:start position:0% +changes but you can kind of see and so +um some of the things you can do create + + align:start position:0% +um some of the things you can do create + + + align:start position:0% +um some of the things you can do create +interactive little systems where you're + + align:start position:0% +interactive little systems where you're + + + align:start position:0% +interactive little systems where you're +scrolling things up and down where + + align:start position:0% +scrolling things up and down where + + + align:start position:0% +scrolling things up and down where +you're hearing um everything but it's + + align:start position:0% +you're hearing um everything but it's + + + align:start position:0% +you're hearing um everything but it's +still a absolutely a work in progress so + + align:start position:0% +still a absolutely a work in progress so + + + align:start position:0% +still a absolutely a work in progress so +if you do + + align:start position:0% +if you do + + + align:start position:0% +if you do +analyze key you get analyze is not a + + align:start position:0% +analyze key you get analyze is not a + + + align:start position:0% +analyze key you get analyze is not a +function so there's still a lot of + + align:start position:0% +function so there's still a lot of + + + align:start position:0% +function so there's still a lot of +things um missing there but there's + + align:start position:0% +things um missing there but there's + + + align:start position:0% +things um missing there but there's +something really nice to being able to + + align:start position:0% +something really nice to being able to + + + align:start position:0% +something really nice to being able to +manipulate with scores in a browser + + align:start position:0% +manipulate with scores in a browser + + + align:start position:0% +manipulate with scores in a browser +stuff the Alternatives that people are + + align:start position:0% +stuff the Alternatives that people are + + + align:start position:0% +stuff the Alternatives that people are +doing right now um tend to be about + + align:start position:0% +doing right now um tend to be about + + + align:start position:0% +doing right now um tend to be about +actually uh using HTML elements to + + align:start position:0% +actually uh using HTML elements to + + + align:start position:0% +actually uh using HTML elements to +represent notes now that you have custom + + align:start position:0% +represent notes now that you have custom + + + align:start position:0% +represent notes now that you have custom +elements and that lets you use your + + align:start position:0% +elements and that lets you use your + + + align:start position:0% +elements and that lets you use your +browsers builtin um get Elements by + + align:start position:0% +browsers builtin um get Elements by + + + align:start position:0% +browsers builtin um get Elements by +class and all these things to move + + align:start position:0% +class and all these things to move + + + align:start position:0% +class and all these things to move +around a score and in theory it should + + align:start position:0% +around a score and in theory it should + + + align:start position:0% +around a score and in theory it should +be uh substantially faster than this or + + align:start position:0% +be uh substantially faster than this or + + + align:start position:0% +be uh substantially faster than this or +at least more + + align:start position:0% +at least more + + + align:start position:0% +at least more +powerful I know if anybody wants to you + + align:start position:0% +powerful I know if anybody wants to you + + + align:start position:0% +powerful I know if anybody wants to you +can play around with with any of this + + align:start position:0% +can play around with with any of this + + + align:start position:0% +can play around with with any of this +for a little bit you can make this a + + align:start position:0% +for a little bit you can make this a + + + align:start position:0% +for a little bit you can make this a +dotted + + align:start position:0% +dotted + + + align:start position:0% +dotted +quarter what I hate is uh duration dot + + align:start position:0% +quarter what I hate is uh duration dot + + + align:start position:0% +quarter what I hate is uh duration dot +dots equals one and nothing's going to + + align:start position:0% +dots equals one and nothing's going to + + + align:start position:0% +dots equals one and nothing's going to +happen until I get rid of this analyze + + align:start position:0% +happen until I get rid of this analyze + + + align:start position:0% +happen until I get rid of this analyze +thing here yep play the round give it a + + align:start position:0% +thing here yep play the round give it a + + + align:start position:0% +thing here yep play the round give it a +78 78 time signature and then um here + + align:start position:0% +78 78 time signature and then um here + + + align:start position:0% +78 78 time signature and then um here +let's let's do this let's create P + + align:start position:0% +let's let's do this let's create P + + + align:start position:0% +let's let's do this let's create P +equals stream dot part oops I'm totally + + align:start position:0% +equals stream dot part oops I'm totally + + + align:start position:0% +equals stream dot part oops I'm totally +in yeah like just being in this class + + align:start position:0% +in yeah like just being in this class + + + align:start position:0% +in yeah like just being in this class +with you all I can't not be in Python + + align:start position:0% +with you all I can't not be in Python + + + align:start position:0% +with you all I can't not be in Python +mode so I'm just going to keep typing + + align:start position:0% +mode so I'm just going to keep typing + + + align:start position:0% +mode so I'm just going to keep typing +Python and then correcting it to + + align:start position:0% +Python and then correcting it to + + + align:start position:0% +Python and then correcting it to +JavaScript until it runs but uh we can + + align:start position:0% +JavaScript until it runs but uh we can + + + align:start position:0% +JavaScript until it runs but uh we can +do something like + + align:start position:0% +do something like + + + align:start position:0% +do something like +for uh let I equals + + align:start position:0% +for uh let I equals + + + align:start position:0% +for uh let I equals +z i is less than four i++ and then oh + + align:start position:0% +z i is less than four i++ and then oh + + + align:start position:0% +z i is less than four i++ and then oh +this pains me as a python + + align:start position:0% +this pains me as a python + + + align:start position:0% +this pains me as a python +um uh as a python person to not have + + align:start position:0% +um uh as a python person to not have + + + align:start position:0% +um uh as a python person to not have +indented code but + + align:start position:0% +indented code but + + + align:start position:0% +indented code but +um actually do we have to call that um + + align:start position:0% +um actually do we have to call that um + + + align:start position:0% +um actually do we have to call that um +we have to call that a measure music 21j + + align:start position:0% +we have to call that a measure music 21j + + + align:start position:0% +we have to call that a measure music 21j +is a lot more strict about such things + + align:start position:0% +is a lot more strict about such things + + + align:start position:0% +is a lot more strict about such things +to + + align:start position:0% + + + + align:start position:0% + +I H what did I do + + align:start position:0% +I H what did I do + + + align:start position:0% +I H what did I do +wrong so hard to tell without + + align:start position:0% +wrong so hard to tell without + + + align:start position:0% +wrong so hard to tell without +indentations but there's this edit + + align:start position:0% +indentations but there's this edit + + + align:start position:0% +indentations but there's this edit +doesn't allow me to hit tab to indent + + align:start position:0% + + + + align:start position:0% + +things here always make your life easier + + align:start position:0% +things here always make your life easier + + + align:start position:0% +things here always make your life easier +get rid of that so you can see + + align:start position:0% +get rid of that so you can see + + + align:start position:0% +get rid of that so you can see +everything on one + + align:start position:0% + + + + align:start position:0% + +page anybody know what I'm M typing here + + align:start position:0% +page anybody know what I'm M typing here + + + align:start position:0% +page anybody know what I'm M typing here +I have a fully baked version over here + + align:start position:0% +I have a fully baked version over here + + + align:start position:0% +I have a fully baked version over here +somewhere on another + + align:start position:0% + + + + align:start position:0% + +tab here we'll go over to the the fully + + align:start position:0% +tab here we'll go over to the the fully + + + align:start position:0% +tab here we'll go over to the the fully +baked one that already works so you can + + align:start position:0% +baked one that already works so you can + + + align:start position:0% +baked one that already works so you can +kind + + align:start position:0% +kind + + + align:start position:0% +kind +of play around with it just saying first + + align:start position:0% +of play around with it just saying first + + + align:start position:0% +of play around with it just saying first +note of each of each measure will be a + + align:start position:0% +note of each of each measure will be a + + + align:start position:0% +note of each of each measure will be a +random number and as we go through we'll + + align:start position:0% +random number and as we go through we'll + + + align:start position:0% +random number and as we go through we'll +just change them and if I make any + + align:start position:0% +just change them and if I make any + + + align:start position:0% +just change them and if I make any +changes here it will automatically give + + align:start position:0% +changes here it will automatically give + + + align:start position:0% +changes here it will automatically give +me a new random number I thought I had + + align:start position:0% +me a new random number I thought I had + + + align:start position:0% +me a new random number I thought I had +it oh + + align:start position:0% +it oh + + + align:start position:0% +it oh +this here I think I have to copy and + + align:start position:0% +this here I think I have to copy and + + + align:start position:0% +this here I think I have to copy and +paste + + align:start position:0% +paste + + + align:start position:0% +paste +what I think happens is + + align:start position:0% +what I think happens is + + + align:start position:0% +what I think happens is +um there we + + align:start position:0% +um there we + + + align:start position:0% +um there we +go and you can do overlapping + + align:start position:0% + + + + align:start position:0% + +things anyhow so it be kind of fun for a + + align:start position:0% +things anyhow so it be kind of fun for a + + + align:start position:0% +things anyhow so it be kind of fun for a +live coding environment if you don't + + align:start position:0% +live coding environment if you don't + + + align:start position:0% +live coding environment if you don't +care about the quality of the music um + + align:start position:0% +care about the quality of the music um + + + align:start position:0% +care about the quality of the music um +coming if you don't care about the + + align:start position:0% +coming if you don't care about the + + + align:start position:0% +coming if you don't care about the +quality of the sound cuz it's not really + + align:start position:0% +quality of the sound cuz it's not really + + + align:start position:0% +quality of the sound cuz it's not really +optimized for sound quality uh but you + + align:start position:0% +optimized for sound quality uh but you + + + align:start position:0% +optimized for sound quality uh but you +could put it out through other + + align:start position:0% +could put it out through other + + + align:start position:0% +could put it out through other +things uh let grab bag topic number one + + align:start position:0% +things uh let grab bag topic number one + + + align:start position:0% +things uh let grab bag topic number one +how to do interactive um how to do + + align:start position:0% +how to do interactive um how to do + + + align:start position:0% +how to do interactive um how to do +interactive programming stuff you can do + + align:start position:0% +interactive programming stuff you can do + + + align:start position:0% +interactive programming stuff you can do +everything uh sorry John you just came + + align:start position:0% +everything uh sorry John you just came + + + align:start position:0% +everything uh sorry John you just came +back in and I'm going just just say look + + align:start position:0% +back in and I'm going just just say look + + + align:start position:0% +back in and I'm going just just say look +you're the only one has anyone else + + align:start position:0% +you're the only one has anyone else + + + align:start position:0% +you're the only one has anyone else +taken interactive music + + align:start position:0% +taken interactive music + + + align:start position:0% +taken interactive music +systems oh you are okay so you have yeah + + align:start position:0% +systems oh you are okay so you have yeah + + + align:start position:0% +systems oh you are okay so you have yeah +so you can put everything into uh a you + + align:start position:0% +so you can put everything into uh a you + + + align:start position:0% +so you can put everything into uh a you +guys mostly use Ki right as your as your + + align:start position:0% +guys mostly use Ki right as your as your + + + align:start position:0% +guys mostly use Ki right as your as your +toolkit so you there are things you can + + align:start position:0% +toolkit so you there are things you can + + + align:start position:0% +toolkit so you there are things you can +do on the on the python side they + + align:start position:0% +do on the on the python side they + + + align:start position:0% +do on the on the python side they +connect up music 21 to things to uh get + + align:start position:0% +connect up music 21 to things to uh get + + + align:start position:0% +connect up music 21 to things to uh get +better sounding interactive um things + + align:start position:0% +better sounding interactive um things + + + align:start position:0% +better sounding interactive um things +but I often find sometimes just the + + align:start position:0% +but I often find sometimes just the + + + align:start position:0% +but I often find sometimes just the +easiest little thing U can be all you + + align:start position:0% +easiest little thing U can be all you + + + align:start position:0% +easiest little thing U can be all you +need okay close these things because + + align:start position:0% +need okay close these things because + + + align:start position:0% +need okay close these things because +otherwise it will eventually just start + + align:start position:0% +otherwise it will eventually just start + + + align:start position:0% +otherwise it will eventually just start +playing again and we have just enough + + align:start position:0% +playing again and we have just enough + + + align:start position:0% +playing again and we have just enough +time for I think for one more topic and + + align:start position:0% +time for I think for one more topic and + + + align:start position:0% +time for I think for one more topic and +then uh I might finally keep my promise + + align:start position:0% +then uh I might finally keep my promise + + + align:start position:0% +then uh I might finally keep my promise +and let you all go a little bit earlier + + align:start position:0% +and let you all go a little bit earlier + + + align:start position:0% +and let you all go a little bit earlier +um okay so the last thing I want to talk + + align:start position:0% +um okay so the last thing I want to talk + + + align:start position:0% +um okay so the last thing I want to talk +about a little bit is music + + align:start position:0% +about a little bit is music + + + align:start position:0% +about a little bit is music +visualization and uh we're going to + + align:start position:0% +visualization and uh we're going to + + + align:start position:0% +visualization and uh we're going to +listen to a piece of music by a + + align:start position:0% +listen to a piece of music by a + + + align:start position:0% +listen to a piece of music by a +contemporary Estonian composer arvo + + align:start position:0% +contemporary Estonian composer arvo + + + align:start position:0% +contemporary Estonian composer arvo +parot and I'm going to ask you + + align:start position:0% +parot and I'm going to ask you + + + align:start position:0% +parot and I'm going to ask you +afterwards to say something about the + + align:start position:0% +afterwards to say something about the + + + align:start position:0% +afterwards to say something about the +structure or the form of this piece and + + align:start position:0% +structure or the form of this piece and + + + align:start position:0% +structure or the form of this piece and +how it works musically first it's a a + + align:start position:0% +how it works musically first it's a a + + + align:start position:0% +how it works musically first it's a a +piece for choir and so it has a text + + align:start position:0% +piece for choir and so it has a text + + + align:start position:0% +piece for choir and so it has a text +it's a actually high high medieval today + + align:start position:0% +it's a actually high high medieval today + + + align:start position:0% +it's a actually high high medieval today +uh it's based on a Gregorian chant of + + align:start position:0% +uh it's based on a Gregorian chant of + + + align:start position:0% +uh it's based on a Gregorian chant of +it's sung in German translation uh o + + align:start position:0% +it's sung in German translation uh o + + + align:start position:0% +it's sung in German translation uh o +Immanuel + + align:start position:0% + + + + align:start position:0% + +and uh the German text is going to be + + align:start position:0% +and uh the German text is going to be + + + align:start position:0% +and uh the German text is going to be +slightly important for that so it's + + align:start position:0% +slightly important for that so it's + + + align:start position:0% +slightly important for that so it's +about a TW minute piece um and long time + + align:start position:0% +about a TW minute piece um and long time + + + align:start position:0% +about a TW minute piece um and long time +of the year for doing it but get + + align:start position:0% +of the year for doing it but get + + + align:start position:0% +of the year for doing it but get +that here we go + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +1988 I think was um one of my favorites + + align:start position:0% +1988 I think was um one of my favorites + + + align:start position:0% +1988 I think was um one of my favorites +um anybody catch anything about the + + align:start position:0% +um anybody catch anything about the + + + align:start position:0% +um anybody catch anything about the +structure you have seen the entire score + + align:start position:0% +structure you have seen the entire score + + + align:start position:0% +structure you have seen the entire score +every single note so we can get + + align:start position:0% +every single note so we can get + + + align:start position:0% +every single note so we can get +something yeah measures always switch + + align:start position:0% +something yeah measures always switch + + + align:start position:0% +something yeah measures always switch +between 1 two and 32 measures always + + align:start position:0% +between 1 two and 32 measures always + + + align:start position:0% +between 1 two and 32 measures always +switch between one two and 32 one two + + align:start position:0% +switch between one two and 32 one two + + + align:start position:0% +switch between one two and 32 one two +and + + align:start position:0% + + + + align:start position:0% + +32 how many sections did the piece have + + align:start position:0% + + + + align:start position:0% + +yeah tell like three seconds nice that's + + align:start position:0% +yeah tell like three seconds nice that's + + + align:start position:0% +yeah tell like three seconds nice that's +actually correct how many people knew + + align:start position:0% +actually correct how many people knew + + + align:start position:0% +actually correct how many people knew +that and how many people were like me + + align:start position:0% +that and how many people were like me + + + align:start position:0% +that and how many people were like me +when they heard this like once twice + + align:start position:0% +when they heard this like once twice + + + align:start position:0% +when they heard this like once twice +three times and didn't fully catch the + + align:start position:0% +three times and didn't fully catch the + + + align:start position:0% +three times and didn't fully catch the +structure I was yeah yeah + + align:start position:0% +structure I was yeah yeah + + + align:start position:0% +structure I was yeah yeah +so fantastic fantastic usually uh so + + align:start position:0% +so fantastic fantastic usually uh so + + + align:start position:0% +so fantastic fantastic usually uh so +yeah there some things in and what voice + + align:start position:0% +yeah there some things in and what voice + + + align:start position:0% +yeah there some things in and what voice +is most Mel what two voices were most + + align:start position:0% +is most Mel what two voices were most + + + align:start position:0% +is most Mel what two voices were most +melodically active + + align:start position:0% +melodically active + + + align:start position:0% +melodically active +yeah middle two I think good ear good + + align:start position:0% +yeah middle two I think good ear good + + + align:start position:0% +yeah middle two I think good ear good +ear this this yall are are really + + align:start position:0% +ear this this yall are are really + + + align:start position:0% +ear this this yall are are really +getting you we should have been doing + + align:start position:0% +getting you we should have been doing + + + align:start position:0% +getting you we should have been doing +more music analysis in class because + + align:start position:0% +more music analysis in class because + + + align:start position:0% +more music analysis in class because +you're getting a lot of things I thought + + align:start position:0% +you're getting a lot of things I thought + + + align:start position:0% +you're getting a lot of things I thought +were going to be extremely hard and some + + align:start position:0% +were going to be extremely hard and some + + + align:start position:0% +were going to be extremely hard and some +at least throughout the room we've had + + align:start position:0% +at least throughout the room we've had + + + align:start position:0% +at least throughout the room we've had +correct answers but I want to uh spend a + + align:start position:0% +correct answers but I want to uh spend a + + + align:start position:0% +correct answers but I want to uh spend a +little bit of time on music um visual by + + align:start position:0% +little bit of time on music um visual by + + + align:start position:0% +little bit of time on music um visual by +the way there are a few uh ad almost + + align:start position:0% +the way there are a few uh ad almost + + + align:start position:0% +the way there are a few uh ad almost +exactly there's one measure of 52 + + align:start position:0% +exactly there's one measure of 52 + + + align:start position:0% +exactly there's one measure of 52 +but yeah there's a couple other things + + align:start position:0% +but yeah there's a couple other things + + + align:start position:0% +but yeah there's a couple other things +but yep so um are we up there yeah go + + align:start position:0% +but yep so um are we up there yeah go + + + align:start position:0% +but yep so um are we up there yeah go +ahead and download um there is the MXL + + align:start position:0% +ahead and download um there is the MXL + + + align:start position:0% +ahead and download um there is the MXL +the XML file music XML file of this + + align:start position:0% +the XML file music XML file of this + + + align:start position:0% +the XML file music XML file of this +piece on canvas and uh take a minute + + align:start position:0% +piece on canvas and uh take a minute + + + align:start position:0% +piece on canvas and uh take a minute +it's it's under copyright but I'm going + + align:start position:0% +it's it's under copyright but I'm going + + + align:start position:0% +it's it's under copyright but I'm going +to assert a claim of fair use for us to + + align:start position:0% +to assert a claim of fair use for us to + + + align:start position:0% +to assert a claim of fair use for us to +be able to uh analyze with it show + + align:start position:0% +be able to uh analyze with it show + + + align:start position:0% +be able to uh analyze with it show +should show you the just the first page + + align:start position:0% +should show you the just the first page + + + align:start position:0% +should show you the just the first page +if you're in Jupiter and + + align:start position:0% +if you're in Jupiter and + + + align:start position:0% +if you're in Jupiter and +more than that if you're + + align:start position:0% + + + + align:start position:0% + +not so this might uh some of these + + align:start position:0% +not so this might uh some of these + + + align:start position:0% +not so this might uh some of these +things might be helpful for + + align:start position:0% +things might be helpful for + + + align:start position:0% +things might be helpful for +um or what we're doing so a little bit + + align:start position:0% +um or what we're doing so a little bit + + + align:start position:0% +um or what we're doing so a little bit +more we're going to be going through the + + align:start position:0% +more we're going to be going through the + + + align:start position:0% +more we're going to be going through the +various + + align:start position:0% +various + + + align:start position:0% +various +um ways of visualizing + + align:start position:0% + + + + align:start position:0% + +I don't think we've maybe I've done a + + align:start position:0% +I don't think we've maybe I've done a + + + align:start position:0% +I don't think we've maybe I've done a +tiny bit of visualization but mostly + + align:start position:0% +tiny bit of visualization but mostly + + + align:start position:0% +tiny bit of visualization but mostly +just on slides I don't think I've + + align:start position:0% + + + + align:start position:0% + +shown we feeling in a good place to move + + align:start position:0% +shown we feeling in a good place to move + + + align:start position:0% +shown we feeling in a good place to move +on now okay so um you know we can do all + + align:start position:0% +on now okay so um you know we can do all + + + align:start position:0% +on now okay so um you know we can do all +the things that um that we normally + + align:start position:0% +the things that um that we normally + + + align:start position:0% +the things that um that we normally +would do we can get the key of the piece + + align:start position:0% +would do we can get the key of the piece + + + align:start position:0% +would do we can get the key of the piece +which I believe + + align:start position:0% +which I believe + + + align:start position:0% +which I believe +changes quite a bit I think if we do U + + align:start position:0% +changes quite a bit I think if we do U + + + align:start position:0% +changes quite a bit I think if we do U +measures 1 through 20. analyze key we + + align:start position:0% +measures 1 through 20. analyze key we + + + align:start position:0% +measures 1 through 20. analyze key we +get something very different no we + + align:start position:0% +get something very different no we + + + align:start position:0% +get something very different no we +don't still get interesting just the key + + align:start position:0% +don't still get interesting just the key + + + align:start position:0% +don't still get interesting just the key +signature changes um okay but now we'll + + align:start position:0% +signature changes um okay but now we'll + + + align:start position:0% +signature changes um okay but now we'll +get into some visualization things so + + align:start position:0% +get into some visualization things so + + + align:start position:0% +get into some visualization things so +the easiest thing you can do with a + + align:start position:0% +the easiest thing you can do with a + + + align:start position:0% +the easiest thing you can do with a +stream um is to do something called plot + + align:start position:0% +stream um is to do something called plot + + + align:start position:0% +stream um is to do something called plot +and plot just gives you um any whatever + + align:start position:0% +and plot just gives you um any whatever + + + align:start position:0% +and plot just gives you um any whatever +you uh sort of a standard + + align:start position:0% +you uh sort of a standard + + + align:start position:0% +you uh sort of a standard +readymade um + + align:start position:0% +readymade um + + + align:start position:0% +readymade um +oops that's why I never do this here uh + + align:start position:0% +oops that's why I never do this here uh + + + align:start position:0% +oops that's why I never do this here uh +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +readymade image sorry it doesn't Zoom + + align:start position:0% +readymade image sorry it doesn't Zoom + + + align:start position:0% +readymade image sorry it doesn't Zoom +the image in but you on here but you + + align:start position:0% +the image in but you on here but you + + + align:start position:0% +the image in but you on here but you +might be able to see something like that + + align:start position:0% +might be able to see something like that + + + align:start position:0% +might be able to see something like that +and so you can see a + + align:start position:0% +and so you can see a + + + align:start position:0% +and so you can see a +relationship of the um various parts + + align:start position:0% +relationship of the um various parts + + + align:start position:0% +relationship of the um various parts +colored in different colors and which + + align:start position:0% +colored in different colors and which + + + align:start position:0% +colored in different colors and which +ones are singing + + align:start position:0% +ones are singing + + + align:start position:0% +ones are singing +what so here the three-part the + + align:start position:0% +what so here the three-part the + + + align:start position:0% +what so here the three-part the +three-fold relationship sorry I'm going + + align:start position:0% +three-fold relationship sorry I'm going + + + align:start position:0% +three-fold relationship sorry I'm going +to have to zoom this out tiny bit so we + + align:start position:0% +to have to zoom this out tiny bit so we + + + align:start position:0% +to have to zoom this out tiny bit so we +can see this again + + align:start position:0% +can see this again + + + align:start position:0% +can see this again +um the three-part relation three section + + align:start position:0% +um the three-part relation three section + + + align:start position:0% +um the three-part relation three section +relationship of the piece becomes very + + align:start position:0% +relationship of the piece becomes very + + + align:start position:0% +relationship of the piece becomes very +clear right you can see that something + + align:start position:0% +clear right you can see that something + + + align:start position:0% +clear right you can see that something +happens at the + + align:start position:0% +happens at the + + + align:start position:0% +happens at the +beginning this increase up here up until + + align:start position:0% +beginning this increase up here up until + + + align:start position:0% +beginning this increase up here up until +a certain point and then a lot of things + + align:start position:0% +a certain point and then a lot of things + + + align:start position:0% +a certain point and then a lot of things +change so what + + align:start position:0% +change so what + + + align:start position:0% +change so what +measure does the third section begin + + align:start position:0% + + + + align:start position:0% + +on yeah somewhere around there so you + + align:start position:0% +on yeah somewhere around there so you + + + align:start position:0% +on yeah somewhere around there so you +can uh 45 I think some 46 44 45 so you + + align:start position:0% +can uh 45 I think some 46 44 45 so you + + + align:start position:0% +can uh 45 I think some 46 44 45 so you +can kind of see something substantial + + align:start position:0% +can kind of see something substantial + + + align:start position:0% +can kind of see something substantial +changes and um here's what Jason pointed + + align:start position:0% +changes and um here's what Jason pointed + + + align:start position:0% +changes and um here's what Jason pointed +out right that um that the inner voices + + align:start position:0% +out right that um that the inner voices + + + align:start position:0% +out right that um that the inner voices +in the second and third sections are the + + align:start position:0% +in the second and third sections are the + + + align:start position:0% +in the second and third sections are the +ones that are + + align:start position:0% +ones that are + + + align:start position:0% +ones that are +very um very + + align:start position:0% +very um very + + + align:start position:0% +very um very +active right so where does second + + align:start position:0% +active right so where does second + + + align:start position:0% +active right so where does second +section begin measure + + align:start position:0% +section begin measure + + + align:start position:0% +section begin measure +13 to + + align:start position:0% +13 to + + + align:start position:0% +13 to +measure 45 so let's let's get this SEC 2 + + align:start position:0% +measure 45 so let's let's get this SEC 2 + + + align:start position:0% +measure 45 so let's let's get this SEC 2 +equals arvo do measures let say 14 to 45 + + align:start position:0% +equals arvo do measures let say 14 to 45 + + + align:start position:0% +equals arvo do measures let say 14 to 45 +44 we'll say SEC 2. plot I think I think + + align:start position:0% +44 we'll say SEC 2. plot I think I think + + + align:start position:0% +44 we'll say SEC 2. plot I think I think +the default is piano roll because that's + + align:start position:0% +the default is piano roll because that's + + + align:start position:0% +the default is piano roll because that's +what most people want so we can look at + + align:start position:0% +what most people want so we can look at + + + align:start position:0% +what most people want so we can look at +section + + align:start position:0% +section + + + align:start position:0% +section +two and we'll say section three was + + align:start position:0% +two and we'll say section three was + + + align:start position:0% +two and we'll say section three was +measures what 45 to + + align:start position:0% +measures what 45 to + + + align:start position:0% +measures what 45 to +76 Section 3 equals arvo + + align:start position:0% +76 Section 3 equals arvo + + + align:start position:0% +76 Section 3 equals arvo +dot + + align:start position:0% +dot + + + align:start position:0% +dot +measures 45 to + + align:start position:0% +measures 45 to + + + align:start position:0% +measures 45 to +76 we can plot + + align:start position:0% + + + + align:start position:0% + +that there's a lot of similarities here + + align:start position:0% +that there's a lot of similarities here + + + align:start position:0% +that there's a lot of similarities here +between section + + align:start position:0% +between section + + + align:start position:0% +between section +two and section + + align:start position:0% + + + + align:start position:0% + +3 what's what's the biggest difference + + align:start position:0% +3 what's what's the biggest difference + + + align:start position:0% +3 what's what's the biggest difference +musically that you can tell from these + + align:start position:0% +musically that you can tell from these + + + align:start position:0% +musically that you can tell from these +charts between section two and section + + align:start position:0% +charts between section two and section + + + align:start position:0% +charts between section two and section +three you'll probably want to go all the + + align:start position:0% +three you'll probably want to go all the + + + align:start position:0% +three you'll probably want to go all the +way back up to your bigger + + align:start position:0% + + + + align:start position:0% + +role over here this side's been mostly + + align:start position:0% +role over here this side's been mostly + + + align:start position:0% +role over here this side's been mostly +quiet yeah section two section almost + + align:start position:0% +quiet yeah section two section almost + + + align:start position:0% +quiet yeah section two section almost +identical but section two is up section + + align:start position:0% +identical but section two is up section + + + align:start position:0% +identical but section two is up section +two and section 3 are almost identical + + align:start position:0% +two and section 3 are almost identical + + + align:start position:0% +two and section 3 are almost identical +but section two is up good can we figure + + align:start position:0% +but section two is up good can we figure + + + align:start position:0% +but section two is up good can we figure +out about how much up it + + align:start position:0% +out about how much up it + + + align:start position:0% +out about how much up it +is look at the key on the + + align:start position:0% +is look at the key on the + + + align:start position:0% +is look at the key on the +side yeah the e to the A and the E to an + + align:start position:0% +side yeah the e to the A and the E to an + + + align:start position:0% +side yeah the e to the A and the E to an +A so it's about about a fifth off in a + + align:start position:0% +A so it's about about a fifth off in a + + + align:start position:0% +A so it's about about a fifth off in a +lot of things except for on the extremes + + align:start position:0% +lot of things except for on the extremes + + + align:start position:0% +lot of things except for on the extremes +but what about the notes in + + align:start position:0% +but what about the notes in + + + align:start position:0% +but what about the notes in +between these moving parts + + align:start position:0% +between these moving parts + + + align:start position:0% +between these moving parts +where are they off what's the + + align:start position:0% +where are they off what's the + + + align:start position:0% +where are they off what's the +relationship + + align:start position:0% + + + + align:start position:0% + +there OCT yeah about yeah an OCT exactly + + align:start position:0% +there OCT yeah about yeah an OCT exactly + + + align:start position:0% +there OCT yeah about yeah an OCT exactly +an octave up so we have things moving + + align:start position:0% +an octave up so we have things moving + + + align:start position:0% +an octave up so we have things moving +now go I'll open up the score one more + + align:start position:0% +now go I'll open up the score one more + + + align:start position:0% +now go I'll open up the score one more +time I know I why I wanted the score + + align:start position:0% +time I know I why I wanted the score + + + align:start position:0% +time I know I why I wanted the score +open so I could keep going to back to + + align:start position:0% +open so I could keep going to back to + + + align:start position:0% +open so I could keep going to back to +this um let me get a no here we go um so + + align:start position:0% +this um let me get a no here we go um so + + + align:start position:0% +this um let me get a no here we go um so +I'll put this in front for a second + + align:start position:0% +I'll put this in front for a second + + + align:start position:0% +I'll put this in front for a second +and sorry now i' now I've lost my my + + align:start position:0% +and sorry now i' now I've lost my my + + + align:start position:0% +and sorry now i' now I've lost my my +train train of thought + + align:start position:0% +train train of thought + + + align:start position:0% +train train of thought +um how easy is it to see which parts are + + align:start position:0% +um how easy is it to see which parts are + + + align:start position:0% +um how easy is it to see which parts are +static and which parts are Mo in Motion + + align:start position:0% +static and which parts are Mo in Motion + + + align:start position:0% +static and which parts are Mo in Motion +in + + align:start position:0% +in + + + align:start position:0% +in +this quite a bit harder so what it what + + align:start position:0% +this quite a bit harder so what it what + + + align:start position:0% +this quite a bit harder so what it what +kind of motion is happening we've + + align:start position:0% +kind of motion is happening we've + + + align:start position:0% +kind of motion is happening we've +identified that it's the inner voices + + align:start position:0% +identified that it's the inner voices + + + align:start position:0% +identified that it's the inner voices +that are in motion + + align:start position:0% +that are in motion + + + align:start position:0% +that are in motion +um what's the + + align:start position:0% +um what's the + + + align:start position:0% +um what's the +pattern now go back to your + + align:start position:0% +pattern now go back to your + + + align:start position:0% +pattern now go back to your +visualization and see if you can figure + + align:start position:0% +visualization and see if you can figure + + + align:start position:0% +visualization and see if you can figure +it + + align:start position:0% +it + + + align:start position:0% +it +out in any of the inner + + align:start position:0% + + + + align:start position:0% + +voices maybe it's easier if you just + + align:start position:0% +voices maybe it's easier if you just + + + align:start position:0% +voices maybe it's easier if you just +look at one of the sections so you can + + align:start position:0% +look at one of the sections so you can + + + align:start position:0% +look at one of the sections so you can +zoom in a little bit + + align:start position:0% +zoom in a little bit + + + align:start position:0% +zoom in a little bit +more John do you want + + align:start position:0% +more John do you want + + + align:start position:0% +more John do you want +to move in + + align:start position:0% +to move in + + + align:start position:0% +to move in +parall they move in parallel first yeah + + align:start position:0% +parall they move in parallel first yeah + + + align:start position:0% +parall they move in parallel first yeah +and looks good and within any given + + align:start position:0% +and looks good and within any given + + + align:start position:0% +and looks good and within any given +voice what's the what's it + + align:start position:0% + + + + align:start position:0% + +doing is it playing Mary had a little + + align:start position:0% +doing is it playing Mary had a little + + + align:start position:0% +doing is it playing Mary had a little +lamp is it jumping around a huge uh + + align:start position:0% +lamp is it jumping around a huge uh + + + align:start position:0% +lamp is it jumping around a huge uh +octave and then coming back down + + align:start position:0% +octave and then coming back down + + + align:start position:0% +octave and then coming back down +Adam they're just playing the same note + + align:start position:0% +Adam they're just playing the same note + + + align:start position:0% +Adam they're just playing the same note +uh not all of them are playing the same + + align:start position:0% +uh not all of them are playing the same + + + align:start position:0% +uh not all of them are playing the same +note these ones are playing the same + + align:start position:0% +note these ones are playing the same + + + align:start position:0% +note these ones are playing the same +note right but what what's what are the + + align:start position:0% +note right but what what's what are the + + + align:start position:0% +note right but what what's what are the +other voices doing these inner + + align:start position:0% +other voices doing these inner + + + align:start position:0% +other voices doing these inner +voices do it go all the way up and then + + align:start position:0% +voices do it go all the way up and then + + + align:start position:0% +voices do it go all the way up and then +all the way yeah I you s repeating right + + align:start position:0% +all the way yeah I you s repeating right + + + align:start position:0% +all the way yeah I you s repeating right +they're repeating what what do they do + + align:start position:0% +they're repeating what what do they do + + + align:start position:0% +they're repeating what what do they do +what what's the pattern yeah stepwise + + align:start position:0% +what what's the pattern yeah stepwise + + + align:start position:0% +what what's the pattern yeah stepwise +stepwise good it's all stepwise which is + + align:start position:0% +stepwise good it's all stepwise which is + + + align:start position:0% +stepwise good it's all stepwise which is +the hard part about piano roll right you + + align:start position:0% +the hard part about piano roll right you + + + align:start position:0% +the hard part about piano roll right you +would want a dionic piano roll at some + + align:start position:0% +would want a dionic piano roll at some + + + align:start position:0% +would want a dionic piano roll at some +point um I think we have that somewhere + + align:start position:0% +point um I think we have that somewhere + + + align:start position:0% +point um I think we have that somewhere +um and it's all step wise and it's even + + align:start position:0% +um and it's all step wise and it's even + + + align:start position:0% +um and it's all step wise and it's even +more than that yeah go Vin it nebor + + align:start position:0% +more than that yeah go Vin it nebor + + + align:start position:0% +more than that yeah go Vin it nebor +tones around a certain page top around + + align:start position:0% +tones around a certain page top around + + + align:start position:0% +tones around a certain page top around +they're all neighbor tones around a + + align:start position:0% +they're all neighbor tones around a + + + align:start position:0% +they're all neighbor tones around a +certain pitch yeah so you can kind of + + align:start position:0% +certain pitch yeah so you can kind of + + + align:start position:0% +certain pitch yeah so you can kind of +top one I can't reach so we'll do the + + align:start position:0% +top one I can't reach so we'll do the + + + align:start position:0% +top one I can't reach so we'll do the +middle one is I guess around e and is it + + align:start position:0% +middle one is I guess around e and is it + + + align:start position:0% +middle one is I guess around e and is it +is there a pattern that you do three ups + + align:start position:0% +is there a pattern that you do three ups + + + align:start position:0% +is there a pattern that you do three ups +and then a down and then what is + + align:start position:0% +and then a down and then what is + + + align:start position:0% +and then a down and then what is +it up then down up then down up then + + align:start position:0% +it up then down up then down up then + + + align:start position:0% +it up then down up then down up then +down so you could almost have a formula + + align:start position:0% +down so you could almost have a formula + + + align:start position:0% +down so you could almost have a formula +um with this in fact uh the the one of + + align:start position:0% +um with this in fact uh the the one of + + + align:start position:0% +um with this in fact uh the the one of +the um other python based music um + + align:start position:0% +the um other python based music um + + + align:start position:0% +the um other python based music um +packages which is more about creating + + align:start position:0% +packages which is more about creating + + + align:start position:0% +packages which is more about creating +algorithmically generable music is + + align:start position:0% +algorithmically generable music is + + + align:start position:0% +algorithmically generable music is +called arvo based on arvo parr's um + + align:start position:0% +called arvo based on arvo parr's um + + + align:start position:0% +called arvo based on arvo parr's um +ability to do this so you can you can + + align:start position:0% +ability to do this so you can you can + + + align:start position:0% +ability to do this so you can you can +download install arvo and um it makes it + + align:start position:0% +download install arvo and um it makes it + + + align:start position:0% +download install arvo and um it makes it +much easier than music 21 does to + + align:start position:0% +much easier than music 21 does to + + + align:start position:0% +much easier than music 21 does to +generate uh here's a motive now spin it + + align:start position:0% +generate uh here's a motive now spin it + + + align:start position:0% +generate uh here's a motive now spin it +out over a certain amount of time while + + align:start position:0% +out over a certain amount of time while + + + align:start position:0% +out over a certain amount of time while +doing something else so yeah so we have + + align:start position:0% +doing something else so yeah so we have + + + align:start position:0% +doing something else so yeah so we have +this thing going up and down and up and + + align:start position:0% +this thing going up and down and up and + + + align:start position:0% +this thing going up and down and up and +down and things like that um by the way + + align:start position:0% +down and things like that um by the way + + + align:start position:0% +down and things like that um by the way +some of the other interesting things + + align:start position:0% +some of the other interesting things + + + align:start position:0% +some of the other interesting things +about the piece that we're not going to + + align:start position:0% +about the piece that we're not going to + + + align:start position:0% +about the piece that we're not going to +visualize music 21 uh are um when does + + align:start position:0% +visualize music 21 uh are um when does + + + align:start position:0% +visualize music 21 uh are um when does +it uh change notes on on any multi- + + align:start position:0% +it uh change notes on on any multi- + + + align:start position:0% +it uh change notes on on any multi- +syllable accented German word which I + + align:start position:0% +syllable accented German word which I + + + align:start position:0% +syllable accented German word which I +think uh sort of interesting here so the + + align:start position:0% +think uh sort of interesting here so the + + + align:start position:0% +think uh sort of interesting here so the +accent always gets the gets the whole + + align:start position:0% +accent always gets the gets the whole + + + align:start position:0% +accent always gets the gets the whole +note and it's always the opposite of + + align:start position:0% +note and it's always the opposite of + + + align:start position:0% +note and it's always the opposite of +whatever it was + + align:start position:0% +whatever it was + + + align:start position:0% +whatever it was +before and then you can kind of see well + + align:start position:0% +before and then you can kind of see well + + + align:start position:0% +before and then you can kind of see well +in section two all of the voices kind of + + align:start position:0% +in section two all of the voices kind of + + + align:start position:0% +in section two all of the voices kind of +play at once and they all rest at once + + align:start position:0% +play at once and they all rest at once + + + align:start position:0% +play at once and they all rest at once +but in section three the top and the + + align:start position:0% +but in section three the top and the + + + align:start position:0% +but in section three the top and the +bottom ones only coming in certain times + + align:start position:0% +bottom ones only coming in certain times + + + align:start position:0% +bottom ones only coming in certain times +the visualization of this helped me in + + align:start position:0% +the visualization of this helped me in + + + align:start position:0% +the visualization of this helped me in +figuring out well when are those times + + align:start position:0% +figuring out well when are those times + + + align:start position:0% +figuring out well when are those times +and it turns out also very strictly + + align:start position:0% +and it turns out also very strictly + + + align:start position:0% +and it turns out also very strictly +generated um that it is + + align:start position:0% +generated um that it is + + + align:start position:0% +generated um that it is +just every other word + + align:start position:0% +just every other word + + + align:start position:0% +just every other word +do they do that's two + + align:start position:0% +do they do that's two + + + align:start position:0% +do they do that's two +words we don't + + align:start position:0% +words we don't + + + align:start position:0% +words we don't +sing next two words derer we sing Oh + + align:start position:0% +sing next two words derer we sing Oh + + + align:start position:0% +sing next two words derer we sing Oh +Come we + + align:start position:0% +Come we + + + align:start position:0% +Come we +don't and there's one exception to it uh + + align:start position:0% +don't and there's one exception to it uh + + + align:start position:0% +don't and there's one exception to it uh +no sorry there isn't an exception on + + align:start position:0% +no sorry there isn't an exception on + + + align:start position:0% +no sorry there isn't an exception on +this one there's some someplace else is + + align:start position:0% +this one there's some someplace else is + + + align:start position:0% +this one there's some someplace else is +an exception on things but I think + + align:start position:0% +an exception on things but I think + + + align:start position:0% +an exception on things but I think +probably set up so that just the number + + align:start position:0% +probably set up so that just the number + + + align:start position:0% +probably set up so that just the number +of words makes it so that God stands + + align:start position:0% +of words makes it so that God stands + + + align:start position:0% +of words makes it so that God stands +alone at the end without accompanyment + + align:start position:0% +alone at the end without accompanyment + + + align:start position:0% +alone at the end without accompanyment +so interesting piece now let's do a tiny + + align:start position:0% +so interesting piece now let's do a tiny + + + align:start position:0% +so interesting piece now let's do a tiny +bit more analysis on it + + align:start position:0% +bit more analysis on it + + + align:start position:0% +bit more analysis on it +um there's a plot that um I could call + + align:start position:0% +um there's a plot that um I could call + + + align:start position:0% +um there's a plot that um I could call +this a cook plot cook because I saw this + + align:start position:0% +this a cook plot cook because I saw this + + + align:start position:0% +this a cook plot cook because I saw this +in now in the reading for Nicholas cook + + align:start position:0% +in now in the reading for Nicholas cook + + + align:start position:0% +in now in the reading for Nicholas cook +um article on computational and + + align:start position:0% +um article on computational and + + + align:start position:0% +um article on computational and +comparative + + align:start position:0% +comparative + + + align:start position:0% +comparative +music computational and comparative + + align:start position:0% +music computational and comparative + + + align:start position:0% +music computational and comparative +musicology I first saw this in a book by + + align:start position:0% +musicology I first saw this in a book by + + + align:start position:0% +musicology I first saw this in a book by +em uh somebody named Emily Dolan so I + + align:start position:0% +em uh somebody named Emily Dolan so I + + + align:start position:0% +em uh somebody named Emily Dolan so I +call it a Dolan graph um even though um + + align:start position:0% +call it a Dolan graph um even though um + + + align:start position:0% +call it a Dolan graph um even though um +and it shows you who is singing where at + + align:start position:0% +and it shows you who is singing where at + + + align:start position:0% +and it shows you who is singing where at +what point which parts are performing + + align:start position:0% +what point which parts are performing + + + align:start position:0% +what point which parts are performing +and do you remember this from the cook + + align:start position:0% +and do you remember this from the cook + + + align:start position:0% +and do you remember this from the cook +it's slightly different graph that he + + align:start position:0% +it's slightly different graph that he + + + align:start position:0% +it's slightly different graph that he +had a slightly different shape size but + + align:start position:0% +had a slightly different shape size but + + + align:start position:0% +had a slightly different shape size but +same type of thing what's being uh + + align:start position:0% +same type of thing what's being uh + + + align:start position:0% +same type of thing what's being uh +depicted + + align:start position:0% +depicted + + + align:start position:0% +depicted +here take a guess what's that Dynamic + + align:start position:0% +here take a guess what's that Dynamic + + + align:start position:0% +here take a guess what's that Dynamic +Dynamics yeah so it's a sort of who's + + align:start position:0% +Dynamics yeah so it's a sort of who's + + + align:start position:0% +Dynamics yeah so it's a sort of who's +playing when and what are the Dynamics + + align:start position:0% +playing when and what are the Dynamics + + + align:start position:0% +playing when and what are the Dynamics +and if you zoom in really closely you + + align:start position:0% +and if you zoom in really closely you + + + align:start position:0% +and if you zoom in really closely you +can see that soprano is always singing a + + align:start position:0% +can see that soprano is always singing a + + + align:start position:0% +can see that soprano is always singing a +tiny bit before the other parts but yeah + + align:start position:0% +tiny bit before the other parts but yeah + + + align:start position:0% +tiny bit before the other parts but yeah +so the piece just sort of builds up to + + align:start position:0% +so the piece just sort of builds up to + + + align:start position:0% +so the piece just sort of builds up to +about two3 point then drops off and just + + align:start position:0% +about two3 point then drops off and just + + + align:start position:0% +about two3 point then drops off and just +very quiet everything after after that + + align:start position:0% +very quiet everything after after that + + + align:start position:0% +very quiet everything after after that +um so there's quite often I think for + + align:start position:0% +um so there's quite often I think for + + + align:start position:0% +um so there's quite often I think for +people who can read music notation uh + + align:start position:0% +people who can read music notation uh + + + align:start position:0% +people who can read music notation uh +graphs and plotting visualization isn't + + align:start position:0% +graphs and plotting visualization isn't + + + align:start position:0% +graphs and plotting visualization isn't +too much of a help but for getting a + + align:start position:0% +too much of a help but for getting a + + + align:start position:0% +too much of a help but for getting a +sense of the form of a large piece very + + align:start position:0% +sense of the form of a large piece very + + + align:start position:0% +sense of the form of a large piece very +quickly these um these tools can be very + + align:start position:0% +quickly these um these tools can be very + + + align:start position:0% +quickly these um these tools can be very +very helpful uh we can kind of see what + + align:start position:0% +very helpful uh we can kind of see what + + + align:start position:0% +very helpful uh we can kind of see what +what notes does he use the most well + + align:start position:0% +what notes does he use the most well + + + align:start position:0% +what notes does he use the most well +obviously those that are going to be um + + align:start position:0% +obviously those that are going to be um + + + align:start position:0% +obviously those that are going to be um +that that the sustained notes are going + + align:start position:0% +that that the sustained notes are going + + + align:start position:0% +that that the sustained notes are going +to come quite a bit but we can + + align:start position:0% +to come quite a bit but we can + + + align:start position:0% +to come quite a bit but we can +see that of the various pitch classes + + align:start position:0% +see that of the various pitch classes + + + align:start position:0% +see that of the various pitch classes +basically there's a reason why it was + + align:start position:0% +basically there's a reason why it was + + + align:start position:0% +basically there's a reason why it was +coming out as a + + align:start position:0% +coming out as a + + + align:start position:0% +coming out as a +major as our + + align:start position:0% +major as our + + + align:start position:0% +major as our +analysis as a definitely winning e + + align:start position:0% + + + + align:start position:0% + +c but almost I guess every surprisingly + + align:start position:0% +c but almost I guess every surprisingly + + + align:start position:0% +c but almost I guess every surprisingly +for a piece that sounds so um consonant + + align:start position:0% +for a piece that sounds so um consonant + + + align:start position:0% +for a piece that sounds so um consonant +in many ways every pitch class is + + align:start position:0% +in many ways every pitch class is + + + align:start position:0% +in many ways every pitch class is +represented at least once there + + align:start position:0% +represented at least once there + + + align:start position:0% +represented at least once there +um let me see which I have a whole bunch + + align:start position:0% +um let me see which I have a whole bunch + + + align:start position:0% +um let me see which I have a whole bunch +of ones that are maybe a little bit less + + align:start position:0% +of ones that are maybe a little bit less + + + align:start position:0% +of ones that are maybe a little bit less +interesting but um we can look at the um + + align:start position:0% +interesting but um we can look at the um + + + align:start position:0% +interesting but um we can look at the um +certain pitches use different uh quarter + + align:start position:0% +certain pitches use different uh quarter + + + align:start position:0% +certain pitches use different uh quarter +different notes more so we can plot a + + align:start position:0% +different notes more so we can plot a + + + align:start position:0% +different notes more so we can plot a +scatter plot and then what we haven't + + align:start position:0% +scatter plot and then what we haven't + + + align:start position:0% +scatter plot and then what we haven't +seen yet is the second and third element + + align:start position:0% +seen yet is the second and third element + + + align:start position:0% +seen yet is the second and third element +uh here um is quarter + + align:start position:0% +uh here um is quarter + + + align:start position:0% +uh here um is quarter +length versus + + align:start position:0% + + + + align:start position:0% + +pitch I think there's other things you + + align:start position:0% +pitch I think there's other things you + + + align:start position:0% +pitch I think there's other things you +can do you can plot around with octave + + align:start position:0% +can do you can plot around with octave + + + align:start position:0% +can do you can plot around with octave +and stuff so these are plot gives you a + + align:start position:0% +and stuff so these are plot gives you a + + + align:start position:0% +and stuff so these are plot gives you a +ready made take in a score and get get + + align:start position:0% +ready made take in a score and get get + + + align:start position:0% +ready made take in a score and get get +some kind of analysis there's two + + align:start position:0% +some kind of analysis there's two + + + align:start position:0% +some kind of analysis there's two +slightly lower level things if you want + + align:start position:0% +slightly lower level things if you want + + + align:start position:0% +slightly lower level things if you want +to if you're thinking of doing + + align:start position:0% +to if you're thinking of doing + + + align:start position:0% +to if you're thinking of doing +visualization in there one call it the + + align:start position:0% +visualization in there one call it the + + + align:start position:0% +visualization in there one call it the +graph which is underlying the plot which + + align:start position:0% +graph which is underlying the plot which + + + align:start position:0% +graph which is underlying the plot which +is the um what you're trying to do and + + align:start position:0% +is the um what you're trying to do and + + + align:start position:0% +is the um what you're trying to do and +what data you want to extract so it's + + align:start position:0% +what data you want to extract so it's + + + align:start position:0% +what data you want to extract so it's +sort of a feature extraction again and + + align:start position:0% +sort of a feature extraction again and + + + align:start position:0% +sort of a feature extraction again and +what do you want to put on each axis so + + align:start position:0% +what do you want to put on each axis so + + + align:start position:0% +what do you want to put on each axis so +there's axes that are defined that you + + align:start position:0% +there's axes that are defined that you + + + align:start position:0% +there's axes that are defined that you +can I don't know we can do let's plot um + + align:start position:0% +can I don't know we can do let's plot um + + + align:start position:0% +can I don't know we can do let's plot um +Pitch against + + align:start position:0% +Pitch against + + + align:start position:0% +Pitch against +Dynamic you know what I yeah + + align:start position:0% +Dynamic you know what I yeah + + + align:start position:0% +Dynamic you know what I yeah +Dynamics does that + + align:start position:0% + + + + align:start position:0% + +work you know what who puts pitch on the + + align:start position:0% +work you know what who puts pitch on the + + + align:start position:0% +work you know what who puts pitch on the +xaxis we'll put Pitch on the Y AIS + + align:start position:0% +xaxis we'll put Pitch on the Y AIS + + + align:start position:0% +xaxis we'll put Pitch on the Y AIS +versus Dynamics swap that + + align:start position:0% +versus Dynamics swap that + + + align:start position:0% +versus Dynamics swap that +around that's why it's having so + + align:start position:0% + + + + align:start position:0% + +trouble so you can see that the oops + + align:start position:0% + + + + align:start position:0% + +that the lowest notes in the pieces only + + align:start position:0% +that the lowest notes in the pieces only + + + align:start position:0% +that the lowest notes in the pieces only +appear on um on the quietest things and + + align:start position:0% +appear on um on the quietest things and + + + align:start position:0% +appear on um on the quietest things and +kind of also look at this terrorist um + + align:start position:0% +kind of also look at this terrorist um + + + align:start position:0% +kind of also look at this terrorist um +initial motion of the piece as the notes + + align:start position:0% +initial motion of the piece as the notes + + + align:start position:0% +initial motion of the piece as the notes +were going up and um and both going up + + align:start position:0% +were going up and um and both going up + + + align:start position:0% +were going up and um and both going up +in pitch and getting higher in volume + + align:start position:0% +in pitch and getting higher in volume + + + align:start position:0% +in pitch and getting higher in volume +and then the very highest um volumes are + + align:start position:0% +and then the very highest um volumes are + + + align:start position:0% +and then the very highest um volumes are +scattered all all throughout but every + + align:start position:0% +scattered all all throughout but every + + + align:start position:0% +scattered all all throughout but every +everything down here shifted up a little + + align:start position:0% +everything down here shifted up a little + + + align:start position:0% +everything down here shifted up a little +bit um just as we + + align:start position:0% +bit um just as we + + + align:start position:0% +bit um just as we +saw think the best thing to do would be + + align:start position:0% +saw think the best thing to do would be + + + align:start position:0% +saw think the best thing to do would be +now that we've thought about the piece + + align:start position:0% +now that we've thought about the piece + + + align:start position:0% +now that we've thought about the piece +thought about its structure listen to it + + align:start position:0% +thought about its structure listen to it + + + align:start position:0% +thought about its structure listen to it +one more time um maybe with the we'll + + align:start position:0% +one more time um maybe with the we'll + + + align:start position:0% +one more time um maybe with the we'll +listen to it with the um piano roll and + + align:start position:0% +listen to it with the um piano roll and + + + align:start position:0% +listen to it with the um piano roll and +see if + + align:start position:0% +see if + + + align:start position:0% +see if +um see if we + + align:start position:0% +um see if we + + + align:start position:0% +um see if we +can oops not that one the the big one + + align:start position:0% +can oops not that one the the big one + + + align:start position:0% +can oops not that one the the big one +and see if we can hear the various parts + + align:start position:0% +and see if we can hear the various parts + + + align:start position:0% +and see if we can hear the various parts +of the piece just as well as we could on + + align:start position:0% +of the piece just as well as we could on + + + align:start position:0% +of the piece just as well as we could on +um with the + + align:start position:0% +um with the + + + align:start position:0% +um with the +score words are harder to tell there's + + align:start position:0% +score words are harder to tell there's + + + align:start position:0% +score words are harder to tell there's +no plot for + + align:start position:0% + + + + align:start position:0% + +that you're mostly color blind Professor + + align:start position:0% +that you're mostly color blind Professor + + + align:start position:0% +that you're mostly color blind Professor +just realized that I used a version of + + align:start position:0% +just realized that I used a version of + + + align:start position:0% +just realized that I used a version of +the plot that does colors not based on + + align:start position:0% +the plot that does colors not based on + + + align:start position:0% +the plot that does colors not based on +the part but just um as a way of being + + align:start position:0% +the part but just um as a way of being + + + align:start position:0% +the part but just um as a way of being +able to see which pitches are which so I + + align:start position:0% +able to see which pitches are which so I + + + align:start position:0% +able to see which pitches are which so I +apologize I made a mistake and said you + + align:start position:0% +apologize I made a mistake and said you + + + align:start position:0% +apologize I made a mistake and said you +could can tell the lines by color but uh + + align:start position:0% +could can tell the lines by color but uh + + + align:start position:0% +could can tell the lines by color but uh +I have to strain to see color so so + + align:start position:0% +I have to strain to see color so so + + + align:start position:0% +I have to strain to see color so so +sorry about U about that but I did just + + align:start position:0% +sorry about U about that but I did just + + + align:start position:0% +sorry about U about that but I did just +while listening to it make one + + align:start position:0% +while listening to it make one + + + align:start position:0% +while listening to it make one +observation this interesting line that + + align:start position:0% +observation this interesting line that + + + align:start position:0% +observation this interesting line that +the E is the very first thing that you + + align:start position:0% +the E is the very first thing that you + + + align:start position:0% +the E is the very first thing that you +hear and it just after a little absence + + align:start position:0% +hear and it just after a little absence + + + align:start position:0% +hear and it just after a little absence +comes back and it's one of the few lines + + align:start position:0% +comes back and it's one of the few lines + + + align:start position:0% +comes back and it's one of the few lines +that's so preminent prominent throughout + + align:start position:0% +that's so preminent prominent throughout + + + align:start position:0% +that's so preminent prominent throughout +there so maybe maybe e is the true sort + + align:start position:0% +there so maybe maybe e is the true sort + + + align:start position:0% +there so maybe maybe e is the true sort +of root point of this piece + + align:start position:0% +of root point of this piece + + + align:start position:0% +of root point of this piece +well thanks everybody um for going + + align:start position:0% +well thanks everybody um for going + + + align:start position:0% +well thanks everybody um for going +through grab bag if you I have more + + align:start position:0% +through grab bag if you I have more + + + align:start position:0% +through grab bag if you I have more +topics that are interest to me but + + align:start position:0% +topics that are interest to me but + + + align:start position:0% +topics that are interest to me but +anything that's interest to you let me + + align:start position:0% +anything that's interest to you let me + + + align:start position:0% +anything that's interest to you let me +know \ No newline at end of file diff --git a/LixwAXsN8vg.txt b/LixwAXsN8vg.txt new file mode 100644 index 0000000000000000000000000000000000000000..2f1239909f116647747e30ae7be869602e67130d --- /dev/null +++ b/LixwAXsN8vg.txt @@ -0,0 +1,1963 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencare at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu in this demonstration we're + + align:start position:0% +ocw.mit.edu in this demonstration we're + + + align:start position:0% +ocw.mit.edu in this demonstration we're +going to show the effect of the light + + align:start position:0% +going to show the effect of the light + + + align:start position:0% +going to show the effect of the light +source on Fringe contrast in a two beam + + align:start position:0% +source on Fringe contrast in a two beam + + + align:start position:0% +source on Fringe contrast in a two beam +interferometer but in particular we want + + align:start position:0% +interferometer but in particular we want + + + align:start position:0% +interferometer but in particular we want +to look at the effect of the spectrum of + + align:start position:0% +to look at the effect of the spectrum of + + + align:start position:0% +to look at the effect of the spectrum of +the light source on Fringe contrast the + + align:start position:0% +the light source on Fringe contrast the + + + align:start position:0% +the light source on Fringe contrast the +setup is here we have a special laser + + align:start position:0% +setup is here we have a special laser + + + align:start position:0% +setup is here we have a special laser +for this uh for this demonstration and + + align:start position:0% +for this uh for this demonstration and + + + align:start position:0% +for this uh for this demonstration and +I'll tell you more about it later the + + align:start position:0% +I'll tell you more about it later the + + + align:start position:0% +I'll tell you more about it later the +light from the + + align:start position:0% +light from the + + + align:start position:0% +light from the +laser is reflected by the mirror here + + align:start position:0% +laser is reflected by the mirror here + + + align:start position:0% +laser is reflected by the mirror here +then we have a + + align:start position:0% +then we have a + + + align:start position:0% +then we have a +polarizer here and then light is + + align:start position:0% +polarizer here and then light is + + + align:start position:0% +polarizer here and then light is +reflected by mirror here this is a beam + + align:start position:0% +reflected by mirror here this is a beam + + + align:start position:0% +reflected by mirror here this is a beam +spitter I explain later and then the + + align:start position:0% +spitter I explain later and then the + + + align:start position:0% +spitter I explain later and then the +light here enters the the Michaelson + + align:start position:0% +light here enters the the Michaelson + + + align:start position:0% +light here enters the the Michaelson +interferometer here's one arm of the + + align:start position:0% +interferometer here's one arm of the + + + align:start position:0% +interferometer here's one arm of the +interferometer and here is the other arm + + align:start position:0% +interferometer and here is the other arm + + + align:start position:0% +interferometer and here is the other arm +of the + + align:start position:0% +of the + + + align:start position:0% +of the +interferometer the beams leaving the + + align:start position:0% +interferometer the beams leaving the + + + align:start position:0% +interferometer the beams leaving the +interferometer are here and then they're + + align:start position:0% +interferometer are here and then they're + + + align:start position:0% +interferometer are here and then they're +reflected by this mirror into this lens + + align:start position:0% +reflected by this mirror into this lens + + + align:start position:0% +reflected by this mirror into this lens +and onto onto the screen now the screen + + align:start position:0% +and onto onto the screen now the screen + + + align:start position:0% +and onto onto the screen now the screen +is uh a little bit dim so let's look at + + align:start position:0% +is uh a little bit dim so let's look at + + + align:start position:0% +is uh a little bit dim so let's look at +an enhanced + + align:start position:0% +an enhanced + + + align:start position:0% +an enhanced +image in the insert as you can see you + + align:start position:0% +image in the insert as you can see you + + + align:start position:0% +image in the insert as you can see you +can see the fringes from the + + align:start position:0% +can see the fringes from the + + + align:start position:0% +can see the fringes from the +interferometer but just to convince you + + align:start position:0% +interferometer but just to convince you + + + align:start position:0% +interferometer but just to convince you +that this is coming from this + + align:start position:0% +that this is coming from this + + + align:start position:0% +that this is coming from this +interferometer I'm going to adjust the + + align:start position:0% +interferometer I'm going to adjust the + + + align:start position:0% +interferometer I'm going to adjust the +alignment in one arm to show you that + + align:start position:0% +alignment in one arm to show you that + + + align:start position:0% +alignment in one arm to show you that +indeed this is associated with with the + + align:start position:0% +indeed this is associated with with the + + + align:start position:0% +indeed this is associated with with the +interferometer here all right now let's + + align:start position:0% +interferometer here all right now let's + + + align:start position:0% +interferometer here all right now let's +look at the light source that we're + + align:start position:0% +look at the light source that we're + + + align:start position:0% +look at the light source that we're +going to + + align:start position:0% +going to + + + align:start position:0% +going to +study this laser here is sort of special + + align:start position:0% +study this laser here is sort of special + + + align:start position:0% +study this laser here is sort of special +it operates in two + + align:start position:0% +it operates in two + + + align:start position:0% +it operates in two +frequencies sometimes three frequencies + + align:start position:0% +frequencies sometimes three frequencies + + + align:start position:0% +frequencies sometimes three frequencies +but the interesting thing about these + + align:start position:0% +but the interesting thing about these + + + align:start position:0% +but the interesting thing about these +frequencies is that they have different + + align:start position:0% +frequencies is that they have different + + + align:start position:0% +frequencies is that they have different +polarizations at least adjacent + + align:start position:0% +polarizations at least adjacent + + + align:start position:0% +polarizations at least adjacent +frequencies have orthogonal + + align:start position:0% +frequencies have orthogonal + + + align:start position:0% +frequencies have orthogonal +polarizations so using a polarizer over + + align:start position:0% +polarizations so using a polarizer over + + + align:start position:0% +polarizations so using a polarizer over +here I can + + align:start position:0% +here I can + + + align:start position:0% +here I can +select either one frequency or two + + align:start position:0% +select either one frequency or two + + + align:start position:0% +select either one frequency or two +frequencies in order to check that + + align:start position:0% +frequencies in order to check that + + + align:start position:0% +frequencies in order to check that +indeed I've selected one frequency or + + align:start position:0% +indeed I've selected one frequency or + + + align:start position:0% +indeed I've selected one frequency or +two frequencies I'm going to sample the + + align:start position:0% +two frequencies I'm going to sample the + + + align:start position:0% +two frequencies I'm going to sample the +the laser beam using this beam splitter + + align:start position:0% +the laser beam using this beam splitter + + + align:start position:0% +the laser beam using this beam splitter +here now I don't know if you can see the + + align:start position:0% +here now I don't know if you can see the + + + align:start position:0% +here now I don't know if you can see the +beam on the on the card is pretty + + align:start position:0% +beam on the on the card is pretty + + + align:start position:0% +beam on the on the card is pretty +weak but this beam is + + align:start position:0% +weak but this beam is + + + align:start position:0% +weak but this beam is +being sent into this Optical Spectrum + + align:start position:0% +being sent into this Optical Spectrum + + + align:start position:0% +being sent into this Optical Spectrum +analyzer which is a scanning fabric Pro + + align:start position:0% +analyzer which is a scanning fabric Pro + + + align:start position:0% +analyzer which is a scanning fabric Pro +interferometer the output of the optical + + align:start position:0% +interferometer the output of the optical + + + align:start position:0% +interferometer the output of the optical +Spectrum analyzer is displayed on the + + align:start position:0% +Spectrum analyzer is displayed on the + + + align:start position:0% +Spectrum analyzer is displayed on the +oscilloscope screen over + + align:start position:0% +oscilloscope screen over + + + align:start position:0% +oscilloscope screen over +here as you can see it is single + + align:start position:0% +here as you can see it is single + + + align:start position:0% +here as you can see it is single +frequency the output of the laser + + align:start position:0% +frequency the output of the laser + + + align:start position:0% +frequency the output of the laser +entering the interferometer is single + + align:start position:0% +entering the interferometer is single + + + align:start position:0% +entering the interferometer is single +frequency now as I change the + + align:start position:0% +frequency now as I change the + + + align:start position:0% +frequency now as I change the +transmission axis of the polarizer here + + align:start position:0% +transmission axis of the polarizer here + + + align:start position:0% +transmission axis of the polarizer here +I can select the other frequency + + align:start position:0% +I can select the other frequency + + + align:start position:0% +I can select the other frequency +or in this case the other + + align:start position:0% +or in this case the other + + + align:start position:0% +or in this case the other +frequencies as shown as shown over + + align:start position:0% +frequencies as shown as shown over + + + align:start position:0% +frequencies as shown as shown over +here sometimes the laser oscillates two + + align:start position:0% +here sometimes the laser oscillates two + + + align:start position:0% +here sometimes the laser oscillates two +frequencies sometimes in three and at + + align:start position:0% +frequencies sometimes in three and at + + + align:start position:0% +frequencies sometimes in three and at +the moment it's oscillating in three if + + align:start position:0% +the moment it's oscillating in three if + + + align:start position:0% +the moment it's oscillating in three if +I go + + align:start position:0% +I go + + + align:start position:0% +I go +back I can I can select one + + align:start position:0% +back I can I can select one + + + align:start position:0% +back I can I can select one +frequency + + align:start position:0% +frequency + + + align:start position:0% +frequency +and + + align:start position:0% +and + + + align:start position:0% +and +halfway rotation of the polarizer 4 5° + + align:start position:0% +halfway rotation of the polarizer 4 5° + + + align:start position:0% +halfway rotation of the polarizer 4 5° +rotation the polarizer I can select more + + align:start position:0% +rotation the polarizer I can select more + + + align:start position:0% +rotation the polarizer I can select more +than one frequency and if I go + + align:start position:0% +than one frequency and if I go + + + align:start position:0% +than one frequency and if I go +completely 90° then I can select uh two + + align:start position:0% +completely 90° then I can select uh two + + + align:start position:0% +completely 90° then I can select uh two +frequencies now let me + + align:start position:0% +frequencies now let me + + + align:start position:0% +frequencies now let me +set my polarizer so that I only have + + align:start position:0% +set my polarizer so that I only have + + + align:start position:0% +set my polarizer so that I only have +only one + + align:start position:0% +only one + + + align:start position:0% +only one +frequency so let's go to the + + align:start position:0% +frequency so let's go to the + + + align:start position:0% +frequency so let's go to the +interferometer and look at the fringes + + align:start position:0% +interferometer and look at the fringes + + + align:start position:0% +interferometer and look at the fringes +as a function of path length difference + + align:start position:0% +as a function of path length difference + + + align:start position:0% +as a function of path length difference +here we are here's the interr ometer + + align:start position:0% +here we are here's the interr ometer + + + align:start position:0% +here we are here's the interr ometer +again and here are the fringes and you + + align:start position:0% +again and here are the fringes and you + + + align:start position:0% +again and here are the fringes and you +can see the contrast is pretty good the + + align:start position:0% +can see the contrast is pretty good the + + + align:start position:0% +can see the contrast is pretty good the +zero over here indicates that this arm + + align:start position:0% +zero over here indicates that this arm + + + align:start position:0% +zero over here indicates that this arm +is equal to to this arm now I'm going to + + align:start position:0% +is equal to to this arm now I'm going to + + + align:start position:0% +is equal to to this arm now I'm going to +vary the length of the arm over + + align:start position:0% +vary the length of the arm over + + + align:start position:0% +vary the length of the arm over +here and you can see that The Fringe + + align:start position:0% +here and you can see that The Fringe + + + align:start position:0% +here and you can see that The Fringe +contrast is pretty + + align:start position:0% +contrast is pretty + + + align:start position:0% +contrast is pretty +good now here I am 11 cm path length + + align:start position:0% +good now here I am 11 cm path length + + + align:start position:0% +good now here I am 11 cm path length +difference fringes are pretty good + + align:start position:0% +difference fringes are pretty good + + + align:start position:0% +difference fringes are pretty good +around + + align:start position:0% +around + + + align:start position:0% +around +20 cm pretty good remember the laser is + + align:start position:0% +20 cm pretty good remember the laser is + + + align:start position:0% +20 cm pretty good remember the laser is +single + + align:start position:0% +single + + + align:start position:0% +single +frequency at present it's about 30 cm + + align:start position:0% +frequency at present it's about 30 cm + + + align:start position:0% +frequency at present it's about 30 cm +difference Fring is pretty good and and + + align:start position:0% +difference Fring is pretty good and and + + + align:start position:0% +difference Fring is pretty good and and +so + + align:start position:0% +so + + + align:start position:0% +so +on The Fringe contrast doesn't doesn't + + align:start position:0% +on The Fringe contrast doesn't doesn't + + + align:start position:0% +on The Fringe contrast doesn't doesn't +deteriorate so let me go + + align:start position:0% +deteriorate so let me go + + + align:start position:0% +deteriorate so let me go +back to the equal + + align:start position:0% +back to the equal + + + align:start position:0% +back to the equal +path condition + + align:start position:0% +path condition + + + align:start position:0% +path condition +so let's look at the scope as I bring in + + align:start position:0% +so let's look at the scope as I bring in + + + align:start position:0% +so let's look at the scope as I bring in +more than one frequency from from the + + align:start position:0% +more than one frequency from from the + + + align:start position:0% +more than one frequency from from the +laser as we can see on the scope we have + + align:start position:0% +laser as we can see on the scope we have + + + align:start position:0% +laser as we can see on the scope we have +one frequency now as I rotate the + + align:start position:0% +one frequency now as I rotate the + + + align:start position:0% +one frequency now as I rotate the +polarizer I can now bring in the other + + align:start position:0% +polarizer I can now bring in the other + + + align:start position:0% +polarizer I can now bring in the other +frequencies so in this position + + align:start position:0% +frequencies so in this position + + + align:start position:0% +frequencies so in this position +essentially we have two dominant + + align:start position:0% +essentially we have two dominant + + + align:start position:0% +essentially we have two dominant +frequency plus a another one now let's + + align:start position:0% +frequency plus a another one now let's + + + align:start position:0% +frequency plus a another one now let's +go back to the interferometer and look + + align:start position:0% +go back to the interferometer and look + + + align:start position:0% +go back to the interferometer and look +at The Fringe contrast as a function + + align:start position:0% +at The Fringe contrast as a function + + + align:start position:0% +at The Fringe contrast as a function +of path length difference with the laser + + align:start position:0% +of path length difference with the laser + + + align:start position:0% +of path length difference with the laser +at several frequencies so here at equal + + align:start position:0% +at several frequencies so here at equal + + + align:start position:0% +at several frequencies so here at equal +path length I can see the fringes are + + align:start position:0% +path length I can see the fringes are + + + align:start position:0% +path length I can see the fringes are +pretty good and then as I go away from + + align:start position:0% +pretty good and then as I go away from + + + align:start position:0% +pretty good and then as I go away from +equal path + + align:start position:0% +equal path + + + align:start position:0% +equal path +length The Fringe contrast begins to + + align:start position:0% +length The Fringe contrast begins to + + + align:start position:0% +length The Fringe contrast begins to +deteriorate and you can see around here + + align:start position:0% +deteriorate and you can see around here + + + align:start position:0% +deteriorate and you can see around here +when I around about 8 or 9 cmers away + + align:start position:0% +when I around about 8 or 9 cmers away + + + align:start position:0% +when I around about 8 or 9 cmers away +The Fringe contrast is pretty bad + + align:start position:0% + + + + align:start position:0% + +here is still + + align:start position:0% +here is still + + + align:start position:0% +here is still +bad bad + + align:start position:0% +bad bad + + + align:start position:0% +bad bad +still again still pretty bad now it + + align:start position:0% +still again still pretty bad now it + + + align:start position:0% +still again still pretty bad now it +picks + + align:start position:0% +picks + + + align:start position:0% +picks +up now Fringe contrast is getting better + + align:start position:0% +up now Fringe contrast is getting better + + + align:start position:0% +up now Fringe contrast is getting better +now at a + + align:start position:0% +now at a + + + align:start position:0% +now at a +position 22 cm that means a path length + + align:start position:0% +position 22 cm that means a path length + + + align:start position:0% +position 22 cm that means a path length +difference of 22 + + align:start position:0% +difference of 22 + + + align:start position:0% +difference of 22 +cm I have as good Fringe contrast as + + align:start position:0% +cm I have as good Fringe contrast as + + + align:start position:0% +cm I have as good Fringe contrast as +before then if I go further + + align:start position:0% + + + + align:start position:0% + +Fringe contrast again + + align:start position:0% +Fringe contrast again + + + align:start position:0% +Fringe contrast again +deteriorates here we see it's pretty + + align:start position:0% +deteriorates here we see it's pretty + + + align:start position:0% +deteriorates here we see it's pretty +pretty much gone over here I'm around 30 + + align:start position:0% +pretty much gone over here I'm around 30 + + + align:start position:0% +pretty much gone over here I'm around 30 +cm path length difference then as I go + + align:start position:0% +cm path length difference then as I go + + + align:start position:0% +cm path length difference then as I go +all the way + + align:start position:0% +all the way + + + align:start position:0% +all the way +to + + align:start position:0% +to + + + align:start position:0% +to +44 CM path difference you can see The + + align:start position:0% +44 CM path difference you can see The + + + align:start position:0% +44 CM path difference you can see The +Fringe contrast is is back again let's + + align:start position:0% +Fringe contrast is is back again let's + + + align:start position:0% +Fringe contrast is is back again let's +go even + + align:start position:0% +go even + + + align:start position:0% +go even +further fridge contrast + + align:start position:0% +further fridge contrast + + + align:start position:0% +further fridge contrast +deteriorates and I think finally if I go + + align:start position:0% +deteriorates and I think finally if I go + + + align:start position:0% +deteriorates and I think finally if I go +to to 66 + + align:start position:0% +to to 66 + + + align:start position:0% +to to 66 +cm Fringe contess comes back but I need + + align:start position:0% +cm Fringe contess comes back but I need + + + align:start position:0% +cm Fringe contess comes back but I need +some + + align:start position:0% +some + + + align:start position:0% +some +Readjustment of the of the beams you can + + align:start position:0% +Readjustment of the of the beams you can + + + align:start position:0% +Readjustment of the of the beams you can +see that though that The Fringe contrast + + align:start position:0% +see that though that The Fringe contrast + + + align:start position:0% +see that though that The Fringe contrast +has been restored and so on so every 22 + + align:start position:0% +has been restored and so on so every 22 + + + align:start position:0% +has been restored and so on so every 22 +cm The Fringe contrast comes back let me + + align:start position:0% +cm The Fringe contrast comes back let me + + + align:start position:0% +cm The Fringe contrast comes back let me +go back again and check around uh let's + + align:start position:0% +go back again and check around uh let's + + + align:start position:0% +go back again and check around uh let's +say 44 CM again Fring contrast is bad + + align:start position:0% +say 44 CM again Fring contrast is bad + + + align:start position:0% +say 44 CM again Fring contrast is bad +around 30 CMS or so I mean I'm sorry at + + align:start position:0% +around 30 CMS or so I mean I'm sorry at + + + align:start position:0% +around 30 CMS or so I mean I'm sorry at +at at 44 CM Fringe contrast pretty good + + align:start position:0% +at at 44 CM Fringe contrast pretty good + + + align:start position:0% +at at 44 CM Fringe contrast pretty good +around 30 cm is pretty bad around 22 cm + + align:start position:0% +around 30 cm is pretty bad around 22 cm + + + align:start position:0% +around 30 cm is pretty bad around 22 cm +is pretty + + align:start position:0% +is pretty + + + align:start position:0% +is pretty +good and around 10 or so CM uh it's + + align:start position:0% +good and around 10 or so CM uh it's + + + align:start position:0% +good and around 10 or so CM uh it's +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +bad + + align:start position:0% +bad + + + align:start position:0% +bad +now clearly The Fringe contrast seems to + + align:start position:0% +now clearly The Fringe contrast seems to + + + align:start position:0% +now clearly The Fringe contrast seems to +be dependent on the spectrum of the + + align:start position:0% +be dependent on the spectrum of the + + + align:start position:0% +be dependent on the spectrum of the +laser just to make sure uh let's stay at + + align:start position:0% +laser just to make sure uh let's stay at + + + align:start position:0% +laser just to make sure uh let's stay at +a position where The Fringe contrast is + + align:start position:0% +a position where The Fringe contrast is + + + align:start position:0% +a position where The Fringe contrast is +pretty bad and let's change the the + + align:start position:0% +pretty bad and let's change the the + + + align:start position:0% +pretty bad and let's change the the +spectrum of the laser going into the + + align:start position:0% +spectrum of the laser going into the + + + align:start position:0% +spectrum of the laser going into the +interferometer let me first adjust the + + align:start position:0% +interferometer let me first adjust the + + + align:start position:0% +interferometer let me first adjust the +position of the Peaks on the + + align:start position:0% +position of the Peaks on the + + + align:start position:0% +position of the Peaks on the +scope and now what I'd like to do is + + align:start position:0% +scope and now what I'd like to do is + + + align:start position:0% +scope and now what I'd like to do is +while we're watching the + + align:start position:0% +while we're watching the + + + align:start position:0% +while we're watching the +contrast I would like now to go back to + + align:start position:0% +contrast I would like now to go back to + + + align:start position:0% +contrast I would like now to go back to +the single frequency condition as you + + align:start position:0% +the single frequency condition as you + + + align:start position:0% +the single frequency condition as you +can see the contrast is is pretty good + + align:start position:0% +can see the contrast is is pretty good + + + align:start position:0% +can see the contrast is is pretty good +and as I I go to the multiple + + align:start position:0% +and as I I go to the multiple + + + align:start position:0% +and as I I go to the multiple +multifrequency position the contrast + + align:start position:0% + + + + align:start position:0% + +disappears so clearly when the laser + + align:start position:0% +disappears so clearly when the laser + + + align:start position:0% +disappears so clearly when the laser +entering the + + align:start position:0% +entering the + + + align:start position:0% +entering the +interferometer has only one frequency + + align:start position:0% +interferometer has only one frequency + + + align:start position:0% +interferometer has only one frequency +contrast is then it's pretty good when + + align:start position:0% +contrast is then it's pretty good when + + + align:start position:0% +contrast is then it's pretty good when +it has several + + align:start position:0% +it has several + + + align:start position:0% +it has several +frequencies at this path length + + align:start position:0% +frequencies at this path length + + + align:start position:0% +frequencies at this path length +difference there's no contrast at + + align:start position:0% +difference there's no contrast at + + + align:start position:0% +difference there's no contrast at +all now let me go to the equal arm + + align:start position:0% +all now let me go to the equal arm + + + align:start position:0% +all now let me go to the equal arm +position let's again look at The Fringe + + align:start position:0% +position let's again look at The Fringe + + + align:start position:0% +position let's again look at The Fringe +contrast as a function of the spectrum + + align:start position:0% +contrast as a function of the spectrum + + + align:start position:0% +contrast as a function of the spectrum +of the laser so if we can look at the + + align:start position:0% +of the laser so if we can look at the + + + align:start position:0% +of the laser so if we can look at the +scope and and + + align:start position:0% +scope and and + + + align:start position:0% +scope and and +the we can look at the scope + + align:start position:0% + + + + align:start position:0% + +and now we have single + + align:start position:0% +and now we have single + + + align:start position:0% +and now we have single +frequency operation The Fringe contast + + align:start position:0% +frequency operation The Fringe contast + + + align:start position:0% +frequency operation The Fringe contast +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +good if you have multiple frequencies + + align:start position:0% + + + + align:start position:0% + +contrast is also pretty good so there's + + align:start position:0% +contrast is also pretty good so there's + + + align:start position:0% +contrast is also pretty good so there's +no change in the in The Fringe contrast + + align:start position:0% +no change in the in The Fringe contrast + + + align:start position:0% +no change in the in The Fringe contrast +with frequency Let Me Now go to 22 cm + + align:start position:0% +with frequency Let Me Now go to 22 cm + + + align:start position:0% +with frequency Let Me Now go to 22 cm +path length + + align:start position:0% +path length + + + align:start position:0% +path length +difference and now again we look at The + + align:start position:0% +difference and now again we look at The + + + align:start position:0% +difference and now again we look at The +Fringe + + align:start position:0% + + + + align:start position:0% + +contrast and its dependence on the + + align:start position:0% +contrast and its dependence on the + + + align:start position:0% +contrast and its dependence on the +spectrum of the light you can see here + + align:start position:0% +spectrum of the light you can see here + + + align:start position:0% +spectrum of the light you can see here +that when let me readjust the fringes a + + align:start position:0% +that when let me readjust the fringes a + + + align:start position:0% +that when let me readjust the fringes a +little bit that's + + align:start position:0% +little bit that's + + + align:start position:0% +little bit that's +it you can see when the laser is a + + align:start position:0% +it you can see when the laser is a + + + align:start position:0% +it you can see when the laser is a +single frequency Fringe contrast is + + align:start position:0% +single frequency Fringe contrast is + + + align:start position:0% +single frequency Fringe contrast is +pretty + + align:start position:0% + + + + align:start position:0% + +good when it has several frequencies + + align:start position:0% +good when it has several frequencies + + + align:start position:0% +good when it has several frequencies +Fringe contrast is also pretty good but + + align:start position:0% +Fringe contrast is also pretty good but + + + align:start position:0% +Fringe contrast is also pretty good but +when I + + align:start position:0% +when I + + + align:start position:0% +when I +am at a position about 10 cm or so away + + align:start position:0% +am at a position about 10 cm or so away + + + align:start position:0% +am at a position about 10 cm or so away +now if we can look at the + + align:start position:0% +now if we can look at the + + + align:start position:0% +now if we can look at the +fringes let + + align:start position:0% + + + + align:start position:0% + +me see the fringes are Fringe contast is + + align:start position:0% +me see the fringes are Fringe contast is + + + align:start position:0% +me see the fringes are Fringe contast is +pretty bad and then again when I go to + + align:start position:0% +pretty bad and then again when I go to + + + align:start position:0% +pretty bad and then again when I go to +single + + align:start position:0% +single + + + align:start position:0% +single +frequency you can see that the fridge + + align:start position:0% +frequency you can see that the fridge + + + align:start position:0% +frequency you can see that the fridge +contrast is pretty good then multiple + + align:start position:0% +contrast is pretty good then multiple + + + align:start position:0% +contrast is pretty good then multiple +frequency Fringe contrast is is pretty + + align:start position:0% +frequency Fringe contrast is is pretty + + + align:start position:0% +frequency Fringe contrast is is pretty +bad so what we have seen is the + + align:start position:0% +bad so what we have seen is the + + + align:start position:0% +bad so what we have seen is the +influence of the spectrum of the laser + + align:start position:0% +influence of the spectrum of the laser + + + align:start position:0% +influence of the spectrum of the laser +light on The Fringe contrast in a two + + align:start position:0% +light on The Fringe contrast in a two + + + align:start position:0% +light on The Fringe contrast in a two +beam interferometer we saw that when the + + align:start position:0% +beam interferometer we saw that when the + + + align:start position:0% +beam interferometer we saw that when the +laser is operating at single frequency + + align:start position:0% +laser is operating at single frequency + + + align:start position:0% +laser is operating at single frequency +The Fringe contrast is unaffected by + + align:start position:0% +The Fringe contrast is unaffected by + + + align:start position:0% +The Fringe contrast is unaffected by +path length difference when the laser + + align:start position:0% +path length difference when the laser + + + align:start position:0% +path length difference when the laser +was oscillating at several frequencies + + align:start position:0% +was oscillating at several frequencies + + + align:start position:0% +was oscillating at several frequencies +we saw that there were + + align:start position:0% +we saw that there were + + + align:start position:0% +we saw that there were +positions where The Fringe contrast went + + align:start position:0% +positions where The Fringe contrast went + + + align:start position:0% +positions where The Fringe contrast went +to almost + + align:start position:0% +to almost + + + align:start position:0% +to almost +zero but The Fringe Co contrast + + align:start position:0% +zero but The Fringe Co contrast + + + align:start position:0% +zero but The Fringe Co contrast +reappeared every 22 + + align:start position:0% +reappeared every 22 + + + align:start position:0% +reappeared every 22 +cm I'd like you to remember that the + + align:start position:0% +cm I'd like you to remember that the + + + align:start position:0% +cm I'd like you to remember that the +laser cavity here let's look at the + + align:start position:0% +laser cavity here let's look at the + + + align:start position:0% +laser cavity here let's look at the +laser cavity the laser cavity + + align:start position:0% +laser cavity the laser cavity + + + align:start position:0% +laser cavity the laser cavity +is uh 22 cm long so maybe there's a + + align:start position:0% +is uh 22 cm long so maybe there's a + + + align:start position:0% +is uh 22 cm long so maybe there's a +connection between the length of the + + align:start position:0% +connection between the length of the + + + align:start position:0% +connection between the length of the +laser cavity and the positions of good + + align:start position:0% +laser cavity and the positions of good + + + align:start position:0% +laser cavity and the positions of good +Fringe contrast in the + + align:start position:0% +Fringe contrast in the + + + align:start position:0% +Fringe contrast in the +interferometer what I'd like you to + + align:start position:0% +interferometer what I'd like you to + + + align:start position:0% +interferometer what I'd like you to +think about is why does Fringe + + align:start position:0% +think about is why does Fringe + + + align:start position:0% +think about is why does Fringe +contrast deteriorate when the laser is + + align:start position:0% +contrast deteriorate when the laser is + + + align:start position:0% +contrast deteriorate when the laser is +oscillating at several frequencies \ No newline at end of file diff --git a/MNhkoylpyNA.txt b/MNhkoylpyNA.txt new file mode 100644 index 0000000000000000000000000000000000000000..33717d54abcd449d0e484f1e9276f3c0bd368644 --- /dev/null +++ b/MNhkoylpyNA.txt @@ -0,0 +1,1597 @@ +ANNOUNCER: The following content +is provided under a + +Creative Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or to view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +HERBERT GROSS: Hi, our lecture +today is entitled + +differentiation of inverse +functions. + +And it pulls together +two previous + +topics that we've discussed. + +Namely, inverse functions +themselves, and secondly, the + +chain rule that we've +discussed just + +a short time ago. + +And perhaps the best way to +introduce the power of + +differentiation of inverse +functions is to start out with + +such a problem. + +Let's actually try to +differentiate a particular + +function, which at least up +until now, we have not been + +able to differentiate. + +The function happens to be y +equals the cube root of 'x'. + +In other words, 'y' equals +'x to the 1/3'. + +Let's find 'dy dx' if 'y' +equals 'x to the 1/3'. + +Now, the whole idea of inverse +functions is what? + +That it gives us a chance +to paraphrase. + +That we can interchange the role +of the dependent and the + +independent variables. + +And like any other form of +paraphrase, even though two + +things may be synonymous, +psychologically one of the two + +may be easier for us to +visualize than the other. + +In particular, in this +particular case, if 'y' equals + +'x to the 1/3', another way +of writing the same + +thing is to say what? + +'x' equals 'y cubed'. + +And now, given that 'x' equals +'y cubed', in other words, + +with treating 'x' as a function +of 'y', we certainly + +know how to differentiate 'y +cubed' with respect to 'y'. + +Namely, we know that for +a positive exponent to + +differentiate, all we have to do +is bring the exponent down + +and replace it by one less. + +In other words, right away what +we can say is that 'dx + +dy' is '3y squared'. + +Now if we use the result of last +time that we talked about + +when we were discussing the +chain rule, and I'll review + +that result in just +a few moments. + +But for the time being, let's +assume that we have the result + +that 'dx dy' is the reciprocal +of 'dy dx'. + +In other words, if 'dy dx' is +'1 over 'dx dy'', that tells + +us that 'dy dx' is '1 +over 3y squared'. + +And I guess to write that in a +more convenient form, that's + +'1/3 y to the minus +2' if you're used + +to exponential notation. + +If we now recall from above that +'y' is equal to 'x to the + +1/3', this can now be written +as ''1/3 x to the 1/3' + +to the minus 2'. + +And we now arrive at an answer +'dy dx' is '1/3 x + +to the minus 2/3'. + +By the way, let me point out +there certainly was nothing + +wrong with leaving our answer +in this particular form. + +It's just conventional that +wherever possible, if the + +original problem was given as +a function of 'x', we would + +like our answer to also +be a function of 'x'. + +I mean, here for example, we +could have said that the + +answer is '1/3 y to the +minus 2', where 'y' + +equals 'x to the 1/3'. + +All we've done here is to fill +this thing in explicitly. + +By the way, there may have +been a tendency-- + +and here's an example of +circular reasoning. + +There may have been a tendency +to say, didn't we already + +learn that to differentiate a +power, we just bring the power + +down and replace +it by one less? + +In other words, if we did that +bringing down the 1/3 would + +give us a factor of +1/3 in front. + +Replacing 1/3 by one less, +1/3 minus 1 is minus 2/3. + +We would then see that 'dy +dx' should be '1/3 x + +to the minus 2/3'. + +Which is exactly what +we got this way. + +The point that we should mention +at this particular + +stage is that the derivative of +'x' to the 'n' being 'nx to + +the 'n - 1'' was proven only +for the case that 'n' is an + +integer, either positive +or negative. + +One uses the binomial theorem +to prove the result for a + +positive integer. + +One uses the quotient rule +to prove the result for a + +negative integer. + +And now, even though I didn't +do this thing in general, I + +think you can see how this +will generalize. + +For fractional exponents, +one uses the + +inverse function idea. + +Namely, we did have to use the +fact that if 'y' is equal to + +'x to the 1/3', 'x' equals +'y cubed' was + +an equivalent equation. + +And we could differentiate +that. + +Now, what is the hang up here, +in so far as how certain are + +we that 'dy dx' and 'dx +dy' are reciprocals? + +You may recall that when we used +the chain rule, we showed + +that if 'y' is a differentiable +function of + +'x', and if 'x' is a +differentiable function of + +'u', then 'y' is a + +differentiable function of 'u'. + +And in particular, 'dy du' is +''dy dx' times 'dx du''. + +And if we now take the +particular case where the + +first variable equals +the third, way 'u' + +equals 'y', we get what? + +'dy dy', which is 1, equals +''dy dx' times 'dx dy''. + +And at first glance, it might +seem that we've proven + +rigorously now the result that +'dx dy' and 'dy dx' are + +reciprocals of each other. + +Product is 1. + +The one logical hang up +that we have right + +now is simply this. + +In the statement of the chain +rule, it did not say that 'y' + +had to be a function of +'x' and 'x' had to be + +a function of 'u'. + +It said 'y' had to be a + +differentiable function of 'x'. + +That was the first variable +had to be a differentiable + +function of the second. + +And the second had to +be a differentiable + +function of the third. + +In other words, coming down to +here, if we know that 'y' is a + +differentiable function of 'x' +and 'y' has an inverse + +function, and if we also knew +that the inverse function was + +differentiable. + +See, in other words, this must +be a differentiable function + +of this and this must be a + +differentiable function of this. + +In other words, the one point +that was missing was is that + +if we knew that if a function +is differentiable, then its + +inverse if it exists, is +also differentiable. + +The chain rule would have given +us a rigorous proof. + +The point that we're missing +though is we do not as yet + +know that the inverse of a +differentiable function is + +also a differentiable +function. + +Now if you recall on our earlier +lecture on inverse + +functions, we pointed out that +there was a rather interesting + +graphical interpretation between +'y' equals 'f of x' + +and 'y' equals 'f +inverse of x'. + +By the way whenever I say, you +may recall, that's just my + +polite way of saying perhaps +you don't, but you'd better + +look it up because we had it. + +So recall that the two curves +are symmetric with respect to + +the line 'y' equals 'x'. + +By the way again, just +a brief aside here. + +Notice that either one of these +functions could have + +been called 'f of x' and the +other one could have been + +called 'f inverse'. + +In other words, just another +piece of brief knowledge here + +that the inverse of the inverse +is the original + +function again. + +In other words, thinking in +terms of our function machine, + +if you interchanged the input +and the output, and then of + +the resulting machine again, +interchange the input and the + +output, you're back to the +original machine again. + +So in this particular diagram, I +certainly could have labeled + +this curve 'y' equals 'f of x' +or 'g of x', then this curve + +here would have been 'y' equals +'g inverse of x'. + +But the important +point is what? + +That 'y' equals 'f of x' and +'y' equals 'f inverse of x' + +are symmetric with respect +to the line 'y equals x'. + +Now you see we have a +particularly simple geometric + +argument as to why an inverse +function should be + +differentiable if the original +function is differentiable. + +Namely, pictorially, what does +it mean to say that a function + +is differentiable? + +It means that when you +plot its graph, + +the graph is smooth. + +In other words, if 'f' is a +differentiable function, the + +curve 'y' equals 'f of x' +will be a smooth curve. + +Now simply ask yourself the +following question. + +If you take a smooth curve and +take its mirror image with + +respect to the line 'y' equals +'x', or for that matter with + +respect to any line, +do you expect the + +curve to become un-smooth? + +You see, in other words, the +mirror image of a smooth curve + +will again, be smooth. + +And that's perhaps the most +intuitive way of picking off + +in your mind why if a function +is differentiable, its inverse + +function will also be +differentiable. + +Of course, as we've seen many +times already in this course, + +we must distinguish between +geometric intuition and + +mathematical analysis. + +That on more occasions than +one, what seemed to be + +happening geometrically was +complicated by something + +unforeseen when we tried to get +the results in terms of + +analytic methods. + +Let me give you an illustration +of this. + +You see, what we're really +saying is, granted that a + +picture can be a good visual +aid, let's suppose we're given + +the curve 'y' equals +'f inverse of x'. + +Well, first of all, what is +that the same as saying? + +It's the same as saying that +'x' equals 'f of y'. + +At any rate, the question +is this. + +We're assuming that 'f' is a +differentiable function. + +What we would like to do is to +prove that 'f inverse' is also + +differentiable. + +Now you see the whole thing +again is that whenever you + +want to prove anything, what +do you mean if you take 'f + +inverse' and differentiate it? + +And by the way, that may look +like a funny notation. + +Think of 'f inverse' as +being one symbol. + +Call it 'g'. + +Call it whatever you want. + +All we're saying is, how would +we, by definition, find the + +derivative of the inverse +function say, + +at 'x' equals 'x1'? + +And the answer is that by +definition, it's just what? + +It's the limit as 'delta +x' approaches 0. + +Same definition as before. + +''f of 'x1 plus 'delta +x' minus 'f of + +x1'' over 'delta x'. + +And in fact, if you want to +write that a little bit more + +explicitly, what is another +way of writing 'delta x'? + +'Delta x', of course, is ''x1 +plus 'delta x' minus x1'. + +Now the idea is-- + +this is 'f inverse'. + +See we want to find the +derivative of 'f inverse'. + +Who cares what the name +of the function is? + +Whatever the name of the +function is, what do you do? + +You compute the function at 'x1 +plus 'delta x', subtract + +off its value at 'x1', and +divide by 'delta x'. + +So by the same definition that +we had the first time we + +defined derivative, this is +the basic definition for + +finding the derivative +of 'f inverse'. + +Now, how do we use the +fact that we already + +know what 'f' is like? + +Remember, we mentioned when we +talked about inverse functions + +before is at the +time you use-- + +the way you really effectively +handle inverse functions is + +when you know properties of +the original function. + +We're not just working blindly +with 'f inverse' here, we're + +working with the case that 'f +inverse' is the inverse of the + +function 'f', and that we know +that 'f' is differentiable. + +And now we want to see if +knowing that 'f' is + +differentiable, can we prove +that 'f inverse' is + +differentiable? + +And you see, the idea is not +really that difficult. + +We can work this thing out step +by step from out little + +diagram over here. + +You see, notice that another +name for 'f inverse of 'x1 + +plus 'delta x'' is 'y1 +plus delta y'. + +Let me just work with what's +in the bracketed + +expression over here. + +See, the numerator is +'y1 plus 'delta y'. + +That's this term. + +Now, what's 'f inverse of x1'? + +As we come up over here, +remember the curve is 'y' + +equals 'f inverse'. + +So 'f inverse of x1' +is just 'y1'. + +Now what's our denominator? + +'x1 plus 'delta x' maps into +'y1 plus 'delta y'. + +Well, the idea is this. + +In terms of inverse functions, +'x1 plus 'delta x' is just the + +back map of 'y1 plus +'delta y'. + +In other words, since +'f inverse'-- + +let's write that down. + +Since 'f inverse of 'x1 plus +'delta x' is equal to 'y1 plus + +'delta y', that's another +way of saying that + +'x1 plus 'delta x'-- + +we might as well write this +because this is what we're + +emphasizing. + +In other words, this +becomes what? + +'x1 plus 'delta x' is just 'f +of 'y1 plus 'delta y''. + +And 'x1' is just 'f of y1'. + +See again, I used the picture +as a visual aid. + +But notice that everything I've +written down here follows + +analytically by my basic +definitions. + +I don't want to overwhelm you +with formal proofs here. + +These are all done +in the text. + +And I think that again, for +those of you who are + +proof-oriented, the proofs are +done excellently enough so + +that you'll get them +from that. + +And for those of you who are not +proof-oriented, an extra + +few minutes here will not make +that much of a difference. + +But what I want you to see over +here is how this thing + +starts to set up now. + +In other words, notice that this +starts to look like what? + +Let me just come over here where +we have some more space. + +This is what? + +The limit as 'delta +x' approaches 0. + +'f 'delta y' over ''f +of 'y1 plus delta + +y' minus 'f of y1''. + +And see, if you look at this +thing, remember 'f' is a + +differentiable function +of 'y'. + +If this had been a 'delta y' +approaching 0, this would have + +just been what? + +If we could assume that as +'delta x' approaches 0, 'delta + +y' approaches 0, this just +would have been what? + +This is the reciprocal of the +derivative of 'f of y' with + +respect to 'y'. + +In other words, this would be +what one would call 'dx dy' + +evaluated at 'y' equals 'y1'. + +This is what? + +''f of 'y1 plus delta y' minus +'f of y1'' over 'delta y' as + +'delta y' approaches 0 +is that derivative. + +And we have what? + +The reciprocal of this thing. + +And in other words, what we will +have proven is that 'dy + +dx' evaluated at 'x' equals +'x1' is the same as the + +reciprocal of 'dx dy' evaluated +at 'y' equals 'y1'. + +The only thing we have to be +sure of in terms of the formal + +proof is to make sure that as +'delta x' approaches 0, 'delta + +y' approaches 0. + +And that is not too difficult +a thing to do. + +As I say, the proof is +done in the book. + +We could do it here, but I think +that that would take + +away from the flavor of what +we're trying to show. + +The idea is it's fine to think +in terms of intuitive ideas. + +In fact, to level with you as +much as I can, of all of my + +mathematician friends who are +outstanding in various aspects + +of mathematics, to my knowledge +not one of them + +works without some sort of +mental picture as to + +what's going on. + +In other words, you can take +something that's very, very + +abstract and somehow or other, +you associate in your mind + +some kind of a visual aid +that gives you a hint as + +to what to do next. + +But once you know what to do +next, you always formulate the + +thing in terms of mathematical +precision. + +In other words, another way of +looking at this-- let's give + +this a broad title. + +Let's call this 'Proof +versus Intuition'. + +And this is a topic that comes +up very, very early in + +mathematics. + +Perhaps the first place that +it's extremely noticeable is + +in the subject called +plane geometry. + +Let me give you a +for instance. + +Let's take a typical +traditional + +plane geometry problem. + +We'l take an isosceles +triangle ABC, + +with AB equal to AC. + +And what we would like to prove +is that the base angles + +of this triangle are equal. + +We'd like to prove that angle +B equals angle C. + +Now you remember how you tackled +this problem in high + +school geometry. + +You said something like this. + +Well, let me draw the +angle bisector here. + +That meets BC at D. AD equals +itself by identity. + +These two angles are equal by +definition of angle bisector. + +Therefore, triangle ABD is +congruent to triangle ACD. + +And corresponding pots of +congruent triangles are equal. + +And you then proved that the +base angles of an isosceles + +triangle were equal. + +Now, at this stage of the game +if you were anything like me, + +what you would have done +has said, this is + +the end of the problem. + +Let's go onto the next one. + +But if you had passed this in +this particular way, you would + +have got a 0. + +And why'd you get a 0? + +Well, if you remember from plane +geometry, there was a + +particular format that +had to be followed. + +It was called the statement +reason format. + +For every statement that +you wrote down, you + +had to give a reason. + +And the reason couldn't be +things like because, or why + +not, or obvious. + +The reasons had to be what? + +Either definitions, or rules, or +previously proven theorems. + +In other words, notice that +even though we never + +emphasized it, back in plane +geometry when you were drawing + +this diagram and getting the +result, that was the geometric + +intuition part. + +In other words, this was +where you showed + +the result was plausible. + +The logic part-- + +and this is why geometry is +being stressed particularly in + +the modern curriculum. + +In terms of logic, notice that +once you had your intuitive + +picture, the statement reason +part followed independently of + +the picture. + +You used the picture to set +yourself up, but the final + +proof hinged on what? + +Having the result follow +purely from the axioms + +themselves. + +From the assumptions. + +And by the way, this is the +basic difference between + +traditional and modern +geometry. + +In modern geometry, let's go +back to the same proof. + +And it's a rather interesting +point and I think you'll see a + +connection between what's +happening in geometry and + +what's happening in calculus. + +You see, remember how +we proved this. + +We said draw the angle bisector +and call this point + +D. And then we went through +this and got this result. + +In modern geometry +they say look it. + +Without looking at the picture, +how do you know that + +D falls between B and C? + +It's obvious in the picture +that it does. + +But if everything has to follow +inescapably from your + +rules when you go through the +statement reason part, then + +unless you have some rule or +definition that tells you that + +D must fall between B and C, +you can't use this result. + +In other words, your result +will be plausible from a + +picture, but not provable +analytically + +So in modern geometry, we +add a few axioms, a few + +rules of the game. + +They're called the axioms of +betweenness, the axioms of + +separation. + +How one point separates other +points and what this thing + +means analytically, so that we +can continue on this way. + +Now you see what I'm driving +at is simply this. + +The Utopian way I think of +learning is to first have an + +intuitive picture of +what's going on. + +Then you proceed gradually to +learn what rigor means. + +As I may have said to you +before, in the language of + +functions, rigor is a function +of the 'rigoree'. + +In other words, if a person is +perfectly willing to accept a + +result, and he's not going to +get into any trouble using it, + +let him use the intuitive +result. + +On the other hand, if you wanted +to teach him later that + +there are pitfalls using his +intuition as a background, + +then we can come ahead and start +to do things in a little + +bit more of a sophisticated +manner. + +Now, you see what I'm driving +at I guess is this. + +If a youngster survives this +procedure of going from the + +intuitive approach to the +rigorous approach to the + +logical difference between +analysis and geometry, he'll + +be in great shape when +he gets to calculus. + +You see, the idea is +exactly the same. + +What we're saying in the +calculus is simply this. + +Given the derivative of an +inverse function, we do it + +first in a way that makes good +geometric sense to us. + +Then to make sure that the +results do not depend on our + +picture, and that our results +can be generalized to more + +variables or to tougher analytic +situations where we + +can't draw the picture, then +we tried to pick up the + +sophistication that allows us to +remove the picture proceed + +purely by analysis. + +What I'm telling you as you read +the text is if you can do + +both, fine. + +Learn the proofs and +the intuition. + +If you have trouble with the +proofs, at least satisfy + +yourself that they're there. + +That they do seem to follow +from the basic axioms and + +other assumptions. + +But meanwhile, rely heavily +on the intuitive results. + +And the important thing being +that you have a picture as to + +what's going on. + +The second aside that +I'd like to make-- + +and in fact, I would like to +conclude our lesson for today + +with this very important +aside-- + +is the following. + +You remember when we were first +learning limits and we + +talked about-- + +well, let me just make +an aside right at + +the beginning here. + +Hate to do that, but it +just occurred to me. + +Remember when we said, let's +compute the limit of 'f of x' + +as 'x' approaches 'a'. + +And our first approach was to +say, OK, let's just replace + +'x' by 'a'. + +And you said, OK, this is fine, +but what happens if you + +get a 0/0 form? + +And the counterargument to that +was, well, if 'f' and 'a' + +are chosen at random, how likely +is it that we're going + +to get a 0/0 form? + +Answer's well, it's not +too likely at all. + +And then the answer to that +was, well, but look it. + +Every time you take a +derivative, you're going to + +get a 0/0 form. + +And so the question +was, in calculus + +0/0 was very important. + +Now we're going to ask the same +kind of a question about + +1:1 functions. + +I guess the best way to +state it is bluntly. + +How likely is it that a given +function f is 1:1? + +For example, if I draw a curve +like this, is this graph 1:1? + +The answer, of course, is no. + +For example, if I pick the point +'y1' over here and come + +across here, I find at least +in this picture, three + +different candidates, three +different "x's". + +'x1', 'x2', and 'x3' +for which what? + +'f of x1' equals 'f of x2', +equals 'f of x3' equals 'y1'. + +And at first glance, you might +be tempted to say, oops, we + +can't apply any of our theory +to this particular function. + +But here's the very +important point. + +Very often in calculus we do not +start with 'y1' and look + +to see whether we have +'x1', 'x2', or 'x3'. + +Very often in calculus we're +starting at something like, + +oh, for the sake of +argument, 'x3'. + +And we say, hey, I wonder +what's going on in a + +neighborhood of 'x3'. + +If you want a fancy word to take +care of that, it's what + +the mathematician calls the +difference between local and + +global properties. + +And those words are exactly +what they sound like. + +Local means in a neighborhood +of a point and global means + +let's look at the curve +in the large. + +And the point is this. + +That very, very often in +calculus, we are not + +interested in what's +happening globally. + +For example, when you're driving +in a car and you're + +driving along say, the New York +Thruway, and you're near + +Albany and somebody says, what's +our gas situation? + +Somehow or other, what your +gas situation was when you + +were near Buffalo has no bearing +on the problem here. + +How full the gas tank is and the +problems involved with a + +full gas tank are local +properties. + +And whether this gets more +abstract or not is irrelevant. + +All we're saying is that in +calculus, very often you're + +dealing with a neighborhood +of a point. + +And notice this, and we'll +do is intuitively. + +The book again, supplies +the rigorous proof. + +Notice that if 'f prime +of x3' here is not 0. + +Well, for the sake of argument, +in this case, we + +notice that the curve +is always rising. + +Notice that with a smooth curve, +if it's rising at a + +particular point, obviously it's +going to be rising in a + +neighborhood of that point. + +Just look at the picture here. + +And what we're saying is this. + +What does it mean for a +function to be 1:1? + +For a function to be 1:1 on an +interval, it's sufficient that + +either 'f prime' never be +negative, or 'f prime' never + +be positive. + +In other words, what +it means is this. + +That as long as the derivative +is not 0, we can find a + +neighborhood, a local +neighborhood, that will make + +that function 1:1 on that +particular neighborhood. + +In other words, once I'm working +with this particular + +neighborhood, and I can't +stress this point enough + +because it's going to come +up over and over again. + +It's going to come up in more +sophisticated forms when we + +deal with functions of +several variables. + +But the idea is what? + +That in a neighborhood of a +point where the derivative is + +not 0, the function may be +viewed as being 1:1. + +You see, the tough part is that +if you start with 'y1', + +you have no way of knowing just +from that whether you + +want a neighborhood near +'x1', or 'x2', or 'x3'. + +But if you know what +neighborhood you want, in a + +sufficiently small neighborhood, +the function + +always behaves like it's 1:1. + +In fact, the only problem that +one runs into is the case + +where at the point in question, +the derivative is 0. + +And I think you can see +pictorially what happens in + +that case right away. + +As soon as the derivative is 0, +notice that no matter how + +small an interval-- well, I +shouldn't say this is a + +possibility. + +Let me show you what +I mean by that. + +Suppose the curve has +a low point here. + +What I'm saying is if the +curve does this, then no + +matter how small an interval +we choose surrounding 'x1', + +the function will not be +1:1 in that interval. + +No matter what interval you pick +here, if you look at the + +image for every point +in the image, there + +are going to be what? + +Two back mappings, two points +that come from here. + +The reason I say you have +to be careful is this. + +You see, you can have a case +where the curve does this. + +It comes in, gets tangent +to the x-axis, and then + +goes down like this. + +You see, at this particular +point, the + +derivative at 0 is 0. + +Yet, the curve is still never +falling in this area. + +This particular curve is 1:1. + +I guess what we're saying here +is that when a derivative is + +0, be careful because something + +like this can happen. + +If the derivative is not 0, +then we know that in the + +neighborhood of the point in +question, as long as the curve + +is smooth, it represents +a 1:1 function. + +And this is what we'll be doing +very, very often in + +calculus, is using neighborhoods +of points at + +which the derivative is not 0. + +Now, what this leads +to is this. + +When you start talking about +things like a derivative being + +0, and intervals and +one-to-oneness, I think you + +can see that this suggests a +rather powerful means or need + +for doing the geometry +of curve plotting. + +This will be the topic of +our next investigation. + +And so until next +time, goodbye. + +ANNOUNCER: Funding for the +publication of this video was + +provided by the Gabriella and +Paul Rosenbaum Foundation. + +Help OCW continue to provide +free and open access to MIT + +courses by making a donation +at ocw.mit.edu/donate. \ No newline at end of file diff --git a/MOdNzHR_tck.txt b/MOdNzHR_tck.txt new file mode 100644 index 0000000000000000000000000000000000000000..29c1372b77b38b216dbc8abd697f65e1a7cb17cf --- /dev/null +++ b/MOdNzHR_tck.txt @@ -0,0 +1,227 @@ +align:start position:0% + +my name is Olivia DEC and I'm a + + align:start position:0% +my name is Olivia DEC and I'm a + + + align:start position:0% +my name is Olivia DEC and I'm a +professor here at MIT in the aeroastro + + align:start position:0% +professor here at MIT in the aeroastro + + + align:start position:0% +professor here at MIT in the aeroastro +department also known as the Department + + align:start position:0% +department also known as the Department + + + align:start position:0% +department also known as the Department +of Aeronautics and astronautics and I've + + align:start position:0% +of Aeronautics and astronautics and I've + + + align:start position:0% +of Aeronautics and astronautics and I've +been in the department since 2001 and my + + align:start position:0% +been in the department since 2001 and my + + + align:start position:0% +been in the department since 2001 and my +passion is Aerospace vehicle anything + + align:start position:0% +passion is Aerospace vehicle anything + + + align:start position:0% +passion is Aerospace vehicle anything +that's flies airplanes Rockets + + align:start position:0% +that's flies airplanes Rockets + + + align:start position:0% +that's flies airplanes Rockets +satellites and uh it's been my passion + + align:start position:0% +satellites and uh it's been my passion + + + align:start position:0% +satellites and uh it's been my passion +since I was a kid so you know I grew up + + align:start position:0% +since I was a kid so you know I grew up + + + align:start position:0% +since I was a kid so you know I grew up +in Switzerland in the in the Alps and + + align:start position:0% +in Switzerland in the in the Alps and + + + align:start position:0% +in Switzerland in the in the Alps and +the Alps especially in the winter time + + align:start position:0% +the Alps especially in the winter time + + + align:start position:0% +the Alps especially in the winter time +when it's a clear night are amazing you + + align:start position:0% +when it's a clear night are amazing you + + + align:start position:0% +when it's a clear night are amazing you +look up at the night sky and you can see + + align:start position:0% +look up at the night sky and you can see + + + align:start position:0% +look up at the night sky and you can see +the stars you can see the Milky Way and + + align:start position:0% +the stars you can see the Milky Way and + + + align:start position:0% +the stars you can see the Milky Way and +as a kid it really inspired me I wanted + + align:start position:0% +as a kid it really inspired me I wanted + + + align:start position:0% +as a kid it really inspired me I wanted +to do something with stars initially I + + align:start position:0% +to do something with stars initially I + + + align:start position:0% +to do something with stars initially I +thought I was going to be an astronomer + + align:start position:0% +thought I was going to be an astronomer + + + align:start position:0% +thought I was going to be an astronomer +but then I really liked building things + + align:start position:0% +but then I really liked building things + + + align:start position:0% +but then I really liked building things +and so Aviation Rockets spacecraft + + align:start position:0% +and so Aviation Rockets spacecraft + + + align:start position:0% +and so Aviation Rockets spacecraft +really became my + + align:start position:0% +really became my + + + align:start position:0% +really became my +passion later I did my military service + + align:start position:0% +passion later I did my military service + + + align:start position:0% +passion later I did my military service +and um I worked on airplanes uh flight + + align:start position:0% +and um I worked on airplanes uh flight + + + align:start position:0% +and um I worked on airplanes uh flight +operations maintenance + + align:start position:0% +operations maintenance + + + align:start position:0% +operations maintenance +repair um really learning airplanes in + + align:start position:0% +repair um really learning airplanes in + + + align:start position:0% +repair um really learning airplanes in +and out the engines the hydraulic system + + align:start position:0% +and out the engines the hydraulic system + + + align:start position:0% +and out the engines the hydraulic system +the avionics working with others and + + align:start position:0% +the avionics working with others and + + + align:start position:0% +the avionics working with others and +Pilots to keep airplanes flying safely + + align:start position:0% +Pilots to keep airplanes flying safely + + + align:start position:0% +Pilots to keep airplanes flying safely +and that really was the origin of my + + align:start position:0% +and that really was the origin of my + + + align:start position:0% +and that really was the origin of my +passion for systems engineering \ No newline at end of file diff --git a/MqocbJ-FPo0.txt b/MqocbJ-FPo0.txt new file mode 100644 index 0000000000000000000000000000000000000000..a29a074fdc3ced71114d3db3e2a5d0cba222d936 --- /dev/null +++ b/MqocbJ-FPo0.txt @@ -0,0 +1,1003 @@ +align:start position:0% + +probability models often involve + + align:start position:0% +probability models often involve + + + align:start position:0% +probability models often involve +infinite sample spaces that is infinite + + align:start position:0% +infinite sample spaces that is infinite + + + align:start position:0% +infinite sample spaces that is infinite +sets but not all sets are of the same + + align:start position:0% +sets but not all sets are of the same + + + align:start position:0% +sets but not all sets are of the same +kind some sets are discrete and we call + + align:start position:0% +kind some sets are discrete and we call + + + align:start position:0% +kind some sets are discrete and we call +them countable and some are continues + + align:start position:0% +them countable and some are continues + + + align:start position:0% +them countable and some are continues +and we call them uncountable + + align:start position:0% +and we call them uncountable + + + align:start position:0% +and we call them uncountable +but what exactly is the difference + + align:start position:0% +but what exactly is the difference + + + align:start position:0% +but what exactly is the difference +between these two types of sets how can + + align:start position:0% +between these two types of sets how can + + + align:start position:0% +between these two types of sets how can +we define it precisely well let us start + + align:start position:0% +we define it precisely well let us start + + + align:start position:0% +we define it precisely well let us start +by first giving a definition of what it + + align:start position:0% +by first giving a definition of what it + + + align:start position:0% +by first giving a definition of what it +means to have a countable set a set will + + align:start position:0% +means to have a countable set a set will + + + align:start position:0% +means to have a countable set a set will +be called countable if its elements can + + align:start position:0% +be called countable if its elements can + + + align:start position:0% +be called countable if its elements can +be put into a one-to-one correspondence + + align:start position:0% +be put into a one-to-one correspondence + + + align:start position:0% +be put into a one-to-one correspondence +with the positive integers this means + + align:start position:0% +with the positive integers this means + + + align:start position:0% +with the positive integers this means +that we look at the elements of that set + + align:start position:0% +that we look at the elements of that set + + + align:start position:0% +that we look at the elements of that set +and we take one element we call it the + + align:start position:0% +and we take one element we call it the + + + align:start position:0% +and we take one element we call it the +first element we take another element we + + align:start position:0% +first element we take another element we + + + align:start position:0% +first element we take another element we +call it the second another we call the + + align:start position:0% +call it the second another we call the + + + align:start position:0% +call it the second another we call the +third element and so on and this way we + + align:start position:0% +third element and so on and this way we + + + align:start position:0% +third element and so on and this way we +will eventually exhaust all of the + + align:start position:0% +will eventually exhaust all of the + + + align:start position:0% +will eventually exhaust all of the +elements of the set so that each one of + + align:start position:0% +elements of the set so that each one of + + + align:start position:0% +elements of the set so that each one of +those elements corresponds to a + + align:start position:0% +those elements corresponds to a + + + align:start position:0% +those elements corresponds to a +particular positive integer namely the + + align:start position:0% +particular positive integer namely the + + + align:start position:0% +particular positive integer namely the +index that appears underneath more + + align:start position:0% +index that appears underneath more + + + align:start position:0% +index that appears underneath more +formally what's happening is that we + + align:start position:0% +formally what's happening is that we + + + align:start position:0% +formally what's happening is that we +take elements of that set that are + + align:start position:0% +take elements of that set that are + + + align:start position:0% +take elements of that set that are +arranged in a sequence we look at the + + align:start position:0% +arranged in a sequence we look at the + + + align:start position:0% +arranged in a sequence we look at the +set which is the entire range of values + + align:start position:0% +set which is the entire range of values + + + align:start position:0% +set which is the entire range of values +of that sequence and we want that + + align:start position:0% +of that sequence and we want that + + + align:start position:0% +of that sequence and we want that +sequence to exhaust the entire set Omega + + align:start position:0% +sequence to exhaust the entire set Omega + + + align:start position:0% +sequence to exhaust the entire set Omega +or in other words in simpler terms we + + align:start position:0% +or in other words in simpler terms we + + + align:start position:0% +or in other words in simpler terms we +want to be able to arrange all the + + align:start position:0% +want to be able to arrange all the + + + align:start position:0% +want to be able to arrange all the +elements of Omega in a sequence so what + + align:start position:0% +elements of Omega in a sequence so what + + + align:start position:0% +elements of Omega in a sequence so what +are some examples of countable sets in a + + align:start position:0% +are some examples of countable sets in a + + + align:start position:0% +are some examples of countable sets in a +trivial sense the positive integers + + align:start position:0% +trivial sense the positive integers + + + align:start position:0% +trivial sense the positive integers +themselves are countable because we can + + align:start position:0% +themselves are countable because we can + + + align:start position:0% +themselves are countable because we can +arrange them in a sequence this is + + align:start position:0% +arrange them in a sequence this is + + + align:start position:0% +arrange them in a sequence this is +almost tautological by the definition + + align:start position:0% +almost tautological by the definition + + + align:start position:0% +almost tautological by the definition +for a more interesting example let's + + align:start position:0% +for a more interesting example let's + + + align:start position:0% +for a more interesting example let's +look at the set of all integers can we + + align:start position:0% +look at the set of all integers can we + + + align:start position:0% +look at the set of all integers can we +arrange them in a sequence yes we can + + align:start position:0% +arrange them in a sequence yes we can + + + align:start position:0% +arrange them in a sequence yes we can +and we can do it in this manner where we + + align:start position:0% +and we can do it in this manner where we + + + align:start position:0% +and we can do it in this manner where we +alternate between positive and negative + + align:start position:0% +alternate between positive and negative + + + align:start position:0% +alternate between positive and negative +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +and this way we're going to cover all + + align:start position:0% +and this way we're going to cover all + + + align:start position:0% +and this way we're going to cover all +the integers and we have arranged them + + align:start position:0% +the integers and we have arranged them + + + align:start position:0% +the integers and we have arranged them +in a sequence how about the set of all + + align:start position:0% +in a sequence how about the set of all + + + align:start position:0% +in a sequence how about the set of all +pairs of positive integers this is less + + align:start position:0% +pairs of positive integers this is less + + + align:start position:0% +pairs of positive integers this is less +clear let us look at this picture this + + align:start position:0% +clear let us look at this picture this + + + align:start position:0% +clear let us look at this picture this +is the set of all pairs of positive + + align:start position:0% +is the set of all pairs of positive + + + align:start position:0% +is the set of all pairs of positive +integers which we understand to continue + + align:start position:0% +integers which we understand to continue + + + align:start position:0% +integers which we understand to continue +indefinitely can we arrange this set in + + align:start position:0% +indefinitely can we arrange this set in + + + align:start position:0% +indefinitely can we arrange this set in +a sequence it turns out that we can and + + align:start position:0% +a sequence it turns out that we can and + + + align:start position:0% +a sequence it turns out that we can and +we can do it by tracing a path of this + + align:start position:0% +we can do it by tracing a path of this + + + align:start position:0% +we can do it by tracing a path of this +kind so you can probably get the sense + + align:start position:0% +kind so you can probably get the sense + + + align:start position:0% +kind so you can probably get the sense +of how this path is going and by + + align:start position:0% +of how this path is going and by + + + align:start position:0% +of how this path is going and by +continuing this way over and over we're + + align:start position:0% +continuing this way over and over we're + + + align:start position:0% +continuing this way over and over we're +going to cover the entire set of all + + align:start position:0% +going to cover the entire set of all + + + align:start position:0% +going to cover the entire set of all +pairs of positive integers so we have + + align:start position:0% +pairs of positive integers so we have + + + align:start position:0% +pairs of positive integers so we have +managed to arrange them in a sequence so + + align:start position:0% +managed to arrange them in a sequence so + + + align:start position:0% +managed to arrange them in a sequence so +the set of all such pairs is indeed a + + align:start position:0% +the set of all such pairs is indeed a + + + align:start position:0% +the set of all such pairs is indeed a +countable set and the same argument can + + align:start position:0% +countable set and the same argument can + + + align:start position:0% +countable set and the same argument can +be extended to argue for the set of all + + align:start position:0% +be extended to argue for the set of all + + + align:start position:0% +be extended to argue for the set of all +triples of positive integers or the set + + align:start position:0% +triples of positive integers or the set + + + align:start position:0% +triples of positive integers or the set +of called quadruples of positive + + align:start position:0% +of called quadruples of positive + + + align:start position:0% +of called quadruples of positive +integers and so on this is actually not + + align:start position:0% +integers and so on this is actually not + + + align:start position:0% +integers and so on this is actually not +just trivial mathematical point that we + + align:start position:0% +just trivial mathematical point that we + + + align:start position:0% +just trivial mathematical point that we +discuss for some curious reason but it + + align:start position:0% +discuss for some curious reason but it + + + align:start position:0% +discuss for some curious reason but it +is because we will often have sample + + align:start position:0% +is because we will often have sample + + + align:start position:0% +is because we will often have sample +spaces that are of this kind and it's + + align:start position:0% +spaces that are of this kind and it's + + + align:start position:0% +spaces that are of this kind and it's +important to know that they are + + align:start position:0% +important to know that they are + + + align:start position:0% +important to know that they are +countable now for a more subtle example + + align:start position:0% +countable now for a more subtle example + + + align:start position:0% +countable now for a more subtle example +let us look at all rational numbers + + align:start position:0% +let us look at all rational numbers + + + align:start position:0% +let us look at all rational numbers +within the range between 0 & 1 what do + + align:start position:0% +within the range between 0 & 1 what do + + + align:start position:0% +within the range between 0 & 1 what do +we mean by rational numbers we mean + + align:start position:0% +we mean by rational numbers we mean + + + align:start position:0% +we mean by rational numbers we mean +those numbers that can be expressed as a + + align:start position:0% +those numbers that can be expressed as a + + + align:start position:0% +those numbers that can be expressed as a +ratio of two integers it turns out that + + align:start position:0% +ratio of two integers it turns out that + + + align:start position:0% +ratio of two integers it turns out that +we can arrange them in a sequence and we + + align:start position:0% +we can arrange them in a sequence and we + + + align:start position:0% +we can arrange them in a sequence and we +can do it as follows + + align:start position:0% +can do it as follows + + + align:start position:0% +can do it as follows +let us first look at rational numbers + + align:start position:0% +let us first look at rational numbers + + + align:start position:0% +let us first look at rational numbers +that have a denominator term of two then + + align:start position:0% +that have a denominator term of two then + + + align:start position:0% +that have a denominator term of two then +look at the rational numbers that have a + + align:start position:0% +look at the rational numbers that have a + + + align:start position:0% +look at the rational numbers that have a +denominator term of three then look at + + align:start position:0% +denominator term of three then look at + + + align:start position:0% +denominator term of three then look at +the rational numbers always within this + + align:start position:0% +the rational numbers always within this + + + align:start position:0% +the rational numbers always within this +range of interest that have a + + align:start position:0% +range of interest that have a + + + align:start position:0% +range of interest that have a +denominator of four + + align:start position:0% +denominator of four + + + align:start position:0% +denominator of four +and then we continue similarly rational + + align:start position:0% +and then we continue similarly rational + + + align:start position:0% +and then we continue similarly rational +numbers that have a denominator of 5 and + + align:start position:0% +numbers that have a denominator of 5 and + + + align:start position:0% +numbers that have a denominator of 5 and +so on this way we're going to exhaust + + align:start position:0% +so on this way we're going to exhaust + + + align:start position:0% +so on this way we're going to exhaust +all the rational numbers actually this + + align:start position:0% +all the rational numbers actually this + + + align:start position:0% +all the rational numbers actually this +number here already appeared there it's + + align:start position:0% +number here already appeared there it's + + + align:start position:0% +number here already appeared there it's +the same number so we do not need to + + align:start position:0% +the same number so we do not need to + + + align:start position:0% +the same number so we do not need to +include this in a sequence but that's + + align:start position:0% +include this in a sequence but that's + + + align:start position:0% +include this in a sequence but that's +not an issue whenever we see in rational + + align:start position:0% +not an issue whenever we see in rational + + + align:start position:0% +not an issue whenever we see in rational +numbers that has already been + + align:start position:0% +numbers that has already been + + + align:start position:0% +numbers that has already been +encountered before we just delete it in + + align:start position:0% +encountered before we just delete it in + + + align:start position:0% +encountered before we just delete it in +the end we end up with a sequence that + + align:start position:0% +the end we end up with a sequence that + + + align:start position:0% +the end we end up with a sequence that +goes over all the possible rational + + align:start position:0% +goes over all the possible rational + + + align:start position:0% +goes over all the possible rational +numbers and so we conclude that the set + + align:start position:0% +numbers and so we conclude that the set + + + align:start position:0% +numbers and so we conclude that the set +of all rational numbers is itself a + + align:start position:0% +of all rational numbers is itself a + + + align:start position:0% +of all rational numbers is itself a +countable set so what kind of set would + + align:start position:0% +countable set so what kind of set would + + + align:start position:0% +countable set so what kind of set would +be uncountable + + align:start position:0% +be uncountable + + + align:start position:0% +be uncountable +an uncountable set by definition is a + + align:start position:0% +an uncountable set by definition is a + + + align:start position:0% +an uncountable set by definition is a +set that is not countable and there are + + align:start position:0% +set that is not countable and there are + + + align:start position:0% +set that is not countable and there are +examples of uncountable sets most + + align:start position:0% +examples of uncountable sets most + + + align:start position:0% +examples of uncountable sets most +prominent continues subsets of the real + + align:start position:0% +prominent continues subsets of the real + + + align:start position:0% +prominent continues subsets of the real +line whenever we have an interval the + + align:start position:0% +line whenever we have an interval the + + + align:start position:0% +line whenever we have an interval the +unit interval or any other interval that + + align:start position:0% +unit interval or any other interval that + + + align:start position:0% +unit interval or any other interval that +has positive lengths that interval is an + + align:start position:0% +has positive lengths that interval is an + + + align:start position:0% +has positive lengths that interval is an +uncountable set and the same is true if + + align:start position:0% +uncountable set and the same is true if + + + align:start position:0% +uncountable set and the same is true if +instead of an interval we look at the + + align:start position:0% +instead of an interval we look at the + + + align:start position:0% +instead of an interval we look at the +entire real line or we look at the + + align:start position:0% +entire real line or we look at the + + + align:start position:0% +entire real line or we look at the +two-dimensional plane or 3 dimensional + + align:start position:0% +two-dimensional plane or 3 dimensional + + + align:start position:0% +two-dimensional plane or 3 dimensional +space and so on so all the usual sets + + align:start position:0% +space and so on so all the usual sets + + + align:start position:0% +space and so on so all the usual sets +that we think of as continuous sets turn + + align:start position:0% +that we think of as continuous sets turn + + + align:start position:0% +that we think of as continuous sets turn +out to be uncountable how do we know + + align:start position:0% +out to be uncountable how do we know + + + align:start position:0% +out to be uncountable how do we know +that they're uncountable there is + + align:start position:0% +that they're uncountable there is + + + align:start position:0% +that they're uncountable there is +actually a brilliant argument that + + align:start position:0% +actually a brilliant argument that + + + align:start position:0% +actually a brilliant argument that +establishes that the unit interval is + + align:start position:0% +establishes that the unit interval is + + + align:start position:0% +establishes that the unit interval is +uncountable and then the argument is + + align:start position:0% +uncountable and then the argument is + + + align:start position:0% +uncountable and then the argument is +easily extended to other cases like the + + align:start position:0% +easily extended to other cases like the + + + align:start position:0% +easily extended to other cases like the +reals and the plain we do not need to + + align:start position:0% +reals and the plain we do not need to + + + align:start position:0% +reals and the plain we do not need to +know how this argument goes for the + + align:start position:0% +know how this argument goes for the + + + align:start position:0% +know how this argument goes for the +purposes of this course but just because + + align:start position:0% +purposes of this course but just because + + + align:start position:0% +purposes of this course but just because +it is so beautiful we will actually be + + align:start position:0% +it is so beautiful we will actually be + + + align:start position:0% +it is so beautiful we will actually be +presenting it to you \ No newline at end of file diff --git a/NfmgFECXqZY.txt b/NfmgFECXqZY.txt new file mode 100644 index 0000000000000000000000000000000000000000..f22742b1648eb0013785d58bd668605e734671a7 --- /dev/null +++ b/NfmgFECXqZY.txt @@ -0,0 +1,11779 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% +so um + + + align:start position:0% +so um +so let's first talk about QED + + align:start position:0% + + + + align:start position:0% + +and we have talked about the Maxwell + + align:start position:0% + + + + align:start position:0% + +action said here is a LaGrange intensity + + align:start position:0% +action said here is a LaGrange intensity + + + align:start position:0% +action said here is a LaGrange intensity +we have F me mu + + align:start position:0% + + + + align:start position:0% + +minus J mu + + align:start position:0% +minus J mu + + + align:start position:0% +minus J mu +Amy + + align:start position:0% +Amy + + + align:start position:0% +Amy +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and jamieu should be a conserved current + + align:start position:0% + + + + align:start position:0% + +because the for the consistency of the + + align:start position:0% +because the for the consistency of the + + + align:start position:0% +because the for the consistency of the +Maxwell equation okay remember JMU has + + align:start position:0% +Maxwell equation okay remember JMU has + + + align:start position:0% +Maxwell equation okay remember JMU has +to be conserved + + align:start position:0% +to be conserved + + + align:start position:0% +to be conserved +so so now the question is what provide + + align:start position:0% +so so now the question is what provide + + + align:start position:0% +so so now the question is what provide +this JMU okay so so now let's imagine + + align:start position:0% +this JMU okay so so now let's imagine + + + align:start position:0% +this JMU okay so so now let's imagine +now let's introduce some other fields + + align:start position:0% +now let's introduce some other fields + + + align:start position:0% +now let's introduce some other fields +now imagine we have some direct + + align:start position:0% +now imagine we have some direct + + + align:start position:0% +now imagine we have some direct +filaments + + align:start position:0% + + + + align:start position:0% + +we have some formionic field service the + + align:start position:0% +we have some formionic field service the + + + align:start position:0% +we have some formionic field service the +lagrangian + + align:start position:0% + + + + align:start position:0% + +okay so this is the lagranging for the + + align:start position:0% +okay so this is the lagranging for the + + + align:start position:0% +okay so this is the lagranging for the +uh for the Iraq formula + + align:start position:0% +uh for the Iraq formula + + + align:start position:0% +uh for the Iraq formula +and then we discussed + + align:start position:0% +and then we discussed + + + align:start position:0% +and then we discussed +that 40 Rock from here + + align:start position:0% +that 40 Rock from here + + + align:start position:0% +that 40 Rock from here +and then there's a conserved current + + align:start position:0% +and then there's a conserved current + + + align:start position:0% +and then there's a conserved current +because there's a global symmetry + + align:start position:0% +because there's a global symmetry + + + align:start position:0% +because there's a global symmetry +let's say U1 Global symmetry + + align:start position:0% + + + + align:start position:0% + +corresponding to psi + + align:start position:0% +corresponding to psi + + + align:start position:0% +corresponding to psi +goes to expression I Alpha Psi + + align:start position:0% +goes to expression I Alpha Psi + + + align:start position:0% +goes to expression I Alpha Psi +with Alpha to be a constant + + align:start position:0% + + + + align:start position:0% + +okay and then this leads to a loser + + align:start position:0% +okay and then this leads to a loser + + + align:start position:0% +okay and then this leads to a loser +current + + align:start position:0% +current + + + align:start position:0% +current +Jamil which is conserved + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now if we want to couple the formulas + + align:start position:0% +so now if we want to couple the formulas + + + align:start position:0% +so now if we want to couple the formulas +to the Maxwell field then it's natural + + align:start position:0% +to the Maxwell field then it's natural + + + align:start position:0% +to the Maxwell field then it's natural +we identify this JMU with this JMU okay + + align:start position:0% +we identify this JMU with this JMU okay + + + align:start position:0% +we identify this JMU with this JMU okay +because both here we need the conserved + + align:start position:0% +because both here we need the conserved + + + align:start position:0% +because both here we need the conserved +current + + align:start position:0% +current + + + align:start position:0% +current +and here we have a conserved current + + align:start position:0% +and here we have a conserved current + + + align:start position:0% +and here we have a conserved current +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so it's natural to write down the + + align:start position:0% +so so it's natural to write down the + + + align:start position:0% +so so it's natural to write down the +theory and then this JB will just + + align:start position:0% +theory and then this JB will just + + + align:start position:0% +theory and then this JB will just +replace by this JMU that's why I use the + + align:start position:0% +replace by this JMU that's why I use the + + + align:start position:0% +replace by this JMU that's why I use the +same notation + + align:start position:0% +same notation + + + align:start position:0% +same notation +so so then that gives us + + align:start position:0% +so so then that gives us + + + align:start position:0% +so so then that gives us +the lagrangian for QED + + align:start position:0% +the lagrangian for QED + + + align:start position:0% +the lagrangian for QED +which is + + align:start position:0% +which is + + + align:start position:0% +which is +we have the Maxwell + + align:start position:0% + + + + align:start position:0% + +which is the free photon + + align:start position:0% +which is the free photon + + + align:start position:0% +which is the free photon +and then we have the free fermium + + align:start position:0% + + + + align:start position:0% + +but then the formula and the photon are + + align:start position:0% +but then the formula and the photon are + + + align:start position:0% +but then the formula and the photon are +coupled together + + align:start position:0% +coupled together + + + align:start position:0% +coupled together +through this + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so now + + align:start position:0% +so so now + + + align:start position:0% +so so now +this is a cubic term okay so now this is + + align:start position:0% +this is a cubic term okay so now this is + + + align:start position:0% +this is a cubic term okay so now this is +the interaction term + + align:start position:0% +the interaction term + + + align:start position:0% +the interaction term +okay so now this is an interaction term + + align:start position:0% +okay so now this is an interaction term + + + align:start position:0% +okay so now this is an interaction term +and this e + + align:start position:0% +and this e + + + align:start position:0% +and this e +can be play two rows okay can be + + align:start position:0% +can be play two rows okay can be + + + align:start position:0% +can be play two rows okay can be +considered as a coupling constant + + align:start position:0% + + + + align:start position:0% + +which essentially the E which + + align:start position:0% +which essentially the E which + + + align:start position:0% +which essentially the E which +just determines the the company strains + + align:start position:0% +just determines the the company strains + + + align:start position:0% +just determines the the company strains +between the PSI and the a okay B is + + align:start position:0% +between the PSI and the a okay B is + + + align:start position:0% +between the PSI and the a okay B is +bigger now of course the carbon is + + align:start position:0% +bigger now of course the carbon is + + + align:start position:0% +bigger now of course the carbon is +stronger okay + + align:start position:0% +stronger okay + + + align:start position:0% +stronger okay +and E can also be considered + + align:start position:0% +and E can also be considered + + + align:start position:0% +and E can also be considered +so place a dual Row one way and one row + + align:start position:0% +so place a dual Row one way and one row + + + align:start position:0% +so place a dual Row one way and one row +is you consider as a coupling and the + + align:start position:0% +is you consider as a coupling and the + + + align:start position:0% +is you consider as a coupling and the +second row is you can consider as a unit + + align:start position:0% +second row is you can consider as a unit + + + align:start position:0% +second row is you can consider as a unit +of charge + + align:start position:0% + + + + align:start position:0% + +because when we talk about the loss + + align:start position:0% +because when we talk about the loss + + + align:start position:0% +because when we talk about the loss +occurrence + + align:start position:0% +occurrence + + + align:start position:0% +occurrence +uh this is conserved you can uh you can + + align:start position:0% +uh this is conserved you can uh you can + + + align:start position:0% +uh this is conserved you can uh you can +multiply this by arbitrary Lumber this + + align:start position:0% +multiply this by arbitrary Lumber this + + + align:start position:0% +multiply this by arbitrary Lumber this +is still considered + + align:start position:0% +is still considered + + + align:start position:0% +is still considered +okay this is still conserved and when we + + align:start position:0% +okay this is still conserved and when we + + + align:start position:0% +okay this is still conserved and when we +multiply uh and here it just means that + + align:start position:0% +multiply uh and here it just means that + + + align:start position:0% +multiply uh and here it just means that +the the unit of this current is given by + + align:start position:0% +the the unit of this current is given by + + + align:start position:0% +the the unit of this current is given by +E okay so so the E plays the two rows + + align:start position:0% +E okay so so the E plays the two rows + + + align:start position:0% +E okay so so the E plays the two rows +here okay + + align:start position:0% + + + + align:start position:0% + +and then of course this e just our + + align:start position:0% +and then of course this e just our + + + align:start position:0% +and then of course this e just our +Standard Electric charge so if you take + + align:start position:0% +Standard Electric charge so if you take + + + align:start position:0% +Standard Electric charge so if you take +it upside to be give to be electron and + + align:start position:0% +it upside to be give to be electron and + + + align:start position:0% +it upside to be give to be electron and +then and then this will be Standard + + align:start position:0% +then and then this will be Standard + + + align:start position:0% +then and then this will be Standard +Electric charge for the electron and + + align:start position:0% +Electric charge for the electron and + + + align:start position:0% +Electric charge for the electron and +then this will be a theory which governs + + align:start position:0% +then this will be a theory which governs + + + align:start position:0% +then this will be a theory which governs +the interaction between the electron and + + align:start position:0% +the interaction between the electron and + + + align:start position:0% +the interaction between the electron and +the photon + + align:start position:0% + + + + align:start position:0% + +any questions on this + + align:start position:0% +any questions on this + + + align:start position:0% +any questions on this +yes + + align:start position:0% + + + + align:start position:0% + +sorry + + align:start position:0% + + + + align:start position:0% + +yeah yeah + + align:start position:0% + + + + align:start position:0% + +that's right that's right yeah yeah so + + align:start position:0% +that's right that's right yeah yeah so + + + align:start position:0% +that's right that's right yeah yeah so +in this framework indeed uh uh this e + + align:start position:0% +in this framework indeed uh uh this e + + + align:start position:0% +in this framework indeed uh uh this e +can be arbitrary and then and then + + align:start position:0% +can be arbitrary and then and then + + + align:start position:0% +can be arbitrary and then and then +different particles can have different + + align:start position:0% +different particles can have different + + + align:start position:0% +different particles can have different +charge for example uh if we couple these + + align:start position:0% +charge for example uh if we couple these + + + align:start position:0% +charge for example uh if we couple these +two electrons this will be e and then if + + align:start position:0% +two electrons this will be e and then if + + + align:start position:0% +two electrons this will be e and then if +we couple this to muon so in principle + + align:start position:0% +we couple this to muon so in principle + + + align:start position:0% +we couple this to muon so in principle +we have some utilda which does not have + + align:start position:0% +we have some utilda which does not have + + + align:start position:0% +we have some utilda which does not have +to be the same as this e indeed and and + + align:start position:0% +to be the same as this e indeed and and + + + align:start position:0% +to be the same as this e indeed and and +it's a highly unusual feature + + align:start position:0% +it's a highly unusual feature + + + align:start position:0% +it's a highly unusual feature +that the uh in in Asia what we observed + + align:start position:0% +that the uh in in Asia what we observed + + + align:start position:0% +that the uh in in Asia what we observed +the charge seemed to be quantized there + + align:start position:0% +the charge seemed to be quantized there + + + align:start position:0% +the charge seemed to be quantized there +seems to be multiple or or yeah of some + + align:start position:0% +seems to be multiple or or yeah of some + + + align:start position:0% +seems to be multiple or or yeah of some +charge and that cannot be explained + + align:start position:0% +charge and that cannot be explained + + + align:start position:0% +charge and that cannot be explained +using this framework it has to be + + align:start position:0% +using this framework it has to be + + + align:start position:0% +using this framework it has to be +explained using some other framework say + + align:start position:0% +explained using some other framework say + + + align:start position:0% +explained using some other framework say +or sometimes called Gran unified theory + + align:start position:0% +or sometimes called Gran unified theory + + + align:start position:0% +or sometimes called Gran unified theory +can be used to explain that yeah + + align:start position:0% +can be used to explain that yeah + + + align:start position:0% +can be used to explain that yeah +other questions + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +just an actual identification + + align:start position:0% +just an actual identification + + + align:start position:0% +just an actual identification +but but like this electronic doesn't + + align:start position:0% +but but like this electronic doesn't + + + align:start position:0% +but but like this electronic doesn't +have this human symmetry for this fair + + align:start position:0% +have this human symmetry for this fair + + + align:start position:0% +have this human symmetry for this fair +enough because it doesn't even exist + + align:start position:0% +enough because it doesn't even exist + + + align:start position:0% +enough because it doesn't even exist +there so yeah yeah + + align:start position:0% + + + + align:start position:0% + +so you're just taking inspiration now to + + align:start position:0% +so you're just taking inspiration now to + + + align:start position:0% +so you're just taking inspiration now to +to add both of them yeah yeah really + + align:start position:0% +to add both of them yeah yeah really + + + align:start position:0% +to add both of them yeah yeah really +yeah that's what we do here we add both + + align:start position:0% +yeah that's what we do here we add both + + + align:start position:0% +yeah that's what we do here we add both +of them yeah + + align:start position:0% + + + + align:start position:0% + +yeah so we have a theory + + align:start position:0% +yeah so we have a theory + + + align:start position:0% +yeah so we have a theory +with a photon and fermium and now the + + align:start position:0% +with a photon and fermium and now the + + + align:start position:0% +with a photon and fermium and now the +coupling is through this J and this J is + + align:start position:0% +coupling is through this J and this J is + + + align:start position:0% +coupling is through this J and this J is +given by this one yeah + + align:start position:0% + + + + align:start position:0% + +yeah okay + + align:start position:0% +yeah okay + + + align:start position:0% +yeah okay +other questions + + align:start position:0% + + + + align:start position:0% + +okay good good + + align:start position:0% +okay good good + + + align:start position:0% +okay good good +so um we can also slightly rewrite this + + align:start position:0% +so um we can also slightly rewrite this + + + align:start position:0% +so um we can also slightly rewrite this +Lagrange in some different way okay so + + align:start position:0% +Lagrange in some different way okay so + + + align:start position:0% +Lagrange in some different way okay so +we can + + align:start position:0% +we can + + + align:start position:0% +we can +lqd + + align:start position:0% +lqd + + + align:start position:0% +lqd +can also be written as in the following + + align:start position:0% +can also be written as in the following + + + align:start position:0% +can also be written as in the following +way + + align:start position:0% +way + + + align:start position:0% +way +okay so we can also rewrite this as one + + align:start position:0% +okay so we can also rewrite this as one + + + align:start position:0% +okay so we can also rewrite this as one +quarter of mu + + align:start position:0% +quarter of mu + + + align:start position:0% +quarter of mu +so this part we don't change + + align:start position:0% +so this part we don't change + + + align:start position:0% +so this part we don't change +but we can actually combine these two + + align:start position:0% +but we can actually combine these two + + + align:start position:0% +but we can actually combine these two +terms together + + align:start position:0% +terms together + + + align:start position:0% +terms together +in the following way we write it as I + + align:start position:0% +in the following way we write it as I + + + align:start position:0% +in the following way we write it as I +PSI bar + + align:start position:0% +PSI bar + + + align:start position:0% +PSI bar +and then comma mu I introduce a new + + align:start position:0% +and then comma mu I introduce a new + + + align:start position:0% +and then comma mu I introduce a new +derivative called D mu + + align:start position:0% +derivative called D mu + + + align:start position:0% +derivative called D mu +minus M PSI + + align:start position:0% +minus M PSI + + + align:start position:0% +minus M PSI +and this D mu + + align:start position:0% +and this D mu + + + align:start position:0% +and this D mu +capital D mu + + align:start position:0% +capital D mu + + + align:start position:0% +capital D mu +PSI is equal to partial mu PSI minus + + align:start position:0% +PSI is equal to partial mu PSI minus + + + align:start position:0% +PSI is equal to partial mu PSI minus +i e a mu PSI + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +so this is the same as that because the + + align:start position:0% +so this is the same as that because the + + + align:start position:0% +so this is the same as that because the +first term here + + align:start position:0% +first term here + + + align:start position:0% +first term here +just give you this term + + align:start position:0% +just give you this term + + + align:start position:0% +just give you this term +and the second term this is + + align:start position:0% +and the second term this is + + + align:start position:0% +and the second term this is +term just give you this e a mu PSI bar I + + align:start position:0% +term just give you this e a mu PSI bar I + + + align:start position:0% +term just give you this e a mu PSI bar I +just give you that + + align:start position:0% +just give you that + + + align:start position:0% +just give you that +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so mathematically these two are just + + align:start position:0% +and so mathematically these two are just + + + align:start position:0% +and so mathematically these two are just +completely equivalent I just like to re + + align:start position:0% +completely equivalent I just like to re + + + align:start position:0% +completely equivalent I just like to re +rewrote it + + align:start position:0% +rewrote it + + + align:start position:0% +rewrote it +but right in this way actually makes one + + align:start position:0% +but right in this way actually makes one + + + align:start position:0% +but right in this way actually makes one +new property of the theory a manifest + + align:start position:0% +new property of the theory a manifest + + + align:start position:0% +new property of the theory a manifest +okay so so this Theory + + align:start position:0% +okay so so this Theory + + + align:start position:0% +okay so so this Theory +[Applause] + + align:start position:0% + + + + align:start position:0% + +so we know that this theory has a gauge + + align:start position:0% +so we know that this theory has a gauge + + + align:start position:0% +so we know that this theory has a gauge +symmetry + + align:start position:0% + + + + align:start position:0% + +but this series we only have a global + + align:start position:0% +but this series we only have a global + + + align:start position:0% +but this series we only have a global +symmetry + + align:start position:0% + + + + align:start position:0% + +okay this area only have a global + + align:start position:0% +okay this area only have a global + + + align:start position:0% +okay this area only have a global +symmetry this Alpha must be a constant + + align:start position:0% +symmetry this Alpha must be a constant + + + align:start position:0% +symmetry this Alpha must be a constant +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now when we combine together + + align:start position:0% + + + + align:start position:0% + +it's another this new lagrangian + + align:start position:0% +it's another this new lagrangian + + + align:start position:0% +it's another this new lagrangian +actually have a new uh uh has a a + + align:start position:0% +actually have a new uh uh has a a + + + align:start position:0% +actually have a new uh uh has a a +has generalized a gauge symmetry okay so + + align:start position:0% +has generalized a gauge symmetry okay so + + + align:start position:0% +has generalized a gauge symmetry okay so +so AO Max + + align:start position:0% +so AO Max + + + align:start position:0% +so AO Max +so l QD + + align:start position:0% +so l QD + + + align:start position:0% +so l QD +is environment + + align:start position:0% + + + + align:start position:0% + +under + + align:start position:0% +under + + + align:start position:0% +under +the following + + align:start position:0% + + + + align:start position:0% + +so you still you take a mu + + align:start position:0% +so you still you take a mu + + + align:start position:0% +so you still you take a mu +goes to a mu plus then partial mu Lambda + + align:start position:0% +goes to a mu plus then partial mu Lambda + + + align:start position:0% +goes to a mu plus then partial mu Lambda +X + + align:start position:0% + + + + align:start position:0% + +and then now you + + align:start position:0% +and then now you + + + align:start position:0% +and then now you +transformed PSI also about local + + align:start position:0% +transformed PSI also about local + + + align:start position:0% +transformed PSI also about local +transformation + + align:start position:0% + + + + align:start position:0% + +you transform it by exponential I + + align:start position:0% +you transform it by exponential I + + + align:start position:0% +you transform it by exponential I +so now this e is electric charging this + + align:start position:0% +so now this e is electric charging this + + + align:start position:0% +so now this e is electric charging this +is different okay + + align:start position:0% + + + + align:start position:0% + +so now you can transform PSI + + align:start position:0% +so now you can transform PSI + + + align:start position:0% +so now you can transform PSI +by actually a local phase + + align:start position:0% +by actually a local phase + + + align:start position:0% +by actually a local phase +actually now it can depend uh this + + align:start position:0% +actually now it can depend uh this + + + align:start position:0% +actually now it can depend uh this +arbitrary function Lambda + + align:start position:0% +arbitrary function Lambda + + + align:start position:0% +arbitrary function Lambda +so you can show that actually this QD is + + align:start position:0% +so you can show that actually this QD is + + + align:start position:0% +so you can show that actually this QD is +in one under this transformation + + align:start position:0% +in one under this transformation + + + align:start position:0% +in one under this transformation +so so if I call this a mu Prime + + align:start position:0% + + + + align:start position:0% + +if I call this beside Prime X + + align:start position:0% +if I call this beside Prime X + + + align:start position:0% +if I call this beside Prime X +okay so you can check yourself + + align:start position:0% +okay so you can check yourself + + + align:start position:0% +okay so you can check yourself +with this transformation + + align:start position:0% +with this transformation + + + align:start position:0% +with this transformation +this demo side + + align:start position:0% + + + + align:start position:0% + +so this stimul + + align:start position:0% +so this stimul + + + align:start position:0% +so this stimul +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +PSI Prime okay so D mu Prime is obtained + + align:start position:0% +PSI Prime okay so D mu Prime is obtained + + + align:start position:0% +PSI Prime okay so D mu Prime is obtained +by by this T mule you replace the uh a + + align:start position:0% +by by this T mule you replace the uh a + + + align:start position:0% +by by this T mule you replace the uh a +mu by mu Prime and then here you you can + + align:start position:0% +mu by mu Prime and then here you you can + + + align:start position:0% +mu by mu Prime and then here you you can +show that this is equal to + + align:start position:0% +show that this is equal to + + + align:start position:0% +show that this is equal to +exponential i e Lambda X + + align:start position:0% +exponential i e Lambda X + + + align:start position:0% +exponential i e Lambda X +Team website + + align:start position:0% +Team website + + + align:start position:0% +Team website +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so it turns out + + align:start position:0% +so it turns out + + + align:start position:0% +so it turns out +in this combination + + align:start position:0% + + + + align:start position:0% + +okay in this combination + + align:start position:0% +okay in this combination + + + align:start position:0% +okay in this combination +so when you make a a such a local + + align:start position:0% +so when you make a a such a local + + + align:start position:0% +so when you make a a such a local +transformation on PSI + + align:start position:0% + + + + align:start position:0% + +when you take the derivative then then + + align:start position:0% +when you take the derivative then then + + + align:start position:0% +when you take the derivative then then +you get the extra term + + align:start position:0% +you get the extra term + + + align:start position:0% +you get the extra term +okay you get the actual term from taking + + align:start position:0% +okay you get the actual term from taking + + + align:start position:0% +okay you get the actual term from taking +the derivative on this Lambda + + align:start position:0% +the derivative on this Lambda + + + align:start position:0% +the derivative on this Lambda +but when you have this combination with + + align:start position:0% +but when you have this combination with + + + align:start position:0% +but when you have this combination with +a mu but a mu also transform this + + align:start position:0% +a mu but a mu also transform this + + + align:start position:0% +a mu but a mu also transform this +additional Lambda terminal Lambda term + + align:start position:0% +additional Lambda terminal Lambda term + + + align:start position:0% +additional Lambda terminal Lambda term +and then this two terms just cancel okay + + align:start position:0% +and then this two terms just cancel okay + + + align:start position:0% +and then this two terms just cancel okay +so in the end uh this D Prime mu a d + + align:start position:0% +so in the end uh this D Prime mu a d + + + align:start position:0% +so in the end uh this D Prime mu a d +Prime mu Prime actually transformed in a + + align:start position:0% +Prime mu Prime actually transformed in a + + + align:start position:0% +Prime mu Prime actually transformed in a +very simple way + + align:start position:0% +very simple way + + + align:start position:0% +very simple way +okay transform in a very simple way yes + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so so this tells you and and then this + + align:start position:0% +so so this tells you and and then this + + + align:start position:0% +so so this tells you and and then this +transform very simply + + align:start position:0% + + + + align:start position:0% + +and then this transform very simply and + + align:start position:0% +and then this transform very simply and + + + align:start position:0% +and then this transform very simply and +say bar just there's no derivative here + + align:start position:0% +say bar just there's no derivative here + + + align:start position:0% +say bar just there's no derivative here +then it's straightforward just transform + + align:start position:0% +then it's straightforward just transform + + + align:start position:0% +then it's straightforward just transform +us the extension balance e and then then + + align:start position:0% +us the extension balance e and then then + + + align:start position:0% +us the extension balance e and then then +we conclude + + align:start position:0% +we conclude + + + align:start position:0% +we conclude +okay so we conclude that lqed + + align:start position:0% +okay so we conclude that lqed + + + align:start position:0% +okay so we conclude that lqed +using varied okay + + align:start position:0% +using varied okay + + + align:start position:0% +using varied okay +under this transformation + + align:start position:0% + + + + align:start position:0% + +okay indeed is invariant okay + + align:start position:0% + + + + align:start position:0% + +so so we call it gate environment + + align:start position:0% +so so we call it gate environment + + + align:start position:0% +so so we call it gate environment +so now this is the a generalized gauge + + align:start position:0% +so now this is the a generalized gauge + + + align:start position:0% +so now this is the a generalized gauge +symmetry which now you also transform + + align:start position:0% +symmetry which now you also transform + + + align:start position:0% +symmetry which now you also transform +the formulas + + align:start position:0% +the formulas + + + align:start position:0% +the formulas +I also transform the formulas + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +any questions on this + + align:start position:0% +any questions on this + + + align:start position:0% +any questions on this +so now we can turn it around + + align:start position:0% +so now we can turn it around + + + align:start position:0% +so now we can turn it around +so so let's uh let us review our logic + + align:start position:0% +so so let's uh let us review our logic + + + align:start position:0% +so so let's uh let us review our logic +okay so so we first start with the + + align:start position:0% +okay so so we first start with the + + + align:start position:0% +okay so so we first start with the +Maxwell Theory so the max will see with + + align:start position:0% +Maxwell Theory so the max will see with + + + align:start position:0% +Maxwell Theory so the max will see with +this J here which you need to provide + + align:start position:0% +this J here which you need to provide + + + align:start position:0% +this J here which you need to provide +and then then from the formionic theory + + align:start position:0% +and then then from the formionic theory + + + align:start position:0% +and then then from the formionic theory +the familiarity you have latio J and + + align:start position:0% +the familiarity you have latio J and + + + align:start position:0% +the familiarity you have latio J and +then we just combine these two Theory + + align:start position:0% +then we just combine these two Theory + + + align:start position:0% +then we just combine these two Theory +and then by replace that J by the by the + + align:start position:0% +and then by replace that J by the by the + + + align:start position:0% +and then by replace that J by the by the +J writes naturally from the formulas + + align:start position:0% +J writes naturally from the formulas + + + align:start position:0% +J writes naturally from the formulas +but it turns out when we combine them + + align:start position:0% +but it turns out when we combine them + + + align:start position:0% +but it turns out when we combine them +together + + align:start position:0% +together + + + align:start position:0% +together +this series actually have a generalized + + align:start position:0% +this series actually have a generalized + + + align:start position:0% +this series actually have a generalized +gauge symmetry which also now can + + align:start position:0% +gauge symmetry which also now can + + + align:start position:0% +gauge symmetry which also now can +transform side locally + + align:start position:0% +transform side locally + + + align:start position:0% +transform side locally +okay you can transform sign locally and + + align:start position:0% +okay you can transform sign locally and + + + align:start position:0% +okay you can transform sign locally and +with this nice structure + + align:start position:0% +with this nice structure + + + align:start position:0% +with this nice structure +okay so this here we have this nice + + align:start position:0% +okay so this here we have this nice + + + align:start position:0% +okay so this here we have this nice +structure and then now uh uh you can uh + + align:start position:0% +structure and then now uh uh you can uh + + + align:start position:0% +structure and then now uh uh you can uh +transform uh upside uh also locally + + align:start position:0% +transform uh upside uh also locally + + + align:start position:0% +transform uh upside uh also locally +so we can also turn this around + + align:start position:0% + + + + align:start position:0% + +so we can say + + align:start position:0% + + + + align:start position:0% + +if we require + + align:start position:0% +if we require + + + align:start position:0% +if we require +so if we call this thing to be star + + align:start position:0% + + + + align:start position:0% + +so if we require + + align:start position:0% + + + + align:start position:0% + +the theory + + align:start position:0% + + + + align:start position:0% + +of a mu + + align:start position:0% +of a mu + + + align:start position:0% +of a mu +and PSI + + align:start position:0% + + + + align:start position:0% + +to be invariant + + align:start position:0% + + + + align:start position:0% + +under + + align:start position:0% + + + + align:start position:0% + +star + + align:start position:0% +star + + + align:start position:0% +star +and then that uniquely + + align:start position:0% +and then that uniquely + + + align:start position:0% +and then that uniquely +these two + + align:start position:0% +these two + + + align:start position:0% +these two +the interaction then there's a bit yeah + + align:start position:0% +the interaction then there's a bit yeah + + + align:start position:0% +the interaction then there's a bit yeah +maybe now you decrease then that leads + + align:start position:0% +maybe now you decrease then that leads + + + align:start position:0% +maybe now you decrease then that leads +to the interaction of the form JMU emu + + align:start position:0% +to the interaction of the form JMU emu + + + align:start position:0% +to the interaction of the form JMU emu +okay it just leads to this kind of + + align:start position:0% +okay it just leads to this kind of + + + align:start position:0% +okay it just leads to this kind of +interaction + + align:start position:0% +interaction + + + align:start position:0% +interaction +okay so so we continue the round we say + + align:start position:0% +okay so so we continue the round we say + + + align:start position:0% +okay so so we continue the round we say +okay let's + + align:start position:0% +okay let's + + + align:start position:0% +okay let's +using a different logic + + align:start position:0% +using a different logic + + + align:start position:0% +using a different logic +we want to couple the photon and the + + align:start position:0% +we want to couple the photon and the + + + align:start position:0% +we want to couple the photon and the +side together + + align:start position:0% +side together + + + align:start position:0% +side together +we want to couple a mu inside together + + align:start position:0% +we want to couple a mu inside together + + + align:start position:0% +we want to couple a mu inside together +and we loaded a mu previously has a + + align:start position:0% +and we loaded a mu previously has a + + + align:start position:0% +and we loaded a mu previously has a +gauge symmetry + + align:start position:0% +gauge symmetry + + + align:start position:0% +gauge symmetry +and now I want to generalize that gauge + + align:start position:0% +and now I want to generalize that gauge + + + align:start position:0% +and now I want to generalize that gauge +symmetry to include the formulas + + align:start position:0% +symmetry to include the formulas + + + align:start position:0% +symmetry to include the formulas +and then and then I require + + align:start position:0% +and then and then I require + + + align:start position:0% +and then and then I require +the full series being varied under this + + align:start position:0% +the full series being varied under this + + + align:start position:0% +the full series being varied under this +symmetry + + align:start position:0% +symmetry + + + align:start position:0% +symmetry +and this requirement then require that + + align:start position:0% +and this requirement then require that + + + align:start position:0% +and this requirement then require that +the interaction between them must have + + align:start position:0% +the interaction between them must have + + + align:start position:0% +the interaction between them must have +this form + + align:start position:0% +this form + + + align:start position:0% +this form +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yeah uh let me write more excretely uh + + align:start position:0% +yeah uh let me write more excretely uh + + + align:start position:0% +yeah uh let me write more excretely uh +in hacking of the form say bar gamma mu + + align:start position:0% +in hacking of the form say bar gamma mu + + + align:start position:0% +in hacking of the form say bar gamma mu +say mu okay so that will lead to this + + align:start position:0% +say mu okay so that will lead to this + + + align:start position:0% +say mu okay so that will lead to this +kind of interaction + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +so the reason this thinking even though + + align:start position:0% +so the reason this thinking even though + + + align:start position:0% +so the reason this thinking even though +this is just rephrase + + align:start position:0% +this is just rephrase + + + align:start position:0% +this is just rephrase +of what we we just did this rephrase is + + align:start position:0% +of what we we just did this rephrase is + + + align:start position:0% +of what we we just did this rephrase is +actually powerful + + align:start position:0% +actually powerful + + + align:start position:0% +actually powerful +okay here it means that when we impose + + align:start position:0% +okay here it means that when we impose + + + align:start position:0% +okay here it means that when we impose +this gauge symmetry + + align:start position:0% + + + + align:start position:0% + +we actually can deduce the interactions + + align:start position:0% + + + + align:start position:0% + +in deduce interactions + + align:start position:0% +in deduce interactions + + + align:start position:0% +in deduce interactions +we can actually reduce interactions just + + align:start position:0% +we can actually reduce interactions just + + + align:start position:0% +we can actually reduce interactions just +by requiring we can fix interactions by + + align:start position:0% +by requiring we can fix interactions by + + + align:start position:0% +by requiring we can fix interactions by +by requiring certain kind of symmetries + + align:start position:0% +by requiring certain kind of symmetries + + + align:start position:0% +by requiring certain kind of symmetries +yes + + align:start position:0% + + + + align:start position:0% + +yeah this was no uh motivates me a a + + align:start position:0% +yeah this was no uh motivates me a a + + + align:start position:0% +yeah this was no uh motivates me a a +Maxwell Siri already have a gauge + + align:start position:0% +Maxwell Siri already have a gauge + + + align:start position:0% +Maxwell Siri already have a gauge +symmetry when I carpeting for me I just + + align:start position:0% +symmetry when I carpeting for me I just + + + align:start position:0% +symmetry when I carpeting for me I just +want to generalize it + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yes + + align:start position:0% + + + + align:start position:0% + +sorry + + align:start position:0% + + + + align:start position:0% + +no the people because we already have + + align:start position:0% +no the people because we already have + + + align:start position:0% +no the people because we already have +this right we just want to generalize + + align:start position:0% +this right we just want to generalize + + + align:start position:0% +this right we just want to generalize +this + + align:start position:0% +this + + + align:start position:0% +this +the max 03 already have this we we just + + align:start position:0% +the max 03 already have this we we just + + + align:start position:0% +the max 03 already have this we we just +need to generalize this to formula and + + align:start position:0% +need to generalize this to formula and + + + align:start position:0% +need to generalize this to formula and +then there's electric generation because + + align:start position:0% +then there's electric generation because + + + align:start position:0% +then there's electric generation because +the formula is already environment under + + align:start position:0% +the formula is already environment under + + + align:start position:0% +the formula is already environment under +the global phase symmetry we just need + + align:start position:0% +the global phase symmetry we just need + + + align:start position:0% +the global phase symmetry we just need +to generalize in the way so that to make + + align:start position:0% +to generalize in the way so that to make + + + align:start position:0% +to generalize in the way so that to make +it local + + align:start position:0% + + + + align:start position:0% + +okay yes + + align:start position:0% + + + + align:start position:0% + +the gauge Transformations on the wave + + align:start position:0% +the gauge Transformations on the wave + + + align:start position:0% +the gauge Transformations on the wave +function is the same yeah is there a + + align:start position:0% +function is the same yeah is there a + + + align:start position:0% +function is the same yeah is there a +reason why that's yeah yeah it's the + + align:start position:0% +reason why that's yeah yeah it's the + + + align:start position:0% +reason why that's yeah yeah it's the +same + + align:start position:0% + + + + align:start position:0% + +um yeah yeah there is a reason because + + align:start position:0% +um yeah yeah there is a reason because + + + align:start position:0% +um yeah yeah there is a reason because +the uh you can uh um + + align:start position:0% + + + + align:start position:0% + +yeah the reason is that the + + align:start position:0% +yeah the reason is that the + + + align:start position:0% +yeah the reason is that the +um + + align:start position:0% +um + + + align:start position:0% +um +uh yeah it's + + align:start position:0% +uh yeah it's + + + align:start position:0% +uh yeah it's +is that the uh + + align:start position:0% +is that the uh + + + align:start position:0% +is that the uh +this when you go to Long writing + + align:start position:0% +this when you go to Long writing + + + align:start position:0% +this when you go to Long writing +visiting case this reduces just to one + + align:start position:0% +visiting case this reduces just to one + + + align:start position:0% +visiting case this reduces just to one +particle quantum mechanics so one + + align:start position:0% +particle quantum mechanics so one + + + align:start position:0% +particle quantum mechanics so one +particle Quantum mechanic should also + + align:start position:0% +particle Quantum mechanic should also + + + align:start position:0% +particle Quantum mechanic should also +have this kind of symmetry + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% +good + + + align:start position:0% +good +so so this is in fact + + align:start position:0% +so so this is in fact + + + align:start position:0% +so so this is in fact +not just a reinterpretation what we are + + align:start position:0% +not just a reinterpretation what we are + + + align:start position:0% +not just a reinterpretation what we are +looking so far this is actually a very + + align:start position:0% +looking so far this is actually a very + + + align:start position:0% +looking so far this is actually a very +deep dynamical principle okay so this is + + align:start position:0% +deep dynamical principle okay so this is + + + align:start position:0% +deep dynamical principle okay so this is +in fact + + align:start position:0% + + + + align:start position:0% + +a dynamical + + align:start position:0% + + + + align:start position:0% + +a deep maybe I'm outside this is a deep + + align:start position:0% +a deep maybe I'm outside this is a deep + + + align:start position:0% +a deep maybe I'm outside this is a deep +dynamical principle + + align:start position:0% + + + + align:start position:0% + +this principle + + align:start position:0% +this principle + + + align:start position:0% +this principle +so so essentially you have gauge + + align:start position:0% +so so essentially you have gauge + + + align:start position:0% +so so essentially you have gauge +interactions gauge symmetries or + + align:start position:0% +interactions gauge symmetries or + + + align:start position:0% +interactions gauge symmetries or +in other words local symmetries + + align:start position:0% + + + + align:start position:0% + +can be used + + align:start position:0% +can be used + + + align:start position:0% +can be used +to determine interactions okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +in other words the interactions + + align:start position:0% +in other words the interactions + + + align:start position:0% +in other words the interactions +all interactions in nature turns out + + align:start position:0% +all interactions in nature turns out + + + align:start position:0% +all interactions in nature turns out +they're related to some gauged images + + align:start position:0% +they're related to some gauged images + + + align:start position:0% +they're related to some gauged images +so so this applies + + align:start position:0% +so so this applies + + + align:start position:0% +so so this applies +to all interactions in nature + + align:start position:0% + + + + align:start position:0% + +so apply so this principle + + align:start position:0% +so apply so this principle + + + align:start position:0% +so apply so this principle +apply to all interactions in nature okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +so here we see in the in the + + align:start position:0% +so here we see in the in the + + + align:start position:0% +so here we see in the in the +electromagnetic interactions + + align:start position:0% +electromagnetic interactions + + + align:start position:0% +electromagnetic interactions +since the same thing happens for the + + align:start position:0% +since the same thing happens for the + + + align:start position:0% +since the same thing happens for the +weeks for the weak interaction same + + align:start position:0% +weeks for the weak interaction same + + + align:start position:0% +weeks for the weak interaction same +thing happens for the strong interaction + + align:start position:0% +thing happens for the strong interaction + + + align:start position:0% +thing happens for the strong interaction +and the same thing happens for Gravity + + align:start position:0% +and the same thing happens for Gravity + + + align:start position:0% +and the same thing happens for Gravity +they all can be formulated as a + + align:start position:0% +they all can be formulated as a + + + align:start position:0% +they all can be formulated as a +consequence of of some local symmetries + + align:start position:0% +consequence of of some local symmetries + + + align:start position:0% +consequence of of some local symmetries +okay some local symmetries + + align:start position:0% +okay some local symmetries + + + align:start position:0% +okay some local symmetries +and the why is that the case we don't + + align:start position:0% +and the why is that the case we don't + + + align:start position:0% +and the why is that the case we don't +really know we don't really understand + + align:start position:0% +really know we don't really understand + + + align:start position:0% +really know we don't really understand +why somehow this dynamical principle + + align:start position:0% +why somehow this dynamical principle + + + align:start position:0% +why somehow this dynamical principle +should be there but but this is just a + + align:start position:0% +should be there but but this is just a + + + align:start position:0% +should be there but but this is just a +fact that all our fundamental + + align:start position:0% +fact that all our fundamental + + + align:start position:0% +fact that all our fundamental +interactions they can all be understood + + align:start position:0% +interactions they can all be understood + + + align:start position:0% +interactions they can all be understood +this way + + align:start position:0% +this way + + + align:start position:0% +this way +so we we roughly understand uh but but + + align:start position:0% +so we we roughly understand uh but but + + + align:start position:0% +so we we roughly understand uh but but +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +but going into that is a will be a long + + align:start position:0% +but going into that is a will be a long + + + align:start position:0% +but going into that is a will be a long +story yes + + align:start position:0% +story yes + + + align:start position:0% +story yes +so people + + align:start position:0% +so people + + + align:start position:0% +so people +say that gauge and variants + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +your Fields by whatever in the series so + + align:start position:0% +your Fields by whatever in the series so + + + align:start position:0% +your Fields by whatever in the series so +how often like an ambiguity in your + + align:start position:0% +how often like an ambiguity in your + + + align:start position:0% +how often like an ambiguity in your +description leads to something very + + align:start position:0% +description leads to something very + + + align:start position:0% +description leads to something very +physical which is yeah yeah exactly so + + align:start position:0% +physical which is yeah yeah exactly so + + + align:start position:0% +physical which is yeah yeah exactly so +so we emphasized So when you say + + align:start position:0% +so we emphasized So when you say + + + align:start position:0% +so we emphasized So when you say +ambiguity it is what we said earlier + + align:start position:0% +ambiguity it is what we said earlier + + + align:start position:0% +ambiguity it is what we said earlier +that the local symmetries or gauge + + align:start position:0% +that the local symmetries or gauge + + + align:start position:0% +that the local symmetries or gauge +symmetry they just + + align:start position:0% +symmetry they just + + + align:start position:0% +symmetry they just +tells you your theory uh the the with + + align:start position:0% +tells you your theory uh the the with + + + align:start position:0% +tells you your theory uh the the with +freedom are redundant + + align:start position:0% +freedom are redundant + + + align:start position:0% +freedom are redundant +okay some of the degrees is not + + align:start position:0% +okay some of the degrees is not + + + align:start position:0% +okay some of the degrees is not +important + + align:start position:0% +important + + + align:start position:0% +important +then you say this should be pretty + + align:start position:0% +then you say this should be pretty + + + align:start position:0% +then you say this should be pretty +artificial right they just tell you have + + align:start position:0% +artificial right they just tell you have + + + align:start position:0% +artificial right they just tell you have +some redundant because Freedom you just + + align:start position:0% +some redundant because Freedom you just + + + align:start position:0% +some redundant because Freedom you just +get rid of them they turned out that + + align:start position:0% +get rid of them they turned out that + + + align:start position:0% +get rid of them they turned out that +they actually yeah uh uh uh yeah so so + + align:start position:0% +they actually yeah uh uh uh yeah so so + + + align:start position:0% +they actually yeah uh uh uh yeah so so +this is this is part of the mystery okay + + align:start position:0% +this is this is part of the mystery okay + + + align:start position:0% +this is this is part of the mystery okay +this is the part of the mystery why + + align:start position:0% +this is the part of the mystery why + + + align:start position:0% +this is the part of the mystery why +somehow uh uh the gauge symmetry leads + + align:start position:0% +somehow uh uh the gauge symmetry leads + + + align:start position:0% +somehow uh uh the gauge symmetry leads +to the interactions yeah + + align:start position:0% +to the interactions yeah + + + align:start position:0% +to the interactions yeah +so so yeah let me just + + align:start position:0% +so so yeah let me just + + + align:start position:0% +so so yeah let me just +yeah it's a long story let me just + + align:start position:0% +yeah it's a long story let me just + + + align:start position:0% +yeah it's a long story let me just +briefly + + align:start position:0% +briefly + + + align:start position:0% +briefly +make some comments here okay so so now + + align:start position:0% +make some comments here okay so so now + + + align:start position:0% +make some comments here okay so so now +we more or less understand + + align:start position:0% +we more or less understand + + + align:start position:0% +we more or less understand +that all these interactions + + align:start position:0% +that all these interactions + + + align:start position:0% +that all these interactions +they all essentially the uh all this + + align:start position:0% +they all essentially the uh all this + + + align:start position:0% +they all essentially the uh all this +important interactions in nature those + + align:start position:0% +important interactions in nature those + + + align:start position:0% +important interactions in nature those +fundamental in actions they all governed + + align:start position:0% +fundamental in actions they all governed + + + align:start position:0% +fundamental in actions they all governed +by some massless particle + + align:start position:0% +by some massless particle + + + align:start position:0% +by some massless particle +okay uh uh the the old government is + + align:start position:0% +okay uh uh the the old government is + + + align:start position:0% +okay uh uh the the old government is +particle but somehow to describes a + + align:start position:0% +particle but somehow to describes a + + + align:start position:0% +particle but somehow to describes a +massless particle + + align:start position:0% +massless particle + + + align:start position:0% +massless particle +you actually require to have some kind + + align:start position:0% +you actually require to have some kind + + + align:start position:0% +you actually require to have some kind +of redundancy to so that you can + + align:start position:0% +of redundancy to so that you can + + + align:start position:0% +of redundancy to so that you can +describe them in a Lorenz cover in the + + align:start position:0% +describe them in a Lorenz cover in the + + + align:start position:0% +describe them in a Lorenz cover in the +way with other without those redundancy + + align:start position:0% +way with other without those redundancy + + + align:start position:0% +way with other without those redundancy +you cannot describe them in the Lawrence + + align:start position:0% +you cannot describe them in the Lawrence + + + align:start position:0% +you cannot describe them in the Lawrence +car in the way so in the sense that's + + align:start position:0% +car in the way so in the sense that's + + + align:start position:0% +car in the way so in the sense that's +where that come from okay yeah yeah but + + align:start position:0% +where that come from okay yeah yeah but + + + align:start position:0% +where that come from okay yeah yeah but +to make the statement which I just said + + align:start position:0% +to make the statement which I just said + + + align:start position:0% +to make the statement which I just said +precise is actually a long story + + align:start position:0% + + + + align:start position:0% + +um we we don't know how to + + align:start position:0% +um we we don't know how to + + + align:start position:0% +um we we don't know how to +so we don't know how to uh there's no + + align:start position:0% +so we don't know how to uh there's no + + + align:start position:0% +so we don't know how to uh there's no +good way to quantize that to give you + + align:start position:0% +good way to quantize that to give you + + + align:start position:0% +good way to quantize that to give you +a nice quantum theory and we also know + + align:start position:0% +a nice quantum theory and we also know + + + align:start position:0% +a nice quantum theory and we also know +that the physically a mu actually plays + + align:start position:0% +that the physically a mu actually plays + + + align:start position:0% +that the physically a mu actually plays +a role and yeah like in situations like + + align:start position:0% +a role and yeah like in situations like + + + align:start position:0% +a role and yeah like in situations like +a hollow bomb effect the Emu Place + + align:start position:0% +a hollow bomb effect the Emu Place + + + align:start position:0% +a hollow bomb effect the Emu Place +important value when e and B is equal to + + align:start position:0% +important value when e and B is equal to + + + align:start position:0% +important value when e and B is equal to +zero so so a mu is a more fundamental + + align:start position:0% +zero so so a mu is a more fundamental + + + align:start position:0% +zero so so a mu is a more fundamental +object + + align:start position:0% +object + + + align:start position:0% +object +than e and P so e and B should be + + align:start position:0% +than e and P so e and B should be + + + align:start position:0% +than e and P so e and B should be +considered as a derived object from from + + align:start position:0% +considered as a derived object from from + + + align:start position:0% +considered as a derived object from from +a mu yeah + + align:start position:0% + + + + align:start position:0% + +other questions yes + + align:start position:0% + + + + align:start position:0% + +I'm not sure I understand your question + + align:start position:0% + + + + align:start position:0% + +yeah no we're not doing any gauge fixing + + align:start position:0% +yeah no we're not doing any gauge fixing + + + align:start position:0% +yeah no we're not doing any gauge fixing +uh here we just uh uh have a uh have a + + align:start position:0% +uh here we just uh uh have a uh have a + + + align:start position:0% +uh here we just uh uh have a uh have a +more generalized uh gauge symmetry we + + align:start position:0% +more generalized uh gauge symmetry we + + + align:start position:0% +more generalized uh gauge symmetry we +are not doing any gauge fixing + + align:start position:0% + + + + align:start position:0% + +but I think + + align:start position:0% + + + + align:start position:0% + +everything yeah + + align:start position:0% + + + + align:start position:0% + +what do you mean by other issues + + align:start position:0% + + + + align:start position:0% + +oh oh oh or or you mean when we yeah no + + align:start position:0% +oh oh oh or or you mean when we yeah no + + + align:start position:0% +oh oh oh or or you mean when we yeah no +no that won't change much because we uh + + align:start position:0% +no that won't change much because we uh + + + align:start position:0% +no that won't change much because we uh +we did before for the gate fixing + + align:start position:0% +we did before for the gate fixing + + + align:start position:0% +we did before for the gate fixing +already it's enough yeah + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now let's talk about another example + + align:start position:0% +so now let's talk about another example + + + align:start position:0% +so now let's talk about another example +so + + align:start position:0% + + + + align:start position:0% + +so if you have a scale of field which is + + align:start position:0% +so if you have a scale of field which is + + + align:start position:0% +so if you have a scale of field which is +charged + + align:start position:0% +charged + + + align:start position:0% +charged +say complex scalar fields + + align:start position:0% +say complex scalar fields + + + align:start position:0% +say complex scalar fields +you can also + + align:start position:0% +you can also + + + align:start position:0% +you can also +couple it to to the photon okay uh uh as + + align:start position:0% +couple it to to the photon okay uh uh as + + + align:start position:0% +couple it to to the photon okay uh uh as +follow as what we did for the for the + + align:start position:0% +follow as what we did for the for the + + + align:start position:0% +follow as what we did for the for the +formulas okay so let's consider if you + + align:start position:0% +formulas okay so let's consider if you + + + align:start position:0% +formulas okay so let's consider if you +have a complex scalar + + align:start position:0% +have a complex scalar + + + align:start position:0% +have a complex scalar +to consider you have a complex scalar + + align:start position:0% + + + + align:start position:0% + +yeah maybe you can also have some + + align:start position:0% +yeah maybe you can also have some + + + align:start position:0% +yeah maybe you can also have some +interaction terms okay + + align:start position:0% +interaction terms okay + + + align:start position:0% +interaction terms okay +so so let's imagine we have some + + align:start position:0% +so so let's imagine we have some + + + align:start position:0% +so so let's imagine we have some +concrete scalar + + align:start position:0% +concrete scalar + + + align:start position:0% +concrete scalar +and so this is invariant on the Phi + + align:start position:0% +and so this is invariant on the Phi + + + align:start position:0% +and so this is invariant on the Phi +goes to again uh there's a global + + align:start position:0% +goes to again uh there's a global + + + align:start position:0% +goes to again uh there's a global +symmetry you want Global symmetry uh + + align:start position:0% +symmetry you want Global symmetry uh + + + align:start position:0% +symmetry you want Global symmetry uh +Alpha equal to constant + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then we have a conserved current + + align:start position:0% + + + + align:start position:0% + +here J mu equal to minus I so again the + + align:start position:0% +here J mu equal to minus I so again the + + + align:start position:0% +here J mu equal to minus I so again the +you lost the current + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +so now + + align:start position:0% +so now + + + align:start position:0% +so now +we can just try to + + align:start position:0% +we can just try to + + + align:start position:0% +we can just try to +do the same trick okay so so let's just + + align:start position:0% +do the same trick okay so so let's just + + + align:start position:0% +do the same trick okay so so let's just +couple this Theory combine this series + + align:start position:0% +couple this Theory combine this series + + + align:start position:0% +couple this Theory combine this series +to the Maxwell Theory okay by identify + + align:start position:0% +to the Maxwell Theory okay by identify + + + align:start position:0% +to the Maxwell Theory okay by identify +that J with this J okay so so naively + + align:start position:0% + + + + align:start position:0% + +so the reason I said Lively because this + + align:start position:0% +so the reason I said Lively because this + + + align:start position:0% +so the reason I said Lively because this +procedure in this case will not work + + align:start position:0% +procedure in this case will not work + + + align:start position:0% +procedure in this case will not work +so now we can consider the scalar QED + + align:start position:0% + + + + align:start position:0% + +say we with Photon couple and and again + + align:start position:0% +say we with Photon couple and and again + + + align:start position:0% +say we with Photon couple and and again +with this malice one half one quarter F + + align:start position:0% +with this malice one half one quarter F + + + align:start position:0% +with this malice one half one quarter F +squared term so it's let me just write + + align:start position:0% +squared term so it's let me just write + + + align:start position:0% +squared term so it's let me just write +the simplified version edges with the F + + align:start position:0% +the simplified version edges with the F + + + align:start position:0% +the simplified version edges with the F +squared and then you then you can add + + align:start position:0% +squared and then you then you can add + + + align:start position:0% +squared and then you then you can add +the scalar LaGrange + + align:start position:0% +the scalar LaGrange + + + align:start position:0% +the scalar LaGrange +okay we're + + align:start position:0% +okay we're + + + align:start position:0% +okay we're +and now Eugene now you add the component + + align:start position:0% +and now Eugene now you add the component + + + align:start position:0% +and now Eugene now you add the component +e and then you can put a mu equal to J + + align:start position:0% +e and then you can put a mu equal to J + + + align:start position:0% +e and then you can put a mu equal to J +mu but with J mu given by this + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +with a mu given by this okay so this is + + align:start position:0% +with a mu given by this okay so this is + + + align:start position:0% +with a mu given by this okay so this is +the value of + + align:start position:0% +the value of + + + align:start position:0% +the value of +so this is the actual thing to do based + + align:start position:0% +so this is the actual thing to do based + + + align:start position:0% +so this is the actual thing to do based +on our ferment story + + align:start position:0% +on our ferment story + + + align:start position:0% +on our ferment story +based on our formula story + + align:start position:0% + + + + align:start position:0% + +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +um + + align:start position:0% + + + + align:start position:0% + +but but now you can check + + align:start position:0% + + + + align:start position:0% + +but now I can easily check + + align:start position:0% + + + + align:start position:0% + +okay so I will not do the exactly check + + align:start position:0% +okay so I will not do the exactly check + + + align:start position:0% +okay so I will not do the exactly check +here you should check yourself + + align:start position:0% +here you should check yourself + + + align:start position:0% +here you should check yourself +this theory is not so let me call this L + + align:start position:0% +this theory is not so let me call this L + + + align:start position:0% +this theory is not so let me call this L +Prime okay L tilde because this is our + + align:start position:0% +Prime okay L tilde because this is our + + + align:start position:0% +Prime okay L tilde because this is our +live series you can check that this L + + align:start position:0% +live series you can check that this L + + + align:start position:0% +live series you can check that this L +tilde + + align:start position:0% + + + + align:start position:0% + +QED + + align:start position:0% +QED + + + align:start position:0% +QED +scalar QD + + align:start position:0% +scalar QD + + + align:start position:0% +scalar QD +is not in warrant + + align:start position:0% + + + + align:start position:0% + +engagement + + align:start position:0% + + + + align:start position:0% + +okay means that you cannot find + + align:start position:0% +okay means that you cannot find + + + align:start position:0% +okay means that you cannot find +you cannot find the transformation on + + align:start position:0% +you cannot find the transformation on + + + align:start position:0% +you cannot find the transformation on +Phi + + align:start position:0% +Phi + + + align:start position:0% +Phi +okay that this hosting is getting + + align:start position:0% +okay that this hosting is getting + + + align:start position:0% +okay that this hosting is getting +variant + + align:start position:0% +variant + + + align:start position:0% +variant +okay this whole thing is getting word + + align:start position:0% +okay this whole thing is getting word + + + align:start position:0% +okay this whole thing is getting word +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +um so for example + + align:start position:0% +um so for example + + + align:start position:0% +um so for example +so it's not getting very for one we can + + align:start position:0% +so it's not getting very for one we can + + + align:start position:0% +so it's not getting very for one we can +check explicitly if you just copy what + + align:start position:0% +check explicitly if you just copy what + + + align:start position:0% +check explicitly if you just copy what +we do here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that this 5X + + align:start position:0% + + + + align:start position:0% + +given by IE Lambda + + align:start position:0% +given by IE Lambda + + + align:start position:0% +given by IE Lambda +x5x so this won't work okay + + align:start position:0% +x5x so this won't work okay + + + align:start position:0% +x5x so this won't work okay +so it's not environment + + align:start position:0% +so it's not environment + + + align:start position:0% +so it's not environment +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yes + + align:start position:0% + + + + align:start position:0% + +no you cannot divided find the same + + align:start position:0% + + + + align:start position:0% + +yeah that's a very good question + + align:start position:0% +yeah that's a very good question + + + align:start position:0% +yeah that's a very good question +so so + + align:start position:0% +so so + + + align:start position:0% +so so +you cannot identify the same + + align:start position:0% +you cannot identify the same + + + align:start position:0% +you cannot identify the same +it's because the + + align:start position:0% +it's because the + + + align:start position:0% +it's because the +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um + + align:start position:0% +um + + + align:start position:0% +um +so naive but you can ask yourself you + + align:start position:0% +so naive but you can ask yourself you + + + align:start position:0% +so naive but you can ask yourself you +say this supposed to be conserved and we + + align:start position:0% +say this supposed to be conserved and we + + + align:start position:0% +say this supposed to be conserved and we +previously said if we have a mutual + + align:start position:0% +previously said if we have a mutual + + + align:start position:0% +previously said if we have a mutual +conserved current distance gate + + align:start position:0% +conserved current distance gate + + + align:start position:0% +conserved current distance gate +environment + + align:start position:0% +environment + + + align:start position:0% +environment +but this is conserved + + align:start position:0% +but this is conserved + + + align:start position:0% +but this is conserved +only when you use the equation motion of + + align:start position:0% +only when you use the equation motion of + + + align:start position:0% +only when you use the equation motion of +this Theory + + align:start position:0% +this Theory + + + align:start position:0% +this Theory +but now when you come for this to to + + align:start position:0% +but now when you come for this to to + + + align:start position:0% +but now when you come for this to to +this Theory then the equation motion for + + align:start position:0% +this Theory then the equation motion for + + + align:start position:0% +this Theory then the equation motion for +Phi changed + + align:start position:0% +Phi changed + + + align:start position:0% +Phi changed +and then and then and then so yeah so no + + align:start position:0% +and then and then and then so yeah so no + + + align:start position:0% +and then and then and then so yeah so no +longer it works okay and so just naively + + align:start position:0% +longer it works okay and so just naively + + + align:start position:0% +longer it works okay and so just naively +do this uh uh uh live redo this is not + + align:start position:0% +do this uh uh uh live redo this is not + + + align:start position:0% +do this uh uh uh live redo this is not +guaranteedable + + align:start position:0% +guaranteedable + + + align:start position:0% +guaranteedable +case + + align:start position:0% +case + + + align:start position:0% +case +it has worked because of the existence + + align:start position:0% +it has worked because of the existence + + + align:start position:0% +it has worked because of the existence +of this imagery + + align:start position:0% +of this imagery + + + align:start position:0% +of this imagery +okay because of the extent of this image + + align:start position:0% + + + + align:start position:0% + +and it turns out this Theory + + align:start position:0% +and it turns out this Theory + + + align:start position:0% +and it turns out this Theory +so so now this area will not be getting + + align:start position:0% +so so now this area will not be getting + + + align:start position:0% +so so now this area will not be getting +warrant + + align:start position:0% +warrant + + + align:start position:0% +warrant +and now this will be backed + + align:start position:0% +and now this will be backed + + + align:start position:0% +and now this will be backed +okay we'll be back because you can no + + align:start position:0% +okay we'll be back because you can no + + + align:start position:0% +okay we'll be back because you can no +longer find any Sim any local symmetry + + align:start position:0% +longer find any Sim any local symmetry + + + align:start position:0% +longer find any Sim any local symmetry +this series is is invariant okay and + + align:start position:0% +this series is is invariant okay and + + + align:start position:0% +this series is is invariant okay and +they just uh uh this is one of + + align:start position:0% +they just uh uh this is one of + + + align:start position:0% +they just uh uh this is one of +generation does not work you cannot find + + align:start position:0% +generation does not work you cannot find + + + align:start position:0% +generation does not work you cannot find +anything you can also not find others + + align:start position:0% +anything you can also not find others + + + align:start position:0% +anything you can also not find others +but this is bad because we said we need + + align:start position:0% +but this is bad because we said we need + + + align:start position:0% +but this is bad because we said we need +gauge symmetry to get rid of unphysical + + align:start position:0% +gauge symmetry to get rid of unphysical + + + align:start position:0% +gauge symmetry to get rid of unphysical +freedom in a meal because mu should only + + align:start position:0% +freedom in a meal because mu should only + + + align:start position:0% +freedom in a meal because mu should only +have two polarization not have four so + + align:start position:0% +have two polarization not have four so + + + align:start position:0% +have two polarization not have four so +we need those gauge symmetries to get + + align:start position:0% +we need those gauge symmetries to get + + + align:start position:0% +we need those gauge symmetries to get +rid of the unphysical decrease feeding + + align:start position:0% +rid of the unphysical decrease feeding + + + align:start position:0% +rid of the unphysical decrease feeding +in a mu but if this cage image is broken + + align:start position:0% +in a mu but if this cage image is broken + + + align:start position:0% +in a mu but if this cage image is broken +by copper to the scalar field + + align:start position:0% +by copper to the scalar field + + + align:start position:0% +by copper to the scalar field +and then this Theory cannot be + + align:start position:0% +and then this Theory cannot be + + + align:start position:0% +and then this Theory cannot be +consistent okay so this is respect + + align:start position:0% +consistent okay so this is respect + + + align:start position:0% +consistent okay so this is respect +okay + + align:start position:0% +okay + + + align:start position:0% +okay +this series back + + align:start position:0% +this series back + + + align:start position:0% +this series back +we can just generalize this principle + + align:start position:0% +we can just generalize this principle + + + align:start position:0% +we can just generalize this principle +okay + + align:start position:0% +okay + + + align:start position:0% +okay +we say let's just impose gauge symmetry + + align:start position:0% +we say let's just impose gauge symmetry + + + align:start position:0% +we say let's just impose gauge symmetry +okay we can just impose each image + + align:start position:0% +okay we can just impose each image + + + align:start position:0% +okay we can just impose each image +so the way out + + align:start position:0% +so the way out + + + align:start position:0% +so the way out +we can just impose the gauge symmetry + + align:start position:0% + + + + align:start position:0% + +impose the theory + + align:start position:0% + + + + align:start position:0% + +to being warrant + + align:start position:0% + + + + align:start position:0% + +under + + align:start position:0% +under + + + align:start position:0% +under +this generally a mu + + align:start position:0% +this generally a mu + + + align:start position:0% +this generally a mu +goes to a mu + + align:start position:0% +goes to a mu + + + align:start position:0% +goes to a mu +plus fashion view Lambda and and the Phi + + align:start position:0% +plus fashion view Lambda and and the Phi + + + align:start position:0% +plus fashion view Lambda and and the Phi +goes to exponential minus + + align:start position:0% +goes to exponential minus + + + align:start position:0% +goes to exponential minus +I Lambda x 5 okay so so we require this + + align:start position:0% +I Lambda x 5 okay so so we require this + + + align:start position:0% +I Lambda x 5 okay so so we require this +to be under that + + align:start position:0% +to be under that + + + align:start position:0% +to be under that +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +so to write a theory environment on this + + align:start position:0% +so to write a theory environment on this + + + align:start position:0% +so to write a theory environment on this +we can just easily follow the inside if + + align:start position:0% +we can just easily follow the inside if + + + align:start position:0% +we can just easily follow the inside if +we already obtained + + align:start position:0% +we already obtained + + + align:start position:0% +we already obtained +from the formula case + + align:start position:0% +from the formula case + + + align:start position:0% +from the formula case +between familiarity case we were told + + align:start position:0% +between familiarity case we were told + + + align:start position:0% +between familiarity case we were told +that this this derivative + + align:start position:0% +that this this derivative + + + align:start position:0% +that this this derivative +this capital D actually transformed + + align:start position:0% +this capital D actually transformed + + + align:start position:0% +this capital D actually transformed +nicely on the side such such + + align:start position:0% +nicely on the side such such + + + align:start position:0% +nicely on the side such such +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +when we make site transformation right + + align:start position:0% +when we make site transformation right + + + align:start position:0% +when we make site transformation right +besides of women or both somewhere it's + + align:start position:0% +besides of women or both somewhere it's + + + align:start position:0% +besides of women or both somewhere it's +a scale of spinner does not play any + + align:start position:0% +a scale of spinner does not play any + + + align:start position:0% +a scale of spinner does not play any +role + + align:start position:0% +role + + + align:start position:0% +role +okay so so we can now just introduce D + + align:start position:0% +okay so so we can now just introduce D + + + align:start position:0% +okay so so we can now just introduce D +Phi + + align:start position:0% + + + + align:start position:0% + +you can just introduce D Phi + + align:start position:0% +you can just introduce D Phi + + + align:start position:0% +you can just introduce D Phi +equal to partial mu Phi + + align:start position:0% +equal to partial mu Phi + + + align:start position:0% +equal to partial mu Phi +minus IE a mu Phi okay we can similarly + + align:start position:0% +minus IE a mu Phi okay we can similarly + + + align:start position:0% +minus IE a mu Phi okay we can similarly +introduce D Phi like this + + align:start position:0% +introduce D Phi like this + + + align:start position:0% +introduce D Phi like this +and now you now Define then transform + + align:start position:0% +and now you now Define then transform + + + align:start position:0% +and now you now Define then transform +nicely under this kind of transformation + + align:start position:0% +nicely under this kind of transformation + + + align:start position:0% +nicely under this kind of transformation +okay so D Phi + + align:start position:0% + + + + align:start position:0% + +okay then transform nicely + + align:start position:0% +okay then transform nicely + + + align:start position:0% +okay then transform nicely +and since this transform nicely and then + + align:start position:0% +and since this transform nicely and then + + + align:start position:0% +and since this transform nicely and then +you can easily write down the LaGrange + + align:start position:0% +you can easily write down the LaGrange + + + align:start position:0% +you can easily write down the LaGrange +okay so so the L + + align:start position:0% +okay so so the L + + + align:start position:0% +okay so so the L +scalar QD + + align:start position:0% +scalar QD + + + align:start position:0% +scalar QD +then can be written as + + align:start position:0% +then can be written as + + + align:start position:0% +then can be written as +minus one quarter F squared + + align:start position:0% +minus one quarter F squared + + + align:start position:0% +minus one quarter F squared +and now + + align:start position:0% +and now + + + align:start position:0% +and now +I + + align:start position:0% +I + + + align:start position:0% +I +instead of the standard derivative + + align:start position:0% +instead of the standard derivative + + + align:start position:0% +instead of the standard derivative +I use this derivative + + align:start position:0% +I use this derivative + + + align:start position:0% +I use this derivative +I use this D derivative capital D + + align:start position:0% +I use this D derivative capital D + + + align:start position:0% +I use this D derivative capital D +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then I have M Square Phi + + align:start position:0% +and then I have M Square Phi + + + align:start position:0% +and then I have M Square Phi +star and the thing I can have five five + + align:start position:0% +star and the thing I can have five five + + + align:start position:0% +star and the thing I can have five five +star + + align:start position:0% +star + + + align:start position:0% +star +okay and so this is will be worried + + align:start position:0% +okay and so this is will be worried + + + align:start position:0% +okay and so this is will be worried +because those don't matter because those + + align:start position:0% +because those don't matter because those + + + align:start position:0% +because those don't matter because those +don't involve in derivatives okay and so + + align:start position:0% +don't involve in derivatives okay and so + + + align:start position:0% +don't involve in derivatives okay and so +yeah + + align:start position:0% + + + + align:start position:0% + +so so this is now getting worried + + align:start position:0% + + + + align:start position:0% + +okay so this D mu + + align:start position:0% + + + + align:start position:0% + +is called covarian derivative okay + + align:start position:0% +is called covarian derivative okay + + + align:start position:0% +is called covarian derivative okay +because it transform nicely + + align:start position:0% +because it transform nicely + + + align:start position:0% +because it transform nicely +under this + + align:start position:0% +under this + + + align:start position:0% +under this +gate transformation so it's called + + align:start position:0% +gate transformation so it's called + + + align:start position:0% +gate transformation so it's called +covariant derivative + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +connection to mathematics + + align:start position:0% +connection to mathematics + + + align:start position:0% +connection to mathematics +and so this is related to a subject + + align:start position:0% +and so this is related to a subject + + + align:start position:0% +and so this is related to a subject +saying differential geometry a deep + + align:start position:0% +saying differential geometry a deep + + + align:start position:0% +saying differential geometry a deep +connection to uh to a sub to to + + align:start position:0% +connection to uh to a sub to to + + + align:start position:0% +connection to uh to a sub to to +differential geometry to a thing in + + align:start position:0% +differential geometry to a thing in + + + align:start position:0% +differential geometry to a thing in +different geometry called connection + + align:start position:0% +different geometry called connection + + + align:start position:0% +different geometry called connection +okay a color connection and yes I will + + align:start position:0% +okay a color connection and yes I will + + + align:start position:0% +okay a color connection and yes I will +not go into that yeah + + align:start position:0% + + + + align:start position:0% + +so so now now let's compare this Theory + + align:start position:0% +so so now now let's compare this Theory + + + align:start position:0% +so so now now let's compare this Theory +with that that naive Theory + + align:start position:0% +with that that naive Theory + + + align:start position:0% +with that that naive Theory +so you can check that L key sqd + + align:start position:0% + + + + align:start position:0% + +is almost that L tilde + + align:start position:0% +is almost that L tilde + + + align:start position:0% +is almost that L tilde +sqd + + align:start position:0% + + + + align:start position:0% + +except this have one more term + + align:start position:0% +except this have one more term + + + align:start position:0% +except this have one more term +so + + align:start position:0% +so + + + align:start position:0% +so +so so the difference + + align:start position:0% +so so the difference + + + align:start position:0% +so so the difference +with the fermian case + + align:start position:0% +with the fermian case + + + align:start position:0% +with the fermian case +the formula only has one derivative + + align:start position:0% +the formula only has one derivative + + + align:start position:0% +the formula only has one derivative +okay and this one does not have + + align:start position:0% +okay and this one does not have + + + align:start position:0% +okay and this one does not have +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +okay and here you have two derivatives + + align:start position:0% +okay and here you have two derivatives + + + align:start position:0% +okay and here you have two derivatives +and each derivative gives you additional + + align:start position:0% +and each derivative gives you additional + + + align:start position:0% +and each derivative gives you additional +a mu + + align:start position:0% +a mu + + + align:start position:0% +a mu +okay so so when you expand this + + align:start position:0% +okay so so when you expand this + + + align:start position:0% +okay so so when you expand this +so here there are four terms + + align:start position:0% +so here there are four terms + + + align:start position:0% +so here there are four terms +okay there are four terms + + align:start position:0% +okay there are four terms + + + align:start position:0% +okay there are four terms +and the three terms are encoded in here + + align:start position:0% + + + + align:start position:0% + +okay three terms are included in here + + align:start position:0% +okay three terms are included in here + + + align:start position:0% +okay three terms are included in here +and here but there's one more term okay + + align:start position:0% +and here but there's one more term okay + + + align:start position:0% +and here but there's one more term okay +it turns out this this one more term + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so actually there's aquatic interaction + + align:start position:0% +so actually there's aquatic interaction + + + align:start position:0% +so actually there's aquatic interaction +between a mu and the five + + align:start position:0% +between a mu and the five + + + align:start position:0% +between a mu and the five +okay so so this only introduce cubic + + align:start position:0% +okay so so this only introduce cubic + + + align:start position:0% +okay so so this only introduce cubic +intaction so if you just have this J mu + + align:start position:0% +intaction so if you just have this J mu + + + align:start position:0% +intaction so if you just have this J mu +a mu you only have cubic induction you + + align:start position:0% +a mu you only have cubic induction you + + + align:start position:0% +a mu you only have cubic induction you +only have two Phi and one a + + align:start position:0% +only have two Phi and one a + + + align:start position:0% +only have two Phi and one a +but but here because of this structure + + align:start position:0% +but but here because of this structure + + + align:start position:0% +but but here because of this structure +you actually have QA also term is 2A and + + align:start position:0% +you actually have QA also term is 2A and + + + align:start position:0% +you actually have QA also term is 2A and +2 5. okay + + align:start position:0% + + + + align:start position:0% + +and when you add this term and then the + + align:start position:0% +and when you add this term and then the + + + align:start position:0% +and when you add this term and then the +whole thing is nice okay + + align:start position:0% + + + + align:start position:0% + +good any questions + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +sorry say it again + + align:start position:0% + + + + align:start position:0% + +because the system by itself not getting + + align:start position:0% +because the system by itself not getting + + + align:start position:0% +because the system by itself not getting +markets + + align:start position:0% +markets + + + align:start position:0% +markets +and families already gauging Market by + + align:start position:0% +and families already gauging Market by + + + align:start position:0% +and families already gauging Market by +itself + + align:start position:0% +itself + + + align:start position:0% +itself +because there's no derivative here and + + align:start position:0% +because there's no derivative here and + + + align:start position:0% +because there's no derivative here and +there's other structure is simple + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah yeah you can you can engineer more + + align:start position:0% +yeah yeah you can you can engineer more + + + align:start position:0% +yeah yeah you can you can engineer more +complicated term but not this kind of + + align:start position:0% +complicated term but not this kind of + + + align:start position:0% +complicated term but not this kind of +term + + align:start position:0% + + + + align:start position:0% + +yeah yeah this is required + + align:start position:0% + + + + align:start position:0% + +yeah you can write down for both fermium + + align:start position:0% +yeah you can write down for both fermium + + + align:start position:0% +yeah you can write down for both fermium +and the scalar case you can write down + + align:start position:0% +and the scalar case you can write down + + + align:start position:0% +and the scalar case you can write down +more complicated terms which are getting + + align:start position:0% +more complicated terms which are getting + + + align:start position:0% +more complicated terms which are getting +variant and uh and the one we wrote down + + align:start position:0% +variant and uh and the one we wrote down + + + align:start position:0% +variant and uh and the one we wrote down +so far just the simplest one + + align:start position:0% +so far just the simplest one + + + align:start position:0% +so far just the simplest one +yeah simplest ways yes + + align:start position:0% + + + + align:start position:0% + +yeah yeah yeah so so so you still + + align:start position:0% +yeah yeah yeah so so so you still + + + align:start position:0% +yeah yeah yeah so so so you still +so when you uh interpret the United + + align:start position:0% +so when you uh interpret the United + + + align:start position:0% +so when you uh interpret the United +current is still this JMU yeah + + align:start position:0% + + + + align:start position:0% + +other questions + + align:start position:0% +other questions + + + align:start position:0% +other questions +okay great + + align:start position:0% +okay great + + + align:start position:0% +okay great +so so now so let me just make a comment + + align:start position:0% +so so now so let me just make a comment + + + align:start position:0% +so so now so let me just make a comment +so in this story + + align:start position:0% +so in this story + + + align:start position:0% +so in this story +not the global charge before okay so now + + align:start position:0% +not the global charge before okay so now + + + align:start position:0% +not the global charge before okay so now +become + + align:start position:0% +become + + + align:start position:0% +become +the uh yeah just emphasize again in the + + align:start position:0% +the uh yeah just emphasize again in the + + + align:start position:0% +the uh yeah just emphasize again in the +scalar case again the the global charge + + align:start position:0% +scalar case again the the global charge + + + align:start position:0% +scalar case again the the global charge +for this global current and now become + + align:start position:0% +for this global current and now become + + + align:start position:0% +for this global current and now become +the the electric charge coupled to the + + align:start position:0% +the the electric charge coupled to the + + + align:start position:0% +the the electric charge coupled to the +electromagnetic fields okay become + + align:start position:0% +electromagnetic fields okay become + + + align:start position:0% +electromagnetic fields okay become +electric charge Capital electromagnetic + + align:start position:0% +electric charge Capital electromagnetic + + + align:start position:0% +electric charge Capital electromagnetic +field okay + + align:start position:0% + + + + align:start position:0% + +okay good so let's draw the uh fireman + + align:start position:0% +okay good so let's draw the uh fireman + + + align:start position:0% +okay good so let's draw the uh fireman +rules okay + + align:start position:0% +rules okay + + + align:start position:0% +rules okay +so from here we can just talk about the + + align:start position:0% +so from here we can just talk about the + + + align:start position:0% +so from here we can just talk about the +fireman rules + + align:start position:0% + + + + align:start position:0% + +so let's first do the formation case + + align:start position:0% +so let's first do the formation case + + + align:start position:0% +so let's first do the formation case +so the rules for fermia is the same as + + align:start position:0% +so the rules for fermia is the same as + + + align:start position:0% +so the rules for fermia is the same as +before the only thing we just need to + + align:start position:0% +before the only thing we just need to + + + align:start position:0% +before the only thing we just need to +write down the uh the propagator for the + + align:start position:0% +write down the uh the propagator for the + + + align:start position:0% +write down the uh the propagator for the +propagators are the same + + align:start position:0% +propagators are the same + + + align:start position:0% +propagators are the same +as previously for for the for the + + align:start position:0% +as previously for for the for the + + + align:start position:0% +as previously for for the for the +Maxwell Theory and for the uh + + align:start position:0% +Maxwell Theory and for the uh + + + align:start position:0% +Maxwell Theory and for the uh +yeah let's first do the QED + + align:start position:0% +yeah let's first do the QED + + + align:start position:0% +yeah let's first do the QED +under the propagator + + align:start position:0% + + + + align:start position:0% + +for a mu + + align:start position:0% +for a mu + + + align:start position:0% +for a mu +and same as before okay + + align:start position:0% +and same as before okay + + + align:start position:0% +and same as before okay +only care about the quadratic Theory I + + align:start position:0% +only care about the quadratic Theory I + + + align:start position:0% +only care about the quadratic Theory I +don't care about interactions same as + + align:start position:0% +don't care about interactions same as + + + align:start position:0% +don't care about interactions same as +before + + align:start position:0% + + + + align:start position:0% + +so we can draw a wavy line corresponding + + align:start position:0% +so we can draw a wavy line corresponding + + + align:start position:0% +so we can draw a wavy line corresponding +to a mu okay and then then the then the + + align:start position:0% +to a mu okay and then then the then the + + + align:start position:0% +to a mu okay and then then the then the +solid line corresponding to say PSI okay + + align:start position:0% +solid line corresponding to say PSI okay + + + align:start position:0% +solid line corresponding to say PSI okay +sorry line goes one into PSI so so this + + align:start position:0% +sorry line goes one into PSI so so this + + + align:start position:0% +sorry line goes one into PSI so so this +is related to AMU propagation this + + align:start position:0% +is related to AMU propagation this + + + align:start position:0% +is related to AMU propagation this +relative side propagation okay + + align:start position:0% + + + + align:start position:0% + +and now the interaction between them + + align:start position:0% +and now the interaction between them + + + align:start position:0% +and now the interaction between them +this interaction between them is given + + align:start position:0% +this interaction between them is given + + + align:start position:0% +this interaction between them is given +by this term + + align:start position:0% + + + + align:start position:0% + +and then these have the structure + + align:start position:0% + + + + align:start position:0% + +you have a one for me and come in + + align:start position:0% +you have a one for me and come in + + + align:start position:0% +you have a one for me and come in +you have two fermions and then couple to + + align:start position:0% +you have two fermions and then couple to + + + align:start position:0% +you have two fermions and then couple to +a photon okay so this is the same very + + align:start position:0% +a photon okay so this is the same very + + + align:start position:0% +a photon okay so this is the same very +similar to this recovery coupling we + + align:start position:0% +similar to this recovery coupling we + + + align:start position:0% +similar to this recovery coupling we +considered before we just now this one + + align:start position:0% +considered before we just now this one + + + align:start position:0% +considered before we just now this one +become a photon + + align:start position:0% +become a photon + + + align:start position:0% +become a photon +okay this one become a photon + + align:start position:0% +okay this one become a photon + + + align:start position:0% +okay this one become a photon +and this effective vertex is given by + + align:start position:0% +and this effective vertex is given by + + + align:start position:0% +and this effective vertex is given by +minus I + + align:start position:0% +minus I + + + align:start position:0% +minus I +E A mu or a gamma mu + + align:start position:0% + + + + align:start position:0% + +Okay so + + align:start position:0% + + + + align:start position:0% + +so matters come from matters here the I + + align:start position:0% +so matters come from matters here the I + + + align:start position:0% +so matters come from matters here the I +come from the eye in the action okay but + + align:start position:0% +come from the eye in the action okay but + + + align:start position:0% +come from the eye in the action okay but +when you do the parts integral action + + align:start position:0% +when you do the parts integral action + + + align:start position:0% +when you do the parts integral action +and you have minus IE and then and then + + align:start position:0% +and you have minus IE and then and then + + + align:start position:0% +and you have minus IE and then and then +side PSI and a mu are taken care of + + align:start position:0% +side PSI and a mu are taken care of + + + align:start position:0% +side PSI and a mu are taken care of +but that's nice and then you only have a + + align:start position:0% +but that's nice and then you only have a + + + align:start position:0% +but that's nice and then you only have a +gamma mu okay + + align:start position:0% +gamma mu okay + + + align:start position:0% +gamma mu okay +so uh so the so the vertex here is the + + align:start position:0% +so uh so the so the vertex here is the + + + align:start position:0% +so uh so the so the vertex here is the +government but pay attention that this + + align:start position:0% +government but pay attention that this + + + align:start position:0% +government but pay attention that this +gamma mu is actually a matrix okay in + + align:start position:0% +gamma mu is actually a matrix okay in + + + align:start position:0% +gamma mu is actually a matrix okay in +the spinner space and so you have to be + + align:start position:0% +the spinner space and so you have to be + + + align:start position:0% +the spinner space and so you have to be +careful when you contract the spindle + + align:start position:0% +careful when you contract the spindle + + + align:start position:0% +careful when you contract the spindle +indices and because now these have spin + + align:start position:0% +indices and because now these have spin + + + align:start position:0% +indices and because now these have spin +indices and it's a matrix okay + + align:start position:0% + + + + align:start position:0% + +good so this is the for the for the + + align:start position:0% +good so this is the for the for the + + + align:start position:0% +good so this is the for the for the +scalar + + align:start position:0% +scalar + + + align:start position:0% +scalar +or for the for the fermium + + align:start position:0% +or for the for the fermium + + + align:start position:0% +or for the for the fermium +and oh yeah so so I should also mention + + align:start position:0% +and oh yeah so so I should also mention + + + align:start position:0% +and oh yeah so so I should also mention +for the external for the external ax + + align:start position:0% + + + + align:start position:0% + +so this is for the um + + align:start position:0% + + + + align:start position:0% + +for the vertices and the propagator + + align:start position:0% + + + + align:start position:0% + +and if we can see the scattering + + align:start position:0% +and if we can see the scattering + + + align:start position:0% +and if we can see the scattering +amplitude + + align:start position:0% + + + + align:start position:0% + +so for skeletal amplitude we mentioned + + align:start position:0% +so for skeletal amplitude we mentioned + + + align:start position:0% +so for skeletal amplitude we mentioned +before for fermium we need to include + + align:start position:0% +before for fermium we need to include + + + align:start position:0% +before for fermium we need to include +the polarization vector + + align:start position:0% +the polarization vector + + + align:start position:0% +the polarization vector +similarly for the photon we also need to + + align:start position:0% +similarly for the photon we also need to + + + align:start position:0% +similarly for the photon we also need to +include the production Vector a + + align:start position:0% +include the production Vector a + + + align:start position:0% +include the production Vector a +partition or a factor + + align:start position:0% +partition or a factor + + + align:start position:0% +partition or a factor +for the external lags okay so so for + + align:start position:0% +for the external lags okay so so for + + + align:start position:0% +for the external lags okay so so for +external Acts + + align:start position:0% + + + + align:start position:0% + +for starting amplitude + + align:start position:0% + + + + align:start position:0% + +so for um + + align:start position:0% +so for um + + + align:start position:0% +so for um +yeah if you calculate the green function + + align:start position:0% +yeah if you calculate the green function + + + align:start position:0% +yeah if you calculate the green function +doesn't matter + + align:start position:0% +doesn't matter + + + align:start position:0% +doesn't matter +you just include external propagator and + + align:start position:0% +you just include external propagator and + + + align:start position:0% +you just include external propagator and +but for the for the scapular amplitude + + align:start position:0% +but for the for the scapular amplitude + + + align:start position:0% +but for the for the scapular amplitude +then we need to include the uh the + + align:start position:0% +then we need to include the uh the + + + align:start position:0% +then we need to include the uh the +polarization Vector for photons + + align:start position:0% +polarization Vector for photons + + + align:start position:0% +polarization Vector for photons +so for the initial state + + align:start position:0% + + + + align:start position:0% + +suppose in the initial State we have say + + align:start position:0% +suppose in the initial State we have say + + + align:start position:0% +suppose in the initial State we have say +some vector k + + align:start position:0% +some vector k + + + align:start position:0% +some vector k +and Alpha so Alpha determines gives this + + align:start position:0% +and Alpha so Alpha determines gives this + + + align:start position:0% +and Alpha so Alpha determines gives this +polarization vector and K is the + + align:start position:0% +polarization vector and K is the + + + align:start position:0% +polarization vector and K is the +momentum + + align:start position:0% +momentum + + + align:start position:0% +momentum +and then we can denote it as + + align:start position:0% +and then we can denote it as + + + align:start position:0% +and then we can denote it as +so Alpha denotes the polarization for + + align:start position:0% +so Alpha denotes the polarization for + + + align:start position:0% +so Alpha denotes the polarization for +the uh and then say we can have a k and + + align:start position:0% +the uh and then say we can have a k and + + + align:start position:0% +the uh and then say we can have a k and +so this is the momentum index so this is + + align:start position:0% +so this is the momentum index so this is + + + align:start position:0% +so this is the momentum index so this is +the momentum Arrow okay + + align:start position:0% +the momentum Arrow okay + + + align:start position:0% +the momentum Arrow okay +and so so this cosine corresponding to + + align:start position:0% + + + + align:start position:0% + +for the initial State then for the final + + align:start position:0% +for the initial State then for the final + + + align:start position:0% +for the initial State then for the final +state + + align:start position:0% + + + + align:start position:0% + +if you have a photon + + align:start position:0% +if you have a photon + + + align:start position:0% +if you have a photon +in the value States + + align:start position:0% +in the value States + + + align:start position:0% +in the value States +like this + + align:start position:0% +like this + + + align:start position:0% +like this +and then again we just have Alpha + + align:start position:0% + + + + align:start position:0% + +and the salomery we show the momentum + + align:start position:0% +and the salomery we show the momentum + + + align:start position:0% +and the salomery we show the momentum +Arrow to come out if you have a final + + align:start position:0% +Arrow to come out if you have a final + + + align:start position:0% +Arrow to come out if you have a final +State and then the polarization Factor + + align:start position:0% +State and then the polarization Factor + + + align:start position:0% +State and then the polarization Factor +will be just this star + + align:start position:0% + + + + align:start position:0% + +just the complex conjugates okay it's + + align:start position:0% +just the complex conjugates okay it's + + + align:start position:0% +just the complex conjugates okay it's +very easy okay + + align:start position:0% +very easy okay + + + align:start position:0% +very easy okay +uh um yeah so so so when you write down + + align:start position:0% +uh um yeah so so so when you write down + + + align:start position:0% +uh um yeah so so so when you write down +the amplitude you just have to be + + align:start position:0% +the amplitude you just have to be + + + align:start position:0% +the amplitude you just have to be +careful uh for the for external Photon + + align:start position:0% +careful uh for the for external Photon + + + align:start position:0% +careful uh for the for external Photon +neck you have to include the + + align:start position:0% +neck you have to include the + + + align:start position:0% +neck you have to include the +polarization vector + + align:start position:0% +polarization vector + + + align:start position:0% +polarization vector +so for scalar QED it's very similar + + align:start position:0% + + + + align:start position:0% + +so here we can introduce + + align:start position:0% +so here we can introduce + + + align:start position:0% +so here we can introduce +a dashed 9 + + align:start position:0% +a dashed 9 + + + align:start position:0% +a dashed 9 +that goes one into a scalar propagator + + align:start position:0% +that goes one into a scalar propagator + + + align:start position:0% +that goes one into a scalar propagator +okay so a corresponding to the scale of + + align:start position:0% +okay so a corresponding to the scale of + + + align:start position:0% +okay so a corresponding to the scale of +propagator okay + + align:start position:0% +propagator okay + + + align:start position:0% +propagator okay +and now this Arrow + + align:start position:0% +and now this Arrow + + + align:start position:0% +and now this Arrow +now has a meaning big big because the + + align:start position:0% +now has a meaning big big because the + + + align:start position:0% +now has a meaning big big because the +scalar has a charge okay a scalar has a + + align:start position:0% +scalar has a charge okay a scalar has a + + + align:start position:0% +scalar has a charge okay a scalar has a +charge + + align:start position:0% +charge + + + align:start position:0% +charge +and so this arrow is not the momentum + + align:start position:0% +and so this arrow is not the momentum + + + align:start position:0% +and so this arrow is not the momentum +Arrow you can do arbitrarily + + align:start position:0% +Arrow you can do arbitrarily + + + align:start position:0% +Arrow you can do arbitrarily +and so so they're so their worries + + align:start position:0% +and so so they're so their worries + + + align:start position:0% +and so so they're so their worries +so and then there's uh uh uh + + align:start position:0% +so and then there's uh uh uh + + + align:start position:0% +so and then there's uh uh uh +yes and then + + align:start position:0% +yes and then + + + align:start position:0% +yes and then +so for QED + + align:start position:0% +so for QED + + + align:start position:0% +so for QED +so let's look at the interaction with + + align:start position:0% +so let's look at the interaction with + + + align:start position:0% +so let's look at the interaction with +the photon and then we have this vertex + + align:start position:0% +the photon and then we have this vertex + + + align:start position:0% +the photon and then we have this vertex +and we also have this vertex + + align:start position:0% +and we also have this vertex + + + align:start position:0% +and we also have this vertex +okay with JMU a cover to that + + align:start position:0% +okay with JMU a cover to that + + + align:start position:0% +okay with JMU a cover to that +okay so so then the then that kind of + + align:start position:0% +okay so so then the then that kind of + + + align:start position:0% +okay so so then the then that kind of +interaction I have the following form so + + align:start position:0% +interaction I have the following form so + + + align:start position:0% +interaction I have the following form so +this JMU coupling is easy + + align:start position:0% +this JMU coupling is easy + + + align:start position:0% +this JMU coupling is easy +we can schematically write it down + + align:start position:0% + + + + align:start position:0% + +so again just you have two Phi + + align:start position:0% +so again just you have two Phi + + + align:start position:0% +so again just you have two Phi +and then couple to a photon okay + + align:start position:0% + + + + align:start position:0% + +Capital photo okay + + align:start position:0% +Capital photo okay + + + align:start position:0% +Capital photo okay +and the and the photon so that vertex so + + align:start position:0% +and the and the photon so that vertex so + + + align:start position:0% +and the and the photon so that vertex so +a mu have index and so we can put the MU + + align:start position:0% +a mu have index and so we can put the MU + + + align:start position:0% +a mu have index and so we can put the MU +here + + align:start position:0% +here + + + align:start position:0% +here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and this vertex is given by minus I + + align:start position:0% + + + + align:start position:0% + +e + + align:start position:0% +e + + + align:start position:0% +e +K plus K Prime mu okay suppose the + + align:start position:0% +K plus K Prime mu okay suppose the + + + align:start position:0% +K plus K Prime mu okay suppose the +momentum here is K and momentum here is + + align:start position:0% +momentum here is K and momentum here is + + + align:start position:0% +momentum here is K and momentum here is +K Prime okay so let's yeah + + align:start position:0% +K Prime okay so let's yeah + + + align:start position:0% +K Prime okay so let's yeah +so the reason you have this K plus K + + align:start position:0% +so the reason you have this K plus K + + + align:start position:0% +so the reason you have this K plus K +Prime mu is because + + align:start position:0% +Prime mu is because + + + align:start position:0% +Prime mu is because +here there's a derivative + + align:start position:0% + + + + align:start position:0% + +actually on Phi and so so this + + align:start position:0% +actually on Phi and so so this + + + align:start position:0% +actually on Phi and so so this +derivative activity on this five gives + + align:start position:0% +derivative activity on this five gives + + + align:start position:0% +derivative activity on this five gives +you a K1 okay and this direction in fact + + align:start position:0% +you a K1 okay and this direction in fact + + + align:start position:0% +you a K1 okay and this direction in fact +give you the K A K Prime okay and and + + align:start position:0% +give you the K A K Prime okay and and + + + align:start position:0% +give you the K A K Prime okay and and +you have the sum of these two terms so + + align:start position:0% +you have the sum of these two terms so + + + align:start position:0% +you have the sum of these two terms so +that's why you have this kind of okay + + align:start position:0% +that's why you have this kind of okay + + + align:start position:0% +that's why you have this kind of okay +for the attack yes + + align:start position:0% + + + + align:start position:0% + +yeah the same + + align:start position:0% +yeah the same + + + align:start position:0% +yeah the same +yeah so for me on uh it external attacks + + align:start position:0% +yeah so for me on uh it external attacks + + + align:start position:0% +yeah so for me on uh it external attacks +the exactly the same as before yeah and + + align:start position:0% +the exactly the same as before yeah and + + + align:start position:0% +the exactly the same as before yeah and +and yeah so we only need to introduce + + align:start position:0% +and yeah so we only need to introduce + + + align:start position:0% +and yeah so we only need to introduce +new rules for photon + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah yeah that rule is exactly the same + + align:start position:0% + + + + align:start position:0% + +that's right that's right yeah so now + + align:start position:0% +that's right that's right yeah so now + + + align:start position:0% +that's right that's right yeah so now +you have just be careful some of the + + align:start position:0% +you have just be careful some of the + + + align:start position:0% +you have just be careful some of the +vertices now including matrices + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah yeah they do yeah yeah for the + + align:start position:0% +yeah yeah they do yeah yeah for the + + + align:start position:0% +yeah yeah they do yeah yeah for the +physical Photon yeah yeah but uh for the + + align:start position:0% +physical Photon yeah yeah but uh for the + + + align:start position:0% +physical Photon yeah yeah but uh for the +physical Photon indeed yeah + + align:start position:0% + + + + align:start position:0% + +oh you can choose it to be complex yeah + + align:start position:0% +oh you can choose it to be complex yeah + + + align:start position:0% +oh you can choose it to be complex yeah +you can for example if you choose a + + align:start position:0% +you can for example if you choose a + + + align:start position:0% +you can for example if you choose a +spherically + + align:start position:0% +spherically + + + align:start position:0% +spherically +a polarization against the complex + + align:start position:0% +a polarization against the complex + + + align:start position:0% +a polarization against the complex +Vector yeah uh for the one we wrote down + + align:start position:0% +Vector yeah uh for the one we wrote down + + + align:start position:0% +Vector yeah uh for the one we wrote down +it's real but then this complex is the + + align:start position:0% +it's real but then this complex is the + + + align:start position:0% +it's real but then this complex is the +same yeah yes + + align:start position:0% + + + + align:start position:0% + +the internal Photon you always just use + + align:start position:0% +the internal Photon you always just use + + + align:start position:0% +the internal Photon you always just use +the internal you just use the photon + + align:start position:0% +the internal you just use the photon + + + align:start position:0% +the internal you just use the photon +propagator + + align:start position:0% +propagator + + + align:start position:0% +propagator +and the photon propagator will include + + align:start position:0% +and the photon propagator will include + + + align:start position:0% +and the photon propagator will include +everything + + align:start position:0% + + + + align:start position:0% + +other questions yes + + align:start position:0% + + + + align:start position:0% + +yeah yeah + + align:start position:0% +yeah yeah + + + align:start position:0% +yeah yeah +you mean the gamma mu + + align:start position:0% +you mean the gamma mu + + + align:start position:0% +you mean the gamma mu +yeah it's just because of spin the + + align:start position:0% +yeah it's just because of spin the + + + align:start position:0% +yeah it's just because of spin the +nature right + + align:start position:0% +nature right + + + align:start position:0% +nature right +okay good + + align:start position:0% +okay good + + + align:start position:0% +okay good +so this vertex so a mu J mu will give + + align:start position:0% +so this vertex so a mu J mu will give + + + align:start position:0% +so this vertex so a mu J mu will give +you this but thanks but we also have + + align:start position:0% +you this but thanks but we also have + + + align:start position:0% +you this but thanks but we also have +with this vertex and this vertex is easy + + align:start position:0% +with this vertex and this vertex is easy + + + align:start position:0% +with this vertex and this vertex is easy +we essentially just have + + align:start position:0% +we essentially just have + + + align:start position:0% +we essentially just have +two fermions or two scalars + + align:start position:0% +two fermions or two scalars + + + align:start position:0% +two fermions or two scalars +but this one + + align:start position:0% +but this one + + + align:start position:0% +but this one +and with two photons okay + + align:start position:0% +and with two photons okay + + + align:start position:0% +and with two photons okay +these two photons + + align:start position:0% +these two photons + + + align:start position:0% +these two photons +and so these have + + align:start position:0% +and so these have + + + align:start position:0% +and so these have +a mu a mu contracted + + align:start position:0% +a mu a mu contracted + + + align:start position:0% +a mu a mu contracted +so if we write mu here + + align:start position:0% +so if we write mu here + + + align:start position:0% +so if we write mu here +and the new here and then we will have + + align:start position:0% +and the new here and then we will have + + + align:start position:0% +and the new here and then we will have +manners okay + + align:start position:0% +manners okay + + + align:start position:0% +manners okay +IE Square + + align:start position:0% +IE Square + + + align:start position:0% +IE Square +is Mu + + align:start position:0% +is Mu + + + align:start position:0% +is Mu +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so so minus I for the same reason and E + + align:start position:0% +so so minus I for the same reason and E + + + align:start position:0% +so so minus I for the same reason and E +squared for the same reason and this a + + align:start position:0% +squared for the same reason and this a + + + align:start position:0% +squared for the same reason and this a +mu contracted so you have a intermediate + + align:start position:0% +mu contracted so you have a intermediate + + + align:start position:0% +mu contracted so you have a intermediate +okay + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% + + + + align:start position:0% + +and the if + + align:start position:0% + + + + align:start position:0% + +depends on what is V here + + align:start position:0% +depends on what is V here + + + align:start position:0% +depends on what is V here +Phi may have some additional interaction + + align:start position:0% +Phi may have some additional interaction + + + align:start position:0% +Phi may have some additional interaction +but suppose V is given by 5 4 + + align:start position:0% +but suppose V is given by 5 4 + + + align:start position:0% +but suppose V is given by 5 4 +okay suppose + + align:start position:0% + + + + align:start position:0% + +suppose V + + align:start position:0% + + + + align:start position:0% + +say c equal to Lambda 4 + + align:start position:0% +say c equal to Lambda 4 + + + align:start position:0% +say c equal to Lambda 4 +and the five five star Square + + align:start position:0% +and the five five star Square + + + align:start position:0% +and the five five star Square +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then + + align:start position:0% +and then + + + align:start position:0% +and then +and then you will also have + + align:start position:0% +and then you will also have + + + align:start position:0% +and then you will also have +interactions like this + + align:start position:0% +interactions like this + + + align:start position:0% +interactions like this +for four scalar interactions + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you have and it's you have two common + + align:start position:0% +you have and it's you have two common + + + align:start position:0% +you have and it's you have two common +two commands Okay + + align:start position:0% + + + + align:start position:0% + +and this will be just minus Island + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +right right come from these terms + + align:start position:0% + + + + align:start position:0% + +come from this term + + align:start position:0% +come from this term + + + align:start position:0% +come from this term +so so this is a mu times J and J have + + align:start position:0% +so so this is a mu times J and J have + + + align:start position:0% +so so this is a mu times J and J have +two fives here + + align:start position:0% + + + + align:start position:0% + +right right + + align:start position:0% + + + + align:start position:0% + +yeah other questions + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah + + align:start position:0% + + + + align:start position:0% + +actually what's the question + + align:start position:0% + + + + align:start position:0% + +no you cannot no because that violates + + align:start position:0% +no you cannot no because that violates + + + align:start position:0% +no you cannot no because that violates +the gauge symmetry yeah yeah so uh so + + align:start position:0% +the gauge symmetry yeah yeah so uh so + + + align:start position:0% +the gauge symmetry yeah yeah so uh so +the cage symmetry is what ensures the + + align:start position:0% +the cage symmetry is what ensures the + + + align:start position:0% +the cage symmetry is what ensures the +photon is mass of this yeah so that's + + align:start position:0% +photon is mass of this yeah so that's + + + align:start position:0% +photon is mass of this yeah so that's +why this is something + + align:start position:0% +why this is something + + + align:start position:0% +why this is something +we don't want to break yeah + + align:start position:0% +we don't want to break yeah + + + align:start position:0% +we don't want to break yeah +other questions + + align:start position:0% + + + + align:start position:0% + +yeah yeah you can combine them just like + + align:start position:0% +yeah yeah you can combine them just like + + + align:start position:0% +yeah yeah you can combine them just like +you have a a theory uh the electric Mark + + align:start position:0% +you have a a theory uh the electric Mark + + + align:start position:0% +you have a a theory uh the electric Mark +that field coupled both to charged + + align:start position:0% +that field coupled both to charged + + + align:start position:0% +that field coupled both to charged +scalar and the charged formulas yeah + + align:start position:0% +scalar and the charged formulas yeah + + + align:start position:0% +scalar and the charged formulas yeah +yeah I can certainly combine them + + align:start position:0% +yeah I can certainly combine them + + + align:start position:0% +yeah I can certainly combine them +uh yeah the reason I'm separating them + + align:start position:0% +uh yeah the reason I'm separating them + + + align:start position:0% +uh yeah the reason I'm separating them +just for convenience yeah + + align:start position:0% + + + + align:start position:0% + +oh you can yeah you can add whatever + + align:start position:0% +oh you can yeah you can add whatever + + + align:start position:0% +oh you can yeah you can add whatever +just every you only have to make sure + + align:start position:0% +just every you only have to make sure + + + align:start position:0% +just every you only have to make sure +things are gate environment + + align:start position:0% +things are gate environment + + + align:start position:0% +things are gate environment +and you can add arbitrary interactions + + align:start position:0% +and you can add arbitrary interactions + + + align:start position:0% +and you can add arbitrary interactions +you want just you have to make sure the + + align:start position:0% +you want just you have to make sure the + + + align:start position:0% +you want just you have to make sure the +environment under those gate + + align:start position:0% +environment under those gate + + + align:start position:0% +environment under those gate +Transformations yeah + + align:start position:0% + + + + align:start position:0% + +with massive frequency + + align:start position:0% +with massive frequency + + + align:start position:0% +with massive frequency +with massive particle a massive photon + + align:start position:0% + + + + align:start position:0% + +no no no you're asking whether the + + align:start position:0% +no no no you're asking whether the + + + align:start position:0% +no no no you're asking whether the +massive Photon copper 2 or um cover to a + + align:start position:0% +massive Photon copper 2 or um cover to a + + + align:start position:0% +massive Photon copper 2 or um cover to a +fermionic field exists + + align:start position:0% +fermionic field exists + + + align:start position:0% +fermionic field exists +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um yeah so + + align:start position:0% +um yeah so + + + align:start position:0% +um yeah so +so this question can be answered in in + + align:start position:0% +so this question can be answered in in + + + align:start position:0% +so this question can be answered in in +several uh uh so so if you just directly + + align:start position:0% +several uh uh so so if you just directly + + + align:start position:0% +several uh uh so so if you just directly +add a mass term + + align:start position:0% +add a mass term + + + align:start position:0% +add a mass term +so let's say let's add the mass term + + align:start position:0% +so let's say let's add the mass term + + + align:start position:0% +so let's say let's add the mass term +for the photon + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this you can immediately + + align:start position:0% +so this you can immediately + + + align:start position:0% +so this you can immediately +check this is not gauge environment so + + align:start position:0% +check this is not gauge environment so + + + align:start position:0% +check this is not gauge environment so +that's the reason we didn't add such a + + align:start position:0% +that's the reason we didn't add such a + + + align:start position:0% +that's the reason we didn't add such a +term to the Maxwell Theory because in + + align:start position:0% +term to the Maxwell Theory because in + + + align:start position:0% +term to the Maxwell Theory because in +the Maxwell series if you add this term + + align:start position:0% +the Maxwell series if you add this term + + + align:start position:0% +the Maxwell series if you add this term +it will violate the gauge symmetry the + + align:start position:0% +it will violate the gauge symmetry the + + + align:start position:0% +it will violate the gauge symmetry the +same reason here so you cannot add such + + align:start position:0% +same reason here so you cannot add such + + + align:start position:0% +same reason here so you cannot add such +a term okay + + align:start position:0% +a term okay + + + align:start position:0% +a term okay +so so you cannot add such a term + + align:start position:0% +so so you cannot add such a term + + + align:start position:0% +so so you cannot add such a term +so this is a root out okay and you + + align:start position:0% +so this is a root out okay and you + + + align:start position:0% +so this is a root out okay and you +cannot add this + + align:start position:0% +cannot add this + + + align:start position:0% +cannot add this +but now you say is it possible + + align:start position:0% +but now you say is it possible + + + align:start position:0% +but now you say is it possible +somehow through some other way that the + + align:start position:0% +somehow through some other way that the + + + align:start position:0% +somehow through some other way that the +photon actually gained Mass + + align:start position:0% +photon actually gained Mass + + + align:start position:0% +photon actually gained Mass +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that's possible + + align:start position:0% +that's possible + + + align:start position:0% +that's possible +that's called the Higgs mechanism that's + + align:start position:0% +that's called the Higgs mechanism that's + + + align:start position:0% +that's called the Higgs mechanism that's +how Hicks got the well priced + + align:start position:0% +how Hicks got the well priced + + + align:start position:0% +how Hicks got the well priced +so and that's come from this term + + align:start position:0% +so and that's come from this term + + + align:start position:0% +so and that's come from this term +so now you imagine somehow this Phi + + align:start position:0% +so now you imagine somehow this Phi + + + align:start position:0% +so now you imagine somehow this Phi +now have a vacuum expectation value + + align:start position:0% +now have a vacuum expectation value + + + align:start position:0% +now have a vacuum expectation value +and now now fire has a constant part + + align:start position:0% +and now now fire has a constant part + + + align:start position:0% +and now now fire has a constant part +if I has a constant part then this + + align:start position:0% +if I has a constant part then this + + + align:start position:0% +if I has a constant part then this +becomes a + + align:start position:0% +becomes a + + + align:start position:0% +becomes a +master + + align:start position:0% +master + + + align:start position:0% +master +for the photon okay and then the photon + + align:start position:0% +for the photon okay and then the photon + + + align:start position:0% +for the photon okay and then the photon +become massive + + align:start position:0% +become massive + + + align:start position:0% +become massive +and actually that's precisely what + + align:start position:0% +and actually that's precisely what + + + align:start position:0% +and actually that's precisely what +happens inside the superconductor + + align:start position:0% +happens inside the superconductor + + + align:start position:0% +happens inside the superconductor +so in every superconductors something + + align:start position:0% +so in every superconductors something + + + align:start position:0% +so in every superconductors something +like this happen + + align:start position:0% +like this happen + + + align:start position:0% +like this happen +okay and and the photon the photon + + align:start position:0% +okay and and the photon the photon + + + align:start position:0% +okay and and the photon the photon +inside the superconductor is massive + + align:start position:0% +inside the superconductor is massive + + + align:start position:0% +inside the superconductor is massive +okay that's a what's responsible for the + + align:start position:0% +okay that's a what's responsible for the + + + align:start position:0% +okay that's a what's responsible for the +for this all rounding effect or a + + align:start position:0% +for this all rounding effect or a + + + align:start position:0% +for this all rounding effect or a +massive effect Etc + + align:start position:0% +massive effect Etc + + + align:start position:0% +massive effect Etc +and and that in the superconductor + + align:start position:0% +and and that in the superconductor + + + align:start position:0% +and and that in the superconductor +that's understood by by Felipe Anderson + + align:start position:0% +that's understood by by Felipe Anderson + + + align:start position:0% +that's understood by by Felipe Anderson +which he uh uh he was + + align:start position:0% +which he uh uh he was + + + align:start position:0% +which he uh uh he was +a little bit unhappy because he thought + + align:start position:0% +a little bit unhappy because he thought + + + align:start position:0% +a little bit unhappy because he thought +he should have claim for the Hicks + + align:start position:0% +he should have claim for the Hicks + + + align:start position:0% +he should have claim for the Hicks +effect + + align:start position:0% +effect + + + align:start position:0% +effect +yeah because he understood it earlier + + align:start position:0% +yeah because he understood it earlier + + + align:start position:0% +yeah because he understood it earlier +and uh yeah but he did understand the + + align:start position:0% +and uh yeah but he did understand the + + + align:start position:0% +and uh yeah but he did understand the +mechanism earlier yeah yeah but Hicks + + align:start position:0% +mechanism earlier yeah yeah but Hicks + + + align:start position:0% +mechanism earlier yeah yeah but Hicks +got a web price because he predicted the + + align:start position:0% +got a web price because he predicted the + + + align:start position:0% +got a web price because he predicted the +particle anyway that's a long story yeah + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +do we give + + align:start position:0% +do we give + + + align:start position:0% +do we give +which factor yeah + + align:start position:0% +which factor yeah + + + align:start position:0% +which factor yeah +you mean we just use the photon + + align:start position:0% +you mean we just use the photon + + + align:start position:0% +you mean we just use the photon +propagator yeah because I don't think + + align:start position:0% +propagator yeah because I don't think + + + align:start position:0% +propagator yeah because I don't think +this is + + align:start position:0% +this is + + + align:start position:0% +this is +yeah yeah at the end of last lecture let + + align:start position:0% +yeah yeah at the end of last lecture let + + + align:start position:0% +yeah yeah at the end of last lecture let +me just write it down so so so the + + align:start position:0% +me just write it down so so so the + + + align:start position:0% +me just write it down so so so the +photon propagator + + align:start position:0% +photon propagator + + + align:start position:0% +photon propagator +so the photon propagator + + align:start position:0% +so the photon propagator + + + align:start position:0% +so the photon propagator +depend on this parameter side + + align:start position:0% +depend on this parameter side + + + align:start position:0% +depend on this parameter side +equal to 1 the photon propagator uh if I + + align:start position:0% +equal to 1 the photon propagator uh if I + + + align:start position:0% +equal to 1 the photon propagator uh if I +call it the MU yeah anyway let me just + + align:start position:0% +call it the MU yeah anyway let me just + + + align:start position:0% +call it the MU yeah anyway let me just +write down fxi equal to one this is just + + align:start position:0% +write down fxi equal to one this is just + + + align:start position:0% +write down fxi equal to one this is just +given by Mita mu mu + + align:start position:0% +given by Mita mu mu + + + align:start position:0% +given by Mita mu mu +K Square minus Epsilon so this Focus I + + align:start position:0% +K Square minus Epsilon so this Focus I + + + align:start position:0% +K Square minus Epsilon so this Focus I +equal to 1. so so so for PSI not equal + + align:start position:0% +equal to 1. so so so for PSI not equal + + + align:start position:0% +equal to 1. so so so for PSI not equal +to 1 uh so yeah so this is focus I equal + + align:start position:0% +to 1 uh so yeah so this is focus I equal + + + align:start position:0% +to 1 uh so yeah so this is focus I equal +to one + + align:start position:0% +to one + + + align:start position:0% +to one +Focus side not equal to one then there + + align:start position:0% +Focus side not equal to one then there + + + align:start position:0% +Focus side not equal to one then there +are some additional terms + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +right + + align:start position:0% + + + + align:start position:0% + +yeah yeah yeah yeah yeah yeah again this + + align:start position:0% +yeah yeah yeah yeah yeah yeah again this + + + align:start position:0% +yeah yeah yeah yeah yeah yeah again this +mechanism is what responsible for the + + align:start position:0% +mechanism is what responsible for the + + + align:start position:0% +mechanism is what responsible for the +weak attacking is short range + + align:start position:0% +weak attacking is short range + + + align:start position:0% +weak attacking is short range +so yeah so the weak interaction started + + align:start position:0% +so yeah so the weak interaction started + + + align:start position:0% +so yeah so the weak interaction started +as mass list particle + + align:start position:0% +as mass list particle + + + align:start position:0% +as mass list particle +but then through the hex mechanism and + + align:start position:0% +but then through the hex mechanism and + + + align:start position:0% +but then through the hex mechanism and +then then the then the analog of a mu + + align:start position:0% +then then the then the analog of a mu + + + align:start position:0% +then then the then the analog of a mu +for the weak interaction become massive + + align:start position:0% +for the weak interaction become massive + + + align:start position:0% +for the weak interaction become massive +and then become short-range yeah yeah + + align:start position:0% +and then become short-range yeah yeah + + + align:start position:0% +and then become short-range yeah yeah +yeah and yeah yeah and yeah + + align:start position:0% +yeah and yeah yeah and yeah + + + align:start position:0% +yeah and yeah yeah and yeah +good other questions + + align:start position:0% +good other questions + + + align:start position:0% +good other questions +yes + + align:start position:0% + + + + align:start position:0% + +um so so in the standard model there's + + align:start position:0% +um so so in the standard model there's + + + align:start position:0% +um so so in the standard model there's +only six is the only scalar field + + align:start position:0% + + + + align:start position:0% + +but you can have some other composite + + align:start position:0% +but you can have some other composite + + + align:start position:0% +but you can have some other composite +scalars like pounds yeah fundamental + + align:start position:0% +scalars like pounds yeah fundamental + + + align:start position:0% +scalars like pounds yeah fundamental +scalars is just the Higgs field + + align:start position:0% +scalars is just the Higgs field + + + align:start position:0% +scalars is just the Higgs field +good + + align:start position:0% +good + + + align:start position:0% +good +okay good so so this uh concludes the + + align:start position:0% +okay good so so this uh concludes the + + + align:start position:0% +okay good so so this uh concludes the +discussion of the QED + + align:start position:0% +discussion of the QED + + + align:start position:0% +discussion of the QED +and now we can now ready just to study + + align:start position:0% +and now we can now ready just to study + + + align:start position:0% +and now we can now ready just to study +the physical processes in QED okay and + + align:start position:0% +the physical processes in QED okay and + + + align:start position:0% +the physical processes in QED okay and +before doing that we need to develop a + + align:start position:0% +before doing that we need to develop a + + + align:start position:0% +before doing that we need to develop a +little bit formalism + + align:start position:0% +little bit formalism + + + align:start position:0% +little bit formalism +uh uh because when we talk about + + align:start position:0% +uh uh because when we talk about + + + align:start position:0% +uh uh because when we talk about +physical processes then we need to make + + align:start position:0% +physical processes then we need to make + + + align:start position:0% +physical processes then we need to make +connection yeah because QED is real life + + align:start position:0% +connection yeah because QED is real life + + + align:start position:0% +connection yeah because QED is real life +okay and then we can uh then we can make + + align:start position:0% +okay and then we can uh then we can make + + + align:start position:0% +okay and then we can uh then we can make +big connection with the real experiments + + align:start position:0% +big connection with the real experiments + + + align:start position:0% +big connection with the real experiments +okay uh to make connection with real + + align:start position:0% +okay uh to make connection with real + + + align:start position:0% +okay uh to make connection with real +experiment we need to develop one more + + align:start position:0% +experiment we need to develop one more + + + align:start position:0% +experiment we need to develop one more +thing + + align:start position:0% +thing + + + align:start position:0% +thing +one more thing + + align:start position:0% +one more thing + + + align:start position:0% +one more thing +so this is the um + + align:start position:0% +so this is the um + + + align:start position:0% +so this is the um +we let you learn how to calculate the + + align:start position:0% +we let you learn how to calculate the + + + align:start position:0% +we let you learn how to calculate the +cross-section + + align:start position:0% + + + + align:start position:0% + +so let's talk about how to calculate + + align:start position:0% +so let's talk about how to calculate + + + align:start position:0% +so let's talk about how to calculate +cross-section so this is a text + + align:start position:0% +cross-section so this is a text + + + align:start position:0% +cross-section so this is a text +regression + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so first let's remind you + + align:start position:0% +so so first let's remind you + + + align:start position:0% +so so first let's remind you +how we calculate how we Define + + align:start position:0% +how we calculate how we Define + + + align:start position:0% +how we calculate how we Define +a cross-action in non-relativity quantum + + align:start position:0% +a cross-action in non-relativity quantum + + + align:start position:0% +a cross-action in non-relativity quantum +mechanics okay in the scattering theory + + align:start position:0% +mechanics okay in the scattering theory + + + align:start position:0% +mechanics okay in the scattering theory +of long-rated with quantum mechanics so + + align:start position:0% +of long-rated with quantum mechanics so + + + align:start position:0% +of long-rated with quantum mechanics so +so in non-related basic quantum + + align:start position:0% +so in non-related basic quantum + + + align:start position:0% +so in non-related basic quantum +mechanics + + align:start position:0% + + + + align:start position:0% + +so you can see that there's a Target + + align:start position:0% + + + + align:start position:0% + +the target is normally considered to be + + align:start position:0% +the target is normally considered to be + + + align:start position:0% +the target is normally considered to be +a point okay here I just make it big so + + align:start position:0% +a point okay here I just make it big so + + + align:start position:0% +a point okay here I just make it big so +that we can see it + + align:start position:0% +that we can see it + + + align:start position:0% +that we can see it +so so here is the target + + align:start position:0% + + + + align:start position:0% + +and then we and then we Define our axis + + align:start position:0% +and then we and then we Define our axis + + + align:start position:0% +and then we and then we Define our axis +the scattering axis which the particle + + align:start position:0% +the scattering axis which the particle + + + align:start position:0% +the scattering axis which the particle +come in + + align:start position:0% +come in + + + align:start position:0% +come in +so this is some incident beam of + + align:start position:0% +so this is some incident beam of + + + align:start position:0% +so this is some incident beam of +particle + + align:start position:0% + + + + align:start position:0% + +okay coming into this direction so say + + align:start position:0% +okay coming into this direction so say + + + align:start position:0% +okay coming into this direction so say +this is a z Direction okay + + align:start position:0% +this is a z Direction okay + + + align:start position:0% +this is a z Direction okay +and uh and the movie in this direction + + align:start position:0% +and uh and the movie in this direction + + + align:start position:0% +and uh and the movie in this direction +to and then then it will interact with + + align:start position:0% +to and then then it will interact with + + + align:start position:0% +to and then then it will interact with +this particle and then we'll scatter + + align:start position:0% +this particle and then we'll scatter + + + align:start position:0% +this particle and then we'll scatter +okay so the particle will scatter and + + align:start position:0% +okay so the particle will scatter and + + + align:start position:0% +okay so the particle will scatter and +then we then we put the detector around + + align:start position:0% +then we then we put the detector around + + + align:start position:0% +then we then we put the detector around +the uh around this uh uh Target particle + + align:start position:0% +the uh around this uh uh Target particle + + + align:start position:0% +the uh around this uh uh Target particle +to decath to detect those scattered + + align:start position:0% +to decath to detect those scattered + + + align:start position:0% +to decath to detect those scattered +particle okay so so for example yeah so + + align:start position:0% +particle okay so so for example yeah so + + + align:start position:0% +particle okay so so for example yeah so +so you should view this uh + + align:start position:0% +so you should view this uh + + + align:start position:0% +so you should view this uh +solid angle here + + align:start position:0% +solid angle here + + + align:start position:0% +solid angle here +okay and so this is the five Direction + + align:start position:0% +okay and so this is the five Direction + + + align:start position:0% +okay and so this is the five Direction +and so so this is the Theta Direction + + align:start position:0% +and so so this is the Theta Direction + + + align:start position:0% +and so so this is the Theta Direction +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so here is the + + align:start position:0% + + + + align:start position:0% + +so so so here is the Theta Direction and + + align:start position:0% +so so so here is the Theta Direction and + + + align:start position:0% +so so so here is the Theta Direction and +this is some small solid angle + + align:start position:0% +this is some small solid angle + + + align:start position:0% +this is some small solid angle +uh uh which is the detector say suppose + + align:start position:0% +uh uh which is the detector say suppose + + + align:start position:0% +uh uh which is the detector say suppose +it's a detector here okay + + align:start position:0% + + + + align:start position:0% + +suppose it is exactly here and then this + + align:start position:0% +suppose it is exactly here and then this + + + align:start position:0% +suppose it is exactly here and then this +detector spread the solid angle + + align:start position:0% +detector spread the solid angle + + + align:start position:0% +detector spread the solid angle +the Omega + + align:start position:0% +the Omega + + + align:start position:0% +the Omega +respect to the Target okay + + align:start position:0% +respect to the Target okay + + + align:start position:0% +respect to the Target okay +so so this is the standard setup for + + align:start position:0% +so so this is the standard setup for + + + align:start position:0% +so so this is the standard setup for +language DV stick for for scattering + + align:start position:0% +language DV stick for for scattering + + + align:start position:0% +language DV stick for for scattering +process in the uh in the + + align:start position:0% +process in the uh in the + + + align:start position:0% +process in the uh in the +non-relativistic mechanics + + align:start position:0% +non-relativistic mechanics + + + align:start position:0% +non-relativistic mechanics +so um so what we measure + + align:start position:0% + + + + align:start position:0% + +what we measure + + align:start position:0% +what we measure + + + align:start position:0% +what we measure +is DN + + align:start position:0% +is DN + + + align:start position:0% +is DN +DT + + align:start position:0% + + + + align:start position:0% + +outgoing particle okay scatter the + + align:start position:0% +outgoing particle okay scatter the + + + align:start position:0% +outgoing particle okay scatter the +particle in the Theta and the five + + align:start position:0% +particle in the Theta and the five + + + align:start position:0% +particle in the Theta and the five +Direction + + align:start position:0% +Direction + + + align:start position:0% +Direction +okay so so so so so this is Theta and + + align:start position:0% +okay so so so so so this is Theta and + + + align:start position:0% +okay so so so so so this is Theta and +the Phi this is where the detector + + align:start position:0% +the Phi this is where the detector + + + align:start position:0% +the Phi this is where the detector +locates okay in the season five + + align:start position:0% +locates okay in the season five + + + align:start position:0% +locates okay in the season five +Direction + + align:start position:0% +Direction + + + align:start position:0% +Direction +so so this is the number + + align:start position:0% + + + + align:start position:0% + +so this dndt is the number of particles + + align:start position:0% + + + + align:start position:0% + +number of scattered particles + + align:start position:0% + + + + align:start position:0% + +number of scientific variable in per + + align:start position:0% +number of scientific variable in per + + + align:start position:0% +number of scientific variable in per +unit time + + align:start position:0% + + + + align:start position:0% + +in the detector + + align:start position:0% + + + + align:start position:0% + +means going registered by the detector + + align:start position:0% +means going registered by the detector + + + align:start position:0% +means going registered by the detector +detective detector at the location + + align:start position:0% + + + + align:start position:0% + +zeta phi okay + + align:start position:0% + + + + align:start position:0% + +so so so so so the question quantity we + + align:start position:0% +so so so so so the question quantity we + + + align:start position:0% +so so so so so the question quantity we +measure is this quantity + + align:start position:0% +measure is this quantity + + + align:start position:0% +measure is this quantity +where we just put the detector there we + + align:start position:0% +where we just put the detector there we + + + align:start position:0% +where we just put the detector there we +just measure particles okay + + align:start position:0% +just measure particles okay + + + align:start position:0% +just measure particles okay +and clearly + + align:start position:0% +and clearly + + + align:start position:0% +and clearly +so so this scene depends on many things + + align:start position:0% +so so this scene depends on many things + + + align:start position:0% +so so this scene depends on many things +okay this quantity depends on many + + align:start position:0% +okay this quantity depends on many + + + align:start position:0% +okay this quantity depends on many +things depending on the interaction + + align:start position:0% +things depending on the interaction + + + align:start position:0% +things depending on the interaction +between the uh between the interaction + + align:start position:0% +between the uh between the interaction + + + align:start position:0% +between the uh between the interaction +between the incident the particle and + + align:start position:0% +between the incident the particle and + + + align:start position:0% +between the incident the particle and +the target Etc + + align:start position:0% +the target Etc + + + align:start position:0% +the target Etc +but it also depends on many other + + align:start position:0% +but it also depends on many other + + + align:start position:0% +but it also depends on many other +kinematic factors okay so for example it + + align:start position:0% +kinematic factors okay so for example it + + + align:start position:0% +kinematic factors okay so for example it +will depend on + + align:start position:0% + + + + align:start position:0% + +this out + + align:start position:0% +this out + + + align:start position:0% +this out +clearly will depend on + + align:start position:0% +clearly will depend on + + + align:start position:0% +clearly will depend on +the uh the number of incident particles + + align:start position:0% + + + + align:start position:0% + +okay so this is the number of incident + + align:start position:0% +okay so this is the number of incident + + + align:start position:0% +okay so this is the number of incident +particle per unit time + + align:start position:0% + + + + align:start position:0% + +if you have more incident particle + + align:start position:0% +if you have more incident particle + + + align:start position:0% +if you have more incident particle +because you will detect more outgoing + + align:start position:0% +because you will detect more outgoing + + + align:start position:0% +because you will detect more outgoing +particle okay + + align:start position:0% +particle okay + + + align:start position:0% +particle okay +and of course this will also + + align:start position:0% +and of course this will also + + + align:start position:0% +and of course this will also +proportional to the Omega the the uh uh + + align:start position:0% +proportional to the Omega the the uh uh + + + align:start position:0% +proportional to the Omega the the uh uh +the the solid angle extended by the + + align:start position:0% +the the solid angle extended by the + + + align:start position:0% +the the solid angle extended by the +detector so if you have a larger + + align:start position:0% +detector so if you have a larger + + + align:start position:0% +detector so if you have a larger +detector of course you will detect more + + align:start position:0% +detector of course you will detect more + + + align:start position:0% +detector of course you will detect more +particles okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +and then we take so if you we divided by + + align:start position:0% +and then we take so if you we divided by + + + align:start position:0% +and then we take so if you we divided by +those kinematic + + align:start position:0% +those kinematic + + + align:start position:0% +those kinematic +obvious kinematic factors away + + align:start position:0% +obvious kinematic factors away + + + align:start position:0% +obvious kinematic factors away +then we will get something more + + align:start position:0% +then we will get something more + + + align:start position:0% +then we will get something more +intrinsic to the interactions okay + + align:start position:0% +intrinsic to the interactions okay + + + align:start position:0% +intrinsic to the interactions okay +so + + align:start position:0% + + + + align:start position:0% + +so we can consider + + align:start position:0% + + + + align:start position:0% + +so we can divide by the Omega and divide + + align:start position:0% +so we can divide by the Omega and divide + + + align:start position:0% +so we can divide by the Omega and divide +it by this scene + + align:start position:0% +it by this scene + + + align:start position:0% +it by this scene +so this object + + align:start position:0% +so this object + + + align:start position:0% +so this object +TN DT + + align:start position:0% +TN DT + + + align:start position:0% +TN DT +then we divide by the Omega per solid + + align:start position:0% +then we divide by the Omega per solid + + + align:start position:0% +then we divide by the Omega per solid +angle out + + align:start position:0% +angle out + + + align:start position:0% +angle out +and if divided by the incident number of + + align:start position:0% +and if divided by the incident number of + + + align:start position:0% +and if divided by the incident number of +particles per unit time + + align:start position:0% +particles per unit time + + + align:start position:0% +particles per unit time +so this should give us + + align:start position:0% +so this should give us + + + align:start position:0% +so this should give us +the probability + + align:start position:0% + + + + align:start position:0% + +of a particle + + align:start position:0% + + + + align:start position:0% + +to be scattered + + align:start position:0% + + + + align:start position:0% + +to see the by Direction + + align:start position:0% + + + + align:start position:0% + +okay so this is the quantity + + align:start position:0% +okay so this is the quantity + + + align:start position:0% +okay so this is the quantity +which captures the effect of the + + align:start position:0% +which captures the effect of the + + + align:start position:0% +which captures the effect of the +interaction + + align:start position:0% +interaction + + + align:start position:0% +interaction +okay so this is a more intrinsic + + align:start position:0% +okay so this is a more intrinsic + + + align:start position:0% +okay so this is a more intrinsic +quantity + + align:start position:0% + + + + align:start position:0% + +but but experimentally this is actually + + align:start position:0% +but but experimentally this is actually + + + align:start position:0% +but but experimentally this is actually +not + + align:start position:0% +not + + + align:start position:0% +not +the thing we directly measure in the + + align:start position:0% +the thing we directly measure in the + + + align:start position:0% +the thing we directly measure in the +experiment but + + align:start position:0% +experiment but + + + align:start position:0% +experiment but +between the experiment it's not easy to + + align:start position:0% +between the experiment it's not easy to + + + align:start position:0% +between the experiment it's not easy to +count the number of the incident + + align:start position:0% +count the number of the incident + + + align:start position:0% +count the number of the incident +particles okay we always consider beam + + align:start position:0% +particles okay we always consider beam + + + align:start position:0% +particles okay we always consider beam +of particles okay we uh + + align:start position:0% +of particles okay we uh + + + align:start position:0% +of particles okay we uh +always consider large number of + + align:start position:0% +always consider large number of + + + align:start position:0% +always consider large number of +particles to be more particles + + align:start position:0% +particles to be more particles + + + align:start position:0% +particles to be more particles +so so experimentally + + align:start position:0% + + + + align:start position:0% + +it's more convenient + + align:start position:0% + + + + align:start position:0% + +we often use is the the incident flux + + align:start position:0% + + + + align:start position:0% + +is the + + align:start position:0% + + + + align:start position:0% + +is a lumbar particle + + align:start position:0% + + + + align:start position:0% + +per unit time and per unit area + + align:start position:0% +per unit time and per unit area + + + align:start position:0% +per unit time and per unit area +okay so we just send the beam and we + + align:start position:0% +okay so we just send the beam and we + + + align:start position:0% +okay so we just send the beam and we +just need to know the density of the + + align:start position:0% +just need to know the density of the + + + align:start position:0% +just need to know the density of the +beam okay so so and so that will give us + + align:start position:0% +beam okay so so and so that will give us + + + align:start position:0% +beam okay so so and so that will give us +the flux okay the number of particles in + + align:start position:0% +the flux okay the number of particles in + + + align:start position:0% +the flux okay the number of particles in +going per unit time and per unit area so + + align:start position:0% +going per unit time and per unit area so + + + align:start position:0% +going per unit time and per unit area so +a is the cross-section of the incident + + align:start position:0% +a is the cross-section of the incident + + + align:start position:0% +a is the cross-section of the incident +beam okay + + align:start position:0% + + + + align:start position:0% + +so now this is the quantity and now we + + align:start position:0% +so now this is the quantity and now we + + + align:start position:0% +so now this is the quantity and now we +have to divide so instead of divided by + + align:start position:0% +have to divide so instead of divided by + + + align:start position:0% +have to divide so instead of divided by +this one we divide by this one okay so + + align:start position:0% +this one we divide by this one okay so + + + align:start position:0% +this one we divide by this one okay so +so now + + align:start position:0% + + + + align:start position:0% + +Omega which + + align:start position:0% +Omega which + + + align:start position:0% +Omega which +is defined to be + + align:start position:0% +is defined to be + + + align:start position:0% +is defined to be +D and + + align:start position:0% +D and + + + align:start position:0% +D and +DT D Omega + + align:start position:0% +DT D Omega + + + align:start position:0% +DT D Omega +out + + align:start position:0% +out + + + align:start position:0% +out +and then you divide it by incident flux + + align:start position:0% +and then you divide it by incident flux + + + align:start position:0% +and then you divide it by incident flux +okay + + align:start position:0% + + + + align:start position:0% + +incident flux per unit time okay + + align:start position:0% +incident flux per unit time okay + + + align:start position:0% +incident flux per unit time okay +so so that's the object we uh we + + align:start position:0% +so so that's the object we uh we + + + align:start position:0% +so so that's the object we uh we +actually mentioned okay + + align:start position:0% +actually mentioned okay + + + align:start position:0% +actually mentioned okay +so this is called the um + + align:start position:0% +so this is called the um + + + align:start position:0% +so this is called the um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so this so some comments on this so the + + align:start position:0% +so this so some comments on this so the + + + align:start position:0% +so this so some comments on this so the +first comment + + align:start position:0% +first comment + + + align:start position:0% +first comment +is that this has dimension of area + + align:start position:0% + + + + align:start position:0% + +so because this thing is dimensionless + + align:start position:0% +so because this thing is dimensionless + + + align:start position:0% +so because this thing is dimensionless +okay this thing is dimension is because + + align:start position:0% +okay this thing is dimension is because + + + align:start position:0% +okay this thing is dimension is because +T canceled but now we have divided by d + + align:start position:0% +T canceled but now we have divided by d + + + align:start position:0% +T canceled but now we have divided by d +a + + align:start position:0% +a + + + align:start position:0% +a +so a going up and then then this has + + align:start position:0% +so a going up and then then this has + + + align:start position:0% +so a going up and then then this has +dimension of area + + align:start position:0% + + + + align:start position:0% + +so the physical meaning of this which + + align:start position:0% +so the physical meaning of this which + + + align:start position:0% +so the physical meaning of this which +I'm sure you learned in your uh in your + + align:start position:0% +I'm sure you learned in your uh in your + + + align:start position:0% +I'm sure you learned in your uh in your +long relativistic quantum mechanics + + align:start position:0% +long relativistic quantum mechanics + + + align:start position:0% +long relativistic quantum mechanics +class + + align:start position:0% +class + + + align:start position:0% +class +you say this gives you + + align:start position:0% + + + + align:start position:0% + +the physical meaning of this + + align:start position:0% +the physical meaning of this + + + align:start position:0% +the physical meaning of this +object so this gives you the effective + + align:start position:0% + + + + align:start position:0% + +area of interaction + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% +so um + + + align:start position:0% +so um +so heuristically you can imagine the + + align:start position:0% +so heuristically you can imagine the + + + align:start position:0% +so heuristically you can imagine the +following + + align:start position:0% +following + + + align:start position:0% +following +so if you imagine the the incident + + align:start position:0% +so if you imagine the the incident + + + align:start position:0% +so if you imagine the the incident +particle + + align:start position:0% +particle + + + align:start position:0% +particle +and this targeted particle they actually + + align:start position:0% +and this targeted particle they actually + + + align:start position:0% +and this targeted particle they actually +have some short range induction okay and + + align:start position:0% +have some short range induction okay and + + + align:start position:0% +have some short range induction okay and +then and the the long intact say say say + + align:start position:0% +then and the the long intact say say say + + + align:start position:0% +then and the the long intact say say say +outside some distance + + align:start position:0% +outside some distance + + + align:start position:0% +outside some distance +and then heuristically and then this + + align:start position:0% +and then heuristically and then this + + + align:start position:0% +and then heuristically and then this +quantities then can be considered + + align:start position:0% +quantities then can be considered + + + align:start position:0% +quantities then can be considered +let's give you the area give you the uh + + align:start position:0% +let's give you the area give you the uh + + + align:start position:0% +let's give you the area give you the uh +the area of interaction + + align:start position:0% +the area of interaction + + + align:start position:0% +the area of interaction +which around this uh uh a Target + + align:start position:0% +which around this uh uh a Target + + + align:start position:0% +which around this uh uh a Target +particle okay + + align:start position:0% +particle okay + + + align:start position:0% +particle okay +to run the target particle so so that's + + align:start position:0% +to run the target particle so so that's + + + align:start position:0% +to run the target particle so so that's +why this D Sigma + + align:start position:0% +why this D Sigma + + + align:start position:0% +why this D Sigma +the Omega is called the differential + + align:start position:0% +the Omega is called the differential + + + align:start position:0% +the Omega is called the differential +cross-action + + align:start position:0% + + + + align:start position:0% + +so the area which going into the + + align:start position:0% +so the area which going into the + + + align:start position:0% +so the area which going into the +direction of Theta Phi + + align:start position:0% +direction of Theta Phi + + + align:start position:0% +direction of Theta Phi +and this Sigma total + + align:start position:0% +and this Sigma total + + + align:start position:0% +and this Sigma total +which defined to be the sigma the Omega + + align:start position:0% +which defined to be the sigma the Omega + + + align:start position:0% +which defined to be the sigma the Omega +U integrated and of all angle + + align:start position:0% +U integrated and of all angle + + + align:start position:0% +U integrated and of all angle +okay so this is a function of C times + + align:start position:0% +okay so this is a function of C times + + + align:start position:0% +okay so this is a function of C times +Phi + + align:start position:0% +Phi + + + align:start position:0% +Phi +and now you integrate over all solid + + align:start position:0% +and now you integrate over all solid + + + align:start position:0% +and now you integrate over all solid +angle and then that gives you the total + + align:start position:0% +angle and then that gives you the total + + + align:start position:0% +angle and then that gives you the total +cross-section + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +this effective area of induction + + align:start position:0% +this effective area of induction + + + align:start position:0% +this effective area of induction +can be seen the very simple uh classical + + align:start position:0% +can be seen the very simple uh classical + + + align:start position:0% +can be seen the very simple uh classical +example + + align:start position:0% +example + + + align:start position:0% +example +so this definition actually is not + + align:start position:0% +so this definition actually is not + + + align:start position:0% +so this definition actually is not +quantum mechanical you can also do it + + align:start position:0% +quantum mechanical you can also do it + + + align:start position:0% +quantum mechanical you can also do it +classically okay it's not restricted to + + align:start position:0% +classically okay it's not restricted to + + + align:start position:0% +classically okay it's not restricted to +Quantum Mechanics this can be defined + + align:start position:0% +Quantum Mechanics this can be defined + + + align:start position:0% +Quantum Mechanics this can be defined +for any scattering event including in In + + align:start position:0% +for any scattering event including in In + + + align:start position:0% +for any scattering event including in In +classical mechanics + + align:start position:0% + + + + align:start position:0% + +so for example + + align:start position:0% +so for example + + + align:start position:0% +so for example +if you have classical scattering + + align:start position:0% + + + + align:start position:0% + +say of some + + align:start position:0% +say of some + + + align:start position:0% +say of some +bullets okay or for beneath ball + + align:start position:0% + + + + align:start position:0% + +and then you find the secret total + + align:start position:0% +and then you find the secret total + + + align:start position:0% +and then you find the secret total +so suppose you have classical + + align:start position:0% +so suppose you have classical + + + align:start position:0% +so suppose you have classical +scattering okay and then you find the + + align:start position:0% +scattering okay and then you find the + + + align:start position:0% +scattering okay and then you find the +sigma total + + align:start position:0% +sigma total + + + align:start position:0% +sigma total +you just the cross section just the the + + align:start position:0% +you just the cross section just the the + + + align:start position:0% +you just the cross section just the the +total area + + align:start position:0% +total area + + + align:start position:0% +total area +total surface area + + align:start position:0% + + + + align:start position:0% + +the cross-section area + + align:start position:0% + + + + align:start position:0% + +of the Billiards okay + + align:start position:0% + + + + align:start position:0% + +because classically + + align:start position:0% +because classically + + + align:start position:0% +because classically +when you hit the video board and hit the + + align:start position:0% +when you hit the video board and hit the + + + align:start position:0% +when you hit the video board and hit the +video okay if you don't hit the video + + align:start position:0% +video okay if you don't hit the video + + + align:start position:0% +video okay if you don't hit the video +board then then you don't change the + + align:start position:0% +board then then you don't change the + + + align:start position:0% +board then then you don't change the +direction + + align:start position:0% +direction + + + align:start position:0% +direction +and then and then the total grossacking + + align:start position:0% +and then and then the total grossacking + + + align:start position:0% +and then and then the total grossacking +just the cross action of the billion + + align:start position:0% +just the cross action of the billion + + + align:start position:0% +just the cross action of the billion +pool + + align:start position:0% +pool + + + align:start position:0% +pool +okay + + align:start position:0% + + + + align:start position:0% + +so so when you go to Quantum + + align:start position:0% +so so when you go to Quantum + + + align:start position:0% +so so when you go to Quantum +Theory and then this is the heuristic + + align:start position:0% +Theory and then this is the heuristic + + + align:start position:0% +Theory and then this is the heuristic +way you understand that some kind + + align:start position:0% +way you understand that some kind + + + align:start position:0% +way you understand that some kind +effective a cross-action + + align:start position:0% +effective a cross-action + + + align:start position:0% +effective a cross-action +for for this target okay and the outside + + align:start position:0% +for for this target okay and the outside + + + align:start position:0% +for for this target okay and the outside +that + + align:start position:0% +that + + + align:start position:0% +that +area then then you no longer have intact + + align:start position:0% +area then then you no longer have intact + + + align:start position:0% +area then then you no longer have intact +yeah ecuristically no longer have + + align:start position:0% +yeah ecuristically no longer have + + + align:start position:0% +yeah ecuristically no longer have +interactions + + align:start position:0% +interactions + + + align:start position:0% +interactions +okay so so so now let me just make two + + align:start position:0% +okay so so so now let me just make two + + + align:start position:0% +okay so so so now let me just make two +quick remark in a relativistic theory + + align:start position:0% + + + + align:start position:0% + +so now we can generalize + + align:start position:0% +so now we can generalize + + + align:start position:0% +so now we can generalize +so this discussion is in the long + + align:start position:0% +so this discussion is in the long + + + align:start position:0% +so this discussion is in the long +relative BC context + + align:start position:0% +relative BC context + + + align:start position:0% +relative BC context +so in the right basic context we + + align:start position:0% +so in the right basic context we + + + align:start position:0% +so in the right basic context we +essentially just have D Sigma + + align:start position:0% +essentially just have D Sigma + + + align:start position:0% +essentially just have D Sigma +cross action + + align:start position:0% +cross action + + + align:start position:0% +cross action +okay from the initial state to final + + align:start position:0% +okay from the initial state to final + + + align:start position:0% +okay from the initial state to final +state + + align:start position:0% +state + + + align:start position:0% +state +okay we no longer have so this is very + + align:start position:0% +okay we no longer have so this is very + + + align:start position:0% +okay we no longer have so this is very +specific we have one particle + + align:start position:0% +specific we have one particle + + + align:start position:0% +specific we have one particle +sketch on the other particle and you + + align:start position:0% +sketch on the other particle and you + + + align:start position:0% +sketch on the other particle and you +this particle scattered away okay + + align:start position:0% +this particle scattered away okay + + + align:start position:0% +this particle scattered away okay +but in but in writeristic you can have + + align:start position:0% +but in but in writeristic you can have + + + align:start position:0% +but in but in writeristic you can have +two particles you can create ten + + align:start position:0% +two particles you can create ten + + + align:start position:0% +two particles you can create ten +thousand particles okay and so this + + align:start position:0% +thousand particles okay and so this + + + align:start position:0% +thousand particles okay and so this +language no longer works okay + + align:start position:0% +language no longer works okay + + + align:start position:0% +language no longer works okay +so so but still you can Define some kind + + align:start position:0% +so so but still you can Define some kind + + + align:start position:0% +so so but still you can Define some kind +of cross-section of initial State Alpha + + align:start position:0% +of cross-section of initial State Alpha + + + align:start position:0% +of cross-section of initial State Alpha +to some final State beta okay + + align:start position:0% +to some final State beta okay + + + align:start position:0% +to some final State beta okay +and so we will be interested in the + + align:start position:0% +and so we will be interested in the + + + align:start position:0% +and so we will be interested in the +in the situation which we have two + + align:start position:0% +in the situation which we have two + + + align:start position:0% +in the situation which we have two +initial particles okay because we uh uh + + align:start position:0% +initial particles okay because we uh uh + + + align:start position:0% +initial particles okay because we uh uh +yeah because experimentally it's + + align:start position:0% +yeah because experimentally it's + + + align:start position:0% +yeah because experimentally it's +convenient just to have two particles + + align:start position:0% +convenient just to have two particles + + + align:start position:0% +convenient just to have two particles +scattering so you have two initial + + align:start position:0% +scattering so you have two initial + + + align:start position:0% +scattering so you have two initial +particles but follow State you can + + align:start position:0% +particles but follow State you can + + + align:start position:0% +particles but follow State you can +be in principle can be arbitrary okay + + align:start position:0% + + + + align:start position:0% + +and the so + + align:start position:0% +and the so + + + align:start position:0% +and the so +so this object + + align:start position:0% +so this object + + + align:start position:0% +so this object +since in the rest of Mystic series it + + align:start position:0% +since in the rest of Mystic series it + + + align:start position:0% +since in the rest of Mystic series it +should be physically observable + + align:start position:0% +should be physically observable + + + align:start position:0% +should be physically observable +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so this should be um + + align:start position:0% +and so this should be um + + + align:start position:0% +and so this should be um +so because this essentially as much of + + align:start position:0% +so because this essentially as much of + + + align:start position:0% +so because this essentially as much of +the probability of the scattering + + align:start position:0% +the probability of the scattering + + + align:start position:0% +the probability of the scattering +so we require this object to be + + align:start position:0% + + + + align:start position:0% + +no renting warrant + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and the symmet + + align:start position:0% +and the symmet + + + align:start position:0% +and the symmet +and also in the relativity you just get + + align:start position:0% +and also in the relativity you just get + + + align:start position:0% +and also in the relativity you just get +the two particles they should + + align:start position:0% +the two particles they should + + + align:start position:0% +the two particles they should +there's no launching of what's the + + align:start position:0% +there's no launching of what's the + + + align:start position:0% +there's no launching of what's the +Target or what is the incident particle + + align:start position:0% +Target or what is the incident particle + + + align:start position:0% +Target or what is the incident particle +so these two particles should have equal + + align:start position:0% +so these two particles should have equal + + + align:start position:0% +so these two particles should have equal +row so this should be symmetric + + align:start position:0% + + + + align:start position:0% + +in one Cube okay + + align:start position:0% +in one Cube okay + + + align:start position:0% +in one Cube okay +so if you exchange one two this cross + + align:start position:0% +so if you exchange one two this cross + + + align:start position:0% +so if you exchange one two this cross +action should be the same + + align:start position:0% +action should be the same + + + align:start position:0% +action should be the same +okay should be the same + + align:start position:0% + + + + align:start position:0% + +so so now if you consider but you can + + align:start position:0% +so so now if you consider but you can + + + align:start position:0% +so so now if you consider but you can +always consider in the rest frame say of + + align:start position:0% +always consider in the rest frame say of + + + align:start position:0% +always consider in the rest frame say of +particle two okay so suppose + + align:start position:0% + + + + align:start position:0% + +we can see that the rest frame + + align:start position:0% + + + + align:start position:0% + +suppose we go into the rest frame of + + align:start position:0% +suppose we go into the rest frame of + + + align:start position:0% +suppose we go into the rest frame of +particle 2 + + align:start position:0% + + + + align:start position:0% + +and then then we roughly have this + + align:start position:0% +and then then we roughly have this + + + align:start position:0% +and then then we roughly have this +situation + + align:start position:0% +situation + + + align:start position:0% +situation +okay so so this is particle two this is + + align:start position:0% +okay so so this is particle two this is + + + align:start position:0% +okay so so this is particle two this is +particle one we come to particle two + + align:start position:0% +particle one we come to particle two + + + align:start position:0% +particle one we come to particle two +and then we should have the uh and then + + align:start position:0% +and then we should have the uh and then + + + align:start position:0% +and then we should have the uh and then +we can again and then in this situation + + align:start position:0% +we can again and then in this situation + + + align:start position:0% +we can again and then in this situation +we can Define the alpha to Beta + + align:start position:0% +we can Define the alpha to Beta + + + align:start position:0% +we can Define the alpha to Beta +based on our language considerations and + + align:start position:0% +based on our language considerations and + + + align:start position:0% +based on our language considerations and +then we consider + + align:start position:0% +then we consider + + + align:start position:0% +then we consider +so here I use the + + align:start position:0% +so here I use the + + + align:start position:0% +so here I use the +probability + + align:start position:0% +probability + + + align:start position:0% +probability +from alpha to Beta DT + + align:start position:0% + + + + align:start position:0% + +okay so this is the essentially replace + + align:start position:0% +okay so this is the essentially replace + + + align:start position:0% +okay so this is the essentially replace +that + + align:start position:0% +that + + + align:start position:0% +that +okay here the final particle only have + + align:start position:0% +okay here the final particle only have + + + align:start position:0% +okay here the final particle only have +one particle so so you can Define sorry + + align:start position:0% +one particle so so you can Define sorry + + + align:start position:0% +one particle so so you can Define sorry +the angle + + align:start position:0% +the angle + + + align:start position:0% +the angle +but if we have but if we have ten + + align:start position:0% +but if we have but if we have ten + + + align:start position:0% +but if we have but if we have ten +thousand particles here + + align:start position:0% +thousand particles here + + + align:start position:0% +thousand particles here +in the beta of course I cannot Define a + + align:start position:0% +in the beta of course I cannot Define a + + + align:start position:0% +in the beta of course I cannot Define a +solid angle okay so so I can just talk + + align:start position:0% +solid angle okay so so I can just talk + + + align:start position:0% +solid angle okay so so I can just talk +about probability from alpha to Beta + + align:start position:0% +about probability from alpha to Beta + + + align:start position:0% +about probability from alpha to Beta +okay + + align:start position:0% +okay + + + align:start position:0% +okay +from alpha to Beta and about previous + + align:start position:0% +from alpha to Beta and about previous + + + align:start position:0% +from alpha to Beta and about previous +time and then again we divide it by + + align:start position:0% +time and then again we divide it by + + + align:start position:0% +time and then again we divide it by +the incident flux of one + + align:start position:0% + + + + align:start position:0% + +okay the incident flux of one okay + + align:start position:0% +okay the incident flux of one okay + + + align:start position:0% +okay the incident flux of one okay +let me just call it in + + align:start position:0% +let me just call it in + + + align:start position:0% +let me just call it in +so NY means the flag the lumbar particle + + align:start position:0% +so NY means the flag the lumbar particle + + + align:start position:0% +so NY means the flag the lumbar particle +of one okay + + align:start position:0% +of one okay + + + align:start position:0% +of one okay +so so + + align:start position:0% +so so + + + align:start position:0% +so so +um + + align:start position:0% +um + + + align:start position:0% +um +yeah so + + align:start position:0% +yeah so + + + align:start position:0% +yeah so +so what we will do + + align:start position:0% +so what we will do + + + align:start position:0% +so what we will do +is that we will first calculate this + + align:start position:0% +is that we will first calculate this + + + align:start position:0% +is that we will first calculate this +object + + align:start position:0% +object + + + align:start position:0% +object +in the rice frame of Q + + align:start position:0% +in the rice frame of Q + + + align:start position:0% +in the rice frame of Q +and then we + + align:start position:0% +and then we + + + align:start position:0% +and then we +and then we construct the low renting + + align:start position:0% +and then we construct the low renting + + + align:start position:0% +and then we construct the low renting +bar in the version of this okay so + + align:start position:0% +bar in the version of this okay so + + + align:start position:0% +bar in the version of this okay so +that's our strategy to uh to Define what + + align:start position:0% +that's our strategy to uh to Define what + + + align:start position:0% +that's our strategy to uh to Define what +will be the right basic and addition of + + align:start position:0% +will be the right basic and addition of + + + align:start position:0% +will be the right basic and addition of +this okay so we will talk we will + + align:start position:0% +this okay so we will talk we will + + + align:start position:0% +this okay so we will talk we will +discuss this next time \ No newline at end of file diff --git a/O0Tw47okZJM.txt b/O0Tw47okZJM.txt new file mode 100644 index 0000000000000000000000000000000000000000..a442fe1b125714029b140759c5eda3a62deaa2c5 --- /dev/null +++ b/O0Tw47okZJM.txt @@ -0,0 +1,10683 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +okay so we're going to continue with our + + align:start position:0% +okay so we're going to continue with our + + + align:start position:0% +okay so we're going to continue with our +discussion of + + align:start position:0% + + + + align:start position:0% + +the spectrum of an operator bounded + + align:start position:0% +the spectrum of an operator bounded + + + align:start position:0% +the spectrum of an operator bounded +linear operator so let me just + + align:start position:0% +linear operator so let me just + + + align:start position:0% +linear operator so let me just +recall from last time the definition + + align:start position:0% +recall from last time the definition + + + align:start position:0% +recall from last time the definition +that if a + + align:start position:0% +that if a + + + align:start position:0% +that if a +and throughout H is a Hilbert space if a + + align:start position:0% +and throughout H is a Hilbert space if a + + + align:start position:0% +and throughout H is a Hilbert space if a +is in a bounded linear operator then + + align:start position:0% +is in a bounded linear operator then + + + align:start position:0% +is in a bounded linear operator then +the resolvent set of a is the set of all + + align:start position:0% +the resolvent set of a is the set of all + + + align:start position:0% +the resolvent set of a is the set of all +lambdas and complex numbers such that a + + align:start position:0% +lambdas and complex numbers such that a + + + align:start position:0% +lambdas and complex numbers such that a +minus Lambda times the identity which I + + align:start position:0% +minus Lambda times the identity which I + + + align:start position:0% +minus Lambda times the identity which I +write as a minus Lambda + + align:start position:0% +write as a minus Lambda + + + align:start position:0% +write as a minus Lambda +is + + align:start position:0% +is + + + align:start position:0% +is +bijective meaning it's one to one and + + align:start position:0% +bijective meaning it's one to one and + + + align:start position:0% +bijective meaning it's one to one and +onto which implies by the open mapping + + align:start position:0% +onto which implies by the open mapping + + + align:start position:0% +onto which implies by the open mapping +theorem that it has a bounded inverse + + align:start position:0% +theorem that it has a bounded inverse + + + align:start position:0% +theorem that it has a bounded inverse +or is equivalent to it having a bounded + + align:start position:0% +or is equivalent to it having a bounded + + + align:start position:0% +or is equivalent to it having a bounded +inverse and the Spectrum + + align:start position:0% +inverse and the Spectrum + + + align:start position:0% +inverse and the Spectrum +of a was + + align:start position:0% + + + + align:start position:0% + +the complement of the resolvent set + + align:start position:0% +the complement of the resolvent set + + + align:start position:0% +the complement of the resolvent set +within the set of complex numbers + + align:start position:0% + + + + align:start position:0% + +and so the spectrum is supposed to be a + + align:start position:0% +and so the spectrum is supposed to be a + + + align:start position:0% +and so the spectrum is supposed to be a +generalization of + + align:start position:0% +generalization of + + + align:start position:0% +generalization of +in finite Dimensions what were called + + align:start position:0% +in finite Dimensions what were called + + + align:start position:0% +in finite Dimensions what were called +the eigenvalues so + + align:start position:0% +the eigenvalues so + + + align:start position:0% +the eigenvalues so +um + + align:start position:0% + + + + align:start position:0% + +and uh so we just + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +call we called Lambda an element of the + + align:start position:0% +call we called Lambda an element of the + + + align:start position:0% +call we called Lambda an element of the +spectrum an eigenvalue + + align:start position:0% + + + + align:start position:0% + +if there exists + + align:start position:0% +if there exists + + + align:start position:0% +if there exists +a u not equal to zero + + align:start position:0% +a u not equal to zero + + + align:start position:0% +a u not equal to zero +such that + + align:start position:0% +such that + + + align:start position:0% +such that +a minus Lambda + + align:start position:0% +a minus Lambda + + + align:start position:0% +a minus Lambda +applied to U is zero in other words a + + align:start position:0% +applied to U is zero in other words a + + + align:start position:0% +applied to U is zero in other words a +minus Lambda is not injective so the + + align:start position:0% +minus Lambda is not injective so the + + + align:start position:0% +minus Lambda is not injective so the +reason for Lambda being in the spectrum + + align:start position:0% +reason for Lambda being in the spectrum + + + align:start position:0% +reason for Lambda being in the spectrum +is that so for uh + + align:start position:0% +is that so for uh + + + align:start position:0% +is that so for uh +a number to be called an eigenvalue is + + align:start position:0% +a number to be called an eigenvalue is + + + align:start position:0% +a number to be called an eigenvalue is +that this operator a minus Lambda has + + align:start position:0% +that this operator a minus Lambda has + + + align:start position:0% +that this operator a minus Lambda has +non-trivial null space in other words + + align:start position:0% +non-trivial null space in other words + + + align:start position:0% +non-trivial null space in other words +there's an it has a + + align:start position:0% +there's an it has a + + + align:start position:0% +there's an it has a +non-zero U so that a u equals Lambda U + + align:start position:0% +non-zero U so that a u equals Lambda U + + + align:start position:0% +non-zero U so that a u equals Lambda U +and we call this uh + + align:start position:0% +and we call this uh + + + align:start position:0% +and we call this uh +thing + + align:start position:0% +thing + + + align:start position:0% +thing +an eigenvector + + align:start position:0% + + + + align:start position:0% + +okay and we saw last time examples of + + align:start position:0% +okay and we saw last time examples of + + + align:start position:0% +okay and we saw last time examples of +an operator that has infinitely many + + align:start position:0% +an operator that has infinitely many + + + align:start position:0% +an operator that has infinitely many +eigenvalues and eigenvectors and also an + + align:start position:0% +eigenvalues and eigenvectors and also an + + + align:start position:0% +eigenvalues and eigenvectors and also an +example of a bounded linear operator + + align:start position:0% +example of a bounded linear operator + + + align:start position:0% +example of a bounded linear operator +which has no eigenvalues and + + align:start position:0% +which has no eigenvalues and + + + align:start position:0% +which has no eigenvalues and +eigenvectors unlike in the case in + + align:start position:0% +eigenvectors unlike in the case in + + + align:start position:0% +eigenvectors unlike in the case in +finite Dimensions where the spectrum is + + align:start position:0% +finite Dimensions where the spectrum is + + + align:start position:0% +finite Dimensions where the spectrum is +exactly the set of eigenvalues of an + + align:start position:0% +exactly the set of eigenvalues of an + + + align:start position:0% +exactly the set of eigenvalues of an +operator + + align:start position:0% +operator + + + align:start position:0% +operator +um oh + + align:start position:0% +um oh + + + align:start position:0% +um oh +now + + align:start position:0% +now + + + align:start position:0% +now +and we also approved at the end of last + + align:start position:0% +and we also approved at the end of last + + + align:start position:0% +and we also approved at the end of last +time so what we could say about these + + align:start position:0% +time so what we could say about these + + + align:start position:0% +time so what we could say about these +two sets or what we could say about the + + align:start position:0% +two sets or what we could say about the + + + align:start position:0% +two sets or what we could say about the +spectrum is that it's a closed set and + + align:start position:0% +spectrum is that it's a closed set and + + + align:start position:0% +spectrum is that it's a closed set and +it's contained within uh the ball of + + align:start position:0% +it's contained within uh the ball of + + + align:start position:0% +it's contained within uh the ball of +radius Norm a and the complex numbers + + align:start position:0% +radius Norm a and the complex numbers + + + align:start position:0% +radius Norm a and the complex numbers +okay + + align:start position:0% +okay + + + align:start position:0% +okay +which means it's a compact set + + align:start position:0% +which means it's a compact set + + + align:start position:0% +which means it's a compact set +and what we could say by taking + + align:start position:0% +and what we could say by taking + + + align:start position:0% +and what we could say by taking +compliments about the resolvent set is + + align:start position:0% +compliments about the resolvent set is + + + align:start position:0% +compliments about the resolvent set is +that it's an open set that contains the + + align:start position:0% +that it's an open set that contains the + + + align:start position:0% +that it's an open set that contains the +exterior to a ball of radius Norm of a + + align:start position:0% +exterior to a ball of radius Norm of a + + + align:start position:0% +exterior to a ball of radius Norm of a +in the complex numbers + + align:start position:0% +in the complex numbers + + + align:start position:0% +in the complex numbers +and that's about all we can say about uh + + align:start position:0% +and that's about all we can say about uh + + + align:start position:0% +and that's about all we can say about uh +the Spectrum in general for now + + align:start position:0% +the Spectrum in general for now + + + align:start position:0% +the Spectrum in general for now +but we can say some quite a lot about + + align:start position:0% +but we can say some quite a lot about + + + align:start position:0% +but we can say some quite a lot about +the spectrum of uh self-adjoin operators + + align:start position:0% +the spectrum of uh self-adjoin operators + + + align:start position:0% +the spectrum of uh self-adjoin operators +and then we can say + + align:start position:0% +and then we can say + + + align:start position:0% +and then we can say +give a pretty complete picture about the + + align:start position:0% +give a pretty complete picture about the + + + align:start position:0% +give a pretty complete picture about the +Spectrum for compact Opera self-adjoined + + align:start position:0% +Spectrum for compact Opera self-adjoined + + + align:start position:0% +Spectrum for compact Opera self-adjoined +compact operators uh but let's first + + align:start position:0% +compact operators uh but let's first + + + align:start position:0% +compact operators uh but let's first +look at self a joint operators so at the + + align:start position:0% +look at self a joint operators so at the + + + align:start position:0% +look at self a joint operators so at the +end of last time + + align:start position:0% + + + + align:start position:0% + +proved that if I have a self a joint and + + align:start position:0% +proved that if I have a self a joint and + + + align:start position:0% +proved that if I have a self a joint and +this is not related to the Spectrum if I + + align:start position:0% +this is not related to the Spectrum if I + + + align:start position:0% +this is not related to the Spectrum if I +have a self-adjoint bounded linear + + align:start position:0% +have a self-adjoint bounded linear + + + align:start position:0% +have a self-adjoint bounded linear +operator on the Hilbert space then for + + align:start position:0% +operator on the Hilbert space then for + + + align:start position:0% +operator on the Hilbert space then for +all you + + align:start position:0% +all you + + + align:start position:0% +all you +a u u + + align:start position:0% +a u u + + + align:start position:0% +a u u +is a real number + + align:start position:0% +is a real number + + + align:start position:0% +is a real number +and + + align:start position:0% +and + + + align:start position:0% +and +we could + + align:start position:0% +we could + + + align:start position:0% +we could +write the norm of a as + + align:start position:0% +write the norm of a as + + + align:start position:0% +write the norm of a as +this quantity soup U equals one of the + + align:start position:0% +this quantity soup U equals one of the + + + align:start position:0% +this quantity soup U equals one of the +absolute value of a u inner product U + + align:start position:0% +absolute value of a u inner product U + + + align:start position:0% +absolute value of a u inner product U +okay + + align:start position:0% + + + + align:start position:0% + +all right so um + + align:start position:0% + + + + align:start position:0% + +now we have the following theorem about + + align:start position:0% +now we have the following theorem about + + + align:start position:0% +now we have the following theorem about +the Spectrum for uh sulf a joint bounded + + align:start position:0% +the Spectrum for uh sulf a joint bounded + + + align:start position:0% +the Spectrum for uh sulf a joint bounded +linear operators + + align:start position:0% +linear operators + + + align:start position:0% +linear operators +on a Hilbert space + + align:start position:0% + + + + align:start position:0% + +so the first is that uh + + align:start position:0% +so the first is that uh + + + align:start position:0% +so the first is that uh +the spectrum is contained in the real + + align:start position:0% +the spectrum is contained in the real + + + align:start position:0% +the spectrum is contained in the real +number line so + + align:start position:0% +number line so + + + align:start position:0% +number line so +um + + align:start position:0% + + + + align:start position:0% + +spectrum of a is contained in the real + + align:start position:0% +spectrum of a is contained in the real + + + align:start position:0% +spectrum of a is contained in the real +number line + + align:start position:0% +number line + + + align:start position:0% +number line +on a + + align:start position:0% +on a + + + align:start position:0% +on a +or in this interval Norm a minus Norm a + + align:start position:0% +or in this interval Norm a minus Norm a + + + align:start position:0% +or in this interval Norm a minus Norm a +to Norm a uh + + align:start position:0% +to Norm a uh + + + align:start position:0% +to Norm a uh +which I'm viewing as a subset of the + + align:start position:0% +which I'm viewing as a subset of the + + + align:start position:0% +which I'm viewing as a subset of the +complex numbers so just a line segment + + align:start position:0% +complex numbers so just a line segment + + + align:start position:0% +complex numbers so just a line segment +from minus dorm a to Norm a as a subset + + align:start position:0% +from minus dorm a to Norm a as a subset + + + align:start position:0% +from minus dorm a to Norm a as a subset +of the complex numbers + + align:start position:0% + + + + align:start position:0% + +and the second is that one of these two + + align:start position:0% +and the second is that one of these two + + + align:start position:0% +and the second is that one of these two +endpoints uh has to be in the Spectrum + + align:start position:0% +endpoints uh has to be in the Spectrum + + + align:start position:0% +endpoints uh has to be in the Spectrum +maybe both but at least one + + align:start position:0% + + + + align:start position:0% + +at least one of plus or minus Norm a + + align:start position:0% +at least one of plus or minus Norm a + + + align:start position:0% +at least one of plus or minus Norm a +is + + align:start position:0% + + + + align:start position:0% + +is in the spectrum of a + + align:start position:0% +is in the spectrum of a + + + align:start position:0% +is in the spectrum of a +okay + + align:start position:0% + + + + align:start position:0% + +Okay so + + align:start position:0% + + + + align:start position:0% + +to establish one we already know uh + + align:start position:0% + + + + align:start position:0% + +since uh the spectrum of a + + align:start position:0% +since uh the spectrum of a + + + align:start position:0% +since uh the spectrum of a +is contained + + align:start position:0% +is contained + + + align:start position:0% +is contained +in those complex numbers with modulus + + align:start position:0% +in those complex numbers with modulus + + + align:start position:0% +in those complex numbers with modulus +less than or equal to the norm of + + align:start position:0% +less than or equal to the norm of + + + align:start position:0% +less than or equal to the norm of +a + + align:start position:0% +a + + + align:start position:0% +a +we just need to show + + align:start position:0% + + + + align:start position:0% + +that the spectrum is contained in the + + align:start position:0% +that the spectrum is contained in the + + + align:start position:0% +that the spectrum is contained in the +real number line + + align:start position:0% +real number line + + + align:start position:0% +real number line +okay then it must be contained in this + + align:start position:0% +okay then it must be contained in this + + + align:start position:0% +okay then it must be contained in this +interval + + align:start position:0% +interval + + + align:start position:0% +interval +okay since it's contained here + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +okay so we'll show that anything off the + + align:start position:0% +okay so we'll show that anything off the + + + align:start position:0% +okay so we'll show that anything off the +real number line + + align:start position:0% +real number line + + + align:start position:0% +real number line +lies in the resolvent okay that's how + + align:start position:0% +lies in the resolvent okay that's how + + + align:start position:0% +lies in the resolvent okay that's how +we'll we'll go about this + + align:start position:0% +we'll we'll go about this + + + align:start position:0% +we'll we'll go about this +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% + + + + align:start position:0% + +we'll show that if Lambda equals + + align:start position:0% +we'll show that if Lambda equals + + + align:start position:0% +we'll show that if Lambda equals +s + + align:start position:0% +s + + + align:start position:0% +s +plus I T with t not equal to zero + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +Lambda is in the resolvent set of a + + align:start position:0% + + + + align:start position:0% + +now uh suppose Lambda has this form + + align:start position:0% +now uh suppose Lambda has this form + + + align:start position:0% +now uh suppose Lambda has this form +then + + align:start position:0% +then + + + align:start position:0% +then +a minus Lambda is equal to a minus s + + align:start position:0% +a minus Lambda is equal to a minus s + + + align:start position:0% +a minus Lambda is equal to a minus s +Plus + + align:start position:0% +Plus + + + align:start position:0% +Plus +or minus sorry i t + + align:start position:0% +or minus sorry i t + + + align:start position:0% +or minus sorry i t +uh which I can write as a tilde minus i + + align:start position:0% +uh which I can write as a tilde minus i + + + align:start position:0% +uh which I can write as a tilde minus i +t with a tilde + + align:start position:0% +t with a tilde + + + align:start position:0% +t with a tilde +a bounded linear operator given by a + + align:start position:0% +a bounded linear operator given by a + + + align:start position:0% +a bounded linear operator given by a +minus s + + align:start position:0% + + + + align:start position:0% + +which + + align:start position:0% +which + + + align:start position:0% +which +is also equal to the adjoint because s + + align:start position:0% +is also equal to the adjoint because s + + + align:start position:0% +is also equal to the adjoint because s +is a real number all right so I should + + align:start position:0% +is a real number all right so I should + + + align:start position:0% +is a real number all right so I should +have said t is not equal to zero and St + + align:start position:0% +have said t is not equal to zero and St + + + align:start position:0% +have said t is not equal to zero and St +real numbers + + align:start position:0% +real numbers + + + align:start position:0% +real numbers +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +a minus Lambda I can write but as a + + align:start position:0% +a minus Lambda I can write but as a + + + align:start position:0% +a minus Lambda I can write but as a +tilde minus i t uh where a tilde is a + + align:start position:0% +tilde minus i t uh where a tilde is a + + + align:start position:0% +tilde minus i t uh where a tilde is a +minus s again a cell for joint operator + + align:start position:0% +minus s again a cell for joint operator + + + align:start position:0% +minus s again a cell for joint operator +all right so if I can do an argument + + align:start position:0% +all right so if I can do an argument + + + align:start position:0% +all right so if I can do an argument +uh for a tilde and show that + + align:start position:0% +uh for a tilde and show that + + + align:start position:0% +uh for a tilde and show that +a tilde minus i t is bijective + + align:start position:0% +a tilde minus i t is bijective + + + align:start position:0% +a tilde minus i t is bijective +then I can conclude a minus s minus i t + + align:start position:0% +then I can conclude a minus s minus i t + + + align:start position:0% +then I can conclude a minus s minus i t +is in is bijective all right + + align:start position:0% +is in is bijective all right + + + align:start position:0% +is in is bijective all right +um + + align:start position:0% +um + + + align:start position:0% +um +why am I doing this because + + align:start position:0% +why am I doing this because + + + align:start position:0% +why am I doing this because +then I can just focus on the one case + + align:start position:0% +then I can just focus on the one case + + + align:start position:0% +then I can just focus on the one case +that s is zero + + align:start position:0% + + + + align:start position:0% + +A minus i t + + align:start position:0% +A minus i t + + + align:start position:0% +A minus i t +is bijective if and only if a minus + + align:start position:0% +is bijective if and only if a minus + + + align:start position:0% +is bijective if and only if a minus +Lambda is bijective + + align:start position:0% + + + + align:start position:0% + +so we only need to consider so I can + + align:start position:0% +so we only need to consider so I can + + + align:start position:0% +so we only need to consider so I can +just work on this thing but instead of + + align:start position:0% +just work on this thing but instead of + + + align:start position:0% +just work on this thing but instead of +writing a tilde over and over again I'll + + align:start position:0% +writing a tilde over and over again I'll + + + align:start position:0% +writing a tilde over and over again I'll +just switch back to a so I only really + + align:start position:0% +just switch back to a so I only really + + + align:start position:0% +just switch back to a so I only really +need to consider the case s equals zero + + align:start position:0% + + + + align:start position:0% + +okay so rather than do the argument for + + align:start position:0% +okay so rather than do the argument for + + + align:start position:0% +okay so rather than do the argument for +a tilde minus i t I'm just going to set + + align:start position:0% +a tilde minus i t I'm just going to set + + + align:start position:0% +a tilde minus i t I'm just going to set +s equal to zero and start doing the + + align:start position:0% +s equal to zero and start doing the + + + align:start position:0% +s equal to zero and start doing the +argument for a minus i t okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +since uh by what we proved or the result + + align:start position:0% +since uh by what we proved or the result + + + align:start position:0% +since uh by what we proved or the result +from last time + + align:start position:0% +from last time + + + align:start position:0% +from last time +so let me just uh + + align:start position:0% + + + + align:start position:0% + +set out what we're gonna + + align:start position:0% + + + + align:start position:0% + +prove uh + + align:start position:0% +prove uh + + + align:start position:0% +prove uh +if a is self-adjoint + + align:start position:0% +if a is self-adjoint + + + align:start position:0% +if a is self-adjoint +then + + align:start position:0% +then + + + align:start position:0% +then +a minus t minus i t is + + align:start position:0% +a minus t minus i t is + + + align:start position:0% +a minus t minus i t is +by objective + + align:start position:0% +by objective + + + align:start position:0% +by objective +for all t uh not equal to zero + + align:start position:0% +for all t uh not equal to zero + + + align:start position:0% +for all t uh not equal to zero +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so once I've proven this claim then I've + + align:start position:0% +so once I've proven this claim then I've + + + align:start position:0% +so once I've proven this claim then I've +proven + + align:start position:0% +proven + + + align:start position:0% +proven +um that uh + + align:start position:0% +um that uh + + + align:start position:0% +um that uh +I've proven my first part of the theorem + + align:start position:0% + + + + align:start position:0% + +okay now + + align:start position:0% + + + + align:start position:0% + +since uh + + align:start position:0% + + + + align:start position:0% + +a u applied to U is real + + align:start position:0% + + + + align:start position:0% + +I get that if I take the imaginary part + + align:start position:0% +I get that if I take the imaginary part + + + align:start position:0% +I get that if I take the imaginary part +of a minus i t + + align:start position:0% +of a minus i t + + + align:start position:0% +of a minus i t +applied to U inner product U + + align:start position:0% +applied to U inner product U + + + align:start position:0% +applied to U inner product U +this is equal to uh + + align:start position:0% + + + + align:start position:0% + +uh Au taking the imaginary part of that + + align:start position:0% +uh Au taking the imaginary part of that + + + align:start position:0% +uh Au taking the imaginary part of that +is just zero so then I get uh minus t + + align:start position:0% +is just zero so then I get uh minus t + + + align:start position:0% +is just zero so then I get uh minus t +um + + align:start position:0% +um + + + align:start position:0% +um +Norm U squared + + align:start position:0% + + + + align:start position:0% + +or which implies that + + align:start position:0% +or which implies that + + + align:start position:0% +or which implies that +um + + align:start position:0% + + + + align:start position:0% + +since T is non-zero we're assuming T is + + align:start position:0% +since T is non-zero we're assuming T is + + + align:start position:0% +since T is non-zero we're assuming T is +non-zero a minus i t times U equals zero + + align:start position:0% +non-zero a minus i t times U equals zero + + + align:start position:0% +non-zero a minus i t times U equals zero +if and only if U equals 0 right because + + align:start position:0% +if and only if U equals 0 right because + + + align:start position:0% +if and only if U equals 0 right because +if this quantity here equals zero then + + align:start position:0% +if this quantity here equals zero then + + + align:start position:0% +if this quantity here equals zero then +this thing here equals zero and + + align:start position:0% +this thing here equals zero and + + + align:start position:0% +this thing here equals zero and +therefore the norm of U has to be zero + + align:start position:0% +therefore the norm of U has to be zero + + + align:start position:0% +therefore the norm of U has to be zero +since T is non-zero so uh + + align:start position:0% +since T is non-zero so uh + + + align:start position:0% +since T is non-zero so uh +the null space of a minus i t is just + + align:start position:0% +the null space of a minus i t is just + + + align:start position:0% +the null space of a minus i t is just +the zero vector and therefore it must + + align:start position:0% +the zero vector and therefore it must + + + align:start position:0% +the zero vector and therefore it must +it's injective right + + align:start position:0% + + + + align:start position:0% + +right is injective it's one to one + + align:start position:0% +right is injective it's one to one + + + align:start position:0% +right is injective it's one to one +all right now we just want to show its + + align:start position:0% +all right now we just want to show its + + + align:start position:0% +all right now we just want to show its +uh bijective or it's surjective + + align:start position:0% +uh bijective or it's surjective + + + align:start position:0% +uh bijective or it's surjective +um okay so similarly + + align:start position:0% + + + + align:start position:0% + +I can prove that uh + + align:start position:0% +I can prove that uh + + + align:start position:0% +I can prove that uh +the adjoint + + align:start position:0% +the adjoint + + + align:start position:0% +the adjoint +of this operator which is in fact a plus + + align:start position:0% +of this operator which is in fact a plus + + + align:start position:0% +of this operator which is in fact a plus +IP + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +injective + + align:start position:0% +injective + + + align:start position:0% +injective +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +uh + + align:start position:0% +uh + + + align:start position:0% +uh +I get that + + align:start position:0% + + + + align:start position:0% + +the orthogonal complement + + align:start position:0% +the orthogonal complement + + + align:start position:0% +the orthogonal complement +to the range of a minus i t so I want to + + align:start position:0% +to the range of a minus i t so I want to + + + align:start position:0% +to the range of a minus i t so I want to +show this equals H to show its + + align:start position:0% +show this equals H to show its + + + align:start position:0% +show this equals H to show its +surjective so the orthogonal complement + + align:start position:0% +surjective so the orthogonal complement + + + align:start position:0% +surjective so the orthogonal complement +of that which is equal to the null space + + align:start position:0% +of that which is equal to the null space + + + align:start position:0% +of that which is equal to the null space +of + + align:start position:0% +of + + + align:start position:0% +of +the adjoint which is + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +equals so since this equals + + align:start position:0% +equals so since this equals + + + align:start position:0% +equals so since this equals +zero + + align:start position:0% +zero + + + align:start position:0% +zero +I include I conclude that + + align:start position:0% +I include I conclude that + + + align:start position:0% +I include I conclude that +the range of a minus i t closure which + + align:start position:0% +the range of a minus i t closure which + + + align:start position:0% +the range of a minus i t closure which +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +range of a minus i t + + align:start position:0% +range of a minus i t + + + align:start position:0% +range of a minus i t +taking the orthogonal complement of the + + align:start position:0% +taking the orthogonal complement of the + + + align:start position:0% +taking the orthogonal complement of the +orthogonal complement so that was part + + align:start position:0% +orthogonal complement so that was part + + + align:start position:0% +orthogonal complement so that was part +of an assignment that if I have a + + align:start position:0% +of an assignment that if I have a + + + align:start position:0% +of an assignment that if I have a +Subspace of the Hilbert space and I take + + align:start position:0% +Subspace of the Hilbert space and I take + + + align:start position:0% +Subspace of the Hilbert space and I take +or let me say here and I take its + + align:start position:0% +or let me say here and I take its + + + align:start position:0% +or let me say here and I take its +orthogonal the orthogonal complement of + + align:start position:0% +orthogonal the orthogonal complement of + + + align:start position:0% +orthogonal the orthogonal complement of +the orthogonal complement I don't get + + align:start position:0% +the orthogonal complement I don't get + + + align:start position:0% +the orthogonal complement I don't get +back the Subspace I get the closure of + + align:start position:0% +back the Subspace I get the closure of + + + align:start position:0% +back the Subspace I get the closure of +the Subspace okay + + align:start position:0% +the Subspace okay + + + align:start position:0% +the Subspace okay +so this is equal to + + align:start position:0% + + + + align:start position:0% + +orthogonal complement of the zero Vector + + align:start position:0% +orthogonal complement of the zero Vector + + + align:start position:0% +orthogonal complement of the zero Vector +which is H + + align:start position:0% +which is H + + + align:start position:0% +which is H +okay so I'll be done showing that a + + align:start position:0% +okay so I'll be done showing that a + + + align:start position:0% +okay so I'll be done showing that a +minus i t is surjective if I can show + + align:start position:0% +minus i t is surjective if I can show + + + align:start position:0% +minus i t is surjective if I can show +that the range is closed because then + + align:start position:0% +that the range is closed because then + + + align:start position:0% +that the range is closed because then +this will just be uh + + align:start position:0% +this will just be uh + + + align:start position:0% +this will just be uh +the range of a minus i t equals h + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +so we just need to show now that uh + + align:start position:0% +so we just need to show now that uh + + + align:start position:0% +so we just need to show now that uh +the range of a minus i t + + align:start position:0% + + + + align:start position:0% + +is closed + + align:start position:0% + + + + align:start position:0% + +so to show it's closed we have to show + + align:start position:0% +so to show it's closed we have to show + + + align:start position:0% +so to show it's closed we have to show +that if we take a sequence of elements + + align:start position:0% +that if we take a sequence of elements + + + align:start position:0% +that if we take a sequence of elements +in here converging to something then + + align:start position:0% +in here converging to something then + + + align:start position:0% +in here converging to something then +that limit is in fact in the set so + + align:start position:0% +that limit is in fact in the set so + + + align:start position:0% +that limit is in fact in the set so +suppose + + align:start position:0% +suppose + + + align:start position:0% +suppose +uh + + align:start position:0% + + + + align:start position:0% + +I have a sequence + + align:start position:0% +I have a sequence + + + align:start position:0% +I have a sequence +of elements u n such that a minus i t + + align:start position:0% +of elements u n such that a minus i t + + + align:start position:0% +of elements u n such that a minus i t +applied to u n converges to an element V + + align:start position:0% +applied to u n converges to an element V + + + align:start position:0% +applied to u n converges to an element V +so my goal is to show that V is in the + + align:start position:0% +so my goal is to show that V is in the + + + align:start position:0% +so my goal is to show that V is in the +range of I A minus i t + + align:start position:0% + + + + align:start position:0% + +so we want to show + + align:start position:0% +so we want to show + + + align:start position:0% +so we want to show +V is in the range + + align:start position:0% + + + + align:start position:0% + +and then we've shown that the range is + + align:start position:0% +and then we've shown that the range is + + + align:start position:0% +and then we've shown that the range is +closed and we're done with the first + + align:start position:0% +closed and we're done with the first + + + align:start position:0% +closed and we're done with the first +part + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +using kind of this argument here we're + + align:start position:0% +using kind of this argument here we're + + + align:start position:0% +using kind of this argument here we're +going to show that the U ins which a + + align:start position:0% +going to show that the U ins which a + + + align:start position:0% +going to show that the U ins which a +priori we don't know converge all we + + align:start position:0% +priori we don't know converge all we + + + align:start position:0% +priori we don't know converge all we +know is that the images of the un's + + align:start position:0% +know is that the images of the un's + + + align:start position:0% +know is that the images of the un's +converge we're going to show that the + + align:start position:0% +converge we're going to show that the + + + align:start position:0% +converge we're going to show that the +UNS actually converge and then that will + + align:start position:0% +UNS actually converge and then that will + + + align:start position:0% +UNS actually converge and then that will +essentially finish the proof + + align:start position:0% + + + + align:start position:0% + +then we have that the absolute value of + + align:start position:0% +then we have that the absolute value of + + + align:start position:0% +then we have that the absolute value of +t uh + + align:start position:0% +t uh + + + align:start position:0% +t uh +U minus u m Norm squared this is by this + + align:start position:0% +U minus u m Norm squared this is by this + + + align:start position:0% +U minus u m Norm squared this is by this +calculation we did over here equal to + + align:start position:0% +calculation we did over here equal to + + + align:start position:0% +calculation we did over here equal to +the absolute value of the image of I + + align:start position:0% +the absolute value of the image of I + + + align:start position:0% +the absolute value of the image of I +mean the imaginary part of + + align:start position:0% +mean the imaginary part of + + + align:start position:0% +mean the imaginary part of +uh + + align:start position:0% +uh + + + align:start position:0% +uh +a minus i t + + align:start position:0% +a minus i t + + + align:start position:0% +a minus i t +u n minus u m + + align:start position:0% +u n minus u m + + + align:start position:0% +u n minus u m +u n minus u m + + align:start position:0% + + + + align:start position:0% + +take the absolute value of all of that + + align:start position:0% + + + + align:start position:0% + +and now uh this is less than or equal to + + align:start position:0% +and now uh this is less than or equal to + + + align:start position:0% +and now uh this is less than or equal to +so the absolute value of the imaginary + + align:start position:0% +so the absolute value of the imaginary + + + align:start position:0% +so the absolute value of the imaginary +part of a complex number is less than or + + align:start position:0% +part of a complex number is less than or + + + align:start position:0% +part of a complex number is less than or +equal to the absolute value of that + + align:start position:0% +equal to the absolute value of that + + + align:start position:0% +equal to the absolute value of that +complex number which by koshy Schwartz I + + align:start position:0% +complex number which by koshy Schwartz I + + + align:start position:0% +complex number which by koshy Schwartz I +can say is less than or equal to a minus + + align:start position:0% +can say is less than or equal to a minus + + + align:start position:0% +can say is less than or equal to a minus +i t + + align:start position:0% +i t + + + align:start position:0% +i t +applied to u n minus u m + + align:start position:0% +applied to u n minus u m + + + align:start position:0% +applied to u n minus u m +but I'll write it as a minus i t + + align:start position:0% + + + + align:start position:0% + +m + + align:start position:0% + + + + align:start position:0% + +times the norm + + align:start position:0% +times the norm + + + align:start position:0% +times the norm +of u n minus um and I started off with a + + align:start position:0% +of u n minus um and I started off with a + + + align:start position:0% +of u n minus um and I started off with a +t + + align:start position:0% +t + + + align:start position:0% +t +which is non-zero times the norm of u n + + align:start position:0% +which is non-zero times the norm of u n + + + align:start position:0% +which is non-zero times the norm of u n +minus u m squared so I get that u n + + align:start position:0% +minus u m squared so I get that u n + + + align:start position:0% +minus u m squared so I get that u n +minus u m so for + + align:start position:0% +minus u m so for + + + align:start position:0% +minus u m so for +that this is less than or equal to 1 + + align:start position:0% +that this is less than or equal to 1 + + + align:start position:0% +that this is less than or equal to 1 +over + + align:start position:0% +over + + + align:start position:0% +over +the absolute value of T times the norm + + align:start position:0% +the absolute value of T times the norm + + + align:start position:0% +the absolute value of T times the norm +of a minus i t applied to u n minus + + align:start position:0% +of a minus i t applied to u n minus + + + align:start position:0% +of a minus i t applied to u n minus +a minus i t applied to u m + + align:start position:0% +a minus i t applied to u m + + + align:start position:0% +a minus i t applied to u m +Norm + + align:start position:0% +Norm + + + align:start position:0% +Norm +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now this thing on the right + + align:start position:0% + + + + align:start position:0% + +or I should say a minus i t applied to u + + align:start position:0% +or I should say a minus i t applied to u + + + align:start position:0% +or I should say a minus i t applied to u +n this is a convergent sequence in + + align:start position:0% +n this is a convergent sequence in + + + align:start position:0% +n this is a convergent sequence in +particular it's a koshy sequence right + + align:start position:0% +particular it's a koshy sequence right + + + align:start position:0% +particular it's a koshy sequence right +so given Epsilon I can find capital N so + + align:start position:0% +so given Epsilon I can find capital N so + + + align:start position:0% +so given Epsilon I can find capital N so +that the norm of this right hand side is + + align:start position:0% +that the norm of this right hand side is + + + align:start position:0% +that the norm of this right hand side is +less than Epsilon times the magnitude of + + align:start position:0% +less than Epsilon times the magnitude of + + + align:start position:0% +less than Epsilon times the magnitude of +t + + align:start position:0% +t + + + align:start position:0% +t +okay and therefore for all capital N + + align:start position:0% +okay and therefore for all capital N + + + align:start position:0% +okay and therefore for all capital N +bigger than or equal to or for all + + align:start position:0% +bigger than or equal to or for all + + + align:start position:0% +bigger than or equal to or for all +little n m bigger than or equal to that + + align:start position:0% +little n m bigger than or equal to that + + + align:start position:0% +little n m bigger than or equal to that +capital N this and Norm will be less + + align:start position:0% +capital N this and Norm will be less + + + align:start position:0% +capital N this and Norm will be less +than Epsilon + + align:start position:0% +than Epsilon + + + align:start position:0% +than Epsilon +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +um + + align:start position:0% + + + + align:start position:0% + +since + + align:start position:0% + + + + align:start position:0% + +this is Koshi + + align:start position:0% +this is Koshi + + + align:start position:0% +this is Koshi +because it's convergent + + align:start position:0% +because it's convergent + + + align:start position:0% +because it's convergent +the previous estimate implies that + + align:start position:0% +the previous estimate implies that + + + align:start position:0% +the previous estimate implies that +sequence U in + + align:start position:0% + + + + align:start position:0% + +is Koshi and since we're in a Hilbert + + align:start position:0% +is Koshi and since we're in a Hilbert + + + align:start position:0% +is Koshi and since we're in a Hilbert +space which means it's complete we can + + align:start position:0% +space which means it's complete we can + + + align:start position:0% +space which means it's complete we can +find a limit of this UNS it exists to U + + align:start position:0% +find a limit of this UNS it exists to U + + + align:start position:0% +find a limit of this UNS it exists to U +an H + + align:start position:0% +an H + + + align:start position:0% +an H +such that u n converges to U + + align:start position:0% +such that u n converges to U + + + align:start position:0% +such that u n converges to U +okay and then we're done now then since + + align:start position:0% +okay and then we're done now then since + + + align:start position:0% +okay and then we're done now then since +a is a bounded linear operator a minus i + + align:start position:0% +a is a bounded linear operator a minus i + + + align:start position:0% +a is a bounded linear operator a minus i +t uh + + align:start position:0% +t uh + + + align:start position:0% +t uh +U or a minus i t applied to U this is + + align:start position:0% +U or a minus i t applied to U this is + + + align:start position:0% +U or a minus i t applied to U this is +equal to the Limit as n goes to Infinity + + align:start position:0% +equal to the Limit as n goes to Infinity + + + align:start position:0% +equal to the Limit as n goes to Infinity +of a minus i t + + align:start position:0% +of a minus i t + + + align:start position:0% +of a minus i t +apply to you in but remember we assumed + + align:start position:0% +apply to you in but remember we assumed + + + align:start position:0% +apply to you in but remember we assumed +that this converges to some element V + + align:start position:0% +that this converges to some element V + + + align:start position:0% +that this converges to some element V +and therefore V is equal to Something + + align:start position:0% +and therefore V is equal to Something + + + align:start position:0% +and therefore V is equal to Something +in the image or in the range of a minus + + align:start position:0% +in the image or in the range of a minus + + + align:start position:0% +in the image or in the range of a minus +i t + + align:start position:0% + + + + align:start position:0% + +V is in the range + + align:start position:0% + + + + align:start position:0% + +and thus the range of a minus i t is + + align:start position:0% +and thus the range of a minus i t is + + + align:start position:0% +and thus the range of a minus i t is +closed and by this + + align:start position:0% +closed and by this + + + align:start position:0% +closed and by this +um + + align:start position:0% + + + + align:start position:0% + +here we conclude that the range of a + + align:start position:0% +here we conclude that the range of a + + + align:start position:0% +here we conclude that the range of a +minus t equals H so a minus i t is + + align:start position:0% +minus t equals H so a minus i t is + + + align:start position:0% +minus t equals H so a minus i t is +bijective + + align:start position:0% + + + + align:start position:0% + +okay and that concludes the proof of the + + align:start position:0% +okay and that concludes the proof of the + + + align:start position:0% +okay and that concludes the proof of the +first property we wanted to do + + align:start position:0% + + + + align:start position:0% + +okay so for the second + + align:start position:0% + + + + align:start position:0% + +uh thing we wanted to show we wanted to + + align:start position:0% +uh thing we wanted to show we wanted to + + + align:start position:0% +uh thing we wanted to show we wanted to +show that at least + + align:start position:0% + + + + align:start position:0% + +one of plus or minus Norm of a + + align:start position:0% +one of plus or minus Norm of a + + + align:start position:0% +one of plus or minus Norm of a +is in the Spectrum + + align:start position:0% +is in the Spectrum + + + align:start position:0% +is in the Spectrum +of a + + align:start position:0% +of a + + + align:start position:0% +of a +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um now + + align:start position:0% +um now + + + align:start position:0% +um now +since uh + + align:start position:0% + + + + align:start position:0% + +the norm of a is equal to + + align:start position:0% +the norm of a is equal to + + + align:start position:0% +the norm of a is equal to +soup over + + align:start position:0% +soup over + + + align:start position:0% +soup over +Norm of U equals one of the absolute + + align:start position:0% +Norm of U equals one of the absolute + + + align:start position:0% +Norm of U equals one of the absolute +value of a u + + align:start position:0% + + + + align:start position:0% + +so a supremum is always characterized by + + align:start position:0% +so a supremum is always characterized by + + + align:start position:0% +so a supremum is always characterized by +being an upper bound and also there + + align:start position:0% +being an upper bound and also there + + + align:start position:0% +being an upper bound and also there +existing a sequence uh + + align:start position:0% +existing a sequence uh + + + align:start position:0% +existing a sequence uh +in the set of things you're taking the + + align:start position:0% +in the set of things you're taking the + + + align:start position:0% +in the set of things you're taking the +supremum of + + align:start position:0% +supremum of + + + align:start position:0% +supremum of +converging to that supremum so that + + align:start position:0% +converging to that supremum so that + + + align:start position:0% +converging to that supremum so that +implies that there exists + + align:start position:0% +implies that there exists + + + align:start position:0% +implies that there exists +a sequence of unit vectors + + align:start position:0% + + + + align:start position:0% + +so that + + align:start position:0% +so that + + + align:start position:0% +so that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +Au inner product U and absolute value + + align:start position:0% +Au inner product U and absolute value + + + align:start position:0% +Au inner product U and absolute value +has to converge to the norm of a so uh + + align:start position:0% +has to converge to the norm of a so uh + + + align:start position:0% +has to converge to the norm of a so uh +in particular a u applied to U has to + + align:start position:0% +in particular a u applied to U has to + + + align:start position:0% +in particular a u applied to U has to +converge to + + align:start position:0% +converge to + + + align:start position:0% +converge to +uh the norm of a or + + align:start position:0% + + + + align:start position:0% + +minus Norm of a + + align:start position:0% +minus Norm of a + + + align:start position:0% +minus Norm of a +as n goes to infinity and there's no n + + align:start position:0% +as n goes to infinity and there's no n + + + align:start position:0% +as n goes to infinity and there's no n +here so + + align:start position:0% +here so + + + align:start position:0% +here so +uh + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +all right so uh + + align:start position:0% + + + + align:start position:0% + +then what is this uh + + align:start position:0% +then what is this uh + + + align:start position:0% +then what is this uh +imply then this implies that + + align:start position:0% +imply then this implies that + + + align:start position:0% +imply then this implies that +for at least one of these choices + + align:start position:0% +for at least one of these choices + + + align:start position:0% +for at least one of these choices +then + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +a uh + + align:start position:0% +a uh + + + align:start position:0% +a uh +plus or minus + + align:start position:0% +plus or minus + + + align:start position:0% +plus or minus +Norm of a + + align:start position:0% +Norm of a + + + align:start position:0% +Norm of a +applied to + + align:start position:0% +applied to + + + align:start position:0% +applied to +u in in a product u n + + align:start position:0% +u in in a product u n + + + align:start position:0% +u in in a product u n +converges to zero + + align:start position:0% +converges to zero + + + align:start position:0% +converges to zero +as n goes to Infinity where here the + + align:start position:0% +as n goes to Infinity where here the + + + align:start position:0% +as n goes to Infinity where here the +plus or minus is chosen uh depending on + + align:start position:0% +plus or minus is chosen uh depending on + + + align:start position:0% +plus or minus is chosen uh depending on +whether this goes to plus or minus the + + align:start position:0% +whether this goes to plus or minus the + + + align:start position:0% +whether this goes to plus or minus the +norm of a so this sign here would be the + + align:start position:0% +norm of a so this sign here would be the + + + align:start position:0% +norm of a so this sign here would be the +opposite of whichever sign the sequence + + align:start position:0% +opposite of whichever sign the sequence + + + align:start position:0% +opposite of whichever sign the sequence +goes to okay + + align:start position:0% + + + + align:start position:0% + +I now claim that this uh + + align:start position:0% +I now claim that this uh + + + align:start position:0% +I now claim that this uh +property here implies that whichever + + align:start position:0% +property here implies that whichever + + + align:start position:0% +property here implies that whichever +sign we have that for that this operator + + align:start position:0% +sign we have that for that this operator + + + align:start position:0% +sign we have that for that this operator +appearing here cannot be invertible and + + align:start position:0% +appearing here cannot be invertible and + + + align:start position:0% +appearing here cannot be invertible and +therefore whichever sign appeared + + align:start position:0% +therefore whichever sign appeared + + + align:start position:0% +therefore whichever sign appeared +here or the opposite sign so let me in + + align:start position:0% +here or the opposite sign so let me in + + + align:start position:0% +here or the opposite sign so let me in +fact stay + + align:start position:0% +fact stay + + + align:start position:0% +fact stay +so the minus corresponds to the plus + + align:start position:0% +so the minus corresponds to the plus + + + align:start position:0% +so the minus corresponds to the plus +sign the plus sign corresponds to the + + align:start position:0% +sign the plus sign corresponds to the + + + align:start position:0% +sign the plus sign corresponds to the +minus sign + + align:start position:0% +minus sign + + + align:start position:0% +minus sign +if we have one of those + + align:start position:0% +if we have one of those + + + align:start position:0% +if we have one of those +so I claim that this property here + + align:start position:0% +so I claim that this property here + + + align:start position:0% +so I claim that this property here +implies that this operator is not + + align:start position:0% +implies that this operator is not + + + align:start position:0% +implies that this operator is not +invertible and therefore one of those is + + align:start position:0% +invertible and therefore one of those is + + + align:start position:0% +invertible and therefore one of those is +in the Spectrum + + align:start position:0% +in the Spectrum + + + align:start position:0% +in the Spectrum +so + + align:start position:0% + + + + align:start position:0% + +suppose instead that a minus plus Norm + + align:start position:0% +suppose instead that a minus plus Norm + + + align:start position:0% +suppose instead that a minus plus Norm +of a + + align:start position:0% +of a + + + align:start position:0% +of a +whichever one appeared is invertible + + align:start position:0% + + + + align:start position:0% + +whichever one + + align:start position:0% +whichever one + + + align:start position:0% +whichever one +does satisfy this is invertible okay + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +um + + align:start position:0% +um + + + align:start position:0% +um +the UNS all have Norm one so one is + + align:start position:0% +the UNS all have Norm one so one is + + + align:start position:0% +the UNS all have Norm one so one is +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +the norm of U in and I can write this as + + align:start position:0% +the norm of U in and I can write this as + + + align:start position:0% +the norm of U in and I can write this as +the norm of a minus plus Norm + + align:start position:0% +the norm of a minus plus Norm + + + align:start position:0% +the norm of a minus plus Norm +a inverse applied to a minus plus Norm a + + align:start position:0% +a inverse applied to a minus plus Norm a + + + align:start position:0% +a inverse applied to a minus plus Norm a +because that's just the identity applied + + align:start position:0% +because that's just the identity applied + + + align:start position:0% +because that's just the identity applied +to u n + + align:start position:0% +to u n + + + align:start position:0% +to u n +and + + align:start position:0% +and + + + align:start position:0% +and +this is less than or equal to the norm + + align:start position:0% +this is less than or equal to the norm + + + align:start position:0% +this is less than or equal to the norm +of the inverse + + align:start position:0% + + + + align:start position:0% + +times the norm of this quantity + + align:start position:0% + + + + align:start position:0% + +and okay so this is a fixed number + + align:start position:0% +and okay so this is a fixed number + + + align:start position:0% +and okay so this is a fixed number +and this thing is converging to zero so + + align:start position:0% +and this thing is converging to zero so + + + align:start position:0% +and this thing is converging to zero so +the right hand side converges to zero + + align:start position:0% +the right hand side converges to zero + + + align:start position:0% +the right hand side converges to zero +but + + align:start position:0% +but + + + align:start position:0% +but +that's one right I have one is less than + + align:start position:0% +that's one right I have one is less than + + + align:start position:0% +that's one right I have one is less than +or equal to zero so that's a + + align:start position:0% +or equal to zero so that's a + + + align:start position:0% +or equal to zero so that's a +contradiction thus uh + + align:start position:0% +contradiction thus uh + + + align:start position:0% +contradiction thus uh +uh a minus or plus Norm of a again where + + align:start position:0% +uh a minus or plus Norm of a again where + + + align:start position:0% +uh a minus or plus Norm of a again where +the minus or plus corresponds to which + + align:start position:0% +the minus or plus corresponds to which + + + align:start position:0% +the minus or plus corresponds to which +uh sine of the norm of a we had that + + align:start position:0% +uh sine of the norm of a we had that + + + align:start position:0% +uh sine of the norm of a we had that +sequence converging to + + align:start position:0% +sequence converging to + + + align:start position:0% +sequence converging to +um + + align:start position:0% + + + + align:start position:0% + +it's not invertible + + align:start position:0% + + + + align:start position:0% + +which implies that uh + + align:start position:0% +which implies that uh + + + align:start position:0% +which implies that uh +plus or minus at least one of these is + + align:start position:0% +plus or minus at least one of these is + + + align:start position:0% +plus or minus at least one of these is +in + + align:start position:0% +in + + + align:start position:0% +in +spec the spectrum of a + + align:start position:0% +spec the spectrum of a + + + align:start position:0% +spec the spectrum of a +right + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now we can in fact do a little bit + + align:start position:0% +now we can in fact do a little bit + + + align:start position:0% +now we can in fact do a little bit +better uh + + align:start position:0% +better uh + + + align:start position:0% +better uh +then + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +you know based on this argument we can + + align:start position:0% +you know based on this argument we can + + + align:start position:0% +you know based on this argument we can +do a little bit better in bounding the + + align:start position:0% +do a little bit better in bounding the + + + align:start position:0% +do a little bit better in bounding the +spectrum of a self-adjoined operator + + align:start position:0% +spectrum of a self-adjoined operator + + + align:start position:0% +spectrum of a self-adjoined operator +than just the the bound that we have + + align:start position:0% + + + + align:start position:0% + +coming from the general theory + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +what do I mean by that + + align:start position:0% + + + + align:start position:0% + +so uh + + align:start position:0% + + + + align:start position:0% + +if a is a self a joint + + align:start position:0% +if a is a self a joint + + + align:start position:0% +if a is a self a joint +bounded operator + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +a minus is equal to the infimum over + + align:start position:0% +a minus is equal to the infimum over + + + align:start position:0% +a minus is equal to the infimum over +All U equals one + + align:start position:0% + + + + align:start position:0% + +a u applied to U + + align:start position:0% +a u applied to U + + + align:start position:0% +a u applied to U +a plus equals the soup + + align:start position:0% + + + + align:start position:0% + +you applied to U + + align:start position:0% + + + + align:start position:0% + +then uh + + align:start position:0% + + + + align:start position:0% + +the spectrum of a + + align:start position:0% +the spectrum of a + + + align:start position:0% +the spectrum of a +is contained so first off then a couple + + align:start position:0% +is contained so first off then a couple + + + align:start position:0% +is contained so first off then a couple +of things + + align:start position:0% +of things + + + align:start position:0% +of things +two things + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +both of these numbers are in the + + align:start position:0% +both of these numbers are in the + + + align:start position:0% +both of these numbers are in the +Spectrum + + align:start position:0% + + + + align:start position:0% + +of a and the spectrum is contained in + + align:start position:0% +of a and the spectrum is contained in + + + align:start position:0% +of a and the spectrum is contained in +this line segment + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so this is something of a tighter bound + + align:start position:0% +so this is something of a tighter bound + + + align:start position:0% +so this is something of a tighter bound +because + + align:start position:0% +because + + + align:start position:0% +because +um + + align:start position:0% +um + + + align:start position:0% +um +a minus is always bigger than or equal + + align:start position:0% +a minus is always bigger than or equal + + + align:start position:0% +a minus is always bigger than or equal +to minus the norm of a just by this + + align:start position:0% +to minus the norm of a just by this + + + align:start position:0% +to minus the norm of a just by this +always being bounded below by the norm + + align:start position:0% +always being bounded below by the norm + + + align:start position:0% +always being bounded below by the norm +of A and A Plus is always bounded above + + align:start position:0% +of A and A Plus is always bounded above + + + align:start position:0% +of A and A Plus is always bounded above +by the norm of a since this is always + + align:start position:0% +by the norm of a since this is always + + + align:start position:0% +by the norm of a since this is always +bounded above by the norm of a so the + + align:start position:0% +bounded above by the norm of a so the + + + align:start position:0% +bounded above by the norm of a so the +soup will be bounded above by that so + + align:start position:0% +soup will be bounded above by that so + + + align:start position:0% +soup will be bounded above by that so +this is a tighter estimate than just a + + align:start position:0% +this is a tighter estimate than just a + + + align:start position:0% +this is a tighter estimate than just a +regular estimate that says the spectrum + + align:start position:0% +regular estimate that says the spectrum + + + align:start position:0% +regular estimate that says the spectrum +is contained inside of uh the interval + + align:start position:0% +is contained inside of uh the interval + + + align:start position:0% +is contained inside of uh the interval +from minus Norm a to Norm a and in fact + + align:start position:0% +from minus Norm a to Norm a and in fact + + + align:start position:0% +from minus Norm a to Norm a and in fact +you get more information uh that not + + align:start position:0% +you get more information uh that not + + + align:start position:0% +you get more information uh that not +just one of the endpoints have to be in + + align:start position:0% +just one of the endpoints have to be in + + + align:start position:0% +just one of the endpoints have to be in +but both of these endpoints are in the + + align:start position:0% +but both of these endpoints are in the + + + align:start position:0% +but both of these endpoints are in the +Spectrum + + align:start position:0% +Spectrum + + + align:start position:0% +Spectrum +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +the proof of this is + + align:start position:0% +the proof of this is + + + align:start position:0% +the proof of this is +just kind of a + + align:start position:0% +just kind of a + + + align:start position:0% +just kind of a +a trick of using what we've done already + + align:start position:0% +a trick of using what we've done already + + + align:start position:0% +a trick of using what we've done already +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% + + + + align:start position:0% + +first note that again + + align:start position:0% +first note that again + + + align:start position:0% +first note that again +by + + align:start position:0% +by + + + align:start position:0% +by +since the absolute value of au and a + + align:start position:0% +since the absolute value of au and a + + + align:start position:0% +since the absolute value of au and a +product U is always less than or equal + + align:start position:0% +product U is always less than or equal + + + align:start position:0% +product U is always less than or equal +to the norm of a + + align:start position:0% + + + + align:start position:0% + +well unit vectors this implies that this + + align:start position:0% +well unit vectors this implies that this + + + align:start position:0% +well unit vectors this implies that this +quantity here is always bounded below by + + align:start position:0% +quantity here is always bounded below by + + + align:start position:0% +quantity here is always bounded below by +Norm of a and bounded above by + + align:start position:0% + + + + align:start position:0% + +Norm of a + + align:start position:0% +Norm of a + + + align:start position:0% +Norm of a +and therefore the infimum of this is + + align:start position:0% +and therefore the infimum of this is + + + align:start position:0% +and therefore the infimum of this is +always bounded from so this is a lower + + align:start position:0% +always bounded from so this is a lower + + + align:start position:0% +always bounded from so this is a lower +Bound for this quantity here so this in + + align:start position:0% +Bound for this quantity here so this in + + + align:start position:0% +Bound for this quantity here so this in +phimum is bigger than it since it's the + + align:start position:0% +phimum is bigger than it since it's the + + + align:start position:0% +phimum is bigger than it since it's the +greatest lower bound + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +least upper bound of these quantities is + + align:start position:0% +least upper bound of these quantities is + + + align:start position:0% +least upper bound of these quantities is +always less than or equal to the norm of + + align:start position:0% +always less than or equal to the norm of + + + align:start position:0% +always less than or equal to the norm of +a + + align:start position:0% +a + + + align:start position:0% +a +so these are actual numbers + + align:start position:0% +so these are actual numbers + + + align:start position:0% +so these are actual numbers +um + + align:start position:0% +um + + + align:start position:0% +um +for one + + align:start position:0% +for one + + + align:start position:0% +for one +okay now + + align:start position:0% + + + + align:start position:0% + +by the definition of a plus or minus + + align:start position:0% + + + + align:start position:0% + +there exists + + align:start position:0% + + + + align:start position:0% + +sequences of unit vectors u n plus or + + align:start position:0% +sequences of unit vectors u n plus or + + + align:start position:0% +sequences of unit vectors u n plus or +minus + + align:start position:0% +minus + + + align:start position:0% +minus +such that a applied to u n plus or minus + + align:start position:0% +such that a applied to u n plus or minus + + + align:start position:0% +such that a applied to u n plus or minus +inner product u n plus or minus + + align:start position:0% +inner product u n plus or minus + + + align:start position:0% +inner product u n plus or minus +converges to a plus or minus + + align:start position:0% +converges to a plus or minus + + + align:start position:0% +converges to a plus or minus +okay now by the the argument we just + + align:start position:0% +okay now by the the argument we just + + + align:start position:0% +okay now by the the argument we just +gave with you know a plus or minus being + + align:start position:0% +gave with you know a plus or minus being + + + align:start position:0% +gave with you know a plus or minus being +uh the norm of a + + align:start position:0% +uh the norm of a + + + align:start position:0% +uh the norm of a +but now we have this + + align:start position:0% +but now we have this + + + align:start position:0% +but now we have this +uh property + + align:start position:0% + + + + align:start position:0% + +I.E + + align:start position:0% +I.E + + + align:start position:0% +I.E +a minus a plus a minus applied to u n + + align:start position:0% +a minus a plus a minus applied to u n + + + align:start position:0% +a minus a plus a minus applied to u n +plus or minus u n plus or minus + + align:start position:0% +plus or minus u n plus or minus + + + align:start position:0% +plus or minus u n plus or minus +converges to zero + + align:start position:0% +converges to zero + + + align:start position:0% +converges to zero +um + + align:start position:0% +um + + + align:start position:0% +um +since I had this property by the + + align:start position:0% +since I had this property by the + + + align:start position:0% +since I had this property by the +previous argument I gave this implies + + align:start position:0% +previous argument I gave this implies + + + align:start position:0% +previous argument I gave this implies +that both a plus and a minus are in the + + align:start position:0% +that both a plus and a minus are in the + + + align:start position:0% +that both a plus and a minus are in the +spectrum of a + + align:start position:0% + + + + align:start position:0% + +since we have for each choice of plus or + + align:start position:0% +since we have for each choice of plus or + + + align:start position:0% +since we have for each choice of plus or +minus a sequence of unit vectors so that + + align:start position:0% +minus a sequence of unit vectors so that + + + align:start position:0% +minus a sequence of unit vectors so that +this quantity here goes to zero a minute + + align:start position:0% +this quantity here goes to zero a minute + + + align:start position:0% +this quantity here goes to zero a minute +ago we could just assert that there was + + align:start position:0% +ago we could just assert that there was + + + align:start position:0% +ago we could just assert that there was +a sequence of unit vectors so for at + + align:start position:0% +a sequence of unit vectors so for at + + + align:start position:0% +a sequence of unit vectors so for at +least one choice of plus or minus the + + align:start position:0% +least one choice of plus or minus the + + + align:start position:0% +least one choice of plus or minus the +norm of a we had this thing going to + + align:start position:0% +norm of a we had this thing going to + + + align:start position:0% +norm of a we had this thing going to +zero but uh for these two numbers + + align:start position:0% +zero but uh for these two numbers + + + align:start position:0% +zero but uh for these two numbers +because it's the infant because this is + + align:start position:0% +because it's the infant because this is + + + align:start position:0% +because it's the infant because this is +the soup we can always find + + align:start position:0% +the soup we can always find + + + align:start position:0% +the soup we can always find +unit vectors so that this quantity is + + align:start position:0% +unit vectors so that this quantity is + + + align:start position:0% +unit vectors so that this quantity is +converging to the soup which is a plus + + align:start position:0% +converging to the soup which is a plus + + + align:start position:0% +converging to the soup which is a plus +this quantity is converging to the Imp + + align:start position:0% +this quantity is converging to the Imp + + + align:start position:0% +this quantity is converging to the Imp +which is a minus + + align:start position:0% +which is a minus + + + align:start position:0% +which is a minus +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so bye + + align:start position:0% + + + + align:start position:0% + +the previous argument + + align:start position:0% + + + + align:start position:0% + +we get that a + + align:start position:0% +we get that a + + + align:start position:0% +we get that a +both a plus or minus + + align:start position:0% +both a plus or minus + + + align:start position:0% +both a plus or minus +are in the spectrum of a + + align:start position:0% +are in the spectrum of a + + + align:start position:0% +are in the spectrum of a +before again I just want to emphasize + + align:start position:0% +before again I just want to emphasize + + + align:start position:0% +before again I just want to emphasize +before we could just say that one of the + + align:start position:0% +before we could just say that one of the + + + align:start position:0% +before we could just say that one of the +Norms of a + + align:start position:0% +Norms of a + + + align:start position:0% +Norms of a +or Plus or + + align:start position:0% +or Plus or + + + align:start position:0% +or Plus or +at least one choice of plus or minus the + + align:start position:0% +at least one choice of plus or minus the + + + align:start position:0% +at least one choice of plus or minus the +norm of a is in the Spectrum here we're + + align:start position:0% +norm of a is in the Spectrum here we're + + + align:start position:0% +norm of a is in the Spectrum here we're +saying both of these numbers are in the + + align:start position:0% +saying both of these numbers are in the + + + align:start position:0% +saying both of these numbers are in the +Spectrum so now what remains is to show + + align:start position:0% +Spectrum so now what remains is to show + + + align:start position:0% +Spectrum so now what remains is to show +that the spectrum is in fact contained + + align:start position:0% +that the spectrum is in fact contained + + + align:start position:0% +that the spectrum is in fact contained +in this interval from a minus a plus + + align:start position:0% + + + + align:start position:0% + +all right so let + + align:start position:0% + + + + align:start position:0% + +let B be their midpoint + + align:start position:0% + + + + align:start position:0% + +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +b equals + + align:start position:0% +b equals + + + align:start position:0% +b equals +a minus B uh times I okay now B is a + + align:start position:0% +a minus B uh times I okay now B is a + + + align:start position:0% +a minus B uh times I okay now B is a +real number because those are two real + + align:start position:0% +real number because those are two real + + + align:start position:0% +real number because those are two real +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +um so capital B is the difference + + align:start position:0% +um so capital B is the difference + + + align:start position:0% +um so capital B is the difference +between a and a is a minus a real number + + align:start position:0% +between a and a is a minus a real number + + + align:start position:0% +between a and a is a minus a real number +times the identity so B is self a joint + + align:start position:0% + + + + align:start position:0% + +and a bounded linear operator on H + + align:start position:0% + + + + align:start position:0% + +so by the previous theorem + + align:start position:0% + + + + align:start position:0% + +we get that + + align:start position:0% +we get that + + + align:start position:0% +we get that +um + + align:start position:0% + + + + align:start position:0% + +the spectrum of B + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +Ed + + align:start position:0% +Ed + + + align:start position:0% +Ed +in the norm of B + + align:start position:0% + + + + align:start position:0% + +so minus normal B normal B + + align:start position:0% +so minus normal B normal B + + + align:start position:0% +so minus normal B normal B +okay + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +it shouldn't uh + + align:start position:0% +it shouldn't uh + + + align:start position:0% +it shouldn't uh +take much thought to to realize that if + + align:start position:0% +take much thought to to realize that if + + + align:start position:0% +take much thought to to realize that if +the spectrum of B which is a shift of a + + align:start position:0% +the spectrum of B which is a shift of a + + + align:start position:0% +the spectrum of B which is a shift of a +by little B is contained in this + + align:start position:0% +by little B is contained in this + + + align:start position:0% +by little B is contained in this +interval then + + align:start position:0% +interval then + + + align:start position:0% +interval then +spec of a + + align:start position:0% +spec of a + + + align:start position:0% +spec of a +is contained in + + align:start position:0% +is contained in + + + align:start position:0% +is contained in +minus Norm of B plus little B + + align:start position:0% +minus Norm of B plus little B + + + align:start position:0% +minus Norm of B plus little B +Norma B plus b + + align:start position:0% +Norma B plus b + + + align:start position:0% +Norma B plus b +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now what's left is to compute the + + align:start position:0% +so now what's left is to compute the + + + align:start position:0% +so now what's left is to compute the +norm of B all right but this is not too + + align:start position:0% +norm of B all right but this is not too + + + align:start position:0% +norm of B all right but this is not too +difficult + + align:start position:0% +difficult + + + align:start position:0% +difficult +um + + align:start position:0% + + + + align:start position:0% + +we have that the normal B + + align:start position:0% +we have that the normal B + + + align:start position:0% +we have that the normal B +this is equal to + + align:start position:0% +this is equal to + + + align:start position:0% +this is equal to +soup of + + align:start position:0% +soup of + + + align:start position:0% +soup of +U equals one + + align:start position:0% +U equals one + + + align:start position:0% +U equals one +the EU applied to U and now I + + align:start position:0% + + + + align:start position:0% + +take the soup over all U equals one and + + align:start position:0% +take the soup over all U equals one and + + + align:start position:0% +take the soup over all U equals one and +let me plug in what a is and B is and + + align:start position:0% +let me plug in what a is and B is and + + + align:start position:0% +let me plug in what a is and B is and +this is a u + + align:start position:0% +this is a u + + + align:start position:0% +this is a u +U minus + + align:start position:0% +U minus + + + align:start position:0% +U minus +a plus minus or a plus minus a minus + + align:start position:0% +a plus minus or a plus minus a minus + + + align:start position:0% +a plus minus or a plus minus a minus +over two + + align:start position:0% +over two + + + align:start position:0% +over two +okay + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +here's a picture here's a minus here's a + + align:start position:0% +here's a picture here's a minus here's a + + + align:start position:0% +here's a picture here's a minus here's a +plus + + align:start position:0% +plus + + + align:start position:0% +plus +a plus is the soup over all of these + + align:start position:0% +a plus is the soup over all of these + + + align:start position:0% +a plus is the soup over all of these +Expressions where U has unit length a + + align:start position:0% +Expressions where U has unit length a + + + align:start position:0% +Expressions where U has unit length a +minus is the Imp over all these + + align:start position:0% +minus is the Imp over all these + + + align:start position:0% +minus is the Imp over all these +Expressions where U has unit length a + + align:start position:0% +Expressions where U has unit length a + + + align:start position:0% +Expressions where U has unit length a +plus plus a minus is the point right in + + align:start position:0% +plus plus a minus is the point right in + + + align:start position:0% +plus plus a minus is the point right in +the middle of them so + + align:start position:0% +the middle of them so + + + align:start position:0% +the middle of them so +what's the biggest this or what's the + + align:start position:0% +what's the biggest this or what's the + + + align:start position:0% +what's the biggest this or what's the +supremum of + + align:start position:0% +supremum of + + + align:start position:0% +supremum of +the difference between these numbers and + + align:start position:0% +the difference between these numbers and + + + align:start position:0% +the difference between these numbers and +the midpoint well it's the + + align:start position:0% +the midpoint well it's the + + + align:start position:0% +the midpoint well it's the +distance given by + + align:start position:0% +distance given by + + + align:start position:0% +distance given by +uh the distance from a plus to the + + align:start position:0% +uh the distance from a plus to the + + + align:start position:0% +uh the distance from a plus to the +midpoint which is equal to the distance + + align:start position:0% +midpoint which is equal to the distance + + + align:start position:0% +midpoint which is equal to the distance +from a minus to the midpoint so which is + + align:start position:0% +from a minus to the midpoint so which is + + + align:start position:0% +from a minus to the midpoint so which is +um a + + align:start position:0% +um a + + + align:start position:0% +um a +plus minus a minus over two + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and since that's the normal B when we + + align:start position:0% +and since that's the normal B when we + + + align:start position:0% +and since that's the normal B when we +plug that into + + align:start position:0% +plug that into + + + align:start position:0% +plug that into +uh + + align:start position:0% +uh + + + align:start position:0% +uh +what we had a minute ago we conclude + + align:start position:0% +what we had a minute ago we conclude + + + align:start position:0% +what we had a minute ago we conclude +that the spectrum is contained in + + align:start position:0% +that the spectrum is contained in + + + align:start position:0% +that the spectrum is contained in +A minus + + align:start position:0% +A minus + + + align:start position:0% +A minus +a plus + + align:start position:0% + + + + align:start position:0% + +a simple core Larry of what we've done + + align:start position:0% +a simple core Larry of what we've done + + + align:start position:0% +a simple core Larry of what we've done +we have this nice little statement about + + align:start position:0% +we have this nice little statement about + + + align:start position:0% +we have this nice little statement about +when exactly + + align:start position:0% +when exactly + + + align:start position:0% +when exactly +a self-adjoint bounded linear operator + + align:start position:0% +a self-adjoint bounded linear operator + + + align:start position:0% +a self-adjoint bounded linear operator +is non-negative so + + align:start position:0% + + + + align:start position:0% + +but a + + align:start position:0% +but a + + + align:start position:0% +but a +be a self a joint bounded linear + + align:start position:0% +be a self a joint bounded linear + + + align:start position:0% +be a self a joint bounded linear +operator on the Hilbert space + + align:start position:0% +operator on the Hilbert space + + + align:start position:0% +operator on the Hilbert space +then + + align:start position:0% + + + + align:start position:0% + +for all you + + align:start position:0% +for all you + + + align:start position:0% +for all you +Au inner product U is bigger than or + + align:start position:0% +Au inner product U is bigger than or + + + align:start position:0% +Au inner product U is bigger than or +equal to zero + + align:start position:0% +equal to zero + + + align:start position:0% +equal to zero +if and only if + + align:start position:0% + + + + align:start position:0% + +the spectrum of a is contained in + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the non-negative numbers + + align:start position:0% +the non-negative numbers + + + align:start position:0% +the non-negative numbers +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +um I'm not even going to write out the + + align:start position:0% +um I'm not even going to write out the + + + align:start position:0% +um I'm not even going to write out the +proof I'm just going to talk my way + + align:start position:0% +proof I'm just going to talk my way + + + align:start position:0% +proof I'm just going to talk my way +through it + + align:start position:0% + + + + align:start position:0% + +so uh let's suppose that Au and a + + align:start position:0% +so uh let's suppose that Au and a + + + align:start position:0% +so uh let's suppose that Au and a +product U is non-negative + + align:start position:0% +product U is non-negative + + + align:start position:0% +product U is non-negative +then uh this number A minus + + align:start position:0% +then uh this number A minus + + + align:start position:0% +then uh this number A minus +is non-negative and therefore the + + align:start position:0% +is non-negative and therefore the + + + align:start position:0% +is non-negative and therefore the +spectrum is contained in a minus a plus + + align:start position:0% +spectrum is contained in a minus a plus + + + align:start position:0% +spectrum is contained in a minus a plus +which is a subset of the non-negative + + align:start position:0% +which is a subset of the non-negative + + + align:start position:0% +which is a subset of the non-negative +real numbers + + align:start position:0% +real numbers + + + align:start position:0% +real numbers +okay + + align:start position:0% +okay + + + align:start position:0% +okay +on the other hand suppose that the + + align:start position:0% +on the other hand suppose that the + + + align:start position:0% +on the other hand suppose that the +spectrum of a is contained in here + + align:start position:0% +spectrum of a is contained in here + + + align:start position:0% +spectrum of a is contained in here +then a minus + + align:start position:0% +then a minus + + + align:start position:0% +then a minus +which is in the Spectrum has to be in + + align:start position:0% +which is in the Spectrum has to be in + + + align:start position:0% +which is in the Spectrum has to be in +the set of non-negative real numbers + + align:start position:0% +the set of non-negative real numbers + + + align:start position:0% +the set of non-negative real numbers +and therefore Au inner product U always + + align:start position:0% +and therefore Au inner product U always + + + align:start position:0% +and therefore Au inner product U always +has to be non-negative since a minus is + + align:start position:0% +has to be non-negative since a minus is + + + align:start position:0% +has to be non-negative since a minus is +the info for all of these + + align:start position:0% +the info for all of these + + + align:start position:0% +the info for all of these +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now we're going to move on to + + align:start position:0% +so now we're going to move on to + + + align:start position:0% +so now we're going to move on to +the spectral theory for + + align:start position:0% +the spectral theory for + + + align:start position:0% +the spectral theory for +not just self-adjoin operators but + + align:start position:0% +not just self-adjoin operators but + + + align:start position:0% +not just self-adjoin operators but +self-adjoined operators that are also + + align:start position:0% +self-adjoined operators that are also + + + align:start position:0% +self-adjoined operators that are also +compact + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +again a natural example is given by uh + + align:start position:0% +again a natural example is given by uh + + + align:start position:0% +again a natural example is given by uh +the inverse of taking the second + + align:start position:0% +the inverse of taking the second + + + align:start position:0% +the inverse of taking the second +derivative along with requiring zero at + + align:start position:0% +derivative along with requiring zero at + + + align:start position:0% +derivative along with requiring zero at +the endpoints this operator I gave last + + align:start position:0% +the endpoints this operator I gave last + + + align:start position:0% +the endpoints this operator I gave last +time + + align:start position:0% +time + + + align:start position:0% +time +that is a bound itself a joint + + align:start position:0% +that is a bound itself a joint + + + align:start position:0% +that is a bound itself a joint +very compact self-adjoined operator + + align:start position:0% +very compact self-adjoined operator + + + align:start position:0% +very compact self-adjoined operator +so all the spectral Theory we developed + + align:start position:0% +so all the spectral Theory we developed + + + align:start position:0% +so all the spectral Theory we developed +for that applies + + align:start position:0% +for that applies + + + align:start position:0% +for that applies +and the Spectrum for that operator ends + + align:start position:0% +and the Spectrum for that operator ends + + + align:start position:0% +and the Spectrum for that operator ends +up being one over the eigenvalues + + align:start position:0% +up being one over the eigenvalues + + + align:start position:0% +up being one over the eigenvalues +corresponding to u double Prime equals + + align:start position:0% +corresponding to u double Prime equals + + + align:start position:0% +corresponding to u double Prime equals +Lambda equals say mu times U with zero + + align:start position:0% +Lambda equals say mu times U with zero + + + align:start position:0% +Lambda equals say mu times U with zero +at the end point so + + align:start position:0% +at the end point so + + + align:start position:0% +at the end point so +um + + align:start position:0% +um + + + align:start position:0% +um +and you'll see that in the assignment or + + align:start position:0% +and you'll see that in the assignment or + + + align:start position:0% +and you'll see that in the assignment or +maybe I'll do it as an example so now + + align:start position:0% +maybe I'll do it as an example so now + + + align:start position:0% +maybe I'll do it as an example so now +we're moving on to + + align:start position:0% + + + + align:start position:0% + +spectral theory for + + align:start position:0% + + + + align:start position:0% + +compact + + align:start position:0% + + + + align:start position:0% + +self-adjoin operators + + align:start position:0% +self-adjoin operators + + + align:start position:0% +self-adjoin operators +which is one of the most again complete + + align:start position:0% +which is one of the most again complete + + + align:start position:0% +which is one of the most again complete +things or + + align:start position:0% +things or + + + align:start position:0% +things or +a class of operators we can say the most + + align:start position:0% +a class of operators we can say the most + + + align:start position:0% +a class of operators we can say the most +about when it comes to the Spectrum + + align:start position:0% +about when it comes to the Spectrum + + + align:start position:0% +about when it comes to the Spectrum +and I'll go ahead and give you + + align:start position:0% + + + + align:start position:0% + +a preview of what we can say about the + + align:start position:0% +a preview of what we can say about the + + + align:start position:0% +a preview of what we can say about the +Spectrum for these operators + + align:start position:0% +Spectrum for these operators + + + align:start position:0% +Spectrum for these operators +uh that it essentially consists of + + align:start position:0% +uh that it essentially consists of + + + align:start position:0% +uh that it essentially consists of +nothing but eigenvalues + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +with the possible exception of zero + + align:start position:0% +with the possible exception of zero + + + align:start position:0% +with the possible exception of zero +being an accumulation point of the + + align:start position:0% +being an accumulation point of the + + + align:start position:0% +being an accumulation point of the +eigenvalues okay so what we'll prove is + + align:start position:0% +eigenvalues okay so what we'll prove is + + + align:start position:0% +eigenvalues okay so what we'll prove is +that the spectrum of a compact + + align:start position:0% +that the spectrum of a compact + + + align:start position:0% +that the spectrum of a compact +self-adjoined operator consists of the + + align:start position:0% +self-adjoined operator consists of the + + + align:start position:0% +self-adjoined operator consists of the +eigenvalues + + align:start position:0% +eigenvalues + + + align:start position:0% +eigenvalues +of this operator + + align:start position:0% +of this operator + + + align:start position:0% +of this operator +along with uh possibly zero + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +zero may or may not be an eigenvalue if + + align:start position:0% +zero may or may not be an eigenvalue if + + + align:start position:0% +zero may or may not be an eigenvalue if +it's not an eigenvalue then it's the + + align:start position:0% +it's not an eigenvalue then it's the + + + align:start position:0% +it's not an eigenvalue then it's the +limit of the eigenvalues and in fact + + align:start position:0% +limit of the eigenvalues and in fact + + + align:start position:0% +limit of the eigenvalues and in fact +so + + align:start position:0% +so + + + align:start position:0% +so +kind of implicit in that statement is + + align:start position:0% +kind of implicit in that statement is + + + align:start position:0% +kind of implicit in that statement is +that the spectrum is in fact accountable + + align:start position:0% +that the spectrum is in fact accountable + + + align:start position:0% +that the spectrum is in fact accountable +for a compact self-adjoined operator so + + align:start position:0% +for a compact self-adjoined operator so + + + align:start position:0% +for a compact self-adjoined operator so +you know why should we expect that + + align:start position:0% +you know why should we expect that + + + align:start position:0% +you know why should we expect that +um + + align:start position:0% +um + + + align:start position:0% +um +or why should we expect such a complete + + align:start position:0% +or why should we expect such a complete + + + align:start position:0% +or why should we expect such a complete +picture in the end we'll also prove that + + align:start position:0% +picture in the end we'll also prove that + + + align:start position:0% +picture in the end we'll also prove that +you can find a basis for H consisting + + align:start position:0% +you can find a basis for H consisting + + + align:start position:0% +you can find a basis for H consisting +entirely of eigenvectors of + + align:start position:0% +entirely of eigenvectors of + + + align:start position:0% +entirely of eigenvectors of +of the operator a which is again + + align:start position:0% +of the operator a which is again + + + align:start position:0% +of the operator a which is again +a + + align:start position:0% +a + + + align:start position:0% +a +generalization to infinite dimensions of + + align:start position:0% +generalization to infinite dimensions of + + + align:start position:0% +generalization to infinite dimensions of +what + + align:start position:0% +what + + + align:start position:0% +what +hopefully you saw in finite Dimensions + + align:start position:0% +hopefully you saw in finite Dimensions + + + align:start position:0% +hopefully you saw in finite Dimensions +but if you didn't our proof will still + + align:start position:0% +but if you didn't our proof will still + + + align:start position:0% +but if you didn't our proof will still +apply to finite Dimensions so why should + + align:start position:0% +apply to finite Dimensions so why should + + + align:start position:0% +apply to finite Dimensions so why should +that then apply to compact self-adjoin + + align:start position:0% +that then apply to compact self-adjoin + + + align:start position:0% +that then apply to compact self-adjoin +operators if you believe it for finite + + align:start position:0% +operators if you believe it for finite + + + align:start position:0% +operators if you believe it for finite +Dimensions well it's because again + + align:start position:0% +Dimensions well it's because again + + + align:start position:0% +Dimensions well it's because again +compact self-adjoined operators are the + + align:start position:0% +compact self-adjoined operators are the + + + align:start position:0% +compact self-adjoined operators are the +norm limit of finite rank operators all + + align:start position:0% +norm limit of finite rank operators all + + + align:start position:0% +norm limit of finite rank operators all +right and finite rank operators again + + align:start position:0% +right and finite rank operators again + + + align:start position:0% +right and finite rank operators again +these just correspond to basically + + align:start position:0% +these just correspond to basically + + + align:start position:0% +these just correspond to basically +matrices we know how to compute the + + align:start position:0% +matrices we know how to compute the + + + align:start position:0% +matrices we know how to compute the +eigenvalues of matrices for finite rank + + align:start position:0% +eigenvalues of matrices for finite rank + + + align:start position:0% +eigenvalues of matrices for finite rank +operators they have a they could have a + + align:start position:0% +operators they have a they could have a + + + align:start position:0% +operators they have a they could have a +very large null space meaning the + + align:start position:0% +very large null space meaning the + + + align:start position:0% +very large null space meaning the +eigenvalue uh zero could be could have a + + align:start position:0% +eigenvalue uh zero could be could have a + + + align:start position:0% +eigenvalue uh zero could be could have a +very large eigenspace but that's the + + align:start position:0% +very large eigenspace but that's the + + + align:start position:0% +very large eigenspace but that's the +point of you know kind of why you expect + + align:start position:0% +point of you know kind of why you expect + + + align:start position:0% +point of you know kind of why you expect +maybe things to carry over to the + + align:start position:0% +maybe things to carry over to the + + + align:start position:0% +maybe things to carry over to the +setting of compact self-adjoined + + align:start position:0% +setting of compact self-adjoined + + + align:start position:0% +setting of compact self-adjoined +operators from what you know in finite + + align:start position:0% +operators from what you know in finite + + + align:start position:0% +operators from what you know in finite +dimensions + + align:start position:0% +dimensions + + + align:start position:0% +dimensions +um + + align:start position:0% +um + + + align:start position:0% +um +okay + + align:start position:0% + + + + align:start position:0% + +so this is not so much a definition as + + align:start position:0% +so this is not so much a definition as + + + align:start position:0% +so this is not so much a definition as +just notation uh + + align:start position:0% + + + + align:start position:0% + +if a is a bounded linear operator + + align:start position:0% +if a is a bounded linear operator + + + align:start position:0% +if a is a bounded linear operator +I will + + align:start position:0% +I will + + + align:start position:0% +I will +denote + + align:start position:0% +denote + + + align:start position:0% +denote +e Lambda to be + + align:start position:0% + + + + align:start position:0% + +null space of a minus Lambda in other + + align:start position:0% +null space of a minus Lambda in other + + + align:start position:0% +null space of a minus Lambda in other +words the set of uh or the Subspace of + + align:start position:0% +words the set of uh or the Subspace of + + + align:start position:0% +words the set of uh or the Subspace of +eigenvectors with eigenvalue Lambda okay + + align:start position:0% +eigenvectors with eigenvalue Lambda okay + + + align:start position:0% +eigenvectors with eigenvalue Lambda okay +which again is the set of U + + align:start position:0% +which again is the set of U + + + align:start position:0% +which again is the set of U +and H such that + + align:start position:0% +and H such that + + + align:start position:0% +and H such that +a minus Lambda + + align:start position:0% +a minus Lambda + + + align:start position:0% +a minus Lambda +U equals zero + + align:start position:0% +U equals zero + + + align:start position:0% +U equals zero +okay + + align:start position:0% + + + + align:start position:0% + +all right so first off + + align:start position:0% + + + + align:start position:0% + +before we get to + + align:start position:0% + + + + align:start position:0% + +classifying the spectral + + align:start position:0% +classifying the spectral + + + align:start position:0% +classifying the spectral +or the spectrum of a compact + + align:start position:0% +or the spectrum of a compact + + + align:start position:0% +or the spectrum of a compact +self-adjoined operator as basically + + align:start position:0% +self-adjoined operator as basically + + + align:start position:0% +self-adjoined operator as basically +consisting of eigenvalues along with + + align:start position:0% +consisting of eigenvalues along with + + + align:start position:0% +consisting of eigenvalues along with +zero we'll first give some kind of + + align:start position:0% +zero we'll first give some kind of + + + align:start position:0% +zero we'll first give some kind of +General + + align:start position:0% +General + + + align:start position:0% +General +um properties of eigenvalues in general + + align:start position:0% +um properties of eigenvalues in general + + + align:start position:0% +um properties of eigenvalues in general +about for a compact itself a joint + + align:start position:0% +about for a compact itself a joint + + + align:start position:0% +about for a compact itself a joint +operator + + align:start position:0% +operator + + + align:start position:0% +operator +so + + align:start position:0% +so + + + align:start position:0% +so +we have the following theorem that uh + + align:start position:0% + + + + align:start position:0% + +suppose + + align:start position:0% +suppose + + + align:start position:0% +suppose +a star a uh + + align:start position:0% + + + + align:start position:0% + +so is a compact self-adjoined operator + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +um + + align:start position:0% +um + + + align:start position:0% +um +few things + + align:start position:0% + + + + align:start position:0% + +if Lambda not equal to zero is + + align:start position:0% +if Lambda not equal to zero is + + + align:start position:0% +if Lambda not equal to zero is +an eigenvalue + + align:start position:0% +an eigenvalue + + + align:start position:0% +an eigenvalue +of a + + align:start position:0% +of a + + + align:start position:0% +of a +then the dimension + + align:start position:0% + + + + align:start position:0% + +of e Lambda the eigen space the the + + align:start position:0% +of e Lambda the eigen space the the + + + align:start position:0% +of e Lambda the eigen space the the +linear Subspace of all vectors that uh + + align:start position:0% +linear Subspace of all vectors that uh + + + align:start position:0% +linear Subspace of all vectors that uh +our eigenvectors of a + + align:start position:0% +our eigenvectors of a + + + align:start position:0% +our eigenvectors of a +this is finite + + align:start position:0% +this is finite + + + align:start position:0% +this is finite +so for for a given eigenvalue the + + align:start position:0% +so for for a given eigenvalue the + + + align:start position:0% +so for for a given eigenvalue the +dimension of the eigenspace is finite + + align:start position:0% + + + + align:start position:0% + +um the second is that if I take two + + align:start position:0% +um the second is that if I take two + + + align:start position:0% +um the second is that if I take two +different + + align:start position:0% +different + + + align:start position:0% +different +eigenvalues uh + + align:start position:0% +eigenvalues uh + + + align:start position:0% +eigenvalues uh +the corresponding eigenspaces are + + align:start position:0% +the corresponding eigenspaces are + + + align:start position:0% +the corresponding eigenspaces are +perpendicular to each other + + align:start position:0% + + + + align:start position:0% + +Lambda 1 does not equal Lambda 2. + + align:start position:0% +Lambda 1 does not equal Lambda 2. + + + align:start position:0% +Lambda 1 does not equal Lambda 2. +uh + + align:start position:0% + + + + align:start position:0% + +eigenvalues of a + + align:start position:0% +eigenvalues of a + + + align:start position:0% +eigenvalues of a +then + + align:start position:0% + + + + align:start position:0% + +e Lambda one + + align:start position:0% + + + + align:start position:0% + +e Lambda 2. + + align:start position:0% + + + + align:start position:0% + +are orthogonal or perpendicular + + align:start position:0% +are orthogonal or perpendicular + + + align:start position:0% +are orthogonal or perpendicular +okay every element in E Lambda 1 is + + align:start position:0% +okay every element in E Lambda 1 is + + + align:start position:0% +okay every element in E Lambda 1 is +orthogonal to every element in E Lambda + + align:start position:0% +orthogonal to every element in E Lambda + + + align:start position:0% +orthogonal to every element in E Lambda +2 and vice versa + + align:start position:0% + + + + align:start position:0% + +and finally + + align:start position:0% + + + + align:start position:0% + +set of non-zero + + align:start position:0% + + + + align:start position:0% + +eigenvalues of a + + align:start position:0% + + + + align:start position:0% + +is either finite + + align:start position:0% + + + + align:start position:0% + +or countable + + align:start position:0% + + + + align:start position:0% + +if it is countable + + align:start position:0% + + + + align:start position:0% + +I.E it's given by + + align:start position:0% +I.E it's given by + + + align:start position:0% +I.E it's given by +a sequence + + align:start position:0% +a sequence + + + align:start position:0% +a sequence +Lambda n + + align:start position:0% +Lambda n + + + align:start position:0% +Lambda n +then + + align:start position:0% + + + + align:start position:0% + +these + + align:start position:0% +these + + + align:start position:0% +these +or if it is countably infinite I should + + align:start position:0% +or if it is countably infinite I should + + + align:start position:0% +or if it is countably infinite I should +say + + align:start position:0% + + + + align:start position:0% + +and I should have said accountably + + align:start position:0% +and I should have said accountably + + + align:start position:0% +and I should have said accountably +infinite here + + align:start position:0% + + + + align:start position:0% + +if it's countably infinite then uh + + align:start position:0% +if it's countably infinite then uh + + + align:start position:0% +if it's countably infinite then uh +they can the eigenvalues converge to + + align:start position:0% +they can the eigenvalues converge to + + + align:start position:0% +they can the eigenvalues converge to +zero + + align:start position:0% + + + + align:start position:0% + +okay in particular this implies that if + + align:start position:0% +okay in particular this implies that if + + + align:start position:0% +okay in particular this implies that if +I have a a compact self-adjoined + + align:start position:0% +I have a a compact self-adjoined + + + align:start position:0% +I have a a compact self-adjoined +operator with infinitely many + + align:start position:0% +operator with infinitely many + + + align:start position:0% +operator with infinitely many +eigenvalues then zero is in the spectrum + + align:start position:0% +eigenvalues then zero is in the spectrum + + + align:start position:0% +eigenvalues then zero is in the spectrum +of + + align:start position:0% +of + + + align:start position:0% +of +this operator + + align:start position:0% +this operator + + + align:start position:0% +this operator +right because + + align:start position:0% +right because + + + align:start position:0% +right because +um + + align:start position:0% +um + + + align:start position:0% +um +the spectrum is a closed set so it's + + align:start position:0% +the spectrum is a closed set so it's + + + align:start position:0% +the spectrum is a closed set so it's +closed undertaking limits and since + + align:start position:0% +closed undertaking limits and since + + + align:start position:0% +closed undertaking limits and since +these are in the Spectrum + + align:start position:0% +these are in the Spectrum + + + align:start position:0% +these are in the Spectrum +the limit has to be in the Spectrum okay + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +proof of one + + align:start position:0% + + + + align:start position:0% + +suppose I have a non-zero eigenvalue and + + align:start position:0% +suppose I have a non-zero eigenvalue and + + + align:start position:0% +suppose I have a non-zero eigenvalue and +towards the contradiction + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +elanda is not finite dimensional + + align:start position:0% +elanda is not finite dimensional + + + align:start position:0% +elanda is not finite dimensional +okay + + align:start position:0% +okay + + + align:start position:0% +okay +then what I can do by the Graham Schmidt + + align:start position:0% +then what I can do by the Graham Schmidt + + + align:start position:0% +then what I can do by the Graham Schmidt +process + + align:start position:0% +process + + + align:start position:0% +process +then there exists + + align:start position:0% + + + + align:start position:0% + +a sequence or a countable collection + + align:start position:0% +a sequence or a countable collection + + + align:start position:0% +a sequence or a countable collection +u n + + align:start position:0% + + + + align:start position:0% + +over to normal + + align:start position:0% + + + + align:start position:0% + +elements + + align:start position:0% +elements + + + align:start position:0% +elements +need Lambda okay so every uh element in + + align:start position:0% +need Lambda okay so every uh element in + + + align:start position:0% +need Lambda okay so every uh element in +the sequence is + + align:start position:0% +the sequence is + + + align:start position:0% +the sequence is +has unit length and it's orthogonal to + + align:start position:0% +has unit length and it's orthogonal to + + + align:start position:0% +has unit length and it's orthogonal to +any other element in the sequence okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +now + + align:start position:0% + + + + align:start position:0% + +since a is a + + align:start position:0% + + + + align:start position:0% + +compact operator + + align:start position:0% + + + + align:start position:0% + +and all of these have unit length + + align:start position:0% +and all of these have unit length + + + align:start position:0% +and all of these have unit length +it follows that a + + align:start position:0% +it follows that a + + + align:start position:0% +it follows that a +applied to U in + + align:start position:0% +applied to U in + + + align:start position:0% +applied to U in +is contained this is a sequence in a + + align:start position:0% +is contained this is a sequence in a + + + align:start position:0% +is contained this is a sequence in a +compact set right so it has a convergent + + align:start position:0% +compact set right so it has a convergent + + + align:start position:0% +compact set right so it has a convergent +subsequence + + align:start position:0% + + + + align:start position:0% + +subsequence + + align:start position:0% +subsequence + + + align:start position:0% +subsequence +a u and J J + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +then + + align:start position:0% +then + + + align:start position:0% +then +a u and J + + align:start position:0% + + + + align:start position:0% + +is Koshi + + align:start position:0% +is Koshi + + + align:start position:0% +is Koshi +but + + align:start position:0% +but + + + align:start position:0% +but +let's actually look at what's the + + align:start position:0% + + + + align:start position:0% + +difference between a + + align:start position:0% +difference between a + + + align:start position:0% +difference between a +two of these in Norm + + align:start position:0% +two of these in Norm + + + align:start position:0% +two of these in Norm +let's make it squared + + align:start position:0% +let's make it squared + + + align:start position:0% +let's make it squared +this is equal to + + align:start position:0% +this is equal to + + + align:start position:0% +this is equal to +Norm of because these are eigenvalues + + align:start position:0% +Norm of because these are eigenvalues + + + align:start position:0% +Norm of because these are eigenvalues +Lambda u n j minus Lambda U and K + + align:start position:0% +Lambda u n j minus Lambda U and K + + + align:start position:0% +Lambda u n j minus Lambda U and K +squared which equals + + align:start position:0% + + + + align:start position:0% + +squared which equals + + align:start position:0% +squared which equals + + + align:start position:0% +squared which equals +2 Lambda squared + + align:start position:0% +2 Lambda squared + + + align:start position:0% +2 Lambda squared +which is a fixed number that's positive + + align:start position:0% +which is a fixed number that's positive + + + align:start position:0% +which is a fixed number that's positive +because Lambda is not equal to zero + + align:start position:0% + + + + align:start position:0% + +left off a part of the + + align:start position:0% +left off a part of the + + + align:start position:0% +left off a part of the +so okay so this what does this imply + + align:start position:0% +so okay so this what does this imply + + + align:start position:0% +so okay so this what does this imply +this implies that the distance between + + align:start position:0% +this implies that the distance between + + + align:start position:0% +this implies that the distance between +any so this is + + align:start position:0% + + + + align:start position:0% + +if I take any two elements in this + + align:start position:0% +if I take any two elements in this + + + align:start position:0% +if I take any two elements in this +subsequence their distance is a constant + + align:start position:0% +subsequence their distance is a constant + + + align:start position:0% +subsequence their distance is a constant +equal to two times Lambda squared and + + align:start position:0% +equal to two times Lambda squared and + + + align:start position:0% +equal to two times Lambda squared and +therefore this is not koshy which is a + + align:start position:0% +therefore this is not koshy which is a + + + align:start position:0% +therefore this is not koshy which is a +contradiction + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +something I forgot to say + + align:start position:0% +something I forgot to say + + + align:start position:0% +something I forgot to say +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +the statement of the theorem + + align:start position:0% + + + + align:start position:0% + +forgive me it's the end of a long day + + align:start position:0% +forgive me it's the end of a long day + + + align:start position:0% +forgive me it's the end of a long day +is that + + align:start position:0% +is that + + + align:start position:0% +is that +eigenvalues have to be real + + align:start position:0% +eigenvalues have to be real + + + align:start position:0% +eigenvalues have to be real +for self-adjoint compact operator so + + align:start position:0% +for self-adjoint compact operator so + + + align:start position:0% +for self-adjoint compact operator so +really for self-adjoined operators + + align:start position:0% +really for self-adjoined operators + + + align:start position:0% +really for self-adjoined operators +uh + + align:start position:0% +uh + + + align:start position:0% +uh +if I could have included it earlier + + align:start position:0% + + + + align:start position:0% + +so the eigenvalues of a self-adjoined + + align:start position:0% +so the eigenvalues of a self-adjoined + + + align:start position:0% +so the eigenvalues of a self-adjoined +operator have to be real why is that + + align:start position:0% +operator have to be real why is that + + + align:start position:0% +operator have to be real why is that +um + + align:start position:0% + + + + align:start position:0% + +since uh + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% + + + + align:start position:0% + +I have something with Norm one + + align:start position:0% +I have something with Norm one + + + align:start position:0% +I have something with Norm one +so if Lambda is an eigenvalue + + align:start position:0% +so if Lambda is an eigenvalue + + + align:start position:0% +so if Lambda is an eigenvalue +it has comes with an eigenvector U with + + align:start position:0% +it has comes with an eigenvector U with + + + align:start position:0% +it has comes with an eigenvector U with +length one so that a u equals Lambda U + + align:start position:0% +length one so that a u equals Lambda U + + + align:start position:0% +length one so that a u equals Lambda U +of course it just has to be a non-zero U + + align:start position:0% +of course it just has to be a non-zero U + + + align:start position:0% +of course it just has to be a non-zero U +but I can normalize it by dividing by + + align:start position:0% +but I can normalize it by dividing by + + + align:start position:0% +but I can normalize it by dividing by +its link + + align:start position:0% + + + + align:start position:0% + +and therefore I get that Lambda which is + + align:start position:0% +and therefore I get that Lambda which is + + + align:start position:0% +and therefore I get that Lambda which is +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +U inner product U this is Norm of U + + align:start position:0% +U inner product U this is Norm of U + + + align:start position:0% +U inner product U this is Norm of U +squared which is one + + align:start position:0% +squared which is one + + + align:start position:0% +squared which is one +Lambda u u and this is equal to complex + + align:start position:0% +Lambda u u and this is equal to complex + + + align:start position:0% +Lambda u u and this is equal to complex +conjugate + + align:start position:0% +conjugate + + + align:start position:0% +conjugate +or let's not do that + + align:start position:0% + + + + align:start position:0% + +this is equal to + + align:start position:0% + + + + align:start position:0% + +a u u which is equal to I take a and it + + align:start position:0% +a u u which is equal to I take a and it + + + align:start position:0% +a u u which is equal to I take a and it +becomes a star U but a star is equal to + + align:start position:0% +becomes a star U but a star is equal to + + + align:start position:0% +becomes a star U but a star is equal to +a so I get u a u since a is Alpha joint + + align:start position:0% +a so I get u a u since a is Alpha joint + + + align:start position:0% +a so I get u a u since a is Alpha joint +and this is equal to U Lambda U and + + align:start position:0% +and this is equal to U Lambda U and + + + align:start position:0% +and this is equal to U Lambda U and +remember uh + + align:start position:0% +remember uh + + + align:start position:0% +remember uh +inner products are + + align:start position:0% +inner products are + + + align:start position:0% +inner products are +conjugate linear in the second entry so + + align:start position:0% +conjugate linear in the second entry so + + + align:start position:0% +conjugate linear in the second entry so +this Lambda pops out but now complex + + align:start position:0% +this Lambda pops out but now complex + + + align:start position:0% +this Lambda pops out but now complex +conjugate so Lambda + + align:start position:0% + + + + align:start position:0% + +so we've shown that the complex + + align:start position:0% +so we've shown that the complex + + + align:start position:0% +so we've shown that the complex +conjugate + + align:start position:0% +conjugate + + + align:start position:0% +conjugate +is equal to uh the original number so + + align:start position:0% +is equal to uh the original number so + + + align:start position:0% +is equal to uh the original number so +Lambda has to be a real number + + align:start position:0% +Lambda has to be a real number + + + align:start position:0% +Lambda has to be a real number +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so that proves part one that + + align:start position:0% +all right so that proves part one that + + + align:start position:0% +all right so that proves part one that +the eigenvalues of a self-adjoin + + align:start position:0% +the eigenvalues of a self-adjoin + + + align:start position:0% +the eigenvalues of a self-adjoin +operator have to be real and the eigen + + align:start position:0% +operator have to be real and the eigen + + + align:start position:0% +operator have to be real and the eigen +spaces of which is what I have just + + align:start position:0% +spaces of which is what I have just + + + align:start position:0% +spaces of which is what I have just +started calling the elandus the + + align:start position:0% +started calling the elandus the + + + align:start position:0% +started calling the elandus the +eigenspace have to be finite dimensional + + align:start position:0% +eigenspace have to be finite dimensional + + + align:start position:0% +eigenspace have to be finite dimensional +for a compact self-adjoined operator + + align:start position:0% + + + + align:start position:0% + +okay so now let's show that + + align:start position:0% +okay so now let's show that + + + align:start position:0% +okay so now let's show that +uh + + align:start position:0% + + + + align:start position:0% + +distinct eigenspaces have to be + + align:start position:0% +distinct eigenspaces have to be + + + align:start position:0% +distinct eigenspaces have to be +orthogonal to each other suppose Lambda + + align:start position:0% +orthogonal to each other suppose Lambda + + + align:start position:0% +orthogonal to each other suppose Lambda +1 does not equal Lambda 2. you + + align:start position:0% + + + + align:start position:0% + +one is in E Lambda One U2 is in e + + align:start position:0% +one is in E Lambda One U2 is in e + + + align:start position:0% +one is in E Lambda One U2 is in e +Lambda 2. + + align:start position:0% + + + + align:start position:0% + +so now what I'd like to show is that the + + align:start position:0% +so now what I'd like to show is that the + + + align:start position:0% +so now what I'd like to show is that the +inner product of U1 with U2 is equal to + + align:start position:0% +inner product of U1 with U2 is equal to + + + align:start position:0% +inner product of U1 with U2 is equal to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +and it's going to be a trick kind of + + align:start position:0% +and it's going to be a trick kind of + + + align:start position:0% +and it's going to be a trick kind of +like I just did here Lambda 1 times U1 + + align:start position:0% +like I just did here Lambda 1 times U1 + + + align:start position:0% +like I just did here Lambda 1 times U1 +U2 + + align:start position:0% +U2 + + + align:start position:0% +U2 +this is equal to + + align:start position:0% +this is equal to + + + align:start position:0% +this is equal to +Lambda 1 U1 U2 this is equal to + + align:start position:0% +Lambda 1 U1 U2 this is equal to + + + align:start position:0% +Lambda 1 U1 U2 this is equal to +a applied to U1 U2 + + align:start position:0% +a applied to U1 U2 + + + align:start position:0% +a applied to U1 U2 +and now I move a over uh to here because + + align:start position:0% +and now I move a over uh to here because + + + align:start position:0% +and now I move a over uh to here because +a is Alpha joint + + align:start position:0% +a is Alpha joint + + + align:start position:0% +a is Alpha joint +all right uh + + align:start position:0% + + + + align:start position:0% + +and a applied to U2 so U2 is in the + + align:start position:0% +and a applied to U2 so U2 is in the + + + align:start position:0% +and a applied to U2 so U2 is in the +second eigenspace so this is equal to U1 + + align:start position:0% +second eigenspace so this is equal to U1 + + + align:start position:0% +second eigenspace so this is equal to U1 +Lambda 2. + + align:start position:0% +Lambda 2. + + + align:start position:0% +Lambda 2. +U2 and because uh Lambda 1 and Lambda 2 + + align:start position:0% +U2 and because uh Lambda 1 and Lambda 2 + + + align:start position:0% +U2 and because uh Lambda 1 and Lambda 2 +have to be real numbers what we've done + + align:start position:0% +have to be real numbers what we've done + + + align:start position:0% +have to be real numbers what we've done +from the first part + + align:start position:0% +from the first part + + + align:start position:0% +from the first part +this Lambda 2 comes all the way out and + + align:start position:0% +this Lambda 2 comes all the way out and + + + align:start position:0% +this Lambda 2 comes all the way out and +remains itself no complex conjugate + + align:start position:0% +remains itself no complex conjugate + + + align:start position:0% +remains itself no complex conjugate +because it's equal to its complex + + align:start position:0% +because it's equal to its complex + + + align:start position:0% +because it's equal to its complex +conjugate + + align:start position:0% +conjugate + + + align:start position:0% +conjugate +and so I started off with Lambda 1 times + + align:start position:0% +and so I started off with Lambda 1 times + + + align:start position:0% +and so I started off with Lambda 1 times +the inner product of U1 U2 and I've + + align:start position:0% +the inner product of U1 U2 and I've + + + align:start position:0% +the inner product of U1 U2 and I've +ended up with Lambda 2 U1 inner product + + align:start position:0% +ended up with Lambda 2 U1 inner product + + + align:start position:0% +ended up with Lambda 2 U1 inner product +with U2 and therefore Lambda 1 minus + + align:start position:0% +with U2 and therefore Lambda 1 minus + + + align:start position:0% +with U2 and therefore Lambda 1 minus +Lambda 2 times the inner product of U1 + + align:start position:0% +Lambda 2 times the inner product of U1 + + + align:start position:0% +Lambda 2 times the inner product of U1 +minus or the inner product of U1 with U2 + + align:start position:0% +minus or the inner product of U1 with U2 + + + align:start position:0% +minus or the inner product of U1 with U2 +equals 0. + + align:start position:0% + + + + align:start position:0% + +okay and Lambda 1 remember we're + + align:start position:0% +okay and Lambda 1 remember we're + + + align:start position:0% +okay and Lambda 1 remember we're +assuming Lambda 1 and Lambda 2 are + + align:start position:0% +assuming Lambda 1 and Lambda 2 are + + + align:start position:0% +assuming Lambda 1 and Lambda 2 are +non-zero or not equal so this quantity + + align:start position:0% +non-zero or not equal so this quantity + + + align:start position:0% +non-zero or not equal so this quantity +here is non-zero so I get that + + align:start position:0% +here is non-zero so I get that + + + align:start position:0% +here is non-zero so I get that +U1 U2 + + align:start position:0% +U1 U2 + + + align:start position:0% +U1 U2 +equals zero and that's the uh + + align:start position:0% +equals zero and that's the uh + + + align:start position:0% +equals zero and that's the uh +uh nope that's not the end that's the + + align:start position:0% +uh nope that's not the end that's the + + + align:start position:0% +uh nope that's not the end that's the +end of number two but not the end of uh + + align:start position:0% +end of number two but not the end of uh + + + align:start position:0% +end of number two but not the end of uh +the proof of this theorem + + align:start position:0% + + + + align:start position:0% + +all right so we're going to prove the + + align:start position:0% +all right so we're going to prove the + + + align:start position:0% +all right so we're going to prove the +last thing that uh the set of non-zero + + align:start position:0% +last thing that uh the set of non-zero + + + align:start position:0% +last thing that uh the set of non-zero +eigenvalues is either finite or + + align:start position:0% +eigenvalues is either finite or + + + align:start position:0% +eigenvalues is either finite or +countable and that uh + + align:start position:0% +countable and that uh + + + align:start position:0% +countable and that uh +if I arrange them in a sequence then the + + align:start position:0% +if I arrange them in a sequence then the + + + align:start position:0% +if I arrange them in a sequence then the +sequence converges to zero + + align:start position:0% + + + + align:start position:0% + +okay so just to have some notation uh + + align:start position:0% +okay so just to have some notation uh + + + align:start position:0% +okay so just to have some notation uh +running around + + align:start position:0% + + + + align:start position:0% + +Capital Lambda let me let this denote uh + + align:start position:0% + + + + align:start position:0% + +those non-zero eigenvalues + + align:start position:0% + + + + align:start position:0% + +all right so what I'd like to claim + + align:start position:0% +all right so what I'd like to claim + + + align:start position:0% +all right so what I'd like to claim +but what I'm going to show + + align:start position:0% +but what I'm going to show + + + align:start position:0% +but what I'm going to show +is that uh + + align:start position:0% + + + + align:start position:0% + +if Lambda n + + align:start position:0% +if Lambda n + + + align:start position:0% +if Lambda n +is + + align:start position:0% +is + + + align:start position:0% +is +a + + align:start position:0% + + + + align:start position:0% + +sequence of + + align:start position:0% + + + + align:start position:0% + +distinct elements + + align:start position:0% +distinct elements + + + align:start position:0% +distinct elements +or distinct uh + + align:start position:0% +or distinct uh + + + align:start position:0% +or distinct uh +eigenvalues + + align:start position:0% +eigenvalues + + + align:start position:0% +eigenvalues +non-zero eigenvalues of a + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +these converge to zero okay so this + + align:start position:0% +these converge to zero okay so this + + + align:start position:0% +these converge to zero okay so this +gives us um + + align:start position:0% +gives us um + + + align:start position:0% +gives us um +so of course okay so the set of non-zero + + align:start position:0% +so of course okay so the set of non-zero + + + align:start position:0% +so of course okay so the set of non-zero +eigen values may be finite fine suppose + + align:start position:0% +eigen values may be finite fine suppose + + + align:start position:0% +eigen values may be finite fine suppose +it's not okay now we're just in the in + + align:start position:0% +it's not okay now we're just in the in + + + align:start position:0% +it's not okay now we're just in the in +the uh setting that + + align:start position:0% +the uh setting that + + + align:start position:0% +the uh setting that +um this that a has infinitely many + + align:start position:0% +um this that a has infinitely many + + + align:start position:0% +um this that a has infinitely many +eigenvalues + + align:start position:0% + + + + align:start position:0% + +um if I can prove this claim then I have + + align:start position:0% +um if I can prove this claim then I have + + + align:start position:0% +um if I can prove this claim then I have +proven two things at once I have proven + + align:start position:0% +proven two things at once I have proven + + + align:start position:0% +proven two things at once I have proven +both that uh the set of non-zero + + align:start position:0% +both that uh the set of non-zero + + + align:start position:0% +both that uh the set of non-zero +eigenvalues is countably infinite + + align:start position:0% +eigenvalues is countably infinite + + + align:start position:0% +eigenvalues is countably infinite +assuming it's infinite + + align:start position:0% +assuming it's infinite + + + align:start position:0% +assuming it's infinite +um and uh they converge to zero so why + + align:start position:0% +um and uh they converge to zero so why + + + align:start position:0% +um and uh they converge to zero so why +does this + + align:start position:0% + + + + align:start position:0% + +so first off if we can show that this + + align:start position:0% +so first off if we can show that this + + + align:start position:0% +so first off if we can show that this +Capital Lambda is countable then this + + align:start position:0% +Capital Lambda is countable then this + + + align:start position:0% +Capital Lambda is countable then this +claim then implies that are countably + + align:start position:0% +claim then implies that are countably + + + align:start position:0% +claim then implies that are countably +infinite then this claim tells me that + + align:start position:0% +infinite then this claim tells me that + + + align:start position:0% +infinite then this claim tells me that +uh the eigenvalues converge to zero + + align:start position:0% +uh the eigenvalues converge to zero + + + align:start position:0% +uh the eigenvalues converge to zero +which is the the last thing I want so + + align:start position:0% +which is the the last thing I want so + + + align:start position:0% +which is the the last thing I want so +all I really need to show is that this + + align:start position:0% +all I really need to show is that this + + + align:start position:0% +all I really need to show is that this +is countable uh using this claim now why + + align:start position:0% +is countable uh using this claim now why + + + align:start position:0% +is countable uh using this claim now why +does this show that Capital Lambda is + + align:start position:0% +does this show that Capital Lambda is + + + align:start position:0% +does this show that Capital Lambda is +accountable + + align:start position:0% +accountable + + + align:start position:0% +accountable +since then if I Define + + align:start position:0% + + + + align:start position:0% + +Lambda sub capital N to be the set of + + align:start position:0% +Lambda sub capital N to be the set of + + + align:start position:0% +Lambda sub capital N to be the set of +non-zero eigenvalues + + align:start position:0% + + + + align:start position:0% + +which are let's say even bigger than or + + align:start position:0% +which are let's say even bigger than or + + + align:start position:0% +which are let's say even bigger than or +equal to 1 over n + + align:start position:0% +equal to 1 over n + + + align:start position:0% +equal to 1 over n +this has to be a finite set + + align:start position:0% +this has to be a finite set + + + align:start position:0% +this has to be a finite set +right if it was infinite then I could + + align:start position:0% +right if it was infinite then I could + + + align:start position:0% +right if it was infinite then I could +find a + + align:start position:0% +find a + + + align:start position:0% +find a +sequence of distinct elements in here + + align:start position:0% +sequence of distinct elements in here + + + align:start position:0% +sequence of distinct elements in here +right + + align:start position:0% +right + + + align:start position:0% +right +and obtain uh or I should say then I can + + align:start position:0% +and obtain uh or I should say then I can + + + align:start position:0% +and obtain uh or I should say then I can +find a subsequent or hold on let me let + + align:start position:0% +find a subsequent or hold on let me let + + + align:start position:0% +find a subsequent or hold on let me let +me stop for a minute + + align:start position:0% +me stop for a minute + + + align:start position:0% +me stop for a minute +um + + align:start position:0% + + + + align:start position:0% + +so my claim is that this is finite + + align:start position:0% +so my claim is that this is finite + + + align:start position:0% +so my claim is that this is finite +we're all in which implies that Lambda + + align:start position:0% +we're all in which implies that Lambda + + + align:start position:0% +we're all in which implies that Lambda +which is the union of + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +accountable Okay so + + align:start position:0% +accountable Okay so + + + align:start position:0% +accountable Okay so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +assuming this claim or assuming what I + + align:start position:0% +assuming this claim or assuming what I + + + align:start position:0% +assuming this claim or assuming what I +wrote here that this is finite for all n + + align:start position:0% +wrote here that this is finite for all n + + + align:start position:0% +wrote here that this is finite for all n +this implies this accountable that's + + align:start position:0% +this implies this accountable that's + + + align:start position:0% +this implies this accountable that's +clear so why do I get this is finite + + align:start position:0% +clear so why do I get this is finite + + + align:start position:0% +clear so why do I get this is finite +this set is finite assuming this claim + + align:start position:0% +this set is finite assuming this claim + + + align:start position:0% +this set is finite assuming this claim +well if this set is infinite then I can + + align:start position:0% +well if this set is infinite then I can + + + align:start position:0% +well if this set is infinite then I can +pick out a sequence of distinct elements + + align:start position:0% +pick out a sequence of distinct elements + + + align:start position:0% +pick out a sequence of distinct elements +in Lambda sub n + + align:start position:0% +in Lambda sub n + + + align:start position:0% +in Lambda sub n +uh that converges okay I could just take + + align:start position:0% +uh that converges okay I could just take + + + align:start position:0% +uh that converges okay I could just take +any sequence and then take a convergent + + align:start position:0% +any sequence and then take a convergent + + + align:start position:0% +any sequence and then take a convergent +subsequence because that sequence has to + + align:start position:0% +subsequence because that sequence has to + + + align:start position:0% +subsequence because that sequence has to +be bounded between 1 over n and the norm + + align:start position:0% +be bounded between 1 over n and the norm + + + align:start position:0% +be bounded between 1 over n and the norm +of a + + align:start position:0% +of a + + + align:start position:0% +of a +but since they're all bigger than or + + align:start position:0% +but since they're all bigger than or + + + align:start position:0% +but since they're all bigger than or +equal to 1 over n that sequence has to + + align:start position:0% +equal to 1 over n that sequence has to + + + align:start position:0% +equal to 1 over n that sequence has to +converge to something that's non-zero + + align:start position:0% +converge to something that's non-zero + + + align:start position:0% +converge to something that's non-zero +but that would contradict the claim + + align:start position:0% +but that would contradict the claim + + + align:start position:0% +but that would contradict the claim +again assuming the claim is true we + + align:start position:0% +again assuming the claim is true we + + + align:start position:0% +again assuming the claim is true we +haven't proved it yet all right so again + + align:start position:0% +haven't proved it yet all right so again + + + align:start position:0% +haven't proved it yet all right so again +from this claim we can then conclude + + align:start position:0% +from this claim we can then conclude + + + align:start position:0% +from this claim we can then conclude +that each of these sets is finite + + align:start position:0% +that each of these sets is finite + + + align:start position:0% +that each of these sets is finite +okay for all in and therefore the set of + + align:start position:0% +okay for all in and therefore the set of + + + align:start position:0% +okay for all in and therefore the set of +non-zero eigenvalues is countable + + align:start position:0% +non-zero eigenvalues is countable + + + align:start position:0% +non-zero eigenvalues is countable +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and if it's countably infinite then + + align:start position:0% +and if it's countably infinite then + + + align:start position:0% +and if it's countably infinite then +again from this claim we conclude that + + align:start position:0% +again from this claim we conclude that + + + align:start position:0% +again from this claim we conclude that +uh the eigenvalues must converge to zero + + align:start position:0% +uh the eigenvalues must converge to zero + + + align:start position:0% +uh the eigenvalues must converge to zero +when I line them up in a sequence + + align:start position:0% +when I line them up in a sequence + + + align:start position:0% +when I line them up in a sequence +okay so the whole proof is reduced to + + align:start position:0% +okay so the whole proof is reduced to + + + align:start position:0% +okay so the whole proof is reduced to +just proving this claim + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so to prove the claim + + align:start position:0% + + + + align:start position:0% + +let you in uh + + align:start position:0% + + + + align:start position:0% + +be Associated uh eigenvectors + + align:start position:0% + + + + align:start position:0% + +so these have unit lengths + + align:start position:0% + + + + align:start position:0% + +and for all n a u n + + align:start position:0% +and for all n a u n + + + align:start position:0% +and for all n a u n +is Lambda U Lambda n u n right we have + + align:start position:0% +is Lambda U Lambda n u n right we have + + + align:start position:0% +is Lambda U Lambda n u n right we have +eigenvalues so we can find eigenvectors + + align:start position:0% +eigenvalues so we can find eigenvectors + + + align:start position:0% +eigenvalues so we can find eigenvectors +with unit length + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +now + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +Lambda n which is equal to + + align:start position:0% +Lambda n which is equal to + + + align:start position:0% +Lambda n which is equal to +or the absolute value of Lambda n is + + align:start position:0% +or the absolute value of Lambda n is + + + align:start position:0% +or the absolute value of Lambda n is +equal to the absolute value of Lambda + + align:start position:0% +equal to the absolute value of Lambda + + + align:start position:0% +equal to the absolute value of Lambda +and uh or the norm of Lambda n applied + + align:start position:0% +and uh or the norm of Lambda n applied + + + align:start position:0% +and uh or the norm of Lambda n applied +to or times u n which is equal to the + + align:start position:0% +to or times u n which is equal to the + + + align:start position:0% +to or times u n which is equal to the +norm of a applied to u n okay what I so + + align:start position:0% +norm of a applied to u n okay what I so + + + align:start position:0% +norm of a applied to u n okay what I so +what I'm going to show is that a applied + + align:start position:0% +what I'm going to show is that a applied + + + align:start position:0% +what I'm going to show is that a applied +to u n converges to zero so if you like + + align:start position:0% +to u n converges to zero so if you like + + + align:start position:0% +to u n converges to zero so if you like +this is + + align:start position:0% +this is + + + align:start position:0% +this is +the final claim that I need to prove so + + align:start position:0% +the final claim that I need to prove so + + + align:start position:0% +the final claim that I need to prove so +if this is claim one + + align:start position:0% + + + + align:start position:0% + +claim one will follow from claim two and + + align:start position:0% +claim one will follow from claim two and + + + align:start position:0% +claim one will follow from claim two and +this little computation right here uh + + align:start position:0% +this little computation right here uh + + + align:start position:0% +this little computation right here uh +where claimed 2 is + + align:start position:0% +where claimed 2 is + + + align:start position:0% +where claimed 2 is +that the norm + + align:start position:0% +that the norm + + + align:start position:0% +that the norm +of a applied to u n again U n's or + + align:start position:0% +of a applied to u n again U n's or + + + align:start position:0% +of a applied to u n again U n's or +eigenvectors with unit length + + align:start position:0% +eigenvectors with unit length + + + align:start position:0% +eigenvectors with unit length +corresponding to the Lambda ends + + align:start position:0% +corresponding to the Lambda ends + + + align:start position:0% +corresponding to the Lambda ends +converge to zero + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so the fact that a applied to these unit + + align:start position:0% +so the fact that a applied to these unit + + + align:start position:0% +so the fact that a applied to these unit +vectors uh converges to zero is + + align:start position:0% +vectors uh converges to zero is + + + align:start position:0% +vectors uh converges to zero is +um + + align:start position:0% +um + + + align:start position:0% +um +not just specific to + + align:start position:0% +not just specific to + + + align:start position:0% +not just specific to +eigenvectors of distinct eigenvalues + + align:start position:0% +eigenvectors of distinct eigenvalues + + + align:start position:0% +eigenvectors of distinct eigenvalues +it's just a property of the compactness + + align:start position:0% +it's just a property of the compactness + + + align:start position:0% +it's just a property of the compactness +of a and the fact that the UNS are an + + align:start position:0% +of a and the fact that the UNS are an + + + align:start position:0% +of a and the fact that the UNS are an +orthonormal sequence okay but they're + + align:start position:0% +orthonormal sequence okay but they're + + + align:start position:0% +orthonormal sequence okay but they're +all unit length and any one element in + + align:start position:0% +all unit length and any one element in + + + align:start position:0% +all unit length and any one element in +the sequence is orthogonal to a + + align:start position:0% +the sequence is orthogonal to a + + + align:start position:0% +the sequence is orthogonal to a +different element in the sequence + + align:start position:0% +different element in the sequence + + + align:start position:0% +different element in the sequence +okay so suppose not suppose claim 2 does + + align:start position:0% +okay so suppose not suppose claim 2 does + + + align:start position:0% +okay so suppose not suppose claim 2 does +not hold + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +just uh you know negating the definition + + align:start position:0% +just uh you know negating the definition + + + align:start position:0% +just uh you know negating the definition +of convergence there exists a Epsilon + + align:start position:0% +of convergence there exists a Epsilon + + + align:start position:0% +of convergence there exists a Epsilon +positive + + align:start position:0% + + + + align:start position:0% + +and uh + + align:start position:0% + + + + align:start position:0% + +we can find a subsequence a u and J + + align:start position:0% +we can find a subsequence a u and J + + + align:start position:0% +we can find a subsequence a u and J +um + + align:start position:0% + + + + align:start position:0% + +such that + + align:start position:0% +such that + + + align:start position:0% +such that +for all J + + align:start position:0% + + + + align:start position:0% + +of a u and J is bigger than or equal to + + align:start position:0% +of a u and J is bigger than or equal to + + + align:start position:0% +of a u and J is bigger than or equal to +Epsilon naught right if you look at the + + align:start position:0% +Epsilon naught right if you look at the + + + align:start position:0% +Epsilon naught right if you look at the +definition of uh + + align:start position:0% +definition of uh + + + align:start position:0% +definition of uh +or the definition of convergence to zero + + align:start position:0% +or the definition of convergence to zero + + + align:start position:0% +or the definition of convergence to zero +and then negate that you can conclude + + align:start position:0% +and then negate that you can conclude + + + align:start position:0% +and then negate that you can conclude +that you can find a subsequence so that + + align:start position:0% +that you can find a subsequence so that + + + align:start position:0% +that you can find a subsequence so that +I have this so there exists some bad + + align:start position:0% +I have this so there exists some bad + + + align:start position:0% +I have this so there exists some bad +Epsilon zero so that I have that + + align:start position:0% +Epsilon zero so that I have that + + + align:start position:0% +Epsilon zero so that I have that +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +all right + + align:start position:0% + + + + align:start position:0% + +since a is a + + align:start position:0% + + + + align:start position:0% + +compact operator there exists a further + + align:start position:0% +compact operator there exists a further + + + align:start position:0% +compact operator there exists a further +subsequence + + align:start position:0% + + + + align:start position:0% + +and let me call it e sub K which is U N + + align:start position:0% +and let me call it e sub K which is U N + + + align:start position:0% +and let me call it e sub K which is U N +Sub J sub k + + align:start position:0% + + + + align:start position:0% + +U and J + + align:start position:0% + + + + align:start position:0% + +such that so remember a applied to U N + + align:start position:0% +such that so remember a applied to U N + + + align:start position:0% +such that so remember a applied to U N +Sub J so + + align:start position:0% +Sub J so + + + align:start position:0% +Sub J so +U N Sub J is a unit length vector and + + align:start position:0% +U N Sub J is a unit length vector and + + + align:start position:0% +U N Sub J is a unit length vector and +therefore a applied to that is contained + + align:start position:0% +therefore a applied to that is contained + + + align:start position:0% +therefore a applied to that is contained +in a compact set assuming a is a compact + + align:start position:0% +in a compact set assuming a is a compact + + + align:start position:0% +in a compact set assuming a is a compact +operator so this must have a convergent + + align:start position:0% +operator so this must have a convergent + + + align:start position:0% +operator so this must have a convergent +subsequence + + align:start position:0% +subsequence + + + align:start position:0% +subsequence +such that + + align:start position:0% +such that + + + align:start position:0% +such that +a applied to e k + + align:start position:0% + + + + align:start position:0% + +is or converges + + align:start position:0% + + + + align:start position:0% + +in H + + align:start position:0% +in H + + + align:start position:0% +in H +and note + + align:start position:0% + + + + align:start position:0% + +a e k since this is just a subsequence + + align:start position:0% +a e k since this is just a subsequence + + + align:start position:0% +a e k since this is just a subsequence +of this sequence + + align:start position:0% +of this sequence + + + align:start position:0% +of this sequence +is bigger than or equal to Epsilon + + align:start position:0% +is bigger than or equal to Epsilon + + + align:start position:0% +is bigger than or equal to Epsilon +naught + + align:start position:0% +naught + + + align:start position:0% +naught +for all k + + align:start position:0% + + + + align:start position:0% + +now since the eks are a subsequence of + + align:start position:0% +now since the eks are a subsequence of + + + align:start position:0% +now since the eks are a subsequence of +an orthonormal sequence it's still an + + align:start position:0% +an orthonormal sequence it's still an + + + align:start position:0% +an orthonormal sequence it's still an +orthonormal sequence okay so note + + align:start position:0% + + + + align:start position:0% + +for all + + align:start position:0% +for all + + + align:start position:0% +for all +K not equal to l and no product e k + + align:start position:0% +K not equal to l and no product e k + + + align:start position:0% +K not equal to l and no product e k +e l which is u + + align:start position:0% +e l which is u + + + align:start position:0% +e l which is u +in + + align:start position:0% +in + + + align:start position:0% +in +k + + align:start position:0% +k + + + align:start position:0% +k +u n l + + align:start position:0% + + + + align:start position:0% + +equals zero and what I'm using here so + + align:start position:0% +equals zero and what I'm using here so + + + align:start position:0% +equals zero and what I'm using here so +of course these are all unit vectors why + + align:start position:0% +of course these are all unit vectors why + + + align:start position:0% +of course these are all unit vectors why +are they orthogonal it's because they + + align:start position:0% +are they orthogonal it's because they + + + align:start position:0% +are they orthogonal it's because they +correspond to distinct eigenvalues + + align:start position:0% +correspond to distinct eigenvalues + + + align:start position:0% +correspond to distinct eigenvalues +distinct non-zero eigenvalues and we + + align:start position:0% +distinct non-zero eigenvalues and we + + + align:start position:0% +distinct non-zero eigenvalues and we +proved that uh that was number two that + + align:start position:0% +proved that uh that was number two that + + + align:start position:0% +proved that uh that was number two that +uh was it number two + + align:start position:0% +uh was it number two + + + align:start position:0% +uh was it number two +yeah that eigenvectors for distinct + + align:start position:0% +yeah that eigenvectors for distinct + + + align:start position:0% +yeah that eigenvectors for distinct +eigenvalues are orthogonal to each other + + align:start position:0% +eigenvalues are orthogonal to each other + + + align:start position:0% +eigenvalues are orthogonal to each other +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so assuming the negation of the claim 2 + + align:start position:0% +so assuming the negation of the claim 2 + + + align:start position:0% +so assuming the negation of the claim 2 +which would prove claim one and finish + + align:start position:0% +which would prove claim one and finish + + + align:start position:0% +which would prove claim one and finish +the proof of this whole theorem + + align:start position:0% +the proof of this whole theorem + + + align:start position:0% +the proof of this whole theorem +I conclude that there exists a sequence + + align:start position:0% +I conclude that there exists a sequence + + + align:start position:0% +I conclude that there exists a sequence +of eigenvectors or orthonormal + + align:start position:0% +of eigenvectors or orthonormal + + + align:start position:0% +of eigenvectors or orthonormal +eigenvectors of a + + align:start position:0% +eigenvectors of a + + + align:start position:0% +eigenvectors of a +so that a e k + + align:start position:0% +so that a e k + + + align:start position:0% +so that a e k +is always bounded below and Norm by + + align:start position:0% +is always bounded below and Norm by + + + align:start position:0% +is always bounded below and Norm by +Epsilon zero + + align:start position:0% +Epsilon zero + + + align:start position:0% +Epsilon zero +okay + + align:start position:0% + + + + align:start position:0% + +and this sequence converges so let + + align:start position:0% +and this sequence converges so let + + + align:start position:0% +and this sequence converges so let +F be the limit + + align:start position:0% + + + + align:start position:0% + +as K goes to Infinity of AEK + + align:start position:0% +as K goes to Infinity of AEK + + + align:start position:0% +as K goes to Infinity of AEK +then + + align:start position:0% +then + + + align:start position:0% +then +Norm of f + + align:start position:0% +Norm of f + + + align:start position:0% +Norm of f +continuity of the norm is equal to the + + align:start position:0% +continuity of the norm is equal to the + + + align:start position:0% +continuity of the norm is equal to the +limit of the Norms of the E case and all + + align:start position:0% +limit of the Norms of the E case and all + + + align:start position:0% +limit of the Norms of the E case and all +of these are above bigger than or equal + + align:start position:0% +of these are above bigger than or equal + + + align:start position:0% +of these are above bigger than or equal +to + + align:start position:0% +to + + + align:start position:0% +to +Epsilon zero so f is non-zero right + + align:start position:0% + + + + align:start position:0% + +in fact we can say a little bit more + + align:start position:0% + + + + align:start position:0% + +than uh in fact + + align:start position:0% +than uh in fact + + + align:start position:0% +than uh in fact +see + + align:start position:0% + + + + align:start position:0% + +so this is kind of useless information I + + align:start position:0% +so this is kind of useless information I + + + align:start position:0% +so this is kind of useless information I +skipped + + align:start position:0% + + + + align:start position:0% + +I didn't write down what I wanted to but + + align:start position:0% +I didn't write down what I wanted to but + + + align:start position:0% +I didn't write down what I wanted to but +okay then + + align:start position:0% +okay then + + + align:start position:0% +okay then +well no I still need that okay no let me + + align:start position:0% +well no I still need that okay no let me + + + align:start position:0% +well no I still need that okay no let me +not + + align:start position:0% +not + + + align:start position:0% +not +let's get rid of that + + align:start position:0% +let's get rid of that + + + align:start position:0% +let's get rid of that +that should still be there so the norm + + align:start position:0% +that should still be there so the norm + + + align:start position:0% +that should still be there so the norm +of f is bigger than or equal to Epsilon + + align:start position:0% +of f is bigger than or equal to Epsilon + + + align:start position:0% +of f is bigger than or equal to Epsilon +zero so Norm of f squared is bigger than + + align:start position:0% +zero so Norm of f squared is bigger than + + + align:start position:0% +zero so Norm of f squared is bigger than +or equal to Epsilon 0 squared + + align:start position:0% + + + + align:start position:0% + +so F in a product f + + align:start position:0% +so F in a product f + + + align:start position:0% +so F in a product f +and by continuity of uh + + align:start position:0% +and by continuity of uh + + + align:start position:0% +and by continuity of uh +in a product that's equal to since the + + align:start position:0% +in a product that's equal to since the + + + align:start position:0% +in a product that's equal to since the +AEK is converge to F uh I will get F + + align:start position:0% +AEK is converge to F uh I will get F + + + align:start position:0% +AEK is converge to F uh I will get F +here and using the fact that + + align:start position:0% +here and using the fact that + + + align:start position:0% +here and using the fact that +a is Alpha joint this is equal to e k + + align:start position:0% + + + + align:start position:0% + +a f + + align:start position:0% +a f + + + align:start position:0% +a f +okay so I have that this limit here + + align:start position:0% + + + + align:start position:0% + +is uh + + align:start position:0% +is uh + + + align:start position:0% +is uh +not negative I mean it's a it's a real + + align:start position:0% +not negative I mean it's a it's a real + + + align:start position:0% +not negative I mean it's a it's a real +number and it's bigger than or equal to + + align:start position:0% + + + + align:start position:0% + +Epsilon 0 squared now here's the problem + + align:start position:0% +Epsilon 0 squared now here's the problem + + + align:start position:0% +Epsilon 0 squared now here's the problem +I have here a sequence of orthonormal + + align:start position:0% +I have here a sequence of orthonormal + + + align:start position:0% +I have here a sequence of orthonormal +vectors right and I know that the sum of + + align:start position:0% +vectors right and I know that the sum of + + + align:start position:0% +vectors right and I know that the sum of +squares of these Fourier coefficients + + align:start position:0% +squares of these Fourier coefficients + + + align:start position:0% +squares of these Fourier coefficients +which are Fourier coefficients for a + + align:start position:0% +which are Fourier coefficients for a + + + align:start position:0% +which are Fourier coefficients for a +applied to f + + align:start position:0% +applied to f + + + align:start position:0% +applied to f +are this sum of squares is finite and + + align:start position:0% +are this sum of squares is finite and + + + align:start position:0% +are this sum of squares is finite and +therefore this has to go to zero and + + align:start position:0% +therefore this has to go to zero and + + + align:start position:0% +therefore this has to go to zero and +that's the contradiction to the Epsilon + + align:start position:0% +that's the contradiction to the Epsilon + + + align:start position:0% +that's the contradiction to the Epsilon +zero squared so by + + align:start position:0% + + + + align:start position:0% + +vessel uh vessels inequality we get that + + align:start position:0% +vessel uh vessels inequality we get that + + + align:start position:0% +vessel uh vessels inequality we get that +sum over k + + align:start position:0% +sum over k + + + align:start position:0% +sum over k +Norm e k + + align:start position:0% +Norm e k + + + align:start position:0% +Norm e k +a f squared this is less than or equal + + align:start position:0% +a f squared this is less than or equal + + + align:start position:0% +a f squared this is less than or equal +to the norm of AFS + + align:start position:0% +to the norm of AFS + + + align:start position:0% +to the norm of AFS +F squared which is finite + + align:start position:0% +F squared which is finite + + + align:start position:0% +F squared which is finite +and since this is a convergent series + + align:start position:0% +and since this is a convergent series + + + align:start position:0% +and since this is a convergent series +the individual terms have to converge to + + align:start position:0% +the individual terms have to converge to + + + align:start position:0% +the individual terms have to converge to +zero + + align:start position:0% + + + + align:start position:0% + +and therefore this uh + + align:start position:0% + + + + align:start position:0% + +equals zero but this + + align:start position:0% +equals zero but this + + + align:start position:0% +equals zero but this +and this are a contradiction + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% + + + + align:start position:0% + +that finishes the proof of this theorem + + align:start position:0% +that finishes the proof of this theorem + + + align:start position:0% +that finishes the proof of this theorem +about the eigenvalues and eigenspaces uh + + align:start position:0% +about the eigenvalues and eigenspaces uh + + + align:start position:0% +about the eigenvalues and eigenspaces uh +for a compact sulfa joint operator + + align:start position:0% + + + + align:start position:0% + +uh all right so I think + + align:start position:0% +uh all right so I think + + + align:start position:0% +uh all right so I think +I think we'll stop there \ No newline at end of file diff --git a/Of68ZXH35o0.txt b/Of68ZXH35o0.txt new file mode 100644 index 0000000000000000000000000000000000000000..2f4b28742a9f2bdbbd785d6ed4ca683768624a9c --- /dev/null +++ b/Of68ZXH35o0.txt @@ -0,0 +1,311 @@ +82% of soldiers in battle suffer from traumatic +limb injuries. Many of these injuries are + +large bone defects. Engineers at MIT are trying +to create materials that mimic the function + +of the bone's natural healing processes. The +structure and properties of these materials + +promote bone regeneration. This video is part +of the Structure-Function-Properties video + +series. The structure, function, and properties +of a system are related and depend on the + +processes that define or create the system. +Hi, my name is Nisarg Shah, and I am a graduate + +student in Professor Paula Hammond's lab in +the chemical engineering department at MIT. + +In the Hammond Lab, we design novel materials +for tissue engineering, gene and drug delivery, + +and energy applications. My research in particular, +focuses on developing and assembling different + +materials for bone tissue regeneration. + +Before watching this video, you should be +familiar with the concepts of pH and pKa, + +and with the common chemical functional groups. +After watching this video, you will be able + +to explain how the concepts of pH and pKa +are useful in the design of materials via + +layer-by-layer assembly. Many of the materials +our lab develops are based on a technique + +called layer-by-layer assembly. Layer- by-layer +assembly utilizes electrostatic interactions + +to create layers of chemical species of alternating +charge. These chemical species could be anything + +-- polymers, proteins, small molecules -- the +key is that they have the appropriate positive + +or negative charge to incorporate them into +the film. + +We assemble these films using a simple dip +method. First, we take our substrate or surface + +that we wish to coat and bombard it with free +radical oxygen in an instrument called a plasma + +cleaner. This not only cleans the surface +of contaminants, but also leaves the surface + +with a negative charge. Next, we take our +substrate and dip it into a solution of positively + +charged molecules. The molecules in solution +bind to the substrate because of Coulombic + +interactions. + +This process is self-adsorption limited, meaning +that once the newly adsorbed layer neutralizes + +the charged sites on the surface, additional +molecules will not bind. This creates layers + +that are on the order of nanometers thick. + +After a rinse step to remove any unbound components, +the substrate is dipped into a solution of + +negatively charged molecules. Interactions +with the charges on the previous layer allow + +a new layer to be deposited. Again, we would +rinse to remove any unbound components. We + +can continue this process and dip our growing +film into solutions of positively and negatively + +charged molecules, with rinse steps in between, +building up our coating layer-by-layer. Many + +of the films I work with have on the order +of 40 layers. We use polymers in many of our + +layers. These long chain, high molecular weight +molecules form more stable layers than small + +molecules. The long polymer chains from one +layer weave through other layers creating + +an interlocking structure. Also, because we +use negatively and positively charged polymers + +in these layers, the polymers ionically crosslink, +adding to the stability of the overall film. + +Polymers whose repeating unit contains a charged +group are called polyelectrolytes. Thus, many + +people refer to the films that we create as +polyelectrolyte multilayers. For every polymer + +or small molecule I incorporate into my layer-by-layer +assembly, I have to be mindful of it's pKa + +and select appropriate assembly conditions +to ensure they have the desired charge. For + +example, one of the polymers that I use in +a layer-by-layer assembly is polyacrylic acid. + +You don't need to worry about it's exact chemical +structure. The important thing to note is + +the repeating carboxylic acid group. Another +polymer that I use in my layer-by-layer assembly + +contains repeating amine groups. Let's say +I'm creating my layer-by-layer assembly at + +a pH equal to 4. If the pKa of the carboxylic +acid groups on our first polymer is approximately + +4.5, and the pKa of the amine groups on our +second polymer is approximately 6.5, what + +would the charge on each of these polymers +be? Pause the video and take a moment to think + +about it. At a pH of 4, some of the carboxylic +acid groups on our first polymer would be + +deprotonated, resulting in a negative charge. +At the same pH, some of the amine groups on + +our second polymer pick up an extra hydrogen, +resulting in a positive charge. Because so + +many molecules could be viable candidates +for incorporation into these films, they are + +being used in a wide variety of applications. +My main interest is using these films in tissue + +engineering applications. + +So, first I have to ask myself, what problem +do I want to solve? Then, I have to ask myself + +how these multilayer films could be useful. +What function do they need to have? What properties + +of the film would help to achieve that function? +Taking all of this into account, how should + +I structure my film? + +One of the problems I became particularly +interested in is that of large bone defects. + +Large bone defects are large gaps in the bone +that result from trauma. + +Although bone is capable of regeneration, +when there are large defects, some sort of + +intervention therapy is needed to bridge the +defect for proper healing. + +These intervention therapies typically involve +taking bone tissue either from another location + +in the patient's body or from a deceased donor +source and grafting it into the defect site. + +While bone taken from the patient may be immune +compatible and be more viable, this method + +has limitations. Tissue injury and trauma +at the site of bone removal causes patients + +pain and long healing times. Bone tissue from +a deceased donor may cause an unfavorable + +immune response. The processes used to prepare +these tissues for implantation may also compromise + +their mechanical properties. + +Our lab had an idea for a possible solution +to this problem. We asked ourselves, can we + +design a scaffold to bridge these large defects +that will stimulate the growth of new bone + +tissue? The idea was to create a rigid, porous +scaffold coated with a multilayer film. The + +multilayer film would deliver biological molecules +that would stimulate the growth of bone both + +on the surface and throughout the scaffold. +Over time, the scaffold would slowly degrade, + +leaving the new bone tissue behind. In selecting +components for both the scaffold and these + +films, we looked to the biological process +of wound healing for inspiration. The idea + +was that if we could mimic the wound healing +process in bone, we could potentially regenerate + +tissue that is mechanically and chemically +identical to native bone tissue. + +The bulk of our scaffold consisted of a polymer +that would slowly degrade when placed in the + +body. This polymer was mixed with calcium +phosphate, a significant component of native + +bone. Our thought was that calcium phosphate +would promote the attachment, growth, and + +migration of cells that produce bone tissue +within the scaffold. + +We then used layer-by-layer assembly to create +a multilayered film on the surface of the + +scaffold. The film contained layers of polymers +and layers of biological molecules that we + +wanted to release into the defect site. One +of the molecules was a protein called bone + +morphogenetic protein-2. This protein is a +growth factor that stimulates mesenchymal + +stem cells from the bone marrow to transform +into bone tissue producing cells. + +The biodegradable properties of the polymers +we used in the film would help to release + +the protein into the surrounding tissue when +the scaffold is implanted. + +In addition to identifying molecules that +would give us the function and properties + +that we desired, we had to choose an assembly +pH that would ensure they had the desired + +charge. + +To test our hypothesis that these materials +would lead to bone growth, we implanted our + +coated scaffold into a rat quadriceps muscle. + +In this model, the scaffold was placed in +a location where bone is not normally found, + +so that we would know that any bone created +on the scaffold was due to the coating. + +Our experiments were successful in that we +saw the deposition of bone minerals and collagen + +on our scaffolds within 4 weeks. Of course, +there are more experiments to be done to see + +if this system will work in the same way in +a large defect site. + +The main lesson I learned in these experiments +was that for bone tissue regeneration to occur, + +my multilayer-coated scaffolds needed to provide +two key functions: to encourage bone producing + +cells to attach, migrate through, and deposit +tissue in the scaffold; and to encourage mesenchymal + +stem cells to transform into bone producing +cells. + +In this video, we hope that you saw how general +chemistry concepts such as pH and pKa continue + +to be useful beyond the classroom and into +research settings. Here, we saw how we need + +We also saw how considering the desired function +and properties of a material can help us rationally + +design its structure. \ No newline at end of file diff --git a/Pfo7r6bjSqI.txt b/Pfo7r6bjSqI.txt new file mode 100644 index 0000000000000000000000000000000000000000..b2685f8433a50ac7c160a86a7c737d6a04b7ada6 --- /dev/null +++ b/Pfo7r6bjSqI.txt @@ -0,0 +1,1675 @@ +ANNOUNCER: Open content is +provided under a creative + +commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation, or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu . + +PROFESSOR JOHN GUTTAG: +Good morning. + +We should start with the +confession, for those of you + +looking at this on +OpenCourseWare, that I'm + +currently lecturing to +an empty auditorium. + +The fifth lecture for 600 this +term, we ran into some + +technical difficulties, which +left us with a recording we + +weren't very satisfied with. + +So, I'm-- this is a redo, and if +you will hear no questions + +from the audience and that's +because there is no audience. + +Nevertheless I will do +my best to pretend. + +I've been told this is a little +bit like giving a + +speech before the US Congress +when C-SPAN is + +the only thing watching. + +OK. + +Computers are supposed to be +good for crunching numbers. + +And we've looked a little bit +at numbers this term, but I + +now want to get into looking +at them in more depth than + +we've been doing. + +Python has two different +kinds of numbers. + +So far, the only kind we've +really paid any attention to + +is type int. + +And those were intended to +mirror the integers, as we all + +learned about starting +in elementary school. + +And they're good for things +that you can count. + +Any place you'd use +whole numbers. + +Interestingly, Python, unlike +some languages, has what are + +called arbitrary precision +integers. + +By that, we mean, you can +make numbers as big as + +you want them to. + +Let's look at an example. + +We'll just take a for a variable +name, and we'll set a + +to be two raised to the +one-thousandth power. + +That, by the way, is a +really big number. + +And now what happens if +we try and display it? + +We get a lot of digits. + +You can see why I'm doing this +on the screen instead of + +writing it on the blackboard. + +I'm not going to ask you whether +you believe this is + +the right answer, trust +me, trust Python. + +I would like you to notice, at +the very end of this is the + +letter L. + +What does that mean? + +It means long. + +That's telling us that it's +representing these-- this + +particular integer in +what it calls it's + +internal long format. + +You needn't worry about that. + +The only thing to say about it +is, when you're dealing with + +long integers, it's a lot less +efficient than when you're + +dealing with smaller numbers. + +And that's all it's kind of +warning you, by printing this + +L. + +About two billion is +the magic number. + +When you get over two billion, +it's now going to deal with + +long integers, so if, for +example, you're trying to deal + +with the US budget deficit, you +will need integers of type + +L. + +OK. + +Let's look at another +interesting example. + +Suppose I said, b equal to two +raised to the nine hundred + +ninety-ninth power. + +I can display b, and it's a +different number, considerably + +smaller, but again, +ending in an L. + +And now, what you think I'll get +if we try a divided by b? + +And remember, we're now doing +integer division. + +Well, let's see. + +We get 2L. + +Well, you'd expect it to be +two, because if you think + +about the meaning of +exponentiation, indeed, the + +difference between raising +something to the nine hundred + +ninety-ninth power and to the +one-thousandth power should + +be, in this case, two, since +that's what we're + +raising to a power. + +Why does it say 2L, right? + +Two is considerably less than +two billion, and that's + +because once you get L, you +stay L. Not particularly + +important, but kind +of worth knowing. + +Well, why am I bothering you +with this whole issue of how + +numbers are represented +in the computer? + +In an ideal world, you would +ignore this completely, and + +just say, numbers do what +numbers are supposed to do. + +But as we're about to see, +sometimes in Python, and in + +fact in every programming +language, things behave + +contrary to what your +intuition suggests. + +And I want to spend a little +time helping you understand + +why this happens. + +So let's look at a different +kind of number. + +And now we're going to look at +what Python, and almost every + +other programming language, +calls type float. + +Which is short for +floating point. + +And that's the way that +programming languages + +typically represent what we +think of as real numbers. + +So, let's look at an example. + +I'm going to set the variable +x to be 0.1, 1/10, and now + +we're going to display x. + +Huh? + +Take a look at this. + +Why isn't it .1? + +Why is it 0.1, a whole bunch +of zeros, and then this + +mysterious one appearing +at the end? + +Is it because Python just wants +to be obnoxious and is + +making life hard? + +No, it has to do with the way +the numbers are represented + +inside the computer. + +Python, like almost every modern +programming language, + +represents numbers using the +i triple e floating point + +standard, and it's +i triple e 754. + +Never again will you have to +remember that it's 754. + +I promise not to ask you that +question on a quiz. + +But that's what they do. + +This is a variant of scientific +notation. + +Something you probably learned +about in high school, as a way + +to represent very +large numbers. + +Typically, the way we do that, +is we represent the numbers in + +the form of a mantissa +and an exponent. + +So we represent a floating point +number as a pair, of a + +mantissa and an exponent. + +And because computers work in +the binary system, it's unlike + +what you probably learned in +high school, where we raise + +ten to some power. + +Here we'll always be raising +two to some power. + +Maybe a little later in the +term, if we talk about + +computer architecture, we'll get +around to explaining why + +computers working binary, but +for now, just assume that they + +do and in fact they + +always have. All right. + +Purists manage to refer to the +mantissa as a significant, but + +I won't do that, because I'm +an old guy and it was a + +mantissa when I first learned +about it and I just can't + +break myself of the habit. + +All right. + +So how does this work? + +Well, when we recognize so-- +when we represent something, + +the mantissa is between +one and two. + +Whoops. + +Strictly less than two, greater +than or equal to one. + +The exponent, is in the +range, -1022 to +1023. + +So this lets us represent +numbers up to about 10 to the + +308th, plus or minus 10 to +the 308th, plus or minus. + +So, quite a large range +of numbers. + +Where did these magic +things come from? + +You know, what-- kind of a +strange numbers to see here. + +Well, it has to do with the fact +that computers typically + +have words in them, and the +words today in a modern + +computer are 64 bits. + +For many years they were 32 +bits, before that they were 16 + +bits, before that they were 8 +bits, they've continually + +grown, but we've been at 64 for +a while and I think we'll + +be stuck at 64 for a while. + +So as we do this, what we do +is, we get one bit for the + +sign-- is it a positive +or negative number?-- + +11 for the exponent, and that +leaves 52 for the mantissa. + +And that basically tells us +how we're storing numbers. + +Hi, are you here for +the 600 lecture? + +There is none today, because we +have a quiz this evening. + +It's now the time that the +lecture would normally have + +started, and a couple of +students who forgot that we + +have a quiz this evening, +instead of a lecture, just + +strolled in, and now +strolled out. + +OK. + +You may never need to know these +constants again, but + +it's worth knowing that they +exist, and that basically, + +this gives us about the +equivalent of seventeen + +decimal digits of precision. + +So we can represent numbers +up to seventeen + +decimal digits long. + +This is an important concept to +understand, that unlike the + +long ints where they can grow +arbitrarily big, when we're + +dealing with floating points, if +we need something more than + +seventeen decimal digits, in +Python at least, we won't be + +able to get it. + +And that's true in +many languages. + +Now the good news is, this is +an enormous number, and it's + +highly unlikely that ever in +your life, you will need more + +precision than that. + +All right. + +Now, let's go back to the 0.1 +mystery that we started at, + +and ask ourselves, why we have +a problem representing that + +number in the computer, hence, +we get something funny out + +from we try and print it back. + +Well, let's look at an easier +problem first. Let's look at + +representing the fraction 1/8. + +That has a nice representation. + +That's equal in decimal to +0.125, and we can represent it + +conveniently in both +base 10 and base 2. + +So if you want to represent +it in base 10, what is it? + +What is that equal to? + +Well, we'll take a mantissa, +1.25, and now we need to + +multiply it by something that +we can represent nicely, and + +in fact that will be +times 10 to the -1. + +So the exponent would simply +be -1, and we have a nice + +representation. + +Suppose we want to represent +it in base 2? + +What would it be? + +1.0 times-- anybody?-- + +Well, 2 to the -3. + +So, in binary notation, that +would be written as 0.001. + +So you see, 1/8 is kind +of a nice number. + +We can represent it nicely in +either base 10 or base 2. + +But how about that pesky +fraction 1/10? + +Well, in base 10, we know +how to represent, it's + +1 times 10 to the-- + +10 to the what?-- + +10 to the 1? + +No. + +But in base 2, it's a problem. + +There is no finite binary number +that exactly represents + +this decimal fraction. + +In fact, if we try and find +the binary number, what we + +find is, we get an infinitely +repeating series. + +Zero zero zero one one zero +zero one one zero + +zero, and et cetera. + +Stop at any finite number of +bits, and you get only an + +approximation to the decimal +fraction 1/10. + +So on most computers, if you +were to print the decimal + +value of the binary +approximation-- and that's + +what we're printing here, +on this screen, right? + +We think in decimal, so Python +quite nicely for us is + +printing things in decimal-- +it would have to display-- + +well I'm not going to write it, +it's a very long number, + +lots of digits-- however, in +Python, whenever we display + +something, it uses the built-in +function repr, short + +for representation, that it +converts the internal + +representation in this case of +a number, to a string, and + +then displays that string in +this case on the screen. + +For floats, it rounds it +to seventeen digits. + +There's that magic number +seventeen again. + +Hence, when it rounds it to +seventeen digits, we get + +exactly what you see in the +bottom of the screen up there. + +Answer to the mystery, why +does it display this? + +Now why should we care? + +Well, it's not so much that +we care about what gets + +displayed, but we have to think +about the implications, + +at least sometimes we have to +think about the implications, + +of what this inexact +representation of numbers + +means when we start doing +more-or-less complex + +computations on those numbers. + +So let's look at a little +example here. + +I'll start by starting the +variable s to 0.0 . + +Notice I'm being careful +to make it a float. + +And then for i in range, let's +see, let's take 10, we'll + +increase s by 0.1 . + +All right, we've done that, +and now, what happens + +when I print s? + +Well, again you don't get +what your intuition + +says you should get. + +Notice the last two digits, +which are eight and nine. + +Well, what's happening here? + +What's happened, is the +error has accumulated. + +I had a small error when I +started, but every time I + +added it, the error got bigger +and it accumulates. + +Sometimes you can get in trouble +in a computation + +because of that. + +Now what happens, by the +way, if I print s? + +That's kind of an interesting +question. + +Notice that it prints one. + +And why is that? + +It's because the print command +has done a rounding here. + +It automatically rounds. + +And that's kind of good, but +it's also kind of bad, because + +that means when you're debugging +your program, you + +can get very confused. + +You say, it says it's one, why +am I getting a different + +answer when I do the +computation? + +And that's because it's +not really one inside. + +So you have to be careful. + +Now mostly, these round-off +errors balance each other out. + +Some floats are slightly higher +than they're supposed + +to be, some are slightly +lower, and in most + +computations it all comes out +in the wash and you get the + +right answer. + +Truth be told, most of the time, +you can avoid worrying + +about these things. + +But, as we say in Latin, +caveat computor. + +Sometimes you have to +worry a little bit. + +Now there is one thing about +floating points about which + +you should always worry. + +And that's really the point I +want to drive home, and that's + +about the meaning +of double equal. + +Let's look at an example +of this. + +So we've before seen the use +of import, so I'm going to + +import math, it gives me some +useful mathematical functions, + +then I'm going to set the +variable a to the + +square root of two. + +Whoops. + +Why didn't this work? + +Because what I should have +said is math dot + +square root of two. + +Explaining to the interpreter +that I want to get the + +function sqrt from +the module math. + +So now I've got a here, and I +can look at what a is, yeah, + +some approximation to the square +root about of two. + +Now here's the interesting +question. + +Suppose I ask about the Boolean +a times a equals + +equals two. + +Now in my heart, I think, if +I've taken the square root of + +number and then I've multiplied +it by itself, I + +could get the original +number back. + +After all, that's the meaning +of square root. + +But by now, you won't be +surprised if the answer of + +this is false, because we know +what we've stored is only an + +approximation to the +square root. + +And that's kind of +interesting. + +So we can see that, by, if I +look at a times a, I'll get + +two point a whole bunch +of zeros and then + +a four at the end. + +So this means, if I've got a +test in my program, in some + +sense it will give me the +unexpected answer false. + +What this tells us, is that it's +very risky to ever use + +the built-in double--equals to +compare floating points, and + +in fact, you should never be +testing for equality, you + +should always be testing +for close enough. + +So typically, what you want to +do in your program, is ask the + +following question: is the +absolute value of a times a + +minus 2.0 less than epsilon? + +If we could easily type Greek, +we'd have written it that way, + +but we can't. + +So that's some small value +chosen to be appropriate for + +the application. + +Saying, if these two things +are within epsilon of each + +other, then I'm going to +treat them as equal. + +And so what I typically do when +I'm writing a Python code + +that's going to deal with +floating point numbers, and I + +do this from time to time, is I +introduce a function called + +almost equal, or near, or pick +your favorite word, that does + +this for me. + +And wherever I would normally +written double x equals y, + +instead I write, near x,y, and +it computes it for me. + +Not a big deal, but keep this +in mind, or as soon as you + +start dealing with numbers, you +will get very frustrated + +in trying to understand what +your program does. + +OK. + +Enough of numbers for a while, +I'm sure some of you will find + +this a relief. + +I now want to get away from +details of floating point, and + +talk about general methods +again, returning to the real + +theme of the course of solving +problems using computers. + +Last week, we looked at the +rather silly problem of + +finding the square root +of a perfect square. + +Well, that's not usually +what you need. + +Let's think about the more +useful problem of finding the + +square root of a real number. + +Well, you've just seen +how you do that. + +You import math and +you call sqrt. + +Let's pretend that we didn't +know that trick, or let's + +pretend it's your job to +introduce-- implement, + +rather-- math. + +And so, you need to figure out +how to implement square root. + +Why might this be a challenge? + +What are some of the issues? + +And there are several. + +One is, what we've just seen +might not be an exact answer. + +For example, the square +root of two. + +So we need to worry about that, +and clearly the way + +we're going to solve that, as +we'll see, is using a concept + +similar to epsilon. + +In fact, we'll even +call it epsilon. + +Another problem with the method +we looked at last time + +is, there we were doing +exhaustive enumeration. + +We were enumerating all the +possible answers, checking + +each one, and if it was +good, stopping. + +Well, the problem with reals, as +opposed to integers, is we + +can't enumerate all guesses. + +And that's because the reals +are uncountable. + +If I ask you to enumerate the +positive integers, you'll say + +one, two, three, four, five. + +If I ask you to enumerate the +reals, the positive reals, + +where do you start? + +One over a billion, +plus who knows? + +Now as we've just seen in fact, +since there's a limit to + +the precision floating point, +technically you can enumerate + +all the floating +point numbers. + +And I say technically, because +if you tried to do that, your + +computation would not terminate +any time soon. + +So even though in some, in +principle you could enumerate + +them, in fact you +really can't. + +And so we think of the floating +points, like the + +reals, as being innumerable. + +Or not innumerable, as to say +as being uncountable. + +So we can't do that. + +So we have to find something +clever, because we're now + +searching a very large space +of possible answers. + +What would, technically +you might call + +a large state space. + +So we're going to take our +previous method of guess and + +check, and replace it by +something called guess, check, + +and improve. + +Previously, we just generated +guesses in some systematic + +way, but without knowing +that we were getting + +closer to the answer. + +Think of the original barnyard +problem with the chickens and + +the heads and the legs, we just +enumerated possibilities, + +but we didn't know that one +guess was better than the + +previous guess. + +Now, we're going to find a way +to do the enumeration where we + +have good reason to believe, +at least with high + +probability, that each +guess is better than + +the previous guess. + +This is what's called successive +approximation. + +And that's a very important +concept. + +Many problems are solved +computationally using + +successive approximation. + +Every successive approximation +method has + +the same rough structure. + +You start with some guess, which +would be the initial + +guess, you then iterate-- and in +a minute I'll tell you why + +I'm doing it this particular +way, over some range. + +I've chosen one hundred, but +doesn't have to be one + +hundred, just some number +there-- if f of x, that is to + +say some some function of my-- + +Whoops, I shouldn't +have said x. + +My notes say x, but it's the +wrong thing-- if f of x, f of + +the guess, is close enough, so +for example, if when I square + +guess, I get close enough to +the number who's root I'm-- + +square root I'm looking for, +then I'll return the guess. + +If it's not close enough, +I'll get a better guess. + +If I do my, in this case, one +hundred iterations, and I've + +not get-- gotten a guess that's +good enough, I'm going + +to quit with some error. + +Saying, wow. + +I thought my method was good +enough that a hundred guesses + +should've gotten me there. + +If it didn't, I may be wrong. + +I always like to have some +limit, so that my program + +can't spin off into the ether, +guessing forever. + +OK. + +Let's look at an example +of that. + +So here's a successive +approximation + +to the square root. + +I've called it square root bi. + +The bi is not a reference to the +sexual preferences of the + +function, but a reference to +the fact that this is an + +example of what's called +a bi-section method. + +The basic idea behind any +bi-section method is the same, + +and we'll see lots of examples +of this semester, is that you + +have some linearly-arranged +space of possible answers. + +And it has the property that if +I take a guess somewhere, + +let's say there, I guess that's +the answer to the + +question, if it turns out that's +not the answer, I can + +easily determine whether the +answer lies to the left or the + +right of the guess. + +So if I guess that 89.12 is the +square root of a number, + +and it turns out not to be the +square root of the number, I + +have a way of saying, is 89.12 +too big or too small. + +If it was too big, then I +know I'd better guess + +some number over here. + +It was too small, then +I'd better guess + +some number over here. + +Why do I call it bi-section? + +Because I'm dividing it in half, +and in general as we'll + +see, when I know what my space +of answers is, I always, as my + +next guess, choose something +half-way along that line. + +So I made a guess, and let's say +was too small, and I know + +the answer is between here and +here, this was too small, I + +now know that the answer is +between here and here, so my + +next guess will be +in the middle. + +The beauty of always guessing +in the middle is, at each + +guess, if it's wrong, I +get to throw out half + +of the state space. + +So I know how long it's going +to take me to search the + +possibilities in some sense, +because I'm getting + +logarithmically progressed. + +This is exactly what we saw when +we looked at recursion in + +some sense, where we solved the +problem by, at each step, + +solving a smaller problem. + +The same problem, but on a +smaller solution space. + +Now as it happens, I'm not +using recursion in this + +implementation we have up on +the screen, I'm doing it + +iteratively but the +idea is the same. + +So we'll take a quick look at +it now, then we'll quit and + +we'll come back to in the next +lecture a little more + +thoroughly. + +I'm going to warn you right +now, that there's a bug in + +this code, and in the next +lecture, we'll see if we can + +discover what that is. + +So, it takes two arguments; x, +the number whose square root + +we're looking for, +and epsilon, how + +close we need to get. + +It assumes that x is +non-negative, and that epsilon + +is greater than zero. + +Why do we need to assume +that's epsilon is + +greater than zero? + +Well, if you made epsilon zero, +and then say, we're + +looking for the square root +of two, we know we'll + +never get an answer. + +So, we want it to be positive, +and then it returns y such + +that y times y is within +epsilon of x. + +It's near, to use the +terminology we used before. + +The next thing we see in the +program, is two assert + +statements. + +This is because I never trust +the people who call my + +functions to do the +right thing. + +Even though I said I'm going to +assume certain things about + +x and epsilon, I'm actually +going to test it. + +And so, I'm going to assert +that x is greater than or + +equal to zero, and that epsilon +is greater than zero. + +What assert does, is it tests +the predicate, say x greater + +than or equal to zero, if it's +true, it does nothing, just + +goes on to the next statement. + +But if it's false, it prints a +message, the string, which is + +my second argument here, and +then the program just stops. + +So rather than my function going +off and doing something + +bizarre, for example running +forever, it just stops with a + +message saying, you called me +with arguments you shouldn't + +have called me with. + +All right, so that's the +specification and then my + +check of the assumptions. + +The next thing it does, is it +looks for a range such that I + +believe I am assured that my +answer lies between the ran-- + +these values, and I'm going to +say, well, my answer will be + +no smaller than zero, and +no bigger than x. + +Now, is this the tightest +possible range? + +Maybe not, but I'm not +too fussy about that. + +I'm just trying to make sure +that I cover the space. + +Then I'll start with a guess, +and again I'm not going to + +worry too much about the guess, +I'm going to take low + +plus high and divide by two, +that is to say, choose + +something in the middle of +this space, and then + +essentially do what +we've got here. + +So it's a little bit more +involved here, I'm going to + +set my counter to one, just to +keep checking, then say, while + +the absolute value of the +guess squared minus x is + +greater than epsilon, that is +to say, why my guess is not + +yet good enough, and the counter +is not greater than a + +hundred, I'll get +the next guess. + +Notice by the way, I have a +print statement here which + +I've commented out, but I sort +of figured that my program + +would not work correctly the +first time, and so, I, when I + +first typed and put in a print +statement, it would let me see + +what was happening each +iteration through this loop, + +so that if it didn't work, I +could get a sense of why not. + +In the next lecture, when we +look for the bug in this + +program, you will see me +uncomment out that print + +statement, but for now, we +go to the next thing. + +And we're here, we know the +guess wasn't good enough, so I + +now say, if the guess squared +was less than x, then I will + +change the low bound +to be the guess. + +Otherwise, I'll change the high +bound to be the guess. + +So I move either the low bound +or I move the high bound, + +either way I'm cutting +the search space + +in half each step. + +I'll get my new guess. + +I'll increment my counter, +and off I go. + +In the happy event that +eventually I get a good enough + +guess, you'll see a-- + +I'll exit the loop. + +When I exit the loop, I checked, +did I exit it because + +I exceeded the counter, +I didn't have + +a good-enough guess. + +If so, I'll print the message +iteration count exceeded. + +Otherwise, I'll print the +result and return it. + +Now again, if I were writing a +square root function to be + +used in another program, I +probably wouldn't bother + +printing the result and the +number of iterations and all + +of that, but again, I'm doing +that here for, because we want + +to see what it's doing. + +All right. + +We'll run it a couple times +and then I'll let + +you out for the day. + +Let's go do this. + +All right. + +We're here. + +Well, notice when I run +it, nothing happens. + +Why did nothing happen? + +Well, nothing happens, it +was just a function. + +Functions don't do anything +until I call them. + +So let's call it. + +Let's call square root bi with +40.001 Took only one at-- + +iteration, that was pretty +fast, estimated two as an + +answer, we're pretty happy +with that answer. + +Let's try another example. + +Let's look at nine. + +I always like to, by the way, +start with questions whose + +answer I know. + +We'll try and get a little +bit more precise. + +Well, all right. + +Here it took eighteen +iterations. + +Didn't actually give me the +answer three, which we know + +happens to be the answer, but it +gave me something that was + +within epsilon of three, so it +meets the specification, so I + +should be perfectly happy. + +Let's look at another example. + +Try a bigger number here. + +All right? + +So I've looked for the square +root of a thousand, here it + +took twenty-nine iterations, +we're kind of creeping up + +there, gave me an estimate. + +Ah, let's look at our infamous +example of two, see + +what it does here. + +Worked around. + +Now, we can see it's actually +working, and I'm getting + +answers that we believe are +good-enough answers, but we + +also see that the speed of +what we talk about as + +convergence-- how many +iterations it takes, the + +number of iterations-- is +variable, and it seems to be + +related to at least two things, +and we'll see more + +about this in the +next lecture. + +The size of the number whose +square root we're looking for, + +and the precision to which +I want the answer. + +Next lecture, we'll look at a, +what's wrong with this one, + +and I would ask you to between +now and the next lecture, + +think about it, see if you can +find the bug yourself, we'll + +look first for the bug, and then +after that, we'll look at + +a better method of finding +the answer. + +Thank you. \ No newline at end of file diff --git a/PlAelAX6gSU.txt b/PlAelAX6gSU.txt new file mode 100644 index 0000000000000000000000000000000000000000..c45a8a8c4d1a5de8bc4c8c196a673cb6123ff4d8 --- /dev/null +++ b/PlAelAX6gSU.txt @@ -0,0 +1,10307 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +we're gonna get started again so where + + align:start position:0% +we're gonna get started again so where + + + align:start position:0% +we're gonna get started again so where +we stopped + + align:start position:0% +we stopped + + + align:start position:0% +we stopped +I had just played you some of the + + align:start position:0% +I had just played you some of the + + + align:start position:0% +I had just played you some of the +results of this texture synthesis + + align:start position:0% +results of this texture synthesis + + + align:start position:0% +results of this texture synthesis +algorithm we all agreed that they + + align:start position:0% +algorithm we all agreed that they + + + align:start position:0% +algorithm we all agreed that they +sounded like pretty realistic and so the + + align:start position:0% +sounded like pretty realistic and so the + + + align:start position:0% +sounded like pretty realistic and so the +whole point of this was that this gives + + align:start position:0% +whole point of this was that this gives + + + align:start position:0% +whole point of this was that this gives +plausibility to the notion that you + + align:start position:0% +plausibility to the notion that you + + + align:start position:0% +plausibility to the notion that you +could be representing these textures + + align:start position:0% +could be representing these textures + + + align:start position:0% +could be representing these textures +with with these sorts of statistics that + + align:start position:0% +with with these sorts of statistics that + + + align:start position:0% +with with these sorts of statistics that +you can compute from a model of what we + + align:start position:0% +you can compute from a model of what we + + + align:start position:0% +you can compute from a model of what we +think encapsulates the signal processing + + align:start position:0% +think encapsulates the signal processing + + + align:start position:0% +think encapsulates the signal processing +in the early auditory system and again + + align:start position:0% +in the early auditory system and again + + + align:start position:0% +in the early auditory system and again +I'll just underscore that via the sort + + align:start position:0% +I'll just underscore that via the sort + + + align:start position:0% +I'll just underscore that via the sort +of cool thing about doing the synthesis + + align:start position:0% +of cool thing about doing the synthesis + + + align:start position:0% +of cool thing about doing the synthesis +is is that there's like an infinite + + align:start position:0% +is is that there's like an infinite + + + align:start position:0% +is is that there's like an infinite +number of ways in which it can fail all + + align:start position:0% +number of ways in which it can fail all + + + align:start position:0% +number of ways in which it can fail all +right and by listening to it and and + + align:start position:0% +right and by listening to it and and + + + align:start position:0% +right and by listening to it and and +convincing yourself that those things + + align:start position:0% +convincing yourself that those things + + + align:start position:0% +convincing yourself that those things +actually sound pretty realistic you + + align:start position:0% +actually sound pretty realistic you + + + align:start position:0% +actually sound pretty realistic you +actually get a pretty powerful sense + + align:start position:0% +actually get a pretty powerful sense + + + align:start position:0% +actually get a pretty powerful sense +that those the the representation is + + align:start position:0% +that those the the representation is + + + align:start position:0% +that those the the representation is +sort of capturing most of what you hear + + align:start position:0% +sort of capturing most of what you hear + + + align:start position:0% +sort of capturing most of what you hear +when you actually listen to that natural + + align:start position:0% +when you actually listen to that natural + + + align:start position:0% +when you actually listen to that natural +sound right and and for instance we + + align:start position:0% +sound right and and for instance we + + + align:start position:0% +sound right and and for instance we +could we could design a classification + + align:start position:0% +could we could design a classification + + + align:start position:0% +could we could design a classification +algorithm that could discriminate + + align:start position:0% +algorithm that could discriminate + + + align:start position:0% +algorithm that could discriminate +between all these different things right + + align:start position:0% +between all these different things right + + + align:start position:0% +between all these different things right +but the point is that they could the + + align:start position:0% +but the point is that they could the + + + align:start position:0% +but the point is that they could the +representation could still not capture + + align:start position:0% +representation could still not capture + + + align:start position:0% +representation could still not capture +all kinds of different things that you + + align:start position:0% +all kinds of different things that you + + + align:start position:0% +all kinds of different things that you +you would hear and by synthesizing + + align:start position:0% +you would hear and by synthesizing + + + align:start position:0% +you would hear and by synthesizing +because of the fact that you can + + align:start position:0% +because of the fact that you can + + + align:start position:0% +because of the fact that you can +potentially fail in any of the possible + + align:start position:0% +potentially fail in any of the possible + + + align:start position:0% +potentially fail in any of the possible +ways right and then listen and observe + + align:start position:0% +ways right and then listen and observe + + + align:start position:0% +ways right and then listen and observe +whether the failure occurs you get a + + align:start position:0% +whether the failure occurs you get a + + + align:start position:0% +whether the failure occurs you get a +pretty powerful method all right but one + + align:start position:0% +pretty powerful method all right but one + + + align:start position:0% +pretty powerful method all right but one +thing that you might be concerned about + + align:start position:0% +thing that you might be concerned about + + + align:start position:0% +thing that you might be concerned about +and this is sort of something that was + + align:start position:0% +and this is sort of something that was + + + align:start position:0% +and this is sort of something that was +annoying me right is that what we've + + align:start position:0% +annoying me right is that what we've + + + align:start position:0% +annoying me right is that what we've +done here is we've imposed a whole bunch + + align:start position:0% +done here is we've imposed a whole bunch + + + align:start position:0% +done here is we've imposed a whole bunch +of statistical constraints right so + + align:start position:0% +of statistical constraints right so + + + align:start position:0% +of statistical constraints right so +we're measuring like there's really + + align:start position:0% +we're measuring like there's really + + + align:start position:0% +we're measuring like there's really +large set of statistics from from the + + align:start position:0% +large set of statistics from from the + + + align:start position:0% +large set of statistics from from the +model right and then generating things + + align:start position:0% +model right and then generating things + + + align:start position:0% +model right and then generating things +that have the same values of those + + align:start position:0% +that have the same values of those + + + align:start position:0% +that have the same values of those +statistics so there's this question of + + align:start position:0% +statistics so there's this question of + + + align:start position:0% +statistics so there's this question of +of whether any set of statistics will do + + align:start position:0% +of whether any set of statistics will do + + + align:start position:0% +of whether any set of statistics will do +and so we wondered what would happen if + + align:start position:0% +and so we wondered what would happen if + + + align:start position:0% +and so we wondered what would happen if +we measured statistics from a model that + + align:start position:0% +we measured statistics from a model that + + + align:start position:0% +we measured statistics from a model that +deviates from what we know about the + + align:start position:0% +deviates from what we know about the + + + align:start position:0% +deviates from what we know about the +biology of the ear so in particular you + + align:start position:0% +biology of the ear so in particular you + + + align:start position:0% +biology of the ear so in particular you +remember that in this model that we set + + align:start position:0% +remember that in this model that we set + + + align:start position:0% +remember that in this model that we set +out there were a bunch of different + + align:start position:0% +out there were a bunch of different + + + align:start position:0% +out there were a bunch of different +stages right + + align:start position:0% +stages right + + + align:start position:0% +stages right +so we've got this initial stage of + + align:start position:0% +so we've got this initial stage of + + + align:start position:0% +so we've got this initial stage of +bandpass filtering there's the process + + align:start position:0% +bandpass filtering there's the process + + + align:start position:0% +bandpass filtering there's the process +of extracting the envelope and then + + align:start position:0% +of extracting the envelope and then + + + align:start position:0% +of extracting the envelope and then +applying amplitude compression and + + align:start position:0% +applying amplitude compression and + + + align:start position:0% +applying amplitude compression and +there's this modulation filtering and in + + align:start position:0% +there's this modulation filtering and in + + + align:start position:0% +there's this modulation filtering and in +each of these cases there are particular + + align:start position:0% +each of these cases there are particular + + + align:start position:0% +each of these cases there are particular +characteristics of the signal processing + + align:start position:0% +characteristics of the signal processing + + + align:start position:0% +characteristics of the signal processing +that's explicitly intended to mimic what + + align:start position:0% +that's explicitly intended to mimic what + + + align:start position:0% +that's explicitly intended to mimic what +we see in biology so in particular that + + align:start position:0% +we see in biology so in particular that + + + align:start position:0% +we see in biology so in particular that +as we noted the kinds of filter banks + + align:start position:0% +as we noted the kinds of filter banks + + + align:start position:0% +as we noted the kinds of filter banks +that you see in biological systems are + + align:start position:0% +that you see in biological systems are + + + align:start position:0% +that you see in biological systems are +better approximated by something that's + + align:start position:0% +better approximated by something that's + + + align:start position:0% +better approximated by something that's +logarithmically spaced then something + + align:start position:0% +logarithmically spaced then something + + + align:start position:0% +logarithmically spaced then something +that's linearly spaced so we remember + + align:start position:0% +that's linearly spaced so we remember + + + align:start position:0% +that's linearly spaced so we remember +remember that picture I showed at the + + align:start position:0% +remember that picture I showed at the + + + align:start position:0% +remember that picture I showed at the +start where we saw that the filters up + + align:start position:0% +start where we saw that the filters up + + + align:start position:0% +start where we saw that the filters up +here were a lot broader than the filters + + align:start position:0% +here were a lot broader than the filters + + + align:start position:0% +here were a lot broader than the filters +down here all right okay and so we can + + align:start position:0% +down here all right okay and so we can + + + align:start position:0% +down here all right okay and so we can +ask well what happens if we swap in a + + align:start position:0% +ask well what happens if we swap in a + + + align:start position:0% +ask well what happens if we swap in a +filter Bank it's linearly spaced it's + + align:start position:0% +filter Bank it's linearly spaced it's + + + align:start position:0% +filter Bank it's linearly spaced it's +sort of more closely analogous to like + + align:start position:0% +sort of more closely analogous to like + + + align:start position:0% +sort of more closely analogous to like +an FFT for instance similarly we can ask + + align:start position:0% +an FFT for instance similarly we can ask + + + align:start position:0% +an FFT for instance similarly we can ask +well what happens if we kind of get rid + + align:start position:0% +well what happens if we kind of get rid + + + align:start position:0% +well what happens if we kind of get rid +of this like nonlinear function here + + align:start position:0% +of this like nonlinear function here + + + align:start position:0% +of this like nonlinear function here +that that's applied to the the amplitude + + align:start position:0% +that that's applied to the the amplitude + + + align:start position:0% +that that's applied to the the amplitude +envelope what and we make the amplitude + + align:start position:0% +envelope what and we make the amplitude + + + align:start position:0% +envelope what and we make the amplitude +response linear instead and so so we did + + align:start position:0% +response linear instead and so so we did + + + align:start position:0% +response linear instead and so so we did +this so you can you can change the + + align:start position:0% +this so you can you can change the + + + align:start position:0% +this so you can you can change the +auditory model and play the exact same + + align:start position:0% +auditory model and play the exact same + + + align:start position:0% +auditory model and play the exact same +game so you can measure statistics from + + align:start position:0% +game so you can measure statistics from + + + align:start position:0% +game so you can measure statistics from +that model and synthesize something from + + align:start position:0% +that model and synthesize something from + + + align:start position:0% +that model and synthesize something from +those statistics and then I'm asked + + align:start position:0% +those statistics and then I'm asked + + + align:start position:0% +those statistics and then I'm asked +whether they sound any different and so + + align:start position:0% +whether they sound any different and so + + + align:start position:0% +whether they sound any different and so +we did an experiment so we would play + + align:start position:0% +we did an experiment so we would play + + + align:start position:0% +we did an experiment so we would play +people on the original sound and from + + align:start position:0% +people on the original sound and from + + + align:start position:0% +people on the original sound and from +that original sound we have two + + align:start position:0% +that original sound we have two + + + align:start position:0% +that original sound we have two +synthetic versions one that's generated + + align:start position:0% +synthetic versions one that's generated + + + align:start position:0% +synthetic versions one that's generated +from the statistics of the model that + + align:start position:0% +from the statistics of the model that + + + align:start position:0% +from the statistics of the model that +replicates biology as best we know how + + align:start position:0% +replicates biology as best we know how + + + align:start position:0% +replicates biology as best we know how +on the other that that is altered in + + align:start position:0% +on the other that that is altered in + + + align:start position:0% +on the other that that is altered in +some way and we would ask people which + + align:start position:0% +some way and we would ask people which + + + align:start position:0% +some way and we would ask people which +of the two synthetic version sounds more + + align:start position:0% +of the two synthetic version sounds more + + + align:start position:0% +of the two synthetic version sounds more +realistic and so there's four conditions + + align:start position:0% +realistic and so there's four conditions + + + align:start position:0% +realistic and so there's four conditions +in this experiment because we could alt + + align:start position:0% +in this experiment because we could alt + + + align:start position:0% +in this experiment because we could alt +do these models in three different ways + + align:start position:0% +do these models in three different ways + + + align:start position:0% +do these models in three different ways +so we could get rid of amplitude + + align:start position:0% +so we could get rid of amplitude + + + align:start position:0% +so we could get rid of amplitude +compression that's the first bar we + + align:start position:0% +compression that's the first bar we + + + align:start position:0% +compression that's the first bar we +could make the cochlea linearly spaced + + align:start position:0% +could make the cochlea linearly spaced + + + align:start position:0% +could make the cochlea linearly spaced +or we could make the modulation filters + + align:start position:0% +or we could make the modulation filters + + + align:start position:0% +or we could make the modulation filters +linearly spaced we could do all three + + align:start position:0% +linearly spaced we could do all three + + + align:start position:0% +linearly spaced we could do all three +and that's the last condition and so + + align:start position:0% +and that's the last condition and so + + + align:start position:0% +and that's the last condition and so +it's being plotted on this axis oops I + + align:start position:0% +it's being plotted on this axis oops I + + + align:start position:0% +it's being plotted on this axis oops I +gave it away is the proportion of trials + + align:start position:0% +gave it away is the proportion of trials + + + align:start position:0% +gave it away is the proportion of trials +on which people said that the synthesis + + align:start position:0% +on which people said that the synthesis + + + align:start position:0% +on which people said that the synthesis +from the biologically plausible model + + align:start position:0% +from the biologically plausible model + + + align:start position:0% +from the biologically plausible model +was more realistic and so if it doesn't + + align:start position:0% +was more realistic and so if it doesn't + + + align:start position:0% +was more realistic and so if it doesn't +matter what statistics you use you + + align:start position:0% +matter what statistics you use you + + + align:start position:0% +matter what statistics you use you +should be right here at this fifty + + align:start position:0% +should be right here at this fifty + + + align:start position:0% +should be right here at this fifty +percent mark in each of these cases I + + align:start position:0% +percent mark in each of these cases I + + + align:start position:0% +percent mark in each of these cases I +mean as you can see in every case people + + align:start position:0% +mean as you can see in every case people + + + align:start position:0% +mean as you can see in every case people +actually report that on average the + + align:start position:0% +actually report that on average the + + + align:start position:0% +actually report that on average the +synthesis from the biologically + + align:start position:0% +synthesis from the biologically + + + align:start position:0% +synthesis from the biologically +plausible model um is more realistic and + + align:start position:0% +plausible model um is more realistic and + + + align:start position:0% +plausible model um is more realistic and +I'll give you a couple of examples so + + align:start position:0% +I'll give you a couple of examples so + + + align:start position:0% +I'll give you a couple of examples so +here's here's crowd noise since + + align:start position:0% +here's here's crowd noise since + + + align:start position:0% +here's here's crowd noise since +sighs from the biologically plausible + + align:start position:0% +sighs from the biologically plausible + + + align:start position:0% +sighs from the biologically plausible +auditory model + + align:start position:0% + + + + align:start position:0% + +and here's the result of doing the exact + + align:start position:0% +and here's the result of doing the exact + + + align:start position:0% +and here's the result of doing the exact +same thing but from the altered model + + align:start position:0% +same thing but from the altered model + + + align:start position:0% +same thing but from the altered model +and this is from this condition here + + align:start position:0% +and this is from this condition here + + + align:start position:0% +and this is from this condition here +where everything is different and you + + align:start position:0% +where everything is different and you + + + align:start position:0% +where everything is different and you +get a letter here it just kind of sounds + + align:start position:0% +get a letter here it just kind of sounds + + + align:start position:0% +get a letter here it just kind of sounds +weird + + align:start position:0% + + + + align:start position:0% + +it's kind of garbled in some way here's + + align:start position:0% +it's kind of garbled in some way here's + + + align:start position:0% +it's kind of garbled in some way here's +some so here's a helicopter synthesized + + align:start position:0% +some so here's a helicopter synthesized + + + align:start position:0% +some so here's a helicopter synthesized +from the biologically plausible model + + align:start position:0% + + + + align:start position:0% + +and here's from the other one doesn't + + align:start position:0% +and here's from the other one doesn't + + + align:start position:0% +and here's from the other one doesn't +sound like the modulations are quite as + + align:start position:0% +sound like the modulations are quite as + + + align:start position:0% +sound like the modulations are quite as +precise and so the the notion here is + + align:start position:0% +precise and so the the notion here is + + + align:start position:0% +precise and so the the notion here is +that we're initializing this procedure + + align:start position:0% +that we're initializing this procedure + + + align:start position:0% +that we're initializing this procedure +with noise and so the output is a + + align:start position:0% +with noise and so the output is a + + + align:start position:0% +with noise and so the output is a +different sound in every case that are + + align:start position:0% +different sound in every case that are + + + align:start position:0% +different sound in every case that are +sharing only the statistical properties + + align:start position:0% +sharing only the statistical properties + + + align:start position:0% +sharing only the statistical properties +and so the statistics that we measure + + align:start position:0% +and so the statistics that we measure + + + align:start position:0% +and so the statistics that we measure +needs to do this in business they define + + align:start position:0% +needs to do this in business they define + + + align:start position:0% +needs to do this in business they define +a class of sounds that include the + + align:start position:0% +a class of sounds that include the + + + align:start position:0% +a class of sounds that include the +original that in fact defines the set as + + align:start position:0% +original that in fact defines the set as + + + align:start position:0% +original that in fact defines the set as +well as a whole bunch of others and when + + align:start position:0% +well as a whole bunch of others and when + + + align:start position:0% +well as a whole bunch of others and when +you run the synthesis you're generating + + align:start position:0% +you run the synthesis you're generating + + + align:start position:0% +you run the synthesis you're generating +one of these other examples and so the + + align:start position:0% +one of these other examples and so the + + + align:start position:0% +one of these other examples and so the +notion is that if the stiches statistics + + align:start position:0% +notion is that if the stiches statistics + + + align:start position:0% +notion is that if the stiches statistics +are measuring what the brain is + + align:start position:0% +are measuring what the brain is + + + align:start position:0% +are measuring what the brain is +measuring well then these examples ought + + align:start position:0% +measuring well then these examples ought + + + align:start position:0% +measuring well then these examples ought +to sound like another example of the + + align:start position:0% +to sound like another example of the + + + align:start position:0% +to sound like another example of the +original sound you ought to be + + align:start position:0% +original sound you ought to be + + + align:start position:0% +original sound you ought to be +generating sort of an equivalence class + + align:start position:0% +generating sort of an equivalence class + + + align:start position:0% +generating sort of an equivalence class +and the idea is that when you are + + align:start position:0% +and the idea is that when you are + + + align:start position:0% +and the idea is that when you are +synthesizing from statistics of this + + align:start position:0% +synthesizing from statistics of this + + + align:start position:0% +synthesizing from statistics of this +non-biological model where it's a + + align:start position:0% +non-biological model where it's a + + + align:start position:0% +non-biological model where it's a +different set right so again it's + + align:start position:0% +different set right so again it's + + + align:start position:0% +different set right so again it's +defined by the original but it contains + + align:start position:0% +defined by the original but it contains + + + align:start position:0% +defined by the original but it contains +different things and they don't sound + + align:start position:0% +different things and they don't sound + + + align:start position:0% +different things and they don't sound +like the original because they're + + align:start position:0% +like the original because they're + + + align:start position:0% +like the original because they're +presumably not defined with the + + align:start position:0% +presumably not defined with the + + + align:start position:0% +presumably not defined with the +measurements that the brain is making I + + align:start position:0% +measurements that the brain is making I + + + align:start position:0% +measurements that the brain is making I +just mentioned to you the fact that the + + align:start position:0% +just mentioned to you the fact that the + + + align:start position:0% +just mentioned to you the fact that the +the procedure will generate a different + + align:start position:0% +the procedure will generate a different + + + align:start position:0% +the procedure will generate a different +signal in each of these cases here you + + align:start position:0% +signal in each of these cases here you + + + align:start position:0% +signal in each of these cases here you +can see the result of synthesizing from + + align:start position:0% +can see the result of synthesizing from + + + align:start position:0% +can see the result of synthesizing from +the statistics of a particular recording + + align:start position:0% +the statistics of a particular recording + + + align:start position:0% +the statistics of a particular recording +of waves and these are three different + + align:start position:0% +of waves and these are three different + + + align:start position:0% +of waves and these are three different +examples and if you sort of inspect + + align:start position:0% +examples and if you sort of inspect + + + align:start position:0% +examples and if you sort of inspect +these you can kind of see that they're + + align:start position:0% +these you can kind of see that they're + + + align:start position:0% +these you can kind of see that they're +all different right they sort of have + + align:start position:0% +all different right they sort of have + + + align:start position:0% +all different right they sort of have +peaks in amplitude in different places + + align:start position:0% +peaks in amplitude in different places + + + align:start position:0% +peaks in amplitude in different places +and stuff but on the other hand they all + + align:start position:0% +and stuff but on the other hand they all + + + align:start position:0% +and stuff but on the other hand they all +kind of look the same in the sense that + + align:start position:0% +kind of look the same in the sense that + + + align:start position:0% +kind of look the same in the sense that +they they have the same textural + + align:start position:0% +they they have the same textural + + + align:start position:0% +they they have the same textural +properties all right that's what's + + align:start position:0% +properties all right that's what's + + + align:start position:0% +properties all right that's what's +supposed to happen and so that the fact + + align:start position:0% +supposed to happen and so that the fact + + + align:start position:0% +supposed to happen and so that the fact +that you have all of these different + + align:start position:0% +that you have all of these different + + + align:start position:0% +that you have all of these different +signals that have the same statistical + + align:start position:0% +signals that have the same statistical + + + align:start position:0% +signals that have the same statistical +properties raises this interesting + + align:start position:0% +properties raises this interesting + + + align:start position:0% +properties raises this interesting +possibility which is that if the brain + + align:start position:0% +possibility which is that if the brain + + + align:start position:0% +possibility which is that if the brain +is just representing time average + + align:start position:0% +is just representing time average + + + align:start position:0% +is just representing time average +statistics we would predict that + + align:start position:0% +statistics we would predict that + + + align:start position:0% +statistics we would predict that +different exemplars of a texture ought + + align:start position:0% +different exemplars of a texture ought + + + align:start position:0% +different exemplars of a texture ought +to be difficult to discriminate and so + + align:start position:0% +to be difficult to discriminate and so + + + align:start position:0% +to be difficult to discriminate and so +this is a the the thing that I'll show + + align:start position:0% +this is a the the thing that I'll show + + + align:start position:0% +this is a the the thing that I'll show +you about next is an experiment that it + + align:start position:0% +you about next is an experiment that it + + + align:start position:0% +you about next is an experiment that it +attempts to test whether this is the + + align:start position:0% +attempts to test whether this is the + + + align:start position:0% +attempts to test whether this is the +case to try to test whether whether + + align:start position:0% +case to try to test whether whether + + + align:start position:0% +case to try to test whether whether +really you are in fact representing + + align:start position:0% +really you are in fact representing + + + align:start position:0% +really you are in fact representing +these textures with with statistics that + + align:start position:0% +these textures with with statistics that + + + align:start position:0% +these textures with with statistics that +summarize their properties by averaging + + align:start position:0% +summarize their properties by averaging + + + align:start position:0% +summarize their properties by averaging +over time and in doing so we're going to + + align:start position:0% +over time and in doing so we're going to + + + align:start position:0% +over time and in doing so we're going to +take advantage of a really simple + + align:start position:0% +take advantage of a really simple + + + align:start position:0% +take advantage of a really simple +statistical phenomenon which is that + + align:start position:0% +statistical phenomenon which is that + + + align:start position:0% +statistical phenomenon which is that +statistics that are + + align:start position:0% +statistics that are + + + align:start position:0% +statistics that are +from small samples are more variable + + align:start position:0% +from small samples are more variable + + + align:start position:0% +from small samples are more variable +than statistics measured from large + + align:start position:0% +than statistics measured from large + + + align:start position:0% +than statistics measured from large +samples and that's what is a exemplified + + align:start position:0% +samples and that's what is a exemplified + + + align:start position:0% +samples and that's what is a exemplified +by the graph that's here on the bottom + + align:start position:0% +by the graph that's here on the bottom + + + align:start position:0% +by the graph that's here on the bottom +so what this graph is plotting is the + + align:start position:0% +so what this graph is plotting is the + + + align:start position:0% +so what this graph is plotting is the +results of an exercise where we took + + align:start position:0% +results of an exercise where we took + + + align:start position:0% +results of an exercise where we took +multiple excerpts of a given texture of + + align:start position:0% +multiple excerpts of a given texture of + + + align:start position:0% +multiple excerpts of a given texture of +a particular duration so you're 40 + + align:start position:0% +a particular duration so you're 40 + + + align:start position:0% +a particular duration so you're 40 +milliseconds 80 160 320 so we get a + + align:start position:0% +milliseconds 80 160 320 so we get a + + + align:start position:0% +milliseconds 80 160 320 so we get a +whole bunch of different excerpts of + + align:start position:0% +whole bunch of different excerpts of + + + align:start position:0% +whole bunch of different excerpts of +that length and then we measure a + + align:start position:0% +that length and then we measure a + + + align:start position:0% +that length and then we measure a +particular statistic from that excerpt + + align:start position:0% +particular statistic from that excerpt + + + align:start position:0% +particular statistic from that excerpt +so in this case it's it's a particular + + align:start position:0% +so in this case it's it's a particular + + + align:start position:0% +so in this case it's it's a particular +cross correlation coefficient for for + + align:start position:0% +cross correlation coefficient for for + + + align:start position:0% +cross correlation coefficient for for +the the envelopes of a pair of sub-bands + + align:start position:0% +the the envelopes of a pair of sub-bands + + + align:start position:0% +the the envelopes of a pair of sub-bands +so we're gonna measure that statistic + + align:start position:0% +so we're gonna measure that statistic + + + align:start position:0% +so we're gonna measure that statistic +and in those different excerpts and then + + align:start position:0% +and in those different excerpts and then + + + align:start position:0% +and in those different excerpts and then +we're just going to try to see how + + align:start position:0% +we're just going to try to see how + + + align:start position:0% +we're just going to try to see how +variable that is across excerpts and + + align:start position:0% +variable that is across excerpts and + + + align:start position:0% +variable that is across excerpts and +that's summarized with the standard + + align:start position:0% +that's summarized with the standard + + + align:start position:0% +that's summarized with the standard +deviation of the statistic and that's + + align:start position:0% +deviation of the statistic and that's + + + align:start position:0% +deviation of the statistic and that's +what's plotted here on the y axis and so + + align:start position:0% +what's plotted here on the y axis and so + + + align:start position:0% +what's plotted here on the y axis and so +the point is that when the excerpts are + + align:start position:0% +the point is that when the excerpts are + + + align:start position:0% +the point is that when the excerpts are +short the statistics are variable so you + + align:start position:0% +short the statistics are variable so you + + + align:start position:0% +short the statistics are variable so you +measure it in one excerpt and then + + align:start position:0% +measure it in one excerpt and then + + + align:start position:0% +measure it in one excerpt and then +another and then another and you don't + + align:start position:0% +another and then another and you don't + + + align:start position:0% +another and then another and you don't +get the same thing all right and so the + + align:start position:0% +get the same thing all right and so the + + + align:start position:0% +get the same thing all right and so the +standard deviation is high and as the + + align:start position:0% +standard deviation is high and as the + + + align:start position:0% +standard deviation is high and as the +excerpt duration increases the + + align:start position:0% +excerpt duration increases the + + + align:start position:0% +excerpt duration increases the +statistics become more consistent they + + align:start position:0% +statistics become more consistent they + + + align:start position:0% +statistics become more consistent they +converge to like the true values of the + + align:start position:0% +converge to like the true values of the + + + align:start position:0% +converge to like the true values of the +station underlying stationary process + + align:start position:0% +station underlying stationary process + + + align:start position:0% +station underlying stationary process +and so the standard deviation kind of + + align:start position:0% +and so the standard deviation kind of + + + align:start position:0% +and so the standard deviation kind of +shrinks alright so we're gonna take + + align:start position:0% +shrinks alright so we're gonna take + + + align:start position:0% +shrinks alright so we're gonna take +advantage of this in in in the + + align:start position:0% +advantage of this in in in the + + + align:start position:0% +advantage of this in in in the +experiments that we'll do all right so + + align:start position:0% +experiments that we'll do all right so + + + align:start position:0% +experiments that we'll do all right so +first to to make sure that or to get + + align:start position:0% +first to to make sure that or to get + + + align:start position:0% +first to to make sure that or to get +plausibility to the notion that people + + align:start position:0% +plausibility to the notion that people + + + align:start position:0% +plausibility to the notion that people +might be able to base judgments on on + + align:start position:0% +might be able to base judgments on on + + + align:start position:0% +might be able to base judgments on on +long term statistics we asked people to + + align:start position:0% +long term statistics we asked people to + + + align:start position:0% +long term statistics we asked people to +discriminate different textures so these + + align:start position:0% +discriminate different textures so these + + + align:start position:0% +discriminate different textures so these +are things that have different long term + + align:start position:0% +are things that have different long term + + + align:start position:0% +are things that have different long term +statistics and so in the experiment + + align:start position:0% +statistics and so in the experiment + + + align:start position:0% +statistics and so in the experiment +people would hear three sounds one of + + align:start position:0% +people would hear three sounds one of + + + align:start position:0% +people would hear three sounds one of +which would be from a particular texture + + align:start position:0% +which would be from a particular texture + + + align:start position:0% +which would be from a particular texture +like rain and then two others of which + + align:start position:0% +like rain and then two others of which + + + align:start position:0% +like rain and then two others of which +would be different examples of a + + align:start position:0% +would be different examples of a + + + align:start position:0% +would be different examples of a +different texture like a stream so you'd + + align:start position:0% +different texture like a stream so you'd + + + align:start position:0% +different texture like a stream so you'd +hear rain stream one stream - and the + + align:start position:0% +hear rain stream one stream - and the + + + align:start position:0% +hear rain stream one stream - and the +task was to say which sound was produced + + align:start position:0% +task was to say which sound was produced + + + align:start position:0% +task was to say which sound was produced +by a different source and so in this + + align:start position:0% +by a different source and so in this + + + align:start position:0% +by a different source and so in this +case the answer would be first alright + + align:start position:0% +case the answer would be first alright + + + align:start position:0% +case the answer would be first alright +and so we gave people this task and we + + align:start position:0% +and so we gave people this task and we + + + align:start position:0% +and so we gave people this task and we +manipulated the duration of the excerpts + + align:start position:0% +manipulated the duration of the excerpts + + + align:start position:0% +manipulated the duration of the excerpts +and so the notion here is that well + + align:start position:0% +and so the notion here is that well + + + align:start position:0% +and so the notion here is that well +given this graph what happens is that + + align:start position:0% +given this graph what happens is that + + + align:start position:0% +given this graph what happens is that +the statistics are very variable for + + align:start position:0% +the statistics are very variable for + + + align:start position:0% +the statistics are very variable for +short excerpts and then they become more + + align:start position:0% +short excerpts and then they become more + + + align:start position:0% +short excerpts and then they become more +consistent um as the excerpt duration + + align:start position:0% +consistent um as the excerpt duration + + + align:start position:0% +consistent um as the excerpt duration +gets longer and so if you're basing your + + align:start position:0% +gets longer and so if you're basing your + + + align:start position:0% +gets longer and so if you're basing your +judgments on the on the statistics + + align:start position:0% +judgments on the on the statistics + + + align:start position:0% +judgments on the on the statistics +computed across the excerpt well then + + align:start position:0% +computed across the excerpt well then + + + align:start position:0% +computed across the excerpt well then +you ought to get better at + + align:start position:0% +you ought to get better at + + + align:start position:0% +you ought to get better at +whether the statistics are the same or + + align:start position:0% +whether the statistics are the same or + + + align:start position:0% +whether the statistics are the same or +different as the excerpt duration gets + + align:start position:0% +different as the excerpt duration gets + + + align:start position:0% +different as the excerpt duration gets +longer all right and so we're gonna plot + + align:start position:0% +longer all right and so we're gonna plot + + + align:start position:0% +longer all right and so we're gonna plot +here is the proportion correct that this + + align:start position:0% +here is the proportion correct that this + + + align:start position:0% +here is the proportion correct that this +task is a function of the excerpt + + align:start position:0% +task is a function of the excerpt + + + align:start position:0% +task is a function of the excerpt +duration and indeed we see that people + + align:start position:0% +duration and indeed we see that people + + + align:start position:0% +duration and indeed we see that people +get better as the duration gets longer + + align:start position:0% +get better as the duration gets longer + + + align:start position:0% +get better as the duration gets longer +so they're not very good when you give + + align:start position:0% +so they're not very good when you give + + + align:start position:0% +so they're not very good when you give +them a really short clip but they get + + align:start position:0% +them a really short clip but they get + + + align:start position:0% +them a really short clip but they get +better and better and as the duration + + align:start position:0% +better and better and as the duration + + + align:start position:0% +better and better and as the duration +increases now of course this is not + + align:start position:0% +increases now of course this is not + + + align:start position:0% +increases now of course this is not +really a particularly exciting result + + align:start position:0% +really a particularly exciting result + + + align:start position:0% +really a particularly exciting result +when you increase the duration you give + + align:start position:0% +when you increase the duration you give + + + align:start position:0% +when you increase the duration you give +people more information and pretty much + + align:start position:0% +people more information and pretty much + + + align:start position:0% +people more information and pretty much +on any story people ought to be getting + + align:start position:0% +on any story people ought to be getting + + + align:start position:0% +on any story people ought to be getting +better right but it's absolutely + + align:start position:0% +better right but it's absolutely + + + align:start position:0% +better right but it's absolutely +consistent with the notion that you + + align:start position:0% +consistent with the notion that you + + + align:start position:0% +consistent with the notion that you +might be basing your judgments on + + align:start position:0% +might be basing your judgments on + + + align:start position:0% +might be basing your judgments on +statistics now the really critical + + align:start position:0% +statistics now the really critical + + + align:start position:0% +statistics now the really critical +experiment is the next one I mean so in + + align:start position:0% +experiment is the next one I mean so in + + + align:start position:0% +experiment is the next one I mean so in +this experiment we gave people different + + align:start position:0% +this experiment we gave people different + + + align:start position:0% +this experiment we gave people different +excerpts of the same texture and we + + align:start position:0% +excerpts of the same texture and we + + + align:start position:0% +excerpts of the same texture and we +asked them to discriminate them so again + + align:start position:0% +asked them to discriminate them so again + + + align:start position:0% +asked them to discriminate them so again +on each trial you hear three sounds but + + align:start position:0% +on each trial you hear three sounds but + + + align:start position:0% +on each trial you hear three sounds but +there are they're they're all excerpts + + align:start position:0% +there are they're they're all excerpts + + + align:start position:0% +there are they're they're all excerpts +from the same texture but two of them + + align:start position:0% +from the same texture but two of them + + + align:start position:0% +from the same texture but two of them +are identical so in this case the last + + align:start position:0% +are identical so in this case the last + + + align:start position:0% +are identical so in this case the last +two are physically identical excerpts of + + align:start position:0% +two are physically identical excerpts of + + + align:start position:0% +two are physically identical excerpts of +for instance rain and the first one is + + align:start position:0% +for instance rain and the first one is + + + align:start position:0% +for instance rain and the first one is +it is a different excerpt of rain and so + + align:start position:0% +it is a different excerpt of rain and so + + + align:start position:0% +it is a different excerpt of rain and so +you just have to say which one is + + align:start position:0% +you just have to say which one is + + + align:start position:0% +you just have to say which one is +different from the other two all right + + align:start position:0% +different from the other two all right + + + align:start position:0% +different from the other two all right +now but maybe the null hypothesis here + + align:start position:0% +now but maybe the null hypothesis here + + + align:start position:0% +now but maybe the null hypothesis here +is what you might expect if you gave + + align:start position:0% +is what you might expect if you gave + + + align:start position:0% +is what you might expect if you gave +this to like a computer algorithm that + + align:start position:0% +this to like a computer algorithm that + + + align:start position:0% +this to like a computer algorithm that +was just limited by sensor noise and so + + align:start position:0% +was just limited by sensor noise and so + + + align:start position:0% +was just limited by sensor noise and so +the notion is that as the excerpt + + align:start position:0% +the notion is that as the excerpt + + + align:start position:0% +the notion is that as the excerpt +duration gets longer you're giving + + align:start position:0% +duration gets longer you're giving + + + align:start position:0% +duration gets longer you're giving +people more information with which to + + align:start position:0% +people more information with which to + + + align:start position:0% +people more information with which to +tell that this one is different from + + align:start position:0% +tell that this one is different from + + + align:start position:0% +tell that this one is different from +from this one so maybe if you listen to + + align:start position:0% +from this one so maybe if you listen to + + + align:start position:0% +from this one so maybe if you listen to +just the beginning it would be hard but + + align:start position:0% +just the beginning it would be hard but + + + align:start position:0% +just the beginning it would be hard but +as you got more information it would it + + align:start position:0% +as you got more information it would it + + + align:start position:0% +as you got more information it would it +would get easier and easier if in + + align:start position:0% +would get easier and easier if in + + + align:start position:0% +would get easier and easier if in +contrast you think that what people + + align:start position:0% +contrast you think that what people + + + align:start position:0% +contrast you think that what people +represent when they hear these sounds + + align:start position:0% +represent when they hear these sounds + + + align:start position:0% +represent when they hear these sounds +are statistics that summarize the + + align:start position:0% +are statistics that summarize the + + + align:start position:0% +are statistics that summarize the +properties over time well I've just + + align:start position:0% +properties over time well I've just + + + align:start position:0% +properties over time well I've just +shown you how the statistics converge to + + align:start position:0% +shown you how the statistics converge to + + + align:start position:0% +shown you how the statistics converge to +fixed values as a duration increases and + + align:start position:0% +fixed values as a duration increases and + + + align:start position:0% +fixed values as a duration increases and +so if what people are representing are + + align:start position:0% +so if what people are representing are + + + align:start position:0% +so if what people are representing are +those statistics you might paradoxically + + align:start position:0% +those statistics you might paradoxically + + + align:start position:0% +those statistics you might paradoxically +think that as the duration increases + + align:start position:0% +think that as the duration increases + + + align:start position:0% +think that as the duration increases +they would get worse at this task and + + align:start position:0% +they would get worse at this task and + + + align:start position:0% +they would get worse at this task and +that's in fact what we find happens so + + align:start position:0% +that's in fact what we find happens so + + + align:start position:0% +that's in fact what we find happens so +people are good at this task when the + + align:start position:0% +people are good at this task when the + + + align:start position:0% +people are good at this task when the +excerpts are very short on the order of + + align:start position:0% +excerpts are very short on the order of + + + align:start position:0% +excerpts are very short on the order of +like 100 milliseconds so they can very + + align:start position:0% +like 100 milliseconds so they can very + + + align:start position:0% +like 100 milliseconds so they can very +easily tell you whether you're which of + + align:start position:0% +easily tell you whether you're which of + + + align:start position:0% +easily tell you whether you're which of +the two excerpts is different I mean as + + align:start position:0% +the two excerpts is different I mean as + + + align:start position:0% +the two excerpts is different I mean as +the duration gets longer and longer um + + align:start position:0% +the duration gets longer and longer um + + + align:start position:0% +the duration gets longer and longer um +they get progressively worse and worse + + align:start position:0% +they get progressively worse and worse + + + align:start position:0% +they get progressively worse and worse +and so we think this is consistent with + + align:start position:0% +and so we think this is consistent with + + + align:start position:0% +and so we think this is consistent with +the idea that when you are hearing a + + align:start position:0% +the idea that when you are hearing a + + + align:start position:0% +the idea that when you are hearing a +texture once the texture is a couple + + align:start position:0% +texture once the texture is a couple + + + align:start position:0% +texture once the texture is a couple +seconds long + + align:start position:0% +seconds long + + + align:start position:0% +seconds long +you're predominantly representing the + + align:start position:0% +you're predominantly representing the + + + align:start position:0% +you're predominantly representing the +statistical properties + + align:start position:0% +statistical properties + + + align:start position:0% +statistical properties +averaging the properties over time and + + align:start position:0% +averaging the properties over time and + + + align:start position:0% +averaging the properties over time and +you lose access to the details that + + align:start position:0% +you lose access to the details that + + + align:start position:0% +you lose access to the details that +differentiate different examples of rain + + align:start position:0% +differentiate different examples of rain + + + align:start position:0% +differentiate different examples of rain +so the exact positions are the raindrops + + align:start position:0% +so the exact positions are the raindrops + + + align:start position:0% +so the exact positions are the raindrops +or the clicks of the fire or what have + + align:start position:0% +or the clicks of the fire or what have + + + align:start position:0% +or the clicks of the fire or what have +you why why should people be unable to + + align:start position:0% +you why why should people be unable to + + + align:start position:0% +you why why should people be unable to +discriminate two examples of rain well + + align:start position:0% +discriminate two examples of rain well + + + align:start position:0% +discriminate two examples of rain well +you might think well these textures are + + align:start position:0% +you might think well these textures are + + + align:start position:0% +you might think well these textures are +just homogeneous right there you know + + align:start position:0% +just homogeneous right there you know + + + align:start position:0% +just homogeneous right there you know +there's just not enough stuff there to + + align:start position:0% +there's just not enough stuff there to + + + align:start position:0% +there's just not enough stuff there to +differentiate them and we know that + + align:start position:0% +differentiate them and we know that + + + align:start position:0% +differentiate them and we know that +that's not true because if you just + + align:start position:0% +that's not true because if you just + + + align:start position:0% +that's not true because if you just +chopped out a little section at random + + align:start position:0% +chopped out a little section at random + + + align:start position:0% +chopped out a little section at random +people can very easily tell you whether + + align:start position:0% +people can very easily tell you whether + + + align:start position:0% +people can very easily tell you whether +it's the same or different right so at a + + align:start position:0% +it's the same or different right so at a + + + align:start position:0% +it's the same or different right so at a +local time scale the details is is very + + align:start position:0% +local time scale the details is is very + + + align:start position:0% +local time scale the details is is very +easily discriminable you might also + + align:start position:0% +easily discriminable you might also + + + align:start position:0% +easily discriminable you might also +imagine that what's happening is that + + align:start position:0% +imagine that what's happening is that + + + align:start position:0% +imagine that what's happening is that +you know over time like you know maybe + + align:start position:0% +you know over time like you know maybe + + + align:start position:0% +you know over time like you know maybe +there's some kind of masking in time or + + align:start position:0% +there's some kind of masking in time or + + + align:start position:0% +there's some kind of masking in time or +that the representation kind of gets + + align:start position:0% +that the representation kind of gets + + + align:start position:0% +that the representation kind of gets +blurred together and in some strange way + + align:start position:0% +blurred together and in some strange way + + + align:start position:0% +blurred together and in some strange way +on the other hand when you give people + + align:start position:0% +on the other hand when you give people + + + align:start position:0% +on the other hand when you give people +sounds that have different statistics + + align:start position:0% +sounds that have different statistics + + + align:start position:0% +sounds that have different statistics +you find that they're just great right + + align:start position:0% +you find that they're just great right + + + align:start position:0% +you find that they're just great right +so they get better and better as the the + + align:start position:0% +so they get better and better as the the + + + align:start position:0% +so they get better and better as the the +stimulus increases and in fact the fact + + align:start position:0% +stimulus increases and in fact the fact + + + align:start position:0% +stimulus increases and in fact the fact +that they continue to get better that + + align:start position:0% +that they continue to get better that + + + align:start position:0% +that they continue to get better that +seems to indicate that the detail that + + align:start position:0% +seems to indicate that the detail that + + + align:start position:0% +seems to indicate that the detail that +is streaming into your ears is being + + align:start position:0% +is streaming into your ears is being + + + align:start position:0% +is streaming into your ears is being +accrued into some representation that + + align:start position:0% +accrued into some representation that + + + align:start position:0% +accrued into some representation that +you have access to and so we think what + + align:start position:0% +you have access to and so we think what + + + align:start position:0% +you have access to and so we think what +we think is happening is that those + + align:start position:0% +we think is happening is that those + + + align:start position:0% +we think is happening is that those +details come in um they're incorporated + + align:start position:0% +details come in um they're incorporated + + + align:start position:0% +details come in um they're incorporated +into your statistical estimates but the + + align:start position:0% +into your statistical estimates but the + + + align:start position:0% +into your statistical estimates but the +fact that you can't tell apart these + + align:start position:0% +fact that you can't tell apart these + + + align:start position:0% +fact that you can't tell apart these +different excerpts means that those do + + align:start position:0% +different excerpts means that those do + + + align:start position:0% +different excerpts means that those do +Tito those details are not otherwise + + align:start position:0% +Tito those details are not otherwise + + + align:start position:0% +Tito those details are not otherwise +retained all right so there are accrued + + align:start position:0% +retained all right so there are accrued + + + align:start position:0% +retained all right so there are accrued +into statistics but then you lose access + + align:start position:0% +into statistics but then you lose access + + + align:start position:0% +into statistics but then you lose access +to the details on their own the point is + + align:start position:0% +to the details on their own the point is + + + align:start position:0% +to the details on their own the point is +that the result as it stands I think + + align:start position:0% +that the result as it stands I think + + + align:start position:0% +that the result as it stands I think +provides evidence for a representation + + align:start position:0% +provides evidence for a representation + + + align:start position:0% +provides evidence for a representation +of time average statistics so the idea + + align:start position:0% +of time average statistics so the idea + + + align:start position:0% +of time average statistics so the idea +is that when the tech - the disease are + + align:start position:0% +is that when the tech - the disease are + + + align:start position:0% +is that when the tech - the disease are +different you can tell things are + + align:start position:0% +different you can tell things are + + + align:start position:0% +different you can tell things are +distinct when they're the same you can't + + align:start position:0% +distinct when they're the same you can't + + + align:start position:0% +distinct when they're the same you can't +and relates to this phenomenon of the + + align:start position:0% +and relates to this phenomenon of the + + + align:start position:0% +and relates to this phenomenon of the +variability of statistics as a function + + align:start position:0% +variability of statistics as a function + + + align:start position:0% +variability of statistics as a function +of sample size so um a couple like + + align:start position:0% +of sample size so um a couple like + + + align:start position:0% +of sample size so um a couple like +control experiments that are probably + + align:start position:0% +control experiments that are probably + + + align:start position:0% +control experiments that are probably +not exactly addressing the question you + + align:start position:0% +not exactly addressing the question you + + + align:start position:0% +not exactly addressing the question you +just raised but but maybe are related so + + align:start position:0% +just raised but but maybe are related so + + + align:start position:0% +just raised but but maybe are related so +one obvious possibility is that the + + align:start position:0% +one obvious possibility is that the + + + align:start position:0% +one obvious possibility is that the +reason that people are good at the + + align:start position:0% +reason that people are good at the + + + align:start position:0% +reason that people are good at the +exemplar discrimination here when the + + align:start position:0% +exemplar discrimination here when the + + + align:start position:0% +exemplar discrimination here when the +excerpts are short and bad here might be + + align:start position:0% +excerpts are short and bad here might be + + + align:start position:0% +excerpts are short and bad here might be +the fact the fact that that maybe your + + align:start position:0% +the fact the fact that that maybe your + + + align:start position:0% +the fact the fact that that maybe your +memory is decaying with time right so + + align:start position:0% +memory is decaying with time right so + + + align:start position:0% +memory is decaying with time right so +the way that we did this experiment + + align:start position:0% +the way that we did this experiment + + + align:start position:0% +the way that we did this experiment +originally was that there was a fixed + + align:start position:0% +originally was that there was a fixed + + + align:start position:0% +originally was that there was a fixed +interest emulation interval so that was + + align:start position:0% +interest emulation interval so that was + + + align:start position:0% +interest emulation interval so that was +the same it was like a couple hundred + + align:start position:0% +the same it was like a couple hundred + + + align:start position:0% +the same it was like a couple hundred +milliseconds in every case and so to + + align:start position:0% +milliseconds in every case and so to + + + align:start position:0% +milliseconds in every case and so to +tell that this is different from this + + align:start position:0% +tell that this is different from this + + + align:start position:0% +tell that this is different from this +well you you know you that the bits that + + align:start position:0% +well you you know you that the bits that + + + align:start position:0% +well you you know you that the bits that +you would have to compare are separated + + align:start position:0% +you would have to compare are separated + + + align:start position:0% +you would have to compare are separated +by a shorter time interval + + align:start position:0% +by a shorter time interval + + + align:start position:0% +by a shorter time interval +or in this case right where they're + + align:start position:0% +or in this case right where they're + + + align:start position:0% +or in this case right where they're +separated by a longer time interval and + + align:start position:0% +separated by a longer time interval and + + + align:start position:0% +separated by a longer time interval and +if you might just imagine that like + + align:start position:0% +if you might just imagine that like + + + align:start position:0% +if you might just imagine that like +memory decays with time you might think + + align:start position:0% +memory decays with time you might think + + + align:start position:0% +memory decays with time you might think +that that would make people worse so we + + align:start position:0% +that that would make people worse so we + + + align:start position:0% +that that would make people worse so we +did a control experiment where we + + align:start position:0% +did a control experiment where we + + + align:start position:0% +did a control experiment where we +equated the inner onset interval alright + + align:start position:0% +equated the inner onset interval alright + + + align:start position:0% +equated the inner onset interval alright +so that the elapsed time between the + + align:start position:0% +so that the elapsed time between the + + + align:start position:0% +so that the elapsed time between the +stuff that you would have to compare in + + align:start position:0% +stuff that you would have to compare in + + + align:start position:0% +stuff that you would have to compare in +order to tell whether something was + + align:start position:0% +order to tell whether something was + + + align:start position:0% +order to tell whether something was +different was the same in the two cases + + align:start position:0% +different was the same in the two cases + + + align:start position:0% +different was the same in the two cases +and that basically makes no difference + + align:start position:0% +and that basically makes no difference + + + align:start position:0% +and that basically makes no difference +right you're still a lot better when the + + align:start position:0% +right you're still a lot better when the + + + align:start position:0% +right you're still a lot better when the +things are short than when they're long + + align:start position:0% +things are short than when they're long + + + align:start position:0% +things are short than when they're long +um and we even we went to pretty great + + align:start position:0% +um and we even we went to pretty great + + + align:start position:0% +um and we even we went to pretty great +lengths to try to help people be able to + + align:start position:0% +lengths to try to help people be able to + + + align:start position:0% +lengths to try to help people be able to +do this with these long adverbs so you + + align:start position:0% +do this with these long adverbs so you + + + align:start position:0% +do this with these long adverbs so you +might also wonder well given that you + + align:start position:0% +might also wonder well given that you + + + align:start position:0% +might also wonder well given that you +can do this with the short excerpts well + + align:start position:0% +can do this with the short excerpts well + + + align:start position:0% +can do this with the short excerpts well +the short excerpts are really just + + align:start position:0% +the short excerpts are really just + + + align:start position:0% +the short excerpts are really just +analogous to like the very beginning of + + align:start position:0% +analogous to like the very beginning of + + + align:start position:0% +analogous to like the very beginning of +these longer excerpts right so why can't + + align:start position:0% +these longer excerpts right so why can't + + + align:start position:0% +these longer excerpts right so why can't +you just listen to the beginning and so + + align:start position:0% +you just listen to the beginning and so + + + align:start position:0% +you just listen to the beginning and so +we tried to help people do just that so + + align:start position:0% +we tried to help people do just that so + + + align:start position:0% +we tried to help people do just that so +in this condition here we put a little + + align:start position:0% +in this condition here we put a little + + + align:start position:0% +in this condition here we put a little +gap between the very beginning excerpt + + align:start position:0% +gap between the very beginning excerpt + + + align:start position:0% +gap between the very beginning excerpt +and the rest of the thing right and we + + align:start position:0% +and the rest of the thing right and we + + + align:start position:0% +and the rest of the thing right and we +just told people all right you know + + align:start position:0% +just told people all right you know + + + align:start position:0% +just told people all right you know +there's gonna be this little thing at + + align:start position:0% +there's gonna be this little thing at + + + align:start position:0% +there's gonna be this little thing at +the start just listen for that and + + align:start position:0% +the start just listen for that and + + + align:start position:0% +the start just listen for that and +people can't do that so we also did it + + align:start position:0% +people can't do that so we also did it + + + align:start position:0% +people can't do that so we also did it +at the end so we put the gap at the end + + align:start position:0% +at the end so we put the gap at the end + + + align:start position:0% +at the end so we put the gap at the end +so again you get this little thing of + + align:start position:0% +so again you get this little thing of + + + align:start position:0% +so again you get this little thing of +the same length as you have in the short + + align:start position:0% +the same length as you have in the short + + + align:start position:0% +the same length as you have in the short +condition and this is performance in + + align:start position:0% +condition and this is performance in + + + align:start position:0% +condition and this is performance in +this cases people are good when it's + + align:start position:0% +this cases people are good when it's + + + align:start position:0% +this cases people are good when it's +short and a lot worse when it's longer + + align:start position:0% +short and a lot worse when it's longer + + + align:start position:0% +short and a lot worse when it's longer +and the presence of the gap doesn't + + align:start position:0% +and the presence of the gap doesn't + + + align:start position:0% +and the presence of the gap doesn't +really seem to make a difference right + + align:start position:0% +really seem to make a difference right + + + align:start position:0% +really seem to make a difference right +so they just yeah you have great trouble + + align:start position:0% +so they just yeah you have great trouble + + + align:start position:0% +so they just yeah you have great trouble +accessing these things another thing + + align:start position:0% +accessing these things another thing + + + align:start position:0% +accessing these things another thing +that's that this sort of relevant and + + align:start position:0% +that's that this sort of relevant and + + + align:start position:0% +that's that this sort of relevant and +related was these experiments that that + + align:start position:0% +related was these experiments that that + + + align:start position:0% +related was these experiments that that +resulted from our thinking about the + + align:start position:0% +resulted from our thinking about the + + + align:start position:0% +resulted from our thinking about the +fact that textures are normally not + + align:start position:0% +fact that textures are normally not + + + align:start position:0% +fact that textures are normally not +generated from our synthesis algorithm + + align:start position:0% +generated from our synthesis algorithm + + + align:start position:0% +generated from our synthesis algorithm +but rather from the superposition of + + align:start position:0% +but rather from the superposition of + + + align:start position:0% +but rather from the superposition of +lots of different sources and so we + + align:start position:0% +lots of different sources and so we + + + align:start position:0% +lots of different sources and so we +wondered what would happen to this + + align:start position:0% +wondered what would happen to this + + + align:start position:0% +wondered what would happen to this +phenomenon if we varied the number of + + align:start position:0% +phenomenon if we varied the number of + + + align:start position:0% +phenomenon if we varied the number of +sources in in a texture so we actually + + align:start position:0% +sources in in a texture so we actually + + + align:start position:0% +sources in in a texture so we actually +generated textures by superimposing + + align:start position:0% +generated textures by superimposing + + + align:start position:0% +generated textures by superimposing +different numbers of sources so in one + + align:start position:0% +different numbers of sources so in one + + + align:start position:0% +different numbers of sources so in one +case we did this with speakers so we we + + align:start position:0% +case we did this with speakers so we we + + + align:start position:0% +case we did this with speakers so we we +wanted to get rid of linguistic effects + + align:start position:0% +wanted to get rid of linguistic effects + + + align:start position:0% +wanted to get rid of linguistic effects +and so we used German speech and people + + align:start position:0% +and so we used German speech and people + + + align:start position:0% +and so we used German speech and people +that didn't speak German so it's like a + + align:start position:0% +that didn't speak German so it's like a + + + align:start position:0% +that didn't speak German so it's like a +German cocktail party that we're gonna + + align:start position:0% +German cocktail party that we're gonna + + + align:start position:0% +German cocktail party that we're gonna +generate so we have one person like this + + align:start position:0% +generate so we have one person like this + + + align:start position:0% +generate so we have one person like this +guitar p.m. and then 29 + + align:start position:0% + + + + align:start position:0% + +roomful of people speaking German right + + align:start position:0% +roomful of people speaking German right + + + align:start position:0% +roomful of people speaking German right +and so we do the exact same experiment + + align:start position:0% +and so we do the exact same experiment + + + align:start position:0% +and so we do the exact same experiment +where we give people different exemplars + + align:start position:0% +where we give people different exemplars + + + align:start position:0% +where we give people different exemplars +of these textures and we ask them to + + align:start position:0% +of these textures and we ask them to + + + align:start position:0% +of these textures and we ask them to +discriminate between them and so what's + + align:start position:0% +discriminate between them and so what's + + + align:start position:0% +discriminate between them and so what's +plotted here is the proportion correct + + align:start position:0% +plotted here is the proportion correct + + + align:start position:0% +plotted here is the proportion correct +as a function of duration we've here + + align:start position:0% +as a function of duration we've here + + + align:start position:0% +as a function of duration we've here +we've reduced it to just two durations + + align:start position:0% +we've reduced it to just two durations + + + align:start position:0% +we've reduced it to just two durations +short and long and there's four + + align:start position:0% +short and long and there's four + + + align:start position:0% +short and long and there's four +different curves corresponding to + + align:start position:0% +different curves corresponding to + + + align:start position:0% +different curves corresponding to +different numbers of speakers in that + + align:start position:0% +different numbers of speakers in that + + + align:start position:0% +different numbers of speakers in that +signal right so the the cyan here is + + align:start position:0% +signal right so the the cyan here is + + + align:start position:0% +signal right so the the cyan here is +what happens with a single speaker and + + align:start position:0% +what happens with a single speaker and + + + align:start position:0% +what happens with a single speaker and +so with a single speaker you actually + + align:start position:0% +so with a single speaker you actually + + + align:start position:0% +so with a single speaker you actually +get better at doing this as a duration + + align:start position:0% +get better at doing this as a duration + + + align:start position:0% +get better at doing this as a duration +increases all right and so that's again + + align:start position:0% +increases all right and so that's again + + + align:start position:0% +increases all right and so that's again +consistent with the null hypothesis that + + align:start position:0% +consistent with the null hypothesis that + + + align:start position:0% +consistent with the null hypothesis that +when there's more information you're + + align:start position:0% +when there's more information you're + + + align:start position:0% +when there's more information you're +actually going to be better able to say + + align:start position:0% +actually going to be better able to say + + + align:start position:0% +actually going to be better able to say +whether something is the same or + + align:start position:0% +whether something is the same or + + + align:start position:0% +whether something is the same or +different but as you increase the number + + align:start position:0% +different but as you increase the number + + + align:start position:0% +different but as you increase the number +of people at the cocktail party so that + + align:start position:0% +of people at the cocktail party so that + + + align:start position:0% +of people at the cocktail party so that +the density of the signal in some sense + + align:start position:0% +the density of the signal in some sense + + + align:start position:0% +the density of the signal in some sense +you can see that performance for the + + align:start position:0% +you can see that performance for the + + + align:start position:0% +you can see that performance for the +short excerpts doesn't really change so + + align:start position:0% +short excerpts doesn't really change so + + + align:start position:0% +short excerpts doesn't really change so +you retain the ability to say whether + + align:start position:0% +you retain the ability to say whether + + + align:start position:0% +you retain the ability to say whether +these things are the same or different + + align:start position:0% +these things are the same or different + + + align:start position:0% +these things are the same or different +but there's this huge interaction and + + align:start position:0% +but there's this huge interaction and + + + align:start position:0% +but there's this huge interaction and +for the long excerpts you get kind of + + align:start position:0% +for the long excerpts you get kind of + + + align:start position:0% +for the long excerpts you get kind of +worse and worse so these impairment at + + align:start position:0% +worse and worse so these impairment at + + + align:start position:0% +worse and worse so these impairment at +long durations is really specific to + + align:start position:0% +long durations is really specific to + + + align:start position:0% +long durations is really specific to +textures doesn't seem to be present for + + align:start position:0% +textures doesn't seem to be present for + + + align:start position:0% +textures doesn't seem to be present for +single sources to make sure that + + align:start position:0% +single sources to make sure that + + + align:start position:0% +single sources to make sure that +phenomenon is not really specific to + + align:start position:0% +phenomenon is not really specific to + + + align:start position:0% +phenomenon is not really specific to +speech we did the exact same thing with + + align:start position:0% +speech we did the exact same thing with + + + align:start position:0% +speech we did the exact same thing with +synthetic drum hits so we just varied + + align:start position:0% +synthetic drum hits so we just varied + + + align:start position:0% +synthetic drum hits so we just varied +the density of a bunch of random drum + + align:start position:0% +the density of a bunch of random drum + + + align:start position:0% +the density of a bunch of random drum +hits like here's five hits per second + + align:start position:0% +hits like here's five hits per second + + + align:start position:0% +hits like here's five hits per second +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +here's 50 all right and you see the + + align:start position:0% +here's 50 all right and you see the + + + align:start position:0% +here's 50 all right and you see the +exact same phenomenon so for the very + + align:start position:0% +exact same phenomenon so for the very + + + align:start position:0% +exact same phenomenon so for the very +sparse issed case you get better as you + + align:start position:0% +sparse issed case you get better as you + + + align:start position:0% +sparse issed case you get better as you +go from the short excerpts to the long + + align:start position:0% +go from the short excerpts to the long + + + align:start position:0% +go from the short excerpts to the long +but then as the density increases you + + align:start position:0% +but then as the density increases you + + + align:start position:0% +but then as the density increases you +see this big interaction and you get + + align:start position:0% +see this big interaction and you get + + + align:start position:0% +see this big interaction and you get +selectively worse here for the for the + + align:start position:0% +selectively worse here for the for the + + + align:start position:0% +selectively worse here for the for the +long duration case okay so um again it's + + align:start position:0% +long duration case okay so um again it's + + + align:start position:0% +long duration case okay so um again it's +worth pointing out that the high + + align:start position:0% +worth pointing out that the high + + + align:start position:0% +worth pointing out that the high +performance at the short with the short + + align:start position:0% +performance at the short with the short + + + align:start position:0% +performance at the short with the short +excerpts indicate that all the stimuli + + align:start position:0% +excerpts indicate that all the stimuli + + + align:start position:0% +excerpts indicate that all the stimuli +have discriminable variation so it's not + + align:start position:0% +have discriminable variation so it's not + + + align:start position:0% +have discriminable variation so it's not +the case that these things are just like + + align:start position:0% +the case that these things are just like + + + align:start position:0% +the case that these things are just like +totally homogeneous and that's why you + + align:start position:0% +totally homogeneous and that's why you + + + align:start position:0% +totally homogeneous and that's why you +can't do it I seems to be a specific + + align:start position:0% +can't do it I seems to be a specific + + + align:start position:0% +can't do it I seems to be a specific +problem with retaining temporal detail + + align:start position:0% +problem with retaining temporal detail + + + align:start position:0% +problem with retaining temporal detail +when the signals are both long and and + + align:start position:0% +when the signals are both long and and + + + align:start position:0% +when the signals are both long and and +texture like okay so what is it what + + align:start position:0% +texture like okay so what is it what + + + align:start position:0% +texture like okay so what is it what +does it mean well good here's the + + align:start position:0% +does it mean well good here's the + + + align:start position:0% +does it mean well good here's the +specular framework and this sort of gets + + align:start position:0% +specular framework and this sort of gets + + + align:start position:0% +specular framework and this sort of gets +back to these questions about working + + align:start position:0% +back to these questions about working + + + align:start position:0% +back to these questions about working +memory and so forth and so this is what + + align:start position:0% +memory and so forth and so this is what + + + align:start position:0% +memory and so forth and so this is what +I the way that I make sense of this + + align:start position:0% +I the way that I make sense of this + + + align:start position:0% +I the way that I make sense of this +stuff and each one of these things is + + align:start position:0% +stuff and each one of these things is + + + align:start position:0% +stuff and each one of these things is +pure speculation or almost pure + + align:start position:0% +pure speculation or almost pure + + + align:start position:0% +pure speculation or almost pure +speculation but I + + align:start position:0% +speculation but I + + + align:start position:0% +speculation but I +I think you need all of them to really + + align:start position:0% +I think you need all of them to really + + + align:start position:0% +I think you need all of them to really +totally make sense of the results it's + + align:start position:0% +totally make sense of the results it's + + + align:start position:0% +totally make sense of the results it's +at least interesting to think about so I + + align:start position:0% +at least interesting to think about so I + + + align:start position:0% +at least interesting to think about so I +think it's plausible that sounds are + + align:start position:0% +think it's plausible that sounds are + + + align:start position:0% +think it's plausible that sounds are +encoded both as sequences of features + + align:start position:0% +encoded both as sequences of features + + + align:start position:0% +encoded both as sequences of features +and with statistics that average + + align:start position:0% +and with statistics that average + + + align:start position:0% +and with statistics that average +information over time and I think that + + align:start position:0% +information over time and I think that + + + align:start position:0% +information over time and I think that +the features that we with which we + + align:start position:0% +the features that we with which we + + + align:start position:0% +the features that we with which we +encode things are engineered to be + + align:start position:0% +encode things are engineered to be + + + align:start position:0% +encode things are engineered to be +sparse for typical natural sound sources + + align:start position:0% +sparse for typical natural sound sources + + + align:start position:0% +sparse for typical natural sound sources +but they end up being dense for textures + + align:start position:0% +but they end up being dense for textures + + + align:start position:0% +but they end up being dense for textures +so the signal comes in you're trying to + + align:start position:0% +so the signal comes in you're trying to + + + align:start position:0% +so the signal comes in you're trying to +model that with a whole bunch of + + align:start position:0% +model that with a whole bunch of + + + align:start position:0% +model that with a whole bunch of +different features that are in some + + align:start position:0% +different features that are in some + + + align:start position:0% +different features that are in some +dictionary you have in your head and for + + align:start position:0% +dictionary you have in your head and for + + + align:start position:0% +dictionary you have in your head and for +a signal like speech your dictionary + + align:start position:0% +a signal like speech your dictionary + + + align:start position:0% +a signal like speech your dictionary +features include things that might be + + align:start position:0% +features include things that might be + + + align:start position:0% +features include things that might be +related to phonemes and so forth and so + + align:start position:0% +related to phonemes and so forth and so + + + align:start position:0% +related to phonemes and so forth and so +for like a single person talking you end + + align:start position:0% +for like a single person talking you end + + + align:start position:0% +for like a single person talking you end +up with this representation that's + + align:start position:0% +up with this representation that's + + + align:start position:0% +up with this representation that's +relatively sparse it's got sort of a + + align:start position:0% +relatively sparse it's got sort of a + + + align:start position:0% +relatively sparse it's got sort of a +small number of feature activations but + + align:start position:0% +small number of feature activations but + + + align:start position:0% +small number of feature activations but +when you get a texture in order to + + align:start position:0% +when you get a texture in order to + + + align:start position:0% +when you get a texture in order to +actually model that signal you need lots + + align:start position:0% +actually model that signal you need lots + + + align:start position:0% +actually model that signal you need lots +and lots and lots of feature + + align:start position:0% +and lots and lots of feature + + + align:start position:0% +and lots and lots of feature +coefficients right in order to in order + + align:start position:0% +coefficients right in order to in order + + + align:start position:0% +coefficients right in order to in order +to actually model the signal and my + + align:start position:0% +to actually model the signal and my + + + align:start position:0% +to actually model the signal and my +hypothesis would be that memory capacity + + align:start position:0% +hypothesis would be that memory capacity + + + align:start position:0% +hypothesis would be that memory capacity +places limits on the number of features + + align:start position:0% +places limits on the number of features + + + align:start position:0% +places limits on the number of features +that can be retained all right so it's + + align:start position:0% +that can be retained all right so it's + + + align:start position:0% +that can be retained all right so it's +not really related to like the duration + + align:start position:0% +not really related to like the duration + + + align:start position:0% +not really related to like the duration +of signal that you can encode per say + + align:start position:0% +of signal that you can encode per say + + + align:start position:0% +of signal that you can encode per say +it's unlike the number of coefficients + + align:start position:0% +it's unlike the number of coefficients + + + align:start position:0% +it's unlike the number of coefficients +that you can retain that you need to + + align:start position:0% +that you can retain that you need to + + + align:start position:0% +that you can retain that you need to +encode that that that signal and the + + align:start position:0% +encode that that that signal and the + + + align:start position:0% +encode that that that signal and the +additional thing I would hypothesize is + + align:start position:0% +additional thing I would hypothesize is + + + align:start position:0% +additional thing I would hypothesize is +that sound is continuously and this is + + align:start position:0% +that sound is continuously and this is + + + align:start position:0% +that sound is continuously and this is +critical obligatory encoded all right so + + align:start position:0% +critical obligatory encoded all right so + + + align:start position:0% +critical obligatory encoded all right so +this stuff comes into your ears you're + + align:start position:0% +this stuff comes into your ears you're + + + align:start position:0% +this stuff comes into your ears you're +continuously projecting it onto this + + align:start position:0% +continuously projecting it onto this + + + align:start position:0% +continuously projecting it onto this +dictionary feature that you have all + + align:start position:0% +dictionary feature that you have all + + + align:start position:0% +dictionary feature that you have all +right and you've got some memory buffer + + align:start position:0% +right and you've got some memory buffer + + + align:start position:0% +right and you've got some memory buffer +within which you can hang on to some + + align:start position:0% +within which you can hang on to some + + + align:start position:0% +within which you can hang on to some +number of those features but then once + + align:start position:0% +number of those features but then once + + + align:start position:0% +number of those features but then once +this once the memory buffer gets gets + + align:start position:0% +this once the memory buffer gets gets + + + align:start position:0% +this once the memory buffer gets gets +exceeded it gets overwritten and so you + + align:start position:0% +exceeded it gets overwritten and so you + + + align:start position:0% +exceeded it gets overwritten and so you +just lose all the stuff that was that + + align:start position:0% +just lose all the stuff that was that + + + align:start position:0% +just lose all the stuff that was that +came before so when your memory capacity + + align:start position:0% +came before so when your memory capacity + + + align:start position:0% +came before so when your memory capacity +for these feature sequences is reached + + align:start position:0% +for these feature sequences is reached + + + align:start position:0% +for these feature sequences is reached +the memory is overwritten by the + + align:start position:0% +the memory is overwritten by the + + + align:start position:0% +the memory is overwritten by the +incoming sound and the only thing you're + + align:start position:0% +incoming sound and the only thing you're + + + align:start position:0% +incoming sound and the only thing you're +left with are these statistics so I'll + + align:start position:0% +left with are these statistics so I'll + + + align:start position:0% +left with are these statistics so I'll +give you one last experiment in the + + align:start position:0% +give you one last experiment in the + + + align:start position:0% +give you one last experiment in the +texture domain and then we'll move on so + + align:start position:0% +texture domain and then we'll move on so + + + align:start position:0% +texture domain and then we'll move on so +this is an experiment where we we + + align:start position:0% +this is an experiment where we we + + + align:start position:0% +this is an experiment where we we +presented people with the original and + + align:start position:0% +presented people with the original and + + + align:start position:0% +presented people with the original and +original recording and then the + + align:start position:0% +original recording and then the + + + align:start position:0% +original recording and then the +synthetic version that we generated from + + align:start position:0% +synthetic version that we generated from + + + align:start position:0% +synthetic version that we generated from +the synthesis algorithm and we just + + align:start position:0% +the synthesis algorithm and we just + + + align:start position:0% +the synthesis algorithm and we just +asked them to rate the realism of the + + align:start position:0% +asked them to rate the realism of the + + + align:start position:0% +asked them to rate the realism of the +synthetic example and so this is just a + + align:start position:0% +synthetic example and so this is just a + + + align:start position:0% +synthetic example and so this is just a +summary of the results of that + + align:start position:0% +summary of the results of that + + + align:start position:0% +summary of the results of that +experiment where we did this for 170 + + align:start position:0% +experiment where we did this for 170 + + + align:start position:0% +experiment where we did this for 170 +different sounds and this is a histogram + + align:start position:0% +different sounds and this is a histogram + + + align:start position:0% +different sounds and this is a histogram +of the average realism rating for each + + align:start position:0% +of the average realism rating for each + + + align:start position:0% +of the average realism rating for each +of those 170 sounds and there's just two + + align:start position:0% +of those 170 sounds and there's just two + + + align:start position:0% +of those 170 sounds and there's just two +points to take away from this right the + + align:start position:0% +points to take away from this right the + + + align:start position:0% +points to take away from this right the +first that there's a big peak up here so + + align:start position:0% +first that there's a big peak up here so + + + align:start position:0% +first that there's a big peak up here so +they rated this the realism on a scale + + align:start position:0% +they rated this the realism on a scale + + + align:start position:0% +they rated this the realism on a scale +of one to seven and so the big peak + + align:start position:0% +of one to seven and so the big peak + + + align:start position:0% +of one to seven and so the big peak +looks like centered at like six means + + align:start position:0% +looks like centered at like six means + + + align:start position:0% +looks like centered at like six means +that the synthesis is working pretty + + align:start position:0% +that the synthesis is working pretty + + + align:start position:0% +that the synthesis is working pretty +well like most of the time and that's + + align:start position:0% +well like most of the time and that's + + + align:start position:0% +well like most of the time and that's +sort of encouraging but there's this + + align:start position:0% +sort of encouraging but there's this + + + align:start position:0% +sort of encouraging but there's this +other interesting thing which is that + + align:start position:0% +other interesting thing which is that + + + align:start position:0% +other interesting thing which is that +there's this long tail down here right + + align:start position:0% +there's this long tail down here right + + + align:start position:0% +there's this long tail down here right +and what this means is that people are + + align:start position:0% +and what this means is that people are + + + align:start position:0% +and what this means is that people are +telling us that this synthetic signal + + align:start position:0% +telling us that this synthetic signal + + + align:start position:0% +telling us that this synthetic signal +that is statistically matched to this + + align:start position:0% +that is statistically matched to this + + + align:start position:0% +that is statistically matched to this +original recording doesn't sound + + align:start position:0% +original recording doesn't sound + + + align:start position:0% +original recording doesn't sound +anything like it I mean that's really + + align:start position:0% +anything like it I mean that's really + + + align:start position:0% +anything like it I mean that's really +interesting because it statistically + + align:start position:0% +interesting because it statistically + + + align:start position:0% +interesting because it statistically +mapped to the original so it's matching + + align:start position:0% +mapped to the original so it's matching + + + align:start position:0% +mapped to the original so it's matching +like all these different dimensions + + align:start position:0% +like all these different dimensions + + + align:start position:0% +like all these different dimensions +right and yet there's still things that + + align:start position:0% +right and yet there's still things that + + + align:start position:0% +right and yet there's still things that +are perceptually missing and that tells + + align:start position:0% +are perceptually missing and that tells + + + align:start position:0% +are perceptually missing and that tells +us that there are things that are + + align:start position:0% +us that there are things that are + + + align:start position:0% +us that there are things that are +important to the brain that are like not + + align:start position:0% +important to the brain that are like not + + + align:start position:0% +important to the brain that are like not +in our model this is a list of the 15 or + + align:start position:0% +in our model this is a list of the 15 or + + + align:start position:0% +in our model this is a list of the 15 or +so sounds that got the lowest realism + + align:start position:0% +so sounds that got the lowest realism + + + align:start position:0% +so sounds that got the lowest realism +ratings and just to make things easy on + + align:start position:0% +ratings and just to make things easy on + + + align:start position:0% +ratings and just to make things easy on +you I'll put labels up next time because + + align:start position:0% +you I'll put labels up next time because + + + align:start position:0% +you I'll put labels up next time because +by and large they tend to fall into sort + + align:start position:0% +by and large they tend to fall into sort + + + align:start position:0% +by and large they tend to fall into sort +of three different categories um sounds + + align:start position:0% +of three different categories um sounds + + + align:start position:0% +of three different categories um sounds +that have some some sort of pitch in + + align:start position:0% +that have some some sort of pitch in + + + align:start position:0% +that have some some sort of pitch in +them + + align:start position:0% +them + + + align:start position:0% +them +sounds like have some kind of rhythmic + + align:start position:0% +sounds like have some kind of rhythmic + + + align:start position:0% +sounds like have some kind of rhythmic +structure and sounds I have + + align:start position:0% +structure and sounds I have + + + align:start position:0% +structure and sounds I have +reverberation um and I'll just I'll play + + align:start position:0% +reverberation um and I'll just I'll play + + + align:start position:0% +reverberation um and I'll just I'll play +you these examples because they're + + align:start position:0% +you these examples because they're + + + align:start position:0% +you these examples because they're +really kind of spectacular failures so + + align:start position:0% +really kind of spectacular failures so + + + align:start position:0% +really kind of spectacular failures so +here's um here I'll play the original + + align:start position:0% +here's um here I'll play the original + + + align:start position:0% +here's um here I'll play the original +version and then the synthetic and + + align:start position:0% +version and then the synthetic and + + + align:start position:0% +version and then the synthetic and +here's the synthetic I'm just warning + + align:start position:0% +here's the synthetic I'm just warning + + + align:start position:0% +here's the synthetic I'm just warning +you bad + + align:start position:0% + + + + align:start position:0% + +here's here's the tapping rhythm really + + align:start position:0% +here's here's the tapping rhythm really + + + align:start position:0% +here's here's the tapping rhythm really +simple but and the synthetic version + + align:start position:0% + + + + align:start position:0% + +alright this is what happens if you uh + + align:start position:0% +alright this is what happens if you uh + + + align:start position:0% +alright this is what happens if you uh +well this is not gonna work very well + + align:start position:0% +well this is not gonna work very well + + + align:start position:0% +well this is not gonna work very well +because we're in an auditorium but I'll + + align:start position:0% +because we're in an auditorium but I'll + + + align:start position:0% +because we're in an auditorium but I'll +try it anyways this is a recording of + + align:start position:0% +try it anyways this is a recording of + + + align:start position:0% +try it anyways this is a recording of +somebody running up a stairwell that's + + align:start position:0% +somebody running up a stairwell that's + + + align:start position:0% +somebody running up a stairwell that's +pretty reverberant and here's the + + align:start position:0% +pretty reverberant and here's the + + + align:start position:0% +pretty reverberant and here's the +synthetic version and it's almost as it + + align:start position:0% +synthetic version and it's almost as it + + + align:start position:0% +synthetic version and it's almost as it +like the echoes don't get put in the + + align:start position:0% +like the echoes don't get put in the + + + align:start position:0% +like the echoes don't get put in the +right place or something and that would + + align:start position:0% +right place or something and that would + + + align:start position:0% +right place or something and that would +sound even worse if this was not an + + align:start position:0% +sound even worse if this was not an + + + align:start position:0% +sound even worse if this was not an +auditorium here's here's what happens + + align:start position:0% +auditorium here's here's what happens + + + align:start position:0% +auditorium here's here's what happens +with music and the synthetic version + + align:start position:0% + + + + align:start position:0% + +and this is what happens with speech a + + align:start position:0% +and this is what happens with speech a + + + align:start position:0% +and this is what happens with speech a +boy fell from the window + + align:start position:0% +boy fell from the window + + + align:start position:0% +boy fell from the window +the wife helped her husband big dogs can + + align:start position:0% +the wife helped her husband big dogs can + + + align:start position:0% +the wife helped her husband big dogs can +be dangerous okay so um in some sense + + align:start position:0% +be dangerous okay so um in some sense + + + align:start position:0% +be dangerous okay so um in some sense +this this is like the most informative + + align:start position:0% +this this is like the most informative + + + align:start position:0% +this this is like the most informative +thing that comes out of this whole + + align:start position:0% +thing that comes out of this whole + + + align:start position:0% +thing that comes out of this whole +effort because again it makes it really + + align:start position:0% +effort because again it makes it really + + + align:start position:0% +effort because again it makes it really +clear what you don't understand right + + align:start position:0% +clear what you don't understand right + + + align:start position:0% +clear what you don't understand right +and in all these cases it was really not + + align:start position:0% +and in all these cases it was really not + + + align:start position:0% +and in all these cases it was really not +obvious a priori + + align:start position:0% +obvious a priori + + + align:start position:0% +obvious a priori +that things would be this bad you know I + + align:start position:0% +that things would be this bad you know I + + + align:start position:0% +that things would be this bad you know I +actually thought it was sort of + + align:start position:0% +actually thought it was sort of + + + align:start position:0% +actually thought it was sort of +plausible that we might be able to + + align:start position:0% +plausible that we might be able to + + + align:start position:0% +plausible that we might be able to +capture pitch with some of these + + align:start position:0% +capture pitch with some of these + + + align:start position:0% +capture pitch with some of these +statistics same with reverb and + + align:start position:0% +statistics same with reverb and + + + align:start position:0% +statistics same with reverb and +certainly some of these simple rhythms I + + align:start position:0% +certainly some of these simple rhythms I + + + align:start position:0% +certainly some of these simple rhythms I +kind of thought that at some of the + + align:start position:0% +kind of thought that at some of the + + + align:start position:0% +kind of thought that at some of the +modulation filters responses and their + + align:start position:0% +modulation filters responses and their + + + align:start position:0% +modulation filters responses and their +correlations would give this to you and + + align:start position:0% +correlations would give this to you and + + + align:start position:0% +correlations would give this to you and +it's not until you actually test this + + align:start position:0% +it's not until you actually test this + + + align:start position:0% +it's not until you actually test this +with synthesis that you realize how bad + + align:start position:0% +with synthesis that you realize how bad + + + align:start position:0% +with synthesis that you realize how bad +this is right and so this really kind of + + align:start position:0% +this is right and so this really kind of + + + align:start position:0% +this is right and so this really kind of +tells you that there's something very + + align:start position:0% +tells you that there's something very + + + align:start position:0% +tells you that there's something very +important that your brain is measuring + + align:start position:0% +important that your brain is measuring + + + align:start position:0% +important that your brain is measuring +that we just don't yet understand and + + align:start position:0% +that we just don't yet understand and + + + align:start position:0% +that we just don't yet understand and +hasn't been built into our model so it + + align:start position:0% +hasn't been built into our model so it + + + align:start position:0% +hasn't been built into our model so it +really sort of identifies the things you + + align:start position:0% +really sort of identifies the things you + + + align:start position:0% +really sort of identifies the things you +need to work on okay so I'm just take + + align:start position:0% +need to work on okay so I'm just take + + + align:start position:0% +need to work on okay so I'm just take +home messages from this this portion of + + align:start position:0% +home messages from this this portion of + + + align:start position:0% +home messages from this this portion of +the lecture so I've argued that sound + + align:start position:0% +the lecture so I've argued that sound + + + align:start position:0% +the lecture so I've argued that sound +synthesis is a powerful tool that can + + align:start position:0% +synthesis is a powerful tool that can + + + align:start position:0% +synthesis is a powerful tool that can +help us test and explore theories of + + align:start position:0% +help us test and explore theories of + + + align:start position:0% +help us test and explore theories of +audition in that the variables that + + align:start position:0% +audition in that the variables that + + + align:start position:0% +audition in that the variables that +produce compelling synthesis are things + + align:start position:0% +produce compelling synthesis are things + + + align:start position:0% +produce compelling synthesis are things +that could possibly underlie perception + + align:start position:0% +that could possibly underlie perception + + + align:start position:0% +that could possibly underlie perception +and conversely that synthesis failures + + align:start position:0% +and conversely that synthesis failures + + + align:start position:0% +and conversely that synthesis failures +are things that point the way to new + + align:start position:0% +are things that point the way to new + + + align:start position:0% +are things that point the way to new +variables that might be important for + + align:start position:0% +variables that might be important for + + + align:start position:0% +variables that might be important for +the the perceptual system i've also + + align:start position:0% +the the perceptual system i've also + + + align:start position:0% +the the perceptual system i've also +argued that textures are a nice point of + + align:start position:0% +argued that textures are a nice point of + + + align:start position:0% +argued that textures are a nice point of +entry for a real world world hearing I + + align:start position:0% +entry for a real world world hearing I + + + align:start position:0% +entry for a real world world hearing I +think what's appealing about them is + + align:start position:0% +think what's appealing about them is + + + align:start position:0% +think what's appealing about them is +that you can actually work with with + + align:start position:0% +that you can actually work with with + + + align:start position:0% +that you can actually work with with +actual like real world like signals and + + align:start position:0% +actual like real world like signals and + + + align:start position:0% +actual like real world like signals and +in all of the complexity that at least + + align:start position:0% +in all of the complexity that at least + + + align:start position:0% +in all of the complexity that at least +exist in that domain and yet work with + + align:start position:0% +exist in that domain and yet work with + + + align:start position:0% +exist in that domain and yet work with +them and generate things that that you + + align:start position:0% +them and generate things that that you + + + align:start position:0% +them and generate things that that you +feel like you can understand and I've + + align:start position:0% +feel like you can understand and I've + + + align:start position:0% +feel like you can understand and I've +argued that many natural sounds may be + + align:start position:0% +argued that many natural sounds may be + + + align:start position:0% +argued that many natural sounds may be +recognized with relatively simple + + align:start position:0% +recognized with relatively simple + + + align:start position:0% +recognized with relatively simple +statistics of early auditory + + align:start position:0% +statistics of early auditory + + + align:start position:0% +statistics of early auditory +representations so the very simplest + + align:start position:0% +representations so the very simplest + + + align:start position:0% +representations so the very simplest +kinds of of statistical representations + + align:start position:0% +kinds of of statistical representations + + + align:start position:0% +kinds of of statistical representations +that you might construct that capture + + align:start position:0% +that you might construct that capture + + + align:start position:0% +that you might construct that capture +things like the spectrum well that on + + align:start position:0% +things like the spectrum well that on + + + align:start position:0% +things like the spectrum well that on +its own is not really that informative + + align:start position:0% +its own is not really that informative + + + align:start position:0% +its own is not really that informative +but if you just go a little bit more + + align:start position:0% +but if you just go a little bit more + + + align:start position:0% +but if you just go a little bit more +complex and into the domain of marginal + + align:start position:0% +complex and into the domain of marginal + + + align:start position:0% +complex and into the domain of marginal +moments and correlations you get + + align:start position:0% +moments and correlations you get + + + align:start position:0% +moments and correlations you get +representations that are pretty powerful + + align:start position:0% +representations that are pretty powerful + + + align:start position:0% +representations that are pretty powerful +and finally I gave you some evidence + + align:start position:0% +and finally I gave you some evidence + + + align:start position:0% +and finally I gave you some evidence +that for textures of moderate length + + align:start position:0% +that for textures of moderate length + + + align:start position:0% +that for textures of moderate length +statistics maybe all that we retain so + + align:start position:0% +statistics maybe all that we retain so + + + align:start position:0% +statistics maybe all that we retain so +there are a lot of interesting open + + align:start position:0% +there are a lot of interesting open + + + align:start position:0% +there are a lot of interesting open +questions + + align:start position:0% +questions + + + align:start position:0% +questions +this domain so one of the big ones I + + align:start position:0% +this domain so one of the big ones I + + + align:start position:0% +this domain so one of the big ones I +think is the the locus of the time + + align:start position:0% +think is the the locus of the time + + + align:start position:0% +think is the the locus of the time +averaging so the I told you about how + + align:start position:0% +averaging so the I told you about how + + + align:start position:0% +averaging so the I told you about how +we've got some evidence in the lab that + + align:start position:0% +we've got some evidence in the lab that + + + align:start position:0% +we've got some evidence in the lab that +the the the timescale of the integration + + align:start position:0% +the the the timescale of the integration + + + align:start position:0% +the the the timescale of the integration +process for computing statistics is on + + align:start position:0% +process for computing statistics is on + + + align:start position:0% +process for computing statistics is on +the order of several seconds and that's + + align:start position:0% +the order of several seconds and that's + + + align:start position:0% +the order of several seconds and that's +a really long time scale relative to + + align:start position:0% +a really long time scale relative to + + + align:start position:0% +a really long time scale relative to +typical time scales in the auditory + + align:start position:0% +typical time scales in the auditory + + + align:start position:0% +typical time scales in the auditory +system and so where exactly that + + align:start position:0% +system and so where exactly that + + + align:start position:0% +system and so where exactly that +happened in the brain I think is very + + align:start position:0% +happened in the brain I think is very + + + align:start position:0% +happened in the brain I think is very +much an open question and kind of an + + align:start position:0% +much an open question and kind of an + + + align:start position:0% +much an open question and kind of an +interesting one and so we'd like to sort + + align:start position:0% +interesting one and so we'd like to sort + + + align:start position:0% +interesting one and so we'd like to sort +of figure out how to get some leverage + + align:start position:0% +of figure out how to get some leverage + + + align:start position:0% +of figure out how to get some leverage +on that there's also a lot of + + align:start position:0% +on that there's also a lot of + + + align:start position:0% +on that there's also a lot of +interesting questions about the + + align:start position:0% +interesting questions about the + + + align:start position:0% +interesting questions about the +relationship to scene analysis so + + align:start position:0% +relationship to scene analysis so + + + align:start position:0% +relationship to scene analysis so +usually you're not hearing a texture in + + align:start position:0% +usually you're not hearing a texture in + + + align:start position:0% +usually you're not hearing a texture in +isolation it's sort of the background to + + align:start position:0% +isolation it's sort of the background to + + + align:start position:0% +isolation it's sort of the background to +like things that maybe you're actually + + align:start position:0% +like things that maybe you're actually + + + align:start position:0% +like things that maybe you're actually +more interested in somebody talking or + + align:start position:0% +more interested in somebody talking or + + + align:start position:0% +more interested in somebody talking or +whatnot and so the relationship between + + align:start position:0% +whatnot and so the relationship between + + + align:start position:0% +whatnot and so the relationship between +these statistical representations and + + align:start position:0% +these statistical representations and + + + align:start position:0% +these statistical representations and +the extraction of individual source + + align:start position:0% +the extraction of individual source + + + align:start position:0% +the extraction of individual source +signals is something that's really open + + align:start position:0% +signals is something that's really open + + + align:start position:0% +signals is something that's really open +and I think kind of kind of interesting + + align:start position:0% +and I think kind of kind of interesting + + + align:start position:0% +and I think kind of kind of interesting +and then there's other these other + + align:start position:0% +and then there's other these other + + + align:start position:0% +and then there's other these other +questions of what kinds of statistics + + align:start position:0% +questions of what kinds of statistics + + + align:start position:0% +questions of what kinds of statistics +would you need to account for some of + + align:start position:0% +would you need to account for some of + + + align:start position:0% +would you need to account for some of +these really profound failures of + + align:start position:0% +these really profound failures of + + + align:start position:0% +these really profound failures of +synthesis okay um so actually one I + + align:start position:0% +synthesis okay um so actually one I + + + align:start position:0% +synthesis okay um so actually one I +think this might be interested + + align:start position:0% +think this might be interested + + + align:start position:0% +think this might be interested +interesting to people so I'll just talk + + align:start position:0% +interesting to people so I'll just talk + + + align:start position:0% +interesting to people so I'll just talk +briefly about this and then we're gonna + + align:start position:0% +briefly about this and then we're gonna + + + align:start position:0% +briefly about this and then we're gonna +have to figure out what to do for the + + align:start position:0% +have to figure out what to do for the + + + align:start position:0% +have to figure out what to do for the +last 20 minutes but one of the reasons I + + align:start position:0% +last 20 minutes but one of the reasons I + + + align:start position:0% +last 20 minutes but one of the reasons I +think I was requested to talk about this + + align:start position:0% +think I was requested to talk about this + + + align:start position:0% +think I was requested to talk about this +is because of the fact that there's been + + align:start position:0% +is because of the fact that there's been + + + align:start position:0% +is because of the fact that there's been +all this work on on texture in the + + align:start position:0% +all this work on on texture in the + + + align:start position:0% +all this work on on texture in the +domain of vision and so it's sort of an + + align:start position:0% +domain of vision and so it's sort of an + + + align:start position:0% +domain of vision and so it's sort of an +interesting case where we can kind of + + align:start position:0% +interesting case where we can kind of + + + align:start position:0% +interesting case where we can kind of +think about similarities and differences + + align:start position:0% +think about similarities and differences + + + align:start position:0% +think about similarities and differences +between sensory systems and so back when + + align:start position:0% +between sensory systems and so back when + + + align:start position:0% +between sensory systems and so back when +we were doing this work as I said this + + align:start position:0% +we were doing this work as I said this + + + align:start position:0% +we were doing this work as I said this +was this was joint work with Aero + + align:start position:0% +was this was joint work with Aero + + + align:start position:0% +was this was joint work with Aero +Simoncelli I was a postdoc in his lab at + + align:start position:0% +Simoncelli I was a postdoc in his lab at + + + align:start position:0% +Simoncelli I was a postdoc in his lab at +NYU and we thought it would be + + align:start position:0% +NYU and we thought it would be + + + align:start position:0% +NYU and we thought it would be +interesting to try to turn the kind of + + align:start position:0% +interesting to try to turn the kind of + + + align:start position:0% +interesting to try to turn the kind of +standard model of visual texture which + + align:start position:0% +standard model of visual texture which + + + align:start position:0% +standard model of visual texture which +was done by Xavier Portilla and arrow a + + align:start position:0% +was done by Xavier Portilla and arrow a + + + align:start position:0% +was done by Xavier Portilla and arrow a +long time ago into sort of the same kind + + align:start position:0% +long time ago into sort of the same kind + + + align:start position:0% +long time ago into sort of the same kind +of diagram that I've been showing you + + align:start position:0% +of diagram that I've been showing you + + + align:start position:0% +of diagram that I've been showing you +and so we actually did this in our paper + + align:start position:0% +and so we actually did this in our paper + + + align:start position:0% +and so we actually did this in our paper +and so this is the one that you've been + + align:start position:0% +and so this is the one that you've been + + + align:start position:0% +and so this is the one that you've been +seeing I'll talk right so you got a + + align:start position:0% +seeing I'll talk right so you got a + + + align:start position:0% +seeing I'll talk right so you got a +sound waveform a stage of filtering this + + align:start position:0% +sound waveform a stage of filtering this + + + align:start position:0% +sound waveform a stage of filtering this +non-linearity to extract the envelope + + align:start position:0% +non-linearity to extract the envelope + + + align:start position:0% +non-linearity to extract the envelope +and compress it and then another stage + + align:start position:0% +and compress it and then another stage + + + align:start position:0% +and compress it and then another stage +of filtering and then there's + + align:start position:0% +of filtering and then there's + + + align:start position:0% +of filtering and then there's +statistical measurements at kind of the + + align:start position:0% +statistical measurements at kind of the + + + align:start position:0% +statistical measurements at kind of the +last two stages of representation and + + align:start position:0% +last two stages of representation and + + + align:start position:0% +last two stages of representation and +this is an analogous diagram that you + + align:start position:0% +this is an analogous diagram that you + + + align:start position:0% +this is an analogous diagram that you +can make for this sort of standard + + align:start position:0% +can make for this sort of standard + + + align:start position:0% +can make for this sort of standard +visual texture a model so we we start + + align:start position:0% +visual texture a model so we we start + + + align:start position:0% +visual texture a model so we we start +out with an image as like beans + + align:start position:0% +out with an image as like beans + + + align:start position:0% +out with an image as like beans +there's center-surround filtering of the + + align:start position:0% +there's center-surround filtering of the + + + align:start position:0% +there's center-surround filtering of the +sort that you would find in the + + align:start position:0% +sort that you would find in the + + + align:start position:0% +sort that you would find in the +or LGN that's that filters things into + + align:start position:0% +or LGN that's that filters things into + + + align:start position:0% +or LGN that's that filters things into +particular spatial frequency bands and + + align:start position:0% +particular spatial frequency bands and + + + align:start position:0% +particular spatial frequency bands and +so that's what you get here so these are + + align:start position:0% +so that's what you get here so these are + + + align:start position:0% +so that's what you get here so these are +these are sub bands again + + align:start position:0% +these are sub bands again + + + align:start position:0% +these are sub bands again +then there's oriented filtering of the + + align:start position:0% +then there's oriented filtering of the + + + align:start position:0% +then there's oriented filtering of the +sort that you you might get vice via + + align:start position:0% +sort that you you might get vice via + + + align:start position:0% +sort that you you might get vice via +simple cells in v1 so then you get the + + align:start position:0% +simple cells in v1 so then you get the + + + align:start position:0% +simple cells in v1 so then you get the +sub bands divided up even finer into + + align:start position:0% +sub bands divided up even finer into + + + align:start position:0% +sub bands divided up even finer into +both spatial frequency and orientation + + align:start position:0% +both spatial frequency and orientation + + + align:start position:0% +both spatial frequency and orientation +and then there's something that's + + align:start position:0% +and then there's something that's + + + align:start position:0% +and then there's something that's +analogous to the extraction of the + + align:start position:0% +analogous to the extraction of the + + + align:start position:0% +analogous to the extraction of the +envelope that would give you something + + align:start position:0% +envelope that would give you something + + + align:start position:0% +envelope that would give you something +like a complex cell alright and so this + + align:start position:0% +like a complex cell alright and so this + + + align:start position:0% +like a complex cell alright and so this +is sort of local amplitude in each of + + align:start position:0% +is sort of local amplitude in each of + + + align:start position:0% +is sort of local amplitude in each of +these different sub bands right so you + + align:start position:0% +these different sub bands right so you + + + align:start position:0% +these different sub bands right so you +can see here the contrast is very high + + align:start position:0% +can see here the contrast is very high + + + align:start position:0% +can see here the contrast is very high +and so you get a high response in this + + align:start position:0% +and so you get a high response in this + + + align:start position:0% +and so you get a high response in this +particular point in the sub band so + + align:start position:0% +particular point in the sub band so + + + align:start position:0% +particular point in the sub band so +again these are this is in the the + + align:start position:0% +again these are this is in the the + + + align:start position:0% +again these are this is in the the +dimensions of space so that's a + + align:start position:0% +dimensions of space so that's a + + + align:start position:0% +dimensions of space so that's a +difference rights as an image so you've + + align:start position:0% +difference rights as an image so you've + + + align:start position:0% +difference rights as an image so you've +got x and y coordinates instead of time + + align:start position:0% +got x and y coordinates instead of time + + + align:start position:0% +got x and y coordinates instead of time +but again there are statistical + + align:start position:0% +but again there are statistical + + + align:start position:0% +but again there are statistical +measurements and there you can actually + + align:start position:0% +measurements and there you can actually + + + align:start position:0% +measurements and there you can actually +relate a lot of them to some of the same + + align:start position:0% +relate a lot of them to some of the same + + + align:start position:0% +relate a lot of them to some of the same +functional forms + + align:start position:0% +functional forms + + + align:start position:0% +functional forms +so there's marginal moments just like we + + align:start position:0% +so there's marginal moments just like we + + + align:start position:0% +so there's marginal moments just like we +were computing from from sound in the + + align:start position:0% +were computing from from sound in the + + + align:start position:0% +were computing from from sound in the +the visual texture model there's an + + align:start position:0% +the visual texture model there's an + + + align:start position:0% +the visual texture model there's an +autocorrelation so that's measuring + + align:start position:0% +autocorrelation so that's measuring + + + align:start position:0% +autocorrelation so that's measuring +spatial correlations which we don't + + align:start position:0% +spatial correlations which we don't + + + align:start position:0% +spatial correlations which we don't +actually have in the in the auditory + + align:start position:0% +actually have in the in the auditory + + + align:start position:0% +actually have in the in the auditory +model but then these correlations across + + align:start position:0% +model but then these correlations across + + + align:start position:0% +model but then these correlations across +different frequency channels so this is + + align:start position:0% +different frequency channels so this is + + + align:start position:0% +different frequency channels so this is +across different spatial frequencies to + + align:start position:0% +across different spatial frequencies to + + + align:start position:0% +across different spatial frequencies to +things tuned to the same orientation and + + align:start position:0% +things tuned to the same orientation and + + + align:start position:0% +things tuned to the same orientation and +this is across orientations and in the + + align:start position:0% +this is across orientations and in the + + + align:start position:0% +this is across orientations and in the +energy domain so a couple interesting + + align:start position:0% +energy domain so a couple interesting + + + align:start position:0% +energy domain so a couple interesting +points to take from this if you just + + align:start position:0% +points to take from this if you just + + + align:start position:0% +points to take from this if you just +sort of look back and forth between + + align:start position:0% +sort of look back and forth between + + + align:start position:0% +sort of look back and forth between +these two pictures the first is that the + + align:start position:0% +these two pictures the first is that the + + + align:start position:0% +these two pictures the first is that the +the statistics that we ended up using in + + align:start position:0% +the statistics that we ended up using in + + + align:start position:0% +the statistics that we ended up using in +the domain of sound are kind of late in + + align:start position:0% +the domain of sound are kind of late in + + + align:start position:0% +the domain of sound are kind of late in +the game all right so they're sort of + + align:start position:0% +the game all right so they're sort of + + + align:start position:0% +the game all right so they're sort of +after this this nonlinear stage that + + align:start position:0% +after this this nonlinear stage that + + + align:start position:0% +after this this nonlinear stage that +extracts amplitude whereas in the visual + + align:start position:0% +extracts amplitude whereas in the visual + + + align:start position:0% +extracts amplitude whereas in the visual +texture model the non-linearity happens + + align:start position:0% +texture model the non-linearity happens + + + align:start position:0% +texture model the non-linearity happens +here and there's all these statistics + + align:start position:0% +here and there's all these statistics + + + align:start position:0% +here and there's all these statistics +that are being measured at these earlier + + align:start position:0% +that are being measured at these earlier + + + align:start position:0% +that are being measured at these earlier +stages before you're you're extracting + + align:start position:0% +stages before you're you're extracting + + + align:start position:0% +stages before you're you're extracting +local amplitude and that's an important + + align:start position:0% +local amplitude and that's an important + + + align:start position:0% +local amplitude and that's an important +difference I think between sounds and + + align:start position:0% +difference I think between sounds and + + + align:start position:0% +difference I think between sounds and +images in that a lot of the action and + + align:start position:0% +images in that a lot of the action and + + + align:start position:0% +images in that a lot of the action and +sound is in the kind of the local + + align:start position:0% +sound is in the kind of the local + + + align:start position:0% +sound is in the kind of the local +amplitude domain whereas there's lots of + + align:start position:0% +amplitude domain whereas there's lots of + + + align:start position:0% +amplitude domain whereas there's lots of +important structure and image images + + align:start position:0% +important structure and image images + + + align:start position:0% +important structure and image images +that has to do with like the sort of + + align:start position:0% +that has to do with like the sort of + + + align:start position:0% +that has to do with like the sort of +local phase that you can't just get from + + align:start position:0% +local phase that you can't just get from + + + align:start position:0% +local phase that you can't just get from +kind of local amplitude measurements but + + align:start position:0% +kind of local amplitude measurements but + + + align:start position:0% +kind of local amplitude measurements but +at sort of a coarse scale the the + + align:start position:0% +at sort of a coarse scale the the + + + align:start position:0% +at sort of a coarse scale the the +the big picture is that we think of + + align:start position:0% +the big picture is that we think of + + + align:start position:0% +the big picture is that we think of +visual texture as being represented with + + align:start position:0% +visual texture as being represented with + + + align:start position:0% +visual texture as being represented with +statistical measurements that average + + align:start position:0% +statistical measurements that average + + + align:start position:0% +statistical measurements that average +across space and we've been arguing that + + align:start position:0% +across space and we've been arguing that + + + align:start position:0% +across space and we've been arguing that +sound texture consists of statistical + + align:start position:0% +sound texture consists of statistical + + + align:start position:0% +sound texture consists of statistical +computations that average across time + + align:start position:0% +computations that average across time + + + align:start position:0% +computations that average across time +that said I was alluding to earlier I + + align:start position:0% +that said I was alluding to earlier I + + + align:start position:0% +that said I was alluding to earlier I +think it's totally plausible that that + + align:start position:0% +think it's totally plausible that that + + + align:start position:0% +think it's totally plausible that that +we should really think about visual + + align:start position:0% +we should really think about visual + + + align:start position:0% +we should really think about visual +texture as something that's potentially + + align:start position:0% +texture as something that's potentially + + + align:start position:0% +texture as something that's potentially +dynamic you know if you're looking at a + + align:start position:0% +dynamic you know if you're looking at a + + + align:start position:0% +dynamic you know if you're looking at a +sheet blowing in the wind or a bunch of + + align:start position:0% +sheet blowing in the wind or a bunch of + + + align:start position:0% +sheet blowing in the wind or a bunch of +people moving in a crowd + + align:start position:0% +people moving in a crowd + + + align:start position:0% +people moving in a crowd +and so there might well be statistics + + align:start position:0% +and so there might well be statistics + + + align:start position:0% +and so there might well be statistics +and the time domain as well that people + + align:start position:0% +and the time domain as well that people + + + align:start position:0% +and the time domain as well that people +just haven't really thought about okay + + align:start position:0% +just haven't really thought about okay + + + align:start position:0% +just haven't really thought about okay +so auditory scene analysis is it's + + align:start position:0% +so auditory scene analysis is it's + + + align:start position:0% +so auditory scene analysis is it's +loosely speaking the process of + + align:start position:0% +loosely speaking the process of + + + align:start position:0% +loosely speaking the process of +inferring events in the world from sound + + align:start position:0% +inferring events in the world from sound + + + align:start position:0% +inferring events in the world from sound +right so in in in almost any kind of + + align:start position:0% +right so in in in almost any kind of + + + align:start position:0% +right so in in in almost any kind of +normal situation there's this sound + + align:start position:0% +normal situation there's this sound + + + align:start position:0% +normal situation there's this sound +signal that comes into your ears and + + align:start position:0% +signal that comes into your ears and + + + align:start position:0% +signal that comes into your ears and +that's the result of multiple causal + + align:start position:0% +that's the result of multiple causal + + + align:start position:0% +that's the result of multiple causal +factors in the world and those can can + + align:start position:0% +factors in the world and those can can + + + align:start position:0% +factors in the world and those can can +be different things in the world that + + align:start position:0% +be different things in the world that + + + align:start position:0% +be different things in the world that +are making sound as we discussed the + + align:start position:0% +are making sound as we discussed the + + + align:start position:0% +are making sound as we discussed the +sound thing also interacts with the + + align:start position:0% +sound thing also interacts with the + + + align:start position:0% +sound thing also interacts with the +environment on the way to your ear and + + align:start position:0% +environment on the way to your ear and + + + align:start position:0% +environment on the way to your ear and +so both of those things contribute the + + align:start position:0% +so both of those things contribute the + + + align:start position:0% +so both of those things contribute the +classic instantiation of this is the + + align:start position:0% +classic instantiation of this is the + + + align:start position:0% +classic instantiation of this is the +cocktail party problem where the notion + + align:start position:0% +cocktail party problem where the notion + + + align:start position:0% +cocktail party problem where the notion +is that there would be multiple sources + + align:start position:0% +is that there would be multiple sources + + + align:start position:0% +is that there would be multiple sources +in the world that the signals from the + + align:start position:0% +in the world that the signals from the + + + align:start position:0% +in the world that the signals from the +two sources sum together into a mixture + + align:start position:0% +two sources sum together into a mixture + + + align:start position:0% +two sources sum together into a mixture +that enters your ear and as a listener + + align:start position:0% +that enters your ear and as a listener + + + align:start position:0% +that enters your ear and as a listener +you're usually interested in individual + + align:start position:0% +you're usually interested in individual + + + align:start position:0% +you're usually interested in individual +sources maybe one of those in particular + + align:start position:0% +sources maybe one of those in particular + + + align:start position:0% +sources maybe one of those in particular +like what somebody that you care about + + align:start position:0% +like what somebody that you care about + + + align:start position:0% +like what somebody that you care about +is saying and so your brain has to take + + align:start position:0% +is saying and so your brain has to take + + + align:start position:0% +is saying and so your brain has to take +that mixed signal and from that to infer + + align:start position:0% +that mixed signal and from that to infer + + + align:start position:0% +that mixed signal and from that to infer +the content of one or more of the + + align:start position:0% +the content of one or more of the + + + align:start position:0% +the content of one or more of the +sources and so this is a classic example + + align:start position:0% +sources and so this is a classic example + + + align:start position:0% +sources and so this is a classic example +of an ill-posed problem and and by that + + align:start position:0% +of an ill-posed problem and and by that + + + align:start position:0% +of an ill-posed problem and and by that +I mean that it's ill-posed because many + + align:start position:0% +I mean that it's ill-posed because many + + + align:start position:0% +I mean that it's ill-posed because many +sets of possible sounds add up to equal + + align:start position:0% +sets of possible sounds add up to equal + + + align:start position:0% +sets of possible sounds add up to equal +the observed mixture so all you have + + align:start position:0% +the observed mixture so all you have + + + align:start position:0% +the observed mixture so all you have +access to is this red guy here right and + + align:start position:0% +access to is this red guy here right and + + + align:start position:0% +access to is this red guy here right and +you'd like to infer the the blue signals + + align:start position:0% +you'd like to infer the the blue signals + + + align:start position:0% +you'd like to infer the the blue signals +which are the true sources that occurred + + align:start position:0% +which are the true sources that occurred + + + align:start position:0% +which are the true sources that occurred +in the world and the problem is that + + align:start position:0% +in the world and the problem is that + + + align:start position:0% +in the world and the problem is that +there are these green signals here which + + align:start position:0% +there are these green signals here which + + + align:start position:0% +there are these green signals here which +also add up to the red signal in fact + + align:start position:0% +also add up to the red signal in fact + + + align:start position:0% +also add up to the red signal in fact +there's like lots and lots and lots of + + align:start position:0% +there's like lots and lots and lots of + + + align:start position:0% +there's like lots and lots and lots of +these right so your brain has to take + + align:start position:0% +these right so your brain has to take + + + align:start position:0% +these right so your brain has to take +the red signal and somehow and for the + + align:start position:0% +the red signal and somehow and for the + + + align:start position:0% +the red signal and somehow and for the +blue ones and so this is analogous to me + + align:start position:0% +blue ones and so this is analogous to me + + + align:start position:0% +blue ones and so this is analogous to me +telling you X plus y equals 17 please + + align:start position:0% +telling you X plus y equals 17 please + + + align:start position:0% +telling you X plus y equals 17 please +solve for X and so obviously if you've + + align:start position:0% +solve for X and so obviously if you've + + + align:start position:0% +solve for X and so obviously if you've +got this on a math test you would + + align:start position:0% +got this on a math test you would + + + align:start position:0% +got this on a math test you would +complain because there's not a unique + + align:start position:0% +complain because there's not a unique + + + align:start position:0% +complain because there's not a unique +solution right you could have one in + + align:start position:0% +solution right you could have one in + + + align:start position:0% +solution right you could have one in +sixteen and two and 15 and three and + + align:start position:0% +sixteen and two and 15 and three and + + + align:start position:0% +sixteen and two and 15 and three and +fourteen and so on and so forth right + + align:start position:0% +fourteen and so on and so forth right + + + align:start position:0% +fourteen and so on and so forth right +but that's exactly the problem that your + + align:start position:0% +but that's exactly the problem that your + + + align:start position:0% +but that's exactly the problem that your +brain is is solving all the time every + + align:start position:0% +brain is is solving all the time every + + + align:start position:0% +brain is is solving all the time every +day + + align:start position:0% +day + + + align:start position:0% +day +when you get a mixture of sounds and the + + align:start position:0% +when you get a mixture of sounds and the + + + align:start position:0% +when you get a mixture of sounds and the +only way that you can solve problems of + + align:start position:0% +only way that you can solve problems of + + + align:start position:0% +only way that you can solve problems of +these these sorts by making assumptions + + align:start position:0% +these these sorts by making assumptions + + + align:start position:0% +these these sorts by making assumptions +about the sound sources and the only way + + align:start position:0% +about the sound sources and the only way + + + align:start position:0% +about the sound sources and the only way +that you would be able to make + + align:start position:0% +that you would be able to make + + + align:start position:0% +that you would be able to make +assumptions about sound sources is if + + align:start position:0% +assumptions about sound sources is if + + + align:start position:0% +assumptions about sound sources is if +real world sound sources have some + + align:start position:0% +real world sound sources have some + + + align:start position:0% +real world sound sources have some +degree of regularity um and in fact they + + align:start position:0% +degree of regularity um and in fact they + + + align:start position:0% +degree of regularity um and in fact they +do and one easy way to see this um is by + + align:start position:0% +do and one easy way to see this um is by + + + align:start position:0% +do and one easy way to see this um is by +generating sounds that are fully random + + align:start position:0% +generating sounds that are fully random + + + align:start position:0% +generating sounds that are fully random +and so the way that you would you would + + align:start position:0% +and so the way that you would you would + + + align:start position:0% +and so the way that you would you would +do this is you would have a random + + align:start position:0% +do this is you would have a random + + + align:start position:0% +do this is you would have a random +number generator he would draw numbers + + align:start position:0% +number generator he would draw numbers + + + align:start position:0% +number generator he would draw numbers +from that and each of those numbers + + align:start position:0% +from that and each of those numbers + + + align:start position:0% +from that and each of those numbers +would form a particular sample and a + + align:start position:0% +would form a particular sample and a + + + align:start position:0% +would form a particular sample and a +sound signal um and then you could play + + align:start position:0% +sound signal um and then you could play + + + align:start position:0% +sound signal um and then you could play +that and listen to it right and so if + + align:start position:0% +that and listen to it right and so if + + + align:start position:0% +that and listen to it right and so if +you did that procedure this is what you + + align:start position:0% +you did that procedure this is what you + + + align:start position:0% +you did that procedure this is what you +would get so those are fully random + + align:start position:0% +would get so those are fully random + + + align:start position:0% +would get so those are fully random +sound signals and so you know we could + + align:start position:0% +sound signals and so you know we could + + + align:start position:0% +sound signals and so you know we could +generate lots and lots of those and the + + align:start position:0% +generate lots and lots of those and the + + + align:start position:0% +generate lots and lots of those and the +point is that with that procedure you + + align:start position:0% +point is that with that procedure you + + + align:start position:0% +point is that with that procedure you +would have to sit there generating these + + align:start position:0% +would have to sit there generating these + + + align:start position:0% +would have to sit there generating these +random sounds for a very very long time + + align:start position:0% +random sounds for a very very long time + + + align:start position:0% +random sounds for a very very long time +before you got something that sounded + + align:start position:0% +before you got something that sounded + + + align:start position:0% +before you got something that sounded +like a real-world sounds right railroad + + align:start position:0% +like a real-world sounds right railroad + + + align:start position:0% +like a real-world sounds right railroad +sounds are like this are this right so + + align:start position:0% +sounds are like this are this right so + + + align:start position:0% +sounds are like this are this right so +the point is that the set of sounds that + + align:start position:0% +the point is that the set of sounds that + + + align:start position:0% +the point is that the set of sounds that +occur in the world are a very very very + + align:start position:0% +occur in the world are a very very very + + + align:start position:0% +occur in the world are a very very very +small portion of the set of all + + align:start position:0% +small portion of the set of all + + + align:start position:0% +small portion of the set of all +physically realizable sound waveforms + + align:start position:0% +physically realizable sound waveforms + + + align:start position:0% +physically realizable sound waveforms +and so the notion is that that's what + + align:start position:0% +and so the notion is that that's what + + + align:start position:0% +and so the notion is that that's what +enables you to hear it's the fact that + + align:start position:0% +enables you to hear it's the fact that + + + align:start position:0% +enables you to hear it's the fact that +you have instantiating the fact that the + + align:start position:0% +you have instantiating the fact that the + + + align:start position:0% +you have instantiating the fact that the +structure of real real tones is not + + align:start position:0% +structure of real real tones is not + + + align:start position:0% +structure of real real tones is not +random and such that when you get a + + align:start position:0% +random and such that when you get a + + + align:start position:0% +random and such that when you get a +mixture of sounds you can actually make + + align:start position:0% +mixture of sounds you can actually make + + + align:start position:0% +mixture of sounds you can actually make +some good guesses as to what the sources + + align:start position:0% +some good guesses as to what the sources + + + align:start position:0% +some good guesses as to what the sources +are all right so we rely on these + + align:start position:0% +are all right so we rely on these + + + align:start position:0% +are all right so we rely on these +regularities in order here so one + + align:start position:0% +regularities in order here so one + + + align:start position:0% +regularities in order here so one +intuitive view of inferring a target + + align:start position:0% +intuitive view of inferring a target + + + align:start position:0% +intuitive view of inferring a target +source from a mixture like this is that + + align:start position:0% +source from a mixture like this is that + + + align:start position:0% +source from a mixture like this is that +you have to do at least a couple things + + align:start position:0% +you have to do at least a couple things + + + align:start position:0% +you have to do at least a couple things +one is to determine the grouping of the + + align:start position:0% +one is to determine the grouping of the + + + align:start position:0% +one is to determine the grouping of the +observed elements and the sound signal + + align:start position:0% +observed elements and the sound signal + + + align:start position:0% +observed elements and the sound signal +and so what what I've done here is for + + align:start position:0% +and so what what I've done here is for + + + align:start position:0% +and so what what I've done here is for +each of these this is that cocktail + + align:start position:0% +each of these this is that cocktail + + + align:start position:0% +each of these this is that cocktail +party problem demo that we saw that we + + align:start position:0% +party problem demo that we saw that we + + + align:start position:0% +party problem demo that we saw that we +heard at the start so we've got one + + align:start position:0% +heard at the start so we've got one + + + align:start position:0% +heard at the start so we've got one +speaker on two three and then seven and + + align:start position:0% +speaker on two three and then seven and + + + align:start position:0% +speaker on two three and then seven and +in the spectrograms + + align:start position:0% +in the spectrograms + + + align:start position:0% +in the spectrograms +I've coded the the pixels either red or + + align:start position:0% +I've coded the the pixels either red or + + + align:start position:0% +I've coded the the pixels either red or +green where they're the pixels are coded + + align:start position:0% +green where they're the pixels are coded + + + align:start position:0% +green where they're the pixels are coded +red if they come from something other + + align:start position:0% +red if they come from something other + + + align:start position:0% +red if they come from something other +than the target source right so like + + align:start position:0% +than the target source right so like + + + align:start position:0% +than the target source right so like +this stuff up here is coming from this + + align:start position:0% +this stuff up here is coming from this + + + align:start position:0% +this stuff up here is coming from this +additional speaker and then the green + + align:start position:0% +additional speaker and then the green + + + align:start position:0% +additional speaker and then the green +bits are the pixels in this in the + + align:start position:0% +bits are the pixels in this in the + + + align:start position:0% +bits are the pixels in this in the +target signal that are masked by the + + align:start position:0% +target signal that are masked by the + + + align:start position:0% +target signal that are masked by the +other signal where the others + + align:start position:0% +other signal where the others + + + align:start position:0% +other signal where the others +actually has higher higher intensity and + + align:start position:0% +actually has higher higher intensity and + + + align:start position:0% +actually has higher higher intensity and +so one notion is that well you have to + + align:start position:0% +so one notion is that well you have to + + + align:start position:0% +so one notion is that well you have to +be able to tell that the red things + + align:start position:0% +be able to tell that the red things + + + align:start position:0% +be able to tell that the red things +actually don't go with the gray things + + align:start position:0% +actually don't go with the gray things + + + align:start position:0% +actually don't go with the gray things +but then you also need to take these + + align:start position:0% +but then you also need to take these + + + align:start position:0% +but then you also need to take these +parts that are green where the other + + align:start position:0% +parts that are green where the other + + + align:start position:0% +parts that are green where the other +source is actually swamp new thing + + align:start position:0% +source is actually swamp new thing + + + align:start position:0% +source is actually swamp new thing +you're interested in and then estimate + + align:start position:0% +you're interested in and then estimate + + + align:start position:0% +you're interested in and then estimate +the content of the target source that's + + align:start position:0% +the content of the target source that's + + + align:start position:0% +the content of the target source that's +at least a very you know sort of naive + + align:start position:0% +at least a very you know sort of naive + + + align:start position:0% +at least a very you know sort of naive +intuitive view of what what has to + + align:start position:0% +intuitive view of what what has to + + + align:start position:0% +intuitive view of what what has to +happen and in both of these cases the + + align:start position:0% +happen and in both of these cases the + + + align:start position:0% +happen and in both of these cases the +only way that you can do this is by + + align:start position:0% +only way that you can do this is by + + + align:start position:0% +only way that you can do this is by +taking advantage of statistical + + align:start position:0% +taking advantage of statistical + + + align:start position:0% +taking advantage of statistical +regularities and sounds so one example + + align:start position:0% +regularities and sounds so one example + + + align:start position:0% +regularities and sounds so one example +of a regularity that that we think might + + align:start position:0% +of a regularity that that we think might + + + align:start position:0% +of a regularity that that we think might +be used to group sound is harmonic + + align:start position:0% +be used to group sound is harmonic + + + align:start position:0% +be used to group sound is harmonic +frequencies so voices and instruments + + align:start position:0% +frequencies so voices and instruments + + + align:start position:0% +frequencies so voices and instruments +and certain other sounds produce + + align:start position:0% +and certain other sounds produce + + + align:start position:0% +and certain other sounds produce +frequencies that are harmonics ie + + align:start position:0% +frequencies that are harmonics ie + + + align:start position:0% +frequencies that are harmonics ie +multiples of a fundamental so here's a + + align:start position:0% +multiples of a fundamental so here's a + + + align:start position:0% +multiples of a fundamental so here's a +schematic power spectrum of some + + align:start position:0% +schematic power spectrum of some + + + align:start position:0% +schematic power spectrum of some +somebody of what might come out of your + + align:start position:0% +somebody of what might come out of your + + + align:start position:0% +somebody of what might come out of your +vocal chords so there's the fundamental + + align:start position:0% +vocal chords so there's the fundamental + + + align:start position:0% +vocal chords so there's the fundamental +frequency here and then all of the + + align:start position:0% +frequency here and then all of the + + + align:start position:0% +frequency here and then all of the +different harmonics and they exhibit + + align:start position:0% +different harmonics and they exhibit + + + align:start position:0% +different harmonics and they exhibit +this very regular structure here + + align:start position:0% +this very regular structure here + + + align:start position:0% +this very regular structure here +similarly this is a 440 on the oboe so + + align:start position:0% +similarly this is a 440 on the oboe so + + + align:start position:0% +similarly this is a 440 on the oboe so +the fundamental frequency is 440 Hertz + + align:start position:0% +the fundamental frequency is 440 Hertz + + + align:start position:0% +the fundamental frequency is 440 Hertz +its concert a but if you look at the + + align:start position:0% +its concert a but if you look at the + + + align:start position:0% +its concert a but if you look at the +power spectrum of that signal you get + + align:start position:0% +power spectrum of that signal you get + + + align:start position:0% +power spectrum of that signal you get +all of these integer multiples of that + + align:start position:0% +all of these integer multiples of that + + + align:start position:0% +all of these integer multiples of that +of that fundamental alright and so the + + align:start position:0% +of that fundamental alright and so the + + + align:start position:0% +of that fundamental alright and so the +way that this happens in speech is that + + align:start position:0% +way that this happens in speech is that + + + align:start position:0% +way that this happens in speech is that +there are these your vocal cords which + + align:start position:0% +there are these your vocal cords which + + + align:start position:0% +there are these your vocal cords which +open and close in this periodic manner + + align:start position:0% +open and close in this periodic manner + + + align:start position:0% +open and close in this periodic manner +they generate a series of sound pulses + + align:start position:0% +they generate a series of sound pulses + + + align:start position:0% +they generate a series of sound pulses +and in the frequency domain that + + align:start position:0% +and in the frequency domain that + + + align:start position:0% +and in the frequency domain that +translates to a harmonic structure no + + align:start position:0% +translates to a harmonic structure no + + + align:start position:0% +translates to a harmonic structure no +I'm not gonna go through this in great + + align:start position:0% +I'm not gonna go through this in great + + + align:start position:0% +I'm not gonna go through this in great +detail + + align:start position:0% +detail + + + align:start position:0% +detail +my necks gonna tell you about speech + + align:start position:0% +my necks gonna tell you about speech + + + align:start position:0% +my necks gonna tell you about speech +alright and so there's there's some + + align:start position:0% +alright and so there's there's some + + + align:start position:0% +alright and so there's there's some +classic evidence that your brain uses + + align:start position:0% +classic evidence that your brain uses + + + align:start position:0% +classic evidence that your brain uses +harmonicity as a grouping cue which is + + align:start position:0% +harmonicity as a grouping cue which is + + + align:start position:0% +harmonicity as a grouping cue which is +that if you take a series of harmonic + + align:start position:0% +that if you take a series of harmonic + + + align:start position:0% +that if you take a series of harmonic +frequencies and you miss tune one of + + align:start position:0% +frequencies and you miss tune one of + + + align:start position:0% +frequencies and you miss tune one of +them your your brain typically causes + + align:start position:0% +them your your brain typically causes + + + align:start position:0% +them your your brain typically causes +you to hear that as a distinct sound + + align:start position:0% +you to hear that as a distinct sound + + + align:start position:0% +you to hear that as a distinct sound +source once the miss tuning becomes + + align:start position:0% +source once the miss tuning becomes + + + align:start position:0% +source once the miss tuning becomes +sufficient here's just a classic demo of + + align:start position:0% +sufficient here's just a classic demo of + + + align:start position:0% +sufficient here's just a classic demo of +that demonstration 18 isolation of a + + align:start position:0% +that demonstration 18 isolation of a + + + align:start position:0% +that demonstration 18 isolation of a +frequency component based on miss uni + + align:start position:0% +frequency component based on miss uni + + + align:start position:0% +frequency component based on miss uni +you are to listen for the third harmonic + + align:start position:0% +you are to listen for the third harmonic + + + align:start position:0% +you are to listen for the third harmonic +of a complex tone first this component + + align:start position:0% +of a complex tone first this component + + + align:start position:0% +of a complex tone first this component +is played alone as a standard then over + + align:start position:0% +is played alone as a standard then over + + + align:start position:0% +is played alone as a standard then over +a series of repetitions it remains at a + + align:start position:0% +a series of repetitions it remains at a + + + align:start position:0% +a series of repetitions it remains at a +constant frequency while the rest of the + + align:start position:0% +constant frequency while the rest of the + + + align:start position:0% +constant frequency while the rest of the +components are gradually lower + + align:start position:0% +components are gradually lower + + + align:start position:0% +components are gradually lower +as a group in steps of 1 percent now + + align:start position:0% +as a group in steps of 1 percent now + + + align:start position:0% +as a group in steps of 1 percent now +after 2 okay and so what you should have + + align:start position:0% +after 2 okay and so what you should have + + + align:start position:0% +after 2 okay and so what you should have +heard and you can tell me whether this + + align:start position:0% +heard and you can tell me whether this + + + align:start position:0% +heard and you can tell me whether this +is the case or not um is that as this + + align:start position:0% +is the case or not um is that as this + + + align:start position:0% +is the case or not um is that as this +thing is miss tuned at some point you + + align:start position:0% +thing is miss tuned at some point you + + + align:start position:0% +thing is miss tuned at some point you +actually start to hear kind of two beeps + + align:start position:0% +actually start to hear kind of two beeps + + + align:start position:0% +actually start to hear kind of two beeps +right there's this there's like the main + + align:start position:0% +right there's this there's like the main + + + align:start position:0% +right there's this there's like the main +tone and then there's this other little + + align:start position:0% +tone and then there's this other little + + + align:start position:0% +tone and then there's this other little +beat right and if you did in the other + + align:start position:0% +beat right and if you did in the other + + + align:start position:0% +beat right and if you did in the other +direction it would it would then reverse + + align:start position:0% + + + + align:start position:0% + +okay um so one other consequence of + + align:start position:0% +okay um so one other consequence of + + + align:start position:0% +okay um so one other consequence of +harmonicity is is and somebody was + + align:start position:0% +harmonicity is is and somebody was + + + align:start position:0% +harmonicity is is and somebody was +asking about this earlier is that your + + align:start position:0% +asking about this earlier is that your + + + align:start position:0% +asking about this earlier is that your +your brain is able to use the harmonics + + align:start position:0% +your brain is able to use the harmonics + + + align:start position:0% +your brain is able to use the harmonics +of the sound in order to infer its pitch + + align:start position:0% +of the sound in order to infer its pitch + + + align:start position:0% +of the sound in order to infer its pitch +so the pitch that you hurt you hear when + + align:start position:0% +so the pitch that you hurt you hear when + + + align:start position:0% +so the pitch that you hurt you hear when +you hear somebody talking um is like a + + align:start position:0% +you hear somebody talking um is like a + + + align:start position:0% +you hear somebody talking um is like a +collective function of all the different + + align:start position:0% +collective function of all the different + + + align:start position:0% +collective function of all the different +harmonics and so one interesting thing + + align:start position:0% +harmonics and so one interesting thing + + + align:start position:0% +harmonics and so one interesting thing +that happens when you miss tuned the + + align:start position:0% +that happens when you miss tuned the + + + align:start position:0% +that happens when you miss tuned the +harmonic is that for very small miss + + align:start position:0% +harmonic is that for very small miss + + + align:start position:0% +harmonic is that for very small miss +tunings that initially causes a bias in + + align:start position:0% +tunings that initially causes a bias in + + + align:start position:0% +tunings that initially causes a bias in +the in your in the perceived pitch and + + align:start position:0% +the in your in the perceived pitch and + + + align:start position:0% +the in your in the perceived pitch and +so that's what's plotted here so this is + + align:start position:0% +so that's what's plotted here so this is + + + align:start position:0% +so that's what's plotted here so this is +a task where somebody hears this complex + + align:start position:0% +a task where somebody hears this complex + + + align:start position:0% +a task where somebody hears this complex +tone that has one of the harmonics + + align:start position:0% +tone that has one of the harmonics + + + align:start position:0% +tone that has one of the harmonics +missed tuned by a little bit and then + + align:start position:0% +missed tuned by a little bit and then + + + align:start position:0% +missed tuned by a little bit and then +they hear another complex don't know + + align:start position:0% +they hear another complex don't know + + + align:start position:0% +they hear another complex don't know +they have to adjust the pitch of the + + align:start position:0% +they have to adjust the pitch of the + + + align:start position:0% +they have to adjust the pitch of the +other one until it sounds the same + + align:start position:0% +other one until it sounds the same + + + align:start position:0% +other one until it sounds the same +alright and so what's being plotted on + + align:start position:0% +alright and so what's being plotted on + + + align:start position:0% +alright and so what's being plotted on +the y-axis in this graph is the average + + align:start position:0% +the y-axis in this graph is the average + + + align:start position:0% +the y-axis in this graph is the average +amount of shift in the pitch match as a + + align:start position:0% +amount of shift in the pitch match as a + + + align:start position:0% +amount of shift in the pitch match as a +function of the shift in that particular + + align:start position:0% +function of the shift in that particular + + + align:start position:0% +function of the shift in that particular +harmonic and for very small missed + + align:start position:0% +harmonic and for very small missed + + + align:start position:0% +harmonic and for very small missed +tunings of like a few percent you can + + align:start position:0% +tunings of like a few percent you can + + + align:start position:0% +tunings of like a few percent you can +see that there's this linear increase in + + align:start position:0% +see that there's this linear increase in + + + align:start position:0% +see that there's this linear increase in +the perceived pitch all right so the + + align:start position:0% +the perceived pitch all right so the + + + align:start position:0% +the perceived pitch all right so the +miss tuning that harmonic causes that + + align:start position:0% +miss tuning that harmonic causes that + + + align:start position:0% +miss tuning that harmonic causes that +the pitch to change but then once the + + align:start position:0% +the pitch to change but then once the + + + align:start position:0% +the pitch to change but then once the +miss tuning exceeds a certain amount you + + align:start position:0% +miss tuning exceeds a certain amount you + + + align:start position:0% +miss tuning exceeds a certain amount you +can actually see that the effect + + align:start position:0% +can actually see that the effect + + + align:start position:0% +can actually see that the effect +reverses and and the the pitch shift + + align:start position:0% +reverses and and the the pitch shift + + + align:start position:0% +reverses and and the the pitch shift +goes away and so we think what's + + align:start position:0% +goes away and so we think what's + + + align:start position:0% +goes away and so we think what's +happening here is that the mechanism in + + align:start position:0% +happening here is that the mechanism in + + + align:start position:0% +happening here is that the mechanism in +your brain that is computing pitch from + + align:start position:0% +your brain that is computing pitch from + + + align:start position:0% +your brain that is computing pitch from +the harmonics somehow realizes that one + + align:start position:0% +the harmonics somehow realizes that one + + + align:start position:0% +the harmonics somehow realizes that one +of those harmonics is miss tune and is + + align:start position:0% +of those harmonics is miss tune and is + + + align:start position:0% +of those harmonics is miss tune and is +not part of the same thing and so it's + + align:start position:0% +not part of the same thing and so it's + + + align:start position:0% +not part of the same thing and so it's +excluded from the computation of pitch + + align:start position:0% +excluded from the computation of pitch + + + align:start position:0% +excluded from the computation of pitch +so the fact that you've segregated those + + align:start position:0% +so the fact that you've segregated those + + + align:start position:0% +so the fact that you've segregated those +sources then + + align:start position:0% +sources then + + + align:start position:0% +sources then +somehow you know happens prior to or in + + align:start position:0% +somehow you know happens prior to or in + + + align:start position:0% +somehow you know happens prior to or in +you know at the same time is that as the + + align:start position:0% +you know at the same time is that as the + + + align:start position:0% +you know at the same time is that as the +the calculation of the pitch here's a + + align:start position:0% +the calculation of the pitch here's a + + + align:start position:0% +the calculation of the pitch here's a +number another classic demonstration of + + align:start position:0% +number another classic demonstration of + + + align:start position:0% +number another classic demonstration of +sounds Federation's related to + + align:start position:0% +sounds Federation's related to + + + align:start position:0% +sounds Federation's related to +harmonicity this is called the Reynolds + + align:start position:0% +harmonicity this is called the Reynolds + + + align:start position:0% +harmonicity this is called the Reynolds +macadam McAdams oboe it's a + + align:start position:0% +macadam McAdams oboe it's a + + + align:start position:0% +macadam McAdams oboe it's a +collaboration between Roger Reynolds and + + align:start position:0% +collaboration between Roger Reynolds and + + + align:start position:0% +collaboration between Roger Reynolds and +Steve McAdams so there's a complex tone + + align:start position:0% +Steve McAdams so there's a complex tone + + + align:start position:0% +Steve McAdams so there's a complex tone +and what's gonna happen here is that the + + align:start position:0% +and what's gonna happen here is that the + + + align:start position:0% +and what's gonna happen here is that the +even harmonics two four six eight etc + + align:start position:0% +even harmonics two four six eight etc + + + align:start position:0% +even harmonics two four six eight etc +will become frequency modulated in a way + + align:start position:0% +will become frequency modulated in a way + + + align:start position:0% +will become frequency modulated in a way +that's coherent I mean so initially + + align:start position:0% +that's coherent I mean so initially + + + align:start position:0% +that's coherent I mean so initially +you'll hear this kind of one thing and + + align:start position:0% +you'll hear this kind of one thing and + + + align:start position:0% +you'll hear this kind of one thing and +then it'll sort of separate into these + + align:start position:0% +then it'll sort of separate into these + + + align:start position:0% +then it'll sort of separate into these +two voices and it's called the oboe + + align:start position:0% +two voices and it's called the oboe + + + align:start position:0% +two voices and it's called the oboe +because the oboe is an instrument that + + align:start position:0% +because the oboe is an instrument that + + + align:start position:0% +because the oboe is an instrument that +has a lot of power at the odd harmonics + + align:start position:0% +has a lot of power at the odd harmonics + + + align:start position:0% +has a lot of power at the odd harmonics +and so you'll hear something it sounds + + align:start position:0% +and so you'll hear something it sounds + + + align:start position:0% +and so you'll hear something it sounds +like an oboe along with something that + + align:start position:0% +like an oboe along with something that + + + align:start position:0% +like an oboe along with something that +maybe is like a voice that has vibrato + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +guys that work for everybody so all + + align:start position:0% +guys that work for everybody so all + + + align:start position:0% +guys that work for everybody so all +these things are they're being affected + + align:start position:0% +these things are they're being affected + + + align:start position:0% +these things are they're being affected +and kind of interesting ways by the + + align:start position:0% +and kind of interesting ways by the + + + align:start position:0% +and kind of interesting ways by the +reverb in this auditorium which which + + align:start position:0% +reverb in this auditorium which which + + + align:start position:0% +reverb in this auditorium which which +will yeah but that that mostly works so + + align:start position:0% +will yeah but that that mostly works so + + + align:start position:0% +will yeah but that that mostly works so +so we've done a little bit of work + + align:start position:0% +so we've done a little bit of work + + + align:start position:0% +so we've done a little bit of work +trying to test whether the brain uses + + align:start position:0% +trying to test whether the brain uses + + + align:start position:0% +trying to test whether the brain uses +harmonicity to segregate actual speech + + align:start position:0% +harmonicity to segregate actual speech + + + align:start position:0% +harmonicity to segregate actual speech +and so very recently it's become + + align:start position:0% +and so very recently it's become + + + align:start position:0% +and so very recently it's become +possible to manipulate speech and change + + align:start position:0% +possible to manipulate speech and change + + + align:start position:0% +possible to manipulate speech and change +its harmonicity and I'm not gonna tell + + align:start position:0% +its harmonicity and I'm not gonna tell + + + align:start position:0% +its harmonicity and I'm not gonna tell +you in detail how this how this works + + align:start position:0% +you in detail how this how this works + + + align:start position:0% +you in detail how this how this works +but we can resynthesize speech in ways + + align:start position:0% +but we can resynthesize speech in ways + + + align:start position:0% +but we can resynthesize speech in ways +that are either harmonic like this this + + align:start position:0% +that are either harmonic like this this + + + align:start position:0% +that are either harmonic like this this +sounds normal + + align:start position:0% +sounds normal + + + align:start position:0% +sounds normal +she's mild and Keith gleaned in her + + align:start position:0% +she's mild and Keith gleaned in her + + + align:start position:0% +she's mild and Keith gleaned in her +beautifully modeled + + align:start position:0% +beautifully modeled + + + align:start position:0% +beautifully modeled +Alec face but we can also resynthesize + + align:start position:0% +Alec face but we can also resynthesize + + + align:start position:0% +Alec face but we can also resynthesize +it so as to make it in a harmonic and if + + align:start position:0% +it so as to make it in a harmonic and if + + + align:start position:0% +it so as to make it in a harmonic and if +you look at the spectra I mean you can + + align:start position:0% +you look at the spectra I mean you can + + + align:start position:0% +you look at the spectra I mean you can +see that the harmonic spacing is no + + align:start position:0% +see that the harmonic spacing is no + + + align:start position:0% +see that the harmonic spacing is no +longer regular alright so we've just + + align:start position:0% +longer regular alright so we've just + + + align:start position:0% +longer regular alright so we've just +added some jitter to the frequencies of + + align:start position:0% +added some jitter to the frequencies of + + + align:start position:0% +added some jitter to the frequencies of +the harmonics and it makes it sound + + align:start position:0% +the harmonics and it makes it sound + + + align:start position:0% +the harmonics and it makes it sound +weird she smiled and teeth gleamed in + + align:start position:0% +weird she smiled and teeth gleamed in + + + align:start position:0% +weird she smiled and teeth gleamed in +her beautifully modeled I love it but + + align:start position:0% +her beautifully modeled I love it but + + + align:start position:0% +her beautifully modeled I love it but +it's it's it's still perfectly + + align:start position:0% +it's it's it's still perfectly + + + align:start position:0% +it's it's it's still perfectly +intelligible alright and that's because + + align:start position:0% +intelligible alright and that's because + + + align:start position:0% +intelligible alright and that's because +the the vocal tract filtering that I + + align:start position:0% +the the vocal tract filtering that I + + + align:start position:0% +the the vocal tract filtering that I +think Hynek is probably gonna tell you + + align:start position:0% +think Hynek is probably gonna tell you + + + align:start position:0% +think Hynek is probably gonna tell you +about this afternoon remains unchanged + + align:start position:0% +about this afternoon remains unchanged + + + align:start position:0% +about this afternoon remains unchanged +and so the notion here is that if you're + + align:start position:0% +and so the notion here is that if you're + + + align:start position:0% +and so the notion here is that if you're +actually using that this harmonic + + align:start position:0% +actually using that this harmonic + + + align:start position:0% +actually using that this harmonic +structure to kind of tell you what parts + + align:start position:0% +structure to kind of tell you what parts + + + align:start position:0% +structure to kind of tell you what parts +of the sound signal belong together well + + align:start position:0% +of the sound signal belong together well + + + align:start position:0% +of the sound signal belong together well +if you got a mixture of two speakers + + align:start position:0% +if you got a mixture of two speakers + + + align:start position:0% +if you got a mixture of two speakers +that were in a harmonic you might think + + align:start position:0% +that were in a harmonic you might think + + + align:start position:0% +that were in a harmonic you might think +that it would be harder to understand + + align:start position:0% +that it would be harder to understand + + + align:start position:0% +that it would be harder to understand +what was being said so we gave people + + align:start position:0% +what was being said so we gave people + + + align:start position:0% +what was being said so we gave people +this this task where we played them + + align:start position:0% +this this task where we played them + + + align:start position:0% +this this task where we played them +words either one word at a time are two + + align:start position:0% +words either one word at a time are two + + + align:start position:0% +words either one word at a time are two +concurrent words and we just asked them + + align:start position:0% +concurrent words and we just asked them + + + align:start position:0% +concurrent words and we just asked them +to type in what they heard and then we + + align:start position:0% +to type in what they heard and then we + + + align:start position:0% +to type in what they heard and then we +just score how much they got correct and + + align:start position:0% +just score how much they got correct and + + + align:start position:0% +just score how much they got correct and +we we did this with a bunch of different + + align:start position:0% +we we did this with a bunch of different + + + align:start position:0% +we we did this with a bunch of different +conditions where we increase the jitter + + align:start position:0% +conditions where we increase the jitter + + + align:start position:0% +conditions where we increase the jitter +so there's harmonic finally here + + align:start position:0% +so there's harmonic finally here + + + align:start position:0% +so there's harmonic finally here +do you object to petting and I don't + + align:start position:0% +do you object to petting and I don't + + + align:start position:0% +do you object to petting and I don't +know why my RA chose this example but + + align:start position:0% +know why my RA chose this example but + + + align:start position:0% +know why my RA chose this example but +whatever it is take it from a corpus + + align:start position:0% +whatever it is take it from a corpus + + + align:start position:0% +whatever it is take it from a corpus +called timet that has a lot of weird + + align:start position:0% +called timet that has a lot of weird + + + align:start position:0% +called timet that has a lot of weird +sentences finally yeah do you object to + + align:start position:0% +sentences finally yeah do you object to + + + align:start position:0% +sentences finally yeah do you object to +petting finally yes + + align:start position:0% +petting finally yes + + + align:start position:0% +petting finally yes +do you object to penny finally here do + + align:start position:0% +do you object to penny finally here do + + + align:start position:0% +do you object to penny finally here do +you object to petting all right so it + + align:start position:0% +you object to petting all right so it + + + align:start position:0% +you object to petting all right so it +kind of gets stranger and stranger + + align:start position:0% +kind of gets stranger and stranger + + + align:start position:0% +kind of gets stranger and stranger +sounding then it bottoms out these are + + align:start position:0% +sounding then it bottoms out these are + + + align:start position:0% +sounding then it bottoms out these are +like ratings of how weird it sounds and + + align:start position:0% +like ratings of how weird it sounds and + + + align:start position:0% +like ratings of how weird it sounds and +these are the results of the recognition + + align:start position:0% +these are the results of the recognition + + + align:start position:0% +these are the results of the recognition +experiment and so what's being plotted + + align:start position:0% +experiment and so what's being plotted + + + align:start position:0% +experiment and so what's being plotted +is the mean number of correct words as a + + align:start position:0% +is the mean number of correct words as a + + + align:start position:0% +is the mean number of correct words as a +function of the deviation from + + align:start position:0% +function of the deviation from + + + align:start position:0% +function of the deviation from +harmonicity so zero here is perfectly + + align:start position:0% +harmonicity so zero here is perfectly + + + align:start position:0% +harmonicity so zero here is perfectly +harmonic and this is increasing jitter + + align:start position:0% +harmonic and this is increasing jitter + + + align:start position:0% +harmonic and this is increasing jitter +and so the interesting thing is that + + align:start position:0% +and so the interesting thing is that + + + align:start position:0% +and so the interesting thing is that +there's no effect on the recognition of + + align:start position:0% +there's no effect on the recognition of + + + align:start position:0% +there's no effect on the recognition of +single words which is below ceiling + + align:start position:0% +single words which is below ceiling + + + align:start position:0% +single words which is below ceiling +because these are single words that are + + align:start position:0% +because these are single words that are + + + align:start position:0% +because these are single words that are +excised from sentences and so they're + + align:start position:0% +excised from sentences and so they're + + + align:start position:0% +excised from sentences and so they're +actually not that easy to understand but + + align:start position:0% +actually not that easy to understand but + + + align:start position:0% +actually not that easy to understand but +when you get people pairs of words you + + align:start position:0% +when you get people pairs of words you + + + align:start position:0% +when you get people pairs of words you +see that they get worse at recognizing + + align:start position:0% +see that they get worse at recognizing + + + align:start position:0% +see that they get worse at recognizing +what was said and then the effect kind + + align:start position:0% +what was said and then the effect kind + + + align:start position:0% +what was said and then the effect kind +of bottoms out so this is consistent + + align:start position:0% +of bottoms out so this is consistent + + + align:start position:0% +of bottoms out so this is consistent +with the notion that your brain is + + align:start position:0% +with the notion that your brain is + + + align:start position:0% +with the notion that your brain is +actually relying in part on the harmonic + + align:start position:0% +actually relying in part on the harmonic + + + align:start position:0% +actually relying in part on the harmonic +structure of the speech in order to pull + + align:start position:0% +structure of the speech in order to pull + + + align:start position:0% +structure of the speech in order to pull +say two concurrent speakers apart and + + align:start position:0% +say two concurrent speakers apart and + + + align:start position:0% +say two concurrent speakers apart and +the other thing to note here though is + + align:start position:0% +the other thing to note here though is + + + align:start position:0% +the other thing to note here though is +that the effect is actually pretty + + align:start position:0% +that the effect is actually pretty + + + align:start position:0% +that the effect is actually pretty +modest right so you're going from like I + + align:start position:0% +modest right so you're going from like I + + + align:start position:0% +modest right so you're going from like I +don't know this is like 0.65 words + + align:start position:0% +don't know this is like 0.65 words + + + align:start position:0% +don't know this is like 0.65 words +correct on a trial down to 0.5 so it's + + align:start position:0% +correct on a trial down to 0.5 so it's + + + align:start position:0% +correct on a trial down to 0.5 so it's +like a 20% reduction and the the miss + + align:start position:0% +like a 20% reduction and the the miss + + + align:start position:0% +like a 20% reduction and the the miss +tuning thing also works with speech this + + align:start position:0% +tuning thing also works with speech this + + + align:start position:0% +tuning thing also works with speech this +is kind of cool so I'm here we've we've + + align:start position:0% +is kind of cool so I'm here we've we've + + + align:start position:0% +is kind of cool so I'm here we've we've +just taken a single harmonic and miss + + align:start position:0% +just taken a single harmonic and miss + + + align:start position:0% +just taken a single harmonic and miss +tuned it and if you listen to that I + + align:start position:0% +tuned it and if you listen to that I + + + align:start position:0% +tuned it and if you listen to that I +think this is this you'll basically + + align:start position:0% +think this is this you'll basically + + + align:start position:0% +think this is this you'll basically +you'll hear the the spoken utterances + + align:start position:0% +you'll hear the the spoken utterances + + + align:start position:0% +you'll hear the the spoken utterances +that it'll sound like there's like some + + align:start position:0% +that it'll sound like there's like some + + + align:start position:0% +that it'll sound like there's like some +whistling sound like on top of it + + align:start position:0% +whistling sound like on top of it + + + align:start position:0% +whistling sound like on top of it +because that's what the the the + + align:start position:0% +because that's what the the the + + + align:start position:0% +because that's what the the the +individual harmonics kind of sounds like + + align:start position:0% +individual harmonics kind of sounds like + + + align:start position:0% +individual harmonics kind of sounds like +on its own so you might have been able + + align:start position:0% +on its own so you might have been able + + + align:start position:0% +on its own so you might have been able +to hear I think this is the that's a + + align:start position:0% +to hear I think this is the that's a + + + align:start position:0% +to hear I think this is the that's a +little quiet but if you listen if you + + align:start position:0% +little quiet but if you listen if you + + + align:start position:0% +little quiet but if you listen if you +listen again yeah so there's this little + + align:start position:0% +listen again yeah so there's this little + + + align:start position:0% +listen again yeah so there's this little +other thing kind of hid hiding there in + + align:start position:0% +other thing kind of hid hiding there in + + + align:start position:0% +other thing kind of hid hiding there in +the background but but it's it's kind of + + align:start position:0% +the background but but it's it's kind of + + + align:start position:0% +the background but but it's it's kind of +hard to hear and that's probably because + + align:start position:0% +hard to hear and that's probably because + + + align:start position:0% +hard to hear and that's probably because +it's particularly in within speech + + align:start position:0% +it's particularly in within speech + + + align:start position:0% +it's particularly in within speech +there's like all these other factors + + align:start position:0% +there's like all these other factors + + + align:start position:0% +there's like all these other factors +that are that are telling you that that + + align:start position:0% +that are that are telling you that that + + + align:start position:0% +that are that are telling you that that +thing is speech and that belongs + + align:start position:0% +thing is speech and that belongs + + + align:start position:0% +thing is speech and that belongs +together and alright let me just wrap up + + align:start position:0% +together and alright let me just wrap up + + + align:start position:0% +together and alright let me just wrap up +here so there's there's a bunch of other + + align:start position:0% +here so there's there's a bunch of other + + + align:start position:0% +here so there's there's a bunch of other +demos of this of this character that I + + align:start position:0% +demos of this of this character that I + + + align:start position:0% +demos of this of this character that I +could kind of I could kind of give you + + align:start position:0% +could kind of I could kind of give you + + + align:start position:0% +could kind of I could kind of give you +about I could tell you about another + + align:start position:0% +about I could tell you about another + + + align:start position:0% +about I could tell you about another +thing that actually matters is + + align:start position:0% +thing that actually matters is + + + align:start position:0% +thing that actually matters is +repetition so if there's something that + + align:start position:0% +repetition so if there's something that + + + align:start position:0% +repetition so if there's something that +that repeats in the signal your brain is + + align:start position:0% +that repeats in the signal your brain is + + + align:start position:0% +that repeats in the signal your brain is +very strongly biased to actually + + align:start position:0% +very strongly biased to actually + + + align:start position:0% +very strongly biased to actually +segregate that from the background so + + align:start position:0% +segregate that from the background so + + + align:start position:0% +segregate that from the background so +this is a demonstration of that in + + align:start position:0% +this is a demonstration of that in + + + align:start position:0% +this is a demonstration of that in +action so what I'm going to be + + align:start position:0% +action so what I'm going to be + + + align:start position:0% +action so what I'm going to be +presenting you with is a sequence of + + align:start position:0% +presenting you with is a sequence of + + + align:start position:0% +presenting you with is a sequence of +mixtures of sounds that will vary in how + + align:start position:0% +mixtures of sounds that will vary in how + + + align:start position:0% +mixtures of sounds that will vary in how +many there are and then at the end + + align:start position:0% +many there are and then at the end + + + align:start position:0% +many there are and then at the end +you're actually going to hear on the the + + align:start position:0% +you're actually going to hear on the the + + + align:start position:0% +you're actually going to hear on the the +the target sound so if I just give you + + align:start position:0% +the target sound so if I just give you + + + align:start position:0% +the target sound so if I just give you +one + + align:start position:0% + + + + align:start position:0% + +alright it doesn't sound like the sound + + align:start position:0% +alright it doesn't sound like the sound + + + align:start position:0% +alright it doesn't sound like the sound +at the end doesn't sound like what you + + align:start position:0% +at the end doesn't sound like what you + + + align:start position:0% +at the end doesn't sound like what you +hear you heard in the in the first thing + + align:start position:0% +hear you heard in the in the first thing + + + align:start position:0% +hear you heard in the in the first thing +but here you can probably start to hear + + align:start position:0% +but here you can probably start to hear + + + align:start position:0% +but here you can probably start to hear +something so each time you're getting + + align:start position:0% +something so each time you're getting + + + align:start position:0% +something so each time you're getting +one of these mixtures and if you just + + align:start position:0% +one of these mixtures and if you just + + + align:start position:0% +one of these mixtures and if you just +get a single mix you can't hear anything + + align:start position:0% +get a single mix you can't hear anything + + + align:start position:0% +get a single mix you can't hear anything +right but just by virtue of the fact + + align:start position:0% +right but just by virtue of the fact + + + align:start position:0% +right but just by virtue of the fact +that there's this latent repeating + + align:start position:0% +that there's this latent repeating + + + align:start position:0% +that there's this latent repeating +structure in there your brain is + + align:start position:0% +structure in there your brain is + + + align:start position:0% +structure in there your brain is +actually able to tell that there's + + align:start position:0% +actually able to tell that there's + + + align:start position:0% +actually able to tell that there's +there's a consistent source and + + align:start position:0% +there's a consistent source and + + + align:start position:0% +there's a consistent source and +segregates that from the background I + + align:start position:0% +segregates that from the background I + + + align:start position:0% +segregates that from the background I +started off by telling you that you know + + align:start position:0% +started off by telling you that you know + + + align:start position:0% +started off by telling you that you know +the only way that you can actually solve + + align:start position:0% +the only way that you can actually solve + + + align:start position:0% +the only way that you can actually solve +this this problem is by incorporating + + align:start position:0% +this this problem is by incorporating + + + align:start position:0% +this this problem is by incorporating +your knowledge of the statistical + + align:start position:0% +your knowledge of the statistical + + + align:start position:0% +your knowledge of the statistical +structure of the world and in yet so far + + align:start position:0% +structure of the world and in yet so far + + + align:start position:0% +structure of the world and in yet so far +the way that the field has really moved + + align:start position:0% +the way that the field has really moved + + + align:start position:0% +the way that the field has really moved +has been to basically just use + + align:start position:0% +has been to basically just use + + + align:start position:0% +has been to basically just use +intuitions you know and so people would + + align:start position:0% +intuitions you know and so people would + + + align:start position:0% +intuitions you know and so people would +look at spectrograms and they say oh + + align:start position:0% +look at spectrograms and they say oh + + + align:start position:0% +look at spectrograms and they say oh +yeah there's like harmonic structure + + align:start position:0% +yeah there's like harmonic structure + + + align:start position:0% +yeah there's like harmonic structure +there's common onset and so then you can + + align:start position:0% +there's common onset and so then you can + + + align:start position:0% +there's common onset and so then you can +do an experiment and show that that has + + align:start position:0% +do an experiment and show that that has + + + align:start position:0% +do an experiment and show that that has +some effect but what we'd really like to + + align:start position:0% +some effect but what we'd really like to + + + align:start position:0% +some effect but what we'd really like to +understand is is how these so called + + align:start position:0% +understand is is how these so called + + + align:start position:0% +understand is is how these so called +grouping cues relate to natural sound + + align:start position:0% +grouping cues relate to natural sound + + + align:start position:0% +grouping cues relate to natural sound +statistics we'd like to know whether + + align:start position:0% +statistics we'd like to know whether + + + align:start position:0% +statistics we'd like to know whether +we're optimal given the nature of + + align:start position:0% +we're optimal given the nature of + + + align:start position:0% +we're optimal given the nature of +real-world sounds we'd like to know + + align:start position:0% +real-world sounds we'd like to know + + + align:start position:0% +real-world sounds we'd like to know +whether these things are actually + + align:start position:0% +whether these things are actually + + + align:start position:0% +whether these things are actually +learned from experience with sound + + align:start position:0% +learned from experience with sound + + + align:start position:0% +learned from experience with sound +whether you're born with them the + + align:start position:0% +whether you're born with them the + + + align:start position:0% +whether you're born with them the +relative importance of these things + + align:start position:0% +relative importance of these things + + + align:start position:0% +relative importance of these things +relative to like knowledge of particular + + align:start position:0% +relative to like knowledge of particular + + + align:start position:0% +relative to like knowledge of particular +sounds like words and so this I really + + align:start position:0% +sounds like words and so this I really + + + align:start position:0% +sounds like words and so this I really +regard this stuff as in its infancy but + + align:start position:0% +regard this stuff as in its infancy but + + + align:start position:0% +regard this stuff as in its infancy but +I think it's really kind of wide open + + align:start position:0% +I think it's really kind of wide open + + + align:start position:0% +I think it's really kind of wide open +and so the sort of take-home messages + + align:start position:0% +and so the sort of take-home messages + + + align:start position:0% +and so the sort of take-home messages +here are that there are grouping cues + + align:start position:0% +here are that there are grouping cues + + + align:start position:0% +here are that there are grouping cues +that the brain uses to take the sound + + align:start position:0% +that the brain uses to take the sound + + + align:start position:0% +that the brain uses to take the sound +energy that comes into your ears and + + align:start position:0% +energy that comes into your ears and + + + align:start position:0% +energy that comes into your ears and +assign it to different sources that are + + align:start position:0% +assign it to different sources that are + + + align:start position:0% +assign it to different sources that are +presumed to be related to statistical + + align:start position:0% +presumed to be related to statistical + + + align:start position:0% +presumed to be related to statistical +regularities of natural sounds some of + + align:start position:0% +regularities of natural sounds some of + + + align:start position:0% +regularities of natural sounds some of +the ones that we know about our chiefly + + align:start position:0% +the ones that we know about our chiefly + + + align:start position:0% +the ones that we know about our chiefly +harmonicity and common onset and + + align:start position:0% +harmonicity and common onset and + + + align:start position:0% +harmonicity and common onset and +repetition I didn't really get to this + + align:start position:0% +repetition I didn't really get to this + + + align:start position:0% +repetition I didn't really get to this +but we also know that the brain infers + + align:start position:0% +but we also know that the brain infers + + + align:start position:0% +but we also know that the brain infers +parts of source signals that are masked + + align:start position:0% +parts of source signals that are masked + + + align:start position:0% +parts of source signals that are masked +by by other sources again using prior + + align:start position:0% +by by other sources again using prior + + + align:start position:0% +by by other sources again using prior +assumptions but um we really need a + + align:start position:0% +assumptions but um we really need a + + + align:start position:0% +assumptions but um we really need a +proper theory in this domain I think + + align:start position:0% +proper theory in this domain I think + + + align:start position:0% +proper theory in this domain I think +both to be able to predict and explain + + align:start position:0% +both to be able to predict and explain + + + align:start position:0% +both to be able to predict and explain +what old word performance and and also I + + align:start position:0% +what old word performance and and also I + + + align:start position:0% +what old word performance and and also I +think to be able to relate what humans + + align:start position:0% +think to be able to relate what humans + + + align:start position:0% +think to be able to relate what humans +are doing in this domain to the machine + + align:start position:0% +are doing in this domain to the machine + + + align:start position:0% +are doing in this domain to the machine +algorithms that we'd like to be able to + + align:start position:0% +algorithms that we'd like to be able to + + + align:start position:0% +algorithms that we'd like to be able to +develop to sort of replicate this sort + + align:start position:0% +develop to sort of replicate this sort + + + align:start position:0% +develop to sort of replicate this sort +of competence and the engineering there + + align:start position:0% +of competence and the engineering there + + + align:start position:0% +of competence and the engineering there +was sort of a brief period of time where + + align:start position:0% +was sort of a brief period of time where + + + align:start position:0% +was sort of a brief period of time where +there were some people in engineering + + align:start position:0% +there were some people in engineering + + + align:start position:0% +there were some people in engineering +that we're kind of trying to relate + + align:start position:0% +that we're kind of trying to relate + + + align:start position:0% +that we're kind of trying to relate +things to biology but by and large that + + align:start position:0% +things to biology but by and large that + + + align:start position:0% +things to biology but by and large that +the fields of sort of diverged + + align:start position:0% +the fields of sort of diverged + + + align:start position:0% +the fields of sort of diverged +I think they really need to come back + + align:start position:0% +I think they really need to come back + + + align:start position:0% +I think they really need to come back +together and so this is gonna be a good + + align:start position:0% +together and so this is gonna be a good + + + align:start position:0% +together and so this is gonna be a good +place for bright young people to work + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/Q5W3J0NChwA.txt b/Q5W3J0NChwA.txt new file mode 100644 index 0000000000000000000000000000000000000000..e5c98c27b363a0e5f1f62fe9b6bc5d61bdb7f925 --- /dev/null +++ b/Q5W3J0NChwA.txt @@ -0,0 +1,323 @@ +align:start position:0% + +so this is + + align:start position:0% +so this is + + + align:start position:0% +so this is +one why this matters for today so look + + align:start position:0% +one why this matters for today so look + + + align:start position:0% +one why this matters for today so look +you know i mentioned that + + align:start position:0% +you know i mentioned that + + + align:start position:0% +you know i mentioned that +getting red was hard back in the day for + + align:start position:0% +getting red was hard back in the day for + + + align:start position:0% +getting red was hard back in the day for +color tv because + + align:start position:0% +color tv because + + + align:start position:0% +color tv because +the red phosphors were difficult to make + + align:start position:0% +the red phosphors were difficult to make + + + align:start position:0% +the red phosphors were difficult to make +for leds it was blue + + align:start position:0% +for leds it was blue + + + align:start position:0% +for leds it was blue +and in fact there was a lot of work + + align:start position:0% +and in fact there was a lot of work + + + align:start position:0% +and in fact there was a lot of work +around gallium nitride here's gallium + + align:start position:0% +around gallium nitride here's gallium + + + align:start position:0% +around gallium nitride here's gallium +nitride in one structure + + align:start position:0% +nitride in one structure + + + align:start position:0% +nitride in one structure +oh notice this there's gallium nitride + + align:start position:0% +oh notice this there's gallium nitride + + + align:start position:0% +oh notice this there's gallium nitride +it's not + + align:start position:0% +it's not + + + align:start position:0% +it's not +on here darn it gallium nitride and + + align:start position:0% +on here darn it gallium nitride and + + + align:start position:0% +on here darn it gallium nitride and +other structures have different gaps + + align:start position:0% +other structures have different gaps + + + align:start position:0% +other structures have different gaps +oh there it is there's one okay but the + + align:start position:0% +oh there it is there's one okay but the + + + align:start position:0% +oh there it is there's one okay but the +point was they wanted blue + + align:start position:0% +point was they wanted blue + + + align:start position:0% +point was they wanted blue +they wanted blue and they needed to make + + align:start position:0% +they wanted blue and they needed to make + + + align:start position:0% +they wanted blue and they needed to make +a material that was both cheap to make + + align:start position:0% +a material that was both cheap to make + + + align:start position:0% +a material that was both cheap to make +and lasted so it didn't like degrade + + align:start position:0% +and lasted so it didn't like degrade + + + align:start position:0% +and lasted so it didn't like degrade +and gave you blue light and that was + + align:start position:0% +and gave you blue light and that was + + + align:start position:0% +and gave you blue light and that was +really hard and that's what the nobel + + align:start position:0% +really hard and that's what the nobel + + + align:start position:0% +really hard and that's what the nobel +prize was given for + + align:start position:0% +prize was given for + + + align:start position:0% +prize was given for +in 2014 because without blue you can't + + align:start position:0% +in 2014 because without blue you can't + + + align:start position:0% +in 2014 because without blue you can't +make white light + + align:start position:0% +make white light + + + align:start position:0% +make white light +right so there's all sorts of + + align:start position:0% +right so there's all sorts of + + + align:start position:0% +right so there's all sorts of +technologies you simply can't go into + + align:start position:0% +technologies you simply can't go into + + + align:start position:0% +technologies you simply can't go into +with leds until you get blue how did it + + align:start position:0% +with leds until you get blue how did it + + + align:start position:0% +with leds until you get blue how did it +happen it happened + + align:start position:0% +happen it happened + + + align:start position:0% +happen it happened +because of chemistry because people + + align:start position:0% +because of chemistry because people + + + align:start position:0% +because of chemistry because people +figured out how to change + + align:start position:0% +figured out how to change + + + align:start position:0% +figured out how to change +the how to take one element and another + + align:start position:0% +the how to take one element and another + + + align:start position:0% +the how to take one element and another +element and then maybe alloy them + + align:start position:0% +element and then maybe alloy them + + + align:start position:0% +element and then maybe alloy them +together maybe you take gallium nitride + + align:start position:0% +together maybe you take gallium nitride + + + align:start position:0% +together maybe you take gallium nitride +and you alloy a little bit of aluminum + + align:start position:0% +and you alloy a little bit of aluminum + + + align:start position:0% +and you alloy a little bit of aluminum +in here and now all of a sudden + + align:start position:0% +in here and now all of a sudden + + + align:start position:0% +in here and now all of a sudden +that means mixing in right now all of a + + align:start position:0% +that means mixing in right now all of a + + + align:start position:0% +that means mixing in right now all of a +sudden you've got a different + + align:start position:0% +sudden you've got a different + + + align:start position:0% +sudden you've got a different +band gap okay band gap engineering + + align:start position:0% +band gap okay band gap engineering + + + align:start position:0% +band gap okay band gap engineering +is really the centerpiece of the + + align:start position:0% +is really the centerpiece of the + + + align:start position:0% +is really the centerpiece of the +semiconductor revolution + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/QOdq7d34f7U.txt b/QOdq7d34f7U.txt new file mode 100644 index 0000000000000000000000000000000000000000..7dd691cf34f201a4d38b3337cfb094062e8e0032 --- /dev/null +++ b/QOdq7d34f7U.txt @@ -0,0 +1,1229 @@ +OK, so what I'd like to do today is pick up where we left + +off last time, + +with respect to how this genetic material actually functions. + + We discussed last time the + +experiments that identified DNA as the fundamental genetic material, + +the transforming principle. We identified the eventual work + +by Crick and Watson's work at the structure of DNA as a double helix. + +We mentioned why that was so tremendously important, + +because it contained within it in principle the secret of replication, + +namely two strands, each of which contained the full information, + +and therefore each of which included in principal serve as a template for + +making the other strand. And that is, after all, the big + +issue about life is how do you, in fact, copy life? And then, I + +mentioned briefly these experiments + +by these post-docs, Matt Meselson and Frank Stahl about + +50 years ago to demonstrate that the semi-conservative model of DNA + +replication was right by virtue of actually labeling DNA during the + +course of its replication in one generation, and demonstrating that + +DNA actually changed in its density when you added in an isotope of + +nitrogen. And, it changed in its density in such a + +way as to be intermediate between what you'd expect from heavy, + +heavy, light, light. You have the intermediate. + +So, that was all good experimental confirmation that this model was + +probably right. But now, how does it really work? + +After all the excitement calms down for a moment you say, + +OK, that's great. We now know in principal it's there, + +but what actually goes on? How is DNA really replicated? + +How is it really read out into information? How does it really, + +as Archibald Garrett noted, and as Beadle and Tatum noted, + +how does it really make protein as well? + +How does it encode the instructions for that? Well, + +that was what was on people's minds in the late '50s. + +And, it was Francis Crick who was the real intellectual thinker about + +this. And, the eventual synthesis that you guys all know, + +because, again, all this stuff gets taught in elementary school these + +days, was encapsulated in the central dogma of molecular biology, + +which I will summarize here diagrammatically. + +The DNA is replicated to make copies of DNA. + +It's read out into the intermediate RNA, and then it is translated into + +protein. This process: translation. This process is called + +transcription. And this process: replication. + +And what I'd like to do is go into some detail today about how each of + +these processes work. Now, at the beginning, + +when people were trying to patch this together, + +it wasn't as obvious as it is to you today, that DNA goes to RNA, + +goes to protein. And, in fact, it was a real struggle to figure out + +what this RNA stuff was doing in the middle, how it could possibly give + +rise to protein. I want to talk about some of that. + +Let me briefly mention, though, Francis Crick's term, + +the central dogma, because it sometimes + +gets criticized, the word dogma there as being like + +religious belief and molecular biologists treated in this way. + +I've read a couple of social scientists who sort of say, + +dogma. In fact, Francis Crick deliberately named this the central + +dogma because he said there was no proof for it at the time it was put + +forward. He put it forward with that word precisely to emphasize + +that this was a working guess. But, it was merely a matter of + +belief that this is sort of how they were putting together the pieces. + +And it was really a question of demonstrating how all these pieces + +work. We still call it the central dogma, but it's now, + +of course, extraordinarily well established. Let's look at this + +first piece. DNA is replicated. All right, so Meselson and Stahl + +tell us that, yeah, the DNA weight look like the new + +strand, the old strand, all that. How would you really + +demonstrate DNA replication? If you wanted to show me that DNA + +replication really happens, this DNA goes to DNA, + +that somehow we had to take a double strand of DNA, + +and it gives rise to, it's one thing to show this in a + +bacterium by adding the nitrogen and all that. The way to really prove + +this was to be in a test tube. In vitro, reconstitute for me DNA + +replication. Show me that in a cell free system, + +you can take DNA, and you can copy it as you would + +expect according to the Crick Watson model here. Well, + +that is what Arthur Kornberg set out to do. Arthur Kornberg was a + +biochemist, and so his interest was crack open the cell, + +and purify an enzyme that was able to copy DNA. Now, + +how do you do that? What cells should you pick? + +Sorry? Why E coli? What a bacteria? It's simple, + +exactly. Good answer. You can grow up a lot of it, + +and presumably, if this DNA replication thing is right, + +it will apply to any organism. So, we'll go with E coli. So, + +what do you do? You just crack open a cell and purify components, + +and throw them in a test tube, and look for DNA synthesis? Well, + +you've got to put something in the test tube. What should we put in + +the test tube? Sorry? Nucleotides, because we think that + +this is going to be made out of nucleotides. So, + +we'd better add some nucleotides to our test tube. + +So, actually, deoxynucleotides, we'll add some DATP, DCTP, DGTP, and + +DTTP, the deoxynucleotide triphosphates, altogether + +known as the DNTPs. OK, that's good. + +So, we're going to take different fractions of the cell. + +We'll add it here. We'll add some nucleotides, and what else should we + +add? Well, if we were going to copy DNA, maybe we ought to put in a DNA + +strand. Let's put in a DNA template. So, let's put in a template + +strand of DNA that we'll copy, + +here we go, and we've got our nucleotides floating around here. + +And, here's our template strand, a single strand of DNA, + +and now we add enzymes, and we hope that it's going to + +somehow copy the DNA. Now, it turns out that that's a + +little bit optimistic because in order to copy the DNA, + +and I think Kornberg had this insight, + +it's helpful to give it a start. So, instead of just adding a single + +template strand, he also added a short complementary + +primer strand with the hope that he would be able to purify an enzyme, + +which even if it couldn't manage to start the synthesis of DNA, + +would be able to extend the synthesis of DNA. + +That's a reasonable thing. Let's not ask for it all at once. + +Maybe it won't be a single fraction. Maybe multiple enzymes would be + +needed to get going. So, he needed a primer strand, + +a template strand, and some nucleotides. And then he added + +fractions, and he looked to see whether he could get incorporation + +of DNA. So now, let's look at this a little more + +closely. The primer strand goes like this. Five prime, ah, + +This direction is going to matter a lot, I told you. + +Phosphate T, phosphate A, phosphate C, phosphate G, phosphate + +T, phosphate A, stop there. Template strand, + +the complement to that , will start in the opposite direction. + +These are anti-parallel. What matches the T: A. Keep + +going: T, G, C, A, T, and phosphate, + +phosphate, phosphate, phosphate, phosphate; I'll stop + +writing the phosphates in a while. Let's say T, A, G, G, C, etc. This + +is the five prime end. That is the three prime end, + +OK? And, this one will go on further, let's say. + +All right, so what is the enzyme that Kornberg hopes to find going to + +do? What's it going to add to the strand? It's going to add an A. + +All right, it wants to put in an A here. So, it's going to take a + +triphosphate, and it's going to catalyze the addition of a + +triphosphate to the growing end of this DNA chain, + +and which is its growing end? The three prime end + +of the chain there, right? It's adding it to the three + +prime carbon there. And, when it does that, + +where is it going to get the energy for catalysis here for this chemical + +reaction here? It's going to get it from the + +dehydration synthesis and the breaking of this triphosphate bond, + +which is a high-energy bond. You'll take off your inorganic + +pyrophosphate and you'll add in an A. That's it. + +Then, it will go off and it'll look for, what, a T, + +a triphosphate with T, DTTP, and then DCTP, etc. + +And it adds them in. This enzyme, this hypothetical enzyme, that can + +polymerize DNA like that is called polymerase. It's all very simple + +stuff. This is DNA polymerase. OK, and the nomenclatures here make + +tremendous sense. This is called DNA polymerase. + +Anyway, Kornberg isolated by a lot of work + +DNA polymerase, and was able to demonstrate that it + +could in fact catalyze this reaction. This was incredibly exciting. + +He got a Nobel Prize for this amongst other things, + +but he really demonstrated that there were proteins that could copy + +DNA according to this double helical model for replication. + +I call your attention to the fact that the replication goes + +five prime to three prime always, ever, all the time. This is + +universal. No one has ever found a DNA polymerization system in nature + +where it goes the other way. And, why would that be? This is + +just a digression. But tell me why that would be? + +Let's take our strand here, T, G, C, A, + +T, T, A, G, C, G, T, why not go this way? + +Why not go, let's say, A, G, C, G. Let's see, what base should + +we put in? We'll take our triphosphate T, right? + +We'll put that in. Let's see, where are we going to get + +the triphosphate bond; where are we going to get the energy? + +The triphosphate's on the wrong end. Oh, that's not a problem because + +when we put this G in, it must be that its triphosphate was + +still there, right? So, now we'll take the next one, + +a triphosphate T, and now why don't we just + +carry out the polymerization using the triphosphate bond, + +the energy from the triphosphate bond, on a growing chain going in + +that direction? That would work, + +right? Just stick this guy here. It'll supply a new triphosphate at + +the end, and that triphosphate can be used to catalyze the next monomer. + +So, what's the problem? You could put the triphosphates on + +the growing chain. If we went this way, + +the triphosphate bond would be on the growing chain, + +rather than in this way the triphosphate is on the monomer. + +But who cares? Who might care? + +If you were designing it, which way would you prefer to do it? + +The one with the energy first, well, why do you care whether the + +triphosphate is on this big, long chain that you've made, or + +whether it's on this monomer because either way you've got a triphosphate + +bond that could be on the monomers floating around, + +or it could be in that last position with the growing chain. Yeah? + +Could be, could be. What kind of mistake might I make? + +Yep. And, you know, what other kind of mistakes can happen? + +What about these high-energy triphosphate bonds: unstable? + +What if they should just spontaneously hydrolyze? + +Oops: big trouble, right? You've lost your + +triphosphate bond, and but what if this one + +spontaneously hydrolyzes? Aren't you in trouble? No, + +get another monomer, right? Clearly, it's no big deal if one of the + +monomers spontaneously hydrolyzes from a triphosphate to a + +monophosphate, but it's a big deal if you've + +invested all of this energy going in the other direction, + +and it should spontaneously hydrolyze. + +So, it makes a great deal more sense to leave that high-energy bond on + +the monomer for the growing polymer rather than on the polymer itself. + +And, in fact, of course, nature hasn't told me why it chose to do + +this. This is my reason why I think nature chose to do this, + +but I think it's very reasonable, and I think it's right. So, this is + +not the way it's done. This is the way it's done, + +and it's always done that way. No one has ever found a case where + +it's not. OK, so now let's look a little more + +closely at DNA replication. Suppose I take not just this teeny + +little piece that Kornberg gives, but suppose I now look at what's + +going on in an organism. An organism might have a big, + +long chromosome. DNA replication is occurring along this chromosome. + +We've got to go five prime to three prime, five prime to three prime. + +Let's suppose there's a primer here. Wait a second, where's the primer + +going to come from? If Kornberg's not there to add the + +primer, what does the organism do? To kind of make one itself, and I'm + +going to need some enzyme to make it. So, what enzyme's going to make it? + +Or, primase: it turns out to be remarkably, coincidentally + +it's primase that makes the primer. It's funny how that works out. And + +so, primase makes the primer, and then what happens? Then, DNA + +polymerase comes along and catalyzes the addition, and works beautifully. + +What about on the other strand? So, it's got a what? + +Why does it have to play catch-up? Let's see, what kind of primer here? + + It's got to go the other way. + +OK, so let's get a primer here. So, but wait a second, now it + +breathes and opens up a little more. We've got to get a primer here. + +And then, when it's going to open up even more we've got to get a primer + +there. See, this guy's going the wrong way. So, + +in fact, this is what happens. When the DNA opens like this, one + +primer here is sufficient to keep going, but here as you begin to open + +this up, the other strand needs the continual addition of new + +primers, and then what happens when this DNA sequence here, + +growing, meets this DNA sequence there? They've got to be ligated + +together. They've got to be joined together. So, + +this is actually getting kind of complicated. We have little DNA + +fragments that have to be ligated together on this strand. + +Now, how are you going to ligate them together? + +Chemically, you've got to catalyze a + +covalent bond between this little growing DNA chain and the previous + +growing DNA chain that was there. How are you going to ligate them? + +Ligase: yes! Coincidentally, it turns out that ligase does that. + +It's just wonderful the way this worked out, that ligase should do + +the ligation, and primase should do the primer, and all that. + +All right, so this goes on and on. Now, this model, which is what + +would be compelled by what we're thinking about is experimentally + +proven. There was a scientist who + +demonstrated that on this strand, this one goes slower, right, because + +it's got to, just as you said, catch up. Playing catch up, this is + +what's called the lagging strand. This guy is called the leading + +strand. The lagging strand plays catch-up to the leading strand. + +And, these little fragments can actually be really, + +truly identified biochemically. They were identified, in fact, by + +somebody called Okazaki. And, do you know what they're + +called, those fragments? Okazaki fragments, + +exactly. That's what they're called. So, that's how it goes, + +and it goes with this continuous replication, and then this + +discontinuous replication there. Now, here's another problem. This + +upset people a lot. Try to take a long chromosome. + +In fact, let's even imagine that it's a circular chromosome like + +bacteria have, a big DNA circle. Imagine trying to replicate this. + +All right, we're going to pull this apart some. We'll start replicating + +as we'll continue to pull this apart, etc., etc., but the problem is that + +we're going to end up with this DNA helix and this DNA helix wrapped + +around each other so that we're going to have double + +helices, or we're going to have interlaced double helices. + +It's really very messy. Topologically, + +if I take a double helix and I copy the two strands, + +and the double helices went around each other 800 times before they got + +to the end and joined up, I've now got two circles of DNA that + +are inextricably linked together with + +what's mathematically called the linking number of 800. + +That's not very good when I try to now divide my cell and say, + +in one chromosome to one cell and one chromosome to the other cell + +because I've got these two long, continuous ropes that are just so + +totally knotted with each other. This bothered people tremendously. + +You can prove, mathematically, some of you take the topology courses + +that there is no way without cutting to pull apart two strings that are + +so intertwined with each other. So, how in the world is life going + +to do that? It's mathematically impossible to do that without + +actually cutting. So, it cuts it because it's got no + +choice, right? There's a theorem that says you + +have to cut it. So, it cuts it. + +You would actually need, it turns out, that if you're + +going to separate out these two different double helices that are + +all wound up around each other, you're going to need to somehow cut + +the DNA, separate it, and pass it through the other side. + +And, you're going to need to do that to un-knot this thing. + +Now, does it change it chemically when you cut it and bring it around + +to the other side of the string? It's still the same molecule, + +right? It's the same DNA, but topologically it's different. + +The two circles are now not linked to 800 times their links, + +799 times, and if I keep doing that, so they are, you could call them + +topoisomers because they differ only in their topology, + +their topoisomers. So, you would need an enzyme that + +actually cuts the DNA, and is clever enough to pass it to + +the other side and then seal it back up, and cut the DNA, + +and pass it through the side and seal it back up. + +What enzyme does that? Topoisomerase does that, + +that's right. And, there are topoisomerase enzymes that cut and + +paste the DNA to resolve this terrible linking number problem. + +So, life has worked all this stuff out, and there's just fascinating + +work that goes on to understand, woops, all of the steps there of DNA + +replication. Now, I mentioned that these are + +actually pretty important things because processes like this are very + +important to rapidly growing cells. It turns out that some very good + +anti-cancer drugs are inhibitors of topoisomerase because rapidly + +growing cancer cells are highly sensitive to the need to continue to + +topologically untangle your DNA. And so, topoisomerase inhibitors + +turn out to be pretty good, well, they're not great, but they + +turned out to be acceptable cancer drugs. + +Here's another issue: fidelity. The fidelity of DNA replication. + +If I'm copying the DNA, I'm going to put in my next base. + +It's a T. I want to put in an A, a G, I want to put in a C; how do I + +get it right? I have my DNA polymerase enzyme here. + +How do I manage to get this right? Why don't I put in a G next to the + +T instead of an A? Well, it's energetically less + +favored, right? Energetically, there's some cost. + +There's a delta G, an energetic difference between the right base + +and the wrong base. Now, if I know delta G, + +I from biochemistry know the equilibrium constant. + +I should be able to calculate, based on the energetic difference + +between putting in the right base and the wrong base how often DNA + +polymerase makes a mistake, and it turns out you can do that. + +It turns out that the equilibrium constant is about 103. + +That means that DNA polymerase, remarkably, gets it right 99.9% of + +the time, it puts it in the right base. Isn't that impressive? + +No, it's terrible. Why is that terrible? Yeah, 99.9% + +this is no Six Sigma performance or anything. This is pretty + +unimpressive stuff. I mean, a typical gene is more than + +1,000 letters. That means we're going to actually + +make a mistake on average in every gene. This won't do. + +So, what happens? Sorry? Well, clearly the energetics say + +that the delta G is only enough to get us a factor of 103. + +We're going to need an additional mechanism, and the additional + +mechanism's a proofreading. It's absolutely right. + +We need to proofread this because we know that initially we're going to + +get it wrong at an unacceptably high rate. And so, + +it turns out that there are two kinds of DNA proofreading that go on. + +First off, DNA polymerase itself has a proofreading activity. + +Whenever DNA polymerase adds a base, it kind of also has an activity that + +will remove a base. So, it doesn't just add bases going + +forward. It also has what's called an + +exonuclease activity that removes bases going backwards. + +Now, that may seem silly, right, because it's adding and + +subtracting, and adding and subtracting, but it adds more than + +it subtracts. And, the trick is that if there's a + +mismatched base, it's much more likely to subtract + +than to add, or much more likely to subtract than if there's not a + +mismatched base. So, the presence of a mismatch + +induces the enzyme to do its removal more than if there was a match. + +In that fashion, DNA polymerase is able to + +substantially increase its proofreading ability to about one + +error in 105 or 106, much better in one in 103. + +Then, it turns out that there are mismatched detection and repair + +enzymes. They come along after DNA polymerase has done its job, + +and they feel along the DNA for any mismatches. Mismatches are going to + +create funny structures. They're going to bulge in some way. + +And, mismatch repair enzymes are able to detect that something's + +funny, and they chop out some sequence, and they get copied back + +in. Now, with the proofreading that comes from these mismatched repair + +enzymes, you can get down to the neighborhood of one mistake + +in about 108 bases. In the course of the human, + +yes? Oh, what a great question! Because, when it has a mistake, + +how does it know who to correct? In bacteria, I can tell you the + +answer. Wouldn't it be cool if you could leave a mark on the old strand? + +If the old strand could be temporarily + +marked in some way so that the enzyme, when it sees a mismatch, + +would also know which strand to cut out and re-synthesize? + +It turns out that bacteria do that. Methylation enzymes actually mark + +the old strand. And, it takes a while before those + +methylation enzymes come along to mark the new strand, + +and it leaves a temporary mark as to who's the old strand. + +I wasn't going to mention that today, but it's a great question. + +So, it leaves breadcrumbs for a while that tells it who's + +the old strand. So, all of this gets worked out. + +Yes? So, the exonucleases go backwards. They go three prime to + +five prime because, that's right, they only work in that + +direction. There are other exos that go in the other direction, + +but this exo on the polymerase go backwards, three prime to five. + +Now, this is not just theoretical stuff. It turns out that about one + +person in 400, that is, probably at least one + +person in this class, is heterozygous for a mutation in + +one of the mismatch repair enzyme genes. One of the genes like MSH-2 + +or MLH-1 that encode the mismatch repair enzymes. + +What do you think happens if you are missing one of your two copies + +of these mismatch repair enzymes? Nothing much. The other copy's + +enough. But, what do you think would happen if by chance a single + +cell in your body were to lose the one remaining working copy of that + +enzyme, the gene-encoded remaining working copy? + +Then it would have no copies. What do you think the response of + +the cell would be? High mutation rates, + +and cancer. It turns out that familial, hereditary, + +nonpolyposis coli, a familial form of colon cancer, + +is caused by, in many cases, mutations in the gene or genes, + +actually, encoding the mismatch repair enzymes. + +So, our theoretical understanding of the central dogma here is an + +incredibly practical disease because getting DNA replication right is + +important. And, that provides a very good proof that + +the difference between 105 or 106 here and 108 accuracy matters a + +great deal, that without that mismatch repair enzyme present in + +the cells, one is in fact going to create new mutations at an + +unacceptably high rate and lead to cancer. I don't know, + +a few other random nice facts about DNA polymerases. + +They're very fast speed. The speed of a DNA polymerase is + +about 2,000 nucleotides per second: very impressive. + +And then, one last point I can't help but mention, + +Arthur Kornberg discovers this enzyme, shows in a test tube, + +it works, people work out, how it works in detail, + +leading strands, lagging strands, topoisomerases, workout + +fidelity, all these kinds of things, great. But Kornberg's enzyme, the + +enzyme he purifies that copies DNA, is it actually the right enzyme? Is + +it the enzyme that the bacterial cells he used actually use to copy + +their DNA? Well, a biochemist would say, + +I cracked open the cell. I purified a component. It's able + +to carry out this function. There you go. But, + +what would the geneticist say? Sorry? Take out the component, + +and demonstrate now what? That the cell can't replicate. + +It's DNA. Until you've shown that, you haven't got the other half of + +the proof. So, of course, some geneticists decided + +to put this to the test. They took many mutant bacteria. + +One at a time, they grew them up, + +and they did Kornberg's purification to purify DNA polymerase. + +This is unbelievably tedious stuff, guys. You've got to take each one. + +You've got to purify it; get DNA polymerase. OK, + +it's there. Next one, next one, next one, next one. + +But, suppose you found a mutant which couldn't make Kornberg's DNA + +polymerase but still grew and replicated its DNA. + +That would prove that Kornberg's enzyme was not essential. + +They did. It turns out that Kornberg's enzyme, + +DNA polymerase 1, although it can replicate DNA in the + +test tube is not the enzyme that cells actually use for their major + +DNA replication. It turns out to be a relatively + +more minor repair enzyme used to fill in gaps. The actual enzyme is + +DNA polymerase 3, not that it matters to you a great + +deal, but this duality between the biochemistry and the genetics is + +very important because just the biochemical side of the story, + +without showing that it was essential to the function in the + +organism misses a very important point there. So, + +the combination of genetics and biochemistry, biochemistry pointed + +us to a class of enzymes. The genetics, then, identifies + +which ones are used for which purposes in vivo, + +which is not that easy to do in the test tube. Anyway, + +I mentioned that, and obviously being a geneticist, + +I like tweaking the biochemists about things like that. + +All right, onward. So, in our picture of DNA replication, + + in our picture of the central dogma, + +we've got DNA goes to DNA, and what about the step of transcription, + +DNA goes to RNA? Well, we've got to copy out our DNA into an + +intermediate molecule called RNA, which is going to then be used as a + +template for protein synthesis. Where do we start? + +Somewhere in here, there's some information. + +We want to make a copy of that information. How do we know where + +to start? Well, there's something. + +There's some information that says start here, right? + +There's a little sign that says, start here. Such a thing is called + +a promoter. And, the promoter, which we'll come and + +talk about more in a while, probably in a lecture or two, + +the promoter says here's the place to start copying the + +DNA into RNA, and it gets copied into the RNA by an + +enzyme that starts here, let's say, I don't know, T, + +A, T, G, G, T, A, T. On the other strand I guess it's going to be A, + +T, A, C, C, A, T, A. It's going to start copying here, + +and it's going to put in an A. Then opposite the A, + +it's going to put in a U, because RNA has U, A, C, C, + +A, U, A, etc., except this time it's doing it not out of DNA but out of + +RNA. How does RNA differ from DNA? So, first off, instead of + +deoxyribose, this is deoxyribose. + +In fact, it's two prime deoxyribose. This is just plain old ribose. + +Remember down there on the two prime carbon, DNA had just a + +hydrogen, whereas RNA has a hydroxyl. + +All right, that's one difference, and it turns out that that hydroxyl + +is important because it would interfere in making long double + +helices of RNA. RNA doesn't make good, + +long double helices. Let's entirely do that, oxygen. + +And, the other major difference between DNA and RNA? + +The only other difference between DNA and RNA is that this has U where + +this has T, and what's the difference between T and U? + +A single methyl group. That's the only difference between + +T and U. In this six-member ring over here, there is a methyl group. + +And here in the six membered ring, there's no methyl group. + +That's it. Why does RNA use U, and DNA use T? Anybody know? + +It's not a big difference. That would be interesting, + +although I don't think it's true. I actually have no idea. I think + +this is fascinating. I've never had a good accounting of + +why it uses U and T. You need to know this, + +and it's true, but I don't actually have a, + +whereas I have a good explanation for this I don't have a good + +explanation for that, although maybe some of my Origin of + +Life colleagues have an explanation. But I've always been a little + +puzzled. Why does it use U instead of T? Anyway, + +I do know why it doesn't have the hydroxyl. Well, + +it has the hydroxyl there. That really does affect the base + +stacking, and all sorts of things like that. All right, + +so you, don't go away, come back. So, the DNA is used as a template + +to copy here a strand of RNA. Some important names: the strand + +that is being copied that is being transcribed is called the + +transcribed strand. This is called the non-transcribed + +strand that makes good sense. This is also called the coding + +strand. And, you will find it in your books as the coding strand. + +Why is it called the non-coding strand? + +This is called the coding strand. Why is the top strand called the + +coding strand? Because the RNA that I copy out + +will have the same sequence as the coding strand, + +except for T's and U's. So, the RNA copy that is made from + + the transcribed strand matches the + +sequence of the non-transcribes strand, or the coding strand. + +So, you will find this confusing, but you will probably find it on + +tests and some things like that to know which strand you're looking at. + +The coding strand is this strand which has the code that ends up, + +but in fact it's the template for the coding strand, + +the complement to the coding strand, the non-coding strand, the + +transcribed strand that is copied. Anyway, I've said that now, and you + +can, So, how does it know where to stop? + +Sorry? Stop codons. Stop codons are actually about translation into + +protein, right, because we're going to come to stop + +codons in a second. There was some start signal there + +called a promoter, which is a start of transcription. + +It turns out there was also a stop signal that says stop of + +transcription. And, you guys haven't probably met + +that before. But, there's a start signal, + +a stop signal, and all over the genome there are these things. + +So, here's some genome. Here's some gene that's got to be read out. + +And, it's read out this way, let's say. This is the coding strand. + +This is what, I'll make two strands here. Now, in the next + +gene over here, does it go in the same direction? + +It might. Or, it might not. It turns out that the orientation of + +genes along the chromosome, which way you read, is not a fixed + +thing across the entire length of the chromosome. + +So, when I refer to the transcribed strand or the non-transcribed strand, + +that's just a local definition that says, with respect to that gene, + +this strand is coding, and this strand is non-coded. + +But with respect to the next gene over, it could be the other way. + +Now, this is not a very orderly way to do things, right? + +If a good engineer did this, they'd probably get all the pieces + +going in line and all that. But life did this, and it turns out + +that evolvable systems, you know, couldn't possibly maintain + +that order. Things are happening all the time, and genes can come in + +any order. In addition, how does RNA polymerase know when to + +turn on the gene? Oh, sorry, what's the enzyme that + +polymerizes RNA? RNA polymerase, yes. + +How does it know when to turn on the gene? How does it turn on the + +right genes in the right tissues? We'll come to that. That's gene + +regulation. That's a big non-trivial thing. + +We'll save that one. All right, so we have all of this + +transcription. Let's now look at the last + +important part of our picture here, which is translation. + +So, RNA goes to protein. So, if RNA goes to protein, + +we take our messenger, our RNA over there. This is an RNA. + +What's the direction it's been copied? Five prime + +to three prime. It's a single strand of RNA that + +we've copied here, a single strand and molecule, + +and let's give it a sequence, A, U, A, C, G, A, U, G, A, A, G, C, C, + +C, etc. Eventually we'll get to U, A, G. How is this RNA interpreted? + +Well, in an abstract sense, the way this RNA is interpreted is + +by a triplet code. The cell could come along and start + +reading three letter codons. But, does it just start anywhere? + +No, it always starts at the same codon, and that codon is A, + +U, G. This is an initiator codon. + +And it encodes a methionine. Then, the next codon down encodes + +lysine, arginine, etc. The interesting challenge is + +how in the world you get from a sequence of nucleotides to a + +sequence of amino acids. So, we have to now get this funny + +translation step between nucleotides and amino acids. + +This concerned people greatly because transcription was pretty + +easy. Transcription was going to be the RNA, actually first + +replication, each nucleotide would match a + +nucleotide on the DNA sequence. Then, RNA polymerization, each + +nucleotide of RNA would match. But how are we going to get amino + +acids to match specific RNA sequences? How are we going to get + +amino acids? Now, this bothered people a great deal. + +And, you know what some of the ideas were? Well, protenase, + +right. Some enzyme, well, + +actually the first ideas were very physical ideas. + +It was that the RNA message there would fold up into some kind of a + +funny shape that would just happen to match a lysine, + +and then the next little bit would fold up to match, + +I don't know, histidine, a methianine, and a serine, + +and a this, because people were thinking the complementarity of DNA + +bases all just physical matching that it would work that the + +amino acids would be directly read off the RNA message. + +But, it was kind of crazy to imagine that because the amino acids + +all have such wildly different physical properties: positive + +charges, negative charges, hydrophilic, hydrophobic, different + +sizes. It just didn't make sense, but it bothered people a great deal. + +But, I would say that a lot of biochemists thought that that was + +sort of how it was going to have to work. The guy who really figured + +out what was going on did it with no experimental data whatsoever. + +He did it by just sitting down and saying, that doesn't make any sense. + +There's got to be another solution. And, that was Francis Crick. + +Francis Crick just had an incredible mind. + +He, Mendel, and a few other people had this incredible insight into + +things. He said, look, this just makes no sense that + +the physical properties are going to do it. He said, + +what's got to be going on is that what I want to put in + +a certain amino acid into a growing protein chain, + +I'm going to take my amino acid here. I'm going to take my codon here, + +and I'm going to build me some kind of an adapter. + +And, this adapter molecule will, in fact, solve the problem. So, he + +said, because Francis Creek, in addition to being brilliant, + +really didn't do any experiments. + +He didn't do any experiments both because he wasn't that fond of doing + +experiments, and because he was legendarily not very good at the + +bench. But, what Francis did was he exhorted all of his colleagues to go + +find the adapter. He had what he called the adapter + +hypothesis. And sure enough, Crick was dead on, just right. + +The adapter hypothesis turned out to be that there was an + +adapter molecule who was made itself out of RNA + +called transfer RNA. And, transfer RNA matched up by + +base pairing to each codon you see, and had amino acids attached to it + +and so the problem of how you mediate between a three-letter code + +of DNA or RNA, of nucleotides, + +and amino acids was solved by a clever intermediate. + +It turned out that they looked, they found the molecule. So, it's + +just one of these great examples of somebody having thought up an idea, + +sent people off to look for it, and it was there. And then, + +of course, you've got to ask, how did the amino acids get stuck + +onto the right transfer RNAs? And the answer is there's a bunch + +of specific enzymes that do precisely that job, + +that look at the transfer RNA, attach the amino acid, and handle + +that whole problem. I will next time briefly end with + +the ribosome, and how those transfer RNAs work to + +catalyze together the protein chain, and then what I want to do is turn + +to how this common picture of DNA, RNA, and protein varies amongst + +organisms. Until next time. \ No newline at end of file diff --git a/R3DI6W9iKtU.txt b/R3DI6W9iKtU.txt new file mode 100644 index 0000000000000000000000000000000000000000..d68d371e9b4a49f6c962f59ad1ace6436673fa1e --- /dev/null +++ b/R3DI6W9iKtU.txt @@ -0,0 +1,8474 @@ +align:start position:0% + +um just very quickly I wanted to you + + align:start position:0% +um just very quickly I wanted to you + + + align:start position:0% +um just very quickly I wanted to you +know I mentioned to you the other day + + align:start position:0% +know I mentioned to you the other day + + + align:start position:0% +know I mentioned to you the other day +that that article about Romney making a + + align:start position:0% +that that article about Romney making a + + + align:start position:0% +that that article about Romney making a +a uh policy statement about embryonic + + align:start position:0% +a uh policy statement about embryonic + + + align:start position:0% +a uh policy statement about embryonic +stem cell research and said that would + + align:start position:0% +stem cell research and said that would + + + align:start position:0% +stem cell research and said that would +you know here was sort of examples of + + align:start position:0% +you know here was sort of examples of + + + align:start position:0% +you know here was sort of examples of +issues we were thinking about in this + + align:start position:0% +issues we were thinking about in this + + + align:start position:0% +issues we were thinking about in this +course that would come into your + + align:start position:0% +course that would come into your + + + align:start position:0% +course that would come into your +ordinary life here's on today's Globe + + align:start position:0% +ordinary life here's on today's Globe + + + align:start position:0% +ordinary life here's on today's Globe +there's a Kennedy rips Romney over stem + + align:start position:0% +there's a Kennedy rips Romney over stem + + + align:start position:0% +there's a Kennedy rips Romney over stem +cell policy this debate is is continuing + + align:start position:0% +cell policy this debate is is continuing + + + align:start position:0% +cell policy this debate is is continuing +it's on the front page of uh of today's + + align:start position:0% +it's on the front page of uh of today's + + + align:start position:0% +it's on the front page of uh of today's +today's Boston Globe we have two people + + align:start position:0% +today's Boston Globe we have two people + + + align:start position:0% +today's Boston Globe we have two people +who probably neither of whom probably + + align:start position:0% +who probably neither of whom probably + + + align:start position:0% +who probably neither of whom probably +have the background in in biology that + + align:start position:0% +have the background in in biology that + + + align:start position:0% +have the background in in biology that +you guys are going to have by the time + + align:start position:0% +you guys are going to have by the time + + + align:start position:0% +you guys are going to have by the time +you finish this course having to Grapple + + align:start position:0% +you finish this course having to Grapple + + + align:start position:0% +you finish this course having to Grapple +with these very serious scientific uh + + align:start position:0% +with these very serious scientific uh + + + align:start position:0% +with these very serious scientific uh +issues that have all kinds of other + + align:start position:0% +issues that have all kinds of other + + + align:start position:0% +issues that have all kinds of other +implications um here's another thing + + align:start position:0% +implications um here's another thing + + + align:start position:0% +implications um here's another thing +this was in yesterday's newspaper this + + align:start position:0% +this was in yesterday's newspaper this + + + align:start position:0% +this was in yesterday's newspaper this +was on I think the second page of the + + align:start position:0% +was on I think the second page of the + + + align:start position:0% +was on I think the second page of the +Boston Globe it's about a curator over + + align:start position:0% +Boston Globe it's about a curator over + + + align:start position:0% +Boston Globe it's about a curator over +at Harvard at the Museum of comparative + + align:start position:0% +at Harvard at the Museum of comparative + + + align:start position:0% +at Harvard at the Museum of comparative +zoology they've got all these different + + align:start position:0% +zoology they've got all these different + + + align:start position:0% +zoology they've got all these different +birds many of you know some of whom are + + align:start position:0% +birds many of you know some of whom are + + + align:start position:0% +birds many of you know some of whom are +extinct in something and now the curator + + align:start position:0% +extinct in something and now the curator + + + align:start position:0% +extinct in something and now the curator +instead of just having them there as a + + align:start position:0% +instead of just having them there as a + + + align:start position:0% +instead of just having them there as a +sort of collection and that's all it is + + align:start position:0% +sort of collection and that's all it is + + + align:start position:0% +sort of collection and that's all it is +is going and getting DNA out of these uh + + align:start position:0% +is going and getting DNA out of these uh + + + align:start position:0% +is going and getting DNA out of these uh +specimens and working back and looking + + align:start position:0% +specimens and working back and looking + + + align:start position:0% +specimens and working back and looking +at gaining you insights from birds that + + align:start position:0% +at gaining you insights from birds that + + + align:start position:0% +at gaining you insights from birds that +don't even you know animals that aren't + + align:start position:0% +don't even you know animals that aren't + + + align:start position:0% +don't even you know animals that aren't +even found on this planet anymore and + + align:start position:0% +even found on this planet anymore and + + + align:start position:0% +even found on this planet anymore and +this one was from uh I didn't want to + + align:start position:0% +this one was from uh I didn't want to + + + align:start position:0% +this one was from uh I didn't want to +show you this in Valentine's Day + + align:start position:0% +show you this in Valentine's Day + + + align:start position:0% +show you this in Valentine's Day +particularly but this is critical this I + + align:start position:0% +particularly but this is critical this I + + + align:start position:0% +particularly but this is critical this I +I don't subscribe to the New York Times + + align:start position:0% +I don't subscribe to the New York Times + + + align:start position:0% +I don't subscribe to the New York Times +but for some reason one appeared in my + + align:start position:0% +but for some reason one appeared in my + + + align:start position:0% +but for some reason one appeared in my +porch on Saturday morning I opened up + + align:start position:0% +porch on Saturday morning I opened up + + + align:start position:0% +porch on Saturday morning I opened up +the first page rare and aggressive HIV + + align:start position:0% +the first page rare and aggressive HIV + + + align:start position:0% +the first page rare and aggressive HIV +reported in New York I'll be talking to + + align:start position:0% +reported in New York I'll be talking to + + + align:start position:0% +reported in New York I'll be talking to +you about the hi V1 virus which is the + + align:start position:0% +you about the hi V1 virus which is the + + + align:start position:0% +you about the hi V1 virus which is the +virus that ends up destroying your your + + align:start position:0% +virus that ends up destroying your your + + + align:start position:0% +virus that ends up destroying your your +some of your immune M your Defender + + align:start position:0% +some of your immune M your Defender + + + align:start position:0% +some of your immune M your Defender +cells and immune system and then people + + align:start position:0% +cells and immune system and then people + + + align:start position:0% +cells and immune system and then people +die of AIDS which is sort of all the + + align:start position:0% +die of AIDS which is sort of all the + + + align:start position:0% +die of AIDS which is sort of all the +other stuff that then happens and it was + + align:start position:0% +other stuff that then happens and it was + + + align:start position:0% +other stuff that then happens and it was +terribly scary when it first showed up + + align:start position:0% +terribly scary when it first showed up + + + align:start position:0% +terribly scary when it first showed up +there was no treatment for it it's like + + align:start position:0% +there was no treatment for it it's like + + + align:start position:0% +there was no treatment for it it's like +that in most of the third world and + + align:start position:0% +that in most of the third world and + + + align:start position:0% +that in most of the third world and +people die if they get it I lost friend + + align:start position:0% +people die if they get it I lost friend + + + align:start position:0% +people die if they get it I lost friend +to it close to it after it first came up + + align:start position:0% +to it close to it after it first came up + + + align:start position:0% +to it close to it after it first came up +then they came up with these various + + align:start position:0% +then they came up with these various + + + align:start position:0% +then they came up with these various +cocktail of different Inhibitors and the + + align:start position:0% +cocktail of different Inhibitors and the + + + align:start position:0% +cocktail of different Inhibitors and the +idea was instead of just having a single + + align:start position:0% +idea was instead of just having a single + + + align:start position:0% +idea was instead of just having a single +drug T drug Target where it would be + + align:start position:0% +drug T drug Target where it would be + + + align:start position:0% +drug T drug Target where it would be +easy for the virus to mutate and as I'll + + align:start position:0% +easy for the virus to mutate and as I'll + + + align:start position:0% +easy for the virus to mutate and as I'll +tell you the HIV mut virus mutates like + + align:start position:0% +tell you the HIV mut virus mutates like + + + align:start position:0% +tell you the HIV mut virus mutates like +crazy instead they' use multiple targets + + align:start position:0% +crazy instead they' use multiple targets + + + align:start position:0% +crazy instead they' use multiple targets +and that's why they do it in sort of + + align:start position:0% +and that's why they do it in sort of + + + align:start position:0% +and that's why they do it in sort of +then the chances of getting mutation is + + align:start position:0% +then the chances of getting mutation is + + + align:start position:0% +then the chances of getting mutation is +is you multiply all these low + + align:start position:0% +is you multiply all these low + + + align:start position:0% +is you multiply all these low +probabilities of getting mutation and + + align:start position:0% +probabilities of getting mutation and + + + align:start position:0% +probabilities of getting mutation and +would hope it would never happen it's + + align:start position:0% +would hope it would never happen it's + + + align:start position:0% +would hope it would never happen it's +happened there in New York is a a uh + + align:start position:0% +happened there in New York is a a uh + + + align:start position:0% +happened there in New York is a a uh +version of HIV 1 that is resistant + + align:start position:0% +version of HIV 1 that is resistant + + + align:start position:0% +version of HIV 1 that is resistant +everything if that spreads which it + + align:start position:0% +everything if that spreads which it + + + align:start position:0% +everything if that spreads which it +probably will it'll be just like what + + align:start position:0% +probably will it'll be just like what + + + align:start position:0% +probably will it'll be just like what +happens with all the bacteria and + + align:start position:0% +happens with all the bacteria and + + + align:start position:0% +happens with all the bacteria and +antibiotics it works for a little while + + align:start position:0% +antibiotics it works for a little while + + + align:start position:0% +antibiotics it works for a little while +natural mutation and natural selection + + align:start position:0% +natural mutation and natural selection + + + align:start position:0% +natural mutation and natural selection +something will happen the organism or + + align:start position:0% +something will happen the organism or + + + align:start position:0% +something will happen the organism or +the virus will change so it's no longer + + align:start position:0% +the virus will change so it's no longer + + + align:start position:0% +the virus will change so it's no longer +resistant so you know for the moment as + + align:start position:0% +resistant so you know for the moment as + + + align:start position:0% +resistant so you know for the moment as +always you know make sure you never + + align:start position:0% +always you know make sure you never + + + align:start position:0% +always you know make sure you never +expose yourself uh to AIDS this would + + align:start position:0% +expose yourself uh to AIDS this would + + + align:start position:0% +expose yourself uh to AIDS this would +take us back just like to before any of + + align:start position:0% +take us back just like to before any of + + + align:start position:0% +take us back just like to before any of +these things were inhibited and the same + + align:start position:0% +these things were inhibited and the same + + + align:start position:0% +these things were inhibited and the same +thing goes right now there strains of + + align:start position:0% +thing goes right now there strains of + + + align:start position:0% +thing goes right now there strains of +microbacterium tuberculosis that are + + align:start position:0% +microbacterium tuberculosis that are + + + align:start position:0% +microbacterium tuberculosis that are +resistant every known antibiotic if you + + align:start position:0% +resistant every known antibiotic if you + + + align:start position:0% +resistant every known antibiotic if you +get that get tuberculosis with that + + align:start position:0% +get that get tuberculosis with that + + + align:start position:0% +get that get tuberculosis with that +thing it's like you were living 200 + + align:start position:0% +thing it's like you were living 200 + + + align:start position:0% +thing it's like you were living 200 +years ago they can't do anything for you + + align:start position:0% +years ago they can't do anything for you + + + align:start position:0% +years ago they can't do anything for you +they put you in a sanatorium but you + + align:start position:0% +they put you in a sanatorium but you + + + align:start position:0% +they put you in a sanatorium but you +can't be cured this is worse this one + + align:start position:0% +can't be cured this is worse this one + + + align:start position:0% +can't be cured this is worse this one +kills you know this is awful this one + + align:start position:0% +kills you know this is awful this one + + + align:start position:0% +kills you know this is awful this one +kills you so just be careful this is + + align:start position:0% +kills you so just be careful this is + + + align:start position:0% +kills you so just be careful this is +just the tip but what always happens + + align:start position:0% +just the tip but what always happens + + + align:start position:0% +just the tip but what always happens +when you have antibiotics or drug + + align:start position:0% +when you have antibiotics or drug + + + align:start position:0% +when you have antibiotics or drug +treatments eventually natural selection + + align:start position:0% +treatments eventually natural selection + + + align:start position:0% +treatments eventually natural selection +mutation will probably produce a variant + + align:start position:0% +mutation will probably produce a variant + + + align:start position:0% +mutation will probably produce a variant +and this looks like it's happening I I + + align:start position:0% +and this looks like it's happening I I + + + align:start position:0% +and this looks like it's happening I I +don't know but I I hope not but I'm + + align:start position:0% +don't know but I I hope not but I'm + + + align:start position:0% +don't know but I I hope not but I'm +afraid this won't be the end of this one + + align:start position:0% +afraid this won't be the end of this one + + + align:start position:0% +afraid this won't be the end of this one +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so some of you I've read some of the + + align:start position:0% +so some of you I've read some of the + + + align:start position:0% +so some of you I've read some of the +comments I'm not terribly surprised that + + align:start position:0% +comments I'm not terribly surprised that + + + align:start position:0% +comments I'm not terribly surprised that +some of you think why is he telling me + + align:start position:0% +some of you think why is he telling me + + + align:start position:0% +some of you think why is he telling me +all this God there was a lot of work for + + align:start position:0% +all this God there was a lot of work for + + + align:start position:0% +all this God there was a lot of work for +tremendously confusing there were all + + align:start position:0% +tremendously confusing there were all + + + align:start position:0% +tremendously confusing there were all +these chemical structures they didn't + + align:start position:0% +these chemical structures they didn't + + + align:start position:0% +these chemical structures they didn't +really get it all seemed somehow out of + + align:start position:0% +really get it all seemed somehow out of + + + align:start position:0% +really get it all seemed somehow out of +this the cell got two molecules of ATP + + align:start position:0% +this the cell got two molecules of ATP + + + align:start position:0% +this the cell got two molecules of ATP +why are we wasting all the time why am I + + align:start position:0% +why are we wasting all the time why am I + + + align:start position:0% +why are we wasting all the time why am I +wasting all this time telling you + + align:start position:0% +wasting all this time telling you + + + align:start position:0% +wasting all this time telling you +about how to get two molecules of ATP + + align:start position:0% +about how to get two molecules of ATP + + + align:start position:0% +about how to get two molecules of ATP +but I mean this is basically so what we + + align:start position:0% +but I mean this is basically so what we + + + align:start position:0% +but I mean this is basically so what we +were we were doing we were looking at + + align:start position:0% +were we were doing we were looking at + + + align:start position:0% +were we were doing we were looking at +glucose which is C6 + + align:start position:0% +glucose which is C6 + + + align:start position:0% +glucose which is C6 +h126 going through this process which + + align:start position:0% +h126 going through this process which + + + align:start position:0% +h126 going through this process which +pathway of 10 + + align:start position:0% +pathway of 10 + + + align:start position:0% +pathway of 10 +enzymatic uh steps and what ends up + + align:start position:0% +enzymatic uh steps and what ends up + + + align:start position:0% +enzymatic uh steps and what ends up +coming out at the other + + align:start position:0% +coming out at the other + + + align:start position:0% +coming out at the other +end is two pyrates and the net yield of + + align:start position:0% +end is two pyrates and the net yield of + + + align:start position:0% +end is two pyrates and the net yield of +that is 2 ATP + + align:start position:0% + + + + align:start position:0% + +plus two molecules of this weird thing + + align:start position:0% +plus two molecules of this weird thing + + + align:start position:0% +plus two molecules of this weird thing +called + + align:start position:0% +called + + + align:start position:0% +called +nadh now I think most of you although a + + align:start position:0% +nadh now I think most of you although a + + + align:start position:0% +nadh now I think most of you although a +few of you still don't seem to have + + align:start position:0% +few of you still don't seem to have + + + align:start position:0% +few of you still don't seem to have +gotten the reason you need to make ATP + + align:start position:0% +gotten the reason you need to make ATP + + + align:start position:0% +gotten the reason you need to make ATP +out of ADP and inorganic phosphate is it + + align:start position:0% +out of ADP and inorganic phosphate is it + + + align:start position:0% +out of ADP and inorganic phosphate is it +stores energy it's you know like having + + align:start position:0% +stores energy it's you know like having + + + align:start position:0% +stores energy it's you know like having +electricity in your house or batteries + + align:start position:0% +electricity in your house or batteries + + + align:start position:0% +electricity in your house or batteries +in your in your flashlight or in your uh + + align:start position:0% +in your in your flashlight or in your uh + + + align:start position:0% +in your in your flashlight or in your uh +iPod or whatever it is you got to have + + align:start position:0% +iPod or whatever it is you got to have + + + align:start position:0% +iPod or whatever it is you got to have +energy in order to do stuff and cells + + align:start position:0% +energy in order to do stuff and cells + + + align:start position:0% +energy in order to do stuff and cells +need it and the major sort of energy + + align:start position:0% +need it and the major sort of energy + + + align:start position:0% +need it and the major sort of energy +Curren they use as ATP and they put most + + align:start position:0% +Curren they use as ATP and they put most + + + align:start position:0% +Curren they use as ATP and they put most +of it by putting squeezing together a + + align:start position:0% +of it by putting squeezing together a + + + align:start position:0% +of it by putting squeezing together a +phosphate up to an ATP making this Bond + + align:start position:0% +phosphate up to an ATP making this Bond + + + align:start position:0% +phosphate up to an ATP making this Bond +that's it's stable unless there's an + + align:start position:0% +that's it's stable unless there's an + + + align:start position:0% +that's it's stable unless there's an +enzyme that'll break it open but there's + + align:start position:0% +enzyme that'll break it open but there's + + + align:start position:0% +enzyme that'll break it open but there's +energy stored in it and they'll drop + + align:start position:0% +energy stored in it and they'll drop + + + align:start position:0% +energy stored in it and they'll drop +downhill and you can use that energy to + + align:start position:0% +downhill and you can use that energy to + + + align:start position:0% +downhill and you can use that energy to +drive other reactions so for life to + + align:start position:0% +drive other reactions so for life to + + + align:start position:0% +drive other reactions so for life to +happen it had to somehow figure out how + + align:start position:0% +happen it had to somehow figure out how + + + align:start position:0% +happen it had to somehow figure out how +to get energy in a form that it could + + align:start position:0% +to get energy in a form that it could + + + align:start position:0% +to get energy in a form that it could +use to do all the biosynthesis that's + + align:start position:0% +use to do all the biosynthesis that's + + + align:start position:0% +use to do all the biosynthesis that's +necessary for Life uh to go on nadh I + + align:start position:0% +necessary for Life uh to go on nadh I + + + align:start position:0% +necessary for Life uh to go on nadh I +showed you the molecule you got a + + align:start position:0% +showed you the molecule you got a + + + align:start position:0% +showed you the molecule you got a +structure the cell makes some number of + + align:start position:0% +structure the cell makes some number of + + + align:start position:0% +structure the cell makes some number of +molecules of that it's around and what + + align:start position:0% +molecules of that it's around and what + + + align:start position:0% +molecules of that it's around and what +happened it comes in it helps some of + + align:start position:0% +happened it comes in it helps some of + + + align:start position:0% +happened it comes in it helps some of +these processes go it ends up it's sort + + align:start position:0% +these processes go it ends up it's sort + + + align:start position:0% +these processes go it ends up it's sort +of like a banking system for electrons + + align:start position:0% +of like a banking system for electrons + + + align:start position:0% +of like a banking system for electrons +if it gets nadh it's got electrons stuck + + align:start position:0% +if it gets nadh it's got electrons stuck + + + align:start position:0% +if it gets nadh it's got electrons stuck +on it there's only a limited number of + + align:start position:0% +on it there's only a limited number of + + + align:start position:0% +on it there's only a limited number of +molecules of nadh in a Cell so if you + + align:start position:0% +molecules of nadh in a Cell so if you + + + align:start position:0% +molecules of nadh in a Cell so if you +put all you make them all the NAD + + align:start position:0% +put all you make them all the NAD + + + align:start position:0% +put all you make them all the NAD +molecules into nadh then you have + + align:start position:0% +molecules into nadh then you have + + + align:start position:0% +molecules into nadh then you have +nowhere else to put electrons and + + align:start position:0% +nowhere else to put electrons and + + + align:start position:0% +nowhere else to put electrons and +everything stop comes to a grinding halt + + align:start position:0% +everything stop comes to a grinding halt + + + align:start position:0% +everything stop comes to a grinding halt +because I was talking about redo + + align:start position:0% +because I was talking about redo + + + align:start position:0% +because I was talking about redo +reactions if you're taking electrons off + + align:start position:0% +reactions if you're taking electrons off + + + align:start position:0% +reactions if you're taking electrons off +somewhere they got to go somewhere else + + align:start position:0% +somewhere they got to go somewhere else + + + align:start position:0% +somewhere they got to go somewhere else +and the cell uses nadh as kind of almost + + align:start position:0% +and the cell uses nadh as kind of almost + + + align:start position:0% +and the cell uses nadh as kind of almost +a currency for passing electrons around + + align:start position:0% +a currency for passing electrons around + + + align:start position:0% +a currency for passing electrons around +in just the same way it uses ATP as a + + align:start position:0% +in just the same way it uses ATP as a + + + align:start position:0% +in just the same way it uses ATP as a +currency for carrying uh energ energy + + align:start position:0% +currency for carrying uh energ energy + + + align:start position:0% +currency for carrying uh energ energy +around from one one form or another now + + align:start position:0% +around from one one form or another now + + + align:start position:0% +around from one one form or another now +the problem was and why this was so + + align:start position:0% +the problem was and why this was so + + + align:start position:0% +the problem was and why this was so +important is this apparently this is I + + align:start position:0% +important is this apparently this is I + + + align:start position:0% +important is this apparently this is I +said this we're basically looking at an + + align:start position:0% +said this we're basically looking at an + + + align:start position:0% +said this we're basically looking at an +evolutionary fossil of some sort because + + align:start position:0% +evolutionary fossil of some sort because + + + align:start position:0% +evolutionary fossil of some sort because +every organism on Earth uses or + + align:start position:0% +every organism on Earth uses or + + + align:start position:0% +every organism on Earth uses or +virtually every organism on Earth uses + + align:start position:0% +virtually every organism on Earth uses + + + align:start position:0% +virtually every organism on Earth uses +uh glycolysis it's in our cytoplasm of + + align:start position:0% +uh glycolysis it's in our cytoplasm of + + + align:start position:0% +uh glycolysis it's in our cytoplasm of +our cells it's in the cytoplasm of + + align:start position:0% +our cells it's in the cytoplasm of + + + align:start position:0% +our cells it's in the cytoplasm of +bacteria it's in the cytoplasm of our + + align:start position:0% +bacteria it's in the cytoplasm of our + + + align:start position:0% +bacteria it's in the cytoplasm of our +Kia it apparently evolves so long ago + + align:start position:0% +Kia it apparently evolves so long ago + + + align:start position:0% +Kia it apparently evolves so long ago +that every form of life on Earth you + + align:start position:0% +that every form of life on Earth you + + + align:start position:0% +that every form of life on Earth you +know depends on this anything that can + + align:start position:0% +know depends on this anything that can + + + align:start position:0% +know depends on this anything that can +can metabolize a a sugar molecule pretty + + align:start position:0% +can metabolize a a sugar molecule pretty + + + align:start position:0% +can metabolize a a sugar molecule pretty +much and so + + align:start position:0% +much and so + + + align:start position:0% +much and so +um it looks complicated it is maybe you + + align:start position:0% +um it looks complicated it is maybe you + + + align:start position:0% +um it looks complicated it is maybe you +could have designed like to tell you + + align:start position:0% +could have designed like to tell you + + + align:start position:0% +could have designed like to tell you +that it's two rea and you make two atps + + align:start position:0% +that it's two rea and you make two atps + + + align:start position:0% +that it's two rea and you make two atps +and it's all simple life isn't often + + align:start position:0% +and it's all simple life isn't often + + + align:start position:0% +and it's all simple life isn't often +simple it's often very complicated it + + align:start position:0% +simple it's often very complicated it + + + align:start position:0% +simple it's often very complicated it +wasn't done by a team of design + + align:start position:0% +wasn't done by a team of design + + + align:start position:0% +wasn't done by a team of design +engineers and building 10an designing + + align:start position:0% +engineers and building 10an designing + + + align:start position:0% +engineers and building 10an designing +and it was done by something that + + align:start position:0% +and it was done by something that + + + align:start position:0% +and it was done by something that +happened with random selection when + + align:start position:0% +happened with random selection when + + + align:start position:0% +happened with random selection when +something finally worked apparently it + + align:start position:0% +something finally worked apparently it + + + align:start position:0% +something finally worked apparently it +got fixed in evolution and even if it + + align:start position:0% +got fixed in evolution and even if it + + + align:start position:0% +got fixed in evolution and even if it +looks clunky I think the other way to + + align:start position:0% +looks clunky I think the other way to + + + align:start position:0% +looks clunky I think the other way to +look at it is to say my isn't that + + align:start position:0% +look at it is to say my isn't that + + + align:start position:0% +look at it is to say my isn't that +almost a I feel a sort of sense of + + align:start position:0% +almost a I feel a sort of sense of + + + align:start position:0% +almost a I feel a sort of sense of +wonder at this point and granted I've + + align:start position:0% +wonder at this point and granted I've + + + align:start position:0% +wonder at this point and granted I've +had a lot of years working in the field + + align:start position:0% +had a lot of years working in the field + + + align:start position:0% +had a lot of years working in the field +that something that complicated could + + align:start position:0% +that something that complicated could + + + align:start position:0% +that something that complicated could +work out and take this molecule of of + + align:start position:0% +work out and take this molecule of of + + + align:start position:0% +work out and take this molecule of of +glucose and make it into two molecules + + align:start position:0% +glucose and make it into two molecules + + + align:start position:0% +glucose and make it into two molecules +of ATP that can then be used to uh allow + + align:start position:0% +of ATP that can then be used to uh allow + + + align:start position:0% +of ATP that can then be used to uh allow +the cell to do synthesis as and I'll + + align:start position:0% +the cell to do synthesis as and I'll + + + align:start position:0% +the cell to do synthesis as and I'll +show you there's a better way you can + + align:start position:0% +show you there's a better way you can + + + align:start position:0% +show you there's a better way you can +use this much more efficiently 18 times + + align:start position:0% +use this much more efficiently 18 times + + + align:start position:0% +use this much more efficiently 18 times +more efficiently if we do respiration + + align:start position:0% +more efficiently if we do respiration + + + align:start position:0% +more efficiently if we do respiration +which we'll talk about today but that + + align:start position:0% +which we'll talk about today but that + + + align:start position:0% +which we'll talk about today but that +needs oxygen and when life started 3.8 + + align:start position:0% +needs oxygen and when life started 3.8 + + + align:start position:0% +needs oxygen and when life started 3.8 +billion years ago or so there was no + + align:start position:0% +billion years ago or so there was no + + + align:start position:0% +billion years ago or so there was no +oxygen so it wasn't an option the + + align:start position:0% +oxygen so it wasn't an option the + + + align:start position:0% +oxygen so it wasn't an option the +initial organisms had to make do with + + align:start position:0% +initial organisms had to make do with + + + align:start position:0% +initial organisms had to make do with +what they with what they found and this + + align:start position:0% +what they with what they found and this + + + align:start position:0% +what they with what they found and this +is this is what developed now the + + align:start position:0% +is this is what developed now the + + + align:start position:0% +is this is what developed now the +problem here so ATP can go off and be + + align:start position:0% +problem here so ATP can go off and be + + + align:start position:0% +problem here so ATP can go off and be +used for lots of things the problem if + + align:start position:0% +used for lots of things the problem if + + + align:start position:0% +used for lots of things the problem if +there's no Oxygen around as I said + + align:start position:0% +there's no Oxygen around as I said + + + align:start position:0% +there's no Oxygen around as I said +there's a limited number of molecules of + + align:start position:0% +there's a limited number of molecules of + + + align:start position:0% +there's a limited number of molecules of +ATP so to make that glycolysis go you're + + align:start position:0% +ATP so to make that glycolysis go you're + + + align:start position:0% +ATP so to make that glycolysis go you're +taking some electrons off and doing that + + align:start position:0% +taking some electrons off and doing that + + + align:start position:0% +taking some electrons off and doing that +oxidation steps you're reducing nadh if + + align:start position:0% +oxidation steps you're reducing nadh if + + + align:start position:0% +oxidation steps you're reducing nadh if +you want that to go as a cycle you got + + align:start position:0% +you want that to go as a cycle you got + + + align:start position:0% +you want that to go as a cycle you got +to somehow regenerate the NAD plus you + + align:start position:0% +to somehow regenerate the NAD plus you + + + align:start position:0% +to somehow regenerate the NAD plus you +can go through another cycle and make + + align:start position:0% +can go through another cycle and make + + + align:start position:0% +can go through another cycle and make +more ATP so there were two variants that + + align:start position:0% +more ATP so there were two variants that + + + align:start position:0% +more ATP so there were two variants that +I told you about if you don't have + + align:start position:0% +I told you about if you don't have + + + align:start position:0% +I told you about if you don't have +oxygen around what uh one of these + + align:start position:0% +oxygen around what uh one of these + + + align:start position:0% +oxygen around what uh one of these +variants yields two + + align:start position:0% + + + + align:start position:0% + +lactate and so the net yield of this is + + align:start position:0% +lactate and so the net yield of this is + + + align:start position:0% +lactate and so the net yield of this is + + align:start position:0% + + + + align:start position:0% + +ATP because what happens in in this part + + align:start position:0% +ATP because what happens in in this part + + + align:start position:0% +ATP because what happens in in this part +is it uses up two molecules of n DH + + align:start position:0% +is it uses up two molecules of n DH + + + align:start position:0% +is it uses up two molecules of n DH +changing the two molecules of pyrovate + + align:start position:0% +changing the two molecules of pyrovate + + + align:start position:0% +changing the two molecules of pyrovate +to two molecules of lactate so that gets + + align:start position:0% +to two molecules of lactate so that gets + + + align:start position:0% +to two molecules of lactate so that gets +rid of this and the net yield of the + + align:start position:0% +rid of this and the net yield of the + + + align:start position:0% +rid of this and the net yield of the +whole thing is two molecules of ATP the + + align:start position:0% +whole thing is two molecules of ATP the + + + align:start position:0% +whole thing is two molecules of ATP the +other way to do it is the way yeast does + + align:start position:0% +other way to do it is the way yeast does + + + align:start position:0% +other way to do it is the way yeast does +it it makes two molecules of + + align:start position:0% +it it makes two molecules of + + + align:start position:0% +it it makes two molecules of +CO2 plus two molecules of + + align:start position:0% +CO2 plus two molecules of + + + align:start position:0% +CO2 plus two molecules of +ethanol and I think when I wrote that on + + align:start position:0% +ethanol and I think when I wrote that on + + + align:start position:0% +ethanol and I think when I wrote that on +the board I forgot I showed you that + + align:start position:0% +the board I forgot I showed you that + + + align:start position:0% +the board I forgot I showed you that +there was acid + + align:start position:0% + + + + align:start position:0% + +alahh we had two molecules of that going + + align:start position:0% +alahh we had two molecules of that going + + + align:start position:0% +alahh we had two molecules of that going +to two molecules of ethanol and I think + + align:start position:0% +to two molecules of ethanol and I think + + + align:start position:0% +to two molecules of ethanol and I think +I forgot to write on the board that it + + align:start position:0% +I forgot to write on the board that it + + + align:start position:0% +I forgot to write on the board that it +used up two molecules of nadh because + + align:start position:0% +used up two molecules of nadh because + + + align:start position:0% +used up two molecules of nadh because +that's important so that's what this + + align:start position:0% +that's important so that's what this + + + align:start position:0% +that's important so that's what this +whole thing is about it achieves the + + align:start position:0% +whole thing is about it achieves the + + + align:start position:0% +whole thing is about it achieves the +same thing and the net yield of this one + + align:start position:0% +same thing and the net yield of this one + + + align:start position:0% +same thing and the net yield of this one +is 2 atps as well so I'm going to talk + + align:start position:0% +is 2 atps as well so I'm going to talk + + + align:start position:0% +is 2 atps as well so I'm going to talk +about photosynthesis later at the end + + align:start position:0% +about photosynthesis later at the end + + + align:start position:0% +about photosynthesis later at the end +latter part of the lecture but if you + + align:start position:0% +latter part of the lecture but if you + + + align:start position:0% +latter part of the lecture but if you +maybe recall the initial sort of thing I + + align:start position:0% +maybe recall the initial sort of thing I + + + align:start position:0% +maybe recall the initial sort of thing I +called release one came up here about + + align:start position:0% +called release one came up here about + + + align:start position:0% +called release one came up here about +3.4 billion years ago later on an + + align:start position:0% +3.4 billion years ago later on an + + + align:start position:0% +3.4 billion years ago later on an +improved version came along that started + + align:start position:0% +improved version came along that started + + + align:start position:0% +improved version came along that started +to generate oxygen now it took billions + + align:start position:0% +to generate oxygen now it took billions + + + align:start position:0% +to generate oxygen now it took billions +of years for us to get to our present + + align:start position:0% +of years for us to get to our present + + + align:start position:0% +of years for us to get to our present +level of oxygen but when oxygen became + + align:start position:0% +level of oxygen but when oxygen became + + + align:start position:0% +level of oxygen but when oxygen became +available in the atmosphere then it was + + align:start position:0% +available in the atmosphere then it was + + + align:start position:0% +available in the atmosphere then it was +um there was a new option for making + + align:start position:0% +um there was a new option for making + + + align:start position:0% +um there was a new option for making +energy and that was instead of taking + + align:start position:0% +energy and that was instead of taking + + + align:start position:0% +energy and that was instead of taking +this nadh and remember there's about 50 + + align:start position:0% +this nadh and remember there's about 50 + + + align:start position:0% +this nadh and remember there's about 50 +kcals per mole of energy in there it's + + align:start position:0% +kcals per mole of energy in there it's + + + align:start position:0% +kcals per mole of energy in there it's +just being thrown away it's not being + + align:start position:0% +just being thrown away it's not being + + + align:start position:0% +just being thrown away it's not being +used at all but if there's oxygen around + + align:start position:0% +used at all but if there's oxygen around + + + align:start position:0% +used at all but if there's oxygen around +there's a new and better + + align:start position:0% +there's a new and better + + + align:start position:0% +there's a new and better +system which you know is respiration + + align:start position:0% +system which you know is respiration + + + align:start position:0% +system which you know is respiration +that's a word you've you've heard you + + align:start position:0% +that's a word you've you've heard you + + + align:start position:0% +that's a word you've you've heard you +know we breathe oxygen we need to + + align:start position:0% +know we breathe oxygen we need to + + + align:start position:0% +know we breathe oxygen we need to +breathe oxygen because we're using the + + align:start position:0% +breathe oxygen because we're using the + + + align:start position:0% +breathe oxygen because we're using the +oxygen to make energy and it's I'll tell + + align:start position:0% +oxygen to make energy and it's I'll tell + + + align:start position:0% +oxygen to make energy and it's I'll tell +you again you don't have to know all the + + align:start position:0% +you again you don't have to know all the + + + align:start position:0% +you again you don't have to know all the +the details but there's a there's a + + align:start position:0% +the details but there's a there's a + + + align:start position:0% +the details but there's a there's a +biochemical cycle called the citric acid + + align:start position:0% + + + + align:start position:0% + +cycle and it goes together with another + + align:start position:0% +cycle and it goes together with another + + + align:start position:0% +cycle and it goes together with another +process that's known as + + align:start position:0% +process that's known as + + + align:start position:0% +process that's known as +oxidative + + align:start position:0% + + + + align:start position:0% + +phosphorilation and so this + + align:start position:0% +phosphorilation and so this + + + align:start position:0% +phosphorilation and so this +is if we have oxygen what we end up with + + align:start position:0% +is if we have oxygen what we end up with + + + align:start position:0% +is if we have oxygen what we end up with +at the end of the day instead of these + + align:start position:0% +at the end of the day instead of these + + + align:start position:0% +at the end of the day instead of these +products is six molecules of CO2 plus + + align:start position:0% +products is six molecules of CO2 plus + + + align:start position:0% +products is six molecules of CO2 plus +six molecules of water but more + + align:start position:0% + + + + align:start position:0% + +importantly 36 + + align:start position:0% + + + + align:start position:0% + +molecules of + + align:start position:0% + + + + align:start position:0% + +ATP so respiration is tremendously + + align:start position:0% +ATP so respiration is tremendously + + + align:start position:0% +ATP so respiration is tremendously +better uh at capturing uh a capturing + + align:start position:0% +better uh at capturing uh a capturing + + + align:start position:0% +better uh at capturing uh a capturing +energy from a from a glucose molecule + + align:start position:0% +energy from a from a glucose molecule + + + align:start position:0% +energy from a from a glucose molecule +and but this is I'll show you in a is a + + align:start position:0% +and but this is I'll show you in a is a + + + align:start position:0% +and but this is I'll show you in a is a +later arriving uh development in res in + + align:start position:0% +later arriving uh development in res in + + + align:start position:0% +later arriving uh development in res in +evolution it had to be because it + + align:start position:0% +evolution it had to be because it + + + align:start position:0% +evolution it had to be because it +required oxygen in the uh in the + + align:start position:0% +required oxygen in the uh in the + + + align:start position:0% +required oxygen in the uh in the +atmosphere and so even though we only + + align:start position:0% +atmosphere and so even though we only + + + align:start position:0% +atmosphere and so even though we only +get two molecules out of ATP we all do + + align:start position:0% +get two molecules out of ATP we all do + + + align:start position:0% +get two molecules out of ATP we all do +it and the other thing it generates is + + align:start position:0% +it and the other thing it generates is + + + align:start position:0% +it and the other thing it generates is +is pyate and as you'll see this process + + align:start position:0% +is pyate and as you'll see this process + + + align:start position:0% +is pyate and as you'll see this process +takes those pyrates that's the starting + + align:start position:0% +takes those pyrates that's the starting + + + align:start position:0% +takes those pyrates that's the starting +material for this part over here okay + + align:start position:0% +material for this part over here okay + + + align:start position:0% +material for this part over here okay +this I hope this is making a bit bit + + align:start position:0% +this I hope this is making a bit bit + + + align:start position:0% +this I hope this is making a bit bit +more sense as to why you've got to keep + + align:start position:0% +more sense as to why you've got to keep + + + align:start position:0% +more sense as to why you've got to keep +your eye on the big picture all you're + + align:start position:0% +your eye on the big picture all you're + + + align:start position:0% +your eye on the big picture all you're +going to see is a whole lot of + + align:start position:0% +going to see is a whole lot of + + + align:start position:0% +going to see is a whole lot of +structures and chemical Transformations + + align:start position:0% +structures and chemical Transformations + + + align:start position:0% +structures and chemical Transformations +that don't make any sense this is all + + align:start position:0% +that don't make any sense this is all + + + align:start position:0% +that don't make any sense this is all +about making any uh ATP and energy and + + align:start position:0% +about making any uh ATP and energy and + + + align:start position:0% +about making any uh ATP and energy and +as we'll see later on um photosynthesis + + align:start position:0% +as we'll see later on um photosynthesis + + + align:start position:0% +as we'll see later on um photosynthesis +in cases that can be something to do + + align:start position:0% +in cases that can be something to do + + + align:start position:0% +in cases that can be something to do +with making um making reducing power for + + align:start position:0% +with making um making reducing power for + + + align:start position:0% +with making um making reducing power for +biosynthesis so uh in order to + + align:start position:0% +biosynthesis so uh in order to + + + align:start position:0% +biosynthesis so uh in order to +understand this though I have to + + align:start position:0% +understand this though I have to + + + align:start position:0% +understand this though I have to +introduce you to another way of thinking + + align:start position:0% +introduce you to another way of thinking + + + align:start position:0% +introduce you to another way of thinking +about energy some of you are still seem + + align:start position:0% +about energy some of you are still seem + + + align:start position:0% +about energy some of you are still seem +to be struggling with the idea that you + + align:start position:0% +to be struggling with the idea that you + + + align:start position:0% +to be struggling with the idea that you +can store energy in a chemical bond but + + align:start position:0% +can store energy in a chemical bond but + + + align:start position:0% +can store energy in a chemical bond but +I think from the comments the majority + + align:start position:0% +I think from the comments the majority + + + align:start position:0% +I think from the comments the majority +of you have that if you're having + + align:start position:0% +of you have that if you're having + + + align:start position:0% +of you have that if you're having +trouble ask your TA or look in sections + + align:start position:0% +trouble ask your TA or look in sections + + + align:start position:0% +trouble ask your TA or look in sections +and stuff but the insight to how this + + align:start position:0% +and stuff but the insight to how this + + + align:start position:0% +and stuff but the insight to how this +part part came even though this process + + align:start position:0% +part part came even though this process + + + align:start position:0% +part part came even though this process +the what underlies this was invented + + align:start position:0% +the what underlies this was invented + + + align:start position:0% +the what underlies this was invented +about roughly 3.4 billion years ago + + align:start position:0% +about roughly 3.4 billion years ago + + + align:start position:0% +about roughly 3.4 billion years ago +scientists didn't begin to even get a + + align:start position:0% +scientists didn't begin to even get a + + + align:start position:0% +scientists didn't begin to even get a +glimmer of how this worked until about + + align:start position:0% +glimmer of how this worked until about + + + align:start position:0% +glimmer of how this worked until about +1961 when there was a scientist named + + align:start position:0% +1961 when there was a scientist named + + + align:start position:0% +1961 when there was a scientist named +Peter Mitchell who got a Nobel Prize + + align:start position:0% + + + + align:start position:0% + +for the Insight that that he had and + + align:start position:0% +for the Insight that that he had and + + + align:start position:0% +for the Insight that that he had and +what he recognized that there were there + + align:start position:0% +what he recognized that there were there + + + align:start position:0% +what he recognized that there were there +sort of three forms of of energy that + + align:start position:0% +sort of three forms of of energy that + + + align:start position:0% +sort of three forms of of energy that +are + + align:start position:0% +are + + + align:start position:0% +are +interconvertible the energy of a + + align:start position:0% +interconvertible the energy of a + + + align:start position:0% +interconvertible the energy of a +chemical + + align:start position:0% +chemical + + + align:start position:0% +chemical +bond and I keep telling you this that + + align:start position:0% +bond and I keep telling you this that + + + align:start position:0% +bond and I keep telling you this that +ATP if we hydrolize that and goes to + + align:start position:0% +ATP if we hydrolize that and goes to + + + align:start position:0% +ATP if we hydrolize that and goes to +ATP plus inorganic phosphate the Delta + + align:start position:0% +ATP plus inorganic phosphate the Delta + + + align:start position:0% +ATP plus inorganic phosphate the Delta +the Delta G Prime Z is about minus 7 + + align:start position:0% +the Delta G Prime Z is about minus 7 + + + align:start position:0% +the Delta G Prime Z is about minus 7 +kilo calories per mole but under + + align:start position:0% +kilo calories per mole but under + + + align:start position:0% +kilo calories per mole but under +physiological conditions + + align:start position:0% + + + + align:start position:0% + +it works out that each ATP gets you + + align:start position:0% +it works out that each ATP gets you + + + align:start position:0% +it works out that each ATP gets you +about 12 kilo calories per mole because + + align:start position:0% +about 12 kilo calories per mole because + + + align:start position:0% +about 12 kilo calories per mole because +life doesn't happen under these under + + align:start position:0% +life doesn't happen under these under + + + align:start position:0% +life doesn't happen under these under +these standard conditions so that's one + + align:start position:0% +these standard conditions so that's one + + + align:start position:0% +these standard conditions so that's one +form of energy we've been talking a lot + + align:start position:0% +form of energy we've been talking a lot + + + align:start position:0% +form of energy we've been talking a lot +about it there's another form of energy + + align:start position:0% +about it there's another form of energy + + + align:start position:0% +about it there's another form of energy +which you probably know intuitively and + + align:start position:0% +which you probably know intuitively and + + + align:start position:0% +which you probably know intuitively and +that is if you have a high concentration + + align:start position:0% +that is if you have a high concentration + + + align:start position:0% +that is if you have a high concentration +of some compound on a side of a sort of + + align:start position:0% +of some compound on a side of a sort of + + + align:start position:0% +of some compound on a side of a sort of +impermeable barrier and a low + + align:start position:0% +impermeable barrier and a low + + + align:start position:0% +impermeable barrier and a low +concentration on the other side High + + align:start position:0% +concentration on the other side High + + + align:start position:0% +concentration on the other side High +concentration of sugar low concentration + + align:start position:0% +concentration of sugar low concentration + + + align:start position:0% +concentration of sugar low concentration +of sugar if you give the system a chance + + align:start position:0% +of sugar if you give the system a chance + + + align:start position:0% +of sugar if you give the system a chance +it'll come to equilibrium so the high + + align:start position:0% +it'll come to equilibrium so the high + + + align:start position:0% +it'll come to equilibrium so the high +the concentrated stuff will flow + + align:start position:0% +the concentrated stuff will flow + + + align:start position:0% +the concentrated stuff will flow +downhill until you're concentrated in + + align:start position:0% +downhill until you're concentrated in + + + align:start position:0% +downhill until you're concentrated in +both sides there's energy you could get + + align:start position:0% +both sides there's energy you could get + + + align:start position:0% +both sides there's energy you could get +out out of that so there's energy + + align:start position:0% +out out of that so there's energy + + + align:start position:0% +out out of that so there's energy +basically stored in a concentration + + align:start position:0% + + + + align:start position:0% + +gradient there's another form which + + align:start position:0% +gradient there's another form which + + + align:start position:0% +gradient there's another form which +you'll probably be familiar certainly to + + align:start position:0% +you'll probably be familiar certainly to + + + align:start position:0% +you'll probably be familiar certainly to +some of you and that's the idea you can + + align:start position:0% +some of you and that's the idea you can + + + align:start position:0% +some of you and that's the idea you can +store energy in an electrical + + align:start position:0% +store energy in an electrical + + + align:start position:0% +store energy in an electrical +gradient if you have + + align:start position:0% +gradient if you have + + + align:start position:0% +gradient if you have +some kind of impermeable barrier and we + + align:start position:0% +some kind of impermeable barrier and we + + + align:start position:0% +some kind of impermeable barrier and we +have a lot of charges on one side and + + align:start position:0% +have a lot of charges on one side and + + + align:start position:0% +have a lot of charges on one side and +less charges on the other side then is + + align:start position:0% +less charges on the other side then is + + + align:start position:0% +less charges on the other side then is +the polarity of an electrical gradient + + align:start position:0% +the polarity of an electrical gradient + + + align:start position:0% +the polarity of an electrical gradient +and that's a form of stored energy now + + align:start position:0% +and that's a form of stored energy now + + + align:start position:0% +and that's a form of stored energy now +it happens that a membrane is + + align:start position:0% +it happens that a membrane is + + + align:start position:0% +it happens that a membrane is +impermeable as I've told you to most + + align:start position:0% +impermeable as I've told you to most + + + align:start position:0% +impermeable as I've told you to most +things uh so you can get a high + + align:start position:0% +things uh so you can get a high + + + align:start position:0% +things uh so you can get a high +concentration of something on one side + + align:start position:0% +concentration of something on one side + + + align:start position:0% +concentration of something on one side +and low concentration in the other and + + align:start position:0% +and low concentration in the other and + + + align:start position:0% +and low concentration in the other and +control by a protein embedded in whether + + align:start position:0% +control by a protein embedded in whether + + + align:start position:0% +control by a protein embedded in whether +those ever get a chance to come across + + align:start position:0% +those ever get a chance to come across + + + align:start position:0% +those ever get a chance to come across +the same idea applies for for an + + align:start position:0% +the same idea applies for for an + + + align:start position:0% +the same idea applies for for an +electrical gradient and in particular of + + align:start position:0% +electrical gradient and in particular of + + + align:start position:0% +electrical gradient and in particular of +Interest the biology or hydrogen ions so + + align:start position:0% +Interest the biology or hydrogen ions so + + + align:start position:0% +Interest the biology or hydrogen ions so +if we have a situation like this we have + + align:start position:0% +if we have a situation like this we have + + + align:start position:0% +if we have a situation like this we have +more hydrogen ions on one side of a + + align:start position:0% +more hydrogen ions on one side of a + + + align:start position:0% +more hydrogen ions on one side of a +membrane than another then we have uh an + + align:start position:0% +membrane than another then we have uh an + + + align:start position:0% +membrane than another then we have uh an +electrical gradient we have a + + align:start position:0% +electrical gradient we have a + + + align:start position:0% +electrical gradient we have a +polarity and so this is the + + align:start position:0% + + + + align:start position:0% + +membrane and + + align:start position:0% +membrane and + + + align:start position:0% +membrane and +uh this so all cells then have + + align:start position:0% + + + + align:start position:0% + +and this is the way it works is this is + + align:start position:0% +and this is the way it works is this is + + + align:start position:0% +and this is the way it works is this is +the outside of the cell and this is the + + align:start position:0% +the outside of the cell and this is the + + + align:start position:0% +the outside of the cell and this is the +inside of the cell so more pluses on the + + align:start position:0% +inside of the cell so more pluses on the + + + align:start position:0% +inside of the cell so more pluses on the +outside hydrogen ions on the outside + + align:start position:0% +outside hydrogen ions on the outside + + + align:start position:0% +outside hydrogen ions on the outside +than the inside and it's about 70 M + + align:start position:0% +than the inside and it's about 70 M + + + align:start position:0% +than the inside and it's about 70 M +volts may not sound that impressive + + align:start position:0% +volts may not sound that impressive + + + align:start position:0% +volts may not sound that impressive +right another way to look at it though + + align:start position:0% +right another way to look at it though + + + align:start position:0% +right another way to look at it though +is the membrane + + align:start position:0% + + + + align:start position:0% + +is about 3 + + align:start position:0% +is about 3 + + + align:start position:0% +is about 3 +nanometers so you say well okay what's + + align:start position:0% +nanometers so you say well okay what's + + + align:start position:0% +nanometers so you say well okay what's +the what's the gradient of of uh + + align:start position:0% +the what's the gradient of of uh + + + align:start position:0% +the what's the gradient of of uh +electrical gradient across that it's + + align:start position:0% +electrical gradient across that it's + + + align:start position:0% +electrical gradient across that it's +about 200,000 + + align:start position:0% +about 200,000 + + + align:start position:0% +about 200,000 +volts per + + align:start position:0% +volts per + + + align:start position:0% +volts per +centimeter and high tension lines are + + align:start position:0% +centimeter and high tension lines are + + + align:start position:0% +centimeter and high tension lines are +you know more like that per mile or + + align:start position:0% +you know more like that per mile or + + + align:start position:0% +you know more like that per mile or +something like that so although it seems + + align:start position:0% +something like that so although it seems + + + align:start position:0% +something like that so although it seems +modest because the membranes you get a + + align:start position:0% +modest because the membranes you get a + + + align:start position:0% +modest because the membranes you get a +very very powerful electron uh + + align:start position:0% +very very powerful electron uh + + + align:start position:0% +very very powerful electron uh +electrical gradient in all cells and so + + align:start position:0% +electrical gradient in all cells and so + + + align:start position:0% +electrical gradient in all cells and so +this is a form of energy and I think + + align:start position:0% +this is a form of energy and I think + + + align:start position:0% +this is a form of energy and I think +this was this was proposed in + + align:start position:0% +this was this was proposed in + + + align:start position:0% +this was this was proposed in +1961 textbooks often say it was adopted + + align:start position:0% +1961 textbooks often say it was adopted + + + align:start position:0% +1961 textbooks often say it was adopted +in the early '70s I went to the postto + + align:start position:0% +in the early '70s I went to the postto + + + align:start position:0% +in the early '70s I went to the postto +at Berkeley in 1975 and people were + + align:start position:0% +at Berkeley in 1975 and people were + + + align:start position:0% +at Berkeley in 1975 and people were +still having arguments about whether + + align:start position:0% +still having arguments about whether + + + align:start position:0% +still having arguments about whether +this really was was the way was this + + align:start position:0% +this really was was the way was this + + + align:start position:0% +this really was was the way was this +really something that was used in nature + + align:start position:0% +really something that was used in nature + + + align:start position:0% +really something that was used in nature +it is and I think one of the one of the + + align:start position:0% +it is and I think one of the one of the + + + align:start position:0% +it is and I think one of the one of the +most dramatic demonstrations that a a + + align:start position:0% +most dramatic demonstrations that a a + + + align:start position:0% +most dramatic demonstrations that a a +proton gradient can be a source of + + align:start position:0% +proton gradient can be a source of + + + align:start position:0% +proton gradient can be a source of +energy comes from uh this sort of thing + + align:start position:0% +energy comes from uh this sort of thing + + + align:start position:0% +energy comes from uh this sort of thing +I showed you how these bacteria these + + align:start position:0% +I showed you how these bacteria these + + + align:start position:0% +I showed you how these bacteria these +are eoli in around with these rotary + + align:start position:0% +are eoli in around with these rotary + + + align:start position:0% +are eoli in around with these rotary +Motors that spin 10 to 100,000 RPM + + align:start position:0% +Motors that spin 10 to 100,000 RPM + + + align:start position:0% +Motors that spin 10 to 100,000 RPM +driving those fella I showed you the + + align:start position:0% +driving those fella I showed you the + + + align:start position:0% +driving those fella I showed you the +picture of the inner membrane of eoli + + align:start position:0% +picture of the inner membrane of eoli + + + align:start position:0% +picture of the inner membrane of eoli +and I mentioned it has a double membrane + + align:start position:0% +and I mentioned it has a double membrane + + + align:start position:0% +and I mentioned it has a double membrane +this is a sort of a protective layer + + align:start position:0% +this is a sort of a protective layer + + + align:start position:0% +this is a sort of a protective layer +you'll see a little bit later in the + + align:start position:0% +you'll see a little bit later in the + + + align:start position:0% +you'll see a little bit later in the +lecture some double membranes again and + + align:start position:0% +lecture some double membranes again and + + + align:start position:0% +lecture some double membranes again and +here's the the motor with the big + + align:start position:0% +here's the the motor with the big + + + align:start position:0% +here's the the motor with the big +propeller the Feller on fella sticking + + align:start position:0% +propeller the Feller on fella sticking + + + align:start position:0% +propeller the Feller on fella sticking +out from it and the way this thing and I + + align:start position:0% +out from it and the way this thing and I + + + align:start position:0% +out from it and the way this thing and I +showed you I guess this picture and then + + align:start position:0% +showed you I guess this picture and then + + + align:start position:0% +showed you I guess this picture and then +this textbook diagram what drives this + + align:start position:0% +this textbook diagram what drives this + + + align:start position:0% +this textbook diagram what drives this +motor is is are uh protons flowing from + + align:start position:0% +motor is is are uh protons flowing from + + + align:start position:0% +motor is is are uh protons flowing from +the outside of the cell through here + + align:start position:0% +the outside of the cell through here + + + align:start position:0% +the outside of the cell through here +through the proteins in here through + + align:start position:0% +through the proteins in here through + + + align:start position:0% +through the proteins in here through +channels in them and that's what + + align:start position:0% +channels in them and that's what + + + align:start position:0% +channels in them and that's what +provides the the torque for the motor + + align:start position:0% +provides the the torque for the motor + + + align:start position:0% +provides the the torque for the motor +that's what drives it it's not ATP or + + align:start position:0% +that's what drives it it's not ATP or + + + align:start position:0% +that's what drives it it's not ATP or +anything it's protons in the outside of + + align:start position:0% +anything it's protons in the outside of + + + align:start position:0% +anything it's protons in the outside of +the inside and there's a very dramatic + + align:start position:0% +the inside and there's a very dramatic + + + align:start position:0% +the inside and there's a very dramatic +demonstration of sort of like you know + + align:start position:0% +demonstration of sort of like you know + + + align:start position:0% +demonstration of sort of like you know +Friday Night horror films if you wanted + + align:start position:0% +Friday Night horror films if you wanted + + + align:start position:0% +Friday Night horror films if you wanted +some well way where people found a way + + align:start position:0% +some well way where people found a way + + + align:start position:0% +some well way where people found a way +of popping it an eoli open so like all + + align:start position:0% +of popping it an eoli open so like all + + + align:start position:0% +of popping it an eoli open so like all +of the cytoplasm run out and then it + + align:start position:0% +of the cytoplasm run out and then it + + + align:start position:0% +of the cytoplasm run out and then it +would recal so what you've got is sort + + align:start position:0% +would recal so what you've got is sort + + + align:start position:0% +would recal so what you've got is sort +of an eoli that is just a shell just the + + align:start position:0% +of an eoli that is just a shell just the + + + align:start position:0% +of an eoli that is just a shell just the +membranes and the proteins embedded in + + align:start position:0% +membranes and the proteins embedded in + + + align:start position:0% +membranes and the proteins embedded in +it and it just sits there at neutral pH + + align:start position:0% +it and it just sits there at neutral pH + + + align:start position:0% +it and it just sits there at neutral pH +if you now acidify the + + align:start position:0% +if you now acidify the + + + align:start position:0% +if you now acidify the +medium what's happening you've created a + + align:start position:0% +medium what's happening you've created a + + + align:start position:0% +medium what's happening you've created a +proton gradient because they're now more + + align:start position:0% +proton gradient because they're now more + + + align:start position:0% +proton gradient because they're now more +protons on the outside and this is just + + align:start position:0% +protons on the outside and this is just + + + align:start position:0% +protons on the outside and this is just +the same P the same picture I showed you + + align:start position:0% +the same P the same picture I showed you + + + align:start position:0% +the same P the same picture I showed you +before but what happens if you do that + + align:start position:0% +before but what happens if you do that + + + align:start position:0% +before but what happens if you do that +experiment is the bacteria start + + align:start position:0% +experiment is the bacteria start + + + align:start position:0% +experiment is the bacteria start +swimming they don't have any insides or + + align:start position:0% +swimming they don't have any insides or + + + align:start position:0% +swimming they don't have any insides or +anything but you have created + + align:start position:0% +anything but you have created + + + align:start position:0% +anything but you have created +artificially a proton gradient and it + + align:start position:0% +artificially a proton gradient and it + + + align:start position:0% +artificially a proton gradient and it +drives the motor and they start swimming + + align:start position:0% +drives the motor and they start swimming + + + align:start position:0% +drives the motor and they start swimming +it's sort of like you know Dead Men + + align:start position:0% +it's sort of like you know Dead Men + + + align:start position:0% +it's sort of like you know Dead Men +Walking or something at a at a bacterial + + align:start position:0% +Walking or something at a at a bacterial + + + align:start position:0% +Walking or something at a at a bacterial +level I think it's a really dramatic + + align:start position:0% +level I think it's a really dramatic + + + align:start position:0% +level I think it's a really dramatic +demonstration of of uh how you can use + + align:start position:0% +demonstration of of uh how you can use + + + align:start position:0% +demonstration of of uh how you can use +the energy of a proton gradient to make + + align:start position:0% +the energy of a proton gradient to make + + + align:start position:0% +the energy of a proton gradient to make +to make energy so the principle that + + align:start position:0% +to make energy so the principle that + + + align:start position:0% +to make energy so the principle that +underlies how respiration works and um + + align:start position:0% +underlies how respiration works and um + + + align:start position:0% +underlies how respiration works and um +photosynthesis works is that you take + + align:start position:0% +photosynthesis works is that you take + + + align:start position:0% +photosynthesis works is that you take +advantage of this combination of + + align:start position:0% +advantage of this combination of + + + align:start position:0% +advantage of this combination of +concentration and electrical gradient + + align:start position:0% +concentration and electrical gradient + + + align:start position:0% +concentration and electrical gradient +and it's known as + + align:start position:0% +and it's known as + + + align:start position:0% +and it's known as +the this is known as the + + align:start position:0% + + + + align:start position:0% + +Chimas osmotic hypothesis because you + + align:start position:0% +Chimas osmotic hypothesis because you + + + align:start position:0% +Chimas osmotic hypothesis because you +have here you have an electrical + + align:start position:0% +have here you have an electrical + + + align:start position:0% +have here you have an electrical +gradient because of the charges you also + + align:start position:0% +gradient because of the charges you also + + + align:start position:0% +gradient because of the charges you also +have a concentration gradient because + + align:start position:0% +have a concentration gradient because + + + align:start position:0% +have a concentration gradient because +you got more hydrogen ions on this side + + align:start position:0% +you got more hydrogen ions on this side + + + align:start position:0% +you got more hydrogen ions on this side +so you can't really separate them and + + align:start position:0% +so you can't really separate them and + + + align:start position:0% +so you can't really separate them and +they're kind of coupled but this idea is + + align:start position:0% +they're kind of coupled but this idea is + + + align:start position:0% +they're kind of coupled but this idea is +that life uses this proton gradient in + + align:start position:0% +that life uses this proton gradient in + + + align:start position:0% +that life uses this proton gradient in +order to make make energy and do some of + + align:start position:0% +order to make make energy and do some of + + + align:start position:0% +order to make make energy and do some of +these energy transactions so here's the + + align:start position:0% +these energy transactions so here's the + + + align:start position:0% +these energy transactions so here's the +sort of principle of how it it's done is + + align:start position:0% +sort of principle of how it it's done is + + + align:start position:0% +sort of principle of how it it's done is +you have a membrane like this then we + + align:start position:0% +you have a membrane like this then we + + + align:start position:0% +you have a membrane like this then we +have a protein and now we're not going + + align:start position:0% +have a protein and now we're not going + + + align:start position:0% +have a protein and now we're not going +to see all the alpha Hiles and beta + + align:start position:0% +to see all the alpha Hiles and beta + + + align:start position:0% +to see all the alpha Hiles and beta +sheets it'll be one of those things we + + align:start position:0% +sheets it'll be one of those things we + + + align:start position:0% +sheets it'll be one of those things we +talked about that that spans the + + align:start position:0% +talked about that that spans the + + + align:start position:0% +talked about that that spans the +membrane the membrane as you might guess + + align:start position:0% +membrane the membrane as you might guess + + + align:start position:0% +membrane the membrane as you might guess +from what you know about it is imper + + align:start position:0% +from what you know about it is imper + + + align:start position:0% +from what you know about it is imper +impermeable to hydrogen ions so that + + align:start position:0% +impermeable to hydrogen ions so that + + + align:start position:0% +impermeable to hydrogen ions so that +what this protein does that's embedded + + align:start position:0% +what this protein does that's embedded + + + align:start position:0% +what this protein does that's embedded +in the membrane it's a proton pump + + align:start position:0% +in the membrane it's a proton pump + + + align:start position:0% +in the membrane it's a proton pump +and if you provide it with energy in + + align:start position:0% +and if you provide it with energy in + + + align:start position:0% +and if you provide it with energy in +some form what it does is it takes a + + align:start position:0% +some form what it does is it takes a + + + align:start position:0% +some form what it does is it takes a +hydrogen ion that's on the inside and it + + align:start position:0% +hydrogen ion that's on the inside and it + + + align:start position:0% +hydrogen ion that's on the inside and it +makes it into a hydrogen + + align:start position:0% +makes it into a hydrogen + + + align:start position:0% +makes it into a hydrogen +ion on the outside there's no chemical + + align:start position:0% +ion on the outside there's no chemical + + + align:start position:0% +ion on the outside there's no chemical +transformation of the proton it's just + + align:start position:0% +transformation of the proton it's just + + + align:start position:0% +transformation of the proton it's just +gone from one side of the membrane to + + align:start position:0% +gone from one side of the membrane to + + + align:start position:0% +gone from one side of the membrane to +the other it's almost like recharging a + + align:start position:0% +the other it's almost like recharging a + + + align:start position:0% +the other it's almost like recharging a +battery or something if you want to + + align:start position:0% +battery or something if you want to + + + align:start position:0% +battery or something if you want to +think about it perhaps in that kind of + + align:start position:0% +think about it perhaps in that kind of + + + align:start position:0% +think about it perhaps in that kind of +way and that's uh then the second stage + + align:start position:0% + + + + align:start position:0% + +is once the proton gradient is + + align:start position:0% +is once the proton gradient is + + + align:start position:0% +is once the proton gradient is +established and you have now many more + + align:start position:0% +established and you have now many more + + + align:start position:0% +established and you have now many more +H+ on the + + align:start position:0% + + + + align:start position:0% + +outside then on the inside then there's + + align:start position:0% +outside then on the inside then there's + + + align:start position:0% +outside then on the inside then there's +another + + align:start position:0% + + + + align:start position:0% + +protein that lets the en lets the + + align:start position:0% +protein that lets the en lets the + + + align:start position:0% +protein that lets the en lets the +proton + + align:start position:0% + + + + align:start position:0% + +flow the proton flows down + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +gradient and therefore is able to come + + align:start position:0% +gradient and therefore is able to come + + + align:start position:0% +gradient and therefore is able to come +back inside the cell now if that's all + + align:start position:0% +back inside the cell now if that's all + + + align:start position:0% +back inside the cell now if that's all +there was to it we wouldn't have + + align:start position:0% +there was to it we wouldn't have + + + align:start position:0% +there was to it we wouldn't have +achieved anything we would have wasted + + align:start position:0% +achieved anything we would have wasted + + + align:start position:0% +achieved anything we would have wasted +energy pumped something out pumped + + align:start position:0% +energy pumped something out pumped + + + align:start position:0% +energy pumped something out pumped +something back but this uh molecule + + align:start position:0% +something back but this uh molecule + + + align:start position:0% +something back but this uh molecule +has an interesting property and that is + + align:start position:0% +has an interesting property and that is + + + align:start position:0% +has an interesting property and that is +the ability of the of the proton to flow + + align:start position:0% +the ability of the of the proton to flow + + + align:start position:0% +the ability of the of the proton to flow +down the gradient uh is obligatorily + + align:start position:0% +down the gradient uh is obligatorily + + + align:start position:0% +down the gradient uh is obligatorily +requires 0 80 p plus uh phospho + + align:start position:0% +requires 0 80 p plus uh phospho + + + align:start position:0% +requires 0 80 p plus uh phospho +inorganic phosphate and as the uh proton + + align:start position:0% +inorganic phosphate and as the uh proton + + + align:start position:0% +inorganic phosphate and as the uh proton +comes down this energy gradient there's + + align:start position:0% +comes down this energy gradient there's + + + align:start position:0% +comes down this energy gradient there's +enough energy given off by that that the + + align:start position:0% +enough energy given off by that that the + + + align:start position:0% +enough energy given off by that that the +cell is able to cap capture it and use + + align:start position:0% +cell is able to cap capture it and use + + + align:start position:0% +cell is able to cap capture it and use +that energy to synthesize a molecule of + + align:start position:0% +that energy to synthesize a molecule of + + + align:start position:0% +that energy to synthesize a molecule of +ATP got it so proton come you do some + + align:start position:0% +ATP got it so proton come you do some + + + align:start position:0% +ATP got it so proton come you do some +energy like from light and + + align:start position:0% +energy like from light and + + + align:start position:0% +energy like from light and +photosynthesis or we'll see in a minute + + align:start position:0% +photosynthesis or we'll see in a minute + + + align:start position:0% +photosynthesis or we'll see in a minute +otherwis dant and then get it outside + + align:start position:0% +otherwis dant and then get it outside + + + align:start position:0% +otherwis dant and then get it outside +once you got the gradient now you can + + align:start position:0% +once you got the gradient now you can + + + align:start position:0% +once you got the gradient now you can +make ATP + + align:start position:0% +make ATP + + + align:start position:0% +make ATP +and actually one of the completely + + align:start position:0% +and actually one of the completely + + + align:start position:0% +and actually one of the completely +remarkable discoveries of of structural + + align:start position:0% +remarkable discoveries of of structural + + + align:start position:0% +remarkable discoveries of of structural +biology this is this is known as an + + align:start position:0% + + + + align:start position:0% + +ATP + + align:start position:0% + + + + align:start position:0% + +synthes it's a + + align:start position:0% +synthes it's a + + + align:start position:0% +synthes it's a +protein it's an enzyme those kinds of + + align:start position:0% +protein it's an enzyme those kinds of + + + align:start position:0% +protein it's an enzyme those kinds of +things we talking about this is also a + + align:start position:0% + + + + align:start position:0% + +protein see all the different things + + align:start position:0% +protein see all the different things + + + align:start position:0% +protein see all the different things +proteins do um uh + + align:start position:0% +proteins do um uh + + + align:start position:0% +proteins do um uh +so this ATP synthes which uses this + + align:start position:0% +so this ATP synthes which uses this + + + align:start position:0% +so this ATP synthes which uses this +energy of the proton gradient to make + + align:start position:0% +energy of the proton gradient to make + + + align:start position:0% +energy of the proton gradient to make +ATP it structure has been worked out and + + align:start position:0% +ATP it structure has been worked out and + + + align:start position:0% +ATP it structure has been worked out and +at a at a level here's part of the + + align:start position:0% +at a at a level here's part of the + + + align:start position:0% +at a at a level here's part of the +crystal structure you can probably see + + align:start position:0% +crystal structure you can probably see + + + align:start position:0% +crystal structure you can probably see +some Alpha heles Beta sheets here's a + + align:start position:0% +some Alpha heles Beta sheets here's a + + + align:start position:0% +some Alpha heles Beta sheets here's a +textbook diagram of it showing the it's + + align:start position:0% +textbook diagram of it showing the it's + + + align:start position:0% +textbook diagram of it showing the it's +upside down from I'm showing you but + + align:start position:0% +upside down from I'm showing you but + + + align:start position:0% +upside down from I'm showing you but +here's a a proton on the inside flowing + + align:start position:0% +here's a a proton on the inside flowing + + + align:start position:0% +here's a a proton on the inside flowing +across and what's remarkable is it turns + + align:start position:0% +across and what's remarkable is it turns + + + align:start position:0% +across and what's remarkable is it turns +out that this uh ATP synthes is + + align:start position:0% +out that this uh ATP synthes is + + + align:start position:0% +out that this uh ATP synthes is +structurally related to the protein + + align:start position:0% +structurally related to the protein + + + align:start position:0% +structurally related to the protein +that's at the heart of that rotary motor + + align:start position:0% +that's at the heart of that rotary motor + + + align:start position:0% +that's at the heart of that rotary motor +that drives the fella and in fact this + + align:start position:0% +that drives the fella and in fact this + + + align:start position:0% +that drives the fella and in fact this +is remember I think I showed you where + + align:start position:0% +is remember I think I showed you where + + + align:start position:0% +is remember I think I showed you where +you could stick the fella to a cover + + align:start position:0% +you could stick the fella to a cover + + + align:start position:0% +you could stick the fella to a cover +slip and the bacteria twirled around so + + align:start position:0% +slip and the bacteria twirled around so + + + align:start position:0% +slip and the bacteria twirled around so +you could actually see they were + + align:start position:0% +you could actually see they were + + + align:start position:0% +you could actually see they were +rotating so people did sort of the + + align:start position:0% +rotating so people did sort of the + + + align:start position:0% +rotating so people did sort of the +equivalent thing they managed to stick + + align:start position:0% +equivalent thing they managed to stick + + + align:start position:0% +equivalent thing they managed to stick +this ATP synthes and then in order to + + align:start position:0% +this ATP synthes and then in order to + + + align:start position:0% +this ATP synthes and then in order to +see you couldn't see that the top part + + align:start position:0% +see you couldn't see that the top part + + + align:start position:0% +see you couldn't see that the top part +was turning but they used some tricky + + align:start position:0% +was turning but they used some tricky + + + align:start position:0% +was turning but they used some tricky +stuff we'll talk about with antibodies + + align:start position:0% +stuff we'll talk about with antibodies + + + align:start position:0% +stuff we'll talk about with antibodies +and something else to attach a long + + align:start position:0% +and something else to attach a long + + + align:start position:0% +and something else to attach a long +filamentous molecule it's is a polymer + + align:start position:0% +filamentous molecule it's is a polymer + + + align:start position:0% +filamentous molecule it's is a polymer +of different of protein called actin + + align:start position:0% +of different of protein called actin + + + align:start position:0% +of different of protein called actin +that's the same stuff we find in our + + align:start position:0% +that's the same stuff we find in our + + + align:start position:0% +that's the same stuff we find in our +muscles and it made it long enough you + + align:start position:0% +muscles and it made it long enough you + + + align:start position:0% +muscles and it made it long enough you +could see that when this thing was + + align:start position:0% +could see that when this thing was + + + align:start position:0% +could see that when this thing was +working that it was twirling around and + + align:start position:0% +working that it was twirling around and + + + align:start position:0% +working that it was twirling around and +so Evolution took the same basic sort of + + align:start position:0% +so Evolution took the same basic sort of + + + align:start position:0% +so Evolution took the same basic sort of +piece of protein machinery and in one + + align:start position:0% +piece of protein machinery and in one + + + align:start position:0% +piece of protein machinery and in one +case it used it to capture the energy of + + align:start position:0% +case it used it to capture the energy of + + + align:start position:0% +case it used it to capture the energy of +a proton gradient and make ATP and in + + align:start position:0% +a proton gradient and make ATP and in + + + align:start position:0% +a proton gradient and make ATP and in +another case it used it to drive this + + align:start position:0% +another case it used it to drive this + + + align:start position:0% +another case it used it to drive this +this propeller if you + + align:start position:0% +this propeller if you + + + align:start position:0% +this propeller if you +will um and here's a sort of a a simple + + align:start position:0% +will um and here's a sort of a a simple + + + align:start position:0% +will um and here's a sort of a a simple +sort of diagram so as the proton flows + + align:start position:0% +sort of diagram so as the proton flows + + + align:start position:0% +sort of diagram so as the proton flows +kind of what happens is this the inner + + align:start position:0% +kind of what happens is this the inner + + + align:start position:0% +kind of what happens is this the inner +part of this thing sort of whirls sort + + align:start position:0% +part of this thing sort of whirls sort + + + align:start position:0% +part of this thing sort of whirls sort +of goes click click and every time it + + align:start position:0% +of goes click click and every time it + + + align:start position:0% +of goes click click and every time it +does it it synthesizes an ATP and it + + align:start position:0% +does it it synthesizes an ATP and it + + + align:start position:0% +does it it synthesizes an ATP and it +sort of takes that energy to push + + align:start position:0% +sort of takes that energy to push + + + align:start position:0% +sort of takes that energy to push +together the uh the ADP and the + + align:start position:0% +together the uh the ADP and the + + + align:start position:0% +together the uh the ADP and the +inorganic phosphate overcoming that + + align:start position:0% +inorganic phosphate overcoming that + + + align:start position:0% +inorganic phosphate overcoming that +activation energy and getting them close + + align:start position:0% +activation energy and getting them close + + + align:start position:0% +activation energy and getting them close +enough that you're able to get that Bond + + align:start position:0% +enough that you're able to get that Bond + + + align:start position:0% +enough that you're able to get that Bond +it's a it's a truly remarkable thing + + align:start position:0% +it's a it's a truly remarkable thing + + + align:start position:0% +it's a it's a truly remarkable thing +this is a somewhat hard concept to grasp + + align:start position:0% +this is a somewhat hard concept to grasp + + + align:start position:0% +this is a somewhat hard concept to grasp +I understand but if you can understand + + align:start position:0% +I understand but if you can understand + + + align:start position:0% +I understand but if you can understand +this interconvertibility between energy + + align:start position:0% +this interconvertibility between energy + + + align:start position:0% +this interconvertibility between energy +in the form of a concent combined + + align:start position:0% +in the form of a concent combined + + + align:start position:0% +in the form of a concent combined +concentration and electrical GR + + align:start position:0% +concentration and electrical GR + + + align:start position:0% +concentration and electrical GR +and ATP and nature goes back and forth + + align:start position:0% +and ATP and nature goes back and forth + + + align:start position:0% +and ATP and nature goes back and forth +and back and forth and it's absolutely + + align:start position:0% +and back and forth and it's absolutely + + + align:start position:0% +and back and forth and it's absolutely +fundamental to life if we didn't have + + align:start position:0% +fundamental to life if we didn't have + + + align:start position:0% +fundamental to life if we didn't have +this stuff going on we couldn't do it + + align:start position:0% +this stuff going on we couldn't do it + + + align:start position:0% +this stuff going on we couldn't do it +you know as I say with glycolysis I wish + + align:start position:0% +you know as I say with glycolysis I wish + + + align:start position:0% +you know as I say with glycolysis I wish +it was simpler but this is the way + + align:start position:0% +it was simpler but this is the way + + + align:start position:0% +it was simpler but this is the way +nature did it this is the way we are and + + align:start position:0% +nature did it this is the way we are and + + + align:start position:0% +nature did it this is the way we are and +if you want know about biology this is + + align:start position:0% +if you want know about biology this is + + + align:start position:0% +if you want know about biology this is +how how it goes and I wouldn't be doing + + align:start position:0% +how how it goes and I wouldn't be doing + + + align:start position:0% +how how it goes and I wouldn't be doing +a Justice if I didn't tell you some of + + align:start position:0% +a Justice if I didn't tell you some of + + + align:start position:0% +a Justice if I didn't tell you some of +the details your MIT students you should + + align:start position:0% +the details your MIT students you should + + + align:start position:0% +the details your MIT students you should +be able to handle I hope some of how uh + + align:start position:0% +be able to handle I hope some of how uh + + + align:start position:0% +be able to handle I hope some of how uh +the world actually works at this at this + + align:start position:0% +the world actually works at this at this + + + align:start position:0% +the world actually works at this at this +kind of level okay now uh with that kind + + align:start position:0% +kind of level okay now uh with that kind + + + align:start position:0% +kind of level okay now uh with that kind +of background now I think we can kind of + + align:start position:0% +of background now I think we can kind of + + + align:start position:0% +of background now I think we can kind of +pretty quickly I can help you begin to + + align:start position:0% +pretty quickly I can help you begin to + + + align:start position:0% +pretty quickly I can help you begin to +see what happens here now remember the + + align:start position:0% +see what happens here now remember the + + + align:start position:0% +see what happens here now remember the +problem up there with glycolysis it + + align:start position:0% +problem up there with glycolysis it + + + align:start position:0% +problem up there with glycolysis it +started when there was no oxygen and + + align:start position:0% +started when there was no oxygen and + + + align:start position:0% +started when there was no oxygen and +therefore it generated these nadhs that + + align:start position:0% +therefore it generated these nadhs that + + + align:start position:0% +therefore it generated these nadhs that +weren't any good you had to just get rid + + align:start position:0% +weren't any good you had to just get rid + + + align:start position:0% +weren't any good you had to just get rid +of them so you took the Pyro organisms + + align:start position:0% +of them so you took the Pyro organisms + + + align:start position:0% +of them so you took the Pyro organisms +learned how to um put them to make + + align:start position:0% +learned how to um put them to make + + + align:start position:0% +learned how to um put them to make +lactate or or ethanol and carbon dioxide + + align:start position:0% +lactate or or ethanol and carbon dioxide + + + align:start position:0% +lactate or or ethanol and carbon dioxide +but if there's oxygen around then + + align:start position:0% +but if there's oxygen around then + + + align:start position:0% +but if there's oxygen around then +there's another um another possibility + + align:start position:0% +there's another um another possibility + + + align:start position:0% +there's another um another possibility +and that is you can combine these + + align:start position:0% +and that is you can combine these + + + align:start position:0% +and that is you can combine these +um these molecules with oxygen so if we + + align:start position:0% +um these molecules with oxygen so if we + + + align:start position:0% +um these molecules with oxygen so if we +take 2 + + align:start position:0% + + + + align:start position:0% + +nadh plus two hydrogen + + align:start position:0% +nadh plus two hydrogen + + + align:start position:0% +nadh plus two hydrogen +ions plus a molecule of oxygen what we + + align:start position:0% +ions plus a molecule of oxygen what we + + + align:start position:0% +ions plus a molecule of oxygen what we +get out is two + + align:start position:0% +get out is two + + + align:start position:0% +get out is two +waters and I think I can show you what's + + align:start position:0% +waters and I think I can show you what's + + + align:start position:0% +waters and I think I can show you what's +going on there kind of Simply if we what + + align:start position:0% +going on there kind of Simply if we what + + + align:start position:0% +going on there kind of Simply if we what +nadh was we got a pair of electrons + + align:start position:0% +nadh was we got a pair of electrons + + + align:start position:0% +nadh was we got a pair of electrons +here and a hydrogen ion well if we took + + align:start position:0% +here and a hydrogen ion well if we took + + + align:start position:0% +here and a hydrogen ion well if we took +that what's that I think you recognize + + align:start position:0% +that what's that I think you recognize + + + align:start position:0% +that what's that I think you recognize +it as a hydrogen a molecule of hydrogen + + align:start position:0% +it as a hydrogen a molecule of hydrogen + + + align:start position:0% +it as a hydrogen a molecule of hydrogen +gas so if you take + + align:start position:0% +gas so if you take + + + align:start position:0% +gas so if you take +nadh and oxygen what the cell is really + + align:start position:0% +nadh and oxygen what the cell is really + + + align:start position:0% +nadh and oxygen what the cell is really +essentially doing it's taking hydrogen + + align:start position:0% +essentially doing it's taking hydrogen + + + align:start position:0% +essentially doing it's taking hydrogen +gas plus oxygen and it's giving two + + align:start position:0% +gas plus oxygen and it's giving two + + + align:start position:0% +gas plus oxygen and it's giving two +waters so it's basically burning + + align:start position:0% +waters so it's basically burning + + + align:start position:0% +waters so it's basically burning +hydrogen I think most of you knew what + + align:start position:0% +hydrogen I think most of you knew what + + + align:start position:0% +hydrogen I think most of you knew what +would happen if I had some a mixture of + + align:start position:0% +would happen if I had some a mixture of + + + align:start position:0% +would happen if I had some a mixture of +hydrogen oxygen up here and check to + + align:start position:0% +hydrogen oxygen up here and check to + + + align:start position:0% +hydrogen oxygen up here and check to +match at it or something we'd have a + + align:start position:0% +match at it or something we'd have a + + + align:start position:0% +match at it or something we'd have a +massive explosion and in fact that's why + + align:start position:0% +massive explosion and in fact that's why + + + align:start position:0% +massive explosion and in fact that's why +there's 50 kilo calories of of energy + + align:start position:0% +there's 50 kilo calories of of energy + + + align:start position:0% +there's 50 kilo calories of of energy +released when that happens and so on an + + align:start position:0% +released when that happens and so on an + + + align:start position:0% +released when that happens and so on an +energy sort of diagram these free- + + align:start position:0% +energy sort of diagram these free- + + + align:start position:0% +energy sort of diagram these free- +energy diagrams we had the 2 + + align:start position:0% +energy diagrams we had the 2 + + + align:start position:0% +energy diagrams we had the 2 +nadh uh here plus the molecule of oxygen + + align:start position:0% +nadh uh here plus the molecule of oxygen + + + align:start position:0% +nadh uh here plus the molecule of oxygen +and down here we have the uh two + + align:start position:0% +and down here we have the uh two + + + align:start position:0% +and down here we have the uh two +molecules of water there is this if that + + align:start position:0% +molecules of water there is this if that + + + align:start position:0% +molecules of water there is this if that +happened in one step it'd be a huge + + align:start position:0% +happened in one step it'd be a huge + + + align:start position:0% +happened in one step it'd be a huge +amount of energy no cell or organism in + + align:start position:0% +amount of energy no cell or organism in + + + align:start position:0% +amount of energy no cell or organism in +Earth has figured out how to do that in + + align:start position:0% +Earth has figured out how to do that in + + + align:start position:0% +Earth has figured out how to do that in +one step and I think some of the + + align:start position:0% +one step and I think some of the + + + align:start position:0% +one step and I think some of the +textbooks liken it to sort of Set It + + align:start position:0% +textbooks liken it to sort of Set It + + + align:start position:0% +textbooks liken it to sort of Set It +would be like setting a stick of + + align:start position:0% +would be like setting a stick of + + + align:start position:0% +would be like setting a stick of +dynamite off in the cell and this is + + align:start position:0% +dynamite off in the cell and this is + + + align:start position:0% +dynamite off in the cell and this is +where one of these things that seemed + + align:start position:0% +where one of these things that seemed + + + align:start position:0% +where one of these things that seemed +um probably like a kind of uninteresting + + align:start position:0% +um probably like a kind of uninteresting + + + align:start position:0% +um probably like a kind of uninteresting +ther thermodynamic property to to some + + align:start position:0% +ther thermodynamic property to to some + + + align:start position:0% +ther thermodynamic property to to some +extent becomes to be really important in + + align:start position:0% +extent becomes to be really important in + + + align:start position:0% +extent becomes to be really important in +understanding biology and that is the + + align:start position:0% +understanding biology and that is the + + + align:start position:0% +understanding biology and that is the +fact that remember I said this this drop + + align:start position:0% +fact that remember I said this this drop + + + align:start position:0% +fact that remember I said this this drop +in energy from reactants the products + + align:start position:0% +in energy from reactants the products + + + align:start position:0% +in energy from reactants the products +was a thermodynamic Pro thermodynamic + + align:start position:0% +was a thermodynamic Pro thermodynamic + + + align:start position:0% +was a thermodynamic Pro thermodynamic +property it didn't matter whether like + + align:start position:0% +property it didn't matter whether like + + + align:start position:0% +property it didn't matter whether like +you skied straight down the hill or you + + align:start position:0% +you skied straight down the hill or you + + + align:start position:0% +you skied straight down the hill or you +came down in a series of little things + + align:start position:0% +came down in a series of little things + + + align:start position:0% +came down in a series of little things +you still got the same amount of energy + + align:start position:0% +you still got the same amount of energy + + + align:start position:0% +you still got the same amount of energy +released going from here down to there + + align:start position:0% +released going from here down to there + + + align:start position:0% +released going from here down to there +so that's in essence what the cell does + + align:start position:0% +so that's in essence what the cell does + + + align:start position:0% +so that's in essence what the cell does +is it breaks this takes this energy and + + align:start position:0% +is it breaks this takes this energy and + + + align:start position:0% +is it breaks this takes this energy and +it breaks it into little packages that + + align:start position:0% +it breaks it into little packages that + + + align:start position:0% +it breaks it into little packages that +it's able to manage in a chemical way + + align:start position:0% +it's able to manage in a chemical way + + + align:start position:0% +it's able to manage in a chemical way +and so instead of coming down at once it + + align:start position:0% +and so instead of coming down at once it + + + align:start position:0% +and so instead of coming down at once it +comes down in a series of steps and + + align:start position:0% +comes down in a series of steps and + + + align:start position:0% +comes down in a series of steps and +every time it flows partway downhill it + + align:start position:0% +every time it flows partway downhill it + + + align:start position:0% +every time it flows partway downhill it +does something and what it does is it + + align:start position:0% +does something and what it does is it + + + align:start position:0% +does something and what it does is it +passes two + + align:start position:0% +passes two + + + align:start position:0% +passes two +electrons to some kind of carrier and + + align:start position:0% +electrons to some kind of carrier and + + + align:start position:0% +electrons to some kind of carrier and +then the two electrons flow downhill a + + align:start position:0% +then the two electrons flow downhill a + + + align:start position:0% +then the two electrons flow downhill a +little bit to another one and then to + + align:start position:0% +little bit to another one and then to + + + align:start position:0% +little bit to another one and then to +another one and what happens when the + + align:start position:0% +another one and what happens when the + + + align:start position:0% +another one and what happens when the +when this these electrons are flowing + + align:start position:0% +when this these electrons are flowing + + + align:start position:0% +when this these electrons are flowing +downhill though is that they drive that + + align:start position:0% +downhill though is that they drive that + + + align:start position:0% +downhill though is that they drive that +proton pump so a proton + + align:start position:0% +proton pump so a proton + + + align:start position:0% +proton pump so a proton +pump takes the proton from being on the + + align:start position:0% +pump takes the proton from being on the + + + align:start position:0% +pump takes the proton from being on the +outside to the inside and then next when + + align:start position:0% +outside to the inside and then next when + + + align:start position:0% +outside to the inside and then next when +the two electrons drop down to the next + + align:start position:0% +the two electrons drop down to the next + + + align:start position:0% +the two electrons drop down to the next +level another H+ goes from out to H+ in + + align:start position:0% +level another H+ goes from out to H+ in + + + align:start position:0% +level another H+ goes from out to H+ in +again + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +um and if you understood what I said + + align:start position:0% +um and if you understood what I said + + + align:start position:0% +um and if you understood what I said +before what the cell can now do is it + + align:start position:0% +before what the cell can now do is it + + + align:start position:0% +before what the cell can now do is it +can + + align:start position:0% +can + + + align:start position:0% +can +make three atps by using that ATP + + align:start position:0% +make three atps by using that ATP + + + align:start position:0% +make three atps by using that ATP +synthesis and now taking advantage of + + align:start position:0% +synthesis and now taking advantage of + + + align:start position:0% +synthesis and now taking advantage of +those three pump proteins and making + + align:start position:0% +those three pump proteins and making + + + align:start position:0% +those three pump proteins and making +them into into three + + align:start position:0% +them into into three + + + align:start position:0% +them into into three +atps and then at the uh at the end of + + align:start position:0% +atps and then at the uh at the end of + + + align:start position:0% +atps and then at the uh at the end of +the day what happens then is you this uh + + align:start position:0% +the day what happens then is you this uh + + + align:start position:0% +the day what happens then is you this uh +these two electrons get together with + + align:start position:0% +these two electrons get together with + + + align:start position:0% +these two electrons get together with +two hydrogen ions plus I'll show it as a + + align:start position:0% +two hydrogen ions plus I'll show it as a + + + align:start position:0% +two hydrogen ions plus I'll show it as a +half of a oxygen here to give + + align:start position:0% +half of a oxygen here to give + + + align:start position:0% +half of a oxygen here to give +you water and what's happening up here + + align:start position:0% +you water and what's happening up here + + + align:start position:0% +you water and what's happening up here +is in essence the molecule of + + align:start position:0% +is in essence the molecule of + + + align:start position:0% +is in essence the molecule of +uh sugar C6 h126 is being burned with + + align:start position:0% +uh sugar C6 h126 is being burned with + + + align:start position:0% +uh sugar C6 h126 is being burned with +six molecules of + + align:start position:0% +six molecules of + + + align:start position:0% +six molecules of +water plus this to give you six + + align:start position:0% +water plus this to give you six + + + align:start position:0% +water plus this to give you six +molecules of + + align:start position:0% +molecules of + + + align:start position:0% +molecules of +CO2 plus six molecules of uh ATP so the + + align:start position:0% +CO2 plus six molecules of uh ATP so the + + + align:start position:0% +CO2 plus six molecules of uh ATP so the +the cell is + + align:start position:0% +the cell is + + + align:start position:0% +the cell is +essentially achieving the same kind of + + align:start position:0% +essentially achieving the same kind of + + + align:start position:0% +essentially achieving the same kind of +thing by this by this process as if it + + align:start position:0% +thing by this by this process as if it + + + align:start position:0% +thing by this by this process as if it +had burned it you'd burned an oxygen + + align:start position:0% +had burned it you'd burned an oxygen + + + align:start position:0% +had burned it you'd burned an oxygen +there's that much potential energy + + align:start position:0% +there's that much potential energy + + + align:start position:0% +there's that much potential energy +released um and in order to the the + + align:start position:0% +released um and in order to the the + + + align:start position:0% +released um and in order to the the +total amount of this change the D Prime + + align:start position:0% +total amount of this change the D Prime + + + align:start position:0% +total amount of this change the D Prime +Z is something of the order I think it's + + align:start position:0% +Z is something of the order I think it's + + + align:start position:0% +Z is something of the order I think it's +minus + + align:start position:0% +minus + + + align:start position:0% +minus +686 kilo calories per mole uh it's able + + align:start position:0% +686 kilo calories per mole uh it's able + + + align:start position:0% +686 kilo calories per mole uh it's able +to capture + + align:start position:0% + + + + align:start position:0% + +respiration captures about + + align:start position:0% +respiration captures about + + + align:start position:0% +respiration captures about +60% of that energy + + align:start position:0% +60% of that energy + + + align:start position:0% +60% of that energy +as + + align:start position:0% +as + + + align:start position:0% +as +ATP this process of + + align:start position:0% +ATP this process of + + + align:start position:0% +ATP this process of +fermentation this is + + align:start position:0% +fermentation this is + + + align:start position:0% +fermentation this is +what these processes that + + align:start position:0% +what these processes that + + + align:start position:0% +what these processes that +happen in the absence of oxygen are + + align:start position:0% +happen in the absence of oxygen are + + + align:start position:0% +happen in the absence of oxygen are +known as + + align:start position:0% +known as + + + align:start position:0% +known as +fermentation as you can see they're much + + align:start position:0% +fermentation as you can see they're much + + + align:start position:0% +fermentation as you can see they're much +much less + + align:start position:0% + + + + align:start position:0% + +efficient it gets more like + + align:start position:0% +efficient it gets more like + + + align:start position:0% +efficient it gets more like +3.3% of the energy + + align:start position:0% +3.3% of the energy + + + align:start position:0% +3.3% of the energy +captured as ATP + + align:start position:0% +captured as ATP + + + align:start position:0% +captured as ATP +P so you can see when oxygen arose in + + align:start position:0% +P so you can see when oxygen arose in + + + align:start position:0% +P so you can see when oxygen arose in +the environment what a huge Boon it was + + align:start position:0% +the environment what a huge Boon it was + + + align:start position:0% +the environment what a huge Boon it was +to life because you could get a lot more + + align:start position:0% +to life because you could get a lot more + + + align:start position:0% +to life because you could get a lot more +energy for the same amount of of + + align:start position:0% +energy for the same amount of of + + + align:start position:0% +energy for the same amount of of +starting material there is one thing + + align:start position:0% +starting material there is one thing + + + align:start position:0% +starting material there is one thing +though that the cell has to do in order + + align:start position:0% +though that the cell has to do in order + + + align:start position:0% +though that the cell has to do in order +to do this it has to do some more + + align:start position:0% +to do this it has to do some more + + + align:start position:0% +to do this it has to do some more +chemistry because it has to take those + + align:start position:0% +chemistry because it has to take those + + + align:start position:0% +chemistry because it has to take those +pyrates and it has to somehow run them + + align:start position:0% +pyrates and it has to somehow run them + + + align:start position:0% +pyrates and it has to somehow run them +through this thing that I'm calling the + + align:start position:0% +through this thing that I'm calling the + + + align:start position:0% +through this thing that I'm calling the +citric acid cycle in oxidative phosphor + + align:start position:0% +citric acid cycle in oxidative phosphor + + + align:start position:0% +citric acid cycle in oxidative phosphor +well the oxidative phosphorilation is + + align:start position:0% +well the oxidative phosphorilation is + + + align:start position:0% +well the oxidative phosphorilation is +basically this chain I've diagrammed you + + align:start position:0% +basically this chain I've diagrammed you + + + align:start position:0% +basically this chain I've diagrammed you +for you here in a schematic way and + + align:start position:0% +for you here in a schematic way and + + + align:start position:0% +for you here in a schematic way and +that's about the level you'll have to + + align:start position:0% +that's about the level you'll have to + + + align:start position:0% +that's about the level you'll have to +understand it I mean physically it's + + align:start position:0% +understand it I mean physically it's + + + align:start position:0% +understand it I mean physically it's +going to be a bunch of proteins stuck in + + align:start position:0% +going to be a bunch of proteins stuck in + + + align:start position:0% +going to be a bunch of proteins stuck in +the membrane and as the electrons get + + align:start position:0% +the membrane and as the electrons get + + + align:start position:0% +the membrane and as the electrons get +passed along they pump a proton as as + + align:start position:0% +passed along they pump a proton as as + + + align:start position:0% +passed along they pump a proton as as +the procedure uh go as the this pathway + + align:start position:0% +the procedure uh go as the this pathway + + + align:start position:0% +the procedure uh go as the this pathway +occurs but the other thing the cells + + align:start position:0% +occurs but the other thing the cells + + + align:start position:0% +occurs but the other thing the cells +have to do is they have to take those + + align:start position:0% +have to do is they have to take those + + + align:start position:0% +have to do is they have to take those +two pyrates and they have to burn them + + align:start position:0% +two pyrates and they have to burn them + + + align:start position:0% +two pyrates and they have to burn them +all the way down to CO2 and uh + + align:start position:0% +all the way down to CO2 and uh + + + align:start position:0% +all the way down to CO2 and uh +and water and what's happening if you + + align:start position:0% +and water and what's happening if you + + + align:start position:0% +and water and what's happening if you +remember that chain of oxidations the + + align:start position:0% +remember that chain of oxidations the + + + align:start position:0% +remember that chain of oxidations the +carbons are being successively oxidized + + align:start position:0% +carbons are being successively oxidized + + + align:start position:0% +carbons are being successively oxidized +all the way up to carbon dioxide you + + align:start position:0% +all the way up to carbon dioxide you + + + align:start position:0% +all the way up to carbon dioxide you +can't be any more oxidized than that if + + align:start position:0% +can't be any more oxidized than that if + + + align:start position:0% +can't be any more oxidized than that if +you're carbon what that must mean is + + align:start position:0% +you're carbon what that must mean is + + + align:start position:0% +you're carbon what that must mean is +something else is getting reduced and + + align:start position:0% +something else is getting reduced and + + + align:start position:0% +something else is getting reduced and +what gets reduced where the electrons go + + align:start position:0% +what gets reduced where the electrons go + + + align:start position:0% +what gets reduced where the electrons go +is nadh's so once oxygen became + + align:start position:0% +is nadh's so once oxygen became + + + align:start position:0% +is nadh's so once oxygen became +available in the atmosphere then the the + + align:start position:0% +available in the atmosphere then the the + + + align:start position:0% +available in the atmosphere then the the +name of the game was to take those two + + align:start position:0% +name of the game was to take those two + + + align:start position:0% +name of the game was to take those two +pyrates and to somehow burn them all the + + align:start position:0% +pyrates and to somehow burn them all the + + + align:start position:0% +pyrates and to somehow burn them all the +way down to here and therefore generate + + align:start position:0% +way down to here and therefore generate + + + align:start position:0% +way down to here and therefore generate +as much nadh as possible if you can make + + align:start position:0% +as much nadh as possible if you can make + + + align:start position:0% +as much nadh as possible if you can make +some atps along the way well and good so + + align:start position:0% +some atps along the way well and good so + + + align:start position:0% +some atps along the way well and good so +there had to be a whole other set of + + align:start position:0% +there had to be a whole other set of + + + align:start position:0% +there had to be a whole other set of +chemical reactions it's every bit as as + + align:start position:0% +chemical reactions it's every bit as as + + + align:start position:0% +chemical reactions it's every bit as as +complicated as glycolysis that emerged + + align:start position:0% +complicated as glycolysis that emerged + + + align:start position:0% +complicated as glycolysis that emerged +in nature that carried out that job and + + align:start position:0% +in nature that carried out that job and + + + align:start position:0% +in nature that carried out that job and +this time I'm not going to take you + + align:start position:0% +this time I'm not going to take you + + + align:start position:0% +this time I'm not going to take you +through all the chemical structures you + + align:start position:0% +through all the chemical structures you + + + align:start position:0% +through all the chemical structures you +can look at it in your textbook and + + align:start position:0% +can look at it in your textbook and + + + align:start position:0% +can look at it in your textbook and +stuff but what I really want you to kind + + align:start position:0% +stuff but what I really want you to kind + + + align:start position:0% +stuff but what I really want you to kind +of take is is to watch keep your eye on + + align:start position:0% +of take is is to watch keep your eye on + + + align:start position:0% +of take is is to watch keep your eye on +on the on the number of + + align:start position:0% +on the on the number of + + + align:start position:0% +on the on the number of +carbons if you look at the structure of + + align:start position:0% +carbons if you look at the structure of + + + align:start position:0% +carbons if you look at the structure of +of pyate you'll see that it's it's three + + align:start position:0% +of pyate you'll see that it's it's three + + + align:start position:0% +of pyate you'll see that it's it's three +three carbons it was + + align:start position:0% +three carbons it was + + + align:start position:0% +three carbons it was +this there's a keto group and an acidic + + align:start position:0% +this there's a keto group and an acidic + + + align:start position:0% +this there's a keto group and an acidic +group so this is almost carbon dioxide + + align:start position:0% +group so this is almost carbon dioxide + + + align:start position:0% +group so this is almost carbon dioxide +it's just one one oxidative step away so + + align:start position:0% +it's just one one oxidative step away so + + + align:start position:0% +it's just one one oxidative step away so +what happens in this cycle is that first + + align:start position:0% +what happens in this cycle is that first + + + align:start position:0% +what happens in this cycle is that first +the carbon dioxide is removed and + + align:start position:0% +the carbon dioxide is removed and + + + align:start position:0% +the carbon dioxide is removed and +this makes it + + align:start position:0% + + + + align:start position:0% + +acetate in essence it's actually join to + + align:start position:0% +acetate in essence it's actually join to + + + align:start position:0% +acetate in essence it's actually join to +something right here and then this feeds + + align:start position:0% +something right here and then this feeds + + + align:start position:0% +something right here and then this feeds +into this thing called the citric acid + + align:start position:0% + + + + align:start position:0% + +cycle and and what it is as I said is + + align:start position:0% +cycle and and what it is as I said is + + + align:start position:0% +cycle and and what it is as I said is +it's a set of chemical reactions that + + align:start position:0% +it's a set of chemical reactions that + + + align:start position:0% +it's a set of chemical reactions that +are designed to take this pyate and burn + + align:start position:0% +are designed to take this pyate and burn + + + align:start position:0% +are designed to take this pyate and burn +it all the way to carbon dioxide and and + + align:start position:0% +it all the way to carbon dioxide and and + + + align:start position:0% +it all the way to carbon dioxide and and +water and to generate as many nadhs in + + align:start position:0% +water and to generate as many nadhs in + + + align:start position:0% +water and to generate as many nadhs in +atps as it can along the way and again I + + align:start position:0% +atps as it can along the way and again I + + + align:start position:0% +atps as it can along the way and again I +wish it was simpler it would be really + + align:start position:0% +wish it was simpler it would be really + + + align:start position:0% +wish it was simpler it would be really +nice if it just did it straight from + + align:start position:0% +nice if it just did it straight from + + + align:start position:0% +nice if it just did it straight from +acetate but instead you'll see if you + + align:start position:0% +acetate but instead you'll see if you + + + align:start position:0% +acetate but instead you'll see if you +look at the TCA cycle is a C4 compound + + align:start position:0% +look at the TCA cycle is a C4 compound + + + align:start position:0% +look at the TCA cycle is a C4 compound +and this gets joined together to give a + + align:start position:0% +and this gets joined together to give a + + + align:start position:0% +and this gets joined together to give a +C6 compound then it oxidizes one of + + align:start position:0% +C6 compound then it oxidizes one of + + + align:start position:0% +C6 compound then it oxidizes one of +these carbons to give a a carbon dioxide + + align:start position:0% +these carbons to give a a carbon dioxide + + + align:start position:0% +these carbons to give a a carbon dioxide +now you're down to C5 does it + + align:start position:0% +now you're down to C5 does it + + + align:start position:0% +now you're down to C5 does it +again another molecule of CO2 you're at + + align:start position:0% +again another molecule of CO2 you're at + + + align:start position:0% +again another molecule of CO2 you're at +C4 and then it takes this C4 carbon + + align:start position:0% +C4 and then it takes this C4 carbon + + + align:start position:0% +C4 and then it takes this C4 carbon +skeleton puts it through some + + align:start position:0% +skeleton puts it through some + + + align:start position:0% +skeleton puts it through some +Transformations that enables the cycle + + align:start position:0% +Transformations that enables the cycle + + + align:start position:0% +Transformations that enables the cycle +to go all over again so basically this + + align:start position:0% +to go all over again so basically this + + + align:start position:0% +to go all over again so basically this +C4 thing just goes through the cycle + + align:start position:0% +C4 thing just goes through the cycle + + + align:start position:0% +C4 thing just goes through the cycle +it's a carrier takes this + + align:start position:0% +it's a carrier takes this + + + align:start position:0% +it's a carrier takes this +C2 right here lets it go be processed to + + align:start position:0% +C2 right here lets it go be processed to + + + align:start position:0% +C2 right here lets it go be processed to +give uh CO2 uh two molecules of CO2 in + + align:start position:0% +give uh CO2 uh two molecules of CO2 in + + + align:start position:0% +give uh CO2 uh two molecules of CO2 in +that process it generates more uh nadh + + align:start position:0% +that process it generates more uh nadh + + + align:start position:0% +that process it generates more uh nadh +uh a bit of ATP and why they're a kind + + align:start position:0% +uh a bit of ATP and why they're a kind + + + align:start position:0% +uh a bit of ATP and why they're a kind +of reduced carrier that you can think of + + align:start position:0% +of reduced carrier that you can think of + + + align:start position:0% +of reduced carrier that you can think of +for the moment largely equivalently to + + align:start position:0% +for the moment largely equivalently to + + + align:start position:0% +for the moment largely equivalently to +um NAD uh + + align:start position:0% +um NAD uh + + + align:start position:0% +um NAD uh +nadh okay now what ha the the entity in + + align:start position:0% +nadh okay now what ha the the entity in + + + align:start position:0% +nadh okay now what ha the the entity in +our cells that carries out this uh + + align:start position:0% +our cells that carries out this uh + + + align:start position:0% +our cells that carries out this uh +process of respiration and + + align:start position:0% + + + + align:start position:0% + +uh of res of of respiration so the + + align:start position:0% +uh of res of of respiration so the + + + align:start position:0% +uh of res of of respiration so the +citric acid cycle and and the + + align:start position:0% +citric acid cycle and and the + + + align:start position:0% +citric acid cycle and and the +mitochondria is not not actually in our + + align:start position:0% +mitochondria is not not actually in our + + + align:start position:0% +mitochondria is not not actually in our +cytoplasm which is perhaps surprising um + + align:start position:0% +cytoplasm which is perhaps surprising um + + + align:start position:0% +cytoplasm which is perhaps surprising um +but all the enzymes for glycolysis are + + align:start position:0% +but all the enzymes for glycolysis are + + + align:start position:0% +but all the enzymes for glycolysis are +so remember my UK simple diagram of the + + align:start position:0% +so remember my UK simple diagram of the + + + align:start position:0% +so remember my UK simple diagram of the +eukariotic cell in the first day we had + + align:start position:0% +eukariotic cell in the first day we had + + + align:start position:0% +eukariotic cell in the first day we had +the nucleus which is a membrane + + align:start position:0% +the nucleus which is a membrane + + + align:start position:0% +the nucleus which is a membrane +compartment that has the the DNA inside + + align:start position:0% +compartment that has the the DNA inside + + + align:start position:0% +compartment that has the the DNA inside +it we'll have more to say about that in + + align:start position:0% +it we'll have more to say about that in + + + align:start position:0% +it we'll have more to say about that in +next lecture or so but then there were + + align:start position:0% +next lecture or so but then there were + + + align:start position:0% +next lecture or so but then there were +some organel and one of them I said was + + align:start position:0% +some organel and one of them I said was + + + align:start position:0% +some organel and one of them I said was +a + + align:start position:0% + + + + align:start position:0% + +mitochondrian and I also said in the + + align:start position:0% +mitochondrian and I also said in the + + + align:start position:0% +mitochondrian and I also said in the +first lecture that that there's pretty + + align:start position:0% +first lecture that that there's pretty + + + align:start position:0% +first lecture that that there's pretty +good evidence now that the mitochondrian + + align:start position:0% +good evidence now that the mitochondrian + + + align:start position:0% +good evidence now that the mitochondrian +arose by some early progenitor or + + align:start position:0% +arose by some early progenitor or + + + align:start position:0% +arose by some early progenitor or +ancestor of a eukariotic cell capturing + + align:start position:0% +ancestor of a eukariotic cell capturing + + + align:start position:0% +ancestor of a eukariotic cell capturing +some kind of uh bacterium it's actually + + align:start position:0% +some kind of uh bacterium it's actually + + + align:start position:0% +some kind of uh bacterium it's actually +one that's sort of kind of related to + + align:start position:0% +one that's sort of kind of related to + + + align:start position:0% +one that's sort of kind of related to +eoli had had double membranes and the + + align:start position:0% +eoli had had double membranes and the + + + align:start position:0% +eoli had had double membranes and the +mitochondria actually still have some of + + align:start position:0% +mitochondria actually still have some of + + + align:start position:0% +mitochondria actually still have some of +their own their own DNA but this is + + align:start position:0% +their own their own DNA but this is + + + align:start position:0% +their own their own DNA but this is +where all the energy all the + + align:start position:0% + + + + align:start position:0% + +enzymes for the citric acid cycle + + align:start position:0% + + + + align:start position:0% + +and um oxidative + + align:start position:0% + + + + align:start position:0% + +phosphorilation are found in the inside + + align:start position:0% +phosphorilation are found in the inside + + + align:start position:0% +phosphorilation are found in the inside +of the the mitochondrian inside of + + align:start position:0% +of the the mitochondrian inside of + + + align:start position:0% +of the the mitochondrian inside of +something that probably used to be a + + align:start position:0% +something that probably used to be a + + + align:start position:0% +something that probably used to be a +free living bacterium in contrast the + + align:start position:0% +free living bacterium in contrast the + + + align:start position:0% +free living bacterium in contrast the +enzymes for + + align:start position:0% +enzymes for + + + align:start position:0% +enzymes for +glycolysis are in What's called the + + align:start position:0% +glycolysis are in What's called the + + + align:start position:0% +glycolysis are in What's called the +cytoplasm of the cell which is sort of + + align:start position:0% +cytoplasm of the cell which is sort of + + + align:start position:0% +cytoplasm of the cell which is sort of +the main the main part of the insides of + + align:start position:0% +the main the main part of the insides of + + + align:start position:0% +the main the main part of the insides of +the cell so you see even here this sort + + align:start position:0% +the cell so you see even here this sort + + + align:start position:0% +the cell so you see even here this sort +of evolutionary history that I kind of + + align:start position:0% +of evolutionary history that I kind of + + + align:start position:0% +of evolutionary history that I kind of +put out across the board the enzymes for + + align:start position:0% +put out across the board the enzymes for + + + align:start position:0% +put out across the board the enzymes for +glycolysis arose so early in EV + + align:start position:0% +glycolysis arose so early in EV + + + align:start position:0% +glycolysis arose so early in EV +Evolution they're in the cytoplasm of + + align:start position:0% +Evolution they're in the cytoplasm of + + + align:start position:0% +Evolution they're in the cytoplasm of +virtually every organism on Earth + + align:start position:0% +virtually every organism on Earth + + + align:start position:0% +virtually every organism on Earth +eukaryotic cells managed to figure out + + align:start position:0% +eukaryotic cells managed to figure out + + + align:start position:0% +eukaryotic cells managed to figure out +how to get 18 times more energy for a + + align:start position:0% +how to get 18 times more energy for a + + + align:start position:0% +how to get 18 times more energy for a +molecule of sugar but in order to do it + + align:start position:0% +molecule of sugar but in order to do it + + + align:start position:0% +molecule of sugar but in order to do it +they kind of had to cheat they took a + + align:start position:0% +they kind of had to cheat they took a + + + align:start position:0% +they kind of had to cheat they took a +bacterium and figured out how to do it + + align:start position:0% +bacterium and figured out how to do it + + + align:start position:0% +bacterium and figured out how to do it +put it inside our own cells and then + + align:start position:0% +put it inside our own cells and then + + + align:start position:0% +put it inside our own cells and then +it's able to run now it's become a part + + align:start position:0% +it's able to run now it's become a part + + + align:start position:0% +it's able to run now it's become a part +of our cell and it's where all this + + align:start position:0% +of our cell and it's where all this + + + align:start position:0% +of our cell and it's where all this +process takes place and if you look at + + align:start position:0% +process takes place and if you look at + + + align:start position:0% +process takes place and if you look at +the structure of a mitochondrian it's + + align:start position:0% +the structure of a mitochondrian it's + + + align:start position:0% +the structure of a mitochondrian it's +actually got two membranes you just saw + + align:start position:0% +actually got two membranes you just saw + + + align:start position:0% +actually got two membranes you just saw +a picture of that in a + + align:start position:0% +a picture of that in a + + + align:start position:0% +a picture of that in a +coli and in fact they sort of kind of + + align:start position:0% +coli and in fact they sort of kind of + + + align:start position:0% +coli and in fact they sort of kind of +involuted a little bit like this and + + align:start position:0% +involuted a little bit like this and + + + align:start position:0% +involuted a little bit like this and +uh so this is an outer membrane of a + + align:start position:0% +uh so this is an outer membrane of a + + + align:start position:0% +uh so this is an outer membrane of a +mitochondrian so I'm basically taking + + align:start position:0% +mitochondrian so I'm basically taking + + + align:start position:0% +mitochondrian so I'm basically taking +this and blowing it up so this is a + + align:start position:0% +this and blowing it up so this is a + + + align:start position:0% +this and blowing it up so this is a +mitochondrian + + align:start position:0% + + + + align:start position:0% + +and the in and the + + align:start position:0% +and the in and the + + + align:start position:0% +and the in and the +out in this case there's an inner + + align:start position:0% + + + + align:start position:0% + +membrane this is where the proton pump + + align:start position:0% +membrane this is where the proton pump + + + align:start position:0% +membrane this is where the proton pump +is located this is where the ATP + + align:start position:0% +is located this is where the ATP + + + align:start position:0% +is located this is where the ATP +synthesis is located and when a + + align:start position:0% +synthesis is located and when a + + + align:start position:0% +synthesis is located and when a +mitochondrian is is working what it's + + align:start position:0% +mitochondrian is is working what it's + + + align:start position:0% +mitochondrian is is working what it's +doing is it's pumping hydrogen ions from + + align:start position:0% +doing is it's pumping hydrogen ions from + + + align:start position:0% +doing is it's pumping hydrogen ions from +its inside which is more or less the + + align:start position:0% +its inside which is more or less the + + + align:start position:0% +its inside which is more or less the +equivalent of a of a cytoplasm it's + + align:start position:0% +equivalent of a of a cytoplasm it's + + + align:start position:0% +equivalent of a of a cytoplasm it's +whatever you to be the cytoplasm of the + + align:start position:0% +whatever you to be the cytoplasm of the + + + align:start position:0% +whatever you to be the cytoplasm of the +original bacterium outside into this + + align:start position:0% +original bacterium outside into this + + + align:start position:0% +original bacterium outside into this +space between the inner and outer + + align:start position:0% +space between the inner and outer + + + align:start position:0% +space between the inner and outer +membranes and then it generates ATP by + + align:start position:0% +membranes and then it generates ATP by + + + align:start position:0% +membranes and then it generates ATP by +flowing flowing back + + align:start position:0% + + + + align:start position:0% + +down okay so there a couple of sort of + + align:start position:0% +down okay so there a couple of sort of + + + align:start position:0% +down okay so there a couple of sort of +things that affect your life that come + + align:start position:0% +things that affect your life that come + + + align:start position:0% +things that affect your life that come +out of this um one of them is uh + + align:start position:0% +out of this um one of them is uh + + + align:start position:0% +out of this um one of them is uh +understanding The Freshman 5 or Freshman + + align:start position:0% +understanding The Freshman 5 or Freshman + + + align:start position:0% +understanding The Freshman 5 or Freshman +15 or whatever it is you come to college + + align:start position:0% +15 or whatever it is you come to college + + + align:start position:0% +15 or whatever it is you come to college +and all of a sudden you you put on a lot + + align:start position:0% +and all of a sudden you you put on a lot + + + align:start position:0% +and all of a sudden you you put on a lot +of weight and sometimes you can figure + + align:start position:0% +of weight and sometimes you can figure + + + align:start position:0% +of weight and sometimes you can figure +it out it's because you ate a lot of Ben + + align:start position:0% +it out it's because you ate a lot of Ben + + + align:start position:0% +it out it's because you ate a lot of Ben +and cherries or a lot of chocolate bars + + align:start position:0% +and cherries or a lot of chocolate bars + + + align:start position:0% +and cherries or a lot of chocolate bars +or something and didn't do as much + + align:start position:0% +or something and didn't do as much + + + align:start position:0% +or something and didn't do as much +exercise another one of you said gee I + + align:start position:0% +exercise another one of you said gee I + + + align:start position:0% +exercise another one of you said gee I +know I understand why I'm not putting on + + align:start position:0% +know I understand why I'm not putting on + + + align:start position:0% +know I understand why I'm not putting on +any weight I do water polo and I guess I + + align:start position:0% +any weight I do water polo and I guess I + + + align:start position:0% +any weight I do water polo and I guess I +must be burning up everything I eat as + + align:start position:0% +must be burning up everything I eat as + + + align:start position:0% +must be burning up everything I eat as +energy and you're right but you can now + + align:start position:0% +energy and you're right but you can now + + + align:start position:0% +energy and you're right but you can now +begin to I can show you at a molecular + + align:start position:0% +begin to I can show you at a molecular + + + align:start position:0% +begin to I can show you at a molecular +level what's happening so what happens + + align:start position:0% +level what's happening so what happens + + + align:start position:0% +level what's happening so what happens +if your your body is everything's + + align:start position:0% +if your your body is everything's + + + align:start position:0% +if your your body is everything's +regulated and it can tell if it needs + + align:start position:0% +regulated and it can tell if it needs + + + align:start position:0% +regulated and it can tell if it needs +cells and your body can tell if it needs + + align:start position:0% +cells and your body can tell if it needs + + + align:start position:0% +cells and your body can tell if it needs +energy if it needs energy and you eat + + align:start position:0% +energy if it needs energy and you eat + + + align:start position:0% +energy if it needs energy and you eat +sugar it runs right through here and it + + align:start position:0% +sugar it runs right through here and it + + + align:start position:0% +sugar it runs right through here and it +makes ATP but if you've eaten enough and + + align:start position:0% +makes ATP but if you've eaten enough and + + + align:start position:0% +makes ATP but if you've eaten enough and +your the things that monitor your your U + + align:start position:0% +your the things that monitor your your U + + + align:start position:0% +your the things that monitor your your U +body say that it's you've got enough ATP + + align:start position:0% +body say that it's you've got enough ATP + + + align:start position:0% +body say that it's you've got enough ATP +then it doesn't keep this uh process uh + + align:start position:0% +then it doesn't keep this uh process uh + + + align:start position:0% +then it doesn't keep this uh process uh +going instead what it does is it stops + + align:start position:0% +going instead what it does is it stops + + + align:start position:0% +going instead what it does is it stops +it and it says instead we're going to + + align:start position:0% +it and it says instead we're going to + + + align:start position:0% +it and it says instead we're going to +put something away for a rainy day which + + align:start position:0% +put something away for a rainy day which + + + align:start position:0% +put something away for a rainy day which +you could see would make a lot of sense + + align:start position:0% +you could see would make a lot of sense + + + align:start position:0% +you could see would make a lot of sense +in evolution you know you'd you want to + + align:start position:0% +in evolution you know you'd you want to + + + align:start position:0% +in evolution you know you'd you want to +if if things are good you just kill the + + align:start position:0% +if if things are good you just kill the + + + align:start position:0% +if if things are good you just kill the +m and you can all eat well for a while + + align:start position:0% +m and you can all eat well for a while + + + align:start position:0% +m and you can all eat well for a while +or something would make sense for your + + align:start position:0% +or something would make sense for your + + + align:start position:0% +or something would make sense for your +body to be able to pack stuff away so + + align:start position:0% +body to be able to pack stuff away so + + + align:start position:0% +body to be able to pack stuff away so +what it does is it intercepts the + + align:start position:0% +what it does is it intercepts the + + + align:start position:0% +what it does is it intercepts the +process at this level at this C2 level + + align:start position:0% +process at this level at this C2 level + + + align:start position:0% +process at this level at this C2 level +the pyate gets to here and instead of + + align:start position:0% +the pyate gets to here and instead of + + + align:start position:0% +the pyate gets to here and instead of +being run through this in + + align:start position:0% +being run through this in + + + align:start position:0% +being run through this in +ATP this acetate or acetal midy which is + + align:start position:0% +ATP this acetate or acetal midy which is + + + align:start position:0% +ATP this acetate or acetal midy which is +a C2 gets run through a cycle of + + align:start position:0% +a C2 gets run through a cycle of + + + align:start position:0% +a C2 gets run through a cycle of +successive two carbon additions and what + + align:start position:0% +successive two carbon additions and what + + + align:start position:0% +successive two carbon additions and what +comes out of that are fatty acids + + align:start position:0% + + + + align:start position:0% + +it also + + align:start position:0% +it also + + + align:start position:0% +it also +takes three + + align:start position:0% + + + + align:start position:0% + +phospho glycer alahh you might remember + + align:start position:0% +phospho glycer alahh you might remember + + + align:start position:0% +phospho glycer alahh you might remember +that that comes that's one of the + + align:start position:0% +that that comes that's one of the + + + align:start position:0% +that that comes that's one of the +products in the stuck in the middle of + + align:start position:0% +products in the stuck in the middle of + + + align:start position:0% +products in the stuck in the middle of +that glycolytic pathway and it makes + + align:start position:0% +that glycolytic pathway and it makes + + + align:start position:0% +that glycolytic pathway and it makes +that into this is a three carbon + + align:start position:0% +that into this is a three carbon + + + align:start position:0% +that into this is a three carbon +compound it makes it into glycerol + + align:start position:0% +compound it makes it into glycerol + + + align:start position:0% +compound it makes it into glycerol +which is a three carbon compound and if + + align:start position:0% +which is a three carbon compound and if + + + align:start position:0% +which is a three carbon compound and if +you look back when we talked about + + align:start position:0% +you look back when we talked about + + + align:start position:0% +you look back when we talked about +lipids a couple of lectures ago you + + align:start position:0% +lipids a couple of lectures ago you + + + align:start position:0% +lipids a couple of lectures ago you +realize what happens if you combine a + + align:start position:0% +realize what happens if you combine a + + + align:start position:0% +realize what happens if you combine a +fatty fatty acids with glycerol then + + align:start position:0% +fatty fatty acids with glycerol then + + + align:start position:0% +fatty fatty acids with glycerol then +you've got fats and in essence I mean + + align:start position:0% +you've got fats and in essence I mean + + + align:start position:0% +you've got fats and in essence I mean +that's what happens you put on we put on + + align:start position:0% +that's what happens you put on we put on + + + align:start position:0% +that's what happens you put on we put on +weight if we eat more than more than + + align:start position:0% +weight if we eat more than more than + + + align:start position:0% +weight if we eat more than more than +we're burning our bodies say okay got as + + align:start position:0% +we're burning our bodies say okay got as + + + align:start position:0% +we're burning our bodies say okay got as +much ATP as we need I'm going to take + + align:start position:0% +much ATP as we need I'm going to take + + + align:start position:0% +much ATP as we need I'm going to take +some of that uh ATP and use it in + + align:start position:0% +some of that uh ATP and use it in + + + align:start position:0% +some of that uh ATP and use it in +in this kind of way + + align:start position:0% +in this kind of way + + + align:start position:0% +in this kind of way +um just SEC here let me + + align:start position:0% + + + + align:start position:0% + +see so there's another thing that + + align:start position:0% +see so there's another thing that + + + align:start position:0% +see so there's another thing that +happens when you're uh physiological + + align:start position:0% +happens when you're uh physiological + + + align:start position:0% +happens when you're uh physiological +thing that we + + align:start position:0% +thing that we + + + align:start position:0% +thing that we +experience well we seem to be stuck at + + align:start position:0% +experience well we seem to be stuck at + + + align:start position:0% +experience well we seem to be stuck at +the moment I won't worry about it um if + + align:start position:0% +the moment I won't worry about it um if + + + align:start position:0% +the moment I won't worry about it um if +you I I've run some marathons I don't + + align:start position:0% +you I I've run some marathons I don't + + + align:start position:0% +you I I've run some marathons I don't +know few of you may have if not almost + + align:start position:0% +know few of you may have if not almost + + + align:start position:0% +know few of you may have if not almost +all of you have heard about hitting the + + align:start position:0% +all of you have heard about hitting the + + + align:start position:0% +all of you have heard about hitting the +wall and it happens in general generally + + align:start position:0% +wall and it happens in general generally + + + align:start position:0% +wall and it happens in general generally +around 21 22 23 miles depends on + + align:start position:0% +around 21 22 23 miles depends on + + + align:start position:0% +around 21 22 23 miles depends on +condition you're doing and + + align:start position:0% +condition you're doing and + + + align:start position:0% +condition you're doing and +physiologically I have experienced + + align:start position:0% +physiologically I have experienced + + + align:start position:0% +physiologically I have experienced +amazing I understand why they call it + + align:start position:0% +amazing I understand why they call it + + + align:start position:0% +amazing I understand why they call it +hitting the wall you're running along + + align:start position:0% +hitting the wall you're running along + + + align:start position:0% +hitting the wall you're running along +you think boy I'm tired but I'm doing + + align:start position:0% +you think boy I'm tired but I'm doing + + + align:start position:0% +you think boy I'm tired but I'm doing +okay and in the space of a quarter mile + + align:start position:0% +okay and in the space of a quarter mile + + + align:start position:0% +okay and in the space of a quarter mile +it's like you bam banged into a brick + + align:start position:0% +it's like you bam banged into a brick + + + align:start position:0% +it's like you bam banged into a brick +wall and you can sort of keep yourself + + align:start position:0% +wall and you can sort of keep yourself + + + align:start position:0% +wall and you can sort of keep yourself +going but some it's a profound + + align:start position:0% +going but some it's a profound + + + align:start position:0% +going but some it's a profound +physiological change and what has + + align:start position:0% +physiological change and what has + + + align:start position:0% +physiological change and what has +happened at that point is you've you've + + align:start position:0% +happened at that point is you've you've + + + align:start position:0% +happened at that point is you've you've +run out of sugar to burn now I told you + + align:start position:0% +run out of sugar to burn now I told you + + + align:start position:0% +run out of sugar to burn now I told you +you can take sugars and you can + + align:start position:0% +you can take sugars and you can + + + align:start position:0% +you can take sugars and you can +polymerize them into glycogen that's one + + align:start position:0% +polymerize them into glycogen that's one + + + align:start position:0% +polymerize them into glycogen that's one +of those polymers with alpha 1 uh 14 + + align:start position:0% +of those polymers with alpha 1 uh 14 + + + align:start position:0% +of those polymers with alpha 1 uh 14 +linkages that's a a sugar storage + + align:start position:0% +linkages that's a a sugar storage + + + align:start position:0% +linkages that's a a sugar storage +molecule so if you start running your + + align:start position:0% +molecule so if you start running your + + + align:start position:0% +molecule so if you start running your +carbo load you try and get as much sugar + + align:start position:0% +carbo load you try and get as much sugar + + + align:start position:0% +carbo load you try and get as much sugar +into glycogen as you possibly can start + + align:start position:0% +into glycogen as you possibly can start + + + align:start position:0% +into glycogen as you possibly can start +running the marathon your body starts + + align:start position:0% +running the marathon your body starts + + + align:start position:0% +running the marathon your body starts +taking that that glycogen and breaking + + align:start position:0% +taking that that glycogen and breaking + + + align:start position:0% +taking that that glycogen and breaking +it down into sugars it runs it through + + align:start position:0% +it down into sugars it runs it through + + + align:start position:0% +it down into sugars it runs it through +that process what happens when you hit + + align:start position:0% +that process what happens when you hit + + + align:start position:0% +that process what happens when you hit +the wall as a human body is most human + + align:start position:0% +the wall as a human body is most human + + + align:start position:0% +the wall as a human body is most human +bodies are designed so that you run out + + align:start position:0% +bodies are designed so that you run out + + + align:start position:0% +bodies are designed so that you run out +of sugar you just can't carbo FL enough + + align:start position:0% +of sugar you just can't carbo FL enough + + + align:start position:0% +of sugar you just can't carbo FL enough +to do 26 miles you can get through 20 or + + align:start position:0% +to do 26 miles you can get through 20 or + + + align:start position:0% +to do 26 miles you can get through 20 or +something there and when you run out of + + align:start position:0% +something there and when you run out of + + + align:start position:0% +something there and when you run out of +that what happens then is your body can + + align:start position:0% +that what happens then is your body can + + + align:start position:0% +that what happens then is your body can +no longer burn sugar so it switched to + + align:start position:0% +no longer burn sugar so it switched to + + + align:start position:0% +no longer burn sugar so it switched to +burning fatty acids and that's less + + align:start position:0% +burning fatty acids and that's less + + + align:start position:0% +burning fatty acids and that's less +efficient and you you really feel it if + + align:start position:0% +efficient and you you really feel it if + + + align:start position:0% +efficient and you you really feel it if +any of you have written done long + + align:start position:0% +any of you have written done long + + + align:start position:0% +any of you have written done long +endurance things or Triathlon or + + align:start position:0% +endurance things or Triathlon or + + + align:start position:0% +endurance things or Triathlon or +anything you've experienced that that + + align:start position:0% +anything you've experienced that that + + + align:start position:0% +anything you've experienced that that +change the final thing just to close for + + align:start position:0% +change the final thing just to close for + + + align:start position:0% +change the final thing just to close for +the lecture for today is one thing you + + align:start position:0% +the lecture for today is one thing you + + + align:start position:0% +the lecture for today is one thing you +can appreciate yeast is somebody that + + align:start position:0% +can appreciate yeast is somebody that + + + align:start position:0% +can appreciate yeast is somebody that +can do both of this both of these things + + align:start position:0% +can do both of this both of these things + + + align:start position:0% +can do both of this both of these things +right it can either + + align:start position:0% +right it can either + + + align:start position:0% +right it can either +grow anerobic + + align:start position:0% + + + + align:start position:0% + +and it makes + + align:start position:0% +and it makes + + + align:start position:0% +and it makes +CO2 plus ethanol or it can grow + + align:start position:0% + + + + align:start position:0% + +aerobically and this gives it two + + align:start position:0% +aerobically and this gives it two + + + align:start position:0% +aerobically and this gives it two +atps per + + align:start position:0% +atps per + + + align:start position:0% +atps per +glucose and this gives it um 36 + + align:start position:0% + + + + align:start position:0% + +atps for glucose so if you were a yeast + + align:start position:0% +atps for glucose so if you were a yeast + + + align:start position:0% +atps for glucose so if you were a yeast +you would have to somehow regulate the + + align:start position:0% +you would have to somehow regulate the + + + align:start position:0% +you would have to somehow regulate the +rate of glycolysis depending on whether + + align:start position:0% +rate of glycolysis depending on whether + + + align:start position:0% +rate of glycolysis depending on whether +it was oxygen around or not and it's + + align:start position:0% +it was oxygen around or not and it's + + + align:start position:0% +it was oxygen around or not and it's +very tricky neat way it happens there's + + align:start position:0% +very tricky neat way it happens there's + + + align:start position:0% +very tricky neat way it happens there's +an enzyme that wouldn't surprise + + align:start position:0% +an enzyme that wouldn't surprise + + + align:start position:0% +an enzyme that wouldn't surprise +you that has an active + + align:start position:0% +you that has an active + + + align:start position:0% +you that has an active +site uh for one of the key steps in the + + align:start position:0% +site uh for one of the key steps in the + + + align:start position:0% +site uh for one of the key steps in the +um in the pathway where it's going from + + align:start position:0% +um in the pathway where it's going from + + + align:start position:0% +um in the pathway where it's going from +fructose one phosphate fructose six + + align:start position:0% +fructose one phosphate fructose six + + + align:start position:0% +fructose one phosphate fructose six +phosphate to F + + align:start position:0% +phosphate to F + + + align:start position:0% +phosphate to F +fructose one six + + align:start position:0% +fructose one six + + + align:start position:0% +fructose one six +diphosphate that's one of the + + align:start position:0% +diphosphate that's one of the + + + align:start position:0% +diphosphate that's one of the +intermediate steps in glycolysis it it's + + align:start position:0% +intermediate steps in glycolysis it it's + + + align:start position:0% +intermediate steps in glycolysis it it's +the the the enzyme that turns out to be + + align:start position:0% +the the the enzyme that turns out to be + + + align:start position:0% +the the the enzyme that turns out to be +rate limiting you can control + + align:start position:0% +rate limiting you can control + + + align:start position:0% +rate limiting you can control +path um passage of something through a + + align:start position:0% +path um passage of something through a + + + align:start position:0% +path um passage of something through a +pathway by just making one step rate + + align:start position:0% +pathway by just making one step rate + + + align:start position:0% +pathway by just making one step rate +limiting so this has a place for the + + align:start position:0% +limiting so this has a place for the + + + align:start position:0% +limiting so this has a place for the +fructose 6 phosphate plus ATP to bind + + align:start position:0% +fructose 6 phosphate plus ATP to bind + + + align:start position:0% +fructose 6 phosphate plus ATP to bind +and it catalyzes the formation of the + + align:start position:0% +and it catalyzes the formation of the + + + align:start position:0% +and it catalyzes the formation of the +fructose 1 six uh diphosphate but that + + align:start position:0% +fructose 1 six uh diphosphate but that + + + align:start position:0% +fructose 1 six uh diphosphate but that +enzyme has to work at UH different rates + + align:start position:0% +enzyme has to work at UH different rates + + + align:start position:0% +enzyme has to work at UH different rates +depending on whether the cell is aerobic + + align:start position:0% +depending on whether the cell is aerobic + + + align:start position:0% +depending on whether the cell is aerobic +or anerobic so what it does is as a + + align:start position:0% +or anerobic so what it does is as a + + + align:start position:0% +or anerobic so what it does is as a +second binding site over here and if it + + align:start position:0% +second binding site over here and if it + + + align:start position:0% +second binding site over here and if it +if it binds ATP + + align:start position:0% +if it binds ATP + + + align:start position:0% +if it binds ATP +ATP this speeds up excuse me slows + + align:start position:0% + + + + align:start position:0% + +down the rate that's catalyzed over here + + align:start position:0% +down the rate that's catalyzed over here + + + align:start position:0% +down the rate that's catalyzed over here +and that's what you'd expect if it's got + + align:start position:0% +and that's what you'd expect if it's got + + + align:start position:0% +and that's what you'd expect if it's got +enough ATP it doesn't need to run + + align:start position:0% +enough ATP it doesn't need to run + + + align:start position:0% +enough ATP it doesn't need to run +glycolysis as fast + + align:start position:0% +glycolysis as fast + + + align:start position:0% +glycolysis as fast +and if it also binds a + + align:start position:0% +and if it also binds a + + + align:start position:0% +and if it also binds a +m or a + + align:start position:0% +m or a + + + align:start position:0% +m or a +DP and that speeds + + align:start position:0% + + + + align:start position:0% + +up the rate so the yeast are able to + + align:start position:0% +up the rate so the yeast are able to + + + align:start position:0% +up the rate so the yeast are able to +monitor the to sort of have a control on + + align:start position:0% +monitor the to sort of have a control on + + + align:start position:0% +monitor the to sort of have a control on +how fast sugar flows through this + + align:start position:0% +how fast sugar flows through this + + + align:start position:0% +how fast sugar flows through this +glycolytic pathway and what they're + + align:start position:0% +glycolytic pathway and what they're + + + align:start position:0% +glycolytic pathway and what they're +really doing is they're monitoring do I + + align:start position:0% +really doing is they're monitoring do I + + + align:start position:0% +really doing is they're monitoring do I +have enough ATP or not and so if they're + + align:start position:0% +have enough ATP or not and so if they're + + + align:start position:0% +have enough ATP or not and so if they're +running with respiration making lots of + + align:start position:0% +running with respiration making lots of + + + align:start position:0% +running with respiration making lots of +stuff they don't need to do glycolysis + + align:start position:0% +stuff they don't need to do glycolysis + + + align:start position:0% +stuff they don't need to do glycolysis +as fast if they're anerobic they have to + + align:start position:0% +as fast if they're anerobic they have to + + + align:start position:0% +as fast if they're anerobic they have to +run it 18 times as fast to get the same + + align:start position:0% +run it 18 times as fast to get the same + + + align:start position:0% +run it 18 times as fast to get the same +amount of energy okay we'll begin the + + align:start position:0% +amount of energy okay we'll begin the + + + align:start position:0% +amount of energy okay we'll begin the +next lecture with uh photosynthesis and + + align:start position:0% +next lecture with uh photosynthesis and + + + align:start position:0% +next lecture with uh photosynthesis and +then we're going to get into a bunch of + + align:start position:0% +then we're going to get into a bunch of + + + align:start position:0% +then we're going to get into a bunch of +molecular biology okay \ No newline at end of file diff --git a/R3uRidfSpc4.txt b/R3uRidfSpc4.txt new file mode 100644 index 0000000000000000000000000000000000000000..f20c1c07cfa301ccafc33230350aade839b8ba3c --- /dev/null +++ b/R3uRidfSpc4.txt @@ -0,0 +1,3195 @@ +PROFESSOR: All right, well, +we've seen how the query + +language works. + +Now, let's talk about how +it's implemented. + +You already pretty much can +guess what's going on there. + +At the bottom of it, there's +a pattern matcher. + +And we looked at a pattern +matcher when we did the + +rule-based control language. + +Just to remind you, here are +some sample patterns. + +This is a pattern that will +match any list of three things + +of which the first is a and the +second is c and the middle + +one can be anything. + +So in this little +pattern-matching syntax, + +there's only one distinction +you make. + +There's either literal things +or variables, and variables + +begin with question mark. + +So this matches any list of +three things of which the + +first is a and the +second is c. + +This one matches any list of +three things of which the + +first is the symbol job. + +The second can be anything. + +And the third is a list of two +things of which the first is + +the symbol computer and the +second can be anything. + +And this one, this next one +matches any list of three + +things, and the only difference +is, here, the third + +list, the first is the symbol +computer, and then there's + +some rest of the list. So this +means two elements and this + +means arbitrary number. + +And our language implementation +isn't even + +going to have to worry about +implementing this dot because + +that's automatically done +by Lisp's reader. + +Remember matchers also have +some consistency in them. + +This match is a list of +three things of which + +the first is a. + +And the second and third can be +anything, but they have to + +be the same thing. + +They're both called x. + +And this matches a list of four +things of which the first + +is the fourth and the second +is the same as the third. + +And this last one matches any +list that begins with a. + +The first thing is a, and the +rest can be anything. + +So that's just a review of +pattern matcher syntax that + +you've already seen. + +And remember, that's implemented +by some procedure + +called match. + +And match takes a pattern and +some data and a dictionary. + +And match asks the question is +there any way to match this + +pattern against this data object +subject to the bindings + +that are already in +this dictionary? + +So, for instance, if we're going +to match the pattern x, + +y, y, x against the data a, b, +b, a subject to a dictionary, + +that says x equals a. + +Then the matcher would say, +yes, that's consistent. + +These match, and it's consistent +with what's in the + +dictionary to say +that x equals a. + +And the result of the match is +the extended dictionary that + +says x equals a and +y equals b. + +So a matcher takes in pattern +data dictionary, puts out an + +extended dictionary if it +matches, or if it doesn't + +match, says that it fails. + +So, for example, if I use the +same pattern here, if I say + +this x, y, y, x match a, b, b, a +with the dictionary y equals + +a, then the matcher would +put out fail. + +Well, you've already seen the +code for a pattern matcher so + +I'm not going to go over it, but +it's the same thing we've + +been doing before. + +You saw that in the system +on rule-based control. + +It's essentially the +same matcher. + +In fact, I think the syntax is +a little bit simpler because + +we're not worrying about +arbitrary constants and + +expressions and things. + +There's just variables +and constants. + +OK, well, given that, what's +a primitive query? + +Primitive query is going to be +a rather complicated thing. + +It's going to be-- + +let's think about the query +job of x is d dot y. + +That's a query we +might type in. + +That's going to be implemented +in the system. + +We'll think of it as +this little box. + +Here's the primitive query. + +What this little box is going +to do is take in two streams + +and put out a stream. + +So the shape of a primitive +query is that it's a thing + +where two streams come in +and one stream goes out. + +What these streams are +going to be is + +down here is the database. + +So we imagine all the things +in the database sort of + +sitting there in a stream and +this thing sucks on them. + +So what are some things that +might be in the database? + +Oh, job of Alyssa is +something and some + +other job is something. + +So imagine all of the facts in +the database sitting there in + +the stream. + +That's what comes in here. + +What comes in here is a stream +of dictionaries. + +So one particular dictionary +might say y equals programmer. + +Now, what the query does when +it gets in a dictionary from + +this stream, it finds all +possible ways of matching the + +query against whatever is coming +in from the database. + +It looks at the query as a +pattern, matches it against + +any fact from the database or +all possible ways of finding + +and matching the database with +respect to this dictionary + +that's coming in. + +So for each fact in the +database, it calls the matcher + +using the pattern, fact, +and dictionary. + +And every time it gets a good +match, it puts out the + +extended dictionary. + +So, for example, if this one +comes in and it finds a match, + +out will come a dictionary that +in this case will have y + +equals programmer and +x equals something. + +y is programmer, x is +something, and d + +is whatever it found. + +And that's all. + +And, of course, it's going to +try this for every fact in the + +dictionary. + +So it might find lots of them. + +It might find another one that +says y equals programmer and x + +equals, and d equals. + +So for one frame coming +in, it might put out-- + +for one dictionary coming in, +it might put out a lot of + +dictionaries, or it might +put out none. + +It might have something +that wouldn't match + +like x equals FOO. + +This one might not match +anything in which case nothing + +will go into this stream +corresponding to this frame. + +Or what you might do is put in +an empty frame, and an empty + +frame says try matching +all ways-- + +find all possible ways of +matching the query against + +something in the database +subject to no previous + +restrictions. + +And if you think about what that +means, that's just the + +computation that's done when you +type in a query right off. + +It tries to find all matches. + +So a primitive query sets +up this mechanism. + +And what the language does, when +you type in the query at + +the top level, it takes this +mechanism, feeds in one single + +empty dictionary, and then for +each thing that comes out + +takes the original query and +instantiates the result with + +all the different dictionaries, +producing a new + +stream of instantiated +patterns here. + +And that's what gets printed +on the terminal. + +That's the basic mechanism +going on there. + +Well, why is that +so complicated? + +You probably can think of a lot +simpler ways to arrange + +this match for a primitive query +rather than having all + +of these streams floating +around. + +And the answer is-- + +you probably guess already. + +The answer is this thing extends +elegantly to implement + +the means of combination. + +So, for instance, suppose I +don't only want to do this. + +I don't want to say who to be +everybody's job description. + +Suppose I want to say AND the +job of x is d dot y and the + +supervisor of x is z. + +Now, supervisor of x is z is +going to be another primitive + +query that has the same shape +to take in a stream of data + +objects, a stream of initial +dictionaries, which are the + +restrictions to try and use when +you match, and it's going + +to put out a stream +of dictionaries. + +So that's what this primitive +query looks like. + +And how do I implement +the AND? + +Well, it's simple. + +I just hook them together. + +I take the output of this one, +and I put that to the + +input of that one. + +And I take the dictionary +here and I fan it out. + +And then you see how that's +going to work, because what's + +going to happen is a frame will +now come in here, which + +has a binding for x, y, and d. + +And then when this one gets +it, it'll say, oh, gee, + +subject to these restrictions, +which now already have values + +in the dictionary for y and +x and d, it looks in the + +database and says, gee, can I +find any supervisor facts? + +And if it finds any, out will +come dictionaries which have + +bindings for y and x +and d and z now. + +And then notice that because the +frames coming in here have + +these restrictions, that's the +thing that assures that when + +you do the AND, this x will mean +the same thing as that x. + +Because by the time something +comes floating in here, x has + +a value that you have to match +against consistently. + +And then you remember from the +code from the matcher, there + +was something in the way the +matcher did dictionaries that + +arrange consistent matches. + +So there's AND. + +The important point to notice +is the general shape. + +Look at what happened: the AND +of two queries, say, P and Q. + +Here's P and Q. The AND +of two queries, well, + +it looks like this. + +Each query takes in a stream +from the database, a stream of + +inputs, and puts out a +stream of outputs. + +And the important point to +notice is that if I draw a box + +around this thing and say this +is AND of P and Q, then that + +box has exactly the same +overall shape. + +It's something that takes in +a stream from the database. + +Here it's going to get fanned +out inside, but from the + +outside you don't see that. + +It takes an input stream and +puts out an output stream. + +So this is AND. + +And then similarly, OR +would look like this. + +OR would-- + +although I didn't show +you examples of OR. + +OR would say can I find all ways +of matching P or Q. So I + +have P and Q. Each will +have their shape. + +And the way OR is implemented +is I'll + +take my database stream. + +I'll fan it out. + +I'll put one into P and one into +Q. I'll take my initial + +query stream coming +in and fan it out. + +So I'll look at all the answers +I might get from P and + +all the answers I might get +from Q, and I'll put them + +through some sort of thing that +appends them or merges + +the result into one stream, and +that's what will come out. + +And this whole thing from +the outside is OR. + +And again, you see it has the +same overall shape when looked + +at from the outside. + +What's NOT? + +NOT works kind of +the same way. + +If I have some query P, I take +the primitive query for P. + +Here, I'm going to implement NOT +P. And NOT's just going to + +act as a filter. + +I'll take in the database and +my original stream of + +dictionaries coming in, and what +NOT P will do is it will + +filter these guys. + +And the way it will filter it, +it will say when I get in a + +dictionary here, I'll find all +the matches, and if I find + +any, I'll throw it away. + +And if I don't find any matches +to something coming in + +here, I'll just pass +that through, so + +NOT is a pure filter. + +So AND is-- + +think of these sort +of electoral + +resistors or something. + +AND is series combination and +OR is parallel combination. + +And then NOT is not going +to extend any + +dictionaries at all. + +It's just going to filter it. + +It's going to throw away +the ones for which it + +finds a way to match. + +And list value is sort +of the same way. + +The filter's a little +more complicated. + +It applies to predicate. + +The major point to notice here, +and it's a major point + +we've looked at before, is +this idea of closure. + +The things that we build as a +means of combination have the + +same overall structure +as the primitive + +things that we're combining. + +So the AND of two things when +looked at from the outside has + +the same shape. + +And what that means is that this +box here could be an AND + +or an OR or a NOT or something +because it has the same shape + +to interface to the +larger things. + +It's the same thing that allowed +us to get complexity + +in the Escher picture language +or allows you to immediately + +build up these complicated +structures just out of pairs. + +It's closure. + +And that's the thing that +allowed me to do what by now + +you took for granted when I +said, gee, there's a query + +which is AND of job and salary, +and I said, oh, + +there's another one, +which is AND of + +job, a NOT of something. + +The fact that I can do that is +a direct consequence of this + +closure principle. + +OK, let's break and +then we'll go on. + +AUDIENCE: Where does the +dictionary come from? + +PROFESSOR: The dictionary +comes initially from + +what you type in. + +So when you start this up, the +first thing it does is set up + +this whole structure. + +It puts in one empty +dictionary. + +And if all you have is one +primitive query, then what + +will come out is a bunch +of dictionaries with + +things filled in. + +The general situation that I +have here is when this is in + +the middle of some nest +of combined things. + +Let's look at the picture +over here. + +This supervisor query gets +in some dictionary. + +Where did this one come from? + +This dictionary came from the +fact that I'm looking at the + +output of this primitive +query. + +So maybe to be very specific, +if I literally typed in just + +this query at the top level, +this AND, what would actually + +happen is it would build this +structure and start up this + +whole thing with one +empty dictionary. + +And now this one would process, +and a whole bunch of + +dictionaries would come out with +x, y's and d's in them. + +Run it through this one. + +So now that's the input +to this one. + +This one would now put +out some other stuff. + +And if this itself were buried +in some larger thing, like an + +OR of something, then +that would go feed + +into the next one. + +So you initially get only one +empty dictionary when you + +start it, but as you're in the +middle of processing these + +compounds things, that's where +these cascades of dictionaries + +start getting generated. + +AUDIENCE: Dictionaries only +come about as a result of + +using the queries? + +Or do they become-- + +do they stay someplace in space +like the database does? + +Are these temporary items? + +PROFESSOR: They're created +temporarily in the matcher. + +Really, they're someplace +in storage. + +Initially, someone creates +a thing called the empty + +dictionary that gets initially +fed to this match procedure, + +and then the match procedure +builds some dictionaries, and + +they get passed on and on. + +AUDIENCE: OK, so they'll +go way after the match? + +PROFESSOR: They'll go +away when no one + +needs them again, yeah. + +AUDIENCE: It appears that the +AND performs some redundant + +searches of the database. + +If the first clause matched, +let's say, the third element + +and not on the first two +elements, the second clause is + +going to look at those first two +elements again, discarding + +them because they don't match. + +The match is already +in the dictionary. + +Would it makes sense to carry +the data element from the + +database along with +the dictionary? + +PROFESSOR: Well, in general, +there are other ways to + +arrange this search, and +there's some analysis + +that you can do. + +I think there's a problem in the +book, which talks about a + +different way that you can +cascade AND to eliminate + +various kinds of redundancies. + +This one is meant to be-- + +was mainly meant to be very +simple so you can see how they + +fit together. + +But you're quite right. + +There are redundancies here +that you can get rid of. + +That's another reason why this +language is somewhat slow. + +There are a lot smarter +things you can do. + +We're just trying to show you +a very simple, in principle, + +implementation. + +AUDIENCE: Did you model this +language on Prolog, or did it + +just come out looking +like Prolog? + +PROFESSOR: Well, Jerry insulted +a whole bunch of + +people yesterday, so I might +as well say that the MIT + +attitude towards Prolog is +something that people did in + +about 1971 and decided that it +wasn't really the right thing + +and stopped. + +So we modeled this on the sort +of natural way that this thing + +was done in about 1971, except +at that point, we didn't do it + +with streams. After we were +using it for about six months, + +we discovered that it had all +these problems, some of which + +I'll talk about later. + +And we said, gee, Prolog must +have fixed those, and then we + +found out that it didn't. + +So this does about the +same thing as Prolog. + +AUDIENCE: Does Prolog +use streams? + +PROFESSOR: No. + +In how it behaves, it behaves +a lot like Prolog. + +Prolog uses a backtracking +strategy. + +But the other thing that's +really good about Prolog that + +makes it a usable thing is that +there's a really very, + +very well-engineered compiler +technology that makes it run + +fast. So although you saw the +merge spitting out these + +answers very, very slowly, a +real Prolog will run very, + +very fast. Because even though +it's sort of doing this, the + +real work that went into +Prolog is a very, very + +excellent compiler effort. + +Let's take a break. + +We've looked at the primitive +queries and the ways that + +streams are used to implement +the means of combination: AND + +and OR and NOT. + +Now, let go on to the means +of abstraction. + +Remember, the means of +abstraction in this + +language are rules. + +So z is a boss in division d +if there's some x who has a + +job in division d and z is +the supervisor of x. + +That's what it means for +someone to be a boss. + +And in effect, if you think +about what we're doing with + +relation to this, there's the +query we wrote-- the job of x + +is in d and the supervisor +of x is z-- + +what we in effect want to do +is take this whole mess and + +draw a box around it and say +this whole thing inside the + +box is boss of z +in division d. + +That's in effect what +we want to do. + +So, for instance, if we've +done that, and we want to + +check whether or not it's true +that Ben Bitdiddle is a boss + +in the computer division, so if +I want to say boss of Ben + +Bitdiddle in the computer +division, imagine typing that + +in as query to the system, in +effect what we want to do is + +set up a dictionary here, which +has z to Ben Bitdiddle + +and d to computer. + +Where did that dictionary +come from? + +Let's look at the slide +for one second. + +That dictionary came from +matching the query that said + +boss of Ben Bitdiddle and +computer onto the conclusion + +of the rule: boss of z and d. + +So we match the query to the +conclusion of the rule. + +That gives us a dictionary, and +that's the thing that we + +would now like to put into +this whole big thing and + +process and see if anything +comes out the other side. + +If anything comes out, +it'll be true. + +That's the basic idea. + +So in general, the way we +implement a rule is we match + +the conclusion of the rule +against something we might + +want to check it's true. + +That match gives us a +dictionary, and with respect + +to that dictionary, we process +the body of the rule. + +Well, that's really all +there is, except for + +two technical points. + +The first technical point is +that I might have said + +something else. + +I might have said who's the boss +in the computer division? + +So I might say boss of who +in computer division. + +And if I did that, what I would +really like to do in + +effect is start up this +dictionary with a match that + +sort of says, well, d +is computer and z is + +whatever who is. + +And our matcher won't +quite do that. + +That's not quite matching +a pattern against data. + +It's matching two patterns and +saying are they consistent or + +not or what ways make +them consistent. + +In other words, what we need +is not quite a pattern + +matcher, but something +a little bit more + +general called a unifier. + +And a unifier is a slight +generalization + +of a pattern matcher. + +What a unifier does is take two +patterns and say what's + +the most general thing you can +substitute for the variables + +in those two patterns to make +them satisfy the pattern + +simultaneously? + +Let me give you an example. + +If I have the pattern +two-element list, which is x + +and x, so I have a two-element +list where both elements are + +the same and otherwise I don't +care what they are, and I + +unify that against the pattern +that says there's a + +two-element list, and the first +one is a and something + +in c and the second one is a +and b and z, then what the + +unifier should tell me is, oh +yeah, in that dictionary, x + +has to be a, b, c, and y has +to be d and z has to be c. + +Those are the restrictions I'd +have to put on the values of + +x, y, and z to make these two +unify, or in other words, to + +make this match x and +make this match x. + +The unifier should be +able to deduce that. + +But the unifier may-- + +there are more complicated +things. + +I might have said something a +little bit more complicated. + +I might have said there's a list +with two elements, and + +they're both the same, and +they should unify against + +something of this form. + +And the unifier should be able +to deduce from that. + +Like that y would have to be +b. y would have to be b. + +Because these two are the same, +so y's got to be b. + +And v here would have to be a. + +And z and w can be anything, +but they have + +to be the same thing. + +And x would have to be b, +followed by a, followed by + +whatever w is or whatever +z is, which is the same. + +So you see, the unifier somehow +has to deduce things + +to unify these patterns. + +So you might think there's some +kind of magic deduction + +going on, but there's not. + +A unifier is basically a very +simple modification of a + +pattern matcher. + +And if you look in the book, +you'll see something like + +three or four lines of code +added to the pattern matcher + +you just saw to handle +the symmetric case. + +Remember, the pattern matcher +has a place where it says is + +this variable matching +a constant. + +And if so, it checks +in the dictionary. + +There's only one other clause in +the unifier, which says is + +this variable matching a +variable, in which case you go + +look in the dictionary and see +if that's consistent with + +what's in the dictionary. + +So all the, quote, deduction +that's in this language, if + +you sort of look at it, sort +of sits in the rule + +applications, which, if you +look at that, sits in the + +unifier, which, if you look at +that under a microscope, sits + +essentially in the +pattern matcher. + +There's no magic at all +going on in there. + +And the, quote, deduction that +you see is just the fact that + +there's this recursion, +which is unwinding the + +matches bit by bit. + +So it looks like this thing is +being very clever, but in + +fact, it's not being +very clever at all. + +There are cases where a unifier + +might have to be clever. + +Let me show you one more. + +Suppose I want to unify a list +of two elements, x and x, with + +a thing that says it's y +followed by a dot y. + +Now, if you think of what that +would have to mean, it would + +have to mean that x had better +be the same as y, but also x + +had better be the same as a list +whose first element is a + +and whose rest is y. + +And if you think about what that +would have to mean, it + +would have to mean that y is +the infinite list of a's. + +In some sense, in order to do +that unification, I have to + +solve the fixed-point equation +cons of a to y is equal to y. + +And in general, I wrote +a very simple one. + +Really doing unification might +have to solve an arbitrary + +fixed-point equation: +f of y equals y. + +And basically, you can't do that +and make the thing finite + +all the time. + +So how does the logic language +handle that? + +The answer is it doesn't. + +It just punts. + +And there's a little check in +the unifier, which says, oh, + +is this one of the hard cases +which when I go to match + +things would involve solving +a fixed-point equation? + +And in this case, I will +throw up my hands. + +And if that check were not in +there, what would happen? + +In most cases is that the +unifier would just go into an + +infinite loop. + +And other logic programming +languages work like that. + +So there's really no magic. + +The easy case is done +in a matcher. + +The hard case is not +done at all. + +And that's about the state +of this technology. + +Let me just say again formally +how rules work now that I + +talked about unifiers. + +So the official definition is +that to apply a rule, we-- + +well, let's start using some +words we've used before. + +Let's talk about sticking +dictionaries into these big + +boxes of query things as +evaluating these large queries + +relative to an environment +or a frame. + +So when you think of that +dictionary, what's the + +dictionary after all? + +It's a bunch of meanings +for symbols. + +That's what we've been calling +frames or environments. + +What does it mean to do some +processing relevant to an + +environment? + +That's what we've been +calling evaluation. + +So we can say the way that you +apply a rule is to evaluate + +the rule body relative to an +environment that's formed by + +unifying the rule conclusion +with the given query. + +And the thing I want you to +notice is the complete formal + +similarity to the net of +circular evaluator or the + +substitution model. + +To apply a procedure, we +evaluate the procedure body + +relative to an environment +that's formed by blinding the + +procedure parameters +to the arguments. + +There's a complete formal +similarity here between the + +rules, rule application, and +procedure application even + +though these things are +very, very different. + +And again, you have the +EVAL APPLY loop. + +EVAL and APPLY. + +So in general, I might be +processing some combined + +expression that will turn into a +rule application, which will + +generate some dictionaries or +frames or environments-- + +whatever you want to call them-- +from match, which will + +then be the input to some big +compound thing like this. + +This has pieces of it and may +have other rule applications. + +And you have essentially the +same cycle even though there's + +nothing here at all that +looks like procedures. + +It really has to do with the +fact you've built a language + +whose means of combination +and abstraction + +unwind in certain ways. + +And then in general, what +happens at the very top level, + +you might have rules in your +database also, so things in + +this database might be rules. + +There are ways to check +that things are true. + +So it might come in here and +have to do a rule check. + +And then there's some control +structure which says, well, + +you look at some rules, and +you look at some data + +elements, and you look at some +rules and data elements, and + +these fan out and out and out. + +So it becomes essentially +impossible to say what order + +it's looking at these things in, +whether it's breadth first + +or depth first or anything. + +And it's even more impossible +because the actual order is + +somehow buried in the delays of +the streams. So what's very + +hard to tell from this is the +order in which it's scanned. + +But what's true, because you're +looking at the stream + +view, is that all of them +eventually get looked at. + +Let me just mention one tiny +technical problem. + +Suppose I tried saying boss of +y is computer, then a funny + +thing would happen. + +As I stuck a dictionary with +y in here, I might get-- + +this y is not the same as that +y, which was the other piece + +of somebody's job description. + +So if I really only did +literally what I said, we'd + +get some variable conflict +problems. So I lied to you a + +little bit. + +Notice that problem is +exactly a problem + +we've run into before. + +It is precisely the need for +local variables in a language. + +When I have the sum of +squares, that x had + +better not be that x. + +That's exactly the same +as this y had + +better not be that y. + +And we know how to solve that. + +That was this whole environment +model, and we + +built chains of frames and all +sorts of things like that. + +There's a much more brutal +way to solve it. + +In the query language, we +didn't even do that. + +We did something completely +brutal. + +We said every time you apply a +rule, rename consistently all + +the variables in the rule to +some new unique names that + +won't conflict with anything. + +That's conceptually simpler, +but really brutal and not + +particularly efficient. + +But notice, we could have +gotten rid of all of our + +environment structures if we +defined for procedures in Lisp + +the same thing. + +If every time we applied +a procedure and did the + +substitution model we renamed +all the variables in the + +procedure, then we never would +have had to worry about local + +variables because they +would never arise. + +OK, well, that would be +inefficient, and it's + +inefficient here in the query +language, too, but we did it + +to keep it simple. + +Let's break for questions. + +AUDIENCE: When you started this +section, you emphasized + +how powerful our APPLY EVAL +model was that we could use it + +for any language. + +And then you say we're going to +have this language which is + +so different. + +It turns out that this language, +as you just pointed + +out, is very much the same. + +I'm wondering if you're arguing +that all languages end + +up coming down to this you can +apply a rule or apply a + +procedure or some +kind of apply? + +PROFESSOR: I would say that +pretty much any language where + +you really are building up these +means of combination and + +giving them simpler names and +you're saying anything of the + +sort, like here's a general kind +of expression, like how + +to square something, almost +anything that you + +would call a procedure. + +If that's got to have +parts, you have to + +unwind those parts. + +You have to have some kind of +organization which says when I + +look at the abstract variables +or tags or whatever you want + +to call them that might stand +for particular things, you + +have to keep track of that, +and that's going to be + +something like an environment. + +And then if you say this part +can have parts which I have to + +unwind, you've got to have +something like this cycle. + +And lots and lots of languages +have that character when they + +sort of get put together +in this way. + +This language again really is +different because there's + +nothing like procedures +on the outside. + +When you go below the surface +and you see the + +implementation, of course, it +starts looking the same. + +But from the outside, it's a +very different world view. + +You're not computing functions +of inputs. + +AUDIENCE: You mentioned earlier +that when you build + +all of these rules in pattern +matcher and with the delayed + +action of streams, you really +have no way to know in what + +order things are evaluated. + +PROFESSOR: Right. + +AUDIENCE: And that would +indicate then that you should + +only express declarative +knowledge that's true for + +all-time, no-time sequence +built into it. + +Otherwise, these things +get all-- + +PROFESSOR: Yes. + +Yes. + +The question is this really is +set up for doing declarative + +knowledge, and as I presented +it-- and I'll show you some of + +the ugly warts under this +after the break. + +As I presented it, it's +just doing logic. + +And in principle, if it were +logic, it wouldn't matter what + +order it's getting done. + +And it's quite true when you +start doing things where you + +have side effects like adding +things to the database and + +taking things out, and we'll see +some others, you use that + +kind of control. + +So, for example, contrasting +with Prolog. + +Say Prolog has various features +where you really + +exploit the order +of evaluation. + +And people write Prolog +programs that way. + +That turns out to be very +complicated in Prolog, + +although if you're +an expert Prolog + +programmer, you can do it. + +However, here I don't think +you can do it at all. + +It's very complicated because +you really are giving up + +control over any prearranged +order of trying things. + +AUDIENCE: Now, that would +indicate then that you have a + +functional mapping. + +And when you started out this +lecture, you said that we + +express the declarative +knowledge which is a relation, + +and we don't talk about the +inputs and the outputs. + +PROFESSOR: Well, there's a +pun on functional, right? + +There's function in the sense +of no side effects and not + +depending on what order +is going on. + +And then there's functional in +the sense of mathematical + +function, which means +input and output. + +And it's just that pun that +you're making, I think. + +AUDIENCE: I'm a little unclear +on what you're doing with + +these two statements, the +two boss statements. + +Is the first one building up +the database and the second + +one a query or-- + +PROFESSOR: OK, I'm sorry. + +What I meant here, if I +type something like + +this in as a query-- + +I should have given an example +way at the very beginning. + +If I type in job, Ben Bitdiddle, +computer wizard, + +what the processing will do is +if it finds a match, it'll + +find a match to that exact +thing, and it'll type out a + +job, Ben Bitdiddle, +computer wizard. + +If it doesn't find a match, +it won't find anything. + +So what I should have said is +the way you use the query + +language to check whether +something is true, remember, + +that's one of the things +you want to do in logic + +programming, is you type in +your query and either that + +comes out or it doesn't. + +So what I was trying to +illustrate here, I wanted to + +start with a very simple +example before + +talking about unifiers. + +So what I should have said, if I +just wanted to check whether + +this is true, I could type that +in and see if anything + +came out + +AUDIENCE: And then +the second one-- + +PROFESSOR: The second one +would be a real query. + +AUDIENCE: A real query, yeah. + +PROFESSOR: What would come out, +see, it would go in here + +say with FOO, and in would go +frame that says z is bound to + +who and d is bound +to computer. + +And this will pass through, and +then by the time it got + +out of here, who would +pick up a binding. + +AUDIENCE: On the unifying thing +there, I still am not + +sure what happens +with who and z. + +If the unifying-- + +the rule here says-- + +OK, so you say that you can't +make question mark equal to + +question mark who. + +PROFESSOR: Right. + +That's what the matcher +can't do. + +But what this will mean to a +unifier is that there's an + +environment with three +variables. + +d here is computer. + +z is whatever who is. + +So if later on in the matcher +routine it said, for example, + +who has to be 3, then when I +looked up in the dictionary, + +it will say, oh, z is 3 because +it's the same as who. + +And that's in some sense the +only thing you need to do to + +extend the unifier +to a matcher. + +AUDIENCE: OK, because it looked +like when you were + +telling how to unify it, it +looked like you would put the + +things together in such a way +that you'd actually solve and + +have a value for both of them. + +And what it looks like now is +that you're actually pass a + +dictionary with two variables +and the variables are linked. + +PROFESSOR: Right. + +It only looks like you're +solving for both of them + +because you're sort of looking +at the whole solution at once. + +If you sort of watch the thing +getting built up recursively, + +it's merely this. + +AUDIENCE: OK, so you +do pass off that + +dictionary with two variables? + +PROFESSOR: That's right. + +AUDIENCE: And link? + +PROFESSOR: Right. + +It just looks like an +ordinary dictionary. + +AUDIENCE: When you're talking +about the unifier, is it that + +there are some cases or some +points that you are not able + +to use by them? + +PROFESSOR: Right. + +AUDIENCE: Can you just by +building the rules or writing + +the forms know in advance if +you are going to be able to + +solve to get the unification +or not? + +Can you add some properties +either to the rules itself or + +to the formula that you're +writing so that you avoid the + +problem of not finding +unification? + +PROFESSOR: I mean, you can +agree, I think, to write in a + +fairly restricted way where +you won't run into it. + +See, because what +you're getting-- + +see, the place where you get +into problems is when you-- + +well, again, you're trying to +match things like that against + +things where these +have structure, + +where a, y, b, y something. + +So this is the kind of +place where you're + +going to get into trouble. + +AUDIENCE: So you can do +that syntactically? + +PROFESSOR: So you can kind of +watch your rules in the kinds + +of things that your writing. + +AUDIENCE: So that's the problem +that the builder of + +the database has to +be concerned? + +PROFESSOR: That's a problem. + +It's a problem either-- not +quite the builder of the + +database, the person who is +expressing the rules, or the + +builder of the database. + +What the unifier actually does +is you can check at the next + +level down when you actually get +to the unifier and you'll + +see in the code where it looks +up in the dictionary. + +If it sort of says what +does y have to be? + +Oh, does y have to be something +that contains a y as + +its expression? + +At that point, the unifier and +say, oh my God, I'm trying to + +solve a fixed-point equation. + +I'll give it up here. + +AUDIENCE: You make the +distinction between the rules + +in the database. + +Are the rules added +to the database? + +PROFESSOR: Yes. + +Yes, I should have said that. + +One way to think about rules +is that they're just other + +things in the database. + +So if you want to check the +things that have to be checked + +in the database, they're kind +of virtual facts that are in + +the database. + +AUDIENCE: But in that +explanation, you made the + +differentiation between database +and the rules itself. + +PROFESSOR: Yeah, I probably +should not have done that. + +The only reason to do that +is in terms of the + +implementation. + +When you look at the +implementation, there's a part + +which says check either +primitive assertions in the + +database or check rules. + +And then the real reason why +you can't tell what order + +things are going to come out +in and is that the rules + +database and the data database +sort of get merged in a kind + +of delayed evaluation way. + +And so that's what makes the +order very complicated. + +OK, let's break. + +We've just seen how the +logic language works + +and how rules work. + +Now, let's turn to a more +profound question. + +What do these things mean? + +That brings us to the subtlest, +most devious part of + +this whole query language +business, and that is that + +it's not quite what +it seems to be. + +AND and OR and NOT and the +logical implication of rules + +are not really the AND and +OR and NOT and logical + +implication of logic. + +Let me give you an +example of that. + +Certainly, if we have two things +in logic, it ought to + +be the case that AND of P and Q +is the same as AND of Q and + +P and that OR of P and Q is the +same as OR of Q and P. But + +let's look here. + +Here's an example. + +Let's talk about somebody +outranking somebody else in + +our little database +organization. + +We'll say s is outranked by b or +if either the supervisor of + +this is b or there's some middle +manager here, that + +supervisor of s is m, and +m is outranked by b. + +So there's one way to define +rule outranked by. + +Or we can write exactly the +same thing, except at the + +bottom here, we reversed the +order of these two clauses. + +And certainly if this were +logic, those ought to mean the + +same thing. + +However, in our particular +implementation, if you say + +something like who's outranked +by Ben Bitdiddle, what you'll + +find is that this rule will +work perfectly well and + +generate answers, whereas +this rule will go + +into an infinite loop. + +And the reason for that is that +this will come in and + +say, oh, who's outranked +by Ben Bitdiddle? + +Find an s which is outranked +by b, where b is Ben + +Bitdiddle, which is going to +happen in it a subproblem. + +Oh gee, find an m such as m is +outranked by Ben Bitdiddle + +with no restrictions on m. + +So this will say in order to +solve this problem, I solve + +exactly the same problem. + +And then after I've solved +that, I'll check for a + +supervisory relationship. + +Whereas this one won't get into +that, because before it + +tries to find this outranked by, +it'll already have had a + +restriction on m here. + +So these two things which ought +to mean the same, in + +fact, one goes into +an infinite loop. + +One does not. + +That's a very extreme case of +a general thing that you'll + +find in logic programming that +if you start changing the + +order of the things in the +ANDs or ORs, you'll find + +tremendous differences +in efficiency. + +And we just saw an infinitely +big difference in efficiency + +and an infinite loop. + +And there are similar things +having to do with the order in + +which you enter rules. + +The order in which it happens +to look at rules in the + +database may vastly change the +efficiency with which it gets + +out answers or, in fact, send +it into an infinite loop for + +some orderings. + +And this whole thing has to do +with the fact that you're + +checking these rules +in some order. + +And some rules may lead to +really long paths of + +implication. + +Others might not. + +And you don't know a priori +which ones are good and which + +ones are bad. + +And there's a whole bunch of +research having to do with + +that, mostly having to do with +thinking about making parallel + +implementations of logic +programming languages. + +And in some sense, what you'd +like to do is check all rules + +in parallel and whichever +ones get answers, + +you bubble them up. + +And if some go down +infinite deductive + +changed, well, you just-- + +you know, memory is cheap and +processors are cheap, and you + +just let them buzz for as +for as long as you want. + +There's a deeper problem, +though, in comparing this + +logic language to real logic. + +The example I just showed you, +it went into an infinite loop + +maybe, but at least it didn't +give the wrong answer. + +There's an actual deeper +problem when we start + +comparing, seriously comparing +this logic language with real + +classical logic. + +So let's sort of review +real classical logic. + +All humans are mortal. + +That's pretty classical logic. + +Then maybe we'll continue +in the very + +best classical tradition. + +We'll say all-- + +let's make it really +classical. + +All Greeks are human, which +has the syllogism that + +Socrates is a Greek. + +And then what do +you write here? + +I think three dots, +classical logic. + +Therefore, then the syllogism, +Socrates is mortal. + +So there's some real honest +classical logic. + +Let's compare that with our +classical logic database. + +So here's a classical +logic database. + +Socrates is a Greek. + +Plato is a Greek. + +Zeus is a Greek, and +Zeus is a god. + +And all humans are mortal. + +To show that something is +mortal, it's enough to show + +that it's human. + +All humans are fallible. + +And all Greeks are humans +is not quite right. + +This says that all Greeks who +are not gods are human. + +So to show something's human, +it's enough to show it's a + +Greek and not a god. + +And the address of any Greek +god is Mount Olympus. + +So there's a little classical +logic database. + +And indeed, that would +work fairly well. + +If we type that in and say is +Socrates mortal or Socrates + +fallible or mortal? + +It'll say yes. + +Is Plato mortal and fallible. + +It'll say yes. + +If we say is Zeus mortal? + +It won't find anything. + +And it'll work perfectly well. + +However, suppose we want +to extend this. + +Let's define what it means for +someone to be a perfect being. + +Let's say rule: a +perfect being. + +And I think this is right. + +If you're up on your medieval +scholastic philosophy, I + +believe that perfect beings +are ones who were neither + +mortal nor fallible. + +AND NOT mortal x, +NOT fallible x. + +So we'll define this system +to teach it what a + +perfect being is. + +And now what we're going to do +is he ask for the address of + +all the perfect beings. + +AND the address of x is +y and x is perfect. + +And so what we're generating +here is the world's most + +exclusive mailing list. For the +address of all the perfect + +things, we might have +typed this in. + +Or we might type in this. + +We'll say AND perfect of x and +the address of x is y. + +Well, suppose we type all that +in and we try this query. + +This query is going to +give us an answer. + +This query will say, yeah, +Mount Olympus. + +This query, in fact, is going +to give us nothing. + +It will say no addresses +of perfect beings. + +Now, why is that? + +Why is there a difference? + +This is not an infinite +loop question. + +This is a different +answer question. + +The reason is that if you +remember the implementation of + +NOT, NOT acted as a filter. + +NOT said I'm going to take some +possible dictionaries, + +some possible frames, some +possible answers, and filter + +out the ones that happened to +satisfy some condition, and + +that's how I implement NOT. + +If you think about what's going +on here, I'll build this + +query box where the output of an +address piece gets fed into + +a perfect piece. + +What will happen is the address +piece will set up some + +things of everyone whose +address I know. + +Those will get filtered by the +NOTs inside perfect here. + +So it will throw out the ones +which happened to be either + +mortal or fallible. + +In the other order what happens +is I set this up, + +started up with an +empty frame. + +The perfect in here doesn't find +anything for the NOTs to + +filter, so nothing comes +out here at all. + +And there's sort of nothing +there that gets fed into the + +address thing. + +So here, I don't +get an answer. + +And again, the reason +for that is NOT + +isn't generating anything. + +NOT's only throwing +out things. + +And if I never started up with +anything, there's nothing for + +it to throw out. + +So out of this thing, I +get the wrong answer. + +How can you fix that? + +Well, there are ways +to fix that. + +So you might say, well, +that's sort of stupid. + +Why are you just doing +all your NOT + +stuff at the beginning? + +The right way to implement NOT +is to realize that when you + +have conditions like NOT, you +should generate all your + +answers first, and then with +each of these dictionaries + +pass along until at the very +end I'll do filtering. + +And there are implementations +of logic languages that work + +like that that solve this +particular problem. + +However, there's a more profound +problem, which is + +which one of these is +the right answer? + +Is it Mount Olympus +or is it nothing? + +So you might say it's Mount +Olympus, because after all, + +Zeus is in that database, +and Zeus was + +neither mortal nor fallible. + +So you might say Zeus wants to +satisfy NOT mortal Zeus or NOT + +fallible Zeus. + +But let's actually look +at that database. + +Let's look at it. + +There's no way-- + +how does it know that Zeus +is not fallible? + +There's nothing in +there about that. + +What's in there is that +humans are fallible. + +How does it know that +Zeus is not mortal? + +There's nothing in +there about that. + +It just said I don't have +any rule, which-- + +the only way I can deduce +something's mortal is if it's + +human, and that's all it really +knows about mortal. + +And in fact, if you remember +your classical mythology, you + +know that the Greek gods were +not mortal but fallible. + +So the answer is not +in the rules there. + +See, why does it deduce that? + +See, Socrates would certainly +not have made + +this error of logic. + +What NOT needs in this +language is not NOT. + +It's not the NOT of logic. + +What NOT needs in this language +is not deducible from + +things in the database as +opposed to not true. + +That's a very big difference. + +Subtle, but big. + +So, in fact, this is perfectly +happy to say not anything that + +it doesn't know about. + +So if you ask it is it not +true that Zeus likes + +chocolate ice cream? + +It will say sure, +it's not true. + +Or anything else or anything +it doesn't know about. + +NOT means not deducible from +the things you've told me. + +In a world where you're +identifying not deducible + +with, in fact, not true, this +is called the closed world + +assumption. + +The closed world assumption. + +Anything that I cannot deduce +from what I know + +is not true, right? + +If I don't know anything about +x, the x isn't true. + +That's very dangerous. + +From a logical point of view, +first of all, it doesn't + +really makes sense. + +Because if I don't know anything +about x, I'm willing + +to say not x. + +But am I willing to +say not not x? + +Well, sure, I don't +know anything + +about that either maybe. + +So not not x is not necessarily +the same as x and + +so on and so on and so on, so +there's some sort of funny + +bias in there. + +So that's sort of funny. + +The second thing, if you start +building up real reasoning + +programs based on this, think +how dangerous that is. + +You're saying I know I'm in a +position to deduce everything + +true that's relevant +to this problem. + +I'm reasoning, and built into my +reasoning mechanism is the + +assumption that anything that I +don't know can't possibly be + +relevant to this +problem, right? + +There are a lot of big +organizations that work like + +that, right? + +Most corporate marketing +divisions work like that. + +You know the consequences +to that. + +So it's very dangerous to start +really typing in these + +big logical implication systems +and going on what they + +say, because they have +this really limiting + +assumption built in. + +So you have to be very, very +careful about that. + +And that's a deep problem. + +That's not a problem about we +can make a little bit cleverer + +implementation and do the +filters and organize the + +infinite loops to make +them go away. + +It's a different kind +of problem. + +It's a different semantics. + +So I think to wrap this up, it's +fair to say that logic + +programming I think is a +terrifically exciting idea, + +the idea that you can bridge +this gap from the imperative + +to the declarative, that you +can start talking about + +relations and really get +tremendous power by going + +above the abstraction +of what's my input + +and what's my output. + +And linked to logic, the problem +is it's a goal that I + +think has yet to be realized. + +And probably one of the very +most interesting research + +questions going on now in +languages is how do you + +somehow make a real +logic language? + +And secondly, how do you bridge +the gap from this world + +of logic and relations to the +worlds of more traditional + +languages and somehow combine +the power of both. + +OK, let's break. + +AUDIENCE: Couldn't you solve +that last problem by having + +the extra rules that imply it? + +The problem here is you have the +definition of something, + +but you don't have the +definition of its opposite. + +If you include in the database +something that says something + +implies mortal x, something +else implies not mortal x, + +haven't you basically +solved the problem? + +PROFESSOR: But the issue +is do you put a finite + +number of those in? + +AUDIENCE: If things are +specified always in pairs-- + +PROFESSOR: But the impression +is then what do + +you do about deduction? + +You can't specify NOTs. + +But the problem is, in a big +system, it turns out that + +might not be a finite +number of things. + +There are also sort +of two issues. + +Partly it might not be finite. + +Partly it might be that's +not what you want. + +So a good example would be +suppose I want to do + +connectivity. + +I want a reason about +connectivity. + +And I'm going to tell you +there's four things: a and b + +and c and d. + +And I'll tell you a is connected +to b and c's + +connected to d. + +And now I'll tell you +is a connected to d? + +That's the question. + +There's an example where I would +like something like the + +closed world assumption. + +That's a tiny toy, but a lot of +times, I want to be able to + +say something like anything +that I haven't told you, + +assume is not true. + +So it's not as simple as you +only want to put in explicit + +NOTs all over the place. + +It's that sometimes it +really isn't clear + +what you even want. + +That having to specify both +everything and not everything + +is too precise, and then you get +down into problems there. + +But there are a lot of +approaches that explicitly put + +in NOTs and reason +based on that. + +So it's a very good idea. + +It's just that then it starts +becoming a little cumbersome + +in the very large problems +you'd like to use. + +AUDIENCE: I'm not sure how +directly related to the + +argument this is, but one of +your points was that one of + +the dangers of the closed rule +is you never really know all + +the things that are there. + +You never really know +all the parts to it. + +Isn't that a major problem +with any programming? + +I always write programs where I +assume that I've got all the + +cases, and so I check for them +all or whatever, and somewhere + +down the road, I find +out that I didn't + +check for one of them. + +PROFESSOR: Well, sure, +it's true. + +But the problem here is it's +that assumption which is the + +thing that you're making if you +believe you're identifying + +this with logic. + +So you're quite right. + +It's a situation you're +never in. + +The problem is if you're +starting to believe that what + +this is doing is logic and you +look at the rules you write + +down and say what can I deduce +from them, you have to be very + +careful to remember that NOT +means something else. + +And it means something else +based on an assumption which + +is probably not true. + +AUDIENCE: Do I understand you +correctly that you cannot fix + +this problem without killing +off all possibilities of + +inference through +altering NOT? + +PROFESSOR: No, that's +not quite right. + +There are other-- + +there are ways to do logic +with real NOTs. + +There are actually +ways to do that. + +But they're very inefficient +as far as anybody knows. + +And they're much more-- + +the, quote, inference in here is +built into this unifier and + +this pattern matching +unification algorithm. + +There are ways to automate +real logical reasoning. + +But it's not based on that, +and logic programming + +languages don't tend to do +that because it's very + +inefficient as far +as anybody knows. + +All right, thank you. \ No newline at end of file diff --git a/R8O0vlHBeNc.txt b/R8O0vlHBeNc.txt new file mode 100644 index 0000000000000000000000000000000000000000..9a47d399078390e15cc0b5152fada3c880949fe8 --- /dev/null +++ b/R8O0vlHBeNc.txt @@ -0,0 +1,16331 @@ +align:start position:0% + +we're + + align:start position:0% +we're + + + align:start position:0% +we're +switching topics + + align:start position:0% +switching topics + + + align:start position:0% +switching topics +so far we focused on + + align:start position:0% +so far we focused on + + + align:start position:0% +so far we focused on +sort of early vision the low level + + align:start position:0% +sort of early vision the low level + + + align:start position:0% +sort of early vision the low level +material what to do with gray levels + + align:start position:0% +material what to do with gray levels + + + align:start position:0% +material what to do with gray levels +how to detect + + align:start position:0% +how to detect + + + align:start position:0% +how to detect +features of certain types in + + align:start position:0% +features of certain types in + + + align:start position:0% +features of certain types in +particular edges and we talked about + + align:start position:0% +particular edges and we talked about + + + align:start position:0% +particular edges and we talked about +very accurately finding edges + + align:start position:0% +very accurately finding edges + + + align:start position:0% +very accurately finding edges +we could continue along that line we + + align:start position:0% +we could continue along that line we + + + align:start position:0% +we could continue along that line we +could talk about finding so-called + + align:start position:0% +could talk about finding so-called + + + align:start position:0% +could talk about finding so-called +interesting points + + align:start position:0% +interesting points + + + align:start position:0% +interesting points +but let's move on to the next stage + + align:start position:0% +but let's move on to the next stage + + + align:start position:0% +but let's move on to the next stage +where we're actually using + + align:start position:0% +where we're actually using + + + align:start position:0% +where we're actually using +that information + + align:start position:0% +that information + + + align:start position:0% +that information +to achieve some + + align:start position:0% +to achieve some + + + align:start position:0% +to achieve some +purpose + + align:start position:0% +purpose + + + align:start position:0% +purpose +and so we'll be talking about + + align:start position:0% +and so we'll be talking about + + + align:start position:0% +and so we'll be talking about +photogrammetry next + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +you know the name is + + align:start position:0% +you know the name is + + + align:start position:0% +you know the name is +composed of two roots which basically + + align:start position:0% +composed of two roots which basically + + + align:start position:0% +composed of two roots which basically +mean + + align:start position:0% +mean + + + align:start position:0% +mean +measurement + + align:start position:0% +measurement + + + align:start position:0% +measurement +and images so it's about measurement + + align:start position:0% +and images so it's about measurement + + + align:start position:0% +and images so it's about measurement +from images + + align:start position:0% +from images + + + align:start position:0% +from images +and it has its origins in + + align:start position:0% +and it has its origins in + + + align:start position:0% +and it has its origins in +right after photography was invented + + align:start position:0% +right after photography was invented + + + align:start position:0% +right after photography was invented +because people saw the potential for + + align:start position:0% +because people saw the potential for + + + align:start position:0% +because people saw the potential for +map making you'd send someone up in a + + align:start position:0% +map making you'd send someone up in a + + + align:start position:0% +map making you'd send someone up in a +hot air balloon which is popular in + + align:start position:0% +hot air balloon which is popular in + + + align:start position:0% +hot air balloon which is popular in +those days + + align:start position:0% +those days + + + align:start position:0% +those days +and then you have a picture + + align:start position:0% +and then you have a picture + + + align:start position:0% +and then you have a picture +which is uh + + align:start position:0% +which is uh + + + align:start position:0% +which is uh +kind of a map if the ground is flat and + + align:start position:0% +kind of a map if the ground is flat and + + + align:start position:0% +kind of a map if the ground is flat and +you have the camera just the right way + + align:start position:0% +you have the camera just the right way + + + align:start position:0% +you have the camera just the right way +if you were over hilly terrain + + align:start position:0% +if you were over hilly terrain + + + align:start position:0% +if you were over hilly terrain +then + + align:start position:0% +then + + + align:start position:0% +then +taking multiple images might allow you + + align:start position:0% +taking multiple images might allow you + + + align:start position:0% +taking multiple images might allow you +to reconstruct that three-dimensional + + align:start position:0% +to reconstruct that three-dimensional + + + align:start position:0% +to reconstruct that three-dimensional +surface + + align:start position:0% +surface + + + align:start position:0% +surface +so that's the kind of thing we'll be + + align:start position:0% +so that's the kind of thing we'll be + + + align:start position:0% +so that's the kind of thing we'll be +looking at + + align:start position:0% +looking at + + + align:start position:0% +looking at +and in particular we're going to talk + + align:start position:0% +and in particular we're going to talk + + + align:start position:0% +and in particular we're going to talk +about four different problems + + align:start position:0% +about four different problems + + + align:start position:0% +about four different problems +which + + align:start position:0% + + + + align:start position:0% + +have the names + + align:start position:0% + + + + align:start position:0% + +and these are just classic uh problems + + align:start position:0% +and these are just classic uh problems + + + align:start position:0% +and these are just classic uh problems +from + + align:start position:0% + + + + align:start position:0% + +photogrammetry + + align:start position:0% + + + + align:start position:0% + +which you know have been reinvented by + + align:start position:0% +which you know have been reinvented by + + + align:start position:0% +which you know have been reinvented by +people in machine vision and different + + align:start position:0% +people in machine vision and different + + + align:start position:0% +people in machine vision and different +given different names but basically + + align:start position:0% +given different names but basically + + + align:start position:0% +given different names but basically +that's what they are + + align:start position:0% +that's what they are + + + align:start position:0% +that's what they are +so + + align:start position:0% +so + + + align:start position:0% +so +this is the one we'll talk about first + + align:start position:0% +this is the one we'll talk about first + + + align:start position:0% +this is the one we'll talk about first +and it's about + + align:start position:0% + + + + align:start position:0% + +finding the relationship between + + align:start position:0% +finding the relationship between + + + align:start position:0% +finding the relationship between +something in 3d and something else in 3d + + align:start position:0% +something in 3d and something else in 3d + + + align:start position:0% +something in 3d and something else in 3d +and it could be for example that + + align:start position:0% +and it could be for example that + + + align:start position:0% +and it could be for example that +we have + + align:start position:0% + + + + align:start position:0% + +two different coordinate systems two + + align:start position:0% +two different coordinate systems two + + + align:start position:0% +two different coordinate systems two +different sensors + + align:start position:0% +different sensors + + + align:start position:0% +different sensors +you know imagine uh autonomous vehicle + + align:start position:0% +you know imagine uh autonomous vehicle + + + align:start position:0% +you know imagine uh autonomous vehicle +with two + + align:start position:0% +with two + + + align:start position:0% +with two +uh laser sensors + + align:start position:0% +uh laser sensors + + + align:start position:0% +uh laser sensors +and we're trying to relate those two + + align:start position:0% +and we're trying to relate those two + + + align:start position:0% +and we're trying to relate those two +coordinate systems + + align:start position:0% +coordinate systems + + + align:start position:0% +coordinate systems +so + + align:start position:0% +so + + + align:start position:0% +so +there you know the different kind of + + align:start position:0% +there you know the different kind of + + + align:start position:0% +there you know the different kind of +tests one is how do you use the + + align:start position:0% +tests one is how do you use the + + + align:start position:0% +tests one is how do you use the +measurements from these two coordinate + + align:start position:0% +measurements from these two coordinate + + + align:start position:0% +measurements from these two coordinate +systems to get 3d information but before + + align:start position:0% +systems to get 3d information but before + + + align:start position:0% +systems to get 3d information but before +you do that you first have to figure out + + align:start position:0% +you do that you first have to figure out + + + align:start position:0% +you do that you first have to figure out +how those two systems are related + + align:start position:0% +how those two systems are related + + + align:start position:0% +how those two systems are related +so you need to find out the coordinate + + align:start position:0% +so you need to find out the coordinate + + + align:start position:0% +so you need to find out the coordinate +transformation from one sensor + + align:start position:0% +transformation from one sensor + + + align:start position:0% +transformation from one sensor +coordinate system to the other + + align:start position:0% +coordinate system to the other + + + align:start position:0% +coordinate system to the other +so that's one kind of problem + + align:start position:0% +so that's one kind of problem + + + align:start position:0% +so that's one kind of problem +and the + + align:start position:0% +and the + + + align:start position:0% +and the +symmetrical + + align:start position:0% +symmetrical + + + align:start position:0% +symmetrical +problem to that is + + align:start position:0% +problem to that is + + + align:start position:0% +problem to that is +where we have a single coordinate system + + align:start position:0% +where we have a single coordinate system + + + align:start position:0% +where we have a single coordinate system +but + + align:start position:0% +but + + + align:start position:0% +but +either they're two objects + + align:start position:0% +either they're two objects + + + align:start position:0% +either they're two objects +or the object moves + + align:start position:0% +or the object moves + + + align:start position:0% +or the object moves +and we want to know the relationship + + align:start position:0% +and we want to know the relationship + + + align:start position:0% +and we want to know the relationship +between before and after + + align:start position:0% +between before and after + + + align:start position:0% +between before and after +and it's actually just + + align:start position:0% +and it's actually just + + + align:start position:0% +and it's actually just +the same problem + + align:start position:0% +the same problem + + + align:start position:0% +the same problem +and we'll + + align:start position:0% +and we'll + + + align:start position:0% +and we'll +talk about that + + align:start position:0% +talk about that + + + align:start position:0% +talk about that +there's some advantages to + + align:start position:0% +there's some advantages to + + + align:start position:0% +there's some advantages to +attacking the + + align:start position:0% +attacking the + + + align:start position:0% +attacking the +tackling the 3d problem first + + align:start position:0% +tackling the 3d problem first + + + align:start position:0% +tackling the 3d problem first +one is that it has a closed form + + align:start position:0% +one is that it has a closed form + + + align:start position:0% +one is that it has a closed form +solution it's always nice + + align:start position:0% +solution it's always nice + + + align:start position:0% +solution it's always nice +even though + + align:start position:0% +even though + + + align:start position:0% +even though +in some sense in machine vision we often + + align:start position:0% +in some sense in machine vision we often + + + align:start position:0% +in some sense in machine vision we often +are more concerned with the second + + align:start position:0% +are more concerned with the second + + + align:start position:0% +are more concerned with the second +problem which is 2d to 2d + + align:start position:0% + + + + align:start position:0% + +right so um + + align:start position:0% +right so um + + + align:start position:0% +right so um +the main sensor we're concerned with is + + align:start position:0% +the main sensor we're concerned with is + + + align:start position:0% +the main sensor we're concerned with is +a camera + + align:start position:0% +a camera + + + align:start position:0% +a camera +and we get images 2d images + + align:start position:0% +and we get images 2d images + + + align:start position:0% +and we get images 2d images +and for example we might have two + + align:start position:0% +and for example we might have two + + + align:start position:0% +and for example we might have two +cameras get two 2d images and we'd like + + align:start position:0% +cameras get two 2d images and we'd like + + + align:start position:0% +cameras get two 2d images and we'd like +to use them to + + align:start position:0% +to use them to + + + align:start position:0% +to use them to +recover + + align:start position:0% +recover + + + align:start position:0% +recover +the third dimension + + align:start position:0% +the third dimension + + + align:start position:0% +the third dimension +so that's you know binocular stereo for + + align:start position:0% +so that's you know binocular stereo for + + + align:start position:0% +so that's you know binocular stereo for +example + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +that's just one application and again + + align:start position:0% +that's just one application and again + + + align:start position:0% +that's just one application and again +there are two types of problems two + + align:start position:0% +there are two types of problems two + + + align:start position:0% +there are two types of problems two +types of applications one is + + align:start position:0% +types of applications one is + + + align:start position:0% +types of applications one is +how do i recover the three-dimensional + + align:start position:0% +how do i recover the three-dimensional + + + align:start position:0% +how do i recover the three-dimensional +information from those two images and + + align:start position:0% +information from those two images and + + + align:start position:0% +information from those two images and +the other one is how do i first + + align:start position:0% +the other one is how do i first + + + align:start position:0% +the other one is how do i first +get the two cameras lined up so that i + + align:start position:0% +get the two cameras lined up so that i + + + align:start position:0% +get the two cameras lined up so that i +can do that what what how do i find the + + align:start position:0% +can do that what what how do i find the + + + align:start position:0% +can do that what what how do i find the +relationship between these two cameras + + align:start position:0% +relationship between these two cameras + + + align:start position:0% +relationship between these two cameras +where they are in space and how they are + + align:start position:0% +where they are in space and how they are + + + align:start position:0% +where they are in space and how they are +rotated + + align:start position:0% +rotated + + + align:start position:0% +rotated +so + + align:start position:0% +so + + + align:start position:0% +so +exterior orientation + + align:start position:0% +exterior orientation + + + align:start position:0% +exterior orientation +so + + align:start position:0% +so + + + align:start position:0% +so +that + + align:start position:0% + + + + align:start position:0% + +is a mixed problem + + align:start position:0% +is a mixed problem + + + align:start position:0% +is a mixed problem +2d to 3d + + align:start position:0% +2d to 3d + + + align:start position:0% +2d to 3d +and + + align:start position:0% +and + + + align:start position:0% +and +this has to do with the situation where + + align:start position:0% +this has to do with the situation where + + + align:start position:0% +this has to do with the situation where +we have uh + + align:start position:0% +we have uh + + + align:start position:0% +we have uh +an image + + align:start position:0% +an image + + + align:start position:0% +an image +and we also have a 3d model of the thing + + align:start position:0% +and we also have a 3d model of the thing + + + align:start position:0% +and we also have a 3d model of the thing +that we're looking at + + align:start position:0% +that we're looking at + + + align:start position:0% +that we're looking at +and so + + align:start position:0% +and so + + + align:start position:0% +and so +we're trying to figure out where we are + + align:start position:0% + + + + align:start position:0% + +and again how we're oriented in space + + align:start position:0% +and again how we're oriented in space + + + align:start position:0% +and again how we're oriented in space +we're going to keep on hearing about + + align:start position:0% +we're going to keep on hearing about + + + align:start position:0% +we're going to keep on hearing about +rotation and orientation because that's + + align:start position:0% +rotation and orientation because that's + + + align:start position:0% +rotation and orientation because that's +a problem in all of these areas + + align:start position:0% +a problem in all of these areas + + + align:start position:0% +a problem in all of these areas +and so i don't know you could imagine a + + align:start position:0% +and so i don't know you could imagine a + + + align:start position:0% +and so i don't know you could imagine a +drone flying over this area + + align:start position:0% +drone flying over this area + + + align:start position:0% +drone flying over this area +and you have a map of this area + + align:start position:0% +and you have a map of this area + + + align:start position:0% +and you have a map of this area +and you're trying to figure out from the + + align:start position:0% +and you're trying to figure out from the + + + align:start position:0% +and you're trying to figure out from the +image + + align:start position:0% +image + + + align:start position:0% +image +where you are + + align:start position:0% +where you are + + + align:start position:0% +where you are +so that be a typical problem of that + + align:start position:0% +so that be a typical problem of that + + + align:start position:0% +so that be a typical problem of that +form or you're on a spacecraft and + + align:start position:0% +form or you're on a spacecraft and + + + align:start position:0% +form or you're on a spacecraft and +you're staring at the stars and you're + + align:start position:0% +you're staring at the stars and you're + + + align:start position:0% +you're staring at the stars and you're +trying to figure out the rotation in + + align:start position:0% +trying to figure out the rotation in + + + align:start position:0% +trying to figure out the rotation in +space of your spacecraft + + align:start position:0% +space of your spacecraft + + + align:start position:0% +space of your spacecraft +and then the last one is + + align:start position:0% +and then the last one is + + + align:start position:0% +and then the last one is +very similar + + align:start position:0% +very similar + + + align:start position:0% +very similar +and i just write it the other way around + + align:start position:0% +and i just write it the other way around + + + align:start position:0% +and i just write it the other way around +3d to 2d + + align:start position:0% +3d to 2d + + + align:start position:0% +3d to 2d +and that is + + align:start position:0% +and that is + + + align:start position:0% +and that is +interior orientation + + align:start position:0% +interior orientation + + + align:start position:0% +interior orientation +exterior interior refers to the camera + + align:start position:0% +exterior interior refers to the camera + + + align:start position:0% +exterior interior refers to the camera +so interior orientation is basically a + + align:start position:0% +so interior orientation is basically a + + + align:start position:0% +so interior orientation is basically a +camera calibration + + align:start position:0% + + + + align:start position:0% + +so we make the camera to certain specs + + align:start position:0% +so we make the camera to certain specs + + + align:start position:0% +so we make the camera to certain specs +you know certain we have the lenses with + + align:start position:0% +you know certain we have the lenses with + + + align:start position:0% +you know certain we have the lenses with +certain focal length and + + align:start position:0% +certain focal length and + + + align:start position:0% +certain focal length and +we have some kind of + + align:start position:0% +we have some kind of + + + align:start position:0% +we have some kind of +metal case that puts the + + align:start position:0% +metal case that puts the + + + align:start position:0% +metal case that puts the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +image in its position relative to the + + align:start position:0% +image in its position relative to the + + + align:start position:0% +image in its position relative to the +lens but it's never going to be exactly + + align:start position:0% +lens but it's never going to be exactly + + + align:start position:0% +lens but it's never going to be exactly +according to spec so in order to make + + align:start position:0% +according to spec so in order to make + + + align:start position:0% +according to spec so in order to make +very precise measurements using these + + align:start position:0% +very precise measurements using these + + + align:start position:0% +very precise measurements using these +cameras uh we need to first figure out + + align:start position:0% +cameras uh we need to first figure out + + + align:start position:0% +cameras uh we need to first figure out +their properties and we already talked + + align:start position:0% +their properties and we already talked + + + align:start position:0% +their properties and we already talked +about finding the principal point and + + align:start position:0% +about finding the principal point and + + + align:start position:0% +about finding the principal point and +that's you know a form of interior + + align:start position:0% +that's you know a form of interior + + + align:start position:0% +that's you know a form of interior +orientation + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +since i have something here i should + + align:start position:0% +since i have something here i should + + + align:start position:0% +since i have something here i should +have something in the last one + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and in terms of applications + + align:start position:0% +and in terms of applications + + + align:start position:0% +and in terms of applications +you know it's kind of obvious we the the + + align:start position:0% +you know it's kind of obvious we the the + + + align:start position:0% +you know it's kind of obvious we the the +original uh application in + + align:start position:0% +original uh application in + + + align:start position:0% +original uh application in +photogrammetry was making topographic + + align:start position:0% +photogrammetry was making topographic + + + align:start position:0% +photogrammetry was making topographic +maps + + align:start position:0% +maps + + + align:start position:0% +maps +so you'd fly a plane + + align:start position:0% +so you'd fly a plane + + + align:start position:0% +so you'd fly a plane +along some predetermined path + + align:start position:0% +along some predetermined path + + + align:start position:0% +along some predetermined path +taking pictures at regular intervals + + align:start position:0% +taking pictures at regular intervals + + + align:start position:0% +taking pictures at regular intervals +and then a person would + + align:start position:0% +and then a person would + + + align:start position:0% +and then a person would +look through + + align:start position:0% +look through + + + align:start position:0% +look through +an instrument that sort of like a + + align:start position:0% +an instrument that sort of like a + + + align:start position:0% +an instrument that sort of like a +binoculars except it's you're presenting + + align:start position:0% +binoculars except it's you're presenting + + + align:start position:0% +binoculars except it's you're presenting +two of these images and the person's eye + + align:start position:0% +two of these images and the person's eye + + + align:start position:0% +two of these images and the person's eye +brain combination + + align:start position:0% +brain combination + + + align:start position:0% +brain combination +um lines them up + + align:start position:0% +um lines them up + + + align:start position:0% +um lines them up +and uh basically determines the height + + align:start position:0% +and uh basically determines the height + + + align:start position:0% +and uh basically determines the height +at any particular point and in order to + + align:start position:0% +at any particular point and in order to + + + align:start position:0% +at any particular point and in order to +plot the map + + align:start position:0% +plot the map + + + align:start position:0% +plot the map +there would be an artificial point where + + align:start position:0% +there would be an artificial point where + + + align:start position:0% +there would be an artificial point where +you've introduced two + + align:start position:0% +you've introduced two + + + align:start position:0% +you've introduced two +in two points in the two images the + + align:start position:0% +in two points in the two images the + + + align:start position:0% +in two points in the two images the +person's looking at + + align:start position:0% +person's looking at + + + align:start position:0% +person's looking at +and their position determines the height + + align:start position:0% +and their position determines the height + + + align:start position:0% +and their position determines the height +and so the person basically places that + + align:start position:0% +and so the person basically places that + + + align:start position:0% +and so the person basically places that +artificial point on the surface they see + + align:start position:0% +artificial point on the surface they see + + + align:start position:0% +artificial point on the surface they see +and moves it around at that height and + + align:start position:0% +and moves it around at that height and + + + align:start position:0% +and moves it around at that height and +thereby creating a contour and of course + + align:start position:0% +thereby creating a contour and of course + + + align:start position:0% +thereby creating a contour and of course +we we don't do that anymore it's all + + align:start position:0% +we we don't do that anymore it's all + + + align:start position:0% +we we don't do that anymore it's all +now automated + + align:start position:0% +now automated + + + align:start position:0% +now automated +using uh correlation and convolution + + align:start position:0% +using uh correlation and convolution + + + align:start position:0% +using uh correlation and convolution +but uh before we do that we need to + + align:start position:0% +but uh before we do that we need to + + + align:start position:0% +but uh before we do that we need to +figure out how the cameras relate to + + align:start position:0% +figure out how the cameras relate to + + + align:start position:0% +figure out how the cameras relate to +each other + + align:start position:0% +each other + + + align:start position:0% +each other +okay um just to give a + + align:start position:0% +okay um just to give a + + + align:start position:0% +okay um just to give a +really simple example + + align:start position:0% +really simple example + + + align:start position:0% +really simple example +of the kind of thing that + + align:start position:0% +of the kind of thing that + + + align:start position:0% +of the kind of thing that +happens in + + align:start position:0% +happens in + + + align:start position:0% +happens in +photogrammetry + + align:start position:0% + + + + align:start position:0% + +so humans have many depth cues + + align:start position:0% +so humans have many depth cues + + + align:start position:0% +so humans have many depth cues +a dozen or so at least + + align:start position:0% +a dozen or so at least + + + align:start position:0% +a dozen or so at least +and we already talked about some of them + + align:start position:0% +and we already talked about some of them + + + align:start position:0% +and we already talked about some of them +we talked about shading and we talked + + align:start position:0% +we talked about shading and we talked + + + align:start position:0% +we talked about shading and we talked +about shape from shading + + align:start position:0% +about shape from shading + + + align:start position:0% +about shape from shading +and another one is binocular stereo so + + align:start position:0% +and another one is binocular stereo so + + + align:start position:0% +and another one is binocular stereo so +if you + + align:start position:0% +if you + + + align:start position:0% +if you +uh talk to the woman or man in the + + align:start position:0% +uh talk to the woman or man in the + + + align:start position:0% +uh talk to the woman or man in the +street + + align:start position:0% +street + + + align:start position:0% +street +and ask them how do we see 3d and + + align:start position:0% +and ask them how do we see 3d and + + + align:start position:0% +and ask them how do we see 3d and +typically say oh we have two eyes so + + align:start position:0% +typically say oh we have two eyes so + + + align:start position:0% +typically say oh we have two eyes so +this is uh + + align:start position:0% +this is uh + + + align:start position:0% +this is uh +important depth q at least from the + + align:start position:0% +important depth q at least from the + + + align:start position:0% +important depth q at least from the +point of view of + + align:start position:0% +point of view of + + + align:start position:0% +point of view of +you know what how people think we see 3d + + align:start position:0% +you know what how people think we see 3d + + + align:start position:0% +you know what how people think we see 3d +even if it's not the most important + + align:start position:0% +even if it's not the most important + + + align:start position:0% +even if it's not the most important +depth cue + + align:start position:0% +depth cue + + + align:start position:0% +depth cue +but let's take a look at that and look + + align:start position:0% +but let's take a look at that and look + + + align:start position:0% +but let's take a look at that and look +at it in a highly simplified special + + align:start position:0% +at it in a highly simplified special + + + align:start position:0% +at it in a highly simplified special +case situation + + align:start position:0% +case situation + + + align:start position:0% +case situation +so in this situation we have two cameras + + align:start position:0% + + + + align:start position:0% + +and we've lined them up + + align:start position:0% +and we've lined them up + + + align:start position:0% +and we've lined them up +so that + + align:start position:0% +so that + + + align:start position:0% +so that +they are perpendicular to the baseline + + align:start position:0% + + + + align:start position:0% + +so each of the optical axis is + + align:start position:0% +so each of the optical axis is + + + align:start position:0% +so each of the optical axis is +perpendicular to the baseline and the + + align:start position:0% +perpendicular to the baseline and the + + + align:start position:0% +perpendicular to the baseline and the +optical axes are parallel + + align:start position:0% +optical axes are parallel + + + align:start position:0% +optical axes are parallel +and the lenses have the same focal + + align:start position:0% +and the lenses have the same focal + + + align:start position:0% +and the lenses have the same focal +length and so on so + + align:start position:0% +length and so on so + + + align:start position:0% +length and so on so +in practice + + align:start position:0% + + + + align:start position:0% + +we need to be more careful we need to + + align:start position:0% +we need to be more careful we need to + + + align:start position:0% +we need to be more careful we need to +allow for + + align:start position:0% +allow for + + + align:start position:0% +allow for +differences between the cameras and + + align:start position:0% +differences between the cameras and + + + align:start position:0% +differences between the cameras and +typically + + align:start position:0% +typically + + + align:start position:0% +typically +it'll be not very practical to perfectly + + align:start position:0% +it'll be not very practical to perfectly + + + align:start position:0% +it'll be not very practical to perfectly +align them up this way + + align:start position:0% +align them up this way + + + align:start position:0% +align them up this way +this + + align:start position:0% +this + + + align:start position:0% +this +someone at draper lab + + align:start position:0% +someone at draper lab + + + align:start position:0% +someone at draper lab +sutro was his name who spent a long time + + align:start position:0% +sutro was his name who spent a long time + + + align:start position:0% +sutro was his name who spent a long time +working on styria for mars rovers long + + align:start position:0% +working on styria for mars rovers long + + + align:start position:0% +working on styria for mars rovers long +before there really was a mars rover + + align:start position:0% +before there really was a mars rover + + + align:start position:0% +before there really was a mars rover +and + + align:start position:0% +and + + + align:start position:0% +and +he was + + align:start position:0% +he was + + + align:start position:0% +he was +concerned with getting these cameras + + align:start position:0% +concerned with getting these cameras + + + align:start position:0% +concerned with getting these cameras +lined up and let's just say that + + align:start position:0% +lined up and let's just say that + + + align:start position:0% +lined up and let's just say that +he never succeeded it's too + + align:start position:0% +he never succeeded it's too + + + align:start position:0% +he never succeeded it's too +difficult to get them lined up + + align:start position:0% +difficult to get them lined up + + + align:start position:0% +difficult to get them lined up +accurately enough + + align:start position:0% +accurately enough + + + align:start position:0% +accurately enough +and so what we're going to do + + align:start position:0% +and so what we're going to do + + + align:start position:0% +and so what we're going to do +later is + + align:start position:0% +later is + + + align:start position:0% +later is +actually figure out how these cameras + + align:start position:0% +actually figure out how these cameras + + + align:start position:0% +actually figure out how these cameras +relate to each other but just to get a + + align:start position:0% +relate to each other but just to get a + + + align:start position:0% +relate to each other but just to get a +feel for this let's look at + + align:start position:0% +feel for this let's look at + + + align:start position:0% +feel for this let's look at +this situation + + align:start position:0% +this situation + + + align:start position:0% +this situation +and we'll pick an origin that's halfway + + align:start position:0% +and we'll pick an origin that's halfway + + + align:start position:0% +and we'll pick an origin that's halfway +between the lenses + + align:start position:0% +between the lenses + + + align:start position:0% +between the lenses +and the baseline + + align:start position:0% +and the baseline + + + align:start position:0% +and the baseline +length is b so + + align:start position:0% +length is b so + + + align:start position:0% +length is b so +b over 2 from each of those + + align:start position:0% +b over 2 from each of those + + + align:start position:0% +b over 2 from each of those +and then let's suppose that they're + + align:start position:0% +and then let's suppose that they're + + + align:start position:0% +and then let's suppose that they're +a distance f + + align:start position:0% +a distance f + + + align:start position:0% +a distance f +from their respective image planes where + + align:start position:0% +from their respective image planes where + + + align:start position:0% +from their respective image planes where +f is as we know + + align:start position:0% +f is as we know + + + align:start position:0% +f is as we know +not the focal length but slightly larger + + align:start position:0% +not the focal length but slightly larger + + + align:start position:0% +not the focal length but slightly larger +and then we pick some point out here + + align:start position:0% + + + + align:start position:0% + +and we'll image it in both + + align:start position:0% +and we'll image it in both + + + align:start position:0% +and we'll image it in both +cameras + + align:start position:0% + + + + align:start position:0% + +we're leaving out the y direction which + + align:start position:0% +we're leaving out the y direction which + + + align:start position:0% +we're leaving out the y direction which +is perpendicular to the blackboard + + align:start position:0% +is perpendicular to the blackboard + + + align:start position:0% +is perpendicular to the blackboard +because that's less interesting from + + align:start position:0% +because that's less interesting from + + + align:start position:0% +because that's less interesting from +this point of view + + align:start position:0% +this point of view + + + align:start position:0% +this point of view +and so up here we have a point that's at + + align:start position:0% +and so up here we have a point that's at + + + align:start position:0% +and so up here we have a point that's at +x and z + + align:start position:0% +x and z + + + align:start position:0% +x and z +and + + align:start position:0% +and + + + align:start position:0% +and +our task + + align:start position:0% +our task + + + align:start position:0% +our task +is + + align:start position:0% +is + + + align:start position:0% +is +from x l and xr the position in those + + align:start position:0% +from x l and xr the position in those + + + align:start position:0% +from x l and xr the position in those +two image plans to determine uh big x + + align:start position:0% +two image plans to determine uh big x + + + align:start position:0% +two image plans to determine uh big x +and big z so + + align:start position:0% +and big z so + + + align:start position:0% +and big z so +we have the two images + + align:start position:0% +we have the two images + + + align:start position:0% +we have the two images +the object does not + + align:start position:0% +the object does not + + + align:start position:0% +the object does not +image in the same place in the two + + align:start position:0% +image in the same place in the two + + + align:start position:0% +image in the same place in the two +images and from the difference we can + + align:start position:0% +images and from the difference we can + + + align:start position:0% +images and from the difference we can +calculate where it is + + align:start position:0% +calculate where it is + + + align:start position:0% +calculate where it is +whereas for a monocular image of course + + align:start position:0% +whereas for a monocular image of course + + + align:start position:0% +whereas for a monocular image of course +we have that scale factor ambiguity we + + align:start position:0% +we have that scale factor ambiguity we + + + align:start position:0% +we have that scale factor ambiguity we +can tell what direction something lies + + align:start position:0% +can tell what direction something lies + + + align:start position:0% +can tell what direction something lies +in but we have no idea how far away it + + align:start position:0% +in but we have no idea how far away it + + + align:start position:0% +in but we have no idea how far away it +is + + align:start position:0% +is + + + align:start position:0% +is +adding the second eye or lens + + align:start position:0% +adding the second eye or lens + + + align:start position:0% +adding the second eye or lens +gives us that ability + + align:start position:0% +gives us that ability + + + align:start position:0% +gives us that ability +well we just use + + align:start position:0% +well we just use + + + align:start position:0% +well we just use +similar triangles + + align:start position:0% + + + + align:start position:0% + +so using similar triangles + + align:start position:0% + + + + align:start position:0% + +right because um + + align:start position:0% +right because um + + + align:start position:0% +right because um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the x and y are relative to this origin + + align:start position:0% + + + + align:start position:0% + +and so if we want to + + align:start position:0% +and so if we want to + + + align:start position:0% +and so if we want to +have the + + align:start position:0% +have the + + + align:start position:0% +have the +this distance + + align:start position:0% +this distance + + + align:start position:0% +this distance +we need to subtract out half the + + align:start position:0% +we need to subtract out half the + + + align:start position:0% +we need to subtract out half the +baseline and similarly on the other side + + align:start position:0% +baseline and similarly on the other side + + + align:start position:0% +baseline and similarly on the other side +we have to add in half the baseline + + align:start position:0% +we have to add in half the baseline + + + align:start position:0% +we have to add in half the baseline +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +two equations uh two unknowns we can + + align:start position:0% +two equations uh two unknowns we can + + + align:start position:0% +two equations uh two unknowns we can +solve + + align:start position:0% + + + + align:start position:0% + +so the depth is + + align:start position:0% +so the depth is + + + align:start position:0% +so the depth is +inversely proportional to the disparity + + align:start position:0% +inversely proportional to the disparity + + + align:start position:0% +inversely proportional to the disparity +so the disparity is the discrepancy in + + align:start position:0% +so the disparity is the discrepancy in + + + align:start position:0% +so the disparity is the discrepancy in +position if you were to superimpose the + + align:start position:0% +position if you were to superimpose the + + + align:start position:0% +position if you were to superimpose the +left and the right image + + align:start position:0% +left and the right image + + + align:start position:0% +left and the right image +and so that gives us directly uh the + + align:start position:0% +and so that gives us directly uh the + + + align:start position:0% +and so that gives us directly uh the +depth the distance + + align:start position:0% +depth the distance + + + align:start position:0% +depth the distance +and that also allows us to + + align:start position:0% +and that also allows us to + + + align:start position:0% +and that also allows us to +determine the sensitivity to error + + align:start position:0% +determine the sensitivity to error + + + align:start position:0% +determine the sensitivity to error +obviously if we're very far away + + align:start position:0% +obviously if we're very far away + + + align:start position:0% +obviously if we're very far away +the disparity will be very small and + + align:start position:0% +the disparity will be very small and + + + align:start position:0% +the disparity will be very small and +then any small error in measuring the + + align:start position:0% +then any small error in measuring the + + + align:start position:0% +then any small error in measuring the +disparity is going to + + align:start position:0% +disparity is going to + + + align:start position:0% +disparity is going to +produce a large error in depth + + align:start position:0% +produce a large error in depth + + + align:start position:0% +produce a large error in depth +so + + align:start position:0% + + + + align:start position:0% + +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +xr plus xl + + align:start position:0% + + + + align:start position:0% + +and again the disparity uh + + align:start position:0% +and again the disparity uh + + + align:start position:0% +and again the disparity uh +comes into it + + align:start position:0% +comes into it + + + align:start position:0% +comes into it +and the baseline + + align:start position:0% +and the baseline + + + align:start position:0% +and the baseline +and now this time we're sort of taking + + align:start position:0% +and now this time we're sort of taking + + + align:start position:0% +and now this time we're sort of taking +an average of the positions + + align:start position:0% + + + + align:start position:0% + +so we can determine the 3d position well + + align:start position:0% +so we can determine the 3d position well + + + align:start position:0% +so we can determine the 3d position well +we've left out y but + + align:start position:0% +we've left out y but + + + align:start position:0% +we've left out y but +that's pretty easy + + align:start position:0% +that's pretty easy + + + align:start position:0% +that's pretty easy +if we have those + + align:start position:0% +if we have those + + + align:start position:0% +if we have those +two + + align:start position:0% +two + + + align:start position:0% +two +measurements + + align:start position:0% +measurements + + + align:start position:0% +measurements +and + + align:start position:0% + + + + align:start position:0% + +one thing is clear if we increase the + + align:start position:0% +one thing is clear if we increase the + + + align:start position:0% +one thing is clear if we increase the +baseline + + align:start position:0% +baseline + + + align:start position:0% +baseline +the disparity gets larger + + align:start position:0% +the disparity gets larger + + + align:start position:0% +the disparity gets larger +and so then + + align:start position:0% +and so then + + + align:start position:0% +and so then +the measurement will be more accurate + + align:start position:0% +the measurement will be more accurate + + + align:start position:0% +the measurement will be more accurate +if we + + align:start position:0% +if we + + + align:start position:0% +if we +increase the focal length + + align:start position:0% +increase the focal length + + + align:start position:0% +increase the focal length +then + + align:start position:0% +then + + + align:start position:0% +then +the + + align:start position:0% +the + + + align:start position:0% +the +disparity will be larger and we improve + + align:start position:0% +disparity will be larger and we improve + + + align:start position:0% +disparity will be larger and we improve +the measurement accuracy but of course + + align:start position:0% +the measurement accuracy but of course + + + align:start position:0% +the measurement accuracy but of course +you + + align:start position:0% +you + + + align:start position:0% +you +have other constraints on these + + align:start position:0% +have other constraints on these + + + align:start position:0% +have other constraints on these +quantities you you don't want the + + align:start position:0% +quantities you you don't want the + + + align:start position:0% +quantities you you don't want the +two cameras to be + + align:start position:0% +two cameras to be + + + align:start position:0% +two cameras to be +too far apart if possible + + align:start position:0% +too far apart if possible + + + align:start position:0% +too far apart if possible +so you know for example in autonomous + + align:start position:0% +so you know for example in autonomous + + + align:start position:0% +so you know for example in autonomous +vehicles + + align:start position:0% +vehicles + + + align:start position:0% +vehicles +it'd be nice if the two cameras could be + + align:start position:0% +it'd be nice if the two cameras could be + + + align:start position:0% +it'd be nice if the two cameras could be +close enough together so you could hide + + align:start position:0% +close enough together so you could hide + + + align:start position:0% +close enough together so you could hide +them behind the rear view mirror + + align:start position:0% +them behind the rear view mirror + + + align:start position:0% +them behind the rear view mirror +rather than have them + + align:start position:0% +rather than have them + + + align:start position:0% +rather than have them +go all the way across + + align:start position:0% +go all the way across + + + align:start position:0% +go all the way across +and if if they are that far apart + + align:start position:0% +and if if they are that far apart + + + align:start position:0% +and if if they are that far apart +then you have a calibration problem + + align:start position:0% +then you have a calibration problem + + + align:start position:0% +then you have a calibration problem +because they're unlikely to stay + + align:start position:0% +because they're unlikely to stay + + + align:start position:0% +because they're unlikely to stay +perfectly lined up over the lifetime of + + align:start position:0% +perfectly lined up over the lifetime of + + + align:start position:0% +perfectly lined up over the lifetime of +the car + + align:start position:0% +the car + + + align:start position:0% +the car +so you'd have to have some automated way + + align:start position:0% +so you'd have to have some automated way + + + align:start position:0% +so you'd have to have some automated way +of rediscovering the relationship + + align:start position:0% +of rediscovering the relationship + + + align:start position:0% +of rediscovering the relationship +between those two coordinate systems + + align:start position:0% +between those two coordinate systems + + + align:start position:0% +between those two coordinate systems +okay so you know this is um + + align:start position:0% +okay so you know this is um + + + align:start position:0% +okay so you know this is um +a very special case + + align:start position:0% +a very special case + + + align:start position:0% +a very special case +not one that one could rely on in + + align:start position:0% +not one that one could rely on in + + + align:start position:0% +not one that one could rely on in +practice as i mentioned and so um we'll + + align:start position:0% +practice as i mentioned and so um we'll + + + align:start position:0% +practice as i mentioned and so um we'll +have to talk about what happens if these + + align:start position:0% +have to talk about what happens if these + + + align:start position:0% +have to talk about what happens if these +two cameras are not + + align:start position:0% +two cameras are not + + + align:start position:0% +two cameras are not +exactly equal and they're not exactly + + align:start position:0% +exactly equal and they're not exactly + + + align:start position:0% +exactly equal and they're not exactly +arranged in this geometry what if + + align:start position:0% +arranged in this geometry what if + + + align:start position:0% +arranged in this geometry what if +there's a rotation between the two + + align:start position:0% +there's a rotation between the two + + + align:start position:0% +there's a rotation between the two +cameras what if the baseline is not + + align:start position:0% +cameras what if the baseline is not + + + align:start position:0% +cameras what if the baseline is not +perpendicular to the optical axis and so + + align:start position:0% +perpendicular to the optical axis and so + + + align:start position:0% +perpendicular to the optical axis and so +on how do you calibrate for that and + + align:start position:0% +on how do you calibrate for that and + + + align:start position:0% +on how do you calibrate for that and +that's going to be + + align:start position:0% +that's going to be + + + align:start position:0% +that's going to be +the topic of later conversation + + align:start position:0% +the topic of later conversation + + + align:start position:0% +the topic of later conversation +so let's dive right in + + align:start position:0% +so let's dive right in + + + align:start position:0% +so let's dive right in +problem number one + + align:start position:0% +problem number one + + + align:start position:0% +problem number one +let's look at absolute orientations + + align:start position:0% + + + + align:start position:0% + +and you know one version of that is we + + align:start position:0% +and you know one version of that is we + + + align:start position:0% +and you know one version of that is we +have two lidars + + align:start position:0% +have two lidars + + + align:start position:0% +have two lidars +laser + + align:start position:0% +laser + + + align:start position:0% +laser +rangefinding + + align:start position:0% +rangefinding + + + align:start position:0% +rangefinding +imaging devices that give us + + align:start position:0% +imaging devices that give us + + + align:start position:0% +imaging devices that give us +3d coordinates + + align:start position:0% +3d coordinates + + + align:start position:0% +3d coordinates +and we're + + align:start position:0% +and we're + + + align:start position:0% +and we're +we're + + align:start position:0% +we're + + + align:start position:0% +we're +going to use + + align:start position:0% +going to use + + + align:start position:0% +going to use +that information to get + + align:start position:0% +that information to get + + + align:start position:0% +that information to get +a picture of the world around + + align:start position:0% +a picture of the world around + + + align:start position:0% +a picture of the world around +our autonomous vehicle or whatever + + align:start position:0% +our autonomous vehicle or whatever + + + align:start position:0% +our autonomous vehicle or whatever +and + + align:start position:0% +and + + + align:start position:0% +and +to do so we need to get the relationship + + align:start position:0% +to do so we need to get the relationship + + + align:start position:0% +to do so we need to get the relationship +between those two + + align:start position:0% +between those two + + + align:start position:0% +between those two +um systems and they're unlikely i mean + + align:start position:0% +um systems and they're unlikely i mean + + + align:start position:0% +um systems and they're unlikely i mean +we try to line them up in some + + align:start position:0% +we try to line them up in some + + + align:start position:0% +we try to line them up in some +reasonable way but + + align:start position:0% +reasonable way but + + + align:start position:0% +reasonable way but +we can't really depend on that + + align:start position:0% +we can't really depend on that + + + align:start position:0% +we can't really depend on that +in the case of the + + align:start position:0% +in the case of the + + + align:start position:0% +in the case of the +topographic reconstruction from aerial + + align:start position:0% +topographic reconstruction from aerial + + + align:start position:0% +topographic reconstruction from aerial +photography + + align:start position:0% +photography + + + align:start position:0% +photography +it's obviously even worse because + + align:start position:0% +it's obviously even worse because + + + align:start position:0% +it's obviously even worse because +the two camera positions + + align:start position:0% +the two camera positions + + + align:start position:0% +the two camera positions +aren't connected by some rigid object + + align:start position:0% +aren't connected by some rigid object + + + align:start position:0% +aren't connected by some rigid object +you know the plane flies along takes a + + align:start position:0% +you know the plane flies along takes a + + + align:start position:0% +you know the plane flies along takes a +picture flies along takes a picture and + + align:start position:0% +picture flies along takes a picture and + + + align:start position:0% +picture flies along takes a picture and +the pilot of course tries to maintain a + + align:start position:0% +the pilot of course tries to maintain a + + + align:start position:0% +the pilot of course tries to maintain a +constant attitude but + + align:start position:0% +constant attitude but + + + align:start position:0% +constant attitude but +the air is not + + align:start position:0% +the air is not + + + align:start position:0% +the air is not +a constant medium so + + align:start position:0% +a constant medium so + + + align:start position:0% +a constant medium so +the orientation of the plane is not + + align:start position:0% +the orientation of the plane is not + + + align:start position:0% +the orientation of the plane is not +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +maintained exactly and so we need to + + align:start position:0% +maintained exactly and so we need to + + + align:start position:0% +maintained exactly and so we need to +compensate for that + + align:start position:0% + + + + align:start position:0% + +notice that in all of this we're + + align:start position:0% +notice that in all of this we're + + + align:start position:0% +notice that in all of this we're +presupposing that we've somehow found + + align:start position:0% +presupposing that we've somehow found + + + align:start position:0% +presupposing that we've somehow found +points + + align:start position:0% +points + + + align:start position:0% +points +that and + + align:start position:0% +that and + + + align:start position:0% +that and +you know we've we've seen how to find + + align:start position:0% +you know we've we've seen how to find + + + align:start position:0% +you know we've we've seen how to find +edges very accurately + + align:start position:0% +edges very accurately + + + align:start position:0% +edges very accurately +and that's + + align:start position:0% +and that's + + + align:start position:0% +and that's +one type of input that we can use + + align:start position:0% +one type of input that we can use + + + align:start position:0% +one type of input that we can use +similarly their methods for finding + + align:start position:0% +similarly their methods for finding + + + align:start position:0% +similarly their methods for finding +quote interesting points + + align:start position:0% +quote interesting points + + + align:start position:0% +quote interesting points +and you know sift + + align:start position:0% +and you know sift + + + align:start position:0% +and you know sift +is an example and um + + align:start position:0% +is an example and um + + + align:start position:0% +is an example and um +i think i have david lowe's paper on the + + align:start position:0% +i think i have david lowe's paper on the + + + align:start position:0% +i think i have david lowe's paper on the +stella site + + align:start position:0% +stella site + + + align:start position:0% +stella site +uh it's a little opaque + + align:start position:0% +uh it's a little opaque + + + align:start position:0% +uh it's a little opaque +and since he wrote it + + align:start position:0% +and since he wrote it + + + align:start position:0% +and since he wrote it +um + + align:start position:0% +um + + + align:start position:0% +um +and patented it + + align:start position:0% +and patented it + + + align:start position:0% +and patented it +um there have been many other + + align:start position:0% +um there have been many other + + + align:start position:0% +um there have been many other +variants + + align:start position:0% +variants + + + align:start position:0% +variants +that typically + + align:start position:0% +that typically + + + align:start position:0% +that typically +are computationally much faster but may + + align:start position:0% +are computationally much faster but may + + + align:start position:0% +are computationally much faster but may +not be as accurate and so on but anyway + + align:start position:0% +not be as accurate and so on but anyway + + + align:start position:0% +not be as accurate and so on but anyway +there's some we're assuming here that + + align:start position:0% +there's some we're assuming here that + + + align:start position:0% +there's some we're assuming here that +there's some way of + + align:start position:0% +there's some way of + + + align:start position:0% +there's some way of +finding interesting points and finding + + align:start position:0% +finding interesting points and finding + + + align:start position:0% +finding interesting points and finding +them again in another image so we're + + align:start position:0% +them again in another image so we're + + + align:start position:0% +them again in another image so we're +sort of leaving aside the the matching + + align:start position:0% +sort of leaving aside the the matching + + + align:start position:0% +sort of leaving aside the the matching +problem uh we're assuming that's been + + align:start position:0% +problem uh we're assuming that's been + + + align:start position:0% +problem uh we're assuming that's been +done + + align:start position:0% +done + + + align:start position:0% +done +and so now we just have the problem of + + align:start position:0% +and so now we just have the problem of + + + align:start position:0% +and so now we just have the problem of +here's a bunch of coordinates in the two + + align:start position:0% +here's a bunch of coordinates in the two + + + align:start position:0% +here's a bunch of coordinates in the two +systems what do we do with it + + align:start position:0% + + + + align:start position:0% + +so i'm going to call these left and + + align:start position:0% +so i'm going to call these left and + + + align:start position:0% +so i'm going to call these left and +right coordinate system just because the + + align:start position:0% +right coordinate system just because the + + + align:start position:0% +right coordinate system just because the +one of the big applications here is to + + align:start position:0% +one of the big applications here is to + + + align:start position:0% +one of the big applications here is to +binocular stereo but of course they + + align:start position:0% +binocular stereo but of course they + + + align:start position:0% +binocular stereo but of course they +could be + + align:start position:0% +could be + + + align:start position:0% +could be +before and after so the vehicle took a + + align:start position:0% +before and after so the vehicle took a + + + align:start position:0% +before and after so the vehicle took a +picture of the world then it moved then + + align:start position:0% +picture of the world then it moved then + + + align:start position:0% +picture of the world then it moved then +it took another picture + + align:start position:0% +it took another picture + + + align:start position:0% +it took another picture +so don't assume that because it's l and + + align:start position:0% +so don't assume that because it's l and + + + align:start position:0% +so don't assume that because it's l and +r + + align:start position:0% +r + + + align:start position:0% +r +that that's um + + align:start position:0% + + + + align:start position:0% + +so here's a point in the environment and + + align:start position:0% +so here's a point in the environment and + + + align:start position:0% +so here's a point in the environment and +we're going to find we'll need more than + + align:start position:0% +we're going to find we'll need more than + + + align:start position:0% +we're going to find we'll need more than +one point so let's put a subscript on + + align:start position:0% +one point so let's put a subscript on + + + align:start position:0% +one point so let's put a subscript on +them + + align:start position:0% +them + + + align:start position:0% +them +and we measure it in this coordinate + + align:start position:0% +and we measure it in this coordinate + + + align:start position:0% +and we measure it in this coordinate +system and we get rli + + align:start position:0% +system and we get rli + + + align:start position:0% +system and we get rli +and we measure it in this and we get the + + align:start position:0% +and we measure it in this and we get the + + + align:start position:0% +and we measure it in this and we get the +vector rri + + align:start position:0% + + + + align:start position:0% + +and again um + + align:start position:0% +and again um + + + align:start position:0% +and again um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +there's this duality where we could be + + align:start position:0% +there's this duality where we could be + + + align:start position:0% +there's this duality where we could be +talking about one object measured in two + + align:start position:0% +talking about one object measured in two + + + align:start position:0% +talking about one object measured in two +different coordinate systems or we could + + align:start position:0% +different coordinate systems or we could + + + align:start position:0% +different coordinate systems or we could +be talking about + + align:start position:0% +be talking about + + + align:start position:0% +be talking about +uh two objects measured in the same + + align:start position:0% +uh two objects measured in the same + + + align:start position:0% +uh two objects measured in the same +coordinate system and this is sort of + + align:start position:0% +coordinate system and this is sort of + + + align:start position:0% +coordinate system and this is sort of +you know like + + align:start position:0% +you know like + + + align:start position:0% +you know like +uh is the camera moving or the object + + align:start position:0% +uh is the camera moving or the object + + + align:start position:0% +uh is the camera moving or the object +moving + + align:start position:0% +moving + + + align:start position:0% +moving +it doesn't matter we just occasionally + + align:start position:0% +it doesn't matter we just occasionally + + + align:start position:0% +it doesn't matter we just occasionally +need to be careful about the sign + + align:start position:0% +need to be careful about the sign + + + align:start position:0% +need to be careful about the sign +because the sign will flip + + align:start position:0% +because the sign will flip + + + align:start position:0% +because the sign will flip +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so + + align:start position:0% +so + + + align:start position:0% +so +now if we know where those coordinate + + align:start position:0% +now if we know where those coordinate + + + align:start position:0% +now if we know where those coordinate +systems are + + align:start position:0% +systems are + + + align:start position:0% +systems are +we have a very happy situation we simply + + align:start position:0% +we have a very happy situation we simply + + + align:start position:0% +we have a very happy situation we simply +project out this ray into 3d and this + + align:start position:0% +project out this ray into 3d and this + + + align:start position:0% +project out this ray into 3d and this +array in 3d find out where they + + align:start position:0% +array in 3d find out where they + + + align:start position:0% +array in 3d find out where they +intersect and we know where + + align:start position:0% +intersect and we know where + + + align:start position:0% +intersect and we know where +p i is that point i + + align:start position:0% +p i is that point i + + + align:start position:0% +p i is that point i +and that's sort of ultimately what we + + align:start position:0% +and that's sort of ultimately what we + + + align:start position:0% +and that's sort of ultimately what we +want to do + + align:start position:0% +want to do + + + align:start position:0% +want to do +and you know they typically won't + + align:start position:0% +and you know they typically won't + + + align:start position:0% +and you know they typically won't +intersect so we'll find the point where + + align:start position:0% +intersect so we'll find the point where + + + align:start position:0% +intersect so we'll find the point where +they + + align:start position:0% +they + + + align:start position:0% +they +have the closest approach + + align:start position:0% + + + + align:start position:0% + +which is + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +where the line connecting them is as + + align:start position:0% +where the line connecting them is as + + + align:start position:0% +where the line connecting them is as +short as possible and that will be + + align:start position:0% +short as possible and that will be + + + align:start position:0% +short as possible and that will be +a line that is perpendicular to both of + + align:start position:0% +a line that is perpendicular to both of + + + align:start position:0% +a line that is perpendicular to both of +them so so there's an interesting uh + + align:start position:0% +them so so there's an interesting uh + + + align:start position:0% +them so so there's an interesting uh +little geometry problem there how to do + + align:start position:0% +little geometry problem there how to do + + + align:start position:0% +little geometry problem there how to do +that + + align:start position:0% +that + + + align:start position:0% +that +uh but right now we're focusing on + + align:start position:0% +uh but right now we're focusing on + + + align:start position:0% +uh but right now we're focusing on +another problem which is before i can + + align:start position:0% +another problem which is before i can + + + align:start position:0% +another problem which is before i can +project these out into the world to find + + align:start position:0% +project these out into the world to find + + + align:start position:0% +project these out into the world to find +their intersection + + align:start position:0% +their intersection + + + align:start position:0% +their intersection +i need to know how these two coordinate + + align:start position:0% +i need to know how these two coordinate + + + align:start position:0% +i need to know how these two coordinate +systems relate to one another and so + + align:start position:0% +systems relate to one another and so + + + align:start position:0% +systems relate to one another and so +how do three dimensional coordinate + + align:start position:0% +how do three dimensional coordinate + + + align:start position:0% +how do three dimensional coordinate +systems relate to each other well + + align:start position:0% +systems relate to each other well + + + align:start position:0% +systems relate to each other well +there's rotation and there's translation + + align:start position:0% +there's rotation and there's translation + + + align:start position:0% +there's rotation and there's translation +and so our job's going to be to find the + + align:start position:0% +and so our job's going to be to find the + + + align:start position:0% +and so our job's going to be to find the +rotation + + align:start position:0% +rotation + + + align:start position:0% +rotation +and to find the translation + + align:start position:0% + + + + align:start position:0% + +and we've talked about this before + + align:start position:0% +and we've talked about this before + + + align:start position:0% +and we've talked about this before +in 3d they're three degrees of freedom + + align:start position:0% +in 3d they're three degrees of freedom + + + align:start position:0% +in 3d they're three degrees of freedom +to rotation + + align:start position:0% +to rotation + + + align:start position:0% +to rotation +and they're three degrees of freedom to + + align:start position:0% +and they're three degrees of freedom to + + + align:start position:0% +and they're three degrees of freedom to +translate them + + align:start position:0% +translate them + + + align:start position:0% +translate them +and that's slightly + + align:start position:0% +and that's slightly + + + align:start position:0% +and that's slightly +surprising uh you know i might say oh + + align:start position:0% +surprising uh you know i might say oh + + + align:start position:0% +surprising uh you know i might say oh +yeah because it's 3d so it's got to be + + align:start position:0% +yeah because it's 3d so it's got to be + + + align:start position:0% +yeah because it's 3d so it's got to be +three but as we mentioned in 2d + + align:start position:0% +three but as we mentioned in 2d + + + align:start position:0% +three but as we mentioned in 2d +rotation only has one degree of freedom + + align:start position:0% +rotation only has one degree of freedom + + + align:start position:0% +rotation only has one degree of freedom +not two + + align:start position:0% +not two + + + align:start position:0% +not two +and in 4d it has six so + + align:start position:0% +and in 4d it has six so + + + align:start position:0% +and in 4d it has six so +it's um it's n times n minus 1 over 2 + + align:start position:0% +it's um it's n times n minus 1 over 2 + + + align:start position:0% +it's um it's n times n minus 1 over 2 +not not n + + align:start position:0% +not not n + + + align:start position:0% +not not n +and it's so it's a + + align:start position:0% +and it's so it's a + + + align:start position:0% +and it's so it's a +fortuitous accident that in 3d you know + + align:start position:0% +fortuitous accident that in 3d you know + + + align:start position:0% +fortuitous accident that in 3d you know +3 times 2 over 2 is 3. so + + align:start position:0% +3 times 2 over 2 is 3. so + + + align:start position:0% +3 times 2 over 2 is 3. so +um it it's slightly confusing it makes + + align:start position:0% +um it it's slightly confusing it makes + + + align:start position:0% +um it it's slightly confusing it makes +it look like rotation is simple + + align:start position:0% +it look like rotation is simple + + + align:start position:0% +it look like rotation is simple +when it isn't so + + align:start position:0% +when it isn't so + + + align:start position:0% +when it isn't so +okay so we're looking for six numbers + + align:start position:0% +okay so we're looking for six numbers + + + align:start position:0% +okay so we're looking for six numbers +and we'll need enough constraint so that + + align:start position:0% +and we'll need enough constraint so that + + + align:start position:0% +and we'll need enough constraint so that +we can find them + + align:start position:0% +we can find them + + + align:start position:0% +we can find them +and so + + align:start position:0% +and so + + + align:start position:0% +and so +let's + + align:start position:0% + + + + align:start position:0% + +so we're looking for a transformation of + + align:start position:0% +so we're looking for a transformation of + + + align:start position:0% +so we're looking for a transformation of +this form + + align:start position:0% +this form + + + align:start position:0% +this form +where + + align:start position:0% +where + + + align:start position:0% +where +this is a translation which is fixed + + align:start position:0% +this is a translation which is fixed + + + align:start position:0% +this is a translation which is fixed +uh that is this formula applies to to + + align:start position:0% +uh that is this formula applies to to + + + align:start position:0% +uh that is this formula applies to to +all the points p i + + align:start position:0% +all the points p i + + + align:start position:0% +all the points p i +p j + + align:start position:0% +p j + + + align:start position:0% +p j +and + + align:start position:0% +and + + + align:start position:0% +and +this is our rotation + + align:start position:0% +this is our rotation + + + align:start position:0% +this is our rotation +and i've purposefully written it this + + align:start position:0% +and i've purposefully written it this + + + align:start position:0% +and i've purposefully written it this +way with a parenthesis to indicate that + + align:start position:0% +way with a parenthesis to indicate that + + + align:start position:0% +way with a parenthesis to indicate that +we are not going to insist on that being + + align:start position:0% +we are not going to insist on that being + + + align:start position:0% +we are not going to insist on that being +represented as an orthonormal matrix + + align:start position:0% +represented as an orthonormal matrix + + + align:start position:0% +represented as an orthonormal matrix +which is what would happen if i just + + align:start position:0% +which is what would happen if i just + + + align:start position:0% +which is what would happen if i just +left out the parenthesis you would + + align:start position:0% +left out the parenthesis you would + + + align:start position:0% +left out the parenthesis you would +assume that i'm talking about a three by + + align:start position:0% +assume that i'm talking about a three by + + + align:start position:0% +assume that i'm talking about a three by +three matrix multiplied by a vector + + align:start position:0% +three matrix multiplied by a vector + + + align:start position:0% +three matrix multiplied by a vector +but we'll be looking at + + align:start position:0% +but we'll be looking at + + + align:start position:0% +but we'll be looking at +other representation and we'll we'll see + + align:start position:0% +other representation and we'll we'll see + + + align:start position:0% +other representation and we'll we'll see +why + + align:start position:0% +why + + + align:start position:0% +why +okay so that's + + align:start position:0% +okay so that's + + + align:start position:0% +okay so that's +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +those are the unknowns + + align:start position:0% + + + + align:start position:0% + +so with an equation like this they're + + align:start position:0% +so with an equation like this they're + + + align:start position:0% +so with an equation like this they're +typically + + align:start position:0% +typically + + + align:start position:0% +typically +sort of two ways of using them the one + + align:start position:0% +sort of two ways of using them the one + + + align:start position:0% +sort of two ways of using them the one +is + + align:start position:0% +is + + + align:start position:0% +is +um you know the rotation and translation + + align:start position:0% +um you know the rotation and translation + + + align:start position:0% +um you know the rotation and translation +you plonk in r of l + + align:start position:0% +you plonk in r of l + + + align:start position:0% +you plonk in r of l +and you compute r of r that's sort of + + align:start position:0% +and you compute r of r that's sort of + + + align:start position:0% +and you compute r of r that's sort of +the the easy thing + + align:start position:0% +the the easy thing + + + align:start position:0% +the the easy thing +and certainly what we use it for but + + align:start position:0% +and certainly what we use it for but + + + align:start position:0% +and certainly what we use it for but +that's easy our problem is different + + align:start position:0% +that's easy our problem is different + + + align:start position:0% +that's easy our problem is different +we know some rlr pairs + + align:start position:0% +we know some rlr pairs + + + align:start position:0% +we know some rlr pairs +that is with the certain points we've + + align:start position:0% +that is with the certain points we've + + + align:start position:0% +that is with the certain points we've +measured in both coordinate system and + + align:start position:0% +measured in both coordinate system and + + + align:start position:0% +measured in both coordinate system and +our job is to find + + align:start position:0% +our job is to find + + + align:start position:0% +our job is to find +the rotation and the translation so + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% +now + + + align:start position:0% +now +before we go on we talk about some + + align:start position:0% +before we go on we talk about some + + + align:start position:0% +before we go on we talk about some +properties of rotation + + align:start position:0% +properties of rotation + + + align:start position:0% +properties of rotation +and + + align:start position:0% +and + + + align:start position:0% +and +we already mentioned them but let me do + + align:start position:0% +we already mentioned them but let me do + + + align:start position:0% +we already mentioned them but let me do +it again so if we represent r as a three + + align:start position:0% +it again so if we represent r as a three + + + align:start position:0% +it again so if we represent r as a three +by three matrix + + align:start position:0% +by three matrix + + + align:start position:0% +by three matrix +it better be orthonormal + + align:start position:0% +it better be orthonormal + + + align:start position:0% +it better be orthonormal +and that means that the + + align:start position:0% +and that means that the + + + align:start position:0% +and that means that the +dot product of rows is zero + + align:start position:0% +dot product of rows is zero + + + align:start position:0% +dot product of rows is zero +and that the dot product of rows with + + align:start position:0% +and that the dot product of rows with + + + align:start position:0% +and that the dot product of rows with +themselves is one + + align:start position:0% +themselves is one + + + align:start position:0% +themselves is one +and so short a quick way of writing that + + align:start position:0% +and so short a quick way of writing that + + + align:start position:0% +and so short a quick way of writing that +is + + align:start position:0% +is + + + align:start position:0% +is +that way + + align:start position:0% +that way + + + align:start position:0% +that way +that is the + + align:start position:0% +that is the + + + align:start position:0% +that is the +matrix times its transpose + + align:start position:0% +matrix times its transpose + + + align:start position:0% +matrix times its transpose +is identity and you can check that that + + align:start position:0% +is identity and you can check that that + + + align:start position:0% +is identity and you can check that that +means that i guess the columns + + align:start position:0% +means that i guess the columns + + + align:start position:0% +means that i guess the columns +if we treat the columns as vectors those + + align:start position:0% +if we treat the columns as vectors those + + + align:start position:0% +if we treat the columns as vectors those +are orthogonal and they're unit unit + + align:start position:0% +are orthogonal and they're unit unit + + + align:start position:0% +are orthogonal and they're unit unit +vectors + + align:start position:0% +vectors + + + align:start position:0% +vectors +and um + + align:start position:0% +and um + + + align:start position:0% +and um +it turns out that you can prove that if + + align:start position:0% +it turns out that you can prove that if + + + align:start position:0% +it turns out that you can prove that if +the columns are have that property then + + align:start position:0% +the columns are have that property then + + + align:start position:0% +the columns are have that property then +the rows have that property so we could + + align:start position:0% +the rows have that property so we could + + + align:start position:0% +the rows have that property so we could +we could also write it as r times r + + align:start position:0% +we could also write it as r times r + + + align:start position:0% +we could also write it as r times r +transpose equals i same thing and then + + align:start position:0% +transpose equals i same thing and then + + + align:start position:0% +transpose equals i same thing and then +you look at this and say wait a minute + + align:start position:0% +you look at this and say wait a minute + + + align:start position:0% +you look at this and say wait a minute +we've got a three by three matrix equals + + align:start position:0% +we've got a three by three matrix equals + + + align:start position:0% +we've got a three by three matrix equals +a three by three matrix that's nine + + align:start position:0% +a three by three matrix that's nine + + + align:start position:0% +a three by three matrix that's nine +constraints + + align:start position:0% +constraints + + + align:start position:0% +constraints +and + + align:start position:0% +and + + + align:start position:0% +and +that seems excessive because we only got + + align:start position:0% +that seems excessive because we only got + + + align:start position:0% +that seems excessive because we only got +nine numbers so if you take out nine + + align:start position:0% +nine numbers so if you take out nine + + + align:start position:0% +nine numbers so if you take out nine +constraints there's nothing left no + + align:start position:0% +constraints there's nothing left no + + + align:start position:0% +constraints there's nothing left no +degrees of freedom well the thing is + + align:start position:0% +degrees of freedom well the thing is + + + align:start position:0% +degrees of freedom well the thing is +that this is a symmetric matrix so it's + + align:start position:0% +that this is a symmetric matrix so it's + + + align:start position:0% +that this is a symmetric matrix so it's +actually only six constraints right + + align:start position:0% +actually only six constraints right + + + align:start position:0% +actually only six constraints right +because the diagonal plus say the top + + align:start position:0% +because the diagonal plus say the top + + + align:start position:0% +because the diagonal plus say the top +right triangle + + align:start position:0% +right triangle + + + align:start position:0% +right triangle +is three plus three is six so there's + + align:start position:0% +is three plus three is six so there's + + + align:start position:0% +is three plus three is six so there's +six constraints + + align:start position:0% +six constraints + + + align:start position:0% +six constraints +the three by three matrix has nine + + align:start position:0% +the three by three matrix has nine + + + align:start position:0% +the three by three matrix has nine +numbers we've got six constraints nine + + align:start position:0% +numbers we've got six constraints nine + + + align:start position:0% +numbers we've got six constraints nine +minus six is three + + align:start position:0% +minus six is three + + + align:start position:0% +minus six is three +uh + + align:start position:0% +uh + + + align:start position:0% +uh +three degrees of freedom so + + align:start position:0% +three degrees of freedom so + + + align:start position:0% +three degrees of freedom so +so uh typically that's where people stop + + align:start position:0% +so uh typically that's where people stop + + + align:start position:0% +so uh typically that's where people stop +that's you know all the conditions we + + align:start position:0% +that's you know all the conditions we + + + align:start position:0% +that's you know all the conditions we +need on the matrix but actually it's not + + align:start position:0% + + + + align:start position:0% + +you need an additional constraint which + + align:start position:0% +you need an additional constraint which + + + align:start position:0% +you need an additional constraint which +is different in that it's not you know + + align:start position:0% +is different in that it's not you know + + + align:start position:0% +is different in that it's not you know +the quality of some number to some value + + align:start position:0% +the quality of some number to some value + + + align:start position:0% +the quality of some number to some value +it's really a single bit of information + + align:start position:0% +it's really a single bit of information + + + align:start position:0% +it's really a single bit of information +and why do we need that + + align:start position:0% +and why do we need that + + + align:start position:0% +and why do we need that +well + + align:start position:0% + + + + align:start position:0% + +here's the example why we need that so + + align:start position:0% +here's the example why we need that so + + + align:start position:0% +here's the example why we need that so +this matrix + + align:start position:0% +this matrix + + + align:start position:0% +this matrix +if you take its transpose it's the same + + align:start position:0% +if you take its transpose it's the same + + + align:start position:0% +if you take its transpose it's the same +matrix and then you multiply it by + + align:start position:0% +matrix and then you multiply it by + + + align:start position:0% +matrix and then you multiply it by +itself you get the identity so this + + align:start position:0% +itself you get the identity so this + + + align:start position:0% +itself you get the identity so this +matrix satisfies that first condition + + align:start position:0% +matrix satisfies that first condition + + + align:start position:0% +matrix satisfies that first condition +but it's not a rotation + + align:start position:0% +but it's not a rotation + + + align:start position:0% +but it's not a rotation +right because it's uh flipping the z + + align:start position:0% +right because it's uh flipping the z + + + align:start position:0% +right because it's uh flipping the z +direction + + align:start position:0% +direction + + + align:start position:0% +direction +so it's a mirror image + + align:start position:0% +so it's a mirror image + + + align:start position:0% +so it's a mirror image +it's uh + + align:start position:0% +it's uh + + + align:start position:0% +it's uh +you know uh i'm standing on the floor + + align:start position:0% +you know uh i'm standing on the floor + + + align:start position:0% +you know uh i'm standing on the floor +and there's another person talking on + + align:start position:0% +and there's another person talking on + + + align:start position:0% +and there's another person talking on +the other side with his feet up + + align:start position:0% +the other side with his feet up + + + align:start position:0% +the other side with his feet up +and um that person's left hand is would + + align:start position:0% +and um that person's left hand is would + + + align:start position:0% +and um that person's left hand is would +be my right hand and so on so + + align:start position:0% +be my right hand and so on so + + + align:start position:0% +be my right hand and so on so +uh no rotation + + align:start position:0% +uh no rotation + + + align:start position:0% +uh no rotation +would turn me into that other person + + align:start position:0% +would turn me into that other person + + + align:start position:0% +would turn me into that other person +right it's like + + align:start position:0% +right it's like + + + align:start position:0% +right it's like +turning your left hand into your right + + align:start position:0% +turning your left hand into your right + + + align:start position:0% +turning your left hand into your right +hand can't be done with just rotation + + align:start position:0% +hand can't be done with just rotation + + + align:start position:0% +hand can't be done with just rotation +can be done trivially with a reflection + + align:start position:0% +can be done trivially with a reflection + + + align:start position:0% +can be done trivially with a reflection +and reflections satisfy this so in order + + align:start position:0% +and reflections satisfy this so in order + + + align:start position:0% +and reflections satisfy this so in order +to eliminate reflections + + align:start position:0% +to eliminate reflections + + + align:start position:0% +to eliminate reflections +um we have to introduce + + align:start position:0% +um we have to introduce + + + align:start position:0% +um we have to introduce +that constraint + + align:start position:0% + + + + align:start position:0% + +so if say we set something up like a + + align:start position:0% +so if say we set something up like a + + + align:start position:0% +so if say we set something up like a +least squares problem we're trying to + + align:start position:0% +least squares problem we're trying to + + + align:start position:0% +least squares problem we're trying to +get these cameras lined up and we make + + align:start position:0% +get these cameras lined up and we make + + + align:start position:0% +get these cameras lined up and we make +some measurements and there's some + + align:start position:0% +some measurements and there's some + + + align:start position:0% +some measurements and there's some +errors that we're trying to minimize + + align:start position:0% +errors that we're trying to minimize + + + align:start position:0% +errors that we're trying to minimize +uh well then we also need to enforce the + + align:start position:0% +uh well then we also need to enforce the + + + align:start position:0% +uh well then we also need to enforce the +orthonormality constraint + + align:start position:0% +orthonormality constraint + + + align:start position:0% +orthonormality constraint +and annoyingly we also need to enforce + + align:start position:0% +and annoyingly we also need to enforce + + + align:start position:0% +and annoyingly we also need to enforce +this constraint and that's hard so + + align:start position:0% +this constraint and that's hard so + + + align:start position:0% +this constraint and that's hard so +that's one reason why we won't be using + + align:start position:0% +that's one reason why we won't be using + + + align:start position:0% +that's one reason why we won't be using +orthonormal matrices much + + align:start position:0% +orthonormal matrices much + + + align:start position:0% +orthonormal matrices much +okay + + align:start position:0% +okay + + + align:start position:0% +okay +oh by the way this means that + + align:start position:0% + + + + align:start position:0% + +that the + + align:start position:0% +that the + + + align:start position:0% +that the +inverse of a rotation matrix is easy to + + align:start position:0% +inverse of a rotation matrix is easy to + + + align:start position:0% +inverse of a rotation matrix is easy to +obtain + + align:start position:0% + + + + align:start position:0% + +i mean we'll use some of these + + align:start position:0% +i mean we'll use some of these + + + align:start position:0% +i mean we'll use some of these +properties as as we go along + + align:start position:0% +properties as as we go along + + + align:start position:0% +properties as as we go along +okay so um one way of uh thinking about + + align:start position:0% +okay so um one way of uh thinking about + + + align:start position:0% +okay so um one way of uh thinking about +this is in terms of a physical model + + align:start position:0% +this is in terms of a physical model + + + align:start position:0% +this is in terms of a physical model +where we have um + + align:start position:0% +where we have um + + + align:start position:0% +where we have um +one you know a cluster of points a cloud + + align:start position:0% +one you know a cluster of points a cloud + + + align:start position:0% +one you know a cluster of points a cloud +of points + + align:start position:0% +of points + + + align:start position:0% +of points +that uh we've uh say + + align:start position:0% +that uh we've uh say + + + align:start position:0% +that uh we've uh say +you know got from the left coordinate + + align:start position:0% +you know got from the left coordinate + + + align:start position:0% +you know got from the left coordinate +system we have a cluster of points from + + align:start position:0% +system we have a cluster of points from + + + align:start position:0% +system we have a cluster of points from +the right coordinate system and we want + + align:start position:0% +the right coordinate system and we want + + + align:start position:0% +the right coordinate system and we want +to superimpose them we want to line them + + align:start position:0% +to superimpose them we want to line them + + + align:start position:0% +to superimpose them we want to line them +up as much as best as possible and one + + align:start position:0% +up as much as best as possible and one + + + align:start position:0% +up as much as best as possible and one +model for that is if this is one of the + + align:start position:0% +model for that is if this is one of the + + + align:start position:0% +model for that is if this is one of the +left-hand coordinate system points + + align:start position:0% +left-hand coordinate system points + + + align:start position:0% +left-hand coordinate system points +and this is one of the right-hand + + align:start position:0% +and this is one of the right-hand + + + align:start position:0% +and this is one of the right-hand +coordinate system points after we've + + align:start position:0% +coordinate system points after we've + + + align:start position:0% +coordinate system points after we've +transformed it + + align:start position:0% +transformed it + + + align:start position:0% +transformed it +we want to make that distance as short + + align:start position:0% +we want to make that distance as short + + + align:start position:0% +we want to make that distance as short +as possible + + align:start position:0% +as possible + + + align:start position:0% +as possible +and in terms of you know physical model + + align:start position:0% +and in terms of you know physical model + + + align:start position:0% +and in terms of you know physical model +we can think of that as a + + align:start position:0% +we can think of that as a + + + align:start position:0% +we can think of that as a +spring that's connecting the two + + align:start position:0% +spring that's connecting the two + + + align:start position:0% +spring that's connecting the two +why is that well because the you know by + + align:start position:0% +why is that well because the you know by + + + align:start position:0% +why is that well because the you know by +hook's law + + align:start position:0% +hook's law + + + align:start position:0% +hook's law +let's call this distance e for error + + align:start position:0% + + + + align:start position:0% + +by hooke's law + + align:start position:0% +by hooke's law + + + align:start position:0% +by hooke's law +the + + align:start position:0% +the + + + align:start position:0% +the +force is proportional to the + + align:start position:0% +force is proportional to the + + + align:start position:0% +force is proportional to the +displacement from the rest length let's + + align:start position:0% +displacement from the rest length let's + + + align:start position:0% +displacement from the rest length let's +assume these springs have a wrist length + + align:start position:0% +assume these springs have a wrist length + + + align:start position:0% +assume these springs have a wrist length +of zero + + align:start position:0% +of zero + + + align:start position:0% +of zero +and then the energy + + align:start position:0% +and then the energy + + + align:start position:0% +and then the energy +is the integral of that + + align:start position:0% + + + + align:start position:0% + +so it's a half the + + align:start position:0% +so it's a half the + + + align:start position:0% +so it's a half the +displacement squared and so we can think + + align:start position:0% +displacement squared and so we can think + + + align:start position:0% +displacement squared and so we can think +of this as an energy minimizing problem + + align:start position:0% +of this as an energy minimizing problem + + + align:start position:0% +of this as an energy minimizing problem +which is what a physical system like + + align:start position:0% +which is what a physical system like + + + align:start position:0% +which is what a physical system like +that would do it would want to + + align:start position:0% +that would do it would want to + + + align:start position:0% +that would do it would want to +adjust itself to minimize the energy and + + align:start position:0% +adjust itself to minimize the energy and + + + align:start position:0% +adjust itself to minimize the energy and +we've run across that in a way in that + + align:start position:0% +we've run across that in a way in that + + + align:start position:0% +we've run across that in a way in that +last patent + + align:start position:0% +last patent + + + align:start position:0% +last patent +not the last the one before last + + align:start position:0% +not the last the one before last + + + align:start position:0% +not the last the one before last +were + + align:start position:0% +were + + + align:start position:0% +were +there was a translation and rotation the + + align:start position:0% +there was a translation and rotation the + + + align:start position:0% +there was a translation and rotation the +scaling based on attraction of points to + + align:start position:0% +scaling based on attraction of points to + + + align:start position:0% +scaling based on attraction of points to +corresponding points and so on + + align:start position:0% +corresponding points and so on + + + align:start position:0% +corresponding points and so on +um + + align:start position:0% +um + + + align:start position:0% +um +okay so we can think of this + + align:start position:0% +okay so we can think of this + + + align:start position:0% +okay so we can think of this +uh we can approach this in a sort of + + align:start position:0% +uh we can approach this in a sort of + + + align:start position:0% +uh we can approach this in a sort of +least squares way so what we're + + align:start position:0% +least squares way so what we're + + + align:start position:0% +least squares way so what we're +trying to do might be this so we define + + align:start position:0% +trying to do might be this so we define + + + align:start position:0% +trying to do might be this so we define +some kind of error + + align:start position:0% + + + + align:start position:0% + +so we choose to transform the + + align:start position:0% +so we choose to transform the + + + align:start position:0% +so we choose to transform the +vector in the left coordinate system + + align:start position:0% +vector in the left coordinate system + + + align:start position:0% +vector in the left coordinate system +by rotation and translation + + align:start position:0% +by rotation and translation + + + align:start position:0% +by rotation and translation +into the coordinate system of the right + + align:start position:0% +into the coordinate system of the right + + + align:start position:0% +into the coordinate system of the right +system and then we compare it with what + + align:start position:0% +system and then we compare it with what + + + align:start position:0% +system and then we compare it with what +we get there and ideally they should be + + align:start position:0% +we get there and ideally they should be + + + align:start position:0% +we get there and ideally they should be +the same and if they're not then we get + + align:start position:0% +the same and if they're not then we get + + + align:start position:0% +the same and if they're not then we get +some sort of error and now this + + align:start position:0% +some sort of error and now this + + + align:start position:0% +some sort of error and now this +introduces some sort of apparent bias + + align:start position:0% +introduces some sort of apparent bias + + + align:start position:0% +introduces some sort of apparent bias +that we're treating one of the two + + align:start position:0% +that we're treating one of the two + + + align:start position:0% +that we're treating one of the two +coordinate systems different from the + + align:start position:0% +coordinate systems different from the + + + align:start position:0% +coordinate systems different from the +other + + align:start position:0% +other + + + align:start position:0% +other +differently from the other and that's um + + align:start position:0% +differently from the other and that's um + + + align:start position:0% +differently from the other and that's um +undesirable you know like + + align:start position:0% +undesirable you know like + + + align:start position:0% +undesirable you know like +why should one coordinate system have + + align:start position:0% +why should one coordinate system have + + + align:start position:0% +why should one coordinate system have +preference over the other so what we + + align:start position:0% +preference over the other so what we + + + align:start position:0% +preference over the other so what we +want to be sure when we're done to check + + align:start position:0% +want to be sure when we're done to check + + + align:start position:0% +want to be sure when we're done to check +that if we had found the transformation + + align:start position:0% +that if we had found the transformation + + + align:start position:0% +that if we had found the transformation +from the + + align:start position:0% +from the + + + align:start position:0% +from the +right to the left system it would be the + + align:start position:0% +right to the left system it would be the + + + align:start position:0% +right to the left system it would be the +exact inverse of what we found going + + align:start position:0% +exact inverse of what we found going + + + align:start position:0% +exact inverse of what we found going +from the left to the right system + + align:start position:0% +from the left to the right system + + + align:start position:0% +from the left to the right system +otherwise there's something wrong and we + + align:start position:0% +otherwise there's something wrong and we + + + align:start position:0% +otherwise there's something wrong and we +already discussed this for example + + align:start position:0% +already discussed this for example + + + align:start position:0% +already discussed this for example +in line fitting you know why + + align:start position:0% +in line fitting you know why + + + align:start position:0% +in line fitting you know why +y equals mx plus c is not desirable + + align:start position:0% +y equals mx plus c is not desirable + + + align:start position:0% +y equals mx plus c is not desirable +because it pretends that there's no + + align:start position:0% +because it pretends that there's no + + + align:start position:0% +because it pretends that there's no +error in x and there's all the error in + + align:start position:0% +error in x and there's all the error in + + + align:start position:0% +error in x and there's all the error in +y + + align:start position:0% +y + + + align:start position:0% +y +when in many of our applications the + + align:start position:0% +when in many of our applications the + + + align:start position:0% +when in many of our applications the +error is in image position which + + align:start position:0% +error is in image position which + + + align:start position:0% +error is in image position which +includes both x and y so + + align:start position:0% +includes both x and y so + + + align:start position:0% +includes both x and y so +similarly here + + align:start position:0% +similarly here + + + align:start position:0% +similarly here +we'll be looking at transformations and + + align:start position:0% +we'll be looking at transformations and + + + align:start position:0% +we'll be looking at transformations and +methods that have that property that + + align:start position:0% +methods that have that property that + + + align:start position:0% +methods that have that property that +there's that symmetry and that symmetry + + align:start position:0% +there's that symmetry and that symmetry + + + align:start position:0% +there's that symmetry and that symmetry +is not apparent in that formula but so + + align:start position:0% +is not apparent in that formula but so + + + align:start position:0% +is not apparent in that formula but so +we'll have to actually check for it + + align:start position:0% +we'll have to actually check for it + + + align:start position:0% +we'll have to actually check for it +okay so what we want to do is of course + + align:start position:0% +okay so what we want to do is of course + + + align:start position:0% +okay so what we want to do is of course +minimize that + + align:start position:0% + + + + align:start position:0% + +and what do we have to play with well + + align:start position:0% +and what do we have to play with well + + + align:start position:0% +and what do we have to play with well +we've got r and we've got uh the + + align:start position:0% +we've got r and we've got uh the + + + align:start position:0% +we've got r and we've got uh the +translation r0 + + align:start position:0% +translation r0 + + + align:start position:0% +translation r0 +so that's sort of in a nutshell uh the + + align:start position:0% +so that's sort of in a nutshell uh the + + + align:start position:0% +so that's sort of in a nutshell uh the +problem we're trying to solve + + align:start position:0% +problem we're trying to solve + + + align:start position:0% +problem we're trying to solve +we've + + align:start position:0% +we've + + + align:start position:0% +we've +we've got a bunch of corresponding + + align:start position:0% +we've got a bunch of corresponding + + + align:start position:0% +we've got a bunch of corresponding +measurements in the two systems + + align:start position:0% +measurements in the two systems + + + align:start position:0% +measurements in the two systems +and we're + + align:start position:0% +and we're + + + align:start position:0% +and we're +trying to find the coordinate + + align:start position:0% +trying to find the coordinate + + + align:start position:0% +trying to find the coordinate +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +between the two systems + + align:start position:0% +between the two systems + + + align:start position:0% +between the two systems +using it and again as i mentioned that's + + align:start position:0% +using it and again as i mentioned that's + + + align:start position:0% +using it and again as i mentioned that's +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +the other way of using those equations + + align:start position:0% +the other way of using those equations + + + align:start position:0% +the other way of using those equations +normally + + align:start position:0% +normally + + + align:start position:0% +normally +normally you would be just going in the + + align:start position:0% +normally you would be just going in the + + + align:start position:0% +normally you would be just going in the +forward direction of the problem you'd + + align:start position:0% +forward direction of the problem you'd + + + align:start position:0% +forward direction of the problem you'd +you know plug in your rl + + align:start position:0% +you know plug in your rl + + + align:start position:0% +you know plug in your rl +rotate translate and you get rr + + align:start position:0% +rotate translate and you get rr + + + align:start position:0% +rotate translate and you get rr +and + + align:start position:0% +and + + + align:start position:0% +and +were then the rotation and translation + + align:start position:0% +were then the rotation and translation + + + align:start position:0% +were then the rotation and translation +are known and what's not known is the + + align:start position:0% +are known and what's not known is the + + + align:start position:0% +are known and what's not known is the +correspondence between the + + align:start position:0% +correspondence between the + + + align:start position:0% +correspondence between the +coordinates of points + + align:start position:0% +coordinates of points + + + align:start position:0% +coordinates of points +and here we're doing the very opposite + + align:start position:0% +and here we're doing the very opposite + + + align:start position:0% +and here we're doing the very opposite +we're assuming that we know the + + align:start position:0% +we're assuming that we know the + + + align:start position:0% +we're assuming that we know the +coordinates of the points pairs of them + + align:start position:0% +coordinates of the points pairs of them + + + align:start position:0% +coordinates of the points pairs of them +and we're trying to find the + + align:start position:0% +and we're trying to find the + + + align:start position:0% +and we're trying to find the +transformation that makes that work + + align:start position:0% +transformation that makes that work + + + align:start position:0% +transformation that makes that work +okay well there are a bunch of methods + + align:start position:0% +okay well there are a bunch of methods + + + align:start position:0% +okay well there are a bunch of methods +we could use to do this + + align:start position:0% +we could use to do this + + + align:start position:0% +we could use to do this +one of them is + + align:start position:0% +one of them is + + + align:start position:0% +one of them is +to separate the problem of finding the + + align:start position:0% +to separate the problem of finding the + + + align:start position:0% +to separate the problem of finding the +translation from the problem of the + + align:start position:0% +translation from the problem of the + + + align:start position:0% +translation from the problem of the +rotation + + align:start position:0% +rotation + + + align:start position:0% +rotation +and actually all of the methods we'll + + align:start position:0% +and actually all of the methods we'll + + + align:start position:0% +and actually all of the methods we'll +look at + + align:start position:0% +look at + + + align:start position:0% +look at +take that approach because it greatly + + align:start position:0% +take that approach because it greatly + + + align:start position:0% +take that approach because it greatly +simplifies the problem + + align:start position:0% +simplifies the problem + + + align:start position:0% +simplifies the problem +uh you know we in each case now only + + align:start position:0% +uh you know we in each case now only + + + align:start position:0% +uh you know we in each case now only +have to deal with three degrees of + + align:start position:0% +have to deal with three degrees of + + + align:start position:0% +have to deal with three degrees of +freedom at a time + + align:start position:0% +freedom at a time + + + align:start position:0% +freedom at a time +and one way we can do that is to + + align:start position:0% +and one way we can do that is to + + + align:start position:0% +and one way we can do that is to +pick some sort of reference point in + + align:start position:0% +pick some sort of reference point in + + + align:start position:0% +pick some sort of reference point in +each of this cloud + + align:start position:0% +each of this cloud + + + align:start position:0% +each of this cloud +point of clouds + + align:start position:0% +point of clouds + + + align:start position:0% +point of clouds +and + + align:start position:0% +and + + + align:start position:0% +and +go with that + + align:start position:0% +go with that + + + align:start position:0% +go with that +and so + + align:start position:0% +and so + + + align:start position:0% +and so +here's a way of + + align:start position:0% +here's a way of + + + align:start position:0% +here's a way of +taking say all of the left points and + + align:start position:0% +taking say all of the left points and + + + align:start position:0% +taking say all of the left points and +constructing a coordinate system in it + + align:start position:0% +constructing a coordinate system in it + + + align:start position:0% +constructing a coordinate system in it +so let's suppose we have 0.1 here so + + align:start position:0% +so let's suppose we have 0.1 here so + + + align:start position:0% +so let's suppose we have 0.1 here so +this is + + align:start position:0% +this is + + + align:start position:0% +this is +a measurement of some point + + align:start position:0% +a measurement of some point + + + align:start position:0% +a measurement of some point +and uh we're going to use that as the + + align:start position:0% +and uh we're going to use that as the + + + align:start position:0% +and uh we're going to use that as the +origin + + align:start position:0% +origin + + + align:start position:0% +origin +so we just out of all the points we've + + align:start position:0% +so we just out of all the points we've + + + align:start position:0% +so we just out of all the points we've +measured we pick one and declare that to + + align:start position:0% +measured we pick one and declare that to + + + align:start position:0% +measured we pick one and declare that to +be the origin okay step one + + align:start position:0% +be the origin okay step one + + + align:start position:0% +be the origin okay step one +then we look at a second point + + align:start position:0% +then we look at a second point + + + align:start position:0% +then we look at a second point +and we connect these two by a line + + align:start position:0% +and we connect these two by a line + + + align:start position:0% +and we connect these two by a line +and that's going to be one of our axes + + align:start position:0% + + + + align:start position:0% + +now the separation between 1 and 2 won't + + align:start position:0% +now the separation between 1 and 2 won't + + + align:start position:0% +now the separation between 1 and 2 won't +be a unit + + align:start position:0% +be a unit + + + align:start position:0% +be a unit +so + + align:start position:0% +so + + + align:start position:0% +so +we don't use the actual difference + + align:start position:0% +we don't use the actual difference + + + align:start position:0% +we don't use the actual difference +between 2 and 1 + + align:start position:0% +between 2 and 1 + + + align:start position:0% +between 2 and 1 +as our coordinate + + align:start position:0% +as our coordinate + + + align:start position:0% +as our coordinate +we normalize it + + align:start position:0% +we normalize it + + + align:start position:0% +we normalize it +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +let's write it over here x hat + + align:start position:0% +let's write it over here x hat + + + align:start position:0% +let's write it over here x hat +unit vector + + align:start position:0% +unit vector + + + align:start position:0% +unit vector +r + + align:start position:0% +r + + + align:start position:0% +r +l two minus r l one + + align:start position:0% + + + + align:start position:0% + +oh sorry let me just define x and then + + align:start position:0% +oh sorry let me just define x and then + + + align:start position:0% +oh sorry let me just define x and then +define x bar in terms of x + + align:start position:0% + + + + align:start position:0% + +save some save some writing + + align:start position:0% +save some save some writing + + + align:start position:0% +save some save some writing +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +now we take a third point + + align:start position:0% +now we take a third point + + + align:start position:0% +now we take a third point +now we can't sort of connect these up + + align:start position:0% +now we can't sort of connect these up + + + align:start position:0% +now we can't sort of connect these up +and say okay that's the y-axis because + + align:start position:0% +and say okay that's the y-axis because + + + align:start position:0% +and say okay that's the y-axis because +then x and y-axis won't be perpendicular + + align:start position:0% +then x and y-axis won't be perpendicular + + + align:start position:0% +then x and y-axis won't be perpendicular +but what we can do is + + align:start position:0% +but what we can do is + + + align:start position:0% +but what we can do is +decide that the plane defined by one two + + align:start position:0% +decide that the plane defined by one two + + + align:start position:0% +decide that the plane defined by one two +and three is the x y plane + + align:start position:0% +and three is the x y plane + + + align:start position:0% +and three is the x y plane +so + + align:start position:0% +so + + + align:start position:0% +so +we can certainly do that and actually uh + + align:start position:0% +we can certainly do that and actually uh + + + align:start position:0% +we can certainly do that and actually uh +we can then based on that idea + + align:start position:0% +we can then based on that idea + + + align:start position:0% +we can then based on that idea +uh we can just remove from + + align:start position:0% +uh we can just remove from + + + align:start position:0% +uh we can just remove from +the vector from one to three + + align:start position:0% +the vector from one to three + + + align:start position:0% +the vector from one to three +the component that is in the direction + + align:start position:0% +the component that is in the direction + + + align:start position:0% +the component that is in the direction +one to two + + align:start position:0% +one to two + + + align:start position:0% +one to two +and what's left is going to be + + align:start position:0% +and what's left is going to be + + + align:start position:0% +and what's left is going to be +automatically perpendicular + + align:start position:0% +automatically perpendicular + + + align:start position:0% +automatically perpendicular +to us and that's + + align:start position:0% +to us and that's + + + align:start position:0% +to us and that's +the y-axis + + align:start position:0% +the y-axis + + + align:start position:0% +the y-axis +so + + align:start position:0% + + + + align:start position:0% + +we pick y equals + + align:start position:0% +we pick y equals + + + align:start position:0% +we pick y equals +rl3 minus rl1 + + align:start position:0% +rl3 minus rl1 + + + align:start position:0% +rl3 minus rl1 +and then we find the component of that + + align:start position:0% +and then we find the component of that + + + align:start position:0% +and then we find the component of that +rl3 minus rl1 + + align:start position:0% +rl3 minus rl1 + + + align:start position:0% +rl3 minus rl1 +in the direction + + align:start position:0% +in the direction + + + align:start position:0% +in the direction +of x hat + + align:start position:0% + + + + align:start position:0% + +right so + + align:start position:0% +right so + + + align:start position:0% +right so +we we pick this vector from one to three + + align:start position:0% +we we pick this vector from one to three + + + align:start position:0% +we we pick this vector from one to three +but we take out a component that's in + + align:start position:0% +but we take out a component that's in + + + align:start position:0% +but we take out a component that's in +the x axis direction + + align:start position:0% +the x axis direction + + + align:start position:0% +the x axis direction +uh which we do simply by taking the dot + + align:start position:0% +uh which we do simply by taking the dot + + + align:start position:0% +uh which we do simply by taking the dot +product of that vector with the unit + + align:start position:0% +product of that vector with the unit + + + align:start position:0% +product of that vector with the unit +vector in the x direction that gives us + + align:start position:0% +vector in the x direction that gives us + + + align:start position:0% +vector in the x direction that gives us +a scalar and then we multiply that by + + align:start position:0% +a scalar and then we multiply that by + + + align:start position:0% +a scalar and then we multiply that by +the unit vector in the x direction so + + align:start position:0% +the unit vector in the x direction so + + + align:start position:0% +the unit vector in the x direction so +that removes uh this component the one + + align:start position:0% +that removes uh this component the one + + + align:start position:0% +that removes uh this component the one +that's parallel to the x-axis and we're + + align:start position:0% +that's parallel to the x-axis and we're + + + align:start position:0% +that's parallel to the x-axis and we're +left with with something that's + + align:start position:0% +left with with something that's + + + align:start position:0% +left with with something that's +perpendicular to the original + + align:start position:0% + + + + align:start position:0% + +and then again we can make a unit vector + + align:start position:0% +and then again we can make a unit vector + + + align:start position:0% +and then again we can make a unit vector +so this won't be a unit vector in + + align:start position:0% +so this won't be a unit vector in + + + align:start position:0% +so this won't be a unit vector in +general of course + + align:start position:0% +general of course + + + align:start position:0% +general of course +okay and it's going to be easy to show + + align:start position:0% +okay and it's going to be easy to show + + + align:start position:0% +okay and it's going to be easy to show +that + + align:start position:0% +that + + + align:start position:0% +that +x dot y dot + + align:start position:0% +x dot y dot + + + align:start position:0% +x dot y dot +is zero + + align:start position:0% +is zero + + + align:start position:0% +is zero +that they're perpendicular to each other + + align:start position:0% +that they're perpendicular to each other + + + align:start position:0% +that they're perpendicular to each other +you can + + align:start position:0% +you can + + + align:start position:0% +you can +check that very easily just by taking + + align:start position:0% +check that very easily just by taking + + + align:start position:0% +check that very easily just by taking +the dot product of this with + + align:start position:0% +the dot product of this with + + + align:start position:0% +the dot product of this with +our definition for x + + align:start position:0% +our definition for x + + + align:start position:0% +our definition for x +well you can just show that + + align:start position:0% +well you can just show that + + + align:start position:0% +well you can just show that +the y vector is perpendicular to the x + + align:start position:0% +the y vector is perpendicular to the x + + + align:start position:0% +the y vector is perpendicular to the x +vector not not the unit + + align:start position:0% +vector not not the unit + + + align:start position:0% +vector not not the unit +okay so um so we have the the origin we + + align:start position:0% +okay so um so we have the the origin we + + + align:start position:0% +okay so um so we have the the origin we +have the x-axis we have the x-y plane + + align:start position:0% +have the x-axis we have the x-y plane + + + align:start position:0% +have the x-axis we have the x-y plane +yeah so we have uh an object and we've + + align:start position:0% +yeah so we have uh an object and we've + + + align:start position:0% +yeah so we have uh an object and we've +identified + + align:start position:0% +identified + + + align:start position:0% +identified +quote interesting points on them on it + + align:start position:0% +quote interesting points on them on it + + + align:start position:0% +quote interesting points on them on it +and we've measured them so it's a cloud + + align:start position:0% +and we've measured them so it's a cloud + + + align:start position:0% +and we've measured them so it's a cloud +of points + + align:start position:0% +of points + + + align:start position:0% +of points +and they could be you know + + align:start position:0% +and they could be you know + + + align:start position:0% +and they could be you know +corners + + align:start position:0% + + + + align:start position:0% + +not edges because edges don't give us + + align:start position:0% +not edges because edges don't give us + + + align:start position:0% +not edges because edges don't give us +full 3d constraint + + align:start position:0% +full 3d constraint + + + align:start position:0% +full 3d constraint +so if you know if our + + align:start position:0% +so if you know if our + + + align:start position:0% +so if you know if our +calibration object or whatever was a + + align:start position:0% +calibration object or whatever was a + + + align:start position:0% +calibration object or whatever was a +cube + + align:start position:0% +cube + + + align:start position:0% +cube +we might very well have + + align:start position:0% +we might very well have + + + align:start position:0% +we might very well have +these points + + align:start position:0% +these points + + + align:start position:0% +these points +or if it's you know someone's head + + align:start position:0% +or if it's you know someone's head + + + align:start position:0% +or if it's you know someone's head +then it might be + + align:start position:0% +then it might be + + + align:start position:0% +then it might be +position of + + align:start position:0% +position of + + + align:start position:0% +position of +the iris of their eye and so on + + align:start position:0% +the iris of their eye and so on + + + align:start position:0% +the iris of their eye and so on +and we've measured those in both + + align:start position:0% +and we've measured those in both + + + align:start position:0% +and we've measured those in both +coordinate systems that's the important + + align:start position:0% +coordinate systems that's the important + + + align:start position:0% +coordinate systems that's the important +thing but right now we're just working + + align:start position:0% +thing but right now we're just working + + + align:start position:0% +thing but right now we're just working +on the left coordinate system + + align:start position:0% +on the left coordinate system + + + align:start position:0% +on the left coordinate system +okay + + align:start position:0% +okay + + + align:start position:0% +okay +well at this point we + + align:start position:0% +well at this point we + + + align:start position:0% +well at this point we +define z to be the cross product of x + + align:start position:0% +define z to be the cross product of x + + + align:start position:0% +define z to be the cross product of x +and y + + align:start position:0% +and y + + + align:start position:0% +and y +because the cross product is + + align:start position:0% +because the cross product is + + + align:start position:0% +because the cross product is +perpendicular to both + + align:start position:0% +perpendicular to both + + + align:start position:0% +perpendicular to both +vectors in the cross product so z is + + align:start position:0% +vectors in the cross product so z is + + + align:start position:0% +vectors in the cross product so z is +going to be perpendicular to both x and + + align:start position:0% +going to be perpendicular to both x and + + + align:start position:0% +going to be perpendicular to both x and +y so now we've got a whole + + align:start position:0% +y so now we've got a whole + + + align:start position:0% +y so now we've got a whole +coordinate system + + align:start position:0% +coordinate system + + + align:start position:0% +coordinate system +we have a triad of unit vectors + + align:start position:0% + + + + align:start position:0% + +that define a coordinate system + + align:start position:0% + + + + align:start position:0% + +so we've done that for the left + + align:start position:0% + + + + align:start position:0% + +and we only need three points so if we + + align:start position:0% +and we only need three points so if we + + + align:start position:0% +and we only need three points so if we +measure the whole bunch of points + + align:start position:0% +measure the whole bunch of points + + + align:start position:0% +measure the whole bunch of points +we don't need them we just need three + + align:start position:0% +we don't need them we just need three + + + align:start position:0% +we don't need them we just need three +and um + + align:start position:0% + + + + align:start position:0% + +now we do the same thing for the right + + align:start position:0% +now we do the same thing for the right + + + align:start position:0% +now we do the same thing for the right +coordinate system + + align:start position:0% +coordinate system + + + align:start position:0% +coordinate system +and you know i'm not going to go through + + align:start position:0% +and you know i'm not going to go through + + + align:start position:0% +and you know i'm not going to go through +the process again i will just get an x r + + align:start position:0% +the process again i will just get an x r + + + align:start position:0% +the process again i will just get an x r +hat a y r hat and a z r hat and i + + align:start position:0% +hat a y r hat and a z r hat and i + + + align:start position:0% +hat a y r hat and a z r hat and i +suppose i should call those + + align:start position:0% + + + + align:start position:0% + +um x left hat + + align:start position:0% +um x left hat + + + align:start position:0% +um x left hat +y left half + + align:start position:0% +y left half + + + align:start position:0% +y left half +and z left hand so + + align:start position:0% +and z left hand so + + + align:start position:0% +and z left hand so +what i do is i take my two cloud + + align:start position:0% +what i do is i take my two cloud + + + align:start position:0% +what i do is i take my two cloud +my two clouds of points + + align:start position:0% +my two clouds of points + + + align:start position:0% +my two clouds of points +measured in these two coordinate systems + + align:start position:0% +measured in these two coordinate systems + + + align:start position:0% +measured in these two coordinate systems +and i use them to build + + align:start position:0% +and i use them to build + + + align:start position:0% +and i use them to build +an axis an x-axis a y-axis and a z-axis + + align:start position:0% +an axis an x-axis a y-axis and a z-axis + + + align:start position:0% +an axis an x-axis a y-axis and a z-axis +and now all i need to do quote all i + + align:start position:0% +and now all i need to do quote all i + + + align:start position:0% +and now all i need to do quote all i +need to do is to + + align:start position:0% +need to do is to + + + align:start position:0% +need to do is to +map those + + align:start position:0% +map those + + + align:start position:0% +map those +unit vectors into each other so + + align:start position:0% +unit vectors into each other so + + + align:start position:0% +unit vectors into each other so +i need to find a transformation that + + align:start position:0% +i need to find a transformation that + + + align:start position:0% +i need to find a transformation that +puts x l into x r + + align:start position:0% +puts x l into x r + + + align:start position:0% +puts x l into x r +and the transformation that puts a y l + + align:start position:0% +and the transformation that puts a y l + + + align:start position:0% +and the transformation that puts a y l +into y r and so on so + + align:start position:0% +into y r and so on so + + + align:start position:0% +into y r and so on so +okay now + + align:start position:0% +okay now + + + align:start position:0% +okay now +because i've artificially removed the + + align:start position:0% +because i've artificially removed the + + + align:start position:0% +because i've artificially removed the +translation + + align:start position:0% +translation + + + align:start position:0% +translation +by picking one of the points as the + + align:start position:0% +by picking one of the points as the + + + align:start position:0% +by picking one of the points as the +origin i don't have to worry about + + align:start position:0% +origin i don't have to worry about + + + align:start position:0% +origin i don't have to worry about +translation + + align:start position:0% +translation + + + align:start position:0% +translation +for the moment i only need to deal with + + align:start position:0% +for the moment i only need to deal with + + + align:start position:0% +for the moment i only need to deal with +rotation i've you know separated that + + align:start position:0% +rotation i've you know separated that + + + align:start position:0% +rotation i've you know separated that +problem + + align:start position:0% +problem + + + align:start position:0% +problem +so i've got then + + align:start position:0% +so i've got then + + + align:start position:0% +so i've got then +x r hat + + align:start position:0% +x r hat + + + align:start position:0% +x r hat +is r x l hat + + align:start position:0% +is r x l hat + + + align:start position:0% +is r x l hat +right so + + align:start position:0% +right so + + + align:start position:0% +right so +the unknown rotation r + + align:start position:0% + + + + align:start position:0% + +uh does this and it also does that + + align:start position:0% +uh does this and it also does that + + + align:start position:0% +uh does this and it also does that +i mean if i just had that first line + + align:start position:0% +i mean if i just had that first line + + + align:start position:0% +i mean if i just had that first line +that wouldn't pin down r because there + + align:start position:0% +that wouldn't pin down r because there + + + align:start position:0% +that wouldn't pin down r because there +are lots of ways of rotating one vector + + align:start position:0% +are lots of ways of rotating one vector + + + align:start position:0% +are lots of ways of rotating one vector +into another it's not unique + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +that's + + align:start position:0% +that's + + + align:start position:0% +that's +what i expect and now my problem is + + align:start position:0% +what i expect and now my problem is + + + align:start position:0% +what i expect and now my problem is +solving for r + + align:start position:0% +solving for r + + + align:start position:0% +solving for r +um so i've got these three vector + + align:start position:0% +um so i've got these three vector + + + align:start position:0% +um so i've got these three vector +matrix equations + + align:start position:0% +matrix equations + + + align:start position:0% +matrix equations +but i think you can see that we can + + align:start position:0% +but i think you can see that we can + + + align:start position:0% +but i think you can see that we can +compose them we can stick them together + + align:start position:0% +compose them we can stick them together + + + align:start position:0% +compose them we can stick them together +into one equation so we could have + + align:start position:0% +into one equation so we could have + + + align:start position:0% +into one equation so we could have +x r hat + + align:start position:0% +x r hat + + + align:start position:0% +x r hat +y r hat + + align:start position:0% +y r hat + + + align:start position:0% +y r hat +z r hat + + align:start position:0% +z r hat + + + align:start position:0% +z r hat +that's now a matrix right because the + + align:start position:0% +that's now a matrix right because the + + + align:start position:0% +that's now a matrix right because the +the in the representation we're using + + align:start position:0% +the in the representation we're using + + + align:start position:0% +the in the representation we're using +these are column vectors + + align:start position:0% +these are column vectors + + + align:start position:0% +these are column vectors +so + + align:start position:0% +so + + + align:start position:0% +so +this is a three by three matrix + + align:start position:0% +this is a three by three matrix + + + align:start position:0% +this is a three by three matrix +and + + align:start position:0% + + + + align:start position:0% + +and the same for the right hand side and + + align:start position:0% +and the same for the right hand side and + + + align:start position:0% +and the same for the right hand side and +i think you'll agree that this single + + align:start position:0% +i think you'll agree that this single + + + align:start position:0% +i think you'll agree that this single +equation + + align:start position:0% +equation + + + align:start position:0% +equation +is equivalent to these separate + + align:start position:0% +is equivalent to these separate + + + align:start position:0% +is equivalent to these separate +equations + + align:start position:0% +equations + + + align:start position:0% +equations +because the uh you know the if i + + align:start position:0% +because the uh you know the if i + + + align:start position:0% +because the uh you know the if i +multiply the matrix by that first vector + + align:start position:0% +multiply the matrix by that first vector + + + align:start position:0% +multiply the matrix by that first vector +i get the first vector over here and so + + align:start position:0% +i get the first vector over here and so + + + align:start position:0% +i get the first vector over here and so +on + + align:start position:0% +on + + + align:start position:0% +on +so + + align:start position:0% +so + + + align:start position:0% +so +that makes the answer trivial that r is + + align:start position:0% + + + + align:start position:0% + +let's see i need to post multiply so + + align:start position:0% + + + + align:start position:0% + +right because if i multiply both sides + + align:start position:0% +right because if i multiply both sides + + + align:start position:0% +right because if i multiply both sides +of that + + align:start position:0% +of that + + + align:start position:0% +of that +equation + + align:start position:0% + + + + align:start position:0% + +up here by the inverse of + + align:start position:0% +up here by the inverse of + + + align:start position:0% +up here by the inverse of +this matrix + + align:start position:0% +this matrix + + + align:start position:0% +this matrix +uh it'll drop out over here it's + + align:start position:0% +uh it'll drop out over here it's + + + align:start position:0% +uh it'll drop out over here it's +multiplied by its own inverse so it + + align:start position:0% +multiplied by its own inverse so it + + + align:start position:0% +multiplied by its own inverse so it +gives identity and then over here on + + align:start position:0% +gives identity and then over here on + + + align:start position:0% +gives identity and then over here on +this side i get this this expression + + align:start position:0% +this side i get this this expression + + + align:start position:0% +this side i get this this expression +does the inverse exist we always ask + + align:start position:0% +does the inverse exist we always ask + + + align:start position:0% +does the inverse exist we always ask +that question you know when does this + + align:start position:0% +that question you know when does this + + + align:start position:0% +that question you know when does this +fail + + align:start position:0% +fail + + + align:start position:0% +fail +well it should because by construction + + align:start position:0% +well it should because by construction + + + align:start position:0% +well it should because by construction +those things are orthogonal to each + + align:start position:0% +those things are orthogonal to each + + + align:start position:0% +those things are orthogonal to each +other so we've got kind of an ideal case + + align:start position:0% +other so we've got kind of an ideal case + + + align:start position:0% +other so we've got kind of an ideal case +where the three columns of the matrix + + align:start position:0% +where the three columns of the matrix + + + align:start position:0% +where the three columns of the matrix +are orthogonal to each other as opposed + + align:start position:0% +are orthogonal to each other as opposed + + + align:start position:0% +are orthogonal to each other as opposed +to being linearly dependent that's the + + align:start position:0% +to being linearly dependent that's the + + + align:start position:0% +to being linearly dependent that's the +other extreme end of the spectrum + + align:start position:0% +other extreme end of the spectrum + + + align:start position:0% +other extreme end of the spectrum +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +so there we are + + align:start position:0% +so there we are + + + align:start position:0% +so there we are +we solve the problem + + align:start position:0% +we solve the problem + + + align:start position:0% +we solve the problem +so + + align:start position:0% +so + + + align:start position:0% +so +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +we said that + + align:start position:0% +we said that + + + align:start position:0% +we said that +if we remove translation for the moment + + align:start position:0% +if we remove translation for the moment + + + align:start position:0% +if we remove translation for the moment +we have three degrees of freedom left to + + align:start position:0% +we have three degrees of freedom left to + + + align:start position:0% +we have three degrees of freedom left to +find + + align:start position:0% +find + + + align:start position:0% +find +and then we said okay we have three + + align:start position:0% +and then we said okay we have three + + + align:start position:0% +and then we said okay we have three +correspondences between the two + + align:start position:0% +correspondences between the two + + + align:start position:0% +correspondences between the two +coordinate system so that sounds about + + align:start position:0% +coordinate system so that sounds about + + + align:start position:0% +coordinate system so that sounds about +right you know three constraints three + + align:start position:0% +right you know three constraints three + + + align:start position:0% +right you know three constraints three +unknowns + + align:start position:0% +unknowns + + + align:start position:0% +unknowns +but those constraints are much more + + align:start position:0% +but those constraints are much more + + + align:start position:0% +but those constraints are much more +powerful because they're not just a + + align:start position:0% +powerful because they're not just a + + + align:start position:0% +powerful because they're not just a +scalar equals a scalar their vector + + align:start position:0% +scalar equals a scalar their vector + + + align:start position:0% +scalar equals a scalar their vector +equals a vector so each of them is worth + + align:start position:0% +equals a vector so each of them is worth + + + align:start position:0% +equals a vector so each of them is worth +three points + + align:start position:0% +three points + + + align:start position:0% +three points +so we actually have you know uh nine + + align:start position:0% +so we actually have you know uh nine + + + align:start position:0% +so we actually have you know uh nine +constraints + + align:start position:0% +constraints + + + align:start position:0% +constraints +we're saying that uh point number one + + align:start position:0% +we're saying that uh point number one + + + align:start position:0% +we're saying that uh point number one +transforms into point number one in the + + align:start position:0% +transforms into point number one in the + + + align:start position:0% +transforms into point number one in the +other system point number two transforms + + align:start position:0% +other system point number two transforms + + + align:start position:0% +other system point number two transforms +into and so on and so each of those are + + align:start position:0% +into and so on and so each of those are + + + align:start position:0% +into and so on and so each of those are +vector equalities you know + + align:start position:0% +vector equalities you know + + + align:start position:0% +vector equalities you know +r of + + align:start position:0% +r of + + + align:start position:0% +r of +l of 1 is going to map into r r of 1 and + + align:start position:0% +l of 1 is going to map into r r of 1 and + + + align:start position:0% +l of 1 is going to map into r r of 1 and +so on so we have + + align:start position:0% +so on so we have + + + align:start position:0% +so on so we have +three vector + + align:start position:0% +three vector + + + align:start position:0% +three vector +vector equalities or if you like + + align:start position:0% +vector equalities or if you like + + + align:start position:0% +vector equalities or if you like +you know how much constraint do you need + + align:start position:0% +you know how much constraint do you need + + + align:start position:0% +you know how much constraint do you need +to pin a point down in 3d well three + + align:start position:0% +to pin a point down in 3d well three + + + align:start position:0% +to pin a point down in 3d well three +constraints right you need x y and z + + align:start position:0% +constraints right you need x y and z + + + align:start position:0% +constraints right you need x y and z +or some other three numbers like + + align:start position:0% +or some other three numbers like + + + align:start position:0% +or some other three numbers like +distances from three + + align:start position:0% +distances from three + + + align:start position:0% +distances from three +i don't know wi-fi routers or something + + align:start position:0% +i don't know wi-fi routers or something + + + align:start position:0% +i don't know wi-fi routers or something +you need three things + + align:start position:0% +you need three things + + + align:start position:0% +you need three things +so in this case we've got nine but wait + + align:start position:0% +so in this case we've got nine but wait + + + align:start position:0% +so in this case we've got nine but wait +a minute the rotation only has three + + align:start position:0% +a minute the rotation only has three + + + align:start position:0% +a minute the rotation only has three +degrees of freedom so what's going on + + align:start position:0% +degrees of freedom so what's going on + + + align:start position:0% +degrees of freedom so what's going on +we it's excessive so we don't need three + + align:start position:0% +we it's excessive so we don't need three + + + align:start position:0% +we it's excessive so we don't need three +points we can just stop with with two + + align:start position:0% +points we can just stop with with two + + + align:start position:0% +points we can just stop with with two +right + + align:start position:0% +right + + + align:start position:0% +right +well but we said with 2 + + align:start position:0% +well but we said with 2 + + + align:start position:0% +well but we said with 2 +we just get the x-axis and then the + + align:start position:0% +we just get the x-axis and then the + + + align:start position:0% +we just get the x-axis and then the +whole thing can still rotate about the + + align:start position:0% +whole thing can still rotate about the + + + align:start position:0% +whole thing can still rotate about the +x-axis so that's not good enough + + align:start position:0% +x-axis so that's not good enough + + + align:start position:0% +x-axis so that's not good enough +we do actually need all three but what's + + align:start position:0% +we do actually need all three but what's + + + align:start position:0% +we do actually need all three but what's +going on is that we're not using all the + + align:start position:0% +going on is that we're not using all the + + + align:start position:0% +going on is that we're not using all the +information we get + + align:start position:0% +information we get + + + align:start position:0% +information we get +right so uh let's make a tally here + + align:start position:0% +right so uh let's make a tally here + + + align:start position:0% +right so uh let's make a tally here +so of the point number one + + align:start position:0% +so of the point number one + + + align:start position:0% +so of the point number one +we are using all three of its uh + + align:start position:0% +we are using all three of its uh + + + align:start position:0% +we are using all three of its uh +components + + align:start position:0% +components + + + align:start position:0% +components +so we use so this provides three + + align:start position:0% +so we use so this provides three + + + align:start position:0% +so we use so this provides three +constraints + + align:start position:0% +constraints + + + align:start position:0% +constraints +um then this one here + + align:start position:0% +um then this one here + + + align:start position:0% +um then this one here +um we're we're not using the distance + + align:start position:0% +um we're we're not using the distance + + + align:start position:0% +um we're we're not using the distance +from one to two we're only using um + + align:start position:0% +from one to two we're only using um + + + align:start position:0% +from one to two we're only using um +the unit vector in that direction so + + align:start position:0% +the unit vector in that direction so + + + align:start position:0% +the unit vector in that direction so +it's a direction so it's really + + align:start position:0% +it's a direction so it's really + + + align:start position:0% +it's a direction so it's really +providing only two + + align:start position:0% +providing only two + + + align:start position:0% +providing only two +and then this one here is even worse + + align:start position:0% +and then this one here is even worse + + + align:start position:0% +and then this one here is even worse +we're actually only using uh one uh + + align:start position:0% +we're actually only using uh one uh + + + align:start position:0% +we're actually only using uh one uh +constraint from that and so the total is + + align:start position:0% +constraint from that and so the total is + + + align:start position:0% +constraint from that and so the total is +three plus 2 plus 1 is 6. oh well that + + align:start position:0% +three plus 2 plus 1 is 6. oh well that + + + align:start position:0% +three plus 2 plus 1 is 6. oh well that +includes the translation so so that + + align:start position:0% +includes the translation so so that + + + align:start position:0% +includes the translation so so that +explains + + align:start position:0% +explains + + + align:start position:0% +explains +some of what's going on + + align:start position:0% +some of what's going on + + + align:start position:0% +some of what's going on +that um + + align:start position:0% +that um + + + align:start position:0% +that um +this particular construction + + align:start position:0% +this particular construction + + + align:start position:0% +this particular construction +does give us a rotation but we're not + + align:start position:0% +does give us a rotation but we're not + + + align:start position:0% +does give us a rotation but we're not +using the information from the points + + align:start position:0% +using the information from the points + + + align:start position:0% +using the information from the points +equally so we've made some arbitrary + + align:start position:0% +equally so we've made some arbitrary + + + align:start position:0% +equally so we've made some arbitrary +decision we picked number one and we're + + align:start position:0% +decision we picked number one and we're + + + align:start position:0% +decision we picked number one and we're +using all of it so that seems wrong + + align:start position:0% +using all of it so that seems wrong + + + align:start position:0% +using all of it so that seems wrong +right because + + align:start position:0% +right because + + + align:start position:0% +right because +i mean who's to say + + align:start position:0% +i mean who's to say + + + align:start position:0% +i mean who's to say +which points + + align:start position:0% +which points + + + align:start position:0% +which points +more important than another i mean there + + align:start position:0% +more important than another i mean there + + + align:start position:0% +more important than another i mean there +might be weight associated with it + + align:start position:0% +might be weight associated with it + + + align:start position:0% +might be weight associated with it +because when you measure them you found + + align:start position:0% +because when you measure them you found + + + align:start position:0% +because when you measure them you found +one point that's really distinctive and + + align:start position:0% +one point that's really distinctive and + + + align:start position:0% +one point that's really distinctive and +you're very certain about where it is + + align:start position:0% +you're very certain about where it is + + + align:start position:0% +you're very certain about where it is +and some other matches that might not be + + align:start position:0% +and some other matches that might not be + + + align:start position:0% +and some other matches that might not be +so good but that that's a different + + align:start position:0% +so good but that that's a different + + + align:start position:0% +so good but that that's a different +issue okay so that's one thing about + + align:start position:0% +issue okay so that's one thing about + + + align:start position:0% +issue okay so that's one thing about +this that's + + align:start position:0% + + + + align:start position:0% + +less than optimal + + align:start position:0% +less than optimal + + + align:start position:0% +less than optimal +so another one is you know what if i had + + align:start position:0% +so another one is you know what if i had + + + align:start position:0% +so another one is you know what if i had +picked + + align:start position:0% +picked + + + align:start position:0% +picked +this point first so this is my one + + align:start position:0% +this point first so this is my one + + + align:start position:0% +this point first so this is my one +and that's my two and that's my three + + align:start position:0% +and that's my two and that's my three + + + align:start position:0% +and that's my two and that's my three +will i get the same transformation + + align:start position:0% +will i get the same transformation + + + align:start position:0% +will i get the same transformation +no + + align:start position:0% +no + + + align:start position:0% +no +i won't get the same transformation + + align:start position:0% +i won't get the same transformation + + + align:start position:0% +i won't get the same transformation +because of i've selectively neglected + + align:start position:0% +because of i've selectively neglected + + + align:start position:0% +because of i've selectively neglected +information and now i am selectively + + align:start position:0% +information and now i am selectively + + + align:start position:0% +information and now i am selectively +neglecting in a different way i'm + + align:start position:0% +neglecting in a different way i'm + + + align:start position:0% +neglecting in a different way i'm +throwing away something else + + align:start position:0% +throwing away something else + + + align:start position:0% +throwing away something else +and so that also tells you that this + + align:start position:0% +and so that also tells you that this + + + align:start position:0% +and so that also tells you that this +isn't + + align:start position:0% +isn't + + + align:start position:0% +isn't +ideal + + align:start position:0% +ideal + + + align:start position:0% +ideal +now in practice also we might be + + align:start position:0% +now in practice also we might be + + + align:start position:0% +now in practice also we might be +inclined to measure more than three + + align:start position:0% +inclined to measure more than three + + + align:start position:0% +inclined to measure more than three +correspondences you know if we have + + align:start position:0% +correspondences you know if we have + + + align:start position:0% +correspondences you know if we have +these two lidars on the vehicle + + align:start position:0% +these two lidars on the vehicle + + + align:start position:0% +these two lidars on the vehicle +uh they're giving us hundreds of uh + + align:start position:0% +uh they're giving us hundreds of uh + + + align:start position:0% +uh they're giving us hundreds of uh +points and uh + + align:start position:0% +points and uh + + + align:start position:0% +points and uh +there will be some error in all of those + + align:start position:0% +there will be some error in all of those + + + align:start position:0% +there will be some error in all of those +measurements but again as we noted if + + align:start position:0% +measurements but again as we noted if + + + align:start position:0% +measurements but again as we noted if +you have lots of points uh least squares + + align:start position:0% +you have lots of points uh least squares + + + align:start position:0% +you have lots of points uh least squares +or some other method can dramatically + + align:start position:0% +or some other method can dramatically + + + align:start position:0% +or some other method can dramatically +improve your accuracy uh you know if you + + align:start position:0% +improve your accuracy uh you know if you + + + align:start position:0% +improve your accuracy uh you know if you +can make use of all of those + + align:start position:0% +can make use of all of those + + + align:start position:0% +can make use of all of those +correspondences so so this doesn't it + + align:start position:0% +correspondences so so this doesn't it + + + align:start position:0% +correspondences so so this doesn't it +just uses three points and yeah you + + align:start position:0% +just uses three points and yeah you + + + align:start position:0% +just uses three points and yeah you +could now repeat it you know picking + + align:start position:0% +could now repeat it you know picking + + + align:start position:0% +could now repeat it you know picking +three other points and do that lots of + + align:start position:0% +three other points and do that lots of + + + align:start position:0% +three other points and do that lots of +different ways and averaging and that + + align:start position:0% +different ways and averaging and that + + + align:start position:0% +different ways and averaging and that +would be better but it would be kuji you + + align:start position:0% +would be better but it would be kuji you + + + align:start position:0% +would be better but it would be kuji you +know ad hoc so + + align:start position:0% +know ad hoc so + + + align:start position:0% +know ad hoc so +okay so ad hoc method number one + + align:start position:0% +okay so ad hoc method number one + + + align:start position:0% +okay so ad hoc method number one +uh it's it's and you know in some sense + + align:start position:0% +uh it's it's and you know in some sense + + + align:start position:0% +uh it's it's and you know in some sense +this might be a way to go if you needed + + align:start position:0% +this might be a way to go if you needed + + + align:start position:0% +this might be a way to go if you needed +an initial guess or if you needed a + + align:start position:0% +an initial guess or if you needed a + + + align:start position:0% +an initial guess or if you needed a +really rough answer + + align:start position:0% +really rough answer + + + align:start position:0% +really rough answer +um + + align:start position:0% +um + + + align:start position:0% +um +say you had a more precise myth so this + + align:start position:0% +say you had a more precise myth so this + + + align:start position:0% +say you had a more precise myth so this +could be like pat quick and + + align:start position:0% +could be like pat quick and + + + align:start position:0% +could be like pat quick and +pat max where you use one to give you a + + align:start position:0% +pat max where you use one to give you a + + + align:start position:0% +pat max where you use one to give you a +fast approximate answer and then you + + align:start position:0% +fast approximate answer and then you + + + align:start position:0% +fast approximate answer and then you +have use that as an initial condition + + align:start position:0% +have use that as an initial condition + + + align:start position:0% +have use that as an initial condition +for something else that gives you a more + + align:start position:0% +for something else that gives you a more + + + align:start position:0% +for something else that gives you a more +precise answer + + align:start position:0% +precise answer + + + align:start position:0% +precise answer +okay so here's method number two + + align:start position:0% + + + + align:start position:0% + +and uh we briefly talked about this in + + align:start position:0% +and uh we briefly talked about this in + + + align:start position:0% +and uh we briefly talked about this in +2d so let me just refresh your memory + + align:start position:0% +2d so let me just refresh your memory + + + align:start position:0% +2d so let me just refresh your memory +because we didn't really spend a lot of + + align:start position:0% +because we didn't really spend a lot of + + + align:start position:0% +because we didn't really spend a lot of +time on it + + align:start position:0% +time on it + + + align:start position:0% +time on it +the idea was that we had some sort of + + align:start position:0% +the idea was that we had some sort of + + + align:start position:0% +the idea was that we had some sort of +blob a binary image + + align:start position:0% +blob a binary image + + + align:start position:0% +blob a binary image +and + + align:start position:0% +and + + + align:start position:0% +and +we're trying to make some measurement on + + align:start position:0% +we're trying to make some measurement on + + + align:start position:0% +we're trying to make some measurement on +it that could help us + + align:start position:0% +it that could help us + + + align:start position:0% +it that could help us +identify or align + + align:start position:0% +identify or align + + + align:start position:0% +identify or align +and + + align:start position:0% +and + + + align:start position:0% +and +we said that one way of doing that is to + + align:start position:0% +we said that one way of doing that is to + + + align:start position:0% +we said that one way of doing that is to +look at the axes of inertia + + align:start position:0% + + + + align:start position:0% + +right so if i have a cloud of points + + align:start position:0% +right so if i have a cloud of points + + + align:start position:0% +right so if i have a cloud of points +as opposed to some sort of + + align:start position:0% +as opposed to some sort of + + + align:start position:0% +as opposed to some sort of +binary image + + align:start position:0% +binary image + + + align:start position:0% +binary image +i can do the same thing i can + + align:start position:0% +i can do the same thing i can + + + align:start position:0% +i can do the same thing i can +find the axes about which the + + align:start position:0% +find the axes about which the + + + align:start position:0% +find the axes about which the +oh wrong way around excuse me + + align:start position:0% +oh wrong way around excuse me + + + align:start position:0% +oh wrong way around excuse me +minimum axis max + + align:start position:0% +minimum axis max + + + align:start position:0% +minimum axis max +so why do i know that's the minimum well + + align:start position:0% +so why do i know that's the minimum well + + + align:start position:0% +so why do i know that's the minimum well +because the inertia depends on the + + align:start position:0% +because the inertia depends on the + + + align:start position:0% +because the inertia depends on the +integral of + + align:start position:0% +integral of + + + align:start position:0% +integral of +the + + align:start position:0% +the + + + align:start position:0% +the +distance + + align:start position:0% +distance + + + align:start position:0% +distance +times the mass + + align:start position:0% +times the mass + + + align:start position:0% +times the mass +distance squared times the mass so it's + + align:start position:0% + + + + align:start position:0% + +let me quote r + + align:start position:0% + + + + align:start position:0% + +and so + + align:start position:0% +and so + + + align:start position:0% +and so +about this axis + + align:start position:0% +about this axis + + + align:start position:0% +about this axis +these distances are all very short so + + align:start position:0% +these distances are all very short so + + + align:start position:0% +these distances are all very short so +the sum of squares of this distance is + + align:start position:0% +the sum of squares of this distance is + + + align:start position:0% +the sum of squares of this distance is +going to be small whereas about this + + align:start position:0% +going to be small whereas about this + + + align:start position:0% +going to be small whereas about this +axis at right angles + + align:start position:0% +axis at right angles + + + align:start position:0% +axis at right angles +a lot of the distances are large so i'm + + align:start position:0% +a lot of the distances are large so i'm + + + align:start position:0% +a lot of the distances are large so i'm +going to get a huge inertia and you can + + align:start position:0% +going to get a huge inertia and you can + + + align:start position:0% +going to get a huge inertia and you can +show that they have to be at right + + align:start position:0% +show that they have to be at right + + + align:start position:0% +show that they have to be at right +angles to each other + + align:start position:0% +angles to each other + + + align:start position:0% +angles to each other +and you can show that you can find them + + align:start position:0% +and you can show that you can find them + + + align:start position:0% +and you can show that you can find them +by finding the eigenvectors and + + align:start position:0% +by finding the eigenvectors and + + + align:start position:0% +by finding the eigenvectors and +eigenvalues of a two by two matrix so + + align:start position:0% +eigenvalues of a two by two matrix so + + + align:start position:0% +eigenvalues of a two by two matrix so +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +2d + + align:start position:0% +2d + + + align:start position:0% +2d +let's go to 3d with the same idea + + align:start position:0% +let's go to 3d with the same idea + + + align:start position:0% +let's go to 3d with the same idea +so there's some sort of object in in + + align:start position:0% +so there's some sort of object in in + + + align:start position:0% +so there's some sort of object in in +space + + align:start position:0% +space + + + align:start position:0% +space +a bunch of points + + align:start position:0% + + + + align:start position:0% + +so we've identified these points + + align:start position:0% +so we've identified these points + + + align:start position:0% +so we've identified these points +and + + align:start position:0% +and + + + align:start position:0% +and +in a way that we can find them again in + + align:start position:0% +in a way that we can find them again in + + + align:start position:0% +in a way that we can find them again in +another image + + align:start position:0% +another image + + + align:start position:0% +another image +and now we're trying to sort of + + align:start position:0% +and now we're trying to sort of + + + align:start position:0% +and now we're trying to sort of +establish a coordinate system + + align:start position:0% +establish a coordinate system + + + align:start position:0% +establish a coordinate system +because we know that once we've got a + + align:start position:0% +because we know that once we've got a + + + align:start position:0% +because we know that once we've got a +coordinate system in the left data and + + align:start position:0% +coordinate system in the left data and + + + align:start position:0% +coordinate system in the left data and +the right data we just have to relate + + align:start position:0% +the right data we just have to relate + + + align:start position:0% +the right data we just have to relate +those two coordinate systems and you + + align:start position:0% +those two coordinate systems and you + + + align:start position:0% +those two coordinate systems and you +know over there we use that method to + + align:start position:0% +know over there we use that method to + + + align:start position:0% +know over there we use that method to +find a coordinate system but we could + + align:start position:0% +find a coordinate system but we could + + + align:start position:0% +find a coordinate system but we could +also look for + + align:start position:0% +also look for + + + align:start position:0% +also look for +axes of + + align:start position:0% +axes of + + + align:start position:0% +axes of +minimum inertia in 3d just as we do in + + align:start position:0% +minimum inertia in 3d just as we do in + + + align:start position:0% +minimum inertia in 3d just as we do in +in 2d + + align:start position:0% +in 2d + + + align:start position:0% +in 2d +and in 3d we're then also going to find + + align:start position:0% +and in 3d we're then also going to find + + + align:start position:0% +and in 3d we're then also going to find +that there's a perpendicular axis + + align:start position:0% +that there's a perpendicular axis + + + align:start position:0% +that there's a perpendicular axis +that has a maximum inertia + + align:start position:0% +that has a maximum inertia + + + align:start position:0% +that has a maximum inertia +and the difference about 3d is that + + align:start position:0% +and the difference about 3d is that + + + align:start position:0% +and the difference about 3d is that +there's a third axis + + align:start position:0% +there's a third axis + + + align:start position:0% +there's a third axis +which is a saddle point + + align:start position:0% +which is a saddle point + + + align:start position:0% +which is a saddle point +so + + align:start position:0% +so + + + align:start position:0% +so +if you move the axis in one direction + + align:start position:0% +if you move the axis in one direction + + + align:start position:0% +if you move the axis in one direction +the inertia gets bigger in a quadratic + + align:start position:0% +the inertia gets bigger in a quadratic + + + align:start position:0% +the inertia gets bigger in a quadratic +way + + align:start position:0% +way + + + align:start position:0% +way +and if you move it in another direction + + align:start position:0% +and if you move it in another direction + + + align:start position:0% +and if you move it in another direction +at right angles the inertia gets smaller + + align:start position:0% +at right angles the inertia gets smaller + + + align:start position:0% +at right angles the inertia gets smaller +in a quadratic way so it's + + align:start position:0% +in a quadratic way so it's + + + align:start position:0% +in a quadratic way so it's +sort of like that + + align:start position:0% +sort of like that + + + align:start position:0% +sort of like that +kind of hard to draw but + + align:start position:0% +kind of hard to draw but + + + align:start position:0% +kind of hard to draw but +here's the idea of the saddle point axis + + align:start position:0% +here's the idea of the saddle point axis + + + align:start position:0% +here's the idea of the saddle point axis +and then if you move it in this + + align:start position:0% +and then if you move it in this + + + align:start position:0% +and then if you move it in this +direction + + align:start position:0% +direction + + + align:start position:0% +direction +the inertia goes down + + align:start position:0% +the inertia goes down + + + align:start position:0% +the inertia goes down +same on this side + + align:start position:0% +same on this side + + + align:start position:0% +same on this side +but then if you move it at right angles + + align:start position:0% +but then if you move it at right angles + + + align:start position:0% +but then if you move it at right angles +then the inertia goes up quadratic + + align:start position:0% +then the inertia goes up quadratic + + + align:start position:0% +then the inertia goes up quadratic +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +so + + align:start position:0% +so + + + align:start position:0% +so +if we can figure out what those axes are + + align:start position:0% + + + + align:start position:0% + +we should be + + align:start position:0% +we should be + + + align:start position:0% +we should be +we should be + + align:start position:0% +we should be + + + align:start position:0% +we should be +well let's do the math it's not not that + + align:start position:0% +well let's do the math it's not not that + + + align:start position:0% +well let's do the math it's not not that +hard + + align:start position:0% +hard + + + align:start position:0% +hard +okay so what we're looking for is + + align:start position:0% +okay so what we're looking for is + + + align:start position:0% +okay so what we're looking for is +uh expression for + + align:start position:0% +uh expression for + + + align:start position:0% +uh expression for +the distance from the axis because again + + align:start position:0% +the distance from the axis because again + + + align:start position:0% +the distance from the axis because again +the the inertia is + + align:start position:0% + + + + align:start position:0% + +the integral of that distance word + + align:start position:0% + + + + align:start position:0% + +over the object so i don't know + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% + + + + align:start position:0% + +that means uh we need to figure out a + + align:start position:0% +that means uh we need to figure out a + + + align:start position:0% +that means uh we need to figure out a +formula for + + align:start position:0% + + + + align:start position:0% + +so this is the point r vector r + + align:start position:0% +so this is the point r vector r + + + align:start position:0% +so this is the point r vector r +and here's the axis and um + + align:start position:0% +and here's the axis and um + + + align:start position:0% +and here's the axis and um +we need to find that distance + + align:start position:0% +we need to find that distance + + + align:start position:0% +we need to find that distance +now i'm going to + + align:start position:0% +now i'm going to + + + align:start position:0% +now i'm going to +cheat a little bit because + + align:start position:0% +cheat a little bit because + + + align:start position:0% +cheat a little bit because +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i'm going to pick the centroid as the + + align:start position:0% +i'm going to pick the centroid as the + + + align:start position:0% +i'm going to pick the centroid as the +origin same trick i want to separate the + + align:start position:0% +origin same trick i want to separate the + + + align:start position:0% +origin same trick i want to separate the +problem of finding the translation from + + align:start position:0% +problem of finding the translation from + + + align:start position:0% +problem of finding the translation from +the problem or finding the rotation and + + align:start position:0% +the problem or finding the rotation and + + + align:start position:0% +the problem or finding the rotation and +we know in 2d that + + align:start position:0% +we know in 2d that + + + align:start position:0% +we know in 2d that +the answer + + align:start position:0% +the answer + + + align:start position:0% +the answer +is that it goes through the centroid + + align:start position:0% +is that it goes through the centroid + + + align:start position:0% +is that it goes through the centroid +and then we had that formula with we + + align:start position:0% +and then we had that formula with we + + + align:start position:0% +and then we had that formula with we +knew the sine and the cosine of the + + align:start position:0% +knew the sine and the cosine of the + + + align:start position:0% +knew the sine and the cosine of the +angle so we could compute the angle + + align:start position:0% +angle so we could compute the angle + + + align:start position:0% +angle so we could compute the angle +okay so we're going to do the same same + + align:start position:0% +okay so we're going to do the same same + + + align:start position:0% +okay so we're going to do the same same +thing here in 3d + + align:start position:0% +thing here in 3d + + + align:start position:0% +thing here in 3d +so + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% + + + + align:start position:0% + +let me blow up that picture a little bit + + align:start position:0% +let me blow up that picture a little bit + + + align:start position:0% +let me blow up that picture a little bit +so this is the distance r this is our + + align:start position:0% +so this is the distance r this is our + + + align:start position:0% +so this is the distance r this is our +vector r this is our axis let's call it + + align:start position:0% +vector r this is our axis let's call it + + + align:start position:0% +vector r this is our axis let's call it +omega hat is the direction of the axis + + align:start position:0% +omega hat is the direction of the axis + + + align:start position:0% +omega hat is the direction of the axis +and + + align:start position:0% +and + + + align:start position:0% +and +and here is r prime + + align:start position:0% + + + + align:start position:0% + +we drop a perpendicular on on the axis + + align:start position:0% +we drop a perpendicular on on the axis + + + align:start position:0% +we drop a perpendicular on on the axis +and what we want to know is the distance + + align:start position:0% +and what we want to know is the distance + + + align:start position:0% +and what we want to know is the distance +between r and r prime so so what is r + + align:start position:0% +between r and r prime so so what is r + + + align:start position:0% +between r and r prime so so what is r +prime + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so let's see we need to + + align:start position:0% +so let's see we need to + + + align:start position:0% +so let's see we need to +find the component + + align:start position:0% +find the component + + + align:start position:0% +find the component +of r in the direction omega + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +okay that's that component and we're + + align:start position:0% +okay that's that component and we're + + + align:start position:0% +okay that's that component and we're +going to subtract that out + + align:start position:0% + + + + align:start position:0% + +no + + align:start position:0% +no + + + align:start position:0% +no +that's i'm already one step ahead let me + + align:start position:0% +that's i'm already one step ahead let me + + + align:start position:0% +that's i'm already one step ahead let me +say r prime is just r projected onto + + align:start position:0% +say r prime is just r projected onto + + + align:start position:0% +say r prime is just r projected onto +omega + + align:start position:0% +omega + + + align:start position:0% +omega +and this is actually our + + align:start position:0% +and this is actually our + + + align:start position:0% +and this is actually our +r minus r prime so + + align:start position:0% +r minus r prime so + + + align:start position:0% +r minus r prime so +so this is the length we're looking for + + align:start position:0% + + + + align:start position:0% + +okay and so we need + + align:start position:0% +okay and so we need + + + align:start position:0% +okay and so we need +we need r squared + + align:start position:0% + + + + align:start position:0% + +don't worry too much about this algebra + + align:start position:0% +don't worry too much about this algebra + + + align:start position:0% +don't worry too much about this algebra +because we won't be using this again but + + align:start position:0% +because we won't be using this again but + + + align:start position:0% +because we won't be using this again but +at least + + align:start position:0% + + + + align:start position:0% + +try and try and follow it + + align:start position:0% +try and try and follow it + + + align:start position:0% +try and try and follow it +so um + + align:start position:0% +so um + + + align:start position:0% +so um +and + + align:start position:0% +and + + + align:start position:0% +and +tell me when i screw up so + + align:start position:0% +tell me when i screw up so + + + align:start position:0% +tell me when i screw up so +if i multiply this out i get r dot r + + align:start position:0% +if i multiply this out i get r dot r + + + align:start position:0% +if i multiply this out i get r dot r +and then i get minus 2 + + align:start position:0% +and then i get minus 2 + + + align:start position:0% +and then i get minus 2 +r dot omega + + align:start position:0% +r dot omega + + + align:start position:0% +r dot omega +square hat squared + + align:start position:0% +square hat squared + + + align:start position:0% +square hat squared +plus r + + align:start position:0% +plus r + + + align:start position:0% +plus r +dot omega hat squared + + align:start position:0% +dot omega hat squared + + + align:start position:0% +dot omega hat squared +uh that's because there's an omega hat + + align:start position:0% +uh that's because there's an omega hat + + + align:start position:0% +uh that's because there's an omega hat +dot omega hat + + align:start position:0% +dot omega hat + + + align:start position:0% +dot omega hat +this is a unit vector so that's just a + + align:start position:0% +this is a unit vector so that's just a + + + align:start position:0% +this is a unit vector so that's just a +one so i can just forget about that + + align:start position:0% +one so i can just forget about that + + + align:start position:0% +one so i can just forget about that +well and since i'm + + align:start position:0% +well and since i'm + + + align:start position:0% +well and since i'm +they're two two things are uh + + align:start position:0% +they're two two things are uh + + + align:start position:0% +they're two two things are uh +have the same form so i end up with + + align:start position:0% +have the same form so i end up with + + + align:start position:0% +have the same form so i end up with +r dot r minus + + align:start position:0% +r dot r minus + + + align:start position:0% +r dot r minus +r dot omega hat squared + + align:start position:0% +r dot omega hat squared + + + align:start position:0% +r dot omega hat squared +so that's my distance from the axis so + + align:start position:0% +so that's my distance from the axis so + + + align:start position:0% +so that's my distance from the axis so +that's what's + + align:start position:0% +that's what's + + + align:start position:0% +that's what's +in the formula for inertia + + align:start position:0% +in the formula for inertia + + + align:start position:0% +in the formula for inertia +and so + + align:start position:0% +and so + + + align:start position:0% +and so +i'm going to then say that the inertia + + align:start position:0% + + + + align:start position:0% + +and what i'm interested in is how that + + align:start position:0% +and what i'm interested in is how that + + + align:start position:0% +and what i'm interested in is how that +varies as i change omega so omega's unit + + align:start position:0% +varies as i change omega so omega's unit + + + align:start position:0% +varies as i change omega so omega's unit +vector they can point in any direction + + align:start position:0% +vector they can point in any direction + + + align:start position:0% +vector they can point in any direction +and i'm looking for the directions where + + align:start position:0% +and i'm looking for the directions where + + + align:start position:0% +and i'm looking for the directions where +that value is it takes on an extremum or + + align:start position:0% +that value is it takes on an extremum or + + + align:start position:0% +that value is it takes on an extremum or +maybe a saddle point + + align:start position:0% +maybe a saddle point + + + align:start position:0% +maybe a saddle point +but you know starting off with just the + + align:start position:0% +but you know starting off with just the + + + align:start position:0% +but you know starting off with just the +minimum i want to find where the minimum + + align:start position:0% +minimum i want to find where the minimum + + + align:start position:0% +minimum i want to find where the minimum +and well that you know doesn't look uh + + align:start position:0% +and well that you know doesn't look uh + + + align:start position:0% +and well that you know doesn't look uh +particularly simple + + align:start position:0% +particularly simple + + + align:start position:0% +particularly simple +um + + align:start position:0% +um + + + align:start position:0% +um +but we can rewrite this so + + align:start position:0% +but we can rewrite this so + + + align:start position:0% +but we can rewrite this so +first of all let me take this and + + align:start position:0% +first of all let me take this and + + + align:start position:0% +first of all let me take this and +rewrite it + + align:start position:0% +rewrite it + + + align:start position:0% +rewrite it +now dot products are + + align:start position:0% +now dot products are + + + align:start position:0% +now dot products are +commutative so + + align:start position:0% +commutative so + + + align:start position:0% +commutative so +i can write it this way + + align:start position:0% + + + + align:start position:0% + +right i can write that and then we have + + align:start position:0% +right i can write that and then we have + + + align:start position:0% +right i can write that and then we have +this notation where + + align:start position:0% +this notation where + + + align:start position:0% +this notation where +we write the dot product in that form + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +these multiplications of the skinny + + align:start position:0% +these multiplications of the skinny + + + align:start position:0% +these multiplications of the skinny +matrices are associative so i can write + + align:start position:0% +matrices are associative so i can write + + + align:start position:0% +matrices are associative so i can write +it that way if i want to and this of + + align:start position:0% +it that way if i want to and this of + + + align:start position:0% +it that way if i want to and this of +course is the dyadic product which we've + + align:start position:0% +course is the dyadic product which we've + + + align:start position:0% +course is the dyadic product which we've +run into a few times before it's a three + + align:start position:0% +run into a few times before it's a three + + + align:start position:0% +run into a few times before it's a three +by three matrix of very special + + align:start position:0% +by three matrix of very special + + + align:start position:0% +by three matrix of very special +struct very simple structure + + align:start position:0% +struct very simple structure + + + align:start position:0% +struct very simple structure +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now for my next step i'd like to rewrite + + align:start position:0% +now for my next step i'd like to rewrite + + + align:start position:0% +now for my next step i'd like to rewrite +this also + + align:start position:0% +this also + + + align:start position:0% +this also +so i'm going to say that's the same as r + + align:start position:0% +so i'm going to say that's the same as r + + + align:start position:0% +so i'm going to say that's the same as r +dot r into omega dot omega + + align:start position:0% +dot r into omega dot omega + + + align:start position:0% +dot r into omega dot omega +well in fact you know i had this over + + align:start position:0% +well in fact you know i had this over + + + align:start position:0% +well in fact you know i had this over +here i just + + align:start position:0% +here i just + + + align:start position:0% +here i just +dropped the omega dot omega because it's + + align:start position:0% +dropped the omega dot omega because it's + + + align:start position:0% +dropped the omega dot omega because it's +one but let me put it back in again + + align:start position:0% +one but let me put it back in again + + + align:start position:0% +one but let me put it back in again +okay then that is r transpose r + + align:start position:0% +okay then that is r transpose r + + + align:start position:0% +okay then that is r transpose r +um + + align:start position:0% +um + + + align:start position:0% +um +omega + + align:start position:0% +omega + + + align:start position:0% +omega +transpose + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% +oh + + + align:start position:0% +oh +sorry so we're going to do the double + + align:start position:0% +sorry so we're going to do the double + + + align:start position:0% +sorry so we're going to do the double +integral of that + + align:start position:0% +integral of that + + + align:start position:0% +integral of that +the triple integral of that + + align:start position:0% +the triple integral of that + + + align:start position:0% +the triple integral of that +and so + + align:start position:0% +and so + + + align:start position:0% +and so +that i can write as + + align:start position:0% +that i can write as + + + align:start position:0% +that i can write as +r dot r into + + align:start position:0% + + + + align:start position:0% + +well this i is the identity matrix and i + + align:start position:0% +well this i is the identity matrix and i + + + align:start position:0% +well this i is the identity matrix and i +wrote the inertia with the blackboard + + align:start position:0% +wrote the inertia with the blackboard + + + align:start position:0% +wrote the inertia with the blackboard +bold eye + + align:start position:0% +bold eye + + + align:start position:0% +bold eye +so that it wouldn't get confused with + + align:start position:0% +so that it wouldn't get confused with + + + align:start position:0% +so that it wouldn't get confused with +this + + align:start position:0% +this + + + align:start position:0% +this +okay so now i've got + + align:start position:0% +okay so now i've got + + + align:start position:0% +okay so now i've got +the whole thing is omega + + align:start position:0% +the whole thing is omega + + + align:start position:0% +the whole thing is omega +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +times omega and i have two terms i have + + align:start position:0% +times omega and i have two terms i have + + + align:start position:0% +times omega and i have two terms i have +uh this thing + + align:start position:0% +uh this thing + + + align:start position:0% +uh this thing +which is the identity matrix + + align:start position:0% +which is the identity matrix + + + align:start position:0% +which is the identity matrix +the integral of + + align:start position:0% +the integral of + + + align:start position:0% +the integral of +r dot r + + align:start position:0% +r dot r + + + align:start position:0% +r dot r +times the identity matrix and then i + + align:start position:0% +times the identity matrix and then i + + + align:start position:0% +times the identity matrix and then i +have this thing which is r + + align:start position:0% +have this thing which is r + + + align:start position:0% +have this thing which is r +r transpose + + align:start position:0% +r transpose + + + align:start position:0% +r transpose +so um given the points + + align:start position:0% +so um given the points + + + align:start position:0% +so um given the points +i can + + align:start position:0% +i can + + + align:start position:0% +i can +well i've written it as an integral of + + align:start position:0% +well i've written it as an integral of + + + align:start position:0% +well i've written it as an integral of +course if we have a finite number of + + align:start position:0% +course if we have a finite number of + + + align:start position:0% +course if we have a finite number of +points it would be just the sum + + align:start position:0% +points it would be just the sum + + + align:start position:0% +points it would be just the sum +so this + + align:start position:0% +so this + + + align:start position:0% +so this +first part is just an identity matrix + + align:start position:0% +first part is just an identity matrix + + + align:start position:0% +first part is just an identity matrix +multiplied by some scalar and this is a + + align:start position:0% +multiplied by some scalar and this is a + + + align:start position:0% +multiplied by some scalar and this is a +dyadic product + + align:start position:0% +dyadic product + + + align:start position:0% +dyadic product +and so + + align:start position:0% + + + + align:start position:0% + +what i'm looking for is an extremum + + align:start position:0% +what i'm looking for is an extremum + + + align:start position:0% +what i'm looking for is an extremum +of that whole expression + + align:start position:0% + + + + align:start position:0% + +now i've run out of + + align:start position:0% +now i've run out of + + + align:start position:0% +now i've run out of +different versions of i so + + align:start position:0% +different versions of i so + + + align:start position:0% +different versions of i so +i don't know let me call it a + + align:start position:0% +i don't know let me call it a + + + align:start position:0% +i don't know let me call it a +so we have something of this form + + align:start position:0% + + + + align:start position:0% + +and i'm looking for let's say a minimum + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +even though it says a this is called the + + align:start position:0% +even though it says a this is called the + + + align:start position:0% +even though it says a this is called the +inertia matrix + + align:start position:0% +inertia matrix + + + align:start position:0% +inertia matrix +so given some three-dimensional shape + + align:start position:0% +so given some three-dimensional shape + + + align:start position:0% +so given some three-dimensional shape +i can compute this three by three + + align:start position:0% +i can compute this three by three + + + align:start position:0% +i can compute this three by three +inertia matrix or given a cloud of + + align:start position:0% +inertia matrix or given a cloud of + + + align:start position:0% +inertia matrix or given a cloud of +points in 3d i can compute this uh this + + align:start position:0% +points in 3d i can compute this uh this + + + align:start position:0% +points in 3d i can compute this uh this +matrix and this is just the detail of + + align:start position:0% +matrix and this is just the detail of + + + align:start position:0% +matrix and this is just the detail of +how to do it uh from the points + + align:start position:0% +how to do it uh from the points + + + align:start position:0% +how to do it uh from the points +and so + + align:start position:0% +and so + + + align:start position:0% +and so +what is that problem well that's just a + + align:start position:0% +what is that problem well that's just a + + + align:start position:0% +what is that problem well that's just a +classic eigenvalue eigenvector problem + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +the the axis i want for the minimization + + align:start position:0% +the the axis i want for the minimization + + + align:start position:0% +the the axis i want for the minimization +is the + + align:start position:0% +is the + + + align:start position:0% +is the +eigenvalue associated with the smallest + + align:start position:0% +eigenvalue associated with the smallest + + + align:start position:0% +eigenvalue associated with the smallest +eigenvalue obviously and then i can look + + align:start position:0% +eigenvalue obviously and then i can look + + + align:start position:0% +eigenvalue obviously and then i can look +for also + + align:start position:0% +for also + + + align:start position:0% +for also +the other axis that maximizes it and + + align:start position:0% +the other axis that maximizes it and + + + align:start position:0% +the other axis that maximizes it and +that's the eigenvector corresponding to + + align:start position:0% +that's the eigenvector corresponding to + + + align:start position:0% +that's the eigenvector corresponding to +the largest eigenvalue and then there's + + align:start position:0% +the largest eigenvalue and then there's + + + align:start position:0% +the largest eigenvalue and then there's +a third one which is in between + + align:start position:0% +a third one which is in between + + + align:start position:0% +a third one which is in between +and those three axes + + align:start position:0% +and those three axes + + + align:start position:0% +and those three axes +um are at right angles to each other or + + align:start position:0% +um are at right angles to each other or + + + align:start position:0% +um are at right angles to each other or +in some nasty cases they're not but we + + align:start position:0% +in some nasty cases they're not but we + + + align:start position:0% +in some nasty cases they're not but we +can make them in that case + + align:start position:0% +can make them in that case + + + align:start position:0% +can make them in that case +at right angles to each other so it's a + + align:start position:0% +at right angles to each other so it's a + + + align:start position:0% +at right angles to each other so it's a +very simple eigenvalue eigenvector + + align:start position:0% +very simple eigenvalue eigenvector + + + align:start position:0% +very simple eigenvalue eigenvector +problem now finding eigenvalues and + + align:start position:0% +problem now finding eigenvalues and + + + align:start position:0% +problem now finding eigenvalues and +eigenvectors of three by three matrices + + align:start position:0% +eigenvectors of three by three matrices + + + align:start position:0% +eigenvectors of three by three matrices +a little bit more work than two by two + + align:start position:0% +a little bit more work than two by two + + + align:start position:0% +a little bit more work than two by two +which we did by hand + + align:start position:0% +which we did by hand + + + align:start position:0% +which we did by hand +but of course the you know you've got + + align:start position:0% +but of course the you know you've got + + + align:start position:0% +but of course the you know you've got +all sorts of tools for doing this kind + + align:start position:0% +all sorts of tools for doing this kind + + + align:start position:0% +all sorts of tools for doing this kind +of stuff and there is actually closed + + align:start position:0% +of stuff and there is actually closed + + + align:start position:0% +of stuff and there is actually closed +form solution uh why well because + + align:start position:0% +form solution uh why well because + + + align:start position:0% +form solution uh why well because +polynomials of degree 3 do have a closed + + align:start position:0% +polynomials of degree 3 do have a closed + + + align:start position:0% +polynomials of degree 3 do have a closed +form solution even though + + align:start position:0% +form solution even though + + + align:start position:0% +form solution even though +we generally only remember the formula + + align:start position:0% +we generally only remember the formula + + + align:start position:0% +we generally only remember the formula +for quadratic + + align:start position:0% +for quadratic + + + align:start position:0% +for quadratic +and + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +so what are we doing so what we've done + + align:start position:0% +so what are we doing so what we've done + + + align:start position:0% +so what are we doing so what we've done +now is we've taken the point cloud in + + align:start position:0% +now is we've taken the point cloud in + + + align:start position:0% +now is we've taken the point cloud in +the left coordinate system and we've + + align:start position:0% +the left coordinate system and we've + + + align:start position:0% +the left coordinate system and we've +built a coordinate system basis in it + + align:start position:0% +built a coordinate system basis in it + + + align:start position:0% +built a coordinate system basis in it +we've got uh we've got three axes that + + align:start position:0% +we've got uh we've got three axes that + + + align:start position:0% +we've got uh we've got three axes that +are right angles to each other + + align:start position:0% +are right angles to each other + + + align:start position:0% +are right angles to each other +and just based on the distribution of + + align:start position:0% +and just based on the distribution of + + + align:start position:0% +and just based on the distribution of +points + + align:start position:0% +points + + + align:start position:0% +points +and so we have a + + align:start position:0% +and so we have a + + + align:start position:0% +and so we have a +left-hand coordinate system + + align:start position:0% +left-hand coordinate system + + + align:start position:0% +left-hand coordinate system +based on on these three vectors + + align:start position:0% +based on on these three vectors + + + align:start position:0% +based on on these three vectors +the ones that minimize the ones that + + align:start position:0% +the ones that minimize the ones that + + + align:start position:0% +the ones that minimize the ones that +maximize and then the ones that that + + align:start position:0% +maximize and then the ones that that + + + align:start position:0% +maximize and then the ones that that +right angle that's uh saddle point + + align:start position:0% +right angle that's uh saddle point + + + align:start position:0% +right angle that's uh saddle point +now we do the same thing for the right + + align:start position:0% +now we do the same thing for the right + + + align:start position:0% +now we do the same thing for the right +hand coordinate system + + align:start position:0% +hand coordinate system + + + align:start position:0% +hand coordinate system +same uh construction + + align:start position:0% +same uh construction + + + align:start position:0% +same uh construction +right we you know if there's an + + align:start position:0% +right we you know if there's an + + + align:start position:0% +right we you know if there's an +elongated point cloud the x-axis is + + align:start position:0% +elongated point cloud the x-axis is + + + align:start position:0% +elongated point cloud the x-axis is +going to be along the length of that + + align:start position:0% +going to be along the length of that + + + align:start position:0% +going to be along the length of that +cloud and so on + + align:start position:0% +cloud and so on + + + align:start position:0% +cloud and so on +um and then we just use the method we + + align:start position:0% +um and then we just use the method we + + + align:start position:0% +um and then we just use the method we +had before + + align:start position:0% +had before + + + align:start position:0% +had before +i guess + + align:start position:0% +i guess + + + align:start position:0% +i guess +it's gone but + + align:start position:0% +it's gone but + + + align:start position:0% +it's gone but +the same method we used for + + align:start position:0% +the same method we used for + + + align:start position:0% +the same method we used for +method number one + + align:start position:0% +method number one + + + align:start position:0% +method number one +and that gives us then a um a different + + align:start position:0% +and that gives us then a um a different + + + align:start position:0% +and that gives us then a um a different +another way of relating the two + + align:start position:0% +another way of relating the two + + + align:start position:0% +another way of relating the two +coordinate systems + + align:start position:0% +coordinate systems + + + align:start position:0% +coordinate systems +uh or relating the two positions of the + + align:start position:0% +uh or relating the two positions of the + + + align:start position:0% +uh or relating the two positions of the +object because those problems are duals + + align:start position:0% +object because those problems are duals + + + align:start position:0% +object because those problems are duals +to each other so this sounds a little + + align:start position:0% +to each other so this sounds a little + + + align:start position:0% +to each other so this sounds a little +bit more reasonable because first of all + + align:start position:0% +bit more reasonable because first of all + + + align:start position:0% +bit more reasonable because first of all +it treats all the points equally they're + + align:start position:0% +it treats all the points equally they're + + + align:start position:0% +it treats all the points equally they're +all thrown into the pot into these sums + + align:start position:0% +all thrown into the pot into these sums + + + align:start position:0% +all thrown into the pot into these sums +we're not you know picking one and using + + align:start position:0% +we're not you know picking one and using + + + align:start position:0% +we're not you know picking one and using +all of its information and only using a + + align:start position:0% +all of its information and only using a + + + align:start position:0% +all of its information and only using a +little bit of the second point + + align:start position:0% +little bit of the second point + + + align:start position:0% +little bit of the second point +also + + align:start position:0% +also + + + align:start position:0% +also +we're using all the points + + align:start position:0% +we're using all the points + + + align:start position:0% +we're using all the points +so and we've constructed a least squares + + align:start position:0% +so and we've constructed a least squares + + + align:start position:0% +so and we've constructed a least squares +problem that performs some sort of + + align:start position:0% +problem that performs some sort of + + + align:start position:0% +problem that performs some sort of +minimization so we're using all of the + + align:start position:0% +minimization so we're using all of the + + + align:start position:0% +minimization so we're using all of the +points um + + align:start position:0% +points um + + + align:start position:0% +points um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so what's the problem + + align:start position:0% +so what's the problem + + + align:start position:0% +so what's the problem +why why is this not + + align:start position:0% +why why is this not + + + align:start position:0% +why why is this not +generally used + + align:start position:0% +generally used + + + align:start position:0% +generally used +well + + align:start position:0% +well + + + align:start position:0% +well +for certain kinds of problems like + + align:start position:0% +for certain kinds of problems like + + + align:start position:0% +for certain kinds of problems like +lining up uh + + align:start position:0% +lining up uh + + + align:start position:0% +lining up uh +cryogenic uh electron microscope images + + align:start position:0% +cryogenic uh electron microscope images + + + align:start position:0% +cryogenic uh electron microscope images +this is fine this uh works + + align:start position:0% +this is fine this uh works + + + align:start position:0% +this is fine this uh works +uh it's not always uh ideal + + align:start position:0% +uh it's not always uh ideal + + + align:start position:0% +uh it's not always uh ideal +and one reason is that it fails under + + align:start position:0% +and one reason is that it fails under + + + align:start position:0% +and one reason is that it fails under +symmetry + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +suppose i have a sphere + + align:start position:0% +suppose i have a sphere + + + align:start position:0% +suppose i have a sphere +it doesn't have a minimum maximum and + + align:start position:0% +it doesn't have a minimum maximum and + + + align:start position:0% +it doesn't have a minimum maximum and +saddle point + + align:start position:0% +saddle point + + + align:start position:0% +saddle point +axis + + align:start position:0% +axis + + + align:start position:0% +axis +because its inertia about any axis is + + align:start position:0% +because its inertia about any axis is + + + align:start position:0% +because its inertia about any axis is +the same + + align:start position:0% +the same + + + align:start position:0% +the same +and then you might say well you know + + align:start position:0% +and then you might say well you know + + + align:start position:0% +and then you might say well you know +that's not that's not fair uh + + align:start position:0% +that's not that's not fair uh + + + align:start position:0% +that's not that's not fair uh +sphere is completely symmetrical so + + align:start position:0% +sphere is completely symmetrical so + + + align:start position:0% +sphere is completely symmetrical so +you know we we have to accept that so we + + align:start position:0% +you know we we have to accept that so we + + + align:start position:0% +you know we we have to accept that so we +might grudgingly + + align:start position:0% +might grudgingly + + + align:start position:0% +might grudgingly +say okay so it doesn't work for a sphere + + align:start position:0% +say okay so it doesn't work for a sphere + + + align:start position:0% +say okay so it doesn't work for a sphere +but that's sort of reasonable + + align:start position:0% +but that's sort of reasonable + + + align:start position:0% +but that's sort of reasonable +well what if i told you that if i give + + align:start position:0% +well what if i told you that if i give + + + align:start position:0% +well what if i told you that if i give +it a tetrahedron + + align:start position:0% +it a tetrahedron + + + align:start position:0% +it a tetrahedron +it it also won't work + + align:start position:0% +it it also won't work + + + align:start position:0% +it it also won't work +turns out if you compute its inertia + + align:start position:0% +turns out if you compute its inertia + + + align:start position:0% +turns out if you compute its inertia +matrix + + align:start position:0% +matrix + + + align:start position:0% +matrix +its uh inertia is the same in all + + align:start position:0% +its uh inertia is the same in all + + + align:start position:0% +its uh inertia is the same in all +directions + + align:start position:0% +directions + + + align:start position:0% +directions +and + + align:start position:0% +and + + + align:start position:0% +and +same with the octahedron + + align:start position:0% +same with the octahedron + + + align:start position:0% +same with the octahedron +so you know the these are just special + + align:start position:0% +so you know the these are just special + + + align:start position:0% +so you know the these are just special +cases i mean they're obviously an + + align:start position:0% +cases i mean they're obviously an + + + align:start position:0% +cases i mean they're obviously an +infinite number of figures that have + + align:start position:0% +infinite number of figures that have + + + align:start position:0% +infinite number of figures that have +that problem again uh the inertia of + + align:start position:0% +that problem again uh the inertia of + + + align:start position:0% +that problem again uh the inertia of +this surprisingly is independent of the + + align:start position:0% +this surprisingly is independent of the + + + align:start position:0% +this surprisingly is independent of the +direction + + align:start position:0% +direction + + + align:start position:0% +direction +even more surprising + + align:start position:0% +even more surprising + + + align:start position:0% +even more surprising +i take a cube + + align:start position:0% +i take a cube + + + align:start position:0% +i take a cube +now you think with a cube you know + + align:start position:0% +now you think with a cube you know + + + align:start position:0% +now you think with a cube you know +they're three well-defined axes so + + align:start position:0% +they're three well-defined axes so + + + align:start position:0% +they're three well-defined axes so +what's going on here well the trouble is + + align:start position:0% +what's going on here well the trouble is + + + align:start position:0% +what's going on here well the trouble is +that the inertia about those three + + align:start position:0% +that the inertia about those three + + + align:start position:0% +that the inertia about those three +well-defined axes are all the same + + align:start position:0% +well-defined axes are all the same + + + align:start position:0% +well-defined axes are all the same +if it's a cube + + align:start position:0% +if it's a cube + + + align:start position:0% +if it's a cube +if it's a brick then you're fine because + + align:start position:0% +if it's a brick then you're fine because + + + align:start position:0% +if it's a brick then you're fine because +the three axes will have different + + align:start position:0% +the three axes will have different + + + align:start position:0% +the three axes will have different +inertias and and you can line things up + + align:start position:0% +inertias and and you can line things up + + + align:start position:0% +inertias and and you can line things up +that way + + align:start position:0% +that way + + + align:start position:0% +that way +so um + + align:start position:0% + + + + align:start position:0% + +but with a cube + + align:start position:0% +but with a cube + + + align:start position:0% +but with a cube +again somewhat surprisingly you can pick + + align:start position:0% +again somewhat surprisingly you can pick + + + align:start position:0% +again somewhat surprisingly you can pick +any axes you get the same inertia + + align:start position:0% + + + + align:start position:0% + +okay so what's going on what what have + + align:start position:0% +okay so what's going on what what have + + + align:start position:0% +okay so what's going on what what have +we lost what have we forgotten well we + + align:start position:0% +we lost what have we forgotten well we + + + align:start position:0% +we lost what have we forgotten well we +haven't used it all the correspondences + + align:start position:0% +haven't used it all the correspondences + + + align:start position:0% +haven't used it all the correspondences +you know we've just taken these in both + + align:start position:0% +you know we've just taken these in both + + + align:start position:0% +you know we've just taken these in both +of these uh well in this particular ad + + align:start position:0% +of these uh well in this particular ad + + + align:start position:0% +of these uh well in this particular ad +hoc method we have taken a point cloud + + align:start position:0% +hoc method we have taken a point cloud + + + align:start position:0% +hoc method we have taken a point cloud +and we've sort of found its elongation + + align:start position:0% +and we've sort of found its elongation + + + align:start position:0% +and we've sort of found its elongation +and we've built these other axes without + + align:start position:0% +and we've built these other axes without + + + align:start position:0% +and we've built these other axes without +thinking about the other point cloud at + + align:start position:0% +thinking about the other point cloud at + + + align:start position:0% +thinking about the other point cloud at +all then we've done the same thing for + + align:start position:0% +all then we've done the same thing for + + + align:start position:0% +all then we've done the same thing for +the other point cloud + + align:start position:0% +the other point cloud + + + align:start position:0% +the other point cloud +but we actually assuming that we know + + align:start position:0% +but we actually assuming that we know + + + align:start position:0% +but we actually assuming that we know +the correspondences so we know that this + + align:start position:0% +the correspondences so we know that this + + + align:start position:0% +the correspondences so we know that this +this point is here and that point is + + align:start position:0% +this point is here and that point is + + + align:start position:0% +this point is here and that point is +there and + + align:start position:0% +there and + + + align:start position:0% +there and +and that's a very different problem + + align:start position:0% +and that's a very different problem + + + align:start position:0% +and that's a very different problem +right + + align:start position:0% +right + + + align:start position:0% +right +because even with a sphere i can line + + align:start position:0% +because even with a sphere i can line + + + align:start position:0% +because even with a sphere i can line +these up correctly + + align:start position:0% +these up correctly + + + align:start position:0% +these up correctly +if i have the correspondences so this is + + align:start position:0% +if i have the correspondences so this is + + + align:start position:0% +if i have the correspondences so this is +kind of a two-edged sword because we'll + + align:start position:0% +kind of a two-edged sword because we'll + + + align:start position:0% +kind of a two-edged sword because we'll +see that there's some methods that don't + + align:start position:0% +see that there's some methods that don't + + + align:start position:0% +see that there's some methods that don't +depend on correspondences they're very + + align:start position:0% +depend on correspondences they're very + + + align:start position:0% +depend on correspondences they're very +uh + + align:start position:0% +uh + + + align:start position:0% +uh +handy they're you know very appealing + + align:start position:0% +handy they're you know very appealing + + + align:start position:0% +handy they're you know very appealing +because if you screw up the + + align:start position:0% +because if you screw up the + + + align:start position:0% +because if you screw up the +correspondences they're not going to be + + align:start position:0% +correspondences they're not going to be + + + align:start position:0% +correspondences they're not going to be +affected + + align:start position:0% +affected + + + align:start position:0% +affected +on the other hand + + align:start position:0% +on the other hand + + + align:start position:0% +on the other hand +you often run into this type of problem + + align:start position:0% +you often run into this type of problem + + + align:start position:0% +you often run into this type of problem +where + + align:start position:0% +where + + + align:start position:0% +where +the method won't give you an answer + + align:start position:0% +the method won't give you an answer + + + align:start position:0% +the method won't give you an answer +because of some symmetry and so they're + + align:start position:0% +because of some symmetry and so they're + + + align:start position:0% +because of some symmetry and so they're +generally not as accurate as methods + + align:start position:0% +generally not as accurate as methods + + + align:start position:0% +generally not as accurate as methods +that do take into account + + align:start position:0% +that do take into account + + + align:start position:0% +that do take into account +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so enough of these ad hoc methods i + + align:start position:0% +so enough of these ad hoc methods i + + + align:start position:0% +so enough of these ad hoc methods i +bring them up partly because people + + align:start position:0% +bring them up partly because people + + + align:start position:0% +bring them up partly because people +actually use them and often don't know + + align:start position:0% +actually use them and often don't know + + + align:start position:0% +actually use them and often don't know +that there's a problem with them + + align:start position:0% +that there's a problem with them + + + align:start position:0% +that there's a problem with them +that's one reason and the other reason + + align:start position:0% +that's one reason and the other reason + + + align:start position:0% +that's one reason and the other reason +is that + + align:start position:0% +is that + + + align:start position:0% +is that +sometimes these are useful to give a + + align:start position:0% +sometimes these are useful to give a + + + align:start position:0% +sometimes these are useful to give a +quick answer + + align:start position:0% +quick answer + + + align:start position:0% +quick answer +uh and it's you know systematic i mean + + align:start position:0% +uh and it's you know systematic i mean + + + align:start position:0% +uh and it's you know systematic i mean +there's no iteration or search or + + align:start position:0% +there's no iteration or search or + + + align:start position:0% +there's no iteration or search or +anything you just uh compute the + + align:start position:0% +anything you just uh compute the + + + align:start position:0% +anything you just uh compute the +eigenvalues and eigenvectors which for + + align:start position:0% +eigenvalues and eigenvectors which for + + + align:start position:0% +eigenvalues and eigenvectors which for +three by three is basically a closed + + align:start position:0% +three by three is basically a closed + + + align:start position:0% +three by three is basically a closed +form operation + + align:start position:0% +form operation + + + align:start position:0% +form operation +okay so let's go back so the the problem + + align:start position:0% +okay so let's go back so the the problem + + + align:start position:0% +okay so let's go back so the the problem +is not the translation + + align:start position:0% +is not the translation + + + align:start position:0% +is not the translation +uh the translation is going to be pretty + + align:start position:0% +uh the translation is going to be pretty + + + align:start position:0% +uh the translation is going to be pretty +easy to deal with so let's focus on the + + align:start position:0% +easy to deal with so let's focus on the + + + align:start position:0% +easy to deal with so let's focus on the +rotation + + align:start position:0% +rotation + + + align:start position:0% +rotation +so generally speaking + + align:start position:0% +so generally speaking + + + align:start position:0% +so generally speaking +we have a bunch of different methods of + + align:start position:0% +we have a bunch of different methods of + + + align:start position:0% +we have a bunch of different methods of +representing rotations so let's first of + + align:start position:0% +representing rotations so let's first of + + + align:start position:0% +representing rotations so let's first of +all look at the properties + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +preserve + + align:start position:0% +preserve + + + align:start position:0% +preserve +dot product + + align:start position:0% + + + + align:start position:0% + +that means + + align:start position:0% + + + + align:start position:0% + +right that's sort of obvious + + align:start position:0% +right that's sort of obvious + + + align:start position:0% +right that's sort of obvious +and that + + align:start position:0% +and that + + + align:start position:0% +and that +has two sort of corollaries one of them + + align:start position:0% +has two sort of corollaries one of them + + + align:start position:0% +has two sort of corollaries one of them +is that + + align:start position:0% +is that + + + align:start position:0% +is that +preserved lengths preserve + + align:start position:0% +preserved lengths preserve + + + align:start position:0% +preserved lengths preserve +lengths which is just what you get if + + align:start position:0% +lengths which is just what you get if + + + align:start position:0% +lengths which is just what you get if +you + + align:start position:0% +you + + + align:start position:0% +you +apply if you make a the same as b + + align:start position:0% + + + + align:start position:0% + +and they preserve angles + + align:start position:0% + + + + align:start position:0% + +right because for example + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +what's interesting is they also preserve + + align:start position:0% +what's interesting is they also preserve + + + align:start position:0% +what's interesting is they also preserve +triple products + + align:start position:0% + + + + align:start position:0% + +so r + + align:start position:0% +so r + + + align:start position:0% +so r +of a + + align:start position:0% + + + + align:start position:0% + +now the triple product of these three + + align:start position:0% +now the triple product of these three + + + align:start position:0% +now the triple product of these three +vectors is just the volume of the + + align:start position:0% +vectors is just the volume of the + + + align:start position:0% +vectors is just the volume of the +parallelepiped + + align:start position:0% +parallelepiped + + + align:start position:0% +parallelepiped +that you draw + + align:start position:0% +that you draw + + + align:start position:0% +that you draw +you know based on suppose this is vector + + align:start position:0% +you know based on suppose this is vector + + + align:start position:0% +you know based on suppose this is vector +a + + align:start position:0% +a + + + align:start position:0% +a +this is vector b + + align:start position:0% +this is vector b + + + align:start position:0% +this is vector b +this is vector c + + align:start position:0% +this is vector c + + + align:start position:0% +this is vector c +you can imagine drawing this + + align:start position:0% +you can imagine drawing this + + + align:start position:0% +you can imagine drawing this +three-dimensional shape which has + + align:start position:0% +three-dimensional shape which has + + + align:start position:0% +three-dimensional shape which has +parallel surfaces but it's generally not + + align:start position:0% +parallel surfaces but it's generally not + + + align:start position:0% +parallel surfaces but it's generally not +a brick it's + + align:start position:0% +a brick it's + + + align:start position:0% +a brick it's +skewed + + align:start position:0% +skewed + + + align:start position:0% +skewed +generally + + align:start position:0% +generally + + + align:start position:0% +generally +and + + align:start position:0% +and + + + align:start position:0% +and +this is the volume of that object + + align:start position:0% + + + + align:start position:0% + +and now imagine taking those three + + align:start position:0% +and now imagine taking those three + + + align:start position:0% +and now imagine taking those three +vectors and rotating them all with the + + align:start position:0% +vectors and rotating them all with the + + + align:start position:0% +vectors and rotating them all with the +same rotation well that just rotates + + align:start position:0% +same rotation well that just rotates + + + align:start position:0% +same rotation well that just rotates +this figure + + align:start position:0% +this figure + + + align:start position:0% +this figure +and it'll retain its volume right and + + align:start position:0% +and it'll retain its volume right and + + + align:start position:0% +and it'll retain its volume right and +that's this quantity so that makes sense + + align:start position:0% +that's this quantity so that makes sense + + + align:start position:0% +that's this quantity so that makes sense +what's important is that it doesn't flip + + align:start position:0% +what's important is that it doesn't flip + + + align:start position:0% +what's important is that it doesn't flip +sign + + align:start position:0% +sign + + + align:start position:0% +sign +if we had replaced that + + align:start position:0% +if we had replaced that + + + align:start position:0% +if we had replaced that +rotation by a reflection + + align:start position:0% +rotation by a reflection + + + align:start position:0% +rotation by a reflection +that triple product would have flipped + + align:start position:0% +that triple product would have flipped + + + align:start position:0% +that triple product would have flipped +sine and you say well what what's a + + align:start position:0% +sine and you say well what what's a + + + align:start position:0% +sine and you say well what what's a +negative volume well it just means that + + align:start position:0% +negative volume well it just means that + + + align:start position:0% +negative volume well it just means that +you don't have the + + align:start position:0% +you don't have the + + + align:start position:0% +you don't have the +vectors + + align:start position:0% +vectors + + + align:start position:0% +vectors +in the sequence of the right-hand rule + + align:start position:0% +in the sequence of the right-hand rule + + + align:start position:0% +in the sequence of the right-hand rule +you have a left-hand rule so you know + + align:start position:0% +you have a left-hand rule so you know + + + align:start position:0% +you have a left-hand rule so you know +it's so i was talking about + + align:start position:0% +it's so i was talking about + + + align:start position:0% +it's so i was talking about +reflection in the ground reversing z + + align:start position:0% +reflection in the ground reversing z + + + align:start position:0% +reflection in the ground reversing z +well obviously now + + align:start position:0% +well obviously now + + + align:start position:0% +well obviously now +if i take that triple product you know i + + align:start position:0% +if i take that triple product you know i + + + align:start position:0% +if i take that triple product you know i +suppose i should write it out a dot b + + align:start position:0% +suppose i should write it out a dot b + + + align:start position:0% +suppose i should write it out a dot b +cross c + + align:start position:0% + + + + align:start position:0% + +and if i flip + + align:start position:0% +and if i flip + + + align:start position:0% +and if i flip +the sign of one of these i'm going to + + align:start position:0% +the sign of one of these i'm going to + + + align:start position:0% +the sign of one of these i'm going to +get a negative sign + + align:start position:0% +get a negative sign + + + align:start position:0% +get a negative sign +so when i say volume um + + align:start position:0% +so when i say volume um + + + align:start position:0% +so when i say volume um +we should really take into account the + + align:start position:0% +we should really take into account the + + + align:start position:0% +we should really take into account the +sign + + align:start position:0% +sign + + + align:start position:0% +sign +so that the magnitude of that quantity + + align:start position:0% +so that the magnitude of that quantity + + + align:start position:0% +so that the magnitude of that quantity +that triple product is the actual volume + + align:start position:0% +that triple product is the actual volume + + + align:start position:0% +that triple product is the actual volume +and the sign of it tells you whether + + align:start position:0% +and the sign of it tells you whether + + + align:start position:0% +and the sign of it tells you whether +it's been flipped from left hand to + + align:start position:0% +it's been flipped from left hand to + + + align:start position:0% +it's been flipped from left hand to +right hand coordinate system + + align:start position:0% + + + + align:start position:0% + +while i have this here + + align:start position:0% +while i have this here + + + align:start position:0% +while i have this here +let me just make sure we understand that + + align:start position:0% +let me just make sure we understand that + + + align:start position:0% +let me just make sure we understand that +there are a large number of equivalent + + align:start position:0% +there are a large number of equivalent + + + align:start position:0% +there are a large number of equivalent +ways of writing the triple product + + align:start position:0% +ways of writing the triple product + + + align:start position:0% +ways of writing the triple product +so + + align:start position:0% +so + + + align:start position:0% +so +in terms of our earlier discussion + + align:start position:0% +in terms of our earlier discussion + + + align:start position:0% +in terms of our earlier discussion +all of this corresponds to + + align:start position:0% +all of this corresponds to + + + align:start position:0% +all of this corresponds to +orthonormality + + align:start position:0% +orthonormality + + + align:start position:0% +orthonormality +and this corresponds to + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +that condition about the determinant + + align:start position:0% +that condition about the determinant + + + align:start position:0% +that condition about the determinant +being greater than one + + align:start position:0% +being greater than one + + + align:start position:0% +being greater than one +okay so that's um + + align:start position:0% +okay so that's um + + + align:start position:0% +okay so that's um +those are all the properties we need uh + + align:start position:0% +those are all the properties we need uh + + + align:start position:0% +those are all the properties we need uh +to proceed so um + + align:start position:0% +to proceed so um + + + align:start position:0% +to proceed so um +now we set it up as a least squares + + align:start position:0% +now we set it up as a least squares + + + align:start position:0% +now we set it up as a least squares +problem we've + + align:start position:0% +problem we've + + + align:start position:0% +problem we've +got correspondences between + + align:start position:0% +got correspondences between + + + align:start position:0% +got correspondences between +vectors measured in the two coordinate + + align:start position:0% +vectors measured in the two coordinate + + + align:start position:0% +vectors measured in the two coordinate +systems + + align:start position:0% +systems + + + align:start position:0% +systems +and we're trying to find the + + align:start position:0% +and we're trying to find the + + + align:start position:0% +and we're trying to find the +transformation between them + + align:start position:0% + + + + align:start position:0% + +so we define some sort of error + + align:start position:0% + + + + align:start position:0% + +okay do i want to start with the + + align:start position:0% +okay do i want to start with the + + + align:start position:0% +okay do i want to start with the +androids oh okay so we've got rr + + align:start position:0% + + + + align:start position:0% + +so that's the transformation uh we're + + align:start position:0% +so that's the transformation uh we're + + + align:start position:0% +so that's the transformation uh we're +dealing with + + align:start position:0% +dealing with + + + align:start position:0% +dealing with +and + + align:start position:0% + + + + align:start position:0% + +we can then define an error + + align:start position:0% + + + + align:start position:0% + +for the ice point + + align:start position:0% + + + + align:start position:0% + +and of course what we're trying to do is + + align:start position:0% +and of course what we're trying to do is + + + align:start position:0% +and of course what we're trying to do is +minimize that error + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +what we have to + + align:start position:0% +what we have to + + + align:start position:0% +what we have to +choose is the offset + + align:start position:0% +choose is the offset + + + align:start position:0% +choose is the offset +and the + + align:start position:0% + + + + align:start position:0% + +rotation okay so um + + align:start position:0% +rotation okay so um + + + align:start position:0% +rotation okay so um +again we're arbitrarily + + align:start position:0% +again we're arbitrarily + + + align:start position:0% +again we're arbitrarily +picking the left coordinate system and + + align:start position:0% +picking the left coordinate system and + + + align:start position:0% +picking the left coordinate system and +mapping it into the right coordinate + + align:start position:0% +mapping it into the right coordinate + + + align:start position:0% +mapping it into the right coordinate +system + + align:start position:0% +system + + + align:start position:0% +system +and then comparing + + align:start position:0% +and then comparing + + + align:start position:0% +and then comparing +the result and + + align:start position:0% +the result and + + + align:start position:0% +the result and +they should be the same ideally there'll + + align:start position:0% +they should be the same ideally there'll + + + align:start position:0% +they should be the same ideally there'll +be some small error in practice so we're + + align:start position:0% +be some small error in practice so we're + + + align:start position:0% +be some small error in practice so we're +trying to make that error as small as + + align:start position:0% +trying to make that error as small as + + + align:start position:0% +trying to make that error as small as +possible and we try and find the + + align:start position:0% +possible and we try and find the + + + align:start position:0% +possible and we try and find the +parameters of the transformation by + + align:start position:0% +parameters of the transformation by + + + align:start position:0% +parameters of the transformation by +minimizing that error + + align:start position:0% +minimizing that error + + + align:start position:0% +minimizing that error +okay now since i know the answer i can + + align:start position:0% +okay now since i know the answer i can + + + align:start position:0% +okay now since i know the answer i can +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +transform things in a way that + + align:start position:0% + + + + align:start position:0% + +simplifies the problem + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +so i just take all of the coordinates in + + align:start position:0% +so i just take all of the coordinates in + + + align:start position:0% +so i just take all of the coordinates in +the left-hand coordinate system add them + + align:start position:0% +the left-hand coordinate system add them + + + align:start position:0% +the left-hand coordinate system add them +up divide by n to get the centroid and i + + align:start position:0% +up divide by n to get the centroid and i + + + align:start position:0% +up divide by n to get the centroid and i +do the same in the right-hand + + align:start position:0% +do the same in the right-hand + + + align:start position:0% +do the same in the right-hand +coordinates and i pick those as the + + align:start position:0% +coordinates and i pick those as the + + + align:start position:0% +coordinates and i pick those as the +origins basically so i'm going to um + + align:start position:0% + + + + align:start position:0% + +subtract out that + + align:start position:0% + + + + align:start position:0% + +okay and this is in + + align:start position:0% +okay and this is in + + + align:start position:0% +okay and this is in +line with the idea that i want to + + align:start position:0% +line with the idea that i want to + + + align:start position:0% +line with the idea that i want to +separate the problem of finding the + + align:start position:0% +separate the problem of finding the + + + align:start position:0% +separate the problem of finding the +translation from finding the rotation so + + align:start position:0% +translation from finding the rotation so + + + align:start position:0% +translation from finding the rotation so +this way i'm going to get rid of the + + align:start position:0% +this way i'm going to get rid of the + + + align:start position:0% +this way i'm going to get rid of the +translation + + align:start position:0% +translation + + + align:start position:0% +translation +we'll worry about it later it's very + + align:start position:0% +we'll worry about it later it's very + + + align:start position:0% +we'll worry about it later it's very +simple + + align:start position:0% +simple + + + align:start position:0% +simple +okay + + align:start position:0% +okay + + + align:start position:0% +okay +by the way while we're + + align:start position:0% + + + + align:start position:0% + +here we might wonder uh + + align:start position:0% +here we might wonder uh + + + align:start position:0% +here we might wonder uh +what that is + + align:start position:0% +what that is + + + align:start position:0% +what that is +so i've changed all the coordinates to + + align:start position:0% +so i've changed all the coordinates to + + + align:start position:0% +so i've changed all the coordinates to +be relative to the centroid + + align:start position:0% +be relative to the centroid + + + align:start position:0% +be relative to the centroid +now i take them all and add them up what + + align:start position:0% +now i take them all and add them up what + + + align:start position:0% +now i take them all and add them up what +what do i get + + align:start position:0% +what do i get + + + align:start position:0% +what do i get +well you could you know + + align:start position:0% +well you could you know + + + align:start position:0% +well you could you know +plug + + align:start position:0% +plug + + + align:start position:0% +plug +this in here + + align:start position:0% +this in here + + + align:start position:0% +this in here +and you're going to get n copies of that + + align:start position:0% +and you're going to get n copies of that + + + align:start position:0% +and you're going to get n copies of that +and you've got the sum of these + + align:start position:0% +and you've got the sum of these + + + align:start position:0% +and you've got the sum of these +and then you look at that formula + + align:start position:0% +and then you look at that formula + + + align:start position:0% +and then you look at that formula +and when you divide by n they all cancel + + align:start position:0% +and when you divide by n they all cancel + + + align:start position:0% +and when you divide by n they all cancel +out right + + align:start position:0% +out right + + + align:start position:0% +out right +so + + align:start position:0% + + + + align:start position:0% + +and it's a vector so + + align:start position:0% +and it's a vector so + + + align:start position:0% +and it's a vector so +so um + + align:start position:0% +so um + + + align:start position:0% +so um +one feature of moving to the centroid is + + align:start position:0% +one feature of moving to the centroid is + + + align:start position:0% +one feature of moving to the centroid is +that now the + + align:start position:0% +that now the + + + align:start position:0% +that now the +the centroids at the origin of the new + + align:start position:0% +the centroids at the origin of the new + + + align:start position:0% +the centroids at the origin of the new +coordinates that makes sense right and + + align:start position:0% +coordinates that makes sense right and + + + align:start position:0% +coordinates that makes sense right and +similarly for the other one + + align:start position:0% +similarly for the other one + + + align:start position:0% +similarly for the other one +and we need this property in a second so + + align:start position:0% +and we need this property in a second so + + + align:start position:0% +and we need this property in a second so +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +so i'm going to plug these new + + align:start position:0% +so i'm going to plug these new + + + align:start position:0% +so i'm going to plug these new +coordinates + + align:start position:0% +coordinates + + + align:start position:0% +coordinates +into my error formula + + align:start position:0% +into my error formula + + + align:start position:0% +into my error formula +so to do that i need to solve this + + align:start position:0% +so to do that i need to solve this + + + align:start position:0% +so to do that i need to solve this +equation for r + + align:start position:0% +equation for r + + + align:start position:0% +equation for r +sub ri + + align:start position:0% +sub ri + + + align:start position:0% +sub ri +well that you know it's hardly worth + + align:start position:0% +well that you know it's hardly worth + + + align:start position:0% +well that you know it's hardly worth +writing out it's it's just moving this + + align:start position:0% +writing out it's it's just moving this + + + align:start position:0% +writing out it's it's just moving this +to the other side + + align:start position:0% +to the other side + + + align:start position:0% +to the other side +and if i make those substitutions then i + + align:start position:0% +and if i make those substitutions then i + + + align:start position:0% +and if i make those substitutions then i +get this + + align:start position:0% +get this + + + align:start position:0% +get this +where + + align:start position:0% +where + + + align:start position:0% +where +the offset now is different + + align:start position:0% + + + + align:start position:0% + +and so my new problem is + + align:start position:0% + + + + align:start position:0% + +and um + + align:start position:0% +and um + + + align:start position:0% +and um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +i can + + align:start position:0% +i can + + + align:start position:0% +i can +so there's a square + + align:start position:0% +so there's a square + + + align:start position:0% +so there's a square +and i can + + align:start position:0% +and i can + + + align:start position:0% +and i can +multiply these out but i i'm going to + + align:start position:0% +multiply these out but i i'm going to + + + align:start position:0% +multiply these out but i i'm going to +group them so i'm going to + + align:start position:0% +group them so i'm going to + + + align:start position:0% +group them so i'm going to +treat this as the difference of that + + align:start position:0% +treat this as the difference of that + + + align:start position:0% +treat this as the difference of that +thing and that thing and then + + align:start position:0% +thing and that thing and then + + + align:start position:0% +thing and that thing and then +undo the square + + align:start position:0% +undo the square + + + align:start position:0% +undo the square +and i get + + align:start position:0% + + + + align:start position:0% + +now the other ways to get here like you + + align:start position:0% +now the other ways to get here like you + + + align:start position:0% +now the other ways to get here like you +can differentiate with respect to the + + align:start position:0% +can differentiate with respect to the + + + align:start position:0% +can differentiate with respect to the +translation + + align:start position:0% + + + + align:start position:0% + +but i think this is the most obvious + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% +now + + + align:start position:0% +now +over here + + align:start position:0% + + + + align:start position:0% + +this whole center term goes away because + + align:start position:0% +this whole center term goes away because + + + align:start position:0% +this whole center term goes away because +it involves the sum of r of sub ri + + align:start position:0% +it involves the sum of r of sub ri + + + align:start position:0% +it involves the sum of r of sub ri +that's zero right + + align:start position:0% +that's zero right + + + align:start position:0% +that's zero right +and then it involves the rotated version + + align:start position:0% +and then it involves the rotated version + + + align:start position:0% +and then it involves the rotated version +of the sum of the rotated division of r + + align:start position:0% +of the sum of the rotated division of r + + + align:start position:0% +of the sum of the rotated division of r +sub li + + align:start position:0% +sub li + + + align:start position:0% +sub li +and we know that um + + align:start position:0% +and we know that um + + + align:start position:0% +and we know that um +that sum is going to be zero as well so + + align:start position:0% +that sum is going to be zero as well so + + + align:start position:0% +that sum is going to be zero as well so +this whole term disappears so that makes + + align:start position:0% +this whole term disappears so that makes + + + align:start position:0% +this whole term disappears so that makes +life a lot simpler + + align:start position:0% + + + + align:start position:0% + +okay so then the next question is + + align:start position:0% +okay so then the next question is + + + align:start position:0% +okay so then the next question is +uh what should we choose for the + + align:start position:0% +uh what should we choose for the + + + align:start position:0% +uh what should we choose for the +offset for the translation + + align:start position:0% +offset for the translation + + + align:start position:0% +offset for the translation +r0 + + align:start position:0% +r0 + + + align:start position:0% +r0 +well this term doesn't depend on r0 of + + align:start position:0% +well this term doesn't depend on r0 of + + + align:start position:0% +well this term doesn't depend on r0 of +the translation at all so forget about + + align:start position:0% +the translation at all so forget about + + + align:start position:0% +the translation at all so forget about +that one for the moment + + align:start position:0% +that one for the moment + + + align:start position:0% +that one for the moment +this one does it depends on the square + + align:start position:0% +this one does it depends on the square + + + align:start position:0% +this one does it depends on the square +of it + + align:start position:0% +of it + + + align:start position:0% +of it +so how do we make it as small as + + align:start position:0% +so how do we make it as small as + + + align:start position:0% +so how do we make it as small as +possible + + align:start position:0% + + + + align:start position:0% + +zero right so + + align:start position:0% + + + + align:start position:0% + +um so now you can see + + align:start position:0% +um so now you can see + + + align:start position:0% +um so now you can see +that um + + align:start position:0% +that um + + + align:start position:0% +that um +a couple of things one of them is + + align:start position:0% +a couple of things one of them is + + + align:start position:0% +a couple of things one of them is +over + + align:start position:0% +over + + + align:start position:0% +over +here we're setting + + align:start position:0% +here we're setting + + + align:start position:0% +here we're setting +we find that the optimum solution has r0 + + align:start position:0% +we find that the optimum solution has r0 + + + align:start position:0% +we find that the optimum solution has r0 +prime 0 which means that this is the + + align:start position:0% +prime 0 which means that this is the + + + align:start position:0% +prime 0 which means that this is the +case + + align:start position:0% +case + + + align:start position:0% +case +r0 is + + align:start position:0% +r0 is + + + align:start position:0% +r0 is +[Music] + + align:start position:0% + + + + align:start position:0% + +so so this is the formula for the + + align:start position:0% +so so this is the formula for the + + + align:start position:0% +so so this is the formula for the +translation + + align:start position:0% + + + + align:start position:0% + +now of course right now we can't use it + + align:start position:0% +now of course right now we can't use it + + + align:start position:0% +now of course right now we can't use it +because we don't know what the rotation + + align:start position:0% +because we don't know what the rotation + + + align:start position:0% +because we don't know what the rotation +is + + align:start position:0% +is + + + align:start position:0% +is +so we don't know what big r is but it's + + align:start position:0% +so we don't know what big r is but it's + + + align:start position:0% +so we don't know what big r is but it's +very intuitive it says that the + + align:start position:0% +very intuitive it says that the + + + align:start position:0% +very intuitive it says that the +translation is the difference between + + align:start position:0% +translation is the difference between + + + align:start position:0% +translation is the difference between +where the centroid is in the right + + align:start position:0% +where the centroid is in the right + + + align:start position:0% +where the centroid is in the right +coordinate system + + align:start position:0% +coordinate system + + + align:start position:0% +coordinate system +and where the left coordinate system + + align:start position:0% +and where the left coordinate system + + + align:start position:0% +and where the left coordinate system +centroid is after you rotate it + + align:start position:0% +centroid is after you rotate it + + + align:start position:0% +centroid is after you rotate it +so it's you know the centroid maps into + + align:start position:0% +so it's you know the centroid maps into + + + align:start position:0% +so it's you know the centroid maps into +the centroid + + align:start position:0% +the centroid + + + align:start position:0% +the centroid +centroid + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +we've accomplished + + align:start position:0% +we've accomplished + + + align:start position:0% +we've accomplished +one objective which is to separate the + + align:start position:0% +one objective which is to separate the + + + align:start position:0% +one objective which is to separate the +problem of finding translation from the + + align:start position:0% +problem of finding translation from the + + + align:start position:0% +problem of finding translation from the +problem of finding rotation and we've um + + align:start position:0% +problem of finding rotation and we've um + + + align:start position:0% +problem of finding rotation and we've um +and then we have a formula there if we + + align:start position:0% +and then we have a formula there if we + + + align:start position:0% +and then we have a formula there if we +ever find the rotation we just go back + + align:start position:0% +ever find the rotation we just go back + + + align:start position:0% +ever find the rotation we just go back +to that formula + + align:start position:0% +to that formula + + + align:start position:0% +to that formula +plug it in to find the + + align:start position:0% +plug it in to find the + + + align:start position:0% +plug it in to find the +translation + + align:start position:0% + + + + align:start position:0% + +okay and then + + align:start position:0% +okay and then + + + align:start position:0% +okay and then +what's left is + + align:start position:0% +what's left is + + + align:start position:0% +what's left is +so basically that gets rid of this term + + align:start position:0% +so basically that gets rid of this term + + + align:start position:0% +so basically that gets rid of this term +as well so so that's gone + + align:start position:0% +as well so so that's gone + + + align:start position:0% +as well so so that's gone +so we're left with this part + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +only worry about rotation so + + align:start position:0% +only worry about rotation so + + + align:start position:0% +only worry about rotation so +so our job is to find + + align:start position:0% + + + + align:start position:0% + +so a new error + + align:start position:0% + + + + align:start position:0% + +right that's just that error term + + align:start position:0% +right that's just that error term + + + align:start position:0% +right that's just that error term +and we're now going to minimize + + align:start position:0% + + + + align:start position:0% + +and that means + + align:start position:0% + + + + align:start position:0% + +so i'm just taking this term and + + align:start position:0% +so i'm just taking this term and + + + align:start position:0% +so i'm just taking this term and +squaring it i suppose i can write this + + align:start position:0% +squaring it i suppose i can write this + + + align:start position:0% +squaring it i suppose i can write this +out here this is + + align:start position:0% + + + + align:start position:0% + +dot + + align:start position:0% +dot + + + align:start position:0% +dot +so i'm just expanding this out + + align:start position:0% + + + + align:start position:0% + +and so + + align:start position:0% +and so + + + align:start position:0% +and so +so from the first two terms here + + align:start position:0% +so from the first two terms here + + + align:start position:0% +so from the first two terms here +i you know the dot product of + + align:start position:0% +i you know the dot product of + + + align:start position:0% +i you know the dot product of +these two gives me that + + align:start position:0% +these two gives me that + + + align:start position:0% +these two gives me that +and then i have the dot product of + + align:start position:0% +and then i have the dot product of + + + align:start position:0% +and then i have the dot product of +that with this that gives me + + align:start position:0% +that with this that gives me + + + align:start position:0% +that with this that gives me +this + + align:start position:0% +this + + + align:start position:0% +this +part which occurs twice and then finally + + align:start position:0% +part which occurs twice and then finally + + + align:start position:0% +part which occurs twice and then finally +i have the dot product of these last + + align:start position:0% +i have the dot product of these last + + + align:start position:0% +i have the dot product of these last +things + + align:start position:0% +things + + + align:start position:0% +things +and + + align:start position:0% +and + + + align:start position:0% +and +since we said that rotation preserves + + align:start position:0% +since we said that rotation preserves + + + align:start position:0% +since we said that rotation preserves +lengths + + align:start position:0% +lengths + + + align:start position:0% +lengths +i might as well compute the length + + align:start position:0% +i might as well compute the length + + + align:start position:0% +i might as well compute the length +before rotation so that's very + + align:start position:0% +before rotation so that's very + + + align:start position:0% +before rotation so that's very +convenient + + align:start position:0% +convenient + + + align:start position:0% +convenient +so these last two collapse into that and + + align:start position:0% +so these last two collapse into that and + + + align:start position:0% +so these last two collapse into that and +r doesn't appear in there + + align:start position:0% +r doesn't appear in there + + + align:start position:0% +r doesn't appear in there +so + + align:start position:0% +so + + + align:start position:0% +so +so this is fixed in the sense that + + align:start position:0% +so this is fixed in the sense that + + + align:start position:0% +so this is fixed in the sense that +it doesn't depend on the rotation + + align:start position:0% +it doesn't depend on the rotation + + + align:start position:0% +it doesn't depend on the rotation +this is fixed + + align:start position:0% +this is fixed + + + align:start position:0% +this is fixed +in that it doesn't depend on the + + align:start position:0% +in that it doesn't depend on the + + + align:start position:0% +in that it doesn't depend on the +rotation + + align:start position:0% +rotation + + + align:start position:0% +rotation +and so + + align:start position:0% +and so + + + align:start position:0% +and so +we now focus on this term + + align:start position:0% +we now focus on this term + + + align:start position:0% +we now focus on this term +except it's got a minus sign + + align:start position:0% +except it's got a minus sign + + + align:start position:0% +except it's got a minus sign +so instead of minimizing we want to + + align:start position:0% +so instead of minimizing we want to + + + align:start position:0% +so instead of minimizing we want to +maximize this + + align:start position:0% +maximize this + + + align:start position:0% +maximize this +so so that's sort of in a nutshell + + align:start position:0% +so so that's sort of in a nutshell + + + align:start position:0% +so so that's sort of in a nutshell +uh our remaining problem + + align:start position:0% +uh our remaining problem + + + align:start position:0% +uh our remaining problem +and with you know if we can do that then + + align:start position:0% +and with you know if we can do that then + + + align:start position:0% +and with you know if we can do that then +we're done and notice how this + + align:start position:0% +we're done and notice how this + + + align:start position:0% +we're done and notice how this +intuitively makes sense + + align:start position:0% +intuitively makes sense + + + align:start position:0% +intuitively makes sense +you know if you imagine that + + align:start position:0% +you know if you imagine that + + + align:start position:0% +you know if you imagine that +think of the + + align:start position:0% +think of the + + + align:start position:0% +think of the +cloud of points and there's a centroid + + align:start position:0% +cloud of points and there's a centroid + + + align:start position:0% +cloud of points and there's a centroid +now connect each of the points in the + + align:start position:0% +now connect each of the points in the + + + align:start position:0% +now connect each of the points in the +cloud of points to the centroid so + + align:start position:0% +cloud of points to the centroid so + + + align:start position:0% +cloud of points to the centroid so +there's a vector from the centroid out + + align:start position:0% +there's a vector from the centroid out + + + align:start position:0% +there's a vector from the centroid out +to each point sort of like a spikey um + + align:start position:0% +to each point sort of like a spikey um + + + align:start position:0% +to each point sort of like a spikey um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +what's the term in sushi + + align:start position:0% +what's the term in sushi + + + align:start position:0% +what's the term in sushi +uni that's it it's uni + + align:start position:0% +uni that's it it's uni + + + align:start position:0% +uni that's it it's uni +it's a sea urchin right it's got these + + align:start position:0% +it's a sea urchin right it's got these + + + align:start position:0% +it's a sea urchin right it's got these +spikes okay and so um + + align:start position:0% +spikes okay and so um + + + align:start position:0% +spikes okay and so um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +what we're doing here is we're taking + + align:start position:0% +what we're doing here is we're taking + + + align:start position:0% +what we're doing here is we're taking +one of these sea urchins and we're + + align:start position:0% +one of these sea urchins and we're + + + align:start position:0% +one of these sea urchins and we're +bringing the other sea urchin into + + align:start position:0% +bringing the other sea urchin into + + + align:start position:0% +bringing the other sea urchin into +alignment and the way we're doing it is + + align:start position:0% +alignment and the way we're doing it is + + + align:start position:0% +alignment and the way we're doing it is +we're saying that corresponding spines + + align:start position:0% +we're saying that corresponding spines + + + align:start position:0% +we're saying that corresponding spines +should have a small angle between them + + align:start position:0% +should have a small angle between them + + + align:start position:0% +should have a small angle between them +their dot product should be large right + + align:start position:0% +their dot product should be large right + + + align:start position:0% +their dot product should be large right +because the dot product between two + + align:start position:0% +because the dot product between two + + + align:start position:0% +because the dot product between two +vectors is proportional to the cosine of + + align:start position:0% +vectors is proportional to the cosine of + + + align:start position:0% +vectors is proportional to the cosine of +the angle so the largest you can make + + align:start position:0% +the angle so the largest you can make + + + align:start position:0% +the angle so the largest you can make +that is one which happens when theta + + align:start position:0% +that is one which happens when theta + + + align:start position:0% +that is one which happens when theta +equals zero so so what's hap this makes + + align:start position:0% +equals zero so so what's hap this makes + + + align:start position:0% +equals zero so so what's hap this makes +perfect sense because we're taking each + + align:start position:0% +perfect sense because we're taking each + + + align:start position:0% +perfect sense because we're taking each +of the corresponding spines of this + + align:start position:0% +of the corresponding spines of this + + + align:start position:0% +of the corresponding spines of this +spiky ball and saying you know put a + + align:start position:0% +spiky ball and saying you know put a + + + align:start position:0% +spiky ball and saying you know put a +contribution in that's proportional to + + align:start position:0% +contribution in that's proportional to + + + align:start position:0% +contribution in that's proportional to +the dot product and make that + + align:start position:0% +the dot product and make that + + + align:start position:0% +the dot product and make that +rotate it to make that as large as + + align:start position:0% +rotate it to make that as large as + + + align:start position:0% +rotate it to make that as large as +possible + + align:start position:0% +possible + + + align:start position:0% +possible +so + + align:start position:0% +so + + + align:start position:0% +so +a whole rotation problem is being + + align:start position:0% +a whole rotation problem is being + + + align:start position:0% +a whole rotation problem is being +simplified down to to this + + align:start position:0% +simplified down to to this + + + align:start position:0% +simplified down to to this +uh if we can solve that + + align:start position:0% +uh if we can solve that + + + align:start position:0% +uh if we can solve that +and so uh well you know one + + align:start position:0% +and so uh well you know one + + + align:start position:0% +and so uh well you know one +we we would calculus people so one thing + + align:start position:0% +we we would calculus people so one thing + + + align:start position:0% +we we would calculus people so one thing +you might think of is + + align:start position:0% + + + + align:start position:0% + +you know we've done this kind of thing + + align:start position:0% +you know we've done this kind of thing + + + align:start position:0% +you know we've done this kind of thing +before we will differentiate with + + align:start position:0% +before we will differentiate with + + + align:start position:0% +before we will differentiate with +respect to r and set the result equal to + + align:start position:0% +respect to r and set the result equal to + + + align:start position:0% +respect to r and set the result equal to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +and + + align:start position:0% +and + + + align:start position:0% +and +well you know that that's + + align:start position:0% +well you know that that's + + + align:start position:0% +well you know that that's +not not quite right because you know r + + align:start position:0% +not not quite right because you know r + + + align:start position:0% +not not quite right because you know r +is not a scalar + + align:start position:0% +is not a scalar + + + align:start position:0% +is not a scalar +it's not even a vector we know how to + + align:start position:0% +it's not even a vector we know how to + + + align:start position:0% +it's not even a vector we know how to +differentiate with respect to vector + + align:start position:0% +differentiate with respect to vector + + + align:start position:0% +differentiate with respect to vector +it's a whole matrix but we could just + + align:start position:0% +it's a whole matrix but we could just + + + align:start position:0% +it's a whole matrix but we could just +take uh the nine elements of the matrix + + align:start position:0% +take uh the nine elements of the matrix + + + align:start position:0% +take uh the nine elements of the matrix +and string them into a nine vector and + + align:start position:0% +and string them into a nine vector and + + + align:start position:0% +and string them into a nine vector and +and differentiate with respect to the + + align:start position:0% +and differentiate with respect to the + + + align:start position:0% +and differentiate with respect to the +nine vector + + align:start position:0% +nine vector + + + align:start position:0% +nine vector +so we could do that the problem is + + align:start position:0% +so we could do that the problem is + + + align:start position:0% +so we could do that the problem is +those nine numbers aren't independent + + align:start position:0% +those nine numbers aren't independent + + + align:start position:0% +those nine numbers aren't independent +they have to satisfy all of those + + align:start position:0% +they have to satisfy all of those + + + align:start position:0% +they have to satisfy all of those +annoying constraints and so it's + + align:start position:0% +annoying constraints and so it's + + + align:start position:0% +annoying constraints and so it's +actually very hard to impose these + + align:start position:0% +actually very hard to impose these + + + align:start position:0% +actually very hard to impose these +constraints subject + + align:start position:0% +constraints subject + + + align:start position:0% +constraints subject +to + + align:start position:0% + + + + align:start position:0% + +r transpose r is i and + + align:start position:0% +r transpose r is i and + + + align:start position:0% +r transpose r is i and +determinant of r is plus one + + align:start position:0% +determinant of r is plus one + + + align:start position:0% +determinant of r is plus one +so you know you can go down that route + + align:start position:0% +so you know you can go down that route + + + align:start position:0% +so you know you can go down that route +but it it gets incredibly messy and so + + align:start position:0% +but it it gets incredibly messy and so + + + align:start position:0% +but it it gets incredibly messy and so +we won't be doing that we'll be looking + + align:start position:0% +we won't be doing that we'll be looking + + + align:start position:0% +we won't be doing that we'll be looking +at um + + align:start position:0% +at um + + + align:start position:0% +at um +other representations for rotation + + align:start position:0% +other representations for rotation + + + align:start position:0% +other representations for rotation +uh where this problem comes out very + + align:start position:0% +uh where this problem comes out very + + + align:start position:0% +uh where this problem comes out very +easily + + align:start position:0% +easily + + + align:start position:0% +easily +but it you know but it's like a lot of + + align:start position:0% +but it you know but it's like a lot of + + + align:start position:0% +but it you know but it's like a lot of +things where there's a bit of a effort + + align:start position:0% +things where there's a bit of a effort + + + align:start position:0% +things where there's a bit of a effort +to + + align:start position:0% +to + + + align:start position:0% +to +develop the technology + + align:start position:0% +develop the technology + + + align:start position:0% +develop the technology +uh the representation once you've got + + align:start position:0% +uh the representation once you've got + + + align:start position:0% +uh the representation once you've got +the representation it's trivial so we'll + + align:start position:0% +the representation it's trivial so we'll + + + align:start position:0% +the representation it's trivial so we'll +spend the next class building up that + + align:start position:0% +spend the next class building up that + + + align:start position:0% +spend the next class building up that +representation + + align:start position:0% +representation + + + align:start position:0% +representation +okay \ No newline at end of file diff --git a/RD9AWDdj-Yk.txt b/RD9AWDdj-Yk.txt new file mode 100644 index 0000000000000000000000000000000000000000..b275778d8397f410d86e99f51a144f695c9ddf16 --- /dev/null +++ b/RD9AWDdj-Yk.txt @@ -0,0 +1,8459 @@ +align:start position:0% + +Sentell + + align:start position:0% +Sentell + + + align:start position:0% +Sentell +survey it this morning about how the + + align:start position:0% +survey it this morning about how the + + + align:start position:0% +survey it this morning about how the +class is going where you thought of a + + align:start position:0% +class is going where you thought of a + + + align:start position:0% +class is going where you thought of a +problem set and I would appreciate if + + align:start position:0% +problem set and I would appreciate if + + + align:start position:0% +problem set and I would appreciate if +you provide us provide me some feedback + + align:start position:0% +you provide us provide me some feedback + + + align:start position:0% +you provide us provide me some feedback +so things you like or don't like about + + align:start position:0% +so things you like or don't like about + + + align:start position:0% +so things you like or don't like about +the class or about the problem said that + + align:start position:0% +the class or about the problem said that + + + align:start position:0% +the class or about the problem said that +was just you last night so it's I can + + align:start position:0% +was just you last night so it's I can + + + align:start position:0% +was just you last night so it's I can +try to adjust to make it more + + align:start position:0% +try to adjust to make it more + + + align:start position:0% +try to adjust to make it more +interesting and useful for all of you + + align:start position:0% + + + + align:start position:0% + +last time we talked about similarities + + align:start position:0% +last time we talked about similarities + + + align:start position:0% +last time we talked about similarities +craft regularity lemma + + align:start position:0% +craft regularity lemma + + + align:start position:0% +craft regularity lemma +so the regularity lemma as I mentioned + + align:start position:0% +so the regularity lemma as I mentioned + + + align:start position:0% +so the regularity lemma as I mentioned +is a extremely powerful tool in modern + + align:start position:0% +is a extremely powerful tool in modern + + + align:start position:0% +is a extremely powerful tool in modern +combinatorics and last time we saw the + + align:start position:0% +combinatorics and last time we saw the + + + align:start position:0% +combinatorics and last time we saw the +statement and the proof of this + + align:start position:0% +statement and the proof of this + + + align:start position:0% +statement and the proof of this +regularity lemma today I want to show + + align:start position:0% +regularity lemma today I want to show + + + align:start position:0% +regularity lemma today I want to show +you how to apply the right dilemma for + + align:start position:0% +you how to apply the right dilemma for + + + align:start position:0% +you how to apply the right dilemma for +extremal applications in particular + + align:start position:0% +extremal applications in particular + + + align:start position:0% +extremal applications in particular +we'll see how to prove + + align:start position:0% +we'll see how to prove + + + align:start position:0% +we'll see how to prove +Rost theorem that I mentioned in the + + align:start position:0% +Rost theorem that I mentioned in the + + + align:start position:0% +Rost theorem that I mentioned in the +very first lecture about subsets of + + align:start position:0% +very first lecture about subsets of + + + align:start position:0% +very first lecture about subsets of +integers lacking three term arithmetic + + align:start position:0% +integers lacking three term arithmetic + + + align:start position:0% +integers lacking three term arithmetic +progressions + + align:start position:0% +progressions + + + align:start position:0% +progressions +first I will you remind you the + + align:start position:0% +first I will you remind you the + + + align:start position:0% +first I will you remind you the +regularity lemma we're always working + + align:start position:0% +regularity lemma we're always working + + + align:start position:0% +regularity lemma we're always working +inside some graph G we say that a pair + + align:start position:0% +inside some graph G we say that a pair + + + align:start position:0% +inside some graph G we say that a pair +of subsets of vertices is epsilon + + align:start position:0% +of subsets of vertices is epsilon + + + align:start position:0% +of subsets of vertices is epsilon +regular if the following holds for all + + align:start position:0% +regular if the following holds for all + + + align:start position:0% +regular if the following holds for all +subsets a of X P of Y neither too small + + align:start position:0% + + + + align:start position:0% + +we have that intensity edge density + + align:start position:0% +we have that intensity edge density + + + align:start position:0% +we have that intensity edge density +between a and B it's very similar to the + + align:start position:0% +between a and B it's very similar to the + + + align:start position:0% +between a and B it's very similar to the +edge density between the ambient sets x + + align:start position:0% +edge density between the ambient sets x + + + align:start position:0% +edge density between the ambient sets x +and y so we had this picture from last + + align:start position:0% +and y so we had this picture from last + + + align:start position:0% +and y so we had this picture from last +time + + align:start position:0% + + + + align:start position:0% + +you have two sets no they don't have to + + align:start position:0% +you have two sets no they don't have to + + + align:start position:0% +you have two sets no they don't have to +be destroyed they could even be the same + + align:start position:0% +be destroyed they could even be the same + + + align:start position:0% +be destroyed they could even be the same +set but for illustration purposes it's + + align:start position:0% +set but for illustration purposes it's + + + align:start position:0% +set but for illustration purposes it's +easier to visualize what's going on if I + + align:start position:0% +easier to visualize what's going on if I + + + align:start position:0% +easier to visualize what's going on if I +draw them as just disjoint subsets so + + align:start position:0% +draw them as just disjoint subsets so + + + align:start position:0% +draw them as just disjoint subsets so +there's some edge density and I said + + align:start position:0% +there's some edge density and I said + + + align:start position:0% +there's some edge density and I said +there Absalon regular if they behave + + align:start position:0% +there Absalon regular if they behave + + + align:start position:0% +there Absalon regular if they behave +random like in the following sense + + align:start position:0% +random like in the following sense + + + align:start position:0% +random like in the following sense +that the edges are somehow distributed + + align:start position:0% +that the edges are somehow distributed + + + align:start position:0% +that the edges are somehow distributed +in a fairly uniform way so that if I + + align:start position:0% +in a fairly uniform way so that if I + + + align:start position:0% +in a fairly uniform way so that if I +look at some smaller subsets a and B / + + align:start position:0% +look at some smaller subsets a and B / + + + align:start position:0% +look at some smaller subsets a and B / +not not too small then the edge + + align:start position:0% +not not too small then the edge + + + align:start position:0% +not not too small then the edge +densities between a and B is very + + align:start position:0% +densities between a and B is very + + + align:start position:0% +densities between a and B is very +similar to the ambient edge densities so + + align:start position:0% +similar to the ambient edge densities so + + + align:start position:0% +similar to the ambient edge densities so +by at most epsilon difference now I need + + align:start position:0% +by at most epsilon difference now I need + + + align:start position:0% +by at most epsilon difference now I need +that a and B are not too small because + + align:start position:0% +that a and B are not too small because + + + align:start position:0% +that a and B are not too small because +if you allow to take for example single + + align:start position:0% +if you allow to take for example single + + + align:start position:0% +if you allow to take for example single +vertices you can easily get densities + + align:start position:0% +vertices you can easily get densities + + + align:start position:0% +vertices you can easily get densities +that are either 0 or 1 so then it's very + + align:start position:0% +that are either 0 or 1 so then it's very + + + align:start position:0% +that are either 0 or 1 so then it's very +hard to make any useful statements so + + align:start position:0% +hard to make any useful statements so + + + align:start position:0% +hard to make any useful statements so +that's why these two conditions are + + align:start position:0% +that's why these two conditions are + + + align:start position:0% +that's why these two conditions are +needed and here the edge density is + + align:start position:0% +needed and here the edge density is + + + align:start position:0% +needed and here the edge density is +defined to be the number of edges with + + align:start position:0% +defined to be the number of edges with + + + align:start position:0% +defined to be the number of edges with +one endpoint in a one endpoint in B + + align:start position:0% +one endpoint in a one endpoint in B + + + align:start position:0% +one endpoint in a one endpoint in B +divided by the product of the sizes of a + + align:start position:0% +divided by the product of the sizes of a + + + align:start position:0% +divided by the product of the sizes of a +and B and we say that a partition of the + + align:start position:0% +and B and we say that a partition of the + + + align:start position:0% +and B and we say that a partition of the +vertex set of the graph is epsilon + + align:start position:0% +vertex set of the graph is epsilon + + + align:start position:0% +vertex set of the graph is epsilon +regular if by summing over all pairs IJ + + align:start position:0% +regular if by summing over all pairs IJ + + + align:start position:0% +regular if by summing over all pairs IJ +such that VI VJ is not epsilon regular + + align:start position:0% +such that VI VJ is not epsilon regular + + + align:start position:0% +such that VI VJ is not epsilon regular +if we sum up the product of these part + + align:start position:0% +if we sum up the product of these part + + + align:start position:0% +if we sum up the product of these part +sizes then this sum is at most an + + align:start position:0% +sizes then this sum is at most an + + + align:start position:0% +sizes then this sum is at most an +epsilon fraction of the total number of + + align:start position:0% +epsilon fraction of the total number of + + + align:start position:0% +epsilon fraction of the total number of +pairs of vertices well the way to think + + align:start position:0% +pairs of vertices well the way to think + + + align:start position:0% +pairs of vertices well the way to think +of this is that there are not too many + + align:start position:0% +of this is that there are not too many + + + align:start position:0% +of this is that there are not too many +irregular parts at least in the case + + align:start position:0% +irregular parts at least in the case + + + align:start position:0% +irregular parts at least in the case +when all the parts are + + align:start position:0% +when all the parts are + + + align:start position:0% +when all the parts are +so you should really think about all of + + align:start position:0% +so you should really think about all of + + + align:start position:0% +so you should really think about all of +them having more or less the same size + + align:start position:0% +them having more or less the same size + + + align:start position:0% +them having more or less the same size +than saying that a most an epsilon + + align:start position:0% +than saying that a most an epsilon + + + align:start position:0% +than saying that a most an epsilon +fraction of them are irregular and the + + align:start position:0% +fraction of them are irregular and the + + + align:start position:0% +fraction of them are irregular and the +main theorem from last time was cemre + + align:start position:0% +main theorem from last time was cemre + + + align:start position:0% +main theorem from last time was cemre +ids regularity lemma and the statement + + align:start position:0% +ids regularity lemma and the statement + + + align:start position:0% +ids regularity lemma and the statement +is that for every epsilon there exists + + align:start position:0% +is that for every epsilon there exists + + + align:start position:0% +is that for every epsilon there exists +some mm M depends only on epsilon and + + align:start position:0% +some mm M depends only on epsilon and + + + align:start position:0% +some mm M depends only on epsilon and +not on the graph that we're about to see + + align:start position:0% +not on the graph that we're about to see + + + align:start position:0% +not on the graph that we're about to see +such that every graph has an epsilon + + align:start position:0% +such that every graph has an epsilon + + + align:start position:0% +such that every graph has an epsilon +regular partition into at most M parts + + align:start position:0% + + + + align:start position:0% + +in particular the number of parts does + + align:start position:0% +in particular the number of parts does + + + align:start position:0% +in particular the number of parts does +not depend on the graph it's for every + + align:start position:0% +not depend on the graph it's for every + + + align:start position:0% +not depend on the graph it's for every +epsilon there's some m and no matter how + + align:start position:0% +epsilon there's some m and no matter how + + + align:start position:0% +epsilon there's some m and no matter how +large the graph there exist a bounded + + align:start position:0% +large the graph there exist a bounded + + + align:start position:0% +large the graph there exist a bounded +size partition that is epsilon regular + + align:start position:0% +size partition that is epsilon regular + + + align:start position:0% +size partition that is epsilon regular +so the proof last time gave us a bound M + + align:start position:0% +so the proof last time gave us a bound M + + + align:start position:0% +so the proof last time gave us a bound M +that is quite large as a function of + + align:start position:0% +that is quite large as a function of + + + align:start position:0% +that is quite large as a function of +Epsilon there's the last time we saw + + align:start position:0% +Epsilon there's the last time we saw + + + align:start position:0% +Epsilon there's the last time we saw +that this M was a power of two's of + + align:start position:0% +that this M was a power of two's of + + + align:start position:0% +that this M was a power of two's of +height essentially polynomial in 1 over + + align:start position:0% +height essentially polynomial in 1 over + + + align:start position:0% +height essentially polynomial in 1 over +Epsilon and I mentioned that you + + align:start position:0% +Epsilon and I mentioned that you + + + align:start position:0% +Epsilon and I mentioned that you +basically cannot improve this bound so + + align:start position:0% +basically cannot improve this bound so + + + align:start position:0% +basically cannot improve this bound so +this bound is more or less best possible + + align:start position:0% +this bound is more or less best possible + + + align:start position:0% +this bound is more or less best possible +up to maybe changing the 5 so in some + + align:start position:0% +up to maybe changing the 5 so in some + + + align:start position:0% +up to maybe changing the 5 so in some +sense the proof that we gave last time + + align:start position:0% +sense the proof that we gave last time + + + align:start position:0% +sense the proof that we gave last time +for similarities graph regularity lemma + + align:start position:0% +for similarities graph regularity lemma + + + align:start position:0% +for similarities graph regularity lemma +was the right proof so that was the + + align:start position:0% +was the right proof so that was the + + + align:start position:0% +was the right proof so that was the +sequence of steps they were the right + + align:start position:0% +sequence of steps they were the right + + + align:start position:0% +sequence of steps they were the right +things to do even though they gave a + + align:start position:0% +things to do even though they gave a + + + align:start position:0% +things to do even though they gave a +terrible bound it's somehow the thing + + align:start position:0% +terrible bound it's somehow the thing + + + align:start position:0% +terrible bound it's somehow the thing +the bound that should come out okay what + + align:start position:0% +the bound that should come out okay what + + + align:start position:0% +the bound that should come out okay what +I want to talk about today is what's a + + align:start position:0% +I want to talk about today is what's a + + + align:start position:0% +I want to talk about today is what's a +regularity partition good form + + align:start position:0% +regularity partition good form + + + align:start position:0% +regularity partition good form +so we did all this work to get a + + align:start position:0% +so we did all this work to get a + + + align:start position:0% +so we did all this work to get a +regularity partition that has all of + + align:start position:0% +regularity partition that has all of + + + align:start position:0% +regularity partition that has all of +these nice definitions but they are + + align:start position:0% +these nice definitions but they are + + + align:start position:0% +these nice definitions but they are +useful for something I said what it it's + + align:start position:0% +useful for something I said what it it's + + + align:start position:0% +useful for something I said what it it's +a useful form and here is the intuition + + align:start position:0% +a useful form and here is the intuition + + + align:start position:0% +a useful form and here is the intuition +that remember the at the beginning of + + align:start position:0% +that remember the at the beginning of + + + align:start position:0% +that remember the at the beginning of +last lecture I mentioned this informal + + align:start position:0% +last lecture I mentioned this informal + + + align:start position:0% +last lecture I mentioned this informal +statement of regularity lemma namely + + align:start position:0% +statement of regularity lemma namely + + + align:start position:0% +statement of regularity lemma namely +that there exists a partition of the + + align:start position:0% +that there exists a partition of the + + + align:start position:0% +that there exists a partition of the +graph so that most pairs look random + + align:start position:0% +graph so that most pairs look random + + + align:start position:0% +graph so that most pairs look random +like so what does random like me so + + align:start position:0% +like so what does random like me so + + + align:start position:0% +like so what does random like me so +random like there's a specific + + align:start position:0% +random like there's a specific + + + align:start position:0% +random like there's a specific +definition but the intuition is that in + + align:start position:0% +definition but the intuition is that in + + + align:start position:0% +definition but the intuition is that in +many aspects especially when it comes to + + align:start position:0% +many aspects especially when it comes to + + + align:start position:0% +many aspects especially when it comes to +counting small patterns the graph in a + + align:start position:0% +counting small patterns the graph in a + + + align:start position:0% +counting small patterns the graph in a +random like setting looks it's very + + align:start position:0% +random like setting looks it's very + + + align:start position:0% +random like setting looks it's very +similar to what happens in a random + + align:start position:0% +similar to what happens in a random + + + align:start position:0% +similar to what happens in a random +graph in a genuine random graph and in + + align:start position:0% +graph in a genuine random graph and in + + + align:start position:0% +graph in a genuine random graph and in +particular if you have three subsets x y + + align:start position:0% +particular if you have three subsets x y + + + align:start position:0% +particular if you have three subsets x y +and z and suppose that the three pairs + + align:start position:0% +and z and suppose that the three pairs + + + align:start position:0% +and z and suppose that the three pairs +are all epsilon regular then you might + + align:start position:0% +are all epsilon regular then you might + + + align:start position:0% +are all epsilon regular then you might +be interested in the number of triangles + + align:start position:0% + + + + align:start position:0% + +with one vertex in each set now if this + + align:start position:0% +with one vertex in each set now if this + + + align:start position:0% +with one vertex in each set now if this +were a genuine random tripartite graph + + align:start position:0% +were a genuine random tripartite graph + + + align:start position:0% +were a genuine random tripartite graph +with a specified edge densities then the + + align:start position:0% +with a specified edge densities then the + + + align:start position:0% +with a specified edge densities then the +number of triangles in such a random + + align:start position:0% +number of triangles in such a random + + + align:start position:0% +number of triangles in such a random +graph is pretty easy to calculate you + + align:start position:0% +graph is pretty easy to calculate you + + + align:start position:0% +graph is pretty easy to calculate you +expect that elissa around the product of + + align:start position:0% +expect that elissa around the product of + + + align:start position:0% +expect that elissa around the product of +the sizes of these vertex sets + + align:start position:0% +the sizes of these vertex sets + + + align:start position:0% +the sizes of these vertex sets +multiplied by their edge densities and + + align:start position:0% +multiplied by their edge densities and + + + align:start position:0% +multiplied by their edge densities and +what we will see is that in this case in + + align:start position:0% +what we will see is that in this case in + + + align:start position:0% +what we will see is that in this case in +that of epsilon regular setting this is + + align:start position:0% +that of epsilon regular setting this is + + + align:start position:0% +that of epsilon regular setting this is +also a true statements a true + + align:start position:0% +also a true statements a true + + + align:start position:0% +also a true statements a true +deterministic statement and that's one + + align:start position:0% +deterministic statement and that's one + + + align:start position:0% +deterministic statement and that's one +of the consequences of epsilon + + align:start position:0% +of the consequences of epsilon + + + align:start position:0% +of the consequences of epsilon +regularity yes question + + align:start position:0% + + + + align:start position:0% + +asking why are we only multiplying the + + align:start position:0% +asking why are we only multiplying the + + + align:start position:0% +asking why are we only multiplying the +sizes of XY and Z so you're asking okay + + align:start position:0% +sizes of XY and Z so you're asking okay + + + align:start position:0% +sizes of XY and Z so you're asking okay +so we're trying to find out how many + + align:start position:0% +so we're trying to find out how many + + + align:start position:0% +so we're trying to find out how many +triangles are there with one vertex in X + + align:start position:0% +triangles are there with one vertex in X + + + align:start position:0% +triangles are there with one vertex in X +one vertex in Y and one vertex in Z + + align:start position:0% +one vertex in Y and one vertex in Z + + + align:start position:0% +one vertex in Y and one vertex in Z +right so if I put these vertices in + + align:start position:0% +right so if I put these vertices in + + + align:start position:0% +right so if I put these vertices in +there one by one then if this were a + + align:start position:0% +there one by one then if this were a + + + align:start position:0% +there one by one then if this were a +random graph I expect that pair to be an + + align:start position:0% +random graph I expect that pair to be an + + + align:start position:0% +random graph I expect that pair to be an +edge with probability D X Y and so on so + + align:start position:0% +edge with probability D X Y and so on so + + + align:start position:0% +edge with probability D X Y and so on so +if the all the edge densities were 1/2 + + align:start position:0% +if the all the edge densities were 1/2 + + + align:start position:0% +if the all the edge densities were 1/2 +then I expect 1/8 of these triples to be + + align:start position:0% +then I expect 1/8 of these triples to be + + + align:start position:0% +then I expect 1/8 of these triples to be +actual triangles and what we're saying + + align:start position:0% +actual triangles and what we're saying + + + align:start position:0% +actual triangles and what we're saying +is that in an epsilon regular setting + + align:start position:0% +is that in an epsilon regular setting + + + align:start position:0% +is that in an epsilon regular setting +that is approximately a true statement + + align:start position:0% + + + + align:start position:0% + +okay so let me formalize this intuition + + align:start position:0% +okay so let me formalize this intuition + + + align:start position:0% +okay so let me formalize this intuition +into an actual statement and this type + + align:start position:0% +into an actual statement and this type + + + align:start position:0% +into an actual statement and this type +of statements are known as counting + + align:start position:0% +of statements are known as counting + + + align:start position:0% +of statements are known as counting +Lamas in literature and in particular + + align:start position:0% +Lamas in literature and in particular + + + align:start position:0% +Lamas in literature and in particular +let's look at the triangle counting them + + align:start position:0% + + + + align:start position:0% + +in a triangle counting lemma okay so + + align:start position:0% +in a triangle counting lemma okay so + + + align:start position:0% +in a triangle counting lemma okay so +we're using the same picture over there + + align:start position:0% +we're using the same picture over there + + + align:start position:0% +we're using the same picture over there +I have three vertex subsets some given + + align:start position:0% +I have three vertex subsets some given + + + align:start position:0% +I have three vertex subsets some given +graph again they don't have to be + + align:start position:0% +graph again they don't have to be + + + align:start position:0% +graph again they don't have to be +destroyed they could overlap but it's + + align:start position:0% +destroyed they could overlap but it's + + + align:start position:0% +destroyed they could overlap but it's +fine to think about that picture over + + align:start position:0% +fine to think about that picture over + + + align:start position:0% +fine to think about that picture over +there and suppose that these three pairs + + align:start position:0% +there and suppose that these three pairs + + + align:start position:0% +there and suppose that these three pairs +of subsets so these three subsets they + + align:start position:0% +of subsets so these three subsets they + + + align:start position:0% +of subsets so these three subsets they +are mutually Epsilon regular + + align:start position:0% + + + + align:start position:0% + +then and for abbreviation let me write + + align:start position:0% +then and for abbreviation let me write + + + align:start position:0% +then and for abbreviation let me write +the sub XY to be the edge density + + align:start position:0% +the sub XY to be the edge density + + + align:start position:0% +the sub XY to be the edge density +between x and y and so on for the other + + align:start position:0% +between x and y and so on for the other + + + align:start position:0% +between x and y and so on for the other +two pairs the conclusion is that the + + align:start position:0% +two pairs the conclusion is that the + + + align:start position:0% +two pairs the conclusion is that the +number of triangles where I'm looking at + + align:start position:0% +number of triangles where I'm looking at + + + align:start position:0% +number of triangles where I'm looking at +triangles and only counting triangles + + align:start position:0% +triangles and only counting triangles + + + align:start position:0% +triangles and only counting triangles +with one specified vertex in X 1 in Y + + align:start position:0% +with one specified vertex in X 1 in Y + + + align:start position:0% +with one specified vertex in X 1 in Y +and one in Z is at least some quantity + + align:start position:0% +and one in Z is at least some quantity + + + align:start position:0% +and one in Z is at least some quantity +so there's a small potential error loss + + align:start position:0% +so there's a small potential error loss + + + align:start position:0% +so there's a small potential error loss +but otherwise the product as I mentioned + + align:start position:0% +but otherwise the product as I mentioned + + + align:start position:0% +but otherwise the product as I mentioned +earlier so it's at least this quantity I + + align:start position:0% +earlier so it's at least this quantity I + + + align:start position:0% +earlier so it's at least this quantity I +mentioned earlier up to your potential + + align:start position:0% +mentioned earlier up to your potential + + + align:start position:0% +mentioned earlier up to your potential +small error because no we're looking at + + align:start position:0% +small error because no we're looking at + + + align:start position:0% +small error because no we're looking at +epsilon regularity so there could be + + align:start position:0% +epsilon regularity so there could be + + + align:start position:0% +epsilon regularity so there could be +some fluctuations in both directions a + + align:start position:0% +some fluctuations in both directions a + + + align:start position:0% +some fluctuations in both directions a +similar statement is also true as an + + align:start position:0% +similar statement is also true as an + + + align:start position:0% +similar statement is also true as an +upper bound but the lower bound will be + + align:start position:0% +upper bound but the lower bound will be + + + align:start position:0% +upper bound but the lower bound will be +more useful so I will show you the proof + + align:start position:0% +more useful so I will show you the proof + + + align:start position:0% +more useful so I will show you the proof +of the lower bound but you you can + + align:start position:0% +of the lower bound but you you can + + + align:start position:0% +of the lower bound but you you can +figure out how to do the upper bound and + + align:start position:0% +figure out how to do the upper bound and + + + align:start position:0% +figure out how to do the upper bound and +later on we'll see a general proof what + + align:start position:0% +later on we'll see a general proof what + + + align:start position:0% +later on we'll see a general proof what +happens instead of triangles if you have + + align:start position:0% +happens instead of triangles if you have + + + align:start position:0% +happens instead of triangles if you have +other sub graphs that you wish to count + + align:start position:0% +other sub graphs that you wish to count + + + align:start position:0% +other sub graphs that you wish to count +so here's the intuition you have a + + align:start position:0% +so here's the intuition you have a + + + align:start position:0% +so here's the intuition you have a +random like setting and we'll formalize + + align:start position:0% +random like setting and we'll formalize + + + align:start position:0% +random like setting and we'll formalize +it in the setting of epsilon regular + + align:start position:0% +it in the setting of epsilon regular + + + align:start position:0% +it in the setting of epsilon regular +pairs okay the question is where does 1 + + align:start position:0% +pairs okay the question is where does 1 + + + align:start position:0% +pairs okay the question is where does 1 +minus epsilon come from you're seeing + + align:start position:0% +minus epsilon come from you're seeing + + + align:start position:0% +minus epsilon come from you're seeing +the proof but you should think of this + + align:start position:0% +the proof but you should think of this + + + align:start position:0% +the proof but you should think of this +as essentially a negligible factor any + + align:start position:0% +as essentially a negligible factor any + + + align:start position:0% +as essentially a negligible factor any +more questions all right so here's how + + align:start position:0% +more questions all right so here's how + + + align:start position:0% +more questions all right so here's how +this proof is going to go + + align:start position:0% + + + + align:start position:0% + +let's look at X and think about its + + align:start position:0% +let's look at X and think about its + + + align:start position:0% +let's look at X and think about its +relationship to Y its epsilon regular + + align:start position:0% +relationship to Y its epsilon regular + + + align:start position:0% +relationship to Y its epsilon regular +and I claim as a result of them being + + align:start position:0% +and I claim as a result of them being + + + align:start position:0% +and I claim as a result of them being +epsilon regular fewer than epsilon + + align:start position:0% +epsilon regular fewer than epsilon + + + align:start position:0% +epsilon regular fewer than epsilon +fraction of X so fewer than this many + + align:start position:0% +fraction of X so fewer than this many + + + align:start position:0% +fraction of X so fewer than this many +vertices in X have a very small number + + align:start position:0% +vertices in X have a very small number + + + align:start position:0% +vertices in X have a very small number +of neighbors in Y because if this were + + align:start position:0% +of neighbors in Y because if this were + + + align:start position:0% +of neighbors in Y because if this were +not the case then you can violate the + + align:start position:0% +not the case then you can violate the + + + align:start position:0% +not the case then you can violate the +condition of epsilon regularity if not + + align:start position:0% +condition of epsilon regularity if not + + + align:start position:0% +condition of epsilon regularity if not +then let's look at this subset which has + + align:start position:0% +then let's look at this subset which has + + + align:start position:0% +then let's look at this subset which has +sighs at least epsilon X and all of them + + align:start position:0% +sighs at least epsilon X and all of them + + + align:start position:0% +sighs at least epsilon X and all of them +have fewer than that number of neighbors + + align:start position:0% +have fewer than that number of neighbors + + + align:start position:0% +have fewer than that number of neighbors +to Y so these two sets so this set X + + align:start position:0% +to Y so these two sets so this set X + + + align:start position:0% +to Y so these two sets so this set X +Prime and Y with witness Nong epsilon + + align:start position:0% +Prime and Y with witness Nong epsilon + + + align:start position:0% +Prime and Y with witness Nong epsilon +regularity so you cannot have too many + + align:start position:0% +regularity so you cannot have too many + + + align:start position:0% +regularity so you cannot have too many +vertices with small degrees going to X + + align:start position:0% +vertices with small degrees going to X + + + align:start position:0% +vertices with small degrees going to X +to go into y okay great and likewise + + align:start position:0% + + + + align:start position:0% + +fewer than epsilon X vertices have a + + align:start position:0% +fewer than epsilon X vertices have a + + + align:start position:0% +fewer than epsilon X vertices have a +small number of neighbors to Z + + align:start position:0% + + + + align:start position:0% + +okay so what does a picture now look + + align:start position:0% +okay so what does a picture now look + + + align:start position:0% +okay so what does a picture now look +like so you have this X and then these + + align:start position:0% +like so you have this X and then these + + + align:start position:0% +like so you have this X and then these +two other sets y&z where I'm going to + + align:start position:0% +two other sets y&z where I'm going to + + + align:start position:0% +two other sets y&z where I'm going to +throw out a small proportion of X less + + align:start position:0% +throw out a small proportion of X less + + + align:start position:0% +throw out a small proportion of X less +than 2 epsilon fraction of X they have + + align:start position:0% +than 2 epsilon fraction of X they have + + + align:start position:0% +than 2 epsilon fraction of X they have +the wrong kinds of degrees and + + align:start position:0% +the wrong kinds of degrees and + + + align:start position:0% +the wrong kinds of degrees and +everything else in here have lots of + + align:start position:0% +everything else in here have lots of + + + align:start position:0% +everything else in here have lots of +neighbors in both Y and in Z in + + align:start position:0% +neighbors in both Y and in Z in + + + align:start position:0% +neighbors in both Y and in Z in +particular for all X up here it has a + + align:start position:0% +particular for all X up here it has a + + + align:start position:0% +particular for all X up here it has a +lot of neighbors to Y lots of neighbors + + align:start position:0% +lot of neighbors to Y lots of neighbors + + + align:start position:0% +lot of neighbors to Y lots of neighbors +to see how many we have at least P sub X + + align:start position:0% +to see how many we have at least P sub X + + + align:start position:0% +to see how many we have at least P sub X +Y minus epsilon Y neighbors to Y and at + + align:start position:0% +Y minus epsilon Y neighbors to Y and at + + + align:start position:0% +Y minus epsilon Y neighbors to Y and at +least P sub X Z minus epsilon times Z + + align:start position:0% +least P sub X Z minus epsilon times Z + + + align:start position:0% +least P sub X Z minus epsilon times Z +neighbors to Z and ok + + align:start position:0% +neighbors to Z and ok + + + align:start position:0% +neighbors to Z and ok +so now realize that missing a hypothesis + + align:start position:0% +so now realize that missing a hypothesis + + + align:start position:0% +so now realize that missing a hypothesis +in the continent let me assume that none + + align:start position:0% +in the continent let me assume that none + + + align:start position:0% +in the continent let me assume that none +of these edge densities are too small + + align:start position:0% + + + + align:start position:0% + +they're all at least two Epsilon so now + + align:start position:0% +they're all at least two Epsilon so now + + + align:start position:0% +they're all at least two Epsilon so now +these guys are at least epsilon + + align:start position:0% +these guys are at least epsilon + + + align:start position:0% +these guys are at least epsilon +fractions of Y & Z so I can apply the + + align:start position:0% +fractions of Y & Z so I can apply the + + + align:start position:0% +fractions of Y & Z so I can apply the +definition of epsilon regularity to the + + align:start position:0% +definition of epsilon regularity to the + + + align:start position:0% +definition of epsilon regularity to the +pair Y Z to deduce that there are lots + + align:start position:0% +pair Y Z to deduce that there are lots + + + align:start position:0% +pair Y Z to deduce that there are lots +of edges between these two sets so over + + align:start position:0% +of edges between these two sets so over + + + align:start position:0% +of edges between these two sets so over +here the number of edges is at least the + + align:start position:0% +here the number of edges is at least the + + + align:start position:0% +here the number of edges is at least the +product of these sizes multiplied by the + + align:start position:0% +product of these sizes multiplied by the + + + align:start position:0% +product of these sizes multiplied by the +edge density between them and by the + + align:start position:0% +edge density between them and by the + + + align:start position:0% +edge density between them and by the +definition of epsilon regularity the + + align:start position:0% +definition of epsilon regularity the + + + align:start position:0% +definition of epsilon regularity the +edge density between these two smaller + + align:start position:0% +edge density between these two smaller + + + align:start position:0% +edge density between these two smaller +these two red sets is at least D of Y Z + + align:start position:0% +these two red sets is at least D of Y Z + + + align:start position:0% +these two red sets is at least D of Y Z +minus Epsilon so putting everything now + + align:start position:0% +minus Epsilon so putting everything now + + + align:start position:0% +minus Epsilon so putting everything now +together we find that the total number + + align:start position:0% +together we find that the total number + + + align:start position:0% +together we find that the total number +of triangles looking at all the possible + + align:start position:0% +of triangles looking at all the possible + + + align:start position:0% +of triangles looking at all the possible +places where X can go these 1 minus 2 + + align:start position:0% +places where X can go these 1 minus 2 + + + align:start position:0% +places where X can go these 1 minus 2 +epsilon times the size of X and I + + align:start position:0% +epsilon times the size of X and I + + + align:start position:0% +epsilon times the size of X and I +multiplied by this factor + + align:start position:0% +multiplied by this factor + + + align:start position:0% +multiplied by this factor +over here so we find the statement up + + align:start position:0% +over here so we find the statement up + + + align:start position:0% +over here so we find the statement up +there so this calculation formalizes the + + align:start position:0% +there so this calculation formalizes the + + + align:start position:0% +there so this calculation formalizes the +intuition now if you have epsilon + + align:start position:0% +intuition now if you have epsilon + + + align:start position:0% +intuition now if you have epsilon +regular pairs then they behave like + + align:start position:0% +regular pairs then they behave like + + + align:start position:0% +regular pairs then they behave like +random settings when it comes to + + align:start position:0% +random settings when it comes to + + + align:start position:0% +random settings when it comes to +counting small patterns namely that of a + + align:start position:0% +counting small patterns namely that of a + + + align:start position:0% +counting small patterns namely that of a +triangle okay so what can we use this + + align:start position:0% +triangle okay so what can we use this + + + align:start position:0% +triangle okay so what can we use this +for the next statement I want to show + + align:start position:0% +for the next statement I want to show + + + align:start position:0% +for the next statement I want to show +you is called a triangle we move all + + align:start position:0% +you is called a triangle we move all + + + align:start position:0% +you is called a triangle we move all +Emma okay so this is a somewhat + + align:start position:0% +Emma okay so this is a somewhat + + + align:start position:0% +Emma okay so this is a somewhat +innocuous looking statement that she's + + align:start position:0% +innocuous looking statement that she's + + + align:start position:0% +innocuous looking statement that she's +surprisingly tricky to proof and part of + + align:start position:0% +surprisingly tricky to proof and part of + + + align:start position:0% +surprisingly tricky to proof and part of +the development of this regularity lemma + + align:start position:0% +the development of this regularity lemma + + + align:start position:0% +the development of this regularity lemma +was to prove similar to triangle removal + + align:start position:0% +was to prove similar to triangle removal + + + align:start position:0% +was to prove similar to triangle removal +Emma this is one in the early + + align:start position:0% +Emma this is one in the early + + + align:start position:0% +Emma this is one in the early +applications of the regularity lemma + + align:start position:0% +applications of the regularity lemma + + + align:start position:0% +applications of the regularity lemma +that's always do to Gousha and + + align:start position:0% +that's always do to Gousha and + + + align:start position:0% +that's always do to Gousha and +similarity back in the 70s here's a + + align:start position:0% +similarity back in the 70s here's a + + + align:start position:0% +similarity back in the 70s here's a +statement for every epsilon there exist + + align:start position:0% +statement for every epsilon there exist + + + align:start position:0% +statement for every epsilon there exist +a delta such that every graph and + + align:start position:0% +a delta such that every graph and + + + align:start position:0% +a delta such that every graph and +vertices with a small number of + + align:start position:0% +vertices with a small number of + + + align:start position:0% +vertices with a small number of +triangles so small number of triangles + + align:start position:0% +triangles so small number of triangles + + + align:start position:0% +triangles so small number of triangles +means a negligible fraction of all the + + align:start position:0% +means a negligible fraction of all the + + + align:start position:0% +means a negligible fraction of all the +possible triples of vertices are actual + + align:start position:0% +possible triples of vertices are actual + + + align:start position:0% +possible triples of vertices are actual +triangles so fewer than Delta and cubed + + align:start position:0% +triangles so fewer than Delta and cubed + + + align:start position:0% +triangles so fewer than Delta and cubed +triangles okay so if you have a graph + + align:start position:0% +triangles okay so if you have a graph + + + align:start position:0% +triangles okay so if you have a graph +with the small number of triangles + + align:start position:0% +with the small number of triangles + + + align:start position:0% +with the small number of triangles +questions can you make a triangle free + + align:start position:0% +questions can you make a triangle free + + + align:start position:0% +questions can you make a triangle free +by getting rid of a small number of + + align:start position:0% +by getting rid of a small number of + + + align:start position:0% +by getting rid of a small number of +edges actually there was already a + + align:start position:0% +edges actually there was already a + + + align:start position:0% +edges actually there was already a +problem on the first problem on the + + align:start position:0% +problem on the first problem on the + + + align:start position:0% +problem on the first problem on the +first homework set that is in that + + align:start position:0% +first homework set that is in that + + + align:start position:0% +first homework set that is in that +spirit but you see this okay so if you + + align:start position:0% +spirit but you see this okay so if you + + + align:start position:0% +spirit but you see this okay so if you +compare what I'm doing here to the + + align:start position:0% +compare what I'm doing here to the + + + align:start position:0% +compare what I'm doing here to the +homework + + align:start position:0% +homework + + + align:start position:0% +homework +you see that there are different scales + + align:start position:0% +you see that there are different scales + + + align:start position:0% +you see that there are different scales +so fewer than Delta and cube triangles + + align:start position:0% +so fewer than Delta and cube triangles + + + align:start position:0% +so fewer than Delta and cube triangles +can be made triangle free by removing + + align:start position:0% + + + + align:start position:0% + +epsilon and squared edges okay so if you + + align:start position:0% +epsilon and squared edges okay so if you + + + align:start position:0% +epsilon and squared edges okay so if you +have a small number of triangles you can + + align:start position:0% +have a small number of triangles you can + + + align:start position:0% +have a small number of triangles you can +get rid of all the triangles by removing + + align:start position:0% +get rid of all the triangles by removing + + + align:start position:0% +get rid of all the triangles by removing +a small number of edges if I put it that + + align:start position:0% +a small number of edges if I put it that + + + align:start position:0% +a small number of edges if I put it that +way actually sounds kind of trivial + + align:start position:0% +way actually sounds kind of trivial + + + align:start position:0% +way actually sounds kind of trivial +right you just get rid of all the + + align:start position:0% +right you just get rid of all the + + + align:start position:0% +right you just get rid of all the +triangles but if you look at the scales + + align:start position:0% +triangles but if you look at the scales + + + align:start position:0% +triangles but if you look at the scales +it's not review at all because there are + + align:start position:0% +it's not review at all because there are + + + align:start position:0% +it's not review at all because there are +only a sub cubic number of triangles so + + align:start position:0% +only a sub cubic number of triangles so + + + align:start position:0% +only a sub cubic number of triangles so +if you take out one edge from each + + align:start position:0% +if you take out one edge from each + + + align:start position:0% +if you take out one edge from each +triangle maybe you got rid of a lot of + + align:start position:0% +triangle maybe you got rid of a lot of + + + align:start position:0% +triangle maybe you got rid of a lot of +edges so this is a very innocent looking + + align:start position:0% +edges so this is a very innocent looking + + + align:start position:0% +edges so this is a very innocent looking +statement but it's actually incredibly + + align:start position:0% +statement but it's actually incredibly + + + align:start position:0% +statement but it's actually incredibly +deep and tricky before jumping to the + + align:start position:0% +deep and tricky before jumping to the + + + align:start position:0% +deep and tricky before jumping to the +proof let me first show you a equivalent + + align:start position:0% +proof let me first show you a equivalent + + + align:start position:0% +proof let me first show you a equivalent +reformulation of the statement that also + + align:start position:0% +reformulation of the statement that also + + + align:start position:0% +reformulation of the statement that also +helps you to think about we know what + + align:start position:0% +helps you to think about we know what + + + align:start position:0% +helps you to think about we know what +this statement is trying to say so the + + align:start position:0% +this statement is trying to say so the + + + align:start position:0% +this statement is trying to say so the +triangle removal emmab can be + + align:start position:0% +triangle removal emmab can be + + + align:start position:0% +triangle removal emmab can be +equivalently stated as saying that every + + align:start position:0% +equivalently stated as saying that every + + + align:start position:0% +equivalently stated as saying that every +end vertex graph with a sub cubic number + + align:start position:0% +end vertex graph with a sub cubic number + + + align:start position:0% +end vertex graph with a sub cubic number +of triangles so little all of n cubed + + align:start position:0% +of triangles so little all of n cubed + + + align:start position:0% +of triangles so little all of n cubed +triangles can be made triangle free + + align:start position:0% + + + + align:start position:0% + +by removing a sub-quadratic namely + + align:start position:0% +by removing a sub-quadratic namely + + + align:start position:0% +by removing a sub-quadratic namely +little o of N squared number of edges + + align:start position:0% + + + + align:start position:0% + +okay so this is an equivalent statement + + align:start position:0% +okay so this is an equivalent statement + + + align:start position:0% +okay so this is an equivalent statement +to what I wrote above although you + + align:start position:0% +to what I wrote above although you + + + align:start position:0% +to what I wrote above although you +actually take some thought to figure out + + align:start position:0% +actually take some thought to figure out + + + align:start position:0% +actually take some thought to figure out +what this is even saying because + + align:start position:0% +what this is even saying because + + + align:start position:0% +what this is even saying because +everybody loves using asymptotic + + align:start position:0% +everybody loves using asymptotic + + + align:start position:0% +everybody loves using asymptotic +notation but there's also ambiguity with + + align:start position:0% +notation but there's also ambiguity with + + + align:start position:0% +notation but there's also ambiguity with +what do you mean by asymptotic notation + + align:start position:0% +what do you mean by asymptotic notation + + + align:start position:0% +what do you mean by asymptotic notation +especially if it appears in the + + align:start position:0% +especially if it appears in the + + + align:start position:0% +especially if it appears in the +hypothesis of a claim okay so so what do + + align:start position:0% +hypothesis of a claim okay so so what do + + + align:start position:0% +hypothesis of a claim okay so so what do +you think this statement means can you + + align:start position:0% +you think this statement means can you + + + align:start position:0% +you think this statement means can you +write out more of a full form so I think + + align:start position:0% +write out more of a full form so I think + + + align:start position:0% +write out more of a full form so I think +of this as a lazy version of trying to + + align:start position:0% +of this as a lazy version of trying to + + + align:start position:0% +of this as a lazy version of trying to +say something right so what do you mean + + align:start position:0% +say something right so what do you mean + + + align:start position:0% +say something right so what do you mean +by having butovo of n cubed triangles + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +okay great so I have sequence of graphs + + align:start position:0% +okay great so I have sequence of graphs + + + align:start position:0% +okay great so I have sequence of graphs +and also you can put some functions in + + align:start position:0% +and also you can put some functions in + + + align:start position:0% +and also you can put some functions in +alright so that's so I'll write down the + + align:start position:0% +alright so that's so I'll write down the + + + align:start position:0% +alright so that's so I'll write down the +statement here but that's kind of the + + align:start position:0% +statement here but that's kind of the + + + align:start position:0% +statement here but that's kind of the +idea were looking at not just a single + + align:start position:0% +idea were looking at not just a single + + + align:start position:0% +idea were looking at not just a single +graph but we're looking at a sequence + + align:start position:0% +graph but we're looking at a sequence + + + align:start position:0% +graph but we're looking at a sequence +another way to say this is that for + + align:start position:0% +another way to say this is that for + + + align:start position:0% +another way to say this is that for +every function FN that is sub-q Bukh so + + align:start position:0% +every function FN that is sub-q Bukh so + + + align:start position:0% +every function FN that is sub-q Bukh so +for example of f of n is n cube divided + + align:start position:0% +for example of f of n is n cube divided + + + align:start position:0% +for example of f of n is n cube divided +by log n there exists some function G + + align:start position:0% +by log n there exists some function G + + + align:start position:0% +by log n there exists some function G +which is sub-quadratic such that if you + + align:start position:0% +which is sub-quadratic such that if you + + + align:start position:0% +which is sub-quadratic such that if you +replace the first one by f of N and the + + align:start position:0% +replace the first one by f of N and the + + + align:start position:0% +replace the first one by f of N and the +second thing by G event and this is a + + align:start position:0% +second thing by G event and this is a + + + align:start position:0% +second thing by G event and this is a +true statement and I leave it to you as + + align:start position:0% +true statement and I leave it to you as + + + align:start position:0% +true statement and I leave it to you as +an exercise and quantify elimination + + align:start position:0% +an exercise and quantify elimination + + + align:start position:0% +an exercise and quantify elimination +let's say to explain why these two + + align:start position:0% +let's say to explain why these two + + + align:start position:0% +let's say to explain why these two +statements are equivalent to each other + + align:start position:0% + + + + align:start position:0% + +all right I want to explain a recipe for + + align:start position:0% +all right I want to explain a recipe for + + + align:start position:0% +all right I want to explain a recipe for +applying similarities regularity lemma + + align:start position:0% +applying similarities regularity lemma + + + align:start position:0% +applying similarities regularity lemma +how does one use the regularity lemma to + + align:start position:0% +how does one use the regularity lemma to + + + align:start position:0% +how does one use the regularity lemma to +proof for statements in graph theory the + + align:start position:0% +proof for statements in graph theory the + + + align:start position:0% +proof for statements in graph theory the +most standard applications of regularity + + align:start position:0% +most standard applications of regularity + + + align:start position:0% +most standard applications of regularity +lemma generally have the following steps + + align:start position:0% + + + + align:start position:0% + +let me call this a recipe and we'll see + + align:start position:0% +let me call this a recipe and we'll see + + + align:start position:0% +let me call this a recipe and we'll see +it a few times + + align:start position:0% + + + + align:start position:0% + +the first step is what we apply + + align:start position:0% +the first step is what we apply + + + align:start position:0% +the first step is what we apply +somewhere these regularity lemma to + + align:start position:0% +somewhere these regularity lemma to + + + align:start position:0% +somewhere these regularity lemma to +obtain a partition so let me call the + + align:start position:0% +obtain a partition so let me call the + + + align:start position:0% +obtain a partition so let me call the +first step partition in the second step + + align:start position:0% +first step partition in the second step + + + align:start position:0% +first step partition in the second step +we look at the partition that we obtain + + align:start position:0% +we look at the partition that we obtain + + + align:start position:0% +we look at the partition that we obtain +and we clean it up so in the partition + + align:start position:0% +and we clean it up so in the partition + + + align:start position:0% +and we clean it up so in the partition +you have some irregular pairs that that + + align:start position:0% +you have some irregular pairs that that + + + align:start position:0% +you have some irregular pairs that that +are undesirable to work with and there + + align:start position:0% +are undesirable to work with and there + + + align:start position:0% +are undesirable to work with and there +are some other pairs that we'll see so + + align:start position:0% +are some other pairs that we'll see so + + + align:start position:0% +are some other pairs that we'll see so +in particular if you our pair involves + + align:start position:0% +in particular if you our pair involves + + + align:start position:0% +in particular if you our pair involves +edges that are fairly sparse or subsets + + align:start position:0% +edges that are fairly sparse or subsets + + + align:start position:0% +edges that are fairly sparse or subsets +of vertices that are fairly small then + + align:start position:0% +of vertices that are fairly small then + + + align:start position:0% +of vertices that are fairly small then +maybe we don't want to touch them + + align:start position:0% +maybe we don't want to touch them + + + align:start position:0% +maybe we don't want to touch them +because they're kind of not so good to + + align:start position:0% +because they're kind of not so good to + + + align:start position:0% +because they're kind of not so good to +deal with so we're going to clean the + + align:start position:0% +deal with so we're going to clean the + + + align:start position:0% +deal with so we're going to clean the +graph by removing edges in irregular + + align:start position:0% +graph by removing edges in irregular + + + align:start position:0% +graph by removing edges in irregular +pairs and low-density pairs + + align:start position:0% + + + + align:start position:0% + +and unless you're using the version of + + align:start position:0% +and unless you're using the version of + + + align:start position:0% +and unless you're using the version of +regularity lemma that allows you to have + + align:start position:0% +regularity lemma that allows you to have + + + align:start position:0% +regularity lemma that allows you to have +equitable parts you also want to get rid + + align:start position:0% +equitable parts you also want to get rid + + + align:start position:0% +equitable parts you also want to get rid +of edges where one of the parts there's + + align:start position:0% +of edges where one of the parts there's + + + align:start position:0% +of edges where one of the parts there's +too small okay + + align:start position:0% + + + + align:start position:0% + +and the third step coders count once + + align:start position:0% +and the third step coders count once + + + align:start position:0% +and the third step coders count once +you've cleaned up the regularity + + align:start position:0% +you've cleaned up the regularity + + + align:start position:0% +you've cleaned up the regularity +partition say well let's try to find + + align:start position:0% +partition say well let's try to find + + + align:start position:0% +partition say well let's try to find +some patterns if you find one pattern in + + align:start position:0% +some patterns if you find one pattern in + + + align:start position:0% +some patterns if you find one pattern in +the cleaned graph and we can use the + + align:start position:0% +the cleaned graph and we can use the + + + align:start position:0% +the cleaned graph and we can use the +counting them up + + align:start position:0% + + + + align:start position:0% + +to find lots of patterns here for the + + align:start position:0% +to find lots of patterns here for the + + + align:start position:0% +to find lots of patterns here for the +purpose of triangle remover lemma and + + align:start position:0% +purpose of triangle remover lemma and + + + align:start position:0% +purpose of triangle remover lemma and +what we've been doing so far pattern + + align:start position:0% +what we've been doing so far pattern + + + align:start position:0% +what we've been doing so far pattern +just means a triangle so we're going to + + align:start position:0% +just means a triangle so we're going to + + + align:start position:0% +just means a triangle so we're going to +use the triangle counting lemma to find + + align:start position:0% +use the triangle counting lemma to find + + + align:start position:0% +use the triangle counting lemma to find +us lots of triangles so we'll see the + + align:start position:0% +us lots of triangles so we'll see the + + + align:start position:0% +us lots of triangles so we'll see the +details in a bit but if we run through + + align:start position:0% +details in a bit but if we run through + + + align:start position:0% +details in a bit but if we run through +this strategy you give me a graph let's + + align:start position:0% +this strategy you give me a graph let's + + + align:start position:0% +this strategy you give me a graph let's +say it so starting from the triangle + + align:start position:0% +say it so starting from the triangle + + + align:start position:0% +say it so starting from the triangle +removal Emma has a small number of + + align:start position:0% +removal Emma has a small number of + + + align:start position:0% +removal Emma has a small number of +triangles you apply the partition clean + + align:start position:0% +triangles you apply the partition clean + + + align:start position:0% +triangles you apply the partition clean +it up and I claim this cleaning removes + + align:start position:0% +it up and I claim this cleaning removes + + + align:start position:0% +it up and I claim this cleaning removes +a small number of edges and it should + + align:start position:0% +a small number of edges and it should + + + align:start position:0% +a small number of edges and it should +result in a triangle free graph because + + align:start position:0% +result in a triangle free graph because + + + align:start position:0% +result in a triangle free graph because +if it did not result in a triangle free + + align:start position:0% +if it did not result in a triangle free + + + align:start position:0% +if it did not result in a triangle free +graph then there's some triangle and + + align:start position:0% +graph then there's some triangle and + + + align:start position:0% +graph then there's some triangle and +from that triangle I can apply the + + align:start position:0% +from that triangle I can apply the + + + align:start position:0% +from that triangle I can apply the +triangle County lemma to get lots of + + align:start position:0% +triangle County lemma to get lots of + + + align:start position:0% +triangle County lemma to get lots of +triangles and now would have violated + + align:start position:0% +triangles and now would have violated + + + align:start position:0% +triangles and now would have violated +the hypothesis of the triangle removal + + align:start position:0% +the hypothesis of the triangle removal + + + align:start position:0% +the hypothesis of the triangle removal +lemma so that's how the proof is going + + align:start position:0% +lemma so that's how the proof is going + + + align:start position:0% +lemma so that's how the proof is going +to go okay so I want to take a very + + align:start position:0% +to go okay so I want to take a very + + + align:start position:0% +to go okay so I want to take a very +quick break and then when we come back + + align:start position:0% +quick break and then when we come back + + + align:start position:0% +quick break and then when we come back +well see the details of how to apply the + + align:start position:0% +well see the details of how to apply the + + + align:start position:0% +well see the details of how to apply the +regularity lemma + + align:start position:0% +regularity lemma + + + align:start position:0% +regularity lemma +are there any questions so far yep okay + + align:start position:0% +are there any questions so far yep okay + + + align:start position:0% +are there any questions so far yep okay +so you're asking about what happens when + + align:start position:0% +so you're asking about what happens when + + + align:start position:0% +so you're asking about what happens when +we remove vertex that are to vertex s + + align:start position:0% +we remove vertex that are to vertex s + + + align:start position:0% +we remove vertex that are to vertex s +that are too small okay you are seen the + + align:start position:0% +that are too small okay you are seen the + + + align:start position:0% +that are too small okay you are seen the +details of the proof so hold on to that + + align:start position:0% +details of the proof so hold on to that + + + align:start position:0% +details of the proof so hold on to that +question for a bit more questions okay + + align:start position:0% +question for a bit more questions okay + + + align:start position:0% +question for a bit more questions okay +so let's see the proof of the triangle + + align:start position:0% +so let's see the proof of the triangle + + + align:start position:0% +so let's see the proof of the triangle +removal MO it so the first step is to + + align:start position:0% +removal MO it so the first step is to + + + align:start position:0% +removal MO it so the first step is to +apply similarities regularity lemma and + + align:start position:0% +apply similarities regularity lemma and + + + align:start position:0% +apply similarities regularity lemma and +find a partition so we'll find a + + align:start position:0% +find a partition so we'll find a + + + align:start position:0% +find a partition so we'll find a +partition that's epsilon over four + + align:start position:0% +partition that's epsilon over four + + + align:start position:0% +partition that's epsilon over four +regular okay so here epsilon is the same + + align:start position:0% +regular okay so here epsilon is the same + + + align:start position:0% +regular okay so here epsilon is the same +epsilon in the statement in the top + + align:start position:0% +epsilon in the statement in the top + + + align:start position:0% +epsilon in the statement in the top +statement of the triangle removal and in + + align:start position:0% +statement of the triangle removal and in + + + align:start position:0% +statement of the triangle removal and in +the second step let's clean the graph by + + align:start position:0% +the second step let's clean the graph by + + + align:start position:0% +the second step let's clean the graph by +removing all edges in so we are going to + + align:start position:0% +removing all edges in so we are going to + + + align:start position:0% +removing all edges in so we are going to +get rid of edges between edges + + align:start position:0% + + + + align:start position:0% + +between VI and DJ whenever VI and VJ + + align:start position:0% + + + + align:start position:0% + +it's not epsilon regular get rid of the + + align:start position:0% +it's not epsilon regular get rid of the + + + align:start position:0% +it's not epsilon regular get rid of the +edges between irregular parts sorry + + align:start position:0% +edges between irregular parts sorry + + + align:start position:0% +edges between irregular parts sorry +epsilon over for regular thank you also + + align:start position:0% +epsilon over for regular thank you also + + + align:start position:0% +epsilon over for regular thank you also +between parts where the edge density is + + align:start position:0% +between parts where the edge density is + + + align:start position:0% +between parts where the edge density is +too small the edge density is less than + + align:start position:0% +too small the edge density is less than + + + align:start position:0% +too small the edge density is less than +epsilon over two get rid of those edges + + align:start position:0% +epsilon over two get rid of those edges + + + align:start position:0% +epsilon over two get rid of those edges +and if one of the two vertex sets has + + align:start position:0% +and if one of the two vertex sets has + + + align:start position:0% +and if one of the two vertex sets has +size too small and here too small means + + align:start position:0% +size too small and here too small means + + + align:start position:0% +size too small and here too small means +epsilon over 4m times the size of and so + + align:start position:0% +epsilon over 4m times the size of and so + + + align:start position:0% +epsilon over 4m times the size of and so +here okay so let me use Big M for the + + align:start position:0% +here okay so let me use Big M for the + + + align:start position:0% +here okay so let me use Big M for the +number of parts so that's the M that + + align:start position:0% +number of parts so that's the M that + + + align:start position:0% +number of parts so that's the M that +comes out of somewhere this regularity + + align:start position:0% +comes out of somewhere this regularity + + + align:start position:0% +comes out of somewhere this regularity +lemma if you like some of the vertex s + + align:start position:0% +lemma if you like some of the vertex s + + + align:start position:0% +lemma if you like some of the vertex s +and B empty it doesn't change the proof + + align:start position:0% +and B empty it doesn't change the proof + + + align:start position:0% +and B empty it doesn't change the proof +and n is the number of vertices in the + + align:start position:0% +and n is the number of vertices in the + + + align:start position:0% +and n is the number of vertices in the +graph and this step you don't really + + align:start position:0% +graph and this step you don't really + + + align:start position:0% +graph and this step you don't really +need the step if you are regular + + align:start position:0% +need the step if you are regular + + + align:start position:0% +need the step if you are regular +partition is equitable okay so let's see + + align:start position:0% +partition is equitable okay so let's see + + + align:start position:0% +partition is equitable okay so let's see +how many vertices how many edges have we + + align:start position:0% +how many vertices how many edges have we + + + align:start position:0% +how many vertices how many edges have we +gotten rid of we want to show that we're + + align:start position:0% +gotten rid of we want to show that we're + + + align:start position:0% +gotten rid of we want to show that we're +not the leading to many edges well in + + align:start position:0% +not the leading to many edges well in + + + align:start position:0% +not the leading to many edges well in +the first step so some the number of + + align:start position:0% +the first step so some the number of + + + align:start position:0% +the first step so some the number of +deleted + + align:start position:0% + + + + align:start position:0% + +Edge's in the first step you see that + + align:start position:0% +Edge's in the first step you see that + + + align:start position:0% +Edge's in the first step you see that +the number of edges deleted is and most + + align:start position:0% +the number of edges deleted is and most + + + align:start position:0% +the number of edges deleted is and most +the sum of product of V I V J's when you + + align:start position:0% +the sum of product of V I V J's when you + + + align:start position:0% +the sum of product of V I V J's when you +sum over IJ such that this pair is not + + align:start position:0% +sum over IJ such that this pair is not + + + align:start position:0% +sum over IJ such that this pair is not +epsilon regular or epsilon for regular + + align:start position:0% +epsilon regular or epsilon for regular + + + align:start position:0% +epsilon regular or epsilon for regular +I'm summing over for regular by the + + align:start position:0% +I'm summing over for regular by the + + + align:start position:0% +I'm summing over for regular by the +definition of an epsilon regular + + align:start position:0% +definition of an epsilon regular + + + align:start position:0% +definition of an epsilon regular +partition this sum here is at most + + align:start position:0% +partition this sum here is at most + + + align:start position:0% +partition this sum here is at most +epsilon over four times N squared in the + + align:start position:0% +epsilon over four times N squared in the + + + align:start position:0% +epsilon over four times N squared in the +second step I'm getting rid of + + align:start position:0% +second step I'm getting rid of + + + align:start position:0% +second step I'm getting rid of +low-density pairs right by the virtue of + + align:start position:0% +low-density pairs right by the virtue of + + + align:start position:0% +low-density pairs right by the virtue of +them being low-density I'm not removing + + align:start position:0% +them being low-density I'm not removing + + + align:start position:0% +them being low-density I'm not removing +so many edges so at most epsilon over + + align:start position:0% +so many edges so at most epsilon over + + + align:start position:0% +so many edges so at most epsilon over +two times and squared edges I'm getting + + align:start position:0% +two times and squared edges I'm getting + + + align:start position:0% +two times and squared edges I'm getting +rid of in the third part you see every + + align:start position:0% +rid of in the third part you see every + + + align:start position:0% +rid of in the third part you see every +time I take a very small piece every + + align:start position:0% +time I take a very small piece every + + + align:start position:0% +time I take a very small piece every +vertex here is adjacent to a most end + + align:start position:0% +vertex here is adjacent to a most end + + + align:start position:0% +vertex here is adjacent to a most end +vertices so the number of such things + + align:start position:0% +vertices so the number of such things + + + align:start position:0% +vertices so the number of such things +such edges I'm getting rid of in the + + align:start position:0% +such edges I'm getting rid of in the + + + align:start position:0% +such edges I'm getting rid of in the +last step is at most this number times + + align:start position:0% +last step is at most this number times + + + align:start position:0% +last step is at most this number times +the number of parts M 10 times n so it's + + align:start position:0% +the number of parts M 10 times n so it's + + + align:start position:0% +the number of parts M 10 times n so it's +at most epsilon over four times N + + align:start position:0% +at most epsilon over four times N + + + align:start position:0% +at most epsilon over four times N +squared okay so here telling you how + + align:start position:0% +squared okay so here telling you how + + + align:start position:0% +squared okay so here telling you how +many edges I've deleted in each step and + + align:start position:0% +many edges I've deleted in each step and + + + align:start position:0% +many edges I've deleted in each step and +in total putting them together we see + + align:start position:0% +in total putting them together we see + + + align:start position:0% +in total putting them together we see +that we get rid of at most epsilon and + + align:start position:0% +that we get rid of at most epsilon and + + + align:start position:0% +that we get rid of at most epsilon and +squared edges from this graph + + align:start position:0% + + + + align:start position:0% + +okay so that's the cleaning step okay so + + align:start position:0% +okay so that's the cleaning step okay so + + + align:start position:0% +okay so that's the cleaning step okay so +we cleaned up the graph by getting rid + + align:start position:0% +we cleaned up the graph by getting rid + + + align:start position:0% +we cleaned up the graph by getting rid +of low-density pears getting rid of + + align:start position:0% +of low-density pears getting rid of + + + align:start position:0% +of low-density pears getting rid of +irregular pears and small vertex s now + + align:start position:0% +irregular pears and small vertex s now + + + align:start position:0% +irregular pears and small vertex s now +suppose after this cleaning some + + align:start position:0% +suppose after this cleaning some + + + align:start position:0% +suppose after this cleaning some +triangle still remains on to the third + + align:start position:0% +triangle still remains on to the third + + + align:start position:0% +triangle still remains on to the third +step + + align:start position:0% +step + + + align:start position:0% +step +so suppose some triangle remains okay so + + align:start position:0% +so suppose some triangle remains okay so + + + align:start position:0% +so suppose some triangle remains okay so +what we're could this triangle set has + + align:start position:0% +what we're could this triangle set has + + + align:start position:0% +what we're could this triangle set has +to be between three parts VI VJ and the + + align:start position:0% +to be between three parts VI VJ and the + + + align:start position:0% +to be between three parts VI VJ and the +K I J and K they don't have to be + + align:start position:0% +K I J and K they don't have to be + + + align:start position:0% +K I J and K they don't have to be +distinct alright so the argument will be + + align:start position:0% +distinct alright so the argument will be + + + align:start position:0% +distinct alright so the argument will be +okay if some of them are the same what's + + align:start position:0% +okay if some of them are the same what's + + + align:start position:0% +okay if some of them are the same what's +easier to draw if they're all different + + align:start position:0% +easier to draw if they're all different + + + align:start position:0% +easier to draw if they're all different +so I have some triangle like that + + align:start position:0% + + + + align:start position:0% + +because these edges have not yet been + + align:start position:0% +because these edges have not yet been + + + align:start position:0% +because these edges have not yet been +deleted in the cleaning step I know that + + align:start position:0% +deleted in the cleaning step I know that + + + align:start position:0% +deleted in the cleaning step I know that +the vertex sets are not too small the + + align:start position:0% +the vertex sets are not too small the + + + align:start position:0% +the vertex sets are not too small the +edge densities are not too small and + + align:start position:0% +edge densities are not too small and + + + align:start position:0% +edge densities are not too small and +they're all regular with each other so + + align:start position:0% +they're all regular with each other so + + + align:start position:0% +they're all regular with each other so +here each pair VI VJ VK is epsilon over + + align:start position:0% +here each pair VI VJ VK is epsilon over + + + align:start position:0% +here each pair VI VJ VK is epsilon over +for regular and edge density at least + + align:start position:0% +for regular and edge density at least + + + align:start position:0% +for regular and edge density at least +epsilon over 2 and now we apply the + + align:start position:0% +epsilon over 2 and now we apply the + + + align:start position:0% +epsilon over 2 and now we apply the +triangle counting lemma and we find that + + align:start position:0% +triangle counting lemma and we find that + + + align:start position:0% +triangle counting lemma and we find that +the number of triangles with one vertex + + align:start position:0% +the number of triangles with one vertex + + + align:start position:0% +the number of triangles with one vertex +in VI one vertex in V J one vertex in VK + + align:start position:0% +in VI one vertex in V J one vertex in VK + + + align:start position:0% +in VI one vertex in V J one vertex in VK +is at least + + align:start position:0% + + + + align:start position:0% + +this quantity here so that's a + + align:start position:0% +this quantity here so that's a + + + align:start position:0% +this quantity here so that's a +correction factor so one over this to + + align:start position:0% +correction factor so one over this to + + + align:start position:0% +correction factor so one over this to +epsilon and then a bunch of density so + + align:start position:0% +epsilon and then a bunch of density so + + + align:start position:0% +epsilon and then a bunch of density so +densities are not too small so I have at + + align:start position:0% +densities are not too small so I have at + + + align:start position:0% +densities are not too small so I have at +least epsilon over four and cubed + + align:start position:0% +least epsilon over four and cubed + + + align:start position:0% +least epsilon over four and cubed +multiplied by the sizes of the vertex + + align:start position:0% +multiplied by the sizes of the vertex + + + align:start position:0% +multiplied by the sizes of the vertex +sets and now I know that use the fact + + align:start position:0% +sets and now I know that use the fact + + + align:start position:0% +sets and now I know that use the fact +that these part sizes are not too small + + align:start position:0% +that these part sizes are not too small + + + align:start position:0% +that these part sizes are not too small +so just in case if I J and K happen to + + align:start position:0% +so just in case if I J and K happen to + + + align:start position:0% +so just in case if I J and K happen to +be the same or two of them happen to be + + align:start position:0% +be the same or two of them happen to be + + + align:start position:0% +be the same or two of them happen to be +the same I might over count the number + + align:start position:0% +the same I might over count the number + + + align:start position:0% +the same I might over count the number +of triangles a little bit but most you + + align:start position:0% +of triangles a little bit but most you + + + align:start position:0% +of triangles a little bit but most you +overcome by a factor six so so that's + + align:start position:0% +overcome by a factor six so so that's + + + align:start position:0% +overcome by a factor six so so that's +okay so if you're worried about that for + + align:start position:0% +okay so if you're worried about that for + + + align:start position:0% +okay so if you're worried about that for +the one over six factor in just in case + + align:start position:0% + + + + align:start position:0% + +IJ K not distinct or if you like in the + + align:start position:0% +IJ K not distinct or if you like in the + + + align:start position:0% +IJ K not distinct or if you like in the +cleaning step you can if you apply the + + align:start position:0% +cleaning step you can if you apply the + + + align:start position:0% +cleaning step you can if you apply the +equitable version of the regularity + + align:start position:0% +equitable version of the regularity + + + align:start position:0% +equitable version of the regularity +lemma you can also get rid of edges be + + align:start position:0% +lemma you can also get rid of edges be + + + align:start position:0% +lemma you can also get rid of edges be +inside the parts but you know there are + + align:start position:0% +inside the parts but you know there are + + + align:start position:0% +inside the parts but you know there are +many ways to do this it's not an + + align:start position:0% +many ways to do this it's not an + + + align:start position:0% +many ways to do this it's not an +important step okay + + align:start position:0% +important step okay + + + align:start position:0% +important step okay +now this quantity let me set it to be + + align:start position:0% +now this quantity let me set it to be + + + align:start position:0% +now this quantity let me set it to be +Delta you see Delta is a function of + + align:start position:0% +Delta you see Delta is a function of + + + align:start position:0% +Delta you see Delta is a function of +epsilon because M is a function of + + align:start position:0% +epsilon because M is a function of + + + align:start position:0% +epsilon because M is a function of +Epsilon + + align:start position:0% + + + + align:start position:0% + +so now looking back at the statement you + + align:start position:0% +so now looking back at the statement you + + + align:start position:0% +so now looking back at the statement you +see for every epsilon there is the Delta + + align:start position:0% +see for every epsilon there is the Delta + + + align:start position:0% +see for every epsilon there is the Delta +such that if your graph has fewer than + + align:start position:0% + + + + align:start position:0% + +abdel tub and cube triangles so then + + align:start position:0% +abdel tub and cube triangles so then + + + align:start position:0% +abdel tub and cube triangles so then +let me get rid of all the all those + + align:start position:0% +let me get rid of all the all those + + + align:start position:0% +let me get rid of all the all those +edges I've gotten rid of fewer than + + align:start position:0% +edges I've gotten rid of fewer than + + + align:start position:0% +edges I've gotten rid of fewer than +epsilon and squared edges and the + + align:start position:0% +epsilon and squared edges and the + + + align:start position:0% +epsilon and squared edges and the +remaining graph should be triangle free + + align:start position:0% +remaining graph should be triangle free + + + align:start position:0% +remaining graph should be triangle free +because if it were not triangle free + + align:start position:0% +because if it were not triangle free + + + align:start position:0% +because if it were not triangle free +then I can find some triangle and that + + align:start position:0% +then I can find some triangle and that + + + align:start position:0% +then I can find some triangle and that +would lead to a lot more triangles so + + align:start position:0% +would lead to a lot more triangles so + + + align:start position:0% +would lead to a lot more triangles so +for example if you said this as Delta + + align:start position:0% +for example if you said this as Delta + + + align:start position:0% +for example if you said this as Delta +over two then this was give you two + + align:start position:0% +over two then this was give you two + + + align:start position:0% +over two then this was give you two +Delta and cube triangles therefore would + + align:start position:0% +Delta and cube triangles therefore would + + + align:start position:0% +Delta and cube triangles therefore would +contradict the hypothesis and that + + align:start position:0% +contradict the hypothesis and that + + + align:start position:0% +contradict the hypothesis and that +finishes the proof of the triangle + + align:start position:0% +finishes the proof of the triangle + + + align:start position:0% +finishes the proof of the triangle +removal Emma right so it's saying that + + align:start position:0% +removal Emma right so it's saying that + + + align:start position:0% +removal Emma right so it's saying that +thus the resulting graph is triangle + + align:start position:0% +thus the resulting graph is triangle + + + align:start position:0% +thus the resulting graph is triangle +free so that's the proof of the triangle + + align:start position:0% +free so that's the proof of the triangle + + + align:start position:0% +free so that's the proof of the triangle +removal lemma so let me recap we start + + align:start position:0% +removal lemma so let me recap we start + + + align:start position:0% +removal lemma so let me recap we start +with a graph apply some radius + + align:start position:0% +with a graph apply some radius + + + align:start position:0% +with a graph apply some radius +regularity lemma and clean up the + + align:start position:0% +regularity lemma and clean up the + + + align:start position:0% +regularity lemma and clean up the +regularity partition by getting rid of + + align:start position:0% +regularity partition by getting rid of + + + align:start position:0% +regularity partition by getting rid of +low-density pairs getting rid of + + align:start position:0% +low-density pairs getting rid of + + + align:start position:0% +low-density pairs getting rid of +irregular pairs and getting rid of edges + + align:start position:0% +irregular pairs and getting rid of edges + + + align:start position:0% +irregular pairs and getting rid of edges +touching a very small vertex set and I + + align:start position:0% +touching a very small vertex set and I + + + align:start position:0% +touching a very small vertex set and I +claim that the resulting graph after + + align:start position:0% +claim that the resulting graph after + + + align:start position:0% +claim that the resulting graph after +cleaning up should be try and go free + + align:start position:0% +cleaning up should be try and go free + + + align:start position:0% +cleaning up should be try and go free +because if we're not triangle free and I + + align:start position:0% +because if we're not triangle free and I + + + align:start position:0% +because if we're not triangle free and I +find some triangle then I should be able + + align:start position:0% +find some triangle then I should be able + + + align:start position:0% +find some triangle then I should be able +to use that triple of vertex s combined + + align:start position:0% +to use that triple of vertex s combined + + + align:start position:0% +to use that triple of vertex s combined +with a triangle counting lemma to + + align:start position:0% +with a triangle counting lemma to + + + align:start position:0% +with a triangle counting lemma to +produce a lot more triangles and that + + align:start position:0% +produce a lot more triangles and that + + + align:start position:0% +produce a lot more triangles and that +would violate the hypothesis of the + + align:start position:0% +would violate the hypothesis of the + + + align:start position:0% +would violate the hypothesis of the +theorem any questions yep + + align:start position:0% + + + + align:start position:0% + +great so questions where am I using + + align:start position:0% +great so questions where am I using + + + align:start position:0% +great so questions where am I using +there exists a triangle if there were no + + align:start position:0% +there exists a triangle if there were no + + + align:start position:0% +there exists a triangle if there were no +triangles then we're done right so the + + align:start position:0% +triangles then we're done right so the + + + align:start position:0% +triangles then we're done right so the +purpose of the triangle the claim in a + + align:start position:0% +purpose of the triangle the claim in a + + + align:start position:0% +purpose of the triangle the claim in a +triangle removal Emma is that you can + + align:start position:0% +triangle removal Emma is that you can + + + align:start position:0% +triangle removal Emma is that you can +get rid of all triangles by removing a + + align:start position:0% +get rid of all triangles by removing a + + + align:start position:0% +get rid of all triangles by removing a +most epsilon and squared edges so okay + + align:start position:0% +most epsilon and squared edges so okay + + + align:start position:0% +most epsilon and squared edges so okay +let me try to answer your question so + + align:start position:0% +let me try to answer your question so + + + align:start position:0% +let me try to answer your question so +why does this proof show that you still + + align:start position:0% +why does this proof show that you still + + + align:start position:0% +why does this proof show that you still +have Delta and cube triangles so I only + + align:start position:0% +have Delta and cube triangles so I only + + + align:start position:0% +have Delta and cube triangles so I only +set Delta at the end but of course you + + align:start position:0% +set Delta at the end but of course you + + + align:start position:0% +set Delta at the end but of course you +can also set Delta in the beginning of + + align:start position:0% +can also set Delta in the beginning of + + + align:start position:0% +can also set Delta in the beginning of +this proof so I'm saying that you do + + align:start position:0% +this proof so I'm saying that you do + + + align:start position:0% +this proof so I'm saying that you do +this step you get rid of epsilon and + + align:start position:0% +this step you get rid of epsilon and + + + align:start position:0% +this step you get rid of epsilon and +squared edges and now I claim after this + + align:start position:0% +squared edges and now I claim after this + + + align:start position:0% +squared edges and now I claim after this +step so I claimed the remaining graph is + + align:start position:0% +step so I claimed the remaining graph is + + + align:start position:0% +step so I claimed the remaining graph is +triangle free if you were not triangle + + align:start position:0% +triangle free if you were not triangle + + + align:start position:0% +triangle free if you were not triangle +free then well have some triangle then + + align:start position:0% +free then well have some triangle then + + + align:start position:0% +free then well have some triangle then +the triangle counting lemma would tell + + align:start position:0% +the triangle counting lemma would tell + + + align:start position:0% +the triangle counting lemma would tell +me there are lots of triangles and that + + align:start position:0% +me there are lots of triangles and that + + + align:start position:0% +me there are lots of triangles and that +would contradict the hypothesis where we + + align:start position:0% +would contradict the hypothesis where we + + + align:start position:0% +would contradict the hypothesis where we +assume that this graph G has a small + + align:start position:0% +assume that this graph G has a small + + + align:start position:0% +assume that this graph G has a small +number of triangles + + align:start position:0% + + + + align:start position:0% + +that's right + + align:start position:0% +that's right + + + align:start position:0% +that's right +so you're saying if you do not have any + + align:start position:0% +so you're saying if you do not have any + + + align:start position:0% +so you're saying if you do not have any +triangles well after the cleaning step + + align:start position:0% +triangles well after the cleaning step + + + align:start position:0% +triangles well after the cleaning step +we have gone rid of all the edges + + align:start position:0% +we have gone rid of all the edges + + + align:start position:0% +we have gone rid of all the edges +between the bad pears and I'm claiming + + align:start position:0% +between the bad pears and I'm claiming + + + align:start position:0% +between the bad pears and I'm claiming +that there is no configuration like this + + align:start position:0% +that there is no configuration like this + + + align:start position:0% +that there is no configuration like this +left and this is the proof right because + + align:start position:0% +left and this is the proof right because + + + align:start position:0% +left and this is the proof right because +if you have some configuration where you + + align:start position:0% +if you have some configuration where you + + + align:start position:0% +if you have some configuration where you +did not delete the edges between these + + align:start position:0% +did not delete the edges between these + + + align:start position:0% +did not delete the edges between these +three parts then you should be able to + + align:start position:0% +three parts then you should be able to + + + align:start position:0% +three parts then you should be able to +get a lot more triangles from the + + align:start position:0% +get a lot more triangles from the + + + align:start position:0% +get a lot more triangles from the +triangle counting lemma you're asking + + align:start position:0% +triangle counting lemma you're asking + + + align:start position:0% +triangle counting lemma you're asking +what happens if there were lots of + + align:start position:0% +what happens if there were lots of + + + align:start position:0% +what happens if there were lots of +triangles inside each VI VJ BK so that + + align:start position:0% +triangles inside each VI VJ BK so that + + + align:start position:0% +triangles inside each VI VJ BK so that +is fine if you find some triangle so + + align:start position:0% +is fine if you find some triangle so + + + align:start position:0% +is fine if you find some triangle so +this picture I J or K they do not have + + align:start position:0% +this picture I J or K they do not have + + + align:start position:0% +this picture I J or K they do not have +to be distinct all right so the same + + align:start position:0% +to be distinct all right so the same + + + align:start position:0% +to be distinct all right so the same +proof works if I J and K some of them + + align:start position:0% +proof works if I J and K some of them + + + align:start position:0% +proof works if I J and K some of them +are equal to each other yeah + + align:start position:0% + + + + align:start position:0% + +so okay you're asking why did I put a + + align:start position:0% +so okay you're asking why did I put a + + + align:start position:0% +so okay you're asking why did I put a +Delta over two just because I for less + + align:start position:0% +Delta over two just because I for less + + + align:start position:0% +Delta over two just because I for less +than or equal to Delta if I put strictly + + align:start position:0% +than or equal to Delta if I put strictly + + + align:start position:0% +than or equal to Delta if I put strictly +less than Delta and I don't need a Delta + + align:start position:0% +less than Delta and I don't need a Delta + + + align:start position:0% +less than Delta and I don't need a Delta +over two okay don't worry about it yes + + align:start position:0% + + + + align:start position:0% + +okay you're asking it's your way to + + align:start position:0% +okay you're asking it's your way to + + + align:start position:0% +okay you're asking it's your way to +generalize the triangle counting lemma + + align:start position:0% +generalize the triangle counting lemma + + + align:start position:0% +generalize the triangle counting lemma +to a general graph so yes we will see + + align:start position:0% +to a general graph so yes we will see + + + align:start position:0% +to a general graph so yes we will see +that not today but I think next time + + align:start position:0% + + + + align:start position:0% + +okay more questions great so why do + + align:start position:0% +okay more questions great so why do + + + align:start position:0% +okay more questions great so why do +people care about the triangle removal + + align:start position:0% +people care about the triangle removal + + + align:start position:0% +people care about the triangle removal +lemma okay so it's a nice maybe somewhat + + align:start position:0% +lemma okay so it's a nice maybe somewhat + + + align:start position:0% +lemma okay so it's a nice maybe somewhat +unintuitive statement but there was a + + align:start position:0% +unintuitive statement but there was a + + + align:start position:0% +unintuitive statement but there was a +very good reason why the statement was + + align:start position:0% +very good reason why the statement was + + + align:start position:0% +very good reason why the statement was +formulated and it's because you can use + + align:start position:0% +formulated and it's because you can use + + + align:start position:0% +formulated and it's because you can use +it to prove Ross theorem so that's what + + align:start position:0% +it to prove Ross theorem so that's what + + + align:start position:0% +it to prove Ross theorem so that's what +I want to explain how to connect this + + align:start position:0% +I want to explain how to connect this + + + align:start position:0% +I want to explain how to connect this +graph theoretic statement to a statement + + align:start position:0% +graph theoretic statement to a statement + + + align:start position:0% +graph theoretic statement to a statement +about three-term a p3 a p3 subsets of + + align:start position:0% +about three-term a p3 a p3 subsets of + + + align:start position:0% +about three-term a p3 a p3 subsets of +integers and this goes back to the very + + align:start position:0% +integers and this goes back to the very + + + align:start position:0% +integers and this goes back to the very +connection between graph theory and + + align:start position:0% +connection between graph theory and + + + align:start position:0% +connection between graph theory and +additive combinatorics that I + + align:start position:0% +additive combinatorics that I + + + align:start position:0% +additive combinatorics that I +highlighted in the first lecture first + + align:start position:0% +highlighted in the first lecture first + + + align:start position:0% +highlighted in the first lecture first +let me state a corollary of the triangle + + align:start position:0% +let me state a corollary of the triangle + + + align:start position:0% +let me state a corollary of the triangle +removal mmm namely that if you have an N + + align:start position:0% +removal mmm namely that if you have an N + + + align:start position:0% +removal mmm namely that if you have an N +vertex graph G where so if so if G and + + align:start position:0% +vertex graph G where so if so if G and + + + align:start position:0% +vertex graph G where so if so if G and +vertex and every edge is in exactly one + + align:start position:0% +vertex and every edge is in exactly one + + + align:start position:0% +vertex and every edge is in exactly one +triangle + + align:start position:0% + + + + align:start position:0% + +then the number of edges of G is little + + align:start position:0% +then the number of edges of G is little + + + align:start position:0% +then the number of edges of G is little +o of N squared these are actually kind + + align:start position:0% +o of N squared these are actually kind + + + align:start position:0% +o of N squared these are actually kind +of strange graphs every edge isn't + + align:start position:0% +of strange graphs every edge isn't + + + align:start position:0% +of strange graphs every edge isn't +exactly one triangle okay + + align:start position:0% + + + + align:start position:0% + +well the number of triangles in G every + + align:start position:0% +well the number of triangles in G every + + + align:start position:0% +well the number of triangles in G every +edge is in exactly one triangle so the + + align:start position:0% +edge is in exactly one triangle so the + + + align:start position:0% +edge is in exactly one triangle so the +number of triangles in G is a number of + + align:start position:0% +number of triangles in G is a number of + + + align:start position:0% +number of triangles in G is a number of +edges divided by three the number of + + align:start position:0% +edges divided by three the number of + + + align:start position:0% +edges divided by three the number of +edges is at most n squared so this + + align:start position:0% +edges is at most n squared so this + + + align:start position:0% +edges is at most n squared so this +quantity is a most quadratic water which + + align:start position:0% +quantity is a most quadratic water which + + + align:start position:0% +quantity is a most quadratic water which +in particular is little Olaf n cubed and + + align:start position:0% +in particular is little Olaf n cubed and + + + align:start position:0% +in particular is little Olaf n cubed and +thus the triangle removal mo tells us + + align:start position:0% +thus the triangle removal mo tells us + + + align:start position:0% +thus the triangle removal mo tells us +that G can be made triangle free by + + align:start position:0% +that G can be made triangle free by + + + align:start position:0% +that G can be made triangle free by +removing little o of N squared edges + + align:start position:0% + + + + align:start position:0% + +on the other hand since every edge is in + + align:start position:0% +on the other hand since every edge is in + + + align:start position:0% +on the other hand since every edge is in +exactly one triangle for how many edges + + align:start position:0% +exactly one triangle for how many edges + + + align:start position:0% +exactly one triangle for how many edges +do you need to remove to get rid of all + + align:start position:0% +do you need to remove to get rid of all + + + align:start position:0% +do you need to remove to get rid of all +the triangles I need to remove at least + + align:start position:0% +the triangles I need to remove at least + + + align:start position:0% +the triangles I need to remove at least +1/3 of the edges need to remove at least + + align:start position:0% +1/3 of the edges need to remove at least + + + align:start position:0% +1/3 of the edges need to remove at least +1/3 of edges to make G triangle free by + + align:start position:0% +1/3 of edges to make G triangle free by + + + align:start position:0% +1/3 of edges to make G triangle free by +putting these two claims together we see + + align:start position:0% +putting these two claims together we see + + + align:start position:0% +putting these two claims together we see +that the number of edges of G must be + + align:start position:0% +that the number of edges of G must be + + + align:start position:0% +that the number of edges of G must be +little off N squared any questions yep + + align:start position:0% + + + + align:start position:0% + +great questions are there not more + + align:start position:0% +great questions are there not more + + + align:start position:0% +great questions are there not more +elementary ways to prove this let me + + align:start position:0% +elementary ways to prove this let me + + + align:start position:0% +elementary ways to prove this let me +make some comments about that the short + + align:start position:0% +make some comments about that the short + + + align:start position:0% +make some comments about that the short +answer is yes but not really and really + + align:start position:0% +answer is yes but not really and really + + + align:start position:0% +answer is yes but not really and really +the answer's no so you can ask what + + align:start position:0% +the answer's no so you can ask what + + + align:start position:0% +the answer's no so you can ask what +about quantitative pounds because you + + align:start position:0% +about quantitative pounds because you + + + align:start position:0% +about quantitative pounds because you +know what is more elementary well it's + + align:start position:0% +know what is more elementary well it's + + + align:start position:0% +know what is more elementary well it's +less elementary it's kind of subjective + + align:start position:0% +less elementary it's kind of subjective + + + align:start position:0% +less elementary it's kind of subjective +but quantitative pounds you know + + align:start position:0% +but quantitative pounds you know + + + align:start position:0% +but quantitative pounds you know +something that is very concrete is hard + + align:start position:0% +something that is very concrete is hard + + + align:start position:0% +something that is very concrete is hard +to argue so if you look at the triangle + + align:start position:0% +to argue so if you look at the triangle + + + align:start position:0% +to argue so if you look at the triangle +removal mmm you can ask how is the + + align:start position:0% +removal mmm you can ask how is the + + + align:start position:0% +removal mmm you can ask how is the +dependence of Delta on Epsilon + + align:start position:0% +dependence of Delta on Epsilon + + + align:start position:0% +dependence of Delta on Epsilon +okay so what does the proof give you + + align:start position:0% +okay so what does the proof give you + + + align:start position:0% +okay so what does the proof give you +where's the bottleneck bottleneck is + + align:start position:0% +where's the bottleneck bottleneck is + + + align:start position:0% +where's the bottleneck bottleneck is +Oasis in the apply application of + + align:start position:0% +Oasis in the apply application of + + + align:start position:0% +Oasis in the apply application of +similarities regularity lemma namely in + + align:start position:0% +similarities regularity lemma namely in + + + align:start position:0% +similarities regularity lemma namely in +this M so none of the other epsilon is + + align:start position:0% +this M so none of the other epsilon is + + + align:start position:0% +this M so none of the other epsilon is +really matter is this M that kills you + + align:start position:0% +really matter is this M that kills you + + + align:start position:0% +really matter is this M that kills you +in terms of quantitative doubts + + align:start position:0% +in terms of quantitative doubts + + + align:start position:0% +in terms of quantitative doubts +so in triangle removal Emma there's + + align:start position:0% +so in triangle removal Emma there's + + + align:start position:0% +so in triangle removal Emma there's +proof gifts 1 over Delta also you can + + align:start position:0% +proof gifts 1 over Delta also you can + + + align:start position:0% +proof gifts 1 over Delta also you can +take 1 over Delta being a power of twos + + align:start position:0% +take 1 over Delta being a power of twos + + + align:start position:0% +take 1 over Delta being a power of twos +of height and most + + align:start position:0% + + + + align:start position:0% + +polynomial in one over epsilon is you're + + align:start position:0% +polynomial in one over epsilon is you're + + + align:start position:0% +polynomial in one over epsilon is you're +a different proof but the best-known + + align:start position:0% +a different proof but the best-known + + + align:start position:0% +a different proof but the best-known +bound so due to Fox is that you can + + align:start position:0% +bound so due to Fox is that you can + + + align:start position:0% +bound so due to Fox is that you can +replace this this height by a different + + align:start position:0% +replace this this height by a different + + + align:start position:0% +replace this this height by a different +height that is a most essentially + + align:start position:0% +height that is a most essentially + + + align:start position:0% +height that is a most essentially +logarithmic in one over epsilon it's + + align:start position:0% +logarithmic in one over epsilon it's + + + align:start position:0% +logarithmic in one over epsilon it's +still a power of two's so we've changed + + align:start position:0% +still a power of two's so we've changed + + + align:start position:0% +still a power of two's so we've changed +some really big number to another purse + + align:start position:0% +some really big number to another purse + + + align:start position:0% +some really big number to another purse +lightly smaller really big number okay + + align:start position:0% +lightly smaller really big number okay + + + align:start position:0% +lightly smaller really big number okay +so this is still an astronomical number + + align:start position:0% +so this is still an astronomical number + + + align:start position:0% +so this is still an astronomical number +for any reasonable epsilon and in terms + + align:start position:0% +for any reasonable epsilon and in terms + + + align:start position:0% +for any reasonable epsilon and in terms +of that corollary basically the only + + align:start position:0% +of that corollary basically the only + + + align:start position:0% +of that corollary basically the only +known proof goes through the triangle + + align:start position:0% +known proof goes through the triangle + + + align:start position:0% +known proof goes through the triangle +removal Emma currently we do not know + + align:start position:0% +removal Emma currently we do not know + + + align:start position:0% +removal Emma currently we do not know +any other approach to this problem and + + align:start position:0% +any other approach to this problem and + + + align:start position:0% +any other approach to this problem and +you'll see later on that well what about + + align:start position:0% +you'll see later on that well what about + + + align:start position:0% +you'll see later on that well what about +you know what's the best thing that we + + align:start position:0% +you know what's the best thing that we + + + align:start position:0% +you know what's the best thing that we +can hope for so it is quite possible + + align:start position:0% +can hope for so it is quite possible + + + align:start position:0% +can hope for so it is quite possible +that there are other proofs that are yet + + align:start position:0% +that there are other proofs that are yet + + + align:start position:0% +that there are other proofs that are yet +to be found + + align:start position:0% +to be found + + + align:start position:0% +to be found +so that's actually no people believe + + align:start position:0% +so that's actually no people believe + + + align:start position:0% +so that's actually no people believe +this that this is not the right proof + + align:start position:0% +this that this is not the right proof + + + align:start position:0% +this that this is not the right proof +that maybe there's some other way to do + + align:start position:0% +that maybe there's some other way to do + + + align:start position:0% +that maybe there's some other way to do +this and the best lower bound which + + align:start position:0% +this and the best lower bound which + + + align:start position:0% +this and the best lower bound which +we'll see either later today or next + + align:start position:0% +we'll see either later today or next + + + align:start position:0% +we'll see either later today or next +time shows that we cannot do better than + + align:start position:0% + + + + align:start position:0% + +one over epsilon being essentially just + + align:start position:0% +one over epsilon being essentially just + + + align:start position:0% +one over epsilon being essentially just +a little bit more than polynomial in + + align:start position:0% +a little bit more than polynomial in + + + align:start position:0% +a little bit more than polynomial in +epsilon so epsilon raised to something + + align:start position:0% +epsilon so epsilon raised to something + + + align:start position:0% +epsilon so epsilon raised to something +that is logarithmic in one over epsilon + + align:start position:0% +that is logarithmic in one over epsilon + + + align:start position:0% +that is logarithmic in one over epsilon +so you can think of this as very not + + align:start position:0% +so you can think of this as very not + + + align:start position:0% +so you can think of this as very not +it's a little bit bigger than polynomial + + align:start position:0% +it's a little bit bigger than polynomial + + + align:start position:0% +it's a little bit bigger than polynomial +in one over epsilon but not that much + + align:start position:0% +in one over epsilon but not that much + + + align:start position:0% +in one over epsilon but not that much +bigger than polynomial one over epsilon + + align:start position:0% +bigger than polynomial one over epsilon + + + align:start position:0% +bigger than polynomial one over epsilon +so there's a very big gap in our + + align:start position:0% +so there's a very big gap in our + + + align:start position:0% +so there's a very big gap in our +knowledge on what is the right + + align:start position:0% +knowledge on what is the right + + + align:start position:0% +knowledge on what is the right +dependence between epsilon and delta in + + align:start position:0% +dependence between epsilon and delta in + + + align:start position:0% +dependence between epsilon and delta in +the triangle removal lemma and that's + + align:start position:0% +the triangle removal lemma and that's + + + align:start position:0% +the triangle removal lemma and that's +one of the it's a major open + + align:start position:0% +one of the it's a major open + + + align:start position:0% +one of the it's a major open +from in extremal combinatorics to close + + align:start position:0% +from in extremal combinatorics to close + + + align:start position:0% +from in extremal combinatorics to close +this gap other questions all right + + align:start position:0% +this gap other questions all right + + + align:start position:0% +this gap other questions all right +so let's prove Ross theorem so let me + + align:start position:0% +so let's prove Ross theorem so let me + + + align:start position:0% +so let's prove Ross theorem so let me +remind you that Roth's theorem which we + + align:start position:0% +remind you that Roth's theorem which we + + + align:start position:0% +remind you that Roth's theorem which we +saw in the very first lecture says that + + align:start position:0% +saw in the very first lecture says that + + + align:start position:0% +saw in the very first lecture says that +if you have a subset of 1 to n that is + + align:start position:0% +if you have a subset of 1 to n that is + + + align:start position:0% +if you have a subset of 1 to n that is +free of 3 term arithmetic progressions + + align:start position:0% + + + + align:start position:0% + +then the size of the set must be + + align:start position:0% +then the size of the set must be + + + align:start position:0% +then the size of the set must be +suppling you alright so what does this + + align:start position:0% +suppling you alright so what does this + + + align:start position:0% +suppling you alright so what does this +have to do with the triangle removal mmm + + align:start position:0% +have to do with the triangle removal mmm + + + align:start position:0% +have to do with the triangle removal mmm +if you remember the first lecture maybe + + align:start position:0% +if you remember the first lecture maybe + + + align:start position:0% +if you remember the first lecture maybe +the connection shouldn't be so + + align:start position:0% +the connection shouldn't be so + + + align:start position:0% +the connection shouldn't be so +surprising what we will do is that we + + align:start position:0% +surprising what we will do is that we + + + align:start position:0% +surprising what we will do is that we +will set up a graph such that you know + + align:start position:0% +will set up a graph such that you know + + + align:start position:0% +will set up a graph such that you know +starting from some arithmetic set such + + align:start position:0% +starting from some arithmetic set such + + + align:start position:0% +starting from some arithmetic set such +that the graph encodes some arithmetic + + align:start position:0% +that the graph encodes some arithmetic + + + align:start position:0% +that the graph encodes some arithmetic +information in particular the three-term + + align:start position:0% +information in particular the three-term + + + align:start position:0% +information in particular the three-term +a piece in your graph in the set + + align:start position:0% +a piece in your graph in the set + + + align:start position:0% +a piece in your graph in the set +correspond to the triangles in the graph + + align:start position:0% +correspond to the triangles in the graph + + + align:start position:0% +correspond to the triangles in the graph +ok so let's set up this graph it will be + + align:start position:0% +ok so let's set up this graph it will be + + + align:start position:0% +ok so let's set up this graph it will be +helpful to view a knot as a subset of + + align:start position:0% +helpful to view a knot as a subset of + + + align:start position:0% +helpful to view a knot as a subset of +the integers it will just be more + + align:start position:0% +the integers it will just be more + + + align:start position:0% +the integers it will just be more +convenient to view it as a subset of a + + align:start position:0% +convenient to view it as a subset of a + + + align:start position:0% +convenient to view it as a subset of a +cyclic group this more yeah I don't have + + align:start position:0% +cyclic group this more yeah I don't have + + + align:start position:0% +cyclic group this more yeah I don't have +to worry about education so much when + + align:start position:0% +to worry about education so much when + + + align:start position:0% +to worry about education so much when +you're working a cyclic group yeah I + + align:start position:0% +you're working a cyclic group yeah I + + + align:start position:0% +you're working a cyclic group yeah I +take m to be 2 n plus 1 so having it odd + + align:start position:0% +take m to be 2 n plus 1 so having it odd + + + align:start position:0% +take m to be 2 n plus 1 so having it odd +makes my life a bit simpler then if a is + + align:start position:0% +makes my life a bit simpler then if a is + + + align:start position:0% +makes my life a bit simpler then if a is +3 AP free subset of 1 to n then I claim + + align:start position:0% +3 AP free subset of 1 to n then I claim + + + align:start position:0% +3 AP free subset of 1 to n then I claim +that a now sitting inside the cyclic + + align:start position:0% +that a now sitting inside the cyclic + + + align:start position:0% +that a now sitting inside the cyclic +group is also 3 AP 3 so the subset of + + align:start position:0% + + + + align:start position:0% + +and what we will do is that we will set + + align:start position:0% +and what we will do is that we will set + + + align:start position:0% +and what we will do is that we will set +up a certain graph so we will set up a + + align:start position:0% +up a certain graph so we will set up a + + + align:start position:0% +up a certain graph so we will set up a +tripartite graph X Y Z and here XY and z + + align:start position:0% +tripartite graph X Y Z and here XY and z + + + align:start position:0% +tripartite graph X Y Z and here XY and z +are going to be M elements whose + + align:start position:0% +are going to be M elements whose + + + align:start position:0% +are going to be M elements whose +vertices are represented by elements of + + align:start position:0% +vertices are represented by elements of + + + align:start position:0% +vertices are represented by elements of +Z mod M and then I need to tell you what + + align:start position:0% +Z mod M and then I need to tell you what + + + align:start position:0% +Z mod M and then I need to tell you what +are the edges of this graph so here are + + align:start position:0% +are the edges of this graph so here are + + + align:start position:0% +are the edges of this graph so here are +the edges by putting an edge between + + align:start position:0% +the edges by putting an edge between + + + align:start position:0% +the edges by putting an edge between +vertex x and y if and only if Y minus X + + align:start position:0% +vertex x and y if and only if Y minus X + + + align:start position:0% +vertex x and y if and only if Y minus X +is an element of a so just it's a rule + + align:start position:0% +is an element of a so just it's a rule + + + align:start position:0% +is an element of a so just it's a rule +for put how to putting the edges and + + align:start position:0% +for put how to putting the edges and + + + align:start position:0% +for put how to putting the edges and +this is basically a KD graph by + + align:start position:0% +this is basically a KD graph by + + + align:start position:0% +this is basically a KD graph by +bipartite variant of a KD graph likewise + + align:start position:0% +bipartite variant of a KD graph likewise + + + align:start position:0% +bipartite variant of a KD graph likewise +I put in the edge between X and Z so + + align:start position:0% +I put in the edge between X and Z so + + + align:start position:0% +I put in the edge between X and Z so +actually let me put X down here and Y up + + align:start position:0% +actually let me put X down here and Y up + + + align:start position:0% +actually let me put X down here and Y up +there so let me put in an edge between y + + align:start position:0% +there so let me put in an edge between y + + + align:start position:0% +there so let me put in an edge between y +and z if I know me if y minus Z minus y + + align:start position:0% +and z if I know me if y minus Z minus y + + + align:start position:0% +and z if I know me if y minus Z minus y +is an element of a and for the very last + + align:start position:0% +is an element of a and for the very last + + + align:start position:0% +is an element of a and for the very last +pair so it's similar but slightly + + align:start position:0% +pair so it's similar but slightly + + + align:start position:0% +pair so it's similar but slightly +different by putting that edge if and + + align:start position:0% +different by putting that edge if and + + + align:start position:0% +different by putting that edge if and +only if Z minus X divided by 2 it's an + + align:start position:0% +only if Z minus X divided by 2 it's an + + + align:start position:0% +only if Z minus X divided by 2 it's an +element of a so because we're in an odd + + align:start position:0% +element of a so because we're in an odd + + + align:start position:0% +element of a so because we're in an odd +cyclic group I can divide by 2 okay so + + align:start position:0% +cyclic group I can divide by 2 okay so + + + align:start position:0% +cyclic group I can divide by 2 okay so +this is a graph right so starting with a + + align:start position:0% +this is a graph right so starting with a + + + align:start position:0% +this is a graph right so starting with a +set a I give you this rule for + + align:start position:0% +set a I give you this rule for + + + align:start position:0% +set a I give you this rule for +constructing this tripartite graph and + + align:start position:0% +constructing this tripartite graph and + + + align:start position:0% +constructing this tripartite graph and +the question now is what are the + + align:start position:0% +the question now is what are the + + + align:start position:0% +the question now is what are the +triangles in this graph if the vertices + + align:start position:0% +triangles in this graph if the vertices + + + align:start position:0% +triangles in this graph if the vertices +X Y Z is a triangle + + align:start position:0% + + + + align:start position:0% + +then these three numbers by definition + + align:start position:0% +then these three numbers by definition + + + align:start position:0% +then these three numbers by definition +because of the edges because they're all + + align:start position:0% +because of the edges because they're all + + + align:start position:0% +because of the edges because they're all +edges in this graph these three numbers + + align:start position:0% +edges in this graph these three numbers + + + align:start position:0% +edges in this graph these three numbers +they all lie in a but now notice that + + align:start position:0% +they all lie in a but now notice that + + + align:start position:0% +they all lie in a but now notice that +these three numbers they form a three + + align:start position:0% +these three numbers they form a three + + + align:start position:0% +these three numbers they form a three +term arithmetic progression because the + + align:start position:0% +term arithmetic progression because the + + + align:start position:0% +term arithmetic progression because the +middle element is the average of the two + + align:start position:0% +middle element is the average of the two + + + align:start position:0% +middle element is the average of the two +others okay but we said that a is a set + + align:start position:0% +others okay but we said that a is a set + + + align:start position:0% +others okay but we said that a is a set +that is three AP three has no three term + + align:start position:0% +that is three AP three has no three term + + + align:start position:0% +that is three AP three has no three term +arithmetic progression so so what must + + align:start position:0% +arithmetic progression so so what must + + + align:start position:0% +arithmetic progression so so what must +be the case so a is three AP free but + + align:start position:0% +be the case so a is three AP free but + + + align:start position:0% +be the case so a is three AP free but +you can still have three a piece using + + align:start position:0% +you can still have three a piece using + + + align:start position:0% +you can still have three a piece using +the same element three times so all the + + align:start position:0% +the same element three times so all the + + + align:start position:0% +the same element three times so all the +three term are automatic progressions + + align:start position:0% +three term are automatic progressions + + + align:start position:0% +three term are automatic progressions +must be of that form so these three + + align:start position:0% +must be of that form so these three + + + align:start position:0% +must be of that form so these three +numbers must then equal to each other in + + align:start position:0% +numbers must then equal to each other in + + + align:start position:0% +numbers must then equal to each other in +particular you see that if you select x + + align:start position:0% +particular you see that if you select x + + + align:start position:0% +particular you see that if you select x +and y it determines e and this equality + + align:start position:0% +and y it determines e and this equality + + + align:start position:0% +and y it determines e and this equality +here is the same as saying that x y&z + + align:start position:0% +here is the same as saying that x y&z + + + align:start position:0% +here is the same as saying that x y&z +they themselves form a three AP in gmod + + align:start position:0% +they themselves form a three AP in gmod + + + align:start position:0% +they themselves form a three AP in gmod +MZ okay so this is precisely the + + align:start position:0% +MZ okay so this is precisely the + + + align:start position:0% +MZ okay so this is precisely the +description of all the triangles in the + + align:start position:0% +description of all the triangles in the + + + align:start position:0% +description of all the triangles in the +graph + + align:start position:0% + + + + align:start position:0% + +okay so all the triangles in the graph G + + align:start position:0% +okay so all the triangles in the graph G + + + align:start position:0% +okay so all the triangles in the graph G +are precisely XYZ where x y and z form a + + align:start position:0% +are precisely XYZ where x y and z form a + + + align:start position:0% +are precisely XYZ where x y and z form a +three term arithmetic progression and in + + align:start position:0% +three term arithmetic progression and in + + + align:start position:0% +three term arithmetic progression and in +particular every edge of G lies in + + align:start position:0% +particular every edge of G lies in + + + align:start position:0% +particular every edge of G lies in +exactly one triangle you give me an edge + + align:start position:0% +exactly one triangle you give me an edge + + + align:start position:0% +exactly one triangle you give me an edge +for example X Y I complete it to a 3 AP + + align:start position:0% +for example X Y I complete it to a 3 AP + + + align:start position:0% +for example X Y I complete it to a 3 AP +XYZ and that's the triangle and that's + + align:start position:0% +XYZ and that's the triangle and that's + + + align:start position:0% +XYZ and that's the triangle and that's +the unique triangle at the edge system + + align:start position:0% +the unique triangle at the edge system + + + align:start position:0% +the unique triangle at the edge system +and likewise if you give me X Z or Y Z I + + align:start position:0% +and likewise if you give me X Z or Y Z I + + + align:start position:0% +and likewise if you give me X Z or Y Z I +can produce for you a unique triangle + + align:start position:0% +can produce for you a unique triangle + + + align:start position:0% +can produce for you a unique triangle +okay so we have this graph it has this + + align:start position:0% +okay so we have this graph it has this + + + align:start position:0% +okay so we have this graph it has this +property that every edge lies in exactly + + align:start position:0% +property that every edge lies in exactly + + + align:start position:0% +property that every edge lies in exactly +one triangle so we can apply the + + align:start position:0% +one triangle so we can apply the + + + align:start position:0% +one triangle so we can apply the +corollary up there to deduce a bound on + + align:start position:0% +corollary up there to deduce a bound on + + + align:start position:0% +corollary up there to deduce a bound on +the total number of edges + + align:start position:0% +the total number of edges + + + align:start position:0% +the total number of edges +well how many edges are there on one + + align:start position:0% +well how many edges are there on one + + + align:start position:0% +well how many edges are there on one +hand we see that because it's a Cayley + + align:start position:0% +hand we see that because it's a Cayley + + + align:start position:0% +hand we see that because it's a Cayley +graph each of the three parts there are + + align:start position:0% +graph each of the three parts there are + + + align:start position:0% +graph each of the three parts there are +three parts here each of the three parts + + align:start position:0% +three parts here each of the three parts + + + align:start position:0% +three parts here each of the three parts +if I start with any vertex I have a + + align:start position:0% +if I start with any vertex I have a + + + align:start position:0% +if I start with any vertex I have a +edges coming out of that vertex to the + + align:start position:0% +edges coming out of that vertex to the + + + align:start position:0% +edges coming out of that vertex to the +next part by the construction on the + + align:start position:0% +next part by the construction on the + + + align:start position:0% +next part by the construction on the +other hand by the corollary up there the + + align:start position:0% +other hand by the corollary up there the + + + align:start position:0% +other hand by the corollary up there the +number of edges has to be little all of + + align:start position:0% +number of edges has to be little all of + + + align:start position:0% +number of edges has to be little all of +em squared and because M is essentially + + align:start position:0% +em squared and because M is essentially + + + align:start position:0% +em squared and because M is essentially +twice and we obtained that the size of a + + align:start position:0% +twice and we obtained that the size of a + + + align:start position:0% +twice and we obtained that the size of a +is little all of em and that proves Ross + + align:start position:0% +is little all of em and that proves Ross + + + align:start position:0% +is little all of em and that proves Ross +theorem + + align:start position:0% + + + + align:start position:0% + +okay so question is why is every edge in + + align:start position:0% +okay so question is why is every edge in + + + align:start position:0% +okay so question is why is every edge in +exactly one triangle so you know what + + align:start position:0% +exactly one triangle so you know what + + + align:start position:0% +exactly one triangle so you know what +all the edges are so this is a + + align:start position:0% +all the edges are so this is a + + + align:start position:0% +all the edges are so this is a +description of what all the edges are + + align:start position:0% +description of what all the edges are + + + align:start position:0% +description of what all the edges are +and what are all the triangles XYZ is a + + align:start position:0% +and what are all the triangles XYZ is a + + + align:start position:0% +and what are all the triangles XYZ is a +triangle + + align:start position:0% +triangle + + + align:start position:0% +triangle +precisely when these three expressions + + align:start position:0% +precisely when these three expressions + + + align:start position:0% +precisely when these three expressions +all line a but notice that these three + + align:start position:0% +all line a but notice that these three + + + align:start position:0% +all line a but notice that these three +expressions they form a three AP because + + align:start position:0% +expressions they form a three AP because + + + align:start position:0% +expressions they form a three AP because +the middle term is the average of the + + align:start position:0% +the middle term is the average of the + + + align:start position:0% +the middle term is the average of the +two others so XYZ it's a triangle if and + + align:start position:0% +two others so XYZ it's a triangle if and + + + align:start position:0% +two others so XYZ it's a triangle if and +only if this equation is true and this + + align:start position:0% +only if this equation is true and this + + + align:start position:0% +only if this equation is true and this +equation is true if and only if X Y Z + + align:start position:0% +equation is true if and only if X Y Z + + + align:start position:0% +equation is true if and only if X Y Z +form as 3 AP in Z mod M so if you just + + align:start position:0% +form as 3 AP in Z mod M so if you just + + + align:start position:0% +form as 3 AP in Z mod M so if you just +read out this equation I have to give + + align:start position:0% +read out this equation I have to give + + + align:start position:0% +read out this equation I have to give +you x and y right so what is Z odds so + + align:start position:0% +you x and y right so what is Z odds so + + + align:start position:0% +you x and y right so what is Z odds so +all the triangles in XYZ are precisely + + align:start position:0% +all the triangles in XYZ are precisely + + + align:start position:0% +all the triangles in XYZ are precisely +given by 3 ApS where one of the + + align:start position:0% +given by 3 ApS where one of the + + + align:start position:0% +given by 3 ApS where one of the +difference is y minus x facing a ok so I + + align:start position:0% +difference is y minus x facing a ok so I + + + align:start position:0% +difference is y minus x facing a ok so I +give you an edge for example X Y such + + align:start position:0% +give you an edge for example X Y such + + + align:start position:0% +give you an edge for example X Y such +that Y minus X facing ape and I claim + + align:start position:0% +that Y minus X facing ape and I claim + + + align:start position:0% +that Y minus X facing ape and I claim +there's a unique Z that completes this + + align:start position:0% +there's a unique Z that completes this + + + align:start position:0% +there's a unique Z that completes this +edge to a triangle and it tells you what + + align:start position:0% +edge to a triangle and it tells you what + + + align:start position:0% +edge to a triangle and it tells you what +that Z is Z has to be the element in Z + + align:start position:0% +that Z is Z has to be the element in Z + + + align:start position:0% +that Z is Z has to be the element in Z +mod M that completes x and y 2 a 3 AP + + align:start position:0% +mod M that completes x and y 2 a 3 AP + + + align:start position:0% +mod M that completes x and y 2 a 3 AP +namely Z is the solution to this + + align:start position:0% +namely Z is the solution to this + + + align:start position:0% +namely Z is the solution to this +equation right there no other Z can work + + align:start position:0% +equation right there no other Z can work + + + align:start position:0% +equation right there no other Z can work +and you can check that Z indeed works in + + align:start position:0% +and you can check that Z indeed works in + + + align:start position:0% +and you can check that Z indeed works in +that all the remaining pairs are edges + + align:start position:0% + + + + align:start position:0% + +so it's something you can check + + align:start position:0% + + + + align:start position:0% + +any more questions alright so starting + + align:start position:0% +any more questions alright so starting + + + align:start position:0% +any more questions alright so starting +with the set a that is three AP free we + + align:start position:0% +with the set a that is three AP free we + + + align:start position:0% +with the set a that is three AP free we +set up this graph with a property that + + align:start position:0% +set up this graph with a property that + + + align:start position:0% +set up this graph with a property that +every edge lies in exactly one triangle + + align:start position:0% +every edge lies in exactly one triangle + + + align:start position:0% +every edge lies in exactly one triangle +and the one triangle basically + + align:start position:0% +and the one triangle basically + + + align:start position:0% +and the one triangle basically +corresponds to the fact that you always + + align:start position:0% +corresponds to the fact that you always + + + align:start position:0% +corresponds to the fact that you always +have this trivial three a piece + + align:start position:0% +have this trivial three a piece + + + align:start position:0% +have this trivial three a piece +repeating the same elements three times + + align:start position:0% +repeating the same elements three times + + + align:start position:0% +repeating the same elements three times +and then by applying this corollary of + + align:start position:0% +and then by applying this corollary of + + + align:start position:0% +and then by applying this corollary of +the triangle removal lemma we deduced + + align:start position:0% +the triangle removal lemma we deduced + + + align:start position:0% +the triangle removal lemma we deduced +that the number of edges in the graph + + align:start position:0% +that the number of edges in the graph + + + align:start position:0% +that the number of edges in the graph +must be sub-quadratic so then the size + + align:start position:0% +must be sub-quadratic so then the size + + + align:start position:0% +must be sub-quadratic so then the size +of a must be sub linear and that proves + + align:start position:0% +of a must be sub linear and that proves + + + align:start position:0% +of a must be sub linear and that proves +ross theorem so we did quite a bit of + + align:start position:0% +ross theorem so we did quite a bit of + + + align:start position:0% +ross theorem so we did quite a bit of +work in proving this theorem similarly + + align:start position:0% +work in proving this theorem similarly + + + align:start position:0% +work in proving this theorem similarly +its regularity lemma counting them I'll + + align:start position:0% +its regularity lemma counting them I'll + + + align:start position:0% +its regularity lemma counting them I'll +remove a lemma and then we set up this + + align:start position:0% +remove a lemma and then we set up this + + + align:start position:0% +remove a lemma and then we set up this +graph it's not an easy theorem later in + + align:start position:0% +graph it's not an easy theorem later in + + + align:start position:0% +graph it's not an easy theorem later in +the course we'll see a different proof + + align:start position:0% +the course we'll see a different proof + + + align:start position:0% +the course we'll see a different proof +of ross theorem that goes through + + align:start position:0% +of ross theorem that goes through + + + align:start position:0% +of ross theorem that goes through +fourier analysis that will look somewhat + + align:start position:0% +fourier analysis that will look somewhat + + + align:start position:0% +fourier analysis that will look somewhat +different but it will have similar + + align:start position:0% +different but it will have similar + + + align:start position:0% +different but it will have similar +themes so we'll also have this team + + align:start position:0% +themes so we'll also have this team + + + align:start position:0% +themes so we'll also have this team +comparing structure and pseudo + + align:start position:0% +comparing structure and pseudo + + + align:start position:0% +comparing structure and pseudo +randomness which comes up in the proof + + align:start position:0% +randomness which comes up in the proof + + + align:start position:0% +randomness which comes up in the proof +in the statement and proof of summary + + align:start position:0% +in the statement and proof of summary + + + align:start position:0% +in the statement and proof of summary +this graft regularity lemma or so there + + align:start position:0% +this graft regularity lemma or so there + + + align:start position:0% +this graft regularity lemma or so there +it's really about understanding what is + + align:start position:0% +it's really about understanding what is + + + align:start position:0% +it's really about understanding what is +the structure of the graph in terms of + + align:start position:0% +the structure of the graph in terms of + + + align:start position:0% +the structure of the graph in terms of +decomposition into parts that look + + align:start position:0% +decomposition into parts that look + + + align:start position:0% +decomposition into parts that look +pseudo-random yeah okay so question is + + align:start position:0% +pseudo-random yeah okay so question is + + + align:start position:0% +pseudo-random yeah okay so question is +why do I call this graph the Kelly graph + + align:start position:0% +why do I call this graph the Kelly graph + + + align:start position:0% +why do I call this graph the Kelly graph +so usually the Cayley graph refers to a + + align:start position:0% +so usually the Cayley graph refers to a + + + align:start position:0% +so usually the Cayley graph refers to a +graph where I give you a group and I + + align:start position:0% +graph where I give you a group and I + + + align:start position:0% +graph where I give you a group and I +give you a subset of the group and I + + align:start position:0% +give you a subset of the group and I + + + align:start position:0% +give you a subset of the group and I +connect to elements if let's say their + + align:start position:0% +connect to elements if let's say their + + + align:start position:0% +connect to elements if let's say their +difference lies in my subset this + + align:start position:0% +difference lies in my subset this + + + align:start position:0% +difference lies in my subset this +basically has that form so it's not + + align:start position:0% +basically has that form so it's not + + + align:start position:0% +basically has that form so it's not +exactly what people mean by a Cayley + + align:start position:0% +exactly what people mean by a Cayley + + + align:start position:0% +exactly what people mean by a Cayley +graph but it has that spirit any more + + align:start position:0% +graph but it has that spirit any more + + + align:start position:0% +graph but it has that spirit any more +questions + + align:start position:0% + + + + align:start position:0% + +okay so earlier I talked about bounds + + align:start position:0% +okay so earlier I talked about bounds + + + align:start position:0% +okay so earlier I talked about bounds +for triangle removal lemma so what about + + align:start position:0% +for triangle removal lemma so what about + + + align:start position:0% +for triangle removal lemma so what about +bounds for Ross theorem what we do know + + align:start position:0% +bounds for Ross theorem what we do know + + + align:start position:0% +bounds for Ross theorem what we do know +somewhat better bounds for Ross theorem + + align:start position:0% +somewhat better bounds for Ross theorem + + + align:start position:0% +somewhat better bounds for Ross theorem +compared to you with this proof so this + + align:start position:0% +compared to you with this proof so this + + + align:start position:0% +compared to you with this proof so this +is somehow it's a nice proof it's a nice + + align:start position:0% +is somehow it's a nice proof it's a nice + + + align:start position:0% +is somehow it's a nice proof it's a nice +graph theoretic proof but it doesn't + + align:start position:0% +graph theoretic proof but it doesn't + + + align:start position:0% +graph theoretic proof but it doesn't +give you very good bounce or it gives + + align:start position:0% +give you very good bounce or it gives + + + align:start position:0% +give you very good bounce or it gives +you balance that they cave very poor T + + align:start position:0% +you balance that they cave very poor T + + + align:start position:0% +you balance that they cave very poor T +as a function of n yeah so what does it + + align:start position:0% +as a function of n yeah so what does it + + + align:start position:0% +as a function of n yeah so what does it +give you as a function event if you were + + align:start position:0% +give you as a function event if you were + + + align:start position:0% +give you as a function event if you were +to replace this little ole by a function + + align:start position:0% +to replace this little ole by a function + + + align:start position:0% +to replace this little ole by a function +of n according to this proof what would + + align:start position:0% +of n according to this proof what would + + + align:start position:0% +of n according to this proof what would +you get and basically asking what is the + + align:start position:0% +you get and basically asking what is the + + + align:start position:0% +you get and basically asking what is the +inverse of the function where you input + + align:start position:0% +inverse of the function where you input + + + align:start position:0% +inverse of the function where you input +some number and it gives you a power of + + align:start position:0% +some number and it gives you a power of + + + align:start position:0% +some number and it gives you a power of +Exponential's of height with that input + + align:start position:0% + + + + align:start position:0% + +let's call the log star so the log star + + align:start position:0% +let's call the log star so the log star + + + align:start position:0% +let's call the log star so the log star +so this is essentially n over the log + + align:start position:0% +so this is essentially n over the log + + + align:start position:0% +so this is essentially n over the log +star event the log star basically is the + + align:start position:0% +star event the log star basically is the + + + align:start position:0% +star event the log star basically is the +number of times you have to take the + + align:start position:0% +number of times you have to take the + + + align:start position:0% +number of times you have to take the +logarithm to get you below one okay so + + align:start position:0% +logarithm to get you below one okay so + + + align:start position:0% +logarithm to get you below one okay so +that's the log star and saying that the + + align:start position:0% +that's the log star and saying that the + + + align:start position:0% +that's the log star and saying that the +log star we know that it grows to + + align:start position:0% +log star we know that it grows to + + + align:start position:0% +log star we know that it grows to +infinity but it's never being observed + + align:start position:0% +infinity but it's never being observed + + + align:start position:0% +infinity but it's never being observed +to do so it's extremely slowing slowly + + align:start position:0% +to do so it's extremely slowing slowly + + + align:start position:0% +to do so it's extremely slowing slowly +growing function any more questions so I + + align:start position:0% +growing function any more questions so I + + + align:start position:0% +growing function any more questions so I +want to okay so next time I want to show + + align:start position:0% +want to okay so next time I want to show + + + align:start position:0% +want to okay so next time I want to show +you a construction that gives you a okay + + align:start position:0% +you a construction that gives you a okay + + + align:start position:0% +you a construction that gives you a okay +so the next time I will show you a + + align:start position:0% +so the next time I will show you a + + + align:start position:0% +so the next time I will show you a +construction that gives you a subset a + + align:start position:0% +construction that gives you a subset a + + + align:start position:0% +construction that gives you a subset a +of n that is fairly large or so you + + align:start position:0% +of n that is fairly large or so you + + + align:start position:0% +of n that is fairly large or so you +might ask okay so you have this upper + + align:start position:0% +might ask okay so you have this upper + + + align:start position:0% +might ask okay so you have this upper +bound but what should the truth be and + + align:start position:0% +bound but what should the truth be and + + + align:start position:0% +bound but what should the truth be and +here's more or less the state of + + align:start position:0% +here's more or less the state of + + + align:start position:0% +here's more or less the state of +knowledge + + align:start position:0% +knowledge + + + align:start position:0% +knowledge +[Applause] + + align:start position:0% + + + + align:start position:0% + +so best bangs + + align:start position:0% + + + + align:start position:0% + +try on rock theorem basically the best + + align:start position:0% +try on rock theorem basically the best + + + align:start position:0% +try on rock theorem basically the best +bounds have the form and divided by + + align:start position:0% +bounds have the form and divided by + + + align:start position:0% +bounds have the form and divided by +basically log n raised to power 1 plus + + align:start position:0% +basically log n raised to power 1 plus + + + align:start position:0% +basically log n raised to power 1 plus +in Toma the precise bounds are deform + + align:start position:0% +in Toma the precise bounds are deform + + + align:start position:0% +in Toma the precise bounds are deform +and over log N and then there's some + + align:start position:0% +and over log N and then there's some + + + align:start position:0% +and over log N and then there's some +extra log log factors but let's not + + align:start position:0% +extra log log factors but let's not + + + align:start position:0% +extra log log factors but let's not +worry about that the best lower bounds + + align:start position:0% +worry about that the best lower bounds + + + align:start position:0% +worry about that the best lower bounds +so we'll see this next time so there + + align:start position:0% +so we'll see this next time so there + + + align:start position:0% +so we'll see this next time so there +exists sets subsets of 1 to n such that + + align:start position:0% + + + + align:start position:0% + +the size of a is at least e to the so n + + align:start position:0% +the size of a is at least e to the so n + + + align:start position:0% +the size of a is at least e to the so n +times + + align:start position:0% +times + + + align:start position:0% +times +ok so first let me say it's pretty close + + align:start position:0% +ok so first let me say it's pretty close + + + align:start position:0% +ok so first let me say it's pretty close +to the exponent is as close to one as + + align:start position:0% +to the exponent is as close to one as + + + align:start position:0% +to the exponent is as close to one as +you can as you wish + + align:start position:0% +you can as you wish + + + align:start position:0% +you can as you wish +there exists as a such that the size of + + align:start position:0% +there exists as a such that the size of + + + align:start position:0% +there exists as a such that the size of +a is n to the 1 minus the whole one and + + align:start position:0% +a is n to the 1 minus the whole one and + + + align:start position:0% +a is n to the 1 minus the whole one and +already this fact is an indication of + + align:start position:0% +already this fact is an indication of + + + align:start position:0% +already this fact is an indication of +the difficulty of the problem because if + + align:start position:0% +the difficulty of the problem because if + + + align:start position:0% +the difficulty of the problem because if +you could prove Ross theorem through + + align:start position:0% +you could prove Ross theorem through + + + align:start position:0% +you could prove Ross theorem through +some fairly elementary techniques like + + align:start position:0% +some fairly elementary techniques like + + + align:start position:0% +some fairly elementary techniques like +using the Cauchy short a bunch of times + + align:start position:0% +using the Cauchy short a bunch of times + + + align:start position:0% +using the Cauchy short a bunch of times +for instance then your experience tells + + align:start position:0% +for instance then your experience tells + + + align:start position:0% +for instance then your experience tells +us that you probably expect some bound + + align:start position:0% +us that you probably expect some bound + + + align:start position:0% +us that you probably expect some bound +that a power saving by replacing the 1 + + align:start position:0% +that a power saving by replacing the 1 + + + align:start position:0% +that a power saving by replacing the 1 +by some smaller number but that's not + + align:start position:0% +by some smaller number but that's not + + + align:start position:0% +by some smaller number but that's not +the case and the fact that that's not + + align:start position:0% +the case and the fact that that's not + + + align:start position:0% +the case and the fact that that's not +the case it's already indication of the + + align:start position:0% +the case it's already indication of the + + + align:start position:0% +the case it's already indication of the +difficulty of of this upper bound of + + align:start position:0% +difficulty of of this upper bound of + + + align:start position:0% +difficulty of of this upper bound of +Ross theorem even getting a little all + + align:start position:0% +Ross theorem even getting a little all + + + align:start position:0% +Ross theorem even getting a little all +right so you don't expect there to be + + align:start position:0% +right so you don't expect there to be + + + align:start position:0% +right so you don't expect there to be +simple proofs getting a little the + + align:start position:0% +simple proofs getting a little the + + + align:start position:0% +simple proofs getting a little the +pound that we'll see next time so what's + + align:start position:0% +pound that we'll see next time so what's + + + align:start position:0% +pound that we'll see next time so what's +your construction which gives you a + + align:start position:0% +your construction which gives you a + + + align:start position:0% +your construction which gives you a +pound that is of this form okay so it's + + align:start position:0% +pound that is of this form okay so it's + + + align:start position:0% +pound that is of this form okay so it's +maybe a little bit hard to think about + + align:start position:0% +maybe a little bit hard to think about + + + align:start position:0% +maybe a little bit hard to think about +how quickly this function grows but I'll + + align:start position:0% +how quickly this function grows but I'll + + + align:start position:0% +how quickly this function grows but I'll +let you think about it now how does this + + align:start position:0% +let you think about it now how does this + + + align:start position:0% +let you think about it now how does this +okay so let's look at this corollary + + align:start position:0% +okay so let's look at this corollary + + + align:start position:0% +okay so let's look at this corollary +here can you see a way to construct a + + align:start position:0% +here can you see a way to construct a + + + align:start position:0% +here can you see a way to construct a +graph which has lots of edges such that + + align:start position:0% +graph which has lots of edges such that + + + align:start position:0% +graph which has lots of edges such that +every edge lies in exactly one triangle + + align:start position:0% + + + + align:start position:0% + +so we did this connection showing how to + + align:start position:0% +so we did this connection showing how to + + + align:start position:0% +so we did this connection showing how to +use this corollary to prove roster but + + align:start position:0% +use this corollary to prove roster but + + + align:start position:0% +use this corollary to prove roster but +you can run the same connection right so + + align:start position:0% +you can run the same connection right so + + + align:start position:0% +you can run the same connection right so +starting from this 3 AP free a we can + + align:start position:0% +starting from this 3 AP free a we can + + + align:start position:0% +starting from this 3 AP free a we can +use that construction to build a graph + + align:start position:0% + + + + align:start position:0% + +and such that graph on n vertices with + + align:start position:0% +and such that graph on n vertices with + + + align:start position:0% +and such that graph on n vertices with +essentially on the water off and the + + align:start position:0% +essentially on the water off and the + + + align:start position:0% +essentially on the water off and the +times the size of a number of edges such + + align:start position:0% +times the size of a number of edges such + + + align:start position:0% +times the size of a number of edges such +that every edge lies in exactly one + + align:start position:0% + + + + align:start position:0% + +triangle so you run the same + + align:start position:0% +triangle so you run the same + + + align:start position:0% +triangle so you run the same +construction and that's this is actually + + align:start position:0% +construction and that's this is actually + + + align:start position:0% +construction and that's this is actually +more or less the only way that we know + + align:start position:0% +more or less the only way that we know + + + align:start position:0% +more or less the only way that we know +how to construct such graphs that are + + align:start position:0% +how to construct such graphs that are + + + align:start position:0% +how to construct such graphs that are +fairly dense so on one hand basically + + align:start position:0% +fairly dense so on one hand basically + + + align:start position:0% +fairly dense so on one hand basically +what I said earlier on one hand you have + + align:start position:0% +what I said earlier on one hand you have + + + align:start position:0% +what I said earlier on one hand you have +this upper bound which is given by the + + align:start position:0% +this upper bound which is given by the + + + align:start position:0% +this upper bound which is given by the +proof of using similarities regularity + + align:start position:0% +proof of using similarities regularity + + + align:start position:0% +proof of using similarities regularity +lemma that gives you a tower in the + + align:start position:0% +lemma that gives you a tower in the + + + align:start position:0% +lemma that gives you a tower in the +upper bound on 1 over Delta and if you + + align:start position:0% +upper bound on 1 over Delta and if you + + + align:start position:0% +upper bound on 1 over Delta and if you +use this construction here 3 AP 3 set to + + align:start position:0% +use this construction here 3 AP 3 set to + + + align:start position:0% +use this construction here 3 AP 3 set to +construct a graph you get this lower + + align:start position:0% +construct a graph you get this lower + + + align:start position:0% +construct a graph you get this lower +bound on delta which is quasi-polynomial + + align:start position:0% +bound on delta which is quasi-polynomial + + + align:start position:0% +bound on delta which is quasi-polynomial +ok and that's that's more or less than + + align:start position:0% +ok and that's that's more or less than + + + align:start position:0% +ok and that's that's more or less than +we know + + align:start position:0% +we know + + + align:start position:0% +we know +so this is weed and it's a major open + + align:start position:0% +so this is weed and it's a major open + + + align:start position:0% +so this is weed and it's a major open +problem to close these two gaps any more + + align:start position:0% +problem to close these two gaps any more + + + align:start position:0% +problem to close these two gaps any more +questions so I want to give you a plan + + align:start position:0% +questions so I want to give you a plan + + + align:start position:0% +questions so I want to give you a plan +on what's coming up ahead so today we + + align:start position:0% +on what's coming up ahead so today we + + + align:start position:0% +on what's coming up ahead so today we +saw one application of similarities + + align:start position:0% +saw one application of similarities + + + align:start position:0% +saw one application of similarities +regularity lemma namely to the triangle + + align:start position:0% +regularity lemma namely to the triangle + + + align:start position:0% +regularity lemma namely to the triangle +removal lemma which has this application + + align:start position:0% +removal lemma which has this application + + + align:start position:0% +removal lemma which has this application +to RAAS terms so we've seen our first + + align:start position:0% +to RAAS terms so we've seen our first + + + align:start position:0% +to RAAS terms so we've seen our first +proof of Rosse theorem and next lecture + + align:start position:0% +proof of Rosse theorem and next lecture + + + align:start position:0% +proof of Rosse theorem and next lecture +and the next couple lectures I want to + + align:start position:0% +and the next couple lectures I want to + + + align:start position:0% +and the next couple lectures I want to +show you a few extensions and + + align:start position:0% +show you a few extensions and + + + align:start position:0% +show you a few extensions and +applications of similarities regularity + + align:start position:0% +applications of similarities regularity + + + align:start position:0% +applications of similarities regularity +lemma so one of the questions today was + + align:start position:0% +lemma so one of the questions today was + + + align:start position:0% +lemma so one of the questions today was +we knew how to count triangles but what + + align:start position:0% +we knew how to count triangles but what + + + align:start position:0% +we knew how to count triangles but what +about other graphs as you can imagine if + + align:start position:0% +about other graphs as you can imagine if + + + align:start position:0% +about other graphs as you can imagine if +you can count triangles then the other + + align:start position:0% +you can count triangles then the other + + + align:start position:0% +you can count triangles then the other +graphs should also be doable using the + + align:start position:0% +graphs should also be doable using the + + + align:start position:0% +graphs should also be doable using the +same ideas and we'll do that so we'll + + align:start position:0% +same ideas and we'll do that so we'll + + + align:start position:0% +same ideas and we'll do that so we'll +see how to count other graphs and we'll + + align:start position:0% +see how to count other graphs and we'll + + + align:start position:0% +see how to count other graphs and we'll +give you a I'll give you a proof of the + + align:start position:0% +give you a I'll give you a proof of the + + + align:start position:0% +give you a I'll give you a proof of the +air - stone Chimel image theorem that we + + align:start position:0% +air - stone Chimel image theorem that we + + + align:start position:0% +air - stone Chimel image theorem that we +do not prove in the first part of this + + align:start position:0% +do not prove in the first part of this + + + align:start position:0% +do not prove in the first part of this +course so gives you an upper bound on + + align:start position:0% +course so gives you an upper bound on + + + align:start position:0% +course so gives you an upper bound on +the extremal number of a graph H that + + align:start position:0% +the extremal number of a graph H that + + + align:start position:0% +the extremal number of a graph H that +depends only on the chromatic number of + + align:start position:0% +depends only on the chromatic number of + + + align:start position:0% +depends only on the chromatic number of +H and then I also mention I will now + + align:start position:0% +H and then I also mention I will now + + + align:start position:0% +H and then I also mention I will now +prove some extensions of the regularity + + align:start position:0% +prove some extensions of the regularity + + + align:start position:0% +prove some extensions of the regularity +lemma to other settings such as - hyper + + align:start position:0% +lemma to other settings such as - hyper + + + align:start position:0% +lemma to other settings such as - hyper +graphs and what that's useful for is + + align:start position:0% +graphs and what that's useful for is + + + align:start position:0% +graphs and what that's useful for is +that it will allow us to deduce + + align:start position:0% +that it will allow us to deduce + + + align:start position:0% +that it will allow us to deduce +generalizations of Ross theorem to + + align:start position:0% +generalizations of Ross theorem to + + + align:start position:0% +generalizations of Ross theorem to +longer arithmetic progressions actual + + align:start position:0% +longer arithmetic progressions actual + + + align:start position:0% +longer arithmetic progressions actual +proving Sammarinese theorem so one way + + align:start position:0% +proving Sammarinese theorem so one way + + + align:start position:0% +proving Sammarinese theorem so one way +to deduce similarities theorem is to use + + align:start position:0% +to deduce similarities theorem is to use + + + align:start position:0% +to deduce similarities theorem is to use +a hyper graph remove ulema + + align:start position:0% +a hyper graph remove ulema + + + align:start position:0% +a hyper graph remove ulema +hyper graph extension of the graph + + align:start position:0% +hyper graph extension of the graph + + + align:start position:0% +hyper graph extension of the graph +remove ulema the triangle removal lemma + + align:start position:0% +remove ulema the triangle removal lemma + + + align:start position:0% +remove ulema the triangle removal lemma +that we saw today it would also let us + + align:start position:0% +that we saw today it would also let us + + + align:start position:0% +that we saw today it would also let us +derive higher dimensional + + align:start position:0% +derive higher dimensional + + + align:start position:0% +derive higher dimensional +generalizations of these theorems so + + align:start position:0% +generalizations of these theorems so + + + align:start position:0% +generalizations of these theorems so +it's a very powerful tool and actually + + align:start position:0% +it's a very powerful tool and actually + + + align:start position:0% +it's a very powerful tool and actually +the hyper graph removal mr has mentioned + + align:start position:0% +the hyper graph removal mr has mentioned + + + align:start position:0% +the hyper graph removal mr has mentioned +in the very first lecture it's a very + + align:start position:0% +in the very first lecture it's a very + + + align:start position:0% +in the very first lecture it's a very +difficult extension of the graph removal + + align:start position:0% +difficult extension of the graph removal + + + align:start position:0% +difficult extension of the graph removal +amount and + + align:start position:0% +amount and + + + align:start position:0% +amount and +hypergraph regularity lemma which can be + + align:start position:0% +hypergraph regularity lemma which can be + + + align:start position:0% +hypergraph regularity lemma which can be +used to prove the hypergraph removal ama + + align:start position:0% +used to prove the hypergraph removal ama + + + align:start position:0% +used to prove the hypergraph removal ama +is a difficult extension of the graph + + align:start position:0% +is a difficult extension of the graph + + + align:start position:0% +is a difficult extension of the graph +regularity lemma okay so we'll see that + + align:start position:0% +regularity lemma okay so we'll see that + + + align:start position:0% +regularity lemma okay so we'll see that +in the next few lectures \ No newline at end of file diff --git a/RJf9jRf-Ekw.txt b/RJf9jRf-Ekw.txt new file mode 100644 index 0000000000000000000000000000000000000000..55c4aac970a3bd3f99adbcb6c2518d96690706ac --- /dev/null +++ b/RJf9jRf-Ekw.txt @@ -0,0 +1,8819 @@ +align:start position:0% + +so um today we're going to get start to + + align:start position:0% +so um today we're going to get start to + + + align:start position:0% +so um today we're going to get start to +get into at least some nitty-gritty + + align:start position:0% +get into at least some nitty-gritty + + + align:start position:0% +get into at least some nitty-gritty +stuff on the course um I think the a + + align:start position:0% +stuff on the course um I think the a + + + align:start position:0% +stuff on the course um I think the a +point I want to just to give you a very + + align:start position:0% +point I want to just to give you a very + + + align:start position:0% +point I want to just to give you a very +broad perspective apart from why biology + + align:start position:0% +broad perspective apart from why biology + + + align:start position:0% +broad perspective apart from why biology +is interesting now I want to talk about + + align:start position:0% +is interesting now I want to talk about + + + align:start position:0% +is interesting now I want to talk about +just very briefly how we study biology I + + align:start position:0% +just very briefly how we study biology I + + + align:start position:0% +just very briefly how we study biology I +sort of talked about it uh the other day + + align:start position:0% +sort of talked about it uh the other day + + + align:start position:0% +sort of talked about it uh the other day +by sort of the levels at which we could + + align:start position:0% +by sort of the levels at which we could + + + align:start position:0% +by sort of the levels at which we could +do it from the biosphere all the way + + align:start position:0% +do it from the biosphere all the way + + + align:start position:0% +do it from the biosphere all the way +down to the molecular level but there's + + align:start position:0% +down to the molecular level but there's + + + align:start position:0% +down to the molecular level but there's +another way of of looking at it and I + + align:start position:0% +another way of of looking at it and I + + + align:start position:0% +another way of of looking at it and I +just want to remind you what I said the + + align:start position:0% +just want to remind you what I said the + + + align:start position:0% +just want to remind you what I said the +other day biology is an experimental + + align:start position:0% + + + + align:start position:0% + +science what we know or think we know at + + align:start position:0% +science what we know or think we know at + + + align:start position:0% +science what we know or think we know at +the moment is because of people having + + align:start position:0% +the moment is because of people having + + + align:start position:0% +the moment is because of people having +made observations designed hypotheses + + align:start position:0% +made observations designed hypotheses + + + align:start position:0% +made observations designed hypotheses +tested them and so on and what you're + + align:start position:0% +tested them and so on and what you're + + + align:start position:0% +tested them and so on and what you're +seeing is sort of the sum of the current + + align:start position:0% +seeing is sort of the sum of the current + + + align:start position:0% +seeing is sort of the sum of the current +state of uh human knowledge when I'm + + align:start position:0% +state of uh human knowledge when I'm + + + align:start position:0% +state of uh human knowledge when I'm +talking to you right now there are + + align:start position:0% +talking to you right now there are + + + align:start position:0% +talking to you right now there are +various two two sort of major + + align:start position:0% +various two two sort of major + + + align:start position:0% +various two two sort of major +disciplines that have been used to get + + align:start position:0% +disciplines that have been used to get + + + align:start position:0% +disciplines that have been used to get +at how biological function works + + align:start position:0% +at how biological function works + + + align:start position:0% +at how biological function works +you as you'll see the main actor for + + align:start position:0% +you as you'll see the main actor for + + + align:start position:0% +you as you'll see the main actor for +many of the things that happen inside of + + align:start position:0% +many of the things that happen inside of + + + align:start position:0% +many of the things that happen inside of +cells and in living organisms are + + align:start position:0% +cells and in living organisms are + + + align:start position:0% +cells and in living organisms are +proteins and we'll be talking what about + + align:start position:0% +proteins and we'll be talking what about + + + align:start position:0% +proteins and we'll be talking what about +what those are and their structures in + + align:start position:0% +what those are and their structures in + + + align:start position:0% +what those are and their structures in +some detail over the next thing but the + + align:start position:0% +some detail over the next thing but the + + + align:start position:0% +some detail over the next thing but the +information is not coded in the proteins + + align:start position:0% +information is not coded in the proteins + + + align:start position:0% +information is not coded in the proteins +the information for coding uh everything + + align:start position:0% +the information for coding uh everything + + + align:start position:0% +the information for coding uh everything +that's in the cell is is in units called + + align:start position:0% +that's in the cell is is in units called + + + align:start position:0% +that's in the cell is is in units called +genes which are made of as you probably + + align:start position:0% +genes which are made of as you probably + + + align:start position:0% +genes which are made of as you probably +all know DNA so there've been + + align:start position:0% +all know DNA so there've been + + + align:start position:0% +all know DNA so there've been +classically there were two approaches + + align:start position:0% +classically there were two approaches + + + align:start position:0% +classically there were two approaches +towards study studying biology in + + align:start position:0% +towards study studying biology in + + + align:start position:0% +towards study studying biology in +detailed ways one was the approach of + + align:start position:0% +detailed ways one was the approach of + + + align:start position:0% +detailed ways one was the approach of +biochemists who basically took whatever + + align:start position:0% +biochemists who basically took whatever + + + align:start position:0% +biochemists who basically took whatever +it was put in a weing blend wearing + + align:start position:0% +it was put in a weing blend wearing + + + align:start position:0% +it was put in a weing blend wearing +blender or something and ripped + + align:start position:0% +blender or something and ripped + + + align:start position:0% +blender or something and ripped +everything into little pieces it's sort + + align:start position:0% +everything into little pieces it's sort + + + align:start position:0% +everything into little pieces it's sort +of like taking the alarm clock and + + align:start position:0% +of like taking the alarm clock and + + + align:start position:0% +of like taking the alarm clock and +shaking it so hard all you got is all + + align:start position:0% +shaking it so hard all you got is all + + + align:start position:0% +shaking it so hard all you got is all +the little bits and once you got it into + + align:start position:0% +the little bits and once you got it into + + + align:start position:0% +the little bits and once you got it into +all little bits then you can purify a + + align:start position:0% +all little bits then you can purify a + + + align:start position:0% +all little bits then you can purify a +little thing like a spring or a little + + align:start position:0% +little thing like a spring or a little + + + align:start position:0% +little thing like a spring or a little +wheel or something and try then to + + align:start position:0% +wheel or something and try then to + + + align:start position:0% +wheel or something and try then to +figure out what that does in the context + + align:start position:0% +figure out what that does in the context + + + align:start position:0% +figure out what that does in the context +of the cell you can get very detailed + + align:start position:0% +of the cell you can get very detailed + + + align:start position:0% +of the cell you can get very detailed +information and this is in a sort of + + align:start position:0% +information and this is in a sort of + + + align:start position:0% +information and this is in a sort of +trivial + + align:start position:0% +trivial + + + align:start position:0% +trivial +way the science of appro discipline of + + align:start position:0% +way the science of appro discipline of + + + align:start position:0% +way the science of appro discipline of +biochemistry um geneticists take a + + align:start position:0% +biochemistry um geneticists take a + + + align:start position:0% +biochemistry um geneticists take a +different sort of + + align:start position:0% + + + + align:start position:0% + +approach what they they do is they take + + align:start position:0% +approach what they they do is they take + + + align:start position:0% +approach what they they do is they take +the living organism and look for a + + align:start position:0% +the living organism and look for a + + + align:start position:0% +the living organism and look for a +variant there's just been one single + + align:start position:0% +variant there's just been one single + + + align:start position:0% +variant there's just been one single +change in that whole um in that whole + + align:start position:0% +change in that whole um in that whole + + + align:start position:0% +change in that whole um in that whole +organism and they study its properties + + align:start position:0% +organism and they study its properties + + + align:start position:0% +organism and they study its properties +and what you learn from that is + + align:start position:0% +and what you learn from that is + + + align:start position:0% +and what you learn from that is +physiologically relevant information and + + align:start position:0% +physiologically relevant information and + + + align:start position:0% +physiologically relevant information and +if you did broke up a car and purified + + align:start position:0% +if you did broke up a car and purified + + + align:start position:0% +if you did broke up a car and purified +the ashtray you could postulate that + + align:start position:0% +the ashtray you could postulate that + + + align:start position:0% +the ashtray you could postulate that +that was really important for the car + + align:start position:0% +that was really important for the car + + + align:start position:0% +that was really important for the car +but if you made a mutant that was + + align:start position:0% +but if you made a mutant that was + + + align:start position:0% +but if you made a mutant that was +missing the ashtray and it still Ren you + + align:start position:0% +missing the ashtray and it still Ren you + + + align:start position:0% +missing the ashtray and it still Ren you +know you you'd learn that that wasn't + + align:start position:0% +know you you'd learn that that wasn't + + + align:start position:0% +know you you'd learn that that wasn't +what was correct and one of the really + + align:start position:0% +what was correct and one of the really + + + align:start position:0% +what was correct and one of the really +powerful things that people could only + + align:start position:0% +powerful things that people could only + + + align:start position:0% +powerful things that people could only +do in very rare instances for a long + + align:start position:0% +do in very rare instances for a long + + + align:start position:0% +do in very rare instances for a long +time was to unite the kinds of + + align:start position:0% +time was to unite the kinds of + + + align:start position:0% +time was to unite the kinds of +observations that biochemist made with + + align:start position:0% +observations that biochemist made with + + + align:start position:0% +observations that biochemist made with +the kinds of observations genetics + + align:start position:0% +the kinds of observations genetics + + + align:start position:0% +the kinds of observations genetics +geneticist made and the explosion in + + align:start position:0% +geneticist made and the explosion in + + + align:start position:0% +geneticist made and the explosion in +knowledge that's happened over the last + + align:start position:0% +knowledge that's happened over the last + + + align:start position:0% +knowledge that's happened over the last +couple of decades uh probably since well + + align:start position:0% +couple of decades uh probably since well + + + align:start position:0% +couple of decades uh probably since well +since probably 1975 when recant DNA came + + align:start position:0% +since probably 1975 when recant DNA came + + + align:start position:0% +since probably 1975 when recant DNA came +in was a whole new realm of sort of a + + align:start position:0% +in was a whole new realm of sort of a + + + align:start position:0% +in was a whole new realm of sort of a +general discipline we call molecular + + align:start position:0% +general discipline we call molecular + + + align:start position:0% +general discipline we call molecular +biology that allowed us to to clone + + align:start position:0% +biology that allowed us to to clone + + + align:start position:0% +biology that allowed us to to clone +genes to sequence them to do many of the + + align:start position:0% +genes to sequence them to do many of the + + + align:start position:0% +genes to sequence them to do many of the +things we'll be talking about but one of + + align:start position:0% +things we'll be talking about but one of + + + align:start position:0% +things we'll be talking about but one of +the real powers in looking at this sort + + align:start position:0% +the real powers in looking at this sort + + + align:start position:0% +the real powers in looking at this sort +of way of about how we study biology is + + align:start position:0% +of way of about how we study biology is + + + align:start position:0% +of way of about how we study biology is +that it suddenly enabled one to uh put + + align:start position:0% +that it suddenly enabled one to uh put + + + align:start position:0% +that it suddenly enabled one to uh put +these two sorts of things together if + + align:start position:0% +these two sorts of things together if + + + align:start position:0% +these two sorts of things together if +you were a biochemist and you purified a + + align:start position:0% +you were a biochemist and you purified a + + + align:start position:0% +you were a biochemist and you purified a +protein and you found out a uh chemical + + align:start position:0% +protein and you found out a uh chemical + + + align:start position:0% +protein and you found out a uh chemical +property that it had and you wondered + + align:start position:0% +property that it had and you wondered + + + align:start position:0% +property that it had and you wondered +what it did in the cell you could + + align:start position:0% +what it did in the cell you could + + + align:start position:0% +what it did in the cell you could +sequence the protein deduce what some of + + align:start position:0% +sequence the protein deduce what some of + + + align:start position:0% +sequence the protein deduce what some of +the DNA sequence was find the gene + + align:start position:0% +the DNA sequence was find the gene + + + align:start position:0% +the DNA sequence was find the gene +disable the gene in the organism look + + align:start position:0% +disable the gene in the organism look + + + align:start position:0% +disable the gene in the organism look +and see if your idea was right or vice + + align:start position:0% +and see if your idea was right or vice + + + align:start position:0% +and see if your idea was right or vice +versa if you were a geneticist and you + + align:start position:0% +versa if you were a geneticist and you + + + align:start position:0% +versa if you were a geneticist and you +found a mutant that had an interesting + + align:start position:0% +found a mutant that had an interesting + + + align:start position:0% +found a mutant that had an interesting +property and you wondered how was + + align:start position:0% +property and you wondered how was + + + align:start position:0% +property and you wondered how was +working then you could clone the gene + + align:start position:0% +working then you could clone the gene + + + align:start position:0% +working then you could clone the gene +look at the protein and try and figure + + align:start position:0% +look at the protein and try and figure + + + align:start position:0% +look at the protein and try and figure +it out and it just that's partly why + + align:start position:0% +it out and it just that's partly why + + + align:start position:0% +it out and it just that's partly why +since about 1975 there's just been this + + align:start position:0% +since about 1975 there's just been this + + + align:start position:0% +since about 1975 there's just been this +absolute upheaval in our knowledge of uh + + align:start position:0% +absolute upheaval in our knowledge of uh + + + align:start position:0% +absolute upheaval in our knowledge of uh +knowledge of biology and we'll be + + align:start position:0% +knowledge of biology and we'll be + + + align:start position:0% +knowledge of biology and we'll be +talking about all of these disciplines + + align:start position:0% +talking about all of these disciplines + + + align:start position:0% +talking about all of these disciplines +here uh as we go through the course um + + align:start position:0% +here uh as we go through the course um + + + align:start position:0% +here uh as we go through the course um +three or four of you were honest enough + + align:start position:0% +three or four of you were honest enough + + + align:start position:0% +three or four of you were honest enough +to say I'd rather be anywhere on Earth + + align:start position:0% +to say I'd rather be anywhere on Earth + + + align:start position:0% +to say I'd rather be anywhere on Earth +but in this class um I'm a senior I + + align:start position:0% +but in this class um I'm a senior I + + + align:start position:0% +but in this class um I'm a senior I +really didn't want to be here and I said + + align:start position:0% +really didn't want to be here and I said + + + align:start position:0% +really didn't want to be here and I said +the other day if you'll come I'll give + + align:start position:0% +the other day if you'll come I'll give + + + align:start position:0% +the other day if you'll come I'll give +you the best I have to try and show you + + align:start position:0% +you the best I have to try and show you + + + align:start position:0% +you the best I have to try and show you +why it's it's um uh I think it's + + align:start position:0% +why it's it's um uh I think it's + + + align:start position:0% +why it's it's um uh I think it's +exciting and why it's so relevant to you + + align:start position:0% +exciting and why it's so relevant to you + + + align:start position:0% +exciting and why it's so relevant to you +and your your life as you go uh looking + + align:start position:0% +and your your life as you go uh looking + + + align:start position:0% +and your your life as you go uh looking +forward uh to moving on with your + + align:start position:0% +forward uh to moving on with your + + + align:start position:0% +forward uh to moving on with your +careers and your family and everything + + align:start position:0% +careers and your family and everything + + + align:start position:0% +careers and your family and everything +else um however don't get even if you're + + align:start position:0% +else um however don't get even if you're + + + align:start position:0% +else um however don't get even if you're +not interested in this course don't get + + align:start position:0% +not interested in this course don't get + + + align:start position:0% +not interested in this course don't get +caught in the Trap because it's we're + + align:start position:0% +caught in the Trap because it's we're + + + align:start position:0% +caught in the Trap because it's we're +not going to be doing differential + + align:start position:0% +not going to be doing differential + + + align:start position:0% +not going to be doing differential +equations that it's easy part of the + + align:start position:0% +equations that it's easy part of the + + + align:start position:0% +equations that it's easy part of the +reason biology is hard is each one of + + align:start position:0% +reason biology is hard is each one of + + + align:start position:0% +reason biology is hard is each one of +these disciplines has a different kind + + align:start position:0% +these disciplines has a different kind + + + align:start position:0% +these disciplines has a different kind +of thinking to be very effective in + + align:start position:0% +of thinking to be very effective in + + + align:start position:0% +of thinking to be very effective in +biology right now you have to be able to + + align:start position:0% +biology right now you have to be able to + + + align:start position:0% +biology right now you have to be able to +think like a chemist what how bonds are + + align:start position:0% +think like a chemist what how bonds are + + + align:start position:0% +think like a chemist what how bonds are +formed and broken and what's reasonable + + align:start position:0% +formed and broken and what's reasonable + + + align:start position:0% +formed and broken and what's reasonable +you need to be able to think in + + align:start position:0% +you need to be able to think in + + + align:start position:0% +you need to be able to think in +threedimensional structures because + + align:start position:0% +threedimensional structures because + + + align:start position:0% +threedimensional structures because +everything happens in 3D and biology is + + align:start position:0% +everything happens in 3D and biology is + + + align:start position:0% +everything happens in 3D and biology is +very much about uh fitting shapes + + align:start position:0% +very much about uh fitting shapes + + + align:start position:0% +very much about uh fitting shapes +together uh genetics is more like + + align:start position:0% +together uh genetics is more like + + + align:start position:0% +together uh genetics is more like +probability and statistics there some of + + align:start position:0% +probability and statistics there some of + + + align:start position:0% +probability and statistics there some of +those logic games that you sort of used + + align:start position:0% +those logic games that you sort of used + + + align:start position:0% +those logic games that you sort of used +to try and do it's more like it's more + + align:start position:0% +to try and do it's more like it's more + + + align:start position:0% +to try and do it's more like it's more +like that uh PCR is I don't know um + + align:start position:0% +like that uh PCR is I don't know um + + + align:start position:0% +like that uh PCR is I don't know um +recombinant DNA all this sort of stuff + + align:start position:0% +recombinant DNA all this sort of stuff + + + align:start position:0% +recombinant DNA all this sort of stuff +it's sort of a strategy kind of game so + + align:start position:0% +it's sort of a strategy kind of game so + + + align:start position:0% +it's sort of a strategy kind of game so +you'll find as you go through this + + align:start position:0% +you'll find as you go through this + + + align:start position:0% +you'll find as you go through this +course that there may be some things + + align:start position:0% +course that there may be some things + + + align:start position:0% +course that there may be some things +that are easy and some that are + + align:start position:0% +that are easy and some that are + + + align:start position:0% +that are easy and some that are +difficult but for you uh easier or + + align:start position:0% +difficult but for you uh easier or + + + align:start position:0% +difficult but for you uh easier or +difficult but you'll need to do a lot of + + align:start position:0% +difficult but you'll need to do a lot of + + + align:start position:0% +difficult but you'll need to do a lot of +different thinking and then at the + + align:start position:0% +different thinking and then at the + + + align:start position:0% +different thinking and then at the +moment you can't do biology anymore by + + align:start position:0% +moment you can't do biology anymore by + + + align:start position:0% +moment you can't do biology anymore by +just being a biochemist or just being a + + align:start position:0% +just being a biochemist or just being a + + + align:start position:0% +just being a biochemist or just being a +geneticist you could in the old days but + + align:start position:0% +geneticist you could in the old days but + + + align:start position:0% +geneticist you could in the old days but +now you got to do it all so where we're + + align:start position:0% +now you got to do it all so where we're + + + align:start position:0% +now you got to do it all so where we're +going to start uh right now will be uh + + align:start position:0% +going to start uh right now will be uh + + + align:start position:0% +going to start uh right now will be uh +with biochemistry and just before I do + + align:start position:0% +with biochemistry and just before I do + + + align:start position:0% +with biochemistry and just before I do +that I just want to show you let's see + + align:start position:0% +that I just want to show you let's see + + + align:start position:0% +that I just want to show you let's see +this uh I wonder if we're going to be + + align:start position:0% +this uh I wonder if we're going to be + + + align:start position:0% +this uh I wonder if we're going to be +able to see these slides with that light + + align:start position:0% +able to see these slides with that light + + + align:start position:0% +able to see these slides with that light +on I think we Poss we'll see whether we + + align:start position:0% +on I think we Poss we'll see whether we + + + align:start position:0% +on I think we Poss we'll see whether we +can do this um so this the green + + align:start position:0% +can do this um so this the green + + + align:start position:0% +can do this um so this the green +fluorescent protein which thanks that's + + align:start position:0% +fluorescent protein which thanks that's + + + align:start position:0% +fluorescent protein which thanks that's +great green fluorescent protein which we + + align:start position:0% +great green fluorescent protein which we + + + align:start position:0% +great green fluorescent protein which we +uh showed you other day is a protein and + + align:start position:0% +uh showed you other day is a protein and + + + align:start position:0% +uh showed you other day is a protein and +we're going to be talking about that and + + align:start position:0% +we're going to be talking about that and + + + align:start position:0% +we're going to be talking about that and +you'll see it's got structures you got + + align:start position:0% +you'll see it's got structures you got + + + align:start position:0% +you'll see it's got structures you got +these sort of sheets and you'll see + + align:start position:0% +these sort of sheets and you'll see + + + align:start position:0% +these sort of sheets and you'll see +little hses and in a couple of days + + align:start position:0% +little hses and in a couple of days + + + align:start position:0% +little hses and in a couple of days +you'll know what this is all about but I + + align:start position:0% +you'll know what this is all about but I + + + align:start position:0% +you'll know what this is all about but I +wanted to uh tell you a couple of things + + align:start position:0% +wanted to uh tell you a couple of things + + + align:start position:0% +wanted to uh tell you a couple of things +just before we get into this this + + align:start position:0% +just before we get into this this + + + align:start position:0% +just before we get into this this +actually was um I showed you that little + + align:start position:0% +actually was um I showed you that little + + + align:start position:0% +actually was um I showed you that little +Barney + + align:start position:0% +Barney + + + align:start position:0% +Barney +thing to try and uh to uh emphasize uh + + align:start position:0% +thing to try and uh to uh emphasize uh + + + align:start position:0% +thing to try and uh to uh emphasize uh +if you looked at Evolution that way you + + align:start position:0% +if you looked at Evolution that way you + + + align:start position:0% +if you looked at Evolution that way you +can see most of it was at the level of + + align:start position:0% +can see most of it was at the level of + + + align:start position:0% +can see most of it was at the level of +single cells and that's why things are + + align:start position:0% +single cells and that's why things are + + + align:start position:0% +single cells and that's why things are +so common when you get down to the + + align:start position:0% +so common when you get down to the + + + align:start position:0% +so common when you get down to the +cellular molecular level I've actually + + align:start position:0% +cellular molecular level I've actually + + + align:start position:0% +cellular molecular level I've actually +done that demo one other place and that + + align:start position:0% +done that demo one other place and that + + + align:start position:0% +done that demo one other place and that +was after um I'm an American Cancer + + align:start position:0% +was after um I'm an American Cancer + + + align:start position:0% +was after um I'm an American Cancer +Society research professor and they + + align:start position:0% +Society research professor and they + + + align:start position:0% +Society research professor and they +asked me to give a a talk for the 50th + + align:start position:0% +asked me to give a a talk for the 50th + + + align:start position:0% +asked me to give a a talk for the 50th +anniversary of the Illinois division of + + align:start position:0% +anniversary of the Illinois division of + + + align:start position:0% +anniversary of the Illinois division of +the American Chemical Society on the + + align:start position:0% +the American Chemical Society on the + + + align:start position:0% +the American Chemical Society on the +importance of of uh basic research and + + align:start position:0% +importance of of uh basic research and + + + align:start position:0% +importance of of uh basic research and +it was after dinner 500 people in + + align:start position:0% +it was after dinner 500 people in + + + align:start position:0% +it was after dinner 500 people in +tuxedos and evening gowns and bottles of + + align:start position:0% +tuxedos and evening gowns and bottles of + + + align:start position:0% +tuxedos and evening gowns and bottles of +wine and they kept shortening my time + + align:start position:0% +wine and they kept shortening my time + + + align:start position:0% +wine and they kept shortening my time +and finally I had 10 minutes to get up + + align:start position:0% +and finally I had 10 minutes to get up + + + align:start position:0% +and finally I had 10 minutes to get up +there in my talks and tell them about + + align:start position:0% +there in my talks and tell them about + + + align:start position:0% +there in my talks and tell them about +the importance of research and basic + + align:start position:0% +the importance of research and basic + + + align:start position:0% +the importance of research and basic +research I finally decided maybe what I + + align:start position:0% +research I finally decided maybe what I + + + align:start position:0% +research I finally decided maybe what I +could do is help them understand why + + align:start position:0% +could do is help them understand why + + + align:start position:0% +could do is help them understand why +when they gave money to to cure cancer + + align:start position:0% +when they gave money to to cure cancer + + + align:start position:0% +when they gave money to to cure cancer +biologists went off scientists went off + + align:start position:0% +biologists went off scientists went off + + + align:start position:0% +biologists went off scientists went off +and studied all these other organisms + + align:start position:0% +and studied all these other organisms + + + align:start position:0% +and studied all these other organisms +fruit flies and everything so I did this + + align:start position:0% +fruit flies and everything so I did this + + + align:start position:0% +fruit flies and everything so I did this +little demo so I was up on the state + + align:start position:0% +little demo so I was up on the state + + + align:start position:0% +little demo so I was up on the state +agage at the Sheran holding the Barney + + align:start position:0% +agage at the Sheran holding the Barney + + + align:start position:0% +agage at the Sheran holding the Barney +and the dinosaur doing what you saw me + + align:start position:0% +and the dinosaur doing what you saw me + + + align:start position:0% +and the dinosaur doing what you saw me +do here and I thought briefly about + + align:start position:0% +do here and I thought briefly about + + + align:start position:0% +do here and I thought briefly about +putting my Tex on just to kind of you + + align:start position:0% +putting my Tex on just to kind of you + + + align:start position:0% +putting my Tex on just to kind of you +know give a little zip to the extra + + align:start position:0% +know give a little zip to the extra + + + align:start position:0% +know give a little zip to the extra +lecture decided not to um because I get + + align:start position:0% +lecture decided not to um because I get + + + align:start position:0% +lecture decided not to um because I get +chalk all over it or something so um if + + align:start position:0% +chalk all over it or something so um if + + + align:start position:0% +chalk all over it or something so um if +you think I'm I'm stupid doing this you + + align:start position:0% +you think I'm I'm stupid doing this you + + + align:start position:0% +you think I'm I'm stupid doing this you +know um my cats thought I was absolutely + + align:start position:0% +know um my cats thought I was absolutely + + + align:start position:0% +know um my cats thought I was absolutely +an idiot afterwards they were very very + + align:start position:0% +an idiot afterwards they were very very + + + align:start position:0% +an idiot afterwards they were very very +puzzled as what was going on okay so I'm + + align:start position:0% +puzzled as what was going on okay so I'm + + + align:start position:0% +puzzled as what was going on okay so I'm +going to start talking in a couple of + + align:start position:0% +going to start talking in a couple of + + + align:start position:0% +going to start talking in a couple of +minutes about calent bonds and you're + + align:start position:0% +minutes about calent bonds and you're + + + align:start position:0% +minutes about calent bonds and you're +going to roll your eyes upwards and + + align:start position:0% +going to roll your eyes upwards and + + + align:start position:0% +going to roll your eyes upwards and +think I've heard about that since I was + + align:start position:0% +think I've heard about that since I was + + + align:start position:0% +think I've heard about that since I was +a baby uh or some of you will think that + + align:start position:0% +a baby uh or some of you will think that + + + align:start position:0% +a baby uh or some of you will think that +but I just want to keep you've got to + + align:start position:0% +but I just want to keep you've got to + + + align:start position:0% +but I just want to keep you've got to +understand something about how the parts + + align:start position:0% +understand something about how the parts + + + align:start position:0% +understand something about how the parts +of that are used in biology are built or + + align:start position:0% +of that are used in biology are built or + + + align:start position:0% +of that are used in biology are built or +it won't make sense and so just to sort + + align:start position:0% +it won't make sense and so just to sort + + + align:start position:0% +it won't make sense and so just to sort +of give you something to sort of keep + + align:start position:0% +of give you something to sort of keep + + + align:start position:0% +of give you something to sort of keep +you going here I want to sort of + + align:start position:0% +you going here I want to sort of + + + align:start position:0% +you going here I want to sort of +foreshadow a couple of things that are + + align:start position:0% +foreshadow a couple of things that are + + + align:start position:0% +foreshadow a couple of things that are +coming here's an example of what happens + + align:start position:0% +coming here's an example of what happens + + + align:start position:0% +coming here's an example of what happens +with genetics this is a single mutation + + align:start position:0% +with genetics this is a single mutation + + + align:start position:0% +with genetics this is a single mutation +in one gene in an individual this woman + + align:start position:0% +in one gene in an individual this woman + + + align:start position:0% +in one gene in an individual this woman +has what's known as verus syndrome + + align:start position:0% +has what's known as verus syndrome + + + align:start position:0% +has what's known as verus syndrome +that's what she looked like as teenager + + align:start position:0% +that's what she looked like as teenager + + + align:start position:0% +that's what she looked like as teenager +that's what she looked like at age 48 + + align:start position:0% +that's what she looked like at age 48 + + + align:start position:0% +that's what she looked like at age 48 +that's one of these mutations that + + align:start position:0% +that's one of these mutations that + + + align:start position:0% +that's one of these mutations that +causes Advanced aging and people are + + align:start position:0% +causes Advanced aging and people are + + + align:start position:0% +causes Advanced aging and people are +working very hard on what that uh uh you + + align:start position:0% +working very hard on what that uh uh you + + + align:start position:0% +working very hard on what that uh uh you +know trying to understand aging during + + align:start position:0% +know trying to understand aging during + + + align:start position:0% +know trying to understand aging during +your time at MIT there are going to be + + align:start position:0% +your time at MIT there are going to be + + + align:start position:0% +your time at MIT there are going to be +they already been some amazing + + align:start position:0% +they already been some amazing + + + align:start position:0% +they already been some amazing +discoveries in The Last 5 Years and it's + + align:start position:0% +discoveries in The Last 5 Years and it's + + + align:start position:0% +discoveries in The Last 5 Years and it's +going to be a time of explosive growth + + align:start position:0% +going to be a time of explosive growth + + + align:start position:0% +going to be a time of explosive growth +that's just one change and it offers a + + align:start position:0% +that's just one change and it offers a + + + align:start position:0% +that's just one change and it offers a +huge clue as to why we age here's + + align:start position:0% +huge clue as to why we age here's + + + align:start position:0% +huge clue as to why we age here's +another example um these are people who + + align:start position:0% +another example um these are people who + + + align:start position:0% +another example um these are people who +have a human condition called called + + align:start position:0% +have a human condition called called + + + align:start position:0% +have a human condition called called +xeroderma pigmentosum and this was the + + align:start position:0% +xeroderma pigmentosum and this was the + + + align:start position:0% +xeroderma pigmentosum and this was the +way they used to look before we + + align:start position:0% +way they used to look before we + + + align:start position:0% +way they used to look before we +understood it they're they're they have + + align:start position:0% +understood it they're they're they have + + + align:start position:0% +understood it they're they're they have +a deficiency in uh handling damage to + + align:start position:0% +a deficiency in uh handling damage to + + + align:start position:0% +a deficiency in uh handling damage to +their DNA that's caused by sunlight so + + align:start position:0% +their DNA that's caused by sunlight so + + + align:start position:0% +their DNA that's caused by sunlight so +if they went out in the sunlight once + + align:start position:0% +if they went out in the sunlight once + + + align:start position:0% +if they went out in the sunlight once +they'd get skin cancer you could see + + align:start position:0% +they'd get skin cancer you could see + + + align:start position:0% +they'd get skin cancer you could see +they get skin lesions and everything + + align:start position:0% +they get skin lesions and everything + + + align:start position:0% +they get skin lesions and everything +else it was due to a defect in just one + + align:start position:0% +else it was due to a defect in just one + + + align:start position:0% +else it was due to a defect in just one +Gene and it took out an important kind + + align:start position:0% +Gene and it took out an important kind + + + align:start position:0% +Gene and it took out an important kind +of DNA uh repair now they know that how + + align:start position:0% +of DNA uh repair now they know that how + + + align:start position:0% +of DNA uh repair now they know that how +it works the kids who do this only go + + align:start position:0% +it works the kids who do this only go + + + align:start position:0% +it works the kids who do this only go +out at night they go to camp at night + + align:start position:0% +out at night they go to camp at night + + + align:start position:0% +out at night they go to camp at night +they call them children of the Moon they + + align:start position:0% +they call them children of the Moon they + + + align:start position:0% +they call them children of the Moon they +look normal and they don't get skin + + align:start position:0% +look normal and they don't get skin + + + align:start position:0% +look normal and they don't get skin +cancer but they have to live a kind of + + align:start position:0% +cancer but they have to live a kind of + + + align:start position:0% +cancer but they have to live a kind of +special life because of this problem and + + align:start position:0% +special life because of this problem and + + + align:start position:0% +special life because of this problem and +people are working on fixing that that's + + align:start position:0% +people are working on fixing that that's + + + align:start position:0% +people are working on fixing that that's +the sort of thing that can come out of + + align:start position:0% +the sort of thing that can come out of + + + align:start position:0% +the sort of thing that can come out of +genetics single change absolutely + + align:start position:0% +genetics single change absolutely + + + align:start position:0% +genetics single change absolutely +dramatic effect but you can sort of make + + align:start position:0% +dramatic effect but you can sort of make + + + align:start position:0% +dramatic effect but you can sort of make +inferences that something important is + + align:start position:0% +inferences that something important is + + + align:start position:0% +inferences that something important is +broken in that individual because the + + align:start position:0% +broken in that individual because the + + + align:start position:0% +broken in that individual because the +rest of us don't have this problem at + + align:start position:0% +rest of us don't have this problem at + + + align:start position:0% +rest of us don't have this problem at +the biochemist um you've you know Watson + + align:start position:0% +the biochemist um you've you know Watson + + + align:start position:0% +the biochemist um you've you know Watson +and Crick and we'll talk more about + + align:start position:0% +and Crick and we'll talk more about + + + align:start position:0% +and Crick and we'll talk more about +their structure of DNA but DNA has to + + align:start position:0% +their structure of DNA but DNA has to + + + align:start position:0% +their structure of DNA but DNA has to +get replicated in fact just in the last + + align:start position:0% +get replicated in fact just in the last + + + align:start position:0% +get replicated in fact just in the last +couple of years we now know that what's + + align:start position:0% +couple of years we now know that what's + + + align:start position:0% +couple of years we now know that what's +wrong with this person is that they're + + align:start position:0% +wrong with this person is that they're + + + align:start position:0% +wrong with this person is that they're +lacking a special DNA copying machine + + align:start position:0% +lacking a special DNA copying machine + + + align:start position:0% +lacking a special DNA copying machine +that is able to copy over strands of DNA + + align:start position:0% +that is able to copy over strands of DNA + + + align:start position:0% +that is able to copy over strands of DNA +that have a have damage in them that's + + align:start position:0% +that have a have damage in them that's + + + align:start position:0% +that have a have damage in them that's +caused by by sunlight it's got a very + + align:start position:0% +caused by by sunlight it's got a very + + + align:start position:0% +caused by by sunlight it's got a very +sort of flexible active sight it can + + align:start position:0% +sort of flexible active sight it can + + + align:start position:0% +sort of flexible active sight it can +accommodate this the bulkiness of this + + align:start position:0% +accommodate this the bulkiness of this + + + align:start position:0% +accommodate this the bulkiness of this +UV induced lesion and so here's a case + + align:start position:0% +UV induced lesion and so here's a case + + + align:start position:0% +UV induced lesion and so here's a case +where we've now United our understanding + + align:start position:0% +where we've now United our understanding + + + align:start position:0% +where we've now United our understanding +of that disease at the ultimate + + align:start position:0% +of that disease at the ultimate + + + align:start position:0% +of that disease at the ultimate +biochemical molecular level and and the + + align:start position:0% +biochemical molecular level and and the + + + align:start position:0% +biochemical molecular level and and the +highlevel human syndrome so that's kind + + align:start position:0% +highlevel human syndrome so that's kind + + + align:start position:0% +highlevel human syndrome so that's kind +of one thing to sort of keep you going + + align:start position:0% +of one thing to sort of keep you going + + + align:start position:0% +of one thing to sort of keep you going +okay so um here's a cell that's the + + align:start position:0% +okay so um here's a cell that's the + + + align:start position:0% +okay so um here's a cell that's the +fundamental unit of life I said the + + align:start position:0% +fundamental unit of life I said the + + + align:start position:0% +fundamental unit of life I said the +other day remember cells carry out + + align:start position:0% +other day remember cells carry out + + + align:start position:0% +other day remember cells carry out +metabolism they do regulated growth they + + align:start position:0% +metabolism they do regulated growth they + + + align:start position:0% +metabolism they do regulated growth they +do reproduction that what's that's what + + align:start position:0% +do reproduction that what's that's what + + + align:start position:0% +do reproduction that what's that's what +makes them different from a uh just a + + align:start position:0% +makes them different from a uh just a + + + align:start position:0% +makes them different from a uh just a +bag of of proteins and nucleic acids and + + align:start position:0% +bag of of proteins and nucleic acids and + + + align:start position:0% +bag of of proteins and nucleic acids and +things and we could think about cells at + + align:start position:0% +things and we could think about cells at + + + align:start position:0% +things and we could think about cells at +a couple of different levels + + align:start position:0% +a couple of different levels + + + align:start position:0% +a couple of different levels +we could think about them in terms of + + align:start position:0% +we could think about them in terms of + + + align:start position:0% +we could think about them in terms of +their atomic composition I guess we can + + align:start position:0% +their atomic composition I guess we can + + + align:start position:0% +their atomic composition I guess we can +see and if we think about that way it's + + align:start position:0% +see and if we think about that way it's + + + align:start position:0% +see and if we think about that way it's +not particularly exciting it's about + + align:start position:0% +not particularly exciting it's about + + + align:start position:0% +not particularly exciting it's about +hydrogen's about 60% Oxygen's about + + align:start position:0% +hydrogen's about 60% Oxygen's about + + + align:start position:0% +hydrogen's about 60% Oxygen's about +20% uh carbons about + + align:start position:0% +20% uh carbons about + + + align:start position:0% +20% uh carbons about +12% nitrogen about 5% and then there's a + + align:start position:0% +12% nitrogen about 5% and then there's a + + + align:start position:0% +12% nitrogen about 5% and then there's a +whole lot of other stuff present at + + align:start position:0% +whole lot of other stuff present at + + + align:start position:0% +whole lot of other stuff present at +lower levels uh phosphorus + + align:start position:0% +lower levels uh phosphorus + + + align:start position:0% +lower levels uh phosphorus +sulfate magnesium manganese + + align:start position:0% +sulfate magnesium manganese + + + align:start position:0% +sulfate magnesium manganese +selenium Etc this isn't a particularly + + align:start position:0% +selenium Etc this isn't a particularly + + + align:start position:0% +selenium Etc this isn't a particularly +helpful way to think about um think + + align:start position:0% +helpful way to think about um think + + + align:start position:0% +helpful way to think about um think +about + + align:start position:0% + + + + align:start position:0% + +cells uh this is uh perhaps a more + + align:start position:0% +cells uh this is uh perhaps a more + + + align:start position:0% +cells uh this is uh perhaps a more +useful way and that's to think about it + + align:start position:0% +useful way and that's to think about it + + + align:start position:0% +useful way and that's to think about it +in terms of molecular + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +composition and we're about 80% water + + align:start position:0% +composition and we're about 80% water + + + align:start position:0% +composition and we're about 80% water +virtually all living organisms more or + + align:start position:0% +virtually all living organisms more or + + + align:start position:0% +virtually all living organisms more or +less the same 80% water as what + + align:start position:0% +less the same 80% water as what + + + align:start position:0% +less the same 80% water as what +ourselves are are made up of and of the + + align:start position:0% +ourselves are are made up of and of the + + + align:start position:0% +ourselves are are made up of and of the +rest of them there are four major + + align:start position:0% +rest of them there are four major + + + align:start position:0% +rest of them there are four major +classes of of macro molecules large + + align:start position:0% +classes of of macro molecules large + + + align:start position:0% +classes of of macro molecules large +biological molecules that make up the + + align:start position:0% +biological molecules that make up the + + + align:start position:0% +biological molecules that make up the +rest of cells and that's what we're + + align:start position:0% +rest of cells and that's what we're + + + align:start position:0% +rest of cells and that's what we're +going to be focusing on a little bit + + align:start position:0% +going to be focusing on a little bit + + + align:start position:0% +going to be focusing on a little bit +there's proteins which I've already + + align:start position:0% +there's proteins which I've already + + + align:start position:0% +there's proteins which I've already +mentioned today that's about 50% of it + + align:start position:0% +mentioned today that's about 50% of it + + + align:start position:0% +mentioned today that's about 50% of it +uh nucleic + + align:start position:0% +uh nucleic + + + align:start position:0% +uh nucleic +acids that's DNA and RNA as we'll say + + align:start position:0% +acids that's DNA and RNA as we'll say + + + align:start position:0% +acids that's DNA and RNA as we'll say +that's about + + align:start position:0% +that's about + + + align:start position:0% +that's about +15% carbohydrates which we'll be talking + + align:start position:0% +15% carbohydrates which we'll be talking + + + align:start position:0% +15% carbohydrates which we'll be talking +about + + align:start position:0% + + + + align:start position:0% + +today lipids + + align:start position:0% +today lipids + + + align:start position:0% +today lipids +about 10% and then there's a bunch of + + align:start position:0% +about 10% and then there's a bunch of + + + align:start position:0% +about 10% and then there's a bunch of +little stuff that is important but uh + + align:start position:0% +little stuff that is important but uh + + + align:start position:0% +little stuff that is important but uh +makes up the remaining amount but to + + align:start position:0% +makes up the remaining amount but to + + + align:start position:0% +makes up the remaining amount but to +understand biology we're really going to + + align:start position:0% +understand biology we're really going to + + + align:start position:0% +understand biology we're really going to +have to try and figure out how cells + + align:start position:0% +have to try and figure out how cells + + + align:start position:0% +have to try and figure out how cells +work we're going to need to talk about + + align:start position:0% +work we're going to need to talk about + + + align:start position:0% +work we're going to need to talk about +the properties of those of those + + align:start position:0% +the properties of those of those + + + align:start position:0% +the properties of those of those +molecules and just say you'll know this + + align:start position:0% +molecules and just say you'll know this + + + align:start position:0% +molecules and just say you'll know this +picture is act this is a was made by + + align:start position:0% +picture is act this is a was made by + + + align:start position:0% +picture is act this is a was made by +somebody at Lawrence Berkeley National + + align:start position:0% +somebody at Lawrence Berkeley National + + + align:start position:0% +somebody at Lawrence Berkeley National +Labs as far as they know she still + + align:start position:0% +Labs as far as they know she still + + + align:start position:0% +Labs as far as they know she still +hasn't published it this is a uh an + + align:start position:0% +hasn't published it this is a uh an + + + align:start position:0% +hasn't published it this is a uh an +image of an actual cell it's made by a + + align:start position:0% +image of an actual cell it's made by a + + + align:start position:0% +image of an actual cell it's made by a +very fancy technique called x-ray + + align:start position:0% +very fancy technique called x-ray + + + align:start position:0% +very fancy technique called x-ray +tomography where she sort of takes a + + align:start position:0% +tomography where she sort of takes a + + + align:start position:0% +tomography where she sort of takes a +zillion little sort of slices and then + + align:start position:0% +zillion little sort of slices and then + + + align:start position:0% +zillion little sort of slices and then +assembles the whole thing this is a + + align:start position:0% +assembles the whole thing this is a + + + align:start position:0% +assembles the whole thing this is a +yeast cell that purple thing which is + + align:start position:0% +yeast cell that purple thing which is + + + align:start position:0% +yeast cell that purple thing which is +artificially colored is the nucleus this + + align:start position:0% +artificially colored is the nucleus this + + + align:start position:0% +artificially colored is the nucleus this +thing in the middle is a big storage + + align:start position:0% +thing in the middle is a big storage + + + align:start position:0% +thing in the middle is a big storage +thing called a vacu in the cell we can't + + align:start position:0% +thing called a vacu in the cell we can't + + + align:start position:0% +thing called a vacu in the cell we can't +see the other cellular components right + + align:start position:0% +see the other cellular components right + + + align:start position:0% +see the other cellular components right +now but that is a real cell it looks + + align:start position:0% +now but that is a real cell it looks + + + align:start position:0% +now but that is a real cell it looks +like like a textbook but it's actually a + + align:start position:0% +like like a textbook but it's actually a + + + align:start position:0% +like like a textbook but it's actually a +yeast cell that got its picture taken by + + align:start position:0% +yeast cell that got its picture taken by + + + align:start position:0% +yeast cell that got its picture taken by +this very fancy thing so as I say we're + + align:start position:0% +this very fancy thing so as I say we're + + + align:start position:0% +this very fancy thing so as I say we're +going to charge right now into starting + + align:start position:0% +going to charge right now into starting + + + align:start position:0% +going to charge right now into starting +to think about these various Force + + align:start position:0% +to think about these various Force + + + align:start position:0% +to think about these various Force +molecular forces that make possible that + + align:start position:0% +molecular forces that make possible that + + + align:start position:0% +molecular forces that make possible that +give these various biomolecules and + + align:start position:0% +give these various biomolecules and + + + align:start position:0% +give these various biomolecules and +biomacromolecules their their properties + + align:start position:0% +biomacromolecules their their properties + + + align:start position:0% +biomacromolecules their their properties +and I just want to give you sort of a a + + align:start position:0% +and I just want to give you sort of a a + + + align:start position:0% +and I just want to give you sort of a a +game plan for how we're going to do this + + align:start position:0% +game plan for how we're going to do this + + + align:start position:0% +game plan for how we're going to do this +um over the next couple of lessons uh + + align:start position:0% +um over the next couple of lessons uh + + + align:start position:0% +um over the next couple of lessons uh +couple of classes they're sort of + + align:start position:0% +couple of classes they're sort of + + + align:start position:0% +couple of classes they're sort of +classes of chemical + + align:start position:0% +classes of chemical + + + align:start position:0% +classes of chemical +forces and + + align:start position:0% +forces and + + + align:start position:0% +forces and +today we'll be talking about Cove valent + + align:start position:0% + + + + align:start position:0% + +bonds and hydrogen bonds and we'll go on + + align:start position:0% +bonds and hydrogen bonds and we'll go on + + + align:start position:0% +bonds and hydrogen bonds and we'll go on +to talk about other ones in the next uh + + align:start position:0% +to talk about other ones in the next uh + + + align:start position:0% +to talk about other ones in the next uh +the next class or two and then we're + + align:start position:0% +the next class or two and then we're + + + align:start position:0% +the next class or two and then we're +going to talk about these + + align:start position:0% + + + + align:start position:0% + +uh biot biological + + align:start position:0% +uh biot biological + + + align:start position:0% +uh biot biological +macromolecules that I just + + align:start position:0% + + + + align:start position:0% + +listed so the proteins actually the + + align:start position:0% +listed so the proteins actually the + + + align:start position:0% +listed so the proteins actually the +order we'll be talking about + + align:start position:0% +order we'll be talking about + + + align:start position:0% +order we'll be talking about +them + + align:start position:0% + + + + align:start position:0% + +carbohydrates nucleic + + align:start position:0% + + + + align:start position:0% + +acids + + align:start position:0% +acids + + + align:start position:0% +acids +proteins and lipids so the way I'm going + + align:start position:0% +proteins and lipids so the way I'm going + + + align:start position:0% +proteins and lipids so the way I'm going +to do this is I can tell you about the + + align:start position:0% +to do this is I can tell you about the + + + align:start position:0% +to do this is I can tell you about the +properties of carbohydrates by just + + align:start position:0% +properties of carbohydrates by just + + + align:start position:0% +properties of carbohydrates by just +talking talk about Cove valent bonds and + + align:start position:0% +talking talk about Cove valent bonds and + + + align:start position:0% +talking talk about Cove valent bonds and +hydrogen bonds so once we've discussed + + align:start position:0% +hydrogen bonds so once we've discussed + + + align:start position:0% +hydrogen bonds so once we've discussed +those we'll go on here and I'll give you + + align:start position:0% +those we'll go on here and I'll give you + + + align:start position:0% +those we'll go on here and I'll give you +a couple of examples and once we've + + align:start position:0% +a couple of examples and once we've + + + align:start position:0% +a couple of examples and once we've +learned some more we'll go on and I'll + + align:start position:0% +learned some more we'll go on and I'll + + + align:start position:0% +learned some more we'll go on and I'll +give you some other examples and as i s + + align:start position:0% +give you some other examples and as i s + + + align:start position:0% +give you some other examples and as i s +said in a second I'm going to say Cove + + align:start position:0% +said in a second I'm going to say Cove + + + align:start position:0% +said in a second I'm going to say Cove +valent bonds it's going to see boring + + align:start position:0% +valent bonds it's going to see boring + + + align:start position:0% +valent bonds it's going to see boring +here's here's just something to sort of + + align:start position:0% +here's here's just something to sort of + + + align:start position:0% +here's here's just something to sort of +keep in we'll get another one in a + + align:start position:0% +keep in we'll get another one in a + + + align:start position:0% +keep in we'll get another one in a +minute um to look ahead why why do we + + align:start position:0% +minute um to look ahead why why do we + + + align:start position:0% +minute um to look ahead why why do we +want to do this sort of stuff I showed + + align:start position:0% +want to do this sort of stuff I showed + + + align:start position:0% +want to do this sort of stuff I showed +you this picture the other day these are + + align:start position:0% +you this picture the other day these are + + + align:start position:0% +you this picture the other day these are +eoli swimming along those things I told + + align:start position:0% +eoli swimming along those things I told + + + align:start position:0% +eoli swimming along those things I told +you are those sort of long spiral Things + + align:start position:0% +you are those sort of long spiral Things + + + align:start position:0% +you are those sort of long spiral Things +Are bundles of protein filaments called + + align:start position:0% +Are bundles of protein filaments called + + + align:start position:0% +Are bundles of protein filaments called +flagella they're being rotated by a + + align:start position:0% +flagella they're being rotated by a + + + align:start position:0% +flagella they're being rotated by a +motor at the end of the the bacterium + + align:start position:0% +motor at the end of the the bacterium + + + align:start position:0% +motor at the end of the the bacterium +that's rotating 10 to 100,000 RPM and + + align:start position:0% +that's rotating 10 to 100,000 RPM and + + + align:start position:0% +that's rotating 10 to 100,000 RPM and +that thing's moving at such a rate so + + align:start position:0% +that thing's moving at such a rate so + + + align:start position:0% +that thing's moving at such a rate so +many body lengths a second that if it + + align:start position:0% +many body lengths a second that if it + + + align:start position:0% +many body lengths a second that if it +was me moving at that speed I'd be going + + align:start position:0% +was me moving at that speed I'd be going + + + align:start position:0% +was me moving at that speed I'd be going +300 mil an hour that many body links so + + align:start position:0% +300 mil an hour that many body links so + + + align:start position:0% +300 mil an hour that many body links so +these are bacteria swimming around um + + align:start position:0% +these are bacteria swimming around um + + + align:start position:0% +these are bacteria swimming around um +the motor that drives them is made of + + align:start position:0% +the motor that drives them is made of + + + align:start position:0% +the motor that drives them is made of +proteins this is a textbook + + align:start position:0% +proteins this is a textbook + + + align:start position:0% +proteins this is a textbook +representation of that motor uh it has + + align:start position:0% +representation of that motor uh it has + + + align:start position:0% +representation of that motor uh it has +has familiar parts to some of you uh it + + align:start position:0% +has familiar parts to some of you uh it + + + align:start position:0% +has familiar parts to some of you uh it +has a rotor there's a bushing there's a + + align:start position:0% +has a rotor there's a bushing there's a + + + align:start position:0% +has a rotor there's a bushing there's a +drive shaft and so on it's got parts + + align:start position:0% +drive shaft and so on it's got parts + + + align:start position:0% +drive shaft and so on it's got parts +that you would recognize uh as an + + align:start position:0% +that you would recognize uh as an + + + align:start position:0% +that you would recognize uh as an +engineer but it's all made out of + + align:start position:0% +engineer but it's all made out of + + + align:start position:0% +engineer but it's all made out of +proteins and that's a textbook diagram + + align:start position:0% +proteins and that's a textbook diagram + + + align:start position:0% +proteins and that's a textbook diagram +what I want to show you in the next + + align:start position:0% +what I want to show you in the next + + + align:start position:0% +what I want to show you in the next +slide is they've taken a whole lot of + + align:start position:0% +slide is they've taken a whole lot of + + + align:start position:0% +slide is they've taken a whole lot of +electron micrographic images of those + + align:start position:0% +electron micrographic images of those + + + align:start position:0% +electron micrographic images of those +things and the resolution isn't so good + + align:start position:0% +things and the resolution isn't so good + + + align:start position:0% +things and the resolution isn't so good +but they averaged a whole bunch of them + + align:start position:0% +but they averaged a whole bunch of them + + + align:start position:0% +but they averaged a whole bunch of them +and this is what it looks + + align:start position:0% +and this is what it looks + + + align:start position:0% +and this is what it looks +like so you can sort of see this is this + + align:start position:0% +like so you can sort of see this is this + + + align:start position:0% +like so you can sort of see this is this +is really is a machine it's built of + + align:start position:0% +is really is a machine it's built of + + + align:start position:0% +is really is a machine it's built of +proteins and to understand how these + + align:start position:0% +proteins and to understand how these + + + align:start position:0% +proteins and to understand how these +machines work you have to understand + + align:start position:0% +machines work you have to understand + + + align:start position:0% +machines work you have to understand +some of these forces so that's why I'm + + align:start position:0% +some of these forces so that's why I'm + + + align:start position:0% +some of these forces so that's why I'm +going to start in and we're going to + + align:start position:0% +going to start in and we're going to + + + align:start position:0% +going to start in and we're going to +begin with coil and bond so that we're + + align:start position:0% +begin with coil and bond so that we're + + + align:start position:0% +begin with coil and bond so that we're +all on the same page right from the + + align:start position:0% +all on the same page right from the + + + align:start position:0% +all on the same page right from the +right from the beginning and another + + align:start position:0% +right from the beginning and another + + + align:start position:0% +right from the beginning and another +aspect as you'll see even though you may + + align:start position:0% +aspect as you'll see even though you may + + + align:start position:0% +aspect as you'll see even though you may +have heard about uh some of these bonds + + align:start position:0% +have heard about uh some of these bonds + + + align:start position:0% +have heard about uh some of these bonds +before there's a new issue that's going + + align:start position:0% +before there's a new issue that's going + + + align:start position:0% +before there's a new issue that's going +to need to uh occupy your your uh your + + align:start position:0% +to need to uh occupy your your uh your + + + align:start position:0% +to need to uh occupy your your uh your +attention and that is what's the + + align:start position:0% +attention and that is what's the + + + align:start position:0% +attention and that is what's the +strength the bond in the context of uh + + align:start position:0% +strength the bond in the context of uh + + + align:start position:0% +strength the bond in the context of uh +temperatures and conditions that are + + align:start position:0% +temperatures and conditions that are + + + align:start position:0% +temperatures and conditions that are +relevant to to life if you can break a + + align:start position:0% +relevant to to life if you can break a + + + align:start position:0% +relevant to to life if you can break a +bond at a th000 deges it doesn't matter + + align:start position:0% +bond at a th000 deges it doesn't matter + + + align:start position:0% +bond at a th000 deges it doesn't matter +because you can't have life at that at + + align:start position:0% +because you can't have life at that at + + + align:start position:0% +because you can't have life at that at +that temperature we got to be thinking + + align:start position:0% +that temperature we got to be thinking + + + align:start position:0% +that temperature we got to be thinking +about a much more restricted uh + + align:start position:0% +about a much more restricted uh + + + align:start position:0% +about a much more restricted uh +temperature sort of range so calent + + align:start position:0% +temperature sort of range so calent + + + align:start position:0% +temperature sort of range so calent +bonds most of you know this is the + + align:start position:0% +bonds most of you know this is the + + + align:start position:0% +bonds most of you know this is the +principal + + align:start position:0% +principal + + + align:start position:0% +principal +force that holds atoms together + + align:start position:0% + + + + align:start position:0% + +it involves a sharing of the + + align:start position:0% + + + + align:start position:0% + +electrons and the you know example you + + align:start position:0% +electrons and the you know example you + + + align:start position:0% +electrons and the you know example you +can all do in your sleep I'm sure if we + + align:start position:0% +can all do in your sleep I'm sure if we + + + align:start position:0% +can all do in your sleep I'm sure if we +take four hydrogen atoms and a carbon + + align:start position:0% +take four hydrogen atoms and a carbon + + + align:start position:0% +take four hydrogen atoms and a carbon +atom we can come up with this + + align:start position:0% + + + + align:start position:0% + +molecule which has four Cove valent + + align:start position:0% +molecule which has four Cove valent + + + align:start position:0% +molecule which has four Cove valent +bonds this is + + align:start position:0% +bonds this is + + + align:start position:0% +bonds this is +methane that's the molecule that that + + align:start position:0% +methane that's the molecule that that + + + align:start position:0% +methane that's the molecule that that +cow saw the other day burps 400 lers of + + align:start position:0% +cow saw the other day burps 400 lers of + + + align:start position:0% +cow saw the other day burps 400 lers of +of those are the little bubbles you see + + align:start position:0% +of those are the little bubbles you see + + + align:start position:0% +of those are the little bubbles you see +coming up when you walk around in a the + + align:start position:0% +coming up when you walk around in a the + + + align:start position:0% +coming up when you walk around in a the +edge of a lake um and it's usually those + + align:start position:0% +edge of a lake um and it's usually those + + + align:start position:0% +edge of a lake um and it's usually those +pairs of electrons as you know are + + align:start position:0% +pairs of electrons as you know are + + + align:start position:0% +pairs of electrons as you know are +usually + + align:start position:0% +usually + + + align:start position:0% +usually +represented like this the typical + + align:start position:0% +represented like this the typical + + + align:start position:0% +represented like this the typical +length is about 0.15 to + + align:start position:0% +length is about 0.15 to + + + align:start position:0% +length is about 0.15 to +0.2 + + align:start position:0% +0.2 + + + align:start position:0% +0.2 +nanometers and the important thing about + + align:start position:0% +nanometers and the important thing about + + + align:start position:0% +nanometers and the important thing about +this these bonds is these are strong + + align:start position:0% + + + + align:start position:0% + +there takes about + + align:start position:0% +there takes about + + + align:start position:0% +there takes about +83 kilo calories per + + align:start position:0% + + + + align:start position:0% + +mole to break a carbon carbon Bond + + align:start position:0% +mole to break a carbon carbon Bond + + + align:start position:0% +mole to break a carbon carbon Bond +so at physiologically relevant + + align:start position:0% + + + + align:start position:0% + +temperatures they don't break + + align:start position:0% + + + + align:start position:0% + +they can they can + + align:start position:0% +they can they can + + + align:start position:0% +they can they can +rotate they can + + align:start position:0% + + + + align:start position:0% + +stretch and they can bend but they're + + align:start position:0% +stretch and they can bend but they're + + + align:start position:0% +stretch and they can bend but they're +not going to break and so if you have a + + align:start position:0% +not going to break and so if you have a + + + align:start position:0% +not going to break and so if you have a +carbon carbon bond in a in a biological + + align:start position:0% +carbon carbon bond in a in a biological + + + align:start position:0% +carbon carbon bond in a in a biological +organism it'll be doing this the carbons + + align:start position:0% +organism it'll be doing this the carbons + + + align:start position:0% +organism it'll be doing this the carbons +will be going this way they'll be + + align:start position:0% +will be going this way they'll be + + + align:start position:0% +will be going this way they'll be +bending back and forth this way but they + + align:start position:0% +bending back and forth this way but they + + + align:start position:0% +bending back and forth this way but they +won't be breaking and to just give you a + + align:start position:0% +won't be breaking and to just give you a + + + align:start position:0% +won't be breaking and to just give you a +sense of how far away they are from + + align:start position:0% +sense of how far away they are from + + + align:start position:0% +sense of how far away they are from +breaking the energy of say one of these + + align:start position:0% +breaking the energy of say one of these + + + align:start position:0% +breaking the energy of say one of these +vibrational modes is about + + align:start position:0% +vibrational modes is about + + + align:start position:0% +vibrational modes is about +0.6 kilo calories per mole so that you + + align:start position:0% +0.6 kilo calories per mole so that you + + + align:start position:0% +0.6 kilo calories per mole so that you +have your the average uh um bond is so + + align:start position:0% +have your the average uh um bond is so + + + align:start position:0% +have your the average uh um bond is so +far away from breaking even though it's + + align:start position:0% +far away from breaking even though it's + + + align:start position:0% +far away from breaking even though it's +a distribution in some more than others + + align:start position:0% +a distribution in some more than others + + + align:start position:0% +a distribution in some more than others +that our our molecules stay together + + align:start position:0% +that our our molecules stay together + + + align:start position:0% +that our our molecules stay together +which is good because we wouldn't want + + align:start position:0% +which is good because we wouldn't want + + + align:start position:0% +which is good because we wouldn't want +our DNA flying apart because the carbon + + align:start position:0% +our DNA flying apart because the carbon + + + align:start position:0% +our DNA flying apart because the carbon +the calent bonds were breaking under + + align:start position:0% +the calent bonds were breaking under + + + align:start position:0% +the calent bonds were breaking under +physiological conditions but that also + + align:start position:0% +physiological conditions but that also + + + align:start position:0% +physiological conditions but that also +uh lead leads us to the need for one of + + align:start position:0% +uh lead leads us to the need for one of + + + align:start position:0% +uh lead leads us to the need for one of +the things you that we'll have to talk + + align:start position:0% +the things you that we'll have to talk + + + align:start position:0% +the things you that we'll have to talk +about because one of the great secrets + + align:start position:0% +about because one of the great secrets + + + align:start position:0% +about because one of the great secrets +of life is that the metabolism all + + align:start position:0% +of life is that the metabolism all + + + align:start position:0% +of life is that the metabolism all +stages of Life involve the making and + + align:start position:0% +stages of Life involve the making and + + + align:start position:0% +stages of Life involve the making and +the breaking of bonds and you can't just + + align:start position:0% +the breaking of bonds and you can't just + + + align:start position:0% +the breaking of bonds and you can't just +add a platinum Catalyst and put it at + + align:start position:0% +add a platinum Catalyst and put it at + + + align:start position:0% +add a platinum Catalyst and put it at +500 degre Centigrade under a th000 + + align:start position:0% +500 degre Centigrade under a th000 + + + align:start position:0% +500 degre Centigrade under a th000 +atmospheres of pressure all the + + align:start position:0% +atmospheres of pressure all the + + + align:start position:0% +atmospheres of pressure all the +chemistry that happens in life has to + + align:start position:0% +chemistry that happens in life has to + + + align:start position:0% +chemistry that happens in life has to +take place in aquous solution pretty + + align:start position:0% +take place in aquous solution pretty + + + align:start position:0% +take place in aquous solution pretty +close to ph7 at at about you know 25 37 + + align:start position:0% +close to ph7 at at about you know 25 37 + + + align:start position:0% +close to ph7 at at about you know 25 37 +de Centigrade there few organisms that + + align:start position:0% +de Centigrade there few organisms that + + + align:start position:0% +de Centigrade there few organisms that +can do it out but most of it's somewhere + + align:start position:0% +can do it out but most of it's somewhere + + + align:start position:0% +can do it out but most of it's somewhere +around body temperature room + + align:start position:0% +around body temperature room + + + align:start position:0% +around body temperature room +temperatures where all that has to take + + align:start position:0% +temperatures where all that has to take + + + align:start position:0% +temperatures where all that has to take +place so what you can see is there had + + align:start position:0% +place so what you can see is there had + + + align:start position:0% +place so what you can see is there had +to be some for or in order for life to + + align:start position:0% +to be some for or in order for life to + + + align:start position:0% +to be some for or in order for life to +occur there had to be some invention + + align:start position:0% +occur there had to be some invention + + + align:start position:0% +occur there had to be some invention +that would let bonds bro be broken and + + align:start position:0% +that would let bonds bro be broken and + + + align:start position:0% +that would let bonds bro be broken and +be formed under physiologically relevant + + align:start position:0% +be formed under physiologically relevant + + + align:start position:0% +be formed under physiologically relevant +conditions and those are enzymes I know + + align:start position:0% +conditions and those are enzymes I know + + + align:start position:0% +conditions and those are enzymes I know +most of you have heard of those we'll + + align:start position:0% +most of you have heard of those we'll + + + align:start position:0% +most of you have heard of those we'll +talk about them in maybe more some level + + align:start position:0% +talk about them in maybe more some level + + + align:start position:0% +talk about them in maybe more some level +that you beyond what some of you have + + align:start position:0% +that you beyond what some of you have + + + align:start position:0% +that you beyond what some of you have +heard anyway but but that keep in mind + + align:start position:0% +heard anyway but but that keep in mind + + + align:start position:0% +heard anyway but but that keep in mind +now that's the driving force for why you + + align:start position:0% +now that's the driving force for why you + + + align:start position:0% +now that's the driving force for why you +need um why we need enzymes because + + align:start position:0% +need um why we need enzymes because + + + align:start position:0% +need um why we need enzymes because +calent bonds are so strong also um + + align:start position:0% +calent bonds are so strong also um + + + align:start position:0% +calent bonds are so strong also um +remind you that there are different + + align:start position:0% +remind you that there are different + + + align:start position:0% +remind you that there are different +types of calent bonds that's a single + + align:start position:0% +types of calent bonds that's a single + + + align:start position:0% +types of calent bonds that's a single +bond this would be a + + align:start position:0% +bond this would be a + + + align:start position:0% +bond this would be a +double bond or a triple bond and they + + align:start position:0% +double bond or a triple bond and they + + + align:start position:0% +double bond or a triple bond and they +get stronger as you share more uh + + align:start position:0% +get stronger as you share more uh + + + align:start position:0% +get stronger as you share more uh +electrons takes gets harder and harder + + align:start position:0% +electrons takes gets harder and harder + + + align:start position:0% +electrons takes gets harder and harder +to break break + + align:start position:0% +to break break + + + align:start position:0% +to break break +them these are called double and triple + + align:start position:0% +them these are called double and triple + + + align:start position:0% +them these are called double and triple +bonds are called unsaturated + + align:start position:0% +bonds are called unsaturated + + + align:start position:0% +bonds are called unsaturated +bonds when we talk about unsaturated + + align:start position:0% +bonds when we talk about unsaturated + + + align:start position:0% +bonds when we talk about unsaturated +fats and things that's because they have + + align:start position:0% +fats and things that's because they have + + + align:start position:0% +fats and things that's because they have +double Bonds in them so olive oil has + + align:start position:0% +double Bonds in them so olive oil has + + + align:start position:0% +double Bonds in them so olive oil has +double Bonds in it and beef fat for + + align:start position:0% +double Bonds in it and beef fat for + + + align:start position:0% +double Bonds in it and beef fat for +example doesn't um other molecules that + + align:start position:0% +example doesn't um other molecules that + + + align:start position:0% +example doesn't um other molecules that +have double bonds that are important are + + align:start position:0% +have double bonds that are important are + + + align:start position:0% +have double bonds that are important are +oxygen and nitrogen gas which is got a + + align:start position:0% +oxygen and nitrogen gas which is got a + + + align:start position:0% +oxygen and nitrogen gas which is got a +triple bond and when Kenny talks to you + + align:start position:0% +triple bond and when Kenny talks to you + + + align:start position:0% +triple bond and when Kenny talks to you +about the nitrogen cycle this is what + + align:start position:0% +about the nitrogen cycle this is what + + + align:start position:0% +about the nitrogen cycle this is what +one of the really important ones + + align:start position:0% +one of the really important ones + + + align:start position:0% +one of the really important ones +thinking about ecology because we all + + align:start position:0% +thinking about ecology because we all + + + align:start position:0% +thinking about ecology because we all +leave all use nitrogen but most + + align:start position:0% +leave all use nitrogen but most + + + align:start position:0% +leave all use nitrogen but most +organisms including themselves and most + + align:start position:0% +organisms including themselves and most + + + align:start position:0% +organisms including themselves and most +things on earth cannot break that bond + + align:start position:0% +things on earth cannot break that bond + + + align:start position:0% +things on earth cannot break that bond +yet we all need nitrogen that has to be + + align:start position:0% +yet we all need nitrogen that has to be + + + align:start position:0% +yet we all need nitrogen that has to be +what they call fixed so it's joined to + + align:start position:0% +what they call fixed so it's joined to + + + align:start position:0% +what they call fixed so it's joined to +something else like ammonia or nitrite + + align:start position:0% +something else like ammonia or nitrite + + + align:start position:0% +something else like ammonia or nitrite +or something like that and that little + + align:start position:0% +or something like that and that little + + + align:start position:0% +or something like that and that little +uh fluorescently labeled bacteria I + + align:start position:0% +uh fluorescently labeled bacteria I + + + align:start position:0% +uh fluorescently labeled bacteria I +showed you invading a plant we'll see it + + align:start position:0% +showed you invading a plant we'll see it + + + align:start position:0% +showed you invading a plant we'll see it +again uh is able to form a symbiosis of + + align:start position:0% +again uh is able to form a symbiosis of + + + align:start position:0% +again uh is able to form a symbiosis of +plant it's one of the few creatures on + + align:start position:0% +plant it's one of the few creatures on + + + align:start position:0% +plant it's one of the few creatures on +Earth that knows how to break that Bond + + align:start position:0% +Earth that knows how to break that Bond + + + align:start position:0% +Earth that knows how to break that Bond +and that's why you can get plants to can + + align:start position:0% +and that's why you can get plants to can + + + align:start position:0% +and that's why you can get plants to can +grow like um peas and beans and alala + + align:start position:0% +grow like um peas and beans and alala + + + align:start position:0% +grow like um peas and beans and alala +and things that can grow with a nitrogen + + align:start position:0% +and things that can grow with a nitrogen + + + align:start position:0% +and things that can grow with a nitrogen +fertilizer because they have a little + + align:start position:0% +fertilizer because they have a little + + + align:start position:0% +fertilizer because they have a little +bacterium who knows how to break that + + align:start position:0% +bacterium who knows how to break that + + + align:start position:0% +bacterium who knows how to break that +Bond and they figured out how to get + + align:start position:0% +Bond and they figured out how to get + + + align:start position:0% +Bond and they figured out how to get +together and collaborate in a + + align:start position:0% +together and collaborate in a + + + align:start position:0% +together and collaborate in a +symbiosis so these bonds are very + + align:start position:0% +symbiosis so these bonds are very + + + align:start position:0% +symbiosis so these bonds are very +important so um there's + + align:start position:0% +important so um there's + + + align:start position:0% +important so um there's +another characteristic of of these bonds + + align:start position:0% +another characteristic of of these bonds + + + align:start position:0% +another characteristic of of these bonds +which is important going to be very + + align:start position:0% +which is important going to be very + + + align:start position:0% +which is important going to be very +important for thinking + + align:start position:0% +important for thinking + + + align:start position:0% +important for thinking +about biology and it's known as + + align:start position:0% +about biology and it's known as + + + align:start position:0% +about biology and it's known as +chirality and it comes from the fact + + align:start position:0% +chirality and it comes from the fact + + + align:start position:0% +chirality and it comes from the fact +that our life on this planet is based on + + align:start position:0% +that our life on this planet is based on + + + align:start position:0% +that our life on this planet is based on +carbon and carbon's ability to form + + align:start position:0% +carbon and carbon's ability to form + + + align:start position:0% +carbon and carbon's ability to form +remarkable kinds of bonds and as you see + + align:start position:0% +remarkable kinds of bonds and as you see + + + align:start position:0% +remarkable kinds of bonds and as you see +over there carbon forms four bonds but + + align:start position:0% +over there carbon forms four bonds but + + + align:start position:0% +over there carbon forms four bonds but +right now we have to start thinking in + + align:start position:0% +right now we have to start thinking in + + + align:start position:0% +right now we have to start thinking in +three-dimensional space because carbon + + align:start position:0% +three-dimensional space because carbon + + + align:start position:0% +three-dimensional space because carbon +is a + + align:start position:0% +is a + + + align:start position:0% +is a +tetrahedron carbon four single bonds + + align:start position:0% + + + + align:start position:0% + +and they're in a + + align:start position:0% + + + + align:start position:0% + +tetrahedral Arrangement so if I lab them + + align:start position:0% +tetrahedral Arrangement so if I lab them + + + align:start position:0% +tetrahedral Arrangement so if I lab them +like this I'm going to this means it's + + align:start position:0% +like this I'm going to this means it's + + + align:start position:0% +like this I'm going to this means it's +coming out of the board sorry A B C and + + align:start position:0% +coming out of the board sorry A B C and + + + align:start position:0% +coming out of the board sorry A B C and +that means it's going back into the + + align:start position:0% +that means it's going back into the + + + align:start position:0% +that means it's going back into the +board so if I do a mirror + + align:start position:0% + + + + align:start position:0% + +image if I look what this would look + + align:start position:0% +image if I look what this would look + + + align:start position:0% +image if I look what this would look +like if I could look at Its Reflection + + align:start position:0% +like if I could look at Its Reflection + + + align:start position:0% +like if I could look at Its Reflection +in a mirror I'd see it would look like + + align:start position:0% + + + + align:start position:0% + +this so these are what are known as + + align:start position:0% +this so these are what are known as + + + align:start position:0% +this so these are what are known as +Optical + + align:start position:0% + + + + align:start position:0% + +isomers and depending on how you are + + align:start position:0% +isomers and depending on how you are + + + align:start position:0% +isomers and depending on how you are +thinking in three dimensions this may be + + align:start position:0% +thinking in three dimensions this may be + + + align:start position:0% +thinking in three dimensions this may be +obvious to you or it may not be obvious + + align:start position:0% +obvious to you or it may not be obvious + + + align:start position:0% +obvious to you or it may not be obvious +to you but you cannot superimpose + + align:start position:0% +to you but you cannot superimpose + + + align:start position:0% +to you but you cannot superimpose +those and this is critical because all + + align:start position:0% +those and this is critical because all + + + align:start position:0% +those and this is critical because all +through biology uh there are carbons + + align:start position:0% +through biology uh there are carbons + + + align:start position:0% +through biology uh there are carbons +that have four different substituents + + align:start position:0% +that have four different substituents + + + align:start position:0% +that have four different substituents +join to them and every time that occurs + + align:start position:0% +join to them and every time that occurs + + + align:start position:0% +join to them and every time that occurs +biology chooses one of those + + align:start position:0% +biology chooses one of those + + + align:start position:0% +biology chooses one of those +arrangements not the other and we have + + align:start position:0% +arrangements not the other and we have + + + align:start position:0% +arrangements not the other and we have +sort of a + + align:start position:0% +sort of a + + + align:start position:0% +sort of a +macro way of perhaps communicating this + + align:start position:0% +macro way of perhaps communicating this + + + align:start position:0% +macro way of perhaps communicating this +so you you've been at the the party at + + align:start position:0% +so you you've been at the the party at + + + align:start position:0% +so you you've been at the the party at +the dorm we were host I was host Masters + + align:start position:0% +the dorm we were host I was host Masters + + + align:start position:0% +the dorm we were host I was host Masters +in mccormic for six years a while back + + align:start position:0% +in mccormic for six years a while back + + + align:start position:0% +in mccormic for six years a while back +so I've lived at least in that + + align:start position:0% +so I've lived at least in that + + + align:start position:0% +so I've lived at least in that +environment it's uh early February + + align:start position:0% +environment it's uh early February + + + align:start position:0% +environment it's uh early February +you're having to go back across the mass + + align:start position:0% +you're having to go back across the mass + + + align:start position:0% +you're having to go back across the mass +that bridge it's minus 20 and the wind + + align:start position:0% +that bridge it's minus 20 and the wind + + + align:start position:0% +that bridge it's minus 20 and the wind +is whipping along and your hands are + + align:start position:0% +is whipping along and your hands are + + + align:start position:0% +is whipping along and your hands are +freezing and you reach into your pocket + + align:start position:0% +freezing and you reach into your pocket + + + align:start position:0% +freezing and you reach into your pocket +to get your gloves and + + align:start position:0% +to get your gloves and + + + align:start position:0% +to get your gloves and +uh-oh two left + + align:start position:0% +uh-oh two left + + + align:start position:0% +uh-oh two left +gloves right there you have the problem + + align:start position:0% +gloves right there you have the problem + + + align:start position:0% +gloves right there you have the problem +that biology as a theme you'll hear over + + align:start position:0% +that biology as a theme you'll hear over + + + align:start position:0% +that biology as a theme you'll hear over +and over again is about fitting shapes + + align:start position:0% +and over again is about fitting shapes + + + align:start position:0% +and over again is about fitting shapes +and your hands are mere images of each + + align:start position:0% +and your hands are mere images of each + + + align:start position:0% +and your hands are mere images of each +other and you could think of the your + + align:start position:0% +other and you could think of the your + + + align:start position:0% +other and you could think of the your +gloves as being sort of a receptor and + + align:start position:0% +gloves as being sort of a receptor and + + + align:start position:0% +gloves as being sort of a receptor and +if the receptors designed to take your + + align:start position:0% +if the receptors designed to take your + + + align:start position:0% +if the receptors designed to take your +right hand you can't or take a left hand + + align:start position:0% +right hand you can't or take a left hand + + + align:start position:0% +right hand you can't or take a left hand +I guess let's say you can't get your + + align:start position:0% +I guess let's say you can't get your + + + align:start position:0% +I guess let's say you can't get your +right hand into the glove it just + + align:start position:0% +right hand into the glove it just + + + align:start position:0% +right hand into the glove it just +doesn't fit and it's at a molecular + + align:start position:0% +doesn't fit and it's at a molecular + + + align:start position:0% +doesn't fit and it's at a molecular +level it's exactly that same thing so + + align:start position:0% +level it's exactly that same thing so + + + align:start position:0% +level it's exactly that same thing so +we're going to have to worry as we + + align:start position:0% +we're going to have to worry as we + + + align:start position:0% +we're going to have to worry as we +go uh through this about not only how + + align:start position:0% +go uh through this about not only how + + + align:start position:0% +go uh through this about not only how +many bonds there are but this is why uh + + align:start position:0% +many bonds there are but this is why uh + + + align:start position:0% +many bonds there are but this is why uh +the exact molecular shape including this + + align:start position:0% +the exact molecular shape including this + + + align:start position:0% +the exact molecular shape including this +Optical isomer issue is going to be very + + align:start position:0% +Optical isomer issue is going to be very + + + align:start position:0% +Optical isomer issue is going to be very +important um there's another very + + align:start position:0% +important um there's another very + + + align:start position:0% +important um there's another very +important principle of of uh calent + + align:start position:0% +important principle of of uh calent + + + align:start position:0% +important principle of of uh calent +bonds that has again huge impact on uh + + align:start position:0% +bonds that has again huge impact on uh + + + align:start position:0% +bonds that has again huge impact on uh +on biology and that concerns how the + + align:start position:0% +on biology and that concerns how the + + + align:start position:0% +on biology and that concerns how the +atoms + + align:start position:0% +atoms + + + align:start position:0% +atoms +involved in the forming the calent bond + + align:start position:0% +involved in the forming the calent bond + + + align:start position:0% +involved in the forming the calent bond +uh think about sharing electrons in some + + align:start position:0% +uh think about sharing electrons in some + + + align:start position:0% +uh think about sharing electrons in some +cases the sharing is pretty much equal + + align:start position:0% +cases the sharing is pretty much equal + + + align:start position:0% +cases the sharing is pretty much equal +it's in a carbon carbon bond that would + + align:start position:0% +it's in a carbon carbon bond that would + + + align:start position:0% +it's in a carbon carbon bond that would +make sense since it's the same thing on + + align:start position:0% +make sense since it's the same thing on + + + align:start position:0% +make sense since it's the same thing on +both sides or a carbon hydrogen bond the + + align:start position:0% +both sides or a carbon hydrogen bond the + + + align:start position:0% +both sides or a carbon hydrogen bond the +the sharing of electrons pretty much the + + align:start position:0% +the sharing of electrons pretty much the + + + align:start position:0% +the sharing of electrons pretty much the +same so the electrons on average are + + align:start position:0% +same so the electrons on average are + + + align:start position:0% +same so the electrons on average are +distributed in between them and this is + + align:start position:0% +distributed in between them and this is + + + align:start position:0% +distributed in between them and this is +what's known as a non-polar Bond + + align:start position:0% + + + + align:start position:0% + +however there are important cases of + + align:start position:0% +however there are important cases of + + + align:start position:0% +however there are important cases of +unequal + + align:start position:0% +unequal + + + align:start position:0% +unequal +sharing and uh the characteristic of an + + align:start position:0% +sharing and uh the characteristic of an + + + align:start position:0% +sharing and uh the characteristic of an +atom that or an element that determines + + align:start position:0% +atom that or an element that determines + + + align:start position:0% +atom that or an element that determines +how the sharing goes is known as electro + + align:start position:0% +how the sharing goes is known as electro + + + align:start position:0% +how the sharing goes is known as electro +negativity and you could think of this + + align:start position:0% +negativity and you could think of this + + + align:start position:0% +negativity and you could think of this +is sort of a euphemism for the + + align:start position:0% + + + + align:start position:0% + +greediness of an atom for electrons + + align:start position:0% + + + + align:start position:0% + +so if you have a oxygen hydrogen bond + + align:start position:0% +so if you have a oxygen hydrogen bond + + + align:start position:0% +so if you have a oxygen hydrogen bond +oxygen is more electr negative than + + align:start position:0% +oxygen is more electr negative than + + + align:start position:0% +oxygen is more electr negative than +hydrogen and what that means is although + + align:start position:0% +hydrogen and what that means is although + + + align:start position:0% +hydrogen and what that means is although +the electrons are still shared this is + + align:start position:0% +the electrons are still shared this is + + + align:start position:0% +the electrons are still shared this is +not an ion or anything the electrons are + + align:start position:0% +not an ion or anything the electrons are + + + align:start position:0% +not an ion or anything the electrons are +shared there's going to be a little bit + + align:start position:0% +shared there's going to be a little bit + + + align:start position:0% +shared there's going to be a little bit +of a negative charge on the oxygen and a + + align:start position:0% +of a negative charge on the oxygen and a + + + align:start position:0% +of a negative charge on the oxygen and a +little bit of a positive charge on the + + align:start position:0% +little bit of a positive charge on the + + + align:start position:0% +little bit of a positive charge on the +hydrogen and that uh means you you know + + align:start position:0% +hydrogen and that uh means you you know + + + align:start position:0% +hydrogen and that uh means you you know +this will have all sorts of consequences + + align:start position:0% +this will have all sorts of consequences + + + align:start position:0% +this will have all sorts of consequences +as you'll see in a minute and there's + + align:start position:0% +as you'll see in a minute and there's + + + align:start position:0% +as you'll see in a minute and there's +one important molecule which we we did + + align:start position:0% +one important molecule which we we did + + + align:start position:0% +one important molecule which we we did +the molecular composition you can see + + align:start position:0% +the molecular composition you can see + + + align:start position:0% +the molecular composition you can see +there's a lot of it around and that's + + align:start position:0% +there's a lot of it around and that's + + + align:start position:0% +there's a lot of it around and that's +water and it's got two o bonds and + + align:start position:0% +water and it's got two o bonds and + + + align:start position:0% +water and it's got two o bonds and +here's where the structure of water is + + align:start position:0% +here's where the structure of water is + + + align:start position:0% +here's where the structure of water is +important that these are not 180 these + + align:start position:0% +important that these are not 180 these + + + align:start position:0% +important that these are not 180 these +two bonds are not 180° opposite to each + + align:start position:0% +two bonds are not 180° opposite to each + + + align:start position:0% +two bonds are not 180° opposite to each +other they're + + align:start position:0% +other they're + + + align:start position:0% +other they're +104.5 de so you end up with a little + + align:start position:0% +104.5 de so you end up with a little + + + align:start position:0% +104.5 de so you end up with a little +negative charge here a little positive + + align:start position:0% +negative charge here a little positive + + + align:start position:0% +negative charge here a little positive +charge here a little positive charge + + align:start position:0% +charge here a little positive charge + + + align:start position:0% +charge here a little positive charge +there and so every single water molecule + + align:start position:0% +there and so every single water molecule + + + align:start position:0% +there and so every single water molecule +sort of has a negative side and more or + + align:start position:0% +sort of has a negative side and more or + + + align:start position:0% +sort of has a negative side and more or +less a positive kind of side and this + + align:start position:0% +less a positive kind of side and this + + + align:start position:0% +less a positive kind of side and this +has consequences because this means that + + align:start position:0% +has consequences because this means that + + + align:start position:0% +has consequences because this means that +the water molecules are going to + + align:start position:0% +the water molecules are going to + + + align:start position:0% +the water molecules are going to +interact and to understand that part + + align:start position:0% +interact and to understand that part + + + align:start position:0% +interact and to understand that part +need to introduce you + + align:start position:0% +need to introduce you + + + align:start position:0% +need to introduce you +to this second + + align:start position:0% + + + + align:start position:0% + +Force which we know is the hydrogen bond + + align:start position:0% + + + + align:start position:0% + +and this is the this is a bond that + + align:start position:0% +and this is the this is a bond that + + + align:start position:0% +and this is the this is a bond that +takes PLC that arises because + + align:start position:0% + + + + align:start position:0% + +of the + + align:start position:0% +of the + + + align:start position:0% +of the +slight positive + + align:start position:0% + + + + align:start position:0% + +charge of an H + + align:start position:0% + + + + align:start position:0% + +bonded to oxygen or + + align:start position:0% + + + + align:start position:0% + +nitrogen and the light negative + + align:start position:0% + + + + align:start position:0% + +charge of the oxygen or the or the + + align:start position:0% +charge of the oxygen or the or the + + + align:start position:0% +charge of the oxygen or the or the +nitrogen itself and right in water we we + + align:start position:0% +nitrogen itself and right in water we we + + + align:start position:0% +nitrogen itself and right in water we we +see this uh be an issue because if we + + align:start position:0% +see this uh be an issue because if we + + + align:start position:0% +see this uh be an issue because if we +have water like this with couple little + + align:start position:0% +have water like this with couple little + + + align:start position:0% +have water like this with couple little +positive little bit of positive charges + + align:start position:0% +positive little bit of positive charges + + + align:start position:0% +positive little bit of positive charges +Here There and a little negative charge + + align:start position:0% +Here There and a little negative charge + + + align:start position:0% +Here There and a little negative charge +here and there's another water + + align:start position:0% +here and there's another water + + + align:start position:0% +here and there's another water +molecule over here little positive + + align:start position:0% +molecule over here little positive + + + align:start position:0% +molecule over here little positive +charge a little negative a little + + align:start position:0% +charge a little negative a little + + + align:start position:0% +charge a little negative a little +positive we can get here is a what's + + align:start position:0% +positive we can get here is a what's + + + align:start position:0% +positive we can get here is a what's +known as a hydrogen + + align:start position:0% +known as a hydrogen + + + align:start position:0% +known as a hydrogen +bond the hydrogen bond is about + + align:start position:0% + + + + align:start position:0% + +12th the + + align:start position:0% + + + + align:start position:0% + +strength of a calent bond and that + + align:start position:0% +strength of a calent bond and that + + + align:start position:0% +strength of a calent bond and that +number is really important because what + + align:start position:0% +number is really important because what + + + align:start position:0% +number is really important because what +that me means is that at temperatures + + align:start position:0% +that me means is that at temperatures + + + align:start position:0% +that me means is that at temperatures +that are relevant for life not all the + + align:start position:0% +that are relevant for life not all the + + + align:start position:0% +that are relevant for life not all the +molecules will have enough energy to + + align:start position:0% +molecules will have enough energy to + + + align:start position:0% +molecules will have enough energy to +break a in a population will have enough + + align:start position:0% +break a in a population will have enough + + + align:start position:0% +break a in a population will have enough +uh energy to break that Bond but some of + + align:start position:0% +uh energy to break that Bond but some of + + + align:start position:0% +uh energy to break that Bond but some of +them will so hydrogen + + align:start position:0% +them will so hydrogen + + + align:start position:0% +them will so hydrogen +bonds uh just write that down so + + align:start position:0% + + + + align:start position:0% + +physiologically relevant + + align:start position:0% + + + + align:start position:0% + +temperatures some molecules + + align:start position:0% + + + + align:start position:0% + +have the energy to + + align:start position:0% + + + + align:start position:0% + +break hydrogen bond and we'll talk about + + align:start position:0% +break hydrogen bond and we'll talk about + + + align:start position:0% +break hydrogen bond and we'll talk about +it next time but probably many of you + + align:start position:0% +it next time but probably many of you + + + align:start position:0% +it next time but probably many of you +know that DNA is made of two strands and + + align:start position:0% +know that DNA is made of two strands and + + + align:start position:0% +know that DNA is made of two strands and +the whole principle of copying the + + align:start position:0% +the whole principle of copying the + + + align:start position:0% +the whole principle of copying the +genetic information is you can pull the + + align:start position:0% +genetic information is you can pull the + + + align:start position:0% +genetic information is you can pull the +strands apart and then copy these comp + + align:start position:0% +strands apart and then copy these comp + + + align:start position:0% +strands apart and then copy these comp +the complimentary information we'll + + align:start position:0% +the complimentary information we'll + + + align:start position:0% +the complimentary information we'll +spend a lot of time talking about that + + align:start position:0% +spend a lot of time talking about that + + + align:start position:0% +spend a lot of time talking about that +but the relevant thing for the moment is + + align:start position:0% +but the relevant thing for the moment is + + + align:start position:0% +but the relevant thing for the moment is +those two strands Each of which are + + align:start position:0% +those two strands Each of which are + + + align:start position:0% +those two strands Each of which are +joined by Cove valent bonds are held + + align:start position:0% +joined by Cove valent bonds are held + + + align:start position:0% +joined by Cove valent bonds are held +together by a whole series of hydrogen + + align:start position:0% +together by a whole series of hydrogen + + + align:start position:0% +together by a whole series of hydrogen +bonds between the different base pairs + + align:start position:0% +bonds between the different base pairs + + + align:start position:0% +bonds between the different base pairs +and so right there sort of is the root + + align:start position:0% +and so right there sort of is the root + + + align:start position:0% +and so right there sort of is the root +of why the cells are able to pull those + + align:start position:0% +of why the cells are able to pull those + + + align:start position:0% +of why the cells are able to pull those +apart put them together and so these + + align:start position:0% +apart put them together and so these + + + align:start position:0% +apart put them together and so these +hydrogen bonds are really really + + align:start position:0% +hydrogen bonds are really really + + + align:start position:0% +hydrogen bonds are really really +important and because we our our life on + + align:start position:0% +important and because we our our life on + + + align:start position:0% +important and because we our our life on +this planet is based in uh we're + + align:start position:0% +this planet is based in uh we're + + + align:start position:0% +this planet is based in uh we're +water-based and the reason water is such + + align:start position:0% +water-based and the reason water is such + + + align:start position:0% +water-based and the reason water is such +a a good solvent is that it is able to + + align:start position:0% +a a good solvent is that it is able to + + + align:start position:0% +a a good solvent is that it is able to +form these hydrogen bonds so this just a + + align:start position:0% +form these hydrogen bonds so this just a + + + align:start position:0% +form these hydrogen bonds so this just a +little movie showing the hydrogen bonds + + align:start position:0% +little movie showing the hydrogen bonds + + + align:start position:0% +little movie showing the hydrogen bonds +little simulation of how they could move + + align:start position:0% +little simulation of how they could move + + + align:start position:0% +little simulation of how they could move +around and um rotate the green thing + + align:start position:0% +around and um rotate the green thing + + + align:start position:0% +around and um rotate the green thing +would be the hydrogen bonds here um this + + align:start position:0% +would be the hydrogen bonds here um this + + + align:start position:0% +would be the hydrogen bonds here um this +is not really a a full representation + + align:start position:0% +is not really a a full representation + + + align:start position:0% +is not really a a full representation +because the uh water molecules are + + align:start position:0% +because the uh water molecules are + + + align:start position:0% +because the uh water molecules are +constantly Changing Partners so they + + align:start position:0% +constantly Changing Partners so they + + + align:start position:0% +constantly Changing Partners so they +form little cages and little shells but + + align:start position:0% +form little cages and little shells but + + + align:start position:0% +form little cages and little shells but +they keep forming hydrogen bonds they'll + + align:start position:0% +they keep forming hydrogen bonds they'll + + + align:start position:0% +they keep forming hydrogen bonds they'll +break one with one water molecule + + align:start position:0% +break one with one water molecule + + + align:start position:0% +break one with one water molecule +immediately reform with another + + align:start position:0% +immediately reform with another + + + align:start position:0% +immediately reform with another +this is a simulation of some that + + align:start position:0% +this is a simulation of some that + + + align:start position:0% +this is a simulation of some that +someone did it's a PC of of what would + + align:start position:0% +someone did it's a PC of of what would + + + align:start position:0% +someone did it's a PC of of what would +happen to water molecules at 0° + + align:start position:0% +happen to water molecules at 0° + + + align:start position:0% +happen to water molecules at 0° +Centigrade where they're liquid so at + + align:start position:0% +Centigrade where they're liquid so at + + + align:start position:0% +Centigrade where they're liquid so at +this point they're they haven't Frozen + + align:start position:0% +this point they're they haven't Frozen + + + align:start position:0% +this point they're they haven't Frozen +but they're just above that and they're + + align:start position:0% +but they're just above that and they're + + + align:start position:0% +but they're just above that and they're +you can sort of get the sense how + + align:start position:0% +you can sort of get the sense how + + + align:start position:0% +you can sort of get the sense how +they're Changing Partners here here's + + align:start position:0% +they're Changing Partners here here's + + + align:start position:0% +they're Changing Partners here here's +another simulation uh done at 100° so + + align:start position:0% +another simulation uh done at 100° so + + + align:start position:0% +another simulation uh done at 100° so +You' be this would be at uh Centigrade + + align:start position:0% +You' be this would be at uh Centigrade + + + align:start position:0% +You' be this would be at uh Centigrade +this would be a boiling temperature what + + align:start position:0% +this would be a boiling temperature what + + + align:start position:0% +this would be a boiling temperature what +you can see now is every now and then + + align:start position:0% +you can see now is every now and then + + + align:start position:0% +you can see now is every now and then +one of the molecules gets enough energy + + align:start position:0% +one of the molecules gets enough energy + + + align:start position:0% +one of the molecules gets enough energy +to break free of these cages and that + + align:start position:0% +to break free of these cages and that + + + align:start position:0% +to break free of these cages and that +when you're watching something boil in a + + align:start position:0% +when you're watching something boil in a + + + align:start position:0% +when you're watching something boil in a +kettle that at a molecular level is + + align:start position:0% +kettle that at a molecular level is + + + align:start position:0% +kettle that at a molecular level is +what's happening is one or another + + align:start position:0% +what's happening is one or another + + + align:start position:0% +what's happening is one or another +molecule is finally getting enough + + align:start position:0% +molecule is finally getting enough + + + align:start position:0% +molecule is finally getting enough +energy to break free of this sort of + + align:start position:0% +energy to break free of this sort of + + + align:start position:0% +energy to break free of this sort of +change of hydrogen + + align:start position:0% +change of hydrogen + + + align:start position:0% +change of hydrogen +um uh bonds that are formed and it's + + align:start position:0% +um uh bonds that are formed and it's + + + align:start position:0% +um uh bonds that are formed and it's +when we go to think about how things + + align:start position:0% +when we go to think about how things + + + align:start position:0% +when we go to think about how things +interact in water when you dissolve + + align:start position:0% +interact in water when you dissolve + + + align:start position:0% +interact in water when you dissolve +sugar in water or something in water you + + align:start position:0% +sugar in water or something in water you + + + align:start position:0% +sugar in water or something in water you +try and dissolve butter in water when + + align:start position:0% +try and dissolve butter in water when + + + align:start position:0% +try and dissolve butter in water when +you stick something into water you have + + align:start position:0% +you stick something into water you have + + + align:start position:0% +you stick something into water you have +to break a whole lot of bonds so there's + + align:start position:0% +to break a whole lot of bonds so there's + + + align:start position:0% +to break a whole lot of bonds so there's +an energy cost to just just simply + + align:start position:0% +an energy cost to just just simply + + + align:start position:0% +an energy cost to just just simply +putting something into water and what + + align:start position:0% +putting something into water and what + + + align:start position:0% +putting something into water and what +makes things dissolve or not is whether + + align:start position:0% +makes things dissolve or not is whether + + + align:start position:0% +makes things dissolve or not is whether +once they're in there they can form + + align:start position:0% +once they're in there they can form + + + align:start position:0% +once they're in there they can form +bonds back again as butter is hydro + + align:start position:0% +bonds back again as butter is hydro + + + align:start position:0% +bonds back again as butter is hydro +carbon and hydrogen bonds there's no + + align:start position:0% +carbon and hydrogen bonds there's no + + + align:start position:0% +carbon and hydrogen bonds there's no +polarity it can't to get it to dissolve + + align:start position:0% +polarity it can't to get it to dissolve + + + align:start position:0% +polarity it can't to get it to dissolve +you'd have to break hydrogen bonds that + + align:start position:0% +you'd have to break hydrogen bonds that + + + align:start position:0% +you'd have to break hydrogen bonds that +costs energy and it can't form any + + align:start position:0% +costs energy and it can't form any + + + align:start position:0% +costs energy and it can't form any +because it's only got non-polar Bonds in + + align:start position:0% +because it's only got non-polar Bonds in + + + align:start position:0% +because it's only got non-polar Bonds in +the butter so the butter floats around + + align:start position:0% +the butter so the butter floats around + + + align:start position:0% +the butter so the butter floats around +on the on the water but this is really + + align:start position:0% +on the on the water but this is really + + + align:start position:0% +on the on the water but this is really +uh a very very important uh very very uh + + align:start position:0% +uh a very very important uh very very uh + + + align:start position:0% +uh a very very important uh very very uh +important force and in fact you know + + align:start position:0% +important force and in fact you know + + + align:start position:0% +important force and in fact you know +this is why when uh uh some of the + + align:start position:0% +this is why when uh uh some of the + + + align:start position:0% +this is why when uh uh some of the +really interesting properties of water + + align:start position:0% +really interesting properties of water + + + align:start position:0% +really interesting properties of water +come from um you all know about surface + + align:start position:0% +come from um you all know about surface + + + align:start position:0% +come from um you all know about surface +tension you've watched little bugs skate + + align:start position:0% +tension you've watched little bugs skate + + + align:start position:0% +tension you've watched little bugs skate +around on the on the surface of the + + align:start position:0% +around on the on the surface of the + + + align:start position:0% +around on the on the surface of the +water this is uh a lizard the ballisk LI + + align:start position:0% +water this is uh a lizard the ballisk LI + + + align:start position:0% +water this is uh a lizard the ballisk LI +lizard that lives in the rainforest of + + align:start position:0% +lizard that lives in the rainforest of + + + align:start position:0% +lizard that lives in the rainforest of +Central and South America and it's uh + + align:start position:0% +Central and South America and it's uh + + + align:start position:0% +Central and South America and it's uh +it's about 2 and 1/2 ft long and it can + + align:start position:0% +it's about 2 and 1/2 ft long and it can + + + align:start position:0% +it's about 2 and 1/2 ft long and it can +take advantage of the surface tension + + align:start position:0% +take advantage of the surface tension + + + align:start position:0% +take advantage of the surface tension +that's due to the hydrogen bonding of + + align:start position:0% +that's due to the hydrogen bonding of + + + align:start position:0% +that's due to the hydrogen bonding of +water to go scooting right across the + + align:start position:0% +water to go scooting right across the + + + align:start position:0% +water to go scooting right across the +water this is not the greatest of of + + align:start position:0% +water this is not the greatest of of + + + align:start position:0% +water this is not the greatest of of +videos it's what I've managed to find so + + align:start position:0% +videos it's what I've managed to find so + + + align:start position:0% +videos it's what I've managed to find so +far but you you get the idea it actually + + align:start position:0% +far but you you get the idea it actually + + + align:start position:0% +far but you you get the idea it actually +runs across the water and that's you're + + align:start position:0% +runs across the water and that's you're + + + align:start position:0% +runs across the water and that's you're +watching the hydrogen bonding in action + + align:start position:0% +watching the hydrogen bonding in action + + + align:start position:0% +watching the hydrogen bonding in action +here um when when I was a grad student + + align:start position:0% +here um when when I was a grad student + + + align:start position:0% +here um when when I was a grad student +my work thesis was on the synthesis of + + align:start position:0% +my work thesis was on the synthesis of + + + align:start position:0% +my work thesis was on the synthesis of +ribooligonucleotides little pieces of + + align:start position:0% +ribooligonucleotides little pieces of + + + align:start position:0% +ribooligonucleotides little pieces of +RNA and I went in a thesis competition + + align:start position:0% +RNA and I went in a thesis competition + + + align:start position:0% +RNA and I went in a thesis competition +to at the end where you were supposed to + + align:start position:0% +to at the end where you were supposed to + + + align:start position:0% +to at the end where you were supposed to +give a talk about your thesis and there + + align:start position:0% +give a talk about your thesis and there + + + align:start position:0% +give a talk about your thesis and there +were four of us and I thought well at + + align:start position:0% +were four of us and I thought well at + + + align:start position:0% +were four of us and I thought well at +least I have a fighting chance and when + + align:start position:0% +least I have a fighting chance and when + + + align:start position:0% +least I have a fighting chance and when +I get in there it turned out one of the + + align:start position:0% +I get in there it turned out one of the + + + align:start position:0% +I get in there it turned out one of the +other people who was competing was the + + align:start position:0% +other people who was competing was the + + + align:start position:0% +other people who was competing was the +guy who studied this lizard so his talk + + align:start position:0% +guy who studied this lizard so his talk + + + align:start position:0% +guy who studied this lizard so his talk +was full of movies of these lizards + + align:start position:0% +was full of movies of these lizards + + + align:start position:0% +was full of movies of these lizards +running back and forth across ponds of + + align:start position:0% +running back and forth across ponds of + + + align:start position:0% +running back and forth across ponds of +water and I thought I'm dead meat but it + + align:start position:0% +water and I thought I'm dead meat but it + + + align:start position:0% +water and I thought I'm dead meat but it +actually turned out I want it so I was + + align:start position:0% +actually turned out I want it so I was + + + align:start position:0% +actually turned out I want it so I was +very surprised but every time I see + + align:start position:0% +very surprised but every time I see + + + align:start position:0% +very surprised but every time I see +something like this it reminds me of it + + align:start position:0% +something like this it reminds me of it + + + align:start position:0% +something like this it reminds me of it +okay and just to remind you too I mean + + align:start position:0% +okay and just to remind you too I mean + + + align:start position:0% +okay and just to remind you too I mean +you may not have been thinking of it in + + align:start position:0% +you may not have been thinking of it in + + + align:start position:0% +you may not have been thinking of it in +this way but you know of course what was + + align:start position:0% +this way but you know of course what was + + + align:start position:0% +this way but you know of course what was +all a fuss about when they sent the + + align:start position:0% +all a fuss about when they sent the + + + align:start position:0% +all a fuss about when they sent the +expeditions to Mars they're looking for + + align:start position:0% +expeditions to Mars they're looking for + + + align:start position:0% +expeditions to Mars they're looking for +traces of water + + align:start position:0% +traces of water + + + align:start position:0% +traces of water +why is that so important it's because + + align:start position:0% +why is that so important it's because + + + align:start position:0% +why is that so important it's because +water has this amazing capacity to form + + align:start position:0% +water has this amazing capacity to form + + + align:start position:0% +water has this amazing capacity to form +hydrogen bonds and be the solvent that + + align:start position:0% +hydrogen bonds and be the solvent that + + + align:start position:0% +hydrogen bonds and be the solvent that +can life go the moon on Triton has + + align:start position:0% +can life go the moon on Triton has + + + align:start position:0% +can life go the moon on Triton has +methane n all non-polar bonds they're + + align:start position:0% +methane n all non-polar bonds they're + + + align:start position:0% +methane n all non-polar bonds they're +talking about raining methane and rivers + + align:start position:0% +talking about raining methane and rivers + + + align:start position:0% +talking about raining methane and rivers +of liquid methane and stuff you might + + align:start position:0% +of liquid methane and stuff you might + + + align:start position:0% +of liquid methane and stuff you might +think about whether it'd be possible to + + align:start position:0% +think about whether it'd be possible to + + + align:start position:0% +think about whether it'd be possible to +design a life form or not or at least + + align:start position:0% +design a life form or not or at least + + + align:start position:0% +design a life form or not or at least +what ways things would have to be + + align:start position:0% +what ways things would have to be + + + align:start position:0% +what ways things would have to be +different okay um we've done enough that + + align:start position:0% +different okay um we've done enough that + + + align:start position:0% +different okay um we've done enough that +I can quickly now introduce you to our + + align:start position:0% +I can quickly now introduce you to our + + + align:start position:0% +I can quickly now introduce you to our +first class of of uh molecules which are + + align:start position:0% + + + + align:start position:0% + +carbohydrates Julie would you mind + + align:start position:0% +carbohydrates Julie would you mind + + + align:start position:0% +carbohydrates Julie would you mind +flipping that uh light back on for a + + align:start position:0% + + + + align:start position:0% + +minute okay so carbohydrates have the + + align:start position:0% +minute okay so carbohydrates have the + + + align:start position:0% +minute okay so carbohydrates have the +general + + align:start position:0% +general + + + align:start position:0% +general +property general formula there + + align:start position:0% +property general formula there + + + align:start position:0% +property general formula there +ch2o and you can have different numbers + + align:start position:0% +ch2o and you can have different numbers + + + align:start position:0% +ch2o and you can have different numbers +of them n minus one + + align:start position:0% + + + + align:start position:0% + +carbons have a CO Bond that's known as a + + align:start position:0% +carbons have a CO Bond that's known as a + + + align:start position:0% +carbons have a CO Bond that's known as a +hydroxy group and one + + align:start position:0% +hydroxy group and one + + + align:start position:0% +hydroxy group and one +carbon has a double bond oxygen which is + + align:start position:0% +carbon has a double bond oxygen which is + + + align:start position:0% +carbon has a double bond oxygen which is +either known as an + + align:start position:0% +either known as an + + + align:start position:0% +either known as an +alahh if it's at the end of a chain or + + align:start position:0% +alahh if it's at the end of a chain or + + + align:start position:0% +alahh if it's at the end of a chain or +as a + + align:start position:0% +as a + + + align:start position:0% +as a +ketone if it's in the + + align:start position:0% +ketone if it's in the + + + align:start position:0% +ketone if it's in the +middle and uh these uh things can come + + align:start position:0% +middle and uh these uh things can come + + + align:start position:0% +middle and uh these uh things can come +in different numbers so if n equal + + align:start position:0% +in different numbers so if n equal + + + align:start position:0% +in different numbers so if n equal +3 it's a it's a triose if it's n equals + + align:start position:0% +3 it's a it's a triose if it's n equals + + + align:start position:0% +3 it's a it's a triose if it's n equals +five it's a pentos the sugars that + + align:start position:0% +five it's a pentos the sugars that + + + align:start position:0% +five it's a pentos the sugars that +you'll see in DNA and RNA are pentoses + + align:start position:0% +you'll see in DNA and RNA are pentoses + + + align:start position:0% +you'll see in DNA and RNA are pentoses +they're five carbon units uh a six + + align:start position:0% +they're five carbon units uh a six + + + align:start position:0% +they're five carbon units uh a six +carbon unit is a a hexos and a very + + align:start position:0% +carbon unit is a a hexos and a very + + + align:start position:0% +carbon unit is a a hexos and a very +common hexos that you're all familiar + + align:start position:0% +common hexos that you're all familiar + + + align:start position:0% +common hexos that you're all familiar +with at least familiar with the name of + + align:start position:0% +with at least familiar with the name of + + + align:start position:0% +with at least familiar with the name of +is is glucose and the structure of + + align:start position:0% +is is glucose and the structure of + + + align:start position:0% +is is glucose and the structure of +glucose in a linear form if I draw it + + align:start position:0% +glucose in a linear form if I draw it + + + align:start position:0% +glucose in a linear form if I draw it +out here it's got the double bond at one + + align:start position:0% +out here it's got the double bond at one + + + align:start position:0% +out here it's got the double bond at one +end so it's an aldah in that case and + + align:start position:0% +end so it's an aldah in that case and + + + align:start position:0% +end so it's an aldah in that case and +then there's an O uh this + + align:start position:0% +then there's an O uh this + + + align:start position:0% +then there's an O uh this +way oh this + + align:start position:0% +way oh this + + + align:start position:0% +way oh this +way + + align:start position:0% +way + + + align:start position:0% +way +oh see 1 2 3 four five six o and it's + + align:start position:0% +oh see 1 2 3 four five six o and it's + + + align:start position:0% +oh see 1 2 3 four five six o and it's +just going off the bottom of the end + + align:start position:0% +just going off the bottom of the end + + + align:start position:0% +just going off the bottom of the end +here bottom of the board for some of you + + align:start position:0% +here bottom of the board for some of you + + + align:start position:0% +here bottom of the board for some of you +probably but we have hydrogens in the + + align:start position:0% +probably but we have hydrogens in the + + + align:start position:0% +probably but we have hydrogens in the +other places now what I had to do in + + align:start position:0% +other places now what I had to do in + + + align:start position:0% +other places now what I had to do in +order + + align:start position:0% +order + + + align:start position:0% +order +to to put up this depiction was kind of + + align:start position:0% +to to put up this depiction was kind of + + + align:start position:0% +to to put up this depiction was kind of +flatten this molecule which you'll know + + align:start position:0% +flatten this molecule which you'll know + + + align:start position:0% +flatten this molecule which you'll know +every one of these is a tetrahedral + + align:start position:0% +every one of these is a tetrahedral + + + align:start position:0% +every one of these is a tetrahedral +Arrangement and flatten it down so I + + align:start position:0% +Arrangement and flatten it down so I + + + align:start position:0% +Arrangement and flatten it down so I +could write it on the board so there are + + align:start position:0% +could write it on the board so there are + + + align:start position:0% +could write it on the board so there are +actually Four chyal + + align:start position:0% + + + + align:start position:0% + +centers in a glucose molecule and + + align:start position:0% +centers in a glucose molecule and + + + align:start position:0% +centers in a glucose molecule and +furthermore this is although this is a + + align:start position:0% +furthermore this is although this is a + + + align:start position:0% +furthermore this is although this is a +representation that you can find in + + align:start position:0% +representation that you can find in + + + align:start position:0% +representation that you can find in +textbooks and I can write it on the + + align:start position:0% +textbooks and I can write it on the + + + align:start position:0% +textbooks and I can write it on the +board that's not how it appears in + + align:start position:0% +board that's not how it appears in + + + align:start position:0% +board that's not how it appears in +nature what happens is that the uh + + align:start position:0% +nature what happens is that the uh + + + align:start position:0% +nature what happens is that the uh +oxygen Here Comes comes up and actually + + align:start position:0% +oxygen Here Comes comes up and actually + + + align:start position:0% +oxygen Here Comes comes up and actually +cyclizes to this carbon and this + + align:start position:0% +cyclizes to this carbon and this + + + align:start position:0% +cyclizes to this carbon and this +hydrogen goes and sits up here and it + + align:start position:0% +hydrogen goes and sits up here and it + + + align:start position:0% +hydrogen goes and sits up here and it +gives you the way glucose is + + align:start position:0% +gives you the way glucose is + + + align:start position:0% +gives you the way glucose is +actually found in solution this would be + + align:start position:0% +actually found in solution this would be + + + align:start position:0% +actually found in solution this would be +uh what's known as beta + + align:start position:0% +uh what's known as beta + + + align:start position:0% +uh what's known as beta +glucose the reason I'm I'm saying beta + + align:start position:0% +glucose the reason I'm I'm saying beta + + + align:start position:0% +glucose the reason I'm I'm saying beta +is we've got a new chyal + + align:start position:0% + + + + align:start position:0% + +center that's formed by this cyclisation + + align:start position:0% +center that's formed by this cyclisation + + + align:start position:0% +center that's formed by this cyclisation +and just to give you a sense of where we + + align:start position:0% +and just to give you a sense of where we + + + align:start position:0% +and just to give you a sense of where we +are this is 1 2 3 4 5 six going this way + + align:start position:0% +are this is 1 2 3 4 5 six going this way + + + align:start position:0% +are this is 1 2 3 4 5 six going this way +and over here it's 1 2 3 4 five and six + + align:start position:0% +and over here it's 1 2 3 4 five and six + + + align:start position:0% +and over here it's 1 2 3 4 five and six +that way and you can sit there and work + + align:start position:0% +that way and you can sit there and work + + + align:start position:0% +that way and you can sit there and work +this out uh yourself afterwards this is + + align:start position:0% +this out uh yourself afterwards this is + + + align:start position:0% +this out uh yourself afterwards this is +known as a + + align:start position:0% + + + + align:start position:0% + +Pinos ring because it's got It's + + align:start position:0% +Pinos ring because it's got It's + + + align:start position:0% +Pinos ring because it's got It's +actually a six-membered ring but you can + + align:start position:0% +actually a six-membered ring but you can + + + align:start position:0% +actually a six-membered ring but you can +see one of the oxygen is now part of the + + align:start position:0% +see one of the oxygen is now part of the + + + align:start position:0% +see one of the oxygen is now part of the +ring and the extra carbon is out + + align:start position:0% +ring and the extra carbon is out + + + align:start position:0% +ring and the extra carbon is out +sticking out here and in solution + + align:start position:0% +sticking out here and in solution + + + align:start position:0% +sticking out here and in solution +because this new chyro center we've now + + align:start position:0% +because this new chyro center we've now + + + align:start position:0% +because this new chyro center we've now +got the the possibility of this thing + + align:start position:0% +got the the possibility of this thing + + + align:start position:0% +got the the possibility of this thing +joining so that the O is up or the O is + + align:start position:0% +joining so that the O is up or the O is + + + align:start position:0% +joining so that the O is up or the O is +down and when it's up the O is up that's + + align:start position:0% +down and when it's up the O is up that's + + + align:start position:0% +down and when it's up the O is up that's +known as the beta form and if the O is + + align:start position:0% +known as the beta form and if the O is + + + align:start position:0% +known as the beta form and if the O is +down that's known as the alpha form so + + align:start position:0% +down that's known as the alpha form so + + + align:start position:0% +down that's known as the alpha form so +again got to keep our eyes on all of + + align:start position:0% +again got to keep our eyes on all of + + + align:start position:0% +again got to keep our eyes on all of +these chwel centers this kind of + + align:start position:0% +these chwel centers this kind of + + + align:start position:0% +these chwel centers this kind of +depiction again is sort of hard to draw + + align:start position:0% +depiction again is sort of hard to draw + + + align:start position:0% +depiction again is sort of hard to draw +so again people tend to sort of flatten + + align:start position:0% +so again people tend to sort of flatten + + + align:start position:0% +so again people tend to sort of flatten +it out and you'll see this kind of + + align:start position:0% +it out and you'll see this kind of + + + align:start position:0% +it out and you'll see this kind of +representation you have to realize it's + + align:start position:0% +representation you have to realize it's + + + align:start position:0% +representation you have to realize it's +representing this is approximately the + + align:start position:0% +representing this is approximately the + + + align:start position:0% +representing this is approximately the +three-dimensional shape shape this is a + + align:start position:0% +three-dimensional shape shape this is a + + + align:start position:0% +three-dimensional shape shape this is a +representation here's beta glucose there + + align:start position:0% +representation here's beta glucose there + + + align:start position:0% +representation here's beta glucose there +now every time that you change a + + align:start position:0% +now every time that you change a + + + align:start position:0% +now every time that you change a +um uh the position of one of these + + align:start position:0% +um uh the position of one of these + + + align:start position:0% +um uh the position of one of these +hydroxy we end up with another + + align:start position:0% +hydroxy we end up with another + + + align:start position:0% +hydroxy we end up with another +um with another sugar so this is beta + + align:start position:0% +um with another sugar so this is beta + + + align:start position:0% +um with another sugar so this is beta +galactose sugar with very different uh + + align:start position:0% +galactose sugar with very different uh + + + align:start position:0% +galactose sugar with very different uh +very different properties and the + + align:start position:0% +very different properties and the + + + align:start position:0% +very different properties and the +difference is here the hydroxy is up + + align:start position:0% +difference is here the hydroxy is up + + + align:start position:0% +difference is here the hydroxy is up +here the hydroxy is down two different + + align:start position:0% +here the hydroxy is down two different + + + align:start position:0% +here the hydroxy is down two different +sugars two different properties but as + + align:start position:0% +sugars two different properties but as + + + align:start position:0% +sugars two different properties but as +simple a difference as that and then + + align:start position:0% +simple a difference as that and then + + + align:start position:0% +simple a difference as that and then +thing that happens in nature is you + + align:start position:0% +thing that happens in nature is you + + + align:start position:0% +thing that happens in nature is you +could over you can join different sugar + + align:start position:0% +could over you can join different sugar + + + align:start position:0% +could over you can join different sugar +molecules together by a principle that + + align:start position:0% +molecules together by a principle that + + + align:start position:0% +molecules together by a principle that +you'll see over and over again and + + align:start position:0% +you'll see over and over again and + + + align:start position:0% +you'll see over and over again and +that's you split out a molecule of water + + align:start position:0% +that's you split out a molecule of water + + + align:start position:0% +that's you split out a molecule of water +and you get a new cove valent Bond where + + align:start position:0% +and you get a new cove valent Bond where + + + align:start position:0% +and you get a new cove valent Bond where +this oxygen joins over to the carbon + + align:start position:0% +this oxygen joins over to the carbon + + + align:start position:0% +this oxygen joins over to the carbon +over here and what that gives you is uh + + align:start position:0% + + + + align:start position:0% + +galactose beta one + + align:start position:0% + + + + align:start position:0% + +for glucose this beta 1 4 glucose is um + + align:start position:0% +for glucose this beta 1 4 glucose is um + + + align:start position:0% +for glucose this beta 1 4 glucose is um +a molecule that you know as lactose or + + align:start position:0% +a molecule that you know as lactose or + + + align:start position:0% +a molecule that you know as lactose or +milk + + align:start position:0% + + + + align:start position:0% + +sugar and part of the reason we know + + align:start position:0% +sugar and part of the reason we know + + + align:start position:0% +sugar and part of the reason we know +about it is because in order to + + align:start position:0% +about it is because in order to + + + align:start position:0% +about it is because in order to +metabolize that you need to have a + + align:start position:0% +metabolize that you need to have a + + + align:start position:0% +metabolize that you need to have a +special enzyme that cuts right here that + + align:start position:0% +special enzyme that cuts right here that + + + align:start position:0% +special enzyme that cuts right here that +enzyme is known as beta galactosidase + + align:start position:0% + + + + align:start position:0% + +that's an + + align:start position:0% +that's an + + + align:start position:0% +that's an +enzyme it's a protein which we'll be + + align:start position:0% +enzyme it's a protein which we'll be + + + align:start position:0% +enzyme it's a protein which we'll be +talking about in the coming lectures and + + align:start position:0% +talking about in the coming lectures and + + + align:start position:0% +talking about in the coming lectures and +it's able to cause this bond to break + + align:start position:0% +it's able to cause this bond to break + + + align:start position:0% +it's able to cause this bond to break +what happens when you become lactose + + align:start position:0% +what happens when you become lactose + + + align:start position:0% +what happens when you become lactose +intolerant is you lose the beta + + align:start position:0% +intolerant is you lose the beta + + + align:start position:0% +intolerant is you lose the beta +galactosides that we all have as a baby + + align:start position:0% +galactosides that we all have as a baby + + + align:start position:0% +galactosides that we all have as a baby +because we need to be able to eat milk + + align:start position:0% +because we need to be able to eat milk + + + align:start position:0% +because we need to be able to eat milk +and if you don't have it then the + + align:start position:0% +and if you don't have it then the + + + align:start position:0% +and if you don't have it then the +lactose passes through your stomach + + align:start position:0% +lactose passes through your stomach + + + align:start position:0% +lactose passes through your stomach +without getting metabolized gets into + + align:start position:0% +without getting metabolized gets into + + + align:start position:0% +without getting metabolized gets into +your intestine with those those 10 to + + align:start position:0% +your intestine with those those 10 to + + + align:start position:0% +your intestine with those those 10 to +the fourth bacteria they metabolize it + + align:start position:0% +the fourth bacteria they metabolize it + + + align:start position:0% +the fourth bacteria they metabolize it +break that bom + + align:start position:0% +break that bom + + + align:start position:0% +break that bom +and then that causes the gas and + + align:start position:0% +and then that causes the gas and + + + align:start position:0% +and then that causes the gas and +discomfort that's associated with + + align:start position:0% +discomfort that's associated with + + + align:start position:0% +discomfort that's associated with +lactose intolerance so all the textbooks + + align:start position:0% +lactose intolerance so all the textbooks + + + align:start position:0% +lactose intolerance so all the textbooks +use + + align:start position:0% +use + + + align:start position:0% +use +um uh lactose as the betag lactosides as + + align:start position:0% +um uh lactose as the betag lactosides as + + + align:start position:0% +um uh lactose as the betag lactosides as +the common enzymes the first time I + + align:start position:0% +the common enzymes the first time I + + + align:start position:0% +the common enzymes the first time I +thought that I that I teach this course + + align:start position:0% +thought that I that I teach this course + + + align:start position:0% +thought that I that I teach this course +I thought boy I have a really good idea + + align:start position:0% +I thought boy I have a really good idea + + + align:start position:0% +I thought boy I have a really good idea +I'm going to come up with a a sample + + align:start position:0% +I'm going to come up with a a sample + + + align:start position:0% +I'm going to come up with a a sample +enzyme that's different but I have to + + align:start position:0% +enzyme that's different but I have to + + + align:start position:0% +enzyme that's different but I have to +learn what it was and it was inspired by + + align:start position:0% +learn what it was and it was inspired by + + + align:start position:0% +learn what it was and it was inspired by +um there's this uh product called bino + + align:start position:0% +um there's this uh product called bino + + + align:start position:0% +um there's this uh product called bino +which is is supposed to reduce the side + + align:start position:0% +which is is supposed to reduce the side + + + align:start position:0% +which is is supposed to reduce the side +effects that are commonly associated + + align:start position:0% +effects that are commonly associated + + + align:start position:0% +effects that are commonly associated +with eating beans which probably many of + + align:start position:0% +with eating beans which probably many of + + + align:start position:0% +with eating beans which probably many of +you are familiar with from summer camps + + align:start position:0% +you are familiar with from summer camps + + + align:start position:0% +you are familiar with from summer camps +and things and the the technical term is + + align:start position:0% +and things and the the technical term is + + + align:start position:0% +and things and the the technical term is +flatulence um but in any case this was + + align:start position:0% +flatulence um but in any case this was + + + align:start position:0% +flatulence um but in any case this was +supposed to be something that reduced + + align:start position:0% +supposed to be something that reduced + + + align:start position:0% +supposed to be something that reduced +flatulence so I thought it's got to be + + align:start position:0% +flatulence so I thought it's got to be + + + align:start position:0% +flatulence so I thought it's got to be +an enzyme I know it it's something to do + + align:start position:0% +an enzyme I know it it's something to do + + + align:start position:0% +an enzyme I know it it's something to do +with oligosaccharides a little change + + align:start position:0% +with oligosaccharides a little change + + + align:start position:0% +with oligosaccharides a little change +the sugar so I I looked at the little + + align:start position:0% +the sugar so I I looked at the little + + + align:start position:0% +the sugar so I I looked at the little +thing of bino and it said hotline any + + align:start position:0% +thing of bino and it said hotline any + + + align:start position:0% +thing of bino and it said hotline any +questions call so I phoned up and said + + align:start position:0% +questions call so I phoned up and said + + + align:start position:0% +questions call so I phoned up and said +hi this kind of an unusual question I'm + + align:start position:0% +hi this kind of an unusual question I'm + + + align:start position:0% +hi this kind of an unusual question I'm +a college professor I'm going to be + + align:start position:0% +a college professor I'm going to be + + + align:start position:0% +a college professor I'm going to be +teaching an introductory biology course + + align:start position:0% +teaching an introductory biology course + + + align:start position:0% +teaching an introductory biology course +and I was wondering if I could find out + + align:start position:0% +and I was wondering if I could find out + + + align:start position:0% +and I was wondering if I could find out +what enzyme you had in bino and what it + + align:start position:0% +what enzyme you had in bino and what it + + + align:start position:0% +what enzyme you had in bino and what it +did to what was in the beans and feeling + + align:start position:0% +did to what was in the beans and feeling + + + align:start position:0% +did to what was in the beans and feeling +and I said you know I really sort of an + + align:start position:0% +and I said you know I really sort of an + + + align:start position:0% +and I said you know I really sort of an +odd question but you know was maybe I + + align:start position:0% +odd question but you know was maybe I + + + align:start position:0% +odd question but you know was maybe I +could talk to one of the scientists in + + align:start position:0% +could talk to one of the scientists in + + + align:start position:0% +could talk to one of the scientists in +the lab and woman says hello Pino and + + align:start position:0% +the lab and woman says hello Pino and + + + align:start position:0% +the lab and woman says hello Pino and +she listens to me and she says yes we + + align:start position:0% +she listens to me and she says yes we + + + align:start position:0% +she listens to me and she says yes we +have a special package we send out to + + align:start position:0% +have a special package we send out to + + + align:start position:0% +have a special package we send out to +college professors and so next thing I + + align:start position:0% +college professors and so next thing I + + + align:start position:0% +college professors and so next thing I +knew I got this huge flood of stuff that + + align:start position:0% +knew I got this huge flood of stuff that + + + align:start position:0% +knew I got this huge flood of stuff that +so I'm now able to quickly tell you why + + align:start position:0% +so I'm now able to quickly tell you why + + + align:start position:0% +so I'm now able to quickly tell you why +beans are The Musical Fruit + + align:start position:0% +beans are The Musical Fruit + + + align:start position:0% +beans are The Musical Fruit +and uh the basis of it is if you join a + + align:start position:0% +and uh the basis of it is if you join a + + + align:start position:0% +and uh the basis of it is if you join a +uh glucose and a fructose together by an + + align:start position:0% +uh glucose and a fructose together by an + + + align:start position:0% +uh glucose and a fructose together by an +alpha12 linkage you get + + align:start position:0% +alpha12 linkage you get + + + align:start position:0% +alpha12 linkage you get +sucrose and you all know that's table + + align:start position:0% +sucrose and you all know that's table + + + align:start position:0% +sucrose and you all know that's table +sugar we can eat + + align:start position:0% +sugar we can eat + + + align:start position:0% +sugar we can eat +sucros no problem but what beans have is + + align:start position:0% +sucros no problem but what beans have is + + + align:start position:0% +sucros no problem but what beans have is +beans have a galactose + + align:start position:0% +beans have a galactose + + + align:start position:0% +beans have a galactose +alpha6 linkage to + + align:start position:0% +alpha6 linkage to + + + align:start position:0% +alpha6 linkage to +sucros or are they actually actually + + align:start position:0% +sucros or are they actually actually + + + align:start position:0% +sucros or are they actually actually +sometimes they have two galactose alpha + + align:start position:0% +sometimes they have two galactose alpha + + + align:start position:0% +sometimes they have two galactose alpha +1 six linkages to sucrose and we can't + + align:start position:0% +1 six linkages to sucrose and we can't + + + align:start position:0% +1 six linkages to sucrose and we can't +metabolize them and it's sort of related + + align:start position:0% +metabolize them and it's sort of related + + + align:start position:0% +metabolize them and it's sort of related +to the same idea as the glucose + + align:start position:0% +to the same idea as the glucose + + + align:start position:0% +to the same idea as the glucose +intolerance that they go through our + + align:start position:0% +intolerance that they go through our + + + align:start position:0% +intolerance that they go through our +stomach and then the bacteria know how + + align:start position:0% +stomach and then the bacteria know how + + + align:start position:0% +stomach and then the bacteria know how +to break that Bond and uh that causes + + align:start position:0% +to break that Bond and uh that causes + + + align:start position:0% +to break that Bond and uh that causes +the problems that you encountered at + + align:start position:0% +the problems that you encountered at + + + align:start position:0% +the problems that you encountered at +summer camp and so what bino turned out + + align:start position:0% +summer camp and so what bino turned out + + + align:start position:0% +summer camp and so what bino turned out +to be is it's a sort of low Tech U + + align:start position:0% +to be is it's a sort of low Tech U + + + align:start position:0% +to be is it's a sort of low Tech U +biotech product it's a f food grade mold + + align:start position:0% +biotech product it's a f food grade mold + + + align:start position:0% +biotech product it's a f food grade mold +called neurospora and it's a very very + + align:start position:0% +called neurospora and it's a very very + + + align:start position:0% +called neurospora and it's a very very +crude preparation of U an + + align:start position:0% +crude preparation of U an + + + align:start position:0% +crude preparation of U an +alpha6 + + align:start position:0% + + + + align:start position:0% + +galactosidase in other words an enzyme + + align:start position:0% +galactosidase in other words an enzyme + + + align:start position:0% +galactosidase in other words an enzyme +that can break that molecule once it + + align:start position:0% +that can break that molecule once it + + + align:start position:0% +that can break that molecule once it +breaks it you have sucrose which we can + + align:start position:0% +breaks it you have sucrose which we can + + + align:start position:0% +breaks it you have sucrose which we can +eat and lactose which we know what to do + + align:start position:0% +eat and lactose which we know what to do + + + align:start position:0% +eat and lactose which we know what to do +with and that's the basis of that so the + + align:start position:0% +with and that's the basis of that so the + + + align:start position:0% +with and that's the basis of that so the +very last thing is um to talk about + + align:start position:0% +very last thing is um to talk about + + + align:start position:0% +very last thing is um to talk about +polysaccharides these come when you join + + align:start position:0% +polysaccharides these come when you join + + + align:start position:0% +polysaccharides these come when you join +together multiple sugars + + align:start position:0% + + + + align:start position:0% + +and as you can appreciate by now there + + align:start position:0% +and as you can appreciate by now there + + + align:start position:0% +and as you can appreciate by now there +are many many ways of joining sugars + + align:start position:0% +are many many ways of joining sugars + + + align:start position:0% +are many many ways of joining sugars +together but suppose we take n glucoses + + align:start position:0% +together but suppose we take n glucoses + + + align:start position:0% +together but suppose we take n glucoses +there's two common ways they can get + + align:start position:0% +there's two common ways they can get + + + align:start position:0% +there's two common ways they can get +joined they can get joined together by + + align:start position:0% +joined they can get joined together by + + + align:start position:0% +joined they can get joined together by +Alpha 14 bonds and these give a + + align:start position:0% +Alpha 14 bonds and these give a + + + align:start position:0% +Alpha 14 bonds and these give a +helical + + align:start position:0% + + + + align:start position:0% + +confirmation and you know these as + + align:start position:0% + + + + align:start position:0% + +starch or glycogen these are energy stor + + align:start position:0% +starch or glycogen these are energy stor + + + align:start position:0% +starch or glycogen these are energy stor +St + + align:start position:0% + + + + align:start position:0% + +molecules and I've run marathons some of + + align:start position:0% +molecules and I've run marathons some of + + + align:start position:0% +molecules and I've run marathons some of +you may have at least some you probably + + align:start position:0% +you may have at least some you probably + + + align:start position:0% +you may have at least some you probably +know about carbo loing what you're + + align:start position:0% +know about carbo loing what you're + + + align:start position:0% +know about carbo loing what you're +trying to do then before you go is + + align:start position:0% +trying to do then before you go is + + + align:start position:0% +trying to do then before you go is +you're eating pasta and everything which + + align:start position:0% +you're eating pasta and everything which + + + align:start position:0% +you're eating pasta and everything which +is full of starches so it's got + + align:start position:0% +is full of starches so it's got + + + align:start position:0% +is full of starches so it's got +polymerized sugars and your body you're + + align:start position:0% +polymerized sugars and your body you're + + + align:start position:0% +polymerized sugars and your body you're +trying to get your body to take these in + + align:start position:0% +trying to get your body to take these in + + + align:start position:0% +trying to get your body to take these in +and polymerize them into glycogen so + + align:start position:0% +and polymerize them into glycogen so + + + align:start position:0% +and polymerize them into glycogen so +your liver is as loaded with the with + + align:start position:0% +your liver is as loaded with the with + + + align:start position:0% +your liver is as loaded with the with +glycogen before you start the race and + + align:start position:0% +glycogen before you start the race and + + + align:start position:0% +glycogen before you start the race and +hitting the wall in a marathon is when + + align:start position:0% +hitting the wall in a marathon is when + + + align:start position:0% +hitting the wall in a marathon is when +you run out of glycogen and then you + + align:start position:0% +you run out of glycogen and then you + + + align:start position:0% +you run out of glycogen and then you +start burning fatty acids and it's no + + align:start position:0% +start burning fatty acids and it's no + + + align:start position:0% +start burning fatty acids and it's no +fun at all but that's what carbal loing + + align:start position:0% +fun at all but that's what carbal loing + + + align:start position:0% +fun at all but that's what carbal loing +is all about is manipulating uh glucoses + + align:start position:0% +is all about is manipulating uh glucoses + + + align:start position:0% +is all about is manipulating uh glucoses +that are in an alpha 14 + + align:start position:0% +that are in an alpha 14 + + + align:start position:0% +that are in an alpha 14 +confirmation if you just make a beta 14 + + align:start position:0% +confirmation if you just make a beta 14 + + + align:start position:0% +confirmation if you just make a beta 14 +confirmation so the only difference + + align:start position:0% +confirmation so the only difference + + + align:start position:0% +confirmation so the only difference +that's happening in The Way We join + + align:start position:0% +that's happening in The Way We join + + + align:start position:0% +that's happening in The Way We join +glucoses together is whether the the + + align:start position:0% +glucoses together is whether the the + + + align:start position:0% +glucoses together is whether the the +hydroxy was up or down when you join the + + align:start position:0% +hydroxy was up or down when you join the + + + align:start position:0% +hydroxy was up or down when you join the +two of them together you get something + + align:start position:0% +two of them together you get something + + + align:start position:0% +two of them together you get something +with uh that's a linear molecule + + align:start position:0% + + + + align:start position:0% + +that forms hydrogen + + align:start position:0% +that forms hydrogen + + + align:start position:0% +that forms hydrogen +bonds between the sugars so you have a a + + align:start position:0% +bonds between the sugars so you have a a + + + align:start position:0% +bonds between the sugars so you have a a +linear chain of of sugars and I'm not + + align:start position:0% +linear chain of of sugars and I'm not + + + align:start position:0% +linear chain of of sugars and I'm not +going to show the details of the + + align:start position:0% +going to show the details of the + + + align:start position:0% +going to show the details of the +hydrogen bond but you have one chain + + align:start position:0% +hydrogen bond but you have one chain + + + align:start position:0% +hydrogen bond but you have one chain +going this way and another chain of + + align:start position:0% +going this way and another chain of + + + align:start position:0% +going this way and another chain of +sugars here and you can get hydrogen + + align:start position:0% +sugars here and you can get hydrogen + + + align:start position:0% +sugars here and you can get hydrogen +bonds between them and you know this is + + align:start position:0% + + + + align:start position:0% + +cellulose so there're two um very + + align:start position:0% +cellulose so there're two um very + + + align:start position:0% +cellulose so there're two um very +important biomolecules that + + align:start position:0% +important biomolecules that + + + align:start position:0% +important biomolecules that +are that are made up of glucose that's + + align:start position:0% +are that are made up of glucose that's + + + align:start position:0% +are that are made up of glucose that's +just some glucose there and if you join + + align:start position:0% +just some glucose there and if you join + + + align:start position:0% +just some glucose there and if you join +them by alpha4 linkages you get starch + + align:start position:0% +them by alpha4 linkages you get starch + + + align:start position:0% +them by alpha4 linkages you get starch +like corn starch which you've all + + align:start position:0% +like corn starch which you've all + + + align:start position:0% +like corn starch which you've all +encountered you join them by hydroxy the + + align:start position:0% +encountered you join them by hydroxy the + + + align:start position:0% +encountered you join them by hydroxy the +other direction you get GL uh get + + align:start position:0% +other direction you get GL uh get + + + align:start position:0% +other direction you get GL uh get +cellulose cellulose is uh important in + + align:start position:0% +cellulose cellulose is uh important in + + + align:start position:0% +cellulose cellulose is uh important in +biology it's what plants make their cell + + align:start position:0% +biology it's what plants make their cell + + + align:start position:0% +biology it's what plants make their cell +walls of that's why you can have trees + + align:start position:0% +walls of that's why you can have trees + + + align:start position:0% +walls of that's why you can have trees +that are so enormously high and one I + + align:start position:0% +that are so enormously high and one I + + + align:start position:0% +that are so enormously high and one I +guess I'll close with one last uh so + + align:start position:0% +guess I'll close with one last uh so + + + align:start position:0% +guess I'll close with one last uh so +most of the paper we get from cellulose + + align:start position:0% +most of the paper we get from cellulose + + + align:start position:0% +most of the paper we get from cellulose +is uh is from trees if you ever try and + + align:start position:0% +is uh is from trees if you ever try and + + + align:start position:0% +is uh is from trees if you ever try and +make make beer or wine or something you + + align:start position:0% +make make beer or wine or something you + + + align:start position:0% +make make beer or wine or something you +probably know you got to keep fruit + + align:start position:0% +probably know you got to keep fruit + + + align:start position:0% +probably know you got to keep fruit +flies away or you get vinegar and the + + align:start position:0% +flies away or you get vinegar and the + + + align:start position:0% +flies away or you get vinegar and the +reason you get vinegar is that there's + + align:start position:0% +reason you get vinegar is that there's + + + align:start position:0% +reason you get vinegar is that there's +the fruit flies carry on their feet a + + align:start position:0% +the fruit flies carry on their feet a + + + align:start position:0% +the fruit flies carry on their feet a +bacterium called acetobacter and it + + align:start position:0% +bacterium called acetobacter and it + + + align:start position:0% +bacterium called acetobacter and it +likes to live at this if you at the + + align:start position:0% +likes to live at this if you at the + + + align:start position:0% +likes to live at this if you at the +surface between the + + align:start position:0% +surface between the + + + align:start position:0% +surface between the +water and the air and what it does then + + align:start position:0% +water and the air and what it does then + + + align:start position:0% +water and the air and what it does then +in order to do that is it makes + + align:start position:0% +in order to do that is it makes + + + align:start position:0% +in order to do that is it makes +cellulose and it floats itself right at + + align:start position:0% +cellulose and it floats itself right at + + + align:start position:0% +cellulose and it floats itself right at +the makes it great thick mat of + + align:start position:0% +the makes it great thick mat of + + + align:start position:0% +the makes it great thick mat of +cellulose and it floats itself right at + + align:start position:0% +cellulose and it floats itself right at + + + align:start position:0% +cellulose and it floats itself right at +the at the air surface inter interface + + align:start position:0% +the at the air surface inter interface + + + align:start position:0% +the at the air surface inter interface +and get a you can get a mat that's half + + align:start position:0% +and get a you can get a mat that's half + + + align:start position:0% +and get a you can get a mat that's half +an inch thick of absolutely perfect + + align:start position:0% +an inch thick of absolutely perfect + + + align:start position:0% +an inch thick of absolutely perfect +cellulose uh and so you don't ever want + + align:start position:0% +cellulose uh and so you don't ever want + + + align:start position:0% +cellulose uh and so you don't ever want +to see that if you're trying to make + + align:start position:0% +to see that if you're trying to make + + + align:start position:0% +to see that if you're trying to make +beer wine or something but it's a + + align:start position:0% +beer wine or something but it's a + + + align:start position:0% +beer wine or something but it's a +bacterium that's making this molecule so + + align:start position:0% +bacterium that's making this molecule so + + + align:start position:0% +bacterium that's making this molecule so +you find it in other places besides + + align:start position:0% +you find it in other places besides + + + align:start position:0% +you find it in other places besides +trees so okay we'll see you on Monday \ No newline at end of file diff --git a/RVc5hXzVFc4.txt b/RVc5hXzVFc4.txt new file mode 100644 index 0000000000000000000000000000000000000000..ecc95775b516b196fbb69911326250f9aa7de3d2 --- /dev/null +++ b/RVc5hXzVFc4.txt @@ -0,0 +1,267 @@ +align:start position:0% + +in this lecture we introduced the + + align:start position:0% +in this lecture we introduced the + + + align:start position:0% +in this lecture we introduced the +Poisson process which is a + + align:start position:0% +Poisson process which is a + + + align:start position:0% +Poisson process which is a +continuous-time analogue of the + + align:start position:0% +continuous-time analogue of the + + + align:start position:0% +continuous-time analogue of the +Bernoulli process one way of thinking + + align:start position:0% +Bernoulli process one way of thinking + + + align:start position:0% +Bernoulli process one way of thinking +about it is as follows time is + + align:start position:0% +about it is as follows time is + + + align:start position:0% +about it is as follows time is +continuous but conceptually we divided + + align:start position:0% +continuous but conceptually we divided + + + align:start position:0% +continuous but conceptually we divided +into a very large number of slots and + + align:start position:0% +into a very large number of slots and + + + align:start position:0% +into a very large number of slots and +during each slot we have a tiny + + align:start position:0% +during each slot we have a tiny + + + align:start position:0% +during each slot we have a tiny +probability of an arrival this + + align:start position:0% +probability of an arrival this + + + align:start position:0% +probability of an arrival this +probability is proportional to the + + align:start position:0% +probability is proportional to the + + + align:start position:0% +probability is proportional to the +length of the slot furthermore we have + + align:start position:0% +length of the slot furthermore we have + + + align:start position:0% +length of the slot furthermore we have +an independence assumption for the + + align:start position:0% +an independence assumption for the + + + align:start position:0% +an independence assumption for the +different slots the Poisson process is a + + align:start position:0% +different slots the Poisson process is a + + + align:start position:0% +different slots the Poisson process is a +very elegant model of arrival processes + + align:start position:0% +very elegant model of arrival processes + + + align:start position:0% +very elegant model of arrival processes +in continuous-time it models many + + align:start position:0% +in continuous-time it models many + + + align:start position:0% +in continuous-time it models many +real-world phenomena and it also has a + + align:start position:0% +real-world phenomena and it also has a + + + align:start position:0% +real-world phenomena and it also has a +very clean mathematical structure that + + align:start position:0% +very clean mathematical structure that + + + align:start position:0% +very clean mathematical structure that +allows us to calculate practically every + + align:start position:0% +allows us to calculate practically every + + + align:start position:0% +allows us to calculate practically every +quantity of interest our development + + align:start position:0% +quantity of interest our development + + + align:start position:0% +quantity of interest our development +will parallel our analysis of the + + align:start position:0% +will parallel our analysis of the + + + align:start position:0% +will parallel our analysis of the +Bernoulli process for example we will + + align:start position:0% +Bernoulli process for example we will + + + align:start position:0% +Bernoulli process for example we will +find the PMF of the number of arrivals + + align:start position:0% +find the PMF of the number of arrivals + + + align:start position:0% +find the PMF of the number of arrivals +during a time interval and the PDF of + + align:start position:0% +during a time interval and the PDF of + + + align:start position:0% +during a time interval and the PDF of +the time of the case arrival we will + + align:start position:0% +the time of the case arrival we will + + + align:start position:0% +the time of the case arrival we will +discuss the memorylessness properties of + + align:start position:0% +discuss the memorylessness properties of + + + align:start position:0% +discuss the memorylessness properties of +the poisson process similar to the case + + align:start position:0% +the poisson process similar to the case + + + align:start position:0% +the poisson process similar to the case +of the Bernoulli process this is just a + + align:start position:0% +of the Bernoulli process this is just a + + + align:start position:0% +of the Bernoulli process this is just a +consequence of the independence + + align:start position:0% +consequence of the independence + + + align:start position:0% +consequence of the independence +assumptions that we are making + + align:start position:0% +assumptions that we are making + + + align:start position:0% +assumptions that we are making +we will then exploit these independence + + align:start position:0% +we will then exploit these independence + + + align:start position:0% +we will then exploit these independence +properties to argue that the inter + + align:start position:0% +properties to argue that the inter + + + align:start position:0% +properties to argue that the inter +arrival times are independent + + align:start position:0% +arrival times are independent + + + align:start position:0% +arrival times are independent +exponential random variables and we will + + align:start position:0% +exponential random variables and we will + + + align:start position:0% +exponential random variables and we will +conclude with a comprehensive example \ No newline at end of file diff --git a/RiRQDZjYkzo.txt b/RiRQDZjYkzo.txt new file mode 100644 index 0000000000000000000000000000000000000000..5d1197ff2d48f5c7f5d5583c7865da5ebfd33423 --- /dev/null +++ b/RiRQDZjYkzo.txt @@ -0,0 +1,1344 @@ +align:start position:0% + +hi everybody welcome back to recitation + + align:start position:0% +hi everybody welcome back to recitation + + + align:start position:0% +hi everybody welcome back to recitation +in lecture you did a bunch of examples + + align:start position:0% +in lecture you did a bunch of examples + + + align:start position:0% +in lecture you did a bunch of examples +of related rates problems so I have a + + align:start position:0% +of related rates problems so I have a + + + align:start position:0% +of related rates problems so I have a +couple more for you to do today um so + + align:start position:0% +couple more for you to do today um so + + + align:start position:0% +couple more for you to do today um so +here we've got Okay so we've got air + + align:start position:0% +here we've got Okay so we've got air + + + align:start position:0% +here we've got Okay so we've got air +being blown into a spherical balloon at + + align:start position:0% +being blown into a spherical balloon at + + + align:start position:0% +being blown into a spherical balloon at +a rate of a th000 cubic centimeters per + + align:start position:0% +a rate of a th000 cubic centimeters per + + + align:start position:0% +a rate of a th000 cubic centimeters per +second so the question is how fast is + + align:start position:0% +second so the question is how fast is + + + align:start position:0% +second so the question is how fast is +the radius growing when the radius is + + align:start position:0% +the radius growing when the radius is + + + align:start position:0% +the radius growing when the radius is +equal to 8 centimeters and then okay so + + align:start position:0% +equal to 8 centimeters and then okay so + + + align:start position:0% +equal to 8 centimeters and then okay so +I've got a second question which is + + align:start position:0% +I've got a second question which is + + + align:start position:0% +I've got a second question which is +about how fast is the surface area + + align:start position:0% +about how fast is the surface area + + + align:start position:0% +about how fast is the surface area +growing at that same time so why don't + + align:start position:0% +growing at that same time so why don't + + + align:start position:0% +growing at that same time so why don't +you take a few minutes work this one out + + align:start position:0% +you take a few minutes work this one out + + + align:start position:0% +you take a few minutes work this one out +for yourself come back and we'll work it + + align:start position:0% +for yourself come back and we'll work it + + + align:start position:0% +for yourself come back and we'll work it +out + + align:start position:0% + + + + align:start position:0% + +together all right welcome back + + align:start position:0% +together all right welcome back + + + align:start position:0% +together all right welcome back +so this question like all related rates + + align:start position:0% +so this question like all related rates + + + align:start position:0% +so this question like all related rates +questions has the property that the + + align:start position:0% +questions has the property that the + + + align:start position:0% +questions has the property that the +calculus is typically very + + align:start position:0% +calculus is typically very + + + align:start position:0% +calculus is typically very +straightforward um but that there's some + + align:start position:0% +straightforward um but that there's some + + + align:start position:0% +straightforward um but that there's some +geometric or algebraic setup so in this + + align:start position:0% +geometric or algebraic setup so in this + + + align:start position:0% +geometric or algebraic setup so in this +in this case it's it's straight up + + align:start position:0% +in this case it's it's straight up + + + align:start position:0% +in this case it's it's straight up +Geometry um so we have a balloon we know + + align:start position:0% +Geometry um so we have a balloon we know + + + align:start position:0% +Geometry um so we have a balloon we know +it's a perfect sphere we know how fast + + align:start position:0% +it's a perfect sphere we know how fast + + + align:start position:0% +it's a perfect sphere we know how fast +the volume is changing so okay so we + + align:start position:0% +the volume is changing so okay so we + + + align:start position:0% +the volume is changing so okay so we +need but we need to know how fast the + + align:start position:0% +need but we need to know how fast the + + + align:start position:0% +need but we need to know how fast the +radius is changing so in order to do + + align:start position:0% +radius is changing so in order to do + + + align:start position:0% +radius is changing so in order to do +that we need to figure out a + + align:start position:0% +that we need to figure out a + + + align:start position:0% +that we need to figure out a +relationship between the radius and the + + align:start position:0% +relationship between the radius and the + + + align:start position:0% +relationship between the radius and the +volume and then we can just do implicit + + align:start position:0% +volume and then we can just do implicit + + + align:start position:0% +volume and then we can just do implicit +differentiation like we've been doing so + + align:start position:0% +differentiation like we've been doing so + + + align:start position:0% +differentiation like we've been doing so +for example Okay so so for a sphere all + + align:start position:0% +for example Okay so so for a sphere all + + + align:start position:0% +for example Okay so so for a sphere all +right this this the setup's not so bad + + align:start position:0% +right this this the setup's not so bad + + + align:start position:0% +right this this the setup's not so bad +for this this first one right so we know + + align:start position:0% +for this this first one right so we know + + + align:start position:0% +for this this first one right so we know +that for a sphere the volume is equal to + + align:start position:0% +that for a sphere the volume is equal to + + + align:start position:0% +that for a sphere the volume is equal to +43 Pi * the radius cubed so that's the + + align:start position:0% +43 Pi * the radius cubed so that's the + + + align:start position:0% +43 Pi * the radius cubed so that's the +the you know relation the the + + align:start position:0% +the you know relation the the + + + align:start position:0% +the you know relation the the +fundamental relationship between the + + align:start position:0% +fundamental relationship between the + + + align:start position:0% +fundamental relationship between the +volume and radius of a sphere and it's + + align:start position:0% +volume and radius of a sphere and it's + + + align:start position:0% +volume and radius of a sphere and it's +true for every sphere everywhere in + + align:start position:0% +true for every sphere everywhere in + + + align:start position:0% +true for every sphere everywhere in +ukian space and we're given also that + + align:start position:0% +ukian space and we're given also that + + + align:start position:0% +ukian space and we're given also that +the volume is changing at a constant + + align:start position:0% +the volume is changing at a constant + + + align:start position:0% +the volume is changing at a constant +rate of a + + align:start position:0% +rate of a + + + align:start position:0% +rate of a +th000 centimeters Cub per second so dvdt + + align:start position:0% +th000 centimeters Cub per second so dvdt + + + align:start position:0% +th000 centimeters Cub per second so dvdt +is just given to be a th000 you know + + align:start position:0% +is just given to be a th000 you know + + + align:start position:0% +is just given to be a th000 you know +leave off the units at this point um so + + align:start position:0% +leave off the units at this point um so + + + align:start position:0% +leave off the units at this point um so +the question is what is drdt that's what + + align:start position:0% +the question is what is drdt that's what + + + align:start position:0% +the question is what is drdt that's what +we're trying to figure out we're trying + + align:start position:0% +we're trying to figure out we're trying + + + align:start position:0% +we're trying to figure out we're trying +to figure out how fast the radius is + + align:start position:0% +to figure out how fast the radius is + + + align:start position:0% +to figure out how fast the radius is +changing at the moment when the radius + + align:start position:0% +changing at the moment when the radius + + + align:start position:0% +changing at the moment when the radius +is equal to 8 cm so how can we do that + + align:start position:0% +is equal to 8 cm so how can we do that + + + align:start position:0% +is equal to 8 cm so how can we do that +well this this fundamental relationship + + align:start position:0% +well this this fundamental relationship + + + align:start position:0% +well this this fundamental relationship +it's an identity it always holds so that + + align:start position:0% +it's an identity it always holds so that + + + align:start position:0% +it's an identity it always holds so that +means we can differentiate it um so if + + align:start position:0% +means we can differentiate it um so if + + + align:start position:0% +means we can differentiate it um so if +we take the + + align:start position:0% +we take the + + + align:start position:0% +we take the +derivative of this identity well V on + + align:start position:0% +derivative of this identity well V on + + + align:start position:0% +derivative of this identity well V on +the left just + + align:start position:0% + + + + align:start position:0% + +becomes dvdt and on the right we want to + + align:start position:0% +becomes dvdt and on the right we want to + + + align:start position:0% +becomes dvdt and on the right we want to +do implicit differentiation so here R is + + align:start position:0% +do implicit differentiation so here R is + + + align:start position:0% +do implicit differentiation so here R is +changing with respect to time R is a + + align:start position:0% +changing with respect to time R is a + + + align:start position:0% +changing with respect to time R is a +function of T well okay so 4/3 pi is a + + align:start position:0% +function of T well okay so 4/3 pi is a + + + align:start position:0% +function of T well okay so 4/3 pi is a +constant so that when we differentiate + + align:start position:0% +constant so that when we differentiate + + + align:start position:0% +constant so that when we differentiate +if nothing happens 4/3 pi and so now we + + align:start position:0% +if nothing happens 4/3 pi and so now we + + + align:start position:0% +if nothing happens 4/3 pi and so now we +differentiate R cubed with respect to T + + align:start position:0% +differentiate R cubed with respect to T + + + align:start position:0% +differentiate R cubed with respect to T +so that gives us + + align:start position:0% +so that gives us + + + align:start position:0% +so that gives us +3 R + + align:start position:0% + + + + align:start position:0% + +2times drdt so that's just the chain + + align:start position:0% +2times drdt so that's just the chain + + + align:start position:0% +2times drdt so that's just the chain +rule in action there and now what we + + align:start position:0% +rule in action there and now what we + + + align:start position:0% +rule in action there and now what we +want is this + + align:start position:0% +want is this + + + align:start position:0% +want is this +drdt right that's that's the thing that + + align:start position:0% +drdt right that's that's the thing that + + + align:start position:0% +drdt right that's that's the thing that +we're looking for is how fast the radius + + align:start position:0% +we're looking for is how fast the radius + + + align:start position:0% +we're looking for is how fast the radius +is growing so that's drdt and we want it + + align:start position:0% +is growing so that's drdt and we want it + + + align:start position:0% +is growing so that's drdt and we want it +at the moment when R is equal to 8 + + align:start position:0% + + + + align:start position:0% + +so when R is equal to 8 + + align:start position:0% +so when R is equal to 8 + + + align:start position:0% +so when R is equal to 8 +this implies that well okay so dvdt is a + + align:start position:0% +this implies that well okay so dvdt is a + + + align:start position:0% +this implies that well okay so dvdt is a +th + + align:start position:0% + + + + align:start position:0% + +always and it implies that okay so it's + + align:start position:0% +always and it implies that okay so it's + + + align:start position:0% +always and it implies that okay so it's +equal to 1,00 is equal to 4/3 pi * 3 * + + align:start position:0% +equal to 1,00 is equal to 4/3 pi * 3 * + + + align:start position:0% +equal to 1,00 is equal to 4/3 pi * 3 * +8^ + + align:start position:0% + + + + align:start position:0% + +sared time + + align:start position:0% +sared time + + + align:start position:0% +sared time +drdt + + align:start position:0% +drdt + + + align:start position:0% +drdt +so at this moment that we're interested + + align:start position:0% +so at this moment that we're interested + + + align:start position:0% +so at this moment that we're interested +in we have this equation to solve for + + align:start position:0% +in we have this equation to solve for + + + align:start position:0% +in we have this equation to solve for +drdt and this is a nice simple equation + + align:start position:0% +drdt and this is a nice simple equation + + + align:start position:0% +drdt and this is a nice simple equation +to solve you just divide through by + + align:start position:0% +to solve you just divide through by + + + align:start position:0% +to solve you just divide through by +everything on the right hand side other + + align:start position:0% +everything on the right hand side other + + + align:start position:0% +everything on the right hand side other +than drdt so this implies that + + align:start position:0% +than drdt so this implies that + + + align:start position:0% +than drdt so this implies that +Dr DT is equal to well okay so I have to + + align:start position:0% +Dr DT is equal to well okay so I have to + + + align:start position:0% +Dr DT is equal to well okay so I have to +divide a thousand by all this stuff I + + align:start position:0% +divide a thousand by all this stuff I + + + align:start position:0% +divide a thousand by all this stuff I +think it works out to something like + + align:start position:0% +think it works out to something like + + + align:start position:0% +think it works out to something like +125 over 32 + + align:start position:0% +125 over 32 + + + align:start position:0% +125 over 32 +Pi all right so that's the exact value + + align:start position:0% +Pi all right so that's the exact value + + + align:start position:0% +Pi all right so that's the exact value +maybe you're interested in sort of + + align:start position:0% +maybe you're interested in sort of + + + align:start position:0% +maybe you're interested in sort of +knowing about how large this is so so + + align:start position:0% +knowing about how large this is so so + + + align:start position:0% +knowing about how large this is so so +well 32 2 pi is pretty close to 100 so + + align:start position:0% +well 32 2 pi is pretty close to 100 so + + + align:start position:0% +well 32 2 pi is pretty close to 100 so +this is about 1.2 + + align:start position:0% +this is about 1.2 + + + align:start position:0% +this is about 1.2 +something so all right so there we go so + + align:start position:0% +something so all right so there we go so + + + align:start position:0% +something so all right so there we go so +that answers the first question at that + + align:start position:0% +that answers the first question at that + + + align:start position:0% +that answers the first question at that +moment the the radius is growing at a + + align:start position:0% +moment the the radius is growing at a + + + align:start position:0% +moment the the radius is growing at a +rate of 125 over 32 Pi cm per second + + align:start position:0% +rate of 125 over 32 Pi cm per second + + + align:start position:0% +rate of 125 over 32 Pi cm per second +okay so now how about the second + + align:start position:0% +okay so now how about the second + + + align:start position:0% +okay so now how about the second +question that we've got here what about + + align:start position:0% +question that we've got here what about + + + align:start position:0% +question that we've got here what about +the surface area so again we we know how + + align:start position:0% +the surface area so again we we know how + + + align:start position:0% +the surface area so again we we know how +fast now the radius is changing and we + + align:start position:0% +fast now the radius is changing and we + + + align:start position:0% +fast now the radius is changing and we +know how fast the volume is changing so + + align:start position:0% +know how fast the volume is changing so + + + align:start position:0% +know how fast the volume is changing so +in order to figure out how fast the + + align:start position:0% +in order to figure out how fast the + + + align:start position:0% +in order to figure out how fast the +surface area is changing we need + + align:start position:0% +surface area is changing we need + + + align:start position:0% +surface area is changing we need +something that relates the surface area + + align:start position:0% +something that relates the surface area + + + align:start position:0% +something that relates the surface area +to either the volume or the radius now + + align:start position:0% +to either the volume or the radius now + + + align:start position:0% +to either the volume or the radius now +the relationship between surface area + + align:start position:0% +the relationship between surface area + + + align:start position:0% +the relationship between surface area +and volume is something that we could + + align:start position:0% +and volume is something that we could + + + align:start position:0% +and volume is something that we could +sort of work out if we had to but it's a + + align:start position:0% +sort of work out if we had to but it's a + + + align:start position:0% +sort of work out if we had to but it's a +lot easier to write down the surface + + align:start position:0% +lot easier to write down the surface + + + align:start position:0% +lot easier to write down the surface +area in terms of the radius so let's do + + align:start position:0% +area in terms of the radius so let's do + + + align:start position:0% +area in terms of the radius so let's do +that um so we + + align:start position:0% +that um so we + + + align:start position:0% +that um so we +have I'm going to I'm going to use the + + align:start position:0% +have I'm going to I'm going to use the + + + align:start position:0% +have I'm going to I'm going to use the +letter s to denote surface area of a + + align:start position:0% +letter s to denote surface area of a + + + align:start position:0% +letter s to denote surface area of a +sphere so again it's a general identity + + align:start position:0% +sphere so again it's a general identity + + + align:start position:0% +sphere so again it's a general identity +you know geometric fact that the surface + + align:start position:0% +you know geometric fact that the surface + + + align:start position:0% +you know geometric fact that the surface +area of a sphere is equal to 4 pi + + align:start position:0% +area of a sphere is equal to 4 pi + + + align:start position:0% +area of a sphere is equal to 4 pi +* the radius squ and this is always true + + align:start position:0% +* the radius squ and this is always true + + + align:start position:0% +* the radius squ and this is always true +and now the thing that we want is the + + align:start position:0% +and now the thing that we want is the + + + align:start position:0% +and now the thing that we want is the +rate of change of the surface area so + + align:start position:0% +rate of change of the surface area so + + + align:start position:0% +rate of change of the surface area so +the rate of change is the derivative so + + align:start position:0% +the rate of change is the derivative so + + + align:start position:0% +the rate of change is the derivative so +we want to compute the derivative here + + align:start position:0% +we want to compute the derivative here + + + align:start position:0% +we want to compute the derivative here +uh dsdt so okay so we just do it so + + align:start position:0% +uh dsdt so okay so we just do it so + + + align:start position:0% +uh dsdt so okay so we just do it so +DS DT is equal to well 4 Pi hangs around + + align:start position:0% +DS DT is equal to well 4 Pi hangs around + + + align:start position:0% +DS DT is equal to well 4 Pi hangs around +and again we we differentiate r s so we + + align:start position:0% +and again we we differentiate r s so we + + + align:start position:0% +and again we we differentiate r s so we +R is a function of T so we have to use + + align:start position:0% +R is a function of T so we have to use + + + align:start position:0% +R is a function of T so we have to use +the chain rule here so this is time 2 + + align:start position:0% +the chain rule here so this is time 2 + + + align:start position:0% +the chain rule here so this is time 2 +R * + + align:start position:0% +R * + + + align:start position:0% +R * +Dr DT so this is an identity so this is + + align:start position:0% +Dr DT so this is an identity so this is + + + align:start position:0% +Dr DT so this is an identity so this is +true always and now we want to know at + + align:start position:0% +true always and now we want to know at + + + align:start position:0% +true always and now we want to know at +this particular moment in time when R is + + align:start position:0% +this particular moment in time when R is + + + align:start position:0% +this particular moment in time when R is +equal to 8 what is dsdt and in order to + + align:start position:0% +equal to 8 what is dsdt and in order to + + + align:start position:0% +equal to 8 what is dsdt and in order to +figure that out well okay so we we just + + align:start position:0% +figure that out well okay so we we just + + + align:start position:0% +figure that out well okay so we we just +have to be able to plug in for + + align:start position:0% +have to be able to plug in for + + + align:start position:0% +have to be able to plug in for +everything else + + align:start position:0% +everything else + + + align:start position:0% +everything else +so so when r equal 8 all right well + + align:start position:0% +so so when r equal 8 all right well + + + align:start position:0% +so so when r equal 8 all right well +luckily now if we if we were just + + align:start position:0% +luckily now if we if we were just + + + align:start position:0% +luckily now if we if we were just +starting this problem from scratch here + + align:start position:0% +starting this problem from scratch here + + + align:start position:0% +starting this problem from scratch here +we'd have a problem which is we wouldn't + + align:start position:0% +we'd have a problem which is we wouldn't + + + align:start position:0% +we'd have a problem which is we wouldn't +know what drdt was but luckily we've + + align:start position:0% +know what drdt was but luckily we've + + + align:start position:0% +know what drdt was but luckily we've +already figured it out right so in in + + align:start position:0% +already figured it out right so in in + + + align:start position:0% +already figured it out right so in in +the first part of the problem so we know + + align:start position:0% +the first part of the problem so we know + + + align:start position:0% +the first part of the problem so we know +that when R is equal to 8 Dr R DT is + + align:start position:0% +that when R is equal to 8 Dr R DT is + + + align:start position:0% +that when R is equal to 8 Dr R DT is +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +125 over 32 Pi did I copy that right yes + + align:start position:0% +125 over 32 Pi did I copy that right yes + + + align:start position:0% +125 over 32 Pi did I copy that right yes +I did okay + + align:start position:0% +I did okay + + + align:start position:0% +I did okay +um so okay so in this case the equation + + align:start position:0% +um so okay so in this case the equation + + + align:start position:0% +um so okay so in this case the equation +we have to solve is just completely + + align:start position:0% +we have to solve is just completely + + + align:start position:0% +we have to solve is just completely +straightforward we just plug in the + + align:start position:0% +straightforward we just plug in the + + + align:start position:0% +straightforward we just plug in the +values and it's already solved for us um + + align:start position:0% +values and it's already solved for us um + + + align:start position:0% +values and it's already solved for us um +so that's nice um so that we + + align:start position:0% +so that's nice um so that we + + + align:start position:0% +so that's nice um so that we +get the DS DT at that moment is equal to + + align:start position:0% +get the DS DT at that moment is equal to + + + align:start position:0% +get the DS DT at that moment is equal to +well okay so it's 4 Pi * + + align:start position:0% +well okay so it's 4 Pi * + + + align:start position:0% +well okay so it's 4 Pi * + + align:start position:0% + + + align:start position:0% +time 8 is the radius + + align:start position:0% +time 8 is the radius + + + align:start position:0% +time 8 is the radius +times + + align:start position:0% +times + + + align:start position:0% +times +125 over + + align:start position:0% +125 over + + + align:start position:0% +125 over +32 pi oh boy and r so we can work this + + align:start position:0% +32 pi oh boy and r so we can work this + + + align:start position:0% +32 pi oh boy and r so we can work this +out if we want I guess that's 32 pi to + + align:start position:0% +out if we want I guess that's 32 pi to + + + align:start position:0% +out if we want I guess that's 32 pi to +cancel so that's equal to + + align:start position:0% +cancel so that's equal to + + + align:start position:0% +cancel so that's equal to +250 and I guess the units there better + + align:start position:0% +250 and I guess the units there better + + + align:start position:0% +250 and I guess the units there better +be ctime squar per second so at this + + align:start position:0% +be ctime squar per second so at this + + + align:start position:0% +be ctime squar per second so at this +moment in time the surface area is + + align:start position:0% +moment in time the surface area is + + + align:start position:0% +moment in time the surface area is +growing by 250 cm squar per second so + + align:start position:0% +growing by 250 cm squar per second so + + + align:start position:0% +growing by 250 cm squar per second so +that's all we had to do so we're all set \ No newline at end of file diff --git a/SR6dDuTbEwo.txt b/SR6dDuTbEwo.txt new file mode 100644 index 0000000000000000000000000000000000000000..839c2f51e7387e5309d13754275f6e7baa83f20f --- /dev/null +++ b/SR6dDuTbEwo.txt @@ -0,0 +1,6491 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so Phil uh is going to do + + align:start position:0% +ocw.mit.edu so Phil uh is going to do + + + align:start position:0% +ocw.mit.edu so Phil uh is going to do +the next three recitations so the first + + align:start position:0% +the next three recitations so the first + + + align:start position:0% +the next three recitations so the first +one today is really going to focus on + + align:start position:0% +one today is really going to focus on + + + align:start position:0% +one today is really going to focus on +how do you actually debug programs onel + + align:start position:0% +how do you actually debug programs onel + + + align:start position:0% +how do you actually debug programs onel +uh how many people + + align:start position:0% +uh how many people + + + align:start position:0% +uh how many people +GDB are familiar with + + align:start position:0% +GDB are familiar with + + + align:start position:0% +GDB are familiar with +GDB okay good so uh there's going to be + + align:start position:0% +GDB okay good so uh there's going to be + + + align:start position:0% +GDB okay good so uh there's going to be +a a mini tutorial on how to run programs + + align:start position:0% +a a mini tutorial on how to run programs + + + align:start position:0% +a a mini tutorial on how to run programs +and attach GDB which is a a debugger + + align:start position:0% +and attach GDB which is a a debugger + + + align:start position:0% +and attach GDB which is a a debugger +that's uh commonly used um for debugging + + align:start position:0% +that's uh commonly used um for debugging + + + align:start position:0% +that's uh commonly used um for debugging +programs we'll show you how to debug PPU + + align:start position:0% +programs we'll show you how to debug PPU + + + align:start position:0% +programs we'll show you how to debug PPU +and spu programs and he's going to talk + + align:start position:0% +and spu programs and he's going to talk + + + align:start position:0% +and spu programs and he's going to talk +a little bit about uh some some other + + align:start position:0% +a little bit about uh some some other + + + align:start position:0% +a little bit about uh some some other +things that might help you in terms of + + align:start position:0% +things that might help you in terms of + + + align:start position:0% +things that might help you in terms of +performance debugging you know finding + + align:start position:0% +performance debugging you know finding + + + align:start position:0% +performance debugging you know finding +out where things are not going as as + + align:start position:0% +out where things are not going as as + + + align:start position:0% +out where things are not going as as +well or as fast as you might expect them + + align:start position:0% +well or as fast as you might expect them + + + align:start position:0% +well or as fast as you might expect them +to go uh and then next two recitations + + align:start position:0% +to go uh and then next two recitations + + + align:start position:0% +to go uh and then next two recitations +which will be next week will focus on + + align:start position:0% +which will be next week will focus on + + + align:start position:0% +which will be next week will focus on +doing some actual performance specific + + align:start position:0% +doing some actual performance specific + + + align:start position:0% +doing some actual performance specific +optimizations so you've written your + + align:start position:0% +optimizations so you've written your + + + align:start position:0% +optimizations so you've written your +program it's working uh well well the + + align:start position:0% +program it's working uh well well the + + + align:start position:0% +program it's working uh well well the +functionality is there but it's not + + align:start position:0% +functionality is there but it's not + + + align:start position:0% +functionality is there but it's not +performing as fast as you might like or + + align:start position:0% +performing as fast as you might like or + + + align:start position:0% +performing as fast as you might like or +you you think you can improve + + align:start position:0% +you you think you can improve + + + align:start position:0% +you you think you can improve +performance a little bit better so what + + align:start position:0% +performance a little bit better so what + + + align:start position:0% +performance a little bit better so what +can you do so he'll show you some tricks + + align:start position:0% +can you do so he'll show you some tricks + + + align:start position:0% +can you do so he'll show you some tricks +and some uh uh some things you can do to + + align:start position:0% +and some uh uh some things you can do to + + + align:start position:0% +and some uh uh some things you can do to +get the performance up uh for some of + + align:start position:0% +get the performance up uh for some of + + + align:start position:0% +get the performance up uh for some of +you have asked about the eclipse + + align:start position:0% +you have asked about the eclipse + + + align:start position:0% +you have asked about the eclipse +debugger uh the Eclipse IDE uh it does + + align:start position:0% +debugger uh the Eclipse IDE uh it does + + + align:start position:0% +debugger uh the Eclipse IDE uh it does +run reasonably slowly on the PlayStation + + align:start position:0% +run reasonably slowly on the PlayStation + + + align:start position:0% +run reasonably slowly on the PlayStation +3's because of M M constraints uh so if + + align:start position:0% +3's because of M M constraints uh so if + + + align:start position:0% +3's because of M M constraints uh so if +you have lots of people trying to use it + + align:start position:0% +you have lots of people trying to use it + + + align:start position:0% +you have lots of people trying to use it +on the eclipse on the PS3 it'll probably + + align:start position:0% +on the eclipse on the PS3 it'll probably + + + align:start position:0% +on the eclipse on the PS3 it'll probably +be unusable so for those of you who are + + align:start position:0% +be unusable so for those of you who are + + + align:start position:0% +be unusable so for those of you who are +interested we'll just do separate + + align:start position:0% +interested we'll just do separate + + + align:start position:0% +interested we'll just do separate +tutorials um offline because I don't + + align:start position:0% +tutorials um offline because I don't + + + align:start position:0% +tutorials um offline because I don't +know how many people actually end up + + align:start position:0% +know how many people actually end up + + + align:start position:0% +know how many people actually end up +using it um other than + + align:start position:0% + + + + align:start position:0% + +that all right so today we'll talk about + + align:start position:0% +that all right so today we'll talk about + + + align:start position:0% +that all right so today we'll talk about +how to run GDB on cell and then we'll + + align:start position:0% +how to run GDB on cell and then we'll + + + align:start position:0% +how to run GDB on cell and then we'll +also do some static profiling where you + + align:start position:0% +also do some static profiling where you + + + align:start position:0% +also do some static profiling where you +can figure fig out when instructions are + + align:start position:0% +can figure fig out when instructions are + + + align:start position:0% +can figure fig out when instructions are +going to be executed and then I'll talk + + align:start position:0% +going to be executed and then I'll talk + + + align:start position:0% +going to be executed and then I'll talk +a little bit about the dynamic profiling + + align:start position:0% +a little bit about the dynamic profiling + + + align:start position:0% +a little bit about the dynamic profiling +tools that we have + + align:start position:0% + + + + align:start position:0% + +available uh so you can use GDB to + + align:start position:0% +available uh so you can use GDB to + + + align:start position:0% +available uh so you can use GDB to +examine the state of your program and + + align:start position:0% +examine the state of your program and + + + align:start position:0% +examine the state of your program and +this can help you figure out uh bugs + + align:start position:0% +this can help you figure out uh bugs + + + align:start position:0% +this can help you figure out uh bugs +that you might have there's two ways + + align:start position:0% +that you might have there's two ways + + + align:start position:0% +that you might have there's two ways +that you can use GDB the first way is uh + + align:start position:0% +that you can use GDB the first way is uh + + + align:start position:0% +that you can use GDB the first way is uh +when your program crashes you can figure + + align:start position:0% +when your program crashes you can figure + + + align:start position:0% +when your program crashes you can figure +out what was happening at the time that + + align:start position:0% +out what was happening at the time that + + + align:start position:0% +out what was happening at the time that +it crashed another way that you can use + + align:start position:0% +it crashed another way that you can use + + + align:start position:0% +it crashed another way that you can use +GDB is to kind of run it from the + + align:start position:0% +GDB is to kind of run it from the + + + align:start position:0% +GDB is to kind of run it from the +beginning you attach GDB to your program + + align:start position:0% +beginning you attach GDB to your program + + + align:start position:0% +beginning you attach GDB to your program +and then you step through all the things + + align:start position:0% +and then you step through all the things + + + align:start position:0% +and then you step through all the things +all the instructions that are being + + align:start position:0% +all the instructions that are being + + + align:start position:0% +all the instructions that are being +executed while the program + + align:start position:0% +executed while the program + + + align:start position:0% +executed while the program +runs now in order for GDB to uh in order + + align:start position:0% +runs now in order for GDB to uh in order + + + align:start position:0% +runs now in order for GDB to uh in order +for GDB to be able to provide useful + + align:start position:0% +for GDB to be able to provide useful + + + align:start position:0% +for GDB to be able to provide useful +information about the state of your + + align:start position:0% +information about the state of your + + + align:start position:0% +information about the state of your +program you have to give it a little + + align:start position:0% +program you have to give it a little + + + align:start position:0% +program you have to give it a little +help you need to compile your program + + align:start position:0% +help you need to compile your program + + + align:start position:0% +help you need to compile your program +using GCC DG uh xlc - G will also work + + align:start position:0% +using GCC DG uh xlc - G will also work + + + align:start position:0% +using GCC DG uh xlc - G will also work +and they put this puts in extra + + align:start position:0% +and they put this puts in extra + + + align:start position:0% +and they put this puts in extra +information into your uh this puts in + + align:start position:0% +information into your uh this puts in + + + align:start position:0% +information into your uh this puts in +some extra information into your program + + align:start position:0% +some extra information into your program + + + align:start position:0% +some extra information into your program +so that when uh when GDB is looking at + + align:start position:0% +so that when uh when GDB is looking at + + + align:start position:0% +so that when uh when GDB is looking at +the state of your program it's able to + + align:start position:0% +the state of your program it's able to + + + align:start position:0% +the state of your program it's able to +figure out what line numbers in the + + align:start position:0% +figure out what line numbers in the + + + align:start position:0% +figure out what line numbers in the +source code that corresponds + + align:start position:0% +source code that corresponds + + + align:start position:0% +source code that corresponds +to uh so you can just add DG manually to + + align:start position:0% +to uh so you can just add DG manually to + + + align:start position:0% +to uh so you can just add DG manually to +your GCC invocations or you can also set + + align:start position:0% +your GCC invocations or you can also set + + + align:start position:0% +your GCC invocations or you can also set +this uh compiler or you can set this + + align:start position:0% +this uh compiler or you can set this + + + align:start position:0% +this uh compiler or you can set this +option in the make file CC opt level and + + align:start position:0% +option in the make file CC opt level and + + + align:start position:0% +option in the make file CC opt level and +set that to CC opt level debug and that + + align:start position:0% +set that to CC opt level debug and that + + + align:start position:0% +set that to CC opt level debug and that +will uh do the same thing as uh adding + + align:start position:0% +will uh do the same thing as uh adding + + + align:start position:0% +will uh do the same thing as uh adding +dasg all right + + align:start position:0% + + + + align:start position:0% + +now uh we have a special version of GDB + + align:start position:0% +now uh we have a special version of GDB + + + align:start position:0% +now uh we have a special version of GDB +available for for our uh use on the cell + + align:start position:0% +available for for our uh use on the cell + + + align:start position:0% +available for for our uh use on the cell +uh PPU GDB is used for debugging uh PPU + + align:start position:0% +uh PPU GDB is used for debugging uh PPU + + + align:start position:0% +uh PPU GDB is used for debugging uh PPU +and spu programs uh after they've been + + align:start position:0% +and spu programs uh after they've been + + + align:start position:0% +and spu programs uh after they've been +linked together and how you invoke it if + + align:start position:0% +linked together and how you invoke it if + + + align:start position:0% +linked together and how you invoke it if +you're going to uh if you're going to + + align:start position:0% +you're going to uh if you're going to + + + align:start position:0% +you're going to uh if you're going to +run your entire program using GDB is you + + align:start position:0% +run your entire program using GDB is you + + + align:start position:0% +run your entire program using GDB is you +type uh PPU dgdb and then the name of + + align:start position:0% +type uh PPU dgdb and then the name of + + + align:start position:0% +type uh PPU dgdb and then the name of +your program and what you get is a GD B + + align:start position:0% +your program and what you get is a GD B + + + align:start position:0% +your program and what you get is a GD B +prompt where you can issue uh additional + + align:start position:0% +prompt where you can issue uh additional + + + align:start position:0% +prompt where you can issue uh additional +commands to the debugger to control + + align:start position:0% +commands to the debugger to control + + + align:start position:0% +commands to the debugger to control +execution of your program and also ask + + align:start position:0% +execution of your program and also ask + + + align:start position:0% +execution of your program and also ask +it ask the debugger to tell you various + + align:start position:0% +it ask the debugger to tell you various + + + align:start position:0% +it ask the debugger to tell you various +things about your + + align:start position:0% +things about your + + + align:start position:0% +things about your +program uh one thing you can do is one + + align:start position:0% +program uh one thing you can do is one + + + align:start position:0% +program uh one thing you can do is one +thing you can do is export spu info + + align:start position:0% +thing you can do is export spu info + + + align:start position:0% +thing you can do is export spu info +equals 1 before you start your program + + align:start position:0% +equals 1 before you start your program + + + align:start position:0% +equals 1 before you start your program +and that will uh that will print some + + align:start position:0% +and that will uh that will print some + + + align:start position:0% +and that will uh that will print some +extra debugging information about when + + align:start position:0% +extra debugging information about when + + + align:start position:0% +extra debugging information about when +threads are being created and + + align:start position:0% + + + + align:start position:0% + +destroyed uh like I mentioned you can + + align:start position:0% +destroyed uh like I mentioned you can + + + align:start position:0% +destroyed uh like I mentioned you can +also + + align:start position:0% +also + + + align:start position:0% +also +uh use GDB to attach to a program that's + + align:start position:0% +uh use GDB to attach to a program that's + + + align:start position:0% +uh use GDB to attach to a program that's +already running and if you want to do + + align:start position:0% +already running and if you want to do + + + align:start position:0% +already running and if you want to do +that you still need to provide the uh + + align:start position:0% +that you still need to provide the uh + + + align:start position:0% +that you still need to provide the uh +executable name and you also provide the + + align:start position:0% +executable name and you also provide the + + + align:start position:0% +executable name and you also provide the +process ID of the program to attach + + align:start position:0% +process ID of the program to attach + + + align:start position:0% +process ID of the program to attach +to + + align:start position:0% +to + + + align:start position:0% +to +and do people know how to get the + + align:start position:0% +and do people know how to get the + + + align:start position:0% +and do people know how to get the +process ID or + + align:start position:0% +process ID or + + + align:start position:0% +process ID or +something how many people don't + + align:start position:0% +something how many people don't + + + align:start position:0% +something how many people don't +know so the easiest way to do it is if + + align:start position:0% +know so the easiest way to do it is if + + + align:start position:0% +know so the easiest way to do it is if +your program is running just type top uh + + align:start position:0% +your program is running just type top uh + + + align:start position:0% +your program is running just type top uh +and that'll actually show you what's + + align:start position:0% +and that'll actually show you what's + + + align:start position:0% +and that'll actually show you what's +running on your machine and be a column + + align:start position:0% +running on your machine and be a column + + + align:start position:0% +running on your machine and be a column +that has the process ID another thing + + align:start position:0% +that has the process ID another thing + + + align:start position:0% +that has the process ID another thing +you can do is just type PS uh we'll add + + align:start position:0% +you can do is just type PS uh we'll add + + + align:start position:0% +you can do is just type PS uh we'll add +those to the reation slides so you can + + align:start position:0% +those to the reation slides so you can + + + align:start position:0% +those to the reation slides so you can +get + + align:start position:0% + + + + align:start position:0% + +that uh so I forgot to mention if + + align:start position:0% +that uh so I forgot to mention if + + + align:start position:0% +that uh so I forgot to mention if +you're uh if you're invoking your + + align:start position:0% +you're uh if you're invoking your + + + align:start position:0% +you're uh if you're invoking your +program with GDB then uh after you type + + align:start position:0% +program with GDB then uh after you type + + + align:start position:0% +program with GDB then uh after you type +ppug GDB uh with your executable name + + align:start position:0% +ppug GDB uh with your executable name + + + align:start position:0% +ppug GDB uh with your executable name +GDB is just going to sit there and wait + + align:start position:0% +GDB is just going to sit there and wait + + + align:start position:0% +GDB is just going to sit there and wait +for instructions and what you can do is + + align:start position:0% +for instructions and what you can do is + + + align:start position:0% +for instructions and what you can do is +type run and that will run your program + + align:start position:0% +type run and that will run your program + + + align:start position:0% +type run and that will run your program +normally uh but the difference is that + + align:start position:0% +normally uh but the difference is that + + + align:start position:0% +normally uh but the difference is that +GDB will uh pick up and GDB will pick up + + align:start position:0% +GDB will uh pick up and GDB will pick up + + + align:start position:0% +GDB will uh pick up and GDB will pick up +if if something goes wrong and then + + align:start position:0% +if if something goes wrong and then + + + align:start position:0% +if if something goes wrong and then +that's where you can step in and look at + + align:start position:0% +that's where you can step in and look at + + + align:start position:0% +that's where you can step in and look at +the program + + align:start position:0% + + + + align:start position:0% + +state so what kind of things can you + + align:start position:0% +state so what kind of things can you + + + align:start position:0% +state so what kind of things can you +figure out about your program + + align:start position:0% +figure out about your program + + + align:start position:0% +figure out about your program +uh anytime you have this GDB prompt and + + align:start position:0% +uh anytime you have this GDB prompt and + + + align:start position:0% +uh anytime you have this GDB prompt and +your program is running you can type BT + + align:start position:0% +your program is running you can type BT + + + align:start position:0% +your program is running you can type BT +to get a to get a stack trace for your + + align:start position:0% +to get a to get a stack trace for your + + + align:start position:0% +to get a to get a stack trace for your +program and this will tell you which + + align:start position:0% +program and this will tell you which + + + align:start position:0% +program and this will tell you which +functions are calling which + + align:start position:0% +functions are calling which + + + align:start position:0% +functions are calling which +functions uh the it's going to give you + + align:start position:0% +functions uh the it's going to give you + + + align:start position:0% +functions uh the it's going to give you +a list of frames and the top one is + + align:start position:0% +a list of frames and the top one is + + + align:start position:0% +a list of frames and the top one is +going to correspond to the deepest level + + align:start position:0% +going to correspond to the deepest level + + + align:start position:0% +going to correspond to the deepest level +of function nesting or the deepest + + align:start position:0% +of function nesting or the deepest + + + align:start position:0% +of function nesting or the deepest +function called in the in the program + + align:start position:0% +function called in the in the program + + + align:start position:0% +function called in the in the program +and of course the last one on the list + + align:start position:0% +and of course the last one on the list + + + align:start position:0% +and of course the last one on the list +is going to be the main or the first + + align:start position:0% +is going to be the main or the first + + + align:start position:0% +is going to be the main or the first +function that was called that make + + align:start position:0% + + + + align:start position:0% + +sense and for each uh for each stack + + align:start position:0% +sense and for each uh for each stack + + + align:start position:0% +sense and for each uh for each stack +frame GDB will tell you uh the name of + + align:start position:0% +frame GDB will tell you uh the name of + + + align:start position:0% +frame GDB will tell you uh the name of +the function and if source code is + + align:start position:0% +the function and if source code is + + + align:start position:0% +the function and if source code is +available it will tell you + + align:start position:0% +available it will tell you + + + align:start position:0% +available it will tell you +uh also which file the function is + + align:start position:0% +uh also which file the function is + + + align:start position:0% +uh also which file the function is +running in right now and at which line + + align:start position:0% +running in right now and at which line + + + align:start position:0% +running in right now and at which line +number and so using that information you + + align:start position:0% +number and so using that information you + + + align:start position:0% +number and so using that information you +can figure out uh exactly you know where + + align:start position:0% +can figure out uh exactly you know where + + + align:start position:0% +can figure out uh exactly you know where +it was that this function called the + + align:start position:0% +it was that this function called the + + + align:start position:0% +it was that this function called the +next function and where it was that each + + align:start position:0% +next function and where it was that each + + + align:start position:0% +next function and where it was that each +function called the the next function + + align:start position:0% +function called the the next function + + + align:start position:0% +function called the the next function +after + + align:start position:0% + + + + align:start position:0% + +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +now now whenever you you've halted the + + align:start position:0% +now now whenever you you've halted the + + + align:start position:0% +now now whenever you you've halted the +program State you can get information + + align:start position:0% +program State you can get information + + + align:start position:0% +program State you can get information +about what the local variables + + align:start position:0% +about what the local variables + + + align:start position:0% +about what the local variables +are and to do that you can type info + + align:start position:0% +are and to do that you can type info + + + align:start position:0% +are and to do that you can type info +locals and it will print a list of all + + align:start position:0% +locals and it will print a list of all + + + align:start position:0% +locals and it will print a list of all +the local variables and their values uh + + align:start position:0% +the local variables and their values uh + + + align:start position:0% +the local variables and their values uh +GDB because it gets annotations from + + align:start position:0% +GDB because it gets annotations from + + + align:start position:0% +GDB because it gets annotations from +from the uh compiled program it knows + + align:start position:0% +from the uh compiled program it knows + + + align:start position:0% +from the uh compiled program it knows +about what data types are associated + + align:start position:0% +about what data types are associated + + + align:start position:0% +about what data types are associated +with which variables and so it will it + + align:start position:0% +with which variables and so it will it + + + align:start position:0% +with which variables and so it will it +will be able to format the values or it + + align:start position:0% +will be able to format the values or it + + + align:start position:0% +will be able to format the values or it +will be able to format the output + + align:start position:0% +will be able to format the output + + + align:start position:0% +will be able to format the output +appropriately so for example uh it knows + + align:start position:0% +appropriately so for example uh it knows + + + align:start position:0% +appropriately so for example uh it knows +that I is an integer whereas if you uh + + align:start position:0% +that I is an integer whereas if you uh + + + align:start position:0% +that I is an integer whereas if you uh +if you had I is for example uh floating + + align:start position:0% +if you had I is for example uh floating + + + align:start position:0% +if you had I is for example uh floating +Point number it would it would print + + align:start position:0% +Point number it would it would print + + + align:start position:0% +Point number it would it would print +that uh floating Point number + + align:start position:0% +that uh floating Point number + + + align:start position:0% +that uh floating Point number +representation + + align:start position:0% +representation + + + align:start position:0% +representation +instead uh instead of looking at single + + align:start position:0% +instead uh instead of looking at single + + + align:start position:0% +instead uh instead of looking at single +variables you can also ask GDB to + + align:start position:0% +variables you can also ask GDB to + + + align:start position:0% +variables you can also ask GDB to +evaluate arbitrary expressions for you + + align:start position:0% +evaluate arbitrary expressions for you + + + align:start position:0% +evaluate arbitrary expressions for you +and this is actually a really powerful + + align:start position:0% +and this is actually a really powerful + + + align:start position:0% +and this is actually a really powerful +facility you can pretty much type any + + align:start position:0% +facility you can pretty much type any + + + align:start position:0% +facility you can pretty much type any +expression that you would be able to use + + align:start position:0% +expression that you would be able to use + + + align:start position:0% +expression that you would be able to use +in C or + + align:start position:0% + + + + align:start position:0% + +C++ + + align:start position:0% + + + + align:start position:0% + +um uh when you type print uh when you + + align:start position:0% +um uh when you type print uh when you + + + align:start position:0% +um uh when you type print uh when you +type print our name GDB will look up + + align:start position:0% +type print our name GDB will look up + + + align:start position:0% +type print our name GDB will look up +that variable name for you but sometimes + + align:start position:0% +that variable name for you but sometimes + + + align:start position:0% +that variable name for you but sometimes +if you have more than one + + align:start position:0% +if you have more than one + + + align:start position:0% +if you have more than one +variable uh if you have if you have more + + align:start position:0% +variable uh if you have if you have more + + + align:start position:0% +variable uh if you have if you have more +than one variable available in your + + align:start position:0% +than one variable available in your + + + align:start position:0% +than one variable available in your +function under the same name for example + + align:start position:0% +function under the same name for example + + + align:start position:0% +function under the same name for example +these variables are in different files + + align:start position:0% +these variables are in different files + + + align:start position:0% +these variables are in different files +or uh different functions on uh + + align:start position:0% +or uh different functions on uh + + + align:start position:0% +or uh different functions on uh +different functions that are all + + align:start position:0% +different functions that are all + + + align:start position:0% +different functions that are all +available then you may need to + + align:start position:0% +available then you may need to + + + align:start position:0% +available then you may need to +disambiguate the variable name and and + + align:start position:0% +disambiguate the variable name and and + + + align:start position:0% +disambiguate the variable name and and +to do that you just precede the variable + + align:start position:0% +to do that you just precede the variable + + + align:start position:0% +to do that you just precede the variable +name with either uh the file name that + + align:start position:0% +name with either uh the file name that + + + align:start position:0% +name with either uh the file name that +you want to use or the function that the + + align:start position:0% +you want to use or the function that the + + + align:start position:0% +you want to use or the function that the +variable occurs in any + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% +questions + + + align:start position:0% +questions +okay and because GDB uh because GDB + + align:start position:0% +okay and because GDB uh because GDB + + + align:start position:0% +okay and because GDB uh because GDB +knows which line number which line + + align:start position:0% +knows which line number which line + + + align:start position:0% +knows which line number which line +numbers the programs uh is executing + + align:start position:0% +numbers the programs uh is executing + + + align:start position:0% +numbers the programs uh is executing +right now then it's able to show you the + + align:start position:0% +right now then it's able to show you the + + + align:start position:0% +right now then it's able to show you the +source code corresponding to the current + + align:start position:0% +source code corresponding to the current + + + align:start position:0% +source code corresponding to the current +uh the current place in the program and + + align:start position:0% +uh the current place in the program and + + + align:start position:0% +uh the current place in the program and +in order to browse the source code if if + + align:start position:0% +in order to browse the source code if if + + + align:start position:0% +in order to browse the source code if if +it's available you just type list + + align:start position:0% +it's available you just type list + + + align:start position:0% +it's available you just type list +uh uh in general whenever GDB has + + align:start position:0% +uh uh in general whenever GDB has + + + align:start position:0% +uh uh in general whenever GDB has +stopped in a certain place you can type + + align:start position:0% +stopped in a certain place you can type + + + align:start position:0% +stopped in a certain place you can type +list to get uh a listing of you know the + + align:start position:0% +list to get uh a listing of you know the + + + align:start position:0% +list to get uh a listing of you know the +source code near that + + align:start position:0% +source code near that + + + align:start position:0% +source code near that +location and what list will do by + + align:start position:0% +location and what list will do by + + + align:start position:0% +location and what list will do by +default is show 10 lines of source code + + align:start position:0% +default is show 10 lines of source code + + + align:start position:0% +default is show 10 lines of source code +near where the program + + align:start position:0% +near where the program + + + align:start position:0% +near where the program +stopped if you type list again it will + + align:start position:0% +stopped if you type list again it will + + + align:start position:0% +stopped if you type list again it will +show 10 lines following that and you can + + align:start position:0% +show 10 lines following that and you can + + + align:start position:0% +show 10 lines following that and you can +keep typing list to to browse the source + + align:start position:0% +keep typing list to to browse the source + + + align:start position:0% +keep typing list to to browse the source +code you can also get this you can also + + align:start position:0% +code you can also get this you can also + + + align:start position:0% +code you can also get this you can also +get the code that's uh that's at a + + align:start position:0% +get the code that's uh that's at a + + + align:start position:0% +get the code that's uh that's at a +particular line number if you want to + + align:start position:0% +particular line number if you want to + + + align:start position:0% +particular line number if you want to +look at another place in your + + align:start position:0% + + + + align:start position:0% + +program all right so this is how to use + + align:start position:0% +program all right so this is how to use + + + align:start position:0% +program all right so this is how to use +GDB to actually control the flow of your + + align:start position:0% +GDB to actually control the flow of your + + + align:start position:0% +GDB to actually control the flow of your +program + + align:start position:0% + + + + align:start position:0% + +um uh if you invoke + + align:start position:0% +um uh if you invoke + + + align:start position:0% +um uh if you invoke +GDB uh if you invoke GDB to to start up + + align:start position:0% +GDB uh if you invoke GDB to to start up + + + align:start position:0% +GDB uh if you invoke GDB to to start up +your program then you can type run and + + align:start position:0% +your program then you can type run and + + + align:start position:0% +your program then you can type run and +that will that will uh run your program + + align:start position:0% +that will that will uh run your program + + + align:start position:0% +that will that will uh run your program +with a normal flow of execution and it + + align:start position:0% +with a normal flow of execution and it + + + align:start position:0% +with a normal flow of execution and it +will only stop when um when errors occur + + align:start position:0% +will only stop when um when errors occur + + + align:start position:0% +will only stop when um when errors occur +but you can use you can use a couple of + + align:start position:0% +but you can use you can use a couple of + + + align:start position:0% +but you can use you can use a couple of +these commands to actually go step by + + align:start position:0% +these commands to actually go step by + + + align:start position:0% +these commands to actually go step by +step through your program and uh and + + align:start position:0% +step through your program and uh and + + + align:start position:0% +step through your program and uh and +wait for one line to be executed and + + align:start position:0% +wait for one line to be executed and + + + align:start position:0% +wait for one line to be executed and +then you know decide whether you want to + + align:start position:0% +then you know decide whether you want to + + + align:start position:0% +then you know decide whether you want to +look at the next line or not uh if you + + align:start position:0% +look at the next line or not uh if you + + + align:start position:0% +look at the next line or not uh if you +want to do this kind of step-by-step + + align:start position:0% +want to do this kind of step-by-step + + + align:start position:0% +want to do this kind of step-by-step +execution uh you start by use you start + + align:start position:0% +execution uh you start by use you start + + + align:start position:0% +execution uh you start by use you start +by using the start command instead of + + align:start position:0% +by using the start command instead of + + + align:start position:0% +by using the start command instead of +the Run command which will run + + align:start position:0% +the Run command which will run + + + align:start position:0% +the Run command which will run +continuously then anytime you want to + + align:start position:0% +continuously then anytime you want to + + + align:start position:0% +continuously then anytime you want to +jump to the next instruction you you can + + align:start position:0% +jump to the next instruction you you can + + + align:start position:0% +jump to the next instruction you you can +use next to get get to the next line in + + align:start position:0% +use next to get get to the next line in + + + align:start position:0% +use next to get get to the next line in +the current + + align:start position:0% +the current + + + align:start position:0% +the current +procedure uh you can also use step which + + align:start position:0% +procedure uh you can also use step which + + + align:start position:0% +procedure uh you can also use step which +will if there are function calls on the + + align:start position:0% +will if there are function calls on the + + + align:start position:0% +will if there are function calls on the +current line it will descend into those + + align:start position:0% +current line it will descend into those + + + align:start position:0% +current line it will descend into those +function calls and show you what's going + + align:start position:0% +function calls and show you what's going + + + align:start position:0% +function calls and show you what's going +on over + + align:start position:0% +on over + + + align:start position:0% +on over +there and uh if you're inside a function + + align:start position:0% +there and uh if you're inside a function + + + align:start position:0% +there and uh if you're inside a function +call you can type finish in order to uh + + align:start position:0% +call you can type finish in order to uh + + + align:start position:0% +call you can type finish in order to uh +in order to jump back to right after the + + align:start position:0% +in order to jump back to right after the + + + align:start position:0% +in order to jump back to right after the +function call ends in the in the caller + + align:start position:0% +function call ends in the in the caller + + + align:start position:0% +function call ends in the in the caller +of that + + align:start position:0% +of that + + + align:start position:0% +of that +function and if you want to stop uh if + + align:start position:0% +function and if you want to stop uh if + + + align:start position:0% +function and if you want to stop uh if +you want to stop line by line execution + + align:start position:0% +you want to stop line by line execution + + + align:start position:0% +you want to stop line by line execution +you can type continue and it will just + + align:start position:0% +you can type continue and it will just + + + align:start position:0% +you can type continue and it will just +uh continue without + + align:start position:0% +uh continue without + + + align:start position:0% +uh continue without +interruptions any + + align:start position:0% + + + + align:start position:0% + +questions basically anytime you use one + + align:start position:0% +questions basically anytime you use one + + + align:start position:0% +questions basically anytime you use one +of these uh line by line commands GDB + + align:start position:0% +of these uh line by line commands GDB + + + align:start position:0% +of these uh line by line commands GDB +will show you the line that you're on + + align:start position:0% +will show you the line that you're on + + + align:start position:0% +will show you the line that you're on +and if the if the + + align:start position:0% +and if the if the + + + align:start position:0% +and if the if the +uh if your program just jumped into a + + align:start position:0% +uh if your program just jumped into a + + + align:start position:0% +uh if your program just jumped into a +new function or something then it will + + align:start position:0% +new function or something then it will + + + align:start position:0% +new function or something then it will +also show you what function and what + + align:start position:0% +also show you what function and what + + + align:start position:0% +also show you what function and what +file you're in so this is very helpful + + align:start position:0% +file you're in so this is very helpful + + + align:start position:0% +file you're in so this is very helpful +for following what's going on in your + + align:start position:0% +for following what's going on in your + + + align:start position:0% +for following what's going on in your +program + + align:start position:0% + + + + align:start position:0% + +okay so in addition to uh just running + + align:start position:0% +okay so in addition to uh just running + + + align:start position:0% +okay so in addition to uh just running +through your program step by step you + + align:start position:0% +through your program step by step you + + + align:start position:0% +through your program step by step you +can also choose to only stop your + + align:start position:0% +can also choose to only stop your + + + align:start position:0% +can also choose to only stop your +program when certain things + + align:start position:0% +program when certain things + + + align:start position:0% +program when certain things +happen so this is very useful for + + align:start position:0% +happen so this is very useful for + + + align:start position:0% +happen so this is very useful for +debugging you know certain pieces of + + align:start position:0% +debugging you know certain pieces of + + + align:start position:0% +debugging you know certain pieces of +code where the code is very deeply + + align:start position:0% +code where the code is very deeply + + + align:start position:0% +code where the code is very deeply +nested inside and you don't want to you + + align:start position:0% +nested inside and you don't want to you + + + align:start position:0% +nested inside and you don't want to you +know step all the way to there you just + + align:start position:0% +know step all the way to there you just + + + align:start position:0% +know step all the way to there you just +want to stop when you get + + align:start position:0% +want to stop when you get + + + align:start position:0% +want to stop when you get +there and GDP allows you to Define break + + align:start position:0% +there and GDP allows you to Define break + + + align:start position:0% +there and GDP allows you to Define break +points which which are places in your + + align:start position:0% +points which which are places in your + + + align:start position:0% +points which which are places in your +source code and once + + align:start position:0% +source code and once + + + align:start position:0% +source code and once +GDB uh once GDB gets to a point of + + align:start position:0% +GDB uh once GDB gets to a point of + + + align:start position:0% +GDB uh once GDB gets to a point of +execution which corresponds to that + + align:start position:0% +execution which corresponds to that + + + align:start position:0% +execution which corresponds to that +point in your source code it will stop + + align:start position:0% +point in your source code it will stop + + + align:start position:0% +point in your source code it will stop +and ask you what to do you can set a + + align:start position:0% +and ask you what to do you can set a + + + align:start position:0% +and ask you what to do you can set a +breakpoint that's associated with any + + align:start position:0% +breakpoint that's associated with any + + + align:start position:0% +breakpoint that's associated with any +particular function in your source code + + align:start position:0% +particular function in your source code + + + align:start position:0% +particular function in your source code +or any + + align:start position:0% +or any + + + align:start position:0% +or any +particular uh oh well what you can do is + + align:start position:0% +particular uh oh well what you can do is + + + align:start position:0% +particular uh oh well what you can do is +if you do break function then it will + + align:start position:0% +if you do break function then it will + + + align:start position:0% +if you do break function then it will +create a new breakpoint and it will stop + + align:start position:0% +create a new breakpoint and it will stop + + + align:start position:0% +create a new breakpoint and it will stop +execution anytime you get to the + + align:start position:0% +execution anytime you get to the + + + align:start position:0% +execution anytime you get to the +beginning the beginning of that function + + align:start position:0% +beginning the beginning of that function + + + align:start position:0% +beginning the beginning of that function +but you can also set break points in the + + align:start position:0% +but you can also set break points in the + + + align:start position:0% +but you can also set break points in the +interior of a function by using line + + align:start position:0% +interior of a function by using line + + + align:start position:0% +interior of a function by using line +numbers all + + align:start position:0% +numbers all + + + align:start position:0% +numbers all +right any + + align:start position:0% + + + + align:start position:0% + +questions now sometimes uh sometimes you + + align:start position:0% +questions now sometimes uh sometimes you + + + align:start position:0% +questions now sometimes uh sometimes you +want a little bit more flexibility than + + align:start position:0% +want a little bit more flexibility than + + + align:start position:0% +want a little bit more flexibility than +that in setting break points suppose you + + align:start position:0% +that in setting break points suppose you + + + align:start position:0% +that in setting break points suppose you +if you only want to set a break point to + + align:start position:0% +if you only want to set a break point to + + + align:start position:0% +if you only want to set a break point to +happen when a certain condition is true + + align:start position:0% +happen when a certain condition is true + + + align:start position:0% +happen when a certain condition is true +uh this is helpful if you're trying to + + align:start position:0% +uh this is helpful if you're trying to + + + align:start position:0% +uh this is helpful if you're trying to +kind of track down a bug then you can + + align:start position:0% +kind of track down a bug then you can + + + align:start position:0% +kind of track down a bug then you can +write break and any of these things and + + align:start position:0% +write break and any of these things and + + + align:start position:0% +write break and any of these things and +then if expression and again you can use + + align:start position:0% +then if expression and again you can use + + + align:start position:0% +then if expression and again you can use +any sort of expression that uh you would + + align:start position:0% +any sort of expression that uh you would + + + align:start position:0% +any sort of expression that uh you would +be able to use in C and what GDB will do + + align:start position:0% +be able to use in C and what GDB will do + + + align:start position:0% +be able to use in C and what GDB will do +is every time execution runs up to that + + align:start position:0% +is every time execution runs up to that + + + align:start position:0% +is every time execution runs up to that +line it will evaluate the expression and + + align:start position:0% +line it will evaluate the expression and + + + align:start position:0% +line it will evaluate the expression and +only if that expression is true will it + + align:start position:0% +only if that expression is true will it + + + align:start position:0% +only if that expression is true will it +will it stop to ask you for + + align:start position:0% +will it stop to ask you for + + + align:start position:0% +will it stop to ask you for +control uh at any at any time you can + + align:start position:0% +control uh at any at any time you can + + + align:start position:0% +control uh at any at any time you can +see which break points are active by + + align:start position:0% +see which break points are active by + + + align:start position:0% +see which break points are active by +doing info breakpoints at the GDB prompt + + align:start position:0% +doing info breakpoints at the GDB prompt + + + align:start position:0% +doing info breakpoints at the GDB prompt +and you can also remove breakpoints at + + align:start position:0% +and you can also remove breakpoints at + + + align:start position:0% +and you can also remove breakpoints at +any time uh when each breakpoint is + + align:start position:0% +any time uh when each breakpoint is + + + align:start position:0% +any time uh when each breakpoint is +created it's given this it's given this + + align:start position:0% +created it's given this it's given this + + + align:start position:0% +created it's given this it's given this +number and the numbers start from one + + align:start position:0% +number and the numbers start from one + + + align:start position:0% +number and the numbers start from one +and to remove a breakpoint you just do + + align:start position:0% +and to remove a breakpoint you just do + + + align:start position:0% +and to remove a breakpoint you just do +remove uh followed by the number that + + align:start position:0% +remove uh followed by the number that + + + align:start position:0% +remove uh followed by the number that +was + + align:start position:0% + + + + align:start position:0% + +assigned uh in addition to braking you + + align:start position:0% +assigned uh in addition to braking you + + + align:start position:0% +assigned uh in addition to braking you +can also set a watch Point what this + + align:start position:0% +can also set a watch Point what this + + + align:start position:0% +can also set a watch Point what this +does is it will halt your program every + + align:start position:0% +does is it will halt your program every + + + align:start position:0% +does is it will halt your program every +time a particular value + + align:start position:0% +time a particular value + + + align:start position:0% +time a particular value +changes and this is this is useful for + + align:start position:0% +changes and this is this is useful for + + + align:start position:0% +changes and this is this is useful for +tracking down certain kinds of bugs if + + align:start position:0% +tracking down certain kinds of bugs if + + + align:start position:0% +tracking down certain kinds of bugs if +you're if you're trying to figure out + + align:start position:0% +you're if you're trying to figure out + + + align:start position:0% +you're if you're trying to figure out +where a certain value for a variable + + align:start position:0% +where a certain value for a variable + + + align:start position:0% +where a certain value for a variable +came from there could potentially be + + align:start position:0% +came from there could potentially be + + + align:start position:0% +came from there could potentially be +many many places in your program where + + align:start position:0% +many many places in your program where + + + align:start position:0% +many many places in your program where +that value is set and you don't want to + + align:start position:0% +that value is set and you don't want to + + + align:start position:0% +that value is set and you don't want to +have to set a break point for all of + + align:start position:0% +have to set a break point for all of + + + align:start position:0% +have to set a break point for all of +those and and watch them so you can + + align:start position:0% +those and and watch them so you can + + + align:start position:0% +those and and watch them so you can +instead set a watch point which will + + align:start position:0% +instead set a watch point which will + + + align:start position:0% +instead set a watch point which will +just tell you when that value is + + align:start position:0% + + + + align:start position:0% + +Set uh watch points work a lot like + + align:start position:0% +Set uh watch points work a lot like + + + align:start position:0% +Set uh watch points work a lot like +breakpoints and you can uh if you do + + align:start position:0% +breakpoints and you can uh if you do + + + align:start position:0% +breakpoints and you can uh if you do +info break points it will also list the + + align:start position:0% +info break points it will also list the + + + align:start position:0% +info break points it will also list the +watch points and I believe you can also + + align:start position:0% +watch points and I believe you can also + + + align:start position:0% +watch points and I believe you can also +remove them the same way with + + align:start position:0% + + + + align:start position:0% + +remove all right so I mentioned how you + + align:start position:0% +remove all right so I mentioned how you + + + align:start position:0% +remove all right so I mentioned how you +can examine your program state by + + align:start position:0% +can examine your program state by + + + align:start position:0% +can examine your program state by +looking at the values of local + + align:start position:0% +looking at the values of local + + + align:start position:0% +looking at the values of local +variables uh if you want a more + + align:start position:0% +variables uh if you want a more + + + align:start position:0% +variables uh if you want a more +low-level view of what's going on in + + align:start position:0% +low-level view of what's going on in + + + align:start position:0% +low-level view of what's going on in +your program you can actually look at + + align:start position:0% +your program you can actually look at + + + align:start position:0% +your program you can actually look at +the raw you can actually look at the raw + + align:start position:0% +the raw you can actually look at the raw + + + align:start position:0% +the raw you can actually look at the raw +memory and uh GDB allows you to specify + + align:start position:0% +memory and uh GDB allows you to specify + + + align:start position:0% +memory and uh GDB allows you to specify +an address and it will tell you + + align:start position:0% +an address and it will tell you + + + align:start position:0% +an address and it will tell you +exactly exactly what data is stored in + + align:start position:0% +exactly exactly what data is stored in + + + align:start position:0% +exactly exactly what data is stored in +the memory at that + + align:start position:0% +the memory at that + + + align:start position:0% +the memory at that +address + + align:start position:0% +address + + + align:start position:0% +address +uh but because there's not necessarily + + align:start position:0% +uh but because there's not necessarily + + + align:start position:0% +uh but because there's not necessarily +annotation info telling GDB uh what kind + + align:start position:0% +annotation info telling GDB uh what kind + + + align:start position:0% +annotation info telling GDB uh what kind +of data is stored at that address and of + + align:start position:0% +of data is stored at that address and of + + + align:start position:0% +of data is stored at that address and of +course there's multiple ways you can + + align:start position:0% +course there's multiple ways you can + + + align:start position:0% +course there's multiple ways you can +interpret uh any particular piece of + + align:start position:0% +interpret uh any particular piece of + + + align:start position:0% +interpret uh any particular piece of +data you'll have to tell GDB exactly how + + align:start position:0% +data you'll have to tell GDB exactly how + + + align:start position:0% +data you'll have to tell GDB exactly how +you want that data to be interpreted so + + align:start position:0% +you want that data to be interpreted so + + + align:start position:0% +you want that data to be interpreted so +you can interpret any particular block + + align:start position:0% +you can interpret any particular block + + + align:start position:0% +you can interpret any particular block +of memory as for example a series of + + align:start position:0% +of memory as for example a series of + + + align:start position:0% +of memory as for example a series of +machine instructions then GDB will tell + + align:start position:0% +machine instructions then GDB will tell + + + align:start position:0% +machine instructions then GDB will tell +you what the instructions are uh as if + + align:start position:0% +you what the instructions are uh as if + + + align:start position:0% +you what the instructions are uh as if +you were looking at as if you were + + align:start position:0% +you were looking at as if you were + + + align:start position:0% +you were looking at as if you were +looking at an an assembly listing uh you + + align:start position:0% +looking at an an assembly listing uh you + + + align:start position:0% +looking at an an assembly listing uh you +can ask GDB to interpret the memory as + + align:start position:0% +can ask GDB to interpret the memory as + + + align:start position:0% +can ask GDB to interpret the memory as +if it were an array of uh an array of + + align:start position:0% +if it were an array of uh an array of + + + align:start position:0% +if it were an array of uh an array of +integers and print them out either in + + align:start position:0% +integers and print them out either in + + + align:start position:0% +integers and print them out either in +HEX or in + + align:start position:0% +HEX or in + + + align:start position:0% +HEX or in +decimal um you can ask GDB + + align:start position:0% +decimal um you can ask GDB + + + align:start position:0% +decimal um you can ask GDB +to uh to + + align:start position:0% +to uh to + + + align:start position:0% +to uh to +uh to display the program or display the + + align:start position:0% +uh to display the program or display the + + + align:start position:0% +uh to display the program or display the +the data as if they were addresses or + + align:start position:0% +the data as if they were addresses or + + + align:start position:0% +the data as if they were addresses or +floating points numbers and how you do + + align:start position:0% +floating points numbers and how you do + + + align:start position:0% +floating points numbers and how you do +this is uh you type X for examine memory + + align:start position:0% +this is uh you type X for examine memory + + + align:start position:0% +this is uh you type X for examine memory +and Slash and then uh the number + + align:start position:0% +and Slash and then uh the number + + + align:start position:0% +and Slash and then uh the number +following is the number of words you + + align:start position:0% +following is the number of words you + + + align:start position:0% +following is the number of words you +want to look + + align:start position:0% +want to look + + + align:start position:0% +want to look +at and then the letter corresponds to + + align:start position:0% +at and then the letter corresponds to + + + align:start position:0% +at and then the letter corresponds to +one of these letters and tells GDB how + + align:start position:0% +one of these letters and tells GDB how + + + align:start position:0% +one of these letters and tells GDB how +to format the output and then the + + align:start position:0% +to format the output and then the + + + align:start position:0% +to format the output and then the +address will be the starting block of + + align:start position:0% +address will be the starting block of + + + align:start position:0% +address will be the starting block of +where you want to start examining + + align:start position:0% +where you want to start examining + + + align:start position:0% +where you want to start examining +memory all right any questions about + + align:start position:0% +memory all right any questions about + + + align:start position:0% +memory all right any questions about +this + + align:start position:0% + + + + align:start position:0% + +okay so I mentioned that at any time + + align:start position:0% +okay so I mentioned that at any time + + + align:start position:0% +okay so I mentioned that at any time +when you stop your program there are + + align:start position:0% +when you stop your program there are + + + align:start position:0% +when you stop your program there are +going to be uh multiple function calls + + align:start position:0% +going to be uh multiple function calls + + + align:start position:0% +going to be uh multiple function calls +which are active corresponding to you + + align:start position:0% +which are active corresponding to you + + + align:start position:0% +which are active corresponding to you +know main which called this other + + align:start position:0% +know main which called this other + + + align:start position:0% +know main which called this other +function which called this other + + align:start position:0% +function which called this other + + + align:start position:0% +function which called this other +function which called wherever your + + align:start position:0% +function which called wherever your + + + align:start position:0% +function which called wherever your +current point of execution is and you + + align:start position:0% +current point of execution is and you + + + align:start position:0% +current point of execution is and you +can actually examine the state for all + + align:start position:0% +can actually examine the state for all + + + align:start position:0% +can actually examine the state for all +of these all of these stack frames + + align:start position:0% +of these all of these stack frames + + + align:start position:0% +of these all of these stack frames +separately um when you do when you do BT + + align:start position:0% +separately um when you do when you do BT + + + align:start position:0% +separately um when you do when you do BT +it's going to give you the list of + + align:start position:0% +it's going to give you the list of + + + align:start position:0% +it's going to give you the list of +frames right and they're going to be + + align:start position:0% +frames right and they're going to be + + + align:start position:0% +frames right and they're going to be +numbered from zero to however many + + align:start position:0% +numbered from zero to however many + + + align:start position:0% +numbered from zero to however many +however many there are and you can jump + + align:start position:0% +however many there are and you can jump + + + align:start position:0% +however many there are and you can jump +to you can jump + + align:start position:0% +to you can jump + + + align:start position:0% +to you can jump +to uh you can jump to any of them by + + align:start position:0% +to uh you can jump to any of them by + + + align:start position:0% +to uh you can jump to any of them by +using frame and the appropriate number + + align:start position:0% +using frame and the appropriate number + + + align:start position:0% +using frame and the appropriate number +and it's going to default to frame zero + + align:start position:0% +and it's going to default to frame zero + + + align:start position:0% +and it's going to default to frame zero +which is the closest to where your + + align:start position:0% +which is the closest to where your + + + align:start position:0% +which is the closest to where your +program is actually executing but you + + align:start position:0% +program is actually executing but you + + + align:start position:0% +program is actually executing but you +can examine the state in frames which + + align:start position:0% +can examine the state in frames which + + + align:start position:0% +can examine the state in frames which +are further + + align:start position:0% +are further + + + align:start position:0% +are further +away so that means when you're + + align:start position:0% +away so that means when you're + + + align:start position:0% +away so that means when you're +evaluating variables each variable only + + align:start position:0% +evaluating variables each variable only + + + align:start position:0% +evaluating variables each variable only +makes sense in the context of a + + align:start position:0% +makes sense in the context of a + + + align:start position:0% +makes sense in the context of a +particular frame and you're able to uh + + align:start position:0% +particular frame and you're able to uh + + + align:start position:0% +particular frame and you're able to uh +go up the call stack to figure out you + + align:start position:0% +go up the call stack to figure out you + + + align:start position:0% +go up the call stack to figure out you +know uh what the value what the value of + + align:start position:0% +know uh what the value what the value of + + + align:start position:0% +know uh what the value what the value of +a particular variable is in this + + align:start position:0% +a particular variable is in this + + + align:start position:0% +a particular variable is in this +function which called this other + + align:start position:0% +function which called this other + + + align:start position:0% +function which called this other +function uh you can also use the + + align:start position:0% +function uh you can also use the + + + align:start position:0% +function uh you can also use the +commands up and down to just jump to the + + align:start position:0% +commands up and down to just jump to the + + + align:start position:0% +commands up and down to just jump to the +uh immediately adjacent uh + + align:start position:0% +uh immediately adjacent uh + + + align:start position:0% +uh immediately adjacent uh +frames all + + align:start position:0% + + + + align:start position:0% + +right okay so you can use GDB from emac + + align:start position:0% +right okay so you can use GDB from emac + + + align:start position:0% +right okay so you can use GDB from emac +as well and emac provides a really handy + + align:start position:0% +as well and emac provides a really handy + + + align:start position:0% +as well and emac provides a really handy +interface for GDB uh if you do MX GDB + + align:start position:0% +interface for GDB uh if you do MX GDB + + + align:start position:0% +interface for GDB uh if you do MX GDB +emex will invoke GDB for you and you're + + align:start position:0% +emex will invoke GDB for you and you're + + + align:start position:0% +emex will invoke GDB for you and you're +going to want to uh when you do this + + align:start position:0% +going to want to uh when you do this + + + align:start position:0% +going to want to uh when you do this +you're going to want to tell emex to use + + align:start position:0% +you're going to want to tell emex to use + + + align:start position:0% +you're going to want to tell emex to use +PPU GDB instead of regular GDB and emx + + align:start position:0% +PPU GDB instead of regular GDB and emx + + + align:start position:0% +PPU GDB instead of regular GDB and emx +will just ask you what you want to + + align:start position:0% +will just ask you what you want to + + + align:start position:0% +will just ask you what you want to +invoke you just want to replace GDB with + + align:start position:0% +invoke you just want to replace GDB with + + + align:start position:0% +invoke you just want to replace GDB with +PPU + + align:start position:0% +PPU + + + align:start position:0% +PPU +GDB uh anytime you're you anytime you're + + align:start position:0% +GDB uh anytime you're you anytime you're + + + align:start position:0% +GDB uh anytime you're you anytime you're +debugging within + + align:start position:0% +debugging within + + + align:start position:0% +debugging within +emac uh if emac has your source code + + align:start position:0% +emac uh if emac has your source code + + + align:start position:0% +emac uh if emac has your source code +files open it will show you the current + + align:start position:0% +files open it will show you the current + + + align:start position:0% +files open it will show you the current +point of execution by drawing a little + + align:start position:0% +point of execution by drawing a little + + + align:start position:0% +point of execution by drawing a little +arrow next to the particular line uh + + align:start position:0% +arrow next to the particular line uh + + + align:start position:0% +arrow next to the particular line uh +next to the particular line in the + + align:start position:0% +next to the particular line in the + + + align:start position:0% +next to the particular line in the +buffer + + align:start position:0% +buffer + + + align:start position:0% +buffer +um you also get a bunch of keyboard + + align:start position:0% +um you also get a bunch of keyboard + + + align:start position:0% +um you also get a bunch of keyboard +shortcuts that you can use to do some + + align:start position:0% +shortcuts that you can use to do some + + + align:start position:0% +shortcuts that you can use to do some +common + + align:start position:0% +common + + + align:start position:0% +common +operations uh you can set break points + + align:start position:0% +operations uh you can set break points + + + align:start position:0% +operations uh you can set break points +with control X space just by uh just by + + align:start position:0% +with control X space just by uh just by + + + align:start position:0% +with control X space just by uh just by +placing your cursor at the particular + + align:start position:0% +placing your cursor at the particular + + + align:start position:0% +placing your cursor at the particular +line that you want to stop at so you + + align:start position:0% +line that you want to stop at so you + + + align:start position:0% +line that you want to stop at so you +don't have to so you don't have to go to + + align:start position:0% +don't have to so you don't have to go to + + + align:start position:0% +don't have to so you don't have to go to +GDB and type break whatever whatever + + align:start position:0% +GDB and type break whatever whatever + + + align:start position:0% +GDB and type break whatever whatever +uh but when you do MX GDB in emex you + + align:start position:0% +uh but when you do MX GDB in emex you + + + align:start position:0% +uh but when you do MX GDB in emex you +get a separate buffer for GDB and so you + + align:start position:0% +get a separate buffer for GDB and so you + + + align:start position:0% +get a separate buffer for GDB and so you +can issue all the commands that you + + align:start position:0% +can issue all the commands that you + + + align:start position:0% +can issue all the commands that you +normally would want + + align:start position:0% + + + + align:start position:0% + +to okay so uh the first thing we're + + align:start position:0% +to okay so uh the first thing we're + + + align:start position:0% +to okay so uh the first thing we're +going to try this should be really quick + + align:start position:0% +going to try this should be really quick + + + align:start position:0% +going to try this should be really quick +uh is we're just going + + align:start position:0% +uh is we're just going + + + align:start position:0% +uh is we're just going +to uh is we're just going to open up a + + align:start position:0% +to uh is we're just going to open up a + + + align:start position:0% +to uh is we're just going to open up a +brief program and make sure you can uh + + align:start position:0% +brief program and make sure you can uh + + + align:start position:0% +brief program and make sure you can uh +invoke GDB on it + + align:start position:0% + + + + align:start position:0% + +oh and you'll have to set uh cell top if + + align:start position:0% +oh and you'll have to set uh cell top if + + + align:start position:0% +oh and you'll have to set uh cell top if +you don't have that set + + align:start position:0% + + + + align:start position:0% + +already uh I'm just going to do the + + align:start position:0% + + + + align:start position:0% + +same how you exit G + + align:start position:0% +same how you exit G + + + align:start position:0% +same how you exit G +oh + + align:start position:0% +oh + + + align:start position:0% +oh +uh uh you can do quit or contr + + align:start position:0% + + + + align:start position:0% + +D + + align:start position:0% + + + + align:start position:0% + +yeah so once once you've attached GDB to + + align:start position:0% +yeah so once once you've attached GDB to + + + align:start position:0% +yeah so once once you've attached GDB to +a program when you exit GDB it will quit + + align:start position:0% +a program when you exit GDB it will quit + + + align:start position:0% +a program when you exit GDB it will quit +the program that you were running unless + + align:start position:0% +the program that you were running unless + + + align:start position:0% +the program that you were running unless +you do detach + + align:start position:0% + + + + align:start position:0% + +first for this one it doesn't really + + align:start position:0% +first for this one it doesn't really + + + align:start position:0% +first for this one it doesn't really +matter because we're looking at a crash + + align:start position:0% +matter because we're looking at a crash + + + align:start position:0% +matter because we're looking at a crash +anyway + + align:start position:0% + + + + align:start position:0% + +uh you can evaluate an expression using + + align:start position:0% + + + + align:start position:0% + +print okay any + + align:start position:0% + + + + align:start position:0% + +questions all right so all I did here + + align:start position:0% +questions all right so all I did here + + + align:start position:0% +questions all right so all I did here +was run and then the program crashes uh + + align:start position:0% +was run and then the program crashes uh + + + align:start position:0% +was run and then the program crashes uh +this is just uh lab + + align:start position:0% +this is just uh lab + + + align:start position:0% +this is just uh lab +one + + align:start position:0% +one + + + align:start position:0% +one +without this is just lab one without the + + align:start position:0% +without this is just lab one without the + + + align:start position:0% +without this is just lab one without the +uh alignment in the control block that + + align:start position:0% +uh alignment in the control block that + + + align:start position:0% +uh alignment in the control block that +you need to to make everything work + + align:start position:0% +you need to to make everything work + + + align:start position:0% +you need to to make everything work +correctly and so all I did here was run + + align:start position:0% +correctly and so all I did here was run + + + align:start position:0% +correctly and so all I did here was run +and then the program crashes and then + + align:start position:0% +and then the program crashes and then + + + align:start position:0% +and then the program crashes and then +print CV and of course uh this thing is + + align:start position:0% +print CV and of course uh this thing is + + + align:start position:0% +print CV and of course uh this thing is +going to be zero because the dma + + align:start position:0% +going to be zero because the dma + + + align:start position:0% +going to be zero because the dma +transfer to do that uh doesn't + + align:start position:0% +transfer to do that uh doesn't + + + align:start position:0% +transfer to do that uh doesn't +work questions + + align:start position:0% + + + + align:start position:0% + +okay so we can exit the the debugger + + align:start position:0% +okay so we can exit the the debugger + + + align:start position:0% +okay so we can exit the the debugger +with control D and it'll ask if you want + + align:start position:0% +with control D and it'll ask if you want + + + align:start position:0% +with control D and it'll ask if you want +to kill the + + align:start position:0% + + + + align:start position:0% + +program + + align:start position:0% + + + + align:start position:0% + +okay so GDB also has features to help + + align:start position:0% +okay so GDB also has features to help + + + align:start position:0% +okay so GDB also has features to help +you with debugging programs that have + + align:start position:0% +you with debugging programs that have + + + align:start position:0% +you with debugging programs that have +multiple threads uh whenever a new + + align:start position:0% +multiple threads uh whenever a new + + + align:start position:0% +multiple threads uh whenever a new +thread is is created or whenever a new + + align:start position:0% +thread is is created or whenever a new + + + align:start position:0% +thread is is created or whenever a new +thread is created or a thread is + + align:start position:0% +thread is created or a thread is + + + align:start position:0% +thread is created or a thread is +destroyed GDB will print a brief message + + align:start position:0% +destroyed GDB will print a brief message + + + align:start position:0% +destroyed GDB will print a brief message +to tell you + + align:start position:0% +to tell you + + + align:start position:0% +to tell you +and uh one important thing is it will + + align:start position:0% +and uh one important thing is it will + + + align:start position:0% +and uh one important thing is it will +print this uh uh lwp number on the + + align:start position:0% +print this uh uh lwp number on the + + + align:start position:0% +print this uh uh lwp number on the +PlayStations and + + align:start position:0% +PlayStations and + + + align:start position:0% +PlayStations and +uh okay so uh to get a list of threads + + align:start position:0% +uh okay so uh to get a list of threads + + + align:start position:0% +uh okay so uh to get a list of threads +you can type info threads and GDB always + + align:start position:0% +you can type info threads and GDB always + + + align:start position:0% +you can type info threads and GDB always +maintains this thing called the current + + align:start position:0% +maintains this thing called the current + + + align:start position:0% +maintains this thing called the current +thread and by default when you do many + + align:start position:0% +thread and by default when you do many + + + align:start position:0% +thread and by default when you do many +other many of these other actions + + align:start position:0% +other many of these other actions + + + align:start position:0% +other many of these other actions +they're going to apply to uh the current + + align:start position:0% +they're going to apply to uh the current + + + align:start position:0% +they're going to apply to uh the current +thread and so to examine things about + + align:start position:0% +thread and so to examine things about + + + align:start position:0% +thread and so to examine things about +other threads you're going to have to + + align:start position:0% +other threads you're going to have to + + + align:start position:0% +other threads you're going to have to +change the thread and to do that you do + + align:start position:0% +change the thread and to do that you do + + + align:start position:0% +change the thread and to do that you do +thread and some number when you do info + + align:start position:0% +thread and some number when you do info + + + align:start position:0% +thread and some number when you do info +threads it's going to give you this list + + align:start position:0% +threads it's going to give you this list + + + align:start position:0% +threads it's going to give you this list +of threads which are numbered uh for + + align:start position:0% +of threads which are numbered uh for + + + align:start position:0% +of threads which are numbered uh for +example 1 two 3 on the left and the lwp + + align:start position:0% +example 1 two 3 on the left and the lwp + + + align:start position:0% +example 1 two 3 on the left and the lwp +numbers that are displayed are going to + + align:start position:0% +numbers that are displayed are going to + + + align:start position:0% +numbers that are displayed are going to +correspond to these that came up when + + align:start position:0% +correspond to these that came up when + + + align:start position:0% +correspond to these that came up when +the threads uh were + + align:start position:0% +the threads uh were + + + align:start position:0% +the threads uh were +started but you're going to have to use + + align:start position:0% +started but you're going to have to use + + + align:start position:0% +started but you're going to have to use +these numbers on the left to switch + + align:start position:0% +these numbers on the left to switch + + + align:start position:0% +these numbers on the left to switch +between threads and when you do info + + align:start position:0% +between threads and when you do info + + + align:start position:0% +between threads and when you do info +threads GD will Mark the current thread + + align:start position:0% +threads GD will Mark the current thread + + + align:start position:0% +threads GD will Mark the current thread +with a star on the left and we'll also + + align:start position:0% +with a star on the left and we'll also + + + align:start position:0% +with a star on the left and we'll also +show you where each thread is executing + + align:start position:0% +show you where each thread is executing + + + align:start position:0% +show you where each thread is executing +right now + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% + + + + align:start position:0% + +does + + align:start position:0% + + + + align:start position:0% + +um uh it will show the procedure and the + + align:start position:0% +um uh it will show the procedure and the + + + align:start position:0% +um uh it will show the procedure and the +file name and line number uh if that if + + align:start position:0% +file name and line number uh if that if + + + align:start position:0% +file name and line number uh if that if +that information is + + align:start position:0% +that information is + + + align:start position:0% +that information is +available you can't find out which + + align:start position:0% +available you can't find out which + + + align:start position:0% +available you can't find out which +that's what I was uh uh + + align:start position:0% + + + + align:start position:0% + +no I don't believe can get that + + align:start position:0% +no I don't believe can get that + + + align:start position:0% +no I don't believe can get that +information + + align:start position:0% + + + + align:start position:0% + +Che David do you + + align:start position:0% +Che David do you + + + align:start position:0% +Che David do you +know + + align:start position:0% + + + + align:start position:0% + +sorry so David says maybe you can do it + + align:start position:0% +sorry so David says maybe you can do it + + + align:start position:0% +sorry so David says maybe you can do it +on simulator but not + + align:start position:0% + + + + align:start position:0% + +on okay + + align:start position:0% +on okay + + + align:start position:0% +on okay +so we're going to try this brief + + align:start position:0% +so we're going to try this brief + + + align:start position:0% +so we're going to try this brief +exercise which is just uh to get you to + + align:start position:0% +exercise which is just uh to get you to + + + align:start position:0% +exercise which is just uh to get you to +work with dealing with multiple + + align:start position:0% +work with dealing with multiple + + + align:start position:0% +work with dealing with multiple +threads um and what you're going to do + + align:start position:0% +threads um and what you're going to do + + + align:start position:0% +threads um and what you're going to do +is load the lab one program which is the + + align:start position:0% +is load the lab one program which is the + + + align:start position:0% +is load the lab one program which is the +correctly working solution for lab one + + align:start position:0% +correctly working solution for lab one + + + align:start position:0% +correctly working solution for lab one +and uh if you'll recall this program has + + align:start position:0% +and uh if you'll recall this program has + + + align:start position:0% +and uh if you'll recall this program has +multiple threads the PPU thread + + align:start position:0% +multiple threads the PPU thread + + + align:start position:0% +multiple threads the PPU thread +maintains an array of control blocks and + + align:start position:0% +maintains an array of control blocks and + + + align:start position:0% +maintains an array of control blocks and +it's going to send the addresses of + + align:start position:0% +it's going to send the addresses of + + + align:start position:0% +it's going to send the addresses of +those control blocks to the spus + + align:start position:0% +those control blocks to the spus + + + align:start position:0% +those control blocks to the spus +so what we're going to do is we're just + + align:start position:0% +so what we're going to do is we're just + + + align:start position:0% +so what we're going to do is we're just +going to set break points at the right + + align:start position:0% +going to set break points at the right + + + align:start position:0% +going to set break points at the right +places to verify that the uh that the + + align:start position:0% +places to verify that the uh that the + + + align:start position:0% +places to verify that the uh that the +first spu thread is getting a control + + align:start position:0% +first spu thread is getting a control + + + align:start position:0% +first spu thread is getting a control +block the control block which is the + + align:start position:0% +block the control block which is the + + + align:start position:0% +block the control block which is the +same as one of the control blocks in the + + align:start position:0% +same as one of the control blocks in the + + + align:start position:0% +same as one of the control blocks in the +PPU program all right any questions + + align:start position:0% +PPU program all right any questions + + + align:start position:0% +PPU program all right any questions +about that this is in Rec 4 lab + + align:start position:0% + + + + align:start position:0% + +one so how we do that so you're going to + + align:start position:0% +one so how we do that so you're going to + + + align:start position:0% +one so how we do that so you're going to +have to run and set break points at the + + align:start position:0% +have to run and set break points at the + + + align:start position:0% +have to run and set break points at the +right places and you're going to want to + + align:start position:0% +right places and you're going to want to + + + align:start position:0% +right places and you're going to want to +set one break point in each thread to be + + align:start position:0% +set one break point in each thread to be + + + align:start position:0% +set one break point in each thread to be +able to examine the value of CB that's + + align:start position:0% +able to examine the value of CB that's + + + align:start position:0% +able to examine the value of CB that's +uh that's being + + align:start position:0% + + + + align:start position:0% + +produced oh yeah + + align:start position:0% + + + + align:start position:0% + +here we have three + + align:start position:0% + + + + align:start position:0% + +right after the recitation um as in as + + align:start position:0% +right after the recitation um as in as + + + align:start position:0% +right after the recitation um as in as +another exercise for those of you who + + align:start position:0% +another exercise for those of you who + + + align:start position:0% +another exercise for those of you who +did get through the way you'll actually + + align:start position:0% +did get through the way you'll actually + + + align:start position:0% +did get through the way you'll actually +run into these problems is you run your + + align:start position:0% +run into these problems is you run your + + + align:start position:0% +run into these problems is you run your +program and you might end up with a bus + + align:start position:0% +program and you might end up with a bus + + + align:start position:0% +program and you might end up with a bus +error so you might want to do is then + + align:start position:0% +error so you might want to do is then + + + align:start position:0% +error so you might want to do is then +launch GDB and you run to the error and + + align:start position:0% +launch GDB and you run to the error and + + + align:start position:0% +launch GDB and you run to the error and +then you trace back in your execution to + + align:start position:0% +then you trace back in your execution to + + + align:start position:0% +then you trace back in your execution to +see uh is my control block value + + align:start position:0% +see uh is my control block value + + + align:start position:0% +see uh is my control block value +matching so you might want to try that + + align:start position:0% +matching so you might want to try that + + + align:start position:0% +matching so you might want to try that +as a second exercise offline um + + align:start position:0% +as a second exercise offline um + + + align:start position:0% +as a second exercise offline um +yes um should we do the static profiling + + align:start position:0% +yes um should we do the static profiling + + + align:start position:0% +yes um should we do the static profiling +thing just go through that but may do + + align:start position:0% +thing just go through that but may do + + + align:start position:0% +thing just go through that but may do +theise + + align:start position:0% + + + + align:start position:0% + +okay uh so one problem that you may have + + align:start position:0% +okay uh so one problem that you may have + + + align:start position:0% +okay uh so one problem that you may have +run into is that uh GDB will remove + + align:start position:0% +run into is that uh GDB will remove + + + align:start position:0% +run into is that uh GDB will remove +break points from threads that exit + + align:start position:0% +break points from threads that exit + + + align:start position:0% +break points from threads that exit +which is a problem if you have more than + + align:start position:0% +which is a problem if you have more than + + + align:start position:0% +which is a problem if you have more than +one thread running the same + + align:start position:0% +one thread running the same + + + align:start position:0% +one thread running the same +program and uh if you're debugging spu + + align:start position:0% +program and uh if you're debugging spu + + + align:start position:0% +program and uh if you're debugging spu +programs GDB May complain about not + + align:start position:0% +programs GDB May complain about not + + + align:start position:0% +programs GDB May complain about not +being able to find the source files but + + align:start position:0% +being able to find the source files but + + + align:start position:0% +being able to find the source files but +uh if you + + align:start position:0% +uh if you + + + align:start position:0% +uh if you +just uh if you just ignore that message + + align:start position:0% +just uh if you just ignore that message + + + align:start position:0% +just uh if you just ignore that message +it seems to find them okay I + + align:start position:0% +it seems to find them okay I + + + align:start position:0% +it seems to find them okay I +think uh you can use Spug GDB to debug + + align:start position:0% +think uh you can use Spug GDB to debug + + + align:start position:0% +think uh you can use Spug GDB to debug +the spu programs by themselves you can + + align:start position:0% +the spu programs by themselves you can + + + align:start position:0% +the spu programs by themselves you can +try that some time + + align:start position:0% + + + + align:start position:0% + +uh okay so actually figuring out what + + align:start position:0% +uh okay so actually figuring out what + + + align:start position:0% +uh okay so actually figuring out what +the errors are unfortunately you don't + + align:start position:0% +the errors are unfortunately you don't + + + align:start position:0% +the errors are unfortunately you don't +get very much information from the + + align:start position:0% +get very much information from the + + + align:start position:0% +get very much information from the +actual errors that occur but maybe + + align:start position:0% +actual errors that occur but maybe + + + align:start position:0% +actual errors that occur but maybe +looking at where the errors are + + align:start position:0% +looking at where the errors are + + + align:start position:0% +looking at where the errors are +occurring can help you figure things out + + align:start position:0% +occurring can help you figure things out + + + align:start position:0% +occurring can help you figure things out +uh if you've run into uh memory + + align:start position:0% +uh if you've run into uh memory + + + align:start position:0% +uh if you've run into uh memory +misalignment problems or the problem + + align:start position:0% +misalignment problems or the problem + + + align:start position:0% +misalignment problems or the problem +in the last recitation where we had uh + + align:start position:0% +in the last recitation where we had uh + + + align:start position:0% +in the last recitation where we had uh +dma transfers that were too big those + + align:start position:0% +dma transfers that were too big those + + + align:start position:0% +dma transfers that were too big those +are all going to be bus errors under + + align:start position:0% +are all going to be bus errors under + + + align:start position:0% +are all going to be bus errors under +various other circumstances you you + + align:start position:0% +various other circumstances you you + + + align:start position:0% +various other circumstances you you +might get segmentation faults + + align:start position:0% +might get segmentation faults + + + align:start position:0% +might get segmentation faults +uh and if you think your program is uh + + align:start position:0% +uh and if you think your program is uh + + + align:start position:0% +uh and if you think your program is uh +running into a deadlock you can also use + + align:start position:0% +running into a deadlock you can also use + + + align:start position:0% +running into a deadlock you can also use +GDB to kind of uh attach to the program + + align:start position:0% +GDB to kind of uh attach to the program + + + align:start position:0% +GDB to kind of uh attach to the program +and then examine the state of that + + align:start position:0% +and then examine the state of that + + + align:start position:0% +and then examine the state of that +program to see you know what's waiting + + align:start position:0% +program to see you know what's waiting + + + align:start position:0% +program to see you know what's waiting +for + + align:start position:0% + + + + align:start position:0% + +what okay so static profiling uh we have + + align:start position:0% +what okay so static profiling uh we have + + + align:start position:0% +what okay so static profiling uh we have +some tools for the cell that will allow + + align:start position:0% +some tools for the cell that will allow + + + align:start position:0% +some tools for the cell that will allow +you + + align:start position:0% +you + + + align:start position:0% +you +to + + align:start position:0% +to + + + align:start position:0% +to +uh we have some tools for the cell that + + align:start position:0% +uh we have some tools for the cell that + + + align:start position:0% +uh we have some tools for the cell that +will allow you to when you have a + + align:start position:0% +will allow you to when you have a + + + align:start position:0% +will allow you to when you have a +sequence of assembly instructions + + align:start position:0% +sequence of assembly instructions + + + align:start position:0% +sequence of assembly instructions +figure out kind of when those + + align:start position:0% +figure out kind of when those + + + align:start position:0% +figure out kind of when those +instructions are going to get scheduled + + align:start position:0% +instructions are going to get scheduled + + + align:start position:0% +instructions are going to get scheduled +and how fast the resulting sequence will + + align:start position:0% +and how fast the resulting sequence will + + + align:start position:0% +and how fast the resulting sequence will +run so in order to take advantage of + + align:start position:0% +run so in order to take advantage of + + + align:start position:0% +run so in order to take advantage of +this you need to use GCC DBS to generate + + align:start position:0% +this you need to use GCC DBS to generate + + + align:start position:0% +this you need to use GCC DBS to generate +your assembly and uh you can also do + + align:start position:0% +your assembly and uh you can also do + + + align:start position:0% +your assembly and uh you can also do +that with + + align:start position:0% +that with + + + align:start position:0% +that with +xlc if you're using our make files you + + align:start position:0% +xlc if you're using our make files you + + + align:start position:0% +xlc if you're using our make files you +can also use make whatever file name dos + + align:start position:0% +can also use make whatever file name dos + + + align:start position:0% +can also use make whatever file name dos +in order to generate the assembly from + + align:start position:0% +in order to generate the assembly from + + + align:start position:0% +in order to generate the assembly from +your uh from your source + + align:start position:0% +your uh from your source + + + align:start position:0% +your uh from your source +code then once you have the s file uh + + align:start position:0% +code then once you have the s file uh + + + align:start position:0% +code then once you have the s file uh +you can run this utility called spu + + align:start position:0% +you can run this utility called spu + + + align:start position:0% +you can run this utility called spu +timing and what spu timing is what spu + + align:start position:0% +timing and what spu timing is what spu + + + align:start position:0% +timing and what spu timing is what spu +timing does is it will take all the + + align:start position:0% +timing does is it will take all the + + + align:start position:0% +timing does is it will take all the +instructions that that are in your + + align:start position:0% +instructions that that are in your + + + align:start position:0% +instructions that that are in your +assembly and figure out the dependencies + + align:start position:0% +assembly and figure out the dependencies + + + align:start position:0% +assembly and figure out the dependencies +between them and then it will figure out + + align:start position:0% +between them and then it will figure out + + + align:start position:0% +between them and then it will figure out +when the earliest point is that each + + align:start position:0% +when the earliest point is that each + + + align:start position:0% +when the earliest point is that each +instruction can get executed and it will + + align:start position:0% +instruction can get executed and it will + + + align:start position:0% +instruction can get executed and it will +print out the schedule that that's + + align:start position:0% +print out the schedule that that's + + + align:start position:0% +print out the schedule that that's +generated so if you provide the dash + + align:start position:0% +generated so if you provide the dash + + + align:start position:0% +generated so if you provide the dash +running + + align:start position:0% +running + + + align:start position:0% +running +count option then it will also show you + + align:start position:0% +count option then it will also show you + + + align:start position:0% +count option then it will also show you +um how many cycles the uh how many + + align:start position:0% +um how many cycles the uh how many + + + align:start position:0% +um how many cycles the uh how many +Cycles in all the entire program will + + align:start position:0% +Cycles in all the entire program will + + + align:start position:0% +Cycles in all the entire program will +take um and the output goes into fil + + align:start position:0% +take um and the output goes into fil + + + align:start position:0% +take um and the output goes into fil +name. s. + + align:start position:0% + + + + align:start position:0% + +timing so for how instructions are + + align:start position:0% +timing so for how instructions are + + + align:start position:0% +timing so for how instructions are +scheduled on cell if you'll recall + + align:start position:0% +scheduled on cell if you'll recall + + + align:start position:0% +scheduled on cell if you'll recall +there's if you if you'll recall there's + + align:start position:0% +there's if you if you'll recall there's + + + align:start position:0% +there's if you if you'll recall there's +two pipelines for different kinds of + + align:start position:0% +two pipelines for different kinds of + + + align:start position:0% +two pipelines for different kinds of +instructions and some instructions can + + align:start position:0% +instructions and some instructions can + + + align:start position:0% +instructions and some instructions can +only run on one or the other of the + + align:start position:0% +only run on one or the other of the + + + align:start position:0% +only run on one or the other of the +pipelines and some instructions can run + + align:start position:0% +pipelines and some instructions can run + + + align:start position:0% +pipelines and some instructions can run +on + + align:start position:0% +on + + + align:start position:0% +on +both now now how cell actually schedules + + align:start position:0% +both now now how cell actually schedules + + + align:start position:0% +both now now how cell actually schedules +those instructions is it's always going + + align:start position:0% +those instructions is it's always going + + + align:start position:0% +those instructions is it's always going +to go in order that the instructions are + + align:start position:0% +to go in order that the instructions are + + + align:start position:0% +to go in order that the instructions are +specified in the uh in the in the + + align:start position:0% +specified in the uh in the in the + + + align:start position:0% +specified in the uh in the in the +binary and whenever there's two + + align:start position:0% +binary and whenever there's two + + + align:start position:0% +binary and whenever there's two +instructions next to each other uh which + + align:start position:0% +instructions next to each other uh which + + + align:start position:0% +instructions next to each other uh which +whenever there's two instructions next + + align:start position:0% +whenever there's two instructions next + + + align:start position:0% +whenever there's two instructions next +to each other and the first instruction + + align:start position:0% +to each other and the first instruction + + + align:start position:0% +to each other and the first instruction +can run on Pipeline zero and the second + + align:start position:0% +can run on Pipeline zero and the second + + + align:start position:0% +can run on Pipeline zero and the second +instruction can run on Pipeline pipeline + + align:start position:0% +instruction can run on Pipeline pipeline + + + align:start position:0% +instruction can run on Pipeline pipeline +one then cell will try and uh schedule + + align:start position:0% +one then cell will try and uh schedule + + + align:start position:0% +one then cell will try and uh schedule +those at the same time and that's called + + align:start position:0% +those at the same time and that's called + + + align:start position:0% +those at the same time and that's called +dual issue so if you were taking + + align:start position:0% +dual issue so if you were taking + + + align:start position:0% +dual issue so if you were taking +advantage of that dual issue all the + + align:start position:0% +advantage of that dual issue all the + + + align:start position:0% +advantage of that dual issue all the +time then potentially you could schedule + + align:start position:0% +time then potentially you could schedule + + + align:start position:0% +time then potentially you could schedule +two instructions every + + align:start position:0% + + + + align:start position:0% + +cycle + + align:start position:0% +cycle + + + align:start position:0% +cycle +um oh yes and and unlike a lot of other + + align:start position:0% +um oh yes and and unlike a lot of other + + + align:start position:0% +um oh yes and and unlike a lot of other +architectures in nowadays cell does not + + align:start position:0% +architectures in nowadays cell does not + + + align:start position:0% +architectures in nowadays cell does not +have Dynamic R Branch prediction all the + + align:start position:0% +have Dynamic R Branch prediction all the + + + align:start position:0% +have Dynamic R Branch prediction all the +branch prediction is encoded inside the + + align:start position:0% +branch prediction is encoded inside the + + + align:start position:0% +branch prediction is encoded inside the +uh all the branch prediction is encoded + + align:start position:0% +uh all the branch prediction is encoded + + + align:start position:0% +uh all the branch prediction is encoded +inside the assembly that you're that + + align:start position:0% +inside the assembly that you're that + + + align:start position:0% +inside the assembly that you're that +you're using so that means for for any + + align:start position:0% +you're using so that means for for any + + + align:start position:0% +you're using so that means for for any +type of loop or whatever you have to be + + align:start position:0% +type of loop or whatever you have to be + + + align:start position:0% +type of loop or whatever you have to be +sure to get the branch prediction right + + align:start position:0% +sure to get the branch prediction right + + + align:start position:0% +sure to get the branch prediction right +if the uh if the branch prediction is + + align:start position:0% +if the uh if the branch prediction is + + + align:start position:0% +if the uh if the branch prediction is +wrong cell is going to end up + + align:start position:0% +wrong cell is going to end up + + + align:start position:0% +wrong cell is going to end up +prefetching instructions along the wrong + + align:start position:0% +prefetching instructions along the wrong + + + align:start position:0% +prefetching instructions along the wrong +line and it's going to have to stall by + + align:start position:0% +line and it's going to have to stall by + + + align:start position:0% +line and it's going to have to stall by +about 20 Cycles when uh when you figure + + align:start position:0% +about 20 Cycles when uh when you figure + + + align:start position:0% +about 20 Cycles when uh when you figure +out uh when it figures out that uh the + + align:start position:0% +out uh when it figures out that uh the + + + align:start position:0% +out uh when it figures out that uh the +branch is + + align:start position:0% + + + + align:start position:0% + +wrong so if you're looking at the + + align:start position:0% +wrong so if you're looking at the + + + align:start position:0% +wrong so if you're looking at the +generated assembly on Cell all the + + align:start position:0% +generated assembly on Cell all the + + + align:start position:0% +generated assembly on Cell all the +instructors are going to be of the form + + align:start position:0% +instructors are going to be of the form + + + align:start position:0% +instructors are going to be of the form +uh operation then the destination uh + + align:start position:0% +uh operation then the destination uh + + + align:start position:0% +uh operation then the destination uh +register and then uh two or more + + align:start position:0% +register and then uh two or more + + + align:start position:0% +register and then uh two or more +sources and if you're trying to figure + + align:start position:0% +sources and if you're trying to figure + + + align:start position:0% +sources and if you're trying to figure +out if you're trying to just kind of + + align:start position:0% +out if you're trying to just kind of + + + align:start position:0% +out if you're trying to just kind of +Orient yourself in the generated + + align:start position:0% +Orient yourself in the generated + + + align:start position:0% +Orient yourself in the generated +assembly there are sometimes these these + + align:start position:0% +assembly there are sometimes these these + + + align:start position:0% +assembly there are sometimes these these +helpful these helpful markers so if + + align:start position:0% +helpful these helpful markers so if + + + align:start position:0% +helpful these helpful markers so if +you're looking at uh if you're looking + + align:start position:0% +you're looking at uh if you're looking + + + align:start position:0% +you're looking at uh if you're looking +at the generated assembly for dist spu + + align:start position:0% +at the generated assembly for dist spu + + + align:start position:0% +at the generated assembly for dist spu +then it's going to have a header at the + + align:start position:0% +then it's going to have a header at the + + + align:start position:0% +then it's going to have a header at the +top which says which files were included + + align:start position:0% +top which says which files were included + + + align:start position:0% +top which says which files were included +inside this uh which files were included + + align:start position:0% +inside this uh which files were included + + + align:start position:0% +inside this uh which files were included +inside this file and then where the + + align:start position:0% +inside this file and then where the + + + align:start position:0% +inside this file and then where the +actual assembly is there will be these + + align:start position:0% +actual assembly is there will be these + + + align:start position:0% +actual assembly is there will be these +markers that say for example uh location + + align:start position:0% +markers that say for example uh location + + + align:start position:0% +markers that say for example uh location +119 and what this means is that uh here + + align:start position:0% +119 and what this means is that uh here + + + align:start position:0% +119 and what this means is that uh here +is the assembly corresponding to file + + align:start position:0% +is the assembly corresponding to file + + + align:start position:0% +is the assembly corresponding to file +one line 19 so that's kind of helpful if + + align:start position:0% +one line 19 so that's kind of helpful if + + + align:start position:0% +one line 19 so that's kind of helpful if +you're trying to uh uh get your bearings + + align:start position:0% +you're trying to uh uh get your bearings + + + align:start position:0% +you're trying to uh uh get your bearings +inside the assembly because otherwise + + align:start position:0% +inside the assembly because otherwise + + + align:start position:0% +inside the assembly because otherwise +it's really hard to make heads or tails + + align:start position:0% +it's really hard to make heads or tails + + + align:start position:0% +it's really hard to make heads or tails +of + + align:start position:0% + + + + align:start position:0% + +questions all right so after you + + align:start position:0% +questions all right so after you + + + align:start position:0% +questions all right so after you +actually run your assembly through the + + align:start position:0% +actually run your assembly through the + + + align:start position:0% +actually run your assembly through the +static profiler it will spit out this + + align:start position:0% +static profiler it will spit out this + + + align:start position:0% +static profiler it will spit out this +schedule and what the schedule shows is + + align:start position:0% +schedule and what the schedule shows is + + + align:start position:0% +schedule and what the schedule shows is +which is which clock Cycles are used for + + align:start position:0% +which is which clock Cycles are used for + + + align:start position:0% +which is which clock Cycles are used for +every single + + align:start position:0% +every single + + + align:start position:0% +every single +instruction uh there's one line for each + + align:start position:0% +instruction uh there's one line for each + + + align:start position:0% +instruction uh there's one line for each +assembly instruction and what it's going + + align:start position:0% +assembly instruction and what it's going + + + align:start position:0% +assembly instruction and what it's going +to do is it's going to print one digit + + align:start position:0% +to do is it's going to print one digit + + + align:start position:0% +to do is it's going to print one digit +in this schedule for each cycle that the + + align:start position:0% +in this schedule for each cycle that the + + + align:start position:0% +in this schedule for each cycle that the +instruction + + align:start position:0% +instruction + + + align:start position:0% +instruction +takes all right so uh so you can kind of + + align:start position:0% +takes all right so uh so you can kind of + + + align:start position:0% +takes all right so uh so you can kind of +think of this this Dimension as the + + align:start position:0% +think of this this Dimension as the + + + align:start position:0% +think of this this Dimension as the +passage of time and uh uh what happens + + align:start position:0% +passage of time and uh uh what happens + + + align:start position:0% +passage of time and uh uh what happens +is that these guys when they get to the + + align:start position:0% +is that these guys when they get to the + + + align:start position:0% +is that these guys when they get to the +right hand side they'll wrap around at + + align:start position:0% +right hand side they'll wrap around at + + + align:start position:0% +right hand side they'll wrap around at +50 columns or + + align:start position:0% +50 columns or + + + align:start position:0% +50 columns or +whatever + + align:start position:0% +whatever + + + align:start position:0% +whatever +and and you'll be able to notice you + + align:start position:0% +and and you'll be able to notice you + + + align:start position:0% +and and you'll be able to notice you +know when these instructions are being + + align:start position:0% +know when these instructions are being + + + align:start position:0% +know when these instructions are being +scheduled and sometimes because + + align:start position:0% +scheduled and sometimes because + + + align:start position:0% +scheduled and sometimes because +sometimes when there's dependencies + + align:start position:0% +sometimes when there's dependencies + + + align:start position:0% +sometimes when there's dependencies +between instructions the instructions + + align:start position:0% +between instructions the instructions + + + align:start position:0% +between instructions the instructions +are not able are not able to get + + align:start position:0% +are not able are not able to get + + + align:start position:0% +are not able are not able to get +scheduled at the uh at the earliest + + align:start position:0% +scheduled at the uh at the earliest + + + align:start position:0% +scheduled at the uh at the earliest +possible time and when that happens + + align:start position:0% +possible time and when that happens + + + align:start position:0% +possible time and when that happens +you'll see these dashes which mean that + + align:start position:0% +you'll see these dashes which mean that + + + align:start position:0% +you'll see these dashes which mean that +the instruction is being stalled to wait + + align:start position:0% +the instruction is being stalled to wait + + + align:start position:0% +the instruction is being stalled to wait +for one of the dependencies in order to + + align:start position:0% +for one of the dependencies in order to + + + align:start position:0% +for one of the dependencies in order to +make your code fast you're going to want + + align:start position:0% +make your code fast you're going to want + + + align:start position:0% +make your code fast you're going to want +to eliminate these uh eliminate these + + align:start position:0% +to eliminate these uh eliminate these + + + align:start position:0% +to eliminate these uh eliminate these +stalls and you can do that to a large + + align:start position:0% +stalls and you can do that to a large + + + align:start position:0% +stalls and you can do that to a large +extent by reordering your + + align:start position:0% + + + + align:start position:0% + +instructions + + align:start position:0% + + + + align:start position:0% + +yep so the point of instruction + + align:start position:0% +yep so the point of instruction + + + align:start position:0% +yep so the point of instruction +scheduling is going to be to to uh + + align:start position:0% +scheduling is going to be to to uh + + + align:start position:0% +scheduling is going to be to to uh +minimize the number of + + align:start position:0% +minimize the number of + + + align:start position:0% +minimize the number of +stalls + + align:start position:0% +stalls + + + align:start position:0% +stalls +and and you can you can do that by if + + align:start position:0% +and and you can you can do that by if + + + align:start position:0% +and and you can you can do that by if +you have instructions uh which are going + + align:start position:0% +you have instructions uh which are going + + + align:start position:0% +you have instructions uh which are going +to be dependencies for other + + align:start position:0% +to be dependencies for other + + + align:start position:0% +to be dependencies for other +instructions you just want to move those + + align:start position:0% +instructions you just want to move those + + + align:start position:0% +instructions you just want to move those +as far up as you + + align:start position:0% +as far up as you + + + align:start position:0% +as far up as you +can so ideally you would get to uh + + align:start position:0% +can so ideally you would get to uh + + + align:start position:0% +can so ideally you would get to uh +instructions for cycle or how many + + align:start position:0% +instructions for cycle or how many + + + align:start position:0% +instructions for cycle or how many +instructions Can you issue for cycle of + + align:start position:0% +instructions Can you issue for cycle of + + + align:start position:0% +instructions Can you issue for cycle of +two because you have dual issue two + + align:start position:0% +two because you have dual issue two + + + align:start position:0% +two because you have dual issue two +pipelines or uh sort of how many cycles + + align:start position:0% +pipelines or uh sort of how many cycles + + + align:start position:0% +pipelines or uh sort of how many cycles +per instruction you would be by a half + + align:start position:0% +per instruction you would be by a half + + + align:start position:0% +per instruction you would be by a half +um cuz you're getting two instructions + + align:start position:0% +um cuz you're getting two instructions + + + align:start position:0% +um cuz you're getting two instructions +for cycle soers is one over two so we we + + align:start position:0% +for cycle soers is one over two so we we + + + align:start position:0% +for cycle soers is one over two so we we +have an exercise that actually has you + + align:start position:0% +have an exercise that actually has you + + + align:start position:0% +have an exercise that actually has you +understand the assembly code and then + + align:start position:0% +understand the assembly code and then + + + align:start position:0% +understand the assembly code and then +doing the instruction reordering so + + align:start position:0% +doing the instruction reordering so + + + align:start position:0% +doing the instruction reordering so +we'll leave that in the slides you can + + align:start position:0% +we'll leave that in the slides you can + + + align:start position:0% +we'll leave that in the slides you can +do it offline but we'll pick up with + + align:start position:0% +do it offline but we'll pick up with + + + align:start position:0% +do it offline but we'll pick up with +this next week uh and go over + + align:start position:0% +this next week uh and go over + + + align:start position:0% +this next week uh and go over +instruction scheduling uh some dma + + align:start position:0% +instruction scheduling uh some dma + + + align:start position:0% +instruction scheduling uh some dma +tricks for improving performance uh and + + align:start position:0% +tricks for improving performance uh and + + + align:start position:0% +tricks for improving performance uh and +in particular thing we'll focus on uh + + align:start position:0% +in particular thing we'll focus on uh + + + align:start position:0% +in particular thing we'll focus on uh +quite rigorously is the calization uh so + + align:start position:0% +quite rigorously is the calization uh so + + + align:start position:0% +quite rigorously is the calization uh so +Phil is going to walk you through how + + align:start position:0% +Phil is going to walk you through how + + + align:start position:0% +Phil is going to walk you through how +you actually cize and get the + + align:start position:0% +you actually cize and get the + + + align:start position:0% +you actually cize and get the +performance from the uh vectorization + + align:start position:0% +performance from the uh vectorization + + + align:start position:0% +performance from the uh vectorization +need INX uh we'll talk a little bit + + align:start position:0% +need INX uh we'll talk a little bit + + + align:start position:0% +need INX uh we'll talk a little bit +about the dynamic profiler um and for + + align:start position:0% +about the dynamic profiler um and for + + + align:start position:0% +about the dynamic profiler um and for +those of you who are still having + + align:start position:0% +those of you who are still having + + + align:start position:0% +those of you who are still having +problems with ggb uh we'll try to + + align:start position:0% +problems with ggb uh we'll try to + + + align:start position:0% +problems with ggb uh we'll try to +resolve those now since that'll probably + + align:start position:0% +resolve those now since that'll probably + + + align:start position:0% +resolve those now since that'll probably +be very useful for your projects um and + + align:start position:0% +be very useful for your projects um and + + + align:start position:0% +be very useful for your projects um and +we installed CVS in main directory on + + align:start position:0% +we installed CVS in main directory on + + + align:start position:0% +we installed CVS in main directory on +every PS3 uh for those of you who + + align:start position:0% +every PS3 uh for those of you who + + + align:start position:0% +every PS3 uh for those of you who +actually want to use it and didn't go + + align:start position:0% +actually want to use it and didn't go + + + align:start position:0% +actually want to use it and didn't go +through a trouble of setting up their + + align:start position:0% +through a trouble of setting up their + + + align:start position:0% +through a trouble of setting up their +own CVS um the CVS is satisfied to + + align:start position:0% +own CVS um the CVS is satisfied to + + + align:start position:0% +own CVS um the CVS is satisfied to +actually notify the local users on that + + align:start position:0% +actually notify the local users on that + + + align:start position:0% +actually notify the local users on that +machine so that would be everybody in + + align:start position:0% +machine so that would be everybody in + + + align:start position:0% +machine so that would be everybody in +your team uh it'll send out an email + + align:start position:0% +your team uh it'll send out an email + + + align:start position:0% +your team uh it'll send out an email +whenever somebody does a check-in uh or + + align:start position:0% +whenever somebody does a check-in uh or + + + align:start position:0% +whenever somebody does a check-in uh or +an import to let them know that uh + + align:start position:0% +an import to let them know that uh + + + align:start position:0% +an import to let them know that uh +there's some new information that they + + align:start position:0% +there's some new information that they + + + align:start position:0% +there's some new information that they +want want to update uh if you don't know + + align:start position:0% +want want to update uh if you don't know + + + align:start position:0% +want want to update uh if you don't know +how to use CVS or one to Qui tutorial + + align:start position:0% +how to use CVS or one to Qui tutorial + + + align:start position:0% +how to use CVS or one to Qui tutorial +just stop by some T will be able to help + + align:start position:0% +just stop by some T will be able to help + + + align:start position:0% +just stop by some T will be able to help +you okay all right that's up here for + + align:start position:0% +you okay all right that's up here for + + + align:start position:0% +you okay all right that's up here for +today \ No newline at end of file diff --git a/SkT7VIul_8A.txt b/SkT7VIul_8A.txt new file mode 100644 index 0000000000000000000000000000000000000000..463d658788fd9b80bac211b9c079b431f6f74ffc --- /dev/null +++ b/SkT7VIul_8A.txt @@ -0,0 +1,403 @@ +align:start position:0% + +in the why this matters because + + align:start position:0% +in the why this matters because + + + align:start position:0% +in the why this matters because +in fact this is one of the things all + + align:start position:0% +in fact this is one of the things all + + + align:start position:0% +in fact this is one of the things all +the way back to hook + + align:start position:0% +the way back to hook + + + align:start position:0% +the way back to hook +and the can his cannonballs and even way + + align:start position:0% +and the can his cannonballs and even way + + + align:start position:0% +and the can his cannonballs and even way +before that + + align:start position:0% +before that + + + align:start position:0% +before that +people notice this stuff does it that i + + align:start position:0% +people notice this stuff does it that i + + + align:start position:0% +people notice this stuff does it that i +broke something + + align:start position:0% +broke something + + + align:start position:0% +broke something +but it always seems to slice in a + + align:start position:0% +but it always seems to slice in a + + + align:start position:0% +but it always seems to slice in a +certain way + + align:start position:0% +certain way + + + align:start position:0% +certain way +why is that why would something always + + align:start position:0% +why is that why would something always + + + align:start position:0% +why is that why would something always +break in the same way every time + + align:start position:0% +break in the same way every time + + + align:start position:0% +break in the same way every time +with the same kind of you know how does + + align:start position:0% +with the same kind of you know how does + + + align:start position:0% +with the same kind of you know how does +it what does whey mean here + + align:start position:0% +it what does whey mean here + + + align:start position:0% +it what does whey mean here +it means like the angles that form right + + align:start position:0% +it means like the angles that form right + + + align:start position:0% +it means like the angles that form right +so why are those angles always kind of + + align:start position:0% +so why are those angles always kind of + + + align:start position:0% +so why are those angles always kind of +the same + + align:start position:0% +the same + + + align:start position:0% +the same +right well it has to do with the + + align:start position:0% +right well it has to do with the + + + align:start position:0% +right well it has to do with the +strength the relative strength + + align:start position:0% +strength the relative strength + + + align:start position:0% +strength the relative strength +of the planes inside of these crystals + + align:start position:0% +of the planes inside of these crystals + + + align:start position:0% +of the planes inside of these crystals +right + + align:start position:0% +right + + + align:start position:0% +right +and in fact here's a beautiful a piece + + align:start position:0% +and in fact here's a beautiful a piece + + + align:start position:0% +and in fact here's a beautiful a piece +of work on stretching a wire + + align:start position:0% +of work on stretching a wire + + + align:start position:0% +of work on stretching a wire +right so here you're taking a wire that + + align:start position:0% +right so here you're taking a wire that + + + align:start position:0% +right so here you're taking a wire that +is crystalline + + align:start position:0% +is crystalline + + + align:start position:0% +is crystalline +and you're pulling it and you can see + + align:start position:0% +and you're pulling it and you can see + + + align:start position:0% +and you're pulling it and you can see +how it breaks + + align:start position:0% +how it breaks + + + align:start position:0% +how it breaks +you can actually see how it breaks it's + + align:start position:0% +you can actually see how it breaks it's + + + align:start position:0% +you can actually see how it breaks it's +breaking along + + align:start position:0% +breaking along + + + align:start position:0% +breaking along +the weakest plane it's breaking along + + align:start position:0% +the weakest plane it's breaking along + + + align:start position:0% +the weakest plane it's breaking along +the weakest plane so if you want to + + align:start position:0% +the weakest plane so if you want to + + + align:start position:0% +the weakest plane so if you want to +think then about + + align:start position:0% +think then about + + + align:start position:0% +think then about +well okay how do i know how to make this + + align:start position:0% +well okay how do i know how to make this + + + align:start position:0% +well okay how do i know how to make this +stronger + + align:start position:0% +stronger + + + align:start position:0% +stronger +for example so it stops breaking you + + align:start position:0% +for example so it stops breaking you + + + align:start position:0% +for example so it stops breaking you +know the weakest link is is + + align:start position:0% +know the weakest link is is + + + align:start position:0% +know the weakest link is is +is the weakest link right that was deep + + align:start position:0% +is the weakest link right that was deep + + + align:start position:0% +is the weakest link right that was deep +and and so yeah so you but so then + + align:start position:0% +and and so yeah so you but so then + + + align:start position:0% +and and so yeah so you but so then +that's the plane of the crystal that i + + align:start position:0% +that's the plane of the crystal that i + + + align:start position:0% +that's the plane of the crystal that i +need to think about + + align:start position:0% +need to think about + + + align:start position:0% +need to think about +how are atoms bonding together or + + align:start position:0% +how are atoms bonding together or + + + align:start position:0% +how are atoms bonding together or +packing in in that plane + + align:start position:0% +packing in in that plane + + + align:start position:0% +packing in in that plane +right this is real stuff this is this + + align:start position:0% +right this is real stuff this is this + + + align:start position:0% +right this is real stuff this is this +comes about + + align:start position:0% +comes about + + + align:start position:0% +comes about +in many of the properties not just the + + align:start position:0% +in many of the properties not just the + + + align:start position:0% +in many of the properties not just the +fracture but in many of the properties + + align:start position:0% +fracture but in many of the properties + + + align:start position:0% +fracture but in many of the properties +of these + + align:start position:0% +of these + + + align:start position:0% +of these +of these materials the the property as i + + align:start position:0% +of these materials the the property as i + + + align:start position:0% +of these materials the the property as i +said before + + align:start position:0% +said before + + + align:start position:0% +said before +depends heavily on which plane you're in + + align:start position:0% +depends heavily on which plane you're in + + + align:start position:0% +depends heavily on which plane you're in +and we'll see that more and more + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/Swo3Lvw7ivg.txt b/Swo3Lvw7ivg.txt new file mode 100644 index 0000000000000000000000000000000000000000..824321449898614bb89ac1a6afa6644c4c0037b2 --- /dev/null +++ b/Swo3Lvw7ivg.txt @@ -0,0 +1,6667 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu of your different facilities + + align:start position:0% +ocw.mit.edu of your different facilities + + + align:start position:0% +ocw.mit.edu of your different facilities +and there are various + + align:start position:0% +and there are various + + + align:start position:0% +and there are various +costs involved that you could use to + + align:start position:0% +costs involved that you could use to + + + align:start position:0% +costs involved that you could use to +make + + align:start position:0% +make + + + align:start position:0% +make +modifications so let's start with hi I'm + + align:start position:0% +modifications so let's start with hi I'm + + + align:start position:0% +modifications so let's start with hi I'm +I'm H mcmanis the co-creator of the lean + + align:start position:0% +I'm H mcmanis the co-creator of the lean + + + align:start position:0% +I'm H mcmanis the co-creator of the lean +Enterprise Value simulation I'm going to + + align:start position:0% +Enterprise Value simulation I'm going to + + + align:start position:0% +Enterprise Value simulation I'm going to +talk a little bit about teaching lean + + align:start position:0% +talk a little bit about teaching lean + + + align:start position:0% +talk a little bit about teaching lean +thinking principles through Hands-On + + align:start position:0% +thinking principles through Hands-On + + + align:start position:0% +thinking principles through Hands-On +learning uh with particular reference to + + align:start position:0% +learning uh with particular reference to + + + align:start position:0% +learning uh with particular reference to +what we do in the lean Academy um + + align:start position:0% +what we do in the lean Academy um + + + align:start position:0% +what we do in the lean Academy um +credited here are Eric rebentish my + + align:start position:0% +credited here are Eric rebentish my + + + align:start position:0% +credited here are Eric rebentish my +co-creator in the lean Enterprise Value + + align:start position:0% +co-creator in the lean Enterprise Value + + + align:start position:0% +co-creator in the lean Enterprise Value +simulation and Earl and Alexis who were + + align:start position:0% +simulation and Earl and Alexis who were + + + align:start position:0% +simulation and Earl and Alexis who were +key in integrating the lean Enterprise + + align:start position:0% +key in integrating the lean Enterprise + + + align:start position:0% +key in integrating the lean Enterprise +Value simulation part of it into the uh + + align:start position:0% +Value simulation part of it into the uh + + + align:start position:0% +Value simulation part of it into the uh +lean Academy the reason we use + + align:start position:0% +lean Academy the reason we use + + + align:start position:0% +lean Academy the reason we use +simulation based education for this is + + align:start position:0% +simulation based education for this is + + + align:start position:0% +simulation based education for this is +that uh teaching lean uh is a difficult + + align:start position:0% +that uh teaching lean uh is a difficult + + + align:start position:0% +that uh teaching lean uh is a difficult +challenge uh a great deal of that is + + align:start position:0% +challenge uh a great deal of that is + + + align:start position:0% +challenge uh a great deal of that is +because it's experience-based and it + + align:start position:0% +because it's experience-based and it + + + align:start position:0% +because it's experience-based and it +depends on a context the context of + + align:start position:0% +depends on a context the context of + + + align:start position:0% +depends on a context the context of +existing industrial and Engineering + + align:start position:0% +existing industrial and Engineering + + + align:start position:0% +existing industrial and Engineering +processes that are not familiar to + + align:start position:0% +processes that are not familiar to + + + align:start position:0% +processes that are not familiar to +students so we really need to give them + + align:start position:0% +students so we really need to give them + + + align:start position:0% +students so we really need to give them +something to think about and work with + + align:start position:0% +something to think about and work with + + + align:start position:0% +something to think about and work with +before a lot of these ideas start to + + align:start position:0% +before a lot of these ideas start to + + + align:start position:0% +before a lot of these ideas start to +make real sense to them so we use + + align:start position:0% +make real sense to them so we use + + + align:start position:0% +make real sense to them so we use +simulation-based education to increase + + align:start position:0% +simulation-based education to increase + + + align:start position:0% +simulation-based education to increase +comprehension to allow them to put the + + align:start position:0% +comprehension to allow them to put the + + + align:start position:0% +comprehension to allow them to put the +ideas together in a more holistic way + + align:start position:0% +ideas together in a more holistic way + + + align:start position:0% +ideas together in a more holistic way +not just bits and pieces of technical + + align:start position:0% +not just bits and pieces of technical + + + align:start position:0% +not just bits and pieces of technical +knowledge but how does it all work + + align:start position:0% +knowledge but how does it all work + + + align:start position:0% +knowledge but how does it all work +together and of course learning through + + align:start position:0% +together and of course learning through + + + align:start position:0% +together and of course learning through +experience getting a tactile feel for + + align:start position:0% +experience getting a tactile feel for + + + align:start position:0% +experience getting a tactile feel for +the material a final thing for a + + align:start position:0% +the material a final thing for a + + + align:start position:0% +the material a final thing for a +intensive event like the lean academy uh + + align:start position:0% +intensive event like the lean academy uh + + + align:start position:0% +intensive event like the lean academy uh +is also just to get the energy level up + + align:start position:0% +is also just to get the energy level up + + + align:start position:0% +is also just to get the energy level up +to give them something to do uh to get + + align:start position:0% +to give them something to do uh to get + + + align:start position:0% +to give them something to do uh to get +their blood pressure up a little bit um + + align:start position:0% +their blood pressure up a little bit um + + + align:start position:0% +their blood pressure up a little bit um +keep them awake and excited and involved + + align:start position:0% +keep them awake and excited and involved + + + align:start position:0% +keep them awake and excited and involved +in the class the simulation is built + + align:start position:0% +in the class the simulation is built + + + align:start position:0% +in the class the simulation is built +around attempting to build Lego + + align:start position:0% +around attempting to build Lego + + + align:start position:0% +around attempting to build Lego +airplanes um that are actually + + align:start position:0% +airplanes um that are actually + + + align:start position:0% +airplanes um that are actually +relatively poorly designed Lego + + align:start position:0% +relatively poorly designed Lego + + + align:start position:0% +relatively poorly designed Lego +airplanes if the criteria for a Lego + + align:start position:0% +airplanes if the criteria for a Lego + + + align:start position:0% +airplanes if the criteria for a Lego +airplane is that it's relatively easy to + + align:start position:0% +airplane is that it's relatively easy to + + + align:start position:0% +airplane is that it's relatively easy to +put together and it stays together once + + align:start position:0% +put together and it stays together once + + + align:start position:0% +put together and it stays together once +you put it + + align:start position:0% +you put it + + + align:start position:0% +you put it +there this is not a very good airplane + + align:start position:0% +there this is not a very good airplane + + + align:start position:0% +there this is not a very good airplane +and it's built in a very unlean way it's + + align:start position:0% +and it's built in a very unlean way it's + + + align:start position:0% +and it's built in a very unlean way it's +built in a legacy uh system which has an + + align:start position:0% +built in a legacy uh system which has an + + + align:start position:0% +built in a legacy uh system which has an +unbalanced production system with + + align:start position:0% +unbalanced production system with + + + align:start position:0% +unbalanced production system with +bottlenecks and other problems a long + + align:start position:0% +bottlenecks and other problems a long + + + align:start position:0% +bottlenecks and other problems a long +supply chain along an uncoordinated + + align:start position:0% +supply chain along an uncoordinated + + + align:start position:0% +supply chain along an uncoordinated +supply chain the Legos actually come + + align:start position:0% +supply chain the Legos actually come + + + align:start position:0% +supply chain the Legos actually come +from uh someplace else that they have to + + align:start position:0% +from uh someplace else that they have to + + + align:start position:0% +from uh someplace else that they have to +be transported to the table where the + + align:start position:0% +be transported to the table where the + + + align:start position:0% +be transported to the table where the +airplanes are built um and there's a lot + + align:start position:0% +airplanes are built um and there's a lot + + + align:start position:0% +airplanes are built um and there's a lot +of paperwork and Communications issues + + align:start position:0% +of paperwork and Communications issues + + + align:start position:0% +of paperwork and Communications issues +in both getting the plane built and then + + align:start position:0% +in both getting the plane built and then + + + align:start position:0% +in both getting the plane built and then +at the end of each round doing the + + align:start position:0% +at the end of each round doing the + + + align:start position:0% +at the end of each round doing the +accounting necessary to figure out + + align:start position:0% +accounting necessary to figure out + + + align:start position:0% +accounting necessary to figure out +whether you actually made money or not + + align:start position:0% +whether you actually made money or not + + + align:start position:0% +whether you actually made money or not +from the airplane the system used in the + + align:start position:0% +from the airplane the system used in the + + + align:start position:0% +from the airplane the system used in the +lean Academy is moderately simple + + align:start position:0% +lean Academy is moderately simple + + + align:start position:0% +lean Academy is moderately simple +we have four manufacturing plants that + + align:start position:0% +we have four manufacturing plants that + + + align:start position:0% +we have four manufacturing plants that +build Tails fuselages wings and final + + align:start position:0% +build Tails fuselages wings and final + + + align:start position:0% +build Tails fuselages wings and final +assemblies to deliver an airplane to the + + align:start position:0% +assemblies to deliver an airplane to the + + + align:start position:0% +assemblies to deliver an airplane to the +customer um we have a supplier quality + + align:start position:0% +customer um we have a supplier quality + + + align:start position:0% +customer um we have a supplier quality +representative uh who interacts with a + + align:start position:0% +representative uh who interacts with a + + + align:start position:0% +representative uh who interacts with a +supply chain consisting of a single + + align:start position:0% +supply chain consisting of a single + + + align:start position:0% +supply chain consisting of a single +dedicated supplier but in a different + + align:start position:0% +dedicated supplier but in a different + + + align:start position:0% +dedicated supplier but in a different +place at a table where the suppliers sit + + align:start position:0% +place at a table where the suppliers sit + + + align:start position:0% +place at a table where the suppliers sit +um so there's a flow of information + + align:start position:0% +um so there's a flow of information + + + align:start position:0% +um so there's a flow of information +between these people and hopefully that + + align:start position:0% +between these people and hopefully that + + + align:start position:0% +between these people and hopefully that +creates a flow of parts of sub + + align:start position:0% +creates a flow of parts of sub + + + align:start position:0% +creates a flow of parts of sub +assemblies and parts uh that result in + + align:start position:0% +assemblies and parts uh that result in + + + align:start position:0% +assemblies and parts uh that result in +some value being delivered and aircraft + + align:start position:0% +some value being delivered and aircraft + + + align:start position:0% +some value being delivered and aircraft +being delivered to the customer the + + align:start position:0% +being delivered to the customer the + + + align:start position:0% +being delivered to the customer the +simulation it's not just a matter of + + align:start position:0% +simulation it's not just a matter of + + + align:start position:0% +simulation it's not just a matter of +building Lego airpl it's actually a + + align:start position:0% +building Lego airpl it's actually a + + + align:start position:0% +building Lego airpl it's actually a +fairly rigidly defined simulation um + + align:start position:0% +fairly rigidly defined simulation um + + + align:start position:0% +fairly rigidly defined simulation um +that has a number of + + align:start position:0% +that has a number of + + + align:start position:0% +that has a number of +features uh for one thing each student + + align:start position:0% +features uh for one thing each student + + + align:start position:0% +features uh for one thing each student +what they're allowed to do is + + align:start position:0% +what they're allowed to do is + + + align:start position:0% +what they're allowed to do is +represented visually uh like this each + + align:start position:0% +represented visually uh like this each + + + align:start position:0% +represented visually uh like this each +student is set is told take these pieces + + align:start position:0% +student is set is told take these pieces + + + align:start position:0% +student is set is told take these pieces +and build that + + align:start position:0% +and build that + + + align:start position:0% +and build that +assembly um this both defines what they + + align:start position:0% +assembly um this both defines what they + + + align:start position:0% +assembly um this both defines what they +need to do visually so it's fairly easy + + align:start position:0% +need to do visually so it's fairly easy + + + align:start position:0% +need to do visually so it's fairly easy +to understand and it's changeable very + + align:start position:0% +to understand and it's changeable very + + + align:start position:0% +to understand and it's changeable very +important this is rather difficult + + align:start position:0% +important this is rather difficult + + + align:start position:0% +important this is rather difficult +assembly to put together the students + + align:start position:0% +assembly to put together the students + + + align:start position:0% +assembly to put together the students +wish to change it they can in an + + align:start position:0% +wish to change it they can in an + + + align:start position:0% +wish to change it they can in an +organized + + align:start position:0% +organized + + + align:start position:0% +organized +way the processes that they do are also + + align:start position:0% +way the processes that they do are also + + + align:start position:0% +way the processes that they do are also +uh constrained by hourglasses it's not a + + align:start position:0% +uh constrained by hourglasses it's not a + + + align:start position:0% +uh constrained by hourglasses it's not a +dexterity contest it's not a race um + + align:start position:0% +dexterity contest it's not a race um + + + align:start position:0% +dexterity contest it's not a race um +it's a process and this process is at + + align:start position:0% +it's a process and this process is at + + + align:start position:0% +it's a process and this process is at +many steps constrained um by the pace of + + align:start position:0% +many steps constrained um by the pace of + + + align:start position:0% +many steps constrained um by the pace of +some hourglasses in particular the + + align:start position:0% +some hourglasses in particular the + + + align:start position:0% +some hourglasses in particular the +assembly operations uh depending on the + + align:start position:0% +assembly operations uh depending on the + + + align:start position:0% +assembly operations uh depending on the +part count hourglasses with different + + align:start position:0% +part count hourglasses with different + + + align:start position:0% +part count hourglasses with different +times are used to represent the actual + + align:start position:0% +times are used to represent the actual + + + align:start position:0% +times are used to represent the actual +Factory operations that are happening + + align:start position:0% +Factory operations that are happening + + + align:start position:0% +Factory operations that are happening +that are simulated by the by the + + align:start position:0% +that are simulated by the by the + + + align:start position:0% +that are simulated by the by the +simulation it's not just a matter of the + + align:start position:0% +simulation it's not just a matter of the + + + align:start position:0% +simulation it's not just a matter of the +students dexterity and so this becomes a + + align:start position:0% +students dexterity and so this becomes a + + + align:start position:0% +students dexterity and so this becomes a +constraint that the students have to + + align:start position:0% +constraint that the students have to + + + align:start position:0% +constraint that the students have to +work with and design uh Solutions + + align:start position:0% +work with and design uh Solutions + + + align:start position:0% +work with and design uh Solutions +around there's a fairly long paperwork + + align:start position:0% +around there's a fairly long paperwork + + + align:start position:0% +around there's a fairly long paperwork +chain and it's fairly clumsy it's not + + align:start position:0% +chain and it's fairly clumsy it's not + + + align:start position:0% +chain and it's fairly clumsy it's not +that hard to learn but it turns out it's + + align:start position:0% +that hard to learn but it turns out it's + + + align:start position:0% +that hard to learn but it turns out it's +not that easy to use uh standard paper + + align:start position:0% +not that easy to use uh standard paper + + + align:start position:0% +not that easy to use uh standard paper +order form here you could think of that + + align:start position:0% +order form here you could think of that + + + align:start position:0% +order form here you could think of that +even as a web form and modern economy + + align:start position:0% +even as a web form and modern economy + + + align:start position:0% +even as a web form and modern economy +but you're just saying I want this many + + align:start position:0% +but you're just saying I want this many + + + align:start position:0% +but you're just saying I want this many +of this part handing it off to your + + align:start position:0% +of this part handing it off to your + + + align:start position:0% +of this part handing it off to your +supplier quality representative who then + + align:start position:0% +supplier quality representative who then + + + align:start position:0% +supplier quality representative who then +hands it to the supplier who has to fill + + align:start position:0% +hands it to the supplier who has to fill + + + align:start position:0% +hands it to the supplier who has to fill +it um and then they have to fill out an + + align:start position:0% +it um and then they have to fill out an + + + align:start position:0% +it um and then they have to fill out an +essentially an invoice sheet that they + + align:start position:0% +essentially an invoice sheet that they + + + align:start position:0% +essentially an invoice sheet that they +send back to you that means that every + + align:start position:0% +send back to you that means that every + + + align:start position:0% +send back to you that means that every +transaction with Legos involves two + + align:start position:0% +transaction with Legos involves two + + + align:start position:0% +transaction with Legos involves two +pieces of paper and one two three four + + align:start position:0% +pieces of paper and one two three four + + + align:start position:0% +pieces of paper and one two three four +steps just to get your parts to build + + align:start position:0% +steps just to get your parts to build + + + align:start position:0% +steps just to get your parts to build +not a very good system but not atypical + + align:start position:0% +not a very good system but not atypical + + + align:start position:0% +not a very good system but not atypical +of the real + + align:start position:0% +of the real + + + align:start position:0% +of the real +world and finally is an accounting + + align:start position:0% +world and finally is an accounting + + + align:start position:0% +world and finally is an accounting +system uh for lean Academy it's a cash + + align:start position:0% +system uh for lean Academy it's a cash + + + align:start position:0% +system uh for lean Academy it's a cash +flow system that tracks all the costs + + align:start position:0% +flow system that tracks all the costs + + + align:start position:0% +flow system that tracks all the costs +involved the fix costs how much does it + + align:start position:0% +involved the fix costs how much does it + + + align:start position:0% +involved the fix costs how much does it +cost to keep your plants open the + + align:start position:0% +cost to keep your plants open the + + + align:start position:0% +cost to keep your plants open the +variable costs how much do those parts + + align:start position:0% +variable costs how much do those parts + + + align:start position:0% +variable costs how much do those parts +cost how much do it cost to do various + + align:start position:0% +cost how much do it cost to do various + + + align:start position:0% +cost how much do it cost to do various +things um and you can figure out whether + + align:start position:0% +things um and you can figure out whether + + + align:start position:0% +things um and you can figure out whether +you're making money or not often you're + + align:start position:0% +you're making money or not often you're + + + align:start position:0% +you're making money or not often you're +not if you don't get out enough + + align:start position:0% +not if you don't get out enough + + + align:start position:0% +not if you don't get out enough +airplanes you don't make any money or if + + align:start position:0% +airplanes you don't make any money or if + + + align:start position:0% +airplanes you don't make any money or if +you do things uh in a in a wasteful way + + align:start position:0% +you do things uh in a in a wasteful way + + + align:start position:0% +you do things uh in a in a wasteful way +if you waste Parts uh you won't make any + + align:start position:0% +if you waste Parts uh you won't make any + + + align:start position:0% +if you waste Parts uh you won't make any +money all right everybody let's check in + + align:start position:0% +money all right everybody let's check in + + + align:start position:0% +money all right everybody let's check in +I'd like to find out how many planes + + align:start position:0% +I'd like to find out how many planes + + + align:start position:0% +I'd like to find out how many planes +each table builds let's start here one + + align:start position:0% +each table builds let's start here one + + + align:start position:0% +each table builds let's start here one +plane one one + + align:start position:0% +plane one one + + + align:start position:0% +plane one one +plane two + + align:start position:0% +plane two + + + align:start position:0% +plane two +planes one plane all right who's making + + align:start position:0% + + + + align:start position:0% + +money let me ask a question is anybody's + + align:start position:0% +money let me ask a question is anybody's + + + align:start position:0% +money let me ask a question is anybody's +manufacturing operations making money + + align:start position:0% +manufacturing operations making money + + + align:start position:0% +manufacturing operations making money +yet no + + align:start position:0% +yet no + + + align:start position:0% +yet no +okay tell me how much money the supplier + + align:start position:0% +okay tell me how much money the supplier + + + align:start position:0% +okay tell me how much money the supplier +is making who is profitable 14 14 okay + + align:start position:0% +is making who is profitable 14 14 okay + + + align:start position:0% +is making who is profitable 14 14 okay +so you're sort of barely profitable + + align:start position:0% +so you're sort of barely profitable + + + align:start position:0% +so you're sort of barely profitable +that's better than being negative all + + align:start position:0% +that's better than being negative all + + + align:start position:0% +that's better than being negative all +right so the supplier might be doing + + align:start position:0% +right so the supplier might be doing + + + align:start position:0% +right so the supplier might be doing +well in that Enterprise but it might be + + align:start position:0% +well in that Enterprise but it might be + + + align:start position:0% +well in that Enterprise but it might be +at the expense of the manufacturing + + align:start position:0% +at the expense of the manufacturing + + + align:start position:0% +at the expense of the manufacturing +portion so this is something that you're + + align:start position:0% +portion so this is something that you're + + + align:start position:0% +portion so this is something that you're +going to think about as you go through + + align:start position:0% +going to think about as you go through + + + align:start position:0% +going to think about as you go through +your simulation so in the lean Academy + + align:start position:0% +your simulation so in the lean Academy + + + align:start position:0% +your simulation so in the lean Academy +we um dedicate one day to the simulation + + align:start position:0% +we um dedicate one day to the simulation + + + align:start position:0% +we um dedicate one day to the simulation +about 2third of the teaching time in + + align:start position:0% +about 2third of the teaching time in + + + align:start position:0% +about 2third of the teaching time in +that day there's some lectures + + align:start position:0% +that day there's some lectures + + + align:start position:0% +that day there's some lectures +interspersed um it happens in 12 minute + + align:start position:0% +interspersed um it happens in 12 minute + + + align:start position:0% +interspersed um it happens in 12 minute +active rounds there 12 12 minutes of + + align:start position:0% +active rounds there 12 12 minutes of + + + align:start position:0% +active rounds there 12 12 minutes of +frenzy uh followed by and uh preceded by + + align:start position:0% +frenzy uh followed by and uh preceded by + + + align:start position:0% +frenzy uh followed by and uh preceded by +in many cases uh time for reflection + + align:start position:0% +in many cases uh time for reflection + + + align:start position:0% +in many cases uh time for reflection +planning financial analysis and so forth + + align:start position:0% +planning financial analysis and so forth + + + align:start position:0% +planning financial analysis and so forth +um and these are separated up into + + align:start position:0% +um and these are separated up into + + + align:start position:0% +um and these are separated up into +basically learning how to how to do the + + align:start position:0% +basically learning how to how to do the + + + align:start position:0% +basically learning how to how to do the +simulation getting past the learning + + align:start position:0% +simulation getting past the learning + + + align:start position:0% +simulation getting past the learning +curve uh understanding how lean process + + align:start position:0% +curve uh understanding how lean process + + + align:start position:0% +curve uh understanding how lean process +improvements can be used to take a + + align:start position:0% +improvements can be used to take a + + + align:start position:0% +improvements can be used to take a +legacy State um and make it lean and + + align:start position:0% +legacy State um and make it lean and + + + align:start position:0% +legacy State um and make it lean and +make it work better um and then a final + + align:start position:0% +make it work better um and then a final + + + align:start position:0% +make it work better um and then a final +round where the uh manufacturing + + align:start position:0% +round where the uh manufacturing + + + align:start position:0% +round where the uh manufacturing +suppliers and also a not simulated but + + align:start position:0% +suppliers and also a not simulated but + + + align:start position:0% +suppliers and also a not simulated but +conceptual Engineering Process is used + + align:start position:0% +conceptual Engineering Process is used + + + align:start position:0% +conceptual Engineering Process is used +to achieve Enterprise Lean by + + align:start position:0% +to achieve Enterprise Lean by + + + align:start position:0% +to achieve Enterprise Lean by +redesigning the airplane tuning the + + align:start position:0% +redesigning the airplane tuning the + + + align:start position:0% +redesigning the airplane tuning the +supply chain to a really high State and + + align:start position:0% +supply chain to a really high State and + + + align:start position:0% +supply chain to a really high State and +seeing what you can do in an almost + + align:start position:0% +seeing what you can do in an almost + + + align:start position:0% +seeing what you can do in an almost +ideal State this is a + + align:start position:0% +ideal State this is a + + + align:start position:0% +ideal State this is a +common uh tool around the industry to go + + align:start position:0% +common uh tool around the industry to go + + + align:start position:0% +common uh tool around the industry to go +and look at other facilities and + + align:start position:0% +and look at other facilities and + + + align:start position:0% +and look at other facilities and +Benchmark yourselves not only with + + align:start position:0% +Benchmark yourselves not only with + + + align:start position:0% +Benchmark yourselves not only with +respect to uh companies that do the same + + align:start position:0% +respect to uh companies that do the same + + + align:start position:0% +respect to uh companies that do the same +thing as you do but also to Benchmark + + align:start position:0% +thing as you do but also to Benchmark + + + align:start position:0% +thing as you do but also to Benchmark +yourself against companies that do other + + align:start position:0% +yourself against companies that do other + + + align:start position:0% +yourself against companies that do other +things but have similar processes to you + + align:start position:0% +things but have similar processes to you + + + align:start position:0% +things but have similar processes to you +so there's a lot to learn by going and + + align:start position:0% +so there's a lot to learn by going and + + + align:start position:0% +so there's a lot to learn by going and +walking around and seeing this and from + + align:start position:0% +walking around and seeing this and from + + + align:start position:0% +walking around and seeing this and from +what I took away from the tables I think + + align:start position:0% +what I took away from the tables I think + + + align:start position:0% +what I took away from the tables I think +we've got two different build to + + align:start position:0% +we've got two different build to + + + align:start position:0% +we've got two different build to +philosophies going on so you'll notice + + align:start position:0% +philosophies going on so you'll notice + + + align:start position:0% +philosophies going on so you'll notice +there are are two kinds of build to + + align:start position:0% +there are are two kinds of build to + + + align:start position:0% +there are are two kinds of build to +packages going on so take a look at that + + align:start position:0% +packages going on so take a look at that + + + align:start position:0% +packages going on so take a look at that +and see what caused somebody else to + + align:start position:0% +and see what caused somebody else to + + + align:start position:0% +and see what caused somebody else to +think differently than what you did I + + align:start position:0% +think differently than what you did I + + + align:start position:0% +think differently than what you did I +also wanted you guys to notice this + + align:start position:0% +also wanted you guys to notice this + + + align:start position:0% +also wanted you guys to notice this +table here because I saw you guys you + + align:start position:0% +table here because I saw you guys you + + + align:start position:0% +table here because I saw you guys you +flipped your bins upside down when you + + align:start position:0% +flipped your bins upside down when you + + + align:start position:0% +flipped your bins upside down when you +were ready for a new one that was your + + align:start position:0% +were ready for a new one that was your + + + align:start position:0% +were ready for a new one that was your +your signals so this was we don't want + + align:start position:0% +your signals so this was we don't want + + + align:start position:0% +your signals so this was we don't want +it anymore this is and that's you do + + align:start position:0% +it anymore this is and that's you do + + + align:start position:0% +it anymore this is and that's you do +want more so I I saw that and I thought + + align:start position:0% +want more so I I saw that and I thought + + + align:start position:0% +want more so I I saw that and I thought +that was an interesting practice anybody + + align:start position:0% +that was an interesting practice anybody + + + align:start position:0% +that was an interesting practice anybody +else have a practice that worked well + + align:start position:0% +else have a practice that worked well + + + align:start position:0% +else have a practice that worked well +for them that might not come out when + + align:start position:0% +for them that might not come out when + + + align:start position:0% +for them that might not come out when +you're doing your table tours and just + + align:start position:0% +you're doing your table tours and just + + + align:start position:0% +you're doing your table tours and just +looking at the static + + align:start position:0% +looking at the static + + + align:start position:0% +looking at the static +display the clock one we use one timer + + align:start position:0% +display the clock one we use one timer + + + align:start position:0% +display the clock one we use one timer +for all four oh + + align:start position:0% +for all four oh + + + align:start position:0% +for all four oh +no no that doesn't count we're all + + align:start position:0% +no no that doesn't count we're all + + + align:start position:0% +no no that doesn't count we're all +synchronized all an + + align:start position:0% +synchronized all an + + + align:start position:0% +synchronized all an +hour so there's a best practice that you + + align:start position:0% +hour so there's a best practice that you + + + align:start position:0% +hour so there's a best practice that you +might consider adop + + align:start position:0% +might consider adop + + + align:start position:0% +might consider adop +did we have a comment from this team + + align:start position:0% +did we have a comment from this team + + + align:start position:0% +did we have a comment from this team +here and then standard sheet so that she + + align:start position:0% +here and then standard sheet so that she + + + align:start position:0% +here and then standard sheet so that she +would be able to identify very quickly + + align:start position:0% +would be able to identify very quickly + + + align:start position:0% +would be able to identify very quickly +okay so did everybody hear that there's + + align:start position:0% +okay so did everybody hear that there's + + + align:start position:0% +okay so did everybody hear that there's +color cating of bins and color cating of + + align:start position:0% +color cating of bins and color cating of + + + align:start position:0% +color cating of bins and color cating of +the different standard orders to try to + + align:start position:0% +the different standard orders to try to + + + align:start position:0% +the different standard orders to try to +match visual inspection and get quality + + align:start position:0% +match visual inspection and get quality + + + align:start position:0% +match visual inspection and get quality +good also color coded the delivery site + + align:start position:0% +good also color coded the delivery site + + + align:start position:0% +good also color coded the delivery site +so the red goes + + align:start position:0% +so the red goes + + + align:start position:0% +so the red goes +bottom so they have three marks of color + + align:start position:0% +bottom so they have three marks of color + + + align:start position:0% +bottom so they have three marks of color +the try to get that all + + align:start position:0% +the try to get that all + + + align:start position:0% +the try to get that all +coordinated other best practices that + + align:start position:0% +coordinated other best practices that + + + align:start position:0% +coordinated other best practices that +won't come out again if you're just + + align:start position:0% +won't come out again if you're just + + + align:start position:0% +won't come out again if you're just +looking + + align:start position:0% +looking + + + align:start position:0% +looking +around yes we to continuous delivery + + align:start position:0% +around yes we to continuous delivery + + + align:start position:0% +around yes we to continuous delivery +cycle up until like cut off time for + + align:start position:0% +cycle up until like cut off time for + + + align:start position:0% +cycle up until like cut off time for +delivery okay because we noticed that + + align:start position:0% +delivery okay because we noticed that + + + align:start position:0% +delivery okay because we noticed that +there was variability and how + + align:start position:0% + + + + align:start position:0% + +long the lean Aerospace initiative which + + align:start position:0% +long the lean Aerospace initiative which + + + align:start position:0% +long the lean Aerospace initiative which +funded all this stuff years ago is the + + align:start position:0% +funded all this stuff years ago is the + + + align:start position:0% +funded all this stuff years ago is the +Consortium of all the airspace companies + + align:start position:0% +Consortium of all the airspace companies + + + align:start position:0% +Consortium of all the airspace companies +and uh the government and in these + + align:start position:0% +and uh the government and in these + + + align:start position:0% +and uh the government and in these +conferences that we have um the the + + align:start position:0% +conferences that we have um the the + + + align:start position:0% +conferences that we have um the the +suppliers the engineers the + + align:start position:0% +suppliers the engineers the + + + align:start position:0% +suppliers the engineers the +manufacturing people get up and make + + align:start position:0% +manufacturing people get up and make + + + align:start position:0% +manufacturing people get up and make +presentations uh to basically show how + + align:start position:0% +presentations uh to basically show how + + + align:start position:0% +presentations uh to basically show how +they do things and that's the benefit of + + align:start position:0% +they do things and that's the benefit of + + + align:start position:0% +they do things and that's the benefit of +this makes the benchmarking a lot easier + + align:start position:0% +this makes the benchmarking a lot easier + + + align:start position:0% +this makes the benchmarking a lot easier +because people basically put their P + + align:start position:0% +because people basically put their P + + + align:start position:0% +because people basically put their P +practices up and everybody benefits and + + align:start position:0% +practices up and everybody benefits and + + + align:start position:0% +practices up and everybody benefits and +that's I mean there an annual fee that + + align:start position:0% +that's I mean there an annual fee that + + + align:start position:0% +that's I mean there an annual fee that +the companies pay that you know supports + + align:start position:0% +the companies pay that you know supports + + + align:start position:0% +the companies pay that you know supports +all that but they in fact get the + + align:start position:0% +all that but they in fact get the + + + align:start position:0% +all that but they in fact get the +advantages of gee we took a tour through + + align:start position:0% +advantages of gee we took a tour through + + + align:start position:0% +advantages of gee we took a tour through +some's Factory and know they got a red + + align:start position:0% +some's Factory and know they got a red + + + align:start position:0% +some's Factory and know they got a red +light that goes on or something like + + align:start position:0% +light that goes on or something like + + + align:start position:0% +light that goes on or something like +that and so all the aerospace companies + + align:start position:0% +that and so all the aerospace companies + + + align:start position:0% +that and so all the aerospace companies +benefit from the conversation and the + + align:start position:0% +benefit from the conversation and the + + + align:start position:0% +benefit from the conversation and the +discussion and the presentations and the + + align:start position:0% +discussion and the presentations and the + + + align:start position:0% +discussion and the presentations and the +factory tours of each other's U uh + + align:start position:0% +factory tours of each other's U uh + + + align:start position:0% +factory tours of each other's U uh +organization the sort of tools that they + + align:start position:0% +organization the sort of tools that they + + + align:start position:0% +organization the sort of tools that they +use + + align:start position:0% +use + + + align:start position:0% +use +um include simple organization um which + + align:start position:0% +um include simple organization um which + + + align:start position:0% +um include simple organization um which +they can use lean principles like 5s and + + align:start position:0% +they can use lean principles like 5s and + + + align:start position:0% +they can use lean principles like 5s and +visual control to clean up their + + align:start position:0% +visual control to clean up their + + + align:start position:0% +visual control to clean up their +workplace just get basic process working + + align:start position:0% +workplace just get basic process working + + + align:start position:0% +workplace just get basic process working +okay um balancing of work workload uh + + align:start position:0% +okay um balancing of work workload uh + + + align:start position:0% +okay um balancing of work workload uh +which can be planned around lean + + align:start position:0% +which can be planned around lean + + + align:start position:0% +which can be planned around lean +principles like Tac time single piece + + align:start position:0% +principles like Tac time single piece + + + align:start position:0% +principles like Tac time single piece +flow which essentially allows them to + + align:start position:0% +flow which essentially allows them to + + + align:start position:0% +flow which essentially allows them to +move work between plants to clear + + align:start position:0% +move work between plants to clear + + + align:start position:0% +move work between plants to clear +bottlenecks and get the get the work + + align:start position:0% +bottlenecks and get the get the work + + + align:start position:0% +bottlenecks and get the get the work +balanced um they can tear down or move + + align:start position:0% +balanced um they can tear down or move + + + align:start position:0% +balanced um they can tear down or move +facilities um again on based on lean + + align:start position:0% +facilities um again on based on lean + + + align:start position:0% +facilities um again on based on lean +principles not just random + + align:start position:0% +principles not just random + + + align:start position:0% +principles not just random +action and they can u u modernize this + + align:start position:0% +action and they can u u modernize this + + + align:start position:0% +action and they can u u modernize this +archaic order system + + align:start position:0% +archaic order system + + + align:start position:0% +archaic order system +um again planned using lean principles + + align:start position:0% +um again planned using lean principles + + + align:start position:0% +um again planned using lean principles +and there's a mechanic in the uh + + align:start position:0% +and there's a mechanic in the uh + + + align:start position:0% +and there's a mechanic in the uh +simulation to allow a paper lless + + align:start position:0% +simulation to allow a paper lless + + + align:start position:0% +simulation to allow a paper lless +there's actually still a little bit of + + align:start position:0% +there's actually still a little bit of + + + align:start position:0% +there's actually still a little bit of +paper but much less uh ordering system + + align:start position:0% +paper but much less uh ordering system + + + align:start position:0% +paper but much less uh ordering system +that would simulate a modern uh + + align:start position:0% +that would simulate a modern uh + + + align:start position:0% +that would simulate a modern uh +web-based um perhaps or certainly + + align:start position:0% +web-based um perhaps or certainly + + + align:start position:0% +web-based um perhaps or certainly +Electronics based uh Inventory + + align:start position:0% +Electronics based uh Inventory + + + align:start position:0% +Electronics based uh Inventory +management system one of the key + + align:start position:0% +management system one of the key + + + align:start position:0% +management system one of the key +features is the simulation allows us uh + + align:start position:0% +features is the simulation allows us uh + + + align:start position:0% +features is the simulation allows us uh +is to use data it's very difficult to go + + align:start position:0% +is to use data it's very difficult to go + + + align:start position:0% +is to use data it's very difficult to go +out to a real aircraft manufacturing + + align:start position:0% +out to a real aircraft manufacturing + + + align:start position:0% +out to a real aircraft manufacturing +plant and play with with it uh with the + + align:start position:0% +plant and play with with it uh with the + + + align:start position:0% +plant and play with with it uh with the +simulation we can play with it in these + + align:start position:0% +simulation we can play with it in these + + + align:start position:0% +simulation we can play with it in these +12 minute rounds and create and use uh + + align:start position:0% +12 minute rounds and create and use uh + + + align:start position:0% +12 minute rounds and create and use uh +data that we've uh that we've collected + + align:start position:0% +data that we've uh that we've collected + + + align:start position:0% +data that we've uh that we've collected +to both plan improvements and track + + align:start position:0% +to both plan improvements and track + + + align:start position:0% +to both plan improvements and track +processes so we can keep track of how + + align:start position:0% +processes so we can keep track of how + + + align:start position:0% +processes so we can keep track of how +long does it take to do things how many + + align:start position:0% +long does it take to do things how many + + + align:start position:0% +long does it take to do things how many +parts are involved um how what's the + + align:start position:0% +parts are involved um how what's the + + + align:start position:0% +parts are involved um how what's the +delay involved in ordering parts Etc and + + align:start position:0% +delay involved in ordering parts Etc and + + + align:start position:0% +delay involved in ordering parts Etc and +we can do that quantitatively and that's + + align:start position:0% +we can do that quantitatively and that's + + + align:start position:0% +we can do that quantitatively and that's +one of the key aspects of most product + + align:start position:0% +one of the key aspects of most product + + + align:start position:0% +one of the key aspects of most product +Improvement techniques is to use the + + align:start position:0% +Improvement techniques is to use the + + + align:start position:0% +Improvement techniques is to use the +data and let it tell you to do not just + + align:start position:0% +data and let it tell you to do not just + + + align:start position:0% +data and let it tell you to do not just +kind of make things up as you go along + + align:start position:0% +kind of make things up as you go along + + + align:start position:0% +kind of make things up as you go along +uh be entirely dependent on on Common + + align:start position:0% +uh be entirely dependent on on Common + + + align:start position:0% +uh be entirely dependent on on Common +Sense or experience to do these uh these + + align:start position:0% +Sense or experience to do these uh these + + + align:start position:0% +Sense or experience to do these uh these +kinds of improvements and this data can + + align:start position:0% +kinds of improvements and this data can + + + align:start position:0% +kinds of improvements and this data can +be incorporated into classic lean tools + + align:start position:0% +be incorporated into classic lean tools + + + align:start position:0% +be incorporated into classic lean tools +like value stream mappings um this is + + align:start position:0% +like value stream mappings um this is + + + align:start position:0% +like value stream mappings um this is +the same data plotted in the classic + + align:start position:0% +the same data plotted in the classic + + + align:start position:0% +the same data plotted in the classic +lean value stream map uh again it gives + + align:start position:0% +lean value stream map uh again it gives + + + align:start position:0% +lean value stream map uh again it gives +them a gives them the opportunity to + + align:start position:0% +them a gives them the opportunity to + + + align:start position:0% +them a gives them the opportunity to +touch a tool to actually use it to + + align:start position:0% +touch a tool to actually use it to + + + align:start position:0% +touch a tool to actually use it to +actually fill out the data um with data + + align:start position:0% +actually fill out the data um with data + + + align:start position:0% +actually fill out the data um with data +that they've collected from a simul from + + align:start position:0% +that they've collected from a simul from + + + align:start position:0% +that they've collected from a simul from +at least a simulated reality and then + + align:start position:0% +at least a simulated reality and then + + + align:start position:0% +at least a simulated reality and then +use that to analyze it um so they can + + align:start position:0% +use that to analyze it um so they can + + + align:start position:0% +use that to analyze it um so they can +find bottlenecks they can find uh + + align:start position:0% +find bottlenecks they can find uh + + + align:start position:0% +find bottlenecks they can find uh +non-value added steps they can find uh + + align:start position:0% +non-value added steps they can find uh + + + align:start position:0% +non-value added steps they can find uh +places where paperwork and lack of + + align:start position:0% +places where paperwork and lack of + + + align:start position:0% +places where paperwork and lack of +synchronization are slowing the process + + align:start position:0% +synchronization are slowing the process + + + align:start position:0% +synchronization are slowing the process +down um and then Focus their + + align:start position:0% +down um and then Focus their + + + align:start position:0% +down um and then Focus their +improvements on those + + align:start position:0% +improvements on those + + + align:start position:0% +improvements on those +areas finally um at the end of the + + align:start position:0% +areas finally um at the end of the + + + align:start position:0% +areas finally um at the end of the +simulation we essentially as we do in + + align:start position:0% +simulation we essentially as we do in + + + align:start position:0% +simulation we essentially as we do in +the real world with uh with lean + + align:start position:0% +the real world with uh with lean + + + align:start position:0% +the real world with uh with lean +thinking ask them to + + align:start position:0% +thinking ask them to + + + align:start position:0% +thinking ask them to +expand their Horizon expand the + + align:start position:0% +expand their Horizon expand the + + + align:start position:0% +expand their Horizon expand the +boundaries of the Enterprise that + + align:start position:0% +boundaries of the Enterprise that + + + align:start position:0% +boundaries of the Enterprise that +they're considering and seeing if they + + align:start position:0% +they're considering and seeing if they + + + align:start position:0% +they're considering and seeing if they +can get bigger payoffs by doing more by + + align:start position:0% +can get bigger payoffs by doing more by + + + align:start position:0% +can get bigger payoffs by doing more by +by bringing in more functions uh in this + + align:start position:0% +by bringing in more functions uh in this + + + align:start position:0% +by bringing in more functions uh in this +case there's not an engineering function + + align:start position:0% +case there's not an engineering function + + + align:start position:0% +case there's not an engineering function +in this simulation but we do allow them + + align:start position:0% +in this simulation but we do allow them + + + align:start position:0% +in this simulation but we do allow them +to redesign the airplane um to cut part + + align:start position:0% +to redesign the airplane um to cut part + + + align:start position:0% +to redesign the airplane um to cut part +count reduce part types fix problems + + align:start position:0% +count reduce part types fix problems + + + align:start position:0% +count reduce part types fix problems +with the airplane make it easier to + + align:start position:0% +with the airplane make it easier to + + + align:start position:0% +with the airplane make it easier to +assemble do all of the things all of the + + align:start position:0% +assemble do all of the things all of the + + + align:start position:0% +assemble do all of the things all of the +U engineering functions that that uh + + align:start position:0% +U engineering functions that that uh + + + align:start position:0% +U engineering functions that that uh +facilitate lean in the real world um and + + align:start position:0% +facilitate lean in the real world um and + + + align:start position:0% +facilitate lean in the real world um and +again touch it understand it understand + + align:start position:0% +again touch it understand it understand + + + align:start position:0% +again touch it understand it understand +it in context and then see how it works + + align:start position:0% +it in context and then see how it works + + + align:start position:0% +it in context and then see how it works +in the final round and again by + + align:start position:0% +in the final round and again by + + + align:start position:0% +in the final round and again by +rebalancing work by redesigning the + + align:start position:0% +rebalancing work by redesigning the + + + align:start position:0% +rebalancing work by redesigning the +airplane um by by changing the facility + + align:start position:0% +airplane um by by changing the facility + + + align:start position:0% +airplane um by by changing the facility +uh organization and further mod + + align:start position:0% +uh organization and further mod + + + align:start position:0% +uh organization and further mod +modernizing the supply chain getting it + + align:start position:0% +modernizing the supply chain getting it + + + align:start position:0% +modernizing the supply chain getting it +getting into a really clean modern just + + align:start position:0% +getting into a really clean modern just + + + align:start position:0% +getting into a really clean modern just +in time supply chain um using the lean + + align:start position:0% +in time supply chain um using the lean + + + align:start position:0% +in time supply chain um using the lean +principles and implementing it on the + + align:start position:0% +principles and implementing it on the + + + align:start position:0% +principles and implementing it on the +simulation + + align:start position:0% +simulation + + + align:start position:0% +simulation +um they can get an outstanding process + + align:start position:0% +um they can get an outstanding process + + + align:start position:0% +um they can get an outstanding process +out of it and that gives them a real + + align:start position:0% +out of it and that gives them a real + + + align:start position:0% +out of it and that gives them a real +intuitive and tactile feel for how lean + + align:start position:0% +intuitive and tactile feel for how lean + + + align:start position:0% +intuitive and tactile feel for how lean +type uh product Improvement principles + + align:start position:0% +type uh product Improvement principles + + + align:start position:0% +type uh product Improvement principles +can be used to not just make a process + + align:start position:0% +can be used to not just make a process + + + align:start position:0% +can be used to not just make a process +better but to make it astonishingly + + align:start position:0% +better but to make it astonishingly + + + align:start position:0% +better but to make it astonishingly +better in a way that they that they + + align:start position:0% +better in a way that they that they + + + align:start position:0% +better in a way that they that they +usually do not think is possible when + + align:start position:0% +usually do not think is possible when + + + align:start position:0% +usually do not think is possible when +they start the simulation another thing + + align:start position:0% +they start the simulation another thing + + + align:start position:0% +they start the simulation another thing +that's uh that's done is throughout the + + align:start position:0% +that's uh that's done is throughout the + + + align:start position:0% +that's uh that's done is throughout the +simulation we embed um learning by doing + + align:start position:0% +simulation we embed um learning by doing + + + align:start position:0% +simulation we embed um learning by doing +sort of mini lessons and this is just a + + align:start position:0% +sort of mini lessons and this is just a + + + align:start position:0% +sort of mini lessons and this is just a +single example con Bond systems uh con + + align:start position:0% +single example con Bond systems uh con + + + align:start position:0% +single example con Bond systems uh con +bonds are a Inventory management um + + align:start position:0% +bonds are a Inventory management um + + + align:start position:0% +bonds are a Inventory management um +ordering um and transport system which + + align:start position:0% +ordering um and transport system which + + + align:start position:0% +ordering um and transport system which +is difficult to lecture to because it's + + align:start position:0% +is difficult to lecture to because it's + + + align:start position:0% +is difficult to lecture to because it's +a very simple thing that does a lot of + + align:start position:0% +a very simple thing that does a lot of + + + align:start position:0% +a very simple thing that does a lot of +that has a lot of different + + align:start position:0% +that has a lot of different + + + align:start position:0% +that has a lot of different +functionalities in the real world and + + align:start position:0% +functionalities in the real world and + + + align:start position:0% +functionalities in the real world and +solves a lot of problems in ways that + + align:start position:0% +solves a lot of problems in ways that + + + align:start position:0% +solves a lot of problems in ways that +are sometimes non-intuitive in the + + align:start position:0% +are sometimes non-intuitive in the + + + align:start position:0% +are sometimes non-intuitive in the +simulation they use con bonds to + + align:start position:0% +simulation they use con bonds to + + + align:start position:0% +simulation they use con bonds to +basically solve their inventory + + align:start position:0% +basically solve their inventory + + + align:start position:0% +basically solve their inventory +management and supply chain problems um + + align:start position:0% +management and supply chain problems um + + + align:start position:0% +management and supply chain problems um +and they get both uh repeated + + align:start position:0% +and they get both uh repeated + + + align:start position:0% +and they get both uh repeated +reintroduction to the concept and what + + align:start position:0% +reintroduction to the concept and what + + + align:start position:0% +reintroduction to the concept and what +they're doing and mentored execution of + + align:start position:0% +they're doing and mentored execution of + + + align:start position:0% +they're doing and mentored execution of +that Concept in the simulated world so + + align:start position:0% +that Concept in the simulated world so + + + align:start position:0% +that Concept in the simulated world so +they really do get an understanding of + + align:start position:0% +they really do get an understanding of + + + align:start position:0% +they really do get an understanding of +how a simple system like conon can serve + + align:start position:0% +how a simple system like conon can serve + + + align:start position:0% +how a simple system like conon can serve +so many functions and solve some of + + align:start position:0% + + + + align:start position:0% + +problems okay so the overall result and + + align:start position:0% +problems okay so the overall result and + + + align:start position:0% +problems okay so the overall result and +this is typical data from a real event + + align:start position:0% +this is typical data from a real event + + + align:start position:0% +this is typical data from a real event +is that they can go from producing no + + align:start position:0% +is that they can go from producing no + + + align:start position:0% +is that they can go from producing no +airplanes or maybe one the first time + + align:start position:0% +airplanes or maybe one the first time + + + align:start position:0% +airplanes or maybe one the first time +they try to producing a dozen the last + + align:start position:0% +they try to producing a dozen the last + + + align:start position:0% +they try to producing a dozen the last +time in the same time and using the same + + align:start position:0% +time in the same time and using the same + + + align:start position:0% +time in the same time and using the same +um same basic capabilities uh is they + + align:start position:0% +um same basic capabilities uh is they + + + align:start position:0% +um same basic capabilities uh is they +never get to throw the hourglasses away + + align:start position:0% +never get to throw the hourglasses away + + + align:start position:0% +never get to throw the hourglasses away +it never turns into a Lego building race + + align:start position:0% +it never turns into a Lego building race + + + align:start position:0% +it never turns into a Lego building race +this isn't just a learning curve what + + align:start position:0% +this isn't just a learning curve what + + + align:start position:0% +this isn't just a learning curve what +they've done is taken the process as it + + align:start position:0% +they've done is taken the process as it + + + align:start position:0% +they've done is taken the process as it +exists and made it much much better and + + align:start position:0% +exists and made it much much better and + + + align:start position:0% +exists and made it much much better and +tracking along with that is uh the + + align:start position:0% +tracking along with that is uh the + + + align:start position:0% +tracking along with that is uh the +financials which go from losing a lot of + + align:start position:0% +financials which go from losing a lot of + + + align:start position:0% +financials which go from losing a lot of +money to making a a lot not surprisingly + + align:start position:0% +money to making a a lot not surprisingly + + + align:start position:0% +money to making a a lot not surprisingly +but again they get a feel for how this + + align:start position:0% +but again they get a feel for how this + + + align:start position:0% +but again they get a feel for how this +kind of production efficiency can lead + + align:start position:0% +kind of production efficiency can lead + + + align:start position:0% +kind of production efficiency can lead +to a financial + + align:start position:0% +to a financial + + + align:start position:0% +to a financial +performance okay so we had a successful + + align:start position:0% +performance okay so we had a successful + + + align:start position:0% +performance okay so we had a successful +U conclusion of our of our simulation + + align:start position:0% +U conclusion of our of our simulation + + + align:start position:0% +U conclusion of our of our simulation +exercise all of our tables managed to + + align:start position:0% +exercise all of our tables managed to + + + align:start position:0% +exercise all of our tables managed to +produce at least eight aircraft uh one + + align:start position:0% +produce at least eight aircraft uh one + + + align:start position:0% +produce at least eight aircraft uh one +table got all the way up to the 12 that + + align:start position:0% +table got all the way up to the 12 that + + + align:start position:0% +table got all the way up to the 12 that +the customer really wanted and we had an + + align:start position:0% +the customer really wanted and we had an + + + align:start position:0% +the customer really wanted and we had an +11 and a 10 everybody got got there by + + align:start position:0% +11 and a 10 everybody got got there by + + + align:start position:0% +11 and a 10 everybody got got there by +by a somewhat different uh route and we + + align:start position:0% +by a somewhat different uh route and we + + + align:start position:0% +by a somewhat different uh route and we +learned some lessons along the way um + + align:start position:0% +learned some lessons along the way um + + + align:start position:0% +learned some lessons along the way um +our group that that produced eight now + + align:start position:0% +our group that that produced eight now + + + align:start position:0% +our group that that produced eight now +that was still better than the than the + + align:start position:0% +that was still better than the than the + + + align:start position:0% +that was still better than the than the +theoretical maximum six they were making + + align:start position:0% +theoretical maximum six they were making + + + align:start position:0% +theoretical maximum six they were making +before um but they didn't meet meet the + + align:start position:0% +before um but they didn't meet meet the + + + align:start position:0% +before um but they didn't meet meet the +theoretical capacity of 12 because they + + align:start position:0% +theoretical capacity of 12 because they + + + align:start position:0% +theoretical capacity of 12 because they +still hadn't ironed out issues with + + align:start position:0% +still hadn't ironed out issues with + + + align:start position:0% +still hadn't ironed out issues with +their supply chain and with coordinating + + align:start position:0% +their supply chain and with coordinating + + + align:start position:0% +their supply chain and with coordinating +it wasn't that they didn't have the + + align:start position:0% +it wasn't that they didn't have the + + + align:start position:0% +it wasn't that they didn't have the +theoretical capacity it was that the + + align:start position:0% +theoretical capacity it was that the + + + align:start position:0% +theoretical capacity it was that the +coordination of the different um + + align:start position:0% +coordination of the different um + + + align:start position:0% +coordination of the different um +components of their Enterprise wasn't + + align:start position:0% +components of their Enterprise wasn't + + + align:start position:0% +components of their Enterprise wasn't +wasn't completely ironed out yet um so + + align:start position:0% +wasn't completely ironed out yet um so + + + align:start position:0% +wasn't completely ironed out yet um so +they they uh didn't meet their + + align:start position:0% +they they uh didn't meet their + + + align:start position:0% +they they uh didn't meet their +production goals very interesting the + + align:start position:0% +production goals very interesting the + + + align:start position:0% +production goals very interesting the +group that made 11 airplanes did get + + align:start position:0% +group that made 11 airplanes did get + + + align:start position:0% +group that made 11 airplanes did get +everything coordinated they did a very + + align:start position:0% +everything coordinated they did a very + + + align:start position:0% +everything coordinated they did a very +good job one order one order was one + + align:start position:0% +good job one order one order was one + + + align:start position:0% +good job one order one order was one +piece short and in a lean system you're + + align:start position:0% +piece short and in a lean system you're + + + align:start position:0% +piece short and in a lean system you're +very vulnerable to that kind of + + align:start position:0% +very vulnerable to that kind of + + + align:start position:0% +very vulnerable to that kind of +disruption that one order that one piece + + align:start position:0% +disruption that one order that one piece + + + align:start position:0% +disruption that one order that one piece +in that one order cost them an airplane + + align:start position:0% +in that one order cost them an airplane + + + align:start position:0% +in that one order cost them an airplane +because it disrupted their uh their + + align:start position:0% +because it disrupted their uh their + + + align:start position:0% +because it disrupted their uh their +synchronization it took them a minute to + + align:start position:0% +synchronization it took them a minute to + + + align:start position:0% +synchronization it took them a minute to +recover that was an airplane uh still + + align:start position:0% +recover that was an airplane uh still + + + align:start position:0% +recover that was an airplane uh still +that doesn't that is a known issue with + + align:start position:0% +that doesn't that is a known issue with + + + align:start position:0% +that doesn't that is a known issue with +Le production systems not necessarily a + + align:start position:0% +Le production systems not necessarily a + + + align:start position:0% +Le production systems not necessarily a +bad thing that uh the the issue the the + + align:start position:0% +bad thing that uh the the issue the the + + + align:start position:0% +bad thing that uh the the issue the the +problem that caused the one order to be + + align:start position:0% +problem that caused the one order to be + + + align:start position:0% +problem that caused the one order to be +bad was surfaced immediately and in the + + align:start position:0% +bad was surfaced immediately and in the + + + align:start position:0% +bad was surfaced immediately and in the +in the future that happened actually + + align:start position:0% +in the future that happened actually + + + align:start position:0% +in the future that happened actually +early in the round and they didn't do it + + align:start position:0% +early in the round and they didn't do it + + + align:start position:0% +early in the round and they didn't do it +again and of course they achieved 11 + + align:start position:0% +again and of course they achieved 11 + + + align:start position:0% +again and of course they achieved 11 +which is a lot better than than seven + + align:start position:0% +which is a lot better than than seven + + + align:start position:0% +which is a lot better than than seven +aircraft and we had one uh group that + + align:start position:0% +aircraft and we had one uh group that + + + align:start position:0% +aircraft and we had one uh group that +was hitting on all cylinders and managed + + align:start position:0% +was hitting on all cylinders and managed + + + align:start position:0% +was hitting on all cylinders and managed +to produce the aircraft a minute that + + align:start position:0% +to produce the aircraft a minute that + + + align:start position:0% +to produce the aircraft a minute that +the customers really wanted um + + align:start position:0% +the customers really wanted um + + + align:start position:0% +the customers really wanted um +interestingly too if we look over the + + align:start position:0% +interestingly too if we look over the + + + align:start position:0% +interestingly too if we look over the +course of the whole day + + align:start position:0% +course of the whole day + + + align:start position:0% +course of the whole day +um the production little bit of + + align:start position:0% +um the production little bit of + + + align:start position:0% +um the production little bit of +variation basically everybody's + + align:start position:0% +variation basically everybody's + + + align:start position:0% +variation basically everybody's +improving production as they go along + + align:start position:0% +improving production as they go along + + + align:start position:0% +improving production as they go along +the financial results uh show some + + align:start position:0% +the financial results uh show some + + + align:start position:0% +the financial results uh show some +interesting detail it's harder to see in + + align:start position:0% +interesting detail it's harder to see in + + + align:start position:0% +interesting detail it's harder to see in +the production diagram um which is that + + align:start position:0% +the production diagram um which is that + + + align:start position:0% +the production diagram um which is that +although everybody's um profit + + align:start position:0% +although everybody's um profit + + + align:start position:0% +although everybody's um profit +improved people took different paths and + + align:start position:0% +improved people took different paths and + + + align:start position:0% +improved people took different paths and +this has been a great class uh for this + + align:start position:0% +this has been a great class uh for this + + + align:start position:0% +this has been a great class uh for this +because basically the paths people took + + align:start position:0% +because basically the paths people took + + + align:start position:0% +because basically the paths people took +pretty much mirror the kinds of things + + align:start position:0% +pretty much mirror the kinds of things + + + align:start position:0% +pretty much mirror the kinds of things +um that can happen in the real world uh + + align:start position:0% +um that can happen in the real world uh + + + align:start position:0% +um that can happen in the real world uh +when you go into Improvement uh events + + align:start position:0% +when you go into Improvement uh events + + + align:start position:0% +when you go into Improvement uh events +uh group number one started out losing a + + align:start position:0% +uh group number one started out losing a + + + align:start position:0% +uh group number one started out losing a +lot of money as soon as they stabilized + + align:start position:0% +lot of money as soon as they stabilized + + + align:start position:0% +lot of money as soon as they stabilized +their traditional process they actually + + align:start position:0% +their traditional process they actually + + + align:start position:0% +their traditional process they actually +managed to make money and when they + + align:start position:0% +managed to make money and when they + + + align:start position:0% +managed to make money and when they +disrupted it trying to lean it out they + + align:start position:0% +disrupted it trying to lean it out they + + + align:start position:0% +disrupted it trying to lean it out they +uh had a had what we call a worse before + + align:start position:0% +uh had a had what we call a worse before + + + align:start position:0% +uh had a had what we call a worse before +better things actually got worse until + + align:start position:0% +better things actually got worse until + + + align:start position:0% +better things actually got worse until +they got better again and stabilized at + + align:start position:0% +they got better again and stabilized at + + + align:start position:0% +they got better again and stabilized at +a high-profit situation um + + align:start position:0% +a high-profit situation um + + + align:start position:0% +a high-profit situation um +group number two showed a much steadier + + align:start position:0% +group number two showed a much steadier + + + align:start position:0% +group number two showed a much steadier +increase in profit um they basically + + align:start position:0% +increase in profit um they basically + + + align:start position:0% +increase in profit um they basically +showed an almost linear Improvement so + + align:start position:0% +showed an almost linear Improvement so + + + align:start position:0% +showed an almost linear Improvement so +they were they were not so disrupted by + + align:start position:0% +they were they were not so disrupted by + + + align:start position:0% +they were they were not so disrupted by +change um didn't didn't come to Quick + + align:start position:0% +change um didn't didn't come to Quick + + + align:start position:0% +change um didn't didn't come to Quick +results but by uh learning slowly and + + align:start position:0% +results but by uh learning slowly and + + + align:start position:0% +results but by uh learning slowly and +steadily as they as they went through + + align:start position:0% +steadily as they as they went through + + + align:start position:0% +steadily as they as they went through +the transformation process managed to + + align:start position:0% +the transformation process managed to + + + align:start position:0% +the transformation process managed to +increase their profits steadily that's + + align:start position:0% +increase their profits steadily that's + + + align:start position:0% +increase their profits steadily that's +nice because that looks good um it's not + + align:start position:0% +nice because that looks good um it's not + + + align:start position:0% +nice because that looks good um it's not +always what happens uh the green the uh + + align:start position:0% +always what happens uh the green the uh + + + align:start position:0% +always what happens uh the green the uh +sorry blue team showed again a typical + + align:start position:0% +sorry blue team showed again a typical + + + align:start position:0% +sorry blue team showed again a typical +reaction they U stabilized and then in + + align:start position:0% +reaction they U stabilized and then in + + + align:start position:0% +reaction they U stabilized and then in +the actual Improvement round the round + + align:start position:0% +the actual Improvement round the round + + + align:start position:0% +the actual Improvement round the round +where they changed things showed at best + + align:start position:0% +where they changed things showed at best + + + align:start position:0% +where they changed things showed at best +steady Financial results so this was + + align:start position:0% +steady Financial results so this was + + + align:start position:0% +steady Financial results so this was +learning in a given state but they would + + align:start position:0% +learning in a given state but they would + + + align:start position:0% +learning in a given state but they would +have maxed out there uh during the um + + align:start position:0% +have maxed out there uh during the um + + + align:start position:0% +have maxed out there uh during the um +transformation they didn't make more + + align:start position:0% +transformation they didn't make more + + + align:start position:0% +transformation they didn't make more +money but that set them up for the uh + + align:start position:0% +money but that set them up for the uh + + + align:start position:0% +money but that set them up for the uh +the next round where they made a lot and + + align:start position:0% +the next round where they made a lot and + + + align:start position:0% +the next round where they made a lot and +again during the next transformation + + align:start position:0% +again during the next transformation + + + align:start position:0% +again during the next transformation +they flattened off again this is a lot + + align:start position:0% +they flattened off again this is a lot + + + align:start position:0% +they flattened off again this is a lot +nicer than that worse before better uh + + align:start position:0% +nicer than that worse before better uh + + + align:start position:0% +nicer than that worse before better uh +but it's still very typical while you're + + align:start position:0% +but it's still very typical while you're + + + align:start position:0% +but it's still very typical while you're +investing the resources while you're + + align:start position:0% +investing the resources while you're + + + align:start position:0% +investing the resources while you're +changing things you can't expect the + + align:start position:0% +changing things you can't expect the + + + align:start position:0% +changing things you can't expect the +dramatic Financial results to happen + + align:start position:0% +dramatic Financial results to happen + + + align:start position:0% +dramatic Financial results to happen +right away what you do is set yourself + + align:start position:0% +right away what you do is set yourself + + + align:start position:0% +right away what you do is set yourself +up for dramatic improvements uh in the + + align:start position:0% +up for dramatic improvements uh in the + + + align:start position:0% +up for dramatic improvements uh in the +next period and we had a final um final + + align:start position:0% +next period and we had a final um final + + + align:start position:0% +next period and we had a final um final +Group which also did the worst before + + align:start position:0% +Group which also did the worst before + + + align:start position:0% +Group which also did the worst before +better thing it had a little bit of a + + align:start position:0% +better thing it had a little bit of a + + + align:start position:0% +better thing it had a little bit of a +unfortunate + + align:start position:0% +unfortunate + + + align:start position:0% +unfortunate +um end result which is the very last + + align:start position:0% +um end result which is the very last + + + align:start position:0% +um end result which is the very last +round they actually had a worse and that + + align:start position:0% +round they actually had a worse and that + + + align:start position:0% +round they actually had a worse and that +was the group that only made the eight + + align:start position:0% +was the group that only made the eight + + + align:start position:0% +was the group that only made the eight +aircraft um they were quite certain uh + + align:start position:0% +aircraft um they were quite certain uh + + + align:start position:0% +aircraft um they were quite certain uh +if we' done another round that they + + align:start position:0% +if we' done another round that they + + + align:start position:0% +if we' done another round that they +could have gotten the 12 and in fact + + align:start position:0% +could have gotten the 12 and in fact + + + align:start position:0% +could have gotten the 12 and in fact +completed their zigzag worse before + + align:start position:0% +completed their zigzag worse before + + + align:start position:0% +completed their zigzag worse before +better + + align:start position:0% +better + + + align:start position:0% +better +Journey so that's a description of the + + align:start position:0% +Journey so that's a description of the + + + align:start position:0% +Journey so that's a description of the +simulation and how it's used um I'm + + align:start position:0% +simulation and how it's used um I'm + + + align:start position:0% +simulation and how it's used um I'm +going to do a brief description of uh + + align:start position:0% +going to do a brief description of uh + + + align:start position:0% +going to do a brief description of uh +the sort of pedagogical goals of the + + align:start position:0% +the sort of pedagogical goals of the + + + align:start position:0% +the sort of pedagogical goals of the +simulation and how we think they've been + + align:start position:0% +simulation and how we think they've been + + + align:start position:0% +simulation and how we think they've been +achieved in the lean uh lean Academy + + align:start position:0% +achieved in the lean uh lean Academy + + + align:start position:0% +achieved in the lean uh lean Academy +context we said that we wanted it to + + align:start position:0% +context we said that we wanted it to + + + align:start position:0% +context we said that we wanted it to +increase the comprehension of + + align:start position:0% +increase the comprehension of + + + align:start position:0% +increase the comprehension of +the U curriculum and there is some + + align:start position:0% +the U curriculum and there is some + + + align:start position:0% +the U curriculum and there is some +literature evidence that that this is + + align:start position:0% +literature evidence that that this is + + + align:start position:0% +literature evidence that that this is +that this works um in + + align:start position:0% +that this works um in + + + align:start position:0% +that this works um in +particular uh in the computer world + + align:start position:0% +particular uh in the computer world + + + align:start position:0% +particular uh in the computer world +people have played computer games versus + + align:start position:0% +people have played computer games versus + + + align:start position:0% +people have played computer games versus +static computer websites and it's been + + align:start position:0% +static computer websites and it's been + + + align:start position:0% +static computer websites and it's been +shown that the little games and these + + align:start position:0% +shown that the little games and these + + + align:start position:0% +shown that the little games and these +are little toy games but the little + + align:start position:0% +are little toy games but the little + + + align:start position:0% +are little toy games but the little +games basically make people uh retain + + align:start position:0% +games basically make people uh retain + + + align:start position:0% +games basically make people uh retain +the material much better um and also if + + align:start position:0% +the material much better um and also if + + + align:start position:0% +the material much better um and also if +you look at Behavior Uh there's been + + align:start position:0% +you look at Behavior Uh there's been + + + align:start position:0% +you look at Behavior Uh there's been +studies on things like healthy diet uh + + align:start position:0% +studies on things like healthy diet uh + + + align:start position:0% +studies on things like healthy diet uh +that people that have learned through + + align:start position:0% +that people that have learned through + + + align:start position:0% +that people that have learned through +game-based learning as opposed to static + + align:start position:0% +game-based learning as opposed to static + + + align:start position:0% +game-based learning as opposed to static +learning uh + + align:start position:0% +learning uh + + + align:start position:0% +learning uh +actually take not not only learn and + + align:start position:0% +actually take not not only learn and + + + align:start position:0% +actually take not not only learn and +retain the information better but it + + align:start position:0% +retain the information better but it + + + align:start position:0% +retain the information better but it +actually affects the outcome um so + + align:start position:0% +actually affects the outcome um so + + + align:start position:0% +actually affects the outcome um so +that's good that evidence is is uh is + + align:start position:0% +that's good that evidence is is uh is + + + align:start position:0% +that's good that evidence is is uh is +there we also hope that uh that there's + + align:start position:0% +there we also hope that uh that there's + + + align:start position:0% +there we also hope that uh that there's +better understanding of the context and + + align:start position:0% +better understanding of the context and + + + align:start position:0% +better understanding of the context and +in the holistic nature of the material + + align:start position:0% +in the holistic nature of the material + + + align:start position:0% +in the holistic nature of the material +and we hope that they learn through + + align:start position:0% +and we hope that they learn through + + + align:start position:0% +and we hope that they learn through +experience that it engages different + + align:start position:0% +experience that it engages different + + + align:start position:0% +experience that it engages different +learning modes um and that it allows + + align:start position:0% +learning modes um and that it allows + + + align:start position:0% +learning modes um and that it allows +them a practice field to actually touch + + align:start position:0% +them a practice field to actually touch + + + align:start position:0% +them a practice field to actually touch +and use the ideas um these are supported + + align:start position:0% +and use the ideas um these are supported + + + align:start position:0% +and use the ideas um these are supported +as goals um but there's not really a + + align:start position:0% +as goals um but there's not really a + + + align:start position:0% +as goals um but there's not really a +whole lot of scientific evidence that + + align:start position:0% +whole lot of scientific evidence that + + + align:start position:0% +whole lot of scientific evidence that +this works intuitively it's the evidence + + align:start position:0% +this works intuitively it's the evidence + + + align:start position:0% +this works intuitively it's the evidence +is pretty powerful and the anecdotal + + align:start position:0% +is pretty powerful and the anecdotal + + + align:start position:0% +is pretty powerful and the anecdotal +experience from the students is is + + align:start position:0% +experience from the students is is + + + align:start position:0% +experience from the students is is +powerful um it's not a proven outcome um + + align:start position:0% +powerful um it's not a proven outcome um + + + align:start position:0% +powerful um it's not a proven outcome um +and we can certainly say that we've + + align:start position:0% +and we can certainly say that we've + + + align:start position:0% +and we can certainly say that we've +observed uh greatly increased student + + align:start position:0% +observed uh greatly increased student + + + align:start position:0% +observed uh greatly increased student +involvement and + + align:start position:0% +involvement and + + + align:start position:0% +involvement and +excitement yeah I mean we were on the + + align:start position:0% +excitement yeah I mean we were on the + + + align:start position:0% +excitement yeah I mean we were on the +same team for the the Lego simulation + + align:start position:0% +same team for the the Lego simulation + + + align:start position:0% +same team for the the Lego simulation +and it was a lot of fun um especially + + align:start position:0% +and it was a lot of fun um especially + + + align:start position:0% +and it was a lot of fun um especially +since we got you know a little + + align:start position:0% +since we got you know a little + + + align:start position:0% +since we got you know a little +competitive with the other teams and + + align:start position:0% +competitive with the other teams and + + + align:start position:0% +competitive with the other teams and +trying to build the most airplanes but + + align:start position:0% +trying to build the most airplanes but + + + align:start position:0% +trying to build the most airplanes but +um and it was really cool you know it's + + align:start position:0% +um and it was really cool you know it's + + + align:start position:0% +um and it was really cool you know it's +something that we played with ever since + + align:start position:0% +something that we played with ever since + + + align:start position:0% +something that we played with ever since +we were little kids and uh you know to + + align:start position:0% +we were little kids and uh you know to + + + align:start position:0% +we were little kids and uh you know to +be able to to build something but then + + align:start position:0% +be able to to build something but then + + + align:start position:0% +be able to to build something but then +apply the lean principles I think was + + align:start position:0% +apply the lean principles I think was + + + align:start position:0% +apply the lean principles I think was +really amazing to see how much we + + align:start position:0% +really amazing to see how much we + + + align:start position:0% +really amazing to see how much we +learned through that it was probably the + + align:start position:0% +learned through that it was probably the + + + align:start position:0% +learned through that it was probably the +best way of demonstrating how a process + + align:start position:0% +best way of demonstrating how a process + + + align:start position:0% +best way of demonstrating how a process +that I thought you know was efficient at + + align:start position:0% +that I thought you know was efficient at + + + align:start position:0% +that I thought you know was efficient at +first and after applying lean we didn't + + align:start position:0% +first and after applying lean we didn't + + + align:start position:0% +first and after applying lean we didn't +think we could make 12 airplanes in 12 + + align:start position:0% +think we could make 12 airplanes in 12 + + + align:start position:0% +think we could make 12 airplanes in 12 +minutes but well we almost made it we + + align:start position:0% +minutes but well we almost made it we + + + align:start position:0% +minutes but well we almost made it we +made 10 but it is possible to do what + + align:start position:0% +made 10 but it is possible to do what + + + align:start position:0% +made 10 but it is possible to do what +some believe is impossible at first and + + align:start position:0% +some believe is impossible at first and + + + align:start position:0% +some believe is impossible at first and +after applying the analysis and getting + + align:start position:0% +after applying the analysis and getting + + + align:start position:0% +after applying the analysis and getting +all the processes down correctly we were + + align:start position:0% +all the processes down correctly we were + + + align:start position:0% +all the processes down correctly we were +getting pretty close I mean it was + + align:start position:0% +getting pretty close I mean it was + + + align:start position:0% +getting pretty close I mean it was +pretty amazing I you know was looking at + + align:start position:0% +pretty amazing I you know was looking at + + + align:start position:0% +pretty amazing I you know was looking at +the chart after and I was like wait we + + align:start position:0% +the chart after and I was like wait we + + + align:start position:0% +the chart after and I was like wait we +really only made one in 12 minutes the + + align:start position:0% +really only made one in 12 minutes the + + + align:start position:0% +really only made one in 12 minutes the +first time and then you know went all to + + align:start position:0% +first time and then you know went all to + + + align:start position:0% +first time and then you know went all to +10 so we're impressed yeah so we think + + align:start position:0% +10 so we're impressed yeah so we think + + + align:start position:0% +10 so we're impressed yeah so we think +this is working we also uh have had very + + align:start position:0% +this is working we also uh have had very + + + align:start position:0% +this is working we also uh have had very +positive + + align:start position:0% +positive + + + align:start position:0% +positive +experience with um basically teaching + + align:start position:0% +experience with um basically teaching + + + align:start position:0% +experience with um basically teaching +complicated systems most of the previous + + align:start position:0% +complicated systems most of the previous + + + align:start position:0% +complicated systems most of the previous +literature evidence was on relatively + + align:start position:0% +literature evidence was on relatively + + + align:start position:0% +literature evidence was on relatively +simple things fact-based uh things um + + align:start position:0% +simple things fact-based uh things um + + + align:start position:0% +simple things fact-based uh things um +we're actually trying to teach a system + + align:start position:0% +we're actually trying to teach a system + + + align:start position:0% +we're actually trying to teach a system +that affects other systems so it's it's + + align:start position:0% +that affects other systems so it's it's + + + align:start position:0% +that affects other systems so it's it's +a complicated uh body of knowledge body + + align:start position:0% +a complicated uh body of knowledge body + + + align:start position:0% +a complicated uh body of knowledge body +of understanding that the students are + + align:start position:0% +of understanding that the students are + + + align:start position:0% +of understanding that the students are +expecting to absorb in a relatively + + align:start position:0% +expecting to absorb in a relatively + + + align:start position:0% +expecting to absorb in a relatively +short time and most of these kind of + + align:start position:0% +short time and most of these kind of + + + align:start position:0% +short time and most of these kind of +systems are not available for + + align:start position:0% +systems are not available for + + + align:start position:0% +systems are not available for +manipulation for teaching purposes you + + align:start position:0% +manipulation for teaching purposes you + + + align:start position:0% +manipulation for teaching purposes you +can't go play with an airplane Factory + + align:start position:0% +can't go play with an airplane Factory + + + align:start position:0% +can't go play with an airplane Factory +um we found that the students have a + + align:start position:0% +um we found that the students have a + + + align:start position:0% +um we found that the students have a +good experience and this experience is + + align:start position:0% +good experience and this experience is + + + align:start position:0% +good experience and this experience is +not limited to this particular + + align:start position:0% +not limited to this particular + + + align:start position:0% +not limited to this particular +simulation although this is a good + + align:start position:0% +simulation although this is a good + + + align:start position:0% +simulation although this is a good +Exemplar of it um if the simulation is + + align:start position:0% +Exemplar of it um if the simulation is + + + align:start position:0% +Exemplar of it um if the simulation is +complex enough to capture the key + + align:start position:0% +complex enough to capture the key + + + align:start position:0% +complex enough to capture the key +features including the emergent + + align:start position:0% +features including the emergent + + + align:start position:0% +features including the emergent +behaviors of the system if it's too + + align:start position:0% +behaviors of the system if it's too + + + align:start position:0% +behaviors of the system if it's too +simple you're not really changing + + align:start position:0% +simple you're not really changing + + + align:start position:0% +simple you're not really changing +anything you're not really changing a + + align:start position:0% +anything you're not really changing a + + + align:start position:0% +anything you're not really changing a +system that that has unexpected + + align:start position:0% +system that that has unexpected + + + align:start position:0% +system that that has unexpected +behaviors so you're not going to capture + + align:start position:0% +behaviors so you're not going to capture + + + align:start position:0% +behaviors so you're not going to capture +this kind of learning um on the other + + align:start position:0% +this kind of learning um on the other + + + align:start position:0% +this kind of learning um on the other +hand it has to be simple enough to have + + align:start position:0% +hand it has to be simple enough to have + + + align:start position:0% +hand it has to be simple enough to have +an acceptable learning curve if it takes + + align:start position:0% +an acceptable learning curve if it takes + + + align:start position:0% +an acceptable learning curve if it takes +three days to learn it's not it's not + + align:start position:0% +three days to learn it's not it's not + + + align:start position:0% +three days to learn it's not it's not +going to be a teaching tool um and of + + align:start position:0% +going to be a teaching tool um and of + + + align:start position:0% +going to be a teaching tool um and of +course it has to be fast enough that you + + align:start position:0% +course it has to be fast enough that you + + + align:start position:0% +course it has to be fast enough that you +can do multiple cycles of learning um + + align:start position:0% +can do multiple cycles of learning um + + + align:start position:0% +can do multiple cycles of learning um +within the teaching period it also has + + align:start position:0% +within the teaching period it also has + + + align:start position:0% +within the teaching period it also has +to be credible uh in the sense that it + + align:start position:0% +to be credible uh in the sense that it + + + align:start position:0% +to be credible uh in the sense that it +can't have artifacts that the students + + align:start position:0% +can't have artifacts that the students + + + align:start position:0% +can't have artifacts that the students +say well um this is not realistic and + + align:start position:0% +say well um this is not realistic and + + + align:start position:0% +say well um this is not realistic and +therefore I will dismiss the experience + + align:start position:0% +therefore I will dismiss the experience + + + align:start position:0% +therefore I will dismiss the experience +because I don't believe it um and it has + + align:start position:0% +because I don't believe it um and it has + + + align:start position:0% +because I don't believe it um and it has +to be fun to keep people engaged um and + + align:start position:0% +to be fun to keep people engaged um and + + + align:start position:0% +to be fun to keep people engaged um and +basically on this set of criteria uh we + + align:start position:0% +basically on this set of criteria uh we + + + align:start position:0% +basically on this set of criteria uh we +think that the the simulation that we + + align:start position:0% +think that the the simulation that we + + + align:start position:0% +think that the the simulation that we +use in the lean Academy um is pretty + + align:start position:0% +use in the lean Academy um is pretty + + + align:start position:0% +use in the lean Academy um is pretty +good students think it's pretty good too + + align:start position:0% +good students think it's pretty good too + + + align:start position:0% +good students think it's pretty good too +um this is feedback from about 200 + + align:start position:0% +um this is feedback from about 200 + + + align:start position:0% +um this is feedback from about 200 +students 194 students over a couple of + + align:start position:0% +students 194 students over a couple of + + + align:start position:0% +students 194 students over a couple of +years of leanies and we consistently get + + align:start position:0% +years of leanies and we consistently get + + + align:start position:0% +years of leanies and we consistently get +the uh the highest score of the types of + + align:start position:0% +the uh the highest score of the types of + + + align:start position:0% +the uh the highest score of the types of +learning + + align:start position:0% +learning + + + align:start position:0% +learning +uh both other Active Learning and + + align:start position:0% +uh both other Active Learning and + + + align:start position:0% +uh both other Active Learning and +lecture materials um that the lean + + align:start position:0% +lecture materials um that the lean + + + align:start position:0% +lecture materials um that the lean +Academy simulation provides positive + + align:start position:0% +Academy simulation provides positive + + + align:start position:0% +Academy simulation provides positive +reinforcement of the concepts that's the + + align:start position:0% +reinforcement of the concepts that's the + + + align:start position:0% +reinforcement of the concepts that's the +that's the wording of the question and + + align:start position:0% +that's the wording of the question and + + + align:start position:0% +that's the wording of the question and +the students agree that that's the case + + align:start position:0% +the students agree that that's the case + + + align:start position:0% +the students agree that that's the case +um just qualitatively we also get U some + + align:start position:0% +um just qualitatively we also get U some + + + align:start position:0% +um just qualitatively we also get U some +written feedback and and verbal feedback + + align:start position:0% +written feedback and and verbal feedback + + + align:start position:0% +written feedback and and verbal feedback +and it appears and again this is this is + + align:start position:0% +and it appears and again this is this is + + + align:start position:0% +and it appears and again this is this is +UN um unprompted we asked them the + + align:start position:0% +UN um unprompted we asked them the + + + align:start position:0% +UN um unprompted we asked them the +general question what do you like about + + align:start position:0% +general question what do you like about + + + align:start position:0% +general question what do you like about +the about the course and what do you + + align:start position:0% +the about the course and what do you + + + align:start position:0% +the about the course and what do you +don't like and what we find is what they + + align:start position:0% +don't like and what we find is what they + + + align:start position:0% +don't like and what we find is what they +like is what we're hoping which is that + + align:start position:0% +like is what we're hoping which is that + + + align:start position:0% +like is what we're hoping which is that +it increases the the comprehension of + + align:start position:0% +it increases the the comprehension of + + + align:start position:0% +it increases the the comprehension of +the curriculum um that the Hands-On + + align:start position:0% +the curriculum um that the Hands-On + + + align:start position:0% +the curriculum um that the Hands-On +learning and practice field experiences + + align:start position:0% +learning and practice field experiences + + + align:start position:0% +learning and practice field experiences +are valuable to them um and and that it + + align:start position:0% +are valuable to them um and and that it + + + align:start position:0% +are valuable to them um and and that it +uh that it increases their involvement + + align:start position:0% +uh that it increases their involvement + + + align:start position:0% +uh that it increases their involvement +and excitement with the + + align:start position:0% +and excitement with the + + + align:start position:0% +and excitement with the +material as well as uh and this was not + + align:start position:0% +material as well as uh and this was not + + + align:start position:0% +material as well as uh and this was not +explicit but it does show up a lot in + + align:start position:0% +explicit but it does show up a lot in + + + align:start position:0% +explicit but it does show up a lot in +the student responses as a team building + + align:start position:0% +the student responses as a team building + + + align:start position:0% +the student responses as a team building +and camaraderie building activity it's + + align:start position:0% +and camaraderie building activity it's + + + align:start position:0% +and camaraderie building activity it's +also very effective and this is just a + + align:start position:0% +also very effective and this is just a + + + align:start position:0% +also very effective and this is just a +numerical breakdown of those kinds of + + align:start position:0% +numerical breakdown of those kinds of + + + align:start position:0% +numerical breakdown of those kinds of +responses um out of + + align:start position:0% +responses um out of + + + align:start position:0% +responses um out of +106 uh written responses um we got a lot + + align:start position:0% +106 uh written responses um we got a lot + + + align:start position:0% +106 uh written responses um we got a lot +of Illuminating a fair number we like + + align:start position:0% +of Illuminating a fair number we like + + + align:start position:0% +of Illuminating a fair number we like +the Hands-On aspect and the excitement + + align:start position:0% +the Hands-On aspect and the excitement + + + align:start position:0% +the Hands-On aspect and the excitement +and bonding were kind of uh uh somewhat + + align:start position:0% +and bonding were kind of uh uh somewhat + + + align:start position:0% +and bonding were kind of uh uh somewhat +secondary but but mentioned as well as a + + align:start position:0% +secondary but but mentioned as well as a + + + align:start position:0% +secondary but but mentioned as well as a +Big Blob is just sort of generic we like + + align:start position:0% +Big Blob is just sort of generic we like + + + align:start position:0% +Big Blob is just sort of generic we like +it but that doesn't that doesn't tell us + + align:start position:0% +it but that doesn't that doesn't tell us + + + align:start position:0% +it but that doesn't that doesn't tell us +a whole bunch about why they like it but + + align:start position:0% +a whole bunch about why they like it but + + + align:start position:0% +a whole bunch about why they like it but +these do and it's kind of what we're + + align:start position:0% +these do and it's kind of what we're + + + align:start position:0% +these do and it's kind of what we're +hoping um caveats always important this + + align:start position:0% +hoping um caveats always important this + + + align:start position:0% +hoping um caveats always important this +evaluation is based on satisfaction not + + align:start position:0% +evaluation is based on satisfaction not + + + align:start position:0% +evaluation is based on satisfaction not +really outcomes we don't track the + + align:start position:0% +really outcomes we don't track the + + + align:start position:0% +really outcomes we don't track the +students in their in their careers as + + align:start position:0% +students in their in their careers as + + + align:start position:0% +students in their in their careers as +aerospace engineers so we uh don't have + + align:start position:0% +aerospace engineers so we uh don't have + + + align:start position:0% +aerospace engineers so we uh don't have +outcome metrics yet um it's cost and + + align:start position:0% +outcome metrics yet um it's cost and + + + align:start position:0% +outcome metrics yet um it's cost and +time intensive to do this kind of thing + + align:start position:0% +time intensive to do this kind of thing + + + align:start position:0% +time intensive to do this kind of thing +you need trained facilitators it takes + + align:start position:0% +you need trained facilitators it takes + + + align:start position:0% +you need trained facilitators it takes +money to set up a a facility to do this + + align:start position:0% +money to set up a a facility to do this + + + align:start position:0% +money to set up a a facility to do this +couple thousand dollars that's the + + align:start position:0% +couple thousand dollars that's the + + + align:start position:0% +couple thousand dollars that's the +startup cost not the per per each + + align:start position:0% +startup cost not the per per each + + + align:start position:0% +startup cost not the per per each +although you do have to pay these people + + align:start position:0% +although you do have to pay these people + + + align:start position:0% +although you do have to pay these people +somehow um they're vulnerable to + + align:start position:0% +somehow um they're vulnerable to + + + align:start position:0% +somehow um they're vulnerable to +disruption um Logistics facility failure + + align:start position:0% +disruption um Logistics facility failure + + + align:start position:0% +disruption um Logistics facility failure +to keep on schedule kind of Errors can + + align:start position:0% +to keep on schedule kind of Errors can + + + align:start position:0% +to keep on schedule kind of Errors can +degrade the uh the experience badly um + + align:start position:0% +degrade the uh the experience badly um + + + align:start position:0% +degrade the uh the experience badly um +our simulation seems to be fairly robust + + align:start position:0% +our simulation seems to be fairly robust + + + align:start position:0% +our simulation seems to be fairly robust +but the uh but in general simulations + + align:start position:0% +but the uh but in general simulations + + + align:start position:0% +but the uh but in general simulations +are vulnerable to disruption and you + + align:start position:0% +are vulnerable to disruption and you + + + align:start position:0% +are vulnerable to disruption and you +can't satisfy every learning style + + align:start position:0% +can't satisfy every learning style + + + align:start position:0% +can't satisfy every learning style +amusingly we've had written feedback + + align:start position:0% +amusingly we've had written feedback + + + align:start position:0% +amusingly we've had written feedback +asking for both more and less simulation + + align:start position:0% +asking for both more and less simulation + + + align:start position:0% +asking for both more and less simulation +because some people feel they need more + + align:start position:0% +because some people feel they need more + + + align:start position:0% +because some people feel they need more +time to uh to um uh internalize the + + align:start position:0% +time to uh to um uh internalize the + + + align:start position:0% +time to uh to um uh internalize the +information information that's there + + align:start position:0% +information information that's there + + + align:start position:0% +information information that's there +others get it quickly um and uh and and + + align:start position:0% +others get it quickly um and uh and and + + + align:start position:0% +others get it quickly um and uh and and +wish they could move on to to other + + align:start position:0% +wish they could move on to to other + + + align:start position:0% +wish they could move on to to other +learning + + align:start position:0% +learning + + + align:start position:0% +learning +modes and another one it's a unexpected + + align:start position:0% +modes and another one it's a unexpected + + + align:start position:0% +modes and another one it's a unexpected +psychological effect is that there's + + align:start position:0% +psychological effect is that there's + + + align:start position:0% +psychological effect is that there's +real stress in the simulated process um + + align:start position:0% +real stress in the simulated process um + + + align:start position:0% +real stress in the simulated process um +and that this sometimes creates + + align:start position:0% +and that this sometimes creates + + + align:start position:0% +and that this sometimes creates +difficulties with people's learning can + + align:start position:0% +difficulties with people's learning can + + + align:start position:0% +difficulties with people's learning can +create competition and bad feeling if + + align:start position:0% +create competition and bad feeling if + + + align:start position:0% +create competition and bad feeling if +it's not managed carefully we've learned + + align:start position:0% +it's not managed carefully we've learned + + + align:start position:0% +it's not managed carefully we've learned +that that's something that that is an + + align:start position:0% +that that's something that that is an + + + align:start position:0% +that that's something that that is an +issue that needs to be that need needs + + align:start position:0% +issue that needs to be that need needs + + + align:start position:0% +issue that needs to be that need needs +to be managed and these by the way are + + align:start position:0% +to be managed and these by the way are + + + align:start position:0% +to be managed and these by the way are +typical issues for teaching Sim ation + + align:start position:0% +typical issues for teaching Sim ation + + + align:start position:0% +typical issues for teaching Sim ation +okay in conclusion of this part we have + + align:start position:0% +okay in conclusion of this part we have + + + align:start position:0% +okay in conclusion of this part we have +a unique simulation of Aerospace + + align:start position:0% +a unique simulation of Aerospace + + + align:start position:0% +a unique simulation of Aerospace +Enterprises a subset of it is used in + + align:start position:0% +Enterprises a subset of it is used in + + + align:start position:0% +Enterprises a subset of it is used in +the lean Academy um we think it + + align:start position:0% +the lean Academy um we think it + + + align:start position:0% +the lean Academy um we think it +works and um it provides a laboratory + + align:start position:0% +works and um it provides a laboratory + + + align:start position:0% +works and um it provides a laboratory +for experiential learning of complex + + align:start position:0% +for experiential learning of complex + + + align:start position:0% +for experiential learning of complex +systems we there's not a whole lot of + + align:start position:0% +systems we there's not a whole lot of + + + align:start position:0% +systems we there's not a whole lot of +work in this area going on um we've had + + align:start position:0% +work in this area going on um we've had + + + align:start position:0% +work in this area going on um we've had +a very good experience with it uh + + align:start position:0% +a very good experience with it uh + + + align:start position:0% +a very good experience with it uh +certainly the feedback that we have from + + align:start position:0% +certainly the feedback that we have from + + + align:start position:0% +certainly the feedback that we have from +our students indicates that it's + + align:start position:0% +our students indicates that it's + + + align:start position:0% +our students indicates that it's +successful um and the caveats that we + + align:start position:0% +successful um and the caveats that we + + + align:start position:0% +successful um and the caveats that we +have for our simulation are typical of + + align:start position:0% +have for our simulation are typical of + + + align:start position:0% +have for our simulation are typical of +learning simulations in general there + + align:start position:0% +learning simulations in general there + + + align:start position:0% +learning simulations in general there +are other aspects of the simulation that + + align:start position:0% +are other aspects of the simulation that + + + align:start position:0% +are other aspects of the simulation that +replicate the entire Enterprise and I'm + + align:start position:0% +replicate the entire Enterprise and I'm + + + align:start position:0% +replicate the entire Enterprise and I'm +going to talk a little bit about each of + + align:start position:0% +going to talk a little bit about each of + + + align:start position:0% +going to talk a little bit about each of +those elements and the simulations are + + align:start position:0% +those elements and the simulations are + + + align:start position:0% +those elements and the simulations are +modular so you can go through the + + align:start position:0% +modular so you can go through the + + + align:start position:0% +modular so you can go through the +manufacturing part or you can go through + + align:start position:0% +manufacturing part or you can go through + + + align:start position:0% +manufacturing part or you can go through +the engineering part depending on what + + align:start position:0% +the engineering part depending on what + + + align:start position:0% +the engineering part depending on what +the learning objectives for the the + + align:start position:0% +the learning objectives for the the + + + align:start position:0% +the learning objectives for the the +course are uh you can combine them in + + align:start position:0% +course are uh you can combine them in + + + align:start position:0% +course are uh you can combine them in +various ways you can combine the + + align:start position:0% +various ways you can combine the + + + align:start position:0% +various ways you can combine the +manufacturing with the engineering to + + align:start position:0% +manufacturing with the engineering to + + + align:start position:0% +manufacturing with the engineering to +teach specific lessons about transition + + align:start position:0% +teach specific lessons about transition + + + align:start position:0% +teach specific lessons about transition +to production and Engineering support uh + + align:start position:0% +to production and Engineering support uh + + + align:start position:0% +to production and Engineering support uh +you can look at just engineering alone + + align:start position:0% +you can look at just engineering alone + + + align:start position:0% +you can look at just engineering alone +if you are interested in understanding + + align:start position:0% +if you are interested in understanding + + + align:start position:0% +if you are interested in understanding +how engineering processes behave in a + + align:start position:0% +how engineering processes behave in a + + + align:start position:0% +how engineering processes behave in a +highly variable environment so there's a + + align:start position:0% +highly variable environment so there's a + + + align:start position:0% +highly variable environment so there's a +lot of flexibility that's built into the + + align:start position:0% +lot of flexibility that's built into the + + + align:start position:0% +lot of flexibility that's built into the +simulation environment so this is the + + align:start position:0% +simulation environment so this is the + + + align:start position:0% +simulation environment so this is the +simulation that you all experienced here + + align:start position:0% +simulation that you all experienced here + + + align:start position:0% +simulation that you all experienced here +in the lean Academy that has the + + align:start position:0% +in the lean Academy that has the + + + align:start position:0% +in the lean Academy that has the +manufacturing core simulation and a + + align:start position:0% +manufacturing core simulation and a + + + align:start position:0% +manufacturing core simulation and a +simplified supplier uh + + align:start position:0% +simplified supplier uh + + + align:start position:0% +simplified supplier uh +uh base with a + + align:start position:0% +uh base with a + + + align:start position:0% +uh base with a +representative if you expand out to the + + align:start position:0% +representative if you expand out to the + + + align:start position:0% +representative if you expand out to the +full supplier simulation you get a much + + align:start position:0% +full supplier simulation you get a much + + + align:start position:0% +full supplier simulation you get a much +richer experience of understanding how + + align:start position:0% +richer experience of understanding how + + + align:start position:0% +richer experience of understanding how +uh ordering and fulfillment processes + + align:start position:0% +uh ordering and fulfillment processes + + + align:start position:0% +uh ordering and fulfillment processes +are dynamic in the + + align:start position:0% +are dynamic in the + + + align:start position:0% +are dynamic in the +Enterprise and uh learning much more + + align:start position:0% +Enterprise and uh learning much more + + + align:start position:0% +Enterprise and uh learning much more +about network uh organization structures + + align:start position:0% +about network uh organization structures + + + align:start position:0% +about network uh organization structures +and the way they behave and how you uh + + align:start position:0% +and the way they behave and how you uh + + + align:start position:0% +and the way they behave and how you uh +how effective uh coordination is + + align:start position:0% +how effective uh coordination is + + + align:start position:0% +how effective uh coordination is +critical to lean + + align:start position:0% + + + + align:start position:0% + +uh for the full Enterprise you can add + + align:start position:0% +uh for the full Enterprise you can add + + + align:start position:0% +uh for the full Enterprise you can add +the Dynamics of uh an engineering system + + align:start position:0% +the Dynamics of uh an engineering system + + + align:start position:0% +the Dynamics of uh an engineering system +that is supporting the manufacturing and + + align:start position:0% +that is supporting the manufacturing and + + + align:start position:0% +that is supporting the manufacturing and +Supply base and this is the full La Sim + + align:start position:0% +Supply base and this is the full La Sim + + + align:start position:0% +Supply base and this is the full La Sim +where the engineering changes that you + + align:start position:0% +where the engineering changes that you + + + align:start position:0% +where the engineering changes that you +made during the course of the redesign + + align:start position:0% +made during the course of the redesign + + + align:start position:0% +made during the course of the redesign +of the airplane were done for + + align:start position:0% +of the airplane were done for + + + align:start position:0% +of the airplane were done for +essentially free in this simulation that + + align:start position:0% +essentially free in this simulation that + + + align:start position:0% +essentially free in this simulation that +you did in the lean academy uh in the + + align:start position:0% +you did in the lean academy uh in the + + + align:start position:0% +you did in the lean academy uh in the +real Enterprise simulation you have to + + align:start position:0% +real Enterprise simulation you have to + + + align:start position:0% +real Enterprise simulation you have to +wait for the engineers to process those + + align:start position:0% +wait for the engineers to process those + + + align:start position:0% +wait for the engineers to process those +jobs and that can lead to all sorts of + + align:start position:0% +jobs and that can lead to all sorts of + + + align:start position:0% +jobs and that can lead to all sorts of +interesting Dynamics amongst the players + + align:start position:0% +interesting Dynamics amongst the players + + + align:start position:0% +interesting Dynamics amongst the players +and uh simulated organizational + + align:start position:0% +and uh simulated organizational + + + align:start position:0% +and uh simulated organizational +structures there's also uh a service and + + align:start position:0% +structures there's also uh a service and + + + align:start position:0% +structures there's also uh a service and +support module that looks at aftermarket + + align:start position:0% +support module that looks at aftermarket + + + align:start position:0% +support module that looks at aftermarket +field support for the products and this + + align:start position:0% +field support for the products and this + + + align:start position:0% +field support for the products and this +introduces a new and interesting uh + + align:start position:0% +introduces a new and interesting uh + + + align:start position:0% +introduces a new and interesting uh +complexities to the Enterprise because + + align:start position:0% +complexities to the Enterprise because + + + align:start position:0% +complexities to the Enterprise because +you know have two main value streams and + + align:start position:0% +you know have two main value streams and + + + align:start position:0% +you know have two main value streams and +sources of revenues you have to + + align:start position:0% +sources of revenues you have to + + + align:start position:0% +sources of revenues you have to +prioritize where you make improvements + + align:start position:0% +prioritize where you make improvements + + + align:start position:0% +prioritize where you make improvements +in the + + align:start position:0% +in the + + + align:start position:0% +in the +Enterprise all right so uh there's + + align:start position:0% +Enterprise all right so uh there's + + + align:start position:0% +Enterprise all right so uh there's +another variant of the simulation that + + align:start position:0% +another variant of the simulation that + + + align:start position:0% +another variant of the simulation that +focuses on just an engineering + + align:start position:0% +focuses on just an engineering + + + align:start position:0% +focuses on just an engineering +organization most engineering + + align:start position:0% +organization most engineering + + + align:start position:0% +organization most engineering +organizations have uh multiple projects + + align:start position:0% +organizations have uh multiple projects + + + align:start position:0% +organizations have uh multiple projects +going on at a given time and they're + + align:start position:0% +going on at a given time and they're + + + align:start position:0% +going on at a given time and they're +competing for resources and those + + align:start position:0% +competing for resources and those + + + align:start position:0% +competing for resources and those +projects aren't always the same so this + + align:start position:0% +projects aren't always the same so this + + + align:start position:0% +projects aren't always the same so this +simulation looks at how you prioritize + + align:start position:0% +simulation looks at how you prioritize + + + align:start position:0% +simulation looks at how you prioritize +projects how you structure the + + align:start position:0% +projects how you structure the + + + align:start position:0% +projects how you structure the +organization how you manage the + + align:start position:0% +organization how you manage the + + + align:start position:0% +organization how you manage the +interactions so that you get the highest + + align:start position:0% +interactions so that you get the highest + + + align:start position:0% +interactions so that you get the highest +throughput through the system and the + + align:start position:0% +throughput through the system and the + + + align:start position:0% +throughput through the system and the +most return on investment for + + align:start position:0% +most return on investment for + + + align:start position:0% +most return on investment for +improvements through uh lean practices + + align:start position:0% +improvements through uh lean practices + + + align:start position:0% +improvements through uh lean practices +so some of the things that were not + + align:start position:0% +so some of the things that were not + + + align:start position:0% +so some of the things that were not +covered in the lean Academy simulation + + align:start position:0% +covered in the lean Academy simulation + + + align:start position:0% +covered in the lean Academy simulation +are uh a more advanced economic system + + align:start position:0% +are uh a more advanced economic system + + + align:start position:0% +are uh a more advanced economic system +that allows you to make tradeoffs to + + align:start position:0% +that allows you to make tradeoffs to + + + align:start position:0% +that allows you to make tradeoffs to +understand what the impact of lean + + align:start position:0% +understand what the impact of lean + + + align:start position:0% +understand what the impact of lean +improvements are and to actually + + align:start position:0% +improvements are and to actually + + + align:start position:0% +improvements are and to actually +calculate financial performance of the + + align:start position:0% +calculate financial performance of the + + + align:start position:0% +calculate financial performance of the +kind that you would typically track with + + align:start position:0% +kind that you would typically track with + + + align:start position:0% +kind that you would typically track with +a real + + align:start position:0% +a real + + + align:start position:0% +a real +company uh there's also a lean + + align:start position:0% +company uh there's also a lean + + + align:start position:0% +company uh there's also a lean +calculator that can be used to evaluate + + align:start position:0% +calculator that can be used to evaluate + + + align:start position:0% +calculator that can be used to evaluate +whether one proposed Improvement effort + + align:start position:0% +whether one proposed Improvement effort + + + align:start position:0% +whether one proposed Improvement effort +is better than another and these are uh + + align:start position:0% +is better than another and these are uh + + + align:start position:0% +is better than another and these are uh +levels of analysis that are uh more + + align:start position:0% +levels of analysis that are uh more + + + align:start position:0% +levels of analysis that are uh more +indepth uh tools that are more + + align:start position:0% +indepth uh tools that are more + + + align:start position:0% +indepth uh tools that are more +sophisticated that can be added onto the + + align:start position:0% +sophisticated that can be added onto the + + + align:start position:0% +sophisticated that can be added onto the +Sim environment so in all it's a fairly + + align:start position:0% +Sim environment so in all it's a fairly + + + align:start position:0% +Sim environment so in all it's a fairly +sophisticated system for teaching the + + align:start position:0% +sophisticated system for teaching the + + + align:start position:0% +sophisticated system for teaching the +impact of lean principles and practices + + align:start position:0% +impact of lean principles and practices + + + align:start position:0% +impact of lean principles and practices +on a uh an Enterprise so there are a + + align:start position:0% +on a uh an Enterprise so there are a + + + align:start position:0% +on a uh an Enterprise so there are a +number of organizations that are using + + align:start position:0% +number of organizations that are using + + + align:start position:0% +number of organizations that are using +the L simulation and its variance and + + align:start position:0% +the L simulation and its variance and + + + align:start position:0% +the L simulation and its variance and +they have a adopted it for their own use + + align:start position:0% +they have a adopted it for their own use + + + align:start position:0% +they have a adopted it for their own use +and are actually uh using it in their + + align:start position:0% +and are actually uh using it in their + + + align:start position:0% +and are actually uh using it in their +own internal training so we have a + + align:start position:0% +own internal training so we have a + + + align:start position:0% +own internal training so we have a +method for actually disseminating these + + align:start position:0% +method for actually disseminating these + + + align:start position:0% +method for actually disseminating these +materials and if there are any questions + + align:start position:0% +materials and if there are any questions + + + align:start position:0% +materials and if there are any questions +about uh adopting the simulation the + + align:start position:0% +about uh adopting the simulation the + + + align:start position:0% +about uh adopting the simulation the +best place to go would be to send a + + align:start position:0% +best place to go would be to send a + + + align:start position:0% +best place to go would be to send a +message to edet at mit.edu + + align:start position:0% +message to edet at mit.edu + + + align:start position:0% +message to edet at mit.edu +and uh you can get more information + + align:start position:0% +and uh you can get more information + + + align:start position:0% +and uh you can get more information +about how you might adopt these uh + + align:start position:0% +about how you might adopt these uh + + + align:start position:0% +about how you might adopt these uh +training + + align:start position:0% + + + + align:start position:0% + +materials for \ No newline at end of file diff --git a/TWedESDFcLQ.txt b/TWedESDFcLQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..7d961018430afe55c21f95fecb1df3ec99891496 --- /dev/null +++ b/TWedESDFcLQ.txt @@ -0,0 +1,1091 @@ +align:start position:0% + +all right so as we have seen in the + + align:start position:0% +all right so as we have seen in the + + + align:start position:0% +all right so as we have seen in the +previous clip another way that initial + + align:start position:0% +previous clip another way that initial + + + align:start position:0% +previous clip another way that initial +conditions may matter is if a chain has + + align:start position:0% +conditions may matter is if a chain has + + + align:start position:0% +conditions may matter is if a chain has +a periodic structure there are many ways + + align:start position:0% +a periodic structure there are many ways + + + align:start position:0% +a periodic structure there are many ways +of defining periodicity some of them are + + align:start position:0% +of defining periodicity some of them are + + + align:start position:0% +of defining periodicity some of them are +more mathematical than others let us + + align:start position:0% +more mathematical than others let us + + + align:start position:0% +more mathematical than others let us +consider on one of the most intuitive + + align:start position:0% +consider on one of the most intuitive + + + align:start position:0% +consider on one of the most intuitive +ways of doing that so here is the + + align:start position:0% +ways of doing that so here is the + + + align:start position:0% +ways of doing that so here is the +definition the states in a recurrent + + align:start position:0% +definition the states in a recurrent + + + align:start position:0% +definition the states in a recurrent +class are periodic if they can be lumped + + align:start position:0% +class are periodic if they can be lumped + + + align:start position:0% +class are periodic if they can be lumped +together or grouped into several + + align:start position:0% +together or grouped into several + + + align:start position:0% +together or grouped into several +subgroups so that all transitions from + + align:start position:0% +subgroups so that all transitions from + + + align:start position:0% +subgroups so that all transitions from +one group lead to the next group so what + + align:start position:0% +one group lead to the next group so what + + + align:start position:0% +one group lead to the next group so what +does that really mean let us try to + + align:start position:0% +does that really mean let us try to + + + align:start position:0% +does that really mean let us try to +parse out this by looking at a given + + align:start position:0% +parse out this by looking at a given + + + align:start position:0% +parse out this by looking at a given +example so here we would have a + + align:start position:0% +example so here we would have a + + + align:start position:0% +example so here we would have a +situation a structure of a diagram in + + align:start position:0% +situation a structure of a diagram in + + + align:start position:0% +situation a structure of a diagram in +which D is equals to 2 whenever you are + + align:start position:0% +which D is equals to 2 whenever you are + + + align:start position:0% +which D is equals to 2 whenever you are +at a given time in a state in that group + + align:start position:0% +at a given time in a state in that group + + + align:start position:0% +at a given time in a state in that group +in the next transition you will go to + + align:start position:0% +in the next transition you will go to + + + align:start position:0% +in the next transition you will go to +that group and if you are in that group + + align:start position:0% +that group and if you are in that group + + + align:start position:0% +that group and if you are in that group +at the next transition you will go to + + align:start position:0% +at the next transition you will go to + + + align:start position:0% +at the next transition you will go to +that group so in some sense there is + + align:start position:0% +that group so in some sense there is + + + align:start position:0% +that group so in some sense there is +periodicity and there is somewhat of a + + align:start position:0% +periodicity and there is somewhat of a + + + align:start position:0% +periodicity and there is somewhat of a +deterministic behavior according to this + + align:start position:0% +deterministic behavior according to this + + + align:start position:0% +deterministic behavior according to this +transition but there is also some + + align:start position:0% +transition but there is also some + + + align:start position:0% +transition but there is also some +randomness left we can be in any of + + align:start position:0% +randomness left we can be in any of + + + align:start position:0% +randomness left we can be in any of +these states within that subgroup but + + align:start position:0% +these states within that subgroup but + + + align:start position:0% +these states within that subgroup but +one thing that is for sure is that + + align:start position:0% +one thing that is for sure is that + + + align:start position:0% +one thing that is for sure is that +whenever at a given time you are into + + align:start position:0% +whenever at a given time you are into + + + align:start position:0% +whenever at a given time you are into +one of these states here in that group + + align:start position:0% +one of these states here in that group + + + align:start position:0% +one of these states here in that group +if the Markov chain has this specific + + align:start position:0% +if the Markov chain has this specific + + + align:start position:0% +if the Markov chain has this specific +structure in the next transition you + + align:start position:0% +structure in the next transition you + + + align:start position:0% +structure in the next transition you +will transition to one of these states + + align:start position:0% +will transition to one of these states + + + align:start position:0% +will transition to one of these states +here and the next transition after you + + align:start position:0% +here and the next transition after you + + + align:start position:0% +here and the next transition after you +will go back here so essentially if your + + align:start position:0% +will go back here so essentially if your + + + align:start position:0% +will go back here so essentially if your +Markov chain started in one of these + + align:start position:0% +Markov chain started in one of these + + + align:start position:0% +Markov chain started in one of these +states here at time N equals zero then + + align:start position:0% +states here at time N equals zero then + + + align:start position:0% +states here at time N equals zero then +at time N equals one it would be here + + align:start position:0% +at time N equals one it would be here + + + align:start position:0% +at time N equals one it would be here +and then at time N equals two it will be + + align:start position:0% +and then at time N equals two it will be + + + align:start position:0% +and then at time N equals two it will be +here times Dement 3 and so and so forth + + align:start position:0% +here times Dement 3 and so and so forth + + + align:start position:0% +here times Dement 3 and so and so forth +so every time you would have an even + + align:start position:0% +so every time you would have an even + + + align:start position:0% +so every time you would have an even +number then you are guaranteed that the + + align:start position:0% +number then you are guaranteed that the + + + align:start position:0% +number then you are guaranteed that the +Markov chain will be in one of these + + align:start position:0% +Markov chain will be in one of these + + + align:start position:0% +Markov chain will be in one of these +states here clearly with this kind of + + align:start position:0% +states here clearly with this kind of + + + align:start position:0% +states here clearly with this kind of +structure it is impossible to have + + align:start position:0% +structure it is impossible to have + + + align:start position:0% +structure it is impossible to have +convergence of the steady state + + align:start position:0% +convergence of the steady state + + + align:start position:0% +convergence of the steady state +probabilities this is another example + + align:start position:0% +probabilities this is another example + + + align:start position:0% +probabilities this is another example +where you would have a structure of a + + align:start position:0% +where you would have a structure of a + + + align:start position:0% +where you would have a structure of a +diagram in which you have a period of 3 + + align:start position:0% +diagram in which you have a period of 3 + + + align:start position:0% +diagram in which you have a period of 3 +here so in that case here D equals 3 so + + align:start position:0% +here so in that case here D equals 3 so + + + align:start position:0% +here so in that case here D equals 3 so +here again if you are in one of these + + align:start position:0% +here again if you are in one of these + + + align:start position:0% +here again if you are in one of these +states at a given time then at the next + + align:start position:0% +states at a given time then at the next + + + align:start position:0% +states at a given time then at the next +time the following transition will + + align:start position:0% +time the following transition will + + + align:start position:0% +time the following transition will +guarantee to bring you in that group and + + align:start position:0% +guarantee to bring you in that group and + + + align:start position:0% +guarantee to bring you in that group and +during the next transition you will go + + align:start position:0% +during the next transition you will go + + + align:start position:0% +during the next transition you will go +to that group and then again here and + + align:start position:0% +to that group and then again here and + + + align:start position:0% +to that group and then again here and +again you will have this kind of + + align:start position:0% +again you will have this kind of + + + align:start position:0% +again you will have this kind of +behavior in a very systematic way so if + + align:start position:0% +behavior in a very systematic way so if + + + align:start position:0% +behavior in a very systematic way so if +you started here at time N equals 0 you + + align:start position:0% +you started here at time N equals 0 you + + + align:start position:0% +you started here at time N equals 0 you +would be in that group here at times n + + align:start position:0% +would be in that group here at times n + + + align:start position:0% +would be in that group here at times n +equals 1 and you would be here at N + + align:start position:0% +equals 1 and you would be here at N + + + align:start position:0% +equals 1 and you would be here at N +equals 2 and again N equals 3 here and + + align:start position:0% +equals 2 and again N equals 3 here and + + + align:start position:0% +equals 2 and again N equals 3 here and +equals 4 and equals 5 6 7 8 and you see + + align:start position:0% +equals 4 and equals 5 6 7 8 and you see + + + align:start position:0% +equals 4 and equals 5 6 7 8 and you see +the pattern if you look at any time in + + align:start position:0% +the pattern if you look at any time in + + + align:start position:0% +the pattern if you look at any time in +the future if the time is of the form 3 + + align:start position:0% +the future if the time is of the form 3 + + + align:start position:0% +the future if the time is of the form 3 +times K for any K greater than equal to + + align:start position:0% +times K for any K greater than equal to + + + align:start position:0% +times K for any K greater than equal to +0 you are guaranteed that your chain + + align:start position:0% +0 you are guaranteed that your chain + + + align:start position:0% +0 you are guaranteed that your chain +will be in one of these states otherwise + + align:start position:0% +will be in one of these states otherwise + + + align:start position:0% +will be in one of these states otherwise +it will be here or here so here again + + align:start position:0% +it will be here or here so here again + + + align:start position:0% +it will be here or here so here again +you do not have convergence so the + + align:start position:0% +you do not have convergence so the + + + align:start position:0% +you do not have convergence so the +steady states because if you are told + + align:start position:0% +steady states because if you are told + + + align:start position:0% +steady states because if you are told +that you started in one of these states + + align:start position:0% +that you started in one of these states + + + align:start position:0% +that you started in one of these states +here then you know that whenever you + + align:start position:0% +here then you know that whenever you + + + align:start position:0% +here then you know that whenever you +have a time that is of the form 3 K plus + + align:start position:0% +have a time that is of the form 3 K plus + + + align:start position:0% +have a time that is of the form 3 K plus +1 you will be here and so the privateeer + + align:start position:0% +1 you will be here and so the privateeer + + + align:start position:0% +1 you will be here and so the privateeer +being here will be 0 alright so we have + + align:start position:0% +being here will be 0 alright so we have + + + align:start position:0% +being here will be 0 alright so we have +been able to explain a little bit what a + + align:start position:0% +been able to explain a little bit what a + + + align:start position:0% +been able to explain a little bit what a +periodic state is using this definition + + align:start position:0% +periodic state is using this definition + + + align:start position:0% +periodic state is using this definition +now given a Markov chain how can we tell + + align:start position:0% +now given a Markov chain how can we tell + + + align:start position:0% +now given a Markov chain how can we tell +whether a Markov chain is periodic or + + align:start position:0% +whether a Markov chain is periodic or + + + align:start position:0% +whether a Markov chain is periodic or +not there are in fact systematic ways of + + align:start position:0% +not there are in fact systematic ways of + + + align:start position:0% +not there are in fact systematic ways of +doing it mathematically but usually + + align:start position:0% +doing it mathematically but usually + + + align:start position:0% +doing it mathematically but usually +within the types of examples we see in + + align:start position:0% +within the types of examples we see in + + + align:start position:0% +within the types of examples we see in +this class most of them it will be easy + + align:start position:0% +this class most of them it will be easy + + + align:start position:0% +this class most of them it will be easy +to see we just eyeball the chain and we + + align:start position:0% +to see we just eyeball the chain and we + + + align:start position:0% +to see we just eyeball the chain and we +tell whether it's parody cannot so let + + align:start position:0% +tell whether it's parody cannot so let + + + align:start position:0% +tell whether it's parody cannot so let +us see if it is that easy to do + + align:start position:0% +us see if it is that easy to do + + + align:start position:0% +us see if it is that easy to do +and consider that chain here okay so + + align:start position:0% +and consider that chain here okay so + + + align:start position:0% +and consider that chain here okay so +let's see is this chain parity cannot I + + align:start position:0% +let's see is this chain parity cannot I + + + align:start position:0% +let's see is this chain parity cannot I +will give you a couple of seconds to + + align:start position:0% +will give you a couple of seconds to + + + align:start position:0% +will give you a couple of seconds to +think about it now I'm gonna help a + + align:start position:0% +think about it now I'm gonna help a + + + align:start position:0% +think about it now I'm gonna help a +little bit I just decide that this one + + align:start position:0% +little bit I just decide that this one + + + align:start position:0% +little bit I just decide that this one +will be red this one will be red this + + align:start position:0% +will be red this one will be red this + + + align:start position:0% +will be red this one will be red this +one will be red and this one will be red + + align:start position:0% +one will be red and this one will be red + + + align:start position:0% +one will be red and this one will be red +now I'm asking the same question what do + + align:start position:0% +now I'm asking the same question what do + + + align:start position:0% +now I'm asking the same question what do +you think well from the structure it is + + align:start position:0% +you think well from the structure it is + + + align:start position:0% +you think well from the structure it is +clear that this Markov chain is periodic + + align:start position:0% +clear that this Markov chain is periodic + + + align:start position:0% +clear that this Markov chain is periodic +and as a period of T equals two in some + + align:start position:0% +and as a period of T equals two in some + + + align:start position:0% +and as a period of T equals two in some +sense the red state here could be one of + + align:start position:0% +sense the red state here could be one of + + + align:start position:0% +sense the red state here could be one of +these group these are the red one the + + align:start position:0% +these group these are the red one the + + + align:start position:0% +these group these are the red one the +white here will be those here and it is + + align:start position:0% +white here will be those here and it is + + + align:start position:0% +white here will be those here and it is +clear if you look at this diagram that + + align:start position:0% +clear if you look at this diagram that + + + align:start position:0% +clear if you look at this diagram that +whenever you are in a red state at the + + align:start position:0% +whenever you are in a red state at the + + + align:start position:0% +whenever you are in a red state at the +next transition you are guaranteed to be + + align:start position:0% +next transition you are guaranteed to be + + + align:start position:0% +next transition you are guaranteed to be +in a white state from this one you will + + align:start position:0% +in a white state from this one you will + + + align:start position:0% +in a white state from this one you will +be in white from this one you will be in + + align:start position:0% +be in white from this one you will be in + + + align:start position:0% +be in white from this one you will be in +a white from this one as well and from + + align:start position:0% +a white from this one as well and from + + + align:start position:0% +a white from this one as well and from +this one as well and whenever you are in + + align:start position:0% +this one as well and whenever you are in + + + align:start position:0% +this one as well and whenever you are in +a white state this one this one this one + + align:start position:0% +a white state this one this one this one + + + align:start position:0% +a white state this one this one this one +this one or this one + + align:start position:0% +this one or this one + + + align:start position:0% +this one or this one +at the next period you can't it to be in + + align:start position:0% +at the next period you can't it to be in + + + align:start position:0% +at the next period you can't it to be in +a red state so this tells you that + + align:start position:0% +a red state so this tells you that + + + align:start position:0% +a red state so this tells you that +sometimes it's not that easy to eyeball + + align:start position:0% +sometimes it's not that easy to eyeball + + + align:start position:0% +sometimes it's not that easy to eyeball +and decide if a Markov chain is periodic + + align:start position:0% +and decide if a Markov chain is periodic + + + align:start position:0% +and decide if a Markov chain is periodic +or not if you have for example lots of + + align:start position:0% +or not if you have for example lots of + + + align:start position:0% +or not if you have for example lots of +lots of states you might have some + + align:start position:0% +lots of states you might have some + + + align:start position:0% +lots of states you might have some +trouble doing this exercise on the other + + align:start position:0% +trouble doing this exercise on the other + + + align:start position:0% +trouble doing this exercise on the other +hand something very useful to know + + align:start position:0% +hand something very useful to know + + + align:start position:0% +hand something very useful to know +sometimes it's extremely easy to tell + + align:start position:0% +sometimes it's extremely easy to tell + + + align:start position:0% +sometimes it's extremely easy to tell +that the chain is not periodic even if + + align:start position:0% +that the chain is not periodic even if + + + align:start position:0% +that the chain is not periodic even if +you have a lot of states what is that + + align:start position:0% +you have a lot of states what is that + + + align:start position:0% +you have a lot of states what is that +case well look at this case here and + + align:start position:0% +case well look at this case here and + + + align:start position:0% +case well look at this case here and +suppose for a moment that you have a + + align:start position:0% +suppose for a moment that you have a + + + align:start position:0% +suppose for a moment that you have a +soft transition here + + align:start position:0% + + + + align:start position:0% + +well in that case you would have a + + align:start position:0% +well in that case you would have a + + + align:start position:0% +well in that case you would have a +transition from a white state to a white + + align:start position:0% +transition from a white state to a white + + + align:start position:0% +transition from a white state to a white +state and you're not guaranteed anymore + + align:start position:0% +state and you're not guaranteed anymore + + + align:start position:0% +state and you're not guaranteed anymore +that from a white state you would go to + + align:start position:0% +that from a white state you would go to + + + align:start position:0% +that from a white state you would go to +a red state in that sense as soon as you + + align:start position:0% +a red state in that sense as soon as you + + + align:start position:0% +a red state in that sense as soon as you +have a self transition the Markov chain + + align:start position:0% +have a self transition the Markov chain + + + align:start position:0% +have a self transition the Markov chain +is a periodic it cannot be periodic so + + align:start position:0% +is a periodic it cannot be periodic so + + + align:start position:0% +is a periodic it cannot be periodic so +whenever you have a self transition this + + align:start position:0% +whenever you have a self transition this + + + align:start position:0% +whenever you have a self transition this +implies that the chain is not periodic + + align:start position:0% +implies that the chain is not periodic + + + align:start position:0% +implies that the chain is not periodic +and usually that's the simplest and + + align:start position:0% +and usually that's the simplest and + + + align:start position:0% +and usually that's the simplest and +easiest way that we can tell most of the + + align:start position:0% +easiest way that we can tell most of the + + + align:start position:0% +easiest way that we can tell most of the +time that the chain is not periodic \ No newline at end of file diff --git a/TgwDg_svSnM.txt b/TgwDg_svSnM.txt new file mode 100644 index 0000000000000000000000000000000000000000..5ab711bf31cf9ea49bb105997bfcad6fc60e4e47 --- /dev/null +++ b/TgwDg_svSnM.txt @@ -0,0 +1,16795 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +welcome back hope everybody had a + + align:start position:0% +welcome back hope everybody had a + + + align:start position:0% +welcome back hope everybody had a +restful break uh spent lots of time + + align:start position:0% +restful break uh spent lots of time + + + align:start position:0% +restful break uh spent lots of time +doing syntax in their spare time + + align:start position:0% +doing syntax in their spare time + + + align:start position:0% +doing syntax in their spare time +um let's do a little syntax now I don't + + align:start position:0% +um let's do a little syntax now I don't + + + align:start position:0% +um let's do a little syntax now I don't +have any announcements uh are there any + + align:start position:0% +have any announcements uh are there any + + + align:start position:0% +have any announcements uh are there any +questions about the things that I'm not + + align:start position:0% +questions about the things that I'm not + + + align:start position:0% +questions about the things that I'm not +announcing things that people are like + + align:start position:0% +announcing things that people are like + + + align:start position:0% +announcing things that people are like +wondering about before we start + + align:start position:0% +wondering about before we start + + + align:start position:0% +wondering about before we start +okay so I just wanted to start with some + + align:start position:0% +okay so I just wanted to start with some + + + align:start position:0% +okay so I just wanted to start with some +review just to remind everybody where we + + align:start position:0% +review just to remind everybody where we + + + align:start position:0% +review just to remind everybody where we +were + + align:start position:0% +were + + + align:start position:0% +were +we were drawing trees like this one + + align:start position:0% +we were drawing trees like this one + + + align:start position:0% +we were drawing trees like this one +um so here's a tree for I will tickle + + align:start position:0% +um so here's a tree for I will tickle + + + align:start position:0% +um so here's a tree for I will tickle +the child with the feather + + align:start position:0% +the child with the feather + + + align:start position:0% +the child with the feather +um it's a tree that has various kinds of + + align:start position:0% +um it's a tree that has various kinds of + + + align:start position:0% +um it's a tree that has various kinds of +information in it about + + align:start position:0% +information in it about + + + align:start position:0% +information in it about +um well various things including uh + + align:start position:0% +um well various things including uh + + + align:start position:0% +um well various things including uh +substrings that we think are treated as + + align:start position:0% +substrings that we think are treated as + + + align:start position:0% +substrings that we think are treated as +constituents for various kinds of + + align:start position:0% +constituents for various kinds of + + + align:start position:0% +constituents for various kinds of +syntactic phenomena so you know this + + align:start position:0% +syntactic phenomena so you know this + + + align:start position:0% +syntactic phenomena so you know this +tree is meant to reflect the fact that + + align:start position:0% +tree is meant to reflect the fact that + + + align:start position:0% +tree is meant to reflect the fact that +this sentence uh first of all has a + + align:start position:0% +this sentence uh first of all has a + + + align:start position:0% +this sentence uh first of all has a +meaning in which I'm going to use a + + align:start position:0% +meaning in which I'm going to use a + + + align:start position:0% +meaning in which I'm going to use a +feather to tickle tickle a child that's + + align:start position:0% +feather to tickle tickle a child that's + + + align:start position:0% +feather to tickle tickle a child that's +the meaning that's been diagrammed here + + align:start position:0% +the meaning that's been diagrammed here + + + align:start position:0% +the meaning that's been diagrammed here +and that if you perform certain + + align:start position:0% +and that if you perform certain + + + align:start position:0% +and that if you perform certain +operations that make it clear that this + + align:start position:0% +operations that make it clear that this + + + align:start position:0% +operations that make it clear that this +is the tree that you've got like + + align:start position:0% +is the tree that you've got like + + + align:start position:0% +is the tree that you've got like +topicalizing the child moving the child + + align:start position:0% +topicalizing the child moving the child + + + align:start position:0% +topicalizing the child moving the child +to the beginning of the sentence you + + align:start position:0% +to the beginning of the sentence you + + + align:start position:0% +to the beginning of the sentence you +know the child I will tickle with the + + align:start position:0% +know the child I will tickle with the + + + align:start position:0% +know the child I will tickle with the +feather uh that that's the only in fact + + align:start position:0% +feather uh that that's the only in fact + + + align:start position:0% +feather uh that that's the only in fact +the only meaning that you can have is + + align:start position:0% +the only meaning that you can have is + + + align:start position:0% +the only meaning that you can have is +the the meaning that goes with this tree + + align:start position:0% +the the meaning that goes with this tree + + + align:start position:0% +the the meaning that goes with this tree +this was all sounding Vaguely Familiar + + align:start position:0% +this was all sounding Vaguely Familiar + + + align:start position:0% +this was all sounding Vaguely Familiar +are there questions about this tree is + + align:start position:0% +are there questions about this tree is + + + align:start position:0% +are there questions about this tree is +anybody looking at this tree and + + align:start position:0% +anybody looking at this tree and + + + align:start position:0% +anybody looking at this tree and +thinking + + align:start position:0% +thinking + + + align:start position:0% +thinking +wait which class am I in again + + align:start position:0% +wait which class am I in again + + + align:start position:0% +wait which class am I in again +what is going on why I'm going to talk + + align:start position:0% +what is going on why I'm going to talk + + + align:start position:0% +what is going on why I'm going to talk +about the stream a little bit of detail + + align:start position:0% +about the stream a little bit of detail + + + align:start position:0% +about the stream a little bit of detail +today but I just want to make sure + + align:start position:0% +today but I just want to make sure + + + align:start position:0% +today but I just want to make sure +there's nothing here that's shocking or + + align:start position:0% +there's nothing here that's shocking or + + + align:start position:0% +there's nothing here that's shocking or +distressing anybody + + align:start position:0% +distressing anybody + + + align:start position:0% +distressing anybody +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +um one of the things we've talked about + + align:start position:0% +um one of the things we've talked about + + + align:start position:0% +um one of the things we've talked about +is that some of the properties of that + + align:start position:0% +is that some of the properties of that + + + align:start position:0% +is that some of the properties of that +tree follow from selection so we have + + align:start position:0% +tree follow from selection so we have + + + align:start position:0% +tree follow from selection so we have +this idea that there's a special kind of + + align:start position:0% +this idea that there's a special kind of + + + align:start position:0% +this idea that there's a special kind of +relation that can hold between uh heads + + align:start position:0% +relation that can hold between uh heads + + + align:start position:0% +relation that can hold between uh heads +so the the smallest things in the tree + + align:start position:0% +so the the smallest things in the tree + + + align:start position:0% +so the the smallest things in the tree +the things that just have words under + + align:start position:0% +the things that just have words under + + + align:start position:0% +the things that just have words under +them things like the verb a relation + + align:start position:0% +them things like the verb a relation + + + align:start position:0% +them things like the verb a relation +that can hold between those heads and + + align:start position:0% +that can hold between those heads and + + + align:start position:0% +that can hold between those heads and +other kinds of phrases in the sentence + + align:start position:0% +other kinds of phrases in the sentence + + + align:start position:0% +other kinds of phrases in the sentence +so we've said that the verb tickle + + align:start position:0% +so we've said that the verb tickle + + + align:start position:0% +so we've said that the verb tickle +selects the object known phrase the + + align:start position:0% +selects the object known phrase the + + + align:start position:0% +selects the object known phrase the +child and what we mean by that is that + + align:start position:0% +child and what we mean by that is that + + + align:start position:0% +child and what we mean by that is that +the relation between the verb tickle and + + align:start position:0% +the relation between the verb tickle and + + + align:start position:0% +the relation between the verb tickle and +the object the child is special in that + + align:start position:0% +the object the child is special in that + + + align:start position:0% +the object the child is special in that +not every verb can be followed by an + + align:start position:0% +not every verb can be followed by an + + + align:start position:0% +not every verb can be followed by an +object so you know you can tickle a + + align:start position:0% +object so you know you can tickle a + + + align:start position:0% +object so you know you can tickle a +child you can devour a child you + + align:start position:0% +child you can devour a child you + + + align:start position:0% +child you can devour a child you +shouldn't but it's grammatical you can + + align:start position:0% +shouldn't but it's grammatical you can + + + align:start position:0% +shouldn't but it's grammatical you can +write a child sort of but there are + + align:start position:0% +write a child sort of but there are + + + align:start position:0% +write a child sort of but there are +other verbs for which you just can't do + + align:start position:0% +other verbs for which you just can't do + + + align:start position:0% +other verbs for which you just can't do +this you can't Thrive the child that + + align:start position:0% +this you can't Thrive the child that + + + align:start position:0% +this you can't Thrive the child that +doesn't make any sense uh so there are + + align:start position:0% +doesn't make any sense uh so there are + + + align:start position:0% +doesn't make any sense uh so there are +some verbs classic way to say this is + + align:start position:0% +some verbs classic way to say this is + + + align:start position:0% +some verbs classic way to say this is +there are some verbs that are transitive + + align:start position:0% +there are some verbs that are transitive + + + align:start position:0% +there are some verbs that are transitive +and others that are intransitive uh so + + align:start position:0% +and others that are intransitive uh so + + + align:start position:0% +and others that are intransitive uh so +in order to know whether you can have an + + align:start position:0% +in order to know whether you can have an + + + align:start position:0% +in order to know whether you can have an +object or not whether the there can be a + + align:start position:0% +object or not whether the there can be a + + + align:start position:0% +object or not whether the there can be a +noun phrase in that position or not the + + align:start position:0% +noun phrase in that position or not the + + + align:start position:0% +noun phrase in that position or not the +sister of the verb you got to know what + + align:start position:0% +sister of the verb you got to know what + + + align:start position:0% +sister of the verb you got to know what +the verb is the verb tells you whether + + align:start position:0% +the verb is the verb tells you whether + + + align:start position:0% +the verb is the verb tells you whether +it needs to have an object or not + + align:start position:0% +it needs to have an object or not + + + align:start position:0% +it needs to have an object or not +um so there's this relation of selection + + align:start position:0% +um so there's this relation of selection + + + align:start position:0% +um so there's this relation of selection +that holds between the verb and the + + align:start position:0% +that holds between the verb and the + + + align:start position:0% +that holds between the verb and the +object uh the idea is when we look up + + align:start position:0% +object uh the idea is when we look up + + + align:start position:0% +object uh the idea is when we look up +words like tickle and devour and write + + align:start position:0% +words like tickle and devour and write + + + align:start position:0% +words like tickle and devour and write +in our mental lexicon uh we'll see + + align:start position:0% +in our mental lexicon uh we'll see + + + align:start position:0% +in our mental lexicon uh we'll see +various things about them including how + + align:start position:0% +various things about them including how + + + align:start position:0% +various things about them including how +they're pronounced uh but also uh + + align:start position:0% +they're pronounced uh but also uh + + + align:start position:0% +they're pronounced uh but also uh +whether they can have objects or not + + align:start position:0% +whether they can have objects or not + + + align:start position:0% +whether they can have objects or not +whether they select for noun phrase + + align:start position:0% +whether they select for noun phrase + + + align:start position:0% +whether they select for noun phrase +sisters or not so when we ask going back + + align:start position:0% +sisters or not so when we ask going back + + + align:start position:0% +sisters or not so when we ask going back +to the tree why is the sister of the + + align:start position:0% +to the tree why is the sister of the + + + align:start position:0% +to the tree why is the sister of the +verb the noun phrase the child + + align:start position:0% +verb the noun phrase the child + + + align:start position:0% +verb the noun phrase the child +the answer one way of interpreting that + + align:start position:0% +the answer one way of interpreting that + + + align:start position:0% +the answer one way of interpreting that +question the answer is well it's because + + align:start position:0% +question the answer is well it's because + + + align:start position:0% +question the answer is well it's because +the verb tickle selects for a noun for + + align:start position:0% +the verb tickle selects for a noun for + + + align:start position:0% +the verb tickle selects for a noun for +his sister and so you give it one now + + align:start position:0% +his sister and so you give it one now + + + align:start position:0% +his sister and so you give it one now +that's why the tree has that bit of + + align:start position:0% +that's why the tree has that bit of + + + align:start position:0% +that's why the tree has that bit of +and we can tell that kind of story about + + align:start position:0% +and we can tell that kind of story about + + + align:start position:0% +and we can tell that kind of story about +a lot of parts of this tree so similarly + + align:start position:0% +a lot of parts of this tree so similarly + + + align:start position:0% +a lot of parts of this tree so similarly +we're going to want to say that the + + align:start position:0% +we're going to want to say that the + + + align:start position:0% +we're going to want to say that the +preposition with selects for a sister + + align:start position:0% +preposition with selects for a sister + + + align:start position:0% +preposition with selects for a sister +that's a noun phrase the feather + + align:start position:0% +that's a noun phrase the feather + + + align:start position:0% +that's a noun phrase the feather +for that matter we'll probably want to + + align:start position:0% +for that matter we'll probably want to + + + align:start position:0% +for that matter we'll probably want to +say that the T will is selecting for a + + align:start position:0% +say that the T will is selecting for a + + + align:start position:0% +say that the T will is selecting for a +verb phrase that's why the T has a verb + + align:start position:0% +verb phrase that's why the T has a verb + + + align:start position:0% +verb phrase that's why the T has a verb +phrase I said sister so there are + + align:start position:0% +phrase I said sister so there are + + + align:start position:0% +phrase I said sister so there are +various places in this tree where a head + + align:start position:0% +various places in this tree where a head + + + align:start position:0% +various places in this tree where a head +has a particular sister and it's because + + align:start position:0% +has a particular sister and it's because + + + align:start position:0% +has a particular sister and it's because +the head is selecting for that as a + + align:start position:0% +the head is selecting for that as a + + + align:start position:0% +the head is selecting for that as a +sister + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +we also said that this relation of + + align:start position:0% +we also said that this relation of + + + align:start position:0% +we also said that this relation of +selection that is something that heads + + align:start position:0% +selection that is something that heads + + + align:start position:0% +selection that is something that heads +can do they can select for properties of + + align:start position:0% +can do they can select for properties of + + + align:start position:0% +can do they can select for properties of +their sister + + align:start position:0% +their sister + + + align:start position:0% +their sister +that sometimes at least they select more + + align:start position:0% +that sometimes at least they select more + + + align:start position:0% +that sometimes at least they select more +specifically than that they select for + + align:start position:0% +specifically than that they select for + + + align:start position:0% +specifically than that they select for +sisters uh where the sister's head has a + + align:start position:0% +sisters uh where the sister's head has a + + + align:start position:0% +sisters uh where the sister's head has a +particular property so I think the + + align:start position:0% +particular property so I think the + + + align:start position:0% +particular property so I think the +example I gave you last time was verb + + align:start position:0% +example I gave you last time was verb + + + align:start position:0% +example I gave you last time was verb +the verb depends where the verb depends + + align:start position:0% +the verb depends where the verb depends + + + align:start position:0% +the verb depends where the verb depends +needs a prepositional phrase sister but + + align:start position:0% +needs a prepositional phrase sister but + + + align:start position:0% +needs a prepositional phrase sister but +it specifically needs a prepositional + + align:start position:0% +it specifically needs a prepositional + + + align:start position:0% +it specifically needs a prepositional +phrase sister in which the preposition + + align:start position:0% +phrase sister in which the preposition + + + align:start position:0% +phrase sister in which the preposition +is on so you have to depend on things + + align:start position:0% +is on so you have to depend on things + + + align:start position:0% +is on so you have to depend on things +you can't depend from them or depend at + + align:start position:0% +you can't depend from them or depend at + + + align:start position:0% +you can't depend from them or depend at +them you can't just have any preposition + + align:start position:0% +them you can't just have any preposition + + + align:start position:0% +them you can't just have any preposition +there has to be has to be on + + align:start position:0% +there has to be has to be on + + + align:start position:0% +there has to be has to be on +um so uh there are verbs like Depend and + + align:start position:0% +um so uh there are verbs like Depend and + + + align:start position:0% +um so uh there are verbs like Depend and +there are many verbs like this uh that + + align:start position:0% +there are many verbs like this uh that + + + align:start position:0% +there are many verbs like this uh that +select for a particular prepositional + + align:start position:0% +select for a particular prepositional + + + align:start position:0% +select for a particular prepositional +phrase sisters but in particular + + align:start position:0% +phrase sisters but in particular + + + align:start position:0% +phrase sisters but in particular +prepositional phrase sisters that have a + + align:start position:0% +prepositional phrase sisters that have a + + + align:start position:0% +prepositional phrase sisters that have a +particular preposition + + align:start position:0% +particular preposition + + + align:start position:0% +particular preposition +sometimes it's less particular than that + + align:start position:0% +sometimes it's less particular than that + + + align:start position:0% +sometimes it's less particular than that +so uh I think in class I said + + align:start position:0% +so uh I think in class I said + + + align:start position:0% +so uh I think in class I said +um I said he said vamping until he could + + align:start position:0% +um I said he said vamping until he could + + + align:start position:0% +um I said he said vamping until he could +get some chalk out that uh the verb put + + align:start position:0% +get some chalk out that uh the verb put + + + align:start position:0% +get some chalk out that uh the verb put +seems to select for a noun phrase sister + + align:start position:0% +seems to select for a noun phrase sister + + + align:start position:0% +seems to select for a noun phrase sister +in a prepositional phrase sister so you + + align:start position:0% +in a prepositional phrase sister so you + + + align:start position:0% +in a prepositional phrase sister so you +put the book + + align:start position:0% +put the book + + + align:start position:0% +put the book +on the table + + align:start position:0% + + + + align:start position:0% + +in the refrigerator + + align:start position:0% + + + + align:start position:0% + +or + + align:start position:0% +or + + + align:start position:0% +or +under the car + + align:start position:0% +under the car + + + align:start position:0% +under the car +or whatever wherever it is you want to + + align:start position:0% +or whatever wherever it is you want to + + + align:start position:0% +or whatever wherever it is you want to +put look + + align:start position:0% +put look + + + align:start position:0% +put look +um so the put has to have a noun phrase + + align:start position:0% +um so the put has to have a noun phrase + + + align:start position:0% +um so the put has to have a noun phrase +object doesn't have to be the book can + + align:start position:0% +object doesn't have to be the book can + + + align:start position:0% +object doesn't have to be the book can +be any noun phrase and then there can be + + align:start position:0% +be any noun phrase and then there can be + + + align:start position:0% +be any noun phrase and then there can be +a prepositional phrase + + align:start position:0% +a prepositional phrase + + + align:start position:0% +a prepositional phrase +put is not like dependent there are a + + align:start position:0% +put is not like dependent there are a + + + align:start position:0% +put is not like dependent there are a +variety of prepositions that can be here + + align:start position:0% +variety of prepositions that can be here + + + align:start position:0% +variety of prepositions that can be here +but you can't just have any preposition + + align:start position:0% +but you can't just have any preposition + + + align:start position:0% +but you can't just have any preposition +here so you can't say put the book + + align:start position:0% +here so you can't say put the book + + + align:start position:0% +here so you can't say put the book +during the party + + align:start position:0% + + + + align:start position:0% + +that's not a that's not a possible + + align:start position:0% +that's not a that's not a possible + + + align:start position:0% +that's not a that's not a possible +sentence + + align:start position:0% +sentence + + + align:start position:0% +sentence +um and we might hope to derive that from + + align:start position:0% +um and we might hope to derive that from + + + align:start position:0% +um and we might hope to derive that from +properties of the meaning of put right + + align:start position:0% +properties of the meaning of put right + + + align:start position:0% +properties of the meaning of put right +so the prepositional phrase that goes + + align:start position:0% +so the prepositional phrase that goes + + + align:start position:0% +so the prepositional phrase that goes +with put needs to specify a location + + align:start position:0% +with put needs to specify a location + + + align:start position:0% +with put needs to specify a location +right uh and during the party doesn't + + align:start position:0% +right uh and during the party doesn't + + + align:start position:0% +right uh and during the party doesn't +specify a location unless we're thinking + + align:start position:0% +specify a location unless we're thinking + + + align:start position:0% +specify a location unless we're thinking +of time as space which as long as syntax + + align:start position:0% +of time as space which as long as syntax + + + align:start position:0% +of time as space which as long as syntax +does not uh Doctor Who I think we're + + align:start position:0% +does not uh Doctor Who I think we're + + + align:start position:0% +does not uh Doctor Who I think we're +okay yeah + + align:start position:0% + + + + align:start position:0% + +oh dear + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um so merge is only binary and that + + align:start position:0% +um so merge is only binary and that + + + align:start position:0% +um so merge is only binary and that +means + + align:start position:0% +means + + + align:start position:0% +means +if we're going to have a tree for these + + align:start position:0% +if we're going to have a tree for these + + + align:start position:0% +if we're going to have a tree for these +kinds of sentences we're going to need + + align:start position:0% +kinds of sentences we're going to need + + + align:start position:0% +kinds of sentences we're going to need +to put the verb put and since we want + + align:start position:0% +to put the verb put and since we want + + + align:start position:0% +to put the verb put and since we want +the noun phrase to be to be next that's + + align:start position:0% +the noun phrase to be to be next that's + + + align:start position:0% +the noun phrase to be to be next that's +what this seems to tell us we'll have a + + align:start position:0% +what this seems to tell us we'll have a + + + align:start position:0% +what this seems to tell us we'll have a +noun phrase here + + align:start position:0% + + + + align:start position:0% + +and then we'll have a prepositional + + align:start position:0% +and then we'll have a prepositional + + + align:start position:0% +and then we'll have a prepositional +phrase + + align:start position:0% + + + + align:start position:0% + +that's one possible answer to your + + align:start position:0% +that's one possible answer to your + + + align:start position:0% +that's one possible answer to your +question if merge is going to be binary + + align:start position:0% + + + + align:start position:0% + +if merge is going to be binary we're + + align:start position:0% +if merge is going to be binary we're + + + align:start position:0% +if merge is going to be binary we're +going to want to say yeah + + align:start position:0% +going to want to say yeah + + + align:start position:0% +going to want to say yeah +put is something that needs two things + + align:start position:0% +put is something that needs two things + + + align:start position:0% +put is something that needs two things +we're going to have to give them to it + + align:start position:0% +we're going to have to give them to it + + + align:start position:0% +we're going to have to give them to it +one at a time we can't give them both to + + align:start position:0% +one at a time we can't give them both to + + + align:start position:0% +one at a time we can't give them both to +it at once otherwise if we wanted to do + + align:start position:0% +it at once otherwise if we wanted to do + + + align:start position:0% +it at once otherwise if we wanted to do +that we would need to use ternary merge + + align:start position:0% +that we would need to use ternary merge + + + align:start position:0% +that we would need to use ternary merge +right we need to merge three things at + + align:start position:0% +right we need to merge three things at + + + align:start position:0% +right we need to merge three things at +once and so we'll merge them one at a + + align:start position:0% +once and so we'll merge them one at a + + + align:start position:0% +once and so we'll merge them one at a +time we'll first give it the noun phrase + + align:start position:0% +time we'll first give it the noun phrase + + + align:start position:0% +time we'll first give it the noun phrase +and then we'll give it the prepositional + + align:start position:0% +and then we'll give it the prepositional + + + align:start position:0% +and then we'll give it the prepositional +phrase why do we first give it the noun + + align:start position:0% +phrase why do we first give it the noun + + + align:start position:0% +phrase why do we first give it the noun +phrase and then the prepositional phrase + + align:start position:0% +phrase and then the prepositional phrase + + + align:start position:0% +phrase and then the prepositional phrase +why don't we say put on the table of the + + align:start position:0% +why don't we say put on the table of the + + + align:start position:0% +why don't we say put on the table of the +book we might actually get to that but + + align:start position:0% +book we might actually get to that but + + + align:start position:0% +book we might actually get to that but +we're not going to get to it today so + + align:start position:0% +we're not going to get to it today so + + + align:start position:0% +we're not going to get to it today so +this is one possible answer to your + + align:start position:0% +this is one possible answer to your + + + align:start position:0% +this is one possible answer to your +question another possible answer to your + + align:start position:0% +question another possible answer to your + + + align:start position:0% +question another possible answer to your +question of course would be to say ah + + align:start position:0% +question of course would be to say ah + + + align:start position:0% +question of course would be to say ah +we've discovered that we were wrong to + + align:start position:0% +we've discovered that we were wrong to + + + align:start position:0% +we've discovered that we were wrong to +say that there's binary merge right that + + align:start position:0% +say that there's binary merge right that + + + align:start position:0% +say that there's binary merge right that +uh here's a place where we need there to + + align:start position:0% +uh here's a place where we need there to + + + align:start position:0% +uh here's a place where we need there to +be eternity merge this is going to + + align:start position:0% +be eternity merge this is going to + + + align:start position:0% +be eternity merge this is going to +interact with things we're going to want + + align:start position:0% +interact with things we're going to want + + + align:start position:0% +interact with things we're going to want +to say about how selection works so I + + align:start position:0% +to say about how selection works so I + + + align:start position:0% +to say about how selection works so I +have now a couple of times said a thing + + align:start position:0% +have now a couple of times said a thing + + + align:start position:0% +have now a couple of times said a thing +gets to select for the properties of its + + align:start position:0% +gets to select for the properties of its + + + align:start position:0% +gets to select for the properties of its +sister right and here it's selecting for + + align:start position:0% +sister right and here it's selecting for + + + align:start position:0% +sister right and here it's selecting for +properties of its sister but this is not + + align:start position:0% +properties of its sister but this is not + + + align:start position:0% +properties of its sister but this is not +its sister right this is something else + + align:start position:0% +its sister right this is something else + + + align:start position:0% +its sister right this is something else +it's it's uh never mind I can't figure + + align:start position:0% +it's it's uh never mind I can't figure + + + align:start position:0% +it's it's uh never mind I can't figure +out the family relation between these + + align:start position:0% +out the family relation between these + + + align:start position:0% +out the family relation between these +two points on the tree it's it's um uh + + align:start position:0% +two points on the tree it's it's um uh + + + align:start position:0% +two points on the tree it's it's um uh +what is it it's its ant yeah the + + align:start position:0% +what is it it's its ant yeah the + + + align:start position:0% +what is it it's its ant yeah the +prepositional phrase is the end of the + + align:start position:0% +prepositional phrase is the end of the + + + align:start position:0% +prepositional phrase is the end of the +verb that's not how how actual + + align:start position:0% +verb that's not how how actual + + + align:start position:0% +verb that's not how how actual +syntacticians talk about this kind of + + align:start position:0% +syntacticians talk about this kind of + + + align:start position:0% +syntacticians talk about this kind of +thing so they're not sisters + + align:start position:0% +thing so they're not sisters + + + align:start position:0% +thing so they're not sisters +um uh so you know two kinds of things we + + align:start position:0% +um uh so you know two kinds of things we + + + align:start position:0% +um uh so you know two kinds of things we +can say oh what we're discovering is uh + + align:start position:0% +can say oh what we're discovering is uh + + + align:start position:0% +can say oh what we're discovering is uh +that we need turn to emerge we need + + align:start position:0% +that we need turn to emerge we need + + + align:start position:0% +that we need turn to emerge we need +these to both be sisters + + align:start position:0% +these to both be sisters + + + align:start position:0% +these to both be sisters +another would be to say oh um we're + + align:start position:0% +another would be to say oh um we're + + + align:start position:0% +another would be to say oh um we're +discovering that uh selection isn't + + align:start position:0% +discovering that uh selection isn't + + + align:start position:0% +discovering that uh selection isn't +necessarily for properties of your + + align:start position:0% +necessarily for properties of your + + + align:start position:0% +necessarily for properties of your +sister it's something more like you + + align:start position:0% +sister it's something more like you + + + align:start position:0% +sister it's something more like you +select things the first things that you + + align:start position:0% +select things the first things that you + + + align:start position:0% +select things the first things that you +merge must be things that you select + + align:start position:0% +merge must be things that you select + + + align:start position:0% +merge must be things that you select +we're going to circle around and talk + + align:start position:0% +we're going to circle around and talk + + + align:start position:0% +we're going to circle around and talk +about that in a second so to say + + align:start position:0% +about that in a second so to say + + + align:start position:0% +about that in a second so to say +something more elaborate about how you + + align:start position:0% +something more elaborate about how you + + + align:start position:0% +something more elaborate about how you +select so that's a really good question + + align:start position:0% +select so that's a really good question + + + align:start position:0% +select so that's a really good question +what we really need to do is develop + + align:start position:0% +what we really need to do is develop + + + align:start position:0% +what we really need to do is develop +tests that will tell us whether this is + + align:start position:0% +tests that will tell us whether this is + + + align:start position:0% +tests that will tell us whether this is +the right tree for something like this + + align:start position:0% +the right tree for something like this + + + align:start position:0% +the right tree for something like this +or whether we would rather have + + align:start position:0% +or whether we would rather have + + + align:start position:0% +or whether we would rather have +something like this where there's a verb + + align:start position:0% +something like this where there's a verb + + + align:start position:0% +something like this where there's a verb +and a noun phrase and prepositional + + align:start position:0% +and a noun phrase and prepositional + + + align:start position:0% +and a noun phrase and prepositional +phrase and merge doesn't have to to be + + align:start position:0% +phrase and merge doesn't have to to be + + + align:start position:0% +phrase and merge doesn't have to to be +binary + + align:start position:0% +binary + + + align:start position:0% +binary +just to cheat a little bit what we'll + + align:start position:0% +just to cheat a little bit what we'll + + + align:start position:0% +just to cheat a little bit what we'll +what we'll find out what we would find + + align:start position:0% +what we'll find out what we would find + + + align:start position:0% +what we'll find out what we would find +out when we develop these kinds of tests + + align:start position:0% +out when we develop these kinds of tests + + + align:start position:0% +out when we develop these kinds of tests +is that this is not the kind of tree + + align:start position:0% +is that this is not the kind of tree + + + align:start position:0% +is that this is not the kind of tree +that we want we want trees + + align:start position:0% +that we want we want trees + + + align:start position:0% +that we want we want trees +but uh we're gonna have to do some work + + align:start position:0% +but uh we're gonna have to do some work + + + align:start position:0% +but uh we're gonna have to do some work +to develop those tests + + align:start position:0% +to develop those tests + + + align:start position:0% +to develop those tests +here we go + + align:start position:0% +here we go + + + align:start position:0% +here we go +oh no + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +like a secret selection inside of it + + align:start position:0% +like a secret selection inside of it + + + align:start position:0% +like a secret selection inside of it +because you could think of board as like + + align:start position:0% +because you could think of board as like + + + align:start position:0% +because you could think of board as like +get on the ship oh + + align:start position:0% + + + + align:start position:0% + +yeah or you could like have this board + + align:start position:0% +yeah or you could like have this board + + + align:start position:0% +yeah or you could like have this board +which kind of includes it inside of it + + align:start position:0% +which kind of includes it inside of it + + + align:start position:0% +which kind of includes it inside of it +like in Spanish + + align:start position:0% +like in Spanish + + + align:start position:0% +like in Spanish +yeah and so it's like + + align:start position:0% +yeah and so it's like + + + align:start position:0% +yeah and so it's like +as + + align:start position:0% +as + + + align:start position:0% +as +a verb that like maybe like + + align:start position:0% + + + + align:start position:0% + +it put the refrigerator everyone knows + + align:start position:0% +it put the refrigerator everyone knows + + + align:start position:0% +it put the refrigerator everyone knows +when you put in the refrigerator yeah + + align:start position:0% +when you put in the refrigerator yeah + + + align:start position:0% +when you put in the refrigerator yeah +yeah I see what you mean so you're + + align:start position:0% +yeah I see what you mean so you're + + + align:start position:0% +yeah I see what you mean so you're +you're pointing out something something + + align:start position:0% +you're pointing out something something + + + align:start position:0% +you're pointing out something something +important which is that um uh here let's + + align:start position:0% +important which is that um uh here let's + + + align:start position:0% +important which is that um uh here let's +do look for you know but in English + + align:start position:0% +do look for you know but in English + + + align:start position:0% +do look for you know but in English +we're going to want to have a verb look + + align:start position:0% +we're going to want to have a verb look + + + align:start position:0% +we're going to want to have a verb look +that selects for a prepositional phrase + + align:start position:0% +that selects for a prepositional phrase + + + align:start position:0% +that selects for a prepositional phrase +uh where the preposition is for + + align:start position:0% + + + + align:start position:0% + +but that there are other languages like + + align:start position:0% +but that there are other languages like + + + align:start position:0% +but that there are other languages like +Spanish in which there's a single verb + + align:start position:0% +Spanish in which there's a single verb + + + align:start position:0% +Spanish in which there's a single verb +that means look for for that matter in + + align:start position:0% +that means look for for that matter in + + + align:start position:0% +that means look for for that matter in +English there's a there's a verb seek + + align:start position:0% +English there's a there's a verb seek + + + align:start position:0% +English there's a there's a verb seek +extended dramatic + + align:start position:0% +extended dramatic + + + align:start position:0% +extended dramatic +uh if I go into a bookstore and say I'm + + align:start position:0% +uh if I go into a bookstore and say I'm + + + align:start position:0% +uh if I go into a bookstore and say I'm +looking for a book that's the normal + + align:start position:0% +looking for a book that's the normal + + + align:start position:0% +looking for a book that's the normal +thing for me to say I could also go into + + align:start position:0% +thing for me to say I could also go into + + + align:start position:0% +thing for me to say I could also go into +a bookstore and say I am seeking a book + + align:start position:0% +a bookstore and say I am seeking a book + + + align:start position:0% +a bookstore and say I am seeking a book +um they would probably direct me to the + + align:start position:0% +um they would probably direct me to the + + + align:start position:0% +um they would probably direct me to the +you know fantasy science fiction section + + align:start position:0% +you know fantasy science fiction section + + + align:start position:0% +you know fantasy science fiction section +you know if I if I did that + + align:start position:0% +you know if I if I did that + + + align:start position:0% +you know if I if I did that +um uh but those are both two ways to say + + align:start position:0% +um uh but those are both two ways to say + + + align:start position:0% +um uh but those are both two ways to say +the same thing + + align:start position:0% +the same thing + + + align:start position:0% +the same thing +um so so maybe you know the way to think + + align:start position:0% +um so so maybe you know the way to think + + + align:start position:0% +um so so maybe you know the way to think +about this is yeah Spanish doesn't have + + align:start position:0% +about this is yeah Spanish doesn't have + + + align:start position:0% +about this is yeah Spanish doesn't have +a verb that means look for it has a verb + + align:start position:0% +a verb that means look for it has a verb + + + align:start position:0% +a verb that means look for it has a verb +that means seek + + align:start position:0% +that means seek + + + align:start position:0% +that means seek +you know there uh uh yeah so or maybe + + align:start position:0% +you know there uh uh yeah so or maybe + + + align:start position:0% +you know there uh uh yeah so or maybe +another way to say this and this is + + align:start position:0% +another way to say this and this is + + + align:start position:0% +another way to say this and this is +going to be important as you guys are + + align:start position:0% +going to be important as you guys are + + + align:start position:0% +going to be important as you guys are +doing uh your work with the languages + + align:start position:0% +doing uh your work with the languages + + + align:start position:0% +doing uh your work with the languages +that you're working on + + align:start position:0% +that you're working on + + + align:start position:0% +that you're working on +um is that you shouldn't necessarily + + align:start position:0% +um is that you shouldn't necessarily + + + align:start position:0% +um is that you shouldn't necessarily +expect the selectional properties of a + + align:start position:0% +expect the selectional properties of a + + + align:start position:0% +expect the selectional properties of a +verb to be the same uh from one language + + align:start position:0% +verb to be the same uh from one language + + + align:start position:0% +verb to be the same uh from one language +to the next that if you are inclined to + + align:start position:0% +to the next that if you are inclined to + + + align:start position:0% +to the next that if you are inclined to +think of Spanish is it with Scott uh as + + align:start position:0% +think of Spanish is it with Scott uh as + + + align:start position:0% +think of Spanish is it with Scott uh as +the equivalent of look for that we want + + align:start position:0% +the equivalent of look for that we want + + + align:start position:0% +the equivalent of look for that we want +to think of of that as as that English + + align:start position:0% +to think of of that as as that English + + + align:start position:0% +to think of of that as as that English +is a verb look that selects for a + + align:start position:0% +is a verb look that selects for a + + + align:start position:0% +is a verb look that selects for a +prepositional phrase Spanish has a verb + + align:start position:0% +prepositional phrase Spanish has a verb + + + align:start position:0% +prepositional phrase Spanish has a verb +that's like seek it selects for uh for a + + align:start position:0% +that's like seek it selects for uh for a + + + align:start position:0% +that's like seek it selects for uh for a +noun phrase + + align:start position:0% +noun phrase + + + align:start position:0% +noun phrase +um yeah so you want to be careful as you + + align:start position:0% +um yeah so you want to be careful as you + + + align:start position:0% +um yeah so you want to be careful as you +are going from language to language uh + + align:start position:0% +are going from language to language uh + + + align:start position:0% +are going from language to language uh +you can't trust selectional restrictions + + align:start position:0% +you can't trust selectional restrictions + + + align:start position:0% +you can't trust selectional restrictions +um + + align:start position:0% +um + + + align:start position:0% +um +and indeed so I've used put as the + + align:start position:0% +and indeed so I've used put as the + + + align:start position:0% +and indeed so I've used put as the +example of a verb that has two things + + align:start position:0% +example of a verb that has two things + + + align:start position:0% +example of a verb that has two things +that it seems to select but there are + + align:start position:0% +that it seems to select but there are + + + align:start position:0% +that it seems to select but there are +probably examples of verbs that select + + align:start position:0% +probably examples of verbs that select + + + align:start position:0% +probably examples of verbs that select +uh uh two things where the two things + + align:start position:0% +uh uh two things where the two things + + + align:start position:0% +uh uh two things where the two things +are say both noun phrases so take a verb + + align:start position:0% +are say both noun phrases so take a verb + + + align:start position:0% +are say both noun phrases so take a verb +like give + + align:start position:0% +like give + + + align:start position:0% +like give +the children + + align:start position:0% + + + + align:start position:0% + +books + + align:start position:0% +books + + + align:start position:0% +books +so here we want there to be two noun + + align:start position:0% +so here we want there to be two noun + + + align:start position:0% +so here we want there to be two noun +phrases uh coming together with give and + + align:start position:0% +phrases uh coming together with give and + + + align:start position:0% +phrases uh coming together with give and +give uh select those it's um it's a + + align:start position:0% +give uh select those it's um it's a + + + align:start position:0% +give uh select those it's um it's a +property of give that it can it can have + + align:start position:0% +property of give that it can it can have + + + align:start position:0% +property of give that it can it can have +two noun phrases after it and not every + + align:start position:0% +two noun phrases after it and not every + + + align:start position:0% +two noun phrases after it and not every +verb can do that put for example can't + + align:start position:0% + + + + align:start position:0% + +you know so even verbs that are fairly + + align:start position:0% +you know so even verbs that are fairly + + + align:start position:0% +you know so even verbs that are fairly +similar in their meaning like donate uh + + align:start position:0% +similar in their meaning like donate uh + + + align:start position:0% +similar in their meaning like donate uh +so you can't donate the children books + + align:start position:0% +so you can't donate the children books + + + align:start position:0% +so you can't donate the children books +you have to donate books to the children + + align:start position:0% +you have to donate books to the children + + + align:start position:0% +you have to donate books to the children +um so yes there uh as so often in this + + align:start position:0% +um so yes there uh as so often in this + + + align:start position:0% +um so yes there uh as so often in this +class I'm showing you the easiest + + align:start position:0% +class I'm showing you the easiest + + + align:start position:0% +class I'm showing you the easiest +examples here and as so often in this + + align:start position:0% +examples here and as so often in this + + + align:start position:0% +examples here and as so often in this +class you guys are immediately saying + + align:start position:0% +class you guys are immediately saying + + + align:start position:0% +class you guys are immediately saying +wait wait what about the complicated + + align:start position:0% +wait wait what about the complicated + + + align:start position:0% +wait wait what about the complicated +examples so yes there are more + + align:start position:0% +examples so yes there are more + + + align:start position:0% +examples so yes there are more +complicated examples we'll try to get to + + align:start position:0% +complicated examples we'll try to get to + + + align:start position:0% +complicated examples we'll try to get to +them cases where you're selecting more + + align:start position:0% +them cases where you're selecting more + + + align:start position:0% +them cases where you're selecting more +than one thing we'll come back to that + + align:start position:0% +than one thing we'll come back to that + + + align:start position:0% +than one thing we'll come back to that +we'll talk about it more now yes + + align:start position:0% + + + + align:start position:0% + +so if we use the technology that we have + + align:start position:0% +so if we use the technology that we have + + + align:start position:0% +so if we use the technology that we have +right now we're kind of compelled to + + align:start position:0% +right now we're kind of compelled to + + + align:start position:0% +right now we're kind of compelled to +have a tree like this one + + align:start position:0% + + + + align:start position:0% + +all right this is capital N because I + + align:start position:0% +all right this is capital N because I + + + align:start position:0% +all right this is capital N because I +knew I was about to write a noun phrase + + align:start position:0% +knew I was about to write a noun phrase + + + align:start position:0% +knew I was about to write a noun phrase +um give the children books you know so + + align:start position:0% +um give the children books you know so + + + align:start position:0% +um give the children books you know so +where uh give needs to to combine with + + align:start position:0% +where uh give needs to to combine with + + + align:start position:0% +where uh give needs to to combine with +two noun phrases and merges binary and + + align:start position:0% +two noun phrases and merges binary and + + + align:start position:0% +two noun phrases and merges binary and +so we'll do binary merge twice + + align:start position:0% +so we'll do binary merge twice + + + align:start position:0% +so we'll do binary merge twice +um that's the kind of tree that we could + + align:start position:0% +um that's the kind of tree that we could + + + align:start position:0% +um that's the kind of tree that we could +draw with the techniques that we have + + align:start position:0% +draw with the techniques that we have + + + align:start position:0% +draw with the techniques that we have +right now + + align:start position:0% +right now + + + align:start position:0% +right now +I I hope I hedged enough in there to + + align:start position:0% +I I hope I hedged enough in there to + + + align:start position:0% +I I hope I hedged enough in there to +make you feel + + align:start position:0% +make you feel + + + align:start position:0% +make you feel +emotionally + + align:start position:0% +emotionally + + + align:start position:0% +emotionally +um grounded enough that if it turns out + + align:start position:0% +um grounded enough that if it turns out + + + align:start position:0% +um grounded enough that if it turns out +later that that's not the right tree + + align:start position:0% +later that that's not the right tree + + + align:start position:0% +later that that's not the right tree +that you won't be too disappointed + + align:start position:0% +that you won't be too disappointed + + + align:start position:0% +that you won't be too disappointed +because we're going to talk more about + + align:start position:0% +because we're going to talk more about + + + align:start position:0% +because we're going to talk more about +this stuff our understanding will get + + align:start position:0% +this stuff our understanding will get + + + align:start position:0% +this stuff our understanding will get +more sophisticated but given everything + + align:start position:0% +more sophisticated but given everything + + + align:start position:0% +more sophisticated but given everything +I'm telling you right now that's the + + align:start position:0% +I'm telling you right now that's the + + + align:start position:0% +I'm telling you right now that's the +tree we expect + + align:start position:0% +tree we expect + + + align:start position:0% +tree we expect +yes + + align:start position:0% + + + + align:start position:0% + +I'm sorry I missed the middle of that uh + + align:start position:0% +I'm sorry I missed the middle of that uh + + + align:start position:0% +I'm sorry I missed the middle of that uh +does do these trees have to have like + + align:start position:0% +does do these trees have to have like + + + align:start position:0% +does do these trees have to have like +exactly each and every word each + + align:start position:0% +exactly each and every word each + + + align:start position:0% +exactly each and every word each +sentence or could it like fill in some + + align:start position:0% +sentence or could it like fill in some + + + align:start position:0% +sentence or could it like fill in some +like uh works like for example I learned + + align:start position:0% +like uh works like for example I learned + + + align:start position:0% +like uh works like for example I learned +in elementary school it's the subject of + + align:start position:0% +in elementary school it's the subject of + + + align:start position:0% +in elementary school it's the subject of +everything I see you oh oh oh could you + + align:start position:0% +everything I see you oh oh oh could you + + + align:start position:0% +everything I see you oh oh oh could you +how + + align:start position:0% + + + + align:start position:0% + +I see + + align:start position:0% +I see + + + align:start position:0% +I see +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um oh I see oh that's a really that's a + + align:start position:0% +um oh I see oh that's a really that's a + + + align:start position:0% +um oh I see oh that's a really that's a +really that's a really interesting and + + align:start position:0% +really that's a really interesting and + + + align:start position:0% +really that's a really interesting and +difficult question + + align:start position:0% +difficult question + + + align:start position:0% +difficult question +um the short answer is yes there are + + align:start position:0% +um the short answer is yes there are + + + align:start position:0% +um the short answer is yes there are +there absolutely are places where we're + + align:start position:0% +there absolutely are places where we're + + + align:start position:0% +there absolutely are places where we're +going to want to say I'm showing you + + align:start position:0% +going to want to say I'm showing you + + + align:start position:0% +going to want to say I'm showing you +trees in which I'm not showing you trees + + align:start position:0% +trees in which I'm not showing you trees + + + align:start position:0% +trees in which I'm not showing you trees +anymore I'm showing you a nebula give me + + align:start position:0% +anymore I'm showing you a nebula give me + + + align:start position:0% +anymore I'm showing you a nebula give me +just a second + + align:start position:0% +just a second + + + align:start position:0% +just a second +um I'm showing you trees in which every + + align:start position:0% +um I'm showing you trees in which every + + + align:start position:0% +um I'm showing you trees in which every +uh terminal node every head has one word + + align:start position:0% +uh terminal node every head has one word + + + align:start position:0% +uh terminal node every head has one word +under it uh and you're wondering could + + align:start position:0% +under it uh and you're wondering could + + + align:start position:0% +under it uh and you're wondering could +it be could there be trees where there + + align:start position:0% +it be could there be trees where there + + + align:start position:0% +it be could there be trees where there +are nodes that don't have anything under + + align:start position:0% +are nodes that don't have anything under + + + align:start position:0% +are nodes that don't have anything under +them or don't have anything pronounced + + align:start position:0% +them or don't have anything pronounced + + + align:start position:0% +them or don't have anything pronounced +under them + + align:start position:0% +under them + + + align:start position:0% +under them +um + + align:start position:0% +um + + + align:start position:0% +um +and indeed uh the short answer is yes + + align:start position:0% +and indeed uh the short answer is yes + + + align:start position:0% +and indeed uh the short answer is yes +there surely are going to be such trees + + align:start position:0% +there surely are going to be such trees + + + align:start position:0% +there surely are going to be such trees +your example is a good one + + align:start position:0% +your example is a good one + + + align:start position:0% +your example is a good one +um + + align:start position:0% +um + + + align:start position:0% +um +do I wanna go off and talk about that + + align:start position:0% +do I wanna go off and talk about that + + + align:start position:0% +do I wanna go off and talk about that +yeah let's talk about that for just a + + align:start position:0% +yeah let's talk about that for just a + + + align:start position:0% +yeah let's talk about that for just a +second + + align:start position:0% +second + + + align:start position:0% +second +um + + align:start position:0% +um + + + align:start position:0% +um +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +we um + + align:start position:0% +we um + + + align:start position:0% +we um +we talked a little bit before we're + + align:start position:0% +we talked a little bit before we're + + + align:start position:0% +we talked a little bit before we're +going to come back to this later but we + + align:start position:0% +going to come back to this later but we + + + align:start position:0% +going to come back to this later but we +talked a little bit before about + + align:start position:0% +talked a little bit before about + + + align:start position:0% +talked a little bit before about +um uh yeah we can do this fast + + align:start position:0% +um uh yeah we can do this fast + + + align:start position:0% +um uh yeah we can do this fast +um uh + + align:start position:0% +um uh + + + align:start position:0% +um uh +constraints on things that pronouns and + + align:start position:0% +constraints on things that pronouns and + + + align:start position:0% +constraints on things that pronouns and +names can refer to so for example we + + align:start position:0% +names can refer to so for example we + + + align:start position:0% +names can refer to so for example we +talked about the fact that if you say + + align:start position:0% +talked about the fact that if you say + + + align:start position:0% +talked about the fact that if you say +she likes + + align:start position:0% +she likes + + + align:start position:0% +she likes +Sally + + align:start position:0% +Sally + + + align:start position:0% +Sally +that's a perfectly fine sentence but it + + align:start position:0% +that's a perfectly fine sentence but it + + + align:start position:0% +that's a perfectly fine sentence but it +can't mean that she and Sally are the + + align:start position:0% +can't mean that she and Sally are the + + + align:start position:0% +can't mean that she and Sally are the +same person + + align:start position:0% +same person + + + align:start position:0% +same person +right so she has to refer to somebody + + align:start position:0% +right so she has to refer to somebody + + + align:start position:0% +right so she has to refer to somebody +other than Sally and we developed a + + align:start position:0% +other than Sally and we developed a + + + align:start position:0% +other than Sally and we developed a +a rule that has that consequence and I + + align:start position:0% +a rule that has that consequence and I + + + align:start position:0% +a rule that has that consequence and I +promised you that we would talk about + + align:start position:0% +promised you that we would talk about + + + align:start position:0% +promised you that we would talk about +that rule in more depth later on + + align:start position:0% +that rule in more depth later on + + + align:start position:0% +that rule in more depth later on +here's another kind of case + + align:start position:0% +here's another kind of case + + + align:start position:0% +here's another kind of case +um if you say something like + + align:start position:0% +um if you say something like + + + align:start position:0% +um if you say something like +Ali + + align:start position:0% + + + + align:start position:0% + +offended herself + + align:start position:0% + + + + align:start position:0% + +there's this special expression herself + + align:start position:0% +there's this special expression herself + + + align:start position:0% +there's this special expression herself +and it has to refer to Sally right so + + align:start position:0% +and it has to refer to Sally right so + + + align:start position:0% +and it has to refer to Sally right so +Sally defended herself means Sally + + align:start position:0% +Sally defended herself means Sally + + + align:start position:0% +Sally defended herself means Sally +defended Sally right so + + align:start position:0% +defended Sally right so + + + align:start position:0% +defended Sally right so +herself refers back to whoever the + + align:start position:0% +herself refers back to whoever the + + + align:start position:0% +herself refers back to whoever the +subject is + + align:start position:0% +subject is + + + align:start position:0% +subject is +um if this had been Mary defended + + align:start position:0% +um if this had been Mary defended + + + align:start position:0% +um if this had been Mary defended +herself well it would have to be Mary + + align:start position:0% +herself well it would have to be Mary + + + align:start position:0% +herself well it would have to be Mary +defending Mary if it had been I defended + + align:start position:0% + + + + align:start position:0% + +myself + + align:start position:0% +myself + + + align:start position:0% +myself +well then you have to use this special + + align:start position:0% +well then you have to use this special + + + align:start position:0% +well then you have to use this special +form of these words these self words + + align:start position:0% +form of these words these self words + + + align:start position:0% +form of these words these self words +they're called reflexives + + align:start position:0% + + + + align:start position:0% + +these reflexives have to refer back to + + align:start position:0% +these reflexives have to refer back to + + + align:start position:0% +these reflexives have to refer back to +something else in the sentence in these + + align:start position:0% +something else in the sentence in these + + + align:start position:0% +something else in the sentence in these +examples they always refer to the + + align:start position:0% +examples they always refer to the + + + align:start position:0% +examples they always refer to the +subject yeah yeah um and they have to do + + align:start position:0% +subject yeah yeah um and they have to do + + + align:start position:0% +subject yeah yeah um and they have to do +that right so you can't say things like + + align:start position:0% +that right so you can't say things like + + + align:start position:0% +that right so you can't say things like +I defended + + align:start position:0% +I defended + + + align:start position:0% +I defended +herself + + align:start position:0% + + + + align:start position:0% + +himself + + align:start position:0% +himself + + + align:start position:0% +himself +right these are out yeah so uh the + + align:start position:0% +right these are out yeah so uh the + + + align:start position:0% +right these are out yeah so uh the +reflexive that's at the end of these + + align:start position:0% +reflexive that's at the end of these + + + align:start position:0% +reflexive that's at the end of these +sentences has to refer back to the + + align:start position:0% +sentences has to refer back to the + + + align:start position:0% +sentences has to refer back to the +subject in these cases + + align:start position:0% +subject in these cases + + + align:start position:0% +subject in these cases +um and the form of the reflexive tells + + align:start position:0% +um and the form of the reflexive tells + + + align:start position:0% +um and the form of the reflexive tells +you something about what the subject is + + align:start position:0% +you something about what the subject is + + + align:start position:0% +you something about what the subject is +so uh you get it it's got this so you + + align:start position:0% +so uh you get it it's got this so you + + + align:start position:0% +so uh you get it it's got this so you +get herself when the subject is you know + + align:start position:0% +get herself when the subject is you know + + + align:start position:0% +get herself when the subject is you know +feminine and third person and you get + + align:start position:0% +feminine and third person and you get + + + align:start position:0% +feminine and third person and you get +myself when the subject is first person + + align:start position:0% +myself when the subject is first person + + + align:start position:0% +myself when the subject is first person +and and if it were you + + align:start position:0% +and and if it were you + + + align:start position:0% +and and if it were you +offended + + align:start position:0% +offended + + + align:start position:0% +offended +it would be defended yourself + + align:start position:0% +it would be defended yourself + + + align:start position:0% +it would be defended yourself +now so this reflexive is telling you + + align:start position:0% +now so this reflexive is telling you + + + align:start position:0% +now so this reflexive is telling you +that it's referring back to you yeah + + align:start position:0% +that it's referring back to you yeah + + + align:start position:0% +that it's referring back to you yeah +this means you defended you now yeah I'm + + align:start position:0% +this means you defended you now yeah I'm + + + align:start position:0% +this means you defended you now yeah I'm +telling you all this because your + + align:start position:0% +telling you all this because your + + + align:start position:0% +telling you all this because your +example from elementary school is a + + align:start position:0% +example from elementary school is a + + + align:start position:0% +example from elementary school is a +really good one if I tell you + + align:start position:0% +really good one if I tell you + + + align:start position:0% +really good one if I tell you +defend yourself + + align:start position:0% + + + + align:start position:0% + +to command + + align:start position:0% +to command + + + align:start position:0% +to command +well everything that we've now learned + + align:start position:0% +well everything that we've now learned + + + align:start position:0% +well everything that we've now learned +about these reflexives leads us to hope + + align:start position:0% +about these reflexives leads us to hope + + + align:start position:0% +about these reflexives leads us to hope +that there's a u in that sentence + + align:start position:0% +that there's a u in that sentence + + + align:start position:0% +that there's a u in that sentence +because well that's what reflexive + + align:start position:0% +because well that's what reflexive + + + align:start position:0% +because well that's what reflexive +seemed to do they refer back to the + + align:start position:0% +seemed to do they refer back to the + + + align:start position:0% +seemed to do they refer back to the +subject and and the they have a forum + + align:start position:0% +subject and and the they have a forum + + + align:start position:0% +subject and and the they have a forum +that tells you something about what the + + align:start position:0% +that tells you something about what the + + + align:start position:0% +that tells you something about what the +subject is in this case they tell you + + align:start position:0% +subject is in this case they tell you + + + align:start position:0% +subject is in this case they tell you +that the subject is you which is what + + align:start position:0% +that the subject is you which is what + + + align:start position:0% +that the subject is you which is what +you were taught in elementary school + + align:start position:0% +you were taught in elementary school + + + align:start position:0% +you were taught in elementary school +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um so you say defend yourself and that's + + align:start position:0% +um so you say defend yourself and that's + + + align:start position:0% +um so you say defend yourself and that's +fine and you cannot say defend himself + + align:start position:0% +fine and you cannot say defend himself + + + align:start position:0% +fine and you cannot say defend himself +defend myself + + align:start position:0% +defend myself + + + align:start position:0% +defend myself +right just as you cannot say you + + align:start position:0% +right just as you cannot say you + + + align:start position:0% +right just as you cannot say you +defended you can say you defended + + align:start position:0% +defended you can say you defended + + + align:start position:0% +defended you can say you defended +yourself but not you defended myself + + align:start position:0% +yourself but not you defended myself + + + align:start position:0% +yourself but not you defended myself +for himself or herself yeah + + align:start position:0% +for himself or herself yeah + + + align:start position:0% +for himself or herself yeah +so indeed there are some good reasons to + + align:start position:0% +so indeed there are some good reasons to + + + align:start position:0% +so indeed there are some good reasons to +think that whoever told you that there's + + align:start position:0% +think that whoever told you that there's + + + align:start position:0% +think that whoever told you that there's +a you in this sentence was right you can + + align:start position:0% +a you in this sentence was right you can + + + align:start position:0% +a you in this sentence was right you can +kind of detect the You by using these + + align:start position:0% +kind of detect the You by using these + + + align:start position:0% +kind of detect the You by using these +reflexives yeah so uh there are indeed + + align:start position:0% +reflexives yeah so uh there are indeed + + + align:start position:0% +reflexives yeah so uh there are indeed +words that are not pronounced uh and if + + align:start position:0% +words that are not pronounced uh and if + + + align:start position:0% +words that are not pronounced uh and if +we were going to draw a tree for defend + + align:start position:0% +we were going to draw a tree for defend + + + align:start position:0% +we were going to draw a tree for defend +yourself we'd probably want to say yeah + + align:start position:0% +yourself we'd probably want to say yeah + + + align:start position:0% +yourself we'd probably want to say yeah +there's a u in subject position and + + align:start position:0% +there's a u in subject position and + + + align:start position:0% +there's a u in subject position and +there would have to be a rule saying + + align:start position:0% +there would have to be a rule saying + + + align:start position:0% +there would have to be a rule saying +don't pronounce that particular you + + align:start position:0% +don't pronounce that particular you + + + align:start position:0% +don't pronounce that particular you +so the shorter answer to your question + + align:start position:0% +so the shorter answer to your question + + + align:start position:0% +so the shorter answer to your question +is yes there are parts of trees that are + + align:start position:0% +is yes there are parts of trees that are + + + align:start position:0% +is yes there are parts of trees that are +not pronounced + + align:start position:0% +not pronounced + + + align:start position:0% +not pronounced +we may get a chance to talk more about + + align:start position:0% +we may get a chance to talk more about + + + align:start position:0% +we may get a chance to talk more about +it + + align:start position:0% +it + + + align:start position:0% +it +all right that was a tangent any other + + align:start position:0% +all right that was a tangent any other + + + align:start position:0% +all right that was a tangent any other +questions + + align:start position:0% +questions + + + align:start position:0% +questions +take us back to this main line here + + align:start position:0% +take us back to this main line here + + + align:start position:0% +take us back to this main line here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +where are we yeah so selection uh head + + align:start position:0% +where are we yeah so selection uh head + + + align:start position:0% +where are we yeah so selection uh head +select for properties of their sisters + + align:start position:0% +select for properties of their sisters + + + align:start position:0% +select for properties of their sisters +although several of you want to know + + align:start position:0% +although several of you want to know + + + align:start position:0% +although several of you want to know +what happens when they seem to have more + + align:start position:0% +what happens when they seem to have more + + + align:start position:0% +what happens when they seem to have more +than one thing that they select and I'm + + align:start position:0% +than one thing that they select and I'm + + + align:start position:0% +than one thing that they select and I'm +trying to well I'm not exactly + + align:start position:0% +trying to well I'm not exactly + + + align:start position:0% +trying to well I'm not exactly +ruthlessly suppressing that question but + + align:start position:0% +ruthlessly suppressing that question but + + + align:start position:0% +ruthlessly suppressing that question but +I'm telling you what we currently seem + + align:start position:0% +I'm telling you what we currently seem + + + align:start position:0% +I'm telling you what we currently seem +to have to say about it and maybe uh + + align:start position:0% +to have to say about it and maybe uh + + + align:start position:0% +to have to say about it and maybe uh +flagging the possibility that we'll have + + align:start position:0% +flagging the possibility that we'll have + + + align:start position:0% +flagging the possibility that we'll have +to say different things later + + align:start position:0% +to say different things later + + + align:start position:0% +to say different things later +okay so far so good + + align:start position:0% +okay so far so good + + + align:start position:0% +okay so far so good +so yeah + + align:start position:0% +so yeah + + + align:start position:0% +so yeah +um right and when selection is for + + align:start position:0% +um right and when selection is for + + + align:start position:0% +um right and when selection is for +something specific so this is the this + + align:start position:0% +something specific so this is the this + + + align:start position:0% +something specific so this is the this +was the point I was trying to make with + + align:start position:0% +was the point I was trying to make with + + + align:start position:0% +was the point I was trying to make with +this slide uh when a verb selects for + + align:start position:0% +this slide uh when a verb selects for + + + align:start position:0% +this slide uh when a verb selects for +something specific uh a verb can for + + align:start position:0% +something specific uh a verb can for + + + align:start position:0% +something specific uh a verb can for +example say I need a prepositional + + align:start position:0% +example say I need a prepositional + + + align:start position:0% +example say I need a prepositional +phrase and I need the preposition to be + + align:start position:0% +phrase and I need the preposition to be + + + align:start position:0% +phrase and I need the preposition to be +on + + align:start position:0% +on + + + align:start position:0% +on +um or I need a prepositional phrase is + + align:start position:0% +um or I need a prepositional phrase is + + + align:start position:0% +um or I need a prepositional phrase is +like put I need a prepositional phrase + + align:start position:0% +like put I need a prepositional phrase + + + align:start position:0% +like put I need a prepositional phrase +and I need the preposition to be + + align:start position:0% +and I need the preposition to be + + + align:start position:0% +and I need the preposition to be +something locative to describe a + + align:start position:0% +something locative to describe a + + + align:start position:0% +something locative to describe a +location yeah + + align:start position:0% +location yeah + + + align:start position:0% +location yeah +um so depend selects for a prepositional + + align:start position:0% +um so depend selects for a prepositional + + + align:start position:0% +um so depend selects for a prepositional +phrase with the head on + + align:start position:0% +phrase with the head on + + + align:start position:0% +phrase with the head on +we're never going to find for example a + + align:start position:0% +we're never going to find for example a + + + align:start position:0% +we're never going to find for example a +verb that selects for a prepositional + + align:start position:0% +verb that selects for a prepositional + + + align:start position:0% +verb that selects for a prepositional +phrase and I don't care what the + + align:start position:0% +phrase and I don't care what the + + + align:start position:0% +phrase and I don't care what the +preposition is but the object must be + + align:start position:0% +preposition is but the object must be + + + align:start position:0% +preposition is but the object must be +tomatoes + + align:start position:0% +tomatoes + + + align:start position:0% +tomatoes +and we won't find anything like that so + + align:start position:0% +and we won't find anything like that so + + + align:start position:0% +and we won't find anything like that so +verb select for their sisters + + align:start position:0% +verb select for their sisters + + + align:start position:0% +verb select for their sisters +sisters in all the cases I'm going to + + align:start position:0% +sisters in all the cases I'm going to + + + align:start position:0% +sisters in all the cases I'm going to +show you + + align:start position:0% +show you + + + align:start position:0% +show you +um they select for their sisters but + + align:start position:0% +um they select for their sisters but + + + align:start position:0% +um they select for their sisters but +what they select specifically is sisters + + align:start position:0% +what they select specifically is sisters + + + align:start position:0% +what they select specifically is sisters +with a particular head they don't say + + align:start position:0% +with a particular head they don't say + + + align:start position:0% +with a particular head they don't say +things like I select for a sister whose + + align:start position:0% +things like I select for a sister whose + + + align:start position:0% +things like I select for a sister whose +compliment you know must be this or + + align:start position:0% +compliment you know must be this or + + + align:start position:0% +compliment you know must be this or +which must contain a tomato or you know + + align:start position:0% +which must contain a tomato or you know + + + align:start position:0% +which must contain a tomato or you know +which must be modified by an adverb you + + align:start position:0% +which must be modified by an adverb you + + + align:start position:0% +which must be modified by an adverb you +know heads don't do things like that + + align:start position:0% +know heads don't do things like that + + + align:start position:0% +know heads don't do things like that +they select few properties of their + + align:start position:0% +they select few properties of their + + + align:start position:0% +they select few properties of their +sisters specifically the heads of their + + align:start position:0% +sisters specifically the heads of their + + + align:start position:0% +sisters specifically the heads of their +sisters + + align:start position:0% +sisters + + + align:start position:0% +sisters +and once we know that this is what I + + align:start position:0% +and once we know that this is what I + + + align:start position:0% +and once we know that this is what I +said in class last time + + align:start position:0% +said in class last time + + + align:start position:0% +said in class last time +we can sort of use that fact about + + align:start position:0% +we can sort of use that fact about + + + align:start position:0% +we can sort of use that fact about +selection uh to detect other heads um so + + align:start position:0% +selection uh to detect other heads um so + + + align:start position:0% +selection uh to detect other heads um so +other kinds of things that seem to be in + + align:start position:0% +other kinds of things that seem to be in + + + align:start position:0% +other kinds of things that seem to be in +this selection relation with other uh + + align:start position:0% +this selection relation with other uh + + + align:start position:0% +this selection relation with other uh +words in the sentence other heads in the + + align:start position:0% +words in the sentence other heads in the + + + align:start position:0% +words in the sentence other heads in the +sentence so when we see other cases + + align:start position:0% +sentence so when we see other cases + + + align:start position:0% +sentence so when we see other cases +where uh there's a particular word in + + align:start position:0% +where uh there's a particular word in + + + align:start position:0% +where uh there's a particular word in +the sentence + + align:start position:0% +the sentence + + + align:start position:0% +the sentence +whose value seems to be determined by + + align:start position:0% +whose value seems to be determined by + + + align:start position:0% +whose value seems to be determined by +another word in the sentence we get to + + align:start position:0% +another word in the sentence we get to + + + align:start position:0% +another word in the sentence we get to +think oh okay maybe that's a selection + + align:start position:0% +think oh okay maybe that's a selection + + + align:start position:0% +think oh okay maybe that's a selection +relation this was the example I gave you + + align:start position:0% +relation this was the example I gave you + + + align:start position:0% +relation this was the example I gave you +last time + + align:start position:0% +last time + + + align:start position:0% +last time +verbs seem to be able to select for + + align:start position:0% +verbs seem to be able to select for + + + align:start position:0% +verbs seem to be able to select for +properties of the Clause that follows + + align:start position:0% +properties of the Clause that follows + + + align:start position:0% +properties of the Clause that follows +them so there are verbs like think that + + align:start position:0% +them so there are verbs like think that + + + align:start position:0% +them so there are verbs like think that +can be followed by a clause not every + + align:start position:0% +can be followed by a clause not every + + + align:start position:0% +can be followed by a clause not every +verb can be followed by a Clause right + + align:start position:0% +verb can be followed by a Clause right + + + align:start position:0% +verb can be followed by a Clause right +so I devoured the pizza Devourer can be + + align:start position:0% +so I devoured the pizza Devourer can be + + + align:start position:0% +so I devoured the pizza Devourer can be +followed by a noun phrase but I devoured + + align:start position:0% +followed by a noun phrase but I devoured + + + align:start position:0% +followed by a noun phrase but I devoured +that I have won the lottery uh it + + align:start position:0% +that I have won the lottery uh it + + + align:start position:0% +that I have won the lottery uh it +doesn't make sense so this looks like a + + align:start position:0% +doesn't make sense so this looks like a + + + align:start position:0% +doesn't make sense so this looks like a +selection relation + + align:start position:0% +selection relation + + + align:start position:0% +selection relation +and specifically it's a selection + + align:start position:0% +and specifically it's a selection + + + align:start position:0% +and specifically it's a selection +relation that's picky about these words + + align:start position:0% +relation that's picky about these words + + + align:start position:0% +relation that's picky about these words +that introduce the Clause that come at + + align:start position:0% +that introduce the Clause that come at + + + align:start position:0% +that introduce the Clause that come at +the beginning of the Clause uh words + + align:start position:0% +the beginning of the Clause uh words + + + align:start position:0% +the beginning of the Clause uh words +like that and whether so think can be + + align:start position:0% +like that and whether so think can be + + + align:start position:0% +like that and whether so think can be +followed by a clause where the word that + + align:start position:0% +followed by a clause where the word that + + + align:start position:0% +followed by a clause where the word that +introduces the Clause is that you can + + align:start position:0% +introduces the Clause is that you can + + + align:start position:0% +introduces the Clause is that you can +say things like I think that I have won + + align:start position:0% +say things like I think that I have won + + + align:start position:0% +say things like I think that I have won +the lottery Wonder can be followed by a + + align:start position:0% +the lottery Wonder can be followed by a + + + align:start position:0% +the lottery Wonder can be followed by a +clause where the word that introduces + + align:start position:0% +clause where the word that introduces + + + align:start position:0% +clause where the word that introduces +the following Clause is whether as in I + + align:start position:0% +the following Clause is whether as in I + + + align:start position:0% +the following Clause is whether as in I +wonder whether I have won the lottery + + align:start position:0% +wonder whether I have won the lottery + + + align:start position:0% +wonder whether I have won the lottery +and these verbs can't be switched so you + + align:start position:0% +and these verbs can't be switched so you + + + align:start position:0% +and these verbs can't be switched so you +can say I think that I have won the + + align:start position:0% +can say I think that I have won the + + + align:start position:0% +can say I think that I have won the +lottery you cannot say I think one + + align:start position:0% +lottery you cannot say I think one + + + align:start position:0% +lottery you cannot say I think one +whether I have won the lottery you can + + align:start position:0% +whether I have won the lottery you can + + + align:start position:0% +whether I have won the lottery you can +say I wonder whether I won the lottery + + align:start position:0% +say I wonder whether I won the lottery + + + align:start position:0% +say I wonder whether I won the lottery +you cannot say I wonder that I have won + + align:start position:0% +you cannot say I wonder that I have won + + + align:start position:0% +you cannot say I wonder that I have won +the lottery + + align:start position:0% +the lottery + + + align:start position:0% +the lottery +and I was saying this looks kind of like + + align:start position:0% +and I was saying this looks kind of like + + + align:start position:0% +and I was saying this looks kind of like +dependent on think needs a clause that + + align:start position:0% +dependent on think needs a clause that + + + align:start position:0% +dependent on think needs a clause that +starts with that Wonder needs a clause + + align:start position:0% +starts with that Wonder needs a clause + + + align:start position:0% +starts with that Wonder needs a clause +that search with weather depends needs a + + align:start position:0% +that search with weather depends needs a + + + align:start position:0% +that search with weather depends needs a +prepositional phrase that has on in it + + align:start position:0% +prepositional phrase that has on in it + + + align:start position:0% +prepositional phrase that has on in it +and just like with depended on we said + + align:start position:0% +and just like with depended on we said + + + align:start position:0% +and just like with depended on we said +yeah depend is selecting for a + + align:start position:0% +yeah depend is selecting for a + + + align:start position:0% +yeah depend is selecting for a +prepositional phrase with a particular + + align:start position:0% +prepositional phrase with a particular + + + align:start position:0% +prepositional phrase with a particular +head uh we get to say oh okay apparently + + align:start position:0% +head uh we get to say oh okay apparently + + + align:start position:0% +head uh we get to say oh okay apparently +that and whether are the heads of the + + align:start position:0% +that and whether are the heads of the + + + align:start position:0% +that and whether are the heads of the +Clause that's getting selected by the + + align:start position:0% +Clause that's getting selected by the + + + align:start position:0% +Clause that's getting selected by the +verb so think and wonder are selecting + + align:start position:0% +verb so think and wonder are selecting + + + align:start position:0% +verb so think and wonder are selecting +for Clauses that are headed by words + + align:start position:0% +for Clauses that are headed by words + + + align:start position:0% +for Clauses that are headed by words +like that and whether we have a word for + + align:start position:0% +like that and whether we have a word for + + + align:start position:0% +like that and whether we have a word for +words like that and whether we call them + + align:start position:0% +words like that and whether we call them + + + align:start position:0% +words like that and whether we call them +complementizers + + align:start position:0% +complementizers + + + align:start position:0% +complementizers +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um + + align:start position:0% +um + + + align:start position:0% +um +I think I apologized for that word last + + align:start position:0% +I think I apologized for that word last + + + align:start position:0% +I think I apologized for that word last +time I'll just apologize for it again + + align:start position:0% +time I'll just apologize for it again + + + align:start position:0% +time I'll just apologize for it again +because it's probably not the word you + + align:start position:0% +because it's probably not the word you + + + align:start position:0% +because it's probably not the word you +learned for those things uh in + + align:start position:0% +learned for those things uh in + + + align:start position:0% +learned for those things uh in +elementary school or High School you + + align:start position:0% +elementary school or High School you + + + align:start position:0% +elementary school or High School you +might have uh heard them called uh + + align:start position:0% +might have uh heard them called uh + + + align:start position:0% +might have uh heard them called uh +conjunctions subordinating conjunctions + + align:start position:0% +conjunctions subordinating conjunctions + + + align:start position:0% +conjunctions subordinating conjunctions +there's lots of things people call them + + align:start position:0% +there's lots of things people call them + + + align:start position:0% +there's lots of things people call them +um but in linguistics we call them + + align:start position:0% +um but in linguistics we call them + + + align:start position:0% +um but in linguistics we call them +complementizers so I'll have to ask you + + align:start position:0% +complementizers so I'll have to ask you + + + align:start position:0% +complementizers so I'll have to ask you +to join me in calling them that + + align:start position:0% +to join me in calling them that + + + align:start position:0% +to join me in calling them that +um so the abbreviation for + + align:start position:0% +um so the abbreviation for + + + align:start position:0% +um so the abbreviation for +complementizer is C uh and the phrase + + align:start position:0% +complementizer is C uh and the phrase + + + align:start position:0% +complementizer is C uh and the phrase +the is the sister of verbs like think + + align:start position:0% +the is the sister of verbs like think + + + align:start position:0% +the is the sister of verbs like think +and wonder is a complementizer phrase a + + align:start position:0% +and wonder is a complementizer phrase a + + + align:start position:0% +and wonder is a complementizer phrase a +CP it's a phrase that's headed by that + + align:start position:0% +CP it's a phrase that's headed by that + + + align:start position:0% +CP it's a phrase that's headed by that +or whether these complimentizers yeah + + align:start position:0% +or whether these complimentizers yeah + + + align:start position:0% +or whether these complimentizers yeah +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so I'll review hopefully it sounds at + + align:start position:0% +so I'll review hopefully it sounds at + + + align:start position:0% +so I'll review hopefully it sounds at +least Vaguely Familiar + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now here we are back at the original + + align:start position:0% +so now here we are back at the original + + + align:start position:0% +so now here we are back at the original +tree I will tickle the child with the + + align:start position:0% +tree I will tickle the child with the + + + align:start position:0% +tree I will tickle the child with the +feather we've talked a lot about + + align:start position:0% +feather we've talked a lot about + + + align:start position:0% +feather we've talked a lot about +selection relations we've said that + + align:start position:0% +selection relations we've said that + + + align:start position:0% +selection relations we've said that +selection relations are relations + + align:start position:0% +selection relations are relations + + + align:start position:0% +selection relations are relations +between heads and uh phrases in many + + align:start position:0% +between heads and uh phrases in many + + + align:start position:0% +between heads and uh phrases in many +cases the sister of the head and in + + align:start position:0% +cases the sister of the head and in + + + align:start position:0% +cases the sister of the head and in +particular selection relations seem to + + align:start position:0% +particular selection relations seem to + + + align:start position:0% +particular selection relations seem to +be picky about when there is pickiness + + align:start position:0% +be picky about when there is pickiness + + + align:start position:0% +be picky about when there is pickiness +about the head of the the phrase that's + + align:start position:0% +about the head of the the phrase that's + + + align:start position:0% +about the head of the the phrase that's +getting selected so we've seen examples + + align:start position:0% +getting selected so we've seen examples + + + align:start position:0% +getting selected so we've seen examples +of that now with prepositional phrases + + align:start position:0% +of that now with prepositional phrases + + + align:start position:0% +of that now with prepositional phrases +and now with complementizer phrases CPS + + align:start position:0% +and now with complementizer phrases CPS + + + align:start position:0% +and now with complementizer phrases CPS +Clauses yeah + + align:start position:0% +Clauses yeah + + + align:start position:0% +Clauses yeah +but and this is near the end of what we + + align:start position:0% +but and this is near the end of what we + + + align:start position:0% +but and this is near the end of what we +did last time + + align:start position:0% +did last time + + + align:start position:0% +did last time +there's more to life than selection + + align:start position:0% +there's more to life than selection + + + align:start position:0% +there's more to life than selection +um not much more but a little more so uh + + align:start position:0% +um not much more but a little more so uh + + + align:start position:0% +um not much more but a little more so uh +uh we don't want to say that tickle or + + align:start position:0% +uh we don't want to say that tickle or + + + align:start position:0% +uh we don't want to say that tickle or +child is selecting with a feather right + + align:start position:0% +child is selecting with a feather right + + + align:start position:0% +child is selecting with a feather right +so uh when I told you that tickle is + + align:start position:0% +so uh when I told you that tickle is + + + align:start position:0% +so uh when I told you that tickle is +selecting the child one of the ways I + + align:start position:0% +selecting the child one of the ways I + + + align:start position:0% +selecting the child one of the ways I +tried to convince you of that was to say + + align:start position:0% +tried to convince you of that was to say + + + align:start position:0% +tried to convince you of that was to say +yeah not every verb can be followed by + + align:start position:0% +yeah not every verb can be followed by + + + align:start position:0% +yeah not every verb can be followed by +an object there are transitive verbs and + + align:start position:0% +an object there are transitive verbs and + + + align:start position:0% +an object there are transitive verbs and +intransitive verbs that's the kind of + + align:start position:0% +intransitive verbs that's the kind of + + + align:start position:0% +intransitive verbs that's the kind of +thing that makes us think we're looking + + align:start position:0% +thing that makes us think we're looking + + + align:start position:0% +thing that makes us think we're looking +at a selection relation + + align:start position:0% +at a selection relation + + + align:start position:0% +at a selection relation +but any verb can be followed by with the + + align:start position:0% +but any verb can be followed by with the + + + align:start position:0% +but any verb can be followed by with the +feather you can do anything with a + + align:start position:0% +feather you can do anything with a + + + align:start position:0% +feather you can do anything with a +feather you can tickle a child with a + + align:start position:0% +feather you can tickle a child with a + + + align:start position:0% +feather you can tickle a child with a +feather or you can devour a child with a + + align:start position:0% +feather or you can devour a child with a + + + align:start position:0% +feather or you can devour a child with a +feather you can write a novel with a + + align:start position:0% +feather you can write a novel with a + + + align:start position:0% +feather you can write a novel with a +feather you can Thrive with a feather + + align:start position:0% +feather you can Thrive with a feather + + + align:start position:0% +feather you can Thrive with a feather +feathers they're just very very flexible + + align:start position:0% +feathers they're just very very flexible + + + align:start position:0% +feathers they're just very very flexible +tools you can do anything with them + + align:start position:0% +tools you can do anything with them + + + align:start position:0% +tools you can do anything with them +again some of these things make more + + align:start position:0% +again some of these things make more + + + align:start position:0% +again some of these things make more +sense than others + + align:start position:0% +sense than others + + + align:start position:0% +sense than others +so it's not clear what you mean when you + + align:start position:0% +so it's not clear what you mean when you + + + align:start position:0% +so it's not clear what you mean when you +say that you will Thrive with a feather + + align:start position:0% +say that you will Thrive with a feather + + + align:start position:0% +say that you will Thrive with a feather +or for that matter well it's actually + + align:start position:0% +or for that matter well it's actually + + + align:start position:0% +or for that matter well it's actually +fairly clear what you mean when you say + + align:start position:0% +fairly clear what you mean when you say + + + align:start position:0% +fairly clear what you mean when you say +you'll devour a child with a feather it + + align:start position:0% +you'll devour a child with a feather it + + + align:start position:0% +you'll devour a child with a feather it +just doesn't bear thinking about too + + align:start position:0% +just doesn't bear thinking about too + + + align:start position:0% +just doesn't bear thinking about too +closely + + align:start position:0% +closely + + + align:start position:0% +closely +um uh but basically you can do anything + + align:start position:0% +um uh but basically you can do anything + + + align:start position:0% +um uh but basically you can do anything +with a feather there's nothing like + + align:start position:0% +with a feather there's nothing like + + + align:start position:0% +with a feather there's nothing like +verbs or transitive and intransitive so + + align:start position:0% +verbs or transitive and intransitive so + + + align:start position:0% +verbs or transitive and intransitive so +this particular prepositional phrase + + align:start position:0% +this particular prepositional phrase + + + align:start position:0% +this particular prepositional phrase +this sort of instrument uh can go + + align:start position:0% +this sort of instrument uh can go + + + align:start position:0% +this sort of instrument uh can go +together with anything + + align:start position:0% +together with anything + + + align:start position:0% +together with anything +and so we don't seem to want to say that + + align:start position:0% +and so we don't seem to want to say that + + + align:start position:0% +and so we don't seem to want to say that +there is a selection relation between + + align:start position:0% +there is a selection relation between + + + align:start position:0% +there is a selection relation between +this prepositional phrase and anything + + align:start position:0% +this prepositional phrase and anything + + + align:start position:0% +this prepositional phrase and anything +at all + + align:start position:0% +at all + + + align:start position:0% +at all +um + + align:start position:0% +um + + + align:start position:0% +um +so there's a distinction that we draw + + align:start position:0% +so there's a distinction that we draw + + + align:start position:0% +so there's a distinction that we draw +between + + align:start position:0% +between + + + align:start position:0% +between +um what are called arguments and what + + align:start position:0% +um what are called arguments and what + + + align:start position:0% +um what are called arguments and what +are called adjuncts so arguments uh like + + align:start position:0% +are called adjuncts so arguments uh like + + + align:start position:0% +are called adjuncts so arguments uh like +the child and I will tickle the child + + align:start position:0% +the child and I will tickle the child + + + align:start position:0% +the child and I will tickle the child +with a feather are things that are + + align:start position:0% +with a feather are things that are + + + align:start position:0% +with a feather are things that are +selected by something in this case the + + align:start position:0% +selected by something in this case the + + + align:start position:0% +selected by something in this case the +verb and adjuncts are just phrases that + + align:start position:0% +verb and adjuncts are just phrases that + + + align:start position:0% +verb and adjuncts are just phrases that +wandered in + + align:start position:0% +wandered in + + + align:start position:0% +wandered in +um they're not selected by anything + + align:start position:0% +um they're not selected by anything + + + align:start position:0% +um they're not selected by anything +they're just there because they want to + + align:start position:0% +they're just there because they want to + + + align:start position:0% +they're just there because they want to +be they're not selected by anything you + + align:start position:0% +be they're not selected by anything you + + + align:start position:0% +be they're not selected by anything you +get to put them in because you feel like + + align:start position:0% +get to put them in because you feel like + + + align:start position:0% +get to put them in because you feel like +it yeah they're often modifiers uh sort + + align:start position:0% +it yeah they're often modifiers uh sort + + + align:start position:0% +it yeah they're often modifiers uh sort +of like this one + + align:start position:0% + + + + align:start position:0% + +okay so there are arguments and then + + align:start position:0% +okay so there are arguments and then + + + align:start position:0% +okay so there are arguments and then +they're adjuncts + + align:start position:0% +they're adjuncts + + + align:start position:0% +they're adjuncts +um how do you tell whether something is + + align:start position:0% +um how do you tell whether something is + + + align:start position:0% +um how do you tell whether something is +an argument or an adjunct I think I + + align:start position:0% +an argument or an adjunct I think I + + + align:start position:0% +an argument or an adjunct I think I +warned you last time this is something + + align:start position:0% +warned you last time this is something + + + align:start position:0% +warned you last time this is something +that people often get confused by and so + + align:start position:0% +that people often get confused by and so + + + align:start position:0% +that people often get confused by and so +I want to be clear about it + + align:start position:0% +I want to be clear about it + + + align:start position:0% +I want to be clear about it +um again when we decided that the child + + align:start position:0% +um again when we decided that the child + + + align:start position:0% +um again when we decided that the child +is selected by tickle what we were doing + + align:start position:0% +is selected by tickle what we were doing + + + align:start position:0% +is selected by tickle what we were doing +was saying not every verb can be + + align:start position:0% +was saying not every verb can be + + + align:start position:0% +was saying not every verb can be +followed by an object so if you're going + + align:start position:0% +followed by an object so if you're going + + + align:start position:0% +followed by an object so if you're going +to have a child right after the verb you + + align:start position:0% +to have a child right after the verb you + + + align:start position:0% +to have a child right after the verb you +have to know what verb it is there are + + align:start position:0% +have to know what verb it is there are + + + align:start position:0% +have to know what verb it is there are +transitive verbs and intransitive verbs + + align:start position:0% +transitive verbs and intransitive verbs + + + align:start position:0% +transitive verbs and intransitive verbs +and some verbs are okay with the + + align:start position:0% +and some verbs are okay with the + + + align:start position:0% +and some verbs are okay with the +following object and others are not + + align:start position:0% +following object and others are not + + + align:start position:0% +following object and others are not +um that's the signature of a selection + + align:start position:0% +um that's the signature of a selection + + + align:start position:0% +um that's the signature of a selection +relation so the arguments are picky + + align:start position:0% +relation so the arguments are picky + + + align:start position:0% +relation so the arguments are picky +about which heads they can combine with + + align:start position:0% +about which heads they can combine with + + + align:start position:0% +about which heads they can combine with +and adjuncts are not what people + + align:start position:0% +and adjuncts are not what people + + + align:start position:0% +and adjuncts are not what people +sometimes get confused about is is + + align:start position:0% +sometimes get confused about is is + + + align:start position:0% +sometimes get confused about is is +thinking that it's sort of the opposite + + align:start position:0% +thinking that it's sort of the opposite + + + align:start position:0% +thinking that it's sort of the opposite +that the pickiness goes in the opposite + + align:start position:0% +that the pickiness goes in the opposite + + + align:start position:0% +that the pickiness goes in the opposite +direction so people think here's a verb + + align:start position:0% +direction so people think here's a verb + + + align:start position:0% +direction so people think here's a verb +that needs to have an object and I've + + align:start position:0% +that needs to have an object and I've + + + align:start position:0% +that needs to have an object and I've +probably said things that led you down + + align:start position:0% +probably said things that led you down + + + align:start position:0% +probably said things that led you down +this Garden Path so there are indeed + + align:start position:0% +this Garden Path so there are indeed + + + align:start position:0% +this Garden Path so there are indeed +verbs that are obligatorily transitive I + + align:start position:0% +verbs that are obligatorily transitive I + + + align:start position:0% +verbs that are obligatorily transitive I +think the example I gave before was + + align:start position:0% +think the example I gave before was + + + align:start position:0% +think the example I gave before was +devour so you know the Dragon + + align:start position:0% +devour so you know the Dragon + + + align:start position:0% +devour so you know the Dragon +devoured + + align:start position:0% + + + + align:start position:0% + +Pizza + + align:start position:0% + + + + align:start position:0% + +we've devoured enough children for one + + align:start position:0% +we've devoured enough children for one + + + align:start position:0% +we've devoured enough children for one +class + + align:start position:0% +class + + + align:start position:0% +class +um possibly too many the the dragon + + align:start position:0% +um possibly too many the the dragon + + + align:start position:0% +um possibly too many the the dragon +Devour the pizza Devourer actually has + + align:start position:0% +Devour the pizza Devourer actually has + + + align:start position:0% +Devour the pizza Devourer actually has +to combine with an object not only is + + align:start position:0% +to combine with an object not only is + + + align:start position:0% +to combine with an object not only is +this a selection relation because not + + align:start position:0% +this a selection relation because not + + + align:start position:0% +this a selection relation because not +just any verb can have an object but + + align:start position:0% +just any verb can have an object but + + + align:start position:0% +just any verb can have an object but +actually Devourer has to combine with an + + align:start position:0% +actually Devourer has to combine with an + + + align:start position:0% +actually Devourer has to combine with an +object it's ungrammatical without the + + align:start position:0% +object it's ungrammatical without the + + + align:start position:0% +object it's ungrammatical without the +pizza so if I take out the pizza it + + align:start position:0% +pizza so if I take out the pizza it + + + align:start position:0% +pizza so if I take out the pizza it +becomes stuck yeah + + align:start position:0% +becomes stuck yeah + + + align:start position:0% +becomes stuck yeah +so the dragon devour that's not a + + align:start position:0% +so the dragon devour that's not a + + + align:start position:0% +so the dragon devour that's not a +sentence + + align:start position:0% + + + + align:start position:0% + +so that's an argument which is actually + + align:start position:0% +so that's an argument which is actually + + + align:start position:0% +so that's an argument which is actually +obligatory Devourer has to be transitive + + align:start position:0% +obligatory Devourer has to be transitive + + + align:start position:0% +obligatory Devourer has to be transitive +but there are plenty of verbs that in + + align:start position:0% +but there are plenty of verbs that in + + + align:start position:0% +but there are plenty of verbs that in +fact it's more common for verbs to be + + align:start position:0% +fact it's more common for verbs to be + + + align:start position:0% +fact it's more common for verbs to be +optionally transitive so uh Devourer + + align:start position:0% +optionally transitive so uh Devourer + + + align:start position:0% +optionally transitive so uh Devourer +needs to have an object but eat which + + align:start position:0% +needs to have an object but eat which + + + align:start position:0% +needs to have an object but eat which +means almost the same thing as devour uh + + align:start position:0% +means almost the same thing as devour uh + + + align:start position:0% +means almost the same thing as devour uh +is it's the transitivity is optional you + + align:start position:0% +is it's the transitivity is optional you + + + align:start position:0% +is it's the transitivity is optional you +can say I ate an apple but you can also + + align:start position:0% +can say I ate an apple but you can also + + + align:start position:0% +can say I ate an apple but you can also +say I ate + + align:start position:0% +say I ate + + + align:start position:0% +say I ate +um obligatory transitive verbs are + + align:start position:0% +um obligatory transitive verbs are + + + align:start position:0% +um obligatory transitive verbs are +actually kind of rare + + align:start position:0% +actually kind of rare + + + align:start position:0% +actually kind of rare +um and the best ones are kind of violent + + align:start position:0% +um and the best ones are kind of violent + + + align:start position:0% +um and the best ones are kind of violent +uh they're things like eviscerate and + + align:start position:0% +uh they're things like eviscerate and + + + align:start position:0% +uh they're things like eviscerate and +you know devour and mutilate those are + + align:start position:0% +you know devour and mutilate those are + + + align:start position:0% +you know devour and mutilate those are +the really clear transitive verbs + + align:start position:0% +the really clear transitive verbs + + + align:start position:0% +the really clear transitive verbs +they're very handy uh in syntax classes + + align:start position:0% +they're very handy uh in syntax classes + + + align:start position:0% +they're very handy uh in syntax classes +yes + + align:start position:0% +yes + + + align:start position:0% +yes +um + + align:start position:0% + + + + align:start position:0% + +sensitive + + align:start position:0% + + + + align:start position:0% + +another or any address + + align:start position:0% +another or any address + + + align:start position:0% +another or any address +we're talking as though any adjunct can + + align:start position:0% +we're talking as though any adjunct can + + + align:start position:0% +we're talking as though any adjunct can +modify anything and um + + align:start position:0% +modify anything and um + + + align:start position:0% +modify anything and um +I mean so this is another one of those + + align:start position:0% +I mean so this is another one of those + + + align:start position:0% +I mean so this is another one of those +places where we have to carefully + + align:start position:0% +places where we have to carefully + + + align:start position:0% +places where we have to carefully +distinguish between syntax and semantics + + align:start position:0% +distinguish between syntax and semantics + + + align:start position:0% +distinguish between syntax and semantics +um there are surely things that it's + + align:start position:0% +um there are surely things that it's + + + align:start position:0% +um there are surely things that it's +very difficult to imagine anybody doing + + align:start position:0% +very difficult to imagine anybody doing + + + align:start position:0% +very difficult to imagine anybody doing +with a feather right but + + align:start position:0% +with a feather right but + + + align:start position:0% +with a feather right but +um those kinds of cases so what's an + + align:start position:0% +um those kinds of cases so what's an + + + align:start position:0% +um those kinds of cases so what's an +example + + align:start position:0% +example + + + align:start position:0% +example +um uh + + align:start position:0% +um uh + + + align:start position:0% +um uh +she she proved for Matt's Last Theorem + + align:start position:0% +she she proved for Matt's Last Theorem + + + align:start position:0% +she she proved for Matt's Last Theorem +with a feather right I don't know how + + align:start position:0% +with a feather right I don't know how + + + align:start position:0% +with a feather right I don't know how +she would do that right + + align:start position:0% +she would do that right + + + align:start position:0% +she would do that right +um but that's a problem that's a math + + align:start position:0% +um but that's a problem that's a math + + + align:start position:0% +um but that's a problem that's a math +problem that's not a syntax problem so + + align:start position:0% +problem that's not a syntax problem so + + + align:start position:0% +problem that's not a syntax problem so +uh the sentence is grammatical uh we + + align:start position:0% +uh the sentence is grammatical uh we + + + align:start position:0% +uh the sentence is grammatical uh we +just can't figure out you know I + + align:start position:0% +just can't figure out you know I + + + align:start position:0% +just can't figure out you know I +wouldn't be able to draw a picture of it + + align:start position:0% +wouldn't be able to draw a picture of it + + + align:start position:0% +wouldn't be able to draw a picture of it +does that make sense so yeah what we're + + align:start position:0% +does that make sense so yeah what we're + + + align:start position:0% +does that make sense so yeah what we're +saying is that that prepositional phrase + + align:start position:0% +saying is that that prepositional phrase + + + align:start position:0% +saying is that that prepositional phrase +can combine with anything in principle + + align:start position:0% +can combine with anything in principle + + + align:start position:0% +can combine with anything in principle +though there may be kinds of + + align:start position:0% +though there may be kinds of + + + align:start position:0% +though there may be kinds of +combinations that will give us meanings + + align:start position:0% +combinations that will give us meanings + + + align:start position:0% +combinations that will give us meanings +that are kind of hard to understand + + align:start position:0% +that are kind of hard to understand + + + align:start position:0% +that are kind of hard to understand +yeah Joseph + + align:start position:0% + + + + align:start position:0% + +Wireless + + align:start position:0% +Wireless + + + align:start position:0% +Wireless +are the most transitive ones I think it + + align:start position:0% +are the most transitive ones I think it + + + align:start position:0% +are the most transitive ones I think it +is yeah yeah there's something about + + align:start position:0% +is yeah yeah there's something about + + + align:start position:0% +is yeah yeah there's something about +violence and transitivity yeah + + align:start position:0% +violence and transitivity yeah + + + align:start position:0% +violence and transitivity yeah +something to think about as you're + + align:start position:0% +something to think about as you're + + + align:start position:0% +something to think about as you're +working on your languages if you want to + + align:start position:0% +working on your languages if you want to + + + align:start position:0% +working on your languages if you want to +um okay so arguments are picky about + + align:start position:0% +um okay so arguments are picky about + + + align:start position:0% +um okay so arguments are picky about +what heads they combine with but there + + align:start position:0% +what heads they combine with but there + + + align:start position:0% +what heads they combine with but there +are uh to to look at things from the + + align:start position:0% +are uh to to look at things from the + + + align:start position:0% +are uh to to look at things from the +other perspective if you're asking for a + + align:start position:0% +other perspective if you're asking for a + + + align:start position:0% +other perspective if you're asking for a +particular head + + align:start position:0% +particular head + + + align:start position:0% +particular head +um if you're if you see a head and it's + + align:start position:0% +um if you're if you see a head and it's + + + align:start position:0% +um if you're if you see a head and it's +followed by a phrase the question to ask + + align:start position:0% +followed by a phrase the question to ask + + + align:start position:0% +followed by a phrase the question to ask +yourself is not is that phrase optional + + align:start position:0% +yourself is not is that phrase optional + + + align:start position:0% +yourself is not is that phrase optional +people often ask that question and it's + + align:start position:0% +people often ask that question and it's + + + align:start position:0% +people often ask that question and it's +it's a question that gets you in the + + align:start position:0% +it's a question that gets you in the + + + align:start position:0% +it's a question that gets you in the +wrong direction there are plenty of + + align:start position:0% +wrong direction there are plenty of + + + align:start position:0% +wrong direction there are plenty of +examples of things that are in fact + + align:start position:0% +examples of things that are in fact + + + align:start position:0% +examples of things that are in fact +arguments but they're optional + + align:start position:0% +arguments but they're optional + + + align:start position:0% +arguments but they're optional +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right + + align:start position:0% + + + + align:start position:0% + +um and then I think this is the last + + align:start position:0% +um and then I think this is the last + + + align:start position:0% +um and then I think this is the last +thing we did last time I was trying to + + align:start position:0% +thing we did last time I was trying to + + + align:start position:0% +thing we did last time I was trying to +illustrate arguments and adjuncts to you + + align:start position:0% +illustrate arguments and adjuncts to you + + + align:start position:0% +illustrate arguments and adjuncts to you +and we sort of got we were in the middle + + align:start position:0% +and we sort of got we were in the middle + + + align:start position:0% +and we sort of got we were in the middle +of deciding on the boat so uh so let's + + align:start position:0% +of deciding on the boat so uh so let's + + + align:start position:0% +of deciding on the boat so uh so let's +decide on the boat again uh fairly + + align:start position:0% +decide on the boat again uh fairly + + + align:start position:0% +decide on the boat again uh fairly +quickly so what we decided was that the + + align:start position:0% +quickly so what we decided was that the + + + align:start position:0% +quickly so what we decided was that the +sentence I decided on the boat can mean + + align:start position:0% +sentence I decided on the boat can mean + + + align:start position:0% +sentence I decided on the boat can mean +at least two things it can mean either I + + align:start position:0% +at least two things it can mean either I + + + align:start position:0% +at least two things it can mean either I +had some decision to make and I made it + + align:start position:0% +had some decision to make and I made it + + + align:start position:0% +had some decision to make and I made it +while I was on the boat right or it + + align:start position:0% +while I was on the boat right or it + + + align:start position:0% +while I was on the boat right or it +could mean I chose the boat right I was + + align:start position:0% +could mean I chose the boat right I was + + + align:start position:0% +could mean I chose the boat right I was +trying to choose between the boat and + + align:start position:0% +trying to choose between the boat and + + + align:start position:0% +trying to choose between the boat and +something else and I chose the boat + + align:start position:0% + + + + align:start position:0% + +um and what we said was uh if we ask the + + align:start position:0% +um and what we said was uh if we ask the + + + align:start position:0% +um and what we said was uh if we ask the +prepositional phrase on the boat is that + + align:start position:0% +prepositional phrase on the boat is that + + + align:start position:0% +prepositional phrase on the boat is that +an argument or an adjunct + + align:start position:0% +an argument or an adjunct + + + align:start position:0% +an argument or an adjunct +um the answer to that question is yes uh + + align:start position:0% +um the answer to that question is yes uh + + + align:start position:0% +um the answer to that question is yes uh +it can be an adjunct I made my decision + + align:start position:0% +it can be an adjunct I made my decision + + + align:start position:0% +it can be an adjunct I made my decision +the when it has the meaning when this + + align:start position:0% +the when it has the meaning when this + + + align:start position:0% +the when it has the meaning when this +sentence means I made my decision while + + align:start position:0% +sentence means I made my decision while + + + align:start position:0% +sentence means I made my decision while +I was on the boat then on the boat is an + + align:start position:0% +I was on the boat then on the boat is an + + + align:start position:0% +I was on the boat then on the boat is an +adjunct uh you can kind of see why just + + align:start position:0% +adjunct uh you can kind of see why just + + + align:start position:0% +adjunct uh you can kind of see why just +like you can do anything with a feather + + align:start position:0% +like you can do anything with a feather + + + align:start position:0% +like you can do anything with a feather +you can do anything on the boat right so + + align:start position:0% +you can do anything on the boat right so + + + align:start position:0% +you can do anything on the boat right so +any Fray You can modify it with on the + + align:start position:0% +any Fray You can modify it with on the + + + align:start position:0% +any Fray You can modify it with on the +boat + + align:start position:0% +boat + + + align:start position:0% +boat +this particular prepositional phrase + + align:start position:0% +this particular prepositional phrase + + + align:start position:0% +this particular prepositional phrase +then is an adjunct in that reading yeah + + align:start position:0% +then is an adjunct in that reading yeah + + + align:start position:0% +then is an adjunct in that reading yeah +have to be careful + + align:start position:0% +have to be careful + + + align:start position:0% +have to be careful +because of course if I say things like + + align:start position:0% +because of course if I say things like + + + align:start position:0% +because of course if I say things like +it depends on the boat + + align:start position:0% + + + + align:start position:0% + +or for that well let's use that one it + + align:start position:0% +or for that well let's use that one it + + + align:start position:0% +or for that well let's use that one it +depends on the boat this is the case + + align:start position:0% +depends on the boat this is the case + + + align:start position:0% +depends on the boat this is the case +where there is a selection relation + + align:start position:0% +where there is a selection relation + + + align:start position:0% +where there is a selection relation +between Depend and on right + + align:start position:0% +between Depend and on right + + + align:start position:0% +between Depend and on right +um we've been talking about that before + + align:start position:0% +um we've been talking about that before + + + align:start position:0% +um we've been talking about that before +that depends select for a prepositional + + align:start position:0% +that depends select for a prepositional + + + align:start position:0% +that depends select for a prepositional +phrase for which the head is on yeah so + + align:start position:0% +phrase for which the head is on yeah so + + + align:start position:0% +phrase for which the head is on yeah so +you can't just look at a prepositional + + align:start position:0% +you can't just look at a prepositional + + + align:start position:0% +you can't just look at a prepositional +if I ask if someone asks you out of the + + align:start position:0% +if I ask if someone asks you out of the + + + align:start position:0% +if I ask if someone asks you out of the +blue is on the boat an argument or an + + align:start position:0% +blue is on the boat an argument or an + + + align:start position:0% +blue is on the boat an argument or an +adjunct the way that's the point of this + + align:start position:0% +adjunct the way that's the point of this + + + align:start position:0% +adjunct the way that's the point of this +slide too the answer is wait what's the + + align:start position:0% +slide too the answer is wait what's the + + + align:start position:0% +slide too the answer is wait what's the +rest of the sentence right because uh + + align:start position:0% +rest of the sentence right because uh + + + align:start position:0% +rest of the sentence right because uh +you have to find out what the + + align:start position:0% +you have to find out what the + + + align:start position:0% +you have to find out what the +relationship is between that + + align:start position:0% +relationship is between that + + + align:start position:0% +relationship is between that +prepositional phrase and the other words + + align:start position:0% +prepositional phrase and the other words + + + align:start position:0% +prepositional phrase and the other words +that are around it yeah + + align:start position:0% +that are around it yeah + + + align:start position:0% +that are around it yeah +so in the reading where I decided on the + + align:start position:0% +so in the reading where I decided on the + + + align:start position:0% +so in the reading where I decided on the +boat means I made my decision while I + + align:start position:0% +boat means I made my decision while I + + + align:start position:0% +boat means I made my decision while I +was on the boat on the boat as an + + align:start position:0% +was on the boat on the boat as an + + + align:start position:0% +was on the boat on the boat as an +adjunct it's just describing the + + align:start position:0% +adjunct it's just describing the + + + align:start position:0% +adjunct it's just describing the +location where uh the rest of the + + align:start position:0% +location where uh the rest of the + + + align:start position:0% +location where uh the rest of the +sentence took place and uh any sentence + + align:start position:0% +sentence took place and uh any sentence + + + align:start position:0% +sentence took place and uh any sentence +can take place on the boat Maybe + + align:start position:0% +can take place on the boat Maybe + + + align:start position:0% +can take place on the boat Maybe +as opposed to uh the reading where it + + align:start position:0% +as opposed to uh the reading where it + + + align:start position:0% +as opposed to uh the reading where it +means I chose the boat + + align:start position:0% +means I chose the boat + + + align:start position:0% +means I chose the boat +there it's an argument because again you + + align:start position:0% +there it's an argument because again you + + + align:start position:0% +there it's an argument because again you +know this the fact that decide on means + + align:start position:0% +know this the fact that decide on means + + + align:start position:0% +know this the fact that decide on means +choose is kind of an idiosyncratic + + align:start position:0% +choose is kind of an idiosyncratic + + + align:start position:0% +choose is kind of an idiosyncratic +property of the verb decide and the + + align:start position:0% +property of the verb decide and the + + + align:start position:0% +property of the verb decide and the +preposition on uh it's like if you look + + align:start position:0% +preposition on uh it's like if you look + + + align:start position:0% +preposition on uh it's like if you look +up decide in the Lexicon uh you know + + align:start position:0% +up decide in the Lexicon uh you know + + + align:start position:0% +up decide in the Lexicon uh you know +it's going to have there we're going to + + align:start position:0% +it's going to have there we're going to + + + align:start position:0% +it's going to have there we're going to +have to list the information that it can + + align:start position:0% +have to list the information that it can + + + align:start position:0% +have to list the information that it can +optionally select an argument that + + align:start position:0% +optionally select an argument that + + + align:start position:0% +optionally select an argument that +starts with on and that the result of + + align:start position:0% +starts with on and that the result of + + + align:start position:0% +starts with on and that the result of +that combination means choose + + align:start position:0% +that combination means choose + + + align:start position:0% +that combination means choose +if you think about other things that + + align:start position:0% +if you think about other things that + + + align:start position:0% +if you think about other things that +mean something pretty similar to decide + + align:start position:0% +mean something pretty similar to decide + + + align:start position:0% +mean something pretty similar to decide +like make up your mind right so I made + + align:start position:0% +like make up your mind right so I made + + + align:start position:0% +like make up your mind right so I made +up my mind on the boat uh only means the + + align:start position:0% +up my mind on the boat uh only means the + + + align:start position:0% +up my mind on the boat uh only means the +first thing I think right if I made up + + align:start position:0% +first thing I think right if I made up + + + align:start position:0% +first thing I think right if I made up +my mind on the boat means I made my + + align:start position:0% +my mind on the boat means I made my + + + align:start position:0% +my mind on the boat means I made my +decision while I was on the boat it + + align:start position:0% +decision while I was on the boat it + + + align:start position:0% +decision while I was on the boat it +doesn't mean I chose the boat right I + + align:start position:0% +doesn't mean I chose the boat right I + + + align:start position:0% +doesn't mean I chose the boat right I +made a choice between the boat and + + align:start position:0% +made a choice between the boat and + + + align:start position:0% +made a choice between the boat and +something else and I chose the boat + + align:start position:0% +something else and I chose the boat + + + align:start position:0% +something else and I chose the boat +right so it's not a property of + + align:start position:0% +right so it's not a property of + + + align:start position:0% +right so it's not a property of +Expressions that mean decide that they + + align:start position:0% +Expressions that mean decide that they + + + align:start position:0% +Expressions that mean decide that they +always combine with on to this it's a + + align:start position:0% +always combine with on to this it's a + + + align:start position:0% +always combine with on to this it's a +idiosyncratic property of decide it's + + align:start position:0% +idiosyncratic property of decide it's + + + align:start position:0% +idiosyncratic property of decide it's +kind of like we have to list for + + align:start position:0% +kind of like we have to list for + + + align:start position:0% +kind of like we have to list for +particular verbs that they're transitive + + align:start position:0% +particular verbs that they're transitive + + + align:start position:0% +particular verbs that they're transitive +or that they're not we have to list for + + align:start position:0% +or that they're not we have to list for + + + align:start position:0% +or that they're not we have to list for +the word decide that it combines with on + + align:start position:0% +the word decide that it combines with on + + + align:start position:0% +the word decide that it combines with on +to give you a meaning that something + + align:start position:0% +to give you a meaning that something + + + align:start position:0% +to give you a meaning that something +like choose I'm sorry I'm talking over + + align:start position:0% +like choose I'm sorry I'm talking over + + + align:start position:0% +like choose I'm sorry I'm talking over +you + + align:start position:0% +you + + + align:start position:0% +you +yes yeah yeah yeah yeah that's a good + + align:start position:0% +yes yeah yeah yeah yeah that's a good + + + align:start position:0% +yes yeah yeah yeah yeah that's a good +another good example so uh you can look + + align:start position:0% +another good example so uh you can look + + + align:start position:0% +another good example so uh you can look +up a look up a reference well so you can + + align:start position:0% +up a look up a reference well so you can + + + align:start position:0% +up a look up a reference well so you can +look up + + align:start position:0% +look up + + + align:start position:0% +look up +um and that up is probably a probably an + + align:start position:0% +um and that up is probably a probably an + + + align:start position:0% +um and that up is probably a probably an +adjunct right uh you can do anything up + + align:start position:0% +adjunct right uh you can do anything up + + + align:start position:0% +adjunct right uh you can do anything up +um but uh to look up a reference the + + align:start position:0% +um but uh to look up a reference the + + + align:start position:0% +um but uh to look up a reference the +fact that that means you know look + + align:start position:0% +fact that that means you know look + + + align:start position:0% +fact that that means you know look +through some stuff and find it that's a + + align:start position:0% +through some stuff and find it that's a + + + align:start position:0% +through some stuff and find it that's a +idiosyncratic fact about looking up and + + align:start position:0% +idiosyncratic fact about looking up and + + + align:start position:0% +idiosyncratic fact about looking up and +uh that's a that's another good example + + align:start position:0% +uh that's a that's another good example + + + align:start position:0% +uh that's a that's another good example +of an argument yeah nice example + + align:start position:0% +of an argument yeah nice example + + + align:start position:0% +of an argument yeah nice example +yep + + align:start position:0% +yep + + + align:start position:0% +yep +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +and then I think this is where we + + align:start position:0% +and then I think this is where we + + + align:start position:0% +and then I think this is where we +stopped uh I asked you to think about + + align:start position:0% +stopped uh I asked you to think about + + + align:start position:0% +stopped uh I asked you to think about +sentences like I decided on the boat on + + align:start position:0% +sentences like I decided on the boat on + + + align:start position:0% +sentences like I decided on the boat on +the plane + + align:start position:0% +the plane + + + align:start position:0% +the plane +and I asked you to suppress your natural + + align:start position:0% +and I asked you to suppress your natural + + + align:start position:0% +and I asked you to suppress your natural +urge to make things more complicated uh + + align:start position:0% +urge to make things more complicated uh + + + align:start position:0% +urge to make things more complicated uh +and to think of Alternatives + + align:start position:0% +and to think of Alternatives + + + align:start position:0% +and to think of Alternatives +um so consider situations in which + + align:start position:0% +um so consider situations in which + + + align:start position:0% +um so consider situations in which +there's only one boat and only one plane + + align:start position:0% +there's only one boat and only one plane + + + align:start position:0% +there's only one boat and only one plane +and neither of them is on the other + + align:start position:0% +and neither of them is on the other + + + align:start position:0% +and neither of them is on the other +right + + align:start position:0% +right + + + align:start position:0% +right +there are two things that you could + + align:start position:0% +there are two things that you could + + + align:start position:0% +there are two things that you could +imagine this meaning + + align:start position:0% +imagine this meaning + + + align:start position:0% +imagine this meaning +it could mean I chose the boat while I + + align:start position:0% +it could mean I chose the boat while I + + + align:start position:0% +it could mean I chose the boat while I +was on the plane or it could mean in + + align:start position:0% +was on the plane or it could mean in + + + align:start position:0% +was on the plane or it could mean in +principle I chose the plane while I was + + align:start position:0% +principle I chose the plane while I was + + + align:start position:0% +principle I chose the plane while I was +on the boat + + align:start position:0% +on the boat + + + align:start position:0% +on the boat +right if we've decided that decide and + + align:start position:0% +right if we've decided that decide and + + + align:start position:0% +right if we've decided that decide and +all on and can combine it in these ways + + align:start position:0% +all on and can combine it in these ways + + + align:start position:0% +all on and can combine it in these ways +but I think + + align:start position:0% +but I think + + + align:start position:0% +but I think +the fact generally was that it only has + + align:start position:0% +the fact generally was that it only has + + + align:start position:0% +the fact generally was that it only has +one of those readings + + align:start position:0% +one of those readings + + + align:start position:0% +one of those readings +is that the reading that people have + + align:start position:0% +is that the reading that people have + + + align:start position:0% +is that the reading that people have +I'll write the readings down one is + + align:start position:0% +I'll write the readings down one is + + + align:start position:0% +I'll write the readings down one is +uh + + align:start position:0% +uh + + + align:start position:0% +uh +chose + + align:start position:0% +chose + + + align:start position:0% +chose +the boat + + align:start position:0% +the boat + + + align:start position:0% +the boat +while + + align:start position:0% +while + + + align:start position:0% +while +on the plane + + align:start position:0% +on the plane + + + align:start position:0% +on the plane +and the other was chose + + align:start position:0% +and the other was chose + + + align:start position:0% +and the other was chose +the plane + + align:start position:0% +the plane + + + align:start position:0% +the plane +while I was on the boat + + align:start position:0% + + + + align:start position:0% + +how many of you can get it to mean this + + align:start position:0% +how many of you can get it to mean this + + + align:start position:0% +how many of you can get it to mean this +first thing + + align:start position:0% + + + + align:start position:0% + +how many of you can get it to me in the + + align:start position:0% +how many of you can get it to me in the + + + align:start position:0% +how many of you can get it to me in the +second thing + + align:start position:0% +second thing + + + align:start position:0% +second thing +a few of you + + align:start position:0% +a few of you + + + align:start position:0% +a few of you +the few of you who can get it to me in + + align:start position:0% +the few of you who can get it to me in + + + align:start position:0% +the few of you who can get it to me in +the second thing please meet with your + + align:start position:0% +the second thing please meet with your + + + align:start position:0% +the second thing please meet with your +classmates after class and get them to + + align:start position:0% +classmates after class and get them to + + + align:start position:0% +classmates after class and get them to +convince you or maybe you could convince + + align:start position:0% +convince you or maybe you could convince + + + align:start position:0% +convince you or maybe you could convince +them that they're wrong + + align:start position:0% +them that they're wrong + + + align:start position:0% +them that they're wrong +I think + + align:start position:0% +I think + + + align:start position:0% +I think +um what we we talked about this a little + + align:start position:0% +um what we we talked about this a little + + + align:start position:0% +um what we we talked about this a little +bit in class possibly that uh if I say + + align:start position:0% +bit in class possibly that uh if I say + + + align:start position:0% +bit in class possibly that uh if I say +for me at least and people should stop + + align:start position:0% +for me at least and people should stop + + + align:start position:0% +for me at least and people should stop +me if this is not true + + align:start position:0% +me if this is not true + + + align:start position:0% +me if this is not true +um I can get it to mean the second thing + + align:start position:0% +um I can get it to mean the second thing + + + align:start position:0% +um I can get it to mean the second thing +but I need an opera score I have to say + + align:start position:0% +but I need an opera score I have to say + + + align:start position:0% +but I need an opera score I have to say +it in a particular way I have to say + + align:start position:0% +it in a particular way I have to say + + + align:start position:0% +it in a particular way I have to say +something like I decided on the boat on + + align:start position:0% +something like I decided on the boat on + + + align:start position:0% +something like I decided on the boat on +the plane there have to be commas and I + + align:start position:0% +the plane there have to be commas and I + + + align:start position:0% +the plane there have to be commas and I +have to kind of squash on the boat a + + align:start position:0% +have to kind of squash on the boat a + + + align:start position:0% +have to kind of squash on the boat a +little bit in order to get it to have + + align:start position:0% +little bit in order to get it to have + + + align:start position:0% +little bit in order to get it to have +this second meaning + + align:start position:0% +this second meaning + + + align:start position:0% +this second meaning +those of you who are considering raising + + align:start position:0% +those of you who are considering raising + + + align:start position:0% +those of you who are considering raising +your hands the second time is that true + + align:start position:0% +your hands the second time is that true + + + align:start position:0% +your hands the second time is that true +of you or are you people who who can + + align:start position:0% +of you or are you people who who can + + + align:start position:0% +of you or are you people who who can +just say I decided on the boat on the + + align:start position:0% +just say I decided on the boat on the + + + align:start position:0% +just say I decided on the boat on the +plane + + align:start position:0% +plane + + + align:start position:0% +plane +and mean this + + align:start position:0% + + + + align:start position:0% + +some of your + + align:start position:0% +some of your + + + align:start position:0% +some of your +raising thumbs and nodding and things + + align:start position:0% +raising thumbs and nodding and things + + + align:start position:0% +raising thumbs and nodding and things +like that is there anybody who that + + align:start position:0% +like that is there anybody who that + + + align:start position:0% +like that is there anybody who that +thing that I just said when I pronounced + + align:start position:0% +thing that I just said when I pronounced + + + align:start position:0% +thing that I just said when I pronounced +it in that particular way is there + + align:start position:0% +it in that particular way is there + + + align:start position:0% +it in that particular way is there +anybody who who did not think oh yeah + + align:start position:0% +anybody who who did not think oh yeah + + + align:start position:0% +anybody who who did not think oh yeah +that's the way I was pronouncing it in + + align:start position:0% +that's the way I was pronouncing it in + + + align:start position:0% +that's the way I was pronouncing it in +my head when I said that I could have it + + align:start position:0% +my head when I said that I could have it + + + align:start position:0% +my head when I said that I could have it +be this way + + align:start position:0% +be this way + + + align:start position:0% +be this way +you say it again is there anybody who if + + align:start position:0% +you say it again is there anybody who if + + + align:start position:0% +you say it again is there anybody who if +you say I decided on the boat on the + + align:start position:0% +you say I decided on the boat on the + + + align:start position:0% +you say I decided on the boat on the +plane + + align:start position:0% +plane + + + align:start position:0% +plane +saying it that way can it mean this the + + align:start position:0% +saying it that way can it mean this the + + + align:start position:0% +saying it that way can it mean this the +second thing + + align:start position:0% +second thing + + + align:start position:0% +second thing +yes + + align:start position:0% +yes + + + align:start position:0% +yes +I + + align:start position:0% + + + + align:start position:0% + +play I still have to say in a different + + align:start position:0% +play I still have to say in a different + + + align:start position:0% +play I still have to say in a different +way + + align:start position:0% + + + + align:start position:0% + +s + + align:start position:0% + + + + align:start position:0% + +oh oh oh I see how do you have to say it + + align:start position:0% +oh oh oh I see how do you have to say it + + + align:start position:0% +oh oh oh I see how do you have to say it +in order to get the second reading + + align:start position:0% +in order to get the second reading + + + align:start position:0% +in order to get the second reading +oh okay fair enough fair enough I this + + align:start position:0% +oh okay fair enough fair enough I this + + + align:start position:0% +oh okay fair enough fair enough I this +is one of many places where um + + align:start position:0% +is one of many places where um + + + align:start position:0% +is one of many places where um +I think I'm going to be content with the + + align:start position:0% +I think I'm going to be content with the + + + align:start position:0% +I think I'm going to be content with the +fact that all of you raised your hands + + align:start position:0% +fact that all of you raised your hands + + + align:start position:0% +fact that all of you raised your hands +when I asked whether it could mean this + + align:start position:0% +when I asked whether it could mean this + + + align:start position:0% +when I asked whether it could mean this +and only a few of you raised your hands + + align:start position:0% +and only a few of you raised your hands + + + align:start position:0% +and only a few of you raised your hands +when I asked whether it could mean this + + align:start position:0% +when I asked whether it could mean this + + + align:start position:0% +when I asked whether it could mean this +I think maybe the ones of you who can + + align:start position:0% +I think maybe the ones of you who can + + + align:start position:0% +I think maybe the ones of you who can +get it to mean this are doing it by + + align:start position:0% +get it to mean this are doing it by + + + align:start position:0% +get it to mean this are doing it by +pronouncing it in a specially + + align:start position:0% +pronouncing it in a specially + + + align:start position:0% +pronouncing it in a specially +interesting way which is itself an + + align:start position:0% +interesting way which is itself an + + + align:start position:0% +interesting way which is itself an +interesting fact right + + align:start position:0% +interesting fact right + + + align:start position:0% +interesting fact right +um there is I think I've alluded to this + + align:start position:0% +um there is I think I've alluded to this + + + align:start position:0% +um there is I think I've alluded to this +a couple of times uh a topic of study + + align:start position:0% +a couple of times uh a topic of study + + + align:start position:0% +a couple of times uh a topic of study +that people work on trying to figure out + + align:start position:0% +that people work on trying to figure out + + + align:start position:0% +that people work on trying to figure out +what the rules are for how the pitch of + + align:start position:0% +what the rules are for how the pitch of + + + align:start position:0% +what the rules are for how the pitch of +your voice Rises and Falls as you speak + + align:start position:0% +your voice Rises and Falls as you speak + + + align:start position:0% +your voice Rises and Falls as you speak +and where you put in pauses and so on + + align:start position:0% +and where you put in pauses and so on + + + align:start position:0% +and where you put in pauses and so on +it's the study of what's sometimes + + align:start position:0% +it's the study of what's sometimes + + + align:start position:0% +it's the study of what's sometimes +called prosody it's very complicated and + + align:start position:0% +called prosody it's very complicated and + + + align:start position:0% +called prosody it's very complicated and +hard but it's really interesting + + align:start position:0% +hard but it's really interesting + + + align:start position:0% +hard but it's really interesting +um so maybe the short thing for me to + + align:start position:0% +um so maybe the short thing for me to + + + align:start position:0% +um so maybe the short thing for me to +say is on the prosody where there's + + align:start position:0% +say is on the prosody where there's + + + align:start position:0% +say is on the prosody where there's +nothing special where we're not doing + + align:start position:0% +nothing special where we're not doing + + + align:start position:0% +nothing special where we're not doing +any pausing or or downgrading of + + align:start position:0% +any pausing or or downgrading of + + + align:start position:0% +any pausing or or downgrading of +anything where we're just reading this + + align:start position:0% +anything where we're just reading this + + + align:start position:0% +anything where we're just reading this +straight through I think everybody + + align:start position:0% +straight through I think everybody + + + align:start position:0% +straight through I think everybody +prefers this to this + + align:start position:0% +prefers this to this + + + align:start position:0% +prefers this to this +let me say that + + align:start position:0% +let me say that + + + align:start position:0% +let me say that +for for the time being + + align:start position:0% +for for the time being + + + align:start position:0% +for for the time being +um so I decided on the boat on the plane + + align:start position:0% +um so I decided on the boat on the plane + + + align:start position:0% +um so I decided on the boat on the plane +when you've got these two on phrases + + align:start position:0% +when you've got these two on phrases + + + align:start position:0% +when you've got these two on phrases +after decide the sort of + + align:start position:0% +after decide the sort of + + + align:start position:0% +after decide the sort of +tendency anyway unless you do fancy + + align:start position:0% +tendency anyway unless you do fancy + + + align:start position:0% +tendency anyway unless you do fancy +prosodic things is to have the first one + + align:start position:0% +prosodic things is to have the first one + + + align:start position:0% +prosodic things is to have the first one +be the argument and the second would be + + align:start position:0% +be the argument and the second would be + + + align:start position:0% +be the argument and the second would be +the adjunct + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so what we're finding out then is that + + align:start position:0% +so what we're finding out then is that + + + align:start position:0% +so what we're finding out then is that +if you've got a head and it has both an + + align:start position:0% +if you've got a head and it has both an + + + align:start position:0% +if you've got a head and it has both an +argument and an adjunct the argument is + + align:start position:0% +argument and an adjunct the argument is + + + align:start position:0% +argument and an adjunct the argument is +closer to the Head + + align:start position:0% +closer to the Head + + + align:start position:0% +closer to the Head +and we're going to come back to that but + + align:start position:0% +and we're going to come back to that but + + + align:start position:0% +and we're going to come back to that but +you know a way to think about it and + + align:start position:0% +you know a way to think about it and + + + align:start position:0% +you know a way to think about it and +we'll come back to it and say this more + + align:start position:0% +we'll come back to it and say this more + + + align:start position:0% +we'll come back to it and say this more +formally in a second it's as though I + + align:start position:0% +formally in a second it's as though I + + + align:start position:0% +formally in a second it's as though I +think I have a tree that I can make use + + align:start position:0% +think I have a tree that I can make use + + + align:start position:0% +think I have a tree that I can make use +of here + + align:start position:0% +of here + + + align:start position:0% +of here +um it's as though if you're gonna have a + + align:start position:0% +um it's as though if you're gonna have a + + + align:start position:0% +um it's as though if you're gonna have a +verb like decide that's going to have + + align:start position:0% +verb like decide that's going to have + + + align:start position:0% +verb like decide that's going to have +two prepositional phrases after it + + align:start position:0% +two prepositional phrases after it + + + align:start position:0% +two prepositional phrases after it +um so and forget what these are for now + + align:start position:0% +um so and forget what these are for now + + + align:start position:0% +um so and forget what these are for now +and also we'll have on the boat + + align:start position:0% + + + + align:start position:0% + +and on the plane + + align:start position:0% +and on the plane + + + align:start position:0% +and on the plane +you know so you've got decide and it's + + align:start position:0% +you know so you've got decide and it's + + + align:start position:0% +you know so you've got decide and it's +going to have two prepositional phrases + + align:start position:0% +going to have two prepositional phrases + + + align:start position:0% +going to have two prepositional phrases +after it and decide optionally select + + align:start position:0% +after it and decide optionally select + + + align:start position:0% +after it and decide optionally select +for a prepositional phrase with on as uh + + align:start position:0% +for a prepositional phrase with on as uh + + + align:start position:0% +for a prepositional phrase with on as uh +as the head what we're saying seeing is + + align:start position:0% +as the head what we're saying seeing is + + + align:start position:0% +as the head what we're saying seeing is +it's as though if you pick the version + + align:start position:0% +it's as though if you pick the version + + + align:start position:0% +it's as though if you pick the version +of decide that so if you decide to have + + align:start position:0% +of decide that so if you decide to have + + + align:start position:0% +of decide that so if you decide to have +it decide select for something + + align:start position:0% +it decide select for something + + + align:start position:0% +it decide select for something +um it's as though when you're merging + + align:start position:0% +um it's as though when you're merging + + + align:start position:0% +um it's as though when you're merging +these two prepositional phrases to + + align:start position:0% +these two prepositional phrases to + + + align:start position:0% +these two prepositional phrases to +projections of the verb you need to + + align:start position:0% +projections of the verb you need to + + + align:start position:0% +projections of the verb you need to +merge the one that's selected first + + align:start position:0% +merge the one that's selected first + + + align:start position:0% +merge the one that's selected first +there's some kind of urgency about this + + align:start position:0% +there's some kind of urgency about this + + + align:start position:0% +there's some kind of urgency about this +selection relation + + align:start position:0% +selection relation + + + align:start position:0% +selection relation +um you don't just get to freely decide + + align:start position:0% +um you don't just get to freely decide + + + align:start position:0% +um you don't just get to freely decide +what order to merge these two + + align:start position:0% +what order to merge these two + + + align:start position:0% +what order to merge these two +prepositional phrases in the argument in + + align:start position:0% +prepositional phrases in the argument in + + + align:start position:0% +prepositional phrases in the argument in +the adjunct you need to hurry up and + + align:start position:0% +the adjunct you need to hurry up and + + + align:start position:0% +the adjunct you need to hurry up and +give it its selectional requirements + + align:start position:0% +give it its selectional requirements + + + align:start position:0% +give it its selectional requirements +something like that and we'll we'll come + + align:start position:0% +something like that and we'll we'll come + + + align:start position:0% +something like that and we'll we'll come +back and talk more about that + + align:start position:0% +back and talk more about that + + + align:start position:0% +back and talk more about that +okay + + align:start position:0% + + + + align:start position:0% + +incidentally well who cares + + align:start position:0% +incidentally well who cares + + + align:start position:0% +incidentally well who cares +um incidentally + + align:start position:0% +um incidentally + + + align:start position:0% +um incidentally +that way of talking about things + + align:start position:0% +that way of talking about things + + + align:start position:0% +that way of talking about things +no sorry let me let me wait until we get + + align:start position:0% +no sorry let me let me wait until we get + + + align:start position:0% +no sorry let me let me wait until we get +more formal about it to to make the next + + align:start position:0% +more formal about it to to make the next + + + align:start position:0% +more formal about it to to make the next +point the next point is that this may + + align:start position:0% +point the next point is that this may + + + align:start position:0% +point the next point is that this may +help us some with the kinds of cases + + align:start position:0% +help us some with the kinds of cases + + + align:start position:0% +help us some with the kinds of cases +that got me to write that tree in the + + align:start position:0% +that got me to write that tree in the + + + align:start position:0% +that got me to write that tree in the +first place the kinds of cases where a + + align:start position:0% +first place the kinds of cases where a + + + align:start position:0% +first place the kinds of cases where a +head seems to select for more than one + + align:start position:0% +head seems to select for more than one + + + align:start position:0% +head seems to select for more than one +thing + + align:start position:0% +thing + + + align:start position:0% +thing +um so we'll come back to that + + align:start position:0% +um so we'll come back to that + + + align:start position:0% +um so we'll come back to that +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +that's where we were last time I think + + align:start position:0% +that's where we were last time I think + + + align:start position:0% +that's where we were last time I think +does anybody have any questions about + + align:start position:0% +does anybody have any questions about + + + align:start position:0% +does anybody have any questions about +any of that has been an attempt to + + align:start position:0% +any of that has been an attempt to + + + align:start position:0% +any of that has been an attempt to +review because I know you've had a week + + align:start position:0% +review because I know you've had a week + + + align:start position:0% +review because I know you've had a week +during which you might not have spent + + align:start position:0% +during which you might not have spent + + + align:start position:0% +during which you might not have spent +every waking moment thinking about + + align:start position:0% +every waking moment thinking about + + + align:start position:0% +every waking moment thinking about +syntax I I don't know why but I guess + + align:start position:0% +syntax I I don't know why but I guess + + + align:start position:0% +syntax I I don't know why but I guess +young people today they have their + + align:start position:0% +young people today they have their + + + align:start position:0% +young people today they have their +priorities there are there other + + align:start position:0% +priorities there are there other + + + align:start position:0% +priorities there are there other +questions about this are there things + + align:start position:0% +questions about this are there things + + + align:start position:0% +questions about this are there things +that aren't clear + + align:start position:0% +that aren't clear + + + align:start position:0% +that aren't clear +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yeah + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so you're wondering + + align:start position:0% +so you're wondering + + + align:start position:0% +so you're wondering +for decide on the on the bows why not do + + align:start position:0% +for decide on the on the bows why not do + + + align:start position:0% +for decide on the on the bows why not do +the side + + align:start position:0% + + + + align:start position:0% + +on and then combine that whole thing + + align:start position:0% +on and then combine that whole thing + + + align:start position:0% +on and then combine that whole thing +with a noun freeze + + align:start position:0% +with a noun freeze + + + align:start position:0% +with a noun freeze +the boat + + align:start position:0% + + + + align:start position:0% + +something like that yeah yeah + + align:start position:0% +something like that yeah yeah + + + align:start position:0% +something like that yeah yeah +um notice that these are making + + align:start position:0% +um notice that these are making + + + align:start position:0% +um notice that these are making +different claims about whether on the + + align:start position:0% +different claims about whether on the + + + align:start position:0% +different claims about whether on the +boat is a constituent or not right + + align:start position:0% +boat is a constituent or not right + + + align:start position:0% +boat is a constituent or not right +and so for example one of the + + align:start position:0% +and so for example one of the + + + align:start position:0% +and so for example one of the +constituency tests that we you fooled + + align:start position:0% +constituency tests that we you fooled + + + align:start position:0% +constituency tests that we you fooled +around with was the one where I'm Amazed + + align:start position:0% +around with was the one where I'm Amazed + + + align:start position:0% +around with was the one where I'm Amazed +by by something that you've said and I + + align:start position:0% +by by something that you've said and I + + + align:start position:0% +by by something that you've said and I +repeat part of what you've said in + + align:start position:0% +repeat part of what you've said in + + + align:start position:0% +repeat part of what you've said in +amazements so if you say I decided on + + align:start position:0% +amazements so if you say I decided on + + + align:start position:0% +amazements so if you say I decided on +the boat I one thing I can surely say is + + align:start position:0% +the boat I one thing I can surely say is + + + align:start position:0% +the boat I one thing I can surely say is +the vote + + align:start position:0% +the vote + + + align:start position:0% +the vote +but I think I can also say on the boat + + align:start position:0% + + + + align:start position:0% + +so I don't think so right yeah so look + + align:start position:0% +so I don't think so right yeah so look + + + align:start position:0% +so I don't think so right yeah so look +up the reference that's a good example + + align:start position:0% +up the reference that's a good example + + + align:start position:0% +up the reference that's a good example +uh look + + align:start position:0% +uh look + + + align:start position:0% +uh look +up + + align:start position:0% +up + + + align:start position:0% +up +reference + + align:start position:0% +reference + + + align:start position:0% +reference +if I'm amazed when you say I looked up + + align:start position:0% +if I'm amazed when you say I looked up + + + align:start position:0% +if I'm amazed when you say I looked up +the reference + + align:start position:0% +the reference + + + align:start position:0% +the reference +if I say up the reference + + align:start position:0% +if I say up the reference + + + align:start position:0% +if I say up the reference +that's weird + + align:start position:0% +that's weird + + + align:start position:0% +that's weird +I have a lifetimes experience being + + align:start position:0% +I have a lifetimes experience being + + + align:start position:0% +I have a lifetimes experience being +weird and that's you know I think that's + + align:start position:0% +weird and that's you know I think that's + + + align:start position:0% +weird and that's you know I think that's +worse than I decided on the boat on the + + align:start position:0% +worse than I decided on the boat on the + + + align:start position:0% +worse than I decided on the boat on the +boat + + align:start position:0% +boat + + + align:start position:0% +boat +I think but yeah that's that's the claim + + align:start position:0% +I think but yeah that's that's the claim + + + align:start position:0% +I think but yeah that's that's the claim +notice there's another difference + + align:start position:0% +notice there's another difference + + + align:start position:0% +notice there's another difference +between look up the reference and decide + + align:start position:0% +between look up the reference and decide + + + align:start position:0% +between look up the reference and decide +on the boat you can also say look the + + align:start position:0% +on the boat you can also say look the + + + align:start position:0% +on the boat you can also say look the +reference up + + align:start position:0% +reference up + + + align:start position:0% +reference up +you cannot say decide the vote on + + align:start position:0% +you cannot say decide the vote on + + + align:start position:0% +you cannot say decide the vote on +so we probably don't want these to be + + align:start position:0% +so we probably don't want these to be + + + align:start position:0% +so we probably don't want these to be +the same yeah + + align:start position:0% +the same yeah + + + align:start position:0% +the same yeah +yeah it's another reason to think that + + align:start position:0% +yeah it's another reason to think that + + + align:start position:0% +yeah it's another reason to think that +they're different + + align:start position:0% +they're different + + + align:start position:0% +they're different +if you're uh familiar with German German + + align:start position:0% +if you're uh familiar with German German + + + align:start position:0% +if you're uh familiar with German German +has a zillion particles like this right + + align:start position:0% +has a zillion particles like this right + + + align:start position:0% +has a zillion particles like this right +here yeah putting things between the + + align:start position:0% +here yeah putting things between the + + + align:start position:0% +here yeah putting things between the +verb and the + + align:start position:0% +verb and the + + + align:start position:0% +verb and the +separable prefix they're called + + align:start position:0% +separable prefix they're called + + + align:start position:0% +separable prefix they're called +yep + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so okay so now hopefully I've got you + + align:start position:0% +so so okay so now hopefully I've got you + + + align:start position:0% +so so okay so now hopefully I've got you +willing to entertain at least + + align:start position:0% +willing to entertain at least + + + align:start position:0% +willing to entertain at least +temporarily the possibility that there + + align:start position:0% +temporarily the possibility that there + + + align:start position:0% +temporarily the possibility that there +are uh things that we can describe as + + align:start position:0% +are uh things that we can describe as + + + align:start position:0% +are uh things that we can describe as +arguments and adjuncts arguments are the + + align:start position:0% +arguments and adjuncts arguments are the + + + align:start position:0% +arguments and adjuncts arguments are the +things that are selected by other heads + + align:start position:0% +things that are selected by other heads + + + align:start position:0% +things that are selected by other heads +adjuncts are phrases that just wandered + + align:start position:0% +adjuncts are phrases that just wandered + + + align:start position:0% +adjuncts are phrases that just wandered +in by mistake uh nothing is selecting + + align:start position:0% +in by mistake uh nothing is selecting + + + align:start position:0% +in by mistake uh nothing is selecting +them they're just here because they want + + align:start position:0% +them they're just here because they want + + + align:start position:0% +them they're just here because they want +to be they're not here because they're + + align:start position:0% +to be they're not here because they're + + + align:start position:0% +to be they're not here because they're +satisfying any needs of anything at all + + align:start position:0% +satisfying any needs of anything at all + + + align:start position:0% +satisfying any needs of anything at all +they're they're parasites basically is + + align:start position:0% +they're they're parasites basically is + + + align:start position:0% +they're they're parasites basically is +what they are they they end up in here + + align:start position:0% +what they are they they end up in here + + + align:start position:0% +what they are they they end up in here +uh inside the the Clause + + align:start position:0% +uh inside the the Clause + + + align:start position:0% +uh inside the the Clause +um and I'm showing you one kind of test + + align:start position:0% +um and I'm showing you one kind of test + + + align:start position:0% +um and I'm showing you one kind of test +for them which is that if you have uh a + + align:start position:0% +for them which is that if you have uh a + + + align:start position:0% +for them which is that if you have uh a +head that is combining both with an + + align:start position:0% +head that is combining both with an + + + align:start position:0% +head that is combining both with an +argument and with an adjunct + + align:start position:0% +argument and with an adjunct + + + align:start position:0% +argument and with an adjunct +it looks like there's at least a + + align:start position:0% +it looks like there's at least a + + + align:start position:0% +it looks like there's at least a +tendency for the argument to want to be + + align:start position:0% +tendency for the argument to want to be + + + align:start position:0% +tendency for the argument to want to be +closer to the head than the adjunct + + align:start position:0% +closer to the head than the adjunct + + + align:start position:0% +closer to the head than the adjunct +right so decide on the boat on the plane + + align:start position:0% +right so decide on the boat on the plane + + + align:start position:0% +right so decide on the boat on the plane +you the argument de-reading the choose + + align:start position:0% +you the argument de-reading the choose + + + align:start position:0% +you the argument de-reading the choose +reading goes with the first one it's + + align:start position:0% +reading goes with the first one it's + + + align:start position:0% +reading goes with the first one it's +that means chose the boat on the plane + + align:start position:0% +that means chose the boat on the plane + + + align:start position:0% +that means chose the boat on the plane +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +I want to show you another test for uh + + align:start position:0% +I want to show you another test for uh + + + align:start position:0% +I want to show you another test for uh +arguments versus adjuncts + + align:start position:0% +arguments versus adjuncts + + + align:start position:0% +arguments versus adjuncts +um here's another sentence I decided on + + align:start position:0% +um here's another sentence I decided on + + + align:start position:0% +um here's another sentence I decided on +the boat and Mary decided on the plane + + align:start position:0% +the boat and Mary decided on the plane + + + align:start position:0% +the boat and Mary decided on the plane +that can mean + + align:start position:0% + + + + align:start position:0% + +at least two things + + align:start position:0% +at least two things + + + align:start position:0% +at least two things +I think possibly four but at least two + + align:start position:0% +I think possibly four but at least two + + + align:start position:0% +I think possibly four but at least two +one thing that it can mean is I chose + + align:start position:0% +one thing that it can mean is I chose + + + align:start position:0% +one thing that it can mean is I chose +the boat and Mary chose the plane + + align:start position:0% +the boat and Mary chose the plane + + + align:start position:0% +the boat and Mary chose the plane +and another thing it can mean is Mary + + align:start position:0% +and another thing it can mean is Mary + + + align:start position:0% +and another thing it can mean is Mary +and I both had decisions to make we had + + align:start position:0% +and I both had decisions to make we had + + + align:start position:0% +and I both had decisions to make we had +to decide whether to major in + + align:start position:0% +to decide whether to major in + + + align:start position:0% +to decide whether to major in +linguistics or not and I made my + + align:start position:0% +linguistics or not and I made my + + + align:start position:0% +linguistics or not and I made my +decision while I was on the boat and she + + align:start position:0% +decision while I was on the boat and she + + + align:start position:0% +decision while I was on the boat and she +made hers while she was on the plane + + align:start position:0% +made hers while she was on the plane + + + align:start position:0% +made hers while she was on the plane +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so it could mean that too + + align:start position:0% + + + + align:start position:0% + +I guess it could also mean I chose the + + align:start position:0% +I guess it could also mean I chose the + + + align:start position:0% +I guess it could also mean I chose the +boat and Mary decided to become a + + align:start position:0% +boat and Mary decided to become a + + + align:start position:0% +boat and Mary decided to become a +Linguistics major while she was on the + + align:start position:0% +Linguistics major while she was on the + + + align:start position:0% +Linguistics major while she was on the +plane + + align:start position:0% +plane + + + align:start position:0% +plane +Maybe + + align:start position:0% +Maybe + + + align:start position:0% +Maybe +I'm not so sure about that but anyway it + + align:start position:0% +I'm not so sure about that but anyway it + + + align:start position:0% +I'm not so sure about that but anyway it +can mean at least those two things yeah + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +consider this sentence I decided on the + + align:start position:0% +consider this sentence I decided on the + + + align:start position:0% +consider this sentence I decided on the +vote and Mary did so on the plane + + align:start position:0% + + + + align:start position:0% + +does that mean two things + + align:start position:0% +does that mean two things + + + align:start position:0% +does that mean two things +I don't think so + + align:start position:0% +I don't think so + + + align:start position:0% +I don't think so +what does that one mean + + align:start position:0% + + + + align:start position:0% + +Joseph + + align:start position:0% + + + + align:start position:0% + +yeah exactly so I made the right + + align:start position:0% +yeah exactly so I made the right + + + align:start position:0% +yeah exactly so I made the right +decision on the boat and married made + + align:start position:0% +decision on the boat and married made + + + align:start position:0% +decision on the boat and married made +the wrong decision on the plane yeah + + align:start position:0% +the wrong decision on the plane yeah + + + align:start position:0% +the wrong decision on the plane yeah +yeah you mean that + + align:start position:0% +yeah you mean that + + + align:start position:0% +yeah you mean that +um + + align:start position:0% +um + + + align:start position:0% +um +yes so there's a phenomenon called VP + + align:start position:0% +yes so there's a phenomenon called VP + + + align:start position:0% +yes so there's a phenomenon called VP +predominalization that is you're you're + + align:start position:0% +predominalization that is you're you're + + + align:start position:0% +predominalization that is you're you're +taking the VP uh decide on or decide I + + align:start position:0% +taking the VP uh decide on or decide I + + + align:start position:0% +taking the VP uh decide on or decide I +guess and you're replacing it with uh do + + align:start position:0% +guess and you're replacing it with uh do + + + align:start position:0% +guess and you're replacing it with uh do +so which is kind of like a pronoun + + align:start position:0% +so which is kind of like a pronoun + + + align:start position:0% +so which is kind of like a pronoun +uh like a pronoun in that it's an + + align:start position:0% +uh like a pronoun in that it's an + + + align:start position:0% +uh like a pronoun in that it's an +expression that can stand in for lots of + + align:start position:0% +expression that can stand in for lots of + + + align:start position:0% +expression that can stand in for lots of +different kinds of verb phrases so just + + align:start position:0% +different kinds of verb phrases so just + + + align:start position:0% +different kinds of verb phrases so just +like you know a pronoun like she can + + align:start position:0% +like you know a pronoun like she can + + + align:start position:0% +like you know a pronoun like she can +stand in for any female person uh do so + + align:start position:0% +stand in for any female person uh do so + + + align:start position:0% +stand in for any female person uh do so +can stand in verb you know lots of kinds + + align:start position:0% +can stand in verb you know lots of kinds + + + align:start position:0% +can stand in verb you know lots of kinds +of verb phrases + + align:start position:0% +of verb phrases + + + align:start position:0% +of verb phrases +um and what we're learning is that if + + align:start position:0% +um and what we're learning is that if + + + align:start position:0% +um and what we're learning is that if +you do that uh the phrase that's outside + + align:start position:0% +you do that uh the phrase that's outside + + + align:start position:0% +you do that uh the phrase that's outside +of do so on the plane + + align:start position:0% +of do so on the plane + + + align:start position:0% +of do so on the plane +um + + align:start position:0% +um + + + align:start position:0% +um +can uh can only be an adjunct it can't + + align:start position:0% +can uh can only be an adjunct it can't + + + align:start position:0% +can uh can only be an adjunct it can't +be an argument + + align:start position:0% +be an argument + + + align:start position:0% +be an argument +there are various ways we could think + + align:start position:0% +there are various ways we could think + + + align:start position:0% +there are various ways we could think +about this + + align:start position:0% +about this + + + align:start position:0% +about this +but here's one + + align:start position:0% +but here's one + + + align:start position:0% +but here's one +could say look + + align:start position:0% +could say look + + + align:start position:0% +could say look +um this is the argument + + align:start position:0% + + + + align:start position:0% + +this is the adjunct + + align:start position:0% +this is the adjunct + + + align:start position:0% +this is the adjunct +we said there's a special relation of + + align:start position:0% +we said there's a special relation of + + + align:start position:0% +we said there's a special relation of +selection between decide and the + + align:start position:0% +selection between decide and the + + + align:start position:0% +selection between decide and the +argument right that doesn't hold between + + align:start position:0% +argument right that doesn't hold between + + + align:start position:0% +argument right that doesn't hold between +decide and the adjunct the adjunct is + + align:start position:0% +decide and the adjunct the adjunct is + + + align:start position:0% +decide and the adjunct the adjunct is +just here because it wants to be so + + align:start position:0% +just here because it wants to be so + + + align:start position:0% +just here because it wants to be so +there's a selection relation between + + align:start position:0% +there's a selection relation between + + + align:start position:0% +there's a selection relation between +these two things and then the adjunct is + + align:start position:0% +these two things and then the adjunct is + + + align:start position:0% +these two things and then the adjunct is +just something you merge because well + + align:start position:0% +just something you merge because well + + + align:start position:0% +just something you merge because well +you've got it and you can merge it + + align:start position:0% +you've got it and you can merge it + + + align:start position:0% +you've got it and you can merge it +um + + align:start position:0% +um + + + align:start position:0% +um +yeah it's what we've been saying and + + align:start position:0% +yeah it's what we've been saying and + + + align:start position:0% +yeah it's what we've been saying and +maybe what we're learning here is that + + align:start position:0% +maybe what we're learning here is that + + + align:start position:0% +maybe what we're learning here is that +yeah decide if you look up the side in + + align:start position:0% +yeah decide if you look up the side in + + + align:start position:0% +yeah decide if you look up the side in +the Lexicon you're going to see that it + + align:start position:0% +the Lexicon you're going to see that it + + + align:start position:0% +the Lexicon you're going to see that it +has the option of selecting for a + + align:start position:0% +has the option of selecting for a + + + align:start position:0% +has the option of selecting for a +prepositional phrase headed by on + + align:start position:0% +prepositional phrase headed by on + + + align:start position:0% +prepositional phrase headed by on +but if you look up do so in the Lexicon + + align:start position:0% +but if you look up do so in the Lexicon + + + align:start position:0% +but if you look up do so in the Lexicon +well it doesn't select anything there + + align:start position:0% +well it doesn't select anything there + + + align:start position:0% +well it doesn't select anything there +aren't any selectional relations with do + + align:start position:0% +aren't any selectional relations with do + + + align:start position:0% +aren't any selectional relations with do +so yeah so do so is kind of blank it + + align:start position:0% +so yeah so do so is kind of blank it + + + align:start position:0% +so yeah so do so is kind of blank it +just means there's a verb phrase and you + + align:start position:0% +just means there's a verb phrase and you + + + align:start position:0% +just means there's a verb phrase and you +know look around at the rest of the + + align:start position:0% +know look around at the rest of the + + + align:start position:0% +know look around at the rest of the +sentence to figure out what the verb + + align:start position:0% +sentence to figure out what the verb + + + align:start position:0% +sentence to figure out what the verb +phrase is yeah but uh there's a verb + + align:start position:0% +phrase is yeah but uh there's a verb + + + align:start position:0% +phrase is yeah but uh there's a verb +phrase so it's not doing any selecting + + align:start position:0% +phrase so it's not doing any selecting + + + align:start position:0% +phrase so it's not doing any selecting +so if you see a prepositional phrase + + align:start position:0% +so if you see a prepositional phrase + + + align:start position:0% +so if you see a prepositional phrase +after do so it's not an argument of + + align:start position:0% +after do so it's not an argument of + + + align:start position:0% +after do so it's not an argument of +anything it had better be an adjunct I + + align:start position:0% +anything it had better be an adjunct I + + + align:start position:0% +anything it had better be an adjunct I +guess that's what we're learning here + + align:start position:0% +guess that's what we're learning here + + + align:start position:0% +guess that's what we're learning here +I told you this is another test for + + align:start position:0% +I told you this is another test for + + + align:start position:0% +I told you this is another test for +arguments and adjuncts if you do VP for + + align:start position:0% +arguments and adjuncts if you do VP for + + + align:start position:0% +arguments and adjuncts if you do VP for +anomalization if you replace the verb + + align:start position:0% +anomalization if you replace the verb + + + align:start position:0% +anomalization if you replace the verb +phrase with do so and you have a phrase + + align:start position:0% +phrase with do so and you have a phrase + + + align:start position:0% +phrase with do so and you have a phrase +left over uh then that thing had better + + align:start position:0% +left over uh then that thing had better + + + align:start position:0% +left over uh then that thing had better +not be an argument it had better be an + + align:start position:0% +not be an argument it had better be an + + + align:start position:0% +not be an argument it had better be an +adjunct yeah + + align:start position:0% +adjunct yeah + + + align:start position:0% +adjunct yeah +the action with arguments and adjunct so + + align:start position:0% +the action with arguments and adjunct so + + + align:start position:0% +the action with arguments and adjunct so +far has been with uh prepositional + + align:start position:0% +far has been with uh prepositional + + + align:start position:0% +far has been with uh prepositional +phrases + + align:start position:0% +phrases + + + align:start position:0% +phrases +um we've talked as though direct objects + + align:start position:0% +um we've talked as though direct objects + + + align:start position:0% +um we've talked as though direct objects +for example are always arguments and so + + align:start position:0% +for example are always arguments and so + + + align:start position:0% +for example are always arguments and so +what we expect is that a direct object + + align:start position:0% +what we expect is that a direct object + + + align:start position:0% +what we expect is that a direct object +will never be able to be left over like + + align:start position:0% +will never be able to be left over like + + + align:start position:0% +will never be able to be left over like +this that is you won't be able to say I + + align:start position:0% +this that is you won't be able to say I + + + align:start position:0% +this that is you won't be able to say I +chose the boat + + align:start position:0% + + + + align:start position:0% + +and Mary did so the plane + + align:start position:0% + + + + align:start position:0% + +right because do so doesn't select for + + align:start position:0% +right because do so doesn't select for + + + align:start position:0% +right because do so doesn't select for +anything direct objects are always + + align:start position:0% +anything direct objects are always + + + align:start position:0% +anything direct objects are always +selected for you get them just if the + + align:start position:0% +selected for you get them just if the + + + align:start position:0% +selected for you get them just if the +verb is a transitive verb then do so + + align:start position:0% +verb is a transitive verb then do so + + + align:start position:0% +verb is a transitive verb then do so +isn't a transitive verb it's almost not + + align:start position:0% +isn't a transitive verb it's almost not + + + align:start position:0% +isn't a transitive verb it's almost not +a verb at all yeah + + align:start position:0% +a verb at all yeah + + + align:start position:0% +a verb at all yeah +yeah does that Accord with people's + + align:start position:0% +yeah does that Accord with people's + + + align:start position:0% +yeah does that Accord with people's +intuitions that you can't say that yeah + + align:start position:0% +intuitions that you can't say that yeah + + + align:start position:0% +intuitions that you can't say that yeah +yeah okay in fact I'm going to Star it + + align:start position:0% +yeah okay in fact I'm going to Star it + + + align:start position:0% +yeah okay in fact I'm going to Star it +before anybody gets the wrong idea + + align:start position:0% +before anybody gets the wrong idea + + + align:start position:0% +before anybody gets the wrong idea +bad sounds bad sound it's no biscuit + + align:start position:0% +bad sounds bad sound it's no biscuit + + + align:start position:0% +bad sounds bad sound it's no biscuit +yep okay + + align:start position:0% + + + + align:start position:0% + +all right so yeah + + align:start position:0% +all right so yeah + + + align:start position:0% +all right so yeah +[Music] + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +good good example + + align:start position:0% + + + + align:start position:0% + +yeah so I chose a boat and marry a plane + + align:start position:0% +yeah so I chose a boat and marry a plane + + + align:start position:0% +yeah so I chose a boat and marry a plane +or + + align:start position:0% +or + + + align:start position:0% +or +I decided on a boat and Mary on a plane + + align:start position:0% +I decided on a boat and Mary on a plane + + + align:start position:0% +I decided on a boat and Mary on a plane +can you say that + + align:start position:0% + + + + align:start position:0% + +I I I live in Somerville and Mary in + + align:start position:0% +I I I live in Somerville and Mary in + + + align:start position:0% +I I I live in Somerville and Mary in +Austin + + align:start position:0% +Austin + + + align:start position:0% +Austin +you can have prepositional phrases in + + align:start position:0% +you can have prepositional phrases in + + + align:start position:0% +you can have prepositional phrases in +this Construction + + align:start position:0% +this Construction + + + align:start position:0% +this Construction +but maybe not selected ones oh because I + + align:start position:0% +but maybe not selected ones oh because I + + + align:start position:0% +but maybe not selected ones oh because I +I decided on the boat and Mary on the + + align:start position:0% +I decided on the boat and Mary on the + + + align:start position:0% +I decided on the boat and Mary on the +plane + + align:start position:0% + + + + align:start position:0% + +it feels kind of Advent to me I don't + + align:start position:0% +it feels kind of Advent to me I don't + + + align:start position:0% +it feels kind of Advent to me I don't +know about you guys yeah + + align:start position:0% + + + + align:start position:0% + +yeah works but it's still + + align:start position:0% +yeah works but it's still + + + align:start position:0% +yeah works but it's still +vague is that what she said + + align:start position:0% +vague is that what she said + + + align:start position:0% +vague is that what she said +it could mean either one okay good I was + + align:start position:0% +it could mean either one okay good I was + + + align:start position:0% +it could mean either one okay good I was +sort of hoping that was true because I + + align:start position:0% +sort of hoping that was true because I + + + align:start position:0% +sort of hoping that was true because I +don't know any reason why it wouldn't be + + align:start position:0% +don't know any reason why it wouldn't be + + + align:start position:0% +don't know any reason why it wouldn't be +able to meet either one + + align:start position:0% +able to meet either one + + + align:start position:0% +able to meet either one +um this is a really interesting uh + + align:start position:0% +um this is a really interesting uh + + + align:start position:0% +um this is a really interesting uh +phenomenon there's a lot of work on it + + align:start position:0% +phenomenon there's a lot of work on it + + + align:start position:0% +phenomenon there's a lot of work on it +it's called The gapping + + align:start position:0% +it's called The gapping + + + align:start position:0% +it's called The gapping +uh and um + + align:start position:0% +uh and um + + + align:start position:0% +uh and um +dissertations have been written yeah + + align:start position:0% +dissertations have been written yeah + + + align:start position:0% +dissertations have been written yeah +interesting stuff yeah + + align:start position:0% + + + + align:start position:0% + +and Mary did so on the plane oh no what + + align:start position:0% +and Mary did so on the plane oh no what + + + align:start position:0% +and Mary did so on the plane oh no what +did Mary do on the plane + + align:start position:0% +did Mary do on the plane + + + align:start position:0% +did Mary do on the plane +oh she chose the vote on the plane oh + + align:start position:0% +oh she chose the vote on the plane oh + + + align:start position:0% +oh she chose the vote on the plane oh +yes well that would be okay + + align:start position:0% +yes well that would be okay + + + align:start position:0% +yes well that would be okay +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +uh I thought you meant that she chose + + align:start position:0% +uh I thought you meant that she chose + + + align:start position:0% +uh I thought you meant that she chose +the plane yes no that's uh no that's + + align:start position:0% +the plane yes no that's uh no that's + + + align:start position:0% +the plane yes no that's uh no that's +absolutely right okay phew + + align:start position:0% +absolutely right okay phew + + + align:start position:0% +absolutely right okay phew +um I yeah that's a nice example I + + align:start position:0% +um I yeah that's a nice example I + + + align:start position:0% +um I yeah that's a nice example I +decided + + align:start position:0% +decided + + + align:start position:0% +decided +on the boat + + align:start position:0% +on the boat + + + align:start position:0% +on the boat +oh here we can use this tree I decided + + align:start position:0% +oh here we can use this tree I decided + + + align:start position:0% +oh here we can use this tree I decided +on the boat and Mary did so on the plane + + align:start position:0% +on the boat and Mary did so on the plane + + + align:start position:0% +on the boat and Mary did so on the plane +I was + + align:start position:0% +I was + + + align:start position:0% +I was +um + + align:start position:0% +um + + + align:start position:0% +um +I was taking that to mean yeah uh decide + + align:start position:0% +I was taking that to mean yeah uh decide + + + align:start position:0% +I was taking that to mean yeah uh decide +in the first Clause is taking an adjunct + + align:start position:0% +in the first Clause is taking an adjunct + + + align:start position:0% +in the first Clause is taking an adjunct +on the boat and in the second Clause + + align:start position:0% +on the boat and in the second Clause + + + align:start position:0% +on the boat and in the second Clause +well do so is uh just replacing the side + + align:start position:0% +well do so is uh just replacing the side + + + align:start position:0% +well do so is uh just replacing the side +and on the plane is another adjunct + + align:start position:0% +and on the plane is another adjunct + + + align:start position:0% +and on the plane is another adjunct +you're saying yeah on the plane is an + + align:start position:0% +you're saying yeah on the plane is an + + + align:start position:0% +you're saying yeah on the plane is an +adjunct all right but do so is replacing + + align:start position:0% +adjunct all right but do so is replacing + + + align:start position:0% +adjunct all right but do so is replacing +the entire verb phrase decide on the + + align:start position:0% +the entire verb phrase decide on the + + + align:start position:0% +the entire verb phrase decide on the +boat where on the boat is an argument + + align:start position:0% +boat where on the boat is an argument + + + align:start position:0% +boat where on the boat is an argument +and yes that's another reading that it + + align:start position:0% +and yes that's another reading that it + + + align:start position:0% +and yes that's another reading that it +ought to be able to have I was just + + align:start position:0% +ought to be able to have I was just + + + align:start position:0% +ought to be able to have I was just +ignoring that reading thank you for + + align:start position:0% +ignoring that reading thank you for + + + align:start position:0% +ignoring that reading thank you for +pulling that reading out and making me + + align:start position:0% +pulling that reading out and making me + + + align:start position:0% +pulling that reading out and making me +pay attention to it you're absolutely + + align:start position:0% +pay attention to it you're absolutely + + + align:start position:0% +pay attention to it you're absolutely +right + + align:start position:0% +right + + + align:start position:0% +right +yeah cool all right so + + align:start position:0% +yeah cool all right so + + + align:start position:0% +yeah cool all right so +yeah arguments versus adjuncts uh decide + + align:start position:0% +yeah arguments versus adjuncts uh decide + + + align:start position:0% +yeah arguments versus adjuncts uh decide +on the boat on the plane uh on the boat + + align:start position:0% +on the boat on the plane uh on the boat + + + align:start position:0% +on the boat on the plane uh on the boat +is an argument it means I chose this + + align:start position:0% +is an argument it means I chose this + + + align:start position:0% +is an argument it means I chose this +means I chose the boat on the plane uh + + align:start position:0% +means I chose the boat on the plane uh + + + align:start position:0% +means I chose the boat on the plane uh +at least on the most natural prosody and + + align:start position:0% +at least on the most natural prosody and + + + align:start position:0% +at least on the most natural prosody and +uh uh + + align:start position:0% +uh uh + + + align:start position:0% +uh uh +We've now seen two ways of + + align:start position:0% +We've now seen two ways of + + + align:start position:0% +We've now seen two ways of +distinguishing arguments from adjuncts + + align:start position:0% +distinguishing arguments from adjuncts + + + align:start position:0% +distinguishing arguments from adjuncts +one is uh if you have anything left over + + align:start position:0% +one is uh if you have anything left over + + + align:start position:0% +one is uh if you have anything left over +after VP predominalization anything + + align:start position:0% +after VP predominalization anything + + + align:start position:0% +after VP predominalization anything +that's outside do so anything that's + + align:start position:0% +that's outside do so anything that's + + + align:start position:0% +that's outside do so anything that's +still there had better be an adjunct and + + align:start position:0% +still there had better be an adjunct and + + + align:start position:0% +still there had better be an adjunct and +not an argument because do so doesn't + + align:start position:0% +not an argument because do so doesn't + + + align:start position:0% +not an argument because do so doesn't +select for things + + align:start position:0% +select for things + + + align:start position:0% +select for things +um and if you have both an argument and + + align:start position:0% +um and if you have both an argument and + + + align:start position:0% +um and if you have both an argument and +an adjunct the argument tends to be + + align:start position:0% +an adjunct the argument tends to be + + + align:start position:0% +an adjunct the argument tends to be +closer to the verb than than the adjunct + + align:start position:0% +closer to the verb than than the adjunct + + + align:start position:0% +closer to the verb than than the adjunct +right those are the two tests that I've + + align:start position:0% +right those are the two tests that I've + + + align:start position:0% +right those are the two tests that I've +that I've given you so far + + align:start position:0% +that I've given you so far + + + align:start position:0% +that I've given you so far +okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +yeah okay and then here's a mini + + align:start position:0% +yeah okay and then here's a mini + + + align:start position:0% +yeah okay and then here's a mini +constituency test that's meant to get + + align:start position:0% +constituency test that's meant to get + + + align:start position:0% +constituency test that's meant to get +you to take seriously the possibility + + align:start position:0% +you to take seriously the possibility + + + align:start position:0% +you to take seriously the possibility +that there is a constituent side on the + + align:start position:0% +that there is a constituent side on the + + + align:start position:0% +that there is a constituent side on the +boat look you can coordinate that + + align:start position:0% +boat look you can coordinate that + + + align:start position:0% +boat look you can coordinate that +constituent with another constituent of + + align:start position:0% +constituent with another constituent of + + + align:start position:0% +constituent with another constituent of +the same kind you can say Mary will + + align:start position:0% +the same kind you can say Mary will + + + align:start position:0% +the same kind you can say Mary will +decide on the boat and read a novel on + + align:start position:0% +decide on the boat and read a novel on + + + align:start position:0% +decide on the boat and read a novel on +the plane it's fine uh so okay the lower + + align:start position:0% +the plane it's fine uh so okay the lower + + + align:start position:0% +the plane it's fine uh so okay the lower +thing is the compliment uh so + + align:start position:0% +thing is the compliment uh so + + + align:start position:0% +thing is the compliment uh so +terminology breaks the lower thing is + + align:start position:0% +terminology breaks the lower thing is + + + align:start position:0% +terminology breaks the lower thing is +the complement uh it's the it's the + + align:start position:0% +the complement uh it's the it's the + + + align:start position:0% +the complement uh it's the it's the +sister of the head + + align:start position:0% +sister of the head + + + align:start position:0% +sister of the head +um so complement is a name that we use + + align:start position:0% +um so complement is a name that we use + + + align:start position:0% +um so complement is a name that we use +for sisters of heads which as we've seen + + align:start position:0% +for sisters of heads which as we've seen + + + align:start position:0% +for sisters of heads which as we've seen +is a position that's kind of privileged + + align:start position:0% +is a position that's kind of privileged + + + align:start position:0% +is a position that's kind of privileged +for things that are for Arguments for + + align:start position:0% +for things that are for Arguments for + + + align:start position:0% +for things that are for Arguments for +things that are selected so + + align:start position:0% +things that are selected so + + + align:start position:0% +things that are selected so +um if there's only going to be one thing + + align:start position:0% +um if there's only going to be one thing + + + align:start position:0% +um if there's only going to be one thing +that can be if there's a sort of + + align:start position:0% +that can be if there's a sort of + + + align:start position:0% +that can be if there's a sort of +competition between an argument and an + + align:start position:0% +competition between an argument and an + + + align:start position:0% +competition between an argument and an +adjunct to be the complement well it's + + align:start position:0% +adjunct to be the complement well it's + + + align:start position:0% +adjunct to be the complement well it's +the argument that's the complement + + align:start position:0% +the argument that's the complement + + + align:start position:0% +the argument that's the complement +that's the thing that gets to be the + + align:start position:0% +that's the thing that gets to be the + + + align:start position:0% +that's the thing that gets to be the +sister that's what we're seeing + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so here's the principle that I + + align:start position:0% +so here's the principle that I + + + align:start position:0% +so here's the principle that I +introduced informally a second ago and + + align:start position:0% +introduced informally a second ago and + + + align:start position:0% +introduced informally a second ago and +I'll now say a little more formally if + + align:start position:0% +I'll now say a little more formally if + + + align:start position:0% +I'll now say a little more formally if +you've got a head that's selecting for + + align:start position:0% +you've got a head that's selecting for + + + align:start position:0% +you've got a head that's selecting for +an argument what we're seeing is uh you + + align:start position:0% +an argument what we're seeing is uh you + + + align:start position:0% +an argument what we're seeing is uh you +need to take care of the selection + + align:start position:0% +need to take care of the selection + + + align:start position:0% +need to take care of the selection +requirements of the head first before + + align:start position:0% +requirements of the head first before + + + align:start position:0% +requirements of the head first before +you do anything else you must first eat + + align:start position:0% +you do anything else you must first eat + + + align:start position:0% +you do anything else you must first eat +your broccoli before you can have your + + align:start position:0% +your broccoli before you can have your + + + align:start position:0% +your broccoli before you can have your +dessert you have to take your core + + align:start position:0% +dessert you have to take your core + + + align:start position:0% +dessert you have to take your core +classes before you can switch to taking + + align:start position:0% +classes before you can switch to taking + + + align:start position:0% +classes before you can switch to taking +all Linguistics classes right that's + + align:start position:0% +all Linguistics classes right that's + + + align:start position:0% +all Linguistics classes right that's +that's the way life is + + align:start position:0% +that's the way life is + + + align:start position:0% +that's the way life is +um so if you're going to read books + + align:start position:0% +um so if you're going to read books + + + align:start position:0% +um so if you're going to read books +quickly + + align:start position:0% +quickly + + + align:start position:0% +quickly +read transitive verb it can have uh + + align:start position:0% +read transitive verb it can have uh + + + align:start position:0% +read transitive verb it can have uh +combined with a noun phrase and so + + align:start position:0% +combined with a noun phrase and so + + + align:start position:0% +combined with a noun phrase and so +you're going to want to give it its noun + + align:start position:0% +you're going to want to give it its noun + + + align:start position:0% +you're going to want to give it its noun +phrase first that's the first thing + + align:start position:0% +phrase first that's the first thing + + + align:start position:0% +phrase first that's the first thing +you'll merge with read quickly is an + + align:start position:0% +you'll merge with read quickly is an + + + align:start position:0% +you'll merge with read quickly is an +adjunct you can do anything quickly it's + + align:start position:0% +adjunct you can do anything quickly it's + + + align:start position:0% +adjunct you can do anything quickly it's +not getting selected by read we won't + + align:start position:0% +not getting selected by read we won't + + + align:start position:0% +not getting selected by read we won't +find verbs that can combine with quickly + + align:start position:0% +find verbs that can combine with quickly + + + align:start position:0% +find verbs that can combine with quickly +and verbs that can't and so yeah + + align:start position:0% +and verbs that can't and so yeah + + + align:start position:0% +and verbs that can't and so yeah +you need to satisfy the needs of read + + align:start position:0% +you need to satisfy the needs of read + + + align:start position:0% +you need to satisfy the needs of read +first before you go merging quickly + + align:start position:0% +first before you go merging quickly + + + align:start position:0% +first before you go merging quickly +which is just kind of an optional thing + + align:start position:0% +which is just kind of an optional thing + + + align:start position:0% +which is just kind of an optional thing +um and that's why the story is going to + + align:start position:0% +um and that's why the story is going to + + + align:start position:0% +um and that's why the story is going to +be we can say he read he read the book + + align:start position:0% +be we can say he read he read the book + + + align:start position:0% +be we can say he read he read the book +quickly but not he read quickly the book + + align:start position:0% +quickly but not he read quickly the book + + + align:start position:0% +quickly but not he read quickly the book +in English + + align:start position:0% +in English + + + align:start position:0% +in English +yeah + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +let me sit down + + align:start position:0% + + + + align:start position:0% + +so you're pointing to the fact that + + align:start position:0% +so you're pointing to the fact that + + + align:start position:0% +so you're pointing to the fact that +there are many languages out there in + + align:start position:0% +there are many languages out there in + + + align:start position:0% +there are many languages out there in +which word order is a lot more flexible + + align:start position:0% +which word order is a lot more flexible + + + align:start position:0% +which word order is a lot more flexible +than it is in English + + align:start position:0% +than it is in English + + + align:start position:0% +than it is in English +um and you know what even in English it + + align:start position:0% +um and you know what even in English it + + + align:start position:0% +um and you know what even in English it +sometimes gets more complicated than + + align:start position:0% +sometimes gets more complicated than + + + align:start position:0% +sometimes gets more complicated than +this so let me show you the ways in + + align:start position:0% +this so let me show you the ways in + + + align:start position:0% +this so let me show you the ways in +which it gets more complicated in + + align:start position:0% +which it gets more complicated in + + + align:start position:0% +which it gets more complicated in +English and uh + + align:start position:0% +English and uh + + + align:start position:0% +English and uh +when we get to that + + align:start position:0% +when we get to that + + + align:start position:0% +when we get to that +we will have a tool that we can use to + + align:start position:0% +we will have a tool that we can use to + + + align:start position:0% +we will have a tool that we can use to +describe what's going on in the + + align:start position:0% +describe what's going on in the + + + align:start position:0% +describe what's going on in the +languages you have in mind yeah + + align:start position:0% +languages you have in mind yeah + + + align:start position:0% +languages you have in mind yeah +so let me just get you to hold off on + + align:start position:0% +so let me just get you to hold off on + + + align:start position:0% +so let me just get you to hold off on +your question for now + + align:start position:0% +your question for now + + + align:start position:0% +your question for now +are there any other questions about this + + align:start position:0% +are there any other questions about this + + + align:start position:0% +are there any other questions about this +so far + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +in fact I think we might be about to do + + align:start position:0% +in fact I think we might be about to do + + + align:start position:0% +in fact I think we might be about to do +it right now yeah so where are we uh + + align:start position:0% +it right now yeah so where are we uh + + + align:start position:0% +it right now yeah so where are we uh +trees are constructed by binary merge + + align:start position:0% +trees are constructed by binary merge + + + align:start position:0% +trees are constructed by binary merge +merge is constrained by selection via + + align:start position:0% +merge is constrained by selection via + + + align:start position:0% +merge is constrained by selection via +this thing I just called the projection + + align:start position:0% +this thing I just called the projection + + + align:start position:0% +this thing I just called the projection +principle which says if a head selects + + align:start position:0% +principle which says if a head selects + + + align:start position:0% +principle which says if a head selects +for something then that should be the + + align:start position:0% +for something then that should be the + + + align:start position:0% +for something then that should be the +first thing you merge + + align:start position:0% +first thing you merge + + + align:start position:0% +first thing you merge +before some of you were tormenting me + + align:start position:0% +before some of you were tormenting me + + + align:start position:0% +before some of you were tormenting me +with questions about heads that seem to + + align:start position:0% +with questions about heads that seem to + + + align:start position:0% +with questions about heads that seem to +be selecting more than one thing and you + + align:start position:0% +be selecting more than one thing and you + + + align:start position:0% +be selecting more than one thing and you +can kind of interpret the projection + + align:start position:0% +can kind of interpret the projection + + + align:start position:0% +can kind of interpret the projection +principle in a way that's that's + + align:start position:0% +principle in a way that's that's + + + align:start position:0% +principle in a way that's that's +sympathetic to that you get to say yeah + + align:start position:0% +sympathetic to that you get to say yeah + + + align:start position:0% +sympathetic to that you get to say yeah +if you have a head that selects for more + + align:start position:0% +if you have a head that selects for more + + + align:start position:0% +if you have a head that selects for more +than one thing you know uh give the + + align:start position:0% +than one thing you know uh give the + + + align:start position:0% +than one thing you know uh give the +children books or put the book on the + + align:start position:0% +children books or put the book on the + + + align:start position:0% +children books or put the book on the +table + + align:start position:0% +table + + + align:start position:0% +table +um uh yeah it has two needs and you had + + align:start position:0% +um uh yeah it has two needs and you had + + + align:start position:0% +um uh yeah it has two needs and you had +better satisfy those needs as fast as + + align:start position:0% +better satisfy those needs as fast as + + + align:start position:0% +better satisfy those needs as fast as +you can modulo binary merge right so uh + + align:start position:0% +you can modulo binary merge right so uh + + + align:start position:0% +you can modulo binary merge right so uh +give it one of its arguments and then it + + align:start position:0% +give it one of its arguments and then it + + + align:start position:0% +give it one of its arguments and then it +still has another argument it needs so + + align:start position:0% +still has another argument it needs so + + + align:start position:0% +still has another argument it needs so +you better merge that one next yeah the + + align:start position:0% +you better merge that one next yeah the + + + align:start position:0% +you better merge that one next yeah the +tools that we have right now make that a + + align:start position:0% +tools that we have right now make that a + + + align:start position:0% +tools that we have right now make that a +possible answer to those kinds of + + align:start position:0% +possible answer to those kinds of + + + align:start position:0% +possible answer to those kinds of +questions + + align:start position:0% +questions + + + align:start position:0% +questions +questions still floating around about + + align:start position:0% +questions still floating around about + + + align:start position:0% +questions still floating around about +whether those are the right trees but + + align:start position:0% +whether those are the right trees but + + + align:start position:0% +whether those are the right trees but +those are the trees we expect right now + + align:start position:0% +those are the trees we expect right now + + + align:start position:0% +those are the trees we expect right now +yep + + align:start position:0% + + + + align:start position:0% + +all right yeah + + align:start position:0% +all right yeah + + + align:start position:0% +all right yeah +yes + + align:start position:0% + + + + align:start position:0% + +it's like kind of like + + align:start position:0% +it's like kind of like + + + align:start position:0% +it's like kind of like +yeah I see what you mean yeah sorry go + + align:start position:0% +yeah I see what you mean yeah sorry go + + + align:start position:0% +yeah I see what you mean yeah sorry go +ahead + + align:start position:0% + + + + align:start position:0% + +uh yes yes yes it is like that that's a + + align:start position:0% +uh yes yes yes it is like that that's a + + + align:start position:0% +uh yes yes yes it is like that that's a +nice way to talk about it + + align:start position:0% +nice way to talk about it + + + align:start position:0% +nice way to talk about it +um so I've been talking as though + + align:start position:0% + + + + align:start position:0% + +see if I can say it + + align:start position:0% +see if I can say it + + + align:start position:0% +see if I can say it +coherently I've been talking as though + + align:start position:0% +coherently I've been talking as though + + + align:start position:0% +coherently I've been talking as though +when we look up give uh + + align:start position:0% +when we look up give uh + + + align:start position:0% +when we look up give uh +you know give is going to say well I + + align:start position:0% +you know give is going to say well I + + + align:start position:0% +you know give is going to say well I +need two noun phrases right or at least + + align:start position:0% +need two noun phrases right or at least + + + align:start position:0% +need two noun phrases right or at least +there's a version of give that takes two + + align:start position:0% +there's a version of give that takes two + + + align:start position:0% +there's a version of give that takes two +noun phrases right you're asking me wait + + align:start position:0% +noun phrases right you're asking me wait + + + align:start position:0% +noun phrases right you're asking me wait +couldn't + + align:start position:0% +couldn't + + + align:start position:0% +couldn't +couldn't well first of all don't we want + + align:start position:0% +couldn't well first of all don't we want + + + align:start position:0% +couldn't well first of all don't we want +to say something more complicated than + + align:start position:0% +to say something more complicated than + + + align:start position:0% +to say something more complicated than +that because we saw this with put as + + align:start position:0% +that because we saw this with put as + + + align:start position:0% +that because we saw this with put as +well it doesn't just want two noun + + align:start position:0% +well it doesn't just want two noun + + + align:start position:0% +well it doesn't just want two noun +phrases it wants two noun phrases in a + + align:start position:0% +phrases it wants two noun phrases in a + + + align:start position:0% +phrases it wants two noun phrases in a +particular order right so uh you want to + + align:start position:0% +particular order right so uh you want to + + + align:start position:0% +particular order right so uh you want to +give the children books you don't want + + align:start position:0% +give the children books you don't want + + + align:start position:0% +give the children books you don't want +to give the books children + + align:start position:0% +to give the books children + + + align:start position:0% +to give the books children +meaning give children books right so the + + align:start position:0% +meaning give children books right so the + + + align:start position:0% +meaning give children books right so the +the first noun phrase in this list is + + align:start position:0% +the first noun phrase in this list is + + + align:start position:0% +the first noun phrase in this list is +the noun phrase that gets the books gets + + align:start position:0% +the noun phrase that gets the books gets + + + align:start position:0% +the noun phrase that gets the books gets +the second noun phrase It's not the + + align:start position:0% +the second noun phrase It's not the + + + align:start position:0% +the second noun phrase It's not the +other way around right and then put the + + align:start position:0% +other way around right and then put the + + + align:start position:0% +other way around right and then put the +book on the table uh put yeah maybe + + align:start position:0% +book on the table uh put yeah maybe + + + align:start position:0% +book on the table uh put yeah maybe +selects for a noun phrase in a + + align:start position:0% +selects for a noun phrase in a + + + align:start position:0% +selects for a noun phrase in a +prepositional phrase uh but you know we + + align:start position:0% +prepositional phrase uh but you know we + + + align:start position:0% +prepositional phrase uh but you know we +need something so we need to say + + align:start position:0% +need something so we need to say + + + align:start position:0% +need something so we need to say +something more structured than that + + align:start position:0% +something more structured than that + + + align:start position:0% +something more structured than that +because it has to be the noun phrase + + align:start position:0% +because it has to be the noun phrase + + + align:start position:0% +because it has to be the noun phrase +first and then the prepositional phrase + + align:start position:0% +first and then the prepositional phrase + + + align:start position:0% +first and then the prepositional phrase +it can't be the other way around and + + align:start position:0% +it can't be the other way around and + + + align:start position:0% +it can't be the other way around and +you're wondering can we say something + + align:start position:0% +you're wondering can we say something + + + align:start position:0% +you're wondering can we say something +like give is a function that takes a + + align:start position:0% +like give is a function that takes a + + + align:start position:0% +like give is a function that takes a +noun phrase and can gets converted into + + align:start position:0% +noun phrase and can gets converted into + + + align:start position:0% +noun phrase and can gets converted into +another function that also takes a noun + + align:start position:0% +another function that also takes a noun + + + align:start position:0% +another function that also takes a noun +phrase something like that right so you + + align:start position:0% +phrase something like that right so you + + + align:start position:0% +phrase something like that right so you +know uh um that's sort of the equivalent + + align:start position:0% +know uh um that's sort of the equivalent + + + align:start position:0% +know uh um that's sort of the equivalent +of creating in or sharing finalization + + align:start position:0% +of creating in or sharing finalization + + + align:start position:0% +of creating in or sharing finalization +or whatever + + align:start position:0% +or whatever + + + align:start position:0% +or whatever +uh if you ever study semantics in my + + align:start position:0% +uh if you ever study semantics in my + + + align:start position:0% +uh if you ever study semantics in my +department I have several German + + align:start position:0% +department I have several German + + + align:start position:0% +department I have several German +semantics colleagues so colleagues whose + + align:start position:0% +semantics colleagues so colleagues whose + + + align:start position:0% +semantics colleagues so colleagues whose +native language is German and they are + + align:start position:0% +native language is German and they are + + + align:start position:0% +native language is German and they are +semanticists + + align:start position:0% +semanticists + + + align:start position:0% +semanticists +um and there were two people who + + align:start position:0% +um and there were two people who + + + align:start position:0% +um and there were two people who +invented + + align:start position:0% +invented + + + align:start position:0% +invented +um the kind of uh functions that he's + + align:start position:0% +um the kind of uh functions that he's + + + align:start position:0% +um the kind of uh functions that he's +talking about where you have a function + + align:start position:0% +talking about where you have a function + + + align:start position:0% +talking about where you have a function +and it changes the function into another + + align:start position:0% +and it changes the function into another + + + align:start position:0% +and it changes the function into another +function that takes another kind of + + align:start position:0% +function that takes another kind of + + + align:start position:0% +function that takes another kind of +thing one of them had the surname Curry + + align:start position:0% +thing one of them had the surname Curry + + + align:start position:0% +thing one of them had the surname Curry +and the other had the surname + + align:start position:0% + + + + align:start position:0% + +uh uh this guy was I think British this + + align:start position:0% +uh uh this guy was I think British this + + + align:start position:0% +uh uh this guy was I think British this +person was German so if most English + + align:start position:0% +person was German so if most English + + + align:start position:0% +person was German so if most English +speakers refer to this as currying in + + align:start position:0% +speakers refer to this as currying in + + + align:start position:0% +speakers refer to this as currying in +but if you are a German you refer to it + + align:start position:0% +but if you are a German you refer to it + + + align:start position:0% +but if you are a German you refer to it +as Shen finkelization + + align:start position:0% +as Shen finkelization + + + align:start position:0% +as Shen finkelization +um uh and uh apparently Shen Finkel + + align:start position:0% +um uh and uh apparently Shen Finkel + + + align:start position:0% +um uh and uh apparently Shen Finkel +discovered it before Curry so the the + + align:start position:0% +discovered it before Curry so the the + + + align:start position:0% +discovered it before Curry so the the +Germans are annoyed by the fact that we + + align:start position:0% +Germans are annoyed by the fact that we + + + align:start position:0% +Germans are annoyed by the fact that we +call it Korean and uh I'm not German so + + align:start position:0% +call it Korean and uh I'm not German so + + + align:start position:0% +call it Korean and uh I'm not German so +I'm not annoyed by you calling it Korean + + align:start position:0% +I'm not annoyed by you calling it Korean + + + align:start position:0% +I'm not annoyed by you calling it Korean +um indeed we clearly want something more + + align:start position:0% +um indeed we clearly want something more + + + align:start position:0% +um indeed we clearly want something more +structured than what I'm giving us yeah + + align:start position:0% +structured than what I'm giving us yeah + + + align:start position:0% +structured than what I'm giving us yeah +and I'm just going to leave your point + + align:start position:0% +and I'm just going to leave your point + + + align:start position:0% +and I'm just going to leave your point +right there yeah so we need we need to + + align:start position:0% +right there yeah so we need we need to + + + align:start position:0% +right there yeah so we need we need to +do something more sophisticated than + + align:start position:0% +do something more sophisticated than + + + align:start position:0% +do something more sophisticated than +what I'm what I'm doing here I keep + + align:start position:0% +what I'm what I'm doing here I keep + + + align:start position:0% +what I'm what I'm doing here I keep +hinting at the fact that we're going to + + align:start position:0% +hinting at the fact that we're going to + + + align:start position:0% +hinting at the fact that we're going to +want to investigate these trees the + + align:start position:0% +want to investigate these trees the + + + align:start position:0% +want to investigate these trees the +trees that I'm showing you and with + + align:start position:0% +trees that I'm showing you and with + + + align:start position:0% +trees that I'm showing you and with +other techniques to find out whether + + align:start position:0% +other techniques to find out whether + + + align:start position:0% +other techniques to find out whether +these are the right uh uh uh + + align:start position:0% +these are the right uh uh uh + + + align:start position:0% +these are the right uh uh uh +constituency structures and when we do + + align:start position:0% +constituency structures and when we do + + + align:start position:0% +constituency structures and when we do +that I think we'll have another reason + + align:start position:0% +that I think we'll have another reason + + + align:start position:0% +that I think we'll have another reason +to revise what I'm telling you now + + align:start position:0% +to revise what I'm telling you now + + + align:start position:0% +to revise what I'm telling you now +so there are several reasons to be + + align:start position:0% +so there are several reasons to be + + + align:start position:0% +so there are several reasons to be +uneasy about what I'm telling you now + + align:start position:0% +uneasy about what I'm telling you now + + + align:start position:0% +uneasy about what I'm telling you now +having I I've shown you a theory which + + align:start position:0% +having I I've shown you a theory which + + + align:start position:0% +having I I've shown you a theory which +works fine as long as heads only have + + align:start position:0% +works fine as long as heads only have + + + align:start position:0% +works fine as long as heads only have +one argument + + align:start position:0% +one argument + + + align:start position:0% +one argument +yeah as soon as they have two arguments + + align:start position:0% +yeah as soon as they have two arguments + + + align:start position:0% +yeah as soon as they have two arguments +these kinds of unsettling questions + + align:start position:0% +these kinds of unsettling questions + + + align:start position:0% +these kinds of unsettling questions +arise yeah + + align:start position:0% +arise yeah + + + align:start position:0% +arise yeah +yeah and we're going to come back to + + align:start position:0% +yeah and we're going to come back to + + + align:start position:0% +yeah and we're going to come back to +them okay + + align:start position:0% +them okay + + + align:start position:0% +them okay +good question + + align:start position:0% +good question + + + align:start position:0% +good question +other questions about this this is great + + align:start position:0% +other questions about this this is great + + + align:start position:0% +other questions about this this is great +I feel like I'm in a graduate seminar + + align:start position:0% +I feel like I'm in a graduate seminar + + + align:start position:0% +I feel like I'm in a graduate seminar +okay all right so uh this is where we + + align:start position:0% +okay all right so uh this is where we + + + align:start position:0% +okay all right so uh this is where we +are then trees are constructed by binary + + align:start position:0% +are then trees are constructed by binary + + + align:start position:0% +are then trees are constructed by binary +merge + + align:start position:0% +merge + + + align:start position:0% +merge +we have the projection principle which + + align:start position:0% +we have the projection principle which + + + align:start position:0% +we have the projection principle which +says if there's a selection relation you + + align:start position:0% +says if there's a selection relation you + + + align:start position:0% +says if there's a selection relation you +need to do that merge relation first + + align:start position:0% +need to do that merge relation first + + + align:start position:0% +need to do that merge relation first +um + + align:start position:0% +um + + + align:start position:0% +um +and that's going to get us contrasts + + align:start position:0% +and that's going to get us contrasts + + + align:start position:0% +and that's going to get us contrasts +like Mary wrote the novel on a + + align:start position:0% +like Mary wrote the novel on a + + + align:start position:0% +like Mary wrote the novel on a +typewriter and versus Mary wrote on the + + align:start position:0% +typewriter and versus Mary wrote on the + + + align:start position:0% +typewriter and versus Mary wrote on the +typewriter the novel where the second + + align:start position:0% +typewriter the novel where the second + + + align:start position:0% +typewriter the novel where the second +one is no good because right is a + + align:start position:0% +one is no good because right is a + + + align:start position:0% +one is no good because right is a +transitive verb has the option of being + + align:start position:0% +transitive verb has the option of being + + + align:start position:0% +transitive verb has the option of being +a transitive verb and when it's a + + align:start position:0% +a transitive verb and when it's a + + + align:start position:0% +a transitive verb and when it's a +transitive verb it uh selects for a + + align:start position:0% +transitive verb it uh selects for a + + + align:start position:0% +transitive verb it uh selects for a +direct object and that's the novel on + + align:start position:0% +direct object and that's the novel on + + + align:start position:0% +direct object and that's the novel on +the typewriter is like with a feather + + align:start position:0% +the typewriter is like with a feather + + + align:start position:0% +the typewriter is like with a feather +you can do anything on a typewriter can + + align:start position:0% +you can do anything on a typewriter can + + + align:start position:0% +you can do anything on a typewriter can +combine with anything so it's an adjunct + + align:start position:0% +combine with anything so it's an adjunct + + + align:start position:0% +combine with anything so it's an adjunct +and so there's no hurry to merge it yep + + align:start position:0% + + + + align:start position:0% + +so we've worked our way to the + + align:start position:0% +so we've worked our way to the + + + align:start position:0% +so we've worked our way to the +conclusion that right when it's + + align:start position:0% +conclusion that right when it's + + + align:start position:0% +conclusion that right when it's +transitive absolutely absolutely has to + + align:start position:0% +transitive absolutely absolutely has to + + + align:start position:0% +transitive absolutely absolutely has to +select uh an object and the object has + + align:start position:0% +select uh an object and the object has + + + align:start position:0% +select uh an object and the object has +to be the first thing you merge together + + align:start position:0% +to be the first thing you merge together + + + align:start position:0% +to be the first thing you merge together +with right + + align:start position:0% +with right + + + align:start position:0% +with right +so it has to be right after right in + + align:start position:0% +so it has to be right after right in + + + align:start position:0% +so it has to be right after right in +English that's why you can say Mary + + align:start position:0% +English that's why you can say Mary + + + align:start position:0% +English that's why you can say Mary +wrote the novel in a typewriter you + + align:start position:0% +wrote the novel in a typewriter you + + + align:start position:0% +wrote the novel in a typewriter you +cannot say Mary wrote on a typewriter + + align:start position:0% +cannot say Mary wrote on a typewriter + + + align:start position:0% +cannot say Mary wrote on a typewriter +the novel The Novel the thing that's + + align:start position:0% +the novel The Novel the thing that's + + + align:start position:0% +the novel The Novel the thing that's +getting written it absolutely has to be + + align:start position:0% +getting written it absolutely has to be + + + align:start position:0% +getting written it absolutely has to be +right next to right + + align:start position:0% + + + + align:start position:0% + +darn + + align:start position:0% +darn + + + align:start position:0% +darn +that last example + + align:start position:0% +that last example + + + align:start position:0% +that last example +looks problematic right + + align:start position:0% +looks problematic right + + + align:start position:0% +looks problematic right +if I ask you what did Mary write on a + + align:start position:0% +if I ask you what did Mary write on a + + + align:start position:0% +if I ask you what did Mary write on a +typewriter we've just worked our way to + + align:start position:0% +typewriter we've just worked our way to + + + align:start position:0% +typewriter we've just worked our way to +the conclusion that right when it takes + + align:start position:0% +the conclusion that right when it takes + + + align:start position:0% +the conclusion that right when it takes +a direct object the direct object has to + + align:start position:0% +a direct object the direct object has to + + + align:start position:0% +a direct object the direct object has to +be the first thing you merge with right + + align:start position:0% +be the first thing you merge with right + + + align:start position:0% +be the first thing you merge with right +it has to be right next to right there + + align:start position:0% +it has to be right next to right there + + + align:start position:0% +it has to be right next to right there +can't be anything intervening between + + align:start position:0% +can't be anything intervening between + + + align:start position:0% +can't be anything intervening between +right and + + align:start position:0% +right and + + + align:start position:0% +right and +uh it's complement the thing that's + + align:start position:0% +uh it's complement the thing that's + + + align:start position:0% +uh it's complement the thing that's +getting written + + align:start position:0% +getting written + + + align:start position:0% +getting written +what's the thing that's getting written + + align:start position:0% +what's the thing that's getting written + + + align:start position:0% +what's the thing that's getting written +in that example what did Mary write on + + align:start position:0% +in that example what did Mary write on + + + align:start position:0% +in that example what did Mary write on +the typewriter Joseph what yeah he's + + align:start position:0% +the typewriter Joseph what yeah he's + + + align:start position:0% +the typewriter Joseph what yeah he's +starting like this sounds like an Abbott + + align:start position:0% +starting like this sounds like an Abbott + + + align:start position:0% +starting like this sounds like an Abbott +and Costello routine yes what's getting + + align:start position:0% +and Costello routine yes what's getting + + + align:start position:0% +and Costello routine yes what's getting +written yes yeah yeah + + align:start position:0% +written yes yeah yeah + + + align:start position:0% +written yes yeah yeah +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +uh but that's not the sister of right + + align:start position:0% +uh but that's not the sister of right + + + align:start position:0% +uh but that's not the sister of right +you know that's nowhere near right it's + + align:start position:0% +you know that's nowhere near right it's + + + align:start position:0% +you know that's nowhere near right it's +way back at the beginning of the + + align:start position:0% +way back at the beginning of the + + + align:start position:0% +way back at the beginning of the +sentence what the heck is going on yeah + + align:start position:0% +sentence what the heck is going on yeah + + + align:start position:0% +sentence what the heck is going on yeah +are you all emotionally distraught + + align:start position:0% +are you all emotionally distraught + + + align:start position:0% +are you all emotionally distraught +that's what I'm trying to do yeah okay + + align:start position:0% +that's what I'm trying to do yeah okay + + + align:start position:0% +that's what I'm trying to do yeah okay +good + + align:start position:0% +good + + + align:start position:0% +good +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +two possible responses oh well we didn't + + align:start position:0% +two possible responses oh well we didn't + + + align:start position:0% +two possible responses oh well we didn't +have time to get too attached to the + + align:start position:0% +have time to get too attached to the + + + align:start position:0% +have time to get too attached to the +rejection principle anyway it was just a + + align:start position:0% +rejection principle anyway it was just a + + + align:start position:0% +rejection principle anyway it was just a +couple of slides ago uh so much for that + + align:start position:0% +couple of slides ago uh so much for that + + + align:start position:0% +couple of slides ago uh so much for that +idea yeah that's one possibility yeah so + + align:start position:0% +idea yeah that's one possibility yeah so + + + align:start position:0% +idea yeah that's one possibility yeah so +apparently + + align:start position:0% +apparently + + + align:start position:0% +apparently +um heads can select for things and they + + align:start position:0% +um heads can select for things and they + + + align:start position:0% +um heads can select for things and they +don't have to be anywhere near it so + + align:start position:0% +don't have to be anywhere near it so + + + align:start position:0% +don't have to be anywhere near it so +well + + align:start position:0% +well + + + align:start position:0% +well +but look here's another possibility we + + align:start position:0% +but look here's another possibility we + + + align:start position:0% +but look here's another possibility we +could say no um + + align:start position:0% +could say no um + + + align:start position:0% +could say no um +the projection principle is right is + + align:start position:0% +the projection principle is right is + + + align:start position:0% +the projection principle is right is +correct + + align:start position:0% +correct + + + align:start position:0% +correct +um + + align:start position:0% +um + + + align:start position:0% +um +should have picked a different verb + + align:start position:0% +should have picked a different verb + + + align:start position:0% +should have picked a different verb +um the injection principle is correct it + + align:start position:0% +um the injection principle is correct it + + + align:start position:0% +um the injection principle is correct it +is true that a verb like right that + + align:start position:0% +is true that a verb like right that + + + align:start position:0% +is true that a verb like right that +selects for an object absolutely has to + + align:start position:0% +selects for an object absolutely has to + + + align:start position:0% +selects for an object absolutely has to +merge with the object first and so + + align:start position:0% +merge with the object first and so + + + align:start position:0% +merge with the object first and so +really what you're doing + + align:start position:0% +really what you're doing + + + align:start position:0% +really what you're doing +when you start to ask a question like + + align:start position:0% +when you start to ask a question like + + + align:start position:0% +when you start to ask a question like +what did Mary write on a typewriter is + + align:start position:0% +what did Mary write on a typewriter is + + + align:start position:0% +what did Mary write on a typewriter is +you are merging right with what what is + + align:start position:0% +you are merging right with what what is + + + align:start position:0% +you are merging right with what what is +starting off as the sister of Rights so + + align:start position:0% +starting off as the sister of Rights so + + + align:start position:0% +starting off as the sister of Rights so +you start off with something more like + + align:start position:0% +you start off with something more like + + + align:start position:0% +you start off with something more like +Mary wrote what on a typewriter + + align:start position:0% + + + + align:start position:0% + +and then apparently there is some + + align:start position:0% +and then apparently there is some + + + align:start position:0% +and then apparently there is some +operation that takes what and puts it + + align:start position:0% +operation that takes what and puts it + + + align:start position:0% +operation that takes what and puts it +somewhere else at the beginning of the + + align:start position:0% +somewhere else at the beginning of the + + + align:start position:0% +somewhere else at the beginning of the +sentence + + align:start position:0% +sentence + + + align:start position:0% +sentence +yeah + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +this is a while ago + + align:start position:0% +this is a while ago + + + align:start position:0% +this is a while ago +um Katarina asked me what about + + align:start position:0% +um Katarina asked me what about + + + align:start position:0% +um Katarina asked me what about +languages where word order is Freer and + + align:start position:0% +languages where word order is Freer and + + + align:start position:0% +languages where word order is Freer and +I said things are about to get more + + align:start position:0% +I said things are about to get more + + + align:start position:0% +I said things are about to get more +complicated + + align:start position:0% +complicated + + + align:start position:0% +complicated +things have now gotten more complicated + + align:start position:0% +things have now gotten more complicated + + + align:start position:0% +things have now gotten more complicated +so yeah there's selection things select + + align:start position:0% +so yeah there's selection things select + + + align:start position:0% +so yeah there's selection things select +for things and when when X selects for y + + align:start position:0% +for things and when when X selects for y + + + align:start position:0% +for things and when when X selects for y +then y needs to merge with X right away + + align:start position:0% +then y needs to merge with X right away + + + align:start position:0% +then y needs to merge with X right away +and there are adjuncts that can merge + + align:start position:0% +and there are adjuncts that can merge + + + align:start position:0% +and there are adjuncts that can merge +wherever they want and there are things + + align:start position:0% +wherever they want and there are things + + + align:start position:0% +wherever they want and there are things +like this movement operations we're + + align:start position:0% +like this movement operations we're + + + align:start position:0% +like this movement operations we're +going to spend some time trying to + + align:start position:0% +going to spend some time trying to + + + align:start position:0% +going to spend some time trying to +convince you that this is true but right + + align:start position:0% +convince you that this is true but right + + + align:start position:0% +convince you that this is true but right +now let me just assert that it's true + + align:start position:0% +now let me just assert that it's true + + + align:start position:0% +now let me just assert that it's true +cases where indeed uh things do merge + + align:start position:0% +cases where indeed uh things do merge + + + align:start position:0% +cases where indeed uh things do merge +just the way we've convinced ourselves + + align:start position:0% +just the way we've convinced ourselves + + + align:start position:0% +just the way we've convinced ourselves +that they do they merge where they + + align:start position:0% +that they do they merge where they + + + align:start position:0% +that they do they merge where they +should they merge as sisters of verbs + + align:start position:0% +should they merge as sisters of verbs + + + align:start position:0% +should they merge as sisters of verbs +but then something else happens and they + + align:start position:0% +but then something else happens and they + + + align:start position:0% +but then something else happens and they +end up somewhere else yeah so there's + + align:start position:0% +end up somewhere else yeah so there's + + + align:start position:0% +end up somewhere else yeah so there's +this operation of movement where you + + align:start position:0% +this operation of movement where you + + + align:start position:0% +this operation of movement where you +take the word what and you move it to + + align:start position:0% +take the word what and you move it to + + + align:start position:0% +take the word what and you move it to +the beginning of the sentence in order + + align:start position:0% +the beginning of the sentence in order + + + align:start position:0% +the beginning of the sentence in order +to form questions like this one notice + + align:start position:0% +to form questions like this one notice + + + align:start position:0% +to form questions like this one notice +that in English and indeed in many + + align:start position:0% +that in English and indeed in many + + + align:start position:0% +that in English and indeed in many +language most languages not all + + align:start position:0% +language most languages not all + + + align:start position:0% +language most languages not all +languages but in many languages + + align:start position:0% +languages but in many languages + + + align:start position:0% +languages but in many languages +if I'm uh Amazed by something you've + + align:start position:0% +if I'm uh Amazed by something you've + + + align:start position:0% +if I'm uh Amazed by something you've +said if you say uh Mary root a proof of + + align:start position:0% +said if you say uh Mary root a proof of + + + align:start position:0% +said if you say uh Mary root a proof of +from us Last Theorem on a typewriter uh + + align:start position:0% +from us Last Theorem on a typewriter uh + + + align:start position:0% +from us Last Theorem on a typewriter uh +I can say Mary wrote on the typewriter + + align:start position:0% +I can say Mary wrote on the typewriter + + + align:start position:0% +I can say Mary wrote on the typewriter +yeah so it actually is possible to say + + align:start position:0% +yeah so it actually is possible to say + + + align:start position:0% +yeah so it actually is possible to say +these words in this order I just have to + + align:start position:0% +these words in this order I just have to + + + align:start position:0% +these words in this order I just have to +be in a particular emotional state I + + align:start position:0% +be in a particular emotional state I + + + align:start position:0% +be in a particular emotional state I +have to be astonished + + align:start position:0% +have to be astonished + + + align:start position:0% +have to be astonished +there's actually cross-linguistically + + align:start position:0% +there's actually cross-linguistically + + + align:start position:0% +there's actually cross-linguistically +extremely common for uh they're called + + align:start position:0% +extremely common for uh they're called + + + align:start position:0% +extremely common for uh they're called +Echo questions uh where if I can't + + align:start position:0% +Echo questions uh where if I can't + + + align:start position:0% +Echo questions uh where if I can't +believe what you just said or if I + + align:start position:0% +believe what you just said or if I + + + align:start position:0% +believe what you just said or if I +couldn't quite hear what you just said + + align:start position:0% +couldn't quite hear what you just said + + + align:start position:0% +couldn't quite hear what you just said +you know if you're telling me on the t + + align:start position:0% +you know if you're telling me on the t + + + align:start position:0% +you know if you're telling me on the t +uh and you say Mary wrote on a + + align:start position:0% +uh and you say Mary wrote on a + + + align:start position:0% +uh and you say Mary wrote on a +typewriter you know there's lots of + + align:start position:0% +typewriter you know there's lots of + + + align:start position:0% +typewriter you know there's lots of +noise in the background and I missed the + + align:start position:0% +noise in the background and I missed the + + + align:start position:0% +noise in the background and I missed the +crucial thing I can say oh Mary wrote + + align:start position:0% +crucial thing I can say oh Mary wrote + + + align:start position:0% +crucial thing I can say oh Mary wrote +water on a typewriter yeah these are + + align:start position:0% +water on a typewriter yeah these are + + + align:start position:0% +water on a typewriter yeah these are +called Echo questions where I'm I'm uh + + align:start position:0% +called Echo questions where I'm I'm uh + + + align:start position:0% +called Echo questions where I'm I'm uh +repeating most of what you just said and + + align:start position:0% +repeating most of what you just said and + + + align:start position:0% +repeating most of what you just said and +replacing part of it with uh with a wh + + align:start position:0% +replacing part of it with uh with a wh + + + align:start position:0% +replacing part of it with uh with a wh +word and it's extremely common + + align:start position:0% +word and it's extremely common + + + align:start position:0% +word and it's extremely common +cross-linguistically for it to be + + align:start position:0% +cross-linguistically for it to be + + + align:start position:0% +cross-linguistically for it to be +possible to leave these words these + + align:start position:0% +possible to leave these words these + + + align:start position:0% +possible to leave these words these +question words like what + + align:start position:0% +question words like what + + + align:start position:0% +question words like what +uh in the positions where you would + + align:start position:0% +uh in the positions where you would + + + align:start position:0% +uh in the positions where you would +expect them to be in those kinds of + + align:start position:0% +expect them to be in those kinds of + + + align:start position:0% +expect them to be in those kinds of +questions in the positions where they + + align:start position:0% +questions in the positions where they + + + align:start position:0% +questions in the positions where they +would be selected it's not Universal + + align:start position:0% +would be selected it's not Universal + + + align:start position:0% +would be selected it's not Universal +actually uh there are languages that + + align:start position:0% +actually uh there are languages that + + + align:start position:0% +actually uh there are languages that +don't let you do that if you're working + + align:start position:0% +don't let you do that if you're working + + + align:start position:0% +don't let you do that if you're working +on language uh it could be interesting + + align:start position:0% +on language uh it could be interesting + + + align:start position:0% +on language uh it could be interesting +to to do some finding out about how it + + align:start position:0% +to to do some finding out about how it + + + align:start position:0% +to to do some finding out about how it +forms these kinds of questions + + align:start position:0% +forms these kinds of questions + + + align:start position:0% +forms these kinds of questions +um + + align:start position:0% +um + + + align:start position:0% +um +okay so lots of questions about what's + + align:start position:0% +okay so lots of questions about what's + + + align:start position:0% +okay so lots of questions about what's +going on in this last example + + align:start position:0% +going on in this last example + + + align:start position:0% +going on in this last example +um there are several reasons to think + + align:start position:0% +um there are several reasons to think + + + align:start position:0% +um there are several reasons to think +that what is ending up in CP + + align:start position:0% +that what is ending up in CP + + + align:start position:0% +that what is ending up in CP +um remember CP it was the thing uh that + + align:start position:0% +um remember CP it was the thing uh that + + + align:start position:0% +um remember CP it was the thing uh that +had heads like weather and that right so + + align:start position:0% +had heads like weather and that right so + + + align:start position:0% +had heads like weather and that right so +we said verbs like no and think and + + align:start position:0% +we said verbs like no and think and + + + align:start position:0% +we said verbs like no and think and +wonder I think was the example I used + + align:start position:0% +wonder I think was the example I used + + + align:start position:0% +wonder I think was the example I used +before they select for Clauses and in + + align:start position:0% +before they select for Clauses and in + + + align:start position:0% +before they select for Clauses and in +particular they select for properties of + + align:start position:0% +particular they select for properties of + + + align:start position:0% +particular they select for properties of +the head of the Clause so + + align:start position:0% +the head of the Clause so + + + align:start position:0% +the head of the Clause so +um uh think can select for a clause + + align:start position:0% +um uh think can select for a clause + + + align:start position:0% +um uh think can select for a clause +that's headed by that that is the + + align:start position:0% +that's headed by that that is the + + + align:start position:0% +that's headed by that that is the +complementizer that's our word for it in + + align:start position:0% +complementizer that's our word for it in + + + align:start position:0% +complementizer that's our word for it in +syntax uh that is the complementizer it + + align:start position:0% +syntax uh that is the complementizer it + + + align:start position:0% +syntax uh that is the complementizer it +introduces that embedded Clause uh I + + align:start position:0% +introduces that embedded Clause uh I + + + align:start position:0% +introduces that embedded Clause uh I +don't know whether he ate the ants + + align:start position:0% +don't know whether he ate the ants + + + align:start position:0% +don't know whether he ate the ants +whether is a complimentizer that can be + + align:start position:0% +whether is a complimentizer that can be + + + align:start position:0% +whether is a complimentizer that can be +selected by no uh you can't think + + align:start position:0% +selected by no uh you can't think + + + align:start position:0% +selected by no uh you can't think +whether he ate the ants and actually + + align:start position:0% +whether he ate the ants and actually + + + align:start position:0% +whether he ate the ants and actually +there are verbs like no that can have + + align:start position:0% +there are verbs like no that can have + + + align:start position:0% +there are verbs like no that can have +either whether or that + + align:start position:0% +either whether or that + + + align:start position:0% +either whether or that +um with a verb like no that can have + + align:start position:0% +um with a verb like no that can have + + + align:start position:0% +um with a verb like no that can have +weather it can also have uh what + + align:start position:0% +weather it can also have uh what + + + align:start position:0% +weather it can also have uh what +immediately following it so you can say + + align:start position:0% +immediately following it so you can say + + + align:start position:0% +immediately following it so you can say +I don't know what he ate + + align:start position:0% +I don't know what he ate + + + align:start position:0% +I don't know what he ate +um + + align:start position:0% +um + + + align:start position:0% +um +and uh notice that if it has what it + + align:start position:0% +and uh notice that if it has what it + + + align:start position:0% +and uh notice that if it has what it +cannot have either that or whether so + + align:start position:0% +cannot have either that or whether so + + + align:start position:0% +cannot have either that or whether so +um uh you can say I know that he ate the + + align:start position:0% +um uh you can say I know that he ate the + + + align:start position:0% +um uh you can say I know that he ate the +ants you can say I know whether he ate + + align:start position:0% +ants you can say I know whether he ate + + + align:start position:0% +ants you can say I know whether he ate +the ants but you cannot say and you can + + align:start position:0% +the ants but you cannot say and you can + + + align:start position:0% +the ants but you cannot say and you can +say I know what he ate you cannot say I + + align:start position:0% +say I know what he ate you cannot say I + + + align:start position:0% +say I know what he ate you cannot say I +know what that he ate or what whether he + + align:start position:0% +know what that he ate or what whether he + + + align:start position:0% +know what that he ate or what whether he +ate right so that and whether and what + + align:start position:0% +ate right so that and whether and what + + + align:start position:0% +ate right so that and whether and what +they all seem to be sort of in the same + + align:start position:0% +they all seem to be sort of in the same + + + align:start position:0% +they all seem to be sort of in the same +slot there they're in the CPE somehow + + align:start position:0% +slot there they're in the CPE somehow + + + align:start position:0% +slot there they're in the CPE somehow +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +we'll see they're not quite in the same + + align:start position:0% +we'll see they're not quite in the same + + + align:start position:0% +we'll see they're not quite in the same +slot but the idea that what ends up + + align:start position:0% +slot but the idea that what ends up + + + align:start position:0% +slot but the idea that what ends up +somewhere in CP uh + + align:start position:0% +somewhere in CP uh + + + align:start position:0% +somewhere in CP uh +has to be part of what's going on here + + align:start position:0% + + + + align:start position:0% + +okay and then + + align:start position:0% +okay and then + + + align:start position:0% +okay and then +as I said I promised you there will be + + align:start position:0% +as I said I promised you there will be + + + align:start position:0% +as I said I promised you there will be +various reasons to think that what + + align:start position:0% +various reasons to think that what + + + align:start position:0% +various reasons to think that what +starts off as the sister of right and + + align:start position:0% +starts off as the sister of right and + + + align:start position:0% +starts off as the sister of right and +moves into CP but one of them is the one + + align:start position:0% +moves into CP but one of them is the one + + + align:start position:0% +moves into CP but one of them is the one +I just went through under certain + + align:start position:0% +I just went through under certain + + + align:start position:0% +I just went through under certain +circumstances communicative + + align:start position:0% +circumstances communicative + + + align:start position:0% +circumstances communicative +circumstances I can say Mary wrote what + + align:start position:0% +circumstances I can say Mary wrote what + + + align:start position:0% +circumstances I can say Mary wrote what +on a typewriter like if I couldn't quite + + align:start position:0% +on a typewriter like if I couldn't quite + + + align:start position:0% +on a typewriter like if I couldn't quite +hear you or if I um if I don't believe + + align:start position:0% +hear you or if I um if I don't believe + + + align:start position:0% +hear you or if I um if I don't believe +what you just said + + align:start position:0% +what you just said + + + align:start position:0% +what you just said +so here's a tree that we're going to + + align:start position:0% +so here's a tree that we're going to + + + align:start position:0% +so here's a tree that we're going to +draw for what will Mary write it's going + + align:start position:0% +draw for what will Mary write it's going + + + align:start position:0% +draw for what will Mary write it's going +to have what starting off as the sister + + align:start position:0% +to have what starting off as the sister + + + align:start position:0% +to have what starting off as the sister +of right right where the projection + + align:start position:0% +of right right where the projection + + + align:start position:0% +of right right where the projection +principle wants it to be right selects + + align:start position:0% +principle wants it to be right selects + + + align:start position:0% +principle wants it to be right selects +for a direct object and it gets one + + align:start position:0% +for a direct object and it gets one + + + align:start position:0% +for a direct object and it gets one +that's the sister of right and then it + + align:start position:0% +that's the sister of right and then it + + + align:start position:0% +that's the sister of right and then it +moves uh to the edge of the CP and so + + align:start position:0% +moves uh to the edge of the CP and so + + + align:start position:0% +moves uh to the edge of the CP and so +that's the kind of tree that we're going + + align:start position:0% +that's the kind of tree that we're going + + + align:start position:0% +that's the kind of tree that we're going +to draw + + align:start position:0% +to draw + + + align:start position:0% +to draw +this phenomenon there's a name for it uh + + align:start position:0% +this phenomenon there's a name for it uh + + + align:start position:0% +this phenomenon there's a name for it uh +it's called wh movement + + align:start position:0% +it's called wh movement + + + align:start position:0% +it's called wh movement +it's called wh movement because these + + align:start position:0% +it's called wh movement because these + + + align:start position:0% +it's called wh movement because these +question words these words like what and + + align:start position:0% +question words these words like what and + + + align:start position:0% +question words these words like what and +where and why and when uh tend to start + + align:start position:0% +where and why and when uh tend to start + + + align:start position:0% +where and why and when uh tend to start +with the letters w and the H in English + + align:start position:0% +with the letters w and the H in English + + + align:start position:0% +with the letters w and the H in English +um who and what and where and when and + + align:start position:0% +um who and what and where and when and + + + align:start position:0% +um who and what and where and when and +why and how which doesn't select start + + align:start position:0% +why and how which doesn't select start + + + align:start position:0% +why and how which doesn't select start +with the words W and H letters w and H + + align:start position:0% +with the words W and H letters w and H + + + align:start position:0% +with the words W and H letters w and H +but it does contain the letters w and H + + align:start position:0% +but it does contain the letters w and H + + + align:start position:0% +but it does contain the letters w and H +just not in the right the right order so + + align:start position:0% +just not in the right the right order so + + + align:start position:0% +just not in the right the right order so +these words are called wh words and + + align:start position:0% +these words are called wh words and + + + align:start position:0% +these words are called wh words and +they're called that it's just a + + align:start position:0% +they're called that it's just a + + + align:start position:0% +they're called that it's just a +technical term in syntax we call these + + align:start position:0% +technical term in syntax we call these + + + align:start position:0% +technical term in syntax we call these +words wh words regardless of the + + align:start position:0% +words wh words regardless of the + + + align:start position:0% +words wh words regardless of the +language we're working in it's a sort of + + align:start position:0% +language we're working in it's a sort of + + + align:start position:0% +language we're working in it's a sort of +embarrassingly anglicentric term yeah so + + align:start position:0% +embarrassingly anglicentric term yeah so + + + align:start position:0% +embarrassingly anglicentric term yeah so +they're called wh words because in + + align:start position:0% +they're called wh words because in + + + align:start position:0% +they're called wh words because in +English they start with w and H the + + align:start position:0% +English they start with w and H the + + + align:start position:0% +English they start with w and H the +language that you're working on they + + align:start position:0% +language that you're working on they + + + align:start position:0% +language that you're working on they +surely will not start with w and H but + + align:start position:0% +surely will not start with w and H but + + + align:start position:0% +surely will not start with w and H but +we're still going to want to call them + + align:start position:0% +we're still going to want to call them + + + align:start position:0% +we're still going to want to call them +wh words and this phenomenon is called + + align:start position:0% +wh words and this phenomenon is called + + + align:start position:0% +wh words and this phenomenon is called +wh movement + + align:start position:0% +wh movement + + + align:start position:0% +wh movement +and it took us linguistically very + + align:start position:0% +and it took us linguistically very + + + align:start position:0% +and it took us linguistically very +common phenomenon uh so uh English + + align:start position:0% +common phenomenon uh so uh English + + + align:start position:0% +common phenomenon uh so uh English +there's English example of it there + + align:start position:0% +there's English example of it there + + + align:start position:0% +there's English example of it there +again what did you put on the table uh + + align:start position:0% +again what did you put on the table uh + + + align:start position:0% +again what did you put on the table uh +here's the Tagalog for what did you put + + align:start position:0% +here's the Tagalog for what did you put + + + align:start position:0% +here's the Tagalog for what did you put +on the table you can see uh the Tagalog + + align:start position:0% +on the table you can see uh the Tagalog + + + align:start position:0% +on the table you can see uh the Tagalog +word for what doesn't begin with w and H + + align:start position:0% +word for what doesn't begin with w and H + + + align:start position:0% +word for what doesn't begin with w and H +uh Tagalog does have W and H but words + + align:start position:0% +uh Tagalog does have W and H but words + + + align:start position:0% +uh Tagalog does have W and H but words +can't start with w and H + + align:start position:0% +can't start with w and H + + + align:start position:0% +can't start with w and H +um and uh there's the finish for uh + + align:start position:0% +um and uh there's the finish for uh + + + align:start position:0% +um and uh there's the finish for uh +where did I put my clothes I should + + align:start position:0% +where did I put my clothes I should + + + align:start position:0% +where did I put my clothes I should +really learn how to say uh what did you + + align:start position:0% +really learn how to say uh what did you + + + align:start position:0% +really learn how to say uh what did you +put on the table and finish I don't know + + align:start position:0% +put on the table and finish I don't know + + + align:start position:0% +put on the table and finish I don't know +why that's my finished example okay so + + align:start position:0% +why that's my finished example okay so + + + align:start position:0% +why that's my finished example okay so +various unrelated languages that have uh + + align:start position:0% +various unrelated languages that have uh + + + align:start position:0% +various unrelated languages that have uh +wh movement it's across linguistically + + align:start position:0% +wh movement it's across linguistically + + + align:start position:0% +wh movement it's across linguistically +very common phenomenon + + align:start position:0% +very common phenomenon + + + align:start position:0% +very common phenomenon +it's not Universal so some of you in + + align:start position:0% +it's not Universal so some of you in + + + align:start position:0% +it's not Universal so some of you in +fact are native speakers of languages in + + align:start position:0% +fact are native speakers of languages in + + + align:start position:0% +fact are native speakers of languages in +which wh words don't move to the left + + align:start position:0% +which wh words don't move to the left + + + align:start position:0% +which wh words don't move to the left +edge of the Clause they just stay where + + align:start position:0% +edge of the Clause they just stay where + + + align:start position:0% +edge of the Clause they just stay where +they are so in Chinese for example uh if + + align:start position:0% +they are so in Chinese for example uh if + + + align:start position:0% +they are so in Chinese for example uh if +you want to say what did Junction buy + + align:start position:0% +you want to say what did Junction buy + + + align:start position:0% +you want to say what did Junction buy +you don't say what to Junction buy or at + + align:start position:0% +you don't say what to Junction buy or at + + + align:start position:0% +you don't say what to Junction buy or at +least you don't have to the standard + + align:start position:0% +least you don't have to the standard + + + align:start position:0% +least you don't have to the standard +thing to say is literally jung-sun + + align:start position:0% +thing to say is literally jung-sun + + + align:start position:0% +thing to say is literally jung-sun +bought what yeah which as I said you can + + align:start position:0% +bought what yeah which as I said you can + + + align:start position:0% +bought what yeah which as I said you can +say in English but only under special + + align:start position:0% +say in English but only under special + + + align:start position:0% +say in English but only under special +circumstances in Chinese that's just the + + align:start position:0% +circumstances in Chinese that's just the + + + align:start position:0% +circumstances in Chinese that's just the +natural way to ask that question is to + + align:start position:0% +natural way to ask that question is to + + + align:start position:0% +natural way to ask that question is to +leave right where it would be yes the + + align:start position:0% +leave right where it would be yes the + + + align:start position:0% +leave right where it would be yes the +the object of the verb yeah and I hear a + + align:start position:0% +the object of the verb yeah and I hear a + + + align:start position:0% +the object of the verb yeah and I hear a +couple more examples uh Buffet which is + + align:start position:0% +couple more examples uh Buffet which is + + + align:start position:0% +couple more examples uh Buffet which is +a language of Cameroon and Hopi which is + + align:start position:0% +a language of Cameroon and Hopi which is + + + align:start position:0% +a language of Cameroon and Hopi which is +a language of the American southwest + + align:start position:0% +a language of the American southwest + + + align:start position:0% +a language of the American southwest +nope + + align:start position:0% + + + + align:start position:0% + +um so there's cross-linguistic variation + + align:start position:0% +um so there's cross-linguistic variation + + + align:start position:0% +um so there's cross-linguistic variation +in how you form wh questions there are + + align:start position:0% +in how you form wh questions there are + + + align:start position:0% +in how you form wh questions there are +languages like English and Finnish and + + align:start position:0% +languages like English and Finnish and + + + align:start position:0% +languages like English and Finnish and +Tagalog and many other languages where + + align:start position:0% +Tagalog and many other languages where + + + align:start position:0% +Tagalog and many other languages where +you take your wh words and you move them + + align:start position:0% +you take your wh words and you move them + + + align:start position:0% +you take your wh words and you move them +to the left edge of CP + + align:start position:0% +to the left edge of CP + + + align:start position:0% +to the left edge of CP +and then there are languages like + + align:start position:0% +and then there are languages like + + + align:start position:0% +and then there are languages like +Chinese and Buffett and Hopi where the + + align:start position:0% +Chinese and Buffett and Hopi where the + + + align:start position:0% +Chinese and Buffett and Hopi where the +wh words just don't move they just stay + + align:start position:0% +wh words just don't move they just stay + + + align:start position:0% +wh words just don't move they just stay +where they would normally go yeah + + align:start position:0% +where they would normally go yeah + + + align:start position:0% +where they would normally go yeah +um wherever they would normally go in + + align:start position:0% +um wherever they would normally go in + + + align:start position:0% +um wherever they would normally go in +the sentence there's no movement going + + align:start position:0% +the sentence there's no movement going + + + align:start position:0% +the sentence there's no movement going +on so uh in Chinese uh if you wanted to + + align:start position:0% +on so uh in Chinese uh if you wanted to + + + align:start position:0% +on so uh in Chinese uh if you wanted to +say jung-sun bought a book instead of + + align:start position:0% +say jung-sun bought a book instead of + + + align:start position:0% +say jung-sun bought a book instead of +what you would just put the word for + + align:start position:0% +what you would just put the word for + + + align:start position:0% +what you would just put the word for +book + + align:start position:0% +book + + + align:start position:0% +book +um it's a Chinese normal word orders + + align:start position:0% +um it's a Chinese normal word orders + + + align:start position:0% +um it's a Chinese normal word orders +subject verb object kind of like English + + align:start position:0% +subject verb object kind of like English + + + align:start position:0% +subject verb object kind of like English +same deal for Buffet uh Hopi has the + + align:start position:0% +same deal for Buffet uh Hopi has the + + + align:start position:0% +same deal for Buffet uh Hopi has the +verb at the end of the sentence so these + + align:start position:0% +verb at the end of the sentence so these + + + align:start position:0% +verb at the end of the sentence so these +wh words these words that mean things + + align:start position:0% +wh words these words that mean things + + + align:start position:0% +wh words these words that mean things +like what and who they're just going + + align:start position:0% +like what and who they're just going + + + align:start position:0% +like what and who they're just going +where the object would normally go in + + align:start position:0% +where the object would normally go in + + + align:start position:0% +where the object would normally go in +these wh Institute languages + + align:start position:0% +these wh Institute languages + + + align:start position:0% +these wh Institute languages +and those are almost the only two + + align:start position:0% +and those are almost the only two + + + align:start position:0% +and those are almost the only two +options take your wh word and move it to + + align:start position:0% +options take your wh word and move it to + + + align:start position:0% +options take your wh word and move it to +the left edge of CP or leave it where it + + align:start position:0% +the left edge of CP or leave it where it + + + align:start position:0% +the left edge of CP or leave it where it +would normally go + + align:start position:0% +would normally go + + + align:start position:0% +would normally go +you can imagine others right so uh for + + align:start position:0% +you can imagine others right so uh for + + + align:start position:0% +you can imagine others right so uh for +example it's not clear that there are + + align:start position:0% +example it's not clear that there are + + + align:start position:0% +example it's not clear that there are +any languages in which you take the wh + + align:start position:0% +any languages in which you take the wh + + + align:start position:0% +any languages in which you take the wh +word and you move it to the end of the + + align:start position:0% +word and you move it to the end of the + + + align:start position:0% +word and you move it to the end of the +Clause I could imagine a language like + + align:start position:0% +Clause I could imagine a language like + + + align:start position:0% +Clause I could imagine a language like +that but it's not clear that there are + + align:start position:0% +that but it's not clear that there are + + + align:start position:0% +that but it's not clear that there are +any languages in which you say you put + + align:start position:0% +any languages in which you say you put + + + align:start position:0% +any languages in which you say you put +on the table what + + align:start position:0% +on the table what + + + align:start position:0% +on the table what +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um I think my next slides make that + + align:start position:0% +um I think my next slides make that + + + align:start position:0% +um I think my next slides make that +observation more complicated and I think + + align:start position:0% +observation more complicated and I think + + + align:start position:0% +observation more complicated and I think +I want to skip them actually so uh so to + + align:start position:0% +I want to skip them actually so uh so to + + + align:start position:0% +I want to skip them actually so uh so to +make this fact more interesting let me + + align:start position:0% +make this fact more interesting let me + + + align:start position:0% +make this fact more interesting let me +show you one other kind of + + align:start position:0% +show you one other kind of + + + align:start position:0% +show you one other kind of +cross-linguistic variation + + align:start position:0% +cross-linguistic variation + + + align:start position:0% +cross-linguistic variation +um I'm not going to do that so let me do + + align:start position:0% +um I'm not going to do that so let me do + + + align:start position:0% +um I'm not going to do that so let me do +that fast we'll come back to this + + align:start position:0% +that fast we'll come back to this + + + align:start position:0% +that fast we'll come back to this +um so because we're running low on time + + align:start position:0% +um so because we're running low on time + + + align:start position:0% +um so because we're running low on time +I want to show you one other one other + + align:start position:0% +I want to show you one other one other + + + align:start position:0% +I want to show you one other one other +quick thing + + align:start position:0% +quick thing + + + align:start position:0% +quick thing +um + + align:start position:0% +um + + + align:start position:0% +um +yeah in the rain in five minutes I'm + + align:start position:0% +yeah in the rain in five minutes I'm + + + align:start position:0% +yeah in the rain in five minutes I'm +gonna set up another thing and then + + align:start position:0% +gonna set up another thing and then + + + align:start position:0% +gonna set up another thing and then +we'll come back and and we'll start here + + align:start position:0% +we'll come back and and we'll start here + + + align:start position:0% +we'll come back and and we'll start here +next time + + align:start position:0% +next time + + + align:start position:0% +next time +um I've been concentrating on wh + + align:start position:0% +um I've been concentrating on wh + + + align:start position:0% +um I've been concentrating on wh +questions where you're only asking about + + align:start position:0% +questions where you're only asking about + + + align:start position:0% +questions where you're only asking about +one thing + + align:start position:0% +one thing + + + align:start position:0% +one thing +in many languages not all languages but + + align:start position:0% +in many languages not all languages but + + + align:start position:0% +in many languages not all languages but +in many languages it's possible to ask + + align:start position:0% +in many languages it's possible to ask + + + align:start position:0% +in many languages it's possible to ask +about more than one thing at the same + + align:start position:0% +about more than one thing at the same + + + align:start position:0% +about more than one thing at the same +time so you can ask questions like what + + align:start position:0% +time so you can ask questions like what + + + align:start position:0% +time so you can ask questions like what +did you give to whom where if I ask you + + align:start position:0% +did you give to whom where if I ask you + + + align:start position:0% +did you give to whom where if I ask you +a question like that what I want is a + + align:start position:0% +a question like that what I want is a + + + align:start position:0% +a question like that what I want is a +list of people and things such that + + align:start position:0% +list of people and things such that + + + align:start position:0% +list of people and things such that +person X got thing X and person y I got + + align:start position:0% +person X got thing X and person y I got + + + align:start position:0% +person X got thing X and person y I got +thing y yeah that's uh that's what I'm + + align:start position:0% +thing y yeah that's uh that's what I'm + + + align:start position:0% +thing y yeah that's uh that's what I'm +asking you if I ask you that kind of + + align:start position:0% +asking you if I ask you that kind of + + + align:start position:0% +asking you if I ask you that kind of +question + + align:start position:0% +question + + + align:start position:0% +question +um + + align:start position:0% + + + + align:start position:0% + +there are again there's some variation + + align:start position:0% +there are again there's some variation + + + align:start position:0% +there are again there's some variation +so English I said is a language with wh + + align:start position:0% +so English I said is a language with wh + + + align:start position:0% +so English I said is a language with wh +movement but it's specifically a + + align:start position:0% +movement but it's specifically a + + + align:start position:0% +movement but it's specifically a +language with wh movement of 1wh so if + + align:start position:0% +language with wh movement of 1wh so if + + + align:start position:0% +language with wh movement of 1wh so if +you want to ask a multiple wh question + + align:start position:0% +you want to ask a multiple wh question + + + align:start position:0% +you want to ask a multiple wh question +you move one of your wh words but you + + align:start position:0% +you move one of your wh words but you + + + align:start position:0% +you move one of your wh words but you +leave the other ones where they are so + + align:start position:0% +leave the other ones where they are so + + + align:start position:0% +leave the other ones where they are so +you say what did you give to whom what + + align:start position:0% +you say what did you give to whom what + + + align:start position:0% +you say what did you give to whom what +did you give to whom when where why how + + align:start position:0% +did you give to whom when where why how + + + align:start position:0% +did you give to whom when where why how +so all your other wh words just stay + + align:start position:0% +so all your other wh words just stay + + + align:start position:0% +so all your other wh words just stay +where they would normally go + + align:start position:0% +where they would normally go + + + align:start position:0% +where they would normally go +there are other languages in which all + + align:start position:0% +there are other languages in which all + + + align:start position:0% +there are other languages in which all +of the wh words move in this big mooing + + align:start position:0% +of the wh words move in this big mooing + + + align:start position:0% +of the wh words move in this big mooing +herd to the beginning of the Clause so + + align:start position:0% +herd to the beginning of the Clause so + + + align:start position:0% +herd to the beginning of the Clause so +in Bulgarian for example you don't ask + + align:start position:0% +in Bulgarian for example you don't ask + + + align:start position:0% +in Bulgarian for example you don't ask +literally what did you give to whom you + + align:start position:0% +literally what did you give to whom you + + + align:start position:0% +literally what did you give to whom you +ask literally what to whom did he give + + align:start position:0% +ask literally what to whom did he give + + + align:start position:0% +ask literally what to whom did he give +so what and to whom are both at the + + align:start position:0% +so what and to whom are both at the + + + align:start position:0% +so what and to whom are both at the +beginning of the sentence there are a + + align:start position:0% +beginning of the sentence there are a + + + align:start position:0% +beginning of the sentence there are a +bunch of languages like this Mohawk is + + align:start position:0% +bunch of languages like this Mohawk is + + + align:start position:0% +bunch of languages like this Mohawk is +another one + + align:start position:0% +another one + + + align:start position:0% +another one +language spoken in uh not too far from + + align:start position:0% +language spoken in uh not too far from + + + align:start position:0% +language spoken in uh not too far from +here + + align:start position:0% +here + + + align:start position:0% +here +um + + align:start position:0% +um + + + align:start position:0% +um +in parts of America and Canada + + align:start position:0% +in parts of America and Canada + + + align:start position:0% +in parts of America and Canada +these are both languages in which uh the + + align:start position:0% +these are both languages in which uh the + + + align:start position:0% +these are both languages in which uh the +wh words all have to move into multiple + + align:start position:0% +wh words all have to move into multiple + + + align:start position:0% +wh words all have to move into multiple +wh question + + align:start position:0% + + + + align:start position:0% + +and again so there's some variation + + align:start position:0% +and again so there's some variation + + + align:start position:0% +and again so there's some variation +between languages there are languages + + align:start position:0% +between languages there are languages + + + align:start position:0% +between languages there are languages +that move one wh word like like English + + align:start position:0% +that move one wh word like like English + + + align:start position:0% +that move one wh word like like English +there are languages that move no bless + + align:start position:0% +there are languages that move no bless + + + align:start position:0% +there are languages that move no bless +you they're languages that move no wh + + align:start position:0% +you they're languages that move no wh + + + align:start position:0% +you they're languages that move no wh +words like Chinese there are languages + + align:start position:0% +words like Chinese there are languages + + + align:start position:0% +words like Chinese there are languages +that move all the wh words like uh + + align:start position:0% +that move all the wh words like uh + + + align:start position:0% +that move all the wh words like uh +Bulgarian or mohawk and again it's not + + align:start position:0% +Bulgarian or mohawk and again it's not + + + align:start position:0% +Bulgarian or mohawk and again it's not +too hard to imagine other options so for + + align:start position:0% +too hard to imagine other options so for + + + align:start position:0% +too hard to imagine other options so for +example you could imagine a language + + align:start position:0% +example you could imagine a language + + + align:start position:0% +example you could imagine a language +that only moved two wh words + + align:start position:0% +that only moved two wh words + + + align:start position:0% +that only moved two wh words +that would be a language where you would + + align:start position:0% +that would be a language where you would + + + align:start position:0% +that would be a language where you would +say uh who what gave to whom to mean who + + align:start position:0% +say uh who what gave to whom to mean who + + + align:start position:0% +say uh who what gave to whom to mean who +gave what to whom yeah + + align:start position:0% +gave what to whom yeah + + + align:start position:0% +gave what to whom yeah +um there aren't any languages like that + + align:start position:0% +um there aren't any languages like that + + + align:start position:0% +um there aren't any languages like that +the only kinds of languages there are + + align:start position:0% +the only kinds of languages there are + + + align:start position:0% +the only kinds of languages there are +are the English kinds so first the + + align:start position:0% +are the English kinds so first the + + + align:start position:0% +are the English kinds so first the +Mandarin kind the Chinese kind where you + + align:start position:0% +Mandarin kind the Chinese kind where you + + + align:start position:0% +Mandarin kind the Chinese kind where you +don't move any of them the English kind + + align:start position:0% +don't move any of them the English kind + + + align:start position:0% +don't move any of them the English kind +where you move one where you say who + + align:start position:0% +where you move one where you say who + + + align:start position:0% +where you move one where you say who +gave what to whom and the Bulgarian + + align:start position:0% +gave what to whom and the Bulgarian + + + align:start position:0% +gave what to whom and the Bulgarian +Mohawk kind where you move them all you + + align:start position:0% +Mohawk kind where you move them all you + + + align:start position:0% +Mohawk kind where you move them all you +say who what to whom gave yeah there + + align:start position:0% +say who what to whom gave yeah there + + + align:start position:0% +say who what to whom gave yeah there +aren't any languages like this that that + + align:start position:0% +aren't any languages like this that that + + + align:start position:0% +aren't any languages like this that that +just moved to or move up to two + + align:start position:0% +just moved to or move up to two + + + align:start position:0% +just moved to or move up to two +you can imagine a language like that but + + align:start position:0% +you can imagine a language like that but + + + align:start position:0% +you can imagine a language like that but +there but there aren't any + + align:start position:0% +there but there aren't any + + + align:start position:0% +there but there aren't any +um and uh let me just leave you with + + align:start position:0% +um and uh let me just leave you with + + + align:start position:0% +um and uh let me just leave you with +this last point and we'll probably take + + align:start position:0% +this last point and we'll probably take + + + align:start position:0% +this last point and we'll probably take +it up here again last next time + + align:start position:0% +it up here again last next time + + + align:start position:0% +it up here again last next time +um + + align:start position:0% +um + + + align:start position:0% +um +uh logical problems language acquisition + + align:start position:0% +uh logical problems language acquisition + + + align:start position:0% +uh logical problems language acquisition +so here's a here's a here's a game we + + align:start position:0% +so here's a here's a here's a game we + + + align:start position:0% +so here's a here's a here's a game we +can play here's a function uh it's a + + align:start position:0% +can play here's a function uh it's a + + + align:start position:0% +can play here's a function uh it's a +function that if you give it one the + + align:start position:0% +function that if you give it one the + + + align:start position:0% +function that if you give it one the +answer is one if you give it two the + + align:start position:0% +answer is one if you give it two the + + + align:start position:0% +answer is one if you give it two the +answer is two if you give it three the + + align:start position:0% +answer is two if you give it three the + + + align:start position:0% +answer is two if you give it three the +answer is three if you give it four the + + align:start position:0% +answer is three if you give it four the + + + align:start position:0% +answer is three if you give it four the +answer is four what do you think the + + align:start position:0% +answer is four what do you think the + + + align:start position:0% +answer is four what do you think the +answer is if you give it five + + align:start position:0% +answer is if you give it five + + + align:start position:0% +answer is if you give it five +five + + align:start position:0% +five + + + align:start position:0% +five +what do you think of any other options + + align:start position:0% +what do you think of any other options + + + align:start position:0% +what do you think of any other options +ha you've fallen into my trap the + + align:start position:0% +ha you've fallen into my trap the + + + align:start position:0% +ha you've fallen into my trap the +function that I actually had in mind was + + align:start position:0% +function that I actually had in mind was + + + align:start position:0% +function that I actually had in mind was +this one + + align:start position:0% +this one + + + align:start position:0% +this one +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +such that the answer is 29 in fact the + + align:start position:0% +such that the answer is 29 in fact the + + + align:start position:0% +such that the answer is 29 in fact the +answer could be anything at all right so + + align:start position:0% +answer could be anything at all right so + + + align:start position:0% +answer could be anything at all right so +this is the kind of uh question you + + align:start position:0% +this is the kind of uh question you + + + align:start position:0% +this is the kind of uh question you +sometimes get asked on standardized + + align:start position:0% +sometimes get asked on standardized + + + align:start position:0% +sometimes get asked on standardized +tests and it's always unfair uh because + + align:start position:0% +tests and it's always unfair uh because + + + align:start position:0% +tests and it's always unfair uh because +the the answer could be anything at all + + align:start position:0% +the the answer could be anything at all + + + align:start position:0% +the the answer could be anything at all +that first thing which I carefully + + align:start position:0% +that first thing which I carefully + + + align:start position:0% +that first thing which I carefully +devised to be zero as long as the thing + + align:start position:0% +devised to be zero as long as the thing + + + align:start position:0% +devised to be zero as long as the thing +I was giving the function was one two + + align:start position:0% +I was giving the function was one two + + + align:start position:0% +I was giving the function was one two +three or four uh you could multiply that + + align:start position:0% +three or four uh you could multiply that + + + align:start position:0% +three or four uh you could multiply that +by anything and so five could be could + + align:start position:0% +by anything and so five could be could + + + align:start position:0% +by anything and so five could be could +be any number yeah + + align:start position:0% +be any number yeah + + + align:start position:0% +be any number yeah +um life is like that a lot there are + + align:start position:0% +um life is like that a lot there are + + + align:start position:0% +um life is like that a lot there are +lots of places where you go through life + + align:start position:0% +lots of places where you go through life + + + align:start position:0% +lots of places where you go through life +and you get a certain number of finite + + align:start position:0% +and you get a certain number of finite + + + align:start position:0% +and you get a certain number of finite +observations of uh how life works and + + align:start position:0% +observations of uh how life works and + + + align:start position:0% +observations of uh how life works and +then you have to make a decision about + + align:start position:0% +then you have to make a decision about + + + align:start position:0% +then you have to make a decision about +what the basic rule is you know so + + align:start position:0% +what the basic rule is you know so + + + align:start position:0% +what the basic rule is you know so +you're doing science let's say you go + + align:start position:0% +you're doing science let's say you go + + + align:start position:0% +you're doing science let's say you go +out there you see uh many white swans + + align:start position:0% +out there you see uh many white swans + + + align:start position:0% +out there you see uh many white swans +um at some point you have to decide have + + align:start position:0% +um at some point you have to decide have + + + align:start position:0% +um at some point you have to decide have +I seen enough white swans but I get to + + align:start position:0% +I seen enough white swans but I get to + + + align:start position:0% +I seen enough white swans but I get to +decide that swans are white right have I + + align:start position:0% +decide that swans are white right have I + + + align:start position:0% +decide that swans are white right have I +seen enough black crows that I get to + + align:start position:0% +seen enough black crows that I get to + + + align:start position:0% +seen enough black crows that I get to +say that crows are black right you never + + align:start position:0% +say that crows are black right you never + + + align:start position:0% +say that crows are black right you never +know maybe the next one is going to be + + align:start position:0% +know maybe the next one is going to be + + + align:start position:0% +know maybe the next one is going to be +purple right or green you know it's just + + align:start position:0% +purple right or green you know it's just + + + align:start position:0% +purple right or green you know it's just +hard to know and this function is sort + + align:start position:0% +hard to know and this function is sort + + + align:start position:0% +hard to know and this function is sort +of a dramatic example of that + + align:start position:0% +of a dramatic example of that + + + align:start position:0% +of a dramatic example of that +imagine just in the remaining seconds + + align:start position:0% +imagine just in the remaining seconds + + + align:start position:0% +imagine just in the remaining seconds +that you are a Bulgarian child + + align:start position:0% +that you are a Bulgarian child + + + align:start position:0% +that you are a Bulgarian child +were any of you Bulgarian children + + align:start position:0% +were any of you Bulgarian children + + + align:start position:0% +were any of you Bulgarian children +okay so just imagine counter factually + + align:start position:0% +okay so just imagine counter factually + + + align:start position:0% +okay so just imagine counter factually +that you were a Bulgarian child + + align:start position:0% +that you were a Bulgarian child + + + align:start position:0% +that you were a Bulgarian child +uh here you are growing up uh hearing + + align:start position:0% +uh here you are growing up uh hearing + + + align:start position:0% +uh here you are growing up uh hearing +your parents uh ask wh questions and + + align:start position:0% +your parents uh ask wh questions and + + + align:start position:0% +your parents uh ask wh questions and +um there's got to be some number in that + + align:start position:0% +um there's got to be some number in that + + + align:start position:0% +um there's got to be some number in that +is the largest number of wh words you + + align:start position:0% +is the largest number of wh words you + + + align:start position:0% +is the largest number of wh words you +ever heard in a question right maybe you + + align:start position:0% +ever heard in a question right maybe you + + + align:start position:0% +ever heard in a question right maybe you +heard your parents say two wh words in a + + align:start position:0% +heard your parents say two wh words in a + + + align:start position:0% +heard your parents say two wh words in a +question maybe you heard them say three + + align:start position:0% +question maybe you heard them say three + + + align:start position:0% +question maybe you heard them say three +it's kind of unlikely that you ever + + align:start position:0% +it's kind of unlikely that you ever + + + align:start position:0% +it's kind of unlikely that you ever +heard them say four or five I mean it + + align:start position:0% +heard them say four or five I mean it + + + align:start position:0% +heard them say four or five I mean it +depends I guess on what your parents + + align:start position:0% +depends I guess on what your parents + + + align:start position:0% +depends I guess on what your parents +line of work was right but there's some + + align:start position:0% +line of work was right but there's some + + + align:start position:0% +line of work was right but there's some +number that's the largest number and + + align:start position:0% +number that's the largest number and + + + align:start position:0% +number that's the largest number and +it's probably different from Bulgarian + + align:start position:0% +it's probably different from Bulgarian + + + align:start position:0% +it's probably different from Bulgarian +to Bulgarian + + align:start position:0% +to Bulgarian + + + align:start position:0% +to Bulgarian +so what we might expect so bulgarians + + align:start position:0% +so what we might expect so bulgarians + + + align:start position:0% +so what we might expect so bulgarians +are sort of in the position you guys + + align:start position:0% +are sort of in the position you guys + + + align:start position:0% +are sort of in the position you guys +were in + + align:start position:0% +were in + + + align:start position:0% +were in +um with that function if you just hear + + align:start position:0% +um with that function if you just hear + + + align:start position:0% +um with that function if you just hear +this let's say what to whom did he give + + align:start position:0% +this let's say what to whom did he give + + + align:start position:0% +this let's say what to whom did he give +uh you got to ask yourself is the rule + + align:start position:0% +uh you got to ask yourself is the rule + + + align:start position:0% +uh you got to ask yourself is the rule +move all the wh phrases is it move two + + align:start position:0% +move all the wh phrases is it move two + + + align:start position:0% +move all the wh phrases is it move two +of the wh pH phrases does it move + + align:start position:0% +of the wh pH phrases does it move + + + align:start position:0% +of the wh pH phrases does it move +maximally three maximally four you know + + align:start position:0% +maximally three maximally four you know + + + align:start position:0% +maximally three maximally four you know +whatever there are literally infinitely + + align:start position:0% +whatever there are literally infinitely + + + align:start position:0% +whatever there are literally infinitely +many rules that are compatible with this + + align:start position:0% +many rules that are compatible with this + + + align:start position:0% +many rules that are compatible with this +data point right + + align:start position:0% +data point right + + + align:start position:0% +data point right +and so you might have expected that + + align:start position:0% +and so you might have expected that + + + align:start position:0% +and so you might have expected that +bulgarians depending on how weird their + + align:start position:0% +bulgarians depending on how weird their + + + align:start position:0% +bulgarians depending on how weird their +parents were would grow up with slightly + + align:start position:0% +parents were would grow up with slightly + + + align:start position:0% +parents were would grow up with slightly +different grammars that you know when + + align:start position:0% +different grammars that you know when + + + align:start position:0% +different grammars that you know when +you took bulgarians and you put them + + align:start position:0% +you took bulgarians and you put them + + + align:start position:0% +you took bulgarians and you put them +into a hyperbaric chamber and you + + align:start position:0% +into a hyperbaric chamber and you + + + align:start position:0% +into a hyperbaric chamber and you +gradually add a wh question wh words to + + align:start position:0% +gradually add a wh question wh words to + + + align:start position:0% +gradually add a wh question wh words to +the questions that they would diverge + + align:start position:0% +the questions that they would diverge + + + align:start position:0% +the questions that they would diverge +you know as the questions got more and + + align:start position:0% +you know as the questions got more and + + + align:start position:0% +you know as the questions got more and +more complicated that there would be the + + align:start position:0% +more complicated that there would be the + + + align:start position:0% +more complicated that there would be the +the two wh bulgarians and the three wh + + align:start position:0% +the two wh bulgarians and the three wh + + + align:start position:0% +the two wh bulgarians and the three wh +bulgarians and the Florida and the five + + align:start position:0% +bulgarians and the Florida and the five + + + align:start position:0% +bulgarians and the Florida and the five +yeah that you would find that out that's + + align:start position:0% +yeah that you would find that out that's + + + align:start position:0% +yeah that you would find that out that's +not what we find out the experiment has + + align:start position:0% +not what we find out the experiment has + + + align:start position:0% +not what we find out the experiment has +been done + + align:start position:0% +been done + + + align:start position:0% +been done +um what you find out is the bulgarians + + align:start position:0% +um what you find out is the bulgarians + + + align:start position:0% +um what you find out is the bulgarians +are all the same they all move all their + + align:start position:0% +are all the same they all move all their + + + align:start position:0% +are all the same they all move all their +wh freezes + + align:start position:0% +wh freezes + + + align:start position:0% +wh freezes +what we think is going on really is that + + align:start position:0% +what we think is going on really is that + + + align:start position:0% +what we think is going on really is that +you know being a human being means + + align:start position:0% +you know being a human being means + + + align:start position:0% +you know being a human being means +having the kind of mind that can put + + align:start position:0% +having the kind of mind that can put + + + align:start position:0% +having the kind of mind that can put +language together in some ways but not + + align:start position:0% +language together in some ways but not + + + align:start position:0% +language together in some ways but not +others + + align:start position:0% +others + + + align:start position:0% +others +um there was never any danger of the + + align:start position:0% +um there was never any danger of the + + + align:start position:0% +um there was never any danger of the +Bulgarian children one entertaining the + + align:start position:0% +Bulgarian children one entertaining the + + + align:start position:0% +Bulgarian children one entertaining the +possibility that the grammar was moved + + align:start position:0% +possibility that the grammar was moved + + + align:start position:0% +possibility that the grammar was moved +to wh phrases they knew that there + + align:start position:0% +to wh phrases they knew that there + + + align:start position:0% +to wh phrases they knew that there +aren't languages like that human + + align:start position:0% +aren't languages like that human + + + align:start position:0% +aren't languages like that human +languages don't work that way this is + + align:start position:0% +languages don't work that way this is + + + align:start position:0% +languages don't work that way this is +what we mean when we talk about + + align:start position:0% +what we mean when we talk about + + + align:start position:0% +what we mean when we talk about +Universal grammar we'll review this next + + align:start position:0% +Universal grammar we'll review this next + + + align:start position:0% +Universal grammar we'll review this next +time because we're out of time but we'll + + align:start position:0% +time because we're out of time but we'll + + + align:start position:0% +time because we're out of time but we'll +talk more about this next time + + align:start position:0% +talk more about this next time + + + align:start position:0% +talk more about this next time +okay \ No newline at end of file diff --git a/TuCYGjp7WKU.txt b/TuCYGjp7WKU.txt new file mode 100644 index 0000000000000000000000000000000000000000..09fb88896bc8e5f553b7a67f6b6727bc0356880f --- /dev/null +++ b/TuCYGjp7WKU.txt @@ -0,0 +1,5307 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% +of MIT courses visit mitop courseware at + + + align:start position:0% +of MIT courses visit mitop courseware at +ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +well last time we had discussed in a + + align:start position:0% +well last time we had discussed in a + + + align:start position:0% +well last time we had discussed in a +very general way the field of digital + + align:start position:0% +very general way the field of digital + + + align:start position:0% +very general way the field of digital +signal processing and hopefully one of + + align:start position:0% +signal processing and hopefully one of + + + align:start position:0% +signal processing and hopefully one of +the things that you were convinced of + + align:start position:0% +the things that you were convinced of + + + align:start position:0% +the things that you were convinced of +was the importance of this set of + + align:start position:0% +was the importance of this set of + + + align:start position:0% +was the importance of this set of +techniques in a general sense what we'd + + align:start position:0% +techniques in a general sense what we'd + + + align:start position:0% +techniques in a general sense what we'd +like to begin on now is a discussion of + + align:start position:0% +like to begin on now is a discussion of + + + align:start position:0% +like to begin on now is a discussion of +some of the details of digital signal + + align:start position:0% +some of the details of digital signal + + + align:start position:0% +some of the details of digital signal +processing and in particular in this + + align:start position:0% +processing and in particular in this + + + align:start position:0% +processing and in particular in this +lecture I would like to introduce the + + align:start position:0% +lecture I would like to introduce the + + + align:start position:0% +lecture I would like to introduce the +class of Des discret time signals and + + align:start position:0% +class of Des discret time signals and + + + align:start position:0% +class of Des discret time signals and +also the class of discreete time + + align:start position:0% +also the class of discreete time + + + align:start position:0% +also the class of discreete time +systems well last time I reminded you + + align:start position:0% +systems well last time I reminded you + + + align:start position:0% +systems well last time I reminded you +that I will be assuming a u familiarity + + align:start position:0% +that I will be assuming a u familiarity + + + align:start position:0% +that I will be assuming a u familiarity +with continuous time signals and systems + + align:start position:0% +with continuous time signals and systems + + + align:start position:0% +with continuous time signals and systems +and what you'll see as we go through + + align:start position:0% +and what you'll see as we go through + + + align:start position:0% +and what you'll see as we go through +this lecture and in fact as we go + + align:start position:0% +this lecture and in fact as we go + + + align:start position:0% +this lecture and in fact as we go +through all of these lectures is a very + + align:start position:0% +through all of these lectures is a very + + + align:start position:0% +through all of these lectures is a very +strong similarity between the + + align:start position:0% +strong similarity between the + + + align:start position:0% +strong similarity between the +results that you're familiar with in the + + align:start position:0% +results that you're familiar with in the + + + align:start position:0% +results that you're familiar with in the +continuous time case and results that + + align:start position:0% +continuous time case and results that + + + align:start position:0% +continuous time case and results that +will develop for the discreet time case + + align:start position:0% +will develop for the discreet time case + + + align:start position:0% +will develop for the discreet time case +obviously of course there will also be + + align:start position:0% +obviously of course there will also be + + + align:start position:0% +obviously of course there will also be +some differences and these differences + + align:start position:0% +some differences and these differences + + + align:start position:0% +some differences and these differences +are important and they'll be important + + align:start position:0% +are important and they'll be important + + + align:start position:0% +are important and they'll be important +to focus on so there will be a great + + align:start position:0% +to focus on so there will be a great + + + align:start position:0% +to focus on so there will be a great +deal of similarity also a few + + align:start position:0% +deal of similarity also a few + + + align:start position:0% +deal of similarity also a few +differences and these few differences + + align:start position:0% +differences and these few differences + + + align:start position:0% +differences and these few differences +are very + + align:start position:0% +are very + + + align:start position:0% +are very +important in the discreet time domain + + align:start position:0% +important in the discreet time domain + + + align:start position:0% +important in the discreet time domain +we're concerned with processing signals + + align:start position:0% +we're concerned with processing signals + + + align:start position:0% +we're concerned with processing signals +that are sequences that is these signals + + align:start position:0% +that are sequences that is these signals + + + align:start position:0% +that are sequences that is these signals +are functions of an integer variable + + align:start position:0% +are functions of an integer variable + + + align:start position:0% +are functions of an integer variable +which we'll call + + align:start position:0% +which we'll call + + + align:start position:0% +which we'll call +n typically we'll depict sequences + + align:start position:0% +n typically we'll depict sequences + + + align:start position:0% +n typically we'll depict sequences +graphically as I've Illustrated here on + + align:start position:0% +graphically as I've Illustrated here on + + + align:start position:0% +graphically as I've Illustrated here on +this first view + + align:start position:0% +this first view + + + align:start position:0% +this first view +graph where I've denoted a general + + align:start position:0% +graph where I've denoted a general + + + align:start position:0% +graph where I've denoted a general +sequence which I call X of + + align:start position:0% +sequence which I call X of + + + align:start position:0% +sequence which I call X of +n a function of the integer variable n + + align:start position:0% +n a function of the integer variable n + + + align:start position:0% +n a function of the integer variable n +and the sequence values I've represented + + align:start position:0% +and the sequence values I've represented + + + align:start position:0% +and the sequence values I've represented +by a bar graph with the height of each + + align:start position:0% +by a bar graph with the height of each + + + align:start position:0% +by a bar graph with the height of each +bar corresponding to the sequence + + align:start position:0% +bar corresponding to the sequence + + + align:start position:0% +bar corresponding to the sequence +value so we have then for example at Nal + + align:start position:0% +value so we have then for example at Nal + + + align:start position:0% +value so we have then for example at Nal +0 a line of height X of 0 at Nal 1 a + + align:start position:0% +0 a line of height X of 0 at Nal 1 a + + + align:start position:0% +0 a line of height X of 0 at Nal 1 a +line of height X of one + + align:start position:0% +line of height X of one + + + align:start position:0% +line of height X of one +Etc of course as I drawn this horizontal + + align:start position:0% +Etc of course as I drawn this horizontal + + + align:start position:0% +Etc of course as I drawn this horizontal +axis I've drawn it as a continuous line + + align:start position:0% +axis I've drawn it as a continuous line + + + align:start position:0% +axis I've drawn it as a continuous line +but it's important to keep in mind that + + align:start position:0% +but it's important to keep in mind that + + + align:start position:0% +but it's important to keep in mind that +the sequences only are defined or only + + align:start position:0% +the sequences only are defined or only + + + align:start position:0% +the sequences only are defined or only +make sense for integer values of the + + align:start position:0% +make sense for integer values of the + + + align:start position:0% +make sense for integer values of the +argument if n is an integer then X of n + + align:start position:0% +argument if n is an integer then X of n + + + align:start position:0% +argument if n is an integer then X of n +makes sense if n is not an integer it's + + align:start position:0% +makes sense if n is not an integer it's + + + align:start position:0% +makes sense if n is not an integer it's +not just that X of n is zero or + + align:start position:0% +not just that X of n is zero or + + + align:start position:0% +not just that X of n is zero or +something like that it simply that X of + + align:start position:0% +something like that it simply that X of + + + align:start position:0% +something like that it simply that X of +n is not defined in other words x of n + + align:start position:0% +n is not defined in other words x of n + + + align:start position:0% +n is not defined in other words x of n +makes sense or is defined for n an + + align:start position:0% +makes sense or is defined for n an + + + align:start position:0% +makes sense or is defined for n an +integer and does not make sense or is + + align:start position:0% +integer and does not make sense or is + + + align:start position:0% +integer and does not make sense or is +not defined if n is not an + + align:start position:0% +not defined if n is not an + + + align:start position:0% +not defined if n is not an +integer so this then is a graphical + + align:start position:0% +integer so this then is a graphical + + + align:start position:0% +integer so this then is a graphical +representation of a general + + align:start position:0% +representation of a general + + + align:start position:0% +representation of a general +sequence and just as in the continuous + + align:start position:0% +sequence and just as in the continuous + + + align:start position:0% +sequence and just as in the continuous +time case we have a number of important + + align:start position:0% +time case we have a number of important + + + align:start position:0% +time case we have a number of important +basic sequences that that we would like + + align:start position:0% +basic sequences that that we would like + + + align:start position:0% +basic sequences that that we would like +to focus + + align:start position:0% +to focus + + + align:start position:0% +to focus +on the first of these that I'd like to + + align:start position:0% +on the first of these that I'd like to + + + align:start position:0% +on the first of these that I'd like to +introduce is the unit sample or impulse + + align:start position:0% +introduce is the unit sample or impulse + + + align:start position:0% +introduce is the unit sample or impulse +sequence will which will denote by Delta + + align:start position:0% +sequence will which will denote by Delta + + + align:start position:0% +sequence will which will denote by Delta +of + + align:start position:0% +of + + + align:start position:0% +of +n the unit sample sequence is a sequence + + align:start position:0% +n the unit sample sequence is a sequence + + + align:start position:0% +n the unit sample sequence is a sequence +whose value is Unity at n equals 0 and + + align:start position:0% +whose value is Unity at n equals 0 and + + + align:start position:0% +whose value is Unity at n equals 0 and +it's equal to zero otherwise that is + + align:start position:0% +it's equal to zero otherwise that is + + + align:start position:0% +it's equal to zero otherwise that is +Delta of nals 1 at n equals 0 and Delta + + align:start position:0% +Delta of nals 1 at n equals 0 and Delta + + + align:start position:0% +Delta of nals 1 at n equals 0 and Delta +of n is equal to zero for n not equal to + + align:start position:0% +of n is equal to zero for n not equal to + + + align:start position:0% +of n is equal to zero for n not equal to +zero the unit sample sequence plays the + + align:start position:0% +zero the unit sample sequence plays the + + + align:start position:0% +zero the unit sample sequence plays the +same role in the discrete time case that + + align:start position:0% +same role in the discrete time case that + + + align:start position:0% +same role in the discrete time case that +the unit impulse time function plays in + + align:start position:0% +the unit impulse time function plays in + + + align:start position:0% +the unit impulse time function plays in +The Continuous time case let me just + + align:start position:0% +The Continuous time case let me just + + + align:start position:0% +The Continuous time case let me just +mention however that the unit sample + + align:start position:0% +mention however that the unit sample + + + align:start position:0% +mention however that the unit sample +sequence is very easily defined there's + + align:start position:0% +sequence is very easily defined there's + + + align:start position:0% +sequence is very easily defined there's +no issue here about the definition in + + align:start position:0% +no issue here about the definition in + + + align:start position:0% +no issue here about the definition in +contrast with the usual mathematical + + align:start position:0% +contrast with the usual mathematical + + + align:start position:0% +contrast with the usual mathematical +problem + + align:start position:0% +problem + + + align:start position:0% +problem +with A continuous time impulse which is + + align:start position:0% +with A continuous time impulse which is + + + align:start position:0% +with A continuous time impulse which is +infinitely big at the origin and zero + + align:start position:0% +infinitely big at the origin and zero + + + align:start position:0% +infinitely big at the origin and zero +every place else but has some area Etc + + align:start position:0% +every place else but has some area Etc + + + align:start position:0% +every place else but has some area Etc +so there's a very precise definition + + align:start position:0% +so there's a very precise definition + + + align:start position:0% +so there's a very precise definition +here of the unit sample or unit impulse + + align:start position:0% +here of the unit sample or unit impulse + + + align:start position:0% +here of the unit sample or unit impulse +sequence and it will play a role similar + + align:start position:0% +sequence and it will play a role similar + + + align:start position:0% +sequence and it will play a role similar +to the unit impulse time function in the + + align:start position:0% +to the unit impulse time function in the + + + align:start position:0% +to the unit impulse time function in the +continuous time + + align:start position:0% +continuous time + + + align:start position:0% +continuous time +case another important basic + + align:start position:0% +case another important basic + + + align:start position:0% +case another important basic +sequence is the unit step sequence which + + align:start position:0% +sequence is the unit step sequence which + + + align:start position:0% +sequence is the unit step sequence which +I'm denoting by U of N and the unit step + + align:start position:0% +I'm denoting by U of N and the unit step + + + align:start position:0% +I'm denoting by U of N and the unit step +sequence is equal to + + align:start position:0% +sequence is equal to + + + align:start position:0% +sequence is equal to +Unity for n greater than or equal to + + align:start position:0% +Unity for n greater than or equal to + + + align:start position:0% +Unity for n greater than or equal to +zero and it's equal to zero for n less + + align:start position:0% +zero and it's equal to zero for n less + + + align:start position:0% +zero and it's equal to zero for n less +than + + align:start position:0% +than + + + align:start position:0% +than +zero so the unit step sequence then is 0 + + align:start position:0% +zero so the unit step sequence then is 0 + + + align:start position:0% +zero so the unit step sequence then is 0 +for n less than zero its Unity its Unity + + align:start position:0% +for n less than zero its Unity its Unity + + + align:start position:0% +for n less than zero its Unity its Unity +for n greater than or equal to zero + + align:start position:0% +for n greater than or equal to zero + + + align:start position:0% +for n greater than or equal to zero +uh this should shouldn't be incidentally + + align:start position:0% +uh this should shouldn't be incidentally + + + align:start position:0% +uh this should shouldn't be incidentally +less than or equal to zero this should + + align:start position:0% +less than or equal to zero this should + + + align:start position:0% +less than or equal to zero this should +be n less than + + align:start position:0% +be n less than + + + align:start position:0% +be n less than +zero and it is again does not have + + align:start position:0% +zero and it is again does not have + + + align:start position:0% +zero and it is again does not have +the difficulties in definition that a + + align:start position:0% +the difficulties in definition that a + + + align:start position:0% +the difficulties in definition that a +continuous time unit step normally + + align:start position:0% +continuous time unit step normally + + + align:start position:0% +continuous time unit step normally +has it's the change in value from Nal + + align:start position:0% +has it's the change in value from Nal + + + align:start position:0% +has it's the change in value from Nal +minus1 to Nal Zer is precisely and + + align:start position:0% +minus1 to Nal Zer is precisely and + + + align:start position:0% +minus1 to Nal Zer is precisely and +easily defined here the unit step is + + align:start position:0% +easily defined here the unit step is + + + align:start position:0% +easily defined here the unit step is +zero here the unit step is one there's + + align:start position:0% +zero here the unit step is one there's + + + align:start position:0% +zero here the unit step is one there's +no issue as there is in the continuous + + align:start position:0% +no issue as there is in the continuous + + + align:start position:0% +no issue as there is in the continuous +time case about + + align:start position:0% + + + + align:start position:0% + +discontinuity just as in the continuous + + align:start position:0% +discontinuity just as in the continuous + + + align:start position:0% +discontinuity just as in the continuous +time case there's a simple relationship + + align:start position:0% +time case there's a simple relationship + + + align:start position:0% +time case there's a simple relationship +between the unit + + align:start position:0% +between the unit + + + align:start position:0% +between the unit +sample or sorry unit impulse and the + + align:start position:0% +sample or sorry unit impulse and the + + + align:start position:0% +sample or sorry unit impulse and the +unit step in the discrete time case + + align:start position:0% +unit step in the discrete time case + + + align:start position:0% +unit step in the discrete time case +there's likewise a simple relationship + + align:start position:0% +there's likewise a simple relationship + + + align:start position:0% +there's likewise a simple relationship +between the unit sample sequence and the + + align:start position:0% +between the unit sample sequence and the + + + align:start position:0% +between the unit sample sequence and the +unit step sequence and in particular the + + align:start position:0% +unit step sequence and in particular the + + + align:start position:0% +unit step sequence and in particular the +unit sample sequence can be obtained + + align:start position:0% +unit sample sequence can be obtained + + + align:start position:0% +unit sample sequence can be obtained +from the unit step sequence by + + align:start position:0% +from the unit step sequence by + + + align:start position:0% +from the unit step sequence by +constructing the first + + align:start position:0% +constructing the first + + + align:start position:0% +constructing the first +difference the unit sample sequence + + align:start position:0% +difference the unit sample sequence + + + align:start position:0% +difference the unit sample sequence +Delta of n is equal to U of n the unit + + align:start position:0% +Delta of n is equal to U of n the unit + + + align:start position:0% +Delta of n is equal to U of n the unit +step minus the unit step delayed by one + + align:start position:0% +step minus the unit step delayed by one + + + align:start position:0% +step minus the unit step delayed by one +sample and we can see that that + + align:start position:0% +sample and we can see that that + + + align:start position:0% +sample and we can see that that +obviously is the case if we look at the + + align:start position:0% +obviously is the case if we look at the + + + align:start position:0% +obviously is the case if we look at the +unit step sequence U of n here we have + + align:start position:0% +unit step sequence U of n here we have + + + align:start position:0% +unit step sequence U of n here we have +the unit step sequence delayed by one so + + align:start position:0% +the unit step sequence delayed by one so + + + align:start position:0% +the unit step sequence delayed by one so +this occurs at n equal 0 this is Nal 1 + + align:start position:0% +this occurs at n equal 0 this is Nal 1 + + + align:start position:0% +this occurs at n equal 0 this is Nal 1 +and clearly the difference between those + + align:start position:0% +and clearly the difference between those + + + align:start position:0% +and clearly the difference between those +two will generate a sample at n equals 0 + + align:start position:0% +two will generate a sample at n equals 0 + + + align:start position:0% +two will generate a sample at n equals 0 +zero of course for n less than zero and + + align:start position:0% +zero of course for n less than zero and + + + align:start position:0% +zero of course for n less than zero and +zero likewise for n greater than zero + + align:start position:0% +zero likewise for n greater than zero + + + align:start position:0% +zero likewise for n greater than zero +because these sequence values will be + + align:start position:0% +because these sequence values will be + + + align:start position:0% +because these sequence values will be +canceled out by those sequence values so + + align:start position:0% +canceled out by those sequence values so + + + align:start position:0% +canceled out by those sequence values so +the unit sample sequence is is the unit + + align:start position:0% +the unit sample sequence is is the unit + + + align:start position:0% +the unit sample sequence is is the unit +step minus a delayed unit step or the + + align:start position:0% +step minus a delayed unit step or the + + + align:start position:0% +step minus a delayed unit step or the +unit sample sequence is equal to the + + align:start position:0% +unit sample sequence is equal to the + + + align:start position:0% +unit sample sequence is equal to the +first difference of the unit step + + align:start position:0% +first difference of the unit step + + + align:start position:0% +first difference of the unit step +sequence similarly we can obtain the + + align:start position:0% +sequence similarly we can obtain the + + + align:start position:0% +sequence similarly we can obtain the +unit step sequence from the unit sample + + align:start position:0% +unit step sequence from the unit sample + + + align:start position:0% +unit step sequence from the unit sample +sequence by constructing a running + + align:start position:0% +sequence by constructing a running + + + align:start position:0% +sequence by constructing a running +sum in particular the unit step sequence + + align:start position:0% +sum in particular the unit step sequence + + + align:start position:0% +sum in particular the unit step sequence +is equal to a running sum of the unit + + align:start position:0% +is equal to a running sum of the unit + + + align:start position:0% +is equal to a running sum of the unit +sample sequence in other words we're + + align:start position:0% +sample sequence in other words we're + + + align:start position:0% +sample sequence in other words we're +constructing here a sum from k equal + + align:start position:0% +constructing here a sum from k equal + + + align:start position:0% +constructing here a sum from k equal +minus infinity to the integer uh to the + + align:start position:0% +minus infinity to the integer uh to the + + + align:start position:0% +minus infinity to the integer uh to the +independent variable n of the sequence + + align:start position:0% +independent variable n of the sequence + + + align:start position:0% +independent variable n of the sequence +Delta of + + align:start position:0% +Delta of + + + align:start position:0% +Delta of +K here we have the sequence Delta of + + align:start position:0% +K here we have the sequence Delta of + + + align:start position:0% +K here we have the sequence Delta of +K if n is less than zero then we're + + align:start position:0% +K if n is less than zero then we're + + + align:start position:0% +K if n is less than zero then we're +adding up sequence values from minus + + align:start position:0% +adding up sequence values from minus + + + align:start position:0% +adding up sequence values from minus +infinity to some negative value of + + align:start position:0% +infinity to some negative value of + + + align:start position:0% +infinity to some negative value of +K and the only values that we collect + + align:start position:0% +K and the only values that we collect + + + align:start position:0% +K and the only values that we collect +when do that or values equal to zero so + + align:start position:0% +when do that or values equal to zero so + + + align:start position:0% +when do that or values equal to zero so +for n less than Z we see that we obtain + + align:start position:0% +for n less than Z we see that we obtain + + + align:start position:0% +for n less than Z we see that we obtain +zero for this sum if n is greater than + + align:start position:0% +zero for this sum if n is greater than + + + align:start position:0% +zero for this sum if n is greater than +zero as I've indicated here then the sum + + align:start position:0% +zero as I've indicated here then the sum + + + align:start position:0% +zero as I've indicated here then the sum +as we collect sequence values from minus + + align:start position:0% +as we collect sequence values from minus + + + align:start position:0% +as we collect sequence values from minus +infinity up to n we collect one nonzero + + align:start position:0% +infinity up to n we collect one nonzero + + + align:start position:0% +infinity up to n we collect one nonzero +sequence value which is equal to one + + align:start position:0% +sequence value which is equal to one + + + align:start position:0% +sequence value which is equal to one +consequently for n greater than zero we + + align:start position:0% +consequently for n greater than zero we + + + align:start position:0% +consequently for n greater than zero we +obtain in this running sum U of n equal + + align:start position:0% +obtain in this running sum U of n equal + + + align:start position:0% +obtain in this running sum U of n equal +to 1 + + align:start position:0% +to 1 + + + align:start position:0% +to 1 +one this plays a role this running sum + + align:start position:0% +one this plays a role this running sum + + + align:start position:0% +one this plays a role this running sum +plays a role similar to the integral in + + align:start position:0% +plays a role similar to the integral in + + + align:start position:0% +plays a role similar to the integral in +the continuous time case and so now we + + align:start position:0% +the continuous time case and so now we + + + align:start position:0% +the continuous time case and so now we +have a relationship between the unit + + align:start position:0% +have a relationship between the unit + + + align:start position:0% +have a relationship between the unit +sample sequence and the unit step + + align:start position:0% +sample sequence and the unit step + + + align:start position:0% +sample sequence and the unit step +sequence there are other basic sequences + + align:start position:0% +sequence there are other basic sequences + + + align:start position:0% +sequence there are other basic sequences +that will play an important role just as + + align:start position:0% +that will play an important role just as + + + align:start position:0% +that will play an important role just as +they do in the continuous time + + align:start position:0% +they do in the continuous time + + + align:start position:0% +they do in the continuous time +case in particular we have the real + + align:start position:0% +case in particular we have the real + + + align:start position:0% +case in particular we have the real +exponential + + align:start position:0% +exponential + + + align:start position:0% +exponential +sequence the sequence X of n is equal to + + align:start position:0% +sequence the sequence X of n is equal to + + + align:start position:0% +sequence the sequence X of n is equal to +Alpha to the + + align:start position:0% +Alpha to the + + + align:start position:0% +Alpha to the +N I've depicted the exponential sequence + + align:start position:0% +N I've depicted the exponential sequence + + + align:start position:0% +N I've depicted the exponential sequence +here for the case in which Alpha is + + align:start position:0% +here for the case in which Alpha is + + + align:start position:0% +here for the case in which Alpha is +positive but less than Unity so that as + + align:start position:0% +positive but less than Unity so that as + + + align:start position:0% +positive but less than Unity so that as +n increases the exponential decreases so + + align:start position:0% +n increases the exponential decreases so + + + align:start position:0% +n increases the exponential decreases so +Alpha to the N if Alpha is between 0o + + align:start position:0% +Alpha to the N if Alpha is between 0o + + + align:start position:0% +Alpha to the N if Alpha is between 0o +and 1 decreases with increasing n if + + align:start position:0% +and 1 decreases with increasing n if + + + align:start position:0% +and 1 decreases with increasing n if +Alpha is greater than one then the + + align:start position:0% +Alpha is greater than one then the + + + align:start position:0% +Alpha is greater than one then the +exponential sequence grows of course + + align:start position:0% +exponential sequence grows of course + + + align:start position:0% +exponential sequence grows of course +exponentially we have also the + + align:start position:0% +exponentially we have also the + + + align:start position:0% +exponentially we have also the +sinusoidal + + align:start position:0% +sinusoidal + + + align:start position:0% +sinusoidal +sequence the general form of the + + align:start position:0% +sequence the general form of the + + + align:start position:0% +sequence the general form of the +sinusoidal sequence is X of n is equal + + align:start position:0% +sinusoidal sequence is X of n is equal + + + align:start position:0% +sinusoidal sequence is X of n is equal +to a cine Omega 0 n plus v f is a phase + + align:start position:0% +to a cine Omega 0 n plus v f is a phase + + + align:start position:0% +to a cine Omega 0 n plus v f is a phase +angle Omega 0 will refer to as the + + align:start position:0% +angle Omega 0 will refer to as the + + + align:start position:0% +angle Omega 0 will refer to as the +frequency a of course is the amplitude + + align:start position:0% +frequency a of course is the amplitude + + + align:start position:0% +frequency a of course is the amplitude +I've Illustrated a sinusoidal sequence + + align:start position:0% +I've Illustrated a sinusoidal sequence + + + align:start position:0% +I've Illustrated a sinusoidal sequence +here for a particular choice of omega0 + + align:start position:0% +here for a particular choice of omega0 + + + align:start position:0% +here for a particular choice of omega0 +and Fe namely Omega 0 = to piun over 4 + + align:start position:0% +and Fe namely Omega 0 = to piun over 4 + + + align:start position:0% +and Fe namely Omega 0 = to piun over 4 +and FAL to minus piun over + + align:start position:0% +and FAL to minus piun over + + + align:start position:0% +and FAL to minus piun over +8 and in looking at this we see that we + + align:start position:0% +8 and in looking at this we see that we + + + align:start position:0% +8 and in looking at this we see that we +get a periodic sequence that is for this + + align:start position:0% +get a periodic sequence that is for this + + + align:start position:0% +get a periodic sequence that is for this +choice of parameters this sequence is + + align:start position:0% +choice of parameters this sequence is + + + align:start position:0% +choice of parameters this sequence is +periodic however an important + + align:start position:0% +periodic however an important + + + align:start position:0% +periodic however an important +distinction between the continuous time + + align:start position:0% +distinction between the continuous time + + + align:start position:0% +distinction between the continuous time +case in the discret time case is that a + + align:start position:0% +case in the discret time case is that a + + + align:start position:0% +case in the discret time case is that a +discrete time sinusoidal signal is not + + align:start position:0% +discrete time sinusoidal signal is not + + + align:start position:0% +discrete time sinusoidal signal is not +necessarily + + align:start position:0% +necessarily + + + align:start position:0% +necessarily +periodic in particular I've Illustrated + + align:start position:0% +periodic in particular I've Illustrated + + + align:start position:0% +periodic in particular I've Illustrated +here another sinusoidal sequence with a + + align:start position:0% +here another sinusoidal sequence with a + + + align:start position:0% +here another sinusoidal sequence with a +different choice for Omega 0 and F in + + align:start position:0% +different choice for Omega 0 and F in + + + align:start position:0% +different choice for Omega 0 and F in +this case Omega 0 equal to 3 pi over + + align:start position:0% +this case Omega 0 equal to 3 pi over + + + align:start position:0% +this case Omega 0 equal to 3 pi over +7 with that choice of Omega 0 these are + + align:start position:0% +7 with that choice of Omega 0 these are + + + align:start position:0% +7 with that choice of Omega 0 these are +the sequence values we obtain and it + + align:start position:0% +the sequence values we obtain and it + + + align:start position:0% +the sequence values we obtain and it +should be obvious + + align:start position:0% +should be obvious + + + align:start position:0% +should be obvious +by examining this sequence that this + + align:start position:0% +by examining this sequence that this + + + align:start position:0% +by examining this sequence that this +sequence is no longer periodic whereas + + align:start position:0% +sequence is no longer periodic whereas + + + align:start position:0% +sequence is no longer periodic whereas +this sequence was so the sinusoidal + + align:start position:0% +this sequence was so the sinusoidal + + + align:start position:0% +this sequence was so the sinusoidal +sequence may or may not be periodic of + + align:start position:0% +sequence may or may not be periodic of + + + align:start position:0% +sequence may or may not be periodic of +course let me remind you that if n was + + align:start position:0% +course let me remind you that if n was + + + align:start position:0% +course let me remind you that if n was +allowed to vary continuously if it was + + align:start position:0% +allowed to vary continuously if it was + + + align:start position:0% +allowed to vary continuously if it was +not an integer variable X of n would be + + align:start position:0% +not an integer variable X of n would be + + + align:start position:0% +not an integer variable X of n would be +periodic the periodicity is lost because + + align:start position:0% +periodic the periodicity is lost because + + + align:start position:0% +periodic the periodicity is lost because +n is now constrained to be an integer + + align:start position:0% +n is now constrained to be an integer + + + align:start position:0% +n is now constrained to be an integer +variable + + align:start position:0% +variable + + + align:start position:0% +variable +and that is one of the important + + align:start position:0% +and that is one of the important + + + align:start position:0% +and that is one of the important +distinctions between continuous time + + align:start position:0% +distinctions between continuous time + + + align:start position:0% +distinctions between continuous time +signals and systems and discrete time + + align:start position:0% +signals and systems and discrete time + + + align:start position:0% +signals and systems and discrete time +signals and + + align:start position:0% +signals and + + + align:start position:0% +signals and +systems another point which I'll suggest + + align:start position:0% +systems another point which I'll suggest + + + align:start position:0% +systems another point which I'll suggest +now uh although it's a point that I'll + + align:start position:0% +now uh although it's a point that I'll + + + align:start position:0% +now uh although it's a point that I'll +want to refer to uh in more detail in + + align:start position:0% +want to refer to uh in more detail in + + + align:start position:0% +want to refer to uh in more detail in +some of the future + + align:start position:0% +some of the future + + + align:start position:0% +some of the future +lectures is that the sinusoidal + + align:start position:0% +lectures is that the sinusoidal + + + align:start position:0% +lectures is that the sinusoidal +sequence + + align:start position:0% +sequence + + + align:start position:0% +sequence +only is is only only + + align:start position:0% +only is is only only + + + align:start position:0% +only is is only only +distinguishable as Omega 0 runs from + + align:start position:0% +distinguishable as Omega 0 runs from + + + align:start position:0% +distinguishable as Omega 0 runs from +over the range 0 to 2 pi or minus pi to + + align:start position:0% +over the range 0 to 2 pi or minus pi to + + + align:start position:0% +over the range 0 to 2 pi or minus pi to +Pi if Omega 0 if we were to replace + + align:start position:0% +Pi if Omega 0 if we were to replace + + + align:start position:0% +Pi if Omega 0 if we were to replace +Omega 0 by Omega 0 + 2 + + align:start position:0% +Omega 0 by Omega 0 + 2 + + + align:start position:0% +Omega 0 by Omega 0 + 2 +pi then we would have in this argument + + align:start position:0% +pi then we would have in this argument + + + align:start position:0% +pi then we would have in this argument +Omega 0 n + 2 pi n the 2 pi n of course + + align:start position:0% +Omega 0 n + 2 pi n the 2 pi n of course + + + align:start position:0% +Omega 0 n + 2 pi n the 2 pi n of course +would have no effect and we'd end up + + align:start position:0% +would have no effect and we'd end up + + + align:start position:0% +would have no effect and we'd end up +with the same sequence so in fact as we + + align:start position:0% +with the same sequence so in fact as we + + + align:start position:0% +with the same sequence so in fact as we +varied Omega 0 between minus pi and plus + + align:start position:0% +varied Omega 0 between minus pi and plus + + + align:start position:0% +varied Omega 0 between minus pi and plus +pi will have seen all of the sinusoidal + + align:start position:0% +pi will have seen all of the sinusoidal + + + align:start position:0% +pi will have seen all of the sinusoidal +sequences with this amplitude and this + + align:start position:0% +sequences with this amplitude and this + + + align:start position:0% +sequences with this amplitude and this +phase that we can possibly + + align:start position:0% + + + + align:start position:0% + +generate one of the + + align:start position:0% +generate one of the + + + align:start position:0% +generate one of the +important aspects of basic this set of + + align:start position:0% +important aspects of basic this set of + + + align:start position:0% +important aspects of basic this set of +basic signals is that they can be used + + align:start position:0% +basic signals is that they can be used + + + align:start position:0% +basic signals is that they can be used +to represent a more General class of + + align:start position:0% +to represent a more General class of + + + align:start position:0% +to represent a more General class of +signals just as in the continuous time + + align:start position:0% +signals just as in the continuous time + + + align:start position:0% +signals just as in the continuous time +case we use use impulses or we use + + align:start position:0% +case we use use impulses or we use + + + align:start position:0% +case we use use impulses or we use +complex exponentials or we use sinusoids + + align:start position:0% +complex exponentials or we use sinusoids + + + align:start position:0% +complex exponentials or we use sinusoids +to represent very general signals we can + + align:start position:0% +to represent very general signals we can + + + align:start position:0% +to represent very general signals we can +develop similar representations here let + + align:start position:0% +develop similar representations here let + + + align:start position:0% +develop similar representations here let +me illustrate this with an + + align:start position:0% +me illustrate this with an + + + align:start position:0% +me illustrate this with an +example where I + + align:start position:0% +example where I + + + align:start position:0% +example where I +consider a general + + align:start position:0% +consider a general + + + align:start position:0% +consider a general +sequence here x of + + align:start position:0% +sequence here x of + + + align:start position:0% +sequence here x of +n the sequence values are X of 0 x of + + align:start position:0% +n the sequence values are X of 0 x of + + + align:start position:0% +n the sequence values are X of 0 x of +One X X of 2 Etc and I mean to suggest + + align:start position:0% +One X X of 2 Etc and I mean to suggest + + + align:start position:0% +One X X of 2 Etc and I mean to suggest +here a very general + + align:start position:0% +here a very general + + + align:start position:0% +here a very general +sequence now I can decompose this + + align:start position:0% +sequence now I can decompose this + + + align:start position:0% +sequence now I can decompose this +sequence into a linear + + align:start position:0% +sequence into a linear + + + align:start position:0% +sequence into a linear +combination of weighted delayed unit + + align:start position:0% +combination of weighted delayed unit + + + align:start position:0% +combination of weighted delayed unit +samples unit sample + + align:start position:0% +samples unit sample + + + align:start position:0% +samples unit sample +sequences by simply extracting + + align:start position:0% +sequences by simply extracting + + + align:start position:0% +sequences by simply extracting +individual sequence values out of X of n + + align:start position:0% +individual sequence values out of X of n + + + align:start position:0% +individual sequence values out of X of n +for + + align:start position:0% +for + + + align:start position:0% +for +example let's consider the sequence x + + align:start position:0% +example let's consider the sequence x + + + align:start position:0% +example let's consider the sequence x +of0 * Delta of n as I've Illustrated + + align:start position:0% +of0 * Delta of n as I've Illustrated + + + align:start position:0% +of0 * Delta of n as I've Illustrated +here x of0 * Delta of n is equal to the + + align:start position:0% +here x of0 * Delta of n is equal to the + + + align:start position:0% +here x of0 * Delta of n is equal to the +original sequence X of n at n equals 0 + + align:start position:0% +original sequence X of n at n equals 0 + + + align:start position:0% +original sequence X of n at n equals 0 +and it's equal to zero + + align:start position:0% + + + + align:start position:0% + +otherwise a second sequence X of 1 * + + align:start position:0% +otherwise a second sequence X of 1 * + + + align:start position:0% +otherwise a second sequence X of 1 * +Delta of N minus1 is a unit sample + + align:start position:0% +Delta of N minus1 is a unit sample + + + align:start position:0% +Delta of N minus1 is a unit sample +sequence delayed by one and having an + + align:start position:0% +sequence delayed by one and having an + + + align:start position:0% +sequence delayed by one and having an +amplitude equal to X of one so this + + align:start position:0% +amplitude equal to X of one so this + + + align:start position:0% +amplitude equal to X of one so this +sequence is equal to this one at n + + align:start position:0% +sequence is equal to this one at n + + + align:start position:0% +sequence is equal to this one at n +equals 1 and it's equal to zero + + align:start position:0% +equals 1 and it's equal to zero + + + align:start position:0% +equals 1 and it's equal to zero +otherwise the sum of these two of course + + align:start position:0% +otherwise the sum of these two of course + + + align:start position:0% +otherwise the sum of these two of course +is equal to this x of n at these two + + align:start position:0% +is equal to this x of n at these two + + + align:start position:0% +is equal to this x of n at these two +values and equal to zero otherwise + + align:start position:0% +values and equal to zero otherwise + + + align:start position:0% +values and equal to zero otherwise +similarly we can consider X of minus1 * + + align:start position:0% +similarly we can consider X of minus1 * + + + align:start position:0% +similarly we can consider X of minus1 * +Delta of n + 1 that's a unit sample at n + + align:start position:0% +Delta of n + 1 that's a unit sample at n + + + align:start position:0% +Delta of n + 1 that's a unit sample at n += -1 with an amplitude of X of minus1 + + align:start position:0% += -1 with an amplitude of X of minus1 + + + align:start position:0% += -1 with an amplitude of X of minus1 +which picks up this this sequence value + + align:start position:0% +which picks up this this sequence value + + + align:start position:0% +which picks up this this sequence value +x ofus 2 * Delta of n + 2 is a unit + + align:start position:0% +x ofus 2 * Delta of n + 2 is a unit + + + align:start position:0% +x ofus 2 * Delta of n + 2 is a unit +sample at n = -2 multiplied by an + + align:start position:0% +sample at n = -2 multiplied by an + + + align:start position:0% +sample at n = -2 multiplied by an +amplitude X of minus 2 which picks up + + align:start position:0% +amplitude X of minus 2 which picks up + + + align:start position:0% +amplitude X of minus 2 which picks up +this sequence + + align:start position:0% +this sequence + + + align:start position:0% +this sequence +value + + align:start position:0% +value + + + align:start position:0% +value +Etc so I think you can see then that as + + align:start position:0% +Etc so I think you can see then that as + + + align:start position:0% +Etc so I think you can see then that as +we add these up what will generate is + + align:start position:0% +we add these up what will generate is + + + align:start position:0% +we add these up what will generate is +this arbitrary sequence X of n in other + + align:start position:0% +this arbitrary sequence X of n in other + + + align:start position:0% +this arbitrary sequence X of n in other +words we can construct X of n an + + align:start position:0% +words we can construct X of n an + + + align:start position:0% +words we can construct X of n an +arbitrary + + align:start position:0% +arbitrary + + + align:start position:0% +arbitrary +sequence as a linear combination of + + align:start position:0% +sequence as a linear combination of + + + align:start position:0% +sequence as a linear combination of +weighted delayed unit + + align:start position:0% +weighted delayed unit + + + align:start position:0% +weighted delayed unit +samples X of 0 * Delta of n plus X of 1 + + align:start position:0% +samples X of 0 * Delta of n plus X of 1 + + + align:start position:0% +samples X of 0 * Delta of n plus X of 1 +* Delta of nus1 plus X of minus1 Delta + + align:start position:0% +* Delta of nus1 plus X of minus1 Delta + + + align:start position:0% +* Delta of nus1 plus X of minus1 Delta +of n + 1 Etc or more generally the sum + + align:start position:0% +of n + 1 Etc or more generally the sum + + + align:start position:0% +of n + 1 Etc or more generally the sum +from Kus Infinity to plus infinity of X + + align:start position:0% +from Kus Infinity to plus infinity of X + + + align:start position:0% +from Kus Infinity to plus infinity of X +of K * Delta of nus K okay this then + + align:start position:0% +of K * Delta of nus K okay this then + + + align:start position:0% +of K * Delta of nus K okay this then +corresponds to a general representation + + align:start position:0% +corresponds to a general representation + + + align:start position:0% +corresponds to a general representation +of an arbitrary sequence in terms of + + align:start position:0% +of an arbitrary sequence in terms of + + + align:start position:0% +of an arbitrary sequence in terms of +weighted delayed unit samples and it's a + + align:start position:0% +weighted delayed unit samples and it's a + + + align:start position:0% +weighted delayed unit samples and it's a +representation that we'll want to refer + + align:start position:0% +representation that we'll want to refer + + + align:start position:0% +representation that we'll want to refer +back to in a few minutes it's not as + + align:start position:0% +back to in a few minutes it's not as + + + align:start position:0% +back to in a few minutes it's not as +I've indicated the only representation + + align:start position:0% +I've indicated the only representation + + + align:start position:0% +I've indicated the only representation +of arbitrary sequences will also be + + align:start position:0% +of arbitrary sequences will also be + + + align:start position:0% +of arbitrary sequences will also be +developing representations in terms of + + align:start position:0% +developing representations in terms of + + + align:start position:0% +developing representations in terms of +complex exponentials or real + + align:start position:0% +complex exponentials or real + + + align:start position:0% +complex exponentials or real +exponentials or in terms of signs and + + align:start position:0% +exponentials or in terms of signs and + + + align:start position:0% +exponentials or in terms of signs and +cosiness okay + + align:start position:0% +cosiness okay + + + align:start position:0% +cosiness okay +that is an introduction to the basic + + align:start position:0% +that is an introduction to the basic + + + align:start position:0% +that is an introduction to the basic +class of signals uh and the notion of + + align:start position:0% +class of signals uh and the notion of + + + align:start position:0% +class of signals uh and the notion of +sequences what I'd like to do now is + + align:start position:0% +sequences what I'd like to do now is + + + align:start position:0% +sequences what I'd like to do now is +focus on the class of discrete time + + align:start position:0% +focus on the class of discrete time + + + align:start position:0% +focus on the class of discrete time +systems and then refer back to some of + + align:start position:0% +systems and then refer back to some of + + + align:start position:0% +systems and then refer back to some of +these results to develop a general + + align:start position:0% +these results to develop a general + + + align:start position:0% +these results to develop a general +representation for a special class of + + align:start position:0% +representation for a special class of + + + align:start position:0% +representation for a special class of +discrete time systems + + align:start position:0% + + + + align:start position:0% + +first of all let me begin with a general + + align:start position:0% +first of all let me begin with a general + + + align:start position:0% +first of all let me begin with a general +system which + + align:start position:0% +system which + + + align:start position:0% +system which +is a discrete time system it has an + + align:start position:0% +is a discrete time system it has an + + + align:start position:0% +is a discrete time system it has an +input which is a sequence X event it has + + align:start position:0% +input which is a sequence X event it has + + + align:start position:0% +input which is a sequence X event it has +an output which is a sequence Y ofen and + + align:start position:0% +an output which is a sequence Y ofen and + + + align:start position:0% +an output which is a sequence Y ofen and +it has a system transformation which + + align:start position:0% +it has a system transformation which + + + align:start position:0% +it has a system transformation which +I've denoted by T + + align:start position:0% +I've denoted by T + + + align:start position:0% +I've denoted by T +of course there isn't much that you can + + align:start position:0% +of course there isn't much that you can + + + align:start position:0% +of course there isn't much that you can +do with the general system uh the + + align:start position:0% +do with the general system uh the + + + align:start position:0% +do with the general system uh the +difficulty with trying to describe a + + align:start position:0% +difficulty with trying to describe a + + + align:start position:0% +difficulty with trying to describe a +general system in general is that there + + align:start position:0% +general system in general is that there + + + align:start position:0% +general system in general is that there +are no properties that you can take + + align:start position:0% +are no properties that you can take + + + align:start position:0% +are no properties that you can take +advantage of so always in characterizing + + align:start position:0% +advantage of so always in characterizing + + + align:start position:0% +advantage of so always in characterizing +systems it's useful to specialize the + + align:start position:0% +systems it's useful to specialize the + + + align:start position:0% +systems it's useful to specialize the +class of systems that is impose + + align:start position:0% +class of systems that is impose + + + align:start position:0% +class of systems that is impose +properties on the system which you can + + align:start position:0% +properties on the system which you can + + + align:start position:0% +properties on the system which you can +exploit to represent the system or to + + align:start position:0% +exploit to represent the system or to + + + align:start position:0% +exploit to represent the system or to +implement the system Etc the special + + align:start position:0% +implement the system Etc the special + + + align:start position:0% +implement the system Etc the special +class that we'll want to consider is the + + align:start position:0% +class that we'll want to consider is the + + + align:start position:0% +class that we'll want to consider is the +class of systems which are first of all + + align:start position:0% +class of systems which are first of all + + + align:start position:0% +class of systems which are first of all +linear and second of all shift and + + align:start position:0% +linear and second of all shift and + + + align:start position:0% +linear and second of all shift and +variant and this class corresponds in + + align:start position:0% +variant and this class corresponds in + + + align:start position:0% +variant and this class corresponds in +the continuous time case to the class of + + align:start position:0% +the continuous time case to the class of + + + align:start position:0% +the continuous time case to the class of +systems that we normally refer to as + + align:start position:0% +systems that we normally refer to as + + + align:start position:0% +systems that we normally refer to as +linear and time + + align:start position:0% +linear and time + + + align:start position:0% +linear and time +invariant uh we'll tend to refer to + + align:start position:0% +invariant uh we'll tend to refer to + + + align:start position:0% +invariant uh we'll tend to refer to +these as linear and shift inv variant + + align:start position:0% +these as linear and shift inv variant + + + align:start position:0% +these as linear and shift inv variant +and for a shorthand notation just + + align:start position:0% +and for a shorthand notation just + + + align:start position:0% +and for a shorthand notation just +Express this as LS + + align:start position:0% +Express this as LS + + + align:start position:0% +Express this as LS +I when I refer to an LSI system what I + + align:start position:0% +I when I refer to an LSI system what I + + + align:start position:0% +I when I refer to an LSI system what I +mean is a system that is linear and + + align:start position:0% +mean is a system that is linear and + + + align:start position:0% +mean is a system that is linear and +shift and variant well let's define + + align:start position:0% +shift and variant well let's define + + + align:start position:0% +shift and variant well let's define +these terms first of all + + align:start position:0% + + + + align:start position:0% + +linearity + + align:start position:0% +linearity + + + align:start position:0% +linearity +linearity states that if I excite the + + align:start position:0% +linearity states that if I excite the + + + align:start position:0% +linearity states that if I excite the +system with a sequence X1 of + + align:start position:0% +system with a sequence X1 of + + + align:start position:0% +system with a sequence X1 of +N and I get at the output a sequence y1 + + align:start position:0% +N and I get at the output a sequence y1 + + + align:start position:0% +N and I get at the output a sequence y1 +of N and if I excite with x X2 of N and + + align:start position:0% +of N and if I excite with x X2 of N and + + + align:start position:0% +of N and if I excite with x X2 of N and +get at the output Y2 of + + align:start position:0% +get at the output Y2 of + + + align:start position:0% +get at the output Y2 of +n then the condition of linearity is + + align:start position:0% +n then the condition of linearity is + + + align:start position:0% +n then the condition of linearity is +that the linear combination ax1 of n + + align:start position:0% +that the linear combination ax1 of n + + + align:start position:0% +that the linear combination ax1 of n +plus bx2 of n produces at the output a + + align:start position:0% +plus bx2 of n produces at the output a + + + align:start position:0% +plus bx2 of n produces at the output a +y1 of n plus b Y2 of n that is the + + align:start position:0% +y1 of n plus b Y2 of n that is the + + + align:start position:0% +y1 of n plus b Y2 of n that is the +response of the system to a sum of + + align:start position:0% +response of the system to a sum of + + + align:start position:0% +response of the system to a sum of +inputs or a linear combination of inputs + + align:start position:0% +inputs or a linear combination of inputs + + + align:start position:0% +inputs or a linear combination of inputs +is a linear combination of the + + align:start position:0% +is a linear combination of the + + + align:start position:0% +is a linear combination of the +corresponding output + + align:start position:0% +corresponding output + + + align:start position:0% +corresponding output +Now by repeated application of just this + + align:start position:0% +Now by repeated application of just this + + + align:start position:0% +Now by repeated application of just this +statement we can make a more general + + align:start position:0% +statement we can make a more general + + + align:start position:0% +statement we can make a more general +statement which is that the sum of a + + align:start position:0% +statement which is that the sum of a + + + align:start position:0% +statement which is that the sum of a +subk * X subk of + + align:start position:0% +subk * X subk of + + + align:start position:0% +subk * X subk of +n produces as an output the + + align:start position:0% +n produces as an output the + + + align:start position:0% +n produces as an output the +sum of a subk Time y subk of + + align:start position:0% +sum of a subk Time y subk of + + + align:start position:0% +sum of a subk Time y subk of +n linearity is stated here of course for + + align:start position:0% +n linearity is stated here of course for + + + align:start position:0% +n linearity is stated here of course for +two inputs but we can obviously extend + + align:start position:0% +two inputs but we can obviously extend + + + align:start position:0% +two inputs but we can obviously extend +that to an arbitrary number of inputs so + + align:start position:0% +that to an arbitrary number of inputs so + + + align:start position:0% +that to an arbitrary number of inputs so +that the statement of linearity as we'll + + align:start position:0% +that the statement of linearity as we'll + + + align:start position:0% +that the statement of linearity as we'll +refer to it will generally be that a + + align:start position:0% +refer to it will generally be that a + + + align:start position:0% +refer to it will generally be that a +general linear combination of inputs + + align:start position:0% +general linear combination of inputs + + + align:start position:0% +general linear combination of inputs +produces at the output the same linear + + align:start position:0% +produces at the output the same linear + + + align:start position:0% +produces at the output the same linear +combination of the corresponding + + align:start position:0% +combination of the corresponding + + + align:start position:0% +combination of the corresponding +outputs so that's the condition of + + align:start position:0% +outputs so that's the condition of + + + align:start position:0% +outputs so that's the condition of +linearity the second condition that we + + align:start position:0% +linearity the second condition that we + + + align:start position:0% +linearity the second condition that we +want to impose on our class of systems + + align:start position:0% +want to impose on our class of systems + + + align:start position:0% +want to impose on our class of systems +is the condition of shift and variance + + align:start position:0% +is the condition of shift and variance + + + align:start position:0% +is the condition of shift and variance +what shift and variance says simply is + + align:start position:0% +what shift and variance says simply is + + + align:start position:0% +what shift and variance says simply is +that if x of n produces y of n then X of + + align:start position:0% +that if x of n produces y of n then X of + + + align:start position:0% +that if x of n produces y of n then X of +n- n0 produces y of nus n0 it's + + align:start position:0% +n- n0 produces y of nus n0 it's + + + align:start position:0% +n- n0 produces y of nus n0 it's +basically a statement that the system + + align:start position:0% +basically a statement that the system + + + align:start position:0% +basically a statement that the system +doesn't particularly care what you call + + align:start position:0% +doesn't particularly care what you call + + + align:start position:0% +doesn't particularly care what you call +n equals z in other words if we shift + + align:start position:0% +n equals z in other words if we shift + + + align:start position:0% +n equals z in other words if we shift +the input in N we shift the output in N + + align:start position:0% +the input in N we shift the output in N + + + align:start position:0% +the input in N we shift the output in N +it's exactly like the condition of time + + align:start position:0% +it's exactly like the condition of time + + + align:start position:0% +it's exactly like the condition of time +invariance in the continuous time + + align:start position:0% +invariance in the continuous time + + + align:start position:0% +invariance in the continuous time +case for example if we excited the + + align:start position:0% +case for example if we excited the + + + align:start position:0% +case for example if we excited the +system with a unit sample to get the + + align:start position:0% +system with a unit sample to get the + + + align:start position:0% +system with a unit sample to get the +unit sample response h of n then the + + align:start position:0% +unit sample response h of n then the + + + align:start position:0% +unit sample response h of n then the +response of the system if the system is + + align:start position:0% +response of the system if the system is + + + align:start position:0% +response of the system if the system is +shift inv variant to a delayed unit + + align:start position:0% +shift inv variant to a delayed unit + + + align:start position:0% +shift inv variant to a delayed unit +sample is the delayed version of the + + align:start position:0% +sample is the delayed version of the + + + align:start position:0% +sample is the delayed version of the +unit sample response so this is shift + + align:start position:0% +unit sample response so this is shift + + + align:start position:0% +unit sample response so this is shift +and variance we had the condition of + + align:start position:0% +and variance we had the condition of + + + align:start position:0% +and variance we had the condition of +linearity the these are two independent + + align:start position:0% +linearity the these are two independent + + + align:start position:0% +linearity the these are two independent +conditions which we'll now want to put + + align:start position:0% +conditions which we'll now want to put + + + align:start position:0% +conditions which we'll now want to put +together to develop a general + + align:start position:0% +together to develop a general + + + align:start position:0% +together to develop a general +representation for linear shift and + + align:start position:0% +representation for linear shift and + + + align:start position:0% +representation for linear shift and +variance + + align:start position:0% +variance + + + align:start position:0% +variance +systems well let me remind you from the + + align:start position:0% +systems well let me remind you from the + + + align:start position:0% +systems well let me remind you from the +last view graph that we had looked at + + align:start position:0% +last view graph that we had looked at + + + align:start position:0% +last view graph that we had looked at +that we had a general representation for + + align:start position:0% +that we had a general representation for + + + align:start position:0% +that we had a general representation for +sequence in terms of weighted delayed + + align:start position:0% +sequence in terms of weighted delayed + + + align:start position:0% +sequence in terms of weighted delayed +unit samples that is previously we had + + align:start position:0% +unit samples that is previously we had + + + align:start position:0% +unit samples that is previously we had +developed the representation X of n of + + align:start position:0% +developed the representation X of n of + + + align:start position:0% +developed the representation X of n of +this form which expresses an arbitrary + + align:start position:0% +this form which expresses an arbitrary + + + align:start position:0% +this form which expresses an arbitrary +sequence in terms of weighted delayed + + align:start position:0% +sequence in terms of weighted delayed + + + align:start position:0% +sequence in terms of weighted delayed +unit + + align:start position:0% +unit + + + align:start position:0% +unit +samples well this then says that X of n + + align:start position:0% +samples well this then says that X of n + + + align:start position:0% +samples well this then says that X of n +is expressed as a linear combination of + + align:start position:0% +is expressed as a linear combination of + + + align:start position:0% +is expressed as a linear combination of +basic inputs and if we restrict + + align:start position:0% +basic inputs and if we restrict + + + align:start position:0% +basic inputs and if we restrict +ourselves to linear systems then the + + align:start position:0% +ourselves to linear systems then the + + + align:start position:0% +ourselves to linear systems then the +output must correspond to the same + + align:start position:0% +output must correspond to the same + + + align:start position:0% +output must correspond to the same +linear combination of the corresponding + + align:start position:0% +linear combination of the corresponding + + + align:start position:0% +linear combination of the corresponding +outputs well Delta of n minus K into a + + align:start position:0% +outputs well Delta of n minus K into a + + + align:start position:0% +outputs well Delta of n minus K into a +linear shift and variant system will + + align:start position:0% +linear shift and variant system will + + + align:start position:0% +linear shift and variant system will +produce at the + + align:start position:0% +produce at the + + + align:start position:0% +produce at the +output by virtue of the property of + + align:start position:0% +output by virtue of the property of + + + align:start position:0% +output by virtue of the property of +shift in + + align:start position:0% +shift in + + + align:start position:0% +shift in +variance the sequence h of n minus + + align:start position:0% +variance the sequence h of n minus + + + align:start position:0% +variance the sequence h of n minus +k and a linear combination of these + + align:start position:0% +k and a linear combination of these + + + align:start position:0% +k and a linear combination of these +delayed unit samples will produce that + + align:start position:0% +delayed unit samples will produce that + + + align:start position:0% +delayed unit samples will produce that +the output by virtue of linearity the + + align:start position:0% +the output by virtue of linearity the + + + align:start position:0% +the output by virtue of linearity the +same linear + + align:start position:0% + + + + align:start position:0% + +combination of the responses to Delta of + + align:start position:0% +combination of the responses to Delta of + + + align:start position:0% +combination of the responses to Delta of +n minus K so if we consider a linear + + align:start position:0% +n minus K so if we consider a linear + + + align:start position:0% +n minus K so if we consider a linear +shift and variance system then because + + align:start position:0% +shift and variance system then because + + + align:start position:0% +shift and variance system then because +of this + + align:start position:0% +of this + + + align:start position:0% +of this +representation we can say that the + + align:start position:0% +representation we can say that the + + + align:start position:0% +representation we can say that the +response due to an arbitrary + + align:start position:0% +response due to an arbitrary + + + align:start position:0% +response due to an arbitrary +input is equal to a linear combination + + align:start position:0% +input is equal to a linear combination + + + align:start position:0% +input is equal to a linear combination +of delayed unit sample + + align:start position:0% +of delayed unit sample + + + align:start position:0% +of delayed unit sample +responses where in general this is a sum + + align:start position:0% +responses where in general this is a sum + + + align:start position:0% +responses where in general this is a sum +from K minus infinity to plus + + align:start position:0% +from K minus infinity to plus + + + align:start position:0% +from K minus infinity to plus +infinity well this is the key result + + align:start position:0% +infinity well this is the key result + + + align:start position:0% +infinity well this is the key result +this is a statement that says that if we + + align:start position:0% +this is a statement that says that if we + + + align:start position:0% +this is a statement that says that if we +talk about linear shift and variance + + align:start position:0% +talk about linear shift and variance + + + align:start position:0% +talk about linear shift and variance +systems then all that we need to know + + align:start position:0% +systems then all that we need to know + + + align:start position:0% +systems then all that we need to know +about the system to characterize it is + + align:start position:0% +about the system to characterize it is + + + align:start position:0% +about the system to characterize it is +its response to a unit sample if we have + + align:start position:0% +its response to a unit sample if we have + + + align:start position:0% +its response to a unit sample if we have +its response to a unit sample we can + + align:start position:0% +its response to a unit sample we can + + + align:start position:0% +its response to a unit sample we can +construct y of n in general that is we + + align:start position:0% +construct y of n in general that is we + + + align:start position:0% +construct y of n in general that is we +can construct the output for an + + align:start position:0% +can construct the output for an + + + align:start position:0% +can construct the output for an +arbitrary input X of + + align:start position:0% +arbitrary input X of + + + align:start position:0% +arbitrary input X of +K this is generally referred to as the + + align:start position:0% +K this is generally referred to as the + + + align:start position:0% +K this is generally referred to as the +convolution + + align:start position:0% +convolution + + + align:start position:0% +convolution +sum in analogy with the convolution + + align:start position:0% +sum in analogy with the convolution + + + align:start position:0% +sum in analogy with the convolution +integral in the continuous time + + align:start position:0% +integral in the continuous time + + + align:start position:0% +integral in the continuous time +case this is one way of writing the + + align:start position:0% +case this is one way of writing the + + + align:start position:0% +case this is one way of writing the +convolution sum there is an alternative + + align:start position:0% +convolution sum there is an alternative + + + align:start position:0% +convolution sum there is an alternative +which is interesting in that it suggests + + align:start position:0% +which is interesting in that it suggests + + + align:start position:0% +which is interesting in that it suggests +some important properties of linear + + align:start position:0% +some important properties of linear + + + align:start position:0% +some important properties of linear +shift and Varan systems and it's + + align:start position:0% +shift and Varan systems and it's + + + align:start position:0% +shift and Varan systems and it's +obtained simply by applying a + + align:start position:0% +obtained simply by applying a + + + align:start position:0% +obtained simply by applying a +substitution of variables to this + + align:start position:0% +substitution of variables to this + + + align:start position:0% +substitution of variables to this +expression in particular suppose that we + + align:start position:0% +expression in particular suppose that we + + + align:start position:0% +expression in particular suppose that we +replace n minus K by the variable + + align:start position:0% +replace n minus K by the variable + + + align:start position:0% +replace n minus K by the variable +r or equivalently k is equal to nus + + align:start position:0% +r or equivalently k is equal to nus + + + align:start position:0% +r or equivalently k is equal to nus +R then what we obtain is y of n is now + + align:start position:0% +R then what we obtain is y of n is now + + + align:start position:0% +R then what we obtain is y of n is now +equal to a sum and this is now a sum on + + align:start position:0% +equal to a sum and this is now a sum on + + + align:start position:0% +equal to a sum and this is now a sum on +R for K we have nus R so this is X of + + align:start position:0% +R for K we have nus R so this is X of + + + align:start position:0% +R for K we have nus R so this is X of +nus R time h of n minus K which is equal + + align:start position:0% +nus R time h of n minus K which is equal + + + align:start position:0% +nus R time h of n minus K which is equal +to R so this is H of + + align:start position:0% +to R so this is H of + + + align:start position:0% +to R so this is H of +R well it's a simple step to take but in + + align:start position:0% +R well it's a simple step to take but in + + + align:start position:0% +R well it's a simple step to take but in +fact what it says is that the system + + align:start position:0% +fact what it says is that the system + + + align:start position:0% +fact what it says is that the system +doesn't particularly care what you call + + align:start position:0% +doesn't particularly care what you call + + + align:start position:0% +doesn't particularly care what you call +the input to the system and what you + + align:start position:0% +the input to the system and what you + + + align:start position:0% +the input to the system and what you +call the unit sample response of the + + align:start position:0% +call the unit sample response of the + + + align:start position:0% +call the unit sample response of the +system said another way it says that + + align:start position:0% +system said another way it says that + + + align:start position:0% +system said another way it says that +convolution is commutative that is if we + + align:start position:0% +convolution is commutative that is if we + + + align:start position:0% +convolution is commutative that is if we +represent the convolution of X of n with + + align:start position:0% +represent the convolution of X of n with + + + align:start position:0% +represent the convolution of X of n with +h of n with an + + align:start position:0% +h of n with an + + + align:start position:0% +h of n with an +asterisk then because of the fact that + + align:start position:0% +asterisk then because of the fact that + + + align:start position:0% +asterisk then because of the fact that +we were able to Interchange the roles of + + align:start position:0% +we were able to Interchange the roles of + + + align:start position:0% +we were able to Interchange the roles of +X of N and H of n that implies + + align:start position:0% +X of N and H of n that implies + + + align:start position:0% +X of N and H of n that implies +essentially that X of n convolved with h + + align:start position:0% +essentially that X of n convolved with h + + + align:start position:0% +essentially that X of n convolved with h +of n is the same thing as as hent + + align:start position:0% +of n is the same thing as as hent + + + align:start position:0% +of n is the same thing as as hent +convolved with X + + align:start position:0% +convolved with X + + + align:start position:0% +convolved with X +ofen that implies as I indicated that if + + align:start position:0% +ofen that implies as I indicated that if + + + align:start position:0% +ofen that implies as I indicated that if +we had a + + align:start position:0% +we had a + + + align:start position:0% +we had a +system with an Impulse response or unit + + align:start position:0% +system with an Impulse response or unit + + + align:start position:0% +system with an Impulse response or unit +sample response h of n an input X of N + + align:start position:0% +sample response h of n an input X of N + + + align:start position:0% +sample response h of n an input X of N +and an output y of n that if I call this + + align:start position:0% +and an output y of n that if I call this + + + align:start position:0% +and an output y of n that if I call this +the input and I call this the unit + + align:start position:0% +the input and I call this the unit + + + align:start position:0% +the input and I call this the unit +sample response as I've done here we + + align:start position:0% +sample response as I've done here we + + + align:start position:0% +sample response as I've done here we +obtain the same output that is H of n + + align:start position:0% +obtain the same output that is H of n + + + align:start position:0% +obtain the same output that is H of n +into a system with unit sample response + + align:start position:0% +into a system with unit sample response + + + align:start position:0% +into a system with unit sample response +X of n gives us at the output y of n + + align:start position:0% +X of n gives us at the output y of n + + + align:start position:0% +X of n gives us at the output y of n +also an implication of that is that + + align:start position:0% +also an implication of that is that + + + align:start position:0% +also an implication of that is that +linear shift and variance systems in + + align:start position:0% +linear shift and variance systems in + + + align:start position:0% +linear shift and variance systems in +Cascade don't particularly care which + + align:start position:0% +Cascade don't particularly care which + + + align:start position:0% +Cascade don't particularly care which +order the systems are cascaded in that + + align:start position:0% +order the systems are cascaded in that + + + align:start position:0% +order the systems are cascaded in that +is if I have a system H1 of n uh that is + + align:start position:0% +is if I have a system H1 of n uh that is + + + align:start position:0% +is if I have a system H1 of n uh that is +with unit sample response H1 of N and + + align:start position:0% +with unit sample response H1 of N and + + + align:start position:0% +with unit sample response H1 of N and +Cascade with a system with unit sample + + align:start position:0% +Cascade with a system with unit sample + + + align:start position:0% +Cascade with a system with unit sample +response respon H2 of N and input X of + + align:start position:0% +response respon H2 of N and input X of + + + align:start position:0% +response respon H2 of N and input X of +n the unit sample response of this + + align:start position:0% +n the unit sample response of this + + + align:start position:0% +n the unit sample response of this +overall system is H1 of n convolved with + + align:start position:0% +overall system is H1 of n convolved with + + + align:start position:0% +overall system is H1 of n convolved with +H2 of + + align:start position:0% +H2 of + + + align:start position:0% +H2 of +n but since convolution is commutative + + align:start position:0% +n but since convolution is commutative + + + align:start position:0% +n but since convolution is commutative +we could just as easily convolve H2 with + + align:start position:0% +we could just as easily convolve H2 with + + + align:start position:0% +we could just as easily convolve H2 with +H1 and that corresponds to a Cascade of + + align:start position:0% +H1 and that corresponds to a Cascade of + + + align:start position:0% +H1 and that corresponds to a Cascade of +the system H2 of n with the system H1 + + align:start position:0% +the system H2 of n with the system H1 + + + align:start position:0% +the system H2 of n with the system H1 +event so simply because of the fact that + + align:start position:0% +event so simply because of the fact that + + + align:start position:0% +event so simply because of the fact that +convolution is + + align:start position:0% + + + + align:start position:0% + +commutative that implies that for + + align:start position:0% +commutative that implies that for + + + align:start position:0% +commutative that implies that for +example that linear shift and variance + + align:start position:0% +example that linear shift and variance + + + align:start position:0% +example that linear shift and variance +systems in Cascade don't particularly + + align:start position:0% +systems in Cascade don't particularly + + + align:start position:0% +systems in Cascade don't particularly +care in which order they're cascaded + + align:start position:0% +care in which order they're cascaded + + + align:start position:0% +care in which order they're cascaded +there are lots of other properties of + + align:start position:0% +there are lots of other properties of + + + align:start position:0% +there are lots of other properties of +convolution and simple properties of + + align:start position:0% +convolution and simple properties of + + + align:start position:0% +convolution and simple properties of +linear shift and variance systems that + + align:start position:0% +linear shift and variance systems that + + + align:start position:0% +linear shift and variance systems that +are are direct consequence of + + align:start position:0% +are are direct consequence of + + + align:start position:0% +are are direct consequence of +convolution and some of the properties + + align:start position:0% +convolution and some of the properties + + + align:start position:0% +convolution and some of the properties +that we've mentioned of convolution and + + align:start position:0% +that we've mentioned of convolution and + + + align:start position:0% +that we've mentioned of convolution and +a number of these we'll see in the + + align:start position:0% +a number of these we'll see in the + + + align:start position:0% +a number of these we'll see in the +lectures as we go along and also a + + align:start position:0% +lectures as we go along and also a + + + align:start position:0% +lectures as we go along and also a +number of them you'll have a chance to + + align:start position:0% +number of them you'll have a chance to + + + align:start position:0% +number of them you'll have a chance to +wrestle with uh in the study + + align:start position:0% +wrestle with uh in the study + + + align:start position:0% +wrestle with uh in the study +guide okay so this is a development of + + align:start position:0% +guide okay so this is a development of + + + align:start position:0% +guide okay so this is a development of +the convolution + + align:start position:0% +the convolution + + + align:start position:0% +the convolution +sum one of the important aspects of the + + align:start position:0% +sum one of the important aspects of the + + + align:start position:0% +sum one of the important aspects of the +convolution + + align:start position:0% +convolution + + + align:start position:0% +convolution +sum is the steps involved in actually + + align:start position:0% +sum is the steps involved in actually + + + align:start position:0% +sum is the steps involved in actually +Computing it that is uh the + + align:start position:0% +Computing it that is uh the + + + align:start position:0% +Computing it that is uh the +manipulations involved in forming this + + align:start position:0% +manipulations involved in forming this + + + align:start position:0% +manipulations involved in forming this +sum and as the last point that I'd like + + align:start position:0% +sum and as the last point that I'd like + + + align:start position:0% +sum and as the last point that I'd like +to make in this lecture I'd like to + + align:start position:0% +to make in this lecture I'd like to + + + align:start position:0% +to make in this lecture I'd like to +illustrate first with a view graph and + + align:start position:0% +illustrate first with a view graph and + + + align:start position:0% +illustrate first with a view graph and +uh then with a movie The computation or + + align:start position:0% +uh then with a movie The computation or + + + align:start position:0% +uh then with a movie The computation or +the implementation of the convolution + + align:start position:0% +the implementation of the convolution + + + align:start position:0% +the implementation of the convolution +sum so let's return to the vi graph + + align:start position:0% + + + + align:start position:0% + +and I've indicated here again the + + align:start position:0% +and I've indicated here again the + + + align:start position:0% +and I've indicated here again the +convolution sum as we've derived it y of + + align:start position:0% +convolution sum as we've derived it y of + + + align:start position:0% +convolution sum as we've derived it y of +n is the sum of X of k h of n minus K + + align:start position:0% +n is the sum of X of k h of n minus K + + + align:start position:0% +n is the sum of X of k h of n minus K +now in implementing the convolution sum + + align:start position:0% +now in implementing the convolution sum + + + align:start position:0% +now in implementing the convolution sum +let me stress that it + + align:start position:0% +let me stress that it + + + align:start position:0% +let me stress that it +is n which is the independent variable + + align:start position:0% +is n which is the independent variable + + + align:start position:0% +is n which is the independent variable +for which we're Computing the output + + align:start position:0% +for which we're Computing the output + + + align:start position:0% +for which we're Computing the output +that is K is just simply a dummy + + align:start position:0% +that is K is just simply a dummy + + + align:start position:0% +that is K is just simply a dummy +variable inside this + + align:start position:0% +variable inside this + + + align:start position:0% +variable inside this +summation well I've Illustrated here uh + + align:start position:0% +summation well I've Illustrated here uh + + + align:start position:0% +summation well I've Illustrated here uh +for a specific example a sequence X of + + align:start position:0% +for a specific example a sequence X of + + + align:start position:0% +for a specific example a sequence X of +K which is a constant from0 to I guess + + align:start position:0% +K which is a constant from0 to I guess + + + align:start position:0% +K which is a constant from0 to I guess +Nal + + align:start position:0% +Nal + + + align:start position:0% +Nal +10 equal to Unity for n equal 0 to 10 + + align:start position:0% +10 equal to Unity for n equal 0 to 10 + + + align:start position:0% +10 equal to Unity for n equal 0 to 10 +and zero otherwise and I've indicated + + align:start position:0% +and zero otherwise and I've indicated + + + align:start position:0% +and zero otherwise and I've indicated +the sequence a little differently here + + align:start position:0% +the sequence a little differently here + + + align:start position:0% +the sequence a little differently here +than I had previously uh since I want to + + align:start position:0% +than I had previously uh since I want to + + + align:start position:0% +than I had previously uh since I want to +distinguish between between the X's the + + align:start position:0% +distinguish between between the X's the + + + align:start position:0% +distinguish between between the X's the +H's and the Y's the sequence X of K I'm + + align:start position:0% +H's and the Y's the sequence X of K I'm + + + align:start position:0% +H's and the Y's the sequence X of K I'm +denoting with little X's uh the sequence + + align:start position:0% +denoting with little X's uh the sequence + + + align:start position:0% +denoting with little X's uh the sequence +H I'll denote with little H's and later + + align:start position:0% +H I'll denote with little H's and later + + + align:start position:0% +H I'll denote with little H's and later +on the sequence y will denote with + + align:start position:0% +on the sequence y will denote with + + + align:start position:0% +on the sequence y will denote with +little y's all right so here we have the + + align:start position:0% +little y's all right so here we have the + + + align:start position:0% +little y's all right so here we have the +sequence a that's this + + align:start position:0% +sequence a that's this + + + align:start position:0% +sequence a that's this +one and plotted as a function of + + align:start position:0% +one and plotted as a function of + + + align:start position:0% +one and plotted as a function of +K here I have the sequence h of K which + + align:start position:0% +K here I have the sequence h of K which + + + align:start position:0% +K here I have the sequence h of K which +I've chosen to be an exponential for K + + align:start position:0% +I've chosen to be an exponential for K + + + align:start position:0% +I've chosen to be an exponential for K +greater than Z and Z for K less than + + align:start position:0% +greater than Z and Z for K less than + + + align:start position:0% +greater than Z and Z for K less than +zero but it's not h of K that we want in + + align:start position:0% +zero but it's not h of K that we want in + + + align:start position:0% +zero but it's not h of K that we want in +this sum it's h of n minus K and what's + + align:start position:0% +this sum it's h of n minus K and what's + + + align:start position:0% +this sum it's h of n minus K and what's +n well n is whatever value of the output + + align:start position:0% +n well n is whatever value of the output + + + align:start position:0% +n well n is whatever value of the output +sequence we're trying to compute so if n + + align:start position:0% +sequence we're trying to compute so if n + + + align:start position:0% +sequence we're trying to compute so if n +was equal to zero for example we would + + align:start position:0% +was equal to zero for example we would + + + align:start position:0% +was equal to zero for example we would +want the sequence h of 0 minus K and + + align:start position:0% +want the sequence h of 0 minus K and + + + align:start position:0% +want the sequence h of 0 minus K and +that's this sequence it's h of K flipped + + align:start position:0% +that's this sequence it's h of K flipped + + + align:start position:0% +that's this sequence it's h of K flipped +around in K because of this minus sign + + align:start position:0% +around in K because of this minus sign + + + align:start position:0% +around in K because of this minus sign +and not shifted one way or the other + + align:start position:0% +and not shifted one way or the other + + + align:start position:0% +and not shifted one way or the other +simply because we have a zero here so + + align:start position:0% +simply because we have a zero here so + + + align:start position:0% +simply because we have a zero here so +here's h of K but that's not what what + + align:start position:0% +here's h of K but that's not what what + + + align:start position:0% +here's h of K but that's not what what +we want it's h of 0 minus K and now to + + align:start position:0% +we want it's h of 0 minus K and now to + + + align:start position:0% +we want it's h of 0 minus K and now to +compute y of Z we would multiply this + + align:start position:0% +compute y of Z we would multiply this + + + align:start position:0% +compute y of Z we would multiply this +sequence by this one and compute the sum + + align:start position:0% +sequence by this one and compute the sum + + + align:start position:0% +sequence by this one and compute the sum +from minus infinity to plus infinity + + align:start position:0% +from minus infinity to plus infinity + + + align:start position:0% +from minus infinity to plus infinity +that would give us the value y of 0 + + align:start position:0% +that would give us the value y of 0 + + + align:start position:0% +that would give us the value y of 0 +for a different value of n we would have + + align:start position:0% +for a different value of n we would have + + + align:start position:0% +for a different value of n we would have +to look at h of n minus k for whichever + + align:start position:0% +to look at h of n minus k for whichever + + + align:start position:0% +to look at h of n minus k for whichever +value of n we were Computing this for + + align:start position:0% +value of n we were Computing this for + + + align:start position:0% +value of n we were Computing this for +for example if n is equal to + + align:start position:0% +for example if n is equal to + + + align:start position:0% +for example if n is equal to +-4 the sequence that we want is H of -4 + + align:start position:0% +-4 the sequence that we want is H of -4 + + + align:start position:0% +-4 the sequence that we want is H of -4 +minus K and that is this sequence + + align:start position:0% +minus K and that is this sequence + + + align:start position:0% +minus K and that is this sequence +shifted to the left by four so to + + align:start position:0% +shifted to the left by four so to + + + align:start position:0% +shifted to the left by four so to +compute y of minus 4 we want this + + align:start position:0% +compute y of minus 4 we want this + + + align:start position:0% +compute y of minus 4 we want this +sequence multiplied by this one and the + + align:start position:0% +sequence multiplied by this one and the + + + align:start position:0% +sequence multiplied by this one and the +sum computed from minus infinity to plus + + align:start position:0% +sum computed from minus infinity to plus + + + align:start position:0% +sum computed from minus infinity to plus +infinity and you can see obviously for + + align:start position:0% +infinity and you can see obviously for + + + align:start position:0% +infinity and you can see obviously for +that particular case that is n equal to + + align:start position:0% +that particular case that is n equal to + + + align:start position:0% +that particular case that is n equal to +minus 4 the product of this and this is + + align:start position:0% +minus 4 the product of this and this is + + + align:start position:0% +minus 4 the product of this and this is +zero and the sum will be equal to + + align:start position:0% +zero and the sum will be equal to + + + align:start position:0% +zero and the sum will be equal to +zero well let's look at this + + align:start position:0% +zero well let's look at this + + + align:start position:0% +zero well let's look at this +example a little more dynamically with a + + align:start position:0% +example a little more dynamically with a + + + align:start position:0% +example a little more dynamically with a +movie that was prepared at Bell + + align:start position:0% +movie that was prepared at Bell + + + align:start position:0% +movie that was prepared at Bell +Telephone Laboratories by Dr Ronald + + align:start position:0% +Telephone Laboratories by Dr Ronald + + + align:start position:0% +Telephone Laboratories by Dr Ronald +schaer + + align:start position:0% + + + + align:start position:0% + +okay the convolution sum then we have is + + align:start position:0% +okay the convolution sum then we have is + + + align:start position:0% +okay the convolution sum then we have is +the sum of X of k h of n minus K and so + + align:start position:0% +the sum of X of k h of n minus K and so + + + align:start position:0% +the sum of X of k h of n minus K and so +what we would like to illustrate is the + + align:start position:0% +what we would like to illustrate is the + + + align:start position:0% +what we would like to illustrate is the +operation of evaluating this sum on the + + align:start position:0% +operation of evaluating this sum on the + + + align:start position:0% +operation of evaluating this sum on the +top we have X of K on the bottom we have + + align:start position:0% +top we have X of K on the bottom we have + + + align:start position:0% +top we have X of K on the bottom we have +H of k h of K being an exponential and + + align:start position:0% +H of k h of K being an exponential and + + + align:start position:0% +H of k h of K being an exponential and +now we see h of minus K namely h of K + + align:start position:0% +now we see h of minus K namely h of K + + + align:start position:0% +now we see h of minus K namely h of K +flipped over as we shift h of K to the + + align:start position:0% +flipped over as we shift h of K to the + + + align:start position:0% +flipped over as we shift h of K to the +left corresponding to n equals minus1 + + align:start position:0% +left corresponding to n equals minus1 + + + align:start position:0% +left corresponding to n equals minus1 +then back to + + align:start position:0% +then back to + + + align:start position:0% +then back to +zero and now to the + + align:start position:0% +zero and now to the + + + align:start position:0% +zero and now to the +right so we have H of 1 minus K and then + + align:start position:0% +right so we have H of 1 minus K and then + + + align:start position:0% +right so we have H of 1 minus K and then +to form y of n we want the product of H + + align:start position:0% +to form y of n we want the product of H + + + align:start position:0% +to form y of n we want the product of H +of minus K shifted with X of K that + + align:start position:0% +of minus K shifted with X of K that + + + align:start position:0% +of minus K shifted with X of K that +product summed from minus infinity to + + align:start position:0% +product summed from minus infinity to + + + align:start position:0% +product summed from minus infinity to +plus infinity so here we see X of K * h + + align:start position:0% +plus infinity so here we see X of K * h + + + align:start position:0% +plus infinity so here we see X of K * h +of 1 - k 2 - K 3 - K etc those + + align:start position:0% +of 1 - k 2 - K 3 - K etc those + + + align:start position:0% +of 1 - k 2 - K 3 - K etc those +multiplied and then summed from minus + + align:start position:0% +multiplied and then summed from minus + + + align:start position:0% +multiplied and then summed from minus +infinity to plus infinity we see during + + align:start position:0% +infinity to plus infinity we see during + + + align:start position:0% +infinity to plus infinity we see during +this portion that more and more values + + align:start position:0% +this portion that more and more values + + + align:start position:0% +this portion that more and more values +of H are engaged with non-zero values of + + align:start position:0% +of H are engaged with non-zero values of + + + align:start position:0% +of H are engaged with non-zero values of +X and so y of n grows until we reach the + + align:start position:0% +X and so y of n grows until we reach the + + + align:start position:0% +X and so y of n grows until we reach the +point where values fall off the end of + + align:start position:0% +point where values fall off the end of + + + align:start position:0% +point where values fall off the end of +the nonzero values of X where y of n + + align:start position:0% +the nonzero values of X where y of n + + + align:start position:0% +the nonzero values of X where y of n +decays + + align:start position:0% +decays + + + align:start position:0% +decays +so this then is an illustration of the + + align:start position:0% +so this then is an illustration of the + + + align:start position:0% +so this then is an illustration of the +linear convolution of X of K with h of + + align:start position:0% + + + + align:start position:0% + +K okay this completes our introduction + + align:start position:0% +K okay this completes our introduction + + + align:start position:0% +K okay this completes our introduction +to discrete time signals and systems + + align:start position:0% +to discrete time signals and systems + + + align:start position:0% +to discrete time signals and systems +there were a number of important points + + align:start position:0% +there were a number of important points + + + align:start position:0% +there were a number of important points +that we've made during this lecture but + + align:start position:0% +that we've made during this lecture but + + + align:start position:0% +that we've made during this lecture but +the key result and the result that it's + + align:start position:0% +the key result and the result that it's + + + align:start position:0% +the key result and the result that it's +important to develop some experience + + align:start position:0% +important to develop some experience + + + align:start position:0% +important to develop some experience +with is the convolution + + align:start position:0% +with is the convolution + + + align:start position:0% +with is the convolution +sum next time we'll introduce some + + align:start position:0% +sum next time we'll introduce some + + + align:start position:0% +sum next time we'll introduce some +additional considerations namely the + + align:start position:0% +additional considerations namely the + + + align:start position:0% +additional considerations namely the +considerations of stability and + + align:start position:0% +considerations of stability and + + + align:start position:0% +considerations of stability and +causality for discrete time systems and + + align:start position:0% +causality for discrete time systems and + + + align:start position:0% +causality for discrete time systems and +we'll also discuss briefly the class of + + align:start position:0% +we'll also discuss briefly the class of + + + align:start position:0% +we'll also discuss briefly the class of +linear shift and variance systems that + + align:start position:0% +linear shift and variance systems that + + + align:start position:0% +linear shift and variance systems that +are represented by linear constant + + align:start position:0% +are represented by linear constant + + + align:start position:0% +are represented by linear constant +coefficient difference equations finally + + align:start position:0% +coefficient difference equations finally + + + align:start position:0% +coefficient difference equations finally +we'll try to tie some of together in and + + align:start position:0% +we'll try to tie some of together in and + + + align:start position:0% +we'll try to tie some of together in and +in particular uh present what will be + + align:start position:0% +in particular uh present what will be + + + align:start position:0% +in particular uh present what will be +called The Frequency response of the + + align:start position:0% +called The Frequency response of the + + + align:start position:0% +called The Frequency response of the +systems and this will eventually lead + + align:start position:0% +systems and this will eventually lead + + + align:start position:0% +systems and this will eventually lead +into a discussion of forier transforms + + align:start position:0% +into a discussion of forier transforms + + + align:start position:0% +into a discussion of forier transforms +thank you + + align:start position:0% + + + + align:start position:0% + +[Music] \ No newline at end of file diff --git a/UI4Hjug3rEc.txt b/UI4Hjug3rEc.txt new file mode 100644 index 0000000000000000000000000000000000000000..964fcbca4d5d3b162f6f169ed20e5312013ef509 --- /dev/null +++ b/UI4Hjug3rEc.txt @@ -0,0 +1,18312 @@ +align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +i'm gonna get started this is lecture 23 + + align:start position:0% +i'm gonna get started this is lecture 23 + + + align:start position:0% +i'm gonna get started this is lecture 23 +uh + + align:start position:0% +uh + + + align:start position:0% +uh +about policy with the evil agent uh the + + align:start position:0% +about policy with the evil agent uh the + + + align:start position:0% +about policy with the evil agent uh the +last lecture of 14 + + align:start position:0% +last lecture of 14 + + + align:start position:0% +last lecture of 14 +uh 13 for better or worse um + + align:start position:0% +uh 13 for better or worse um + + + align:start position:0% +uh 13 for better or worse um +okay so what's the plan for today we're + + align:start position:0% +okay so what's the plan for today we're + + + align:start position:0% +okay so what's the plan for today we're +going to talk about + + align:start position:0% +going to talk about + + + align:start position:0% +going to talk about +paternalism what is paternalism reasons + + align:start position:0% +paternalism what is paternalism reasons + + + align:start position:0% +paternalism what is paternalism reasons +for paternalism uh + + align:start position:0% +for paternalism uh + + + align:start position:0% +for paternalism uh +why it might be popular or or not + + align:start position:0% +why it might be popular or or not + + + align:start position:0% +why it might be popular or or not +we're going to talk about a specific + + align:start position:0% +we're going to talk about a specific + + + align:start position:0% +we're going to talk about a specific +example of uh + + align:start position:0% +example of uh + + + align:start position:0% +example of uh +what was coined as uh libertarian + + align:start position:0% +what was coined as uh libertarian + + + align:start position:0% +what was coined as uh libertarian +paternalism i'll explain more which is + + align:start position:0% +paternalism i'll explain more which is + + + align:start position:0% +paternalism i'll explain more which is +to save more tomorrow plan what's good + + align:start position:0% +to save more tomorrow plan what's good + + + align:start position:0% +to save more tomorrow plan what's good +about this + + align:start position:0% +about this + + + align:start position:0% +about this +specific example and we'll discuss that + + align:start position:0% +specific example and we'll discuss that + + + align:start position:0% +specific example and we'll discuss that +and finally + + align:start position:0% +and finally + + + align:start position:0% +and finally +we'll talk about market solutions often + + align:start position:0% +we'll talk about market solutions often + + + align:start position:0% +we'll talk about market solutions often +it's sort of + + align:start position:0% +it's sort of + + + align:start position:0% +it's sort of +one solution that's all conventions to + + align:start position:0% +one solution that's all conventions to + + + align:start position:0% +one solution that's all conventions to +say well why can't the market + + align:start position:0% +say well why can't the market + + + align:start position:0% +say well why can't the market +solve these kinds of issues and we're + + align:start position:0% +solve these kinds of issues and we're + + + align:start position:0% +solve these kinds of issues and we're +going to talk about uh why that may or + + align:start position:0% +going to talk about uh why that may or + + + align:start position:0% +going to talk about uh why that may or +may not be a good idea + + align:start position:0% +may not be a good idea + + + align:start position:0% +may not be a good idea +okay so then let me just ask very simply + + align:start position:0% +okay so then let me just ask very simply + + + align:start position:0% +okay so then let me just ask very simply +to start + + align:start position:0% +to start + + + align:start position:0% +to start +with um from your classes if you're + + align:start position:0% +with um from your classes if you're + + + align:start position:0% +with um from your classes if you're +taking in economics and otherwise + + align:start position:0% +taking in economics and otherwise + + + align:start position:0% +taking in economics and otherwise +what are some reasons for government + + align:start position:0% +what are some reasons for government + + + align:start position:0% +what are some reasons for government +policies + + align:start position:0% +policies + + + align:start position:0% +policies +um you know and doesn't mean that he + + align:start position:0% +um you know and doesn't mean that he + + + align:start position:0% +um you know and doesn't mean that he +necessarily endorse those reasons but + + align:start position:0% +necessarily endorse those reasons but + + + align:start position:0% +necessarily endorse those reasons but +what are reasons why the government + + align:start position:0% +what are reasons why the government + + + align:start position:0% +what are reasons why the government +why we might want the government to + + align:start position:0% +why we might want the government to + + + align:start position:0% +why we might want the government to +engage in in + + align:start position:0% +engage in in + + + align:start position:0% +engage in in +uh economic or other sort of government + + align:start position:0% +uh economic or other sort of government + + + align:start position:0% +uh economic or other sort of government +policies + + align:start position:0% +policies + + + align:start position:0% +policies +yes so one uh reason might be that + + align:start position:0% +yes so one uh reason might be that + + + align:start position:0% +yes so one uh reason might be that +people don't quite know um + + align:start position:0% +people don't quite know um + + + align:start position:0% +people don't quite know um +what's good for them and so we can + + align:start position:0% +what's good for them and so we can + + + align:start position:0% +what's good for them and so we can +potentially help them + + align:start position:0% +potentially help them + + + align:start position:0% +potentially help them +by doing so that's of course the reason + + align:start position:0% +by doing so that's of course the reason + + + align:start position:0% +by doing so that's of course the reason +uh uh that's of course we're gonna talk + + align:start position:0% +uh uh that's of course we're gonna talk + + + align:start position:0% +uh uh that's of course we're gonna talk +about + + align:start position:0% +about + + + align:start position:0% +about +today let me rephrase my question um + + align:start position:0% +today let me rephrase my question um + + + align:start position:0% +today let me rephrase my question um +in neoclassical economics what are + + align:start position:0% +in neoclassical economics what are + + + align:start position:0% +in neoclassical economics what are +reasons for the government + + align:start position:0% +reasons for the government + + + align:start position:0% +reasons for the government +to engage so the behavioral ones are of + + align:start position:0% +to engage so the behavioral ones are of + + + align:start position:0% +to engage so the behavioral ones are of +course what we're going to call like + + align:start position:0% +course what we're going to call like + + + align:start position:0% +course what we're going to call like +internalities which is essentially + + align:start position:0% +internalities which is essentially + + + align:start position:0% +internalities which is essentially +people misoptimize in certain ways + + align:start position:0% +people misoptimize in certain ways + + + align:start position:0% +people misoptimize in certain ways +but one of the neoclassical reasons to + + align:start position:0% +but one of the neoclassical reasons to + + + align:start position:0% +but one of the neoclassical reasons to +for the government to to + + align:start position:0% +for the government to to + + + align:start position:0% +for the government to to +engage so like this would be things like + + align:start position:0% +engage so like this would be things like + + + align:start position:0% +engage so like this would be things like +um + + align:start position:0% +um + + + align:start position:0% +um +externalities this could be individuals + + align:start position:0% +externalities this could be individuals + + + align:start position:0% +externalities this could be individuals +uh causing externalities + + align:start position:0% +uh causing externalities + + + align:start position:0% +uh causing externalities +externalities essentially is a fancy + + align:start position:0% +externalities essentially is a fancy + + + align:start position:0% +externalities essentially is a fancy +word for like + + align:start position:0% +word for like + + + align:start position:0% +word for like +people causing some positive or negative + + align:start position:0% +people causing some positive or negative + + + align:start position:0% +people causing some positive or negative +effects on others that they might not be + + align:start position:0% +effects on others that they might not be + + + align:start position:0% +effects on others that they might not be +able to + + align:start position:0% +able to + + + align:start position:0% +able to +internalize this could be smokers or + + align:start position:0% +internalize this could be smokers or + + + align:start position:0% +internalize this could be smokers or +individuals doing that + + align:start position:0% +individuals doing that + + + align:start position:0% +individuals doing that +uh like for example smoking you might + + align:start position:0% +uh like for example smoking you might + + + align:start position:0% +uh like for example smoking you might +cause health effects on others + + align:start position:0% +cause health effects on others + + + align:start position:0% +cause health effects on others +uh could be also farms polluting the + + align:start position:0% +uh could be also farms polluting the + + + align:start position:0% +uh could be also farms polluting the +environment or polluting sort of like um + + align:start position:0% +environment or polluting sort of like um + + + align:start position:0% +environment or polluting sort of like um +water or some other sources of other + + align:start position:0% +water or some other sources of other + + + align:start position:0% +water or some other sources of other +people polluting + + align:start position:0% +people polluting + + + align:start position:0% +people polluting +in otherwise the air and so on and so + + align:start position:0% +in otherwise the air and so on and so + + + align:start position:0% +in otherwise the air and so on and so +forth which might be bad for others + + align:start position:0% +forth which might be bad for others + + + align:start position:0% +forth which might be bad for others +health + + align:start position:0% +health + + + align:start position:0% +health +and to the extent that the firm or + + align:start position:0% +and to the extent that the firm or + + + align:start position:0% +and to the extent that the firm or +others are not sort of taking + + align:start position:0% +others are not sort of taking + + + align:start position:0% +others are not sort of taking +that into account that'll lead to + + align:start position:0% +that into account that'll lead to + + + align:start position:0% +that into account that'll lead to +socially um suboptimal outcomes now the + + align:start position:0% +socially um suboptimal outcomes now the + + + align:start position:0% +socially um suboptimal outcomes now the +government would say well + + align:start position:0% +government would say well + + + align:start position:0% +government would say well +let's tax that because we want to make + + align:start position:0% +let's tax that because we want to make + + + align:start position:0% +let's tax that because we want to make +sure that people are + + align:start position:0% +sure that people are + + + align:start position:0% +sure that people are +taking into account these these uh + + align:start position:0% +taking into account these these uh + + + align:start position:0% +taking into account these these uh +externalities and with the optimal tax + + align:start position:0% +externalities and with the optimal tax + + + align:start position:0% +externalities and with the optimal tax +schedule potentially at least you can + + align:start position:0% +schedule potentially at least you can + + + align:start position:0% +schedule potentially at least you can +get back to the first faster so some + + align:start position:0% +get back to the first faster so some + + + align:start position:0% +get back to the first faster so some +at least you can improve off potentially + + align:start position:0% +at least you can improve off potentially + + + align:start position:0% +at least you can improve off potentially +so usually the the theorems about like + + align:start position:0% +so usually the the theorems about like + + + align:start position:0% +so usually the the theorems about like +free markets etc + + align:start position:0% +free markets etc + + + align:start position:0% +free markets etc +they essentially will the free market + + align:start position:0% +they essentially will the free market + + + align:start position:0% +they essentially will the free market +will achieve that things are efficient + + align:start position:0% +will achieve that things are efficient + + + align:start position:0% +will achieve that things are efficient +or potentially under some conditions + + align:start position:0% +or potentially under some conditions + + + align:start position:0% +or potentially under some conditions +but what the market will not typically + + align:start position:0% +but what the market will not typically + + + align:start position:0% +but what the market will not typically +achieve + + align:start position:0% +achieve + + + align:start position:0% +achieve +is sort of some form of equity and sort + + align:start position:0% +is sort of some form of equity and sort + + + align:start position:0% +is sort of some form of equity and sort +of to the extent that we + + align:start position:0% +of to the extent that we + + + align:start position:0% +of to the extent that we +are interested in that you might want to + + align:start position:0% +are interested in that you might want to + + + align:start position:0% +are interested in that you might want to +engage in social security insurance + + align:start position:0% +engage in social security insurance + + + align:start position:0% +engage in social security insurance +program unemployment insurance + + align:start position:0% +program unemployment insurance + + + align:start position:0% +program unemployment insurance +and so on and so forth so if you have + + align:start position:0% +and so on and so forth so if you have + + + align:start position:0% +and so on and so forth so if you have +lots of competition + + align:start position:0% +lots of competition + + + align:start position:0% +lots of competition +the prices will fall down to often + + align:start position:0% +the prices will fall down to often + + + align:start position:0% +the prices will fall down to often +marginal costs and that's good for + + align:start position:0% +marginal costs and that's good for + + + align:start position:0% +marginal costs and that's good for +consumers because stuff is cheap + + align:start position:0% +consumers because stuff is cheap + + + align:start position:0% +consumers because stuff is cheap +he could only one firm the firm the + + align:start position:0% +he could only one firm the firm the + + + align:start position:0% +he could only one firm the firm the +monopolist in the most stuck + + align:start position:0% +monopolist in the most stuck + + + align:start position:0% +monopolist in the most stuck +in case the monopolist will charge above + + align:start position:0% +in case the monopolist will charge above + + + align:start position:0% +in case the monopolist will charge above +um a marginal cost + + align:start position:0% +um a marginal cost + + + align:start position:0% +um a marginal cost +so prices will be higher fewer things + + align:start position:0% +so prices will be higher fewer things + + + align:start position:0% +so prices will be higher fewer things +will be sold and people will be + + align:start position:0% +will be sold and people will be + + + align:start position:0% +will be sold and people will be +um less happy about that and sort of + + align:start position:0% +um less happy about that and sort of + + + align:start position:0% +um less happy about that and sort of +then there's sort of this + + align:start position:0% +then there's sort of this + + + align:start position:0% +then there's sort of this +the anti-trust in 1420 as you say + + align:start position:0% +the anti-trust in 1420 as you say + + + align:start position:0% +the anti-trust in 1420 as you say +exactly nancy rose and others are + + align:start position:0% +exactly nancy rose and others are + + + align:start position:0% +exactly nancy rose and others are +working on that uh and their trust + + align:start position:0% +working on that uh and their trust + + + align:start position:0% +working on that uh and their trust +commissions et cetera + + align:start position:0% +commissions et cetera + + + align:start position:0% +commissions et cetera +china essentially make sure uh there's + + align:start position:0% +china essentially make sure uh there's + + + align:start position:0% +china essentially make sure uh there's +sufficient competition in markets + + align:start position:0% +sufficient competition in markets + + + align:start position:0% +sufficient competition in markets +because do you think that's good for + + align:start position:0% +because do you think that's good for + + + align:start position:0% +because do you think that's good for +welfare + + align:start position:0% +welfare + + + align:start position:0% +welfare +so there's uh other sort of market + + align:start position:0% +so there's uh other sort of market + + + align:start position:0% +so there's uh other sort of market +failures for example + + align:start position:0% +failures for example + + + align:start position:0% +failures for example +um public goods um uh parks and so on + + align:start position:0% +um public goods um uh parks and so on + + + align:start position:0% +um public goods um uh parks and so on +the government might want to provide + + align:start position:0% +the government might want to provide + + + align:start position:0% +the government might want to provide +that because in general people might + + align:start position:0% +that because in general people might + + + align:start position:0% +that because in general people might +under under um provide that + + align:start position:0% +under under um provide that + + + align:start position:0% +under under um provide that +could be also other things like + + align:start position:0% +could be also other things like + + + align:start position:0% +could be also other things like +information markets for information tend + + align:start position:0% +information markets for information tend + + + align:start position:0% +information markets for information tend +to fail the reason being that + + align:start position:0% +to fail the reason being that + + + align:start position:0% +to fail the reason being that +uh uh when i come up with an idea that's + + align:start position:0% +uh uh when i come up with an idea that's + + + align:start position:0% +uh uh when i come up with an idea that's +is useful for a lot of people i might + + align:start position:0% +is useful for a lot of people i might + + + align:start position:0% +is useful for a lot of people i might +not be able to internalize the rents + + align:start position:0% +not be able to internalize the rents + + + align:start position:0% +not be able to internalize the rents +from that + + align:start position:0% +from that + + + align:start position:0% +from that +instead of i'm under investing therefore + + align:start position:0% +instead of i'm under investing therefore + + + align:start position:0% +instead of i'm under investing therefore +in + + align:start position:0% +in + + + align:start position:0% +in +r d and so on so now i think we have all + + align:start position:0% +r d and so on so now i think we have all + + + align:start position:0% +r d and so on so now i think we have all +all the things i have on my list as + + align:start position:0% +all the things i have on my list as + + + align:start position:0% +all the things i have on my list as +macroeconomic policy as can just mention + + align:start position:0% +macroeconomic policy as can just mention + + + align:start position:0% +macroeconomic policy as can just mention +the federal reserve might + + align:start position:0% +the federal reserve might + + + align:start position:0% +the federal reserve might +be uh that's interest rate there might + + align:start position:0% +be uh that's interest rate there might + + + align:start position:0% +be uh that's interest rate there might +be fiscal stimulus + + align:start position:0% +be fiscal stimulus + + + align:start position:0% +be fiscal stimulus +competition policy that's what everyone + + align:start position:0% +competition policy that's what everyone + + + align:start position:0% +competition policy that's what everyone +just mentioned then there's just + + align:start position:0% +just mentioned then there's just + + + align:start position:0% +just mentioned then there's just +redistribution social insurance i think + + align:start position:0% +redistribution social insurance i think + + + align:start position:0% +redistribution social insurance i think +that's what um + + align:start position:0% +that's what um + + + align:start position:0% +that's what um +justin said on employment insurance + + align:start position:0% +justin said on employment insurance + + + align:start position:0% +justin said on employment insurance +social security and so on + + align:start position:0% +social security and so on + + + align:start position:0% +social security and so on +and then there might be uh externality + + align:start position:0% +and then there might be uh externality + + + align:start position:0% +and then there might be uh externality +that's what natalie said um + + align:start position:0% +that's what natalie said um + + + align:start position:0% +that's what natalie said um +uh uh cigarette taxes and other sort of + + align:start position:0% +uh uh cigarette taxes and other sort of + + + align:start position:0% +uh uh cigarette taxes and other sort of +market failures + + align:start position:0% +market failures + + + align:start position:0% +market failures +such as uh innovation that's um what + + align:start position:0% +such as uh innovation that's um what + + + align:start position:0% +such as uh innovation that's um what +uh jose uh as well said what we're gonna + + align:start position:0% +uh jose uh as well said what we're gonna + + + align:start position:0% +uh jose uh as well said what we're gonna +focus on now is + + align:start position:0% +focus on now is + + + align:start position:0% +focus on now is +none of these things which uh and that's + + align:start position:0% +none of these things which uh and that's + + + align:start position:0% +none of these things which uh and that's +getting back to what we said um at the + + align:start position:0% +getting back to what we said um at the + + + align:start position:0% +getting back to what we said um at the +very beginning which is + + align:start position:0% +very beginning which is + + + align:start position:0% +very beginning which is +internalities so that's a not a + + align:start position:0% +internalities so that's a not a + + + align:start position:0% +internalities so that's a not a +traditional way for governments to + + align:start position:0% +traditional way for governments to + + + align:start position:0% +traditional way for governments to +to engage in if you went back like 20 + + align:start position:0% +to engage in if you went back like 20 + + + align:start position:0% +to engage in if you went back like 20 +years from now the government that there + + align:start position:0% +years from now the government that there + + + align:start position:0% +years from now the government that there +would be no such + + align:start position:0% +would be no such + + + align:start position:0% +would be no such +very few such considerations but more + + align:start position:0% +very few such considerations but more + + + align:start position:0% +very few such considerations but more +recently + + align:start position:0% +recently + + + align:start position:0% +recently +in part perhaps because as a consequence + + align:start position:0% +in part perhaps because as a consequence + + + align:start position:0% +in part perhaps because as a consequence +of the rise of people economics + + align:start position:0% +of the rise of people economics + + + align:start position:0% +of the rise of people economics +people are much more interested now in + + align:start position:0% +people are much more interested now in + + + align:start position:0% +people are much more interested now in +uh internalities and what are + + align:start position:0% +uh internalities and what are + + + align:start position:0% +uh internalities and what are +internalities + + align:start position:0% +internalities + + + align:start position:0% +internalities +it's essentially sort of similar to to + + align:start position:0% +it's essentially sort of similar to to + + + align:start position:0% +it's essentially sort of similar to to +accenture + + align:start position:0% +accenture + + + align:start position:0% +accenture +the coin is very similar uh instead of + + align:start position:0% +the coin is very similar uh instead of + + + align:start position:0% +the coin is very similar uh instead of +um + + align:start position:0% +um + + + align:start position:0% +um +causing damage or not um internalizing + + align:start position:0% +causing damage or not um internalizing + + + align:start position:0% +causing damage or not um internalizing +sufficiently uh effects on other people + + align:start position:0% +sufficiently uh effects on other people + + + align:start position:0% +sufficiently uh effects on other people +this is now effects on + + align:start position:0% +this is now effects on + + + align:start position:0% +this is now effects on +your future self essentially and so the + + align:start position:0% +your future self essentially and so the + + + align:start position:0% +your future self essentially and so the +kotoma does not fully or properly + + align:start position:0% +kotoma does not fully or properly + + + align:start position:0% +kotoma does not fully or properly +internalize all the costs and or + + align:start position:0% +internalize all the costs and or + + + align:start position:0% +internalize all the costs and or +benefits + + align:start position:0% +benefits + + + align:start position:0% +benefits +she imposes on her uh future potential + + align:start position:0% +she imposes on her uh future potential + + + align:start position:0% +she imposes on her uh future potential +um itself + + align:start position:0% +um itself + + + align:start position:0% +um itself +and if the government is sort of not + + align:start position:0% +and if the government is sort of not + + + align:start position:0% +and if the government is sort of not +confident that that's the case well then + + align:start position:0% +confident that that's the case well then + + + align:start position:0% +confident that that's the case well then +the government might want to + + align:start position:0% +the government might want to + + + align:start position:0% +the government might want to +to intervene now what's paternalism but + + align:start position:0% +to intervene now what's paternalism but + + + align:start position:0% +to intervene now what's paternalism but +journalism is essentially + + align:start position:0% +journalism is essentially + + + align:start position:0% +journalism is essentially +um a version of that there's a very + + align:start position:0% +um a version of that there's a very + + + align:start position:0% +um a version of that there's a very +convoluted um + + align:start position:0% +convoluted um + + + align:start position:0% +convoluted um +definition by the american webster um + + align:start position:0% +definition by the american webster um + + + align:start position:0% +definition by the american webster um +dictionary which i'm not going to read + + align:start position:0% +dictionary which i'm not going to read + + + align:start position:0% +dictionary which i'm not going to read +to you but it's you know at least one + + align:start position:0% +to you but it's you know at least one + + + align:start position:0% +to you but it's you know at least one +definition and + + align:start position:0% +definition and + + + align:start position:0% +definition and +there's a better one from david lipson + + align:start position:0% +there's a better one from david lipson + + + align:start position:0% +there's a better one from david lipson +um which is an attempt to influence or + + align:start position:0% +um which is an attempt to influence or + + + align:start position:0% +um which is an attempt to influence or +control uh people's conduct + + align:start position:0% +control uh people's conduct + + + align:start position:0% +control uh people's conduct +for their own good in other words when + + align:start position:0% +for their own good in other words when + + + align:start position:0% +for their own good in other words when +the motivation for the intervention is + + align:start position:0% +the motivation for the intervention is + + + align:start position:0% +the motivation for the intervention is +not about + + align:start position:0% +not about + + + align:start position:0% +not about +externalities so it's to say if we try + + align:start position:0% +externalities so it's to say if we try + + + align:start position:0% +externalities so it's to say if we try +to affect people's behavior for their + + align:start position:0% +to affect people's behavior for their + + + align:start position:0% +to affect people's behavior for their +own good in some ways and that sort of + + align:start position:0% +own good in some ways and that sort of + + + align:start position:0% +own good in some ways and that sort of +assumes of course + + align:start position:0% +assumes of course + + + align:start position:0% +assumes of course +that people are not fully optimizing in + + align:start position:0% +that people are not fully optimizing in + + + align:start position:0% +that people are not fully optimizing in +certain ways + + align:start position:0% +certain ways + + + align:start position:0% +certain ways +not when it comes to like their effects + + align:start position:0% +not when it comes to like their effects + + + align:start position:0% +not when it comes to like their effects +on others but + + align:start position:0% +on others but + + + align:start position:0% +on others but +rather the effects on themselves + + align:start position:0% +rather the effects on themselves + + + align:start position:0% +rather the effects on themselves +okay so there is a question + + align:start position:0% + + + + align:start position:0% + +now when is um + + align:start position:0% +now when is um + + + align:start position:0% +now when is um +paternalism warm that we can sort of go + + align:start position:0% +paternalism warm that we can sort of go + + + align:start position:0% +paternalism warm that we can sort of go +through the list of + + align:start position:0% +through the list of + + + align:start position:0% +through the list of +um topics that we discussed in the class + + align:start position:0% +um topics that we discussed in the class + + + align:start position:0% +um topics that we discussed in the class +and it's important to understand that + + align:start position:0% +and it's important to understand that + + + align:start position:0% +and it's important to understand that +like not all of these topics + + align:start position:0% +like not all of these topics + + + align:start position:0% +like not all of these topics +are in fact warranting intervention for + + align:start position:0% +are in fact warranting intervention for + + + align:start position:0% +are in fact warranting intervention for +example if you think people have certain + + align:start position:0% +example if you think people have certain + + + align:start position:0% +example if you think people have certain +risk preferences + + align:start position:0% +risk preferences + + + align:start position:0% +risk preferences +reference dependent preferences or + + align:start position:0% +reference dependent preferences or + + + align:start position:0% +reference dependent preferences or +social preferences that's not a bias or + + align:start position:0% +social preferences that's not a bias or + + + align:start position:0% +social preferences that's not a bias or +problem that we need to fix people care + + align:start position:0% +problem that we need to fix people care + + + align:start position:0% +problem that we need to fix people care +about + + align:start position:0% +about + + + align:start position:0% +about +others and that's just the way their + + align:start position:0% +others and that's just the way their + + + align:start position:0% +others and that's just the way their +utility function is like + + align:start position:0% +utility function is like + + + align:start position:0% +utility function is like +and then you kind of make sure that + + align:start position:0% +and then you kind of make sure that + + + align:start position:0% +and then you kind of make sure that +people can optimize + + align:start position:0% +people can optimize + + + align:start position:0% +people can optimize +their uh optimize accordingly + + align:start position:0% +their uh optimize accordingly + + + align:start position:0% +their uh optimize accordingly +that's not necessarily a bias or a + + align:start position:0% +that's not necessarily a bias or a + + + align:start position:0% +that's not necessarily a bias or a +problem + + align:start position:0% +problem + + + align:start position:0% +problem +of course if there's problems with + + align:start position:0% +of course if there's problems with + + + align:start position:0% +of course if there's problems with +self-control problems where people are + + align:start position:0% +self-control problems where people are + + + align:start position:0% +self-control problems where people are +timing consistent preferences we might + + align:start position:0% +timing consistent preferences we might + + + align:start position:0% +timing consistent preferences we might +want to sort of help people + + align:start position:0% +want to sort of help people + + + align:start position:0% +want to sort of help people +that assumes of course that we know + + align:start position:0% +that assumes of course that we know + + + align:start position:0% +that assumes of course that we know +which self is the one we want to + + align:start position:0% +which self is the one we want to + + + align:start position:0% +which self is the one we want to +to support uh there's lots of + + align:start position:0% +to support uh there's lots of + + + align:start position:0% +to support uh there's lots of +space here when you think about + + align:start position:0% +space here when you think about + + + align:start position:0% +space here when you think about +non-standard beliefs for people to uh + + align:start position:0% +non-standard beliefs for people to uh + + + align:start position:0% +non-standard beliefs for people to uh +make mistakes so for our governments and + + align:start position:0% +make mistakes so for our governments and + + + align:start position:0% +make mistakes so for our governments and +others to intervene + + align:start position:0% +others to intervene + + + align:start position:0% +others to intervene +this would be limited attention also + + align:start position:0% +this would be limited attention also + + + align:start position:0% +this would be limited attention also +things like memory where people just + + align:start position:0% +things like memory where people just + + + align:start position:0% +things like memory where people just +forget stuff + + align:start position:0% +forget stuff + + + align:start position:0% +forget stuff +um learning failures people just have + + align:start position:0% +um learning failures people just have + + + align:start position:0% +um learning failures people just have +wrong information over optimism over + + align:start position:0% +wrong information over optimism over + + + align:start position:0% +wrong information over optimism over +confidence + + align:start position:0% +confidence + + + align:start position:0% +confidence +projection and attribution bias these + + align:start position:0% +projection and attribution bias these + + + align:start position:0% +projection and attribution bias these +are all essentially people that make + + align:start position:0% +are all essentially people that make + + + align:start position:0% +are all essentially people that make +mistakes in some ways + + align:start position:0% +mistakes in some ways + + + align:start position:0% +mistakes in some ways +and to the extent that they make these + + align:start position:0% +and to the extent that they make these + + + align:start position:0% +and to the extent that they make these +mistakes we might want to intervene + + align:start position:0% +mistakes we might want to intervene + + + align:start position:0% +mistakes we might want to intervene +importantly we discussed this already + + align:start position:0% +importantly we discussed this already + + + align:start position:0% +importantly we discussed this already +motivated beliefs + + align:start position:0% +motivated beliefs + + + align:start position:0% +motivated beliefs +are not necessarily a reason or want to + + align:start position:0% +are not necessarily a reason or want to + + + align:start position:0% +are not necessarily a reason or want to +be very careful with that + + align:start position:0% +be very careful with that + + + align:start position:0% +be very careful with that +that is as we said previously when we + + align:start position:0% +that is as we said previously when we + + + align:start position:0% +that is as we said previously when we +talked about health issues for example + + align:start position:0% +talked about health issues for example + + + align:start position:0% +talked about health issues for example +so if somebody + + align:start position:0% +so if somebody + + + align:start position:0% +so if somebody +does not want to know their health + + align:start position:0% +does not want to know their health + + + align:start position:0% +does not want to know their health +status because they want to feel happy + + align:start position:0% +status because they want to feel happy + + + align:start position:0% +status because they want to feel happy +or make themselves + + align:start position:0% +or make themselves + + + align:start position:0% +or make themselves +think that they're happy and they don't + + align:start position:0% +think that they're happy and they don't + + + align:start position:0% +think that they're happy and they don't +want to know that + + align:start position:0% +want to know that + + + align:start position:0% +want to know that +uh because you know they want to have a + + align:start position:0% +uh because you know they want to have a + + + align:start position:0% +uh because you know they want to have a +few years of their lives in which they + + align:start position:0% +few years of their lives in which they + + + align:start position:0% +few years of their lives in which they +think you know can we loot themselves + + align:start position:0% +think you know can we loot themselves + + + align:start position:0% +think you know can we loot themselves +and thinking they're happy + + align:start position:0% +and thinking they're happy + + + align:start position:0% +and thinking they're happy +they're healthy and happy um it's not + + align:start position:0% +they're healthy and happy um it's not + + + align:start position:0% +they're healthy and happy um it's not +obvious + + align:start position:0% +obvious + + + align:start position:0% +obvious +that they're making a mistake in a sense + + align:start position:0% +that they're making a mistake in a sense + + + align:start position:0% +that they're making a mistake in a sense +they could be making a mistake because + + align:start position:0% +they could be making a mistake because + + + align:start position:0% +they could be making a mistake because +potentially there could be health + + align:start position:0% +potentially there could be health + + + align:start position:0% +potentially there could be health +investments or health behaviors that + + align:start position:0% +investments or health behaviors that + + + align:start position:0% +investments or health behaviors that +they could engage in to improve their + + align:start position:0% +they could engage in to improve their + + + align:start position:0% +they could engage in to improve their +behavior + + align:start position:0% +behavior + + + align:start position:0% +behavior +but it could also just be that look + + align:start position:0% +but it could also just be that look + + + align:start position:0% +but it could also just be that look +there's actually not much one can do + + align:start position:0% +there's actually not much one can do + + + align:start position:0% +there's actually not much one can do +and so now there's if you intervene we + + align:start position:0% +and so now there's if you intervene we + + + align:start position:0% +and so now there's if you intervene we +might actually make things worse + + align:start position:0% +might actually make things worse + + + align:start position:0% +might actually make things worse +because there's somebody who actually + + align:start position:0% +because there's somebody who actually + + + align:start position:0% +because there's somebody who actually +doesn't even want to know um what's + + align:start position:0% +doesn't even want to know um what's + + + align:start position:0% +doesn't even want to know um what's +going on that's + + align:start position:0% +going on that's + + + align:start position:0% +going on that's +often that's actually the case but i'm + + align:start position:0% +often that's actually the case but i'm + + + align:start position:0% +often that's actually the case but i'm +sort of just flagging that for motivated + + align:start position:0% +sort of just flagging that for motivated + + + align:start position:0% +sort of just flagging that for motivated +beliefs + + align:start position:0% +beliefs + + + align:start position:0% +beliefs +when people derive utility from beliefs + + align:start position:0% +when people derive utility from beliefs + + + align:start position:0% +when people derive utility from beliefs +things get + + align:start position:0% +things get + + + align:start position:0% +things get +tricky quite easily let me talk about + + align:start position:0% +tricky quite easily let me talk about + + + align:start position:0% +tricky quite easily let me talk about +non-standard decision-making gender + + align:start position:0% +non-standard decision-making gender + + + align:start position:0% +non-standard decision-making gender +discrimination there's a clear case for + + align:start position:0% +discrimination there's a clear case for + + + align:start position:0% +discrimination there's a clear case for +for intervention that people don't get + + align:start position:0% +for intervention that people don't get + + + align:start position:0% +for intervention that people don't get +treated the right way + + align:start position:0% +treated the right way + + + align:start position:0% +treated the right way +as they should or any other + + align:start position:0% +as they should or any other + + + align:start position:0% +as they should or any other +discrimination + + align:start position:0% +discrimination + + + align:start position:0% +discrimination +um and then we talked about these other + + align:start position:0% +um and then we talked about these other + + + align:start position:0% +um and then we talked about these other +um aspects here of course then default + + align:start position:0% +um aspects here of course then default + + + align:start position:0% +um aspects here of course then default +frames and not just are not sort of + + align:start position:0% +frames and not just are not sort of + + + align:start position:0% +frames and not just are not sort of +necessarily reasons to intervene these + + align:start position:0% +necessarily reasons to intervene these + + + align:start position:0% +necessarily reasons to intervene these +are more like + + align:start position:0% +are more like + + + align:start position:0% +are more like +instruments that we can use to intervene + + align:start position:0% +instruments that we can use to intervene + + + align:start position:0% +instruments that we can use to intervene +you can sort of set defaults or frames + + align:start position:0% +you can sort of set defaults or frames + + + align:start position:0% +you can sort of set defaults or frames +or not just in certain ways that help us + + align:start position:0% +or not just in certain ways that help us + + + align:start position:0% +or not just in certain ways that help us +to make people make different choices in + + align:start position:0% +to make people make different choices in + + + align:start position:0% +to make people make different choices in +ways that are potentially + + align:start position:0% +ways that are potentially + + + align:start position:0% +ways that are potentially +fairly cheap and then also in ways that + + align:start position:0% +fairly cheap and then also in ways that + + + align:start position:0% +fairly cheap and then also in ways that +don't really necessarily distort + + align:start position:0% +don't really necessarily distort + + + align:start position:0% +don't really necessarily distort +behaviors of everyone i'm going to get + + align:start position:0% +behaviors of everyone i'm going to get + + + align:start position:0% +behaviors of everyone i'm going to get +back to that in a second + + align:start position:0% +back to that in a second + + + align:start position:0% +back to that in a second +when it comes to like poverty and mental + + align:start position:0% +when it comes to like poverty and mental + + + align:start position:0% +when it comes to like poverty and mental +health these are more like + + align:start position:0% +health these are more like + + + align:start position:0% +health these are more like +aspects where we say if poverty affects + + align:start position:0% +aspects where we say if poverty affects + + + align:start position:0% +aspects where we say if poverty affects +people's decision-making and causes + + align:start position:0% +people's decision-making and causes + + + align:start position:0% +people's decision-making and causes +behavioral biases or low productivity + + align:start position:0% +behavioral biases or low productivity + + + align:start position:0% +behavioral biases or low productivity +and so on then things like hash + + align:start position:0% +and so on then things like hash + + + align:start position:0% +and so on then things like hash +transfers and the why + + align:start position:0% +transfers and the why + + + align:start position:0% +transfers and the why +uh might help that's necessarily not + + align:start position:0% +uh might help that's necessarily not + + + align:start position:0% +uh might help that's necessarily not +sure that + + align:start position:0% +sure that + + + align:start position:0% +sure that +counts as like paternalism that's more + + align:start position:0% +counts as like paternalism that's more + + + align:start position:0% +counts as like paternalism that's more +like sort of support programs + + align:start position:0% +like sort of support programs + + + align:start position:0% +like sort of support programs +and then i think like happiness and + + align:start position:0% +and then i think like happiness and + + + align:start position:0% +and then i think like happiness and +mental health here you could think about + + align:start position:0% +mental health here you could think about + + + align:start position:0% +mental health here you could think about +um if you think people are misoptimizing + + align:start position:0% +um if you think people are misoptimizing + + + align:start position:0% +um if you think people are misoptimizing +in certain ways if they sort of under + + align:start position:0% +in certain ways if they sort of under + + + align:start position:0% +in certain ways if they sort of under +use um uh psychological services or if + + align:start position:0% +use um uh psychological services or if + + + align:start position:0% +use um uh psychological services or if +they sort of misoptimize in various ways + + align:start position:0% +they sort of misoptimize in various ways + + + align:start position:0% +they sort of misoptimize in various ways +we think you know they could be + + align:start position:0% +we think you know they could be + + + align:start position:0% +we think you know they could be +experimenting more they could be doing + + align:start position:0% +experimenting more they could be doing + + + align:start position:0% +experimenting more they could be doing +more things to + + align:start position:0% +more things to + + + align:start position:0% +more things to +improve their own happiness perhaps + + align:start position:0% +improve their own happiness perhaps + + + align:start position:0% +improve their own happiness perhaps +there's some ways in which you could + + align:start position:0% +there's some ways in which you could + + + align:start position:0% +there's some ways in which you could +push people to + + align:start position:0% +push people to + + + align:start position:0% +push people to +to experiment more and try to figure + + align:start position:0% +to experiment more and try to figure + + + align:start position:0% +to experiment more and try to figure +that out notice that i'm sort of + + align:start position:0% +that out notice that i'm sort of + + + align:start position:0% +that out notice that i'm sort of +careful here in my wording i'm saying + + align:start position:0% +careful here in my wording i'm saying + + + align:start position:0% +careful here in my wording i'm saying +pushing people to experiment and trying + + align:start position:0% +pushing people to experiment and trying + + + align:start position:0% +pushing people to experiment and trying +things out + + align:start position:0% +things out + + + align:start position:0% +things out +as opposed to like pushing people to do + + align:start position:0% +as opposed to like pushing people to do + + + align:start position:0% +as opposed to like pushing people to do +certain things for example + + align:start position:0% +certain things for example + + + align:start position:0% +certain things for example +if you say people should be working more + + align:start position:0% +if you say people should be working more + + + align:start position:0% +if you say people should be working more +um and their work should be + + align:start position:0% +um and their work should be + + + align:start position:0% +um and their work should be +working last and wow it's very hard for + + align:start position:0% +working last and wow it's very hard for + + + align:start position:0% +working last and wow it's very hard for +the government to actually understand + + align:start position:0% +the government to actually understand + + + align:start position:0% +the government to actually understand +what's good and bad + + align:start position:0% +what's good and bad + + + align:start position:0% +what's good and bad +um but it could be like people are maybe + + align:start position:0% +um but it could be like people are maybe + + + align:start position:0% +um but it could be like people are maybe +working too much and we could sort of + + align:start position:0% +working too much and we could sort of + + + align:start position:0% +working too much and we could sort of +push them towards trying to think about + + align:start position:0% +push them towards trying to think about + + + align:start position:0% +push them towards trying to think about +it and then see that what do they want + + align:start position:0% +it and then see that what do they want + + + align:start position:0% +it and then see that what do they want +to experiment and sort of learn more + + align:start position:0% +to experiment and sort of learn more + + + align:start position:0% +to experiment and sort of learn more +could they perhaps be happier by doing + + align:start position:0% +could they perhaps be happier by doing + + + align:start position:0% +could they perhaps be happier by doing +so + + align:start position:0% +so + + + align:start position:0% +so +any questions on this + + align:start position:0% + + + + align:start position:0% + +so then um there's different forms of + + align:start position:0% +so then um there's different forms of + + + align:start position:0% +so then um there's different forms of +paternalisms + + align:start position:0% +paternalisms + + + align:start position:0% +paternalisms +that you can think about just hard + + align:start position:0% +that you can think about just hard + + + align:start position:0% +that you can think about just hard +paternalism and there's soft paternalism + + align:start position:0% +paternalism and there's soft paternalism + + + align:start position:0% +paternalism and there's soft paternalism +now what's hard journalism essentially + + align:start position:0% +now what's hard journalism essentially + + + align:start position:0% +now what's hard journalism essentially +forcing choices on people + + align:start position:0% +forcing choices on people + + + align:start position:0% +forcing choices on people +changing prices significantly mandate + + align:start position:0% +changing prices significantly mandate + + + align:start position:0% +changing prices significantly mandate +choices or procedures + + align:start position:0% +choices or procedures + + + align:start position:0% +choices or procedures +outlaw products or including um taxes so + + align:start position:0% +outlaw products or including um taxes so + + + align:start position:0% +outlaw products or including um taxes so +you think of taxes sort of changing + + align:start position:0% +you think of taxes sort of changing + + + align:start position:0% +you think of taxes sort of changing +prices + + align:start position:0% +prices + + + align:start position:0% +prices +uh you can make things cheaper you can + + align:start position:0% +uh you can make things cheaper you can + + + align:start position:0% +uh you can make things cheaper you can +make things more expensive to people + + align:start position:0% +make things more expensive to people + + + align:start position:0% +make things more expensive to people +for people you can subsidize things you + + align:start position:0% +for people you can subsidize things you + + + align:start position:0% +for people you can subsidize things you +can outlaw a prop + + align:start position:0% + + + + align:start position:0% + +like up paternal agreement really + + align:start position:0% +like up paternal agreement really + + + align:start position:0% +like up paternal agreement really +significantly changing people's + + align:start position:0% +significantly changing people's + + + align:start position:0% +significantly changing people's +uh optimization problem uh in pretty + + align:start position:0% +uh optimization problem uh in pretty + + + align:start position:0% +uh optimization problem uh in pretty +harsh ways + + align:start position:0% +harsh ways + + + align:start position:0% +harsh ways +by essentially changing prices + + align:start position:0% +by essentially changing prices + + + align:start position:0% +by essentially changing prices +potentially + + align:start position:0% +potentially + + + align:start position:0% +potentially +um making some options infinitely + + align:start position:0% +um making some options infinitely + + + align:start position:0% +um making some options infinitely +expensive right it's just to say look + + align:start position:0% +expensive right it's just to say look + + + align:start position:0% +expensive right it's just to say look +i'm i'm just not allowing you to buy + + align:start position:0% +i'm i'm just not allowing you to buy + + + align:start position:0% +i'm i'm just not allowing you to buy +certain goods + + align:start position:0% +certain goods + + + align:start position:0% +certain goods +you can think of the price as just being + + align:start position:0% +you can think of the price as just being + + + align:start position:0% +you can think of the price as just being +infinitely expensive for those goods so + + align:start position:0% +infinitely expensive for those goods so + + + align:start position:0% +infinitely expensive for those goods so +that's hard for journalism + + align:start position:0% +that's hard for journalism + + + align:start position:0% +that's hard for journalism +now in contrast there's other forms of + + align:start position:0% +now in contrast there's other forms of + + + align:start position:0% +now in contrast there's other forms of +soft paternalism + + align:start position:0% +soft paternalism + + + align:start position:0% +soft paternalism +there's two versions of that there's + + align:start position:0% +there's two versions of that there's + + + align:start position:0% +there's two versions of that there's +what's called libertarian paternalism + + align:start position:0% +what's called libertarian paternalism + + + align:start position:0% +what's called libertarian paternalism +which is what + + align:start position:0% +which is what + + + align:start position:0% +which is what +sailor and sunstein are are known for + + align:start position:0% +sailor and sunstein are are known for + + + align:start position:0% +sailor and sunstein are are known for +which are essentially policies that + + align:start position:0% +which are essentially policies that + + + align:start position:0% +which are essentially policies that +constructively influence behavior while + + align:start position:0% +constructively influence behavior while + + + align:start position:0% +constructively influence behavior while +preserving or nearly preserving freedom + + align:start position:0% +preserving or nearly preserving freedom + + + align:start position:0% +preserving or nearly preserving freedom +of choice but that's essentially + + align:start position:0% +of choice but that's essentially + + + align:start position:0% +of choice but that's essentially +not just that we talked about previously + + align:start position:0% +not just that we talked about previously + + + align:start position:0% +not just that we talked about previously +that's essentially just saying like + + align:start position:0% +that's essentially just saying like + + + align:start position:0% +that's essentially just saying like +you can choose whatever you want but i'm + + align:start position:0% +you can choose whatever you want but i'm + + + align:start position:0% +you can choose whatever you want but i'm +trying to influence your behavior in + + align:start position:0% +trying to influence your behavior in + + + align:start position:0% +trying to influence your behavior in +certain ways + + align:start position:0% +certain ways + + + align:start position:0% +certain ways +that push you towards some options or + + align:start position:0% +that push you towards some options or + + + align:start position:0% +that push you towards some options or +some outcomes that we think are + + align:start position:0% +some outcomes that we think are + + + align:start position:0% +some outcomes that we think are +better than others right notice that the + + align:start position:0% +better than others right notice that the + + + align:start position:0% +better than others right notice that the +government or the policy maker needs to + + align:start position:0% +government or the policy maker needs to + + + align:start position:0% +government or the policy maker needs to +be very clear on what's good and what's + + align:start position:0% +be very clear on what's good and what's + + + align:start position:0% +be very clear on what's good and what's +bad and then sort of try to understand + + align:start position:0% +bad and then sort of try to understand + + + align:start position:0% +bad and then sort of try to understand +okay do you think here's some good + + align:start position:0% +okay do you think here's some good + + + align:start position:0% +okay do you think here's some good +behavior that we have identified + + align:start position:0% +behavior that we have identified + + + align:start position:0% +behavior that we have identified +let's now try to push you towards that + + align:start position:0% +let's now try to push you towards that + + + align:start position:0% +let's now try to push you towards that +direction + + align:start position:0% +direction + + + align:start position:0% +direction +but since we're kind of unsure what + + align:start position:0% +but since we're kind of unsure what + + + align:start position:0% +but since we're kind of unsure what +what people want um we're not sort of + + align:start position:0% +what people want um we're not sort of + + + align:start position:0% +what people want um we're not sort of +trying to exclude some option for some + + align:start position:0% +trying to exclude some option for some + + + align:start position:0% +trying to exclude some option for some +people because we might + + align:start position:0% +people because we might + + + align:start position:0% +people because we might +make things to worse for some people but + + align:start position:0% +make things to worse for some people but + + + align:start position:0% +make things to worse for some people but +instead just try to push you towards + + align:start position:0% +instead just try to push you towards + + + align:start position:0% +instead just try to push you towards +that + + align:start position:0% +that + + + align:start position:0% +that +um very much related to that is what's + + align:start position:0% +um very much related to that is what's + + + align:start position:0% +um very much related to that is what's +called a symmetric paternalism this is + + align:start position:0% +called a symmetric paternalism this is + + + align:start position:0% +called a symmetric paternalism this is +um + + align:start position:0% +um + + + align:start position:0% +um +the term from camera at all which are + + align:start position:0% +the term from camera at all which are + + + align:start position:0% +the term from camera at all which are +policies that help people who make + + align:start position:0% +policies that help people who make + + + align:start position:0% +policies that help people who make +mistakes while interfering minimally + + align:start position:0% +mistakes while interfering minimally + + + align:start position:0% +mistakes while interfering minimally +with people who um behave optimally that + + align:start position:0% +with people who um behave optimally that + + + align:start position:0% +with people who um behave optimally that +is to say + + align:start position:0% +is to say + + + align:start position:0% +is to say +you want to be careful um if you see + + align:start position:0% +you want to be careful um if you see + + + align:start position:0% +you want to be careful um if you see +people start + + align:start position:0% +people start + + + align:start position:0% +people start +doing certain things you want to be + + align:start position:0% +doing certain things you want to be + + + align:start position:0% +doing certain things you want to be +careful not to make things + + align:start position:0% +careful not to make things + + + align:start position:0% +careful not to make things +worse for some people suppose some + + align:start position:0% +worse for some people suppose some + + + align:start position:0% +worse for some people suppose some +people + + align:start position:0% +people + + + align:start position:0% +people +for a share of the people like half of + + align:start position:0% +for a share of the people like half of + + + align:start position:0% +for a share of the people like half of +the population is to the behavioral + + align:start position:0% +the population is to the behavioral + + + align:start position:0% +the population is to the behavioral +agents they make a bunch of mistakes + + align:start position:0% +agents they make a bunch of mistakes + + + align:start position:0% +agents they make a bunch of mistakes +and half of the population doesn't make + + align:start position:0% +and half of the population doesn't make + + + align:start position:0% +and half of the population doesn't make +mistakes at all + + align:start position:0% +mistakes at all + + + align:start position:0% +mistakes at all +now you could say and some people are + + align:start position:0% +now you could say and some people are + + + align:start position:0% +now you could say and some people are +smoking and some people are not smoking + + align:start position:0% +smoking and some people are not smoking + + + align:start position:0% +smoking and some people are not smoking +each of these + + align:start position:0% +each of these + + + align:start position:0% +each of these +you might sort of say well the smokers + + align:start position:0% +you might sort of say well the smokers + + + align:start position:0% +you might sort of say well the smokers +are making mistakes the behavioral + + align:start position:0% +are making mistakes the behavioral + + + align:start position:0% +are making mistakes the behavioral +smokers are making mistakes so let's + + align:start position:0% +smokers are making mistakes so let's + + + align:start position:0% +smokers are making mistakes so let's +help them + + align:start position:0% +help them + + + align:start position:0% +help them +so they can attack smoking right now + + align:start position:0% +so they can attack smoking right now + + + align:start position:0% +so they can attack smoking right now +what's going to happen is well you might + + align:start position:0% +what's going to happen is well you might + + + align:start position:0% +what's going to happen is well you might +sort of improve some outcomes for those + + align:start position:0% +sort of improve some outcomes for those + + + align:start position:0% +sort of improve some outcomes for those +people + + align:start position:0% +people + + + align:start position:0% +people +and that might be good but there will be + + align:start position:0% +and that might be good but there will be + + + align:start position:0% +and that might be good but there will be +other people who just like smoking and + + align:start position:0% +other people who just like smoking and + + + align:start position:0% +other people who just like smoking and +they're just happy they're very happy to + + align:start position:0% +they're just happy they're very happy to + + + align:start position:0% +they're just happy they're very happy to +smoke and they know that they're health + + align:start position:0% +smoke and they know that they're health + + + align:start position:0% +smoke and they know that they're health +risks but they decide to smoke anyway + + align:start position:0% +risks but they decide to smoke anyway + + + align:start position:0% +risks but they decide to smoke anyway +if you now start attack smoking you're + + align:start position:0% +if you now start attack smoking you're + + + align:start position:0% +if you now start attack smoking you're +going to distort their choices and make + + align:start position:0% +going to distort their choices and make + + + align:start position:0% +going to distort their choices and make +things worse off + + align:start position:0% +things worse off + + + align:start position:0% +things worse off +for them so uh in particular + + align:start position:0% +for them so uh in particular + + + align:start position:0% +for them so uh in particular +isometric paternalism is trying to avoid + + align:start position:0% +isometric paternalism is trying to avoid + + + align:start position:0% +isometric paternalism is trying to avoid +that + + align:start position:0% +that + + + align:start position:0% +that +by essentially saying like look we will + + align:start position:0% +by essentially saying like look we will + + + align:start position:0% +by essentially saying like look we will +try to + + align:start position:0% +try to + + + align:start position:0% +try to +come up with some some policies to make + + align:start position:0% +come up with some some policies to make + + + align:start position:0% +come up with some some policies to make +things better for some people + + align:start position:0% +things better for some people + + + align:start position:0% +things better for some people +but we want to be very careful not to + + align:start position:0% +but we want to be very careful not to + + + align:start position:0% +but we want to be very careful not to +make things worse um for others in + + align:start position:0% +make things worse um for others in + + + align:start position:0% +make things worse um for others in +particular people who are already + + align:start position:0% +particular people who are already + + + align:start position:0% +particular people who are already +optimizing + + align:start position:0% +optimizing + + + align:start position:0% +optimizing +anyway okay and so libertarian + + align:start position:0% +anyway okay and so libertarian + + + align:start position:0% +anyway okay and so libertarian +paternalism is a version of that or it's + + align:start position:0% +paternalism is a version of that or it's + + + align:start position:0% +paternalism is a version of that or it's +just very closely related with + + align:start position:0% +just very closely related with + + + align:start position:0% +just very closely related with +essentially to say + + align:start position:0% +essentially to say + + + align:start position:0% +essentially to say +if you preserve or nearly preserve + + align:start position:0% +if you preserve or nearly preserve + + + align:start position:0% +if you preserve or nearly preserve +freedom of choice + + align:start position:0% +freedom of choice + + + align:start position:0% +freedom of choice +then it often follows that you're not + + align:start position:0% +then it often follows that you're not + + + align:start position:0% +then it often follows that you're not +going to make things + + align:start position:0% +going to make things + + + align:start position:0% +going to make things +um worse for people optimizing anyway + + align:start position:0% +um worse for people optimizing anyway + + + align:start position:0% +um worse for people optimizing anyway +right because if somebody's optimizing + + align:start position:0% +right because if somebody's optimizing + + + align:start position:0% +right because if somebody's optimizing +anyway and i'm just essentially sort of + + align:start position:0% +anyway and i'm just essentially sort of + + + align:start position:0% +anyway and i'm just essentially sort of +just providing small nudges one way or + + align:start position:0% +just providing small nudges one way or + + + align:start position:0% +just providing small nudges one way or +the other + + align:start position:0% +the other + + + align:start position:0% +the other +then often i'm not going to make things + + align:start position:0% +then often i'm not going to make things + + + align:start position:0% +then often i'm not going to make things +worse for people optimizing anyway + + align:start position:0% +worse for people optimizing anyway + + + align:start position:0% +worse for people optimizing anyway +that's not necessarily always the case + + align:start position:0% +that's not necessarily always the case + + + align:start position:0% +that's not necessarily always the case +but it's pretty much + + align:start position:0% +but it's pretty much + + + align:start position:0% +but it's pretty much +closely related i'm saying there could + + align:start position:0% +closely related i'm saying there could + + + align:start position:0% +closely related i'm saying there could +be some people who just smoke they have + + align:start position:0% +be some people who just smoke they have + + + align:start position:0% +be some people who just smoke they have +like five cigarettes a day and one + + align:start position:0% +like five cigarettes a day and one + + + align:start position:0% +like five cigarettes a day and one +cigarette a day and there could be + + align:start position:0% +cigarette a day and there could be + + + align:start position:0% +cigarette a day and there could be +there could be suppose there's two types + + align:start position:0% +there could be suppose there's two types + + + align:start position:0% +there could be suppose there's two types +of people there's one type of people who + + align:start position:0% +of people there's one type of people who + + + align:start position:0% +of people there's one type of people who +are essentially + + align:start position:0% +are essentially + + + align:start position:0% +are essentially +making mistakes uh there have + + align:start position:0% +making mistakes uh there have + + + align:start position:0% +making mistakes uh there have +internalities in the sense that + + align:start position:0% +internalities in the sense that + + + align:start position:0% +internalities in the sense that +misunderstand the consequences of + + align:start position:0% +misunderstand the consequences of + + + align:start position:0% +misunderstand the consequences of +smoking for their future self + + align:start position:0% +smoking for their future self + + + align:start position:0% +smoking for their future self +these are people who make mistakes now + + align:start position:0% +these are people who make mistakes now + + + align:start position:0% +these are people who make mistakes now +those people we might want to help + + align:start position:0% +those people we might want to help + + + align:start position:0% +those people we might want to help +by increasing the price of smoking by + + align:start position:0% +by increasing the price of smoking by + + + align:start position:0% +by increasing the price of smoking by +taxing it or in other ways + + align:start position:0% +taxing it or in other ways + + + align:start position:0% +taxing it or in other ways +okay but there could be other people who + + align:start position:0% +okay but there could be other people who + + + align:start position:0% +okay but there could be other people who +essentially are fully aware of the + + align:start position:0% +essentially are fully aware of the + + + align:start position:0% +essentially are fully aware of the +consequences of smoking for the future + + align:start position:0% +consequences of smoking for the future + + + align:start position:0% +consequences of smoking for the future +health + + align:start position:0% +health + + + align:start position:0% +health +and those are optimizing and they're + + align:start position:0% +and those are optimizing and they're + + + align:start position:0% +and those are optimizing and they're +essentially in the optimization + + align:start position:0% +essentially in the optimization + + + align:start position:0% +essentially in the optimization +to decide that smoking is optimal for + + align:start position:0% +to decide that smoking is optimal for + + + align:start position:0% +to decide that smoking is optimal for +them + + align:start position:0% + + + + align:start position:0% + +those people might be made worse off by + + align:start position:0% +those people might be made worse off by + + + align:start position:0% +those people might be made worse off by +cigarette taxes because essentially + + align:start position:0% +cigarette taxes because essentially + + + align:start position:0% +cigarette taxes because essentially +what would you do with those taxes or + + align:start position:0% +what would you do with those taxes or + + + align:start position:0% +what would you do with those taxes or +any other taxes you distort people's + + align:start position:0% +any other taxes you distort people's + + + align:start position:0% +any other taxes you distort people's +behaviors + + align:start position:0% +behaviors + + + align:start position:0% +behaviors +and um you know then we have a situation + + align:start position:0% +and um you know then we have a situation + + + align:start position:0% +and um you know then we have a situation +where + + align:start position:0% +where + + + align:start position:0% +where +we have potentially made some people + + align:start position:0% +we have potentially made some people + + + align:start position:0% +we have potentially made some people +better off but also other people worse + + align:start position:0% +better off but also other people worse + + + align:start position:0% +better off but also other people worse +off + + align:start position:0% +off + + + align:start position:0% +off +and a lot of people would then be upset + + align:start position:0% +and a lot of people would then be upset + + + align:start position:0% +and a lot of people would then be upset +or like unhappy about this because you + + align:start position:0% +or like unhappy about this because you + + + align:start position:0% +or like unhappy about this because you +know + + align:start position:0% +know + + + align:start position:0% +know +we say like look there's people who + + align:start position:0% +we say like look there's people who + + + align:start position:0% +we say like look there's people who +screw up their choices or they don't + + align:start position:0% +screw up their choices or they don't + + + align:start position:0% +screw up their choices or they don't +know what they're doing + + align:start position:0% +know what they're doing + + + align:start position:0% +know what they're doing +uh they're trying to help them but now + + align:start position:0% +uh they're trying to help them but now + + + align:start position:0% +uh they're trying to help them but now +that comes at the cost of others who are + + align:start position:0% +that comes at the cost of others who are + + + align:start position:0% +that comes at the cost of others who are +actually perfectly optimizing and in + + align:start position:0% +actually perfectly optimizing and in + + + align:start position:0% +actually perfectly optimizing and in +some sense that gets you in trouble + + align:start position:0% +some sense that gets you in trouble + + + align:start position:0% +some sense that gets you in trouble +because you know they will be unhappy + + align:start position:0% +because you know they will be unhappy + + + align:start position:0% +because you know they will be unhappy +people on the other + + align:start position:0% +people on the other + + + align:start position:0% +people on the other +side of it potentially quite a few of + + align:start position:0% +side of it potentially quite a few of + + + align:start position:0% +side of it potentially quite a few of +them all right + + align:start position:0% +them all right + + + align:start position:0% +them all right +so what are not arguments against + + align:start position:0% +so what are not arguments against + + + align:start position:0% +so what are not arguments against +paternalism or + + align:start position:0% +paternalism or + + + align:start position:0% +paternalism or +you know why is paternalism bad you + + align:start position:0% +you know why is paternalism bad you + + + align:start position:0% +you know why is paternalism bad you +might sort of say um + + align:start position:0% +might sort of say um + + + align:start position:0% +might sort of say um +that sounds all pretty good but like now + + align:start position:0% +that sounds all pretty good but like now + + + align:start position:0% +that sounds all pretty good but like now +you try to actually implement this + + align:start position:0% +you try to actually implement this + + + align:start position:0% +you try to actually implement this +uh what's bad about it + + align:start position:0% + + + + align:start position:0% + +so one typical argument is to say well + + align:start position:0% +so one typical argument is to say well + + + align:start position:0% +so one typical argument is to say well +people make mistakes + + align:start position:0% +people make mistakes + + + align:start position:0% +people make mistakes +well the government is made out of + + align:start position:0% +well the government is made out of + + + align:start position:0% +well the government is made out of +people and so + + align:start position:0% +people and so + + + align:start position:0% +people and so +uh how do we know that the people who + + align:start position:0% +uh how do we know that the people who + + + align:start position:0% +uh how do we know that the people who +are in the government actually know + + align:start position:0% +are in the government actually know + + + align:start position:0% +are in the government actually know +better + + align:start position:0% +better + + + align:start position:0% +better +than people uh uh choose for themselves + + align:start position:0% +than people uh uh choose for themselves + + + align:start position:0% +than people uh uh choose for themselves +and so if then the government + + align:start position:0% +and so if then the government + + + align:start position:0% +and so if then the government +uh is is also making mistakes then + + align:start position:0% +uh is is also making mistakes then + + + align:start position:0% +uh is is also making mistakes then +essentially choosing for others + + align:start position:0% +essentially choosing for others + + + align:start position:0% +essentially choosing for others +it's not clear that it makes things + + align:start position:0% +it's not clear that it makes things + + + align:start position:0% +it's not clear that it makes things +better or it could make things + + align:start position:0% +better or it could make things + + + align:start position:0% +better or it could make things +worse in particular if you think that + + align:start position:0% +worse in particular if you think that + + + align:start position:0% +worse in particular if you think that +the government + + align:start position:0% +the government + + + align:start position:0% +the government +doesn't have enough information so i + + align:start position:0% +doesn't have enough information so i + + + align:start position:0% +doesn't have enough information so i +know what's best for me + + align:start position:0% +know what's best for me + + + align:start position:0% +know what's best for me +and so therefore um i'm best equipped to + + align:start position:0% +and so therefore um i'm best equipped to + + + align:start position:0% +and so therefore um i'm best equipped to +make decisions for myself because you + + align:start position:0% +make decisions for myself because you + + + align:start position:0% +make decisions for myself because you +might potentially + + align:start position:0% +might potentially + + + align:start position:0% +might potentially +in particular if there's hydrogenated + + align:start position:0% +in particular if there's hydrogenated + + + align:start position:0% +in particular if there's hydrogenated +you might make people some people better + + align:start position:0% +you might make people some people better + + + align:start position:0% +you might make people some people better +off but that might come at the cost of + + align:start position:0% +off but that might come at the cost of + + + align:start position:0% +off but that might come at the cost of +some others + + align:start position:0% +some others + + + align:start position:0% +some others +and then it's not clear that on average + + align:start position:0% +and then it's not clear that on average + + + align:start position:0% +and then it's not clear that on average +your overall be making things better + + align:start position:0% +your overall be making things better + + + align:start position:0% +your overall be making things better +and that's a very important in + + align:start position:0% +and that's a very important in + + + align:start position:0% +and that's a very important in +particular + + align:start position:0% +particular + + + align:start position:0% +particular +um that comes up a lot in if you think + + align:start position:0% +um that comes up a lot in if you think + + + align:start position:0% +um that comes up a lot in if you think +1475 for example which is political + + align:start position:0% +1475 for example which is political + + + align:start position:0% +1475 for example which is political +economy + + align:start position:0% +economy + + + align:start position:0% +economy +that would come up because you know + + align:start position:0% +that would come up because you know + + + align:start position:0% +that would come up because you know +while we might want to help people we're + + align:start position:0% +while we might want to help people we're + + + align:start position:0% +while we might want to help people we're +going to give people money but then the + + align:start position:0% +going to give people money but then the + + + align:start position:0% +going to give people money but then the +government gets essentially a + + align:start position:0% +government gets essentially a + + + align:start position:0% +government gets essentially a +village government or whatever gets like + + align:start position:0% +village government or whatever gets like + + + align:start position:0% +village government or whatever gets like +captured by elites + + align:start position:0% +captured by elites + + + align:start position:0% +captured by elites +to keep the money for themselves and so + + align:start position:0% +to keep the money for themselves and so + + + align:start position:0% +to keep the money for themselves and so +the more + + align:start position:0% +the more + + + align:start position:0% +the more +um they give the more opportunity they + + align:start position:0% +um they give the more opportunity they + + + align:start position:0% +um they give the more opportunity they +give for that box with different + + align:start position:0% +give for that box with different + + + align:start position:0% +give for that box with different +government resources and power + + align:start position:0% +government resources and power + + + align:start position:0% +government resources and power +the more opportunities to uh for misuse + + align:start position:0% +the more opportunities to uh for misuse + + + align:start position:0% +the more opportunities to uh for misuse +and corruption and so on and so forth + + align:start position:0% +and corruption and so on and so forth + + + align:start position:0% +and corruption and so on and so forth +right so that's essentially saying that + + align:start position:0% +right so that's essentially saying that + + + align:start position:0% +right so that's essentially saying that +so there's one class of argument is to + + align:start position:0% +so there's one class of argument is to + + + align:start position:0% +so there's one class of argument is to +say well even if the government wanted + + align:start position:0% +say well even if the government wanted + + + align:start position:0% +say well even if the government wanted +to + + align:start position:0% +to + + + align:start position:0% +to +do the very best for people if the + + align:start position:0% +do the very best for people if the + + + align:start position:0% +do the very best for people if the +government wanted eyes for + + align:start position:0% +government wanted eyes for + + + align:start position:0% +government wanted eyes for +for for for its citizens that would be + + align:start position:0% +for for for its citizens that would be + + + align:start position:0% +for for for its citizens that would be +hard to do because it doesn't know how + + align:start position:0% +hard to do because it doesn't know how + + + align:start position:0% +hard to do because it doesn't know how +to do that it has inherent problems with + + align:start position:0% +to do that it has inherent problems with + + + align:start position:0% +to do that it has inherent problems with +that + + align:start position:0% +that + + + align:start position:0% +that +because of uh heterogeneity knowledge + + align:start position:0% +because of uh heterogeneity knowledge + + + align:start position:0% +because of uh heterogeneity knowledge +issues and so on and so forth + + align:start position:0% +issues and so on and so forth + + + align:start position:0% +issues and so on and so forth +um and then there's a second second type + + align:start position:0% +um and then there's a second second type + + + align:start position:0% +um and then there's a second second type +of argument which um + + align:start position:0% +of argument which um + + + align:start position:0% +of argument which um +um uh chad just mentioned which is + + align:start position:0% +um uh chad just mentioned which is + + + align:start position:0% +um uh chad just mentioned which is +well who's there to say that the + + align:start position:0% +well who's there to say that the + + + align:start position:0% +well who's there to say that the +government is actually + + align:start position:0% +government is actually + + + align:start position:0% +government is actually +benevolent and actually wants people to + + align:start position:0% +benevolent and actually wants people to + + + align:start position:0% +benevolent and actually wants people to +be better off maybe that just + + align:start position:0% +be better off maybe that just + + + align:start position:0% +be better off maybe that just +want to get rich and so on and so forth + + align:start position:0% +want to get rich and so on and so forth + + + align:start position:0% +want to get rich and so on and so forth +and so now if we let them make choices + + align:start position:0% +and so now if we let them make choices + + + align:start position:0% +and so now if we let them make choices +then that opens the door for corruption + + align:start position:0% +then that opens the door for corruption + + + align:start position:0% +then that opens the door for corruption +misuse of money and so on and so forth + + align:start position:0% +misuse of money and so on and so forth + + + align:start position:0% +misuse of money and so on and so forth +so there's sort of a slippery slope + + align:start position:0% +so there's sort of a slippery slope + + + align:start position:0% +so there's sort of a slippery slope +argument to say well there's some things + + align:start position:0% +argument to say well there's some things + + + align:start position:0% +argument to say well there's some things +which i'm going to argue for some things + + align:start position:0% +which i'm going to argue for some things + + + align:start position:0% +which i'm going to argue for some things +it's pretty clear that + + align:start position:0% +it's pretty clear that + + + align:start position:0% +it's pretty clear that +we can make big things better or make + + align:start position:0% +we can make big things better or make + + + align:start position:0% +we can make big things better or make +people some people at least better off + + align:start position:0% +people some people at least better off + + + align:start position:0% +people some people at least better off +without hurting others and there's so + + align:start position:0% +without hurting others and there's so + + + align:start position:0% +without hurting others and there's so +some cases where you say let's + + align:start position:0% +some cases where you say let's + + + align:start position:0% +some cases where you say let's +have the government do that or whatever + + align:start position:0% +have the government do that or whatever + + + align:start position:0% +have the government do that or whatever +the set policies that help people + + align:start position:0% +the set policies that help people + + + align:start position:0% +the set policies that help people +by the way it doesn't have to be + + align:start position:0% +by the way it doesn't have to be + + + align:start position:0% +by the way it doesn't have to be +necessarily the government but + + align:start position:0% +necessarily the government but + + + align:start position:0% +necessarily the government but +also be like company + + align:start position:0% + + + + align:start position:0% + +um but then you know i said well once we + + align:start position:0% +um but then you know i said well once we + + + align:start position:0% +um but then you know i said well once we +start with like some things and they're + + align:start position:0% +start with like some things and they're + + + align:start position:0% +start with like some things and they're +gonna do more things and at some point + + align:start position:0% +gonna do more things and at some point + + + align:start position:0% +gonna do more things and at some point +they reach points for like the + + align:start position:0% +they reach points for like the + + + align:start position:0% +they reach points for like the +government actually doesn't know what + + align:start position:0% +government actually doesn't know what + + + align:start position:0% +government actually doesn't know what +they're doing and then they make things + + align:start position:0% +they're doing and then they make things + + + align:start position:0% +they're doing and then they make things +um worse off so i have a bunch of + + align:start position:0% +um worse off so i have a bunch of + + + align:start position:0% +um worse off so i have a bunch of +different + + align:start position:0% +different + + + align:start position:0% +different +um arguments here i think you mentioned + + align:start position:0% +um arguments here i think you mentioned + + + align:start position:0% +um arguments here i think you mentioned +quite a few of them + + align:start position:0% +quite a few of them + + + align:start position:0% +quite a few of them +uh there's informational issues sort of + + align:start position:0% +uh there's informational issues sort of + + + align:start position:0% +uh there's informational issues sort of +not understanding preferences people are + + align:start position:0% +not understanding preferences people are + + + align:start position:0% +not understanding preferences people are +optimizing anyway + + align:start position:0% +optimizing anyway + + + align:start position:0% +optimizing anyway +there's this is what carmen said you + + align:start position:0% +there's this is what carmen said you + + + align:start position:0% +there's this is what carmen said you +know or we discussed previously that + + align:start position:0% +know or we discussed previously that + + + align:start position:0% +know or we discussed previously that +people + + align:start position:0% +people + + + align:start position:0% +people +some people's choices might be distorted + + align:start position:0% +some people's choices might be distorted + + + align:start position:0% +some people's choices might be distorted +so these are issues of heterogeneity + + align:start position:0% +so these are issues of heterogeneity + + + align:start position:0% +so these are issues of heterogeneity +often + + align:start position:0% +often + + + align:start position:0% +often +uh then the sort of the government is + + align:start position:0% +uh then the sort of the government is + + + align:start position:0% +uh then the sort of the government is +terrible and wastes money anyway + + align:start position:0% +terrible and wastes money anyway + + + align:start position:0% +terrible and wastes money anyway +um the government doesn't have like + + align:start position:0% +um the government doesn't have like + + + align:start position:0% +um the government doesn't have like +people's best + + align:start position:0% +people's best + + + align:start position:0% +people's best +interests and minds just regulatory + + align:start position:0% +interests and minds just regulatory + + + align:start position:0% +interests and minds just regulatory +capture i think + + align:start position:0% +capture i think + + + align:start position:0% +capture i think +this is also what um uh chad mentioned + + align:start position:0% +this is also what um uh chad mentioned + + + align:start position:0% +this is also what um uh chad mentioned +uh freedom of choice then there's some + + align:start position:0% +uh freedom of choice then there's some + + + align:start position:0% +uh freedom of choice then there's some +other arguments which is freedom of + + align:start position:0% +other arguments which is freedom of + + + align:start position:0% +other arguments which is freedom of +choice matters per se that's a little + + align:start position:0% +choice matters per se that's a little + + + align:start position:0% +choice matters per se that's a little +trickier to address but just here look + + align:start position:0% +trickier to address but just here look + + + align:start position:0% +trickier to address but just here look +that's just + + align:start position:0% +that's just + + + align:start position:0% +that's just +i want to choose for myself and i don't + + align:start position:0% +i want to choose for myself and i don't + + + align:start position:0% +i want to choose for myself and i don't +want the government to tell me anything + + align:start position:0% +want the government to tell me anything + + + align:start position:0% +want the government to tell me anything +and that's important by itself this is + + align:start position:0% +and that's important by itself this is + + + align:start position:0% +and that's important by itself this is +not about the outcome this is about the + + align:start position:0% +not about the outcome this is about the + + + align:start position:0% +not about the outcome this is about the +freedom of choice mattering itself + + align:start position:0% +freedom of choice mattering itself + + + align:start position:0% +freedom of choice mattering itself +um then there's a similarly there's + + align:start position:0% +um then there's a similarly there's + + + align:start position:0% +um then there's a similarly there's +arguments about the good people just + + align:start position:0% +arguments about the good people just + + + align:start position:0% +arguments about the good people just +don't like hard paternalism they just + + align:start position:0% +don't like hard paternalism they just + + + align:start position:0% +don't like hard paternalism they just +don't like to be told or like + + align:start position:0% +don't like to be told or like + + + align:start position:0% +don't like to be told or like +certain options uh to be + + align:start position:0% +certain options uh to be + + + align:start position:0% +certain options uh to be +excluded for those reasons perhaps + + align:start position:0% +excluded for those reasons perhaps + + + align:start position:0% +excluded for those reasons perhaps +partially because they don't want the + + align:start position:0% +partially because they don't want the + + + align:start position:0% +partially because they don't want the +government to be + + align:start position:0% +government to be + + + align:start position:0% +government to be +powerful and then there's finally + + align:start position:0% +powerful and then there's finally + + + align:start position:0% +powerful and then there's finally +there's some sort of practical problems + + align:start position:0% +there's some sort of practical problems + + + align:start position:0% +there's some sort of practical problems +which is + + align:start position:0% +which is + + + align:start position:0% +which is +you know once we agree that we want sort + + align:start position:0% +you know once we agree that we want sort + + + align:start position:0% +you know once we agree that we want sort +of some paternalistic policies + + align:start position:0% +of some paternalistic policies + + + align:start position:0% +of some paternalistic policies +which policy should we choose and how do + + align:start position:0% +which policy should we choose and how do + + + align:start position:0% +which policy should we choose and how do +we know what it would which is better + + align:start position:0% +we know what it would which is better + + + align:start position:0% +we know what it would which is better +than another i'm going to get back to + + align:start position:0% +than another i'm going to get back to + + + align:start position:0% +than another i'm going to get back to +that in a bit as well + + align:start position:0% +that in a bit as well + + + align:start position:0% +that in a bit as well +there's also practical implementation + + align:start position:0% +there's also practical implementation + + + align:start position:0% +there's also practical implementation +problems just to say the government even + + align:start position:0% +problems just to say the government even + + + align:start position:0% +problems just to say the government even +if the government wanted to do the right + + align:start position:0% +if the government wanted to do the right + + + align:start position:0% +if the government wanted to do the right +things + + align:start position:0% +things + + + align:start position:0% +things +the government is often like inefficient + + align:start position:0% +the government is often like inefficient + + + align:start position:0% +the government is often like inefficient +and so on and so forth and so it's + + align:start position:0% +and so on and so forth and so it's + + + align:start position:0% +and so on and so forth and so it's +just costly to do and practically it's + + align:start position:0% +just costly to do and practically it's + + + align:start position:0% +just costly to do and practically it's +just hard to do certain things + + align:start position:0% +just hard to do certain things + + + align:start position:0% +just hard to do certain things +now what are arguments in favor i'm + + align:start position:0% +now what are arguments in favor i'm + + + align:start position:0% +now what are arguments in favor i'm +going to just + + align:start position:0% +going to just + + + align:start position:0% +going to just +speed things up a bit so the arguments + + align:start position:0% +speed things up a bit so the arguments + + + align:start position:0% +speed things up a bit so the arguments +in paper are often like very simple + + align:start position:0% +in paper are often like very simple + + + align:start position:0% +in paper are often like very simple +which is that people make mistakes + + align:start position:0% +which is that people make mistakes + + + align:start position:0% +which is that people make mistakes +people screw up and they can help them + + align:start position:0% +people screw up and they can help them + + + align:start position:0% +people screw up and they can help them +potentially screw up less + + align:start position:0% +potentially screw up less + + + align:start position:0% +potentially screw up less +um people often also don't like to + + align:start position:0% +um people often also don't like to + + + align:start position:0% +um people often also don't like to +necessarily make choose choices for + + align:start position:0% +necessarily make choose choices for + + + align:start position:0% +necessarily make choose choices for +themselves that could be just because + + align:start position:0% +themselves that could be just because + + + align:start position:0% +themselves that could be just because +they don't + + align:start position:0% +they don't + + + align:start position:0% +they don't +like doing it it could also be just it's + + align:start position:0% +like doing it it could also be just it's + + + align:start position:0% +like doing it it could also be just it's +costly to do that and that's just + + align:start position:0% +costly to do that and that's just + + + align:start position:0% +costly to do that and that's just +there's some activities that are just + + align:start position:0% +there's some activities that are just + + + align:start position:0% +there's some activities that are just +hard to do + + align:start position:0% +hard to do + + + align:start position:0% +hard to do +and i'd rather have somebody regulate + + align:start position:0% +and i'd rather have somebody regulate + + + align:start position:0% +and i'd rather have somebody regulate +this for me as opposed to like + + align:start position:0% +this for me as opposed to like + + + align:start position:0% +this for me as opposed to like +me having to choose or make these + + align:start position:0% +me having to choose or make these + + + align:start position:0% +me having to choose or make these +choices all for myself + + align:start position:0% +choices all for myself + + + align:start position:0% +choices all for myself +an example would be suppose you know + + align:start position:0% +an example would be suppose you know + + + align:start position:0% +an example would be suppose you know +there's like insurance plans or some + + align:start position:0% +there's like insurance plans or some + + + align:start position:0% +there's like insurance plans or some +form of like retirement plans and so on + + align:start position:0% +form of like retirement plans and so on + + + align:start position:0% +form of like retirement plans and so on +if there's some options that are just + + align:start position:0% +if there's some options that are just + + + align:start position:0% +if there's some options that are just +terrible and they just would be + + align:start position:0% +terrible and they just would be + + + align:start position:0% +terrible and they just would be +exploiting me and making me worse off + + align:start position:0% +exploiting me and making me worse off + + + align:start position:0% +exploiting me and making me worse off +i could probably figure it out if you + + align:start position:0% +i could probably figure it out if you + + + align:start position:0% +i could probably figure it out if you +gave me these plans and like i spent + + align:start position:0% +gave me these plans and like i spent + + + align:start position:0% +gave me these plans and like i spent +like a day + + align:start position:0% +like a day + + + align:start position:0% +like a day +um studying them but you know i have + + align:start position:0% +um studying them but you know i have + + + align:start position:0% +um studying them but you know i have +like better stuff to do and i'd rather + + align:start position:0% +like better stuff to do and i'd rather + + + align:start position:0% +like better stuff to do and i'd rather +have somebody else screen out sort of + + align:start position:0% +have somebody else screen out sort of + + + align:start position:0% +have somebody else screen out sort of +the bad plans + + align:start position:0% +the bad plans + + + align:start position:0% +the bad plans +and sort of then offer me sort of the + + align:start position:0% +and sort of then offer me sort of the + + + align:start position:0% +and sort of then offer me sort of the +the choices that + + align:start position:0% +the choices that + + + align:start position:0% +the choices that +try to not exploit me and then make + + align:start position:0% +try to not exploit me and then make + + + align:start position:0% +try to not exploit me and then make +maybe + + align:start position:0% +maybe + + + align:start position:0% +maybe +some choices from a limited set that's + + align:start position:0% +some choices from a limited set that's + + + align:start position:0% +some choices from a limited set that's +not to say i couldn't do it but it's + + align:start position:0% +not to say i couldn't do it but it's + + + align:start position:0% +not to say i couldn't do it but it's +just sort of saying it's inefficient for + + align:start position:0% +just sort of saying it's inefficient for + + + align:start position:0% +just sort of saying it's inefficient for +me to + + align:start position:0% +me to + + + align:start position:0% +me to +to deal with these things um on my own + + align:start position:0% +to deal with these things um on my own + + + align:start position:0% +to deal with these things um on my own +now and then finally and this is i think + + align:start position:0% +now and then finally and this is i think + + + align:start position:0% +now and then finally and this is i think +one of the most important arguments is + + align:start position:0% +one of the most important arguments is + + + align:start position:0% +one of the most important arguments is +that + + align:start position:0% + + + + align:start position:0% + +there are a lot of soft paternalism + + align:start position:0% +there are a lot of soft paternalism + + + align:start position:0% +there are a lot of soft paternalism +regimes where people can opt out + + align:start position:0% +regimes where people can opt out + + + align:start position:0% +regimes where people can opt out +and are unaffected potentially so when + + align:start position:0% +and are unaffected potentially so when + + + align:start position:0% +and are unaffected potentially so when +you go back to like the previous + + align:start position:0% +you go back to like the previous + + + align:start position:0% +you go back to like the previous +concerns + + align:start position:0% +concerns + + + align:start position:0% +concerns +um that people might have these are + + align:start position:0% +um that people might have these are + + + align:start position:0% +um that people might have these are +often arguments against hard + + align:start position:0% +often arguments against hard + + + align:start position:0% +often arguments against hard +journalism these are often things about + + align:start position:0% +journalism these are often things about + + + align:start position:0% +journalism these are often things about +like government wasting money and so on + + align:start position:0% +like government wasting money and so on + + + align:start position:0% +like government wasting money and so on +and so forth + + align:start position:0% +and so forth + + + align:start position:0% +and so forth +if this is about like sending reminders + + align:start position:0% +if this is about like sending reminders + + + align:start position:0% +if this is about like sending reminders +or like + + align:start position:0% +or like + + + align:start position:0% +or like +phrasing letters in one way versus + + align:start position:0% +phrasing letters in one way versus + + + align:start position:0% +phrasing letters in one way versus +another in some simple ways + + align:start position:0% +another in some simple ways + + + align:start position:0% +another in some simple ways +or putting food or putting apples next + + align:start position:0% +or putting food or putting apples next + + + align:start position:0% +or putting food or putting apples next +to like the counter versus like candy + + align:start position:0% +to like the counter versus like candy + + + align:start position:0% +to like the counter versus like candy +bars + + align:start position:0% +bars + + + align:start position:0% +bars +this is not about the government taking + + align:start position:0% +this is not about the government taking + + + align:start position:0% +this is not about the government taking +over or like restricting people's free + + align:start position:0% +over or like restricting people's free + + + align:start position:0% +over or like restricting people's free +choice + + align:start position:0% +choice + + + align:start position:0% +choice +it's rather to say which trying to make + + align:start position:0% +it's rather to say which trying to make + + + align:start position:0% +it's rather to say which trying to make +people better off in some simple ways + + align:start position:0% +people better off in some simple ways + + + align:start position:0% +people better off in some simple ways +you need to do and um + + align:start position:0% +you need to do and um + + + align:start position:0% +you need to do and um +and so a lot of these uh criticism or + + align:start position:0% +and so a lot of these uh criticism or + + + align:start position:0% +and so a lot of these uh criticism or +arguments go away once you go into like + + align:start position:0% +arguments go away once you go into like + + + align:start position:0% +arguments go away once you go into like +soft paternalism um + + align:start position:0% +soft paternalism um + + + align:start position:0% +soft paternalism um +territory and so then um + + align:start position:0% +territory and so then um + + + align:start position:0% +territory and so then um +at the end of the day i think it's hard + + align:start position:0% +at the end of the day i think it's hard + + + align:start position:0% +at the end of the day i think it's hard +to make arguments often for + + align:start position:0% +to make arguments often for + + + align:start position:0% +to make arguments often for +journalism because you need to be very + + align:start position:0% +journalism because you need to be very + + + align:start position:0% +journalism because you need to be very +confident things right + + align:start position:0% +confident things right + + + align:start position:0% +confident things right +it's much easier to argue for + + align:start position:0% +it's much easier to argue for + + + align:start position:0% +it's much easier to argue for +self-paternalism + + align:start position:0% +self-paternalism + + + align:start position:0% +self-paternalism +simple policies that are not expensive + + align:start position:0% +simple policies that are not expensive + + + align:start position:0% +simple policies that are not expensive +that arguably are not + + align:start position:0% +that arguably are not + + + align:start position:0% +that arguably are not +hurting a lot of people but make at + + align:start position:0% +hurting a lot of people but make at + + + align:start position:0% +hurting a lot of people but make at +least some people um better off + + align:start position:0% +least some people um better off + + + align:start position:0% +least some people um better off +um now i think uh so it's a little hard + + align:start position:0% +um now i think uh so it's a little hard + + + align:start position:0% +um now i think uh so it's a little hard +to see maybe um but + + align:start position:0% +to see maybe um but + + + align:start position:0% +to see maybe um but +sometimes it's actually quite hard to + + align:start position:0% +sometimes it's actually quite hard to + + + align:start position:0% +sometimes it's actually quite hard to +figure out whether people are making + + align:start position:0% +figure out whether people are making + + + align:start position:0% +figure out whether people are making +mistakes + + align:start position:0% +mistakes + + + align:start position:0% +mistakes +this is for example here um uh um + + align:start position:0% +this is for example here um uh um + + + align:start position:0% +this is for example here um uh um +a survey from gallup that looks at + + align:start position:0% +a survey from gallup that looks at + + + align:start position:0% +a survey from gallup that looks at +americans and looks at like + + align:start position:0% +americans and looks at like + + + align:start position:0% +americans and looks at like +um people uh who call themselves very or + + align:start position:0% +um people uh who call themselves very or + + + align:start position:0% +um people uh who call themselves very or +somewhat overweight versus + + align:start position:0% +somewhat overweight versus + + + align:start position:0% +somewhat overweight versus +the percentage who are overweight and + + align:start position:0% +the percentage who are overweight and + + + align:start position:0% +the percentage who are overweight and +obese by some standards by the cdc and + + align:start position:0% +obese by some standards by the cdc and + + + align:start position:0% +obese by some standards by the cdc and +so on + + align:start position:0% +so on + + + align:start position:0% +so on +and so here you see essentially that + + align:start position:0% +and so here you see essentially that + + + align:start position:0% +and so here you see essentially that +people tend to + + align:start position:0% +people tend to + + + align:start position:0% +people tend to +uh the fraction war of these + + align:start position:0% + + + + align:start position:0% + +tends to be quite high intensity + + align:start position:0% +tends to be quite high intensity + + + align:start position:0% +tends to be quite high intensity +increasing by people's perception of + + align:start position:0% +increasing by people's perception of + + + align:start position:0% +increasing by people's perception of +that might be + + align:start position:0% +that might be + + + align:start position:0% +that might be +not necessarily the case now in some + + align:start position:0% +not necessarily the case now in some + + + align:start position:0% +not necessarily the case now in some +ways like who are we to sort of say that + + align:start position:0% +ways like who are we to sort of say that + + + align:start position:0% +ways like who are we to sort of say that +people should change their behaviors or + + align:start position:0% +people should change their behaviors or + + + align:start position:0% +people should change their behaviors or +that they're making mistakes so in some + + align:start position:0% +that they're making mistakes so in some + + + align:start position:0% +that they're making mistakes so in some +situations at least it's quite tricky to + + align:start position:0% +situations at least it's quite tricky to + + + align:start position:0% +situations at least it's quite tricky to +figure out + + align:start position:0% +figure out + + + align:start position:0% +figure out +what's a mistake and what's not and what + + align:start position:0% +what's a mistake and what's not and what + + + align:start position:0% +what's a mistake and what's not and what +to be do or not + + align:start position:0% +to be do or not + + + align:start position:0% +to be do or not +and again you get into tricky issues um + + align:start position:0% +and again you get into tricky issues um + + + align:start position:0% +and again you get into tricky issues um +when it comes to particular for + + align:start position:0% +when it comes to particular for + + + align:start position:0% +when it comes to particular for +different selves and self-control where + + align:start position:0% +different selves and self-control where + + + align:start position:0% +different selves and self-control where +again who are we just saying that uh + + align:start position:0% +again who are we just saying that uh + + + align:start position:0% +again who are we just saying that uh +somebody should lose weight or change + + align:start position:0% +somebody should lose weight or change + + + align:start position:0% +somebody should lose weight or change +their behavior in certain ways + + align:start position:0% +their behavior in certain ways + + + align:start position:0% +their behavior in certain ways +um when perhaps um that's not in their + + align:start position:0% +um when perhaps um that's not in their + + + align:start position:0% +um when perhaps um that's not in their +best interest or that's not what they're + + align:start position:0% +best interest or that's not what they're + + + align:start position:0% +best interest or that's not what they're +doing maybe they're fully optimizing + + align:start position:0% +doing maybe they're fully optimizing + + + align:start position:0% +doing maybe they're fully optimizing +and how how would we even know that + + align:start position:0% +and how how would we even know that + + + align:start position:0% +and how how would we even know that +that's not the case + + align:start position:0% +that's not the case + + + align:start position:0% +that's not the case +now what are some forms of paternalisms + + align:start position:0% +now what are some forms of paternalisms + + + align:start position:0% +now what are some forms of paternalisms +that are quite + + align:start position:0% +that are quite + + + align:start position:0% +that are quite +um popular there's lots of examples of + + align:start position:0% +um popular there's lots of examples of + + + align:start position:0% +um popular there's lots of examples of +in fact quite popular + + align:start position:0% +in fact quite popular + + + align:start position:0% +in fact quite popular +paternalism there's social security + + align:start position:0% +paternalism there's social security + + + align:start position:0% +paternalism there's social security +there's healthcare program for retirees + + align:start position:0% +there's healthcare program for retirees + + + align:start position:0% +there's healthcare program for retirees +including medicare which tends to be + + align:start position:0% +including medicare which tends to be + + + align:start position:0% +including medicare which tends to be +quite popular + + align:start position:0% +quite popular + + + align:start position:0% +quite popular +uh there's often restrictions of um + + align:start position:0% +uh there's often restrictions of um + + + align:start position:0% +uh there's often restrictions of um +investment menus and 401k savings plans + + align:start position:0% +investment menus and 401k savings plans + + + align:start position:0% +investment menus and 401k savings plans +where essentially that's precisely what + + align:start position:0% +where essentially that's precisely what + + + align:start position:0% +where essentially that's precisely what +i was just saying is where + + align:start position:0% +i was just saying is where + + + align:start position:0% +i was just saying is where +um essentially just bad plans so + + align:start position:0% +um essentially just bad plans so + + + align:start position:0% +um essentially just bad plans so +dominated plants are often just excluded + + align:start position:0% +dominated plants are often just excluded + + + align:start position:0% +dominated plants are often just excluded +um there's often consumer safety + + align:start position:0% +um there's often consumer safety + + + align:start position:0% +um there's often consumer safety +regulations that the fda + + align:start position:0% +regulations that the fda + + + align:start position:0% +regulations that the fda +essentially certain drugs cannot be + + align:start position:0% +essentially certain drugs cannot be + + + align:start position:0% +essentially certain drugs cannot be +offered like you cannot take certain + + align:start position:0% +offered like you cannot take certain + + + align:start position:0% +offered like you cannot take certain +drugs + + align:start position:0% +drugs + + + align:start position:0% +drugs +the government essentially just sort of + + align:start position:0% +the government essentially just sort of + + + align:start position:0% +the government essentially just sort of +if they're not being safe + + align:start position:0% +if they're not being safe + + + align:start position:0% +if they're not being safe +um there's mandatory education and many + + align:start position:0% +um there's mandatory education and many + + + align:start position:0% +um there's mandatory education and many +places you have to go to school you + + align:start position:0% +places you have to go to school you + + + align:start position:0% +places you have to go to school you +can't just sort of say i'm just + + align:start position:0% +can't just sort of say i'm just + + + align:start position:0% +can't just sort of say i'm just +sort of uh um i'm + + align:start position:0% +sort of uh um i'm + + + align:start position:0% +sort of uh um i'm +my kid is sort of learning at the forest + + align:start position:0% +my kid is sort of learning at the forest + + + align:start position:0% +my kid is sort of learning at the forest +that's sort of not an option + + align:start position:0% +that's sort of not an option + + + align:start position:0% +that's sort of not an option +um often that's to do with also like + + align:start position:0% +um often that's to do with also like + + + align:start position:0% +um often that's to do with also like +protection of miners in some ways + + align:start position:0% +protection of miners in some ways + + + align:start position:0% +protection of miners in some ways +um then there's cigarette taxes or sin + + align:start position:0% +um then there's cigarette taxes or sin + + + align:start position:0% +um then there's cigarette taxes or sin +taxes that's + + align:start position:0% +taxes that's + + + align:start position:0% +taxes that's +often called that's also hard + + align:start position:0% +often called that's also hard + + + align:start position:0% +often called that's also hard +paternalism notice that here you're + + align:start position:0% +paternalism notice that here you're + + + align:start position:0% +paternalism notice that here you're +changing people's prices + + align:start position:0% +changing people's prices + + + align:start position:0% +changing people's prices +uh in many places uh prostitution + + align:start position:0% +uh in many places uh prostitution + + + align:start position:0% +uh in many places uh prostitution +polygamy + + align:start position:0% +polygamy + + + align:start position:0% +polygamy +are are banned these are like hard bands + + align:start position:0% +are are banned these are like hard bands + + + align:start position:0% +are are banned these are like hard bands +so you can just you're just not allowed + + align:start position:0% +so you can just you're just not allowed + + + align:start position:0% +so you can just you're just not allowed +to like um + + align:start position:0% +to like um + + + align:start position:0% +to like um +marry three spouses um uh + + align:start position:0% +marry three spouses um uh + + + align:start position:0% +marry three spouses um uh +mandating face mask interestingly it + + align:start position:0% +mandating face mask interestingly it + + + align:start position:0% +mandating face mask interestingly it +seems to me that that's hard paternalism + + align:start position:0% +seems to me that that's hard paternalism + + + align:start position:0% +seems to me that that's hard paternalism +as you have for example in uh + + align:start position:0% +as you have for example in uh + + + align:start position:0% +as you have for example in uh +in cambridge i think that the punishment + + align:start position:0% +in cambridge i think that the punishment + + + align:start position:0% +in cambridge i think that the punishment +is currently 300 if you go outside and + + align:start position:0% +is currently 300 if you go outside and + + + align:start position:0% +is currently 300 if you go outside and +don't wear a face mask + + align:start position:0% +don't wear a face mask + + + align:start position:0% +don't wear a face mask +i'm pretty sure in cambridge that's + + align:start position:0% +i'm pretty sure in cambridge that's + + + align:start position:0% +i'm pretty sure in cambridge that's +quite popular notice of course that's + + align:start position:0% +quite popular notice of course that's + + + align:start position:0% +quite popular notice of course that's +not true in all states + + align:start position:0% +not true in all states + + + align:start position:0% +not true in all states +and so on so there might be some + + align:start position:0% +and so on so there might be some + + + align:start position:0% +and so on so there might be some +policies that are very much popular + + align:start position:0% +policies that are very much popular + + + align:start position:0% +policies that are very much popular +in some places but not at all in others + + align:start position:0% +in some places but not at all in others + + + align:start position:0% +in some places but not at all in others +there's also some um soft paternalism + + align:start position:0% +there's also some um soft paternalism + + + align:start position:0% +there's also some um soft paternalism +that tends to be quite + + align:start position:0% +that tends to be quite + + + align:start position:0% +that tends to be quite +um popular um there's some places where + + align:start position:0% +um popular um there's some places where + + + align:start position:0% +um popular um there's some places where +like it's not clear whether it's like + + align:start position:0% +like it's not clear whether it's like + + + align:start position:0% +like it's not clear whether it's like +hard versus soft paternalism what + + align:start position:0% +hard versus soft paternalism what + + + align:start position:0% +hard versus soft paternalism what +exactly the definition is + + align:start position:0% +exactly the definition is + + + align:start position:0% +exactly the definition is +things like banning junk food and school + + align:start position:0% +things like banning junk food and school + + + align:start position:0% +things like banning junk food and school +vending machines you can call that sort + + align:start position:0% +vending machines you can call that sort + + + align:start position:0% +vending machines you can call that sort +of heart paternalism because you take + + align:start position:0% +of heart paternalism because you take + + + align:start position:0% +of heart paternalism because you take +away + + align:start position:0% +away + + + align:start position:0% +away +options but of course it doesn't really + + align:start position:0% +options but of course it doesn't really + + + align:start position:0% +options but of course it doesn't really +uh prevent you from bringing in candy to + + align:start position:0% +uh prevent you from bringing in candy to + + + align:start position:0% +uh prevent you from bringing in candy to +school anyway so like call that hardest + + align:start position:0% +school anyway so like call that hardest + + + align:start position:0% +school anyway so like call that hardest +off patrols and um i don't really care + + align:start position:0% +off patrols and um i don't really care + + + align:start position:0% +off patrols and um i don't really care +about that tends to be quite + + align:start position:0% +about that tends to be quite + + + align:start position:0% +about that tends to be quite +a popular policy uh calorie disclosure + + align:start position:0% +a popular policy uh calorie disclosure + + + align:start position:0% +a popular policy uh calorie disclosure +laws which essentially just + + align:start position:0% +laws which essentially just + + + align:start position:0% +laws which essentially just +saying like you have to put in some + + align:start position:0% +saying like you have to put in some + + + align:start position:0% +saying like you have to put in some +information for our customers + + align:start position:0% +information for our customers + + + align:start position:0% +information for our customers +which could be easily available you can + + align:start position:0% +which could be easily available you can + + + align:start position:0% +which could be easily available you can +just look it up online or the like + + align:start position:0% +just look it up online or the like + + + align:start position:0% +just look it up online or the like +and things like default enrollment in + + align:start position:0% +and things like default enrollment in + + + align:start position:0% +and things like default enrollment in +401ks dating span all tend to be quite + + align:start position:0% +401ks dating span all tend to be quite + + + align:start position:0% +401ks dating span all tend to be quite +popular now and for some + + align:start position:0% +popular now and for some + + + align:start position:0% +popular now and for some +goods you know there's like huge um um + + align:start position:0% +goods you know there's like huge um um + + + align:start position:0% +goods you know there's like huge um um +uh taxes for example cigarette taxes + + align:start position:0% +uh taxes for example cigarette taxes + + + align:start position:0% +uh taxes for example cigarette taxes +tend to be extremely high + + align:start position:0% +tend to be extremely high + + + align:start position:0% +tend to be extremely high +this is from 2019 um notice that there's + + align:start position:0% +this is from 2019 um notice that there's + + + align:start position:0% +this is from 2019 um notice that there's +huge variation across + + align:start position:0% +huge variation across + + + align:start position:0% +huge variation across +um places if you look at like you know + + align:start position:0% +um places if you look at like you know + + + align:start position:0% +um places if you look at like you know +some places here these are like some of + + align:start position:0% +some places here these are like some of + + + align:start position:0% +some places here these are like some of +the highest + + align:start position:0% +the highest + + + align:start position:0% +the highest +um uh uh such as um connecticut's uh + + align:start position:0% +um uh uh such as um connecticut's uh + + + align:start position:0% +um uh uh such as um connecticut's uh +including massachusetts it's three four + + align:start position:0% +including massachusetts it's three four + + + align:start position:0% +including massachusetts it's three four +um dollars per pack of cigarettes + + align:start position:0% +um dollars per pack of cigarettes + + + align:start position:0% +um dollars per pack of cigarettes +in addition there's also like a dollar + + align:start position:0% +in addition there's also like a dollar + + + align:start position:0% +in addition there's also like a dollar +from the federal government + + align:start position:0% +from the federal government + + + align:start position:0% +from the federal government +then there's some other places including + + align:start position:0% +then there's some other places including + + + align:start position:0% +then there's some other places including +um uh + + align:start position:0% +um uh + + + align:start position:0% +um uh +you know uh uh north dakota or like + + align:start position:0% +you know uh uh north dakota or like + + + align:start position:0% +you know uh uh north dakota or like +um north carolina and so on where + + align:start position:0% +um north carolina and so on where + + + align:start position:0% +um north carolina and so on where +cigarette taxes are extremely + + align:start position:0% +cigarette taxes are extremely + + + align:start position:0% +cigarette taxes are extremely +low so that's kind of quite interesting + + align:start position:0% +low so that's kind of quite interesting + + + align:start position:0% +low so that's kind of quite interesting +because it sort of + + align:start position:0% +because it sort of + + + align:start position:0% +because it sort of +it says you know here's a policy that + + align:start position:0% +it says you know here's a policy that + + + align:start position:0% +it says you know here's a policy that +depending on your view + + align:start position:0% +depending on your view + + + align:start position:0% +depending on your view +of how people make choices governments + + align:start position:0% +of how people make choices governments + + + align:start position:0% +of how people make choices governments +make very different decisions + + align:start position:0% +make very different decisions + + + align:start position:0% +make very different decisions +and presumably that has to do with like + + align:start position:0% +and presumably that has to do with like + + + align:start position:0% +and presumably that has to do with like +freedom of choice + + align:start position:0% +freedom of choice + + + align:start position:0% +freedom of choice +or uh the popularity of that choice + + align:start position:0% +or uh the popularity of that choice + + + align:start position:0% +or uh the popularity of that choice +itself + + align:start position:0% +itself + + + align:start position:0% +itself +in the specific state of course it also + + align:start position:0% +in the specific state of course it also + + + align:start position:0% +in the specific state of course it also +has to do with potentially + + align:start position:0% +has to do with potentially + + + align:start position:0% +has to do with potentially +um the party and so on uh similarly + + align:start position:0% +um the party and so on uh similarly + + + align:start position:0% +um the party and so on uh similarly +there's also an aspiration in + + align:start position:0% +there's also an aspiration in + + + align:start position:0% +there's also an aspiration in +state alcohol taxes um they're in fact + + align:start position:0% +state alcohol taxes um they're in fact + + + align:start position:0% +state alcohol taxes um they're in fact +um they're very like hugely uh + + align:start position:0% +um they're very like hugely uh + + + align:start position:0% +um they're very like hugely uh +particular sort of + + align:start position:0% +particular sort of + + + align:start position:0% +particular sort of +you find some states where like the um + + align:start position:0% +you find some states where like the um + + + align:start position:0% +you find some states where like the um +the + + align:start position:0% +the + + + align:start position:0% +the +taxes per per gallon or like you know + + align:start position:0% +taxes per per gallon or like you know + + + align:start position:0% +taxes per per gallon or like you know +twenty thirty dollars and some other + + align:start position:0% +twenty thirty dollars and some other + + + align:start position:0% +twenty thirty dollars and some other +states where it's like essentially close + + align:start position:0% +states where it's like essentially close + + + align:start position:0% +states where it's like essentially close +to zero + + align:start position:0% +to zero + + + align:start position:0% +to zero +um notice that there's also a bunch of + + align:start position:0% +um notice that there's also a bunch of + + + align:start position:0% +um notice that there's also a bunch of +other um + + align:start position:0% +other um + + + align:start position:0% +other um +blue laws as they're referred to which + + align:start position:0% +blue laws as they're referred to which + + + align:start position:0% +blue laws as they're referred to which +is things like on certain days you're + + align:start position:0% +is things like on certain days you're + + + align:start position:0% +is things like on certain days you're +not allowed to sell alcohol + + align:start position:0% +not allowed to sell alcohol + + + align:start position:0% +not allowed to sell alcohol +uh and so on now that's kind of + + align:start position:0% +uh and so on now that's kind of + + + align:start position:0% +uh and so on now that's kind of +interesting because that sort of + + align:start position:0% +interesting because that sort of + + + align:start position:0% +interesting because that sort of +additional restrictions + + align:start position:0% +additional restrictions + + + align:start position:0% +additional restrictions +um uh which would tend to be quite + + align:start position:0% +um uh which would tend to be quite + + + align:start position:0% +um uh which would tend to be quite +um inefficient in various ways that is + + align:start position:0% +um inefficient in various ways that is + + + align:start position:0% +um inefficient in various ways that is +to say + + align:start position:0% +to say + + + align:start position:0% +to say +so economists would tend to think that + + align:start position:0% +so economists would tend to think that + + + align:start position:0% +so economists would tend to think that +like if there's certain behavior that + + align:start position:0% +like if there's certain behavior that + + + align:start position:0% +like if there's certain behavior that +you don't want people to engage in + + align:start position:0% +you don't want people to engage in + + + align:start position:0% +you don't want people to engage in +we should tax it um instead um you could + + align:start position:0% +we should tax it um instead um you could + + + align:start position:0% +we should tax it um instead um you could +essentially sort of outlaw it in certain + + align:start position:0% +essentially sort of outlaw it in certain + + + align:start position:0% +essentially sort of outlaw it in certain +ways that tends to be quite inefficient + + align:start position:0% +ways that tends to be quite inefficient + + + align:start position:0% +ways that tends to be quite inefficient +because often people find ways to get + + align:start position:0% +because often people find ways to get + + + align:start position:0% +because often people find ways to get +any way plus the government does not get + + align:start position:0% +any way plus the government does not get + + + align:start position:0% +any way plus the government does not get +any taxes or revenue + + align:start position:0% +any taxes or revenue + + + align:start position:0% +any taxes or revenue +um from that now + + align:start position:0% +um from that now + + + align:start position:0% +um from that now +what are some unpopular um paternalism + + align:start position:0% +what are some unpopular um paternalism + + + align:start position:0% +what are some unpopular um paternalism +or things that people don't like + + align:start position:0% +or things that people don't like + + + align:start position:0% +or things that people don't like +quickly i think that's exactly right so + + align:start position:0% +quickly i think that's exactly right so + + + align:start position:0% +quickly i think that's exactly right so +one of them is helmets and + + align:start position:0% +one of them is helmets and + + + align:start position:0% +one of them is helmets and +seat belts so there often + + align:start position:0% +seat belts so there often + + + align:start position:0% +seat belts so there often +it's there's no externality here this is + + align:start position:0% +it's there's no externality here this is + + + align:start position:0% +it's there's no externality here this is +essentially just like something to + + align:start position:0% +essentially just like something to + + + align:start position:0% +essentially just like something to +protect yourself + + align:start position:0% +protect yourself + + + align:start position:0% +protect yourself +now they tend to be quite unpopular in + + align:start position:0% +now they tend to be quite unpopular in + + + align:start position:0% +now they tend to be quite unpopular in +many places + + align:start position:0% +many places + + + align:start position:0% +many places +um it's not quite clear why that is + + align:start position:0% +um it's not quite clear why that is + + + align:start position:0% +um it's not quite clear why that is +so often it's sort of a thing that's not + + align:start position:0% +so often it's sort of a thing that's not + + + align:start position:0% +so often it's sort of a thing that's not +cool or like a sort of some social norms + + align:start position:0% +cool or like a sort of some social norms + + + align:start position:0% +cool or like a sort of some social norms +or in some ways where people sort of + + align:start position:0% +or in some ways where people sort of + + + align:start position:0% +or in some ways where people sort of +think + + align:start position:0% +think + + + align:start position:0% +think +it's like another thing they want to do + + align:start position:0% +it's like another thing they want to do + + + align:start position:0% +it's like another thing they want to do +it's like uh sort of explaining to my + + align:start position:0% +it's like uh sort of explaining to my + + + align:start position:0% +it's like uh sort of explaining to my +14 year or 15 year old niece to wear + + align:start position:0% +14 year or 15 year old niece to wear + + + align:start position:0% +14 year or 15 year old niece to wear +like a helmet is sort of very hard + + align:start position:0% +like a helmet is sort of very hard + + + align:start position:0% +like a helmet is sort of very hard +and then she would say yes yes but then + + align:start position:0% +and then she would say yes yes but then + + + align:start position:0% +and then she would say yes yes but then +like drive around like ride her bike + + align:start position:0% +like drive around like ride her bike + + + align:start position:0% +like drive around like ride her bike +around the corner and then take it off + + align:start position:0% +around the corner and then take it off + + + align:start position:0% +around the corner and then take it off +and sort of you know and so on + + align:start position:0% +and sort of you know and so on + + + align:start position:0% +and sort of you know and so on +so that seems to be about sort of + + align:start position:0% +so that seems to be about sort of + + + align:start position:0% +so that seems to be about sort of +something about + + align:start position:0% +something about + + + align:start position:0% +something about +personal trade-offs between risk and + + align:start position:0% +personal trade-offs between risk and + + + align:start position:0% +personal trade-offs between risk and +rewards in some ways where + + align:start position:0% +rewards in some ways where + + + align:start position:0% +rewards in some ways where +uh you know the government of some + + align:start position:0% +uh you know the government of some + + + align:start position:0% +uh you know the government of some +people um might just + + align:start position:0% +people um might just + + + align:start position:0% +people um might just +not value the benefits of + + align:start position:0% +not value the benefits of + + + align:start position:0% +not value the benefits of +looking cool or whatever sufficiently or + + align:start position:0% +looking cool or whatever sufficiently or + + + align:start position:0% +looking cool or whatever sufficiently or +as much as the individual itself and + + align:start position:0% +as much as the individual itself and + + + align:start position:0% +as much as the individual itself and +then they tend to be sort of um + + align:start position:0% +then they tend to be sort of um + + + align:start position:0% +then they tend to be sort of um +uh unhappy about it of course the + + align:start position:0% +uh unhappy about it of course the + + + align:start position:0% +uh unhappy about it of course the +alternative way of putting this is that + + align:start position:0% +alternative way of putting this is that + + + align:start position:0% +alternative way of putting this is that +the individual itself + + align:start position:0% +the individual itself + + + align:start position:0% +the individual itself +is underestimating the risk potentially + + align:start position:0% +is underestimating the risk potentially + + + align:start position:0% +is underestimating the risk potentially +of doesn't take into account how bad it + + align:start position:0% +of doesn't take into account how bad it + + + align:start position:0% +of doesn't take into account how bad it +would be to actually have a bicycle + + align:start position:0% +would be to actually have a bicycle + + + align:start position:0% +would be to actually have a bicycle +accident + + align:start position:0% +accident + + + align:start position:0% +accident +right but that's essentially something + + align:start position:0% +right but that's essentially something + + + align:start position:0% +right but that's essentially something +about people + + align:start position:0% +about people + + + align:start position:0% +about people +disagreeing with the government with + + align:start position:0% +disagreeing with the government with + + + align:start position:0% +disagreeing with the government with +their parents or the like about + + align:start position:0% +their parents or the like about + + + align:start position:0% +their parents or the like about +the risk versus reward or cost benefits + + align:start position:0% +the risk versus reward or cost benefits + + + align:start position:0% +the risk versus reward or cost benefits +of certain actions + + align:start position:0% +of certain actions + + + align:start position:0% +of certain actions +and there seems to be disagreement and + + align:start position:0% +and there seems to be disagreement and + + + align:start position:0% +and there seems to be disagreement and +then you could sort of mandate that but + + align:start position:0% +then you could sort of mandate that but + + + align:start position:0% +then you could sort of mandate that but +that + + align:start position:0% +that + + + align:start position:0% +that +leads to unhappiness because they're + + align:start position:0% +leads to unhappiness because they're + + + align:start position:0% +leads to unhappiness because they're +precisely that disagreement + + align:start position:0% +precisely that disagreement + + + align:start position:0% +precisely that disagreement +now the wearing mask is in some + + align:start position:0% +now the wearing mask is in some + + + align:start position:0% +now the wearing mask is in some +sense quite similar there it's quite + + align:start position:0% +sense quite similar there it's quite + + + align:start position:0% +sense quite similar there it's quite +different and what's different here is + + align:start position:0% +different and what's different here is + + + align:start position:0% +different and what's different here is +that there's externalities right so + + align:start position:0% +that there's externalities right so + + + align:start position:0% +that there's externalities right so +their externalities here are + + align:start position:0% +their externalities here are + + + align:start position:0% +their externalities here are +that certain people benefit a lot from + + align:start position:0% +that certain people benefit a lot from + + + align:start position:0% +that certain people benefit a lot from +having their shops open + + align:start position:0% +having their shops open + + + align:start position:0% +having their shops open +or like being able to sell things + + align:start position:0% +or like being able to sell things + + + align:start position:0% +or like being able to sell things +and others are affected a lot so in + + align:start position:0% +and others are affected a lot so in + + + align:start position:0% +and others are affected a lot so in +particular the elderly + + align:start position:0% +particular the elderly + + + align:start position:0% +particular the elderly +might might be disproportionately + + align:start position:0% +might might be disproportionately + + + align:start position:0% +might might be disproportionately +affected and sort of might essentially + + align:start position:0% +affected and sort of might essentially + + + align:start position:0% +affected and sort of might essentially +uh the number of people who will die + + align:start position:0% +uh the number of people who will die + + + align:start position:0% +uh the number of people who will die +will clearly if people are not wearing + + align:start position:0% +will clearly if people are not wearing + + + align:start position:0% +will clearly if people are not wearing +masks or if shops are not a few people + + align:start position:0% +masks or if shops are not a few people + + + align:start position:0% +masks or if shops are not a few people +are + + align:start position:0% +are + + + align:start position:0% +are +running out of outside or meeting and so + + align:start position:0% +running out of outside or meeting and so + + + align:start position:0% +running out of outside or meeting and so +on and so forth + + align:start position:0% +on and so forth + + + align:start position:0% +on and so forth +um but there's others who are really um + + align:start position:0% +um but there's others who are really um + + + align:start position:0% +um but there's others who are really um +for whom that's really costly because + + align:start position:0% +for whom that's really costly because + + + align:start position:0% +for whom that's really costly because +their businesses are not open + + align:start position:0% +their businesses are not open + + + align:start position:0% +their businesses are not open +and they like now that could be there + + align:start position:0% +and they like now that could be there + + + align:start position:0% +and they like now that could be there +could be + + align:start position:0% +could be + + + align:start position:0% +could be +entirely rational um issues + + align:start position:0% +entirely rational um issues + + + align:start position:0% +entirely rational um issues +um where you might say well um uh people + + align:start position:0% +um where you might say well um uh people + + + align:start position:0% +um where you might say well um uh people +just don't care about certain uh + + align:start position:0% +just don't care about certain uh + + + align:start position:0% +just don't care about certain uh +other groups of the society and + + align:start position:0% +other groups of the society and + + + align:start position:0% +other groups of the society and +therefore you want to have your shop + + align:start position:0% +therefore you want to have your shop + + + align:start position:0% +therefore you want to have your shop +open and you + + align:start position:0% +open and you + + + align:start position:0% +open and you +don't want to be told um that what that + + align:start position:0% +don't want to be told um that what that + + + align:start position:0% +don't want to be told um that what that +you should be doing that + + align:start position:0% +you should be doing that + + + align:start position:0% +you should be doing that +there could be also mistakes in the + + align:start position:0% +there could be also mistakes in the + + + align:start position:0% +there could be also mistakes in the +sense that people just don't understand + + align:start position:0% +sense that people just don't understand + + + align:start position:0% +sense that people just don't understand +necessarily these externalities they + + align:start position:0% +necessarily these externalities they + + + align:start position:0% +necessarily these externalities they +might sort of say well + + align:start position:0% +might sort of say well + + + align:start position:0% +might sort of say well +um i'm not effective and i'll be just + + align:start position:0% +um i'm not effective and i'll be just + + + align:start position:0% +um i'm not effective and i'll be just +fine that might be actually + + align:start position:0% +fine that might be actually + + + align:start position:0% +fine that might be actually +the risk for themselves is not that high + + align:start position:0% +the risk for themselves is not that high + + + align:start position:0% +the risk for themselves is not that high +but of course there's + + align:start position:0% +but of course there's + + + align:start position:0% +but of course there's +um large externalities and others that + + align:start position:0% +um large externalities and others that + + + align:start position:0% +um large externalities and others that +they might sort of not appreciate or not + + align:start position:0% +they might sort of not appreciate or not + + + align:start position:0% +they might sort of not appreciate or not +take into account + + align:start position:0% +take into account + + + align:start position:0% +take into account +uh exactly so so chad carmen is saying + + align:start position:0% +uh exactly so so chad carmen is saying + + + align:start position:0% +uh exactly so so chad carmen is saying +speed limits uh similarly are similar to + + align:start position:0% +speed limits uh similarly are similar to + + + align:start position:0% +speed limits uh similarly are similar to +that + + align:start position:0% +that + + + align:start position:0% +that +because they're sort of like i'm driving + + align:start position:0% +because they're sort of like i'm driving + + + align:start position:0% +because they're sort of like i'm driving +but there's affect yourself but also + + align:start position:0% +but there's affect yourself but also + + + align:start position:0% +but there's affect yourself but also +um in certain accidents + + align:start position:0% +um in certain accidents + + + align:start position:0% +um in certain accidents +and so um why is that or what + + align:start position:0% +and so um why is that or what + + + align:start position:0% +and so um why is that or what +so how do we think about + + align:start position:0% +so how do we think about + + + align:start position:0% +so how do we think about +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +to say so i mentioned here + + align:start position:0% +to say so i mentioned here + + + align:start position:0% +to say so i mentioned here +and this is an example so here we have + + align:start position:0% +and this is an example so here we have + + + align:start position:0% +and this is an example so here we have +um we think sort of sicknesses + + align:start position:0% +um we think sort of sicknesses + + + align:start position:0% +um we think sort of sicknesses +are quite um popular and why is that + + align:start position:0% +are quite um popular and why is that + + + align:start position:0% +are quite um popular and why is that +popular and why is the + + align:start position:0% +popular and why is the + + + align:start position:0% +popular and why is the +uh making certain drugs illegal + + align:start position:0% +uh making certain drugs illegal + + + align:start position:0% +uh making certain drugs illegal +why is that unpopular what's the problem + + align:start position:0% +why is that unpopular what's the problem + + + align:start position:0% +why is that unpopular what's the problem +here + + align:start position:0% +here + + + align:start position:0% +here +so i think there's when you think about + + align:start position:0% +so i think there's when you think about + + + align:start position:0% +so i think there's when you think about +when you do like economic + + align:start position:0% +when you do like economic + + + align:start position:0% +when you do like economic +analysis of that there's essential you + + align:start position:0% +analysis of that there's essential you + + + align:start position:0% +analysis of that there's essential you +can think of this + + align:start position:0% +can think of this + + + align:start position:0% +can think of this +might be externality values might + + align:start position:0% +might be externality values might + + + align:start position:0% +might be externality values might +actually much lower than for + + align:start position:0% +actually much lower than for + + + align:start position:0% +actually much lower than for +smoking or drinking because uh drunk + + align:start position:0% +smoking or drinking because uh drunk + + + align:start position:0% +smoking or drinking because uh drunk +driving and so on is very + + align:start position:0% +driving and so on is very + + + align:start position:0% +driving and so on is very +lethal there might be also some + + align:start position:0% +lethal there might be also some + + + align:start position:0% +lethal there might be also some +expertise from + + align:start position:0% +expertise from + + + align:start position:0% +expertise from +smoking weed um but um uh the + + align:start position:0% +smoking weed um but um uh the + + + align:start position:0% +smoking weed um but um uh the +externalities are surely looking for + + align:start position:0% +externalities are surely looking for + + + align:start position:0% +externalities are surely looking for +preferred drinking now then there could + + align:start position:0% +preferred drinking now then there could + + + align:start position:0% +preferred drinking now then there could +be melodies but again for internalities + + align:start position:0% +be melodies but again for internalities + + + align:start position:0% +be melodies but again for internalities +usually the solution would be just the + + align:start position:0% +usually the solution would be just the + + + align:start position:0% +usually the solution would be just the +typical sin taxes and so on you would + + align:start position:0% +typical sin taxes and so on you would + + + align:start position:0% +typical sin taxes and so on you would +say well you want to tax it + + align:start position:0% +say well you want to tax it + + + align:start position:0% +say well you want to tax it +sure but then you at least would get + + align:start position:0% +sure but then you at least would get + + + align:start position:0% +sure but then you at least would get +some revenue you would increase the + + align:start position:0% +some revenue you would increase the + + + align:start position:0% +some revenue you would increase the +price you would get some revenue for the + + align:start position:0% +price you would get some revenue for the + + + align:start position:0% +price you would get some revenue for the +government + + align:start position:0% +government + + + align:start position:0% +government +um plus you would lower people's + + align:start position:0% +um plus you would lower people's + + + align:start position:0% +um plus you would lower people's +consumption um + + align:start position:0% +consumption um + + + align:start position:0% +consumption um +in addition there's all this stuff about + + align:start position:0% +in addition there's all this stuff about + + + align:start position:0% +in addition there's all this stuff about +like um + + align:start position:0% +like um + + + align:start position:0% +like um +locking people up unnecessarily by + + align:start position:0% +locking people up unnecessarily by + + + align:start position:0% +locking people up unnecessarily by +making it illegal essentially you create + + align:start position:0% +making it illegal essentially you create + + + align:start position:0% +making it illegal essentially you create +like a large prisoner + + align:start position:0% +like a large prisoner + + + align:start position:0% +like a large prisoner +population and so on which surely is for + + align:start position:0% +population and so on which surely is for + + + align:start position:0% +population and so on which surely is for +society so once you sort of have like + + align:start position:0% +society so once you sort of have like + + + align:start position:0% +society so once you sort of have like +these + + align:start position:0% +these + + + align:start position:0% +these +policies there's actually not a lot of + + align:start position:0% +policies there's actually not a lot of + + + align:start position:0% +policies there's actually not a lot of +reasons for + + align:start position:0% +reasons for + + + align:start position:0% +reasons for +uh for outlawing these are sort of tend + + align:start position:0% +uh for outlawing these are sort of tend + + + align:start position:0% +uh for outlawing these are sort of tend +to be + + align:start position:0% +to be + + + align:start position:0% +to be +um sort of gut reactions or some sort of + + align:start position:0% +um sort of gut reactions or some sort of + + + align:start position:0% +um sort of gut reactions or some sort of +judgments that were made at some point + + align:start position:0% +judgments that were made at some point + + + align:start position:0% +judgments that were made at some point +there's some lobby arguing in favor of + + align:start position:0% +there's some lobby arguing in favor of + + + align:start position:0% +there's some lobby arguing in favor of +alcohol and maybe less of a lobby + + align:start position:0% +alcohol and maybe less of a lobby + + + align:start position:0% +alcohol and maybe less of a lobby +arguing for other drugs + + align:start position:0% +arguing for other drugs + + + align:start position:0% +arguing for other drugs +um but as you say you know the sentiment + + align:start position:0% +um but as you say you know the sentiment + + + align:start position:0% +um but as you say you know the sentiment +has very much changed and it seems to be + + align:start position:0% +has very much changed and it seems to be + + + align:start position:0% +has very much changed and it seems to be +like sooner or later + + align:start position:0% +like sooner or later + + + align:start position:0% +like sooner or later +pretty much all states are moving uh + + align:start position:0% +pretty much all states are moving uh + + + align:start position:0% +pretty much all states are moving uh +towards + + align:start position:0% +towards + + + align:start position:0% +towards +south asia and that leads to essentially + + align:start position:0% +south asia and that leads to essentially + + + align:start position:0% +south asia and that leads to essentially +potential government + + align:start position:0% +potential government + + + align:start position:0% +potential government +uh uh revenues um + + align:start position:0% +uh uh revenues um + + + align:start position:0% +uh uh revenues um +as well so i think one argument perhaps + + align:start position:0% +as well so i think one argument perhaps + + + align:start position:0% +as well so i think one argument perhaps +that one could make is sort of these + + align:start position:0% +that one could make is sort of these + + + align:start position:0% +that one could make is sort of these +gateway direct + + align:start position:0% +gateway direct + + + align:start position:0% +gateway direct +arguments which you know i don't think + + align:start position:0% +arguments which you know i don't think + + + align:start position:0% +arguments which you know i don't think +there's actually that much + + align:start position:0% +there's actually that much + + + align:start position:0% +there's actually that much +evidence for that but you say well + + align:start position:0% +evidence for that but you say well + + + align:start position:0% +evidence for that but you say well +actually sort of um + + align:start position:0% +actually sort of um + + + align:start position:0% +actually sort of um +uh mariana might not be so bad by itself + + align:start position:0% +uh mariana might not be so bad by itself + + + align:start position:0% +uh mariana might not be so bad by itself +but perhaps it leads to like other words + + align:start position:0% +but perhaps it leads to like other words + + + align:start position:0% +but perhaps it leads to like other words +it's not obvious at all that + + align:start position:0% +it's not obvious at all that + + + align:start position:0% +it's not obvious at all that +legalization um of that + + align:start position:0% +legalization um of that + + + align:start position:0% +legalization um of that +so hey it's not obvious that that's + + align:start position:0% +so hey it's not obvious that that's + + + align:start position:0% +so hey it's not obvious that that's +necessarily true but b it's all obvious + + align:start position:0% +necessarily true but b it's all obvious + + + align:start position:0% +necessarily true but b it's all obvious +that making it legal + + align:start position:0% +that making it legal + + + align:start position:0% +that making it legal +versus illegal changes that rationale + + align:start position:0% +versus illegal changes that rationale + + + align:start position:0% +versus illegal changes that rationale +because + + align:start position:0% +because + + + align:start position:0% +because +when it's illegal lots of people are + + align:start position:0% +when it's illegal lots of people are + + + align:start position:0% +when it's illegal lots of people are +using drugs anyway and maybe it makes it + + align:start position:0% +using drugs anyway and maybe it makes it + + + align:start position:0% +using drugs anyway and maybe it makes it +even more + + align:start position:0% +even more + + + align:start position:0% +even more +and maybe sort of more dangerous um + + align:start position:0% +and maybe sort of more dangerous um + + + align:start position:0% +and maybe sort of more dangerous um +potentially + + align:start position:0% +potentially + + + align:start position:0% +potentially +but i think it's important to sort of + + align:start position:0% +but i think it's important to sort of + + + align:start position:0% +but i think it's important to sort of +realize that some of these policies are + + align:start position:0% +realize that some of these policies are + + + align:start position:0% +realize that some of these policies are +very much like sort of + + align:start position:0% +very much like sort of + + + align:start position:0% +very much like sort of +in some ways arbitrary um based on some + + align:start position:0% +in some ways arbitrary um based on some + + + align:start position:0% +in some ways arbitrary um based on some +legacy or some lobbies and so on and so + + align:start position:0% +legacy or some lobbies and so on and so + + + align:start position:0% +legacy or some lobbies and so on and so +forth + + align:start position:0% +forth + + + align:start position:0% +forth +and what's important here is that the + + align:start position:0% +and what's important here is that the + + + align:start position:0% +and what's important here is that the +the popularity itself then also will + + align:start position:0% +the popularity itself then also will + + + align:start position:0% +the popularity itself then also will +affect policies in some ways + + align:start position:0% +affect policies in some ways + + + align:start position:0% +affect policies in some ways +like you know as you say you know the + + align:start position:0% +like you know as you say you know the + + + align:start position:0% +like you know as you say you know the +public sentiment has shifted in various + + align:start position:0% +public sentiment has shifted in various + + + align:start position:0% +public sentiment has shifted in various +in some ways stuff will become legal uh + + align:start position:0% +in some ways stuff will become legal uh + + + align:start position:0% +in some ways stuff will become legal uh +as a result of that and once you do it + + align:start position:0% +as a result of that and once you do it + + + align:start position:0% +as a result of that and once you do it +in some states and things seem fine and + + align:start position:0% +in some states and things seem fine and + + + align:start position:0% +in some states and things seem fine and +the states make a bunch of money from it + + align:start position:0% +the states make a bunch of money from it + + + align:start position:0% +the states make a bunch of money from it +a lot of other states eventually will + + align:start position:0% +a lot of other states eventually will + + + align:start position:0% +a lot of other states eventually will +follow um + + align:start position:0% +follow um + + + align:start position:0% +follow um +in part because it's also you know much + + align:start position:0% +in part because it's also you know much + + + align:start position:0% +in part because it's also you know much +harder to + + align:start position:0% +harder to + + + align:start position:0% +harder to +enforce laws if you have a bunch of + + align:start position:0% +enforce laws if you have a bunch of + + + align:start position:0% +enforce laws if you have a bunch of +surrounding states where you can + + align:start position:0% +surrounding states where you can + + + align:start position:0% +surrounding states where you can +um buy stuff legally and that makes it + + align:start position:0% +um buy stuff legally and that makes it + + + align:start position:0% +um buy stuff legally and that makes it +of course trickier than to sort of + + align:start position:0% +of course trickier than to sort of + + + align:start position:0% +of course trickier than to sort of +enforce the law um + + align:start position:0% +enforce the law um + + + align:start position:0% +enforce the law um +anyway um i have some other unpopular + + align:start position:0% +anyway um i have some other unpopular + + + align:start position:0% +anyway um i have some other unpopular +uh uh examples of popular paternalism + + align:start position:0% +uh uh examples of popular paternalism + + + align:start position:0% +uh uh examples of popular paternalism +um junk food bans um + + align:start position:0% +um junk food bans um + + + align:start position:0% +um junk food bans um +junk food taxes and some of these things + + align:start position:0% +junk food taxes and some of these things + + + align:start position:0% +junk food taxes and some of these things +again are changing over time so + + align:start position:0% +again are changing over time so + + + align:start position:0% +again are changing over time so +like you know um uh i might well be that + + align:start position:0% +like you know um uh i might well be that + + + align:start position:0% +like you know um uh i might well be that +um things are + + align:start position:0% +um things are + + + align:start position:0% +um things are +are different in 10 20 years from now uh + + align:start position:0% +are different in 10 20 years from now uh + + + align:start position:0% +are different in 10 20 years from now uh +gambling laws pornography laws + + align:start position:0% +gambling laws pornography laws + + + align:start position:0% +gambling laws pornography laws +uh other kinds of syntaxes um + + align:start position:0% +uh other kinds of syntaxes um + + + align:start position:0% +uh other kinds of syntaxes um +mandating face masks again and some + + align:start position:0% +mandating face masks again and some + + + align:start position:0% +mandating face masks again and some +states are just really really popular + + align:start position:0% +states are just really really popular + + + align:start position:0% +states are just really really popular +and people on the streets + + align:start position:0% +and people on the streets + + + align:start position:0% +and people on the streets +um protesting against it which is quite + + align:start position:0% +um protesting against it which is quite + + + align:start position:0% +um protesting against it which is quite +um quite interesting john cena + + align:start position:0% +um quite interesting john cena + + + align:start position:0% +um quite interesting john cena +might be but often it is the case that + + align:start position:0% +might be but often it is the case that + + + align:start position:0% +might be but often it is the case that +there are + + align:start position:0% +there are + + + align:start position:0% +there are +some forms of there is real economic + + align:start position:0% +some forms of there is real economic + + + align:start position:0% +some forms of there is real economic +interests + + align:start position:0% +interests + + + align:start position:0% +interests +um behind that often and perhaps um + + align:start position:0% +um behind that often and perhaps um + + + align:start position:0% +um behind that often and perhaps um +again that could be very much fully + + align:start position:0% +again that could be very much fully + + + align:start position:0% +again that could be very much fully +rational uh it could also be that people + + align:start position:0% +rational uh it could also be that people + + + align:start position:0% +rational uh it could also be that people +might misunderstand the externalities + + align:start position:0% +might misunderstand the externalities + + + align:start position:0% +might misunderstand the externalities +that are + + align:start position:0% +that are + + + align:start position:0% +that are +at play um there's some other sort of + + align:start position:0% +at play um there's some other sort of + + + align:start position:0% +at play um there's some other sort of +kinds of heart paternalism that's also + + align:start position:0% +kinds of heart paternalism that's also + + + align:start position:0% +kinds of heart paternalism that's also +kind of unpopular and also not a + + align:start position:0% +kind of unpopular and also not a + + + align:start position:0% +kind of unpopular and also not a +particular efficient thing to do + + align:start position:0% +particular efficient thing to do + + + align:start position:0% +particular efficient thing to do +which is things like the ban on 16-ounce + + align:start position:0% +which is things like the ban on 16-ounce + + + align:start position:0% +which is things like the ban on 16-ounce +sodas + + align:start position:0% +sodas + + + align:start position:0% +sodas +which is kind of like a weird thing to + + align:start position:0% +which is kind of like a weird thing to + + + align:start position:0% +which is kind of like a weird thing to +do if you think about it because you can + + align:start position:0% +do if you think about it because you can + + + align:start position:0% +do if you think about it because you can +just buy smaller + + align:start position:0% +just buy smaller + + + align:start position:0% +just buy smaller +smaller bottles of the leg and it tends + + align:start position:0% +smaller bottles of the leg and it tends + + + align:start position:0% +smaller bottles of the leg and it tends +to be quite inefficient + + align:start position:0% +to be quite inefficient + + + align:start position:0% +to be quite inefficient +um um overall uh here's a + + align:start position:0% +um um overall uh here's a + + + align:start position:0% +um um overall uh here's a +signs for for for seat belts + + align:start position:0% +signs for for for seat belts + + + align:start position:0% +signs for for for seat belts +um now okay so here's the + + align:start position:0% +um now okay so here's the + + + align:start position:0% +um now okay so here's the +legalization which also does massive um + + align:start position:0% +legalization which also does massive um + + + align:start position:0% +legalization which also does massive um +variation of prostates + + align:start position:0% +variation of prostates + + + align:start position:0% +variation of prostates +now there's some um nudges and some + + align:start position:0% +now there's some um nudges and some + + + align:start position:0% +now there's some um nudges and some +policies have + + align:start position:0% +policies have + + + align:start position:0% +policies have +massive impacts and we studied at least + + align:start position:0% +massive impacts and we studied at least + + + align:start position:0% +massive impacts and we studied at least +some of this for example this was + + align:start position:0% +some of this for example this was + + + align:start position:0% +some of this for example this was +automatic enrollment there there's + + align:start position:0% +automatic enrollment there there's + + + align:start position:0% +automatic enrollment there there's +essentially + + align:start position:0% +essentially + + + align:start position:0% +essentially +a huge swing towards that essentially + + align:start position:0% +a huge swing towards that essentially + + + align:start position:0% +a huge swing towards that essentially +lots of + + align:start position:0% +lots of + + + align:start position:0% +lots of +companies and so on they're now using + + align:start position:0% +companies and so on they're now using + + + align:start position:0% +companies and so on they're now using +that and + + align:start position:0% +that and + + + align:start position:0% +that and +the fraction of people who are uh uh + + align:start position:0% +the fraction of people who are uh uh + + + align:start position:0% +the fraction of people who are uh uh +participating in retirement plans is way + + align:start position:0% +participating in retirement plans is way + + + align:start position:0% +participating in retirement plans is way +higher than the fraction + + align:start position:0% +higher than the fraction + + + align:start position:0% +higher than the fraction +of people when there's voluntary there's + + align:start position:0% +of people when there's voluntary there's + + + align:start position:0% +of people when there's voluntary there's +other policies which are quite simple + + align:start position:0% +other policies which are quite simple + + + align:start position:0% +other policies which are quite simple +policies + + align:start position:0% +policies + + + align:start position:0% +policies +um uh which are things um + + align:start position:0% +um uh which are things um + + + align:start position:0% +um uh which are things um +uh trying to get people to appear in + + align:start position:0% +uh trying to get people to appear in + + + align:start position:0% +uh trying to get people to appear in +court + + align:start position:0% +court + + + align:start position:0% +court +there essentially lots of + + align:start position:0% +there essentially lots of + + + align:start position:0% +there essentially lots of +lots of um uh + + align:start position:0% +lots of um uh + + + align:start position:0% +lots of um uh +people who have to appear in court um + + align:start position:0% +people who have to appear in court um + + + align:start position:0% +people who have to appear in court um +for like initial court hearings + + align:start position:0% +for like initial court hearings + + + align:start position:0% +for like initial court hearings +tend to not show up in those meetings + + align:start position:0% +tend to not show up in those meetings + + + align:start position:0% +tend to not show up in those meetings +and as you can imagine that's not a + + align:start position:0% +and as you can imagine that's not a + + + align:start position:0% +and as you can imagine that's not a +great idea because you know that that + + align:start position:0% +great idea because you know that that + + + align:start position:0% +great idea because you know that that +essentially leads to like + + align:start position:0% +essentially leads to like + + + align:start position:0% +essentially leads to like +uh potentially really bad consequences + + align:start position:0% +uh potentially really bad consequences + + + align:start position:0% +uh potentially really bad consequences +now what you can essentially just do is + + align:start position:0% +now what you can essentially just do is + + + align:start position:0% +now what you can essentially just do is +try to + + align:start position:0% +try to + + + align:start position:0% +try to +do very simple policies and there's a + + align:start position:0% +do very simple policies and there's a + + + align:start position:0% +do very simple policies and there's a +very nice paper by obelious and others + + align:start position:0% +very nice paper by obelious and others + + + align:start position:0% +very nice paper by obelious and others +who looks at this + + align:start position:0% +who looks at this + + + align:start position:0% +who looks at this +you can sort of change the forms you can + + align:start position:0% +you can sort of change the forms you can + + + align:start position:0% +you can sort of change the forms you can +phrase things differently + + align:start position:0% +phrase things differently + + + align:start position:0% +phrase things differently +that essentially tries to nudge people + + align:start position:0% +that essentially tries to nudge people + + + align:start position:0% +that essentially tries to nudge people +in the right direction + + align:start position:0% +in the right direction + + + align:start position:0% +in the right direction +um you can also do things like text + + align:start position:0% +um you can also do things like text + + + align:start position:0% +um you can also do things like text +message reminders and the text messages + + align:start position:0% +message reminders and the text messages + + + align:start position:0% +message reminders and the text messages +window just says your court date + + align:start position:0% +window just says your court date + + + align:start position:0% +window just says your court date +is on may 22 at 9am + + align:start position:0% +is on may 22 at 9am + + + align:start position:0% +is on may 22 at 9am +please show up and you remind people to + + align:start position:0% +please show up and you remind people to + + + align:start position:0% +please show up and you remind people to +do that + + align:start position:0% +do that + + + align:start position:0% +do that +and what you get essentially is that you + + align:start position:0% +and what you get essentially is that you + + + align:start position:0% +and what you get essentially is that you +get large + + align:start position:0% +get large + + + align:start position:0% +get large +decreases in timely court appearances or + + align:start position:0% +decreases in timely court appearances or + + + align:start position:0% +decreases in timely court appearances or +non-appearances where the fraction won't + + align:start position:0% +non-appearances where the fraction won't + + + align:start position:0% +non-appearances where the fraction won't +show up in court to their own court + + align:start position:0% +show up in court to their own court + + + align:start position:0% +show up in court to their own court +hearing + + align:start position:0% + + + + align:start position:0% + +decreases a lot by using very very + + align:start position:0% +decreases a lot by using very very + + + align:start position:0% +decreases a lot by using very very +simple + + align:start position:0% +simple + + + align:start position:0% +simple +policies once you do those kinds of + + align:start position:0% +policies once you do those kinds of + + + align:start position:0% +policies once you do those kinds of +policies presumably + + align:start position:0% +policies presumably + + + align:start position:0% +policies presumably +much to say against this policy in the + + align:start position:0% +much to say against this policy in the + + + align:start position:0% +much to say against this policy in the +sense that + + align:start position:0% +sense that + + + align:start position:0% +sense that +uh you might say well so hey you're not + + align:start position:0% +uh you might say well so hey you're not + + + align:start position:0% +uh you might say well so hey you're not +restricting anybody's choices + + align:start position:0% +restricting anybody's choices + + + align:start position:0% +restricting anybody's choices +you're also not really making anybody + + align:start position:0% +you're also not really making anybody + + + align:start position:0% +you're also not really making anybody +worse off by sending some text message + + align:start position:0% +worse off by sending some text message + + + align:start position:0% +worse off by sending some text message +reminders there might be some small + + align:start position:0% +reminders there might be some small + + + align:start position:0% +reminders there might be some small +inconveniences of receiving these text + + align:start position:0% +inconveniences of receiving these text + + + align:start position:0% +inconveniences of receiving these text +messages which are kind of + + align:start position:0% +messages which are kind of + + + align:start position:0% +messages which are kind of +annoying in spam for some people but + + align:start position:0% +annoying in spam for some people but + + + align:start position:0% +annoying in spam for some people but +overall like nobody is really made off + + align:start position:0% +overall like nobody is really made off + + + align:start position:0% +overall like nobody is really made off +by + + align:start position:0% +by + + + align:start position:0% +by +by this it's a very cheap thing to do so + + align:start position:0% +by this it's a very cheap thing to do so + + + align:start position:0% +by this it's a very cheap thing to do so +there's not a lot of + + align:start position:0% +there's not a lot of + + + align:start position:0% +there's not a lot of +arguments against such policies where + + align:start position:0% +arguments against such policies where + + + align:start position:0% +arguments against such policies where +you say look here's a policy that's + + align:start position:0% +you say look here's a policy that's + + + align:start position:0% +you say look here's a policy that's +extremely cheap to do some people are + + align:start position:0% +extremely cheap to do some people are + + + align:start position:0% +extremely cheap to do some people are +benefiting presumably showing up in + + align:start position:0% +benefiting presumably showing up in + + + align:start position:0% +benefiting presumably showing up in +court is a good thing + + align:start position:0% +court is a good thing + + + align:start position:0% +court is a good thing +for your court hearing and it's cheap + + align:start position:0% +for your court hearing and it's cheap + + + align:start position:0% +for your court hearing and it's cheap +things to do + + align:start position:0% +things to do + + + align:start position:0% +things to do +um and the benefits are potentially + + align:start position:0% +um and the benefits are potentially + + + align:start position:0% +um and the benefits are potentially +large because you'll now be prevent some + + align:start position:0% +large because you'll now be prevent some + + + align:start position:0% +large because you'll now be prevent some +people for + + align:start position:0% +people for + + + align:start position:0% +people for +from uh essentially ending up in jail + + align:start position:0% +from uh essentially ending up in jail + + + align:start position:0% +from uh essentially ending up in jail +for uh uh + + align:start position:0% +for uh uh + + + align:start position:0% +for uh uh +too long or for unnecessary time because + + align:start position:0% +too long or for unnecessary time because + + + align:start position:0% +too long or for unnecessary time because +they failed to appear to their hearings + + align:start position:0% +they failed to appear to their hearings + + + align:start position:0% +they failed to appear to their hearings +okay but to them i think it's also + + align:start position:0% +okay but to them i think it's also + + + align:start position:0% +okay but to them i think it's also +important so there's some examples that + + align:start position:0% +important so there's some examples that + + + align:start position:0% +important so there's some examples that +essentially show large effects including + + align:start position:0% +essentially show large effects including + + + align:start position:0% +essentially show large effects including +automatic enrollment + + align:start position:0% +automatic enrollment + + + align:start position:0% +automatic enrollment +including things like text messages or + + align:start position:0% +including things like text messages or + + + align:start position:0% +including things like text messages or +some uh + + align:start position:0% +some uh + + + align:start position:0% +some uh +interventions to induce court + + align:start position:0% +interventions to induce court + + + align:start position:0% +interventions to induce court +appearances + + align:start position:0% +appearances + + + align:start position:0% +appearances +um but it's important to understand that + + align:start position:0% +um but it's important to understand that + + + align:start position:0% +um but it's important to understand that +not everything always works + + align:start position:0% +not everything always works + + + align:start position:0% +not everything always works +what you sort of see often or what i've + + align:start position:0% +what you sort of see often or what i've + + + align:start position:0% +what you sort of see often or what i've +shown you + + align:start position:0% +shown you + + + align:start position:0% +shown you +are examples of successful examples of + + align:start position:0% +are examples of successful examples of + + + align:start position:0% +are examples of successful examples of +stuff that works + + align:start position:0% +stuff that works + + + align:start position:0% +stuff that works +but there's some examples just don't + + align:start position:0% +but there's some examples just don't + + + align:start position:0% +but there's some examples just don't +work at all so here's an example of a + + align:start position:0% +work at all so here's an example of a + + + align:start position:0% +work at all so here's an example of a +clinical trial which is called the heart + + align:start position:0% +clinical trial which is called the heart + + + align:start position:0% +clinical trial which is called the heart +strong randomized + + align:start position:0% +strong randomized + + + align:start position:0% +strong randomized +clinical trial which gave people + + align:start position:0% +clinical trial which gave people + + + align:start position:0% +clinical trial which gave people +essentially like a kitchen sink of + + align:start position:0% +essentially like a kitchen sink of + + + align:start position:0% +essentially like a kitchen sink of +things that we think are all good things + + align:start position:0% +things that we think are all good things + + + align:start position:0% +things that we think are all good things +to do + + align:start position:0% +to do + + + align:start position:0% +to do +this is stuff like reminders financial + + align:start position:0% +this is stuff like reminders financial + + + align:start position:0% +this is stuff like reminders financial +incentives social support + + align:start position:0% +incentives social support + + + align:start position:0% +incentives social support +and so on and so forth for people + + align:start position:0% +and so on and so forth for people + + + align:start position:0% +and so on and so forth for people +essentially who had heart attacks + + align:start position:0% +essentially who had heart attacks + + + align:start position:0% +essentially who had heart attacks +by giving them like wireless models + + align:start position:0% +by giving them like wireless models + + + align:start position:0% +by giving them like wireless models +lottery based incentives + + align:start position:0% +lottery based incentives + + + align:start position:0% +lottery based incentives +uh and again social support by sort of + + align:start position:0% +uh and again social support by sort of + + + align:start position:0% +uh and again social support by sort of +having um + + align:start position:0% +having um + + + align:start position:0% +having um +friends and family to to help them and + + align:start position:0% +friends and family to to help them and + + + align:start position:0% +friends and family to to help them and +essentially that did exactly + + align:start position:0% +essentially that did exactly + + + align:start position:0% +essentially that did exactly +nothing for people and sort of had no + + align:start position:0% +nothing for people and sort of had no + + + align:start position:0% +nothing for people and sort of had no +effect whatsoever + + align:start position:0% +effect whatsoever + + + align:start position:0% +effect whatsoever +so it's not to say that like we think + + align:start position:0% +so it's not to say that like we think + + + align:start position:0% +so it's not to say that like we think +like everything works always and like we + + align:start position:0% +like everything works always and like we + + + align:start position:0% +like everything works always and like we +should just always nudge people and + + align:start position:0% +should just always nudge people and + + + align:start position:0% +should just always nudge people and +provide incentives and so on and so + + align:start position:0% +provide incentives and so on and so + + + align:start position:0% +provide incentives and so on and so +forth + + align:start position:0% +forth + + + align:start position:0% +forth +it's something that like might work but + + align:start position:0% +it's something that like might work but + + + align:start position:0% +it's something that like might work but +in fact there's no reason to think that + + align:start position:0% +in fact there's no reason to think that + + + align:start position:0% +in fact there's no reason to think that +it might always work + + align:start position:0% +it might always work + + + align:start position:0% +it might always work +in some situations this might be helpful + + align:start position:0% +in some situations this might be helpful + + + align:start position:0% +in some situations this might be helpful +and others um + + align:start position:0% +and others um + + + align:start position:0% +and others um +not more concerningly there's also + + align:start position:0% +not more concerningly there's also + + + align:start position:0% +not more concerningly there's also +recently and there's a very recent paper + + align:start position:0% +recently and there's a very recent paper + + + align:start position:0% +recently and there's a very recent paper +from stefano lavina that just came out + + align:start position:0% +from stefano lavina that just came out + + + align:start position:0% +from stefano lavina that just came out +like a week ago that looks at um + + align:start position:0% +like a week ago that looks at um + + + align:start position:0% +like a week ago that looks at um +academic studies and nudged units + + align:start position:0% +academic studies and nudged units + + + align:start position:0% +academic studies and nudged units +that's to say what they're trying to do + + align:start position:0% +that's to say what they're trying to do + + + align:start position:0% +that's to say what they're trying to do +is look at treatment effects in academic + + align:start position:0% +is look at treatment effects in academic + + + align:start position:0% +is look at treatment effects in academic +studies that are published in papers + + align:start position:0% +studies that are published in papers + + + align:start position:0% +studies that are published in papers +which are papers like yeah uh the the + + align:start position:0% +which are papers like yeah uh the the + + + align:start position:0% +which are papers like yeah uh the the +stuff that we saw on default effects and + + align:start position:0% +stuff that we saw on default effects and + + + align:start position:0% +stuff that we saw on default effects and +so on which is carol at all is one of + + align:start position:0% +so on which is carol at all is one of + + + align:start position:0% +so on which is carol at all is one of +the following key savings one + + align:start position:0% +the following key savings one + + + align:start position:0% +the following key savings one +there's here's the um the study on fafsa + + align:start position:0% +there's here's the um the study on fafsa + + + align:start position:0% +there's here's the um the study on fafsa +enrollment that i showed you + + align:start position:0% +enrollment that i showed you + + + align:start position:0% +enrollment that i showed you +there's some changing order of + + align:start position:0% +there's some changing order of + + + align:start position:0% +there's some changing order of +menu orders in buffet line for healthier + + align:start position:0% +menu orders in buffet line for healthier + + + align:start position:0% +menu orders in buffet line for healthier +food consumption so there's a bunch of + + align:start position:0% +food consumption so there's a bunch of + + + align:start position:0% +food consumption so there's a bunch of +sort of papers that usually you would + + align:start position:0% +sort of papers that usually you would + + + align:start position:0% +sort of papers that usually you would +teach in like a typical class + + align:start position:0% +teach in like a typical class + + + align:start position:0% +teach in like a typical class +and what you see here is on the x-axis + + align:start position:0% +and what you see here is on the x-axis + + + align:start position:0% +and what you see here is on the x-axis +or so on the y-axis you see treatment + + align:start position:0% +or so on the y-axis you see treatment + + + align:start position:0% +or so on the y-axis you see treatment +effects and percentage points + + align:start position:0% +effects and percentage points + + + align:start position:0% +effects and percentage points +on the x-axis you see the control group + + align:start position:0% +on the x-axis you see the control group + + + align:start position:0% +on the x-axis you see the control group +take up which is to say + + align:start position:0% +take up which is to say + + + align:start position:0% +take up which is to say +if you don't do anything what does the + + align:start position:0% +if you don't do anything what does the + + + align:start position:0% +if you don't do anything what does the +control group do + + align:start position:0% +control group do + + + align:start position:0% +control group do +and what you see is pretty large effect + + align:start position:0% +and what you see is pretty large effect + + + align:start position:0% +and what you see is pretty large effect +in many of these studies that are + + align:start position:0% +in many of these studies that are + + + align:start position:0% +in many of these studies that are +published there's some questions on this + + align:start position:0% +published there's some questions on this + + + align:start position:0% +published there's some questions on this +is like u-shaped or inverse you whatever + + align:start position:0% +is like u-shaped or inverse you whatever + + + align:start position:0% +is like u-shaped or inverse you whatever +let's ignore that for a second but + + align:start position:0% +let's ignore that for a second but + + + align:start position:0% +let's ignore that for a second but +overall what you see is pretty large + + align:start position:0% +overall what you see is pretty large + + + align:start position:0% +overall what you see is pretty large +treatment effects in + + align:start position:0% +treatment effects in + + + align:start position:0% +treatment effects in +situations when you then look at + + align:start position:0% +situations when you then look at + + + align:start position:0% +situations when you then look at +and this is like 20 cl6 trials and set + + align:start position:0% +and this is like 20 cl6 trials and set + + + align:start position:0% +and this is like 20 cl6 trials and set +71 different + + align:start position:0% +71 different + + + align:start position:0% +71 different +nudges here when you instead look at + + align:start position:0% +nudges here when you instead look at + + + align:start position:0% +nudges here when you instead look at +uh nudge units so what are nudge units + + align:start position:0% +uh nudge units so what are nudge units + + + align:start position:0% +uh nudge units so what are nudge units +these are essentially + + align:start position:0% +these are essentially + + + align:start position:0% +these are essentially +for example the uk government has the + + align:start position:0% +for example the uk government has the + + + align:start position:0% +for example the uk government has the +uh what's called the bit the behavioral + + align:start position:0% +uh what's called the bit the behavioral + + + align:start position:0% +uh what's called the bit the behavioral +insights team + + align:start position:0% +insights team + + + align:start position:0% +insights team +which essentially is a team inside the + + align:start position:0% +which essentially is a team inside the + + + align:start position:0% +which essentially is a team inside the +uk government + + align:start position:0% +uk government + + + align:start position:0% +uk government +that tries to support or like nudge + + align:start position:0% +that tries to support or like nudge + + + align:start position:0% +that tries to support or like nudge +people to make better choices that's + + align:start position:0% +people to make better choices that's + + + align:start position:0% +people to make better choices that's +very much sort of like + + align:start position:0% +very much sort of like + + + align:start position:0% +very much sort of like +coming from the nudge movement from + + align:start position:0% +coming from the nudge movement from + + + align:start position:0% +coming from the nudge movement from +failure and so on that sort of like + + align:start position:0% +failure and so on that sort of like + + + align:start position:0% +failure and so on that sort of like +advise the uk government to set this up + + align:start position:0% +advise the uk government to set this up + + + align:start position:0% +advise the uk government to set this up +and they're now nudging away because the + + align:start position:0% +and they're now nudging away because the + + + align:start position:0% +and they're now nudging away because the +government is really happy about cheap + + align:start position:0% +government is really happy about cheap + + + align:start position:0% +government is really happy about cheap +stuff that doesn't cost + + align:start position:0% +stuff that doesn't cost + + + align:start position:0% +stuff that doesn't cost +very much but potentially has like large + + align:start position:0% +very much but potentially has like large + + + align:start position:0% +very much but potentially has like large +benefits + + align:start position:0% +benefits + + + align:start position:0% +benefits +now what then um + + align:start position:0% +now what then um + + + align:start position:0% +now what then um +what they then also do often is they + + align:start position:0% +what they then also do often is they + + + align:start position:0% +what they then also do often is they +evaluate their + + align:start position:0% +evaluate their + + + align:start position:0% +evaluate their +interventions in part because they try + + align:start position:0% +interventions in part because they try + + + align:start position:0% +interventions in part because they try +to figure out what works best + + align:start position:0% +to figure out what works best + + + align:start position:0% +to figure out what works best +now when you look at these interventions + + align:start position:0% +now when you look at these interventions + + + align:start position:0% +now when you look at these interventions +you see essentially that the + + align:start position:0% +you see essentially that the + + + align:start position:0% +you see essentially that the +treatment effects in those kinds of + + align:start position:0% +treatment effects in those kinds of + + + align:start position:0% +treatment effects in those kinds of +interventions tend to be much larger + + align:start position:0% +interventions tend to be much larger + + + align:start position:0% +interventions tend to be much larger +than on the left if you look at the + + align:start position:0% +than on the left if you look at the + + + align:start position:0% +than on the left if you look at the +right there's a bunch of stuff on just + + align:start position:0% +right there's a bunch of stuff on just + + + align:start position:0% +right there's a bunch of stuff on just +massive bunch of points that are pretty + + align:start position:0% +massive bunch of points that are pretty + + + align:start position:0% +massive bunch of points that are pretty +high above 10 20 + + align:start position:0% +high above 10 20 + + + align:start position:0% +high above 10 20 +when you look to the right essentially + + align:start position:0% +when you look to the right essentially + + + align:start position:0% +when you look to the right essentially +you see almost everything is between + + align:start position:0% +you see almost everything is between + + + align:start position:0% +you see almost everything is between +zero and ten percent + + align:start position:0% +zero and ten percent + + + align:start position:0% +zero and ten percent +uh a lot of it seems to be not + + align:start position:0% +uh a lot of it seems to be not + + + align:start position:0% +uh a lot of it seems to be not +statistically significantly differently + + align:start position:0% +statistically significantly differently + + + align:start position:0% +statistically significantly differently +from + + align:start position:0% +from + + + align:start position:0% +from +uh different from zero so that should + + align:start position:0% +uh different from zero so that should + + + align:start position:0% +uh different from zero so that should +give us some pause + + align:start position:0% +give us some pause + + + align:start position:0% +give us some pause +uh in the sense of like we should be + + align:start position:0% +uh in the sense of like we should be + + + align:start position:0% +uh in the sense of like we should be +careful and and sort of necessarily + + align:start position:0% +careful and and sort of necessarily + + + align:start position:0% +careful and and sort of necessarily +recommending a bunch of stuff to + + align:start position:0% +recommending a bunch of stuff to + + + align:start position:0% +recommending a bunch of stuff to +governments and saying like we should + + align:start position:0% +governments and saying like we should + + + align:start position:0% +governments and saying like we should +always nudge and so on and so forth + + align:start position:0% +always nudge and so on and so forth + + + align:start position:0% +always nudge and so on and so forth +um what's going on here well some of + + align:start position:0% +um what's going on here well some of + + + align:start position:0% +um what's going on here well some of +this could be about + + align:start position:0% +this could be about + + + align:start position:0% +this could be about +uh publication bias like essentially + + align:start position:0% +uh publication bias like essentially + + + align:start position:0% +uh publication bias like essentially +there's a bunch of studies that are + + align:start position:0% +there's a bunch of studies that are + + + align:start position:0% +there's a bunch of studies that are +being run and what's being published is + + align:start position:0% +being run and what's being published is + + + align:start position:0% +being run and what's being published is +essentially stuff that's highly + + align:start position:0% +essentially stuff that's highly + + + align:start position:0% +essentially stuff that's highly +significant and flashy and important + + align:start position:0% +significant and flashy and important + + + align:start position:0% +significant and flashy and important +there could be also issues with + + align:start position:0% +there could be also issues with + + + align:start position:0% +there could be also issues with +implementation that maybe what's done + + align:start position:0% +implementation that maybe what's done + + + align:start position:0% +implementation that maybe what's done +with researchers + + align:start position:0% +with researchers + + + align:start position:0% +with researchers +is sort of implemented better + + align:start position:0% +is sort of implemented better + + + align:start position:0% +is sort of implemented better +potentially + + align:start position:0% +potentially + + + align:start position:0% +potentially +and maybe what's done at scale it's just + + align:start position:0% +and maybe what's done at scale it's just + + + align:start position:0% +and maybe what's done at scale it's just +harder to do a nudge units and harder to + + align:start position:0% +harder to do a nudge units and harder to + + + align:start position:0% +harder to do a nudge units and harder to +carefully and then the effects might be + + align:start position:0% +carefully and then the effects might be + + + align:start position:0% +carefully and then the effects might be +lower not to say that governments + + align:start position:0% +lower not to say that governments + + + align:start position:0% +lower not to say that governments +shouldn't nudge in the sense that like + + align:start position:0% +shouldn't nudge in the sense that like + + + align:start position:0% +shouldn't nudge in the sense that like +if they would if there are effects of + + align:start position:0% +if they would if there are effects of + + + align:start position:0% +if they would if there are effects of +the order of magnitude of something like + + align:start position:0% +the order of magnitude of something like + + + align:start position:0% +the order of magnitude of something like + + align:start position:0% + + + align:start position:0% +and that's really percentage points and + + align:start position:0% +and that's really percentage points and + + + align:start position:0% +and that's really percentage points and +that's really cheap to do you should + + align:start position:0% +that's really cheap to do you should + + + align:start position:0% +that's really cheap to do you should +probably do it anyway + + align:start position:0% +probably do it anyway + + + align:start position:0% +probably do it anyway +um but it's just the same not just are + + align:start position:0% +um but it's just the same not just are + + + align:start position:0% +um but it's just the same not just are +not the magic bullet that sort of + + align:start position:0% +not the magic bullet that sort of + + + align:start position:0% +not the magic bullet that sort of +changed everything that the government + + align:start position:0% +changed everything that the government + + + align:start position:0% +changed everything that the government +should always engage on them + + align:start position:0% +should always engage on them + + + align:start position:0% +should always engage on them +and it's quite important in fact for the + + align:start position:0% +and it's quite important in fact for the + + + align:start position:0% +and it's quite important in fact for the +government or governments or any sort of + + align:start position:0% +government or governments or any sort of + + + align:start position:0% +government or governments or any sort of +these + + align:start position:0% +these + + + align:start position:0% +these +policy units and firms by the way the + + align:start position:0% +policy units and firms by the way the + + + align:start position:0% +policy units and firms by the way the +exact same thing + + align:start position:0% +exact same thing + + + align:start position:0% +exact same thing +to try and figure out what works and + + align:start position:0% +to try and figure out what works and + + + align:start position:0% +to try and figure out what works and +what doesn't and not just rely on the + + align:start position:0% +what doesn't and not just rely on the + + + align:start position:0% +what doesn't and not just rely on the +academic evidence that + + align:start position:0% +academic evidence that + + + align:start position:0% +academic evidence that +uh might sort of be more proof of + + align:start position:0% +uh might sort of be more proof of + + + align:start position:0% +uh might sort of be more proof of +concept rather than sort of something + + align:start position:0% +concept rather than sort of something + + + align:start position:0% +concept rather than sort of something +that + + align:start position:0% +that + + + align:start position:0% +that +evaluates cost effectiveness any + + align:start position:0% +evaluates cost effectiveness any + + + align:start position:0% +evaluates cost effectiveness any +questions on this + + align:start position:0% + + + + align:start position:0% + +now another question this is a little + + align:start position:0% +now another question this is a little + + + align:start position:0% +now another question this is a little +blurry um another question you might ask + + align:start position:0% +blurry um another question you might ask + + + align:start position:0% +blurry um another question you might ask +um and you might have seen these kinds + + align:start position:0% +um and you might have seen these kinds + + + align:start position:0% +um and you might have seen these kinds +of letters before + + align:start position:0% +of letters before + + + align:start position:0% +of letters before +whether everybody wants to be notched + + align:start position:0% +whether everybody wants to be notched + + + align:start position:0% +whether everybody wants to be notched +and so what um there's a very + + align:start position:0% +and so what um there's a very + + + align:start position:0% +and so what um there's a very +famous study by alcott and others that + + align:start position:0% +famous study by alcott and others that + + + align:start position:0% +famous study by alcott and others that +look at + + align:start position:0% +look at + + + align:start position:0% +look at +energy comparisons that's a study done + + align:start position:0% +energy comparisons that's a study done + + + align:start position:0% +energy comparisons that's a study done +with o power of the company + + align:start position:0% +with o power of the company + + + align:start position:0% +with o power of the company +um that essentially tries to reduce + + align:start position:0% +um that essentially tries to reduce + + + align:start position:0% +um that essentially tries to reduce +energy usage + + align:start position:0% +energy usage + + + align:start position:0% +energy usage +and the way this works is what you do is + + align:start position:0% +and the way this works is what you do is + + + align:start position:0% +and the way this works is what you do is +um you send people + + align:start position:0% +um you send people + + + align:start position:0% +um you send people +these kinds of letters and i'm getting + + align:start position:0% +these kinds of letters and i'm getting + + + align:start position:0% +these kinds of letters and i'm getting +these letters um too that sort of says + + align:start position:0% +these letters um too that sort of says + + + align:start position:0% +these letters um too that sort of says +here's your + + align:start position:0% +here's your + + + align:start position:0% +here's your +um here's your energy consumption in the + + align:start position:0% +um here's your energy consumption in the + + + align:start position:0% +um here's your energy consumption in the +last + + align:start position:0% +last + + + align:start position:0% +last +month the month last year here is + + align:start position:0% +month the month last year here is + + + align:start position:0% +month the month last year here is +um all of your neighbors so it's a + + align:start position:0% +um all of your neighbors so it's a + + + align:start position:0% +um all of your neighbors so it's a +comparison you see + + align:start position:0% +comparison you see + + + align:start position:0% +comparison you see +this the blue bars like how much did you + + align:start position:0% +this the blue bars like how much did you + + + align:start position:0% +this the blue bars like how much did you +use and the + + align:start position:0% +use and the + + + align:start position:0% +use and the +the gray bars like how much did all of + + align:start position:0% +the gray bars like how much did all of + + + align:start position:0% +the gray bars like how much did all of +your neighbors use + + align:start position:0% +your neighbors use + + + align:start position:0% +your neighbors use +and then there's the green bar that sort + + align:start position:0% +and then there's the green bar that sort + + + align:start position:0% +and then there's the green bar that sort +of says how much do efficient neighbors + + align:start position:0% +of says how much do efficient neighbors + + + align:start position:0% +of says how much do efficient neighbors +use + + align:start position:0% +use + + + align:start position:0% +use +and then there's like smileys where you + + align:start position:0% +and then there's like smileys where you + + + align:start position:0% +and then there's like smileys where you +have like uh two smileys if you're doing + + align:start position:0% +have like uh two smileys if you're doing + + + align:start position:0% +have like uh two smileys if you're doing +great one smiley if you're doing good + + align:start position:0% +great one smiley if you're doing good + + + align:start position:0% +great one smiley if you're doing good +like this + + align:start position:0% +like this + + + align:start position:0% +like this +fellow here and then there's no smiley i + + align:start position:0% +fellow here and then there's no smiley i + + + align:start position:0% +fellow here and then there's no smiley i +guess if you're + + align:start position:0% +guess if you're + + + align:start position:0% +guess if you're +if you're not doing well sometimes + + align:start position:0% +if you're not doing well sometimes + + + align:start position:0% +if you're not doing well sometimes +there's also like a sad smiley if you're + + align:start position:0% +there's also like a sad smiley if you're + + + align:start position:0% +there's also like a sad smiley if you're +using lots of energy and so on + + align:start position:0% +using lots of energy and so on + + + align:start position:0% +using lots of energy and so on +and so then there's some essentially + + align:start position:0% +and so then there's some essentially + + + align:start position:0% +and so then there's some essentially +what this is trying to do is trying to + + align:start position:0% +what this is trying to do is trying to + + + align:start position:0% +what this is trying to do is trying to +provide some social comparison here + + align:start position:0% +provide some social comparison here + + + align:start position:0% +provide some social comparison here +it's a very cheap policy to do in + + align:start position:0% +it's a very cheap policy to do in + + + align:start position:0% +it's a very cheap policy to do in +particular um + + align:start position:0% +particular um + + + align:start position:0% +particular um +when you're sending sort of energy bills + + align:start position:0% +when you're sending sort of energy bills + + + align:start position:0% +when you're sending sort of energy bills +anyway it's very cheap to sort of add + + align:start position:0% +anyway it's very cheap to sort of add + + + align:start position:0% +anyway it's very cheap to sort of add +this at the top + + align:start position:0% +this at the top + + + align:start position:0% +this at the top +where essentially you're sending people + + align:start position:0% +where essentially you're sending people + + + align:start position:0% +where essentially you're sending people +energy bills anyway and now you're sort + + align:start position:0% +energy bills anyway and now you're sort + + + align:start position:0% +energy bills anyway and now you're sort +of adding the social comparison to try + + align:start position:0% +of adding the social comparison to try + + + align:start position:0% +of adding the social comparison to try +to nudge people to use less energy + + align:start position:0% +to nudge people to use less energy + + + align:start position:0% +to nudge people to use less energy +um there's a question of why the company + + align:start position:0% +um there's a question of why the company + + + align:start position:0% +um there's a question of why the company +might do that but that's sort of like a + + align:start position:0% +might do that but that's sort of like a + + + align:start position:0% +might do that but that's sort of like a +separate + + align:start position:0% +separate + + + align:start position:0% +separate +issue and what you see here is when you + + align:start position:0% +issue and what you see here is when you + + + align:start position:0% +issue and what you see here is when you +look at + + align:start position:0% +look at + + + align:start position:0% +look at +people when you look at treatment + + align:start position:0% +people when you look at treatment + + + align:start position:0% +people when you look at treatment +effects there tends to be + + align:start position:0% +effects there tends to be + + + align:start position:0% +effects there tends to be +clear treatment effects at least some + + align:start position:0% +clear treatment effects at least some + + + align:start position:0% +clear treatment effects at least some +treatment effects of + + align:start position:0% +treatment effects of + + + align:start position:0% +treatment effects of +providing this kind of information + + align:start position:0% +providing this kind of information + + + align:start position:0% +providing this kind of information +reduces + + align:start position:0% +reduces + + + align:start position:0% +reduces +overall energy + + align:start position:0% +overall energy + + + align:start position:0% +overall energy +consumption of rcts that people have + + align:start position:0% +consumption of rcts that people have + + + align:start position:0% +consumption of rcts that people have +now one question you might ask is well + + align:start position:0% +now one question you might ask is well + + + align:start position:0% +now one question you might ask is well +shouldn't we + + align:start position:0% +shouldn't we + + + align:start position:0% +shouldn't we +then always do this so what's the reason + + align:start position:0% +then always do this so what's the reason + + + align:start position:0% +then always do this so what's the reason +not to do that and it turns out + + align:start position:0% +not to do that and it turns out + + + align:start position:0% +not to do that and it turns out +not everybody um wants to be notched so + + align:start position:0% +not everybody um wants to be notched so + + + align:start position:0% +not everybody um wants to be notched so +here's an intervention where + + align:start position:0% +here's an intervention where + + + align:start position:0% +here's an intervention where +now again alcott and co-author have now + + align:start position:0% +now again alcott and co-author have now + + + align:start position:0% +now again alcott and co-author have now +in fact asked people about would you + + align:start position:0% +in fact asked people about would you + + + align:start position:0% +in fact asked people about would you +like to receive these letters + + align:start position:0% +like to receive these letters + + + align:start position:0% +like to receive these letters +and what they ask is would you like to + + align:start position:0% +and what they ask is would you like to + + + align:start position:0% +and what they ask is would you like to +receive these kinds of social + + align:start position:0% +receive these kinds of social + + + align:start position:0% +receive these kinds of social +comparisons + + align:start position:0% +comparisons + + + align:start position:0% +comparisons +and what they ask is um uh what's your + + align:start position:0% +and what they ask is um uh what's your + + + align:start position:0% +and what they ask is um uh what's your +positive willingness to pay for it + + align:start position:0% +positive willingness to pay for it + + + align:start position:0% +positive willingness to pay for it +so would you like to have a dollar + + align:start position:0% +so would you like to have a dollar + + + align:start position:0% +so would you like to have a dollar +versus these reports + + align:start position:0% +versus these reports + + + align:start position:0% +versus these reports +boy so a dollar no no reports versus um + + align:start position:0% +boy so a dollar no no reports versus um + + + align:start position:0% +boy so a dollar no no reports versus um +just receiving the reports + + align:start position:0% +just receiving the reports + + + align:start position:0% +just receiving the reports +what is people's willingness to pay but + + align:start position:0% +what is people's willingness to pay but + + + align:start position:0% +what is people's willingness to pay but +they also ask their willingness to pay + + align:start position:0% +they also ask their willingness to pay + + + align:start position:0% +they also ask their willingness to pay +not to receive these reports that is to + + align:start position:0% +not to receive these reports that is to + + + align:start position:0% +not to receive these reports that is to +say i could either tell you + + align:start position:0% +say i could either tell you + + + align:start position:0% +say i could either tell you +i i would ask you like you receive a + + align:start position:0% +i i would ask you like you receive a + + + align:start position:0% +i i would ask you like you receive a +dollar um + + align:start position:0% +dollar um + + + align:start position:0% +dollar um +at no reports or um uh or sorry + + align:start position:0% +at no reports or um uh or sorry + + + align:start position:0% +at no reports or um uh or sorry +you receive zero dollars and no reports + + align:start position:0% +you receive zero dollars and no reports + + + align:start position:0% +you receive zero dollars and no reports +or received a dollar and the reports and + + align:start position:0% +or received a dollar and the reports and + + + align:start position:0% +or received a dollar and the reports and +some people sort of turned that down + + align:start position:0% +some people sort of turned that down + + + align:start position:0% +some people sort of turned that down +which essentially implies that they'd + + align:start position:0% +which essentially implies that they'd + + + align:start position:0% +which essentially implies that they'd +rather have one + + align:start position:0% +rather have one + + + align:start position:0% +rather have one +or less and no reports they are willing + + align:start position:0% +or less and no reports they are willing + + + align:start position:0% +or less and no reports they are willing +to pay not to receive these reports + + align:start position:0% +to pay not to receive these reports + + + align:start position:0% +to pay not to receive these reports +and this is what you see here on the + + align:start position:0% +and this is what you see here on the + + + align:start position:0% +and this is what you see here on the +left is essentially people's willingness + + align:start position:0% +left is essentially people's willingness + + + align:start position:0% +left is essentially people's willingness +to pay for home reports + + align:start position:0% +to pay for home reports + + + align:start position:0% +to pay for home reports +so there are quite a few people here on + + align:start position:0% +so there are quite a few people here on + + + align:start position:0% +so there are quite a few people here on +the right who have positive willingness + + align:start position:0% +the right who have positive willingness + + + align:start position:0% +the right who have positive willingness +to pay they think it's kind of useful + + align:start position:0% +to pay they think it's kind of useful + + + align:start position:0% +to pay they think it's kind of useful +it's kind of interesting maybe it helps + + align:start position:0% +it's kind of interesting maybe it helps + + + align:start position:0% +it's kind of interesting maybe it helps +them reduce their energy consumption + + align:start position:0% +them reduce their energy consumption + + + align:start position:0% +them reduce their energy consumption +maybe that motivates them in certain + + align:start position:0% +maybe that motivates them in certain + + + align:start position:0% +maybe that motivates them in certain +ways + + align:start position:0% +ways + + + align:start position:0% +ways +but some people are just like saying + + align:start position:0% +but some people are just like saying + + + align:start position:0% +but some people are just like saying +essentially i do not want these reports + + align:start position:0% +essentially i do not want these reports + + + align:start position:0% +essentially i do not want these reports +the reason being that essentially it's + + align:start position:0% +the reason being that essentially it's + + + align:start position:0% +the reason being that essentially it's +kind of just annoying to like + + align:start position:0% +kind of just annoying to like + + + align:start position:0% +kind of just annoying to like +get nag all the time if you want to sort + + align:start position:0% +get nag all the time if you want to sort + + + align:start position:0% +get nag all the time if you want to sort +of maybe in some cases you just don't + + align:start position:0% +of maybe in some cases you just don't + + + align:start position:0% +of maybe in some cases you just don't +have a lot of choice + + align:start position:0% +have a lot of choice + + + align:start position:0% +have a lot of choice +in some cases maybe you just like to use + + align:start position:0% +in some cases maybe you just like to use + + + align:start position:0% +in some cases maybe you just like to use +lots of energy for whatever reason + + align:start position:0% +lots of energy for whatever reason + + + align:start position:0% +lots of energy for whatever reason +and it's really annoying to be told all + + align:start position:0% +and it's really annoying to be told all + + + align:start position:0% +and it's really annoying to be told all +the time that you're like neighbor is + + align:start position:0% +the time that you're like neighbor is + + + align:start position:0% +the time that you're like neighbor is +really better than you are + + align:start position:0% +really better than you are + + + align:start position:0% +really better than you are +uh makes people look just uncomfortable + + align:start position:0% +uh makes people look just uncomfortable + + + align:start position:0% +uh makes people look just uncomfortable +and makes them unhappy and so on and so + + align:start position:0% +and makes them unhappy and so on and so + + + align:start position:0% +and makes them unhappy and so on and so +forth + + align:start position:0% +forth + + + align:start position:0% +forth +uh maybe it makes them feel guilty who + + align:start position:0% +uh maybe it makes them feel guilty who + + + align:start position:0% +uh maybe it makes them feel guilty who +knows um + + align:start position:0% +knows um + + + align:start position:0% +knows um +maybe just don't want to think about it + + align:start position:0% +maybe just don't want to think about it + + + align:start position:0% +maybe just don't want to think about it +but importantly + + align:start position:0% +but importantly + + + align:start position:0% +but importantly +there are some people who just do not + + align:start position:0% +there are some people who just do not + + + align:start position:0% +there are some people who just do not +want to be nudged + + align:start position:0% +want to be nudged + + + align:start position:0% +want to be nudged +and i think that's important um because + + align:start position:0% +and i think that's important um because + + + align:start position:0% +and i think that's important um because +you know when you think back about the + + align:start position:0% +you know when you think back about the + + + align:start position:0% +you know when you think back about the +libertarian paternalism or the + + align:start position:0% +libertarian paternalism or the + + + align:start position:0% +libertarian paternalism or the +soft paternalism criteria asymmetric + + align:start position:0% +soft paternalism criteria asymmetric + + + align:start position:0% +soft paternalism criteria asymmetric +paternalism that we + + align:start position:0% +paternalism that we + + + align:start position:0% +paternalism that we +talked about well what the asymmetric + + align:start position:0% +talked about well what the asymmetric + + + align:start position:0% +talked about well what the asymmetric +paternalism would say is we should not + + align:start position:0% +paternalism would say is we should not + + + align:start position:0% +paternalism would say is we should not +make anybody + + align:start position:0% +make anybody + + + align:start position:0% +make anybody +um worse off so now if you send all + + align:start position:0% +um worse off so now if you send all + + + align:start position:0% +um worse off so now if you send all +these letters and make actually people + + align:start position:0% +these letters and make actually people + + + align:start position:0% +these letters and make actually people +feel people + + align:start position:0% +feel people + + + align:start position:0% +feel people +uncomfortable then in fact we are + + align:start position:0% +uncomfortable then in fact we are + + + align:start position:0% +uncomfortable then in fact we are +potentially making people + + align:start position:0% +potentially making people + + + align:start position:0% +potentially making people +um worse up and you can think about some + + align:start position:0% +um worse up and you can think about some + + + align:start position:0% +um worse up and you can think about some +other types of + + align:start position:0% +other types of + + + align:start position:0% +other types of +uh intervention if you think about if + + align:start position:0% +uh intervention if you think about if + + + align:start position:0% +uh intervention if you think about if +you got like letters from my tells you + + align:start position:0% +you got like letters from my tells you + + + align:start position:0% +you got like letters from my tells you +all the time how are you doing compared + + align:start position:0% +all the time how are you doing compared + + + align:start position:0% +all the time how are you doing compared +to + + align:start position:0% +to + + + align:start position:0% +to +um classmates of + + align:start position:0% +um classmates of + + + align:start position:0% +um classmates of +um uh uh study efforts in terms of like + + align:start position:0% +um uh uh study efforts in terms of like + + + align:start position:0% +um uh uh study efforts in terms of like +problem sets and changes and so on + + align:start position:0% +problem sets and changes and so on + + + align:start position:0% +problem sets and changes and so on +um potentially you know that would + + align:start position:0% +um potentially you know that would + + + align:start position:0% +um potentially you know that would +likely + + align:start position:0% +likely + + + align:start position:0% +likely +increase study efforts in some ways and + + align:start position:0% +increase study efforts in some ways and + + + align:start position:0% +increase study efforts in some ways and +we would perhaps increase learning in + + align:start position:0% +we would perhaps increase learning in + + + align:start position:0% +we would perhaps increase learning in +some ways + + align:start position:0% +some ways + + + align:start position:0% +some ways +but it's not clear at all that we would + + align:start position:0% +but it's not clear at all that we would + + + align:start position:0% +but it's not clear at all that we would +increase welfare because maybe everybody + + align:start position:0% +increase welfare because maybe everybody + + + align:start position:0% +increase welfare because maybe everybody +would be even more stressed and + + align:start position:0% +would be even more stressed and + + + align:start position:0% +would be even more stressed and +everybody would sort of + + align:start position:0% +everybody would sort of + + + align:start position:0% +everybody would sort of +be less happy and so on and so forth at + + align:start position:0% +be less happy and so on and so forth at + + + align:start position:0% +be less happy and so on and so forth at +least + + align:start position:0% +least + + + align:start position:0% +least +in some cases um + + align:start position:0% +in some cases um + + + align:start position:0% +in some cases um +yeah so um actually so jenna is asking a + + align:start position:0% +yeah so um actually so jenna is asking a + + + align:start position:0% +yeah so um actually so jenna is asking a +question about like who's unhappy about + + align:start position:0% +question about like who's unhappy about + + + align:start position:0% +question about like who's unhappy about +this + + align:start position:0% +this + + + align:start position:0% +this +um i think + + align:start position:0% + + + + align:start position:0% + +what's so inside so the isometric + + align:start position:0% +what's so inside so the isometric + + + align:start position:0% +what's so inside so the isometric +paternalism is just to say + + align:start position:0% +paternalism is just to say + + + align:start position:0% +paternalism is just to say +suppose there are some people who are + + align:start position:0% +suppose there are some people who are + + + align:start position:0% +suppose there are some people who are +just very happy with that choice about + + align:start position:0% +just very happy with that choice about + + + align:start position:0% +just very happy with that choice about +using logi + + align:start position:0% +using logi + + + align:start position:0% +using logi +and they just don't want to be nudged + + align:start position:0% +and they just don't want to be nudged + + + align:start position:0% +and they just don't want to be nudged +they don't want to they're fully + + align:start position:0% +they don't want to they're fully + + + align:start position:0% +they don't want to they're fully +rationally choosing this + + align:start position:0% +rationally choosing this + + + align:start position:0% +rationally choosing this +maybe they know sort of deep down in + + align:start position:0% +maybe they know sort of deep down in + + + align:start position:0% +maybe they know sort of deep down in +their heart and it's bad to like uh ruin + + align:start position:0% +their heart and it's bad to like uh ruin + + + align:start position:0% +their heart and it's bad to like uh ruin +the + + align:start position:0% +the + + + align:start position:0% +the +the planets and climate and so on and so + + align:start position:0% +the planets and climate and so on and so + + + align:start position:0% +the planets and climate and so on and so +forth but they really made a choice that + + align:start position:0% +forth but they really made a choice that + + + align:start position:0% +forth but they really made a choice that +they want + + align:start position:0% +they want + + + align:start position:0% +they want +lots of energy those people are not the + + align:start position:0% +lots of energy those people are not the + + + align:start position:0% +lots of energy those people are not the +people who want to receive any letters + + align:start position:0% +people who want to receive any letters + + + align:start position:0% +people who want to receive any letters +so things geometric patronalism would + + align:start position:0% +so things geometric patronalism would + + + align:start position:0% +so things geometric patronalism would +say + + align:start position:0% +say + + + align:start position:0% +say +we should just leave them alone they + + align:start position:0% +we should just leave them alone they + + + align:start position:0% +we should just leave them alone they +should just be doing whatever they want + + align:start position:0% +should just be doing whatever they want + + + align:start position:0% +should just be doing whatever they want +to do + + align:start position:0% +to do + + + align:start position:0% +to do +and us sending them letters to make them + + align:start position:0% +and us sending them letters to make them + + + align:start position:0% +and us sending them letters to make them +feel bad if they don't even change their + + align:start position:0% +feel bad if they don't even change their + + + align:start position:0% +feel bad if they don't even change their +behavior anyway + + align:start position:0% +behavior anyway + + + align:start position:0% +behavior anyway +or even if they would change their + + align:start position:0% +or even if they would change their + + + align:start position:0% +or even if they would change their +behavior that's not for us to say and we + + align:start position:0% +behavior that's not for us to say and we + + + align:start position:0% +behavior that's not for us to say and we +should just leave them alone because you + + align:start position:0% +should just leave them alone because you + + + align:start position:0% +should just leave them alone because you +make them worse off by receiving these + + align:start position:0% +make them worse off by receiving these + + + align:start position:0% +make them worse off by receiving these +letters + + align:start position:0% +letters + + + align:start position:0% +letters +by the revealed preference to say + + align:start position:0% +by the revealed preference to say + + + align:start position:0% +by the revealed preference to say +they're willing to pay not to receive + + align:start position:0% +they're willing to pay not to receive + + + align:start position:0% +they're willing to pay not to receive +these letters + + align:start position:0% +these letters + + + align:start position:0% +these letters +now there could be some situations where + + align:start position:0% +now there could be some situations where + + + align:start position:0% +now there could be some situations where +people who have potentially large + + align:start position:0% +people who have potentially large + + + align:start position:0% +people who have potentially large +treatment effects these are people who + + align:start position:0% +treatment effects these are people who + + + align:start position:0% +treatment effects these are people who +use lots of + + align:start position:0% +use lots of + + + align:start position:0% +use lots of +energy and they just don't know about it + + align:start position:0% +energy and they just don't know about it + + + align:start position:0% +energy and they just don't know about it +and those we want to sort of + + align:start position:0% +and those we want to sort of + + + align:start position:0% +and those we want to sort of +send them letters and push them but i + + align:start position:0% +send them letters and push them but i + + + align:start position:0% +send them letters and push them but i +think the whole point of the paternalism + + align:start position:0% +think the whole point of the paternalism + + + align:start position:0% +think the whole point of the paternalism +is metropolitan + + align:start position:0% +is metropolitan + + + align:start position:0% +is metropolitan +is to say we shouldn't make anybody + + align:start position:0% +is to say we shouldn't make anybody + + + align:start position:0% +is to say we shouldn't make anybody +worse off so if somebody + + align:start position:0% +worse off so if somebody + + + align:start position:0% +worse off so if somebody +reveals to us by their preference which + + align:start position:0% +reveals to us by their preference which + + + align:start position:0% +reveals to us by their preference which +is what these fellows are doing here + + align:start position:0% +is what these fellows are doing here + + + align:start position:0% +is what these fellows are doing here +that they really don't want to receive + + align:start position:0% +that they really don't want to receive + + + align:start position:0% +that they really don't want to receive +these letters we should um + + align:start position:0% +these letters we should um + + + align:start position:0% +these letters we should um +uh respect that and so the one then one + + align:start position:0% +uh respect that and so the one then one + + + align:start position:0% +uh respect that and so the one then one +potential solution here is then to say + + align:start position:0% +potential solution here is then to say + + + align:start position:0% +potential solution here is then to say +well why don't we just let people opt + + align:start position:0% +well why don't we just let people opt + + + align:start position:0% +well why don't we just let people opt +out but you just say okay + + align:start position:0% +out but you just say okay + + + align:start position:0% +out but you just say okay +you send people these letters and then + + align:start position:0% +you send people these letters and then + + + align:start position:0% +you send people these letters and then +you have to click on something or like + + align:start position:0% +you have to click on something or like + + + align:start position:0% +you have to click on something or like +you have to sort of opt in or opt out + + align:start position:0% +you have to sort of opt in or opt out + + + align:start position:0% +you have to sort of opt in or opt out +and then maybe people who really don't + + align:start position:0% +and then maybe people who really don't + + + align:start position:0% +and then maybe people who really don't +want to receive these letters + + align:start position:0% +want to receive these letters + + + align:start position:0% +want to receive these letters +we can essentially just um let them be + + align:start position:0% +we can essentially just um let them be + + + align:start position:0% +we can essentially just um let them be +that there's no judgment here in terms + + align:start position:0% +that there's no judgment here in terms + + + align:start position:0% +that there's no judgment here in terms +of like is that socially + + align:start position:0% +of like is that socially + + + align:start position:0% +of like is that socially +uh like what do we want to do when is + + align:start position:0% +uh like what do we want to do when is + + + align:start position:0% +uh like what do we want to do when is +this a good or bad thing + + align:start position:0% +this a good or bad thing + + + align:start position:0% +this a good or bad thing +this is just to say we should respect + + align:start position:0% +this is just to say we should respect + + + align:start position:0% +this is just to say we should respect +people's um uh preferences in certain + + align:start position:0% +people's um uh preferences in certain + + + align:start position:0% +people's um uh preferences in certain +ways + + align:start position:0% +ways + + + align:start position:0% +ways +does that make sense + + align:start position:0% + + + + align:start position:0% + +um now the next question you might ask + + align:start position:0% +um now the next question you might ask + + + align:start position:0% +um now the next question you might ask +is well + + align:start position:0% +is well + + + align:start position:0% +is well +what form should paternalism take and + + align:start position:0% +what form should paternalism take and + + + align:start position:0% +what form should paternalism take and +that's the thing sometimes + + align:start position:0% +that's the thing sometimes + + + align:start position:0% +that's the thing sometimes +it's important because you know you + + align:start position:0% +it's important because you know you + + + align:start position:0% +it's important because you know you +could uh take 401k savings policies + + align:start position:0% +could uh take 401k savings policies + + + align:start position:0% +could uh take 401k savings policies +you can come up with a lot of different + + align:start position:0% +you can come up with a lot of different + + + align:start position:0% +you can come up with a lot of different +options in which you could design your + + align:start position:0% +options in which you could design your + + + align:start position:0% +options in which you could design your +um um your 401k savings policies + + align:start position:0% +um um your 401k savings policies + + + align:start position:0% +um um your 401k savings policies +you could say you could have like active + + align:start position:0% +you could say you could have like active + + + align:start position:0% +you could say you could have like active +decisions you could have defaults for + + align:start position:0% +decisions you could have defaults for + + + align:start position:0% +decisions you could have defaults for +participation + + align:start position:0% +participation + + + align:start position:0% +participation +you have like defaults for less + + align:start position:0% +you have like defaults for less + + + align:start position:0% +you have like defaults for less +information + + align:start position:0% +information + + + align:start position:0% +information +you have like a personal financial + + align:start position:0% +you have like a personal financial + + + align:start position:0% +you have like a personal financial +planner um sitting down with you + + align:start position:0% +planner um sitting down with you + + + align:start position:0% +planner um sitting down with you +you might have like a minimum amount of + + align:start position:0% +you might have like a minimum amount of + + + align:start position:0% +you might have like a minimum amount of +this is like as hard paternal as minimum + + align:start position:0% +this is like as hard paternal as minimum + + + align:start position:0% +this is like as hard paternal as minimum +amount of non-zero for one key savings + + align:start position:0% +amount of non-zero for one key savings + + + align:start position:0% +amount of non-zero for one key savings +trade merchants just force people to + + align:start position:0% +trade merchants just force people to + + + align:start position:0% +trade merchants just force people to +save + + align:start position:0% +save + + + align:start position:0% +save +and it's important to say it's it's not + + align:start position:0% +and it's important to say it's it's not + + + align:start position:0% +and it's important to say it's it's not +just about paternalism versus + + align:start position:0% +just about paternalism versus + + + align:start position:0% +just about paternalism versus +non-paternalism once you get into the + + align:start position:0% +non-paternalism once you get into the + + + align:start position:0% +non-paternalism once you get into the +paternalism realm it's actually very + + align:start position:0% +paternalism realm it's actually very + + + align:start position:0% +paternalism realm it's actually very +hard to figure out + + align:start position:0% +hard to figure out + + + align:start position:0% +hard to figure out +what you do because there's so many + + align:start position:0% +what you do because there's so many + + + align:start position:0% +what you do because there's so many +different options and it's hard to + + align:start position:0% +different options and it's hard to + + + align:start position:0% +different options and it's hard to +tell which one is better than the other + + align:start position:0% +tell which one is better than the other + + + align:start position:0% +tell which one is better than the other +more generally even it's actually quite + + align:start position:0% +more generally even it's actually quite + + + align:start position:0% +more generally even it's actually quite +hard to come up with any like + + align:start position:0% +hard to come up with any like + + + align:start position:0% +hard to come up with any like +non-paternalism option that is to say + + align:start position:0% +non-paternalism option that is to say + + + align:start position:0% +non-paternalism option that is to say +you can think of like all the options + + align:start position:0% +you can think of like all the options + + + align:start position:0% +you can think of like all the options +that are there in some sense once you + + align:start position:0% +that are there in some sense once you + + + align:start position:0% +that are there in some sense once you +think that defaults affect people's + + align:start position:0% +think that defaults affect people's + + + align:start position:0% +think that defaults affect people's +decisions + + align:start position:0% +decisions + + + align:start position:0% +decisions +the no um savings default is also a form + + align:start position:0% +the no um savings default is also a form + + + align:start position:0% +the no um savings default is also a form +of paternalism in some sense you say you + + align:start position:0% +of paternalism in some sense you say you + + + align:start position:0% +of paternalism in some sense you say you +choose something for people + + align:start position:0% +choose something for people + + + align:start position:0% +choose something for people +and that's going to push them to not + + align:start position:0% +and that's going to push them to not + + + align:start position:0% +and that's going to push them to not +safe or you choose to hide + + align:start position:0% +safe or you choose to hide + + + align:start position:0% +safe or you choose to hide +like there's nothing special about the + + align:start position:0% +like there's nothing special about the + + + align:start position:0% +like there's nothing special about the +zero + + align:start position:0% +zero + + + align:start position:0% +zero +we also have a ten percent savings + + align:start position:0% +we also have a ten percent savings + + + align:start position:0% +we also have a ten percent savings +default and so it's almost like regard + + align:start position:0% +default and so it's almost like regard + + + align:start position:0% +default and so it's almost like regard +is + + align:start position:0% +is + + + align:start position:0% +is +it's important to understand that + + align:start position:0% +it's important to understand that + + + align:start position:0% +it's important to understand that +regardless what choice you choose you're + + align:start position:0% +regardless what choice you choose you're + + + align:start position:0% +regardless what choice you choose you're +going to affect + + align:start position:0% +going to affect + + + align:start position:0% +going to affect +people's choices and their behaviors in + + align:start position:0% +people's choices and their behaviors in + + + align:start position:0% +people's choices and their behaviors in +certain ways and so + + align:start position:0% +certain ways and so + + + align:start position:0% +certain ways and so +that sort of means essentially that um + + align:start position:0% +that sort of means essentially that um + + + align:start position:0% +that sort of means essentially that um +you have to take a stance + + align:start position:0% +you have to take a stance + + + align:start position:0% +you have to take a stance +in which you sort of change affect + + align:start position:0% +in which you sort of change affect + + + align:start position:0% +in which you sort of change affect +people's behavior + + align:start position:0% +people's behavior + + + align:start position:0% +people's behavior +in a way just saying like we're just + + align:start position:0% +in a way just saying like we're just + + + align:start position:0% +in a way just saying like we're just +choosing a zero + + align:start position:0% +choosing a zero + + + align:start position:0% +choosing a zero +savings defaults and something's just a + + align:start position:0% +savings defaults and something's just a + + + align:start position:0% +savings defaults and something's just a +cop-out + + align:start position:0% +cop-out + + + align:start position:0% +cop-out +because even the zero savings default is + + align:start position:0% +because even the zero savings default is + + + align:start position:0% +because even the zero savings default is +affecting people's behavior um + + align:start position:0% +affecting people's behavior um + + + align:start position:0% +affecting people's behavior um +quite a bit so in a way the discussion + + align:start position:0% +quite a bit so in a way the discussion + + + align:start position:0% +quite a bit so in a way the discussion +should rather be about like + + align:start position:0% +should rather be about like + + + align:start position:0% +should rather be about like +what is the optimal way of the optimal + + align:start position:0% +what is the optimal way of the optimal + + + align:start position:0% +what is the optimal way of the optimal +paternalism + + align:start position:0% +paternalism + + + align:start position:0% +paternalism +soft paternalism i would argue rather + + align:start position:0% +soft paternalism i would argue rather + + + align:start position:0% +soft paternalism i would argue rather +than sort of saying paternalism versus + + align:start position:0% +than sort of saying paternalism versus + + + align:start position:0% +than sort of saying paternalism versus +not because regardless of what option + + align:start position:0% +not because regardless of what option + + + align:start position:0% +not because regardless of what option +you choose you're going to affect + + align:start position:0% +you choose you're going to affect + + + align:start position:0% +you choose you're going to affect +behaviors in certain ways + + align:start position:0% +behaviors in certain ways + + + align:start position:0% +behaviors in certain ways +because precisely the way you provide + + align:start position:0% +because precisely the way you provide + + + align:start position:0% +because precisely the way you provide +information to people on the default + + align:start position:0% +information to people on the default + + + align:start position:0% +information to people on the default +frames etc + + align:start position:0% +frames etc + + + align:start position:0% +frames etc +affect people's choices does that make + + align:start position:0% +affect people's choices does that make + + + align:start position:0% +affect people's choices does that make +sense + + align:start position:0% + + + + align:start position:0% + +okay so here's a very quick example of + + align:start position:0% +okay so here's a very quick example of + + + align:start position:0% +okay so here's a very quick example of +like a very + + align:start position:0% +like a very + + + align:start position:0% +like a very +useful and and hopefully example of + + align:start position:0% +useful and and hopefully example of + + + align:start position:0% +useful and and hopefully example of +libertarian + + align:start position:0% +libertarian + + + align:start position:0% +libertarian +paternalism that has been quite + + align:start position:0% +paternalism that has been quite + + + align:start position:0% +paternalism that has been quite +successful + + align:start position:0% +successful + + + align:start position:0% +successful +the theology bernardi uh uh were + + align:start position:0% +the theology bernardi uh uh were + + + align:start position:0% +the theology bernardi uh uh were +asked to design a forward key savings + + align:start position:0% +asked to design a forward key savings + + + align:start position:0% +asked to design a forward key savings +for a company + + align:start position:0% +for a company + + + align:start position:0% +for a company +that wanted to increase its employees + + align:start position:0% +that wanted to increase its employees + + + align:start position:0% +that wanted to increase its employees +savings + + align:start position:0% +savings + + + align:start position:0% +savings +so the companies hired a financial + + align:start position:0% +so the companies hired a financial + + + align:start position:0% +so the companies hired a financial +advisor the employers could sit down + + align:start position:0% +advisor the employers could sit down + + + align:start position:0% +advisor the employers could sit down +with the advisor to violate the + + align:start position:0% +with the advisor to violate the + + + align:start position:0% +with the advisor to violate the +financial situation + + align:start position:0% +financial situation + + + align:start position:0% +financial situation +plan so for those who agreed to talk to + + align:start position:0% +plan so for those who agreed to talk to + + + align:start position:0% +plan so for those who agreed to talk to +the advisor the reviser + + align:start position:0% +the advisor the reviser + + + align:start position:0% +the advisor the reviser +he i guess in this case recommended a + + align:start position:0% +he i guess in this case recommended a + + + align:start position:0% +he i guess in this case recommended a +savings rate some agreed to implement + + align:start position:0% +savings rate some agreed to implement + + + align:start position:0% +savings rate some agreed to implement +this and then bernardi and taylor got + + align:start position:0% +this and then bernardi and taylor got + + + align:start position:0% +this and then bernardi and taylor got +the leftovers so that's + + align:start position:0% +the leftovers so that's + + + align:start position:0% +the leftovers so that's +arguably that's um sort of negatively + + align:start position:0% +arguably that's um sort of negatively + + + align:start position:0% +arguably that's um sort of negatively +selected + + align:start position:0% +selected + + + align:start position:0% +selected +uh towards um saving um a lot + + align:start position:0% +uh towards um saving um a lot + + + align:start position:0% +uh towards um saving um a lot +now what's the then the smart the save + + align:start position:0% +now what's the then the smart the save + + + align:start position:0% +now what's the then the smart the save +more tomorrow plan + + align:start position:0% +more tomorrow plan + + + align:start position:0% +more tomorrow plan +uh employees were then approached about + + align:start position:0% +uh employees were then approached about + + + align:start position:0% +uh employees were then approached about +increasing their contribution rate um + + align:start position:0% +increasing their contribution rate um + + + align:start position:0% +increasing their contribution rate um +uh uh one typical time before the next + + align:start position:0% +uh uh one typical time before the next + + + align:start position:0% +uh uh one typical time before the next +scheduled pay rates so that's to say + + align:start position:0% +scheduled pay rates so that's to say + + + align:start position:0% +scheduled pay rates so that's to say +before the next scheduled periods they + + align:start position:0% +before the next scheduled periods they + + + align:start position:0% +before the next scheduled periods they +were essentially asked about + + align:start position:0% +were essentially asked about + + + align:start position:0% +were essentially asked about +whether they would like to join + + align:start position:0% +whether they would like to join + + + align:start position:0% +whether they would like to join +voluntarily and if they wanted to do + + align:start position:0% +voluntarily and if they wanted to do + + + align:start position:0% +voluntarily and if they wanted to do +um they their contribution to the plan + + align:start position:0% +um they their contribution to the plan + + + align:start position:0% +um they their contribution to the plan +was going to be increased beginning with + + align:start position:0% +was going to be increased beginning with + + + align:start position:0% +was going to be increased beginning with +the first paycheck after the race + + align:start position:0% +the first paycheck after the race + + + align:start position:0% +the first paycheck after the race +so that's to say if i told you like in + + align:start position:0% +so that's to say if i told you like in + + + align:start position:0% +so that's to say if i told you like in +december you're going to get a pay raise + + align:start position:0% +december you're going to get a pay raise + + + align:start position:0% +december you're going to get a pay raise +would you like to increase your + + align:start position:0% +would you like to increase your + + + align:start position:0% +would you like to increase your +contribution + + align:start position:0% +contribution + + + align:start position:0% +contribution +then once you receive that pay raise and + + align:start position:0% +then once you receive that pay raise and + + + align:start position:0% +then once you receive that pay raise and +so then + + align:start position:0% +so then + + + align:start position:0% +so then +um you could choose like a or there's a + + align:start position:0% +um you could choose like a or there's a + + + align:start position:0% +um you could choose like a or there's a +preset maximum + + align:start position:0% +preset maximum + + + align:start position:0% +preset maximum +and then what would happen is the + + align:start position:0% +and then what would happen is the + + + align:start position:0% +and then what would happen is the +contribution rate would automatically + + align:start position:0% +contribution rate would automatically + + + align:start position:0% +contribution rate would automatically +increase + + align:start position:0% +increase + + + align:start position:0% +increase +over time with each pay raise that you + + align:start position:0% +over time with each pay raise that you + + + align:start position:0% +over time with each pay raise that you +would receive like suppose your pay + + align:start position:0% +would receive like suppose your pay + + + align:start position:0% +would receive like suppose your pay +raise is like say five percent or three + + align:start position:0% +raise is like say five percent or three + + + align:start position:0% +raise is like say five percent or three +percent + + align:start position:0% +percent + + + align:start position:0% +percent +what you would get then is like um uh + + align:start position:0% +what you would get then is like um uh + + + align:start position:0% +what you would get then is like um uh +suppose it's three percent you + + align:start position:0% +suppose it's three percent you + + + align:start position:0% +suppose it's three percent you +have like only like a two percent + + align:start position:0% +have like only like a two percent + + + align:start position:0% +have like only like a two percent +increase in your pay rate pay + + align:start position:0% +increase in your pay rate pay + + + align:start position:0% +increase in your pay rate pay +and one percent or one percentage point + + align:start position:0% +and one percent or one percentage point + + + align:start position:0% +and one percent or one percentage point +if you pay would then go towards the + + align:start position:0% +if you pay would then go towards the + + + align:start position:0% +if you pay would then go towards the +retirement contribution + + align:start position:0% +retirement contribution + + + align:start position:0% +retirement contribution +importantly the employee can opt out of + + align:start position:0% +importantly the employee can opt out of + + + align:start position:0% +importantly the employee can opt out of +the plan at any point in time by + + align:start position:0% +the plan at any point in time by + + + align:start position:0% +the plan at any point in time by +essentially just + + align:start position:0% +essentially just + + + align:start position:0% +essentially just +making a phone call or um the like + + align:start position:0% +making a phone call or um the like + + + align:start position:0% +making a phone call or um the like +now why is this plan um a + + align:start position:0% +now why is this plan um a + + + align:start position:0% +now why is this plan um a +libertarian paternalism well because of + + align:start position:0% +libertarian paternalism well because of + + + align:start position:0% +libertarian paternalism well because of +aspects two and four + + align:start position:0% +aspects two and four + + + align:start position:0% +aspects two and four +right it's voluntary so you can do + + align:start position:0% +right it's voluntary so you can do + + + align:start position:0% +right it's voluntary so you can do +whatever you want you you can you don't + + align:start position:0% +whatever you want you you can you don't + + + align:start position:0% +whatever you want you you can you don't +have to choose + + align:start position:0% +have to choose + + + align:start position:0% +have to choose +this at all you can essentially decline + + align:start position:0% +this at all you can essentially decline + + + align:start position:0% +this at all you can essentially decline +it you can also opt out at any point in + + align:start position:0% +it you can also opt out at any point in + + + align:start position:0% +it you can also opt out at any point in +time so it's + + align:start position:0% +time so it's + + + align:start position:0% +time so it's +arguably nobody is worse made worse off + + align:start position:0% +arguably nobody is worse made worse off + + + align:start position:0% +arguably nobody is worse made worse off +because you essentially what we're doing + + align:start position:0% +because you essentially what we're doing + + + align:start position:0% +because you essentially what we're doing +here is + + align:start position:0% +here is + + + align:start position:0% +here is +um increasing people's options but say + + align:start position:0% +um increasing people's options but say + + + align:start position:0% +um increasing people's options but say +here's an option for you to like + + align:start position:0% +here's an option for you to like + + + align:start position:0% +here's an option for you to like +increase to saving automatically over + + align:start position:0% +increase to saving automatically over + + + align:start position:0% +increase to saving automatically over +time + + align:start position:0% +time + + + align:start position:0% +time +um and you can leave it out you can + + align:start position:0% +um and you can leave it out you can + + + align:start position:0% +um and you can leave it out you can +leave it whenever you would like um to + + align:start position:0% +leave it whenever you would like um to + + + align:start position:0% +leave it whenever you would like um to +do so arguably nobody should be worse + + align:start position:0% +do so arguably nobody should be worse + + + align:start position:0% +do so arguably nobody should be worse +off + + align:start position:0% +off + + + align:start position:0% +off +on uh by this and potentially some + + align:start position:0% +on uh by this and potentially some + + + align:start position:0% +on uh by this and potentially some +people are made + + align:start position:0% +people are made + + + align:start position:0% +people are made +better off um quite a bit and that's + + align:start position:0% +better off um quite a bit and that's + + + align:start position:0% +better off um quite a bit and that's +exactly what you see here + + align:start position:0% +exactly what you see here + + + align:start position:0% +exactly what you see here +essentially um when you look at the + + align:start position:0% +essentially um when you look at the + + + align:start position:0% +essentially um when you look at the +people who joined the smart plan + + align:start position:0% +people who joined the smart plan + + + align:start position:0% +people who joined the smart plan +um notice that this is not random here + + align:start position:0% +um notice that this is not random here + + + align:start position:0% +um notice that this is not random here +so there's some you know + + align:start position:0% +so there's some you know + + + align:start position:0% +so there's some you know +concerns about identification but + + align:start position:0% +concerns about identification but + + + align:start position:0% +concerns about identification but +setting that aside + + align:start position:0% +setting that aside + + + align:start position:0% +setting that aside +um if you look at the people who again + + align:start position:0% +um if you look at the people who again + + + align:start position:0% +um if you look at the people who again +like arguably are negatively selected + + align:start position:0% +like arguably are negatively selected + + + align:start position:0% +like arguably are negatively selected +these are people + + align:start position:0% +these are people + + + align:start position:0% +these are people +who declined um + + align:start position:0% +who declined um + + + align:start position:0% +who declined um +the financial consult and they + + align:start position:0% +the financial consult and they + + + align:start position:0% +the financial consult and they +essentially increased their savings + + align:start position:0% +essentially increased their savings + + + align:start position:0% +essentially increased their savings +dramatically + + align:start position:0% +dramatically + + + align:start position:0% +dramatically +uh as a consequence of this smart plan + + align:start position:0% +uh as a consequence of this smart plan + + + align:start position:0% +uh as a consequence of this smart plan +and now the smart plan has been + + align:start position:0% +and now the smart plan has been + + + align:start position:0% +and now the smart plan has been +introduced or implemented in quite a few + + align:start position:0% +introduced or implemented in quite a few + + + align:start position:0% +introduced or implemented in quite a few +um + + align:start position:0% +um + + + align:start position:0% +um +places but anyway that's not the point + + align:start position:0% +places but anyway that's not the point + + + align:start position:0% +places but anyway that's not the point +here i wanted to say + + align:start position:0% +here i wanted to say + + + align:start position:0% +here i wanted to say +um what's good about the plan is well + + align:start position:0% +um what's good about the plan is well + + + align:start position:0% +um what's good about the plan is well +it's a smart plan uh + + align:start position:0% +it's a smart plan uh + + + align:start position:0% +it's a smart plan uh +not just because of the acronym but also + + align:start position:0% +not just because of the acronym but also + + + align:start position:0% +not just because of the acronym but also +because it's using um + + align:start position:0% +because it's using um + + + align:start position:0% +because it's using um +behavioral principles or stuff that we + + align:start position:0% +behavioral principles or stuff that we + + + align:start position:0% +behavioral principles or stuff that we +learned in class um + + align:start position:0% +learned in class um + + + align:start position:0% +learned in class um +uh quite a bit and carefully so what are + + align:start position:0% +uh quite a bit and carefully so what are + + + align:start position:0% +uh quite a bit and carefully so what are +these principles so why is this a useful + + align:start position:0% +these principles so why is this a useful + + + align:start position:0% +these principles so why is this a useful +plan + + align:start position:0% +plan + + + align:start position:0% +plan +um to use and i'm gonna sort of show you + + align:start position:0% +um to use and i'm gonna sort of show you + + + align:start position:0% +um to use and i'm gonna sort of show you +again what the plan is + + align:start position:0% +again what the plan is + + + align:start position:0% +again what the plan is +what's clever about this plan what is it + + align:start position:0% +what's clever about this plan what is it + + + align:start position:0% +what's clever about this plan what is it +using carefully + + align:start position:0% + + + + align:start position:0% + +by the way i don't know if you can hear + + align:start position:0% +by the way i don't know if you can hear + + + align:start position:0% +by the way i don't know if you can hear +this background noise this is my + + align:start position:0% +this background noise this is my + + + align:start position:0% +this background noise this is my +neighbor has engaged in various + + align:start position:0% +neighbor has engaged in various + + + align:start position:0% +neighbor has engaged in various +uh home uh home uh improvement project + + align:start position:0% +uh home uh home uh improvement project + + + align:start position:0% +uh home uh home uh improvement project +projects + + align:start position:0% +projects + + + align:start position:0% +projects +since the quarantine um uh um + + align:start position:0% +since the quarantine um uh um + + + align:start position:0% +since the quarantine um uh um +i've so far um refrain from + + align:start position:0% +i've so far um refrain from + + + align:start position:0% +i've so far um refrain from +uh complaining about it because i don't + + align:start position:0% +uh complaining about it because i don't + + + align:start position:0% +uh complaining about it because i don't +know what's going on in their lives + + align:start position:0% +know what's going on in their lives + + + align:start position:0% +know what's going on in their lives +otherwise and um + + align:start position:0% +otherwise and um + + + align:start position:0% +otherwise and um +maybe that's sort of a way of uh dealing + + align:start position:0% +maybe that's sort of a way of uh dealing + + + align:start position:0% +maybe that's sort of a way of uh dealing +with stress + + align:start position:0% +with stress + + + align:start position:0% +with stress +and so on you can hear this the default + + align:start position:0% +and so on you can hear this the default + + + align:start position:0% +and so on you can hear this the default +once you + + align:start position:0% +once you + + + align:start position:0% +once you +opt in the default is for your uh pay + + align:start position:0% +opt in the default is for your uh pay + + + align:start position:0% +opt in the default is for your uh pay +writing + + align:start position:0% +writing + + + align:start position:0% +writing +the the contribution rate to increase so + + align:start position:0% +the the contribution rate to increase so + + + align:start position:0% +the the contribution rate to increase so +the default is essentially working + + align:start position:0% +the default is essentially working + + + align:start position:0% +the default is essentially working +towards + + align:start position:0% +towards + + + align:start position:0% +towards +increasing people's savings okay so + + align:start position:0% +increasing people's savings okay so + + + align:start position:0% +increasing people's savings okay so +there's two things going on here one is + + align:start position:0% +there's two things going on here one is + + + align:start position:0% +there's two things going on here one is +prison buys when you say well yeah in + + align:start position:0% +prison buys when you say well yeah in + + + align:start position:0% +prison buys when you say well yeah in +the future i want to save more + + align:start position:0% +the future i want to save more + + + align:start position:0% +the future i want to save more +so precisely that's kind of great + + align:start position:0% +so precisely that's kind of great + + + align:start position:0% +so precisely that's kind of great +because you know now like the future + + align:start position:0% +because you know now like the future + + + align:start position:0% +because you know now like the future +itself will be virtuous and so on so + + align:start position:0% +itself will be virtuous and so on so + + + align:start position:0% +itself will be virtuous and so on so +people are present bias that will help + + align:start position:0% +people are present bias that will help + + + align:start position:0% +people are present bias that will help +and then um there's also just the the + + align:start position:0% +and then um there's also just the the + + + align:start position:0% +and then um there's also just the the +part that's about + + align:start position:0% +part that's about + + + align:start position:0% +part that's about +uh uh paycheck increases remember people + + align:start position:0% +uh uh paycheck increases remember people + + + align:start position:0% +uh uh paycheck increases remember people +tend to be philosophers + + align:start position:0% +tend to be philosophers + + + align:start position:0% +tend to be philosophers +so um what this plan is also + + align:start position:0% +so um what this plan is also + + + align:start position:0% +so um what this plan is also +accomplishing is like so if i'm asking + + align:start position:0% +accomplishing is like so if i'm asking + + + align:start position:0% +accomplishing is like so if i'm asking +you right now today would you like to + + align:start position:0% +you right now today would you like to + + + align:start position:0% +you right now today would you like to +increase your savings rate + + align:start position:0% +increase your savings rate + + + align:start position:0% +increase your savings rate +well not only are you press buyers but + + align:start position:0% +well not only are you press buyers but + + + align:start position:0% +well not only are you press buyers but +also you're gonna have like a cut in + + align:start position:0% +also you're gonna have like a cut in + + + align:start position:0% +also you're gonna have like a cut in +your paycheck and people hate cuts in + + align:start position:0% +your paycheck and people hate cuts in + + + align:start position:0% +your paycheck and people hate cuts in +their paychecks + + align:start position:0% +their paychecks + + + align:start position:0% +their paychecks +so instead it's saying like well in the + + align:start position:0% +so instead it's saying like well in the + + + align:start position:0% +so instead it's saying like well in the +future your rates will be lower + + align:start position:0% +future your rates will be lower + + + align:start position:0% +future your rates will be lower +and people are less averse to reducing + + align:start position:0% +and people are less averse to reducing + + + align:start position:0% +and people are less averse to reducing +those + + align:start position:0% +those + + + align:start position:0% +those +um increases um compared to + + align:start position:0% +um increases um compared to + + + align:start position:0% +um increases um compared to +experiencing pay cuts so that's i think + + align:start position:0% +experiencing pay cuts so that's i think + + + align:start position:0% +experiencing pay cuts so that's i think +what we have here so this is essentially + + align:start position:0% +what we have here so this is essentially + + + align:start position:0% +what we have here so this is essentially +prison bias is helping + + align:start position:0% +prison bias is helping + + + align:start position:0% +prison bias is helping +then there's reference dependence and + + align:start position:0% +then there's reference dependence and + + + align:start position:0% +then there's reference dependence and +then there's defaults that help + + align:start position:0% +then there's defaults that help + + + align:start position:0% +then there's defaults that help +people switching out or some form of + + align:start position:0% +people switching out or some form of + + + align:start position:0% +people switching out or some form of +present bias but people precisely as we + + align:start position:0% +present bias but people precisely as we + + + align:start position:0% +present bias but people precisely as we +said previously people are not switching + + align:start position:0% +said previously people are not switching + + + align:start position:0% +said previously people are not switching +out of those kinds of plans + + align:start position:0% +out of those kinds of plans + + + align:start position:0% +out of those kinds of plans +so if you think that's a good thing to + + align:start position:0% +so if you think that's a good thing to + + + align:start position:0% +so if you think that's a good thing to +increase people's savings here that's + + align:start position:0% +increase people's savings here that's + + + align:start position:0% +increase people's savings here that's +something + + align:start position:0% +something + + + align:start position:0% +something +because people might actually + + align:start position:0% +because people might actually + + + align:start position:0% +because people might actually +procrastinate switching out of it once + + align:start position:0% +procrastinate switching out of it once + + + align:start position:0% +procrastinate switching out of it once +they're in in the first place + + align:start position:0% +they're in in the first place + + + align:start position:0% +they're in in the first place +so that seems to be like a a great + + align:start position:0% +so that seems to be like a a great + + + align:start position:0% +so that seems to be like a a great +example because not only is it + + align:start position:0% +example because not only is it + + + align:start position:0% +example because not only is it +preserving libertarian uh or is it is it + + align:start position:0% +preserving libertarian uh or is it is it + + + align:start position:0% +preserving libertarian uh or is it is it +preserving people's free choice and not + + align:start position:0% +preserving people's free choice and not + + + align:start position:0% +preserving people's free choice and not +people + + align:start position:0% +people + + + align:start position:0% +people +making people um uh worse off but also + + align:start position:0% +making people um uh worse off but also + + + align:start position:0% +making people um uh worse off but also +it's using in a smart way + + align:start position:0% +it's using in a smart way + + + align:start position:0% +it's using in a smart way +um behavioral um principles okay + + align:start position:0% +um behavioral um principles okay + + + align:start position:0% +um behavioral um principles okay +let me briefly talk about the market and + + align:start position:0% +let me briefly talk about the market and + + + align:start position:0% +let me briefly talk about the market and +we talked about this a little bit + + align:start position:0% +we talked about this a little bit + + + align:start position:0% +we talked about this a little bit +already previously but i want to sort of + + align:start position:0% +already previously but i want to sort of + + + align:start position:0% +already previously but i want to sort of +make this um + + align:start position:0% +make this um + + + align:start position:0% +make this um +explicit so one um argument that often + + align:start position:0% +explicit so one um argument that often + + + align:start position:0% +explicit so one um argument that often +comes + + align:start position:0% +comes + + + align:start position:0% +comes +in particular out of other um is well + + align:start position:0% +in particular out of other um is well + + + align:start position:0% +in particular out of other um is well +um if people have self-control problems + + align:start position:0% +um if people have self-control problems + + + align:start position:0% +um if people have self-control problems +or other issues well will not the market + + align:start position:0% +or other issues well will not the market + + + align:start position:0% +or other issues well will not the market +come up with some goods or some + + align:start position:0% +come up with some goods or some + + + align:start position:0% +come up with some goods or some +solutions that will help people right + + align:start position:0% +solutions that will help people right + + + align:start position:0% +solutions that will help people right +after all there's like money to be made + + align:start position:0% +after all there's like money to be made + + + align:start position:0% +after all there's like money to be made +um in improving people's choices + + align:start position:0% +um in improving people's choices + + + align:start position:0% +um in improving people's choices +so if really self-control problems so + + align:start position:0% +so if really self-control problems so + + + align:start position:0% +so if really self-control problems so +the like are really important + + align:start position:0% +the like are really important + + + align:start position:0% +the like are really important +why is not having anybody coming up with + + align:start position:0% +why is not having anybody coming up with + + + align:start position:0% +why is not having anybody coming up with +a market solution and sort of a great + + align:start position:0% +a market solution and sort of a great + + + align:start position:0% +a market solution and sort of a great +product that helps people and then + + align:start position:0% +product that helps people and then + + + align:start position:0% +product that helps people and then +they're going to make a lot of money + + align:start position:0% +they're going to make a lot of money + + + align:start position:0% +they're going to make a lot of money +um from doing so and so in particular if + + align:start position:0% +um from doing so and so in particular if + + + align:start position:0% +um from doing so and so in particular if +consumers are feeling + + align:start position:0% +consumers are feeling + + + align:start position:0% +consumers are feeling +sophisticated then they demand uh ways + + align:start position:0% +sophisticated then they demand uh ways + + + align:start position:0% +sophisticated then they demand uh ways +to change the consumption + + align:start position:0% +to change the consumption + + + align:start position:0% +to change the consumption +and then there will be somebody who's + + align:start position:0% +and then there will be somebody who's + + + align:start position:0% +and then there will be somebody who's +providing that good + + align:start position:0% +providing that good + + + align:start position:0% +providing that good +and you know if the welfare effects of + + align:start position:0% +and you know if the welfare effects of + + + align:start position:0% +and you know if the welfare effects of +those kinds of + + align:start position:0% +those kinds of + + + align:start position:0% +those kinds of +uh uh self-control or other distortions + + align:start position:0% +uh uh self-control or other distortions + + + align:start position:0% +uh uh self-control or other distortions +are large well then you can make a lot + + align:start position:0% +are large well then you can make a lot + + + align:start position:0% +are large well then you can make a lot +of money from helping people + + align:start position:0% +of money from helping people + + + align:start position:0% +of money from helping people +improve their behavior so what's what's + + align:start position:0% +improve their behavior so what's what's + + + align:start position:0% +improve their behavior so what's what's +problematic with this + + align:start position:0% + + + + align:start position:0% + +um uh line of argument well the market + + align:start position:0% +um uh line of argument well the market + + + align:start position:0% +um uh line of argument well the market +is precisely part of the problem well so + + align:start position:0% +is precisely part of the problem well so + + + align:start position:0% +is precisely part of the problem well so +on the one hand you sort of say if you + + align:start position:0% +on the one hand you sort of say if you + + + align:start position:0% +on the one hand you sort of say if you +try to + + align:start position:0% +try to + + + align:start position:0% +try to +so this is google and this is quite a + + align:start position:0% +so this is google and this is quite a + + + align:start position:0% +so this is google and this is quite a +while ago but you know uh + + align:start position:0% +while ago but you know uh + + + align:start position:0% +while ago but you know uh +right now it's in some sense more + + align:start position:0% +right now it's in some sense more + + + align:start position:0% +right now it's in some sense more +sophisticated ways and there's lots of + + align:start position:0% +sophisticated ways and there's lots of + + + align:start position:0% +sophisticated ways and there's lots of +targeting going on + + align:start position:0% +targeting going on + + + align:start position:0% +targeting going on +but if you google impulsive credit card + + align:start position:0% +but if you google impulsive credit card + + + align:start position:0% +but if you google impulsive credit card +spending what you're going to get is a + + align:start position:0% +spending what you're going to get is a + + + align:start position:0% +spending what you're going to get is a +bunch of advice to help you with that + + align:start position:0% +bunch of advice to help you with that + + + align:start position:0% +bunch of advice to help you with that +but at the same time you also get a + + align:start position:0% +but at the same time you also get a + + + align:start position:0% +but at the same time you also get a +bunch of credit card offers that are + + align:start position:0% +bunch of credit card offers that are + + + align:start position:0% +bunch of credit card offers that are +like you're going to get targeted + + align:start position:0% +like you're going to get targeted + + + align:start position:0% +like you're going to get targeted +eventually by + + align:start position:0% +eventually by + + + align:start position:0% +eventually by +companies that might essentially + + align:start position:0% +companies that might essentially + + + align:start position:0% +companies that might essentially +precisely exploit you + + align:start position:0% +precisely exploit you + + + align:start position:0% +precisely exploit you +so on the one hand you there will be a + + align:start position:0% +so on the one hand you there will be a + + + align:start position:0% +so on the one hand you there will be a +side of the market you will potentially + + align:start position:0% +side of the market you will potentially + + + align:start position:0% +side of the market you will potentially +help you + + align:start position:0% +help you + + + align:start position:0% +help you +but there's another side of the market + + align:start position:0% +but there's another side of the market + + + align:start position:0% +but there's another side of the market +will you want to to exploit you + + align:start position:0% +will you want to to exploit you + + + align:start position:0% +will you want to to exploit you +and uh importantly what the market will + + align:start position:0% +and uh importantly what the market will + + + align:start position:0% +and uh importantly what the market will +do is firms will try to target naive + + align:start position:0% +do is firms will try to target naive + + + align:start position:0% +do is firms will try to target naive +people and you might remember this from + + align:start position:0% +people and you might remember this from + + + align:start position:0% +people and you might remember this from +lectures + + align:start position:0% +lectures + + + align:start position:0% +lectures +five and six where essentially firms + + align:start position:0% +five and six where essentially firms + + + align:start position:0% +five and six where essentially firms +precisely try to find people um + + align:start position:0% +precisely try to find people um + + + align:start position:0% +precisely try to find people um +um who are perhaps um left sophisticated + + align:start position:0% +um who are perhaps um left sophisticated + + + align:start position:0% +um who are perhaps um left sophisticated +financially in other ways + + align:start position:0% +financially in other ways + + + align:start position:0% +financially in other ways +so the firms are precisely trying to + + align:start position:0% +so the firms are precisely trying to + + + align:start position:0% +so the firms are precisely trying to +target naive people because those are + + align:start position:0% +target naive people because those are + + + align:start position:0% +target naive people because those are +the people you can exploit + + align:start position:0% +the people you can exploit + + + align:start position:0% +the people you can exploit +moreover the naives are the ones who + + align:start position:0% +moreover the naives are the ones who + + + align:start position:0% +moreover the naives are the ones who +will think + + align:start position:0% +will think + + + align:start position:0% +will think +well i don't have any problems so i + + align:start position:0% +well i don't have any problems so i + + + align:start position:0% +well i don't have any problems so i +don't actually need any goods or any + + align:start position:0% +don't actually need any goods or any + + + align:start position:0% +don't actually need any goods or any +sort of products that might help you + + align:start position:0% +sort of products that might help you + + + align:start position:0% +sort of products that might help you +so not only are they being targeted by + + align:start position:0% +so not only are they being targeted by + + + align:start position:0% +so not only are they being targeted by +people who try to + + align:start position:0% +people who try to + + + align:start position:0% +people who try to +decide to screw them over but also they + + align:start position:0% +decide to screw them over but also they + + + align:start position:0% +decide to screw them over but also they +actually + + align:start position:0% +actually + + + align:start position:0% +actually +are um reluctant to seek help because + + align:start position:0% +are um reluctant to seek help because + + + align:start position:0% +are um reluctant to seek help because +precisely + + align:start position:0% +precisely + + + align:start position:0% +precisely +um uh uh they think they're not even + + align:start position:0% +um uh uh they think they're not even + + + align:start position:0% +um uh uh they think they're not even +they think it's not even necessary to + + align:start position:0% +they think it's not even necessary to + + + align:start position:0% +they think it's not even necessary to +seek help + + align:start position:0% +seek help + + + align:start position:0% +seek help +so even a firm who wants to help has + + align:start position:0% +so even a firm who wants to help has + + + align:start position:0% +so even a firm who wants to help has +trouble making money with us because + + align:start position:0% +trouble making money with us because + + + align:start position:0% +trouble making money with us because +people + + align:start position:0% +people + + + align:start position:0% +people +if they're naive will not necessarily + + align:start position:0% +if they're naive will not necessarily + + + align:start position:0% +if they're naive will not necessarily +understand that + + align:start position:0% +understand that + + + align:start position:0% +understand that +um help is required and that's precisely + + align:start position:0% +um help is required and that's precisely + + + align:start position:0% +um help is required and that's precisely +the tension that we see in many markets + + align:start position:0% +the tension that we see in many markets + + + align:start position:0% +the tension that we see in many markets +where there's some firms who might want + + align:start position:0% +where there's some firms who might want + + + align:start position:0% +where there's some firms who might want +to + + align:start position:0% +to + + + align:start position:0% +to +help and support in this case + + align:start position:0% +help and support in this case + + + align:start position:0% +help and support in this case +self-control that's also true for other + + align:start position:0% +self-control that's also true for other + + + align:start position:0% +self-control that's also true for other +um issues but there's on the other side + + align:start position:0% +um issues but there's on the other side + + + align:start position:0% +um issues but there's on the other side +funds that try to break down uh the + + align:start position:0% +funds that try to break down uh the + + + align:start position:0% +funds that try to break down uh the +self-control from consumers precisely + + align:start position:0% +self-control from consumers precisely + + + align:start position:0% +self-control from consumers precisely +because they can make much much a bunch + + align:start position:0% +because they can make much much a bunch + + + align:start position:0% +because they can make much much a bunch +of money + + align:start position:0% +of money + + + align:start position:0% +of money +um from that and so now um + + align:start position:0% +um from that and so now um + + + align:start position:0% +um from that and so now um +uh the second part then severely limits + + align:start position:0% +uh the second part then severely limits + + + align:start position:0% +uh the second part then severely limits +the market's ability to provide + + align:start position:0% +the market's ability to provide + + + align:start position:0% +the market's ability to provide +self-control because it's essentially + + align:start position:0% +self-control because it's essentially + + + align:start position:0% +self-control because it's essentially +too forced to start work + + align:start position:0% +too forced to start work + + + align:start position:0% +too forced to start work +now the government of course can sort of + + align:start position:0% +now the government of course can sort of + + + align:start position:0% +now the government of course can sort of +uh try to address this and this is what + + align:start position:0% +uh try to address this and this is what + + + align:start position:0% +uh try to address this and this is what +behavioral io would be about behavioral + + align:start position:0% +behavioral io would be about behavioral + + + align:start position:0% +behavioral io would be about behavioral +i o would be about saying + + align:start position:0% +i o would be about saying + + + align:start position:0% +i o would be about saying +uh industrial organization which would + + align:start position:0% +uh industrial organization which would + + + align:start position:0% +uh industrial organization which would +be well there's behavioral consumers + + align:start position:0% +be well there's behavioral consumers + + + align:start position:0% +be well there's behavioral consumers +there's firms to try to + + align:start position:0% +there's firms to try to + + + align:start position:0% +there's firms to try to +exploit consumers now the government is + + align:start position:0% +exploit consumers now the government is + + + align:start position:0% +exploit consumers now the government is +trying to support + + align:start position:0% +trying to support + + + align:start position:0% +trying to support +um or like by some form of regulation + + align:start position:0% +um or like by some form of regulation + + + align:start position:0% +um or like by some form of regulation +trying to + + align:start position:0% +trying to + + + align:start position:0% +trying to +help customers particular things like + + align:start position:0% +help customers particular things like + + + align:start position:0% +help customers particular things like +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +consumer financial protection bureau and + + align:start position:0% +consumer financial protection bureau and + + + align:start position:0% +consumer financial protection bureau and +so on trying to help + + align:start position:0% +so on trying to help + + + align:start position:0% +so on trying to help +um consumers not to get exploited by + + align:start position:0% +um consumers not to get exploited by + + + align:start position:0% +um consumers not to get exploited by +banning advertising by capping interest + + align:start position:0% +banning advertising by capping interest + + + align:start position:0% +banning advertising by capping interest +rates and so on and so forth + + align:start position:0% +rates and so on and so forth + + + align:start position:0% +rates and so on and so forth +also by for example um + + align:start position:0% +also by for example um + + + align:start position:0% +also by for example um +mandating disclosure and so on and so + + align:start position:0% +mandating disclosure and so on and so + + + align:start position:0% +mandating disclosure and so on and so +forth + + align:start position:0% +forth + + + align:start position:0% +forth +um now um i'm going to say one final + + align:start position:0% +um now um i'm going to say one final + + + align:start position:0% +um now um i'm going to say one final +thing about nudges um which is + + align:start position:0% +thing about nudges um which is + + + align:start position:0% +thing about nudges um which is +on the one hand we talked about nudges + + align:start position:0% +on the one hand we talked about nudges + + + align:start position:0% +on the one hand we talked about nudges +in the sense of saying + + align:start position:0% +in the sense of saying + + + align:start position:0% +in the sense of saying +look there's some behavior that we're + + align:start position:0% +look there's some behavior that we're + + + align:start position:0% +look there's some behavior that we're +trying to improve which would be like + + align:start position:0% +trying to improve which would be like + + + align:start position:0% +trying to improve which would be like +you know suppose people keep forgetting + + align:start position:0% +you know suppose people keep forgetting + + + align:start position:0% +you know suppose people keep forgetting +um certain things to take their + + align:start position:0% +um certain things to take their + + + align:start position:0% +um certain things to take their +medication or to appear in court + + align:start position:0% +medication or to appear in court + + + align:start position:0% +medication or to appear in court +let's send reminders to um + + align:start position:0% +let's send reminders to um + + + align:start position:0% +let's send reminders to um +uh to to improve behaviors you can set + + align:start position:0% +uh to to improve behaviors you can set + + + align:start position:0% +uh to to improve behaviors you can set +defaults in certain ways and so on and + + align:start position:0% +defaults in certain ways and so on and + + + align:start position:0% +defaults in certain ways and so on and +so forth + + align:start position:0% +so forth + + + align:start position:0% +so forth +which is policies to improve good + + align:start position:0% +which is policies to improve good + + + align:start position:0% +which is policies to improve good +behaviors + + align:start position:0% +behaviors + + + align:start position:0% +behaviors +assuming that the person who makes those + + align:start position:0% +assuming that the person who makes those + + + align:start position:0% +assuming that the person who makes those +choices but has been + + align:start position:0% +choices but has been + + + align:start position:0% +choices but has been +benevolent in certain ways now on the + + align:start position:0% +benevolent in certain ways now on the + + + align:start position:0% +benevolent in certain ways now on the +other hand of course + + align:start position:0% +other hand of course + + + align:start position:0% +other hand of course +firms can use the same techniques on the + + align:start position:0% +firms can use the same techniques on the + + + align:start position:0% +firms can use the same techniques on the +same um + + align:start position:0% +same um + + + align:start position:0% +same um +approaches to do the exact opposites and + + align:start position:0% +approaches to do the exact opposites and + + + align:start position:0% +approaches to do the exact opposites and +just to harm people and this is what um + + align:start position:0% +just to harm people and this is what um + + + align:start position:0% +just to harm people and this is what um +uh uh thalain sunstein calls sludges + + align:start position:0% +uh uh thalain sunstein calls sludges + + + align:start position:0% +uh uh thalain sunstein calls sludges +which essentially is like using these + + align:start position:0% +which essentially is like using these + + + align:start position:0% +which essentially is like using these +nudges and + + align:start position:0% +nudges and + + + align:start position:0% +nudges and +and bad ways by um trying to push people + + align:start position:0% +and bad ways by um trying to push people + + + align:start position:0% +and bad ways by um trying to push people +in wrong directions + + align:start position:0% +in wrong directions + + + align:start position:0% +in wrong directions +so an example of that would be offering + + align:start position:0% +so an example of that would be offering + + + align:start position:0% +so an example of that would be offering +rebates on a product + + align:start position:0% +rebates on a product + + + align:start position:0% +rebates on a product +and then having people customers to + + align:start position:0% +and then having people customers to + + + align:start position:0% +and then having people customers to +require to + + align:start position:0% +require to + + + align:start position:0% +require to +to mail in forms of delight and you may + + align:start position:0% +to mail in forms of delight and you may + + + align:start position:0% +to mail in forms of delight and you may +have encountered these and wondering + + align:start position:0% +have encountered these and wondering + + + align:start position:0% +have encountered these and wondering +like why i have to + + align:start position:0% +like why i have to + + + align:start position:0% +like why i have to +mail in this form and this is kind of + + align:start position:0% +mail in this form and this is kind of + + + align:start position:0% +mail in this form and this is kind of +tedious and then you end up not doing it + + align:start position:0% + + + + align:start position:0% + +you want to think oh i'm getting like + + align:start position:0% +you want to think oh i'm getting like + + + align:start position:0% +you want to think oh i'm getting like +this great discount + + align:start position:0% +this great discount + + + align:start position:0% +this great discount +and then actually never send it in + + align:start position:0% +and then actually never send it in + + + align:start position:0% +and then actually never send it in +because then they don't have to actually + + align:start position:0% +because then they don't have to actually + + + align:start position:0% +because then they don't have to actually +pay + + align:start position:0% +pay + + + align:start position:0% +pay +they can sell you the good but then you + + align:start position:0% +they can sell you the good but then you + + + align:start position:0% +they can sell you the good but then you +don't have to actually they don't have + + align:start position:0% +don't have to actually they don't have + + + align:start position:0% +don't have to actually they don't have +to give you the discount at the end of + + align:start position:0% +to give you the discount at the end of + + + align:start position:0% +to give you the discount at the end of +the day + + align:start position:0% +the day + + + align:start position:0% +the day +so there's a bunch of types of uh cases + + align:start position:0% +so there's a bunch of types of uh cases + + + align:start position:0% +so there's a bunch of types of uh cases +both from the private sector but also + + align:start position:0% +both from the private sector but also + + + align:start position:0% +both from the private sector but also +from the public sector such as things + + align:start position:0% +from the public sector such as things + + + align:start position:0% +from the public sector such as things +says voter registration + + align:start position:0% +says voter registration + + + align:start position:0% +says voter registration +when you think about it why is voter + + align:start position:0% +when you think about it why is voter + + + align:start position:0% +when you think about it why is voter +division hard in certain places + + align:start position:0% +division hard in certain places + + + align:start position:0% +division hard in certain places +well the reason why it's hard is because + + align:start position:0% +well the reason why it's hard is because + + + align:start position:0% +well the reason why it's hard is because +certain parties and groups do not want + + align:start position:0% +certain parties and groups do not want + + + align:start position:0% +certain parties and groups do not want +certain types of groups of people to + + align:start position:0% +certain types of groups of people to + + + align:start position:0% +certain types of groups of people to +vote + + align:start position:0% +vote + + + align:start position:0% +vote +and those are essentially deliberate + + align:start position:0% +and those are essentially deliberate + + + align:start position:0% +and those are essentially deliberate +ways of making it hard for people to to + + align:start position:0% +ways of making it hard for people to to + + + align:start position:0% +ways of making it hard for people to to +make choices that are arguably good for + + align:start position:0% +make choices that are arguably good for + + + align:start position:0% +make choices that are arguably good for +them or for society + + align:start position:0% +them or for society + + + align:start position:0% +them or for society +and that's what they learned sunshine + + align:start position:0% +and that's what they learned sunshine + + + align:start position:0% +and that's what they learned sunshine +would call sludges + + align:start position:0% +would call sludges + + + align:start position:0% +would call sludges +and then here it's important to realize + + align:start position:0% +and then here it's important to realize + + + align:start position:0% +and then here it's important to realize +that it's in fact + + align:start position:0% +that it's in fact + + + align:start position:0% +that it's in fact +identifying and eliminating such sludges + + align:start position:0% +identifying and eliminating such sludges + + + align:start position:0% +identifying and eliminating such sludges +which essentially are + + align:start position:0% +which essentially are + + + align:start position:0% +which essentially are +certain ways that make it hard for + + align:start position:0% +certain ways that make it hard for + + + align:start position:0% +certain ways that make it hard for +people to make good choices for + + align:start position:0% +people to make good choices for + + + align:start position:0% +people to make good choices for +themselves or for society + + align:start position:0% +themselves or for society + + + align:start position:0% +themselves or for society +can be equally important or perhaps as + + align:start position:0% +can be equally important or perhaps as + + + align:start position:0% +can be equally important or perhaps as +important as sort of + + align:start position:0% +important as sort of + + + align:start position:0% +important as sort of +implementing nudges to improve people's + + align:start position:0% +implementing nudges to improve people's + + + align:start position:0% +implementing nudges to improve people's +behavior in certain ways so it's not + + align:start position:0% +behavior in certain ways so it's not + + + align:start position:0% +behavior in certain ways so it's not +just about sort of taking behavior where + + align:start position:0% +just about sort of taking behavior where + + + align:start position:0% +just about sort of taking behavior where +people on their own screw up in certain + + align:start position:0% +people on their own screw up in certain + + + align:start position:0% +people on their own screw up in certain +ways and trying to improve them and + + align:start position:0% +ways and trying to improve them and + + + align:start position:0% +ways and trying to improve them and +trying to help them + + align:start position:0% +trying to help them + + + align:start position:0% +trying to help them +but rather helping people uh being + + align:start position:0% +but rather helping people uh being + + + align:start position:0% +but rather helping people uh being +misdirected in certain ways + + align:start position:0% +misdirected in certain ways + + + align:start position:0% +misdirected in certain ways +um to to be exploited + + align:start position:0% +um to to be exploited + + + align:start position:0% +um to to be exploited +and in many cases in particular in + + align:start position:0% +and in many cases in particular in + + + align:start position:0% +and in many cases in particular in +companies identifying those kinds of + + align:start position:0% +companies identifying those kinds of + + + align:start position:0% +companies identifying those kinds of +sludges + + align:start position:0% +sludges + + + align:start position:0% +sludges +and uh calling companies out gets it + + align:start position:0% +and uh calling companies out gets it + + + align:start position:0% +and uh calling companies out gets it +pretty far + + align:start position:0% +pretty far + + + align:start position:0% +pretty far +gets you pretty far in some sense on + + align:start position:0% +gets you pretty far in some sense on + + + align:start position:0% +gets you pretty far in some sense on +social media but like + + align:start position:0% +social media but like + + + align:start position:0% +social media but like +once called out companies often back + + align:start position:0% +once called out companies often back + + + align:start position:0% +once called out companies often back +down and try to reduce them because they + + align:start position:0% +down and try to reduce them because they + + + align:start position:0% +down and try to reduce them because they +did + + align:start position:0% +did + + + align:start position:0% +did +they don't want to have bad reputations + + align:start position:0% +they don't want to have bad reputations + + + align:start position:0% +they don't want to have bad reputations +of exploiting um + + align:start position:0% +of exploiting um + + + align:start position:0% +of exploiting um +customers okay so let me sort of + + align:start position:0% +customers okay so let me sort of + + + align:start position:0% +customers okay so let me sort of +summarize the lecture and then briefly + + align:start position:0% +summarize the lecture and then briefly + + + align:start position:0% +summarize the lecture and then briefly +and two minutes the whole class + + align:start position:0% +and two minutes the whole class + + + align:start position:0% +and two minutes the whole class +um so some forms of particular soft + + align:start position:0% +um so some forms of particular soft + + + align:start position:0% +um so some forms of particular soft +paternalism can ambiguously improve + + align:start position:0% +paternalism can ambiguously improve + + + align:start position:0% +paternalism can ambiguously improve +welfare and we should be quite excited + + align:start position:0% +welfare and we should be quite excited + + + align:start position:0% +welfare and we should be quite excited +about them and they can help quite a bit + + align:start position:0% +about them and they can help quite a bit + + + align:start position:0% +about them and they can help quite a bit +now on the other end not just can also + + align:start position:0% +now on the other end not just can also + + + align:start position:0% +now on the other end not just can also +make things worse in particular if the + + align:start position:0% +make things worse in particular if the + + + align:start position:0% +make things worse in particular if the +government doesn't know + + align:start position:0% +government doesn't know + + + align:start position:0% +government doesn't know +what's good for people and we want to be + + align:start position:0% +what's good for people and we want to be + + + align:start position:0% +what's good for people and we want to be +careful and nudging + + align:start position:0% +careful and nudging + + + align:start position:0% +careful and nudging +there's some examples happen in class + + align:start position:0% +there's some examples happen in class + + + align:start position:0% +there's some examples happen in class +but there's also some + + align:start position:0% +but there's also some + + + align:start position:0% +but there's also some +examples of nudges actually backfiring + + align:start position:0% +examples of nudges actually backfiring + + + align:start position:0% +examples of nudges actually backfiring +now in addition to that some people + + align:start position:0% +now in addition to that some people + + + align:start position:0% +now in addition to that some people +dislike being mentioned + + align:start position:0% +dislike being mentioned + + + align:start position:0% +dislike being mentioned +we should respect that and take that + + align:start position:0% +we should respect that and take that + + + align:start position:0% +we should respect that and take that +into account we try to maximize + + align:start position:0% +into account we try to maximize + + + align:start position:0% +into account we try to maximize +utility remember as opposed to like um + + align:start position:0% +utility remember as opposed to like um + + + align:start position:0% +utility remember as opposed to like um +certain behaviors or take up of certain + + align:start position:0% +certain behaviors or take up of certain + + + align:start position:0% +certain behaviors or take up of certain +outcomes and you want to be careful not + + align:start position:0% +outcomes and you want to be careful not + + + align:start position:0% +outcomes and you want to be careful not +to make people worse off + + align:start position:0% +to make people worse off + + + align:start position:0% +to make people worse off +in helping people opt out of certain + + align:start position:0% +in helping people opt out of certain + + + align:start position:0% +in helping people opt out of certain +languages or certain + + align:start position:0% +languages or certain + + + align:start position:0% +languages or certain +events should be quite helpful in + + align:start position:0% +events should be quite helpful in + + + align:start position:0% +events should be quite helpful in +addition the market does not solve + + align:start position:0% +addition the market does not solve + + + align:start position:0% +addition the market does not solve +everything + + align:start position:0% +everything + + + align:start position:0% +everything +so we should not have faith in like the + + align:start position:0% +so we should not have faith in like the + + + align:start position:0% +so we should not have faith in like the +market solving things in particular the + + align:start position:0% +market solving things in particular the + + + align:start position:0% +market solving things in particular the +market might um uh make things worse + + align:start position:0% +market might um uh make things worse + + + align:start position:0% +market might um uh make things worse +um finally uh reducing sludges can go a + + align:start position:0% +um finally uh reducing sludges can go a + + + align:start position:0% +um finally uh reducing sludges can go a +long way in improving behavior um + + align:start position:0% +long way in improving behavior um + + + align:start position:0% +long way in improving behavior um +overall now a big picture summary of + + align:start position:0% +overall now a big picture summary of + + + align:start position:0% +overall now a big picture summary of +this class um + + align:start position:0% +this class um + + + align:start position:0% +this class um +what is it in one slide that i want you + + align:start position:0% +what is it in one slide that i want you + + + align:start position:0% +what is it in one slide that i want you +to take away and have + + align:start position:0% +to take away and have + + + align:start position:0% +to take away and have +i've learned of course things are more + + align:start position:0% +i've learned of course things are more + + + align:start position:0% +i've learned of course things are more +complicated but let me give you like a + + align:start position:0% +complicated but let me give you like a + + + align:start position:0% +complicated but let me give you like a +very brief summary so one psychological + + align:start position:0% +very brief summary so one psychological + + + align:start position:0% +very brief summary so one psychological +considerations are or can be quite + + align:start position:0% +considerations are or can be quite + + + align:start position:0% +considerations are or can be quite +important in a lot of economic choices + + align:start position:0% +important in a lot of economic choices + + + align:start position:0% +important in a lot of economic choices +and behaviors we should take them + + align:start position:0% +and behaviors we should take them + + + align:start position:0% +and behaviors we should take them +very seriously for you personally i + + align:start position:0% +very seriously for you personally i + + + align:start position:0% +very seriously for you personally i +think that means in some ways + + align:start position:0% +think that means in some ways + + + align:start position:0% +think that means in some ways +understanding your own biases and + + align:start position:0% +understanding your own biases and + + + align:start position:0% +understanding your own biases and +mistakes and issues better and try to + + align:start position:0% +mistakes and issues better and try to + + + align:start position:0% +mistakes and issues better and try to +improve decision making + + align:start position:0% +improve decision making + + + align:start position:0% +improve decision making +seems quite important that's true for + + align:start position:0% +seems quite important that's true for + + + align:start position:0% +seems quite important that's true for +short run or simple sort of + + align:start position:0% +short run or simple sort of + + + align:start position:0% +short run or simple sort of +considerations such as you know how to + + align:start position:0% +considerations such as you know how to + + + align:start position:0% +considerations such as you know how to +deal with procrastination and exercising + + align:start position:0% +deal with procrastination and exercising + + + align:start position:0% +deal with procrastination and exercising +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +it's also true for long run + + align:start position:0% +it's also true for long run + + + align:start position:0% +it's also true for long run +considerations like which which jobs do + + align:start position:0% +considerations like which which jobs do + + + align:start position:0% +considerations like which which jobs do +you want to have which friends do you + + align:start position:0% +you want to have which friends do you + + + align:start position:0% +you want to have which friends do you +want to keep and so on and so forth + + align:start position:0% +want to keep and so on and so forth + + + align:start position:0% +want to keep and so on and so forth +uh it could make you perfect you're + + align:start position:0% +uh it could make you perfect you're + + + align:start position:0% +uh it could make you perfect you're +unhappy in the future + + align:start position:0% +unhappy in the future + + + align:start position:0% +unhappy in the future +and you want to be quite mindful um + + align:start position:0% +and you want to be quite mindful um + + + align:start position:0% +and you want to be quite mindful um +about that + + align:start position:0% +about that + + + align:start position:0% +about that +small changes or like thinking about + + align:start position:0% +small changes or like thinking about + + + align:start position:0% +small changes or like thinking about +things um for a while can make big + + align:start position:0% +things um for a while can make big + + + align:start position:0% +things um for a while can make big +differences + + align:start position:0% +differences + + + align:start position:0% +differences +so i think i very much encourage you to + + align:start position:0% +so i think i very much encourage you to + + + align:start position:0% +so i think i very much encourage you to +introspect be more mindful and mindful + + align:start position:0% +introspect be more mindful and mindful + + + align:start position:0% +introspect be more mindful and mindful +and your choices + + align:start position:0% +and your choices + + + align:start position:0% +and your choices +um as i said last time experimenting + + align:start position:0% +um as i said last time experimenting + + + align:start position:0% +um as i said last time experimenting +seeking advice + + align:start position:0% +seeking advice + + + align:start position:0% +seeking advice +including psychological support and so + + align:start position:0% +including psychological support and so + + + align:start position:0% +including psychological support and so +on seem to be quite helpful + + align:start position:0% +on seem to be quite helpful + + + align:start position:0% +on seem to be quite helpful +at the same time you also shouldn't + + align:start position:0% +at the same time you also shouldn't + + + align:start position:0% +at the same time you also shouldn't +stress too much and sort of just try to + + align:start position:0% +stress too much and sort of just try to + + + align:start position:0% +stress too much and sort of just try to +be happy + + align:start position:0% +be happy + + + align:start position:0% +be happy +and don't be too harsh on yourself uh + + align:start position:0% +and don't be too harsh on yourself uh + + + align:start position:0% +and don't be too harsh on yourself uh +often people are doing quite well + + align:start position:0% +often people are doing quite well + + + align:start position:0% +often people are doing quite well +already um overall + + align:start position:0% +already um overall + + + align:start position:0% +already um overall +it's also worth understanding that + + align:start position:0% +it's also worth understanding that + + + align:start position:0% +it's also worth understanding that +sometimes it's actually easier to help + + align:start position:0% +sometimes it's actually easier to help + + + align:start position:0% +sometimes it's actually easier to help +your friends or others than yourself + + align:start position:0% +your friends or others than yourself + + + align:start position:0% +your friends or others than yourself +it's often easier to see in others how + + align:start position:0% +it's often easier to see in others how + + + align:start position:0% +it's often easier to see in others how +they're mis-optimizing + + align:start position:0% +they're mis-optimizing + + + align:start position:0% +they're mis-optimizing +and how to improve their behaviors so in + + align:start position:0% +and how to improve their behaviors so in + + + align:start position:0% +and how to improve their behaviors so in +some ways helping others + + align:start position:0% +some ways helping others + + + align:start position:0% +some ways helping others +um might be in fact one of the things + + align:start position:0% +um might be in fact one of the things + + + align:start position:0% +um might be in fact one of the things +you might have taken away + + align:start position:0% +you might have taken away + + + align:start position:0% +you might have taken away +from this class um and then finally you + + align:start position:0% +from this class um and then finally you + + + align:start position:0% +from this class um and then finally you +know you want to think about in + + align:start position:0% +know you want to think about in + + + align:start position:0% +know you want to think about in +particular when you think about like + + align:start position:0% +particular when you think about like + + + align:start position:0% +particular when you think about like +designs of teams working with others + + align:start position:0% +designs of teams working with others + + + align:start position:0% +designs of teams working with others +incentives products and so on if you try + + align:start position:0% +incentives products and so on if you try + + + align:start position:0% +incentives products and so on if you try +to design an app or any website or + + align:start position:0% +to design an app or any website or + + + align:start position:0% +to design an app or any website or +thinking about psychological + + align:start position:0% +thinking about psychological + + + align:start position:0% +thinking about psychological +considerations of designing things + + align:start position:0% +considerations of designing things + + + align:start position:0% +considerations of designing things +is quite important that you should take + + align:start position:0% +is quite important that you should take + + + align:start position:0% +is quite important that you should take +those things + + align:start position:0% +those things + + + align:start position:0% +those things +into account um somebody was asking + + align:start position:0% +into account um somebody was asking + + + align:start position:0% +into account um somebody was asking +about books to read so i just sort of + + align:start position:0% +about books to read so i just sort of + + + align:start position:0% +about books to read so i just sort of +added them here + + align:start position:0% +added them here + + + align:start position:0% +added them here +i was planning to say a little bit more + + align:start position:0% +i was planning to say a little bit more + + + align:start position:0% +i was planning to say a little bit more +but i'm sort of out of time so i'm just + + align:start position:0% +but i'm sort of out of time so i'm just + + + align:start position:0% +but i'm sort of out of time so i'm just +leaving this here i'll try to add like a + + align:start position:0% +leaving this here i'll try to add like a + + + align:start position:0% +leaving this here i'll try to add like a +couple of sentences for each of + + align:start position:0% +couple of sentences for each of + + + align:start position:0% +couple of sentences for each of +um there are some quite amazing books + + align:start position:0% +um there are some quite amazing books + + + align:start position:0% +um there are some quite amazing books +that you can read + + align:start position:0% + + + + align:start position:0% + +in particular for example chaldini's 93 + + align:start position:0% +in particular for example chaldini's 93 + + + align:start position:0% +in particular for example chaldini's 93 +influence books is amazing book to read + + align:start position:0% +influence books is amazing book to read + + + align:start position:0% +influence books is amazing book to read +daeneryeli has really nice books + + align:start position:0% +daeneryeli has really nice books + + + align:start position:0% +daeneryeli has really nice books +including predictably irrational + + align:start position:0% +including predictably irrational + + + align:start position:0% +including predictably irrational +some of these are more basic um than + + align:start position:0% +some of these are more basic um than + + + align:start position:0% +some of these are more basic um than +others + + align:start position:0% +others + + + align:start position:0% +others +um if you're interested in poverty milan + + align:start position:0% +um if you're interested in poverty milan + + + align:start position:0% +um if you're interested in poverty milan +athena and shafir's scarcity book is + + align:start position:0% +athena and shafir's scarcity book is + + + align:start position:0% +athena and shafir's scarcity book is +really an amazing um + + align:start position:0% +really an amazing um + + + align:start position:0% +really an amazing um +uh read and then danny kahneman's uh + + align:start position:0% +uh read and then danny kahneman's uh + + + align:start position:0% +uh read and then danny kahneman's uh +thinking fast and slow + + align:start position:0% +thinking fast and slow + + + align:start position:0% +thinking fast and slow +um it's also like um uh extremely + + align:start position:0% +um it's also like um uh extremely + + + align:start position:0% +um it's also like um uh extremely +insightful and interesting + + align:start position:0% +insightful and interesting + + + align:start position:0% +insightful and interesting +um of course there's other brooks for + + align:start position:0% +um of course there's other brooks for + + + align:start position:0% +um of course there's other brooks for +example dick taylor talks about the + + align:start position:0% +example dick taylor talks about the + + + align:start position:0% +example dick taylor talks about the +history of behavioral economics + + align:start position:0% +history of behavioral economics + + + align:start position:0% +history of behavioral economics +uh lewis uh is the what's called the + + align:start position:0% +uh lewis uh is the what's called the + + + align:start position:0% +uh lewis uh is the what's called the +undoing project which is about + + align:start position:0% +undoing project which is about + + + align:start position:0% +undoing project which is about +uh conor mcgregor's friendship and how + + align:start position:0% +uh conor mcgregor's friendship and how + + + align:start position:0% +uh conor mcgregor's friendship and how +they sort of essentially came to + + align:start position:0% +they sort of essentially came to + + + align:start position:0% +they sort of essentially came to +uh in some really important ways uh + + align:start position:0% +uh in some really important ways uh + + + align:start position:0% +uh in some really important ways uh +revolutionizing + + align:start position:0% +revolutionizing + + + align:start position:0% +revolutionizing +uh some parts of economics so there's + + align:start position:0% +uh some parts of economics so there's + + + align:start position:0% +uh some parts of economics so there's +lots of things to read + + align:start position:0% +lots of things to read + + + align:start position:0% +lots of things to read +uh if you're interested in any of these + + align:start position:0% +uh if you're interested in any of these + + + align:start position:0% +uh if you're interested in any of these +just let me know i'm very happy to + + align:start position:0% +just let me know i'm very happy to + + + align:start position:0% +just let me know i'm very happy to +to to chat so that's that's pretty much + + align:start position:0% +to to chat so that's that's pretty much + + + align:start position:0% +to to chat so that's that's pretty much +all i have to say i have lots of fun + + align:start position:0% +all i have to say i have lots of fun + + + align:start position:0% +all i have to say i have lots of fun +uh teaching this class i know this + + align:start position:0% +uh teaching this class i know this + + + align:start position:0% +uh teaching this class i know this +semester was was tricky and difficult + + align:start position:0% +semester was was tricky and difficult + + + align:start position:0% +semester was was tricky and difficult +um for many of us i i uh every um time i + + align:start position:0% +um for many of us i i uh every um time i + + + align:start position:0% +um for many of us i i uh every um time i +teach this class i'm surprised how much + + align:start position:0% +teach this class i'm surprised how much + + + align:start position:0% +teach this class i'm surprised how much +i learned i hope you learned some useful + + align:start position:0% +i learned i hope you learned some useful + + + align:start position:0% +i learned i hope you learned some useful +things too + + align:start position:0% +things too + + + align:start position:0% +things too +um i guess uh this is from last time so + + align:start position:0% +um i guess uh this is from last time so + + + align:start position:0% +um i guess uh this is from last time so +there's no course evaluations this this + + align:start position:0% +there's no course evaluations this this + + + align:start position:0% +there's no course evaluations this this +year + + align:start position:0% +year + + + align:start position:0% +year +we might do an informal or informal one + + align:start position:0% +we might do an informal or informal one + + + align:start position:0% +we might do an informal or informal one +um to just want to try to think about uh + + align:start position:0% +um to just want to try to think about uh + + + align:start position:0% +um to just want to try to think about uh +learn more about what you thought we did + + align:start position:0% +learn more about what you thought we did + + + align:start position:0% +learn more about what you thought we did +already in informal + + align:start position:0% +already in informal + + + align:start position:0% +already in informal +relationship but that was assuming that + + align:start position:0% +relationship but that was assuming that + + + align:start position:0% +relationship but that was assuming that +there will be actual evaluations this + + align:start position:0% +there will be actual evaluations this + + + align:start position:0% +there will be actual evaluations this +semester + + align:start position:0% +semester + + + align:start position:0% +semester +unfortunately mit has sort of canceled + + align:start position:0% +unfortunately mit has sort of canceled + + + align:start position:0% +unfortunately mit has sort of canceled +them this year uh i think to be mindful + + align:start position:0% +them this year uh i think to be mindful + + + align:start position:0% +them this year uh i think to be mindful +for some people are particularly + + align:start position:0% +for some people are particularly + + + align:start position:0% +for some people are particularly +affected by + + align:start position:0% +affected by + + + align:start position:0% +affected by +um uh uh the quarantine and so on uh + + align:start position:0% +um uh uh the quarantine and so on uh + + + align:start position:0% +um uh uh the quarantine and so on uh +come to my office hours you have + + align:start position:0% +come to my office hours you have + + + align:start position:0% +come to my office hours you have +questions + + align:start position:0% +questions + + + align:start position:0% +questions +um uh i have some europe opportunities + + align:start position:0% +um uh i have some europe opportunities + + + align:start position:0% +um uh i have some europe opportunities +some of you have already applied to + + align:start position:0% +some of you have already applied to + + + align:start position:0% +some of you have already applied to +those there's been um quite a bit of + + align:start position:0% +those there's been um quite a bit of + + + align:start position:0% +those there's been um quite a bit of +interest um so if you have already + + align:start position:0% +interest um so if you have already + + + align:start position:0% +interest um so if you have already +applied i'll get back to you + + align:start position:0% +applied i'll get back to you + + + align:start position:0% +applied i'll get back to you +soon but any case come and talk to me um + + align:start position:0% +soon but any case come and talk to me um + + + align:start position:0% +soon but any case come and talk to me um +if you're interested i hope you learn + + align:start position:0% +if you're interested i hope you learn + + + align:start position:0% +if you're interested i hope you learn +more economics and if you hope you take + + align:start position:0% +more economics and if you hope you take + + + align:start position:0% +more economics and if you hope you take +psychological considerations and those + + align:start position:0% +psychological considerations and those + + + align:start position:0% +psychological considerations and those +uh economic issues quite seriously so + + align:start position:0% +uh economic issues quite seriously so + + + align:start position:0% +uh economic issues quite seriously so +thank you very much + + align:start position:0% +thank you very much + + + align:start position:0% +thank you very much +you \ No newline at end of file diff --git a/UUKTIhxznF0.txt b/UUKTIhxznF0.txt new file mode 100644 index 0000000000000000000000000000000000000000..18ed5c0a1a3043d149b522c673f57f64d5010b93 --- /dev/null +++ b/UUKTIhxznF0.txt @@ -0,0 +1,3868 @@ +The following content is +provided under a Creative + +Commons license. + +Your support help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: So today, we're going +to talk a bit more about + +parallelism and about how you +get performance out of + +parallel codes. + +And also, we're going to take +a little bit of a tour + +underneath the Cilk++ runtime +system so you can get an idea + +of what's going on underneath +and why it is that when you + +code stuff, how it is that it +gets mapped, scheduled on the + +processors. + +So when people talk about +parallelism, one of the first + +things that often comes up is +what's called Amdahl's Law. + +Gene Amdahl was the architect +of the IBM360 computers who + +then left IBM and formed his +own company that made + +competing machines and he made +the following observation + +about parallel computing, +he said-- + +and I'm paraphrasing here-- + +half your application is +parallel and half is serial. + +You can't get more than a factor +of two speed up, no + +matter how many processors +it runs on. + +So if you think about it, if +it's half parallel and you + +managed to make that parallel +part run in zero time, still + +the serial part will be half of +the time and you only get a + +factor of two speedup. + +You can generalize that to say +if some fraction alpha can be + +run in parallel and the rest +must be run serially, the + +speedup is at most 1 +over 1 minus alpha. + +OK, so this was used in the +1980s in particular to say why + +it was that parallel computing +had no future, because you + +simply weren't going to be able +to get very much speedups + +from parallel computing. + +You're going to spend extra +hardware on the parallel parts + +of the system and yet you might +be limited in terms of + +how much parallelism there is +in a particular application + +and you wouldn't get +very much speedup. + +You wouldn't get the bang for +the buck, if you will. + +So things have changed today +that make that not quite the + +same story. + +The first thing is that with +multicore computers, it is + +pretty much just as inexpensive +to produce a p + +processor right now, like six +processor machine as it is a + +one processor machine. + +so it's not like you're actually +paying for those + +extra processing cores. + +They come for free. + +Because what else are you're +going to use that silicon for? + +And the other thing is that +we've had a large growth of + +understanding of problems +for which there's ample + +parallelism, where that +amount of time is, + +in fact, quite small. + +And the main place these things +come from, it turns + +out, this analysis is kind of a +throughput kind of analysis. + +OK, it says, gee, I only get +50% speedup for that + +application, but what most +people care about in most + +interactive applications, at +least for a client side + +programming, is response time. + +And for any problem that you +have that has a response time + +that's too long and its compute +intensive, using + +parallelism to make it so that +the response is much zippier + +is definitely worthwhile. + +And so this is true, even for +things like game programs. + +So in game programs, they don't +have quite a response + +time problem, they have what's +called a time box problem, + +where you have a certain +amount of time-- + +13 milliseconds typically-- + +because you need some slop to +make sure that you can go from + +one frame to another, but about +13 milliseconds to do a + +rendering of whatever the frame +is that the game player + +is going to see on his computer +or her computer. + +And so in that time, you want to +do as much as you possibly + +can, and so there's a big +opportunity there to take + +advantage of parallelism in +order to do more, have more + +quality graphics, have better +AI, have better physics and + +all the other components that +make up a game engine. + +But one of the issues +with Amdahl's Law-- + +and this analysis is a cogent +analysis that Amdahl made-- + +but one of the issues here is +that it doesn't really say + +anything about how fast +you can expect your + +application to run. + +In other words, this is a nice +sort of thing, but who really + +can decompose their application +into the serial + +part and the part that +can be parallel? + +Well fortunately, there's been a +lot of work in the theory of + +parallel systems to answer this +question, and we're going + +to go over some of that really +outstanding research that + +helps us understand what +parallelism is. + +So we're going to talk a +little bit about what + +parallelism is and come up with +a very specific measure + +of parallelism, quantify +parallelism, OK? + +We're also going to talk a +little bit about scheduling + +theory and how the Cilk++ +runtime system works. + +And then we're going to have +a little chess lesson. + +So who here plays chess? + +Nobody plays chess anymore. + +Who plays Angry Birds? + +[LAUGHTER] + +OK. + +So you don't have to know +anything about chess to learn + +this chess lesson, that's OK. + +So we'll start out with +what is parallelism? + +So let's recall first the +basics of Cilk++. + +So here's the example of the +lousy Fibonacci that everybody + +parallelizes because it's +good didactically. + +We have the Cilk spawn statement +that says that the + +child can execute in parallel +with the parent caller and the + +sync that says don't go past +this point until all your + +spawn children have returned. + +And that's a local sync, +that's just a + +sync for that function. + +It's not a sync across +the whole machine. + +So some of you may have had +experience with open MP + +barriers, for example, +that's a sync + +across the whole machine. + +This is not, this is just a +local sync for this function + +saying when I sync, make sure +all my children have returned + +before going past this point. + +And just remember also that Cilk +keywords grant permission + +for parallel execution. + +They don't command parallel +execution. + +OK so we can always execute +our code serially + +if we choose to. + +Yes? + +AUDIENCE: [UNINTELLIGIBLE] + +Can't this runtime figure that +spawning an extra child would + +be more expensive? + +Can't it like look at +this and be like-- + +PROFESSOR: We'll go into it. + +I'll show you how it works +later in the lecture. + +I'll show you how it works and +then we can talk about what + +knobs you have to tune, OK? + +So it's helpful to have +an execution model for + +something like this. + +And so we're going to look at +an abstract execution model, + +which is basically asking what +does the instruction trace + +look like for this program? + +So normally when you execute a +program, you can imagine one + +instruction executing +after the other. + +And if it's a serial program, +all those instructions + +essentially form a long chain. + +Well there's a similar thing for +parallel computers, which + +is that instead of a chain as +you'll see, it gets bushier + +and it's going to be a directed +acyclic graph. + +So let's take a look +at how we do this. + +So we'll the example +of fib of four. + +So what we're going to do +is start out here with a + +rectangle here that I want you +think about as sort of a + +function call activation +record. + +So it's a record on a stack. + +It's got variables associated +with it. + +The only variable I'm going to +keep track of is n, so that's + +what the four is there. + +OK, so we're going to +do fib of four. + +So we've got in this activation +frame, we have the + +variable four and now what I've +done is I've color coded + +the fib function here and into +the parts that are all serial. + +So there's a serial part up to +where it spawns, then there's + +recursively calling the fib and +then there's returning. + +So there's sort of three parts +to this function, each of + +which is, in fact, a chain +of serial instruction. + +I'm going to collapse those +chains into a single circle + +here that I'm going +to call a strand. + +OK, now what we do is we execute +the strand, which + +corresponds to executing the +instructions and advancing the + +program calendar up until +the point we hit this + +fib of n minus 1. + +At that point, I basically +call fib of n minus 1. + +So in this case, it's now +going to be fib of 3. + +So that means I create a child +and start executing in the + +child, this prefix part +of the function. + +However, unlike I were doing an +ordinary function call, I + +would make this call and then +this guy would just sit here + +and wait until this +frame was done. + +But since it's a spawn, what +happens is I'm actually going + +to continue executing in the +parent and execute, in fact, + +the green part. + +So in this case, evaluating +the arguments, etc. + +Then it's going to spawn here, +but this guy, in fact, is + +going to what it does when it +gets here is it evaluates n + +minus 2, it does a call +of fib of n minus 2. + +So I've indicated that this was +a called frame by showing + +it in a light color. + +So these are spawn, spawn, +call, meanwhile + +this thing is going. + +So at this point, we now have +one, two, three things that + +are operating in parallel +at the same time. + +We keep going on, OK? + +So this guy that does a spawn +and has a continuation, this + +one does a call, but while +he's doing a call, he's + +waiting for the return +so he doesn't start + +executing the successor. + +He stalled at the +Cilk sink here. + +And we keep executing and so +as you can see, what's + +happening is we're actually +creating a directed acyclic + +graph of these strands. + +So here basically, this guy was +able to execute because + +both of the children, one that +he had spawned and one that he + +had called, have returned. + +And so this fella, therefore, +is able then + +to execute the return. + +OK, so the addition of x plus y +in particular, and then the + +return to the parent. + +And so what we end up with is of +all these serial chains of + +instructions that are +represented by these strands, + +all these circles, they're +embedded in the call tree like + +you would have in an ordinary +serial execution. + +You have a call tree that you +execute up and down, you walk + +it like a stack normally. + +Now, in fact, what we have is +embedded in there is the + +parallel execution which form a +DAG, directed acyclic graph. + +So when you start thinking in +parallel, you have to start + +thinking about the DAG as your +execution model, not a chain + +of instructions. + +And the nice thing about this +particular execution model + +we're going to be looking at is +nowhere did I say how many + +processors we were running on. + +This is a processor +oblivious model. + +It doesn't know how many +processors you're running on. + +We simply in the execution +model, are thinking about + +abstractly what can run in +parallel, not what actually + +does run in parallel +in an execution. + +So any questions about +this execution model? + +OK. + +So just so that we have some +terminology, so the parallel + +instruction stream is a DAG +with vertices and edges. + +Each vertex is a strand, OK? + +Which is a sequence of +instructions not containing a + +call spawn sync, a return or +thrown exception, if you're + +doing exceptions. + +We're not going to really talk +about exceptions much. + +So they are supported in the +software that we'll be using, + +but for most part, we're +not going to have + +to worry about them. + +OK so there's an initial strand +where you start, and a + +final strand where you end. + +Then each edge is a spawn or +a call or return or what's + +called a continue edge or a +continuation edge, which goes + +from the parent, when a parent +spawns something to the next + +instruction after the spawn. + +So we can classify the edges +in that fashion. + +And I've only explain this for +spawm and sync, as you recall + +from last time, we also talked +about Cilk four. + +It turns out Cilk four is +converted to spawns and syncs + +using a recursive divide +and conquer approach. + +We'll talk about that next +time on Thursday. + +So we'll talk more about Cilk +four and how it's implemented + +and the implications of how +loop parallelism works. + +So at the fundamental level, +the runtime system is only + +concerned about spawns +and syncs. + +Now given that we have a DAG, +so I've taken away the call + +tree and just left the strands +of a computation. + +It's actually not the same as +the computation we saw before. + +We would like to understand, +is this a good parallel + +program or not? + +Based on if I understand +the logical + +parallelism that I've exposed. + +So how much parallelism do +you think is in here? + +Give me a number. + +How many processors does it +make sense to run this on? + +Five? + +That's as parallel as it gets. + +Let's take a look. + +We're going to do an analysis. + +At the end of it, we'll know +what the answer is. + +So for that, let tp be the +execution time on p processors + +for this particular program. + +It turns but there +are two measures + +that are really important. + +The first is called the work. + +OK, so of course, we know +that real machines + +have caches, etc. + +Let's forget all of that. + +Just very simple algorithmic +model where every strand, + +let's say, costs us unit time +as opposed to in practice, + +they may be many instructions +and so forth. + +We can take that into account. + +Let's take that into +account separately. + +So T1 is the work. + +It's the time it if I had to +execute it on one processor, + +I've got to do all the +work that's in here. + +So what's the work of this +particular computation? + +I think it's 18, right? + +Yeah, 18. + +So T1 is the work. + +So even though I'm executing a +parallel, I could it execute + +it serially and then T1 is the +amount of work it would take. + +The other measure is called the +span, and sometimes called + +critical path length or +computational depth. + +And it corresponds to the +longest path of dependencies + +in the DAG. + +We call it T infinity because +even if you had an infinite + +number of processors, you still +can't do this one until + +you finish that one. + +You can't do this one until you +finish that one, can't do + +this one till you've finished +that one and so forth. + +So even with an infinite number +of processors, I still + +wouldn't go faster +than the span. + +So that's why we denote +by T infinity. + +So these are the two +important measures. + +Now what we're really +interested in is + +Tp for a given p. + +As you'll see, we actually can +get some bounds on the + +performance on p processors just +by looking at the work, + +the span and the number of +processors we're executing on. + +So the first bound is +the following, it's + +called the Work Law. + +The Work Law says that the time +on p processors is at + +least the time on one processor +divided by p. + +So why does that Work +Law make sense? + +What's that saying? + +Sorry? + +AUDIENCE: Like work is +conserved sort of? + +I mean, you have to do the +same amount of work. + +PROFESSOR: You have to do the +same amount of work, so on + +every time step, you can get +p pieces of work done. + +So if you're running for fewer +than T1 over p steps, you've + +done less than T1 work +over and time Tp. + +So you won't have done all +the work if you run + +for less than this. + +So the time must be at least +Tp, time Tp must be at + +least T1 over p. + +You only get to do p +work on one step. + +Is that pretty clear? + +The second one should be even +clearer, the Span Law. + +On p processors, you're not +going to go faster than if you + +had an infinite number of +processors because the + +infinite processor could always +use fewer processors if + +it's scheduled. + +Once again, this is a +very simple model. + +We're not taking into account +scheduling, we're not taking + +into account overheads or +whatever, just a simple + +conceptual model for +understanding parallelism. + +So any questions about +these two laws? + +There's going to be a couple +of formulas in this lecture + +today that you should write +down and play with. + +So these two, they may seem +simple, but these are hugely + +important formulas. + +So you should know that Tp is at +least T1 over p, that's the + +Work Law and that Tp is +at least T infinity. + +Those are bounds on how fast +you could execute. + +Do I have a question +in that back there? + +OK so let's see what happens +to work in span in terms of + +how we can understand our +programs and decompose them. + +So suppose that I have a +computation A followed by + +computation B and I connect +them in series. + +What happens to the work? + +How does the work of all this +whole thing correspond to the + +work of A and the work of B? + +What's that? + +AUDIENCE: [UNINTELLIGIBLE] + +PROFESSOR: Yeah, add +them together. + +You get T1 of A plus T1 of B. +Take the work of this and the + +work of this. + +OK, that's pretty easy. + +What about the span? + +So the span is the longest +path of dependencies. + +What happens to the span +when I connect + +two things in a series? + +Yeah, it just sums as well +because I take whatever the + +longest path is from here to +here and then the longest one + +from here to here, +it just adds. + +But now let's look at parallel +composition, So now suppose + +that I can execute these +two things in parallel. + +What happens to the work? + +It just adds, just as before. + +The work always adds. + +The work is easy because +it's additive. + +What happens to the span? + +What's that? + +AUDIENCE: [UNINTELLIGIBLE] + +PROFESSOR: It's the +max of the spans. + +Right, so whatever is the +longest, whichever one of + +these ones has a longer span, +that's going to be + +the span of the total. + +Does that give you some +Intuition So we're going to + +see when we analyze the spans of +things that in fact, we're + +going to see maxes occurring +all over the place. + +So speedup is defined +to be T1 over Tp. + +So speedup is how much faster am +I on p processors than I am + +on one processor? + +Pretty easy. + +So if T1 over Tp is equal to +p, we say we have perfect + +linear speedup, or +linear speedup. + +That's good, right? + +Because if I put on use p +processors, I'd like to have + +things go p times faster. + +OK, that would be +the ideal world. + +If T1 over Tp, which is the +speedup, is greater than p, + +that says we have super +linear speedup. + +And in our model, we don't get +that because of the work law. + +Because the work law says Tp is +greater than or equal to T1 + +over p and just do a little +algebra here, you get T1 over + +Tp must be less than +or equal to p. + +So you can't get super +linear speedup. + +In practice, there are +situations where you can get + +super linear speedup due +to caching effects and + +a variety of things. + +We'll talk about some +of those things. + +But in this simple model, +we don't get + +that kind of behavior. + +And of course, the case I left +out is the common case, which + +is the T1 over Tp is less than +p, and that's very common + +people write code which doesn't + +give them linear speedup. + +We're mostly interested in +getting linear speedup here. + +That's our goal. + +So that we're getting the most +bang for the buck out of the + +processors we're using. + +OK, parallelism. + +So we're finally to the point +where I can talk about + +parallelism and give a +quantitative definition of + +parallelism. + +So the Span Law says that Tp is +at least T infinity, right? + +The time on p processors is at +least the time on an infinite + +number of processors. + +So the maximum possible speedup, +that's T1 over Tp, + +given T1 and T infinity +is T1 over T infinity. + +And we call that the +parallelism. + +It's the maximum amount +of speedup we + +could possibly attain. + +So we have the speedup and the +speedup by the Span Law that + +says this is the maximum amount +we can get, we could + +also view it as if I look along +the critical path of the + +computation. + +It's sort of what's the average +amount of work at + +every level. + +The work, the total amount of +stuff here divided by that + +length there that sort of tells +us the width, what's the + +average amount of stuff that's +going on in every step. + +So for this example, +what is the-- + +I forgot to put this +on my slide-- + +what is the parallelism of +this particular DAG here? + +Two, right? + +So the span has length nine-- +this is assuming everything + +was unit time-- + +obviously in reality, when you +have more instructions, you in + +fact would make it be whatever +the length of this was in + +terms of number of instructions +or what have you, + +of execution time of +all these things. + +So this is length 9, there's +18 things here, + +parallelism is 2. + +So we can quantify parallelism +precisely. + +We'll see why it's important +to quantify it. + +So that the maximum speedup +we're going to get when we run + +this application. + +Here's another example +we did before. + +Fib of four. + +So let's assume again that +each strand takes + +unit time to execute. + +So what is the work in this +particular computation? + +Assume every strand takes unit +time to execute, which of + +course it doesn't, but-- + +anybody care to hazard +a guess? + +17, yeah, because there's four +nodes here that have 3 plus 5. + +So 3 times 4 plus 5 is 17. + +So the work is 17. + +OK, what's the span? + +This one's tricky. + +Too bad it's not a little +bit more focused. + +What the span? + +AUDIENCE: 8. + +PROFESSOR: 8, that's correct. + +Who got 7? + +Yeah, so I got 7 when I did this +and then I looked harder + +and it was 8. + +It's 8, so here it is. + +Here's the span. + +There is goes. + +Ooh that little sidestep there, +that's what makes it 8. + +OK so basically, it comes down +here and I had gone down like + +that when I did it, but in fact, +you've got to go over + +and back up. + +So it's actually 8. + +So that says that the +parallelism is a little bit + +more than 2, 2 and 1/8. + +What that says is that if +I use many more than two + +processors, I can't get linear +speedup anymore. + +I'm only going to get marginal +performance gains. + +If I use more than 2, because +the maximum speedup I can get + +is like 2.125 if I had an +infinite number of processors. + +So any questions about this? + +So this by the way deceptively +simple and yet, if you don't + +play around with it a little +bit, you can get + +confused very easily. + +Deceptively simple, +very powerful to + +be able to do this. + +So here we have for the analysis +of parallelism, one + +of the things that we have going +for us in using the Cilk + +tool suite is a program called +Cilkview, which has a + +scalability analyzer. + +And it is like the race detector +that I talked to you + +about last time in that it uses +dynamic instrumentation. + +So you run it under Cilkview, +it's like running it under + +[? Valgrhen ?] + +for example, or what have you. + +So basically you run your +program under it, and it + +analyzes your program +for scalability. + +It computes the work and span of +your program to derive some + +upper bounds on parallel +performance and it also + +estimates a scheduling overhead +to compute what's + +called a burden span +for lower bounds. + +So let's take a look. + +So here's, for example, here's +a quick sort program. + +So let's just see this +is a c++ program. + +So here we're using a template +so that the type of items that + +I'm sorting I can make +be a variable. + +So tightening-- can we shut +the back door there? + +One of the TAs? + +Somebody run up to-- + +thank you. + +So we have the variable T And +we're going to quick sort from + +the beginning to the +end of the array. + +And what we do is, just as +you're familiar with quick + +sort, if there's actually +something to be sorted, more + +than one thing, then we find the +middle by partitioning the + +thing and this is a bit +of a c++ magic to + +find the middle element. + +And then the important part +from our point of view is + +after we've done this partition, +we quick sort the + +first part of the array, from +beginning to middle and then + +from the beginning plus 1 or +the middle, whichever is + +greater to the end. + +And then we sync. + +So what we're doing is quick +sort where we're spawning off + +the two sub problems to +be solved in parallel + +recursively. + +So they're going to execute in +parallel and they're going to + +execute in parallel +and so forth. + +So a fairly natural thing to +divide, to do divide and + +conquer on quick sort because +the two some problems can be + +operated on independently. + +We just sort them recursively. + +But we can sort them +in parallel. + +OK, so suppose that we are +sorting 100,000 numbers. + +How much parallelism do you +think is in this code? + +So remember that we're getting +this recursive stuff done. + +How many people think-- + +well, it's not going +to be more than + +100,000, I promise you. + +So how many people think more +than a million parallels? + +Raise your hand, more +than a million? + +And how many people think +more than 100,000? + +And how many people think +more than 10,000? + +OK, between the two. + +More than 1,000? + +OK, how about more than 100? + +100 to 1,000? + +How about 10 to 100? + +How about between 1 and 10? + +So a lot of people think +between 1 and 10. + +Why do you think that there's +so little parallels in this? + +You don't have to justify +yourself, OK. + +Well let's see how much there +is according to Cilkview. + +So here's the type of output +that you'll get. + +You'll get a graphical curve. + +You'll also get a +textual output. + +But this is sort of the +graphical output. + +And this is basically showing +what the running time here is. + +So the first thing it shows is +it will actually run your + +program, benchmark your program, +on in this case, up + +to 8 course. + +We ran it. + +So we ran up to 8 course and +give you what your measured + +speedup is. + +So the second thing is it +tells you the parallels. + +If you can't read that +it's, 11.21. + +So we get about 11. + +Why do you think it's +not higher? + +What's that? + +AUDIENCE: It's the log. + +PROFESSOR: What's the log? + +AUDIENCE: [UNINTELLIGIBLE] + +PROFESSOR: Yeah, but you're +doing the two things in + +parallel, right? + +We'll actually analyze this. + +So it has to do with the fact +that the partition routine is + +a serial piece of code +and it's big. + +So the initial partitioning +takes you 100,000-- + +sorry, 100 million steps +of doing a partition-- + +before you get to do any +parallelism at all. + +And we'll see that +in just a minute. + +So it gives you the +parallelism. + +It also plots this. + +So this is the parallelism. + +Notice that's the same +number, 11.21 is + +plotted as this bound. + +So it tells you the span law and +it tells you the work law. + +This is the linear speedup. + +If you were having linear +speedup, this is what your + +program would give you. + +So it gives you these two +bounds, the work law and span + +law on your speedup. + +And then it also computes +what's called a burden + +parallelism, estimating +scheduling overheads to sort + +of give you a lower bound. + +Now that's not to say that +your numbers can't fall + +outside this range. + +But when they do, it will tell +you essentially what the + +issues are with your program. + +And we'll discuss how you +diagnose some of those issues. + +Actually that's in one of the +handouts that we've provided. + +I think that's in one +of the handouts. + +If not, we'll make sure it's +among the handouts. + +So basically, this gives you a +range for what you can expect. + +So the important thing here is +to notice here for example, + +that we're losing performance, +but it's not due to the + +parallelism, to the work law. + +Basically, in some sense, what's +happening is we are + +losing it because the Span Law +because we're starting to + +approach the point where the +span is going to be the issue. + +So we'll talk more about this. + +So the main thing is you have +a tool that can tell you the + +work and span and so that you +can analyze your own programs + +to understand are you bounded +by parallelism, for example, + +in particular, in the code +that you've written. + +OK let's do a theoretical +analysis of this to understand + +why that number is small. + +So the main thing here is that +the expected work, as you + +recall, of quick sort +is order n log n. + +You tend to do order n log n +work, you partition and then + +you're solving two problems +of the same size. + +If you actually draw out the +recursion tree, it's log + +height with linear amount of +work on every level for n log + +end total work. + +The expected span, however, is +order n because the partition + +routine is a serial program that +partitions up the thing + +of size n in order n time. + +So when you compute the +parallelism, you get + +parallelism of order log n +and log n is kind of puny + +parallelism, and that's our +technical word for it. + +So puny parallelism is what +we get out of quick sort. + +So it turns out there +are lots of things + +that you can analyze. + +Here's just a selection of +some of the interesting + +practical algorithms and the +kinds of analyses that you can + +do showing that, for example, +with merge sort you can do it + +with work n log n. + +You can get a span of log qn and +so then the parallelism is + +the ratio of the two. + +In fact, you can actually +theoretically get log squared + +n span, but that's not as +practical an algorithm as the + +one that gives you +log cubed n. + +And you can go through and there +are a whole bunch of + +algorithms for which you can +get very good parallelism. + +So all of these, if you look +at the ratio of these, the + +parallelism is quite high. + +So let's talk a little bit +about what's going on + +underneath and why parallelism +is important. + +So when you describe your +program in Cilk, you express + +the potential parallelism +of your application. + +You don't say exactly how it's +going to be scheduled, that's + +done by the Cilk++ scheduler, +which maps the strands + +dynamically onto the processors +at run time. + +So it's going to do the load +balancing and everything + +necessary to balance your +computation off the number of + +processors. + +We want to understand how that +process works, because that's + +going to help us to understand +how it is that we can build + +codes that will map very +effectively on to the number + +of processors. + +Now it turns out that the theory +of the distributed + +schedulers such as is in +Cilk++ is complicated. + +I'll wave my hands about it +towards the end, but the + +analysis of it is advanced. + +You have to take a graduate +course to get that stuff. + +So instead, we're going to +explore the ideas with a + +centralized, much simpler, +scheduler which serves as a + +surrogate for understanding +what's going on. + +So the basic idea of almost all +scheduling theory in this + +domain is greedy scheduling. + +And so this is-- by the way, +we're coming to the second + +thing you have to understand +really well in order to be + +able to generate good code, +the second sort + +of theoretical thing-- + +so the idea of a greedy +scheduler is you want to do as + +much work as possible +on each step. + +So the idea here is let's take +a look, for example, suppose + +that we've executed this part +of the DAG already. + +Then there are certain number +of strands that are ready to + +execute, meaning all their +predecessors have exited. + +How many strands are ready +to execute on this DAG? + +Five, right? + +These guys. + +So those five strands are +ready to execute. + +So the idea is-- and let me +illustrate for p equals 3-- + +the idea is to understand the +execution in terms of two + +types of steps. + +So in a greed schedule, you +always do as much as possible. + +So is what would be called a +complete step because I can + +schedule all three processors +to have some work + +to do on that step. + +So which are the best three guys +to be able to execute? + +Yes, so I'm not sure what the +best three are, but for sure, + +you want to get this guy +and this guy, right? + +Maybe that guy's not, +but this guy, you + +definitely want to execute. + +And these guys, I guess, OK. + +So in a greedy schedule, no, +you're not allowed to look to + +see which ones are +the best execute. + +You don't know what the future +is, the scheduler isn't going + +to know what the future is so it +just executes any p course. + +You just execute any p course. + +In this case, I executed +the p strand. + +In this case, I executed these +three guys even though they + +weren't necessarily the best. + +And in a greedy scheduler, it +doesn't look to see what's the + +best one to execute, it +just executes as many + +as it can this case. + +In this case, it's p. + +Now we have what's called +an incomplete step. + +Notice nothing got enabled. + +That was sort of too bad. + +So there's only two guys +that are ready to go. + +What do you think happens if +I have an incomplete step, + +namely p strands are +ready, fewer than + +p strands are ready? + +I just to execute all of +them, as many as I can. + +Run all of them. + +So that's what a greedy +scheduler does. + +Just at every step, it executes +as many as it can and + +we can classify the steps as +ones which are complete, + +meaning we used all our +processors versus incomplete, + +meaning we only used a subset +of our processors in + +scheduling it. + +So that's what a greedy +scheduler does. + +Now the important thing, +which is the + +analysis of this program. + +And this is, by the way, the +single most important thing in + +scheduling theory but you're +going to ever learn is this + +particular theory. + +It goes all the way back to +1968 and what it basically + +says it is any greedy scheduler +achieves a bound of + +T1 over p plus T infinity. + +So why is that an interesting +upper bound? + +Yeah? + +AUDIENCE: That says that it's +got the refinement of what you + +said before, even if you add as +many processors as you can, + +basically you're bounded +by T infinity. + +PROFESSOR: Yeah. + +AUDIENCE: It's compulsory. + +PROFESSOR: So basically, each +of these, this term here is + +the term in the Work Law. + +This is the term in the Span +Law, and we're saying you can + +always achieve the sum of those +two lower bounds as an + +upper bound. + +So let's see how we do this and +then we'll look at some of + +the implications. + +Question, do you have +a question? + +No? + +So here's the proof that +you meet this. + +So that the proof says-- +and I'll illustrate + +for P equals 3-- + +how many complete steps +could we have? + +So I'll argue that the number +of complete steps is at + +most T1 over p. + +Why is that? + +Every complete step +performs p work. + +So if I had more complete steps +than T1 over p, I'd be + +doing more than T1 work. + +But I only have T1 work to do. + +OK, so the maximum number of +complete steps I could have is + +at most T1 over p. + +Do people follow that? + +So the trickier part of the +proof, which is not all that + +tricky but it's a little bit +trickier, is the other side. + +How many incomplete steps +could I have? + +So we execute those. + +So I claim that the number of +incomplete steps is bounded by + +the critical path length, +by the span. + +Why is that? + +Well let's take a look at +the part of DAG that + +has yet to be executed. + +So that this gray part here. + +There's some span associated +with that. + +In this case, it's this +longest path. + +When I execute all of the ready +threads that are ready + +to go, I guarantee to reduce +the span of that unexecuted + +DAG by at least one. + +So as I do here, so I reduce +it by one when I execute. + +So if I have a complete step, +I don't guaranteed to reduce + +the span of the unexecuted DAG, +because I may execute + +things as I showed you in this +example, you don't actually + +advance anything. + +But I execute all the ready +threads on an incomplete step, + +and that's going to +reduce it by one. + +So the number of incomplete +steps is at most infinity. + +So the total number of steps +is at most the sum. + +So as I say, this proof you +should understand in your + +sleep because it's the most +important scheduling theory + +proof that you're going to +probably see in your lifetime. + +It's very old, and really, very, +very simple and yet, + +there's a huge amount of +scheduling theory if you have + +a look at scheduling theory, +that comes out of this just + +making this same problem more +complicated and more real and + +more interesting and so forth. + +But this is really the crux +of what's going on. + +Any questions about +this proof? + +So one corollary of the greedy +scheduling algorithm is that + +any greedy scheduler achieves +within a factor of two of + +optimal scheduling. + +So let's see why that is. + +So it's guaranteed as an upper +bound to get within a factor + +of two of optimal. + +So here's the proof. + +So let's Tp star be the +execution time produced by the + +optimal scheduler. + +This is the schedule that knows +the whole DAG in advance + +and can schedule things exactly +where they need to be + +scheduled to minimize the +total amount of time. + +Now even though the optimal +scheduler can schedule very + +officially, it's still +bound by the Work Law + +and the Span Law. + +So therefore, Tp star has still +got to be greater than + +T1 over p and greater than +T infinity by the + +Work and Span Laws. + +Even though it's optimal, every +scheduler must obey the + +Work Laws and Spam Law. + +So then we have, by the greedy +scheduling theorem, Tp is at + +most T1 over p plus +T infinity. + +Well that's at most twice the +maximum of these two values, + +whichever is larger. + +I've just plugged in to get the +maximum of those two and + +that's at most, by +this equation, + +twice the optimal time. + +So this is a very simple +corollary says oh, greedy + +scheduling is actually +pretty good. + +It's not optimal, +in fact, optimal + +scheduling is mP complete. + +Very hard problem to solve. + +But getting within a factor +of two, you just do greedy + +scheduling, it works +just fine. + +More importantly is the next +corollary, which has to do is + +when do you get linear +speedup? + +And this is, I think, the +most important thing + +to get out of this. + +So any greedy scheduler achieves +near perfect linear + +speedup whenever-- + +what's this thing on +the left-hand side? + +What's the name we +call that?-- + +the parallelism, right? + +That's the parallelism, is much +bigger than the number of + +processors you're running on. + +So if the number of processors +are running on is smaller than + +the parallelism of your code +says you can expect near + +perfect linear speedup. + +OK, so what does that say you +want to do in your program? + +You want to make sure you have +ample parallelism and then the + +scheduler will be able to +schedule it so that you get + +near perfect linear speedup. + +Let's see why that's true. + +So T1 over T infinity is much +bigger than p is equivalent to + +saying that T infinity is much +less than T1 over p. + +That's just algebra. + +Well what does that mean? + +The greedy scheduling theorem +says Tp is at most T1 over p + +plus T infinity. + +We just said that if we have +this condition, then T + +infinity is very small compared +to T1 over p. + +So if this is negligible, +then the whole thing is + +about T1 over p. + +Well that just says that +the speedup is about p. + +So the name of the game is to +make sure that your span is + +relatively short compared to +the amount of work per + +processor that you're doing. + +And in that case, you'll +get linear speedup. + +And that happens when you've +got enough parallelism + +compared to the number +processors you're running on. + +Any questions about this? + +This is like the most important +thing you're going + +to learn about parallel +computing. + +Everything else we're going to +do is going to be derivatives + +of this, so if you don't +understand this, you have a + +hard time with the +other stuff. + +So in some sense, it's +deceptively simple, right? + +We just have a few variables, +T1, Tp, T infinity, p, there's + +not much else going on. + +But there are these bounds and +these elegant theorems that + +tell us something about how no +matter what the shape of the + +DAG is or whatever, these two +values, the work and the span, + +really characterize very closely +where it is that you + +can expect to get +linear speedup. + +Any questions? + +OK, good. + +So the quantity T1 over PT +infinity, so what is that? + +That's just the parallelism +divided by p. + +That's called the parallel +slackness. + +So this parallel slackness is +10, means you have 10 times + +more parallelism than +processors. + +So if you have high slackness, +you can expect + +to get linear speedup. + +If you have low slackness, +don't expect + +to get linear speedup. + +OK. + +Now the scheduler we're using +is not a greedy scheduler. + +It's better in many ways, +because it's a distributed, + +what's called work stealing +scheduler and I'll show you + +how it works in a little bit. + +But it's based on +the same theory. + +Even though it's a more +complicated scheduler from an + +analytical point of view, it's +really based on the same + +theory as greedy scheduling. + +It guarantees that the time on +p processors is at most T1 + +over p plus order T infinity. + +So there's a constant here. + +And it's a randomized scheduler, +so it actually only + +guarantees this in +expectation. + +It actually guarantees very +close to this with high + +probability. + +OK so the difference is the big +O, but if you look at any + +of the formulas that we did with +the greedy scheduler, the + +fact that there's a constant +there doesn't really matter. + +You get the same effect, it just +means that the slackness + +that you need to get linear +speedup has to not only + +overcome the T infinity, it's +also got to overcome the + +constant there. + +And empirically, it actually +turns out this is not bad as + +an estimate using the +greedy bound. + +Not bad as an estimate, so this +is sort of a model that + +we'll take as if we're +doing things + +with a greedy scheduler. + +And that will be very close for +what we're actually going + +to see in practice with +the Cilk++ scheduler. + +So once again, it means near +perfect linear speedup as long + +as p is much less than T1 over +T infinity generally. + +And so Cilkview allows us to +measure T1 and T infinity. + +So that's going to be good, +because then we can figure out + +what our parallelism is and look +to see how we're running + +on typically 12 cores, how much +parallels do we have? + +If our parallelism is 12, we +don't have a lot of slackness. + +We won't get very +good speedup. + +But if we have a parallelism +of say, 10 times more, say + +120, we should get very, very +good parallelism, very, very + +good speedup on 12 cores. + +We should get close to +perfect speedup. + +So let's talk about the runtime +system and how this + +work stealing scheduler works, +because it different + +from the other one. + +And this will be helpful also +for understanding when you + +program these things what +you can expect. + +So the basic idea of the +schedule is there's two + +strategies the people have +explored for doing scheduling. + +One is called work sharing, +which is not what Cilk++ does. + +But let me explain what work +sharing is because it's + +helpful to contrast it +with work stealing. + +So in works sharing, what you do +is when you spawn off some + +work, you say let me go find +some low utilized processor + +and put that worked there +for it to operate on. + +The problem with work sharing +is that you have to do some + +communication and +synchronization every time you + +do a spawn. + +Every time you do a spawn, +you're going to go out. + +This is kind of what +Pthreads does, when + +you do Pthread create. + +It goes out and says OK, let me +create all of the things it + +needs to do and get it schedule +then on a processor. + +Work stealing, on the +other hand, takes + +the opposite approach. + +Whenever it spawns work, it's +just going to keep that work + +local to it, but make it +available for stealing. + +A processor that runs out of +work is going to go looking + +for work to steal, +to bring back. + +The advantage of work stealing +is that the processor doesn't + +do any synchronization +except when it's + +actually load balancing. + +So if all of the processors have +ample work to do, then + +what happens is there's no +overhead for scheduling + +whatsoever. + +They all just crank away. + +And so you get very, very low +overheads when there's ample + +work to do on each processor. + +So let's see how this works. + +So the particular way that +it maintains it is that + +basically, each processor +maintains a work deck. + +So a deck is a double-ended +queue of the ready strands. + +It manipulates the bottom of +the deck like a stack. + +So what that says is, for +example, here, we had a spawn + +followed by two calls. + +And basically, it's operating +just as it would have to + +operate in an ordinary stack, +an ordinary call stack. + +So, for example, this guy says +call, well it pushes a frame + +on the bottom of the call +stack just like normal. + +It says spawn, it pushes +a spawn frame on the + +bottom of the deck. + +In fact, of course, it's running +in parallel, so you + +can have a bunch of guys that +are both calling and spawning + +and they all push whatever +their frames are. + +When somebody says return, +you just pop it off. + +So in the common case, each of +these guys is just executing + +the code serially the way +that it would normally + +executing in C or C++. + +However, if somebody runs out +of work, then it becomes a + +thief and it looks for a victim +and the strategy that's + +used by Cilk++ is to +look at random. + +It says let me just go to +any other processor + +or any other workers-- + +I call these workers-- + +and grab away some +of their work. + +But when it grabs it away, what +it does is it steals it + +from the opposite end of the +deck from where this + +particular victim is actually +doing its work. + +So it steals the oldest +stuff first. + +So it moves that over and now +here what it's doing is it's + +stealing up to the point +that it spawns. + +So it steals from the top of the +deck down to where there's + +a spawn on top. + +Yes? + +AUDIENCE: Is there always +a spawn on the + +top of every deck? + +PROFESSOR: Close, +almost always. + +Yes, so I think that you could +say that there are. + +So the initial deck does not +have a spawn on top of it, but + +you could imagine that it did. + +And then when you steal, you're +always stealing from + +the top down to a spawn. + +If there isn't something, if +this is just a call here, this + +cannot any longer be stolen. + +There's no work there to be +stolen because this is just a + +single execution, there's +nothing that's been spawned + +off at this point. + +This is the result of having +been spawned as opposed to + +that it's doing a spawn. + +So yes, basically +you're right. + +There's a spawn on the top. + +So it basically steals that +off and then it resumes + +execution afterwards and starts +then operating just + +like an ordinary deck. + +So the theorem that you can +prove for this type of + +scheduler is that if you have +sufficient parallelism, so you + +all know what parallelism is at +this point, you can prove + +that the workers steal +infrequently. + +So in a a typical execution, you +might have a few hundred + +load balancing operations of +this nature for something + +which is doing billions and +billions of instructions. + +So you steal infrequently. + +If you're stealing infrequently +and all the rest + +of the time you're just +executing like the C or C++, + +hey, now you've got linear +speedup because you've got all + +of these guys working +all the time. + +And so as I say, the main thing +to understand is that + +there's this work stealing +scheduler running underneath. + +It's more complicated to +analyze then the greedy + +scheduler, but it gives you +pretty much the same + +qualitative kinds of results. + +And the idea then is that the +stealing occurs infrequently + +so you get linear speedup. + +So the idea then is just as with +greedy scheduling, make + +sure you have enough +parallelism, because then the + +load balancing is a small +fraction of the time these + +processors are spending +executing the code. + +Because whenever it's doing +things like work stealing, + +it's not working on your code +executing, making it go fast. + +It's doing bookkeeping and +overhead and stuff. + +So you want to make sure +that stays low. + +So any questions about that? + +So specifically, we +have these bounds. + +You have achieved this expected +running time, which I + +mentioned before. + +Let me give you a pseudo-proof +of this. + +So this is not a real proof +because it ignores things like + +independence of probabilities. + +So when you do a probability +analysis, you're not allowed + +to multiply probabilities unless +they're independent. + +So anyway, here I'm multiplying +probabilities that + +are independent. + +So the idea is you can +view a processor as + +either working or stealing. + +So it goes into one +of two modes. + +It's going to be stealing +if it's run out of work, + +otherwise it's working. + +So the total time all processors +spend working is + +T1, hooray, that's +at least a bound. + +Now it turns out that every +steal has a 1 over p chance of + +reducing the span by one. + +So you can prove that of all of +the work that's in the top + +of all those decks that those +are where any of the ready + +threads are going to be there +are in a position of reducing + +the span if you execute them. + +And so whenever you steal, you +have a 1 over p chance of + +hitting the guy that matters +for the span + +of unexecuted DAG. + +So the same kind of thing +as in theory. + +You have a 1 over p chance. + +So the expected cost of all +steals is order PT infinity. + +So this is true, but not +for this reason. + +But it's kind, the intuition +is right. + +So therefore the cost of all +steals is PT infinity and the + +cost of the work is T1, so +that's the total amount of + +work and time spent stealing +by all the p processors. + +So to get the time spent doing +that, we divide by p, because + +they're p processors. + +And when I do that, I get T1 +over p plus order T infinity. + +So that's kind of where that +bound is coming from. + +So you can see what's important +here is that the + +term, that order T infinity +term, this the one where all + +the overhead of scheduling +and synchronization is. + +There's no overhead for +scheduling and synchronization + +in the T1 over p term. + +The only overhead there is to do +things like mark the frames + +as being a steel frame or +a spawn frame and do the + +bookkeeping of the deck as +you're executing so the spawn + +can be implemented +very cheaply. + +Now in addition to the +scheduling things, there are + +some other things to understand +a little bit about + +the scheduler and that is that +it supports the C, C++ rule + +for pointers. + +So remember in C and C++, you +can pass a pointer to stack + +space down, but you can't pass +a pointer to stack space back + +to your parent, right? + +Because it popped off. + +So if you think about a C or +C++ execution, let's say we + +have this call structure here. + +A really cannot see any of the +stack space of B,C,D or E. So + +this is what A gets to see. + +And B, meanwhile, can see A +space, because that's down on + +the stack, but it can't see C, D +or E. Particularly if you're + +executing this serially, it +can't see C because C hasn't + +executed yet when B executes. + +However, C, it turns out, +the same thing. + +I can't see any of the variables +that might be + +allocated in the space +for B when I'm + +executing here on a stack. + +You can see them in a heap, but +not on the stack, because + +B has been popped off at that +point and so forth. + +So this is basically the normal +rule, the normal views + +of stack that you +get in C or C++. + +In Cilk++, you get exactly the +same behavior except that + +multiple ones of these views +may exist at the same time. + +So if, for example, B and C are +both executing at the same + +time, they each will +see their own stack + +space and a stack space. + +And so the cactus stack +maintains that fiction that + +you can sort of look at your +ancestors and see your + +ancestors, but now +it's maintained. + +It's called a cactus stack +because it's kind of like a + +tree structure upside down, like +a what's the name of that + +big cactus out West? + +Yes, saguaro. + +The saguaro cactus, yep. + +This kind of looks like that +if you look at the stacks. + +This leads to a very powerful +bound on how much space your + +program is using. + +So normally, if you do a greedy +scheduler, you could + +end up using gobs more space +then you would in a serial + +execution, gobs more +stack space. + +In Cilk++ programs, +you have a bound. + +It's p times s1 is the maximum +amount of stack space you'll + +ever use where s1 is +the stack space + +used by serial execution. + +So if you can keep your serial +execution to use a reasonable + +amount of stack space-- +and usually it does-- + +then in parallel, you don't +use more than p times that + +amount of stack space. + +And the proof for that is sort +of by induction, which + +basically says there's a +property called the Busy + +Leaves Property that says that +if you have a leaf that's + +being worked on but hasn't +been completed-- + +so I've indicated those by the +purple and pink ones-- + +then if it's a leaf, it has +a worker executing on it. + +And so therefore, if you look at +how much stack space you're + +using, each of these guys can +trace up and they may double + +count the stack space, but it'll +still be bounded by p + +times the depth that they're +at, or p times s1, which is + +the maximum amount. + +So it has good space bounds. + +That's not so crucial for you +folks to know as a practical + +matter, but it would be +if this didn't hold. + +If this didn't hold, then you +would have more programming + +problems than you'll have. + +The implications of this work +stealing scheduler is + +interesting from the linguistic +point of view, + +because you can write a code +like this, so for i gets one + +to a billion, spawn some +sub-routine foo + +of i and then sync. + +So one way of executing this, +the way that the work sharing + +schedulers tend to do this, +is they say oh, I've got a + +billion tasks to do. + +So let me create a billion tasks +and now schedule them + +and the space just vrooms to +store all those billion tasks, + +it gets to be huge. + +Now of course, they have some +strategies they can use to + +reduce it by bunching tasks +together and so forth. + +But in principle, you got a +billion pieces of work to do + +even if you execute +on one processor. + +Whereas in the work stealing +type execution, what happens + +is you execute this in +fact depth research. + +So basically, you're going to +execute foo of 1 and then + +you'll return. + +And then you'll increment i and +you'll execute foo of 2, + +and you'll return. + +At no time are you using more +than in this case two stack + +frames, one for this routine +here and one for foo because + +you basically keep going up. + +You're using your stack up on +demand, rather than creating + +all the work up front +to be scheduled. + +So the work stealing scheduler +is very good from + +that point of view. + +The tricky thing for people +to understand is that if + +executing on multiple +processors, when you do Cilk + +spawn, the processor, the worker +that you're running on, + +is going to execute foo of 1. + +The next statement-- + +which would basically +be incrementing the + +counter and so forth-- + +is executed by whatever +processor comes in and steals + +that continuation. + +So if you had two processors, +they're each going to + +basically be executing. + +The first processor isn't the +one that excuse everything in + +this function. + +This function has its execution +shared, the strands + +are going to be shared where the +first part of it would be + +done by processor one and the +latter part of it would be + +done by processor two. + +And then when processor one +finishes this off, it might go + +back and steal back from +processor two. + +So the important thing there is +it's generating its stack + +needs sort of on demand rather +than all up front, and that + +keeps the amount of stack space +small as it executes. + +So the moral is it's better to +steal your parents from their + +children than stealing children +from their parents. + +So that's the advantage of +doing this sort of parent + +stealing, because you're always +doing the frame which + +is an ancestor of where that +worker is working and that + +means resuming a function +right in the middle on a + +different processor. + +That's kind of the magic of the +technologies is how do you + +actually move a stack frame from +one place to another and + +resume it in the middle? + +Let's finish up here with +a chess lesson. + +I promised a chess lesson, +so we might as well do + +some fun and games. + +We have a lot of experience at +MIT with chess programs. + +We've had a lot of success, +probably our closest one was + +Star Socrates 2.0, which took +second place in the world + +computer chess championship +running on an 1824 node Intel + +Paragon, so a big supercomputer +running with a + +Cilk scheduler. + +We actually almost won that +competition, and it's a sad + +story that maybe be sometime +around dinner or something I + +will tell you the sad story +behind it, but I'm not going + +to tell you why we didn't +take first place. + +And we've had a bunch of other +successes over the years. + +Right now our chess programming +is dormant, we're + +not doing that in my group +anymore, but in the past, we + +had some very strong chess +playing programs. + +So what we did with Star +Socrates, which is one of our + +programs, was we wanted to +understand the Cilk scheduler. + +And so what we did is we ran +a whole bunch of different + +positions on different numbers +of processors which ran for + +different amounts of time. + +We wanted to plot them all on +the same chart, and here's our + +strategy for doing it. + +What decided to do was do a +standard speedup curve. + +So a standard speedup curve says +let's plot the number of + +processors along this axis and +the speed up along that axis. + +But in order to fit all these +things on the same processor + +curve, what we did was we +normalize the speedup. + +So what's the maximum pot? + +So here's the speedup. + +If you look the numerator +here, this is the + +speedup, T1 over Tp. + +What we did is we normalized +by the parallelism. + +So we said what fraction of +perfect speedup can we get? + +So here one says that I got +exactly a speedup, this is the + +maximum possible speed up that +I can get because the maximum + +possible value of T1 over +p is T1 over T infinity. + +So that's sort of the maximum. + +On this axis, we said how +many processors are + +you running on it? + +Well, we looked at +that relative to + +essentially the slackness. + +So notice by normalizing, we +essentially have here the + +inverse of the slackness. + +So 1 here says that I'm running +on exactly the same + +number of processors +as my parallelism. + +A tenth here says I've got a +slackness of 10, I'm running + +on 10 times fewer processors +then parallelism. + +Out here, I'm saying I got way +more processors than I have + +parallelism. + +So I plotted all the points. + +So it doesn't show up very well +here, but all those green + +points, there are a lot of green +points here, that's our + +performance, measured +performance. + +You can sort of see they're +green there, not the best + +color for this projector. + +So we plot on this essentially +the Work Law and the Span Law. + +So this is the Work Law, it says +linear speedup, and this + +is the Span Law. + +And you can see that we're +getting very close to perfect + +linear speedup as long as our +slackness is 10 or greater. + +See that? + +It's hugging that curve +really tightly. + +As we approach a slackness of 1, +you can see that it starts + +to go away from the linear +speedup curve. + +So for this program, if you +look, it says, gee, if we were + +running with 10 time, slackness +of 10, 10 times more + +parallelism than processors, +we're getting almost perfect + +linear speedup in the number of +processors we're running on + +across a wide range of number +of processors, wide range of + +benchmarks for this +chess program. + +And in fact, this curve +is the curve. + +This is not an interpolation +here, but rather it is just + +the greedy scheduling curve, +and you can see it does a + +pretty good job of going through +all the points here. + +Greedy scheduling does a pretty +good job of predicting + +the performance. + +The other thing you should +notice is that although things + +are very tight down here, as +you approach up here, they + +start getting more spread. + +And the reason is that as you +start having more of the span + +mattering in the calculation, +that's where all the + +synchronization, communication, +all the + +overhead of actually doing the +mechanics of moving a frame + +from one processor to another +take into account, so you get + +a lot more spread as +you go up here. + +So that's just the first +part of the lesson. + +The first part was, oh, the +theory works out in practice + +for real programs. + +You have like 10 times more +parallelisms than processors, + +you're going to do a +pretty good job of + +getting linear speedup. + +So that says you guys should be +shooting for parallelisms + +on the order of 100 for +running on 12 cores. + +Somewhere in that vicinity you +should be doing pretty well if + +you've got parallelism +of 100 when you + +measure it for your codes. + +So we normalize by the +parallel there. + +Now the real lesson though was +understanding how to use + +things like work and span to +make decisions in the design + +of our program. + +So as it turned out, Socrates +for this particular + +competition was to run on a +512 processor connection + +machine at the University +of Illinois. + +So this was in the mid +in the early 1990's. + +It was one of the most powerful +machines in the + +world, and this thing is +probably more powerful today. + +But in those days, it was a +pretty powerful machine. + +I don't know whether this +thing is, but this thing + +probably I'm pretty sure +is more powerful. + +So this was a big machine. + +However here at MIT, we didn't +have a great big + +machine like that. + +We only had a 32 +processor CM5. + +So we were developing on a +little machine expecting to + +run on a big machine. + +So one of the developers +proposed to change the program + +that produced a speedup of over +20% on the MIT machine. + +So we said, oh that's pretty +good, 25% improvement. + +But we did a back of the +envelope calculation and + +rejected that improvement +because we were able to use + +work and span to predict the +behavior on the big machine. + +So let's see how that worked +out, why that worked out. + +So I've fudged these numbers so +that they're easy to do the + +math on and easy +to understand. + +The real numbers actually though +did sort out very, very + +similar to what I'm saying, +just they weren't round + +numbers like I'm going +to give you. + +So the original program +ran for let's say 65 + +seconds on 32 cores. + +The proposed program ran for +40 seconds on 32 cores. + +Sounds like a good improvement +to me. + +Let's go for the +faster program. + +Well, let's hold your horses. + +Let's take a look at our +performance model based on + +greedy scheduling. + +That Tp is T1 over +p plus infinity. + +What component we really need to +understand the scale this, + +what component of each of +these things is work + +and which is span? + +Because that's how we're going +to be able to predict what's + +going to happen on +the big machine. + +So indeed, this original program +had a work of 2048 + +seconds and a span +of one second. + +Now chess, it turns out, is a +non-deterministic type of + +program where you use +speculative parallelism, and + +so in order to get more +parallelism, you can sacrifice + +and do more work versus +less work. + +So this one over here that we +improved it to had less work + +on the benchmark, but it +had a longer span. + +So it had less work +but a longer span. + +So when we actually were going +to run this, well first of + +all, we did the calculation +and it actually came out + +pretty close. + +I was kind of surprised how +close the theory matched. + +We actually on 32 processors +when you do the work spanned + +calculation, you get the 65 +seconds on a 32 processor + +machine, here we +had 40 seconds. + +But now what happens when we +scale this to the big machine? + +Here we scaled it +to 512 cores. + +So now we take the work divided +by the number of + +processors, 512, plus 1, that's +5 seconds for this. + +Here we have the work but we now +have a much larger span. + +So we have two seconds of work +for processor, but now eight + +seconds of span for a +total of 10 seconds. + +So had we made this quote +"improvement," our code would + +have been half as fast. + +It would not have scaled. + +And so the point is that work +and span typically will beat + +running times for predicting +scalability of performance. + +So you can measure a particular +thing, but what you + +really want to know is this +thing this going to scale and + +how is it going to scale +into the future. + +So people building multicore +applications today want to + +know that they coded up. + +They don't want to be told in +two years that they've got to + +recode it all because the +number of cores doubled. + +They want to have some +future-proof notion that hey, + +there's a lot of parallelism +in this program. + +So work and span, work +and span, eat it, + +drink it, sleep it. + +Work and span, work and span, +work and span, work and span, + +work and span, OK? + +Work and span. \ No newline at end of file diff --git a/Uic47mwXNuQ.txt b/Uic47mwXNuQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..9115bfcb2d683c88f4f62c34a18bc6a5fc6c4b0b --- /dev/null +++ b/Uic47mwXNuQ.txt @@ -0,0 +1,14834 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop coreware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu thanks for coming out this + + align:start position:0% +ocw.mit.edu thanks for coming out this + + + align:start position:0% +ocw.mit.edu thanks for coming out this +is going to be + + align:start position:0% +is going to be + + + align:start position:0% +is going to be +hardcore uh nonlinear spectroscopy boot + + align:start position:0% +hardcore uh nonlinear spectroscopy boot + + + align:start position:0% +hardcore uh nonlinear spectroscopy boot +camp we're going to try and make it + + align:start position:0% +camp we're going to try and make it + + + align:start position:0% +camp we're going to try and make it +through as much material as possible Pro + + align:start position:0% +through as much material as possible Pro + + + align:start position:0% +through as much material as possible Pro +my problem is I've got this week to do + + align:start position:0% +my problem is I've got this week to do + + + align:start position:0% +my problem is I've got this week to do +it which means we're going to cram in as + + align:start position:0% +it which means we're going to cram in as + + + align:start position:0% +it which means we're going to cram in as +much as we can and so here's what I was + + align:start position:0% +much as we can and so here's what I was + + + align:start position:0% +much as we can and so here's what I was +um after the kind of material that I + + align:start position:0% +um after the kind of material that I + + + align:start position:0% +um after the kind of material that I +wanted to go through and we'll see how + + align:start position:0% +wanted to go through and we'll see how + + + align:start position:0% +wanted to go through and we'll see how +far we get um in ter oh yeah and one + + align:start position:0% +far we get um in ter oh yeah and one + + + align:start position:0% +far we get um in ter oh yeah and one +thing I forgot in terms of scheduling uh + + align:start position:0% +thing I forgot in terms of scheduling uh + + + align:start position:0% +thing I forgot in terms of scheduling uh +there's been a mistake with the + + align:start position:0% +there's been a mistake with the + + + align:start position:0% +there's been a mistake with the +scheduling tomorrow I have I have a + + align:start position:0% +scheduling tomorrow I have I have a + + + align:start position:0% +scheduling tomorrow I have I have a +different lecture to give tomorrow at uh + + align:start position:0% +different lecture to give tomorrow at uh + + + align:start position:0% +different lecture to give tomorrow at uh +at noon so uh we won't be doing this at + + align:start position:0% +at noon so uh we won't be doing this at + + + align:start position:0% +at noon so uh we won't be doing this at +noon tomorrow and um instead unless uh + + align:start position:0% +noon tomorrow and um instead unless uh + + + align:start position:0% +noon tomorrow and um instead unless uh +you hear differently from me by email + + align:start position:0% +you hear differently from me by email + + + align:start position:0% +you hear differently from me by email +then uh just um let's plan that the next + + align:start position:0% +then uh just um let's plan that the next + + + align:start position:0% +then uh just um let's plan that the next +one will be Thursday at uh 9:00 a.m. as + + align:start position:0% +one will be Thursday at uh 9:00 a.m. as + + + align:start position:0% +one will be Thursday at uh 9:00 a.m. as +scheduled okay um okay so uh I'm going + + align:start position:0% +scheduled okay um okay so uh I'm going + + + align:start position:0% +scheduled okay um okay so uh I'm going +to try and + + align:start position:0% +to try and + + + align:start position:0% +to try and +do uh as much as we can and my feeling + + align:start position:0% +do uh as much as we can and my feeling + + + align:start position:0% +do uh as much as we can and my feeling +is sort of the uh top 75% of this board + + align:start position:0% +is sort of the uh top 75% of this board + + + align:start position:0% +is sort of the uh top 75% of this board +is probably what we'll get to so the + + align:start position:0% +is probably what we'll get to so the + + + align:start position:0% +is probably what we'll get to so the +ideas um I'd like to spend uh today + + align:start position:0% +ideas um I'd like to spend uh today + + + align:start position:0% +ideas um I'd like to spend uh today +we're going to spend a I don't know + + align:start position:0% +we're going to spend a I don't know + + + align:start position:0% +we're going to spend a I don't know +probably an hour and a half we'll kind + + align:start position:0% +probably an hour and a half we'll kind + + + align:start position:0% +probably an hour and a half we'll kind +of break in between for 20 minutes or + + align:start position:0% +of break in between for 20 minutes or + + + align:start position:0% +of break in between for 20 minutes or +something like that at least long enough + + align:start position:0% +something like that at least long enough + + + align:start position:0% +something like that at least long enough +to get some coffee and what I'd like to + + align:start position:0% +to get some coffee and what I'd like to + + + align:start position:0% +to get some coffee and what I'd like to +work through is basically some + + align:start position:0% +work through is basically some + + + align:start position:0% +work through is basically some +introductory material and some formalism + + align:start position:0% +introductory material and some formalism + + + align:start position:0% +introductory material and some formalism +which is um what is nonlinear + + align:start position:0% +which is um what is nonlinear + + + align:start position:0% +which is um what is nonlinear +spectroscopy why would you want to do it + + align:start position:0% +spectroscopy why would you want to do it + + + align:start position:0% +spectroscopy why would you want to do it +um and then talk specifically about + + align:start position:0% +um and then talk specifically about + + + align:start position:0% +um and then talk specifically about +coherent nonlinear spectroscopy because + + align:start position:0% +coherent nonlinear spectroscopy because + + + align:start position:0% +coherent nonlinear spectroscopy because +that's really what the emphasis of this + + align:start position:0% +that's really what the emphasis of this + + + align:start position:0% +that's really what the emphasis of this +discussion will be uh and then go + + align:start position:0% +discussion will be uh and then go + + + align:start position:0% +discussion will be uh and then go +through sort of just the methods that we + + align:start position:0% +through sort of just the methods that we + + + align:start position:0% +through sort of just the methods that we +use to you know describe what happens + + align:start position:0% +use to you know describe what happens + + + align:start position:0% +use to you know describe what happens +and and in particular I think one thing + + align:start position:0% +and and in particular I think one thing + + + align:start position:0% +and and in particular I think one thing +that's very useful for getting into the + + align:start position:0% +that's very useful for getting into the + + + align:start position:0% +that's very useful for getting into the +business is diagrammatic peration Theory + + align:start position:0% +business is diagrammatic peration Theory + + + align:start position:0% +business is diagrammatic peration Theory +uh so then the good fraction of the + + align:start position:0% +uh so then the good fraction of the + + + align:start position:0% +uh so then the good fraction of the +remaining lectures are going to you know + + align:start position:0% +remaining lectures are going to you know + + + align:start position:0% +remaining lectures are going to you know +involve these next three topics so um in + + align:start position:0% +involve these next three topics so um in + + + align:start position:0% +involve these next three topics so um in +particular we're going to spend a lot of + + align:start position:0% +particular we're going to spend a lot of + + + align:start position:0% +particular we're going to spend a lot of +time talking about third order nonlinear + + align:start position:0% +time talking about third order nonlinear + + + align:start position:0% +time talking about third order nonlinear +spectroscopy and I'll Define that also + + align:start position:0% +spectroscopy and I'll Define that also + + + align:start position:0% +spectroscopy and I'll Define that also +but that's the good fraction of methods + + align:start position:0% +but that's the good fraction of methods + + + align:start position:0% +but that's the good fraction of methods +that people use um and you can pretty + + align:start position:0% +that people use um and you can pretty + + + align:start position:0% +that people use um and you can pretty +much map the you know large fraction of + + align:start position:0% +much map the you know large fraction of + + + align:start position:0% +much map the you know large fraction of +things that everyone does onto this kind + + align:start position:0% +things that everyone does onto this kind + + + align:start position:0% +things that everyone does onto this kind +of a spectroscopy um and I'll I'll try + + align:start position:0% +of a spectroscopy um and I'll I'll try + + + align:start position:0% +of a spectroscopy um and I'll I'll try +and point out that that means not just + + align:start position:0% +and point out that that means not just + + + align:start position:0% +and point out that that means not just +what is done in my group and in Keith + + align:start position:0% +what is done in my group and in Keith + + + align:start position:0% +what is done in my group and in Keith +Nelson's group but that in fact what + + align:start position:0% +Nelson's group but that in fact what + + + align:start position:0% +Nelson's group but that in fact what +every spectroscopy group here on campus + + align:start position:0% +every spectroscopy group here on campus + + + align:start position:0% +every spectroscopy group here on campus +does um that's anything more advanced + + align:start position:0% +does um that's anything more advanced + + + align:start position:0% +does um that's anything more advanced +than stuffing something into an ftir or + + align:start position:0% +than stuffing something into an ftir or + + + align:start position:0% +than stuffing something into an ftir or +uvv can be sort of mapped onto thinking + + align:start position:0% +uvv can be sort of mapped onto thinking + + + align:start position:0% +uvv can be sort of mapped onto thinking +in terms of nor third order + + align:start position:0% +in terms of nor third order + + + align:start position:0% +in terms of nor third order +spectroscopy and then uh a bit about + + align:start position:0% +spectroscopy and then uh a bit about + + + align:start position:0% +spectroscopy and then uh a bit about +two-dimensional spectroscopy we + + align:start position:0% +two-dimensional spectroscopy we + + + align:start position:0% +two-dimensional spectroscopy we +will that is uh actually nothing new to + + align:start position:0% +will that is uh actually nothing new to + + + align:start position:0% +will that is uh actually nothing new to +that thinking this is it's just a new + + align:start position:0% +that thinking this is it's just a new + + + align:start position:0% +that thinking this is it's just a new +way of thinking about old ideas in terms + + align:start position:0% +way of thinking about old ideas in terms + + + align:start position:0% +way of thinking about old ideas in terms +of um uh you know a two-dimensional + + align:start position:0% +of um uh you know a two-dimensional + + + align:start position:0% +of um uh you know a two-dimensional +spectrum and then so that's sort of to + + align:start position:0% +spectrum and then so that's sort of to + + + align:start position:0% +spectrum and then so that's sort of to +find kind of some of the prominent + + align:start position:0% +find kind of some of the prominent + + + align:start position:0% +find kind of some of the prominent +methods and then you know how we're + + align:start position:0% +methods and then you know how we're + + + align:start position:0% +methods and then you know how we're +going to make use of those kinds of + + align:start position:0% +going to make use of those kinds of + + + align:start position:0% +going to make use of those kinds of +things and and this just in a very + + align:start position:0% +things and and this just in a very + + + align:start position:0% +things and and this just in a very +general sense I'd like to give you a + + align:start position:0% +general sense I'd like to give you a + + + align:start position:0% +general sense I'd like to give you a +feeling for how we make use of these + + align:start position:0% +feeling for how we make use of these + + + align:start position:0% +feeling for how we make use of these +things in terms of studying molecular + + align:start position:0% +things in terms of studying molecular + + + align:start position:0% +things in terms of studying molecular +structure molecular Dynamics and then + + align:start position:0% +structure molecular Dynamics and then + + + align:start position:0% +structure molecular Dynamics and then +for condensed phase problems + + align:start position:0% +for condensed phase problems + + + align:start position:0% +for condensed phase problems +fluctuations and things okay after that + + align:start position:0% +fluctuations and things okay after that + + + align:start position:0% +fluctuations and things okay after that +there's some stuff that's up in the air + + align:start position:0% +there's some stuff that's up in the air + + + align:start position:0% +there's some stuff that's up in the air +it's like how far can we get and also + + align:start position:0% +it's like how far can we get and also + + + align:start position:0% +it's like how far can we get and also +depending a little bit on interest I + + align:start position:0% +depending a little bit on interest I + + + align:start position:0% +depending a little bit on interest I +have a feeling we're not going to be + + align:start position:0% +have a feeling we're not going to be + + + align:start position:0% +have a feeling we're not going to be +able to get any further than that this + + align:start position:0% +able to get any further than that this + + + align:start position:0% +able to get any further than that this +week so you know if there's a lot of + + align:start position:0% +week so you know if there's a lot of + + + align:start position:0% +week so you know if there's a lot of +interest we might be able to go um + + align:start position:0% +interest we might be able to go um + + + align:start position:0% +interest we might be able to go um +schedule some other lectures later on + + align:start position:0% +schedule some other lectures later on + + + align:start position:0% +schedule some other lectures later on +it'll have to be for quite a bit later + + align:start position:0% +it'll have to be for quite a bit later + + + align:start position:0% +it'll have to be for quite a bit later +on uh and I was thinking something like + + align:start position:0% +on uh and I was thinking something like + + + align:start position:0% +on uh and I was thinking something like +coherent nonlinear Ramen methods might + + align:start position:0% +coherent nonlinear Ramen methods might + + + align:start position:0% +coherent nonlinear Ramen methods might +be another good topic to go through um + + align:start position:0% +be another good topic to go through um + + + align:start position:0% +be another good topic to go through um +the influence of orientation and + + align:start position:0% +the influence of orientation and + + + align:start position:0% +the influence of orientation and +polarization on nonlinear spectroscopy + + align:start position:0% +polarization on nonlinear spectroscopy + + + align:start position:0% +polarization on nonlinear spectroscopy +is another big thing lots of people make + + align:start position:0% +is another big thing lots of people make + + + align:start position:0% +is another big thing lots of people make +use of and then um also surface + + align:start position:0% +use of and then um also surface + + + align:start position:0% +use of and then um also surface +selective nonlinear spectroscopies also + + align:start position:0% +selective nonlinear spectroscopies also + + + align:start position:0% +selective nonlinear spectroscopies also +would be a great topic uh and if you're + + align:start position:0% +would be a great topic uh and if you're + + + align:start position:0% +would be a great topic uh and if you're +really interested in that one I think I + + align:start position:0% +really interested in that one I think I + + + align:start position:0% +really interested in that one I think I +would beat on the gentleman in the + + align:start position:0% +would beat on the gentleman in the + + + align:start position:0% +would beat on the gentleman in the +corner up there because we'd like to + + align:start position:0% +corner up there because we'd like to + + + align:start position:0% +corner up there because we'd like to +coers Paul into giving that particular + + align:start position:0% +coers Paul into giving that particular + + + align:start position:0% +coers Paul into giving that particular +one I'm by the way I'm I'm beating on + + align:start position:0% +one I'm by the way I'm I'm beating on + + + align:start position:0% +one I'm by the way I'm I'm beating on +Dave blank from the University of + + align:start position:0% +Dave blank from the University of + + + align:start position:0% +Dave blank from the University of +Minnesota at the moment on giving the + + align:start position:0% +Minnesota at the moment on giving the + + + align:start position:0% +Minnesota at the moment on giving the +ramen one he's going to be giv the + + align:start position:0% +ramen one he's going to be giv the + + + align:start position:0% +ramen one he's going to be giv the +modern Optics seminar in two weeks and I + + align:start position:0% +modern Optics seminar in two weeks and I + + + align:start position:0% +modern Optics seminar in two weeks and I +told him come early give us a lecture + + align:start position:0% +told him come early give us a lecture + + + align:start position:0% +told him come early give us a lecture +he's because he's a pro at those methods + + align:start position:0% +he's because he's a pro at those methods + + + align:start position:0% +he's because he's a pro at those methods +so we'll see how this will develops but + + align:start position:0% +so we'll see how this will develops but + + + align:start position:0% +so we'll see how this will develops but +an important thing is um give me lots of + + align:start position:0% +an important thing is um give me lots of + + + align:start position:0% +an important thing is um give me lots of +feedback on you know what's uh what you + + align:start position:0% +feedback on you know what's uh what you + + + align:start position:0% +feedback on you know what's uh what you +like what's important what You' like to + + align:start position:0% + + + + align:start position:0% + +see all + + align:start position:0% +see all + + + align:start position:0% +see all +right + + align:start position:0% +right + + + align:start position:0% +right +so let's + + align:start position:0% +so let's + + + align:start position:0% +so let's +see where shall we + + align:start position:0% + + + + align:start position:0% + +start um okay I guess + + align:start position:0% + + + + align:start position:0% + +uh I guess a good spot is what is + + align:start position:0% +uh I guess a good spot is what is + + + align:start position:0% +uh I guess a good spot is what is +nonlinear + + align:start position:0% + + + + align:start position:0% + +spectroscopy what I don't want you to do + + align:start position:0% +spectroscopy what I don't want you to do + + + align:start position:0% +spectroscopy what I don't want you to do +is to get hung up in definitions about + + align:start position:0% +is to get hung up in definitions about + + + align:start position:0% +is to get hung up in definitions about +what it is because it means many things + + align:start position:0% +what it is because it means many things + + + align:start position:0% +what it is because it means many things +to many different people um when you + + align:start position:0% +to many different people um when you + + + align:start position:0% +to many different people um when you +might ask what's linear spectroscopy and + + align:start position:0% +might ask what's linear spectroscopy and + + + align:start position:0% +might ask what's linear spectroscopy and +they just sort of a working definition + + align:start position:0% +they just sort of a working definition + + + align:start position:0% +they just sort of a working definition +is um that uh I want to understand how + + align:start position:0% +is um that uh I want to understand how + + + align:start position:0% +is um that uh I want to understand how +matter interacts with one incident light + + align:start position:0% +matter interacts with one incident light + + + align:start position:0% +matter interacts with one incident light +field on the sample so spectroscopy in + + align:start position:0% +field on the sample so spectroscopy in + + + align:start position:0% +field on the sample so spectroscopy in +general we just think of it as studying + + align:start position:0% +general we just think of it as studying + + + align:start position:0% +general we just think of it as studying +the properties of matter um by + + align:start position:0% +the properties of matter um by + + + align:start position:0% +the properties of matter um by +irradiating it with light some uh which + + align:start position:0% +irradiating it with light some uh which + + + align:start position:0% +irradiating it with light some uh which +you know has a number of variables that + + align:start position:0% +you know has a number of variables that + + + align:start position:0% +you know has a number of variables that +we can control like frequency and + + align:start position:0% +we can control like frequency and + + + align:start position:0% +we can control like frequency and +amplitude and polarization phase and so + + align:start position:0% +amplitude and polarization phase and so + + + align:start position:0% +amplitude and polarization phase and so +on and manipulating any one of those + + align:start position:0% +on and manipulating any one of those + + + align:start position:0% +on and manipulating any one of those +variables and radiating the system with + + align:start position:0% +variables and radiating the system with + + + align:start position:0% +variables and radiating the system with +one light field that's sort of what we + + align:start position:0% +one light field that's sort of what we + + + align:start position:0% +one light field that's sort of what we +think of as linear spectroscopy okay so + + align:start position:0% +think of as linear spectroscopy okay so + + + align:start position:0% +think of as linear spectroscopy okay so +what is nonlinear then well it can it + + align:start position:0% +what is nonlinear then well it can it + + + align:start position:0% +what is nonlinear then well it can it +means many things to many people um and + + align:start position:0% +means many things to many people um and + + + align:start position:0% +means many things to many people um and +all of them are right uh there one is uh + + align:start position:0% +all of them are right uh there one is uh + + + align:start position:0% +all of them are right uh there one is uh +thinking that um how one uh acts on the + + align:start position:0% +thinking that um how one uh acts on the + + + align:start position:0% +thinking that um how one uh acts on the +matter with the light field is not uh + + align:start position:0% +matter with the light field is not uh + + + align:start position:0% +matter with the light field is not uh +proportional to the intensity of the + + align:start position:0% +proportional to the intensity of the + + + align:start position:0% +proportional to the intensity of the +light field so with traditional uh + + align:start position:0% +light field so with traditional uh + + + align:start position:0% +light field so with traditional uh +absorption Ramen scattering and + + align:start position:0% +absorption Ramen scattering and + + + align:start position:0% +absorption Ramen scattering and +fluoresence Method we think of how the + + align:start position:0% +fluoresence Method we think of how the + + + align:start position:0% +fluoresence Method we think of how the +matter responds is linear in the + + align:start position:0% +matter responds is linear in the + + + align:start position:0% +matter responds is linear in the +exitation pl and if you drive things + + align:start position:0% +exitation pl and if you drive things + + + align:start position:0% +exitation pl and if you drive things +hard enough no it's not so that could be + + align:start position:0% +hard enough no it's not so that could be + + + align:start position:0% +hard enough no it's not so that could be +nonlinear um we're uh we can treat those + + align:start position:0% +nonlinear um we're uh we can treat those + + + align:start position:0% +nonlinear um we're uh we can treat those +effects with the things we talk about + + align:start position:0% +effects with the things we talk about + + + align:start position:0% +effects with the things we talk about +but that's not what we're going to be + + align:start position:0% +but that's not what we're going to be + + + align:start position:0% +but that's not what we're going to be +dealing with we're talking about the + + align:start position:0% +dealing with we're talking about the + + + align:start position:0% +dealing with we're talking about the +case where one um interacts uh this with + + align:start position:0% +case where one um interacts uh this with + + + align:start position:0% +case where one um interacts uh this with +the system using multiple light + + align:start position:0% +the system using multiple light + + + align:start position:0% +the system using multiple light +Fields um Each of which you can control + + align:start position:0% +Fields um Each of which you can control + + + align:start position:0% +Fields um Each of which you can control +independently Each of which you have + + align:start position:0% +independently Each of which you have + + + align:start position:0% +independently Each of which you have +independent control of things like uh + + align:start position:0% +independent control of things like uh + + + align:start position:0% +independent control of things like uh +time variable Ables frequency + + align:start position:0% +time variable Ables frequency + + + align:start position:0% +time variable Ables frequency +polarization phase + + align:start position:0% +polarization phase + + + align:start position:0% +polarization phase +Etc and uh watching how the sample + + align:start position:0% +Etc and uh watching how the sample + + + align:start position:0% +Etc and uh watching how the sample +responds to that um so uh in in that + + align:start position:0% +responds to that um so uh in in that + + + align:start position:0% +responds to that um so uh in in that +and you know what may be a little + + align:start position:0% +and you know what may be a little + + + align:start position:0% +and you know what may be a little +confusing we're actually going to use + + align:start position:0% +confusing we're actually going to use + + + align:start position:0% +confusing we're actually going to use +linear response Theory to describe + + align:start position:0% +linear response Theory to describe + + + align:start position:0% +linear response Theory to describe +nonlinear spectroscopy and this should + + align:start position:0% +nonlinear spectroscopy and this should + + + align:start position:0% +nonlinear spectroscopy and this should +not confuse you what it means is that we + + align:start position:0% +not confuse you what it means is that we + + + align:start position:0% +not confuse you what it means is that we +will still treat matter as responding + + align:start position:0% +will still treat matter as responding + + + align:start position:0% +will still treat matter as responding +linearly to a particular light + + align:start position:0% +linearly to a particular light + + + align:start position:0% +linearly to a particular light +field but it may be that there are many + + align:start position:0% +field but it may be that there are many + + + align:start position:0% +field but it may be that there are many +light fields that come into the sample + + align:start position:0% +light fields that come into the sample + + + align:start position:0% +light fields that come into the sample +um and the nonlinearity arises from um + + align:start position:0% +um and the nonlinearity arises from um + + + align:start position:0% +um and the nonlinearity arises from um +you know the multiple Fields okay so + + align:start position:0% +you know the multiple Fields okay so + + + align:start position:0% +you know the multiple Fields okay so +that + + align:start position:0% +that + + + align:start position:0% +that +um uh that uh + + align:start position:0% + + + + align:start position:0% + +is what we're after and to be a little + + align:start position:0% +is what we're after and to be a little + + + align:start position:0% +is what we're after and to be a little +bit more precise about it not multiple + + align:start position:0% +bit more precise about it not multiple + + + align:start position:0% +bit more precise about it not multiple +light Fields per se but multiple light + + align:start position:0% +light Fields per se but multiple light + + + align:start position:0% +light Fields per se but multiple light +inter interactions because um as you + + align:start position:0% +inter interactions because um as you + + + align:start position:0% +inter interactions because um as you +might imagine there can be many + + align:start position:0% +might imagine there can be many + + + align:start position:0% +might imagine there can be many +interactions uh of the matter with just + + align:start position:0% +interactions uh of the matter with just + + + align:start position:0% +interactions uh of the matter with just +one of the incident Fields so that's + + align:start position:0% +one of the incident Fields so that's + + + align:start position:0% +one of the incident Fields so that's +what we're after so to put this sort of + + align:start position:0% +what we're after so to put this sort of + + + align:start position:0% +what we're after so to put this sort of +into a more precise way of saying it is + + align:start position:0% +into a more precise way of saying it is + + + align:start position:0% +into a more precise way of saying it is +you know with linear spectroscopy we can + + align:start position:0% +you know with linear spectroscopy we can + + + align:start position:0% +you know with linear spectroscopy we can +almost always just um write + + align:start position:0% + + + + align:start position:0% + +the the response of the system in some + + align:start position:0% +the the response of the system in some + + + align:start position:0% +the the response of the system in some +way is + + align:start position:0% +way is + + + align:start position:0% +way is +proportional to a matrix element + + align:start position:0% +proportional to a matrix element + + + align:start position:0% +proportional to a matrix element +squared this says that a light field + + align:start position:0% +squared this says that a light field + + + align:start position:0% +squared this says that a light field +creates superpositions of say an initial + + align:start position:0% +creates superpositions of say an initial + + + align:start position:0% +creates superpositions of say an initial +and a final State and uh our our view + + align:start position:0% +and a final State and uh our our view + + + align:start position:0% +and a final State and uh our our view +into the matter is dictated by a matrix + + align:start position:0% +into the matter is dictated by a matrix + + + align:start position:0% +into the matter is dictated by a matrix +element squared um so you know writing + + align:start position:0% +element squared um so you know writing + + + align:start position:0% +element squared um so you know writing +this out a little bit more explicitly + + align:start position:0% + + + + align:start position:0% + +we are always talking about + + align:start position:0% +we are always talking about + + + align:start position:0% +we are always talking about +two uh Matrix elements and for linear + + align:start position:0% +two uh Matrix elements and for linear + + + align:start position:0% +two uh Matrix elements and for linear +techniques these are really just one is + + align:start position:0% +techniques these are really just one is + + + align:start position:0% +techniques these are really just one is +the conjugate of the other and when we + + align:start position:0% +the conjugate of the other and when we + + + align:start position:0% +the conjugate of the other and when we +get to nonlinear spectroscopy we're + + align:start position:0% +get to nonlinear spectroscopy we're + + + align:start position:0% +get to nonlinear spectroscopy we're +saying that we are going to have + + align:start position:0% +saying that we are going to have + + + align:start position:0% +saying that we are going to have +multiple Matrix + + align:start position:0% +multiple Matrix + + + align:start position:0% +multiple Matrix +elements um that is there will be three + + align:start position:0% +elements um that is there will be three + + + align:start position:0% +elements um that is there will be three +or more and this means that uh there + + align:start position:0% +or more and this means that uh there + + + align:start position:0% +or more and this means that uh there +isn't sort of this nice uh clean + + align:start position:0% +isn't sort of this nice uh clean + + + align:start position:0% +isn't sort of this nice uh clean +symmetry that one sees in um the linear + + align:start position:0% +symmetry that one sees in um the linear + + + align:start position:0% +symmetry that one sees in um the linear +spectroscopies did you have a question + + align:start position:0% +spectroscopies did you have a question + + + align:start position:0% +spectroscopies did you have a question +okay so for instance you know you might + + align:start position:0% +okay so for instance you know you might + + + align:start position:0% +okay so for instance you know you might +imagine things of the or of the nature a + + align:start position:0% +imagine things of the or of the nature a + + + align:start position:0% +imagine things of the or of the nature a +mu b b u c c u a you know they the + + align:start position:0% +mu b b u c c u a you know they the + + + align:start position:0% +mu b b u c c u a you know they the +moment you've got three or more then you + + align:start position:0% +moment you've got three or more then you + + + align:start position:0% +moment you've got three or more then you +know you're in the nonlinear + + align:start position:0% +know you're in the nonlinear + + + align:start position:0% +know you're in the nonlinear +spectroscopy business + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +right okay um + + align:start position:0% + + + + align:start position:0% + +all right so I'd say then the the next + + align:start position:0% +all right so I'd say then the the next + + + align:start position:0% +all right so I'd say then the the next +thing is why do + + align:start position:0% + + + + align:start position:0% + +it + + align:start position:0% +it + + + align:start position:0% +it +um so whoever came up with the term + + align:start position:0% +um so whoever came up with the term + + + align:start position:0% +um so whoever came up with the term +spectroscopy I don't know who it was but + + align:start position:0% +spectroscopy I don't know who it was but + + + align:start position:0% +spectroscopy I don't know who it was but +it's a brilliant name for how you + + align:start position:0% +it's a brilliant name for how you + + + align:start position:0% +it's a brilliant name for how you +understand you know study light with + + align:start position:0% +understand you know study light with + + + align:start position:0% +understand you know study light with +matter because um spectron is the Latin + + align:start position:0% +matter because um spectron is the Latin + + + align:start position:0% +matter because um spectron is the Latin +word for Spirit or + + align:start position:0% +word for Spirit or + + + align:start position:0% +word for Spirit or +ghost and the scopion is to see and so + + align:start position:0% +ghost and the scopion is to see and so + + + align:start position:0% +ghost and the scopion is to see and so +it's sort of implying look I'm trying to + + align:start position:0% +it's sort of implying look I'm trying to + + + align:start position:0% +it's sort of implying look I'm trying to +look at the Spirit or the ghost of the + + align:start position:0% +look at the Spirit or the ghost of the + + + align:start position:0% +look at the Spirit or the ghost of the +molecule and this is exactly you know + + align:start position:0% +molecule and this is exactly you know + + + align:start position:0% +molecule and this is exactly you know +this really gets at everything that + + align:start position:0% +this really gets at everything that + + + align:start position:0% +this really gets at everything that +spectroscopy is about you don't see + + align:start position:0% +spectroscopy is about you don't see + + + align:start position:0% +spectroscopy is about you don't see +molecules right we are not Imaging you + + align:start position:0% +molecules right we are not Imaging you + + + align:start position:0% +molecules right we are not Imaging you +study matter indirectly you tease out + + align:start position:0% +study matter indirectly you tease out + + + align:start position:0% +study matter indirectly you tease out +information by Shining Light on it and + + align:start position:0% +information by Shining Light on it and + + + align:start position:0% +information by Shining Light on it and +watch and see how that light or how the + + align:start position:0% +watch and see how that light or how the + + + align:start position:0% +watch and see how that light or how the +matter is changed by that + + align:start position:0% +matter is changed by that + + + align:start position:0% +matter is changed by that +interaction um but you still don't know + + align:start position:0% +interaction um but you still don't know + + + align:start position:0% +interaction um but you still don't know +what those molecules are doing your + + align:start position:0% +what those molecules are doing your + + + align:start position:0% +what those molecules are doing your +ability to get information about the + + align:start position:0% +ability to get information about the + + + align:start position:0% +ability to get information about the +structure and dynamics of a of a + + align:start position:0% +structure and dynamics of a of a + + + align:start position:0% +structure and dynamics of a of a +molecule is really predicated entirely + + align:start position:0% +molecule is really predicated entirely + + + align:start position:0% +molecule is really predicated entirely +on a model so um at the this we don't + + align:start position:0% +on a model so um at the this we don't + + + align:start position:0% +on a model so um at the this we don't +make enough out of this but spectroscopy + + align:start position:0% +make enough out of this but spectroscopy + + + align:start position:0% +make enough out of this but spectroscopy +and modeling are inseparable and um one + + align:start position:0% +and modeling are inseparable and um one + + + align:start position:0% +and modeling are inseparable and um one +is the other okay you don't always think + + align:start position:0% +is the other okay you don't always think + + + align:start position:0% +is the other okay you don't always think +about it that way very often the the + + align:start position:0% +about it that way very often the the + + + align:start position:0% +about it that way very often the the +model is so ingrained in your way of + + align:start position:0% +model is so ingrained in your way of + + + align:start position:0% +model is so ingrained in your way of +thinking about it and so taken for + + align:start position:0% +thinking about it and so taken for + + + align:start position:0% +thinking about it and so taken for +granted that you just don't even think + + align:start position:0% +granted that you just don't even think + + + align:start position:0% +granted that you just don't even think +about it right the fact that uh you know + + align:start position:0% +about it right the fact that uh you know + + + align:start position:0% +about it right the fact that uh you know +I have harmonic oscillator selection + + align:start position:0% +I have harmonic oscillator selection + + + align:start position:0% +I have harmonic oscillator selection +roles that you know that my vibrations + + align:start position:0% +roles that you know that my vibrations + + + align:start position:0% +roles that you know that my vibrations +or harmonic oscillators or or things + + align:start position:0% +or harmonic oscillators or or things + + + align:start position:0% +or harmonic oscillators or or things +like that and um that goes for basically + + align:start position:0% +like that and um that goes for basically + + + align:start position:0% +like that and um that goes for basically +any kind of spectroscop I would even say + + align:start position:0% +any kind of spectroscop I would even say + + + align:start position:0% +any kind of spectroscop I would even say +that for x-ray + + align:start position:0% +that for x-ray + + + align:start position:0% +that for x-ray +crystallography you are Shining Light on + + align:start position:0% +crystallography you are Shining Light on + + + align:start position:0% +crystallography you are Shining Light on +matter and you do have a model that you + + align:start position:0% +matter and you do have a model that you + + + align:start position:0% +matter and you do have a model that you +are fitting your observable to it turns + + align:start position:0% +are fitting your observable to it turns + + + align:start position:0% +are fitting your observable to it turns +out that the constraints are very high + + align:start position:0% +out that the constraints are very high + + + align:start position:0% +out that the constraints are very high +in that case + + align:start position:0% +in that case + + + align:start position:0% +in that case +um you you're going to put together a + + align:start position:0% +um you you're going to put together a + + + align:start position:0% +um you you're going to put together a +model calculate an observable and see + + align:start position:0% +model calculate an observable and see + + + align:start position:0% +model calculate an observable and see +how it matches so every spectroscopy + + align:start position:0% +how it matches so every spectroscopy + + + align:start position:0% +how it matches so every spectroscopy +does this what you whether you're + + align:start position:0% +does this what you whether you're + + + align:start position:0% +does this what you whether you're +thinking about it or not okay so why + + align:start position:0% +thinking about it or not okay so why + + + align:start position:0% +thinking about it or not okay so why +this gets it why to do it uh + + align:start position:0% +this gets it why to do it uh + + + align:start position:0% +this gets it why to do it uh +particularly for really complex system + + align:start position:0% +particularly for really complex system + + + align:start position:0% +particularly for really complex system +so the more degrees of freedom you put + + align:start position:0% +so the more degrees of freedom you put + + + align:start position:0% +so the more degrees of freedom you put +together um you know we talk about this + + align:start position:0% +together um you know we talk about this + + + align:start position:0% +together um you know we talk about this +a lot for condensed phase problems but + + align:start position:0% +a lot for condensed phase problems but + + + align:start position:0% +a lot for condensed phase problems but +it's just the same for many degrees of + + align:start position:0% +it's just the same for many degrees of + + + align:start position:0% +it's just the same for many degrees of +freedom in gas phase problems that the + + align:start position:0% +freedom in gas phase problems that the + + + align:start position:0% +freedom in gas phase problems that the +more degrees of freedom you have the + + align:start position:0% +more degrees of freedom you have the + + + align:start position:0% +more degrees of freedom you have the +more ingested your spectrum becomes the + + align:start position:0% +more ingested your spectrum becomes the + + + align:start position:0% +more ingested your spectrum becomes the +more difficult it is to interpret the + + align:start position:0% +more difficult it is to interpret the + + + align:start position:0% +more difficult it is to interpret the +relationships between different spectral + + align:start position:0% +relationships between different spectral + + + align:start position:0% +relationships between different spectral +features and that's at the root of + + align:start position:0% +features and that's at the root of + + + align:start position:0% +features and that's at the root of +trying to get out the structure or the + + align:start position:0% +trying to get out the structure or the + + + align:start position:0% +trying to get out the structure or the +Dynamics of the system um so what uh it + + align:start position:0% +Dynamics of the system um so what uh it + + + align:start position:0% +Dynamics of the system um so what uh it +really is about is developing a more + + align:start position:0% +really is about is developing a more + + + align:start position:0% +really is about is developing a more +constraints on your modeling um + + align:start position:0% + + + + align:start position:0% + +and you I you can say this different + + align:start position:0% +and you I you can say this different + + + align:start position:0% +and you I you can say this different +ways you can say it when I take a linear + + align:start position:0% +ways you can say it when I take a linear + + + align:start position:0% +ways you can say it when I take a linear +Spectrum + + align:start position:0% + + + + align:start position:0% + +um when I take a linear Spectrum it's + + align:start position:0% +um when I take a linear Spectrum it's + + + align:start position:0% +um when I take a linear Spectrum it's +ambiguous I get a broad featureless line + + align:start position:0% +ambiguous I get a broad featureless line + + + align:start position:0% +ambiguous I get a broad featureless line +shape I don't know how to interpret it + + align:start position:0% +shape I don't know how to interpret it + + + align:start position:0% +shape I don't know how to interpret it +that's just another way of saying + + align:start position:0% +that's just another way of saying + + + align:start position:0% +that's just another way of saying +exactly the same thing right so + + align:start position:0% +exactly the same thing right so + + + align:start position:0% +exactly the same thing right so +um uh so um there's many ways of saying + + align:start position:0% +um uh so um there's many ways of saying + + + align:start position:0% +um uh so um there's many ways of saying +this one is is uh defeat inhomogeneous + + align:start position:0% +this one is is uh defeat inhomogeneous + + + align:start position:0% +this one is is uh defeat inhomogeneous +broadening + + align:start position:0% + + + + align:start position:0% + +um you know this this is a topic that + + align:start position:0% +um you know this this is a topic that + + + align:start position:0% +um you know this this is a topic that +many um condens pH problems have to deal + + align:start position:0% +many um condens pH problems have to deal + + + align:start position:0% +many um condens pH problems have to deal +with if I have a broad featureless line + + align:start position:0% +with if I have a broad featureless line + + + align:start position:0% +with if I have a broad featureless line +shape + + align:start position:0% +shape + + + align:start position:0% +shape +um what are the ways you you know attack + + align:start position:0% +um what are the ways you you know attack + + + align:start position:0% +um what are the ways you you know attack +looking at a spectrum well there's + + align:start position:0% +looking at a spectrum well there's + + + align:start position:0% +looking at a spectrum well there's +always three observables there's you + + align:start position:0% +always three observables there's you + + + align:start position:0% +always three observables there's you +know resonance frequency and amplitud + + align:start position:0% +know resonance frequency and amplitud + + + align:start position:0% +know resonance frequency and amplitud +ude and line width those are the kinds + + align:start position:0% +ude and line width those are the kinds + + + align:start position:0% +ude and line width those are the kinds +of things that we uh try to get a handle + + align:start position:0% +of things that we uh try to get a handle + + + align:start position:0% +of things that we uh try to get a handle +on but you know uh in terms of Dynamics + + align:start position:0% +on but you know uh in terms of Dynamics + + + align:start position:0% +on but you know uh in terms of Dynamics +we're very often interested in line + + align:start position:0% +we're very often interested in line + + + align:start position:0% +we're very often interested in line +withd and the question is is this + + align:start position:0% +withd and the question is is this + + + align:start position:0% +withd and the question is is this +telling me anything about Dynamics it is + + align:start position:0% +telling me anything about Dynamics it is + + + align:start position:0% +telling me anything about Dynamics it is +is this really a homogeneous line or is + + align:start position:0% +is this really a homogeneous line or is + + + align:start position:0% +is this really a homogeneous line or is +this really just a superposition of many + + align:start position:0% +this really just a superposition of many + + + align:start position:0% +this really just a superposition of many +molecules you know behaving maybe quite + + align:start position:0% +molecules you know behaving maybe quite + + + align:start position:0% +molecules you know behaving maybe quite +differently you know regular Spectrum + + align:start position:0% +differently you know regular Spectrum + + + align:start position:0% +differently you know regular Spectrum +doesn't tell you that um + + align:start position:0% +doesn't tell you that um + + + align:start position:0% +doesn't tell you that um +it also may be things about uh you're + + align:start position:0% +it also may be things about uh you're + + + align:start position:0% +it also may be things about uh you're +trying to establish spectral + + align:start position:0% + + + + align:start position:0% + +correlations you know so there the + + align:start position:0% +correlations you know so there the + + + align:start position:0% +correlations you know so there the +question is okay imagine I've got a + + align:start position:0% +question is okay imagine I've got a + + + align:start position:0% +question is okay imagine I've got a +spectrum that's got two resonances in + + align:start position:0% +spectrum that's got two resonances in + + + align:start position:0% +spectrum that's got two resonances in +it and you go in with uh little or no + + align:start position:0% + + + + align:start position:0% + +knowledge so there's an ambiguity in the + + align:start position:0% +knowledge so there's an ambiguity in the + + + align:start position:0% +knowledge so there's an ambiguity in the +Spectrum and it + + align:start position:0% +Spectrum and it + + + align:start position:0% +Spectrum and it +says um the fact that I have two peaks + + align:start position:0% +says um the fact that I have two peaks + + + align:start position:0% +says um the fact that I have two peaks +how do I + + align:start position:0% +how do I + + + align:start position:0% +how do I +establish whether or not those Peaks um + + align:start position:0% +establish whether or not those Peaks um + + + align:start position:0% +establish whether or not those Peaks um +report on let's say one or two molecules + + align:start position:0% +report on let's say one or two molecules + + + align:start position:0% +report on let's say one or two molecules +right do I have a resonance that arises + + align:start position:0% +right do I have a resonance that arises + + + align:start position:0% +right do I have a resonance that arises +from one species and a second resonance + + align:start position:0% +from one species and a second resonance + + + align:start position:0% +from one species and a second resonance +that + + align:start position:0% +that + + + align:start position:0% +that +arises from + + align:start position:0% +arises from + + + align:start position:0% +arises from +another or in fact do these two um + + align:start position:0% +another or in fact do these two um + + + align:start position:0% +another or in fact do these two um +transitions both arise from the same + + align:start position:0% +transitions both arise from the same + + + align:start position:0% +transitions both arise from the same +molecule as the result of a um MO + + align:start position:0% +molecule as the result of a um MO + + + align:start position:0% +molecule as the result of a um MO +interaction or maybe other separate + + align:start position:0% +interaction or maybe other separate + + + align:start position:0% +interaction or maybe other separate +molecules but do they encode some sort + + align:start position:0% +molecules but do they encode some sort + + + align:start position:0% +molecules but do they encode some sort +of a coupling right so you could imagine + + align:start position:0% +of a coupling right so you could imagine + + + align:start position:0% +of a coupling right so you could imagine +having States you know A and B coupling + + align:start position:0% +having States you know A and B coupling + + + align:start position:0% +having States you know A and B coupling +these + + align:start position:0% +these + + + align:start position:0% +these +together just lead to you know new + + align:start position:0% +together just lead to you know new + + + align:start position:0% +together just lead to you know new +States one and two and sort of in an + + align:start position:0% +States one and two and sort of in an + + + align:start position:0% +States one and two and sort of in an +igen state representation then we end up + + align:start position:0% +igen state representation then we end up + + + align:start position:0% +igen state representation then we end up +with the two resonance say from these + + align:start position:0% +with the two resonance say from these + + + align:start position:0% +with the two resonance say from these +couple States I can't distinguish those + + align:start position:0% +couple States I can't distinguish those + + + align:start position:0% +couple States I can't distinguish those +kinds of scenarios from uh a linear + + align:start position:0% +kinds of scenarios from uh a linear + + + align:start position:0% +kinds of scenarios from uh a linear +Spectrum so this this is just sort of an + + align:start position:0% +Spectrum so this this is just sort of an + + + align:start position:0% +Spectrum so this this is just sort of an +example there's many ambiguities that + + align:start position:0% +example there's many ambiguities that + + + align:start position:0% +example there's many ambiguities that +come from a traditional spectrum and how + + align:start position:0% +come from a traditional spectrum and how + + + align:start position:0% +come from a traditional spectrum and how +do you get rid of it + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay um well I think we'll see quite a + + align:start position:0% +okay um well I think we'll see quite a + + + align:start position:0% +okay um well I think we'll see quite a +few of those + + align:start position:0% +few of those + + + align:start position:0% +few of those +examples + + align:start position:0% + + + + align:start position:0% + +okay don't hesitate to interrupt me with + + align:start position:0% +okay don't hesitate to interrupt me with + + + align:start position:0% +okay don't hesitate to interrupt me with +questions I don't to be great to have + + align:start position:0% +questions I don't to be great to have + + + align:start position:0% +questions I don't to be great to have +conversation about any stuff that uh you + + align:start position:0% +conversation about any stuff that uh you + + + align:start position:0% +conversation about any stuff that uh you +don't don't follow okay the the what + + align:start position:0% +don't don't follow okay the the what + + + align:start position:0% +don't don't follow okay the the what +we're going to + + align:start position:0% + + + + align:start position:0% + +spend most of our time on is coherent + + align:start position:0% +spend most of our time on is coherent + + + align:start position:0% +spend most of our time on is coherent +nonlinear spectroscopy all right so that + + align:start position:0% +nonlinear spectroscopy all right so that + + + align:start position:0% +nonlinear spectroscopy all right so that +this is going to be a subset uh you know + + align:start position:0% +this is going to be a subset uh you know + + + align:start position:0% +this is going to be a subset uh you know +of what nonlinear spectroscopies are + + align:start position:0% +of what nonlinear spectroscopies are + + + align:start position:0% +of what nonlinear spectroscopies are +um so what do I mean by coherent + + align:start position:0% +um so what do I mean by coherent + + + align:start position:0% +um so what do I mean by coherent +nonlinear + + align:start position:0% +nonlinear + + + align:start position:0% +nonlinear +spectroscopy um in short there's two + + align:start position:0% +spectroscopy um in short there's two + + + align:start position:0% +spectroscopy um in short there's two +ways of thinking um how matter will + + align:start position:0% +ways of thinking um how matter will + + + align:start position:0% +ways of thinking um how matter will +respond once you've radiated with light + + align:start position:0% +respond once you've radiated with light + + + align:start position:0% +respond once you've radiated with light +field and one of these will call + + align:start position:0% +field and one of these will call + + + align:start position:0% +field and one of these will call +coherent and the other will call + + align:start position:0% +coherent and the other will call + + + align:start position:0% +coherent and the other will call +spontaneous um and it really just has to + + align:start position:0% +spontaneous um and it really just has to + + + align:start position:0% +spontaneous um and it really just has to +do with once you have used a light field + + align:start position:0% +do with once you have used a light field + + + align:start position:0% +do with once you have used a light field +to drive dipoles in your sample how do + + align:start position:0% +to drive dipoles in your sample how do + + + align:start position:0% +to drive dipoles in your sample how do +they emit light or how how do they uh + + align:start position:0% +they emit light or how how do they uh + + + align:start position:0% +they emit light or how how do they uh +respond to that light field one of them + + align:start position:0% +respond to that light field one of them + + + align:start position:0% +respond to that light field one of them +one of these possibilities is that they + + align:start position:0% +one of these possibilities is that they + + + align:start position:0% +one of these possibilities is that they +uh radiate all independently and this is + + align:start position:0% +uh radiate all independently and this is + + + align:start position:0% +uh radiate all independently and this is +just sort of spontaneous emission types + + align:start position:0% +just sort of spontaneous emission types + + + align:start position:0% +just sort of spontaneous emission types +of + + align:start position:0% + + + + align:start position:0% + +processes and and from that point of + + align:start position:0% +processes and and from that point of + + + align:start position:0% +processes and and from that point of +view we would think of that as you know + + align:start position:0% +view we would think of that as you know + + + align:start position:0% +view we would think of that as you know +the intensity of light that we observe + + align:start position:0% +the intensity of light that we observe + + + align:start position:0% +the intensity of light that we observe +after the radiation is going to be in + + align:start position:0% +after the radiation is going to be in + + + align:start position:0% +after the radiation is going to be in +some way proportional to sort of summing + + align:start position:0% +some way proportional to sort of summing + + + align:start position:0% +some way proportional to sort of summing +over + + align:start position:0% +over + + + align:start position:0% +over +the um you know the radiation pattern + + align:start position:0% +the um you know the radiation pattern + + + align:start position:0% +the um you know the radiation pattern +from Individual + + align:start position:0% +from Individual + + + align:start position:0% +from Individual +dipoles individual independent dipoles + + align:start position:0% +dipoles individual independent dipoles + + + align:start position:0% +dipoles individual independent dipoles +and it's going to depend on detection + + align:start position:0% +and it's going to depend on detection + + + align:start position:0% +and it's going to depend on detection +geometry and things like this you know + + align:start position:0% +geometry and things like this you know + + + align:start position:0% +geometry and things like this you know +and each one of these dipoles is going + + align:start position:0% +and each one of these dipoles is going + + + align:start position:0% +and each one of these dipoles is going +to follow just a + + align:start position:0% +to follow just a + + + align:start position:0% +to follow just a +classical um dipole radiation pattern + + align:start position:0% +classical um dipole radiation pattern + + + align:start position:0% +classical um dipole radiation pattern +something that looks + + align:start position:0% + + + + align:start position:0% + +um um let's + + align:start position:0% +um um let's + + + align:start position:0% +um um let's +see you know the electric field will + + align:start position:0% +see you know the electric field will + + + align:start position:0% +see you know the electric field will +look something + + align:start position:0% + + + + align:start position:0% + +that is you know if I have a dipole + + align:start position:0% +that is you know if I have a dipole + + + align:start position:0% +that is you know if I have a dipole +aligned along say the Z Direction then + + align:start position:0% +aligned along say the Z Direction then + + + align:start position:0% +aligned along say the Z Direction then +I'm really going + + align:start position:0% +I'm really going + + + align:start position:0% +I'm really going +to radiate + + align:start position:0% +to radiate + + + align:start position:0% +to radiate +light um in then orthogonal + + align:start position:0% +light um in then orthogonal + + + align:start position:0% +light um in then orthogonal +Direction okay and so I I get light + + align:start position:0% +Direction okay and so I I get light + + + align:start position:0% +Direction okay and so I I get light +emission from all directions so what + + align:start position:0% +emission from all directions so what + + + align:start position:0% +emission from all directions so what +we're talking about in for spontaneous + + align:start position:0% +we're talking about in for spontaneous + + + align:start position:0% +we're talking about in for spontaneous +spectroscopies are things like Ramen + + align:start position:0% +spectroscopies are things like Ramen + + + align:start position:0% +spectroscopies are things like Ramen +spontaneous Ramen scattering fluorescent + + align:start position:0% +spontaneous Ramen scattering fluorescent + + + align:start position:0% +spontaneous Ramen scattering fluorescent +spectroscopy phosphor us and those sorts + + align:start position:0% +spectroscopy phosphor us and those sorts + + + align:start position:0% +spectroscopy phosphor us and those sorts +of things okay so um okay then + + align:start position:0% + + + + align:start position:0% + +uh coherent just refers to the case + + align:start position:0% +uh coherent just refers to the case + + + align:start position:0% +uh coherent just refers to the case +where we have an external light field it + + align:start position:0% +where we have an external light field it + + + align:start position:0% +where we have an external light field it +acts to + + align:start position:0% +acts to + + + align:start position:0% +acts to +drive um + + align:start position:0% +drive um + + + align:start position:0% +drive um +a let's say imagine we have a light + + align:start position:0% +a let's say imagine we have a light + + + align:start position:0% +a let's say imagine we have a light +field incident on the sample we have a + + align:start position:0% +field incident on the sample we have a + + + align:start position:0% +field incident on the sample we have a +sample that may have you know + + align:start position:0% +sample that may have you know + + + align:start position:0% +sample that may have you know +uh number of dipoles but it drives each + + align:start position:0% +uh number of dipoles but it drives each + + + align:start position:0% +uh number of dipoles but it drives each +one of these molecules within your + + align:start position:0% +one of these molecules within your + + + align:start position:0% +one of these molecules within your +sample to uh creating a macroscopic + + align:start position:0% +sample to uh creating a macroscopic + + + align:start position:0% +sample to uh creating a macroscopic +phase coherent polarization that is all + + align:start position:0% +phase coherent polarization that is all + + + align:start position:0% +phase coherent polarization that is all +of these dipoles are oscillating with a + + align:start position:0% +of these dipoles are oscillating with a + + + align:start position:0% +of these dipoles are oscillating with a +well-defined phase relationship + + align:start position:0% +well-defined phase relationship + + + align:start position:0% +well-defined phase relationship +macroscopically there is an oscillating + + align:start position:0% +macroscopically there is an oscillating + + + align:start position:0% +macroscopically there is an oscillating +dipole we'll call the + + align:start position:0% +dipole we'll call the + + + align:start position:0% +dipole we'll call the +polarization and that radiates a + + align:start position:0% +polarization and that radiates a + + + align:start position:0% +polarization and that radiates a +field + + align:start position:0% +field + + + align:start position:0% +field +um uh remember that an accelerated + + align:start position:0% +um uh remember that an accelerated + + + align:start position:0% +um uh remember that an accelerated +charge radiates a fi much like this but + + align:start position:0% +charge radiates a fi much like this but + + + align:start position:0% +charge radiates a fi much like this but +now because of the phase relationship + + align:start position:0% +now because of the phase relationship + + + align:start position:0% +now because of the phase relationship +there is constructive interference of + + align:start position:0% +there is constructive interference of + + + align:start position:0% +there is constructive interference of +all of these microscopic light fields in + + align:start position:0% +all of these microscopic light fields in + + + align:start position:0% +all of these microscopic light fields in +one particular + + align:start position:0% +one particular + + + align:start position:0% +one particular +direction so there's a you know we have + + align:start position:0% +direction so there's a you know we have + + + align:start position:0% +direction so there's a you know we have +a transmitted beam but in addition there + + align:start position:0% +a transmitted beam but in addition there + + + align:start position:0% +a transmitted beam but in addition there +is + + align:start position:0% +is + + + align:start position:0% +is +um you know + + align:start position:0% +um you know + + + align:start position:0% +um you know +a signal that's radiated and it has a + + align:start position:0% +a signal that's radiated and it has a + + + align:start position:0% +a signal that's radiated and it has a +well-defined uh direction of well- + + align:start position:0% +well-defined uh direction of well- + + + align:start position:0% +well-defined uh direction of well- +defined wave + + align:start position:0% +defined wave + + + align:start position:0% +defined wave +Vector okay so this actually you may not + + align:start position:0% +Vector okay so this actually you may not + + + align:start position:0% +Vector okay so this actually you may not +have thought about it this way but when + + align:start position:0% +have thought about it this way but when + + + align:start position:0% +have thought about it this way but when +you do an absorption experiment it is a + + align:start position:0% +you do an absorption experiment it is a + + + align:start position:0% +you do an absorption experiment it is a +coherent spectroscopy in that sense and + + align:start position:0% +coherent spectroscopy in that sense and + + + align:start position:0% +coherent spectroscopy in that sense and +we'll talk a little bit about this + + align:start position:0% +we'll talk a little bit about this + + + align:start position:0% +we'll talk a little bit about this +slightly different way of viewing + + align:start position:0% +slightly different way of viewing + + + align:start position:0% +slightly different way of viewing +absorption that it really reflects + + align:start position:0% +absorption that it really reflects + + + align:start position:0% +absorption that it really reflects +a a signal radiated by coherently + + align:start position:0% +a a signal radiated by coherently + + + align:start position:0% +a a signal radiated by coherently +radiated by oscillators of your sample + + align:start position:0% +radiated by oscillators of your sample + + + align:start position:0% +radiated by oscillators of your sample +which propagates collinearly with your + + align:start position:0% +which propagates collinearly with your + + + align:start position:0% +which propagates collinearly with your +transmitted field but they're out of + + align:start position:0% +transmitted field but they're out of + + + align:start position:0% +transmitted field but they're out of +phase with one another and destructive + + align:start position:0% +phase with one another and destructive + + + align:start position:0% +phase with one another and destructive +interference Is What You observe as + + align:start position:0% +interference Is What You observe as + + + align:start position:0% +interference Is What You observe as +absorption it's just a slightly + + align:start position:0% +absorption it's just a slightly + + + align:start position:0% +absorption it's just a slightly +different picture of the same process + + align:start position:0% +different picture of the same process + + + align:start position:0% +different picture of the same process +okay um so we're we're going to be + + align:start position:0% +okay um so we're we're going to be + + + align:start position:0% +okay um so we're we're going to be +dealing with these sorts of coherent + + align:start position:0% +dealing with these sorts of coherent + + + align:start position:0% +dealing with these sorts of coherent +experiments um and + + align:start position:0% +experiments um and + + + align:start position:0% +experiments um and +they but also for the case where the + + align:start position:0% +they but also for the case where the + + + align:start position:0% +they but also for the case where the +polarization that's created in the + + align:start position:0% +polarization that's created in the + + + align:start position:0% +polarization that's created in the +sample arises from many electric field + + align:start position:0% +sample arises from many electric field + + + align:start position:0% +sample arises from many electric field +um interactions Okay so + + align:start position:0% + + + + align:start position:0% + +um so nonlinear Spectros be will be we + + align:start position:0% +um so nonlinear Spectros be will be we + + + align:start position:0% +um so nonlinear Spectros be will be we +have a macroscopic + + align:start position:0% +have a macroscopic + + + align:start position:0% +have a macroscopic +polarization it's created by many fields + + align:start position:0% +polarization it's created by many fields + + + align:start position:0% +polarization it's created by many fields +that um enter the + + align:start position:0% + + + + align:start position:0% + +sample um they lead to a well- defined + + align:start position:0% +sample um they lead to a well- defined + + + align:start position:0% +sample um they lead to a well- defined +directional + + align:start position:0% + + + + align:start position:0% + +signal um that's radiated as result of + + align:start position:0% +signal um that's radiated as result of + + + align:start position:0% +signal um that's radiated as result of +all those and each of these fields then + + align:start position:0% +all those and each of these fields then + + + align:start position:0% +all those and each of these fields then +will be specified by some particular + + align:start position:0% +will be specified by some particular + + + align:start position:0% +will be specified by some particular +frequency some time ordering phase and + + align:start position:0% +frequency some time ordering phase and + + + align:start position:0% +frequency some time ordering phase and +so + + align:start position:0% +so + + + align:start position:0% +so +on okay so is it a good picture to have + + align:start position:0% +on okay so is it a good picture to have + + + align:start position:0% +on okay so is it a good picture to have +a completely spontaneous you know system + + align:start position:0% +a completely spontaneous you know system + + + align:start position:0% +a completely spontaneous you know system +and a completely coherent system or in + + align:start position:0% +and a completely coherent system or in + + + align:start position:0% +and a completely coherent system or in +any real experimental + + align:start position:0% +any real experimental + + + align:start position:0% +any real experimental +system does one sort of almost no matter + + align:start position:0% +system does one sort of almost no matter + + + align:start position:0% +system does one sort of almost no matter +what have some degree of coherence even + + align:start position:0% +what have some degree of coherence even + + + align:start position:0% +what have some degree of coherence even +if you're using incoherent light as you + + align:start position:0% +if you're using incoherent light as you + + + align:start position:0% +if you're using incoherent light as you +can make and no matter what you have + + align:start position:0% +can make and no matter what you have + + + align:start position:0% +can make and no matter what you have +some + + align:start position:0% +some + + + align:start position:0% +some +spontaneous no matter how strongly you + + align:start position:0% +spontaneous no matter how strongly you + + + align:start position:0% +spontaneous no matter how strongly you +polarize that's um so that's an + + align:start position:0% +polarize that's um so that's an + + + align:start position:0% +polarize that's um so that's an +excellent question the idea is you at + + align:start position:0% +excellent question the idea is you at + + + align:start position:0% +excellent question the idea is you at +all times you always have both + + align:start position:0% +all times you always have both + + + align:start position:0% +all times you always have both +contributions so when you put a light + + align:start position:0% +contributions so when you put a light + + + align:start position:0% +contributions so when you put a light +field into a sample you will always have + + align:start position:0% +field into a sample you will always have + + + align:start position:0% +field into a sample you will always have +both spontaneous and coherent radiation + + align:start position:0% +both spontaneous and coherent radiation + + + align:start position:0% +both spontaneous and coherent radiation +coming out um as you might imagine the + + align:start position:0% +coming out um as you might imagine the + + + align:start position:0% +coming out um as you might imagine the +degree to which I see one or another + + align:start position:0% +degree to which I see one or another + + + align:start position:0% +degree to which I see one or another +depends on how coherent their radiation + + align:start position:0% +depends on how coherent their radiation + + + align:start position:0% +depends on how coherent their radiation +is so def phasing plays a really big + + align:start position:0% +is so def phasing plays a really big + + + align:start position:0% +is so def phasing plays a really big +role in determining how much of one or + + align:start position:0% +role in determining how much of one or + + + align:start position:0% +role in determining how much of one or +the other you you get in electronic + + align:start position:0% +the other you you get in electronic + + + align:start position:0% +the other you you get in electronic +spectroscopy in condensed phases def + + align:start position:0% +spectroscopy in condensed phases def + + + align:start position:0% +spectroscopy in condensed phases def +phasing is an extremely rapid process + + align:start position:0% +phasing is an extremely rapid process + + + align:start position:0% +phasing is an extremely rapid process +and hence you get + + align:start position:0% +and hence you get + + + align:start position:0% +and hence you get +fluoresence um as the dominant emission + + align:start position:0% +fluoresence um as the dominant emission + + + align:start position:0% +fluoresence um as the dominant emission +process um and so spontaneous is you + + align:start position:0% +process um and so spontaneous is you + + + align:start position:0% +process um and so spontaneous is you +know overwhelmingly you know the large + + align:start position:0% +know overwhelmingly you know the large + + + align:start position:0% +know overwhelmingly you know the large +contributor in electronic + + align:start position:0% +contributor in electronic + + + align:start position:0% +contributor in electronic +systems um uh in vibrational systems the + + align:start position:0% +systems um uh in vibrational systems the + + + align:start position:0% +systems um uh in vibrational systems the +fact that the radi of Lifetime is so + + align:start position:0% +fact that the radi of Lifetime is so + + + align:start position:0% +fact that the radi of Lifetime is so +incredibly long and that intermolecular + + align:start position:0% +incredibly long and that intermolecular + + + align:start position:0% +incredibly long and that intermolecular +interactions are so much stronger means + + align:start position:0% +interactions are so much stronger means + + + align:start position:0% +interactions are so much stronger means +that um they uh relax very rapidly + + align:start position:0% +that um they uh relax very rapidly + + + align:start position:0% +that um they uh relax very rapidly +non-radiatively and that means that the + + align:start position:0% +non-radiatively and that means that the + + + align:start position:0% +non-radiatively and that means that the +response is almost always dominated by + + align:start position:0% +response is almost always dominated by + + + align:start position:0% +response is almost always dominated by +the coherent part there's uh many cases + + align:start position:0% +the coherent part there's uh many cases + + + align:start position:0% +the coherent part there's uh many cases +where people have actually made use of + + align:start position:0% +where people have actually made use of + + + align:start position:0% +where people have actually made use of +the fact that you can look at both + + align:start position:0% +the fact that you can look at both + + + align:start position:0% +the fact that you can look at both +simultaneously and use that to deduce a + + align:start position:0% +simultaneously and use that to deduce a + + + align:start position:0% +simultaneously and use that to deduce a +lot of information about the inter + + align:start position:0% +lot of information about the inter + + + align:start position:0% +lot of information about the inter +molecular interaction so if you look at + + align:start position:0% +molecular interaction so if you look at + + + align:start position:0% +molecular interaction so if you look at +resonance Ramen scattering and compare + + align:start position:0% +resonance Ramen scattering and compare + + + align:start position:0% +resonance Ramen scattering and compare +the coherent and the incoherent + + align:start position:0% +the coherent and the incoherent + + + align:start position:0% +the coherent and the incoherent +scattering profiles you can make a lot + + align:start position:0% +scattering profiles you can make a lot + + + align:start position:0% +scattering profiles you can make a lot +of use of that to tell you about + + align:start position:0% + + + + align:start position:0% + +Dynamics the other thing uh that you + + align:start position:0% +Dynamics the other thing uh that you + + + align:start position:0% +Dynamics the other thing uh that you +were getting at I'll talk more about + + align:start position:0% +were getting at I'll talk more about + + + align:start position:0% +were getting at I'll talk more about +this later is the you tend to think of + + align:start position:0% +this later is the you tend to think of + + + align:start position:0% +this later is the you tend to think of +say I do a UV Vis or an infrared + + align:start position:0% +say I do a UV Vis or an infrared + + + align:start position:0% +say I do a UV Vis or an infrared +Spectrum with a lamp you don't think of + + align:start position:0% +Spectrum with a lamp you don't think of + + + align:start position:0% +Spectrum with a lamp you don't think of +that as a coherent light source + + align:start position:0% +that as a coherent light source + + + align:start position:0% +that as a coherent light source +nonetheless I'm calling that a coherent + + align:start position:0% +nonetheless I'm calling that a coherent + + + align:start position:0% +nonetheless I'm calling that a coherent +spectroscopy because it is true that the + + align:start position:0% +spectroscopy because it is true that the + + + align:start position:0% +spectroscopy because it is true that the +coherence of the incoming light + + align:start position:0% +coherence of the incoming light + + + align:start position:0% +coherence of the incoming light +itself you know is scrambled very + + align:start position:0% +itself you know is scrambled very + + + align:start position:0% +itself you know is scrambled very +rapidly but that light sets up coherent + + align:start position:0% +rapidly but that light sets up coherent + + + align:start position:0% +rapidly but that light sets up coherent +oscillations in the sample and that's + + align:start position:0% +oscillations in the sample and that's + + + align:start position:0% +oscillations in the sample and that's +exactly what you measure when you do an + + align:start position:0% +exactly what you measure when you do an + + + align:start position:0% +exactly what you measure when you do an +measure the interferogram in an ftir + + align:start position:0% +measure the interferogram in an ftir + + + align:start position:0% +measure the interferogram in an ftir +interferometer is you're measuring the + + align:start position:0% +interferometer is you're measuring the + + + align:start position:0% +interferometer is you're measuring the +coherence in the of the dipoles in your + + align:start position:0% + + + + align:start position:0% + +sample okay so uh one thing um I I want + + align:start position:0% +sample okay so uh one thing um I I want + + + align:start position:0% +sample okay so uh one thing um I I want +to point out is that there there there's + + align:start position:0% +to point out is that there there there's + + + align:start position:0% +to point out is that there there there's +certainly spontaneous nonlinear + + align:start position:0% +certainly spontaneous nonlinear + + + align:start position:0% +certainly spontaneous nonlinear +spectroscopies right and and I would say + + align:start position:0% +spectroscopies right and and I would say + + + align:start position:0% +spectroscopies right and and I would say +that there's lots of those that are done + + align:start position:0% +that there's lots of those that are done + + + align:start position:0% +that there's lots of those that are done +it's you know I detect my signal with + + align:start position:0% +it's you know I detect my signal with + + + align:start position:0% +it's you know I detect my signal with +spontaneous emission say or uh um or + + align:start position:0% +spontaneous emission say or uh um or + + + align:start position:0% +spontaneous emission say or uh um or +with some other sort of + + align:start position:0% +with some other sort of + + + align:start position:0% +with some other sort of +uh you maybe the sample reports somehow + + align:start position:0% +uh you maybe the sample reports somehow + + + align:start position:0% +uh you maybe the sample reports somehow +differently to you photo thermally or + + align:start position:0% +differently to you photo thermally or + + + align:start position:0% +differently to you photo thermally or +electron emission or something like that + + align:start position:0% +electron emission or something like that + + + align:start position:0% +electron emission or something like that +those would be coherent but if you're + + align:start position:0% +those would be coherent but if you're + + + align:start position:0% +those would be coherent but if you're +acting on the sample with multiple + + align:start position:0% +acting on the sample with multiple + + + align:start position:0% +acting on the sample with multiple +fields and looking at the response and + + align:start position:0% +fields and looking at the response and + + + align:start position:0% +fields and looking at the response and +that's still that's still uh coherent uh + + align:start position:0% +that's still that's still uh coherent uh + + + align:start position:0% +that's still that's still uh coherent uh +that's incoherent nonlinear spectroscopy + + align:start position:0% +that's incoherent nonlinear spectroscopy + + + align:start position:0% +that's incoherent nonlinear spectroscopy +but we're going to deal primarily with + + align:start position:0% +but we're going to deal primarily with + + + align:start position:0% +but we're going to deal primarily with +this and you'll see there's a real clear + + align:start position:0% +this and you'll see there's a real clear + + + align:start position:0% +this and you'll see there's a real clear +mapping from one to the + + align:start position:0% +mapping from one to the + + + align:start position:0% +mapping from one to the +other + + align:start position:0% +other + + + align:start position:0% +other +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Music] + + align:start position:0% + + + + align:start position:0% + +um okay I would + + align:start position:0% +um okay I would + + + align:start position:0% +um okay I would +uh I'd like to dig in in then a little + + align:start position:0% +uh I'd like to dig in in then a little + + + align:start position:0% +uh I'd like to dig in in then a little +bit into this formalism about what the + + align:start position:0% +bit into this formalism about what the + + + align:start position:0% +bit into this formalism about what the +nonlinear polarization is that is how do + + align:start position:0% +nonlinear polarization is that is how do + + + align:start position:0% +nonlinear polarization is that is how do +you set up a macroscopic + + align:start position:0% +you set up a macroscopic + + + align:start position:0% +you set up a macroscopic +oscillating um collection coherently + + align:start position:0% +oscillating um collection coherently + + + align:start position:0% +oscillating um collection coherently +oscillating collection of dipoles in the + + align:start position:0% +oscillating collection of dipoles in the + + + align:start position:0% +oscillating collection of dipoles in the +sample and so uh the + + align:start position:0% +sample and so uh the + + + align:start position:0% +sample and so uh the +polarization will take it really to be a + + align:start position:0% +polarization will take it really to be a + + + align:start position:0% +polarization will take it really to be a +macroscopic uh property it's basically + + align:start position:0% +macroscopic uh property it's basically + + + align:start position:0% +macroscopic uh property it's basically +an ensemble average you know a + + align:start position:0% +an ensemble average you know a + + + align:start position:0% +an ensemble average you know a +macroscopic average over the dipoles of + + align:start position:0% +macroscopic average over the dipoles of + + + align:start position:0% +macroscopic average over the dipoles of +your sample so we'll just just really + + align:start position:0% +your sample so we'll just just really + + + align:start position:0% +your sample so we'll just just really +just take it as a suing over all the + + align:start position:0% +just take it as a suing over all the + + + align:start position:0% +just take it as a suing over all the +diap um in your sample and those are + + align:start position:0% +diap um in your sample and those are + + + align:start position:0% +diap um in your sample and those are +going to just going to be distributed + + align:start position:0% +going to just going to be distributed + + + align:start position:0% +going to just going to be distributed +through space m is just my count for um + + align:start position:0% +through space m is just my count for um + + + align:start position:0% +through space m is just my count for um +a particular molecule in my sample let's + + align:start position:0% +a particular molecule in my sample let's + + + align:start position:0% +a particular molecule in my sample let's +say and for any one molecule then + + align:start position:0% +say and for any one molecule then + + + align:start position:0% +say and for any one molecule then +there's going to be um a molecular + + align:start position:0% +there's going to be um a molecular + + + align:start position:0% +there's going to be um a molecular +dipole moment and we'll just take that + + align:start position:0% +dipole moment and we'll just take that + + + align:start position:0% +dipole moment and we'll just take that +to be a some over charges within the + + align:start position:0% +to be a some over charges within the + + + align:start position:0% +to be a some over charges within the +molecule + + align:start position:0% + + + + align:start position:0% + +okay so this is sort of our view of uh + + align:start position:0% +okay so this is sort of our view of uh + + + align:start position:0% +okay so this is sort of our view of uh +um the dipole moment of the system and + + align:start position:0% +um the dipole moment of the system and + + + align:start position:0% +um the dipole moment of the system and +the macroscopic + + align:start position:0% +the macroscopic + + + align:start position:0% +the macroscopic +polarization okay um in the case of + + align:start position:0% +polarization okay um in the case of + + + align:start position:0% +polarization okay um in the case of +linear + + align:start position:0% +linear + + + align:start position:0% +linear +spectroscopy we uh + + align:start position:0% +spectroscopy we uh + + + align:start position:0% +spectroscopy we uh +associate um the polarization as related + + align:start position:0% +associate um the polarization as related + + + align:start position:0% +associate um the polarization as related +to the + + align:start position:0% +to the + + + align:start position:0% +to the +susceptibility times uh the incident + + align:start position:0% +susceptibility times uh the incident + + + align:start position:0% +susceptibility times uh the incident +electric field so this is a frequency + + align:start position:0% +electric field so this is a frequency + + + align:start position:0% +electric field so this is a frequency +domain representation of how we um + + align:start position:0% +domain representation of how we um + + + align:start position:0% +domain representation of how we um +describe the polarization in requires an + + align:start position:0% +describe the polarization in requires an + + + align:start position:0% +describe the polarization in requires an +ensemble average over all of these + + align:start position:0% +ensemble average over all of these + + + align:start position:0% +ensemble average over all of these +dipoles and that's expressed through a + + align:start position:0% +dipoles and that's expressed through a + + + align:start position:0% +dipoles and that's expressed through a +susceptibility which is complex quantity + + align:start position:0% +susceptibility which is complex quantity + + + align:start position:0% +susceptibility which is complex quantity +its real and imaginary Parts reflect the + + align:start position:0% +its real and imaginary Parts reflect the + + + align:start position:0% +its real and imaginary Parts reflect the +you know the dispersive and absorptive + + align:start position:0% +you know the dispersive and absorptive + + + align:start position:0% +you know the dispersive and absorptive +parts of the response of your system and + + align:start position:0% +parts of the response of your system and + + + align:start position:0% +parts of the response of your system and +this is just the frequency domain + + align:start position:0% +this is just the frequency domain + + + align:start position:0% +this is just the frequency domain +version of the linear response function + + align:start position:0% +version of the linear response function + + + align:start position:0% +version of the linear response function +that uh We've Ted talked about that in + + align:start position:0% +that uh We've Ted talked about that in + + + align:start position:0% +that uh We've Ted talked about that in +574 we can also say that this is related + + align:start position:0% + + + + align:start position:0% + +to it's a really a convolution over the + + align:start position:0% +to it's a really a convolution over the + + + align:start position:0% +to it's a really a convolution over the +linear response function with the + + align:start position:0% +linear response function with the + + + align:start position:0% +linear response function with the +incident uh electric field okay so the + + align:start position:0% +incident uh electric field okay so the + + + align:start position:0% +incident uh electric field okay so the +susceptibility and the linear response + + align:start position:0% +susceptibility and the linear response + + + align:start position:0% +susceptibility and the linear response +fun function these are two identical + + align:start position:0% +fun function these are two identical + + + align:start position:0% +fun function these are two identical +manifestations of the response of + + align:start position:0% +manifestations of the response of + + + align:start position:0% +manifestations of the response of +dipoles um to electromagnetic radiation + + align:start position:0% +dipoles um to electromagnetic radiation + + + align:start position:0% +dipoles um to electromagnetic radiation +just one that's in the frequency domain + + align:start position:0% +just one that's in the frequency domain + + + align:start position:0% +just one that's in the frequency domain +one is in the time domain you know we + + align:start position:0% +one is in the time domain you know we + + + align:start position:0% +one is in the time domain you know we +would just get um the susceptibility + + align:start position:0% +would just get um the susceptibility + + + align:start position:0% +would just get um the susceptibility +from a foro transform + + align:start position:0% +from a foro transform + + + align:start position:0% +from a foro transform +of uh the linear response function + + align:start position:0% + + + + align:start position:0% + +okay okay so so um either of these + + align:start position:0% +okay okay so so um either of these + + + align:start position:0% +okay okay so so um either of these +methods just use for say an absorption + + align:start position:0% +methods just use for say an absorption + + + align:start position:0% +methods just use for say an absorption +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +okay okay + + align:start position:0% +okay okay + + + align:start position:0% +okay okay +now + + align:start position:0% +now + + + align:start position:0% +now +um now the next connection I'd like to + + align:start position:0% +um now the next connection I'd like to + + + align:start position:0% +um now the next connection I'd like to +make is the polarization to this + + align:start position:0% +make is the polarization to this + + + align:start position:0% +make is the polarization to this +radiated signal field that is you know + + align:start position:0% +radiated signal field that is you know + + + align:start position:0% +radiated signal field that is you know +how is it that an oscillating + + align:start position:0% +how is it that an oscillating + + + align:start position:0% +how is it that an oscillating +polarization acts as a source for a + + align:start position:0% + + + + align:start position:0% + +signal + + align:start position:0% +signal + + + align:start position:0% +signal +and um so the idea is we're used to + + align:start position:0% +and um so the idea is we're used to + + + align:start position:0% +and um so the idea is we're used to +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +um uh wave equations let's write one for + + align:start position:0% +um uh wave equations let's write one for + + + align:start position:0% +um uh wave equations let's write one for +a free electron magnetic + + align:start position:0% + + + + align:start position:0% + +wave uh plane + + align:start position:0% + + + + align:start position:0% + +wave so this is the equation of motion + + align:start position:0% +wave so this is the equation of motion + + + align:start position:0% +wave so this is the equation of motion +we'll write just for a plain + + align:start position:0% +we'll write just for a plain + + + align:start position:0% +we'll write just for a plain +electromagnetic wave propagating with a + + align:start position:0% +electromagnetic wave propagating with a + + + align:start position:0% +electromagnetic wave propagating with a +particular wave vector + + align:start position:0% +particular wave vector + + + align:start position:0% +particular wave vector +uh oscillating both with a particular + + align:start position:0% +uh oscillating both with a particular + + + align:start position:0% +uh oscillating both with a particular +frequency and with a particular + + align:start position:0% +frequency and with a particular + + + align:start position:0% +frequency and with a particular +periodicity we call the + + align:start position:0% +periodicity we call the + + + align:start position:0% +periodicity we call the +wavelength we we solve that to get you + + align:start position:0% +wavelength we we solve that to get you + + + align:start position:0% +wavelength we we solve that to get you +know our um typical plane wave + + align:start position:0% +know our um typical plane wave + + + align:start position:0% +know our um typical plane wave +Solutions um if we're trying to now talk + + align:start position:0% +Solutions um if we're trying to now talk + + + align:start position:0% +Solutions um if we're trying to now talk +about how such a wave gets uh radiated + + align:start position:0% +about how such a wave gets uh radiated + + + align:start position:0% +about how such a wave gets uh radiated +by a dipole say in this form we can + + align:start position:0% +by a dipole say in this form we can + + + align:start position:0% +by a dipole say in this form we can +think of this polarization now as an um + + align:start position:0% +think of this polarization now as an um + + + align:start position:0% +think of this polarization now as an um +a charge source and if we talk about the + + align:start position:0% +a charge source and if we talk about the + + + align:start position:0% +a charge source and if we talk about the +acceleration of those charges those will + + align:start position:0% +acceleration of those charges those will + + + align:start position:0% +acceleration of those charges those will +act to Radia a field so we can + + align:start position:0% +act to Radia a field so we can + + + align:start position:0% +act to Radia a field so we can +really rather than just saying this this + + align:start position:0% +really rather than just saying this this + + + align:start position:0% +really rather than just saying this this +wave propagates an isolation we can say + + align:start position:0% +wave propagates an isolation we can say + + + align:start position:0% +wave propagates an isolation we can say +instead that it oscillates as the result + + align:start position:0% +instead that it oscillates as the result + + + align:start position:0% +instead that it oscillates as the result +of a source and that + + align:start position:0% +of a source and that + + + align:start position:0% +of a source and that +source is just the the polarization so + + align:start position:0% +source is just the the polarization so + + + align:start position:0% +source is just the the polarization so +let me + + align:start position:0% +let me + + + align:start position:0% +let me +see um + + align:start position:0% + + + + align:start position:0% + +okay so now here's my accelerating + + align:start position:0% +okay so now here's my accelerating + + + align:start position:0% +okay so now here's my accelerating +charges and they're acting as a source + + align:start position:0% +charges and they're acting as a source + + + align:start position:0% +charges and they're acting as a source +for this field and the solutions to this + + align:start position:0% +for this field and the solutions to this + + + align:start position:0% +for this field and the solutions to this +look very similar to the the kinds of um + + align:start position:0% +look very similar to the the kinds of um + + + align:start position:0% +look very similar to the the kinds of um +plane wave solutions that you're used to + + align:start position:0% +plane wave solutions that you're used to + + + align:start position:0% +plane wave solutions that you're used to +we now say that there's a you know the + + align:start position:0% +we now say that there's a you know the + + + align:start position:0% +we now say that there's a you know the +macroscopic polarization in the + + align:start position:0% +macroscopic polarization in the + + + align:start position:0% +macroscopic polarization in the +sample has a Time profile and a um + + align:start position:0% +sample has a Time profile and a um + + + align:start position:0% +sample has a Time profile and a um +space and + + align:start position:0% +space and + + + align:start position:0% +space and +frequency response that looks just like + + align:start position:0% +frequency response that looks just like + + + align:start position:0% +frequency response that looks just like +a plain wave + + align:start position:0% + + + + align:start position:0% + +solution + + align:start position:0% +solution + + + align:start position:0% +solution +okay so uh we have a sort of a Time + + align:start position:0% +okay so uh we have a sort of a Time + + + align:start position:0% +okay so uh we have a sort of a Time +profile to these oscillating charges + + align:start position:0% +profile to these oscillating charges + + + align:start position:0% +profile to these oscillating charges +um the and + + align:start position:0% +um the and + + + align:start position:0% +um the and +these you know these oscillations have a + + align:start position:0% +these you know these oscillations have a + + + align:start position:0% +these you know these oscillations have a +well- defined uh Direction and frequency + + align:start position:0% +well- defined uh Direction and frequency + + + align:start position:0% +well- defined uh Direction and frequency +as and that results from + + align:start position:0% +as and that results from + + + align:start position:0% +as and that results from +uh if you take this polarization this + + align:start position:0% +uh if you take this polarization this + + + align:start position:0% +uh if you take this polarization this +leads to predicting you know which wave + + align:start position:0% +leads to predicting you know which wave + + + align:start position:0% +leads to predicting you know which wave +will this light field propagate and that + + align:start position:0% +will this light field propagate and that + + + align:start position:0% +will this light field propagate and that +follows sort of a uh parallel solution + + align:start position:0% +follows sort of a uh parallel solution + + + align:start position:0% +follows sort of a uh parallel solution +or + + align:start position:0% + + + + align:start position:0% + +okay so here's the oscillating + + align:start position:0% +okay so here's the oscillating + + + align:start position:0% +okay so here's the oscillating +polarization solving uh this wave + + align:start position:0% +polarization solving uh this wave + + + align:start position:0% +polarization solving uh this wave +equation gives you sort of what the + + align:start position:0% +equation gives you sort of what the + + + align:start position:0% +equation gives you sort of what the +shape of the radiated signal is and the + + align:start position:0% +shape of the radiated signal is and the + + + align:start position:0% +shape of the radiated signal is and the +wave Vector of this polarization and the + + align:start position:0% +wave Vector of this polarization and the + + + align:start position:0% +wave Vector of this polarization and the +signal need not be the same in fact the + + align:start position:0% +signal need not be the same in fact the + + + align:start position:0% +signal need not be the same in fact the +relationship between these two um sort + + align:start position:0% +relationship between these two um sort + + + align:start position:0% +relationship between these two um sort +of gives you the directionality of the + + align:start position:0% +of gives you the directionality of the + + + align:start position:0% +of gives you the directionality of the +signal so we go back over here + + align:start position:0% + + + + align:start position:0% + +okay now when you calculate uh when you + + align:start position:0% +okay now when you calculate uh when you + + + align:start position:0% +okay now when you calculate uh when you +integrate this uh equation over a + + align:start position:0% +integrate this uh equation over a + + + align:start position:0% +integrate this uh equation over a +macroscopic sample that has a length + + align:start position:0% +macroscopic sample that has a length + + + align:start position:0% +macroscopic sample that has a length +L um and where + + align:start position:0% +L um and where + + + align:start position:0% +L um and where +L is is much greater than the wavelength + + align:start position:0% +L is is much greater than the wavelength + + + align:start position:0% +L is is much greater than the wavelength +of light so you need enough it needs to + + align:start position:0% +of light so you need enough it needs to + + + align:start position:0% +of light so you need enough it needs to +be a large enough sample that you can + + align:start position:0% +be a large enough sample that you can + + + align:start position:0% +be a large enough sample that you can +have many oscillations of the field to + + align:start position:0% +have many oscillations of the field to + + + align:start position:0% +have many oscillations of the field to +establish constructive and destructive + + align:start position:0% +establish constructive and destructive + + + align:start position:0% +establish constructive and destructive +interferences between dipole but at the + + align:start position:0% +interferences between dipole but at the + + + align:start position:0% +interferences between dipole but at the +same time we're working in the electric + + align:start position:0% +same time we're working in the electric + + + align:start position:0% +same time we're working in the electric +dipole + + align:start position:0% +dipole + + + align:start position:0% +dipole +approximation so Lambda is much greater + + align:start position:0% +approximation so Lambda is much greater + + + align:start position:0% +approximation so Lambda is much greater +than + + align:start position:0% +than + + + align:start position:0% +than +the the sort of size of the molecular + + align:start position:0% +the the sort of size of the molecular + + + align:start position:0% +the the sort of size of the molecular +charge + + align:start position:0% +charge + + + align:start position:0% +charge +distributions okay um then you obtain + + align:start position:0% +distributions okay um then you obtain + + + align:start position:0% +distributions okay um then you obtain +this kind of a relationship between the + + align:start position:0% +this kind of a relationship between the + + + align:start position:0% +this kind of a relationship between the +radiated signal and the oscillating + + align:start position:0% +radiated signal and the oscillating + + + align:start position:0% +radiated signal and the oscillating +polarization in the sample um and the + + align:start position:0% +polarization in the sample um and the + + + align:start position:0% +polarization in the sample um and the +thing I want to point out here is that + + align:start position:0% +thing I want to point out here is that + + + align:start position:0% +thing I want to point out here is that +um it depends on these phase matching + + align:start position:0% +um it depends on these phase matching + + + align:start position:0% +um it depends on these phase matching +terms here where Delta K is really the + + align:start position:0% +terms here where Delta K is really the + + + align:start position:0% +terms here where Delta K is really the +phase mismatch between the wave Vector + + align:start position:0% +phase mismatch between the wave Vector + + + align:start position:0% +phase mismatch between the wave Vector +of the + + align:start position:0% +of the + + + align:start position:0% +of the +polarization and that of the field and + + align:start position:0% +polarization and that of the field and + + + align:start position:0% +polarization and that of the field and +this just says there is going to be a + + align:start position:0% +this just says there is going to be a + + + align:start position:0% +this just says there is going to be a +well- defined Direction um you know I + + align:start position:0% +well- defined Direction um you know I + + + align:start position:0% +well- defined Direction um you know I +may have + + align:start position:0% + + + + align:start position:0% + +multiple incident fields + + align:start position:0% +multiple incident fields + + + align:start position:0% +multiple incident fields +that come into this sample with well + + align:start position:0% +that come into this sample with well + + + align:start position:0% +that come into this sample with well +defined phase + + align:start position:0% + + + + align:start position:0% + +relationships the net result of this + + align:start position:0% +relationships the net result of this + + + align:start position:0% +relationships the net result of this +will be that there is some + + align:start position:0% +will be that there is some + + + align:start position:0% +will be that there is some +net uh wave Vector in the sample and + + align:start position:0% +net uh wave Vector in the sample and + + + align:start position:0% +net uh wave Vector in the sample and +that is going to act as a + + align:start position:0% +that is going to act as a + + + align:start position:0% +that is going to act as a +source for a signal field um whose + + align:start position:0% +source for a signal field um whose + + + align:start position:0% +source for a signal field um whose +direction will be sharply peaked as + + align:start position:0% +direction will be sharply peaked as + + + align:start position:0% +direction will be sharply peaked as +given by this sync function in a + + align:start position:0% +given by this sync function in a + + + align:start position:0% +given by this sync function in a +direction um given uh by the um + + align:start position:0% +direction um given uh by the um + + + align:start position:0% +direction um given uh by the um +polarization wave Vector + + align:start position:0% + + + + align:start position:0% + +okay I'm a little confused just thinking + + align:start position:0% +okay I'm a little confused just thinking + + + align:start position:0% +okay I'm a little confused just thinking +about a limiting case uh if you had one + + align:start position:0% +about a limiting case uh if you had one + + + align:start position:0% +about a limiting case uh if you had one +molecule yep then sort of by definition + + align:start position:0% +molecule yep then sort of by definition + + + align:start position:0% +molecule yep then sort of by definition +you had a a macroscopic polarization + + align:start position:0% +you had a a macroscopic polarization + + + align:start position:0% +you had a a macroscopic polarization +there only one no that's that this + + align:start position:0% +there only one no that's that this + + + align:start position:0% +there only one no that's that this +really um holds for an ensemble so I + + align:start position:0% +really um holds for an ensemble so I + + + align:start position:0% +really um holds for an ensemble so I +mean there's actually a lot of + + align:start position:0% +mean there's actually a lot of + + + align:start position:0% +mean there's actually a lot of +interesting questions that come about + + align:start position:0% +interesting questions that come about + + + align:start position:0% +interesting questions that come about +you know can you have or how do you see + + align:start position:0% +you know can you have or how do you see + + + align:start position:0% +you know can you have or how do you see +nonlinear behavior in a single dipole or + + align:start position:0% +nonlinear behavior in a single dipole or + + + align:start position:0% +nonlinear behavior in a single dipole or +how would you see absorption in a single + + align:start position:0% +how would you see absorption in a single + + + align:start position:0% +how would you see absorption in a single +dipole and uh that's that's something we + + align:start position:0% +dipole and uh that's that's something we + + + align:start position:0% +dipole and uh that's that's something we +won't get into what we're talking about + + align:start position:0% +won't get into what we're talking about + + + align:start position:0% +won't get into what we're talking about +here can the idea of uh the phase + + align:start position:0% +here can the idea of uh the phase + + + align:start position:0% +here can the idea of uh the phase +matching and the coherent radiation that + + align:start position:0% +matching and the coherent radiation that + + + align:start position:0% +matching and the coherent radiation that +we're talking about is intrinsic and + + align:start position:0% +we're talking about is intrinsic and + + + align:start position:0% +we're talking about is intrinsic and +having a you know large Ensemble of many + + align:start position:0% +having a you know large Ensemble of many + + + align:start position:0% +having a you know large Ensemble of many +coherently radiating di so um so right + + align:start position:0% +coherently radiating di so um so right + + + align:start position:0% +coherently radiating di so um so right +so it uh I think in describing a single + + align:start position:0% +so it uh I think in describing a single + + + align:start position:0% +so it uh I think in describing a single +molecule Behavior you have to start from + + align:start position:0% +molecule Behavior you have to start from + + + align:start position:0% +molecule Behavior you have to start from +scratch and do this differently so this + + align:start position:0% +scratch and do this differently so this + + + align:start position:0% +scratch and do this differently so this +is how we view the spontaneous is sort + + align:start position:0% +is how we view the spontaneous is sort + + + align:start position:0% +is how we view the spontaneous is sort +of how we would view the single molecule + + align:start position:0% +of how we would view the single molecule + + + align:start position:0% +of how we would view the single molecule +you know behavior um that there's really + + align:start position:0% +you know behavior um that there's really + + + align:start position:0% +you know behavior um that there's really +independent radiation from each + + align:start position:0% +independent radiation from each + + + align:start position:0% +independent radiation from each +dipole um so right this by definition an + + align:start position:0% +dipole um so right this by definition an + + + align:start position:0% +dipole um so right this by definition an +ensemble + + align:start position:0% + + + + align:start position:0% + +approach and that raises all kinds of + + align:start position:0% +approach and that raises all kinds of + + + align:start position:0% +approach and that raises all kinds of +Interest in questions about how similar + + align:start position:0% +Interest in questions about how similar + + + align:start position:0% +Interest in questions about how similar +are the individual molecules to the + + align:start position:0% +are the individual molecules to the + + + align:start position:0% +are the individual molecules to the +behavior of The Ensemble how do you + + align:start position:0% +behavior of The Ensemble how do you + + + align:start position:0% +behavior of The Ensemble how do you +reconstruct that okay so um one thing + + align:start position:0% +reconstruct that okay so um one thing + + + align:start position:0% +reconstruct that okay so um one thing +that comes um out of all of this some + + align:start position:0% +that comes um out of all of this some + + + align:start position:0% +that comes um out of all of this some +bookkeeping you you know you will be + + align:start position:0% +bookkeeping you you know you will be + + + align:start position:0% +bookkeeping you you know you will be +able to keep track of well what + + align:start position:0% +able to keep track of well what + + + align:start position:0% +able to keep track of well what +direction does this signal go and what + + align:start position:0% +direction does this signal go and what + + + align:start position:0% +direction does this signal go and what +frequency does it have and you know + + align:start position:0% +frequency does it have and you know + + + align:start position:0% +frequency does it have and you know +we'll + + align:start position:0% +we'll + + + align:start position:0% +we'll +establish that you know the wave Vector + + align:start position:0% +establish that you know the wave Vector + + + align:start position:0% +establish that you know the wave Vector +of the signal is going to in some way be + + align:start position:0% +of the signal is going to in some way be + + + align:start position:0% +of the signal is going to in some way be +related + + align:start position:0% +related + + + align:start position:0% +related +to a sum + + align:start position:0% +to a sum + + + align:start position:0% +to a sum +or difference over all of the incident + + align:start position:0% +or difference over all of the incident + + + align:start position:0% +or difference over all of the incident +wave vectors into your sample the + + align:start position:0% +wave vectors into your sample the + + + align:start position:0% +wave vectors into your sample the +whether that takes on plus or minus is + + align:start position:0% +whether that takes on plus or minus is + + + align:start position:0% +whether that takes on plus or minus is +going to depend a lot on whether you + + align:start position:0% +going to depend a lot on whether you + + + align:start position:0% +going to depend a lot on whether you +have absorption or stimulated emission + + align:start position:0% +have absorption or stimulated emission + + + align:start position:0% +have absorption or stimulated emission +processes for instance and this is + + align:start position:0% +processes for instance and this is + + + align:start position:0% +processes for instance and this is +really just a reflection of uh the + + align:start position:0% +really just a reflection of uh the + + + align:start position:0% +really just a reflection of uh the +uh principle of momentum + + align:start position:0% +uh principle of momentum + + + align:start position:0% +uh principle of momentum +conservation for the sample um and for + + align:start position:0% +conservation for the sample um and for + + + align:start position:0% +conservation for the sample um and for +you know for the whole sequence of light + + align:start position:0% +you know for the whole sequence of light + + + align:start position:0% +you know for the whole sequence of light +interaction and similarly there has to + + align:start position:0% +interaction and similarly there has to + + + align:start position:0% +interaction and similarly there has to +be sort of an energy conservation + + align:start position:0% +be sort of an energy conservation + + + align:start position:0% +be sort of an energy conservation +statement and that will be reflected by + + align:start position:0% +statement and that will be reflected by + + + align:start position:0% +statement and that will be reflected by +the fact that the frequency of the + + align:start position:0% +the fact that the frequency of the + + + align:start position:0% +the fact that the frequency of the +radiated light is going to be related to + + align:start position:0% +radiated light is going to be related to + + + align:start position:0% +radiated light is going to be related to +some uh sums and differences over the + + align:start position:0% +some uh sums and differences over the + + + align:start position:0% +some uh sums and differences over the +frequencies of the incident field and + + align:start position:0% +frequencies of the incident field and + + + align:start position:0% +frequencies of the incident field and +this + + align:start position:0% + + + + align:start position:0% + +is we'll also establish what gives um + + align:start position:0% +is we'll also establish what gives um + + + align:start position:0% +is we'll also establish what gives um +rise to this energy conservation + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +all + + align:start position:0% + + + + align:start position:0% + +right a couple of more couple more + + align:start position:0% +right a couple of more couple more + + + align:start position:0% +right a couple of more couple more +definitions so for our work um what + + align:start position:0% +definitions so for our work um what + + + align:start position:0% +definitions so for our work um what +we're going to be doing is working with + + align:start position:0% +we're going to be doing is working with + + + align:start position:0% +we're going to be doing is working with +a + + align:start position:0% +a + + + align:start position:0% +a +uh + + align:start position:0% +uh + + + align:start position:0% +uh +semiclassical uh description of the + + align:start position:0% +semiclassical uh description of the + + + align:start position:0% +semiclassical uh description of the +light matter + + align:start position:0% +light matter + + + align:start position:0% +light matter +interaction and what we mean by that is + + align:start position:0% +interaction and what we mean by that is + + + align:start position:0% +interaction and what we mean by that is +that this is all going to be handled by + + align:start position:0% +that this is all going to be handled by + + + align:start position:0% +that this is all going to be handled by +taking a hamiltonian for the system to + + align:start position:0% +taking a hamiltonian for the system to + + + align:start position:0% +taking a hamiltonian for the system to +be a sum of two + + align:start position:0% +be a sum of two + + + align:start position:0% +be a sum of two +parts one is a hamiltonian that for the + + align:start position:0% +parts one is a hamiltonian that for the + + + align:start position:0% +parts one is a hamiltonian that for the +matter in your system and we'll you know + + align:start position:0% +matter in your system and we'll you know + + + align:start position:0% +matter in your system and we'll you know +we'll come up with various forms of what + + align:start position:0% +we'll come up with various forms of what + + + align:start position:0% +we'll come up with various forms of what +this hamiltonian might look like but uh + + align:start position:0% +this hamiltonian might look like but uh + + + align:start position:0% +this hamiltonian might look like but uh +the molecules are here and then we have + + align:start position:0% +the molecules are here and then we have + + + align:start position:0% +the molecules are here and then we have +an external + + align:start position:0% +an external + + + align:start position:0% +an external +potential um this is the external light + + align:start position:0% +potential um this is the external light + + + align:start position:0% +potential um this is the external light +Fields they act on the molecules + + align:start position:0% +Fields they act on the molecules + + + align:start position:0% +Fields they act on the molecules +creating uh coherent + + align:start position:0% +creating uh coherent + + + align:start position:0% +creating uh coherent +superpositions um and this these light + + align:start position:0% +superpositions um and this these light + + + align:start position:0% +superpositions um and this these light +Fields will just be treated like that an + + align:start position:0% +Fields will just be treated like that an + + + align:start position:0% +Fields will just be treated like that an +external potential we're not going to be + + align:start position:0% +external potential we're not going to be + + + align:start position:0% +external potential we're not going to be +calculating you know how the matter + + align:start position:0% +calculating you know how the matter + + + align:start position:0% +calculating you know how the matter +changes the light Fields uh we are just + + align:start position:0% +changes the light Fields uh we are just + + + align:start position:0% +changes the light Fields uh we are just +going and you know the matter will not + + align:start position:0% +going and you know the matter will not + + + align:start position:0% +going and you know the matter will not +influence them in any strong way they + + align:start position:0% +influence them in any strong way they + + + align:start position:0% +influence them in any strong way they +just act on the matter okay there's no + + align:start position:0% +just act on the matter okay there's no + + + align:start position:0% +just act on the matter okay there's no +we are not going to be taking care of + + align:start position:0% +we are not going to be taking care of + + + align:start position:0% +we are not going to be taking care of +energy conservation between the matter + + align:start position:0% +energy conservation between the matter + + + align:start position:0% +energy conservation between the matter +and the light for instance okay this + + align:start position:0% +and the light for instance okay this + + + align:start position:0% +and the light for instance okay this +external potential is going to be + + align:start position:0% +external potential is going to be + + + align:start position:0% +external potential is going to be +written sort of in the dipole + + align:start position:0% +written sort of in the dipole + + + align:start position:0% +written sort of in the dipole +approximation + + align:start position:0% + + + + align:start position:0% + +um it's going to be you know related to + + align:start position:0% +um it's going to be you know related to + + + align:start position:0% +um it's going to be you know related to +the dipole moment of the sample and uh + + align:start position:0% +the dipole moment of the sample and uh + + + align:start position:0% +the dipole moment of the sample and uh +the incid the incident electric field + + align:start position:0% +the incid the incident electric field + + + align:start position:0% +the incid the incident electric field +now in general I just want you to notice + + align:start position:0% +now in general I just want you to notice + + + align:start position:0% +now in general I just want you to notice +with this that you know when we say this + + align:start position:0% +with this that you know when we say this + + + align:start position:0% +with this that you know when we say this +we now can mean this incident field is + + align:start position:0% +we now can mean this incident field is + + + align:start position:0% +we now can mean this incident field is +that may be the superposition of many + + align:start position:0% +that may be the superposition of many + + + align:start position:0% +that may be the superposition of many +different fields okay maybe not just one + + align:start position:0% +different fields okay maybe not just one + + + align:start position:0% +different fields okay maybe not just one +all right + + align:start position:0% + + + + align:start position:0% + +um okay and um we're going to be + + align:start position:0% +um okay and um we're going to be + + + align:start position:0% +um okay and um we're going to be +treating a lot of this in the + + align:start position:0% +treating a lot of this in the + + + align:start position:0% +treating a lot of this in the +interaction picture that we uh developed + + align:start position:0% +interaction picture that we uh developed + + + align:start position:0% +interaction picture that we uh developed +in + + align:start position:0% +in + + + align:start position:0% +in +574 so that uh we're really going to be + + align:start position:0% +574 so that uh we're really going to be + + + align:start position:0% +574 so that uh we're really going to be +talking about the time evolution of the + + align:start position:0% +talking about the time evolution of the + + + align:start position:0% +talking about the time evolution of the +dipole moment of the sample and um + + align:start position:0% +dipole moment of the sample and um + + + align:start position:0% +dipole moment of the sample and um +remember we'll we've written that + + align:start position:0% + + + + align:start position:0% + +as time evolution of the dipole moment + + align:start position:0% +as time evolution of the dipole moment + + + align:start position:0% +as time evolution of the dipole moment +under the material + + align:start position:0% +under the material + + + align:start position:0% +under the material +hamiltonian okay and you'll you'll + + align:start position:0% +hamiltonian okay and you'll you'll + + + align:start position:0% +hamiltonian okay and you'll you'll +notice this is not going to be the last + + align:start position:0% +notice this is not going to be the last + + + align:start position:0% +notice this is not going to be the last +time that I forget to put H bars in I'm + + align:start position:0% +time that I forget to put H bars in I'm + + + align:start position:0% +time that I forget to put H bars in I'm +particularly forgetful with h + + align:start position:0% +particularly forgetful with h + + + align:start position:0% +particularly forgetful with h +bars um and okay just for the record + + align:start position:0% +bars um and okay just for the record + + + align:start position:0% +bars um and okay just for the record +that I know + + align:start position:0% +that I know + + + align:start position:0% +that I know +them + + align:start position:0% +them + + + align:start position:0% +them +um and what we are going to do is assume + + align:start position:0% +um and what we are going to do is assume + + + align:start position:0% +um and what we are going to do is assume +that + + align:start position:0% +that + + + align:start position:0% +that +uh that there's just a direct + + align:start position:0% +uh that there's just a direct + + + align:start position:0% +uh that there's just a direct +correlation between the + + align:start position:0% +correlation between the + + + align:start position:0% +correlation between the +polarization and a non equilibrium + + align:start position:0% +polarization and a non equilibrium + + + align:start position:0% +polarization and a non equilibrium +average over the uh you + + align:start position:0% +average over the uh you + + + align:start position:0% +average over the uh you +know microscopic dipole moment for the + + align:start position:0% +know microscopic dipole moment for the + + + align:start position:0% +know microscopic dipole moment for the +system + + align:start position:0% + + + + align:start position:0% + +okay all + + align:start position:0% +okay all + + + align:start position:0% +okay all +right any uh any questions has popped + + align:start position:0% + + + + align:start position:0% + +up all + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +right okay let's um so now just to get + + align:start position:0% +right okay let's um so now just to get + + + align:start position:0% +right okay let's um so now just to get +started Let's uh talk a bit + + align:start position:0% +started Let's uh talk a bit + + + align:start position:0% +started Let's uh talk a bit +about just a a a linear absorption + + align:start position:0% +about just a a a linear absorption + + + align:start position:0% +about just a a a linear absorption +experiment um and and just sort of work + + align:start position:0% +experiment um and and just sort of work + + + align:start position:0% +experiment um and and just sort of work +through what hopefully is pretty + + align:start position:0% +through what hopefully is pretty + + + align:start position:0% +through what hopefully is pretty +comfortable to you did you have a + + align:start position:0% +comfortable to you did you have a + + + align:start position:0% +comfortable to you did you have a +question so you're just say that the + + align:start position:0% +question so you're just say that the + + + align:start position:0% +question so you're just say that the +polarization is going to be we're going + + align:start position:0% +polarization is going to be we're going + + + align:start position:0% +polarization is going to be we're going +to think of it as a Time average off the + + align:start position:0% +to think of it as a Time average off the + + + align:start position:0% +to think of it as a Time average off the +that a time it it's a non-equilibrium + + align:start position:0% +that a time it it's a non-equilibrium + + + align:start position:0% +that a time it it's a non-equilibrium +Ensemble + + align:start position:0% +Ensemble + + + align:start position:0% +Ensemble +average yeah so I mean we're we're + + align:start position:0% +average yeah so I mean we're we're + + + align:start position:0% +average yeah so I mean we're we're +basically it's just another way of + + align:start position:0% +basically it's just another way of + + + align:start position:0% +basically it's just another way of +saying what I wrote up here right you + + align:start position:0% +saying what I wrote up here right you + + + align:start position:0% +saying what I wrote up here right you +know that at any moment in time you do a + + align:start position:0% +know that at any moment in time you do a + + + align:start position:0% +know that at any moment in time you do a +um an average over the position of all + + align:start position:0% +um an average over the position of all + + + align:start position:0% +um an average over the position of all +the charges in your sample + + align:start position:0% +the charges in your sample + + + align:start position:0% +the charges in your sample +microscopically and + + align:start position:0% +microscopically and + + + align:start position:0% +microscopically and +um and and I'm using the bar for non-e + + align:start position:0% +um and and I'm using the bar for non-e + + + align:start position:0% +um and and I'm using the bar for non-e +equilibrium just because I want to + + align:start position:0% +equilibrium just because I want to + + + align:start position:0% +equilibrium just because I want to +use + + align:start position:0% +use + + + align:start position:0% +use +uh this is a uh the brackets as an + + align:start position:0% +uh this is a uh the brackets as an + + + align:start position:0% +uh this is a uh the brackets as an +equilibrium + + align:start position:0% + + + + align:start position:0% + +average but you know how it's basically + + align:start position:0% +average but you know how it's basically + + + align:start position:0% +average but you know how it's basically +how do the dipoles respond after you hit + + align:start position:0% +how do the dipoles respond after you hit + + + align:start position:0% +how do the dipoles respond after you hit +the equilibrium system you know with the + + align:start position:0% +the equilibrium system you know with the + + + align:start position:0% +the equilibrium system you know with the +light + + align:start position:0% + + + + align:start position:0% + +okay all right so um I I just wanted to + + align:start position:0% +okay all right so um I I just wanted to + + + align:start position:0% +okay all right so um I I just wanted to +talk about this idea of um uh linear + + align:start position:0% +talk about this idea of um uh linear + + + align:start position:0% +talk about this idea of um uh linear +spectroscopy as a as a coherent method + + align:start position:0% +spectroscopy as a as a coherent method + + + align:start position:0% +spectroscopy as a as a coherent method +so back to I've got a macroscopic sample + + align:start position:0% +so back to I've got a macroscopic sample + + + align:start position:0% +so back to I've got a macroscopic sample +I'm going to have + + align:start position:0% +I'm going to have + + + align:start position:0% +I'm going to have +uh incident radiation uh come into the + + align:start position:0% +uh incident radiation uh come into the + + + align:start position:0% +uh incident radiation uh come into the +sample I usually characterize it by some + + align:start position:0% +sample I usually characterize it by some + + + align:start position:0% +sample I usually characterize it by some +sort of an + + align:start position:0% +sort of an + + + align:start position:0% +sort of an +intensity um and that's related to + + align:start position:0% +intensity um and that's related to + + + align:start position:0% +intensity um and that's related to +you know the modulus squared of the + + align:start position:0% +you know the modulus squared of the + + + align:start position:0% +you know the modulus squared of the +electric field um and we and I'd like to + + align:start position:0% +electric field um and we and I'd like to + + + align:start position:0% +electric field um and we and I'd like to +sort of establish the idea that you now + + align:start position:0% +sort of establish the idea that you now + + + align:start position:0% +sort of establish the idea that you now +we're going to have an oscillating + + align:start position:0% +we're going to have an oscillating + + + align:start position:0% +we're going to have an oscillating +polarization that um those accelerated + + align:start position:0% +polarization that um those accelerated + + + align:start position:0% +polarization that um those accelerated +dipoles induced By the Light field are + + align:start position:0% +dipoles induced By the Light field are + + + align:start position:0% +dipoles induced By the Light field are +actually going to uh lead to radiated + + align:start position:0% +actually going to uh lead to radiated + + + align:start position:0% +actually going to uh lead to radiated +light and if you say that there's an + + align:start position:0% +light and if you say that there's an + + + align:start position:0% +light and if you say that there's an +incident wave Vector to the light coming + + align:start position:0% +incident wave Vector to the light coming + + + align:start position:0% +incident wave Vector to the light coming +in we want to establish that the the + + align:start position:0% +in we want to establish that the the + + + align:start position:0% +in we want to establish that the the +outgoing wave Vector is the same as the + + align:start position:0% +outgoing wave Vector is the same as the + + + align:start position:0% +outgoing wave Vector is the same as the +incoming wave Vector um and it just + + align:start position:0% +incoming wave Vector um and it just + + + align:start position:0% +incoming wave Vector um and it just +happens + + align:start position:0% +happens + + + align:start position:0% +happens +to coincide with the wave Vector for the + + align:start position:0% +to coincide with the wave Vector for the + + + align:start position:0% +to coincide with the wave Vector for the +outgoing uh for the transmitted light + + align:start position:0% +outgoing uh for the transmitted light + + + align:start position:0% +outgoing uh for the transmitted light +and that there's actually a destructive + + align:start position:0% +and that there's actually a destructive + + + align:start position:0% +and that there's actually a destructive +interference between these two fields + + align:start position:0% +interference between these two fields + + + align:start position:0% +interference between these two fields +that looks like + + align:start position:0% +that looks like + + + align:start position:0% +that looks like +absorption okay so and the way we + + align:start position:0% +absorption okay so and the way we + + + align:start position:0% +absorption okay so and the way we +measure that in a traditional absorption + + align:start position:0% +measure that in a traditional absorption + + + align:start position:0% +measure that in a traditional absorption +experiment is that you know we measure + + align:start position:0% +experiment is that you know we measure + + + align:start position:0% +experiment is that you know we measure +intensities there's the int it of the + + align:start position:0% +intensities there's the int it of the + + + align:start position:0% +intensities there's the int it of the +outgoing + + align:start position:0% + + + + align:start position:0% + +light that's just going to be some + + align:start position:0% +light that's just going to be some + + + align:start position:0% +light that's just going to be some +change Delta I on top of the incident + + align:start position:0% +change Delta I on top of the incident + + + align:start position:0% +change Delta I on top of the incident +L okay and + + align:start position:0% +L okay and + + + align:start position:0% +L okay and +uh I out is again related to the modulus + + align:start position:0% +uh I out is again related to the modulus + + + align:start position:0% +uh I out is again related to the modulus +squared of + + align:start position:0% +squared of + + + align:start position:0% +squared of +the um of well let me see + + align:start position:0% +the um of well let me see + + + align:start position:0% +the um of well let me see +yeah some over all the outgoing fields + + align:start position:0% + + + + align:start position:0% + +um okay so um we've sort of established + + align:start position:0% +um okay so um we've sort of established + + + align:start position:0% +um okay so um we've sort of established +before that in a traditional picture of + + align:start position:0% +before that in a traditional picture of + + + align:start position:0% +before that in a traditional picture of +the um polarization and therefore the um + + align:start position:0% +the um polarization and therefore the um + + + align:start position:0% +the um polarization and therefore the um +radiated signal out of the sample is + + align:start position:0% +radiated signal out of the sample is + + + align:start position:0% +radiated signal out of the sample is +proportional to the susceptibility so + + align:start position:0% +proportional to the susceptibility so + + + align:start position:0% +proportional to the susceptibility so +let's uh think a little bit about what + + align:start position:0% +let's uh think a little bit about what + + + align:start position:0% +let's uh think a little bit about what +the intensity of the outgoing light + + align:start position:0% +the intensity of the outgoing light + + + align:start position:0% +the intensity of the outgoing light +looks like there's really two fields + + align:start position:0% +looks like there's really two fields + + + align:start position:0% +looks like there's really two fields +that are going to come out of the sample + + align:start position:0% + + + + align:start position:0% + +there's the outgoing + + align:start position:0% +there's the outgoing + + + align:start position:0% +there's the outgoing +field and then there's a radiated signal + + align:start position:0% +field and then there's a radiated signal + + + align:start position:0% +field and then there's a radiated signal +field and we're going to observe the + + align:start position:0% +field and we're going to observe the + + + align:start position:0% +field and we're going to observe the +intensity so the modulus square of that + + align:start position:0% +intensity so the modulus square of that + + + align:start position:0% +intensity so the modulus square of that +sum and this is going to we know this + + align:start position:0% +sum and this is going to we know this + + + align:start position:0% +sum and this is going to we know this +sort of from our + + align:start position:0% +sort of from our + + + align:start position:0% +sort of from our +um description here that um I guess I + + align:start position:0% +um description here that um I guess I + + + align:start position:0% +um description here that um I guess I +didn't point it out before but notice + + align:start position:0% +didn't point it out before but notice + + + align:start position:0% +didn't point it out before but notice +that there is an eye out here that means + + align:start position:0% +that there is an eye out here that means + + + align:start position:0% +that there is an eye out here that means +we've got a 90° phase shift between the + + align:start position:0% +we've got a 90° phase shift between the + + + align:start position:0% +we've got a 90° phase shift between the +oscillations of the polarization + + align:start position:0% +oscillations of the polarization + + + align:start position:0% +oscillations of the polarization +and the signal field + + align:start position:0% +and the signal field + + + align:start position:0% +and the signal field +okay and and I mean that that shouldn't + + align:start position:0% +okay and and I mean that that shouldn't + + + align:start position:0% +okay and and I mean that that shouldn't +come as you know any big surprise you + + align:start position:0% +come as you know any big surprise you + + + align:start position:0% +come as you know any big surprise you +know the the uh biggest Fields is when + + align:start position:0% +know the the uh biggest Fields is when + + + align:start position:0% +know the the uh biggest Fields is when +you have the fastest motion of the + + align:start position:0% +you have the fastest motion of the + + + align:start position:0% +you have the fastest motion of the +charges and there's this 90° + + align:start position:0% +charges and there's this 90° + + + align:start position:0% +charges and there's this 90° +relationship with how fast the you know + + align:start position:0% +relationship with how fast the you know + + + align:start position:0% +relationship with how fast the you know +they um the charges are moving and the + + align:start position:0% +they um the charges are moving and the + + + align:start position:0% +they um the charges are moving and the +magnitude of the signal field so what + + align:start position:0% +magnitude of the signal field so what + + + align:start position:0% +magnitude of the signal field so what +we're saying is + + align:start position:0% +we're saying is + + + align:start position:0% +we're saying is +um uh we're just going to write this now + + align:start position:0% +um uh we're just going to write this now + + + align:start position:0% +um uh we're just going to write this now +in terms of the polarization in the + + align:start position:0% +in terms of the polarization in the + + + align:start position:0% +in terms of the polarization in the +sample okay and now we'll make the + + align:start position:0% +sample okay and now we'll make the + + + align:start position:0% +sample okay and now we'll make the +approximation also + + align:start position:0% +approximation also + + + align:start position:0% +approximation also +um that uh this transmitted light field + + align:start position:0% +um that uh this transmitted light field + + + align:start position:0% +um that uh this transmitted light field +that the interaction is so weak that + + align:start position:0% +that the interaction is so weak that + + + align:start position:0% +that the interaction is so weak that +this transmitted light field is really + + align:start position:0% +this transmitted light field is really + + + align:start position:0% +this transmitted light field is really +not changed at all that it's really + + align:start position:0% +not changed at all that it's really + + + align:start position:0% +not changed at all that it's really +identical to the incoming + + align:start position:0% +identical to the incoming + + + align:start position:0% +identical to the incoming +field um so this is approximately equal + + align:start position:0% +field um so this is approximately equal + + + align:start position:0% +field um so this is approximately equal +to + + align:start position:0% +to + + + align:start position:0% +to +incident okay and now for the + + align:start position:0% +incident okay and now for the + + + align:start position:0% +incident okay and now for the +polarization this is just the + + align:start position:0% +polarization this is just the + + + align:start position:0% +polarization this is just the +susceptibility times the incident + + align:start position:0% + + + + align:start position:0% + +field okay and + + align:start position:0% + + + + align:start position:0% + +uh so what do we have + + align:start position:0% + + + + align:start position:0% + +let's see if we sort of + + align:start position:0% + + + + align:start position:0% + +substitute uh just recognize that the + + align:start position:0% +substitute uh just recognize that the + + + align:start position:0% +substitute uh just recognize that the +susceptibility is composed of a real and + + align:start position:0% +susceptibility is composed of a real and + + + align:start position:0% +susceptibility is composed of a real and +an imaginary + + align:start position:0% +an imaginary + + + align:start position:0% +an imaginary +part and we uh substitute that in here + + align:start position:0% +part and we uh substitute that in here + + + align:start position:0% +part and we uh substitute that in here +and really evaluate all of our terms the + + align:start position:0% +and really evaluate all of our terms the + + + align:start position:0% +and really evaluate all of our terms the +two leading terms + + align:start position:0% + + + + align:start position:0% + +uh we can you know factor out the + + align:start position:0% +uh we can you know factor out the + + + align:start position:0% +uh we can you know factor out the +intensity of the incident light + + align:start position:0% +intensity of the incident light + + + align:start position:0% +intensity of the incident light +field and the leading term is just one + + align:start position:0% +field and the leading term is just one + + + align:start position:0% +field and the leading term is just one +next term is just twice the imaginary + + align:start position:0% +next term is just twice the imaginary + + + align:start position:0% +next term is just twice the imaginary +part of the + + align:start position:0% +part of the + + + align:start position:0% +part of the +susceptibility and this just sort of + + align:start position:0% +susceptibility and this just sort of + + + align:start position:0% +susceptibility and this just sort of +confirms this you know idea we've uh at + + align:start position:0% +confirms this you know idea we've uh at + + + align:start position:0% +confirms this you know idea we've uh at +least in 574 we've established this + + align:start position:0% +least in 574 we've established this + + + align:start position:0% +least in 574 we've established this +before that uh it is the imaginary part + + align:start position:0% +before that uh it is the imaginary part + + + align:start position:0% +before that uh it is the imaginary part +of the susceptibility the imaginary part + + align:start position:0% +of the susceptibility the imaginary part + + + align:start position:0% +of the susceptibility the imaginary part +of um the response that tells you about + + align:start position:0% +of um the response that tells you about + + + align:start position:0% +of um the response that tells you about +uh the absorption of light uh the + + align:start position:0% +uh the absorption of light uh the + + + align:start position:0% +uh the absorption of light uh the +absorption of energy from the light + + align:start position:0% +absorption of energy from the light + + + align:start position:0% +absorption of energy from the light +field okay so and this is why there's + + align:start position:0% +field okay so and this is why there's + + + align:start position:0% +field okay so and this is why there's +even though there's all these Square + + align:start position:0% +even though there's all these Square + + + align:start position:0% +even though there's all these Square +relationships uh you know between the + + align:start position:0% +relationships uh you know between the + + + align:start position:0% +relationships uh you know between the +fields and the intensities You observe + + align:start position:0% +fields and the intensities You observe + + + align:start position:0% +fields and the intensities You observe +this is why there is a linear + + align:start position:0% +this is why there is a linear + + + align:start position:0% +this is why there is a linear +relationship between intensity + + align:start position:0% +relationship between intensity + + + align:start position:0% +relationship between intensity +changes and uh the response of the + + align:start position:0% + + + + align:start position:0% + +system all right so how how do we go + + align:start position:0% +system all right so how how do we go + + + align:start position:0% +system all right so how how do we go +about um Des any questions um how do we + + align:start position:0% +about um Des any questions um how do we + + + align:start position:0% +about um Des any questions um how do we +go about describing this as we you know + + align:start position:0% +go about describing this as we you know + + + align:start position:0% +go about describing this as we you know +go forward um you know we there are many + + align:start position:0% +go forward um you know we there are many + + + align:start position:0% +go forward um you know we there are many +ways of dealing with the nonlinear + + align:start position:0% +ways of dealing with the nonlinear + + + align:start position:0% +ways of dealing with the nonlinear +response uh in a Time domain picture + + align:start position:0% +response uh in a Time domain picture + + + align:start position:0% +response uh in a Time domain picture +it's very nice to treat it in terms of a + + align:start position:0% +it's very nice to treat it in terms of a + + + align:start position:0% +it's very nice to treat it in terms of a +response function right so um think of + + align:start position:0% + + + + align:start position:0% + +so so the linear response function here + + align:start position:0% +so so the linear response function here + + + align:start position:0% +so so the linear response function here +there's a step response to enforce + + align:start position:0% +there's a step response to enforce + + + align:start position:0% +there's a step response to enforce +causality but it's related to + + align:start position:0% +causality but it's related to + + + align:start position:0% +causality but it's related to +correlation functions in the dipole + + align:start position:0% +correlation functions in the dipole + + + align:start position:0% +correlation functions in the dipole +operator those the time dependence there + + align:start position:0% +operator those the time dependence there + + + align:start position:0% +operator those the time dependence there +is as we've defined before it's under + + align:start position:0% +is as we've defined before it's under + + + align:start position:0% +is as we've defined before it's under +the material hamiltonian but you can see + + align:start position:0% +the material hamiltonian but you can see + + + align:start position:0% +the material hamiltonian but you can see +that we have a couple of different + + align:start position:0% +that we have a couple of different + + + align:start position:0% +that we have a couple of different +correlations functions here we sometimes + + align:start position:0% +correlations functions here we sometimes + + + align:start position:0% +correlations functions here we sometimes +write this as C minus C star it's just + + align:start position:0% +write this as C minus C star it's just + + + align:start position:0% +write this as C minus C star it's just +the order of these operators now you + + align:start position:0% +the order of these operators now you + + + align:start position:0% +the order of these operators now you +know if you're evaluating a um in in + + align:start position:0% +know if you're evaluating a um in in + + + align:start position:0% +know if you're evaluating a um in in +linear response this is an equilibrium + + align:start position:0% +linear response this is an equilibrium + + + align:start position:0% +linear response this is an equilibrium +Ensemble average is performed over this + + align:start position:0% +Ensemble average is performed over this + + + align:start position:0% +Ensemble average is performed over this +product of operators you know we might + + align:start position:0% +product of operators you know we might + + + align:start position:0% +product of operators you know we might +think of this + + align:start position:0% + + + + align:start position:0% + +as + + align:start position:0% +as + + + align:start position:0% +as +n over + + align:start position:0% + + + + align:start position:0% + +um but and and uh sort of encoded in all + + align:start position:0% +um but and and uh sort of encoded in all + + + align:start position:0% +um but and and uh sort of encoded in all +of this is the fact that you're always + + align:start position:0% +of this is the fact that you're always + + + align:start position:0% +of this is the fact that you're always +keeping track of the evolution of um at + + align:start position:0% +keeping track of the evolution of um at + + + align:start position:0% +keeping track of the evolution of um at +least two different coherences when you + + align:start position:0% +least two different coherences when you + + + align:start position:0% +least two different coherences when you +evaluate you know how a system behaves + + align:start position:0% +evaluate you know how a system behaves + + + align:start position:0% +evaluate you know how a system behaves +and sometimes we've written this also as + + align:start position:0% +and sometimes we've written this also as + + + align:start position:0% +and sometimes we've written this also as +this may be a superposition of a wave + + align:start position:0% +this may be a superposition of a wave + + + align:start position:0% +this may be a superposition of a wave +pack get propagating on the ground uh + + align:start position:0% +pack get propagating on the ground uh + + + align:start position:0% +pack get propagating on the ground uh +state of your system and on the excited + + align:start position:0% +state of your system and on the excited + + + align:start position:0% +state of your system and on the excited +state of your + + align:start position:0% +state of your + + + align:start position:0% +state of your +system so keeping track of how the + + align:start position:0% +system so keeping track of how the + + + align:start position:0% +system so keeping track of how the +system evolves is already getting a + + align:start position:0% +system evolves is already getting a + + + align:start position:0% +system evolves is already getting a +little bit tricky here and when you go + + align:start position:0% +little bit tricky here and when you go + + + align:start position:0% +little bit tricky here and when you go +to nonlinear spectroscopy where you have + + align:start position:0% +to nonlinear spectroscopy where you have + + + align:start position:0% +to nonlinear spectroscopy where you have +to sort of establish what the phase + + align:start position:0% +to sort of establish what the phase + + + align:start position:0% +to sort of establish what the phase +relationships are between different + + align:start position:0% +relationships are between different + + + align:start position:0% +relationships are between different +coherences after you know another + + align:start position:0% +coherences after you know another + + + align:start position:0% +coherences after you know another +electric field is applied to the sample + + align:start position:0% +electric field is applied to the sample + + + align:start position:0% +electric field is applied to the sample +uh bookkeeping starts to become really + + align:start position:0% +uh bookkeeping starts to become really + + + align:start position:0% +uh bookkeeping starts to become really +complicated and this is is part of the + + align:start position:0% +complicated and this is is part of the + + + align:start position:0% +complicated and this is is part of the +motivation for using the density Matrix + + align:start position:0% +motivation for using the density Matrix + + + align:start position:0% +motivation for using the density Matrix +to um describe nonlinear response it's + + align:start position:0% +to um describe nonlinear response it's + + + align:start position:0% +to um describe nonlinear response it's +um it becomes much more practical as a + + align:start position:0% +um it becomes much more practical as a + + + align:start position:0% +um it becomes much more practical as a +bookkeeping tool and it also for + + align:start position:0% +bookkeeping tool and it also for + + + align:start position:0% +bookkeeping tool and it also for +condensed phase problems it turns out to + + align:start position:0% +condensed phase problems it turns out to + + + align:start position:0% +condensed phase problems it turns out to +have other advantages in terms of + + align:start position:0% +have other advantages in terms of + + + align:start position:0% +have other advantages in terms of +talking about uh + + align:start position:0% + + + + align:start position:0% + +Dynamics okay so now going back to + + align:start position:0% +Dynamics okay so now going back to + + + align:start position:0% +Dynamics okay so now going back to +um linear + + align:start position:0% + + + + align:start position:0% + +spectroscopy let's let's + + align:start position:0% +spectroscopy let's let's + + + align:start position:0% +spectroscopy let's let's +um look at how we' treat the Dynamics + + align:start position:0% + + + + align:start position:0% + +there okay so the equation of motion + + align:start position:0% +there okay so the equation of motion + + + align:start position:0% +there okay so the equation of motion +rather than using the Schrodinger + + align:start position:0% +rather than using the Schrodinger + + + align:start position:0% +rather than using the Schrodinger +equation we'll use the Louisville + + align:start position:0% +equation we'll use the Louisville + + + align:start position:0% +equation we'll use the Louisville +equation so equation of motion for the + + align:start position:0% +equation so equation of motion for the + + + align:start position:0% +equation so equation of motion for the +uh density Matrix I'm just being very + + align:start position:0% +uh density Matrix I'm just being very + + + align:start position:0% +uh density Matrix I'm just being very +explicit at the moment won't be later + + align:start position:0% +explicit at the moment won't be later + + + align:start position:0% +explicit at the moment won't be later +that we're writing everything in the + + align:start position:0% +that we're writing everything in the + + + align:start position:0% +that we're writing everything in the +interaction picture so that is the time + + align:start position:0% +interaction picture so that is the time + + + align:start position:0% +interaction picture so that is the time +evolution of this uh density Matrix um + + align:start position:0% +evolution of this uh density Matrix um + + + align:start position:0% +evolution of this uh density Matrix um +you know follows just like the rest um + + align:start position:0% +you know follows just like the rest um + + + align:start position:0% +you know follows just like the rest um +of The + + align:start position:0% +of The + + + align:start position:0% +of The +Operators um and the uh this is the + + align:start position:0% +Operators um and the uh this is the + + + align:start position:0% +Operators um and the uh this is the +interaction picture + + align:start position:0% +interaction picture + + + align:start position:0% +interaction picture +hamiltonian which um also comes from the + + align:start position:0% +hamiltonian which um also comes from the + + + align:start position:0% +hamiltonian which um also comes from the +transformation of this + + align:start position:0% +transformation of this + + + align:start position:0% +transformation of this +interaction okay the solutions to this + + align:start position:0% +interaction okay the solutions to this + + + align:start position:0% +interaction okay the solutions to this +so there's another way of writing this + + align:start position:0% +so there's another way of writing this + + + align:start position:0% +so there's another way of writing this +also + + align:start position:0% + + + + align:start position:0% + +um G is a super operator and it just + + align:start position:0% +um G is a super operator and it just + + + align:start position:0% +um G is a super operator and it just +implies exactly the same thing taking + + align:start position:0% +implies exactly the same thing taking + + + align:start position:0% +implies exactly the same thing taking +the commutator um with this interaction + + align:start position:0% +the commutator um with this interaction + + + align:start position:0% +the commutator um with this interaction +picture antonian okay so this is a Time + + align:start position:0% + + + + align:start position:0% + +propagator um now we can integrate this + + align:start position:0% +propagator um now we can integrate this + + + align:start position:0% +propagator um now we can integrate this +uh equation directly and this sort of + + align:start position:0% +uh equation directly and this sort of + + + align:start position:0% +uh equation directly and this sort of +forms the uh basis for a perturbative + + align:start position:0% +forms the uh basis for a perturbative + + + align:start position:0% +forms the uh basis for a perturbative +expansion of the density Matrix and this + + align:start position:0% +expansion of the density Matrix and this + + + align:start position:0% +expansion of the density Matrix and this +is going to be one of the tools we make + + align:start position:0% +is going to be one of the tools we make + + + align:start position:0% +is going to be one of the tools we make +a lot of use of right we are and this is + + align:start position:0% +a lot of use of right we are and this is + + + align:start position:0% +a lot of use of right we are and this is +the origin of talking about you know + + align:start position:0% +the origin of talking about you know + + + align:start position:0% +the origin of talking about you know +what order is a particular nonlinear + + align:start position:0% +what order is a particular nonlinear + + + align:start position:0% +what order is a particular nonlinear +spectroscopy how many light field + + align:start position:0% +spectroscopy how many light field + + + align:start position:0% +spectroscopy how many light field +interactions uh come into + + align:start position:0% +interactions uh come into + + + align:start position:0% +interactions uh come into +it + + align:start position:0% + + + + align:start position:0% + +so so I'm just doing a direct + + align:start position:0% +so so I'm just doing a direct + + + align:start position:0% +so so I'm just doing a direct +integration of + + align:start position:0% +integration of + + + align:start position:0% +integration of +this um equation + + align:start position:0% + + + + align:start position:0% + +T this in in and of itself is not a very + + align:start position:0% +T this in in and of itself is not a very + + + align:start position:0% +T this in in and of itself is not a very +practical equation because it is a + + align:start position:0% +practical equation because it is a + + + align:start position:0% +practical equation because it is a +function of + + align:start position:0% +function of + + + align:start position:0% +function of +itself um but uh this forms the basis + + align:start position:0% +itself um but uh this forms the basis + + + align:start position:0% +itself um but uh this forms the basis +for doing an iterative + + align:start position:0% +for doing an iterative + + + align:start position:0% +for doing an iterative +substitution of um this equation into + + align:start position:0% +substitution of um this equation into + + + align:start position:0% +substitution of um this equation into +itself and what you get is a + + align:start position:0% +itself and what you get is a + + + align:start position:0% +itself and what you get is a +perturbation series expansion which in + + align:start position:0% +perturbation series expansion which in + + + align:start position:0% +perturbation series expansion which in +which each + + align:start position:0% +which each + + + align:start position:0% +which each +term contains increasingly more and more + + align:start position:0% +term contains increasingly more and more + + + align:start position:0% +term contains increasingly more and more +interactions with the external light + + align:start position:0% +interactions with the external light + + + align:start position:0% +interactions with the external light +field so the first order solution is + + align:start position:0% +field so the first order solution is + + + align:start position:0% +field so the first order solution is +really to suggest that uh this term here + + align:start position:0% +really to suggest that uh this term here + + + align:start position:0% +really to suggest that uh this term here +is just the equilibrium density Matrix + + align:start position:0% +is just the equilibrium density Matrix + + + align:start position:0% +is just the equilibrium density Matrix +that you just have one light field + + align:start position:0% +that you just have one light field + + + align:start position:0% +that you just have one light field +interacting with the uh system and then + + align:start position:0% +interacting with the uh system and then + + + align:start position:0% +interacting with the uh system and then +watch the response to that um or uh if + + align:start position:0% +watch the response to that um or uh if + + + align:start position:0% +watch the response to that um or uh if +you're talking about nonlinear + + align:start position:0% +you're talking about nonlinear + + + align:start position:0% +you're talking about nonlinear +spectroscopies then you perform this + + align:start position:0% +spectroscopies then you perform this + + + align:start position:0% +spectroscopies then you perform this +iterative substitution multiple times up + + align:start position:0% +iterative substitution multiple times up + + + align:start position:0% +iterative substitution multiple times up +to the order that's relevant for your + + align:start position:0% +to the order that's relevant for your + + + align:start position:0% +to the order that's relevant for your +purposes um and + + align:start position:0% +purposes um and + + + align:start position:0% +purposes um and +uh right and then at the end what you're + + align:start position:0% +uh right and then at the end what you're + + + align:start position:0% +uh right and then at the end what you're +going to want is + + align:start position:0% +going to want is + + + align:start position:0% +going to want is +to + + align:start position:0% + + + + align:start position:0% + +um let's see at the end of the day when + + align:start position:0% +um let's see at the end of the day when + + + align:start position:0% +um let's see at the end of the day when +you want to look at an observable and + + align:start position:0% +you want to look at an observable and + + + align:start position:0% +you want to look at an observable and +calculate the polarization you're + + align:start position:0% +calculate the polarization you're + + + align:start position:0% +calculate the polarization you're +interested in you're going to + + align:start position:0% + + + + align:start position:0% + +Trace over the density Matrix and the + + align:start position:0% +Trace over the density Matrix and the + + + align:start position:0% +Trace over the density Matrix and the +dipole + + align:start position:0% +dipole + + + align:start position:0% +dipole +operator that's take the expectation + + align:start position:0% +operator that's take the expectation + + + align:start position:0% +operator that's take the expectation +value of the dipole operator at the end + + align:start position:0% +value of the dipole operator at the end + + + align:start position:0% +value of the dipole operator at the end +of all that + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so + + align:start position:0% + + + + align:start position:0% + +um so I I have to do it at least once + + align:start position:0% +um so I I have to do it at least once + + + align:start position:0% +um so I I have to do it at least once +let me um write it out in its gory + + align:start position:0% +let me um write it out in its gory + + + align:start position:0% +let me um write it out in its gory +detail um because we're going to use + + align:start position:0% +detail um because we're going to use + + + align:start position:0% +detail um because we're going to use +this quite a bit in general this um + + align:start position:0% +this quite a bit in general this um + + + align:start position:0% +this quite a bit in general this um +perturbative solution can be written as + + align:start position:0% +perturbative solution can be written as + + + align:start position:0% +perturbative solution can be written as +a sum of terms that we write as say the + + align:start position:0% +a sum of terms that we write as say the + + + align:start position:0% +a sum of terms that we write as say the +zeroth order first order second order + + align:start position:0% +zeroth order first order second order + + + align:start position:0% +zeroth order first order second order +and so on expansion in the density + + align:start position:0% +and so on expansion in the density + + + align:start position:0% +and so on expansion in the density +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +right Row one is the linear response it + + align:start position:0% +right Row one is the linear response it + + + align:start position:0% +right Row one is the linear response it +should look just like our traditional + + align:start position:0% +should look just like our traditional + + + align:start position:0% +should look just like our traditional +linear response function that I just + + align:start position:0% +linear response function that I just + + + align:start position:0% +linear response function that I just +erased + + align:start position:0% + + + + align:start position:0% + +um and the um the idea is the Assumption + + align:start position:0% +um and the um the idea is the Assumption + + + align:start position:0% +um and the um the idea is the Assumption +in all these problems is that we're + + align:start position:0% +in all these problems is that we're + + + align:start position:0% +in all these problems is that we're +going to initiate the system in a state + + align:start position:0% +going to initiate the system in a state + + + align:start position:0% +going to initiate the system in a state +of thermal equilibrium we'll call that + + align:start position:0% +of thermal equilibrium we'll call that + + + align:start position:0% +of thermal equilibrium we'll call that +row EQ and in fact the the zero order + + align:start position:0% +row EQ and in fact the the zero order + + + align:start position:0% +row EQ and in fact the the zero order +density Matrix is also row + + align:start position:0% +density Matrix is also row + + + align:start position:0% +density Matrix is also row +EQ um we're integrating over the time + + align:start position:0% +EQ um we're integrating over the time + + + align:start position:0% +EQ um we're integrating over the time +development of the system under one time + + align:start position:0% +development of the system under one time + + + align:start position:0% +development of the system under one time +variable + + align:start position:0% +variable + + + align:start position:0% +variable +T1 row + + align:start position:0% + + + + align:start position:0% + +two is going to now look like a Time + + align:start position:0% +two is going to now look like a Time + + + align:start position:0% +two is going to now look like a Time +ordered + + align:start position:0% + + + + align:start position:0% + +expression and it's going to involve + + align:start position:0% +expression and it's going to involve + + + align:start position:0% +expression and it's going to involve +nested + + align:start position:0% + + + + align:start position:0% + +commentators let's y That's fine okay so + + align:start position:0% +commentators let's y That's fine okay so + + + align:start position:0% +commentators let's y That's fine okay so +I mean I think you'll see sort of how + + align:start position:0% +I mean I think you'll see sort of how + + + align:start position:0% +I mean I think you'll see sort of how +this uh develops that you have a um yeah + + align:start position:0% +this uh develops that you have a um yeah + + + align:start position:0% +this uh develops that you have a um yeah +I guess what I one thing I should point + + align:start position:0% +I guess what I one thing I should point + + + align:start position:0% +I guess what I one thing I should point +out here is these + + align:start position:0% +out here is these + + + align:start position:0% +out here is these +time variables in this linear case as + + align:start position:0% +time variables in this linear case as + + + align:start position:0% +time variables in this linear case as +time + + align:start position:0% +time + + + align:start position:0% +time +progresses we're going to make an + + align:start position:0% +progresses we're going to make an + + + align:start position:0% +progresses we're going to make an +observation of the state of the system + + align:start position:0% +observation of the state of the system + + + align:start position:0% +observation of the state of the system +at time + + align:start position:0% +at time + + + align:start position:0% +at time +T and we're going to relate that to + + align:start position:0% +T and we're going to relate that to + + + align:start position:0% +T and we're going to relate that to +everything that preceded that time we're + + align:start position:0% +everything that preceded that time we're + + + align:start position:0% +everything that preceded that time we're +going to do that by integrating over a + + align:start position:0% +going to do that by integrating over a + + + align:start position:0% +going to do that by integrating over a +variable um T1 T1 is a a Time Point + + align:start position:0% +variable um T1 T1 is a a Time Point + + + align:start position:0% +variable um T1 T1 is a a Time Point +preceding T and that point is the point + + align:start position:0% +preceding T and that point is the point + + + align:start position:0% +preceding T and that point is the point +at which one integrate interacts with + + align:start position:0% +at which one integrate interacts with + + + align:start position:0% +at which one integrate interacts with +the light field and drives the dipoles + + align:start position:0% +the light field and drives the dipoles + + + align:start position:0% +the light field and drives the dipoles +of the sample and the behavior at T is + + align:start position:0% +of the sample and the behavior at T is + + + align:start position:0% +of the sample and the behavior at T is +just the integrated history over that + + align:start position:0% +just the integrated history over that + + + align:start position:0% +just the integrated history over that +single interaction the second order + + align:start position:0% +single interaction the second order + + + align:start position:0% +single interaction the second order +response just takes it a step further + + align:start position:0% +response just takes it a step further + + + align:start position:0% +response just takes it a step further +but includes you know the fact that + + align:start position:0% +but includes you know the fact that + + + align:start position:0% +but includes you know the fact that +there is a specific time ordering + + align:start position:0% +there is a specific time ordering + + + align:start position:0% +there is a specific time ordering +enforced um by the limits of this + + align:start position:0% +enforced um by the limits of this + + + align:start position:0% +enforced um by the limits of this +integral that T1 must precede T2 which + + align:start position:0% +integral that T1 must precede T2 which + + + align:start position:0% +integral that T1 must precede T2 which +must precede the point of observation T + + align:start position:0% +must precede the point of observation T + + + align:start position:0% +must precede the point of observation T +um and we're going to + + align:start position:0% +um and we're going to + + + align:start position:0% +um and we're going to +integrate T1 up for all values up to T2 + + align:start position:0% +integrate T1 up for all values up to T2 + + + align:start position:0% +integrate T1 up for all values up to T2 +and say that first + + align:start position:0% +and say that first + + + align:start position:0% +and say that first +interaction must preced a second light + + align:start position:0% +interaction must preced a second light + + + align:start position:0% +interaction must preced a second light +field interaction which must pred + + align:start position:0% +field interaction which must pred + + + align:start position:0% +field interaction which must pred +observing the + + align:start position:0% + + + + align:start position:0% + +system um so let's see terms of um + + align:start position:0% +system um so let's see terms of um + + + align:start position:0% +system um so let's see terms of um +the going so we're going to make use of + + align:start position:0% +the going so we're going to make use of + + + align:start position:0% +the going so we're going to make use of +many of these terms but now just going + + align:start position:0% +many of these terms but now just going + + + align:start position:0% +many of these terms but now just going +back briefly to the case of linear + + align:start position:0% +back briefly to the case of linear + + + align:start position:0% +back briefly to the case of linear +spectroscopy um you know the + + align:start position:0% +spectroscopy um you know the + + + align:start position:0% +spectroscopy um you know the +polarization of the system which is in + + align:start position:0% +polarization of the system which is in + + + align:start position:0% +polarization of the system which is in +turn proportional to the signal that you + + align:start position:0% +turn proportional to the signal that you + + + align:start position:0% +turn proportional to the signal that you +see this just comes from tracing over + + align:start position:0% +see this just comes from tracing over + + + align:start position:0% +see this just comes from tracing over +the product of + + align:start position:0% +the product of + + + align:start position:0% +the product of +the density Matrix times the first order + + align:start position:0% +the density Matrix times the first order + + + align:start position:0% +the density Matrix times the first order +expansion of the um dens sorry dipole + + align:start position:0% +expansion of the um dens sorry dipole + + + align:start position:0% +expansion of the um dens sorry dipole +operator and the first order expansion + + align:start position:0% +operator and the first order expansion + + + align:start position:0% +operator and the first order expansion +of the density Matrix we substitute this + + align:start position:0% +of the density Matrix we substitute this + + + align:start position:0% +of the density Matrix we substitute this +into + + align:start position:0% + + + + align:start position:0% + +here let's see this is we're going to + + align:start position:0% +here let's see this is we're going to + + + align:start position:0% +here let's see this is we're going to +start the system at equilibrium so our + + align:start position:0% +start the system at equilibrium so our + + + align:start position:0% +start the system at equilibrium so our +initial point point is minus + + align:start position:0% +initial point point is minus + + + align:start position:0% +initial point point is minus +infinity + + align:start position:0% + + + + align:start position:0% + +T1 + + align:start position:0% +T1 + + + align:start position:0% +T1 +row this is row + + align:start position:0% + + + + align:start position:0% + +EQ and uh now we can let's + + align:start position:0% + + + + align:start position:0% + +see right okay now we can manipulate + + align:start position:0% +see right okay now we can manipulate + + + align:start position:0% +see right okay now we can manipulate +things around a little bit um and also + + align:start position:0% +things around a little bit um and also + + + align:start position:0% +things around a little bit um and also +switch integration + + align:start position:0% +switch integration + + + align:start position:0% +switch integration +variables um we're the way we're going + + align:start position:0% +variables um we're the way we're going + + + align:start position:0% +variables um we're the way we're going +to label time variables is T's will + + align:start position:0% +to label time variables is T's will + + + align:start position:0% +to label time variables is T's will +refer to a point of interaction and a + + align:start position:0% +refer to a point of interaction and a + + + align:start position:0% +refer to a point of interaction and a +point of observation and we'll use to As + + align:start position:0% +point of observation and we'll use to As + + + align:start position:0% +point of observation and we'll use to As +Time intervals the difference between + + align:start position:0% +Time intervals the difference between + + + align:start position:0% +Time intervals the difference between +those two so let's define um to one as + + align:start position:0% +those two so let's define um to one as + + + align:start position:0% +those two so let's define um to one as +being T + + align:start position:0% +being T + + + align:start position:0% +being T +minus T1 and I'll let you do sort of a + + align:start position:0% +minus T1 and I'll let you do sort of a + + + align:start position:0% +minus T1 and I'll let you do sort of a +the variable transformation here and you + + align:start position:0% +the variable transformation here and you + + + align:start position:0% +the variable transformation here and you +can uh convince yourself after + + align:start position:0% +can uh convince yourself after + + + align:start position:0% +can uh convince yourself after +substituting um minus + + align:start position:0% +substituting um minus + + + align:start position:0% +substituting um minus +mui of + + align:start position:0% +mui of + + + align:start position:0% +mui of +t1. + + align:start position:0% +t1. + + + align:start position:0% +t1. +E1 what this looks like + + align:start position:0% + + + + align:start position:0% + +okay and so just by comparing these you + + align:start position:0% +okay and so just by comparing these you + + + align:start position:0% +okay and so just by comparing these you +can see we sort of recover what we + + align:start position:0% +can see we sort of recover what we + + + align:start position:0% +can see we sort of recover what we +expect as the response function so this + + align:start position:0% +expect as the response function so this + + + align:start position:0% +expect as the response function so this +IH + + align:start position:0% +IH + + + align:start position:0% +IH +Bar times the uh Trace over + + align:start position:0% +Bar times the uh Trace over + + + align:start position:0% +Bar times the uh Trace over +the commutator and the dipole + + align:start position:0% +the commutator and the dipole + + + align:start position:0% +the commutator and the dipole +operator at time zero and time T times + + align:start position:0% +operator at time zero and time T times + + + align:start position:0% +operator at time zero and time T times +the equilibrium density Matrix this is + + align:start position:0% +the equilibrium density Matrix this is + + + align:start position:0% +the equilibrium density Matrix this is +just the linear response + + align:start position:0% +just the linear response + + + align:start position:0% +just the linear response +function + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so okay uh okay so we've uh written it + + align:start position:0% +so okay uh okay so we've uh written it + + + align:start position:0% +so okay uh okay so we've uh written it +this way and now just to wrap this part + + align:start position:0% +this way and now just to wrap this part + + + align:start position:0% +this way and now just to wrap this part +up let me write this out EXP explicitly + + align:start position:0% +up let me write this out EXP explicitly + + + align:start position:0% +up let me write this out EXP explicitly +just so we're clear about what this + + align:start position:0% +just so we're clear about what this + + + align:start position:0% +just so we're clear about what this +thing really means cuz sometimes it + + align:start position:0% +thing really means cuz sometimes it + + + align:start position:0% +thing really means cuz sometimes it +seems to be a bit you know + + align:start position:0% +seems to be a bit you know + + + align:start position:0% +seems to be a bit you know +abstract + + align:start position:0% + + + + align:start position:0% + +um now what we are saying there is that + + align:start position:0% +um now what we are saying there is that + + + align:start position:0% +um now what we are saying there is that +you know the response + + align:start position:0% + + + + align:start position:0% + +function is really a sum over two + + align:start position:0% +function is really a sum over two + + + align:start position:0% +function is really a sum over two +correlation functions + + align:start position:0% +correlation functions + + + align:start position:0% +correlation functions +C of to minus C star of + + align:start position:0% +C of to minus C star of + + + align:start position:0% +C of to minus C star of +to and and that correlation function can + + align:start position:0% +to and and that correlation function can + + + align:start position:0% +to and and that correlation function can +be + + align:start position:0% + + + + align:start position:0% + +written + + align:start position:0% + + + + align:start position:0% + +as a trace over the product of operators + + align:start position:0% +as a trace over the product of operators + + + align:start position:0% +as a trace over the product of operators +in the sort of traditional time ordered + + align:start position:0% +in the sort of traditional time ordered + + + align:start position:0% +in the sort of traditional time ordered +Direction and if you're more interested + + align:start position:0% +Direction and if you're more interested + + + align:start position:0% +Direction and if you're more interested +in the uh wave Vector representation + + align:start position:0% +in the uh wave Vector representation + + + align:start position:0% +in the uh wave Vector representation +what we're talking about then + + align:start position:0% +what we're talking about then + + + align:start position:0% +what we're talking about then +is written in the igen state System igen + + align:start position:0% +is written in the igen state System igen + + + align:start position:0% +is written in the igen state System igen +state representation + + align:start position:0% + + + + align:start position:0% + +same sort of thing okay when you see row + + align:start position:0% +same sort of thing okay when you see row + + + align:start position:0% +same sort of thing okay when you see row +EQ that should just be telling you + + align:start position:0% +EQ that should just be telling you + + + align:start position:0% +EQ that should just be telling you +you're doing a equilibrium thermal + + align:start position:0% +you're doing a equilibrium thermal + + + align:start position:0% +you're doing a equilibrium thermal +average and uh now the you know what the + + align:start position:0% + + + + align:start position:0% + +um conjugate of this correlation + + align:start position:0% +um conjugate of this correlation + + + align:start position:0% +um conjugate of this correlation +function we think of that as just + + align:start position:0% +function we think of that as just + + + align:start position:0% +function we think of that as just +replacing the time ordering as you know + + align:start position:0% +replacing the time ordering as you know + + + align:start position:0% +replacing the time ordering as you know +negative time but uh you know sort of + + align:start position:0% +negative time but uh you know sort of + + + align:start position:0% +negative time but uh you know sort of +recognize that what that really looks + + align:start position:0% +recognize that what that really looks + + + align:start position:0% +recognize that what that really looks +like in terms of the density + + align:start position:0% +like in terms of the density + + + align:start position:0% +like in terms of the density +Matrix is now the density Matrix is + + align:start position:0% +Matrix is now the density Matrix is + + + align:start position:0% +Matrix is now the density Matrix is +sandwiched between two + + align:start position:0% +sandwiched between two + + + align:start position:0% +sandwiched between two +operators and and so this is sort of the + + align:start position:0% +operators and and so this is sort of the + + + align:start position:0% +operators and and so this is sort of the +start um and so in this case it really + + align:start position:0% +start um and so in this case it really + + + align:start position:0% +start um and so in this case it really +refers to just flipping the order of + + align:start position:0% +refers to just flipping the order of + + + align:start position:0% +refers to just flipping the order of +operators in this thermal average but um + + align:start position:0% +operators in this thermal average but um + + + align:start position:0% +operators in this thermal average but um +you know this is sort of the start to + + align:start position:0% +you know this is sort of the start to + + + align:start position:0% +you know this is sort of the start to +how you think about keeping track of + + align:start position:0% +how you think about keeping track of + + + align:start position:0% +how you think about keeping track of +what's happening in the density Matrix + + align:start position:0% +what's happening in the density Matrix + + + align:start position:0% +what's happening in the density Matrix +which turns to be good for bookkeeping + + align:start position:0% +which turns to be good for bookkeeping + + + align:start position:0% +which turns to be good for bookkeeping +remember that you know one sort of uh + + align:start position:0% +remember that you know one sort of uh + + + align:start position:0% +remember that you know one sort of uh +starts with the system at equilibrium in + + align:start position:0% +starts with the system at equilibrium in + + + align:start position:0% +starts with the system at equilibrium in +some particular State call it the ground + + align:start position:0% +some particular State call it the ground + + + align:start position:0% +some particular State call it the ground +state and now what you see is that this + + align:start position:0% +state and now what you see is that this + + + align:start position:0% +state and now what you see is that this +correlation function really reflects the + + align:start position:0% +correlation function really reflects the + + + align:start position:0% +correlation function really reflects the +fact that when was going to have time + + align:start position:0% +fact that when was going to have time + + + align:start position:0% +fact that when was going to have time +evolving dipole operators + + align:start position:0% +evolving dipole operators + + + align:start position:0% +evolving dipole operators +acting um either on the uh cats the wave + + align:start position:0% +acting um either on the uh cats the wave + + + align:start position:0% +acting um either on the uh cats the wave +functions of the system or on their + + align:start position:0% +functions of the system or on their + + + align:start position:0% +functions of the system or on their +conjugates um and that you know how the + + align:start position:0% +conjugates um and that you know how the + + + align:start position:0% +conjugates um and that you know how the +system behaves is going to depend on + + align:start position:0% +system behaves is going to depend on + + + align:start position:0% +system behaves is going to depend on +many terms + + align:start position:0% +many terms + + + align:start position:0% +many terms +Each of which differs sort of by phase + + align:start position:0% +Each of which differs sort of by phase + + + align:start position:0% +Each of which differs sort of by phase +relationships between which way you know + + align:start position:0% +relationships between which way you know + + + align:start position:0% +relationships between which way you know +is your dipole operator acting on the + + align:start position:0% +is your dipole operator acting on the + + + align:start position:0% +is your dipole operator acting on the +state of your system um for for linear + + align:start position:0% +state of your system um for for linear + + + align:start position:0% +state of your system um for for linear +spectroscopies that doesn't you know + + align:start position:0% +spectroscopies that doesn't you know + + + align:start position:0% +spectroscopies that doesn't you know +matter too much but the moment you have + + align:start position:0% +matter too much but the moment you have + + + align:start position:0% +matter too much but the moment you have +more than one time variable to worry + + align:start position:0% +more than one time variable to worry + + + align:start position:0% +more than one time variable to worry +about it's very important then to keep + + align:start position:0% +about it's very important then to keep + + + align:start position:0% +about it's very important then to keep +track of how the phase of how your + + align:start position:0% +track of how the phase of how your + + + align:start position:0% +track of how the phase of how your +system evolves between one time period + + align:start position:0% +system evolves between one time period + + + align:start position:0% +system evolves between one time period +and + + align:start position:0% + + + + align:start position:0% + +another like to now take the next step + + align:start position:0% +another like to now take the next step + + + align:start position:0% +another like to now take the next step +to talking about the nonlinear + + align:start position:0% +to talking about the nonlinear + + + align:start position:0% +to talking about the nonlinear +polarization we're basically going to do + + align:start position:0% +polarization we're basically going to do + + + align:start position:0% +polarization we're basically going to do +uh the same thing that we um did using + + align:start position:0% +uh the same thing that we um did using + + + align:start position:0% +uh the same thing that we um did using +the density Matrix for the linear case + + align:start position:0% +the density Matrix for the linear case + + + align:start position:0% +the density Matrix for the linear case +um what I want you to + + align:start position:0% +um what I want you to + + + align:start position:0% +um what I want you to +identify is that uh just the in general + + align:start position:0% +identify is that uh just the in general + + + align:start position:0% +identify is that uh just the in general +the polarization in the sample if you + + align:start position:0% +the polarization in the sample if you + + + align:start position:0% +the polarization in the sample if you +treat this within uh the framework of + + align:start position:0% +treat this within uh the framework of + + + align:start position:0% +treat this within uh the framework of +linear response and perturbation Theory + + align:start position:0% +linear response and perturbation Theory + + + align:start position:0% +linear response and perturbation Theory +the way we have we can also then expand + + align:start position:0% +the way we have we can also then expand + + + align:start position:0% +the way we have we can also then expand +the polarization + + align:start position:0% + + + + align:start position:0% + +in orders of the incident electric + + align:start position:0% + + + + align:start position:0% + +field and we'll be spending a lot of + + align:start position:0% +field and we'll be spending a lot of + + + align:start position:0% +field and we'll be spending a lot of +this is sort of our bookkeeping linear + + align:start position:0% +this is sort of our bookkeeping linear + + + align:start position:0% +this is sort of our bookkeeping linear +spectroscopy is usually what we + + align:start position:0% +spectroscopy is usually what we + + + align:start position:0% +spectroscopy is usually what we +associate with uh linear response just + + align:start position:0% +associate with uh linear response just + + + align:start position:0% +associate with uh linear response just +in one field P1 we're going to talk a + + align:start position:0% +in one field P1 we're going to talk a + + + align:start position:0% +in one field P1 we're going to talk a +lot about third order + + align:start position:0% +lot about third order + + + align:start position:0% +lot about third order +expansions um and what we mean when we + + align:start position:0% +expansions um and what we mean when we + + + align:start position:0% +expansions um and what we mean when we +write this is you know + + align:start position:0% +write this is you know + + + align:start position:0% +write this is you know +we recognize that the polarization is is + + align:start position:0% +we recognize that the polarization is is + + + align:start position:0% +we recognize that the polarization is is +just a trace over the dipole operator at + + align:start position:0% +just a trace over the dipole operator at + + + align:start position:0% +just a trace over the dipole operator at +time T and uh the uh density + + align:start position:0% +time T and uh the uh density + + + align:start position:0% +time T and uh the uh density +Matrix and that we can now do a perative + + align:start position:0% +Matrix and that we can now do a perative + + + align:start position:0% +Matrix and that we can now do a perative +expansion of the density Matrix and that + + align:start position:0% +expansion of the density Matrix and that + + + align:start position:0% +expansion of the density Matrix and that +Maps directly onto the um what I've + + align:start position:0% +Maps directly onto the um what I've + + + align:start position:0% +Maps directly onto the um what I've +written up top here + + align:start position:0% + + + + align:start position:0% + +so the terms we've got here are just + + align:start position:0% +so the terms we've got here are just + + + align:start position:0% +so the terms we've got here are just +these uh expansions in the um uh density + + align:start position:0% +these uh expansions in the um uh density + + + align:start position:0% +these uh expansions in the um uh density +Matrix two different orders Each of + + align:start position:0% +Matrix two different orders Each of + + + align:start position:0% +Matrix two different orders Each of +which is just characterized by a certain + + align:start position:0% +which is just characterized by a certain + + + align:start position:0% +which is just characterized by a certain +number of field interactions now made + + align:start position:0% +number of field interactions now made + + + align:start position:0% +number of field interactions now made +the mistake of um erasing the other one + + align:start position:0% +the mistake of um erasing the other one + + + align:start position:0% +the mistake of um erasing the other one +let me just throw down the second order + + align:start position:0% +let me just throw down the second order + + + align:start position:0% +let me just throw down the second order +term again just uh so that we have + + align:start position:0% +term again just uh so that we have + + + align:start position:0% +term again just uh so that we have +something to look + + align:start position:0% + + + + align:start position:0% + +at this is the uh + + align:start position:0% +at this is the uh + + + align:start position:0% +at this is the uh +time time ordered interaction + + align:start position:0% +time time ordered interaction + + + align:start position:0% +time time ordered interaction +nested commutators in field interactions + + align:start position:0% + + + + align:start position:0% + +okay one thing I failed to mention + + align:start position:0% +okay one thing I failed to mention + + + align:start position:0% +okay one thing I failed to mention +earlier is that uh even though we are + + align:start position:0% +earlier is that uh even though we are + + + align:start position:0% +earlier is that uh even though we are +talking about a nonlinear response we + + align:start position:0% +talking about a nonlinear response we + + + align:start position:0% +talking about a nonlinear response we +still talk about this as being linear + + align:start position:0% +still talk about this as being linear + + + align:start position:0% +still talk about this as being linear +response Theory so that there is still a + + align:start position:0% +response Theory so that there is still a + + + align:start position:0% +response Theory so that there is still a +simple linear interaction between how + + align:start position:0% +simple linear interaction between how + + + align:start position:0% +simple linear interaction between how +the system behaves when you have an + + align:start position:0% +the system behaves when you have an + + + align:start position:0% +the system behaves when you have an +interaction with one of these fields the + + align:start position:0% +interaction with one of these fields the + + + align:start position:0% +interaction with one of these fields the +nonlinearity really comes about from + + align:start position:0% +nonlinearity really comes about from + + + align:start position:0% +nonlinearity really comes about from +that the fact that there are multiple + + align:start position:0% +that the fact that there are multiple + + + align:start position:0% +that the fact that there are multiple +linear interactions + + align:start position:0% + + + + align:start position:0% + +uh okay so what I'd like to do is + + align:start position:0% +uh okay so what I'd like to do is + + + align:start position:0% +uh okay so what I'd like to do is +connect this with um a nonlinear + + align:start position:0% +connect this with um a nonlinear + + + align:start position:0% +connect this with um a nonlinear +response function and that's really + + align:start position:0% +response function and that's really + + + align:start position:0% +response function and that's really +going to end up being the um sort of the + + align:start position:0% +going to end up being the um sort of the + + + align:start position:0% +going to end up being the um sort of the +business end of doing nonlinear + + align:start position:0% +business end of doing nonlinear + + + align:start position:0% +business end of doing nonlinear +spectroscopy um it's really what we talk + + align:start position:0% +spectroscopy um it's really what we talk + + + align:start position:0% +spectroscopy um it's really what we talk +about as the kind of connection to what + + align:start position:0% +about as the kind of connection to what + + + align:start position:0% +about as the kind of connection to what +molecules are doing uh in the sample uh + + align:start position:0% +molecules are doing uh in the sample uh + + + align:start position:0% +molecules are doing uh in the sample uh +and that + + align:start position:0% + + + + align:start position:0% + +um let's + + align:start position:0% +um let's + + + align:start position:0% +um let's +see just one one thing that uh you may + + align:start position:0% +see just one one thing that uh you may + + + align:start position:0% +see just one one thing that uh you may +have done or you may not have done but + + align:start position:0% +have done or you may not have done but + + + align:start position:0% +have done or you may not have done but +is worth doing is um to sort of just + + align:start position:0% +is worth doing is um to sort of just + + + align:start position:0% +is worth doing is um to sort of just +develop a classical description of the + + align:start position:0% +develop a classical description of the + + + align:start position:0% +develop a classical description of the +of a nonlinear response function um very + + align:start position:0% +of a nonlinear response function um very + + + align:start position:0% +of a nonlinear response function um very +much the way you would do it just for a + + align:start position:0% +much the way you would do it just for a + + + align:start position:0% +much the way you would do it just for a +linear response do you have a question + + align:start position:0% +linear response do you have a question + + + align:start position:0% +linear response do you have a question +the brackets are unbalanced and that + + align:start position:0% +the brackets are unbalanced and that + + + align:start position:0% +the brackets are unbalanced and that +just what it's not quite the + + align:start position:0% +just what it's not quite the + + + align:start position:0% +just what it's not quite the +same + + align:start position:0% +same + + + align:start position:0% +same +sorry okay should be okay + + align:start position:0% +sorry okay should be okay + + + align:start position:0% +sorry okay should be okay +thanks uh yeah keep me on my toes + + align:start position:0% +thanks uh yeah keep me on my toes + + + align:start position:0% +thanks uh yeah keep me on my toes +I'm uh I don't I don't put a 100% + + align:start position:0% +I'm uh I don't I don't put a 100% + + + align:start position:0% +I'm uh I don't I don't put a 100% +guarantee on what I write + + align:start position:0% + + + + align:start position:0% + +um so just in general for for any sort + + align:start position:0% +um so just in general for for any sort + + + align:start position:0% +um so just in general for for any sort +of form of you know how a system would + + align:start position:0% +of form of you know how a system would + + + align:start position:0% +of form of you know how a system would +respond to multiple actions of an + + align:start position:0% +respond to multiple actions of an + + + align:start position:0% +respond to multiple actions of an +external potential you know and you want + + align:start position:0% +external potential you know and you want + + + align:start position:0% +external potential you know and you want +to describe what happens at some time to + + align:start position:0% +to describe what happens at some time to + + + align:start position:0% +to describe what happens at some time to +as a result of what happened before it + + align:start position:0% +as a result of what happened before it + + + align:start position:0% +as a result of what happened before it +you sort of expect that the change you + + align:start position:0% +you sort of expect that the change you + + + align:start position:0% +you sort of expect that the change you +know uh in the expectation value of any + + align:start position:0% +know uh in the expectation value of any + + + align:start position:0% +know uh in the expectation value of any +sort of internal operator is going to + + align:start position:0% +sort of internal operator is going to + + + align:start position:0% +sort of internal operator is going to +look it's going to have a lot of + + align:start position:0% +look it's going to have a lot of + + + align:start position:0% +look it's going to have a lot of +similarity to what we've uh written here + + align:start position:0% +similarity to what we've uh written here + + + align:start position:0% +similarity to what we've uh written here +just um you know really follows a um + + align:start position:0% +just um you know really follows a um + + + align:start position:0% +just um you know really follows a um +looks very similar to Expressions that + + align:start position:0% +looks very similar to Expressions that + + + align:start position:0% +looks very similar to Expressions that +one gets from pertubation Theory + + align:start position:0% + + + + align:start position:0% + +so just in general you think you say + + align:start position:0% +so just in general you think you say + + + align:start position:0% +so just in general you think you say +that look uh I'm going to Define some + + align:start position:0% +that look uh I'm going to Define some + + + align:start position:0% +that look uh I'm going to Define some +sort of a response function in this case + + align:start position:0% +sort of a response function in this case + + + align:start position:0% +sort of a response function in this case +I'm going to have two two external + + align:start position:0% +I'm going to have two two external + + + align:start position:0% +I'm going to have two two external +potentials so I'm going to call it a + + align:start position:0% +potentials so I'm going to call it a + + + align:start position:0% +potentials so I'm going to call it a +second order response and there's going + + align:start position:0% +second order response and there's going + + + align:start position:0% +second order response and there's going +to be some arbitrary uh form to you know + + align:start position:0% +to be some arbitrary uh form to you know + + + align:start position:0% +to be some arbitrary uh form to you know +what this external potential looks like + + align:start position:0% +what this external potential looks like + + + align:start position:0% +what this external potential looks like +um but I have independent control over + + align:start position:0% +um but I have independent control over + + + align:start position:0% +um but I have independent control over +both of them uh and how they act on the + + align:start position:0% +both of them uh and how they act on the + + + align:start position:0% +both of them uh and how they act on the +system how my system looks at time T is + + align:start position:0% +system how my system looks at time T is + + + align:start position:0% +system how my system looks at time T is +going to depend on integrating over the + + align:start position:0% +going to depend on integrating over the + + + align:start position:0% +going to depend on integrating over the +full history of this uh uh system uh and + + align:start position:0% +full history of this uh uh system uh and + + + align:start position:0% +full history of this uh uh system uh and +we are through the limits on this + + align:start position:0% +we are through the limits on this + + + align:start position:0% +we are through the limits on this +integral we enforce that this response + + align:start position:0% +integral we enforce that this response + + + align:start position:0% +integral we enforce that this response +function requires that you know this uh + + align:start position:0% +function requires that you know this uh + + + align:start position:0% +function requires that you know this uh +first field precedes the second field + + align:start position:0% +first field precedes the second field + + + align:start position:0% +first field precedes the second field +and then we have to integrate over the + + align:start position:0% +and then we have to integrate over the + + + align:start position:0% +and then we have to integrate over the +full time history of those interactions + + align:start position:0% +full time history of those interactions + + + align:start position:0% +full time history of those interactions +so um + + align:start position:0% +so um + + + align:start position:0% +so um +taking uh this uh type of form of the + + align:start position:0% +taking uh this uh type of form of the + + + align:start position:0% +taking uh this uh type of form of the +response function and then now comparing + + align:start position:0% +response function and then now comparing + + + align:start position:0% +response function and then now comparing +it uh to the let's compare it say to the + + align:start position:0% +it uh to the let's compare it say to the + + + align:start position:0% +it uh to the let's compare it say to the +second order + + align:start position:0% + + + + align:start position:0% + +polarization uh which we would get + + align:start position:0% +polarization uh which we would get + + + align:start position:0% +polarization uh which we would get +basically by uh inserting this expansion + + align:start position:0% +basically by uh inserting this expansion + + + align:start position:0% +basically by uh inserting this expansion +up + + align:start position:0% +up + + + align:start position:0% +up +into this term + + align:start position:0% +into this term + + + align:start position:0% +into this term +here + + align:start position:0% + + + + align:start position:0% + +um let's see maybe I should G + + align:start position:0% + + + + align:start position:0% + +okay so now what we're going to do is + + align:start position:0% +okay so now what we're going to do is + + + align:start position:0% +okay so now what we're going to do is +just + + align:start position:0% +just + + + align:start position:0% +just +explicitly insert what um you know the + + align:start position:0% +explicitly insert what um you know the + + + align:start position:0% +explicitly insert what um you know the +form of the interaction with the light + + align:start position:0% +form of the interaction with the light + + + align:start position:0% +form of the interaction with the light +field in each case it takes on the form + + align:start position:0% +field in each case it takes on the form + + + align:start position:0% +field in each case it takes on the form +mu. e of course the dipole operators are + + align:start position:0% +mu. e of course the dipole operators are + + + align:start position:0% +mu. e of course the dipole operators are +time dependent here that's sort of what + + align:start position:0% +time dependent here that's sort of what + + + align:start position:0% +time dependent here that's sort of what +uh this is uh meant to uh Express and + + align:start position:0% +uh this is uh meant to uh Express and + + + align:start position:0% +uh this is uh meant to uh Express and +now we can sort of simplify this a + + align:start position:0% +now we can sort of simplify this a + + + align:start position:0% +now we can sort of simplify this a +little + + align:start position:0% +little + + + align:start position:0% +little +bit and I'm going to do a couple of + + align:start position:0% +bit and I'm going to do a couple of + + + align:start position:0% +bit and I'm going to do a couple of +manipul ations at the same time and let + + align:start position:0% +manipul ations at the same time and let + + + align:start position:0% +manipul ations at the same time and let +you sort out the details yourself um + + align:start position:0% +you sort out the details yourself um + + + align:start position:0% +you sort out the details yourself um +switching + + align:start position:0% +switching + + + align:start position:0% +switching +variables as we did before so let's + + align:start position:0% + + + + align:start position:0% + +see let me take it one step at a time + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +now I've got to be + + align:start position:0% + + + + align:start position:0% + +careful okay so what have I done here + + align:start position:0% +careful okay so what have I done here + + + align:start position:0% +careful okay so what have I done here +one thing so all I've done is a + + align:start position:0% +one thing so all I've done is a + + + align:start position:0% +one thing so all I've done is a +substitution and then I've uh brought in + + align:start position:0% +substitution and then I've uh brought in + + + align:start position:0% +substitution and then I've uh brought in +this operator and I've made use of + + align:start position:0% +this operator and I've made use of + + + align:start position:0% +this operator and I've made use of +something we U + + align:start position:0% +something we U + + + align:start position:0% +something we U +thr of sort of shuffling the nesting of + + align:start position:0% +thr of sort of shuffling the nesting of + + + align:start position:0% +thr of sort of shuffling the nesting of +operators just want you to remember + + align:start position:0% +operators just want you to remember + + + align:start position:0% +operators just want you to remember +that if you + + align:start position:0% +that if you + + + align:start position:0% +that if you +write nested operators nested left that + + align:start position:0% +write nested operators nested left that + + + align:start position:0% +write nested operators nested left that +you can just switch the ordering Nest + + align:start position:0% +you can just switch the ordering Nest + + + align:start position:0% +you can just switch the ordering Nest +them + + align:start position:0% + + + + align:start position:0% + +right and those are you know evaluating + + align:start position:0% +right and those are you know evaluating + + + align:start position:0% +right and those are you know evaluating +those are equivalent so I've done that + + align:start position:0% +those are equivalent so I've done that + + + align:start position:0% +those are equivalent so I've done that +over here also and it's it's basically + + align:start position:0% +over here also and it's it's basically + + + align:start position:0% +over here also and it's it's basically +sort of to isolate our equilibrium + + align:start position:0% +sort of to isolate our equilibrium + + + align:start position:0% +sort of to isolate our equilibrium +density + + align:start position:0% +density + + + align:start position:0% +density +Matrix okay the next step is to switch + + align:start position:0% +Matrix okay the next step is to switch + + + align:start position:0% +Matrix okay the next step is to switch +variables um and it's here we have + + align:start position:0% +variables um and it's here we have + + + align:start position:0% +variables um and it's here we have +written the history of the system in + + align:start position:0% +written the history of the system in + + + align:start position:0% +written the history of the system in +terms of the time point of the + + align:start position:0% +terms of the time point of the + + + align:start position:0% +terms of the time point of the +interaction of the electric field and we + + align:start position:0% +interaction of the electric field and we + + + align:start position:0% +interaction of the electric field and we +want to switch to time intervals between + + align:start position:0% +want to switch to time intervals between + + + align:start position:0% +want to switch to time intervals between +subsequent interactions okay so what + + align:start position:0% +subsequent interactions okay so what + + + align:start position:0% +subsequent interactions okay so what +we're going to do is um Define these + + align:start position:0% +we're going to do is um Define these + + + align:start position:0% +we're going to do is um Define these +variables + + align:start position:0% +variables + + + align:start position:0% +variables +um we're going to say uh + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +T2 is equal to + + align:start position:0% +T2 is equal to + + + align:start position:0% +T2 is equal to +T minus to 2 okay so we're um just + + align:start position:0% +T minus to 2 okay so we're um just + + + align:start position:0% +T minus to 2 okay so we're um just +trying to write time points in terms of + + align:start position:0% +trying to write time points in terms of + + + align:start position:0% +trying to write time points in terms of +time intervals okay and T1 is going to + + align:start position:0% +time intervals okay and T1 is going to + + + align:start position:0% +time intervals okay and T1 is going to +be T minus to 2 minus to + + align:start position:0% +be T minus to 2 minus to + + + align:start position:0% +be T minus to 2 minus to +1 all + + align:start position:0% +1 all + + + align:start position:0% +1 all +right um if you now rewrite just sort of + + align:start position:0% +right um if you now rewrite just sort of + + + align:start position:0% +right um if you now rewrite just sort of +the this basic form of the response + + align:start position:0% +the this basic form of the response + + + align:start position:0% +the this basic form of the response +function it sort of takes the + + align:start position:0% + + + + align:start position:0% + +form oops let me erase this + + align:start position:0% +form oops let me erase this + + + align:start position:0% +form oops let me erase this +[Music] + + align:start position:0% + + + + align:start position:0% + +okay so this is just sort of taking this + + align:start position:0% +okay so this is just sort of taking this + + + align:start position:0% +okay so this is just sort of taking this +general form and uh switching variables + + align:start position:0% +general form and uh switching variables + + + align:start position:0% +general form and uh switching variables +um and now we're going to do the same + + align:start position:0% +um and now we're going to do the same + + + align:start position:0% +um and now we're going to do the same +thing to our second order + + align:start position:0% + + + + align:start position:0% + +polarization let's see where I put + + align:start position:0% + + + + align:start position:0% + +that okay + + align:start position:0% + + + + align:start position:0% + +uh oh this is going to be on over each + + align:start position:0% + + + + align:start position:0% + +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so one thing I want to point out is uh + + align:start position:0% +so one thing I want to point out is uh + + + align:start position:0% +so one thing I want to point out is uh +you know that integration limits now + + align:start position:0% +you know that integration limits now + + + align:start position:0% +you know that integration limits now +talking in terms of time intervals looks + + align:start position:0% +talking in terms of time intervals looks + + + align:start position:0% +talking in terms of time intervals looks +a bit simple but we still have enforced + + align:start position:0% +a bit simple but we still have enforced + + + align:start position:0% +a bit simple but we still have enforced +causality over here um just uh sort of + + align:start position:0% +causality over here um just uh sort of + + + align:start position:0% +causality over here um just uh sort of +by how we've written our time variables + + align:start position:0% +by how we've written our time variables + + + align:start position:0% +by how we've written our time variables +we still enforce that uh T1 uh to 1 is a + + align:start position:0% +we still enforce that uh T1 uh to 1 is a + + + align:start position:0% +we still enforce that uh T1 uh to 1 is a +time interval that precedes to 2 we have + + align:start position:0% +time interval that precedes to 2 we have + + + align:start position:0% +time interval that precedes to 2 we have +to integrate over the full history uh + + align:start position:0% +to integrate over the full history uh + + + align:start position:0% +to integrate over the full history uh +for all possible interactions prior to + + align:start position:0% +for all possible interactions prior to + + + align:start position:0% +for all possible interactions prior to +observing so zero refers to sort of um + + align:start position:0% +observing so zero refers to sort of um + + + align:start position:0% +observing so zero refers to sort of um +the latest possible time and infinity + + align:start position:0% +the latest possible time and infinity + + + align:start position:0% +the latest possible time and infinity +sort of the earliest possible longest uh + + align:start position:0% +sort of the earliest possible longest uh + + + align:start position:0% +sort of the earliest possible longest uh +time interval before uh in this way of + + align:start position:0% +time interval before uh in this way of + + + align:start position:0% +time interval before uh in this way of +looking at it + + align:start position:0% +looking at it + + + align:start position:0% +looking at it +whatever the value of to 2 is you still + + align:start position:0% +whatever the value of to 2 is you still + + + align:start position:0% +whatever the value of to 2 is you still +have to integrate over all possible + + align:start position:0% +have to integrate over all possible + + + align:start position:0% +have to integrate over all possible +values of to one prior to it + + align:start position:0% + + + + align:start position:0% + +now comparing that to what you get from + + align:start position:0% +now comparing that to what you get from + + + align:start position:0% +now comparing that to what you get from +the second order polarization you know + + align:start position:0% +the second order polarization you know + + + align:start position:0% +the second order polarization you know +what we have is something that looks + + align:start position:0% +what we have is something that looks + + + align:start position:0% +what we have is something that looks +analogous to what you see for a linear + + align:start position:0% +analogous to what you see for a linear + + + align:start position:0% +analogous to what you see for a linear +case it's clear that this nested bunch + + align:start position:0% +case it's clear that this nested bunch + + + align:start position:0% +case it's clear that this nested bunch +of dipole operators is the second order + + align:start position:0% +of dipole operators is the second order + + + align:start position:0% +of dipole operators is the second order +response + + align:start position:0% +response + + + align:start position:0% +response +function okay uh and so this is going to + + align:start position:0% +function okay uh and so this is going to + + + align:start position:0% +function okay uh and so this is going to +describe how the uh system evolves now + + align:start position:0% +describe how the uh system evolves now + + + align:start position:0% +describe how the uh system evolves now +this starts to look really messy and at + + align:start position:0% +this starts to look really messy and at + + + align:start position:0% +this starts to look really messy and at +the end of the day this is exactly why + + align:start position:0% +the end of the day this is exactly why + + + align:start position:0% +the end of the day this is exactly why +we have to start coming up with + + align:start position:0% +we have to start coming up with + + + align:start position:0% +we have to start coming up with +bookkeeping tricks is that you can see + + align:start position:0% +bookkeeping tricks is that you can see + + + align:start position:0% +bookkeeping tricks is that you can see +that what this represents is that you + + align:start position:0% +that what this represents is that you + + + align:start position:0% +that what this represents is that you +are you have really in this particular + + align:start position:0% +are you have really in this particular + + + align:start position:0% +are you have really in this particular +case here let me write the response + + align:start position:0% +case here let me write the response + + + align:start position:0% +case here let me write the response +function you know + + align:start position:0% + + + + align:start position:0% + +explicitly + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +age um now when we write the response + + align:start position:0% +age um now when we write the response + + + align:start position:0% +age um now when we write the response +function explicitly now we do have to + + align:start position:0% +function explicitly now we do have to + + + align:start position:0% +function explicitly now we do have to +remind you that we are that uh you have + + align:start position:0% +remind you that we are that uh you have + + + align:start position:0% +remind you that we are that uh you have +to enforce causality there's a step + + align:start position:0% +to enforce causality there's a step + + + align:start position:0% +to enforce causality there's a step +response here that ensures that the time + + align:start position:0% +response here that ensures that the time + + + align:start position:0% +response here that ensures that the time +variables tow are always + + align:start position:0% +variables tow are always + + + align:start position:0% +variables tow are always +positive um + + align:start position:0% + + + + align:start position:0% + +so uh what I want you to see here is + + align:start position:0% +so uh what I want you to see here is + + + align:start position:0% +so uh what I want you to see here is +you've got actually four separate + + align:start position:0% +you've got actually four separate + + + align:start position:0% +you've got actually four separate +correlation functions that are in this + + align:start position:0% +correlation functions that are in this + + + align:start position:0% +correlation functions that are in this +expression right we had two when we + + align:start position:0% +expression right we had two when we + + + align:start position:0% +expression right we had two when we +wrote out the linear response form a COR + + align:start position:0% +wrote out the linear response form a COR + + + align:start position:0% +wrote out the linear response form a COR +a dipole correlation function and its + + align:start position:0% +a dipole correlation function and its + + + align:start position:0% +a dipole correlation function and its +conjugate it's complex conjugate in this + + align:start position:0% +conjugate it's complex conjugate in this + + + align:start position:0% +conjugate it's complex conjugate in this +case we have four different correlation + + align:start position:0% +case we have four different correlation + + + align:start position:0% +case we have four different correlation +functions they all just differ by the + + align:start position:0% +functions they all just differ by the + + + align:start position:0% +functions they all just differ by the +time order + + align:start position:0% +time order + + + align:start position:0% +time order +of these dipole + + align:start position:0% + + + + align:start position:0% + +operators so let's + + align:start position:0% +operators so let's + + + align:start position:0% +operators so let's +um as you might imagine this makes uh + + align:start position:0% +um as you might imagine this makes uh + + + align:start position:0% +um as you might imagine this makes uh +keeping track of everything that's going + + align:start position:0% +keeping track of everything that's going + + + align:start position:0% +keeping track of everything that's going +on a little bit complicated imagine + + align:start position:0% +on a little bit complicated imagine + + + align:start position:0% +on a little bit complicated imagine +going to fifth + + align:start position:0% +going to fifth + + + align:start position:0% +going to fifth +order okay + + align:start position:0% +order okay + + + align:start position:0% +order okay +um let's take a brief look at that let's + + align:start position:0% +um let's take a brief look at that let's + + + align:start position:0% +um let's take a brief look at that let's +see yeah actually let me um just to sort + + align:start position:0% +see yeah actually let me um just to sort + + + align:start position:0% +see yeah actually let me um just to sort +of make a little bit of contact to + + align:start position:0% +of make a little bit of contact to + + + align:start position:0% +of make a little bit of contact to +you know how we would write this in a + + align:start position:0% +you know how we would write this in a + + + align:start position:0% +you know how we would write this in a +wave Vector + + align:start position:0% + + + + align:start position:0% + +representation in the igen states of + + align:start position:0% +representation in the igen states of + + + align:start position:0% +representation in the igen states of +the system hamiltonian + + align:start position:0% + + + + align:start position:0% + +okay just an equilibrium thermal average + + align:start position:0% +okay just an equilibrium thermal average + + + align:start position:0% +okay just an equilibrium thermal average +over this product of operators + + align:start position:0% +over this product of operators + + + align:start position:0% +over this product of operators +okay now there is a there is a Time + + align:start position:0% +okay now there is a there is a Time + + + align:start position:0% +okay now there is a there is a Time +ordering enforced in this product of + + align:start position:0% +ordering enforced in this product of + + + align:start position:0% +ordering enforced in this product of +operators um and it may not be quite + + align:start position:0% +operators um and it may not be quite + + + align:start position:0% +operators um and it may not be quite +apparent there so it's sometimes helpful + + align:start position:0% +apparent there so it's sometimes helpful + + + align:start position:0% +apparent there so it's sometimes helpful +to sort of piece this apart and take a + + align:start position:0% +to sort of piece this apart and take a + + + align:start position:0% +to sort of piece this apart and take a +look at them individually a little bit + + align:start position:0% +look at them individually a little bit + + + align:start position:0% +look at them individually a little bit +just to sort of get a sense for what's + + align:start position:0% +just to sort of get a sense for what's + + + align:start position:0% +just to sort of get a sense for what's +going on um + + align:start position:0% + + + + align:start position:0% + +let's see + + align:start position:0% + + + + align:start position:0% + +well let's um let's take one of the + + align:start position:0% +well let's um let's take one of the + + + align:start position:0% +well let's um let's take one of the +possible four terms that come out of + + align:start position:0% +possible four terms that come out of + + + align:start position:0% +possible four terms that come out of +this um let's look explicitly at one + + align:start position:0% +this um let's look explicitly at one + + + align:start position:0% +this um let's look explicitly at one +that uh looks + + align:start position:0% + + + + align:start position:0% + +like we'll call it + + align:start position:0% +like we'll call it + + + align:start position:0% +like we'll call it +q1 and this looks like the trace it + + align:start position:0% +q1 and this looks like the trace it + + + align:start position:0% +q1 and this looks like the trace it +would be the leading term when you + + align:start position:0% +would be the leading term when you + + + align:start position:0% +would be the leading term when you +expand all of these + + align:start position:0% +expand all of these + + + align:start position:0% +expand all of these +out where you maintain the time ordering + + align:start position:0% +out where you maintain the time ordering + + + align:start position:0% +out where you maintain the time ordering +as it's written there + + align:start position:0% + + + + align:start position:0% + +use + + align:start position:0% +use + + + align:start position:0% +use +okay so um this uh says that we have a + + align:start position:0% +okay so um this uh says that we have a + + + align:start position:0% +okay so um this uh says that we have a +sequence of interactions with the + + align:start position:0% +sequence of interactions with the + + + align:start position:0% +sequence of interactions with the +electric field there is a diple uh + + align:start position:0% +electric field there is a diple uh + + + align:start position:0% +electric field there is a diple uh +operator that acts on the system and + + align:start position:0% +operator that acts on the system and + + + align:start position:0% +operator that acts on the system and +then there's going to be some time + + align:start position:0% +then there's going to be some time + + + align:start position:0% +then there's going to be some time +Evolution this + + align:start position:0% +Evolution this + + + align:start position:0% +Evolution this +operator uh you know remembering that + + align:start position:0% +operator uh you know remembering that + + + align:start position:0% +operator uh you know remembering that +when we write the interaction rep uh + + align:start position:0% +when we write the interaction rep uh + + + align:start position:0% +when we write the interaction rep uh +representation of the dipole operator + + align:start position:0% +representation of the dipole operator + + + align:start position:0% +representation of the dipole operator +we're time evolving under the material + + align:start position:0% + + + + align:start position:0% + +Hamilton or alternatively we can write + + align:start position:0% +Hamilton or alternatively we can write + + + align:start position:0% +Hamilton or alternatively we can write +that in terms of the time propagator you + + align:start position:0% +that in terms of the time propagator you + + + align:start position:0% +that in terms of the time propagator you +not we have an in between each of these + + align:start position:0% +not we have an in between each of these + + + align:start position:0% +not we have an in between each of these +these interactions we evolve for some + + align:start position:0% +these interactions we evolve for some + + + align:start position:0% +these interactions we evolve for some +period of time here's our first period + + align:start position:0% +period of time here's our first period + + + align:start position:0% +period of time here's our first period +of evolution to one this is the first + + align:start position:0% +of evolution to one this is the first + + + align:start position:0% +of evolution to one this is the first +time interval and then there's a second + + align:start position:0% +time interval and then there's a second + + + align:start position:0% +time interval and then there's a second +time interval it ISS uh whatever follows + + align:start position:0% +time interval it ISS uh whatever follows + + + align:start position:0% +time interval it ISS uh whatever follows +T1 that's to 1 to 1 plus to 2 so let's + + align:start position:0% +T1 that's to 1 to 1 plus to 2 so let's + + + align:start position:0% +T1 that's to 1 to 1 plus to 2 so let's +um actually go ahead and write out the + + align:start position:0% +um actually go ahead and write out the + + + align:start position:0% +um actually go ahead and write out the +time propagation explicitly right so + + align:start position:0% +time propagation explicitly right so + + + align:start position:0% +time propagation explicitly right so +what we + + align:start position:0% +what we + + + align:start position:0% +what we +got here + + align:start position:0% +got here + + + align:start position:0% +got here +is Trace + + align:start position:0% + + + + align:start position:0% + +okay here's uh really just writing out + + align:start position:0% +okay here's uh really just writing out + + + align:start position:0% +okay here's uh really just writing out +the time propagators and just a dipole + + align:start position:0% +the time propagators and just a dipole + + + align:start position:0% +the time propagators and just a dipole +operator and uh then the next thing + + align:start position:0% +operator and uh then the next thing + + + align:start position:0% +operator and uh then the next thing +we're going to do here is + + align:start position:0% +we're going to do here is + + + align:start position:0% +we're going to do here is +uh you know recognize that this product + + align:start position:0% +uh you know recognize that this product + + + align:start position:0% +uh you know recognize that this product +of the time propagator over both time + + align:start position:0% +of the time propagator over both time + + + align:start position:0% +of the time propagator over both time +periods times the time reversal operator + + align:start position:0% +periods times the time reversal operator + + + align:start position:0% +periods times the time reversal operator +for T1 this is + + align:start position:0% +for T1 this is + + + align:start position:0% +for T1 this is +just just time propagation during the + + align:start position:0% +just just time propagation during the + + + align:start position:0% +just just time propagation during the +second + + align:start position:0% +second + + + align:start position:0% +second +interval okay let's + + align:start position:0% +interval okay let's + + + align:start position:0% +interval okay let's +see and we'll also recognize over here + + align:start position:0% +see and we'll also recognize over here + + + align:start position:0% +see and we'll also recognize over here +that this product of time Evolution + + align:start position:0% +that this product of time Evolution + + + align:start position:0% +that this product of time Evolution +during to one and to two this is just a + + align:start position:0% +during to one and to two this is just a + + + align:start position:0% +during to one and to two this is just a +product of two separate time + + align:start position:0% +product of two separate time + + + align:start position:0% +product of two separate time +propagators for the individual + + align:start position:0% + + + + align:start position:0% + +periods + + align:start position:0% + + + + align:start position:0% + +okay and then the next thing we'll do is + + align:start position:0% +okay and then the next thing we'll do is + + + align:start position:0% +okay and then the next thing we'll do is +remember + + align:start position:0% +remember + + + align:start position:0% +remember +that um there is a cyclic invariance to + + align:start position:0% +that um there is a cyclic invariance to + + + align:start position:0% +that um there is a cyclic invariance to +the trace so that if we write the if we + + align:start position:0% +the trace so that if we write the if we + + + align:start position:0% +the trace so that if we write the if we +want to evaluate the trace of a product + + align:start position:0% +want to evaluate the trace of a product + + + align:start position:0% +want to evaluate the trace of a product +of many matrices + + align:start position:0% +of many matrices + + + align:start position:0% +of many matrices +ABC this is identical no matter how you + + align:start position:0% +ABC this is identical no matter how you + + + align:start position:0% +ABC this is identical no matter how you +invert the order as long as you keep + + align:start position:0% +invert the order as long as you keep + + + align:start position:0% +invert the order as long as you keep +track of doing it + + align:start position:0% + + + + align:start position:0% + +cyclically uh c a b b c a all right so + + align:start position:0% +cyclically uh c a b b c a all right so + + + align:start position:0% +cyclically uh c a b b c a all right so +we're going to bring over this set of + + align:start position:0% +we're going to bring over this set of + + + align:start position:0% +we're going to bring over this set of +time + + align:start position:0% +time + + + align:start position:0% +time +propagators over to the other side + + align:start position:0% + + + + align:start position:0% + +okay so this is a just a different way + + align:start position:0% +okay so this is a just a different way + + + align:start position:0% +okay so this is a just a different way +of uh representing you know what uh is + + align:start position:0% +of uh representing you know what uh is + + + align:start position:0% +of uh representing you know what uh is +going on in the system what this + + align:start position:0% +going on in the system what this + + + align:start position:0% +going on in the system what this +expression says is when I perform an + + align:start position:0% +expression says is when I perform an + + + align:start position:0% +expression says is when I perform an +experiment I begin at equilibrium in a + + align:start position:0% +experiment I begin at equilibrium in a + + + align:start position:0% +experiment I begin at equilibrium in a +certain State that's this equilibrium + + align:start position:0% +certain State that's this equilibrium + + + align:start position:0% +certain State that's this equilibrium +density + + align:start position:0% +density + + + align:start position:0% +density +Matrix the next uh process is that + + align:start position:0% +Matrix the next uh process is that + + + align:start position:0% +Matrix the next uh process is that +there's an interaction with the light + + align:start position:0% +there's an interaction with the light + + + align:start position:0% +there's an interaction with the light +field so step one is that um my dipole + + align:start position:0% +field so step one is that um my dipole + + + align:start position:0% +field so step one is that um my dipole +operator acts on this state and + + align:start position:0% +operator acts on this state and + + + align:start position:0% +operator acts on this state and +uh creates a superposition with some + + align:start position:0% +uh creates a superposition with some + + + align:start position:0% +uh creates a superposition with some +other + + align:start position:0% +other + + + align:start position:0% +other +state then my um then I evolve the + + align:start position:0% +state then my um then I evolve the + + + align:start position:0% +state then my um then I evolve the +system forward in time so just + + align:start position:0% +system forward in time so just + + + align:start position:0% +system forward in time so just +recognizing that the time + + align:start position:0% +recognizing that the time + + + align:start position:0% +recognizing that the time +evolution of the density Matrix then in + + align:start position:0% +evolution of the density Matrix then in + + + align:start position:0% +evolution of the density Matrix then in +its superposition State during to one is + + align:start position:0% +its superposition State during to one is + + + align:start position:0% +its superposition State during to one is +just un of to + + align:start position:0% +just un of to + + + align:start position:0% +just un of to +one time + + align:start position:0% +one time + + + align:start position:0% +one time +row + + align:start position:0% +row + + + align:start position:0% +row +un okay then the second so this uh + + align:start position:0% +un okay then the second so this uh + + + align:start position:0% +un okay then the second so this uh +second sandwich of time propagators + + align:start position:0% +second sandwich of time propagators + + + align:start position:0% +second sandwich of time propagators +propagates the density Matrix forward in + + align:start position:0% +propagates the density Matrix forward in + + + align:start position:0% +propagates the density Matrix forward in +time at after that time period we again + + align:start position:0% +time at after that time period we again + + + align:start position:0% +time at after that time period we again +we have a dipole operator here and it + + align:start position:0% +we have a dipole operator here and it + + + align:start position:0% +we have a dipole operator here and it +acts from the left to the right on the + + align:start position:0% +acts from the left to the right on the + + + align:start position:0% +acts from the left to the right on the +density + + align:start position:0% +density + + + align:start position:0% +density +Matrix and then after that interaction + + align:start position:0% +Matrix and then after that interaction + + + align:start position:0% +Matrix and then after that interaction +the system again gets propagated forward + + align:start position:0% +the system again gets propagated forward + + + align:start position:0% +the system again gets propagated forward +in time under you not this time where + + align:start position:0% +in time under you not this time where + + + align:start position:0% +in time under you not this time where +the time variable is to to the second + + align:start position:0% +the time variable is to to the second + + + align:start position:0% +the time variable is to to the second +period + + align:start position:0% +period + + + align:start position:0% +period +at the end of all of + + align:start position:0% +at the end of all of + + + align:start position:0% +at the end of all of +that we multiply by a third density + + align:start position:0% +that we multiply by a third density + + + align:start position:0% +that we multiply by a third density +operator and Trace over the + + align:start position:0% +operator and Trace over the + + + align:start position:0% +operator and Trace over the +Matrix okay so what uh + + align:start position:0% +Matrix okay so what uh + + + align:start position:0% +Matrix okay so what uh +is when this sort of gets at how you + + align:start position:0% +is when this sort of gets at how you + + + align:start position:0% +is when this sort of gets at how you +read these sorts of processes it + + align:start position:0% +read these sorts of processes it + + + align:start position:0% +read these sorts of processes it +reflects um that there is a sequence of + + align:start position:0% +reflects um that there is a sequence of + + + align:start position:0% +reflects um that there is a sequence of +interactions and that uh there's free + + align:start position:0% +interactions and that uh there's free + + + align:start position:0% +interactions and that uh there's free +evolution of the system in the absence + + align:start position:0% +evolution of the system in the absence + + + align:start position:0% +evolution of the system in the absence +of light field in between those + + align:start position:0% +of light field in between those + + + align:start position:0% +of light field in between those +interactions + + align:start position:0% + + + + align:start position:0% + +now what makes the different terms + + align:start position:0% +now what makes the different terms + + + align:start position:0% +now what makes the different terms +different Let's uh um let's take a look + + align:start position:0% +different Let's uh um let's take a look + + + align:start position:0% +different Let's uh um let's take a look +at that um before I leave one uh I + + align:start position:0% +at that um before I leave one uh I + + + align:start position:0% +at that um before I leave one uh I +should also point out there's one other + + align:start position:0% +should also point out there's one other + + + align:start position:0% +should also point out there's one other +way of um writing this kind of an + + align:start position:0% +way of um writing this kind of an + + + align:start position:0% +way of um writing this kind of an +equation + + align:start position:0% +equation + + + align:start position:0% +equation +um it's sometimes written you know + + align:start position:0% +um it's sometimes written you know + + + align:start position:0% +um it's sometimes written you know +explicitly as a Time + + align:start position:0% + + + + align:start position:0% + +propagator just remembering the solution + + align:start position:0% +propagator just remembering the solution + + + align:start position:0% +propagator just remembering the solution +to your + + align:start position:0% +to your + + + align:start position:0% +to your +um Louisville + + align:start position:0% + + + + align:start position:0% + +equation we can sort of encapsulate all + + align:start position:0% +equation we can sort of encapsulate all + + + align:start position:0% +equation we can sort of encapsulate all +that picture by writing it really in + + align:start position:0% +that picture by writing it really in + + + align:start position:0% +that picture by writing it really in +terms of a Time propagator G which sort + + align:start position:0% +terms of a Time propagator G which sort + + + align:start position:0% +terms of a Time propagator G which sort +of + + align:start position:0% +of + + + align:start position:0% +of +um has this + + align:start position:0% +um has this + + + align:start position:0% +um has this +uh you know that is the super operator + + align:start position:0% +uh you know that is the super operator + + + align:start position:0% +uh you know that is the super operator +that involves a m Matrix okay + + align:start position:0% +that involves a m Matrix okay + + + align:start position:0% +that involves a m Matrix okay +okay so now to compare terms let's go to + + align:start position:0% +okay so now to compare terms let's go to + + + align:start position:0% +okay so now to compare terms let's go to +another one which varies a little bit by + + align:start position:0% +another one which varies a little bit by + + + align:start position:0% +another one which varies a little bit by +the uh order of these operators the time + + align:start position:0% +the uh order of these operators the time + + + align:start position:0% +the uh order of these operators the time +ordering um so let's look at the next + + align:start position:0% +ordering um so let's look at the next + + + align:start position:0% +ordering um so let's look at the next +term in an expansion just call that one + + align:start position:0% +term in an expansion just call that one + + + align:start position:0% +term in an expansion just call that one +Q2 and let's look at one that um where + + align:start position:0% +Q2 and let's look at one that um where + + + align:start position:0% +Q2 and let's look at one that um where +we've + + align:start position:0% +we've + + + align:start position:0% +we've +got time zero here on the left + + align:start position:0% + + + + align:start position:0% + +okay now we can perform the same uh sort + + align:start position:0% +okay now we can perform the same uh sort + + + align:start position:0% +okay now we can perform the same uh sort +of + + align:start position:0% +of + + + align:start position:0% +of +manipulations um in this case uh the the + + align:start position:0% +manipulations um in this case uh the the + + + align:start position:0% +manipulations um in this case uh the the +first strategy is really just to + + align:start position:0% +first strategy is really just to + + + align:start position:0% +first strategy is really just to +move the zero operator over here the + + align:start position:0% +move the zero operator over here the + + + align:start position:0% +move the zero operator over here the +thing we have to remember is uh in + + align:start position:0% +thing we have to remember is uh in + + + align:start position:0% +thing we have to remember is uh in +evaluating these things is to enforce + + align:start position:0% +evaluating these things is to enforce + + + align:start position:0% +evaluating these things is to enforce +causality that is zero has to preed to 1 + + align:start position:0% +causality that is zero has to preed to 1 + + + align:start position:0% +causality that is zero has to preed to 1 +has to precede to 1 plus to 2 so in + + align:start position:0% +has to precede to 1 plus to 2 so in + + + align:start position:0% +has to precede to 1 plus to 2 so in +evaluating these things and then + + align:start position:0% +evaluating these things and then + + + align:start position:0% +evaluating these things and then +propagating the system forward you have + + align:start position:0% +propagating the system forward you have + + + align:start position:0% +propagating the system forward you have +to make sure to enforce that so the only + + align:start position:0% +to make sure to enforce that so the only + + + align:start position:0% +to make sure to enforce that so the only +way to enforce that this is the first + + align:start position:0% +way to enforce that this is the first + + + align:start position:0% +way to enforce that this is the first +operator is to act on the BR side sorry + + align:start position:0% +operator is to act on the BR side sorry + + + align:start position:0% +operator is to act on the BR side sorry +the BR side of the density Matrix so + + align:start position:0% +the BR side of the density Matrix so + + + align:start position:0% +the BR side of the density Matrix so +remember with this density Matrix you + + align:start position:0% +remember with this density Matrix you + + + align:start position:0% +remember with this density Matrix you +can think of it as this outer + + align:start position:0% +can think of it as this outer + + + align:start position:0% +can think of it as this outer +product um and this is equivalent to + + align:start position:0% +product um and this is equivalent to + + + align:start position:0% +product um and this is equivalent to +writing Trace UI to 1 plus to2 + + align:start position:0% +writing Trace UI to 1 plus to2 + + + align:start position:0% +writing Trace UI to 1 plus to2 +mui of to 1 row + + align:start position:0% +mui of to 1 row + + + align:start position:0% +mui of to 1 row +EQ mui of + + align:start position:0% +EQ mui of + + + align:start position:0% +EQ mui of +zero okay so now the action as opposed + + align:start position:0% +zero okay so now the action as opposed + + + align:start position:0% +zero okay so now the action as opposed +to up here where the dipole operator + + align:start position:0% +to up here where the dipole operator + + + align:start position:0% +to up here where the dipole operator +initially acted from the left to the + + align:start position:0% +initially acted from the left to the + + + align:start position:0% +initially acted from the left to the +right + + align:start position:0% +right + + + align:start position:0% +right +acting on the uh cat side of this + + align:start position:0% +acting on the uh cat side of this + + + align:start position:0% +acting on the uh cat side of this +density + + align:start position:0% +density + + + align:start position:0% +density +Matrix in this case it's the + + align:start position:0% +Matrix in this case it's the + + + align:start position:0% +Matrix in this case it's the +conjugate so here the um + + align:start position:0% +conjugate so here the um + + + align:start position:0% +conjugate so here the um +yeah the dipole operator is acting on + + align:start position:0% +yeah the dipole operator is acting on + + + align:start position:0% +yeah the dipole operator is acting on +the bro side of the density Matrix and + + align:start position:0% +the bro side of the density Matrix and + + + align:start position:0% +the bro side of the density Matrix and +so this really just reflects the fact + + align:start position:0% +so this really just reflects the fact + + + align:start position:0% +so this really just reflects the fact +we're keeping track of the fact that uh + + align:start position:0% +we're keeping track of the fact that uh + + + align:start position:0% +we're keeping track of the fact that uh +um there are different possibilities for + + align:start position:0% +um there are different possibilities for + + + align:start position:0% +um there are different possibilities for +the permutations of the phase of how + + align:start position:0% +the permutations of the phase of how + + + align:start position:0% +the permutations of the phase of how +coherences evolve once you start to have + + align:start position:0% +coherences evolve once you start to have + + + align:start position:0% +coherences evolve once you start to have +multiple time periods so this one is + + align:start position:0% +multiple time periods so this one is + + + align:start position:0% +multiple time periods so this one is +just um reflecting interaction first on + + align:start position:0% +just um reflecting interaction first on + + + align:start position:0% +just um reflecting interaction first on +the bra side here and then the second + + align:start position:0% +the bra side here and then the second + + + align:start position:0% +the bra side here and then the second +interaction is going to be from the cat + + align:start position:0% +interaction is going to be from the cat + + + align:start position:0% +interaction is going to be from the cat +side now you know we didn't keep track + + align:start position:0% +side now you know we didn't keep track + + + align:start position:0% +side now you know we didn't keep track +of this for linear spectroscopy wasn't + + align:start position:0% +of this for linear spectroscopy wasn't + + + align:start position:0% +of this for linear spectroscopy wasn't +necessary really but now what this uh + + align:start position:0% +necessary really but now what this uh + + + align:start position:0% +necessary really but now what this uh +encodes is the fact that the way um a + + align:start position:0% +encodes is the fact that the way um a + + + align:start position:0% +encodes is the fact that the way um a +coherence + + align:start position:0% +coherence + + + align:start position:0% +coherence +evolves uh whether you talk about this + + align:start position:0% +evolves uh whether you talk about this + + + align:start position:0% +evolves uh whether you talk about this +as you know a positive or negative + + align:start position:0% +as you know a positive or negative + + + align:start position:0% +as you know a positive or negative +complex exponential whether you think + + align:start position:0% +complex exponential whether you think + + + align:start position:0% +complex exponential whether you think +about this as phase acquired whether you + + align:start position:0% +about this as phase acquired whether you + + + align:start position:0% +about this as phase acquired whether you +you know think about this as positive + + align:start position:0% +you know think about this as positive + + + align:start position:0% +you know think about this as positive +time or negative time um we do in + + align:start position:0% +time or negative time um we do in + + + align:start position:0% +time or negative time um we do in +different time periods have to keep + + align:start position:0% +different time periods have to keep + + + align:start position:0% +different time periods have to keep +track of how one coherence evolves with + + align:start position:0% +track of how one coherence evolves with + + + align:start position:0% +track of how one coherence evolves with +respect to the other + + align:start position:0% +respect to the other + + + align:start position:0% +respect to the other +okay so what I want to get at here is + + align:start position:0% +okay so what I want to get at here is + + + align:start position:0% +okay so what I want to get at here is +that each one of these uh correlation + + align:start position:0% +that each one of these uh correlation + + + align:start position:0% +that each one of these uh correlation +functions that you see there they just + + align:start position:0% +functions that you see there they just + + + align:start position:0% +functions that you see there they just +differ by the time ordering of um of + + align:start position:0% +differ by the time ordering of um of + + + align:start position:0% +differ by the time ordering of um of +these interactions right and that + + align:start position:0% +these interactions right and that + + + align:start position:0% +these interactions right and that +q1 um is what we would call a c cat + + align:start position:0% +q1 um is what we would call a c cat + + + align:start position:0% +q1 um is what we would call a c cat +interaction right both both dipole + + align:start position:0% +interaction right both both dipole + + + align:start position:0% +interaction right both both dipole +operators act on the cat side of the + + align:start position:0% +operators act on the cat side of the + + + align:start position:0% +operators act on the cat side of the +density Matrix the the phase acquired by + + align:start position:0% +density Matrix the the phase acquired by + + + align:start position:0% +density Matrix the the phase acquired by +the system is locked it's additive you + + align:start position:0% +the system is locked it's additive you + + + align:start position:0% +the system is locked it's additive you +prop in the same way during the first + + align:start position:0% +prop in the same way during the first + + + align:start position:0% +prop in the same way during the first +period as you do during the + + align:start position:0% +period as you do during the + + + align:start position:0% +period as you do during the +second Q2 is + + align:start position:0% +second Q2 is + + + align:start position:0% +second Q2 is +a a braet Time ordering if you write out + + align:start position:0% +a a braet Time ordering if you write out + + + align:start position:0% +a a braet Time ordering if you write out +the other two you'll find that they are + + align:start position:0% +the other two you'll find that they are + + + align:start position:0% +the other two you'll find that they are +the conjugates of these two correlation + + align:start position:0% +the conjugates of these two correlation + + + align:start position:0% +the conjugates of these two correlation +functions + + align:start position:0% +functions + + + align:start position:0% +functions +so uh Q3 is going to be a k + + align:start position:0% +so uh Q3 is going to be a k + + + align:start position:0% +so uh Q3 is going to be a k +bra and bra and K bra these are just + + align:start position:0% +bra and bra and K bra these are just + + + align:start position:0% +bra and bra and K bra these are just +complex conjugates of one + + align:start position:0% +complex conjugates of one + + + align:start position:0% +complex conjugates of one +another Q4 is going to be bra + + align:start position:0% +another Q4 is going to be bra + + + align:start position:0% +another Q4 is going to be bra +bra okay so in the linear case of linear + + align:start position:0% +bra okay so in the linear case of linear + + + align:start position:0% +bra okay so in the linear case of linear +spectroscopy it was related to one + + align:start position:0% +spectroscopy it was related to one + + + align:start position:0% +spectroscopy it was related to one +correlation function and its complex + + align:start position:0% +correlation function and its complex + + + align:start position:0% +correlation function and its complex +conjugate in the case of second order + + align:start position:0% +conjugate in the case of second order + + + align:start position:0% +conjugate in the case of second order +nonlinear spectroscopy the response is + + align:start position:0% +nonlinear spectroscopy the response is + + + align:start position:0% +nonlinear spectroscopy the response is +related to two different correlation + + align:start position:0% +related to two different correlation + + + align:start position:0% +related to two different correlation +functions that are distinct and + + align:start position:0% +functions that are distinct and + + + align:start position:0% +functions that are distinct and +different plus their complex conjugates + + align:start position:0% +different plus their complex conjugates + + + align:start position:0% +different plus their complex conjugates +okay and so we might you know we'll also + + align:start position:0% +okay and so we might you know we'll also + + + align:start position:0% +okay and so we might you know we'll also +write that um sort of in a form that + + align:start position:0% +write that um sort of in a form that + + + align:start position:0% +write that um sort of in a form that +looks like the second order response + + align:start position:0% +looks like the second order response + + + align:start position:0% +looks like the second order response +H + + align:start position:0% + + + + align:start position:0% + +baral 1 to + + align:start position:0% +baral 1 to + + + align:start position:0% +baral 1 to +2 Q + + align:start position:0% +2 Q + + + align:start position:0% +2 Q +Alpha + + align:start position:0% +Alpha + + + align:start position:0% +Alpha +to + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + +Star okay and each one of these cues + + align:start position:0% +Star okay and each one of these cues + + + align:start position:0% +Star okay and each one of these cues +then is explicitly one type of + + align:start position:0% +then is explicitly one type of + + + align:start position:0% +then is explicitly one type of +correlation function of the form up here + + align:start position:0% +correlation function of the form up here + + + align:start position:0% +correlation function of the form up here +just the time ordering of + + align:start position:0% +just the time ordering of + + + align:start position:0% +just the time ordering of +operators + + align:start position:0% + + + + align:start position:0% + +okay any questions folks so I have one + + align:start position:0% +okay any questions folks so I have one + + + align:start position:0% +okay any questions folks so I have one +broad question about this kind of + + align:start position:0% +broad question about this kind of + + + align:start position:0% +broad question about this kind of +formalism so I I I always feel like I + + align:start position:0% +formalism so I I I always feel like I + + + align:start position:0% +formalism so I I I always feel like I +understand this mathematically but I + + align:start position:0% +understand this mathematically but I + + + align:start position:0% +understand this mathematically but I +have some + + align:start position:0% +have some + + + align:start position:0% +have some +trouble getting a physical intuition out + + align:start position:0% +trouble getting a physical intuition out + + + align:start position:0% +trouble getting a physical intuition out +of it because when I think of a real + + align:start position:0% +of it because when I think of a real + + + align:start position:0% +of it because when I think of a real +experiment you know I think of lasers + + align:start position:0% +experiment you know I think of lasers + + + align:start position:0% +experiment you know I think of lasers +which we haven't mentioned here and I + + align:start position:0% +which we haven't mentioned here and I + + + align:start position:0% +which we haven't mentioned here and I +feel like you + + align:start position:0% +feel like you + + + align:start position:0% +feel like you +know when you put specific times on this + + align:start position:0% +know when you put specific times on this + + + align:start position:0% +know when you put specific times on this +it's almost as if these are Delta + + align:start position:0% +it's almost as if these are Delta + + + align:start position:0% +it's almost as if these are Delta +functions of electric field right + + align:start position:0% +functions of electric field right + + + align:start position:0% +functions of electric field right +whereas you know real electric Fields + + align:start position:0% +whereas you know real electric Fields + + + align:start position:0% +whereas you know real electric Fields +you know have some temporal extent and + + align:start position:0% +you know have some temporal extent and + + + align:start position:0% +you know have some temporal extent and +right so how do we sort of translate + + align:start position:0% +right so how do we sort of translate + + + align:start position:0% +right so how do we sort of translate +from this notation right to thinking in + + align:start position:0% +from this notation right to thinking in + + + align:start position:0% +from this notation right to thinking in +terms of operators as you know literally + + align:start position:0% +terms of operators as you know literally + + + align:start position:0% +terms of operators as you know literally +you know equipment and observables as + + align:start position:0% +you know equipment and observables as + + + align:start position:0% +you know equipment and observables as +things we actually observe I I agree + + align:start position:0% +things we actually observe I I agree + + + align:start position:0% +things we actually observe I I agree +with you we're we're running through + + align:start position:0% +with you we're we're running through + + + align:start position:0% +with you we're we're running through +formalism now which really has very + + align:start position:0% +formalism now which really has very + + + align:start position:0% +formalism now which really has very +little intuition until you start working + + align:start position:0% +little intuition until you start working + + + align:start position:0% +little intuition until you start working +through specific experiments but I mean + + align:start position:0% +through specific experiments but I mean + + + align:start position:0% +through specific experiments but I mean +as far as your question goes um in much + + align:start position:0% +as far as your question goes um in much + + + align:start position:0% +as far as your question goes um in much +the same way that you can come up with + + align:start position:0% +the same way that you can come up with + + + align:start position:0% +the same way that you can come up with +the time or frequency domain + + align:start position:0% +the time or frequency domain + + + align:start position:0% +the time or frequency domain +representations of linear uh Spectra in + + align:start position:0% +representations of linear uh Spectra in + + + align:start position:0% +representations of linear uh Spectra in +terms of a susceptibility for the + + align:start position:0% +terms of a susceptibility for the + + + align:start position:0% +terms of a susceptibility for the +frequency domain or a response function + + align:start position:0% +frequency domain or a response function + + + align:start position:0% +frequency domain or a response function +for the time domain there will be + + align:start position:0% +for the time domain there will be + + + align:start position:0% +for the time domain there will be +similar sorts of fora transform + + align:start position:0% +similar sorts of fora transform + + + align:start position:0% +similar sorts of fora transform +relationships here that allow you to + + align:start position:0% +relationships here that allow you to + + + align:start position:0% +relationships here that allow you to +cast the nonlinear response either in + + align:start position:0% +cast the nonlinear response either in + + + align:start position:0% +cast the nonlinear response either in +terms of a Time sequence of interactions + + align:start position:0% +terms of a Time sequence of interactions + + + align:start position:0% +terms of a Time sequence of interactions +or in terms of products of multiple + + align:start position:0% +or in terms of products of multiple + + + align:start position:0% +or in terms of products of multiple +resonant denominators if you like the + + align:start position:0% +resonant denominators if you like the + + + align:start position:0% +resonant denominators if you like the +frequency domain representation um so + + align:start position:0% +frequency domain representation um so + + + align:start position:0% +frequency domain representation um so +that's sort of a simple version to it + + align:start position:0% +that's sort of a simple version to it + + + align:start position:0% +that's sort of a simple version to it +but uh you know what what you're really + + align:start position:0% +but uh you know what what you're really + + + align:start position:0% +but uh you know what what you're really +getting at is actually encoded in this + + align:start position:0% +getting at is actually encoded in this + + + align:start position:0% +getting at is actually encoded in this +expression for the polarization because + + align:start position:0% +expression for the polarization because + + + align:start position:0% +expression for the polarization because +um that's really what these terms + + align:start position:0% +um that's really what these terms + + + align:start position:0% +um that's really what these terms +reflect these are the shape of arbitrary + + align:start position:0% +reflect these are the shape of arbitrary + + + align:start position:0% +reflect these are the shape of arbitrary +they're of arbitrary form these are the + + align:start position:0% +they're of arbitrary form these are the + + + align:start position:0% +they're of arbitrary form these are the +shape of the electric Fields driving the + + align:start position:0% +shape of the electric Fields driving the + + + align:start position:0% +shape of the electric Fields driving the +system these could be brief pulses they + + align:start position:0% +system these could be brief pulses they + + + align:start position:0% +system these could be brief pulses they +could also be continuous monochromatic + + align:start position:0% +could also be continuous monochromatic + + + align:start position:0% +could also be continuous monochromatic +waves uh and those you know you would + + align:start position:0% +waves uh and those you know you would + + + align:start position:0% +waves uh and those you know you would +necessarily have to enforce time + + align:start position:0% +necessarily have to enforce time + + + align:start position:0% +necessarily have to enforce time +ordering and act on those uh and that + + align:start position:0% +ordering and act on those uh and that + + + align:start position:0% +ordering and act on those uh and that +turns into a 4A transform then right and + + align:start position:0% +turns into a 4A transform then right and + + + align:start position:0% +turns into a 4A transform then right and +so we'll we will go through some details + + align:start position:0% +so we'll we will go through some details + + + align:start position:0% +so we'll we will go through some details +I think that + + align:start position:0% +I think that + + + align:start position:0% +I think that +develop thanks \ No newline at end of file diff --git a/Unzc731iCUY.txt b/Unzc731iCUY.txt new file mode 100644 index 0000000000000000000000000000000000000000..5e67701a47000c0b984c54e2296613856871456b --- /dev/null +++ b/Unzc731iCUY.txt @@ -0,0 +1,10971 @@ +align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +the uh uniform code of military + + align:start position:0% +the uh uniform code of military + + + align:start position:0% +the uh uniform code of military +Justice specifies Court marshal for any + + align:start position:0% +Justice specifies Court marshal for any + + + align:start position:0% +Justice specifies Court marshal for any +officer who sends a soldier into battle + + align:start position:0% +officer who sends a soldier into battle + + + align:start position:0% +officer who sends a soldier into battle +without a weapon + + align:start position:0% +without a weapon + + + align:start position:0% +without a weapon +there ought to be a similar protection + + align:start position:0% +there ought to be a similar protection + + + align:start position:0% +there ought to be a similar protection +for students because students shouldn't + + align:start position:0% +for students because students shouldn't + + + align:start position:0% +for students because students shouldn't +go out into life without an ability to + + align:start position:0% +go out into life without an ability to + + + align:start position:0% +go out into life without an ability to +communicate and that's because your + + align:start position:0% +communicate and that's because your + + + align:start position:0% +communicate and that's because your +success in life will be determined + + align:start position:0% +success in life will be determined + + + align:start position:0% +success in life will be determined +largely by your ability to speak your + + align:start position:0% +largely by your ability to speak your + + + align:start position:0% +largely by your ability to speak your +ability to write and the quality of your + + align:start position:0% +ability to write and the quality of your + + + align:start position:0% +ability to write and the quality of your +ideas in that + + align:start position:0% +ideas in that + + + align:start position:0% +ideas in that +order I know that I can be successful in + + align:start position:0% +order I know that I can be successful in + + + align:start position:0% +order I know that I can be successful in +this + + align:start position:0% +this + + + align:start position:0% +this +because the quality of + + align:start position:0% +because the quality of + + + align:start position:0% +because the quality of +communication your speaking your writing + + align:start position:0% +communication your speaking your writing + + + align:start position:0% +communication your speaking your writing +is largely determined by this + + align:start position:0% +is largely determined by this + + + align:start position:0% +is largely determined by this +formula it's a matter of how much + + align:start position:0% +formula it's a matter of how much + + + align:start position:0% +formula it's a matter of how much +knowledge you have how much you practice + + align:start position:0% +knowledge you have how much you practice + + + align:start position:0% +knowledge you have how much you practice +with that knowledge and you're inherent + + align:start position:0% +with that knowledge and you're inherent + + + align:start position:0% +with that knowledge and you're inherent +talent and notice that the tea is very + + align:start position:0% +talent and notice that the tea is very + + + align:start position:0% +talent and notice that the tea is very +small what really matters is what you + + align:start position:0% +small what really matters is what you + + + align:start position:0% +small what really matters is what you +know this point came to me U suddenly a + + align:start position:0% +know this point came to me U suddenly a + + + align:start position:0% +know this point came to me U suddenly a +few decades ago when I was skiing at Sun + + align:start position:0% +few decades ago when I was skiing at Sun + + + align:start position:0% +few decades ago when I was skiing at Sun +Valley I had heard that it was celebrity + + align:start position:0% +Valley I had heard that it was celebrity + + + align:start position:0% +Valley I had heard that it was celebrity +weekend and one of the celebrities was + + align:start position:0% +weekend and one of the celebrities was + + + align:start position:0% +weekend and one of the celebrities was +a was Mary L Reon famous Olympic gymnast + + align:start position:0% +a was Mary L Reon famous Olympic gymnast + + + align:start position:0% +a was Mary L Reon famous Olympic gymnast +perfect tens in the vault and I heard + + align:start position:0% +perfect tens in the vault and I heard + + + align:start position:0% +perfect tens in the vault and I heard +that she was an novice at skiing so when + + align:start position:0% +that she was an novice at skiing so when + + + align:start position:0% +that she was an novice at skiing so when +the opportune moment arrived I looked + + align:start position:0% +the opportune moment arrived I looked + + + align:start position:0% +the opportune moment arrived I looked +over on a novice slope and saw this + + align:start position:0% +over on a novice slope and saw this + + + align:start position:0% +over on a novice slope and saw this +young woman who when she became + + align:start position:0% +young woman who when she became + + + align:start position:0% +young woman who when she became +unbalanced went like that and I said + + align:start position:0% +unbalanced went like that and I said + + + align:start position:0% +unbalanced went like that and I said +that's got to be her that must be the + + align:start position:0% +that's got to be her that must be the + + + align:start position:0% +that's got to be her that must be the +gymnast but then it occurred to me I'm a + + align:start position:0% +gymnast but then it occurred to me I'm a + + + align:start position:0% +gymnast but then it occurred to me I'm a +much better skier than she is and she's + + align:start position:0% +much better skier than she is and she's + + + align:start position:0% +much better skier than she is and she's +an Olympic Athlete not only an ordinary + + align:start position:0% +an Olympic Athlete not only an ordinary + + + align:start position:0% +an Olympic Athlete not only an ordinary +Olympic Athlete an outstanding + + align:start position:0% +Olympic Athlete an outstanding + + + align:start position:0% +Olympic Athlete an outstanding +one and I was a better skier because I + + align:start position:0% +one and I was a better skier because I + + + align:start position:0% +one and I was a better skier because I +had the K and I had the p and all she + + align:start position:0% +had the K and I had the p and all she + + + align:start position:0% +had the K and I had the p and all she +had was the tea so you can get a lot + + align:start position:0% +had was the tea so you can get a lot + + + align:start position:0% +had was the tea so you can get a lot +better than people who may have inherent + + align:start position:0% +better than people who may have inherent + + + align:start position:0% +better than people who may have inherent +talents if you have the right amount of + + align:start position:0% +talents if you have the right amount of + + + align:start position:0% +talents if you have the right amount of +knowledge so that's what my objective is + + align:start position:0% +knowledge so that's what my objective is + + + align:start position:0% +knowledge so that's what my objective is +today and here's my promise today you + + align:start position:0% +today and here's my promise today you + + + align:start position:0% +today and here's my promise today you +will see + + align:start position:0% +will see + + + align:start position:0% +will see +some examples of what you can put in + + align:start position:0% +some examples of what you can put in + + + align:start position:0% +some examples of what you can put in +your + + align:start position:0% +your + + + align:start position:0% +your +armorium of speaking techniques + + align:start position:0% +armorium of speaking techniques + + + align:start position:0% +armorium of speaking techniques +and it will be the casee that someone of + + align:start position:0% +and it will be the casee that someone of + + + align:start position:0% +and it will be the casee that someone of +those examples some urtic some technique + + align:start position:0% +those examples some urtic some technique + + + align:start position:0% +those examples some urtic some technique +maybe only one will make will be the one + + align:start position:0% +maybe only one will make will be the one + + + align:start position:0% +maybe only one will make will be the one +that gets you the + + align:start position:0% +that gets you the + + + align:start position:0% +that gets you the +job and so this is a very nonlinear + + align:start position:0% +job and so this is a very nonlinear + + + align:start position:0% +job and so this is a very nonlinear +process you never know when it's going + + align:start position:0% +process you never know when it's going + + + align:start position:0% +process you never know when it's going +to happen but that is my promise by the + + align:start position:0% +to happen but that is my promise by the + + + align:start position:0% +to happen but that is my promise by the +end of the next 60 Minutes you'll been + + align:start position:0% +end of the next 60 Minutes you'll been + + + align:start position:0% +end of the next 60 Minutes you'll been +exposed to a lot of ideas some of which + + align:start position:0% +exposed to a lot of ideas some of which + + + align:start position:0% +exposed to a lot of ideas some of which +you'll incorporate into your own + + align:start position:0% +you'll incorporate into your own + + + align:start position:0% +you'll incorporate into your own +repertoire and they will ensure that you + + align:start position:0% +repertoire and they will ensure that you + + + align:start position:0% +repertoire and they will ensure that you +get the maximum + + align:start position:0% +get the maximum + + + align:start position:0% +get the maximum +opportunity to uh have your + + align:start position:0% +opportunity to uh have your + + + align:start position:0% +opportunity to uh have your +ideas uh valued and accepted by the + + align:start position:0% +ideas uh valued and accepted by the + + + align:start position:0% +ideas uh valued and accepted by the +people you speak with now in order to do + + align:start position:0% +people you speak with now in order to do + + + align:start position:0% +people you speak with now in order to do +that we have to have a rule of + + align:start position:0% +that we have to have a rule of + + + align:start position:0% +that we have to have a rule of +Engagement and that + + align:start position:0% +Engagement and that + + + align:start position:0% +Engagement and that +is no laptops no cell phones so if you + + align:start position:0% +is no laptops no cell phones so if you + + + align:start position:0% +is no laptops no cell phones so if you +could close those I'll start up as soon + + align:start position:0% +could close those I'll start up as soon + + + align:start position:0% +could close those I'll start up as soon +as you're + + align:start position:0% +as you're + + + align:start position:0% +as you're +done some people ask why that uh is a is + + align:start position:0% +done some people ask why that uh is a is + + + align:start position:0% +done some people ask why that uh is a is +a rule + + align:start position:0% +a rule + + + align:start position:0% +a rule +engagement and the answer is we humans + + align:start position:0% +engagement and the answer is we humans + + + align:start position:0% +engagement and the answer is we humans +only have one language processor and if + + align:start position:0% +only have one language processor and if + + + align:start position:0% +only have one language processor and if +your language processor is engage could + + align:start position:0% +your language processor is engage could + + + align:start position:0% +your language processor is engage could +you shut the laptop please if your + + align:start position:0% +you shut the laptop please if your + + + align:start position:0% +you shut the laptop please if your +language processor is engaged browsing + + align:start position:0% +language processor is engaged browsing + + + align:start position:0% +language processor is engaged browsing +the web or reading your email you're + + align:start position:0% +the web or reading your email you're + + + align:start position:0% +the web or reading your email you're +distracted and worse yet you distract + + align:start position:0% +distracted and worse yet you distract + + + align:start position:0% +distracted and worse yet you distract +all the people around you Studies have + + align:start position:0% +all the people around you Studies have + + + align:start position:0% +all the people around you Studies have +shown that and worse yet if I see a open + + align:start position:0% +shown that and worse yet if I see a open + + + align:start position:0% +shown that and worse yet if I see a open +laptop somewhere back there or up here + + align:start position:0% +laptop somewhere back there or up here + + + align:start position:0% +laptop somewhere back there or up here +it drives me nuts and I do a worse job + + align:start position:0% +it drives me nuts and I do a worse job + + + align:start position:0% +it drives me nuts and I do a worse job +and so that ensures that all of your + + align:start position:0% +and so that ensures that all of your + + + align:start position:0% +and so that ensures that all of your +friends who were who are paying + + align:start position:0% +friends who were who are paying + + + align:start position:0% +friends who were who are paying +attention uh don't get the performance + + align:start position:0% +attention uh don't get the performance + + + align:start position:0% +attention uh don't get the performance +that they came to + + align:start position:0% +that they came to + + + align:start position:0% +that they came to +have so that's it for Preamble let's get + + align:start position:0% +have so that's it for Preamble let's get + + + align:start position:0% +have so that's it for Preamble let's get +started first thing to talk about of + + align:start position:0% +started first thing to talk about of + + + align:start position:0% +started first thing to talk about of +course is how to + + align:start position:0% + + + + align:start position:0% + +start some people think the right thing + + align:start position:0% +start some people think the right thing + + + align:start position:0% +start some people think the right thing +to do is to start a talk + + align:start position:0% +to do is to start a talk + + + align:start position:0% +to do is to start a talk +a + + align:start position:0% + + + + align:start position:0% + +joke I don't recommend + + align:start position:0% + + + + align:start position:0% + +it and the reason is that in the + + align:start position:0% +it and the reason is that in the + + + align:start position:0% +it and the reason is that in the +beginning of a talk people are still + + align:start position:0% +beginning of a talk people are still + + + align:start position:0% +beginning of a talk people are still +putting their laptops away they're + + align:start position:0% +putting their laptops away they're + + + align:start position:0% +putting their laptops away they're +becoming adjusted to your speaking + + align:start position:0% +becoming adjusted to your speaking + + + align:start position:0% +becoming adjusted to your speaking +parameters to your vocal + + align:start position:0% +parameters to your vocal + + + align:start position:0% +parameters to your vocal +parameters and they're not ready for a + + align:start position:0% +parameters and they're not ready for a + + + align:start position:0% +parameters and they're not ready for a +joke so it doesn't work very well they + + align:start position:0% +joke so it doesn't work very well they + + + align:start position:0% +joke so it doesn't work very well they +usually fall + + align:start position:0% +usually fall + + + align:start position:0% +usually fall +flat what you want to do instead is + + align:start position:0% +flat what you want to do instead is + + + align:start position:0% +flat what you want to do instead is +start with empowerment + + align:start position:0% + + + + align:start position:0% + +promise you want to tell people what + + align:start position:0% +promise you want to tell people what + + + align:start position:0% +promise you want to tell people what +they're going to know at the end of the + + align:start position:0% +they're going to know at the end of the + + + align:start position:0% +they're going to know at the end of the +hour that they didn't know at the + + align:start position:0% +hour that they didn't know at the + + + align:start position:0% +hour that they didn't know at the +beginning of the hour it's an + + align:start position:0% +beginning of the hour it's an + + + align:start position:0% +beginning of the hour it's an +empowerment promise it's the reason for + + align:start position:0% +empowerment promise it's the reason for + + + align:start position:0% +empowerment promise it's the reason for +being + + align:start position:0% +being + + + align:start position:0% +being +here uh what would be an example oh I + + align:start position:0% +here uh what would be an example oh I + + + align:start position:0% +here uh what would be an example oh I +see at the end of this 60 Minutes you + + align:start position:0% +see at the end of this 60 Minutes you + + + align:start position:0% +see at the end of this 60 Minutes you +will know things about speaking you + + align:start position:0% +will know things about speaking you + + + align:start position:0% +will know things about speaking you +don't know now and something among those + + align:start position:0% +don't know now and something among those + + + align:start position:0% +don't know now and something among those +things you know will be make a + + align:start position:0% +things you know will be make a + + + align:start position:0% +things you know will be make a +difference in your life yeah that's an + + align:start position:0% +difference in your life yeah that's an + + + align:start position:0% +difference in your life yeah that's an +empowerment promise so that's the best + + align:start position:0% +empowerment promise so that's the best + + + align:start position:0% +empowerment promise so that's the best +way to + + align:start position:0% +way to + + + align:start position:0% +way to +start so now that I've talked a little + + align:start position:0% +start so now that I've talked a little + + + align:start position:0% +start so now that I've talked a little +bit about how to start what I want to do + + align:start position:0% +bit about how to start what I want to do + + + align:start position:0% +bit about how to start what I want to do +is give you some samples of tics that + + align:start position:0% +is give you some samples of tics that + + + align:start position:0% +is give you some samples of tics that +are always on my mind when I give a + + align:start position:0% +are always on my mind when I give a + + + align:start position:0% +are always on my mind when I give a +talk and first of these + + align:start position:0% +talk and first of these + + + align:start position:0% +talk and first of these +tics is that it's a good idea to cycle + + align:start position:0% +tics is that it's a good idea to cycle + + + align:start position:0% +tics is that it's a good idea to cycle +on the + + align:start position:0% +on the + + + align:start position:0% +on the +subject go around it go around it again + + align:start position:0% +subject go around it go around it again + + + align:start position:0% +subject go around it go around it again +go around + + align:start position:0% +go around + + + align:start position:0% +go around +again some people say tell them what you + + align:start position:0% +again some people say tell them what you + + + align:start position:0% +again some people say tell them what you +want to tell + + align:start position:0% +want to tell + + + align:start position:0% +want to tell +them tell them again and then tell them + + align:start position:0% +them tell them again and then tell them + + + align:start position:0% +them tell them again and then tell them +a third time as if + + align:start position:0% +a third time as if + + + align:start position:0% +a third time as if +people weren't intelligent but the point + + align:start position:0% +people weren't intelligent but the point + + + align:start position:0% +people weren't intelligent but the point +is the reason is well there are many + + align:start position:0% +is the reason is well there are many + + + align:start position:0% +is the reason is well there are many +reasons one of which is at any given + + align:start position:0% +reasons one of which is at any given + + + align:start position:0% +reasons one of which is at any given +moment about 20% of you will be fogged + + align:start position:0% +moment about 20% of you will be fogged + + + align:start position:0% +moment about 20% of you will be fogged +out no matter what the lecture is so if + + align:start position:0% +out no matter what the lecture is so if + + + align:start position:0% +out no matter what the lecture is so if +you want to ensure that the probability + + align:start position:0% +you want to ensure that the probability + + + align:start position:0% +you want to ensure that the probability +that everybody gets it is high you need + + align:start position:0% +that everybody gets it is high you need + + + align:start position:0% +that everybody gets it is high you need +to say it three + + align:start position:0% +to say it three + + + align:start position:0% +to say it three +times so cycling is one of the things + + align:start position:0% +times so cycling is one of the things + + + align:start position:0% +times so cycling is one of the things +that I always think about when I give a + + align:start position:0% +that I always think about when I give a + + + align:start position:0% +that I always think about when I give a +talk another thing I think about is in + + align:start position:0% +talk another thing I think about is in + + + align:start position:0% +talk another thing I think about is in +explaining my idea I want to build a + + align:start position:0% +explaining my idea I want to build a + + + align:start position:0% +explaining my idea I want to build a +fence around + + align:start position:0% + + + + align:start position:0% + +it so that it's not confused with + + align:start position:0% +it so that it's not confused with + + + align:start position:0% +it so that it's not confused with +somebody else's idea so if you were from + + align:start position:0% +somebody else's idea so if you were from + + + align:start position:0% +somebody else's idea so if you were from +Mars and I was teaching you about what + + align:start position:0% +Mars and I was teaching you about what + + + align:start position:0% +Mars and I was teaching you about what +an arch is I might say to you well + + align:start position:0% +an arch is I might say to you well + + + align:start position:0% +an arch is I might say to you well +that's an arch and that's not to be + + align:start position:0% +that's an arch and that's not to be + + + align:start position:0% +that's an arch and that's not to be +confused with some other things that + + align:start position:0% +confused with some other things that + + + align:start position:0% +confused with some other things that +other people might think is an AR this + + align:start position:0% +other people might think is an AR this + + + align:start position:0% +other people might think is an AR this +is not an AR + + align:start position:0% + + + + align:start position:0% + +Arch that's not an arch I'm building a + + align:start position:0% +Arch that's not an arch I'm building a + + + align:start position:0% +Arch that's not an arch I'm building a +fence around my idea so that it can be + + align:start position:0% +fence around my idea so that it can be + + + align:start position:0% +fence around my idea so that it can be +distinguished from somebody else's idea + + align:start position:0% +distinguished from somebody else's idea + + + align:start position:0% +distinguished from somebody else's idea +so in a more technical sense I might say + + align:start position:0% +so in a more technical sense I might say + + + align:start position:0% +so in a more technical sense I might say +well my algorithm might similar might + + align:start position:0% +well my algorithm might similar might + + + align:start position:0% +well my algorithm might similar might +seem similar to Jones's algorithm except + + align:start position:0% +seem similar to Jones's algorithm except + + + align:start position:0% +seem similar to Jones's algorithm except +his is exponential and mine's linear + + align:start position:0% +his is exponential and mine's linear + + + align:start position:0% +his is exponential and mine's linear +that's putting a fence around your idea + + align:start position:0% +that's putting a fence around your idea + + + align:start position:0% +that's putting a fence around your idea +so that people can not be confused about + + align:start position:0% +so that people can not be confused about + + + align:start position:0% +so that people can not be confused about +how it might relate to something + + align:start position:0% +how it might relate to something + + + align:start position:0% +how it might relate to something +else the third thing on this list of + + align:start position:0% +else the third thing on this list of + + + align:start position:0% +else the third thing on this list of +samples + + align:start position:0% +samples + + + align:start position:0% +samples +is the idea of verbal + + align:start position:0% + + + + align:start position:0% + +punctuation and the idea here is that + + align:start position:0% +punctuation and the idea here is that + + + align:start position:0% +punctuation and the idea here is that +because people will uh occasionally fog + + align:start position:0% +because people will uh occasionally fog + + + align:start position:0% +because people will uh occasionally fog +out and need to get back on the bus you + + align:start position:0% +out and need to get back on the bus you + + + align:start position:0% +out and need to get back on the bus you +need to provide some Landmark places + + align:start position:0% +need to provide some Landmark places + + + align:start position:0% +need to provide some Landmark places +where you're announcing that it's a good + + align:start position:0% +where you're announcing that it's a good + + + align:start position:0% +where you're announcing that it's a good +time to get back on + + align:start position:0% +time to get back on + + + align:start position:0% +time to get back on +so I might in this talk say something + + align:start position:0% +so I might in this talk say something + + + align:start position:0% +so I might in this talk say something +about this being my + + align:start position:0% +about this being my + + + align:start position:0% +about this being my +outline the first thing we're going to + + align:start position:0% +outline the first thing we're going to + + + align:start position:0% +outline the first thing we're going to +do is talk about how to start then we're + + align:start position:0% +do is talk about how to start then we're + + + align:start position:0% +do is talk about how to start then we're +going to deal with these four samples + + align:start position:0% +going to deal with these four samples + + + align:start position:0% +going to deal with these four samples +and among these four samples I've talked + + align:start position:0% +and among these four samples I've talked + + + align:start position:0% +and among these four samples I've talked +about the first idea that's cycling the + + align:start position:0% +about the first idea that's cycling the + + + align:start position:0% +about the first idea that's cycling the +second idea building a and now the third + + align:start position:0% +second idea building a and now the third + + + align:start position:0% +second idea building a and now the third +idea is build is verbal + + align:start position:0% +idea is build is verbal + + + align:start position:0% +idea is build is verbal +punctuation so I'm enumerating I'm + + align:start position:0% +punctuation so I'm enumerating I'm + + + align:start position:0% +punctuation so I'm enumerating I'm +providing numbers I'm giving you a sense + + align:start position:0% +providing numbers I'm giving you a sense + + + align:start position:0% +providing numbers I'm giving you a sense +that there's a seam in the talk and you + + align:start position:0% +that there's a seam in the talk and you + + + align:start position:0% +that there's a seam in the talk and you +can get back back on + + align:start position:0% + + + + align:start position:0% + +okay so now we're on a + + align:start position:0% +okay so now we're on a + + + align:start position:0% +okay so now we're on a +roll uh and since we're on a + + align:start position:0% +roll uh and since we're on a + + + align:start position:0% +roll uh and since we're on a +roll can you uh guess what fourth idea + + align:start position:0% +roll can you uh guess what fourth idea + + + align:start position:0% +roll can you uh guess what fourth idea +might be here an idea that helps people + + align:start position:0% +might be here an idea that helps people + + + align:start position:0% +might be here an idea that helps people +get back on the + + align:start position:0% + + + + align:start position:0% + +bus yes ask question ask a question yes + + align:start position:0% +bus yes ask question ask a question yes + + + align:start position:0% +bus yes ask question ask a question yes +thank + + align:start position:0% +thank + + + align:start position:0% +thank +you so ask a question + + align:start position:0% + + + + align:start position:0% + +and so I will ask a question how how + + align:start position:0% +and so I will ask a question how how + + + align:start position:0% +and so I will ask a question how how +much dead air can there be how long can + + align:start position:0% +much dead air can there be how long can + + + align:start position:0% +much dead air can there be how long can +I pause uh I counted 7 Seconds it seems + + align:start position:0% +I pause uh I counted 7 Seconds it seems + + + align:start position:0% +I pause uh I counted 7 Seconds it seems +like an eternity to me to wait and not + + align:start position:0% +like an eternity to me to wait and not + + + align:start position:0% +like an eternity to me to wait and not +say anything for 10 for 7 seconds but + + align:start position:0% +say anything for 10 for 7 seconds but + + + align:start position:0% +say anything for 10 for 7 seconds but +that's the the standard amount of time + + align:start position:0% +that's the the standard amount of time + + + align:start position:0% +that's the the standard amount of time +you can wait for an answer and of course + + align:start position:0% +you can wait for an answer and of course + + + align:start position:0% +you can wait for an answer and of course +the question has to be carefully chosen + + align:start position:0% +the question has to be carefully chosen + + + align:start position:0% +the question has to be carefully chosen +it can't be too obvious because then + + align:start position:0% +it can't be too obvious because then + + + align:start position:0% +it can't be too obvious because then +people will be embarrassed to say what + + align:start position:0% +people will be embarrassed to say what + + + align:start position:0% +people will be embarrassed to say what +the answer is can't be too hard because + + align:start position:0% +the answer is can't be too hard because + + + align:start position:0% +the answer is can't be too hard because +nobody will have anything to + + align:start position:0% +nobody will have anything to + + + align:start position:0% +nobody will have anything to +say so here are some sample eristics you + + align:start position:0% +say so here are some sample eristics you + + + align:start position:0% +say so here are some sample eristics you +can put in your armorium and build up + + align:start position:0% +can put in your armorium and build up + + + align:start position:0% +can put in your armorium and build up +your your repertoire of uh ideas about + + align:start position:0% +your your repertoire of uh ideas about + + + align:start position:0% +your your repertoire of uh ideas about +presentation and now if this persuades + + align:start position:0% +presentation and now if this persuades + + + align:start position:0% +presentation and now if this persuades +you that there is something to know that + + align:start position:0% +you that there is something to know that + + + align:start position:0% +you that there is something to know that +there there is knowledge then I've + + align:start position:0% +there there is knowledge then I've + + + align:start position:0% +there there is knowledge then I've +already succeeded because what I want to + + align:start position:0% +already succeeded because what I want to + + + align:start position:0% +already succeeded because what I want to +convince you of is if you watch the + + align:start position:0% +convince you of is if you watch the + + + align:start position:0% +convince you of is if you watch the +speakers you admire and feel are + + align:start position:0% +speakers you admire and feel are + + + align:start position:0% +speakers you admire and feel are +effective and ask yourselves why they're + + align:start position:0% +effective and ask yourselves why they're + + + align:start position:0% +effective and ask yourselves why they're +successful then you can build up your + + align:start position:0% +successful then you can build up your + + + align:start position:0% +successful then you can build up your +own personal repertoire and develop your + + align:start position:0% +own personal repertoire and develop your + + + align:start position:0% +own personal repertoire and develop your +own personal style and that's that's my + + align:start position:0% +own personal style and that's that's my + + + align:start position:0% +own personal style and that's that's my +fundamental + + align:start position:0% +fundamental + + + align:start position:0% +fundamental +objective and the rest of this talk is + + align:start position:0% +objective and the rest of this talk is + + + align:start position:0% +objective and the rest of this talk is +about some of the things that are in my + + align:start position:0% +about some of the things that are in my + + + align:start position:0% +about some of the things that are in my +arm inventorium that I think are + + align:start position:0% +arm inventorium that I think are + + + align:start position:0% +arm inventorium that I think are +effective so next thing on our agenda as + + align:start position:0% +effective so next thing on our agenda as + + + align:start position:0% +effective so next thing on our agenda as +we start to discuss these other things + + align:start position:0% +we start to discuss these other things + + + align:start position:0% +we start to discuss these other things +is a discussion of time and place so + + align:start position:0% +is a discussion of time and place so + + + align:start position:0% +is a discussion of time and place so +what do you think is a good time to have + + align:start position:0% +what do you think is a good time to have + + + align:start position:0% +what do you think is a good time to have +a lecture + + align:start position:0% + + + + align:start position:0% + +11:00 a.m. + + align:start position:0% + + + + align:start position:0% + +yeah and the reason + + align:start position:0% + + + + align:start position:0% + +is most people at MIT are awake by then + + align:start position:0% +is most people at MIT are awake by then + + + align:start position:0% +is most people at MIT are awake by then +and hardly anyone is going back to + + align:start position:0% +and hardly anyone is going back to + + + align:start position:0% +and hardly anyone is going back to +sleep it's not right after a meal people + + align:start position:0% +sleep it's not right after a meal people + + + align:start position:0% +sleep it's not right after a meal people +aren't fatigued from this or that it's a + + align:start position:0% +aren't fatigued from this or that it's a + + + align:start position:0% +aren't fatigued from this or that it's a +great time to have a + + align:start position:0% +great time to have a + + + align:start position:0% +great time to have a +lecture so that brings me next to the + + align:start position:0% +lecture so that brings me next to the + + + align:start position:0% +lecture so that brings me next to the +question of what about the place and the + + align:start position:0% +question of what about the place and the + + + align:start position:0% +question of what about the place and the +most important thing about the place is + + align:start position:0% +most important thing about the place is + + + align:start position:0% +most important thing about the place is +that it be well + + align:start position:0% + + + + align:start position:0% + +lit this room is well + + align:start position:0% +lit this room is well + + + align:start position:0% +lit this room is well +lit problem with the other kinds of + + align:start position:0% +lit problem with the other kinds of + + + align:start position:0% +lit problem with the other kinds of +rooms is that we + + align:start position:0% +rooms is that we + + + align:start position:0% +rooms is that we +humans uh whenever the lights go down or + + align:start position:0% +humans uh whenever the lights go down or + + + align:start position:0% +humans uh whenever the lights go down or +whe whenever the room is dimly lighted + + align:start position:0% +whe whenever the room is dimly lighted + + + align:start position:0% +whe whenever the room is dimly lighted +it signals that we should go to sleep so + + align:start position:0% +it signals that we should go to sleep so + + + align:start position:0% +it signals that we should go to sleep so +whenever I go somewhere to give a talk + + align:start position:0% +whenever I go somewhere to give a talk + + + align:start position:0% +whenever I go somewhere to give a talk +even today the first thing I do when I + + align:start position:0% +even today the first thing I do when I + + + align:start position:0% +even today the first thing I do when I +speak to the audiovisual people is say + + align:start position:0% +speak to the audiovisual people is say + + + align:start position:0% +speak to the audiovisual people is say +keep the lights full + + align:start position:0% + + + + align:start position:0% + +up oh they might + + align:start position:0% +up oh they might + + + align:start position:0% +up oh they might +reply people will see the slides better + + align:start position:0% +reply people will see the slides better + + + align:start position:0% +reply people will see the slides better +if we turn the lights off and then I + + align:start position:0% +if we turn the lights off and then I + + + align:start position:0% +if we turn the lights off and then I +reply it's extremely hard to see slides + + align:start position:0% +reply it's extremely hard to see slides + + + align:start position:0% +reply it's extremely hard to see slides +through closed + + align:start position:0% + + + + align:start position:0% + +eyelids what else can you say about the + + align:start position:0% +eyelids what else can you say about the + + + align:start position:0% +eyelids what else can you say about the +place well the place should be + + align:start position:0% + + + + align:start position:0% + +cased and I mean that in the clal sense + + align:start position:0% +cased and I mean that in the clal sense + + + align:start position:0% +cased and I mean that in the clal sense +of like uh if you're robbing a bank you + + align:start position:0% +of like uh if you're robbing a bank you + + + align:start position:0% +of like uh if you're robbing a bank you +would go to the bank you know some some + + align:start position:0% +would go to the bank you know some some + + + align:start position:0% +would go to the bank you know some some +occasions before to see what it's like + + align:start position:0% +occasions before to see what it's like + + + align:start position:0% +occasions before to see what it's like +so there are no surprises when you uh + + align:start position:0% +so there are no surprises when you uh + + + align:start position:0% +so there are no surprises when you uh +when you do your + + align:start position:0% +when you do your + + + align:start position:0% +when you do your +robbery so uh whenever I go somewhere to + + align:start position:0% +robbery so uh whenever I go somewhere to + + + align:start position:0% +robbery so uh whenever I go somewhere to +speak the first thing I ask my host to + + align:start position:0% +speak the first thing I ask my host to + + + align:start position:0% +speak the first thing I ask my host to +do is to take me to the place where I'll + + align:start position:0% +do is to take me to the place where I'll + + + align:start position:0% +do is to take me to the place where I'll +be speaking so that there any + + align:start position:0% +be speaking so that there any + + + align:start position:0% +be speaking so that there any +weirdnesses I'll be able to + + align:start position:0% +weirdnesses I'll be able to + + + align:start position:0% +weirdnesses I'll be able to +um to deal with it uh sometimes it might + + align:start position:0% +um to deal with it uh sometimes it might + + + align:start position:0% +um to deal with it uh sometimes it might +require some intervention some time it + + align:start position:0% +require some intervention some time it + + + align:start position:0% +require some intervention some time it +just might require me to understand what + + align:start position:0% +just might require me to understand what + + + align:start position:0% +just might require me to understand what +the challenges are so when I came here + + align:start position:0% +the challenges are so when I came here + + + align:start position:0% +the challenges are so when I came here +this morning I did what I typically do I + + align:start position:0% +this morning I did what I typically do I + + + align:start position:0% +this morning I did what I typically do I +imagined that all the seats were filled + + align:start position:0% +imagined that all the seats were filled + + + align:start position:0% +imagined that all the seats were filled +with disinterested farm + + align:start position:0% +with disinterested farm + + + align:start position:0% +with disinterested farm +animals that way I knew that no matter + + align:start position:0% +animals that way I knew that no matter + + + align:start position:0% +animals that way I knew that no matter +how bad it was it wouldn't be as bad as + + align:start position:0% + + + + align:start position:0% + +that so uh finally it should be + + align:start position:0% +that so uh finally it should be + + + align:start position:0% +that so uh finally it should be +reasonably it should be reasonably + + align:start position:0% +reasonably it should be reasonably + + + align:start position:0% +reasonably it should be reasonably +populated + + align:start position:0% + + + + align:start position:0% + +it should + + align:start position:0% +it should + + + align:start position:0% +it should +be it should be the case that you know + + align:start position:0% +be it should be the case that you know + + + align:start position:0% +be it should be the case that you know +if there are 10 people in this Hall + + align:start position:0% +if there are 10 people in this Hall + + + align:start position:0% +if there are 10 people in this Hall +everyone would be wondering what's going + + align:start position:0% +everyone would be wondering what's going + + + align:start position:0% +everyone would be wondering what's going +on that's so much more interesting that + + align:start position:0% +on that's so much more interesting that + + + align:start position:0% +on that's so much more interesting that +nobody's here so you want to get a right + + align:start position:0% +nobody's here so you want to get a right + + + align:start position:0% +nobody's here so you want to get a right +siiz place that's doesn't have to be + + align:start position:0% +siiz place that's doesn't have to be + + + align:start position:0% +siiz place that's doesn't have to be +packed but it has to be more than half + + align:start position:0% +packed but it has to be more than half + + + align:start position:0% +packed but it has to be more than half +full so those are some thoughts about uh + + align:start position:0% +full so those are some thoughts about uh + + + align:start position:0% +full so those are some thoughts about uh +time and place next thing I want to talk + + align:start position:0% +time and place next thing I want to talk + + + align:start position:0% +time and place next thing I want to talk +about is uh subject of uh bo boards and + + align:start position:0% +about is uh subject of uh bo boards and + + + align:start position:0% +about is uh subject of uh bo boards and +props and + + align:start position:0% + + + + align:start position:0% + +slides well these are the tools of the + + align:start position:0% +slides well these are the tools of the + + + align:start position:0% +slides well these are the tools of the +trade uh I uh believe that this is the + + align:start position:0% +trade uh I uh believe that this is the + + + align:start position:0% +trade uh I uh believe that this is the +uh this is the the right tool for uh + + align:start position:0% +uh this is the the right tool for uh + + + align:start position:0% +uh this is the the right tool for uh +speaking when your purpose is uh + + align:start position:0% +speaking when your purpose is uh + + + align:start position:0% +speaking when your purpose is uh +informing uh the slides are good when + + align:start position:0% +informing uh the slides are good when + + + align:start position:0% +informing uh the slides are good when +your purpose is uh exposing but this is + + align:start position:0% +your purpose is uh exposing but this is + + + align:start position:0% +your purpose is uh exposing but this is +what I use when I'm informing teaching + + align:start position:0% +what I use when I'm informing teaching + + + align:start position:0% +what I use when I'm informing teaching +lecturing + + align:start position:0% +lecturing + + + align:start position:0% +lecturing +and there are several reasons why I use + + align:start position:0% +and there are several reasons why I use + + + align:start position:0% +and there are several reasons why I use +it for one thing when you use the board + + align:start position:0% +it for one thing when you use the board + + + align:start position:0% +it for one thing when you use the board +you have a Graphic + + align:start position:0% + + + + align:start position:0% + +quality it's the case that when you have + + align:start position:0% +quality it's the case that when you have + + + align:start position:0% +quality it's the case that when you have +a board then you can easily exploit the + + align:start position:0% +a board then you can easily exploit the + + + align:start position:0% +a board then you can easily exploit the +fact that you can use Graphics in your + + align:start position:0% +fact that you can use Graphics in your + + + align:start position:0% +fact that you can use Graphics in your +presentation so that's the graphic + + align:start position:0% +presentation so that's the graphic + + + align:start position:0% +presentation so that's the graphic +quality that I like and next thing I + + align:start position:0% +quality that I like and next thing I + + + align:start position:0% +quality that I like and next thing I +like is like a speed property + + align:start position:0% + + + + align:start position:0% + +the speed with which you write on the + + align:start position:0% +the speed with which you write on the + + + align:start position:0% +the speed with which you write on the +Blackboard is approximately the speed at + + align:start position:0% +Blackboard is approximately the speed at + + + align:start position:0% +Blackboard is approximately the speed at +which people can absorb ideas if you go + + align:start position:0% +which people can absorb ideas if you go + + + align:start position:0% +which people can absorb ideas if you go +flipping through a bunch of slides + + align:start position:0% +flipping through a bunch of slides + + + align:start position:0% +flipping through a bunch of slides +nobody can go that + + align:start position:0% + + + + align:start position:0% + +fast finally one great property of a + + align:start position:0% +fast finally one great property of a + + + align:start position:0% +fast finally one great property of a +board is that it's can be a + + align:start position:0% + + + + align:start position:0% + +Target many people + + align:start position:0% +Target many people + + + align:start position:0% +Target many people +who are novices at speaking find + + align:start position:0% +who are novices at speaking find + + + align:start position:0% +who are novices at speaking find +themselves uh suddenly aware of their + + align:start position:0% +themselves uh suddenly aware of their + + + align:start position:0% +themselves uh suddenly aware of their +hands it's as if their hands were + + align:start position:0% +hands it's as if their hands were + + + align:start position:0% +hands it's as if their hands were +private parts that shouldn't be exposed + + align:start position:0% +private parts that shouldn't be exposed + + + align:start position:0% +private parts that shouldn't be exposed +in public so right away they go into the + + align:start position:0% +in public so right away they go into the + + + align:start position:0% +in public so right away they go into the +pockets and this is considered insulting + + align:start position:0% +pockets and this is considered insulting + + + align:start position:0% +pockets and this is considered insulting +in some parts of the world or + + align:start position:0% +in some parts of the world or + + + align:start position:0% +in some parts of the world or +alternatively maybe the hands will go in + + align:start position:0% +alternatively maybe the hands will go in + + + align:start position:0% +alternatively maybe the hands will go in +in back like this I was once in a + + align:start position:0% +in back like this I was once in a + + + align:start position:0% +in back like this I was once in a +Convent in + + align:start position:0% +Convent in + + + align:start position:0% +Convent in +Serbia and uh my uh host U well we were + + align:start position:0% +Serbia and uh my uh host U well we were + + + align:start position:0% +Serbia and uh my uh host U well we were +as soon as we entered a nun came up to + + align:start position:0% +as soon as we entered a nun came up to + + + align:start position:0% +as soon as we entered a nun came up to +us and offered us a refreshment and I + + align:start position:0% +us and offered us a refreshment and I + + + align:start position:0% +us and offered us a refreshment and I +was about to say no thank you when he + + align:start position:0% +was about to say no thank you when he + + + align:start position:0% +was about to say no thank you when he +said eat that stuff or + + align:start position:0% +said eat that stuff or + + + align:start position:0% +said eat that stuff or +die it's a question of local custom and + + align:start position:0% +die it's a question of local custom and + + + align:start position:0% +die it's a question of local custom and +and politeness but then uh before + + align:start position:0% +and politeness but then uh before + + + align:start position:0% +and politeness but then uh before +anything happened there uh the nun + + align:start position:0% +anything happened there uh the nun + + + align:start position:0% +anything happened there uh the nun +pulled my hands off like this because it + + align:start position:0% +pulled my hands off like this because it + + + align:start position:0% +pulled my hands off like this because it +was extraordinarily insulting in that + + align:start position:0% +was extraordinarily insulting in that + + + align:start position:0% +was extraordinarily insulting in that +culture to have your hands behind your + + align:start position:0% +culture to have your hands behind your + + + align:start position:0% +culture to have your hands behind your +back so uh why is that well it's it's + + align:start position:0% +back so uh why is that well it's it's + + + align:start position:0% +back so uh why is that well it's it's +usually supposed that that's what that + + align:start position:0% +usually supposed that that's what that + + + align:start position:0% +usually supposed that that's what that +has to do with whether you're concealing + + align:start position:0% +has to do with whether you're concealing + + + align:start position:0% +has to do with whether you're concealing +a weapon so if your hands are in your + + align:start position:0% +a weapon so if your hands are in your + + + align:start position:0% +a weapon so if your hands are in your +pockets behind your back then um it + + align:start position:0% +pockets behind your back then um it + + + align:start position:0% +pockets behind your back then um it +looks like you might have a weapon and + + align:start position:0% +looks like you might have a weapon and + + + align:start position:0% +looks like you might have a weapon and +that's what I mean by The Virtue one of + + align:start position:0% +that's what I mean by The Virtue one of + + + align:start position:0% +that's what I mean by The Virtue one of +these virtues of the board now you have + + align:start position:0% +these virtues of the board now you have + + + align:start position:0% +these virtues of the board now you have +something to do with your hands you can + + align:start position:0% +something to do with your hands you can + + + align:start position:0% +something to do with your hands you can +point out the + + align:start position:0% + + + + align:start position:0% + +stuff I was once watching Seymour paper + + align:start position:0% +stuff I was once watching Seymour paper + + + align:start position:0% +stuff I was once watching Seymour paper +give a lecture I thought it was terrific + + align:start position:0% +give a lecture I thought it was terrific + + + align:start position:0% +give a lecture I thought it was terrific +so I went a second time first time to + + align:start position:0% +so I went a second time first time to + + + align:start position:0% +so I went a second time first time to +absorb the content second time to note + + align:start position:0% +absorb the content second time to note + + + align:start position:0% +absorb the content second time to note +the style + + align:start position:0% +the style + + + align:start position:0% +the style +and what I discovered is that papet was + + align:start position:0% +and what I discovered is that papet was + + + align:start position:0% +and what I discovered is that papet was +constantly pointing at the board and + + align:start position:0% +constantly pointing at the board and + + + align:start position:0% +constantly pointing at the board and +then I thought about a little while and + + align:start position:0% +then I thought about a little while and + + + align:start position:0% +then I thought about a little while and +I noted that none of the stuff he was + + align:start position:0% +I noted that none of the stuff he was + + + align:start position:0% +I noted that none of the stuff he was +pointing to had anything to do with what + + align:start position:0% +pointing to had anything to do with what + + + align:start position:0% +pointing to had anything to do with what +he was + + align:start position:0% + + + + align:start position:0% + +saying nevertheless it was a effective + + align:start position:0% + + + + align:start position:0% + +technique so that's a just a little bit + + align:start position:0% +technique so that's a just a little bit + + + align:start position:0% +technique so that's a just a little bit +about the the virtue of of of black + + align:start position:0% +about the the virtue of of of black + + + align:start position:0% +about the the virtue of of of black +boards and now I want to talk about + + align:start position:0% +boards and now I want to talk about + + + align:start position:0% +boards and now I want to talk about +props you know the custodians of + + align:start position:0% +props you know the custodians of + + + align:start position:0% +props you know the custodians of +knowledge about props s are the + + align:start position:0% +knowledge about props s are the + + + align:start position:0% +knowledge about props s are the +playwrights many decades ago I saw a + + align:start position:0% +playwrights many decades ago I saw a + + + align:start position:0% +playwrights many decades ago I saw a +play by Hinrich Ipson it was head of + + align:start position:0% +play by Hinrich Ipson it was head of + + + align:start position:0% +play by Hinrich Ipson it was head of +gabbler I remember vaguely there was + + align:start position:0% +gabbler I remember vaguely there was + + + align:start position:0% +gabbler I remember vaguely there was +about a woman in an unhappy marriage and + + align:start position:0% +about a woman in an unhappy marriage and + + + align:start position:0% +about a woman in an unhappy marriage and +her husband was in competition for an + + align:start position:0% +her husband was in competition for an + + + align:start position:0% +her husband was in competition for an +academic job with somebody else and he + + align:start position:0% +academic job with somebody else and he + + + align:start position:0% +academic job with somebody else and he +was going to lose partly because he was + + align:start position:0% +was going to lose partly because he was + + + align:start position:0% +was going to lose partly because he was +boring and partly because the competitor + + align:start position:0% +boring and partly because the competitor + + + align:start position:0% +boring and partly because the competitor +had just written a magnificent book by + + align:start position:0% +had just written a magnificent book by + + + align:start position:0% +had just written a magnificent book by +the way this is back in the days before + + align:start position:0% +the way this is back in the days before + + + align:start position:0% +the way this is back in the days before +they were copying machines and comp + + align:start position:0% +they were copying machines and comp + + + align:start position:0% +they were copying machines and comp +computers any anyhow as the play + + align:start position:0% +computers any anyhow as the play + + + align:start position:0% +computers any anyhow as the play +opens there's a pot bellied + + align:start position:0% + + + + align:start position:0% + +stove and in the beginning of the + + align:start position:0% +stove and in the beginning of the + + + align:start position:0% +stove and in the beginning of the +play uh the putt belly stove with its + + align:start position:0% +play uh the putt belly stove with its + + + align:start position:0% +play uh the putt belly stove with its +open door just has some uh slightly + + align:start position:0% +open door just has some uh slightly + + + align:start position:0% +open door just has some uh slightly +glowing + + align:start position:0% +glowing + + + align:start position:0% +glowing +Embers but the P stove is always there + + align:start position:0% +Embers but the P stove is always there + + + align:start position:0% +Embers but the P stove is always there +and it tension mounts in the play + + align:start position:0% +and it tension mounts in the play + + + align:start position:0% +and it tension mounts in the play +uh and you see this manuscript this prop + + align:start position:0% +uh and you see this manuscript this prop + + + align:start position:0% +uh and you see this manuscript this prop +that Ipson so artfully used you just + + align:start position:0% +that Ipson so artfully used you just + + + align:start position:0% +that Ipson so artfully used you just +know that something's going to happen + + align:start position:0% +know that something's going to happen + + + align:start position:0% +know that something's going to happen +because as the play goes on the Fire + + align:start position:0% +because as the play goes on the Fire + + + align:start position:0% +because as the play goes on the Fire +gets bigger and hotter and finally all + + align:start position:0% +gets bigger and hotter and finally all + + + align:start position:0% +gets bigger and hotter and finally all +consuming and you just know that that + + align:start position:0% +consuming and you just know that that + + + align:start position:0% +consuming and you just know that that +manuscript is going to go into that + + align:start position:0% +manuscript is going to go into that + + + align:start position:0% +manuscript is going to go into that +fire it's memorable thing it's what I + + align:start position:0% +fire it's memorable thing it's what I + + + align:start position:0% +fire it's memorable thing it's what I +remember about + + align:start position:0% +remember about + + + align:start position:0% +remember about +play so the play rights have got this + + align:start position:0% +play so the play rights have got this + + + align:start position:0% +play so the play rights have got this +all figured out + + align:start position:0% +all figured out + + + align:start position:0% +all figured out +uh but on the other hand they're not the + + align:start position:0% +uh but on the other hand they're not the + + + align:start position:0% +uh but on the other hand they're not the +only people who can use props here's an + + align:start position:0% +only people who can use props here's an + + + align:start position:0% +only people who can use props here's an +example of the use of a prop also due to + + align:start position:0% +example of the use of a prop also due to + + + align:start position:0% +example of the use of a prop also due to +sear paper he was talking about how it's + + align:start position:0% +sear paper he was talking about how it's + + + align:start position:0% +sear paper he was talking about how it's +important to look at the problem in the + + align:start position:0% +important to look at the problem in the + + + align:start position:0% +important to look at the problem in the +right way and here's an example that uh + + align:start position:0% +right way and here's an example that uh + + + align:start position:0% +right way and here's an example that uh +not only teaches that but makes it + + align:start position:0% +not only teaches that but makes it + + + align:start position:0% +not only teaches that but makes it +possible for you to embarrass your + + align:start position:0% +possible for you to embarrass your + + + align:start position:0% +possible for you to embarrass your +friends in mechanical engineering so + + align:start position:0% +friends in mechanical engineering so + + + align:start position:0% +friends in mechanical engineering so +here's here's what you do take this + + align:start position:0% +here's here's what you do take this + + + align:start position:0% +here's here's what you do take this +bicycle wheel you start it spinning and + + align:start position:0% +bicycle wheel you start it spinning and + + + align:start position:0% +bicycle wheel you start it spinning and +then you put some + + align:start position:0% +then you put some + + + align:start position:0% +then you put some +torque on the axle or + + align:start position:0% +torque on the axle or + + + align:start position:0% +torque on the axle or +equivalently you blow on the edge and + + align:start position:0% +equivalently you blow on the edge and + + + align:start position:0% +equivalently you blow on the edge and +the issue is does it go that way or does + + align:start position:0% +the issue is does it go that way or does + + + align:start position:0% +the issue is does it go that way or does +it go that way now the mechanical + + align:start position:0% +it go that way now the mechanical + + + align:start position:0% +it go that way now the mechanical +engineers will immediately say oh yes I + + align:start position:0% +engineers will immediately say oh yes I + + + align:start position:0% +engineers will immediately say oh yes I +see right hand screw and they'll put + + align:start position:0% +see right hand screw and they'll put + + + align:start position:0% +see right hand screw and they'll put +their fingers in this position but + + align:start position:0% +their fingers in this position but + + + align:start position:0% +their fingers in this position but +forget exactly how to align their + + align:start position:0% +forget exactly how to align their + + + align:start position:0% +forget exactly how to align their +fingers with various aspects of the + + align:start position:0% +fingers with various aspects of the + + + align:start position:0% +fingers with various aspects of the +problem and so it's you usually the case + + align:start position:0% +problem and so it's you usually the case + + + align:start position:0% +problem and so it's you usually the case +that they get it right with about a 50% + + align:start position:0% +that they get it right with about a 50% + + + align:start position:0% +that they get it right with about a 50% +probability so they um very fancy + + align:start position:0% +probability so they um very fancy + + + align:start position:0% +probability so they um very fancy +education gets them up to the point + + align:start position:0% +education gets them up to the point + + + align:start position:0% +education gets them up to the point +where they're equivalent to flipping a + + align:start position:0% +where they're equivalent to flipping a + + + align:start position:0% +where they're equivalent to flipping a +coin but it doesn't have to be that way + + align:start position:0% +coin but it doesn't have to be that way + + + align:start position:0% +coin but it doesn't have to be that way +because you can think about the problem + + align:start position:0% +because you can think about the problem + + + align:start position:0% +because you can think about the problem +a little differently so here's what you + + align:start position:0% +a little differently so here's what you + + + align:start position:0% +a little differently so here's what you +do you take some duct tape and you uh + + align:start position:0% +do you take some duct tape and you uh + + + align:start position:0% +do you take some duct tape and you uh +put it around part of the wheel like + + align:start position:0% +put it around part of the wheel like + + + align:start position:0% +put it around part of the wheel like +that and now you start to think about + + align:start position:0% +that and now you start to think about + + + align:start position:0% +that and now you start to think about +not the whole wheel but just the little + + align:start position:0% +not the whole wheel but just the little + + + align:start position:0% +not the whole wheel but just the little +piece that's underneath the duct tape so + + align:start position:0% +piece that's underneath the duct tape so + + + align:start position:0% +piece that's underneath the duct tape so +here that piece comes rolling over the + + align:start position:0% +here that piece comes rolling over the + + + align:start position:0% +here that piece comes rolling over the +top and at this point you blow on it + + align:start position:0% +top and at this point you blow on it + + + align:start position:0% +top and at this point you blow on it +with a puff of air forgetting about the + + align:start position:0% +with a puff of air forgetting about the + + + align:start position:0% +with a puff of air forgetting about the +rest of the wheel what happens to that + + align:start position:0% +rest of the wheel what happens to that + + + align:start position:0% +rest of the wheel what happens to that +little piece that's under the duct tape + + align:start position:0% +little piece that's under the duct tape + + + align:start position:0% +little piece that's under the duct tape +it must want to go that way cuz you bang + + align:start position:0% +it must want to go that way cuz you bang + + + align:start position:0% +it must want to go that way cuz you bang +on it like that it's already going down + + align:start position:0% +on it like that it's already going down + + + align:start position:0% +on it like that it's already going down +like that and what about the next piece + + align:start position:0% +like that and what about the next piece + + + align:start position:0% +like that and what about the next piece +same thing next piece same thing so the + + align:start position:0% +same thing next piece same thing so the + + + align:start position:0% +same thing next piece same thing so the +only thing that can happen is the wheel + + align:start position:0% +only thing that can happen is the wheel + + + align:start position:0% +only thing that can happen is the wheel +goes over like that and so now you'll + + align:start position:0% +goes over like that and so now you'll + + + align:start position:0% +goes over like that and so now you'll +never Wonder again because you're + + align:start position:0% +never Wonder again because you're + + + align:start position:0% +never Wonder again because you're +thinking about the problem in the right + + align:start position:0% +thinking about the problem in the right + + + align:start position:0% +thinking about the problem in the right +way and it's + + align:start position:0% +way and it's + + + align:start position:0% +way and it's +demonstrated by the use of a + + align:start position:0% + + + + align:start position:0% + +problem you can try this after we're + + align:start position:0% + + + + align:start position:0% + +done another example I like to remember + + align:start position:0% +done another example I like to remember + + + align:start position:0% +done another example I like to remember +is one from when I was taking + + align:start position:0% +is one from when I was taking + + + align:start position:0% +is one from when I was taking +801 Alan Lazarus was the instructor at + + align:start position:0% +801 Alan Lazarus was the instructor at + + + align:start position:0% +801 Alan Lazarus was the instructor at +the time and he was talking about the + + align:start position:0% +the time and he was talking about the + + + align:start position:0% +the time and he was talking about the +conservation of energy kinetic and + + align:start position:0% +conservation of energy kinetic and + + + align:start position:0% +conservation of energy kinetic and +potential + + align:start position:0% +potential + + + align:start position:0% +potential +and there was a long wire in the ceiling + + align:start position:0% +and there was a long wire in the ceiling + + + align:start position:0% +and there was a long wire in the ceiling +in 26 100 attached to a much bigger + + align:start position:0% +in 26 100 attached to a much bigger + + + align:start position:0% +in 26 100 attached to a much bigger +steel Ball but one not un like this and + + align:start position:0% +steel Ball but one not un like this and + + + align:start position:0% +steel Ball but one not un like this and +Lazarus uh took the + + align:start position:0% +Lazarus uh took the + + + align:start position:0% +Lazarus uh took the +ball up against the wall like this he + + align:start position:0% +ball up against the wall like this he + + + align:start position:0% +ball up against the wall like this he +put his head flat against the wall to + + align:start position:0% +put his head flat against the wall to + + + align:start position:0% +put his head flat against the wall to +steady + + align:start position:0% +steady + + + align:start position:0% +steady +himself and then uh he let go and the + + align:start position:0% +himself and then uh he let go and the + + + align:start position:0% +himself and then uh he let go and the +Pendulum takes many seconds ago over and + + align:start position:0% +Pendulum takes many seconds ago over and + + + align:start position:0% +Pendulum takes many seconds ago over and +back and then uh gently uh kisses + + align:start position:0% +back and then uh gently uh kisses + + + align:start position:0% +back and then uh gently uh kisses +lazarus's + + align:start position:0% +lazarus's + + + align:start position:0% +lazarus's +nose and so you have many seconds to + + align:start position:0% +nose and so you have many seconds to + + + align:start position:0% +nose and so you have many seconds to +think this guy really believes in the + + align:start position:0% +think this guy really believes in the + + + align:start position:0% +think this guy really believes in the +conservation of + + align:start position:0% + + + + align:start position:0% + +energy um do not try this at + + align:start position:0% +energy um do not try this at + + + align:start position:0% +energy um do not try this at +home the problem is that uh first time + + align:start position:0% +home the problem is that uh first time + + + align:start position:0% +home the problem is that uh first time +you do this you may not just let go + + align:start position:0% +you do this you may not just let go + + + align:start position:0% +you do this you may not just let go +there's a natural human tendency to push + + align:start position:0% + + + + align:start position:0% + +so uh that's a little bit on a subject + + align:start position:0% +so uh that's a little bit on a subject + + + align:start position:0% +so uh that's a little bit on a subject +of + + align:start position:0% + + + + align:start position:0% + +props you know it's interesting whenever + + align:start position:0% +props you know it's interesting whenever + + + align:start position:0% +props you know it's interesting whenever +surveys are taken students always say + + align:start position:0% +surveys are taken students always say + + + align:start position:0% +surveys are taken students always say +more chalk less + + align:start position:0% +more chalk less + + + align:start position:0% +more chalk less +PowerPoint and uh why would that be uh + + align:start position:0% +PowerPoint and uh why would that be uh + + + align:start position:0% +PowerPoint and uh why would that be uh +props are always also very + + align:start position:0% +props are always also very + + + align:start position:0% +props are always also very +effective why would that be uh I'll give + + align:start position:0% +effective why would that be uh I'll give + + + align:start position:0% +effective why would that be uh I'll give +you my Lunatic Fringe view on this it um + + align:start position:0% +you my Lunatic Fringe view on this it um + + + align:start position:0% +you my Lunatic Fringe view on this it um +has to do with + + align:start position:0% +has to do with + + + align:start position:0% +has to do with +uh what I would call + + align:start position:0% + + + + align:start position:0% + +empathetic + + align:start position:0% +empathetic + + + align:start position:0% +empathetic +mirroring when you're sitting up there + + align:start position:0% +mirroring when you're sitting up there + + + align:start position:0% +mirroring when you're sitting up there +watching me right on the board all those + + align:start position:0% +watching me right on the board all those + + + align:start position:0% +watching me right on the board all those +little mirror neurons in your head I + + align:start position:0% +little mirror neurons in your head I + + + align:start position:0% +little mirror neurons in your head I +believe become actuated and you can feel + + align:start position:0% +believe become actuated and you can feel + + + align:start position:0% +believe become actuated and you can feel +yourself writing on the Blackboard and + + align:start position:0% +yourself writing on the Blackboard and + + + align:start position:0% +yourself writing on the Blackboard and +even more so uh when I uh talk about + + align:start position:0% +even more so uh when I uh talk about + + + align:start position:0% +even more so uh when I uh talk about +this steel ball going that way and this + + align:start position:0% +this steel ball going that way and this + + + align:start position:0% +this steel ball going that way and this +way you can you can you can feel the + + align:start position:0% +way you can you can you can feel the + + + align:start position:0% +way you can you can you can feel the +ball as if you were me and you can't do + + align:start position:0% +ball as if you were me and you can't do + + + align:start position:0% +ball as if you were me and you can't do +that with a slide you can't do it with a + + align:start position:0% +that with a slide you can't do it with a + + + align:start position:0% +that with a slide you can't do it with a +picture you need to see see it uh in in + + align:start position:0% +picture you need to see see it uh in in + + + align:start position:0% +picture you need to see see it uh in in +the physical world that's why I think + + align:start position:0% +the physical world that's why I think + + + align:start position:0% +the physical world that's why I think +that oh yes of course it's it's there + + align:start position:0% +that oh yes of course it's it's there + + + align:start position:0% +that oh yes of course it's it's there +there speed questions involved too that + + align:start position:0% +there speed questions involved too that + + + align:start position:0% +there speed questions involved too that +have to be separated out but I think the + + align:start position:0% +have to be separated out but I think the + + + align:start position:0% +have to be separated out but I think the +empathetic mirroring is why props and + + align:start position:0% +empathetic mirroring is why props and + + + align:start position:0% +empathetic mirroring is why props and +the use of a Blackboard are so + + align:start position:0% +the use of a Blackboard are so + + + align:start position:0% +the use of a Blackboard are so +effective + + align:start position:0% +effective + + + align:start position:0% +effective +well let's + + align:start position:0% +well let's + + + align:start position:0% +well let's +see oh yes there is one more thing by + + align:start position:0% +see oh yes there is one more thing by + + + align:start position:0% +see oh yes there is one more thing by +way of uh the tools and that has to do + + align:start position:0% +way of uh the tools and that has to do + + + align:start position:0% +way of uh the tools and that has to do +with the uh use of + + align:start position:0% + + + + align:start position:0% + +slides I repeat I think they're for + + align:start position:0% +slides I repeat I think they're for + + + align:start position:0% +slides I repeat I think they're for +exposing ideas not for teaching ideas + + align:start position:0% +exposing ideas not for teaching ideas + + + align:start position:0% +exposing ideas not for teaching ideas +but that's what we do in a job talk or + + align:start position:0% +but that's what we do in a job talk or + + + align:start position:0% +but that's what we do in a job talk or +conference talk we expose ideas we don't + + align:start position:0% +conference talk we expose ideas we don't + + + align:start position:0% +conference talk we expose ideas we don't +teach them so let me tell you a little + + align:start position:0% +teach them so let me tell you a little + + + align:start position:0% +teach them so let me tell you a little +bit about my views on that + + align:start position:0% +bit about my views on that + + + align:start position:0% +bit about my views on that +um I remember once I was + + align:start position:0% +um I remember once I was + + + align:start position:0% +um I remember once I was +um in um Terminal + + align:start position:0% +um in um Terminal + + + align:start position:0% +um in um Terminal +A had Logan airport I just come back + + align:start position:0% +A had Logan airport I just come back + + + align:start position:0% +A had Logan airport I just come back +from a really miserable conference and + + align:start position:0% +from a really miserable conference and + + + align:start position:0% +from a really miserable conference and +the flight was really horrible it was + + align:start position:0% +the flight was really horrible it was + + + align:start position:0% +the flight was really horrible it was +one of those that feels like an + + align:start position:0% +one of those that feels like an + + + align:start position:0% +one of those that feels like an +unbalanced washing machine and for the + + align:start position:0% +unbalanced washing machine and for the + + + align:start position:0% +unbalanced washing machine and for the +only time in my life I decided to uh + + align:start position:0% +only time in my life I decided to uh + + + align:start position:0% +only time in my life I decided to uh +stop on my way to my car and have a cup + + align:start position:0% +stop on my way to my car and have a cup + + + align:start position:0% +stop on my way to my car and have a cup +of coffee and relax a little bit and I + + align:start position:0% +of coffee and relax a little bit and I + + + align:start position:0% +of coffee and relax a little bit and I +as I was there for a few minutes uh + + align:start position:0% +as I was there for a few minutes uh + + + align:start position:0% +as I was there for a few minutes uh +someone came up to me and said uh are + + align:start position:0% +someone came up to me and said uh are + + + align:start position:0% +someone came up to me and said uh are +you Professor + + align:start position:0% +you Professor + + + align:start position:0% +you Professor +Winston I think so I + + align:start position:0% +Winston I think so I + + + align:start position:0% +Winston I think so I +said I don't know I guess I was trying + + align:start position:0% +said I don't know I guess I was trying + + + align:start position:0% +said I don't know I guess I was trying +to be funny in any event uh he said I'm + + align:start position:0% +to be funny in any event uh he said I'm + + + align:start position:0% +to be funny in any event uh he said I'm +on my way to Europe to give a job talk + + align:start position:0% +on my way to Europe to give a job talk + + + align:start position:0% +on my way to Europe to give a job talk +would you mind critiquing my + + align:start position:0% +would you mind critiquing my + + + align:start position:0% +would you mind critiquing my +slides not at all I said you have too + + align:start position:0% +slides not at all I said you have too + + + align:start position:0% +slides not at all I said you have too +many and they have too many + + align:start position:0% +many and they have too many + + + align:start position:0% +many and they have too many +words how did you know he said thinking + + align:start position:0% +words how did you know he said thinking + + + align:start position:0% +words how did you know he said thinking +perhaps I'd seen a talk of his before I + + align:start position:0% +perhaps I'd seen a talk of his before I + + + align:start position:0% +perhaps I'd seen a talk of his before I +hadn't uh my reply was because it's + + align:start position:0% +hadn't uh my reply was because it's + + + align:start position:0% +hadn't uh my reply was because it's +always true there are always too many + + align:start position:0% +always true there are always too many + + + align:start position:0% +always true there are always too many +slides always too many words so let me + + align:start position:0% +slides always too many words so let me + + + align:start position:0% +slides always too many words so let me +show you some extreme examples of how + + align:start position:0% +show you some extreme examples of how + + + align:start position:0% +show you some extreme examples of how +not to use + + align:start position:0% + + + + align:start position:0% + +slides well for this demonstration I + + align:start position:0% +slides well for this demonstration I + + + align:start position:0% +slides well for this demonstration I +need to be uh way over + + align:start position:0% + + + + align:start position:0% + +here um and uh when I get over here then + + align:start position:0% +here um and uh when I get over here then + + + align:start position:0% +here um and uh when I get over here then +I can start to say things like + + align:start position:0% +I can start to say things like + + + align:start position:0% +I can start to say things like +U one of the things you shouldn't do is + + align:start position:0% +U one of the things you shouldn't do is + + + align:start position:0% +U one of the things you shouldn't do is +read your + + align:start position:0% +read your + + + align:start position:0% +read your +transparencies people in your audience + + align:start position:0% +transparencies people in your audience + + + align:start position:0% +transparencies people in your audience +know how to read and reading will just + + align:start position:0% +know how to read and reading will just + + + align:start position:0% +know how to read and reading will just +annoy them also you should be sure that + + align:start position:0% +annoy them also you should be sure that + + + align:start position:0% +annoy them also you should be sure that +you have only a few words on each + + align:start position:0% +you have only a few words on each + + + align:start position:0% +you have only a few words on each +transparency and that the words are easy + + align:start position:0% +transparency and that the words are easy + + + align:start position:0% +transparency and that the words are easy +to read and I hope it driving you + + align:start position:0% +to read and I hope it driving you + + + align:start position:0% +to read and I hope it driving you +crazy because I'm committing uh all + + align:start position:0% +crazy because I'm committing uh all + + + align:start position:0% +crazy because I'm committing uh all +kinds of crimes the first of which is + + align:start position:0% +kinds of crimes the first of which is + + + align:start position:0% +kinds of crimes the first of which is +that there are too many words on this + + align:start position:0% +that there are too many words on this + + + align:start position:0% +that there are too many words on this +slide second of which is I'm way over + + align:start position:0% +slide second of which is I'm way over + + + align:start position:0% +slide second of which is I'm way over +there and it slides away over there so + + align:start position:0% +there and it slides away over there so + + + align:start position:0% +there and it slides away over there so +you get into this uh tennis match + + align:start position:0% +you get into this uh tennis match + + + align:start position:0% +you get into this uh tennis match +feeling of uh shifting back and forth + + align:start position:0% +feeling of uh shifting back and forth + + + align:start position:0% +feeling of uh shifting back and forth +between the slide and the speaker you + + align:start position:0% +between the slide and the speaker you + + + align:start position:0% +between the slide and the speaker you +want the slides to be uh condiments to + + align:start position:0% +want the slides to be uh condiments to + + + align:start position:0% +want the slides to be uh condiments to +what you're saying not the main event or + + align:start position:0% +what you're saying not the main event or + + + align:start position:0% +what you're saying not the main event or +the opposite way around so how can we + + align:start position:0% +the opposite way around so how can we + + + align:start position:0% +the opposite way around so how can we +fix this step number one is to get rid + + align:start position:0% +fix this step number one is to get rid + + + align:start position:0% +fix this step number one is to get rid +of the background junk that's always + + align:start position:0% +of the background junk that's always + + + align:start position:0% +of the background junk that's always +distraction uh step number two is to get + + align:start position:0% +distraction uh step number two is to get + + + align:start position:0% +distraction uh step number two is to get +rid of the + + align:start position:0% +rid of the + + + align:start position:0% +rid of the +words when I reduceed the the words to + + align:start position:0% +words when I reduceed the the words to + + + align:start position:0% +words when I reduceed the the words to +these then everything I + + align:start position:0% +these then everything I + + + align:start position:0% +these then everything I +read a previous time I'm not licensed to + + align:start position:0% +read a previous time I'm not licensed to + + + align:start position:0% +read a previous time I'm not licensed to +say because it's not on the slide I'm + + align:start position:0% +say because it's not on the slide I'm + + + align:start position:0% +say because it's not on the slide I'm +not reading my slides anymore but I'm + + align:start position:0% +not reading my slides anymore but I'm + + + align:start position:0% +not reading my slides anymore but I'm +saying what was written on the slides in + + align:start position:0% +saying what was written on the slides in + + + align:start position:0% +saying what was written on the slides in +a previous + + align:start position:0% +a previous + + + align:start position:0% +a previous +example so what else can we do to + + align:start position:0% +example so what else can we do to + + + align:start position:0% +example so what else can we do to +simplify + + align:start position:0% +simplify + + + align:start position:0% +simplify +this well we can get rid of the logos we + + align:start position:0% +this well we can get rid of the logos we + + + align:start position:0% +this well we can get rid of the logos we +don't need + + align:start position:0% +don't need + + + align:start position:0% +don't need +them + + align:start position:0% +them + + + align:start position:0% +them +simplification what else can we + + align:start position:0% +simplification what else can we + + + align:start position:0% +simplification what else can we +do get rid of the + + align:start position:0% +do get rid of the + + + align:start position:0% +do get rid of the +title now I want to talk to you about + + align:start position:0% +title now I want to talk to you about + + + align:start position:0% +title now I want to talk to you about +some rules for slide preparation I'm + + align:start position:0% +some rules for slide preparation I'm + + + align:start position:0% +some rules for slide preparation I'm +telling you the title doesn't have to be + + align:start position:0% +telling you the title doesn't have to be + + + align:start position:0% +telling you the title doesn't have to be +up there by reducing the number of words + + align:start position:0% +up there by reducing the number of words + + + align:start position:0% +up there by reducing the number of words +on the slide I'm allowing you pay more + + align:start position:0% +on the slide I'm allowing you pay more + + + align:start position:0% +on the slide I'm allowing you pay more +attention to me unless to what's written + + align:start position:0% +attention to me unless to what's written + + + align:start position:0% +attention to me unless to what's written +on the + + align:start position:0% +on the + + + align:start position:0% +on the +slide I mentioned it before we have only + + align:start position:0% +slide I mentioned it before we have only + + + align:start position:0% +slide I mentioned it before we have only +one language processor and we can either + + align:start position:0% +one language processor and we can either + + + align:start position:0% +one language processor and we can either +use it to read stuff or to listen to the + + align:start position:0% +use it to read stuff or to listen to the + + + align:start position:0% +use it to read stuff or to listen to the +speaker and so if we have too many words + + align:start position:0% +speaker and so if we have too many words + + + align:start position:0% +speaker and so if we have too many words +on the slide forces people in the + + align:start position:0% +on the slide forces people in the + + + align:start position:0% +on the slide forces people in the +audience to read this stuff and not + + align:start position:0% + + + + align:start position:0% + +listen student of mine did an experiment + + align:start position:0% +listen student of mine did an experiment + + + align:start position:0% +listen student of mine did an experiment +a few years ago uh he taught some + + align:start position:0% +a few years ago uh he taught some + + + align:start position:0% +a few years ago uh he taught some +students some + + align:start position:0% +students some + + + align:start position:0% +students some +um web based programming + + align:start position:0% +um web based programming + + + align:start position:0% +um web based programming +ideas half the information was on slides + + align:start position:0% +ideas half the information was on slides + + + align:start position:0% +ideas half the information was on slides +he said the other half and then for a + + align:start position:0% +he said the other half and then for a + + + align:start position:0% +he said the other half and then for a +control group he reversed it and the + + align:start position:0% +control group he reversed it and the + + + align:start position:0% +control group he reversed it and the +question was what did the subjects that + + align:start position:0% +question was what did the subjects that + + + align:start position:0% +question was what did the subjects that +is to say freshman in his fraternity + + align:start position:0% +is to say freshman in his fraternity + + + align:start position:0% +is to say freshman in his fraternity +what did the subjects remember + + align:start position:0% +what did the subjects remember + + + align:start position:0% +what did the subjects remember +best what he + + align:start position:0% +best what he + + + align:start position:0% +best what he +said or what they read on the + + align:start position:0% +said or what they read on the + + + align:start position:0% +said or what they read on the +slide and the answer + + align:start position:0% +slide and the answer + + + align:start position:0% +slide and the answer +is what they read on the + + align:start position:0% +is what they read on the + + + align:start position:0% +is what they read on the +slide when their slides have a lot of + + align:start position:0% +slide when their slides have a lot of + + + align:start position:0% +slide when their slides have a lot of +material on it they don't pay attention + + align:start position:0% +material on it they don't pay attention + + + align:start position:0% +material on it they don't pay attention +to the speaker in fact in the after + + align:start position:0% +to the speaker in fact in the after + + + align:start position:0% +to the speaker in fact in the after +Action Report one of the subjects said I + + align:start position:0% +Action Report one of the subjects said I + + + align:start position:0% +Action Report one of the subjects said I +wish you hadn't talked so much it was + + align:start position:0% + + + + align:start position:0% + +distracting well that last item is + + align:start position:0% +distracting well that last item is + + + align:start position:0% +distracting well that last item is +eliminate + + align:start position:0% +eliminate + + + align:start position:0% +eliminate +clutter I hear some clutter no no no + + align:start position:0% +clutter I hear some clutter no no no + + + align:start position:0% +clutter I hear some clutter no no no +reason even for those + + align:start position:0% +reason even for those + + + align:start position:0% +reason even for those +bullets so the too many words problem is + + align:start position:0% +bullets so the too many words problem is + + + align:start position:0% +bullets so the too many words problem is +a consequence of h a crime Microsoft has + + align:start position:0% +a consequence of h a crime Microsoft has + + + align:start position:0% +a consequence of h a crime Microsoft has +committed by allowing you to use funds + + align:start position:0% +committed by allowing you to use funds + + + align:start position:0% +committed by allowing you to use funds +that are too small + + align:start position:0% +that are too small + + + align:start position:0% +that are too small +so you should all have a sample slide + + align:start position:0% +so you should all have a sample slide + + + align:start position:0% +so you should all have a sample slide +like this that you can use to determine + + align:start position:0% +like this that you can use to determine + + + align:start position:0% +like this that you can use to determine +what the minimum Fun Size is that's + + align:start position:0% +what the minimum Fun Size is that's + + + align:start position:0% +what the minimum Fun Size is that's +that's easily leisurable shiv what do + + align:start position:0% +that's easily leisurable shiv what do + + + align:start position:0% +that's easily leisurable shiv what do +you think of + + align:start position:0% +you think of + + + align:start position:0% +you think of +those which size is right what's that + + align:start position:0% +those which size is right what's that + + + align:start position:0% +those which size is right what's that +size is right yeah minimum maybe 40 or + + align:start position:0% +size is right yeah minimum maybe 40 or + + + align:start position:0% +size is right yeah minimum maybe 40 or +50 yeah he says 40 or 50 I think it's + + align:start position:0% +50 yeah he says 40 or 50 I think it's + + + align:start position:0% +50 yeah he says 40 or 50 I think it's +about right 35 is get too small not + + align:start position:0% +about right 35 is get too small not + + + align:start position:0% +about right 35 is get too small not +necessarily because you can't read it + + align:start position:0% +necessarily because you can't read it + + + align:start position:0% +necessarily because you can't read it +but because it because you're probably + + align:start position:0% +but because it because you're probably + + + align:start position:0% +but because it because you're probably +using it to get too many words on the + + align:start position:0% +using it to get too many words on the + + + align:start position:0% +using it to get too many words on the +slide what other crimes do we + + align:start position:0% +slide what other crimes do we + + + align:start position:0% +slide what other crimes do we +have well we have the laser pointer + + align:start position:0% +have well we have the laser pointer + + + align:start position:0% +have well we have the laser pointer +crime not for that I you know in the old + + align:start position:0% +crime not for that I you know in the old + + + align:start position:0% +crime not for that I you know in the old +days when we didn't have laser pointers + + align:start position:0% +days when we didn't have laser pointers + + + align:start position:0% +days when we didn't have laser pointers +we used wooden ones and people would go + + align:start position:0% +we used wooden ones and people would go + + + align:start position:0% +we used wooden ones and people would go +waving these things around + + align:start position:0% + + + + align:start position:0% + +and pretty soon it became almost like a + + align:start position:0% +and pretty soon it became almost like a + + + align:start position:0% +and pretty soon it became almost like a +the CH swirling contest so here's what + + align:start position:0% +the CH swirling contest so here's what + + + align:start position:0% +the CH swirling contest so here's what +here's what I recommended in the old + + align:start position:0% +here's what I recommended in the old + + + align:start position:0% +here's what I recommended in the old +days for dealing with this kind of + + align:start position:0% + + + + align:start position:0% + +pointer this example of used of a + + align:start position:0% + + + + align:start position:0% + +prop Jim glass up there saw this talk + + align:start position:0% +prop Jim glass up there saw this talk + + + align:start position:0% +prop Jim glass up there saw this talk +about 20 years ago and uh so oh yeah I + + align:start position:0% +about 20 years ago and uh so oh yeah I + + + align:start position:0% +about 20 years ago and uh so oh yeah I +remembered that talk that's the one + + align:start position:0% +remembered that talk that's the one + + + align:start position:0% +remembered that talk that's the one +where you broke the + + align:start position:0% +where you broke the + + + align:start position:0% +where you broke the +pointer it's amazing how props uh tend + + align:start position:0% +pointer it's amazing how props uh tend + + + align:start position:0% +pointer it's amazing how props uh tend +to be the things that are + + align:start position:0% +to be the things that are + + + align:start position:0% +to be the things that are +remembered well now oh we don't have uh + + align:start position:0% +remembered well now oh we don't have uh + + + align:start position:0% +remembered well now oh we don't have uh +we don't have physical pointers anymore + + align:start position:0% +we don't have physical pointers anymore + + + align:start position:0% +we don't have physical pointers anymore +we've got uh we got laser pointers + + align:start position:0% +we've got uh we got laser pointers + + + align:start position:0% +we've got uh we got laser pointers +that's a Wonder more people aren't + + align:start position:0% +that's a Wonder more people aren't + + + align:start position:0% +that's a Wonder more people aren't +driven into epileptic fits over this + + align:start position:0% +driven into epileptic fits over this + + + align:start position:0% +driven into epileptic fits over this +sort of stuff but here's what tends to + + align:start position:0% +sort of stuff but here's what tends to + + + align:start position:0% +sort of stuff but here's what tends to +happen look at that it's a lovely + + align:start position:0% +happen look at that it's a lovely + + + align:start position:0% +happen look at that it's a lovely +recursive picture and I can become part + + align:start position:0% +recursive picture and I can become part + + + align:start position:0% +recursive picture and I can become part +of it by putting that laser beam right + + align:start position:0% +of it by putting that laser beam right + + + align:start position:0% +of it by putting that laser beam right +on the back of my head up + + align:start position:0% + + + + align:start position:0% + +there and what do you see + + align:start position:0% +there and what do you see + + + align:start position:0% +there and what do you see +you see the back of my + + align:start position:0% +you see the back of my + + + align:start position:0% +you see the back of my +head I'm have no eye contact no + + align:start position:0% +head I'm have no eye contact no + + + align:start position:0% +head I'm have no eye contact no +engagement nothing I was sitting with a + + align:start position:0% +engagement nothing I was sitting with a + + + align:start position:0% +engagement nothing I was sitting with a +student watching a talk one day and she + + align:start position:0% +student watching a talk one day and she + + + align:start position:0% +student watching a talk one day and she +said you know what we could all leave + + align:start position:0% +said you know what we could all leave + + + align:start position:0% +said you know what we could all leave +and he wouldn't + + align:start position:0% + + + + align:start position:0% + +know so what happens when you use a + + align:start position:0% +know so what happens when you use a + + + align:start position:0% +know so what happens when you use a +laser pointer you can't use a laser + + align:start position:0% +laser pointer you can't use a laser + + + align:start position:0% +laser pointer you can't use a laser +pointer without turning your head and + + align:start position:0% +pointer without turning your head and + + + align:start position:0% +pointer without turning your head and +pointing it at something and when you do + + align:start position:0% +pointing it at something and when you do + + + align:start position:0% +pointing it at something and when you do +that you lose uh you lose contact with + + align:start position:0% +that you lose uh you lose contact with + + + align:start position:0% +that you lose uh you lose contact with +the audience you don't want to do it so + + align:start position:0% +the audience you don't want to do it so + + + align:start position:0% +the audience you don't want to do it so +what do you do if you need to need to + + align:start position:0% +what do you do if you need to need to + + + align:start position:0% +what do you do if you need to need to +identify something in your image and you + + align:start position:0% +identify something in your image and you + + + align:start position:0% +identify something in your image and you +don't want to point at it with a laser + + align:start position:0% +don't want to point at it with a laser + + + align:start position:0% +don't want to point at it with a laser +this is what you do put a little arrow + + align:start position:0% +this is what you do put a little arrow + + + align:start position:0% +this is what you do put a little arrow +on there and say now look at that guy + + align:start position:0% +on there and say now look at that guy + + + align:start position:0% +on there and say now look at that guy +number one at the end of Arrow number + + align:start position:0% +number one at the end of Arrow number + + + align:start position:0% +number one at the end of Arrow number +one you don't need to have laser pointer + + align:start position:0% +one you don't need to have laser pointer + + + align:start position:0% +one you don't need to have laser pointer +to do + + align:start position:0% + + + + align:start position:0% + +that the to heavy + + align:start position:0% +that the to heavy + + + align:start position:0% +that the to heavy +crime when people ask me to review a + + align:start position:0% +crime when people ask me to review a + + + align:start position:0% +crime when people ask me to review a +presentation I ask them to print it out + + align:start position:0% +presentation I ask them to print it out + + + align:start position:0% +presentation I ask them to print it out +and lay it out on a table + + align:start position:0% + + + + align:start position:0% + +when they do that it's easy to see + + align:start position:0% +when they do that it's easy to see + + + align:start position:0% +when they do that it's easy to see +whether the talk is too heavy too much + + align:start position:0% +whether the talk is too heavy too much + + + align:start position:0% +whether the talk is too heavy too much +text not enough air not enough white + + align:start position:0% +text not enough air not enough white + + + align:start position:0% +text not enough air not enough white +space not enough + + align:start position:0% +space not enough + + + align:start position:0% +space not enough +imagery this is a good example of uh + + align:start position:0% +imagery this is a good example of uh + + + align:start position:0% +imagery this is a good example of uh +such a talk way too + + align:start position:0% +such a talk way too + + + align:start position:0% +such a talk way too +heavy uh the uh presenter has taken + + align:start position:0% +heavy uh the uh presenter has taken + + + align:start position:0% +heavy uh the uh presenter has taken +advantage of uh small font sizes to get + + align:start position:0% +advantage of uh small font sizes to get + + + align:start position:0% +advantage of uh small font sizes to get +as much on the slide as he + + align:start position:0% + + + + align:start position:0% + +wanted lots of crimes here but uh the + + align:start position:0% +wanted lots of crimes here but uh the + + + align:start position:0% +wanted lots of crimes here but uh the +too heaviness the fact that it's too + + align:start position:0% +too heaviness the fact that it's too + + + align:start position:0% +too heaviness the fact that it's too +heavy is what I wanted to illustrate so + + align:start position:0% +heavy is what I wanted to illustrate so + + + align:start position:0% +heavy is what I wanted to illustrate so +here by contrast another talk one I gave + + align:start position:0% +here by contrast another talk one I gave + + + align:start position:0% +here by contrast another talk one I gave +a few years ago it's not it wasn't a + + align:start position:0% +a few years ago it's not it wasn't a + + + align:start position:0% +a few years ago it's not it wasn't a +deeply technical talk but I show it to + + align:start position:0% +deeply technical talk but I show it to + + + align:start position:0% +deeply technical talk but I show it to +you + + align:start position:0% +you + + + align:start position:0% +you +because there's air in + + align:start position:0% +because there's air in + + + align:start position:0% +because there's air in +it it's mostly pictures of things there + + align:start position:0% +it it's mostly pictures of things there + + + align:start position:0% +it it's mostly pictures of things there +are three or four slides that have text + + align:start position:0% +are three or four slides that have text + + + align:start position:0% +are three or four slides that have text +on them but when I come to those I give + + align:start position:0% +on them but when I come to those I give + + + align:start position:0% +on them but when I come to those I give +the audience time to read them and + + align:start position:0% +the audience time to read them and + + + align:start position:0% +the audience time to read them and +they're there because they might have + + align:start position:0% +they're there because they might have + + + align:start position:0% +they're there because they might have +have some historical significance the + + align:start position:0% +have some historical significance the + + + align:start position:0% +have some historical significance the +first slide with a lot of text on it is + + align:start position:0% +first slide with a lot of text on it is + + + align:start position:0% +first slide with a lot of text on it is +a extraction from the + + align:start position:0% +a extraction from the + + + align:start position:0% +a extraction from the +1957 from the for the from the proposal + + align:start position:0% +1957 from the for the from the proposal + + + align:start position:0% +1957 from the for the from the proposal +for the 1957 AI conference at Dartmouth + + align:start position:0% +for the 1957 AI conference at Dartmouth + + + align:start position:0% +for the 1957 AI conference at Dartmouth +extraordinarily interesting event and + + align:start position:0% +extraordinarily interesting event and + + + align:start position:0% +extraordinarily interesting event and +that + + align:start position:0% +that + + + align:start position:0% +that +historical extraction from The Proposal + + align:start position:0% +historical extraction from The Proposal + + + align:start position:0% +historical extraction from The Proposal +helps drive that point + + align:start position:0% +helps drive that point + + + align:start position:0% +helps drive that point +home what else have we got here oh yeah + + align:start position:0% +home what else have we got here oh yeah + + + align:start position:0% +home what else have we got here oh yeah +your vocabulary word for the day this is + + align:start position:0% +your vocabulary word for the day this is + + + align:start position:0% +your vocabulary word for the day this is +an NAX Lon + + align:start position:0% +an NAX Lon + + + align:start position:0% +an NAX Lon +what that means is this is the kind of + + align:start position:0% +what that means is this is the kind of + + + align:start position:0% +what that means is this is the kind of +slide you can get away with exactly once + + align:start position:0% +slide you can get away with exactly once + + + align:start position:0% +slide you can get away with exactly once +in your + + align:start position:0% +in your + + + align:start position:0% +in your +presentation this is a slide that got + + align:start position:0% +presentation this is a slide that got + + + align:start position:0% +presentation this is a slide that got +some currency some years ago because it + + align:start position:0% +some currency some years ago because it + + + align:start position:0% +some currency some years ago because it +shows the + + align:start position:0% +shows the + + + align:start position:0% +shows the +complexity of um governing in + + align:start position:0% +complexity of um governing in + + + align:start position:0% +complexity of um governing in +Afghanistan by showing how impossibly + + align:start position:0% +Afghanistan by showing how impossibly + + + align:start position:0% +Afghanistan by showing how impossibly +complex it is it's something we you in + + align:start position:0% +complex it is it's something we you in + + + align:start position:0% +complex it is it's something we you in +the audience can't understand and and + + align:start position:0% +the audience can't understand and and + + + align:start position:0% +the audience can't understand and and +that's the point but you can't have many + + align:start position:0% +that's the point but you can't have many + + + align:start position:0% +that's the point but you can't have many +of these you can have one per work one + + align:start position:0% +of these you can have one per work one + + + align:start position:0% +of these you can have one per work one +per presentation one per paper one per + + align:start position:0% +per presentation one per paper one per + + + align:start position:0% +per presentation one per paper one per +book that's what it that's what epex Lan + + align:start position:0% +book that's what it that's what epex Lan + + + align:start position:0% +book that's what it that's what epex Lan +is and this is an example of + + align:start position:0% +is and this is an example of + + + align:start position:0% +is and this is an example of +it well I've shown you some crimes and + + align:start position:0% +it well I've shown you some crimes and + + + align:start position:0% +it well I've shown you some crimes and +so you might be asking do these crimes + + align:start position:0% +so you might be asking do these crimes + + + align:start position:0% +so you might be asking do these crimes +actually + + align:start position:0% +actually + + + align:start position:0% +actually +occur so + + align:start position:0% +occur so + + + align:start position:0% +occur so +um they + + align:start position:0% + + + + align:start position:0% + +do there's the hands in the pockets + + align:start position:0% + + + + align:start position:0% + +crime there's a um crime and time and + + align:start position:0% +crime there's a um crime and time and + + + align:start position:0% +crime there's a um crime and time and +place selection + + align:start position:0% +place selection + + + align:start position:0% +place selection +here this is how you get to the BTO + + align:start position:0% +here this is how you get to the BTO + + + align:start position:0% +here this is how you get to the BTO +theater first thing you do is you get + + align:start position:0% +theater first thing you do is you get + + + align:start position:0% +theater first thing you do is you get +down these steps over at the media + + align:start position:0% +down these steps over at the media + + + align:start position:0% +down these steps over at the media +lab then you cross this large open + + align:start position:0% +lab then you cross this large open + + + align:start position:0% +lab then you cross this large open +space then you turn right down this + + align:start position:0% +space then you turn right down this + + + align:start position:0% +space then you turn right down this +Corridor this point whenever I go in + + align:start position:0% +Corridor this point whenever I go in + + + align:start position:0% +Corridor this point whenever I go in +there I wonder if if there are torture + + align:start position:0% +there I wonder if if there are torture + + + align:start position:0% +there I wonder if if there are torture +implements around the corner and then + + align:start position:0% +implements around the corner and then + + + align:start position:0% +implements around the corner and then +when you get in there you get into this + + align:start position:0% +when you get in there you get into this + + + align:start position:0% +when you get in there you get into this +dark gloomy place so it's well- named + + align:start position:0% +dark gloomy place so it's well- named + + + align:start position:0% +dark gloomy place so it's well- named +what when they call it the baros theater + + align:start position:0% +what when they call it the baros theater + + + align:start position:0% +what when they call it the baros theater +because it's a place where you can watch + + align:start position:0% +because it's a place where you can watch + + + align:start position:0% +because it's a place where you can watch +a movie but it's not a place where you + + align:start position:0% +a movie but it's not a place where you + + + align:start position:0% +a movie but it's not a place where you +can give a + + align:start position:0% + + + + align:start position:0% + +talk now on a subject that doesn't + + align:start position:0% +talk now on a subject that doesn't + + + align:start position:0% +talk now on a subject that doesn't +happen here's a talk I attended a while + + align:start position:0% +happen here's a talk I attended a while + + + align:start position:0% +happen here's a talk I attended a while +back in + + align:start position:0% +back in + + + align:start position:0% +back in +stada notice that the speaker is H far + + align:start position:0% +stada notice that the speaker is H far + + + align:start position:0% +stada notice that the speaker is H far +away from the slides speaker is using a + + align:start position:0% +away from the slides speaker is using a + + + align:start position:0% +away from the slides speaker is using a +laser + + align:start position:0% +laser + + + align:start position:0% +laser +pointer and you say to me + + align:start position:0% +pointer and you say to me + + + align:start position:0% +pointer and you say to me +well what's happening here it's by the + + align:start position:0% +well what's happening here it's by the + + + align:start position:0% +well what's happening here it's by the +way the 80th 80th slide in the + + align:start position:0% +way the 80th 80th slide in the + + + align:start position:0% +way the 80th 80th slide in the +presentation notice that it stent with + + align:start position:0% +presentation notice that it stent with + + + align:start position:0% +presentation notice that it stent with +words this is the first of 10 conclusion + + align:start position:0% + + + + align:start position:0% + +slides so uh what's the audience + + align:start position:0% +slides so uh what's the audience + + + align:start position:0% +slides so uh what's the audience +reaction that's the sponsor of the + + align:start position:0% +reaction that's the sponsor of the + + + align:start position:0% +reaction that's the sponsor of the +meeting he's reading his + + align:start position:0% +meeting he's reading his + + + align:start position:0% +meeting he's reading his +email this is the co-sponsor of the + + align:start position:0% +email this is the co-sponsor of the + + + align:start position:0% +email this is the co-sponsor of the +meeting he's examining the lunch + + align:start position:0% +meeting he's examining the lunch + + + align:start position:0% +meeting he's examining the lunch +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +menu what about this person + + align:start position:0% + + + + align:start position:0% + +this person looks like he's paying + + align:start position:0% +this person looks like he's paying + + + align:start position:0% +this person looks like he's paying +attention but this because it's a still + + align:start position:0% +attention but this because it's a still + + + align:start position:0% +attention but this because it's a still +picture if you were to see a video what + + align:start position:0% +picture if you were to see a video what + + + align:start position:0% +picture if you were to see a video what +you would see is something like + + align:start position:0% + + + + align:start position:0% + +this so yeah it it it does + + align:start position:0% +this so yeah it it it does + + + align:start position:0% +this so yeah it it it does +happen well now uh that's a a quick + + align:start position:0% +happen well now uh that's a a quick + + + align:start position:0% +happen well now uh that's a a quick +review of of tools now I want to talk + + align:start position:0% +review of of tools now I want to talk + + + align:start position:0% +review of of tools now I want to talk +about some special cases + + align:start position:0% + + + + align:start position:0% + +we could talk a little bit about uh + + align:start position:0% +we could talk a little bit about uh + + + align:start position:0% +we could talk a little bit about uh +informing or to say it another way doing + + align:start position:0% +informing or to say it another way doing + + + align:start position:0% +informing or to say it another way doing +what I'm doing + + align:start position:0% +what I'm doing + + + align:start position:0% +what I'm doing +now but I'll just say a few words about + + align:start position:0% +now but I'll just say a few words about + + + align:start position:0% +now but I'll just say a few words about +that uh in that kind of in that kind of + + align:start position:0% +that uh in that kind of in that kind of + + + align:start position:0% +that uh in that kind of in that kind of +presentation you want to start with a + + align:start position:0% +presentation you want to start with a + + + align:start position:0% +presentation you want to start with a +promise like I did for this for this uh + + align:start position:0% +promise like I did for this for this uh + + + align:start position:0% +promise like I did for this for this uh +for this hour that we're going through + + align:start position:0% +for this hour that we're going through + + + align:start position:0% +for this hour that we're going through +now but then it comes to the question of + + align:start position:0% +now but then it comes to the question of + + + align:start position:0% +now but then it comes to the question of +how do you inspire + + align:start position:0% +how do you inspire + + + align:start position:0% +how do you inspire +people I've given this talk for a long + + align:start position:0% +people I've given this talk for a long + + + align:start position:0% +people I've given this talk for a long +time and a few years ago um uh our + + align:start position:0% +time and a few years ago um uh our + + + align:start position:0% +time and a few years ago um uh our +department chairman said would you + + align:start position:0% +department chairman said would you + + + align:start position:0% +department chairman said would you +please give this talk to uh a new + + align:start position:0% +please give this talk to uh a new + + + align:start position:0% +please give this talk to uh a new +faculty and be sure to emphasize what it + + align:start position:0% +faculty and be sure to emphasize what it + + + align:start position:0% +faculty and be sure to emphasize what it +takes to inspire students and strangely + + align:start position:0% +takes to inspire students and strangely + + + align:start position:0% +takes to inspire students and strangely +I hadn't thought about that question + + align:start position:0% +I hadn't thought about that question + + + align:start position:0% +I hadn't thought about that question +before so I started a survey I talked to + + align:start position:0% +before so I started a survey I talked to + + + align:start position:0% +before so I started a survey I talked to +some of my incoming freshman advises and + + align:start position:0% +some of my incoming freshman advises and + + + align:start position:0% +some of my incoming freshman advises and +I talked to senior faculty and + + align:start position:0% +I talked to senior faculty and + + + align:start position:0% +I talked to senior faculty and +everything in between about how they've + + align:start position:0% +everything in between about how they've + + + align:start position:0% +everything in between about how they've +been + + align:start position:0% +been + + + align:start position:0% +been +inspired what I found from the uh + + align:start position:0% +inspired what I found from the uh + + + align:start position:0% +inspired what I found from the uh +incoming freshman is that they were + + align:start position:0% +incoming freshman is that they were + + + align:start position:0% +incoming freshman is that they were +inspired by some high school teacher who + + align:start position:0% +inspired by some high school teacher who + + + align:start position:0% +inspired by some high school teacher who +told them they could do it + + align:start position:0% +told them they could do it + + + align:start position:0% +told them they could do it +what I found in the senior + + align:start position:0% +what I found in the senior + + + align:start position:0% +what I found in the senior +faculty they um were inspired by someone + + align:start position:0% +faculty they um were inspired by someone + + + align:start position:0% +faculty they um were inspired by someone +who helped them to see a problem in a + + align:start position:0% +who helped them to see a problem in a + + + align:start position:0% +who helped them to see a problem in a +new way and what I saw from + + align:start position:0% +new way and what I saw from + + + align:start position:0% +new way and what I saw from +everyone is that they were + + align:start position:0% +everyone is that they were + + + align:start position:0% +everyone is that they were +inspired when someone exhibited passion + + align:start position:0% +inspired when someone exhibited passion + + + align:start position:0% +inspired when someone exhibited passion +about what they were + + align:start position:0% +about what they were + + + align:start position:0% +about what they were +doing exhibited passion about what they + + align:start position:0% +doing exhibited passion about what they + + + align:start position:0% +doing exhibited passion about what they +were + + align:start position:0% +were + + + align:start position:0% +were +doing yeah so that's uh that's one one + + align:start position:0% +doing yeah so that's uh that's one one + + + align:start position:0% +doing yeah so that's uh that's one one +way to be inspiring + + align:start position:0% +way to be inspiring + + + align:start position:0% +way to be inspiring +it's easy for me because you know I do + + align:start position:0% +it's easy for me because you know I do + + + align:start position:0% +it's easy for me because you know I do +artificial + + align:start position:0% +artificial + + + align:start position:0% +artificial +intelligence um and uh how how can you + + align:start position:0% +intelligence um and uh how how can you + + + align:start position:0% +intelligence um and uh how how can you +not be interested in artificial + + align:start position:0% +not be interested in artificial + + + align:start position:0% +not be interested in artificial +intelligence right I mean if you're not + + align:start position:0% +intelligence right I mean if you're not + + + align:start position:0% +intelligence right I mean if you're not +interested in artificial intelligence + + align:start position:0% +interested in artificial intelligence + + + align:start position:0% +interested in artificial intelligence +you're probably not interested in + + align:start position:0% +you're probably not interested in + + + align:start position:0% +you're probably not interested in +interesting + + align:start position:0% + + + + align:start position:0% + +things so uh when I'm lecturing uh in my + + align:start position:0% +things so uh when I'm lecturing uh in my + + + align:start position:0% +things so uh when I'm lecturing uh in my +AI class it's natural for me to talk + + align:start position:0% +AI class it's natural for me to talk + + + align:start position:0% +AI class it's natural for me to talk +about what I think is cool and how + + align:start position:0% +about what I think is cool and how + + + align:start position:0% +about what I think is cool and how +exciting some new idea is uh so that's + + align:start position:0% +exciting some new idea is uh so that's + + + align:start position:0% +exciting some new idea is uh so that's +the kind of that's the kind of + + align:start position:0% +the kind of that's the kind of + + + align:start position:0% +the kind of that's the kind of +expression of passion that makes a + + align:start position:0% +expression of passion that makes a + + + align:start position:0% +expression of passion that makes a +difference uh while informing with + + align:start position:0% +difference uh while informing with + + + align:start position:0% +difference uh while informing with +respect to this question of of of + + align:start position:0% + + + + align:start position:0% + +inspiring oh yeah and of course during + + align:start position:0% +inspiring oh yeah and of course during + + + align:start position:0% +inspiring oh yeah and of course during +this promise phase you can also Express + + align:start position:0% +this promise phase you can also Express + + + align:start position:0% +this promise phase you can also Express +how cool stuff is let me give you an + + align:start position:0% +how cool stuff is let me give you an + + + align:start position:0% +how cool stuff is let me give you an +example of a lecture that starts this + + align:start position:0% +example of a lecture that starts this + + + align:start position:0% +example of a lecture that starts this +way I'm talking about resource + + align:start position:0% +way I'm talking about resource + + + align:start position:0% +way I'm talking about resource +allocation it's the same sort of stuff + + align:start position:0% +allocation it's the same sort of stuff + + + align:start position:0% +allocation it's the same sort of stuff +you would think of when you're s it's + + align:start position:0% +you would think of when you're s it's + + + align:start position:0% +you would think of when you're s it's +the same sort of ideas you would need if + + align:start position:0% +the same sort of ideas you would need if + + + align:start position:0% +the same sort of ideas you would need if +you're + + align:start position:0% +you're + + + align:start position:0% +you're +allocating a aircraft to a flight + + align:start position:0% +allocating a aircraft to a flight + + + align:start position:0% +allocating a aircraft to a flight +schedule or trying to schedule a factory + + align:start position:0% +schedule or trying to schedule a factory + + + align:start position:0% +schedule or trying to schedule a factory +or something like that but the example + + align:start position:0% +or something like that but the example + + + align:start position:0% +or something like that but the example +is putting colors on the states in the + + align:start position:0% +is putting colors on the states in the + + + align:start position:0% +is putting colors on the states in the +United States without any bordering + + align:start position:0% +United States without any bordering + + + align:start position:0% +United States without any bordering +states having the same color so here it + + align:start position:0% + + + + align:start position:0% + +goes this is what I show in the + + align:start position:0% +goes this is what I show in the + + + align:start position:0% +goes this is what I show in the +beginning of the class this is a way of + + align:start position:0% +beginning of the class this is a way of + + + align:start position:0% +beginning of the class this is a way of +doing that coloring and you might say + + align:start position:0% +doing that coloring and you might say + + + align:start position:0% +doing that coloring and you might say +well why don't we wait till it + + align:start position:0% +well why don't we wait till it + + + align:start position:0% +well why don't we wait till it +finishes would you like to do that no + + align:start position:0% + + + + align:start position:0% + +well we're not going to wait till it + + align:start position:0% +well we're not going to wait till it + + + align:start position:0% +well we're not going to wait till it +finishes because the sun will have + + align:start position:0% +finishes because the sun will have + + + align:start position:0% +finishes because the sun will have +exploded and consumed the Earth before + + align:start position:0% +exploded and consumed the Earth before + + + align:start position:0% +exploded and consumed the Earth before +this program + + align:start position:0% +this program + + + align:start position:0% +this program +finishes but with a slight adjustment to + + align:start position:0% +finishes but with a slight adjustment to + + + align:start position:0% +finishes but with a slight adjustment to +how the program works which I tell my + + align:start position:0% +how the program works which I tell my + + + align:start position:0% +how the program works which I tell my +students you will understand in the next + + align:start position:0% +students you will understand in the next + + + align:start position:0% +students you will understand in the next +50 minutes this is what you + + align:start position:0% + + + + align:start position:0% + +get Isn't that cool you know you got you + + align:start position:0% +get Isn't that cool you know you got you + + + align:start position:0% +get Isn't that cool you know you got you +got to be you got to be amazed by stuff + + align:start position:0% +got to be you got to be amazed by stuff + + + align:start position:0% +got to be you got to be amazed by stuff +that takes a computation from longer + + align:start position:0% +that takes a computation from longer + + + align:start position:0% +that takes a computation from longer +than the lifetime of the solar system + + align:start position:0% +than the lifetime of the solar system + + + align:start position:0% +than the lifetime of the solar system +into a few seconds so that's what I mean + + align:start position:0% +into a few seconds so that's what I mean + + + align:start position:0% +into a few seconds so that's what I mean +by providing a promise up front and + + align:start position:0% +by providing a promise up front and + + + align:start position:0% +by providing a promise up front and +expressing some passion about what + + align:start position:0% +expressing some passion about what + + + align:start position:0% +expressing some passion about what +you're talking + + align:start position:0% +you're talking + + + align:start position:0% +you're talking +about well the last item in this little + + align:start position:0% +about well the last item in this little + + + align:start position:0% +about well the last item in this little +block here is uh uh it has to do with + + align:start position:0% +block here is uh uh it has to do with + + + align:start position:0% +block here is uh uh it has to do with +what people think that they do at MIT + + align:start position:0% +what people think that they do at MIT + + + align:start position:0% +what people think that they do at MIT +you ask a faculty what the most + + align:start position:0% +you ask a faculty what the most + + + align:start position:0% +you ask a faculty what the most +important purpose is and they'll say + + align:start position:0% +important purpose is and they'll say + + + align:start position:0% +important purpose is and they'll say +well uh the most important thing I do is + + align:start position:0% +well uh the most important thing I do is + + + align:start position:0% +well uh the most important thing I do is +teach people how to + + align:start position:0% +teach people how to + + + align:start position:0% +teach people how to +think and then uh you say oh that's + + align:start position:0% +think and then uh you say oh that's + + + align:start position:0% +think and then uh you say oh that's +great how do you teach people how to + + align:start position:0% +great how do you teach people how to + + + align:start position:0% +great how do you teach people how to +think Blank + + align:start position:0% +think Blank + + + align:start position:0% +think Blank +Stare no one can quite respond to that + + align:start position:0% +Stare no one can quite respond to that + + + align:start position:0% +Stare no one can quite respond to that +part that natural next question so how + + align:start position:0% +part that natural next question so how + + + align:start position:0% +part that natural next question so how +do you teach people how to think + + align:start position:0% +do you teach people how to think + + + align:start position:0% +do you teach people how to think +well I believe that we are storytelling + + align:start position:0% +well I believe that we are storytelling + + + align:start position:0% +well I believe that we are storytelling +animals and that uh we start to + + align:start position:0% +animals and that uh we start to + + + align:start position:0% +animals and that uh we start to +developing our story understanding and + + align:start position:0% +developing our story understanding and + + + align:start position:0% +developing our story understanding and +manipulating skills with fairy tales in + + align:start position:0% +manipulating skills with fairy tales in + + + align:start position:0% +manipulating skills with fairy tales in +childhood and continue on through + + align:start position:0% +childhood and continue on through + + + align:start position:0% +childhood and continue on through +professional schools like law business + + align:start position:0% +professional schools like law business + + + align:start position:0% +professional schools like law business +medicine engineer everything and we + + align:start position:0% +medicine engineer everything and we + + + align:start position:0% +medicine engineer everything and we +continue doing that throughout life so + + align:start position:0% +continue doing that throughout life so + + + align:start position:0% +continue doing that throughout life so +if uh that is what thinking is all about + + align:start position:0% +if uh that is what thinking is all about + + + align:start position:0% +if uh that is what thinking is all about +then when you want to teach people how + + align:start position:0% +then when you want to teach people how + + + align:start position:0% +then when you want to teach people how +to think you provide them with the + + align:start position:0% +to think you provide them with the + + + align:start position:0% +to think you provide them with the +stories they need to know the questions + + align:start position:0% +stories they need to know the questions + + + align:start position:0% +stories they need to know the questions +they need to ask about those stories + + align:start position:0% +they need to ask about those stories + + + align:start position:0% +they need to ask about those stories +mechanisms for analyzing those stories + + align:start position:0% +mechanisms for analyzing those stories + + + align:start position:0% +mechanisms for analyzing those stories +ways of putting stories together ways of + + align:start position:0% +ways of putting stories together ways of + + + align:start position:0% +ways of putting stories together ways of +evaluating + + align:start position:0% +evaluating + + + align:start position:0% +evaluating +how reliable the story is and that's + + align:start position:0% +how reliable the story is and that's + + + align:start position:0% +how reliable the story is and that's +what I think you need to do when you + + align:start position:0% +what I think you need to do when you + + + align:start position:0% +what I think you need to do when you +teach people how to + + align:start position:0% +teach people how to + + + align:start position:0% +teach people how to +think but that's all about education and + + align:start position:0% +think but that's all about education and + + + align:start position:0% +think but that's all about education and +uh many of you here not necessarily for + + align:start position:0% +uh many of you here not necessarily for + + + align:start position:0% +uh many of you here not necessarily for +that but rather for uh for this part for + + align:start position:0% +that but rather for uh for this part for + + + align:start position:0% +that but rather for uh for this part for +persuading which breaks down into + + align:start position:0% +persuading which breaks down into + + + align:start position:0% +persuading which breaks down into +several categories oral exams not shown + + align:start position:0% +several categories oral exams not shown + + + align:start position:0% +several categories oral exams not shown +job talks getting famous I won't say + + align:start position:0% +job talks getting famous I won't say + + + align:start position:0% +job talks getting famous I won't say +much about oral exams other than the + + align:start position:0% +much about oral exams other than the + + + align:start position:0% +much about oral exams other than the +fact that they used to be a lot scarier + + align:start position:0% +fact that they used to be a lot scarier + + + align:start position:0% +fact that they used to be a lot scarier +than they are today in the old + + align:start position:0% +than they are today in the old + + + align:start position:0% +than they are today in the old +days um + + align:start position:0% +days um + + + align:start position:0% +days um +reading the literature in a foreign + + align:start position:0% +reading the literature in a foreign + + + align:start position:0% +reading the literature in a foreign +language was a part of that and there + + align:start position:0% +language was a part of that and there + + + align:start position:0% +language was a part of that and there +was a a high failure rate and when you + + align:start position:0% +was a a high failure rate and when you + + + align:start position:0% +was a a high failure rate and when you +look at when you look back on those uh + + align:start position:0% +look at when you look back on those uh + + + align:start position:0% +look at when you look back on those uh +on those failures the most uh usual + + align:start position:0% +on those failures the most uh usual + + + align:start position:0% +on those failures the most uh usual +reason for people failing an oral exam + + align:start position:0% +reason for people failing an oral exam + + + align:start position:0% +reason for people failing an oral exam +is failure to situate and a failure to + + align:start position:0% +is failure to situate and a failure to + + + align:start position:0% +is failure to situate and a failure to +practice by situate I mean it's + + align:start position:0% +practice by situate I mean it's + + + align:start position:0% +practice by situate I mean it's +important to talk about your research + + align:start position:0% +important to talk about your research + + + align:start position:0% +important to talk about your research +and context uh this is a problem that's + + align:start position:0% +and context uh this is a problem that's + + + align:start position:0% +and context uh this is a problem that's +being pursued all over the world there + + align:start position:0% +being pursued all over the world there + + + align:start position:0% +being pursued all over the world there +hasn't been any progress before me in + + align:start position:0% +hasn't been any progress before me in + + + align:start position:0% +hasn't been any progress before me in +past 30 + + align:start position:0% +past 30 + + + align:start position:0% +past 30 +years um everyone is looking for a + + align:start position:0% +years um everyone is looking for a + + + align:start position:0% +years um everyone is looking for a +solution because it will have impact on + + align:start position:0% +solution because it will have impact on + + + align:start position:0% +solution because it will have impact on +so many other things so that's situating + + align:start position:0% +so many other things so that's situating + + + align:start position:0% +so many other things so that's situating +in time and place and field and then as + + align:start position:0% +in time and place and field and then as + + + align:start position:0% +in time and place and field and then as +far as practice is + + align:start position:0% +far as practice is + + + align:start position:0% +far as practice is +concerned yes practice is important but + + align:start position:0% +concerned yes practice is important but + + + align:start position:0% +concerned yes practice is important but +that doesn't mean uh showing your slides + + align:start position:0% +that doesn't mean uh showing your slides + + + align:start position:0% +that doesn't mean uh showing your slides +to the people who share an office with + + align:start position:0% +to the people who share an office with + + + align:start position:0% +to the people who share an office with +the problem with that is that um if + + align:start position:0% +the problem with that is that um if + + + align:start position:0% +the problem with that is that um if +people know what you're doing they will + + align:start position:0% +people know what you're doing they will + + + align:start position:0% +people know what you're doing they will +hallucinate that there's material in + + align:start position:0% +hallucinate that there's material in + + + align:start position:0% +hallucinate that there's material in +your presentation that isn't there it it + + align:start position:0% +your presentation that isn't there it it + + + align:start position:0% +your presentation that isn't there it it +isn't + + align:start position:0% +isn't + + + align:start position:0% +isn't +there a variation on the scene by the + + align:start position:0% +there a variation on the scene by the + + + align:start position:0% +there a variation on the scene by the +way is your faculty supervisor is not a + + align:start position:0% +way is your faculty supervisor is not a + + + align:start position:0% +way is your faculty supervisor is not a +very good person to help you debug a + + align:start position:0% +very good person to help you debug a + + + align:start position:0% +very good person to help you debug a +talk because they in fact know what + + align:start position:0% +talk because they in fact know what + + + align:start position:0% +talk because they in fact know what +you're doing and they will in fact + + align:start position:0% +you're doing and they will in fact + + + align:start position:0% +you're doing and they will in fact +hallucinate there's material in your + + align:start position:0% +hallucinate there's material in your + + + align:start position:0% +hallucinate there's material in your +presentation that isn't there so you + + align:start position:0% +presentation that isn't there so you + + + align:start position:0% +presentation that isn't there so you +need to get together some friends who + + align:start position:0% +need to get together some friends who + + + align:start position:0% +need to get together some friends who +don't know what you're doing and have + + align:start position:0% +don't know what you're doing and have + + + align:start position:0% +don't know what you're doing and have +them well you start the practice session + + align:start position:0% +them well you start the practice session + + + align:start position:0% +them well you start the practice session +by saying if you can't make me cry I + + align:start position:0% +by saying if you can't make me cry I + + + align:start position:0% +by saying if you can't make me cry I +won't value you as a friend friend + + align:start position:0% +won't value you as a friend friend + + + align:start position:0% +won't value you as a friend friend +anymore and then when you get to the + + align:start position:0% +anymore and then when you get to the + + + align:start position:0% +anymore and then when you get to the +faculty uh on a uh oral exam it will be + + align:start position:0% +faculty uh on a uh oral exam it will be + + + align:start position:0% +faculty uh on a uh oral exam it will be +easy you see + + align:start position:0% +easy you see + + + align:start position:0% +easy you see +um difficulty the amount of flack you + + align:start position:0% +um difficulty the amount of flack you + + + align:start position:0% +um difficulty the amount of flack you +get from somebody is proportional to age + + align:start position:0% +get from somebody is proportional to age + + + align:start position:0% +get from somebody is proportional to age +the older somebody is the more uh the + + align:start position:0% +the older somebody is the more uh the + + + align:start position:0% +the older somebody is the more uh the +more they understand where they are in + + align:start position:0% +more they understand where they are in + + + align:start position:0% +more they understand where they are in +the world but but the young people are + + align:start position:0% +the world but but the young people are + + + align:start position:0% +the world but but the young people are +trying to show the old people how smart + + align:start position:0% +trying to show the old people how smart + + + align:start position:0% +trying to show the old people how smart +they are so so sobly vicious so whenever + + align:start position:0% +they are so so sobly vicious so whenever + + + align:start position:0% +they are so so sobly vicious so whenever +you have an opportunity to have an + + align:start position:0% +you have an opportunity to have an + + + align:start position:0% +you have an opportunity to have an +examining committee that's full of + + align:start position:0% +examining committee that's full of + + + align:start position:0% +examining committee that's full of +people with gray hair that's what you + + align:start position:0% +people with gray hair that's what you + + + align:start position:0% +people with gray hair that's what you +want well that's just a word or two + + align:start position:0% +want well that's just a word or two + + + align:start position:0% +want well that's just a word or two +about something I haven't listed here + + align:start position:0% +about something I haven't listed here + + + align:start position:0% +about something I haven't listed here +let's get into the subject of job talks + + align:start position:0% +let's get into the subject of job talks + + + align:start position:0% +let's get into the subject of job talks +so I was + + align:start position:0% +so I was + + + align:start position:0% +so I was +um sitting in a bar uh many years ago uh + + align:start position:0% +um sitting in a bar uh many years ago uh + + + align:start position:0% +um sitting in a bar uh many years ago uh +in uh San Diego I was a member of the + + align:start position:0% +in uh San Diego I was a member of the + + + align:start position:0% +in uh San Diego I was a member of the +Navy science board and I was saying with + + align:start position:0% +Navy science board and I was saying with + + + align:start position:0% +Navy science board and I was saying with +a couple of uh my colleagues on the + + align:start position:0% +a couple of uh my colleagues on the + + + align:start position:0% +a couple of uh my colleagues on the +board uh Dolores Eder from the + + align:start position:0% +board uh Dolores Eder from the + + + align:start position:0% +board uh Dolores Eder from the +University of Colorado uh she made me so + + align:start position:0% +University of Colorado uh she made me so + + + align:start position:0% +University of Colorado uh she made me so +jealous I could spit because she written + + align:start position:0% +jealous I could spit because she written + + + align:start position:0% +jealous I could spit because she written +21 books and I'd only written + + align:start position:0% +21 books and I'd only written + + + align:start position:0% +21 books and I'd only written +177 and then the other one was + + align:start position:0% +177 and then the other one was + + + align:start position:0% +177 and then the other one was +uh bill welon from the University of + + align:start position:0% +uh bill welon from the University of + + + align:start position:0% +uh bill welon from the University of +Texas he was a electrom magnetism guy + + align:start position:0% +Texas he was a electrom magnetism guy + + + align:start position:0% +Texas he was a electrom magnetism guy +and he know knew how to use rail guns to + + align:start position:0% +and he know knew how to use rail guns to + + + align:start position:0% +and he know knew how to use rail guns to +to drive steel rods through tank armor + + align:start position:0% +to drive steel rods through tank armor + + + align:start position:0% +to drive steel rods through tank armor +these are interesting people so I said + + align:start position:0% +these are interesting people so I said + + + align:start position:0% +these are interesting people so I said +um what do you look for uh in a uh + + align:start position:0% +um what do you look for uh in a uh + + + align:start position:0% +um what do you look for uh in a uh +faculty + + align:start position:0% +faculty + + + align:start position:0% +faculty +candidate and uh within a one microc + + align:start position:0% +candidate and uh within a one microc + + + align:start position:0% +candidate and uh within a one microc +Dolores said they have to show us + + align:start position:0% +Dolores said they have to show us + + + align:start position:0% +Dolores said they have to show us +they've got some kind of + + align:start position:0% +they've got some kind of + + + align:start position:0% +they've got some kind of +vision quickly followed by Bill who said + + align:start position:0% +vision quickly followed by Bill who said + + + align:start position:0% +vision quickly followed by Bill who said +they have to show us that they've done + + align:start position:0% + + + + align:start position:0% + +something oh that sounds good I said and + + align:start position:0% +something oh that sounds good I said and + + + align:start position:0% +something oh that sounds good I said and +then I said to them how long does the + + align:start position:0% +then I said to them how long does the + + + align:start position:0% +then I said to them how long does the +candidate have to establish these two + + align:start position:0% +candidate have to establish these two + + + align:start position:0% +candidate have to establish these two +things what do you think + + align:start position:0% +things what do you think + + + align:start position:0% +things what do you think +compare your answer to + + align:start position:0% + + + + align:start position:0% + +theirs 5 + + align:start position:0% +theirs 5 + + + align:start position:0% +theirs 5 +minutes so if you haven't expressed your + + align:start position:0% +minutes so if you haven't expressed your + + + align:start position:0% +minutes so if you haven't expressed your +vision if you haven't told people that + + align:start position:0% +vision if you haven't told people that + + + align:start position:0% +vision if you haven't told people that +you've done something in five minutes + + align:start position:0% +you've done something in five minutes + + + align:start position:0% +you've done something in five minutes +you're you you've already lost so you + + align:start position:0% +you're you you've already lost so you + + + align:start position:0% +you're you you've already lost so you +you have to be able to do that and let + + align:start position:0% +you have to be able to do that and let + + + align:start position:0% +you have to be able to do that and let +me just mention a couple of things in + + align:start position:0% +me just mention a couple of things in + + + align:start position:0% +me just mention a couple of things in +that + + align:start position:0% +that + + + align:start position:0% +that +connection here which is you know the + + align:start position:0% +connection here which is you know the + + + align:start position:0% +connection here which is you know the +vision is in part a problem that + + align:start position:0% +vision is in part a problem that + + + align:start position:0% +vision is in part a problem that +somebody cares about + + align:start position:0% + + + + align:start position:0% + +and something new in your + + align:start position:0% + + + + align:start position:0% + +approach so the problem is understanding + + align:start position:0% +approach so the problem is understanding + + + align:start position:0% +approach so the problem is understanding +the nature of human intelligence and the + + align:start position:0% +the nature of human intelligence and the + + + align:start position:0% +the nature of human intelligence and the +approach is asking questions about what + + align:start position:0% +approach is asking questions about what + + + align:start position:0% +approach is asking questions about what +makes us different from chimpanzees and + + align:start position:0% +makes us different from chimpanzees and + + + align:start position:0% +makes us different from chimpanzees and +neandertals is it merely a matter of + + align:start position:0% +neandertals is it merely a matter of + + + align:start position:0% +neandertals is it merely a matter of +quantity or we just a little bit smarter + + align:start position:0% +quantity or we just a little bit smarter + + + align:start position:0% +quantity or we just a little bit smarter +in some continuous way or do we have + + align:start position:0% +in some continuous way or do we have + + + align:start position:0% +in some continuous way or do we have +something that's fundamentally different + + align:start position:0% +something that's fundamentally different + + + align:start position:0% +something that's fundamentally different +the chimpan Tendencies don't have and + + align:start position:0% +the chimpan Tendencies don't have and + + + align:start position:0% +the chimpan Tendencies don't have and +the Andals either and the answer is yes + + align:start position:0% +the Andals either and the answer is yes + + + align:start position:0% +the Andals either and the answer is yes +we do have something different we are + + align:start position:0% +we do have something different we are + + + align:start position:0% +we do have something different we are +symbolic + + align:start position:0% +symbolic + + + align:start position:0% +symbolic +creatures and because we're symbolic + + align:start position:0% +creatures and because we're symbolic + + + align:start position:0% +creatures and because we're symbolic +creatures we can + + align:start position:0% +creatures we can + + + align:start position:0% +creatures we can +um we can uh build symbolic descriptions + + align:start position:0% +um we can uh build symbolic descriptions + + + align:start position:0% +um we can uh build symbolic descriptions +of relations and events we can string + + align:start position:0% +of relations and events we can string + + + align:start position:0% +of relations and events we can string +them together and make stories and + + align:start position:0% +them together and make stories and + + + align:start position:0% +them together and make stories and +because we can make stories that's what + + align:start position:0% +because we can make stories that's what + + + align:start position:0% +because we can make stories that's what +makes us different so that's that's + + align:start position:0% +makes us different so that's that's + + + align:start position:0% +makes us different so that's that's +that's my stump speech that's how I + + align:start position:0% +that's my stump speech that's how I + + + align:start position:0% +that's my stump speech that's how I +start most of my talks on my my own + + align:start position:0% +start most of my talks on my my own + + + align:start position:0% +start most of my talks on my my own +personal + + align:start position:0% +personal + + + align:start position:0% +personal +research how do you express the notion + + align:start position:0% +research how do you express the notion + + + align:start position:0% +research how do you express the notion +that you've done + + align:start position:0% +that you've done + + + align:start position:0% +that you've done +something by listing the steps that need + + align:start position:0% +something by listing the steps that need + + + align:start position:0% +something by listing the steps that need +to be taken in order to achieve the + + align:start position:0% +to be taken in order to achieve the + + + align:start position:0% +to be taken in order to achieve the +solution to that problem you don't have + + align:start position:0% +solution to that problem you don't have + + + align:start position:0% +solution to that problem you don't have +to have done all of those steps but you + + align:start position:0% +to have done all of those steps but you + + + align:start position:0% +to have done all of those steps but you +can say here's here's what needs to be + + align:start position:0% +can say here's here's what needs to be + + + align:start position:0% +can say here's here's what needs to be +done an example here's what needs to be + + align:start position:0% +done an example here's what needs to be + + + align:start position:0% +done an example here's what needs to be +done we need to specify some Behavior we + + align:start position:0% +done we need to specify some Behavior we + + + align:start position:0% +done we need to specify some Behavior we +need to enumerate the constraints that + + align:start position:0% +need to enumerate the constraints that + + + align:start position:0% +need to enumerate the constraints that +make it possible to deal with that + + align:start position:0% +make it possible to deal with that + + + align:start position:0% +make it possible to deal with that +behavior we have to implement a system + + align:start position:0% +behavior we have to implement a system + + + align:start position:0% +behavior we have to implement a system +because we're engineers and we don't + + align:start position:0% +because we're engineers and we don't + + + align:start position:0% +because we're engineers and we don't +think that we've understood something + + align:start position:0% +think that we've understood something + + + align:start position:0% +think that we've understood something +unless we can build it and we've built + + align:start position:0% +unless we can build it and we've built + + + align:start position:0% +unless we can build it and we've built +such a system and we're about to + + align:start position:0% +such a system and we're about to + + + align:start position:0% +such a system and we're about to +demonstrate it to you today that would + + align:start position:0% +demonstrate it to you today that would + + + align:start position:0% +demonstrate it to you today that would +be an example of enumerating series of + + align:start position:0% +be an example of enumerating series of + + + align:start position:0% +be an example of enumerating series of +steps needed to realize the + + align:start position:0% +steps needed to realize the + + + align:start position:0% +steps needed to realize the +vision so then blah blah blah blah blah + + align:start position:0% +vision so then blah blah blah blah blah + + + align:start position:0% +vision so then blah blah blah blah blah +blah blah blah blah and then you + + align:start position:0% +blah blah blah blah and then you + + + align:start position:0% +blah blah blah blah and then you +conclude by you conclude by enumerating + + align:start position:0% +conclude by you conclude by enumerating + + + align:start position:0% +conclude by you conclude by enumerating +your contributions + + align:start position:0% + + + + align:start position:0% + +it's kind of mirror of of these steps + + align:start position:0% +it's kind of mirror of of these steps + + + align:start position:0% +it's kind of mirror of of these steps +and helps to establish that you've done + + align:start position:0% +and helps to establish that you've done + + + align:start position:0% +and helps to establish that you've done +something so that's a kind of general + + align:start position:0% +something so that's a kind of general + + + align:start position:0% +something so that's a kind of general +purpose framework for doing a technical + + align:start position:0% +purpose framework for doing a technical + + + align:start position:0% +purpose framework for doing a technical +talk + + align:start position:0% +talk + + + align:start position:0% +talk +now only a few more things left to do + + align:start position:0% +now only a few more things left to do + + + align:start position:0% +now only a few more things left to do +today uh getting famous is the next item + + align:start position:0% +today uh getting famous is the next item + + + align:start position:0% +today uh getting famous is the next item +on our agenda because once you've got + + align:start position:0% +on our agenda because once you've got + + + align:start position:0% +on our agenda because once you've got +the job you need to think a little bit + + align:start position:0% +the job you need to think a little bit + + + align:start position:0% +the job you need to think a little bit +about how you're going to be recognized + + align:start position:0% +about how you're going to be recognized + + + align:start position:0% +about how you're going to be recognized +for what you + + align:start position:0% +for what you + + + align:start position:0% +for what you +do so + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +well first of all why should you care + + align:start position:0% +well first of all why should you care + + + align:start position:0% +well first of all why should you care +about getting + + align:start position:0% +about getting + + + align:start position:0% +about getting +famous I thought about this um in + + align:start position:0% +famous I thought about this um in + + + align:start position:0% +famous I thought about this um in +connection with + + align:start position:0% +connection with + + + align:start position:0% +connection with +a fundraising event I attended + + align:start position:0% + + + + align:start position:0% + +once fundraising event for raising money + + align:start position:0% +once fundraising event for raising money + + + align:start position:0% +once fundraising event for raising money +to save Venice from going underwater and + + align:start position:0% +to save Venice from going underwater and + + + align:start position:0% +to save Venice from going underwater and +having all of its art destroyed anyway I + + align:start position:0% +having all of its art destroyed anyway I + + + align:start position:0% +having all of its art destroyed anyway I +was sitting here + + align:start position:0% +was sitting here + + + align:start position:0% +was sitting here +and JC was sitting + + align:start position:0% +and JC was sitting + + + align:start position:0% +and JC was sitting +here that was uh Julia the late Julia + + align:start position:0% + + + + align:start position:0% + +Child and as the evening wore on more + + align:start position:0% +Child and as the evening wore on more + + + align:start position:0% +Child and as the evening wore on more +and more people would come up and ask + + align:start position:0% +and more people would come up and ask + + + align:start position:0% +and more people would come up and ask +Julia to autograph something or Express + + align:start position:0% +Julia to autograph something or Express + + + align:start position:0% +Julia to autograph something or Express +a a feeling that she had changed their + + align:start position:0% +a a feeling that she had changed their + + + align:start position:0% +a a feeling that she had changed their +life and it just happened over and over + + align:start position:0% +life and it just happened over and over + + + align:start position:0% +life and it just happened over and over +again So eventually I turned to Julia + + align:start position:0% +again So eventually I turned to Julia + + + align:start position:0% +again So eventually I turned to Julia +and I said Miss child is it fun to be + + align:start position:0% +and I said Miss child is it fun to be + + + align:start position:0% +and I said Miss child is it fun to be +famous and she thought about it for a + + align:start position:0% +famous and she thought about it for a + + + align:start position:0% +famous and she thought about it for a +second and she said you get used to + + align:start position:0% +second and she said you get used to + + + align:start position:0% +second and she said you get used to +it but you know what occurred to me you + + align:start position:0% +it but you know what occurred to me you + + + align:start position:0% +it but you know what occurred to me you +never get used to being + + align:start position:0% +never get used to being + + + align:start position:0% +never get used to being +ignored so it's you know it's it's + + align:start position:0% +ignored so it's you know it's it's + + + align:start position:0% +ignored so it's you know it's it's +here's a way to think about it your + + align:start position:0% +here's a way to think about it your + + + align:start position:0% +here's a way to think about it your +ideas are like your children and you + + align:start position:0% +ideas are like your children and you + + + align:start position:0% +ideas are like your children and you +don't want them to go into the world in + + align:start position:0% +don't want them to go into the world in + + + align:start position:0% +don't want them to go into the world in +rags so what you want to do is to be + + align:start position:0% +rags so what you want to do is to be + + + align:start position:0% +rags so what you want to do is to be +sure that you have + + align:start position:0% +sure that you have + + + align:start position:0% +sure that you have +these techniques these mechanisms these + + align:start position:0% +these techniques these mechanisms these + + + align:start position:0% +these techniques these mechanisms these +thoughts about how to present the ideas + + align:start position:0% +thoughts about how to present the ideas + + + align:start position:0% +thoughts about how to present the ideas +that you have so that they're recognized + + align:start position:0% +that you have so that they're recognized + + + align:start position:0% +that you have so that they're recognized +for the value that that is in them so + + align:start position:0% +for the value that that is in them so + + + align:start position:0% +for the value that that is in them so +that's why it's a legitimate thing to + + align:start position:0% +that's why it's a legitimate thing to + + + align:start position:0% +that's why it's a legitimate thing to +concern yourself with the with + + align:start position:0% +concern yourself with the with + + + align:start position:0% +concern yourself with the with +packaging now how do you get uh + + align:start position:0% +packaging now how do you get uh + + + align:start position:0% +packaging now how do you get uh +remembered well there's something I like + + align:start position:0% +remembered well there's something I like + + + align:start position:0% +remembered well there's something I like +to call Winston star and every one of + + align:start position:0% +to call Winston star and every one of + + + align:start position:0% +to call Winston star and every one of +the items I'm about to articulate has a + + align:start position:0% +the items I'm about to articulate has a + + + align:start position:0% +the items I'm about to articulate has a +starts with an + + align:start position:0% +starts with an + + + align:start position:0% +starts with an +S so if you want your presentation ideas + + align:start position:0% +S so if you want your presentation ideas + + + align:start position:0% +S so if you want your presentation ideas +to be remembered one of the things you + + align:start position:0% +to be remembered one of the things you + + + align:start position:0% +to be remembered one of the things you +need to do is to make sure that you have + + align:start position:0% +need to do is to make sure that you have + + + align:start position:0% +need to do is to make sure that you have +some kind of + + align:start position:0% +some kind of + + + align:start position:0% +some kind of +symbol associated with your work so this + + align:start position:0% +symbol associated with your work so this + + + align:start position:0% +symbol associated with your work so this +Arch example is actually from my PhD + + align:start position:0% +Arch example is actually from my PhD + + + align:start position:0% +Arch example is actually from my PhD +thesis many many years ago + + align:start position:0% +thesis many many years ago + + + align:start position:0% +thesis many many years ago +and in the course of uh my work uh at + + align:start position:0% +and in the course of uh my work uh at + + + align:start position:0% +and in the course of uh my work uh at +that time uh this work on Arch learning + + align:start position:0% +that time uh this work on Arch learning + + + align:start position:0% +that time uh this work on Arch learning +became mildly famous and I didn't know + + align:start position:0% +became mildly famous and I didn't know + + + align:start position:0% +became mildly famous and I didn't know +why it was only many years later that I + + align:start position:0% +why it was only many years later that I + + + align:start position:0% +why it was only many years later that I +realized that that work accidentally had + + align:start position:0% +realized that that work accidentally had + + + align:start position:0% +realized that that work accidentally had +all of the elements on this star so the + + align:start position:0% +all of the elements on this star so the + + + align:start position:0% +all of the elements on this star so the +first element is that there was a kind + + align:start position:0% +first element is that there was a kind + + + align:start position:0% +first element is that there was a kind +of symbol it's the arch + + align:start position:0% + + + + align:start position:0% + +itself next thing you need is some kind + + align:start position:0% +itself next thing you need is some kind + + + align:start position:0% +itself next thing you need is some kind +of + + align:start position:0% + + + + align:start position:0% + +slogan a kind of phrase that provides a + + align:start position:0% +slogan a kind of phrase that provides a + + + align:start position:0% +slogan a kind of phrase that provides a +handle on the work and in this case the + + align:start position:0% +handle on the work and in this case the + + + align:start position:0% +handle on the work and in this case the +phrase was one shot + + align:start position:0% + + + + align:start position:0% + +learning and it was one shot because the + + align:start position:0% +learning and it was one shot because the + + + align:start position:0% +learning and it was one shot because the +program I wrote learned something + + align:start position:0% +program I wrote learned something + + + align:start position:0% +program I wrote learned something +definite from every example that was + + align:start position:0% +definite from every example that was + + + align:start position:0% +definite from every example that was +presented to us so in going from a model + + align:start position:0% +presented to us so in going from a model + + + align:start position:0% +presented to us so in going from a model +based on this configuration to something + + align:start position:0% +based on this configuration to something + + + align:start position:0% +based on this configuration to something +that isn't an arch based on that + + align:start position:0% +that isn't an arch based on that + + + align:start position:0% +that isn't an arch based on that +configuration the program learned that + + align:start position:0% +configuration the program learned that + + + align:start position:0% +configuration the program learned that +it has to be on top one shot + + align:start position:0% +it has to be on top one shot + + + align:start position:0% +it has to be on top one shot +learning so that's a + + align:start position:0% +learning so that's a + + + align:start position:0% +learning so that's a +simple slogan now we need a + + align:start position:0% + + + + align:start position:0% + +surprise yeah the surprise is you don't + + align:start position:0% +surprise yeah the surprise is you don't + + + align:start position:0% +surprise yeah the surprise is you don't +need a million examples of something to + + align:start position:0% +need a million examples of something to + + + align:start position:0% +need a million examples of something to +learn you can do it with one example if + + align:start position:0% +learn you can do it with one example if + + + align:start position:0% +learn you can do it with one example if +you're smart enough to make use of that + + align:start position:0% +you're smart enough to make use of that + + + align:start position:0% +you're smart enough to make use of that +example appropriately so that was the + + align:start position:0% +example appropriately so that was the + + + align:start position:0% +example appropriately so that was the +surprise you can learn something + + align:start position:0% +surprise you can learn something + + + align:start position:0% +surprise you can learn something +definite from each + + align:start position:0% +definite from each + + + align:start position:0% +definite from each +example next item was a Salient + + align:start position:0% + + + + align:start position:0% + +idea now when I say Salient idea I don't + + align:start position:0% +idea now when I say Salient idea I don't + + + align:start position:0% +idea now when I say Salient idea I don't +mean important what I mean is an idea + + align:start position:0% +mean important what I mean is an idea + + + align:start position:0% +mean important what I mean is an idea +that sticks + + align:start position:0% +that sticks + + + align:start position:0% +that sticks +out + + align:start position:0% +out + + + align:start position:0% +out +uh some some thesis funnily enough have + + align:start position:0% +uh some some thesis funnily enough have + + + align:start position:0% +uh some some thesis funnily enough have +too many good ideas and you don't know + + align:start position:0% +too many good ideas and you don't know + + + align:start position:0% +too many good ideas and you don't know +what it's all about because which one is + + align:start position:0% +what it's all about because which one is + + + align:start position:0% +what it's all about because which one is +it it so you need an idea that sticks + + align:start position:0% +it it so you need an idea that sticks + + + align:start position:0% +it it so you need an idea that sticks +out and the idea that stuck out + + align:start position:0% +out and the idea that stuck out + + + align:start position:0% +out and the idea that stuck out +here was a notion of a near + + align:start position:0% + + + + align:start position:0% + +miss you see this is not an arch but it + + align:start position:0% +miss you see this is not an arch but it + + + align:start position:0% +miss you see this is not an arch but it +doesn't miss by much so it's a near + + align:start position:0% +doesn't miss by much so it's a near + + + align:start position:0% +doesn't miss by much so it's a near +Miss + + align:start position:0% +Miss + + + align:start position:0% +Miss +finally you need to tell the + + align:start position:0% +finally you need to tell the + + + align:start position:0% +finally you need to tell the +story of how you did it how it works why + + align:start position:0% +story of how you did it how it works why + + + align:start position:0% +story of how you did it how it works why +it's + + align:start position:0% +it's + + + align:start position:0% +it's +important so that's + + align:start position:0% +important so that's + + + align:start position:0% +important so that's +um a bit on uh how to not so much get + + align:start position:0% +um a bit on uh how to not so much get + + + align:start position:0% +um a bit on uh how to not so much get +famous but how to ensure that your work + + align:start position:0% +famous but how to ensure that your work + + + align:start position:0% +famous but how to ensure that your work +is + + align:start position:0% +is + + + align:start position:0% +is +recognized well that that we're almost + + align:start position:0% +recognized well that that we're almost + + + align:start position:0% +recognized well that that we're almost +finished because now we're we're down to + + align:start position:0% +finished because now we're we're down to + + + align:start position:0% +finished because now we're we're down to +this last item which is U how to + + align:start position:0% +this last item which is U how to + + + align:start position:0% +this last item which is U how to +stop and when we come to that there's a + + align:start position:0% +stop and when we come to that there's a + + + align:start position:0% +stop and when we come to that there's a +question of all right well what is the + + align:start position:0% +question of all right well what is the + + + align:start position:0% +question of all right well what is the +final + + align:start position:0% + + + + align:start position:0% + +slide and what are the final words + + align:start position:0% + + + + align:start position:0% + +so for the final slide let me give you + + align:start position:0% +so for the final slide let me give you + + + align:start position:0% +so for the final slide let me give you +some examples of + + align:start position:0% + + + + align:start position:0% + +possibilities how about this + + align:start position:0% + + + + align:start position:0% + +one well you might see that + + align:start position:0% +one well you might see that + + + align:start position:0% +one well you might see that +slide and + + align:start position:0% + + + + align:start position:0% + +uh think to yourself there are thousand + + align:start position:0% +uh think to yourself there are thousand + + + align:start position:0% +uh think to yourself there are thousand +faculty at + + align:start position:0% +faculty at + + + align:start position:0% +faculty at +MIT nice piece of work but not so much + + align:start position:0% +MIT nice piece of work but not so much + + + align:start position:0% +MIT nice piece of work but not so much +but it's only a tiny any piece of work + + align:start position:0% +but it's only a tiny any piece of work + + + align:start position:0% +but it's only a tiny any piece of work +if you divide by a + + align:start position:0% +if you divide by a + + + align:start position:0% +if you divide by a +thousand so when you show a whole + + align:start position:0% +thousand so when you show a whole + + + align:start position:0% +thousand so when you show a whole +gigantic list of collaborators at the + + align:start position:0% +gigantic list of collaborators at the + + + align:start position:0% +gigantic list of collaborators at the +end of a talk it's a kind of it's a it's + + align:start position:0% +end of a talk it's a kind of it's a it's + + + align:start position:0% +end of a talk it's a kind of it's a it's +it's it's a kind of let down because it + + align:start position:0% +it's it's a kind of let down because it + + + align:start position:0% +it's it's a kind of let down because it +suggests that nobody knows well did you + + align:start position:0% +suggests that nobody knows well did you + + + align:start position:0% +suggests that nobody knows well did you +do anything + + align:start position:0% +do anything + + + align:start position:0% +do anything +significant now you got to you got to + + align:start position:0% +significant now you got to you got to + + + align:start position:0% +significant now you got to you got to +recognize your collaborators right so + + align:start position:0% +recognize your collaborators right so + + + align:start position:0% +recognize your collaborators right so +where do you do that not on the last + + align:start position:0% +where do you do that not on the last + + + align:start position:0% +where do you do that not on the last +slide on the first slide all this was on + + align:start position:0% +slide on the first slide all this was on + + + align:start position:0% +slide on the first slide all this was on +the first slide these are the + + align:start position:0% +the first slide these are the + + + align:start position:0% +the first slide these are the +collaborators so you don't want to put + + align:start position:0% +collaborators so you don't want to put + + + align:start position:0% +collaborators so you don't want to put +them at the end you don't want a slide + + align:start position:0% +them at the end you don't want a slide + + + align:start position:0% +them at the end you don't want a slide +like this + + align:start position:0% +like this + + + align:start position:0% +like this +how about this + + align:start position:0% +how about this + + + align:start position:0% +how about this +one this is the worst possible way to + + align:start position:0% +one this is the worst possible way to + + + align:start position:0% +one this is the worst possible way to +end a + + align:start position:0% +end a + + + align:start position:0% +end a +talk because this slide can be up there + + align:start position:0% +talk because this slide can be up there + + + align:start position:0% +talk because this slide can be up there +for 20 minutes I've seen it happen it + + align:start position:0% +for 20 minutes I've seen it happen it + + + align:start position:0% +for 20 minutes I've seen it happen it +squanders real estate it squanders an + + align:start position:0% +squanders real estate it squanders an + + + align:start position:0% +squanders real estate it squanders an +opportunity to tell people who you are + + align:start position:0% +opportunity to tell people who you are + + + align:start position:0% +opportunity to tell people who you are +it's it's + + align:start position:0% + + + + align:start position:0% + +just what about this one + + align:start position:0% + + + + align:start position:0% + +I often see it I've never seen anybody + + align:start position:0% +I often see it I've never seen anybody + + + align:start position:0% +I often see it I've never seen anybody +write it + + align:start position:0% +write it + + + align:start position:0% +write it +down also it wastes + + align:start position:0% + + + + align:start position:0% + +opportunity oh my + + align:start position:0% +opportunity oh my + + + align:start position:0% +opportunity oh my +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +God even + + align:start position:0% + + + + align:start position:0% + +worse all of these slides do nothing for + + align:start position:0% +worse all of these slides do nothing for + + + align:start position:0% +worse all of these slides do nothing for +you they waste an opportunity for you to + + align:start position:0% +you they waste an opportunity for you to + + + align:start position:0% +you they waste an opportunity for you to +tell people to leave people with what + + align:start position:0% +tell people to leave people with what + + + align:start position:0% +tell people to leave people with what +you with who you + + align:start position:0% +you with who you + + + align:start position:0% +you with who you +are well well what about + + align:start position:0% +are well well what about + + + align:start position:0% +are well well what about +this this a good + + align:start position:0% +this this a good + + + align:start position:0% +this this a good +one it might seem so at first but here's + + align:start position:0% +one it might seem so at first but here's + + + align:start position:0% +one it might seem so at first but here's +the + + align:start position:0% + + + + align:start position:0% + +problem if you say these are my + + align:start position:0% +problem if you say these are my + + + align:start position:0% +problem if you say these are my +conclusions these are perfectly + + align:start position:0% +conclusions these are perfectly + + + align:start position:0% +conclusions these are perfectly +legitimate conclusions that nobody cares + + align:start position:0% +legitimate conclusions that nobody cares + + + align:start position:0% +legitimate conclusions that nobody cares +about what they care about is what you + + align:start position:0% +about what they care about is what you + + + align:start position:0% +about what they care about is what you +have done and that's why your final + + align:start position:0% +have done and that's why your final + + + align:start position:0% +have done and that's why your final +slide should have this + + align:start position:0% +slide should have this + + + align:start position:0% +slide should have this +label + + align:start position:0% +label + + + align:start position:0% +label +contributions it's a mirror of what I + + align:start position:0% +contributions it's a mirror of what I + + + align:start position:0% +contributions it's a mirror of what I +said over there about how job talks on + + align:start position:0% +said over there about how job talks on + + + align:start position:0% +said over there about how job talks on +to ought to be like a sandwich and the + + align:start position:0% +to ought to be like a sandwich and the + + + align:start position:0% +to ought to be like a sandwich and the +final Slide the one that's up there + + align:start position:0% +final Slide the one that's up there + + + align:start position:0% +final Slide the one that's up there +while people are asking questions and + + align:start position:0% +while people are asking questions and + + + align:start position:0% +while people are asking questions and +filing out it ought to be the one that + + align:start position:0% +filing out it ought to be the one that + + + align:start position:0% +filing out it ought to be the one that +has your contributions on + + align:start position:0% +has your contributions on + + + align:start position:0% +has your contributions on +it here's an example from my own stump + + align:start position:0% +it here's an example from my own stump + + + align:start position:0% +it here's an example from my own stump +speech yeah this is what uh I talk about + + align:start position:0% +speech yeah this is what uh I talk about + + + align:start position:0% +speech yeah this is what uh I talk about +a lot yes here are the things that I + + align:start position:0% +a lot yes here are the things that I + + + align:start position:0% +a lot yes here are the things that I +typically + + align:start position:0% + + + + align:start position:0% + +demonstrate and I wait for people to + + align:start position:0% +demonstrate and I wait for people to + + + align:start position:0% +demonstrate and I wait for people to +read it and then the final element there + + align:start position:0% +read it and then the final element there + + + align:start position:0% +read it and then the final element there +is this is what we get out of + + align:start position:0% +is this is what we get out of + + + align:start position:0% +is this is what we get out of +it so that's a example of a contribution + + align:start position:0% +it so that's a example of a contribution + + + align:start position:0% +it so that's a example of a contribution +line all right + + align:start position:0% +line all right + + + align:start position:0% +line all right +now what about the other part you know + + align:start position:0% +now what about the other part you know + + + align:start position:0% +now what about the other part you know +you got your final slide slide up there + + align:start position:0% +you got your final slide slide up there + + + align:start position:0% +you got your final slide slide up there +it's a contribution slide somehow you + + align:start position:0% +it's a contribution slide somehow you + + + align:start position:0% +it's a contribution slide somehow you +have to tell people you're + + align:start position:0% +have to tell people you're + + + align:start position:0% +have to tell people you're +finished so uh let's check out a few + + align:start position:0% + + + + align:start position:0% + +possibilities one thing you could + + align:start position:0% +possibilities one thing you could + + + align:start position:0% +possibilities one thing you could +do in the final words is you could uh + + align:start position:0% +do in the final words is you could uh + + + align:start position:0% +do in the final words is you could uh +tell a joke + + align:start position:0% + + + + align:start position:0% + +it's + + align:start position:0% +it's + + + align:start position:0% +it's +okay by the time you're done people have + + align:start position:0% +okay by the time you're done people have + + + align:start position:0% +okay by the time you're done people have +adjusted themselves to your voice + + align:start position:0% +adjusted themselves to your voice + + + align:start position:0% +adjusted themselves to your voice +parameters they're ready for a + + align:start position:0% + + + + align:start position:0% + +joke I was sitting in another bar this + + align:start position:0% +joke I was sitting in another bar this + + + align:start position:0% +joke I was sitting in another bar this +time in Austin Texas with a colleague of + + align:start position:0% +time in Austin Texas with a colleague of + + + align:start position:0% +time in Austin Texas with a colleague of +mine named Doug lenat and Doug's a + + align:start position:0% +mine named Doug lenat and Doug's a + + + align:start position:0% +mine named Doug lenat and Doug's a +fantastic speaker and so I said uh to + + align:start position:0% +fantastic speaker and so I said uh to + + + align:start position:0% +fantastic speaker and so I said uh to +Doug Doug you're a fantastic speaker + + align:start position:0% +Doug Doug you're a fantastic speaker + + + align:start position:0% +Doug Doug you're a fantastic speaker +what's your secret and he said oh + + align:start position:0% +what's your secret and he said oh + + + align:start position:0% +what's your secret and he said oh +I always uh finish with a joke and that + + align:start position:0% +I always uh finish with a joke and that + + + align:start position:0% +I always uh finish with a joke and that +way people think they've had fun the + + align:start position:0% +way people think they've had fun the + + + align:start position:0% +way people think they've had fun the +whole + + align:start position:0% + + + + align:start position:0% + +time so yeah a joke will work down + + align:start position:0% +time so yeah a joke will work down + + + align:start position:0% +time so yeah a joke will work down +there how about uh this + + align:start position:0% + + + + align:start position:0% + +one thank + + align:start position:0% +one thank + + + align:start position:0% +one thank +you I don't recommend it + + align:start position:0% +you I don't recommend it + + + align:start position:0% +you I don't recommend it +it's a weak move you will not go to hell + + align:start position:0% +it's a weak move you will not go to hell + + + align:start position:0% +it's a weak move you will not go to hell +if you conclude your talk by saying + + align:start position:0% +if you conclude your talk by saying + + + align:start position:0% +if you conclude your talk by saying +thank you but it's a weak move and + + align:start position:0% +thank you but it's a weak move and + + + align:start position:0% +thank you but it's a weak move and +here's + + align:start position:0% +here's + + + align:start position:0% +here's +why when you say thank you even worse + + align:start position:0% +why when you say thank you even worse + + + align:start position:0% +why when you say thank you even worse +thank you for listening it suggests that + + align:start position:0% +thank you for listening it suggests that + + + align:start position:0% +thank you for listening it suggests that +everybody has stayed that long out of + + align:start position:0% +everybody has stayed that long out of + + + align:start position:0% +everybody has stayed that long out of +politeness and that they had a profound + + align:start position:0% +politeness and that they had a profound + + + align:start position:0% +politeness and that they had a profound +desire to be somewhere else but they're + + align:start position:0% +desire to be somewhere else but they're + + + align:start position:0% +desire to be somewhere else but they're +so polite they stuck it out and that's + + align:start position:0% +so polite they stuck it out and that's + + + align:start position:0% +so polite they stuck it out and that's +what you're thanking them + + align:start position:0% +what you're thanking them + + + align:start position:0% +what you're thanking them +for so once wild Applause has started + + align:start position:0% +for so once wild Applause has started + + + align:start position:0% +for so once wild Applause has started +you can mouth a thank you and it's not + + align:start position:0% +you can mouth a thank you and it's not + + + align:start position:0% +you can mouth a thank you and it's not +there's nothing wrong with that but the + + align:start position:0% +there's nothing wrong with that but the + + + align:start position:0% +there's nothing wrong with that but the +last thing you do do should not be + + align:start position:0% +last thing you do do should not be + + + align:start position:0% +last thing you do do should not be +saying thank + + align:start position:0% +saying thank + + + align:start position:0% +saying thank +you now do you say to me well doesn't + + align:start position:0% +you now do you say to me well doesn't + + + align:start position:0% +you now do you say to me well doesn't +everybody say thank you well what + + align:start position:0% +everybody say thank you well what + + + align:start position:0% +everybody say thank you well what +everybody does is not necessarily the + + align:start position:0% +everybody does is not necessarily the + + + align:start position:0% +everybody does is not necessarily the +right + + align:start position:0% +right + + + align:start position:0% +right +thing and I'd like to illustrate how + + align:start position:0% +thing and I'd like to illustrate how + + + align:start position:0% +thing and I'd like to illustrate how +some talks can end without saying thank + + align:start position:0% +some talks can end without saying thank + + + align:start position:0% +some talks can end without saying thank +you I like to draw from political + + align:start position:0% +you I like to draw from political + + + align:start position:0% +you I like to draw from political +speeches but the ones that I've heard + + align:start position:0% +speeches but the ones that I've heard + + + align:start position:0% +speeches but the ones that I've heard +recently aren't so good + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +so I'm going to have to go go back a + + align:start position:0% +so I'm going to have to go go back a + + + align:start position:0% +so I'm going to have to go go back a +little bit so here's a Governor Christie + + align:start position:0% +little bit so here's a Governor Christie + + + align:start position:0% +little bit so here's a Governor Christie +he uh gave the U Republican keynote + + align:start position:0% +he uh gave the U Republican keynote + + + align:start position:0% +he uh gave the U Republican keynote +address one year uh this is the end of + + align:start position:0% +address one year uh this is the end of + + + align:start position:0% +address one year uh this is the end of +his talk let's see what he + + align:start position:0% + + + + align:start position:0% + +does and together everybody together we + + align:start position:0% +does and together everybody together we + + + align:start position:0% +does and together everybody together we +will stand up once again for American + + align:start position:0% +will stand up once again for American + + + align:start position:0% +will stand up once again for American +greatness for our children and + + align:start position:0% +greatness for our children and + + + align:start position:0% +greatness for our children and +grandchildren God bless you and God + + align:start position:0% +grandchildren God bless you and God + + + align:start position:0% +grandchildren God bless you and God +bless + + align:start position:0% + + + + align:start position:0% + +America that's some a classic + + align:start position:0% +America that's some a classic + + + align:start position:0% +America that's some a classic +benediction ending God bless you God + + align:start position:0% +benediction ending God bless you God + + + align:start position:0% +benediction ending God bless you God +Bless + + align:start position:0% +Bless + + + align:start position:0% +Bless +America now I I don't want to be + + align:start position:0% +America now I I don't want to be + + + align:start position:0% +America now I I don't want to be +partisan about this so I think I better + + align:start position:0% +partisan about this so I think I better + + + align:start position:0% +partisan about this so I think I better +switch to the keynote address in the Dem + + align:start position:0% +switch to the keynote address in the Dem + + + align:start position:0% +switch to the keynote address in the Dem +Democratic + + align:start position:0% +Democratic + + + align:start position:0% +Democratic +Convention I was delivered that year by + + align:start position:0% +Convention I was delivered that year by + + + align:start position:0% +Convention I was delivered that year by +by Bill Clinton who knows something + + align:start position:0% +by Bill Clinton who knows something + + + align:start position:0% +by Bill Clinton who knows something +about how to + + align:start position:0% + + + + align:start position:0% + +speak if that is what you want if that + + align:start position:0% +speak if that is what you want if that + + + align:start position:0% +speak if that is what you want if that +is what you believe you must vote and + + align:start position:0% +is what you believe you must vote and + + + align:start position:0% +is what you believe you must vote and +you must reelect President Barack Obama + + align:start position:0% +you must reelect President Barack Obama + + + align:start position:0% +you must reelect President Barack Obama +God bless you and God bless + + align:start position:0% + + + + align:start position:0% + +America now watch this let's go back a + + align:start position:0% +America now watch this let's go back a + + + align:start position:0% +America now watch this let's go back a +little bit and redo it what I want you + + align:start position:0% +little bit and redo it what I want you + + + align:start position:0% +little bit and redo it what I want you +to see is that at one point he seems to + + align:start position:0% +to see is that at one point he seems to + + + align:start position:0% +to see is that at one point he seems to +be almost pressing his lips together + + align:start position:0% +be almost pressing his lips together + + + align:start position:0% +be almost pressing his lips together +forcing himself not to say thank you and + + align:start position:0% +forcing himself not to say thank you and + + + align:start position:0% +forcing himself not to say thank you and +then there's another place where he does + + align:start position:0% +then there's another place where he does + + + align:start position:0% +then there's another place where he does +a little salute so watch for those this + + align:start position:0% +a little salute so watch for those this + + + align:start position:0% +a little salute so watch for those this +time + + align:start position:0% +time + + + align:start position:0% +time +around if that that is what you want if + + align:start position:0% +around if that that is what you want if + + + align:start position:0% +around if that that is what you want if +that is what you believe you must vote + + align:start position:0% +that is what you believe you must vote + + + align:start position:0% +that is what you believe you must vote +and you must reelect President Barack + + align:start position:0% +and you must reelect President Barack + + + align:start position:0% +and you must reelect President Barack +Obama God bless you and God bless + + align:start position:0% +Obama God bless you and God bless + + + align:start position:0% +Obama God bless you and God bless +America everybody's pursing his + + align:start position:0% +America everybody's pursing his + + + align:start position:0% +America everybody's pursing his +lips there's a + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +SL yeah I think that's pretty good now + + align:start position:0% +SL yeah I think that's pretty good now + + + align:start position:0% +SL yeah I think that's pretty good now +what are we going to take away from this + + align:start position:0% +what are we going to take away from this + + + align:start position:0% +what are we going to take away from this +well um I suppose I can conclude this + + align:start position:0% +well um I suppose I can conclude this + + + align:start position:0% +well um I suppose I can conclude this +talked by saying uh God bless you and + + align:start position:0% +talked by saying uh God bless you and + + + align:start position:0% +talked by saying uh God bless you and +God + + align:start position:0% +God + + + align:start position:0% +God +bless Institute of Technology but uh it + + align:start position:0% +bless Institute of Technology but uh it + + + align:start position:0% +bless Institute of Technology but uh it +might not work so well but what what you + + align:start position:0% +might not work so well but what what you + + + align:start position:0% +might not work so well but what what you +can't get out of this is you don't have + + align:start position:0% +can't get out of this is you don't have + + + align:start position:0% +can't get out of this is you don't have +to say thank you there are other things + + align:start position:0% +to say thank you there are other things + + + align:start position:0% +to say thank you there are other things +you can do and you know it's interesting + + align:start position:0% +you can do and you know it's interesting + + + align:start position:0% +you can do and you know it's interesting +that uh over time people figure this out + + align:start position:0% +that uh over time people figure this out + + + align:start position:0% +that uh over time people figure this out +and there's some stock ways of ending + + align:start position:0% +and there's some stock ways of ending + + + align:start position:0% +and there's some stock ways of ending +things so uh in the Catholic church in a + + align:start position:0% +things so uh in the Catholic church in a + + + align:start position:0% +things so uh in the Catholic church in a +good old Latin + + align:start position:0% +good old Latin + + + align:start position:0% +good old Latin +Mass it landed with it + + align:start position:0% +Mass it landed with it + + + align:start position:0% +Mass it landed with it +Miss EST + + align:start position:0% +Miss EST + + + align:start position:0% +Miss EST +which translates approximately to okay + + align:start position:0% +which translates approximately to okay + + + align:start position:0% +which translates approximately to okay +the mass is over you can go home + + align:start position:0% +the mass is over you can go home + + + align:start position:0% +the mass is over you can go home +now and of course uh at the musical + + align:start position:0% +now and of course uh at the musical + + + align:start position:0% +now and of course uh at the musical +concerts uh you know that uh it's time + + align:start position:0% +concerts uh you know that uh it's time + + + align:start position:0% +concerts uh you know that uh it's time +to clap not at the end of the song but + + align:start position:0% +to clap not at the end of the song but + + + align:start position:0% +to clap not at the end of the song but +rather when the uh conductor goes over + + align:start position:0% +rather when the uh conductor goes over + + + align:start position:0% +rather when the uh conductor goes over +and shakes hands with the concert Master + + align:start position:0% +and shakes hands with the concert Master + + + align:start position:0% +and shakes hands with the concert Master +those are conventions that tell you that + + align:start position:0% +those are conventions that tell you that + + + align:start position:0% +those are conventions that tell you that +the that the event is + + align:start position:0% +the that the event is + + + align:start position:0% +the that the event is +over so uh + + align:start position:0% +over so uh + + + align:start position:0% +over so uh +those are all possibilities for here but + + align:start position:0% +those are all possibilities for here but + + + align:start position:0% +those are all possibilities for here but +one more possibility and that is that + + align:start position:0% +one more possibility and that is that + + + align:start position:0% +one more possibility and that is that +you + + align:start position:0% + + + + align:start position:0% + +can salute the audience and by that I + + align:start position:0% +can salute the audience and by that I + + + align:start position:0% +can salute the audience and by that I +mean you can say something about how how + + align:start position:0% +mean you can say something about how how + + + align:start position:0% +mean you can say something about how how +much you value your time and a place so + + align:start position:0% +much you value your time and a place so + + + align:start position:0% +much you value your time and a place so +I could say well it's been a a great fun + + align:start position:0% +I could say well it's been a a great fun + + + align:start position:0% +I could say well it's been a a great fun +being here uh it's been uh fascinating + + align:start position:0% +being here uh it's been uh fascinating + + + align:start position:0% +being here uh it's been uh fascinating +to see what you folks are doing here at + + align:start position:0% +to see what you folks are doing here at + + + align:start position:0% +to see what you folks are doing here at +MIT I've been uh what stimulated uh and + + align:start position:0% +MIT I've been uh what stimulated uh and + + + align:start position:0% +MIT I've been uh what stimulated uh and +and provoked by the kinds of questions + + align:start position:0% +and provoked by the kinds of questions + + + align:start position:0% +and provoked by the kinds of questions +you been ask has been really great and + + align:start position:0% +you been ask has been really great and + + + align:start position:0% +you been ask has been really great and +and and I look forward to coming back on + + align:start position:0% +and and I look forward to coming back on + + + align:start position:0% +and and I look forward to coming back on +many occasions in the future so that + + align:start position:0% +many occasions in the future so that + + + align:start position:0% +many occasions in the future so that +salutes the audience you can do + + align:start position:0% + + + + align:start position:0% + +that well there it is um you know what + + align:start position:0% +that well there it is um you know what + + + align:start position:0% +that well there it is um you know what +uh I'm glad you're here and and the + + align:start position:0% +uh I'm glad you're here and and the + + + align:start position:0% +uh I'm glad you're here and and the +reason is by being here I think you have + + align:start position:0% +reason is by being here I think you have + + + align:start position:0% +reason is by being here I think you have +demonstrated an understanding that how + + align:start position:0% +demonstrated an understanding that how + + + align:start position:0% +demonstrated an understanding that how +you present and how you package your + + align:start position:0% +you present and how you package your + + + align:start position:0% +you present and how you package your +ideas is an important thing + + align:start position:0% +ideas is an important thing + + + align:start position:0% +ideas is an important thing +and I salute you for + + align:start position:0% +and I salute you for + + + align:start position:0% +and I salute you for +that and uh I uh suggest that you uh + + align:start position:0% +that and uh I uh suggest that you uh + + + align:start position:0% +that and uh I uh suggest that you uh +come back again and bring your friends + + align:start position:0% +come back again and bring your friends + + + align:start position:0% +come back again and bring your friends +[Applause] \ No newline at end of file diff --git a/UxMpn92vGXs.txt b/UxMpn92vGXs.txt new file mode 100644 index 0000000000000000000000000000000000000000..6dc65af705a8751903e8ba63a57f3c09167d1f73 --- /dev/null +++ b/UxMpn92vGXs.txt @@ -0,0 +1,14107 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu + + align:start position:0% +ocw.mit.edu + + + align:start position:0% +ocw.mit.edu +okay um welcome to class some very quick + + align:start position:0% +okay um welcome to class some very quick + + + align:start position:0% +okay um welcome to class some very quick +announcements we had the date wrong on + + align:start position:0% +announcements we had the date wrong on + + + align:start position:0% +announcements we had the date wrong on +the vision statement the vision + + align:start position:0% +the vision statement the vision + + + align:start position:0% +the vision statement the vision +statement you guys worked on on Monday + + align:start position:0% +statement you guys worked on on Monday + + + align:start position:0% +statement you guys worked on on Monday +is due today we had the date wrong in + + align:start position:0% +is due today we had the date wrong in + + + align:start position:0% +is due today we had the date wrong in +Stellar so um we're going it will not be + + align:start position:0% +Stellar so um we're going it will not be + + + align:start position:0% +Stellar so um we're going it will not be +late as long as it's turned in by + + align:start position:0% +late as long as it's turned in by + + + align:start position:0% +late as long as it's turned in by +tomorrow morning we have adjusted the + + align:start position:0% +tomorrow morning we have adjusted the + + + align:start position:0% +tomorrow morning we have adjusted the +date on on stellers unette shows the + + align:start position:0% +date on on stellers unette shows the + + + align:start position:0% +date on on stellers unette shows the +real date but since we made that mistake + + align:start position:0% +real date but since we made that mistake + + + align:start position:0% +real date but since we made that mistake +it's not late until tomorrow but we will + + align:start position:0% +it's not late until tomorrow but we will + + + align:start position:0% +it's not late until tomorrow but we will +expect them all in by the end of the day + + align:start position:0% +expect them all in by the end of the day + + + align:start position:0% +expect them all in by the end of the day +today um secondly um things that are due + + align:start position:0% +today um secondly um things that are due + + + align:start position:0% +today um secondly um things that are due +next Monday you will be expected to be + + align:start position:0% +next Monday you will be expected to be + + + align:start position:0% +next Monday you will be expected to be +turning in a prodct backlog we're going + + align:start position:0% +turning in a prodct backlog we're going + + + align:start position:0% +turning in a prodct backlog we're going +to work on creating a product backlog in + + align:start position:0% +to work on creating a product backlog in + + + align:start position:0% +to work on creating a product backlog in +class today and then you will have some + + align:start position:0% +class today and then you will have some + + + align:start position:0% +class today and then you will have some +time to refine it and think about it as + + align:start position:0% +time to refine it and think about it as + + + align:start position:0% +time to refine it and think about it as +you're working on the project over the + + align:start position:0% +you're working on the project over the + + + align:start position:0% +you're working on the project over the +weekend + + align:start position:0% +weekend + + + align:start position:0% +weekend +um if you have made one one thing you + + align:start position:0% +um if you have made one one thing you + + + align:start position:0% +um if you have made one one thing you +should be working on along the way + + align:start position:0% +should be working on along the way + + + align:start position:0% +should be working on along the way +remember you may require a design change + + align:start position:0% +remember you may require a design change + + + align:start position:0% +remember you may require a design change +log for this project as well so you + + align:start position:0% +log for this project as well so you + + + align:start position:0% +log for this project as well so you +should have already started it because + + align:start position:0% +should have already started it because + + + align:start position:0% +should have already started it because +you probably made some design decisions + + align:start position:0% +you probably made some design decisions + + + align:start position:0% +you probably made some design decisions +in your meeting on Monday so don't + + align:start position:0% +in your meeting on Monday so don't + + + align:start position:0% +in your meeting on Monday so don't +forget that and don't don't try to do it + + align:start position:0% +forget that and don't don't try to do it + + + align:start position:0% +forget that and don't don't try to do it +at the end + + align:start position:0% +at the end + + + align:start position:0% +at the end +um I think that's all the + + align:start position:0% +um I think that's all the + + + align:start position:0% +um I think that's all the +announcements yeah okay um so today's + + align:start position:0% +announcements yeah okay um so today's + + + align:start position:0% +announcements yeah okay um so today's +class is going to be we're going to + + align:start position:0% +class is going to be we're going to + + + align:start position:0% +class is going to be we're going to +start talking about project management + + align:start position:0% +start talking about project management + + + align:start position:0% +start talking about project management +um what we are trying to do with project + + align:start position:0% +um what we are trying to do with project + + + align:start position:0% +um what we are trying to do with project +management is give you the just in time + + align:start position:0% +management is give you the just in time + + + align:start position:0% +management is give you the just in time +version of it which is to say we're + + align:start position:0% +version of it which is to say we're + + + align:start position:0% +version of it which is to say we're +trying to give you the pieces of project + + align:start position:0% +trying to give you the pieces of project + + + align:start position:0% +trying to give you the pieces of project +management you need for the project + + align:start position:0% +management you need for the project + + + align:start position:0% +management you need for the project +you're on right now in the state it's on + + align:start position:0% +you're on right now in the state it's on + + + align:start position:0% +you're on right now in the state it's on +and we're going to do just in time + + align:start position:0% +and we're going to do just in time + + + align:start position:0% +and we're going to do just in time +project management for project two and + + align:start position:0% +project management for project two and + + + align:start position:0% +project management for project two and +then on Project three we're expect you + + align:start position:0% +then on Project three we're expect you + + + align:start position:0% +then on Project three we're expect you +to use all those pieces from the + + align:start position:0% +to use all those pieces from the + + + align:start position:0% +to use all those pieces from the +beginning and all the way through on + + align:start position:0% +beginning and all the way through on + + + align:start position:0% +beginning and all the way through on +your own so that you'll have had a a + + align:start position:0% +your own so that you'll have had a a + + + align:start position:0% +your own so that you'll have had a a +walkthrough on Project two a practice + + align:start position:0% +walkthrough on Project two a practice + + + align:start position:0% +walkthrough on Project two a practice +run on Project three and then on Project + + align:start position:0% +run on Project three and then on Project + + + align:start position:0% +run on Project three and then on Project +four hopefully you will need it and it + + align:start position:0% +four hopefully you will need it and it + + + align:start position:0% +four hopefully you will need it and it +will all work that's sort of the + + align:start position:0% +will all work that's sort of the + + + align:start position:0% +will all work that's sort of the +philosophy so we are giving it out to + + align:start position:0% +philosophy so we are giving it out to + + + align:start position:0% +philosophy so we are giving it out to +you in bits and pieces and I acknowledge + + align:start position:0% +you in bits and pieces and I acknowledge + + + align:start position:0% +you in bits and pieces and I acknowledge +that um I suspect that between between + + align:start position:0% +that um I suspect that between between + + + align:start position:0% +that um I suspect that between between +today's lecture and Monday's lecture we + + align:start position:0% +today's lecture and Monday's lecture we + + + align:start position:0% +today's lecture and Monday's lecture we +will have covered sort of the whole all + + align:start position:0% +will have covered sort of the whole all + + + align:start position:0% +will have covered sort of the whole all +the things we expect you to be doing as + + align:start position:0% +the things we expect you to be doing as + + + align:start position:0% +the things we expect you to be doing as +far as project management but today's + + align:start position:0% +far as project management but today's + + + align:start position:0% +far as project management but today's +lecture is sort of the first half and + + align:start position:0% +lecture is sort of the first half and + + + align:start position:0% +lecture is sort of the first half and +then Mondays will be the second half and + + align:start position:0% +then Mondays will be the second half and + + + align:start position:0% +then Mondays will be the second half and +tidying it all + + align:start position:0% +tidying it all + + + align:start position:0% +tidying it all +up + + align:start position:0% +up + + + align:start position:0% +up +um so we're going to do a brief history + + align:start position:0% +um so we're going to do a brief history + + + align:start position:0% +um so we're going to do a brief history +of how how project manage management was + + align:start position:0% +of how how project manage management was + + + align:start position:0% +of how how project manage management was +done in the past in the software + + align:start position:0% +done in the past in the software + + + align:start position:0% +done in the past in the software +industry we're going to talk about agile + + align:start position:0% +industry we're going to talk about agile + + + align:start position:0% +industry we're going to talk about agile +which is where many software companies + + align:start position:0% +which is where many software companies + + + align:start position:0% +which is where many software companies +are using now or are moving to with + + align:start position:0% +are using now or are moving to with + + + align:start position:0% +are using now or are moving to with +various levels of success not all of + + align:start position:0% +various levels of success not all of + + + align:start position:0% +various levels of success not all of +them + + align:start position:0% +them + + + align:start position:0% +them +unfortunately um then we're going to + + align:start position:0% +unfortunately um then we're going to + + + align:start position:0% +unfortunately um then we're going to +start getting into the nitty-gritty of + + align:start position:0% +start getting into the nitty-gritty of + + + align:start position:0% +start getting into the nitty-gritty of +the agile management system that our lab + + align:start position:0% +the agile management system that our lab + + + align:start position:0% +the agile management system that our lab +is most familiar with which is + + align:start position:0% +is most familiar with which is + + + align:start position:0% +is most familiar with which is +Scrum um and we'll start walking through + + align:start position:0% +Scrum um and we'll start walking through + + + align:start position:0% +Scrum um and we'll start walking through +all the aspects of scrum we will + + align:start position:0% +all the aspects of scrum we will + + + align:start position:0% +all the aspects of scrum we will +concentrate today on product backlogs + + align:start position:0% +concentrate today on product backlogs + + + align:start position:0% +concentrate today on product backlogs +we'll take a break from our lecture and + + align:start position:0% +we'll take a break from our lecture and + + + align:start position:0% +we'll take a break from our lecture and +you guys will have the opportunity in + + align:start position:0% +you guys will have the opportunity in + + + align:start position:0% +you guys will have the opportunity in +about a half an hour to make your own + + align:start position:0% +about a half an hour to make your own + + + align:start position:0% +about a half an hour to make your own +product backlogs and then do very quick + + align:start position:0% +product backlogs and then do very quick + + + align:start position:0% +product backlogs and then do very quick +presentations of sort of okay here are + + align:start position:0% +presentations of sort of okay here are + + + align:start position:0% +presentations of sort of okay here are +the top features that we found in our + + align:start position:0% +the top features that we found in our + + + align:start position:0% +the top features that we found in our +product backlog when we sat down and + + align:start position:0% +product backlog when we sat down and + + + align:start position:0% +product backlog when we sat down and +actually thought about our game um then + + align:start position:0% +actually thought about our game um then + + + align:start position:0% +actually thought about our game um then +unfortunately I will get up and start + + align:start position:0% +unfortunately I will get up and start + + + align:start position:0% +unfortunately I will get up and start +talking again + + align:start position:0% +talking again + + + align:start position:0% +talking again +we'll go over the meetings in scrum um + + align:start position:0% +we'll go over the meetings in scrum um + + + align:start position:0% +we'll go over the meetings in scrum um +how they run and what they are and why + + align:start position:0% +how they run and what they are and why + + + align:start position:0% +how they run and what they are and why +you do them and their level of + + align:start position:0% +you do them and their level of + + + align:start position:0% +you do them and their level of +importance and when we hit the end of + + align:start position:0% +importance and when we hit the end of + + + align:start position:0% +importance and when we hit the end of +that we'll have you run a small one + + align:start position:0% +that we'll have you run a small one + + + align:start position:0% +that we'll have you run a small one +yourself and then we will actually get + + align:start position:0% +yourself and then we will actually get + + + align:start position:0% +yourself and then we will actually get +to use the rest of time in class for + + align:start position:0% +to use the rest of time in class for + + + align:start position:0% +to use the rest of time in class for +working in your groups and working on + + align:start position:0% +working in your groups and working on + + + align:start position:0% +working in your groups and working on +your + + align:start position:0% +your + + + align:start position:0% +your +projects okay all right and any + + align:start position:0% +projects okay all right and any + + + align:start position:0% +projects okay all right and any +questions and let's + + align:start position:0% +questions and let's + + + align:start position:0% +questions and let's +go I can now now that now that we have + + align:start position:0% +go I can now now that now that we have + + + align:start position:0% +go I can now now that now that we have +the class interest guys I can mostly + + align:start position:0% +the class interest guys I can mostly + + + align:start position:0% +the class interest guys I can mostly +skip that slide + + align:start position:0% +skip that slide + + + align:start position:0% +skip that slide +um okay so you all took this class to + + align:start position:0% +um okay so you all took this class to + + + align:start position:0% +um okay so you all took this class to +learn how to create video games we + + align:start position:0% +learn how to create video games we + + + align:start position:0% +learn how to create video games we +however created this class to teach + + align:start position:0% +however created this class to teach + + + align:start position:0% +however created this class to teach +project management in video games um + + align:start position:0% +project management in video games um + + + align:start position:0% +project management in video games um +fortunately we're all going to get what + + align:start position:0% +fortunately we're all going to get what + + + align:start position:0% +fortunately we're all going to get what +we want because you really do need some + + align:start position:0% +we want because you really do need some + + + align:start position:0% +we want because you really do need some +good project management skills to + + align:start position:0% +good project management skills to + + + align:start position:0% +good project management skills to +successfully make video + + align:start position:0% +successfully make video + + + align:start position:0% +successfully make video +games um the better your project + + align:start position:0% +games um the better your project + + + align:start position:0% +games um the better your project +management the better your chances of + + align:start position:0% +management the better your chances of + + + align:start position:0% +management the better your chances of +coming out with a good game it won't + + align:start position:0% +coming out with a good game it won't + + + align:start position:0% +coming out with a good game it won't +guarantee it you need a lot of other + + align:start position:0% +guarantee it you need a lot of other + + + align:start position:0% +guarantee it you need a lot of other +good things as well but I can pretty + + align:start position:0% +good things as well but I can pretty + + + align:start position:0% +good things as well but I can pretty +much guarantee that without any project + + align:start position:0% +much guarantee that without any project + + + align:start position:0% +much guarantee that without any project +management you're attempt to make a game + + align:start position:0% +management you're attempt to make a game + + + align:start position:0% +management you're attempt to make a game +is going to fail um so so do try to + + align:start position:0% +is going to fail um so so do try to + + + align:start position:0% +is going to fail um so so do try to +listen I know this is some of the less + + align:start position:0% +listen I know this is some of the less + + + align:start position:0% +listen I know this is some of the less +interesting stuff we cover especially + + align:start position:0% +interesting stuff we cover especially + + + align:start position:0% +interesting stuff we cover especially +coming after the high of prototyping in + + align:start position:0% +coming after the high of prototyping in + + + align:start position:0% +coming after the high of prototyping in +making games but this is just as + + align:start position:0% +making games but this is just as + + + align:start position:0% +making games but this is just as +important as + + align:start position:0% + + + + align:start position:0% + +prototyping so what is project + + align:start position:0% +prototyping so what is project + + + align:start position:0% +prototyping so what is project +management let's start by explaining + + align:start position:0% +management let's start by explaining + + + align:start position:0% +management let's start by explaining +what the heck I'm talking about um + + align:start position:0% +what the heck I'm talking about um + + + align:start position:0% +what the heck I'm talking about um +project management is the work on the + + align:start position:0% +project management is the work on the + + + align:start position:0% +project management is the work on the +project that's devoted to planning + + align:start position:0% +project that's devoted to planning + + + align:start position:0% +project that's devoted to planning +organizing securing motivating and + + align:start position:0% +organizing securing motivating and + + + align:start position:0% +organizing securing motivating and +controlling the resources to + + align:start position:0% +controlling the resources to + + + align:start position:0% +controlling the resources to +successfully complete a project + + align:start position:0% +successfully complete a project + + + align:start position:0% +successfully complete a project +um you've all heard of fast good cheap + + align:start position:0% +um you've all heard of fast good cheap + + + align:start position:0% +um you've all heard of fast good cheap +pick two um most projects are actually + + align:start position:0% +pick two um most projects are actually + + + align:start position:0% +pick two um most projects are actually +kind of luckily if they manage to choose + + align:start position:0% +kind of luckily if they manage to choose + + + align:start position:0% +kind of luckily if they manage to choose +one and it's project management that + + align:start position:0% +one and it's project management that + + + align:start position:0% +one and it's project management that +allows them to figure out whether + + align:start position:0% +allows them to figure out whether + + + align:start position:0% +allows them to figure out whether +they're going to be fast or good or good + + align:start position:0% +they're going to be fast or good or good + + + align:start position:0% +they're going to be fast or good or good +or cheap or + + align:start position:0% +or cheap or + + + align:start position:0% +or cheap or +whatever um project management is all + + align:start position:0% +whatever um project management is all + + + align:start position:0% +whatever um project management is all +about predicting I know that the + + align:start position:0% +about predicting I know that the + + + align:start position:0% +about predicting I know that the +definition up there says controlling but + + align:start position:0% +definition up there says controlling but + + + align:start position:0% +definition up there says controlling but +you really can't control a whole lot of + + align:start position:0% +you really can't control a whole lot of + + + align:start position:0% +you really can't control a whole lot of +things what you can do is you can make + + align:start position:0% +things what you can do is you can make + + + align:start position:0% +things what you can do is you can make +some estimates make some predictions + + align:start position:0% +some estimates make some predictions + + + align:start position:0% +some estimates make some predictions +plan for the risks you're going to run + + align:start position:0% +plan for the risks you're going to run + + + align:start position:0% +plan for the risks you're going to run +into and then deal with them so it's + + align:start position:0% +into and then deal with them so it's + + + align:start position:0% +into and then deal with them so it's +really about predicting what you're + + align:start position:0% +really about predicting what you're + + + align:start position:0% +really about predicting what you're +going to need to do when you're going to + + align:start position:0% +going to need to do when you're going to + + + align:start position:0% +going to need to do when you're going to +need to do it and how you're going to + + align:start position:0% +need to do it and how you're going to + + + align:start position:0% +need to do it and how you're going to +need to do + + align:start position:0% +need to do + + + align:start position:0% +need to do +it + + align:start position:0% + + + + align:start position:0% + +um if you follow game and other large + + align:start position:0% +um if you follow game and other large + + + align:start position:0% +um if you follow game and other large +software project releases you know how + + align:start position:0% +software project releases you know how + + + align:start position:0% +software project releases you know how +rarely they actually manage to come out + + align:start position:0% +rarely they actually manage to come out + + + align:start position:0% +rarely they actually manage to come out +on time with all of their features games + + align:start position:0% +on time with all of their features games + + + align:start position:0% +on time with all of their features games +are especially famous for coming out + + align:start position:0% +are especially famous for coming out + + + align:start position:0% +are especially famous for coming out +late for being over budget and for often + + align:start position:0% +late for being over budget and for often + + + align:start position:0% +late for being over budget and for often +underd delivering the shiny things that + + align:start position:0% +underd delivering the shiny things that + + + align:start position:0% +underd delivering the shiny things that +they had mentioned can anybody think of + + align:start position:0% +they had mentioned can anybody think of + + + align:start position:0% +they had mentioned can anybody think of +a couple of of games recently that have + + align:start position:0% +a couple of of games recently that have + + + align:start position:0% +a couple of of games recently that have +done that + + align:start position:0% + + + + align:start position:0% + +no + + align:start position:0% +no + + + align:start position:0% +no +mm yeah the the + + align:start position:0% + + + + align:start position:0% + +new + + align:start position:0% +new + + + align:start position:0% +new +yep okay definitions they vary but yeah + + align:start position:0% +yep okay definitions they vary but yeah + + + align:start position:0% +yep okay definitions they vary but yeah +it's it is really really common for + + align:start position:0% +it's it is really really common for + + + align:start position:0% +it's it is really really common for +games to come out late and over + + align:start position:0% +games to come out late and over + + + align:start position:0% +games to come out late and over +budget um here's another one anybody + + align:start position:0% +budget um here's another one anybody + + + align:start position:0% +budget um here's another one anybody +name a AAA game that shift on time I'm + + align:start position:0% +name a AAA game that shift on time I'm + + + align:start position:0% +name a AAA game that shift on time I'm +not actually sure I can do this one + + align:start position:0% +not actually sure I can do this one + + + align:start position:0% +not actually sure I can do this one +with all the features that they + + align:start position:0% +with all the features that they + + + align:start position:0% +with all the features that they +predicted can anyone name + + align:start position:0% +predicted can anyone name + + + align:start position:0% +predicted can anyone name +one + + align:start position:0% + + + + align:start position:0% + +hm Call of Duty Call of Duty okay that's + + align:start position:0% +hm Call of Duty Call of Duty okay that's + + + align:start position:0% +hm Call of Duty Call of Duty okay that's +impressive okay so so how do you manage + + align:start position:0% +impressive okay so so how do you manage + + + align:start position:0% +impressive okay so so how do you manage +to plan what you're going to need to do + + align:start position:0% +to plan what you're going to need to do + + + align:start position:0% +to plan what you're going to need to do +get all of your resoures in order have + + align:start position:0% +get all of your resoures in order have + + + align:start position:0% +get all of your resoures in order have +them all in the right place at the right + + align:start position:0% +them all in the right place at the right + + + align:start position:0% +them all in the right place at the right +time and get them working + + align:start position:0% +time and get them working + + + align:start position:0% +time and get them working +together the old model of doing this + + align:start position:0% +together the old model of doing this + + + align:start position:0% +together the old model of doing this +which is which is actually the model + + align:start position:0% +which is which is actually the model + + + align:start position:0% +which is which is actually the model +that I worked at in several Studios and + + align:start position:0% +that I worked at in several Studios and + + + align:start position:0% +that I worked at in several Studios and +I've seen several other Studios that use + + align:start position:0% +I've seen several other Studios that use + + + align:start position:0% +I've seen several other Studios that use +it and it doesn't work very well but the + + align:start position:0% +it and it doesn't work very well but the + + + align:start position:0% +it and it doesn't work very well but the +the sort of the model that things + + align:start position:0% +the sort of the model that things + + + align:start position:0% +the sort of the model that things +started with in the industry and Grew + + align:start position:0% +started with in the industry and Grew + + + align:start position:0% +started with in the industry and Grew +From is waterall and I want to talk + + align:start position:0% +From is waterall and I want to talk + + + align:start position:0% +From is waterall and I want to talk +about that because it's where some + + align:start position:0% +about that because it's where some + + + align:start position:0% +about that because it's where some +studios some studios still are and it's + + align:start position:0% +studios some studios still are and it's + + + align:start position:0% +studios some studios still are and it's +where a lot of software projects still + + align:start position:0% +where a lot of software projects still + + + align:start position:0% +where a lot of software projects still +are and so it's good to understand what + + align:start position:0% +are and so it's good to understand what + + + align:start position:0% +are and so it's good to understand what +the history of project management is so + + align:start position:0% +the history of project management is so + + + align:start position:0% +the history of project management is so +you understand some of the problems that + + align:start position:0% +you understand some of the problems that + + + align:start position:0% +you understand some of the problems that +were found in that model that the agile + + align:start position:0% +were found in that model that the agile + + + align:start position:0% +were found in that model that the agile +model is trying to fix um agile has its + + align:start position:0% +model is trying to fix um agile has its + + + align:start position:0% +model is trying to fix um agile has its +own problems and we'll talk about them + + align:start position:0% +own problems and we'll talk about them + + + align:start position:0% +own problems and we'll talk about them +but let's start with + + align:start position:0% +but let's start with + + + align:start position:0% +but let's start with +waterfall so the very traditional + + align:start position:0% +waterfall so the very traditional + + + align:start position:0% +waterfall so the very traditional +tool um is waterfall where you prepare + + align:start position:0% +tool um is waterfall where you prepare + + + align:start position:0% +tool um is waterfall where you prepare +for every stage you sort of finish every + + align:start position:0% +for every stage you sort of finish every + + + align:start position:0% +for every stage you sort of finish every +stage 100% And then you move on to the + + align:start position:0% +stage 100% And then you move on to the + + + align:start position:0% +stage 100% And then you move on to the +next stage um to see what happens um you + + align:start position:0% +next stage um to see what happens um you + + + align:start position:0% +next stage um to see what happens um you +first you need your spec you need your + + align:start position:0% +first you need your spec you need your + + + align:start position:0% +first you need your spec you need your +requirements um which in game design is + + align:start position:0% +requirements um which in game design is + + + align:start position:0% +requirements um which in game design is +sort of your concept and your design + + align:start position:0% +sort of your concept and your design + + + align:start position:0% +sort of your concept and your design +phase you figure out what you want to + + align:start position:0% +phase you figure out what you want to + + + align:start position:0% +phase you figure out what you want to +make you figure out what all the + + align:start position:0% +make you figure out what all the + + + align:start position:0% +make you figure out what all the +features are you also figure out other + + align:start position:0% +features are you also figure out other + + + align:start position:0% +features are you also figure out other +constraints like what is your budget how + + align:start position:0% +constraints like what is your budget how + + + align:start position:0% +constraints like what is your budget how +long you're going to take what can the + + align:start position:0% +long you're going to take what can the + + + align:start position:0% +long you're going to take what can the +people on your team actually do if you + + align:start position:0% +people on your team actually do if you + + + align:start position:0% +people on your team actually do if you +don't have a physics programmer you + + align:start position:0% +don't have a physics programmer you + + + align:start position:0% +don't have a physics programmer you +probably don't want to make a physics + + align:start position:0% +probably don't want to make a physics + + + align:start position:0% +probably don't want to make a physics +game all that sort of pulling all those + + align:start position:0% +game all that sort of pulling all those + + + align:start position:0% +game all that sort of pulling all those +constraints together to make a design + + align:start position:0% +constraints together to make a design + + + align:start position:0% +constraints together to make a design +that is reasonable that works with the + + align:start position:0% +that is reasonable that works with the + + + align:start position:0% +that is reasonable that works with the +things that you think you're going to + + align:start position:0% +things that you think you're going to + + + align:start position:0% +things that you think you're going to +have to work + + align:start position:0% +have to work + + + align:start position:0% +have to work +with um that concepting design is going + + align:start position:0% +with um that concepting design is going + + + align:start position:0% +with um that concepting design is going +to flow into pre-production where you + + align:start position:0% +to flow into pre-production where you + + + align:start position:0% +to flow into pre-production where you +sat there and you made a whole lot of + + align:start position:0% +sat there and you made a whole lot of + + + align:start position:0% +sat there and you made a whole lot of +assumptions and design and concepting in + + align:start position:0% +assumptions and design and concepting in + + + align:start position:0% +assumptions and design and concepting in +pre-production you test them in very + + align:start position:0% +pre-production you test them in very + + + align:start position:0% +pre-production you test them in very +small scale usually you figure out if + + align:start position:0% +small scale usually you figure out if + + + align:start position:0% +small scale usually you figure out if +people can actually do the things they + + align:start position:0% +people can actually do the things they + + + align:start position:0% +people can actually do the things they +said they were going to do you figure + + align:start position:0% +said they were going to do you figure + + + align:start position:0% +said they were going to do you figure +out if the software you were going to + + align:start position:0% +out if the software you were going to + + + align:start position:0% +out if the software you were going to +buy is actually going to work or not and + + align:start position:0% +buy is actually going to work or not and + + + align:start position:0% +buy is actually going to work or not and +all those other details using the data + + align:start position:0% +all those other details using the data + + + align:start position:0% +all those other details using the data +you gathered in pre-production you + + align:start position:0% +you gathered in pre-production you + + + align:start position:0% +you gathered in pre-production you +create a whole lot of big fancy + + align:start position:0% +create a whole lot of big fancy + + + align:start position:0% +create a whole lot of big fancy +schedules and using those schedules you + + align:start position:0% +schedules and using those schedules you + + + align:start position:0% +schedules and using those schedules you +hire up your team and you go into + + align:start position:0% +hire up your team and you go into + + + align:start position:0% +hire up your team and you go into +production and you implement everything + + align:start position:0% +production and you implement everything + + + align:start position:0% +production and you implement everything +and you get it all Built Well you get + + align:start position:0% +and you get it all Built Well you get + + + align:start position:0% +and you get it all Built Well you get +most of it built + + align:start position:0% +most of it built + + + align:start position:0% +most of it built +um then you go into then in game in game + + align:start position:0% +um then you go into then in game in game + + + align:start position:0% +um then you go into then in game in game +processes you go into Alpha when you've + + align:start position:0% +processes you go into Alpha when you've + + + align:start position:0% +processes you go into Alpha when you've +got most of your features in and that's + + align:start position:0% +got most of your features in and that's + + + align:start position:0% +got most of your features in and that's +when you usually bring on a few small + + align:start position:0% +when you usually bring on a few small + + + align:start position:0% +when you usually bring on a few small +testers to do a little bit of testing + + align:start position:0% +testers to do a little bit of testing + + + align:start position:0% +testers to do a little bit of testing +and make sure your code is working the + + align:start position:0% +and make sure your code is working the + + + align:start position:0% +and make sure your code is working the +way you expected it to then when you've + + align:start position:0% +way you expected it to then when you've + + + align:start position:0% +way you expected it to then when you've +got all your features in and it's mostly + + align:start position:0% +got all your features in and it's mostly + + + align:start position:0% +got all your features in and it's mostly +working you go into beta you bring on + + align:start position:0% +working you go into beta you bring on + + + align:start position:0% +working you go into beta you bring on +more testers um in big studies these + + align:start position:0% +more testers um in big studies these + + + align:start position:0% +more testers um in big studies these +days it's often common to have you know + + align:start position:0% +days it's often common to have you know + + + align:start position:0% +days it's often common to have you know +open betas if you're looking at a + + align:start position:0% +open betas if you're looking at a + + + align:start position:0% +open betas if you're looking at a +massive some sort of massive um game + + align:start position:0% +massive some sort of massive um game + + + align:start position:0% +massive some sort of massive um game +where you you're not going to hire + + align:start position:0% +where you you're not going to hire + + + align:start position:0% +where you you're not going to hire +100,000 testers so what you do is you + + align:start position:0% +100,000 testers so what you do is you + + + align:start position:0% +100,000 testers so what you do is you +have an open beta and you let people + + align:start position:0% +have an open beta and you let people + + + align:start position:0% +have an open beta and you let people +come and play your game for free in + + align:start position:0% +come and play your game for free in + + + align:start position:0% +come and play your game for free in +exchange for testing it um that + + align:start position:0% +exchange for testing it um that + + + align:start position:0% +exchange for testing it um that +hopefully Nails out the rest of your big + + align:start position:0% +hopefully Nails out the rest of your big + + + align:start position:0% +hopefully Nails out the rest of your big +problems and then you ship + + align:start position:0% +problems and then you ship + + + align:start position:0% +problems and then you ship +it does anyone see the big problem with + + align:start position:0% +it does anyone see the big problem with + + + align:start position:0% +it does anyone see the big problem with +games in this + + align:start position:0% + + + + align:start position:0% + +model it's a little subtle so it's easy + + align:start position:0% +model it's a little subtle so it's easy + + + align:start position:0% +model it's a little subtle so it's easy +to miss it's okay if you don't but + + align:start position:0% + + + + align:start position:0% + +yeah you have to + + align:start position:0% + + + + align:start position:0% + +keep that that is it all the almost all + + align:start position:0% +keep that that is it all the almost all + + + align:start position:0% +keep that that is it all the almost all +of the testing is here at the end at + + align:start position:0% +of the testing is here at the end at + + + align:start position:0% +of the testing is here at the end at +beta it's a little late to change your + + align:start position:0% +beta it's a little late to change your + + + align:start position:0% +beta it's a little late to change your +design if you're + + align:start position:0% +design if you're + + + align:start position:0% +design if you're +doing all of your testing at the end if + + align:start position:0% +doing all of your testing at the end if + + + align:start position:0% +doing all of your testing at the end if +you're doing all your testing at the end + + align:start position:0% +you're doing all your testing at the end + + + align:start position:0% +you're doing all your testing at the end +the team can't respond to it they can't + + align:start position:0% +the team can't respond to it they can't + + + align:start position:0% +the team can't respond to it they can't +fix things and that is where a lot of + + align:start position:0% +fix things and that is where a lot of + + + align:start position:0% +fix things and that is where a lot of +schedules get stretched out and a lot of + + align:start position:0% +schedules get stretched out and a lot of + + + align:start position:0% +schedules get stretched out and a lot of +budgets get stretched out because all of + + align:start position:0% +budgets get stretched out because all of + + + align:start position:0% +budgets get stretched out because all of +the planning you had goes out the door + + align:start position:0% +the planning you had goes out the door + + + align:start position:0% +the planning you had goes out the door +somewhere around early Alpha and you + + align:start position:0% +somewhere around early Alpha and you + + + align:start position:0% +somewhere around early Alpha and you +have to start reworking your whole + + align:start position:0% +have to start reworking your whole + + + align:start position:0% +have to start reworking your whole +system um + + align:start position:0% +system um + + + align:start position:0% +system um +the problem here is of course you can't + + align:start position:0% +the problem here is of course you can't + + + align:start position:0% +the problem here is of course you can't +predict fun um you can't design an + + align:start position:0% +predict fun um you can't design an + + + align:start position:0% +predict fun um you can't design an +engaging experience without interacting + + align:start position:0% +engaging experience without interacting + + + align:start position:0% +engaging experience without interacting +with the people who are going to be + + align:start position:0% +with the people who are going to be + + + align:start position:0% +with the people who are going to be +using it which means not just the people + + align:start position:0% +using it which means not just the people + + + align:start position:0% +using it which means not just the people +on your team not just the small group of + + align:start position:0% +on your team not just the small group of + + + align:start position:0% +on your team not just the small group of +pre-prod I mean in waterfall they do do + + align:start position:0% +pre-prod I mean in waterfall they do do + + + align:start position:0% +pre-prod I mean in waterfall they do do +testing and in in pre-production you + + align:start position:0% +testing and in in pre-production you + + + align:start position:0% +testing and in in pre-production you +test in design you test but you're + + align:start position:0% +test in design you test but you're + + + align:start position:0% +test in design you test but you're +almost always testing with a very small + + align:start position:0% +almost always testing with a very small + + + align:start position:0% +almost always testing with a very small +group of people the other designers on + + align:start position:0% +group of people the other designers on + + + align:start position:0% +group of people the other designers on +your team the other people in your + + align:start position:0% +your team the other people in your + + + align:start position:0% +your team the other people in your +company you're not going for any big + + align:start position:0% +company you're not going for any big + + + align:start position:0% +company you're not going for any big +testing you're not going for any user + + align:start position:0% +testing you're not going for any user + + + align:start position:0% +testing you're not going for any user +testing you're not finding out how the + + align:start position:0% +testing you're not finding out how the + + + align:start position:0% +testing you're not finding out how the +people are actually going to use your + + align:start position:0% +people are actually going to use your + + + align:start position:0% +people are actually going to use your +product are going to react to it um so + + align:start position:0% +product are going to react to it um so + + + align:start position:0% +product are going to react to it um so +it's it's in many ways it's doomed to + + align:start position:0% +it's it's in many ways it's doomed to + + + align:start position:0% +it's it's in many ways it's doomed to +fail there's not a lot you can do about + + align:start position:0% +fail there's not a lot you can do about + + + align:start position:0% +fail there's not a lot you can do about +it um none of these projects are none of + + align:start position:0% +it um none of these projects are none of + + + align:start position:0% +it um none of these projects are none of +these problems are actually unique to + + align:start position:0% +these problems are actually unique to + + + align:start position:0% +these problems are actually unique to +games it's why big software projects + + align:start position:0% +games it's why big software projects + + + align:start position:0% +games it's why big software projects +often run over budget and run into a lot + + align:start position:0% +often run over budget and run into a lot + + + align:start position:0% +often run over budget and run into a lot +of feature creep but games have the + + align:start position:0% +of feature creep but games have the + + + align:start position:0% +of feature creep but games have the +really unique problem that their primary + + align:start position:0% +really unique problem that their primary + + + align:start position:0% +really unique problem that their primary +feature their primary goal is to be + + align:start position:0% +feature their primary goal is to be + + + align:start position:0% +feature their primary goal is to be +interesting and engaging to use if you + + align:start position:0% +interesting and engaging to use if you + + + align:start position:0% +interesting and engaging to use if you +are looking at business software and + + align:start position:0% +are looking at business software and + + + align:start position:0% +are looking at business software and +it's hard to use and it's annoying but + + align:start position:0% +it's hard to use and it's annoying but + + + align:start position:0% +it's hard to use and it's annoying but +it does all the calculations you need + + align:start position:0% +it does all the calculations you need + + + align:start position:0% +it does all the calculations you need +and it's the one that the tech + + align:start position:0% +and it's the one that the tech + + + align:start position:0% +and it's the one that the tech +department bought and and deployed + + align:start position:0% +department bought and and deployed + + + align:start position:0% +department bought and and deployed +you're going to use it there's just no + + align:start position:0% +you're going to use it there's just no + + + align:start position:0% +you're going to use it there's just no +getting around it but nobody has to play + + align:start position:0% +getting around it but nobody has to play + + + align:start position:0% +getting around it but nobody has to play +Call of Duty nobody has to turn on a + + align:start position:0% +Call of Duty nobody has to turn on a + + + align:start position:0% +Call of Duty nobody has to turn on a +particular game on their phone and play + + align:start position:0% +particular game on their phone and play + + + align:start position:0% +particular game on their phone and play +it so if a game fails in that sort of + + align:start position:0% +it so if a game fails in that sort of + + + align:start position:0% +it so if a game fails in that sort of +user connection it has completely failed + + align:start position:0% +user connection it has completely failed + + + align:start position:0% +user connection it has completely failed +there's there's nothing else you can do + + align:start position:0% +there's there's nothing else you can do + + + align:start position:0% +there's there's nothing else you can do +um it really kind of comes down to if + + align:start position:0% +um it really kind of comes down to if + + + align:start position:0% +um it really kind of comes down to if +your users aren't happy it's not a good + + align:start position:0% +your users aren't happy it's not a good + + + align:start position:0% +your users aren't happy it's not a good +game Your Design changes your schedule + + align:start position:0% +game Your Design changes your schedule + + + align:start position:0% +game Your Design changes your schedule +changes and your project management has + + align:start position:0% +changes and your project management has + + + align:start position:0% +changes and your project management has +now all of the time you put in project + + align:start position:0% +now all of the time you put in project + + + align:start position:0% +now all of the time you put in project +management has mostly been a waste of + + align:start position:0% +management has mostly been a waste of + + + align:start position:0% +management has mostly been a waste of +time + + align:start position:0% +time + + + align:start position:0% +time +um so what do you do + + align:start position:0% +um so what do you do + + + align:start position:0% +um so what do you do +instead first of all you think about + + align:start position:0% +instead first of all you think about + + + align:start position:0% +instead first of all you think about +building design iteration into your + + align:start position:0% +building design iteration into your + + + align:start position:0% +building design iteration into your +project management model you assume that + + align:start position:0% +project management model you assume that + + + align:start position:0% +project management model you assume that +you're going to be iterating and + + align:start position:0% +you're going to be iterating and + + + align:start position:0% +you're going to be iterating and +changing your design all the way around + + align:start position:0% +changing your design all the way around + + + align:start position:0% +changing your design all the way around +um that is where agile that is what the + + align:start position:0% +um that is where agile that is what the + + + align:start position:0% +um that is where agile that is what the +agile project + + align:start position:0% +agile project + + + align:start position:0% +agile project +management movement I guess is the right + + align:start position:0% +management movement I guess is the right + + + align:start position:0% +management movement I guess is the right +way to put it um was invented from there + + align:start position:0% +way to put it um was invented from there + + + align:start position:0% +way to put it um was invented from there +are actually several different types of + + align:start position:0% +are actually several different types of + + + align:start position:0% +are actually several different types of +project management that call themselves + + align:start position:0% +project management that call themselves + + + align:start position:0% +project management that call themselves +agile and there are several different + + align:start position:0% +agile and there are several different + + + align:start position:0% +agile and there are several different +techniques and tricks that call + + align:start position:0% +techniques and tricks that call + + + align:start position:0% +techniques and tricks that call +themselves agile um the one thing that + + align:start position:0% +themselves agile um the one thing that + + + align:start position:0% +themselves agile um the one thing that +they have in common is that they try to + + align:start position:0% +they have in common is that they try to + + + align:start position:0% +they have in common is that they try to +follow the agile Manifesto which is + + align:start position:0% +follow the agile Manifesto which is + + + align:start position:0% +follow the agile Manifesto which is +individuals and directions over + + align:start position:0% +individuals and directions over + + + align:start position:0% +individuals and directions over +processes and + + align:start position:0% +processes and + + + align:start position:0% +processes and +tools um does anyone want to + + align:start position:0% +tools um does anyone want to + + + align:start position:0% +tools um does anyone want to +well let's just go ahead working + + align:start position:0% +well let's just go ahead working + + + align:start position:0% +well let's just go ahead working +software over comprehensive + + align:start position:0% +software over comprehensive + + + align:start position:0% +software over comprehensive +documentation customer collaboration + + align:start position:0% +documentation customer collaboration + + + align:start position:0% +documentation customer collaboration +over contract negotiation and responding + + align:start position:0% +over contract negotiation and responding + + + align:start position:0% +over contract negotiation and responding +to change over following a + + align:start position:0% +to change over following a + + + align:start position:0% +to change over following a +plan + + align:start position:0% +plan + + + align:start position:0% +plan +um so for the first one individuals in + + align:start position:0% +um so for the first one individuals in + + + align:start position:0% +um so for the first one individuals in +interactions means it's better to get up + + align:start position:0% +interactions means it's better to get up + + + align:start position:0% +interactions means it's better to get up +and talk to someone than to send a whole + + align:start position:0% +and talk to someone than to send a whole + + + align:start position:0% +and talk to someone than to send a whole +lot of change requests over um working + + align:start position:0% +lot of change requests over um working + + + align:start position:0% +lot of change requests over um working +software that's why we ask for paper + + align:start position:0% +software that's why we ask for paper + + + align:start position:0% +software that's why we ask for paper +prototypes um and vision statements + + align:start position:0% +prototypes um and vision statements + + + align:start position:0% +prototypes um and vision statements +instead of a big F instead of a big fat + + align:start position:0% +instead of a big F instead of a big fat + + + align:start position:0% +instead of a big F instead of a big fat +design document it's why we want to see + + align:start position:0% +design document it's why we want to see + + + align:start position:0% +design document it's why we want to see +what it's doing rather than having you + + align:start position:0% +what it's doing rather than having you + + + align:start position:0% +what it's doing rather than having you +tell us what it will + + align:start position:0% +tell us what it will + + + align:start position:0% +tell us what it will +do um you don't really have so much + + align:start position:0% +do um you don't really have so much + + + align:start position:0% +do um you don't really have so much +customer collaboration so you don't have + + align:start position:0% +customer collaboration so you don't have + + + align:start position:0% +customer collaboration so you don't have +to worry about signing contracts and + + align:start position:0% +to worry about signing contracts and + + + align:start position:0% +to worry about signing contracts and +getting people to observe Milestones + + align:start position:0% +getting people to observe Milestones + + + align:start position:0% +getting people to observe Milestones +that's less of a less of a problem in a + + align:start position:0% +that's less of a less of a problem in a + + + align:start position:0% +that's less of a less of a problem in a +class specifically um and responding to + + align:start position:0% +class specifically um and responding to + + + align:start position:0% +class specifically um and responding to +change over following a plan means that + + align:start position:0% +change over following a plan means that + + + align:start position:0% +change over following a plan means that +if you discover what you're doing isn't + + align:start position:0% +if you discover what you're doing isn't + + + align:start position:0% +if you discover what you're doing isn't +going isn't working you sit down and you + + align:start position:0% +going isn't working you sit down and you + + + align:start position:0% +going isn't working you sit down and you +figure out how to fix it rather than + + align:start position:0% +figure out how to fix it rather than + + + align:start position:0% +figure out how to fix it rather than +continuing to go down the rabbit hole um + + align:start position:0% +continuing to go down the rabbit hole um + + + align:start position:0% +continuing to go down the rabbit hole um +and a lot of + + align:start position:0% +and a lot of + + + align:start position:0% +and a lot of +I just want to to state that everything + + align:start position:0% +I just want to to state that everything + + + align:start position:0% +I just want to to state that everything +on this are good things to do even the + + align:start position:0% +on this are good things to do even the + + + align:start position:0% +on this are good things to do even the +things that are sort of uh lower in + + align:start position:0% +things that are sort of uh lower in + + + align:start position:0% +things that are sort of uh lower in +priority it's good to have processes and + + align:start position:0% +priority it's good to have processes and + + + align:start position:0% +priority it's good to have processes and +tools but but it's more important that + + align:start position:0% +tools but but it's more important that + + + align:start position:0% +tools but but it's more important that +you have good interaction between the + + align:start position:0% +you have good interaction between the + + + align:start position:0% +you have good interaction between the +individuals in your group if you are + + align:start position:0% +individuals in your group if you are + + + align:start position:0% +individuals in your group if you are +saying no I can't actually get up and + + align:start position:0% +saying no I can't actually get up and + + + align:start position:0% +saying no I can't actually get up and +talk to this person because we have a + + align:start position:0% +talk to this person because we have a + + + align:start position:0% +talk to this person because we have a +process that we have to follow then you + + align:start position:0% +process that we have to follow then you + + + align:start position:0% +process that we have to follow then you +are now prioritizing incorrect at least + + align:start position:0% +are now prioritizing incorrect at least + + + align:start position:0% +are now prioritizing incorrect at least +according to the to to the + + align:start position:0% +according to the to to the + + + align:start position:0% +according to the to to the +actual Manifesto and I guess to are + + align:start position:0% +actual Manifesto and I guess to are + + + align:start position:0% +actual Manifesto and I guess to are +customers where where your customers + + align:start position:0% +customers where where your customers + + + align:start position:0% +customers where where your customers +where the instructors a lot of your + + align:start position:0% +where the instructors a lot of your + + + align:start position:0% +where the instructors a lot of your +classmates are going to be people who + + align:start position:0% +classmates are going to be people who + + + align:start position:0% +classmates are going to be people who +are going to play a games um and you + + align:start position:0% +are going to play a games um and you + + + align:start position:0% +are going to play a games um and you +want and customer collaboration is + + align:start position:0% +want and customer collaboration is + + + align:start position:0% +want and customer collaboration is +important in that sense because if you + + align:start position:0% +important in that sense because if you + + + align:start position:0% +important in that sense because if you +just replace that with work with your + + align:start position:0% +just replace that with work with your + + + align:start position:0% +just replace that with work with your +players right work work with the people + + align:start position:0% +players right work work with the people + + + align:start position:0% +players right work work with the people +who are going to play your game um and + + align:start position:0% +who are going to play your game um and + + + align:start position:0% +who are going to play your game um and +uh yes we did specify this is what we + + align:start position:0% +uh yes we did specify this is what we + + + align:start position:0% +uh yes we did specify this is what we +want you to see + + align:start position:0% +want you to see + + + align:start position:0% +want you to see +this is what want to see in the game + + align:start position:0% +this is what want to see in the game + + + align:start position:0% +this is what want to see in the game +that you want you're going to create + + align:start position:0% +that you want you're going to create + + + align:start position:0% +that you want you're going to create +that's like a contract well that's + + align:start position:0% +that's like a contract well that's + + + align:start position:0% +that's like a contract well that's +that's less important that actually + + align:start position:0% +that's less important that actually + + + align:start position:0% +that's less important that actually +coming and talking to us about problems + + align:start position:0% +coming and talking to us about problems + + + align:start position:0% +coming and talking to us about problems +that you might be having and might have + + align:start position:0% +that you might be having and might have + + + align:start position:0% +that you might be having and might have +trouble with don't just use our syllabus + + align:start position:0% +trouble with don't just use our syllabus + + + align:start position:0% +trouble with don't just use our syllabus +at a lottery list of things that you + + align:start position:0% +at a lottery list of things that you + + + align:start position:0% +at a lottery list of things that you +have to do and just be done with that + + align:start position:0% +have to do and just be done with that + + + align:start position:0% +have to do and just be done with that +talk to us yeah yeah thank + + align:start position:0% +talk to us yeah yeah thank + + + align:start position:0% +talk to us yeah yeah thank +you um so sort of the sort of model the + + align:start position:0% +you um so sort of the sort of model the + + + align:start position:0% +you um so sort of the sort of model the +model of making a software project I + + align:start position:0% +model of making a software project I + + + align:start position:0% +model of making a software project I +keep wanting to say a game but this is + + align:start position:0% +keep wanting to say a game but this is + + + align:start position:0% +keep wanting to say a game but this is +for for any any software actually an + + align:start position:0% +for for any any software actually an + + + align:start position:0% +for for any any software actually an +agile model is that the project start + + align:start position:0% +agile model is that the project start + + + align:start position:0% +agile model is that the project start +you've got your vision and your idea of + + align:start position:0% +you've got your vision and your idea of + + + align:start position:0% +you've got your vision and your idea of +what you're making and then on every + + align:start position:0% +what you're making and then on every + + + align:start position:0% +what you're making and then on every +iteration you go through every step + + align:start position:0% +iteration you go through every step + + + align:start position:0% +iteration you go through every step +essentially of the waterfall process you + + align:start position:0% +essentially of the waterfall process you + + + align:start position:0% +essentially of the waterfall process you +do a little bit of design a little bit + + align:start position:0% +do a little bit of design a little bit + + + align:start position:0% +do a little bit of design a little bit +of of detailed design you do a little + + align:start position:0% +of of detailed design you do a little + + + align:start position:0% +of of detailed design you do a little +bit of implementation of that particular + + align:start position:0% +bit of implementation of that particular + + + align:start position:0% +bit of implementation of that particular +chunk of the design you've just created + + align:start position:0% +chunk of the design you've just created + + + align:start position:0% +chunk of the design you've just created +then you spend some time testing it to + + align:start position:0% +then you spend some time testing it to + + + align:start position:0% +then you spend some time testing it to +make sure that a it works the way you + + align:start position:0% +make sure that a it works the way you + + + align:start position:0% +make sure that a it works the way you +expect it to and B it's achieving the + + align:start position:0% +expect it to and B it's achieving the + + + align:start position:0% +expect it to and B it's achieving the +result you want to get I.E the feature + + align:start position:0% +result you want to get I.E the feature + + + align:start position:0% +result you want to get I.E the feature +does what you expect it to do as far as + + align:start position:0% +does what you expect it to do as far as + + + align:start position:0% +does what you expect it to do as far as +improving the quality of your project um + + align:start position:0% +improving the quality of your project um + + + align:start position:0% +improving the quality of your project um +then you spend some time reviewing what + + align:start position:0% +then you spend some time reviewing what + + + align:start position:0% +then you spend some time reviewing what +your overall project is doing is it + + align:start position:0% +your overall project is doing is it + + + align:start position:0% +your overall project is doing is it +still going in the same direction you + + align:start position:0% +still going in the same direction you + + + align:start position:0% +still going in the same direction you +thought it would be going at the start + + align:start position:0% +thought it would be going at the start + + + align:start position:0% +thought it would be going at the start +of project is that the direction you + + align:start position:0% +of project is that the direction you + + + align:start position:0% +of project is that the direction you +want to be going in and then you can + + align:start position:0% +want to be going in and then you can + + + align:start position:0% +want to be going in and then you can +modify your plan accordingly and you + + align:start position:0% +modify your plan accordingly and you + + + align:start position:0% +modify your plan accordingly and you +start over with another + + align:start position:0% +start over with another + + + align:start position:0% +start over with another +iteration + + align:start position:0% + + + + align:start position:0% + +um the S the big Sav you have here and + + align:start position:0% +um the S the big Sav you have here and + + + align:start position:0% +um the S the big Sav you have here and +the the way in which agile management + + align:start position:0% +the the way in which agile management + + + align:start position:0% +the the way in which agile management +save tends to save time over waterfall + + align:start position:0% +save tends to save time over waterfall + + + align:start position:0% +save tends to save time over waterfall +Management in this project is you spend + + align:start position:0% +Management in this project is you spend + + + align:start position:0% +Management in this project is you spend +less time designing features that people + + align:start position:0% +less time designing features that people + + + align:start position:0% +less time designing features that people +don't want and more time working on the + + align:start position:0% +don't want and more time working on the + + + align:start position:0% +don't want and more time working on the +features that people do want and that's + + align:start position:0% +features that people do want and that's + + + align:start position:0% +features that people do want and that's +actually where the big time save is + + align:start position:0% +actually where the big time save is + + + align:start position:0% +actually where the big time save is +agile can't make you write code faster + + align:start position:0% +agile can't make you write code faster + + + align:start position:0% +agile can't make you write code faster +what it can do is make sure that the + + align:start position:0% +what it can do is make sure that the + + + align:start position:0% +what it can do is make sure that the +code you're writing is the code you want + + align:start position:0% +code you're writing is the code you want + + + align:start position:0% +code you're writing is the code you want +as opposed to the code that you end up + + align:start position:0% +as opposed to the code that you end up + + + align:start position:0% +as opposed to the code that you end up +cutting at the end of the + + align:start position:0% +cutting at the end of the + + + align:start position:0% +cutting at the end of the +project um some caveat before we start + + align:start position:0% +project um some caveat before we start + + + align:start position:0% +project um some caveat before we start +actually talking about how this applies + + align:start position:0% +actually talking about how this applies + + + align:start position:0% +actually talking about how this applies +to you in your project um agile is good + + align:start position:0% +to you in your project um agile is good + + + align:start position:0% +to you in your project um agile is good +not perfect which means once you've + + align:start position:0% +not perfect which means once you've + + + align:start position:0% +not perfect which means once you've +learned the tools and processes for + + align:start position:0% +learned the tools and processes for + + + align:start position:0% +learned the tools and processes for +Agile development you will want to keep + + align:start position:0% +Agile development you will want to keep + + + align:start position:0% +Agile development you will want to keep +adjusting and improving them you may + + align:start position:0% +adjusting and improving them you may + + + align:start position:0% +adjusting and improving them you may +discover that we're going to give you a + + align:start position:0% +discover that we're going to give you a + + + align:start position:0% +discover that we're going to give you a +set of outlines and a Baker's list of + + align:start position:0% +set of outlines and a Baker's list of + + + align:start position:0% +set of outlines and a Baker's list of +things to follow a recipe to do good + + align:start position:0% +things to follow a recipe to do good + + + align:start position:0% +things to follow a recipe to do good +project management and you may discover + + align:start position:0% +project management and you may discover + + + align:start position:0% +project management and you may discover +that following some portions of this + + align:start position:0% +that following some portions of this + + + align:start position:0% +that following some portions of this +recipe does not work well for the group + + align:start position:0% +recipe does not work well for the group + + + align:start position:0% +recipe does not work well for the group +you're in well the right thing to do is + + align:start position:0% +you're in well the right thing to do is + + + align:start position:0% +you're in well the right thing to do is +to set those pieces aside and figure out + + align:start position:0% +to set those pieces aside and figure out + + + align:start position:0% +to set those pieces aside and figure out +a way to work around it um a good agile + + align:start position:0% +a way to work around it um a good agile + + + align:start position:0% +a way to work around it um a good agile +team is always adjusting their processes + + align:start position:0% +team is always adjusting their processes + + + align:start position:0% +team is always adjusting their processes +and trying to improve + + align:start position:0% +and trying to improve + + + align:start position:0% +and trying to improve +them um another + + align:start position:0% +them um another + + + align:start position:0% +them um another +big um agile assumes that all of your + + align:start position:0% +big um agile assumes that all of your + + + align:start position:0% +big um agile assumes that all of your +developers are + + align:start position:0% +developers are + + + align:start position:0% +developers are +interchangeable which they're not right + + align:start position:0% +interchangeable which they're not right + + + align:start position:0% +interchangeable which they're not right +different programmers have different + + align:start position:0% +different programmers have different + + + align:start position:0% +different programmers have different +skills and on a game project + + align:start position:0% +skills and on a game project + + + align:start position:0% +skills and on a game project +especially um you have people who can do + + align:start position:0% +especially um you have people who can do + + + align:start position:0% +especially um you have people who can do +art you have people who are better at + + align:start position:0% +art you have people who are better at + + + align:start position:0% +art you have people who are better at +design you have people who are better at + + align:start position:0% +design you have people who are better at + + + align:start position:0% +design you have people who are better at +X or Y Z they're not all interchangeable + + align:start position:0% +X or Y Z they're not all interchangeable + + + align:start position:0% +X or Y Z they're not all interchangeable +which means that it takes more work to + + align:start position:0% +which means that it takes more work to + + + align:start position:0% +which means that it takes more work to +set up what your task set that you can + + align:start position:0% +set up what your task set that you can + + + align:start position:0% +set up what your task set that you can +get done in any particular period of + + align:start position:0% +get done in any particular period of + + + align:start position:0% +get done in any particular period of +time um on a project than pure agile was + + align:start position:0% +time um on a project than pure agile was + + + align:start position:0% +time um on a project than pure agile was +agile says okay you've got this list of + + align:start position:0% +agile says okay you've got this list of + + + align:start position:0% +agile says okay you've got this list of +tasks you've got you've got enough time + + align:start position:0% +tasks you've got you've got enough time + + + align:start position:0% +tasks you've got you've got enough time +to do them they'll get done when you're + + align:start position:0% +to do them they'll get done when you're + + + align:start position:0% +to do them they'll get done when you're +making a game you have to look more + + align:start position:0% +making a game you have to look more + + + align:start position:0% +making a game you have to look more +closely at the dependencies and who can + + align:start position:0% +closely at the dependencies and who can + + + align:start position:0% +closely at the dependencies and who can +get each of those tasks done to make + + align:start position:0% +get each of those tasks done to make + + + align:start position:0% +get each of those tasks done to make +sure that you have not in + + align:start position:0% +sure that you have not in + + + align:start position:0% +sure that you have not in +fact arranged for two of your part two + + align:start position:0% +fact arranged for two of your part two + + + align:start position:0% +fact arranged for two of your part two +of your team members to do nothing this + + align:start position:0% +of your team members to do nothing this + + + align:start position:0% +of your team members to do nothing this +Sprint and two of your team members to + + align:start position:0% +Sprint and two of your team members to + + + align:start position:0% +Sprint and two of your team members to +do twice as much as they actually have + + align:start position:0% +do twice as much as they actually have + + + align:start position:0% +do twice as much as they actually have +time for Sprint is the iteration cycle I + + align:start position:0% +time for Sprint is the iteration cycle I + + + align:start position:0% +time for Sprint is the iteration cycle I +will explain it again later I'm trying + + align:start position:0% +will explain it again later I'm trying + + + align:start position:0% +will explain it again later I'm trying +not to jump ahead and use jargon I + + align:start position:0% +not to jump ahead and use jargon I + + + align:start position:0% +not to jump ahead and use jargon I +haven't introduced but it's sometimes a + + align:start position:0% +haven't introduced but it's sometimes a + + + align:start position:0% +haven't introduced but it's sometimes a +challenge um let me know if I use a + + align:start position:0% +challenge um let me know if I use a + + + align:start position:0% +challenge um let me know if I use a +phrase that you don't understand because + + align:start position:0% +phrase that you don't understand because + + + align:start position:0% +phrase that you don't understand because +I will explain it or redefine it for you + + align:start position:0% +I will explain it or redefine it for you + + + align:start position:0% +I will explain it or redefine it for you +um finally and this is a problem you're + + align:start position:0% +um finally and this is a problem you're + + + align:start position:0% +um finally and this is a problem you're +likely to run into a little bit less in + + align:start position:0% +likely to run into a little bit less in + + + align:start position:0% +likely to run into a little bit less in +class but you are more likely to run out + + align:start position:0% +class but you are more likely to run out + + + align:start position:0% +class but you are more likely to run out +run into when you go into the outside + + align:start position:0% +run into when you go into the outside + + + align:start position:0% +run into when you go into the outside +world and you work on teams with + + align:start position:0% +world and you work on teams with + + + align:start position:0% +world and you work on teams with +different people um people trained in + + align:start position:0% +different people um people trained in + + + align:start position:0% +different people um people trained in +different disciplines communicate + + align:start position:0% +different disciplines communicate + + + align:start position:0% +different disciplines communicate +differently they have different + + align:start position:0% +differently they have different + + + align:start position:0% +differently they have different +terminology um on game teams this is + + align:start position:0% +terminology um on game teams this is + + + align:start position:0% +terminology um on game teams this is +really hard because you will often find + + align:start position:0% +really hard because you will often find + + + align:start position:0% +really hard because you will often find +and I'm not actually trying to + + align:start position:0% +and I'm not actually trying to + + + align:start position:0% +and I'm not actually trying to +stereotype you know all programmers talk + + align:start position:0% +stereotype you know all programmers talk + + + align:start position:0% +stereotype you know all programmers talk +like this or all artists talk like that + + align:start position:0% +like this or all artists talk like that + + + align:start position:0% +like this or all artists talk like that +but it is the case that the people who + + align:start position:0% +but it is the case that the people who + + + align:start position:0% +but it is the case that the people who +do programming and the people who are + + align:start position:0% +do programming and the people who are + + + align:start position:0% +do programming and the people who are +creating your assets be they art or + + align:start position:0% +creating your assets be they art or + + + align:start position:0% +creating your assets be they art or +design or audio often will talk past + + align:start position:0% +design or audio often will talk past + + + align:start position:0% +design or audio often will talk past +each other on specific problems the + + align:start position:0% +each other on specific problems the + + + align:start position:0% +each other on specific problems the +artists will not be able to explain why + + align:start position:0% +artists will not be able to explain why + + + align:start position:0% +artists will not be able to explain why +they can't meet the programmer's + + align:start position:0% +they can't meet the programmer's + + + align:start position:0% +they can't meet the programmer's +technical requirements and the + + align:start position:0% +technical requirements and the + + + align:start position:0% +technical requirements and the +programmers will be unwilling to figure + + align:start position:0% +programmers will be unwilling to figure + + + align:start position:0% +programmers will be unwilling to figure +out why it is the artist can't meet + + align:start position:0% +out why it is the artist can't meet + + + align:start position:0% +out why it is the artist can't meet +those technical requirements they've + + align:start position:0% +those technical requirements they've + + + align:start position:0% +those technical requirements they've +given the technical requirements why + + align:start position:0% +given the technical requirements why + + + align:start position:0% +given the technical requirements why +don't you just make something that works + + align:start position:0% +don't you just make something that works + + + align:start position:0% +don't you just make something that works +in it um since agile depends on really + + align:start position:0% +in it um since agile depends on really + + + align:start position:0% +in it um since agile depends on really +good communication and the willingness + + align:start position:0% +good communication and the willingness + + + align:start position:0% +good communication and the willingness +to solve problems like this this can + + align:start position:0% +to solve problems like this this can + + + align:start position:0% +to solve problems like this this can +create a huge tie-up especially in an + + align:start position:0% +create a huge tie-up especially in an + + + align:start position:0% +create a huge tie-up especially in an +agile team it can can pretty much stop + + align:start position:0% +agile team it can can pretty much stop + + + align:start position:0% +agile team it can can pretty much stop +anything from getting done so that's + + align:start position:0% +anything from getting done so that's + + + align:start position:0% +anything from getting done so that's +another big red flag to be aware of when + + align:start position:0% +another big red flag to be aware of when + + + align:start position:0% +another big red flag to be aware of when +you're using these + + align:start position:0% + + + + align:start position:0% + +methods okay so there are more than one + + align:start position:0% +methods okay so there are more than one + + + align:start position:0% +methods okay so there are more than one +there's more than one agile system the + + align:start position:0% +there's more than one agile system the + + + align:start position:0% +there's more than one agile system the +one that we use that we have the people + + align:start position:0% +one that we use that we have the people + + + align:start position:0% +one that we use that we have the people +who work in our Labs as europs use is + + align:start position:0% +who work in our Labs as europs use is + + + align:start position:0% +who work in our Labs as europs use is +called scrum is anybody familiar with + + align:start position:0% +called scrum is anybody familiar with + + + align:start position:0% +called scrum is anybody familiar with +scrum yay there's a few people anybody + + align:start position:0% +scrum yay there's a few people anybody + + + align:start position:0% +scrum yay there's a few people anybody +used it at internships and things like + + align:start position:0% +used it at internships and things like + + + align:start position:0% +used it at internships and things like +that + + align:start position:0% +that + + + align:start position:0% +that +okay all right so you guys you guys can + + align:start position:0% +okay all right so you guys you guys can + + + align:start position:0% +okay all right so you guys you guys can +help your teams out a little bit + + align:start position:0% +help your teams out a little bit + + + align:start position:0% +help your teams out a little bit +hopefully so scrum has three buzzwords + + align:start position:0% +hopefully so scrum has three buzzwords + + + align:start position:0% +hopefully so scrum has three buzzwords +and I may as well go ahead and call them + + align:start position:0% +and I may as well go ahead and call them + + + align:start position:0% +and I may as well go ahead and call them +buzzwords because that's really what + + align:start position:0% +buzzwords because that's really what + + + align:start position:0% +buzzwords because that's really what +they are that are supposed to Define it + + align:start position:0% +they are that are supposed to Define it + + + align:start position:0% +they are that are supposed to Define it +and let you understand what what it is + + align:start position:0% +and let you understand what what it is + + + align:start position:0% +and let you understand what what it is +about um they are transparency + + align:start position:0% +about um they are transparency + + + align:start position:0% +about um they are transparency +inspection and adaptability you can + + align:start position:0% +inspection and adaptability you can + + + align:start position:0% +inspection and adaptability you can +think of them a scrums vision statement + + align:start position:0% +think of them a scrums vision statement + + + align:start position:0% +think of them a scrums vision statement +um much shorter than a document um + + align:start position:0% +um much shorter than a document um + + + align:start position:0% +um much shorter than a document um +essentially if you are doing scrum right + + align:start position:0% +essentially if you are doing scrum right + + + align:start position:0% +essentially if you are doing scrum right +um all of your decisions and processes + + align:start position:0% +um all of your decisions and processes + + + align:start position:0% +um all of your decisions and processes +are transparent everyone on the team who + + align:start position:0% +are transparent everyone on the team who + + + align:start position:0% +are transparent everyone on the team who +needs to be involved in a decision is + + align:start position:0% +needs to be involved in a decision is + + + align:start position:0% +needs to be involved in a decision is +and anyone on the team who wants to + + align:start position:0% +and anyone on the team who wants to + + + align:start position:0% +and anyone on the team who wants to +understand why something was done can no + + align:start position:0% +understand why something was done can no + + + align:start position:0% +understand why something was done can no +one on the team should be able to say at + + align:start position:0% +one on the team should be able to say at + + + align:start position:0% +one on the team should be able to say at +any point well no one told me about that + + align:start position:0% +any point well no one told me about that + + + align:start position:0% +any point well no one told me about that +um because it's both the team's + + align:start position:0% +um because it's both the team's + + + align:start position:0% +um because it's both the team's +responsibility to share information and + + align:start position:0% +responsibility to share information and + + + align:start position:0% +responsibility to share information and +each team member's responsibility to + + align:start position:0% +each team member's responsibility to + + + align:start position:0% +each team member's responsibility to +stay + + align:start position:0% +stay + + + align:start position:0% +stay +informed um everything done by the team + + align:start position:0% +informed um everything done by the team + + + align:start position:0% +informed um everything done by the team +is inspected at some point um decisions + + align:start position:0% +is inspected at some point um decisions + + + align:start position:0% +is inspected at some point um decisions +processes team actions deliverables code + + align:start position:0% +processes team actions deliverables code + + + align:start position:0% +processes team actions deliverables code +um the team thinks proactively about + + align:start position:0% +um the team thinks proactively about + + + align:start position:0% +um the team thinks proactively about +what they're doing how they're doing it + + align:start position:0% +what they're doing how they're doing it + + + align:start position:0% +what they're doing how they're doing it +and if the team discovers a problem uh + + align:start position:0% +and if the team discovers a problem uh + + + align:start position:0% +and if the team discovers a problem uh +for example the build keeps being broken + + align:start position:0% +for example the build keeps being broken + + + align:start position:0% +for example the build keeps being broken +every night the team doesn't just say oh + + align:start position:0% +every night the team doesn't just say oh + + + align:start position:0% +every night the team doesn't just say oh +we'll work around it instead it takes + + align:start position:0% +we'll work around it instead it takes + + + align:start position:0% +we'll work around it instead it takes +the responsibility of figuring out how + + align:start position:0% +the responsibility of figuring out how + + + align:start position:0% +the responsibility of figuring out how +why and fixing not just the broken build + + align:start position:0% +why and fixing not just the broken build + + + align:start position:0% +why and fixing not just the broken build +but the processes that led to the broken + + align:start position:0% +but the processes that led to the broken + + + align:start position:0% +but the processes that led to the broken +build and finally um which feeds back + + align:start position:0% +build and finally um which feeds back + + + align:start position:0% +build and finally um which feeds back +into the other two the team is willing + + align:start position:0% +into the other two the team is willing + + + align:start position:0% +into the other two the team is willing +to adapt any processes and decisions to + + align:start position:0% +to adapt any processes and decisions to + + + align:start position:0% +to adapt any processes and decisions to +the reality they're actually dealing + + align:start position:0% +the reality they're actually dealing + + + align:start position:0% +the reality they're actually dealing +with when they find a structural problem + + align:start position:0% +with when they find a structural problem + + + align:start position:0% +with when they find a structural problem +you know for example how does art assets + + align:start position:0% +you know for example how does art assets + + + align:start position:0% +you know for example how does art assets +get in the game well right now we're + + align:start position:0% +get in the game well right now we're + + + align:start position:0% +get in the game well right now we're +having the programmers handload them in + + align:start position:0% +having the programmers handload them in + + + align:start position:0% +having the programmers handload them in +and we're losing six hours of programmer + + align:start position:0% +and we're losing six hours of programmer + + + align:start position:0% +and we're losing six hours of programmer +time every week um instead they sit down + + align:start position:0% +time every week um instead they sit down + + + align:start position:0% +time every week um instead they sit down +and say well how do we fix this do we + + align:start position:0% +and say well how do we fix this do we + + + align:start position:0% +and say well how do we fix this do we +take 12 hours next Sprint to code up a + + align:start position:0% +take 12 hours next Sprint to code up a + + + align:start position:0% +take 12 hours next Sprint to code up a +tool that allows the artist to put it in + + align:start position:0% +tool that allows the artist to put it in + + + align:start position:0% +tool that allows the artist to put it in +and then we'll save all that time going + + align:start position:0% +and then we'll save all that time going + + + align:start position:0% +and then we'll save all that time going +forward do we teach the artists how to + + align:start position:0% +forward do we teach the artists how to + + + align:start position:0% +forward do we teach the artists how to +put the co put their art indirectly I've + + align:start position:0% +put the co put their art indirectly I've + + + align:start position:0% +put the co put their art indirectly I've +had this + + align:start position:0% +had this + + + align:start position:0% +had this +discussion um on on a team in which we + + align:start position:0% +discussion um on on a team in which we + + + align:start position:0% +discussion um on on a team in which we +were losing an awful lot of time to Art + + align:start position:0% +were losing an awful lot of time to Art + + + align:start position:0% +were losing an awful lot of time to Art +to programmers putting art in game and + + align:start position:0% +to programmers putting art in game and + + + align:start position:0% +to programmers putting art in game and +the programmers were convinced it would + + align:start position:0% +the programmers were convinced it would + + + align:start position:0% +the programmers were convinced it would +be faster just keep it putting it in + + align:start position:0% +be faster just keep it putting it in + + + align:start position:0% +be faster just keep it putting it in +because it would take too long to teach + + align:start position:0% +because it would take too long to teach + + + align:start position:0% +because it would take too long to teach +the artists how to do it despite the + + align:start position:0% +the artists how to do it despite the + + + align:start position:0% +the artists how to do it despite the +fact that it was eating eight or 12 + + align:start position:0% +fact that it was eating eight or 12 + + + align:start position:0% +fact that it was eating eight or 12 +hours of programmer + + align:start position:0% +hours of programmer + + + align:start position:0% +hours of programmer +time every week I still think they were + + align:start position:0% +time every week I still think they were + + + align:start position:0% +time every week I still think they were +wrong anyway um note that I keep saying + + align:start position:0% +wrong anyway um note that I keep saying + + + align:start position:0% +wrong anyway um note that I keep saying +team and team members + + align:start position:0% +team and team members + + + align:start position:0% +team and team members +um in scrum the responsibility for + + align:start position:0% +um in scrum the responsibility for + + + align:start position:0% +um in scrum the responsibility for +project management doesn't sit with a + + align:start position:0% +project management doesn't sit with a + + + align:start position:0% +project management doesn't sit with a +producer or design lead or the + + align:start position:0% +producer or design lead or the + + + align:start position:0% +producer or design lead or the +programming lead it's the team's + + align:start position:0% +programming lead it's the team's + + + align:start position:0% +programming lead it's the team's +responsibility um Guided by the team + + align:start position:0% +responsibility um Guided by the team + + + align:start position:0% +responsibility um Guided by the team +members to manage their own project um + + align:start position:0% +members to manage their own project um + + + align:start position:0% +members to manage their own project um +that doesn't mean that a scrum team gets + + align:start position:0% +that doesn't mean that a scrum team gets + + + align:start position:0% +that doesn't mean that a scrum team gets +to do whatever they want um they still + + align:start position:0% +to do whatever they want um they still + + + align:start position:0% +to do whatever they want um they still +have constraints requirements + + align:start position:0% +have constraints requirements + + + align:start position:0% +have constraints requirements +expectations project handouts um handed + + align:start position:0% +expectations project handouts um handed + + + align:start position:0% +expectations project handouts um handed +down to them from managers clients + + align:start position:0% +down to them from managers clients + + + align:start position:0% +down to them from managers clients +instructors and other people um but in + + align:start position:0% +instructors and other people um but in + + + align:start position:0% +instructors and other people um but in +exchange for taking responsibility for + + align:start position:0% +exchange for taking responsibility for + + + align:start position:0% +exchange for taking responsibility for +the project management scrum teams do + + align:start position:0% +the project management scrum teams do + + + align:start position:0% +the project management scrum teams do +get to explain to the producers managers + + align:start position:0% +get to explain to the producers managers + + + align:start position:0% +get to explain to the producers managers +Executives and outside forces just how + + align:start position:0% +Executives and outside forces just how + + + align:start position:0% +Executives and outside forces just how +much they think they can achieve in a + + align:start position:0% +much they think they can achieve in a + + + align:start position:0% +much they think they can achieve in a +given time so you can go ahead and ask a + + align:start position:0% +given time so you can go ahead and ask a + + + align:start position:0% +given time so you can go ahead and ask a +scrum team for the sky the Earth the + + align:start position:0% +scrum team for the sky the Earth the + + + align:start position:0% +scrum team for the sky the Earth the +stars and the moon and an experienced + + align:start position:0% +stars and the moon and an experienced + + + align:start position:0% +stars and the moon and an experienced +and empowered scrum team will explain + + align:start position:0% +and empowered scrum team will explain + + + align:start position:0% +and empowered scrum team will explain +that okay in that time and on that + + align:start position:0% +that okay in that time and on that + + + align:start position:0% +that okay in that time and on that +budget we can get you a terrarium with a + + align:start position:0% +budget we can get you a terrarium with a + + + align:start position:0% +budget we can get you a terrarium with a +fancy + + align:start position:0% + + + + align:start position:0% + +NightLight um so how does this work um + + align:start position:0% +NightLight um so how does this work um + + + align:start position:0% +NightLight um so how does this work um +with with + + align:start position:0% +with with + + + align:start position:0% +with with +vocabulary there may or may not be a + + align:start position:0% +vocabulary there may or may not be a + + + align:start position:0% +vocabulary there may or may not be a +quiz later um so the project cycle this + + align:start position:0% +quiz later um so the project cycle this + + + align:start position:0% +quiz later um so the project cycle this +is the cycle of a whole project with the + + align:start position:0% +is the cycle of a whole project with the + + + align:start position:0% +is the cycle of a whole project with the +internal cycle right there in the Middle + + align:start position:0% +internal cycle right there in the Middle + + + align:start position:0% +internal cycle right there in the Middle +where you can see it um looking at it + + align:start position:0% +where you can see it um looking at it + + + align:start position:0% +where you can see it um looking at it +from sort of the whole Project Life + + align:start position:0% +from sort of the whole Project Life + + + align:start position:0% +from sort of the whole Project Life +you've got pregame Sprint which is let + + align:start position:0% +you've got pregame Sprint which is let + + + align:start position:0% +you've got pregame Sprint which is let +me start with this let me start with + + align:start position:0% +me start with this let me start with + + + align:start position:0% +me start with this let me start with +what a Sprint is um so a Sprint is is + + align:start position:0% +what a Sprint is um so a Sprint is is + + + align:start position:0% +what a Sprint is um so a Sprint is is +the way that a scrum project divides up + + align:start position:0% +the way that a scrum project divides up + + + align:start position:0% +the way that a scrum project divides up +its design iteration Cycles um Sprint + + align:start position:0% +its design iteration Cycles um Sprint + + + align:start position:0% +its design iteration Cycles um Sprint +length depends on the project and what + + align:start position:0% +length depends on the project and what + + + align:start position:0% +length depends on the project and what +the team wants one month was an early + + align:start position:0% +the team wants one month was an early + + + align:start position:0% +the team wants one month was an early +standard but a lot of people are now + + align:start position:0% +standard but a lot of people are now + + + align:start position:0% +standard but a lot of people are now +using two weeks instead in this class we + + align:start position:0% +using two weeks instead in this class we + + + align:start position:0% +using two weeks instead in this class we +encourage onee Sprints given the length + + align:start position:0% +encourage onee Sprints given the length + + + align:start position:0% +encourage onee Sprints given the length +of the projects and the sort of reality + + align:start position:0% +of the projects and the sort of reality + + + align:start position:0% +of the projects and the sort of reality +of how much you can or can't get done in + + align:start position:0% +of how much you can or can't get done in + + + align:start position:0% +of how much you can or can't get done in +a week um so a six-month project can be + + align:start position:0% +a week um so a six-month project can be + + + align:start position:0% +a week um so a six-month project can be +divided into six one month Sprints 12 + + align:start position:0% +divided into six one month Sprints 12 + + + align:start position:0% +divided into six one month Sprints 12 +two week Sprints depending on what the + + align:start position:0% +two week Sprints depending on what the + + + align:start position:0% +two week Sprints depending on what the +team wants to + + align:start position:0% +team wants to + + + align:start position:0% +team wants to +do um so much like a waterfall project + + align:start position:0% +do um so much like a waterfall project + + + align:start position:0% +do um so much like a waterfall project +you've got your design and vision time + + align:start position:0% +you've got your design and vision time + + + align:start position:0% +you've got your design and vision time +you've got your development time and + + align:start position:0% +you've got your development time and + + + align:start position:0% +you've got your development time and +then you've got your wrapper + + align:start position:0% +then you've got your wrapper + + + align:start position:0% +then you've got your wrapper +time your your uh Vision time is going + + align:start position:0% +time your your uh Vision time is going + + + align:start position:0% +time your your uh Vision time is going +to be when you're coming up with the + + align:start position:0% +to be when you're coming up with the + + + align:start position:0% +to be when you're coming up with the +idea and the overall outline that's in + + align:start position:0% +idea and the overall outline that's in + + + align:start position:0% +idea and the overall outline that's in +many ways that's what you did on Monday + + align:start position:0% +many ways that's what you did on Monday + + + align:start position:0% +many ways that's what you did on Monday +right that was kind of you formed teams + + align:start position:0% +right that was kind of you formed teams + + + align:start position:0% +right that was kind of you formed teams +you got a vision statement some people + + align:start position:0% +you got a vision statement some people + + + align:start position:0% +you got a vision statement some people +were even sitting around and making + + align:start position:0% +were even sitting around and making + + + align:start position:0% +were even sitting around and making +feature lists that's really your pregame + + align:start position:0% +feature lists that's really your pregame + + + align:start position:0% +feature lists that's really your pregame +staging Sprint right there um in the + + align:start position:0% +staging Sprint right there um in the + + + align:start position:0% +staging Sprint right there um in the +development Sprints that's when you're + + align:start position:0% +development Sprints that's when you're + + + align:start position:0% +development Sprints that's when you're +actually making the game + + align:start position:0% +actually making the game + + + align:start position:0% +actually making the game +and you're taking a couple of features + + align:start position:0% +and you're taking a couple of features + + + align:start position:0% +and you're taking a couple of features +every Sprint you're getting them working + + align:start position:0% +every Sprint you're getting them working + + + align:start position:0% +every Sprint you're getting them working +you're testing them and then you're + + align:start position:0% +you're testing them and then you're + + + align:start position:0% +you're testing them and then you're +moving on and grabbing a few more + + align:start position:0% +moving on and grabbing a few more + + + align:start position:0% +moving on and grabbing a few more +features getting them working and + + align:start position:0% +features getting them working and + + + align:start position:0% +features getting them working and +testing them until it all comes + + align:start position:0% +testing them until it all comes + + + align:start position:0% +testing them until it all comes +together + + align:start position:0% + + + + align:start position:0% + +um see product backlog has anybody here + + align:start position:0% +um see product backlog has anybody here + + + align:start position:0% +um see product backlog has anybody here +does anybody here know what a product + + align:start position:0% +does anybody here know what a product + + + align:start position:0% +does anybody here know what a product +backlog is can you go ahead and tell + + align:start position:0% + + + + align:start position:0% + +meur ex exactly actually not in a Sprint + + align:start position:0% +meur ex exactly actually not in a Sprint + + + align:start position:0% +meur ex exactly actually not in a Sprint +in the in the overall project yeah the + + align:start position:0% +in the in the overall project yeah the + + + align:start position:0% +in the in the overall project yeah the +product backlog is in fact the feature + + align:start position:0% +product backlog is in fact the feature + + + align:start position:0% +product backlog is in fact the feature +list for the whole for the whole thing + + align:start position:0% +list for the whole for the whole thing + + + align:start position:0% +list for the whole for the whole thing +um once you've got it you take bits of + + align:start position:0% +um once you've got it you take bits of + + + align:start position:0% +um once you've got it you take bits of +it off to make your Sprint backlog the + + align:start position:0% +it off to make your Sprint backlog the + + + align:start position:0% +it off to make your Sprint backlog the +Sprint backlog is what gets done in + + align:start position:0% +Sprint backlog is what gets done in + + + align:start position:0% +Sprint backlog is what gets done in +every + + align:start position:0% +every + + + align:start position:0% +every +Sprint um eventually hopefully your + + align:start position:0% +Sprint um eventually hopefully your + + + align:start position:0% +Sprint um eventually hopefully your +product backlog has hit zero and some + + align:start position:0% +product backlog has hit zero and some + + + align:start position:0% +product backlog has hit zero and some +teams I'm afraid that your teams are + + align:start position:0% +teams I'm afraid that your teams are + + + align:start position:0% +teams I'm afraid that your teams are +probably not going to have the luxury of + + align:start position:0% +probably not going to have the luxury of + + + align:start position:0% +probably not going to have the luxury of +this um take what's called a wrapper + + align:start position:0% +this um take what's called a wrapper + + + align:start position:0% +this um take what's called a wrapper +Sprint or two to kind of hardening you + + align:start position:0% +Sprint or two to kind of hardening you + + + align:start position:0% +Sprint or two to kind of hardening you +can think of it as polish and hardening + + align:start position:0% +can think of it as polish and hardening + + + align:start position:0% +can think of it as polish and hardening +taking the time where you're not putting + + align:start position:0% +taking the time where you're not putting + + + align:start position:0% +taking the time where you're not putting +in any new features but you're making + + align:start position:0% +in any new features but you're making + + + align:start position:0% +in any new features but you're making +sure that all the systems really work do + + align:start position:0% +sure that all the systems really work do + + + align:start position:0% +sure that all the systems really work do +work they're kind of kind of a Shakedown + + align:start position:0% +work they're kind of kind of a Shakedown + + + align:start position:0% +work they're kind of kind of a Shakedown +Cruise + + align:start position:0% +Cruise + + + align:start position:0% +Cruise +um so that is the overall project + + align:start position:0% +um so that is the overall project + + + align:start position:0% +um so that is the overall project +plan and what does it look like on the + + align:start position:0% +plan and what does it look like on the + + + align:start position:0% +plan and what does it look like on the +inside of the + + align:start position:0% +inside of the + + + align:start position:0% +inside of the +Sprint um let me see if I can see what + + align:start position:0% +Sprint um let me see if I can see what + + + align:start position:0% +Sprint um let me see if I can see what +that looks like there we go um + + align:start position:0% +that looks like there we go um + + + align:start position:0% +that looks like there we go um +so here we have our big pile of + + align:start position:0% +so here we have our big pile of + + + align:start position:0% +so here we have our big pile of +definitions um so since you're doing a + + align:start position:0% +definitions um so since you're doing a + + + align:start position:0% +definitions um so since you're doing a +little bit of project planning design + + align:start position:0% +little bit of project planning design + + + align:start position:0% +little bit of project planning design +implementation and testing in every + + align:start position:0% +implementation and testing in every + + + align:start position:0% +implementation and testing in every +Sprint you have to figure out when and + + align:start position:0% +Sprint you have to figure out when and + + + align:start position:0% +Sprint you have to figure out when and +where you're doing those things scrum + + align:start position:0% +where you're doing those things scrum + + + align:start position:0% +where you're doing those things scrum +has a fairly I don't want to say rigid + + align:start position:0% +has a fairly I don't want to say rigid + + + align:start position:0% +has a fairly I don't want to say rigid +but they do have a very well- defined + + align:start position:0% +but they do have a very well- defined + + + align:start position:0% +but they do have a very well- defined +set of processes and tools to do that + + align:start position:0% +set of processes and tools to do that + + + align:start position:0% +set of processes and tools to do that +with + + align:start position:0% +with + + + align:start position:0% +with +um so to handle project planning and + + align:start position:0% +um so to handle project planning and + + + align:start position:0% +um so to handle project planning and +communication every spent involves a set + + align:start position:0% +communication every spent involves a set + + + align:start position:0% +communication every spent involves a set +of standardized meetings Sprint planning + + align:start position:0% +of standardized meetings Sprint planning + + + align:start position:0% +of standardized meetings Sprint planning +daily scrum Sprint review and the + + align:start position:0% +daily scrum Sprint review and the + + + align:start position:0% +daily scrum Sprint review and the +retrospective um to handle the features + + align:start position:0% +retrospective um to handle the features + + + align:start position:0% +retrospective um to handle the features +in task management scrum teams create + + align:start position:0% +in task management scrum teams create + + + align:start position:0% +in task management scrum teams create +and use a set of tools artifacts is what + + align:start position:0% +and use a set of tools artifacts is what + + + align:start position:0% +and use a set of tools artifacts is what +it's called of um the product backlog + + align:start position:0% +it's called of um the product backlog + + + align:start position:0% +it's called of um the product backlog +the Sprint backlog the task list and a + + align:start position:0% +the Sprint backlog the task list and a + + + align:start position:0% +the Sprint backlog the task list and a +scrum + + align:start position:0% +scrum + + + align:start position:0% +scrum +board um at the start of its development + + align:start position:0% +board um at the start of its development + + + align:start position:0% +board um at the start of its development +sprit the team turns to its product + + align:start position:0% +sprit the team turns to its product + + + align:start position:0% +sprit the team turns to its product +backlog which is like we said the + + align:start position:0% +backlog which is like we said the + + + align:start position:0% +backlog which is like we said the +feature + + align:start position:0% +feature + + + align:start position:0% +feature +list um hold what's called a Sprint + + align:start position:0% +list um hold what's called a Sprint + + + align:start position:0% +list um hold what's called a Sprint +planning meeting um in which they decide + + align:start position:0% +planning meeting um in which they decide + + + align:start position:0% +planning meeting um in which they decide +just how many of those items they can + + align:start position:0% +just how many of those items they can + + + align:start position:0% +just how many of those items they can +get + + align:start position:0% +get + + + align:start position:0% +get +done that list of items that they're + + align:start position:0% +done that list of items that they're + + + align:start position:0% +done that list of items that they're +moving from their Sprint from their + + align:start position:0% +moving from their Sprint from their + + + align:start position:0% +moving from their Sprint from their +product backlog becomes the Sprint + + align:start position:0% +product backlog becomes the Sprint + + + align:start position:0% +product backlog becomes the Sprint +backlog from there they break those + + align:start position:0% +backlog from there they break those + + + align:start position:0% +backlog from there they break those +features cuz features coming off a + + align:start position:0% +features cuz features coming off a + + + align:start position:0% +features cuz features coming off a +backlog usually fairly large so they'll + + align:start position:0% +backlog usually fairly large so they'll + + + align:start position:0% +backlog usually fairly large so they'll +break them down into much smaller items + + align:start position:0% +break them down into much smaller items + + + align:start position:0% +break them down into much smaller items +called tasks um a task is just a chunk + + align:start position:0% +called tasks um a task is just a chunk + + + align:start position:0% +called tasks um a task is just a chunk +of work that you can estimate fairly + + align:start position:0% +of work that you can estimate fairly + + + align:start position:0% +of work that you can estimate fairly +well um having gotten that big list of + + align:start position:0% +well um having gotten that big list of + + + align:start position:0% +well um having gotten that big list of +tasks they start working their way + + align:start position:0% +tasks they start working their way + + + align:start position:0% +tasks they start working their way +through it um every day while they're + + align:start position:0% +through it um every day while they're + + + align:start position:0% +through it um every day while they're +working on the project you'll hold a + + align:start position:0% +working on the project you'll hold a + + + align:start position:0% +working on the project you'll hold a +daily scrum meeting where you talk about + + align:start position:0% +daily scrum meeting where you talk about + + + align:start position:0% +daily scrum meeting where you talk about +what you're doing how you're doing it + + align:start position:0% +what you're doing how you're doing it + + + align:start position:0% +what you're doing how you're doing it +what you hope to get done um at the end + + align:start position:0% +what you hope to get done um at the end + + + align:start position:0% +what you hope to get done um at the end +of the Sprint you end up having a Sprint + + align:start position:0% +of the Sprint you end up having a Sprint + + + align:start position:0% +of the Sprint you end up having a Sprint +review where you take a look at what + + align:start position:0% +review where you take a look at what + + + align:start position:0% +review where you take a look at what +you've got done you compared what you + + align:start position:0% +you've got done you compared what you + + + align:start position:0% +you've got done you compared what you +wanted to get done with what you + + align:start position:0% +wanted to get done with what you + + + align:start position:0% +wanted to get done with what you +actually did you go ahead and you adjust + + align:start position:0% +actually did you go ahead and you adjust + + + align:start position:0% +actually did you go ahead and you adjust +your product backlog if you need to and + + align:start position:0% +your product backlog if you need to and + + + align:start position:0% +your product backlog if you need to and +then you hold a retrospective meaning + + align:start position:0% +then you hold a retrospective meaning + + + align:start position:0% +then you hold a retrospective meaning +and that's where instead of T talking + + align:start position:0% +and that's where instead of T talking + + + align:start position:0% +and that's where instead of T talking +about the product in specifically you're + + align:start position:0% +about the product in specifically you're + + + align:start position:0% +about the product in specifically you're +talking about the team and the processes + + align:start position:0% +talking about the team and the processes + + + align:start position:0% +talking about the team and the processes +that's where that's where agile tries to + + align:start position:0% +that's where that's where agile tries to + + + align:start position:0% +that's where that's where agile tries to +improve the way the team is working + + align:start position:0% +improve the way the team is working + + + align:start position:0% +improve the way the team is working +together is the retrospective meeting um + + align:start position:0% +together is the retrospective meeting um + + + align:start position:0% +together is the retrospective meeting um +and then you're ready for a new Sprint + + align:start position:0% +and then you're ready for a new Sprint + + + align:start position:0% +and then you're ready for a new Sprint +planning meeting and the whole thing + + align:start position:0% +planning meeting and the whole thing + + + align:start position:0% +planning meeting and the whole thing +starts over + + align:start position:0% + + + + align:start position:0% + +again okay I'm almost done throwing + + align:start position:0% +again okay I'm almost done throwing + + + align:start position:0% +again okay I'm almost done throwing +vocabulary at you and then I'll go back + + align:start position:0% +vocabulary at you and then I'll go back + + + align:start position:0% +vocabulary at you and then I'll go back +and make sure that I actually did Define + + align:start position:0% +and make sure that I actually did Define + + + align:start position:0% +and make sure that I actually did Define +all the vocabulary I've used um so on + + align:start position:0% +all the vocabulary I've used um so on + + + align:start position:0% +all the vocabulary I've used um so on +the team I claimed that the team was + + align:start position:0% +the team I claimed that the team was + + + align:start position:0% +the team I claimed that the team was +responsible for all of its um project + + align:start position:0% +responsible for all of its um project + + + align:start position:0% +responsible for all of its um project +management that's not quite true um + + align:start position:0% +management that's not quite true um + + + align:start position:0% +management that's not quite true um +teams typically have three kinds of + + align:start position:0% +teams typically have three kinds of + + + align:start position:0% +teams typically have three kinds of +members there's your sort of average + + align:start position:0% +members there's your sort of average + + + align:start position:0% +members there's your sort of average +everyday team member who is someone on + + align:start position:0% +everyday team member who is someone on + + + align:start position:0% +everyday team member who is someone on +the team working to keep things things + + align:start position:0% +the team working to keep things things + + + align:start position:0% +the team working to keep things things +running um the team has a product owner + + align:start position:0% +running um the team has a product owner + + + align:start position:0% +running um the team has a product owner +may have a product owner in classic + + align:start position:0% +may have a product owner in classic + + + align:start position:0% +may have a product owner in classic +scrum you always have a product owner um + + align:start position:0% +scrum you always have a product owner um + + + align:start position:0% +scrum you always have a product owner um +your teams probably won't it's much + + align:start position:0% +your teams probably won't it's much + + + align:start position:0% +your teams probably won't it's much +harder to have a product owner on a um + + align:start position:0% +harder to have a product owner on a um + + + align:start position:0% +harder to have a product owner on a um +student team and the reason for that is + + align:start position:0% +student team and the reason for that is + + + align:start position:0% +student team and the reason for that is +because the product owner is the person + + align:start position:0% +because the product owner is the person + + + align:start position:0% +because the product owner is the person +who holds the sole vision of the product + + align:start position:0% +who holds the sole vision of the product + + + align:start position:0% +who holds the sole vision of the product +um for classic scrum teams the product + + align:start position:0% +um for classic scrum teams the product + + + align:start position:0% +um for classic scrum teams the product +owner is the person who creates the + + align:start position:0% +owner is the person who creates the + + + align:start position:0% +owner is the person who creates the +product backlog helps them prioritize it + + align:start position:0% +product backlog helps them prioritize it + + + align:start position:0% +product backlog helps them prioritize it +and lets them know which of their + + align:start position:0% +and lets them know which of their + + + align:start position:0% +and lets them know which of their +features are the most important and + + align:start position:0% +features are the most important and + + + align:start position:0% +features are the most important and +whether or not the features as + + align:start position:0% +whether or not the features as + + + align:start position:0% +whether or not the features as +implemented are working the way they + + align:start position:0% +implemented are working the way they + + + align:start position:0% +implemented are working the way they +need to um your team may be lucky enough + + align:start position:0% +need to um your team may be lucky enough + + + align:start position:0% +need to um your team may be lucky enough +to have someone who has a good enough + + align:start position:0% +to have someone who has a good enough + + + align:start position:0% +to have someone who has a good enough +grasp of the project and if you do it's + + align:start position:0% +grasp of the project and if you do it's + + + align:start position:0% +grasp of the project and if you do it's +really really + + align:start position:0% +really really + + + align:start position:0% +really really +valuable um it's really helpful to have + + align:start position:0% +valuable um it's really helpful to have + + + align:start position:0% +valuable um it's really helpful to have +one person who you can tune to and say + + align:start position:0% +one person who you can tune to and say + + + align:start position:0% +one person who you can tune to and say +is this going to work or is this working + + align:start position:0% +is this going to work or is this working + + + align:start position:0% +is this going to work or is this working +or is this what we had in mind um and + + align:start position:0% +or is this what we had in mind um and + + + align:start position:0% +or is this what we had in mind um and +have one person answer that instead of + + align:start position:0% +have one person answer that instead of + + + align:start position:0% +have one person answer that instead of +having a big debate over whether it does + + align:start position:0% +having a big debate over whether it does + + + align:start position:0% +having a big debate over whether it does +or not um but on student teams it's it + + align:start position:0% +or not um but on student teams it's it + + + align:start position:0% +or not um but on student teams it's it +can be really hard to have someone in + + align:start position:0% +can be really hard to have someone in + + + align:start position:0% +can be really hard to have someone in +that + + align:start position:0% +that + + + align:start position:0% +that +position um so that's your product owner + + align:start position:0% +position um so that's your product owner + + + align:start position:0% +position um so that's your product owner +the other unique person on your team is + + align:start position:0% +the other unique person on your team is + + + align:start position:0% +the other unique person on your team is +a scrum master and you will need one of + + align:start position:0% +a scrum master and you will need one of + + + align:start position:0% +a scrum master and you will need one of +those + + align:start position:0% +those + + + align:start position:0% +those +um the scrum Master is the lucky person + + align:start position:0% +um the scrum Master is the lucky person + + + align:start position:0% +um the scrum Master is the lucky person +who runs the meetings serves is the + + align:start position:0% +who runs the meetings serves is the + + + align:start position:0% +who runs the meetings serves is the +facilitator and the mediator and is in + + align:start position:0% +facilitator and the mediator and is in + + + align:start position:0% +facilitator and the mediator and is in +charge of making sure that scrum is + + align:start position:0% +charge of making sure that scrum is + + + align:start position:0% +charge of making sure that scrum is +followed and the team is working + + align:start position:0% +followed and the team is working + + + align:start position:0% +followed and the team is working +reasonably + + align:start position:0% +reasonably + + + align:start position:0% +reasonably +smoothly um they frequently get stuck + + align:start position:0% +smoothly um they frequently get stuck + + + align:start position:0% +smoothly um they frequently get stuck +with updating product backlogs Sprint + + align:start position:0% +with updating product backlogs Sprint + + + align:start position:0% +with updating product backlogs Sprint +backlogs task lists scrum boards + + align:start position:0% +backlogs task lists scrum boards + + + align:start position:0% +backlogs task lists scrum boards +whatever recordkeeping paraphernalia the + + align:start position:0% +whatever recordkeeping paraphernalia the + + + align:start position:0% +whatever recordkeeping paraphernalia the +team feels it needs to have um setting + + align:start position:0% +team feels it needs to have um setting + + + align:start position:0% +team feels it needs to have um setting +up meetings and making sure they happen + + align:start position:0% +up meetings and making sure they happen + + + align:start position:0% +up meetings and making sure they happen +um try to think of your the scrum Master + + align:start position:0% +um try to think of your the scrum Master + + + align:start position:0% +um try to think of your the scrum Master +as a bit of the team coach and as the + + align:start position:0% +as a bit of the team coach and as the + + + align:start position:0% +as a bit of the team coach and as the +keeper of documents rather at than as + + align:start position:0% +keeper of documents rather at than as + + + align:start position:0% +keeper of documents rather at than as +the producer or the person in charge of + + align:start position:0% +the producer or the person in charge of + + + align:start position:0% +the producer or the person in charge of +the project um just trying to keep the + + align:start position:0% +the project um just trying to keep the + + + align:start position:0% +the project um just trying to keep the +backlog SE straight keeping meetings + + align:start position:0% +backlog SE straight keeping meetings + + + align:start position:0% +backlog SE straight keeping meetings +flowing and keeping communication + + align:start position:0% +flowing and keeping communication + + + align:start position:0% +flowing and keeping communication +flowing is a lot of work for one person + + align:start position:0% +flowing is a lot of work for one person + + + align:start position:0% +flowing is a lot of work for one person +you don't also want to burden that + + align:start position:0% +you don't also want to burden that + + + align:start position:0% +you don't also want to burden that +person with being in charge of leading + + align:start position:0% +person with being in charge of leading + + + align:start position:0% +person with being in charge of leading +the team and making all the final + + align:start position:0% +the team and making all the final + + + align:start position:0% +the team and making all the final +decisions if you can find a way to to + + align:start position:0% +decisions if you can find a way to to + + + align:start position:0% +decisions if you can find a way to to +try they they they often end up drifting + + align:start position:0% +try they they they often end up drifting + + + align:start position:0% +try they they they often end up drifting +together and we see a lot and we often + + align:start position:0% +together and we see a lot and we often + + + align:start position:0% +together and we see a lot and we often +make the slip of calling the person who + + align:start position:0% +make the slip of calling the person who + + + align:start position:0% +make the slip of calling the person who +serving is the team scrum Master as the + + align:start position:0% +serving is the team scrum Master as the + + + align:start position:0% +serving is the team scrum Master as the +producer see if you can try to keep + + align:start position:0% +producer see if you can try to keep + + + align:start position:0% +producer see if you can try to keep +those two roles separate if you can let + + align:start position:0% +those two roles separate if you can let + + + align:start position:0% +those two roles separate if you can let +the scrum Master just be the person + + align:start position:0% +the scrum Master just be the person + + + align:start position:0% +the scrum Master just be the person +keeping the team running and you can let + + align:start position:0% +keeping the team running and you can let + + + align:start position:0% +keeping the team running and you can let +someone else step into that kind of + + align:start position:0% +someone else step into that kind of + + + align:start position:0% +someone else step into that kind of +vision holder guide the team role + + align:start position:0% +vision holder guide the team role + + + align:start position:0% +vision holder guide the team role +okay um all right I think that that is + + align:start position:0% +okay um all right I think that that is + + + align:start position:0% +okay um all right I think that that is +in fact what I have to say + + align:start position:0% +in fact what I have to say + + + align:start position:0% +in fact what I have to say +on on that and + + align:start position:0% +on on that and + + + align:start position:0% +on on that and +so do everybody think they have at least + + align:start position:0% +so do everybody think they have at least + + + align:start position:0% +so do everybody think they have at least +a definition or an idea for all of these + + align:start position:0% +a definition or an idea for all of these + + + align:start position:0% +a definition or an idea for all of these +words here's the quiz later you + + align:start position:0% + + + + align:start position:0% + +see that's + + align:start position:0% +see that's + + + align:start position:0% +see that's +hm okay should I be mean and choose the + + align:start position:0% +hm okay should I be mean and choose the + + + align:start position:0% +hm okay should I be mean and choose the +one that I haven't defined that nobody + + align:start position:0% +one that I haven't defined that nobody + + + align:start position:0% +one that I haven't defined that nobody +admitted + + align:start position:0% +admitted + + + align:start position:0% +admitted +to okay who can tell me what a scrum + + align:start position:0% +to okay who can tell me what a scrum + + + align:start position:0% +to okay who can tell me what a scrum +board is + + align:start position:0% + + + + align:start position:0% + +is that + + align:start position:0% +is that + + + align:start position:0% +is that +just you have everything all theas to + + align:start position:0% +just you have everything all theas to + + + align:start position:0% +just you have everything all theas to +be that they that's exactly what it is + + align:start position:0% +be that they that's exactly what it is + + + align:start position:0% +be that they that's exactly what it is +so um what a scrum board + + align:start position:0% +so um what a scrum board + + + align:start position:0% +so um what a scrum board +is what a scrum board is is it's + + align:start position:0% +is what a scrum board is is it's + + + align:start position:0% +is what a scrum board is is it's +frequently if you've got a team that all + + align:start position:0% +frequently if you've got a team that all + + + align:start position:0% +frequently if you've got a team that all +works in the same place it's it's + + align:start position:0% +works in the same place it's it's + + + align:start position:0% +works in the same place it's it's +usually a physical big physical board + + align:start position:0% +usually a physical big physical board + + + align:start position:0% +usually a physical big physical board +that you have room to put cards with all + + align:start position:0% +that you have room to put cards with all + + + align:start position:0% +that you have room to put cards with all +the tasks on it on and you just have it + + align:start position:0% +the tasks on it on and you just have it + + + align:start position:0% +the tasks on it on and you just have it +divided up into sections to show the + + align:start position:0% +divided up into sections to show the + + + align:start position:0% +divided up into sections to show the +status of each task um by using a scrum + + align:start position:0% +status of each task um by using a scrum + + + align:start position:0% +status of each task um by using a scrum +board teams can figure out exactly how + + align:start position:0% +board teams can figure out exactly how + + + align:start position:0% +board teams can figure out exactly how +far long they are what the state of + + align:start position:0% +far long they are what the state of + + + align:start position:0% +far long they are what the state of +their project is by just looking at the + + align:start position:0% +their project is by just looking at the + + + align:start position:0% +their project is by just looking at the +board um teams that are going to end up + + align:start position:0% +board um teams that are going to end up + + + align:start position:0% +board um teams that are going to end up +working in a much more distributed + + align:start position:0% +working in a much more distributed + + + align:start position:0% +working in a much more distributed +fashion and who don't have designated + + align:start position:0% +fashion and who don't have designated + + + align:start position:0% +fashion and who don't have designated +place to sort of leave a scrum board + + align:start position:0% +place to sort of leave a scrum board + + + align:start position:0% +place to sort of leave a scrum board +setup for example you guys are not going + + align:start position:0% +setup for example you guys are not going + + + align:start position:0% +setup for example you guys are not going +to be able to put scrum boards up on the + + align:start position:0% +to be able to put scrum boards up on the + + + align:start position:0% +to be able to put scrum boards up on the +back of the classroom and come in and + + align:start position:0% +back of the classroom and come in and + + + align:start position:0% +back of the classroom and come in and +check up on them every couple of days + + align:start position:0% +check up on them every couple of days + + + align:start position:0% +check up on them every couple of days +there are a couple of um on online + + align:start position:0% +there are a couple of um on online + + + align:start position:0% +there are a couple of um on online +options and I will talk about them when + + align:start position:0% +options and I will talk about them when + + + align:start position:0% +options and I will talk about them when +I actually talk about scrum boards a + + align:start position:0% +I actually talk about scrum boards a + + + align:start position:0% +I actually talk about scrum boards a +little bit more and I'm asking you to + + align:start position:0% +little bit more and I'm asking you to + + + align:start position:0% +little bit more and I'm asking you to +get one set up just just on curiosity + + align:start position:0% +get one set up just just on curiosity + + + align:start position:0% +get one set up just just on curiosity +who's already got something like that + + align:start position:0% +who's already got something like that + + + align:start position:0% +who's already got something like that +like a online site with all your tasks + + align:start position:0% +like a online site with all your tasks + + + align:start position:0% +like a online site with all your tasks +on it um we're using Trello Trello uses + + align:start position:0% +on it um we're using Trello Trello uses + + + align:start position:0% +on it um we're using Trello Trello uses +exactly a scrumb style visual + + align:start position:0% +exactly a scrumb style visual + + + align:start position:0% +exactly a scrumb style visual +representation there's also a scrum + + align:start position:0% +representation there's also a scrum + + + align:start position:0% +representation there's also a scrum +plugin for Trello for Chrome that you + + align:start position:0% +plugin for Trello for Chrome that you + + + align:start position:0% +plugin for Trello for Chrome that you +can get like points here I did not know + + align:start position:0% +can get like points here I did not know + + + align:start position:0% +can get like points here I did not know +that that's oh that's new it's called Uh + + align:start position:0% +that that's oh that's new it's called Uh + + + align:start position:0% +that that's oh that's new it's called Uh +SC for or something + + align:start position:0% + + + + align:start position:0% + +what else I I another hand what are you + + align:start position:0% +what else I I another hand what are you + + + align:start position:0% +what else I I another hand what are you +using a okay I so so so is that just + + align:start position:0% +using a okay I so so so is that just + + + align:start position:0% +using a okay I so so so is that just +does it also have like a card like + + align:start position:0% +does it also have like a card like + + + align:start position:0% +does it also have like a card like +representation or is it more like + + align:start position:0% + + + + align:start position:0% + +spreadsheet the multiplayer + + align:start position:0% + + + + align:start position:0% + +list yeah I haven't I haven't used that + + align:start position:0% +list yeah I haven't I haven't used that + + + align:start position:0% +list yeah I haven't I haven't used that +site I don't know + + align:start position:0% +site I don't know + + + align:start position:0% +site I don't know +don't we any other Alternatives yeah um + + align:start position:0% +don't we any other Alternatives yeah um + + + align:start position:0% +don't we any other Alternatives yeah um +I will actually talk about scrum boards + + align:start position:0% +I will actually talk about scrum boards + + + align:start position:0% +I will actually talk about scrum boards +and a little bit more when we actually + + align:start position:0% +and a little bit more when we actually + + + align:start position:0% +and a little bit more when we actually +have gotten around to making our Sprint + + align:start position:0% +have gotten around to making our Sprint + + + align:start position:0% +have gotten around to making our Sprint +backlogs and task lists and talking + + align:start position:0% +backlogs and task lists and talking + + + align:start position:0% +backlogs and task lists and talking +about the techniques you use to make + + align:start position:0% +about the techniques you use to make + + + align:start position:0% +about the techniques you use to make +them okay so we're we're finally + + align:start position:0% +them okay so we're we're finally + + + align:start position:0% +them okay so we're we're finally +actually getting to the action part of + + align:start position:0% +actually getting to the action part of + + + align:start position:0% +actually getting to the action part of +this of this story and I'm lying there + + align:start position:0% +this of this story and I'm lying there + + + align:start position:0% +this of this story and I'm lying there +I'm not actually going to talk about + + align:start position:0% +I'm not actually going to talk about + + + align:start position:0% +I'm not actually going to talk about +time boxing right now um I went back and + + align:start position:0% +time boxing right now um I went back and + + + align:start position:0% +time boxing right now um I went back and +updated my my lecture without updating + + align:start position:0% +updated my my lecture without updating + + + align:start position:0% +updated my my lecture without updating +my slides but we are going to talk about + + align:start position:0% +my slides but we are going to talk about + + + align:start position:0% +my slides but we are going to talk about +user stories so let's talk about how you + + align:start position:0% +user stories so let's talk about how you + + + align:start position:0% +user stories so let's talk about how you +make a product backlog because it is not + + align:start position:0% +make a product backlog because it is not + + + align:start position:0% +make a product backlog because it is not +just a feature list there's actually + + align:start position:0% +just a feature list there's actually + + + align:start position:0% +just a feature list there's actually +some very important differences between + + align:start position:0% +some very important differences between + + + align:start position:0% +some very important differences between +a feature list and a product backlog + + align:start position:0% +a feature list and a product backlog + + + align:start position:0% +a feature list and a product backlog +that makes a product backlog a manage a + + align:start position:0% +that makes a product backlog a manage a + + + align:start position:0% +that makes a product backlog a manage a +product management tool as well as a + + align:start position:0% +product management tool as well as a + + + align:start position:0% +product management tool as well as a +design + + align:start position:0% +design + + + align:start position:0% +design +tool so um it's an organized prioritized + + align:start position:0% +tool so um it's an organized prioritized + + + align:start position:0% +tool so um it's an organized prioritized +feature list so the team always knows + + align:start position:0% +feature list so the team always knows + + + align:start position:0% +feature list so the team always knows +what the most important next feature is + + align:start position:0% +what the most important next feature is + + + align:start position:0% +what the most important next feature is +um so if I actually sat down and looked + + align:start position:0% +um so if I actually sat down and looked + + + align:start position:0% +um so if I actually sat down and looked +at one of the product backlogs you + + align:start position:0% +at one of the product backlogs you + + + align:start position:0% +at one of the product backlogs you +turned in every feature in your game + + align:start position:0% +turned in every feature in your game + + + align:start position:0% +turned in every feature in your game +should be described or mentioned in the + + align:start position:0% +should be described or mentioned in the + + + align:start position:0% +should be described or mentioned in the +product backlog um and each item should + + align:start position:0% +product backlog um and each item should + + + align:start position:0% +product backlog um and each item should +have a priority status indicating how + + align:start position:0% +have a priority status indicating how + + + align:start position:0% +have a priority status indicating how +important it is when are you going to do + + align:start position:0% +important it is when are you going to do + + + align:start position:0% +important it is when are you going to do +it are you going to do it first or you + + align:start position:0% +it are you going to do it first or you + + + align:start position:0% +it are you going to do it first or you +going to do it last is this is what's + + align:start position:0% +going to do it last is this is what's + + + align:start position:0% +going to do it last is this is what's +going to get or is this the one that's + + align:start position:0% +going to get or is this the one that's + + + align:start position:0% +going to get or is this the one that's +going to get cut when you realize you + + align:start position:0% +going to get cut when you realize you + + + align:start position:0% +going to get cut when you realize you +don't have time to finish the + + align:start position:0% +don't have time to finish the + + + align:start position:0% +don't have time to finish the +project + + align:start position:0% +project + + + align:start position:0% +project +um so how do you decide what goes into + + align:start position:0% +um so how do you decide what goes into + + + align:start position:0% +um so how do you decide what goes into +it and how do you estimate and how do + + align:start position:0% +it and how do you estimate and how do + + + align:start position:0% +it and how do you estimate and how do +you + + align:start position:0% +you + + + align:start position:0% +you +um prioritize there's the big + + align:start position:0% +um prioritize there's the big + + + align:start position:0% +um prioritize there's the big +question um so here is a sample project + + align:start position:0% +question um so here is a sample project + + + align:start position:0% +question um so here is a sample project +backlog it's not for a game but it's for + + align:start position:0% +backlog it's not for a game but it's for + + + align:start position:0% +backlog it's not for a game but it's for +some sort of login page or something but + + align:start position:0% +some sort of login page or something but + + + align:start position:0% +some sort of login page or something but +it it serves pretty much the same + + align:start position:0% +it it serves pretty much the same + + + align:start position:0% +it it serves pretty much the same +purpose um at a minimum this is sort of + + align:start position:0% +purpose um at a minimum this is sort of + + + align:start position:0% +purpose um at a minimum this is sort of +the minimum you should have in your + + align:start position:0% +the minimum you should have in your + + + align:start position:0% +the minimum you should have in your +product backlog um some people get + + align:start position:0% +product backlog um some people get + + + align:start position:0% +product backlog um some people get +fancier and include extra and include + + align:start position:0% +fancier and include extra and include + + + align:start position:0% +fancier and include extra and include +lots of extra information but that's not + + align:start position:0% +lots of extra information but that's not + + + align:start position:0% +lots of extra information but that's not +necessary um keeping it simple + + align:start position:0% +necessary um keeping it simple + + + align:start position:0% +necessary um keeping it simple +especially to start will make your life + + align:start position:0% +especially to start will make your life + + + align:start position:0% +especially to start will make your life +a little bit easier if you discover + + align:start position:0% +a little bit easier if you discover + + + align:start position:0% +a little bit easier if you discover +there's more information you want to + + align:start position:0% +there's more information you want to + + + align:start position:0% +there's more information you want to +track here go ahead and do that but + + align:start position:0% +track here go ahead and do that but + + + align:start position:0% +track here go ahead and do that but +start with the basics um the basics are + + align:start position:0% +start with the basics um the basics are + + + align:start position:0% +start with the basics um the basics are +an ID number ID number is not its + + align:start position:0% +an ID number ID number is not its + + + align:start position:0% +an ID number ID number is not its +priority it's actually in the order of + + align:start position:0% +priority it's actually in the order of + + + align:start position:0% +priority it's actually in the order of +which we T we thought the Fe thought of + + align:start position:0% +which we T we thought the Fe thought of + + + align:start position:0% +which we T we thought the Fe thought of +the features this is the fifth feature + + align:start position:0% +the features this is the fifth feature + + + align:start position:0% +the features this is the fifth feature +we thought of um IDs come in useful when + + align:start position:0% +we thought of um IDs come in useful when + + + align:start position:0% +we thought of um IDs come in useful when +you start moving tasks off of your + + align:start position:0% +you start moving tasks off of your + + + align:start position:0% +you start moving tasks off of your +backlog and into your Sprint backlog and + + align:start position:0% +backlog and into your Sprint backlog and + + + align:start position:0% +backlog and into your Sprint backlog and +breaking them down into smaller tasks so + + align:start position:0% +breaking them down into smaller tasks so + + + align:start position:0% +breaking them down into smaller tasks so +you can use your ID number to know oh + + align:start position:0% +you can use your ID number to know oh + + + align:start position:0% +you can use your ID number to know oh +yes this project this this feature is + + align:start position:0% +yes this project this this feature is + + + align:start position:0% +yes this project this this feature is +the same as is on the product backlog + + align:start position:0% +the same as is on the product backlog + + + align:start position:0% +the same as is on the product backlog +and all of these eight tasks that it + + align:start position:0% +and all of these eight tasks that it + + + align:start position:0% +and all of these eight tasks that it +came out of it are all related to each + + align:start position:0% +came out of it are all related to each + + + align:start position:0% +came out of it are all related to each +other because they all still have the ID + + align:start position:0% +other because they all still have the ID + + + align:start position:0% +other because they all still have the ID +number that goes back to the original + + align:start position:0% +number that goes back to the original + + + align:start position:0% +number that goes back to the original +product + + align:start position:0% +product + + + align:start position:0% +product +backlog um then you need a description + + align:start position:0% +backlog um then you need a description + + + align:start position:0% +backlog um then you need a description +um this backlog is using user stories + + align:start position:0% +um this backlog is using user stories + + + align:start position:0% +um this backlog is using user stories +which I will explain in a moment um but + + align:start position:0% +which I will explain in a moment um but + + + align:start position:0% +which I will explain in a moment um but +they all have sort of the same pattern + + align:start position:0% +they all have sort of the same pattern + + + align:start position:0% +they all have sort of the same pattern +um as an unauthorized user I want to + + align:start position:0% +um as an unauthorized user I want to + + + align:start position:0% +um as an unauthorized user I want to +create a new account as a authorized + + align:start position:0% +create a new account as a authorized + + + align:start position:0% +create a new account as a authorized +user I want to as an unauthorized user I + + align:start position:0% +user I want to as an unauthorized user I + + + align:start position:0% +user I want to as an unauthorized user I +want to so + + align:start position:0% +want to so + + + align:start position:0% +want to so +that um so there's your description of + + align:start position:0% +that um so there's your description of + + + align:start position:0% +that um so there's your description of +what the feature is then you need an + + align:start position:0% +what the feature is then you need an + + + align:start position:0% +what the feature is then you need an +estimation of how big a job this is for + + align:start position:0% +estimation of how big a job this is for + + + align:start position:0% +estimation of how big a job this is for +the product backlog we don't actually + + align:start position:0% +the product backlog we don't actually + + + align:start position:0% +the product backlog we don't actually +recommend trying to do really fine + + align:start position:0% +recommend trying to do really fine + + + align:start position:0% +recommend trying to do really fine +estimation um they're using numbers in + + align:start position:0% +estimation um they're using numbers in + + + align:start position:0% +estimation um they're using numbers in +this backlog I I should make a new one + + align:start position:0% +this backlog I I should make a new one + + + align:start position:0% +this backlog I I should make a new one +that uses my preferred system which is + + align:start position:0% +that uses my preferred system which is + + + align:start position:0% +that uses my preferred system which is +actually just using the words small + + align:start position:0% +actually just using the words small + + + align:start position:0% +actually just using the words small +medium large extra + + align:start position:0% +medium large extra + + + align:start position:0% +medium large extra +large and how big is small I'm not + + align:start position:0% +large and how big is small I'm not + + + align:start position:0% +large and how big is small I'm not +really sure when you certainly when you + + align:start position:0% +really sure when you certainly when you + + + align:start position:0% +really sure when you certainly when you +first create your backlog you won't be + + align:start position:0% +first create your backlog you won't be + + + align:start position:0% +first create your backlog you won't be +really sure either but you can probably + + align:start position:0% +really sure either but you can probably + + + align:start position:0% +really sure either but you can probably +tell the difference between a small + + align:start position:0% +tell the difference between a small + + + align:start position:0% +tell the difference between a small +feature and a medium feature and an + + align:start position:0% +feature and a medium feature and an + + + align:start position:0% +feature and a medium feature and an +extra large feature um so when you go + + align:start position:0% +extra large feature um so when you go + + + align:start position:0% +extra large feature um so when you go +through and you write down all your + + align:start position:0% +through and you write down all your + + + align:start position:0% +through and you write down all your +features you can say what are all the + + align:start position:0% +features you can say what are all the + + + align:start position:0% +features you can say what are all the +smallest features here and call those + + align:start position:0% +smallest features here and call those + + + align:start position:0% +smallest features here and call those +small what's what's bigger than that + + align:start position:0% +small what's what's bigger than that + + + align:start position:0% +small what's what's bigger than that +that's probably a medium what's the + + align:start position:0% +that's probably a medium what's the + + + align:start position:0% +that's probably a medium what's the +biggest feature I can see here make that + + align:start position:0% +biggest feature I can see here make that + + + align:start position:0% +biggest feature I can see here make that +a large when you're making the product + + align:start position:0% +a large when you're making the product + + + align:start position:0% +a large when you're making the product +backlog it really is you don't want to + + align:start position:0% +backlog it really is you don't want to + + + align:start position:0% +backlog it really is you don't want to +spend a lot of time figuring out + + align:start position:0% +spend a lot of time figuring out + + + align:start position:0% +spend a lot of time figuring out +estimation and trying to figure out + + align:start position:0% +estimation and trying to figure out + + + align:start position:0% +estimation and trying to figure out +exactly how many hours it's going to + + align:start position:0% +exactly how many hours it's going to + + + align:start position:0% +exactly how many hours it's going to +take and how many subtasks are involved + + align:start position:0% +take and how many subtasks are involved + + + align:start position:0% +take and how many subtasks are involved +what you want to do is get a feel for + + align:start position:0% +what you want to do is get a feel for + + + align:start position:0% +what you want to do is get a feel for +the overall size of the features and a + + align:start position:0% +the overall size of the features and a + + + align:start position:0% +the overall size of the features and a +feel for how big they are in relation to + + align:start position:0% +feel for how big they are in relation to + + + align:start position:0% +feel for how big they are in relation to +each other because if you're fairly good + + align:start position:0% +each other because if you're fairly good + + + align:start position:0% +each other because if you're fairly good +at saying this is a about the same size + + align:start position:0% +at saying this is a about the same size + + + align:start position:0% +at saying this is a about the same size +feature as this and this is about the + + align:start position:0% +feature as this and this is about the + + + align:start position:0% +feature as this and this is about the +same size feature as that once you + + align:start position:0% +same size feature as that once you + + + align:start position:0% +same size feature as that once you +realize that feature a took you 3 hours + + align:start position:0% +realize that feature a took you 3 hours + + + align:start position:0% +realize that feature a took you 3 hours +and you have four other small features + + align:start position:0% +and you have four other small features + + + align:start position:0% +and you have four other small features +it's not that hard to go oh so that's a + + align:start position:0% +it's not that hard to go oh so that's a + + + align:start position:0% +it's not that hard to go oh so that's a +total of about 12 hours between those + + align:start position:0% +total of about 12 hours between those + + + align:start position:0% +total of about 12 hours between those +four features + + align:start position:0% +four features + + + align:start position:0% +four features +right + + align:start position:0% + + + + align:start position:0% + +um so that is that is the format of a of + + align:start position:0% +um so that is that is the format of a of + + + align:start position:0% +um so that is that is the format of a of +a back of a of a product backlog are + + align:start position:0% +a back of a of a product backlog are + + + align:start position:0% +a back of a of a product backlog are +there any + + align:start position:0% + + + + align:start position:0% + +questions no okay just want to point out + + align:start position:0% +questions no okay just want to point out + + + align:start position:0% +questions no okay just want to point out +occasionally you come across a feature + + align:start position:0% +occasionally you come across a feature + + + align:start position:0% +occasionally you come across a feature +that's actually not one feature that's + + align:start position:0% +that's actually not one feature that's + + + align:start position:0% +that's actually not one feature that's +actually a whole bunch all rolled up in + + align:start position:0% +actually a whole bunch all rolled up in + + + align:start position:0% +actually a whole bunch all rolled up in +one like multiplayer or something like + + align:start position:0% +one like multiplayer or something like + + + align:start position:0% +one like multiplayer or something like +that nwork it's not a single line + + align:start position:0% +that nwork it's not a single line + + + align:start position:0% +that nwork it's not a single line +feature it's a whole bunch of different + + align:start position:0% +feature it's a whole bunch of different + + + align:start position:0% +feature it's a whole bunch of different +things so so that's you know uh if you + + align:start position:0% +things so so that's you know uh if you + + + align:start position:0% +things so so that's you know uh if you +if you come across features that clearly + + align:start position:0% +if you come across features that clearly + + + align:start position:0% +if you come across features that clearly +dwarf everything else that you've got on + + align:start position:0% +dwarf everything else that you've got on + + + align:start position:0% +dwarf everything else that you've got on +your list you should try to break those + + align:start position:0% +your list you should try to break those + + + align:start position:0% +your list you should try to break those +down into small large chunks uh so it + + align:start position:0% +down into small large chunks uh so it + + + align:start position:0% +down into small large chunks uh so it +could be like multiplayer login you know + + align:start position:0% +could be like multiplayer login you know + + + align:start position:0% +could be like multiplayer login you know +multiplayer uh matchmaking you know all + + align:start position:0% +multiplayer uh matchmaking you know all + + + align:start position:0% +multiplayer uh matchmaking you know all +these things are separate features but I + + align:start position:0% +these things are separate features but I + + + align:start position:0% +these things are separate features but I +will say that when you're making your + + align:start position:0% +will say that when you're making your + + + align:start position:0% +will say that when you're making your +first pass at a product backlog it's + + align:start position:0% +first pass at a product backlog it's + + + align:start position:0% +first pass at a product backlog it's +okay to stick multiplayer on there as a + + align:start position:0% +okay to stick multiplayer on there as a + + + align:start position:0% +okay to stick multiplayer on there as a +feature and then right next to it extra + + align:start position:0% +feature and then right next to it extra + + + align:start position:0% +feature and then right next to it extra +EXT extra large and realize you're going + + align:start position:0% +EXT extra large and realize you're going + + + align:start position:0% +EXT extra large and realize you're going +to come back and break it down later + + align:start position:0% +to come back and break it down later + + + align:start position:0% +to come back and break it down later +when you're making your first po pic + + align:start position:0% +when you're making your first po pic + + + align:start position:0% +when you're making your first po pic +backlog you don't want to be worrying + + align:start position:0% +backlog you don't want to be worrying + + + align:start position:0% +backlog you don't want to be worrying +about well what are all the little sub + + align:start position:0% +about well what are all the little sub + + + align:start position:0% +about well what are all the little sub +features of multiplayer um but you do + + align:start position:0% +features of multiplayer um but you do + + + align:start position:0% +features of multiplayer um but you do +want to go ahead and acknowledge that oh + + align:start position:0% +want to go ahead and acknowledge that oh + + + align:start position:0% +want to go ahead and acknowledge that oh +my gosh we've just you know put + + align:start position:0% +my gosh we've just you know put + + + align:start position:0% +my gosh we've just you know put +something ginormous on the list um and + + align:start position:0% +something ginormous on the list um and + + + align:start position:0% +something ginormous on the list um and +using a very rough estimation tool lets + + align:start position:0% +using a very rough estimation tool lets + + + align:start position:0% +using a very rough estimation tool lets +you do that and move on to getting all + + align:start position:0% +you do that and move on to getting all + + + align:start position:0% +you do that and move on to getting all +of your features in and then you can + + align:start position:0% +of your features in and then you can + + + align:start position:0% +of your features in and then you can +come back and honestly estimate them a + + align:start position:0% +come back and honestly estimate them a + + + align:start position:0% +come back and honestly estimate them a +lot more finely when you're actually + + align:start position:0% +lot more finely when you're actually + + + align:start position:0% +lot more finely when you're actually +thinking that you might put them in or + + align:start position:0% +thinking that you might put them in or + + + align:start position:0% +thinking that you might put them in or +when you're actually determining what + + align:start position:0% +when you're actually determining what + + + align:start position:0% +when you're actually determining what +their overall priority is and how badly + + align:start position:0% +their overall priority is and how badly + + + align:start position:0% +their overall priority is and how badly +you want + + align:start position:0% +you want + + + align:start position:0% +you want +them because if you end up deciding you + + align:start position:0% +them because if you end up deciding you + + + align:start position:0% +them because if you end up deciding you +want to drop multiplayer there's no + + align:start position:0% +want to drop multiplayer there's no + + + align:start position:0% +want to drop multiplayer there's no +point in having spent a lot of time drop + + align:start position:0% +point in having spent a lot of time drop + + + align:start position:0% +point in having spent a lot of time drop +dividing it up into 12 or 14 different + + align:start position:0% + + + + align:start position:0% + +features all right so I mentioned user + + align:start position:0% +features all right so I mentioned user + + + align:start position:0% +features all right so I mentioned user +stories and I did not actually Define + + align:start position:0% +stories and I did not actually Define + + + align:start position:0% +stories and I did not actually Define +them very well and that's because I was + + align:start position:0% +them very well and that's because I was + + + align:start position:0% +them very well and that's because I was +going to come along and Define them here + + align:start position:0% +going to come along and Define them here + + + align:start position:0% +going to come along and Define them here +so a user story is just a very specific + + align:start position:0% +so a user story is just a very specific + + + align:start position:0% +so a user story is just a very specific +way to describe a feature it is I think + + align:start position:0% +way to describe a feature it is I think + + + align:start position:0% +way to describe a feature it is I think +unique to scrum although there may be + + align:start position:0% +unique to scrum although there may be + + + align:start position:0% +unique to scrum although there may be +other agile methodologies that have + + align:start position:0% +other agile methodologies that have + + + align:start position:0% +other agile methodologies that have +stolen it as a way of describing a + + align:start position:0% +stolen it as a way of describing a + + + align:start position:0% +stolen it as a way of describing a +feature um and we're going to ask you to + + align:start position:0% +feature um and we're going to ask you to + + + align:start position:0% +feature um and we're going to ask you to +use user stories for project two at + + align:start position:0% +use user stories for project two at + + + align:start position:0% +use user stories for project two at +least just to get you familiar with it + + align:start position:0% +least just to get you familiar with it + + + align:start position:0% +least just to get you familiar with it +and to understand why we think they're + + align:start position:0% +and to understand why we think they're + + + align:start position:0% +and to understand why we think they're +they're a neat idea you may end up + + align:start position:0% +they're a neat idea you may end up + + + align:start position:0% +they're a neat idea you may end up +deciding that you don't like them and + + align:start position:0% +deciding that you don't like them and + + + align:start position:0% +deciding that you don't like them and +that's okay but we want you to at least + + align:start position:0% +that's okay but we want you to at least + + + align:start position:0% +that's okay but we want you to at least +experiment with them + + align:start position:0% +experiment with them + + + align:start position:0% +experiment with them +so the goal of a user story is to help + + align:start position:0% +so the goal of a user story is to help + + + align:start position:0% +so the goal of a user story is to help +you phrase your feature in a clearly + + align:start position:0% +you phrase your feature in a clearly + + + align:start position:0% +you phrase your feature in a clearly +testable and understandable manner to + + align:start position:0% +testable and understandable manner to + + + align:start position:0% +testable and understandable manner to +someone who did not help you write the + + align:start position:0% +someone who did not help you write the + + + align:start position:0% +someone who did not help you write the +document + + align:start position:0% +document + + + align:start position:0% +document +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so a user story follows the formula of + + align:start position:0% +so a user story follows the formula of + + + align:start position:0% +so a user story follows the formula of +as the person who is going to use this + + align:start position:0% +as the person who is going to use this + + + align:start position:0% +as the person who is going to use this +feature which could be the user it could + + align:start position:0% +feature which could be the user it could + + + align:start position:0% +feature which could be the user it could +be the designer if you're creating a + + align:start position:0% +be the designer if you're creating a + + + align:start position:0% +be the designer if you're creating a +level editor could be the artist if + + align:start position:0% +level editor could be the artist if + + + align:start position:0% +level editor could be the artist if +you're creating something for them it + + align:start position:0% +you're creating something for them it + + + align:start position:0% +you're creating something for them it +could be another set of coders if you're + + align:start position:0% +could be another set of coders if you're + + + align:start position:0% +could be another set of coders if you're +creating tools but the important thing + + align:start position:0% +creating tools but the important thing + + + align:start position:0% +creating tools but the important thing +is to recognize who are you making this + + align:start position:0% +is to recognize who are you making this + + + align:start position:0% +is to recognize who are you making this +feature for and who is going to use it + + align:start position:0% +feature for and who is going to use it + + + align:start position:0% +feature for and who is going to use it +um then you want to describe what it's + + align:start position:0% +um then you want to describe what it's + + + align:start position:0% +um then you want to describe what it's +going to do and that description should + + align:start position:0% +going to do and that description should + + + align:start position:0% +going to do and that description should +be something you can + + align:start position:0% +be something you can + + + align:start position:0% +be something you can +test + + align:start position:0% +test + + + align:start position:0% +test +um so that when someone goes ahead and + + align:start position:0% +um so that when someone goes ahead and + + + align:start position:0% +um so that when someone goes ahead and +gets this completed feature on the other + + align:start position:0% +gets this completed feature on the other + + + align:start position:0% +gets this completed feature on the other +end they can go in as pretending to be + + align:start position:0% +end they can go in as pretending to be + + + align:start position:0% +end they can go in as pretending to be +whoever that person is use that feature + + align:start position:0% +whoever that person is use that feature + + + align:start position:0% +whoever that person is use that feature +and confirm that it works + + align:start position:0% +and confirm that it works + + + align:start position:0% +and confirm that it works +Works finally you want the end the end + + align:start position:0% +Works finally you want the end the end + + + align:start position:0% +Works finally you want the end the end +third which is so + + align:start position:0% +third which is so + + + align:start position:0% +third which is so +that explain the reason why you want the + + align:start position:0% +that explain the reason why you want the + + + align:start position:0% +that explain the reason why you want the +feature there what is the purpose of + + align:start position:0% +feature there what is the purpose of + + + align:start position:0% +feature there what is the purpose of +this feature in your game what is it + + align:start position:0% + + + + align:start position:0% + +achieving can anybody think about why + + align:start position:0% +achieving can anybody think about why + + + align:start position:0% +achieving can anybody think about why +this is an interesting or useful format + + align:start position:0% +this is an interesting or useful format + + + align:start position:0% +this is an interesting or useful format +for stating a feature in can you see any + + align:start position:0% +for stating a feature in can you see any + + + align:start position:0% +for stating a feature in can you see any +benefits in it I can go ahead and tell + + align:start position:0% +benefits in it I can go ahead and tell + + + align:start position:0% +benefits in it I can go ahead and tell +you what we think the benefits are but + + align:start position:0% +you what we think the benefits are but + + + align:start position:0% +you what we think the benefits are but +I'm wondering if you guys can think of + + align:start position:0% + + + + align:start position:0% + +any it's testable and focused on + + align:start position:0% +any it's testable and focused on + + + align:start position:0% +any it's testable and focused on +theer or other + + align:start position:0% +theer or other + + + align:start position:0% +theer or other +relevant yep that's that's + + align:start position:0% + + + + align:start position:0% + +one okay um so it's testable which means + + align:start position:0% +one okay um so it's testable which means + + + align:start position:0% +one okay um so it's testable which means +that you can confirm it's working it's + + align:start position:0% +that you can confirm it's working it's + + + align:start position:0% +that you can confirm it's working it's +focused on the person who's going to use + + align:start position:0% +focused on the person who's going to use + + + align:start position:0% +focused on the person who's going to use +it we're going back to that sort of you + + align:start position:0% +it we're going back to that sort of you + + + align:start position:0% +it we're going back to that sort of you +know user user oriented creation of of + + align:start position:0% +know user user oriented creation of of + + + align:start position:0% +know user user oriented creation of of +product and finally having the reason + + align:start position:0% +product and finally having the reason + + + align:start position:0% +product and finally having the reason +there means that if the person who + + align:start position:0% +there means that if the person who + + + align:start position:0% +there means that if the person who +originally asked for the feature did not + + align:start position:0% +originally asked for the feature did not + + + align:start position:0% +originally asked for the feature did not +understand the game well enough and + + align:start position:0% +understand the game well enough and + + + align:start position:0% +understand the game well enough and +asked for a lousy feature or one that + + align:start position:0% +asked for a lousy feature or one that + + + align:start position:0% +asked for a lousy feature or one that +doesn't work well with the game the + + align:start position:0% +doesn't work well with the game the + + + align:start position:0% +doesn't work well with the game the +person who is going to implement it can + + align:start position:0% +person who is going to implement it can + + + align:start position:0% +person who is going to implement it can +come back and say hey you asked for a + + align:start position:0% +come back and say hey you asked for a + + + align:start position:0% +come back and say hey you asked for a +physics engine but you want it so the + + align:start position:0% +physics engine but you want it so the + + + align:start position:0% +physics engine but you want it so the +player can drop rocks over the O into a + + align:start position:0% +player can drop rocks over the O into a + + + align:start position:0% +player can drop rocks over the O into a +pool and watch the Rocks + + align:start position:0% +pool and watch the Rocks + + + align:start position:0% +pool and watch the Rocks +sink that's the only use of your physics + + align:start position:0% +sink that's the only use of your physics + + + align:start position:0% +sink that's the only use of your physics +engine we could make this a lot faster + + align:start position:0% +engine we could make this a lot faster + + + align:start position:0% +engine we could make this a lot faster +and easier iier if I write an animation + + align:start position:0% +and easier iier if I write an animation + + + align:start position:0% +and easier iier if I write an animation +hack that shows this happening and we + + align:start position:0% +hack that shows this happening and we + + + align:start position:0% +hack that shows this happening and we +can give you some sliders to control how + + align:start position:0% +can give you some sliders to control how + + + align:start position:0% +can give you some sliders to control how +fast it falls dep depending on the + + align:start position:0% +fast it falls dep depending on the + + + align:start position:0% +fast it falls dep depending on the +weight of the + + align:start position:0% +weight of the + + + align:start position:0% +weight of the +rock um and it's people will often say + + align:start position:0% +rock um and it's people will often say + + + align:start position:0% +rock um and it's people will often say +they want + + align:start position:0% +they want + + + align:start position:0% +they want +something that is bigger or smaller or + + align:start position:0% +something that is bigger or smaller or + + + align:start position:0% +something that is bigger or smaller or +doesn't actually do what they want it to + + align:start position:0% +doesn't actually do what they want it to + + + align:start position:0% +doesn't actually do what they want it to +do it's really common when you're + + align:start position:0% +do it's really common when you're + + + align:start position:0% +do it's really common when you're +writing features it happens all the time + + align:start position:0% +writing features it happens all the time + + + align:start position:0% +writing features it happens all the time +and so having that reason there means + + align:start position:0% +and so having that reason there means + + + align:start position:0% +and so having that reason there means +that the team can go back and do a + + align:start position:0% +that the team can go back and do a + + + align:start position:0% +that the team can go back and do a +double check when they actually go to + + align:start position:0% +double check when they actually go to + + + align:start position:0% +double check when they actually go to +implement it that the thing that's being + + align:start position:0% +implement it that the thing that's being + + + align:start position:0% +implement it that the thing that's being +asked for is something that is really + + align:start position:0% +asked for is something that is really + + + align:start position:0% +asked for is something that is really +needed and it so it puts it puts a + + align:start position:0% +needed and it so it puts it puts a + + + align:start position:0% +needed and it so it puts it puts a +double check right back in the feature + + align:start position:0% +double check right back in the feature + + + align:start position:0% +double check right back in the feature +and it's it's not as good as going back + + align:start position:0% +and it's it's not as good as going back + + + align:start position:0% +and it's it's not as good as going back +and talking to the person who wrote the + + align:start position:0% +and talking to the person who wrote the + + + align:start position:0% +and talking to the person who wrote the +feature but it's at least a uh a warning + + align:start position:0% +feature but it's at least a uh a warning + + + align:start position:0% +feature but it's at least a uh a warning +signal telling you that you might might + + align:start position:0% +signal telling you that you might might + + + align:start position:0% +signal telling you that you might might +want to go talk to someone and make sure + + align:start position:0% +want to go talk to someone and make sure + + + align:start position:0% +want to go talk to someone and make sure +this is really what they need and really + + align:start position:0% +this is really what they need and really + + + align:start position:0% +this is really what they need and really +what they + + align:start position:0% + + + + align:start position:0% + +want so I think I already just went over + + align:start position:0% +want so I think I already just went over + + + align:start position:0% +want so I think I already just went over +this + + align:start position:0% +this + + + align:start position:0% +this +so because user stories have that check + + align:start position:0% +so because user stories have that check + + + align:start position:0% +so because user stories have that check +in them + + align:start position:0% + + + + align:start position:0% + +you can make sure you're actually doing + + align:start position:0% +you can make sure you're actually doing + + + align:start position:0% +you can make sure you're actually doing +the work you want to do and not some + + align:start position:0% +the work you want to do and not some + + + align:start position:0% +the work you want to do and not some +other work agile one of the things that + + align:start position:0% +other work agile one of the things that + + + align:start position:0% +other work agile one of the things that +agile is really try and do is focus on + + align:start position:0% +agile is really try and do is focus on + + + align:start position:0% +agile is really try and do is focus on +making sure that you're not doing extra + + align:start position:0% +making sure that you're not doing extra + + + align:start position:0% +making sure that you're not doing extra +work you're not doing work that doesn't + + align:start position:0% +work you're not doing work that doesn't + + + align:start position:0% +work you're not doing work that doesn't +need to be done that's going to get cut + + align:start position:0% +need to be done that's going to get cut + + + align:start position:0% +need to be done that's going to get cut +later on and so a lot of the tools and a + + align:start position:0% +later on and so a lot of the tools and a + + + align:start position:0% +later on and so a lot of the tools and a +lot of the processes and a lot of the + + align:start position:0% +lot of the processes and a lot of the + + + align:start position:0% +lot of the processes and a lot of the +language and a lot of the meetings are + + align:start position:0% +language and a lot of the meetings are + + + align:start position:0% +language and a lot of the meetings are +all about making sure that before you go + + align:start position:0% +all about making sure that before you go + + + align:start position:0% +all about making sure that before you go +out and put a lot of time into something + + align:start position:0% +out and put a lot of time into something + + + align:start position:0% +out and put a lot of time into something +it's really the thing that you want to + + align:start position:0% +it's really the thing that you want to + + + align:start position:0% +it's really the thing that you want to +be + + align:start position:0% +be + + + align:start position:0% +be +doing okay and user stories are just one + + align:start position:0% +doing okay and user stories are just one + + + align:start position:0% +doing okay and user stories are just one +more way to add that check into your + + align:start position:0% + + + + align:start position:0% + +process + + align:start position:0% +process + + + align:start position:0% +process +um I'm going to skip on time boxing + + align:start position:0% +um I'm going to skip on time boxing + + + align:start position:0% +um I'm going to skip on time boxing +right now because I've got a better + + align:start position:0% +right now because I've got a better + + + align:start position:0% +right now because I've got a better +discussion it's more relevant to + + align:start position:0% +discussion it's more relevant to + + + align:start position:0% +discussion it's more relevant to +meetings um and I'd rather talk about it + + align:start position:0% +meetings um and I'd rather talk about it + + + align:start position:0% +meetings um and I'd rather talk about it +in meetings so we'll skip talking about + + align:start position:0% +in meetings so we'll skip talking about + + + align:start position:0% +in meetings so we'll skip talking about +it there okay that is that is actually + + align:start position:0% +it there okay that is that is actually + + + align:start position:0% +it there okay that is that is actually +the first two-thirds of the lecture for + + align:start position:0% +the first two-thirds of the lecture for + + + align:start position:0% +the first two-thirds of the lecture for +today and I was going to propose that we + + align:start position:0% +today and I was going to propose that we + + + align:start position:0% +today and I was going to propose that we +take a 10-minute break and when you come + + align:start position:0% +take a 10-minute break and when you come + + + align:start position:0% +take a 10-minute break and when you come +back it will be time to make + + align:start position:0% +back it will be time to make + + + align:start position:0% +back it will be time to make +um a product backlog for your team um + + align:start position:0% +um a product backlog for your team um + + + align:start position:0% +um a product backlog for your team um +we're going to give you half an hour to + + align:start position:0% +we're going to give you half an hour to + + + align:start position:0% +we're going to give you half an hour to +do it in um and that half an hour will + + align:start position:0% +do it in um and that half an hour will + + + align:start position:0% +do it in um and that half an hour will +also include the time to prepare a + + align:start position:0% +also include the time to prepare a + + + align:start position:0% +also include the time to prepare a +two-minute presentation on what the top + + align:start position:0% +two-minute presentation on what the top + + + align:start position:0% +two-minute presentation on what the top +features for your product are and what + + align:start position:0% +features for your product are and what + + + align:start position:0% +features for your product are and what +your an updated vision statement for + + align:start position:0% +your an updated vision statement for + + + align:start position:0% +your an updated vision statement for +your game since I'm things may have + + align:start position:0% +your game since I'm things may have + + + align:start position:0% +your game since I'm things may have +shifted a bit when you added new people + + align:start position:0% +shifted a bit when you added new people + + + align:start position:0% +shifted a bit when you added new people +no visual aids just come up talk for up + + align:start position:0% +no visual aids just come up talk for up + + + align:start position:0% +no visual aids just come up talk for up +to 2 minutes it's okay if you talk for + + align:start position:0% +to 2 minutes it's okay if you talk for + + + align:start position:0% +to 2 minutes it's okay if you talk for +Less the faster we get through + + align:start position:0% +Less the faster we get through + + + align:start position:0% +Less the faster we get through +presentations the faster we get to other + + align:start position:0% +presentations the faster we get to other + + + align:start position:0% +presentations the faster we get to other +things um and then we'll move on to + + align:start position:0% +things um and then we'll move on to + + + align:start position:0% +things um and then we'll move on to +talking about meanings is there a + + align:start position:0% +talking about meanings is there a + + + align:start position:0% +talking about meanings is there a +s sample backlog on Stellar there is not + + align:start position:0% +s sample backlog on Stellar there is not + + + align:start position:0% +s sample backlog on Stellar there is not +a sample backlog on Stellar I think I + + align:start position:0% +a sample backlog on Stellar I think I + + + align:start position:0% +a sample backlog on Stellar I think I +think there is you think there is put it + + align:start position:0% +think there is you think there is put it + + + align:start position:0% +think there is you think there is put it +up the time get back okay + + align:start position:0% +up the time get back okay + + + align:start position:0% +up the time get back okay +UMES yeah in many ways I actually Mo I + + align:start position:0% +UMES yeah in many ways I actually Mo I + + + align:start position:0% +UMES yeah in many ways I actually Mo I +actually recommend you going to Google + + align:start position:0% +actually recommend you going to Google + + + align:start position:0% +actually recommend you going to Google +and create a a Google spreadsheet give + + align:start position:0% +and create a a Google spreadsheet give + + + align:start position:0% +and create a a Google spreadsheet give +it an idea ID + + align:start position:0% +it an idea ID + + + align:start position:0% +it an idea ID +and priority and status and go on from + + align:start position:0% +and priority and status and go on from + + + align:start position:0% +and priority and status and go on from +there but + + align:start position:0% +there but + + + align:start position:0% +there but +yeah okay slect back hm is it there yeah + + align:start position:0% +yeah okay slect back hm is it there yeah + + + align:start position:0% +yeah okay slect back hm is it there yeah +sample product backlog okay it is there + + align:start position:0% +sample product backlog okay it is there + + + align:start position:0% +sample product backlog okay it is there +thank you Rick I forgot to check on + + align:start position:0% +thank you Rick I forgot to check on + + + align:start position:0% +thank you Rick I forgot to check on +Stellar all right um that said it + + align:start position:0% +Stellar all right um that said it + + + align:start position:0% +Stellar all right um that said it +is2 come back in 10 minutes and start + + align:start position:0% +is2 come back in 10 minutes and start + + + align:start position:0% +is2 come back in 10 minutes and start +working on your product backlogs but go + + align:start position:0% +working on your product backlogs but go + + + align:start position:0% +working on your product backlogs but go +stretch your legs a little bit okay um + + align:start position:0% +stretch your legs a little bit okay um + + + align:start position:0% +stretch your legs a little bit okay um +so it's 202 + + align:start position:0% +so it's 202 + + + align:start position:0% +so it's 202 +um if you not already sitting in your + + align:start position:0% +um if you not already sitting in your + + + align:start position:0% +um if you not already sitting in your +project groups you should probably go + + align:start position:0% +project groups you should probably go + + + align:start position:0% +project groups you should probably go +ahead and get together in your in your + + align:start position:0% +ahead and get together in your in your + + + align:start position:0% +ahead and get together in your in your +project teams um at + + align:start position:0% +project teams um at + + + align:start position:0% +project teams um at +232 2:35 we'll give you some time to + + align:start position:0% +232 2:35 we'll give you some time to + + + align:start position:0% +232 2:35 we'll give you some time to +move around at 2:35 we will go ahead and + + align:start position:0% +move around at 2:35 we will go ahead and + + + align:start position:0% +move around at 2:35 we will go ahead and +we'll we'll make a list for signing up + + align:start position:0% +we'll we'll make a list for signing up + + + align:start position:0% +we'll we'll make a list for signing up +and we'll run through the presentations + + align:start position:0% +and we'll run through the presentations + + + align:start position:0% +and we'll run through the presentations +okay if there are any questions or you + + align:start position:0% +okay if there are any questions or you + + + align:start position:0% +okay if there are any questions or you +want to know what's going on if you like + + align:start position:0% +want to know what's going on if you like + + + align:start position:0% +want to know what's going on if you like +some advice we'll be all hanging on down + + align:start position:0% +some advice we'll be all hanging on down + + + align:start position:0% +some advice we'll be all hanging on down +here + + align:start position:0% +here + + + align:start position:0% +here +um so please feel free to come and ask + + align:start position:0% +um so please feel free to come and ask + + + align:start position:0% +um so please feel free to come and ask +us for any advice or any help or + + align:start position:0% +us for any advice or any help or + + + align:start position:0% +us for any advice or any help or +anything you need + + align:start position:0% +anything you need + + + align:start position:0% +anything you need +okay + + align:start position:0% + + + + align:start position:0% + +okay ah one moment let + + align:start position:0% + + + + align:start position:0% + +me you don't need you don't need that + + align:start position:0% +me you don't need you don't need that + + + align:start position:0% +me you don't need you don't need that +plug in right now okay um so let's go + + align:start position:0% +plug in right now okay um so let's go + + + align:start position:0% +plug in right now okay um so let's go +ahead is every I'm guessing everybody's + + align:start position:0% +ahead is every I'm guessing everybody's + + + align:start position:0% +ahead is every I'm guessing everybody's +ready for + + align:start position:0% +ready for + + + align:start position:0% +ready for +presentations okay then let's ask C + + align:start position:0% +presentations okay then let's ask C + + + align:start position:0% +presentations okay then let's ask C +castic to come on + + align:start position:0% + + + + align:start position:0% + +down okay so the goal of comcastic is to + + align:start position:0% +down okay so the goal of comcastic is to + + + align:start position:0% +down okay so the goal of comcastic is to +be able to place um internet service + + align:start position:0% +be able to place um internet service + + + align:start position:0% +be able to place um internet service +stations in a town so that you can + + align:start position:0% +stations in a town so that you can + + + align:start position:0% +stations in a town so that you can +service the neighborhood and get money + + align:start position:0% +service the neighborhood and get money + + + align:start position:0% +service the neighborhood and get money +and then eventually you want to build + + align:start position:0% +and then eventually you want to build + + + align:start position:0% +and then eventually you want to build +your Monopoly cable Empire to become + + align:start position:0% +your Monopoly cable Empire to become + + + align:start position:0% +your Monopoly cable Empire to become +very wealthy and so the core features + + align:start position:0% +very wealthy and so the core features + + + align:start position:0% +very wealthy and so the core features +that are necessary in order to enable + + align:start position:0% +that are necessary in order to enable + + + align:start position:0% +that are necessary in order to enable +this are um being able to look at the + + align:start position:0% +this are um being able to look at the + + + align:start position:0% +this are um being able to look at the +town map you need to be able to place + + align:start position:0% +town map you need to be able to place + + + align:start position:0% +town map you need to be able to place +pieces you need to be able to rotate the + + align:start position:0% +pieces you need to be able to rotate the + + + align:start position:0% +pieces you need to be able to rotate the +pieces because the orientation doesn't + + align:start position:0% +pieces because the orientation doesn't + + + align:start position:0% +pieces because the orientation doesn't +matter um you also need to be able to + + align:start position:0% +matter um you also need to be able to + + + align:start position:0% +matter um you also need to be able to +have some kind of turn mechanics you + + align:start position:0% +have some kind of turn mechanics you + + + align:start position:0% +have some kind of turn mechanics you +want like an end turn button or + + align:start position:0% +want like an end turn button or + + + align:start position:0% +want like an end turn button or +something that happens when you place a + + align:start position:0% +something that happens when you place a + + + align:start position:0% +something that happens when you place a +piece um and that will also uh give you + + align:start position:0% +piece um and that will also uh give you + + + align:start position:0% +piece um and that will also uh give you +the money result for that turn you also + + align:start position:0% +the money result for that turn you also + + + align:start position:0% +the money result for that turn you also +need to be able to know how much money + + align:start position:0% +need to be able to know how much money + + + align:start position:0% +need to be able to know how much money +you have and be able to place pieces + + align:start position:0% +you have and be able to place pieces + + + align:start position:0% +you have and be able to place pieces +only in legal spots and to be able to + + align:start position:0% +only in legal spots and to be able to + + + align:start position:0% +only in legal spots and to be able to +start the game quit the game things like + + align:start position:0% +start the game quit the game things like + + + align:start position:0% +start the game quit the game things like +that so those are V core features ofas + + align:start position:0% +that so those are V core features ofas + + + align:start position:0% +that so those are V core features ofas +thank + + align:start position:0% + + + + align:start position:0% + +you all right blind + + align:start position:0% + + + + align:start position:0% + +aliens uh blind aliens team goal is to + + align:start position:0% +aliens uh blind aliens team goal is to + + + align:start position:0% +aliens uh blind aliens team goal is to +create a creepy and enthralling game and + + align:start position:0% +create a creepy and enthralling game and + + + align:start position:0% +create a creepy and enthralling game and +in order to do that we first need to + + align:start position:0% +in order to do that we first need to + + + align:start position:0% +in order to do that we first need to +have really basic structure which is + + align:start position:0% +have really basic structure which is + + + align:start position:0% +have really basic structure which is +what we're going to focus on this week + + align:start position:0% +what we're going to focus on this week + + + align:start position:0% +what we're going to focus on this week +we're going to focus on having a uh + + align:start position:0% +we're going to focus on having a uh + + + align:start position:0% +we're going to focus on having a uh +first a start menu where we can just say + + align:start position:0% +first a start menu where we can just say + + + align:start position:0% +first a start menu where we can just say +the instructions really fast and input + + align:start position:0% +the instructions really fast and input + + + align:start position:0% +the instructions really fast and input +the number of aliens which is going to + + align:start position:0% +the number of aliens which is going to + + + align:start position:0% +the number of aliens which is going to +be important for testing because you + + align:start position:0% +be important for testing because you + + + align:start position:0% +be important for testing because you +know you need to be able to change + + align:start position:0% +know you need to be able to change + + + align:start position:0% +know you need to be able to change +things quickly and then we're going to + + align:start position:0% +things quickly and then we're going to + + + align:start position:0% +things quickly and then we're going to +have the main screen a character + + align:start position:0% +have the main screen a character + + + align:start position:0% +have the main screen a character +character movement aliens alien movement + + align:start position:0% +character movement aliens alien movement + + + align:start position:0% +character movement aliens alien movement +and then this weekend we're going to get + + align:start position:0% +and then this weekend we're going to get + + + align:start position:0% +and then this weekend we're going to get +up together work on those interactions + + align:start position:0% +up together work on those interactions + + + align:start position:0% +up together work on those interactions +of those aliens in the character and + + align:start position:0% +of those aliens in the character and + + + align:start position:0% +of those aliens in the character and +then work on shooting um so that's what + + align:start position:0% +then work on shooting um so that's what + + + align:start position:0% +then work on shooting um so that's what +what we're focusing on thank + + align:start position:0% + + + + align:start position:0% + +you all right + + align:start position:0% + + + + align:start position:0% + +Wonder hi uh so for plunder winds um + + align:start position:0% +Wonder hi uh so for plunder winds um + + + align:start position:0% +Wonder hi uh so for plunder winds um +we're implementing a similar game to our + + align:start position:0% +we're implementing a similar game to our + + + align:start position:0% +we're implementing a similar game to our +Pro paper prototype so we're a + + align:start position:0% +Pro paper prototype so we're a + + + align:start position:0% +Pro paper prototype so we're a +grid-based or tile based um turn based + + align:start position:0% +grid-based or tile based um turn based + + + align:start position:0% +grid-based or tile based um turn based +game and built around three core + + align:start position:0% +game and built around three core + + + align:start position:0% +game and built around three core +mechanics + + align:start position:0% +mechanics + + + align:start position:0% +mechanics +or core mechanics are a random encounter + + align:start position:0% +or core mechanics are a random encounter + + + align:start position:0% +or core mechanics are a random encounter +mechanic where every Square possibly has + + align:start position:0% +mechanic where every Square possibly has + + + align:start position:0% +mechanic where every Square possibly has +either treasure or Pirates a um an + + align:start position:0% +either treasure or Pirates a um an + + + align:start position:0% +either treasure or Pirates a um an +exploration mechanic where you reveal + + align:start position:0% +exploration mechanic where you reveal + + + align:start position:0% +exploration mechanic where you reveal +the risk level of nearby tiles and so + + align:start position:0% +the risk level of nearby tiles and so + + + align:start position:0% +the risk level of nearby tiles and so +that can change like what Pirates will + + align:start position:0% +that can change like what Pirates will + + + align:start position:0% +that can change like what Pirates will +do to you if you actually land on that + + align:start position:0% +do to you if you actually land on that + + + align:start position:0% +do to you if you actually land on that +square something like that and then a + + align:start position:0% +square something like that and then a + + + align:start position:0% +square something like that and then a +wind mechanic which controls which + + align:start position:0% +wind mechanic which controls which + + + align:start position:0% +wind mechanic which controls which +directions you can + + align:start position:0% +directions you can + + + align:start position:0% +directions you can +move and so uh our gols for this week + + align:start position:0% +move and so uh our gols for this week + + + align:start position:0% +move and so uh our gols for this week +are to try and Implement as much of our + + align:start position:0% +are to try and Implement as much of our + + + align:start position:0% +are to try and Implement as much of our +core mechanics as possible so that uh we + + align:start position:0% +core mechanics as possible so that uh we + + + align:start position:0% +core mechanics as possible so that uh we +can possibly like look into uh look into + + align:start position:0% +can possibly like look into uh look into + + + align:start position:0% +can possibly like look into uh look into +stretch goals for our games like + + align:start position:0% +stretch goals for our games like + + + align:start position:0% +stretch goals for our games like +possibly implementing one or two unique + + align:start position:0% +possibly implementing one or two unique + + + align:start position:0% +possibly implementing one or two unique +abilities to improve playability over + + align:start position:0% +abilities to improve playability over + + + align:start position:0% +abilities to improve playability over +the following next week thank + + align:start position:0% + + + + align:start position:0% + +you lost + + align:start position:0% + + + + align:start position:0% + +underground um L Underground + + align:start position:0% + + + + align:start position:0% + +scar for a second uh the goal is to well + + align:start position:0% +scar for a second uh the goal is to well + + + align:start position:0% +scar for a second uh the goal is to well +for the goal overall goal is to create a + + align:start position:0% +for the goal overall goal is to create a + + + align:start position:0% +for the goal overall goal is to create a +game that people will like it will be + + align:start position:0% +game that people will like it will be + + + align:start position:0% +game that people will like it will be +random and it will allow exploration our + + align:start position:0% +random and it will allow exploration our + + + align:start position:0% +random and it will allow exploration our +goals for the weekend are to create the + + align:start position:0% +goals for the weekend are to create the + + + align:start position:0% +goals for the weekend are to create the +basic Bare Bones you can walk around the + + align:start position:0% +basic Bare Bones you can walk around the + + + align:start position:0% +basic Bare Bones you can walk around the +map you can drop bombs it's make the + + align:start position:0% +map you can drop bombs it's make the + + + align:start position:0% +map you can drop bombs it's make the +most basic part out and then build up on + + align:start position:0% +most basic part out and then build up on + + + align:start position:0% +most basic part out and then build up on +everything else uh the features that + + align:start position:0% +everything else uh the features that + + + align:start position:0% +everything else uh the features that +we're thinking of planning + + align:start position:0% +we're thinking of planning + + + align:start position:0% +we're thinking of planning +the most important features of the game + + align:start position:0% +the most important features of the game + + + align:start position:0% +the most important features of the game +which are the ones that we'll be working + + align:start position:0% +which are the ones that we'll be working + + + align:start position:0% +which are the ones that we'll be working +on this weekend are will just be um + + align:start position:0% +on this weekend are will just be um + + + align:start position:0% +on this weekend are will just be um +being able to move around the + + align:start position:0% +being able to move around the + + + align:start position:0% +being able to move around the +board uh a board a general board uh + + align:start position:0% +board uh a board a general board uh + + + align:start position:0% +board uh a board a general board uh +dropping bombs + + align:start position:0% +dropping bombs + + + align:start position:0% +dropping bombs +and possibly the most basic nice looking + + align:start position:0% +and possibly the most basic nice looking + + + align:start position:0% +and possibly the most basic nice looking +art that we + + align:start position:0% + + + + align:start position:0% + +can fever + + align:start position:0% +can fever + + + align:start position:0% +can fever +Evolution just a quick Point uh the the + + align:start position:0% +Evolution just a quick Point uh the the + + + align:start position:0% +Evolution just a quick Point uh the the +most basic art that you can is probably + + align:start position:0% +most basic art that you can is probably + + + align:start position:0% +most basic art that you can is probably +not the nicest looking art you can make + + align:start position:0% +not the nicest looking art you can make + + + align:start position:0% +not the nicest looking art you can make +so just go for + + align:start position:0% +so just go for + + + align:start position:0% +so just go for +basic figure nice can + + align:start position:0% + + + + align:start position:0% + +come all right so Beaver Revolution is a + + align:start position:0% +come all right so Beaver Revolution is a + + + align:start position:0% +come all right so Beaver Revolution is a +2d turn-based game where you're trying + + align:start position:0% +2d turn-based game where you're trying + + + align:start position:0% +2d turn-based game where you're trying +to progress your beaver colony and one + + align:start position:0% +to progress your beaver colony and one + + + align:start position:0% +to progress your beaver colony and one +of our main core mechanics of this game + + align:start position:0% +of our main core mechanics of this game + + + align:start position:0% +of our main core mechanics of this game +is that you have three different choices + + align:start position:0% +is that you have three different choices + + + align:start position:0% +is that you have three different choices +you can make every turn in order to + + align:start position:0% +you can make every turn in order to + + + align:start position:0% +you can make every turn in order to +progress to one of the many wi + + align:start position:0% +progress to one of the many wi + + + align:start position:0% +progress to one of the many wi +conditions we have in the game so this + + align:start position:0% +conditions we have in the game so this + + + align:start position:0% +conditions we have in the game so this +is going to be one of our main focus for + + align:start position:0% +is going to be one of our main focus for + + + align:start position:0% +is going to be one of our main focus for +this week weekend we want to be able to + + align:start position:0% +this week weekend we want to be able to + + + align:start position:0% +this week weekend we want to be able to +implement a board want to be able to + + align:start position:0% +implement a board want to be able to + + + align:start position:0% +implement a board want to be able to +sort of Select how to build our dams and + + align:start position:0% +sort of Select how to build our dams and + + + align:start position:0% +sort of Select how to build our dams and +we want to make it really easy to + + align:start position:0% +we want to make it really easy to + + + align:start position:0% +we want to make it really easy to +incorporate the three different choices + + align:start position:0% +incorporate the three different choices + + + align:start position:0% +incorporate the three different choices +we have every turn so our main focus + + align:start position:0% +we have every turn so our main focus + + + align:start position:0% +we have every turn so our main focus +will be um also on creating a UI which + + align:start position:0% +will be um also on creating a UI which + + + align:start position:0% +will be um also on creating a UI which +makes it really easy to sort of figure + + align:start position:0% +makes it really easy to sort of figure + + + align:start position:0% +makes it really easy to sort of figure +out what you can do um what sort of + + align:start position:0% +out what you can do um what sort of + + + align:start position:0% +out what you can do um what sort of +resources you have like how far is your + + align:start position:0% +resources you have like how far is your + + + align:start position:0% +resources you have like how far is your +beaver calling progressing and I think + + align:start position:0% +beaver calling progressing and I think + + + align:start position:0% +beaver calling progressing and I think +um our second um main mechanic which is + + align:start position:0% +um our second um main mechanic which is + + + align:start position:0% +um our second um main mechanic which is +including the ravenous factors such as + + align:start position:0% +including the ravenous factors such as + + + align:start position:0% +including the ravenous factors such as +the + + align:start position:0% +the + + + align:start position:0% +the +disasters and uh you know like that kind + + align:start position:0% +disasters and uh you know like that kind + + + align:start position:0% +disasters and uh you know like that kind +of stuff that sort of stuff can be added + + align:start position:0% +of stuff that sort of stuff can be added + + + align:start position:0% +of stuff that sort of stuff can be added +on later in sort of the project we don't + + align:start position:0% +on later in sort of the project we don't + + + align:start position:0% +on later in sort of the project we don't +need a focus on now right now we just + + align:start position:0% +need a focus on now right now we just + + + align:start position:0% +need a focus on now right now we just +want to focus on making sure we can play + + align:start position:0% +want to focus on making sure we can play + + + align:start position:0% +want to focus on making sure we can play +through the game making sure that it's + + align:start position:0% +through the game making sure that it's + + + align:start position:0% +through the game making sure that it's +not confusing to the player and that you + + align:start position:0% +not confusing to the player and that you + + + align:start position:0% +not confusing to the player and that you +can do it without sort of adding any + + align:start position:0% +can do it without sort of adding any + + + align:start position:0% +can do it without sort of adding any +sort of of the uh features that require + + align:start position:0% +sort of of the uh features that require + + + align:start position:0% +sort of of the uh features that require +more balance + + align:start position:0% + + + + align:start position:0% + +modu + + align:start position:0% + + + + align:start position:0% + +dice hi we're Maji dice we want to make + + align:start position:0% +dice hi we're Maji dice we want to make + + + align:start position:0% +dice hi we're Maji dice we want to make +a fun engaging puzzle game where the + + align:start position:0% +a fun engaging puzzle game where the + + + align:start position:0% +a fun engaging puzzle game where the +player moves around a dice on a board to + + align:start position:0% +player moves around a dice on a board to + + + align:start position:0% +player moves around a dice on a board to +try and using modulo arithmetic create + + align:start position:0% +try and using modulo arithmetic create + + + align:start position:0% +try and using modulo arithmetic create +zeros and set up combo chains so our + + align:start position:0% +zeros and set up combo chains so our + + + align:start position:0% +zeros and set up combo chains so our +goal for the first week is first of all + + align:start position:0% +goal for the first week is first of all + + + align:start position:0% +goal for the first week is first of all +just set up the board and the dice so + + align:start position:0% +just set up the board and the dice so + + + align:start position:0% +just set up the board and the dice so +that the player can see what they're + + align:start position:0% +that the player can see what they're + + + align:start position:0% +that the player can see what they're +doing and then our immediate following + + align:start position:0% +doing and then our immediate following + + + align:start position:0% +doing and then our immediate following +goal is to incentivize players create + + align:start position:0% +goal is to incentivize players create + + + align:start position:0% +goal is to incentivize players create +combos so that multiple moves earns them + + align:start position:0% +combos so that multiple moves earns them + + + align:start position:0% +combos so that multiple moves earns them +like create zeros in a row and we want + + align:start position:0% +like create zeros in a row and we want + + + align:start position:0% +like create zeros in a row and we want +to do this by like you know giving them + + align:start position:0% +to do this by like you know giving them + + + align:start position:0% +to do this by like you know giving them +more points and like having a pretty UI + + align:start position:0% +more points and like having a pretty UI + + + align:start position:0% +more points and like having a pretty UI +so that they're incentified to set up + + align:start position:0% +so that they're incentified to set up + + + align:start position:0% +so that they're incentified to set up +and do this sort of fun + + align:start position:0% + + + + align:start position:0% + +stuff barkle + + align:start position:0% + + + + align:start position:0% + +Redemption okay sparkly Redemption to + + align:start position:0% +Redemption okay sparkly Redemption to + + + align:start position:0% +Redemption okay sparkly Redemption to +the Real Time game where you shoot + + align:start position:0% +the Real Time game where you shoot + + + align:start position:0% +the Real Time game where you shoot +monsters and pick up sparkly and the + + align:start position:0% +monsters and pick up sparkly and the + + + align:start position:0% +monsters and pick up sparkly and the +important thing is that when you pick up + + align:start position:0% +important thing is that when you pick up + + + align:start position:0% +important thing is that when you pick up +sparkly you either get a different + + align:start position:0% +sparkly you either get a different + + + align:start position:0% +sparkly you either get a different +weapon or the monsters change their + + align:start position:0% +weapon or the monsters change their + + + align:start position:0% +weapon or the monsters change their +behavior that means the core thing we + + align:start position:0% +behavior that means the core thing we + + + align:start position:0% +behavior that means the core thing we +really need to implement is to have a + + align:start position:0% +really need to implement is to have a + + + align:start position:0% +really need to implement is to have a +mighty you can move around have monsters + + align:start position:0% +mighty you can move around have monsters + + + align:start position:0% +mighty you can move around have monsters +with at least two different behaviors + + align:start position:0% +with at least two different behaviors + + + align:start position:0% +with at least two different behaviors +because the swapping is important and + + align:start position:0% +because the swapping is important and + + + align:start position:0% +because the swapping is important and +have sparkly that you can pick up Theos + + align:start position:0% +have sparkly that you can pick up Theos + + + align:start position:0% +have sparkly that you can pick up Theos +needs at least two different attacks so + + align:start position:0% +needs at least two different attacks so + + + align:start position:0% +needs at least two different attacks so +that's probably what we're going to + + align:start position:0% +that's probably what we're going to + + + align:start position:0% +that's probably what we're going to +focus on at this time um I guess it also + + align:start position:0% +focus on at this time um I guess it also + + + align:start position:0% +focus on at this time um I guess it also +be sort of important to have it be + + align:start position:0% +be sort of important to have it be + + + align:start position:0% +be sort of important to have it be +easily visible at a glance the + + align:start position:0% +easily visible at a glance the + + + align:start position:0% +easily visible at a glance the +difference what the current monster + + align:start position:0% +difference what the current monster + + + align:start position:0% +difference what the current monster +behavior is what your current attack is + + align:start position:0% +behavior is what your current attack is + + + align:start position:0% +behavior is what your current attack is +and I guess how many sparkly you have + + align:start position:0% +and I guess how many sparkly you have + + + align:start position:0% +and I guess how many sparkly you have +and uh so I guess it's not the most most + + align:start position:0% +and uh so I guess it's not the most most + + + align:start position:0% +and uh so I guess it's not the most most +critical thing to have + + align:start position:0% +critical thing to have + + + align:start position:0% +critical thing to have +this week but we'll probably also kind + + align:start position:0% +this week but we'll probably also kind + + + align:start position:0% +this week but we'll probably also kind +of try and get it so that you can at + + align:start position:0% +of try and get it so that you can at + + + align:start position:0% +of try and get it so that you can at +least see what's going on and not just + + align:start position:0% +least see what's going on and not just + + + align:start position:0% +least see what's going on and not just +have to sort of guess at it + + align:start position:0% + + + + align:start position:0% + +all right if we + + align:start position:0% + + + + align:start position:0% + +can okay + + align:start position:0% +can okay + + + align:start position:0% +can okay +so we did product backlogs um you did + + align:start position:0% +so we did product backlogs um you did + + + align:start position:0% +so we did product backlogs um you did +what was sort of the in somewh you you + + align:start position:0% +what was sort of the in somewh you you + + + align:start position:0% +what was sort of the in somewh you you +on on Monday you did a fair chunk of + + align:start position:0% +on on Monday you did a fair chunk of + + + align:start position:0% +on on Monday you did a fair chunk of +your Sprint plan of your planning Sprint + + align:start position:0% +your Sprint plan of your planning Sprint + + + align:start position:0% +your Sprint plan of your planning Sprint +you finished up sort of the second half + + align:start position:0% +you finished up sort of the second half + + + align:start position:0% +you finished up sort of the second half +of that today by getting a product + + align:start position:0% +of that today by getting a product + + + align:start position:0% +of that today by getting a product +backlog pulled together um + + align:start position:0% +backlog pulled together um + + + align:start position:0% +backlog pulled together um +to close out today I'm going to just I'm + + align:start position:0% +to close out today I'm going to just I'm + + + align:start position:0% +to close out today I'm going to just I'm +going to talk about the uh the meetings + + align:start position:0% +going to talk about the uh the meetings + + + align:start position:0% +going to talk about the uh the meetings +that are involved involved in scrum + + align:start position:0% +that are involved involved in scrum + + + align:start position:0% +that are involved involved in scrum +we're not actually going to have you + + align:start position:0% +we're not actually going to have you + + + align:start position:0% +we're not actually going to have you +hold them all here because a wouldn't be + + align:start position:0% +hold them all here because a wouldn't be + + + align:start position:0% +hold them all here because a wouldn't be +very useful it would take a lot of time + + align:start position:0% +very useful it would take a lot of time + + + align:start position:0% +very useful it would take a lot of time +and because we're because we're + + align:start position:0% +and because we're because we're + + + align:start position:0% +and because we're because we're +introducing scrum alongside the project + + align:start position:0% +introducing scrum alongside the project + + + align:start position:0% +introducing scrum alongside the project +they don't the timing doesn't fall well + + align:start position:0% +they don't the timing doesn't fall well + + + align:start position:0% +they don't the timing doesn't fall well +as we introduce things would be the + + align:start position:0% +as we introduce things would be the + + + align:start position:0% +as we introduce things would be the +right way to put it we are hoping you + + align:start position:0% +right way to put it we are hoping you + + + align:start position:0% +right way to put it we are hoping you +will use these meetings things in + + align:start position:0% +will use these meetings things in + + + align:start position:0% +will use these meetings things in +Project 3 um as you start planning out + + align:start position:0% +Project 3 um as you start planning out + + + align:start position:0% +Project 3 um as you start planning out +your project and figuring things out so + + align:start position:0% +your project and figuring things out so + + + align:start position:0% +your project and figuring things out so +I do want to talk about how you run the + + align:start position:0% +I do want to talk about how you run the + + + align:start position:0% +I do want to talk about how you run the +meetings we talked about that occur + + align:start position:0% +meetings we talked about that occur + + + align:start position:0% +meetings we talked about that occur +within a scrum + + align:start position:0% +within a scrum + + + align:start position:0% +within a scrum +cycle um but first i'm just going to + + align:start position:0% +cycle um but first i'm just going to + + + align:start position:0% +cycle um but first i'm just going to +talk about meetings um and meetings as a + + align:start position:0% +talk about meetings um and meetings as a + + + align:start position:0% +talk about meetings um and meetings as a +Force for good as opposed to how most of + + align:start position:0% +Force for good as opposed to how most of + + + align:start position:0% +Force for good as opposed to how most of +us probably think of them which is let's + + align:start position:0% +us probably think of them which is let's + + + align:start position:0% +us probably think of them which is let's +be honest as a force for evil um as a + + align:start position:0% +be honest as a force for evil um as a + + + align:start position:0% +be honest as a force for evil um as a +force for evil they suck away a lot of + + align:start position:0% +force for evil they suck away a lot of + + + align:start position:0% +force for evil they suck away a lot of +time if you have a six-person team and + + align:start position:0% +time if you have a six-person team and + + + align:start position:0% +time if you have a six-person team and +you have a 1-hour meeting that's 6 hours + + align:start position:0% +you have a 1-hour meeting that's 6 hours + + + align:start position:0% +you have a 1-hour meeting that's 6 hours +of work gone so you want to make sure + + align:start position:0% +of work gone so you want to make sure + + + align:start position:0% +of work gone so you want to make sure +that those six hours of work are + + align:start position:0% +that those six hours of work are + + + align:start position:0% +that those six hours of work are +actually good and useful hours of + + align:start position:0% +actually good and useful hours of + + + align:start position:0% +actually good and useful hours of +work um there are three primary tools to + + align:start position:0% +work um there are three primary tools to + + + align:start position:0% +work um there are three primary tools to +do this + + align:start position:0% +do this + + + align:start position:0% +do this +um that we're going to talk about here + + align:start position:0% +um that we're going to talk about here + + + align:start position:0% +um that we're going to talk about here +we're going to talk about time boxing + + align:start position:0% +we're going to talk about time boxing + + + align:start position:0% +we're going to talk about time boxing +having a clear agenda and having + + align:start position:0% +having a clear agenda and having + + + align:start position:0% +having a clear agenda and having +involved + + align:start position:0% +involved + + + align:start position:0% +involved +participants um has anybody heard here + + align:start position:0% +participants um has anybody heard here + + + align:start position:0% +participants um has anybody heard here +here heard of time boxing and do you + + align:start position:0% +here heard of time boxing and do you + + + align:start position:0% +here heard of time boxing and do you +know what that that concept + + align:start position:0% + + + + align:start position:0% + +is okay time boxing is when you decide + + align:start position:0% +is okay time boxing is when you decide + + + align:start position:0% +is okay time boxing is when you decide +before you have the meeting or before + + align:start position:0% +before you have the meeting or before + + + align:start position:0% +before you have the meeting or before +you start any particular activity how + + align:start position:0% +you start any particular activity how + + + align:start position:0% +you start any particular activity how +much time you're going to let it take um + + align:start position:0% +much time you're going to let it take um + + + align:start position:0% +much time you're going to let it take um +you give your you give the task a Time + + align:start position:0% +you give your you give the task a Time + + + align:start position:0% +you give your you give the task a Time +budget and you don't exceed that time + + align:start position:0% +budget and you don't exceed that time + + + align:start position:0% +budget and you don't exceed that time +budget um for example Sprints are just + + align:start position:0% +budget um for example Sprints are just + + + align:start position:0% +budget um for example Sprints are just +one big time box um you're defining that + + align:start position:0% +one big time box um you're defining that + + + align:start position:0% +one big time box um you're defining that +here's a set of things we're going to + + align:start position:0% +here's a set of things we're going to + + + align:start position:0% +here's a set of things we're going to +get done we have a week to do them in + + align:start position:0% +get done we have a week to do them in + + + align:start position:0% +get done we have a week to do them in +when we're done with that week we're + + align:start position:0% +when we're done with that week we're + + + align:start position:0% +when we're done with that week we're +going to stop and see how much we got + + align:start position:0% +going to stop and see how much we got + + + align:start position:0% +going to stop and see how much we got +done and we're going to move on from + + align:start position:0% +done and we're going to move on from + + + align:start position:0% +done and we're going to move on from +there and + + align:start position:0% +there and + + + align:start position:0% +there and +re-evaluate meetings can do this too um + + align:start position:0% +re-evaluate meetings can do this too um + + + align:start position:0% +re-evaluate meetings can do this too um +and all meetings in scrum should be time + + align:start position:0% +and all meetings in scrum should be time + + + align:start position:0% +and all meetings in scrum should be time +boxed it's actually it's one of the it's + + align:start position:0% +boxed it's actually it's one of the it's + + + align:start position:0% +boxed it's actually it's one of the it's +one of the classic scrum rules is that + + align:start position:0% +one of the classic scrum rules is that + + + align:start position:0% +one of the classic scrum rules is that +meetings are time boxed they have a + + align:start position:0% +meetings are time boxed they have a + + + align:start position:0% +meetings are time boxed they have a +limited amount of time that you spend on + + align:start position:0% +limited amount of time that you spend on + + + align:start position:0% +limited amount of time that you spend on +them um + + align:start position:0% +them um + + + align:start position:0% +them um +time boxing acknowledges that there sort + + align:start position:0% +time boxing acknowledges that there sort + + + align:start position:0% +time boxing acknowledges that there sort +of a maximum amount of time you can + + align:start position:0% +of a maximum amount of time you can + + + align:start position:0% +of a maximum amount of time you can +spend on any particular problem before + + align:start position:0% +spend on any particular problem before + + + align:start position:0% +spend on any particular problem before +any time after that is + + align:start position:0% +any time after that is + + + align:start position:0% +any time after that is +wasted + + align:start position:0% +wasted + + + align:start position:0% +wasted +um it does mean that you won't always + + align:start position:0% +um it does mean that you won't always + + + align:start position:0% +um it does mean that you won't always +reach the perfect solution because after + + align:start position:0% +reach the perfect solution because after + + + align:start position:0% +reach the perfect solution because after +you've been talking if you've given + + align:start position:0% +you've been talking if you've given + + + align:start position:0% +you've been talking if you've given +yourself an hour to discuss a problem + + align:start position:0% +yourself an hour to discuss a problem + + + align:start position:0% +yourself an hour to discuss a problem +and you've talked about it for an hour + + align:start position:0% +and you've talked about it for an hour + + + align:start position:0% +and you've talked about it for an hour +and you haven't quite come to a great + + align:start position:0% +and you haven't quite come to a great + + + align:start position:0% +and you haven't quite come to a great +solution you stop talking anyway you + + align:start position:0% +solution you stop talking anyway you + + + align:start position:0% +solution you stop talking anyway you +decide what the most reasonable solution + + align:start position:0% +decide what the most reasonable solution + + + align:start position:0% +decide what the most reasonable solution +you've talked about is and you go ahead + + align:start position:0% +you've talked about is and you go ahead + + + align:start position:0% +you've talked about is and you go ahead +and do that um it's sort of an Implement + + align:start position:0% +and do that um it's sort of an Implement + + + align:start position:0% +and do that um it's sort of an Implement +it's a implementation of the theory that + + align:start position:0% +it's a implementation of the theory that + + + align:start position:0% +it's a implementation of the theory that +the perfect is the enemy of the good it + + align:start position:0% +the perfect is the enemy of the good it + + + align:start position:0% +the perfect is the enemy of the good it +may be that you talk if you went ahead + + align:start position:0% +may be that you talk if you went ahead + + + align:start position:0% +may be that you talk if you went ahead +and talked for another hour you would + + align:start position:0% +and talked for another hour you would + + + align:start position:0% +and talked for another hour you would +find the perfect and ideal solution to + + align:start position:0% +find the perfect and ideal solution to + + + align:start position:0% +find the perfect and ideal solution to +the problem but it's also very possible + + align:start position:0% +the problem but it's also very possible + + + align:start position:0% +the problem but it's also very possible +that you're just going to spend another + + align:start position:0% +that you're just going to spend another + + + align:start position:0% +that you're just going to spend another +hour talking about it it may be better + + align:start position:0% +hour talking about it it may be better + + + align:start position:0% +hour talking about it it may be better +and it usually is better to go ahead + + align:start position:0% +and it usually is better to go ahead + + + align:start position:0% +and it usually is better to go ahead +with the best solution you came up with + + align:start position:0% +with the best solution you came up with + + + align:start position:0% +with the best solution you came up with +and start implementing that and see how + + align:start position:0% +and start implementing that and see how + + + align:start position:0% +and start implementing that and see how +it works so that's the idea behind time + + align:start position:0% +it works so that's the idea behind time + + + align:start position:0% +it works so that's the idea behind time +boxing um clear agendas if you don't + + align:start position:0% +boxing um clear agendas if you don't + + + align:start position:0% +boxing um clear agendas if you don't +know why you're having a meeting you + + align:start position:0% +know why you're having a meeting you + + + align:start position:0% +know why you're having a meeting you +probably shouldn't be having it um the + + align:start position:0% +probably shouldn't be having it um the + + + align:start position:0% +probably shouldn't be having it um the +meetings that + + align:start position:0% +meetings that + + + align:start position:0% +meetings that +scrum recommends come with a built-in + + align:start position:0% +scrum recommends come with a built-in + + + align:start position:0% +scrum recommends come with a built-in +agenda for what you want to do um you'll + + align:start position:0% +agenda for what you want to do um you'll + + + align:start position:0% +agenda for what you want to do um you'll +probably have to have other meetings + + align:start position:0% +probably have to have other meetings + + + align:start position:0% +probably have to have other meetings +because at some point you'll have to + + align:start position:0% +because at some point you'll have to + + + align:start position:0% +because at some point you'll have to +talk about to figure out how your + + align:start position:0% +talk about to figure out how your + + + align:start position:0% +talk about to figure out how your +version control is working or how this + + align:start position:0% +version control is working or how this + + + align:start position:0% +version control is working or how this +feature is working or how the art assets + + align:start position:0% +feature is working or how the art assets + + + align:start position:0% +feature is working or how the art assets +go into the game or what kind of sound + + align:start position:0% +go into the game or what kind of sound + + + align:start position:0% +go into the game or what kind of sound +assets you're going to have um before + + align:start position:0% +assets you're going to have um before + + + align:start position:0% +assets you're going to have um before +you go ahead and have that meeting make + + align:start position:0% +you go ahead and have that meeting make + + + align:start position:0% +you go ahead and have that meeting make +sure you know what the goal of it is + + align:start position:0% +sure you know what the goal of it is + + + align:start position:0% +sure you know what the goal of it is +what you want to come out of it with and + + align:start position:0% +what you want to come out of it with and + + + align:start position:0% +what you want to come out of it with and +honestly Fading Into the next Point who + + align:start position:0% +honestly Fading Into the next Point who + + + align:start position:0% +honestly Fading Into the next Point who +actually needs to be there at the + + align:start position:0% +actually needs to be there at the + + + align:start position:0% +actually needs to be there at the +meeting um not all meetings require the + + align:start position:0% +meeting um not all meetings require the + + + align:start position:0% +meeting um not all meetings require the +whole team a lot of meetings are really + + align:start position:0% +whole team a lot of meetings are really + + + align:start position:0% +whole team a lot of meetings are really +good as just one-on-one conversations or + + align:start position:0% +good as just one-on-one conversations or + + + align:start position:0% +good as just one-on-one conversations or +or just a small group of people a + + align:start position:0% +or just a small group of people a + + + align:start position:0% +or just a small group of people a +subgroup of people who are working on a + + align:start position:0% +subgroup of people who are working on a + + + align:start position:0% +subgroup of people who are working on a +particular task can get together and + + align:start position:0% +particular task can get together and + + + align:start position:0% +particular task can get together and +talk about it without including everyone + + align:start position:0% +talk about it without including everyone + + + align:start position:0% +talk about it without including everyone +else um the other half of involved + + align:start position:0% +else um the other half of involved + + + align:start position:0% +else um the other half of involved +participants is if you are in a meeting + + align:start position:0% +participants is if you are in a meeting + + + align:start position:0% +participants is if you are in a meeting +be in the meeting + + align:start position:0% +be in the meeting + + + align:start position:0% +be in the meeting +don't don't be coding in the background + + align:start position:0% +don't don't be coding in the background + + + align:start position:0% +don't don't be coding in the background +um don't be checking your cell phone and + + align:start position:0% +um don't be checking your cell phone and + + + align:start position:0% +um don't be checking your cell phone and +texting something don't work on a + + align:start position:0% +texting something don't work on a + + + align:start position:0% +texting something don't work on a +problem set go ahead and be there um + + align:start position:0% +problem set go ahead and be there um + + + align:start position:0% +problem set go ahead and be there um +except that you have dedicated the next + + align:start position:0% +except that you have dedicated the next + + + align:start position:0% +except that you have dedicated the next +15 or 20 minutes to working with your + + align:start position:0% +15 or 20 minutes to working with your + + + align:start position:0% +15 or 20 minutes to working with your +co-workers to solve this particular + + align:start position:0% +co-workers to solve this particular + + + align:start position:0% +co-workers to solve this particular +problem get the problem solved get the + + align:start position:0% +problem get the problem solved get the + + + align:start position:0% +problem get the problem solved get the +meeting over and then get back to doing + + align:start position:0% +meeting over and then get back to doing + + + align:start position:0% +meeting over and then get back to doing +useful things um so those really are + + align:start position:0% +useful things um so those really are + + + align:start position:0% +useful things um so those really are +those really are the ways to make + + align:start position:0% +those really are the ways to make + + + align:start position:0% +those really are the ways to make +meetings useful and to make them work + + align:start position:0% +meetings useful and to make them work + + + align:start position:0% +meetings useful and to make them work +for you rather than working against you + + align:start position:0% +for you rather than working against you + + + align:start position:0% +for you rather than working against you +all right that said I'm now going to go + + align:start position:0% +all right that said I'm now going to go + + + align:start position:0% +all right that said I'm now going to go +ahead and talk a little bit about each + + align:start position:0% +ahead and talk a little bit about each + + + align:start position:0% +ahead and talk a little bit about each +of the meetings um so the starting the + + align:start position:0% +of the meetings um so the starting the + + + align:start position:0% +of the meetings um so the starting the +Sprint planning meeting which you've + + align:start position:0% +Sprint planning meeting which you've + + + align:start position:0% +Sprint planning meeting which you've +actually already mostly done right um we + + align:start position:0% +actually already mostly done right um we + + + align:start position:0% +actually already mostly done right um we +will do it in class on youve already + + align:start position:0% +will do it in class on youve already + + + align:start position:0% +will do it in class on youve already +done a good chunk of that which is + + align:start position:0% +done a good chunk of that which is + + + align:start position:0% +done a good chunk of that which is +making the product backlog we're going + + align:start position:0% +making the product backlog we're going + + + align:start position:0% +making the product backlog we're going +to do this on Monday we're actually + + align:start position:0% +to do this on Monday we're actually + + + align:start position:0% +to do this on Monday we're actually +going to go ahead and take your product + + align:start position:0% +going to go ahead and take your product + + + align:start position:0% +going to go ahead and take your product +backlog and break it down into a Sprint + + align:start position:0% +backlog and break it down into a Sprint + + + align:start position:0% +backlog and break it down into a Sprint +task list and start making tasks so we + + align:start position:0% +task list and start making tasks so we + + + align:start position:0% +task list and start making tasks so we +will have a in-class Sprint planning + + align:start position:0% +will have a in-class Sprint planning + + + align:start position:0% +will have a in-class Sprint planning +meeting for your next Sprint next week + + align:start position:0% +meeting for your next Sprint next week + + + align:start position:0% +meeting for your next Sprint next week +um but a Sprint planning meeting sets + + align:start position:0% +um but a Sprint planning meeting sets + + + align:start position:0% +um but a Sprint planning meeting sets +the team's goals for the + + align:start position:0% +the team's goals for the + + + align:start position:0% +the team's goals for the +Sprint um and has the deliverable its + + align:start position:0% +Sprint um and has the deliverable its + + + align:start position:0% +Sprint um and has the deliverable its +goal of a Sprint backlog and an + + align:start position:0% +goal of a Sprint backlog and an + + + align:start position:0% +goal of a Sprint backlog and an +estimated task list for the Sprint so + + align:start position:0% +estimated task list for the Sprint so + + + align:start position:0% +estimated task list for the Sprint so +you know exactly how many hours of work + + align:start position:0% +you know exactly how many hours of work + + + align:start position:0% +you know exactly how many hours of work +you think you are going to get done over + + align:start position:0% +you think you are going to get done over + + + align:start position:0% +you think you are going to get done over +the next week um and it is time box to + + align:start position:0% +the next week um and it is time box to + + + align:start position:0% +the next week um and it is time box to +one to two hours for a team your size 1 + + align:start position:0% +one to two hours for a team your size 1 + + + align:start position:0% +one to two hours for a team your size 1 +hour is probably good for an + + align:start position:0% +hour is probably good for an + + + align:start position:0% +hour is probably good for an +inexperienced team your size one and a + + align:start position:0% +inexperienced team your size one and a + + + align:start position:0% +inexperienced team your size one and a +half hours might actually better + + align:start position:0% +half hours might actually better + + + align:start position:0% +half hours might actually better +um so the better you the the more you do + + align:start position:0% +um so the better you the the more you do + + + align:start position:0% +um so the better you the the more you do +this the faster you get at it because + + align:start position:0% +this the faster you get at it because + + + align:start position:0% +this the faster you get at it because +the easier it + + align:start position:0% +the easier it + + + align:start position:0% +the easier it +gets + + align:start position:0% +gets + + + align:start position:0% +gets +um at the end of the Sprint on the very + + align:start position:0% +um at the end of the Sprint on the very + + + align:start position:0% +um at the end of the Sprint on the very +on the other side of it is the Sprint + + align:start position:0% +on the other side of it is the Sprint + + + align:start position:0% +on the other side of it is the Sprint +review meeting um it has the + + align:start position:0% +review meeting um it has the + + + align:start position:0% +review meeting um it has the +deliverables of demonstrating your + + align:start position:0% +deliverables of demonstrating your + + + align:start position:0% +deliverables of demonstrating your +working product in this case your + + align:start position:0% +working product in this case your + + + align:start position:0% +working product in this case your +finished project two um it is a chance + + align:start position:0% +finished project two um it is a chance + + + align:start position:0% +finished project two um it is a chance +for you to for your team to stop and + + align:start position:0% +for you to for your team to stop and + + + align:start position:0% +for you to for your team to stop and +review and evaluate your product and + + align:start position:0% +review and evaluate your product and + + + align:start position:0% +review and evaluate your product and +decide if that's actually what you want + + align:start position:0% +decide if that's actually what you want + + + align:start position:0% +decide if that's actually what you want +if you have clients to go ahead and say + + align:start position:0% +if you have clients to go ahead and say + + + align:start position:0% +if you have clients to go ahead and say +yes that's what we want keep working in + + align:start position:0% +yes that's what we want keep working in + + + align:start position:0% +yes that's what we want keep working in +that direction or to say oh my gosh this + + align:start position:0% +that direction or to say oh my gosh this + + + align:start position:0% +that direction or to say oh my gosh this +is exactly not what we were thinking of + + align:start position:0% +is exactly not what we were thinking of + + + align:start position:0% +is exactly not what we were thinking of +quick change everything um so the other + + align:start position:0% +quick change everything um so the other + + + align:start position:0% +quick change everything um so the other +thing you do in the Sprint review + + align:start position:0% +thing you do in the Sprint review + + + align:start position:0% +thing you do in the Sprint review +meeting after you review the product is + + align:start position:0% +meeting after you review the product is + + + align:start position:0% +meeting after you review the product is +change and update your product backlog + + align:start position:0% +change and update your product backlog + + + align:start position:0% +change and update your product backlog +because it may be some of the features + + align:start position:0% +because it may be some of the features + + + align:start position:0% +because it may be some of the features +that you thought were really important + + align:start position:0% +that you thought were really important + + + align:start position:0% +that you thought were really important +before you went into the Sprint have + + align:start position:0% +before you went into the Sprint have + + + align:start position:0% +before you went into the Sprint have +turned out to be less important or it + + align:start position:0% +turned out to be less important or it + + + align:start position:0% +turned out to be less important or it +might be that you thought of five new + + align:start position:0% +might be that you thought of five new + + + align:start position:0% +might be that you thought of five new +features that you really need to put + + align:start position:0% +features that you really need to put + + + align:start position:0% +features that you really need to put +into the game and that it's worth + + align:start position:0% +into the game and that it's worth + + + align:start position:0% +into the game and that it's worth +cutting some of the other features you + + align:start position:0% +cutting some of the other features you + + + align:start position:0% +cutting some of the other features you +already had on the list um so the Sprint + + align:start position:0% +already had on the list um so the Sprint + + + align:start position:0% +already had on the list um so the Sprint +review meeting sets up your Sprint + + align:start position:0% +review meeting sets up your Sprint + + + align:start position:0% +review meeting sets up your Sprint +planning meeting by getting your product + + align:start position:0% +planning meeting by getting your product + + + align:start position:0% +planning meeting by getting your product +backlog in shape to go and prepare for + + align:start position:0% +backlog in shape to go and prepare for + + + align:start position:0% +backlog in shape to go and prepare for +the next Sprint it also is time boxed um + + align:start position:0% +the next Sprint it also is time boxed um + + + align:start position:0% +the next Sprint it also is time boxed um +to about one hour again for a team year + + align:start position:0% +to about one hour again for a team year + + + align:start position:0% +to about one hour again for a team year +size um the other end of the other end + + align:start position:0% +size um the other end of the other end + + + align:start position:0% +size um the other end of the other end +of Sprint meeting is the retrospective + + align:start position:0% +of Sprint meeting is the retrospective + + + align:start position:0% +of Sprint meeting is the retrospective +which is not the same as the Sprint + + align:start position:0% +which is not the same as the Sprint + + + align:start position:0% +which is not the same as the Sprint +review a lot of teams try to smash a + + align:start position:0% +review a lot of teams try to smash a + + + align:start position:0% +review a lot of teams try to smash a +Sprint review meeting and a + + align:start position:0% +Sprint review meeting and a + + + align:start position:0% +Sprint review meeting and a +retrospective meeting into the same one + + align:start position:0% +retrospective meeting into the same one + + + align:start position:0% +retrospective meeting into the same one +and they have very different purposes + + align:start position:0% +and they have very different purposes + + + align:start position:0% +and they have very different purposes +the Sprint review meeting is all about + + align:start position:0% +the Sprint review meeting is all about + + + align:start position:0% +the Sprint review meeting is all about +reviewing your product the retrospective + + align:start position:0% +reviewing your product the retrospective + + + align:start position:0% +reviewing your product the retrospective +is about reviewing your process it's + + align:start position:0% +is about reviewing your process it's + + + align:start position:0% +is about reviewing your process it's +about talking about the + + align:start position:0% +about talking about the + + + align:start position:0% +about talking about the +team um ideally it kind of recognizes + + align:start position:0% +team um ideally it kind of recognizes + + + align:start position:0% +team um ideally it kind of recognizes +the things that went right the things + + align:start position:0% +the things that went right the things + + + align:start position:0% +the things that went right the things +that went wrong and generates a short + + align:start position:0% +that went wrong and generates a short + + + align:start position:0% +that went wrong and generates a short +list um at least one or two items of + + align:start position:0% +list um at least one or two items of + + + align:start position:0% +list um at least one or two items of +things to do differently next time + + align:start position:0% +things to do differently next time + + + align:start position:0% +things to do differently next time +because they will improve the things + + align:start position:0% +because they will improve the things + + + align:start position:0% +because they will improve the things +that happened + + align:start position:0% +that happened + + + align:start position:0% +that happened +um so it's it's a forward-looking + + align:start position:0% +um so it's it's a forward-looking + + + align:start position:0% +um so it's it's a forward-looking +meeting despite its name its the name is + + align:start position:0% +meeting despite its name its the name is + + + align:start position:0% +meeting despite its name its the name is +retrospective it's looking back at what + + align:start position:0% +retrospective it's looking back at what + + + align:start position:0% +retrospective it's looking back at what +happened in the past to see what you can + + align:start position:0% +happened in the past to see what you can + + + align:start position:0% +happened in the past to see what you can +do better in the future if you do your + + align:start position:0% +do better in the future if you do your + + + align:start position:0% +do better in the future if you do your +team retrospective well it actually will + + align:start position:0% +team retrospective well it actually will + + + align:start position:0% +team retrospective well it actually will +be a lot of what we're asking for in our + + align:start position:0% +be a lot of what we're asking for in our + + + align:start position:0% +be a lot of what we're asking for in our +postmortem writeups because really + + align:start position:0% +postmortem writeups because really + + + align:start position:0% +postmortem writeups because really +that's what we're that's what we're + + align:start position:0% +that's what we're that's what we're + + + align:start position:0% +that's what we're that's what we're +looking for in the post-mortems is + + align:start position:0% +looking for in the post-mortems is + + + align:start position:0% +looking for in the post-mortems is +understanding what you did why you did + + align:start position:0% +understanding what you did why you did + + + align:start position:0% +understanding what you did why you did +it how it could be improved um we want + + align:start position:0% +it how it could be improved um we want + + + align:start position:0% +it how it could be improved um we want +to know what sinkholes you fell into and + + align:start position:0% +to know what sinkholes you fell into and + + + align:start position:0% +to know what sinkholes you fell into and +how you climbed out of them and how you + + align:start position:0% +how you climbed out of them and how you + + + align:start position:0% +how you climbed out of them and how you +would build a bridge over the sinkhole + + align:start position:0% +would build a bridge over the sinkhole + + + align:start position:0% +would build a bridge over the sinkhole +next time so you don't fall into + + align:start position:0% + + + + align:start position:0% + +it finally there's the daily scrum and + + align:start position:0% +it finally there's the daily scrum and + + + align:start position:0% +it finally there's the daily scrum and +this is the meeting that happens + + align:start position:0% +this is the meeting that happens + + + align:start position:0% +this is the meeting that happens +regularly over the Sprint every day or + + align:start position:0% +regularly over the Sprint every day or + + + align:start position:0% +regularly over the Sprint every day or +if your team is not meeting every day + + align:start position:0% +if your team is not meeting every day + + + align:start position:0% +if your team is not meeting every day +every time your team meets um so the + + align:start position:0% +every time your team meets um so the + + + align:start position:0% +every time your team meets um so the +daily scrum the goal of the daily scrum + + align:start position:0% +daily scrum the goal of the daily scrum + + + align:start position:0% +daily scrum the goal of the daily scrum +is to keep the team accountable to each + + align:start position:0% +is to keep the team accountable to each + + + align:start position:0% +is to keep the team accountable to each +other and to encourage communication + + align:start position:0% +other and to encourage communication + + + align:start position:0% +other and to encourage communication +across the team um if everyone's being + + align:start position:0% +across the team um if everyone's being + + + align:start position:0% +across the team um if everyone's being +honest at the daily scrum there's really + + align:start position:0% +honest at the daily scrum there's really + + + align:start position:0% +honest at the daily scrum there's really +no excuse for anyone to not know the + + align:start position:0% +no excuse for anyone to not know the + + + align:start position:0% +no excuse for anyone to not know the +full state of the project um especially + + align:start position:0% +full state of the project um especially + + + align:start position:0% +full state of the project um especially +when it's combined with a a scrum board + + align:start position:0% +when it's combined with a a scrum board + + + align:start position:0% +when it's combined with a a scrum board +with all the tasks up um daily scrums + + align:start position:0% +with all the tasks up um daily scrums + + + align:start position:0% +with all the tasks up um daily scrums +are also actually called daily standups + + align:start position:0% +are also actually called daily standups + + + align:start position:0% +are also actually called daily standups +because a lot of teams do them standing + + align:start position:0% +because a lot of teams do them standing + + + align:start position:0% +because a lot of teams do them standing +up in order to keep them + + align:start position:0% +up in order to keep them + + + align:start position:0% +up in order to keep them +short + + align:start position:0% +short + + + align:start position:0% +short +um classically It's Time boxed at 15 + + align:start position:0% +um classically It's Time boxed at 15 + + + align:start position:0% +um classically It's Time boxed at 15 +minutes for teams your size 5 to six + + align:start position:0% +minutes for teams your size 5 to six + + + align:start position:0% +minutes for teams your size 5 to six +minutes is probably actually enough + + align:start position:0% +minutes is probably actually enough + + + align:start position:0% +minutes is probably actually enough +because all each person has to do is + + align:start position:0% +because all each person has to do is + + + align:start position:0% +because all each person has to do is +stand stand up and answer these three + + align:start position:0% +stand stand up and answer these three + + + align:start position:0% +stand stand up and answer these three +questions um what did you do yesterday + + align:start position:0% +questions um what did you do yesterday + + + align:start position:0% +questions um what did you do yesterday +or since our last meeting so what have + + align:start position:0% +or since our last meeting so what have + + + align:start position:0% +or since our last meeting so what have +you gotten done um what are you going to + + align:start position:0% +you gotten done um what are you going to + + + align:start position:0% +you gotten done um what are you going to +do today what's on your task list and + + align:start position:0% +do today what's on your task list and + + + align:start position:0% +do today what's on your task list and +finally what is keeping you from getting + + align:start position:0% +finally what is keeping you from getting + + + align:start position:0% +finally what is keeping you from getting +things + + align:start position:0% +things + + + align:start position:0% +things +done um What's blocking you how come you + + align:start position:0% +done um What's blocking you how come you + + + align:start position:0% +done um What's blocking you how come you +can't get things done and sometimes the + + align:start position:0% +can't get things done and sometimes the + + + align:start position:0% +can't get things done and sometimes the +answer is nothing and sometimes the + + align:start position:0% +answer is nothing and sometimes the + + + align:start position:0% +answer is nothing and sometimes the +answer is something in which case it + + align:start position:0% +answer is something in which case it + + + align:start position:0% +answer is something in which case it +needs to get dealt with the place where + + align:start position:0% +needs to get dealt with the place where + + + align:start position:0% +needs to get dealt with the place where +daily scrums often go wrong and end up + + align:start position:0% +daily scrums often go wrong and end up + + + align:start position:0% +daily scrums often go wrong and end up +taking longer than their 5 minutes or 15 + + align:start position:0% +taking longer than their 5 minutes or 15 + + + align:start position:0% +taking longer than their 5 minutes or 15 +minutes is when people start mentioning + + align:start position:0% +minutes is when people start mentioning + + + align:start position:0% +minutes is when people start mentioning +what they're being blocked by and + + align:start position:0% +what they're being blocked by and + + + align:start position:0% +what they're being blocked by and +everyone jumps in to help them solve the + + align:start position:0% +everyone jumps in to help them solve the + + + align:start position:0% +everyone jumps in to help them solve the +problem that's not actually what you do + + align:start position:0% +problem that's not actually what you do + + + align:start position:0% +problem that's not actually what you do +at a daily scrum you don't solve the + + align:start position:0% +at a daily scrum you don't solve the + + + align:start position:0% +at a daily scrum you don't solve the +problem with the daily scrum you mention + + align:start position:0% +problem with the daily scrum you mention + + + align:start position:0% +problem with the daily scrum you mention +it someone makes a note of it so + + align:start position:0% +it someone makes a note of it so + + + align:start position:0% +it someone makes a note of it so +everyone's aware of it you get the + + align:start position:0% +everyone's aware of it you get the + + + align:start position:0% +everyone's aware of it you get the +meeting over and then the people who + + align:start position:0% +meeting over and then the people who + + + align:start position:0% +meeting over and then the people who +actually need to be involved to solve + + align:start position:0% +actually need to be involved to solve + + + align:start position:0% +actually need to be involved to solve +the problem talk to solve the problem + + align:start position:0% +the problem talk to solve the problem + + + align:start position:0% +the problem talk to solve the problem +it's once again it's it's invoking that + + align:start position:0% +it's once again it's it's invoking that + + + align:start position:0% +it's once again it's it's invoking that +principle of if you don't need to be at + + align:start position:0% +principle of if you don't need to be at + + + align:start position:0% +principle of if you don't need to be at +a meeting don't be at a meeting right um + + align:start position:0% +a meeting don't be at a meeting right um + + + align:start position:0% +a meeting don't be at a meeting right um +so that is my comment on daily scrums + + align:start position:0% +so that is my comment on daily scrums + + + align:start position:0% +so that is my comment on daily scrums +and I was going to have you guys try and + + align:start position:0% +and I was going to have you guys try and + + + align:start position:0% +and I was going to have you guys try and +do one today but I actually don't think + + align:start position:0% +do one today but I actually don't think + + + align:start position:0% +do one today but I actually don't think +that would be very useful um I think + + align:start position:0% +that would be very useful um I think + + + align:start position:0% +that would be very useful um I think +you've already really probably done a + + align:start position:0% +you've already really probably done a + + + align:start position:0% +you've already really probably done a +lot of that in sitting down and talking + + align:start position:0% +lot of that in sitting down and talking + + + align:start position:0% +lot of that in sitting down and talking +about your product backlogs so I think I + + align:start position:0% +about your product backlogs so I think I + + + align:start position:0% +about your product backlogs so I think I +would prefer to go ahead and close out + + align:start position:0% +would prefer to go ahead and close out + + + align:start position:0% +would prefer to go ahead and close out +my lecture here and give you the rest of + + align:start position:0% +my lecture here and give you the rest of + + + align:start position:0% +my lecture here and give you the rest of +the hour to continue working on your + + align:start position:0% +the hour to continue working on your + + + align:start position:0% +the hour to continue working on your +teams on your projects one thing we can + + align:start position:0% +teams on your projects one thing we can + + + align:start position:0% +teams on your projects one thing we can +recommend is that since most of your + + align:start position:0% +recommend is that since most of your + + + align:start position:0% +recommend is that since most of your +teams seem to be planning a meeting up + + align:start position:0% +teams seem to be planning a meeting up + + + align:start position:0% +teams seem to be planning a meeting up +sometime between now and Monday and I + + align:start position:0% +sometime between now and Monday and I + + + align:start position:0% +sometime between now and Monday and I +will suddenly encourage that plan to do + + align:start position:0% +will suddenly encourage that plan to do + + + align:start position:0% +will suddenly encourage that plan to do +this during that next meeting yes it's + + align:start position:0% +this during that next meeting yes it's + + + align:start position:0% +this during that next meeting yes it's +on a weekend if it's on Friday if it's + + align:start position:0% +on a weekend if it's on Friday if it's + + + align:start position:0% +on a weekend if it's on Friday if it's +tomorrow whenever that is do this and + + align:start position:0% +tomorrow whenever that is do this and + + + align:start position:0% +tomorrow whenever that is do this and +ask every single person these three + + align:start position:0% +ask every single person these three + + + align:start position:0% +ask every single person these three +questions of and be prepared personally + + align:start position:0% +questions of and be prepared personally + + + align:start position:0% +questions of and be prepared personally +prepared to answer all of these pre + + align:start position:0% +prepared to answer all of these pre + + + align:start position:0% +prepared to answer all of these pre +questions the thing that can be blocking + + align:start position:0% +questions the thing that can be blocking + + + align:start position:0% +questions the thing that can be blocking +you is you've got a horrible head cold + + align:start position:0% +you is you've got a horrible head cold + + + align:start position:0% +you is you've got a horrible head cold +you know uh your computer you know just + + align:start position:0% +you know uh your computer you know just + + + align:start position:0% +you know uh your computer you know just +fried my mine just my my hard drive just + + align:start position:0% +fried my mine just my my hard drive just + + + align:start position:0% +fried my mine just my my hard drive just +di uh you know uh I can't I have a + + align:start position:0% +di uh you know uh I can't I have a + + + align:start position:0% +di uh you know uh I can't I have a +problem with my with game engine you + + align:start position:0% +problem with my with game engine you + + + align:start position:0% +problem with my with game engine you +know and there's probably somebody else + + align:start position:0% +know and there's probably somebody else + + + align:start position:0% +know and there's probably somebody else +on a team who can help you figure that + + align:start position:0% +on a team who can help you figure that + + + align:start position:0% +on a team who can help you figure that +out be very honest about that could be + + align:start position:0% +out be very honest about that could be + + + align:start position:0% +out be very honest about that could be +in other class is you know giving you + + align:start position:0% +in other class is you know giving you + + + align:start position:0% +in other class is you know giving you +problems that's also a perfectly fine + + align:start position:0% +problems that's also a perfectly fine + + + align:start position:0% +problems that's also a perfectly fine +answer you want your team to know what's + + align:start position:0% +answer you want your team to know what's + + + align:start position:0% +answer you want your team to know what's +preventing you from getting something um + + align:start position:0% +preventing you from getting something um + + + align:start position:0% +preventing you from getting something um +the other thing you should do um over + + align:start position:0% +the other thing you should do um over + + + align:start position:0% +the other thing you should do um over +this weekend and have chosen by the time + + align:start position:0% +this weekend and have chosen by the time + + + align:start position:0% +this weekend and have chosen by the time +you come in on Monday is a scrum Master + + align:start position:0% +you come in on Monday is a scrum Master + + + align:start position:0% +you come in on Monday is a scrum Master +for your + + align:start position:0% +for your + + + align:start position:0% +for your +team and from the instructor's point of + + align:start position:0% +team and from the instructor's point of + + + align:start position:0% +team and from the instructor's point of +view um that's the person who is + + align:start position:0% +view um that's the person who is + + + align:start position:0% +view um that's the person who is +primarily responsible for uploading + + align:start position:0% +primarily responsible for uploading + + + align:start position:0% +primarily responsible for uploading +documents Vision documents product + + align:start position:0% +documents Vision documents product + + + align:start position:0% +documents Vision documents product +backlogs design change logs um making + + align:start position:0% +backlogs design change logs um making + + + align:start position:0% +backlogs design change logs um making +sure that we have a link to your project + + align:start position:0% +sure that we have a link to your project + + + align:start position:0% +sure that we have a link to your project +when the project is done because we + + align:start position:0% +when the project is done because we + + + align:start position:0% +when the project is done because we +don't need everyone on the team to do + + align:start position:0% +don't need everyone on the team to do + + + align:start position:0% +don't need everyone on the team to do +all to do the joint team Turnin we + + align:start position:0% +all to do the joint team Turnin we + + + align:start position:0% +all to do the joint team Turnin we +really only need one person to do it um + + align:start position:0% +really only need one person to do it um + + + align:start position:0% +really only need one person to do it um +from the team's point of view should be + + align:start position:0% +from the team's point of view should be + + + align:start position:0% +from the team's point of view should be +the person helping you do + + align:start position:0% +the person helping you do + + + align:start position:0% +the person helping you do +scrum um and that's all I have for today + + align:start position:0% +scrum um and that's all I have for today + + + align:start position:0% +scrum um and that's all I have for today +so do you have anything else Rick um + + align:start position:0% +so do you have anything else Rick um + + + align:start position:0% +so do you have anything else Rick um +deadlines so turn in your vision + + align:start position:0% +deadlines so turn in your vision + + + align:start position:0% +deadlines so turn in your vision +documents the ones you just worked on + + align:start position:0% +documents the ones you just worked on + + + align:start position:0% +documents the ones you just worked on +that you updated with your new team uh + + align:start position:0% +that you updated with your new team uh + + + align:start position:0% +that you updated with your new team uh +turn them into Stellar by the end of + + align:start position:0% +turn them into Stellar by the end of + + + align:start position:0% +turn them into Stellar by the end of +class um I was telling people since we + + align:start position:0% +class um I was telling people since we + + + align:start position:0% +class um I was telling people since we +had the date wrong in case something + + align:start position:0% +had the date wrong in case something + + + align:start position:0% +had the date wrong in case something +went horribly R they had until the end + + align:start position:0% +went horribly R they had until the end + + + align:start position:0% +went horribly R they had until the end +of the day today if I were + + align:start position:0% +of the day today if I were + + + align:start position:0% +of the day today if I were +to rather be the original PowerPoint + + align:start position:0% +to rather be the original PowerPoint + + + align:start position:0% +to rather be the original PowerPoint +leure or PDF slide of not both you get + + align:start position:0% + + + + align:start position:0% + +might + + align:start position:0% +might + + + align:start position:0% +might +not but it's open \ No newline at end of file diff --git a/VT2o4KCEbes.txt b/VT2o4KCEbes.txt new file mode 100644 index 0000000000000000000000000000000000000000..26ebf10f8b3333adf8bb0e459993537f5c6771fc --- /dev/null +++ b/VT2o4KCEbes.txt @@ -0,0 +1,12707 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay let's get started I hope everybody + + align:start position:0% +okay let's get started I hope everybody + + + align:start position:0% +okay let's get started I hope everybody +had a great long weekend so I'm teaching + + align:start position:0% +had a great long weekend so I'm teaching + + + align:start position:0% +had a great long weekend so I'm teaching +today and today we're gonna be talking + + align:start position:0% +today and today we're gonna be talking + + + align:start position:0% +today and today we're gonna be talking +about transactions so just to recap + + align:start position:0% +about transactions so just to recap + + + align:start position:0% +about transactions so just to recap +where we've been so far + + align:start position:0% +where we've been so far + + + align:start position:0% +where we've been so far +taja's sort of explained signatures in + + align:start position:0% +taja's sort of explained signatures in + + + align:start position:0% +taja's sort of explained signatures in +Bitcoin in particular RSA and ECDSA and + + align:start position:0% +Bitcoin in particular RSA and ECDSA and + + + align:start position:0% +Bitcoin in particular RSA and ECDSA and +told us a little bit about Merkle trees + + align:start position:0% +told us a little bit about Merkle trees + + + align:start position:0% +told us a little bit about Merkle trees +and so these are some of the underlying + + align:start position:0% +and so these are some of the underlying + + + align:start position:0% +and so these are some of the underlying +primitives that we need to know about in + + align:start position:0% +primitives that we need to know about in + + + align:start position:0% +primitives that we need to know about in +order to understand how most of the + + align:start position:0% +order to understand how most of the + + + align:start position:0% +order to understand how most of the +block chains today are constructed okay + + align:start position:0% +block chains today are constructed okay + + + align:start position:0% +block chains today are constructed okay +so we spent a bit of time talking about + + align:start position:0% +so we spent a bit of time talking about + + + align:start position:0% +so we spent a bit of time talking about +the underlying primitives now let's + + align:start position:0% +the underlying primitives now let's + + + align:start position:0% +the underlying primitives now let's +start to put them together a little bit + + align:start position:0% +start to put them together a little bit + + + align:start position:0% +start to put them together a little bit +and to understand what goes into a + + align:start position:0% +and to understand what goes into a + + + align:start position:0% +and to understand what goes into a +blockchain so if you recall this is a + + align:start position:0% +blockchain so if you recall this is a + + + align:start position:0% +blockchain so if you recall this is a +slide that had just shown before and I'm + + align:start position:0% +slide that had just shown before and I'm + + + align:start position:0% +slide that had just shown before and I'm +really sorry about this quadrant but I + + align:start position:0% +really sorry about this quadrant but I + + + align:start position:0% +really sorry about this quadrant but I +don't know I don't think I could control + + align:start position:0% +don't know I don't think I could control + + + align:start position:0% +don't know I don't think I could control +this individually so we'll definitely + + align:start position:0% +this individually so we'll definitely + + + align:start position:0% +this individually so we'll definitely +post the slides of course but let me + + align:start position:0% +post the slides of course but let me + + + align:start position:0% +post the slides of course but let me +know if something is really confusing + + align:start position:0% +know if something is really confusing + + + align:start position:0% +know if something is really confusing +just raise your hand so this is + + align:start position:0% +just raise your hand so this is + + + align:start position:0% +just raise your hand so this is +something that you guys have seen before + + align:start position:0% +something that you guys have seen before + + + align:start position:0% +something that you guys have seen before +and it's like a very sort of rough + + align:start position:0% +and it's like a very sort of rough + + + align:start position:0% +and it's like a very sort of rough +approximation of a hash chain okay so + + align:start position:0% +approximation of a hash chain okay so + + + align:start position:0% +approximation of a hash chain okay so +what we have here is we have this + + align:start position:0% +what we have here is we have this + + + align:start position:0% +what we have here is we have this +doesn't actually show the previous but + + align:start position:0% +doesn't actually show the previous but + + + align:start position:0% +doesn't actually show the previous but +what we have here is we have some + + align:start position:0% +what we have here is we have some + + + align:start position:0% +what we have here is we have some +message we have an on such that when you + + align:start position:0% +message we have an on such that when you + + + align:start position:0% +message we have an on such that when you +hash these three things together you get + + align:start position:0% +hash these three things together you get + + + align:start position:0% +hash these three things together you get +this hash value which has a certain + + align:start position:0% +this hash value which has a certain + + + align:start position:0% +this hash value which has a certain +number of leading zeros at the beginning + + align:start position:0% +number of leading zeros at the beginning + + + align:start position:0% +number of leading zeros at the beginning +in this case it's two leading zeros and + + align:start position:0% +in this case it's two leading zeros and + + + align:start position:0% +in this case it's two leading zeros and +when we construct the next block we + + align:start position:0% +when we construct the next block we + + + align:start position:0% +when we construct the next block we +point to implicitly point to this + + align:start position:0% +point to implicitly point to this + + + align:start position:0% +point to implicitly point to this +previous block by including that hash + + align:start position:0% +previous block by including that hash + + + align:start position:0% +previous block by including that hash +inside of this when we produce this hash + + align:start position:0% +inside of this when we produce this hash + + + align:start position:0% +inside of this when we produce this hash +so note that there isn't actually a + + align:start position:0% +so note that there isn't actually a + + + align:start position:0% +so note that there isn't actually a +physical pointer or memory address + + align:start position:0% +physical pointer or memory address + + + align:start position:0% +physical pointer or memory address +pointer type thing connecting these two + + align:start position:0% +pointer type thing connecting these two + + + align:start position:0% +pointer type thing connecting these two +things together and note that this block + + align:start position:0% +things together and note that this block + + + align:start position:0% +things together and note that this block +does not actually contain the hash of + + align:start position:0% +does not actually contain the hash of + + + align:start position:0% +does not actually contain the hash of +itself but we are sort of implicitly + + align:start position:0% +itself but we are sort of implicitly + + + align:start position:0% +itself but we are sort of implicitly +pointing to this by including the hash + + align:start position:0% +pointing to this by including the hash + + + align:start position:0% +pointing to this by including the hash +of this block in the following block + + align:start position:0% +of this block in the following block + + + align:start position:0% +of this block in the following block +okay and so on over here again this is a + + align:start position:0% +okay and so on over here again this is a + + + align:start position:0% +okay and so on over here again this is a +different message at different knots and + + align:start position:0% +different message at different knots and + + + align:start position:0% +different message at different knots and +it includes the hash of this block + + align:start position:0% +it includes the hash of this block + + + align:start position:0% +it includes the hash of this block +instead of the one before and by + + align:start position:0% +instead of the one before and by + + + align:start position:0% +instead of the one before and by +including the hash of this block it's + + align:start position:0% +including the hash of this block it's + + + align:start position:0% +including the hash of this block it's +also implicitly including the hash of + + align:start position:0% +also implicitly including the hash of + + + align:start position:0% +also implicitly including the hash of +this block because that's right here and + + align:start position:0% +this block because that's right here and + + + align:start position:0% +this block because that's right here and +what we're gonna see is that if you + + align:start position:0% +what we're gonna see is that if you + + + align:start position:0% +what we're gonna see is that if you +change anything about the previous + + align:start position:0% +change anything about the previous + + + align:start position:0% +change anything about the previous +blocks in the blockchain for example if + + align:start position:0% +blocks in the blockchain for example if + + + align:start position:0% +blocks in the blockchain for example if +you changed this message then you know + + align:start position:0% +you changed this message then you know + + + align:start position:0% +you changed this message then you know +you're going to need to change the knots + + align:start position:0% +you're going to need to change the knots + + + align:start position:0% +you're going to need to change the knots +in order to get the hash to compute + + align:start position:0% +in order to get the hash to compute + + + align:start position:0% +in order to get the hash to compute +right it's gonna be a different hash and + + align:start position:0% +right it's gonna be a different hash and + + + align:start position:0% +right it's gonna be a different hash and +that change is gonna trickle down + + align:start position:0% +that change is gonna trickle down + + + align:start position:0% +that change is gonna trickle down +through the entire blockchain and so + + align:start position:0% +through the entire blockchain and so + + + align:start position:0% +through the entire blockchain and so +that's what makes these things what we + + align:start position:0% +that's what makes these things what we + + + align:start position:0% +that's what makes these things what we +call tamper proof the fact that there + + align:start position:0% +call tamper proof the fact that there + + + align:start position:0% +call tamper proof the fact that there +are these hashes these hashes are + + align:start position:0% +are these hashes these hashes are + + + align:start position:0% +are these hashes these hashes are +collision collision resistant and so + + align:start position:0% +collision collision resistant and so + + + align:start position:0% +collision collision resistant and so +it's very difficult you can't really + + align:start position:0% +it's very difficult you can't really + + + align:start position:0% +it's very difficult you can't really +compute something out you can't change + + align:start position:0% +compute something out you can't change + + + align:start position:0% +compute something out you can't change +what's in the past without having it + + align:start position:0% +what's in the past without having it + + + align:start position:0% +what's in the past without having it +reflected in the future so now let's go + + align:start position:0% +reflected in the future so now let's go + + + align:start position:0% +reflected in the future so now let's go +into a little bit more detail about + + align:start position:0% +into a little bit more detail about + + + align:start position:0% +into a little bit more detail about +exactly what this message thing is okay + + align:start position:0% +exactly what this message thing is okay + + + align:start position:0% +exactly what this message thing is okay +we've talked about the previous hash + + align:start position:0% +we've talked about the previous hash + + + align:start position:0% +we've talked about the previous hash +pointers we've talked about the nonce + + align:start position:0% +pointers we've talked about the nonce + + + align:start position:0% +pointers we've talked about the nonce +we've talked about proof of work but + + align:start position:0% +we've talked about proof of work but + + + align:start position:0% +we've talked about proof of work but +what actually goes inside of a block + + align:start position:0% +what actually goes inside of a block + + + align:start position:0% +what actually goes inside of a block +well we have this general we've kind of + + align:start position:0% +well we have this general we've kind of + + + align:start position:0% +well we have this general we've kind of +been alluding to it but what goes inside + + align:start position:0% +been alluding to it but what goes inside + + + align:start position:0% +been alluding to it but what goes inside +a block are transactions we're trying to + + align:start position:0% +a block are transactions we're trying to + + + align:start position:0% +a block are transactions we're trying to +build a payment system here so what do + + align:start position:0% +build a payment system here so what do + + + align:start position:0% +build a payment system here so what do +we need to have in a transaction what + + align:start position:0% +we need to have in a transaction what + + + align:start position:0% +we need to have in a transaction what +should a transaction look like yes okay + + align:start position:0% +should a transaction look like yes okay + + + align:start position:0% +should a transaction look like yes okay +inputs and outputs maybe even like a + + align:start position:0% +inputs and outputs maybe even like a + + + align:start position:0% +inputs and outputs maybe even like a +higher level here like semantically what + + align:start position:0% +higher level here like semantically what + + + align:start position:0% +higher level here like semantically what +do we want in a transaction yep okay a + + align:start position:0% +do we want in a transaction yep okay a + + + align:start position:0% +do we want in a transaction yep okay a +sender a receiver an amount anybody else + + align:start position:0% +sender a receiver an amount anybody else + + + align:start position:0% +sender a receiver an amount anybody else +okay an ID some way of referencing it + + align:start position:0% +okay an ID some way of referencing it + + + align:start position:0% +okay an ID some way of referencing it +anybody else + + align:start position:0% +anybody else + + + align:start position:0% +anybody else +yep + + align:start position:0% + + + + align:start position:0% + +a proof that it's a legit transaction + + align:start position:0% +a proof that it's a legit transaction + + + align:start position:0% +a proof that it's a legit transaction +right so um exactly so what we need is + + align:start position:0% +right so um exactly so what we need is + + + align:start position:0% +right so um exactly so what we need is +those things that you guys just said we + + align:start position:0% +those things that you guys just said we + + + align:start position:0% +those things that you guys just said we +need to know the amount how much of this + + align:start position:0% +need to know the amount how much of this + + + align:start position:0% +need to know the amount how much of this +coin we're transferring we need to know + + align:start position:0% +coin we're transferring we need to know + + + align:start position:0% +coin we're transferring we need to know +where it's coming from and in particular + + align:start position:0% +where it's coming from and in particular + + + align:start position:0% +where it's coming from and in particular +we need an authorization of some sort + + align:start position:0% +we need an authorization of some sort + + + align:start position:0% +we need an authorization of some sort +that that user actually authorized the + + align:start position:0% +that that user actually authorized the + + + align:start position:0% +that that user actually authorized the +spend and we need who were paying and so + + align:start position:0% +spend and we need who were paying and so + + + align:start position:0% +spend and we need who were paying and so +unfortunately this is in the dark part + + align:start position:0% +unfortunately this is in the dark part + + + align:start position:0% +unfortunately this is in the dark part +but this is sort of like you know a + + align:start position:0% +but this is sort of like you know a + + + align:start position:0% +but this is sort of like you know a +little rough sketch of a transaction and + + align:start position:0% +little rough sketch of a transaction and + + + align:start position:0% +little rough sketch of a transaction and +we have Alice who's spending $5 to Bob + + align:start position:0% +we have Alice who's spending $5 to Bob + + + align:start position:0% +we have Alice who's spending $5 to Bob +and we have this authorization here + + align:start position:0% +and we have this authorization here + + + align:start position:0% +and we have this authorization here +okay and this authorization given we + + align:start position:0% +okay and this authorization given we + + + align:start position:0% +okay and this authorization given we +just learned about signatures signatures + + align:start position:0% +just learned about signatures signatures + + + align:start position:0% +just learned about signatures signatures +are a great way to do authorization + + align:start position:0% +are a great way to do authorization + + + align:start position:0% +are a great way to do authorization +because it's something that only Alice + + align:start position:0% +because it's something that only Alice + + + align:start position:0% +because it's something that only Alice +can produce right so um I don't know if + + align:start position:0% +can produce right so um I don't know if + + + align:start position:0% +can produce right so um I don't know if +you can see this but there question + + align:start position:0% +you can see this but there question + + + align:start position:0% +you can see this but there question +marks here so what should Alice sign to + + align:start position:0% +marks here so what should Alice sign to + + + align:start position:0% +marks here so what should Alice sign to +show that she authorized this + + align:start position:0% +show that she authorized this + + + align:start position:0% +show that she authorized this +transaction what do you think would be a + + align:start position:0% +transaction what do you think would be a + + + align:start position:0% +transaction what do you think would be a +good thing what is a good message for + + align:start position:0% +good thing what is a good message for + + + align:start position:0% +good thing what is a good message for +her to sign for her to indicate her + + align:start position:0% +her to sign for her to indicate her + + + align:start position:0% +her to sign for her to indicate her +authority her her desire to produce this + + align:start position:0% +authority her her desire to produce this + + + align:start position:0% +authority her her desire to produce this +transaction and spend her funds her + + align:start position:0% +transaction and spend her funds her + + + align:start position:0% +transaction and spend her funds her +private key she should sign her private + + align:start position:0% +private key she should sign her private + + + align:start position:0% +private key she should sign her private +key okay the whole transaction okay so + + align:start position:0% +key okay the whole transaction okay so + + + align:start position:0% +key okay the whole transaction okay so +let's talk about signing the private key + + align:start position:0% +let's talk about signing the private key + + + align:start position:0% +let's talk about signing the private key +let's say that she did sign her private + + align:start position:0% +let's say that she did sign her private + + + align:start position:0% +let's say that she did sign her private +key okay the problem with a signature is + + align:start position:0% +key okay the problem with a signature is + + + align:start position:0% +key okay the problem with a signature is +that in order to tell if the signatures + + align:start position:0% +that in order to tell if the signatures + + + align:start position:0% +that in order to tell if the signatures +valid you need the thing that you signed + + align:start position:0% +valid you need the thing that you signed + + + align:start position:0% +valid you need the thing that you signed +so she would have to include her private + + align:start position:0% +so she would have to include her private + + + align:start position:0% +so she would have to include her private +key which would then share her private + + align:start position:0% +key which would then share her private + + + align:start position:0% +key which would then share her private +key with everyone which isn't really a + + align:start position:0% +key with everyone which isn't really a + + + align:start position:0% +key with everyone which isn't really a +good way for her to use her public and + + align:start position:0% +good way for her to use her public and + + + align:start position:0% +good way for her to use her public and +private key she couldn't certainly sign + + align:start position:0% +private key she couldn't certainly sign + + + align:start position:0% +private key she couldn't certainly sign +the transaction and the nice thing about + + align:start position:0% +the transaction and the nice thing about + + + align:start position:0% +the transaction and the nice thing about +signing the transaction this is all blue + + align:start position:0% +signing the transaction this is all blue + + + align:start position:0% +signing the transaction this is all blue +indicating that she's signing it is that + + align:start position:0% +indicating that she's signing it is that + + + align:start position:0% +indicating that she's signing it is that +she's signing all three of these things + + align:start position:0% +she's signing all three of these things + + + align:start position:0% +she's signing all three of these things +as well right she's saying I want to pay + + align:start position:0% +as well right she's saying I want to pay + + + align:start position:0% +as well right she's saying I want to pay +Bob I want to pay Bob five dollars now + + align:start position:0% +Bob I want to pay Bob five dollars now + + + align:start position:0% +Bob I want to pay Bob five dollars now +what's a problem with signing the + + align:start position:0% +what's a problem with signing the + + + align:start position:0% +what's a problem with signing the +transaction yes + + align:start position:0% +transaction yes + + + align:start position:0% +transaction yes +so that is an excellent point you could + + align:start position:0% +so that is an excellent point you could + + + align:start position:0% +so that is an excellent point you could +keep using it if you were Bob and we'll + + align:start position:0% +keep using it if you were Bob and we'll + + + align:start position:0% +keep using it if you were Bob and we'll +get into that a little bit later but + + align:start position:0% +get into that a little bit later but + + + align:start position:0% +get into that a little bit later but +another problem here is the way that + + align:start position:0% +another problem here is the way that + + + align:start position:0% +another problem here is the way that +I've shown it right now she's signing + + align:start position:0% +I've shown it right now she's signing + + + align:start position:0% +I've shown it right now she's signing +the signature the signature is kind of + + align:start position:0% +the signature the signature is kind of + + + align:start position:0% +the signature the signature is kind of +part of the transaction and so you want + + align:start position:0% +part of the transaction and so you want + + + align:start position:0% +part of the transaction and so you want +to make sure that you're you're not you + + align:start position:0% +to make sure that you're you're not you + + + align:start position:0% +to make sure that you're you're not you +know when you sign a transaction you're + + align:start position:0% +know when you sign a transaction you're + + + align:start position:0% +know when you sign a transaction you're +signing everything but the signature + + align:start position:0% +signing everything but the signature + + + align:start position:0% +signing everything but the signature +right because you can't produce the + + align:start position:0% +right because you can't produce the + + + align:start position:0% +right because you can't produce the +signature you can't sign the signature + + align:start position:0% +signature you can't sign the signature + + + align:start position:0% +signature you can't sign the signature +without knowing what the signature is it + + align:start position:0% +without knowing what the signature is it + + + align:start position:0% +without knowing what the signature is it +would be like a whole new type of proof + + align:start position:0% +would be like a whole new type of proof + + + align:start position:0% +would be like a whole new type of proof +of work on the transaction so I don't + + align:start position:0% +of work on the transaction so I don't + + + align:start position:0% +of work on the transaction so I don't +know if you can see this but this says + + align:start position:0% +know if you can see this but this says + + + align:start position:0% +know if you can see this but this says +transaction - signature and in fact you + + align:start position:0% +transaction - signature and in fact you + + + align:start position:0% +transaction - signature and in fact you +know we can even make that a little bit + + align:start position:0% +know we can even make that a little bit + + + align:start position:0% +know we can even make that a little bit +easier by turning that into a hash of + + align:start position:0% +easier by turning that into a hash of + + + align:start position:0% +easier by turning that into a hash of +the transaction not including the + + align:start position:0% +the transaction not including the + + + align:start position:0% +the transaction not including the +signature because that sort of brings a + + align:start position:0% +signature because that sort of brings a + + + align:start position:0% +signature because that sort of brings a +message down to a smaller thing and from + + align:start position:0% +message down to a smaller thing and from + + + align:start position:0% +message down to a smaller thing and from +what we know about hash functions you + + align:start position:0% +what we know about hash functions you + + + align:start position:0% +what we know about hash functions you +can't really given given a message and a + + align:start position:0% +can't really given given a message and a + + + align:start position:0% +can't really given given a message and a +hash of that message it's difficult to + + align:start position:0% +hash of that message it's difficult to + + + align:start position:0% +hash of that message it's difficult to +produce another message that would hash + + align:start position:0% +produce another message that would hash + + + align:start position:0% +produce another message that would hash +to the same thing so this hash serves as + + align:start position:0% +to the same thing so this hash serves as + + + align:start position:0% +to the same thing so this hash serves as +kind of an identifier for the + + align:start position:0% +kind of an identifier for the + + + align:start position:0% +kind of an identifier for the +transaction as a whole in fact Bitcoin + + align:start position:0% +transaction as a whole in fact Bitcoin + + + align:start position:0% +transaction as a whole in fact Bitcoin +uses the hash of this as the transaction + + align:start position:0% +uses the hash of this as the transaction + + + align:start position:0% +uses the hash of this as the transaction +ID so this is how we refer to + + align:start position:0% +ID so this is how we refer to + + + align:start position:0% +ID so this is how we refer to +transactions and it's a nice small thing + + align:start position:0% +transactions and it's a nice small thing + + + align:start position:0% +transactions and it's a nice small thing +to sign which indicates Alice's intent + + align:start position:0% +to sign which indicates Alice's intent + + + align:start position:0% +to sign which indicates Alice's intent +to spend her funds so one thing that I + + align:start position:0% +to spend her funds so one thing that I + + + align:start position:0% +to spend her funds so one thing that I +kind of want to go into a little bit is + + align:start position:0% +kind of want to go into a little bit is + + + align:start position:0% +kind of want to go into a little bit is +that there's a couple different ways for + + align:start position:0% +that there's a couple different ways for + + + align:start position:0% +that there's a couple different ways for +thinking about transactions and what + + align:start position:0% +thinking about transactions and what + + + align:start position:0% +thinking about transactions and what +transactions actually look like and how + + align:start position:0% +transactions actually look like and how + + + align:start position:0% +transactions actually look like and how +they're stored and how we sort of + + align:start position:0% +they're stored and how we sort of + + + align:start position:0% +they're stored and how we sort of +specify coins and to the most natural + + align:start position:0% +specify coins and to the most natural + + + align:start position:0% +specify coins and to the most natural +model to me anyway not to everybody + + align:start position:0% +model to me anyway not to everybody + + + align:start position:0% +model to me anyway not to everybody +perhaps is what I call the account based + + align:start position:0% +perhaps is what I call the account based + + + align:start position:0% +perhaps is what I call the account based +model so it's kind of like what we were + + align:start position:0% +model so it's kind of like what we were + + + align:start position:0% +model so it's kind of like what we were +doing before when we saw the banks and + + align:start position:0% +doing before when we saw the banks and + + + align:start position:0% +doing before when we saw the banks and +we were talking about banks keeping + + align:start position:0% +we were talking about banks keeping + + + align:start position:0% +we were talking about banks keeping +track of how many how much funds people + + align:start position:0% +track of how many how much funds people + + + align:start position:0% +track of how many how much funds people +have and this is sort of how you and I + + align:start position:0% +have and this is sort of how you and I + + + align:start position:0% +have and this is sort of how you and I +might think of our own bank accounts I + + align:start position:0% +might think of our own bank accounts I + + + align:start position:0% +might think of our own bank accounts I +think in my bank account as having a + + align:start position:0% +think in my bank account as having a + + + align:start position:0% +think in my bank account as having a +certain amount of funds in it right and + + align:start position:0% +certain amount of funds in it right and + + + align:start position:0% +certain amount of funds in it right and +so in the account based model users have + + align:start position:0% +so in the account based model users have + + + align:start position:0% +so in the account based model users have +certain amounts or balances associated + + align:start position:0% +certain amounts or balances associated + + + align:start position:0% +certain amounts or balances associated +with their with their user names and + + align:start position:0% +with their with their user names and + + + align:start position:0% +with their with their user names and +when a transaction comes in like Alice + + align:start position:0% +when a transaction comes in like Alice + + + align:start position:0% +when a transaction comes in like Alice +wants to give five dollars to Bob then + + align:start position:0% +wants to give five dollars to Bob then + + + align:start position:0% +wants to give five dollars to Bob then +what might happen is that the the nodes + + align:start position:0% +what might happen is that the the nodes + + + align:start position:0% +what might happen is that the the nodes +and the network which are all + + align:start position:0% +and the network which are all + + + align:start position:0% +and the network which are all +maintaining sort of an in a unified way + + align:start position:0% +maintaining sort of an in a unified way + + + align:start position:0% +maintaining sort of an in a unified way +this balance sheet will end up saying + + align:start position:0% +this balance sheet will end up saying + + + align:start position:0% +this balance sheet will end up saying +okay Alice had ten and Bob had zero + + align:start position:0% +okay Alice had ten and Bob had zero + + + align:start position:0% +okay Alice had ten and Bob had zero +Alice wants to give $5 to Bob let's + + align:start position:0% +Alice wants to give $5 to Bob let's + + + align:start position:0% +Alice wants to give $5 to Bob let's +subtract five from Alice's account and + + align:start position:0% +subtract five from Alice's account and + + + align:start position:0% +subtract five from Alice's account and +give it to Bob and so what the nodes + + align:start position:0% +give it to Bob and so what the nodes + + + align:start position:0% +give it to Bob and so what the nodes +would do here to see if this transaction + + align:start position:0% +would do here to see if this transaction + + + align:start position:0% +would do here to see if this transaction +was valid would be they would check the + + align:start position:0% +was valid would be they would check the + + + align:start position:0% +was valid would be they would check the +signature to make sure that Alice + + align:start position:0% +signature to make sure that Alice + + + align:start position:0% +signature to make sure that Alice +actually authorized this transaction and + + align:start position:0% +actually authorized this transaction and + + + align:start position:0% +actually authorized this transaction and +they would also make sure that Alice had + + align:start position:0% +they would also make sure that Alice had + + + align:start position:0% +they would also make sure that Alice had +the funds to spend and in the account + + align:start position:0% +the funds to spend and in the account + + + align:start position:0% +the funds to spend and in the account +based model the way that you check to + + align:start position:0% +based model the way that you check to + + + align:start position:0% +based model the way that you check to +see if Alice has the funds to spend is + + align:start position:0% +see if Alice has the funds to spend is + + + align:start position:0% +see if Alice has the funds to spend is +you literally look at her balance and + + align:start position:0% +you literally look at her balance and + + + align:start position:0% +you literally look at her balance and +you look at the amount she wants to + + align:start position:0% +you look at the amount she wants to + + + align:start position:0% +you look at the amount she wants to +spend and you make sure that if she + + align:start position:0% +spend and you make sure that if she + + + align:start position:0% +spend and you make sure that if she +spends that amount the balance won't go + + align:start position:0% +spends that amount the balance won't go + + + align:start position:0% +spends that amount the balance won't go +below zero so this is actually the model + + align:start position:0% +below zero so this is actually the model + + + align:start position:0% +below zero so this is actually the model +that aetherium uses it's not the model + + align:start position:0% +that aetherium uses it's not the model + + + align:start position:0% +that aetherium uses it's not the model +that Bitcoin uses so just sort of to + + align:start position:0% +that Bitcoin uses so just sort of to + + + align:start position:0% +that Bitcoin uses so just sort of to +summarize you store a list of accounts + + align:start position:0% +summarize you store a list of accounts + + + align:start position:0% +summarize you store a list of accounts +and balances a transaction is valid if + + align:start position:0% +and balances a transaction is valid if + + + align:start position:0% +and balances a transaction is valid if +there's a balance in the account and + + align:start position:0% +there's a balance in the account and + + + align:start position:0% +there's a balance in the account and +then when a transaction is processed you + + align:start position:0% +then when a transaction is processed you + + + align:start position:0% +then when a transaction is processed you +debit the sender and credit the receiver + + align:start position:0% +debit the sender and credit the receiver + + + align:start position:0% +debit the sender and credit the receiver +so very straightforward now so like I + + align:start position:0% +so very straightforward now so like I + + + align:start position:0% +so very straightforward now so like I +said this is the way that etherium works + + align:start position:0% +said this is the way that etherium works + + + align:start position:0% +said this is the way that etherium works +and it's it's a little bit more natural + + align:start position:0% +and it's it's a little bit more natural + + + align:start position:0% +and it's it's a little bit more natural +I think to think about but this is not + + align:start position:0% +I think to think about but this is not + + + align:start position:0% +I think to think about but this is not +the way Bitcoin works actually Bitcoin + + align:start position:0% +the way Bitcoin works actually Bitcoin + + + align:start position:0% +the way Bitcoin works actually Bitcoin +has a very different model of coins and + + align:start position:0% +has a very different model of coins and + + + align:start position:0% +has a very different model of coins and +of transactions and I I think the you + + align:start position:0% +of transactions and I I think the you + + + align:start position:0% +of transactions and I I think the you +know when I was learning about how + + align:start position:0% +know when I was learning about how + + + align:start position:0% +know when I was learning about how +Bitcoin worked and how aetherium worked + + align:start position:0% +Bitcoin worked and how aetherium worked + + + align:start position:0% +Bitcoin worked and how aetherium worked +I found bitcoins model a little bit + + align:start position:0% +I found bitcoins model a little bit + + + align:start position:0% +I found bitcoins model a little bit +unnatural until I went through this + + align:start position:0% +unnatural until I went through this + + + align:start position:0% +unnatural until I went through this +exercise of thinking about something + + align:start position:0% +exercise of thinking about something + + + align:start position:0% +exercise of thinking about something +called replay attacks and this is what + + align:start position:0% +called replay attacks and this is what + + + align:start position:0% +called replay attacks and this is what +Isan mentioned earlier right which is + + align:start position:0% +Isan mentioned earlier right which is + + + align:start position:0% +Isan mentioned earlier right which is +when you have this transaction and you + + align:start position:0% +when you have this transaction and you + + + align:start position:0% +when you have this transaction and you +know you you send it to the network and + + align:start position:0% +know you you send it to the network and + + + align:start position:0% +know you you send it to the network and +the network processes the transaction + + align:start position:0% +the network processes the transaction + + + align:start position:0% +the network processes the transaction +and debits alice and credits Bob what is + + align:start position:0% +and debits alice and credits Bob what is + + + align:start position:0% +and debits alice and credits Bob what is +to prevent you know a malicious agent + + align:start position:0% +to prevent you know a malicious agent + + + align:start position:0% +to prevent you know a malicious agent +from noticing that transaction and + + align:start position:0% +from noticing that transaction and + + + align:start position:0% +from noticing that transaction and +rebroadcasting it again to the network + + align:start position:0% +rebroadcasting it again to the network + + + align:start position:0% +rebroadcasting it again to the network +so basically repeatedly debiting alice + + align:start position:0% +so basically repeatedly debiting alice + + + align:start position:0% +so basically repeatedly debiting alice +until until she doesn't have any funds + + align:start position:0% +until until she doesn't have any funds + + + align:start position:0% +until until she doesn't have any funds +left so can you guys think of a way to + + align:start position:0% +left so can you guys think of a way to + + + align:start position:0% +left so can you guys think of a way to +maybe get around this what would you do + + align:start position:0% +maybe get around this what would you do + + + align:start position:0% +maybe get around this what would you do +how would you how would you prevent this + + align:start position:0% +how would you how would you prevent this + + + align:start position:0% +how would you how would you prevent this +replay attack yes + + align:start position:0% + + + + align:start position:0% + +so one thing is adding a time sure time + + align:start position:0% +so one thing is adding a time sure time + + + align:start position:0% +so one thing is adding a time sure time +is a little bit tricky because of the + + align:start position:0% +is a little bit tricky because of the + + + align:start position:0% +is a little bit tricky because of the +nature of the system maybe you know but + + align:start position:0% +nature of the system maybe you know but + + + align:start position:0% +nature of the system maybe you know but +but a time is like a pretty good idea a + + align:start position:0% +but a time is like a pretty good idea a + + + align:start position:0% +but a time is like a pretty good idea a +unique number of some kind certainly + + align:start position:0% +unique number of some kind certainly + + + align:start position:0% +unique number of some kind certainly +would help because that way if you saw a + + align:start position:0% +would help because that way if you saw a + + + align:start position:0% +would help because that way if you saw a +transaction with the same unique nut + + align:start position:0% +transaction with the same unique nut + + + align:start position:0% +transaction with the same unique nut +with the same number then you'd know + + align:start position:0% +with the same number then you'd know + + + align:start position:0% +with the same number then you'd know +okay this transaction has been seen + + align:start position:0% +okay this transaction has been seen + + + align:start position:0% +okay this transaction has been seen +before this is a repeat this is a + + align:start position:0% +before this is a repeat this is a + + + align:start position:0% +before this is a repeat this is a +rebroadcast this is not something I + + align:start position:0% +rebroadcast this is not something I + + + align:start position:0% +rebroadcast this is not something I +should process so if you actually does + + align:start position:0% +should process so if you actually does + + + align:start position:0% +should process so if you actually does +something like this there is sort of + + align:start position:0% +something like this there is sort of + + + align:start position:0% +something like this there is sort of +this like this number included in every + + align:start position:0% +this like this number included in every + + + align:start position:0% +this like this number included in every +transaction but the tricky part about + + align:start position:0% +transaction but the tricky part about + + + align:start position:0% +transaction but the tricky part about +the way that aetherium does this and + + align:start position:0% +the way that aetherium does this and + + + align:start position:0% +the way that aetherium does this and +we're gonna learn more about aetherium + + align:start position:0% +we're gonna learn more about aetherium + + + align:start position:0% +we're gonna learn more about aetherium +later on in the course we're gonna have + + align:start position:0% +later on in the course we're gonna have + + + align:start position:0% +later on in the course we're gonna have +a guest lecturer come in and teach us + + align:start position:0% +a guest lecturer come in and teach us + + + align:start position:0% +a guest lecturer come in and teach us +about that is that it requires you to + + align:start position:0% +about that is that it requires you to + + + align:start position:0% +about that is that it requires you to +keep track of all of the numbers you've + + align:start position:0% +keep track of all of the numbers you've + + + align:start position:0% +keep track of all of the numbers you've +seen and you have to do this per user + + align:start position:0% +seen and you have to do this per user + + + align:start position:0% +seen and you have to do this per user +and so all the nodes in the network have + + align:start position:0% +and so all the nodes in the network have + + + align:start position:0% +and so all the nodes in the network have +to keep track of all of the nonces that + + align:start position:0% +to keep track of all of the nonces that + + + align:start position:0% +to keep track of all of the nonces that +they've seen per user and so you know if + + align:start position:0% +they've seen per user and so you know if + + + align:start position:0% +they've seen per user and so you know if +a user uses aetherium ones and then goes + + align:start position:0% +a user uses aetherium ones and then goes + + + align:start position:0% +a user uses aetherium ones and then goes +away all of the nodes have to keep that + + align:start position:0% +away all of the nodes have to keep that + + + align:start position:0% +away all of the nodes have to keep that +state forever essentially just in case + + align:start position:0% +state forever essentially just in case + + + align:start position:0% +state forever essentially just in case +you know someone comes back and + + align:start position:0% +you know someone comes back and + + + align:start position:0% +you know someone comes back and +rebroadcasts another transaction so um a + + align:start position:0% +rebroadcasts another transaction so um a + + + align:start position:0% +rebroadcasts another transaction so um a +Bitcoin like I said and I keep saying + + align:start position:0% +Bitcoin like I said and I keep saying + + + align:start position:0% +Bitcoin like I said and I keep saying +does something and there's nothing wrong + + align:start position:0% +does something and there's nothing wrong + + + align:start position:0% +does something and there's nothing wrong +with this with this model we'll sort of + + align:start position:0% +with this with this model we'll sort of + + + align:start position:0% +with this with this model we'll sort of +compare and contrast like I said it's + + align:start position:0% +compare and contrast like I said it's + + + align:start position:0% +compare and contrast like I said it's +what aetherium uses but I think that + + align:start position:0% +what aetherium uses but I think that + + + align:start position:0% +what aetherium uses but I think that +this was part of the motivation for why + + align:start position:0% +this was part of the motivation for why + + + align:start position:0% +this was part of the motivation for why +Bitcoin was designed the way that it was + + align:start position:0% +Bitcoin was designed the way that it was + + + align:start position:0% +Bitcoin was designed the way that it was +and so Bickman uses this idea called + + align:start position:0% +and so Bickman uses this idea called + + + align:start position:0% +and so Bickman uses this idea called +unspent transaction outputs so you'll + + align:start position:0% +unspent transaction outputs so you'll + + + align:start position:0% +unspent transaction outputs so you'll +notice like over here we don't have any + + align:start position:0% +notice like over here we don't have any + + + align:start position:0% +notice like over here we don't have any +notion of a coin per se you know they're + + align:start position:0% +notion of a coin per se you know they're + + + align:start position:0% +notion of a coin per se you know they're +just amounts and amounts are debited and + + align:start position:0% +just amounts and amounts are debited and + + + align:start position:0% +just amounts and amounts are debited and +credited and if Alice spends two Bob and + + align:start position:0% +credited and if Alice spends two Bob and + + + align:start position:0% +credited and if Alice spends two Bob and +Alice spends - Carol and they come in + + align:start position:0% +Alice spends - Carol and they come in + + + align:start position:0% +Alice spends - Carol and they come in +different orders either one could happen + + align:start position:0% +different orders either one could happen + + + align:start position:0% +different orders either one could happen +first you know there's no notion of like + + align:start position:0% +first you know there's no notion of like + + + align:start position:0% +first you know there's no notion of like +Carol gets these coins and Bob gets + + align:start position:0% +Carol gets these coins and Bob gets + + + align:start position:0% +Carol gets these coins and Bob gets +these coins but Bitcoin is a little bit + + align:start position:0% +these coins but Bitcoin is a little bit + + + align:start position:0% +these coins but Bitcoin is a little bit +different all coins are not the same and + + align:start position:0% +different all coins are not the same and + + + align:start position:0% +different all coins are not the same and +when you're spending you don't just + + align:start position:0% +when you're spending you don't just + + + align:start position:0% +when you're spending you don't just +include an amount you refer back to the + + align:start position:0% +include an amount you refer back to the + + + align:start position:0% +include an amount you refer back to the +specific coin that you are spending okay + + align:start position:0% +specific coin that you are spending okay + + + align:start position:0% +specific coin that you are spending okay +so you actually have to refer to + + align:start position:0% +so you actually have to refer to + + + align:start position:0% +so you actually have to refer to +coin in order to spend it and this is + + align:start position:0% +coin in order to spend it and this is + + + align:start position:0% +coin in order to spend it and this is +the really weird part + + align:start position:0% +the really weird part + + + align:start position:0% +the really weird part +coins are created or destroyed consumed + + align:start position:0% +coins are created or destroyed consumed + + + align:start position:0% +coins are created or destroyed consumed +and and then new coins are created every + + align:start position:0% +and and then new coins are created every + + + align:start position:0% +and and then new coins are created every +transaction okay so whenever you spend + + align:start position:0% +transaction okay so whenever you spend + + + align:start position:0% +transaction okay so whenever you spend +your Bitcoin you have to spend it in its + + align:start position:0% +your Bitcoin you have to spend it in its + + + align:start position:0% +your Bitcoin you have to spend it in its +entirety that bitcoin is then destroyed + + align:start position:0% +entirety that bitcoin is then destroyed + + + align:start position:0% +entirety that bitcoin is then destroyed +and new coins are created and there's a + + align:start position:0% +and new coins are created and there's a + + + align:start position:0% +and new coins are created and there's a +rule in the entire system that a coin + + align:start position:0% +rule in the entire system that a coin + + + align:start position:0% +rule in the entire system that a coin +can only be spent once so let's go into + + align:start position:0% +can only be spent once so let's go into + + + align:start position:0% +can only be spent once so let's go into +exact we'll go into exactly what that + + align:start position:0% +exact we'll go into exactly what that + + + align:start position:0% +exact we'll go into exactly what that +looks like in a transaction but I want + + align:start position:0% +looks like in a transaction but I want + + + align:start position:0% +looks like in a transaction but I want +to know if there are any questions about + + align:start position:0% +to know if there are any questions about + + + align:start position:0% +to know if there are any questions about +that first about that idea yes yeah + + align:start position:0% +that first about that idea yes yeah + + + align:start position:0% +that first about that idea yes yeah +that's a great question so the question + + align:start position:0% +that's a great question so the question + + + align:start position:0% +that's a great question so the question +is aren't coins fungible so first of all + + align:start position:0% +is aren't coins fungible so first of all + + + align:start position:0% +is aren't coins fungible so first of all +coins aren't fungible actually they they + + align:start position:0% +coins aren't fungible actually they they + + + align:start position:0% +coins aren't fungible actually they they +they're very specific you can you can + + align:start position:0% +they're very specific you can you can + + + align:start position:0% +they're very specific you can you can +like see a coin but you can like the + + align:start position:0% +like see a coin but you can like the + + + align:start position:0% +like see a coin but you can like the +question about can you know what happens + + align:start position:0% +question about can you know what happens + + + align:start position:0% +question about can you know what happens +if you want to only want to spend part + + align:start position:0% +if you want to only want to spend part + + + align:start position:0% +if you want to only want to spend part +of a coin is a great question and we'll + + align:start position:0% +of a coin is a great question and we'll + + + align:start position:0% +of a coin is a great question and we'll +see how you do that in in the way that + + align:start position:0% +see how you do that in in the way that + + + align:start position:0% +see how you do that in in the way that +the transaction is constructed but the + + align:start position:0% +the transaction is constructed but the + + + align:start position:0% +the transaction is constructed but the +short answer is if you want to spend + + align:start position:0% +short answer is if you want to spend + + + align:start position:0% +short answer is if you want to spend +part of a coin you have to spend the + + align:start position:0% +part of a coin you have to spend the + + + align:start position:0% +part of a coin you have to spend the +whole coin spend the part that you want + + align:start position:0% +whole coin spend the part that you want + + + align:start position:0% +whole coin spend the part that you want +to someone else and then spend the rest + + align:start position:0% +to someone else and then spend the rest + + + align:start position:0% +to someone else and then spend the rest +of it back to yourself creating a new + + align:start position:0% +of it back to yourself creating a new + + + align:start position:0% +of it back to yourself creating a new +coin in the process yes whoever you say + + align:start position:0% +coin in the process yes whoever you say + + + align:start position:0% +coin in the process yes whoever you say +should own the new ones when you're when + + align:start position:0% +should own the new ones when you're when + + + align:start position:0% +should own the new ones when you're when +so the transaction consumes coins and + + align:start position:0% +so the transaction consumes coins and + + + align:start position:0% +so the transaction consumes coins and +creates new ones as payment and as the + + align:start position:0% +creates new ones as payment and as the + + + align:start position:0% +creates new ones as payment and as the +creator of that transaction is the + + align:start position:0% +creator of that transaction is the + + + align:start position:0% +creator of that transaction is the +spender I will decide who should get the + + align:start position:0% +spender I will decide who should get the + + + align:start position:0% +spender I will decide who should get the +new coins and I'll show you details of + + align:start position:0% +new coins and I'll show you details of + + + align:start position:0% +new coins and I'll show you details of +this in a moment + + align:start position:0% + + + + align:start position:0% + +no not exactly full balance in the + + align:start position:0% +no not exactly full balance in the + + + align:start position:0% +no not exactly full balance in the +account so let's uh let's let's go a + + align:start position:0% +account so let's uh let's let's go a + + + align:start position:0% +account so let's uh let's let's go a +little bit further to look at what's + + align:start position:0% +little bit further to look at what's + + + align:start position:0% +little bit further to look at what's +happening here because Bitcoin doesn't + + align:start position:0% +happening here because Bitcoin doesn't + + + align:start position:0% +happening here because Bitcoin doesn't +actually keep track of balances so let's + + align:start position:0% +actually keep track of balances so let's + + + align:start position:0% +actually keep track of balances so let's +take a look at what a transaction + + align:start position:0% +take a look at what a transaction + + + align:start position:0% +take a look at what a transaction +actually looks like okay so a + + align:start position:0% +actually looks like okay so a + + + align:start position:0% +actually looks like okay so a +transaction has many different parts but + + align:start position:0% +transaction has many different parts but + + + align:start position:0% +transaction has many different parts but +we're gonna focus on two parts which is + + align:start position:0% +we're gonna focus on two parts which is + + + align:start position:0% +we're gonna focus on two parts which is +the inputs and the outputs and here I'm + + align:start position:0% +the inputs and the outputs and here I'm + + + align:start position:0% +the inputs and the outputs and here I'm +showing a transaction with one input and + + align:start position:0% +showing a transaction with one input and + + + align:start position:0% +showing a transaction with one input and +one output okay + + align:start position:0% +one output okay + + + align:start position:0% +one output okay +now an input actually refers back to + + align:start position:0% +now an input actually refers back to + + + align:start position:0% +now an input actually refers back to +another transactions output so let's + + align:start position:0% +another transactions output so let's + + + align:start position:0% +another transactions output so let's +assume and we'll get into how this is + + align:start position:0% +assume and we'll get into how this is + + + align:start position:0% +assume and we'll get into how this is +done later but let's assume that there + + align:start position:0% +done later but let's assume that there + + + align:start position:0% +done later but let's assume that there +are coins in the system okay let's just + + align:start position:0% +are coins in the system okay let's just + + + align:start position:0% +are coins in the system okay let's just +assume that some coins have been created + + align:start position:0% +assume that some coins have been created + + + align:start position:0% +assume that some coins have been created +out of nowhere let's say in particular + + align:start position:0% +out of nowhere let's say in particular + + + align:start position:0% +out of nowhere let's say in particular +that maybe 12.5 coins have been created + + align:start position:0% +that maybe 12.5 coins have been created + + + align:start position:0% +that maybe 12.5 coins have been created +out of nowhere and so there's a + + align:start position:0% +out of nowhere and so there's a + + + align:start position:0% +out of nowhere and so there's a +transaction that outputs 12.5 coins to + + align:start position:0% +transaction that outputs 12.5 coins to + + + align:start position:0% +transaction that outputs 12.5 coins to +Alice and Alice wants to spend those + + align:start position:0% +Alice and Alice wants to spend those + + + align:start position:0% +Alice and Alice wants to spend those +coins and so Alice would create a new + + align:start position:0% +coins and so Alice would create a new + + + align:start position:0% +coins and so Alice would create a new +transaction that points back to the + + align:start position:0% +transaction that points back to the + + + align:start position:0% +transaction that points back to the +transaction where she received those + + align:start position:0% +transaction where she received those + + + align:start position:0% +transaction where she received those +coins and the way that she points back + + align:start position:0% +coins and the way that she points back + + + align:start position:0% +coins and the way that she points back +to that is using the transaction ID of + + align:start position:0% +to that is using the transaction ID of + + + align:start position:0% +to that is using the transaction ID of +the previous transaction which you + + align:start position:0% +the previous transaction which you + + + align:start position:0% +the previous transaction which you +remember she's the hash the index + + align:start position:0% +remember she's the hash the index + + + align:start position:0% +remember she's the hash the index +meaning which output of the previous + + align:start position:0% +meaning which output of the previous + + + align:start position:0% +meaning which output of the previous +transaction she's intending to spend and + + align:start position:0% +transaction she's intending to spend and + + + align:start position:0% +transaction she's intending to spend and +something called a script sig which is + + align:start position:0% +something called a script sig which is + + + align:start position:0% +something called a script sig which is +her authorization to spend that output + + align:start position:0% +her authorization to spend that output + + + align:start position:0% +her authorization to spend that output +so this is how alice refers back to the + + align:start position:0% +so this is how alice refers back to the + + + align:start position:0% +so this is how alice refers back to the +output she wants to spend and when I say + + align:start position:0% +output she wants to spend and when I say + + + align:start position:0% +output she wants to spend and when I say +coin I'm referring to outputs + + align:start position:0% +coin I'm referring to outputs + + + align:start position:0% +coin I'm referring to outputs +okay so outputs can be for different + + align:start position:0% +okay so outputs can be for different + + + align:start position:0% +okay so outputs can be for different +amounts output you know you could create + + align:start position:0% +amounts output you know you could create + + + align:start position:0% +amounts output you know you could create +an output you could spend 12.5 coins and + + align:start position:0% +an output you could spend 12.5 coins and + + + align:start position:0% +an output you could spend 12.5 coins and +create many different outputs of many + + align:start position:0% +create many different outputs of many + + + align:start position:0% +create many different outputs of many +different amounts and send them to + + align:start position:0% +different amounts and send them to + + + align:start position:0% +different amounts and send them to +different people if you wanted to so + + align:start position:0% +different people if you wanted to so + + + align:start position:0% +different people if you wanted to so +this is the format of a transaction + + align:start position:0% +this is the format of a transaction + + + align:start position:0% +this is the format of a transaction +there's an input which points back to a + + align:start position:0% +there's an input which points back to a + + + align:start position:0% +there's an input which points back to a +previous transactions output that you're + + align:start position:0% +previous transactions output that you're + + + align:start position:0% +previous transactions output that you're +intending to spend and then the way that + + align:start position:0% +intending to spend and then the way that + + + align:start position:0% +intending to spend and then the way that +you spend it you're consuming that + + align:start position:0% +you spend it you're consuming that + + + align:start position:0% +you spend it you're consuming that +output essentially by pointing back to + + align:start position:0% +output essentially by pointing back to + + + align:start position:0% +output essentially by pointing back to +it with this input the way that you + + align:start position:0% +it with this input the way that you + + + align:start position:0% +it with this input the way that you +spend it is by producing a new output + + align:start position:0% +spend it is by producing a new output + + + align:start position:0% +spend it is by producing a new output +okay and again this transaction just + + align:start position:0% +okay and again this transaction just + + + align:start position:0% +okay and again this transaction just +doesn't want input + + align:start position:0% +doesn't want input + + + align:start position:0% +doesn't want input +one output it could have many and the + + align:start position:0% +one output it could have many and the + + + align:start position:0% +one output it could have many and the +output that you produce has something + + align:start position:0% +output that you produce has something + + + align:start position:0% +output that you produce has something +called a script pub key what the script + + align:start position:0% +called a script pub key what the script + + + align:start position:0% +called a script pub key what the script +pub key is the script pump key is a way + + align:start position:0% +pub key is the script pump key is a way + + + align:start position:0% +pub key is the script pump key is a way +of specifying the conditions under which + + align:start position:0% +of specifying the conditions under which + + + align:start position:0% +of specifying the conditions under which +this output can be redeemed so in its + + align:start position:0% +this output can be redeemed so in its + + + align:start position:0% +this output can be redeemed so in its +simplest sense you might have the script + + align:start position:0% +simplest sense you might have the script + + + align:start position:0% +simplest sense you might have the script +cig merely be a signature just alice's + + align:start position:0% +cig merely be a signature just alice's + + + align:start position:0% +cig merely be a signature just alice's +signature saying i have the right to + + align:start position:0% +signature saying i have the right to + + + align:start position:0% +signature saying i have the right to +spend this and if alice is spending too + + align:start position:0% +spend this and if alice is spending too + + + align:start position:0% +spend this and if alice is spending too +bob then maybe the script pub key would + + align:start position:0% +bob then maybe the script pub key would + + + align:start position:0% +bob then maybe the script pub key would +actually just be Bob's public key and + + align:start position:0% +actually just be Bob's public key and + + + align:start position:0% +actually just be Bob's public key and +the implied meaning there would be + + align:start position:0% +the implied meaning there would be + + + align:start position:0% +the implied meaning there would be +anyone who could produce a signature of + + align:start position:0% +anyone who could produce a signature of + + + align:start position:0% +anyone who could produce a signature of +the corresponding private key with that + + align:start position:0% +the corresponding private key with that + + + align:start position:0% +the corresponding private key with that +public key could then spend this output + + align:start position:0% + + + + align:start position:0% + +one thing is that these two things + + align:start position:0% +one thing is that these two things + + + align:start position:0% +one thing is that these two things +together the previous transaction ID and + + align:start position:0% +together the previous transaction ID and + + + align:start position:0% +together the previous transaction ID and +the index serves to uniquely identify an + + align:start position:0% +the index serves to uniquely identify an + + + align:start position:0% +the index serves to uniquely identify an +output so these two things uniquely + + align:start position:0% +output so these two things uniquely + + + align:start position:0% +output so these two things uniquely +identify some money to spend okay and + + align:start position:0% +identify some money to spend okay and + + + align:start position:0% +identify some money to spend okay and +the value that's specified in the output + + align:start position:0% +the value that's specified in the output + + + align:start position:0% +the value that's specified in the output +is actually specified in something + + align:start position:0% +is actually specified in something + + + align:start position:0% +is actually specified in something +called satoshis and there are 10 to the + + align:start position:0% +called satoshis and there are 10 to the + + + align:start position:0% +called satoshis and there are 10 to the +8th satoshis in one Bitcoin so the value + + align:start position:0% +8th satoshis in one Bitcoin so the value + + + align:start position:0% +8th satoshis in one Bitcoin so the value +doesn't have any decimal places in it it + + align:start position:0% +doesn't have any decimal places in it it + + + align:start position:0% +doesn't have any decimal places in it it +is always an integer an output is what + + align:start position:0% +is always an integer an output is what + + + align:start position:0% +is always an integer an output is what +I'm referring to when I say the word + + align:start position:0% +I'm referring to when I say the word + + + align:start position:0% +I'm referring to when I say the word +coin so questions on this sort of + + align:start position:0% +coin so questions on this sort of + + + align:start position:0% +coin so questions on this sort of +general set up yes + + align:start position:0% +general set up yes + + + align:start position:0% +general set up yes +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +sure um okay the index is I remember how + + align:start position:0% +sure um okay the index is I remember how + + + align:start position:0% +sure um okay the index is I remember how +I said there could be multiple outputs + + align:start position:0% +I said there could be multiple outputs + + + align:start position:0% +I said there could be multiple outputs +the index simply refers to which output + + align:start position:0% +the index simply refers to which output + + + align:start position:0% +the index simply refers to which output +in the previous transaction you're + + align:start position:0% +in the previous transaction you're + + + align:start position:0% +in the previous transaction you're +talking about was there a question back + + align:start position:0% +talking about was there a question back + + + align:start position:0% +talking about was there a question back +there + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +sure yes we'll get to that in a moment + + align:start position:0% +sure yes we'll get to that in a moment + + + align:start position:0% +sure yes we'll get to that in a moment +actually but maybe I could just draw one + + align:start position:0% +actually but maybe I could just draw one + + + align:start position:0% +actually but maybe I could just draw one +on the board so so you could certainly + + align:start position:0% +on the board so so you could certainly + + + align:start position:0% +on the board so so you could certainly +have a transaction that has multiple + + align:start position:0% +have a transaction that has multiple + + + align:start position:0% +have a transaction that has multiple +outputs okay + + align:start position:0% +outputs okay + + + align:start position:0% +outputs okay +and so this input here would refer back + + align:start position:0% +and so this input here would refer back + + + align:start position:0% +and so this input here would refer back +to some previous transactions outputs + + align:start position:0% + + + + align:start position:0% + +and let's say that this was for example + + align:start position:0% +and let's say that this was for example + + + align:start position:0% +and let's say that this was for example +20 Bitcoin okay then + + align:start position:0% +20 Bitcoin okay then + + + align:start position:0% +20 Bitcoin okay then +this needs to consume 20 Bitcoin and it + + align:start position:0% +this needs to consume 20 Bitcoin and it + + + align:start position:0% +this needs to consume 20 Bitcoin and it +can spread that 20 Bitcoin out in any + + align:start position:0% +can spread that 20 Bitcoin out in any + + + align:start position:0% +can spread that 20 Bitcoin out in any +way that it wants and there's some + + align:start position:0% +way that it wants and there's some + + + align:start position:0% +way that it wants and there's some +details here that we're gonna get to in + + align:start position:0% +details here that we're gonna get to in + + + align:start position:0% +details here that we're gonna get to in +a moment + + align:start position:0% +a moment + + + align:start position:0% +a moment +but basically you have that 20 here you + + align:start position:0% +but basically you have that 20 here you + + + align:start position:0% +but basically you have that 20 here you +could send five here ten here five here + + align:start position:0% +could send five here ten here five here + + + align:start position:0% +could send five here ten here five here +and each of these outputs would have its + + align:start position:0% +and each of these outputs would have its + + + align:start position:0% +and each of these outputs would have its +own script pub key its own rules for how + + align:start position:0% +own script pub key its own rules for how + + + align:start position:0% +own script pub key its own rules for how +to redeem it and each output has its own + + align:start position:0% +to redeem it and each output has its own + + + align:start position:0% +to redeem it and each output has its own +amount yep that's a good question so um + + align:start position:0% +amount yep that's a good question so um + + + align:start position:0% +amount yep that's a good question so um +if we if you go back to the slide where + + align:start position:0% +if we if you go back to the slide where + + + align:start position:0% +if we if you go back to the slide where +I sort of was showing this is where the + + align:start position:0% +I sort of was showing this is where the + + + align:start position:0% +I sort of was showing this is where the +name chain comes from here so what we're + + align:start position:0% +name chain comes from here so what we're + + + align:start position:0% +name chain comes from here so what we're +talking about right now is what goes + + align:start position:0% +talking about right now is what goes + + + align:start position:0% +talking about right now is what goes +inside each block and what goes inside + + align:start position:0% +inside each block and what goes inside + + + align:start position:0% +inside each block and what goes inside +each block are transactions so for the + + align:start position:0% +each block are transactions so for the + + + align:start position:0% +each block are transactions so for the +moment you can pretend like each block + + align:start position:0% +moment you can pretend like each block + + + align:start position:0% +moment you can pretend like each block +only has one transaction in it but a + + align:start position:0% +only has one transaction in it but a + + + align:start position:0% +only has one transaction in it but a +block can contain a set of transactions + + align:start position:0% +block can contain a set of transactions + + + align:start position:0% +block can contain a set of transactions +but the chain part comes from how we + + align:start position:0% +but the chain part comes from how we + + + align:start position:0% +but the chain part comes from how we +actually chained these blocks of + + align:start position:0% +actually chained these blocks of + + + align:start position:0% +actually chained these blocks of +transactions together + + align:start position:0% + + + + align:start position:0% + +okay so let's talk about script zigs and + + align:start position:0% +okay so let's talk about script zigs and + + + align:start position:0% +okay so let's talk about script zigs and +script pub keys a little bit more so + + align:start position:0% +script pub keys a little bit more so + + + align:start position:0% +script pub keys a little bit more so +script pub keys like I said are in the + + align:start position:0% +script pub keys like I said are in the + + + align:start position:0% +script pub keys like I said are in the +outputs and you can think of them as + + align:start position:0% +outputs and you can think of them as + + + align:start position:0% +outputs and you can think of them as +predicates so script pub keys specify a + + align:start position:0% +predicates so script pub keys specify a + + + align:start position:0% +predicates so script pub keys specify a +predicate on how someone can redeem this + + align:start position:0% +predicate on how someone can redeem this + + + align:start position:0% +predicate on how someone can redeem this +output okay so remember transaction can + + align:start position:0% +output okay so remember transaction can + + + align:start position:0% +output okay so remember transaction can +have multiple inputs multiple outputs + + align:start position:0% +have multiple inputs multiple outputs + + + align:start position:0% +have multiple inputs multiple outputs +each output has its own script pub key + + align:start position:0% +each output has its own script pub key + + + align:start position:0% +each output has its own script pub key +script SIG's + + align:start position:0% +script SIG's + + + align:start position:0% +script SIG's +which are in the inputs help satisfy the + + align:start position:0% +which are in the inputs help satisfy the + + + align:start position:0% +which are in the inputs help satisfy the +predicate that's specified in the script + + align:start position:0% +predicate that's specified in the script + + + align:start position:0% +predicate that's specified in the script +pub key so we would have a script pump + + align:start position:0% +pub key so we would have a script pump + + + align:start position:0% +pub key so we would have a script pump +key here and we would have a script sig + + align:start position:0% +key here and we would have a script sig + + + align:start position:0% +key here and we would have a script sig +here and this script sig if this is a + + align:start position:0% +here and this script sig if this is a + + + align:start position:0% +here and this script sig if this is a +valid transaction would explain how to + + align:start position:0% +valid transaction would explain how to + + + align:start position:0% +valid transaction would explain how to +satisfy the script pub key so the script + + align:start position:0% +satisfy the script pub key so the script + + + align:start position:0% +satisfy the script pub key so the script +pub key would set up a predicate on the + + align:start position:0% +pub key would set up a predicate on the + + + align:start position:0% +pub key would set up a predicate on the +output the most common predicate is + + align:start position:0% +output the most common predicate is + + + align:start position:0% +output the most common predicate is +produce a signature and a public key + + align:start position:0% +produce a signature and a public key + + + align:start position:0% +produce a signature and a public key +that satisfies this hash and the script + + align:start position:0% +that satisfies this hash and the script + + + align:start position:0% +that satisfies this hash and the script +sig would provide the information + + align:start position:0% +sig would provide the information + + + align:start position:0% +sig would provide the information +necessary to satisfy that predicate so + + align:start position:0% +necessary to satisfy that predicate so + + + align:start position:0% +necessary to satisfy that predicate so +what does it mean to have money in this + + align:start position:0% +what does it mean to have money in this + + + align:start position:0% +what does it mean to have money in this +system what does it mean to be able to + + align:start position:0% +system what does it mean to be able to + + + align:start position:0% +system what does it mean to be able to +spend money what does it mean for Alice + + align:start position:0% +spend money what does it mean for Alice + + + align:start position:0% +spend money what does it mean for Alice +to be able to transfer money to Bob it + + align:start position:0% +to be able to transfer money to Bob it + + + align:start position:0% +to be able to transfer money to Bob it +means Alice know some information that + + align:start position:0% +means Alice know some information that + + + align:start position:0% +means Alice know some information that +allows her to produce a satisfying + + align:start position:0% +allows her to produce a satisfying + + + align:start position:0% +allows her to produce a satisfying +script sig for some outputs out there + + align:start position:0% +script sig for some outputs out there + + + align:start position:0% +script sig for some outputs out there +that's what having money means it's not + + align:start position:0% +that's what having money means it's not + + + align:start position:0% +that's what having money means it's not +an account balance so questions on that + + align:start position:0% +an account balance so questions on that + + + align:start position:0% +an account balance so questions on that +because it's a little non-intuitive but + + align:start position:0% +because it's a little non-intuitive but + + + align:start position:0% +because it's a little non-intuitive but +the important thing to note here is the + + align:start position:0% +the important thing to note here is the + + + align:start position:0% +the important thing to note here is the +nodes in the Bitcoin network are not + + align:start position:0% +nodes in the Bitcoin network are not + + + align:start position:0% +nodes in the Bitcoin network are not +keeping track of how much money you have + + align:start position:0% +keeping track of how much money you have + + + align:start position:0% +keeping track of how much money you have +it's your job to keep track of how much + + align:start position:0% +it's your job to keep track of how much + + + align:start position:0% +it's your job to keep track of how much +money you have or a wallets job and + + align:start position:0% +money you have or a wallets job and + + + align:start position:0% +money you have or a wallets job and +we'll talk more about wallets later and + + align:start position:0% +we'll talk more about wallets later and + + + align:start position:0% +we'll talk more about wallets later and +the way that you do that is by knowing + + align:start position:0% +the way that you do that is by knowing + + + align:start position:0% +the way that you do that is by knowing +how many outputs there are out there + + align:start position:0% +how many outputs there are out there + + + align:start position:0% +how many outputs there are out there +that you can actually + + align:start position:0% +that you can actually + + + align:start position:0% +that you can actually +that you have the knowledge to redeem + + align:start position:0% +that you have the knowledge to redeem + + + align:start position:0% +that you have the knowledge to redeem +like I said a transaction can have + + align:start position:0% +like I said a transaction can have + + + align:start position:0% +like I said a transaction can have +multiple inputs and multiple outputs and + + align:start position:0% +multiple inputs and multiple outputs and + + + align:start position:0% +multiple inputs and multiple outputs and +each input comes with its own script sig + + align:start position:0% +each input comes with its own script sig + + + align:start position:0% +each input comes with its own script sig +and each output comes with its own + + align:start position:0% +and each output comes with its own + + + align:start position:0% +and each output comes with its own +script pub key so it's not that there's + + align:start position:0% +script pub key so it's not that there's + + + align:start position:0% +script pub key so it's not that there's +one script sig in one script pub key for + + align:start position:0% +one script sig in one script pub key for + + + align:start position:0% +one script sig in one script pub key for +the entire transaction a transaction can + + align:start position:0% +the entire transaction a transaction can + + + align:start position:0% +the entire transaction a transaction can +actually spend multiple different + + align:start position:0% +actually spend multiple different + + + align:start position:0% +actually spend multiple different +outputs and produce multiple different + + align:start position:0% +outputs and produce multiple different + + + align:start position:0% +outputs and produce multiple different +new outputs and these outputs could have + + align:start position:0% +new outputs and these outputs could have + + + align:start position:0% +new outputs and these outputs could have +nothing to do with each other here this + + align:start position:0% +nothing to do with each other here this + + + align:start position:0% +nothing to do with each other here this +input might point to a previous output + + align:start position:0% +input might point to a previous output + + + align:start position:0% +input might point to a previous output +that Alice knows how to spend and this + + align:start position:0% +that Alice knows how to spend and this + + + align:start position:0% +that Alice knows how to spend and this +input might point to a previous output + + align:start position:0% +input might point to a previous output + + + align:start position:0% +input might point to a previous output +the Carol knows how to spend and you can + + align:start position:0% +the Carol knows how to spend and you can + + + align:start position:0% +the Carol knows how to spend and you can +actually combine both of those into the + + align:start position:0% +actually combine both of those into the + + + align:start position:0% +actually combine both of those into the +same transaction assuming you can + + align:start position:0% +same transaction assuming you can + + + align:start position:0% +same transaction assuming you can +produce a transaction with the right + + align:start position:0% +produce a transaction with the right + + + align:start position:0% +produce a transaction with the right +script 6 now Alice and Carol might have + + align:start position:0% +script 6 now Alice and Carol might have + + + align:start position:0% +script 6 now Alice and Carol might have +to talk to each other in order to + + align:start position:0% +to talk to each other in order to + + + align:start position:0% +to talk to each other in order to +produce this transaction because it's + + align:start position:0% +produce this transaction because it's + + + align:start position:0% +produce this transaction because it's +going to need both signatures but they + + align:start position:0% +going to need both signatures but they + + + align:start position:0% +going to need both signatures but they +could do it great question so you know + + align:start position:0% +could do it great question so you know + + + align:start position:0% +could do it great question so you know +what prevents people from shuffling + + align:start position:0% +what prevents people from shuffling + + + align:start position:0% +what prevents people from shuffling +around the inputs and the outputs well + + align:start position:0% +around the inputs and the outputs well + + + align:start position:0% +around the inputs and the outputs well +part of it is because this is serialized + + align:start position:0% +part of it is because this is serialized + + + align:start position:0% +part of it is because this is serialized +into a transaction and that transaction + + align:start position:0% +into a transaction and that transaction + + + align:start position:0% +into a transaction and that transaction +is hashed and then these signatures are + + align:start position:0% +is hashed and then these signatures are + + + align:start position:0% +is hashed and then these signatures are +on that transaction hash remember we saw + + align:start position:0% +on that transaction hash remember we saw + + + align:start position:0% +on that transaction hash remember we saw +that from a few slides before so if you + + align:start position:0% +that from a few slides before so if you + + + align:start position:0% +that from a few slides before so if you +were to flip around the order or if you + + align:start position:0% +were to flip around the order or if you + + + align:start position:0% +were to flip around the order or if you +were to trying to change any bits in + + align:start position:0% +were to trying to change any bits in + + + align:start position:0% +were to trying to change any bits in +here and change the pub key you would + + align:start position:0% +here and change the pub key you would + + + align:start position:0% +here and change the pub key you would +end up changing the hash of the + + align:start position:0% +end up changing the hash of the + + + align:start position:0% +end up changing the hash of the +transaction and this signature would no + + align:start position:0% +transaction and this signature would no + + + align:start position:0% +transaction and this signature would no +longer be valid and something also + + align:start position:0% +longer be valid and something also + + + align:start position:0% +longer be valid and something also +that's important to note only valid + + align:start position:0% +that's important to note only valid + + + align:start position:0% +that's important to note only valid +transactions get accepted to the + + align:start position:0% +transactions get accepted to the + + + align:start position:0% +transactions get accepted to the +blockchain so all of the nodes are + + align:start position:0% +blockchain so all of the nodes are + + + align:start position:0% +blockchain so all of the nodes are +checking to make sure that the script + + align:start position:0% +checking to make sure that the script + + + align:start position:0% +checking to make sure that the script +pub keys and these scripts IG's work out + + align:start position:0% +pub keys and these scripts IG's work out + + + align:start position:0% +pub keys and these scripts IG's work out +and I'll show you the rules that they're + + align:start position:0% +and I'll show you the rules that they're + + + align:start position:0% +and I'll show you the rules that they're +checking in just a moment + + align:start position:0% +checking in just a moment + + + align:start position:0% +checking in just a moment +and so it's it's if anything doesn't + + align:start position:0% +and so it's it's if anything doesn't + + + align:start position:0% +and so it's it's if anything doesn't +match if this signature is not a valid + + align:start position:0% +match if this signature is not a valid + + + align:start position:0% +match if this signature is not a valid +script sig for whatever output it's + + align:start position:0% +script sig for whatever output it's + + + align:start position:0% +script sig for whatever output it's +pointing to this is an invalid + + align:start position:0% +pointing to this is an invalid + + + align:start position:0% +pointing to this is an invalid +transaction no one will accept it in + + align:start position:0% +transaction no one will accept it in + + + align:start position:0% +transaction no one will accept it in +fact most nodes won't even pass it + + align:start position:0% +fact most nodes won't even pass it + + + align:start position:0% +fact most nodes won't even pass it +around and it will not get into the + + align:start position:0% +around and it will not get into the + + + align:start position:0% +around and it will not get into the +blockchain or if it does get into the + + align:start position:0% +blockchain or if it does get into the + + + align:start position:0% +blockchain or if it does get into the +blockchain all of the nodes were + + align:start position:0% +blockchain all of the nodes were + + + align:start position:0% +blockchain all of the nodes were +following the rules of the network will + + align:start position:0% +following the rules of the network will + + + align:start position:0% +following the rules of the network will +ignore it because if a transaction is + + align:start position:0% +ignore it because if a transaction is + + + align:start position:0% +ignore it because if a transaction is +invalid it means the entire block is + + align:start position:0% +invalid it means the entire block is + + + align:start position:0% +invalid it means the entire block is +invalid + + align:start position:0% +invalid + + + align:start position:0% +invalid +and it means any chain building off that + + align:start position:0% +and it means any chain building off that + + + align:start position:0% +and it means any chain building off that +block is also invalid so nodes that are + + align:start position:0% +block is also invalid so nodes that are + + + align:start position:0% +block is also invalid so nodes that are +following the rules of the network which + + align:start position:0% +following the rules of the network which + + + align:start position:0% +following the rules of the network which +are these should be valid will not + + align:start position:0% +are these should be valid will not + + + align:start position:0% +are these should be valid will not +listen to that and will completely + + align:start position:0% +listen to that and will completely + + + align:start position:0% +listen to that and will completely +ignore that entire chain so here's + + align:start position:0% +ignore that entire chain so here's + + + align:start position:0% +ignore that entire chain so here's +another visual of sort of what it looks + + align:start position:0% +another visual of sort of what it looks + + + align:start position:0% +another visual of sort of what it looks +like to have and this is not what the + + align:start position:0% +like to have and this is not what the + + + align:start position:0% +like to have and this is not what the +blockchain looks like I want to be clear + + align:start position:0% +blockchain looks like I want to be clear + + + align:start position:0% +blockchain looks like I want to be clear +the blockchain is just a set of blocks + + align:start position:0% +the blockchain is just a set of blocks + + + align:start position:0% +the blockchain is just a set of blocks +pointing to previous blocks what we have + + align:start position:0% +pointing to previous blocks what we have + + + align:start position:0% +pointing to previous blocks what we have +here is more sort of like the logical + + align:start position:0% +here is more sort of like the logical + + + align:start position:0% +here is more sort of like the logical +representation of what a transaction + + align:start position:0% +representation of what a transaction + + + align:start position:0% +representation of what a transaction +looks like so you have a transaction + + align:start position:0% +looks like so you have a transaction + + + align:start position:0% +looks like so you have a transaction +right here and you have two inputs in + + align:start position:0% +right here and you have two inputs in + + + align:start position:0% +right here and you have two inputs in +this transaction and the first one is + + align:start position:0% +this transaction and the first one is + + + align:start position:0% +this transaction and the first one is +pointing to the second output of this + + align:start position:0% +pointing to the second output of this + + + align:start position:0% +pointing to the second output of this +previous transaction that happened over + + align:start position:0% +previous transaction that happened over + + + align:start position:0% +previous transaction that happened over +here so this transaction has a hash and + + align:start position:0% +here so this transaction has a hash and + + + align:start position:0% +here so this transaction has a hash and +you know maybe this is the hash of the + + align:start position:0% +you know maybe this is the hash of the + + + align:start position:0% +you know maybe this is the hash of the +entire transaction and so in order to + + align:start position:0% +entire transaction and so in order to + + + align:start position:0% +entire transaction and so in order to +spend that output over there you specify + + align:start position:0% +spend that output over there you specify + + + align:start position:0% +spend that output over there you specify +the hash you specify the index so 0 1 2 + + align:start position:0% +the hash you specify the index so 0 1 2 + + + align:start position:0% +the hash you specify the index so 0 1 2 +you specify this index right here and + + align:start position:0% +you specify this index right here and + + + align:start position:0% +you specify this index right here and +you provide a script sig that will + + align:start position:0% +you provide a script sig that will + + + align:start position:0% +you provide a script sig that will +validate according to whatever the + + align:start position:0% +validate according to whatever the + + + align:start position:0% +validate according to whatever the +script pub key is for that output so + + align:start position:0% +script pub key is for that output so + + + align:start position:0% +script pub key is for that output so +note here this transaction doesn't care + + align:start position:0% +note here this transaction doesn't care + + + align:start position:0% +note here this transaction doesn't care +what those outputs are at all it's not + + align:start position:0% +what those outputs are at all it's not + + + align:start position:0% +what those outputs are at all it's not +using those it's not looking at those + + align:start position:0% +using those it's not looking at those + + + align:start position:0% +using those it's not looking at those +someone else might spend those someone + + align:start position:0% +someone else might spend those someone + + + align:start position:0% +someone else might spend those someone +else might not spend those it's just + + align:start position:0% +else might not spend those it's just + + + align:start position:0% +else might not spend those it's just +spending this one right here and in the + + align:start position:0% +spending this one right here and in the + + + align:start position:0% +spending this one right here and in the +act of spending this one right here it + + align:start position:0% +act of spending this one right here it + + + align:start position:0% +act of spending this one right here it +doesn't make those other ones invalid in + + align:start position:0% +doesn't make those other ones invalid in + + + align:start position:0% +doesn't make those other ones invalid in +the simplest form those could still be + + align:start position:0% +the simplest form those could still be + + + align:start position:0% +the simplest form those could still be +spent by someone else so outputs are + + align:start position:0% +spent by someone else so outputs are + + + align:start position:0% +spent by someone else so outputs are +consumed separately so here it's + + align:start position:0% +consumed separately so here it's + + + align:start position:0% +consumed separately so here it's +pointing to a different transaction the + + align:start position:0% +pointing to a different transaction the + + + align:start position:0% +pointing to a different transaction the +transaction with this hash and so it + + align:start position:0% +transaction with this hash and so it + + + align:start position:0% +transaction with this hash and so it +specifies the transaction ID and then it + + align:start position:0% +specifies the transaction ID and then it + + + align:start position:0% +specifies the transaction ID and then it +specifies which output in that + + align:start position:0% +specifies which output in that + + + align:start position:0% +specifies which output in that +transaction it's spending in this case + + align:start position:0% +transaction it's spending in this case + + + align:start position:0% +transaction it's spending in this case +it's the third one so it has index two + + align:start position:0% +it's the third one so it has index two + + + align:start position:0% +it's the third one so it has index two +and it provides a satisfying script sig + + align:start position:0% +and it provides a satisfying script sig + + + align:start position:0% +and it provides a satisfying script sig +for this output which might be total it + + align:start position:0% +for this output which might be total it + + + align:start position:0% +for this output which might be total it +probably is totally different than the + + align:start position:0% +probably is totally different than the + + + align:start position:0% +probably is totally different than the +satisfying script sig for that output so + + align:start position:0% +satisfying script sig for that output so + + + align:start position:0% +satisfying script sig for that output so +this is what this transaction has to + + align:start position:0% +this is what this transaction has to + + + align:start position:0% +this is what this transaction has to +specify in order to spend those outputs + + align:start position:0% +specify in order to spend those outputs + + + align:start position:0% +specify in order to spend those outputs +and it can produce whatever new outputs + + align:start position:0% +and it can produce whatever new outputs + + + align:start position:0% +and it can produce whatever new outputs +it wants to produce under certain rules + + align:start position:0% + + + + align:start position:0% + +not whole box so actually points to + + align:start position:0% +not whole box so actually points to + + + align:start position:0% +not whole box so actually points to +something else um this box what do you + + align:start position:0% +something else um this box what do you + + + align:start position:0% +something else um this box what do you +mean when you say points - this is + + align:start position:0% +mean when you say points - this is + + + align:start position:0% +mean when you say points - this is +something that will be inside of the + + align:start position:0% +something that will be inside of the + + + align:start position:0% +something that will be inside of the +blockchain inside of a block in the + + align:start position:0% +blockchain inside of a block in the + + + align:start position:0% +blockchain inside of a block in the +blockchain so this doesn't actually + + align:start position:0% +blockchain so this doesn't actually + + + align:start position:0% +blockchain so this doesn't actually +point to anything it contains hashes + + align:start position:0% +point to anything it contains hashes + + + align:start position:0% +point to anything it contains hashes +like literally it just contains these + + align:start position:0% +like literally it just contains these + + + align:start position:0% +like literally it just contains these +bytes these hashes of the transactions + + align:start position:0% +bytes these hashes of the transactions + + + align:start position:0% +bytes these hashes of the transactions +that it's spending and those are kind of + + align:start position:0% +that it's spending and those are kind of + + + align:start position:0% +that it's spending and those are kind of +like a pointer in a sense but when it + + align:start position:0% +like a pointer in a sense but when it + + + align:start position:0% +like a pointer in a sense but when it +comes to the entire blockchain this is + + align:start position:0% +comes to the entire blockchain this is + + + align:start position:0% +comes to the entire blockchain this is +one part of one block yeah I know can + + align:start position:0% +one part of one block yeah I know can + + + align:start position:0% +one part of one block yeah I know can +you guys see this at all can you still + + align:start position:0% +you guys see this at all can you still + + + align:start position:0% +you guys see this at all can you still +see that or no okay good okay great yeah + + align:start position:0% +see that or no okay good okay great yeah + + + align:start position:0% +see that or no okay good okay great yeah +you had your hand up + + align:start position:0% + + + + align:start position:0% + +that was sort of more like an idealized + + align:start position:0% +that was sort of more like an idealized + + + align:start position:0% +that was sort of more like an idealized +transaction so this is what a + + align:start position:0% +transaction so this is what a + + + align:start position:0% +transaction so this is what a +transaction actually looks like the + + align:start position:0% +transaction actually looks like the + + + align:start position:0% +transaction actually looks like the +transaction but when you sign the + + align:start position:0% +transaction but when you sign the + + + align:start position:0% +transaction but when you sign the +transaction you don't sign the script + + align:start position:0% +transaction you don't sign the script + + + align:start position:0% +transaction you don't sign the script +six because the script says include the + + align:start position:0% +six because the script says include the + + + align:start position:0% +six because the script says include the +signature of the transaction and it's + + align:start position:0% +signature of the transaction and it's + + + align:start position:0% +signature of the transaction and it's +important to note the scripts tag + + align:start position:0% +important to note the scripts tag + + + align:start position:0% +important to note the scripts tag +includes the signature of the + + align:start position:0% +includes the signature of the + + + align:start position:0% +includes the signature of the +transaction as a whole not just this + + align:start position:0% +transaction as a whole not just this + + + align:start position:0% +transaction as a whole not just this +part of it yes great question so um you + + align:start position:0% +part of it yes great question so um you + + + align:start position:0% +part of it yes great question so um you +know okay I said that there's this rule + + align:start position:0% +know okay I said that there's this rule + + + align:start position:0% +know okay I said that there's this rule +that outputs are supposed to only be + + align:start position:0% +that outputs are supposed to only be + + + align:start position:0% +that outputs are supposed to only be +consumed once but I can definitely + + align:start position:0% +consumed once but I can definitely + + + align:start position:0% +consumed once but I can definitely +produce another transaction which points + + align:start position:0% +produce another transaction which points + + + align:start position:0% +produce another transaction which points +back to that output I could send it to + + align:start position:0% +back to that output I could send it to + + + align:start position:0% +back to that output I could send it to +the network and what would happen is the + + align:start position:0% +the network and what would happen is the + + + align:start position:0% +the network and what would happen is the +nodes in the network assuming they're + + align:start position:0% +nodes in the network assuming they're + + + align:start position:0% +nodes in the network assuming they're +following consensus rules would note + + align:start position:0% +following consensus rules would note + + + align:start position:0% +following consensus rules would note +that this had already been spent so if + + align:start position:0% +that this had already been spent so if + + + align:start position:0% +that this had already been spent so if +this is already if they've already seen + + align:start position:0% +this is already if they've already seen + + + align:start position:0% +this is already if they've already seen +a transaction a valid transaction that + + align:start position:0% +a transaction a valid transaction that + + + align:start position:0% +a transaction a valid transaction that +consumes an output they will not accept + + align:start position:0% +consumes an output they will not accept + + + align:start position:0% +consumes an output they will not accept +another transaction that tries to spend + + align:start position:0% +another transaction that tries to spend + + + align:start position:0% +another transaction that tries to spend +the same output that's what's known as a + + align:start position:0% +the same output that's what's known as a + + + align:start position:0% +the same output that's what's known as a +double spend and so all the nodes in the + + align:start position:0% +double spend and so all the nodes in the + + + align:start position:0% +double spend and so all the nodes in the +network together are maintaining this + + align:start position:0% +network together are maintaining this + + + align:start position:0% +network together are maintaining this +rule great question yes you know this + + align:start position:0% +rule great question yes you know this + + + align:start position:0% +rule great question yes you know this +seems kind of annoying right like you + + align:start position:0% +seems kind of annoying right like you + + + align:start position:0% +seems kind of annoying right like you +you see this transaction and okay + + align:start position:0% +you see this transaction and okay + + + align:start position:0% +you see this transaction and okay +there's some random bytes in here and + + align:start position:0% +there's some random bytes in here and + + + align:start position:0% +there's some random bytes in here and +some you know a signature and how am I + + align:start position:0% +some you know a signature and how am I + + + align:start position:0% +some you know a signature and how am I +supposed to figure out what this goes to + + align:start position:0% +supposed to figure out what this goes to + + + align:start position:0% +supposed to figure out what this goes to +right how am I supposed to figure out + + align:start position:0% +right how am I supposed to figure out + + + align:start position:0% +right how am I supposed to figure out +you know whether this is a valid + + align:start position:0% +you know whether this is a valid + + + align:start position:0% +you know whether this is a valid +transaction whether it's been spent or + + align:start position:0% +transaction whether it's been spent or + + + align:start position:0% +transaction whether it's been spent or +not and the answer is that every single + + align:start position:0% +not and the answer is that every single + + + align:start position:0% +not and the answer is that every single +node is maintaining a lot of data + + align:start position:0% +node is maintaining a lot of data + + + align:start position:0% +node is maintaining a lot of data +structures in order to make this faster + + align:start position:0% +structures in order to make this faster + + + align:start position:0% +structures in order to make this faster +and in fact they're maintaining a data + + align:start position:0% +and in fact they're maintaining a data + + + align:start position:0% +and in fact they're maintaining a data +structure called the outs the UT exocet + + align:start position:0% +structure called the outs the UT exocet + + + align:start position:0% +structure called the outs the UT exocet +and I'll tell you a little bit about the + + align:start position:0% +and I'll tell you a little bit about the + + + align:start position:0% +and I'll tell you a little bit about the +UT Exocet in a minute but really the + + align:start position:0% +UT Exocet in a minute but really the + + + align:start position:0% +UT Exocet in a minute but really the +I'll tell you how its created in a + + align:start position:0% +I'll tell you how its created in a + + + align:start position:0% +I'll tell you how its created in a +moment yes + + align:start position:0% + + + + align:start position:0% + +sure um so I'm not gonna go into how a + + align:start position:0% +sure um so I'm not gonna go into how a + + + align:start position:0% +sure um so I'm not gonna go into how a +block is how what a block is composed of + + align:start position:0% +block is how what a block is composed of + + + align:start position:0% +block is how what a block is composed of +I'm not gonna go into help what a block + + align:start position:0% +I'm not gonna go into help what a block + + + align:start position:0% +I'm not gonna go into help what a block +is composed of but we will tomorrow yes + + align:start position:0% + + + + align:start position:0% + +yes I I'm sorry could you say yes yes + + align:start position:0% +yes I I'm sorry could you say yes yes + + + align:start position:0% +yes I I'm sorry could you say yes yes +there's a different script say for each + + align:start position:0% +there's a different script say for each + + + align:start position:0% +there's a different script say for each +input there's a different script sig for + + align:start position:0% +input there's a different script sig for + + + align:start position:0% +input there's a different script sig for +each input but that's cryptic signs most + + align:start position:0% +each input but that's cryptic signs most + + + align:start position:0% +each input but that's cryptic signs most +of the transaction so the scripts say + + align:start position:0% +of the transaction so the scripts say + + + align:start position:0% +of the transaction so the scripts say +there's a different one because the + + align:start position:0% +there's a different one because the + + + align:start position:0% +there's a different one because the +because different outputs could have + + align:start position:0% +because different outputs could have + + + align:start position:0% +because different outputs could have +different satisfying conditions but the + + align:start position:0% +different satisfying conditions but the + + + align:start position:0% +different satisfying conditions but the +script sig has to sign a message right + + align:start position:0% +script sig has to sign a message right + + + align:start position:0% +script sig has to sign a message right +or has to produce something actually + + align:start position:0% +or has to produce something actually + + + align:start position:0% +or has to produce something actually +we're gonna go into a few specific + + align:start position:0% +we're gonna go into a few specific + + + align:start position:0% +we're gonna go into a few specific +script SIG's and I think it'll be a lot + + align:start position:0% +script SIG's and I think it'll be a lot + + + align:start position:0% +script SIG's and I think it'll be a lot +clearer exactly what this is because + + align:start position:0% +clearer exactly what this is because + + + align:start position:0% +clearer exactly what this is because +it's not clear right now what goes in + + align:start position:0% +it's not clear right now what goes in + + + align:start position:0% +it's not clear right now what goes in +the script so you're in the script punky + + align:start position:0% +the script so you're in the script punky + + + align:start position:0% +the script so you're in the script punky +so this is sort of like a logical + + align:start position:0% +so this is sort of like a logical + + + align:start position:0% +so this is sort of like a logical +representation of what a transaction + + align:start position:0% +representation of what a transaction + + + align:start position:0% +representation of what a transaction +looks like it refers to the previous + + align:start position:0% +looks like it refers to the previous + + + align:start position:0% +looks like it refers to the previous +transaction that it's spending from and + + align:start position:0% +transaction that it's spending from and + + + align:start position:0% +transaction that it's spending from and +the important things to note here are + + align:start position:0% +the important things to note here are + + + align:start position:0% +the important things to note here are +you can spend you don't have to spend + + align:start position:0% +you can spend you don't have to spend + + + align:start position:0% +you can spend you don't have to spend +all of the outputs in a transaction you + + align:start position:0% +all of the outputs in a transaction you + + + align:start position:0% +all of the outputs in a transaction you +can just spend one but you must consume + + align:start position:0% +can just spend one but you must consume + + + align:start position:0% +can just spend one but you must consume +that output entirely and produce when + + align:start position:0% +that output entirely and produce when + + + align:start position:0% +that output entirely and produce when +you produce your new outputs and so this + + align:start position:0% +you produce your new outputs and so this + + + align:start position:0% +you produce your new outputs and so this +is what's actually like this is the JSON + + align:start position:0% +is what's actually like this is the JSON + + + align:start position:0% +is what's actually like this is the JSON +representation of a transaction in + + align:start position:0% +representation of a transaction in + + + align:start position:0% +representation of a transaction in +Bitcoin okay and so this is probably + + align:start position:0% +Bitcoin okay and so this is probably + + + align:start position:0% +Bitcoin okay and so this is probably +pretty hard to read and I don't think + + align:start position:0% +pretty hard to read and I don't think + + + align:start position:0% +pretty hard to read and I don't think +it's worth it to try to look at + + align:start position:0% +it's worth it to try to look at + + + align:start position:0% +it's worth it to try to look at +everything in great detail but when we + + align:start position:0% +everything in great detail but when we + + + align:start position:0% +everything in great detail but when we +have the slides up you can take a look + + align:start position:0% +have the slides up you can take a look + + + align:start position:0% +have the slides up you can take a look +at this and this is literally what goes + + align:start position:0% +at this and this is literally what goes + + + align:start position:0% +at this and this is literally what goes +inside a transaction and there are a few + + align:start position:0% +inside a transaction and there are a few + + + align:start position:0% +inside a transaction and there are a few +fields that I'm not talking about here + + align:start position:0% +fields that I'm not talking about here + + + align:start position:0% +fields that I'm not talking about here +one is the version and another is the + + align:start position:0% +one is the version and another is the + + + align:start position:0% +one is the version and another is the +lock time and I think when we talk these + + align:start position:0% +lock time and I think when we talk these + + + align:start position:0% +lock time and I think when we talk these +scripts the script Punkie and scripts it + + align:start position:0% +scripts the script Punkie and scripts it + + + align:start position:0% +scripts the script Punkie and scripts it +can actually get quite interesting and + + align:start position:0% +can actually get quite interesting and + + + align:start position:0% +can actually get quite interesting and +quite complex that's what makes + + align:start position:0% +quite complex that's what makes + + + align:start position:0% +quite complex that's what makes +bitcoins so cool and I think when we get + + align:start position:0% +bitcoins so cool and I think when we get + + + align:start position:0% +bitcoins so cool and I think when we get +into that discussion about all the + + align:start position:0% +into that discussion about all the + + + align:start position:0% +into that discussion about all the +different things that can go into that + + align:start position:0% +different things that can go into that + + + align:start position:0% +different things that can go into that +then we'll talk a little bit more about + + align:start position:0% +then we'll talk a little bit more about + + + align:start position:0% +then we'll talk a little bit more about +what and lock time is or lock time is + + align:start position:0% +what and lock time is or lock time is + + + align:start position:0% +what and lock time is or lock time is +but the the short answer is the lock + + align:start position:0% +but the the short answer is the lock + + + align:start position:0% +but the the short answer is the lock +time tells you at what point in time + + align:start position:0% +time tells you at what point in time + + + align:start position:0% +time tells you at what point in time +this transaction is valid so until that + + align:start position:0% +this transaction is valid so until that + + + align:start position:0% +this transaction is valid so until that +lot of time happens the transaction is + + align:start position:0% +lot of time happens the transaction is + + + align:start position:0% +lot of time happens the transaction is +not valid and can't be included in the + + align:start position:0% +not valid and can't be included in the + + + align:start position:0% +not valid and can't be included in the +blockchain so this transaction is a lot + + align:start position:0% +blockchain so this transaction is a lot + + + align:start position:0% +blockchain so this transaction is a lot +of time of zero meaning it's valid + + align:start position:0% +of time of zero meaning it's valid + + + align:start position:0% +of time of zero meaning it's valid +immediately and can be included in the + + align:start position:0% +immediately and can be included in the + + + align:start position:0% +immediately and can be included in the +blockchain so here this has one input + + align:start position:0% +blockchain so here this has one input + + + align:start position:0% +blockchain so here this has one input +the input has the transaction ID and the + + align:start position:0% +the input has the transaction ID and the + + + align:start position:0% +the input has the transaction ID and the +index so that's zero so it's spending + + align:start position:0% +index so that's zero so it's spending + + + align:start position:0% +index so that's zero so it's spending +the first output of whatever that + + align:start position:0% +the first output of whatever that + + + align:start position:0% +the first output of whatever that +transaction is and it has some scripting + + align:start position:0% +transaction is and it has some scripting + + + align:start position:0% +transaction is and it has some scripting +which is empty so and then this is the + + align:start position:0% +which is empty so and then this is the + + + align:start position:0% +which is empty so and then this is the +output that it's producing its spending + + align:start position:0% +output that it's producing its spending + + + align:start position:0% +output that it's producing its spending +49.99 bitcoins from that previous output + + align:start position:0% +49.99 bitcoins from that previous output + + + align:start position:0% +49.99 bitcoins from that previous output +output and it's spending it to a new + + align:start position:0% +output and it's spending it to a new + + + align:start position:0% +output and it's spending it to a new +output and these are the rules for + + align:start position:0% +output and these are the rules for + + + align:start position:0% +output and these are the rules for +redeeming with this new output let's + + align:start position:0% +redeeming with this new output let's + + + align:start position:0% +redeeming with this new output let's +talk about consensus rules so I keep + + align:start position:0% +talk about consensus rules so I keep + + + align:start position:0% +talk about consensus rules so I keep +using the word valid right this + + align:start position:0% +using the word valid right this + + + align:start position:0% +using the word valid right this +transaction is valid this transactions + + align:start position:0% +transaction is valid this transactions + + + align:start position:0% +transaction is valid this transactions +invalid and so there are these implicit + + align:start position:0% +invalid and so there are these implicit + + + align:start position:0% +invalid and so there are these implicit +rules to Bitcoin which are defined by + + align:start position:0% +rules to Bitcoin which are defined by + + + align:start position:0% +rules to Bitcoin which are defined by +the software which state what makes a + + align:start position:0% +the software which state what makes a + + + align:start position:0% +the software which state what makes a +valid transaction or a valid block for + + align:start position:0% +valid transaction or a valid block for + + + align:start position:0% +valid transaction or a valid block for +transactions specifically the sum of the + + align:start position:0% +transactions specifically the sum of the + + + align:start position:0% +transactions specifically the sum of the +inputs has to be less than or equal to + + align:start position:0% +inputs has to be less than or equal to + + + align:start position:0% +inputs has to be less than or equal to +the sum of the outputs so you can't + + align:start position:0% +the sum of the outputs so you can't + + + align:start position:0% +the sum of the outputs so you can't +create money out of nowhere you have to + + align:start position:0% +create money out of nowhere you have to + + + align:start position:0% +create money out of nowhere you have to +actually you can't spend more than + + align:start position:0% +actually you can't spend more than + + + align:start position:0% +actually you can't spend more than +you're putting into a transaction and + + align:start position:0% +you're putting into a transaction and + + + align:start position:0% +you're putting into a transaction and +why less than or equal to fees exactly + + align:start position:0% +why less than or equal to fees exactly + + + align:start position:0% +why less than or equal to fees exactly +so the difference in the outputs and the + + align:start position:0% +so the difference in the outputs and the + + + align:start position:0% +so the difference in the outputs and the +inputs is implicit and it's a fee that + + align:start position:0% +inputs is implicit and it's a fee that + + + align:start position:0% +inputs is implicit and it's a fee that +essentially just goes to the miner the + + align:start position:0% +essentially just goes to the miner the + + + align:start position:0% +essentially just goes to the miner the +person who produces the block there is + + align:start position:0% +person who produces the block there is + + + align:start position:0% +person who produces the block there is +one exception to this rule it's a + + align:start position:0% +one exception to this rule it's a + + + align:start position:0% +one exception to this rule it's a +transaction called the coinbase + + align:start position:0% +transaction called the coinbase + + + align:start position:0% +transaction called the coinbase +transaction no relation to the company + + align:start position:0% +transaction no relation to the company + + + align:start position:0% +transaction no relation to the company +it's not named after the company I think + + align:start position:0% +it's not named after the company I think + + + align:start position:0% +it's not named after the company I think +the company is named after it but it's + + align:start position:0% +the company is named after it but it's + + + align:start position:0% +the company is named after it but it's +the first transaction in a block and + + align:start position:0% +the first transaction in a block and + + + align:start position:0% +the first transaction in a block and +it's the transaction that gives out the + + align:start position:0% +it's the transaction that gives out the + + + align:start position:0% +it's the transaction that gives out the +block reward so the first transaction in + + align:start position:0% +block reward so the first transaction in + + + align:start position:0% +block reward so the first transaction in +a block is the transit is special it + + align:start position:0% +a block is the transit is special it + + + align:start position:0% +a block is the transit is special it +doesn't have any inputs or it does have + + align:start position:0% +doesn't have any inputs or it does have + + + align:start position:0% +doesn't have any inputs or it does have +puts but they're meaningless and it + + align:start position:0% +puts but they're meaningless and it + + + align:start position:0% +puts but they're meaningless and it +produces the block rewards so right now + + align:start position:0% +produces the block rewards so right now + + + align:start position:0% +produces the block rewards so right now +the block reward is 12.5 bitcoins so + + align:start position:0% +the block reward is 12.5 bitcoins so + + + align:start position:0% +the block reward is 12.5 bitcoins so +every time a block is produced every one + + align:start position:0% +every time a block is produced every one + + + align:start position:0% +every time a block is produced every one +every time someone solves that + + align:start position:0% +every time someone solves that + + + align:start position:0% +every time someone solves that +proof-of-work puzzle and produces a + + align:start position:0% +proof-of-work puzzle and produces a + + + align:start position:0% +proof-of-work puzzle and produces a +block they include a transaction at the + + align:start position:0% +block they include a transaction at the + + + align:start position:0% +block they include a transaction at the +very beginning that usually gives + + align:start position:0% +very beginning that usually gives + + + align:start position:0% +very beginning that usually gives +themselves 12.5 Bitcoin plus whatever + + align:start position:0% +themselves 12.5 Bitcoin plus whatever + + + align:start position:0% +themselves 12.5 Bitcoin plus whatever +fees are implicit in all of the trend in + + align:start position:0% +fees are implicit in all of the trend in + + + align:start position:0% +fees are implicit in all of the trend in +as the sum of all of the transactions in + + align:start position:0% +as the sum of all of the transactions in + + + align:start position:0% +as the sum of all of the transactions in +the block so this invariant must be + + align:start position:0% +the block so this invariant must be + + + align:start position:0% +the block so this invariant must be +maintained except for the coinbase + + align:start position:0% +maintained except for the coinbase + + + align:start position:0% +maintained except for the coinbase +transaction of which there's one in + + align:start position:0% +transaction of which there's one in + + + align:start position:0% +transaction of which there's one in +every block and then this invariant must + + align:start position:0% +every block and then this invariant must + + + align:start position:0% +every block and then this invariant must +also be maintained which oh yes sorry + + align:start position:0% +also be maintained which oh yes sorry + + + align:start position:0% +also be maintained which oh yes sorry +the people creating the transaction + + align:start position:0% +the people creating the transaction + + + align:start position:0% +the people creating the transaction +determine the fees so when I create a + + align:start position:0% +determine the fees so when I create a + + + align:start position:0% +determine the fees so when I create a +transaction I'm specifying which outputs + + align:start position:0% +transaction I'm specifying which outputs + + + align:start position:0% +transaction I'm specifying which outputs +I'm spending and putting them in my + + align:start position:0% +I'm spending and putting them in my + + + align:start position:0% +I'm spending and putting them in my +inputs and I'm producing the outputs so + + align:start position:0% +inputs and I'm producing the outputs so + + + align:start position:0% +inputs and I'm producing the outputs so +I could you know I just have to maintain + + align:start position:0% +I could you know I just have to maintain + + + align:start position:0% +I could you know I just have to maintain +that invariant right so let's say that + + align:start position:0% +that invariant right so let's say that + + + align:start position:0% +that invariant right so let's say that +I'm spending an import worth five + + align:start position:0% +I'm spending an import worth five + + + align:start position:0% +I'm spending an import worth five +Bitcoin I could produce an output worth + + align:start position:0% +Bitcoin I could produce an output worth + + + align:start position:0% +Bitcoin I could produce an output worth +five Bitcoin meaning that the fee is + + align:start position:0% +five Bitcoin meaning that the fee is + + + align:start position:0% +five Bitcoin meaning that the fee is +zero it's very unlikely that my + + align:start position:0% +zero it's very unlikely that my + + + align:start position:0% +zero it's very unlikely that my +transaction would get accepted into the + + align:start position:0% +transaction would get accepted into the + + + align:start position:0% +transaction would get accepted into the +blockchain with a fee of zero it's + + align:start position:0% +blockchain with a fee of zero it's + + + align:start position:0% +blockchain with a fee of zero it's +possible sure but if I'm not mining + + align:start position:0% +possible sure but if I'm not mining + + + align:start position:0% +possible sure but if I'm not mining +myself why would a miner take my + + align:start position:0% +myself why would a miner take my + + + align:start position:0% +myself why would a miner take my +transaction when they could take a + + align:start position:0% +transaction when they could take a + + + align:start position:0% +transaction when they could take a +transaction that has a higher fee + + align:start position:0% +transaction that has a higher fee + + + align:start position:0% +transaction that has a higher fee +associated with it and the fee is + + align:start position:0% +associated with it and the fee is + + + align:start position:0% +associated with it and the fee is +implicit it's the difference between the + + align:start position:0% +implicit it's the difference between the + + + align:start position:0% +implicit it's the difference between the +sum of the inputs and the sum of the + + align:start position:0% +sum of the inputs and the sum of the + + + align:start position:0% +sum of the inputs and the sum of the +outputs any other questions at this + + align:start position:0% +outputs any other questions at this + + + align:start position:0% +outputs any other questions at this +point the fee is okay the fee is + + align:start position:0% +point the fee is okay the fee is + + + align:start position:0% +point the fee is okay the fee is +implicit so when you so in the inputs + + align:start position:0% +implicit so when you so in the inputs + + + align:start position:0% +implicit so when you so in the inputs +you're consuming so let's let's use this + + align:start position:0% +you're consuming so let's let's use this + + + align:start position:0% +you're consuming so let's let's use this +example right here okay so here we're + + align:start position:0% +example right here okay so here we're + + + align:start position:0% +example right here okay so here we're +consuming this output which has 20 + + align:start position:0% +consuming this output which has 20 + + + align:start position:0% +consuming this output which has 20 +Bitcoin in it right so implicitly this + + align:start position:0% +Bitcoin in it right so implicitly this + + + align:start position:0% +Bitcoin in it right so implicitly this +thing has 20 Bitcoin to spend alright + + align:start position:0% +thing has 20 Bitcoin to spend alright + + + align:start position:0% +thing has 20 Bitcoin to spend alright +now before I had it set up as five ten + + align:start position:0% +now before I had it set up as five ten + + + align:start position:0% +now before I had it set up as five ten +five right and so 20 needs to be greater + + align:start position:0% +five right and so 20 needs to be greater + + + align:start position:0% +five right and so 20 needs to be greater +than or equal to 5 plus ten plus five + + align:start position:0% +than or equal to 5 plus ten plus five + + + align:start position:0% +than or equal to 5 plus ten plus five +and it is great 20 + + align:start position:0% +and it is great 20 + + + align:start position:0% +and it is great 20 +greater than or equal to 20 what I could + + align:start position:0% +greater than or equal to 20 what I could + + + align:start position:0% +greater than or equal to 20 what I could +do is I could change this number to a 4 + + align:start position:0% +do is I could change this number to a 4 + + + align:start position:0% +do is I could change this number to a 4 +and so what this means is notice that + + align:start position:0% +and so what this means is notice that + + + align:start position:0% +and so what this means is notice that +this adds up to 19 now where did that + + align:start position:0% +this adds up to 19 now where did that + + + align:start position:0% +this adds up to 19 now where did that +one Bitcoin go that one Bitcoin + + align:start position:0% +one Bitcoin go that one Bitcoin + + + align:start position:0% +one Bitcoin go that one Bitcoin +implicitly goes to whoever produces the + + align:start position:0% +implicitly goes to whoever produces the + + + align:start position:0% +implicitly goes to whoever produces the +block in which that contains this + + align:start position:0% +block in which that contains this + + + align:start position:0% +block in which that contains this +transaction yeah you're right sorry that + + align:start position:0% +transaction yeah you're right sorry that + + + align:start position:0% +transaction yeah you're right sorry that +should be greater than or equal to sorry + + align:start position:0% +should be greater than or equal to sorry + + + align:start position:0% +should be greater than or equal to sorry +about that + + align:start position:0% +about that + + + align:start position:0% +about that +so another invariant that needs to be + + align:start position:0% +so another invariant that needs to be + + + align:start position:0% +so another invariant that needs to be +maintained is that this output has not + + align:start position:0% +maintained is that this output has not + + + align:start position:0% +maintained is that this output has not +already been referenced in another + + align:start position:0% +already been referenced in another + + + align:start position:0% +already been referenced in another +transaction in another valid transaction + + align:start position:0% +transaction in another valid transaction + + + align:start position:0% +transaction in another valid transaction +and then as I alluded to a final + + align:start position:0% +and then as I alluded to a final + + + align:start position:0% +and then as I alluded to a final +invariant is around the lock time so + + align:start position:0% +invariant is around the lock time so + + + align:start position:0% +invariant is around the lock time so +let's go into an example of how this + + align:start position:0% +let's go into an example of how this + + + align:start position:0% +let's go into an example of how this +actually works + + align:start position:0% +actually works + + + align:start position:0% +actually works +this script sig and script pub key thing + + align:start position:0% +this script sig and script pub key thing + + + align:start position:0% +this script sig and script pub key thing +so I haven't really gone into detail yet + + align:start position:0% +so I haven't really gone into detail yet + + + align:start position:0% +so I haven't really gone into detail yet +about what this is I sort of implied + + align:start position:0% +about what this is I sort of implied + + + align:start position:0% +about what this is I sort of implied +that this specified a key and the + + align:start position:0% +that this specified a key and the + + + align:start position:0% +that this specified a key and the +specified a signature but what does this + + align:start position:0% +specified a signature but what does this + + + align:start position:0% +specified a signature but what does this +actually look like and I mean I think + + align:start position:0% +actually look like and I mean I think + + + align:start position:0% +actually look like and I mean I think +this is really really interesting + + align:start position:0% +this is really really interesting + + + align:start position:0% +this is really really interesting +actually because Bitcoin lets you + + align:start position:0% +actually because Bitcoin lets you + + + align:start position:0% +actually because Bitcoin lets you +specify lots of different script pub + + align:start position:0% +specify lots of different script pub + + + align:start position:0% +specify lots of different script pub +keys and lots of different script SIG's + + align:start position:0% +keys and lots of different script SIG's + + + align:start position:0% +keys and lots of different script SIG's +and so this gives you this kind of + + align:start position:0% +and so this gives you this kind of + + + align:start position:0% +and so this gives you this kind of +flexibility so that you can program in + + align:start position:0% +flexibility so that you can program in + + + align:start position:0% +flexibility so that you can program in +different kinds of conditions on what it + + align:start position:0% +different kinds of conditions on what it + + + align:start position:0% +different kinds of conditions on what it +takes to redeem a transaction so we're + + align:start position:0% +takes to redeem a transaction so we're + + + align:start position:0% +takes to redeem a transaction so we're +just going to talk about a couple very + + align:start position:0% +just going to talk about a couple very + + + align:start position:0% +just going to talk about a couple very +simple ones because to get into sort of + + align:start position:0% +simple ones because to get into sort of + + + align:start position:0% +simple ones because to get into sort of +more complex stuff we need to go really + + align:start position:0% +more complex stuff we need to go really + + + align:start position:0% +more complex stuff we need to go really +deep into this word script so basically + + align:start position:0% +deep into this word script so basically + + + align:start position:0% +deep into this word script so basically +the script pub key and the script sig + + align:start position:0% +the script pub key and the script sig + + + align:start position:0% +the script pub key and the script sig +are composed of op codes so Bitcoin has + + align:start position:0% +are composed of op codes so Bitcoin has + + + align:start position:0% +are composed of op codes so Bitcoin has +a little less than 200 op codes and you + + align:start position:0% +a little less than 200 op codes and you + + + align:start position:0% +a little less than 200 op codes and you +write the coin scripts using these op + + align:start position:0% +write the coin scripts using these op + + + align:start position:0% +write the coin scripts using these op +codes so let's talk about the most + + align:start position:0% +codes so let's talk about the most + + + align:start position:0% +codes so let's talk about the most +common Bitcoin script which is paid a + + align:start position:0% +common Bitcoin script which is paid a + + + align:start position:0% +common Bitcoin script which is paid a +pub key hash + + align:start position:0% +pub key hash + + + align:start position:0% +pub key hash +so the idea here is you want to send + + align:start position:0% +so the idea here is you want to send + + + align:start position:0% +so the idea here is you want to send +money to a public key so Alice has Bob's + + align:start position:0% +money to a public key so Alice has Bob's + + + align:start position:0% +money to a public key so Alice has Bob's +public key and Alice wants to pay Bob + + align:start position:0% +public key and Alice wants to pay Bob + + + align:start position:0% +public key and Alice wants to pay Bob +and so Alice wants to send money to + + align:start position:0% +and so Alice wants to send money to + + + align:start position:0% +and so Alice wants to send money to +Bob's public key well the reason that + + align:start position:0% +Bob's public key well the reason that + + + align:start position:0% +Bob's public key well the reason that +this is called pub key hash I thought + + align:start position:0% +this is called pub key hash I thought + + + align:start position:0% +this is called pub key hash I thought +what keys are kind of big and there's + + align:start position:0% +what keys are kind of big and there's + + + align:start position:0% +what keys are kind of big and there's +this nice you can kind of like make this + + align:start position:0% +this nice you can kind of like make this + + + align:start position:0% +this nice you can kind of like make this +nice observation that you don't + + align:start position:0% +nice observation that you don't + + + align:start position:0% +nice observation that you don't +necessarily have to put the whole public + + align:start position:0% +necessarily have to put the whole public + + + align:start position:0% +necessarily have to put the whole public +key in the output you can put a hash of + + align:start position:0% +key in the output you can put a hash of + + + align:start position:0% +key in the output you can put a hash of +the public key in the output and I think + + align:start position:0% +the public key in the output and I think + + + align:start position:0% +the public key in the output and I think +Taj already talked about this when he + + align:start position:0% +Taj already talked about this when he + + + align:start position:0% +Taj already talked about this when he +was talking about Bitcoin addresses so + + align:start position:0% +was talking about Bitcoin addresses so + + + align:start position:0% +was talking about Bitcoin addresses so +the script pub key is instructions on + + align:start position:0% +the script pub key is instructions on + + + align:start position:0% +the script pub key is instructions on +how to verify a signature of a public + + align:start position:0% +how to verify a signature of a public + + + align:start position:0% +how to verify a signature of a public +key that has been hashed and the script + + align:start position:0% +key that has been hashed and the script + + + align:start position:0% +key that has been hashed and the script +sig is that signature and the actual + + align:start position:0% +sig is that signature and the actual + + + align:start position:0% +sig is that signature and the actual +public key the preimage of the hash + + align:start position:0% +public key the preimage of the hash + + + align:start position:0% +public key the preimage of the hash +public key and this is what that looks + + align:start position:0% +public key and this is what that looks + + + align:start position:0% +public key and this is what that looks +like so this is literally the script pub + + align:start position:0% +like so this is literally the script pub + + + align:start position:0% +like so this is literally the script pub +key for a paid a pub key hash input or + + align:start position:0% +key for a paid a pub key hash input or + + + align:start position:0% +key for a paid a pub key hash input or +output and this is literally the script + + align:start position:0% +output and this is literally the script + + + align:start position:0% +output and this is literally the script +sig that would you would use to redeem + + align:start position:0% +sig that would you would use to redeem + + + align:start position:0% +sig that would you would use to redeem +that output so this right here would go + + align:start position:0% +that output so this right here would go + + + align:start position:0% +that output so this right here would go +inside one of these and it would set the + + align:start position:0% +inside one of these and it would set the + + + align:start position:0% +inside one of these and it would set the +conditions under which you could redeem + + align:start position:0% +conditions under which you could redeem + + + align:start position:0% +conditions under which you could redeem +this output and this right here would go + + align:start position:0% +this output and this right here would go + + + align:start position:0% +this output and this right here would go +inside the input of the transaction + + align:start position:0% +inside the input of the transaction + + + align:start position:0% +inside the input of the transaction +that's redeeming it and let's take a + + align:start position:0% +that's redeeming it and let's take a + + + align:start position:0% +that's redeeming it and let's take a +look at how this actually works okay so + + align:start position:0% +look at how this actually works okay so + + + align:start position:0% +look at how this actually works okay so +what the Bitcoin script interpreter does + + align:start position:0% +what the Bitcoin script interpreter does + + + align:start position:0% +what the Bitcoin script interpreter does +is when it's evaluating whether or not a + + align:start position:0% +is when it's evaluating whether or not a + + + align:start position:0% +is when it's evaluating whether or not a +transaction is valid it takes a look at + + align:start position:0% +transaction is valid it takes a look at + + + align:start position:0% +transaction is valid it takes a look at +the input and it looks at which previous + + align:start position:0% +the input and it looks at which previous + + + align:start position:0% +the input and it looks at which previous +transaction it's looking at and which + + align:start position:0% +transaction it's looking at and which + + + align:start position:0% +transaction it's looking at and which +index the output is and it grabs the + + align:start position:0% +index the output is and it grabs the + + + align:start position:0% +index the output is and it grabs the +script pub key well first of all and + + align:start position:0% +script pub key well first of all and + + + align:start position:0% +script pub key well first of all and +make sure that output hasn't already + + align:start position:0% +make sure that output hasn't already + + + align:start position:0% +make sure that output hasn't already +been spent then it grabs the script pub + + align:start position:0% +been spent then it grabs the script pub + + + align:start position:0% +been spent then it grabs the script pub +key and it takes the script sig and it + + align:start position:0% +key and it takes the script sig and it + + + align:start position:0% +key and it takes the script sig and it +puts them on top of each other just like + + align:start position:0% +puts them on top of each other just like + + + align:start position:0% +puts them on top of each other just like +this so that's the script steak up there + + align:start position:0% +this so that's the script steak up there + + + align:start position:0% +this so that's the script steak up there +this is a script pub key down here and + + align:start position:0% +this is a script pub key down here and + + + align:start position:0% +this is a script pub key down here and +it runs this combined script through of + + align:start position:0% +it runs this combined script through of + + + align:start position:0% +it runs this combined script through of +the Bitcoin script interpreter which is + + align:start position:0% +the Bitcoin script interpreter which is + + + align:start position:0% +the Bitcoin script interpreter which is +based on a stack model so it starts + + align:start position:0% +based on a stack model so it starts + + + align:start position:0% +based on a stack model so it starts +pushing things on to the stack it starts + + align:start position:0% +pushing things on to the stack it starts + + + align:start position:0% +pushing things on to the stack it starts +at the very top and it starts pushing + + align:start position:0% +at the very top and it starts pushing + + + align:start position:0% +at the very top and it starts pushing +these items onto the stack and + + align:start position:0% +these items onto the stack and + + + align:start position:0% +these items onto the stack and +evaluating them and so the rules are + + align:start position:0% +evaluating them and so the rules are + + + align:start position:0% +evaluating them and so the rules are +that constants get pushed onto the stack + + align:start position:0% +that constants get pushed onto the stack + + + align:start position:0% +that constants get pushed onto the stack +and then operations and these things + + align:start position:0% +and then operations and these things + + + align:start position:0% +and then operations and these things +right here are operations op do pop hash + + align:start position:0% +right here are operations op do pop hash + + + align:start position:0% +right here are operations op do pop hash +160 people verify and op check sig these + + align:start position:0% +160 people verify and op check sig these + + + align:start position:0% +160 people verify and op check sig these +are all Bitcoin op codes operations have + + align:start position:0% +are all Bitcoin op codes operations have + + + align:start position:0% +are all Bitcoin op codes operations have +different rules as to how they're + + align:start position:0% +different rules as to how they're + + + align:start position:0% +different rules as to how they're +evaluated and what they consume off of + + align:start position:0% +evaluated and what they consume off of + + + align:start position:0% +evaluated and what they consume off of +the stack so the first thing is a + + align:start position:0% +the stack so the first thing is a + + + align:start position:0% +the stack so the first thing is a +signature we're gonna pop the signature + + align:start position:0% +signature we're gonna pop the signature + + + align:start position:0% +signature we're gonna pop the signature +and push it onto the stack because it is + + align:start position:0% +and push it onto the stack because it is + + + align:start position:0% +and push it onto the stack because it is +a it is a constant so this would be the + + align:start position:0% +a it is a constant so this would be the + + + align:start position:0% +a it is a constant so this would be the +signature that Alice might produce in + + align:start position:0% +signature that Alice might produce in + + + align:start position:0% +signature that Alice might produce in +order to spend her output then same + + align:start position:0% +order to spend her output then same + + + align:start position:0% +order to spend her output then same +thing with the pub key because the pub + + align:start position:0% +thing with the pub key because the pub + + + align:start position:0% +thing with the pub key because the pub +key is also a constant then we're gonna + + align:start position:0% +key is also a constant then we're gonna + + + align:start position:0% +key is also a constant then we're gonna +take this first like now okay we're done + + align:start position:0% +take this first like now okay we're done + + + align:start position:0% +take this first like now okay we're done +with constants for the moment and the + + align:start position:0% +with constants for the moment and the + + + align:start position:0% +with constants for the moment and the +next thing on the stack is op do op Duke + + align:start position:0% +next thing on the stack is op do op Duke + + + align:start position:0% +next thing on the stack is op do op Duke +does basically exactly what it sounds + + align:start position:0% +does basically exactly what it sounds + + + align:start position:0% +does basically exactly what it sounds +like it takes the thing that's currently + + align:start position:0% +like it takes the thing that's currently + + + align:start position:0% +like it takes the thing that's currently +on the top of the stack and it + + align:start position:0% +on the top of the stack and it + + + align:start position:0% +on the top of the stack and it +duplicates it so the way that we consume + + align:start position:0% +duplicates it so the way that we consume + + + align:start position:0% +duplicates it so the way that we consume +up do is we take this pub key and we + + align:start position:0% +up do is we take this pub key and we + + + align:start position:0% +up do is we take this pub key and we +create another copy of the pub key the + + align:start position:0% +create another copy of the pub key the + + + align:start position:0% +create another copy of the pub key the +next up is op hash 160 also does exactly + + align:start position:0% +next up is op hash 160 also does exactly + + + align:start position:0% +next up is op hash 160 also does exactly +what it sounds like + + align:start position:0% +what it sounds like + + + align:start position:0% +what it sounds like +it takes what's on the top of the stack + + align:start position:0% +it takes what's on the top of the stack + + + align:start position:0% +it takes what's on the top of the stack +it hashes it and it pushes that hash + + align:start position:0% +it hashes it and it pushes that hash + + + align:start position:0% +it hashes it and it pushes that hash +onto the top of the stack so after we + + align:start position:0% +onto the top of the stack so after we + + + align:start position:0% +onto the top of the stack so after we +run op hash 160 this is what our hash + + align:start position:0% +run op hash 160 this is what our hash + + + align:start position:0% +run op hash 160 this is what our hash +will this is what our stack will look + + align:start position:0% +will this is what our stack will look + + + align:start position:0% +will this is what our stack will look +like next thing is a constant so we take + + align:start position:0% +like next thing is a constant so we take + + + align:start position:0% +like next thing is a constant so we take +that constant which is a it which should + + align:start position:0% +that constant which is a it which should + + + align:start position:0% +that constant which is a it which should +be which is the hash of the pub key so + + align:start position:0% +be which is the hash of the pub key so + + + align:start position:0% +be which is the hash of the pub key so +this is the address that this money is + + align:start position:0% +this is the address that this money is + + + align:start position:0% +this is the address that this money is +being sent to essentially and we put + + align:start position:0% +being sent to essentially and we put + + + align:start position:0% +being sent to essentially and we put +that on the top of the stack and then we + + align:start position:0% +that on the top of the stack and then we + + + align:start position:0% +that on the top of the stack and then we +run this operation called op equal + + align:start position:0% +run this operation called op equal + + + align:start position:0% +run this operation called op equal +verify whenever an op code ends with + + align:start position:0% +verify whenever an op code ends with + + + align:start position:0% +verify whenever an op code ends with +verify it means that it's a little bit + + align:start position:0% +verify it means that it's a little bit + + + align:start position:0% +verify it means that it's a little bit +special it means that it has the ability + + align:start position:0% +special it means that it has the ability + + + align:start position:0% +special it means that it has the ability +to + + align:start position:0% +to + + + align:start position:0% +to +if it fails break out of the entire + + align:start position:0% +if it fails break out of the entire + + + align:start position:0% +if it fails break out of the entire +script execution and immediately cause + + align:start position:0% +script execution and immediately cause + + + align:start position:0% +script execution and immediately cause +transaction validation to fail so op + + align:start position:0% +transaction validation to fail so op + + + align:start position:0% +transaction validation to fail so op +equal verified does what it sounds like + + align:start position:0% +equal verified does what it sounds like + + + align:start position:0% +equal verified does what it sounds like +it checks to make sure that the two + + align:start position:0% +it checks to make sure that the two + + + align:start position:0% +it checks to make sure that the two +things on the top of the stack are equal + + align:start position:0% +things on the top of the stack are equal + + + align:start position:0% +things on the top of the stack are equal +and if they're not equal then it + + align:start position:0% +and if they're not equal then it + + + align:start position:0% +and if they're not equal then it +immediately fails validation so you'll + + align:start position:0% +immediately fails validation so you'll + + + align:start position:0% +immediately fails validation so you'll +note that what the two things at the top + + align:start position:0% +note that what the two things at the top + + + align:start position:0% +note that what the two things at the top +of this let's go back to what the two + + align:start position:0% +of this let's go back to what the two + + + align:start position:0% +of this let's go back to what the two +things on the top of the stack are right + + align:start position:0% +things on the top of the stack are right + + + align:start position:0% +things on the top of the stack are right +now okay so we pushed the cig we pushed + + align:start position:0% +now okay so we pushed the cig we pushed + + + align:start position:0% +now okay so we pushed the cig we pushed +a pub key we duplicated that pub key and + + align:start position:0% +a pub key we duplicated that pub key and + + + align:start position:0% +a pub key we duplicated that pub key and +these are from the script sig so this is + + align:start position:0% +these are from the script sig so this is + + + align:start position:0% +these are from the script sig so this is +from whoever's redeeming the transaction + + align:start position:0% +from whoever's redeeming the transaction + + + align:start position:0% +from whoever's redeeming the transaction +okay so whoever's redeeming the + + align:start position:0% +okay so whoever's redeeming the + + + align:start position:0% +okay so whoever's redeeming the +transaction has put a copy of this of + + align:start position:0% +transaction has put a copy of this of + + + align:start position:0% +transaction has put a copy of this of +this pub key on there and now that pub + + align:start position:0% +this pub key on there and now that pub + + + align:start position:0% +this pub key on there and now that pub +keys on the stack twice we hashed the + + align:start position:0% +keys on the stack twice we hashed the + + + align:start position:0% +keys on the stack twice we hashed the +pub key and then we put we pushed the + + align:start position:0% +pub key and then we put we pushed the + + + align:start position:0% +pub key and then we put we pushed the +hash that was specified in the part of + + align:start position:0% +hash that was specified in the part of + + + align:start position:0% +hash that was specified in the part of +the transact and the previous + + align:start position:0% +the transact and the previous + + + align:start position:0% +the transact and the previous +transaction that set up the rules for + + align:start position:0% +transaction that set up the rules for + + + align:start position:0% +transaction that set up the rules for +how to spend this okay and then op equal + + align:start position:0% +how to spend this okay and then op equal + + + align:start position:0% +how to spend this okay and then op equal +verify make sure that these things are + + align:start position:0% +verify make sure that these things are + + + align:start position:0% +verify make sure that these things are +actually the same and if they're not the + + align:start position:0% +actually the same and if they're not the + + + align:start position:0% +actually the same and if they're not the +same then it'll fail that verify check + + align:start position:0% +same then it'll fail that verify check + + + align:start position:0% +same then it'll fail that verify check +in the entire transaction validation + + align:start position:0% +in the entire transaction validation + + + align:start position:0% +in the entire transaction validation +will abort and it's an invalid + + align:start position:0% +will abort and it's an invalid + + + align:start position:0% +will abort and it's an invalid +transaction so let's assume that they're + + align:start position:0% +transaction so let's assume that they're + + + align:start position:0% +transaction so let's assume that they're +the same okay great then op equal verify + + align:start position:0% +the same okay great then op equal verify + + + align:start position:0% +the same okay great then op equal verify +can't then we continue transaction + + align:start position:0% +can't then we continue transaction + + + align:start position:0% +can't then we continue transaction +validation and now we're left with this + + align:start position:0% +validation and now we're left with this + + + align:start position:0% +validation and now we're left with this +op check sig pub key SiC and this does + + align:start position:0% +op check sig pub key SiC and this does + + + align:start position:0% +op check sig pub key SiC and this does +exactly what you think it might do it + + align:start position:0% +exactly what you think it might do it + + + align:start position:0% +exactly what you think it might do it +pops two things off the stack checks to + + align:start position:0% +pops two things off the stack checks to + + + align:start position:0% +pops two things off the stack checks to +make sure that the signature is a valid + + align:start position:0% +make sure that the signature is a valid + + + align:start position:0% +make sure that the signature is a valid +signature for this pub key and if it is + + align:start position:0% +signature for this pub key and if it is + + + align:start position:0% +signature for this pub key and if it is +it pushes true on to the stack and if + + align:start position:0% +it pushes true on to the stack and if + + + align:start position:0% +it pushes true on to the stack and if +there is a true on top of the stack in + + align:start position:0% +there is a true on top of the stack in + + + align:start position:0% +there is a true on top of the stack in +fact I think it's if there's any + + align:start position:0% +fact I think it's if there's any + + + align:start position:0% +fact I think it's if there's any +constant on top of the stack when we've + + align:start position:0% +constant on top of the stack when we've + + + align:start position:0% +constant on top of the stack when we've +consumed all of the parts of our script + + align:start position:0% +consumed all of the parts of our script + + + align:start position:0% +consumed all of the parts of our script +say again script pub key then this + + align:start position:0% +say again script pub key then this + + + align:start position:0% +say again script pub key then this +transaction this returns true and we in + + align:start position:0% +transaction this returns true and we in + + + align:start position:0% +transaction this returns true and we in +the veldt and the transaction is + + align:start position:0% +the veldt and the transaction is + + + align:start position:0% +the veldt and the transaction is +considered valid + + align:start position:0% + + + + align:start position:0% + +so let's this is a lot and and I know + + align:start position:0% +so let's this is a lot and and I know + + + align:start position:0% +so let's this is a lot and and I know +this is kind of complicated so let's + + align:start position:0% +this is kind of complicated so let's + + + align:start position:0% +this is kind of complicated so let's +sort of step through this one more time + + align:start position:0% +sort of step through this one more time + + + align:start position:0% +sort of step through this one more time +and there's just a couple + + align:start position:0% +and there's just a couple + + + align:start position:0% +and there's just a couple +things that I want to make clear this + + align:start position:0% +things that I want to make clear this + + + align:start position:0% +things that I want to make clear this +part right here is set up in the output + + align:start position:0% +part right here is set up in the output + + + align:start position:0% +part right here is set up in the output +of whatever transaction we're spending + + align:start position:0% +of whatever transaction we're spending + + + align:start position:0% +of whatever transaction we're spending +so if Alice creates this transaction and + + align:start position:0% +so if Alice creates this transaction and + + + align:start position:0% +so if Alice creates this transaction and +she's spending to Bob then Alice would + + align:start position:0% +she's spending to Bob then Alice would + + + align:start position:0% +she's spending to Bob then Alice would +put whose pub key here hash of a pub key + + align:start position:0% +put whose pub key here hash of a pub key + + + align:start position:0% +put whose pub key here hash of a pub key +actually right so Alice would put the + + align:start position:0% +actually right so Alice would put the + + + align:start position:0% +actually right so Alice would put the +hash of bob's cup key here and it when + + align:start position:0% +hash of bob's cup key here and it when + + + align:start position:0% +hash of bob's cup key here and it when +Bob's redeeming what would go in the + + align:start position:0% +Bob's redeeming what would go in the + + + align:start position:0% +Bob's redeeming what would go in the +input that needs to redeem that output + + align:start position:0% + + + + align:start position:0% + +sorry I can't hear Bob's signature and + + align:start position:0% +sorry I can't hear Bob's signature and + + + align:start position:0% +sorry I can't hear Bob's signature and +the pub key that corresponds to that + + align:start position:0% +the pub key that corresponds to that + + + align:start position:0% +the pub key that corresponds to that +signature because all we have is a hash + + align:start position:0% +signature because all we have is a hash + + + align:start position:0% +signature because all we have is a hash +so those are the things that would get + + align:start position:0% +so those are the things that would get + + + align:start position:0% +so those are the things that would get +put on top of the stack so up there we + + align:start position:0% +put on top of the stack so up there we + + + align:start position:0% +put on top of the stack so up there we +have Bob signature and we have Bob's pub + + align:start position:0% +have Bob signature and we have Bob's pub + + + align:start position:0% +have Bob signature and we have Bob's pub +key again those get pushed onto the + + align:start position:0% +key again those get pushed onto the + + + align:start position:0% +key again those get pushed onto the +stack because they're constants + + align:start position:0% +stack because they're constants + + + align:start position:0% +stack because they're constants +duplicated hash the top copy over the + + align:start position:0% +duplicated hash the top copy over the + + + align:start position:0% +duplicated hash the top copy over the +hash make sure that they're equal and + + align:start position:0% +hash make sure that they're equal and + + + align:start position:0% +hash make sure that they're equal and +then check the signature and this is a + + align:start position:0% +then check the signature and this is a + + + align:start position:0% +then check the signature and this is a +paid a pub key hash script it is the + + align:start position:0% +paid a pub key hash script it is the + + + align:start position:0% +paid a pub key hash script it is the +most common script in Bitcoin and this + + align:start position:0% +most common script in Bitcoin and this + + + align:start position:0% +most common script in Bitcoin and this +is this basically the standard way of + + align:start position:0% +is this basically the standard way of + + + align:start position:0% +is this basically the standard way of +spending money are there questions about + + align:start position:0% +spending money are there questions about + + + align:start position:0% +spending money are there questions about +this yes + + align:start position:0% + + + + align:start position:0% + +yeah that's a great question so um let's + + align:start position:0% +yeah that's a great question so um let's + + + align:start position:0% +yeah that's a great question so um let's +say that we didn't have this equal + + align:start position:0% +say that we didn't have this equal + + + align:start position:0% +say that we didn't have this equal +verify here then what could a malicious + + align:start position:0% +verify here then what could a malicious + + + align:start position:0% +verify here then what could a malicious +spender possibly do that's a good + + align:start position:0% +spender possibly do that's a good + + + align:start position:0% +spender possibly do that's a good +question I don't think that would matter + + align:start position:0% +question I don't think that would matter + + + align:start position:0% +question I don't think that would matter +I'm not sure would it matter it's faster + + align:start position:0% +I'm not sure would it matter it's faster + + + align:start position:0% +I'm not sure would it matter it's faster +to verify the two hashes are equal the + + align:start position:0% +to verify the two hashes are equal the + + + align:start position:0% +to verify the two hashes are equal the +checks take operation takes a yes yes + + align:start position:0% +checks take operation takes a yes yes + + + align:start position:0% +checks take operation takes a yes yes +every single node on the network is + + align:start position:0% +every single node on the network is + + + align:start position:0% +every single node on the network is +running the Bitcoin script interpreter + + align:start position:0% +running the Bitcoin script interpreter + + + align:start position:0% +running the Bitcoin script interpreter +inside of it and the Bitcoin script + + align:start position:0% +inside of it and the Bitcoin script + + + align:start position:0% +inside of it and the Bitcoin script +interpreter is known as is what's called + + align:start position:0% +interpreter is known as is what's called + + + align:start position:0% +interpreter is known as is what's called +consensus critical so if two nodes have + + align:start position:0% +consensus critical so if two nodes have + + + align:start position:0% +consensus critical so if two nodes have +slightly different script interpreters + + align:start position:0% +slightly different script interpreters + + + align:start position:0% +slightly different script interpreters +that would interpret this in different + + align:start position:0% +that would interpret this in different + + + align:start position:0% +that would interpret this in different +ways the network would have a consensus + + align:start position:0% +ways the network would have a consensus + + + align:start position:0% +ways the network would have a consensus +failure yes peanut booking is a thing + + align:start position:0% +failure yes peanut booking is a thing + + + align:start position:0% +failure yes peanut booking is a thing +actually and paid aha punky hash is + + align:start position:0% +actually and paid aha punky hash is + + + align:start position:0% +actually and paid aha punky hash is +considered better and the reason for + + align:start position:0% +considered better and the reason for + + + align:start position:0% +considered better and the reason for +that is kind of subtle actually it's + + align:start position:0% +that is kind of subtle actually it's + + + align:start position:0% +that is kind of subtle actually it's +because um so the hash of the pub key is + + align:start position:0% +because um so the hash of the pub key is + + + align:start position:0% +because um so the hash of the pub key is +smaller than the pub key right and this + + align:start position:0% +smaller than the pub key right and this + + + align:start position:0% +smaller than the pub key right and this +is definitely going on the blockchain we + + align:start position:0% +is definitely going on the blockchain we + + + align:start position:0% +is definitely going on the blockchain we +don't know if this is gonna go on the + + align:start position:0% +don't know if this is gonna go on the + + + align:start position:0% +don't know if this is gonna go on the +blockchain or not not all outputs are + + align:start position:0% +blockchain or not not all outputs are + + + align:start position:0% +blockchain or not not all outputs are +consumed so let's put the small stuff + + align:start position:0% +consumed so let's put the small stuff + + + align:start position:0% +consumed so let's put the small stuff +here and the big stuff over here it's + + align:start position:0% +here and the big stuff over here it's + + + align:start position:0% +here and the big stuff over here it's +about saving space also the set of + + align:start position:0% +about saving space also the set of + + + align:start position:0% +about saving space also the set of +unspent transaction outputs is something + + align:start position:0% +unspent transaction outputs is something + + + align:start position:0% +unspent transaction outputs is something +that every node has to maintain it's + + align:start position:0% +that every node has to maintain it's + + + align:start position:0% +that every node has to maintain it's +very important you are referring to it + + align:start position:0% +very important you are referring to it + + + align:start position:0% +very important you are referring to it +quite a bit this is not something that + + align:start position:0% +quite a bit this is not something that + + + align:start position:0% +quite a bit this is not something that +every node has to maintain and so you + + align:start position:0% +every node has to maintain and so you + + + align:start position:0% +every node has to maintain and so you +you want to make this smaller even at + + align:start position:0% +you want to make this smaller even at + + + align:start position:0% +you want to make this smaller even at +the expense of making this bigger yes + + align:start position:0% + + + + align:start position:0% + +public events crew doesn't actually + + align:start position:0% +public events crew doesn't actually + + + align:start position:0% +public events crew doesn't actually +verify could you accidentally sign a + + align:start position:0% +verify could you accidentally sign a + + + align:start position:0% +verify could you accidentally sign a +transaction that has a public keep of + + align:start position:0% +transaction that has a public keep of + + + align:start position:0% +transaction that has a public keep of +script that doesn't verify let me see if + + align:start position:0% +script that doesn't verify let me see if + + + align:start position:0% +script that doesn't verify let me see if +this answers your question so here is an + + align:start position:0% +this answers your question so here is an + + + align:start position:0% +this answers your question so here is an +example of an unspent about put okay + + align:start position:0% +example of an unspent about put okay + + + align:start position:0% +example of an unspent about put okay +the unspin double output has an + + align:start position:0% +the unspin double output has an + + + align:start position:0% +the unspin double output has an +opportune as the first instruction of + + align:start position:0% +opportune as the first instruction of + + + align:start position:0% +opportune as the first instruction of +its script pub key opera turn does what + + align:start position:0% +its script pub key opera turn does what + + + align:start position:0% +its script pub key opera turn does what +you might think it does which means when + + align:start position:0% +you might think it does which means when + + + align:start position:0% +you might think it does which means when +you evaluate it + + align:start position:0% +you evaluate it + + + align:start position:0% +you evaluate it +it returns immediately and says invalid + + align:start position:0% +it returns immediately and says invalid + + + align:start position:0% +it returns immediately and says invalid +and so if you have one of these in your + + align:start position:0% +and so if you have one of these in your + + + align:start position:0% +and so if you have one of these in your +transaction in your script pub key + + align:start position:0% +transaction in your script pub key + + + align:start position:0% +transaction in your script pub key +there's no script cig that could + + align:start position:0% +there's no script cig that could + + + align:start position:0% +there's no script cig that could +possibly redeem the script pub key you + + align:start position:0% +possibly redeem the script pub key you + + + align:start position:0% +possibly redeem the script pub key you +could create a anything you wanted and + + align:start position:0% +could create a anything you wanted and + + + align:start position:0% +could create a anything you wanted and +no matter what you put on there would + + align:start position:0% +no matter what you put on there would + + + align:start position:0% +no matter what you put on there would +never be it would never evaluate to true + + align:start position:0% +never be it would never evaluate to true + + + align:start position:0% +never be it would never evaluate to true +there's no way to actually redeem the + + align:start position:0% +there's no way to actually redeem the + + + align:start position:0% +there's no way to actually redeem the +script pump key in this output does that + + align:start position:0% +script pump key in this output does that + + + align:start position:0% +script pump key in this output does that +answer your question okay + + align:start position:0% + + + + align:start position:0% + +well that's the next slide so yes this + + align:start position:0% +well that's the next slide so yes this + + + align:start position:0% +well that's the next slide so yes this +is what's called an anyone can spend + + align:start position:0% +is what's called an anyone can spend + + + align:start position:0% +is what's called an anyone can spend +output okay the simplest anyone can + + align:start position:0% +output okay the simplest anyone can + + + align:start position:0% +output okay the simplest anyone can +spend output is just an empty script + + align:start position:0% +spend output is just an empty script + + + align:start position:0% +spend output is just an empty script +pucky because a script sig that has op + + align:start position:0% +pucky because a script sig that has op + + + align:start position:0% +pucky because a script sig that has op +true in it would evaluate to true notice + + align:start position:0% +true in it would evaluate to true notice + + + align:start position:0% +true in it would evaluate to true notice +here there's no public keys there's no + + align:start position:0% +here there's no public keys there's no + + + align:start position:0% +here there's no public keys there's no +signatures + + align:start position:0% +signatures + + + align:start position:0% +signatures +there's no hashes of public keys the + + align:start position:0% +there's no hashes of public keys the + + + align:start position:0% +there's no hashes of public keys the +script pub key doesn't actually specify + + align:start position:0% +script pub key doesn't actually specify + + + align:start position:0% +script pub key doesn't actually specify +any public keys and so but when you + + align:start position:0% +any public keys and so but when you + + + align:start position:0% +any public keys and so but when you +evaluate this right here you push up + + align:start position:0% +evaluate this right here you push up + + + align:start position:0% +evaluate this right here you push up +true on to the stack and then you would + + align:start position:0% +true on to the stack and then you would + + + align:start position:0% +true on to the stack and then you would +finish and there would be a true up true + + align:start position:0% +finish and there would be a true up true + + + align:start position:0% +finish and there would be a true up true +would push sorry off true would push a + + align:start position:0% +would push sorry off true would push a + + + align:start position:0% +would push sorry off true would push a +true on to the sack and then when you + + align:start position:0% +true on to the sack and then when you + + + align:start position:0% +true on to the sack and then when you +finish there would be a true on the + + align:start position:0% +finish there would be a true on the + + + align:start position:0% +finish there would be a true on the +stack meaning this is valid yep yeah so + + align:start position:0% +stack meaning this is valid yep yeah so + + + align:start position:0% +stack meaning this is valid yep yeah so +um so this is an anyone can spend output + + align:start position:0% +um so this is an anyone can spend output + + + align:start position:0% +um so this is an anyone can spend output +and this is a no one can spend output + + align:start position:0% +and this is a no one can spend output + + + align:start position:0% +and this is a no one can spend output +and yeah there's no public keys in here + + align:start position:0% +and yeah there's no public keys in here + + + align:start position:0% +and yeah there's no public keys in here +there's no signatures in there so you + + align:start position:0% +there's no signatures in there so you + + + align:start position:0% +there's no signatures in there so you +can totally create outputs that have + + align:start position:0% +can totally create outputs that have + + + align:start position:0% +can totally create outputs that have +nothing to do with signatures or maybe + + align:start position:0% +nothing to do with signatures or maybe + + + align:start position:0% +nothing to do with signatures or maybe +have you develop verify multiple + + align:start position:0% +have you develop verify multiple + + + align:start position:0% +have you develop verify multiple +signatures which we're not gonna go into + + align:start position:0% +signatures which we're not gonna go into + + + align:start position:0% +signatures which we're not gonna go into +right now but it's also possible + + align:start position:0% +right now but it's also possible + + + align:start position:0% +right now but it's also possible +yes yes yes yes again there are fewer + + align:start position:0% +yes yes yes yes again there are fewer + + + align:start position:0% +yes yes yes yes again there are fewer +than 200 opcodes the number of standard + + align:start position:0% +than 200 opcodes the number of standard + + + align:start position:0% +than 200 opcodes the number of standard +op codes is even smaller meaning that + + align:start position:0% +op codes is even smaller meaning that + + + align:start position:0% +op codes is even smaller meaning that +there's a very small number that you can + + align:start position:0% +there's a very small number that you can + + + align:start position:0% +there's a very small number that you can +use in your scripts and script pub keys + + align:start position:0% +use in your scripts and script pub keys + + + align:start position:0% +use in your scripts and script pub keys +and it it's definitely possible if you + + align:start position:0% +and it it's definitely possible if you + + + align:start position:0% +and it it's definitely possible if you +write some weird script pub key or some + + align:start position:0% +write some weird script pub key or some + + + align:start position:0% +write some weird script pub key or some +weird script cig to accidentally create + + align:start position:0% +weird script cig to accidentally create + + + align:start position:0% +weird script cig to accidentally create +outputs that are never spendable or to + + align:start position:0% +outputs that are never spendable or to + + + align:start position:0% +outputs that are never spendable or to +accidentally create outputs that could + + align:start position:0% +accidentally create outputs that could + + + align:start position:0% +accidentally create outputs that could +be spent by someone else so there's a + + align:start position:0% +be spent by someone else so there's a + + + align:start position:0% +be spent by someone else so there's a +standard set of script pub keys to use + + align:start position:0% +standard set of script pub keys to use + + + align:start position:0% +standard set of script pub keys to use +and I would not recommend going outside + + align:start position:0% +and I would not recommend going outside + + + align:start position:0% +and I would not recommend going outside +that set except for in the lab that + + align:start position:0% +that set except for in the lab that + + + align:start position:0% +that set except for in the lab that +you're gonna do because we have some + + align:start position:0% +you're gonna do because we have some + + + align:start position:0% +you're gonna do because we have some +more fun ones in there + + align:start position:0% +more fun ones in there + + + align:start position:0% +more fun ones in there +yes sure Pena's script cash I don't + + align:start position:0% +yes sure Pena's script cash I don't + + + align:start position:0% +yes sure Pena's script cash I don't +actually have slides on peda script cash + + align:start position:0% +actually have slides on peda script cash + + + align:start position:0% +actually have slides on peda script cash +so I'm not sure that we can do a good + + align:start position:0% +so I'm not sure that we can do a good + + + align:start position:0% +so I'm not sure that we can do a good +job of explaining it right now but the + + align:start position:0% +job of explaining it right now but the + + + align:start position:0% +job of explaining it right now but the +idea behind peda script hash is that + + align:start position:0% +idea behind peda script hash is that + + + align:start position:0% +idea behind peda script hash is that +yeah I don't have I don't have the the + + align:start position:0% +yeah I don't have I don't have the the + + + align:start position:0% +yeah I don't have I don't have the the +slides for it but the idea is that + + align:start position:0% +slides for it but the idea is that + + + align:start position:0% +slides for it but the idea is that +you're going to put instead of instead + + align:start position:0% +you're going to put instead of instead + + + align:start position:0% +you're going to put instead of instead +of this particular script pub key here + + align:start position:0% +of this particular script pub key here + + + align:start position:0% +of this particular script pub key here +you're gonna have a script pub key that + + align:start position:0% +you're gonna have a script pub key that + + + align:start position:0% +you're gonna have a script pub key that +includes a hash of a script and then the + + align:start position:0% +includes a hash of a script and then the + + + align:start position:0% +includes a hash of a script and then the +script sig has to produce that script + + align:start position:0% +script sig has to produce that script + + + align:start position:0% +script sig has to produce that script +you know and it has to match that hash + + align:start position:0% +you know and it has to match that hash + + + align:start position:0% +you know and it has to match that hash +and the whole thing has to verify it's + + align:start position:0% +and the whole thing has to verify it's + + + align:start position:0% +and the whole thing has to verify it's +the rough idea behind peda script cache + + align:start position:0% +the rough idea behind peda script cache + + + align:start position:0% +the rough idea behind peda script cache +and I can we can produce an example of + + align:start position:0% +and I can we can produce an example of + + + align:start position:0% +and I can we can produce an example of +that for you tomorrow but the cool thing + + align:start position:0% +that for you tomorrow but the cool thing + + + align:start position:0% +that for you tomorrow but the cool thing +about that is you don't even know what + + align:start position:0% +about that is you don't even know what + + + align:start position:0% +about that is you don't even know what +you have to do to redeem this output + + align:start position:0% +you have to do to redeem this output + + + align:start position:0% +you have to do to redeem this output +right so someone has to produce a script + + align:start position:0% +right so someone has to produce a script + + + align:start position:0% +right so someone has to produce a script +that when combined that has the same + + align:start position:0% +that when combined that has the same + + + align:start position:0% +that when combined that has the same +hash and when combined with the script + + align:start position:0% +hash and when combined with the script + + + align:start position:0% +hash and when combined with the script +pub key will evaluate to true yeah so so + + align:start position:0% +pub key will evaluate to true yeah so so + + + align:start position:0% +pub key will evaluate to true yeah so so +um the script sig and the script pub he + + align:start position:0% +um the script sig and the script pub he + + + align:start position:0% +um the script sig and the script pub he +literally just get concatenated together + + align:start position:0% +literally just get concatenated together + + + align:start position:0% +literally just get concatenated together +and then evaluated is one thing so yeah + + align:start position:0% +and then evaluated is one thing so yeah + + + align:start position:0% +and then evaluated is one thing so yeah +it would it would just go through the + + align:start position:0% +it would it would just go through the + + + align:start position:0% +it would it would just go through the +same thing question any more questions + + align:start position:0% + + + + align:start position:0% + +so what do you guys think is this good + + align:start position:0% +so what do you guys think is this good + + + align:start position:0% +so what do you guys think is this good +is this bad + + align:start position:0% + + + + align:start position:0% + +yeah that's a great question so the + + align:start position:0% +yeah that's a great question so the + + + align:start position:0% +yeah that's a great question so the +question is could you Dawson network by + + align:start position:0% +question is could you Dawson network by + + + align:start position:0% +question is could you Dawson network by +creating transactions that are not + + align:start position:0% +creating transactions that are not + + + align:start position:0% +creating transactions that are not +spendable you can't really daus the + + align:start position:0% +spendable you can't really daus the + + + align:start position:0% +spendable you can't really daus the +network per se so um so this is an + + align:start position:0% +network per se so um so this is an + + + align:start position:0% +network per se so um so this is an +example of a transaction that's not + + align:start position:0% +example of a transaction that's not + + + align:start position:0% +example of a transaction that's not +expendable and see how it has this opera + + align:start position:0% +expendable and see how it has this opera + + + align:start position:0% +expendable and see how it has this opera +turn that says whatever there is this + + align:start position:0% +turn that says whatever there is this + + + align:start position:0% +turn that says whatever there is this +pattern of people who like to store + + align:start position:0% +pattern of people who like to store + + + align:start position:0% +pattern of people who like to store +things in the Bitcoin blockchain because + + align:start position:0% +things in the Bitcoin blockchain because + + + align:start position:0% +things in the Bitcoin blockchain because +it's there and it's very highly + + align:start position:0% +it's there and it's very highly + + + align:start position:0% +it's there and it's very highly +replicated and so one type of + + align:start position:0% +replicated and so one type of + + + align:start position:0% +replicated and so one type of +transaction that a lot of people make is + + align:start position:0% +transaction that a lot of people make is + + + align:start position:0% +transaction that a lot of people make is +an opportune with a hash of some data in + + align:start position:0% +an opportune with a hash of some data in + + + align:start position:0% +an opportune with a hash of some data in +it or some data in it these are unspun + + align:start position:0% +it or some data in it these are unspun + + + align:start position:0% +it or some data in it these are unspun +double outputs that will live on the + + align:start position:0% +double outputs that will live on the + + + align:start position:0% +double outputs that will live on the +Bitcoin blockchain forever and will be + + align:start position:0% +Bitcoin blockchain forever and will be + + + align:start position:0% +Bitcoin blockchain forever and will be +part of the you TXO set possibly forever + + align:start position:0% + + + + align:start position:0% + +generally Bitcoin developers discourage + + align:start position:0% +generally Bitcoin developers discourage + + + align:start position:0% +generally Bitcoin developers discourage +using Bitcoin in this way because it + + align:start position:0% +using Bitcoin in this way because it + + + align:start position:0% +using Bitcoin in this way because it +does bloat the you TXO set that said + + align:start position:0% +does bloat the you TXO set that said + + + align:start position:0% +does bloat the you TXO set that said +there's nothing to prevent you from + + align:start position:0% +there's nothing to prevent you from + + + align:start position:0% +there's nothing to prevent you from +doing it if you want to pay the fees you + + align:start position:0% +doing it if you want to pay the fees you + + + align:start position:0% +doing it if you want to pay the fees you +know that okay things I didn't know that + + align:start position:0% +know that okay things I didn't know that + + + align:start position:0% +know that okay things I didn't know that +they weren't kept in the UT access it + + align:start position:0% + + + + align:start position:0% + +okay I didn't know that those weren't + + align:start position:0% +okay I didn't know that those weren't + + + align:start position:0% +okay I didn't know that those weren't +included in the UT Exocet so that's good + + align:start position:0% +included in the UT Exocet so that's good + + + align:start position:0% +included in the UT Exocet so that's good +so then it doesn't block the UT Exocet + + align:start position:0% +so then it doesn't block the UT Exocet + + + align:start position:0% +so then it doesn't block the UT Exocet +it just goes in the blockchain and you + + align:start position:0% +it just goes in the blockchain and you + + + align:start position:0% +it just goes in the blockchain and you +paid the feet put your transaction in + + align:start position:0% +paid the feet put your transaction in + + + align:start position:0% +paid the feet put your transaction in +the blockchain so good for you yes + + align:start position:0% + + + + align:start position:0% + +that's a great question so why have this + + align:start position:0% +that's a great question so why have this + + + align:start position:0% +that's a great question so why have this +weird opcode thing right I mean what + + align:start position:0% +weird opcode thing right I mean what + + + align:start position:0% +weird opcode thing right I mean what +kind of sense does this make so the + + align:start position:0% +kind of sense does this make so the + + + align:start position:0% +kind of sense does this make so the +problem with a general programming + + align:start position:0% +problem with a general programming + + + align:start position:0% +problem with a general programming +language is it's really easy to shoot + + align:start position:0% +language is it's really easy to shoot + + + align:start position:0% +language is it's really easy to shoot +yourself in the foot it's really easy to + + align:start position:0% +yourself in the foot it's really easy to + + + align:start position:0% +yourself in the foot it's really easy to +write a program that you think you know + + align:start position:0% +write a program that you think you know + + + align:start position:0% +write a program that you think you know +how many of you have had a bug in your + + align:start position:0% +how many of you have had a bug in your + + + align:start position:0% +how many of you have had a bug in your +program ever please all of you should + + align:start position:0% +program ever please all of you should + + + align:start position:0% +program ever please all of you should +probably raise their hands right so and + + align:start position:0% +probably raise their hands right so and + + + align:start position:0% +probably raise their hands right so and +how many of you have had bugs in your + + align:start position:0% +how many of you have had bugs in your + + + align:start position:0% +how many of you have had bugs in your +program that showed up a lot later than + + align:start position:0% +program that showed up a lot later than + + + align:start position:0% +program that showed up a lot later than +you thought they would when you thought + + align:start position:0% +you thought they would when you thought + + + align:start position:0% +you thought they would when you thought +your program didn't have any bugs right + + align:start position:0% +your program didn't have any bugs right + + + align:start position:0% +your program didn't have any bugs right +so these things once you put them out + + align:start position:0% +so these things once you put them out + + + align:start position:0% +so these things once you put them out +there + + align:start position:0% +there + + + align:start position:0% +there +these script cookies and script once you + + align:start position:0% +these script cookies and script once you + + + align:start position:0% +these script cookies and script once you +put these transactions out there they're + + align:start position:0% +put these transactions out there they're + + + align:start position:0% +put these transactions out there they're +out there you cannot take them back + + align:start position:0% +out there you cannot take them back + + + align:start position:0% +out there you cannot take them back +well not easily ah and you know they + + align:start position:0% +well not easily ah and you know they + + + align:start position:0% +well not easily ah and you know they +might execute in ways that you didn't + + align:start position:0% +might execute in ways that you didn't + + + align:start position:0% +might execute in ways that you didn't +anticipate them executing the more + + align:start position:0% +anticipate them executing the more + + + align:start position:0% +anticipate them executing the more +complicated the script you write the + + align:start position:0% +complicated the script you write the + + + align:start position:0% +complicated the script you write the +more likely it is that there's some hole + + align:start position:0% +more likely it is that there's some hole + + + align:start position:0% +more likely it is that there's some hole +in your script some way of satisfying it + + align:start position:0% +in your script some way of satisfying it + + + align:start position:0% +in your script some way of satisfying it +that you didn't anticipate that could + + align:start position:0% +that you didn't anticipate that could + + + align:start position:0% +that you didn't anticipate that could +end up stealing your money right so with + + align:start position:0% +end up stealing your money right so with + + + align:start position:0% +end up stealing your money right so with +a general programming language rule you + + align:start position:0% +a general programming language rule you + + + align:start position:0% +a general programming language rule you +might think oh well at least you know + + align:start position:0% +might think oh well at least you know + + + align:start position:0% +might think oh well at least you know +these op codes are super tricky and + + align:start position:0% +these op codes are super tricky and + + + align:start position:0% +these op codes are super tricky and +weird and I don't understand them at + + align:start position:0% +weird and I don't understand them at + + + align:start position:0% +weird and I don't understand them at +least with the general programming + + align:start position:0% +least with the general programming + + + align:start position:0% +least with the general programming +language I'm more likely to write + + align:start position:0% +language I'm more likely to write + + + align:start position:0% +language I'm more likely to write +correct things right + + align:start position:0% +correct things right + + + align:start position:0% +correct things right +you know actually having the strange + + align:start position:0% +you know actually having the strange + + + align:start position:0% +you know actually having the strange +opcode language has a lot of benefits so + + align:start position:0% +opcode language has a lot of benefits so + + + align:start position:0% +opcode language has a lot of benefits so +number one it's not turing-complete + + align:start position:0% +number one it's not turing-complete + + + align:start position:0% +number one it's not turing-complete +you know exactly how much CPU is it is + + align:start position:0% +you know exactly how much CPU is it is + + + align:start position:0% +you know exactly how much CPU is it is +going to take to run these scripts + + align:start position:0% +going to take to run these scripts + + + align:start position:0% +going to take to run these scripts +because of because of the nature of the + + align:start position:0% +because of because of the nature of the + + + align:start position:0% +because of because of the nature of the +opcodes and the language you you there's + + align:start position:0% +opcodes and the language you you there's + + + align:start position:0% +opcodes and the language you you there's +no for loops in here you know you can't + + align:start position:0% +no for loops in here you know you can't + + + align:start position:0% +no for loops in here you know you can't +just run a while that takes forever + + align:start position:0% +just run a while that takes forever + + + align:start position:0% +just run a while that takes forever +these the this is a stack based language + + align:start position:0% +these the this is a stack based language + + + align:start position:0% +these the this is a stack based language +and so it's very easy to tell how long a + + align:start position:0% +and so it's very easy to tell how long a + + + align:start position:0% +and so it's very easy to tell how long a +transaction is actually gonna take to + + align:start position:0% +transaction is actually gonna take to + + + align:start position:0% +transaction is actually gonna take to +execute and this is really important + + align:start position:0% +execute and this is really important + + + align:start position:0% +execute and this is really important +because every node in the network has to + + align:start position:0% +because every node in the network has to + + + align:start position:0% +because every node in the network has to +execute these things so you don't want a + + align:start position:0% +execute these things so you don't want a + + + align:start position:0% +execute these things so you don't want a +script sneaking in there that's going to + + align:start position:0% +script sneaking in there that's going to + + + align:start position:0% +script sneaking in there that's going to +you know take hours to execute it's also + + align:start position:0% +you know take hours to execute it's also + + + align:start position:0% +you know take hours to execute it's also +you can look at the number of op codes + + align:start position:0% +you can look at the number of op codes + + + align:start position:0% +you can look at the number of op codes +in the script and + + align:start position:0% +in the script and + + + align:start position:0% +in the script and +like I said get a rough sense of how + + align:start position:0% +like I said get a rough sense of how + + + align:start position:0% +like I said get a rough sense of how +expensive it's gonna be and that's why + + align:start position:0% +expensive it's gonna be and that's why + + + align:start position:0% +expensive it's gonna be and that's why +there are limits on the number of + + align:start position:0% +there are limits on the number of + + + align:start position:0% +there are limits on the number of +opcodes you can have in a script it's + + align:start position:0% +opcodes you can have in a script it's + + + align:start position:0% +opcodes you can have in a script it's +very difficult to do that if you have a + + align:start position:0% +very difficult to do that if you have a + + + align:start position:0% +very difficult to do that if you have a +more general programming language so + + align:start position:0% +more general programming language so + + + align:start position:0% +more general programming language so +those are a couple of reasons and I mean + + align:start position:0% +those are a couple of reasons and I mean + + + align:start position:0% +those are a couple of reasons and I mean +I think it's important to point out that + + align:start position:0% +I think it's important to point out that + + + align:start position:0% +I think it's important to point out that +aetherium which does have a more general + + align:start position:0% +aetherium which does have a more general + + + align:start position:0% +aetherium which does have a more general +programming language they're constantly + + align:start position:0% +programming language they're constantly + + + align:start position:0% +programming language they're constantly +problems popping up where people are + + align:start position:0% +problems popping up where people are + + + align:start position:0% +problems popping up where people are +taking advantage of transit of contracts + + align:start position:0% +taking advantage of transit of contracts + + + align:start position:0% +taking advantage of transit of contracts +even fairly well understood ones are so + + align:start position:0% +even fairly well understood ones are so + + + align:start position:0% +even fairly well understood ones are so +called you know we thought they were + + align:start position:0% +called you know we thought they were + + + align:start position:0% +called you know we thought they were +well understood and figuring out how to + + align:start position:0% +well understood and figuring out how to + + + align:start position:0% +well understood and figuring out how to +freeze people's funds or steal people's + + align:start position:0% +freeze people's funds or steal people's + + + align:start position:0% +freeze people's funds or steal people's +funds so that's the motivation behind + + align:start position:0% +funds so that's the motivation behind + + + align:start position:0% +funds so that's the motivation behind +this sort of strange language are there + + align:start position:0% +this sort of strange language are there + + + align:start position:0% +this sort of strange language are there +any other questions I don't understand + + align:start position:0% +any other questions I don't understand + + + align:start position:0% +any other questions I don't understand +them right now and I do want to stress + + align:start position:0% +them right now and I do want to stress + + + align:start position:0% +them right now and I do want to stress +when you're dealing with real money so + + align:start position:0% +when you're dealing with real money so + + + align:start position:0% +when you're dealing with real money so +not in the lab for this class you want + + align:start position:0% +not in the lab for this class you want + + + align:start position:0% +not in the lab for this class you want +to stick with very standard scripts you + + align:start position:0% +to stick with very standard scripts you + + + align:start position:0% +to stick with very standard scripts you +don't want to write super crazy weird + + align:start position:0% +don't want to write super crazy weird + + + align:start position:0% +don't want to write super crazy weird +tricky scripts or if you do you want to + + align:start position:0% +tricky scripts or if you do you want to + + + align:start position:0% +tricky scripts or if you do you want to +get them vetted very carefully + + align:start position:0% +get them vetted very carefully + + + align:start position:0% +get them vetted very carefully +yes great question so the there are two + + align:start position:0% +yes great question so the there are two + + + align:start position:0% +yes great question so the there are two +levels at which things can be enabled or + + align:start position:0% +levels at which things can be enabled or + + + align:start position:0% +levels at which things can be enabled or +disabled in Bitcoin so first there's the + + align:start position:0% +disabled in Bitcoin so first there's the + + + align:start position:0% +disabled in Bitcoin so first there's the +validation rules so what makes a + + align:start position:0% +validation rules so what makes a + + + align:start position:0% +validation rules so what makes a +transaction valid or not valid right and + + align:start position:0% +transaction valid or not valid right and + + + align:start position:0% +transaction valid or not valid right and +that meaning that if a transaction is + + align:start position:0% +that meaning that if a transaction is + + + align:start position:0% +that meaning that if a transaction is +invalid and it's in a block that whole + + align:start position:0% +invalid and it's in a block that whole + + + align:start position:0% +invalid and it's in a block that whole +block is invalid if a transaction is + + align:start position:0% +block is invalid if a transaction is + + + align:start position:0% +block is invalid if a transaction is +invalid and in a block and that block is + + align:start position:0% +invalid and in a block and that block is + + + align:start position:0% +invalid and in a block and that block is +in a block chain that entire block chain + + align:start position:0% +in a block chain that entire block chain + + + align:start position:0% +in a block chain that entire block chain +is invalid so there's there's that level + + align:start position:0% +is invalid so there's there's that level + + + align:start position:0% +is invalid so there's there's that level +and we're going to talk about sort of + + align:start position:0% +and we're going to talk about sort of + + + align:start position:0% +and we're going to talk about sort of +how those rules change and who sets + + align:start position:0% +how those rules change and who sets + + + align:start position:0% +how those rules change and who sets +those rules but you can consider them + + align:start position:0% +those rules but you can consider them + + + align:start position:0% +those rules but you can consider them +sort of for now being set by the the + + align:start position:0% +sort of for now being set by the the + + + align:start position:0% +sort of for now being set by the the +code the Bitcoin core or the Bitcoin + + align:start position:0% +code the Bitcoin core or the Bitcoin + + + align:start position:0% +code the Bitcoin core or the Bitcoin +software which specifies what is valid + + align:start position:0% +software which specifies what is valid + + + align:start position:0% +software which specifies what is valid +and what is invalid + + align:start position:0% +and what is invalid + + + align:start position:0% +and what is invalid +but there's another level at which you + + align:start position:0% +but there's another level at which you + + + align:start position:0% +but there's another level at which you +can you can you can sort of adjust what + + align:start position:0% +can you can you can sort of adjust what + + + align:start position:0% +can you can you can sort of adjust what +is what sort of ends up getting accepted + + align:start position:0% +is what sort of ends up getting accepted + + + align:start position:0% +is what sort of ends up getting accepted +or not accepted and that is what is + + align:start position:0% +or not accepted and that is what is + + + align:start position:0% +or not accepted and that is what is +transmitted over the peer-to-peer + + align:start position:0% +transmitted over the peer-to-peer + + + align:start position:0% +transmitted over the peer-to-peer +network so there are transactions that + + align:start position:0% +network so there are transactions that + + + align:start position:0% +network so there are transactions that +are valid but are what's known as non + + align:start position:0% +are valid but are what's known as non + + + align:start position:0% +are valid but are what's known as non +standard and that transaction if it gets + + align:start position:0% +standard and that transaction if it gets + + + align:start position:0% +standard and that transaction if it gets +into a block that block is still valid + + align:start position:0% +into a block that block is still valid + + + align:start position:0% +into a block that block is still valid +but the nodes in the network if it sees + + align:start position:0% +but the nodes in the network if it sees + + + align:start position:0% +but the nodes in the network if it sees +that transaction won't relay them around + + align:start position:0% +that transaction won't relay them around + + + align:start position:0% +that transaction won't relay them around +so you'd have to like be a minor and + + align:start position:0% +so you'd have to like be a minor and + + + align:start position:0% +so you'd have to like be a minor and +actually decide I want this transaction + + align:start position:0% +actually decide I want this transaction + + + align:start position:0% +actually decide I want this transaction +in a block and mine that block and if + + align:start position:0% +in a block and mine that block and if + + + align:start position:0% +in a block and mine that block and if +you do that everyone will consider it a + + align:start position:0% +you do that everyone will consider it a + + + align:start position:0% +you do that everyone will consider it a +valid block okay fine but no one will + + align:start position:0% +valid block okay fine but no one will + + + align:start position:0% +valid block okay fine but no one will +actually send your transaction around + + align:start position:0% +actually send your transaction around + + + align:start position:0% +actually send your transaction around +and so the you know if you're not a + + align:start position:0% +and so the you know if you're not a + + + align:start position:0% +and so the you know if you're not a +money or yourself the odds of it getting + + align:start position:0% +money or yourself the odds of it getting + + + align:start position:0% +money or yourself the odds of it getting +into the blockchain are very low and so + + align:start position:0% +into the blockchain are very low and so + + + align:start position:0% +into the blockchain are very low and so +those are the two sets of rules the + + align:start position:0% +those are the two sets of rules the + + + align:start position:0% +those are the two sets of rules the +peer-to-peer rules are more restrictive + + align:start position:0% +peer-to-peer rules are more restrictive + + + align:start position:0% +peer-to-peer rules are more restrictive +than the validation rules okay so we + + align:start position:0% +than the validation rules okay so we + + + align:start position:0% +than the validation rules okay so we +already kind of started talking about + + align:start position:0% +already kind of started talking about + + + align:start position:0% +already kind of started talking about +this a little bit you know what are the + + align:start position:0% +this a little bit you know what are the + + + align:start position:0% +this a little bit you know what are the +benefits of UTX those and what are the + + align:start position:0% +benefits of UTX those and what are the + + + align:start position:0% +benefits of UTX those and what are the +downsides of UT exo's so one of the + + align:start position:0% +downsides of UT exo's so one of the + + + align:start position:0% +downsides of UT exo's so one of the +benefits of UT exo's is that but you + + align:start position:0% +benefits of UT exo's is that but you + + + align:start position:0% +benefits of UT exo's is that but you +guys see how they help with with replay + + align:start position:0% +guys see how they help with with replay + + + align:start position:0% +guys see how they help with with replay +attacks I can sure I can copy this + + align:start position:0% +attacks I can sure I can copy this + + + align:start position:0% +attacks I can sure I can copy this +transaction and put multiple out there + + align:start position:0% +transaction and put multiple out there + + + align:start position:0% +transaction and put multiple out there +but you're only allowed to spend an + + align:start position:0% +but you're only allowed to spend an + + + align:start position:0% +but you're only allowed to spend an +output once and once you consume that + + align:start position:0% +output once and once you consume that + + + align:start position:0% +output once and once you consume that +output that's it so you can't really do + + align:start position:0% +output that's it so you can't really do + + + align:start position:0% +output that's it so you can't really do +replay attacks in this model so it's a + + align:start position:0% +replay attacks in this model so it's a + + + align:start position:0% +replay attacks in this model so it's a +very sort of elegant way of getting rid + + align:start position:0% +very sort of elegant way of getting rid + + + align:start position:0% +very sort of elegant way of getting rid +of the replay attack problem without + + align:start position:0% +of the replay attack problem without + + + align:start position:0% +of the replay attack problem without +having to store a nonce per account in + + align:start position:0% +having to store a nonce per account in + + + align:start position:0% +having to store a nonce per account in +your system another benefit is that you + + align:start position:0% +your system another benefit is that you + + + align:start position:0% +your system another benefit is that you +know you can actually get a little bit + + align:start position:0% +know you can actually get a little bit + + + align:start position:0% +know you can actually get a little bit +better privacy with this UT EXO system + + align:start position:0% +better privacy with this UT EXO system + + + align:start position:0% +better privacy with this UT EXO system +because you don't have to use the same + + align:start position:0% +because you don't have to use the same + + + align:start position:0% +because you don't have to use the same +public key for all of your transactions + + align:start position:0% +public key for all of your transactions + + + align:start position:0% +public key for all of your transactions +you can generate new ones every single + + align:start position:0% +you can generate new ones every single + + + align:start position:0% +you can generate new ones every single +time and then combine ut EXO's from + + align:start position:0% +time and then combine ut EXO's from + + + align:start position:0% +time and then combine ut EXO's from +different things into I mean you're + + align:start position:0% +different things into I mean you're + + + align:start position:0% +different things into I mean you're +gonna have to combine them anyway even + + align:start position:0% +gonna have to combine them anyway even + + + align:start position:0% +gonna have to combine them anyway even +if they did spend at the same public key + + align:start position:0% +if they did spend at the same public key + + + align:start position:0% +if they did spend at the same public key +so why not generate fresh ones all the + + align:start position:0% +so why not generate fresh ones all the + + + align:start position:0% +so why not generate fresh ones all the +time and it becomes a little bit harder + + align:start position:0% +time and it becomes a little bit harder + + + align:start position:0% +time and it becomes a little bit harder +to track who you're spending and who + + align:start position:0% +to track who you're spending and who + + + align:start position:0% +to track who you're spending and who +you're paying to and the account based + + align:start position:0% +you're paying to and the account based + + + align:start position:0% +you're paying to and the account based +model you need to have you know it's + + align:start position:0% +model you need to have you know it's + + + align:start position:0% +model you need to have you know it's +more likely that all of your funds are + + align:start position:0% +more likely that all of your funds are + + + align:start position:0% +more likely that all of your funds are +gonna be in one account in order to make + + align:start position:0% +gonna be in one account in order to make + + + align:start position:0% +gonna be in one account in order to make +a spend now Adele + + align:start position:0% +a spend now Adele + + + align:start position:0% +a spend now Adele +of UT EXO's is that they're complicated + + align:start position:0% +of UT EXO's is that they're complicated + + + align:start position:0% +of UT EXO's is that they're complicated +so when I first heard about UT EXO's and + + align:start position:0% +so when I first heard about UT EXO's and + + + align:start position:0% +so when I first heard about UT EXO's and +I first understood how Bitcoin worked I + + align:start position:0% +I first understood how Bitcoin worked I + + + align:start position:0% +I first understood how Bitcoin worked I +was like why does Bitcoin work this way + + align:start position:0% +was like why does Bitcoin work this way + + + align:start position:0% +was like why does Bitcoin work this way +this makes zero sense an account based + + align:start position:0% +this makes zero sense an account based + + + align:start position:0% +this makes zero sense an account based +model would be so much easier and I mean + + align:start position:0% +model would be so much easier and I mean + + + align:start position:0% +model would be so much easier and I mean +I think for wallet providers and for for + + align:start position:0% +I think for wallet providers and for for + + + align:start position:0% +I think for wallet providers and for for +people who are writing user software it + + align:start position:0% +people who are writing user software it + + + align:start position:0% +people who are writing user software it +is easier to deal with an account based + + align:start position:0% +is easier to deal with an account based + + + align:start position:0% +is easier to deal with an account based +model than a UT EXO model because people + + align:start position:0% +model than a UT EXO model because people + + + align:start position:0% +model than a UT EXO model because people +who are writing Bitcoin wallets software + + align:start position:0% +who are writing Bitcoin wallets software + + + align:start position:0% +who are writing Bitcoin wallets software +have to keep track of all of your UT X + + align:start position:0% +have to keep track of all of your UT X + + + align:start position:0% +have to keep track of all of your UT X +OS and then figure out how to combine + + align:start position:0% +OS and then figure out how to combine + + + align:start position:0% +OS and then figure out how to combine +them to get the amount that you want to + + align:start position:0% +them to get the amount that you want to + + + align:start position:0% +them to get the amount that you want to +spend and make sure that they produce + + align:start position:0% +spend and make sure that they produce + + + align:start position:0% +spend and make sure that they produce +what are called change outputs the right + + align:start position:0% +what are called change outputs the right + + + align:start position:0% +what are called change outputs the right +way so you don't like accidentally lose + + align:start position:0% +way so you don't like accidentally lose + + + align:start position:0% +way so you don't like accidentally lose +some of your money because you're + + align:start position:0% +some of your money because you're + + + align:start position:0% +some of your money because you're +spending an output that has a hundred + + align:start position:0% +spending an output that has a hundred + + + align:start position:0% +spending an output that has a hundred +Bitcoin but you're only paying someone + + align:start position:0% +Bitcoin but you're only paying someone + + + align:start position:0% +Bitcoin but you're only paying someone +one Bitcoin you better make sure you + + align:start position:0% +one Bitcoin you better make sure you + + + align:start position:0% +one Bitcoin you better make sure you +have that 99 Bitcoin output in there + + align:start position:0% +have that 99 Bitcoin output in there + + + align:start position:0% +have that 99 Bitcoin output in there +going back to you right so it just makes + + align:start position:0% +going back to you right so it just makes + + + align:start position:0% +going back to you right so it just makes +everything a little bit more complicated + + align:start position:0% +everything a little bit more complicated + + + align:start position:0% +everything a little bit more complicated +you can't you know you can't just spend + + align:start position:0% +you can't you know you can't just spend + + + align:start position:0% +you can't you know you can't just spend +the amount you want to spend you have to + + align:start position:0% +the amount you want to spend you have to + + + align:start position:0% +the amount you want to spend you have to +find these outputs and combine them in + + align:start position:0% +find these outputs and combine them in + + + align:start position:0% +find these outputs and combine them in +the right way and and and figure all of + + align:start position:0% +the right way and and and figure all of + + + align:start position:0% +the right way and and and figure all of +this stuff out another problem is around + + align:start position:0% +this stuff out another problem is around + + + align:start position:0% +this stuff out another problem is around +fungibility so this is why I say that + + align:start position:0% +fungibility so this is why I say that + + + align:start position:0% +fungibility so this is why I say that +bitcoins not fungible because of these + + align:start position:0% +bitcoins not fungible because of these + + + align:start position:0% +bitcoins not fungible because of these +outputs and the fact that you have to + + align:start position:0% +outputs and the fact that you have to + + + align:start position:0% +outputs and the fact that you have to +point back to the output that you're + + align:start position:0% +point back to the output that you're + + + align:start position:0% +point back to the output that you're +going to spend which ends up creating + + align:start position:0% +going to spend which ends up creating + + + align:start position:0% +going to spend which ends up creating +what's called a transaction graph so you + + align:start position:0% +what's called a transaction graph so you + + + align:start position:0% +what's called a transaction graph so you +can sort of see how things are chained + + align:start position:0% +can sort of see how things are chained + + + align:start position:0% +can sort of see how things are chained +together and you can actually discern + + align:start position:0% +together and you can actually discern + + + align:start position:0% +together and you can actually discern +quite a bit of information about what's + + align:start position:0% +quite a bit of information about what's + + + align:start position:0% +quite a bit of information about what's +going on in the network and in fact the + + align:start position:0% +going on in the network and in fact the + + + align:start position:0% +going on in the network and in fact the +FBI has used the transaction graph in + + align:start position:0% +FBI has used the transaction graph in + + + align:start position:0% +FBI has used the transaction graph in +some of its cases around Silk Road to + + align:start position:0% +some of its cases around Silk Road to + + + align:start position:0% +some of its cases around Silk Road to +see where Bitcoin was moving and there + + align:start position:0% +see where Bitcoin was moving and there + + + align:start position:0% +see where Bitcoin was moving and there +are many companies out there chain + + align:start position:0% +are many companies out there chain + + + align:start position:0% +are many companies out there chain +analysis elliptic that provides services + + align:start position:0% +analysis elliptic that provides services + + + align:start position:0% +analysis elliptic that provides services +based around the fact that bitcoins + + align:start position:0% +based around the fact that bitcoins + + + align:start position:0% +based around the fact that bitcoins +transaction graph is totally open and so + + align:start position:0% +transaction graph is totally open and so + + + align:start position:0% +transaction graph is totally open and so +you can you can sort of see how coins + + align:start position:0% +you can you can sort of see how coins + + + align:start position:0% +you can you can sort of see how coins +are moving around so in addition to the + + align:start position:0% +are moving around so in addition to the + + + align:start position:0% +are moving around so in addition to the +transaction graph problem you kind of + + align:start position:0% +transaction graph problem you kind of + + + align:start position:0% +transaction graph problem you kind of +lose this aspect of fungibility in the + + align:start position:0% +lose this aspect of fungibility in the + + + align:start position:0% +lose this aspect of fungibility in the +sense that let's say that I know that + + align:start position:0% +sense that let's say that I know that + + + align:start position:0% +sense that let's say that I know that +for whatever reason these coins came + + align:start position:0% +for whatever reason these coins came + + + align:start position:0% +for whatever reason these coins came +from let's say like I don't know a + + align:start position:0% +from let's say like I don't know a + + + align:start position:0% +from let's say like I don't know a +terrorist or something like that you + + align:start position:0% +terrorist or something like that you + + + align:start position:0% +terrorist or something like that you +then know exactly where those coins are + + align:start position:0% +then know exactly where those coins are + + + align:start position:0% +then know exactly where those coins are +going and you can kind of see the chain + + align:start position:0% +going and you can kind of see the chain + + + align:start position:0% +going and you can kind of see the chain +of transaction + + align:start position:0% +of transaction + + + align:start position:0% +of transaction +that come off of those coins and it sort + + align:start position:0% +that come off of those coins and it sort + + + align:start position:0% +that come off of those coins and it sort +of creates a potential opportunity for + + align:start position:0% +of creates a potential opportunity for + + + align:start position:0% +of creates a potential opportunity for +someone to blacklist coins or you might + + align:start position:0% +someone to blacklist coins or you might + + + align:start position:0% +someone to blacklist coins or you might +decide that you know you like coins that + + align:start position:0% +decide that you know you like coins that + + + align:start position:0% +decide that you know you like coins that +were produced that are that are fresher + + align:start position:0% +were produced that are that are fresher + + + align:start position:0% +were produced that are that are fresher +than other coins so there's this ability + + align:start position:0% +than other coins so there's this ability + + + align:start position:0% +than other coins so there's this ability +to distinguish between coins which is a + + align:start position:0% +to distinguish between coins which is a + + + align:start position:0% +to distinguish between coins which is a +little bit troublesome because + + align:start position:0% +little bit troublesome because + + + align:start position:0% +little bit troublesome because +fungibility is is generally considered a + + align:start position:0% +fungibility is is generally considered a + + + align:start position:0% +fungibility is is generally considered a +very good property for money to have and + + align:start position:0% +very good property for money to have and + + + align:start position:0% +very good property for money to have and +this is not entirely functional but + + align:start position:0% +this is not entirely functional but + + + align:start position:0% +this is not entirely functional but +people are working on that + + align:start position:0% + + + + align:start position:0% + +any other questions I alluded to this + + align:start position:0% +any other questions I alluded to this + + + align:start position:0% +any other questions I alluded to this +earlier but every single node that's + + align:start position:0% +earlier but every single node that's + + + align:start position:0% +earlier but every single node that's +running the Bitcoin software keeps this + + align:start position:0% +running the Bitcoin software keeps this + + + align:start position:0% +running the Bitcoin software keeps this +data structure called the UT Exocet so + + align:start position:0% +data structure called the UT Exocet so + + + align:start position:0% +data structure called the UT Exocet so +these are all of the outstanding unspent + + align:start position:0% +these are all of the outstanding unspent + + + align:start position:0% +these are all of the outstanding unspent +transaction outputs it's all the coins + + align:start position:0% +transaction outputs it's all the coins + + + align:start position:0% +transaction outputs it's all the coins +in the system all the money in the + + align:start position:0% +in the system all the money in the + + + align:start position:0% +in the system all the money in the +system that's available to be spent the + + align:start position:0% +system that's available to be spent the + + + align:start position:0% +system that's available to be spent the +way that this is computed is when a + + align:start position:0% +way that this is computed is when a + + + align:start position:0% +way that this is computed is when a +Bitcoin node comes online and starts to + + align:start position:0% +Bitcoin node comes online and starts to + + + align:start position:0% +Bitcoin node comes online and starts to +download the blockchain they run through + + align:start position:0% +download the blockchain they run through + + + align:start position:0% +download the blockchain they run through +the blockchain and continuously add and + + align:start position:0% +the blockchain and continuously add and + + + align:start position:0% +the blockchain and continuously add and +remove things from the UT Exocet to + + align:start position:0% +remove things from the UT Exocet to + + + align:start position:0% +remove things from the UT Exocet to +produce a UT Exocet that is valid for + + align:start position:0% +produce a UT Exocet that is valid for + + + align:start position:0% +produce a UT Exocet that is valid for +whatever the last block is that it's + + align:start position:0% +whatever the last block is that it's + + + align:start position:0% +whatever the last block is that it's +seen when a new block comes in node runs + + align:start position:0% +seen when a new block comes in node runs + + + align:start position:0% +seen when a new block comes in node runs +through the block and again removes and + + align:start position:0% +through the block and again removes and + + + align:start position:0% +through the block and again removes and +adds things to the UT exocet as + + align:start position:0% +adds things to the UT exocet as + + + align:start position:0% +adds things to the UT exocet as +necessary right now there's about I know + + align:start position:0% +necessary right now there's about I know + + + align:start position:0% +necessary right now there's about I know +60 million UT X OS in the UT Exocet a + + align:start position:0% +60 million UT X OS in the UT Exocet a + + + align:start position:0% +60 million UT X OS in the UT Exocet a +lot of them unfortunately well a lot a + + align:start position:0% +lot of them unfortunately well a lot a + + + align:start position:0% +lot of them unfortunately well a lot a +lot bye sigh look by like in terms of + + align:start position:0% +lot bye sigh look by like in terms of + + + align:start position:0% +lot bye sigh look by like in terms of +bytes of the UT Exocet a lot of them are + + align:start position:0% +bytes of the UT Exocet a lot of them are + + + align:start position:0% +bytes of the UT Exocet a lot of them are +very small and are unlikely to get spent + + align:start position:0% +very small and are unlikely to get spent + + + align:start position:0% +very small and are unlikely to get spent +very soon so that's kind of a bummer the + + align:start position:0% +very soon so that's kind of a bummer the + + + align:start position:0% +very soon so that's kind of a bummer the +you take so said is about three + + align:start position:0% +you take so said is about three + + + align:start position:0% +you take so said is about three +gigabytes right now I think and so every + + align:start position:0% +gigabytes right now I think and so every + + + align:start position:0% +gigabytes right now I think and so every +node in Bitcoin in addition to storing + + align:start position:0% +node in Bitcoin in addition to storing + + + align:start position:0% +node in Bitcoin in addition to storing +the blockchain stores this UT Exocet and + + align:start position:0% +the blockchain stores this UT Exocet and + + + align:start position:0% +the blockchain stores this UT Exocet and +uses the state structure to very quickly + + align:start position:0% +uses the state structure to very quickly + + + align:start position:0% +uses the state structure to very quickly +tell if a transaction is a double spend + + align:start position:0% +tell if a transaction is a double spend + + + align:start position:0% +tell if a transaction is a double spend +or not any questions about the UT X I + + align:start position:0% +or not any questions about the UT X I + + + align:start position:0% +or not any questions about the UT X I +said yesterday + + align:start position:0% + + + + align:start position:0% + +that's a good question how do you avoid + + align:start position:0% +that's a good question how do you avoid + + + align:start position:0% +that's a good question how do you avoid +having small transactions accumulate + + align:start position:0% +having small transactions accumulate + + + align:start position:0% +having small transactions accumulate +over time I don't know the answer to + + align:start position:0% +over time I don't know the answer to + + + align:start position:0% +over time I don't know the answer to +that question it's kind of a bummer + + align:start position:0% +that question it's kind of a bummer + + + align:start position:0% +that question it's kind of a bummer +the it's not really in people's interest + + align:start position:0% +the it's not really in people's interest + + + align:start position:0% +the it's not really in people's interest +to generate those transactions because + + align:start position:0% +to generate those transactions because + + + align:start position:0% +to generate those transactions because +you're creating I haven't talked about + + align:start position:0% +you're creating I haven't talked about + + + align:start position:0% +you're creating I haven't talked about +how fees are computed yet but fees are + + align:start position:0% +how fees are computed yet but fees are + + + align:start position:0% +how fees are computed yet but fees are +measured according to the resources that + + align:start position:0% +measured according to the resources that + + + align:start position:0% +measured according to the resources that +a transaction takes up in the system + + align:start position:0% +a transaction takes up in the system + + + align:start position:0% +a transaction takes up in the system +during fees are measured according to + + align:start position:0% +during fees are measured according to + + + align:start position:0% +during fees are measured according to +the size of the transaction so if you + + align:start position:0% +the size of the transaction so if you + + + align:start position:0% +the size of the transaction so if you +have to combine a whole bunch of tiny + + align:start position:0% +have to combine a whole bunch of tiny + + + align:start position:0% +have to combine a whole bunch of tiny +outputs in order to get a big enough sum + + align:start position:0% +outputs in order to get a big enough sum + + + align:start position:0% +outputs in order to get a big enough sum +you're gonna have to pay more in fees so + + align:start position:0% +you're gonna have to pay more in fees so + + + align:start position:0% +you're gonna have to pay more in fees so +it's not really in your interest to + + align:start position:0% +it's not really in your interest to + + + align:start position:0% +it's not really in your interest to +produce a lot of these tiny things but + + align:start position:0% +produce a lot of these tiny things but + + + align:start position:0% +produce a lot of these tiny things but +there's not really a good way of + + align:start position:0% +there's not really a good way of + + + align:start position:0% +there's not really a good way of +stopping it and in fact there have been + + align:start position:0% +stopping it and in fact there have been + + + align:start position:0% +stopping it and in fact there have been +services in the past like Satoshi dice + + align:start position:0% +services in the past like Satoshi dice + + + align:start position:0% +services in the past like Satoshi dice +and whatnot that have created a ton of + + align:start position:0% +and whatnot that have created a ton of + + + align:start position:0% +and whatnot that have created a ton of +very tiny outputs and uploaded the UTX + + align:start position:0% +very tiny outputs and uploaded the UTX + + + align:start position:0% +very tiny outputs and uploaded the UTX +is that I don't know Taj if you have any + + align:start position:0% +is that I don't know Taj if you have any + + + align:start position:0% +is that I don't know Taj if you have any +insight onto how to stop that from + + align:start position:0% +insight onto how to stop that from + + + align:start position:0% +insight onto how to stop that from +happening other than the fees other than + + align:start position:0% +happening other than the fees other than + + + align:start position:0% +happening other than the fees other than +the fees yeah yes + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so I'm not sure in the account B's model + + align:start position:0% +so I'm not sure in the account B's model + + + align:start position:0% +so I'm not sure in the account B's model +we'll find out more about this when we + + align:start position:0% +we'll find out more about this when we + + + align:start position:0% +we'll find out more about this when we +get to the etherium section of the class + + align:start position:0% +get to the etherium section of the class + + + align:start position:0% +get to the etherium section of the class +how you combine spending from different + + align:start position:0% +how you combine spending from different + + + align:start position:0% +how you combine spending from different +accounts but but Bitcoin makes it very + + align:start position:0% +accounts but but Bitcoin makes it very + + + align:start position:0% +accounts but but Bitcoin makes it very +easy to combine spending from different + + align:start position:0% +easy to combine spending from different + + + align:start position:0% +easy to combine spending from different +pub keys and the account based model I + + align:start position:0% +pub keys and the account based model I + + + align:start position:0% +pub keys and the account based model I +could imagine it being a slightly more + + align:start position:0% +could imagine it being a slightly more + + + align:start position:0% +could imagine it being a slightly more +complicated process but that's a good + + align:start position:0% +complicated process but that's a good + + + align:start position:0% +complicated process but that's a good +point yes you could definitely create a + + align:start position:0% +point yes you could definitely create a + + + align:start position:0% +point yes you could definitely create a +lot of accounts with a lot of small + + align:start position:0% +lot of accounts with a lot of small + + + align:start position:0% +lot of accounts with a lot of small +balance but if you want to spend a lot + + align:start position:0% +balance but if you want to spend a lot + + + align:start position:0% +balance but if you want to spend a lot +you're gonna have to somehow accumulate + + align:start position:0% +you're gonna have to somehow accumulate + + + align:start position:0% +you're gonna have to somehow accumulate +all of that spending remember I talked + + align:start position:0% +all of that spending remember I talked + + + align:start position:0% +all of that spending remember I talked +about how there is like one special + + align:start position:0% +about how there is like one special + + + align:start position:0% +about how there is like one special +transaction in every block called the + + align:start position:0% +transaction in every block called the + + + align:start position:0% +transaction in every block called the +coinbase transaction and this + + align:start position:0% +coinbase transaction and this + + + align:start position:0% +coinbase transaction and this +transaction does not have to follow all + + align:start position:0% +transaction does not have to follow all + + + align:start position:0% +transaction does not have to follow all +of the rules specified before so this is + + align:start position:0% +of the rules specified before so this is + + + align:start position:0% +of the rules specified before so this is +kind of like a hard coded exception into + + align:start position:0% +kind of like a hard coded exception into + + + align:start position:0% +kind of like a hard coded exception into +how Bitcoin works that there can be this + + align:start position:0% +how Bitcoin works that there can be this + + + align:start position:0% +how Bitcoin works that there can be this +one transaction in every block called + + align:start position:0% +one transaction in every block called + + + align:start position:0% +one transaction in every block called +the coinbase transaction it is the first + + align:start position:0% +the coinbase transaction it is the first + + + align:start position:0% +the coinbase transaction it is the first +transaction the coinbase transaction has + + align:start position:0% +transaction the coinbase transaction has + + + align:start position:0% +transaction the coinbase transaction has +exactly one input and that input needs + + align:start position:0% +exactly one input and that input needs + + + align:start position:0% +exactly one input and that input needs +to have certain field this input does + + align:start position:0% +to have certain field this input does + + + align:start position:0% +to have certain field this input does +not point to a previous output ok this + + align:start position:0% +not point to a previous output ok this + + + align:start position:0% +not point to a previous output ok this +input is essentially empty this is the + + align:start position:0% +input is essentially empty this is the + + + align:start position:0% +input is essentially empty this is the +transaction that doles out the block + + align:start position:0% +transaction that doles out the block + + + align:start position:0% +transaction that doles out the block +reward so this is the transaction that + + align:start position:0% +reward so this is the transaction that + + + align:start position:0% +reward so this is the transaction that +the block reward used to be 50 Bitcoin + + align:start position:0% +the block reward used to be 50 Bitcoin + + + align:start position:0% +the block reward used to be 50 Bitcoin +25 bitcoins 50 bitcoins now it's 12.5 + + align:start position:0% +25 bitcoins 50 bitcoins now it's 12.5 + + + align:start position:0% +25 bitcoins 50 bitcoins now it's 12.5 +bitcoins per block this is the + + align:start position:0% +bitcoins per block this is the + + + align:start position:0% +bitcoins per block this is the +transaction that doles out that 12.5 + + align:start position:0% +transaction that doles out that 12.5 + + + align:start position:0% +transaction that doles out that 12.5 +bitcoins plus the fees of the block so + + align:start position:0% +bitcoins plus the fees of the block so + + + align:start position:0% +bitcoins plus the fees of the block so +it has exactly one input and that input + + align:start position:0% +it has exactly one input and that input + + + align:start position:0% +it has exactly one input and that input +has all zeros for the previous + + align:start position:0% +has all zeros for the previous + + + align:start position:0% +has all zeros for the previous +transaction ID and then ffff for the + + align:start position:0% +transaction ID and then ffff for the + + + align:start position:0% +transaction ID and then ffff for the +index into that previous transaction ID + + align:start position:0% +index into that previous transaction ID + + + align:start position:0% +index into that previous transaction ID +I think the script sig can basically be + + align:start position:0% +I think the script sig can basically be + + + align:start position:0% +I think the script sig can basically be +whatever you want it's not evaluated it + + align:start position:0% +whatever you want it's not evaluated it + + + align:start position:0% +whatever you want it's not evaluated it +might have to be valid I'm not sure and + + align:start position:0% +might have to be valid I'm not sure and + + + align:start position:0% +might have to be valid I'm not sure and +then its output is in satoshis so this + + align:start position:0% +then its output is in satoshis so this + + + align:start position:0% +then its output is in satoshis so this +is 12.5 Bitcoin because remember a + + align:start position:0% +is 12.5 Bitcoin because remember a + + + align:start position:0% +is 12.5 Bitcoin because remember a +Bitcoin is 10 to the 8th satoshis so + + align:start position:0% +Bitcoin is 10 to the 8th satoshis so + + + align:start position:0% +Bitcoin is 10 to the 8th satoshis so +this is 12.5 Bitcoin plus here are the + + align:start position:0% +this is 12.5 Bitcoin plus here are the + + + align:start position:0% +this is 12.5 Bitcoin plus here are the +fees from that block and you probably if + + align:start position:0% +fees from that block and you probably if + + + align:start position:0% +fees from that block and you probably if +you're the one so the miner is the one + + align:start position:0% +you're the one so the miner is the one + + + align:start position:0% +you're the one so the miner is the one +who creates this + + align:start position:0% +who creates this + + + align:start position:0% +who creates this +action and the miner who creates this + + align:start position:0% +action and the miner who creates this + + + align:start position:0% +action and the miner who creates this +transaction probably wants to give + + align:start position:0% +transaction probably wants to give + + + align:start position:0% +transaction probably wants to give +themselves the Bitcoin and the block + + align:start position:0% +themselves the Bitcoin and the block + + + align:start position:0% +themselves the Bitcoin and the block +award and so would specify in here a + + align:start position:0% +award and so would specify in here a + + + align:start position:0% +award and so would specify in here a +script pub key that they could redeem + + align:start position:0% + + + + align:start position:0% + +note that this also has the nice + + align:start position:0% +note that this also has the nice + + + align:start position:0% +note that this also has the nice +property of making well I don't know if + + align:start position:0% +property of making well I don't know if + + + align:start position:0% +property of making well I don't know if +it's a nice property but all the blocks + + align:start position:0% +it's a nice property but all the blocks + + + align:start position:0% +it's a nice property but all the blocks +that people work on are actually + + align:start position:0% +that people work on are actually + + + align:start position:0% +that people work on are actually +different because each book in each + + align:start position:0% +different because each book in each + + + align:start position:0% +different because each book in each +block the coinbase transaction is going + + align:start position:0% +block the coinbase transaction is going + + + align:start position:0% +block the coinbase transaction is going +to be different because each person's + + align:start position:0% +to be different because each person's + + + align:start position:0% +to be different because each person's +trying to pay themselves for the + + align:start position:0% +trying to pay themselves for the + + + align:start position:0% +trying to pay themselves for the +different miners yes great question so + + align:start position:0% +different miners yes great question so + + + align:start position:0% +different miners yes great question so +um what would happen if a miner put like + + align:start position:0% +um what would happen if a miner put like + + + align:start position:0% +um what would happen if a miner put like +100 bitcoins in there any idea so what's + + align:start position:0% +100 bitcoins in there any idea so what's + + + align:start position:0% +100 bitcoins in there any idea so what's +keeping that at 12.5 bitcoins is the + + align:start position:0% +keeping that at 12.5 bitcoins is the + + + align:start position:0% +keeping that at 12.5 bitcoins is the +same thing that's keeping invalid + + align:start position:0% +same thing that's keeping invalid + + + align:start position:0% +same thing that's keeping invalid +transactions out of the blockchain which + + align:start position:0% +transactions out of the blockchain which + + + align:start position:0% +transactions out of the blockchain which +is the consensus rules of Bitcoin it + + align:start position:0% +is the consensus rules of Bitcoin it + + + align:start position:0% +is the consensus rules of Bitcoin it +says in the code that at this point in + + align:start position:0% +says in the code that at this point in + + + align:start position:0% +says in the code that at this point in +time given the block height where we are + + align:start position:0% +time given the block height where we are + + + align:start position:0% +time given the block height where we are +that number should be no larger than + + align:start position:0% +that number should be no larger than + + + align:start position:0% +that number should be no larger than +12.5 plus the fees in the transaction + + align:start position:0% +12.5 plus the fees in the transaction + + + align:start position:0% +12.5 plus the fees in the transaction +and if a miner put a different number in + + align:start position:0% +and if a miner put a different number in + + + align:start position:0% +and if a miner put a different number in +there a higher they can put a lower + + align:start position:0% +there a higher they can put a lower + + + align:start position:0% +there a higher they can put a lower +number that's fine they'll end up + + align:start position:0% +number that's fine they'll end up + + + align:start position:0% +number that's fine they'll end up +burning some Bitcoin which is + + align:start position:0% +burning some Bitcoin which is + + + align:start position:0% +burning some Bitcoin which is +unfortunate but if they try to put + + align:start position:0% +unfortunate but if they try to put + + + align:start position:0% +unfortunate but if they try to put +something higher in there the network + + align:start position:0% +something higher in there the network + + + align:start position:0% +something higher in there the network +will regard it as invalid because the + + align:start position:0% +will regard it as invalid because the + + + align:start position:0% +will regard it as invalid because the +network is running a set of rules and we + + align:start position:0% +network is running a set of rules and we + + + align:start position:0% +network is running a set of rules and we +are in this class going to get to what + + align:start position:0% +are in this class going to get to what + + + align:start position:0% +are in this class going to get to what +happens when you want to change that set + + align:start position:0% +happens when you want to change that set + + + align:start position:0% +happens when you want to change that set +of rules which gets really tricky but + + align:start position:0% +of rules which gets really tricky but + + + align:start position:0% +of rules which gets really tricky but +right now assume that the network is + + align:start position:0% +right now assume that the network is + + + align:start position:0% +right now assume that the network is +running the set of rules they're all + + align:start position:0% +running the set of rules they're all + + + align:start position:0% +running the set of rules they're all +checking they're all validating and so + + align:start position:0% +checking they're all validating and so + + + align:start position:0% +checking they're all validating and so +the answer is the network would reject + + align:start position:0% +the answer is the network would reject + + + align:start position:0% +the answer is the network would reject +this block if there was a higher number + + align:start position:0% +this block if there was a higher number + + + align:start position:0% +this block if there was a higher number +in there so this is kind of fun because + + align:start position:0% +in there so this is kind of fun because + + + align:start position:0% +in there so this is kind of fun because +you can sort of put whatever you want in + + align:start position:0% +you can sort of put whatever you want in + + + align:start position:0% +you can sort of put whatever you want in +here + + align:start position:0% +here + + + align:start position:0% +here +and so miners like to put advertisements + + align:start position:0% +and so miners like to put advertisements + + + align:start position:0% +and so miners like to put advertisements +in there and there actually was a pit + + align:start position:0% +in there and there actually was a pit + + + align:start position:0% +in there and there actually was a pit +there was like a time I don't know if + + align:start position:0% +there was like a time I don't know if + + + align:start position:0% +there was like a time I don't know if +you can still do this where you could + + align:start position:0% +you can still do this where you could + + + align:start position:0% +you can still do this where you could +literally buy the space from miners and + + align:start position:0% +literally buy the space from miners and + + + align:start position:0% +literally buy the space from miners and +put whatever you wanted in there so you + + align:start position:0% +put whatever you wanted in there so you + + + align:start position:0% +put whatever you wanted in there so you +could put your name + + align:start position:0% +could put your name + + + align:start position:0% +could put your name +or you know like ask someone to marry + + align:start position:0% +or you know like ask someone to marry + + + align:start position:0% +or you know like ask someone to marry +you or whatever you know you might want + + align:start position:0% +you or whatever you know you might want + + + align:start position:0% +you or whatever you know you might want +to do to put in the Bitcoin blockchain + + align:start position:0% +to do to put in the Bitcoin blockchain + + + align:start position:0% +to do to put in the Bitcoin blockchain +for all eternity but yeah so so miners + + align:start position:0% +for all eternity but yeah so so miners + + + align:start position:0% +for all eternity but yeah so so miners +like to put fun things in the script zig + + align:start position:0% +like to put fun things in the script zig + + + align:start position:0% +like to put fun things in the script zig +and maybe we could we could show them + + align:start position:0% +and maybe we could we could show them + + + align:start position:0% +and maybe we could we could show them +some of those things later or you could + + align:start position:0% +some of those things later or you could + + + align:start position:0% +some of those things later or you could +go look yourself + + align:start position:0% +go look yourself + + + align:start position:0% +go look yourself +[Music] \ No newline at end of file diff --git a/Vp_AzDGQyrA.txt b/Vp_AzDGQyrA.txt new file mode 100644 index 0000000000000000000000000000000000000000..d81a8562aaf17a1860228cd2355094acf9d45e22 --- /dev/null +++ b/Vp_AzDGQyrA.txt @@ -0,0 +1,18547 @@ +align:start position:0% + +okay hello everybody + + align:start position:0% +okay hello everybody + + + align:start position:0% +okay hello everybody +we'll get started + + align:start position:0% +we'll get started + + + align:start position:0% +we'll get started +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +just recapping what we did + + align:start position:0% +just recapping what we did + + + align:start position:0% +just recapping what we did +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +a + + align:start position:0% +a + + + align:start position:0% +a +in the last lecture on tuesday + + align:start position:0% +in the last lecture on tuesday + + + align:start position:0% +in the last lecture on tuesday +we um + + align:start position:0% +we um + + + align:start position:0% +we um +had a + + align:start position:0% +had a + + + align:start position:0% +had a +it was kind of a two is the second part + + align:start position:0% +it was kind of a two is the second part + + + align:start position:0% +it was kind of a two is the second part +of a two lecture sequence on the + + align:start position:0% +of a two lecture sequence on the + + + align:start position:0% +of a two lecture sequence on the +hierarchy theorem + + align:start position:0% +hierarchy theorem + + + align:start position:0% +hierarchy theorem +higher hierarchy theorems for time and + + align:start position:0% +higher hierarchy theorems for time and + + + align:start position:0% +higher hierarchy theorems for time and +space + + align:start position:0% +space + + + align:start position:0% +space +and using the hierarchy theorems to show + + align:start position:0% +and using the hierarchy theorems to show + + + align:start position:0% +and using the hierarchy theorems to show +that there are that there is a problem + + align:start position:0% +that there are that there is a problem + + + align:start position:0% +that there are that there is a problem +which is + + align:start position:0% +which is + + + align:start position:0% +which is +intractable that's provably outside of + + align:start position:0% +intractable that's provably outside of + + + align:start position:0% +intractable that's provably outside of +polynomial time + + align:start position:0% +polynomial time + + + align:start position:0% +polynomial time +and that was this equivalence problem + + align:start position:0% +and that was this equivalence problem + + + align:start position:0% +and that was this equivalence problem +for regular expressions with + + align:start position:0% +for regular expressions with + + + align:start position:0% +for regular expressions with +exponentiation + + align:start position:0% +exponentiation + + + align:start position:0% +exponentiation +and then we had a short discussion + + align:start position:0% +and then we had a short discussion + + + align:start position:0% +and then we had a short discussion +about oracles + + align:start position:0% +about oracles + + + align:start position:0% +about oracles +and the possibility that similar methods + + align:start position:0% +and the possibility that similar methods + + + align:start position:0% +and the possibility that similar methods +might you might be used to show that + + align:start position:0% +might you might be used to show that + + + align:start position:0% +might you might be used to show that +satisfiability is outside of p which + + align:start position:0% +satisfiability is outside of p which + + + align:start position:0% +satisfiability is outside of p which +would then of course solve the p versus + + align:start position:0% +would then of course solve the p versus + + + align:start position:0% +would then of course solve the p versus +mp problem and argued that um + + align:start position:0% +mp problem and argued that um + + + align:start position:0% +mp problem and argued that um +it seems unlikely + + align:start position:0% +it seems unlikely + + + align:start position:0% +it seems unlikely +um this kind of a meta theorem not not a + + align:start position:0% +um this kind of a meta theorem not not a + + + align:start position:0% +um this kind of a meta theorem not not a +well uh + + align:start position:0% +well uh + + + align:start position:0% +well uh +well-defined notion + + align:start position:0% +well-defined notion + + + align:start position:0% +well-defined notion +but seems unlikely that the methods that + + align:start position:0% +but seems unlikely that the methods that + + + align:start position:0% +but seems unlikely that the methods that +were used for proving + + align:start position:0% +were used for proving + + + align:start position:0% +were used for proving +the um + + align:start position:0% +the um + + + align:start position:0% +the um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the intractability of um + + align:start position:0% +the intractability of um + + + align:start position:0% +the intractability of um +equivalence of regular expressions with + + align:start position:0% +equivalence of regular expressions with + + + align:start position:0% +equivalence of regular expressions with +exponentiation could be used to solve p + + align:start position:0% +exponentiation could be used to solve p + + + align:start position:0% +exponentiation could be used to solve p +versus np at least um the the + + align:start position:0% +versus np at least um the the + + + align:start position:0% +versus np at least um the the +diagonalization method kind of in a pure + + align:start position:0% +diagonalization method kind of in a pure + + + align:start position:0% +diagonalization method kind of in a pure +form whatever that means uh that's not + + align:start position:0% +form whatever that means uh that's not + + + align:start position:0% +form whatever that means uh that's not +going to be um enough + + align:start position:0% +going to be um enough + + + align:start position:0% +going to be um enough +so today we're going to + + align:start position:0% +so today we're going to + + + align:start position:0% +so today we're going to +shift gears again begin a somewhat + + align:start position:0% +shift gears again begin a somewhat + + + align:start position:0% +shift gears again begin a somewhat +different topic which is really kind of + + align:start position:0% +different topic which is really kind of + + + align:start position:0% +different topic which is really kind of +um going to be our uh + + align:start position:0% +um going to be our uh + + + align:start position:0% +um going to be our uh +again a + + align:start position:0% +again a + + + align:start position:0% +again a +few lectures on probabilistic + + align:start position:0% +few lectures on probabilistic + + + align:start position:0% +few lectures on probabilistic +computation which is going to wrap round + + align:start position:0% +computation which is going to wrap round + + + align:start position:0% +computation which is going to wrap round +out the semester for us + + align:start position:0% +out the semester for us + + + align:start position:0% +out the semester for us +um and we're going to start by talking + + align:start position:0% +um and we're going to start by talking + + + align:start position:0% +um and we're going to start by talking +about a different model of computation + + align:start position:0% +about a different model of computation + + + align:start position:0% +about a different model of computation +which allows for uh probabilis + + align:start position:0% +which allows for uh probabilis + + + align:start position:0% +which allows for uh probabilis +probabilism in the + + align:start position:0% +probabilism in the + + + align:start position:0% +probabilism in the +measuring the amount of probabilism or + + align:start position:0% +measuring the amount of probabilism or + + + align:start position:0% +measuring the amount of probabilism or +measuring the probability allowing for + + align:start position:0% +measuring the probability allowing for + + + align:start position:0% +measuring the probability allowing for +probabilism in the computation + + align:start position:0% +probabilism in the computation + + + align:start position:0% +probabilism in the computation +define an associated complexity class uh + + align:start position:0% +define an associated complexity class uh + + + align:start position:0% +define an associated complexity class uh +this class bpp + + align:start position:0% +this class bpp + + + align:start position:0% +this class bpp +and then start to start the discussion + + align:start position:0% +and then start to start the discussion + + + align:start position:0% +and then start to start the discussion +of an example um + + align:start position:0% +of an example um + + + align:start position:0% +of an example um +about something called branching + + align:start position:0% +about something called branching + + + align:start position:0% +about something called branching +programs + + align:start position:0% +programs + + + align:start position:0% +programs +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so uh with that in mind um + + align:start position:0% +so uh with that in mind um + + + align:start position:0% +so uh with that in mind um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um + + align:start position:0% +um + + + align:start position:0% +um +a + + align:start position:0% +a + + + align:start position:0% +a +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so we're gonna start off by defining + + align:start position:0% +so we're gonna start off by defining + + + align:start position:0% +so we're gonna start off by defining +the notion of a probabilistic + + align:start position:0% +the notion of a probabilistic + + + align:start position:0% +the notion of a probabilistic +turing machine or ptm + + align:start position:0% +turing machine or ptm + + + align:start position:0% +turing machine or ptm +um a probabilistic turing machine is a + + align:start position:0% +um a probabilistic turing machine is a + + + align:start position:0% +um a probabilistic turing machine is a +lot like + + align:start position:0% +lot like + + + align:start position:0% +lot like +the way we have thought about + + align:start position:0% +the way we have thought about + + + align:start position:0% +the way we have thought about +non-deterministic touring machines + + align:start position:0% +non-deterministic touring machines + + + align:start position:0% +non-deterministic touring machines +in that it's a kind of a machine that + + align:start position:0% +in that it's a kind of a machine that + + + align:start position:0% +in that it's a kind of a machine that +can have multiple choices multiple ways + + align:start position:0% +can have multiple choices multiple ways + + + align:start position:0% +can have multiple choices multiple ways +to go + + align:start position:0% +to go + + + align:start position:0% +to go +in its computation so there's not just + + align:start position:0% +in its computation so there's not just + + + align:start position:0% +in its computation so there's not just +going to be a fixed uh deterministic + + align:start position:0% +going to be a fixed uh deterministic + + + align:start position:0% +going to be a fixed uh deterministic +path + + align:start position:0% +path + + + align:start position:0% +path +um of its computation but there's going + + align:start position:0% +um of its computation but there's going + + + align:start position:0% +um of its computation but there's going +to be a tree of possibilities um and for + + align:start position:0% +to be a tree of possibilities um and for + + + align:start position:0% +to be a tree of possibilities um and for +our purposes we're going to limit the + + align:start position:0% +our purposes we're going to limit the + + + align:start position:0% +our purposes we're going to limit the +branching in that tree to be either + + align:start position:0% +branching in that tree to be either + + + align:start position:0% +branching in that tree to be either +um a step of the computation where + + align:start position:0% +um a step of the computation where + + + align:start position:0% +um a step of the computation where +there's no branching where it's a + + align:start position:0% +there's no branching where it's a + + + align:start position:0% +there's no branching where it's a +deterministic step + + align:start position:0% +deterministic step + + + align:start position:0% +deterministic step +uh as shown over here um so every step + + align:start position:0% +uh as shown over here um so every step + + + align:start position:0% +uh as shown over here um so every step +of the way leads uniquely to the next + + align:start position:0% +of the way leads uniquely to the next + + + align:start position:0% +of the way leads uniquely to the next +step + + align:start position:0% +step + + + align:start position:0% +step +or there might be some steps which have + + align:start position:0% +or there might be some steps which have + + + align:start position:0% +or there might be some steps which have +a choice and we're only going to allow + + align:start position:0% +a choice and we're only going to allow + + + align:start position:0% +a choice and we're only going to allow +for these purposes uh to keep life + + align:start position:0% +for these purposes uh to keep life + + + align:start position:0% +for these purposes uh to keep life +simple + + align:start position:0% +simple + + + align:start position:0% +simple +um having only uh a choice among two + + align:start position:0% +um having only uh a choice among two + + + align:start position:0% +um having only uh a choice among two +possibilities + + align:start position:0% +possibilities + + + align:start position:0% +possibilities +um + + align:start position:0% +um + + + align:start position:0% +um +and we'll associate to that + + align:start position:0% +and we'll associate to that + + + align:start position:0% +and we'll associate to that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um + + align:start position:0% +um + + + align:start position:0% +um +the notion of a + + align:start position:0% +the notion of a + + + align:start position:0% +the notion of a +probability that each choice will have a + + align:start position:0% +probability that each choice will have a + + + align:start position:0% +probability that each choice will have a +50 50 chance of getting taken + + align:start position:0% +50 50 chance of getting taken + + + align:start position:0% +50 50 chance of getting taken +and this kind of corresponds with the + + align:start position:0% +and this kind of corresponds with the + + + align:start position:0% +and this kind of corresponds with the +way some of us or some of you think + + align:start position:0% +way some of us or some of you think + + + align:start position:0% +way some of us or some of you think +about non-determinism which is not + + align:start position:0% +about non-determinism which is not + + + align:start position:0% +about non-determinism which is not +exactly right up and up until this point + + align:start position:0% +exactly right up and up until this point + + + align:start position:0% +exactly right up and up until this point +is that the machine is kind of taking a + + align:start position:0% +is that the machine is kind of taking a + + + align:start position:0% +is that the machine is kind of taking a +random branch it really we don't think + + align:start position:0% +random branch it really we don't think + + + align:start position:0% +random branch it really we don't think +about it randomly until now now we're + + align:start position:0% +about it randomly until now now we're + + + align:start position:0% +about it randomly until now now we're +going to think about the machine as + + align:start position:0% +going to think about the machine as + + + align:start position:0% +going to think about the machine as +actually taking + + align:start position:0% +actually taking + + + align:start position:0% +actually taking +sort of picking a random choice among + + align:start position:0% +sort of picking a random choice among + + + align:start position:0% +sort of picking a random choice among +all the different branches that it could + + align:start position:0% +all the different branches that it could + + + align:start position:0% +all the different branches that it could +make um and picking the choice kind of + + align:start position:0% +make um and picking the choice kind of + + + align:start position:0% +make um and picking the choice kind of +uniformly by flipping a coin every time + + align:start position:0% +uniformly by flipping a coin every time + + + align:start position:0% +uniformly by flipping a coin every time +it has an option of which way to go + + align:start position:0% +it has an option of which way to go + + + align:start position:0% +it has an option of which way to go +uh + + align:start position:0% +uh + + + align:start position:0% +uh +now you could + + align:start position:0% +now you could + + + align:start position:0% +now you could +define i'm getting a question here uh + + align:start position:0% +define i'm getting a question here uh + + + align:start position:0% +define i'm getting a question here uh +the uh a machine that has several + + align:start position:0% +the uh a machine that has several + + + align:start position:0% +the uh a machine that has several +different ways to more than two ways to + + align:start position:0% +different ways to more than two ways to + + + align:start position:0% +different ways to more than two ways to +go and then you would need to have a + + align:start position:0% +go and then you would need to have a + + + align:start position:0% +go and then you would need to have a +three-way coin a four-way coin and so on + + align:start position:0% +three-way coin a four-way coin and so on + + + align:start position:0% +three-way coin a four-way coin and so on +and you could define it all of that that + + align:start position:0% +and you could define it all of that that + + + align:start position:0% +and you could define it all of that that +way + + align:start position:0% +way + + + align:start position:0% +way +as well but it doesn't end up giving you + + align:start position:0% +as well but it doesn't end up giving you + + + align:start position:0% +as well but it doesn't end up giving you +anything different or anything uh + + align:start position:0% +anything different or anything uh + + + align:start position:0% +anything different or anything uh +interesting or new for uh for the kinds + + align:start position:0% +interesting or new for uh for the kinds + + + align:start position:0% +interesting or new for uh for the kinds +of things we're going to be discussing + + align:start position:0% +of things we're going to be discussing + + + align:start position:0% +of things we're going to be discussing +so and it's just going to be simpler to + + align:start position:0% +so and it's just going to be simpler to + + + align:start position:0% +so and it's just going to be simpler to +keep the discussion limited to the case + + align:start position:0% +keep the discussion limited to the case + + + align:start position:0% +keep the discussion limited to the case +where the machine can only have two + + align:start position:0% +where the machine can only have two + + + align:start position:0% +where the machine can only have two +possibilities um if it's going to be + + align:start position:0% +possibilities um if it's going to be + + + align:start position:0% +possibilities um if it's going to be +having a choice at all or or just one + + align:start position:0% +having a choice at all or or just one + + + align:start position:0% +having a choice at all or or just one +possibility when there's no choice + + align:start position:0% +possibility when there's no choice + + + align:start position:0% +possibility when there's no choice +okay so um so now we're going to have to + + align:start position:0% +okay so um so now we're going to have to + + + align:start position:0% +okay so um so now we're going to have to +talk about the probability of a + + align:start position:0% +talk about the probability of a + + + align:start position:0% +talk about the probability of a +the machine taking a sum branch of its + + align:start position:0% +the machine taking a sum branch of its + + + align:start position:0% +the machine taking a sum branch of its +computation so you imagine here here is + + align:start position:0% +computation so you imagine here here is + + + align:start position:0% +computation so you imagine here here is +the same computation tree that we've + + align:start position:0% +the same computation tree that we've + + + align:start position:0% +the same computation tree that we've +seen before in the case of ordinary + + align:start position:0% +seen before in the case of ordinary + + + align:start position:0% +seen before in the case of ordinary +non-deterministic machines where you + + align:start position:0% +non-deterministic machines where you + + + align:start position:0% +non-deterministic machines where you +have m on w there could be several + + align:start position:0% +have m on w there could be several + + + align:start position:0% +have m on w there could be several +different ways to go and there might be + + align:start position:0% +different ways to go and there might be + + + align:start position:0% +different ways to go and there might be +some particular branch but now we want + + align:start position:0% +some particular branch but now we want + + + align:start position:0% +some particular branch but now we want +to talk about the probability that the + + align:start position:0% +to talk about the probability that the + + + align:start position:0% +to talk about the probability that the +machine actually ends up picking that + + align:start position:0% +machine actually ends up picking that + + + align:start position:0% +machine actually ends up picking that +branch + + align:start position:0% +branch + + + align:start position:0% +branch +and it's going to be + + align:start position:0% +and it's going to be + + + align:start position:0% +and it's going to be +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know when we talk about + + align:start position:0% +you know when we talk about + + + align:start position:0% +you know when we talk about +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the machine having a choice of ways to + + align:start position:0% +the machine having a choice of ways to + + + align:start position:0% +the machine having a choice of ways to +go we're going to associate that with a + + align:start position:0% +go we're going to associate that with a + + + align:start position:0% +go we're going to associate that with a +coin flip so we're going to call that a + + align:start position:0% +coin flip so we're going to call that a + + + align:start position:0% +coin flip so we're going to call that a +coin flip step when the machine has a + + align:start position:0% +coin flip step when the machine has a + + + align:start position:0% +coin flip step when the machine has a +possibility of ways to go and so on a + + align:start position:0% +possibility of ways to go and so on a + + + align:start position:0% +possibility of ways to go and so on a +particular branch + + align:start position:0% +particular branch + + + align:start position:0% +particular branch +the probability of that branch occurring + + align:start position:0% +the probability of that branch occurring + + + align:start position:0% +the probability of that branch occurring +is going to be one over two to the + + align:start position:0% +is going to be one over two to the + + + align:start position:0% +is going to be one over two to the +number of coin flips + + align:start position:0% +number of coin flips + + + align:start position:0% +number of coin flips +coin flip states on that branch + + align:start position:0% +coin flip states on that branch + + + align:start position:0% +coin flip states on that branch +and the reason for i mean this is kind + + align:start position:0% +and the reason for i mean this is kind + + + align:start position:0% +and the reason for i mean this is kind +of the the + + align:start position:0% +of the the + + + align:start position:0% +of the the +the definition that makes sense um in + + align:start position:0% +the definition that makes sense um in + + + align:start position:0% +the definition that makes sense um in +that if you imagine looking at the + + align:start position:0% +that if you imagine looking at the + + + align:start position:0% +that if you imagine looking at the +computation tree here and here is the + + align:start position:0% +computation tree here and here is the + + + align:start position:0% +computation tree here and here is the +branch that we're focusing on um of + + align:start position:0% +branch that we're focusing on um of + + + align:start position:0% +branch that we're focusing on um of +interest + + align:start position:0% +interest + + + align:start position:0% +interest +every time there's a coin flip on that + + align:start position:0% +every time there's a coin flip on that + + + align:start position:0% +every time there's a coin flip on that +branch + + align:start position:0% +branch + + + align:start position:0% +branch +there's a 50 50 chance of taking a + + align:start position:0% +there's a 50 50 chance of taking a + + + align:start position:0% +there's a 50 50 chance of taking a +different branch or staying on that + + align:start position:0% +different branch or staying on that + + + align:start position:0% +different branch or staying on that +branch + + align:start position:0% +branch + + + align:start position:0% +branch +so the more coin flips there are on some + + align:start position:0% +so the more coin flips there are on some + + + align:start position:0% +so the more coin flips there are on some +particular branch the less likely that + + align:start position:0% +particular branch the less likely that + + + align:start position:0% +particular branch the less likely that +branch would be the one that the machine + + align:start position:0% +branch would be the one that the machine + + + align:start position:0% +branch would be the one that the machine +actually actually ends up taking taking + + align:start position:0% +actually actually ends up taking taking + + + align:start position:0% +actually actually ends up taking taking +and so it's going to be one over two to + + align:start position:0% +and so it's going to be one over two to + + + align:start position:0% +and so it's going to be one over two to +the number of coin flips + + align:start position:0% +the number of coin flips + + + align:start position:0% +the number of coin flips +and that's the way we're defining it + + align:start position:0% +and that's the way we're defining it + + + align:start position:0% +and that's the way we're defining it +now once we have that notion + + align:start position:0% +now once we have that notion + + + align:start position:0% +now once we have that notion +we can also talk about the probability + + align:start position:0% +we can also talk about the probability + + + align:start position:0% +we can also talk about the probability +that the machine ends up accepting + + align:start position:0% +that the machine ends up accepting + + + align:start position:0% +that the machine ends up accepting +because each as before each of these + + align:start position:0% +because each as before each of these + + + align:start position:0% +because each as before each of these +branches is going to end up + + align:start position:0% +branches is going to end up + + + align:start position:0% +branches is going to end up +at an accept state or reject state i'm + + align:start position:0% +at an accept state or reject state i'm + + + align:start position:0% +at an accept state or reject state i'm +thinking about this only in terms of + + align:start position:0% +thinking about this only in terms of + + + align:start position:0% +thinking about this only in terms of +deciders + + align:start position:0% +deciders + + + align:start position:0% +deciders +and + + align:start position:0% +and + + + align:start position:0% +and +the probability of + + align:start position:0% +the probability of + + + align:start position:0% +the probability of +the machine accepting here is just going + + align:start position:0% +the machine accepting here is just going + + + align:start position:0% +the machine accepting here is just going +to be the sum over all probabilities of + + align:start position:0% +to be the sum over all probabilities of + + + align:start position:0% +to be the sum over all probabilities of +the branches that end up accepting + + align:start position:0% +the branches that end up accepting + + + align:start position:0% +the branches that end up accepting +so just add up all of those + + align:start position:0% +so just add up all of those + + + align:start position:0% +so just add up all of those +probabilities of a branch leading to an + + align:start position:0% +probabilities of a branch leading to an + + + align:start position:0% +probabilities of a branch leading to an +accept and we'll call that the + + align:start position:0% +accept and we'll call that the + + + align:start position:0% +accept and we'll call that the +probability that the machine accepts its + + align:start position:0% +probability that the machine accepts its + + + align:start position:0% +probability that the machine accepts its +input + + align:start position:0% +input + + + align:start position:0% +input +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and the probability that the machine + + align:start position:0% +and the probability that the machine + + + align:start position:0% +and the probability that the machine +rejects is going to be one minus the + + align:start position:0% +rejects is going to be one minus the + + + align:start position:0% +rejects is going to be one minus the +probability that it accepts + + align:start position:0% +probability that it accepts + + + align:start position:0% +probability that it accepts +because it's going to the machine um on + + align:start position:0% +because it's going to the machine um on + + + align:start position:0% +because it's going to the machine um on +every branch is either either going to + + align:start position:0% +every branch is either either going to + + + align:start position:0% +every branch is either either going to +do one or the other + + align:start position:0% +do one or the other + + + align:start position:0% +do one or the other +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +now if you're thinking about a + + align:start position:0% +now if you're thinking about a + + + align:start position:0% +now if you're thinking about a +particular language + + align:start position:0% +particular language + + + align:start position:0% +particular language +that the machine is trying to decide + + align:start position:0% +that the machine is trying to decide + + + align:start position:0% +that the machine is trying to decide +this probabilistic machine now is trying + + align:start position:0% +this probabilistic machine now is trying + + + align:start position:0% +this probabilistic machine now is trying +to decide + + align:start position:0% +to decide + + + align:start position:0% +to decide +um you know + + align:start position:0% + + + + align:start position:0% + +on on each input + + align:start position:0% +on on each input + + + align:start position:0% +on on each input +some of the branches of the machine may + + align:start position:0% +some of the branches of the machine may + + + align:start position:0% +some of the branches of the machine may +not may give the correct answer they're + + align:start position:0% +not may give the correct answer they're + + + align:start position:0% +not may give the correct answer they're +going to accept when the input is in the + + align:start position:0% +going to accept when the input is in the + + + align:start position:0% +going to accept when the input is in the +language other branches may give the + + align:start position:0% +language other branches may give the + + + align:start position:0% +language other branches may give the +wrong answer they may reject when the + + align:start position:0% +wrong answer they may reject when the + + + align:start position:0% +wrong answer they may reject when the +input is in the language and vice versa + + align:start position:0% +input is in the language and vice versa + + + align:start position:0% +input is in the language and vice versa +so there's going to be a possibility of + + align:start position:0% +so there's going to be a possibility of + + + align:start position:0% +so there's going to be a possibility of +error now in the machine in any + + align:start position:0% +error now in the machine in any + + + align:start position:0% +error now in the machine in any +particular branch it might actually give + + align:start position:0% +particular branch it might actually give + + + align:start position:0% +particular branch it might actually give +the wrong answer + + align:start position:0% +the wrong answer + + + align:start position:0% +the wrong answer +and what we're going to say is bound + + align:start position:0% +and what we're going to say is bound + + + align:start position:0% +and what we're going to say is bound +that error + + align:start position:0% +that error + + + align:start position:0% +that error +over all possible inputs + + align:start position:0% +over all possible inputs + + + align:start position:0% +over all possible inputs +um and so and uh + + align:start position:0% +um and so and uh + + + align:start position:0% +um and so and uh +we'll say that the machine for any + + align:start position:0% +we'll say that the machine for any + + + align:start position:0% +we'll say that the machine for any +epsilon greater than or equal to zero + + align:start position:0% +epsilon greater than or equal to zero + + + align:start position:0% +epsilon greater than or equal to zero +um we will say that the machine decides + + align:start position:0% +um we will say that the machine decides + + + align:start position:0% +um we will say that the machine decides +the language with error probability + + align:start position:0% +the language with error probability + + + align:start position:0% +the language with error probability +epsilon + + align:start position:0% +epsilon + + + align:start position:0% +epsilon +if that's the worst that can possibly + + align:start position:0% +if that's the worst that can possibly + + + align:start position:0% +if that's the worst that can possibly +happen you know if every + + align:start position:0% +happen you know if every + + + align:start position:0% +happen you know if every +um for every input the machine gives the + + align:start position:0% +um for every input the machine gives the + + + align:start position:0% +um for every input the machine gives the +wrong answer + + align:start position:0% +wrong answer + + + align:start position:0% +wrong answer +with probability at most epsilon + + align:start position:0% + + + + align:start position:0% + +um equivalently if you like to spell it + + align:start position:0% +um equivalently if you like to spell it + + + align:start position:0% +um equivalently if you like to spell it +out a little bit more + + align:start position:0% +out a little bit more + + + align:start position:0% +out a little bit more +you know + + align:start position:0% + + + + align:start position:0% + +a little differently + + align:start position:0% +a little differently + + + align:start position:0% +a little differently +for + + align:start position:0% +for + + + align:start position:0% +for +strings that are in the language the + + align:start position:0% +strings that are in the language the + + + align:start position:0% +strings that are in the language the +probability that the machine rejects + + align:start position:0% +probability that the machine rejects + + + align:start position:0% +probability that the machine rejects +that input is going to be at most + + align:start position:0% +that input is going to be at most + + + align:start position:0% +that input is going to be at most +epsilon and for strings in the language + + align:start position:0% +epsilon and for strings in the language + + + align:start position:0% +epsilon and for strings in the language +the probability of for strings not in + + align:start position:0% +the probability of for strings not in + + + align:start position:0% +the probability of for strings not in +the language the probability that + + align:start position:0% +the language the probability that + + + align:start position:0% +the language the probability that +accepts is a most epsilon + + align:start position:0% +accepts is a most epsilon + + + align:start position:0% +accepts is a most epsilon +so again this is + + align:start position:0% +so again this is + + + align:start position:0% +so again this is +the machine doing the the thing that + + align:start position:0% +the machine doing the the thing that + + + align:start position:0% +the machine doing the the thing that +it's not supposed to be doing for things + + align:start position:0% +it's not supposed to be doing for things + + + align:start position:0% +it's not supposed to be doing for things +in the language it should be rejecting + + align:start position:0% +in the language it should be rejecting + + + align:start position:0% +in the language it should be rejecting +very rarely for things not in the + + align:start position:0% +very rarely for things not in the + + + align:start position:0% +very rarely for things not in the +language it should be accepting very + + align:start position:0% +language it should be accepting very + + + align:start position:0% +language it should be accepting very +rarely and that's what this bound is + + align:start position:0% +rarely and that's what this bound is + + + align:start position:0% +rarely and that's what this bound is +doing for you + + align:start position:0% +doing for you + + + align:start position:0% +doing for you +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so let's just see uh + + align:start position:0% +so let's just see uh + + + align:start position:0% +so let's just see uh +so we'll talk about so i'm getting some + + align:start position:0% +so we'll talk about so i'm getting some + + + align:start position:0% +so we'll talk about so i'm getting some +questions here about um + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so let me just look at these one second + + align:start position:0% +so let me just look at these one second + + + align:start position:0% +so let me just look at these one second +here + + align:start position:0% +here + + + align:start position:0% +here +the + + align:start position:0% + + + + align:start position:0% + +yeah so + + align:start position:0% +yeah so + + + align:start position:0% +yeah so +probability zero so there's a + + align:start position:0% +probability zero so there's a + + + align:start position:0% +probability zero so there's a +possibility that the machine have might + + align:start position:0% +possibility that the machine have might + + + align:start position:0% +possibility that the machine have might +have a probability zero say of accepting + + align:start position:0% +have a probability zero say of accepting + + + align:start position:0% +have a probability zero say of accepting +that means there are no branches that + + align:start position:0% +that means there are no branches that + + + align:start position:0% +that means there are no branches that +end up accepting or probability zero of + + align:start position:0% +end up accepting or probability zero of + + + align:start position:0% +end up accepting or probability zero of +rejecting there were no rejecting + + align:start position:0% +rejecting there were no rejecting + + + align:start position:0% +rejecting there were no rejecting +branches + + align:start position:0% +branches + + + align:start position:0% +branches +um but i think we're going to talk in a + + align:start position:0% +um but i think we're going to talk in a + + + align:start position:0% +um but i think we're going to talk in a +minute about the connection between this + + align:start position:0% +minute about the connection between this + + + align:start position:0% +minute about the connection between this +and and the standard notion of np + + align:start position:0% +and and the standard notion of np + + + align:start position:0% +and and the standard notion of np +um so just hold off on that for a second + + align:start position:0% +um so just hold off on that for a second + + + align:start position:0% +um so just hold off on that for a second +uh + + align:start position:0% +uh + + + align:start position:0% +uh +also about what what about the you know + + align:start position:0% +also about what what about the you know + + + align:start position:0% +also about what what about the you know +the um the possibility that the machine + + align:start position:0% +the um the possibility that the machine + + + align:start position:0% +the um the possibility that the machine +is you know + + align:start position:0% +is you know + + + align:start position:0% +is you know +being a decider or running in a certain + + align:start position:0% +being a decider or running in a certain + + + align:start position:0% +being a decider or running in a certain +amount of time um so we will look at + + align:start position:0% +amount of time um so we will look at + + + align:start position:0% +amount of time um so we will look at +time-bounded machines + + align:start position:0% +time-bounded machines + + + align:start position:0% +time-bounded machines +in a second um + + align:start position:0% +in a second um + + + align:start position:0% +in a second um +on the next slide or two um talking + + align:start position:0% +on the next slide or two um talking + + + align:start position:0% +on the next slide or two um talking +about machines that run in polynomial + + align:start position:0% +about machines that run in polynomial + + + align:start position:0% +about machines that run in polynomial +time so that means all branches have to + + align:start position:0% +time so that means all branches have to + + + align:start position:0% +time so that means all branches have to +halt within some polynomial number of + + align:start position:0% +halt within some polynomial number of + + + align:start position:0% +halt within some polynomial number of +steps um so that's where we're going + + align:start position:0% +steps um so that's where we're going + + + align:start position:0% +steps um so that's where we're going +but for the time being we're only + + align:start position:0% +but for the time being we're only + + + align:start position:0% +but for the time being we're only +looking at the siders where the machine + + align:start position:0% +looking at the siders where the machine + + + align:start position:0% +looking at the siders where the machine +has to hold on every branch + + align:start position:0% +has to hold on every branch + + + align:start position:0% +has to hold on every branch +but some branches might run for a long + + align:start position:0% +but some branches might run for a long + + + align:start position:0% +but some branches might run for a long +time but + + align:start position:0% +time but + + + align:start position:0% +time but +for now we're not going to be thinking + + align:start position:0% +for now we're not going to be thinking + + + align:start position:0% +for now we're not going to be thinking +about machines that have branches that + + align:start position:0% +about machines that have branches that + + + align:start position:0% +about machines that have branches that +run um forever where all of our machines + + align:start position:0% +run um forever where all of our machines + + + align:start position:0% +run um forever where all of our machines +are deciders so they they hold on every + + align:start position:0% +are deciders so they they hold on every + + + align:start position:0% +are deciders so they they hold on every +branch + + align:start position:0% +branch + + + align:start position:0% +branch +see there's anything else here no so why + + align:start position:0% +see there's anything else here no so why + + + align:start position:0% +see there's anything else here no so why +don't i move on so let's define now + + align:start position:0% +don't i move on so let's define now + + + align:start position:0% +don't i move on so let's define now +the class bpp + + align:start position:0% +the class bpp + + + align:start position:0% +the class bpp +using this notion of a probabilistic + + align:start position:0% +using this notion of a probabilistic + + + align:start position:0% +using this notion of a probabilistic +turing machine which is now going to be + + align:start position:0% +turing machine which is now going to be + + + align:start position:0% +turing machine which is now going to be +running in polynomial time + + align:start position:0% +running in polynomial time + + + align:start position:0% +running in polynomial time +so bpp is going to be another one of + + align:start position:0% +so bpp is going to be another one of + + + align:start position:0% +so bpp is going to be another one of +these complexity classes a collection of + + align:start position:0% +these complexity classes a collection of + + + align:start position:0% +these complexity classes a collection of +languages like p and np and p space and + + align:start position:0% +languages like p and np and p space and + + + align:start position:0% +languages like p and np and p space and +so on and um but it's going to be now + + align:start position:0% +so on and um but it's going to be now + + + align:start position:0% +so on and um but it's going to be now +associated with the capabilities of + + align:start position:0% +associated with the capabilities of + + + align:start position:0% +associated with the capabilities of +these probabilistic machines the kinds + + align:start position:0% +these probabilistic machines the kinds + + + align:start position:0% +these probabilistic machines the kinds +of languages that they can do + + align:start position:0% +of languages that they can do + + + align:start position:0% +of languages that they can do +so we'll say the class bpp + + align:start position:0% +so we'll say the class bpp + + + align:start position:0% +so we'll say the class bpp +is the set of languages a + + align:start position:0% +is the set of languages a + + + align:start position:0% +is the set of languages a +such that there's some probabilistic + + align:start position:0% +such that there's some probabilistic + + + align:start position:0% +such that there's some probabilistic +polynomial time + + align:start position:0% +polynomial time + + + align:start position:0% +polynomial time +during machines so all branches have to + + align:start position:0% +during machines so all branches have to + + + align:start position:0% +during machines so all branches have to +halt within you know to the k for some k + + align:start position:0% +halt within you know to the k for some k + + + align:start position:0% +halt within you know to the k for some k +so some polynomial time + + align:start position:0% +so some polynomial time + + + align:start position:0% +so some polynomial time +polynomial time probabilistic turing + + align:start position:0% +polynomial time probabilistic turing + + + align:start position:0% +polynomial time probabilistic turing +machine decides a with error possibility + + align:start position:0% +machine decides a with error possibility + + + align:start position:0% +machine decides a with error possibility +at most one-third + + align:start position:0% + + + + align:start position:0% + +so in other words + + align:start position:0% +so in other words + + + align:start position:0% +so in other words +when it's accepting + + align:start position:0% +when it's accepting + + + align:start position:0% +when it's accepting +for some for strings in the language the + + align:start position:0% +for some for strings in the language the + + + align:start position:0% +for some for strings in the language the +machine has to reject with at most + + align:start position:0% +machine has to reject with at most + + + align:start position:0% +machine has to reject with at most +one-third so saying it equivalently for + + align:start position:0% +one-third so saying it equivalently for + + + align:start position:0% +one-third so saying it equivalently for +strings in the language it has to accept + + align:start position:0% +strings in the language it has to accept + + + align:start position:0% +strings in the language it has to accept +with two-thirds probability and for + + align:start position:0% +with two-thirds probability and for + + + align:start position:0% +with two-thirds probability and for +strings not in the language it has to + + align:start position:0% +strings not in the language it has to + + + align:start position:0% +strings not in the language it has to +reject what two-thirds probability at + + align:start position:0% +reject what two-thirds probability at + + + align:start position:0% +reject what two-thirds probability at +least + + align:start position:0% +least + + + align:start position:0% +least +in both cases + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +okay + + align:start position:0% + + + + align:start position:0% + +somehow ended up with + + align:start position:0% +somehow ended up with + + + align:start position:0% +somehow ended up with +didn't check my animation here but okay + + align:start position:0% +didn't check my animation here but okay + + + align:start position:0% +didn't check my animation here but okay +that's fine so there is a um + + align:start position:0% +that's fine so there is a um + + + align:start position:0% +that's fine so there is a um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +now if you look at the one-third here in + + align:start position:0% +now if you look at the one-third here in + + + align:start position:0% +now if you look at the one-third here in +the definition + + align:start position:0% +the definition + + + align:start position:0% +the definition +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know it seems strange to define a + + align:start position:0% +you know it seems strange to define a + + + align:start position:0% +you know it seems strange to define a +complexity class in terms of some + + align:start position:0% +complexity class in terms of some + + + align:start position:0% +complexity class in terms of some +arbitrary constant like one-third why + + align:start position:0% +arbitrary constant like one-third why + + + align:start position:0% +arbitrary constant like one-third why +didn't we use one-quarter + + align:start position:0% +didn't we use one-quarter + + + align:start position:0% +didn't we use one-quarter +you know or uh + + align:start position:0% +you know or uh + + + align:start position:0% +you know or uh +you know one-tenth in the definition of + + align:start position:0% +you know one-tenth in the definition of + + + align:start position:0% +you know one-tenth in the definition of +bpp + + align:start position:0% +bpp + + + align:start position:0% +bpp +and say the machine has to get have an + + align:start position:0% +and say the machine has to get have an + + + align:start position:0% +and say the machine has to get have an +error with at most one tenth or one + + align:start position:0% +error with at most one tenth or one + + + align:start position:0% +error with at most one tenth or one +hundredth uh + + align:start position:0% +hundredth uh + + + align:start position:0% +hundredth uh +well it doesn't matter + + align:start position:0% +well it doesn't matter + + + align:start position:0% +well it doesn't matter +and that's the point of this uh + + align:start position:0% +and that's the point of this uh + + + align:start position:0% +and that's the point of this uh +next statement called the amplification + + align:start position:0% +next statement called the amplification + + + align:start position:0% +next statement called the amplification +lemma + + align:start position:0% +lemma + + + align:start position:0% +lemma +which says that + + align:start position:0% +which says that + + + align:start position:0% +which says that +um + + align:start position:0% +um + + + align:start position:0% +um +you can always if you have a machine + + align:start position:0% +you can always if you have a machine + + + align:start position:0% +you can always if you have a machine +that's running in a certain + + align:start position:0% +that's running in a certain + + + align:start position:0% +that's running in a certain +uh + + align:start position:0% +uh + + + align:start position:0% +uh +a polynomial time that's running within + + align:start position:0% +a polynomial time that's running within + + + align:start position:0% +a polynomial time that's running within +this with a certain error which it is + + align:start position:0% +this with a certain error which it is + + + align:start position:0% +this with a certain error which it is +most one-half if you have an error + + align:start position:0% +most one-half if you have an error + + + align:start position:0% +most one-half if you have an error +one-half it's not interesting because + + align:start position:0% +one-half it's not interesting because + + + align:start position:0% +one-half it's not interesting because +the machine + + align:start position:0% +the machine + + + align:start position:0% +the machine +could just flip a coin for every uh + + align:start position:0% +could just flip a coin for every uh + + + align:start position:0% +could just flip a coin for every uh +input and it could get uh the right + + align:start position:0% +input and it could get uh the right + + + align:start position:0% +input and it could get uh the right +answer with it with probability one-half + + align:start position:0% +answer with it with probability one-half + + + align:start position:0% +answer with it with probability one-half +so probability one-half is not + + align:start position:0% +so probability one-half is not + + + align:start position:0% +so probability one-half is not +interesting you have to have probability + + align:start position:0% +interesting you have to have probability + + + align:start position:0% +interesting you have to have probability +strictly less than one-half for the + + align:start position:0% +strictly less than one-half for the + + + align:start position:0% +strictly less than one-half for the +machine to actually be doing something + + align:start position:0% +machine to actually be doing something + + + align:start position:0% +machine to actually be doing something +that's meaningful about that language + + align:start position:0% +that's meaningful about that language + + + align:start position:0% +that's meaningful about that language +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +if you have a + + align:start position:0% +if you have a + + + align:start position:0% +if you have a +probabilistic turing machine that has + + align:start position:0% +probabilistic turing machine that has + + + align:start position:0% +probabilistic turing machine that has +error + + align:start position:0% +error + + + align:start position:0% +error +let's say epsilon one which is at most + + align:start position:0% +let's say epsilon one which is at most + + + align:start position:0% +let's say epsilon one which is at most +one half which is less than one half + + align:start position:0% + + + + align:start position:0% + +then you can convert that to any + + align:start position:0% +then you can convert that to any + + + align:start position:0% +then you can convert that to any +error probability you want + + align:start position:0% +error probability you want + + + align:start position:0% +error probability you want +for some other + + align:start position:0% +for some other + + + align:start position:0% +for some other +polynomial time probabilistic turing + + align:start position:0% +polynomial time probabilistic turing + + + align:start position:0% +polynomial time probabilistic turing +machine so you can make that error which + + align:start position:0% +machine so you can make that error which + + + align:start position:0% +machine so you can make that error which +maybe starts out as one-third and you + + align:start position:0% +maybe starts out as one-third and you + + + align:start position:0% +maybe starts out as one-third and you +can drive that error down to one out of + + align:start position:0% +can drive that error down to one out of + + + align:start position:0% +can drive that error down to one out of +one over or google + + align:start position:0% +one over or google + + + align:start position:0% +one over or google +um + + align:start position:0% +um + + + align:start position:0% +um +and seriously you can really make the + + align:start position:0% +and seriously you can really make the + + + align:start position:0% +and seriously you can really make the +error extremely extremely small + + align:start position:0% + + + + align:start position:0% + +using a very simple procedure + + align:start position:0% +using a very simple procedure + + + align:start position:0% +using a very simple procedure +and and that's simply this + + align:start position:0% +and and that's simply this + + + align:start position:0% +and and that's simply this +so if you're starting out with a machine + + align:start position:0% +so if you're starting out with a machine + + + align:start position:0% +so if you're starting out with a machine +that has an error possibility of + + align:start position:0% +that has an error possibility of + + + align:start position:0% +that has an error possibility of +one-third say so that means + + align:start position:0% +one-third say so that means + + + align:start position:0% +one-third say so that means +two-thirds of the time it's going to get + + align:start position:0% +two-thirds of the time it's going to get + + + align:start position:0% +two-thirds of the time it's going to get +the right answer and at most one-third + + align:start position:0% +the right answer and at most one-third + + + align:start position:0% +the right answer and at most one-third +of the time at least two-thirds of the + + align:start position:0% +of the time at least two-thirds of the + + + align:start position:0% +of the time at least two-thirds of the +time the right answer most one-third of + + align:start position:0% +time the right answer most one-third of + + + align:start position:0% +time the right answer most one-third of +the time the the incorrect answer + + align:start position:0% +the time the the incorrect answer + + + align:start position:0% +the time the the incorrect answer +whether that's accepting or rejecting + + align:start position:0% +whether that's accepting or rejecting + + + align:start position:0% +whether that's accepting or rejecting +um and now you want to get that answer + + align:start position:0% +um and now you want to get that answer + + + align:start position:0% +um and now you want to get that answer +down to be something much that error + + align:start position:0% +down to be something much that error + + + align:start position:0% +down to be something much that error +down to something much smaller + + align:start position:0% +down to something much smaller + + + align:start position:0% +down to something much smaller +um + + align:start position:0% +um + + + align:start position:0% +um +the the idea is you just you're going to + + align:start position:0% +the the idea is you just you're going to + + + align:start position:0% +the the idea is you just you're going to +take that machine + + align:start position:0% +take that machine + + + align:start position:0% +take that machine +and you're + + align:start position:0% +and you're + + + align:start position:0% +and you're +going to run it multiple times + + align:start position:0% +going to run it multiple times + + + align:start position:0% +going to run it multiple times +it's kind of with independent runs if + + align:start position:0% +it's kind of with independent runs if + + + align:start position:0% +it's kind of with independent runs if +that me if you want to think about it + + align:start position:0% +that me if you want to think about it + + + align:start position:0% +that me if you want to think about it +you sort of more formally speaking but + + align:start position:0% +you sort of more formally speaking but + + + align:start position:0% +you sort of more formally speaking but +it's sort of intuitive you're just going + + align:start position:0% +it's sort of intuitive you're just going + + + align:start position:0% +it's sort of intuitive you're just going +to run the machine + + align:start position:0% +to run the machine + + + align:start position:0% +to run the machine +uh tossing your coins + + align:start position:0% +uh tossing your coins + + + align:start position:0% +uh tossing your coins +um + + align:start position:0% +um + + + align:start position:0% +um +uh instead of just running it once + + align:start position:0% +uh instead of just running it once + + + align:start position:0% +uh instead of just running it once +you're going to run the machine 100 + + align:start position:0% +you're going to run the machine 100 + + + align:start position:0% +you're going to run the machine 100 +times or or a million times but you can + + align:start position:0% +times or or a million times but you can + + + align:start position:0% +times or or a million times but you can +do that so it's a constant factor + + align:start position:0% +do that so it's a constant factor + + + align:start position:0% +do that so it's a constant factor +and even a thousand times is going to be + + align:start position:0% +and even a thousand times is going to be + + + align:start position:0% +and even a thousand times is going to be +enough to increase your confidence in + + align:start position:0% +enough to increase your confidence in + + + align:start position:0% +enough to increase your confidence in +the result tremendously because + + align:start position:0% +the result tremendously because + + + align:start position:0% +the result tremendously because +if you run the machine a thousand times + + align:start position:0% +if you run the machine a thousand times + + + align:start position:0% +if you run the machine a thousand times +and 600 of those times the mach the + + align:start position:0% +and 600 of those times the mach the + + + align:start position:0% +and 600 of those times the mach the +machine accepts and 400 of the time the + + align:start position:0% +machine accepts and 400 of the time the + + + align:start position:0% +machine accepts and 400 of the time the +machine rejects + + align:start position:0% +machine rejects + + + align:start position:0% +machine rejects +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it's very powerful evidence that this + + align:start position:0% +it's very powerful evidence that this + + + align:start position:0% +it's very powerful evidence that this +machine is biased toward accepting that + + align:start position:0% +machine is biased toward accepting that + + + align:start position:0% +machine is biased toward accepting that +it's accepting most of the time + + align:start position:0% +it's accepting most of the time + + + align:start position:0% +it's accepting most of the time +um so it's um was + + align:start position:0% +um so it's um was + + + align:start position:0% +um so it's um was +uh + + align:start position:0% +uh + + + align:start position:0% +uh +if it had an error + + align:start position:0% +if it had an error + + + align:start position:0% +if it had an error +probability of most one-third um + + align:start position:0% +probability of most one-third um + + + align:start position:0% +probability of most one-third um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the the probability that you're + + align:start position:0% +the the probability that you're + + + align:start position:0% +the the probability that you're +seeing it except + + align:start position:0% +seeing it except + + + align:start position:0% +seeing it except +600 times when really two-thirds of the + + align:start position:0% +600 times when really two-thirds of the + + + align:start position:0% +600 times when really two-thirds of the +time it's rejecting overall + + align:start position:0% +time it's rejecting overall + + + align:start position:0% +time it's rejecting overall +is extremely unlikely + + align:start position:0% +is extremely unlikely + + + align:start position:0% +is extremely unlikely +um and you can calculate that uh which + + align:start position:0% +um and you can calculate that uh which + + + align:start position:0% +um and you can calculate that uh which +we're not going to bother to do but it's + + align:start position:0% +we're not going to bother to do but it's + + + align:start position:0% +we're not going to bother to do but it's +a routine probability calculation uh to + + align:start position:0% +a routine probability calculation uh to + + + align:start position:0% +a routine probability calculation uh to +show that the the probability that if + + align:start position:0% +show that the the probability that if + + + align:start position:0% +show that the the probability that if +you run it a whole bunch of times and + + align:start position:0% +you run it a whole bunch of times and + + + align:start position:0% +you run it a whole bunch of times and +you see the majority coming up + + align:start position:0% +you see the majority coming up + + + align:start position:0% +you see the majority coming up +um which is not the + + align:start position:0% +um which is not the + + + align:start position:0% +um which is not the +not the right answer that's extremely + + align:start position:0% +not the right answer that's extremely + + + align:start position:0% +not the right answer that's extremely +the + + align:start position:0% +the + + + align:start position:0% +the +the probability of that is extremely + + align:start position:0% +the probability of that is extremely + + + align:start position:0% +the probability of that is extremely +small + + align:start position:0% +small + + + align:start position:0% +small +um + + align:start position:0% +um + + + align:start position:0% +um +so i'm not saying that very clearly but + + align:start position:0% +so i'm not saying that very clearly but + + + align:start position:0% +so i'm not saying that very clearly but +um + + align:start position:0% +um + + + align:start position:0% +um +the the the + + align:start position:0% +the the the + + + align:start position:0% +the the the +the method here is you're going to + + align:start position:0% +the method here is you're going to + + + align:start position:0% +the method here is you're going to +take your original machine + + align:start position:0% +take your original machine + + + align:start position:0% +take your original machine +which has error probability one-third + + align:start position:0% +which has error probability one-third + + + align:start position:0% +which has error probability one-third +or whatever it whatever it is some you + + align:start position:0% +or whatever it whatever it is some you + + + align:start position:0% +or whatever it whatever it is some you +know you know maybe + + align:start position:0% +know you know maybe + + + align:start position:0% +know you know maybe +has error probability 49 + + align:start position:0% +has error probability 49 + + + align:start position:0% +has error probability 49 +and you run it uh for a large number of + + align:start position:0% +and you run it uh for a large number of + + + align:start position:0% +and you run it uh for a large number of +times and then you take the majority + + align:start position:0% +times and then you take the majority + + + align:start position:0% +times and then you take the majority +vote + + align:start position:0% +vote + + + align:start position:0% +vote +and + + align:start position:0% +and + + + align:start position:0% +and +it you're kind of sampling the the + + align:start position:0% +it you're kind of sampling the the + + + align:start position:0% +it you're kind of sampling the the +outcomes of this machine and if you take + + align:start position:0% +outcomes of this machine and if you take + + + align:start position:0% +outcomes of this machine and if you take +enough samples it's overwhelmingly + + align:start position:0% +enough samples it's overwhelmingly + + + align:start position:0% +enough samples it's overwhelmingly +likely since you're just doing them + + align:start position:0% +likely since you're just doing them + + + align:start position:0% +likely since you're just doing them +uniformly you're taking those samples + + align:start position:0% +uniformly you're taking those samples + + + align:start position:0% +uniformly you're taking those samples +uniformly it's overwhelmingly likely + + align:start position:0% +uniformly it's overwhelmingly likely + + + align:start position:0% +uniformly it's overwhelmingly likely +that you're going to be seeing the + + align:start position:0% +that you're going to be seeing the + + + align:start position:0% +that you're going to be seeing the +predominant one come up more often um + + align:start position:0% +predominant one come up more often um + + + align:start position:0% +predominant one come up more often um +and exactly what that right value is + + align:start position:0% +and exactly what that right value is + + + align:start position:0% +and exactly what that right value is +we're not going to bother to calculate + + align:start position:0% +we're not going to bother to calculate + + + align:start position:0% +we're not going to bother to calculate +but that's something that + + align:start position:0% +but that's something that + + + align:start position:0% +but that's something that +you know if you i will i'll refer you to + + align:start position:0% +you know if you i will i'll refer you to + + + align:start position:0% +you know if you i will i'll refer you to +the textbook or you know that's the kind + + align:start position:0% +the textbook or you know that's the kind + + + align:start position:0% +the textbook or you know that's the kind +of thing that comes up in any elementary + + align:start position:0% +of thing that comes up in any elementary + + + align:start position:0% +of thing that comes up in any elementary +probability book and it's sort of very + + align:start position:0% +probability book and it's sort of very + + + align:start position:0% +probability book and it's sort of very +intuitive so i don't want to spend the + + align:start position:0% +intuitive so i don't want to spend the + + + align:start position:0% +intuitive so i don't want to spend the +time and do that calculation which is + + align:start position:0% +time and do that calculation which is + + + align:start position:0% +time and do that calculation which is +not all that interesting + + align:start position:0% +not all that interesting + + + align:start position:0% +not all that interesting +um + + align:start position:0% + + + + align:start position:0% + +uh okay so just one quick question here + + align:start position:0% +uh okay so just one quick question here + + + align:start position:0% +uh okay so just one quick question here +that i'm getting + + align:start position:0% +that i'm getting + + + align:start position:0% +that i'm getting +what happens if you bound if the error + + align:start position:0% +what happens if you bound if the error + + + align:start position:0% +what happens if you bound if the error +is greater than a half i don't think + + align:start position:0% +is greater than a half i don't think + + + align:start position:0% +is greater than a half i don't think +that because we're bounding the error so + + align:start position:0% +that because we're bounding the error so + + + align:start position:0% +that because we're bounding the error so +we're not saying the error actually is + + align:start position:0% +we're not saying the error actually is + + + align:start position:0% +we're not saying the error actually is +one you know like sixty percent on + + align:start position:0% +one you know like sixty percent on + + + align:start position:0% +one you know like sixty percent on +everything because then if you knew the + + align:start position:0% +everything because then if you knew the + + + align:start position:0% +everything because then if you knew the +error was sixty percent + + align:start position:0% +error was sixty percent + + + align:start position:0% +error was sixty percent +guaranteed you can always just flip the + + align:start position:0% +guaranteed you can always just flip the + + + align:start position:0% +guaranteed you can always just flip the +flip your answer around and get your um + + align:start position:0% +flip your answer around and get your um + + + align:start position:0% +flip your answer around and get your um +error to be 40 + + align:start position:0% +error to be 40 + + + align:start position:0% +error to be 40 +but you know i'm saying the error is + + align:start position:0% +but you know i'm saying the error is + + + align:start position:0% +but you know i'm saying the error is +that most + + align:start position:0% +that most + + + align:start position:0% +that most +whatever epsilon is and so um if it's + + align:start position:0% +whatever epsilon is and so um if it's + + + align:start position:0% +whatever epsilon is and so um if it's +you're saying the error is at most 60 + + align:start position:0% +you're saying the error is at most 60 + + + align:start position:0% +you're saying the error is at most 60 +percent it doesn't tell you anything + + align:start position:0% +percent it doesn't tell you anything + + + align:start position:0% +percent it doesn't tell you anything +um + + align:start position:0% +um + + + align:start position:0% +um +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +[Music] + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +another question is does the + + align:start position:0% +another question is does the + + + align:start position:0% +another question is does the +amplification lemma also justify that + + align:start position:0% +amplification lemma also justify that + + + align:start position:0% +amplification lemma also justify that +the choice of model with binary + + align:start position:0% +the choice of model with binary + + + align:start position:0% +the choice of model with binary +branching choices is equivalent to any + + align:start position:0% +branching choices is equivalent to any + + + align:start position:0% +branching choices is equivalent to any +other + + align:start position:0% +other + + + align:start position:0% +other +perhaps you could say that um + + align:start position:0% +perhaps you could say that um + + + align:start position:0% +perhaps you could say that um +because you can change those + + align:start position:0% +because you can change those + + + align:start position:0% +because you can change those +you know if you had through a three-way + + align:start position:0% +you know if you had through a three-way + + + align:start position:0% +you know if you had through a three-way +branching um you can simulate that with + + align:start position:0% +branching um you can simulate that with + + + align:start position:0% +branching um you can simulate that with +two-way branching to any accuracy that + + align:start position:0% +two-way branching to any accuracy that + + + align:start position:0% +two-way branching to any accuracy that +you want um + + align:start position:0% +you want um + + + align:start position:0% +you want um +you know + + align:start position:0% +you know + + + align:start position:0% +you know +not going to get it down to zero but + + align:start position:0% +not going to get it down to zero but + + + align:start position:0% +not going to get it down to zero but +you're going to get it very close + + align:start position:0% +you're going to get it very close + + + align:start position:0% +you're going to get it very close +um so it's + + align:start position:0% +um so it's + + + align:start position:0% +um so it's +maybe it's the amplification level maybe + + align:start position:0% +maybe it's the amplification level maybe + + + align:start position:0% +maybe it's the amplification level maybe +it's + + align:start position:0% +it's + + + align:start position:0% +it's +yeah sort of all related um + + align:start position:0% +yeah sort of all related um + + + align:start position:0% +yeah sort of all related um +okay let's move on um + + align:start position:0% +okay let's move on um + + + align:start position:0% +okay let's move on um +so + + align:start position:0% + + + + align:start position:0% + +the way that it's helpful to think about + + align:start position:0% +the way that it's helpful to think about + + + align:start position:0% +the way that it's helpful to think about +this class let's let's contrast it with + + align:start position:0% +this class let's let's contrast it with + + + align:start position:0% +this class let's let's contrast it with +the other model of non-deterministic + + align:start position:0% +the other model of non-deterministic + + + align:start position:0% +the other model of non-deterministic +computation that we have is + + align:start position:0% +computation that we have is + + + align:start position:0% +computation that we have is +non-determinism is np + + align:start position:0% +non-determinism is np + + + align:start position:0% +non-determinism is np +uh so non-deterministic then the model + + align:start position:0% +uh so non-deterministic then the model + + + align:start position:0% +uh so non-deterministic then the model +of non-deterministic polynomial time + + align:start position:0% +of non-deterministic polynomial time + + + align:start position:0% +of non-deterministic polynomial time +computation was np um the other class + + align:start position:0% +computation was np um the other class + + + align:start position:0% +computation was np um the other class +and um + + align:start position:0% +and um + + + align:start position:0% +and um +so the way + + align:start position:0% +so the way + + + align:start position:0% +so the way +it's i think one way to look at to think + + align:start position:0% +it's i think one way to look at to think + + + align:start position:0% +it's i think one way to look at to think +about non-determinism in the case of np + + align:start position:0% +about non-determinism in the case of np + + + align:start position:0% +about non-determinism in the case of np +is + + align:start position:0% +is + + + align:start position:0% +is +for strings in the language for your np + + align:start position:0% +for strings in the language for your np + + + align:start position:0% +for strings in the language for your np +turing machine + + align:start position:0% +turing machine + + + align:start position:0% +turing machine +there's at least one accepting branch + + align:start position:0% +there's at least one accepting branch + + + align:start position:0% +there's at least one accepting branch +so i'm indicating the accepting ones in + + align:start position:0% +so i'm indicating the accepting ones in + + + align:start position:0% +so i'm indicating the accepting ones in +green and the non-accepting one the + + align:start position:0% +green and the non-accepting one the + + + align:start position:0% +green and the non-accepting one the +rejecting branches in red + + align:start position:0% +rejecting branches in red + + + align:start position:0% +rejecting branches in red +so you could have + + align:start position:0% +so you could have + + + align:start position:0% +so you could have +almost all of the branches be rejecting + + align:start position:0% +almost all of the branches be rejecting + + + align:start position:0% +almost all of the branches be rejecting +branches um + + align:start position:0% +branches um + + + align:start position:0% +branches um +for strings in the language as long as + + align:start position:0% +for strings in the language as long as + + + align:start position:0% +for strings in the language as long as +there is at least one accepting branch + + align:start position:0% +there is at least one accepting branch + + + align:start position:0% +there is at least one accepting branch +that's just the way non-determinism + + align:start position:0% +that's just the way non-determinism + + + align:start position:0% +that's just the way non-determinism +works the accepting branch overrules all + + align:start position:0% +works the accepting branch overrules all + + + align:start position:0% +works the accepting branch overrules all +the all of the others it's only when + + align:start position:0% +the all of the others it's only when + + + align:start position:0% +the all of the others it's only when +you're not in the language that you that + + align:start position:0% +you're not in the language that you that + + + align:start position:0% +you're not in the language that you that +all of the branches turn out to have to + + align:start position:0% +all of the branches turn out to have to + + + align:start position:0% +all of the branches turn out to have to +be rejecting that's when the rejecting + + align:start position:0% +be rejecting that's when the rejecting + + + align:start position:0% +be rejecting that's when the rejecting +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +you know it's it has no accepting branch + + align:start position:0% +you know it's it has no accepting branch + + + align:start position:0% +you know it's it has no accepting branch +to overroll it + + align:start position:0% +to overroll it + + + align:start position:0% +to overroll it +um but the situation for bpp is a little + + align:start position:0% +um but the situation for bpp is a little + + + align:start position:0% +um but the situation for bpp is a little +different it is is different um there + + align:start position:0% +different it is is different um there + + + align:start position:0% +different it is is different um there +it's kind of majority majority rules + + align:start position:0% +it's kind of majority majority rules + + + align:start position:0% +it's kind of majority majority rules +so um + + align:start position:0% +so um + + + align:start position:0% +so um +in the case for strings in the language + + align:start position:0% +in the case for strings in the language + + + align:start position:0% +in the case for strings in the language +you you need to have + + align:start position:0% +you you need to have + + + align:start position:0% +you you need to have +a large or you know the the overwhelming + + align:start position:0% +a large or you know the the overwhelming + + + align:start position:0% +a large or you know the the overwhelming +majority of the + + align:start position:0% +majority of the + + + align:start position:0% +majority of the +branches have to be accepting and for + + align:start position:0% +branches have to be accepting and for + + + align:start position:0% +branches have to be accepting and for +strings not in the language the + + align:start position:0% +strings not in the language the + + + align:start position:0% +strings not in the language the +overwhelming majority have to be + + align:start position:0% +overwhelming majority have to be + + + align:start position:0% +overwhelming majority have to be +rejecting + + align:start position:0% +rejecting + + + align:start position:0% +rejecting +what you're not going to allow in the + + align:start position:0% +what you're not going to allow in the + + + align:start position:0% +what you're not going to allow in the +case of + + align:start position:0% +case of + + + align:start position:0% +case of +bpp is kind of you know + + align:start position:0% +bpp is kind of you know + + + align:start position:0% +bpp is kind of you know +an in-between + + align:start position:0% +an in-between + + + align:start position:0% +an in-between +uh + + align:start position:0% +uh + + + align:start position:0% +uh +state where it's sort of 50-50 + + align:start position:0% +state where it's sort of 50-50 + + + align:start position:0% +state where it's sort of 50-50 +um or very very close to 50-50 um those + + align:start position:0% +um or very very close to 50-50 um those + + + align:start position:0% +um or very very close to 50-50 um those +kinds of machines are not + + align:start position:0% +kinds of machines are not + + + align:start position:0% +kinds of machines are not +don't qualify as + + align:start position:0% + + + + align:start position:0% + +uh deciding a language in bpp they + + align:start position:0% +uh deciding a language in bpp they + + + align:start position:0% +uh deciding a language in bpp they +always have to kind of lean one way or + + align:start position:0% +always have to kind of lean one way or + + + align:start position:0% +always have to kind of lean one way or +lean the other way for every input + + align:start position:0% +lean the other way for every input + + + align:start position:0% +lean the other way for every input +otherwise you won't be able to do the + + align:start position:0% +otherwise you won't be able to do the + + + align:start position:0% +otherwise you won't be able to do the +amplification so need to have some bias + + align:start position:0% +amplification so need to have some bias + + + align:start position:0% +amplification so need to have some bias +um away from in half in + + align:start position:0% +um away from in half in + + + align:start position:0% +um away from in half in +in accepting or rejecting + + align:start position:0% +in accepting or rejecting + + + align:start position:0% +in accepting or rejecting +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +let me so i was going to ask a check-in + + align:start position:0% +let me so i was going to ask a check-in + + + align:start position:0% +let me so i was going to ask a check-in +i think at this point yes let's + + align:start position:0% +i think at this point yes let's + + + align:start position:0% +i think at this point yes let's +so just thinking about bpp i hope i was + + align:start position:0% +so just thinking about bpp i hope i was + + + align:start position:0% +so just thinking about bpp i hope i was +clear so if there's questions about that + + align:start position:0% +clear so if there's questions about that + + + align:start position:0% +clear so if there's questions about that +i think i've + + align:start position:0% +i think i've + + + align:start position:0% +i think i've +somehow didn't + + align:start position:0% + + + + align:start position:0% + +i'm not sure i described it totally well + + align:start position:0% +i'm not sure i described it totally well + + + align:start position:0% +i'm not sure i described it totally well +here um so i'm going to ask a few + + align:start position:0% +here um so i'm going to ask a few + + + align:start position:0% +here um so i'm going to ask a few +questions about ppp but if you have any + + align:start position:0% +questions about ppp but if you have any + + + align:start position:0% +questions about ppp but if you have any +questions for me first + + align:start position:0% +questions for me first + + + align:start position:0% +questions for me first +go ahead + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +okay why don't we just run the check-in + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +let me launch this and then i can answer + + align:start position:0% +let me launch this and then i can answer + + + align:start position:0% +let me launch this and then i can answer +questions as you're asking + + align:start position:0% +questions as you're asking + + + align:start position:0% +questions as you're asking +did i start that yeah + + align:start position:0% +did i start that yeah + + + align:start position:0% +did i start that yeah +okay so you have to um + + align:start position:0% +okay so you have to um + + + align:start position:0% +okay so you have to um +check all of these that you think are + + align:start position:0% +check all of these that you think are + + + align:start position:0% +check all of these that you think are +true + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +can you think of non-deterministic + + align:start position:0% +can you think of non-deterministic + + + align:start position:0% +can you think of non-deterministic +turing machines as try all branches at + + align:start position:0% +turing machines as try all branches at + + + align:start position:0% +turing machines as try all branches at +once + + align:start position:0% +once + + + align:start position:0% +once +and get the right answer + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +and bp is guess only one or uh i guess + + align:start position:0% +and bp is guess only one or uh i guess + + + align:start position:0% +and bp is guess only one or uh i guess +only one branch i don't know um + + align:start position:0% +only one branch i don't know um + + + align:start position:0% +only one branch i don't know um +you know i would say a little + + align:start position:0% +you know i would say a little + + + align:start position:0% +you know i would say a little +differently i would say i i would think + + align:start position:0% +differently i would say i i would think + + + align:start position:0% +differently i would say i i would think +of non-determinism as you can still just + + align:start position:0% +of non-determinism as you can still just + + + align:start position:0% +of non-determinism as you can still just +try one branch but you always guess the + + align:start position:0% +try one branch but you always guess the + + + align:start position:0% +try one branch but you always guess the +right one + + align:start position:0% +right one + + + align:start position:0% +right one +um + + align:start position:0% +um + + + align:start position:0% +um +so there's some sort of a you know + + align:start position:0% +so there's some sort of a you know + + + align:start position:0% +so there's some sort of a you know +magical power that allows you always to + + align:start position:0% +magical power that allows you always to + + + align:start position:0% +magical power that allows you always to +guess the right answer if there's a + + align:start position:0% +guess the right answer if there's a + + + align:start position:0% +guess the right answer if there's a +right guess uh if you're in the language + + align:start position:0% +right guess uh if you're in the language + + + align:start position:0% +right guess uh if you're in the language +uh in the case of bpp + + align:start position:0% +uh in the case of bpp + + + align:start position:0% +uh in the case of bpp +you're going to be um picking a random + + align:start position:0% +you're going to be um picking a random + + + align:start position:0% +you're going to be um picking a random +branch no matter what + + align:start position:0% +branch no matter what + + + align:start position:0% +branch no matter what +and you know that the random branch is + + align:start position:0% +and you know that the random branch is + + + align:start position:0% +and you know that the random branch is +likely to give the right answer but not + + align:start position:0% +likely to give the right answer but not + + + align:start position:0% +likely to give the right answer but not +guaranteed + + align:start position:0% +guaranteed + + + align:start position:0% +guaranteed +and the implication the amplification + + align:start position:0% +and the implication the amplification + + + align:start position:0% +and the implication the amplification +limit tells you you can arrange things + + align:start position:0% +limit tells you you can arrange things + + + align:start position:0% +limit tells you you can arrange things +so that it's extremely likely + + align:start position:0% +so that it's extremely likely + + + align:start position:0% +so that it's extremely likely +that the random branch is going to give + + align:start position:0% +that the random branch is going to give + + + align:start position:0% +that the random branch is going to give +you the right answer + + align:start position:0% +you the right answer + + + align:start position:0% +you the right answer +okay let's see how we doing on our uh + + align:start position:0% +okay let's see how we doing on our uh + + + align:start position:0% +okay let's see how we doing on our uh +check-in here + + align:start position:0% +check-in here + + + align:start position:0% +check-in here +um + + align:start position:0% +um + + + align:start position:0% +um +got a lot of vote we've got a lot of + + align:start position:0% +got a lot of vote we've got a lot of + + + align:start position:0% +got a lot of vote we've got a lot of +support for all candidates + + align:start position:0% +support for all candidates + + + align:start position:0% +support for all candidates +um + + align:start position:0% + + + + align:start position:0% + +and um + + align:start position:0% + + + + align:start position:0% + +i'll give you give you another uh + + align:start position:0% + + + + align:start position:0% + +a little bit of time here because + + align:start position:0% +a little bit of time here because + + + align:start position:0% +a little bit of time here because +there's a bunch of questions almost like + + align:start position:0% +there's a bunch of questions almost like + + + align:start position:0% +there's a bunch of questions almost like +four check-ins at once + + align:start position:0% +four check-ins at once + + + align:start position:0% +four check-ins at once +um + + align:start position:0% +um + + + align:start position:0% +um +but we have two more check real + + align:start position:0% +but we have two more check real + + + align:start position:0% +but we have two more check real +check-ins coming + + align:start position:0% +check-ins coming + + + align:start position:0% +check-ins coming +later um + + align:start position:0% +later um + + + align:start position:0% +later um +okay so why don't we uh come and + + align:start position:0% +okay so why don't we uh come and + + + align:start position:0% +okay so why don't we uh come and +let's uh give another 10 seconds and + + align:start position:0% +let's uh give another 10 seconds and + + + align:start position:0% +let's uh give another 10 seconds and +then i'm going to stop + + align:start position:0% + + + + align:start position:0% + +closing down + + align:start position:0% +closing down + + + align:start position:0% +closing down +one two three + + align:start position:0% +one two three + + + align:start position:0% +one two three +close + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so uh we've got a lot of support here uh + + align:start position:0% +so uh we've got a lot of support here uh + + + align:start position:0% +so uh we've got a lot of support here uh +and in fact + + align:start position:0% +and in fact + + + align:start position:0% +and in fact +that's good because all of them are true + + align:start position:0% +that's good because all of them are true + + + align:start position:0% +that's good because all of them are true +um + + align:start position:0% +um + + + align:start position:0% +um +some of them are easier to see than + + align:start position:0% +some of them are easier to see than + + + align:start position:0% +some of them are easier to see than +others + + align:start position:0% +others + + + align:start position:0% +others +so first of all c is very easy to see um + + align:start position:0% +so first of all c is very easy to see um + + + align:start position:0% +so first of all c is very easy to see um +because that that's a going to be a + + align:start position:0% +because that that's a going to be a + + + align:start position:0% +because that that's a going to be a +machine that has the correct answer all + + align:start position:0% +machine that has the correct answer all + + + align:start position:0% +machine that has the correct answer all +of it all of the time so that's error + + align:start position:0% +of it all of the time so that's error + + + align:start position:0% +of it all of the time so that's error +probability zero + + align:start position:0% +probability zero + + + align:start position:0% +probability zero +um on both accepting and rejecting + + align:start position:0% +um on both accepting and rejecting + + + align:start position:0% +um on both accepting and rejecting +um + + align:start position:0% +um + + + align:start position:0% +um +this is a little harder d is a little + + align:start position:0% +this is a little harder d is a little + + + align:start position:0% +this is a little harder d is a little +bit harder to see that's in p space but + + align:start position:0% +bit harder to see that's in p space but + + + align:start position:0% +bit harder to see that's in p space but +you know you could + + align:start position:0% +you know you could + + + align:start position:0% +you know you could +calculate for every branch + + align:start position:0% +calculate for every branch + + + align:start position:0% +calculate for every branch +um what its probability is and you can + + align:start position:0% +um what its probability is and you can + + + align:start position:0% +um what its probability is and you can +just go through all the branches and add + + align:start position:0% +just go through all the branches and add + + + align:start position:0% +just go through all the branches and add +up all those probabilities in a p-space + + align:start position:0% +up all those probabilities in a p-space + + + align:start position:0% +up all those probabilities in a p-space +machine + + align:start position:0% +machine + + + align:start position:0% +machine +so um you have to think about a little + + align:start position:0% +so um you have to think about a little + + + align:start position:0% +so um you have to think about a little +bit but d is not too hard to see either + + align:start position:0% +bit but d is not too hard to see either + + + align:start position:0% +bit but d is not too hard to see either +closure under complement + + align:start position:0% +closure under complement + + + align:start position:0% +closure under complement +if you just take your + + align:start position:0% +if you just take your + + + align:start position:0% +if you just take your +your bpp machine and you flip the answer + + align:start position:0% +your bpp machine and you flip the answer + + + align:start position:0% +your bpp machine and you flip the answer +on every branch + + align:start position:0% +on every branch + + + align:start position:0% +on every branch +um that's typically doesn't work in + + align:start position:0% +um that's typically doesn't work in + + + align:start position:0% +um that's typically doesn't work in +non-determined ordinary non-determinism + + align:start position:0% +non-determined ordinary non-determinism + + + align:start position:0% +non-determined ordinary non-determinism +but it does work here + + align:start position:0% +but it does work here + + + align:start position:0% +but it does work here +because it's going to change a bias + + align:start position:0% +because it's going to change a bias + + + align:start position:0% +because it's going to change a bias +toward accepting into a bias toward + + align:start position:0% +toward accepting into a bias toward + + + align:start position:0% +toward accepting into a bias toward +rejecting and vice versa so bpp is + + align:start position:0% +rejecting and vice versa so bpp is + + + align:start position:0% +rejecting and vice versa so bpp is +closed under compliment + + align:start position:0% +closed under compliment + + + align:start position:0% +closed under compliment +uh and closure under union it kind of + + align:start position:0% +uh and closure under union it kind of + + + align:start position:0% +uh and closure under union it kind of +follows from the amplification level as + + align:start position:0% +follows from the amplification level as + + + align:start position:0% +follows from the amplification level as +long as you can make the probability + + align:start position:0% +long as you can make the probability + + + align:start position:0% +long as you can make the probability +extremely small + + align:start position:0% +extremely small + + + align:start position:0% +extremely small +then you can just run the two different + + align:start position:0% +then you can just run the two different + + + align:start position:0% +then you can just run the two different +machines + + align:start position:0% +machines + + + align:start position:0% +machines +and + + align:start position:0% +and + + + align:start position:0% +and +even though the they each might make a + + align:start position:0% +even though the they each might make a + + + align:start position:0% +even though the they each might make a +mistake cumulatively the total + + align:start position:0% +mistake cumulatively the total + + + align:start position:0% +mistake cumulatively the total +the probability that each one of them + + align:start position:0% +the probability that each one of them + + + align:start position:0% +the probability that each one of them +that either of them will make a mistake + + align:start position:0% +that either of them will make a mistake + + + align:start position:0% +that either of them will make a mistake +is still small and so you can just run + + align:start position:0% +is still small and so you can just run + + + align:start position:0% +is still small and so you can just run +to the two machines and take the or of + + align:start position:0% +to the two machines and take the or of + + + align:start position:0% +to the two machines and take the or of +the responses that they get and it's + + align:start position:0% +the responses that they get and it's + + + align:start position:0% +the responses that they get and it's +still very likely to give the right + + align:start position:0% +still very likely to give the right + + + align:start position:0% +still very likely to give the right +answer for the union + + align:start position:0% +answer for the union + + + align:start position:0% +answer for the union +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +let's continue + + align:start position:0% +let's continue + + + align:start position:0% +let's continue +uh so what i'm going to do now + + align:start position:0% +uh so what i'm going to do now + + + align:start position:0% +uh so what i'm going to do now +for the rest of the lecture uh is and + + align:start position:0% +for the rest of the lecture uh is and + + + align:start position:0% +for the rest of the lecture uh is and +it's actually going to spill over into + + align:start position:0% +it's actually going to spill over into + + + align:start position:0% +it's actually going to spill over into +the lecture after thanksgiving because + + align:start position:0% +the lecture after thanksgiving because + + + align:start position:0% +the lecture after thanksgiving because +this is going to introduce an important + + align:start position:0% +this is going to introduce an important + + + align:start position:0% +this is going to introduce an important +method for us + + align:start position:0% +method for us + + + align:start position:0% +method for us +is to look at an example of a problem + + align:start position:0% +is to look at an example of a problem + + + align:start position:0% +is to look at an example of a problem +that's in bpp + + align:start position:0% +that's in bpp + + + align:start position:0% +that's in bpp +um i love to teach things by using + + align:start position:0% +um i love to teach things by using + + + align:start position:0% +um i love to teach things by using +examples um and so this is a very good + + align:start position:0% +examples um and so this is a very good + + + align:start position:0% +examples um and so this is a very good +example because it has a lot of meat to + + align:start position:0% +example because it has a lot of meat to + + + align:start position:0% +example because it has a lot of meat to +it + + align:start position:0% +it + + + align:start position:0% +it +and it's a very interesting example in + + align:start position:0% +and it's a very interesting example in + + + align:start position:0% +and it's a very interesting example in +general proving things in bpp which are + + align:start position:0% +general proving things in bpp which are + + + align:start position:0% +general proving things in bpp which are +not trivially there because they're + + align:start position:0% +not trivially there because they're + + + align:start position:0% +not trivially there because they're +already in p they tend to be uh somewhat + + align:start position:0% +already in p they tend to be uh somewhat + + + align:start position:0% +already in p they tend to be uh somewhat +more involved than um + + align:start position:0% +more involved than um + + + align:start position:0% +more involved than um +uh some of the other algorithms we've + + align:start position:0% +uh some of the other algorithms we've + + + align:start position:0% +uh some of the other algorithms we've +seen so there are no simple examples of + + align:start position:0% +seen so there are no simple examples of + + + align:start position:0% +seen so there are no simple examples of +problems in bpp + + align:start position:0% +problems in bpp + + + align:start position:0% +problems in bpp +which are not already in p + + align:start position:0% +which are not already in p + + + align:start position:0% +which are not already in p +um + + align:start position:0% +um + + + align:start position:0% +um +so this is uh + + align:start position:0% +so this is uh + + + align:start position:0% +so this is uh +one example that we're going to go + + align:start position:0% +one example that we're going to go + + + align:start position:0% +one example that we're going to go +through of a problem in bpp that's not + + align:start position:0% +through of a problem in bpp that's not + + + align:start position:0% +through of a problem in bpp that's not +known to bnp + + align:start position:0% +known to bnp + + + align:start position:0% +known to bnp +of course things could collapse down um + + align:start position:0% +of course things could collapse down um + + + align:start position:0% +of course things could collapse down um +but uh uh + + align:start position:0% +but uh uh + + + align:start position:0% +but uh uh +as star as far as we know + + align:start position:0% +as star as far as we know + + + align:start position:0% +as star as far as we know +this is + + align:start position:0% +this is + + + align:start position:0% +this is +um not this language is not in p so + + align:start position:0% +um not this language is not in p so + + + align:start position:0% +um not this language is not in p so +let's let's see what the language is + + align:start position:0% +let's let's see what the language is + + + align:start position:0% +let's let's see what the language is +has to do with these things called + + align:start position:0% +has to do with these things called + + + align:start position:0% +has to do with these things called +branching programs the branching program + + align:start position:0% +branching programs the branching program + + + align:start position:0% +branching programs the branching program +is a structure that looks like this + + align:start position:0% +is a structure that looks like this + + + align:start position:0% +is a structure that looks like this +so let's understand what the pieces are + + align:start position:0% +so let's understand what the pieces are + + + align:start position:0% +so let's understand what the pieces are +first of all it's a graph directed graph + + align:start position:0% + + + + align:start position:0% + +and uh we're not we're not going to + + align:start position:0% +and uh we're not we're not going to + + + align:start position:0% +and uh we're not we're not going to +allow and there is are no cycles allowed + + align:start position:0% +allow and there is are no cycles allowed + + + align:start position:0% +allow and there is are no cycles allowed +in this graph it's a directed acyclic + + align:start position:0% +in this graph it's a directed acyclic + + + align:start position:0% +in this graph it's a directed acyclic +graph + + align:start position:0% +graph + + + align:start position:0% +graph +um + + align:start position:0% +um + + + align:start position:0% +um +so you can no loops allowed + + align:start position:0% +so you can no loops allowed + + + align:start position:0% +so you can no loops allowed +and + + align:start position:0% +and + + + align:start position:0% +and +the nodes are in two categories + + align:start position:0% +the nodes are in two categories + + + align:start position:0% +the nodes are in two categories +there are query nodes which are labeled + + align:start position:0% +there are query nodes which are labeled + + + align:start position:0% +there are query nodes which are labeled +with a variable letter + + align:start position:0% +with a variable letter + + + align:start position:0% +with a variable letter +and output nodes which are labeled + + align:start position:0% +and output nodes which are labeled + + + align:start position:0% +and output nodes which are labeled +either zero or one + + align:start position:0% +either zero or one + + + align:start position:0% +either zero or one +and lastly there is a one of the query + + align:start position:0% +and lastly there is a one of the query + + + align:start position:0% +and lastly there is a one of the query +nodes is going to be or one of the nodes + + align:start position:0% +nodes is going to be or one of the nodes + + + align:start position:0% +nodes is going to be or one of the nodes +is going to be designated as a start + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so what you do + + align:start position:0% +and so what you do + + + align:start position:0% +and so what you do +is + + align:start position:0% +is + + + align:start position:0% +is +the way um + + align:start position:0% +the way um + + + align:start position:0% +the way um +this is a model of computation um and + + align:start position:0% +this is a model of computation um and + + + align:start position:0% +this is a model of computation um and +the way we actually use + + align:start position:0% +the way we actually use + + + align:start position:0% +the way we actually use +a branching program + + align:start position:0% +a branching program + + + align:start position:0% +a branching program +is we + + align:start position:0% + + + + align:start position:0% + +have some assignment to the variables + + align:start position:0% +have some assignment to the variables + + + align:start position:0% +have some assignment to the variables +that's going to be the input + + align:start position:0% +that's going to be the input + + + align:start position:0% +that's going to be the input +so you take all of the the variables + + align:start position:0% +so you take all of the the variables + + + align:start position:0% +so you take all of the the variables +there are three variables in this case + + align:start position:0% +there are three variables in this case + + + align:start position:0% +there are three variables in this case +um x1 x2 and x3 you assign you give them + + align:start position:0% +um x1 x2 and x3 you assign you give them + + + align:start position:0% +um x1 x2 and x3 you assign you give them +some truth assignment um so x let's + + align:start position:0% +some truth assignment um so x let's + + + align:start position:0% +some truth assignment um so x let's +let's say zeros and one so x1 is zero x1 + + align:start position:0% +let's say zeros and one so x1 is zero x1 + + + align:start position:0% +let's say zeros and one so x1 is zero x1 +is one or whatever + + align:start position:0% +is one or whatever + + + align:start position:0% +is one or whatever +and + + align:start position:0% +and + + + align:start position:0% +and +once you have the truth assignment you + + align:start position:0% +once you have the truth assignment you + + + align:start position:0% +once you have the truth assignment you +start + + align:start position:0% +start + + + align:start position:0% +start +at the start variable + + align:start position:0% +at the start variable + + + align:start position:0% +at the start variable +and you + + align:start position:0% +and you + + + align:start position:0% +and you +and you look at its label + + align:start position:0% + + + + align:start position:0% + +and you see what value the input has + + align:start position:0% +and you see what value the input has + + + align:start position:0% +and you see what value the input has +assigned to that variable + + align:start position:0% +assigned to that variable + + + align:start position:0% +assigned to that variable +so if x1 assigned + + align:start position:0% +so if x1 assigned + + + align:start position:0% +so if x1 assigned +a one you're going to follow down the + + align:start position:0% +a one you're going to follow down the + + + align:start position:0% +a one you're going to follow down the +one branch but assigned to zero you + + align:start position:0% +one branch but assigned to zero you + + + align:start position:0% +one branch but assigned to zero you +follow you go down the zero branch and + + align:start position:0% +follow you go down the zero branch and + + + align:start position:0% +follow you go down the zero branch and +then when you get down to the + + align:start position:0% +then when you get down to the + + + align:start position:0% +then when you get down to the +next node + + align:start position:0% +next node + + + align:start position:0% +next node +that's another + + align:start position:0% +that's another + + + align:start position:0% +that's another +variable that you're going to have to + + align:start position:0% +variable that you're going to have to + + + align:start position:0% +variable that you're going to have to +query depending upon what the input + + align:start position:0% +query depending upon what the input + + + align:start position:0% +query depending upon what the input +assignment is + + align:start position:0% +assignment is + + + align:start position:0% +assignment is +and you're just going to + + align:start position:0% +and you're just going to + + + align:start position:0% +and you're just going to +continue that process + + align:start position:0% +continue that process + + + align:start position:0% +continue that process +because there are no cycles + + align:start position:0% +because there are no cycles + + + align:start position:0% +because there are no cycles +you're going to end up at one of the + + align:start position:0% +you're going to end up at one of the + + + align:start position:0% +you're going to end up at one of the +output nodes because all of the variable + + align:start position:0% +output nodes because all of the variable + + + align:start position:0% +output nodes because all of the variable +nodes all the all the query nodes + + align:start position:0% +nodes all the all the query nodes + + + align:start position:0% +nodes all the all the query nodes +have + + align:start position:0% +have + + + align:start position:0% +have +two outgoing edges one labeled zero one + + align:start position:0% +two outgoing edges one labeled zero one + + + align:start position:0% +two outgoing edges one labeled zero one +labeled one + + align:start position:0% +labeled one + + + align:start position:0% +labeled one +so you're gonna eventually end up at an + + align:start position:0% +so you're gonna eventually end up at an + + + align:start position:0% +so you're gonna eventually end up at an +output node and that's going to be the + + align:start position:0% +output node and that's going to be the + + + align:start position:0% +output node and that's going to be the +output of the branching program + + align:start position:0% +output of the branching program + + + align:start position:0% +output of the branching program +so we'll do let's do a quick example + + align:start position:0% +so we'll do let's do a quick example + + + align:start position:0% +so we'll do let's do a quick example +so if x1 is 1 x2 is 0 and x3 is 1. + + align:start position:0% +so if x1 is 1 x2 is 0 and x3 is 1. + + + align:start position:0% +so if x1 is 1 x2 is 0 and x3 is 1. +so we again we start at the start + + align:start position:0% +so we again we start at the start + + + align:start position:0% +so we again we start at the start +variable the start node that has the + + align:start position:0% +variable the start node that has the + + + align:start position:0% +variable the start node that has the +indicated with the + + align:start position:0% +indicated with the + + + align:start position:0% +indicated with the +arrow coming in from nowhere so you're + + align:start position:0% +arrow coming in from nowhere so you're + + + align:start position:0% +arrow coming in from nowhere so you're +going to start at x1 + + align:start position:0% +going to start at x1 + + + align:start position:0% +going to start at x1 +uh + + align:start position:0% + + + + align:start position:0% + +the node labeled x1 so you have to look + + align:start position:0% +the node labeled x1 so you have to look + + + align:start position:0% +the node labeled x1 so you have to look +and see what is x1 in the input it's a + + align:start position:0% +and see what is x1 in the input it's a + + + align:start position:0% +and see what is x1 in the input it's a +1. so you're going to follow down the + + align:start position:0% +1. so you're going to follow down the + + + align:start position:0% +1. so you're going to follow down the +one branch + + align:start position:0% +one branch + + + align:start position:0% +one branch +now you see the next node oh that's an + + align:start position:0% +now you see the next node oh that's an + + + align:start position:0% +now you see the next node oh that's an +x3 + + align:start position:0% +x3 + + + align:start position:0% +x3 +see what's x3 in the input x3 is a 1. + + align:start position:0% +see what's x3 in the input x3 is a 1. + + + align:start position:0% +see what's x3 in the input x3 is a 1. +so you go down to one branch again + + align:start position:0% +so you go down to one branch again + + + align:start position:0% +so you go down to one branch again +now you have an x2 node take a look at + + align:start position:0% +now you have an x2 node take a look at + + + align:start position:0% +now you have an x2 node take a look at +the input x2 is a zero you follow the + + align:start position:0% +the input x2 is a zero you follow the + + + align:start position:0% +the input x2 is a zero you follow the +zero branch now you're at an output + + align:start position:0% +zero branch now you're at an output + + + align:start position:0% +zero branch now you're at an output +branch output node so that's a zero and + + align:start position:0% +branch output node so that's a zero and + + + align:start position:0% +branch output node so that's a zero and +that's the output of the of the of this + + align:start position:0% +that's the output of the of the of this + + + align:start position:0% +that's the output of the of the of this +computation so + + align:start position:0% +computation so + + + align:start position:0% +computation so +um writing it this way and thinking + + align:start position:0% +um writing it this way and thinking + + + align:start position:0% +um writing it this way and thinking +about it as a boolean function which + + align:start position:0% +about it as a boolean function which + + + align:start position:0% +about it as a boolean function which +maps you know strings of zeros and ones + + align:start position:0% +maps you know strings of zeros and ones + + + align:start position:0% +maps you know strings of zeros and ones +we have f of one zero one representing + + align:start position:0% +we have f of one zero one representing + + + align:start position:0% +we have f of one zero one representing +those that assign that assignment that + + align:start position:0% +those that assign that assignment that + + + align:start position:0% +those that assign that assignment that +equals zero that was the output and + + align:start position:0% +equals zero that was the output and + + + align:start position:0% +equals zero that was the output and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +that's the output of this computation + + align:start position:0% +that's the output of this computation + + + align:start position:0% +that's the output of this computation +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +so important to underst we're going to + + align:start position:0% +so important to underst we're going to + + + align:start position:0% +so important to underst we're going to +spend a lot of time + + align:start position:0% +spend a lot of time + + + align:start position:0% +spend a lot of time +you know talking about branching + + align:start position:0% +you know talking about branching + + + align:start position:0% +you know talking about branching +programs so it's critical to understand + + align:start position:0% +programs so it's critical to understand + + + align:start position:0% +programs so it's critical to understand +this model i think it's fairly simple + + align:start position:0% +this model i think it's fairly simple + + + align:start position:0% +this model i think it's fairly simple +but if you didn't get it please ask + + align:start position:0% + + + + align:start position:0% + +we can easily correct up any + + align:start position:0% +we can easily correct up any + + + align:start position:0% +we can easily correct up any +misunderstanding at this point + + align:start position:0% + + + + align:start position:0% + +it's not exactly the same as a dfa + + align:start position:0% +it's not exactly the same as a dfa + + + align:start position:0% +it's not exactly the same as a dfa +dfas for one thing can take inputs of + + align:start position:0% +dfas for one thing can take inputs of + + + align:start position:0% +dfas for one thing can take inputs of +any length + + align:start position:0% +any length + + + align:start position:0% +any length +um + + align:start position:0% +um + + + align:start position:0% +um +this + + align:start position:0% +this + + + align:start position:0% +this +this has inputs of some particular + + align:start position:0% +this has inputs of some particular + + + align:start position:0% +this has inputs of some particular +length + + align:start position:0% +length + + + align:start position:0% +length +where the branching program has some + + align:start position:0% +where the branching program has some + + + align:start position:0% +where the branching program has some +fixed number of variables + + align:start position:0% +fixed number of variables + + + align:start position:0% +fixed number of variables +this one has three so this only takes + + align:start position:0% +this one has three so this only takes + + + align:start position:0% +this one has three so this only takes +inputs of length three um so there's + + align:start position:0% +inputs of length three um so there's + + + align:start position:0% +inputs of length three um so there's +maybe some connection to thinking these + + align:start position:0% +maybe some connection to thinking these + + + align:start position:0% +maybe some connection to thinking these +estates and so on but it's a different + + align:start position:0% +estates and so on but it's a different + + + align:start position:0% +estates and so on but it's a different +model + + align:start position:0% +model + + + align:start position:0% +model +so now we'll say that two branching + + align:start position:0% +so now we'll say that two branching + + + align:start position:0% +so now we'll say that two branching +programs + + align:start position:0% +programs + + + align:start position:0% +programs +um + + align:start position:0% +um + + + align:start position:0% +um +okay let me just ask one more question + + align:start position:0% +okay let me just ask one more question + + + align:start position:0% +okay let me just ask one more question +not all nodes need to be used right + + align:start position:0% +not all nodes need to be used right + + + align:start position:0% +not all nodes need to be used right +um + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +there's no requirement that all nodes + + align:start position:0% +there's no requirement that all nodes + + + align:start position:0% +there's no requirement that all nodes +need to be used and that even could be + + align:start position:0% +need to be used and that even could be + + + align:start position:0% +need to be used and that even could be +inaccessible nodes i'm not preventing + + align:start position:0% +inaccessible nodes i'm not preventing + + + align:start position:0% +inaccessible nodes i'm not preventing +that uh that could be okay um so on the + + align:start position:0% +that uh that could be okay um so on the + + + align:start position:0% +that uh that could be okay um so on the +particular branch certainly you're not + + align:start position:0% +particular branch certainly you're not + + + align:start position:0% +particular branch certainly you're not +gonna you know when you're executing + + align:start position:0% +gonna you know when you're executing + + + align:start position:0% +gonna you know when you're executing +this + + align:start position:0% +this + + + align:start position:0% +this +branching program on an input obvious + + align:start position:0% +branching program on an input obvious + + + align:start position:0% +branching program on an input obvious +certainly you're to have a path that's + + align:start position:0% +certainly you're to have a path that's + + + align:start position:0% +certainly you're to have a path that's +going to only use some part of the + + align:start position:0% +going to only use some part of the + + + align:start position:0% +going to only use some part of the +tree + + align:start position:0% +tree + + + align:start position:0% +tree +part of the graph + + align:start position:0% +part of the graph + + + align:start position:0% +part of the graph +but + + align:start position:0% +but + + + align:start position:0% +but +there might be some + + align:start position:0% +there might be some + + + align:start position:0% +there might be some +paths that can + + align:start position:0% +paths that can + + + align:start position:0% +paths that can +can never occur + + align:start position:0% +can never occur + + + align:start position:0% +can never occur +you know so if you went down x equal to + + align:start position:0% +you know so if you went down x equal to + + + align:start position:0% +you know so if you went down x equal to +one here and then x three was zero + + align:start position:0% +one here and then x three was zero + + + align:start position:0% +one here and then x three was zero +now you're re-reading x one so you'd + + align:start position:0% +now you're re-reading x one so you'd + + + align:start position:0% +now you're re-reading x one so you'd +never you could you wouldn't go down + + align:start position:0% +never you could you wouldn't go down + + + align:start position:0% +never you could you wouldn't go down +this branch + + align:start position:0% +this branch + + + align:start position:0% +this branch +unless you + + align:start position:0% +unless you + + + align:start position:0% +unless you +i think all of the branches in this + + align:start position:0% +i think all of the branches in this + + + align:start position:0% +i think all of the branches in this +particular branching program could get + + align:start position:0% +particular branching program could get + + + align:start position:0% +particular branching program could get +used but i didn't check that so maybe + + align:start position:0% +used but i didn't check that so maybe + + + align:start position:0% +used but i didn't check that so maybe +i'm wrong um + + align:start position:0% +i'm wrong um + + + align:start position:0% +i'm wrong um +okay so let's continue two branching + + align:start position:0% +okay so let's continue two branching + + + align:start position:0% +okay so let's continue two branching +programs may may or may not compute the + + align:start position:0% +programs may may or may not compute the + + + align:start position:0% +programs may may or may not compute the +same function + + align:start position:0% +same function + + + align:start position:0% +same function +um we'll say they're equivalent if they + + align:start position:0% +um we'll say they're equivalent if they + + + align:start position:0% +um we'll say they're equivalent if they +do + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% + + + + align:start position:0% + +two + + align:start position:0% +two + + + align:start position:0% +two +branching programs can be equivalent + + align:start position:0% +branching programs can be equivalent + + + align:start position:0% +branching programs can be equivalent +even though they superficially look + + align:start position:0% +even though they superficially look + + + align:start position:0% +even though they superficially look +different from one another + + align:start position:0% +different from one another + + + align:start position:0% +different from one another +and we're interested in the + + align:start position:0% +and we're interested in the + + + align:start position:0% +and we're interested in the +computational problem of given two of + + align:start position:0% +computational problem of given two of + + + align:start position:0% +computational problem of given two of +these branching programs do they compute + + align:start position:0% +these branching programs do they compute + + + align:start position:0% +these branching programs do they compute +the same function do they in other words + + align:start position:0% +the same function do they in other words + + + align:start position:0% +the same function do they in other words +do they always give the same answer + + align:start position:0% +do they always give the same answer + + + align:start position:0% +do they always give the same answer +um on the setting of the input uh + + align:start position:0% +um on the setting of the input uh + + + align:start position:0% +um on the setting of the input uh +so we'll define the associated language + + align:start position:0% +so we'll define the associated language + + + align:start position:0% +so we'll define the associated language +equivalence problem for branching + + align:start position:0% +equivalence problem for branching + + + align:start position:0% +equivalence problem for branching +programs says that you're given two of + + align:start position:0% +programs says that you're given two of + + + align:start position:0% +programs says that you're given two of +these branching programs and they're + + align:start position:0% +these branching programs and they're + + + align:start position:0% +these branching programs and they're +equivalent to be in the language we're + + align:start position:0% +equivalent to be in the language we're + + + align:start position:0% +equivalent to be in the language we're +going to sometimes write equivalence + + align:start position:0% +going to sometimes write equivalence + + + align:start position:0% +going to sometimes write equivalence +using the mathematical notation of the + + align:start position:0% +using the mathematical notation of the + + + align:start position:0% +using the mathematical notation of the +three lined equals equal sign + + align:start position:0% +three lined equals equal sign + + + align:start position:0% +three lined equals equal sign +the equivalence sign + + align:start position:0% +the equivalence sign + + + align:start position:0% +the equivalence sign +okay that means they compute the same + + align:start position:0% +okay that means they compute the same + + + align:start position:0% +okay that means they compute the same +they always give the same answer + + align:start position:0% +they always give the same answer + + + align:start position:0% +they always give the same answer +now that problem + + align:start position:0% +now that problem + + + align:start position:0% +now that problem +turns out to be cohen p + + align:start position:0% +turns out to be cohen p + + + align:start position:0% +turns out to be cohen p +complete i've asked you to show on your + + align:start position:0% +complete i've asked you to show on your + + + align:start position:0% +complete i've asked you to show on your +homework i believe + + align:start position:0% +homework i believe + + + align:start position:0% +homework i believe +um + + align:start position:0% +um + + + align:start position:0% +um +this is not a super hard reduction um + + align:start position:0% +this is not a super hard reduction um + + + align:start position:0% +this is not a super hard reduction um +it's the in comp complete by the way is + + align:start position:0% +it's the in comp complete by the way is + + + align:start position:0% +it's the in comp complete by the way is +the complement of an mp complete problem + + align:start position:0% +the complement of an mp complete problem + + + align:start position:0% +the complement of an mp complete problem +or equivalently it's a problem to which + + align:start position:0% +or equivalently it's a problem to which + + + align:start position:0% +or equivalently it's a problem to which +all co np problems are polynomial time + + align:start position:0% +all co np problems are polynomial time + + + align:start position:0% +all co np problems are polynomial time +reducible and it's in coin + + align:start position:0% +reducible and it's in coin + + + align:start position:0% +reducible and it's in coin +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so + + align:start position:0% +so + + + align:start position:0% +so +uh + + align:start position:0% + + + + align:start position:0% + +this is coin p complete + + align:start position:0% +this is coin p complete + + + align:start position:0% +this is coin p complete +and + + align:start position:0% + + + + align:start position:0% + +that's for you to show um + + align:start position:0% +that's for you to show um + + + align:start position:0% +that's for you to show um +but that has an important + + align:start position:0% +but that has an important + + + align:start position:0% +but that has an important +significance for us right now + + align:start position:0% +significance for us right now + + + align:start position:0% +significance for us right now +um because if you if + + align:start position:0% +um because if you if + + + align:start position:0% +um because if you if +you know looking at the question of + + align:start position:0% +you know looking at the question of + + + align:start position:0% +you know looking at the question of +whether this problem is in bpp + + align:start position:0% +whether this problem is in bpp + + + align:start position:0% +whether this problem is in bpp +the fact that it's coin + + align:start position:0% +the fact that it's coin + + + align:start position:0% +the fact that it's coin +co np complete suggests that the answer + + align:start position:0% +co np complete suggests that the answer + + + align:start position:0% +co np complete suggests that the answer +is no + + align:start position:0% +is no + + + align:start position:0% +is no +because + + align:start position:0% +because + + + align:start position:0% +because +if + + align:start position:0% +if + + + align:start position:0% +if +a co np complete or np complete problem + + align:start position:0% +a co np complete or np complete problem + + + align:start position:0% +a co np complete or np complete problem +more in bpp + + align:start position:0% +more in bpp + + + align:start position:0% +more in bpp +because everything else in np or cmp is + + align:start position:0% +because everything else in np or cmp is + + + align:start position:0% +because everything else in np or cmp is +reducible to that problem then all of + + align:start position:0% +reducible to that problem then all of + + + align:start position:0% +reducible to that problem then all of +those np or co-np problems would be in + + align:start position:0% +those np or co-np problems would be in + + + align:start position:0% +those np or co-np problems would be in +bpp for the exactly the same reason that + + align:start position:0% +bpp for the exactly the same reason that + + + align:start position:0% +bpp for the exactly the same reason that +we've seen before + + align:start position:0% +we've seen before + + + align:start position:0% +we've seen before +um and that's not known to be the case + + align:start position:0% +um and that's not known to be the case + + + align:start position:0% +um and that's not known to be the case +and not believed to be the case um + + align:start position:0% +and not believed to be the case um + + + align:start position:0% +and not believed to be the case um +so + + align:start position:0% +so + + + align:start position:0% +so +uh we don't expect that a co-mp complete + + align:start position:0% +uh we don't expect that a co-mp complete + + + align:start position:0% +uh we don't expect that a co-mp complete +problem is going to be in bpp um that + + align:start position:0% +problem is going to be in bpp um that + + + align:start position:0% +problem is going to be in bpp um that +would be you know an amazing uh and + + align:start position:0% +would be you know an amazing uh and + + + align:start position:0% +would be you know an amazing uh and +surprising uh + + align:start position:0% +surprising uh + + + align:start position:0% +surprising uh +uh result so um + + align:start position:0% +uh result so um + + + align:start position:0% +uh result so um +because i i hope i made it clear in my + + align:start position:0% +because i i hope i made it clear in my + + + align:start position:0% +because i i hope i made it clear in my +previous um you know in previous + + align:start position:0% +previous um you know in previous + + + align:start position:0% +previous um you know in previous +discussion that + + align:start position:0% +discussion that + + + align:start position:0% +discussion that +you know the bpp from a practical + + align:start position:0% +you know the bpp from a practical + + + align:start position:0% +you know the bpp from a practical +standpoint is very close to being like p + + align:start position:0% +standpoint is very close to being like p + + + align:start position:0% +standpoint is very close to being like p +um because you can make the error + + align:start position:0% +um because you can make the error + + + align:start position:0% +um because you can make the error +probability of the machine so incredibly + + align:start position:0% +probability of the machine so incredibly + + + align:start position:0% +probability of the machine so incredibly +low + + align:start position:0% +low + + + align:start position:0% +low +um + + align:start position:0% +um + + + align:start position:0% +um +that + + align:start position:0% +that + + + align:start position:0% +that +you know it's a comparable + + align:start position:0% +you know it's a comparable + + + align:start position:0% +you know it's a comparable +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know if you run the machine and the + + align:start position:0% +you know if you run the machine and the + + + align:start position:0% +you know if you run the machine and the +error probability is like one over + + align:start position:0% +error probability is like one over + + + align:start position:0% +error probability is like one over +google um + + align:start position:0% +google um + + + align:start position:0% +google um +then it's sort of + + align:start position:0% +then it's sort of + + + align:start position:0% +then it's sort of +even greater than the probability that + + align:start position:0% +even greater than the probability that + + + align:start position:0% +even greater than the probability that +some alpha particle came in and flipped + + align:start position:0% +some alpha particle came in and flipped + + + align:start position:0% +some alpha particle came in and flipped +the value of what some internal uh + + align:start position:0% +the value of what some internal uh + + + align:start position:0% +the value of what some internal uh +memory cell in your in your computation + + align:start position:0% +memory cell in your in your computation + + + align:start position:0% +memory cell in your in your computation +so if you have an extremely low error + + align:start position:0% +so if you have an extremely low error + + + align:start position:0% +so if you have an extremely low error +probability it's pretty good from a + + align:start position:0% +probability it's pretty good from a + + + align:start position:0% +probability it's pretty good from a +practical standpoint um + + align:start position:0% + + + + align:start position:0% + +so it would be amazing if np problems + + align:start position:0% +so it would be amazing if np problems + + + align:start position:0% +so it would be amazing if np problems +were solvable in bpp um + + align:start position:0% +were solvable in bpp um + + + align:start position:0% +were solvable in bpp um +so + + align:start position:0% +so + + + align:start position:0% +so +this is not the language we're going to + + align:start position:0% +this is not the language we're going to + + + align:start position:0% +this is not the language we're going to +use as our example we're going to look + + align:start position:0% +use as our example we're going to look + + + align:start position:0% +use as our example we're going to look +at a related restricted version of this + + align:start position:0% +at a related restricted version of this + + + align:start position:0% +at a related restricted version of this +problem about equivalence for branching + + align:start position:0% +problem about equivalence for branching + + + align:start position:0% +problem about equivalence for branching +programs and that i'm going to introduce + + align:start position:0% +programs and that i'm going to introduce + + + align:start position:0% +programs and that i'm going to introduce +right now + + align:start position:0% +right now + + + align:start position:0% +right now +okay any questions here + + align:start position:0% +okay any questions here + + + align:start position:0% +okay any questions here +don't see any questions + + align:start position:0% +don't see any questions + + + align:start position:0% +don't see any questions +um + + align:start position:0% + + + + align:start position:0% + +fading out + + align:start position:0% +fading out + + + align:start position:0% +fading out +uh okay + + align:start position:0% +uh okay + + + align:start position:0% +uh okay +um + + align:start position:0% +um + + + align:start position:0% +um +so let's move on + + align:start position:0% +so let's move on + + + align:start position:0% +so let's move on +so we're going to talk about branching + + align:start position:0% +so we're going to talk about branching + + + align:start position:0% +so we're going to talk about branching +programs that are what are called read + + align:start position:0% +programs that are what are called read + + + align:start position:0% +programs that are what are called read +once + + align:start position:0% +once + + + align:start position:0% +once +read once branching programs + + align:start position:0% +read once branching programs + + + align:start position:0% +read once branching programs +and those are simply branching programs + + align:start position:0% +and those are simply branching programs + + + align:start position:0% +and those are simply branching programs +that are not allowed to re-read + + align:start position:0% +that are not allowed to re-read + + + align:start position:0% +that are not allowed to re-read +an input that they've previously read + + align:start position:0% +an input that they've previously read + + + align:start position:0% +an input that they've previously read +so for example + + align:start position:0% +so for example + + + align:start position:0% +so for example +is this + + align:start position:0% +is this + + + align:start position:0% +is this +branching program a read once branching + + align:start position:0% +branching program a read once branching + + + align:start position:0% +branching program a read once branching +program + + align:start position:0% +program + + + align:start position:0% +program +no + + align:start position:0% +no + + + align:start position:0% +no +this branching program is not a read + + align:start position:0% +this branching program is not a read + + + align:start position:0% +this branching program is not a read +once branching program because + + align:start position:0% +once branching program because + + + align:start position:0% +once branching program because +um + + align:start position:0% +um + + + align:start position:0% +um +you can + + align:start position:0% +you can + + + align:start position:0% +you can +find a path that's going to cause you to + + align:start position:0% +find a path that's going to cause you to + + + align:start position:0% +find a path that's going to cause you to +read the same variable more than once so + + align:start position:0% +read the same variable more than once so + + + align:start position:0% +read the same variable more than once so +it's not going to be a read once + + align:start position:0% +it's not going to be a read once + + + align:start position:0% +it's not going to be a read once +um so over here let's not read once + + align:start position:0% +um so over here let's not read once + + + align:start position:0% +um so over here let's not read once +because there's two + + align:start position:0% +because there's two + + + align:start position:0% +because there's two +occurrences of an x1 on the same branch + + align:start position:0% +occurrences of an x1 on the same branch + + + align:start position:0% +occurrences of an x1 on the same branch +now you might ask why would anybody want + + align:start position:0% +now you might ask why would anybody want + + + align:start position:0% +now you might ask why would anybody want +to do that because you've already read + + align:start position:0% +to do that because you've already read + + + align:start position:0% +to do that because you've already read +the value of x1 well i mean in the case + + align:start position:0% +the value of x1 well i mean in the case + + + align:start position:0% +the value of x1 well i mean in the case +of this particular branching program + + align:start position:0% +of this particular branching program + + + align:start position:0% +of this particular branching program +there might be a value because you could + + align:start position:0% +there might be a value because you could + + + align:start position:0% +there might be a value because you could +have got to this x x1 branch by going + + align:start position:0% +have got to this x x1 branch by going + + + align:start position:0% +have got to this x x1 branch by going +this way or that way + + align:start position:0% +this way or that way + + + align:start position:0% +this way or that way +um + + align:start position:0% +um + + + align:start position:0% +um +but that's a separate question + + align:start position:0% +but that's a separate question + + + align:start position:0% +but that's a separate question +if we restrict our attention + + align:start position:0% +if we restrict our attention + + + align:start position:0% +if we restrict our attention +to read once branching programs then the + + align:start position:0% +to read once branching programs then the + + + align:start position:0% +to read once branching programs then the +problem of testing equivalence becomes + + align:start position:0% +problem of testing equivalence becomes + + + align:start position:0% +problem of testing equivalence becomes +uh + + align:start position:0% +uh + + + align:start position:0% +uh +very different in character + + align:start position:0% +very different in character + + + align:start position:0% +very different in character +and in fact we're going to give a + + align:start position:0% +and in fact we're going to give a + + + align:start position:0% +and in fact we're going to give a +probabilistic algorithm uh + + align:start position:0% +probabilistic algorithm uh + + + align:start position:0% +probabilistic algorithm uh +a bpp algorithm to solve that problem + + align:start position:0% +a bpp algorithm to solve that problem + + + align:start position:0% +a bpp algorithm to solve that problem +so the equivalence problem for read once + + align:start position:0% +so the equivalence problem for read once + + + align:start position:0% +so the equivalence problem for read once +branching programs which are not allowed + + align:start position:0% +branching programs which are not allowed + + + align:start position:0% +branching programs which are not allowed +to re-read variables on any path + + align:start position:0% +to re-read variables on any path + + + align:start position:0% +to re-read variables on any path +um that's interestingly going to be + + align:start position:0% +um that's interestingly going to be + + + align:start position:0% +um that's interestingly going to be +solvable with a probabilistic + + align:start position:0% +solvable with a probabilistic + + + align:start position:0% +solvable with a probabilistic +uh polynomial time algorithm you know + + align:start position:0% +uh polynomial time algorithm you know + + + align:start position:0% +uh polynomial time algorithm you know +with a small error probability + + align:start position:0% +with a small error probability + + + align:start position:0% +with a small error probability +um + + align:start position:0% +um + + + align:start position:0% +um +so i'm going to run a check in now but + + align:start position:0% +so i'm going to run a check in now but + + + align:start position:0% +so i'm going to run a check in now but +let's make sure we're all together on + + align:start position:0% +let's make sure we're all together on + + + align:start position:0% +let's make sure we're all together on +this so i got a good question here can + + align:start position:0% +this so i got a good question here can + + + align:start position:0% +this so i got a good question here can +every boolean function be described by a + + align:start position:0% +every boolean function be described by a + + + align:start position:0% +every boolean function be described by a +branching program yes + + align:start position:0% +branching program yes + + + align:start position:0% +branching program yes +that's an easy exercise but you can make + + align:start position:0% +that's an easy exercise but you can make + + + align:start position:0% +that's an easy exercise but you can make +branch branching programs are um they + + align:start position:0% +branch branching programs are um they + + + align:start position:0% +branch branching programs are um they +may be large + + align:start position:0% +may be large + + + align:start position:0% +may be large +uh you can describe any boolean function + + align:start position:0% +uh you can describe any boolean function + + + align:start position:0% +uh you can describe any boolean function +with some branching program + + align:start position:0% +with some branching program + + + align:start position:0% +with some branching program +that's not hard to show + + align:start position:0% +that's not hard to show + + + align:start position:0% +that's not hard to show +um + + align:start position:0% +um + + + align:start position:0% +um +other questions are we all together on + + align:start position:0% +other questions are we all together on + + + align:start position:0% +other questions are we all together on +understanding what read once means and + + align:start position:0% +understanding what read once means and + + + align:start position:0% +understanding what read once means and +branching programs and all that stuff + + align:start position:0% +branching programs and all that stuff + + + align:start position:0% +branching programs and all that stuff +this is a good time to ask if you're not + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +okay so let's do the check-in + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +as i pointed out we will show that the + + align:start position:0% +as i pointed out we will show that the + + + align:start position:0% +as i pointed out we will show that the +equivalence for read once branching + + align:start position:0% +equivalence for read once branching + + + align:start position:0% +equivalence for read once branching +programs is solvable in bpp + + align:start position:0% +programs is solvable in bpp + + + align:start position:0% +programs is solvable in bpp +can we use that to solve the general + + align:start position:0% +can we use that to solve the general + + + align:start position:0% +can we use that to solve the general +case for branching programs + + align:start position:0% +case for branching programs + + + align:start position:0% +case for branching programs +by converting branch general branching + + align:start position:0% +by converting branch general branching + + + align:start position:0% +by converting branch general branching +programs to read once branching programs + + align:start position:0% +programs to read once branching programs + + + align:start position:0% +programs to read once branching programs +and then run running the read once test + + align:start position:0% +and then run running the read once test + + + align:start position:0% +and then run running the read once test +so + + align:start position:0% +so + + + align:start position:0% +so +what do you think + + align:start position:0% +what do you think + + + align:start position:0% +what do you think +okay i'm seeing a lot of uh + + align:start position:0% +okay i'm seeing a lot of uh + + + align:start position:0% +okay i'm seeing a lot of uh +correct answers here um so let's let's + + align:start position:0% +correct answers here um so let's let's + + + align:start position:0% +correct answers here um so let's let's +wrap this one one up quickly + + align:start position:0% +wrap this one one up quickly + + + align:start position:0% +wrap this one one up quickly +um + + align:start position:0% + + + + align:start position:0% + +another 10 seconds please + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +ready are we all ready + + align:start position:0% +ready are we all ready + + + align:start position:0% +ready are we all ready +one two three closing + + align:start position:0% + + + + align:start position:0% + +all right yes + + align:start position:0% +all right yes + + + align:start position:0% +all right yes +most of you have + + align:start position:0% +most of you have + + + align:start position:0% +most of you have +uh + + align:start position:0% +uh + + + align:start position:0% +uh +answered correctly um + + align:start position:0% +answered correctly um + + + align:start position:0% +answered correctly um +well answer a is not a very good answer + + align:start position:0% +well answer a is not a very good answer + + + align:start position:0% +well answer a is not a very good answer +because we already commented on the + + align:start position:0% +because we already commented on the + + + align:start position:0% +because we already commented on the +previous slide that we don't know how to + + align:start position:0% +previous slide that we don't know how to + + + align:start position:0% +previous slide that we don't know how to +do + + align:start position:0% +do + + + align:start position:0% +do +the general case in bpp so it would be + + align:start position:0% +the general case in bpp so it would be + + + align:start position:0% +the general case in bpp so it would be +kind of surprising if right here i'm + + align:start position:0% +kind of surprising if right here i'm + + + align:start position:0% +kind of surprising if right here i'm +saying yes we could do it + + align:start position:0% +saying yes we could do it + + + align:start position:0% +saying yes we could do it +by using the restricted case so + + align:start position:0% + + + + align:start position:0% + +you know i think a + + align:start position:0% +you know i think a + + + align:start position:0% +you know i think a +better answer would be to one of the + + align:start position:0% +better answer would be to one of the + + + align:start position:0% +better answer would be to one of the +no's but + + align:start position:0% +no's but + + + align:start position:0% +no's but +as i did comment you can always convert + + align:start position:0% +as i did comment you can always convert + + + align:start position:0% +as i did comment you can always convert +you can always do any uh boolean + + align:start position:0% +you can always do any uh boolean + + + align:start position:0% +you can always do any uh boolean +function uh with a + + align:start position:0% + + + + align:start position:0% + +well maybe i didn't say it for read once + + align:start position:0% +well maybe i didn't say it for read once + + + align:start position:0% +well maybe i didn't say it for read once +branching programs but you even read + + align:start position:0% +branching programs but you even read + + + align:start position:0% +branching programs but you even read +once branching programs can do any + + align:start position:0% +once branching programs can do any + + + align:start position:0% +once branching programs can do any +compute any boolean function um so the + + align:start position:0% +compute any boolean function um so the + + + align:start position:0% +compute any boolean function um so the +the conversion is possible but in + + align:start position:0% +the conversion is possible but in + + + align:start position:0% +the conversion is possible but in +general will not be polynomial time and + + align:start position:0% +general will not be polynomial time and + + + align:start position:0% +general will not be polynomial time and +you can if you imagine you've been + + align:start position:0% +you can if you imagine you've been + + + align:start position:0% +you can if you imagine you've been +trying to do the conversion over here + + align:start position:0% +trying to do the conversion over here + + + align:start position:0% +trying to do the conversion over here +you could convert this branching program + + align:start position:0% +you could convert this branching program + + + align:start position:0% +you could convert this branching program +to read once um but you'd have to + + align:start position:0% +to read once um but you'd have to + + + align:start position:0% +to read once um but you'd have to +basically separate the two + + align:start position:0% +basically separate the two + + + align:start position:0% +basically separate the two +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um + + align:start position:0% +um + + + align:start position:0% +um +you know instead of re-reading the x1 + + align:start position:0% +you know instead of re-reading the x1 + + + align:start position:0% +you know instead of re-reading the x1 +you could remember that x1 value but + + align:start position:0% +you could remember that x1 value but + + + align:start position:0% +you could remember that x1 value but +then you would not be you couldn't + + align:start position:0% +then you would not be you couldn't + + + align:start position:0% +then you would not be you couldn't +reconverge over here you'd have to keep + + align:start position:0% +reconverge over here you'd have to keep + + + align:start position:0% +reconverge over here you'd have to keep +those two those two + + align:start position:0% +those two those two + + + align:start position:0% +those two those two +threads of the those two branches of the + + align:start position:0% +threads of the those two branches of the + + + align:start position:0% +threads of the those two branches of the +computation apart + + align:start position:0% +computation apart + + + align:start position:0% +computation apart +those two paths apart from one another + + align:start position:0% +those two paths apart from one another + + + align:start position:0% +those two paths apart from one another +and already the branching program would + + align:start position:0% +and already the branching program would + + + align:start position:0% +and already the branching program would +start to increase in size by doing that + + align:start position:0% +start to increase in size by doing that + + + align:start position:0% +start to increase in size by doing that +um + + align:start position:0% +um + + + align:start position:0% +um +and um + + align:start position:0% +and um + + + align:start position:0% +and um +so in general + + align:start position:0% +so in general + + + align:start position:0% +so in general +conversion converting is possible but it + + align:start position:0% +conversion converting is possible but it + + + align:start position:0% +conversion converting is possible but it +requires a big expansion a big + + align:start position:0% +requires a big expansion a big + + + align:start position:0% +requires a big expansion a big +increase in the size + + align:start position:0% +increase in the size + + + align:start position:0% +increase in the size +and then we will + + align:start position:0% +and then we will + + + align:start position:0% +and then we will +not allow a polynomial time algorithm + + align:start position:0% +not allow a polynomial time algorithm + + + align:start position:0% +not allow a polynomial time algorithm +anymore even in probabilistic in the + + align:start position:0% +anymore even in probabilistic in the + + + align:start position:0% +anymore even in probabilistic in the +probabilistic case + + align:start position:0% +probabilistic case + + + align:start position:0% +probabilistic case +um + + align:start position:0% +um + + + align:start position:0% +um +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so now let's start to look at the + + align:start position:0% +so now let's start to look at the + + + align:start position:0% +so now let's start to look at the +possibility of showing that this + + align:start position:0% +possibility of showing that this + + + align:start position:0% +possibility of showing that this +equivalence problem is solvable in bpp + + align:start position:0% +equivalence problem is solvable in bpp + + + align:start position:0% +equivalence problem is solvable in bpp +and it's going to take us in kind of + + align:start position:0% +and it's going to take us in kind of + + + align:start position:0% +and it's going to take us in kind of +a strange direction but let's let's try + + align:start position:0% +a strange direction but let's let's try + + + align:start position:0% +a strange direction but let's let's try +to get our intuition going first by + + align:start position:0% +to get our intuition going first by + + + align:start position:0% +to get our intuition going first by +doing something + + align:start position:0% +doing something + + + align:start position:0% +doing something +which seems like the most obvious + + align:start position:0% +which seems like the most obvious + + + align:start position:0% +which seems like the most obvious +obvious approach + + align:start position:0% +obvious approach + + + align:start position:0% +obvious approach +um + + align:start position:0% +um + + + align:start position:0% +um +so here + + align:start position:0% +so here + + + align:start position:0% +so here +uh so we're gonna + + align:start position:0% +uh so we're gonna + + + align:start position:0% +uh so we're gonna +give a + + align:start position:0% +give a + + + align:start position:0% +give a +an algorithm now um + + align:start position:0% +an algorithm now um + + + align:start position:0% +an algorithm now um +uh which is going to be an attempt + + align:start position:0% +uh which is going to be an attempt + + + align:start position:0% +uh which is going to be an attempt +it's not going to work but nevertheless + + align:start position:0% +it's not going to work but nevertheless + + + align:start position:0% +it's not going to work but nevertheless +it's going to have the germ of the right + + align:start position:0% +it's going to have the germ of the right + + + align:start position:0% +it's going to have the germ of the right +idea or the or the + + align:start position:0% +idea or the or the + + + align:start position:0% +idea or the or the +not the germ but the beginning of the + + align:start position:0% +not the germ but the beginning of the + + + align:start position:0% +not the germ but the beginning of the +right way to think about it + + align:start position:0% +right way to think about it + + + align:start position:0% +right way to think about it +so here are the two branching read once + + align:start position:0% +so here are the two branching read once + + + align:start position:0% +so here are the two branching read once +branching programs are b1 and b2 + + align:start position:0% +branching programs are b1 and b2 + + + align:start position:0% +branching programs are b1 and b2 +and i want to see + + align:start position:0% +and i want to see + + + align:start position:0% +and i want to see +do they compute the same function or not + + align:start position:0% +do they compute the same function or not + + + align:start position:0% +do they compute the same function or not +um so one thing you might try + + align:start position:0% +um so one thing you might try + + + align:start position:0% +um so one thing you might try +is just running them on a bunch of + + align:start position:0% +is just running them on a bunch of + + + align:start position:0% +is just running them on a bunch of +randomly selected + + align:start position:0% +randomly selected + + + align:start position:0% +randomly selected +assignments or inputs + + align:start position:0% +assignments or inputs + + + align:start position:0% +assignments or inputs +all right so you're going to you can + + align:start position:0% +all right so you're going to you can + + + align:start position:0% +all right so you're going to you can +just um + + align:start position:0% +just um + + + align:start position:0% +just um +take two randomness input assignments + + align:start position:0% +take two randomness input assignments + + + align:start position:0% +take two randomness input assignments +just take x1 + + align:start position:0% +just take x1 + + + align:start position:0% +just take x1 +flip a coin to say it's one of zero x do + + align:start position:0% +flip a coin to say it's one of zero x do + + + align:start position:0% +flip a coin to say it's one of zero x do +the same for x two and so on + + align:start position:0% +the same for x two and so on + + + align:start position:0% +the same for x two and so on +um then you get some input assignment + + align:start position:0% +um then you get some input assignment + + + align:start position:0% +um then you get some input assignment +you run the two branching programs on + + align:start position:0% +you run the two branching programs on + + + align:start position:0% +you run the two branching programs on +that assignment + + align:start position:0% +that assignment + + + align:start position:0% +that assignment +and maybe that doesn't give you know + + align:start position:0% +and maybe that doesn't give you know + + + align:start position:0% +and maybe that doesn't give you know +even if they agree it doesn't give you a + + align:start position:0% +even if they agree it doesn't give you a + + + align:start position:0% +even if they agree it doesn't give you a +lot of confidence that you got the right + + align:start position:0% +lot of confidence that you got the right + + + align:start position:0% +lot of confidence that you got the right +answer uh + + align:start position:0% +answer uh + + + align:start position:0% +answer uh +that they're really equivalent so you do + + align:start position:0% +that they're really equivalent so you do + + + align:start position:0% +that they're really equivalent so you do +it a hundred times whatever some some + + align:start position:0% +it a hundred times whatever some some + + + align:start position:0% +it a hundred times whatever some some +number of times um + + align:start position:0% +number of times um + + + align:start position:0% +number of times um +and + + align:start position:0% +and + + + align:start position:0% +and +of course + + align:start position:0% +of course + + + align:start position:0% +of course +if + + align:start position:0% +if + + + align:start position:0% +if +they uh ever disagree + + align:start position:0% +they uh ever disagree + + + align:start position:0% +they uh ever disagree +on some assignment on one of those + + align:start position:0% +on some assignment on one of those + + + align:start position:0% +on some assignment on one of those +assignments then you know they're not + + align:start position:0% +assignments then you know they're not + + + align:start position:0% +assignments then you know they're not +equivalent and you can immediately + + align:start position:0% +equivalent and you can immediately + + + align:start position:0% +equivalent and you can immediately +reject + + align:start position:0% +reject + + + align:start position:0% +reject +um + + align:start position:0% +um + + + align:start position:0% +um +but + + align:start position:0% +but + + + align:start position:0% +but +uh what i'd like to say is if they + + align:start position:0% +uh what i'd like to say is if they + + + align:start position:0% +uh what i'd like to say is if they +agree + + align:start position:0% +agree + + + align:start position:0% +agree +on those + + align:start position:0% +on those + + + align:start position:0% +on those +you know hundred + + align:start position:0% +you know hundred + + + align:start position:0% +you know hundred +tries those hundred assignments there + + align:start position:0% +tries those hundred assignments there + + + align:start position:0% +tries those hundred assignments there +then + + align:start position:0% +then + + + align:start position:0% +then +there then they are um + + align:start position:0% +there then they are um + + + align:start position:0% +there then they are um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +at least i'll i haven't found a place + + align:start position:0% +at least i'll i haven't found a place + + + align:start position:0% +at least i'll i haven't found a place +where they disagree so i'm gonna say + + align:start position:0% +where they disagree so i'm gonna say + + + align:start position:0% +where they disagree so i'm gonna say +that they're equivalent + + align:start position:0% +that they're equivalent + + + align:start position:0% +that they're equivalent +is that a reasonable thing uh to do + + align:start position:0% +is that a reasonable thing uh to do + + + align:start position:0% +is that a reasonable thing uh to do +well it might be + + align:start position:0% +well it might be + + + align:start position:0% +well it might be +uh it depends on k um + + align:start position:0% +uh it depends on k um + + + align:start position:0% +uh it depends on k um +so the critical thing is what value of k + + align:start position:0% +so the critical thing is what value of k + + + align:start position:0% +so the critical thing is what value of k +should you pick + + align:start position:0% +should you pick + + + align:start position:0% +should you pick +which is going to be big enough to allow + + align:start position:0% +which is going to be big enough to allow + + + align:start position:0% +which is going to be big enough to allow +us to draw the conclusion that if you + + align:start position:0% +us to draw the conclusion that if you + + + align:start position:0% +us to draw the conclusion that if you +run it for k times and you never see a + + align:start position:0% +run it for k times and you never see a + + + align:start position:0% +run it for k times and you never see a +difference + + align:start position:0% +difference + + + align:start position:0% +difference +then you can + + align:start position:0% +then you can + + + align:start position:0% +then you can +conclude + + align:start position:0% +conclude + + + align:start position:0% +conclude +with good confidence that the two + + align:start position:0% +with good confidence that the two + + + align:start position:0% +with good confidence that the two +branching programs are equivalent + + align:start position:0% +branching programs are equivalent + + + align:start position:0% +branching programs are equivalent +because + + align:start position:0% +because + + + align:start position:0% +because +you've tried to look for + + align:start position:0% +you've tried to look for + + + align:start position:0% +you've tried to look for +a difference and you never found one + + align:start position:0% +a difference and you never found one + + + align:start position:0% +a difference and you never found one +well the thing is is that + + align:start position:0% +well the thing is is that + + + align:start position:0% +well the thing is is that +um + + align:start position:0% +um + + + align:start position:0% +um +k is going to have to be pretty big + + align:start position:0% +k is going to have to be pretty big + + + align:start position:0% +k is going to have to be pretty big +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so + + align:start position:0% +so + + + align:start position:0% +so +looking at it this way if the two + + align:start position:0% +looking at it this way if the two + + + align:start position:0% +looking at it this way if the two +branching programs were equivalent + + align:start position:0% + + + + align:start position:0% + +then certainly they're always going to + + align:start position:0% +then certainly they're always going to + + + align:start position:0% +then certainly they're always going to +give the same value + + align:start position:0% +give the same value + + + align:start position:0% +give the same value +um + + align:start position:0% +um + + + align:start position:0% +um +so the probability that the machine + + align:start position:0% +so the probability that the machine + + + align:start position:0% +so the probability that the machine +accepts is going to be one and that's + + align:start position:0% +accepts is going to be one and that's + + + align:start position:0% +accepts is going to be one and that's +good + + align:start position:0% +good + + + align:start position:0% +good +because we want for + + align:start position:0% +because we want for + + + align:start position:0% +because we want for +this is a case when we're in the + + align:start position:0% +this is a case when we're in the + + + align:start position:0% +this is a case when we're in the +language we want the probability of + + align:start position:0% +language we want the probability of + + + align:start position:0% +language we want the probability of +acceptance to be high and here the + + align:start position:0% +acceptance to be high and here the + + + align:start position:0% +acceptance to be high and here the +probability of acceptance is actually + + align:start position:0% +probability of acceptance is actually + + + align:start position:0% +probability of acceptance is actually +one + + align:start position:0% +one + + + align:start position:0% +one +so it's always going to accept when the + + align:start position:0% +so it's always going to accept when the + + + align:start position:0% +so it's always going to accept when the +two uh branching + + align:start position:0% +two uh branching + + + align:start position:0% +two uh branching +programs were equivalent + + align:start position:0% +programs were equivalent + + + align:start position:0% +programs were equivalent +but what happens when the branching + + align:start position:0% +but what happens when the branching + + + align:start position:0% +but what happens when the branching +programs are not equivalent + + align:start position:0% +programs are not equivalent + + + align:start position:0% +programs are not equivalent +now we want the probability of rejection + + align:start position:0% +now we want the probability of rejection + + + align:start position:0% +now we want the probability of rejection +to be high the probability of acceptance + + align:start position:0% +to be high the probability of acceptance + + + align:start position:0% +to be high the probability of acceptance +should be very low + + align:start position:0% +should be very low + + + align:start position:0% +should be very low +um + + align:start position:0% +um + + + align:start position:0% +um +right so if if they're not equivalent we + + align:start position:0% +right so if if they're not equivalent we + + + align:start position:0% +right so if if they're not equivalent we +want the probability that the machine + + align:start position:0% +want the probability that the machine + + + align:start position:0% +want the probability that the machine +rejects is going to be + + align:start position:0% +rejects is going to be + + + align:start position:0% +rejects is going to be +high if they're not equivalent because + + align:start position:0% +high if they're not equivalent because + + + align:start position:0% +high if they're not equivalent because +that that's what the correct answer is + + align:start position:0% +that that's what the correct answer is + + + align:start position:0% +that that's what the correct answer is +well the only way the machine is going + + align:start position:0% +well the only way the machine is going + + + align:start position:0% +well the only way the machine is going +to reject + + align:start position:0% +to reject + + + align:start position:0% +to reject +if it finds + + align:start position:0% +if it finds + + + align:start position:0% +if it finds +um a place + + align:start position:0% +um a place + + + align:start position:0% +um a place +where the two branching programs + + align:start position:0% +where the two branching programs + + + align:start position:0% +where the two branching programs +disagree + + align:start position:0% +disagree + + + align:start position:0% +disagree +but but + + align:start position:0% +but but + + + align:start position:0% +but but +those two branching programs even though + + align:start position:0% +those two branching programs even though + + + align:start position:0% +those two branching programs even though +not equivalent + + align:start position:0% +not equivalent + + + align:start position:0% +not equivalent +might disagree rarely + + align:start position:0% +might disagree rarely + + + align:start position:0% +might disagree rarely +they might only disagree on one input + + align:start position:0% +they might only disagree on one input + + + align:start position:0% +they might only disagree on one input +assignment out of the two to the end + + align:start position:0% +assignment out of the two to the end + + + align:start position:0% +assignment out of the two to the end +possibilities + + align:start position:0% +possibilities + + + align:start position:0% +possibilities +so these two inequivalent branching + + align:start position:0% +so these two inequivalent branching + + + align:start position:0% +so these two inequivalent branching +programs might agree almost everywhere + + align:start position:0% +programs might agree almost everywhere + + + align:start position:0% +programs might agree almost everywhere +just except at one place and then that's + + align:start position:0% +just except at one place and then that's + + + align:start position:0% +just except at one place and then that's +enough for them not to be equivalent but + + align:start position:0% +enough for them not to be equivalent but + + + align:start position:0% +enough for them not to be equivalent but +the problem is that if you're just going + + align:start position:0% +the problem is that if you're just going + + + align:start position:0% +the problem is that if you're just going +to do random sampling + + align:start position:0% +to do random sampling + + + align:start position:0% +to do random sampling +um the likelihood of finding that one + + align:start position:0% +um the likelihood of finding that one + + + align:start position:0% +um the likelihood of finding that one +exceptional place where the two disagree + + align:start position:0% +exceptional place where the two disagree + + + align:start position:0% +exceptional place where the two disagree +is very low you're going to have to do + + align:start position:0% +is very low you're going to have to do + + + align:start position:0% +is very low you're going to have to do +an enormous number of samples before + + align:start position:0% +an enormous number of samples before + + + align:start position:0% +an enormous number of samples before +you're likely to actually to to to find + + align:start position:0% +you're likely to actually to to to find + + + align:start position:0% +you're likely to actually to to to find +that uh that point of difference um and + + align:start position:0% +that uh that point of difference um and + + + align:start position:0% +that uh that point of difference um and +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +in order to be confident that you're + + align:start position:0% +in order to be confident that you're + + + align:start position:0% +in order to be confident that you're +going to find that difference if there + + align:start position:0% +going to find that difference if there + + + align:start position:0% +going to find that difference if there +is one you're going to have to do + + align:start position:0% +is one you're going to have to do + + + align:start position:0% +is one you're going to have to do +exponentially many samples and you don't + + align:start position:0% +exponentially many samples and you don't + + + align:start position:0% +exponentially many samples and you don't +have time to do that with a polynomial + + align:start position:0% +have time to do that with a polynomial + + + align:start position:0% +have time to do that with a polynomial +time algorithm + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +you're just going to have to flip too + + align:start position:0% +you're just going to have to flip too + + + align:start position:0% +you're just going to have to flip too +many coins you have to run too many + + align:start position:0% +many coins you have to run too many + + + align:start position:0% +many coins you have to run too many +different + + align:start position:0% + + + + align:start position:0% + +samples + + align:start position:0% +samples + + + align:start position:0% +samples +different assignments through these two + + align:start position:0% +different assignments through these two + + + align:start position:0% +different assignments through these two +machines + + align:start position:0% +machines + + + align:start position:0% +machines +and um because they're almost + + align:start position:0% +and um because they're almost + + + align:start position:0% +and um because they're almost +they're different but they're almost the + + align:start position:0% +they're different but they're almost the + + + align:start position:0% +they're different but they're almost the +same + + align:start position:0% +same + + + align:start position:0% +same +um + + align:start position:0% +um + + + align:start position:0% +um +so we're going to need to find a + + align:start position:0% +so we're going to need to find a + + + align:start position:0% +so we're going to need to find a +different method + + align:start position:0% +different method + + + align:start position:0% +different method +and + + align:start position:0% +and + + + align:start position:0% +and +um the the idea is we're going to run + + align:start position:0% +um the the idea is we're going to run + + + align:start position:0% +um the the idea is we're going to run +these two + + align:start position:0% +these two + + + align:start position:0% +these two +branching programs + + align:start position:0% +branching programs + + + align:start position:0% +branching programs +in some crazy way + + align:start position:0% +in some crazy way + + + align:start position:0% +in some crazy way +instead of running them on zeros and + + align:start position:0% +instead of running them on zeros and + + + align:start position:0% +instead of running them on zeros and +ones that we've been we've been doing it + + align:start position:0% +ones that we've been we've been doing it + + + align:start position:0% +ones that we've been we've been doing it +so far we're going to feed in + + align:start position:0% +so far we're going to feed in + + + align:start position:0% +so far we're going to feed in +values for the variables + + align:start position:0% +values for the variables + + + align:start position:0% +values for the variables +which are non-boolean + + align:start position:0% +which are non-boolean + + + align:start position:0% +which are non-boolean +they are going to be going to set x1 to + + align:start position:0% +they are going to be going to set x1 to + + + align:start position:0% +they are going to be going to set x1 to +2 x3 to 7 + + align:start position:0% +2 x3 to 7 + + + align:start position:0% +2 x3 to 7 +x + + align:start position:0% +x + + + align:start position:0% +x +4 to 15. + + align:start position:0% +4 to 15. + + + align:start position:0% +4 to 15. +of course that doesn't seem to make any + + align:start position:0% +of course that doesn't seem to make any + + + align:start position:0% +of course that doesn't seem to make any +sense but it's nevertheless going to + + align:start position:0% +sense but it's nevertheless going to + + + align:start position:0% +sense but it's nevertheless going to +turn out to be useful a useful thing to + + align:start position:0% +turn out to be useful a useful thing to + + + align:start position:0% +turn out to be useful a useful thing to +do and it's going to give us some + + align:start position:0% +do and it's going to give us some + + + align:start position:0% +do and it's going to give us some +insight into + + align:start position:0% +insight into + + + align:start position:0% +insight into +the equivalence or equivalence of these + + align:start position:0% +the equivalence or equivalence of these + + + align:start position:0% +the equivalence or equivalence of these +branching programs um + + align:start position:0% + + + + align:start position:0% + +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so let's just i think are we at the end + + align:start position:0% +so let's just i think are we at the end + + + align:start position:0% +so let's just i think are we at the end +yeah we're at the break here so why + + align:start position:0% +yeah we're at the break here so why + + + align:start position:0% +yeah we're at the break here so why +don't i i'm getting some questions + + align:start position:0% +don't i i'm getting some questions + + + align:start position:0% +don't i i'm getting some questions +coming in which is great um i will + + align:start position:0% +coming in which is great um i will + + + align:start position:0% +coming in which is great um i will +answer those questions but why don't i + + align:start position:0% +answer those questions but why don't i + + + align:start position:0% +answer those questions but why don't i +start off our uh + + align:start position:0% +start off our uh + + + align:start position:0% +start off our uh +break and then um + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% + + + + align:start position:0% + +there's a question about whether these + + align:start position:0% +there's a question about whether these + + + align:start position:0% +there's a question about whether these +this machine runs deterministically or + + align:start position:0% +this machine runs deterministically or + + + align:start position:0% +this machine runs deterministically or +not so which machine are we talking + + align:start position:0% +not so which machine are we talking + + + align:start position:0% +not so which machine are we talking +about + + align:start position:0% +about + + + align:start position:0% +about +so the branching programs themselves + + align:start position:0% +so the branching programs themselves + + + align:start position:0% +so the branching programs themselves +that they'd run deterministically you + + align:start position:0% +that they'd run deterministically you + + + align:start position:0% +that they'd run deterministically you +give them an assignment to the um to the + + align:start position:0% +give them an assignment to the um to the + + + align:start position:0% +give them an assignment to the um to the +input variables + + align:start position:0% +input variables + + + align:start position:0% +input variables +that's going to determine a path through + + align:start position:0% +that's going to determine a path through + + + align:start position:0% +that's going to determine a path through +each branching program + + align:start position:0% +each branching program + + + align:start position:0% +each branching program +which is eventually going to output a + + align:start position:0% +which is eventually going to output a + + + align:start position:0% +which is eventually going to output a +zero or a one + + align:start position:0% +zero or a one + + + align:start position:0% +zero or a one +and you want to know do those two + + align:start position:0% +and you want to know do those two + + + align:start position:0% +and you want to know do those two +branching programs always give the same + + align:start position:0% +branching programs always give the same + + + align:start position:0% +branching programs always give the same +value no matter what the input was + + align:start position:0% +value no matter what the input was + + + align:start position:0% +value no matter what the input was +but the branching programs themselves + + align:start position:0% +but the branching programs themselves + + + align:start position:0% +but the branching programs themselves +were deterministic + + align:start position:0% +were deterministic + + + align:start position:0% +were deterministic +um now the machine that's trying to + + align:start position:0% +um now the machine that's trying to + + + align:start position:0% +um now the machine that's trying to +make the determination of whether those + + align:start position:0% +make the determination of whether those + + + align:start position:0% +make the determination of whether those +two branching programs are equivalent + + align:start position:0% +two branching programs are equivalent + + + align:start position:0% +two branching programs are equivalent +that machine that we're going to be + + align:start position:0% +that machine that we're going to be + + + align:start position:0% +that machine that we're going to be +arguing is going to be a probabilistic + + align:start position:0% +arguing is going to be a probabilistic + + + align:start position:0% +arguing is going to be a probabilistic +machine so it's a kind of + + align:start position:0% +machine so it's a kind of + + + align:start position:0% +machine so it's a kind of +non-deterministic machine that's going + + align:start position:0% +non-deterministic machine that's going + + + align:start position:0% +non-deterministic machine that's going +to have different possible ways to go + + align:start position:0% +to have different possible ways to go + + + align:start position:0% +to have different possible ways to go +depending upon the outcome if it's of + + align:start position:0% +depending upon the outcome if it's of + + + align:start position:0% +depending upon the outcome if it's of +its coin tosses + + align:start position:0% +its coin tosses + + + align:start position:0% +its coin tosses +so it you can think of as + + align:start position:0% +so it you can think of as + + + align:start position:0% +so it you can think of as +non-determinist you know + + align:start position:0% +non-determinist you know + + + align:start position:0% +non-determinist you know +non-determinism in the ordinary sense + + align:start position:0% +non-determinism in the ordinary sense + + + align:start position:0% +non-determinism in the ordinary sense +about how like that it has a tree of + + align:start position:0% +about how like that it has a tree of + + + align:start position:0% +about how like that it has a tree of +possibilities + + align:start position:0% +possibilities + + + align:start position:0% +possibilities +but um now + + align:start position:0% +but um now + + + align:start position:0% +but um now +you know the way we're thinking about + + align:start position:0% +you know the way we're thinking about + + + align:start position:0% +you know the way we're thinking about +acceptance is different you know that + + align:start position:0% +acceptance is different you know that + + + align:start position:0% +acceptance is different you know that +instead of accepting if there's just one + + align:start position:0% +instead of accepting if there's just one + + + align:start position:0% +instead of accepting if there's just one +uh accept branch + + align:start position:0% +uh accept branch + + + align:start position:0% +uh accept branch +the machine for it to accept um has to + + align:start position:0% +the machine for it to accept um has to + + + align:start position:0% +the machine for it to accept um has to +have a majority of the branches be + + align:start position:0% +have a majority of the branches be + + + align:start position:0% +have a majority of the branches be +accepting um + + align:start position:0% +accepting um + + + align:start position:0% +accepting um +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +you know + + align:start position:0% +you know + + + align:start position:0% +you know +so it's it's + + align:start position:0% +so it's it's + + + align:start position:0% +so it's it's +there's some similarities but some + + align:start position:0% +there's some similarities but some + + + align:start position:0% +there's some similarities but some +differences with the usual way we think + + align:start position:0% +differences with the usual way we think + + + align:start position:0% +differences with the usual way we think +of non-determinism + + align:start position:0% +of non-determinism + + + align:start position:0% +of non-determinism +so what's the motivation behind + + align:start position:0% +so what's the motivation behind + + + align:start position:0% +so what's the motivation behind +introducing this type of turing machine + + align:start position:0% +introducing this type of turing machine + + + align:start position:0% +introducing this type of turing machine +well i mean there's a lot + + align:start position:0% + + + + align:start position:0% + +i guess there are two motivations + + align:start position:0% +i guess there are two motivations + + + align:start position:0% +i guess there are two motivations +uh + + align:start position:0% +uh + + + align:start position:0% +uh +probabilistic algorithms sometimes + + align:start position:0% +probabilistic algorithms sometimes + + + align:start position:0% +probabilistic algorithms sometimes +called monte carlo algorithms um + + align:start position:0% +called monte carlo algorithms um + + + align:start position:0% +called monte carlo algorithms um +uh turn out to be useful in practice for + + align:start position:0% +uh turn out to be useful in practice for + + + align:start position:0% +uh turn out to be useful in practice for +a variety of things + + align:start position:0% +a variety of things + + + align:start position:0% +a variety of things +and um + + align:start position:0% +and um + + + align:start position:0% +and um +so that led to + + align:start position:0% +so that led to + + + align:start position:0% +so that led to +um + + align:start position:0% +um + + + align:start position:0% +um +people to think about them in the + + align:start position:0% +people to think about them in the + + + align:start position:0% +people to think about them in the +context of complexity + + align:start position:0% +context of complexity + + + align:start position:0% +context of complexity +um they're related in some ways to + + align:start position:0% +um they're related in some ways to + + + align:start position:0% +um they're related in some ways to +quantum computers which are also + + align:start position:0% +quantum computers which are also + + + align:start position:0% +quantum computers which are also +probabilistic in in a somewhat different + + align:start position:0% +probabilistic in in a somewhat different + + + align:start position:0% +probabilistic in in a somewhat different +way um but they also have a very nice um + + align:start position:0% +way um but they also have a very nice um + + + align:start position:0% +way um but they also have a very nice um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +formulation in complexity theory + + align:start position:0% +formulation in complexity theory + + + align:start position:0% +formulation in complexity theory +so complexity theorists like to think + + align:start position:0% +so complexity theorists like to think + + + align:start position:0% +so complexity theorists like to think +about probabilistic computation because + + align:start position:0% +about probabilistic computation because + + + align:start position:0% +about probabilistic computation because +i mean you can do interesting things + + align:start position:0% +i mean you can do interesting things + + + align:start position:0% +i mean you can do interesting things +with probabilistic machines and the + + align:start position:0% +with probabilistic machines and the + + + align:start position:0% +with probabilistic machines and the +complexity classes associated are also + + align:start position:0% +complexity classes associated are also + + + align:start position:0% +complexity classes associated are also +interesting so as you'll see + + align:start position:0% +interesting so as you'll see + + + align:start position:0% +interesting so as you'll see +it leads us in an interesting direction + + align:start position:0% +it leads us in an interesting direction + + + align:start position:0% +it leads us in an interesting direction +uh to consider how to solve this problem + + align:start position:0% +uh to consider how to solve this problem + + + align:start position:0% +uh to consider how to solve this problem +this read once branching program problem + + align:start position:0% +this read once branching program problem + + + align:start position:0% +this read once branching program problem +equivalence + + align:start position:0% +equivalence + + + align:start position:0% +equivalence +with a probabilistic machine it's just + + align:start position:0% +with a probabilistic machine it's just + + + align:start position:0% +with a probabilistic machine it's just +just an interesting um algorithm that + + align:start position:0% +just an interesting um algorithm that + + + align:start position:0% +just an interesting um algorithm that +we're going to come up with + + align:start position:0% +we're going to come up with + + + align:start position:0% +we're going to come up with +um + + align:start position:0% + + + + align:start position:0% + +so in our pro in our proof attempt where + + align:start position:0% +so in our pro in our proof attempt where + + + align:start position:0% +so in our pro in our proof attempt where +did we use the probabilistic nature for + + align:start position:0% +did we use the probabilistic nature for + + + align:start position:0% +did we use the probabilistic nature for +bpp because we're running the two + + align:start position:0% +bpp because we're running the two + + + align:start position:0% +bpp because we're running the two +branching programs on a random input + + align:start position:0% +branching programs on a random input + + + align:start position:0% +branching programs on a random input +um + + align:start position:0% + + + + align:start position:0% + +i mean + + align:start position:0% +i mean + + + align:start position:0% +i mean +so you know you have your two branching + + align:start position:0% +so you know you have your two branching + + + align:start position:0% +so you know you have your two branching +programs you pick a random + + align:start position:0% +programs you pick a random + + + align:start position:0% +programs you pick a random +input to run those two branching + + align:start position:0% +input to run those two branching + + + align:start position:0% +input to run those two branching +programs and you see what they do + + align:start position:0% +programs and you see what they do + + + align:start position:0% +programs and you see what they do +that's where that's why it's + + align:start position:0% +that's where that's why it's + + + align:start position:0% +that's where that's why it's +probabilistic + + align:start position:0% +probabilistic + + + align:start position:0% +probabilistic +when you're thinking about random + + align:start position:0% +when you're thinking about random + + + align:start position:0% +when you're thinking about random +behavior of the machine + + align:start position:0% +behavior of the machine + + + align:start position:0% +behavior of the machine +it's a um that's a probabilistic machine + + align:start position:0% +it's a um that's a probabilistic machine + + + align:start position:0% +it's a um that's a probabilistic machine +so each branch of the machine + + align:start position:0% +so each branch of the machine + + + align:start position:0% +so each branch of the machine +is going to be like the way we normally + + align:start position:0% +is going to be like the way we normally + + + align:start position:0% +is going to be like the way we normally +think about non-determinism somebody's + + align:start position:0% +think about non-determinism somebody's + + + align:start position:0% +think about non-determinism somebody's +asking whether + + align:start position:0% +asking whether + + + align:start position:0% +asking whether +we think of the complexity of the + + align:start position:0% +we think of the complexity of the + + + align:start position:0% +we think of the complexity of the +machine in terms of all of the branches + + align:start position:0% +machine in terms of all of the branches + + + align:start position:0% +machine in terms of all of the branches +of the machine + + align:start position:0% +of the machine + + + align:start position:0% +of the machine +or + + align:start position:0% +or + + + align:start position:0% +or +um each branch separately it's we always + + align:start position:0% +um each branch separately it's we always + + + align:start position:0% +um each branch separately it's we always +think about for non-deterministic + + align:start position:0% +think about for non-deterministic + + + align:start position:0% +think about for non-deterministic +machines each branch separately + + align:start position:0% +machines each branch separately + + + align:start position:0% +machines each branch separately +um i'm not totally sure i understand the + + align:start position:0% +um i'm not totally sure i understand the + + + align:start position:0% +um i'm not totally sure i understand the +question there so are all the inputs + + align:start position:0% +question there so are all the inputs + + + align:start position:0% +question there so are all the inputs +built in and we randomly choose one + + align:start position:0% +built in and we randomly choose one + + + align:start position:0% +built in and we randomly choose one +through coin flips + + align:start position:0% +through coin flips + + + align:start position:0% +through coin flips +not sure i understand that question + + align:start position:0% +not sure i understand that question + + + align:start position:0% +not sure i understand that question +either we're given as input the two + + align:start position:0% +either we're given as input the two + + + align:start position:0% +either we're given as input the two +branching programs + + align:start position:0% +branching programs + + + align:start position:0% +branching programs +and then we flip coins you know kind of + + align:start position:0% +and then we flip coins you know kind of + + + align:start position:0% +and then we flip coins you know kind of +using our non-determinism + + align:start position:0% +using our non-determinism + + + align:start position:0% +using our non-determinism +you can think about it equivalent in + + align:start position:0% +you can think about it equivalent in + + + align:start position:0% +you can think about it equivalent in +terms of coin flips to choose the values + + align:start position:0% +terms of coin flips to choose the values + + + align:start position:0% +terms of coin flips to choose the values +of the variables so now we have a set of + + align:start position:0% +of the variables so now we have a set of + + + align:start position:0% +of the variables so now we have a set of +variable + + align:start position:0% +variable + + + align:start position:0% +variable +inputs to the + + align:start position:0% +inputs to the + + + align:start position:0% +inputs to the +values of the variables + + align:start position:0% +values of the variables + + + align:start position:0% +values of the variables +and we use that to + + align:start position:0% +and we use that to + + + align:start position:0% +and we use that to +um as input to the branching programs to + + align:start position:0% +um as input to the branching programs to + + + align:start position:0% +um as input to the branching programs to +see what whether they + + align:start position:0% +see what whether they + + + align:start position:0% +see what whether they +to see what answers they give and we in + + align:start position:0% +to see what answers they give and we in + + + align:start position:0% +to see what answers they give and we in +particular whether they give the same + + align:start position:0% +particular whether they give the same + + + align:start position:0% +particular whether they give the same +answer on that randomly chosen uh input + + align:start position:0% +answer on that randomly chosen uh input + + + align:start position:0% +answer on that randomly chosen uh input +let's move on um + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so now sort of moving us toward + + align:start position:0% +so now sort of moving us toward + + + align:start position:0% +so now sort of moving us toward +um + + align:start position:0% +um + + + align:start position:0% +um +the actual bpp algorithm for uh + + align:start position:0% +the actual bpp algorithm for uh + + + align:start position:0% +the actual bpp algorithm for uh +um read once branching program + + align:start position:0% +um read once branching program + + + align:start position:0% +um read once branching program +equivalence + + align:start position:0% +equivalence + + + align:start position:0% +equivalence +testing um + + align:start position:0% +testing um + + + align:start position:0% +testing um +we have to think about + + align:start position:0% +we have to think about + + + align:start position:0% +we have to think about +a different way + + align:start position:0% +a different way + + + align:start position:0% +a different way +to + + align:start position:0% +to + + + align:start position:0% +to +um + + align:start position:0% + + + + align:start position:0% + +we need an alternate way of thinking + + align:start position:0% +we need an alternate way of thinking + + + align:start position:0% +we need an alternate way of thinking +about + + align:start position:0% +about + + + align:start position:0% +about +the computation of a branching program + + align:start position:0% +the computation of a branching program + + + align:start position:0% +the computation of a branching program +it's going to look very similar but it's + + align:start position:0% +it's going to look very similar but it's + + + align:start position:0% +it's going to look very similar but it's +going to lead us in a direction that's + + align:start position:0% +going to lead us in a direction that's + + + align:start position:0% +going to lead us in a direction that's +going to allow us to talk about this + + align:start position:0% +going to allow us to talk about this + + + align:start position:0% +going to allow us to talk about this +um these non-boolean inputs that i refer + + align:start position:0% +um these non-boolean inputs that i refer + + + align:start position:0% +um these non-boolean inputs that i refer +to um just kind of where we're going + + align:start position:0% +to um just kind of where we're going + + + align:start position:0% +to um just kind of where we're going +we're going to be simulating branching + + align:start position:0% +we're going to be simulating branching + + + align:start position:0% +we're going to be simulating branching +programs with polynomials + + align:start position:0% +programs with polynomials + + + align:start position:0% +programs with polynomials +if that helps you sort of as an + + align:start position:0% +if that helps you sort of as an + + + align:start position:0% +if that helps you sort of as an +overarching plan but we'll we'll get + + align:start position:0% +overarching plan but we'll we'll get + + + align:start position:0% +overarching plan but we'll we'll get +there a little slowly + + align:start position:0% +there a little slowly + + + align:start position:0% +there a little slowly +so okay here's a branching program + + align:start position:0% +so okay here's a branching program + + + align:start position:0% +so okay here's a branching program +read once branching program um we're not + + align:start position:0% +read once branching program um we're not + + + align:start position:0% +read once branching program um we're not +going to use the read once feature uh + + align:start position:0% +going to use the read once feature uh + + + align:start position:0% +going to use the read once feature uh +just yet but we'll that'll come later + + align:start position:0% +just yet but we'll that'll come later + + + align:start position:0% +just yet but we'll that'll come later +but anyway here's a branching program + + align:start position:0% +but anyway here's a branching program + + + align:start position:0% +but anyway here's a branching program +um + + align:start position:0% + + + + align:start position:0% + +and um + + align:start position:0% +and um + + + align:start position:0% +and um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +oh here's my branch and i + + align:start position:0% +oh here's my branch and i + + + align:start position:0% +oh here's my branch and i +put crashed here + + align:start position:0% +put crashed here + + + align:start position:0% +put crashed here +start that again + + align:start position:0% +start that again + + + align:start position:0% +start that again +um + + align:start position:0% + + + + align:start position:0% + +okay so we take an input + + align:start position:0% +okay so we take an input + + + align:start position:0% +okay so we take an input +um whatever it is um + + align:start position:0% +um whatever it is um + + + align:start position:0% +um whatever it is um +and + + align:start position:0% +and + + + align:start position:0% +and +thinking about the computation of the + + align:start position:0% +thinking about the computation of the + + + align:start position:0% +thinking about the computation of the +branching process so we're not thinking + + align:start position:0% +branching process so we're not thinking + + + align:start position:0% +branching process so we're not thinking +about the algorithm right now we're just + + align:start position:0% +about the algorithm right now we're just + + + align:start position:0% +about the algorithm right now we're just +thinking about branching programs for + + align:start position:0% +thinking about branching programs for + + + align:start position:0% +thinking about branching programs for +the minute we're going to get back to + + align:start position:0% +the minute we're going to get back to + + + align:start position:0% +the minute we're going to get back to +the algorithm later + + align:start position:0% +the algorithm later + + + align:start position:0% +the algorithm later +so the branching program follows a path + + align:start position:0% +so the branching program follows a path + + + align:start position:0% +so the branching program follows a path +as i indicated when you have a + + align:start position:0% +as i indicated when you have a + + + align:start position:0% +as i indicated when you have a +particular input your x1 is 0 + + align:start position:0% +particular input your x1 is 0 + + + align:start position:0% +particular input your x1 is 0 +x2 is 1 + + align:start position:0% +x2 is 1 + + + align:start position:0% +x2 is 1 +x3 is 1 so the output is going to be 1 + + align:start position:0% +x3 is 1 so the output is going to be 1 + + + align:start position:0% +x3 is 1 so the output is going to be 1 +in this case + + align:start position:0% +in this case + + + align:start position:0% +in this case +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +the way i want to think about this a + + align:start position:0% +the way i want to think about this a + + + align:start position:0% +the way i want to think about this a +little differently + + align:start position:0% +little differently + + + align:start position:0% +little differently +is i want to label all of the nodes and + + align:start position:0% +is i want to label all of the nodes and + + + align:start position:0% +is i want to label all of the nodes and +all of the edges + + align:start position:0% +all of the edges + + + align:start position:0% +all of the edges +uh with a value + + align:start position:0% +uh with a value + + + align:start position:0% +uh with a value +that tells me whether or not this yellow + + align:start position:0% +that tells me whether or not this yellow + + + align:start position:0% +that tells me whether or not this yellow +path went through that node or edge + + align:start position:0% +path went through that node or edge + + + align:start position:0% +path went through that node or edge +it's going to be just a + + align:start position:0% +it's going to be just a + + + align:start position:0% +it's going to be just a +doing the same but + + align:start position:0% +doing the same but + + + align:start position:0% +doing the same but +you may think this is no difference at + + align:start position:0% +you may think this is no difference at + + + align:start position:0% +you may think this is no difference at +all but i want to label all the all of + + align:start position:0% +all but i want to label all the all of + + + align:start position:0% +all but i want to label all the all of +the things on the yellow path + + align:start position:0% +the things on the yellow path + + + align:start position:0% +the things on the yellow path +i'm going to label them or the one + + align:start position:0% +i'm going to label them or the one + + + align:start position:0% +i'm going to label them or the one +and all of the things that are not on + + align:start position:0% +and all of the things that are not on + + + align:start position:0% +and all of the things that are not on +the yellow path + + align:start position:0% +the yellow path + + + align:start position:0% +the yellow path +i'm going to label with a zero + + align:start position:0% +i'm going to label with a zero + + + align:start position:0% +i'm going to label with a zero +so i'm keeping those trying to keep + + align:start position:0% +so i'm keeping those trying to keep + + + align:start position:0% +so i'm keeping those trying to keep +those labels apart from the original + + align:start position:0% +those labels apart from the original + + + align:start position:0% +those labels apart from the original +branching program + + align:start position:0% +branching program + + + align:start position:0% +branching program +which are written in white these labels + + align:start position:0% +which are written in white these labels + + + align:start position:0% +which are written in white these labels +are written yellow + + align:start position:0% +are written yellow + + + align:start position:0% +are written yellow +but these labels have to do with the + + align:start position:0% +but these labels have to do with the + + + align:start position:0% +but these labels have to do with the +execution of the branching program on an + + align:start position:0% +execution of the branching program on an + + + align:start position:0% +execution of the branching program on an +input + + align:start position:0% +input + + + align:start position:0% +input +so once i have an input that's going to + + align:start position:0% +so once i have an input that's going to + + + align:start position:0% +so once i have an input that's going to +determine a one or a zero + + align:start position:0% +determine a one or a zero + + + align:start position:0% +determine a one or a zero +label + + align:start position:0% +label + + + align:start position:0% +label +for every node and edge + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +if we want to look at the output from + + align:start position:0% +if we want to look at the output from + + + align:start position:0% +if we want to look at the output from +this branching program after we have + + align:start position:0% +this branching program after we have + + + align:start position:0% +this branching program after we have +that labeling we only have to look at + + align:start position:0% +that labeling we only have to look at + + + align:start position:0% +that labeling we only have to look at +the label of the one output node because + + align:start position:0% +the label of the one output node because + + + align:start position:0% +the label of the one output node because +that's if that one has a one on it that + + align:start position:0% +that's if that one has a one on it that + + + align:start position:0% +that's if that one has a one on it that +means that the path went through that + + align:start position:0% +means that the path went through that + + + align:start position:0% +means that the path went through that +one and so therefore we should output + + align:start position:0% +one and so therefore we should output + + + align:start position:0% +one and so therefore we should output +output output uh the output is one + + align:start position:0% +output output uh the output is one + + + align:start position:0% +output output uh the output is one +um + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so + + align:start position:0% +so + + + align:start position:0% +so +i'm going to give you another way of + + align:start position:0% +i'm going to give you another way of + + + align:start position:0% +i'm going to give you another way of +assigning that instead of just coming + + align:start position:0% +assigning that instead of just coming + + + align:start position:0% +assigning that instead of just coming +finding the path first and then coming + + align:start position:0% +finding the path first and then coming + + + align:start position:0% +finding the path first and then coming +up with the labeling afterward i'm going + + align:start position:0% +up with the labeling afterward i'm going + + + align:start position:0% +up with the labeling afterward i'm going +to give you a different way of coming up + + align:start position:0% +to give you a different way of coming up + + + align:start position:0% +to give you a different way of coming up +with that labeling kind of building it + + align:start position:0% +with that labeling kind of building it + + + align:start position:0% +with that labeling kind of building it +up inductively starting at the start + + align:start position:0% +up inductively starting at the start + + + align:start position:0% +up inductively starting at the start +node and building up that labeling + + align:start position:0% +node and building up that labeling + + + align:start position:0% +node and building up that labeling +you'll see what i mean + + align:start position:0% +you'll see what i mean + + + align:start position:0% +you'll see what i mean +by my example + + align:start position:0% +by my example + + + align:start position:0% +by my example +so if i have a label on this node + + align:start position:0% +so if i have a label on this node + + + align:start position:0% +so if i have a label on this node +so i already know + + align:start position:0% +so i already know + + + align:start position:0% +so i already know +whether or not the path went through + + align:start position:0% +whether or not the path went through + + + align:start position:0% +whether or not the path went through +that node + + align:start position:0% +that node + + + align:start position:0% +that node +you know label 1 means the path went + + align:start position:0% +you know label 1 means the path went + + + align:start position:0% +you know label 1 means the path went +through it label 0 means the path + + align:start position:0% +through it label 0 means the path + + + align:start position:0% +through it label 0 means the path +doesn't it does not go through it + + align:start position:0% +doesn't it does not go through it + + + align:start position:0% +doesn't it does not go through it +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +that's going to tell me how to label the + + align:start position:0% +that's going to tell me how to label the + + + align:start position:0% +that's going to tell me how to label the +two outgoing edges + + align:start position:0% +two outgoing edges + + + align:start position:0% +two outgoing edges +so if i'm if i've already labeled this + + align:start position:0% +so if i'm if i've already labeled this + + + align:start position:0% +so if i'm if i've already labeled this +with a where a is a zero or one then + + align:start position:0% +with a where a is a zero or one then + + + align:start position:0% +with a where a is a zero or one then +uh + + align:start position:0% +uh + + + align:start position:0% +uh +what what expression should i use + + align:start position:0% +what what expression should i use + + + align:start position:0% +what what expression should i use +um + + align:start position:0% +um + + + align:start position:0% +um +to how do + + align:start position:0% +to how do + + + align:start position:0% +to how do +under what circumstances will i label + + align:start position:0% +under what circumstances will i label + + + align:start position:0% +under what circumstances will i label +what's what's the right label for this + + align:start position:0% +what's what's the right label for this + + + align:start position:0% +what's what's the right label for this +one outgoing edge here + + align:start position:0% +one outgoing edge here + + + align:start position:0% +one outgoing edge here +well if a is zero + + align:start position:0% +well if a is zero + + + align:start position:0% +well if a is zero +that means the pair we know the path did + + align:start position:0% +that means the pair we know the path did + + + align:start position:0% +that means the pair we know the path did +not go through this node so there's no + + align:start position:0% +not go through this node so there's no + + + align:start position:0% +not go through this node so there's no +way it could go through that edge + + align:start position:0% +way it could go through that edge + + + align:start position:0% +way it could go through that edge +similarly + + align:start position:0% +similarly + + + align:start position:0% +similarly +if x i + + align:start position:0% +if x i + + + align:start position:0% +if x i +is a zero + + align:start position:0% +is a zero + + + align:start position:0% +is a zero +that means even if we did go through + + align:start position:0% +that means even if we did go through + + + align:start position:0% +that means even if we did go through +that node + + align:start position:0% +that node + + + align:start position:0% +that node +the path would go through the other edge + + align:start position:0% +the path would go through the other edge + + + align:start position:0% +the path would go through the other edge +other outgoing edge and not to this one + + align:start position:0% +other outgoing edge and not to this one + + + align:start position:0% +other outgoing edge and not to this one +so that tells us that the boolean + + align:start position:0% +so that tells us that the boolean + + + align:start position:0% +so that tells us that the boolean +expression which describes the value the + + align:start position:0% +expression which describes the value the + + + align:start position:0% +expression which describes the value the +label of this uh node in the execution + + align:start position:0% +label of this uh node in the execution + + + align:start position:0% +label of this uh node in the execution +is going to be the and + + align:start position:0% +is going to be the and + + + align:start position:0% +is going to be the and +of the + + align:start position:0% +of the + + + align:start position:0% +of the +the value on the node and the um the + + align:start position:0% +the value on the node and the um the + + + align:start position:0% +the value on the node and the um the +query variable of that node + + align:start position:0% +query variable of that node + + + align:start position:0% +query variable of that node +now + + align:start position:0% +now + + + align:start position:0% +now +think about what's the right way to + + align:start position:0% +think about what's the right way to + + + align:start position:0% +think about what's the right way to +label the other edge + + align:start position:0% +label the other edge + + + align:start position:0% +label the other edge +the the execution value of the other + + align:start position:0% +the the execution value of the other + + + align:start position:0% +the the execution value of the other +edge + + align:start position:0% +edge + + + align:start position:0% +edge +again you have to have go through this + + align:start position:0% +again you have to have go through this + + + align:start position:0% +again you have to have go through this +node so a has to be one but now you want + + align:start position:0% +node so a has to be one but now you want + + + align:start position:0% +node so a has to be one but now you want +x i to be 0 in order to go through that + + align:start position:0% +x i to be 0 in order to go through that + + + align:start position:0% +x i to be 0 in order to go through that +edge so that means it's going to be a + + align:start position:0% +edge so that means it's going to be a + + + align:start position:0% +edge so that means it's going to be a +and the complement of x i + + align:start position:0% + + + + align:start position:0% + +okay so this is going to just tell me + + align:start position:0% +okay so this is going to just tell me + + + align:start position:0% +okay so this is going to just tell me +this i'm writing a formula for how we're + + align:start position:0% +this i'm writing a formula for how we're + + + align:start position:0% +this i'm writing a formula for how we're +labeling these uh these edges + + align:start position:0% +labeling these uh these edges + + + align:start position:0% +labeling these uh these edges +based on the label of the of the parent + + align:start position:0% +based on the label of the of the parent + + + align:start position:0% +based on the label of the of the parent +node + + align:start position:0% +node + + + align:start position:0% +node +similarly if i have a bunch of edges + + align:start position:0% +similarly if i have a bunch of edges + + + align:start position:0% +similarly if i have a bunch of edges +where i already know the values the + + align:start position:0% +where i already know the values the + + + align:start position:0% +where i already know the values the +labels uh the execution levels there + + align:start position:0% +labels uh the execution levels there + + + align:start position:0% +labels uh the execution levels there +let's say so i have a1 a2 and a3 what is + + align:start position:0% +let's say so i have a1 a2 and a3 what is + + + align:start position:0% +let's say so i have a1 a2 and a3 what is +the right label to put on this node + + align:start position:0% +the right label to put on this node + + + align:start position:0% +the right label to put on this node +um + + align:start position:0% +um + + + align:start position:0% +um +well if any one of those is a one + + align:start position:0% +well if any one of those is a one + + + align:start position:0% +well if any one of those is a one +that means the path went through that + + align:start position:0% +that means the path went through that + + + align:start position:0% +that means the path went through that +edge and so therefore it's going to go + + align:start position:0% +edge and so therefore it's going to go + + + align:start position:0% +edge and so therefore it's going to go +through that node + + align:start position:0% +through that node + + + align:start position:0% +through that node +so that tells us that the label to put + + align:start position:0% +so that tells us that the label to put + + + align:start position:0% +so that tells us that the label to put +on that node is the or + + align:start position:0% +on that node is the or + + + align:start position:0% +on that node is the or +of the labels on the incoming edges + + align:start position:0% +of the labels on the incoming edges + + + align:start position:0% +of the labels on the incoming edges +okay + + align:start position:0% +okay + + + align:start position:0% +okay +questions on this + + align:start position:0% + + + + align:start position:0% + +so now this is kind of setting the stage + + align:start position:0% +so now this is kind of setting the stage + + + align:start position:0% +so now this is kind of setting the stage +for + + align:start position:0% +for + + + align:start position:0% +for +starting to think about this + + align:start position:0% +starting to think about this + + + align:start position:0% +starting to think about this +um + + align:start position:0% +um + + + align:start position:0% +um +more toward polynomials instead instead + + align:start position:0% +more toward polynomials instead instead + + + align:start position:0% +more toward polynomials instead instead +of using a boolean algebra + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% +so um + + + align:start position:0% +so um +quite i'm getting question how do we + + align:start position:0% +quite i'm getting question how do we + + + align:start position:0% +quite i'm getting question how do we +know what the execution path is which + + align:start position:0% +know what the execution path is which + + + align:start position:0% +know what the execution path is which +nodes to label we're going to be + + align:start position:0% +nodes to label we're going to be + + + align:start position:0% +nodes to label we're going to be +labeling all of the nodes + + align:start position:0% +labeling all of the nodes + + + align:start position:0% +labeling all of the nodes +so we start off with labeling the uh + + align:start position:0% +so we start off with labeling the uh + + + align:start position:0% +so we start off with labeling the uh +did i say that here we should we start + + align:start position:0% +did i say that here we should we start + + + align:start position:0% +did i say that here we should we start +up i didn't say but i should have we + + align:start position:0% +up i didn't say but i should have we + + + align:start position:0% +up i didn't say but i should have we +label the the start node with one that + + align:start position:0% +label the the start node with one that + + + align:start position:0% +label the the start node with one that +because the path always goes through the + + align:start position:0% +because the path always goes through the + + + align:start position:0% +because the path always goes through the +start node so without even talking about + + align:start position:0% +start node so without even talking about + + + align:start position:0% +start node so without even talking about +a path we just label the start node 1. + + align:start position:0% +a path we just label the start node 1. + + + align:start position:0% +a path we just label the start node 1. +maybe we'll do an example of this also + + align:start position:0% +maybe we'll do an example of this also + + + align:start position:0% +maybe we'll do an example of this also +but + + align:start position:0% +but + + + align:start position:0% +but +now once we label this star this node 1 + + align:start position:0% +now once we label this star this node 1 + + + align:start position:0% +now once we label this star this node 1 +we have an expression + + align:start position:0% +we have an expression + + + align:start position:0% +we have an expression +that tells us + + align:start position:0% +that tells us + + + align:start position:0% +that tells us +how to label the two outgoing um the two + + align:start position:0% +how to label the two outgoing um the two + + + align:start position:0% +how to label the two outgoing um the two +outgoing edges this edge and that edge + + align:start position:0% +outgoing edges this edge and that edge + + + align:start position:0% +outgoing edges this edge and that edge +um + + align:start position:0% +um + + + align:start position:0% +um +and i'm doing it without + + align:start position:0% +and i'm doing it without + + + align:start position:0% +and i'm doing it without +knowing the values of the variables i'm + + align:start position:0% +knowing the values of the variables i'm + + + align:start position:0% +knowing the values of the variables i'm +doing it kind of i'm just making an + + align:start position:0% +doing it kind of i'm just making an + + + align:start position:0% +doing it kind of i'm just making an +expression uh which is going to describe + + align:start position:0% +expression uh which is going to describe + + + align:start position:0% +expression uh which is going to describe +what those labels would be + + align:start position:0% +what those labels would be + + + align:start position:0% +what those labels would be +once you tell me what the input + + align:start position:0% +once you tell me what the input + + + align:start position:0% +once you tell me what the input +assignment is + + align:start position:0% + + + + align:start position:0% + +okay so i'm just sort of it's almost + + align:start position:0% +okay so i'm just sort of it's almost + + + align:start position:0% +okay so i'm just sort of it's almost +like a symbolic execution here i'm just + + align:start position:0% +like a symbolic execution here i'm just + + + align:start position:0% +like a symbolic execution here i'm just +writing down the different expressions + + align:start position:0% +writing down the different expressions + + + align:start position:0% +writing down the different expressions +for how to calculate what these things + + align:start position:0% +for how to calculate what these things + + + align:start position:0% +for how to calculate what these things +should be + + align:start position:0% +should be + + + align:start position:0% +should be +um + + align:start position:0% +um + + + align:start position:0% +um +let's + + align:start position:0% +let's + + + align:start position:0% +let's +let me um + + align:start position:0% +let me um + + + align:start position:0% +let me um +maybe this will become clearer as we + + align:start position:0% +maybe this will become clearer as we + + + align:start position:0% +maybe this will become clearer as we +continue + + align:start position:0% +continue + + + align:start position:0% +continue +so the poll now this is the big idea of + + align:start position:0% +so the poll now this is the big idea of + + + align:start position:0% +so the poll now this is the big idea of +this proof um + + align:start position:0% +this proof um + + + align:start position:0% +this proof um +we're going to use something called + + align:start position:0% +we're going to use something called + + + align:start position:0% +we're going to use something called +arithmetization + + align:start position:0% +arithmetization + + + align:start position:0% +arithmetization +we're going to convert from thinking + + align:start position:0% +we're going to convert from thinking + + + align:start position:0% +we're going to convert from thinking +about things in the boolean world to + + align:start position:0% +about things in the boolean world to + + + align:start position:0% +about things in the boolean world to +thinking about things in the + + align:start position:0% +thinking about things in the + + + align:start position:0% +thinking about things in the +arithmetical world where we you have + + align:start position:0% +arithmetical world where we you have + + + align:start position:0% +arithmetical world where we you have +arithmetic + + align:start position:0% +arithmetic + + + align:start position:0% +arithmetic +over integers let's say for now um + + align:start position:0% +over integers let's say for now um + + + align:start position:0% +over integers let's say for now um +so instead of ands and ors we're going + + align:start position:0% +so instead of ands and ors we're going + + + align:start position:0% +so instead of ands and ors we're going +to be talking about pluses and times + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +we're going to the way we're going to + + align:start position:0% +we're going to the way we're going to + + + align:start position:0% +we're going to the way we're going to +make the bridge + + align:start position:0% +make the bridge + + + align:start position:0% +make the bridge +is bishop by showing how to simulate the + + align:start position:0% +is bishop by showing how to simulate the + + + align:start position:0% +is bishop by showing how to simulate the +ands and ors + + align:start position:0% +ands and ors + + + align:start position:0% +ands and ors +the hand and or operations with the plus + + align:start position:0% +the hand and or operations with the plus + + + align:start position:0% +the hand and or operations with the plus +and times operations + + align:start position:0% +and times operations + + + align:start position:0% +and times operations +um + + align:start position:0% +um + + + align:start position:0% +um +so um + + align:start position:0% +so um + + + align:start position:0% +so um +assuming + + align:start position:0% +assuming + + + align:start position:0% +assuming +one means true and zero means false + + align:start position:0% + + + + align:start position:0% + +if you have + + align:start position:0% +if you have + + + align:start position:0% +if you have +the expression a and b + + align:start position:0% +the expression a and b + + + align:start position:0% +the expression a and b +as a boolean expression + + align:start position:0% +as a boolean expression + + + align:start position:0% +as a boolean expression +we can represent that as a times b + + align:start position:0% +we can represent that as a times b + + + align:start position:0% +we can represent that as a times b +using arithmetic + + align:start position:0% +using arithmetic + + + align:start position:0% +using arithmetic +because + + align:start position:0% + + + + align:start position:0% + +um it has it computes exactly the same + + align:start position:0% +um it has it computes exactly the same + + + align:start position:0% +um it has it computes exactly the same +value + + align:start position:0% +value + + + align:start position:0% +value +when we have um + + align:start position:0% +when we have um + + + align:start position:0% +when we have um +the boolean + + align:start position:0% +the boolean + + + align:start position:0% +the boolean +representation of true and false uh + + align:start position:0% +representation of true and false uh + + + align:start position:0% +representation of true and false uh +being one and zero + + align:start position:0% +being one and zero + + + align:start position:0% +being one and zero +so you know + + align:start position:0% +so you know + + + align:start position:0% +so you know +one and one + + align:start position:0% +one and one + + + align:start position:0% +one and one +is one + + align:start position:0% +is one + + + align:start position:0% +is one +and one times one is one + + align:start position:0% +and one times one is one + + + align:start position:0% +and one times one is one +and anything else you know one and zero + + align:start position:0% +and anything else you know one and zero + + + align:start position:0% +and anything else you know one and zero +zero and one zero and zero + + align:start position:0% +zero and one zero and zero + + + align:start position:0% +zero and one zero and zero +if you if you applied the times operator + + align:start position:0% +if you if you applied the times operator + + + align:start position:0% +if you if you applied the times operator +you're going to get the same value so + + align:start position:0% +you're going to get the same value so + + + align:start position:0% +you're going to get the same value so +times is very much like and in this + + align:start position:0% +times is very much like and in this + + + align:start position:0% +times is very much like and in this +sense + + align:start position:0% +sense + + + align:start position:0% +sense +okay we're going to write it as just a b + + align:start position:0% +okay we're going to write it as just a b + + + align:start position:0% +okay we're going to write it as just a b +usually without the time symbol + + align:start position:0% + + + + align:start position:0% + +so if we have a complement + + align:start position:0% +so if we have a complement + + + align:start position:0% +so if we have a complement +how would we simulate that + + align:start position:0% +how would we simulate that + + + align:start position:0% +how would we simulate that +with arithmetic + + align:start position:0% +with arithmetic + + + align:start position:0% +with arithmetic +well + + align:start position:0% +well + + + align:start position:0% +well +again + + align:start position:0% +again + + + align:start position:0% +again +here we're just flipping one and zero + + align:start position:0% + + + + align:start position:0% + +in using the complement operation that's + + align:start position:0% +in using the complement operation that's + + + align:start position:0% +in using the complement operation that's +going to be the same as subtracting the + + align:start position:0% +going to be the same as subtracting the + + + align:start position:0% +going to be the same as subtracting the +value from one that also flips it from + + align:start position:0% +value from one that also flips it from + + + align:start position:0% +value from one that also flips it from +uh + + align:start position:0% +uh + + + align:start position:0% +uh +between one and zero + + align:start position:0% +between one and zero + + + align:start position:0% +between one and zero +um how about or if you have a or b + + align:start position:0% +um how about or if you have a or b + + + align:start position:0% +um how about or if you have a or b +well um + + align:start position:0% +well um + + + align:start position:0% +well um +it's slightly more complicated + + align:start position:0% +it's slightly more complicated + + + align:start position:0% +it's slightly more complicated +because you use a plus b + + align:start position:0% +because you use a plus b + + + align:start position:0% +because you use a plus b +um + + align:start position:0% +um + + + align:start position:0% +um +but + + align:start position:0% +but + + + align:start position:0% +but +you have to subtract off the product + + align:start position:0% +you have to subtract off the product + + + align:start position:0% +you have to subtract off the product +because + + align:start position:0% +because + + + align:start position:0% +because +what you want is this this + + align:start position:0% +what you want is this this + + + align:start position:0% +what you want is this this +simulation should be + + align:start position:0% +simulation should be + + + align:start position:0% +simulation should be +give you exactly the same value so what + + align:start position:0% +give you exactly the same value so what + + + align:start position:0% +give you exactly the same value so what +if you have one or one + + align:start position:0% +if you have one or one + + + align:start position:0% +if you have one or one +you want that to be a one a one answer + + align:start position:0% +you want that to be a one a one answer + + + align:start position:0% +you want that to be a one a one answer +you don't want it to be a two + + align:start position:0% +you don't want it to be a two + + + align:start position:0% +you don't want it to be a two +so you have to subtract off the product + + align:start position:0% +so you have to subtract off the product + + + align:start position:0% +so you have to subtract off the product +um + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and the goal is is to have a faithful + + align:start position:0% +and the goal is is to have a faithful + + + align:start position:0% +and the goal is is to have a faithful +simulation + + align:start position:0% +simulation + + + align:start position:0% +simulation +of the and and or by using plus and + + align:start position:0% +of the and and or by using plus and + + + align:start position:0% +of the and and or by using plus and +times so you get exactly the same + + align:start position:0% +times so you get exactly the same + + + align:start position:0% +times so you get exactly the same +answers out + + align:start position:0% +answers out + + + align:start position:0% +answers out +when you put in boolean values here + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um + + align:start position:0% +um + + + align:start position:0% +um +just to say where we're going + + align:start position:0% +just to say where we're going + + + align:start position:0% +just to say where we're going +what this is going to + + align:start position:0% +what this is going to + + + align:start position:0% +what this is going to +um + + align:start position:0% +um + + + align:start position:0% +um +you know it sounds it's superficially we + + align:start position:0% +you know it sounds it's superficially we + + + align:start position:0% +you know it sounds it's superficially we +haven't really done anything + + align:start position:0% +haven't really done anything + + + align:start position:0% +haven't really done anything +um + + align:start position:0% +um + + + align:start position:0% +um +this is + + align:start position:0% +this is + + + align:start position:0% +this is +but um + + align:start position:0% +but um + + + align:start position:0% +but um +what this is going to enable us to do is + + align:start position:0% +what this is going to enable us to do is + + + align:start position:0% +what this is going to enable us to do is +plug in values which are not boolean + + align:start position:0% +plug in values which are not boolean + + + align:start position:0% +plug in values which are not boolean +because you know it doesn't make sense + + align:start position:0% +because you know it doesn't make sense + + + align:start position:0% +because you know it doesn't make sense +to talk about it makes sense to talk + + align:start position:0% +to talk about it makes sense to talk + + + align:start position:0% +to talk about it makes sense to talk +about one and zero but it doesn't make + + align:start position:0% +about one and zero but it doesn't make + + + align:start position:0% +about one and zero but it doesn't make +sense to talk about two and three + + align:start position:0% +sense to talk about two and three + + + align:start position:0% +sense to talk about two and three +but it does talk it makes sense to talk + + align:start position:0% +but it does talk it makes sense to talk + + + align:start position:0% +but it does talk it makes sense to talk +about two times three + + align:start position:0% +about two times three + + + align:start position:0% +about two times three +and that's going to be + + align:start position:0% +and that's going to be + + + align:start position:0% +and that's going to be +a useful + + align:start position:0% +a useful + + + align:start position:0% +a useful +um okay so let's just see + + align:start position:0% +um okay so let's just see + + + align:start position:0% +um okay so let's just see +um + + align:start position:0% + + + + align:start position:0% + +remember + + align:start position:0% +remember + + + align:start position:0% +remember +that that + + align:start position:0% +that that + + + align:start position:0% +that that +that um + + align:start position:0% +that um + + + align:start position:0% +that um +that inductive labeling procedure that i + + align:start position:0% +that inductive labeling procedure that i + + + align:start position:0% +that inductive labeling procedure that i +described before + + align:start position:0% +described before + + + align:start position:0% +described before +um where i labeled gave the execution + + align:start position:0% +um where i labeled gave the execution + + + align:start position:0% +um where i labeled gave the execution +labels on the edges + + align:start position:0% +labels on the edges + + + align:start position:0% +labels on the edges +depending upon the label of the parent + + align:start position:0% +depending upon the label of the parent + + + align:start position:0% +depending upon the label of the parent +node and which node which variable is + + align:start position:0% +node and which node which variable is + + + align:start position:0% +node and which node which variable is +being queried um so + + align:start position:0% +being queried um so + + + align:start position:0% +being queried um so +if i know that this value is an a but + + align:start position:0% +if i know that this value is an a but + + + align:start position:0% +if i know that this value is an a but +now the + + align:start position:0% +now the + + + align:start position:0% +now the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so i'm just going to write this down + + align:start position:0% +so i'm just going to write this down + + + align:start position:0% +so i'm just going to write this down +using uh arithmetic instead of using + + align:start position:0% +using uh arithmetic instead of using + + + align:start position:0% +using uh arithmetic instead of using +boolean uh + + align:start position:0% +boolean uh + + + align:start position:0% +boolean uh +operations + + align:start position:0% +operations + + + align:start position:0% +operations +uh so before we have this was a an a and + + align:start position:0% +uh so before we have this was a an a and + + + align:start position:0% +uh so before we have this was a an a and +x i if you remember from the previous + + align:start position:0% +x i if you remember from the previous + + + align:start position:0% +x i if you remember from the previous +slide + + align:start position:0% +slide + + + align:start position:0% +slide +um now what are we going to use instead + + align:start position:0% +um now what are we going to use instead + + + align:start position:0% +um now what are we going to use instead +because we're going to use this + + align:start position:0% +because we're going to use this + + + align:start position:0% +because we're going to use this +conversion here instead of and we're + + align:start position:0% +conversion here instead of and we're + + + align:start position:0% +conversion here instead of and we're +going to use multiplication + + align:start position:0% +going to use multiplication + + + align:start position:0% +going to use multiplication +that's just a times x i + + align:start position:0% +that's just a times x i + + + align:start position:0% +that's just a times x i +what about on this side + + align:start position:0% +what about on this side + + + align:start position:0% +what about on this side +here was + + align:start position:0% +here was + + + align:start position:0% +here was +a and the complement of x i + + align:start position:0% +a and the complement of x i + + + align:start position:0% +a and the complement of x i +now the complement of x i is one minus x + + align:start position:0% +now the complement of x i is one minus x + + + align:start position:0% +now the complement of x i is one minus x +i + + align:start position:0% +i + + + align:start position:0% +i +in the uh arithmetically so this becomes + + align:start position:0% +in the uh arithmetically so this becomes + + + align:start position:0% +in the uh arithmetically so this becomes +a times one minus x i + + align:start position:0% +a times one minus x i + + + align:start position:0% +a times one minus x i +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +similarly + + align:start position:0% +similarly + + + align:start position:0% +similarly +here + + align:start position:0% +here + + + align:start position:0% +here +we did the or + + align:start position:0% +we did the or + + + align:start position:0% +we did the or +to get the label on the node from its + + align:start position:0% +to get the label on the node from its + + + align:start position:0% +to get the label on the node from its +the labels of its incoming edges + + align:start position:0% +the labels of its incoming edges + + + align:start position:0% +the labels of its incoming edges +now we're going to do something a little + + align:start position:0% +now we're going to do something a little + + + align:start position:0% +now we're going to do something a little +strange um because we have a formula + + align:start position:0% +strange um because we have a formula + + + align:start position:0% +strange um because we have a formula +here for or + + align:start position:0% +here for or + + + align:start position:0% +here for or +but for technical reasons that will come + + align:start position:0% +but for technical reasons that will come + + + align:start position:0% +but for technical reasons that will come +up later + + align:start position:0% +up later + + + align:start position:0% +up later +this is not a convenient representation + + align:start position:0% +this is not a convenient representation + + + align:start position:0% +this is not a convenient representation +for us + + align:start position:0% +for us + + + align:start position:0% +for us +what i'm going to use instead of this + + align:start position:0% +what i'm going to use instead of this + + + align:start position:0% +what i'm going to use instead of this +one i'm just going to simply say + + align:start position:0% +one i'm just going to simply say + + + align:start position:0% +one i'm just going to simply say +just take the sum + + align:start position:0% +just take the sum + + + align:start position:0% +just take the sum +why is that good enough + + align:start position:0% + + + + align:start position:0% + +in this case this is still going to be a + + align:start position:0% +in this case this is still going to be a + + + align:start position:0% +in this case this is still going to be a +faithful representation and give the + + align:start position:0% +faithful representation and give the + + + align:start position:0% +faithful representation and give the +right answer all of the time + + align:start position:0% +right answer all of the time + + + align:start position:0% +right answer all of the time +and that's because + + align:start position:0% +and that's because + + + align:start position:0% +and that's because +for our + + align:start position:0% +for our + + + align:start position:0% +for our +branching programs + + align:start position:0% +branching programs + + + align:start position:0% +branching programs +read once or otherwise read once is not + + align:start position:0% +read once or otherwise read once is not + + + align:start position:0% +read once or otherwise read once is not +coming in yet + + align:start position:0% + + + + align:start position:0% + +for our branching programs + + align:start position:0% +for our branching programs + + + align:start position:0% +for our branching programs +they're a cyclic + + align:start position:0% +they're a cyclic + + + align:start position:0% +they're a cyclic +so they can never enter a node on two + + align:start position:0% +so they can never enter a node on two + + + align:start position:0% +so they can never enter a node on two +different paths + + align:start position:0% +different paths + + + align:start position:0% +different paths +there's at most one way to come into a + + align:start position:0% +there's at most one way to come into a + + + align:start position:0% +there's at most one way to come into a +node uh um on a path through the on an + + align:start position:0% +node uh um on a path through the on an + + + align:start position:0% +node uh um on a path through the on an +execution path through the branching + + align:start position:0% +execution path through the branching + + + align:start position:0% +execution path through the branching +program if it comes in through uh + + align:start position:0% +program if it comes in through uh + + + align:start position:0% +program if it comes in through uh +through to this edge + + align:start position:0% +through to this edge + + + align:start position:0% +through to this edge +um + + align:start position:0% +um + + + align:start position:0% +um +there's no way for it to for this edge + + align:start position:0% +there's no way for it to for this edge + + + align:start position:0% +there's no way for it to for this edge +to also have a path because that means + + align:start position:0% +to also have a path because that means + + + align:start position:0% +to also have a path because that means +you have to go out and come back + + align:start position:0% +you have to go out and come back + + + align:start position:0% +you have to go out and come back +and and + + align:start position:0% + + + + align:start position:0% + +have a cycle + + align:start position:0% +have a cycle + + + align:start position:0% +have a cycle +in the branching program which is + + align:start position:0% +in the branching program which is + + + align:start position:0% +in the branching program which is +disallowed so at most one of these edges + + align:start position:0% +disallowed so at most one of these edges + + + align:start position:0% +disallowed so at most one of these edges +can have the path go through it + + align:start position:0% +can have the path go through it + + + align:start position:0% +can have the path go through it +so at most one of these a's + + align:start position:0% +so at most one of these a's + + + align:start position:0% +so at most one of these a's +can be a one the others are going to be + + align:start position:0% +can be a one the others are going to be + + + align:start position:0% +can be a one the others are going to be +zero and therefore just taking the sum + + align:start position:0% +zero and therefore just taking the sum + + + align:start position:0% +zero and therefore just taking the sum +is going to give us a value of either 0 + + align:start position:0% +is going to give us a value of either 0 + + + align:start position:0% +is going to give us a value of either 0 +or 1 but it's never going to give a + + align:start position:0% +or 1 but it's never going to give a + + + align:start position:0% +or 1 but it's never going to give a +value higher and so you don't have to + + align:start position:0% +value higher and so you don't have to + + + align:start position:0% +value higher and so you don't have to +subtract off these product terms + + align:start position:0% +subtract off these product terms + + + align:start position:0% +subtract off these product terms +okay a little bit complicated here if + + align:start position:0% +okay a little bit complicated here if + + + align:start position:0% +okay a little bit complicated here if +you didn't totally get that + + align:start position:0% +you didn't totally get that + + + align:start position:0% +you didn't totally get that +um don't worry for now + + align:start position:0% +um don't worry for now + + + align:start position:0% +um don't worry for now +you know we're um + + align:start position:0% +you know we're um + + + align:start position:0% +you know we're um +you know more concerned that you get the + + align:start position:0% +you know more concerned that you get the + + + align:start position:0% +you know more concerned that you get the +the big picture of what's going on + + align:start position:0% +the big picture of what's going on + + + align:start position:0% +the big picture of what's going on +um + + align:start position:0% + + + + align:start position:0% + +okay so um + + align:start position:0% +okay so um + + + align:start position:0% +okay so um +i think we're almost + + align:start position:0% +i think we're almost + + + align:start position:0% +i think we're almost +um + + align:start position:0% +um + + + align:start position:0% +um +let me just see how far we are + + align:start position:0% +let me just see how far we are + + + align:start position:0% +let me just see how far we are +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so i'm just going to work through an + + align:start position:0% +so i'm just going to work through an + + + align:start position:0% +so i'm just going to work through an +example and i think that'll bring us uh + + align:start position:0% +example and i think that'll bring us uh + + + align:start position:0% +example and i think that'll bring us uh +let's just see any questions here + + align:start position:0% +let's just see any questions here + + + align:start position:0% +let's just see any questions here +not seeing any + + align:start position:0% +not seeing any + + + align:start position:0% +not seeing any +it means you're either all + + align:start position:0% +it means you're either all + + + align:start position:0% +it means you're either all +totally understanding or or you're + + align:start position:0% +totally understanding or or you're + + + align:start position:0% +totally understanding or or you're +totally lost i never can tell + + align:start position:0% +totally lost i never can tell + + + align:start position:0% +totally lost i never can tell +um so feel free to ask a question if + + align:start position:0% +um so feel free to ask a question if + + + align:start position:0% +um so feel free to ask a question if +you're even if you're confused um + + align:start position:0% +you're even if you're confused um + + + align:start position:0% +you're even if you're confused um +you know i'll do my best + + align:start position:0% +you know i'll do my best + + + align:start position:0% +you know i'll do my best +okay maybe this example might help + + align:start position:0% +okay maybe this example might help + + + align:start position:0% +okay maybe this example might help +um + + align:start position:0% +um + + + align:start position:0% +um +so now what we're going to do is using + + align:start position:0% +so now what we're going to do is using + + + align:start position:0% +so now what we're going to do is using +this sort of arithmetical + + align:start position:0% +this sort of arithmetical + + + align:start position:0% +this sort of arithmetical +view + + align:start position:0% +view + + + align:start position:0% +view +of the way i + + align:start position:0% +of the way i + + + align:start position:0% +of the way i +branching program's computation um you + + align:start position:0% +branching program's computation um you + + + align:start position:0% +branching program's computation um you +know + + align:start position:0% +know + + + align:start position:0% +know +is executed when when we're running it + + align:start position:0% +is executed when when we're running it + + + align:start position:0% +is executed when when we're running it +uh um + + align:start position:0% +uh um + + + align:start position:0% +uh um +you know an input through it um this is + + align:start position:0% +you know an input through it um this is + + + align:start position:0% +you know an input through it um this is +going to allow us now to give a meaning + + align:start position:0% +going to allow us now to give a meaning + + + align:start position:0% +going to allow us now to give a meaning +to running the branching program on + + align:start position:0% +to running the branching program on + + + align:start position:0% +to running the branching program on +non-boolean inputs so maybe this example + + align:start position:0% +non-boolean inputs so maybe this example + + + align:start position:0% +non-boolean inputs so maybe this example +will illustrate that + + align:start position:0% +will illustrate that + + + align:start position:0% +will illustrate that +um + + align:start position:0% + + + + align:start position:0% + +so let's just take this particular + + align:start position:0% +so let's just take this particular + + + align:start position:0% +so let's just take this particular +branching program here + + align:start position:0% +branching program here + + + align:start position:0% +branching program here +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +this branching program it's just on two + + align:start position:0% +this branching program it's just on two + + + align:start position:0% +this branching program it's just on two +variables x1 and x2 and actually + + align:start position:0% +variables x1 and x2 and actually + + + align:start position:0% +variables x1 and x2 and actually +computes a familiar function + + align:start position:0% +computes a familiar function + + + align:start position:0% +computes a familiar function +this is the exclusive or function if you + + align:start position:0% +this is the exclusive or function if you + + + align:start position:0% +this is the exclusive or function if you +look at it for a minute you'll see that + + align:start position:0% +look at it for a minute you'll see that + + + align:start position:0% +look at it for a minute you'll see that +this is going to give you + + align:start position:0% +this is going to give you + + + align:start position:0% +this is going to give you +x1 exclusive or x2 + + align:start position:0% +x1 exclusive or x2 + + + align:start position:0% +x1 exclusive or x2 +so it's going to be + + align:start position:0% +so it's going to be + + + align:start position:0% +so it's going to be +one if either of the x1 or x2 are one + + align:start position:0% +one if either of the x1 or x2 are one + + + align:start position:0% +one if either of the x1 or x2 are one +but it's going to be zero if they're + + align:start position:0% +but it's going to be zero if they're + + + align:start position:0% +but it's going to be zero if they're +both one that's what this branching + + align:start position:0% +both one that's what this branching + + + align:start position:0% +both one that's what this branching +program computes + + align:start position:0% +program computes + + + align:start position:0% +program computes +now but let's take a + + align:start position:0% +now but let's take a + + + align:start position:0% +now but let's take a +look um at running this branching + + align:start position:0% +look um at running this branching + + + align:start position:0% +look um at running this branching +program instead of on the + + align:start position:0% +program instead of on the + + + align:start position:0% +program instead of on the +usual boolean values let's run it on x1 + + align:start position:0% +usual boolean values let's run it on x1 + + + align:start position:0% +usual boolean values let's run it on x1 +equal to 2 and x2 equal to 3. + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um + + align:start position:0% +um + + + align:start position:0% +um +you know a common confusion + + align:start position:0% +you know a common confusion + + + align:start position:0% +you know a common confusion +might be that you're looking you know + + align:start position:0% +might be that you're looking you know + + + align:start position:0% +might be that you're looking you know +when you do the x1 query you're looking + + align:start position:0% +when you do the x1 query you're looking + + + align:start position:0% +when you do the x1 query you're looking +for + + align:start position:0% +for + + + align:start position:0% +for +another + + align:start position:0% +another + + + align:start position:0% +another +outgoing edge which is labeled two no + + align:start position:0% +outgoing edge which is labeled two no + + + align:start position:0% +outgoing edge which is labeled two no +that's not what i'm doing what i'm doing + + align:start position:0% +that's not what i'm doing what i'm doing + + + align:start position:0% +that's not what i'm doing what i'm doing +here is i'm somehow + + align:start position:0% +here is i'm somehow + + + align:start position:0% +here is i'm somehow +uh through this execution + + align:start position:0% +uh through this execution + + + align:start position:0% +uh through this execution +by assigning these other values i'm kind + + align:start position:0% +by assigning these other values i'm kind + + + align:start position:0% +by assigning these other values i'm kind +of blending together the computation of + + align:start position:0% +of blending together the computation of + + + align:start position:0% +of blending together the computation of +x x + + align:start position:0% +x x + + + align:start position:0% +x x +uh 1 equal to 0 and x1 equal to 1 + + align:start position:0% +uh 1 equal to 0 and x1 equal to 1 + + + align:start position:0% +uh 1 equal to 0 and x1 equal to 1 +together + + align:start position:0% +together + + + align:start position:0% +together +i don't know if that makes any sense but + + align:start position:0% +i don't know if that makes any sense but + + + align:start position:0% +i don't know if that makes any sense but +let's look through the example + + align:start position:0% +let's look through the example + + + align:start position:0% +let's look through the example +um so first of all these are the + + align:start position:0% +um so first of all these are the + + + align:start position:0% +um so first of all these are the +labeling rules that i had from + + align:start position:0% +labeling rules that i had from + + + align:start position:0% +labeling rules that i had from +uh the previous slide when i + + align:start position:0% +uh the previous slide when i + + + align:start position:0% +uh the previous slide when i +used plus and times instead of and or + + align:start position:0% +used plus and times instead of and or + + + align:start position:0% +used plus and times instead of and or +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now i'm going to show you how to use + + align:start position:0% +now i'm going to show you how to use + + + align:start position:0% +now i'm going to show you how to use +that to label the nodes and edges of + + align:start position:0% +that to label the nodes and edges of + + + align:start position:0% +that to label the nodes and edges of +this graph based on this input + + align:start position:0% +this graph based on this input + + + align:start position:0% +this graph based on this input +and that'll determine an output + + align:start position:0% +and that'll determine an output + + + align:start position:0% +and that'll determine an output +would be the value on the uh + + align:start position:0% +would be the value on the uh + + + align:start position:0% +would be the value on the uh +the one node + + align:start position:0% +the one node + + + align:start position:0% +the one node +okay so we always start out by labeling + + align:start position:0% +okay so we always start out by labeling + + + align:start position:0% +okay so we always start out by labeling +the start node with one + + align:start position:0% +the start node with one + + + align:start position:0% +the start node with one +that's just the rule + + align:start position:0% +that's just the rule + + + align:start position:0% +that's just the rule +um + + align:start position:0% +um + + + align:start position:0% +um +and + + align:start position:0% +and + + + align:start position:0% +and +uh okay + + align:start position:0% +uh okay + + + align:start position:0% +uh okay +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +let's let's think about it together + + align:start position:0% +let's let's think about it together + + + align:start position:0% +let's let's think about it together +before i blurt out the answer + + align:start position:0% +before i blurt out the answer + + + align:start position:0% +before i blurt out the answer +what's going to be the label on + + align:start position:0% +what's going to be the label on + + + align:start position:0% +what's going to be the label on +this edge + + align:start position:0% +this edge + + + align:start position:0% +this edge +so this is one of the outgoing edges uh + + align:start position:0% +so this is one of the outgoing edges uh + + + align:start position:0% +so this is one of the outgoing edges uh +from a node that already has a label so + + align:start position:0% +from a node that already has a label so + + + align:start position:0% +from a node that already has a label so +that's going to be this case here + + align:start position:0% +that's going to be this case here + + + align:start position:0% +that's going to be this case here +and what we do is if we take we take the + + align:start position:0% +and what we do is if we take we take the + + + align:start position:0% +and what we do is if we take we take the +label of that node + + align:start position:0% +label of that node + + + align:start position:0% +label of that node +and since it's a one edge that's + + align:start position:0% +and since it's a one edge that's + + + align:start position:0% +and since it's a one edge that's +outgoing + + align:start position:0% +outgoing + + + align:start position:0% +outgoing +we multiply that label + + align:start position:0% +we multiply that label + + + align:start position:0% +we multiply that label +by um the value + + align:start position:0% +by um the value + + + align:start position:0% +by um the value +of uh that + + align:start position:0% +of uh that + + + align:start position:0% +of uh that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +variable + + align:start position:0% +variable + + + align:start position:0% +variable +of the the assignment to that variable + + align:start position:0% +of the the assignment to that variable + + + align:start position:0% +of the the assignment to that variable +so x1 is two + + align:start position:0% +so x1 is two + + + align:start position:0% +so x1 is two +so we take the the it's good this the a + + align:start position:0% +so we take the the it's good this the a + + + align:start position:0% +so we take the the it's good this the a +here is one + + align:start position:0% +here is one + + + align:start position:0% +here is one +x1 is a assigned to two so it's going to + + align:start position:0% +x1 is a assigned to two so it's going to + + + align:start position:0% +x1 is a assigned to two so it's going to +be one times two + + align:start position:0% +be one times two + + + align:start position:0% +be one times two +is going to be the value + + align:start position:0% +is going to be the value + + + align:start position:0% +is going to be the value +the execution value we put on this edge + + align:start position:0% +the execution value we put on this edge + + + align:start position:0% +the execution value we put on this edge +so it's going to be 2. + + align:start position:0% + + + + align:start position:0% + +what's going to be the value we put on + + align:start position:0% +what's going to be the value we put on + + + align:start position:0% +what's going to be the value we put on +the other edge the other edge the 0 + + align:start position:0% +the other edge the other edge the 0 + + + align:start position:0% +the other edge the other edge the 0 +outgoing edge from x1 + + align:start position:0% +outgoing edge from x1 + + + align:start position:0% +outgoing edge from x1 +so once you think about that for a + + align:start position:0% +so once you think about that for a + + + align:start position:0% +so once you think about that for a +second + + align:start position:0% + + + + align:start position:0% + +so now we're going to use this + + align:start position:0% +so now we're going to use this + + + align:start position:0% +so now we're going to use this +expression + + align:start position:0% +expression + + + align:start position:0% +expression +it's a times 1 minus x i + + align:start position:0% +it's a times 1 minus x i + + + align:start position:0% +it's a times 1 minus x i +and so x i again is two so one minus x i + + align:start position:0% +and so x i again is two so one minus x i + + + align:start position:0% +and so x i again is two so one minus x i +is one minus two + + align:start position:0% +is one minus two + + + align:start position:0% +is one minus two +um + + align:start position:0% +um + + + align:start position:0% +um +does that mean that's how complementary + + align:start position:0% +does that mean that's how complementary + + + align:start position:0% +does that mean that's how complementary +but okay let's say that so it's one + + align:start position:0% +but okay let's say that so it's one + + + align:start position:0% +but okay let's say that so it's one +minus 2 so that's minus 1 times the + + align:start position:0% +minus 2 so that's minus 1 times the + + + align:start position:0% +minus 2 so that's minus 1 times the +label + + align:start position:0% +label + + + align:start position:0% +label +1 here so you get minus 1 as the label + + align:start position:0% +1 here so you get minus 1 as the label + + + align:start position:0% +1 here so you get minus 1 as the label +on this edge + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% + + + + align:start position:0% + +keep in mind + + align:start position:0% +keep in mind + + + align:start position:0% +keep in mind +that if i had plugged in and this is + + align:start position:0% +that if i had plugged in and this is + + + align:start position:0% +that if i had plugged in and this is +very important if i had plugged in + + align:start position:0% +very important if i had plugged in + + + align:start position:0% +very important if i had plugged in +boolean values here + + align:start position:0% +boolean values here + + + align:start position:0% +boolean values here +i would be getting out the same boolean + + align:start position:0% +i would be getting out the same boolean + + + align:start position:0% +i would be getting out the same boolean +values that you would get just by + + align:start position:0% +values that you would get just by + + + align:start position:0% +values that you would get just by +following through the path + + align:start position:0% +following through the path + + + align:start position:0% +following through the path +you know the things on the path would be + + align:start position:0% +you know the things on the path would be + + + align:start position:0% +you know the things on the path would be +one the things off the path would be + + align:start position:0% +one the things off the path would be + + + align:start position:0% +one the things off the path would be +zero + + align:start position:0% +zero + + + align:start position:0% +zero +um + + align:start position:0% +um + + + align:start position:0% +um +but uh + + align:start position:0% +but uh + + + align:start position:0% +but uh +but with what's kind of uh what's + + align:start position:0% +but with what's kind of uh what's + + + align:start position:0% +but with what's kind of uh what's +happening here is that + + align:start position:0% +happening here is that + + + align:start position:0% +happening here is that +there's still a meaning + + align:start position:0% +there's still a meaning + + + align:start position:0% +there's still a meaning +when the inputs are not boolean + + align:start position:0% +when the inputs are not boolean + + + align:start position:0% +when the inputs are not boolean +so let's continue here how about what's + + align:start position:0% +so let's continue here how about what's + + + align:start position:0% +so let's continue here how about what's +going to be the value on this node + + align:start position:0% + + + + align:start position:0% + +so think with me i think it will help + + align:start position:0% +so think with me i think it will help + + + align:start position:0% +so think with me i think it will help +you + + align:start position:0% +you + + + align:start position:0% +you +so + + align:start position:0% +so + + + align:start position:0% +so +now we're using this rule here we add up + + align:start position:0% +now we're using this rule here we add up + + + align:start position:0% +now we're using this rule here we add up +all the values on the incoming edges + + align:start position:0% +all the values on the incoming edges + + + align:start position:0% +all the values on the incoming edges +there's only one incoming edge which is + + align:start position:0% +there's only one incoming edge which is + + + align:start position:0% +there's only one incoming edge which is +value two so that means this guy's going + + align:start position:0% +value two so that means this guy's going + + + align:start position:0% +value two so that means this guy's going +to get a two and similar on this one + + align:start position:0% +to get a two and similar on this one + + + align:start position:0% +to get a two and similar on this one +this guy's going to get a minus one + + align:start position:0% +this guy's going to get a minus one + + + align:start position:0% +this guy's going to get a minus one +now let's take a look at this edge + + align:start position:0% +now let's take a look at this edge + + + align:start position:0% +now let's take a look at this edge +so this is a the zero outgoing edge from + + align:start position:0% +so this is a the zero outgoing edge from + + + align:start position:0% +so this is a the zero outgoing edge from +a node label two with with label x2 + + align:start position:0% +a node label two with with label x2 + + + align:start position:0% +a node label two with with label x2 +so this is the zero outgoing edge + + align:start position:0% +so this is the zero outgoing edge + + + align:start position:0% +so this is the zero outgoing edge +the node the label is two so it's going + + align:start position:0% +the node the label is two so it's going + + + align:start position:0% +the node the label is two so it's going +to be two times + + align:start position:0% +to be two times + + + align:start position:0% +to be two times +one minus the x2 value x2 is 3 so 1 + + align:start position:0% +one minus the x2 value x2 is 3 so 1 + + + align:start position:0% +one minus the x2 value x2 is 3 so 1 +minus 3 is minus 2. it's going to be 2 + + align:start position:0% +minus 3 is minus 2. it's going to be 2 + + + align:start position:0% +minus 3 is minus 2. it's going to be 2 +times -2 + + align:start position:0% +times -2 + + + align:start position:0% +times -2 +which is minus 4. + + align:start position:0% +which is minus 4. + + + align:start position:0% +which is minus 4. +so similarly you can get the value here + + align:start position:0% +so similarly you can get the value here + + + align:start position:0% +so similarly you can get the value here +the value on the the + + align:start position:0% +the value on the the + + + align:start position:0% +the value on the the +one outgoing edge is going to be + + align:start position:0% +one outgoing edge is going to be + + + align:start position:0% +one outgoing edge is going to be +2 times + + align:start position:0% +2 times + + + align:start position:0% +2 times +x the x2 value which is 3 so that's + + align:start position:0% +x the x2 value which is 3 so that's + + + align:start position:0% +x the x2 value which is 3 so that's +going to be 6. + + align:start position:0% +going to be 6. + + + align:start position:0% +going to be 6. +and these two here + + align:start position:0% + + + + align:start position:0% + +uh um + + align:start position:0% +uh um + + + align:start position:0% +uh um +so you know now we have a minus one + + align:start position:0% +so you know now we have a minus one + + + align:start position:0% +so you know now we have a minus one +and the outgoing is a + + align:start position:0% +and the outgoing is a + + + align:start position:0% +and the outgoing is a +it's a it's a zero edge so it's one + + align:start position:0% +it's a it's a zero edge so it's one + + + align:start position:0% +it's a it's a zero edge so it's one +minus three + + align:start position:0% +minus three + + + align:start position:0% +minus three +and here it's going to be one times + + align:start position:0% +and here it's going to be one times + + + align:start position:0% +and here it's going to be one times +minus three + + align:start position:0% +minus three + + + align:start position:0% +minus three +no + + align:start position:0% +no + + + align:start position:0% +no +1 times 3 i'm sorry 1 times 3. + + align:start position:0% +1 times 3 i'm sorry 1 times 3. + + + align:start position:0% +1 times 3 i'm sorry 1 times 3. +um + + align:start position:0% +um + + + align:start position:0% +um +so you get the out the answer is minus + + align:start position:0% +so you get the out the answer is minus + + + align:start position:0% +so you get the out the answer is minus +3. so now what's the label on the zero + + align:start position:0% +3. so now what's the label on the zero + + + align:start position:0% +3. so now what's the label on the zero +output edge + + align:start position:0% +output edge + + + align:start position:0% +output edge +so you have to add in add up the two + + align:start position:0% +so you have to add in add up the two + + + align:start position:0% +so you have to add in add up the two +incoming edges here so we have + + align:start position:0% +incoming edges here so we have + + + align:start position:0% +incoming edges here so we have +uh this + + align:start position:0% +uh this + + + align:start position:0% +uh this +this edge here was a two + + align:start position:0% + + + + align:start position:0% + +this edge coming in here is a six so + + align:start position:0% +this edge coming in here is a six so + + + align:start position:0% +this edge coming in here is a six so +it's going to be two plus six + + align:start position:0% +it's going to be two plus six + + + align:start position:0% +it's going to be two plus six +it's eight and what about this edge this + + align:start position:0% +it's eight and what about this edge this + + + align:start position:0% +it's eight and what about this edge this +node here this is an important node + + align:start position:0% +node here this is an important node + + + align:start position:0% +node here this is an important node +because this is going to be the output + + align:start position:0% +because this is going to be the output + + + align:start position:0% +because this is going to be the output +so + + align:start position:0% +so + + + align:start position:0% +so +it has + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know minus three coming in + + align:start position:0% +you know minus three coming in + + + align:start position:0% +you know minus three coming in +and a minus four coming in so you add + + align:start position:0% +and a minus four coming in so you add + + + align:start position:0% +and a minus four coming in so you add +those together + + align:start position:0% +those together + + + align:start position:0% +those together +you get a minus seven + + align:start position:0% +you get a minus seven + + + align:start position:0% +you get a minus seven +i mean you may wonder + + align:start position:0% +i mean you may wonder + + + align:start position:0% +i mean you may wonder +what + + align:start position:0% +what + + + align:start position:0% +what +what the world is going on here um + + align:start position:0% +what the world is going on here um + + + align:start position:0% +what the world is going on here um +just a lot of mumbo jumbo uh + + align:start position:0% +just a lot of mumbo jumbo uh + + + align:start position:0% +just a lot of mumbo jumbo uh +but we're gonna make sense of all this + + align:start position:0% +but we're gonna make sense of all this + + + align:start position:0% +but we're gonna make sense of all this +not today uh we're gonna have to argue + + align:start position:0% +not today uh we're gonna have to argue + + + align:start position:0% +not today uh we're gonna have to argue +why this is + + align:start position:0% +why this is + + + align:start position:0% +why this is +what the meaning that we're gonna get + + align:start position:0% +what the meaning that we're gonna get + + + align:start position:0% +what the meaning that we're gonna get +out of this is gonna be + + align:start position:0% +out of this is gonna be + + + align:start position:0% +out of this is gonna be +um but the point point is + + align:start position:0% +um but the point point is + + + align:start position:0% +um but the point point is +that + + align:start position:0% +that + + + align:start position:0% +that +this is going to lead to a new algorithm + + align:start position:0% +this is going to lead to a new algorithm + + + align:start position:0% +this is going to lead to a new algorithm +for testing this is again getting back + + align:start position:0% +for testing this is again getting back + + + align:start position:0% +for testing this is again getting back +to what we were + + align:start position:0% +to what we were + + + align:start position:0% +to what we were +doing + + align:start position:0% +doing + + + align:start position:0% +doing +this is + + align:start position:0% +this is + + + align:start position:0% +this is +the equivalence problem for read once + + align:start position:0% +the equivalence problem for read once + + + align:start position:0% +the equivalence problem for read once +branching programs so now what the new + + align:start position:0% +branching programs so now what the new + + + align:start position:0% +branching programs so now what the new +algorithm is going to do is going to + + align:start position:0% +algorithm is going to do is going to + + + align:start position:0% +algorithm is going to do is going to +pick a random non-boolean assignment + + align:start position:0% +pick a random non-boolean assignment + + + align:start position:0% +pick a random non-boolean assignment +so it's going to randomly assign + + align:start position:0% +so it's going to randomly assign + + + align:start position:0% +so it's going to randomly assign +values to the x's + + align:start position:0% +values to the x's + + + align:start position:0% +values to the x's +and to some non-boolean values instead + + align:start position:0% +and to some non-boolean values instead + + + align:start position:0% +and to some non-boolean values instead +of zeros and ones we're going to plug in + + align:start position:0% +of zeros and ones we're going to plug in + + + align:start position:0% +of zeros and ones we're going to plug in +random + + align:start position:0% +random + + + align:start position:0% +random +integer values we'll make that clear + + align:start position:0% +integer values we'll make that clear + + + align:start position:0% +integer values we'll make that clear +next time what's what this what the + + align:start position:0% +next time what's what this what the + + + align:start position:0% +next time what's what this what the +domain is going to be + + align:start position:0% +domain is going to be + + + align:start position:0% +domain is going to be +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and then once we have that non-boolean + + align:start position:0% +and then once we have that non-boolean + + + align:start position:0% +and then once we have that non-boolean +assignment we're going to value b1 and + + align:start position:0% +assignment we're going to value b1 and + + + align:start position:0% +assignment we're going to value b1 and +b2 + + align:start position:0% +b2 + + + align:start position:0% +b2 +and if they disagree + + align:start position:0% +and if they disagree + + + align:start position:0% +and if they disagree +out there in that extended + + align:start position:0% +out there in that extended + + + align:start position:0% +out there in that extended +domain + + align:start position:0% +domain + + + align:start position:0% +domain +then we have to show that they're not + + align:start position:0% +then we have to show that they're not + + + align:start position:0% +then we have to show that they're not +equivalent and will reject + + align:start position:0% +equivalent and will reject + + + align:start position:0% +equivalent and will reject +and we'll also show that + + align:start position:0% +and we'll also show that + + + align:start position:0% +and we'll also show that +if they were equivalent + + align:start position:0% +if they were equivalent + + + align:start position:0% +if they were equivalent +then even when we evaluate them + + align:start position:0% + + + + align:start position:0% + +then we have to show that if if they're + + align:start position:0% +then we have to show that if if they're + + + align:start position:0% +then we have to show that if if they're +not equivalent that they're very likely + + align:start position:0% +not equivalent that they're very likely + + + align:start position:0% +not equivalent that they're very likely +to to have a difference in the + + align:start position:0% +to to have a difference in the + + + align:start position:0% +to to have a difference in the +non-boolean uh domain and so um if they + + align:start position:0% +non-boolean uh domain and so um if they + + + align:start position:0% +non-boolean uh domain and so um if they +agree it it + + align:start position:0% +agree it it + + + align:start position:0% +agree it it +it gives you evidence that the two are + + align:start position:0% +it gives you evidence that the two are + + + align:start position:0% +it gives you evidence that the two are +really equivalent + + align:start position:0% +really equivalent + + + align:start position:0% +really equivalent +um so the completeness proof will come + + align:start position:0% +um so the completeness proof will come + + + align:start position:0% +um so the completeness proof will come +after thanksgiving so with that um i'm + + align:start position:0% +after thanksgiving so with that um i'm + + + align:start position:0% +after thanksgiving so with that um i'm +gonna wish you all a nice uh break um oh + + align:start position:0% +gonna wish you all a nice uh break um oh + + + align:start position:0% +gonna wish you all a nice uh break um oh +we have a check in here sorry + + align:start position:0% +we have a check in here sorry + + + align:start position:0% +we have a check in here sorry +oh yeah this is a good one + + align:start position:0% +oh yeah this is a good one + + + align:start position:0% +oh yeah this is a good one +i don't know how if you're following me + + align:start position:0% +i don't know how if you're following me + + + align:start position:0% +i don't know how if you're following me +uh but + + align:start position:0% +uh but + + + align:start position:0% +uh but +um if i plug in one for x1 + + align:start position:0% +um if i plug in one for x1 + + + align:start position:0% +um if i plug in one for x1 +and y for x2 + + align:start position:0% +and y for x2 + + + align:start position:0% +and y for x2 +does it do the inputs in the assignment + + align:start position:0% +does it do the inputs in the assignment + + + align:start position:0% +does it do the inputs in the assignment +need to be distinct no + + align:start position:0% +need to be distinct no + + + align:start position:0% +need to be distinct no +it could be the same value + + align:start position:0% +it could be the same value + + + align:start position:0% +it could be the same value +i could be + + align:start position:0% +i could be + + + align:start position:0% +i could be +uh two and two here that's perfectly + + align:start position:0% +uh two and two here that's perfectly + + + align:start position:0% +uh two and two here that's perfectly +valid + + align:start position:0% +valid + + + align:start position:0% +valid +but here i'm going to plug in 1 for x1 + + align:start position:0% +but here i'm going to plug in 1 for x1 + + + align:start position:0% +but here i'm going to plug in 1 for x1 +i'm going to plug in a + + align:start position:0% +i'm going to plug in a + + + align:start position:0% +i'm going to plug in a +variable for x2 y + + align:start position:0% +variable for x2 y + + + align:start position:0% +variable for x2 y +and i'm going to do the whole + + align:start position:0% +and i'm going to do the whole + + + align:start position:0% +and i'm going to do the whole +calculation that i just did and now + + align:start position:0% +calculation that i just did and now + + + align:start position:0% +calculation that i just did and now +what's going to be the output + + align:start position:0% + + + + align:start position:0% + +and i mean this looks like a pain to + + align:start position:0% +and i mean this looks like a pain to + + + align:start position:0% +and i mean this looks like a pain to +figure out you could do it it looks like + + align:start position:0% +figure out you could do it it looks like + + + align:start position:0% +figure out you could do it it looks like +a pain but let me give you a big hint + + align:start position:0% +a pain but let me give you a big hint + + + align:start position:0% +a pain but let me give you a big hint +um + + align:start position:0% +um + + + align:start position:0% +um +remember that this thing + + align:start position:0% +remember that this thing + + + align:start position:0% +remember that this thing +is supposed to be calculating the + + align:start position:0% +is supposed to be calculating the + + + align:start position:0% +is supposed to be calculating the +original branching program calculates + + align:start position:0% +original branching program calculates + + + align:start position:0% +original branching program calculates +the exclusive or function + + align:start position:0% +the exclusive or function + + + align:start position:0% +the exclusive or function +and that means when i plug in + + align:start position:0% +and that means when i plug in + + + align:start position:0% +and that means when i plug in +um a boolean value + + align:start position:0% +um a boolean value + + + align:start position:0% +um a boolean value +i should get the exclusive or value + + align:start position:0% +i should get the exclusive or value + + + align:start position:0% +i should get the exclusive or value +coming out + + align:start position:0% +coming out + + + align:start position:0% +coming out +so if i already know that x1 is one + + align:start position:0% +so if i already know that x1 is one + + + align:start position:0% +so if i already know that x1 is one +which of these is consistent + + align:start position:0% +which of these is consistent + + + align:start position:0% +which of these is consistent +with getting + + align:start position:0% +with getting + + + align:start position:0% +with getting +a value + + align:start position:0% +a value + + + align:start position:0% +a value +uh that the exclusive or function would + + align:start position:0% +uh that the exclusive or function would + + + align:start position:0% +uh that the exclusive or function would +compute + + align:start position:0% +compute + + + align:start position:0% +compute +so let me launch the poll on that + + align:start position:0% + + + + align:start position:0% + +so we're at a time + + align:start position:0% + + + + align:start position:0% + +so let's just let this run for another + + align:start position:0% +so let's just let this run for another + + + align:start position:0% +so let's just let this run for another +10 seconds + + align:start position:0% +10 seconds + + + align:start position:0% +10 seconds +okay + + align:start position:0% +okay + + + align:start position:0% +okay +i'm going to close this + + align:start position:0% +i'm going to close this + + + align:start position:0% +i'm going to close this +ready + + align:start position:0% +ready + + + align:start position:0% +ready +um + + align:start position:0% + + + + align:start position:0% + +yes indeed + + align:start position:0% +yes indeed + + + align:start position:0% +yes indeed +a is the right answer because that's one + + align:start position:0% +a is the right answer because that's one + + + align:start position:0% +a is the right answer because that's one +if i know that one variable is one then + + align:start position:0% +if i know that one variable is one then + + + align:start position:0% +if i know that one variable is one then +the exclusive or + + align:start position:0% +the exclusive or + + + align:start position:0% +the exclusive or +is going to be the complement of the + + align:start position:0% +is going to be the complement of the + + + align:start position:0% +is going to be the complement of the +other variable + + align:start position:0% +other variable + + + align:start position:0% +other variable +which is one minus y so that's what you + + align:start position:0% +which is one minus y so that's what you + + + align:start position:0% +which is one minus y so that's what you +would get if you calculated this + + align:start position:0% +would get if you calculated this + + + align:start position:0% +would get if you calculated this +um + + align:start position:0% +um + + + align:start position:0% +um +because this is what we did today + + align:start position:0% +because this is what we did today + + + align:start position:0% +because this is what we did today +and um + + align:start position:0% +and um + + + align:start position:0% +and um +feel free to ask questions so let me + + align:start position:0% +feel free to ask questions so let me + + + align:start position:0% +feel free to ask questions so let me +just so we're going to spend a good + + align:start position:0% +just so we're going to spend a good + + + align:start position:0% +just so we're going to spend a good +chunk i'll review this + + align:start position:0% +chunk i'll review this + + + align:start position:0% +chunk i'll review this +what we've done so far but then we're + + align:start position:0% +what we've done so far but then we're + + + align:start position:0% +what we've done so far but then we're +going to carry it forward and spend a + + align:start position:0% +going to carry it forward and spend a + + + align:start position:0% +going to carry it forward and spend a +good chunk of tuesday's lecture after + + align:start position:0% +good chunk of tuesday's lecture after + + + align:start position:0% +good chunk of tuesday's lecture after +the + + align:start position:0% +the + + + align:start position:0% +the +thanksgiving break uh proving that this + + align:start position:0% +thanksgiving break uh proving that this + + + align:start position:0% +thanksgiving break uh proving that this +uh procedure that i just subscribed + + align:start position:0% +uh procedure that i just subscribed + + + align:start position:0% +uh procedure that i just subscribed +worked and works and it's um + + align:start position:0% +worked and works and it's um + + + align:start position:0% +worked and works and it's um +it's an interesting but somewhat + + align:start position:0% +it's an interesting but somewhat + + + align:start position:0% +it's an interesting but somewhat +you know it's not such an easy proof uh + + align:start position:0% +you know it's not such an easy proof uh + + + align:start position:0% +you know it's not such an easy proof uh +so we're going to spend the try to do it + + align:start position:0% +so we're going to spend the try to do it + + + align:start position:0% +so we're going to spend the try to do it +slowly and clearly and then um but this + + align:start position:0% +slowly and clearly and then um but this + + + align:start position:0% +slowly and clearly and then um but this +notion of arithmetization is going to be + + align:start position:0% +notion of arithmetization is going to be + + + align:start position:0% +notion of arithmetization is going to be +this is this was + + align:start position:0% +this is this was + + + align:start position:0% +this is this was +you know + + align:start position:0% +you know + + + align:start position:0% +you know +it's it's an important notion in + + align:start position:0% +it's it's an important notion in + + + align:start position:0% +it's it's an important notion in +complexity and so um we'll + + align:start position:0% +complexity and so um we'll + + + align:start position:0% +complexity and so um we'll +we'll see it again coming up in another + + align:start position:0% +we'll see it again coming up in another + + + align:start position:0% +we'll see it again coming up in another +proof afterwards + + align:start position:0% +proof afterwards + + + align:start position:0% +proof afterwards +in about interactive proof systems + + align:start position:0% +in about interactive proof systems + + + align:start position:0% +in about interactive proof systems +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so please ask questions + + align:start position:0% +so please ask questions + + + align:start position:0% +so please ask questions +so the output is the value of the one + + align:start position:0% +so the output is the value of the one + + + align:start position:0% +so the output is the value of the one +output one state yes + + align:start position:0% +output one state yes + + + align:start position:0% +output one state yes +that was a question i got + + align:start position:0% +that was a question i got + + + align:start position:0% +that was a question i got +other questions + + align:start position:0% +other questions + + + align:start position:0% +other questions +somebody's saying minus seven is not the + + align:start position:0% +somebody's saying minus seven is not the + + + align:start position:0% +somebody's saying minus seven is not the +xor of two and three + + align:start position:0% + + + + align:start position:0% + +what is the xor of two and three + + align:start position:0% +what is the xor of two and three + + + align:start position:0% +what is the xor of two and three +so by the way i i should say we kind of + + align:start position:0% +so by the way i i should say we kind of + + + align:start position:0% +so by the way i i should say we kind of +ran a little short on time i'm not + + align:start position:0% +ran a little short on time i'm not + + + align:start position:0% +ran a little short on time i'm not +saying that we discovered some + + align:start position:0% +saying that we discovered some + + + align:start position:0% +saying that we discovered some +fundamental new truth about xor here + + align:start position:0% +fundamental new truth about xor here + + + align:start position:0% +fundamental new truth about xor here +um because that would be bizarre + + align:start position:0% +um because that would be bizarre + + + align:start position:0% +um because that would be bizarre +it really depends on the arbitrary + + align:start position:0% +it really depends on the arbitrary + + + align:start position:0% +it really depends on the arbitrary +decision that we made to say true is one + + align:start position:0% +decision that we made to say true is one + + + align:start position:0% +decision that we made to say true is one +and false is zero + + align:start position:0% +and false is zero + + + align:start position:0% +and false is zero +we could have come up with a different + + align:start position:0% +we could have come up with a different + + + align:start position:0% +we could have come up with a different +representation for true and false and + + align:start position:0% +representation for true and false and + + + align:start position:0% +representation for true and false and +then you would get a different value + + align:start position:0% +then you would get a different value + + + align:start position:0% +then you would get a different value +for xor coming out of that you know from + + align:start position:0% +for xor coming out of that you know from + + + align:start position:0% +for xor coming out of that you know from +the arithmetization that i just + + align:start position:0% +the arithmetization that i just + + + align:start position:0% +the arithmetization that i just +described um + + align:start position:0% +described um + + + align:start position:0% +described um +but uh for this particular way of + + align:start position:0% +but uh for this particular way of + + + align:start position:0% +but uh for this particular way of +representing true and false that's how + + align:start position:0% +representing true and false that's how + + + align:start position:0% +representing true and false that's how +xor and this particular branching + + align:start position:0% +xor and this particular branching + + + align:start position:0% +xor and this particular branching +program that's how uh + + align:start position:0% +program that's how uh + + + align:start position:0% +program that's how uh +what how xor evaluates + + align:start position:0% +what how xor evaluates + + + align:start position:0% +what how xor evaluates +the the remainder of the proof so + + align:start position:0% +the the remainder of the proof so + + + align:start position:0% +the the remainder of the proof so +somebody's asking which is it which is + + align:start position:0% +somebody's asking which is it which is + + + align:start position:0% +somebody's asking which is it which is +true the fundamental theorem of algebra + + align:start position:0% +true the fundamental theorem of algebra + + + align:start position:0% +true the fundamental theorem of algebra +which talks about polynomials and the + + align:start position:0% +which talks about polynomials and the + + + align:start position:0% +which talks about polynomials and the +number of roots that you can have that's + + align:start position:0% +number of roots that you can have that's + + + align:start position:0% +number of roots that you can have that's +going to be that's going to be critical + + align:start position:0% +going to be that's going to be critical + + + align:start position:0% +going to be that's going to be critical +um + + align:start position:0% +um + + + align:start position:0% +um +uh so the that is the fundamental + + align:start position:0% +uh so the that is the fundamental + + + align:start position:0% +uh so the that is the fundamental +theorem of algebra that's where we're + + align:start position:0% +theorem of algebra that's where we're + + + align:start position:0% +theorem of algebra that's where we're +going good good question + + align:start position:0% +going good good question + + + align:start position:0% +going good good question +well you know so the + + align:start position:0% +well you know so the + + + align:start position:0% +well you know so the +somebody's complaining that you know + + align:start position:0% +somebody's complaining that you know + + + align:start position:0% +somebody's complaining that you know +we're not taking the + + align:start position:0% +we're not taking the + + + align:start position:0% +we're not taking the +digit + + align:start position:0% +digit + + + align:start position:0% +digit +binary representation of two and three + + align:start position:0% +binary representation of two and three + + + align:start position:0% +binary representation of two and three +and taking the + + align:start position:0% +and taking the + + + align:start position:0% +and taking the +bit by bit + + align:start position:0% +bit by bit + + + align:start position:0% +bit by bit +um + + align:start position:0% +um + + + align:start position:0% +um +xor well that's i'm not + + align:start position:0% +xor well that's i'm not + + + align:start position:0% +xor well that's i'm not +you know + + align:start position:0% +you know + + + align:start position:0% +you know +binary representation is not a part of + + align:start position:0% +binary representation is not a part of + + + align:start position:0% +binary representation is not a part of +this + + align:start position:0% +this + + + align:start position:0% +this +we're thinking of these as two elements + + align:start position:0% +we're thinking of these as two elements + + + align:start position:0% +we're thinking of these as two elements +of a field + + align:start position:0% +of a field + + + align:start position:0% +of a field +um of a finite field which we'll talk + + align:start position:0% +um of a finite field which we'll talk + + + align:start position:0% +um of a finite field which we'll talk +about later + + align:start position:0% +about later + + + align:start position:0% +about later +represent the binary representation is + + align:start position:0% +represent the binary representation is + + + align:start position:0% +represent the binary representation is +isn't + + align:start position:0% +isn't + + + align:start position:0% +isn't +is not is not entering into this + + align:start position:0% +is not is not entering into this + + + align:start position:0% +is not is not entering into this +discussion + + align:start position:0% +discussion + + + align:start position:0% +discussion +um + + align:start position:0% +um + + + align:start position:0% +um +so talk about why just doing the sum is + + align:start position:0% +so talk about why just doing the sum is + + + align:start position:0% +so talk about why just doing the sum is +enough + + align:start position:0% +enough + + + align:start position:0% +enough +um + + align:start position:0% + + + + align:start position:0% + +i think that was + + align:start position:0% +i think that was + + + align:start position:0% +i think that was +so why is it i mean here it is why is + + align:start position:0% +so why is it i mean here it is why is + + + align:start position:0% +so why is it i mean here it is why is +just doing the sum when i'm + + align:start position:0% +just doing the sum when i'm + + + align:start position:0% +just doing the sum when i'm +looking at the um + + align:start position:0% +looking at the um + + + align:start position:0% +looking at the um +the + + align:start position:0% +the + + + align:start position:0% +the +how to describe the value of this node + + align:start position:0% +how to describe the value of this node + + + align:start position:0% +how to describe the value of this node +based upon the values of all the + + align:start position:0% +based upon the values of all the + + + align:start position:0% +based upon the values of all the +incoming nodes + + align:start position:0% +incoming nodes + + + align:start position:0% +incoming nodes +and remember the point of the the + + align:start position:0% +and remember the point of the the + + + align:start position:0% +and remember the point of the the +starting point of this is that we have + + align:start position:0% +starting point of this is that we have + + + align:start position:0% +starting point of this is that we have +to faithfully represent the boolean + + align:start position:0% +to faithfully represent the boolean + + + align:start position:0% +to faithfully represent the boolean +logic with the arithmetic + + align:start position:0% +logic with the arithmetic + + + align:start position:0% +logic with the arithmetic +and then we're going to use that and + + align:start position:0% +and then we're going to use that and + + + align:start position:0% +and then we're going to use that and +extend it to non-boolean values but as a + + align:start position:0% +extend it to non-boolean values but as a + + + align:start position:0% +extend it to non-boolean values but as a +starting point we have to faithfully + + align:start position:0% +starting point we have to faithfully + + + align:start position:0% +starting point we have to faithfully +represent the boolean values + + align:start position:0% +represent the boolean values + + + align:start position:0% +represent the boolean values +now the boolean values + + align:start position:0% +now the boolean values + + + align:start position:0% +now the boolean values +on the incoming edges at most one of + + align:start position:0% +on the incoming edges at most one of + + + align:start position:0% +on the incoming edges at most one of +them can be + + align:start position:0% +them can be + + + align:start position:0% +them can be +can be a one + + align:start position:0% +can be a one + + + align:start position:0% +can be a one +because + + align:start position:0% +because + + + align:start position:0% +because +the ones correspond to the + + align:start position:0% +the ones correspond to the + + + align:start position:0% +the ones correspond to the +edges + + align:start position:0% +edges + + + align:start position:0% +edges +of the execution path + + align:start position:0% +of the execution path + + + align:start position:0% +of the execution path +and you can't make an execution path + + align:start position:0% +and you can't make an execution path + + + align:start position:0% +and you can't make an execution path +um that's going to have two + + align:start position:0% +um that's going to have two + + + align:start position:0% +um that's going to have two +branches + + align:start position:0% +branches + + + align:start position:0% +branches +that's going to go through a node twice + + align:start position:0% +that's going to go through a node twice + + + align:start position:0% +that's going to go through a node twice +because then you have a loop + + align:start position:0% +because then you have a loop + + + align:start position:0% +because then you have a loop +and we don't have there's no cycles + + align:start position:0% +and we don't have there's no cycles + + + align:start position:0% +and we don't have there's no cycles +allowed + + align:start position:0% +allowed + + + align:start position:0% +allowed +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so i think where it's at four + + align:start position:0% +so i think where it's at four + + + align:start position:0% +so i think where it's at four +um + + align:start position:0% +um + + + align:start position:0% +um +i want to say farewell to all you all + + align:start position:0% +i want to say farewell to all you all + + + align:start position:0% +i want to say farewell to all you all +have a great uh week and i'll see you + + align:start position:0% +have a great uh week and i'll see you + + + align:start position:0% +have a great uh week and i'll see you +when you get back + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/WUxImdA7k8E.txt b/WUxImdA7k8E.txt new file mode 100644 index 0000000000000000000000000000000000000000..d0bfbc10352fc88172b94dcc1ed8bfe8e94cbf87 --- /dev/null +++ b/WUxImdA7k8E.txt @@ -0,0 +1,386 @@ +IAN HUTCHINSON: Let's +just finish this + +off by cleaning up this +plot and saving it. + +In the first case, I don't +have any labels on my axes. + +That's bad. + +Let me put some +labels on my axes. + +X-label is the way you do this. + +And in this case I have a +very simple label that I want. + +And the same thing, +presumably for Y-label. + +That will at least +put some labels on. + +Aren't they horribly small? + +But they are there. + +Now, I want to improve +this plot in general. + +Let me point out another +thing that I want to do. + +I don't want to have +hold on permanently, + +so let me put hold off +after the second plot. + +And that's going to avoid +difficulties in the future. + +So I'm just going to save that. + +Now in order to improve +the size of the labels + +and so forth that's +involved with this, + +there are a number +of things one can do. + +And in general, I'm going to +do this for many of my plots. + +And so what I want +to do is I want + +to illustrate the fact +that my script-- which + +is called fitting.m, +can call another script. + +And it can call as +many scripts as I like. + +The script I'm going to call, +I have in my editor already. + +It's called plot defaults. + +Plot defaults.m. + +And here are some +mysterious calls + +that you will find out +only by reading the help + +files in general. + +By the way, in Octave +there's all kinds of help + +that you can find out by +typing things like, help. + +But in general it's more +useful usually to use doc. + +And so we could do +doc, let's say a plat + +and it would then +bring me to a place + +in the documentation, where +the documentation for plot + +is described. + +MathLab has got +its own help system + +and you can use that to +look up various things. + +I could do doc of, +let's say, set, + +and it will show +me what these set + +commands that are in this +file plot defaults are doing. + +The syntax is +complicated and it's not + +worth us dwelling +on it at the moment. + +Let me just explain +what it's going to do. + +First of all it's going to +set the default access label + +font size to be bigger, 20. + +Second thing it's +going to do is it's + +going to make the width of +the lines of the axes two + +instead of one because +the axes on these plots + +may well be better +if they're thicker. + +In general these plots tend to +come up with rather thin lines. + +That's useful generally, but the +most useful thing to fix these + +plots, and to get the labelling +to be a decent size turns out + +to be to shrink the size of +the plot leave the font size + +the same. + +So what this command +does is it basically + +sets the paper units, the paper +orientation, and the paper size + +to be three inches by four +inches, height versus width. + +And then it sets the paper +position in such a way + +that we aren't +writing off the paper. + +As I said, all of this is subtle +and you wouldn't necessarily + +want to know all +the details of this. + +I'll happily make this +file available to you. + +But all I have to do +in order to execute + +those commands in that +file, plot defaults, + +is write the command +plot defaults. + +And I'm going to do that +before my first plot. + +So plot defaults +should read in that + +file that I was just +looking at, this file, + +and execute the commands in it. + +Notice, by the way, +comments, very important. + +Because these commands +are mysterious, + +I put some commentary +to remind you + +what they're supposed to +be doing next to them, + +and the way the +comment is defined + +is by having a percent line +at the beginning of the line, + +or actually anywhere else +in the line for that matter. + +OK. + +Let's save this new +file and run it again. + +And lo and behold it's run. + +Probably-- I may not have +several of the defaults right + +because I've been doing a +number of things in this Octave + +session. + +If I get tired of +this Octave session-- + +I've run 25 different commands +on it, it's telling me-- + +and I want to +start a fresh, it's + +sometimes helpful to start +a new, fresh session. + +I can do this very +straightforwardly, + +we're just saying, exit, and +then starting over again. + +That's one way to be sure you've +got a nice, fresh session. + +One of the nicest +things about Octave + +is it actually still remembers +what your commands were, + +even though you've +got a new session. + +So here's what the plot +looks like, in the case + +when I run it with plot +defaults and executed before any + +of other plotting commands. + +So the plot defaults needs to +happen before anything else. + +And now what you see is +much better, much bigger + +at any rate labels on the +axes, et cetera, et cetera. + +Things aren't perfect. + +There's a little y is crashed +with the x there, but anyway. + +You can tweak around with +those to your heart's content. + +If this were fine, my final +plot, what I wanted to save, + +one of the ways I +could save it would + +be to do some kind of screen +capture on this window + +that I'm plotting it in. + +That would give me a rather +cumbersome and not very pretty + +plot. + +There is another way of +plotting, of saving this plot. + +And that is to use +the command print. + +So print is actually +printing out the plotting. + +One has to tell print +what format one wants. + +Supposing I want EPS +format, I could say D EPS. + +And suppose that I know what +file I want to save it into, + +I could, for example, write +fitted.EPS, like that. + +So this tells it to print out +this plot into an EPS file, + +which is then named fitted.EPS. + +Let's see what happens. + +Nothing obvious, +except that if I now + +look in the directory, which in +Octave I can do by typing LS, + +there is a file +called fitted EPS. + +I don't want to get out +of my Octave session. + +I'm in the same directory here. + +Here it is, fitted EPS. + +Let's have a look at that +file using ghost view, + +and there it is. + +This is now a good quality +file that I might be + +proud to show to my professor. + +It's actually not in color. + +That's because I use EPS. + +I think it's EPS C for color. + +Let me try it. + +Let's run that again and now +look at it again, and see, + +yes, it's color. + +Now it's color. + +So that's how to get +a plot and to save + +it looking halfway decent. + +And that's where we'll end. \ No newline at end of file diff --git a/We570M74cXE.txt b/We570M74cXE.txt new file mode 100644 index 0000000000000000000000000000000000000000..d4377ab9b2d914d13705b2d071994795570d8b91 --- /dev/null +++ b/We570M74cXE.txt @@ -0,0 +1,9067 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so this is our last 10:34 lecture of the + + align:start position:0% +so this is our last 10:34 lecture of the + + + align:start position:0% +so this is our last 10:34 lecture of the +year and we're just gonna use it for + + align:start position:0% +year and we're just gonna use it for + + + align:start position:0% +year and we're just gonna use it for +review so I'm gonna give a brief recap + + align:start position:0% +review so I'm gonna give a brief recap + + + align:start position:0% +review so I'm gonna give a brief recap +of the course we've done a lot actually + + align:start position:0% +of the course we've done a lot actually + + + align:start position:0% +of the course we've done a lot actually +I hope you've learned a lot over the + + align:start position:0% +I hope you've learned a lot over the + + + align:start position:0% +I hope you've learned a lot over the +course of the term we've had lots of + + align:start position:0% +course of the term we've had lots of + + + align:start position:0% +course of the term we've had lots of +opportunities to practice with different + + align:start position:0% +opportunities to practice with different + + + align:start position:0% +opportunities to practice with different +numerical methods I've checked in from + + align:start position:0% +numerical methods I've checked in from + + + align:start position:0% +numerical methods I've checked in from +time to time on the homework submissions + + align:start position:0% +time to time on the homework submissions + + + align:start position:0% +time to time on the homework submissions +and really impressed with the quality of + + align:start position:0% +and really impressed with the quality of + + + align:start position:0% +and really impressed with the quality of +the work that the class is produced as a + + align:start position:0% +the work that the class is produced as a + + + align:start position:0% +the work that the class is produced as a +whole it tells me that you guys do + + align:start position:0% +whole it tells me that you guys do + + + align:start position:0% +whole it tells me that you guys do +understand what you're doing that you + + align:start position:0% +understand what you're doing that you + + + align:start position:0% +understand what you're doing that you +can apply these methods to problems of + + align:start position:0% +can apply these methods to problems of + + + align:start position:0% +can apply these methods to problems of +engineering interests and I hope that + + align:start position:0% +engineering interests and I hope that + + + align:start position:0% +engineering interests and I hope that +the things you've learned over the + + align:start position:0% +the things you've learned over the + + + align:start position:0% +the things you've learned over the +course of the term can be applied to + + align:start position:0% +course of the term can be applied to + + + align:start position:0% +course of the term can be applied to +your research down the road right that's + + align:start position:0% +your research down the road right that's + + + align:start position:0% +your research down the road right that's +sort of the goal here whether you do + + align:start position:0% +sort of the goal here whether you do + + + align:start position:0% +sort of the goal here whether you do +experiments or modeling or theory at + + align:start position:0% +experiments or modeling or theory at + + + align:start position:0% +experiments or modeling or theory at +some point computation is gonna play a + + align:start position:0% +some point computation is gonna play a + + + align:start position:0% +some point computation is gonna play a +role you should feel comfortable after + + align:start position:0% +role you should feel comfortable after + + + align:start position:0% +role you should feel comfortable after +the things that we've done in this + + align:start position:0% +the things that we've done in this + + + align:start position:0% +the things that we've done in this +course on reaching back to these tools + + align:start position:0% +course on reaching back to these tools + + + align:start position:0% +course on reaching back to these tools +and utilizing them to either solve + + align:start position:0% +and utilizing them to either solve + + + align:start position:0% +and utilizing them to either solve +simple transport models of a drug + + align:start position:0% +simple transport models of a drug + + + align:start position:0% +simple transport models of a drug +delivery problem that you're working on + + align:start position:0% +delivery problem that you're working on + + + align:start position:0% +delivery problem that you're working on +or fitting data reliably doing + + align:start position:0% +or fitting data reliably doing + + + align:start position:0% +or fitting data reliably doing +hypothesis testing of models versus data + + align:start position:0% +hypothesis testing of models versus data + + + align:start position:0% +hypothesis testing of models versus data +you have the tools now to do that the + + align:start position:0% +you have the tools now to do that the + + + align:start position:0% +you have the tools now to do that the +homework assignments that you've + + align:start position:0% +homework assignments that you've + + + align:start position:0% +homework assignments that you've +completed over the course of the term + + align:start position:0% +completed over the course of the term + + + align:start position:0% +completed over the course of the term +sort of lay out the framework in which + + align:start position:0% +sort of lay out the framework in which + + + align:start position:0% +sort of lay out the framework in which +that can be done and and you seem very + + align:start position:0% +that can be done and and you seem very + + + align:start position:0% +that can be done and and you seem very +competent okay well test that confidence + + align:start position:0% +competent okay well test that confidence + + + align:start position:0% +competent okay well test that confidence +on a final exam which is a Monday from + + align:start position:0% +on a final exam which is a Monday from + + + align:start position:0% +on a final exam which is a Monday from +9:00 to 12:00 a.m. it's not in Walker + + align:start position:0% +9:00 to 12:00 a.m. it's not in Walker + + + align:start position:0% +9:00 to 12:00 a.m. it's not in Walker +though okay it's in 56 154 I'll remind + + align:start position:0% +though okay it's in 56 154 I'll remind + + + align:start position:0% +though okay it's in 56 154 I'll remind +you of that again at the end but it's + + align:start position:0% +you of that again at the end but it's + + + align:start position:0% +you of that again at the end but it's +not in Walker so don't show up there at + + align:start position:0% +not in Walker so don't show up there at + + + align:start position:0% +not in Walker so don't show up there at +9:00 a.m. you'll be taking the wrong + + align:start position:0% +9:00 a.m. you'll be taking the wrong + + + align:start position:0% +9:00 a.m. you'll be taking the wrong +final exam it's in 56 there's gonna be a + + align:start position:0% +final exam it's in 56 there's gonna be a + + + align:start position:0% +final exam it's in 56 there's gonna be a +review session with the TAS on Friday + + align:start position:0% +review session with the TAS on Friday + + + align:start position:0% +review session with the TAS on Friday +it's gonna be in this room it's gonna be + + align:start position:0% +it's gonna be in this room it's gonna be + + + align:start position:0% +it's gonna be in this room it's gonna be +from 10 to 12 a.m. and the TAS asked me + + align:start position:0% +from 10 to 12 a.m. and the TAS asked me + + + align:start position:0% +from 10 to 12 a.m. and the TAS asked me +to ask you to review your grade on + + align:start position:0% +to ask you to review your grade on + + + align:start position:0% +to ask you to review your grade on +stellar make sure that everything is + + align:start position:0% +stellar make sure that everything is + + + align:start position:0% +stellar make sure that everything is +entered accurately okay so check that + + align:start position:0% +entered accurately okay so check that + + + align:start position:0% +entered accurately okay so check that +your assignment grades match the grades + + align:start position:0% +your assignment grades match the grades + + + align:start position:0% +your assignment grades match the grades +that are entered there check that your + + align:start position:0% +that are entered there check that your + + + align:start position:0% +that are entered there check that your +quiz grades match the grades that are + + align:start position:0% +quiz grades match the grades that are + + + align:start position:0% +quiz grades match the grades that are +entered there + + align:start position:0% +entered there + + + align:start position:0% +entered there +you're gonna take your final on Monday + + align:start position:0% +you're gonna take your final on Monday + + + align:start position:0% +you're gonna take your final on Monday +and we're gonna grade it on Tuesday and + + align:start position:0% +and we're gonna grade it on Tuesday and + + + align:start position:0% +and we're gonna grade it on Tuesday and +submit your final grades because some of + + align:start position:0% +submit your final grades because some of + + + align:start position:0% +submit your final grades because some of +us have to travel right after the final + + align:start position:0% +us have to travel right after the final + + + align:start position:0% +us have to travel right after the final +exam period so we want to make sure + + align:start position:0% +exam period so we want to make sure + + + align:start position:0% +exam period so we want to make sure +everything is as accurate as possible + + align:start position:0% +everything is as accurate as possible + + + align:start position:0% +everything is as accurate as possible +when we enter the final the final data + + align:start position:0% +when we enter the final the final data + + + align:start position:0% +when we enter the final the final data +okay good + + align:start position:0% + + + + align:start position:0% + +okay so course recap I've done a lot + + align:start position:0% +okay so course recap I've done a lot + + + align:start position:0% +okay so course recap I've done a lot +this term actually right you should be + + align:start position:0% +this term actually right you should be + + + align:start position:0% +this term actually right you should be +really pleased with yourself for having + + align:start position:0% +really pleased with yourself for having + + + align:start position:0% +really pleased with yourself for having +made it this far any one of these + + align:start position:0% +made it this far any one of these + + + align:start position:0% +made it this far any one of these +subjects could comprise an entire course + + align:start position:0% +subjects could comprise an entire course + + + align:start position:0% +subjects could comprise an entire course +in and of itself and you've gotten a + + align:start position:0% +in and of itself and you've gotten a + + + align:start position:0% +in and of itself and you've gotten a +broad overview of all of them so I + + align:start position:0% +broad overview of all of them so I + + + align:start position:0% +broad overview of all of them so I +remind you we started with linear + + align:start position:0% +remind you we started with linear + + + align:start position:0% +remind you we started with linear +algebra I told you the first day that + + align:start position:0% +algebra I told you the first day that + + + align:start position:0% +algebra I told you the first day that +linear algebra would be the underpinning + + align:start position:0% +linear algebra would be the underpinning + + + align:start position:0% +linear algebra would be the underpinning +of all the numerical methods that we + + align:start position:0% +of all the numerical methods that we + + + align:start position:0% +of all the numerical methods that we +utilize along the way and that was true + + align:start position:0% +utilize along the way and that was true + + + align:start position:0% +utilize along the way and that was true +I didn't lie you really wanted to + + align:start position:0% +I didn't lie you really wanted to + + + align:start position:0% +I didn't lie you really wanted to +understand linear algebra well if you + + align:start position:0% +understand linear algebra well if you + + + align:start position:0% +understand linear algebra well if you +were gonna solve any problems + + align:start position:0% +were gonna solve any problems + + + align:start position:0% +were gonna solve any problems +numerically we moved on to things that + + align:start position:0% +numerically we moved on to things that + + + align:start position:0% +numerically we moved on to things that +were more interesting from an + + align:start position:0% +were more interesting from an + + + align:start position:0% +were more interesting from an +engineering context systems of nonlinear + + align:start position:0% +engineering context systems of nonlinear + + + align:start position:0% +engineering context systems of nonlinear +equations an optimization right so being + + align:start position:0% +equations an optimization right so being + + + align:start position:0% +equations an optimization right so being +able to solve engineering problems being + + align:start position:0% +able to solve engineering problems being + + + align:start position:0% +able to solve engineering problems being +able to do engineering design by + + align:start position:0% +able to do engineering design by + + + align:start position:0% +able to do engineering design by +optimizing over various uncontrolled + + align:start position:0% +optimizing over various uncontrolled + + + align:start position:0% +optimizing over various uncontrolled +degrees of freedom is important we did + + align:start position:0% +degrees of freedom is important we did + + + align:start position:0% +degrees of freedom is important we did +both constrained and unconstrained + + align:start position:0% +both constrained and unconstrained + + + align:start position:0% +both constrained and unconstrained +optimization and we moved on to dynamics + + align:start position:0% +optimization and we moved on to dynamics + + + align:start position:0% +optimization and we moved on to dynamics +we did OD initial value problems and D + + align:start position:0% +we did OD initial value problems and D + + + align:start position:0% +we did OD initial value problems and D +AES which are the combination of + + align:start position:0% +AES which are the combination of + + + align:start position:0% +AES which are the combination of +non-linear equations and initial value + + align:start position:0% +non-linear equations and initial value + + + align:start position:0% +non-linear equations and initial value +problems we discussed boundary value + + align:start position:0% +problems we discussed boundary value + + + align:start position:0% +problems we discussed boundary value +problems and partial differential + + align:start position:0% +problems and partial differential + + + align:start position:0% +problems and partial differential +equations which largely are a class of + + align:start position:0% +equations which largely are a class of + + + align:start position:0% +equations which largely are a class of +boundary value problems as well at least + + align:start position:0% +boundary value problems as well at least + + + align:start position:0% +boundary value problems as well at least +the ones that chemical engineers are + + align:start position:0% +the ones that chemical engineers are + + + align:start position:0% +the ones that chemical engineers are +typically interested in and we switched + + align:start position:0% +typically interested in and we switched + + + align:start position:0% +typically interested in and we switched +a little bit we went into probability + + align:start position:0% +a little bit we went into probability + + + align:start position:0% +a little bit we went into probability +and models and data and then we came + + align:start position:0% +and models and data and then we came + + + align:start position:0% +and models and data and then we came +back to more modeling in the form of + + align:start position:0% +back to more modeling in the form of + + + align:start position:0% +back to more modeling in the form of +stochastic simulation and all along this + + align:start position:0% +stochastic simulation and all along this + + + align:start position:0% +stochastic simulation and all along this +was threaded through with lots and lots + + align:start position:0% +was threaded through with lots and lots + + + align:start position:0% +was threaded through with lots and lots +of MATLAB so please to do programming if + + align:start position:0% +of MATLAB so please to do programming if + + + align:start position:0% +of MATLAB so please to do programming if +you didn't know that before + + align:start position:0% +you didn't know that before + + + align:start position:0% +you didn't know that before +MATLAB my labs actually a very useful + + align:start position:0% +MATLAB my labs actually a very useful + + + align:start position:0% +MATLAB my labs actually a very useful +programming tool to know it's not so + + align:start position:0% +programming tool to know it's not so + + + align:start position:0% +programming tool to know it's not so +specific you know there aren't specific + + align:start position:0% +specific you know there aren't specific + + + align:start position:0% +specific you know there aren't specific +quirks in details you need to understand + + align:start position:0% +quirks in details you need to understand + + + align:start position:0% +quirks in details you need to understand +like you would with a lower level + + align:start position:0% +like you would with a lower level + + + align:start position:0% +like you would with a lower level +programming language like C or Fortran + + align:start position:0% +programming language like C or Fortran + + + align:start position:0% +programming language like C or Fortran +it's very high level and the concepts + + align:start position:0% +it's very high level and the concepts + + + align:start position:0% +it's very high level and the concepts +that you utilize there can be translated + + align:start position:0% +that you utilize there can be translated + + + align:start position:0% +that you utilize there can be translated +to other programming languages as well + + align:start position:0% +to other programming languages as well + + + align:start position:0% +to other programming languages as well +so you may find at some point in your + + align:start position:0% +so you may find at some point in your + + + align:start position:0% +so you may find at some point in your +research you want to do a lot of data + + align:start position:0% +research you want to do a lot of data + + + align:start position:0% +research you want to do a lot of data +handling my labs not great for handling + + align:start position:0% +handling my labs not great for handling + + + align:start position:0% +handling my labs not great for handling +data actually parsing large data sets is + + align:start position:0% +data actually parsing large data sets is + + + align:start position:0% +data actually parsing large data sets is +quite difficult and + + align:start position:0% +quite difficult and + + + align:start position:0% +quite difficult and +but there are toolkits that are built + + align:start position:0% +but there are toolkits that are built + + + align:start position:0% +but there are toolkits that are built +into programming environments like + + align:start position:0% +into programming environments like + + + align:start position:0% +into programming environments like +Python that are very efficient at doing + + align:start position:0% +Python that are very efficient at doing + + + align:start position:0% +Python that are very efficient at doing +that and Python is also underpinned by + + align:start position:0% +that and Python is also underpinned by + + + align:start position:0% +that and Python is also underpinned by +similar numerical methods that are + + align:start position:0% +similar numerical methods that are + + + align:start position:0% +similar numerical methods that are +readily accessible what everything you + + align:start position:0% +readily accessible what everything you + + + align:start position:0% +readily accessible what everything you +learned in MATLAB can be applied there + + align:start position:0% +learned in MATLAB can be applied there + + + align:start position:0% +learned in MATLAB can be applied there +as well right so you should have a broad + + align:start position:0% +as well right so you should have a broad + + + align:start position:0% +as well right so you should have a broad +understanding of how to draft an + + align:start position:0% +understanding of how to draft an + + + align:start position:0% +understanding of how to draft an +algorithm how to modularize code right + + align:start position:0% +algorithm how to modularize code right + + + align:start position:0% +algorithm how to modularize code right +how do you integrate several different + + align:start position:0% +how do you integrate several different + + + align:start position:0% +how do you integrate several different +numerical methods together to form a + + align:start position:0% +numerical methods together to form a + + + align:start position:0% +numerical methods together to form a +solution to a more complex problem so we + + align:start position:0% +solution to a more complex problem so we + + + align:start position:0% +solution to a more complex problem so we +did linear algebra this was the basis of + + align:start position:0% +did linear algebra this was the basis of + + + align:start position:0% +did linear algebra this was the basis of +all the problem solving we did + + align:start position:0% +all the problem solving we did + + + align:start position:0% +all the problem solving we did +principally it was concerned with the + + align:start position:0% +principally it was concerned with the + + + align:start position:0% +principally it was concerned with the +solution of systems of linear equations + + align:start position:0% +solution of systems of linear equations + + + align:start position:0% +solution of systems of linear equations +though oftentimes that's sort of + + align:start position:0% +though oftentimes that's sort of + + + align:start position:0% +though oftentimes that's sort of +disguised it isn't a direct system of + + align:start position:0% +disguised it isn't a direct system of + + + align:start position:0% +disguised it isn't a direct system of +linear equations we're trying to solve + + align:start position:0% +linear equations we're trying to solve + + + align:start position:0% +linear equations we're trying to solve +but somehow we need to decompose a + + align:start position:0% +but somehow we need to decompose a + + + align:start position:0% +but somehow we need to decompose a +matrix and in the process of decomposing + + align:start position:0% +matrix and in the process of decomposing + + + align:start position:0% +matrix and in the process of decomposing +it we're essentially doing solution of + + align:start position:0% +it we're essentially doing solution of + + + align:start position:0% +it we're essentially doing solution of +systems of linear equations one thing we + + align:start position:0% +systems of linear equations one thing we + + + align:start position:0% +systems of linear equations one thing we +were really concerned with was how + + align:start position:0% +were really concerned with was how + + + align:start position:0% +were really concerned with was how +linear algebra operations scale with the + + align:start position:0% +linear algebra operations scale with the + + + align:start position:0% +linear algebra operations scale with the +size of the problem that we're + + align:start position:0% +size of the problem that we're + + + align:start position:0% +size of the problem that we're +interested in right the bigger the + + align:start position:0% +interested in right the bigger the + + + align:start position:0% +interested in right the bigger the +system of equations gets right the + + align:start position:0% +system of equations gets right the + + + align:start position:0% +system of equations gets right the +slower the calculation is going to be + + align:start position:0% +slower the calculation is going to be + + + align:start position:0% +slower the calculation is going to be +and how slow can that get right this + + align:start position:0% +and how slow can that get right this + + + align:start position:0% +and how slow can that get right this +will introduce fundamental limits on + + align:start position:0% +will introduce fundamental limits on + + + align:start position:0% +will introduce fundamental limits on +what we can do computationally when we + + align:start position:0% +what we can do computationally when we + + + align:start position:0% +what we can do computationally when we +try to solve partial differential + + align:start position:0% +try to solve partial differential + + + align:start position:0% +try to solve partial differential +equations and we decompose them into + + align:start position:0% +equations and we decompose them into + + + align:start position:0% +equations and we decompose them into +linear equations and we have huge + + align:start position:0% +linear equations and we have huge + + + align:start position:0% +linear equations and we have huge +numbers of states that we'd like to be + + align:start position:0% +numbers of states that we'd like to be + + + align:start position:0% +numbers of states that we'd like to be +able to resolve with that partial + + align:start position:0% +able to resolve with that partial + + + align:start position:0% +able to resolve with that partial +differential equation or the problem can + + align:start position:0% +differential equation or the problem can + + + align:start position:0% +differential equation or the problem can +get so complex so fast that a computer + + align:start position:0% +get so complex so fast that a computer + + + align:start position:0% +get so complex so fast that a computer +can't approaches so being able to + + align:start position:0% +can't approaches so being able to + + + align:start position:0% +can't approaches so being able to +estimate the computational cost of these + + align:start position:0% +estimate the computational cost of these + + + align:start position:0% +estimate the computational cost of these +operations is critical for deciding + + align:start position:0% +operations is critical for deciding + + + align:start position:0% +operations is critical for deciding +whether problem is feasible or + + align:start position:0% +whether problem is feasible or + + + align:start position:0% +whether problem is feasible or +unfeasible right you'd like to know that + + align:start position:0% +unfeasible right you'd like to know that + + + align:start position:0% +unfeasible right you'd like to know that +before you start writing down a + + align:start position:0% +before you start writing down a + + + align:start position:0% +before you start writing down a +numerical solution to the problem so we + + align:start position:0% +numerical solution to the problem so we + + + align:start position:0% +numerical solution to the problem so we +focused a lot on that there was + + align:start position:0% +focused a lot on that there was + + + align:start position:0% +focused a lot on that there was +fundamentals like arithmetic solving + + align:start position:0% +fundamentals like arithmetic solving + + + align:start position:0% +fundamentals like arithmetic solving +linear equations numerically using + + align:start position:0% +linear equations numerically using + + + align:start position:0% +linear equations numerically using +Gaussian elimination for example we + + align:start position:0% +Gaussian elimination for example we + + + align:start position:0% +Gaussian elimination for example we +discussed decomposition in the form of + + align:start position:0% +discussed decomposition in the form of + + + align:start position:0% +discussed decomposition in the form of +eigenvalues and eigenvectors and more + + align:start position:0% +eigenvalues and eigenvectors and more + + + align:start position:0% +eigenvalues and eigenvectors and more +generally the singular value + + align:start position:0% +generally the singular value + + + align:start position:0% +generally the singular value +decomposition and we discussed briefly + + align:start position:0% +decomposition and we discussed briefly + + + align:start position:0% +decomposition and we discussed briefly +iterative solutions of linear equations + + align:start position:0% +iterative solutions of linear equations + + + align:start position:0% +iterative solutions of linear equations +that was sort of our segue into + + align:start position:0% +that was sort of our segue into + + + align:start position:0% +that was sort of our segue into +iterative solutions of nonlinear + + align:start position:0% +iterative solutions of nonlinear + + + align:start position:0% +iterative solutions of nonlinear +equations as well so that was things + + align:start position:0% +equations as well so that was things + + + align:start position:0% +equations as well so that was things +like the + + align:start position:0% +like the + + + align:start position:0% +like the +Koby method or the gauss-seidel method + + align:start position:0% +Koby method or the gauss-seidel method + + + align:start position:0% +Koby method or the gauss-seidel method +which were ways of the really operator + + align:start position:0% +which were ways of the really operator + + + align:start position:0% +which were ways of the really operator +splitting methods of the same sort of + + align:start position:0% +splitting methods of the same sort of + + + align:start position:0% +splitting methods of the same sort of +classes we talked about in PDEs where we + + align:start position:0% +classes we talked about in PDEs where we + + + align:start position:0% +classes we talked about in PDEs where we +took that matrix and we split it into + + align:start position:0% +took that matrix and we split it into + + + align:start position:0% +took that matrix and we split it into +different parts we split it in a way + + align:start position:0% +different parts we split it in a way + + + align:start position:0% +different parts we split it in a way +that would make it convenient to solve a + + align:start position:0% +that would make it convenient to solve a + + + align:start position:0% +that would make it convenient to solve a +simpler system of linear equations and + + align:start position:0% +simpler system of linear equations and + + + align:start position:0% +simpler system of linear equations and +depending on the properties of the + + align:start position:0% +depending on the properties of the + + + align:start position:0% +depending on the properties of the +matrix that that solution might be + + align:start position:0% +matrix that that solution might be + + + align:start position:0% +matrix that that solution might be +achievable or not achievable right the + + align:start position:0% +achievable or not achievable right the + + + align:start position:0% +achievable or not achievable right the +iterative method may not converge but + + align:start position:0% +iterative method may not converge but + + + align:start position:0% +iterative method may not converge but +for certain classes of problems we could + + align:start position:0% +for certain classes of problems we could + + + align:start position:0% +for certain classes of problems we could +guarantee that it would converge and it + + align:start position:0% +guarantee that it would converge and it + + + align:start position:0% +guarantee that it would converge and it +might do it very quickly things we + + align:start position:0% +might do it very quickly things we + + + align:start position:0% +might do it very quickly things we +didn't cover but that are important I + + align:start position:0% +didn't cover but that are important I + + + align:start position:0% +didn't cover but that are important I +think there's a notion called linear + + align:start position:0% +think there's a notion called linear + + + align:start position:0% +think there's a notion called linear +operator theory which is an extension of + + align:start position:0% +operator theory which is an extension of + + + align:start position:0% +operator theory which is an extension of +linear algebra to infinite dimensions + + align:start position:0% +linear algebra to infinite dimensions + + + align:start position:0% +linear algebra to infinite dimensions +you've seen some of this already in your + + align:start position:0% +you've seen some of this already in your + + + align:start position:0% +you've seen some of this already in your +transport class for example where you + + align:start position:0% +transport class for example where you + + + align:start position:0% +transport class for example where you +solve differential equations with sets + + align:start position:0% +solve differential equations with sets + + + align:start position:0% +solve differential equations with sets +of functions right you have some + + align:start position:0% +of functions right you have some + + + align:start position:0% +of functions right you have some +infinite set of functions that you solve + + align:start position:0% +infinite set of functions that you solve + + + align:start position:0% +infinite set of functions that you solve +a differential equation with an ordinary + + align:start position:0% +a differential equation with an ordinary + + + align:start position:0% +a differential equation with an ordinary +differential equation or a partial + + align:start position:0% +differential equation or a partial + + + align:start position:0% +differential equation or a partial +differential equation and all of the + + align:start position:0% +differential equation and all of the + + + align:start position:0% +differential equation and all of the +underpinnings of that fall under linear + + align:start position:0% +underpinnings of that fall under linear + + + align:start position:0% +underpinnings of that fall under linear +operator theory which is an extension of + + align:start position:0% +operator theory which is an extension of + + + align:start position:0% +operator theory which is an extension of +what you've learned already for linear + + align:start position:0% +what you've learned already for linear + + + align:start position:0% +what you've learned already for linear +algebra we talked about Gaussian + + align:start position:0% +algebra we talked about Gaussian + + + align:start position:0% +algebra we talked about Gaussian +elimination and the Lu decomposition + + align:start position:0% +elimination and the Lu decomposition + + + align:start position:0% +elimination and the Lu decomposition +you'll find in the literature there are + + align:start position:0% +you'll find in the literature there are + + + align:start position:0% +you'll find in the literature there are +lots of matrix decomposition methods and + + align:start position:0% +lots of matrix decomposition methods and + + + align:start position:0% +lots of matrix decomposition methods and +the ones that are chosen are chosen for + + align:start position:0% +the ones that are chosen are chosen for + + + align:start position:0% +the ones that are chosen are chosen for +often problems specific reasons so + + align:start position:0% +often problems specific reasons so + + + align:start position:0% +often problems specific reasons so +there's things like the QR decomposition + + align:start position:0% +there's things like the QR decomposition + + + align:start position:0% +there's things like the QR decomposition +or the CH eleska decomposition or the + + align:start position:0% +or the CH eleska decomposition or the + + + align:start position:0% +or the CH eleska decomposition or the +Schur decomposition these are these are + + align:start position:0% +Schur decomposition these are these are + + + align:start position:0% +Schur decomposition these are these are +technical terms you can look them up and + + align:start position:0% +technical terms you can look them up and + + + align:start position:0% +technical terms you can look them up and +you should feel confident that if you + + align:start position:0% +you should feel confident that if you + + + align:start position:0% +you should feel confident that if you +read about them you should be able to + + align:start position:0% +read about them you should be able to + + + align:start position:0% +read about them you should be able to +understand them given the basis and + + align:start position:0% +understand them given the basis and + + + align:start position:0% +understand them given the basis and +linear algebra you have now but we + + align:start position:0% +linear algebra you have now but we + + + align:start position:0% +linear algebra you have now but we +didn't look at those in particular and + + align:start position:0% +didn't look at those in particular and + + + align:start position:0% +didn't look at those in particular and +the state of the art and linear algebra + + align:start position:0% +the state of the art and linear algebra + + + align:start position:0% +the state of the art and linear algebra +and solving systems of linear equations + + align:start position:0% +and solving systems of linear equations + + + align:start position:0% +and solving systems of linear equations +lies in what I referred to as Krylov + + align:start position:0% +lies in what I referred to as Krylov + + + align:start position:0% +lies in what I referred to as Krylov +subspace methods we talked about + + align:start position:0% +subspace methods we talked about + + + align:start position:0% +subspace methods we talked about +conjugate gradient is an iterative + + align:start position:0% +conjugate gradient is an iterative + + + align:start position:0% +conjugate gradient is an iterative +method for linear equations there's a + + align:start position:0% +method for linear equations there's a + + + align:start position:0% +method for linear equations there's a +broader view of that that's this Krylov + + align:start position:0% +broader view of that that's this Krylov + + + align:start position:0% +broader view of that that's this Krylov +sub Krylov subspace method you may see + + align:start position:0% +sub Krylov subspace method you may see + + + align:start position:0% +sub Krylov subspace method you may see +that in the literature from time to time + + align:start position:0% +that in the literature from time to time + + + align:start position:0% +that in the literature from time to time +it's a more same or a more nuanced + + align:start position:0% +it's a more same or a more nuanced + + + align:start position:0% +it's a more same or a more nuanced +discussion of linear dependence of + + align:start position:0% +discussion of linear dependence of + + + align:start position:0% +discussion of linear dependence of +columns in in a matrix and or linear + + align:start position:0% +columns in in a matrix and or linear + + + align:start position:0% +columns in in a matrix and or linear +independence and how + + align:start position:0% +independence and how + + + align:start position:0% +independence and how +can take advantage of that to rapidly + + align:start position:0% +can take advantage of that to rapidly + + + align:start position:0% +can take advantage of that to rapidly +generate iterative solutions to those + + align:start position:0% +generate iterative solutions to those + + + align:start position:0% +generate iterative solutions to those +equations ok any questions about linear + + align:start position:0% +equations ok any questions about linear + + + align:start position:0% +equations ok any questions about linear +algebra no things are clear you've done + + align:start position:0% +algebra no things are clear you've done + + + align:start position:0% +algebra no things are clear you've done +a lot of it this term systems of + + align:start position:0% +a lot of it this term systems of + + + align:start position:0% +a lot of it this term systems of +nonlinear equations so these are of + + align:start position:0% +nonlinear equations so these are of + + + align:start position:0% +nonlinear equations so these are of +course essential for any engineering + + align:start position:0% +course essential for any engineering + + + align:start position:0% +course essential for any engineering +problems of practical importance right + + align:start position:0% +problems of practical importance right + + + align:start position:0% +problems of practical importance right +linear equations tend to be easy to + + align:start position:0% +linear equations tend to be easy to + + + align:start position:0% +linear equations tend to be easy to +solve + + align:start position:0% +solve + + + align:start position:0% +solve +overall most engineering problems that + + align:start position:0% +overall most engineering problems that + + + align:start position:0% +overall most engineering problems that +are interesting are nonlinear by nature + + align:start position:0% +are interesting are nonlinear by nature + + + align:start position:0% +are interesting are nonlinear by nature +that's what makes them interesting and + + align:start position:0% +that's what makes them interesting and + + + align:start position:0% +that's what makes them interesting and +we also saw later on that solving + + align:start position:0% +we also saw later on that solving + + + align:start position:0% +we also saw later on that solving +systems of nonlinear equations was + + align:start position:0% +systems of nonlinear equations was + + + align:start position:0% +systems of nonlinear equations was +intimately associated with optimization + + align:start position:0% +intimately associated with optimization + + + align:start position:0% +intimately associated with optimization +right and so we discussed fundamentals + + align:start position:0% +right and so we discussed fundamentals + + + align:start position:0% +right and so we discussed fundamentals +like convergence of sequences and the + + align:start position:0% +like convergence of sequences and the + + + align:start position:0% +like convergence of sequences and the +rate of convergence of those sequences + + align:start position:0% +rate of convergence of those sequences + + + align:start position:0% +rate of convergence of those sequences +stopping criteria for iterative methods + + align:start position:0% +stopping criteria for iterative methods + + + align:start position:0% +stopping criteria for iterative methods +the best sort of non-linear equation + + align:start position:0% +the best sort of non-linear equation + + + align:start position:0% +the best sort of non-linear equation +solvers in multiple you know with + + align:start position:0% +solvers in multiple you know with + + + align:start position:0% +solvers in multiple you know with +multiple equations and multiple unknowns + + align:start position:0% +multiple equations and multiple unknowns + + + align:start position:0% +multiple equations and multiple unknowns +are newton raphson type methods right + + align:start position:0% +are newton raphson type methods right + + + align:start position:0% +are newton raphson type methods right +they're the ones that are gonna if we're + + align:start position:0% +they're the ones that are gonna if we're + + + align:start position:0% +they're the ones that are gonna if we're +close enough to a solution give us + + align:start position:0% +close enough to a solution give us + + + align:start position:0% +close enough to a solution give us +quadratic convergence which is often + + align:start position:0% +quadratic convergence which is often + + + align:start position:0% +quadratic convergence which is often +more than we deserve it's an + + align:start position:0% +more than we deserve it's an + + + align:start position:0% +more than we deserve it's an +exceptionally fast but it's not globally + + align:start position:0% +exceptionally fast but it's not globally + + + align:start position:0% +exceptionally fast but it's not globally +convergent sort of methodology so we + + align:start position:0% +convergent sort of methodology so we + + + align:start position:0% +convergent sort of methodology so we +also discuss quasi newton raphson + + align:start position:0% +also discuss quasi newton raphson + + + align:start position:0% +also discuss quasi newton raphson +methods that can help enhance the + + align:start position:0% +methods that can help enhance the + + + align:start position:0% +methods that can help enhance the +convergence of newton raphson and then + + align:start position:0% +convergence of newton raphson and then + + + align:start position:0% +convergence of newton raphson and then +we knew that we needed good initial + + align:start position:0% +we knew that we needed good initial + + + align:start position:0% +we knew that we needed good initial +guesses for solving these problems we + + align:start position:0% +guesses for solving these problems we + + + align:start position:0% +guesses for solving these problems we +don't know how many solutions there are + + align:start position:0% +don't know how many solutions there are + + + align:start position:0% +don't know how many solutions there are +we have no idea where they're located + + align:start position:0% +we have no idea where they're located + + + align:start position:0% +we have no idea where they're located +and so we talked about homotopy and + + align:start position:0% +and so we talked about homotopy and + + + align:start position:0% +and so we talked about homotopy and +bifurcation as ways of generating those + + align:start position:0% +bifurcation as ways of generating those + + + align:start position:0% +bifurcation as ways of generating those +initial guesses and ways of tracking + + align:start position:0% +initial guesses and ways of tracking + + + align:start position:0% +initial guesses and ways of tracking +multiple routes or multiple solutions to + + align:start position:0% +multiple routes or multiple solutions to + + + align:start position:0% +multiple routes or multiple solutions to +the system of equations I mentioned + + align:start position:0% +the system of equations I mentioned + + + align:start position:0% +the system of equations I mentioned +briefly during that lecture the concept + + align:start position:0% +briefly during that lecture the concept + + + align:start position:0% +briefly during that lecture the concept +of arc length continuation which is a + + align:start position:0% +of arc length continuation which is a + + + align:start position:0% +of arc length continuation which is a +more advanced sort of homotopy method we + + align:start position:0% +more advanced sort of homotopy method we + + + align:start position:0% +more advanced sort of homotopy method we +didn't get to discuss that in detail + + align:start position:0% +didn't get to discuss that in detail + + + align:start position:0% +didn't get to discuss that in detail +because actually arc length continuation + + align:start position:0% +because actually arc length continuation + + + align:start position:0% +because actually arc length continuation +is a the underlying equation for arc + + align:start position:0% +is a the underlying equation for arc + + + align:start position:0% +is a the underlying equation for arc +length continuation is a Dae okay it's a + + align:start position:0% +length continuation is a Dae okay it's a + + + align:start position:0% +length continuation is a Dae okay it's a +fully implicit Dae that one has to solve + + align:start position:0% +fully implicit Dae that one has to solve + + + align:start position:0% +fully implicit Dae that one has to solve +in order to track the solution path as a + + align:start position:0% +in order to track the solution path as a + + + align:start position:0% +in order to track the solution path as a +function of the cantata peeper ammeter + + align:start position:0% +function of the cantata peeper ammeter + + + align:start position:0% +function of the cantata peeper ammeter +okay so we we didn't cover this we + + align:start position:0% +okay so we we didn't cover this we + + + align:start position:0% +okay so we we didn't cover this we +didn't try to solve any arc length + + align:start position:0% +didn't try to solve any arc length + + + align:start position:0% +didn't try to solve any arc length +continuation problem so it's very common + + align:start position:0% +continuation problem so it's very common + + + align:start position:0% +continuation problem so it's very common +math + + align:start position:0% +math + + + align:start position:0% +math +that's applied to solutions of nonlinear + + align:start position:0% +that's applied to solutions of nonlinear + + + align:start position:0% +that's applied to solutions of nonlinear +equations and we moved on to + + align:start position:0% +equations and we moved on to + + + align:start position:0% +equations and we moved on to +optimization right so we need this for + + align:start position:0% +optimization right so we need this for + + + align:start position:0% +optimization right so we need this for +design we use this for model fitting + + align:start position:0% +design we use this for model fitting + + + align:start position:0% +design we use this for model fitting +right and we discussed both + + align:start position:0% +right and we discussed both + + + align:start position:0% +right and we discussed both +unconstrained and constrained + + align:start position:0% +unconstrained and constrained + + + align:start position:0% +unconstrained and constrained +optimization in the unconstrained + + align:start position:0% +optimization in the unconstrained + + + align:start position:0% +optimization in the unconstrained +context we derived optimality conditions + + align:start position:0% +context we derived optimality conditions + + + align:start position:0% +context we derived optimality conditions +how do we know that we found the + + align:start position:0% +how do we know that we found the + + + align:start position:0% +how do we know that we found the +solution to this problem at least a + + align:start position:0% +solution to this problem at least a + + + align:start position:0% +solution to this problem at least a +locally optimal solution and then we + + align:start position:0% +locally optimal solution and then we + + + align:start position:0% +locally optimal solution and then we +discuss steepest descent methods that + + align:start position:0% +discuss steepest descent methods that + + + align:start position:0% +discuss steepest descent methods that +could get us to that solution with + + align:start position:0% +could get us to that solution with + + + align:start position:0% +could get us to that solution with +linear conversions we discussed + + align:start position:0% +linear conversions we discussed + + + align:start position:0% +linear conversions we discussed +newton-raphson methods that can get us + + align:start position:0% +newton-raphson methods that can get us + + + align:start position:0% +newton-raphson methods that can get us +that solution with quadratic convergence + + align:start position:0% +that solution with quadratic convergence + + + align:start position:0% +that solution with quadratic convergence +we discuss dogleg methods that are + + align:start position:0% +we discuss dogleg methods that are + + + align:start position:0% +we discuss dogleg methods that are +heuristic by nature but meant to mix the + + align:start position:0% +heuristic by nature but meant to mix the + + + align:start position:0% +heuristic by nature but meant to mix the +properties of steepest descent and + + align:start position:0% +properties of steepest descent and + + + align:start position:0% +properties of steepest descent and +newton-raphson to give us reliable + + align:start position:0% +newton-raphson to give us reliable + + + align:start position:0% +newton-raphson to give us reliable +convergence no matter how far we are + + align:start position:0% +convergence no matter how far we are + + + align:start position:0% +convergence no matter how far we are +from the solution we moved on to + + align:start position:0% +from the solution we moved on to + + + align:start position:0% +from the solution we moved on to +constrained optimization and those came + + align:start position:0% +constrained optimization and those came + + + align:start position:0% +constrained optimization and those came +those problems came in two types rate + + align:start position:0% +those problems came in two types rate + + + align:start position:0% +those problems came in two types rate +equality constraints and inequality + + align:start position:0% +equality constraints and inequality + + + align:start position:0% +equality constraints and inequality +constraints and we discussed the method + + align:start position:0% +constraints and we discussed the method + + + align:start position:0% +constraints and we discussed the method +of LaGrange multipliers to handle + + align:start position:0% +of LaGrange multipliers to handle + + + align:start position:0% +of LaGrange multipliers to handle +equality constraints we discussed + + align:start position:0% +equality constraints we discussed + + + align:start position:0% +equality constraints we discussed +interior point methods to handle + + align:start position:0% +interior point methods to handle + + + align:start position:0% +interior point methods to handle +inequality constraints and their mixture + + align:start position:0% +inequality constraints and their mixture + + + align:start position:0% +inequality constraints and their mixture +to handle a combination of equality and + + align:start position:0% +to handle a combination of equality and + + + align:start position:0% +to handle a combination of equality and +inequality constraints we left out a lot + + align:start position:0% +inequality constraints we left out a lot + + + align:start position:0% +inequality constraints we left out a lot +right optimization is a huge field so + + align:start position:0% +right optimization is a huge field so + + + align:start position:0% +right optimization is a huge field so +there's special classes of problems + + align:start position:0% +there's special classes of problems + + + align:start position:0% +there's special classes of problems +called linear programs which are solved + + align:start position:0% +called linear programs which are solved + + + align:start position:0% +called linear programs which are solved +in a particular fashion these are + + align:start position:0% +in a particular fashion these are + + + align:start position:0% +in a particular fashion these are +problems that have a linear dependence + + align:start position:0% +problems that have a linear dependence + + + align:start position:0% +problems that have a linear dependence +on the design variables there's problems + + align:start position:0% +on the design variables there's problems + + + align:start position:0% +on the design variables there's problems +called integer programs right where the + + align:start position:0% +called integer programs right where the + + + align:start position:0% +called integer programs right where the +design variables can only take on + + align:start position:0% +design variables can only take on + + + align:start position:0% +design variables can only take on +integer values these might be very + + align:start position:0% +integer values these might be very + + + align:start position:0% +integer values these might be very +important you can imagine trying to + + align:start position:0% +important you can imagine trying to + + + align:start position:0% +important you can imagine trying to +design a plant and asking what integer + + align:start position:0% +design a plant and asking what integer + + + align:start position:0% +design a plant and asking what integer +number of heat exchangers or separators + + align:start position:0% +number of heat exchangers or separators + + + align:start position:0% +number of heat exchangers or separators +is optimal right associated with + + align:start position:0% +is optimal right associated with + + + align:start position:0% +is optimal right associated with +constraint optimization and inequality + + align:start position:0% +constraint optimization and inequality + + + align:start position:0% +constraint optimization and inequality +constraints there there's an equivalent + + align:start position:0% +constraints there there's an equivalent + + + align:start position:0% +constraints there there's an equivalent +set of optimality conditions so we + + align:start position:0% +set of optimality conditions so we + + + align:start position:0% +set of optimality conditions so we +didn't try to derive they're called the + + align:start position:0% +didn't try to derive they're called the + + + align:start position:0% +didn't try to derive they're called the +KKT conditions so this comes up a lot in + + align:start position:0% +KKT conditions so this comes up a lot in + + + align:start position:0% +KKT conditions so this comes up a lot in +literature so sort of the fundamentals + + align:start position:0% +literature so sort of the fundamentals + + + align:start position:0% +literature so sort of the fundamentals +of knowing that you found the optimum to + + align:start position:0% +of knowing that you found the optimum to + + + align:start position:0% +of knowing that you found the optimum to +the inequality constrained problem + + align:start position:0% +the inequality constrained problem + + + align:start position:0% +the inequality constrained problem +they're not difficult to derive but we + + align:start position:0% +they're not difficult to derive but we + + + align:start position:0% +they're not difficult to derive but we +have a limited amount of time in the + + align:start position:0% +have a limited amount of time in the + + + align:start position:0% +have a limited amount of time in the +class it's something fundamental that's + + align:start position:0% +class it's something fundamental that's + + + align:start position:0% +class it's something fundamental that's +sort of missing and then these + + align:start position:0% +sort of missing and then these + + + align:start position:0% +sort of missing and then these +two methods all find local optima but + + align:start position:0% +two methods all find local optima but + + + align:start position:0% +two methods all find local optima but +oftentimes were interested in global + + align:start position:0% +oftentimes were interested in global + + + align:start position:0% +oftentimes were interested in global +optimization instead and that's not + + align:start position:0% +optimization instead and that's not + + + align:start position:0% +optimization instead and that's not +something that we discussed at all + + align:start position:0% +something that we discussed at all + + + align:start position:0% +something that we discussed at all +that's that's quite complicated and + + align:start position:0% +that's that's quite complicated and + + + align:start position:0% +that's that's quite complicated and +beyond the scope of the course but + + align:start position:0% +beyond the scope of the course but + + + align:start position:0% +beyond the scope of the course but +things like genetic algorithms that's a + + align:start position:0% +things like genetic algorithms that's a + + + align:start position:0% +things like genetic algorithms that's a +term that'll come up a lot that's one + + align:start position:0% +term that'll come up a lot that's one + + + align:start position:0% +term that'll come up a lot that's one +way of trying to seek out global Optima + + align:start position:0% +way of trying to seek out global Optima + + + align:start position:0% +way of trying to seek out global Optima +in the landscape okay + + align:start position:0% +in the landscape okay + + + align:start position:0% +in the landscape okay +ODI VP right so now we want to move from + + align:start position:0% +ODI VP right so now we want to move from + + + align:start position:0% +ODI VP right so now we want to move from +static engineering situations to + + align:start position:0% +static engineering situations to + + + align:start position:0% +static engineering situations to +dynamics okay and we were really + + align:start position:0% +dynamics okay and we were really + + + align:start position:0% +dynamics okay and we were really +concerned when modeling dynamics with + + align:start position:0% +concerned when modeling dynamics with + + + align:start position:0% +concerned when modeling dynamics with +both the accuracy and the stability of + + align:start position:0% +both the accuracy and the stability of + + + align:start position:0% +both the accuracy and the stability of +these methods we were concerned about + + align:start position:0% +these methods we were concerned about + + + align:start position:0% +these methods we were concerned about +stability with other algorithms to write + + align:start position:0% +stability with other algorithms to write + + + align:start position:0% +stability with other algorithms to write +for solutions of non-linear equations we + + align:start position:0% +for solutions of non-linear equations we + + + align:start position:0% +for solutions of non-linear equations we +were concerned with whether the + + align:start position:0% +were concerned with whether the + + + align:start position:0% +were concerned with whether the +newton-raphson method would converge or + + align:start position:0% +newton-raphson method would converge or + + + align:start position:0% +newton-raphson method would converge or +not that's a stability issue in a sense + + align:start position:0% +not that's a stability issue in a sense + + + align:start position:0% +not that's a stability issue in a sense +okay so we're convert we're concerned + + align:start position:0% +okay so we're convert we're concerned + + + align:start position:0% +okay so we're convert we're concerned +with stability there but here we really + + align:start position:0% +with stability there but here we really + + + align:start position:0% +with stability there but here we really +focused on it in detail in part because + + align:start position:0% +focused on it in detail in part because + + + align:start position:0% +focused on it in detail in part because +some of these differential equations are + + align:start position:0% +some of these differential equations are + + + align:start position:0% +some of these differential equations are +inherently unstable okay in engineering + + align:start position:0% +inherently unstable okay in engineering + + + align:start position:0% +inherently unstable okay in engineering +circumstances that happens and we would + + align:start position:0% +circumstances that happens and we would + + + align:start position:0% +circumstances that happens and we would +be unwilling to accept unstable + + align:start position:0% +be unwilling to accept unstable + + + align:start position:0% +be unwilling to accept unstable +solutions in situations where the + + align:start position:0% +solutions in situations where the + + + align:start position:0% +solutions in situations where the +equations themselves are stable okay and + + align:start position:0% +equations themselves are stable okay and + + + align:start position:0% +equations themselves are stable okay and +the case of newton-raphson we could do + + align:start position:0% +the case of newton-raphson we could do + + + align:start position:0% +the case of newton-raphson we could do +these sorts of quasi newton raphson + + align:start position:0% +these sorts of quasi newton raphson + + + align:start position:0% +these sorts of quasi newton raphson +methods to change the path the solution + + align:start position:0% +methods to change the path the solution + + + align:start position:0% +methods to change the path the solution +follows okay and we didn't really care + + align:start position:0% +follows okay and we didn't really care + + + align:start position:0% +follows okay and we didn't really care +what path that followed but here the + + align:start position:0% +what path that followed but here the + + + align:start position:0% +what path that followed but here the +path is important okay we're not free to + + align:start position:0% +path is important okay we're not free to + + + align:start position:0% +path is important okay we're not free to +change the path so the method itself has + + align:start position:0% +change the path so the method itself has + + + align:start position:0% +change the path so the method itself has +to be inherently stable so we discussed + + align:start position:0% +to be inherently stable so we discussed + + + align:start position:0% +to be inherently stable so we discussed +numerical integration we discussed two + + align:start position:0% +numerical integration we discussed two + + + align:start position:0% +numerical integration we discussed two +classes method explicit methods and + + align:start position:0% +classes method explicit methods and + + + align:start position:0% +classes method explicit methods and +implicit methods so explicitly mentioned + + align:start position:0% +implicit methods so explicitly mentioned + + + align:start position:0% +implicit methods so explicitly mentioned +these these explicit runge-kutta + + align:start position:0% +these these explicit runge-kutta + + + align:start position:0% +these these explicit runge-kutta +formulas that been derive for all sorts + + align:start position:0% +formulas that been derive for all sorts + + + align:start position:0% +formulas that been derive for all sorts +of accuracy levels both local truncation + + align:start position:0% +of accuracy levels both local truncation + + + align:start position:0% +of accuracy levels both local truncation +error and global truncation error + + align:start position:0% +error and global truncation error + + + align:start position:0% +error and global truncation error +explicit methods unfortunately you can't + + align:start position:0% +explicit methods unfortunately you can't + + + align:start position:0% +explicit methods unfortunately you can't +guarantee that they're always stable + + align:start position:0% +guarantee that they're always stable + + + align:start position:0% +guarantee that they're always stable +right they lack a property called a + + align:start position:0% +right they lack a property called a + + + align:start position:0% +right they lack a property called a +stability implicit methods on the other + + align:start position:0% +stability implicit methods on the other + + + align:start position:0% +stability implicit methods on the other +hand can be can be made to be stable + + align:start position:0% +hand can be can be made to be stable + + + align:start position:0% +hand can be can be made to be stable +under all circumstances okay + + align:start position:0% +under all circumstances okay + + + align:start position:0% +under all circumstances okay +so one of those is the backward Euler + + align:start position:0% +so one of those is the backward Euler + + + align:start position:0% +so one of those is the backward Euler +method that's a nice one to use the + + align:start position:0% +method that's a nice one to use the + + + align:start position:0% +method that's a nice one to use the +penalty for using these implicit methods + + align:start position:0% +penalty for using these implicit methods + + + align:start position:0% +penalty for using these implicit methods +is you likely have to solve a nonlinear + + align:start position:0% +is you likely have to solve a nonlinear + + + align:start position:0% +is you likely have to solve a nonlinear +equation at each time step so there's a + + align:start position:0% +equation at each time step so there's a + + + align:start position:0% +equation at each time step so there's a +cost that they associated with enhancing + + align:start position:0% +cost that they associated with enhancing + + + align:start position:0% +cost that they associated with enhancing +stability we discussed local and global + + align:start position:0% +stability we discussed local and global + + + align:start position:0% +stability we discussed local and global +truncation error and we talked about + + align:start position:0% +truncation error and we talked about + + + align:start position:0% +truncation error and we talked about +stiffness and linear stability criteria + + align:start position:0% +stiffness and linear stability criteria + + + align:start position:0% +stiffness and linear stability criteria +so linearizing the ordinary differential + + align:start position:0% +so linearizing the ordinary differential + + + align:start position:0% +so linearizing the ordinary differential +equation assessing with the eigen values + + align:start position:0% +equation assessing with the eigen values + + + align:start position:0% +equation assessing with the eigen values +associated with the Jacobian of that + + align:start position:0% +associated with the Jacobian of that + + + align:start position:0% +associated with the Jacobian of that +linearization is and using those eigen + + align:start position:0% +linearization is and using those eigen + + + align:start position:0% +linearization is and using those eigen +values to tell us for example what kind + + align:start position:0% +values to tell us for example what kind + + + align:start position:0% +values to tell us for example what kind +of time steps we need with our method in + + align:start position:0% +of time steps we need with our method in + + + align:start position:0% +of time steps we need with our method in +order to achieve stable integration and + + align:start position:0% +order to achieve stable integration and + + + align:start position:0% +order to achieve stable integration and +time things we didn't cover that are + + align:start position:0% +time things we didn't cover that are + + + align:start position:0% +time things we didn't cover that are +sort of interesting and maybe important + + align:start position:0% +sort of interesting and maybe important + + + align:start position:0% +sort of interesting and maybe important +in engineering contexts one of those is + + align:start position:0% +in engineering contexts one of those is + + + align:start position:0% +in engineering contexts one of those is +event location you may want to know the + + align:start position:0% +event location you may want to know the + + + align:start position:0% +event location you may want to know the +time at which something happens right so + + align:start position:0% +time at which something happens right so + + + align:start position:0% +time at which something happens right so +I may want to know when does the + + align:start position:0% +I may want to know when does the + + + align:start position:0% +I may want to know when does the +solution hit a certain point in time + + align:start position:0% +solution hit a certain point in time + + + align:start position:0% +solution hit a certain point in time +okay maybe I even want to change my + + align:start position:0% +okay maybe I even want to change my + + + align:start position:0% +okay maybe I even want to change my +dynamics when the solution hits a + + align:start position:0% +dynamics when the solution hits a + + + align:start position:0% +dynamics when the solution hits a +particular point in time it's a there's + + align:start position:0% +particular point in time it's a there's + + + align:start position:0% +particular point in time it's a there's +a broader class of methods that can do + + align:start position:0% +a broader class of methods that can do + + + align:start position:0% +a broader class of methods that can do +that they're built into MATLAB to + + align:start position:0% +that they're built into MATLAB to + + + align:start position:0% +that they're built into MATLAB to +actually you can set up these events and + + align:start position:0% +actually you can set up these events and + + + align:start position:0% +actually you can set up these events and +change have the dynamics change or have + + align:start position:0% +change have the dynamics change or have + + + align:start position:0% +change have the dynamics change or have +a report than an event occurred okay but + + align:start position:0% +a report than an event occurred okay but + + + align:start position:0% +a report than an event occurred okay but +we didn't really discuss that at all and + + align:start position:0% +we didn't really discuss that at all and + + + align:start position:0% +we didn't really discuss that at all and +there you know in numerical computing + + align:start position:0% +there you know in numerical computing + + + align:start position:0% +there you know in numerical computing +parallelization is important for + + align:start position:0% +parallelization is important for + + + align:start position:0% +parallelization is important for +studying classes of big problems it's + + align:start position:0% +studying classes of big problems it's + + + align:start position:0% +studying classes of big problems it's +sort of funny but you can even do + + align:start position:0% +sort of funny but you can even do + + + align:start position:0% +sort of funny but you can even do +parallelization in time okay so this is + + align:start position:0% +parallelization in time okay so this is + + + align:start position:0% +parallelization in time okay so this is +something that's been discussed for a + + align:start position:0% +something that's been discussed for a + + + align:start position:0% +something that's been discussed for a +long time and for certain classes of + + align:start position:0% +long time and for certain classes of + + + align:start position:0% +long time and for certain classes of +problems it offers computational + + align:start position:0% +problems it offers computational + + + align:start position:0% +problems it offers computational +advantages over serial integration of + + align:start position:0% +advantages over serial integration of + + + align:start position:0% +advantages over serial integration of +the dynamics of a no dibp so you can + + align:start position:0% +the dynamics of a no dibp so you can + + + align:start position:0% +the dynamics of a no dibp so you can +imagine how do you parallel lies in time + + align:start position:0% +imagine how do you parallel lies in time + + + align:start position:0% +imagine how do you parallel lies in time +so you can take the time window that + + align:start position:0% +so you can take the time window that + + + align:start position:0% +so you can take the time window that +you're interested in and cut it up into + + align:start position:0% +you're interested in and cut it up into + + + align:start position:0% +you're interested in and cut it up into +different slices and you could try to + + align:start position:0% +different slices and you could try to + + + align:start position:0% +different slices and you could try to +solve in parallel the dynamics over each + + align:start position:0% +solve in parallel the dynamics over each + + + align:start position:0% +solve in parallel the dynamics over each +of those slices but for each slice you + + align:start position:0% +of those slices but for each slice you + + + align:start position:0% +of those slices but for each slice you +need an initial condition that has to be + + align:start position:0% +need an initial condition that has to be + + + align:start position:0% +need an initial condition that has to be +precisely prescribed okay and you don't + + align:start position:0% +precisely prescribed okay and you don't + + + align:start position:0% +precisely prescribed okay and you don't +know those initial conditions that's + + align:start position:0% +know those initial conditions that's + + + align:start position:0% +know those initial conditions that's +what the serial integration would tell + + align:start position:0% +what the serial integration would tell + + + align:start position:0% +what the serial integration would tell +you a one way of doing parallel in time + + align:start position:0% +you a one way of doing parallel in time + + + align:start position:0% +you a one way of doing parallel in time +is to say well those initial conditions + + align:start position:0% +is to say well those initial conditions + + + align:start position:0% +is to say well those initial conditions +are unknown + + align:start position:0% +are unknown + + + align:start position:0% +are unknown +and they match up to the terminal + + align:start position:0% +and they match up to the terminal + + + align:start position:0% +and they match up to the terminal +conditions of the previous slice so why + + align:start position:0% +conditions of the previous slice so why + + + align:start position:0% +conditions of the previous slice so why +not wrap this serial integration process + + align:start position:0% +not wrap this serial integration process + + + align:start position:0% +not wrap this serial integration process +in a newton-raphson solver to determine + + align:start position:0% +in a newton-raphson solver to determine + + + align:start position:0% +in a newton-raphson solver to determine +each of these points for certain classes + + align:start position:0% +each of these points for certain classes + + + align:start position:0% +each of these points for certain classes +of problem certain ODI VPS that are + + align:start position:0% +of problem certain ODI VPS that are + + + align:start position:0% +of problem certain ODI VPS that are +inherently stable you can do that and + + align:start position:0% +inherently stable you can do that and + + + align:start position:0% +inherently stable you can do that and +you can get a computational speed-up + + align:start position:0% +you can get a computational speed-up + + + align:start position:0% +you can get a computational speed-up +over over a serial integration just by + + align:start position:0% +over over a serial integration just by + + + align:start position:0% +over over a serial integration just by +doing the integration for each of these + + align:start position:0% +doing the integration for each of these + + + align:start position:0% +doing the integration for each of these +slices on different computers and + + align:start position:0% +slices on different computers and + + + align:start position:0% +slices on different computers and +bringing all the results together right + + align:start position:0% +bringing all the results together right + + + align:start position:0% +bringing all the results together right +the bigger the farmer computers you have + + align:start position:0% +the bigger the farmer computers you have + + + align:start position:0% +the bigger the farmer computers you have +the more slices you can utilize that's + + align:start position:0% +the more slices you can utilize that's + + + align:start position:0% +the more slices you can utilize that's +sort of interesting right parallel in + + align:start position:0% +sort of interesting right parallel in + + + align:start position:0% +sort of interesting right parallel in +time it it's bizarre because we usually + + align:start position:0% +time it it's bizarre because we usually + + + align:start position:0% +time it it's bizarre because we usually +think of time integration as being sort + + align:start position:0% +think of time integration as being sort + + + align:start position:0% +think of time integration as being sort +of causal right I have to know where I + + align:start position:0% +of causal right I have to know where I + + + align:start position:0% +of causal right I have to know where I +was to predict where I'm going but you + + align:start position:0% +was to predict where I'm going but you + + + align:start position:0% +was to predict where I'm going but you +can actually divide these things up and + + align:start position:0% +can actually divide these things up and + + + align:start position:0% +can actually divide these things up and +more sophisticated more sophisticated + + align:start position:0% +more sophisticated more sophisticated + + + align:start position:0% +more sophisticated more sophisticated +ways we talked about be de or PB VPS and + + align:start position:0% +ways we talked about be de or PB VPS and + + + align:start position:0% +ways we talked about be de or PB VPS and +PD es okay we treated them as the same + + align:start position:0% +PD es okay we treated them as the same + + + align:start position:0% +PD es okay we treated them as the same +class of problem broadly usually when + + align:start position:0% +class of problem broadly usually when + + + align:start position:0% +class of problem broadly usually when +engineers chemical engineers are looking + + align:start position:0% +engineers chemical engineers are looking + + + align:start position:0% +engineers chemical engineers are looking +at these problems were where it in + + align:start position:0% +at these problems were where it in + + + align:start position:0% +at these problems were where it in +spatial variation of some sort of a + + align:start position:0% +spatial variation of some sort of a + + + align:start position:0% +spatial variation of some sort of a +conserved quantity so momentum or energy + + align:start position:0% +conserved quantity so momentum or energy + + + align:start position:0% +conserved quantity so momentum or energy +or concentration of a species or mass + + align:start position:0% +or concentration of a species or mass + + + align:start position:0% +or concentration of a species or mass +and here we were also concerned with + + align:start position:0% +and here we were also concerned with + + + align:start position:0% +and here we were also concerned with +both the accuracy and stability of + + align:start position:0% +both the accuracy and stability of + + + align:start position:0% +both the accuracy and stability of +method stability now for when we had + + align:start position:0% +method stability now for when we had + + + align:start position:0% +method stability now for when we had +also time integration of the solution in + + align:start position:0% +also time integration of the solution in + + + align:start position:0% +also time integration of the solution in +addition to spatial variation and so for + + align:start position:0% +addition to spatial variation and so for + + + align:start position:0% +addition to spatial variation and so for +B VPS we talked about shooting methods + + align:start position:0% +B VPS we talked about shooting methods + + + align:start position:0% +B VPS we talked about shooting methods +right so can I recast a boundary value + + align:start position:0% +right so can I recast a boundary value + + + align:start position:0% +right so can I recast a boundary value +problem in one dimension as an initial + + align:start position:0% +problem in one dimension as an initial + + + align:start position:0% +problem in one dimension as an initial +value problem with an unknown okay + + align:start position:0% +value problem with an unknown okay + + + align:start position:0% +value problem with an unknown okay +that's a very common way of solving + + align:start position:0% +that's a very common way of solving + + + align:start position:0% +that's a very common way of solving +these problems and they are sometimes + + align:start position:0% +these problems and they are sometimes + + + align:start position:0% +these problems and they are sometimes +stable and sometimes not when they're + + align:start position:0% +stable and sometimes not when they're + + + align:start position:0% +stable and sometimes not when they're +unstable you can do what's called + + align:start position:0% +unstable you can do what's called + + + align:start position:0% +unstable you can do what's called +multiple shooting where you divide the + + align:start position:0% +multiple shooting where you divide the + + + align:start position:0% +multiple shooting where you divide the +domain up into subdomains and you shoot + + align:start position:0% +domain up into subdomains and you shoot + + + align:start position:0% +domain up into subdomains and you shoot +from the initial condition of each of + + align:start position:0% +from the initial condition of each of + + + align:start position:0% +from the initial condition of each of +those subdomains it looks exactly like + + align:start position:0% +those subdomains it looks exactly like + + + align:start position:0% +those subdomains it looks exactly like +the parallel and time integration that I + + align:start position:0% +the parallel and time integration that I + + + align:start position:0% +the parallel and time integration that I +described for you before and then you + + align:start position:0% +described for you before and then you + + + align:start position:0% +described for you before and then you +try to match up the initial conditions + + align:start position:0% +try to match up the initial conditions + + + align:start position:0% +try to match up the initial conditions +with the terminal conditions to get a + + align:start position:0% +with the terminal conditions to get a + + + align:start position:0% +with the terminal conditions to get a +continuous solution then we discussed + + align:start position:0% +continuous solution then we discussed + + + align:start position:0% +continuous solution then we discussed +relaxation methods for solution of B VPS + + align:start position:0% +relaxation methods for solution of B VPS + + + align:start position:0% +relaxation methods for solution of B VPS +and PDE so colocation golurk in + + align:start position:0% +and PDE so colocation golurk in + + + align:start position:0% +and PDE so colocation golurk in +colocation you'll recall was we want to + + align:start position:0% +colocation you'll recall was we want to + + + align:start position:0% +colocation you'll recall was we want to +try to satisfy the governing equation + + align:start position:0% +try to satisfy the governing equation + + + align:start position:0% +try to satisfy the governing equation +various points in the solution domain + + align:start position:0% +various points in the solution domain + + + align:start position:0% +various points in the solution domain +right so we might write we might write + + align:start position:0% +right so we might write we might write + + + align:start position:0% +right so we might write we might write +our solution as the superposition of a + + align:start position:0% +our solution as the superposition of a + + + align:start position:0% +our solution as the superposition of a +set of functions and then try to satisfy + + align:start position:0% +set of functions and then try to satisfy + + + align:start position:0% +set of functions and then try to satisfy +at various points that we've laid out in + + align:start position:0% +at various points that we've laid out in + + + align:start position:0% +at various points that we've laid out in +the domains maybe there's even an + + align:start position:0% +the domains maybe there's even an + + + align:start position:0% +the domains maybe there's even an +optimal place to put all these points in + + align:start position:0% +optimal place to put all these points in + + + align:start position:0% +optimal place to put all these points in +order to minimize the the error in the + + align:start position:0% +order to minimize the the error in the + + + align:start position:0% +order to minimize the the error in the +solution okay + + align:start position:0% +solution okay + + + align:start position:0% +solution okay +golurk in instead we tried to try to + + align:start position:0% +golurk in instead we tried to try to + + + align:start position:0% +golurk in instead we tried to try to +make the projection right of the error + + align:start position:0% +make the projection right of the error + + + align:start position:0% +make the projection right of the error +in our equations on different different + + align:start position:0% +in our equations on different different + + + align:start position:0% +in our equations on different different +orthogonal functions that represented + + align:start position:0% +orthogonal functions that represented + + + align:start position:0% +orthogonal functions that represented +the solution b0 so that was sort of a + + align:start position:0% +the solution b0 so that was sort of a + + + align:start position:0% +the solution b0 so that was sort of a +global error that we tried to minimize + + align:start position:0% +global error that we tried to minimize + + + align:start position:0% +global error that we tried to minimize +over different orthogonal functions + + align:start position:0% +over different orthogonal functions + + + align:start position:0% +over different orthogonal functions +whereas collocation is sort of a local + + align:start position:0% +whereas collocation is sort of a local + + + align:start position:0% +whereas collocation is sort of a local +error that we're trying to minimize a + + align:start position:0% +error that we're trying to minimize a + + + align:start position:0% +error that we're trying to minimize a +local truncation error that we're trying + + align:start position:0% +local truncation error that we're trying + + + align:start position:0% +local truncation error that we're trying +to minimize we discussed find a + + align:start position:0% +to minimize we discussed find a + + + align:start position:0% +to minimize we discussed find a +difference in finite volume methods as + + align:start position:0% +difference in finite volume methods as + + + align:start position:0% +difference in finite volume methods as +well so ways of discretizing the + + align:start position:0% +well so ways of discretizing the + + + align:start position:0% +well so ways of discretizing the +equations find a difference I would say + + align:start position:0% +equations find a difference I would say + + + align:start position:0% +equations find a difference I would say +is the easiest one to reach for okay if + + align:start position:0% +is the easiest one to reach for okay if + + + align:start position:0% +is the easiest one to reach for okay if +you had to pick a quick and dirty method + + align:start position:0% +you had to pick a quick and dirty method + + + align:start position:0% +you had to pick a quick and dirty method +to try to get a solution finite + + align:start position:0% +to try to get a solution finite + + + align:start position:0% +to try to get a solution finite +difference can be really easy to go to + + align:start position:0% +difference can be really easy to go to + + + align:start position:0% +difference can be really easy to go to +ok it's easy to figure out how big the + + align:start position:0% +ok it's easy to figure out how big the + + + align:start position:0% +ok it's easy to figure out how big the +errors are in your finite difference + + align:start position:0% +errors are in your finite difference + + + align:start position:0% +errors are in your finite difference +method but it may not be the optimal + + align:start position:0% +method but it may not be the optimal + + + align:start position:0% +method but it may not be the optimal +approach to the problem for certain + + align:start position:0% +approach to the problem for certain + + + align:start position:0% +approach to the problem for certain +geometry is finite volume is really far + + align:start position:0% +geometry is finite volume is really far + + + align:start position:0% +geometry is finite volume is really far +more preferable because it's easy test + + align:start position:0% +more preferable because it's easy test + + + align:start position:0% +more preferable because it's easy test +to make the fluxes through surfaces of + + align:start position:0% +to make the fluxes through surfaces of + + + align:start position:0% +to make the fluxes through surfaces of +funny shapes where your grid shape now + + align:start position:0% +funny shapes where your grid shape now + + + align:start position:0% +funny shapes where your grid shape now +conforms to your geometry finite volume + + align:start position:0% +conforms to your geometry finite volume + + + align:start position:0% +conforms to your geometry finite volume +also had the advantage of being strictly + + align:start position:0% +also had the advantage of being strictly + + + align:start position:0% +also had the advantage of being strictly +conservative right so I can never gain + + align:start position:0% +conservative right so I can never gain + + + align:start position:0% +conservative right so I can never gain +or lose a conserved quantity and the + + align:start position:0% +or lose a conserved quantity and the + + + align:start position:0% +or lose a conserved quantity and the +finite volume method at least within the + + align:start position:0% +finite volume method at least within the + + + align:start position:0% +finite volume method at least within the +numerical error and that isn't true of + + align:start position:0% +numerical error and that isn't true of + + + align:start position:0% +numerical error and that isn't true of +finite difference or finite element so + + align:start position:0% +finite difference or finite element so + + + align:start position:0% +finite difference or finite element so +if I'm concerned about those things + + align:start position:0% +if I'm concerned about those things + + + align:start position:0% +if I'm concerned about those things +finite volume is really the approach to + + align:start position:0% +finite volume is really the approach to + + + align:start position:0% +finite volume is really the approach to +use and you'll find about so you know + + align:start position:0% +use and you'll find about so you know + + + align:start position:0% +use and you'll find about so you know +one fluid mechanical solver that's + + align:start position:0% +one fluid mechanical solver that's + + + align:start position:0% +one fluid mechanical solver that's +freely available you could go download + + align:start position:0% +freely available you could go download + + + align:start position:0% +freely available you could go download +and use it use it today and it's widely + + align:start position:0% +and use it use it today and it's widely + + + align:start position:0% +and use it use it today and it's widely +used in research is open foam and that's + + align:start position:0% +used in research is open foam and that's + + + align:start position:0% +used in research is open foam and that's +all based on the finite volume method + + align:start position:0% +all based on the finite volume method + + + align:start position:0% +all based on the finite volume method +right so they're trying to conserve + + align:start position:0% +right so they're trying to conserve + + + align:start position:0% +right so they're trying to conserve +momentum conserve mass and conserve + + align:start position:0% +momentum conserve mass and conserve + + + align:start position:0% +momentum conserve mass and conserve +energy associated with the fluid right + + align:start position:0% +energy associated with the fluid right + + + align:start position:0% +energy associated with the fluid right +open foam is good at drawing bizarre + + align:start position:0% +open foam is good at drawing bizarre + + + align:start position:0% +open foam is good at drawing bizarre +grids of the domain + + align:start position:0% +grids of the domain + + + align:start position:0% +grids of the domain +be very accurate integration of fluid + + align:start position:0% +be very accurate integration of fluid + + + align:start position:0% +be very accurate integration of fluid +mechanical equations and it's good at + + align:start position:0% +mechanical equations and it's good at + + + align:start position:0% +mechanical equations and it's good at +doing that because it uses finite volume + + align:start position:0% +doing that because it uses finite volume + + + align:start position:0% +doing that because it uses finite volume +you discussed the method of lines which + + align:start position:0% +you discussed the method of lines which + + + align:start position:0% +you discussed the method of lines which +was a way of discretizing space but + + align:start position:0% +was a way of discretizing space but + + + align:start position:0% +was a way of discretizing space but +leaving the time dimension undisguised + + align:start position:0% +leaving the time dimension undisguised + + + align:start position:0% +leaving the time dimension undisguised +and then applying OD ivp methods for + + align:start position:0% +and then applying OD ivp methods for + + + align:start position:0% +and then applying OD ivp methods for +solving right solving in time it's an + + align:start position:0% +solving right solving in time it's an + + + align:start position:0% +solving right solving in time it's an +incredibly useful way to approach those + + align:start position:0% +incredibly useful way to approach those + + + align:start position:0% +incredibly useful way to approach those +problems because it leverages expertise + + align:start position:0% +problems because it leverages expertise + + + align:start position:0% +problems because it leverages expertise +in two different techniques right + + align:start position:0% +in two different techniques right + + + align:start position:0% +in two different techniques right +they're specialized methods for doing + + align:start position:0% +they're specialized methods for doing + + + align:start position:0% +they're specialized methods for doing +time integration with some spatial + + align:start position:0% +time integration with some spatial + + + align:start position:0% +time integration with some spatial +discretization that are vetted for their + + align:start position:0% +discretization that are vetted for their + + + align:start position:0% +discretization that are vetted for their +stability properties and their accuracy + + align:start position:0% +stability properties and their accuracy + + + align:start position:0% +stability properties and their accuracy +and the third those are fine but I would + + align:start position:0% +and the third those are fine but I would + + + align:start position:0% +and the third those are fine but I would +say they're a little antiquated they're + + align:start position:0% +say they're a little antiquated they're + + + align:start position:0% +say they're a little antiquated they're +reliable for particular classes of + + align:start position:0% +reliable for particular classes of + + + align:start position:0% +reliable for particular classes of +problems but for general problems you + + align:start position:0% +problems but for general problems you + + + align:start position:0% +problems but for general problems you +may not have any idea whether they're + + align:start position:0% +may not have any idea whether they're + + + align:start position:0% +may not have any idea whether they're +gonna work or not whereas method of + + align:start position:0% +gonna work or not whereas method of + + + align:start position:0% +gonna work or not whereas method of +lines may be a really good approach to a + + align:start position:0% +lines may be a really good approach to a + + + align:start position:0% +lines may be a really good approach to a +you know to a parabolic partial + + align:start position:0% +you know to a parabolic partial + + + align:start position:0% +you know to a parabolic partial +differential equation you're working + + align:start position:0% +differential equation you're working + + + align:start position:0% +differential equation you're working +with where you can just rely on the + + align:start position:0% +with where you can just rely on the + + + align:start position:0% +with where you can just rely on the +adaptive time stepping and air control + + align:start position:0% +adaptive time stepping and air control + + + align:start position:0% +adaptive time stepping and air control +and an OD IVP solver to keep everything + + align:start position:0% +and an OD IVP solver to keep everything + + + align:start position:0% +and an OD IVP solver to keep everything +stable in time that you integrate + + align:start position:0% +stable in time that you integrate + + + align:start position:0% +stable in time that you integrate +forward we did application of commercial + + align:start position:0% +forward we did application of commercial + + + align:start position:0% +forward we did application of commercial +software so use COMSOL to solve a + + align:start position:0% +software so use COMSOL to solve a + + + align:start position:0% +software so use COMSOL to solve a +problem I don't know would you say was + + align:start position:0% +problem I don't know would you say was + + + align:start position:0% +problem I don't know would you say was +COMSOL easier to use than writing your + + align:start position:0% +COMSOL easier to use than writing your + + + align:start position:0% +COMSOL easier to use than writing your +own MATLAB code harder to use than + + align:start position:0% +own MATLAB code harder to use than + + + align:start position:0% +own MATLAB code harder to use than +writing your own MATLAB code do you + + align:start position:0% +writing your own MATLAB code do you + + + align:start position:0% +writing your own MATLAB code do you +think no easier to use but the result I + + align:start position:0% +think no easier to use but the result I + + + align:start position:0% +think no easier to use but the result I +would say it wasn't as good without some + + align:start position:0% +would say it wasn't as good without some + + + align:start position:0% +would say it wasn't as good without some +careful refinement of the COMSOL + + align:start position:0% +careful refinement of the COMSOL + + + align:start position:0% +careful refinement of the COMSOL +solution right so you really for that + + align:start position:0% +solution right so you really for that + + + align:start position:0% +solution right so you really for that +particular problem if you wanted a + + align:start position:0% +particular problem if you wanted a + + + align:start position:0% +particular problem if you wanted a +solution that looked like your MATLAB + + align:start position:0% +solution that looked like your MATLAB + + + align:start position:0% +solution that looked like your MATLAB +solution that was carefully resolved in + + align:start position:0% +solution that was carefully resolved in + + + align:start position:0% +solution that was carefully resolved in +space you really had to go in and refine + + align:start position:0% +space you really had to go in and refine + + + align:start position:0% +space you really had to go in and refine +the grid in particular places right so + + align:start position:0% +the grid in particular places right so + + + align:start position:0% +the grid in particular places right so +it gets gets harder and harder the more + + align:start position:0% +it gets gets harder and harder the more + + + align:start position:0% +it gets gets harder and harder the more +detail you want but it's a it's an easy + + align:start position:0% +detail you want but it's a it's an easy + + + align:start position:0% +detail you want but it's a it's an easy +way to get an answer you should check + + align:start position:0% +way to get an answer you should check + + + align:start position:0% +way to get an answer you should check +whether that answer is right by + + align:start position:0% +whether that answer is right by + + + align:start position:0% +whether that answer is right by +comparing it with other methods you + + align:start position:0% +comparing it with other methods you + + + align:start position:0% +comparing it with other methods you +can't guarantee that it's giving you the + + align:start position:0% +can't guarantee that it's giving you the + + + align:start position:0% +can't guarantee that it's giving you the +right result either okay give you an + + align:start position:0% +right result either okay give you an + + + align:start position:0% +right result either okay give you an +example I had I'd mentioned an unsteady + + align:start position:0% +example I had I'd mentioned an unsteady + + + align:start position:0% +example I had I'd mentioned an unsteady +advection diffusion problem to one of my + + align:start position:0% +advection diffusion problem to one of my + + + align:start position:0% +advection diffusion problem to one of my +grad + + align:start position:0% +grad + + + align:start position:0% +grad +students and he's very good with COMSOL + + align:start position:0% +students and he's very good with COMSOL + + + align:start position:0% +students and he's very good with COMSOL +it was quite I mentioned that it was a + + align:start position:0% +it was quite I mentioned that it was a + + + align:start position:0% +it was quite I mentioned that it was a +hard problem because their boundary + + align:start position:0% +hard problem because their boundary + + + align:start position:0% +hard problem because their boundary +layers and the boundary layers changed + + align:start position:0% +layers and the boundary layers changed + + + align:start position:0% +layers and the boundary layers changed +thickness and time and resolving those + + align:start position:0% +thickness and time and resolving those + + + align:start position:0% +thickness and time and resolving those +things can be can be quite challenging + + align:start position:0% +things can be can be quite challenging + + + align:start position:0% +things can be can be quite challenging +without any physical insight well I + + align:start position:0% +without any physical insight well I + + + align:start position:0% +without any physical insight well I +thought they think I could just do it in + + align:start position:0% +thought they think I could just do it in + + + align:start position:0% +thought they think I could just do it in +COMSOL and he he he tried it and COMSOL + + align:start position:0% +COMSOL and he he he tried it and COMSOL + + + align:start position:0% +COMSOL and he he he tried it and COMSOL +was happy to report a solution in time + + align:start position:0% +was happy to report a solution in time + + + align:start position:0% +was happy to report a solution in time +and space but the solution was + + align:start position:0% +and space but the solution was + + + align:start position:0% +and space but the solution was +nonsensical right we could visualize it + + align:start position:0% +nonsensical right we could visualize it + + + align:start position:0% +nonsensical right we could visualize it +and see that it didn't look like what + + align:start position:0% +and see that it didn't look like what + + + align:start position:0% +and see that it didn't look like what +other numerical solutions look like and + + align:start position:0% +other numerical solutions look like and + + + align:start position:0% +other numerical solutions look like and +in certain limits didn't correspond to + + align:start position:0% +in certain limits didn't correspond to + + + align:start position:0% +in certain limits didn't correspond to +what those solutions are known to be in + + align:start position:0% +what those solutions are known to be in + + + align:start position:0% +what those solutions are known to be in +those limits so you know that the the + + align:start position:0% +those limits so you know that the the + + + align:start position:0% +those limits so you know that the the +black box is great in that it reports an + + align:start position:0% +black box is great in that it reports an + + + align:start position:0% +black box is great in that it reports an +answer but it can also be really + + align:start position:0% +answer but it can also be really + + + align:start position:0% +answer but it can also be really +problematic as well so maybe have + + align:start position:0% +problematic as well so maybe have + + + align:start position:0% +problematic as well so maybe have +expertise with counsel you can get a + + align:start position:0% +expertise with counsel you can get a + + + align:start position:0% +expertise with counsel you can get a +solution to converge for a difficult + + align:start position:0% +solution to converge for a difficult + + + align:start position:0% +solution to converge for a difficult +problem but you should really have other + + align:start position:0% +problem but you should really have other + + + align:start position:0% +problem but you should really have other +methodologies that let you assess how + + align:start position:0% +methodologies that let you assess how + + + align:start position:0% +methodologies that let you assess how +assess the quality of that solution + + align:start position:0% +assess the quality of that solution + + + align:start position:0% +assess the quality of that solution +right for simple problems simple + + align:start position:0% +right for simple problems simple + + + align:start position:0% +right for simple problems simple +elliptic problems and simple parabolic + + align:start position:0% +elliptic problems and simple parabolic + + + align:start position:0% +elliptic problems and simple parabolic +problems it's going to do great because + + align:start position:0% +problems it's going to do great because + + + align:start position:0% +problems it's going to do great because +it's built to eat those for breakfast + + align:start position:0% +it's built to eat those for breakfast + + + align:start position:0% +it's built to eat those for breakfast +but for complicated engineering problems + + align:start position:0% +but for complicated engineering problems + + + align:start position:0% +but for complicated engineering problems +you've got to vet your solutions okay Oh + + align:start position:0% +you've got to vet your solutions okay Oh + + + align:start position:0% +you've got to vet your solutions okay Oh +what didn't we cover we didn't talk + + align:start position:0% +what didn't we cover we didn't talk + + + align:start position:0% +what didn't we cover we didn't talk +about hyperbolic equations not really we + + align:start position:0% +about hyperbolic equations not really we + + + align:start position:0% +about hyperbolic equations not really we +talked a little bit about advection + + align:start position:0% +talked a little bit about advection + + + align:start position:0% +talked a little bit about advection +equations okay which have a hyperbolic + + align:start position:0% +equations okay which have a hyperbolic + + + align:start position:0% +equations okay which have a hyperbolic +character associated with them so you + + align:start position:0% +character associated with them so you + + + align:start position:0% +character associated with them so you +have like a pulse of solute and it's + + align:start position:0% +have like a pulse of solute and it's + + + align:start position:0% +have like a pulse of solute and it's +affected along in time and you want that + + align:start position:0% +affected along in time and you want that + + + align:start position:0% +affected along in time and you want that +advection to be stable so you want to + + align:start position:0% +advection to be stable so you want to + + + align:start position:0% +advection to be stable so you want to +use things like upwind differencing to + + align:start position:0% +use things like upwind differencing to + + + align:start position:0% +use things like upwind differencing to +ensure that stability but there's a + + align:start position:0% +ensure that stability but there's a + + + align:start position:0% +ensure that stability but there's a +broader class of hyperbolic problems + + align:start position:0% +broader class of hyperbolic problems + + + align:start position:0% +broader class of hyperbolic problems +that relate to things like the motion of + + align:start position:0% +that relate to things like the motion of + + + align:start position:0% +that relate to things like the motion of +waves okay in elastic solids we don't + + align:start position:0% +waves okay in elastic solids we don't + + + align:start position:0% +waves okay in elastic solids we don't +typically encounter those in chemical + + align:start position:0% +typically encounter those in chemical + + + align:start position:0% +typically encounter those in chemical +engineering but Chemical Engineering is + + align:start position:0% +engineering but Chemical Engineering is + + + align:start position:0% +engineering but Chemical Engineering is +a broad discipline it may be your your + + align:start position:0% +a broad discipline it may be your your + + + align:start position:0% +a broad discipline it may be your your +engineering soft materials for some sort + + align:start position:0% +engineering soft materials for some sort + + + align:start position:0% +engineering soft materials for some sort +of device and you want to look at the + + align:start position:0% +of device and you want to look at the + + + align:start position:0% +of device and you want to look at the +elastic response of that material that + + align:start position:0% +elastic response of that material that + + + align:start position:0% +elastic response of that material that +the PDEs that govern that are a + + align:start position:0% +the PDEs that govern that are a + + + align:start position:0% +the PDEs that govern that are a +completely different class than the ones + + align:start position:0% +completely different class than the ones + + + align:start position:0% +completely different class than the ones +that we typically look at they're not + + align:start position:0% +that we typically look at they're not + + + align:start position:0% +that we typically look at they're not +parabolic they're not elliptic they're + + align:start position:0% +parabolic they're not elliptic they're + + + align:start position:0% +parabolic they're not elliptic they're +hyperbolic and they have these wave-like + + align:start position:0% +hyperbolic and they have these wave-like + + + align:start position:0% +hyperbolic and they have these wave-like +solutions associated with them there + + align:start position:0% +solutions associated with them there + + + align:start position:0% +solutions associated with them there +particular solution methods in order to + + align:start position:0% +particular solution methods in order to + + + align:start position:0% +particular solution methods in order to +be stable and accurate and then there + + align:start position:0% +be stable and accurate and then there + + + align:start position:0% +be stable and accurate and then there +are all sorts of specialized methods + + align:start position:0% +are all sorts of specialized methods + + + align:start position:0% +are all sorts of specialized methods +that are dreamed up to apply to maybe a + + align:start position:0% +that are dreamed up to apply to maybe a + + + align:start position:0% +that are dreamed up to apply to maybe a +broad class of problems but they're it's + + align:start position:0% +broad class of problems but they're it's + + + align:start position:0% +broad class of problems but they're it's +kind of hard to ensure that they're + + align:start position:0% +kind of hard to ensure that they're + + + align:start position:0% +kind of hard to ensure that they're +gonna work but nonetheless you you'll + + align:start position:0% +gonna work but nonetheless you you'll + + + align:start position:0% +gonna work but nonetheless you you'll +see a lot of this out in the literature + + align:start position:0% +see a lot of this out in the literature + + + align:start position:0% +see a lot of this out in the literature +so they're things called multi grid + + align:start position:0% +so they're things called multi grid + + + align:start position:0% +so they're things called multi grid +methods they try to discretize a partial + + align:start position:0% +methods they try to discretize a partial + + + align:start position:0% +methods they try to discretize a partial +differential equation with different + + align:start position:0% +differential equation with different + + + align:start position:0% +differential equation with different +levels of fineness and use coarse + + align:start position:0% +levels of fineness and use coarse + + + align:start position:0% +levels of fineness and use coarse +solutions as initial guesses for finer + + align:start position:0% +solutions as initial guesses for finer + + + align:start position:0% +solutions as initial guesses for finer +and finer solutions in space for some + + align:start position:0% +and finer solutions in space for some + + + align:start position:0% +and finer solutions in space for some +problems this works great in fact you + + align:start position:0% +problems this works great in fact you + + + align:start position:0% +problems this works great in fact you +can show that it's you know that it can + + align:start position:0% +can show that it's you know that it can + + + align:start position:0% +can show that it's you know that it can +work as well as is possible + + align:start position:0% +work as well as is possible + + + align:start position:0% +work as well as is possible +so depending on like the size of the + + align:start position:0% +so depending on like the size of the + + + align:start position:0% +so depending on like the size of the +problem you can you say have endpoints + + align:start position:0% +problem you can you say have endpoints + + + align:start position:0% +problem you can you say have endpoints +of which you want to find the solution + + align:start position:0% +of which you want to find the solution + + + align:start position:0% +of which you want to find the solution +you can find it in order n time with + + align:start position:0% +you can find it in order n time with + + + align:start position:0% +you can find it in order n time with +some of these methods okay depending on + + align:start position:0% +some of these methods okay depending on + + + align:start position:0% +some of these methods okay depending on +the particular problem you're looking at + + align:start position:0% +the particular problem you're looking at + + + align:start position:0% +the particular problem you're looking at +which is that's good but oftentimes + + align:start position:0% +which is that's good but oftentimes + + + align:start position:0% +which is that's good but oftentimes +engineering problems aren't of that sort + + align:start position:0% +engineering problems aren't of that sort + + + align:start position:0% +engineering problems aren't of that sort +there's something more complicated going + + align:start position:0% +there's something more complicated going + + + align:start position:0% +there's something more complicated going +on and it's hard to ensure that you get + + align:start position:0% +on and it's hard to ensure that you get + + + align:start position:0% +on and it's hard to ensure that you get +those sorts of rates of convergence but + + align:start position:0% +those sorts of rates of convergence but + + + align:start position:0% +those sorts of rates of convergence but +nonetheless they exist and something + + align:start position:0% +nonetheless they exist and something + + + align:start position:0% +nonetheless they exist and something +that we we didn't cover you should be + + align:start position:0% +that we we didn't cover you should be + + + align:start position:0% +that we we didn't cover you should be +aware of we did da EES so now we coupled + + align:start position:0% +aware of we did da EES so now we coupled + + + align:start position:0% +aware of we did da EES so now we coupled +ODI VPS with nonlinear algebraic + + align:start position:0% +ODI VPS with nonlinear algebraic + + + align:start position:0% +ODI VPS with nonlinear algebraic +equations most dynamic engineering + + align:start position:0% +equations most dynamic engineering + + + align:start position:0% +equations most dynamic engineering +problems are of this type we showed the + + align:start position:0% +problems are of this type we showed the + + + align:start position:0% +problems are of this type we showed the +days are really an issue with model + + align:start position:0% +days are really an issue with model + + + align:start position:0% +days are really an issue with model +formulation ultimately right we write + + align:start position:0% +formulation ultimately right we write + + + align:start position:0% +formulation ultimately right we write +down conservation equations and we write + + align:start position:0% +down conservation equations and we write + + + align:start position:0% +down conservation equations and we write +down certain constraints on those + + align:start position:0% +down certain constraints on those + + + align:start position:0% +down certain constraints on those +conservation equations the constraints + + align:start position:0% +conservation equations the constraints + + + align:start position:0% +conservation equations the constraints +can be specifications like we want + + align:start position:0% +can be specifications like we want + + + align:start position:0% +can be specifications like we want +particular flow rates in certain places + + align:start position:0% +particular flow rates in certain places + + + align:start position:0% +particular flow rates in certain places +or they can be fundamental they can be + + align:start position:0% +or they can be fundamental they can be + + + align:start position:0% +or they can be fundamental they can be +thermodynamic constraints on the + + align:start position:0% +thermodynamic constraints on the + + + align:start position:0% +thermodynamic constraints on the +coexistence of different different + + align:start position:0% +coexistence of different different + + + align:start position:0% +coexistence of different different +phases of a particular material in a + + align:start position:0% +phases of a particular material in a + + + align:start position:0% +phases of a particular material in a +particular unit operation if we could + + align:start position:0% +particular unit operation if we could + + + align:start position:0% +particular unit operation if we could +solve those constraints for certain + + align:start position:0% +solve those constraints for certain + + + align:start position:0% +solve those constraints for certain +unknowns and substitute them in the + + align:start position:0% +unknowns and substitute them in the + + + align:start position:0% +unknowns and substitute them in the +equations we might be able to produce + + align:start position:0% +equations we might be able to produce + + + align:start position:0% +equations we might be able to produce +ODI vp's probably we can't come up with + + align:start position:0% +ODI vp's probably we can't come up with + + + align:start position:0% +ODI vp's probably we can't come up with +those solutions so instead we've always + + align:start position:0% +those solutions so instead we've always + + + align:start position:0% +those solutions so instead we've always +got this coupled system of initial value + + align:start position:0% +got this coupled system of initial value + + + align:start position:0% +got this coupled system of initial value +problems with nonlinear equations okay + + align:start position:0% +problems with nonlinear equations okay + + + align:start position:0% +problems with nonlinear equations okay +so you have that sort of a circumstance + + align:start position:0% +so you have that sort of a circumstance + + + align:start position:0% +so you have that sort of a circumstance +how should you think about that one way + + align:start position:0% +how should you think about that one way + + + align:start position:0% +how should you think about that one way +to think about it was to say that the + + align:start position:0% +to think about it was to say that the + + + align:start position:0% +to think about it was to say that the +algebraic equations are essentially + + align:start position:0% +algebraic equations are essentially + + + align:start position:0% +algebraic equations are essentially +infinitely stiff right they have to be + + align:start position:0% +infinitely stiff right they have to be + + + align:start position:0% +infinitely stiff right they have to be +imposed exactly at every time step + + align:start position:0% +imposed exactly at every time step + + + align:start position:0% +imposed exactly at every time step +they never relax in time with the finite + + align:start position:0% +they never relax in time with the finite + + + align:start position:0% +they never relax in time with the finite +time constant so we knew that those + + align:start position:0% +time constant so we knew that those + + + align:start position:0% +time constant so we knew that those +sorts of methods are hard to resolve + + align:start position:0% +sorts of methods are hard to resolve + + + align:start position:0% +sorts of methods are hard to resolve +with typical OD solvers and we tried to + + align:start position:0% +with typical OD solvers and we tried to + + + align:start position:0% +with typical OD solvers and we tried to +assess that by computing something + + align:start position:0% +assess that by computing something + + + align:start position:0% +assess that by computing something +called the differential index so we + + align:start position:0% +called the differential index so we + + + align:start position:0% +called the differential index so we +asked how many times do I have to take + + align:start position:0% +asked how many times do I have to take + + + align:start position:0% +asked how many times do I have to take +derivatives of the algebraic equations + + align:start position:0% +derivatives of the algebraic equations + + + align:start position:0% +derivatives of the algebraic equations +or any new algebraic constraints in + + align:start position:0% +or any new algebraic constraints in + + + align:start position:0% +or any new algebraic constraints in +order to get a system of ordinary + + align:start position:0% +order to get a system of ordinary + + + align:start position:0% +order to get a system of ordinary +differential equations that represent + + align:start position:0% +differential equations that represent + + + align:start position:0% +differential equations that represent +the same model I may want to solve that + + align:start position:0% +the same model I may want to solve that + + + align:start position:0% +the same model I may want to solve that +system of ordinary differential + + align:start position:0% +system of ordinary differential + + + align:start position:0% +system of ordinary differential +equations or I may just want to know the + + align:start position:0% +equations or I may just want to know the + + + align:start position:0% +equations or I may just want to know the +differential index so that I can choose + + align:start position:0% +differential index so that I can choose + + + align:start position:0% +differential index so that I can choose +a particular method to solve this + + align:start position:0% +a particular method to solve this + + + align:start position:0% +a particular method to solve this +problem we saw the higher the index was + + align:start position:0% +problem we saw the higher the index was + + + align:start position:0% +problem we saw the higher the index was +the more sensitive the solution was to + + align:start position:0% +the more sensitive the solution was to + + + align:start position:0% +the more sensitive the solution was to +perturbations in different input + + align:start position:0% +perturbations in different input + + + align:start position:0% +perturbations in different input +variables right so the differential + + align:start position:0% +variables right so the differential + + + align:start position:0% +variables right so the differential +index played an important role in + + align:start position:0% +index played an important role in + + + align:start position:0% +index played an important role in +telling us something physical about the + + align:start position:0% +telling us something physical about the + + + align:start position:0% +telling us something physical about the +problem and the responses that could be + + align:start position:0% +problem and the responses that could be + + + align:start position:0% +problem and the responses that could be +elicited by da e systems we also talked + + align:start position:0% +elicited by da e systems we also talked + + + align:start position:0% +elicited by da e systems we also talked +about consistent initialization right I + + align:start position:0% +about consistent initialization right I + + + align:start position:0% +about consistent initialization right I +need to prescribe the initial conditions + + align:start position:0% +need to prescribe the initial conditions + + + align:start position:0% +need to prescribe the initial conditions +for all the differential and algebraic + + align:start position:0% +for all the differential and algebraic + + + align:start position:0% +for all the differential and algebraic +variables can I prescribe any of those + + align:start position:0% +variables can I prescribe any of those + + + align:start position:0% +variables can I prescribe any of those +independently well the answer is + + align:start position:0% +independently well the answer is + + + align:start position:0% +independently well the answer is +actually no right depending on the + + align:start position:0% +actually no right depending on the + + + align:start position:0% +actually no right depending on the +differential index there are underlying + + align:start position:0% +differential index there are underlying + + + align:start position:0% +differential index there are underlying +algebraic constraints that have to be + + align:start position:0% +algebraic constraints that have to be + + + align:start position:0% +algebraic constraints that have to be +satisfied at all points in time and if + + align:start position:0% +satisfied at all points in time and if + + + align:start position:0% +satisfied at all points in time and if +they're not then that can break the + + align:start position:0% +they're not then that can break the + + + align:start position:0% +they're not then that can break the +method that's trying to integrate the DA + + align:start position:0% +method that's trying to integrate the DA + + + align:start position:0% +method that's trying to integrate the DA +e so you have to prescribe the initial + + align:start position:0% +e so you have to prescribe the initial + + + align:start position:0% +e so you have to prescribe the initial +conditions consistently right if they're + + align:start position:0% +conditions consistently right if they're + + + align:start position:0% +conditions consistently right if they're +not prescribed consistently and you go + + align:start position:0% +not prescribed consistently and you go + + + align:start position:0% +not prescribed consistently and you go +to a piece of commercial software it may + + align:start position:0% +to a piece of commercial software it may + + + align:start position:0% +to a piece of commercial software it may +give an error it may tell you nothing + + align:start position:0% +give an error it may tell you nothing + + + align:start position:0% +give an error it may tell you nothing +you may get a reasonable results or an + + align:start position:0% +you may get a reasonable results or an + + + align:start position:0% +you may get a reasonable results or an +unreasonable result it really depends on + + align:start position:0% +unreasonable result it really depends on + + + align:start position:0% +unreasonable result it really depends on +the methodology so it's up to you to + + align:start position:0% +the methodology so it's up to you to + + + align:start position:0% +the methodology so it's up to you to +know in advance that this is an + + align:start position:0% +know in advance that this is an + + + align:start position:0% +know in advance that this is an +important aspect of the problem we saw + + align:start position:0% +important aspect of the problem we saw + + + align:start position:0% +important aspect of the problem we saw +the index 1 da EES typically right index + + align:start position:0% +the index 1 da EES typically right index + + + align:start position:0% +the index 1 da EES typically right index +2 da s can be converted into index 1 da + + align:start position:0% +2 da s can be converted into index 1 da + + + align:start position:0% +2 da s can be converted into index 1 da +es and solve pretty easily index 3 and + + align:start position:0% +es and solve pretty easily index 3 and + + + align:start position:0% +es and solve pretty easily index 3 and +bigger da es are difficult because of + + align:start position:0% +bigger da es are difficult because of + + + align:start position:0% +bigger da es are difficult because of +their high sensitivity so there's + + align:start position:0% +their high sensitivity so there's + + + align:start position:0% +their high sensitivity so there's +special software that's out there I + + align:start position:0% +special software that's out there I + + + align:start position:0% +special software that's out there I +mentioned some of it during our da + + align:start position:0% +mentioned some of it during our da + + + align:start position:0% +mentioned some of it during our da +lecture and that's really what you want + + align:start position:0% +lecture and that's really what you want + + + align:start position:0% +lecture and that's really what you want +to reach for if you have a high index + + align:start position:0% +to reach for if you have a high index + + + align:start position:0% +to reach for if you have a high index +DAA examples we're able to craft all + + align:start position:0% +DAA examples we're able to craft all + + + align:start position:0% +DAA examples we're able to craft all +sorts of examples where we + + align:start position:0% +sorts of examples where we + + + align:start position:0% +sorts of examples where we +tried to do funny things about with + + align:start position:0% +tried to do funny things about with + + + align:start position:0% +tried to do funny things about with +causality where you try to you know you + + align:start position:0% +causality where you try to you know you + + + align:start position:0% +causality where you try to you know you +try to control the input you try to + + align:start position:0% +try to control the input you try to + + + align:start position:0% +try to control the input you try to +change the input by affecting the output + + align:start position:0% +change the input by affecting the output + + + align:start position:0% +change the input by affecting the output +which doesn't doesn't make a lot of + + align:start position:0% +which doesn't doesn't make a lot of + + + align:start position:0% +which doesn't doesn't make a lot of +sense but that led to very high index + + align:start position:0% +sense but that led to very high index + + + align:start position:0% +sense but that led to very high index +daes + + align:start position:0% +daes + + + align:start position:0% +daes +mechanical systems often have very high + + align:start position:0% +mechanical systems often have very high + + + align:start position:0% +mechanical systems often have very high +index DA's associated with the + + align:start position:0% +index DA's associated with the + + + align:start position:0% +index DA's associated with the +mechanical constraints typically lead to + + align:start position:0% +mechanical constraints typically lead to + + + align:start position:0% +mechanical constraints typically lead to +index 3 daes okay so these pop up in + + align:start position:0% +index 3 daes okay so these pop up in + + + align:start position:0% +index 3 daes okay so these pop up in +places that are important and being able + + align:start position:0% +places that are important and being able + + + align:start position:0% +places that are important and being able +to look at the model and assess the + + align:start position:0% +to look at the model and assess the + + + align:start position:0% +to look at the model and assess the +index of it is is kind of essential we + + align:start position:0% +index of it is is kind of essential we + + + align:start position:0% +index of it is is kind of essential we +do probability right so the physical + + align:start position:0% +do probability right so the physical + + + align:start position:0% +do probability right so the physical +world has inherent uncertainty right + + align:start position:0% +world has inherent uncertainty right + + + align:start position:0% +world has inherent uncertainty right +such as uncertainty in our ability to + + align:start position:0% +such as uncertainty in our ability to + + + align:start position:0% +such as uncertainty in our ability to +measure things but fundamental physical + + align:start position:0% +measure things but fundamental physical + + + align:start position:0% +measure things but fundamental physical +uncertainty is built-in to the world + + align:start position:0% +uncertainty is built-in to the world + + + align:start position:0% +uncertainty is built-in to the world +around us so measurements have + + align:start position:0% +around us so measurements have + + + align:start position:0% +around us so measurements have +uncontrolled or even uncontrollable + + align:start position:0% +uncontrolled or even uncontrollable + + + align:start position:0% +uncontrolled or even uncontrollable +sensitivities to this uncertainty and we + + align:start position:0% +sensitivities to this uncertainty and we + + + align:start position:0% +sensitivities to this uncertainty and we +wanted to know how to handle it so we + + align:start position:0% +wanted to know how to handle it so we + + + align:start position:0% +wanted to know how to handle it so we +talked about things like sources of + + align:start position:0% +talked about things like sources of + + + align:start position:0% +talked about things like sources of +randomness we did fundamentals + + align:start position:0% +randomness we did fundamentals + + + align:start position:0% +randomness we did fundamentals +maybe this overlapped with 10:40 but I + + align:start position:0% +maybe this overlapped with 10:40 but I + + + align:start position:0% +maybe this overlapped with 10:40 but I +think overlap is good because people + + align:start position:0% +think overlap is good because people + + + align:start position:0% +think overlap is good because people +humans tend to have bad intuition about + + align:start position:0% +humans tend to have bad intuition about + + + align:start position:0% +humans tend to have bad intuition about +probability in general so we discuss + + align:start position:0% +probability in general so we discuss + + + align:start position:0% +probability in general so we discuss +probability densities means covariances + + align:start position:0% +probability densities means covariances + + + align:start position:0% +probability densities means covariances +expected values joint probabilities + + align:start position:0% +expected values joint probabilities + + + align:start position:0% +expected values joint probabilities +conditional probabilities we talked + + align:start position:0% +conditional probabilities we talked + + + align:start position:0% +conditional probabilities we talked +about common probability densities you + + align:start position:0% +about common probability densities you + + + align:start position:0% +about common probability densities you +covered the central limit theorem you + + align:start position:0% +covered the central limit theorem you + + + align:start position:0% +covered the central limit theorem you +talked about the difference between + + align:start position:0% +talked about the difference between + + + align:start position:0% +talked about the difference between +sample averages and the population mean + + align:start position:0% +sample averages and the population mean + + + align:start position:0% +sample averages and the population mean +okay one thing that's important that I + + align:start position:0% +okay one thing that's important that I + + + align:start position:0% +okay one thing that's important that I +don't think that gets covered much in + + align:start position:0% +don't think that gets covered much in + + + align:start position:0% +don't think that gets covered much in +detail but if you're gonna be working + + align:start position:0% +detail but if you're gonna be working + + + align:start position:0% +detail but if you're gonna be working +with randomness computationally + + align:start position:0% +with randomness computationally + + + align:start position:0% +with randomness computationally +oftentimes you have to generate random + + align:start position:0% +oftentimes you have to generate random + + + align:start position:0% +oftentimes you have to generate random +numbers and you'd like to generate good + + align:start position:0% +numbers and you'd like to generate good + + + align:start position:0% +numbers and you'd like to generate good +random numbers in terms of computer + + align:start position:0% +random numbers in terms of computer + + + align:start position:0% +random numbers in terms of computer +doesn't generate doesn't generate proper + + align:start position:0% +doesn't generate doesn't generate proper + + + align:start position:0% +doesn't generate doesn't generate proper +random numbers only pseudo-random + + align:start position:0% +random numbers only pseudo-random + + + align:start position:0% +random numbers only pseudo-random +numbers and these generators have + + align:start position:0% +numbers and these generators have + + + align:start position:0% +numbers and these generators have +various properties associated with them + + align:start position:0% +various properties associated with them + + + align:start position:0% +various properties associated with them +and some of them are good and some of + + align:start position:0% +and some of them are good and some of + + + align:start position:0% +and some of them are good and some of +them are bad and you want to use good + + align:start position:0% +them are bad and you want to use good + + + align:start position:0% +them are bad and you want to use good +ones so if you have to generate random + + align:start position:0% +ones so if you have to generate random + + + align:start position:0% +ones so if you have to generate random +numbers for your research you'd like to + + align:start position:0% +numbers for your research you'd like to + + + align:start position:0% +numbers for your research you'd like to +know that they are high-quality right + + align:start position:0% +know that they are high-quality right + + + align:start position:0% +know that they are high-quality right +that the sequence of numbers that's + + align:start position:0% +that the sequence of numbers that's + + + align:start position:0% +that the sequence of numbers that's +being generated doesn't repeat over the + + align:start position:0% +being generated doesn't repeat over the + + + align:start position:0% +being generated doesn't repeat over the +time that you're using it that it won't + + align:start position:0% +time that you're using it that it won't + + + align:start position:0% +time that you're using it that it won't +repeat over or overlap over many + + align:start position:0% +repeat over or overlap over many + + + align:start position:0% +repeat over or overlap over many +different uses + + align:start position:0% +different uses + + + align:start position:0% +different uses +of this methodology right so high + + align:start position:0% +of this methodology right so high + + + align:start position:0% +of this methodology right so high +quality random numbers are important we + + align:start position:0% +quality random numbers are important we + + + align:start position:0% +quality random numbers are important we +discuss models versus data right so we + + align:start position:0% +discuss models versus data right so we + + + align:start position:0% +discuss models versus data right so we +wanted to regress estimate parameters + + align:start position:0% +wanted to regress estimate parameters + + + align:start position:0% +wanted to regress estimate parameters +from the data okay we wanted to do + + align:start position:0% +from the data okay we wanted to do + + + align:start position:0% +from the data okay we wanted to do +things like hypothesis testing right I + + align:start position:0% +things like hypothesis testing right I + + + align:start position:0% +things like hypothesis testing right I +have a model is the model consistent + + align:start position:0% +have a model is the model consistent + + + align:start position:0% +have a model is the model consistent +with the data or is it not consistent + + align:start position:0% +with the data or is it not consistent + + + align:start position:0% +with the data or is it not consistent +with the data so you covered things like + + align:start position:0% +with the data so you covered things like + + + align:start position:0% +with the data so you covered things like +linear and non-linear least squares + + align:start position:0% +linear and non-linear least squares + + + align:start position:0% +linear and non-linear least squares +maximum likelihood estimates confidence + + align:start position:0% +maximum likelihood estimates confidence + + + align:start position:0% +maximum likelihood estimates confidence +intervals found using the chi-squared + + align:start position:0% +intervals found using the chi-squared + + + align:start position:0% +intervals found using the chi-squared +distribution right we did Bayes theorem + + align:start position:0% +distribution right we did Bayes theorem + + + align:start position:0% +distribution right we did Bayes theorem +and Bayesian parameter estimation as + + align:start position:0% +and Bayesian parameter estimation as + + + align:start position:0% +and Bayesian parameter estimation as +well right so a way of using prior + + align:start position:0% +well right so a way of using prior + + + align:start position:0% +well right so a way of using prior +information about parameter values to + + align:start position:0% +information about parameter values to + + + align:start position:0% +information about parameter values to +estimate better estimate the probability + + align:start position:0% +estimate better estimate the probability + + + align:start position:0% +estimate better estimate the probability +that those parameters will take on + + align:start position:0% +that those parameters will take on + + + align:start position:0% +that those parameters will take on +values given the data okay we didn't + + align:start position:0% +values given the data okay we didn't + + + align:start position:0% +values given the data okay we didn't +cover design of experiments that's a + + align:start position:0% +cover design of experiments that's a + + + align:start position:0% +cover design of experiments that's a +10:55 one topic right but there are + + align:start position:0% +10:55 one topic right but there are + + + align:start position:0% +10:55 one topic right but there are +specific ways that one can design the + + align:start position:0% +specific ways that one can design the + + + align:start position:0% +specific ways that one can design the +experiment which data values do I take + + align:start position:0% +experiment which data values do I take + + + align:start position:0% +experiment which data values do I take +in order to make the fitting of + + align:start position:0% +in order to make the fitting of + + + align:start position:0% +in order to make the fitting of +parameters optimal right and there are + + align:start position:0% +parameters optimal right and there are + + + align:start position:0% +parameters optimal right and there are +other problems besides regression that + + align:start position:0% +other problems besides regression that + + + align:start position:0% +other problems besides regression that +are important but we don't typically + + align:start position:0% +are important but we don't typically + + + align:start position:0% +are important but we don't typically +utilize those in chemical engineering so + + align:start position:0% +utilize those in chemical engineering so + + + align:start position:0% +utilize those in chemical engineering so +one of those is classification so if I + + align:start position:0% +one of those is classification so if I + + + align:start position:0% +one of those is classification so if I +have a series of points and I do + + align:start position:0% +have a series of points and I do + + + align:start position:0% +have a series of points and I do +regression and in some sense asking for + + align:start position:0% +regression and in some sense asking for + + + align:start position:0% +regression and in some sense asking for +like what's the best curve do to this + + align:start position:0% +like what's the best curve do to this + + + align:start position:0% +like what's the best curve do to this +model that can be drawn through those + + align:start position:0% +model that can be drawn through those + + + align:start position:0% +model that can be drawn through those +points right what parameter values give + + align:start position:0% +points right what parameter values give + + + align:start position:0% +points right what parameter values give +me the curve that's closest to all these + + align:start position:0% +me the curve that's closest to all these + + + align:start position:0% +me the curve that's closest to all these +points those least squares + + align:start position:0% +points those least squares + + + align:start position:0% +points those least squares +classification might ask instead what's + + align:start position:0% +classification might ask instead what's + + + align:start position:0% +classification might ask instead what's +the curve that divides these points most + + align:start position:0% +the curve that divides these points most + + + align:start position:0% +the curve that divides these points most +evenly or sits farthest from all these + + align:start position:0% +evenly or sits farthest from all these + + + align:start position:0% +evenly or sits farthest from all these +points in an equal amount instead right + + align:start position:0% +points in an equal amount instead right + + + align:start position:0% +points in an equal amount instead right +which line which side of this line do + + align:start position:0% +which line which side of this line do + + + align:start position:0% +which line which side of this line do +the points sit on right are they have + + align:start position:0% +the points sit on right are they have + + + align:start position:0% +the points sit on right are they have +type A or type B it's kind of a related + + align:start position:0% +type A or type B it's kind of a related + + + align:start position:0% +type A or type B it's kind of a related +problem to regression but it's a + + align:start position:0% +problem to regression but it's a + + + align:start position:0% +problem to regression but it's a +different sort of problem ok the same + + align:start position:0% +different sort of problem ok the same + + + align:start position:0% +different sort of problem ok the same +sorts of methods can be applied to + + align:start position:0% +sorts of methods can be applied to + + + align:start position:0% +sorts of methods can be applied to +classification that you apply to doing + + align:start position:0% +classification that you apply to doing + + + align:start position:0% +classification that you apply to doing +regression and parameter estimation + + align:start position:0% +regression and parameter estimation + + + align:start position:0% +regression and parameter estimation +that's it's an important problem and + + align:start position:0% +that's it's an important problem and + + + align:start position:0% +that's it's an important problem and +then we finished up with stochastic + + align:start position:0% +then we finished up with stochastic + + + align:start position:0% +then we finished up with stochastic +simulation right so you know you learned + + align:start position:0% +simulation right so you know you learned + + + align:start position:0% +simulation right so you know you learned +that sampling of random processes can be + + align:start position:0% +that sampling of random processes can be + + + align:start position:0% +that sampling of random processes can be +used for engineering calculations and + + align:start position:0% +used for engineering calculations and + + + align:start position:0% +used for engineering calculations and +they're even in herre + + align:start position:0% +they're even in herre + + + align:start position:0% +they're even in herre +random physical processes that you might + + align:start position:0% +random physical processes that you might + + + align:start position:0% +random physical processes that you might +want to model reliably okay so we did + + align:start position:0% +want to model reliably okay so we did + + + align:start position:0% +want to model reliably okay so we did +metropolis Monte Carlo this was a way of + + align:start position:0% +metropolis Monte Carlo this was a way of + + + align:start position:0% +metropolis Monte Carlo this was a way of +basically computing high dimensional + + align:start position:0% +basically computing high dimensional + + + align:start position:0% +basically computing high dimensional +integrals that's what it boiled down to + + align:start position:0% +integrals that's what it boiled down to + + + align:start position:0% +integrals that's what it boiled down to +where we wanted to sample from different + + align:start position:0% +where we wanted to sample from different + + + align:start position:0% +where we wanted to sample from different +places in the domain weighted by some + + align:start position:0% +places in the domain weighted by some + + + align:start position:0% +places in the domain weighted by some +probability density function okay you + + align:start position:0% +probability density function okay you + + + align:start position:0% +probability density function okay you +did kinetic Monte Carlo which is really + + align:start position:0% +did kinetic Monte Carlo which is really + + + align:start position:0% +did kinetic Monte Carlo which is really +sort of event-driven algorithm right you + + align:start position:0% +sort of event-driven algorithm right you + + + align:start position:0% +sort of event-driven algorithm right you +are expecting that certain events are + + align:start position:0% +are expecting that certain events are + + + align:start position:0% +are expecting that certain events are +going to occur with certain rates okay + + align:start position:0% +going to occur with certain rates okay + + + align:start position:0% +going to occur with certain rates okay +they're actually they're non stochastic + + align:start position:0% +they're actually they're non stochastic + + + align:start position:0% +they're actually they're non stochastic +versions of that the same sort of + + align:start position:0% +versions of that the same sort of + + + align:start position:0% +versions of that the same sort of +adventure of an algorithm I think should + + align:start position:0% +adventure of an algorithm I think should + + + align:start position:0% +adventure of an algorithm I think should +happen at certain points in time and + + align:start position:0% +happen at certain points in time and + + + align:start position:0% +happen at certain points in time and +rather than integrating the dynamics of + + align:start position:0% +rather than integrating the dynamics of + + + align:start position:0% +rather than integrating the dynamics of +the system all along these points in + + align:start position:0% +the system all along these points in + + + align:start position:0% +the system all along these points in +time I just advance the dynamics till + + align:start position:0% +time I just advance the dynamics till + + + align:start position:0% +time I just advance the dynamics till +the next event occurs that event occurs + + align:start position:0% +the next event occurs that event occurs + + + align:start position:0% +the next event occurs that event occurs +right I keep a list of what the next + + align:start position:0% +right I keep a list of what the next + + + align:start position:0% +right I keep a list of what the next +event is gonna be and I followed those + + align:start position:0% +event is gonna be and I followed those + + + align:start position:0% +event is gonna be and I followed those +events along so could be something like + + align:start position:0% +events along so could be something like + + + align:start position:0% +events along so could be something like +like billiard balls on a table right I + + align:start position:0% +like billiard balls on a table right I + + + align:start position:0% +like billiard balls on a table right I +know when the billiard I know the + + align:start position:0% +know when the billiard I know the + + + align:start position:0% +know when the billiard I know the +trajectories of the billiard balls given + + align:start position:0% +trajectories of the billiard balls given + + + align:start position:0% +trajectories of the billiard balls given +their position and their momenta and all + + align:start position:0% +their position and their momenta and all + + + align:start position:0% +their position and their momenta and all +I need to do is keep track of when they + + align:start position:0% +I need to do is keep track of when they + + + align:start position:0% +I need to do is keep track of when they +collide and where they're gonna go next + + align:start position:0% +collide and where they're gonna go next + + + align:start position:0% +collide and where they're gonna go next +and what the next events are going to be + + align:start position:0% +and what the next events are going to be + + + align:start position:0% +and what the next events are going to be +kinetic Monte Carlo is the same thing so + + align:start position:0% +kinetic Monte Carlo is the same thing so + + + align:start position:0% +kinetic Monte Carlo is the same thing so +if the events are now stochastic they + + align:start position:0% +if the events are now stochastic they + + + align:start position:0% +if the events are now stochastic they +occur with prescribed rates okay and so + + align:start position:0% +occur with prescribed rates okay and so + + + align:start position:0% +occur with prescribed rates okay and so +I just need to sample from this + + align:start position:0% +I just need to sample from this + + + align:start position:0% +I just need to sample from this +distribution of rates to get the right + + align:start position:0% +distribution of rates to get the right + + + align:start position:0% +distribution of rates to get the right +sequence of events there's how many + + align:start position:0% +sequence of events there's how many + + + align:start position:0% +sequence of events there's how many +things about kinetic Monte Carlo so + + align:start position:0% +things about kinetic Monte Carlo so + + + align:start position:0% +things about kinetic Monte Carlo so +applied to applied to chemical kinetics + + align:start position:0% +applied to applied to chemical kinetics + + + align:start position:0% +applied to applied to chemical kinetics +you can estimate these rates reasonably + + align:start position:0% +you can estimate these rates reasonably + + + align:start position:0% +you can estimate these rates reasonably +well you gotta know the rates for this + + align:start position:0% +well you gotta know the rates for this + + + align:start position:0% +well you gotta know the rates for this +process to look right if you don't have + + align:start position:0% +process to look right if you don't have + + + align:start position:0% +process to look right if you don't have +the rates correct or you don't have the + + align:start position:0% +the rates correct or you don't have the + + + align:start position:0% +the rates correct or you don't have the +relative magnitudes of the rates then + + align:start position:0% +relative magnitudes of the rates then + + + align:start position:0% +relative magnitudes of the rates then +then the simulation is kind of + + align:start position:0% +then the simulation is kind of + + + align:start position:0% +then the simulation is kind of +meaningless right the result is going to + + align:start position:0% +meaningless right the result is going to + + + align:start position:0% +meaningless right the result is going to +be going to be nonsense or garbage and + + align:start position:0% +be going to be nonsense or garbage and + + + align:start position:0% +be going to be nonsense or garbage and +so there's going to be limitations on + + align:start position:0% +so there's going to be limitations on + + + align:start position:0% +so there's going to be limitations on +your ability to do this based upon how + + align:start position:0% +your ability to do this based upon how + + + align:start position:0% +your ability to do this based upon how +accurately you can estimate these rates + + align:start position:0% +accurately you can estimate these rates + + + align:start position:0% +accurately you can estimate these rates +okay it also means that if you know that + + align:start position:0% +okay it also means that if you know that + + + align:start position:0% +okay it also means that if you know that +there's disparities in the rates say one + + align:start position:0% +there's disparities in the rates say one + + + align:start position:0% +there's disparities in the rates say one +rate is very high and one rate is very + + align:start position:0% +rate is very high and one rate is very + + + align:start position:0% +rate is very high and one rate is very +low you can make certain assumptions + + align:start position:0% +low you can make certain assumptions + + + align:start position:0% +low you can make certain assumptions +about the process things that happen + + align:start position:0% +about the process things that happen + + + align:start position:0% +about the process things that happen +very quickly you may treat as though + + align:start position:0% +very quickly you may treat as though + + + align:start position:0% +very quickly you may treat as though +they're equilibrated and not try to + + align:start position:0% +they're equilibrated and not try to + + + align:start position:0% +they're equilibrated and not try to +resolve them at all and look more at + + align:start position:0% +resolve them at all and look more at + + + align:start position:0% +resolve them at all and look more at +infrequent processes that occur slower + + align:start position:0% +infrequent processes that occur slower + + + align:start position:0% +infrequent processes that occur slower +rates so there + + align:start position:0% +rates so there + + + align:start position:0% +rates so there +sort of right the position with which + + align:start position:0% +sort of right the position with which + + + align:start position:0% +sort of right the position with which +you have to know these things is + + align:start position:0% +you have to know these things is + + + align:start position:0% +you have to know these things is +important the relative rates are what's + + align:start position:0% +important the relative rates are what's + + + align:start position:0% +important the relative rates are what's +really important in these problems and + + align:start position:0% +really important in these problems and + + + align:start position:0% +really important in these problems and +you want to get them right in order to + + align:start position:0% +you want to get them right in order to + + + align:start position:0% +you want to get them right in order to +resolve these physical processes + + align:start position:0% +resolve these physical processes + + + align:start position:0% +resolve these physical processes +correctly let me discuss molecular + + align:start position:0% +correctly let me discuss molecular + + + align:start position:0% +correctly let me discuss molecular +dynamics after that which is another + + align:start position:0% +dynamics after that which is another + + + align:start position:0% +dynamics after that which is another +type of stochastic simulation + + align:start position:0% +type of stochastic simulation + + + align:start position:0% +type of stochastic simulation +methodology here you just integrate the + + align:start position:0% +methodology here you just integrate the + + + align:start position:0% +methodology here you just integrate the +equations of motion associated with that + + align:start position:0% +equations of motion associated with that + + + align:start position:0% +equations of motion associated with that +whatever particles you're interested in + + align:start position:0% +whatever particles you're interested in + + + align:start position:0% +whatever particles you're interested in +okay kinetic Monte Carlo and molecular + + align:start position:0% +okay kinetic Monte Carlo and molecular + + + align:start position:0% +okay kinetic Monte Carlo and molecular +dynamics so fundamentally far from + + align:start position:0% +dynamics so fundamentally far from + + + align:start position:0% +dynamics so fundamentally far from +equilibrium but may relax towards + + align:start position:0% +equilibrium but may relax towards + + + align:start position:0% +equilibrium but may relax towards +equilibrium depending on what + + align:start position:0% +equilibrium depending on what + + + align:start position:0% +equilibrium depending on what +constraints you put on the the + + align:start position:0% +constraints you put on the the + + + align:start position:0% +constraints you put on the the +particular rate processes that you're + + align:start position:0% +particular rate processes that you're + + + align:start position:0% +particular rate processes that you're +modeling metropolis Monte Carlo is + + align:start position:0% +modeling metropolis Monte Carlo is + + + align:start position:0% +modeling metropolis Monte Carlo is +usually sampling and underlying if we're + + align:start position:0% +usually sampling and underlying if we're + + + align:start position:0% +usually sampling and underlying if we're +applying it in the statistical + + align:start position:0% +applying it in the statistical + + + align:start position:0% +applying it in the statistical +mechanical sense it's usually sampling + + align:start position:0% +mechanical sense it's usually sampling + + + align:start position:0% +mechanical sense it's usually sampling +and underlying equilibrium Boltzmann + + align:start position:0% +and underlying equilibrium Boltzmann + + + align:start position:0% +and underlying equilibrium Boltzmann +distribution okay so they they often get + + align:start position:0% +distribution okay so they they often get + + + align:start position:0% +distribution okay so they they often get +used in fundamentally different + + align:start position:0% +used in fundamentally different + + + align:start position:0% +used in fundamentally different +different ways as well + + align:start position:0% +different ways as well + + + align:start position:0% +different ways as well +we didn't cover stochastic differential + + align:start position:0% +we didn't cover stochastic differential + + + align:start position:0% +we didn't cover stochastic differential +equations so depending on depending on + + align:start position:0% +equations so depending on depending on + + + align:start position:0% +equations so depending on depending on +which degrees of freedom you want to + + align:start position:0% +which degrees of freedom you want to + + + align:start position:0% +which degrees of freedom you want to +represent in a model like molecular + + align:start position:0% +represent in a model like molecular + + + align:start position:0% +represent in a model like molecular +dynamics okay there may be some degrees + + align:start position:0% +dynamics okay there may be some degrees + + + align:start position:0% +dynamics okay there may be some degrees +of freedom you you simply don't care + + align:start position:0% +of freedom you you simply don't care + + + align:start position:0% +of freedom you you simply don't care +about but they have an influence on the + + align:start position:0% +about but they have an influence on the + + + align:start position:0% +about but they have an influence on the +problem so in my research for example we + + align:start position:0% +problem so in my research for example we + + + align:start position:0% +problem so in my research for example we +model nanoparticles and particulates + + align:start position:0% +model nanoparticles and particulates + + + align:start position:0% +model nanoparticles and particulates +we're not very interested in the details + + align:start position:0% +we're not very interested in the details + + + align:start position:0% +we're not very interested in the details +of the solvent surrounding these + + align:start position:0% +of the solvent surrounding these + + + align:start position:0% +of the solvent surrounding these +particles there's a huge disparity in + + align:start position:0% +particles there's a huge disparity in + + + align:start position:0% +particles there's a huge disparity in +length scales associated with + + align:start position:0% +length scales associated with + + + align:start position:0% +length scales associated with +nanoparticles and the molecular + + align:start position:0% +nanoparticles and the molecular + + + align:start position:0% +nanoparticles and the molecular +dimensions of the solvent that surrounds + + align:start position:0% +dimensions of the solvent that surrounds + + + align:start position:0% +dimensions of the solvent that surrounds +them the solvent has an influence + + align:start position:0% +them the solvent has an influence + + + align:start position:0% +them the solvent has an influence +nonetheless it's fluctuating all the + + align:start position:0% +nonetheless it's fluctuating all the + + + align:start position:0% +nonetheless it's fluctuating all the +time right solvent molecules are + + align:start position:0% +time right solvent molecules are + + + align:start position:0% +time right solvent molecules are +colliding with these particles and + + align:start position:0% +colliding with these particles and + + + align:start position:0% +colliding with these particles and +they're imparting momentum one way of + + align:start position:0% +they're imparting momentum one way of + + + align:start position:0% +they're imparting momentum one way of +resolving a system like that without + + align:start position:0% +resolving a system like that without + + + align:start position:0% +resolving a system like that without +having to look explicitly at the solvent + + align:start position:0% +having to look explicitly at the solvent + + + align:start position:0% +having to look explicitly at the solvent +is to try to integrate out the solvent + + align:start position:0% +is to try to integrate out the solvent + + + align:start position:0% +is to try to integrate out the solvent +degrees of freedom and treat those + + align:start position:0% +degrees of freedom and treat those + + + align:start position:0% +degrees of freedom and treat those +collisions of the solvent with this + + align:start position:0% +collisions of the solvent with this + + + align:start position:0% +collisions of the solvent with this +particle in a stochastic sense okay so + + align:start position:0% +particle in a stochastic sense okay so + + + align:start position:0% +particle in a stochastic sense okay so +at various points in time there's + + align:start position:0% +at various points in time there's + + + align:start position:0% +at various points in time there's +momentum that's randomly transferred to + + align:start position:0% +momentum that's randomly transferred to + + + align:start position:0% +momentum that's randomly transferred to +particles dispersed in a solvent the + + align:start position:0% +particles dispersed in a solvent the + + + align:start position:0% +particles dispersed in a solvent the +physical manifestation of that is + + align:start position:0% +physical manifestation of that is + + + align:start position:0% +physical manifestation of that is +Brownian motion right when you look at + + align:start position:0% +Brownian motion right when you look at + + + align:start position:0% +Brownian motion right when you look at +small particles in a fluid you see them + + align:start position:0% +small particles in a fluid you see them + + + align:start position:0% +small particles in a fluid you see them +diffuser + + align:start position:0% +diffuser + + + align:start position:0% +diffuser +and that's that's where that's coming + + align:start position:0% +and that's that's where that's coming + + + align:start position:0% +and that's that's where that's coming +from so you can simulate processes like + + align:start position:0% +from so you can simulate processes like + + + align:start position:0% +from so you can simulate processes like +that without having to resolve molecular + + align:start position:0% +that without having to resolve molecular + + + align:start position:0% +that without having to resolve molecular +scales so as you go up in scale you've + + align:start position:0% +scales so as you go up in scale you've + + + align:start position:0% +scales so as you go up in scale you've +integrated out degrees of freedom but + + align:start position:0% +integrated out degrees of freedom but + + + align:start position:0% +integrated out degrees of freedom but +often times that innit that introduces + + align:start position:0% +often times that innit that introduces + + + align:start position:0% +often times that innit that introduces +inherent stochasticity in the underlying + + align:start position:0% +inherent stochasticity in the underlying + + + align:start position:0% +inherent stochasticity in the underlying +dynamics of whatever you're trying to + + align:start position:0% +dynamics of whatever you're trying to + + + align:start position:0% +dynamics of whatever you're trying to +model that's very interesting + + align:start position:0% +model that's very interesting + + + align:start position:0% +model that's very interesting +and then for Monte Carlo methods there's + + align:start position:0% +and then for Monte Carlo methods there's + + + align:start position:0% +and then for Monte Carlo methods there's +advanced sampling methods and we didn't + + align:start position:0% +advanced sampling methods and we didn't + + + align:start position:0% +advanced sampling methods and we didn't +discuss any of these in detail but you + + align:start position:0% +discuss any of these in detail but you + + + align:start position:0% +discuss any of these in detail but you +saw some of this with with the model you + + align:start position:0% +saw some of this with with the model you + + + align:start position:0% +saw some of this with with the model you +saw with the problem you approached in + + align:start position:0% +saw with the problem you approached in + + + align:start position:0% +saw with the problem you approached in +your homework where you had two sort of + + align:start position:0% +your homework where you had two sort of + + + align:start position:0% +your homework where you had two sort of +populations or two peaks in the + + align:start position:0% +populations or two peaks in the + + + align:start position:0% +populations or two peaks in the +probability distribution that were + + align:start position:0% +probability distribution that were + + + align:start position:0% +probability distribution that were +widely separated and it may be hard for + + align:start position:0% +widely separated and it may be hard for + + + align:start position:0% +widely separated and it may be hard for +a Monte Carlo method to traverse between + + align:start position:0% +a Monte Carlo method to traverse between + + + align:start position:0% +a Monte Carlo method to traverse between +those peaks and umbrella sampling is a + + align:start position:0% +those peaks and umbrella sampling is a + + + align:start position:0% +those peaks and umbrella sampling is a +way of biasing the probability + + align:start position:0% +way of biasing the probability + + + align:start position:0% +way of biasing the probability +distribution to make those paths from + + align:start position:0% +distribution to make those paths from + + + align:start position:0% +distribution to make those paths from +one peak to another more probable okay + + align:start position:0% +one peak to another more probable okay + + + align:start position:0% +one peak to another more probable okay +so this is a way of seeking out rare + + align:start position:0% +so this is a way of seeking out rare + + + align:start position:0% +so this is a way of seeking out rare +events okay like the transitions between + + align:start position:0% +events okay like the transitions between + + + align:start position:0% +events okay like the transitions between +these two these two different + + align:start position:0% +these two these two different + + + align:start position:0% +these two these two different +populations and it's it's pretty + + align:start position:0% +populations and it's it's pretty + + + align:start position:0% +populations and it's it's pretty +important ultimately for exploring + + align:start position:0% +important ultimately for exploring + + + align:start position:0% +important ultimately for exploring +complex high dimensional spaces but you + + align:start position:0% +complex high dimensional spaces but you + + + align:start position:0% +complex high dimensional spaces but you +you have to understand something about + + align:start position:0% +you have to understand something about + + + align:start position:0% +you have to understand something about +the underlying physics in order to + + align:start position:0% +the underlying physics in order to + + + align:start position:0% +the underlying physics in order to +figure out the biases needed to enhance + + align:start position:0% +figure out the biases needed to enhance + + + align:start position:0% +figure out the biases needed to enhance +the sampling so it's so quite + + align:start position:0% +the sampling so it's so quite + + + align:start position:0% +the sampling so it's so quite +complicated okay so I remind you your + + align:start position:0% +complicated okay so I remind you your + + + align:start position:0% +complicated okay so I remind you your +final exam right it's Monday + + align:start position:0% +final exam right it's Monday + + + align:start position:0% +final exam right it's Monday +it's in 56 154 at 9:00 a.m. okay don't + + align:start position:0% +it's in 56 154 at 9:00 a.m. okay don't + + + align:start position:0% +it's in 56 154 at 9:00 a.m. okay don't +show up the locker it's not going to be + + align:start position:0% +show up the locker it's not going to be + + + align:start position:0% +show up the locker it's not going to be +there it's three hours it's gonna be + + align:start position:0% +there it's three hours it's gonna be + + + align:start position:0% +there it's three hours it's gonna be +comprehensive you can expect roughly one + + align:start position:0% +comprehensive you can expect roughly one + + + align:start position:0% +comprehensive you can expect roughly one +problem for each thematic topic we've + + align:start position:0% +problem for each thematic topic we've + + + align:start position:0% +problem for each thematic topic we've +written it now I think it's against a + + align:start position:0% +written it now I think it's against a + + + align:start position:0% +written it now I think it's against a +nine problems long so we're we're in the + + align:start position:0% +nine problems long so we're we're in the + + + align:start position:0% +nine problems long so we're we're in the +process of revising it for difficulty in + + align:start position:0% +process of revising it for difficulty in + + + align:start position:0% +process of revising it for difficulty in +time it's gonna be a short answer format + + align:start position:0% +time it's gonna be a short answer format + + + align:start position:0% +time it's gonna be a short answer format +we sort of aim at 10 to 15 minutes per + + align:start position:0% +we sort of aim at 10 to 15 minutes per + + + align:start position:0% +we sort of aim at 10 to 15 minutes per +problem right I think that's the sort of + + align:start position:0% +problem right I think that's the sort of + + + align:start position:0% +problem right I think that's the sort of +time frame you should be looking at the + + align:start position:0% +time frame you should be looking at the + + + align:start position:0% +time frame you should be looking at the +problems are structured in such a way + + align:start position:0% +problems are structured in such a way + + + align:start position:0% +problems are structured in such a way +that that's about how long they should + + align:start position:0% +that that's about how long they should + + + align:start position:0% +that that's about how long they should +take you should use that guide your + + align:start position:0% +take you should use that guide your + + + align:start position:0% +take you should use that guide your +temporal budget on the exam right it's + + align:start position:0% +temporal budget on the exam right it's + + + align:start position:0% +temporal budget on the exam right it's +taking too long + + align:start position:0% +taking too long + + + align:start position:0% +taking too long +switch to something else don't let + + align:start position:0% +switch to something else don't let + + + align:start position:0% +switch to something else don't let +yourself get hung up focusing on one + + align:start position:0% +yourself get hung up focusing on one + + + align:start position:0% +yourself get hung up focusing on one +thing move around and come back to it + + align:start position:0% +thing move around and come back to it + + + align:start position:0% +thing move around and come back to it +later there'll be some fundamentals + + align:start position:0% +later there'll be some fundamentals + + + align:start position:0% +later there'll be some fundamentals +right there's gonna be some translation + + align:start position:0% +right there's gonna be some translation + + + align:start position:0% +right there's gonna be some translation +of engineering + + align:start position:0% +of engineering + + + align:start position:0% +of engineering +to numerix and there's gonna be some + + align:start position:0% +to numerix and there's gonna be some + + + align:start position:0% +to numerix and there's gonna be some +MATLAB okay so it'll look like a blend + + align:start position:0% +MATLAB okay so it'll look like a blend + + + align:start position:0% +MATLAB okay so it'll look like a blend +of the first exam in the second exam + + align:start position:0% + + + + align:start position:0% + +yeah yeah yeah yeah we know computer so + + align:start position:0% +yeah yeah yeah yeah we know computer so + + + align:start position:0% +yeah yeah yeah yeah we know computer so +you just you know write a little + + align:start position:0% +you just you know write a little + + + align:start position:0% +you just you know write a little +write a little script you know we've + + align:start position:0% +write a little script you know we've + + + align:start position:0% +write a little script you know we've +asked problems like that before + + align:start position:0% +asked problems like that before + + + align:start position:0% +asked problems like that before +it'll be at the same the same type yes I + + align:start position:0% +it'll be at the same the same type yes I + + + align:start position:0% +it'll be at the same the same type yes I +think there's nine yeah I think that's + + align:start position:0% +think there's nine yeah I think that's + + + align:start position:0% +think there's nine yeah I think that's +well that's how many we've written now I + + align:start position:0% +well that's how many we've written now I + + + align:start position:0% +well that's how many we've written now I +don't I don't I'm not planning I'm + + align:start position:0% +don't I don't I'm not planning I'm + + + align:start position:0% +don't I don't I'm not planning I'm +writing anymore + + align:start position:0% +writing anymore + + + align:start position:0% +writing anymore +plus or minus one yeah what's that oh + + align:start position:0% +plus or minus one yeah what's that oh + + + align:start position:0% +plus or minus one yeah what's that oh +sure no there there listen if we gave + + align:start position:0% +sure no there there listen if we gave + + + align:start position:0% +sure no there there listen if we gave +you nine problems of the same length as + + align:start position:0% +you nine problems of the same length as + + + align:start position:0% +you nine problems of the same length as +on the first two quizzes you wouldn't + + align:start position:0% +on the first two quizzes you wouldn't + + + align:start position:0% +on the first two quizzes you wouldn't +get through the problem so they're not + + align:start position:0% +get through the problem so they're not + + + align:start position:0% +get through the problem so they're not +written to be so long but there are + + align:start position:0% +written to be so long but there are + + + align:start position:0% +written to be so long but there are +multiple parts but multiple parts are + + align:start position:0% +multiple parts but multiple parts are + + + align:start position:0% +multiple parts but multiple parts are +usually intended to guide you to the + + align:start position:0% +usually intended to guide you to the + + + align:start position:0% +usually intended to guide you to the +solution we're looking for usually we're + + align:start position:0% +solution we're looking for usually we're + + + align:start position:0% +solution we're looking for usually we're +testing for a particular understanding + + align:start position:0% +testing for a particular understanding + + + align:start position:0% +testing for a particular understanding +it also helps you out when there are + + align:start position:0% +it also helps you out when there are + + + align:start position:0% +it also helps you out when there are +multiple parts means there's lots of + + align:start position:0% +multiple parts means there's lots of + + + align:start position:0% +multiple parts means there's lots of +partial credit available right you have + + align:start position:0% +partial credit available right you have + + + align:start position:0% +partial credit available right you have +to get the whole thing he's gonna get + + align:start position:0% +to get the whole thing he's gonna get + + + align:start position:0% +to get the whole thing he's gonna get +two out of three parts you did pretty + + align:start position:0% +two out of three parts you did pretty + + + align:start position:0% +two out of three parts you did pretty +good okay more questions + + align:start position:0% + + + + align:start position:0% + +yes that's right yeah yeah they're not + + align:start position:0% +yes that's right yeah yeah they're not + + + align:start position:0% +yes that's right yeah yeah they're not +they're not they're not multiple-choice + + align:start position:0% +they're not they're not multiple-choice + + + align:start position:0% +they're not they're not multiple-choice +or false there's only you know you got a + + align:start position:0% +or false there's only you know you got a + + + align:start position:0% +or false there's only you know you got a +short answer I think you know the the + + align:start position:0% +short answer I think you know the the + + + align:start position:0% +short answer I think you know the the +the level of detail means means you want + + align:start position:0% +the level of detail means means you want + + + align:start position:0% +the level of detail means means you want +to hit a level of detail that shows us + + align:start position:0% +to hit a level of detail that shows us + + + align:start position:0% +to hit a level of detail that shows us +you understand what you're talking about + + align:start position:0% +you understand what you're talking about + + + align:start position:0% +you understand what you're talking about +right we don't need we don't need pages + + align:start position:0% +right we don't need we don't need pages + + + align:start position:0% +right we don't need we don't need pages +of information on these things but we + + align:start position:0% +of information on these things but we + + + align:start position:0% +of information on these things but we +need to have enough information that we + + align:start position:0% +need to have enough information that we + + + align:start position:0% +need to have enough information that we +can see you know what you're doing right + + align:start position:0% +can see you know what you're doing right + + + align:start position:0% +can see you know what you're doing right +we're trying to assess your + + align:start position:0% +we're trying to assess your + + + align:start position:0% +we're trying to assess your +understanding of the material that's all + + align:start position:0% + + + + align:start position:0% + +or questions + + align:start position:0% + + + + align:start position:0% + +no more questions okay well good it's + + align:start position:0% +no more questions okay well good it's + + + align:start position:0% +no more questions okay well good it's +been a real pleasure teaching you guys + + align:start position:0% +been a real pleasure teaching you guys + + + align:start position:0% +been a real pleasure teaching you guys +I'm really pleased with the outcome of + + align:start position:0% +I'm really pleased with the outcome of + + + align:start position:0% +I'm really pleased with the outcome of +this course I think this is my third + + align:start position:0% +this course I think this is my third + + + align:start position:0% +this course I think this is my third +time teaching and I think this is the + + align:start position:0% +time teaching and I think this is the + + + align:start position:0% +time teaching and I think this is the +strongest group that I've seen come + + align:start position:0% +strongest group that I've seen come + + + align:start position:0% +strongest group that I've seen come +through + + align:start position:0% +through + + + align:start position:0% +through +10:34 so you guys should should be + + align:start position:0% +10:34 so you guys should should be + + + align:start position:0% +10:34 so you guys should should be +really proud of yourselves okay good all + + align:start position:0% +really proud of yourselves okay good all + + + align:start position:0% +really proud of yourselves okay good all +right good luck + + align:start position:0% +right good luck + + + align:start position:0% +right good luck +[Applause] \ No newline at end of file diff --git a/X6ilT3uUOBo.txt b/X6ilT3uUOBo.txt new file mode 100644 index 0000000000000000000000000000000000000000..39fcc2483f0d16a9345066f748877c06c0a1f6d6 --- /dev/null +++ b/X6ilT3uUOBo.txt @@ -0,0 +1,10424 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencare at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right I'm going to start + + align:start position:0% +ocw.mit.edu all right I'm going to start + + + align:start position:0% +ocw.mit.edu all right I'm going to start +today by talking about so what have we + + align:start position:0% +today by talking about so what have we + + + align:start position:0% +today by talking about so what have we +been doing what have we actually done + + align:start position:0% +been doing what have we actually done + + + align:start position:0% +been doing what have we actually done +over the last few lectures and I'm going + + align:start position:0% +over the last few lectures and I'm going + + + align:start position:0% +over the last few lectures and I'm going +to suggest that what we've done is we've + + align:start position:0% +to suggest that what we've done is we've + + + align:start position:0% +to suggest that what we've done is we've +outlined a lot of the basic elements of + + align:start position:0% +outlined a lot of the basic elements of + + + align:start position:0% +outlined a lot of the basic elements of +programming a lot of the basic elements + + align:start position:0% +programming a lot of the basic elements + + + align:start position:0% +programming a lot of the basic elements +we're going to need to write code and I + + align:start position:0% +we're going to need to write code and I + + + align:start position:0% +we're going to need to write code and I +want to just highlight it for you + + align:start position:0% +want to just highlight it for you + + + align:start position:0% +want to just highlight it for you +because we're going to come back and + + align:start position:0% +because we're going to come back and + + + align:start position:0% +because we're going to come back and +look at it so I'm going to suggest that + + align:start position:0% +look at it so I'm going to suggest that + + + align:start position:0% +look at it so I'm going to suggest that +we've looked at three different kinds of + + align:start position:0% +we've looked at three different kinds of + + + align:start position:0% +we've looked at three different kinds of +things right we've talked about + + align:start position:0% + + + + align:start position:0% + +data we've talked about + + align:start position:0% + + + + align:start position:0% + +operations and we've talked about + + align:start position:0% +operations and we've talked about + + + align:start position:0% +operations and we've talked about +commands or + + align:start position:0% + + + + align:start position:0% + +statements right data is what we expect + + align:start position:0% +statements right data is what we expect + + + align:start position:0% +statements right data is what we expect +it's our way of representing + + align:start position:0% +it's our way of representing + + + align:start position:0% +it's our way of representing +fundamentally the kinds of of + + align:start position:0% +fundamentally the kinds of of + + + align:start position:0% +fundamentally the kinds of of +information we want to move around and + + align:start position:0% +information we want to move around and + + + align:start position:0% +information we want to move around and +here I'm going to suggest we've seen + + align:start position:0% +here I'm going to suggest we've seen + + + align:start position:0% +here I'm going to suggest we've seen +numbers we've seen + + align:start position:0% +numbers we've seen + + + align:start position:0% +numbers we've seen +strings and I'm going to add booleans + + align:start position:0% +strings and I'm going to add booleans + + + align:start position:0% +strings and I'm going to add booleans +here as well there a third kind of value + + align:start position:0% +here as well there a third kind of value + + + align:start position:0% +here as well there a third kind of value +that we saw when we started talking + + align:start position:0% +that we saw when we started talking + + + align:start position:0% +that we saw when we started talking +about + + align:start position:0% +about + + + align:start position:0% +about +conditionals we saw associated with that + + align:start position:0% +conditionals we saw associated with that + + + align:start position:0% +conditionals we saw associated with that +primitive data we have ways of taking + + align:start position:0% +primitive data we have ways of taking + + + align:start position:0% +primitive data we have ways of taking +data in and creating new kinds of data + + align:start position:0% +data in and creating new kinds of data + + + align:start position:0% +data in and creating new kinds of data +out or new versions of data out so we + + align:start position:0% +out or new versions of data out so we + + + align:start position:0% +out or new versions of data out so we +have operations + + align:start position:0% +have operations + + + align:start position:0% +have operations +things like addition and multiplication + + align:start position:0% +things like addition and multiplication + + + align:start position:0% +things like addition and multiplication +which we saw not only apply to numbers + + align:start position:0% +which we saw not only apply to numbers + + + align:start position:0% +which we saw not only apply to numbers +but we can use them on things like + + align:start position:0% +but we can use them on things like + + + align:start position:0% +but we can use them on things like +strings and we're going to come back to + + align:start position:0% +strings and we're going to come back to + + + align:start position:0% +strings and we're going to come back to +them again can't use them on booleans + + align:start position:0% +them again can't use them on booleans + + + align:start position:0% +them again can't use them on booleans +they have a different set of things they + + align:start position:0% +they have a different set of things they + + + align:start position:0% +they have a different set of things they +do things like and and + + align:start position:0% +do things like and and + + + align:start position:0% +do things like and and +or and of course there's a bunch of + + align:start position:0% +or and of course there's a bunch of + + + align:start position:0% +or and of course there's a bunch of +other ones in there I'm not going to put + + align:start position:0% +other ones in there I'm not going to put + + + align:start position:0% +other ones in there I'm not going to put +them all up but we're building up a + + align:start position:0% +them all up but we're building up a + + + align:start position:0% +them all up but we're building up a +little collection if you like of those + + align:start position:0% +little collection if you like of those + + + align:start position:0% +little collection if you like of those +operations and then the main thing we've + + align:start position:0% +operations and then the main thing we've + + + align:start position:0% +operations and then the main thing we've +done is we've talked about commands and + + align:start position:0% +done is we've talked about commands and + + + align:start position:0% +done is we've talked about commands and +I'm going to suggest we've seen now four + + align:start position:0% +I'm going to suggest we've seen now four + + + align:start position:0% +I'm going to suggest we've seen now four +different things + + align:start position:0% +different things + + + align:start position:0% +different things +we' seen an assignment how to bind a + + align:start position:0% +we' seen an assignment how to bind a + + + align:start position:0% +we' seen an assignment how to bind a +name to a + + align:start position:0% +name to a + + + align:start position:0% +name to a +value we've seen input and + + align:start position:0% + + + + align:start position:0% + +output print for output for example and + + align:start position:0% +output print for output for example and + + + align:start position:0% +output print for output for example and +and raw input for + + align:start position:0% +and raw input for + + + align:start position:0% +and raw input for +input we've seen + + align:start position:0% + + + + align:start position:0% + +conditionals or set another way branches + + align:start position:0% +conditionals or set another way branches + + + align:start position:0% +conditionals or set another way branches +ways of changing the flow of control + + align:start position:0% +ways of changing the flow of control + + + align:start position:0% +ways of changing the flow of control +through that sequence of instructions + + align:start position:0% +through that sequence of instructions + + + align:start position:0% +through that sequence of instructions +we're building up and the last thing we + + align:start position:0% +we're building up and the last thing we + + + align:start position:0% +we're building up and the last thing we +added were Loop + + align:start position:0% + + + + align:start position:0% + +mechanisms and here we saw while it's + + align:start position:0% +mechanisms and here we saw while it's + + + align:start position:0% +mechanisms and here we saw while it's +the first example we've + + align:start position:0% + + + + align:start position:0% + +seen that's what we've done so far now + + align:start position:0% +seen that's what we've done so far now + + + align:start position:0% +seen that's what we've done so far now +interestingly this set of instructions + + align:start position:0% +interestingly this set of instructions + + + align:start position:0% +interestingly this set of instructions +is actually quite powerful we're going + + align:start position:0% +is actually quite powerful we're going + + + align:start position:0% +is actually quite powerful we're going +to come back to that later on in terms + + align:start position:0% +to come back to that later on in terms + + + align:start position:0% +to come back to that later on in terms +of what we can do with it but what we've + + align:start position:0% +of what we can do with it but what we've + + + align:start position:0% +of what we can do with it but what we've +really done is given that basis we're + + align:start position:0% +really done is given that basis we're + + + align:start position:0% +really done is given that basis we're +now talking about how do we write Comm + + align:start position:0% +now talking about how do we write Comm + + + align:start position:0% +now talking about how do we write Comm +common patterns of code how do we write + + align:start position:0% +common patterns of code how do we write + + + align:start position:0% +common patterns of code how do we write +things that solve particular kinds of + + align:start position:0% +things that solve particular kinds of + + + align:start position:0% +things that solve particular kinds of +problems so what I want you to do is to + + align:start position:0% +problems so what I want you to do is to + + + align:start position:0% +problems so what I want you to do is to +keep in mind those are the basis we + + align:start position:0% +keep in mind those are the basis we + + + align:start position:0% +keep in mind those are the basis we +ought to be able to do a lot with that + + align:start position:0% +ought to be able to do a lot with that + + + align:start position:0% +ought to be able to do a lot with that +basis but what we're really interested + + align:start position:0% +basis but what we're really interested + + + align:start position:0% +basis but what we're really interested +in is not filling out a whole bunch of + + align:start position:0% +in is not filling out a whole bunch of + + + align:start position:0% +in is not filling out a whole bunch of +other things in here but how do we put + + align:start position:0% +other things in here but how do we put + + + align:start position:0% +other things in here but how do we put +them together into common templates + + align:start position:0% +them together into common templates + + + align:start position:0% +them together into common templates +we're going to do that + + align:start position:0% +we're going to do that + + + align:start position:0% +we're going to do that +today second thing we've been doing I + + align:start position:0% +today second thing we've been doing I + + + align:start position:0% +today second thing we've been doing I +want to highlight for you is we've along + + align:start position:0% +want to highlight for you is we've along + + + align:start position:0% +want to highlight for you is we've along +the way mostly just verbally rather than + + align:start position:0% +the way mostly just verbally rather than + + + align:start position:0% +the way mostly just verbally rather than +writing it down but we've been talking + + align:start position:0% +writing it down but we've been talking + + + align:start position:0% +writing it down but we've been talking +about Good + + align:start position:0% +about Good + + + align:start position:0% +about Good +style good programming style right + + align:start position:0% +style good programming style right + + + align:start position:0% +style good programming style right +things that we all to do as you put + + align:start position:0% +things that we all to do as you put + + + align:start position:0% +things that we all to do as you put +these pieces together in order to give + + align:start position:0% +these pieces together in order to give + + + align:start position:0% +these pieces together in order to give +you really good code and you should be + + align:start position:0% +you really good code and you should be + + + align:start position:0% +you really good code and you should be +collecting those together give you some + + align:start position:0% +collecting those together give you some + + + align:start position:0% +collecting those together give you some +examples what have we talked about we've + + align:start position:0% +examples what have we talked about we've + + + align:start position:0% +examples what have we talked about we've +talked about things like using comments + + align:start position:0% +talked about things like using comments + + + align:start position:0% +talked about things like using comments +to highlight what you're doing in the + + align:start position:0% +to highlight what you're doing in the + + + align:start position:0% +to highlight what you're doing in the +code to make it easier to debug uh we + + align:start position:0% +code to make it easier to debug uh we + + + align:start position:0% +code to make it easier to debug uh we +talked about type discipline the notion + + align:start position:0% +talked about type discipline the notion + + + align:start position:0% +talked about type discipline the notion +that you should check the types of + + align:start position:0% +that you should check the types of + + + align:start position:0% +that you should check the types of +operat sorry types of operands before + + align:start position:0% +operat sorry types of operands before + + + align:start position:0% +operat sorry types of operands before +you app operators to them to make sure + + align:start position:0% +you app operators to them to make sure + + + align:start position:0% +you app operators to them to make sure +that they're what the code is expecting + + align:start position:0% +that they're what the code is expecting + + + align:start position:0% +that they're what the code is expecting +we talked about descriptive use of good + + align:start position:0% +we talked about descriptive use of good + + + align:start position:0% +we talked about descriptive use of good +variable names as a way in essence of + + align:start position:0% +variable names as a way in essence of + + + align:start position:0% +variable names as a way in essence of +documenting your code + + align:start position:0% +documenting your code + + + align:start position:0% +documenting your code +fourth one we talked about was this idea + + align:start position:0% +fourth one we talked about was this idea + + + align:start position:0% +fourth one we talked about was this idea +of testing all possible branches through + + align:start position:0% +of testing all possible branches through + + + align:start position:0% +of testing all possible branches through +a piece of code if it's got conditionals + + align:start position:0% +a piece of code if it's got conditionals + + + align:start position:0% +a piece of code if it's got conditionals +in it to make sure that every possible + + align:start position:0% +in it to make sure that every possible + + + align:start position:0% +in it to make sure that every possible +input is going to give you an output + + align:start position:0% +input is going to give you an output + + + align:start position:0% +input is going to give you an output +that you actually want to see so you + + align:start position:0% +that you actually want to see so you + + + align:start position:0% +that you actually want to see so you +know you can start writing your own kind + + align:start position:0% +know you can start writing your own kind + + + align:start position:0% +know you can start writing your own kind +of Mis manners book if you like of you + + align:start position:0% +of Mis manners book if you like of you + + + align:start position:0% +of Mis manners book if you like of you +know what are good programming you know + + align:start position:0% +know what are good programming you know + + + align:start position:0% +know what are good programming you know +I don't know what you call them John + + align:start position:0% +I don't know what you call them John + + + align:start position:0% +I don't know what you call them John +good programming hygiene good + + align:start position:0% +good programming hygiene good + + + align:start position:0% +good programming hygiene good +programming style good programming + + align:start position:0% +programming style good programming + + + align:start position:0% +programming style good programming +practices things that you want to do to + + align:start position:0% +practices things that you want to do to + + + align:start position:0% +practices things that you want to do to +write good + + align:start position:0% +write good + + + align:start position:0% +write good +code okay what we're going to do today + + align:start position:0% +code okay what we're going to do today + + + align:start position:0% +code okay what we're going to do today +is we're going to start now building up + + align:start position:0% +is we're going to start now building up + + + align:start position:0% +is we're going to start now building up +Beyond just these pieces although + + align:start position:0% +Beyond just these pieces although + + + align:start position:0% +Beyond just these pieces although +they're valuable to start creating two + + align:start position:0% +they're valuable to start creating two + + + align:start position:0% +they're valuable to start creating two +things one common patterns of code that + + align:start position:0% +things one common patterns of code that + + + align:start position:0% +things one common patterns of code that +tackle certain classes of problems and + + align:start position:0% +tackle certain classes of problems and + + + align:start position:0% +tackle certain classes of problems and +secondly we're going to talk about tools + + align:start position:0% +secondly we're going to talk about tools + + + align:start position:0% +secondly we're going to talk about tools +you can use to help understand those + + align:start position:0% +you can use to help understand those + + + align:start position:0% +you can use to help understand those +pieces of + + align:start position:0% +pieces of + + + align:start position:0% +pieces of +things okay so last time around we + + align:start position:0% +things okay so last time around we + + + align:start position:0% +things okay so last time around we +talked about or introduced if you like + + align:start position:0% +talked about or introduced if you like + + + align:start position:0% +talked about or introduced if you like +iterative + + align:start position:0% +iterative + + + align:start position:0% +iterative +programs and I want to generalize that + + align:start position:0% +programs and I want to generalize that + + + align:start position:0% +programs and I want to generalize that +for a second + + align:start position:0% + + + + align:start position:0% + +because we're going to come back and use + + align:start position:0% +because we're going to come back and use + + + align:start position:0% +because we're going to come back and use +this a + + align:start position:0% + + + + align:start position:0% + +lot and I want to do a very high level + + align:start position:0% +lot and I want to do a very high level + + + align:start position:0% +lot and I want to do a very high level +description of what goes into an + + align:start position:0% +description of what goes into an + + + align:start position:0% +description of what goes into an +interative program or how I would think + + align:start position:0% +interative program or how I would think + + + align:start position:0% +interative program or how I would think +about this right and I know if John + + align:start position:0% +about this right and I know if John + + + align:start position:0% +about this right and I know if John +disagrees with me he'll tell me but this + + align:start position:0% +disagrees with me he'll tell me but this + + + align:start position:0% +disagrees with me he'll tell me but this +is my way of thinking about it if I'm + + align:start position:0% +is my way of thinking about it if I'm + + + align:start position:0% +is my way of thinking about it if I'm +going to try and decide how to tackle a + + align:start position:0% +going to try and decide how to tackle a + + + align:start position:0% +going to try and decide how to tackle a +problem in an iterative manner here are + + align:start position:0% +problem in an iterative manner here are + + + align:start position:0% +problem in an iterative manner here are +the steps I'm going to go through first + + align:start position:0% +the steps I'm going to go through first + + + align:start position:0% +the steps I'm going to go through first +thing I'm going to do is I'm going to + + align:start position:0% + + + + align:start position:0% + +choose the variable + + align:start position:0% +choose the variable + + + align:start position:0% +choose the variable +that's going to + + align:start position:0% + + + + align:start position:0% + +count what do what in the world do I + + align:start position:0% +count what do what in the world do I + + + align:start position:0% +count what do what in the world do I +mean by that I'm thinking about a + + align:start position:0% +mean by that I'm thinking about a + + + align:start position:0% +mean by that I'm thinking about a +problem I'm going to show you an example + + align:start position:0% +problem I'm going to show you an example + + + align:start position:0% +problem I'm going to show you an example +in a second first thing I'm going to do + + align:start position:0% +in a second first thing I'm going to do + + + align:start position:0% +in a second first thing I'm going to do +is say what is the thing that's going to + + align:start position:0% +is say what is the thing that's going to + + + align:start position:0% +is say what is the thing that's going to +change every time I run through the same + + align:start position:0% +change every time I run through the same + + + align:start position:0% +change every time I run through the same +set of code what is counting my way + + align:start position:0% +set of code what is counting my way + + + align:start position:0% +set of code what is counting my way +through this process now I'm putting qu + + align:start position:0% +through this process now I'm putting qu + + + align:start position:0% +through this process now I'm putting qu +counting double quotes not to make it a + + align:start position:0% +counting double quotes not to make it a + + + align:start position:0% +counting double quotes not to make it a +string but to say this is count + + align:start position:0% +string but to say this is count + + + align:start position:0% +string but to say this is count +generically it could be counting one by + + align:start position:0% +generically it could be counting one by + + + align:start position:0% +generically it could be counting one by +one through the integers it could also + + align:start position:0% +one through the integers it could also + + + align:start position:0% +one through the integers it could also +be taking a collection of data and going + + align:start position:0% +be taking a collection of data and going + + + align:start position:0% +be taking a collection of data and going +through them one by one it could be + + align:start position:0% +through them one by one it could be + + + align:start position:0% +through them one by one it could be +doing counting in some other mechanism + + align:start position:0% +doing counting in some other mechanism + + + align:start position:0% +doing counting in some other mechanism +but what's the variable that I want to + + align:start position:0% +but what's the variable that I want to + + + align:start position:0% +but what's the variable that I want to +use second thing I do I need to + + align:start position:0% +use second thing I do I need to + + + align:start position:0% +use second thing I do I need to +initialize + + align:start position:0% +initialize + + + align:start position:0% +initialize +it and I need to initialize it outside + + align:start position:0% +it and I need to initialize it outside + + + align:start position:0% +it and I need to initialize it outside +of the + + align:start position:0% +of the + + + align:start position:0% +of the +loop that is where do I want to start + + align:start position:0% +loop that is where do I want to start + + + align:start position:0% +loop that is where do I want to start +and I need to make sure I have a command + + align:start position:0% +and I need to make sure I have a command + + + align:start position:0% +and I need to make sure I have a command +that sets that up the third thing I'm + + align:start position:0% +that sets that up the third thing I'm + + + align:start position:0% +that sets that up the third thing I'm +going to do is I need to set + + align:start position:0% +going to do is I need to set + + + align:start position:0% +going to do is I need to set +up the Right End test + + align:start position:0% +up the Right End test + + + align:start position:0% +up the Right End test +how do I know when I'm done with the + + align:start position:0% +how do I know when I'm done with the + + + align:start position:0% +how do I know when I'm done with the +loop and obviously that ought to involve + + align:start position:0% +loop and obviously that ought to involve + + + align:start position:0% +loop and obviously that ought to involve +the variable in some way or it's not + + align:start position:0% +the variable in some way or it's not + + + align:start position:0% +the variable in some way or it's not +going to make a lot of sense so this + + align:start position:0% +going to make a lot of sense so this + + + align:start position:0% +going to make a lot of sense so this +includes the variable since that's the + + align:start position:0% +includes the variable since that's the + + + align:start position:0% +includes the variable since that's the +thing that's + + align:start position:0% +thing that's + + + align:start position:0% +thing that's +changing all right the fourth thing I'm + + align:start position:0% +changing all right the fourth thing I'm + + + align:start position:0% +changing all right the fourth thing I'm +going to do is I'm going to then + + align:start position:0% +going to do is I'm going to then + + + align:start position:0% +going to do is I'm going to then +construct the block of + + align:start position:0% + + + + align:start position:0% + +code and I want to remind you that block + + align:start position:0% +code and I want to remind you that block + + + align:start position:0% +code and I want to remind you that block +of code is a set of instructions the + + align:start position:0% +of code is a set of instructions the + + + align:start position:0% +of code is a set of instructions the +same set of instructions that are going + + align:start position:0% +same set of instructions that are going + + + align:start position:0% +same set of instructions that are going +to be done each time through the loop + + align:start position:0% +to be done each time through the loop + + + align:start position:0% +to be done each time through the loop +all that's going to change is the Val + + align:start position:0% +all that's going to change is the Val + + + align:start position:0% +all that's going to change is the Val +the variable or the value of some data + + align:start position:0% +the variable or the value of some data + + + align:start position:0% +the variable or the value of some data +structures and remind you that inside of + + align:start position:0% +structures and remind you that inside of + + + align:start position:0% +structures and remind you that inside of +here I better be changing the + + align:start position:0% + + + + align:start position:0% + +variable right if that variable that's + + align:start position:0% +variable right if that variable that's + + + align:start position:0% +variable right if that variable that's +counting is not changing I'm going to be + + align:start position:0% +counting is not changing I'm going to be + + + align:start position:0% +counting is not changing I'm going to be +stuck in an infinite Loop so I auto exp + + align:start position:0% +stuck in an infinite Loop so I auto exp + + + align:start position:0% +stuck in an infinite Loop so I auto exp +yeah expct right expect somewhere in + + align:start position:0% +yeah expct right expect somewhere in + + + align:start position:0% +yeah expct right expect somewhere in +there a change of that variable all + + align:start position:0% +there a change of that variable all + + + align:start position:0% +there a change of that variable all +right and then the last thing I want to + + align:start position:0% +right and then the last thing I want to + + + align:start position:0% +right and then the last thing I want to +do is just decide you know what do I do + + align:start position:0% +do is just decide you know what do I do + + + align:start position:0% +do is just decide you know what do I do +when I'm done + + align:start position:0% + + + + align:start position:0% + +okay I know it looks boring but it's a + + align:start position:0% +okay I know it looks boring but it's a + + + align:start position:0% +okay I know it looks boring but it's a +structure of the things I want to think + + align:start position:0% +structure of the things I want to think + + + align:start position:0% +structure of the things I want to think +about when I go through trying to take a + + align:start position:0% +about when I go through trying to take a + + + align:start position:0% +about when I go through trying to take a +problem and mapping it into an iterative + + align:start position:0% +problem and mapping it into an iterative + + + align:start position:0% +problem and mapping it into an iterative +program those are the things I want to + + align:start position:0% +program those are the things I want to + + + align:start position:0% +program those are the things I want to +see if I go along all right so let me + + align:start position:0% +see if I go along all right so let me + + + align:start position:0% +see if I go along all right so let me +give you an + + align:start position:0% +give you an + + + align:start position:0% +give you an +example um I'm given an integer that's a + + align:start position:0% +example um I'm given an integer that's a + + + align:start position:0% +example um I'm given an integer that's a +perfect square and I want to write a + + align:start position:0% +perfect square and I want to write a + + + align:start position:0% +perfect square and I want to write a +little piece of code that's going to + + align:start position:0% +little piece of code that's going to + + + align:start position:0% +little piece of code that's going to +find the square root of it right so I'm + + align:start position:0% +find the square root of it right so I'm + + + align:start position:0% +find the square root of it right so I'm +cheating a little I know it's a perfect + + align:start position:0% +cheating a little I know it's a perfect + + + align:start position:0% +cheating a little I know it's a perfect +square somebody's given it to me come + + align:start position:0% +square somebody's given it to me come + + + align:start position:0% +square somebody's given it to me come +back in a second to generalize so what + + align:start position:0% +back in a second to generalize so what + + + align:start position:0% +back in a second to generalize so what +would the steps be that I'd use to walk + + align:start position:0% +would the steps be that I'd use to walk + + + align:start position:0% +would the steps be that I'd use to walk +through it well if I think about these + + align:start position:0% +through it well if I think about these + + + align:start position:0% +through it well if I think about these +steps here's an easy way to do it let's + + align:start position:0% +steps here's an easy way to do it let's + + + align:start position:0% +steps here's an easy way to do it let's +start at one let's call X the thing I'm + + align:start position:0% +start at one let's call X the thing I'm + + + align:start position:0% +start at one let's call X the thing I'm +trying to find the square root of let's + + align:start position:0% +trying to find the square root of let's + + + align:start position:0% +trying to find the square root of let's +start at one square it okay if it's not + + align:start position:0% +start at one square it okay if it's not + + + align:start position:0% +start at one square it okay if it's not +greater than x take two square it if + + align:start position:0% +greater than x take two square it if + + + align:start position:0% +greater than x take two square it if +it's not greater than next take three + + align:start position:0% +it's not greater than next take three + + + align:start position:0% +it's not greater than next take three +Square it and keep going until the + + align:start position:0% +Square it and keep going until the + + + align:start position:0% +Square it and keep going until the +square of one of those integers is + + align:start position:0% +square of one of those integers is + + + align:start position:0% +square of one of those integers is +greater than or equal to sorry it's just + + align:start position:0% +greater than or equal to sorry it's just + + + align:start position:0% +greater than or equal to sorry it's just +greater than x okay why am I doing that + + align:start position:0% +greater than x okay why am I doing that + + + align:start position:0% +greater than x okay why am I doing that +when I get greater than x I've gone past + + align:start position:0% +when I get greater than x I've gone past + + + align:start position:0% +when I get greater than x I've gone past +the place where I want to be and + + align:start position:0% +the place where I want to be and + + + align:start position:0% +the place where I want to be and +obviously when I get to something whose + + align:start position:0% +obviously when I get to something whose + + + align:start position:0% +obviously when I get to something whose +square is equal to X I got the answer I + + align:start position:0% +square is equal to X I got the answer I + + + align:start position:0% +square is equal to X I got the answer I +want and I kick it out so notice what + + align:start position:0% +want and I kick it out so notice what + + + align:start position:0% +want and I kick it out so notice what +I've done I've identified the thing I'm + + align:start position:0% +I've done I've identified the thing I'm + + + align:start position:0% +I've done I've identified the thing I'm +going to use to count something some + + align:start position:0% +going to use to count something some + + + align:start position:0% +going to use to count something some +variable that's going to Discount the + + align:start position:0% +variable that's going to Discount the + + + align:start position:0% +variable that's going to Discount the +integers I've identified the nend test + + align:start position:0% +integers I've identified the nend test + + + align:start position:0% +integers I've identified the nend test +which is when that square is bigger than + + align:start position:0% +which is when that square is bigger than + + + align:start position:0% +which is when that square is bigger than +the thing I'm looking for I've + + align:start position:0% +the thing I'm looking for I've + + + align:start position:0% +the thing I'm looking for I've +identified basically what I want to do + + align:start position:0% +identified basically what I want to do + + + align:start position:0% +identified basically what I want to do +inside the loop which is simply keep + + align:start position:0% +inside the loop which is simply keep + + + align:start position:0% +inside the loop which is simply keep +changing that variable and I didn't say + + align:start position:0% +changing that variable and I didn't say + + + align:start position:0% +changing that variable and I didn't say +what I want to do and I'm done + + align:start position:0% +what I want to do and I'm done + + + align:start position:0% +what I want to do and I'm done +essentially print out the answer + + align:start position:0% +essentially print out the answer + + + align:start position:0% +essentially print out the answer +okay so how could I code this up well + + align:start position:0% +okay so how could I code this up well + + + align:start position:0% +okay so how could I code this up well +you might think let's just jump in and + + align:start position:0% +you might think let's just jump in and + + + align:start position:0% +you might think let's just jump in and +write some code I don't want to quite do + + align:start position:0% +write some code I don't want to quite do + + + align:start position:0% +write some code I don't want to quite do +that though because I want to show you + + align:start position:0% +that though because I want to show you + + + align:start position:0% +that though because I want to show you +another tool that's valuable for + + align:start position:0% +another tool that's valuable for + + + align:start position:0% +another tool that's valuable for +thinking about how to structure the Cod + + align:start position:0% +thinking about how to structure the Cod + + + align:start position:0% +thinking about how to structure the Cod +and that is something called a + + align:start position:0% + + + + align:start position:0% + +flowchart + + align:start position:0% +flowchart + + + align:start position:0% +flowchart +now people of Professor good tags in my + + align:start position:0% +now people of Professor good tags in my + + + align:start position:0% +now people of Professor good tags in my +age unfortunately remember flowcharts + + align:start position:0% +age unfortunately remember flowcharts + + + align:start position:0% +age unfortunately remember flowcharts +back as they say on The Simpsons back in + + align:start position:0% +back as they say on The Simpsons back in + + + align:start position:0% +back as they say on The Simpsons back in +the day back in the 60s John right + + align:start position:0% +the day back in the 60s John right + + + align:start position:0% +the day back in the 60s John right +really good programmers have these + + align:start position:0% +really good programmers have these + + + align:start position:0% +really good programmers have these +wonderful little plastic stencils I + + align:start position:0% +wonderful little plastic stencils I + + + align:start position:0% +wonderful little plastic stencils I +tried to find mine I couldn't find it + + align:start position:0% +tried to find mine I couldn't find it + + + align:start position:0% +tried to find mine I couldn't find it +it's a little stencil with little cutout + + align:start position:0% +it's a little stencil with little cutout + + + align:start position:0% +it's a little stencil with little cutout +shapes on it that you use to draw flow + + align:start position:0% +shapes on it that you use to draw flow + + + align:start position:0% +shapes on it that you use to draw flow +charts I'm going to show you in a second + + align:start position:0% +charts I'm going to show you in a second + + + align:start position:0% +charts I'm going to show you in a second +and you tucked it right in here next to + + align:start position:0% +and you tucked it right in here next to + + + align:start position:0% +and you tucked it right in here next to +your pocket protector with all your pens + + align:start position:0% +your pocket protector with all your pens + + + align:start position:0% +your pocket protector with all your pens +in it you know so your belt was also + + align:start position:0% +in it you know so your belt was also + + + align:start position:0% +in it you know so your belt was also +about this high and your glasses were + + align:start position:0% +about this high and your glasses were + + + align:start position:0% +about this high and your glasses were +this thick you know we have few of those + + align:start position:0% +this thick you know we have few of those + + + align:start position:0% +this thick you know we have few of those +nerds left we mostly keep them in the + + align:start position:0% +nerds left we mostly keep them in the + + + align:start position:0% +nerds left we mostly keep them in the +museum but that was what you did with + + align:start position:0% +museum but that was what you did with + + + align:start position:0% +museum but that was what you did with +the + + align:start position:0% +the + + + align:start position:0% +the +flowchart despite making a bad joke + + align:start position:0% +flowchart despite making a bad joke + + + align:start position:0% +flowchart despite making a bad joke +about it we're going to do the same + + align:start position:0% +about it we're going to do the same + + + align:start position:0% +about it we're going to do the same +thing here we're going to chart out a + + align:start position:0% +thing here we're going to chart out a + + + align:start position:0% +thing here we're going to chart out a +little bit of what should go into + + align:start position:0% +little bit of what should go into + + + align:start position:0% +little bit of what should go into +actually making this thing work so + + align:start position:0% +actually making this thing work so + + + align:start position:0% +actually making this thing work so +here's a simple flowchart that I'm going + + align:start position:0% +here's a simple flowchart that I'm going + + + align:start position:0% +here's a simple flowchart that I'm going +to use to capture what I just described + + align:start position:0% +to use to capture what I just described + + + align:start position:0% +to use to capture what I just described +and I'm going to and again I'm actually + + align:start position:0% +and I'm going to and again I'm actually + + + align:start position:0% +and I'm going to and again I'm actually +going to do it the way they used to do + + align:start position:0% +going to do it the way they used to do + + + align:start position:0% +going to do it the way they used to do +it I'm going to draw a rectangle with + + align:start position:0% +it I'm going to draw a rectangle with + + + align:start position:0% +it I'm going to draw a rectangle with +rounded + + align:start position:0% +rounded + + + align:start position:0% +rounded +Corners that's my starting point and + + align:start position:0% +Corners that's my starting point and + + + align:start position:0% +Corners that's my starting point and +then what did I say to do I said I need + + align:start position:0% +then what did I say to do I said I need + + + align:start position:0% +then what did I say to do I said I need +to identify a variable I'm going to give + + align:start position:0% +to identify a variable I'm going to give + + + align:start position:0% +to identify a variable I'm going to give +it a name let's just call it a ANS for + + align:start position:0% +it a name let's just call it a ANS for + + + align:start position:0% +it a name let's just call it a ANS for +answer and I need to initialize it so + + align:start position:0% +answer and I need to initialize it so + + + align:start position:0% +answer and I need to initialize it so +I'm going to come down and in a square + + align:start position:0% + + + + align:start position:0% + +box I'm going to initialize answer to + + align:start position:0% +box I'm going to initialize answer to + + + align:start position:0% +box I'm going to initialize answer to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +I now want to run through the loop + + align:start position:0% +I now want to run through the loop + + + align:start position:0% +I now want to run through the loop +what's the first thing I do in a loop I + + align:start position:0% +what's the first thing I do in a loop I + + + align:start position:0% +what's the first thing I do in a loop I +test an end test so the flowchart says + + align:start position:0% +test an end test so the flowchart says + + + align:start position:0% +test an end test so the flowchart says +and the tradition was to do this in a + + align:start position:0% +and the tradition was to do this in a + + + align:start position:0% +and the tradition was to do this in a +diamond + + align:start position:0% +diamond + + + align:start position:0% +diamond +shape I'm going to check if answer times + + align:start position:0% +shape I'm going to check if answer times + + + align:start position:0% +shape I'm going to check if answer times +answer uh which way did I want to do + + align:start position:0% +answer uh which way did I want to do + + + align:start position:0% +answer uh which way did I want to do +this is less than or equal to + + align:start position:0% + + + + align:start position:0% + +X now that's a test there two + + align:start position:0% +X now that's a test there two + + + align:start position:0% +X now that's a test there two +possibilities if the answer is + + align:start position:0% + + + + align:start position:0% + +yes that I'm still looking for the + + align:start position:0% +yes that I'm still looking for the + + + align:start position:0% +yes that I'm still looking for the +answer what do I want to do well I don't + + align:start position:0% +answer what do I want to do well I don't + + + align:start position:0% +answer what do I want to do well I don't +have to do anything other than change + + align:start position:0% +have to do anything other than change + + + align:start position:0% +have to do anything other than change +the counter so I'm going to go to + + align:start position:0% +the counter so I'm going to go to + + + align:start position:0% +the counter so I'm going to go to +answer is answer + + + align:start position:0% +answer is answer + + + + align:start position:0% +answer is answer + +one + + align:start position:0% +one + + + align:start position:0% +one +and I'm going to do it + + align:start position:0% +and I'm going to do it + + + align:start position:0% +and I'm going to do it +again eventually if I've done this right + + align:start position:0% +again eventually if I've done this right + + + align:start position:0% +again eventually if I've done this right +that that test is + + align:start position:0% +that that test is + + + align:start position:0% +that that test is +no and I wonder iFly ran out of room + + align:start position:0% +no and I wonder iFly ran out of room + + + align:start position:0% +no and I wonder iFly ran out of room +here in which case I'm going to go to a + + align:start position:0% +here in which case I'm going to go to a + + + align:start position:0% +here in which case I'm going to go to a +print statement which was always done in + + align:start position:0% +print statement which was always done in + + + align:start position:0% +print statement which was always done in +a trapezoid + + align:start position:0% + + + + align:start position:0% + +I'm going to print out answer and I + + align:start position:0% +I'm going to print out answer and I + + + align:start position:0% +I'm going to print out answer and I +should have put a box below it that says + + align:start position:0% +should have put a box below it that says + + + align:start position:0% +should have put a box below it that says +stop + + align:start position:0% +stop + + + align:start position:0% +stop +okay wow but notice what I got here + + align:start position:0% +okay wow but notice what I got here + + + align:start position:0% +okay wow but notice what I got here +actually this is a useful tool for + + align:start position:0% +actually this is a useful tool for + + + align:start position:0% +actually this is a useful tool for +visualizing how I'm trying to put it + + align:start position:0% +visualizing how I'm trying to put it + + + align:start position:0% +visualizing how I'm trying to put it +together because it lets me see where + + align:start position:0% +together because it lets me see where + + + align:start position:0% +together because it lets me see where +the loop is right there it lets me see + + align:start position:0% +the loop is right there it lets me see + + + align:start position:0% +the loop is right there it lets me see +the end test it lets me make sure that + + align:start position:0% +the end test it lets me make sure that + + + align:start position:0% +the end test it lets me make sure that +I'm in fact initializing the variable + + align:start position:0% +I'm in fact initializing the variable + + + align:start position:0% +I'm in fact initializing the variable +and I'm checking the right things as I + + align:start position:0% +and I'm checking the right things as I + + + align:start position:0% +and I'm checking the right things as I +go along and the idea of this flowchart + + align:start position:0% +go along and the idea of this flowchart + + + align:start position:0% +go along and the idea of this flowchart +is if you start you know little ball + + align:start position:0% +is if you start you know little ball + + + align:start position:0% +is if you start you know little ball +bearing here it's going to roll down + + align:start position:0% +bearing here it's going to roll down + + + align:start position:0% +bearing here it's going to roll down +setting up an assignment statement and + + align:start position:0% +setting up an assignment statement and + + + align:start position:0% +setting up an assignment statement and +then depending on here it's like there's + + align:start position:0% +then depending on here it's like there's + + + align:start position:0% +then depending on here it's like there's +a pair of flippers in there does the + + align:start position:0% +a pair of flippers in there does the + + + align:start position:0% +a pair of flippers in there does the +test it sets the ball this way to change + + align:start position:0% +test it sets the ball this way to change + + + align:start position:0% +test it sets the ball this way to change +it to ants plus one and comes back + + align:start position:0% +it to ants plus one and comes back + + + align:start position:0% +it to ants plus one and comes back +around eventually it's going to drop + + align:start position:0% +around eventually it's going to drop + + + align:start position:0% +around eventually it's going to drop +through and print out the + + align:start position:0% +through and print out the + + + align:start position:0% +through and print out the +answer reason I'm going to show you this + + align:start position:0% +answer reason I'm going to show you this + + + align:start position:0% +answer reason I'm going to show you this +flowchart I'm going to do one other + + align:start position:0% +flowchart I'm going to do one other + + + align:start position:0% +flowchart I'm going to do one other +example in a second but I want to show + + align:start position:0% +example in a second but I want to show + + + align:start position:0% +example in a second but I want to show +you a comparison remember last time we + + align:start position:0% +you a comparison remember last time we + + + align:start position:0% +you a comparison remember last time we +wrote this simple piece of code to print + + align:start position:0% +wrote this simple piece of code to print + + + align:start position:0% +wrote this simple piece of code to print +out even or odd if um you know xit was + + align:start position:0% +out even or odd if um you know xit was + + + align:start position:0% +out even or odd if um you know xit was +in fact even or odd so let me show you + + align:start position:0% +in fact even or odd so let me show you + + + align:start position:0% +in fact even or odd so let me show you +what a flowchart for that would look + + align:start position:0% +what a flowchart for that would look + + + align:start position:0% +what a flowchart for that would look +like because I want to make a comp + + align:start position:0% +like because I want to make a comp + + + align:start position:0% +like because I want to make a comp +parison Point + + align:start position:0% + + + + align:start position:0% + +here if I were to do a flowchart for + + align:start position:0% +here if I were to do a flowchart for + + + align:start position:0% +here if I were to do a flowchart for +that + + align:start position:0% +that + + + align:start position:0% +that +one would do the + + align:start position:0% + + + + align:start position:0% + +following remind you that the test here + + align:start position:0% +following remind you that the test here + + + align:start position:0% +following remind you that the test here +was we took X if that's what we're + + align:start position:0% +was we took X if that's what we're + + + align:start position:0% +was we took X if that's what we're +looking for did integer division by two + + align:start position:0% +looking for did integer division by two + + + align:start position:0% +looking for did integer division by two +multiplied it by two and we checked to + + align:start position:0% +multiplied it by two and we checked to + + + align:start position:0% +multiplied it by two and we checked to +see that was the same as X if the answer + + align:start position:0% +see that was the same as X if the answer + + + align:start position:0% +see that was the same as X if the answer +is + + align:start position:0% +is + + + align:start position:0% +is +yes then we did a + + align:start position:0% + + + + align:start position:0% + +print of + + align:start position:0% +print of + + + align:start position:0% +print of +even if the answer was + + align:start position:0% + + + + align:start position:0% + +no we did a print of + + align:start position:0% + + + + align:start position:0% + +odd and then we carried + + align:start position:0% + + + + align:start position:0% + +on again wow but there's an important + + align:start position:0% +on again wow but there's an important + + + align:start position:0% +on again wow but there's an important +point here remember last time I said + + align:start position:0% +point here remember last time I said + + + align:start position:0% +point here remember last time I said +that there's different kinds of + + align:start position:0% +that there's different kinds of + + + align:start position:0% +that there's different kinds of +complexity in our code and I suggested + + align:start position:0% +complexity in our code and I suggested + + + align:start position:0% +complexity in our code and I suggested +for simple branching programs the amount + + align:start position:0% +for simple branching programs the amount + + + align:start position:0% +for simple branching programs the amount +of time it takes to run that program is + + align:start position:0% +of time it takes to run that program is + + + align:start position:0% +of time it takes to run that program is +in essence bounded by the number of + + align:start position:0% +in essence bounded by the number of + + + align:start position:0% +in essence bounded by the number of +instructions because you only execute + + align:start position:0% +instructions because you only execute + + + align:start position:0% +instructions because you only execute +each instruction at most once didn't + + align:start position:0% +each instruction at most once didn't + + + align:start position:0% +each instruction at most once didn't +depend on the size of the input and you + + align:start position:0% +depend on the size of the input and you + + + align:start position:0% +depend on the size of the input and you +can see that there I start off either I + + align:start position:0% +can see that there I start off either I + + + align:start position:0% +can see that there I start off either I +take this path and carry on or I take + + align:start position:0% +take this path and carry on or I take + + + align:start position:0% +take this path and carry on or I take +that path and carry on but each box if + + align:start position:0% +that path and carry on but each box if + + + align:start position:0% +that path and carry on but each box if +you like gets touched exactly once the + + align:start position:0% +you like gets touched exactly once the + + + align:start position:0% +you like gets touched exactly once the +other hand look go this + + align:start position:0% +other hand look go this + + + align:start position:0% +other hand look go this +one this depends now on the size of X + + align:start position:0% +one this depends now on the size of X + + + align:start position:0% +one this depends now on the size of X +right because what am I going to do I'm + + align:start position:0% +right because what am I going to do I'm + + + align:start position:0% +right because what am I going to do I'm +going to come down and say is an S less + + align:start position:0% +going to come down and say is an S less + + + align:start position:0% +going to come down and say is an S less +than or equal to X if it is I'm going to + + align:start position:0% +than or equal to X if it is I'm going to + + + align:start position:0% +than or equal to X if it is I'm going to +go around and execute that statement + + align:start position:0% +go around and execute that statement + + + align:start position:0% +go around and execute that statement +check it again and go around and execute + + align:start position:0% +check it again and go around and execute + + + align:start position:0% +check it again and go around and execute +that so I'm going to cycle around that + + align:start position:0% +that so I'm going to cycle around that + + + align:start position:0% +that so I'm going to cycle around that +Loop there enough times to get to the + + align:start position:0% +Loop there enough times to get to the + + + align:start position:0% +Loop there enough times to get to the +answer and that number of times is going + + align:start position:0% +answer and that number of times is going + + + align:start position:0% +answer and that number of times is going +to depend on the input so as I change + + align:start position:0% +to depend on the input so as I change + + + align:start position:0% +to depend on the input so as I change +the input I'm going to change the + + align:start position:0% +the input I'm going to change the + + + align:start position:0% +the input I'm going to change the +complexity of the code now this happens + + align:start position:0% +complexity of the code now this happens + + + align:start position:0% +complexity of the code now this happens +to be what we would call a linear + + align:start position:0% +to be what we would call a linear + + + align:start position:0% +to be what we would call a linear +process because the number of times I go + + align:start position:0% +process because the number of times I go + + + align:start position:0% +process because the number of times I go +around the loop is directly related to + + align:start position:0% +around the loop is directly related to + + + align:start position:0% +around the loop is directly related to +the size of the argument if I double the + + align:start position:0% +the size of the argument if I double the + + + align:start position:0% +the size of the argument if I double the +argument I'm going to double the number + + align:start position:0% +argument I'm going to double the number + + + align:start position:0% +argument I'm going to double the number +of times I go around the loop if I + + align:start position:0% +of times I go around the loop if I + + + align:start position:0% +of times I go around the loop if I +increase it by five I'm going to + + align:start position:0% +increase it by five I'm going to + + + align:start position:0% +increase it by five I'm going to +increase by five the number of times I + + align:start position:0% +increase by five the number of times I + + + align:start position:0% +increase by five the number of times I +go around the loop we'll see later on + + align:start position:0% +go around the loop we'll see later on + + + align:start position:0% +go around the loop we'll see later on +there are classes of computation that + + align:start position:0% +there are classes of computation that + + + align:start position:0% +there are classes of computation that +are inherently much more complex we hate + + align:start position:0% +are inherently much more complex we hate + + + align:start position:0% +are inherently much more complex we hate +them because they're costly but they're + + align:start position:0% +them because they're costly but they're + + + align:start position:0% +them because they're costly but they're +sometimes inherently that way but you + + align:start position:0% +sometimes inherently that way but you + + + align:start position:0% +sometimes inherently that way but you +can see the compar between these + + align:start position:0% +can see the compar between these + + + align:start position:0% +can see the compar between these +two okay now having done that let's + + align:start position:0% +two okay now having done that let's + + + align:start position:0% +two okay now having done that let's +build this + + align:start position:0% + + + + align:start position:0% + +code my machine will come back up there + + align:start position:0% +code my machine will come back up there + + + align:start position:0% +code my machine will come back up there +we + + align:start position:0% +we + + + align:start position:0% +we +go so I'm going to now go ahead and + + align:start position:0% +go so I'm going to now go ahead and + + + align:start position:0% +go so I'm going to now go ahead and +write a little piece of code and I put + + align:start position:0% +write a little piece of code and I put + + + align:start position:0% +write a little piece of code and I put +it here and I hope you can actually see + + align:start position:0% +it here and I hope you can actually see + + + align:start position:0% +it here and I hope you can actually see +these better this + + align:start position:0% +these better this + + + align:start position:0% +these better this +time let me + + align:start position:0% +time let me + + + align:start position:0% +time let me +uncomment that + + align:start position:0% +uncomment that + + + align:start position:0% +uncomment that +region right so there's basically an + + align:start position:0% +region right so there's basically an + + + align:start position:0% +region right so there's basically an +encapsulation of that code right it says + + align:start position:0% +encapsulation of that code right it says + + + align:start position:0% +encapsulation of that code right it says +if I look at + + align:start position:0% +if I look at + + + align:start position:0% +if I look at +this where am I right here I've got some + + align:start position:0% +this where am I right here I've got some + + + align:start position:0% +this where am I right here I've got some +value for x initially I'm going to set + + align:start position:0% +value for x initially I'm going to set + + + align:start position:0% +value for x initially I'm going to set +answer to zero just like there and + + align:start position:0% +answer to zero just like there and + + + align:start position:0% +answer to zero just like there and +there's my Loop there's the test which + + align:start position:0% +there's my Loop there's the test which + + + align:start position:0% +there's my Loop there's the test which +is right like that is answer squar less + + align:start position:0% +is right like that is answer squar less + + + align:start position:0% +is right like that is answer squar less +than or equal to X if it is ah there's + + align:start position:0% +than or equal to X if it is ah there's + + + align:start position:0% +than or equal to X if it is ah there's +the block corresponding to the loop + + align:start position:0% +the block corresponding to the loop + + + align:start position:0% +the block corresponding to the loop +chains answer and eventually I'm done + + align:start position:0% +chains answer and eventually I'm done + + + align:start position:0% +chains answer and eventually I'm done +with all this thing I'm just going to + + align:start position:0% +with all this thing I'm just going to + + + align:start position:0% +with all this thing I'm just going to +print answer + + align:start position:0% +print answer + + + align:start position:0% +print answer +out okay all right let me show you one + + align:start position:0% +out okay all right let me show you one + + + align:start position:0% +out okay all right let me show you one +other tool that I want to use which is + + align:start position:0% +other tool that I want to use which is + + + align:start position:0% +other tool that I want to use which is +written that piece of cod ought to check + + align:start position:0% +written that piece of cod ought to check + + + align:start position:0% +written that piece of cod ought to check +it well I could just run it but another + + align:start position:0% +it well I could just run it but another + + + align:start position:0% +it well I could just run it but another +useful thing to do as I'm especially as + + align:start position:0% +useful thing to do as I'm especially as + + + align:start position:0% +useful thing to do as I'm especially as +I want to debug these things is to + + align:start position:0% +I want to debug these things is to + + + align:start position:0% +I want to debug these things is to +simulate that + + align:start position:0% +simulate that + + + align:start position:0% +simulate that +code and I'm going to do this because as + + align:start position:0% +code and I'm going to do this because as + + + align:start position:0% +code and I'm going to do this because as +Professor good tag noticed to me + + align:start position:0% +Professor good tag noticed to me + + + align:start position:0% +Professor good tag noticed to me +students seem reluctant to do this I + + align:start position:0% +students seem reluctant to do this I + + + align:start position:0% +students seem reluctant to do this I +guess it's not Macho enough John to just + + align:start position:0% +guess it's not Macho enough John to just + + + align:start position:0% +guess it's not Macho enough John to just +you know uh you know go off and do + + align:start position:0% +you know uh you know go off and do + + + align:start position:0% +you know uh you know go off and do +things by hand you ought to just run + + align:start position:0% +things by hand you ought to just run + + + align:start position:0% +things by hand you ought to just run +them but it's a valuable tool to get + + align:start position:0% +them but it's a valuable tool to get + + + align:start position:0% +them but it's a valuable tool to get +into so let me do that + + align:start position:0% +into so let me do that + + + align:start position:0% +into so let me do that +here like get pants I'm doing such a + + align:start position:0% +here like get pants I'm doing such a + + + align:start position:0% +here like get pants I'm doing such a +great job I got to say when I I've got + + align:start position:0% +great job I got to say when I I've got + + + align:start position:0% +great job I got to say when I I've got +two sons now aged 18 and 20 they used to + + align:start position:0% +two sons now aged 18 and 20 they used to + + + align:start position:0% +two sons now aged 18 and 20 they used to +think I had the coolest job in the world + + align:start position:0% +think I had the coolest job in the world + + + align:start position:0% +think I had the coolest job in the world +because I came home covered in chalk now + + align:start position:0% +because I came home covered in chalk now + + + align:start position:0% +because I came home covered in chalk now +they have a different opinion that you + + align:start position:0% +they have a different opinion that you + + + align:start position:0% +they have a different opinion that you +can probably figure + + align:start position:0% +can probably figure + + + align:start position:0% +can probably figure +out all right simulate the code what I + + align:start position:0% +out all right simulate the code what I + + + align:start position:0% +out all right simulate the code what I +mean by that is pick a simple set of + + align:start position:0% +mean by that is pick a simple set of + + + align:start position:0% +mean by that is pick a simple set of +values and let's walk through it to see + + align:start position:0% +values and let's walk through it to see + + + align:start position:0% +values and let's walk through it to see +what happens and this is useful because + + align:start position:0% +what happens and this is useful because + + + align:start position:0% +what happens and this is useful because +it's going to allow me to a make sure + + align:start position:0% +it's going to allow me to a make sure + + + align:start position:0% +it's going to allow me to a make sure +that I've got something that's going to + + align:start position:0% +that I've got something that's going to + + + align:start position:0% +that I've got something that's going to +terminate it's going to let me make sure + + align:start position:0% +terminate it's going to let me make sure + + + align:start position:0% +terminate it's going to let me make sure +that I'm fact I'm doing the right kinds + + align:start position:0% +that I'm fact I'm doing the right kinds + + + align:start position:0% +that I'm fact I'm doing the right kinds +of updates I could do this by the way by + + align:start position:0% +of updates I could do this by the way by + + + align:start position:0% +of updates I could do this by the way by +running the code and putting print + + align:start position:0% +running the code and putting print + + + align:start position:0% +running the code and putting print +statements in in various places as well + + align:start position:0% +statements in in various places as well + + + align:start position:0% +statements in in various places as well +but the hand simulation is valuable so + + align:start position:0% +but the hand simulation is valuable so + + + align:start position:0% +but the hand simulation is valuable so +let me just start it what do I have here + + align:start position:0% +let me just start it what do I have here + + + align:start position:0% +let me just start it what do I have here +I need the variable + + align:start position:0% +I need the variable + + + align:start position:0% +I need the variable +ANS I need + + align:start position:0% +ANS I need + + + align:start position:0% +ANS I need +X and I need a ANS time a s s time an + + align:start position:0% +X and I need a ANS time a s s time an + + + align:start position:0% +X and I need a ANS time a s s time an +right those are the three things that + + align:start position:0% +right those are the three things that + + + align:start position:0% +right those are the three things that +are involved in this computation and I + + align:start position:0% +are involved in this computation and I + + + align:start position:0% +are involved in this computation and I +picked something reasonably simple + + align:start position:0% +picked something reasonably simple + + + align:start position:0% +picked something reasonably simple +answer starts at zero I set up X I think + + align:start position:0% +answer starts at zero I set up X I think + + + align:start position:0% +answer starts at zero I set up X I think +to be 16 there so what does the loop say + + align:start position:0% +to be 16 there so what does the loop say + + + align:start position:0% +to be 16 there so what does the loop say +I can either look at my flowchart or I + + align:start position:0% +I can either look at my flowchart or I + + + align:start position:0% +I can either look at my flowchart or I +look at the code look at the flowchart + + align:start position:0% +look at the code look at the flowchart + + + align:start position:0% +look at the code look at the flowchart +it says I'm at this point look at answer + + align:start position:0% +it says I'm at this point look at answer + + + align:start position:0% +it says I'm at this point look at answer +squ is it less than or equal to sorry + + align:start position:0% +squ is it less than or equal to sorry + + + align:start position:0% +squ is it less than or equal to sorry +first of all answer squared is zero is + + align:start position:0% +first of all answer squared is zero is + + + align:start position:0% +first of all answer squared is zero is +it less than or equal to X yes so what + + align:start position:0% +it less than or equal to X yes so what + + + align:start position:0% +it less than or equal to X yes so what +do I do change + + align:start position:0% +do I do change + + + align:start position:0% +do I do change +answer X doesn't change back around to + + align:start position:0% +answer X doesn't change back around to + + + align:start position:0% +answer X doesn't change back around to +the test what's the answer squared it's + + align:start position:0% +the test what's the answer squared it's + + + align:start position:0% +the test what's the answer squared it's +one it's it less than or equal to 16 + + align:start position:0% +one it's it less than or equal to 16 + + + align:start position:0% +one it's it less than or equal to 16 +sure run the loop again answer becomes + + align:start position:0% +sure run the loop again answer becomes + + + align:start position:0% +sure run the loop again answer becomes +two x stays 16 answered squared is four + + align:start position:0% +two x stays 16 answered squared is four + + + align:start position:0% +two x stays 16 answered squared is four +is that less than or equal to 16 yes + + align:start position:0% +is that less than or equal to 16 yes + + + align:start position:0% +is that less than or equal to 16 yes +aren't you glad I didn't pick x equal + + align:start position:0% +aren't you glad I didn't pick x equal + + + align:start position:0% +aren't you glad I didn't pick x equal + + align:start position:0% + + + align:start position:0% +all right answer goes up by one answer + + align:start position:0% +all right answer goes up by one answer + + + align:start position:0% +all right answer goes up by one answer +squared is n still less than or equal to + + align:start position:0% +squared is n still less than or equal to + + + align:start position:0% +squared is n still less than or equal to +16 answer goes to four x stays the same + + align:start position:0% +16 answer goes to four x stays the same + + + align:start position:0% +16 answer goes to four x stays the same +4^ SAR is 16 is 16 less than or equal to + + align:start position:0% +4^ SAR is 16 is 16 less than or equal to + + + align:start position:0% +4^ SAR is 16 is 16 less than or equal to +16 yes so answer goes to five answer + + align:start position:0% +16 yes so answer goes to five answer + + + align:start position:0% +16 yes so answer goes to five answer +squar becomes 25 ah that is now no + + align:start position:0% +squar becomes 25 ah that is now no + + + align:start position:0% +squar becomes 25 ah that is now no +longer true here so I print out five + + align:start position:0% +longer true here so I print out five + + + align:start position:0% +longer true here so I print out five +right sure sare < TK of 16 is 5 + + align:start position:0% +right sure sare < TK of 16 is 5 + + + align:start position:0% +right sure sare < TK of 16 is 5 +it's Bush economics + + align:start position:0% +it's Bush economics + + + align:start position:0% +it's Bush economics +okay I know I'm not supposed to make it + + align:start position:0% +okay I know I'm not supposed to make it + + + align:start position:0% +okay I know I'm not supposed to make it +bad jokes like that what + + align:start position:0% +bad jokes like that what + + + align:start position:0% +bad jokes like that what +happened + + align:start position:0% + + + + align:start position:0% + +yeah doesn't stop at the right place + + align:start position:0% +yeah doesn't stop at the right place + + + align:start position:0% +yeah doesn't stop at the right place +thank you exactly right my bug here is + + align:start position:0% +thank you exactly right my bug here is + + + align:start position:0% +thank you exactly right my bug here is +right there let me find my + + align:start position:0% + + + + align:start position:0% + +cursor I probably want that right I want + + align:start position:0% +cursor I probably want that right I want + + + align:start position:0% +cursor I probably want that right I want +less than rather than less than or equal + + align:start position:0% +less than rather than less than or equal + + + align:start position:0% +less than rather than less than or equal +to this is an easy bug to come up with + + align:start position:0% +to this is an easy bug to come up with + + + align:start position:0% +to this is an easy bug to come up with +but imagine if you don't do the test + + align:start position:0% +but imagine if you don't do the test + + + align:start position:0% +but imagine if you don't do the test +you're going to get answers out that + + align:start position:0% +you're going to get answers out that + + + align:start position:0% +you're going to get answers out that +don't make any sense and in fact if we + + align:start position:0% +don't make any sense and in fact if we + + + align:start position:0% +don't make any sense and in fact if we +just go ahead and run this now hopefully + + align:start position:0% +just go ahead and run this now hopefully + + + align:start position:0% +just go ahead and run this now hopefully +we get + + align:start position:0% +we get + + + align:start position:0% +we get +out oops + + align:start position:0% +out oops + + + align:start position:0% +out oops +sorry I'm going to have to change this + + align:start position:0% +sorry I'm going to have to change this + + + align:start position:0% +sorry I'm going to have to change this +quickly I still have some things + + align:start position:0% +quickly I still have some things + + + align:start position:0% +quickly I still have some things +uncommented at the bottom yeah there + + align:start position:0% +uncommented at the bottom yeah there + + + align:start position:0% +uncommented at the bottom yeah there +they are I don't think we need that + + align:start position:0% +they are I don't think we need that + + + align:start position:0% +they are I don't think we need that +yet all right we will comment those out + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so why did I do it it's a simple example + + align:start position:0% +so why did I do it it's a simple example + + + align:start position:0% +so why did I do it it's a simple example +I agree but notice what I just did it + + align:start position:0% +I agree but notice what I just did it + + + align:start position:0% +I agree but notice what I just did it +allowed me to highlight is the code + + align:start position:0% +allowed me to highlight is the code + + + align:start position:0% +allowed me to highlight is the code +doing the right thing I spotted an error + + align:start position:0% +doing the right thing I spotted an error + + + align:start position:0% +doing the right thing I spotted an error +here I could have spotted it by running + + align:start position:0% +here I could have spotted it by running + + + align:start position:0% +here I could have spotted it by running +it on different test sets and using + + align:start position:0% +it on different test sets and using + + + align:start position:0% +it on different test sets and using +print statement another way doing it but + + align:start position:0% +print statement another way doing it but + + + align:start position:0% +print statement another way doing it but +this idea of at least simulating it on + + align:start position:0% +this idea of at least simulating it on + + + align:start position:0% +this idea of at least simulating it on +SIMPLE examples lets you check a couple + + align:start position:0% +SIMPLE examples lets you check a couple + + + align:start position:0% +SIMPLE examples lets you check a couple +of important questions and in fact now + + align:start position:0% +of important questions and in fact now + + + align:start position:0% +of important questions and in fact now +let me ask those two questions about + + align:start position:0% +let me ask those two questions about + + + align:start position:0% +let me ask those two questions about +this piece of code first question is for + + align:start position:0% +this piece of code first question is for + + + align:start position:0% +this piece of code first question is for +what values of integers we're going to + + align:start position:0% +what values of integers we're going to + + + align:start position:0% +what values of integers we're going to +assume integers but for what values of X + + align:start position:0% +assume integers but for what values of X + + + align:start position:0% +assume integers but for what values of X +does this code + + align:start position:0% +does this code + + + align:start position:0% +does this code +terminate and the second question is for + + align:start position:0% +terminate and the second question is for + + + align:start position:0% +terminate and the second question is for +what values of X does it give me back + + align:start position:0% +what values of X does it give me back + + + align:start position:0% +what values of X does it give me back +the right answer all right first + + align:start position:0% +the right answer all right first + + + align:start position:0% +the right answer all right first +question what values of X does it + + align:start position:0% +question what values of X does it + + + align:start position:0% +question what values of X does it +terminate again assume X is an + + align:start position:0% + + + + align:start position:0% + +integer well break it down into pieces + + align:start position:0% +integer well break it down into pieces + + + align:start position:0% +integer well break it down into pieces +suppose X is POS positive does it + + align:start position:0% +suppose X is POS positive does it + + + align:start position:0% +suppose X is POS positive does it +terminate sure right because answer + + align:start position:0% +terminate sure right because answer + + + align:start position:0% +terminate sure right because answer +starts out at zero so answer squared is + + align:start position:0% +starts out at zero so answer squared is + + + align:start position:0% +starts out at zero so answer squared is +zero at each time through the loop + + align:start position:0% +zero at each time through the loop + + + align:start position:0% +zero at each time through the loop +answer is increasing that means at some + + align:start position:0% +answer is increasing that means at some + + + align:start position:0% +answer is increasing that means at some +point in some finite number of steps + + align:start position:0% +point in some finite number of steps + + + align:start position:0% +point in some finite number of steps +answer squared has got to get bigger + + align:start position:0% +answer squared has got to get bigger + + + align:start position:0% +answer squared has got to get bigger +than x if x is positive so for positive + + align:start position:0% +than x if x is positive so for positive + + + align:start position:0% +than x if x is positive so for positive +integers it terminates and it probably I + + align:start position:0% +integers it terminates and it probably I + + + align:start position:0% +integers it terminates and it probably I +think we could deduce Returns the right + + align:start position:0% +think we could deduce Returns the right + + + align:start position:0% +think we could deduce Returns the right +answer here right X is negative X is + + align:start position:0% +answer here right X is negative X is + + + align:start position:0% +answer here right X is negative X is +minus 16 + + align:start position:0% +minus 16 + + + align:start position:0% +minus 16 +does this code + + align:start position:0% + + + + align:start position:0% + +terminate boy I feel like Arnold + + align:start position:0% +terminate boy I feel like Arnold + + + align:start position:0% +terminate boy I feel like Arnold +Schwarzenegger here does this + + align:start position:0% +Schwarzenegger here does this + + + align:start position:0% +Schwarzenegger here does this +terminate + + align:start position:0% + + + + align:start position:0% + +somebody ah thank you so it does + + align:start position:0% +somebody ah thank you so it does + + + align:start position:0% +somebody ah thank you so it does +terminate right you're sitting too far + + align:start position:0% +terminate right you're sitting too far + + + align:start position:0% +terminate right you're sitting too far +back let me try oh too far sorry come + + align:start position:0% +back let me try oh too far sorry come + + + align:start position:0% +back let me try oh too far sorry come +and get me one later if you can't find + + align:start position:0% +and get me one later if you can't find + + + align:start position:0% +and get me one later if you can't find +it yes it stops at the first step right + + align:start position:0% +it yes it stops at the first step right + + + align:start position:0% +it yes it stops at the first step right +let's look at it it says if answer sorry + + align:start position:0% +let's look at it it says if answer sorry + + + align:start position:0% +let's look at it it says if answer sorry +the X is - 16 answer is zero is 0 less + + align:start position:0% +the X is - 16 answer is zero is 0 less + + + align:start position:0% +the X is - 16 answer is zero is 0 less +than- 16 no so what does it do it prints + + align:start position:0% +than- 16 no so what does it do it prints + + + align:start position:0% +than- 16 no so what does it do it prints +out + + align:start position:0% +out + + + align:start position:0% +out +zero ah so that now answers my second + + align:start position:0% +zero ah so that now answers my second + + + align:start position:0% +zero ah so that now answers my second +question it does terminate but does it + + align:start position:0% +question it does terminate but does it + + + align:start position:0% +question it does terminate but does it +give me the right answer no right it + + align:start position:0% +give me the right answer no right it + + + align:start position:0% +give me the right answer no right it +gives me an answer and imagine I'm using + + align:start position:0% +gives me an answer and imagine I'm using + + + align:start position:0% +gives me an answer and imagine I'm using +this somewhere else you know is going to + + align:start position:0% +this somewhere else you know is going to + + + align:start position:0% +this somewhere else you know is going to +go off and say gee the the the square + + align:start position:0% +go off and say gee the the the square + + + align:start position:0% +go off and say gee the the the square +root of minus 16 is zero well it really + + align:start position:0% +root of minus 16 is zero well it really + + + align:start position:0% +root of minus 16 is zero well it really +should be you know an imaginary number + + align:start position:0% +should be you know an imaginary number + + + align:start position:0% +should be you know an imaginary number +but this is not a valuable thing to have + + align:start position:0% +but this is not a valuable thing to have + + + align:start position:0% +but this is not a valuable thing to have +come back and so that's the second thing + + align:start position:0% +come back and so that's the second thing + + + align:start position:0% +come back and so that's the second thing +I've just highlighted here is that I now + + align:start position:0% +I've just highlighted here is that I now + + + align:start position:0% +I've just highlighted here is that I now +have the ability to check whether it + + align:start position:0% +have the ability to check whether it + + + align:start position:0% +have the ability to check whether it +does the right thing and those are two + + align:start position:0% +does the right thing and those are two + + + align:start position:0% +does the right thing and those are two +things that you'd like to do with every + + align:start position:0% +things that you'd like to do with every + + + align:start position:0% +things that you'd like to do with every +looping construct you write you'd like + + align:start position:0% +looping construct you write you'd like + + + align:start position:0% +looping construct you write you'd like +to be able to assure yourselves that it + + align:start position:0% +to be able to assure yourselves that it + + + align:start position:0% +to be able to assure yourselves that it +will always terminate and then the + + align:start position:0% +will always terminate and then the + + + align:start position:0% +will always terminate and then the +second thing you'd like to do is to + + align:start position:0% +second thing you'd like to do is to + + + align:start position:0% +second thing you'd like to do is to +assure yourself that it does give you + + align:start position:0% +assure yourself that it does give you + + + align:start position:0% +assure yourself that it does give you +back a reasonable answer we started to + + align:start position:0% +back a reasonable answer we started to + + + align:start position:0% +back a reasonable answer we started to +talk about ways to do the former it's + + align:start position:0% +talk about ways to do the former it's + + + align:start position:0% +talk about ways to do the former it's +looking at the end test it's looking at + + align:start position:0% +looking at the end test it's looking at + + + align:start position:0% +looking at the end test it's looking at +the kinds of conditions you're going to + + align:start position:0% +the kinds of conditions you're going to + + + align:start position:0% +the kinds of conditions you're going to +put in for the latter this is a place + + align:start position:0% +put in for the latter this is a place + + + align:start position:0% +put in for the latter this is a place +where running test cases would would do + + align:start position:0% +where running test cases would would do + + + align:start position:0% +where running test cases would would do +a good job of helping you with that + + align:start position:0% +a good job of helping you with that + + + align:start position:0% +a good job of helping you with that +nonetheless having done that let's look + + align:start position:0% +nonetheless having done that let's look + + + align:start position:0% +nonetheless having done that let's look +at a better way to write this which + + align:start position:0% +at a better way to write this which + + + align:start position:0% +at a better way to write this which +is right here and is also I think on + + align:start position:0% +is right here and is also I think on + + + align:start position:0% +is right here and is also I think on +your sheet I'm going to uncomment that + + align:start position:0% +your sheet I'm going to uncomment that + + + align:start position:0% +your sheet I'm going to uncomment that +I'm going to comment this one + + align:start position:0% + + + + align:start position:0% + +out all right so let's look at this code + + align:start position:0% +out all right so let's look at this code + + + align:start position:0% +out all right so let's look at this code +for a + + align:start position:0% +for a + + + align:start position:0% +for a +second notice what this does certainly + + align:start position:0% +second notice what this does certainly + + + align:start position:0% +second notice what this does certainly +the heart of it right in here is still + + align:start position:0% +the heart of it right in here is still + + + align:start position:0% +the heart of it right in here is still +the same thing but notice what this does + + align:start position:0% +the same thing but notice what this does + + + align:start position:0% +the same thing but notice what this does +the first thing it does is it says let's + + align:start position:0% +the first thing it does is it says let's + + + align:start position:0% +the first thing it does is it says let's +check and make sure X is greater than or + + align:start position:0% +check and make sure X is greater than or + + + align:start position:0% +check and make sure X is greater than or +equal to zero if it isn't notice what's + + align:start position:0% +equal to zero if it isn't notice what's + + + align:start position:0% +equal to zero if it isn't notice what's +going to happen none of that block is + + align:start position:0% +going to happen none of that block is + + + align:start position:0% +going to happen none of that block is +going to get executed and it's going to + + align:start position:0% +going to get executed and it's going to + + + align:start position:0% +going to get executed and it's going to +come down here and print out a useful + + align:start position:0% +come down here and print out a useful + + + align:start position:0% +come down here and print out a useful +piece of information which says hey you + + align:start position:0% +piece of information which says hey you + + + align:start position:0% +piece of information which says hey you +gave me a negative number I don't know + + align:start position:0% +gave me a negative number I don't know + + + align:start position:0% +gave me a negative number I don't know +how to do + + align:start position:0% +how to do + + + align:start position:0% +how to do +this if it is in fact positive then + + align:start position:0% +this if it is in fact positive then + + + align:start position:0% +this if it is in fact positive then +we're going to go in here but now notice + + align:start position:0% +we're going to go in here but now notice + + + align:start position:0% +we're going to go in here but now notice +what we're doing here there's the basic + + align:start position:0% +what we're doing here there's the basic + + + align:start position:0% +what we're doing here there's the basic +thing we did before right we're checking + + align:start position:0% +thing we did before right we're checking + + + align:start position:0% +thing we did before right we're checking +the end test and incrementing actually + + align:start position:0% +the end test and incrementing actually + + + align:start position:0% +the end test and incrementing actually +was going to I commented that out for a + + align:start position:0% +was going to I commented that out for a + + + align:start position:0% +was going to I commented that out for a +reason you'll see in a second but + + align:start position:0% +reason you'll see in a second but + + + align:start position:0% +reason you'll see in a second but +normally I would keep this on which + + align:start position:0% +normally I would keep this on which + + + align:start position:0% +normally I would keep this on which +would let me at each step see what it's + + align:start position:0% +would let me at each step see what it's + + + align:start position:0% +would let me at each step see what it's +doing if I ran this it would print out + + align:start position:0% +doing if I ran this it would print out + + + align:start position:0% +doing if I ran this it would print out +each step which is helping me make sure + + align:start position:0% +each step which is helping me make sure + + + align:start position:0% +each step which is helping me make sure +that it's incrementing the right way + + align:start position:0% +that it's incrementing the right way + + + align:start position:0% +that it's incrementing the right way +okay once it gets to the end of that + + align:start position:0% +okay once it gets to the end of that + + + align:start position:0% +okay once it gets to the end of that +what's it going to do it's going to come + + align:start position:0% +what's it going to do it's going to come + + + align:start position:0% +what's it going to do it's going to come +down here and + + align:start position:0% +down here and + + + align:start position:0% +down here and +oh what's that + + align:start position:0% +oh what's that + + + align:start position:0% +oh what's that +doing well I cheated when I started I + + align:start position:0% +doing well I cheated when I started I + + + align:start position:0% +doing well I cheated when I started I +said Somebody's giv me a perfect square + + align:start position:0% +said Somebody's giv me a perfect square + + + align:start position:0% +said Somebody's giv me a perfect square +I'm looking for the square root of it + + align:start position:0% +I'm looking for the square root of it + + + align:start position:0% +I'm looking for the square root of it +but suppose I gave this thing 15 and + + align:start position:0% +but suppose I gave this thing 15 and + + + align:start position:0% +but suppose I gave this thing 15 and +asked it to run it' still give me an + + align:start position:0% +asked it to run it' still give me an + + + align:start position:0% +asked it to run it' still give me an +answer it just would not be the answer + + align:start position:0% +answer it just would not be the answer + + + align:start position:0% +answer it just would not be the answer +on I'm looking for so now in this case + + align:start position:0% +on I'm looking for so now in this case + + + align:start position:0% +on I'm looking for so now in this case +this code is going to when we get here + + align:start position:0% +this code is going to when we get here + + + align:start position:0% +this code is going to when we get here +check and if you haven't seen that + + align:start position:0% +check and if you haven't seen that + + + align:start position:0% +check and if you haven't seen that +strange thing there that explanation + + align:start position:0% +strange thing there that explanation + + + align:start position:0% +strange thing there that explanation +point in computer e called a bang it + + align:start position:0% +point in computer e called a bang it + + + align:start position:0% +point in computer e called a bang it +says if answer star answer is not equal + + align:start position:0% +says if answer star answer is not equal + + + align:start position:0% +says if answer star answer is not equal +to + + align:start position:0% +to + + + align:start position:0% +to +X right what's that say it says I've + + align:start position:0% +X right what's that say it says I've + + + align:start position:0% +X right what's that say it says I've +already gotten to the end of the loop + + align:start position:0% +already gotten to the end of the loop + + + align:start position:0% +already gotten to the end of the loop +I'm now past where I want it to be and + + align:start position:0% +I'm now past where I want it to be and + + + align:start position:0% +I'm now past where I want it to be and +I'm going to check to make sure that in + + align:start position:0% +I'm going to check to make sure that in + + + align:start position:0% +I'm going to check to make sure that in +fact this really is a perfect square if + + align:start position:0% +fact this really is a perfect square if + + + align:start position:0% +fact this really is a perfect square if +it isn't print out something that says + + align:start position:0% +it isn't print out something that says + + + align:start position:0% +it isn't print out something that says +Ah you gave me something that wasn't a + + align:start position:0% +Ah you gave me something that wasn't a + + + align:start position:0% +Ah you gave me something that wasn't a +perfect square and only if that is true + + align:start position:0% +perfect square and only if that is true + + + align:start position:0% +perfect square and only if that is true +and I'm going to print out the + + align:start position:0% +and I'm going to print out the + + + align:start position:0% +and I'm going to print out the +answer it's the same computation but + + align:start position:0% +answer it's the same computation but + + + align:start position:0% +answer it's the same computation but +this is a nice way of writing it often + + align:start position:0% +this is a nice way of writing it often + + + align:start position:0% +this is a nice way of writing it often +called Defensive + + align:start position:0% + + + + align:start position:0% + +programming and I think we have lots of + + align:start position:0% +programming and I think we have lots of + + + align:start position:0% +programming and I think we have lots of +variations on it I don't know John what + + align:start position:0% +variations on it I don't know John what + + + align:start position:0% +variations on it I don't know John what +your favorite is for the definition of + + align:start position:0% +your favorite is for the definition of + + + align:start position:0% +your favorite is for the definition of +defensive programing for me it says make + + align:start position:0% +defensive programing for me it says make + + + align:start position:0% +defensive programing for me it says make +sure that I'm going through all possible + + align:start position:0% +sure that I'm going through all possible + + + align:start position:0% +sure that I'm going through all possible +paths through the code make sure I'm + + align:start position:0% +paths through the code make sure I'm + + + align:start position:0% +paths through the code make sure I'm +printing out or or returning if you like + + align:start position:0% +printing out or or returning if you like + + + align:start position:0% +printing out or or returning if you like +useful information for each style sorry + + align:start position:0% +useful information for each style sorry + + + align:start position:0% +useful information for each style sorry +for each path through the code make sure + + align:start position:0% +for each path through the code make sure + + + align:start position:0% +for each path through the code make sure +that for all possible inputs there is a + + align:start position:0% +that for all possible inputs there is a + + + align:start position:0% +that for all possible inputs there is a +path through the code or a way to get + + align:start position:0% +path through the code or a way to get + + + align:start position:0% +path through the code or a way to get +through the code that does not cause an + + align:start position:0% +through the code that does not cause an + + + align:start position:0% +through the code that does not cause an +error or an infinite Loop what else + + align:start position:0% +error or an infinite Loop what else + + + align:start position:0% +error or an infinite Loop what else +would you add + + align:start position:0% +would you add + + + align:start position:0% +would you add +John well I I we'll come back to this + + align:start position:0% +John well I I we'll come back to this + + + align:start position:0% +John well I I we'll come back to this +later in the term and talk it in some + + align:start position:0% +later in the term and talk it in some + + + align:start position:0% +later in the term and talk it in some +detail about particular techniques the + + align:start position:0% +detail about particular techniques the + + + align:start position:0% +detail about particular techniques the +basic idea of defensive programming is + + align:start position:0% +basic idea of defensive programming is + + + align:start position:0% +basic idea of defensive programming is +to assume that a if you're getting + + align:start position:0% +to assume that a if you're getting + + + align:start position:0% +to assume that a if you're getting +inputs from a user they won't + + align:start position:0% +inputs from a user they won't + + + align:start position:0% +inputs from a user they won't +necessarily give you the input you've + + align:start position:0% +necessarily give you the input you've + + + align:start position:0% +necessarily give you the input you've +asked for so if you ask for a positive + + align:start position:0% +asked for so if you ask for a positive + + + align:start position:0% +asked for so if you ask for a positive +number don't count on them giving you + + align:start position:0% +number don't count on them giving you + + + align:start position:0% +number don't count on them giving you +one right and B if you're using a piece + + align:start position:0% +one right and B if you're using a piece + + + align:start position:0% +one right and B if you're using a piece +of a program written by a programmer who + + align:start position:0% +of a program written by a programmer who + + + align:start position:0% +of a program written by a programmer who +is not perfect perhaps yourself uh there + + align:start position:0% +is not perfect perhaps yourself uh there + + + align:start position:0% +is not perfect perhaps yourself uh there +could be mistakes in that program and so + + align:start position:0% +could be mistakes in that program and so + + + align:start position:0% +could be mistakes in that program and so +you write your program under the + + align:start position:0% +you write your program under the + + + align:start position:0% +you write your program under the +assumption that not only might the user + + align:start position:0% +assumption that not only might the user + + + align:start position:0% +assumption that not only might the user +make a mistake other parts of your + + align:start position:0% +make a mistake other parts of your + + + align:start position:0% +make a mistake other parts of your +program might make a mistake and you + + align:start position:0% +program might make a mistake and you + + + align:start position:0% +program might make a mistake and you +just put in lots of different tests + + align:start position:0% +just put in lots of different tests + + + align:start position:0% +just put in lots of different tests +under the assumption that you'd rather + + align:start position:0% +under the assumption that you'd rather + + + align:start position:0% +under the assumption that you'd rather +catch that something has gone wrong than + + align:start position:0% +catch that something has gone wrong than + + + align:start position:0% +catch that something has gone wrong than +have it go wrong and not know it and + + align:start position:0% +have it go wrong and not know it and + + + align:start position:0% +have it go wrong and not know it and +we'll talk later in the term about + + align:start position:0% +we'll talk later in the term about + + + align:start position:0% +we'll talk later in the term about +dozens of different tricks but the main + + align:start position:0% +dozens of different tricks but the main + + + align:start position:0% +dozens of different tricks but the main +thing to keep in mind is the general + + align:start position:0% +thing to keep in mind is the general + + + align:start position:0% +thing to keep in mind is the general +principle that people are + + align:start position:0% +principle that people are + + + align:start position:0% +principle that people are +dumb and we'll make mistakes and + + align:start position:0% +dumb and we'll make mistakes and + + + align:start position:0% +dumb and we'll make mistakes and +therefore you write your program so that + + align:start position:0% +therefore you write your program so that + + + align:start position:0% +therefore you write your program so that +catastrophes don't occur when those + + align:start position:0% +catastrophes don't occur when those + + + align:start position:0% +catastrophes don't occur when those +mistakes are made + + align:start position:0% +mistakes are made + + + align:start position:0% +mistakes are made +good and as John said we're going to + + align:start position:0% +good and as John said we're going to + + + align:start position:0% +good and as John said we're going to +come back to it but that's what + + align:start position:0% +come back to it but that's what + + + align:start position:0% +come back to it but that's what +basically the goal here and and uh you + + align:start position:0% +basically the goal here and and uh you + + + align:start position:0% +basically the goal here and and uh you +saw me put my hands up when I said + + align:start position:0% +saw me put my hands up when I said + + + align:start position:0% +saw me put my hands up when I said +stupid programmer I've certainly written + + align:start position:0% +stupid programmer I've certainly written + + + align:start position:0% +stupid programmer I've certainly written +code that has this problem I've tried to + + align:start position:0% +code that has this problem I've tried to + + + align:start position:0% +code that has this problem I've tried to +use my own code that has this problem + + align:start position:0% +use my own code that has this problem + + + align:start position:0% +use my own code that has this problem +and good to sorry good hygiene I'm going + + align:start position:0% +and good to sorry good hygiene I'm going + + + align:start position:0% +and good to sorry good hygiene I'm going +to use that word again here of getting + + align:start position:0% +to use that word again here of getting + + + align:start position:0% +to use that word again here of getting +into the habit of writing defensive code + + align:start position:0% +into the habit of writing defensive code + + + align:start position:0% +into the habit of writing defensive code +up front it's part of that collection of + + align:start position:0% +up front it's part of that collection of + + + align:start position:0% +up front it's part of that collection of +things that you ought to do is a great + + align:start position:0% +things that you ought to do is a great + + + align:start position:0% +things that you ought to do is a great +thing to do I stress it in particular + + align:start position:0% +thing to do I stress it in particular + + + align:start position:0% +thing to do I stress it in particular +because I know you're all going to get + + align:start position:0% +because I know you're all going to get + + + align:start position:0% +because I know you're all going to get +into this stage you got a problem set + + align:start position:0% +into this stage you got a problem set + + + align:start position:0% +into this stage you got a problem set +due in a couple of hours you're still + + align:start position:0% +due in a couple of hours you're still + + + align:start position:0% +due in a couple of hours you're still +writing the code you don't want to waste + + align:start position:0% +writing the code you don't want to waste + + + align:start position:0% +writing the code you don't want to waste +time and I'm going to use quotes on + + align:start position:0% +time and I'm going to use quotes on + + + align:start position:0% +time and I'm going to use quotes on +waste time doing those extra things to + + align:start position:0% +waste time doing those extra things to + + + align:start position:0% +waste time doing those extra things to +do the defensive programming you just + + align:start position:0% +do the defensive programming you just + + + align:start position:0% +do the defensive programming you just +want to get the darn thing done it's a + + align:start position:0% +want to get the darn thing done it's a + + + align:start position:0% +want to get the darn thing done it's a +bad habit to get into because when you + + align:start position:0% +bad habit to get into because when you + + + align:start position:0% +bad habit to get into because when you +come back to it it may haunt you later + + align:start position:0% +come back to it it may haunt you later + + + align:start position:0% +come back to it it may haunt you later +on down the road so really get into that + + align:start position:0% +on down the road so really get into that + + + align:start position:0% +on down the road so really get into that +notion of trying to be defensive as you + + align:start position:0% +notion of trying to be defensive as you + + + align:start position:0% +notion of trying to be defensive as you +program okay the other thing I want to + + align:start position:0% +program okay the other thing I want to + + + align:start position:0% +program okay the other thing I want to +say here is that this + + align:start position:0% +say here is that this + + + align:start position:0% +say here is that this +style of program we just wrote is + + align:start position:0% +style of program we just wrote is + + + align:start position:0% +style of program we just wrote is +actually a very common + + align:start position:0% +actually a very common + + + align:start position:0% +actually a very common +one and we're going to give it a nice + + align:start position:0% +one and we're going to give it a nice + + + align:start position:0% +one and we're going to give it a nice +little + + align:start position:0% + + + + align:start position:0% + +name often referred to as exhaustive + + align:start position:0% +name often referred to as exhaustive + + + align:start position:0% +name often referred to as exhaustive +enumeration + + align:start position:0% +enumeration + + + align:start position:0% +enumeration +what does that mean it says I'm + + align:start position:0% +what does that mean it says I'm + + + align:start position:0% +what does that mean it says I'm +literally walking through all possible + + align:start position:0% +literally walking through all possible + + + align:start position:0% +literally walking through all possible +values some parameter some element of + + align:start position:0% +values some parameter some element of + + + align:start position:0% +values some parameter some element of +the computation testing everything until + + align:start position:0% +the computation testing everything until + + + align:start position:0% +the computation testing everything until +I find the right answer right so it's + + align:start position:0% +I find the right answer right so it's + + + align:start position:0% +I find the right answer right so it's +you know again I can even write that + + align:start position:0% +you know again I can even write that + + + align:start position:0% +you know again I can even write that +down essentially saying + + align:start position:0% + + + + align:start position:0% + +try all reasonable + + align:start position:0% + + + + align:start position:0% + +values until you find the solution + + align:start position:0% + + + + align:start position:0% + +and you might say well wait a minute + + align:start position:0% +and you might say well wait a minute + + + align:start position:0% +and you might say well wait a minute +isn't that going to be really + + align:start position:0% +isn't that going to be really + + + align:start position:0% +isn't that going to be really +expensive and the answer is yeah I guess + + align:start position:0% +expensive and the answer is yeah I guess + + + align:start position:0% +expensive and the answer is yeah I guess +if you want to search you know all the + + align:start position:0% +if you want to search you know all the + + + align:start position:0% +if you want to search you know all the +pages on Google one by one yes probably + + align:start position:0% +pages on Google one by one yes probably + + + align:start position:0% +pages on Google one by one yes probably +it's going to take a while but there are + + align:start position:0% +it's going to take a while but there are + + + align:start position:0% +it's going to take a while but there are +an awful lot of computations for which + + align:start position:0% +an awful lot of computations for which + + + align:start position:0% +an awful lot of computations for which +this is the right way to do it you just + + align:start position:0% +this is the right way to do it you just + + + align:start position:0% +this is the right way to do it you just +want to exhaustively go through things + + align:start position:0% +want to exhaustively go through things + + + align:start position:0% +want to exhaustively go through things +and just to give you a sense of that let + + align:start position:0% +and just to give you a sense of that let + + + align:start position:0% +and just to give you a sense of that let +me show you an example I'm going to + + align:start position:0% +me show you an example I'm going to + + + align:start position:0% +me show you an example I'm going to +change + + align:start position:0% + + + + align:start position:0% + +this right a nice big number + + align:start position:0% + + + + align:start position:0% + +you know computers are fast these days I + + align:start position:0% +you know computers are fast these days I + + + align:start position:0% +you know computers are fast these days I +can make this even bigger it's going to + + align:start position:0% +can make this even bigger it's going to + + + align:start position:0% +can make this even bigger it's going to +do it fairly quickly so it really is + + align:start position:0% +do it fairly quickly so it really is + + + align:start position:0% +do it fairly quickly so it really is +quick to do this it doesn't mean that + + align:start position:0% +quick to do this it doesn't mean that + + + align:start position:0% +quick to do this it doesn't mean that +exhaustive numeration is a bad idea it + + align:start position:0% +exhaustive numeration is a bad idea it + + + align:start position:0% +exhaustive numeration is a bad idea it +is often the right idea to use so we've + + align:start position:0% +is often the right idea to use so we've + + + align:start position:0% +is often the right idea to use so we've +seen one example of this this idea of + + align:start position:0% +seen one example of this this idea of + + + align:start position:0% +seen one example of this this idea of +walking through all the integers looking + + align:start position:0% +walking through all the integers looking + + + align:start position:0% +walking through all the integers looking +for the square root let's look at some + + align:start position:0% +for the square root let's look at some + + + align:start position:0% +for the square root let's look at some +other examples in order to try and see + + align:start position:0% +other examples in order to try and see + + + align:start position:0% +other examples in order to try and see +other ways in which we could do + + align:start position:0% +other ways in which we could do + + + align:start position:0% +other ways in which we could do +it + + align:start position:0% +it + + + align:start position:0% +it +okay particular let's go over to here + + align:start position:0% +okay particular let's go over to here + + + align:start position:0% +okay particular let's go over to here +and let me show you a second example + + align:start position:0% +and let me show you a second example + + + align:start position:0% +and let me show you a second example +again let me comment that + + align:start position:0% + + + + align:start position:0% + +out here's another problem that I'd like + + align:start position:0% +out here's another problem that I'd like + + + align:start position:0% +out here's another problem that I'd like +to + + align:start position:0% +to + + + align:start position:0% +to +solve suppose I want to find all the + + align:start position:0% +solve suppose I want to find all the + + + align:start position:0% +solve suppose I want to find all the +divisors of some integer I want to U + + align:start position:0% +divisors of some integer I want to U + + + align:start position:0% +divisors of some integer I want to U +figure out what all the divisor are that + + align:start position:0% +figure out what all the divisor are that + + + align:start position:0% +figure out what all the divisor are that +go evenly into it again the same kind of + + align:start position:0% +go evenly into it again the same kind of + + + align:start position:0% +go evenly into it again the same kind of +reasoning says given some value x i + + align:start position:0% +reasoning says given some value x i + + + align:start position:0% +reasoning says given some value x i +happened to pick a small one here what's + + align:start position:0% +happened to pick a small one here what's + + + align:start position:0% +happened to pick a small one here what's +an easy way to do this well let's just + + align:start position:0% +an easy way to do this well let's just + + + align:start position:0% +an easy way to do this well let's just +start at one that's my VAR I'm going to + + align:start position:0% +start at one that's my VAR I'm going to + + + align:start position:0% +start at one that's my VAR I'm going to +change and check does it divide evenly + + align:start position:0% +change and check does it divide evenly + + + align:start position:0% +change and check does it divide evenly +into X if it does print it out move on + + align:start position:0% +into X if it does print it out move on + + + align:start position:0% +into X if it does print it out move on +to the next one print it out so again I + + align:start position:0% +to the next one print it out so again I + + + align:start position:0% +to the next one print it out so again I +can do the same kind of thing here you + + align:start position:0% +can do the same kind of thing here you + + + align:start position:0% +can do the same kind of thing here you +can see that in fact let's just run it + + align:start position:0% +can see that in fact let's just run it + + + align:start position:0% +can see that in fact let's just run it +to make sure it does the right + + align:start position:0% + + + + align:start position:0% + +thing okay in fact if I go back to the + + align:start position:0% +thing okay in fact if I go back to the + + + align:start position:0% +thing okay in fact if I go back to the +code what did I decide to do here I say + + align:start position:0% +code what did I decide to do here I say + + + align:start position:0% +code what did I decide to do here I say +starting with an initialization of I + + align:start position:0% +starting with an initialization of I + + + align:start position:0% +starting with an initialization of I +there's my first step as equal to one + + align:start position:0% +there's my first step as equal to one + + + align:start position:0% +there's my first step as equal to one +I'm going to walk through a little Loop + + align:start position:0% +I'm going to walk through a little Loop + + + align:start position:0% +I'm going to walk through a little Loop +where I check as long first of all as + + align:start position:0% +where I check as long first of all as + + + align:start position:0% +where I check as long first of all as +long as eyes less than x so there's my n + + align:start position:0% +long as eyes less than x so there's my n + + + align:start position:0% +long as eyes less than x so there's my n +test I'm going to do something and in + + align:start position:0% +test I'm going to do something and in + + + align:start position:0% +test I'm going to do something and in +this case the something is I'm going to + + align:start position:0% +this case the something is I'm going to + + + align:start position:0% +this case the something is I'm going to +look to see if I divides X evenly so + + align:start position:0% +look to see if I divides X evenly so + + + align:start position:0% +look to see if I divides X evenly so +I'll remind you that amp sorry that + + align:start position:0% +I'll remind you that amp sorry that + + + align:start position:0% +I'll remind you that amp sorry that +percent sign there that says if x + + align:start position:0% +percent sign there that says if x + + + align:start position:0% +percent sign there that says if x +divided by I has zero remainder because + + align:start position:0% +divided by I has zero remainder because + + + align:start position:0% +divided by I has zero remainder because +this gives me back the remainder if + + align:start position:0% +this gives me back the remainder if + + + align:start position:0% +this gives me back the remainder if +that's equal to zero print something out + + align:start position:0% +that's equal to zero print something out + + + align:start position:0% +that's equal to zero print something out +ah and there's my nice + + align:start position:0% +ah and there's my nice + + + align:start position:0% +ah and there's my nice +increment simple little piece of code + + align:start position:0% +increment simple little piece of code + + + align:start position:0% +increment simple little piece of code +notice again exactly the same form I + + align:start position:0% +notice again exactly the same form I + + + align:start position:0% +notice again exactly the same form I +picked the thing I wanted to vary I + + align:start position:0% +picked the thing I wanted to vary I + + + align:start position:0% +picked the thing I wanted to vary I +initialize it outside the loop I have a + + align:start position:0% +initialize it outside the loop I have a + + + align:start position:0% +initialize it outside the loop I have a +test to see when I'm done + + align:start position:0% +test to see when I'm done + + + align:start position:0% +test to see when I'm done +and then I got a set of instructions I'm + + align:start position:0% +and then I got a set of instructions I'm + + + align:start position:0% +and then I got a set of instructions I'm +doing every time inside the loop in this + + align:start position:0% +doing every time inside the loop in this + + + align:start position:0% +doing every time inside the loop in this +case it's doing the the check on the + + align:start position:0% +case it's doing the the check on the + + + align:start position:0% +case it's doing the the check on the +remainder and printing them out and when + + align:start position:0% +remainder and printing them out and when + + + align:start position:0% +remainder and printing them out and when +I'm done with the whole thing sorry and + + align:start position:0% +I'm done with the whole thing sorry and + + + align:start position:0% +I'm done with the whole thing sorry and +the increment of the variable and then + + align:start position:0% +the increment of the variable and then + + + align:start position:0% +the increment of the variable and then +when I'm done I just not returning + + align:start position:0% +when I'm done I just not returning + + + align:start position:0% +when I'm done I just not returning +anything + + align:start position:0% +anything + + + align:start position:0% +anything +out okay so now you've seen two simple + + align:start position:0% +out okay so now you've seen two simple + + + align:start position:0% +out okay so now you've seen two simple +examples let me generalize this in this + + align:start position:0% +examples let me generalize this in this + + + align:start position:0% +examples let me generalize this in this +case my increment was just adding one to + + align:start position:0% +case my increment was just adding one to + + + align:start position:0% +case my increment was just adding one to +an integer it's a pretty straightforward + + align:start position:0% +an integer it's a pretty straightforward + + + align:start position:0% +an integer it's a pretty straightforward +thing to do but you can imagine thinking + + align:start position:0% +thing to do but you can imagine thinking + + + align:start position:0% +thing to do but you can imagine thinking +about this a little differently if I + + align:start position:0% +about this a little differently if I + + + align:start position:0% +about this a little differently if I +somehow had a collection + + align:start position:0% +somehow had a collection + + + align:start position:0% +somehow had a collection +an ordered collection of all the + + align:start position:0% +an ordered collection of all the + + + align:start position:0% +an ordered collection of all the +integers from 1 to + + align:start position:0% +integers from 1 to + + + align:start position:0% +integers from 1 to +10 I could imagine doing the same thing + + align:start position:0% +10 I could imagine doing the same thing + + + align:start position:0% +10 I could imagine doing the same thing +where now what I'm doing is I'm starting + + align:start position:0% +where now what I'm doing is I'm starting + + + align:start position:0% +where now what I'm doing is I'm starting +with the first element of that + + align:start position:0% +with the first element of that + + + align:start position:0% +with the first element of that +collection doing something going to the + + align:start position:0% +collection doing something going to the + + + align:start position:0% +collection doing something going to the +next element doing something going to + + align:start position:0% +next element doing something going to + + + align:start position:0% +next element doing something going to +the next element doing something I'm + + align:start position:0% +the next element doing something I'm + + + align:start position:0% +the next element doing something I'm +just walking through the sequence of + + align:start position:0% +just walking through the sequence of + + + align:start position:0% +just walking through the sequence of +elements right and I haven't said yet + + align:start position:0% +elements right and I haven't said yet + + + align:start position:0% +elements right and I haven't said yet +how do I get that collection but you + + align:start position:0% +how do I get that collection but you + + + align:start position:0% +how do I get that collection but you +could certainly conceptualize that if I + + align:start position:0% +could certainly conceptualize that if I + + + align:start position:0% +could certainly conceptualize that if I +had that collection that would be a nice + + align:start position:0% +had that collection that would be a nice + + + align:start position:0% +had that collection that would be a nice +thing to do that is a more common + + align:start position:0% +thing to do that is a more common + + + align:start position:0% +thing to do that is a more common +pattern that is basically saying given + + align:start position:0% +pattern that is basically saying given + + + align:start position:0% +pattern that is basically saying given +some collection of data I I want to have + + align:start position:0% +some collection of data I I want to have + + + align:start position:0% +some collection of data I I want to have +a again a looping mechanism where now my + + align:start position:0% +a again a looping mechanism where now my + + + align:start position:0% +a again a looping mechanism where now my +process is walk through this the The + + align:start position:0% +process is walk through this the The + + + align:start position:0% +process is walk through this the The +Collection one element at a time and for + + align:start position:0% +Collection one element at a time and for + + + align:start position:0% +Collection one element at a time and for +that we + + align:start position:0% +that we + + + align:start position:0% +that we +have a particular + + align:start position:0% +have a particular + + + align:start position:0% +have a particular +construct called a for loop it's going + + align:start position:0% +construct called a for loop it's going + + + align:start position:0% +construct called a for loop it's going +to do exactly that for us it's going to + + align:start position:0% +to do exactly that for us it's going to + + + align:start position:0% +to do exactly that for us it's going to +be more General than this we're going to + + align:start position:0% +be more General than this we're going to + + + align:start position:0% +be more General than this we're going to +come back to that in fact Professor gag + + align:start position:0% +come back to that in fact Professor gag + + + align:start position:0% +come back to that in fact Professor gag +is going to pick this up in a couple of + + align:start position:0% +is going to pick this up in a couple of + + + align:start position:0% +is going to pick this up in a couple of +lectures but we can talk right now about + + align:start position:0% +lectures but we can talk right now about + + + align:start position:0% +lectures but we can talk right now about +the basic form the form of a for Loop + + align:start position:0% +the basic form the form of a for Loop + + + align:start position:0% +the basic form the form of a for Loop +says for and I'm going to put little + + align:start position:0% +says for and I'm going to put little + + + align:start position:0% +says for and I'm going to put little +angle braces in here again to say for + + align:start position:0% +angle braces in here again to say for + + + align:start position:0% +angle braces in here again to say for +some variable I'm going name I want to + + align:start position:0% +some variable I'm going name I want to + + + align:start position:0% +some variable I'm going name I want to +get to it + + align:start position:0% +get to it + + + align:start position:0% +get to it +in some + + align:start position:0% + + + + align:start position:0% + +collection and then I have a block of + + align:start position:0% + + + + align:start position:0% + +code and what it's saying semantically + + align:start position:0% +code and what it's saying semantically + + + align:start position:0% +code and what it's saying semantically +is using that variable as my placeholder + + align:start position:0% +is using that variable as my placeholder + + + align:start position:0% +is using that variable as my placeholder +have it walk through this collection + + align:start position:0% +have it walk through this collection + + + align:start position:0% +have it walk through this collection +starting at the first thing execute that + + align:start position:0% +starting at the first thing execute that + + + align:start position:0% +starting at the first thing execute that +code then the next thing execute that + + align:start position:0% +code then the next thing execute that + + + align:start position:0% +code then the next thing execute that +code and so on one of the advantages of + + align:start position:0% +code and so on one of the advantages of + + + align:start position:0% +code and so on one of the advantages of +this advantages of this is that I don't + + align:start position:0% +this advantages of this is that I don't + + + align:start position:0% +this advantages of this is that I don't +have to worry about explicitly updating + + align:start position:0% +have to worry about explicitly updating + + + align:start position:0% +have to worry about explicitly updating +my variable it happens for me + + align:start position:0% +my variable it happens for me + + + align:start position:0% +my variable it happens for me +automatically and that's very nice + + align:start position:0% +automatically and that's very nice + + + align:start position:0% +automatically and that's very nice +because this allows me to be sure that + + align:start position:0% +because this allows me to be sure that + + + align:start position:0% +because this allows me to be sure that +my for Loop is going to + + align:start position:0% +my for Loop is going to + + + align:start position:0% +my for Loop is going to +terminate because as long as this + + align:start position:0% +terminate because as long as this + + + align:start position:0% +terminate because as long as this +collection is finite this thing is just + + align:start position:0% +collection is finite this thing is just + + + align:start position:0% +collection is finite this thing is just +going to walk through them all right so + + align:start position:0% +going to walk through them all right so + + + align:start position:0% +going to walk through them all right so +if I show you for example I'm going to + + align:start position:0% +if I show you for example I'm going to + + + align:start position:0% +if I show you for example I'm going to +comment this one + + align:start position:0% +comment this one + + + align:start position:0% +comment this one +out in my usual + + align:start position:0% +out in my usual + + + align:start position:0% +out in my usual +Manner and let's look at + + align:start position:0% +Manner and let's look at + + + align:start position:0% +Manner and let's look at +uncommenting + + align:start position:0% + + + + align:start position:0% + +that there's the same piece of cod now I + + align:start position:0% +that there's the same piece of cod now I + + + align:start position:0% +that there's the same piece of cod now I +slung something by you or snuck + + align:start position:0% +slung something by you or snuck + + + align:start position:0% +slung something by you or snuck +something by you which is I hadn't said + + align:start position:0% +something by you which is I hadn't said + + + align:start position:0% +something by you which is I hadn't said +how to + + align:start position:0% +how to + + + align:start position:0% +how to +generate the set of integers from 1 to + + align:start position:0% +generate the set of integers from 1 to + + + align:start position:0% +generate the set of integers from 1 to +10 so range is a built-in python + + align:start position:0% +10 so range is a built-in python + + + align:start position:0% +10 so range is a built-in python +function we're going to come back to it + + align:start position:0% +function we're going to come back to it + + + align:start position:0% +function we're going to come back to it +in a second for now just think of it as + + align:start position:0% +in a second for now just think of it as + + + align:start position:0% +in a second for now just think of it as +saying it gives you all the integers + + align:start position:0% +saying it gives you all the integers + + + align:start position:0% +saying it gives you all the integers +from one up to but not including + + align:start position:0% +from one up to but not including + + + align:start position:0% +from one up to but not including +X okay but now you can see the form this + + align:start position:0% +X okay but now you can see the form this + + + align:start position:0% +X okay but now you can see the form this +now says okay let I start as the first + + align:start position:0% +now says okay let I start as the first + + + align:start position:0% +now says okay let I start as the first +thing in there which is one and then do + + align:start position:0% +thing in there which is one and then do + + + align:start position:0% +thing in there which is one and then do +exactly as I did before the same thing + + align:start position:0% +exactly as I did before the same thing + + + align:start position:0% +exactly as I did before the same thing +but notice I don't need to say how to + + align:start position:0% +but notice I don't need to say how to + + + align:start position:0% +but notice I don't need to say how to +increment it it's happening + + align:start position:0% +increment it it's happening + + + align:start position:0% +increment it it's happening +automatically for me okay in fact if I + + align:start position:0% +automatically for me okay in fact if I + + + align:start position:0% +automatically for me okay in fact if I +run + + align:start position:0% + + + + align:start position:0% + +it does the same thing which is what I + + align:start position:0% +it does the same thing which is what I + + + align:start position:0% +it does the same thing which is what I +would + + align:start position:0% +would + + + align:start position:0% +would +expect + + align:start position:0% +expect + + + align:start position:0% +expect +okay now the advantage of the + + align:start position:0% +okay now the advantage of the + + + align:start position:0% +okay now the advantage of the +four as I said is that it + + align:start position:0% +four as I said is that it + + + align:start position:0% +four as I said is that it +has if you like a cleaner way of reading + + align:start position:0% +has if you like a cleaner way of reading + + + align:start position:0% +has if you like a cleaner way of reading +it I don't have to worry about do I + + align:start position:0% +it I don't have to worry about do I + + + align:start position:0% +it I don't have to worry about do I +initialize it did I forget to initialize + + align:start position:0% +initialize it did I forget to initialize + + + align:start position:0% +initialize it did I forget to initialize +it outside the loop it happens + + align:start position:0% +it outside the loop it happens + + + align:start position:0% +it outside the loop it happens +automatically just by the syntax of it + + align:start position:0% +automatically just by the syntax of it + + + align:start position:0% +automatically just by the syntax of it +right there that it's going to start + + align:start position:0% +right there that it's going to start + + + align:start position:0% +right there that it's going to start +with the first element I don't have to + + align:start position:0% +with the first element I don't have to + + + align:start position:0% +with the first element I don't have to +worry about did I remember to put the + + align:start position:0% +worry about did I remember to put the + + + align:start position:0% +worry about did I remember to put the +increment and it's going to + + align:start position:0% +increment and it's going to + + + align:start position:0% +increment and it's going to +automatically walk its way through there + + align:start position:0% +automatically walk its way through there + + + align:start position:0% +automatically walk its way through there +second advantage of the four is that + + align:start position:0% +second advantage of the four is that + + + align:start position:0% +second advantage of the four is that +right now we're thinking about it just + + align:start position:0% +right now we're thinking about it just + + + align:start position:0% +right now we're thinking about it just +as a sequence of integers we could + + align:start position:0% +as a sequence of integers we could + + + align:start position:0% +as a sequence of integers we could +imagine it's just counting its way + + align:start position:0% +imagine it's just counting its way + + + align:start position:0% +imagine it's just counting its way +through but we're going to see very + + align:start position:0% +through but we're going to see very + + + align:start position:0% +through but we're going to see very +shortly that in fact those collections + + align:start position:0% +shortly that in fact those collections + + + align:start position:0% +shortly that in fact those collections +could be arbitrary going to have other + + align:start position:0% +could be arbitrary going to have other + + + align:start position:0% +could be arbitrary going to have other +ways of building them but it could be a + + align:start position:0% +ways of building them but it could be a + + + align:start position:0% +ways of building them but it could be a +collection of all the Primes H there's + + align:start position:0% +collection of all the Primes H there's + + + align:start position:0% +collection of all the Primes H there's +an interesting thing to do it could be a + + align:start position:0% +an interesting thing to do it could be a + + + align:start position:0% +an interesting thing to do it could be a +collection of uh you know I don't know + + align:start position:0% +collection of uh you know I don't know + + + align:start position:0% +collection of uh you know I don't know +batting averages of somebody or other it + + align:start position:0% +batting averages of somebody or other it + + + align:start position:0% +batting averages of somebody or other it +could be arbitrary collections that + + align:start position:0% +could be arbitrary collections that + + + align:start position:0% +could be arbitrary collections that +you've come up with in other ways the + + align:start position:0% +you've come up with in other ways the + + + align:start position:0% +you've come up with in other ways the +four is again going to let you walk + + align:start position:0% +four is again going to let you walk + + + align:start position:0% +four is again going to let you walk +through that thing so it does not have + + align:start position:0% +through that thing so it does not have + + + align:start position:0% +through that thing so it does not have +to be something that could be described + + align:start position:0% +to be something that could be described + + + align:start position:0% +to be something that could be described +procedurally such as add one to to to + + align:start position:0% +procedurally such as add one to to to + + + align:start position:0% +procedurally such as add one to to to +the previous element it could be any + + align:start position:0% +the previous element it could be any + + + align:start position:0% +the previous element it could be any +arbitrary collection and if I were to + + align:start position:0% +arbitrary collection and if I were to + + + align:start position:0% +arbitrary collection and if I were to +use that and again I just put it on your + + align:start position:0% +use that and again I just put it on your + + + align:start position:0% +use that and again I just put it on your +handout I could go back and rewrite that + + align:start position:0% +handout I could go back and rewrite that + + + align:start position:0% +handout I could go back and rewrite that +thing that I had previously for finding + + align:start position:0% +thing that I had previously for finding + + + align:start position:0% +thing that I had previously for finding +the the the square roots of the perfect + + align:start position:0% +the the the square roots of the perfect + + + align:start position:0% +the the the square roots of the perfect +squares just using the for Loop + + align:start position:0% +squares just using the for Loop + + + align:start position:0% +squares just using the for Loop +okay what I want to do though is go on + + align:start position:0% +okay what I want to do though is go on + + + align:start position:0% +okay what I want to do though is go on +to or sorry go back + + align:start position:0% +to or sorry go back + + + align:start position:0% +to or sorry go back +to my divisor example and I got a set of + + align:start position:0% +to my divisor example and I got a set of + + + align:start position:0% +to my divisor example and I got a set of +try again I got a number I want to find + + align:start position:0% +try again I got a number I want to find + + + align:start position:0% +try again I got a number I want to find +the divisor right now what my code is + + align:start position:0% +the divisor right now what my code is + + + align:start position:0% +the divisor right now what my code is +doing is it's printing them out for me + + align:start position:0% +doing is it's printing them out for me + + + align:start position:0% +doing is it's printing them out for me +which is + + align:start position:0% +which is + + + align:start position:0% +which is +useful but imagine I actually wanted to + + align:start position:0% +useful but imagine I actually wanted to + + + align:start position:0% +useful but imagine I actually wanted to +gather them together I wanted to collect + + align:start position:0% +gather them together I wanted to collect + + + align:start position:0% +gather them together I wanted to collect +them so I could do something with them + + align:start position:0% +them so I could do something with them + + + align:start position:0% +them so I could do something with them +might want to add them up might want to + + align:start position:0% +might want to add them up might want to + + + align:start position:0% +might want to add them up might want to +multiply them together might want to do + + align:start position:0% +multiply them together might want to do + + + align:start position:0% +multiply them together might want to do +I don't know something else with it find + + align:start position:0% +I don't know something else with it find + + + align:start position:0% +I don't know something else with it find +common divisors of of things by looking + + align:start position:0% +common divisors of of things by looking + + + align:start position:0% +common divisors of of things by looking +at them I need in fact a way to make + + align:start position:0% +at them I need in fact a way to make + + + align:start position:0% +at them I need in fact a way to make +explicit what I hinted at with range is + + align:start position:0% +explicit what I hinted at with range is + + + align:start position:0% +explicit what I hinted at with range is +I need a way to collect things together + + align:start position:0% +I need a way to collect things together + + + align:start position:0% +I need a way to collect things together +and that's going to be the first of our + + align:start position:0% +and that's going to be the first of our + + + align:start position:0% +and that's going to be the first of our +more compound data structures and we + + align:start position:0% +more compound data structures and we + + + align:start position:0% +more compound data structures and we +have exactly such a structure and it's + + align:start position:0% +have exactly such a structure and it's + + + align:start position:0% +have exactly such a structure and it's +called a + + align:start position:0% + + + + align:start position:0% + +tupal this is an ordered sequence + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% +of + + + align:start position:0% +of +elements now I'm going to actually add + + align:start position:0% +elements now I'm going to actually add + + + align:start position:0% +elements now I'm going to actually add +something to it that's going to make + + align:start position:0% +something to it that's going to make + + + align:start position:0% +something to it that's going to make +sense in a little while or in a couple + + align:start position:0% +sense in a little while or in a couple + + + align:start position:0% +sense in a little while or in a couple +of lectures which is it is + + align:start position:0% + + + + align:start position:0% + +immutable meaning I cannot change it and + + align:start position:0% +immutable meaning I cannot change it and + + + align:start position:0% +immutable meaning I cannot change it and +we'll see why that's important later on + + align:start position:0% +we'll see why that's important later on + + + align:start position:0% +we'll see why that's important later on +but for now a tupal is this ordered + + align:start position:0% +but for now a tupal is this ordered + + + align:start position:0% +but for now a tupal is this ordered +sequence of + + align:start position:0% +sequence of + + + align:start position:0% +sequence of +structures okay and how do I create them + + align:start position:0% +structures okay and how do I create them + + + align:start position:0% +structures okay and how do I create them +well the representation + + align:start position:0% +well the representation + + + align:start position:0% +well the representation +is + + align:start position:0% +is + + + align:start position:0% +is +following a square bracket + + align:start position:0% + + + + align:start position:0% + +followed by a sequence of elements + + align:start position:0% +followed by a sequence of elements + + + align:start position:0% +followed by a sequence of elements +separated by commas followed by closed + + align:start position:0% +separated by commas followed by closed + + + align:start position:0% +separated by commas followed by closed +square + + align:start position:0% +square + + + align:start position:0% +square +bracket and that is literally what I + + align:start position:0% +bracket and that is literally what I + + + align:start position:0% +bracket and that is literally what I +said it is an ordered sequence of + + align:start position:0% +said it is an ordered sequence of + + + align:start position:0% +said it is an ordered sequence of +elements and you can see where they + + align:start position:0% +elements and you can see where they + + + align:start position:0% +elements and you can see where they +are okay so let me do a little example + + align:start position:0% +are okay so let me do a little example + + + align:start position:0% +are okay so let me do a little example +of this if I go back over here let's + + align:start position:0% + + + + align:start position:0% + +define can't type + + align:start position:0% + + + + align:start position:0% + +I can look at the value of test it's an + + align:start position:0% +I can look at the value of test it's an + + + align:start position:0% +I can look at the value of test it's an +ordered sequence I need to get elements + + align:start position:0% +ordered sequence I need to get elements + + + align:start position:0% +ordered sequence I need to get elements +out of it and so again I have a way of + + align:start position:0% +out of it and so again I have a way of + + + align:start position:0% +out of it and so again I have a way of +doing that in particular I can ask for + + align:start position:0% +doing that in particular I can ask for + + + align:start position:0% +doing that in particular I can ask for +the zeroth element of test again notice + + align:start position:0% +the zeroth element of test again notice + + + align:start position:0% +the zeroth element of test again notice +I'm putting a square bracket around + + align:start position:0% +I'm putting a square bracket around + + + align:start position:0% +I'm putting a square bracket around +it and it gives me I know this sounds + + align:start position:0% +it and it gives me I know this sounds + + + align:start position:0% +it and it gives me I know this sounds +confusing but this is a long tradition + + align:start position:0% +confusing but this is a long tradition + + + align:start position:0% +confusing but this is a long tradition +it gives me uh + + align:start position:0% + + + + align:start position:0% + +yes sorry + + align:start position:0% + + + + align:start position:0% + +I created a list here ah thank + + align:start position:0% +I created a list here ah thank + + + align:start position:0% +I created a list here ah thank +you I'm glad you guys are on top of it + + align:start position:0% +you I'm glad you guys are on top of it + + + align:start position:0% +you I'm glad you guys are on top of it +you're saying I + + align:start position:0% +you're saying I + + + align:start position:0% +you're saying I +want that is that right John yes okay + + align:start position:0% +want that is that right John yes okay + + + align:start position:0% +want that is that right John yes okay +sorry you're going to see why this was a + + align:start position:0% +sorry you're going to see why this was a + + + align:start position:0% +sorry you're going to see why this was a +mistake in a little while I did not want + + align:start position:0% +mistake in a little while I did not want + + + align:start position:0% +mistake in a little while I did not want +to make a list I wanted to create a tupo + + align:start position:0% +to make a list I wanted to create a tupo + + + align:start position:0% +to make a list I wanted to create a tupo +thank you for catching it I want pen not + + align:start position:0% +thank you for catching it I want pen not + + + align:start position:0% +thank you for catching it I want pen not +square brackets there you'll also see in + + align:start position:0% +square brackets there you'll also see in + + + align:start position:0% +square brackets there you'll also see in +a little while why both of these things + + align:start position:0% +a little while why both of these things + + + align:start position:0% +a little while why both of these things +would work this way but it's not what I + + align:start position:0% +would work this way but it's not what I + + + align:start position:0% +would work this way but it's not what I +wanted okay so I guess I should go back + + align:start position:0% +wanted okay so I guess I should go back + + + align:start position:0% +wanted okay so I guess I should go back +and let me do this correctly this + + align:start position:0% + + + + align:start position:0% + +way again I can look at + + align:start position:0% +way again I can look at + + + align:start position:0% +way again I can look at +test and I guess test now if I want to + + align:start position:0% +test and I guess test now if I want to + + + align:start position:0% +test and I guess test now if I want to +get the element + + align:start position:0% +get the element + + + align:start position:0% +get the element +out angle bracket or square bracket I + + align:start position:0% +out angle bracket or square bracket I + + + align:start position:0% +out angle bracket or square bracket I +still want square bracket that's what I + + align:start position:0% +still want square bracket that's what I + + + align:start position:0% +still want square bracket that's what I +thought okay now I can go back to where + + align:start position:0% +thought okay now I can go back to where + + + align:start position:0% +thought okay now I can go back to where +I was which is this strange piece of + + align:start position:0% +I was which is this strange piece of + + + align:start position:0% +I was which is this strange piece of +History which is we start counting at + + align:start position:0% +History which is we start counting at + + + align:start position:0% +History which is we start counting at +zero so the I hate to say it this way + + align:start position:0% +zero so the I hate to say it this way + + + align:start position:0% +zero so the I hate to say it this way +the first element of this tupal is at + + align:start position:0% +the first element of this tupal is at + + + align:start position:0% +the first element of this tupal is at +position zero or index zero okay so I + + align:start position:0% +position zero or index zero okay so I + + + align:start position:0% +position zero or index zero okay so I +can get the zeroth one out I can get + + align:start position:0% +can get the zeroth one out I can get + + + align:start position:0% +can get the zeroth one out I can get +um if I do two I get the third thing out + + align:start position:0% +um if I do two I get the third thing out + + + align:start position:0% +um if I do two I get the third thing out +because I go 0 one two notice however if + + align:start position:0% +because I go 0 one two notice however if + + + align:start position:0% +because I go 0 one two notice however if +I + + align:start position:0% +I + + + align:start position:0% +I +do something that tries to go + + align:start position:0% +do something that tries to go + + + align:start position:0% +do something that tries to go +outside of the length of the tupal it + + align:start position:0% +outside of the length of the tupal it + + + align:start position:0% +outside of the length of the tupal it +complains which is + + align:start position:0% +complains which is + + + align:start position:0% +complains which is +right tuples also have another nice + + align:start position:0% +right tuples also have another nice + + + align:start position:0% +right tuples also have another nice +structure which is I can go the other + + align:start position:0% +structure which is I can go the other + + + align:start position:0% +structure which is I can go the other +direction which is if I want to get the + + align:start position:0% +direction which is if I want to get the + + + align:start position:0% +direction which is if I want to get the +last + + align:start position:0% +last + + + align:start position:0% +last +element of that tupal I give it a + + align:start position:0% +element of that tupal I give it a + + + align:start position:0% +element of that tupal I give it a +negative index imagine you think of it + + align:start position:0% +negative index imagine you think of it + + + align:start position:0% +negative index imagine you think of it +as it's starting right just before the + + align:start position:0% +as it's starting right just before the + + + align:start position:0% +as it's starting right just before the +beginning of the thing if I give it a + + align:start position:0% +beginning of the thing if I give it a + + + align:start position:0% +beginning of the thing if I give it a +zero it's going to take the first one if + + align:start position:0% +zero it's going to take the first one if + + + align:start position:0% +zero it's going to take the first one if +I give it a one it's going to take the + + align:start position:0% +I give it a one it's going to take the + + + align:start position:0% +I give it a one it's going to take the +next one but I can go the other + + align:start position:0% +next one but I can go the other + + + align:start position:0% +next one but I can go the other +direction and if I give it a minus one + + align:start position:0% +direction and if I give it a minus one + + + align:start position:0% +direction and if I give it a minus one +it picks up the last element of the + + align:start position:0% +it picks up the last element of the + + + align:start position:0% +it picks up the last element of the +Tuple and again I can go minus + + align:start position:0% +Tuple and again I can go minus + + + align:start position:0% +Tuple and again I can go minus +two to go back so this is what we would + + align:start position:0% +two to go back so this is what we would + + + align:start position:0% +two to go back so this is what we would +call + + align:start position:0% + + + + align:start position:0% + +selection we can do things like + + align:start position:0% +selection we can do things like + + + align:start position:0% +selection we can do things like +Fu of zero to get out the particular + + align:start position:0% +Fu of zero to get out the particular + + + align:start position:0% +Fu of zero to get out the particular +element I can also pick up pieces of + + align:start position:0% +element I can also pick up pieces of + + + align:start position:0% +element I can also pick up pieces of +that um tupo and again I want to show + + align:start position:0% +that um tupo and again I want to show + + + align:start position:0% +that um tupo and again I want to show +you the format here if I give it this + + align:start position:0% +you the format here if I give it this + + + align:start position:0% +you the format here if I give it this +strange expression this is saying I want + + align:start position:0% +strange expression this is saying I want + + + align:start position:0% +strange expression this is saying I want +to get the piece of the tupal starting + + align:start position:0% +to get the piece of the tupal starting + + + align:start position:0% +to get the piece of the tupal starting +at index one which is going to be the + + align:start position:0% +at index one which is going to be the + + + align:start position:0% +at index one which is going to be the +second element and going up to but not + + align:start position:0% +second element and going up to but not + + + align:start position:0% +second element and going up to but not +including index + + align:start position:0% +including index + + + align:start position:0% +including index +3 and it gives me back that piece or + + align:start position:0% +3 and it gives me back that piece or + + + align:start position:0% +3 and it gives me back that piece or +actually a copy of that piece of the + + align:start position:0% +actually a copy of that piece of the + + + align:start position:0% +actually a copy of that piece of the +tupo okay this is called + + align:start position:0% + + + + align:start position:0% + +slicing and then just to complete + + align:start position:0% +slicing and then just to complete + + + align:start position:0% +slicing and then just to complete +there's two other nice things you can do + + align:start position:0% +there's two other nice things you can do + + + align:start position:0% +there's two other nice things you can do +with slices or you can get the beginning + + align:start position:0% +with slices or you can get the beginning + + + align:start position:0% +with slices or you can get the beginning +or the + + align:start position:0% +or the + + + align:start position:0% +or the +end of a tupal so for example if I say + + align:start position:0% +end of a tupal so for example if I say + + + align:start position:0% +end of a tupal so for example if I say +test and I don't give it a start but I + + align:start position:0% +test and I don't give it a start but I + + + align:start position:0% +test and I don't give it a start but I +give it an end it gives me all the + + align:start position:0% +give it an end it gives me all the + + + align:start position:0% +give it an end it gives me all the +elements up to that + + align:start position:0% +elements up to that + + + align:start position:0% +elements up to that +point and I can obviously do the other + + align:start position:0% +point and I can obviously do the other + + + align:start position:0% +point and I can obviously do the other +direction which + + align:start position:0% + + + + align:start position:0% + +is I can say skip + + align:start position:0% +is I can say skip + + + align:start position:0% +is I can say skip +to index two and all the remaining + + align:start position:0% +to index two and all the remaining + + + align:start position:0% +to index two and all the remaining +pieces and this lets me slice out if you + + align:start position:0% +pieces and this lets me slice out if you + + + align:start position:0% +pieces and this lets me slice out if you +like a front part or a back part or a + + align:start position:0% +like a front part or a back part or a + + + align:start position:0% +like a front part or a back part or a +middle part of of the tupal as I go + + align:start position:0% +middle part of of the tupal as I go + + + align:start position:0% +middle part of of the tupal as I go +along what in the world does that have + + align:start position:0% +along what in the world does that have + + + align:start position:0% +along what in the world does that have +to do with with my U divisor example + + align:start position:0% +to do with with my U divisor example + + + align:start position:0% +to do with with my U divisor example +well actually before I do that let me in + + align:start position:0% +well actually before I do that let me in + + + align:start position:0% +well actually before I do that let me in +fact fill in a piece here which is + + align:start position:0% +fact fill in a piece here which is + + + align:start position:0% +fact fill in a piece here which is +remember I said range we could think of + + align:start position:0% +remember I said range we could think of + + + align:start position:0% +remember I said range we could think of +conceptually + + align:start position:0% +conceptually + + + align:start position:0% +conceptually +as a tuple or sorry as a as a sequence + + align:start position:0% +as a tuple or sorry as a as a sequence + + + align:start position:0% +as a tuple or sorry as a as a sequence +of these things in fact it gives me back + + align:start position:0% +of these things in fact it gives me back + + + align:start position:0% +of these things in fact it gives me back +and now I hate this it's actually a list + + align:start position:0% +and now I hate this it's actually a list + + + align:start position:0% +and now I hate this it's actually a list +it's not a uh a tupal but for now think + + align:start position:0% +it's not a uh a tupal but for now think + + + align:start position:0% +it's not a uh a tupal but for now think +of it is giving you back an explicit + + align:start position:0% +of it is giving you back an explicit + + + align:start position:0% +of it is giving you back an explicit +version of that uh representation of all + + align:start position:0% +version of that uh representation of all + + + align:start position:0% +version of that uh representation of all +those elements you'll see why I'm going + + align:start position:0% +those elements you'll see why I'm going + + + align:start position:0% +those elements you'll see why I'm going +to make that distinction in a couple of + + align:start position:0% +to make that distinction in a couple of + + + align:start position:0% +to make that distinction in a couple of +lectures all right what does this have + + align:start position:0% +lectures all right what does this have + + + align:start position:0% +lectures all right what does this have +to do with my divisor example this says + + align:start position:0% +to do with my divisor example this says + + + align:start position:0% +to do with my divisor example this says +I can make tupal but imagine now I'm + + align:start position:0% +I can make tupal but imagine now I'm + + + align:start position:0% +I can make tupal but imagine now I'm +going back to my divisor example and I + + align:start position:0% +going back to my divisor example and I + + + align:start position:0% +going back to my divisor example and I +want to gather up the elements as I go + + align:start position:0% +want to gather up the elements as I go + + + align:start position:0% +want to gather up the elements as I go +along I ought to be able to do that by + + align:start position:0% +along I ought to be able to do that by + + + align:start position:0% +along I ought to be able to do that by +in fact just adding the pieces in and + + align:start position:0% +in fact just adding the pieces in and + + + align:start position:0% +in fact just adding the pieces in and +that's what I'm going to do over + + align:start position:0% +that's what I'm going to do over + + + align:start position:0% +that's what I'm going to do over +here which + + align:start position:0% +here which + + + align:start position:0% +here which +is let me comment that + + align:start position:0% + + + + align:start position:0% + +out let + + align:start position:0% +out let + + + align:start position:0% +out let +me uncomment that and I guess I need the + + align:start position:0% +me uncomment that and I guess I need the + + + align:start position:0% +me uncomment that and I guess I need the +same thing here right I need + + align:start position:0% +same thing here right I need + + + align:start position:0% +same thing here right I need +um PR's + + align:start position:0% +um PR's + + + align:start position:0% +um PR's +not thank you you can tell I'm an + + align:start position:0% +not thank you you can tell I'm an + + + align:start position:0% +not thank you you can tell I'm an +oldtime list Packer I really do love + + align:start position:0% +oldtime list Packer I really do love + + + align:start position:0% +oldtime list Packer I really do love +these things + + align:start position:0% + + + + align:start position:0% + +and is that right John okay so my + + align:start position:0% +and is that right John okay so my + + + align:start position:0% +and is that right John okay so my +apologies that your handout is wrong I + + align:start position:0% +apologies that your handout is wrong I + + + align:start position:0% +apologies that your handout is wrong I +did not think to check about the + + align:start position:0% +did not think to check about the + + + align:start position:0% +did not think to check about the +difference between these things + + align:start position:0% +difference between these things + + + align:start position:0% +difference between these things +nonetheless having done that let's look + + align:start position:0% +nonetheless having done that let's look + + + align:start position:0% +nonetheless having done that let's look +at what I'm going to do I now want to + + align:start position:0% +at what I'm going to do I now want to + + + align:start position:0% +at what I'm going to do I now want to +run a loop where I need to collect + + align:start position:0% +run a loop where I need to collect + + + align:start position:0% +run a loop where I need to collect +things together I'm going to give a name + + align:start position:0% +things together I'm going to give a name + + + align:start position:0% +things together I'm going to give a name +to that and what you see there is I'm + + align:start position:0% +to that and what you see there is I'm + + + align:start position:0% +to that and what you see there is I'm +going to call divisors initially an + + align:start position:0% +going to call divisors initially an + + + align:start position:0% +going to call divisors initially an +empty tupo something that has nothing in + + align:start position:0% +empty tupo something that has nothing in + + + align:start position:0% +empty tupo something that has nothing in +it right here and then I'm going to run + + align:start position:0% +it right here and then I'm going to run + + + align:start position:0% +it right here and then I'm going to run +through the same loop as before going + + align:start position:0% +through the same loop as before going + + + align:start position:0% +through the same loop as before going +through this set of things doing the + + align:start position:0% +through this set of things doing the + + + align:start position:0% +through this set of things doing the +check and now what would I like to do + + align:start position:0% +check and now what would I like to do + + + align:start position:0% +check and now what would I like to do +every time I find a diviser I'd like to + + align:start position:0% +every time I find a diviser I'd like to + + + align:start position:0% +every time I find a diviser I'd like to +gather it together so I'm going to + + align:start position:0% +gather it together so I'm going to + + + align:start position:0% +gather it together so I'm going to +create a tuple of one element the value + + align:start position:0% +create a tuple of one element the value + + + align:start position:0% +create a tuple of one element the value +of I and then ah cool there's that + + align:start position:0% +of I and then ah cool there's that + + + align:start position:0% +of I and then ah cool there's that +addition operation that's badly + + align:start position:0% +addition operation that's badly + + + align:start position:0% +addition operation that's badly +overloaded this is why Professor gag + + align:start position:0% +overloaded this is why Professor gag + + + align:start position:0% +overloaded this is why Professor gag +likes it and I don't given that this is + + align:start position:0% +likes it and I don't given that this is + + + align:start position:0% +likes it and I don't given that this is +a tupal and that's a tupal I can just + + align:start position:0% +a tupal and that's a tupal I can just + + + align:start position:0% +a tupal and that's a tupal I can just +add them together that is concatenate + + align:start position:0% +add them together that is concatenate + + + align:start position:0% +add them together that is concatenate +them if you like one on the end of it + + align:start position:0% +them if you like one on the end of it + + + align:start position:0% +them if you like one on the end of it +and if I keep doing that when I'm done + + align:start position:0% +and if I keep doing that when I'm done + + + align:start position:0% +and if I keep doing that when I'm done +divisor will be a collection of things + + align:start position:0% +divisor will be a collection of things + + + align:start position:0% +divisor will be a collection of things +so let me just run + + align:start position:0% + + + + align:start position:0% + +it all right uh this is what I get for + + align:start position:0% +it all right uh this is what I get for + + + align:start position:0% +it all right uh this is what I get for +trying to + + align:start position:0% +trying to + + + align:start position:0% +trying to +be ah thank you right + + align:start position:0% +be ah thank you right + + + align:start position:0% +be ah thank you right +there all right we'll try try this + + align:start position:0% + + + + align:start position:0% + +again + + align:start position:0% + + + + align:start position:0% + +okay and there are the set of advisers + + align:start position:0% +okay and there are the set of advisers + + + align:start position:0% +okay and there are the set of advisers +thank you for catch who did that + + align:start position:0% +thank you for catch who did that + + + align:start position:0% +thank you for catch who did that +somebody + + align:start position:0% +somebody + + + align:start position:0% +somebody +gets no yours thank you nice catch too + + align:start position:0% +gets no yours thank you nice catch too + + + align:start position:0% +gets no yours thank you nice catch too +by the way all right so now that you can + + align:start position:0% +by the way all right so now that you can + + + align:start position:0% +by the way all right so now that you can +see that I can screw up programming + + align:start position:0% +see that I can screw up programming + + + align:start position:0% +see that I can screw up programming +which I just did but we fixed it on the + + align:start position:0% +which I just did but we fixed it on the + + + align:start position:0% +which I just did but we fixed it on the +Fly thank you what have we done we've + + align:start position:0% +Fly thank you what have we done we've + + + align:start position:0% +Fly thank you what have we done we've +now got a way of collecting things + + align:start position:0% +now got a way of collecting things + + + align:start position:0% +now got a way of collecting things +together right and this is the first + + align:start position:0% +together right and this is the first + + + align:start position:0% +together right and this is the first +version of Something we'd like to use + + align:start position:0% +version of Something we'd like to use + + + align:start position:0% +version of Something we'd like to use +use have now that I've got that bound as + + align:start position:0% +use have now that I've got that bound as + + + align:start position:0% +use have now that I've got that bound as +a name I could go in and do things with + + align:start position:0% +a name I could go in and do things with + + + align:start position:0% +a name I could go in and do things with +that I could go in and say give me the + + align:start position:0% +that I could go in and say give me the + + + align:start position:0% +that I could go in and say give me the +fourth divisor give me the the second + + align:start position:0% +fourth divisor give me the the second + + + align:start position:0% +fourth divisor give me the the second +through fifth divisor again as I + + align:start position:0% +through fifth divisor again as I + + + align:start position:0% +through fifth divisor again as I +suggested if I got two integers I want + + align:start position:0% +suggested if I got two integers I want + + + align:start position:0% +suggested if I got two integers I want +to find common divisors I could take + + align:start position:0% +to find common divisors I could take + + + align:start position:0% +to find common divisors I could take +those two lists and walk through them + + align:start position:0% +those two lists and walk through them + + + align:start position:0% +those two lists and walk through them +shouldn't say list those two tuples and + + align:start position:0% +shouldn't say list those two tuples and + + + align:start position:0% +shouldn't say list those two tuples and +walk through them to find the pieces + + align:start position:0% +walk through them to find the pieces + + + align:start position:0% +walk through them to find the pieces +that match up so I've got a way now of + + align:start position:0% +that match up so I've got a way now of + + + align:start position:0% +that match up so I've got a way now of +gathering data + + align:start position:0% +gathering data + + + align:start position:0% +gathering data +together the last thing I want to do is + + align:start position:0% +together the last thing I want to do is + + + align:start position:0% +together the last thing I want to do is +to say all right now that we've got this + + align:start position:0% +to say all right now that we've got this + + + align:start position:0% +to say all right now that we've got this +idea of being able to collect things + + align:start position:0% +idea of being able to collect things + + + align:start position:0% +idea of being able to collect things +into collections we got the ability now + + align:start position:0% +into collections we got the ability now + + + align:start position:0% +into collections we got the ability now +to use looping structures as we did be + + align:start position:0% +to use looping structures as we did be + + + align:start position:0% +to use looping structures as we did be +as we did before but they can walk down + + align:start position:0% +as we did before but they can walk down + + + align:start position:0% +as we did before but they can walk down +them doing things to them where else + + align:start position:0% +them doing things to them where else + + + align:start position:0% +them doing things to them where else +might we have this need to do things + + align:start position:0% +might we have this need to do things + + + align:start position:0% +might we have this need to do things +with looping + + align:start position:0% +with looping + + + align:start position:0% +with looping +structures and I'm going to suggest + + align:start position:0% +structures and I'm going to suggest + + + align:start position:0% +structures and I'm going to suggest +you've already seen it what's a + + align:start position:0% +you've already seen it what's a + + + align:start position:0% +you've already seen it what's a +string well at some level it is an + + align:start position:0% +string well at some level it is an + + + align:start position:0% +string well at some level it is an +ordered sequence of characters + + align:start position:0% +ordered sequence of characters + + + align:start position:0% +ordered sequence of characters +right now it is not represented the same + + align:start position:0% +right now it is not represented the same + + + align:start position:0% +right now it is not represented the same +way you don't see strings inside these + + align:start position:0% +way you don't see strings inside these + + + align:start position:0% +way you don't see strings inside these +open pands and closed PS You Don't See + + align:start position:0% +open pands and closed PS You Don't See + + + align:start position:0% +open pands and closed PS You Don't See +strings with you know commas between + + align:start position:0% +strings with you know commas between + + + align:start position:0% +strings with you know commas between +them but it has the same kind of + + align:start position:0% +them but it has the same kind of + + + align:start position:0% +them but it has the same kind of +property it is an ordered sequence of + + align:start position:0% +property it is an ordered sequence of + + + align:start position:0% +property it is an ordered sequence of +characters we'd like to do the same + + align:start position:0% +characters we'd like to do the same + + + align:start position:0% +characters we'd like to do the same +thing with strings that is we'd like to + + align:start position:0% +thing with strings that is we'd like to + + + align:start position:0% +thing with strings that is we'd like to +be able to get pieces of them out we'd + + align:start position:0% +be able to get pieces of them out we'd + + + align:start position:0% +be able to get pieces of them out we'd +like to be able to add them together or + + align:start position:0% +like to be able to add them together or + + + align:start position:0% +like to be able to add them together or +concatenate them together we'd like to + + align:start position:0% +concatenate them together we'd like to + + + align:start position:0% +concatenate them together we'd like to +be able to slice them and in fact we + + align:start position:0% + + + + align:start position:0% + +can so + + align:start position:0% + + + + align:start position:0% + +strings also support + + align:start position:0% + + + + align:start position:0% + +things like + + align:start position:0% +things like + + + align:start position:0% +things like +selection + + align:start position:0% + + + + align:start position:0% + +slicing and a set of other parameters or + + align:start position:0% +slicing and a set of other parameters or + + + align:start position:0% +slicing and a set of other parameters or +other properties and let's just look at + + align:start position:0% +other properties and let's just look at + + + align:start position:0% +other properties and let's just look at +that again if I go back here let me + + align:start position:0% +that again if I go back here let me + + + align:start position:0% +that again if I go back here let me +comment this + + align:start position:0% + + + + align:start position:0% + +out right here are a pair of strings + + align:start position:0% +out right here are a pair of strings + + + align:start position:0% +out right here are a pair of strings +that I've set + + align:start position:0% + + + + align:start position:0% + +up S1 and + + align:start position:0% +up S1 and + + + align:start position:0% +up S1 and +S2 okay let me just run these so we can + + align:start position:0% +S2 okay let me just run these so we can + + + align:start position:0% +S2 okay let me just run these so we can +go back over + + align:start position:0% +go back over + + + align:start position:0% +go back over +here so I can see the value of S1 it's a + + align:start position:0% +here so I can see the value of S1 it's a + + + align:start position:0% +here so I can see the value of S1 it's a +string I can do things + + align:start position:0% +string I can do things + + + align:start position:0% +string I can do things +like S1 and S2 as we saw before it + + align:start position:0% +like S1 and S2 as we saw before it + + + align:start position:0% +like S1 and S2 as we saw before it +simply concatenates them together and + + align:start position:0% +simply concatenates them together and + + + align:start position:0% +simply concatenates them together and +gives me back a longer string but I can + + align:start position:0% +gives me back a longer string but I can + + + align:start position:0% +gives me back a longer string but I can +also ask for parts of this so I can for + + align:start position:0% +also ask for parts of this so I can for + + + align:start position:0% +also ask for parts of this so I can for +example say give + + align:start position:0% + + + + align:start position:0% + +me the first element of string one + + align:start position:0% +me the first element of string one + + + align:start position:0% +me the first element of string one +S1 ah it's exactly what we would have + + align:start position:0% +S1 ah it's exactly what we would have + + + align:start position:0% +S1 ah it's exactly what we would have +thought if this was repres represented + + align:start position:0% +thought if this was repres represented + + + align:start position:0% +thought if this was repres represented +as an ordered sequence of things okay I + + align:start position:0% +as an ordered sequence of things okay I + + + align:start position:0% +as an ordered sequence of things okay I +should have said first it's index zero + + align:start position:0% +should have said first it's index zero + + + align:start position:0% +should have said first it's index zero +the first one I can similarly go in and + + align:start position:0% +the first one I can similarly go in and + + + align:start position:0% +the first one I can similarly go in and +say I'd like all the + + align:start position:0% +say I'd like all the + + + align:start position:0% +say I'd like all the +things + + align:start position:0% +things + + + align:start position:0% +things +ah between index two and index 4 and + + align:start position:0% +ah between index two and index 4 and + + + align:start position:0% +ah between index two and index 4 and +again remember what that does index two + + align:start position:0% +again remember what that does index two + + + align:start position:0% +again remember what that does index two +say start at 012 so a b ah C and then it + + align:start position:0% +say start at 012 so a b ah C and then it + + + align:start position:0% +say start at 012 so a b ah C and then it +goes up to but not including an index + + align:start position:0% +goes up to but not including an index + + + align:start position:0% +goes up to but not including an index +four so it gets c and d and then it + + align:start position:0% +four so it gets c and d and then it + + + align:start position:0% +four so it gets c and d and then it +stops I can similarly just as I did with + + align:start position:0% +stops I can similarly just as I did with + + + align:start position:0% +stops I can similarly just as I did with +the tupal I can ask for + + align:start position:0% +the tupal I can ask for + + + align:start position:0% +the tupal I can ask for +everything up + + align:start position:0% +everything up + + + align:start position:0% +everything up +to some point or I can ask for + + align:start position:0% +to some point or I can ask for + + + align:start position:0% +to some point or I can ask for +everything starting at some point and + + align:start position:0% +everything starting at some point and + + + align:start position:0% +everything starting at some point and +carrying + + align:start position:0% +carrying + + + align:start position:0% +carrying +on now what you're seeing here then is + + align:start position:0% +on now what you're seeing here then is + + + align:start position:0% +on now what you're seeing here then is +the beginning of complex data structures + + align:start position:0% +the beginning of complex data structures + + + align:start position:0% +the beginning of complex data structures +and the nice thing is that there's a + + align:start position:0% +and the nice thing is that there's a + + + align:start position:0% +and the nice thing is that there's a +shared Behavior there just as I can have + + align:start position:0% +shared Behavior there just as I can have + + + align:start position:0% +shared Behavior there just as I can have +tupal as an ordered collection of things + + align:start position:0% +tupal as an ordered collection of things + + + align:start position:0% +tupal as an ordered collection of things +strings behave as an ordered collection + + align:start position:0% +strings behave as an ordered collection + + + align:start position:0% +strings behave as an ordered collection +of things so I can start thinking about + + align:start position:0% +of things so I can start thinking about + + + align:start position:0% +of things so I can start thinking about +doing manipulation on strings I can con + + align:start position:0% +doing manipulation on strings I can con + + + align:start position:0% +doing manipulation on strings I can con +can concatenate them together I can find + + align:start position:0% +can concatenate them together I can find + + + align:start position:0% +can concatenate them together I can find +pieces in side of them I could actually + + align:start position:0% +pieces in side of them I could actually + + + align:start position:0% +pieces in side of them I could actually +do things with them and let me show you + + align:start position:0% +do things with them and let me show you + + + align:start position:0% +do things with them and let me show you +just a simple little example of + + align:start position:0% +just a simple little example of + + + align:start position:0% +just a simple little example of +something I might want to + + align:start position:0% +something I might want to + + + align:start position:0% +something I might want to +do + + align:start position:0% +do + + + align:start position:0% +do +right suppose I + + align:start position:0% + + + + align:start position:0% + +take and I better comment this one out + + align:start position:0% +take and I better comment this one out + + + align:start position:0% +take and I better comment this one out +it's going to spit it out let me comment + + align:start position:0% +it's going to spit it out let me comment + + + align:start position:0% +it's going to spit it out let me comment +that + + align:start position:0% +that + + + align:start position:0% +that +out suppose I take a number I like to + + align:start position:0% +out suppose I take a number I like to + + + align:start position:0% +out suppose I take a number I like to +add up all the digits inside of the + + align:start position:0% +add up all the digits inside of the + + + align:start position:0% +add up all the digits inside of the +number I can use the tools I've just + + align:start position:0% +number I can use the tools I've just + + + align:start position:0% +number I can use the tools I've just +described in order to capture that so + + align:start position:0% +described in order to capture that so + + + align:start position:0% +described in order to capture that so +what would I want to to do I'd like to + + align:start position:0% +what would I want to to do I'd like to + + + align:start position:0% +what would I want to to do I'd like to +somehow walk down each of the digits one + + align:start position:0% +somehow walk down each of the digits one + + + align:start position:0% +somehow walk down each of the digits one +at a time and add them up Ah that's a + + align:start position:0% +at a time and add them up Ah that's a + + + align:start position:0% +at a time and add them up Ah that's a +looping mechanism right I need to have + + align:start position:0% +looping mechanism right I need to have + + + align:start position:0% +looping mechanism right I need to have +some way of walking through them an easy + + align:start position:0% +some way of walking through them an easy + + + align:start position:0% +some way of walking through them an easy +way to do it would be inside of a four + + align:start position:0% +way to do it would be inside of a four + + + align:start position:0% +way to do it would be inside of a four +and what would I like to do well I need + + align:start position:0% +and what would I like to do well I need + + + align:start position:0% +and what would I like to do well I need +to take that number and I'm going to + + align:start position:0% +to take that number and I'm going to + + + align:start position:0% +to take that number and I'm going to +turn it into a string so notice what I'm + + align:start position:0% +turn it into a string so notice what I'm + + + align:start position:0% +turn it into a string so notice what I'm +going to do right here I'm going to take + + align:start position:0% +going to do right here I'm going to take + + + align:start position:0% +going to do right here I'm going to take +that number and convert it into a string + + align:start position:0% +that number and convert it into a string + + + align:start position:0% +that number and convert it into a string +that's an example of that type + + align:start position:0% +that's an example of that type + + + align:start position:0% +that's an example of that type +conversion we did earlier on by doing + + align:start position:0% +conversion we did earlier on by doing + + + align:start position:0% +conversion we did earlier on by doing +that it makes it possible for me to + + align:start position:0% +that it makes it possible for me to + + + align:start position:0% +that it makes it possible for me to +treat it as an ordered sequence of + + align:start position:0% +treat it as an ordered sequence of + + + align:start position:0% +treat it as an ordered sequence of +characters and so what's the loop going + + align:start position:0% +characters and so what's the loop going + + + align:start position:0% +characters and so what's the loop going +to do it's going to say for C which was + + align:start position:0% +to do it's going to say for C which was + + + align:start position:0% +to do it's going to say for C which was +my name for the character in that string + + align:start position:0% +my name for the character in that string + + + align:start position:0% +my name for the character in that string +that means starting at the first one I'm + + align:start position:0% +that means starting at the first one I'm + + + align:start position:0% +that means starting at the first one I'm +going to do something to it and what I'm + + align:start position:0% +going to do something to it and what I'm + + + align:start position:0% +going to do something to it and what I'm +going to do I'm going to take that + + align:start position:0% +going to do I'm going to take that + + + align:start position:0% +going to do I'm going to take that +character convert it back into an + + align:start position:0% +character convert it back into an + + + align:start position:0% +character convert it back into an +integer and add it into some digits and + + align:start position:0% +integer and add it into some digits and + + + align:start position:0% +integer and add it into some digits and +I've done a little Shand here which is I + + align:start position:0% +I've done a little Shand here which is I + + + align:start position:0% +I've done a little Shand here which is I +should have said some digits is equal to + + align:start position:0% +should have said some digits is equal to + + + align:start position:0% +should have said some digits is equal to +some digits plus this but that little + + align:start position:0% +some digits plus this but that little + + + align:start position:0% +some digits plus this but that little +short hand there is doing exactly the + + align:start position:0% +short hand there is doing exactly the + + + align:start position:0% +short hand there is doing exactly the +same thing it is adding that value into + + align:start position:0% +same thing it is adding that value into + + + align:start position:0% +same thing it is adding that value into +some digits and putting it back into or + + align:start position:0% +some digits and putting it back into or + + + align:start position:0% +some digits and putting it back into or +signing it back into some digits and + + align:start position:0% +signing it back into some digits and + + + align:start position:0% +signing it back into some digits and +I'll just walk through that Loop and + + align:start position:0% +I'll just walk through that Loop and + + + align:start position:0% +I'll just walk through that Loop and +when I'm done I can print out what the + + align:start position:0% +when I'm done I can print out what the + + + align:start position:0% +when I'm done I can print out what the +total thing + + align:start position:0% +total thing + + + align:start position:0% +total thing +does and if I do + + align:start position:0% +does and if I do + + + align:start position:0% +does and if I do +that I get out what I would + + align:start position:0% +that I get out what I would + + + align:start position:0% +that I get out what I would +expect so what have I + + align:start position:0% +expect so what have I + + + align:start position:0% +expect so what have I +done we've now generalized the idea of + + align:start position:0% +done we've now generalized the idea of + + + align:start position:0% +done we've now generalized the idea of +iteration into this little pattern and + + align:start position:0% +iteration into this little pattern and + + + align:start position:0% +iteration into this little pattern and +again as I said this is my version of it + + align:start position:0% +again as I said this is my version of it + + + align:start position:0% +again as I said this is my version of it +but you can see every one of the + + align:start position:0% +but you can see every one of the + + + align:start position:0% +but you can see every one of the +examples we've used so far has that + + align:start position:0% +examples we've used so far has that + + + align:start position:0% +examples we've used so far has that +pattern to it figure out what I'm trying + + align:start position:0% +pattern to it figure out what I'm trying + + + align:start position:0% +pattern to it figure out what I'm trying +to walk through what's the collection of + + align:start position:0% +to walk through what's the collection of + + + align:start position:0% +to walk through what's the collection of +things I'm trying to walk through figure + + align:start position:0% +things I'm trying to walk through figure + + + align:start position:0% +things I'm trying to walk through figure +out what I want to do at each stage + + align:start position:0% +out what I want to do at each stage + + + align:start position:0% +out what I want to do at each stage +figure out what the end test is figure + + align:start position:0% +figure out what the end test is figure + + + align:start position:0% +figure out what the end test is figure +out what I'm going to do at the end of + + align:start position:0% +out what I'm going to do at the end of + + + align:start position:0% +out what I'm going to do at the end of +it I can write it explicitly I can write + + align:start position:0% +it I can write it explicitly I can write + + + align:start position:0% +it I can write it explicitly I can write +it inside of a for Loop and we've + + align:start position:0% +it inside of a for Loop and we've + + + align:start position:0% +it inside of a for Loop and we've +started to add and we'll see a lot more + + align:start position:0% +started to add and we'll see a lot more + + + align:start position:0% +started to add and we'll see a lot more +of this examples of collections of of + + align:start position:0% +of this examples of collections of of + + + align:start position:0% +of this examples of collections of of +structures so that we don't just have to + + align:start position:0% +structures so that we don't just have to + + + align:start position:0% +structures so that we don't just have to +do something that can be easily + + align:start position:0% +do something that can be easily + + + align:start position:0% +do something that can be easily +described as walking through a set of + + align:start position:0% +described as walking through a set of + + + align:start position:0% +described as walking through a set of +things but can actually be a collection + + align:start position:0% +things but can actually be a collection + + + align:start position:0% +things but can actually be a collection +that you walk through the last thing I + + align:start position:0% +that you walk through the last thing I + + + align:start position:0% +that you walk through the last thing I +want to point out to you + + align:start position:0% + + + + align:start position:0% + +is I started out with this + + align:start position:0% +is I started out with this + + + align:start position:0% +is I started out with this +list I haven't added anything to the + + align:start position:0% +list I haven't added anything to the + + + align:start position:0% +list I haven't added anything to the +list right I mean I've got a different + + align:start position:0% +list right I mean I've got a different + + + align:start position:0% +list right I mean I've got a different +kind of looping mechanism I I guess I + + align:start position:0% +kind of looping mechanism I I guess I + + + align:start position:0% +kind of looping mechanism I I guess I +should say that's not quite true I've + + align:start position:0% +should say that's not quite true I've + + + align:start position:0% +should say that's not quite true I've +added the ability to have more complex + + align:start position:0% +added the ability to have more complex + + + align:start position:0% +added the ability to have more complex +data structures here but I dropped a + + align:start position:0% +data structures here but I dropped a + + + align:start position:0% +data structures here but I dropped a +hint in the first lecture about what you + + align:start position:0% +hint in the first lecture about what you + + + align:start position:0% +hint in the first lecture about what you +could compute with things and in fact if + + align:start position:0% +could compute with things and in fact if + + + align:start position:0% +could compute with things and in fact if +you think for a second about that list + + align:start position:0% +you think for a second about that list + + + align:start position:0% +you think for a second about that list +you could ask what can I compute with + + align:start position:0% +you could ask what can I compute with + + + align:start position:0% +you could ask what can I compute with +just that set of constructs and the + + align:start position:0% +just that set of constructs and the + + + align:start position:0% +just that set of constructs and the +answer is basically anything this is an + + align:start position:0% +answer is basically anything this is an + + + align:start position:0% +answer is basically anything this is an +example of what is referred to + + align:start position:0% +example of what is referred to + + + align:start position:0% +example of what is referred to +frequently as being a turing + + align:start position:0% +frequently as being a turing + + + align:start position:0% +frequently as being a turing +complete language right is to say with + + align:start position:0% +complete language right is to say with + + + align:start position:0% +complete language right is to say with +just those set of constructs anything + + align:start position:0% +just those set of constructs anything + + + align:start position:0% +just those set of constructs anything +you can describe Al algorithmically you + + align:start position:0% +you can describe Al algorithmically you + + + align:start position:0% +you can describe Al algorithmically you +can compute with that set of + + align:start position:0% +can compute with that set of + + + align:start position:0% +can compute with that set of +constructs so there's good news and bad + + align:start position:0% +constructs so there's good news and bad + + + align:start position:0% +constructs so there's good news and bad +news the good news is it sounds like + + align:start position:0% +news the good news is it sounds like + + + align:start position:0% +news the good news is it sounds like +we're done class is canceled until final + + align:start position:0% +we're done class is canceled until final + + + align:start position:0% +we're done class is canceled until final +exam because this is all you need to + + align:start position:0% +exam because this is all you need to + + + align:start position:0% +exam because this is all you need to +know right the bad news is of course + + align:start position:0% +know right the bad news is of course + + + align:start position:0% +know right the bad news is of course +that's not true the real issue is to + + align:start position:0% +that's not true the real issue is to + + + align:start position:0% +that's not true the real issue is to +figure out how to build constructs out + + align:start position:0% +figure out how to build constructs out + + + align:start position:0% +figure out how to build constructs out +of this that tackle particular problems + + align:start position:0% +of this that tackle particular problems + + + align:start position:0% +of this that tackle particular problems +but the fundamental basics of + + align:start position:0% +but the fundamental basics of + + + align:start position:0% +but the fundamental basics of +computation are just captured in that + + align:start position:0% +computation are just captured in that + + + align:start position:0% +computation are just captured in that +set of + + align:start position:0% +set of + + + align:start position:0% +set of +mechanisms all right we'll see you next + + align:start position:0% +mechanisms all right we'll see you next + + + align:start position:0% +mechanisms all right we'll see you next +time \ No newline at end of file diff --git a/Ye4vL7u6N2g.txt b/Ye4vL7u6N2g.txt new file mode 100644 index 0000000000000000000000000000000000000000..b890a234bb49a9bc07329b231f2ac9e42a7f4562 --- /dev/null +++ b/Ye4vL7u6N2g.txt @@ -0,0 +1,2851 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +mitopencourseware@ocw.mit.edu. + +PROFESSOR: So today what we're +going to do is continue our + +discussion of supply +and demand. + +This is sort of introduction +week, if you will. + +We've kind of talked about +supply and demand, and you + +guys, rightly, immediately +were on to where do those + +curves come from. + +And that's what we'll +start next week. + +But what I want to do today is +talk some more about what + +determines the shapes of supply +and demand curves and + +just think about an overview of +how we think about supply + +and demand interacting in a +market and what determines how + +responsive individuals and +firms are to prices. + +And, once again, remember +everyone should have a handout + +that you should have picked up +in the back on your way in. + +So everyone should +have a handout. + +What we talked about last time +was the sort of qualitative + +effects, the qualitative version +of the supply and + +demand model. + +We talked about what happens +when a supply curve shifts, + +what happens when a demand +curve shifts. + +We talked about how either a +supply shock or a demand shock + +could lead to the price +being increased. + +But they could have very +different effects on + +quantity, et cetera. + +What we didn't talk about is +how big these effects are. + +I made up some numbers. + +I threw them on the graphs. + +But I didn't talk about where +the size of those + +effects come from. + +And where they come from is the +shapes of the supply and + +demand curve. + +And that's what we'll talk about +today is what determines + +the shapes of supply +and demand curves. + +And that will be the focus +of today's lecture. + +I'll talk both theoretically +about what determines these + +shapes and empirically about +how economists go about + +figuring out the shapes of +supply and demand curves. + +So, to think about this, let's +start with Figure 3-1, which + +is a standard market diagram +we had last time. + +With an initial equilibrium at +point E1, with an initial + +price P1 and a quantity Q1. + +That's the equilibrium +that's stable. + +Because at that price P1, +consumers demand Q1 units, and + +suppliers are willing +to provide Q1 units. + +So that's a stable +equilibrium. + +Now we have some supply shift. + +Last time we talked +about somehow a + +pork-specific drought. + +That leads the supply +to shift inward. + +So the supply curve +rises to S2. + +At that new price, initially, +you would have excess demand. + +But quickly the price increases +to shut off that + +excess demand. + +And you end up with a new +equilibrium with a higher + +price, P2, and a lower +quantity Q2, and new + +equilibrium point E2. + +OK? + +And we talked that through +last time. + +What I want to talk about this +time is well, what determines + +the size of that shift from Q1 +to Q2 and that price increase + +from P1 to P2? + +What's going to determine it +is the elasticity of supply + +and demand. + +The elasticity of supply and +demand is how much do supply + +and demand respond? + +Do the quantities supplied and +the quantities demanded + +respond when the +price changes? + +When we say, how elastic is +demand, what we mean is how + +sensitive to price is the +quantity demanded. + +Or, alternatively, what is the +slope of that demand curve? + +So the slope of the demand curve +will be the sensitivity + +of quantity demanded to the +price consumers face. + +And that will determine the +market responsiveness. + +In economics, it's always true +that the best way to think + +about things is to +go to extremes. + +You have to remember that +extremes don't exist in the + +real world. + +But it's a useful +teaching device + +to think about extremes. + +So let's think about one extreme +case in Figure 3-2. + +Let's think about the case of +perfectly inelastic demand. + +Perfectly inelastic demand, +that's where there's no + +elasticity of demand. + +What that means is that demand +for a good is unchanged + +regardless of the price. + +So perfectly inelastic demand is +a case where demand for the + +good is unchanged regardless +of the price. + +That would lead you to have a +vertical demand curve at a + +given quantity. + +What this says is regardless +of the price, people always + +demand Q. + +Can anyone tell me what +would cause demand to + +be perfectly inelastic? + +In what types of situations +would demand be-- + +it's never perfectly +inelastic-- + +would demand be relatively +inelastic? + +Yeah? + +AUDIENCE: [INAUDIBLE PHRASE]. + +PROFESSOR: It's all +about substitutes. + +When there's no substitutes, +when there's nowhere to go, it + +doesn't matter what +the price is. + +When there's no substitutes, +demand will be perfectly + +inelastic, because you have to +have Q. It doesn't matter what + +the price is. + +Because there's no substitute +for that good. + +So if you wanted amount Q of +that good for any reason, + +you're always going to +want that amount Q + +no matter the price. + +So a perfectly inelastic good +would have no substitutes. + +So you'd always want +Q no matter what. + +Can anyone think +of an example? + +There's no perfectly inelastic +good in the world. + +But what sorts of goods? + +Yeah? + +AUDIENCE: Medicines. + +PROFESSOR: Medicines. + +Now, not necessarily +all medicines. + +So give me an example of a +medicine which would be more + +or less inelastic. + +So I don't even need +a medical name. + +What sort of treatments? + +AUDIENCE: Like heart +attack maybe? + +PROFESSOR: Yeah, something which +is sort of lifesaving. + +The best thing that we often use +is insulin for diabetics. + +Diabetics without getting that +insulin to manage their + +diabetes will die. + +That seems like that's something +where there's not a + +whole lot of substitutes. + +The substitute is dying. + +So basically that's +where demand + +is relatively inelastic. + +Or a heart transplant, when you +get a heart transplant or + +any kind of transplant, you have +medicine you take so you + +don't reject the transplanted +organ. + +That sort of medicine demand +should be very inelastic. + +Elastic drug, well, +our favorite + +example is always Viagra. + +It's something where you'd think +that you can probably + +survive without it. + +And people would want less +Viagra if you charged a lot + +more for it than if you +charged less for it. + +So elasticity is going to be +about substitutability. + +And that's going to determine +inelastic demand. + +Now, what happens with inelastic +demand when there's + +a supply shock? + +When supply increases, +what happens? + +Well, in that case, there can +never be excess demand, + +because demand doesn't change. + +So all that happens is +price just increases. + +If there's inelastic demand, +and there's a supply shock, + +then all that happens is an +increase in price and no + +change in quantity. + +So with inelastic demand, +quantity doesn't change for a + +price increase. + +Price just goes up. + +From a supply shock, prices +just goes up. + +Now, let's consider +the opposite. + +Let's look at Figure +3-3 and think about + +perfectly elastic demand. + +Perfectly elastic demand is +demand where consumers, + +essentially, don't care +about the quantity. + +They just care about +the price. + +That is, there are infinitely +good substitutes. + +A perfectly elastically demanded +good would be one + +where there are, essentially, +perfect substitutes. + +An inelastic good is where +there's no substitute. + +A perfectly elastic good would +be where there's perfect + +substitutes. + +Technically, if a good is +perfectly elastically + +demanded, then you are +completely indifferent between + +that good and a substitute. + +Well, if you're completely +indifferent, then if the price + +changed at all, you would +immediately switch. + +And so the price can't change. + +What's an example? + +Once again, there's no +good example of a + +perfectly elastic good. + +Yeah? + +AUDIENCE: Candy. + +PROFESSOR: What? + +AUDIENCE: Candy. + +PROFESSOR: Candy. + +OK. + +So you've got your +Wrigley's gum. + +I like the sugar-free, +minty gum. + +You've got Orbit and Eclipse. + +And I go to the store, and +they're all pretty much the + +same price. + +If Orbit was more than Eclipse, +I just buy Eclipse. + +They're the same. + +They're minty gum. + +It doesn't make a difference. + +So basically the price +is the same. + +If there's a supply shock, I +don't know, they're made with + +the same shit. + +But let's say that Eclipse has +some magic ingredient. + +And let's say the Eclipse magic +ingredient got more + +expensive, so the supply +curve shifted up. + +Well, Eclipse could not respond +by raising its price. + +Because I just switched +to Orbit. + +Or we often think of McDonald's +and Burger King. + +Now, they're less perfect + +substitutes, but pretty perfect. + +If McDonald's started charging +$10 for a hamburger, you + +wouldn't go there anymore. + +You'd go to Burger King. + +So if there's a supply shock to +a provider that's facing a + +perfectly elastic demand curve, +they cannot raise their + +price, because people +will just switch. + +So quantity will fall a lot. + +Because if I'm supplying Eclipse +gum, and it suddenly + +costs a lot more to produce +Eclipse gum, but I can't raise + +my price, because I will lose +all my business to Orbit, I'm + +just going to produce +a lot less Eclipse. + +Because I'm losing money now. + +So with perfectly inelastic +demand, the + +quantity didn't change. + +With perfectly elastic demand, +we saw a big quantity change. + +So, more generally, what +determines the quantity change + +in response to a price change +is the elasticity. + +More generally, we're between +these two cases of perfectly + +elastic and perfectly +inelastic. + +And what's going to determine +the price change is going to + +be the price elasticity of +demand epsilon which is going + +to be the percentage change in +quantity for each percentage + +change in price or, in calculus +terms, dQ/dP. + +So it's, basically, the +percentage change in quantity + +for the percentage +change in price. + +So, for example, if for every 1% +increase in price quantity + +falls 2%, that is a price +elasticity of + +demand of minus 2. + +The price elasticity of demand +is the percentage change in + +quantity for the percentage +change in price. + +So inelastic demand is +an epsilon of 0. + +There is no change in quantity +when price changes. + +Perfectly elastic demand is an +epsilon of negative infinity. + +Any epsilon change in price +leads to a negative infinite + +change in quantity. + +Immediately, the quantity +goes to 0 if you try + +to raise your price. + +So the price elasticity of +demand will typically be + +between 0 and negative +infinity. + +And the larger it is the more +quantity will change when + +prices change. + +Questions about that? + +Yeah? + +AUDIENCE: So that formula, +shouldn't it be dQ/dP times + +P/Q because dQ/dP just refers to +the change of the quantity + +with respect to price, not + +necessarily the percent change. + +PROFESSOR: Yeah, you're right. + +I was trying to get too fancy +with my calculus. + +You're right. + +Let's just stick with the +non-calculus formula. + +I never should deviate +from my notes. + +So let's just stick with the +non-calculus formula. + +OK, other questions +about this? + +OK. + +So, basically, that's +the elasticity. + +That's going to be +the elasticity. + +Now, an interesting point about +elasticity is now, we're + +not going to get into +producer theory + +for a couple of lectures. + +But as a little peek ahead about +producer theory, let's + +think about how elasticity +determines the money that + +producers make from selling +their goods. + +Well, if a producer sells Q +goods at a price P, they make + +revenues R. Revenues are the +price times the quantity. + +The amount of money a producer +makes when it sells goods, its + +revenues, this isn't +its profits. + +We're not having profits. + +It's just the amount of money +it makes, not the amount of + +money it takes home at +the end of the day. + +I'm ignoring the cost +of making the goods. + +The amount of total +revenues it makes + +is price times quantity. + +Well, we can then say that the +change in revenues with + +respect to price is what? + +It's Q plus dQ, plus delta Q-- +let me put it this way to make + +my math clearer-- + +plus P times delta Q over delta +P. That's how revenues + +change with respect to price. + +Or, in other words, plugging +in from the elasticity + +formula, delta R over delta P +equals Q times 1 plus epsilon. + +So, in other words, what this +says is that if you're a + +producer, and you're trying to +decide whether to raise your + +price, whether that will +increase revenues, it all + +depends on the elasticity. + +If the elasticity is between +0 and minus 1, then raising + +prices will raise revenues. + +If the elasticity is greater +than minus 1, then raising + +prices will lower revenues. + +We're often faced with the issue +of why did they charge + +this much for this good, or +should they raise their prices + +or not raise their price. + +Well, that's all about the +elasticity of demand. + +The elasticity of demand will +determine whether they're + +going to make more money by +raising their price or lose + +money by raising their price. + +For Eclipse gum, their +elasticity of demand is well + +above minus 1 in absolute value, +so they're going to + +lose money by raising +their price. + +If they take the current level +of Eclipse, for every penny + +they raise, they'll +lose money. + +For insulin, for every +penny they raise, + +they'll make money. + +And then you might say well, +then how come the price of + +insulin isn't infinity +and the price of + +Eclipse gum isn't zero? + +Well, that's what we'll talk +about in a few weeks. + +Because it also depends on the +costs of producing it. + +But at the end of the day, +that's what's going to + +determine the money that's made +by producers when they + +change their prices. + +Questions about that? + +OK. + +So now, that's how we think +about the shape + +of supply and demand. + +The shape of supply and demand +is determined by these + +elasticities. + +So now we have to get into OK, +well, where do we get these + +elasticities from? + +And that is the main topic of +empirical economics which is + +estimating these kinds of +elasticities, estimating these + +types of elasticities. + +So one of the first distinctions +I drew in the + +lectures is between theoretical +economics and + +empirical economics. + +Theoretical economics can tell +us this is what a graph looks + +like and supply and demand. + +Theoretical economics can't +really tell us how big, for + +example, an elasticity +is going to be. + +It can tell us, there's more +substitutes or less + +substitutes so we +can rank them. + +We know the elasticity for +Eclipse gum has got to be + +higher than the elasticity +for insulin. + +But from the theoretical model, +we can't say what the + +elasticity actually is. + +To say what an elasticity +actually is, we need to go to + +an empirical model. + +We actually need to bring data +to bear on the question. + +And this is very difficult. + +Because here we face the +fundamental conundrum facing + +the empirical economist which +is distinguishing causation + +from correlation. + +And the whole guts of empirical +economics is all + +about this question, +distinguishing causation from + +correlation. + +The classic story that +illustrates this, it's due to + +my colleague, Frank Fisher, +from a textbook many years + +ago, was the story of in ancient +Russia there was a + +cholera outbreak, and many +people were dying. + +So the government decided to +send doctors out to try to + +solve the problem. + +And where there were +more people sick, + +they sent more doctors. + +Well, the peasants said, +wait a second. + +We observe that where there's +more doctors, more people are + +dying from cholera. + +So the doctors must be +causing the cholera. + +So they rose up and killed +the doctors. + +The peasants confused causation +with correlation. + +They thought that the fact that +you saw more people dying + +where there's more doctors +meant that doctors were + +causing the disease. + +Clearly that's wrong. + +That's why they were peasants. + +But it's not just peasants +that make this mistake. + +For example, in 1988, Harvard +University, our illustrious + +neighbor to the south, +I guess, west, + +east, I don't know. + +Which way is Harvard? + +I don't know directions, +down the street. + +A Harvard University dean +conducted an interview with a + +set of freshmen. + +And they found that those +that had taken + +SAT preparation courses-- + +now, you all took SAT +preparation courses. + +But in 1988, not everyone did. + +Those who'd taken SAT +preparation courses scored an + +average of 63 points lower-- + +this was back when the +SAT was 1600 points-- + +63 points lower on their SATs +then those that had not taken + +preparation courses. + +The dean concluded that +preparation courses were + +unhelpful, and that the testing +industry was preying + +on the insecurities +of students to + +provide a useless service. + +Why was the dean confusing +causation with correlation? + +What did the dean get wrong in +drawing that conclusion? + +Yeah? + +AUDIENCE: What had probably +happened is the students who + +got worse scores realized that +they wanted to try and improve + +their scores by taking +an SAT prep class. + +So that's why there is a lower +average score for the people + +who had taken the class. + +PROFESSOR: Generally, the people +who needed the help the + +most took the most courses. + +And so they had an underlying +lower score. + +So, in fact, you can't tell +anything from the fact that + +the people who took the prep +course scored worse. + +It's just another excellent +example of confusing causation + +with correlation. + +And that's another example. + +Another example I like quite +a lot is studies of + +breastfeeding. + +There are numbers of studies of +breastfeeding, especially + +in developing countries, where +they found that the longer + +children were breastfed +the sicker they were. + +So they concluded that + +breastfeeding was bad for kids. + +Well, that's not the truth. + +The truth is the sicker kids +need to be breastfed more, + +because breastfeeding is +actually good for kids. + +And they just confused the +causation with the + +correlation. + +Now, these are all +fun examples. + +But the truth is this is a +common mistake made by + +citizens, policy makers, +everyone in the real world. + +It's taking two things that move +together and assuming one + +causes the other. + +And this is the fundamental +conundrum facing empirical + +economics in trying to address +these kinds of things like + +measuring elasticities. + +So to understand that, let's +think about the issue of + +trying to estimate the +elasticity of demand for pork. + +Let's say you have the exciting +job of estimating the + +elasticity of demand for pork. + +That's your assignment. + +Well, you say, wait a second. + +What we learned in class, as +shown in Figure 3-4, is that + +the price of pork can rise for +very different reasons. + +Figure 3-4, we start at an +initial equilibrium like E1 + +with a quantity like +Q1 and a price P1. + +Now, imagine that there was a +shift in demand, because the + +price of beef rose, remember? + +The price of beef rose. + +That shifted demand +from D1 to D2. + +What did that lead to? + +A higher price and a +higher quantity. + +So if you took that diagram-- + +forget the supply shift for a +minute, just imagine that's + +the change-- + +and you said, aha. + +I can measure the elasticity. + +I see here there's a +change in price. + +I can then look at how +quantity changed. + +And I'll get the elasticity +right after all. + +It's delta Q over Q +or delta P over P. + +So I just look, and I take Q2 +prime minus Q1 over Q1. + +That's the percentage change +in Q. I take P2 + +over P1 over P1. + +That's the percentage +change in price. + +And what do I get? + +A wrong signed elasticity +is what I get. + +I get a positive elasticity, +because Q is going up + +and P is going up. + +Why? + +Because I'm confusing causation +with correlation. + +It's not the price change that +caused quantity to change. + +In fact, it's the opposite. + +It's a taste shift, which caused +quantity to increase + +which drove up the price. + +It was a demand increase which +caused the quantity demanded + +to increase which drove +up the price. + +So it's the quantity driving +the price, not the price + +driving the quantity. + +So if you looked at that simple +example, as many people + +in the real world do, they'd +say, hey, look. + +Higher prices cause +higher quantities. + +You're getting the +wrong answer. + +Because you're confusing +correlation which is the + +higher price is correlated +with the higher quantity. + +Because there was a common +factor causing both of them + +which is the demand shift +and not causation. + +The higher price did not cause +the higher quantity. + +What do we need to do? + +We need to distinguish why +the price increased. + +We need to distinguish +why the price + +increased to measure this. + +If, instead, we looked at a +shift in supply such as the + +case that's shifting from +S1 to S2 and moving the + +equilibrium from E1 to +E2, then you would + +get the right answer. + +Because then you'd say, look. + +Something independent +to consumers + +shifted up the price. + +Some shock to the supply of +pork shifted up the price. + +And we saw that their quantity +fell as a result. + +What's the key? + +The key is that to measure an +elasticity of demand, you're + +measuring the slope of +the demand curve. + +So you need to shift along a +demand curve, not shift the + +demand curve itself. + +So if you look at this figure, +what's the concept we want? + +We want the slope of +the demand curve. + +Well, you get that by shifting +from E1 to E2, because you + +shift along the demand curve. + +So by looking at what happens +to quantity as price rises + +from E1 to E2, you get the slope +of the demand curve. + +You get that delta Q over +delta P you want. + +But from E1 to E2 prime, you're +not shifting along the + +demand curve. + +You're actually measuring the +elasticity of supply. + +You're measuring the elasticity +of supply. + +You're shifting along +a supply curve. + +So you're actually answering a +different question, a relevant + +question, but a different one. + +That question is, what's the +elasticity of supply? + +How willing are pork producers +to supply pork as + +the price goes up? + +So it's the same delta Q over +delta P. But here we did the + +elasticity of demand. + +There's a corresponding +elasticity of supply which is + +measured the same way. + +It's delta Q over delta +P, but it's for a + +different kind of shock. + +It's what you get from moving +along the supply curve. + +So if we went from E1 to E2 +prime, we can use that to + +measure the elasticity of supply +or the slope of the + +supply curve. + +And we do that if something +shifts demand to move us along + +the supply curve. + +From E1 to E2, we measure the +elasticity of demand as + +something shifts supply +and moves us + +along the demand curve. + +So what we need to measure the +elasticity of demand is + +something which shifts +supply but does not, + +itself, affect demand. + +And the best example of this +that we use in economics, a + +great example, is government +policy which comes along and + +changes the supply conditions +for a good. + +So, for example, let's think +about a tax on pork. + +So if you go to Figure 3-5, +imagine the government came + +along and taxed pork. + +The government comes along +and taxes pork. + +Let's think about what +a tax on pork does. + +The government comes along, and +let's say the pork market + +is initially in equilibrium +at $3.30 with 220 million + +kilograms of pork sold. + +Now the government comes along +and says that it's going to + +charge $1.05 in tax for every +kilogram of pork. + +So it's going to impose +a tax of $1.05 + +per kilogram on producers. + +So it's saying to producers of +pork, for every kilogram of + +pork you sell, you have +to send a check to the + +government for $1.05. + +For every kilogram of pork you +sell, you have to send a check + +to the government for $1.05. + +Now, somebody talk me through +how a supplier + +thinks through that. + +How does a supplier +react to that? + +What do they think? + +They're initially happy at +E1 selling 220 million + +kilograms at $3.30. + +What happens when the government +comes in and says + +you have to pay $1.05 for every + +kilogram of pork you sell? + +What happens? + +Yeah. + +AUDIENCE: The producer decides +that the current amount of + +money they have will not be able +to buy as much inputs to + +create their products. + +So they can produce less. + +PROFESSOR: Exactly. + +So, in other words, the cost +of producing just rose. + +So what do they do? + +So, in other words, what they +say is look, effectively, if I + +was happy before selling 220 +million kilograms at $3.30, to + +keep me equally happy selling +220 million kilograms, I'm + +going to have to raise +the price. + +We should add this to +graph, actually. + +If you draw a vertical line up +for me, one to the S2 curve. + +Draw a little dashed line up +from the E1 to the S2 curve + +and then over. + +That price intersection +will be $4.35. + +So in other words, if you want +me to keep producing 220 + +million kilograms of pork, +I'm going to have + +to get $4.35 a kilogram. + +And you might say, what gives +you the right to get that? + +And it's not about rights. + +It's about what producers +are willing to do. + +That same mathematics, that same +supply curve that tells + +us they're willing to sell 220 +million kilograms at $3.30 + +says, if you want them to keep +selling 220 million kilograms + +but also pay $1.05 to the +government, they're going to + +have to get $4.35 a kilogram. + +So what happens is that's +a supply shift. + +And with the same reaction +we saw last time with the + +drought, the price goes up, +consumers demand less, and you + +reach a new equilibrium +at the price E2. + +You reach a new equilibrium +where you sell 206 million + +kilograms for a price +of $4.00. + +So someone tell me how I use +this example to find + +elasticity of demand. + +Yeah. + +AUDIENCE: I guess you need to +know that the change in price + +traveled along the +demand curve. + +So you know that it's not +[INAUDIBLE PHRASE]. + +PROFESSOR: OK, so tell me. + +You don't have to do the +math in your head. + +But how would I compute it? + +AUDIENCE: You would take E1 and +E2, and then you would do + +the price over the +quantity change. + +PROFESSOR: Right, exactly. + +So the quantity change delta +Q over Q, is what? + +It's minus 14 over 220. + +It fell by 14 million +kilograms over 220. + +The price change, delta P +over P, the price rose + +from $3.30 to $4.00. + +So the price change is +$0.70 over $3.30. + +And using those, you +end up with a price + +elasticity of minus 0.3. + +Or, in other words, there's +a 6.4% change in quantity. + +This is minus 6.4% for a +21% change in price. + +So quantity falls by 6.4% when +price goes up by 21%. + +That's a price elasticity +of minus 0.3. + +Or that's a relatively +inelastic demand. + +It's not perfectly inelastic, +but it's relatively inelastic. + +In other words, at that point, +pork producers could make + +money by raising the price. + +Now, you might say well, +why didn't they? + +That's something we'll discuss +in a couple weeks. + +But at that point, demand +is relatively inelastic. + +And you've got a convincing +estimate, because you moved + +along that demand curve. + +You used the supply shift. + +Now, we're going to talk about +taxation much, much later in + +the semester. + +Let me just talk for one minute +about what we learned + +from this graph. + +What happens? + +Well, the shaded area is the +money the government raises + +from its tax. + +The government has a tax +of $1.05 at 206 million + +kilograms. So it raises $1.05 +times 206 million kilograms + +which is that shaded area. + +There are two points to note the +we'll come back to later + +in the semester. + +The first point to note is the +amount of money the government + +raises will depend directly on +the elasticity of demand. + +Can anyone tell me how much +money the government would + +raise if you had a perfectly +inelastic demand? + +Yeah. + +AUDIENCE: [INAUDIBLE PHRASE]. + +PROFESSOR: Right. + +If we think about this demand +curve being perfectly flat, if + +we think about this demand curve +being perfectly flat, + +then basically the producer +can't charge any more for + +their good. + +So it's going to depend on +whether the producer is + +willing to sell at $1.05 less +and how much less they're + +willing to sell. + +If they're willing to sell a +lot less, they're going to + +make a lot less money. + +It's going to be where that +second supply curve intersects + +a flat demand curve. + +So that quantity is going +to be a lot smaller. + +We don't have it +on the diagram. + +But you see where that dashed +line at $3.30 intersects S2, + +that's way to the left. + +Quantity is going to fall +a ton in this market. + +When quantity falls, the +government is going to raise a + +lot less money. + +Because the government +raises $1.05 on every + +unit sold at the end. + +So if the government taxes +very elastically demanded + +goods, it's going to +raise less money. + +If it taxes inelastically +demanded goods like insulin, + +it's going to raise more money, +because the quantity + +doesn't change. + +Yeah. + +AUDIENCE: So cigarettes are +relatively inelastic. + +PROFESSOR: Yes, exactly. + +Cigarettes are relatively +inelastic. + +The elasticity is around +minus 0.5. + +So the government will actually +raise money by + +raising the cigarette tax. + +Those of us, as good liberals, +think we should tax yachts. + +Let's tax yachts. + +Only rich guy have yachts. + +The problem is yachts are + +incredibly elastically demanded. + +So you raise a lot less money +taxing yachts than you think. + +Because guys buy fewer yachts, +and you don't raise as much + +money as you think you would. + +You still raise some, and it +still may be worth it. + +But you raise less +than you think. + +So that's one sort of +observation about this. + +It's basically how much money +you'll raise will be a + +function of how elastic +the demand is. + +The other important observation +to make is why + +it's actually hard for +governments to figure out how + +much money they're going +to raise for a tax. + +Because, to figure it out, +they need to know these + +elasticities. + +That is, the naive thing to do +would have been to say what? + +Well, we're selling 220 million +kilograms of pork. + +That's $1.05. + +We're going to tax +each kilogram. + +So that's 220 million +times $1.05. + +And that's how much +money we raise. + +Well, that's wrong, we +know, because that + +assumes inelastic demand. + +If demand's elastic, they'll +raise less than that. + +Well, if we want to figure out +how much a government is going + +to raise from a tax, they've +got to know what these + +elasticities are. + +And those are actually pretty +hard things to know. + +So that's why there's +uncertainty. + +That's why when politicians will +say, this tax will raise + +x and you'll hear the New York +Times report, the tax will + +raise x, that is a guess. + +Those are guesses, because +they depend on our best + +estimate of the key elasticities +that determine + +how people respond. + +Yeah. + +AUDIENCE: But in Washington +you have tax + +cuts that raise money. + +PROFESSOR: Well, some +claim you do. + +You don't actually. + +But some claim you have tax +cuts that raise money. + +That's because they think the +elasticity is very large. + +If the elasticity is +large enough, a tax + +cut can raise money. + +So, basically, that's all about +that some people think + +that elasticities are large +enough that tax + +cuts can raise money. + +Those people are wrong. + +But that's what they claim. + +Yeah. + +AUDIENCE: [INAUDIBLE PHRASE]. + +PROFESSOR: Yes. + +Excellent point. + +You'll go through that +in section on Friday. + +So what I've done is I've done +an example of a constant + +elasticity curve. + +Actually, I've done something +here which is logically + +inconsistent. + +This curve is linear which means +it can't be constant + +elasticity. + +If it's constant elasticity, +it would have to curve. + +So what I've estimated here +is a local elasticity. + +I have estimated the elasticity + +around that price change. + +But the elasticity, if this +curve is true, would be + +different at different +points on this curve. + +If the elasticity is going to +be constant all over the + +curve, and you're going to do +a constant elasticity of + +demand, that's going to +be a curve that bends, + +not a linear curve. + +So a linear demand curve +is not constant + +elasticity of demand. + +We will typically ignore that +issue and focus on local + +elasticities. + +But that is an important +issue. + +We'll discuss that in section +on Friday, the difference + +between constant elasticity of +demand curves and linear + +demand curves. + +But, typically, we're think +about local changes. + +So if it's local enough, it +doesn't really matter. + +But, for a broad change, it will +matter what the shape of + +the curve is. + +Good point. + +Other questions? + +OK. + +Let me then turn to another +problem we face + +in empirical economics. + +So this is an example of a +problem we're facing in + +empirical economics. + +Let me turn to an example of +another problem we face in + +empirical economics estimating +elasticities. + +It is that individuals often +choose the price they face. + +Individuals, typically, often +don't just face a price that's + +given to them. + +And then you can say, OK, +they're given a price, and we + +see how they respond. + +They often choose the +price they face. + +Let me explain what +I mean by that. + +A classic example of an +elasticity that matters a lot + +for policies is the elasticity +of demand for medical care, + +the elasticity of demand +for medical care. + +That is how much less medical +care will you use if you have + +to pay for it? + +So, for example, most of us have +insurance through MIT or + +maybe through our parents. + +And the way health insurance +works is you pay a certain + +amount per month or your parents +do, and, in return, + +that health insurance covers the +cost of your medical care, + +most of it. + +But, typically, you have +to pay some of it. + +So how many people have +gone to the doctor in + +the last six months? + +Did you have to pay something? + +How much did you pay? + +Did you pay a copayment? + +No? + +None of you? + +Yeah. + +How much did you pay? + +AUDIENCE: I think like $20. + +PROFESSOR: $20, $10, $5, that's +what's called the + +copayment, or $0. + +Most insurance these days has +what's called copayments. + +A copayment is what you pay +when you go to the doctor. + +Insurance picks up the +rest. You don't know. + +You didn't know how much the +whole doctor visit cost. You + +just went, you gave +them your card. + +They said your copayment +is $20. + +You gave them $20. + +You don't know. + +The visit might have cost $100, +$200, $500, $1,000. + +You don't know. + +Your insurer picks up the rest. +You pay the copayment. + +Copayments are rapidly on the +rise in health insurance. + +There's a rapid rise +in copayments. + +Increasingly, insurers are +saying, look, health care + +costs are out of control. + +One way we're going to combat +them is by making people bear + +more of the cost +that they use. + +I could go on forever about +how I'm a health care + +economist. I could go on about +health care forever. + +But just to fix ideas on why +this is an issue, in 1950, the + +US economy spent 5% of our gross +domestic product, 5% of + +our size of the economy +went to health care. + +Today it's 17%. + +By 2075, it's projected +to be 40%. + +That is of every dollar that's +made in America, $0.40 will go + +to medical care. + +By 100 years later, +it's about 100%. + +Literally, if we do nothing, +the entire economy will be + +health care. + +Obviously, that can't happen. + +We've got to deal with this. + +And one way that insurers and +some policy makers are saying + +we need to deal with this is we +need to make consumers bear + +more of the costs of +their medical care. + +We need to make consumers pay +more when they go to the + +doctor, so that they understand +the consequences of + +their decision. + +Well, if we're going to do that, +a key question we need + +to know is well, does it +affect their behavior? + +If we make consumers pay more, +and it doesn't at all affect + +their demand for medical care-- +it's just a tax on + +them, essentially-- + +then that's different than if +it causes them to use less + +medical care. + +It may be good, may be bad. + +We'll come back to that. + +But the key empirical question +is what is the elasticity of + +demand for medical care? + +If you pay $20 and you pay $0, +how much less like are you to + +use the doctor when you pay $20 +versus when you pay $0. + +Well, we can all introspect +this and think about it. + +But, in fact, to answer this we +have to go to the data and + +ask, well, what's +the difference? + +So people, for many years, +went to the data. + +And they said, look, there's all +sorts of differences out + +there across people and what +they pay for their copayments. + +Some people have insurance where +they pay nothing, some + +where they have $20. + +Some people have what they call +high-deductible plans. + +A deductible plan is where you +pay the full cost of your + +visits until you reach +some limit. + +So a $2000 deductible plan will +be one where you pay all + +of your medical costs until +you've spent $2,000. + +It's a big copayment. + +So we look across those people, +and people did. + +And they found, look, the people +that have plans where + +they spend more for health care, +where they have a high + +copayment, use a lot less health +care than where they + +don't have to spend anything. + +The elasticity of demand +looks very, very high. + +What is wrong with +those studies? + +What is wrong with the +conclusion those people drew? + +They drew it by comparing people +who had plans where + +they paid a lot to go to the +doctor, and therefore use a + +lot less care to people who +didn't pay anything when they + +went to the doctor and +used a lot more care. + +I pick the $20 person, because +I picked on you already. + +AUDIENCE: Probably they chose +to have a high-deductible + +plan, because they don't often +go to the doctor already. + +PROFESSOR: The rational choice, +if you're young and + +healthy, for almost everyone in +this room, is going to be a + +very high-deductible, +high copayment plan. + +Because it will cost you less +money, because the insurer is + +shifting the money to you. + +But you don't use the +doctor anyway. + +So who cares? + +So the healthier people are +going to choose the plans + +where they pay more. + +So, of course, you're going to +find in the plans where people + +pay more they use less +medical care. + +But is it because they're paying +more, or is it because + +healthy guys choose +those plans? + +It's causation versus +correlation. + +We don't know. + +Well, how can we figure +that out? + +Well, if we were doctors, what +we'd do-- real doctors, not a + +doctor like me, a real doctor, +a medical doctor-- + +what we'd do is we'd run +a randomized trial. + +So if doctors want to figure +out whether a drug works or + +not, they don't just look at +guys who take the drug versus + +guys who don't. + +They run a randomized trial. + +They randomly assign some people +to take the drug and + +some people not. + +Now, when you run a randomized +trial, by definition, you get + +a causal effect. + +Well, this room isn't +quite big enough. + +We all know the law +of large numbers. + +But imagine there were four +times as many people in this + +room or five times as many +people in this room. + +OK? + +And I had you come +up to the front. + +I flipped a coin and said half +of you are going to take the + +drug, and half of you +are not, randomly by + +the flip of a coin. + +Then, by definition, any +statistically noticeable + +differences I get between the +group the takes the drug and + +the group that doesn't is +caused by the drug. + +And how do I know that? + +Because I know the groups are +otherwise identical by the law + +of large numbers. + +By the law of large numbers, I +know that as long as I have + +enough people, they're +identical. + +So if the only difference +between them is that one's + +taking the drug and one's not, +that's a randomized trial. + +That would be how I could solve +the causation versus + +correlation problem. + +In medicine, thousands of +randomized trials every day + +are being run. + +In fact, the FDA, before it +will approve a drug, will + +typically require a +randomized trial. + +Well, in the social sciences, +it's harder to + +run randomized trials. + +Because we're actually trying +to understand things like + +people's demand for medical +care, not whether a + +drug works or not. + +But, in fact, one of the most +famous social randomized + +trials in history was called +the RAND Health Insurance + +Experiment run in the 1970s. + +This is where some innovative +health economists who + +understood this problem that +we laid out about the fact + +that you can't just compare more +or less generous health + +insurance policies, actually +randomized health insurance + +policies across people. + +They recruited volunteers, and +they literally said, we're + +going to randomize. + +Some people are going to have +policies where the health care + +is free, and some people are +going to have policies where + +they have to pay, essentially, +all the costs of health care. + +So they, essentially, randomized +across these + +different groups. + +And, therefore, they can +assess what the price + +elasticity was. + +Because they knew the price +difference between groups. + +For one, the price was zero. + +For one, the price was one. + +They actually had a range of +prices they varied it across. + +They could look at the quantity +response, and they + +knew that was a quantity +response to the price, because + +people weren't choosing +their prices. + +The prices were being +assigned to them. + +What did they find? + +Well, they found that medical +demand is elastic, although + +not as elastic as the +previous study. + +It's somewhat elastic. + +It's not as elastic as the +previous studies found. + +They found that the elasticity +of demand for medical care is + +around minus 0.2. + +So when the price goes up, +people use less medical care + +but not that much less. + +Now, let's be clear. + +Remember what elasticity is. + +That delta Q over Q. The same +study showed that if you take + +someone who paid nothing and +make them pay almost + +everything, their utilization of +medical care falls by 45%. + +That's consistent with that +small elasticity. + +Because that's a huge delta +P, percent delta P. So, + +basically, that's comes to the +question about local versus + +global elasticities. + +So it's not saying that +prices don't matter. + +But it's not a very, very +elastically demanded good. + +So that's how they measure +that price of + +elasticity of demand. + +That experiment, which was run +over 35 years ago now, that + +result drives much of what +we do in health policy. + +So a lot of the estimates that +we saw for the recently passed + +health reform bill +derived from how + +do we get that estimate. + +We'll have to figure out how +people are going to respond + +with their medical care when we +give them health insurance. + +The recently passed health care +bill just gave 32 million + +people health insurance. + +Well, how are they going +to respond to + +having health insurance? + +We go back to the RAND estimates +and say, well, we + +have this elasticity +of demand. + +We know what we're doing +to the price. + +We figure out how much medical +care is going to go up. + +But here's the other thing. + +Here's the question in +the lecture that + +that we'll close with. + +Is that a good thing or a bad +thing that medical care fell + +when the price went up? + +And how would we tell +whether it's a good + +thing or a bad thing? + +So we know when we raise +the price, people use + +less medical care. + +How can we tell if that's a +good thing or a bad thing? + +In the same experiment, +how could we tell? + +What could we do? + +Yeah. + +AUDIENCE: Maybe you'll get +death rates or like-- + +PROFESSOR: You look +at their health. + +You say, look, the +same trial can + +answer a different question. + +We know that when you charge +someone for health + +care, they use less. + +Well, are they sicker? + +The answer, not at all. + +People use less health +and were no sicker. + +Why? + +Because we waste a huge amount +of health care in the US. + +A huge amount of health +care is wasted. + +So, in fact, we could cut back +quite a lot on health care, + +and we'd be no sicker. + +And that's what the RAND +experiment showed, that we can + +charge people to use +medical providers. + +And they'll use less medical +care, and they won't be sicker + +as a result. + +Which suggests that, actually, +as we try to think about + +getting our health care costs +under control in America, + +making people pay something to +go to the doctor is not a + +crazy thing to be +thinking about. + +How much? + +Well that depends on efficiency +versus equity. + +We can't make someone who has no +income pay $1,000 to go to + +the doctor. + +That, clearly, is a mistake. + +But we can take a rich guy like +me and make me pay $50 to + +go to the doctor. + +There's no reason +not to do that. + +So, basically, that's a lesson +of how you can use elasticity + +of demand to help inform +the kind of + +policies we need to make. + +OK, let me stop there. + +By the way, if you at all find +this stuff interesting, and + +you haven't yet read +Freakonomics-- + +how many of you have +read Freakonomics? + +That's amazing. + +OK. + +If you haven't read +Freakonomics, you should. + +It's a great book. + +If you're lazy, the movie +is coming out. + +And Freakonomics the movie +is premiering on + +Friday the 30th at LSC. + +So if you're interested in +learning more about empirical + +tools in economics, you can +watch Freakonomics the movie + +on Friday the 30th. \ No newline at end of file diff --git a/Ykep0YaxgYw.txt b/Ykep0YaxgYw.txt new file mode 100644 index 0000000000000000000000000000000000000000..d92724324d2a64dbf9f643cfb74792ff0f47a86f --- /dev/null +++ b/Ykep0YaxgYw.txt @@ -0,0 +1,233 @@ +User-mode programs need to communicate with +the OS to request service or get access to + +useful OS data like the time of day. + +But if they're running in a different MMU +context than the OS, they don't have direct + +access to OS code and data. + +And that might be bad idea in any case: +the OS is usually responsible for implementing + +security and access policies and other users +of the system would be upset if any random + +user program could circumvent those protections. + +What's needed is the ability for user-mode +programs to call OS code at specific entry + +points, using registers or the user-mode virtual +memory to send or receive information. + +We'd use these "supervisor calls" to access +a well-documented and secure OS application + +programming interface (API). + +An example of such an interface is POSIX (https://en.wikipedia.org/wiki/POSIX), +a standard interface implemented by many Unix-like + +operating systems. + +As it turns out, we have a way of transferring +control from a user-mode program to a specific + +OS handler - just execute an illegal instruction! + +We'll adopt the convention of using illegal +instructions with an opcode field of 1 to + +serve as supervisor calls. + +The low order bits of these SVC instructions +will contain an index indicating which SVC + +service we're trying to access. + +Let's see how this would work. + +Here's our user-mode/kernel-mode diagram again. + +Note that the user-mode programs contain supervisor +calls with different indices, which when executed + +are intended to serve as requests for different +OS services. + +When an SVC instruction is executed, the hardware +detects the opcode field of 1 as an illegal + +instruction and triggers an exception that +runs the OS IllOp handler, as we saw in the + +previous segment. + +The handler saves the process state in the +temporary storage area, then dispatches to + +the appropriate handler based on the opcode +field. + +This handler can access the user's registers +in the temporary storage area, or using the + +appropriate OS subroutines can access the +contents of any user-mode virtual address. + +If information is to be returned to the user, +the return values can be stored in the temporary + +storage area, overwriting, say, the saved +contents of the user's R0 register. + +Then, when the handler completes, the potentially-updated +saved register values are reloaded into the + +CPU registers +and execution of the user-mode program resumes + +at the instruction following the supervisor +call. + +In the previous segment we saw how the illegal +instruction handler uses a dispatch table + +to choose the appropriate sub-handler depending +on the opcode field of the illegal instruction. + +In this slide we see the sub-handler for SVC +instructions, i.e., those with an opcode field + +of 1. + +This code uses the low-order bits of the instruction +to access another dispatch table to select + +the appropriate code for each of the eight +possible SVCs. + +Our Tiny OS only has a meagre selection of +simple services. + +A real OS would have SVCs for accessing files, +dealing with network connections, managing + +virtual memory, spawning new processes, and +so on. + +Here's the code for resuming execution of +the user-mode process when the SVC handler + +is done: +simply restore the saved values for the registers + +and JMP to resume execution at the instruction +following the SVC instruction. + +There are times when for some reason the SVC +request cannot be completed and the request + +should be retried in the future. + +For example, the ReadCh SVC returns the next +character typed by the user, but if no character + +has yet been typed, the OS cannot complete +the request at this time. + +In this case, the SVC handler should branch +to I_Wait, which arranges for the SVC instruction + +to be re-executed next time this process runs +and then calls Scheduler() to run the next + +process. + +This gives all the other processes a chance +to run before the SVC is tried again, hopefully + +this time successfully. + +You can see that this code also serves as +the implementation for two different SVCs! + +A process can give up the remainder of its +current execution time slice by calling the + +Yield() SVC. + +This simply causes the OS to call Scheduler(), +suspending execution of the current process + +until its next turn in the round-robin scheduling +process. + +And to stop execution, a process can call +the Halt() SVC. + +Looking at the implementation, we can see +that "halt" is a bit of misnomer. + +What really happens is that the system arranges +to re-execute the Halt() SVC each time the + +process is scheduled, which then causes the +OS to schedule the next process for execution. + +The process appears to halt since the instruction +following the Halt() SVC is never executed. + +Adding new SVC handlers is straightforward. + +First we need to define new SVC macros for +use in user-mode programs. + +In this example, we're defining SVCs for getting +and setting the time of day. + +Since these are the eighth and ninth SVCs, +we need to make a small adjustment to the + +SVC dispatch code and then add the appropriate +entries to the end of the dispatch table. + +The code for the new handlers is equally straightforward. + +The handler can access the value of the program's +R0 by looking at the correct entry in the + +UserMState temporary holding area. + +It just takes a few instructions to implement +the desired operations. + +The SVC mechanism provides controlled access +to OS services and data. + +As we'll see in a few lectures, it'll be useful +that SVC handlers can't be interrupted since + +they are running in supervisor mode where +interrupts are disabled. + +So, for example, if we need to increment a +value in main memory, using a LD/ADDC/ST sequence, + +but we want to ensure no other process execution +intervenes between the LD and the ST, + +we can encapsulate the required functionality +as an SVC, which is guaranteed to be uninterruptible. + +We've made an excellent start at exploring +the implementation of a simple time-shared + +operating system. + +We'll continue the exploration in the next +lecture when we see how the OS deals with + +external input/output devices. \ No newline at end of file diff --git a/Zk91WpvA0-c.txt b/Zk91WpvA0-c.txt new file mode 100644 index 0000000000000000000000000000000000000000..8467cb348b3a64b9e8eb5ec85fceb30428aaa74a --- /dev/null +++ b/Zk91WpvA0-c.txt @@ -0,0 +1,14243 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following content is provided by MIT +open courseware under a Creative Commons + + align:start position:0% +open courseware under a Creative Commons + + + align:start position:0% +open courseware under a Creative Commons +license additional information about our + + align:start position:0% +license additional information about our + + + align:start position:0% +license additional information about our +license and MIT open courseware in + + align:start position:0% +license and MIT open courseware in + + + align:start position:0% +license and MIT open courseware in +general is available at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu uh next week this is our + + align:start position:0% +ocw.mit.edu uh next week this is our + + + align:start position:0% +ocw.mit.edu uh next week this is our +next to last lecture I'll be giving uh + + align:start position:0% +next to last lecture I'll be giving uh + + + align:start position:0% +next to last lecture I'll be giving uh +the last lecture in the series next + + align:start position:0% +the last lecture in the series next + + + align:start position:0% +the last lecture in the series next +Monday night at 6 um and the title of my + + align:start position:0% +Monday night at 6 um and the title of my + + + align:start position:0% +Monday night at 6 um and the title of my +talk is uh to see is the root of idea + + align:start position:0% +talk is uh to see is the root of idea + + + align:start position:0% +talk is uh to see is the root of idea +in fact uh the word idea comes from the + + align:start position:0% +in fact uh the word idea comes from the + + + align:start position:0% +in fact uh the word idea comes from the +Greek verb to see uh so I'll be talking + + align:start position:0% +Greek verb to see uh so I'll be talking + + + align:start position:0% +Greek verb to see uh so I'll be talking +both about my own work and reflecting on + + align:start position:0% +both about my own work and reflecting on + + + align:start position:0% +both about my own work and reflecting on +the series uh as a whole but tonight we + + align:start position:0% +the series uh as a whole but tonight we + + + align:start position:0% +the series uh as a whole but tonight we +have with us lesie Tuttle who has had a + + align:start position:0% +have with us lesie Tuttle who has had a + + + align:start position:0% +have with us lesie Tuttle who has had a +couple of different careers she started + + align:start position:0% +couple of different careers she started + + + align:start position:0% +couple of different careers she started +out in the first 10 years as a + + align:start position:0% +out in the first 10 years as a + + + align:start position:0% +out in the first 10 years as a +photojournalist working for a Turkish + + align:start position:0% +photojournalist working for a Turkish + + + align:start position:0% +photojournalist working for a Turkish +development + + align:start position:0% +development + + + align:start position:0% +development +foundation and uh Oxfam America + + align:start position:0% +foundation and uh Oxfam America + + + align:start position:0% +foundation and uh Oxfam America +photographing in turkey and then she + + align:start position:0% +photographing in turkey and then she + + + align:start position:0% +photographing in turkey and then she +came back to the US got her MBA and + + align:start position:0% +came back to the US got her MBA and + + + align:start position:0% +came back to the US got her MBA and +worked for 8 years setting up uh uh + + align:start position:0% +worked for 8 years setting up uh uh + + + align:start position:0% +worked for 8 years setting up uh uh +nonprofit firm here in um Cambridge + + align:start position:0% +nonprofit firm here in um Cambridge + + + align:start position:0% +nonprofit firm here in um Cambridge +called consens the consensus building + + align:start position:0% +called consens the consensus building + + + align:start position:0% +called consens the consensus building +Institute in 2000 she was contacted by + + align:start position:0% +Institute in 2000 she was contacted by + + + align:start position:0% +Institute in 2000 she was contacted by +one of the + + align:start position:0% +one of the + + + align:start position:0% +one of the +children uh who was living in London uh + + align:start position:0% +children uh who was living in London uh + + + align:start position:0% +children uh who was living in London uh +in 2000 one of the children that she had + + align:start position:0% +in 2000 one of the children that she had + + + align:start position:0% +in 2000 one of the children that she had +photographed in the Turkish V one of of + + align:start position:0% +photographed in the Turkish V one of of + + + align:start position:0% +photographed in the Turkish V one of of +the Turkish villages in the + + align:start position:0% +the Turkish villages in the + + + align:start position:0% +the Turkish villages in the +1970s because he knew that she had these + + align:start position:0% +1970s because he knew that she had these + + + align:start position:0% +1970s because he knew that she had these +photographs of his village and there was + + align:start position:0% +photographs of his village and there was + + + align:start position:0% +photographs of his village and there was +a photography exhibit being organized in + + align:start position:0% +a photography exhibit being organized in + + + align:start position:0% +a photography exhibit being organized in +London of the past 50 years of this + + align:start position:0% +London of the past 50 years of this + + + align:start position:0% +London of the past 50 years of this +particular Turkish Village they invited + + align:start position:0% +particular Turkish Village they invited + + + align:start position:0% +particular Turkish Village they invited +Lesley to contribute photographs to this + + align:start position:0% +Lesley to contribute photographs to this + + + align:start position:0% +Lesley to contribute photographs to this +exhibit and curious she decided to go + + align:start position:0% +exhibit and curious she decided to go + + + align:start position:0% +exhibit and curious she decided to go +back to the Turkish Village and + + align:start position:0% +back to the Turkish Village and + + + align:start position:0% +back to the Turkish Village and +reacquaint herself with the people there + + align:start position:0% +reacquaint herself with the people there + + + align:start position:0% +reacquaint herself with the people there +and that started off on a whole other + + align:start position:0% +and that started off on a whole other + + + align:start position:0% +and that started off on a whole other +project which she's going to share with + + align:start position:0% +project which she's going to share with + + + align:start position:0% +project which she's going to share with +you tonight um the early photographs in + + align:start position:0% +you tonight um the early photographs in + + + align:start position:0% +you tonight um the early photographs in +the 1970s being in black and white and + + align:start position:0% +the 1970s being in black and white and + + + align:start position:0% +the 1970s being in black and white and +the more recent work since 2000 is in + + align:start position:0% +the more recent work since 2000 is in + + + align:start position:0% +the more recent work since 2000 is in +color welcome Wesley thank + + align:start position:0% +color welcome Wesley thank + + + align:start position:0% +color welcome Wesley thank +you well um I have talked for about 45 + + align:start position:0% +you well um I have talked for about 45 + + + align:start position:0% +you well um I have talked for about 45 +minutes and show you about a 100 + + align:start position:0% +minutes and show you about a 100 + + + align:start position:0% +minutes and show you about a 100 +photographs sometimes quickly and + + align:start position:0% +photographs sometimes quickly and + + + align:start position:0% +photographs sometimes quickly and +sometimes pausing to more to say about + + align:start position:0% +sometimes pausing to more to say about + + + align:start position:0% +sometimes pausing to more to say about +certain ones and then I look forward to + + align:start position:0% +certain ones and then I look forward to + + + align:start position:0% +certain ones and then I look forward to +Professor robot's commentary and I'm + + align:start position:0% +Professor robot's commentary and I'm + + + align:start position:0% +Professor robot's commentary and I'm +happy that there are people here not + + align:start position:0% +happy that there are people here not + + + align:start position:0% +happy that there are people here not +just from this academic world but from + + align:start position:0% +just from this academic world but from + + + align:start position:0% +just from this academic world but from +other worlds of TV and radio production + + align:start position:0% +other worlds of TV and radio production + + + align:start position:0% +other worlds of TV and radio production +that might also join in to make the + + align:start position:0% +that might also join in to make the + + + align:start position:0% +that might also join in to make the +conversation um + + align:start position:0% +conversation um + + + align:start position:0% +conversation um +Lively + + align:start position:0% +Lively + + + align:start position:0% +Lively +so let me + + align:start position:0% +so let me + + + align:start position:0% +so let me +begin + + align:start position:0% +begin + + + align:start position:0% +begin +um today is May 1st International + + align:start position:0% +um today is May 1st International + + + align:start position:0% +um today is May 1st International +workers day I mentioned this because I'm + + align:start position:0% +workers day I mentioned this because I'm + + + align:start position:0% +workers day I mentioned this because I'm +thinking about how profound being in a + + align:start position:0% +thinking about how profound being in a + + + align:start position:0% +thinking about how profound being in a +certain place at a certain time can be + + align:start position:0% +certain place at a certain time can be + + + align:start position:0% +certain place at a certain time can be +in terms of experiencing catalytic + + align:start position:0% +in terms of experiencing catalytic + + + align:start position:0% +in terms of experiencing catalytic +public events on this day in + + align:start position:0% +public events on this day in + + + align:start position:0% +public events on this day in +1977 I was in tuxum square Istanbul's + + align:start position:0% +1977 I was in tuxum square Istanbul's + + + align:start position:0% +1977 I was in tuxum square Istanbul's +largest modern Square along with + + align:start position:0% +largest modern Square along with + + + align:start position:0% +largest modern Square along with +thousands of families students and + + align:start position:0% +thousands of families students and + + + align:start position:0% +thousands of families students and +workers who were out there in a holiday + + align:start position:0% +workers who were out there in a holiday + + + align:start position:0% +workers who were out there in a holiday +mood to celebrate International workers + + align:start position:0% +mood to celebrate International workers + + + align:start position:0% +mood to celebrate International workers +day it was during a period of political + + align:start position:0% +day it was during a period of political + + + align:start position:0% +day it was during a period of political +Anarchy so some say it was the CIA and + + align:start position:0% +Anarchy so some say it was the CIA and + + + align:start position:0% +Anarchy so some say it was the CIA and +some say it was the Turkish military who + + align:start position:0% +some say it was the Turkish military who + + + align:start position:0% +some say it was the Turkish military who +allowed snipers to go to the rooftops of + + align:start position:0% +allowed snipers to go to the rooftops of + + + align:start position:0% +allowed snipers to go to the rooftops of +the hotels in talkx him and fire shots + + align:start position:0% +the hotels in talkx him and fire shots + + + align:start position:0% +the hotels in talkx him and fire shots +down upon the crowd causing panic and + + align:start position:0% +down upon the crowd causing panic and + + + align:start position:0% +down upon the crowd causing panic and +Stampede although I'd been in protests + + align:start position:0% +Stampede although I'd been in protests + + + align:start position:0% +Stampede although I'd been in protests +and riots in the US during the Vietnam + + align:start position:0% +and riots in the US during the Vietnam + + + align:start position:0% +and riots in the US during the Vietnam +era I'd never feed for my feared for my + + align:start position:0% +era I'd never feed for my feared for my + + + align:start position:0% +era I'd never feed for my feared for my +life quite as much as I did Den in there + + align:start position:0% +life quite as much as I did Den in there + + + align:start position:0% +life quite as much as I did Den in there +34 people were killed and many were + + align:start position:0% +34 people were killed and many were + + + align:start position:0% +34 people were killed and many were +crushed and + + align:start position:0% +crushed and + + + align:start position:0% +crushed and +injured there are May 1st 911s and + + align:start position:0% +injured there are May 1st 911s and + + + align:start position:0% +injured there are May 1st 911s and +hurricane katrinas in many of our Lives + + align:start position:0% +hurricane katrinas in many of our Lives + + + align:start position:0% +hurricane katrinas in many of our Lives +when being there at a certain place and + + align:start position:0% +when being there at a certain place and + + + align:start position:0% +when being there at a certain place and +then at a specific moment makes makes + + align:start position:0% +then at a specific moment makes makes + + + align:start position:0% +then at a specific moment makes makes +for unforgettable and irrevocable + + align:start position:0% +for unforgettable and irrevocable + + + align:start position:0% +for unforgettable and irrevocable +drama however I'm not here to talk about + + align:start position:0% +drama however I'm not here to talk about + + + align:start position:0% +drama however I'm not here to talk about +a single abrupt life-changing event + + align:start position:0% +a single abrupt life-changing event + + + align:start position:0% +a single abrupt life-changing event +rather I'm here to describe significant + + align:start position:0% +rather I'm here to describe significant + + + align:start position:0% +rather I'm here to describe significant +changes that occurred in over 30 women + + align:start position:0% +changes that occurred in over 30 women + + + align:start position:0% +changes that occurred in over 30 women +uh 30 years to a group of people that + + align:start position:0% +uh 30 years to a group of people that + + + align:start position:0% +uh 30 years to a group of people that +all came from the same place I will show + + align:start position:0% +all came from the same place I will show + + + align:start position:0% +all came from the same place I will show +the place they came from where they went + + align:start position:0% +the place they came from where they went + + + align:start position:0% +the place they came from where they went +and how migration changed + + align:start position:0% +and how migration changed + + + align:start position:0% +and how migration changed +them this is the story about how change + + align:start position:0% +them this is the story about how change + + + align:start position:0% +them this is the story about how change +of place can cause dramatic shifts in + + align:start position:0% +of place can cause dramatic shifts in + + + align:start position:0% +of place can cause dramatic shifts in +people's + + align:start position:0% +people's + + + align:start position:0% +people's +lives it's not news to any of you that + + align:start position:0% +lives it's not news to any of you that + + + align:start position:0% +lives it's not news to any of you that +Urban migration changes how people think + + align:start position:0% +Urban migration changes how people think + + + align:start position:0% +Urban migration changes how people think +and live as city planners Architects and + + align:start position:0% +and live as city planners Architects and + + + align:start position:0% +and live as city planners Architects and +21st century citizens this phenomena is + + align:start position:0% +21st century citizens this phenomena is + + + align:start position:0% +21st century citizens this phenomena is +very + + align:start position:0% +very + + + align:start position:0% +very +apparent I'm not a sociologist a visual + + align:start position:0% +apparent I'm not a sociologist a visual + + + align:start position:0% +apparent I'm not a sociologist a visual +Anthropologist or a city planner I'm a + + align:start position:0% +Anthropologist or a city planner I'm a + + + align:start position:0% +Anthropologist or a city planner I'm a +photojournalist in the 70s and 80s I + + align:start position:0% +photojournalist in the 70s and 80s I + + + align:start position:0% +photojournalist in the 70s and 80s I +worked for 10 years for not for-profits + + align:start position:0% +worked for 10 years for not for-profits + + + align:start position:0% +worked for 10 years for not for-profits +including Oxfam America where my job was + + align:start position:0% +including Oxfam America where my job was + + + align:start position:0% +including Oxfam America where my job was +to show through individual stories in + + align:start position:0% +to show through individual stories in + + + align:start position:0% +to show through individual stories in +pictures and words how economic and + + align:start position:0% +pictures and words how economic and + + + align:start position:0% +pictures and words how economic and +social development might occur starting + + align:start position:0% +social development might occur starting + + + align:start position:0% +social development might occur starting +from the bottom up we were very + + align:start position:0% +from the bottom up we were very + + + align:start position:0% +from the bottom up we were very +idealistic there is an ongoing debate in + + align:start position:0% +idealistic there is an ongoing debate in + + + align:start position:0% +idealistic there is an ongoing debate in +photojournalism or social documentary + + align:start position:0% +photojournalism or social documentary + + + align:start position:0% +photojournalism or social documentary +photography about the role of the + + align:start position:0% +photography about the role of the + + + align:start position:0% +photography about the role of the +photographer the photographer's ability + + align:start position:0% +photographer the photographer's ability + + + align:start position:0% +photographer the photographer's ability +or even attempt to be objective and + + align:start position:0% +or even attempt to be objective and + + + align:start position:0% +or even attempt to be objective and +about the vit Al ity or effectiveness of + + align:start position:0% +about the vit Al ity or effectiveness of + + + align:start position:0% +about the vit Al ity or effectiveness of +telling stories with an agenda in mind + + align:start position:0% +telling stories with an agenda in mind + + + align:start position:0% +telling stories with an agenda in mind +it interests me to discuss these issues + + align:start position:0% +it interests me to discuss these issues + + + align:start position:0% +it interests me to discuss these issues +and I would gladly do so as I'm not an + + align:start position:0% +and I would gladly do so as I'm not an + + + align:start position:0% +and I would gladly do so as I'm not an +academic I have no claim to a + + align:start position:0% +academic I have no claim to a + + + align:start position:0% +academic I have no claim to a +significant statistical pool or a + + align:start position:0% +significant statistical pool or a + + + align:start position:0% +significant statistical pool or a +generalized Theory but this position I + + align:start position:0% +generalized Theory but this position I + + + align:start position:0% +generalized Theory but this position I +will defend and present here is that by + + align:start position:0% +will defend and present here is that by + + + align:start position:0% +will defend and present here is that by +sharing the stories of things we have + + align:start position:0% +sharing the stories of things we have + + + align:start position:0% +sharing the stories of things we have +personally witnessed we may be able to + + align:start position:0% +personally witnessed we may be able to + + + align:start position:0% +personally witnessed we may be able to +deepen and broaden other people's view + + align:start position:0% +deepen and broaden other people's view + + + align:start position:0% +deepen and broaden other people's view +as the world views of the world just as + + align:start position:0% +as the world views of the world just as + + + align:start position:0% +as the world views of the world just as +storytelling reaches from one generation + + align:start position:0% +storytelling reaches from one generation + + + align:start position:0% +storytelling reaches from one generation +to the next in all cultures and in many + + align:start position:0% +to the next in all cultures and in many + + + align:start position:0% +to the next in all cultures and in many +forms often with lasting lessons and + + align:start position:0% +forms often with lasting lessons and + + + align:start position:0% +forms often with lasting lessons and +insights worth + + align:start position:0% +insights worth + + + align:start position:0% +insights worth +sharing my claim my story in words and + + align:start position:0% +sharing my claim my story in words and + + + align:start position:0% +sharing my claim my story in words and +photographs is about how Urban migration + + align:start position:0% +photographs is about how Urban migration + + + align:start position:0% +photographs is about how Urban migration +made feminists out of very traditional + + align:start position:0% +made feminists out of very traditional + + + align:start position:0% +made feminists out of very traditional +village women this is something I + + align:start position:0% +village women this is something I + + + align:start position:0% +village women this is something I +discovered and I decided I wanted to + + align:start position:0% +discovered and I decided I wanted to + + + align:start position:0% +discovered and I decided I wanted to +show it to others these stories are also + + align:start position:0% +show it to others these stories are also + + + align:start position:0% +show it to others these stories are also +about + + align:start position:0% +about + + + align:start position:0% +about +the oops the + + align:start position:0% +the oops the + + + align:start position:0% +the oops the +little that's goodbye um these stories + + align:start position:0% +little that's goodbye um these stories + + + align:start position:0% +little that's goodbye um these stories +are also about how the impact of and + + align:start position:0% +are also about how the impact of and + + + align:start position:0% +are also about how the impact of and +outcomes of migration vary for different + + align:start position:0% +outcomes of migration vary for different + + + align:start position:0% +outcomes of migration vary for different +individuals depending upon who they are + + align:start position:0% +individuals depending upon who they are + + + align:start position:0% +individuals depending upon who they are +and where they + + align:start position:0% +and where they + + + align:start position:0% +and where they +went it appears from the women that I + + align:start position:0% +went it appears from the women that I + + + align:start position:0% +went it appears from the women that I +met that going to a major city in + + align:start position:0% +met that going to a major city in + + + align:start position:0% +met that going to a major city in +another country might not provide as + + align:start position:0% +another country might not provide as + + + align:start position:0% +another country might not provide as +great an improvement as migrating to a + + align:start position:0% +great an improvement as migrating to a + + + align:start position:0% +great an improvement as migrating to a +city in your own country in this case + + align:start position:0% +city in your own country in this case + + + align:start position:0% +city in your own country in this case +turkey then there are those who + + align:start position:0% +turkey then there are those who + + + align:start position:0% +turkey then there are those who +ultimately um return to the Village the + + align:start position:0% +ultimately um return to the Village the + + + align:start position:0% +ultimately um return to the Village the +way people recollect The Village Life is + + align:start position:0% +way people recollect The Village Life is + + + align:start position:0% +way people recollect The Village Life is +also a part of the story along with + + align:start position:0% +also a part of the story along with + + + align:start position:0% +also a part of the story along with +their General Reflections about what has + + align:start position:0% +their General Reflections about what has + + + align:start position:0% +their General Reflections about what has +been lost and what has been gained by + + align:start position:0% +been lost and what has been gained by + + + align:start position:0% +been lost and what has been gained by +the move to urban + + align:start position:0% +the move to urban + + + align:start position:0% +the move to urban +areas lastly I will look at the meaning + + align:start position:0% +areas lastly I will look at the meaning + + + align:start position:0% +areas lastly I will look at the meaning +of the V that the village holds for some + + align:start position:0% +of the V that the village holds for some + + + align:start position:0% +of the V that the village holds for some +of these people + + align:start position:0% +of these people + + + align:start position:0% +of these people +today if these stories serve no other + + align:start position:0% +today if these stories serve no other + + + align:start position:0% +today if these stories serve no other +purpose than to challenge you to rethink + + align:start position:0% +purpose than to challenge you to rethink + + + align:start position:0% +purpose than to challenge you to rethink +your assumptions and I'm borrowing this + + align:start position:0% +your assumptions and I'm borrowing this + + + align:start position:0% +your assumptions and I'm borrowing this +phrase from Martin creger who was here + + align:start position:0% +phrase from Martin creger who was here + + + align:start position:0% +phrase from Martin creger who was here +last week then I think it will be worth + + align:start position:0% +last week then I think it will be worth + + + align:start position:0% +last week then I think it will be worth +the effort the subtitle by the way that + + align:start position:0% +the effort the subtitle by the way that + + + align:start position:0% +the effort the subtitle by the way that +I've always wanted to use the story for + + align:start position:0% +I've always wanted to use the story for + + + align:start position:0% +I've always wanted to use the story for +these stories is don't judge a Woman by + + align:start position:0% +these stories is don't judge a Woman by + + + align:start position:0% +these stories is don't judge a Woman by +her + + align:start position:0% + + + + align:start position:0% + +headscarf the people you're about to see + + align:start position:0% +headscarf the people you're about to see + + + align:start position:0% +headscarf the people you're about to see +were all born in the same Village Top + + align:start position:0% +were all born in the same Village Top + + + align:start position:0% +were all born in the same Village Top +parich near seas in central turkey all + + align:start position:0% +parich near seas in central turkey all + + + align:start position:0% +parich near seas in central turkey all +of the black and white photos are from + + align:start position:0% +of the black and white photos are from + + + align:start position:0% +of the black and white photos are from +1974 to 1978 everything in color is from + + align:start position:0% +1974 to 1978 everything in color is from + + + align:start position:0% +1974 to 1978 everything in color is from +2000 to + + align:start position:0% +2000 to + + + align:start position:0% +2000 to +2004 I was working in the 1970s as a + + align:start position:0% +2004 I was working in the 1970s as a + + + align:start position:0% +2004 I was working in the 1970s as a +photojournalist um for a Turkish + + align:start position:0% +photojournalist um for a Turkish + + + align:start position:0% +photojournalist um for a Turkish +development foundation based in anara + + align:start position:0% +development foundation based in anara + + + align:start position:0% +development foundation based in anara +one of my colleagues vas was from this + + align:start position:0% +one of my colleagues vas was from this + + + align:start position:0% +one of my colleagues vas was from this +Village in central anatolio where he + + align:start position:0% +Village in central anatolio where he + + + align:start position:0% +Village in central anatolio where he +brought me and introduced me to the + + align:start position:0% +brought me and introduced me to the + + + align:start position:0% +brought me and introduced me to the +people and to the + + align:start position:0% +people and to the + + + align:start position:0% +people and to the +place a key character in this story is + + align:start position:0% +place a key character in this story is + + + align:start position:0% +place a key character in this story is +fim may I met fim May on my first visit + + align:start position:0% +fim may I met fim May on my first visit + + + align:start position:0% +fim may I met fim May on my first visit +to top parich in + + align:start position:0% +to top parich in + + + align:start position:0% +to top parich in +1975 fim May and I were both 25 years + + align:start position:0% +1975 fim May and I were both 25 years + + + align:start position:0% +1975 fim May and I were both 25 years +old only I was a single American and she + + align:start position:0% +old only I was a single American and she + + + align:start position:0% +old only I was a single American and she +had been married at age 13 and was + + align:start position:0% +had been married at age 13 and was + + + align:start position:0% +had been married at age 13 and was +pregnant with her sixth + + align:start position:0% +pregnant with her sixth + + + align:start position:0% +pregnant with her sixth +child but there she was harvesting wheat + + align:start position:0% +child but there she was harvesting wheat + + + align:start position:0% +child but there she was harvesting wheat +with a side in the middle of the field + + align:start position:0% +with a side in the middle of the field + + + align:start position:0% +with a side in the middle of the field +in the midday Sun she dropped everything + + align:start position:0% +in the midday Sun she dropped everything + + + align:start position:0% +in the midday Sun she dropped everything +and made us tea right out there in the + + align:start position:0% +and made us tea right out there in the + + + align:start position:0% +and made us tea right out there in the +middle of the + + align:start position:0% +middle of the + + + align:start position:0% +middle of the +field I looked at her with + + align:start position:0% +field I looked at her with + + + align:start position:0% +field I looked at her with +awe uh she says about herself and some + + align:start position:0% +awe uh she says about herself and some + + + align:start position:0% +awe uh she says about herself and some +of the + + align:start position:0% +of the + + + align:start position:0% +of the +woman of the her friends at the time + + align:start position:0% +woman of the her friends at the time + + + align:start position:0% +woman of the her friends at the time +that the work was on the back of the + + align:start position:0% +that the work was on the back of the + + + align:start position:0% +that the work was on the back of the +women that we were like + + align:start position:0% +women that we were like + + + align:start position:0% +women that we were like +Stones a bond of friendship grew between + + align:start position:0% +Stones a bond of friendship grew between + + + align:start position:0% +Stones a bond of friendship grew between +us and even though I left the country + + align:start position:0% +us and even though I left the country + + + align:start position:0% +us and even though I left the country +for more than two decades she and the + + align:start position:0% +for more than two decades she and the + + + align:start position:0% +for more than two decades she and the +other women haunted me I needed to see + + align:start position:0% +other women haunted me I needed to see + + + align:start position:0% +other women haunted me I needed to see +what had become of them 25 years later I + + align:start position:0% +what had become of them 25 years later I + + + align:start position:0% +what had become of them 25 years later I +went back to fim's Village to find out + + align:start position:0% +went back to fim's Village to find out + + + align:start position:0% +went back to fim's Village to find out +whether our friendship had been + + align:start position:0% +whether our friendship had been + + + align:start position:0% +whether our friendship had been +ephemeral as it turned out our + + align:start position:0% +ephemeral as it turned out our + + + align:start position:0% +ephemeral as it turned out our +connection was + + align:start position:0% +connection was + + + align:start position:0% +connection was +immediate she told me about the major + + align:start position:0% +immediate she told me about the major + + + align:start position:0% +immediate she told me about the major +transitions in her life she had been + + align:start position:0% +transitions in her life she had been + + + align:start position:0% +transitions in her life she had been +elected The Village me leader the MTAR + + align:start position:0% +elected The Village me leader the MTAR + + + align:start position:0% +elected The Village me leader the MTAR +her children had migrated to Turkish + + align:start position:0% +her children had migrated to Turkish + + + align:start position:0% +her children had migrated to Turkish +cities and + + align:start position:0% +cities and + + + align:start position:0% +cities and +England what the + + align:start position:0% +England what the + + + align:start position:0% +England what the +name topar is near conal Andor + + align:start position:0% +name topar is near conal Andor + + + align:start position:0% +name topar is near conal Andor +sias + + align:start position:0% +sias + + + align:start position:0% +sias +um after hearing and seeing uh the + + align:start position:0% +um after hearing and seeing uh the + + + align:start position:0% +um after hearing and seeing uh the +dramatic changes that I had occurred in + + align:start position:0% +dramatic changes that I had occurred in + + + align:start position:0% +dramatic changes that I had occurred in +the village including the end of of + + align:start position:0% +the village including the end of of + + + align:start position:0% +the village including the end of of +animal husbandry I set about to tell her + + align:start position:0% +animal husbandry I set about to tell her + + + align:start position:0% +animal husbandry I set about to tell her +story and to tell the story of the other + + align:start position:0% +story and to tell the story of the other + + + align:start position:0% +story and to tell the story of the other +village women + + align:start position:0% +village women + + + align:start position:0% +village women +let's start by looking back at Village + + align:start position:0% +let's start by looking back at Village + + + align:start position:0% +let's start by looking back at Village +Life in this place in the + + align:start position:0% +Life in this place in the + + + align:start position:0% +Life in this place in the +1970s topar dit is a is a Kurdish + + align:start position:0% +1970s topar dit is a is a Kurdish + + + align:start position:0% +1970s topar dit is a is a Kurdish +Village and therefore it was settled in + + align:start position:0% +Village and therefore it was settled in + + + align:start position:0% +Village and therefore it was settled in +a Hidden Valley so the Turkish milissa + + align:start position:0% +a Hidden Valley so the Turkish milissa + + + align:start position:0% +a Hidden Valley so the Turkish milissa +couldn't find them when they were + + align:start position:0% +couldn't find them when they were + + + align:start position:0% +couldn't find them when they were +looking for conscripts and + + align:start position:0% +looking for conscripts and + + + align:start position:0% +looking for conscripts and +taxes this Village was inaccessible by + + align:start position:0% +taxes this Village was inaccessible by + + + align:start position:0% +taxes this Village was inaccessible by +public transportation perhaps a two-hour + + align:start position:0% +public transportation perhaps a two-hour + + + align:start position:0% +public transportation perhaps a two-hour +walk to the nearest ride there was no + + align:start position:0% +walk to the nearest ride there was no + + + align:start position:0% +walk to the nearest ride there was no +electricity until + + align:start position:0% +electricity until + + + align:start position:0% +electricity until +1985 there was one Central Village well + + align:start position:0% +1985 there was one Central Village well + + + align:start position:0% +1985 there was one Central Village well +over a period of 30 years there was + + align:start position:0% +over a period of 30 years there was + + + align:start position:0% +over a period of 30 years there was +never more than a primary school mostly + + align:start position:0% +never more than a primary school mostly + + + align:start position:0% +never more than a primary school mostly +attended by boys and now there's no + + align:start position:0% +attended by boys and now there's no + + + align:start position:0% +attended by boys and now there's no +school at + + align:start position:0% +school at + + + align:start position:0% +school at +all The Village's subsistence came from + + align:start position:0% +all The Village's subsistence came from + + + align:start position:0% +all The Village's subsistence came from +animal husbandry mostly sheep and goats + + align:start position:0% +animal husbandry mostly sheep and goats + + + align:start position:0% +animal husbandry mostly sheep and goats +but with some families having a few cows + + align:start position:0% +but with some families having a few cows + + + align:start position:0% +but with some families having a few cows +and + + align:start position:0% +and + + + align:start position:0% +and +chickens people ate meat perhaps once a + + align:start position:0% +chickens people ate meat perhaps once a + + + align:start position:0% +chickens people ate meat perhaps once a +meet or when a visitor like myself + + align:start position:0% +meet or when a visitor like myself + + + align:start position:0% +meet or when a visitor like myself +appeared they produced cheese and milk + + align:start position:0% +appeared they produced cheese and milk + + + align:start position:0% +appeared they produced cheese and milk +and uh yogurt rather they grew wheat and + + align:start position:0% +and uh yogurt rather they grew wheat and + + + align:start position:0% +and uh yogurt rather they grew wheat and +barley and did some seasonal tradings + + align:start position:0% +barley and did some seasonal tradings + + + align:start position:0% +barley and did some seasonal tradings +with the vendors in town for tea and + + align:start position:0% +with the vendors in town for tea and + + + align:start position:0% +with the vendors in town for tea and +sugar and + + align:start position:0% +sugar and + + + align:start position:0% +sugar and +kosene the winters were long and harsh + + align:start position:0% +kosene the winters were long and harsh + + + align:start position:0% +kosene the winters were long and harsh +and + + align:start position:0% +and + + + align:start position:0% +and +isolating + + align:start position:0% +isolating + + + align:start position:0% +isolating +uh dried dung was the main source of + + align:start position:0% +uh dried dung was the main source of + + + align:start position:0% +uh dried dung was the main source of +fuel and um during the past 100 years + + align:start position:0% +fuel and um during the past 100 years + + + align:start position:0% +fuel and um during the past 100 years +most of the surrounding trees um had + + align:start position:0% +most of the surrounding trees um had + + + align:start position:0% +most of the surrounding trees um had +been cut down they had once been + + align:start position:0% +been cut down they had once been + + + align:start position:0% +been cut down they had once been +available for building the home + + align:start position:0% +available for building the home + + + align:start position:0% +available for building the home +construction and posts such as these + + align:start position:0% +construction and posts such as these + + + align:start position:0% +construction and posts such as these +with the um interesting post and beam + + align:start position:0% +with the um interesting post and beam + + + align:start position:0% +with the um interesting post and beam +possibly a design comes from Iran you + + align:start position:0% +possibly a design comes from Iran you + + + align:start position:0% +possibly a design comes from Iran you +might uh Architects might tell me more + + align:start position:0% +might uh Architects might tell me more + + + align:start position:0% +might uh Architects might tell me more +about that but the houses consisted of a + + align:start position:0% +about that but the houses consisted of a + + + align:start position:0% +about that but the houses consisted of a +kitchen storage room such as this and an + + align:start position:0% +kitchen storage room such as this and an + + + align:start position:0% +kitchen storage room such as this and an +indoor + + align:start position:0% +indoor + + + align:start position:0% +indoor +stable and then there'd be a living room + + align:start position:0% +stable and then there'd be a living room + + + align:start position:0% +stable and then there'd be a living room +with the divon around the edge the D I + + align:start position:0% +with the divon around the edge the D I + + + align:start position:0% +with the divon around the edge the D I +believe is a a Persian word used in + + align:start position:0% +believe is a a Persian word used in + + + align:start position:0% +believe is a a Persian word used in +Turkish for that structure along the + + align:start position:0% +Turkish for that structure along the + + + align:start position:0% +Turkish for that structure along the +outer wall that's used for both um + + align:start position:0% +outer wall that's used for both um + + + align:start position:0% +outer wall that's used for both um +sitting and + + align:start position:0% +sitting and + + + align:start position:0% +sitting and +sleeping the population of the nearest + + align:start position:0% +sleeping the population of the nearest + + + align:start position:0% +sleeping the population of the nearest +um town was Sunni Turk who prohibited + + align:start position:0% +um town was Sunni Turk who prohibited + + + align:start position:0% +um town was Sunni Turk who prohibited +the Kurdish children from coming to + + align:start position:0% +the Kurdish children from coming to + + + align:start position:0% +the Kurdish children from coming to +their schools and also just shunned them + + align:start position:0% +their schools and also just shunned them + + + align:start position:0% +their schools and also just shunned them +in + + align:start position:0% +in + + + align:start position:0% +in +general this Prejudice was doubled + + align:start position:0% +general this Prejudice was doubled + + + align:start position:0% +general this Prejudice was doubled +because these Kurds were + + align:start position:0% +because these Kurds were + + + align:start position:0% +because these Kurds were +alivi and a sect that although Muslim + + align:start position:0% +alivi and a sect that although Muslim + + + align:start position:0% +alivi and a sect that although Muslim +were to the sunnis as within + + align:start position:0% +were to the sunnis as within + + + align:start position:0% +were to the sunnis as within +protestantism the unitarians are of the + + align:start position:0% +protestantism the unitarians are of the + + + align:start position:0% +protestantism the unitarians are of the +Baptist so um the migration out of the + + align:start position:0% +Baptist so um the migration out of the + + + align:start position:0% +Baptist so um the migration out of the +village to Turkish and European cities + + align:start position:0% +village to Turkish and European cities + + + align:start position:0% +village to Turkish and European cities +began in the 70s and accelerated in the + + align:start position:0% +began in the 70s and accelerated in the + + + align:start position:0% +began in the 70s and accelerated in the +80s by 1990 all of the able-bodied men + + align:start position:0% +80s by 1990 all of the able-bodied men + + + align:start position:0% +80s by 1990 all of the able-bodied men +and families had left the village and + + align:start position:0% +and families had left the village and + + + align:start position:0% +and families had left the village and +animal husbandry had ceased the weaving + + align:start position:0% +animal husbandry had ceased the weaving + + + align:start position:0% +animal husbandry had ceased the weaving +of rugs and the alivi ceremonial + + align:start position:0% +of rugs and the alivi ceremonial + + + align:start position:0% +of rugs and the alivi ceremonial +practices also came to an end only the + + align:start position:0% +practices also came to an end only the + + + align:start position:0% +practices also came to an end only the +elderly and a few isolated families + + align:start position:0% +elderly and a few isolated families + + + align:start position:0% +elderly and a few isolated families +stayed in the village year round most + + align:start position:0% +stayed in the village year round most + + + align:start position:0% +stayed in the village year round most +people maintain their ties by returning + + align:start position:0% +people maintain their ties by returning + + + align:start position:0% +people maintain their ties by returning +for summer + + align:start position:0% +for summer + + + align:start position:0% +for summer +visits I'd add in aide that when I + + align:start position:0% +visits I'd add in aide that when I + + + align:start position:0% +visits I'd add in aide that when I +showed this picture in the village in + + align:start position:0% +showed this picture in the village in + + + align:start position:0% +showed this picture in the village in +the year 2000 everyone who looked at it + + align:start position:0% +the year 2000 everyone who looked at it + + + align:start position:0% +the year 2000 everyone who looked at it +said they're all + + align:start position:0% + + + + align:start position:0% + +dead when I returned to the Village I + + align:start position:0% +dead when I returned to the Village I + + + align:start position:0% +dead when I returned to the Village I +looked for women I had known and + + align:start position:0% +looked for women I had known and + + + align:start position:0% +looked for women I had known and +photographed in the 70s I interviewed + + align:start position:0% +photographed in the 70s I interviewed + + + align:start position:0% +photographed in the 70s I interviewed +them to find out what they what had + + align:start position:0% +them to find out what they what had + + + align:start position:0% +them to find out what they what had +happened in their lives kiraz here in + + align:start position:0% +happened in their lives kiraz here in + + + align:start position:0% +happened in their lives kiraz here in +the center was one of those who bounced + + align:start position:0% +the center was one of those who bounced + + + align:start position:0% +the center was one of those who bounced +back and forth between the city and + + align:start position:0% +back and forth between the city and + + + align:start position:0% +back and forth between the city and +Village over the years here's a bit of + + align:start position:0% +Village over the years here's a bit of + + + align:start position:0% +Village over the years here's a bit of +her history and her own words + + align:start position:0% +her history and her own words + + + align:start position:0% +her history and her own words +we worked as agricultural workers When + + align:start position:0% +we worked as agricultural workers When + + + align:start position:0% +we worked as agricultural workers When +We Were Young Girls we used to go from + + align:start position:0% +We Were Young Girls we used to go from + + + align:start position:0% +We Were Young Girls we used to go from +the village to Seas to work in the + + align:start position:0% +the village to Seas to work in the + + + align:start position:0% +the village to Seas to work in the +fields we were very poor we used to go + + align:start position:0% +fields we were very poor we used to go + + + align:start position:0% +fields we were very poor we used to go +work and bring back some food they would + + align:start position:0% +work and bring back some food they would + + + align:start position:0% +work and bring back some food they would +give us bread and sugar we made our + + align:start position:0% +give us bread and sugar we made our + + + align:start position:0% +give us bread and sugar we made our +living on these things then I got + + align:start position:0% +living on these things then I got + + + align:start position:0% +living on these things then I got +married and moved to Adon with my + + align:start position:0% +married and moved to Adon with my + + + align:start position:0% +married and moved to Adon with my +husband I didn't go to work in the + + align:start position:0% +husband I didn't go to work in the + + + align:start position:0% +husband I didn't go to work in the +fields after I was married I cleaned + + align:start position:0% +fields after I was married I cleaned + + + align:start position:0% +fields after I was married I cleaned +houses I cleaned Windows Doors I wiped + + align:start position:0% +houses I cleaned Windows Doors I wiped + + + align:start position:0% +houses I cleaned Windows Doors I wiped +floors I did laundry with my hands that + + align:start position:0% +floors I did laundry with my hands that + + + align:start position:0% +floors I did laundry with my hands that +and my husband died we didn't have any + + align:start position:0% +and my husband died we didn't have any + + + align:start position:0% +and my husband died we didn't have any +money I brought his body to the village + + align:start position:0% +money I brought his body to the village + + + align:start position:0% +money I brought his body to the village +with help of the neighbors I was left + + align:start position:0% +with help of the neighbors I was left + + + align:start position:0% +with help of the neighbors I was left +alone to look after my four children + + align:start position:0% +alone to look after my four children + + + align:start position:0% +alone to look after my four children +without a husband I suffered many + + align:start position:0% +without a husband I suffered many + + + align:start position:0% +without a husband I suffered many +hardships I sometimes went to Adonna and + + align:start position:0% +hardships I sometimes went to Adonna and + + + align:start position:0% +hardships I sometimes went to Adonna and +sometimes stayed in the village I didn't + + align:start position:0% +sometimes stayed in the village I didn't + + + align:start position:0% +sometimes stayed in the village I didn't +let go of my land I protected my land I + + align:start position:0% +let go of my land I protected my land I + + + align:start position:0% +let go of my land I protected my land I +grew poppers in the fields and sold them + + align:start position:0% +grew poppers in the fields and sold them + + + align:start position:0% +grew poppers in the fields and sold them +we had sheep at one point I came back to + + align:start position:0% +we had sheep at one point I came back to + + + align:start position:0% +we had sheep at one point I came back to +the Village sold the sheep and bought a + + align:start position:0% +the Village sold the sheep and bought a + + + align:start position:0% +the Village sold the sheep and bought a +tractor we also sold rugs + + align:start position:0% +tractor we also sold rugs + + + align:start position:0% +tractor we also sold rugs +yes we are better off now nowadays + + align:start position:0% +yes we are better off now nowadays + + + align:start position:0% +yes we are better off now nowadays +everybody can go to school everybody + + align:start position:0% +everybody can go to school everybody + + + align:start position:0% +everybody can go to school everybody +works I managed to live with the help of + + align:start position:0% +works I managed to live with the help of + + + align:start position:0% +works I managed to live with the help of +my daughters one daughter is in Germany + + align:start position:0% +my daughters one daughter is in Germany + + + align:start position:0% +my daughters one daughter is in Germany +with her husband another in Canada but + + align:start position:0% +with her husband another in Canada but + + + align:start position:0% +with her husband another in Canada but +she's divorced the third went to Israel + + align:start position:0% +she's divorced the third went to Israel + + + align:start position:0% +she's divorced the third went to Israel +to work I don't even have a pension my + + align:start position:0% +to work I don't even have a pension my + + + align:start position:0% +to work I don't even have a pension my +sons are very poor one works but they + + align:start position:0% +sons are very poor one works but they + + + align:start position:0% +sons are very poor one works but they +can only feed themselves well to speak + + align:start position:0% +can only feed themselves well to speak + + + align:start position:0% +can only feed themselves well to speak +the truth it is my daughters who give + + align:start position:0% +the truth it is my daughters who give + + + align:start position:0% +the truth it is my daughters who give +help to their mother not my sons I get + + align:start position:0% +help to their mother not my sons I get + + + align:start position:0% +help to their mother not my sons I get +along with the help of my daughters + + align:start position:0% +along with the help of my daughters + + + align:start position:0% +along with the help of my daughters +30 years ago the women earned no cash + + align:start position:0% +30 years ago the women earned no cash + + + align:start position:0% +30 years ago the women earned no cash +had no control of family wealth and if + + align:start position:0% +had no control of family wealth and if + + + align:start position:0% +had no control of family wealth and if +they had cash they never would have been + + align:start position:0% +they had cash they never would have been + + + align:start position:0% +they had cash they never would have been +able to decide on their own to give part + + align:start position:0% +able to decide on their own to give part + + + align:start position:0% +able to decide on their own to give part +of their income to their mothers instead + + align:start position:0% +of their income to their mothers instead + + + align:start position:0% +of their income to their mothers instead +of their husbands or + + align:start position:0% + + + + align:start position:0% + +fathers here's my friend + + align:start position:0% + + + + align:start position:0% + +fim with her daughter semma in 1975 on + + align:start position:0% +fim with her daughter semma in 1975 on + + + align:start position:0% +fim with her daughter semma in 1975 on +the left and on the right is SEO with + + align:start position:0% +the left and on the right is SEO with + + + align:start position:0% +the left and on the right is SEO with +her son in 2001 + + align:start position:0% +her son in 2001 + + + align:start position:0% +her son in 2001 +fim May says of + + align:start position:0% +fim May says of + + + align:start position:0% +fim May says of +marriage I was married in the + + align:start position:0% +marriage I was married in the + + + align:start position:0% +marriage I was married in the +old-fashioned way by an arranged + + align:start position:0% +old-fashioned way by an arranged + + + align:start position:0% +old-fashioned way by an arranged +marriage I was born in 1951 and married + + align:start position:0% +marriage I was born in 1951 and married + + + align:start position:0% +marriage I was born in 1951 and married +in + + align:start position:0% +in + + + align:start position:0% +in +1964 it's very hard to be married at + + align:start position:0% +1964 it's very hard to be married at + + + align:start position:0% +1964 it's very hard to be married at +such a young age young girls were + + align:start position:0% +such a young age young girls were + + + align:start position:0% +such a young age young girls were +married off to men whom they' never met + + align:start position:0% +married off to men whom they' never met + + + align:start position:0% +married off to men whom they' never met +before women had no right to speak no + + align:start position:0% +before women had no right to speak no + + + align:start position:0% +before women had no right to speak no +bride was allowed to speak with their + + align:start position:0% +bride was allowed to speak with their + + + align:start position:0% +bride was allowed to speak with their +Elders it was only a nod for yes and a + + align:start position:0% +Elders it was only a nod for yes and a + + + align:start position:0% +Elders it was only a nod for yes and a +for no now young people choose their own + + align:start position:0% +for no now young people choose their own + + + align:start position:0% +for no now young people choose their own +Partners they can speak openly and at + + align:start position:0% +Partners they can speak openly and at + + + align:start position:0% +Partners they can speak openly and at +the dinner table together two daughters + + align:start position:0% +the dinner table together two daughters + + + align:start position:0% +the dinner table together two daughters +got married to the men of their my two + + align:start position:0% +got married to the men of their my two + + + align:start position:0% +got married to the men of their my two +daughters got married to the men of + + align:start position:0% +daughters got married to the men of + + + align:start position:0% +daughters got married to the men of +their choice they fell in love they told + + align:start position:0% +their choice they fell in love they told + + + align:start position:0% +their choice they fell in love they told +us we consented they were both happily + + align:start position:0% +us we consented they were both happily + + + align:start position:0% +us we consented they were both happily +married this next woman chake a neighbor + + align:start position:0% +married this next woman chake a neighbor + + + align:start position:0% +married this next woman chake a neighbor +of f mid in the 70s has a typical + + align:start position:0% +of f mid in the 70s has a typical + + + align:start position:0% +of f mid in the 70s has a typical +migration story here is chake making + + align:start position:0% +migration story here is chake making + + + align:start position:0% +migration story here is chake making +bread in the old way uh + + align:start position:0% +bread in the old way uh + + + align:start position:0% +bread in the old way uh +then by that Hearth and then 25 years + + align:start position:0% +then by that Hearth and then 25 years + + + align:start position:0% +then by that Hearth and then 25 years +later in front of the same Hearth that + + align:start position:0% +later in front of the same Hearth that + + + align:start position:0% +later in front of the same Hearth that +is no longer in use in the village + + align:start position:0% +is no longer in use in the village + + + align:start position:0% +is no longer in use in the village +she migrated to the city with her + + align:start position:0% +she migrated to the city with her + + + align:start position:0% +she migrated to the city with her +husband and children they live in a + + align:start position:0% +husband and children they live in a + + + align:start position:0% +husband and children they live in a +modest concrete block house with modern + + align:start position:0% +modest concrete block house with modern + + + align:start position:0% +modest concrete block house with modern +appliances she has spent the last 25 + + align:start position:0% +appliances she has spent the last 25 + + + align:start position:0% +appliances she has spent the last 25 +years cleaning houses in order to pay + + align:start position:0% +years cleaning houses in order to pay + + + align:start position:0% +years cleaning houses in order to pay +for the children's education and to + + align:start position:0% +for the children's education and to + + + align:start position:0% +for the children's education and to +afford a city + + align:start position:0% +afford a city + + + align:start position:0% +afford a city +home here's her son naaza as a child + + align:start position:0% +home here's her son naaza as a child + + + align:start position:0% +home here's her son naaza as a child +with the Lambs in the village and now + + align:start position:0% +with the Lambs in the village and now + + + align:start position:0% +with the Lambs in the village and now +seated in the center he's a University + + align:start position:0% +seated in the center he's a University + + + align:start position:0% +seated in the center he's a University +graduate ch's daughter sbel is seen here + + align:start position:0% +graduate ch's daughter sbel is seen here + + + align:start position:0% +graduate ch's daughter sbel is seen here +in the village in her youth now she sits + + align:start position:0% +in the village in her youth now she sits + + + align:start position:0% +in the village in her youth now she sits +with her mother in cel's fancily + + align:start position:0% +with her mother in cel's fancily + + + align:start position:0% +with her mother in cel's fancily +furnished living room Cel has worked in + + align:start position:0% +furnished living room Cel has worked in + + + align:start position:0% +furnished living room Cel has worked in +retail stores and is active in a Le left + + align:start position:0% +retail stores and is active in a Le left + + + align:start position:0% +retail stores and is active in a Le left +leaning aliv political + + align:start position:0% +leaning aliv political + + + align:start position:0% +leaning aliv political +party her husband is Turkish he runs a + + align:start position:0% +party her husband is Turkish he runs a + + + align:start position:0% +party her husband is Turkish he runs a +record store and doesn't speak a word of + + align:start position:0% +record store and doesn't speak a word of + + + align:start position:0% +record store and doesn't speak a word of +Kurdish the fact that Sabel is working + + align:start position:0% +Kurdish the fact that Sabel is working + + + align:start position:0% +Kurdish the fact that Sabel is working +that she engages in political activity + + align:start position:0% +that she engages in political activity + + + align:start position:0% +that she engages in political activity +that she has married a Turk and that she + + align:start position:0% +that she has married a Turk and that she + + + align:start position:0% +that she has married a Turk and that she +insists she will not have children were + + align:start position:0% +insists she will not have children were + + + align:start position:0% +insists she will not have children were +all Unthinkable ideas for her mother's + + align:start position:0% +all Unthinkable ideas for her mother's + + + align:start position:0% +all Unthinkable ideas for her mother's +generation and for centuries of + + align:start position:0% +generation and for centuries of + + + align:start position:0% +generation and for centuries of +generations before + + align:start position:0% + + + + align:start position:0% + +them the material wealth and Comforts + + align:start position:0% +them the material wealth and Comforts + + + align:start position:0% +them the material wealth and Comforts +that come with City Life are one of the + + align:start position:0% +that come with City Life are one of the + + + align:start position:0% +that come with City Life are one of the +most obvious and common + + align:start position:0% +most obvious and common + + + align:start position:0% +most obvious and common +improvements the backbreaking labor that + + align:start position:0% +improvements the backbreaking labor that + + + align:start position:0% +improvements the backbreaking labor that +characterized women's work in the + + align:start position:0% +characterized women's work in the + + + align:start position:0% +characterized women's work in the +village is lessened by the running water + + align:start position:0% +village is lessened by the running water + + + align:start position:0% +village is lessened by the running water +electricity + + align:start position:0% +electricity + + + align:start position:0% +electricity +appliances available in the + + align:start position:0% +appliances available in the + + + align:start position:0% +appliances available in the +city that these possessions are + + align:start position:0% +city that these possessions are + + + align:start position:0% +city that these possessions are +cherished in this way is + + align:start position:0% + + + + align:start position:0% + +understandable how however much of the + + align:start position:0% +understandable how however much of the + + + align:start position:0% +understandable how however much of the +population that initially moved to the + + align:start position:0% +population that initially moved to the + + + align:start position:0% +population that initially moved to the +city maintained a village style life in + + align:start position:0% +city maintained a village style life in + + + align:start position:0% +city maintained a village style life in +their neighborhoods their ghettos here + + align:start position:0% +their neighborhoods their ghettos here + + + align:start position:0% +their neighborhoods their ghettos here +in the city of Adonna with a population + + align:start position:0% +in the city of Adonna with a population + + + align:start position:0% +in the city of Adonna with a population +of nearly 2 million the wom the women + + align:start position:0% +of nearly 2 million the wom the women + + + align:start position:0% +of nearly 2 million the wom the women +gather to wash and dry Peppers together + + align:start position:0% +gather to wash and dry Peppers together + + + align:start position:0% +gather to wash and dry Peppers together +in the street just as they might have in + + align:start position:0% +in the street just as they might have in + + + align:start position:0% +in the street just as they might have in +the + + align:start position:0% +the + + + align:start position:0% +the +village bread making for special + + align:start position:0% +village bread making for special + + + align:start position:0% +village bread making for special +occasions takes place in the street the + + align:start position:0% +occasions takes place in the street the + + + align:start position:0% +occasions takes place in the street the +male only kabane is also + + align:start position:0% +male only kabane is also + + + align:start position:0% +male only kabane is also +there sunna once a resident of topar + + align:start position:0% +there sunna once a resident of topar + + + align:start position:0% +there sunna once a resident of topar +ditch is seen here on her Rooftop in + + align:start position:0% +ditch is seen here on her Rooftop in + + + align:start position:0% +ditch is seen here on her Rooftop in +Adonna where she has cleaned other + + align:start position:0% +Adonna where she has cleaned other + + + align:start position:0% +Adonna where she has cleaned other +people's houses for several decades + + align:start position:0% +people's houses for several decades + + + align:start position:0% +people's houses for several decades +while her husband had a job in the + + align:start position:0% +while her husband had a job in the + + + align:start position:0% +while her husband had a job in the +city this the exterior of her home is in + + align:start position:0% +city this the exterior of her home is in + + + align:start position:0% +city this the exterior of her home is in +an old neighborhood inhabited by + + align:start position:0% +an old neighborhood inhabited by + + + align:start position:0% +an old neighborhood inhabited by +hundreds of people from toich on the + + align:start position:0% +hundreds of people from toich on the + + + align:start position:0% +hundreds of people from toich on the +outside is a blue concrete block and on + + align:start position:0% +outside is a blue concrete block and on + + + align:start position:0% +outside is a blue concrete block and on +the inside some notion of Italian roko + + align:start position:0% +the inside some notion of Italian roko + + + align:start position:0% +the inside some notion of Italian roko +in a parlor were only holiday guests + + align:start position:0% +in a parlor were only holiday guests + + + align:start position:0% +in a parlor were only holiday guests +that entertained and here sunna's mother + + align:start position:0% +that entertained and here sunna's mother + + + align:start position:0% +that entertained and here sunna's mother +in the family woman with the ever + + align:start position:0% +in the family woman with the ever + + + align:start position:0% +in the family woman with the ever +present always on + + align:start position:0% +present always on + + + align:start position:0% +present always on +television one of sunna's daughters is a + + align:start position:0% +television one of sunna's daughters is a + + + align:start position:0% +television one of sunna's daughters is a +trained in textile design and has eloped + + align:start position:0% +trained in textile design and has eloped + + + align:start position:0% +trained in textile design and has eloped +much to sunna's dismay toble with an + + align:start position:0% +much to sunna's dismay toble with an + + + align:start position:0% +much to sunna's dismay toble with an +older man one son left for England when + + align:start position:0% +older man one son left for England when + + + align:start position:0% +older man one son left for England when +he was 16 and he's been driving a red + + align:start position:0% +he was 16 and he's been driving a red + + + align:start position:0% +he was 16 and he's been driving a red +double-decker bus while supporting a + + align:start position:0% +double-decker bus while supporting a + + + align:start position:0% +double-decker bus while supporting a +family there he doesn't visit because if + + align:start position:0% +family there he doesn't visit because if + + + align:start position:0% +family there he doesn't visit because if +he came back he would have to do a + + align:start position:0% +he came back he would have to do a + + + align:start position:0% +he came back he would have to do a +two-year military service in + + align:start position:0% +two-year military service in + + + align:start position:0% +two-year military service in +Turkey the other son and daughter-in-law + + align:start position:0% +Turkey the other son and daughter-in-law + + + align:start position:0% +Turkey the other son and daughter-in-law +run a kebab shop in + + align:start position:0% +run a kebab shop in + + + align:start position:0% +run a kebab shop in +Adonna sunna and her husband are retired + + align:start position:0% +Adonna sunna and her husband are retired + + + align:start position:0% +Adonna sunna and her husband are retired +now spending half of the year in the + + align:start position:0% +now spending half of the year in the + + + align:start position:0% +now spending half of the year in the +retirement home they built back in the + + align:start position:0% +retirement home they built back in the + + + align:start position:0% +retirement home they built back in the +village that has a swimming pool for the + + align:start position:0% +village that has a swimming pool for the + + + align:start position:0% +village that has a swimming pool for the +grandkids water solar water heaters and + + align:start position:0% +grandkids water solar water heaters and + + + align:start position:0% +grandkids water solar water heaters and +two satellite + + align:start position:0% + + + + align:start position:0% + +dishes for many um for many from the + + align:start position:0% +dishes for many um for many from the + + + align:start position:0% +dishes for many um for many from the +generation that moved to the city and + + align:start position:0% +generation that moved to the city and + + + align:start position:0% +generation that moved to the city and +got their education there + + align:start position:0% +got their education there + + + align:start position:0% +got their education there +the recreated life of the village LIF + + align:start position:0% +the recreated life of the village LIF + + + align:start position:0% +the recreated life of the village LIF +style in the city the of their parents + + align:start position:0% +style in the city the of their parents + + + align:start position:0% +style in the city the of their parents +is + + align:start position:0% +is + + + align:start position:0% +is +unacceptable so they have tried to move + + align:start position:0% +unacceptable so they have tried to move + + + align:start position:0% +unacceptable so they have tried to move +away from those tight-knit communities + + align:start position:0% +away from those tight-knit communities + + + align:start position:0% +away from those tight-knit communities +in the city and have sought a new + + align:start position:0% +in the city and have sought a new + + + align:start position:0% +in the city and have sought a new +lifestyle in a new + + align:start position:0% +lifestyle in a new + + + align:start position:0% +lifestyle in a new +setting that's Leila here she is + + align:start position:0% +setting that's Leila here she is + + + align:start position:0% +setting that's Leila here she is +entertaining her mother and sunna in a + + align:start position:0% +entertaining her mother and sunna in a + + + align:start position:0% +entertaining her mother and sunna in a +high-rise in her high-rise home they all + + align:start position:0% +high-rise in her high-rise home they all + + + align:start position:0% +high-rise in her high-rise home they all +once lived in top parage although her + + align:start position:0% +once lived in top parage although her + + + align:start position:0% +once lived in top parage although her +mother is a literate Leila has a + + align:start position:0% +mother is a literate Leila has a + + + align:start position:0% +mother is a literate Leila has a +university degree and teaches high + + align:start position:0% +university degree and teaches high + + + align:start position:0% +university degree and teaches high +school art her husband is an engineer + + align:start position:0% +school art her husband is an engineer + + + align:start position:0% +school art her husband is an engineer +whom Leia Leila chose when she married + + align:start position:0% +whom Leia Leila chose when she married + + + align:start position:0% +whom Leia Leila chose when she married +him at + + align:start position:0% +him at + + + align:start position:0% +him at +26 in Lila's words we are not very close + + align:start position:0% +26 in Lila's words we are not very close + + + align:start position:0% +26 in Lila's words we are not very close +to the people who migrated from the + + align:start position:0% +to the people who migrated from the + + + align:start position:0% +to the people who migrated from the +village they we don't want to be close + + align:start position:0% +village they we don't want to be close + + + align:start position:0% +village they we don't want to be close +to them you know about that culture the + + align:start position:0% +to them you know about that culture the + + + align:start position:0% +to them you know about that culture the +background of that Society it's not a + + align:start position:0% +background of that Society it's not a + + + align:start position:0% +background of that Society it's not a +very modern society we wanted to raise + + align:start position:0% +very modern society we wanted to raise + + + align:start position:0% +very modern society we wanted to raise +our child in a more developed Society + + align:start position:0% +our child in a more developed Society + + + align:start position:0% +our child in a more developed Society +we've become aware of the advantage of + + align:start position:0% +we've become aware of the advantage of + + + align:start position:0% +we've become aware of the advantage of +living in a developed an environment + + align:start position:0% +living in a developed an environment + + + align:start position:0% +living in a developed an environment +with different + + align:start position:0% +with different + + + align:start position:0% +with different +people in contrast here's Lea's mother + + align:start position:0% +people in contrast here's Lea's mother + + + align:start position:0% +people in contrast here's Lea's mother +who sums up her life this way with my + + align:start position:0% +who sums up her life this way with my + + + align:start position:0% +who sums up her life this way with my +mother and father I had a very simple + + align:start position:0% +mother and father I had a very simple + + + align:start position:0% +mother and father I had a very simple +Village Life cattle sheep cows I never + + align:start position:0% +Village Life cattle sheep cows I never + + + align:start position:0% +Village Life cattle sheep cows I never +went to school of course there was no + + align:start position:0% +went to school of course there was no + + + align:start position:0% +went to school of course there was no +school when I was a child the school was + + align:start position:0% +school when I was a child the school was + + + align:start position:0% +school when I was a child the school was +built later my mother and father + + align:start position:0% +built later my mother and father + + + align:start position:0% +built later my mother and father +couldn't afford to send me away to + + align:start position:0% +couldn't afford to send me away to + + + align:start position:0% +couldn't afford to send me away to +school they didn't care much about + + align:start position:0% +school they didn't care much about + + + align:start position:0% +school they didn't care much about +sending girls to school I got married + + align:start position:0% +sending girls to school I got married + + + align:start position:0% +sending girls to school I got married +when I was 15 then I came to Adonna we + + align:start position:0% +when I was 15 then I came to Adonna we + + + align:start position:0% +when I was 15 then I came to Adonna we +suffered a lot we were poor I had three + + align:start position:0% +suffered a lot we were poor I had three + + + align:start position:0% +suffered a lot we were poor I had three +babies I worked as a house cleaner I had + + align:start position:0% +babies I worked as a house cleaner I had + + + align:start position:0% +babies I worked as a house cleaner I had +to Bear all the expenses and the burdens + + align:start position:0% +to Bear all the expenses and the burdens + + + align:start position:0% +to Bear all the expenses and the burdens +of sending two children to school we + + align:start position:0% +of sending two children to school we + + + align:start position:0% +of sending two children to school we +only worked just like slaves and now we + + align:start position:0% +only worked just like slaves and now we + + + align:start position:0% +only worked just like slaves and now we +have a normal life not rich not poor my + + align:start position:0% +have a normal life not rich not poor my + + + align:start position:0% +have a normal life not rich not poor my +daughter is a teacher my son is a + + align:start position:0% +daughter is a teacher my son is a + + + align:start position:0% +daughter is a teacher my son is a +veterinarian we're doing well in the + + align:start position:0% +veterinarian we're doing well in the + + + align:start position:0% +veterinarian we're doing well in the +past women didn't have any rights it's + + align:start position:0% +past women didn't have any rights it's + + + align:start position:0% +past women didn't have any rights it's +better now + + align:start position:0% + + + + align:start position:0% + +here is fim's oldest daughter Elvin seen + + align:start position:0% +here is fim's oldest daughter Elvin seen + + + align:start position:0% +here is fim's oldest daughter Elvin seen +in a CH as a child in the photo um on + + align:start position:0% +in a CH as a child in the photo um on + + + align:start position:0% +in a CH as a child in the photo um on +the leftand photo in the center roow + + align:start position:0% +the leftand photo in the center roow + + + align:start position:0% +the leftand photo in the center roow +back and more recently on the right she + + align:start position:0% +back and more recently on the right she + + + align:start position:0% +back and more recently on the right she +lives in the city of ismet on the shores + + align:start position:0% +lives in the city of ismet on the shores + + + align:start position:0% +lives in the city of ismet on the shores +of the marous sea about an hour east of + + align:start position:0% +of the marous sea about an hour east of + + + align:start position:0% +of the marous sea about an hour east of +Istanbul the marmar sea is the large + + align:start position:0% +Istanbul the marmar sea is the large + + + align:start position:0% +Istanbul the marmar sea is the large +body of water between the Bosphorus and + + align:start position:0% +body of water between the Bosphorus and + + + align:start position:0% +body of water between the Bosphorus and +before the dardel that separates the + + align:start position:0% +before the dardel that separates the + + + align:start position:0% +before the dardel that separates the +Black Sea from the + + align:start position:0% +Black Sea from the + + + align:start position:0% +Black Sea from the +Mediterranean right over the earthquake + + align:start position:0% +Mediterranean right over the earthquake + + + align:start position:0% +Mediterranean right over the earthquake +fault + + align:start position:0% +fault + + + align:start position:0% +fault +Elvin grew up in the village where she + + align:start position:0% +Elvin grew up in the village where she + + + align:start position:0% +Elvin grew up in the village where she +got a few years of schooling for a time + + align:start position:0% +got a few years of schooling for a time + + + align:start position:0% +got a few years of schooling for a time +she was sent to relatives in Istanbul to + + align:start position:0% +she was sent to relatives in Istanbul to + + + align:start position:0% +she was sent to relatives in Istanbul to +attend high school then she cared for + + align:start position:0% +attend high school then she cared for + + + align:start position:0% +attend high school then she cared for +her older brother Ali's first child as + + align:start position:0% +her older brother Ali's first child as + + + align:start position:0% +her older brother Ali's first child as +its mother for 5 years when Ali and his + + align:start position:0% +its mother for 5 years when Ali and his + + + align:start position:0% +its mother for 5 years when Ali and his +wife migrated illegally to + + align:start position:0% +wife migrated illegally to + + + align:start position:0% +wife migrated illegally to +England eventually Elvin met and got + + align:start position:0% +England eventually Elvin met and got + + + align:start position:0% +England eventually Elvin met and got +engaged to a man whose family had left + + align:start position:0% +engaged to a man whose family had left + + + align:start position:0% +engaged to a man whose family had left +the village when he was young they + + align:start position:0% +the village when he was young they + + + align:start position:0% +the village when he was young they +courted and she followed him where his + + align:start position:0% +courted and she followed him where his + + + align:start position:0% +courted and she followed him where his +medical studies led him over many years + + align:start position:0% +medical studies led him over many years + + + align:start position:0% +medical studies led him over many years +she completed a University degree in + + align:start position:0% +she completed a University degree in + + + align:start position:0% +she completed a University degree in +high school man in hotel + + align:start position:0% +high school man in hotel + + + align:start position:0% +high school man in hotel +management here are some of her thoughts + + align:start position:0% +management here are some of her thoughts + + + align:start position:0% +management here are some of her thoughts +about the change between the + + align:start position:0% + + + + align:start position:0% + +generations our generation is the bridge + + align:start position:0% +generations our generation is the bridge + + + align:start position:0% +generations our generation is the bridge +between these two + + align:start position:0% +between these two + + + align:start position:0% +between these two +generations I would tell if I were to + + align:start position:0% +generations I would tell if I were to + + + align:start position:0% +generations I would tell if I were to +tell my child this whole process in the + + align:start position:0% +tell my child this whole process in the + + + align:start position:0% +tell my child this whole process in the +future he would not understand it the + + align:start position:0% +future he would not understand it the + + + align:start position:0% +future he would not understand it the +generation prior to ours thought that + + align:start position:0% +generation prior to ours thought that + + + align:start position:0% +generation prior to ours thought that +having children was for making them work + + align:start position:0% +having children was for making them work + + + align:start position:0% +having children was for making them work +and to take care of their parents in + + align:start position:0% +and to take care of their parents in + + + align:start position:0% +and to take care of their parents in +their old age parents wanted their + + align:start position:0% +their old age parents wanted their + + + align:start position:0% +their old age parents wanted their +children to become their guarantees for + + align:start position:0% +children to become their guarantees for + + + align:start position:0% +children to become their guarantees for +their future support raising kids was an + + align:start position:0% +their future support raising kids was an + + + align:start position:0% +their future support raising kids was an +analogous to raising + + align:start position:0% +analogous to raising + + + align:start position:0% +analogous to raising +workers after our generation this + + align:start position:0% +workers after our generation this + + + align:start position:0% +workers after our generation this +mentality was not the same because + + align:start position:0% +mentality was not the same because + + + align:start position:0% +mentality was not the same because +people understood the importance of + + align:start position:0% +people understood the importance of + + + align:start position:0% +people understood the importance of +Education regarding decisions from every + + align:start position:0% +Education regarding decisions from every + + + align:start position:0% +Education regarding decisions from every +aspect my father used to make a decision + + align:start position:0% +aspect my father used to make a decision + + + align:start position:0% +aspect my father used to make a decision +and my mother used to obey it at that + + align:start position:0% +and my mother used to obey it at that + + + align:start position:0% +and my mother used to obey it at that +time many girls were sent outside the + + align:start position:0% +time many girls were sent outside the + + + align:start position:0% +time many girls were sent outside the +village so they could continue their + + align:start position:0% +village so they could continue their + + + align:start position:0% +village so they could continue their +education when my father father went + + align:start position:0% +education when my father father went + + + align:start position:0% +education when my father father went +outside the village had different + + align:start position:0% +outside the village had different + + + align:start position:0% +outside the village had different +friends saw different Lifestyles he + + align:start position:0% +friends saw different Lifestyles he + + + align:start position:0% +friends saw different Lifestyles he +understood what people that when people + + align:start position:0% +understood what people that when people + + + align:start position:0% +understood what people that when people +studied more they would become more + + align:start position:0% +studied more they would become more + + + align:start position:0% +studied more they would become more +powerful all this influenced his + + align:start position:0% +powerful all this influenced his + + + align:start position:0% +powerful all this influenced his +changing my father made the decision I + + align:start position:0% +changing my father made the decision I + + + align:start position:0% +changing my father made the decision I +would go to Istanbul and attend + + align:start position:0% +would go to Istanbul and attend + + + align:start position:0% +would go to Istanbul and attend +Secondary School Frankly Speaking my + + align:start position:0% +Secondary School Frankly Speaking my + + + align:start position:0% +Secondary School Frankly Speaking my +mother wasn't consulted at + + align:start position:0% +mother wasn't consulted at + + + align:start position:0% +mother wasn't consulted at +all in my married life we have a + + align:start position:0% +all in my married life we have a + + + align:start position:0% +all in my married life we have a +democracy from every aspect if we have + + align:start position:0% +democracy from every aspect if we have + + + align:start position:0% +democracy from every aspect if we have +to make a final decision about something + + align:start position:0% +to make a final decision about something + + + align:start position:0% +to make a final decision about something +we absolutely talk our marriage is a + + align:start position:0% +we absolutely talk our marriage is a + + + align:start position:0% +we absolutely talk our marriage is a +dialogue it's essential we can even talk + + align:start position:0% +dialogue it's essential we can even talk + + + align:start position:0% +dialogue it's essential we can even talk +about a very trivial detail if I have to + + align:start position:0% +about a very trivial detail if I have to + + + align:start position:0% +about a very trivial detail if I have to +persuade him to do something for sure I + + align:start position:0% +persuade him to do something for sure I + + + align:start position:0% +persuade him to do something for sure I +will do so and vice + + align:start position:0% +will do so and vice + + + align:start position:0% +will do so and vice +versa Elvin lives in the high-rise + + align:start position:0% +versa Elvin lives in the high-rise + + + align:start position:0% +versa Elvin lives in the high-rise +complex but she chooses to go to the + + align:start position:0% +complex but she chooses to go to the + + + align:start position:0% +complex but she chooses to go to the +green grocery down the road instead of + + align:start position:0% +green grocery down the road instead of + + + align:start position:0% +green grocery down the road instead of +the nearby + + align:start position:0% + + + + align:start position:0% + +supermarket now let's go from elvin's + + align:start position:0% +supermarket now let's go from elvin's + + + align:start position:0% +supermarket now let's go from elvin's +market and ismet to a market in + + align:start position:0% +market and ismet to a market in + + + align:start position:0% +market and ismet to a market in +London in the back the cafe Millenium is + + align:start position:0% +London in the back the cafe Millenium is + + + align:start position:0% +London in the back the cafe Millenium is +elvin's older brother Ali's Cafe they + + align:start position:0% +elvin's older brother Ali's Cafe they + + + align:start position:0% +elvin's older brother Ali's Cafe they +serve British breakfast all day in + + align:start position:0% +serve British breakfast all day in + + + align:start position:0% +serve British breakfast all day in +kebabs Ali is the um the boy in the + + align:start position:0% +kebabs Ali is the um the boy in the + + + align:start position:0% +kebabs Ali is the um the boy in the +front right and his the uh siblings in + + align:start position:0% +front right and his the uh siblings in + + + align:start position:0% +front right and his the uh siblings in +the village in + + align:start position:0% + + + + align:start position:0% + +1976 this is where he lives in public + + align:start position:0% +1976 this is where he lives in public + + + align:start position:0% +1976 this is where he lives in public +housing in London the BMW in the front + + align:start position:0% +housing in London the BMW in the front + + + align:start position:0% +housing in London the BMW in the front +is + + align:start position:0% +is + + + align:start position:0% +is +his he came to London on false visas + + align:start position:0% +his he came to London on false visas + + + align:start position:0% +his he came to London on false visas +with his wife wife 12 years ago he left + + align:start position:0% +with his wife wife 12 years ago he left + + + align:start position:0% +with his wife wife 12 years ago he left +his infant son with Elvin because they + + align:start position:0% +his infant son with Elvin because they + + + align:start position:0% +his infant son with Elvin because they +had no insurance that the assurance that + + align:start position:0% +had no insurance that the assurance that + + + align:start position:0% +had no insurance that the assurance that +the journey would be safe or that they + + align:start position:0% +the journey would be safe or that they + + + align:start position:0% +the journey would be safe or that they +would be able to sustain themselves once + + align:start position:0% +would be able to sustain themselves once + + + align:start position:0% +would be able to sustain themselves once +they arrived for seven years they worked + + align:start position:0% +they arrived for seven years they worked + + + align:start position:0% +they arrived for seven years they worked +15 to 18 hours a day in a sweat shop by + + align:start position:0% +15 to 18 hours a day in a sweat shop by + + + align:start position:0% +15 to 18 hours a day in a sweat shop by +day and doing sewing pieace work at + + align:start position:0% +day and doing sewing pieace work at + + + align:start position:0% +day and doing sewing pieace work at +night this way they paid off the gang + + align:start position:0% +night this way they paid off the gang + + + align:start position:0% +night this way they paid off the gang +the 5,000 per person it cost them to get + + align:start position:0% +the 5,000 per person it cost them to get + + + align:start position:0% +the 5,000 per person it cost them to get +into + + align:start position:0% +into + + + align:start position:0% +into +England in addition Ali and his wife + + align:start position:0% +England in addition Ali and his wife + + + align:start position:0% +England in addition Ali and his wife +worked to pay pay for his two brothers + + align:start position:0% +worked to pay pay for his two brothers + + + align:start position:0% +worked to pay pay for his two brothers +and youngest sister Bazar to come in on + + align:start position:0% +and youngest sister Bazar to come in on + + + align:start position:0% +and youngest sister Bazar to come in on +false visas one of them brought in his + + align:start position:0% +false visas one of them brought in his + + + align:start position:0% +false visas one of them brought in his +son Arif then 5 years old as their + + align:start position:0% +son Arif then 5 years old as their + + + align:start position:0% +son Arif then 5 years old as their +own this is a Victorian building + + align:start position:0% +own this is a Victorian building + + + align:start position:0% +own this is a Victorian building +converted into a mosque in one of the + + align:start position:0% +converted into a mosque in one of the + + + align:start position:0% +converted into a mosque in one of the +Turkish neighborhoods in London there + + align:start position:0% +Turkish neighborhoods in London there + + + align:start position:0% +Turkish neighborhoods in London there +are an estimated 300,000 Turks and Kurds + + align:start position:0% +are an estimated 300,000 Turks and Kurds + + + align:start position:0% +are an estimated 300,000 Turks and Kurds +living in London most of the first + + align:start position:0% +living in London most of the first + + + align:start position:0% +living in London most of the first +generation like Ali stay in their + + align:start position:0% +generation like Ali stay in their + + + align:start position:0% +generation like Ali stay in their +neighborhood speak hardly any English + + align:start position:0% +neighborhood speak hardly any English + + + align:start position:0% +neighborhood speak hardly any English +and survive on employment generated with + + align:start position:0% +and survive on employment generated with + + + align:start position:0% +and survive on employment generated with +within the + + align:start position:0% +within the + + + align:start position:0% +within the +community the British policy is that if + + align:start position:0% +community the British policy is that if + + + align:start position:0% +community the British policy is that if +you declare yourself a political Refugee + + align:start position:0% +you declare yourself a political Refugee + + + align:start position:0% +you declare yourself a political Refugee +and do not leave England uh tur yeah do + + align:start position:0% +and do not leave England uh tur yeah do + + + align:start position:0% +and do not leave England uh tur yeah do +not leave England for turkey for 10 + + align:start position:0% +not leave England for turkey for 10 + + + align:start position:0% +not leave England for turkey for 10 +years you are granted British + + align:start position:0% +years you are granted British + + + align:start position:0% +years you are granted British +citizenship Ali lived in England for 10 + + align:start position:0% +citizenship Ali lived in England for 10 + + + align:start position:0% +citizenship Ali lived in England for 10 +years without returning to + + align:start position:0% +years without returning to + + + align:start position:0% +years without returning to +Turkey what does this policy mean for + + align:start position:0% +Turkey what does this policy mean for + + + align:start position:0% +Turkey what does this policy mean for +fim their mother it means that of her + + align:start position:0% +fim their mother it means that of her + + + align:start position:0% +fim their mother it means that of her +six children she has not seen four of + + align:start position:0% +six children she has not seen four of + + + align:start position:0% +six children she has not seen four of +them for 10 years the British would not + + align:start position:0% +them for 10 years the British would not + + + align:start position:0% +them for 10 years the British would not +Grant her an official Vis VIs visit a + + align:start position:0% +Grant her an official Vis VIs visit a + + + align:start position:0% +Grant her an official Vis VIs visit a +visa to visit + + align:start position:0% +visa to visit + + + align:start position:0% +visa to visit +them Ali reflects about the impact of + + align:start position:0% +them Ali reflects about the impact of + + + align:start position:0% +them Ali reflects about the impact of +immigration on himself his siblings um + + align:start position:0% +immigration on himself his siblings um + + + align:start position:0% +immigration on himself his siblings um +and his family and these Reflections I + + align:start position:0% +and his family and these Reflections I + + + align:start position:0% +and his family and these Reflections I +think provide some insight on how others + + align:start position:0% +think provide some insight on how others + + + align:start position:0% +think provide some insight on how others +in his situation might feel surely he + + align:start position:0% +in his situation might feel surely he + + + align:start position:0% +in his situation might feel surely he +doesn't speak for everyone but the + + align:start position:0% +doesn't speak for everyone but the + + + align:start position:0% +doesn't speak for everyone but the +concerns he expresses provide a succinct + + align:start position:0% +concerns he expresses provide a succinct + + + align:start position:0% +concerns he expresses provide a succinct +summary of the cost and tradeoffs many + + align:start position:0% +summary of the cost and tradeoffs many + + + align:start position:0% +summary of the cost and tradeoffs many +immigrants knowingly or unknowingly + + align:start position:0% +immigrants knowingly or unknowingly + + + align:start position:0% +immigrants knowingly or unknowingly +encounter + + align:start position:0% +encounter + + + align:start position:0% +encounter +uh for this reason and because of the + + align:start position:0% +uh for this reason and because of the + + + align:start position:0% +uh for this reason and because of the +clear way he articulates the issue I + + align:start position:0% +clear way he articulates the issue I + + + align:start position:0% +clear way he articulates the issue I +will share with you a lengthy portion of + + align:start position:0% +will share with you a lengthy portion of + + + align:start position:0% +will share with you a lengthy portion of +it 2004 interview I had with + + align:start position:0% + + + + align:start position:0% + +him this is + + align:start position:0% +him this is + + + align:start position:0% +him this is +Ali why was our desire to go abroad so + + align:start position:0% +Ali why was our desire to go abroad so + + + align:start position:0% +Ali why was our desire to go abroad so +great well we got Hoodwinked our friends + + align:start position:0% +great well we got Hoodwinked our friends + + + align:start position:0% +great well we got Hoodwinked our friends +dazzled us not telling us the whole + + align:start position:0% +dazzled us not telling us the whole + + + align:start position:0% +dazzled us not telling us the whole +truth about their lives there what + + align:start position:0% +truth about their lives there what + + + align:start position:0% +truth about their lives there what +conditions they had suffered they + + align:start position:0% +conditions they had suffered they + + + align:start position:0% +conditions they had suffered they +implied with their behavior and dress + + align:start position:0% +implied with their behavior and dress + + + align:start position:0% +implied with their behavior and dress +that the life what the lifestyle was + + align:start position:0% +that the life what the lifestyle was + + + align:start position:0% +that the life what the lifestyle was +there was wasn't really the people who + + align:start position:0% +there was wasn't really the people who + + + align:start position:0% +there was wasn't really the people who +first experienced difficulties abroad + + align:start position:0% +first experienced difficulties abroad + + + align:start position:0% +first experienced difficulties abroad +didn't tell about these things to other + + align:start position:0% +didn't tell about these things to other + + + align:start position:0% +didn't tell about these things to other +people on the contrary they exhibit Only + + align:start position:0% +people on the contrary they exhibit Only + + + align:start position:0% +people on the contrary they exhibit Only +The Good Side nice clothes food jewelry + + align:start position:0% +The Good Side nice clothes food jewelry + + + align:start position:0% +The Good Side nice clothes food jewelry +things they hadn't seen before which + + align:start position:0% +things they hadn't seen before which + + + align:start position:0% +things they hadn't seen before which +were very attractive to the people this + + align:start position:0% +were very attractive to the people this + + + align:start position:0% +were very attractive to the people this +arises from our ignorance and + + align:start position:0% +arises from our ignorance and + + + align:start position:0% +arises from our ignorance and +unconsciousness in our society Keeping + + align:start position:0% +unconsciousness in our society Keeping + + + align:start position:0% +unconsciousness in our society Keeping +Up With the Jones still persist as was + + align:start position:0% +Up With the Jones still persist as was + + + align:start position:0% +Up With the Jones still persist as was +the case with people going to Istanbul + + align:start position:0% +the case with people going to Istanbul + + + align:start position:0% +the case with people going to Istanbul +from The Villages this time the same + + align:start position:0% +from The Villages this time the same + + + align:start position:0% +from The Villages this time the same +thing happened with the people going + + align:start position:0% +thing happened with the people going + + + align:start position:0% +thing happened with the people going +abroad giving false images about life + + align:start position:0% +abroad giving false images about life + + + align:start position:0% +abroad giving false images about life +there these people caused the creation + + align:start position:0% +there these people caused the creation + + + align:start position:0% +there these people caused the creation +of a False Image like money was + + align:start position:0% +of a False Image like money was + + + align:start position:0% +of a False Image like money was +collected either from the trees or off + + align:start position:0% +collected either from the trees or off + + + align:start position:0% +collected either from the trees or off +the street so + + align:start position:0% +the street so + + + align:start position:0% +the street so +easy we went to the big city for all the + + align:start position:0% +easy we went to the big city for all the + + + align:start position:0% +easy we went to the big city for all the +same reason turkey's resources are + + align:start position:0% +same reason turkey's resources are + + + align:start position:0% +same reason turkey's resources are +insufficient people started this + + align:start position:0% +insufficient people started this + + + align:start position:0% +insufficient people started this +adventure with the hopes of attaining + + align:start position:0% +adventure with the hopes of attaining + + + align:start position:0% +adventure with the hopes of attaining +better possibilities and living + + align:start position:0% +better possibilities and living + + + align:start position:0% +better possibilities and living +conditions in other countries and other + + align:start position:0% +conditions in other countries and other + + + align:start position:0% +conditions in other countries and other +lands maybe some of us did get better + + align:start position:0% +lands maybe some of us did get better + + + align:start position:0% +lands maybe some of us did get better +conditions economically we did get some + + align:start position:0% +conditions economically we did get some + + + align:start position:0% +conditions economically we did get some +material benefits this we all starting + + align:start position:0% +material benefits this we all starting + + + align:start position:0% +material benefits this we all starting +with me have to think about maybe some + + align:start position:0% +with me have to think about maybe some + + + align:start position:0% +with me have to think about maybe some +of us earned money but was this the sole + + align:start position:0% +of us earned money but was this the sole + + + align:start position:0% +of us earned money but was this the sole +aim of our coming here the important + + align:start position:0% +aim of our coming here the important + + + align:start position:0% +aim of our coming here the important +part is what we lost morally in our + + align:start position:0% +part is what we lost morally in our + + + align:start position:0% +part is what we lost morally in our +values we were introduced to money here + + align:start position:0% +values we were introduced to money here + + + align:start position:0% +values we were introduced to money here +there were times when I said I wish I + + align:start position:0% +there were times when I said I wish I + + + align:start position:0% +there were times when I said I wish I +had money but now I criticize myself and + + align:start position:0% +had money but now I criticize myself and + + + align:start position:0% +had money but now I criticize myself and +I hate money all right one has to have + + align:start position:0% +I hate money all right one has to have + + + align:start position:0% +I hate money all right one has to have +enough money to live on but if it only + + align:start position:0% +enough money to live on but if it only + + + align:start position:0% +enough money to live on but if it only +is a means now I'm asking first to + + align:start position:0% +is a means now I'm asking first to + + + align:start position:0% +is a means now I'm asking first to +myself and then to all the community did + + align:start position:0% +myself and then to all the community did + + + align:start position:0% +myself and then to all the community did +money make you happy instead we lost our + + align:start position:0% +money make you happy instead we lost our + + + align:start position:0% +money make you happy instead we lost our +values customs and traditions dances + + align:start position:0% +values customs and traditions dances + + + align:start position:0% +values customs and traditions dances +music our respect our love what money + + align:start position:0% +music our respect our love what money + + + align:start position:0% +music our respect our love what money +can bring these back to us there used to + + align:start position:0% +can bring these back to us there used to + + + align:start position:0% +can bring these back to us there used to +be respect for the elderly there were + + align:start position:0% +be respect for the elderly there were + + + align:start position:0% +be respect for the elderly there were +good human relations there was no money + + align:start position:0% +good human relations there was no money + + + align:start position:0% +good human relations there was no money +but there were moral values I lived + + align:start position:0% +but there were moral values I lived + + + align:start position:0% +but there were moral values I lived +these things myself in Turkey I didn't + + align:start position:0% +these things myself in Turkey I didn't + + + align:start position:0% +these things myself in Turkey I didn't +watch these things in movies or read + + align:start position:0% +watch these things in movies or read + + + align:start position:0% +watch these things in movies or read +them in books I know this from my own + + align:start position:0% +them in books I know this from my own + + + align:start position:0% +them in books I know this from my own +experience I'm not objecting to the way + + align:start position:0% +experience I'm not objecting to the way + + + align:start position:0% +experience I'm not objecting to the way +other societies live + + align:start position:0% +other societies live + + + align:start position:0% +other societies live +a British child acts according to how + + align:start position:0% +a British child acts according to how + + + align:start position:0% +a British child acts according to how +he's brought up that's only normal but + + align:start position:0% +he's brought up that's only normal but + + + align:start position:0% +he's brought up that's only normal but +why should I try to imitate their lives + + align:start position:0% +why should I try to imitate their lives + + + align:start position:0% +why should I try to imitate their lives +why should we immediately want to + + align:start position:0% +why should we immediately want to + + + align:start position:0% +why should we immediately want to +assimilate into British culture none of + + align:start position:0% +assimilate into British culture none of + + + align:start position:0% +assimilate into British culture none of +us adults can even speak English we have + + align:start position:0% +us adults can even speak English we have + + + align:start position:0% +us adults can even speak English we have +lost control of the children they are + + align:start position:0% +lost control of the children they are + + + align:start position:0% +lost control of the children they are +the ones speaking English we need them + + align:start position:0% +the ones speaking English we need them + + + align:start position:0% +the ones speaking English we need them +to interpret for us at the schools and + + align:start position:0% +to interpret for us at the schools and + + + align:start position:0% +to interpret for us at the schools and +they can easily fool us who is guilty if + + align:start position:0% +they can easily fool us who is guilty if + + + align:start position:0% +they can easily fool us who is guilty if +you don't teach your culture to your + + align:start position:0% +you don't teach your culture to your + + + align:start position:0% +you don't teach your culture to your +children in the end life isn't about + + align:start position:0% +children in the end life isn't about + + + align:start position:0% +children in the end life isn't about +earning money wearing nice clothes and + + align:start position:0% +earning money wearing nice clothes and + + + align:start position:0% +earning money wearing nice clothes and +riding in nice cars many here enjoy + + align:start position:0% +riding in nice cars many here enjoy + + + align:start position:0% +riding in nice cars many here enjoy +their residents permit but they don't + + align:start position:0% +their residents permit but they don't + + + align:start position:0% +their residents permit but they don't +don't they feel insulted when they are + + align:start position:0% +don't they feel insulted when they are + + + align:start position:0% +don't they feel insulted when they are +treated as second class citizens in the + + align:start position:0% +treated as second class citizens in the + + + align:start position:0% +treated as second class citizens in the +airports at Customs people with British + + align:start position:0% +airports at Customs people with British + + + align:start position:0% +airports at Customs people with British +passports just pass by while the others + + align:start position:0% +passports just pass by while the others + + + align:start position:0% +passports just pass by while the others +wait in cues isn't this a double + + align:start position:0% +wait in cues isn't this a double + + + align:start position:0% +wait in cues isn't this a double +standard look at the lives of my parents + + align:start position:0% +standard look at the lives of my parents + + + align:start position:0% +standard look at the lives of my parents +jair and + + align:start position:0% +jair and + + + align:start position:0% +jair and +fim no washing machine no dishwasher no + + align:start position:0% +fim no washing machine no dishwasher no + + + align:start position:0% +fim no washing machine no dishwasher no +car their children have all of these + + align:start position:0% +car their children have all of these + + + align:start position:0% +car their children have all of these +they have everything appliances + + align:start position:0% +they have everything appliances + + + align:start position:0% +they have everything appliances +instruments vehicles but here if we go + + align:start position:0% +instruments vehicles but here if we go + + + align:start position:0% +instruments vehicles but here if we go +back to the same point what is important + + align:start position:0% +back to the same point what is important + + + align:start position:0% +back to the same point what is important +here whose moral values were more + + align:start position:0% +here whose moral values were more + + + align:start position:0% +here whose moral values were more +precious who is more worthy as a human + + align:start position:0% +precious who is more worthy as a human + + + align:start position:0% +precious who is more worthy as a human +being who is more admired more + + align:start position:0% +being who is more admired more + + + align:start position:0% +being who is more admired more +trustworthy more dependable as a friend + + align:start position:0% +trustworthy more dependable as a friend + + + align:start position:0% +trustworthy more dependable as a friend +who keeps his promises or how he hosts a + + align:start position:0% +who keeps his promises or how he hosts a + + + align:start position:0% +who keeps his promises or how he hosts a +guest in his house we can conclude that + + align:start position:0% +guest in his house we can conclude that + + + align:start position:0% +guest in his house we can conclude that +money is not everything a human being is + + align:start position:0% +money is not everything a human being is + + + align:start position:0% +money is not everything a human being is +a human being no matter if he has money + + align:start position:0% +a human being no matter if he has money + + + align:start position:0% +a human being no matter if he has money +or not in some ways fim May in the + + align:start position:0% +or not in some ways fim May in the + + + align:start position:0% +or not in some ways fim May in the +village has lived a better + + align:start position:0% +village has lived a better + + + align:start position:0% +village has lived a better +life here is fim May's youngest daughter + + align:start position:0% +life here is fim May's youngest daughter + + + align:start position:0% +life here is fim May's youngest daughter +be gazar in a London Cafe the school in + + align:start position:0% +be gazar in a London Cafe the school in + + + align:start position:0% +be gazar in a London Cafe the school in +the village had closed by the time she + + align:start position:0% +the village had closed by the time she + + + align:start position:0% +the village had closed by the time she +was old enough to go this was in part + + align:start position:0% +was old enough to go this was in part + + + align:start position:0% +was old enough to go this was in part +due to the fact that most of the + + align:start position:0% +due to the fact that most of the + + + align:start position:0% +due to the fact that most of the +families had migrated out of the village + + align:start position:0% +families had migrated out of the village + + + align:start position:0% +families had migrated out of the village +and only returned in the summer so she + + align:start position:0% +and only returned in the summer so she + + + align:start position:0% +and only returned in the summer so she +was sent to be living with relatives in + + align:start position:0% +was sent to be living with relatives in + + + align:start position:0% +was sent to be living with relatives in +Adon to attend school however at aged 16 + + align:start position:0% +Adon to attend school however at aged 16 + + + align:start position:0% +Adon to attend school however at aged 16 +before she finished high school Ali sent + + align:start position:0% +before she finished high school Ali sent + + + align:start position:0% +before she finished high school Ali sent +for her to come to England she's 24 now + + align:start position:0% +for her to come to England she's 24 now + + + align:start position:0% +for her to come to England she's 24 now +8 years into the 10 before she can + + align:start position:0% +8 years into the 10 before she can + + + align:start position:0% +8 years into the 10 before she can +return to Turkey and see her mother + + align:start position:0% +return to Turkey and see her mother + + + align:start position:0% +return to Turkey and see her mother +again she is supported by her brother + + align:start position:0% +again she is supported by her brother + + + align:start position:0% +again she is supported by her brother +working sometimes in the + + align:start position:0% +working sometimes in the + + + align:start position:0% +working sometimes in the +cafe her main passion is Kurdish and + + align:start position:0% +cafe her main passion is Kurdish and + + + align:start position:0% +cafe her main passion is Kurdish and +Turkish folk music which she learned + + align:start position:0% +Turkish folk music which she learned + + + align:start position:0% +Turkish folk music which she learned +first from her father who you see now + + align:start position:0% +first from her father who you see now + + + align:start position:0% +first from her father who you see now +with his saws back in the 70s she + + align:start position:0% +with his saws back in the 70s she + + + align:start position:0% +with his saws back in the 70s she +continues to practice and to sing with + + align:start position:0% +continues to practice and to sing with + + + align:start position:0% +continues to practice and to sing with +her brothers and London her dream is to + + align:start position:0% +her brothers and London her dream is to + + + align:start position:0% +her brothers and London her dream is to +make a cassette but she is dissatisfied + + align:start position:0% +make a cassette but she is dissatisfied + + + align:start position:0% +make a cassette but she is dissatisfied +about trying to make their music in a + + align:start position:0% +about trying to make their music in a + + + align:start position:0% +about trying to make their music in a +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +country she says I want to be involved + + align:start position:0% +country she says I want to be involved + + + align:start position:0% +country she says I want to be involved +in music to communicate with other + + align:start position:0% +in music to communicate with other + + + align:start position:0% +in music to communicate with other +people via music + + align:start position:0% +people via music + + + align:start position:0% +people via music +when it comes to the words and the + + align:start position:0% +when it comes to the words and the + + + align:start position:0% +when it comes to the words and the +message a certain kind of music can be + + align:start position:0% +message a certain kind of music can be + + + align:start position:0% +message a certain kind of music can be +best understood only by the people who + + align:start position:0% +best understood only by the people who + + + align:start position:0% +best understood only by the people who +live in that country you can be much + + align:start position:0% +live in that country you can be much + + + align:start position:0% +live in that country you can be much +more productive when you're in your own + + align:start position:0% +more productive when you're in your own + + + align:start position:0% +more productive when you're in your own +country and its music but here so far + + align:start position:0% +country and its music but here so far + + + align:start position:0% +country and its music but here so far +away from home one is only inspired to + + align:start position:0% +away from home one is only inspired to + + + align:start position:0% +away from home one is only inspired to +write songs about missing home and after + + align:start position:0% +write songs about missing home and after + + + align:start position:0% +write songs about missing home and after +a while that's not + + align:start position:0% +a while that's not + + + align:start position:0% +a while that's not +enough my mind is always in Turkey every + + align:start position:0% +enough my mind is always in Turkey every + + + align:start position:0% +enough my mind is always in Turkey every +moment I live in this country we have + + align:start position:0% +moment I live in this country we have + + + align:start position:0% +moment I live in this country we have +always lived a half and half + + align:start position:0% +always lived a half and half + + + align:start position:0% +always lived a half and half +dissatisfied life what I want now most + + align:start position:0% +dissatisfied life what I want now most + + + align:start position:0% +dissatisfied life what I want now most +is to be able to go there to satisfy my + + align:start position:0% +is to be able to go there to satisfy my + + + align:start position:0% +is to be able to go there to satisfy my +longings we live between two cultures + + align:start position:0% +longings we live between two cultures + + + align:start position:0% +longings we live between two cultures +which adds extra responsibilities leaves + + align:start position:0% +which adds extra responsibilities leaves + + + align:start position:0% +which adds extra responsibilities leaves +us depressed and discouraged it is + + align:start position:0% +us depressed and discouraged it is + + + align:start position:0% +us depressed and discouraged it is +ironic that with so many more + + align:start position:0% +ironic that with so many more + + + align:start position:0% +ironic that with so many more +opportunities we end up being so much + + align:start position:0% +opportunities we end up being so much + + + align:start position:0% +opportunities we end up being so much +more + + align:start position:0% +more + + + align:start position:0% +more +negative here is cenon also one of the + + align:start position:0% +negative here is cenon also one of the + + + align:start position:0% +negative here is cenon also one of the +fim sons who came to London like bezar + + align:start position:0% +fim sons who came to London like bezar + + + align:start position:0% +fim sons who came to London like bezar +he is a musician he is the Babe in arms + + align:start position:0% +he is a musician he is the Babe in arms + + + align:start position:0% +he is a musician he is the Babe in arms +with fim on the right for while he and + + align:start position:0% +with fim on the right for while he and + + + align:start position:0% +with fim on the right for while he and +Ali ran a music school in London to + + align:start position:0% +Ali ran a music school in London to + + + align:start position:0% +Ali ran a music school in London to +teach the local kids Kurdish and Turkish + + align:start position:0% +teach the local kids Kurdish and Turkish + + + align:start position:0% +teach the local kids Kurdish and Turkish +folk music and how to play the S it was + + align:start position:0% +folk music and how to play the S it was + + + align:start position:0% +folk music and how to play the S it was +a gathering place for the Youth of the + + align:start position:0% +a gathering place for the Youth of the + + + align:start position:0% +a gathering place for the Youth of the +community but it didn't pay the rent so + + align:start position:0% +community but it didn't pay the rent so + + + align:start position:0% +community but it didn't pay the rent so +it eventually shut down cenan plays + + align:start position:0% +it eventually shut down cenan plays + + + align:start position:0% +it eventually shut down cenan plays +sometimes at nightclubs in the Turkish + + align:start position:0% +sometimes at nightclubs in the Turkish + + + align:start position:0% +sometimes at nightclubs in the Turkish +neighborhoods he is talented musically + + align:start position:0% +neighborhoods he is talented musically + + + align:start position:0% +neighborhoods he is talented musically +and very Charming but I haven't been + + align:start position:0% +and very Charming but I haven't been + + + align:start position:0% +and very Charming but I haven't been +able to get a straight answer out of him + + align:start position:0% +able to get a straight answer out of him + + + align:start position:0% +able to get a straight answer out of him +about what he how he spends his days + + align:start position:0% + + + + align:start position:0% + +now I want to return with you to top + + align:start position:0% +now I want to return with you to top + + + align:start position:0% +now I want to return with you to top +parage to see after 30 years of + + align:start position:0% +parage to see after 30 years of + + + align:start position:0% +parage to see after 30 years of +migration who remains there and what + + align:start position:0% +migration who remains there and what + + + align:start position:0% +migration who remains there and what +their views + + align:start position:0% + + + + align:start position:0% + +are here's fim's father-in-law Hassan + + align:start position:0% +are here's fim's father-in-law Hassan + + + align:start position:0% +are here's fim's father-in-law Hassan +Baba one of the reasons fim stays in the + + align:start position:0% +Baba one of the reasons fim stays in the + + + align:start position:0% +Baba one of the reasons fim stays in the +village is to take care of him he + + align:start position:0% +village is to take care of him he + + + align:start position:0% +village is to take care of him he +refuses to live in the city in an + + align:start position:0% +refuses to live in the city in an + + + align:start position:0% +refuses to live in the city in an +interview he said to me I don't like + + align:start position:0% +interview he said to me I don't like + + + align:start position:0% +interview he said to me I don't like +cities the village life is good enough + + align:start position:0% +cities the village life is good enough + + + align:start position:0% +cities the village life is good enough +for me dry bread cold water that's good + + align:start position:0% +for me dry bread cold water that's good + + + align:start position:0% +for me dry bread cold water that's good +enough the mountain bird doesn't fit in + + align:start position:0% +enough the mountain bird doesn't fit in + + + align:start position:0% +enough the mountain bird doesn't fit in +a Vineyard and a Vineyard bird doesn't + + align:start position:0% +a Vineyard and a Vineyard bird doesn't + + + align:start position:0% +a Vineyard and a Vineyard bird doesn't +belong in the + + align:start position:0% + + + + align:start position:0% + +mountain this is Hassan Baba in 1976 + + align:start position:0% +mountain this is Hassan Baba in 1976 + + + align:start position:0% +mountain this is Hassan Baba in 1976 +with his late wife when I asked him + + align:start position:0% +with his late wife when I asked him + + + align:start position:0% +with his late wife when I asked him +about the changes he'd seen at his + + align:start position:0% +about the changes he'd seen at his + + + align:start position:0% +about the changes he'd seen at his +lifetime he commented in the past the + + align:start position:0% +lifetime he commented in the past the + + + align:start position:0% +lifetime he commented in the past the +women wouldn't go about with their heads + + align:start position:0% +women wouldn't go about with their heads + + + align:start position:0% +women wouldn't go about with their heads +uncovered a bride wouldn't go out for a + + align:start position:0% +uncovered a bride wouldn't go out for a + + + align:start position:0% +uncovered a bride wouldn't go out for a +month now it is all free there is a + + align:start position:0% +month now it is all free there is a + + + align:start position:0% +month now it is all free there is a +civilized understanding old heads become + + align:start position:0% +civilized understanding old heads become + + + align:start position:0% +civilized understanding old heads become +new heads but the old days were Heaven + + align:start position:0% +new heads but the old days were Heaven + + + align:start position:0% +new heads but the old days were Heaven +compared to today there was goodness and + + align:start position:0% +compared to today there was goodness and + + + align:start position:0% +compared to today there was goodness and +blessing there was Humanity the elders + + align:start position:0% +blessing there was Humanity the elders + + + align:start position:0% +blessing there was Humanity the elders +and the young people were aware of the + + align:start position:0% +and the young people were aware of the + + + align:start position:0% +and the young people were aware of the +difference and the distance between them + + align:start position:0% +difference and the distance between them + + + align:start position:0% +difference and the distance between them +and respected each other I am much older + + align:start position:0% +and respected each other I am much older + + + align:start position:0% +and respected each other I am much older +than you but whoever you are what it all + + align:start position:0% +than you but whoever you are what it all + + + align:start position:0% +than you but whoever you are what it all +comes down to is good manners honor + + align:start position:0% +comes down to is good manners honor + + + align:start position:0% +comes down to is good manners honor +kindness and + + align:start position:0% + + + + align:start position:0% + +mercy Hanam shimshek fim's nextdoor + + align:start position:0% +mercy Hanam shimshek fim's nextdoor + + + align:start position:0% +mercy Hanam shimshek fim's nextdoor +neighbor recently became a widow she + + align:start position:0% +neighbor recently became a widow she + + + align:start position:0% +neighbor recently became a widow she +refuses to move to the city um on her + + align:start position:0% +refuses to move to the city um on her + + + align:start position:0% +refuses to move to the city um on her +son's invite as long as she can take + + align:start position:0% +son's invite as long as she can take + + + align:start position:0% +son's invite as long as she can take +care of herself in the + + align:start position:0% +care of herself in the + + + align:start position:0% +care of herself in the +village a few years ago her eldest + + align:start position:0% +village a few years ago her eldest + + + align:start position:0% +village a few years ago her eldest +daughter was politically who was + + align:start position:0% +daughter was politically who was + + + align:start position:0% +daughter was politically who was +politically active got involved in + + align:start position:0% +politically active got involved in + + + align:start position:0% +politically active got involved in +Terrorist activities and was shot dead + + align:start position:0% +Terrorist activities and was shot dead + + + align:start position:0% +Terrorist activities and was shot dead +she reflects on the old + + align:start position:0% +she reflects on the old + + + align:start position:0% +she reflects on the old +times before there was great poverty + + align:start position:0% +times before there was great poverty + + + align:start position:0% +times before there was great poverty +even though we suffered a lot we still + + align:start position:0% +even though we suffered a lot we still + + + align:start position:0% +even though we suffered a lot we still +longed for those days we we were better + + align:start position:0% +longed for those days we we were better + + + align:start position:0% +longed for those days we we were better +we were happier then we were all + + align:start position:0% +we were happier then we were all + + + align:start position:0% +we were happier then we were all +together then with our children now + + align:start position:0% +together then with our children now + + + align:start position:0% +together then with our children now +conditions may be much better but there + + align:start position:0% +conditions may be much better but there + + + align:start position:0% +conditions may be much better but there +is no family just + + align:start position:0% + + + + align:start position:0% + +loneliness there are also younger people + + align:start position:0% +loneliness there are also younger people + + + align:start position:0% +loneliness there are also younger people +and families who return to the Village + + align:start position:0% +and families who return to the Village + + + align:start position:0% +and families who return to the Village +from months at a time this young woman + + align:start position:0% +from months at a time this young woman + + + align:start position:0% +from months at a time this young woman +is chidam she spent her part of her + + align:start position:0% +is chidam she spent her part of her + + + align:start position:0% +is chidam she spent her part of her +youth in the village and then got a few + + align:start position:0% +youth in the village and then got a few + + + align:start position:0% +youth in the village and then got a few +years education while living in Adonna + + align:start position:0% +years education while living in Adonna + + + align:start position:0% +years education while living in Adonna +her parents took them with her to Israel + + align:start position:0% +her parents took them with her to Israel + + + align:start position:0% +her parents took them with her to Israel +when she was 15 she worked there as a + + align:start position:0% +when she was 15 she worked there as a + + + align:start position:0% +when she was 15 she worked there as a +babysitter in a house cleaner until the + + align:start position:0% +babysitter in a house cleaner until the + + + align:start position:0% +babysitter in a house cleaner until the +age of 22 she was impressed with the + + align:start position:0% +age of 22 she was impressed with the + + + align:start position:0% +age of 22 she was impressed with the +orderliness and the lifestyle in Israel + + align:start position:0% +orderliness and the lifestyle in Israel + + + align:start position:0% +orderliness and the lifestyle in Israel +and would like to return + + align:start position:0% +and would like to return + + + align:start position:0% +and would like to return +there however now she's engaged and + + align:start position:0% +there however now she's engaged and + + + align:start position:0% +there however now she's engaged and +waiting out her time before the wedding + + align:start position:0% +waiting out her time before the wedding + + + align:start position:0% +waiting out her time before the wedding +with the v in the village with her + + align:start position:0% +with the v in the village with her + + + align:start position:0% +with the v in the village with her +grandmother she and her mother are still + + align:start position:0% +grandmother she and her mother are still + + + align:start position:0% +grandmother she and her mother are still +recovering from a traumatic experience + + align:start position:0% +recovering from a traumatic experience + + + align:start position:0% +recovering from a traumatic experience +um due to the earthquake that CLA the + + align:start position:0% +um due to the earthquake that CLA the + + + align:start position:0% +um due to the earthquake that CLA the +live claimed the lives of 30,000 in + + align:start position:0% +live claimed the lives of 30,000 in + + + align:start position:0% +live claimed the lives of 30,000 in +1999 jum and her mother were in the same + + align:start position:0% +1999 jum and her mother were in the same + + + align:start position:0% +1999 jum and her mother were in the same +apartment in yivo with jum's brother and + + align:start position:0% +apartment in yivo with jum's brother and + + + align:start position:0% +apartment in yivo with jum's brother and +Uncle when the earthquake occurred the + + align:start position:0% +Uncle when the earthquake occurred the + + + align:start position:0% +Uncle when the earthquake occurred the +men were crushed to death when the + + align:start position:0% +men were crushed to death when the + + + align:start position:0% +men were crushed to death when the +building collapsed jam and her mother + + align:start position:0% +building collapsed jam and her mother + + + align:start position:0% +building collapsed jam and her mother +were + + align:start position:0% +were + + + align:start position:0% +were +saved Jam will move to Istanbul where + + align:start position:0% +saved Jam will move to Istanbul where + + + align:start position:0% +saved Jam will move to Istanbul where +her fiance Works after the wedding but + + align:start position:0% +her fiance Works after the wedding but + + + align:start position:0% +her fiance Works after the wedding but +for now she is happy with the Village + + align:start position:0% +for now she is happy with the Village + + + align:start position:0% +for now she is happy with the Village +Life socializing with all the younger + + align:start position:0% +Life socializing with all the younger + + + align:start position:0% +Life socializing with all the younger +people that come as vacationers during + + align:start position:0% +people that come as vacationers during + + + align:start position:0% +people that come as vacationers during +the summer + + align:start position:0% + + + + align:start position:0% + +months fim however still lives in topar + + align:start position:0% +months fim however still lives in topar + + + align:start position:0% +months fim however still lives in topar +ditch year round with a few dozen + + align:start position:0% +ditch year round with a few dozen + + + align:start position:0% +ditch year round with a few dozen +households mostly elderly who stay + + align:start position:0% +households mostly elderly who stay + + + align:start position:0% +households mostly elderly who stay +through the + + align:start position:0% +through the + + + align:start position:0% +through the +winter after her husband died she + + align:start position:0% +winter after her husband died she + + + align:start position:0% +winter after her husband died she +stepped forward and got herself elected + + align:start position:0% +stepped forward and got herself elected + + + align:start position:0% +stepped forward and got herself elected +to become the first female Village head + + align:start position:0% +to become the first female Village head + + + align:start position:0% +to become the first female Village head +the mkar to have a female mkar brought + + align:start position:0% +the mkar to have a female mkar brought + + + align:start position:0% +the mkar to have a female mkar brought +broke with centuries of + + align:start position:0% +broke with centuries of + + + align:start position:0% +broke with centuries of +tradition this is her living room from + + align:start position:0% +tradition this is her living room from + + + align:start position:0% +tradition this is her living room from +which she conducts Village business as a + + align:start position:0% +which she conducts Village business as a + + + align:start position:0% +which she conducts Village business as a +MTAR she has made major improvements + + align:start position:0% +MTAR she has made major improvements + + + align:start position:0% +MTAR she has made major improvements +including road construction of new + + align:start position:0% +including road construction of new + + + align:start position:0% +including road construction of new +Central well and water system and the + + align:start position:0% +Central well and water system and the + + + align:start position:0% +Central well and water system and the +construction of a village + + align:start position:0% +construction of a village + + + align:start position:0% +construction of a village +house her does her husband died + + align:start position:0% +house her does her husband died + + + align:start position:0% +house her does her husband died +tragically 10 years ago so f Way wears + + align:start position:0% +tragically 10 years ago so f Way wears + + + align:start position:0% +tragically 10 years ago so f Way wears +mostly the traditional black of widows + + align:start position:0% +mostly the traditional black of widows + + + align:start position:0% +mostly the traditional black of widows +but has introduced a few muted colors + + align:start position:0% +but has introduced a few muted colors + + + align:start position:0% +but has introduced a few muted colors +and pants into her + + align:start position:0% +and pants into her + + + align:start position:0% +and pants into her +wardrobe fim talks to her children in + + align:start position:0% +wardrobe fim talks to her children in + + + align:start position:0% +wardrobe fim talks to her children in +England by the phone and watches the uh + + align:start position:0% +England by the phone and watches the uh + + + align:start position:0% +England by the phone and watches the uh +the videotapes that they + + align:start position:0% +the videotapes that they + + + align:start position:0% +the videotapes that they +send the Wonder of this woman is that + + align:start position:0% +send the Wonder of this woman is that + + + align:start position:0% +send the Wonder of this woman is that +she has made these dramatic changes + + align:start position:0% +she has made these dramatic changes + + + align:start position:0% +she has made these dramatic changes +without migrating herself this this is + + align:start position:0% +without migrating herself this this is + + + align:start position:0% +without migrating herself this this is +how she expresses herself about + + align:start position:0% +how she expresses herself about + + + align:start position:0% +how she expresses herself about +migrating to do work in the + + align:start position:0% +migrating to do work in the + + + align:start position:0% +migrating to do work in the +city F the changes started about 30 + + align:start position:0% +city F the changes started about 30 + + + align:start position:0% +city F the changes started about 30 +years ago when people including my + + align:start position:0% +years ago when people including my + + + align:start position:0% +years ago when people including my +husband went to work in the city he did + + align:start position:0% +husband went to work in the city he did + + + align:start position:0% +husband went to work in the city he did +not want his children to stay in the + + align:start position:0% +not want his children to stay in the + + + align:start position:0% +not want his children to stay in the +village and just be Farmers or Shepherds + + align:start position:0% +village and just be Farmers or Shepherds + + + align:start position:0% +village and just be Farmers or Shepherds +like himself we moved to the city but we + + align:start position:0% +like himself we moved to the city but we + + + align:start position:0% +like himself we moved to the city but we +couldn't + + align:start position:0% +couldn't + + + align:start position:0% +couldn't +manage I can do any kind of hard Village + + align:start position:0% +manage I can do any kind of hard Village + + + align:start position:0% +manage I can do any kind of hard Village +work but the city work forgive me + + align:start position:0% +work but the city work forgive me + + + align:start position:0% +work but the city work forgive me +cleaning toilets and watching other + + align:start position:0% +cleaning toilets and watching other + + + align:start position:0% +cleaning toilets and watching other +people's underwear where I couldn't go + + align:start position:0% +people's underwear where I couldn't go + + + align:start position:0% +people's underwear where I couldn't go +along with that that kind of work + + align:start position:0% +along with that that kind of work + + + align:start position:0% +along with that that kind of work +affects a person's Pride so we move back + + align:start position:0% +affects a person's Pride so we move back + + + align:start position:0% +affects a person's Pride so we move back +to the + + align:start position:0% +to the + + + align:start position:0% +to the +village in the summer The Village fills + + align:start position:0% +village in the summer The Village fills + + + align:start position:0% +village in the summer The Village fills +up with families from the cities who + + align:start position:0% +up with families from the cities who + + + align:start position:0% +up with families from the cities who +rebuild old houses adding appliances and + + align:start position:0% +rebuild old houses adding appliances and + + + align:start position:0% +rebuild old houses adding appliances and +satellite + + align:start position:0% +satellite + + + align:start position:0% +satellite +dishes they hold celebrations for + + align:start position:0% +dishes they hold celebrations for + + + align:start position:0% +dishes they hold celebrations for +weddings and circum circumcisions and + + align:start position:0% +weddings and circum circumcisions and + + + align:start position:0% +weddings and circum circumcisions and +the anniversary of their dead with the + + align:start position:0% +the anniversary of their dead with the + + + align:start position:0% +the anniversary of their dead with the +ceremonies and village-wide banquets + + align:start position:0% +ceremonies and village-wide banquets + + + align:start position:0% +ceremonies and village-wide banquets +many people who have died in the cities + + align:start position:0% +many people who have died in the cities + + + align:start position:0% +many people who have died in the cities +are brought back to the Village to be + + align:start position:0% +are brought back to the Village to be + + + align:start position:0% +are brought back to the Village to be +buried the old traditional gravestones + + align:start position:0% +buried the old traditional gravestones + + + align:start position:0% +buried the old traditional gravestones +are being replaced with elaborate marble + + align:start position:0% +are being replaced with elaborate marble + + + align:start position:0% +are being replaced with elaborate marble +ones similar to those in the seen in the + + align:start position:0% +ones similar to those in the seen in the + + + align:start position:0% +ones similar to those in the seen in the +modern + + align:start position:0% +modern + + + align:start position:0% +modern +cities here is jair's Tombstone paid for + + align:start position:0% +cities here is jair's Tombstone paid for + + + align:start position:0% +cities here is jair's Tombstone paid for +by fim's children living abroad who + + align:start position:0% +by fim's children living abroad who + + + align:start position:0% +by fim's children living abroad who +could not return to Turkey to attend the + + align:start position:0% +could not return to Turkey to attend the + + + align:start position:0% +could not return to Turkey to attend the +funeral this procession walks to the + + align:start position:0% +funeral this procession walks to the + + + align:start position:0% +funeral this procession walks to the +graveyard to sacrifice a lamb that will + + align:start position:0% +graveyard to sacrifice a lamb that will + + + align:start position:0% +graveyard to sacrifice a lamb that will +contribute to the meal that the family + + align:start position:0% +contribute to the meal that the family + + + align:start position:0% +contribute to the meal that the family +of the remembered dead PR prepares for + + align:start position:0% +of the remembered dead PR prepares for + + + align:start position:0% +of the remembered dead PR prepares for +the hundreds of people who come to the + + align:start position:0% +the hundreds of people who come to the + + + align:start position:0% +the hundreds of people who come to the +memorial the dead man was a young + + align:start position:0% +memorial the dead man was a young + + + align:start position:0% +memorial the dead man was a young +political activist who was shot a year + + align:start position:0% +political activist who was shot a year + + + align:start position:0% +political activist who was shot a year +ago his memory is honored prayers are + + align:start position:0% +ago his memory is honored prayers are + + + align:start position:0% +ago his memory is honored prayers are +said bridges are sung and the community + + align:start position:0% +said bridges are sung and the community + + + align:start position:0% +said bridges are sung and the community +Comforts all of those who have loved + + align:start position:0% +Comforts all of those who have loved + + + align:start position:0% +Comforts all of those who have loved +ones who were buried + + align:start position:0% +ones who were buried + + + align:start position:0% +ones who were buried +there at first glance the words most of + + align:start position:0% +there at first glance the words most of + + + align:start position:0% +there at first glance the words most of +us that would Ed to describe this place + + align:start position:0% +us that would Ed to describe this place + + + align:start position:0% +us that would Ed to describe this place +this Village topar ditch are in the + + align:start position:0% +this Village topar ditch are in the + + + align:start position:0% +this Village topar ditch are in the +middle of nowhere or for God + + align:start position:0% +middle of nowhere or for God + + + align:start position:0% +middle of nowhere or for God +forsaken it takes 16 hours and three + + align:start position:0% +forsaken it takes 16 hours and three + + + align:start position:0% +forsaken it takes 16 hours and three +different buses to get from topar ditch + + align:start position:0% +different buses to get from topar ditch + + + align:start position:0% +different buses to get from topar ditch +from + + align:start position:0% + + + + align:start position:0% + +Istanbul why do people come back what is + + align:start position:0% +Istanbul why do people come back what is + + + align:start position:0% +Istanbul why do people come back what is +special about this place what meaning + + align:start position:0% +special about this place what meaning + + + align:start position:0% +special about this place what meaning +does it have to them that they cannot + + align:start position:0% +does it have to them that they cannot + + + align:start position:0% +does it have to them that they cannot +find in Istanbul or Adonna or + + align:start position:0% +find in Istanbul or Adonna or + + + align:start position:0% +find in Istanbul or Adonna or +London no one is returning to 10 sheep + + align:start position:0% +London no one is returning to 10 sheep + + + align:start position:0% +London no one is returning to 10 sheep +the rugs that were made her once will + + align:start position:0% +the rugs that were made her once will + + + align:start position:0% +the rugs that were made her once will +never be woven again eventually none of + + align:start position:0% +never be woven again eventually none of + + + align:start position:0% +never be woven again eventually none of +the elderly will remain for the + + align:start position:0% +the elderly will remain for the + + + align:start position:0% +the elderly will remain for the +winter but I imagine that Ali and be + + align:start position:0% +winter but I imagine that Ali and be + + + align:start position:0% +winter but I imagine that Ali and be +gazar will try to describe the spirit of + + align:start position:0% +gazar will try to describe the spirit of + + + align:start position:0% +gazar will try to describe the spirit of +topar dit in the songs that they will + + align:start position:0% +topar dit in the songs that they will + + + align:start position:0% +topar dit in the songs that they will +write I began by saying that I would + + align:start position:0% +write I began by saying that I would + + + align:start position:0% +write I began by saying that I would +show you how Urban migration made + + align:start position:0% +show you how Urban migration made + + + align:start position:0% +show you how Urban migration made +feminists out of traditional village + + align:start position:0% +feminists out of traditional village + + + align:start position:0% +feminists out of traditional village +women this was the discovery I made and + + align:start position:0% +women this was the discovery I made and + + + align:start position:0% +women this was the discovery I made and +the finding that encouraged me to tell + + align:start position:0% +the finding that encouraged me to tell + + + align:start position:0% +the finding that encouraged me to tell +their + + align:start position:0% +their + + + align:start position:0% +their +stories I purposely use the term + + align:start position:0% +stories I purposely use the term + + + align:start position:0% +stories I purposely use the term +feminist to provoke discussion about + + align:start position:0% +feminist to provoke discussion about + + + align:start position:0% +feminist to provoke discussion about +what these women have achieved no one + + align:start position:0% +what these women have achieved no one + + + align:start position:0% +what these women have achieved no one +had ever used the word feminist in their + + align:start position:0% +had ever used the word feminist in their + + + align:start position:0% +had ever used the word feminist in their +conversations with me they have never + + align:start position:0% +conversations with me they have never + + + align:start position:0% +conversations with me they have never +been no one in these pictures they have + + align:start position:0% +been no one in these pictures they have + + + align:start position:0% +been no one in these pictures they have +never been a part of any organized + + align:start position:0% +never been a part of any organized + + + align:start position:0% +never been a part of any organized +feminist + + align:start position:0% +feminist + + + align:start position:0% +feminist +organization yet in my view they are + + align:start position:0% +organization yet in my view they are + + + align:start position:0% +organization yet in my view they are +feminist by their actions and by their + + align:start position:0% +feminist by their actions and by their + + + align:start position:0% +feminist by their actions and by their +accomplishments in the light of the + + align:start position:0% +accomplishments in the light of the + + + align:start position:0% +accomplishments in the light of the +centuries theyve of tradition they've + + align:start position:0% +centuries theyve of tradition they've + + + align:start position:0% +centuries theyve of tradition they've +had to + + align:start position:0% +had to + + + align:start position:0% +had to +overcome for the older generation of + + align:start position:0% +overcome for the older generation of + + + align:start position:0% +overcome for the older generation of +illiterate women such as chak this + + align:start position:0% +illiterate women such as chak this + + + align:start position:0% +illiterate women such as chak this +pursuit of a feminist path involved + + align:start position:0% +pursuit of a feminist path involved + + + align:start position:0% +pursuit of a feminist path involved +taking a job outside the home receiving + + align:start position:0% +taking a job outside the home receiving + + + align:start position:0% +taking a job outside the home receiving +wages and controlling a part or all of + + align:start position:0% +wages and controlling a part or all of + + + align:start position:0% +wages and controlling a part or all of +the money and participating in key + + align:start position:0% +the money and participating in key + + + align:start position:0% +the money and participating in key +economic decisions affecting the + + align:start position:0% +economic decisions affecting the + + + align:start position:0% +economic decisions affecting the +family for their daughter's generation + + align:start position:0% +family for their daughter's generation + + + align:start position:0% +family for their daughter's generation +feminist action involved insisting on an + + align:start position:0% +feminist action involved insisting on an + + + align:start position:0% +feminist action involved insisting on an +education choosing their own husbands + + align:start position:0% +education choosing their own husbands + + + align:start position:0% +education choosing their own husbands +and marrying later in life so that they + + align:start position:0% +and marrying later in life so that they + + + align:start position:0% +and marrying later in life so that they +could finish their education it also + + align:start position:0% +could finish their education it also + + + align:start position:0% +could finish their education it also +involved taking advantage of health + + align:start position:0% +involved taking advantage of health + + + align:start position:0% +involved taking advantage of health +services including + + align:start position:0% +services including + + + align:start position:0% +services including +contraception both in the village and in + + align:start position:0% +contraception both in the village and in + + + align:start position:0% +contraception both in the village and in +the city women for the first time joined + + align:start position:0% +the city women for the first time joined + + + align:start position:0% +the city women for the first time joined +political organizations and took or took + + align:start position:0% +political organizations and took or took + + + align:start position:0% +political organizations and took or took +political + + align:start position:0% + + + + align:start position:0% + +office once my efforts to document their + + align:start position:0% +office once my efforts to document their + + + align:start position:0% +office once my efforts to document their +stories were underway the most + + align:start position:0% +stories were underway the most + + + align:start position:0% +stories were underway the most +surprising thing I discovered was that + + align:start position:0% +surprising thing I discovered was that + + + align:start position:0% +surprising thing I discovered was that +the women who migrated to England + + align:start position:0% +the women who migrated to England + + + align:start position:0% +the women who migrated to England +experienced far fewer improvements in + + align:start position:0% +experienced far fewer improvements in + + + align:start position:0% +experienced far fewer improvements in +their lives other than material + + align:start position:0% +their lives other than material + + + align:start position:0% +their lives other than material +conference than the women who migrated + + align:start position:0% +conference than the women who migrated + + + align:start position:0% +conference than the women who migrated +within turkey to Turkish cities their + + align:start position:0% +within turkey to Turkish cities their + + + align:start position:0% +within turkey to Turkish cities their +lack of training and limits on their job + + align:start position:0% +lack of training and limits on their job + + + align:start position:0% +lack of training and limits on their job +opportunities in England restricted + + align:start position:0% +opportunities in England restricted + + + align:start position:0% +opportunities in England restricted +their personal development and + + align:start position:0% +their personal development and + + + align:start position:0% +their personal development and +Independence I assume that language and + + align:start position:0% +Independence I assume that language and + + + align:start position:0% +Independence I assume that language and +social barriers are the reason for this + + align:start position:0% +social barriers are the reason for this + + + align:start position:0% +social barriers are the reason for this +it will be interesting to see what + + align:start position:0% +it will be interesting to see what + + + align:start position:0% +it will be interesting to see what +changes and we might dare to call them + + align:start position:0% +changes and we might dare to call them + + + align:start position:0% +changes and we might dare to call them +improvements that their children who + + align:start position:0% +improvements that their children who + + + align:start position:0% +improvements that their children who +have grown up in British schools might + + align:start position:0% + + + + align:start position:0% + +experience when we ask the question what + + align:start position:0% +experience when we ask the question what + + + align:start position:0% +experience when we ask the question what +part of your Traditions do you want to + + align:start position:0% +part of your Traditions do you want to + + + align:start position:0% +part of your Traditions do you want to +leave behind and what part do you want + + align:start position:0% +leave behind and what part do you want + + + align:start position:0% +leave behind and what part do you want +to hold on + + align:start position:0% +to hold on + + + align:start position:0% +to hold on +to there are many answers spanning the + + align:start position:0% +to there are many answers spanning the + + + align:start position:0% +to there are many answers spanning the +gamut from those who have been starting + + align:start position:0% +gamut from those who have been starting + + + align:start position:0% +gamut from those who have been starting +started to mythologize the life of the + + align:start position:0% +started to mythologize the life of the + + + align:start position:0% +started to mythologize the life of the +village and those who want nothing to do + + align:start position:0% +village and those who want nothing to do + + + align:start position:0% +village and those who want nothing to do +with the past it will be intriguing to + + align:start position:0% +with the past it will be intriguing to + + + align:start position:0% +with the past it will be intriguing to +see which qualities of visual Vis sorry + + align:start position:0% +see which qualities of visual Vis sorry + + + align:start position:0% +see which qualities of visual Vis sorry +visual life are retained and transformed + + align:start position:0% +visual life are retained and transformed + + + align:start position:0% +visual life are retained and transformed +in the context of Modern urban + + align:start position:0% +in the context of Modern urban + + + align:start position:0% +in the context of Modern urban +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +settings I hope you've enjoyed meeting + + align:start position:0% +settings I hope you've enjoyed meeting + + + align:start position:0% +settings I hope you've enjoyed meeting +my friends all of them took the trouble + + align:start position:0% +my friends all of them took the trouble + + + align:start position:0% +my friends all of them took the trouble +to share their stories with me I think + + align:start position:0% +to share their stories with me I think + + + align:start position:0% +to share their stories with me I think +at least in part because they were proud + + align:start position:0% +at least in part because they were proud + + + align:start position:0% +at least in part because they were proud +of how much they had accomplished + + align:start position:0% +of how much they had accomplished + + + align:start position:0% +of how much they had accomplished +I consider it my J my honor to um share + + align:start position:0% +I consider it my J my honor to um share + + + align:start position:0% +I consider it my J my honor to um share +their accomplishments and tell their + + align:start position:0% +their accomplishments and tell their + + + align:start position:0% +their accomplishments and tell their +stories to the broadest possible + + align:start position:0% +stories to the broadest possible + + + align:start position:0% +stories to the broadest possible +audience I hope I've take I've shaken + + align:start position:0% +audience I hope I've take I've shaken + + + align:start position:0% +audience I hope I've take I've shaken +your assumptions about the impact of + + align:start position:0% +your assumptions about the impact of + + + align:start position:0% +your assumptions about the impact of +rural to Urban migration and the power + + align:start position:0% +rural to Urban migration and the power + + + align:start position:0% +rural to Urban migration and the power +of Turkish village women to change their + + align:start position:0% +of Turkish village women to change their + + + align:start position:0% +of Turkish village women to change their +lives thanks + + align:start position:0% + + + + align:start position:0% + +this lecture is + + align:start position:0% +this lecture is + + + align:start position:0% +this lecture is +co-sponsored uh by the city design and + + align:start position:0% +co-sponsored uh by the city design and + + + align:start position:0% +co-sponsored uh by the city design and +development program and by the Aon + + align:start position:0% +development program and by the Aon + + + align:start position:0% +development program and by the Aon +program for architecture at MIT and I've + + align:start position:0% +program for architecture at MIT and I've + + + align:start position:0% +program for architecture at MIT and I've +asked nassa rat who's the director of + + align:start position:0% +asked nassa rat who's the director of + + + align:start position:0% +asked nassa rat who's the director of +the program professor of architecture + + align:start position:0% +the program professor of architecture + + + align:start position:0% +the program professor of architecture +here at MIT to make some comments before + + align:start position:0% +here at MIT to make some comments before + + + align:start position:0% +here at MIT to make some comments before +we open uh the floor to General + + align:start position:0% +we open uh the floor to General + + + align:start position:0% +we open uh the floor to General +discussion thank + + align:start position:0% +discussion thank + + + align:start position:0% +discussion thank +you and couldn't have chosen a worse + + align:start position:0% +you and couldn't have chosen a worse + + + align:start position:0% +you and couldn't have chosen a worse +person than me to make these comments + + align:start position:0% +person than me to make these comments + + + align:start position:0% +person than me to make these comments +but I'll make them nonetheless um + + align:start position:0% +but I'll make them nonetheless um + + + align:start position:0% +but I'll make them nonetheless um +thank you Leslie it was very beautiful I + + align:start position:0% +thank you Leslie it was very beautiful I + + + align:start position:0% +thank you Leslie it was very beautiful I +should start by saying that the visual + + align:start position:0% +should start by saying that the visual + + + align:start position:0% +should start by saying that the visual +quality of your images are really + + align:start position:0% +quality of your images are really + + + align:start position:0% +quality of your images are really +stupendous and I enjoyed them + + align:start position:0% +stupendous and I enjoyed them + + + align:start position:0% +stupendous and I enjoyed them +tremendously I also enjoyed the way you + + align:start position:0% +tremendously I also enjoyed the way you + + + align:start position:0% +tremendously I also enjoyed the way you +woven your narrative your narrative is + + align:start position:0% +woven your narrative your narrative is + + + align:start position:0% +woven your narrative your narrative is +actually flowing in + + align:start position:0% +actually flowing in + + + align:start position:0% +actually flowing in +extremely story-like way although you + + align:start position:0% +extremely story-like way although you + + + align:start position:0% +extremely story-like way although you +are using social sciences tools of + + align:start position:0% +are using social sciences tools of + + + align:start position:0% +are using social sciences tools of +interviewing and sort of like bringing + + align:start position:0% +interviewing and sort of like bringing + + + align:start position:0% +interviewing and sort of like bringing +in the interviews in and you even use + + align:start position:0% +in the interviews in and you even use + + + align:start position:0% +in the interviews in and you even use +statistics every now and then and you + + align:start position:0% +statistics every now and then and you + + + align:start position:0% +statistics every now and then and you +use actually all sorts of like hard data + + align:start position:0% +use actually all sorts of like hard data + + + align:start position:0% +use actually all sorts of like hard data +but nonetheless I guess actually most of + + align:start position:0% +but nonetheless I guess actually most of + + + align:start position:0% +but nonetheless I guess actually most of +us have enjoyed it more as a story than + + align:start position:0% +us have enjoyed it more as a story than + + + align:start position:0% +us have enjoyed it more as a story than +anything else listening to what she's + + align:start position:0% +anything else listening to what she's + + + align:start position:0% +anything else listening to what she's +saying so thank you for that I have two + + align:start position:0% +saying so thank you for that I have two + + + align:start position:0% +saying so thank you for that I have two +comments one is to speak about + + align:start position:0% +comments one is to speak about + + + align:start position:0% +comments one is to speak about +immigration and of course actually I + + align:start position:0% +immigration and of course actually I + + + align:start position:0% +immigration and of course actually I +know something about it myself I am an + + align:start position:0% +know something about it myself I am an + + + align:start position:0% +know something about it myself I am an +immigrant myself probably actually half + + align:start position:0% +immigrant myself probably actually half + + + align:start position:0% +immigrant myself probably actually half +of you are immigrants or planning to be + + align:start position:0% +of you are immigrants or planning to be + + + align:start position:0% +of you are immigrants or planning to be +if you are not + + align:start position:0% +if you are not + + + align:start position:0% +if you are not +already + + align:start position:0% +already + + + align:start position:0% +already +um and + + align:start position:0% + + + + align:start position:0% + +uh what you light + + align:start position:0% + + + + align:start position:0% + +I sorry about that I'm going to make few + + align:start position:0% +I sorry about that I'm going to make few + + + align:start position:0% +I sorry about that I'm going to make few +comments on immigration some of them are + + align:start position:0% +comments on immigration some of them are + + + align:start position:0% +comments on immigration some of them are +scholarly and and based basically on my + + align:start position:0% +scholarly and and based basically on my + + + align:start position:0% +scholarly and and based basically on my +profession as a historian and uh some of + + align:start position:0% +profession as a historian and uh some of + + + align:start position:0% +profession as a historian and uh some of +them are personal and perhaps actually a + + align:start position:0% +them are personal and perhaps actually a + + + align:start position:0% +them are personal and perhaps actually a +little bit even um um existential um the + + align:start position:0% +little bit even um um existential um the + + + align:start position:0% +little bit even um um existential um the +historical one I kept on thinking while + + align:start position:0% +historical one I kept on thinking while + + + align:start position:0% +historical one I kept on thinking while +I was listening that we are now + + align:start position:0% +I was listening that we are now + + + align:start position:0% +I was listening that we are now +constantly being bared with the notion + + align:start position:0% +constantly being bared with the notion + + + align:start position:0% +constantly being bared with the notion +of immigrants around the world $150 + + align:start position:0% +of immigrants around the world $150 + + + align:start position:0% +of immigrants around the world $150 +million million dollars 150 million + + align:start position:0% +million million dollars 150 million + + + align:start position:0% +million million dollars 150 million +individuals are at this point in time + + align:start position:0% +individuals are at this point in time + + + align:start position:0% +individuals are at this point in time +supposedly immigrants in different + + align:start position:0% +supposedly immigrants in different + + + align:start position:0% +supposedly immigrants in different +places in the um first world coming from + + align:start position:0% +places in the um first world coming from + + + align:start position:0% +places in the um first world coming from +the third world a humongous number we + + align:start position:0% +the third world a humongous number we + + + align:start position:0% +the third world a humongous number we +are supposed to constantly think of it + + align:start position:0% +are supposed to constantly think of it + + + align:start position:0% +are supposed to constantly think of it +as a problem of course all of you are + + align:start position:0% +as a problem of course all of you are + + + align:start position:0% +as a problem of course all of you are +aware of the fact that today is not just + + align:start position:0% +aware of the fact that today is not just + + + align:start position:0% +aware of the fact that today is not just +the 1st of May and the international uh + + align:start position:0% +the 1st of May and the international uh + + + align:start position:0% +the 1st of May and the international uh +Labor day but also is the day of protest + + align:start position:0% +Labor day but also is the day of protest + + + align:start position:0% +Labor day but also is the day of protest +about the new immigration laws um all of + + align:start position:0% +about the new immigration laws um all of + + + align:start position:0% +about the new immigration laws um all of +us have witnessed since 911 the changes + + align:start position:0% +us have witnessed since 911 the changes + + + align:start position:0% +us have witnessed since 911 the changes +the tightening of immigration laws in + + align:start position:0% +the tightening of immigration laws in + + + align:start position:0% +the tightening of immigration laws in +the West and as a matter of fact + + align:start position:0% +the West and as a matter of fact + + + align:start position:0% +the West and as a matter of fact +actually even the the mere tarity and + + align:start position:0% +actually even the the mere tarity and + + + align:start position:0% +actually even the the mere tarity and +and and in a sense actually even the + + align:start position:0% +and and in a sense actually even the + + + align:start position:0% +and and in a sense actually even the +mere uh hypocrisy of the policy makers + + align:start position:0% +mere uh hypocrisy of the policy makers + + + align:start position:0% +mere uh hypocrisy of the policy makers +in the first world about who they are + + align:start position:0% +in the first world about who they are + + + align:start position:0% +in the first world about who they are +going to let in and who they're not + + align:start position:0% +going to let in and who they're not + + + align:start position:0% +going to let in and who they're not +going to let in and sort of like somehow + + align:start position:0% +going to let in and sort of like somehow + + + align:start position:0% +going to let in and sort of like somehow +categorizing people in different ways + + align:start position:0% +categorizing people in different ways + + + align:start position:0% +categorizing people in different ways +people with high degrees in sciences and + + align:start position:0% +people with high degrees in sciences and + + + align:start position:0% +people with high degrees in sciences and +engineering and Computer Sciences are + + align:start position:0% +engineering and Computer Sciences are + + + align:start position:0% +engineering and Computer Sciences are +welcome in in many places as a matter of + + align:start position:0% +welcome in in many places as a matter of + + + align:start position:0% +welcome in in many places as a matter of +fact the US is copying the German + + align:start position:0% +fact the US is copying the German + + + align:start position:0% +fact the US is copying the German +immigration law many of you probably + + align:start position:0% +immigration law many of you probably + + + align:start position:0% +immigration law many of you probably +know that in the way we are moving now + + align:start position:0% +know that in the way we are moving now + + + align:start position:0% +know that in the way we are moving now +but all of that is just bringing to my + + align:start position:0% +but all of that is just bringing to my + + + align:start position:0% +but all of that is just bringing to my +mind something else it's funny how short + + align:start position:0% +mind something else it's funny how short + + + align:start position:0% +mind something else it's funny how short +our Collective memories + + align:start position:0% +our Collective memories + + + align:start position:0% +our Collective memories +are Europe is actually the place that + + align:start position:0% +are Europe is actually the place that + + + align:start position:0% +are Europe is actually the place that +have produced the most number of + + align:start position:0% +have produced the most number of + + + align:start position:0% +have produced the most number of +immigrants in history Europe is the one + + align:start position:0% +immigrants in history Europe is the one + + + align:start position:0% +immigrants in history Europe is the one +that actually for four centuries solved + + align:start position:0% +that actually for four centuries solved + + + align:start position:0% +that actually for four centuries solved +all of its problems by sending people + + align:start position:0% +all of its problems by sending people + + + align:start position:0% +all of its problems by sending people +out and in a sense actually colonizing + + align:start position:0% +out and in a sense actually colonizing + + + align:start position:0% +out and in a sense actually colonizing +the rest of the discovered word or the + + align:start position:0% +the rest of the discovered word or the + + + align:start position:0% +the rest of the discovered word or the +word that is being discovered and some + + align:start position:0% +word that is being discovered and some + + + align:start position:0% +word that is being discovered and some +of the word that was already discovered + + align:start position:0% +of the word that was already discovered + + + align:start position:0% +of the word that was already discovered +and sort of like Europeans or people of + + align:start position:0% +and sort of like Europeans or people of + + + align:start position:0% +and sort of like Europeans or people of +European Origins claiming that the + + align:start position:0% +European Origins claiming that the + + + align:start position:0% +European Origins claiming that the +people living in it were not worth it or + + align:start position:0% +people living in it were not worth it or + + + align:start position:0% +people living in it were not worth it or +didn't deserve it or whatever it is so + + align:start position:0% +didn't deserve it or whatever it is so + + + align:start position:0% +didn't deserve it or whatever it is so +we remove them and take their place so + + align:start position:0% +we remove them and take their place so + + + align:start position:0% +we remove them and take their place so +immigration is really not a new hisory + + align:start position:0% +immigration is really not a new hisory + + + align:start position:0% +immigration is really not a new hisory +new story in the world it's a very very + + align:start position:0% +new story in the world it's a very very + + + align:start position:0% +new story in the world it's a very very +old story in the world and the + + align:start position:0% +old story in the world and the + + + align:start position:0% +old story in the world and the +immigration story that we were looking + + align:start position:0% +immigration story that we were looking + + + align:start position:0% +immigration story that we were looking +at here + + align:start position:0% +at here + + + align:start position:0% +at here +today is part of this sort of like + + align:start position:0% +today is part of this sort of like + + + align:start position:0% +today is part of this sort of like +continuous movement of humanity over all + + align:start position:0% +continuous movement of humanity over all + + + align:start position:0% +continuous movement of humanity over all +of its time I mean from the beginning on + + align:start position:0% +of its time I mean from the beginning on + + + align:start position:0% +of its time I mean from the beginning on +but I struck by your comparison between + + align:start position:0% +but I struck by your comparison between + + + align:start position:0% +but I struck by your comparison between +people moving to the cities in turkey + + align:start position:0% +people moving to the cities in turkey + + + align:start position:0% +people moving to the cities in turkey +and of course people moving to London + + align:start position:0% +and of course people moving to London + + + align:start position:0% +and of course people moving to London +most of the examples that we've looked + + align:start position:0% +most of the examples that we've looked + + + align:start position:0% +most of the examples that we've looked +at are in London and that led me to + + align:start position:0% +at are in London and that led me to + + + align:start position:0% +at are in London and that led me to +reflect upon my own case and uh I was + + align:start position:0% +reflect upon my own case and uh I was + + + align:start position:0% +reflect upon my own case and uh I was +wondering I mean I for example and I + + align:start position:0% +wondering I mean I for example and I + + + align:start position:0% +wondering I mean I for example and I +this is sort of like a bit of personal + + align:start position:0% +this is sort of like a bit of personal + + + align:start position:0% +this is sort of like a bit of personal +history I stayed in this country after I + + align:start position:0% +history I stayed in this country after I + + + align:start position:0% +history I stayed in this country after I +finished my education not because of the + + align:start position:0% +finished my education not because of the + + + align:start position:0% +finished my education not because of the +economic benefits of being in this + + align:start position:0% +economic benefits of being in this + + + align:start position:0% +economic benefits of being in this +country but because of what is probably + + align:start position:0% +country but because of what is probably + + + align:start position:0% +country but because of what is probably +going to be uh uh to turn out to be an + + align:start position:0% +going to be uh uh to turn out to be an + + + align:start position:0% +going to be uh uh to turn out to be an +extremely false belief that this country + + align:start position:0% +extremely false belief that this country + + + align:start position:0% +extremely false belief that this country +provides me with the freedom that I was + + align:start position:0% +provides me with the freedom that I was + + + align:start position:0% +provides me with the freedom that I was +lacking in the country that I'm coming + + align:start position:0% +lacking in the country that I'm coming + + + align:start position:0% +lacking in the country that I'm coming +from because as you all know actually at + + align:start position:0% +from because as you all know actually at + + + align:start position:0% +from because as you all know actually at +this point in time someone like me + + align:start position:0% +this point in time someone like me + + + align:start position:0% +this point in time someone like me +cannot really Express himself freely in + + align:start position:0% +cannot really Express himself freely in + + + align:start position:0% +cannot really Express himself freely in +this country as a matter of fact I can't + + align:start position:0% +this country as a matter of fact I can't + + + align:start position:0% +this country as a matter of fact I can't +tell you my real opinion now here uh + + align:start position:0% +tell you my real opinion now here uh + + + align:start position:0% +tell you my real opinion now here uh +despite the fact that we believe that we + + align:start position:0% +despite the fact that we believe that we + + + align:start position:0% +despite the fact that we believe that we +are living in a free environment um so + + align:start position:0% +are living in a free environment um so + + + align:start position:0% +are living in a free environment um so +having said that uh of course there we + + align:start position:0% +having said that uh of course there we + + + align:start position:0% +having said that uh of course there we +have an extremely classical story of + + align:start position:0% +have an extremely classical story of + + + align:start position:0% +have an extremely classical story of +immigration of uh people who are going + + align:start position:0% +immigration of uh people who are going + + + align:start position:0% +immigration of uh people who are going +to improve their lot in life and of + + align:start position:0% +to improve their lot in life and of + + + align:start position:0% +to improve their lot in life and of +course actually she paying the heavy + + align:start position:0% +course actually she paying the heavy + + + align:start position:0% +course actually she paying the heavy +price the uh + + align:start position:0% +price the uh + + + align:start position:0% +price the uh +um the FF seller in Central Square some + + align:start position:0% +um the FF seller in Central Square some + + + align:start position:0% +um the FF seller in Central Square some +years ago my wife and I stopped there + + align:start position:0% +years ago my wife and I stopped there + + + align:start position:0% +years ago my wife and I stopped there +and somebody told us that in Central + + align:start position:0% +and somebody told us that in Central + + + align:start position:0% +and somebody told us that in Central +Square there's this like fabulous place + + align:start position:0% +Square there's this like fabulous place + + + align:start position:0% +Square there's this like fabulous place +that prepares for Just Like Home home + + align:start position:0% +that prepares for Just Like Home home + + + align:start position:0% +that prepares for Just Like Home home +for me is Syria for my wife it's Egypt + + align:start position:0% +for me is Syria for my wife it's Egypt + + + align:start position:0% +for me is Syria for my wife it's Egypt +so we actually have different opinions + + align:start position:0% +so we actually have different opinions + + + align:start position:0% +so we actually have different opinions +about what f is the Egyptians call it + + align:start position:0% +about what f is the Egyptians call it + + + align:start position:0% +about what f is the Egyptians call it +it's made differently and so on and so + + align:start position:0% +it's made differently and so on and so + + + align:start position:0% +it's made differently and so on and so +forth so we wanted to compare we landed + + align:start position:0% +forth so we wanted to compare we landed + + + align:start position:0% +forth so we wanted to compare we landed +there it was a shop owned by a ser + + align:start position:0% +there it was a shop owned by a ser + + + align:start position:0% +there it was a shop owned by a ser +still is as a matter of fact it's in + + align:start position:0% +still is as a matter of fact it's in + + + align:start position:0% +still is as a matter of fact it's in +Central Square and the person that was + + align:start position:0% +Central Square and the person that was + + + align:start position:0% +Central Square and the person that was +preparing the FL was Egyptian so it was + + align:start position:0% +preparing the FL was Egyptian so it was + + + align:start position:0% +preparing the FL was Egyptian so it was +it was exactly what we were looking + + align:start position:0% +it was exactly what we were looking + + + align:start position:0% +it was exactly what we were looking +for the guy said he was working 15 hours + + align:start position:0% +for the guy said he was working 15 hours + + + align:start position:0% +for the guy said he was working 15 hours +today exactly the same as the kids of + + align:start position:0% +today exactly the same as the kids of + + + align:start position:0% +today exactly the same as the kids of +faime he was making + + align:start position:0% +faime he was making + + + align:start position:0% +faime he was making +$70 or so and his expenses were $75 a + + align:start position:0% +$70 or so and his expenses were $75 a + + + align:start position:0% +$70 or so and his expenses were $75 a +day so he was actually borrowing from + + align:start position:0% +day so he was actually borrowing from + + + align:start position:0% +day so he was actually borrowing from +the owner of the business and he had + + align:start position:0% +the owner of the business and he had + + + align:start position:0% +the owner of the business and he had +been here for 2 years and he hadn't + + align:start position:0% +been here for 2 years and he hadn't + + + align:start position:0% +been here for 2 years and he hadn't +saved a single penny of course he was + + align:start position:0% +saved a single penny of course he was + + + align:start position:0% +saved a single penny of course he was +indebted to the owner of the business he + + align:start position:0% +indebted to the owner of the business he + + + align:start position:0% +indebted to the owner of the business he +was working way above his capacity and I + + align:start position:0% +was working way above his capacity and I + + + align:start position:0% +was working way above his capacity and I +said well what are you doing where you + + align:start position:0% +said well what are you doing where you + + + align:start position:0% +said well what are you doing where you +came from he said I came from Alexandria + + align:start position:0% +came from he said I came from Alexandria + + + align:start position:0% +came from he said I came from Alexandria +and I owned a shoe shop there and I'm + + align:start position:0% +and I owned a shoe shop there and I'm + + + align:start position:0% +and I owned a shoe shop there and I'm +like what brought you here it's the same + + align:start position:0% +like what brought you here it's the same + + + align:start position:0% +like what brought you here it's the same +question I mean here we have examples in + + align:start position:0% +question I mean here we have examples in + + + align:start position:0% +question I mean here we have examples in +Turkey of people who went to Turkish + + align:start position:0% +Turkey of people who went to Turkish + + + align:start position:0% +Turkey of people who went to Turkish +cities and made it and somehow improved + + align:start position:0% +cities and made it and somehow improved + + + align:start position:0% +cities and made it and somehow improved +their lives there and people who went + + align:start position:0% +their lives there and people who went + + + align:start position:0% +their lives there and people who went +looking for ways to improve in their + + align:start position:0% +looking for ways to improve in their + + + align:start position:0% +looking for ways to improve in their +lives elsewhere in in in in the West in + + align:start position:0% +lives elsewhere in in in in the West in + + + align:start position:0% +lives elsewhere in in in in the West in +this case who did not improve their + + align:start position:0% +this case who did not improve their + + + align:start position:0% +this case who did not improve their +lives as a matter of fact actually they + + align:start position:0% +lives as a matter of fact actually they + + + align:start position:0% +lives as a matter of fact actually they +sacrificed their lives these are people + + align:start position:0% +sacrificed their lives these are people + + + align:start position:0% +sacrificed their lives these are people +who have lived in England for 10 years + + align:start position:0% +who have lived in England for 10 years + + + align:start position:0% +who have lived in England for 10 years +without the ability of being of of going + + align:start position:0% +without the ability of being of of going + + + align:start position:0% +without the ability of being of of going +back home totally deprived economically + + align:start position:0% +back home totally deprived economically + + + align:start position:0% +back home totally deprived economically +totally deprived socially feeling + + align:start position:0% +totally deprived socially feeling + + + align:start position:0% +totally deprived socially feeling +alienated Ali's testimony is is heroin + + align:start position:0% +alienated Ali's testimony is is heroin + + + align:start position:0% +alienated Ali's testimony is is heroin +and uh and and what's what's the + + align:start position:0% +and uh and and what's what's the + + + align:start position:0% +and uh and and what's what's the +ultimate Aim so I don't know I mean + + align:start position:0% +ultimate Aim so I don't know I mean + + + align:start position:0% +ultimate Aim so I don't know I mean +perhaps actually your message shouldn't + + align:start position:0% +perhaps actually your message shouldn't + + + align:start position:0% +perhaps actually your message shouldn't +be don't misjudge women but your message + + align:start position:0% +be don't misjudge women but your message + + + align:start position:0% +be don't misjudge women but your message +should be going to IM immigrant + + align:start position:0% +should be going to IM immigrant + + + align:start position:0% +should be going to IM immigrant +communities or communities that are + + align:start position:0% +communities or communities that are + + + align:start position:0% +communities or communities that are +planning to send immigrants and tell + + align:start position:0% +planning to send immigrants and tell + + + align:start position:0% +planning to send immigrants and tell +them watch out before you send out your + + align:start position:0% +them watch out before you send out your + + + align:start position:0% +them watch out before you send out your +your immigrants perhaps that's not the + + align:start position:0% +your immigrants perhaps that's not the + + + align:start position:0% +your immigrants perhaps that's not the +best solution the last point that I want + + align:start position:0% +best solution the last point that I want + + + align:start position:0% +best solution the last point that I want +to make and this is actually a direct + + align:start position:0% +to make and this is actually a direct + + + align:start position:0% +to make and this is actually a direct +comment on something that you + + align:start position:0% +comment on something that you + + + align:start position:0% +comment on something that you +said + + align:start position:0% + + + + align:start position:0% + +uh you said that at uh what what you + + align:start position:0% +uh you said that at uh what what you + + + align:start position:0% +uh you said that at uh what what you +were doing you were a photojournalist 30 + + align:start position:0% +were doing you were a photojournalist 30 + + + align:start position:0% +were doing you were a photojournalist 30 +years ago and you were trying to + + align:start position:0% +years ago and you were trying to + + + align:start position:0% +years ago and you were trying to +document how economic and social + + align:start position:0% +document how economic and social + + + align:start position:0% +document how economic and social +development work from the bottom up + + align:start position:0% +development work from the bottom up + + + align:start position:0% +development work from the bottom up +and then you commented and you said we + + align:start position:0% +and then you commented and you said we + + + align:start position:0% +and then you commented and you said we +were idealist then or idealistic then + + align:start position:0% +were idealist then or idealistic then + + + align:start position:0% +were idealist then or idealistic then +and I would like to comment on that I + + align:start position:0% +and I would like to comment on that I + + + align:start position:0% +and I would like to comment on that I +would like to comment actually for the + + align:start position:0% +would like to comment actually for the + + + align:start position:0% +would like to comment actually for the +students the rest of us are rot and it's + + align:start position:0% +students the rest of us are rot and it's + + + align:start position:0% +students the rest of us are rot and it's +not going to have it's not going to help + + align:start position:0% +not going to have it's not going to help + + + align:start position:0% +not going to have it's not going to help +we already are somehow gone but those of + + align:start position:0% +we already are somehow gone but those of + + + align:start position:0% +we already are somehow gone but those of +you who are here for idealistic reasons + + align:start position:0% +you who are here for idealistic reasons + + + align:start position:0% +you who are here for idealistic reasons +and I went to school and I stayed in + + align:start position:0% +and I went to school and I stayed in + + + align:start position:0% +and I went to school and I stayed in +this country for idealistic reasons stay + + align:start position:0% +this country for idealistic reasons stay + + + align:start position:0% +this country for idealistic reasons stay +idealistic we need to be idealistic I + + align:start position:0% +idealistic we need to be idealistic I + + + align:start position:0% +idealistic we need to be idealistic I +mean what's the opposite of idealistic + + align:start position:0% +mean what's the opposite of idealistic + + + align:start position:0% +mean what's the opposite of idealistic +if I may ask Leslie I mean if we were + + align:start position:0% +if I may ask Leslie I mean if we were + + + align:start position:0% +if I may ask Leslie I mean if we were +idealistic then what are we today what + + align:start position:0% +idealistic then what are we today what + + + align:start position:0% +idealistic then what are we today what +is it exactly that we have moved into to + + align:start position:0% +is it exactly that we have moved into to + + + align:start position:0% +is it exactly that we have moved into to +me actually it's really Bleak what we + + align:start position:0% +me actually it's really Bleak what we + + + align:start position:0% +me actually it's really Bleak what we +have become what pragmatic I guess + + align:start position:0% +have become what pragmatic I guess + + + align:start position:0% +have become what pragmatic I guess +that's the word is that what the word + + align:start position:0% +that's the word is that what the word + + + align:start position:0% +that's the word is that what the word +that we usually think of as the opposite + + align:start position:0% +that we usually think of as the opposite + + + align:start position:0% +that we usually think of as the opposite +of + + align:start position:0% +of + + + align:start position:0% +of +idealistic idealism is what really moves + + align:start position:0% +idealistic idealism is what really moves + + + align:start position:0% +idealistic idealism is what really moves +the world it's not pragmatism and it's + + align:start position:0% +the world it's not pragmatism and it's + + + align:start position:0% +the world it's not pragmatism and it's +not really success in whatever it is + + align:start position:0% +not really success in whatever it is + + + align:start position:0% +not really success in whatever it is +that we are successful in is this + + align:start position:0% +that we are successful in is this + + + align:start position:0% +that we are successful in is this +ability to actually face up to problems + + align:start position:0% +ability to actually face up to problems + + + align:start position:0% +ability to actually face up to problems +that seem to be insurmountable think of + + align:start position:0% +that seem to be insurmountable think of + + + align:start position:0% +that seem to be insurmountable think of +totally totally totally unrealistic + + align:start position:0% +totally totally totally unrealistic + + + align:start position:0% +totally totally totally unrealistic +solutions to them and go about find + + align:start position:0% +solutions to them and go about find + + + align:start position:0% +solutions to them and go about find +pursuing and doing these Solutions so + + align:start position:0% +pursuing and doing these Solutions so + + + align:start position:0% +pursuing and doing these Solutions so +those of you who are younger than 40 in + + align:start position:0% +those of you who are younger than 40 in + + + align:start position:0% +those of you who are younger than 40 in +the audience stay idealistic those of us + + align:start position:0% +the audience stay idealistic those of us + + + align:start position:0% +the audience stay idealistic those of us +who are above I don't know I mean some + + align:start position:0% +who are above I don't know I mean some + + + align:start position:0% +who are above I don't know I mean some +of us perhaps still have it in their + + align:start position:0% +of us perhaps still have it in their + + + align:start position:0% +of us perhaps still have it in their +heart do clearly does but the rest of us + + align:start position:0% +heart do clearly does but the rest of us + + + align:start position:0% +heart do clearly does but the rest of us +I'm not sure I speak for myself I became + + align:start position:0% +I'm not sure I speak for myself I became + + + align:start position:0% +I'm not sure I speak for myself I became +somewhat pragmatic thank you for + + align:start position:0% +somewhat pragmatic thank you for + + + align:start position:0% +somewhat pragmatic thank you for +reminding me of what + + align:start position:0% + + + + align:start position:0% + +I someone wants to turn up the lights + + align:start position:0% +I someone wants to turn up the lights + + + align:start position:0% +I someone wants to turn up the lights +and ask some questions or raise some + + align:start position:0% +and ask some questions or raise some + + + align:start position:0% +and ask some questions or raise some +issues + + align:start position:0% + + + + align:start position:0% + +yeah do you want to stand up and speak + + align:start position:0% +yeah do you want to stand up and speak + + + align:start position:0% +yeah do you want to stand up and speak +loudly + + align:start position:0% + + + + align:start position:0% + +and you explain the story + + align:start position:0% +and you explain the story + + + align:start position:0% +and you explain the story +of to us and in this story I think they + + align:start position:0% +of to us and in this story I think they + + + align:start position:0% +of to us and in this story I think they +live in a very small uh Village it + + align:start position:0% +live in a very small uh Village it + + + align:start position:0% +live in a very small uh Village it +should be less than 2,000 because I am a + + align:start position:0% +should be less than 2,000 because I am a + + + align:start position:0% +should be less than 2,000 because I am a +I visited most of the part of the turkey + + align:start position:0% +I visited most of the part of the turkey + + + align:start position:0% +I visited most of the part of the turkey +I am see this part this part of the + + align:start position:0% +I am see this part this part of the + + + align:start position:0% +I am see this part this part of the +turkey yet and you point out a lot of + + align:start position:0% +turkey yet and you point out a lot of + + + align:start position:0% +turkey yet and you point out a lot of +problems and made sensitive problems + + align:start position:0% +problems and made sensitive problems + + + align:start position:0% +problems and made sensitive problems +woman issues + + align:start position:0% +woman issues + + + align:start position:0% +woman issues +immigration and migration + + align:start position:0% +immigration and migration + + + align:start position:0% +immigration and migration +and feminism and Kurdish problem and + + align:start position:0% +and feminism and Kurdish problem and + + + align:start position:0% +and feminism and Kurdish problem and +Turkish problem and also Al Al problem + + align:start position:0% +Turkish problem and also Al Al problem + + + align:start position:0% +Turkish problem and also Al Al problem +and these are very sensitive issues and + + align:start position:0% +and these are very sensitive issues and + + + align:start position:0% +and these are very sensitive issues and +from one family + + align:start position:0% +from one family + + + align:start position:0% +from one family +perspective I think it is not uh how can + + align:start position:0% +perspective I think it is not uh how can + + + align:start position:0% +perspective I think it is not uh how can +I say it is not correct to make + + align:start position:0% +I say it is not correct to make + + + align:start position:0% +I say it is not correct to make +generalization about these sensitive + + align:start position:0% +generalization about these sensitive + + + align:start position:0% +generalization about these sensitive +issues you cannot do that with this + + align:start position:0% +issues you cannot do that with this + + + align:start position:0% +issues you cannot do that with this +information and and also you are not + + align:start position:0% +information and and also you are not + + + align:start position:0% +information and and also you are not +using any + + align:start position:0% +using any + + + align:start position:0% +using any +social + + align:start position:0% +social + + + align:start position:0% +social +um scientific + + align:start position:0% +um scientific + + + align:start position:0% +um scientific +method with from one family perspective + + align:start position:0% +method with from one family perspective + + + align:start position:0% +method with from one family perspective +you cannot make + + align:start position:0% +you cannot make + + + align:start position:0% +you cannot make +generalization I think at the end of + + align:start position:0% +generalization I think at the end of + + + align:start position:0% +generalization I think at the end of +your + + align:start position:0% +your + + + align:start position:0% +your +presentation it is not clear to me still + + align:start position:0% +presentation it is not clear to me still + + + align:start position:0% +presentation it is not clear to me still +what is your conclusion about image + + align:start position:0% +what is your conclusion about image + + + align:start position:0% +what is your conclusion about image +issue well you brought up a lot of + + align:start position:0% +issue well you brought up a lot of + + + align:start position:0% +issue well you brought up a lot of +things and maybe I can briefly respond + + align:start position:0% +things and maybe I can briefly respond + + + align:start position:0% +things and maybe I can briefly respond +on a few points um I think I started by + + align:start position:0% +on a few points um I think I started by + + + align:start position:0% +on a few points um I think I started by +saying I am not a social scientist I'm + + align:start position:0% +saying I am not a social scientist I'm + + + align:start position:0% +saying I am not a social scientist I'm +telling stories from one place um as I + + align:start position:0% +telling stories from one place um as I + + + align:start position:0% +telling stories from one place um as I +said to Professor B I'm not interested + + align:start position:0% +said to Professor B I'm not interested + + + align:start position:0% +said to Professor B I'm not interested +in influencing uh Urban policy or you + + align:start position:0% +in influencing uh Urban policy or you + + + align:start position:0% +in influencing uh Urban policy or you +know this my goal is actually directed + + align:start position:0% +know this my goal is actually directed + + + align:start position:0% +know this my goal is actually directed +to a very different different audience + + align:start position:0% +to a very different different audience + + + align:start position:0% +to a very different different audience +than than you um my goal is to take some + + align:start position:0% +than than you um my goal is to take some + + + align:start position:0% +than than you um my goal is to take some +women's stories and I would like to take + + align:start position:0% +women's stories and I would like to take + + + align:start position:0% +women's stories and I would like to take +these stories to in a book form and an + + align:start position:0% +these stories to in a book form and an + + + align:start position:0% +these stories to in a book form and an +exhibit form to public libraries in the + + align:start position:0% +exhibit form to public libraries in the + + + align:start position:0% +exhibit form to public libraries in the +United States to give some of the + + align:start position:0% +United States to give some of the + + + align:start position:0% +United States to give some of the +American public an idea about how these + + align:start position:0% +American public an idea about how these + + + align:start position:0% +American public an idea about how these +women have radically changed their lives + + align:start position:0% +women have radically changed their lives + + + align:start position:0% +women have radically changed their lives +and have done things which I think the + + align:start position:0% +and have done things which I think the + + + align:start position:0% +and have done things which I think the +typical stereotyped idea of the Muslim + + align:start position:0% +typical stereotyped idea of the Muslim + + + align:start position:0% +typical stereotyped idea of the Muslim +woman that we get in the press that is + + align:start position:0% +woman that we get in the press that is + + + align:start position:0% +woman that we get in the press that is +so stereotypical and + + align:start position:0% +so stereotypical and + + + align:start position:0% +so stereotypical and +bizarre well I you know if I'm a + + align:start position:0% +bizarre well I you know if I'm a + + + align:start position:0% +bizarre well I you know if I'm a +photojournalist and find any if you if + + align:start position:0% +photojournalist and find any if you if + + + align:start position:0% +photojournalist and find any if you if +you want to you know if you want to go + + align:start position:0% +you want to you know if you want to go + + + align:start position:0% +you want to you know if you want to go +to + + align:start position:0% +to + + + align:start position:0% +to +um New Orleans and photograph all the + + align:start position:0% +um New Orleans and photograph all the + + + align:start position:0% +um New Orleans and photograph all the +people who are building nice houses or + + align:start position:0% +people who are building nice houses or + + + align:start position:0% +people who are building nice houses or +you go to New Orleans and photograph all + + align:start position:0% +you go to New Orleans and photograph all + + + align:start position:0% +you go to New Orleans and photograph all +the houses that haven't been rebuilt I I + + align:start position:0% +the houses that haven't been rebuilt I I + + + align:start position:0% +the houses that haven't been rebuilt I I +don't claim to have a comprehensive view + + align:start position:0% +don't claim to have a comprehensive view + + + align:start position:0% +don't claim to have a comprehensive view +um I am not making + + align:start position:0% +um I am not making + + + align:start position:0% +um I am not making +any assumptions about um people beyond + + align:start position:0% +any assumptions about um people beyond + + + align:start position:0% +any assumptions about um people beyond +the ones that I've had contact with but + + align:start position:0% +the ones that I've had contact with but + + + align:start position:0% +the ones that I've had contact with but +I as I said in the beginning I think + + align:start position:0% +I as I said in the beginning I think + + + align:start position:0% +I as I said in the beginning I think +think that for the purpose + + align:start position:0% +think that for the purpose + + + align:start position:0% +think that for the purpose +of making some human contact between + + align:start position:0% +of making some human contact between + + + align:start position:0% +of making some human contact between +cultures there is I believe there's an + + align:start position:0% +cultures there is I believe there's an + + + align:start position:0% +cultures there is I believe there's an +advantage to telling stories about + + align:start position:0% +advantage to telling stories about + + + align:start position:0% +advantage to telling stories about +individuals not social science + + align:start position:0% +individuals not social science + + + align:start position:0% +individuals not social science +statistics that's up to the academics + + align:start position:0% +statistics that's up to the academics + + + align:start position:0% +statistics that's up to the academics +and that if if I could make some impact + + align:start position:0% +and that if if I could make some impact + + + align:start position:0% +and that if if I could make some impact +with opening up the minds of some people + + align:start position:0% +with opening up the minds of some people + + + align:start position:0% +with opening up the minds of some people +in other parts of the country about um + + align:start position:0% +in other parts of the country about um + + + align:start position:0% +in other parts of the country about um +Muslim women that they would have more + + align:start position:0% +Muslim women that they would have more + + + align:start position:0% +Muslim women that they would have more +compassion for this one family then + + align:start position:0% +compassion for this one family then + + + align:start position:0% +compassion for this one family then +that's the extent of my goal um it's + + align:start position:0% +that's the extent of my goal um it's + + + align:start position:0% +that's the extent of my goal um it's +storytelling it's not social science um + + align:start position:0% +storytelling it's not social science um + + + align:start position:0% +storytelling it's not social science um +you + + align:start position:0% +you + + + align:start position:0% +you +know I I don't + + align:start position:0% +know I I don't + + + align:start position:0% +know I I don't +uh it's one you know there's one Village + + align:start position:0% +uh it's one you know there's one Village + + + align:start position:0% +uh it's one you know there's one Village +it's a small village um and I'm very + + align:start position:0% +it's a small village um and I'm very + + + align:start position:0% +it's a small village um and I'm very +very aware of sensitivity around + + align:start position:0% +very aware of sensitivity around + + + align:start position:0% +very aware of sensitivity around +discussing Kurds or Alves and I took the + + align:start position:0% +discussing Kurds or Alves and I took the + + + align:start position:0% +discussing Kurds or Alves and I took the +freedom to say some of those things in + + align:start position:0% +freedom to say some of those things in + + + align:start position:0% +freedom to say some of those things in +this room because I thought I could + + align:start position:0% +this room because I thought I could + + + align:start position:0% +this room because I thought I could +probably say it um but those + + align:start position:0% +probably say it um but those + + + align:start position:0% +probably say it um but those +are those are people whom for whom + + align:start position:0% +are those are people whom for whom + + + align:start position:0% +are those are people whom for whom +that's a Kurdish Village and they've + + align:start position:0% +that's a Kurdish Village and they've + + + align:start position:0% +that's a Kurdish Village and they've +experienced a lot of discrimination and + + align:start position:0% +experienced a lot of discrimination and + + + align:start position:0% +experienced a lot of discrimination and +um it's a bigger topic we could discuss + + align:start position:0% +um it's a bigger topic we could discuss + + + align:start position:0% +um it's a bigger topic we could discuss +you know discrimination against Kurds in + + align:start position:0% +you know discrimination against Kurds in + + + align:start position:0% +you know discrimination against Kurds in +Turkey over many hours with many social + + align:start position:0% +Turkey over many hours with many social + + + align:start position:0% +Turkey over many hours with many social +scientists but um these are the personal + + align:start position:0% +scientists but um these are the personal + + + align:start position:0% +scientists but um these are the personal +stories that have and how it's impacted + + align:start position:0% +stories that have and how it's impacted + + + align:start position:0% +stories that have and how it's impacted +them in fact one of the things that they + + align:start position:0% +them in fact one of the things that they + + + align:start position:0% +them in fact one of the things that they +said about the Kurdish women who went to + + align:start position:0% +said about the Kurdish women who went to + + + align:start position:0% +said about the Kurdish women who went to +Adonna is that that often they got jobs + + align:start position:0% +Adonna is that that often they got jobs + + + align:start position:0% +Adonna is that that often they got jobs +that the Turkish women wouldn't get + + align:start position:0% +that the Turkish women wouldn't get + + + align:start position:0% +that the Turkish women wouldn't get +because their husbands allowed them to + + align:start position:0% +because their husbands allowed them to + + + align:start position:0% +because their husbands allowed them to +work in other people's homes whereas + + align:start position:0% +work in other people's homes whereas + + + align:start position:0% +work in other people's homes whereas +some of the Turkish women in that area + + align:start position:0% +some of the Turkish women in that area + + + align:start position:0% +some of the Turkish women in that area +had + + align:start position:0% +had + + + align:start position:0% +had +stricter house rules and didn't get to + + align:start position:0% +stricter house rules and didn't get to + + + align:start position:0% +stricter house rules and didn't get to +go out and clean other people's homes I + + align:start position:0% +go out and clean other people's homes I + + + align:start position:0% +go out and clean other people's homes I +mean there's more to it + + align:start position:0% +mean there's more to it + + + align:start position:0% +mean there's more to it +yes can we run the discussion yes in the + + align:start position:0% +yes can we run the discussion yes in the + + + align:start position:0% +yes can we run the discussion yes in the +back + + align:start position:0% +back + + + align:start position:0% +back +yeah Osama um + + align:start position:0% +yeah Osama um + + + align:start position:0% +yeah Osama um +I saw one common threat in the story was + + align:start position:0% +I saw one common threat in the story was + + + align:start position:0% +I saw one common threat in the story was +the pursuit of Education especially in + + align:start position:0% +the pursuit of Education especially in + + + align:start position:0% +the pursuit of Education especially in +the uh the children of the new + + align:start position:0% +the uh the children of the new + + + align:start position:0% +the uh the children of the new +immigrants and I'm wondering uh at what + + align:start position:0% +immigrants and I'm wondering uh at what + + + align:start position:0% +immigrants and I'm wondering uh at what +stage was the fruit of education on the + + align:start position:0% +stage was the fruit of education on the + + + align:start position:0% +stage was the fruit of education on the +minds of these immigrants whether in the + + align:start position:0% +minds of these immigrants whether in the + + + align:start position:0% +minds of these immigrants whether in the +village and that was one of the strong + + align:start position:0% +village and that was one of the strong + + + align:start position:0% +village and that was one of the strong +motivating factors to move to the city + + align:start position:0% +motivating factors to move to the city + + + align:start position:0% +motivating factors to move to the city +life whether in London or in modern + + align:start position:0% +life whether in London or in modern + + + align:start position:0% +life whether in London or in modern +turkey cities or whether that uh + + align:start position:0% +turkey cities or whether that uh + + + align:start position:0% +turkey cities or whether that uh +education route was was thought upon + + align:start position:0% +education route was was thought upon + + + align:start position:0% +education route was was thought upon +more after the fact after moving into + + align:start position:0% +more after the fact after moving into + + + align:start position:0% +more after the fact after moving into +the big cities after realizing that that + + align:start position:0% +the big cities after realizing that that + + + align:start position:0% +the big cities after realizing that that +is more of the key toward success in + + align:start position:0% +is more of the key toward success in + + + align:start position:0% +is more of the key toward success in +those areas I think um one of the things + + align:start position:0% +those areas I think um one of the things + + + align:start position:0% +those areas I think um one of the things +that happened was at least out of this + + align:start position:0% +that happened was at least out of this + + + align:start position:0% +that happened was at least out of this +particular Village a lot of the men as + + align:start position:0% +particular Village a lot of the men as + + + align:start position:0% +particular Village a lot of the men as +it often happens went to work in the + + align:start position:0% +it often happens went to work in the + + + align:start position:0% +it often happens went to work in the +city first and they as jier said sort of + + align:start position:0% +city first and they as jier said sort of + + + align:start position:0% +city first and they as jier said sort of +started to understand what education + + align:start position:0% +started to understand what education + + + align:start position:0% +started to understand what education +could offer their children as well as + + align:start position:0% +could offer their children as well as + + + align:start position:0% +could offer their children as well as +knowing that they didn't want their + + align:start position:0% +knowing that they didn't want their + + + align:start position:0% +knowing that they didn't want their +children to be Shepherds so um I I mean + + align:start position:0% +children to be Shepherds so um I I mean + + + align:start position:0% +children to be Shepherds so um I I mean +I don't think you could + + align:start position:0% +I don't think you could + + + align:start position:0% +I don't think you could +say um that it suddenly dawned on them + + align:start position:0% +say um that it suddenly dawned on them + + + align:start position:0% +say um that it suddenly dawned on them +and then they moved it was a sort of a + + align:start position:0% +and then they moved it was a sort of a + + + align:start position:0% +and then they moved it was a sort of a +so process where people were coming back + + align:start position:0% +so process where people were coming back + + + align:start position:0% +so process where people were coming back +and forth between the village and the + + align:start position:0% +and forth between the village and the + + + align:start position:0% +and forth between the village and the +city seasonally and began to sort of + + align:start position:0% +city seasonally and began to sort of + + + align:start position:0% +city seasonally and began to sort of +understand and you know you people here + + align:start position:0% +understand and you know you people here + + + align:start position:0% +understand and you know you people here +know much more about this urbanization + + align:start position:0% +know much more about this urbanization + + + align:start position:0% +know much more about this urbanization +process then I could begin to expound on + + align:start position:0% +process then I could begin to expound on + + + align:start position:0% +process then I could begin to expound on +but at least from the instance here it + + align:start position:0% +but at least from the instance here it + + + align:start position:0% +but at least from the instance here it +was very clear that those people coming + + align:start position:0% +was very clear that those people coming + + + align:start position:0% +was very clear that those people coming +back from the city had a big influence + + align:start position:0% +back from the city had a big influence + + + align:start position:0% +back from the city had a big influence +as well as sometimes they um they began + + align:start position:0% +as well as sometimes they um they began + + + align:start position:0% +as well as sometimes they um they began +to send out a few services to these + + align:start position:0% +to send out a few services to these + + + align:start position:0% +to send out a few services to these +places who had never ever gotten any + + align:start position:0% +places who had never ever gotten any + + + align:start position:0% +places who had never ever gotten any +Services there began to be nurses and + + align:start position:0% +Services there began to be nurses and + + + align:start position:0% +Services there began to be nurses and +some teachers who came with ideas that + + align:start position:0% +some teachers who came with ideas that + + + align:start position:0% +some teachers who came with ideas that +had influence but I still think it's + + align:start position:0% +had influence but I still think it's + + + align:start position:0% +had influence but I still think it's +kind of an astounding thing that in such + + align:start position:0% +kind of an astounding thing that in such + + + align:start position:0% +kind of an astounding thing that in such +a short amount of time that amount of + + align:start position:0% +a short amount of time that amount of + + + align:start position:0% +a short amount of time that amount of +change could take place yeah um I just + + align:start position:0% +change could take place yeah um I just + + + align:start position:0% +change could take place yeah um I just +wanted to disagree my friend here I + + align:start position:0% +wanted to disagree my friend here I + + + align:start position:0% +wanted to disagree my friend here I +think um some of these larger issues are + + align:start position:0% +think um some of these larger issues are + + + align:start position:0% +think um some of these larger issues are +best understood in their personal + + align:start position:0% +best understood in their personal + + + align:start position:0% +best understood in their personal +effects on people and I really applaud + + align:start position:0% +effects on people and I really applaud + + + align:start position:0% +effects on people and I really applaud +your approach um of looking at + + align:start position:0% +your approach um of looking at + + + align:start position:0% +your approach um of looking at +individuals and how it affects their + + align:start position:0% +individuals and how it affects their + + + align:start position:0% +individuals and how it affects their +lives how the cish issue elev issue + + align:start position:0% +lives how the cish issue elev issue + + + align:start position:0% +lives how the cish issue elev issue +women's issue affect their lives + + align:start position:0% +women's issue affect their lives + + + align:start position:0% +women's issue affect their lives +individually because I think that's + + align:start position:0% +individually because I think that's + + + align:start position:0% +individually because I think that's +where we begin to make change um my + + align:start position:0% +where we begin to make change um my + + + align:start position:0% +where we begin to make change um my +family story is very similar to this + + align:start position:0% +family story is very similar to this + + + align:start position:0% +family story is very similar to this +family story and um I think it does + + align:start position:0% +family story and um I think it does + + + align:start position:0% +family story and um I think it does +really wonderfully show larger Trends + + align:start position:0% +really wonderfully show larger Trends + + + align:start position:0% +really wonderfully show larger Trends +which many many many families change uh + + align:start position:0% +which many many many families change uh + + + align:start position:0% +which many many many families change uh +many many families have experienced uh + + align:start position:0% +many many families have experienced uh + + + align:start position:0% +many many families have experienced uh +in their lives um I also want to ask you + + align:start position:0% +in their lives um I also want to ask you + + + align:start position:0% +in their lives um I also want to ask you +about you mentioned that there was a + + align:start position:0% +about you mentioned that there was a + + + align:start position:0% +about you mentioned that there was a +television on all the time how did You + + align:start position:0% +television on all the time how did You + + + align:start position:0% +television on all the time how did You +observe people's lives changing through + + align:start position:0% +observe people's lives changing through + + + align:start position:0% +observe people's lives changing through +the TV I wondered if you had any + + align:start position:0% +the TV I wondered if you had any + + + align:start position:0% +the TV I wondered if you had any +Recollections on that + + align:start position:0% +Recollections on that + + + align:start position:0% +Recollections on that +well unfortunately I wasn't um in the + + align:start position:0% +well unfortunately I wasn't um in the + + + align:start position:0% +well unfortunately I wasn't um in the +village when electricity arrived in that + + align:start position:0% +village when electricity arrived in that + + + align:start position:0% +village when electricity arrived in that +Village I had been in another Village in + + align:start position:0% +Village I had been in another Village in + + + align:start position:0% +Village I had been in another Village in +the south in the 70s when electricity + + align:start position:0% +the south in the 70s when electricity + + + align:start position:0% +the south in the 70s when electricity +got there a lot sooner and um what it + + align:start position:0% +got there a lot sooner and um what it + + + align:start position:0% +got there a lot sooner and um what it +brought in were all those images of + + align:start position:0% +brought in were all those images of + + + align:start position:0% +brought in were all those images of +women that were really unacceptable in + + align:start position:0% +women that were really unacceptable in + + + align:start position:0% +women that were really unacceptable in +Village culture I mean the ladies in the + + align:start position:0% +Village culture I mean the ladies in the + + + align:start position:0% +Village culture I mean the ladies in the +with less clothing on and the soap + + align:start position:0% +with less clothing on and the soap + + + align:start position:0% +with less clothing on and the soap +operas with these bizarre situations and + + align:start position:0% +operas with these bizarre situations and + + + align:start position:0% +operas with these bizarre situations and +you know um you know it's an exposure to + + align:start position:0% +you know um you know it's an exposure to + + + align:start position:0% +you know um you know it's an exposure to +a broader audience and um so I you know + + align:start position:0% +a broader audience and um so I you know + + + align:start position:0% +a broader audience and um so I you know +I I can't um I think that the influence + + align:start position:0% +I I can't um I think that the influence + + + align:start position:0% +I I can't um I think that the influence +you know it began it begins to do all of + + align:start position:0% +you know it began it begins to do all of + + + align:start position:0% +you know it began it begins to do all of +this cultural globalization if you will + + align:start position:0% +this cultural globalization if you will + + + align:start position:0% +this cultural globalization if you will +but + + align:start position:0% +but + + + align:start position:0% +but +um then the the women with the TV on + + align:start position:0% +um then the the women with the TV on + + + align:start position:0% +um then the the women with the TV on +that was in the city what's really + + align:start position:0% +that was in the city what's really + + + align:start position:0% +that was in the city what's really +interesting about being in the Middle + + align:start position:0% +interesting about being in the Middle + + + align:start position:0% +interesting about being in the Middle +East as many of you know is that you can + + align:start position:0% +East as many of you know is that you can + + + align:start position:0% +East as many of you know is that you can +get television channels from 12 + + align:start position:0% +get television channels from 12 + + + align:start position:0% +get television channels from 12 +different countries you know you I mean + + align:start position:0% +different countries you know you I mean + + + align:start position:0% +different countries you know you I mean +it's it's a lot more open-minded than + + align:start position:0% +it's it's a lot more open-minded than + + + align:start position:0% +it's it's a lot more open-minded than +what we have on our television in that + + align:start position:0% +what we have on our television in that + + + align:start position:0% +what we have on our television in that +you can hear um broadcasts from + + align:start position:0% +you can hear um broadcasts from + + + align:start position:0% +you can hear um broadcasts from +radically different views so I imagine + + align:start position:0% +radically different views so I imagine + + + align:start position:0% +radically different views so I imagine +that has a big impact as + + align:start position:0% +that has a big impact as + + + align:start position:0% +that has a big impact as +well anyone + + align:start position:0% +well anyone + + + align:start position:0% +well anyone +else yes Connie you mentioned the + + align:start position:0% +else yes Connie you mentioned the + + + align:start position:0% +else yes Connie you mentioned the +incredible uh amount of change between + + align:start position:0% +incredible uh amount of change between + + + align:start position:0% +incredible uh amount of change between +these two generations really that hit me + + align:start position:0% +these two generations really that hit me + + + align:start position:0% +these two generations really that hit me +just so fundamentally how the mothers + + align:start position:0% +just so fundamentally how the mothers + + + align:start position:0% +just so fundamentally how the mothers +the daughters within that period of time + + align:start position:0% +the daughters within that period of time + + + align:start position:0% +the daughters within that period of time +the the transition the life changes they + + align:start position:0% +the the transition the life changes they + + + align:start position:0% +the the transition the life changes they +went through I wonder if there was a + + align:start position:0% +went through I wonder if there was a + + + align:start position:0% +went through I wonder if there was a +political context generally within + + align:start position:0% +political context generally within + + + align:start position:0% +political context generally within +turkey I my limited knowledge of Adam + + align:start position:0% +turkey I my limited knowledge of Adam + + + align:start position:0% +turkey I my limited knowledge of Adam +Turk and what he was trying to do to + + align:start position:0% +Turk and what he was trying to do to + + + align:start position:0% +Turk and what he was trying to do to +modernize the country I I just wonder if + + align:start position:0% +modernize the country I I just wonder if + + + align:start position:0% +modernize the country I I just wonder if +there was a momentum that was supported + + align:start position:0% +there was a momentum that was supported + + + align:start position:0% +there was a momentum that was supported +outside of even their cultural sort of + + align:start position:0% +outside of even their cultural sort of + + + align:start position:0% +outside of even their cultural sort of +intimate + + align:start position:0% +intimate + + + align:start position:0% +intimate +Circle that would have supported those + + align:start position:0% +Circle that would have supported those + + + align:start position:0% +Circle that would have supported those +changes well actually that one of the + + align:start position:0% +changes well actually that one of the + + + align:start position:0% +changes well actually that one of the +first photographs that I showed at the + + align:start position:0% +first photographs that I showed at the + + + align:start position:0% +first photographs that I showed at the +beginning was um they weren't really + + align:start position:0% +beginning was um they weren't really + + + align:start position:0% +beginning was um they weren't really +village women they were women in the + + align:start position:0% +village women they were women in the + + + align:start position:0% +village women they were women in the +city in in 1975 who were marching it it + + align:start position:0% +city in in 1975 who were marching it it + + + align:start position:0% +city in in 1975 who were marching it it +wasn't Mayday it was International + + align:start position:0% +wasn't Mayday it was International + + + align:start position:0% +wasn't Mayday it was International +women's day um so you know there I I I + + align:start position:0% +women's day um so you know there I I I + + + align:start position:0% +women's day um so you know there I I I +would hate to try to capitalize um + + align:start position:0% +would hate to try to capitalize um + + + align:start position:0% +would hate to try to capitalize um +several decades of Turkish social and + + align:start position:0% +several decades of Turkish social and + + + align:start position:0% +several decades of Turkish social and +political history especially um but um + + align:start position:0% +political history especially um but um + + + align:start position:0% +political history especially um but um +there were there were certainly + + align:start position:0% +there were there were certainly + + + align:start position:0% +there were there were certainly +movements within the cities there are + + align:start position:0% +movements within the cities there are + + + align:start position:0% +movements within the cities there are +certainly academic feminists in Istanbul + + align:start position:0% +certainly academic feminists in Istanbul + + + align:start position:0% +certainly academic feminists in Istanbul +who um you know you would be very + + align:start position:0% +who um you know you would be very + + + align:start position:0% +who um you know you would be very +comfortable with 30 years ago discussing + + align:start position:0% +comfortable with 30 years ago discussing + + + align:start position:0% +comfortable with 30 years ago discussing +your ideas with and the extent to which + + align:start position:0% +your ideas with and the extent to which + + + align:start position:0% +your ideas with and the extent to which +those ideas reach out to a village that + + align:start position:0% +those ideas reach out to a village that + + + align:start position:0% +those ideas reach out to a village that +is 600 miles away and inaccessible is it + + align:start position:0% +is 600 miles away and inaccessible is it + + + align:start position:0% +is 600 miles away and inaccessible is it +it seems to me that the the transitions + + align:start position:0% +it seems to me that the the transitions + + + align:start position:0% +it seems to me that the the transitions +that have happened sort of globally in + + align:start position:0% +that have happened sort of globally in + + + align:start position:0% +that have happened sort of globally in +terms of of change change are a function + + align:start position:0% +terms of of change change are a function + + + align:start position:0% +terms of of change change are a function +of this interaction between the village + + align:start position:0% +of this interaction between the village + + + align:start position:0% +of this interaction between the village +and the city and um you can find in + + align:start position:0% +and the city and um you can find in + + + align:start position:0% +and the city and um you can find in +Turkey you know in the in the 7s there + + align:start position:0% +Turkey you know in the in the 7s there + + + align:start position:0% +Turkey you know in the in the 7s there +was there was tremendous political + + align:start position:0% +was there was tremendous political + + + align:start position:0% +was there was tremendous political +Anarchy and upheaval and then there were + + align:start position:0% +Anarchy and upheaval and then there were + + + align:start position:0% +Anarchy and upheaval and then there were +coups and you know the the the political + + align:start position:0% +coups and you know the the the political + + + align:start position:0% +coups and you know the the the political +history um is a part of it but you know + + align:start position:0% +history um is a part of it but you know + + + align:start position:0% +history um is a part of it but you know +I'd be I I couldn't begin to tell you + + align:start position:0% +I'd be I I couldn't begin to tell you + + + align:start position:0% +I'd be I I couldn't begin to tell you +what were the specific catalysts that + + align:start position:0% +what were the specific catalysts that + + + align:start position:0% +what were the specific catalysts that +you know lead from one thing to another + + align:start position:0% +you know lead from one thing to another + + + align:start position:0% +you know lead from one thing to another +and + + align:start position:0% +and + + + align:start position:0% +and +yes my name is Colin Clark I was a Peace + + align:start position:0% +yes my name is Colin Clark I was a Peace + + + align:start position:0% +yes my name is Colin Clark I was a Peace +Corp volunteer in Turkey in the 1960s a + + align:start position:0% +Corp volunteer in Turkey in the 1960s a + + + align:start position:0% +Corp volunteer in Turkey in the 1960s a +teacher um in the Southeastern turkey in + + align:start position:0% +teacher um in the Southeastern turkey in + + + align:start position:0% +teacher um in the Southeastern turkey in +the kurish area and just I mean in this + + align:start position:0% +the kurish area and just I mean in this + + + align:start position:0% +the kurish area and just I mean in this +question of what was going on + + align:start position:0% +question of what was going on + + + align:start position:0% +question of what was going on +politically or what what the Turkish + + align:start position:0% +politically or what what the Turkish + + + align:start position:0% +politically or what what the Turkish +government was + + align:start position:0% +government was + + + align:start position:0% +government was +perhaps uh doing there were um there + + align:start position:0% +perhaps uh doing there were um there + + + align:start position:0% +perhaps uh doing there were um there +were women teachers sent out all over + + align:start position:0% +were women teachers sent out all over + + + align:start position:0% +were women teachers sent out all over +turkey I mean I was I happen to be an + + align:start position:0% +turkey I mean I was I happen to be an + + + align:start position:0% +turkey I mean I was I happen to be an +American but there were Turkish women + + align:start position:0% +American but there were Turkish women + + + align:start position:0% +American but there were Turkish women +teachers sent out into very small rural + + align:start position:0% +teachers sent out into very small rural + + + align:start position:0% +teachers sent out into very small rural +areas not necessarily to Villages but + + align:start position:0% +areas not necessarily to Villages but + + + align:start position:0% +areas not necessarily to Villages but +small towns where they had middle + + align:start position:0% +small towns where they had middle + + + align:start position:0% +small towns where they had middle +schools and where probably 20 years + + align:start position:0% +schools and where probably 20 years + + + align:start position:0% +schools and where probably 20 years +earlier it would have been just totally + + align:start position:0% +earlier it would have been just totally + + + align:start position:0% +earlier it would have been just totally +unheard of so those kinds + + align:start position:0% +unheard of so those kinds + + + align:start position:0% +unheard of so those kinds +of + + align:start position:0% +of + + + align:start position:0% +of +experiences you know from the point of + + align:start position:0% +experiences you know from the point of + + + align:start position:0% +experiences you know from the point of +view of the people in rural areas uh + + align:start position:0% +view of the people in rural areas uh + + + align:start position:0% +view of the people in rural areas uh +certainly must have affected them to see + + align:start position:0% +certainly must have affected them to see + + + align:start position:0% +certainly must have affected them to see +you know young women um coming as + + align:start position:0% +you know young women um coming as + + + align:start position:0% +you know young women um coming as +teachers and nurses and and so on so + + align:start position:0% +teachers and nurses and and so on so + + + align:start position:0% +teachers and nurses and and so on so +that's that's another way that change + + align:start position:0% +that's that's another way that change + + + align:start position:0% +that's that's another way that change +comes about and I would also say on the + + align:start position:0% +comes about and I would also say on the + + + align:start position:0% +comes about and I would also say on the +whole question of of migration it's not + + align:start position:0% +whole question of of migration it's not + + + align:start position:0% +whole question of of migration it's not +only that people want to go to the city + + align:start position:0% +only that people want to go to the city + + + align:start position:0% +only that people want to go to the city +I mean it's clear that there isn't the + + align:start position:0% +I mean it's clear that there isn't the + + + align:start position:0% +I mean it's clear that there isn't the +kind of work that people were doing in + + align:start position:0% +kind of work that people were doing in + + + align:start position:0% +kind of work that people were doing in +The Villages 40 years ago is not there + + align:start position:0% +The Villages 40 years ago is not there + + + align:start position:0% +The Villages 40 years ago is not there +to be done anymore it's you know Turkey + + align:start position:0% +to be done anymore it's you know Turkey + + + align:start position:0% +to be done anymore it's you know Turkey +is managing to provide itself with food + + align:start position:0% +is managing to provide itself with food + + + align:start position:0% +is managing to provide itself with food +and and meat and so on but the the the + + align:start position:0% +and and meat and so on but the the the + + + align:start position:0% +and and meat and so on but the the the +human labor required to do that is much + + align:start position:0% +human labor required to do that is much + + + align:start position:0% +human labor required to do that is much +much less so it's inevitable that people + + align:start position:0% +much less so it's inevitable that people + + + align:start position:0% +much less so it's inevitable that people +for whatever reasons individuals have + + align:start position:0% +for whatever reasons individuals have + + + align:start position:0% +for whatever reasons individuals have +you know this since a worldwide um + + align:start position:0% +you know this since a worldwide um + + + align:start position:0% +you know this since a worldwide um +phenomenon and you know there the + + align:start position:0% +phenomenon and you know there the + + + align:start position:0% +phenomenon and you know there the +individual stories which are interesting + + align:start position:0% +individual stories which are interesting + + + align:start position:0% +individual stories which are interesting +but the whole um thing was inevitable + + align:start position:0% +but the whole um thing was inevitable + + + align:start position:0% +but the whole um thing was inevitable +anyway the emping out of the countryside + + align:start position:0% +anyway the emping out of the countryside + + + align:start position:0% +anyway the emping out of the countryside +and the growth of cities and I'd like to + + align:start position:0% +and the growth of cities and I'd like to + + + align:start position:0% +and the growth of cities and I'd like to +turn to the the other part of our our + + align:start position:0% +turn to the the other part of our our + + + align:start position:0% +turn to the the other part of our our +series here is on photography is + + align:start position:0% +series here is on photography is + + + align:start position:0% +series here is on photography is +inquiry + + align:start position:0% +inquiry + + + align:start position:0% +inquiry +um how marvelously your photograph + + align:start position:0% +um how marvelously your photograph + + + align:start position:0% +um how marvelously your photograph +showed the value of Photography in uh + + align:start position:0% +showed the value of Photography in uh + + + align:start position:0% +showed the value of Photography in uh +capturing these two times 30 years + + align:start position:0% +capturing these two times 30 years + + + align:start position:0% +capturing these two times 30 years +apart uh and your eye is + + align:start position:0% +apart uh and your eye is + + + align:start position:0% +apart uh and your eye is +really an extraordinary eye with a + + align:start position:0% +really an extraordinary eye with a + + + align:start position:0% +really an extraordinary eye with a +sensitivity to uh the every + + align:start position:0% +sensitivity to uh the every + + + align:start position:0% +sensitivity to uh the every +day um the fact that as a 25y old you + + align:start position:0% +day um the fact that as a 25y old you + + + align:start position:0% +day um the fact that as a 25y old you +laid the foundation in black and white + + align:start position:0% +laid the foundation in black and white + + + align:start position:0% +laid the foundation in black and white +photography uh for what you were able to + + align:start position:0% +photography uh for what you were able to + + + align:start position:0% +photography uh for what you were able to +come back and build on 30 years later uh + + align:start position:0% +come back and build on 30 years later uh + + + align:start position:0% +come back and build on 30 years later uh +is a testimony to your you know your + + align:start position:0% +is a testimony to your you know your + + + align:start position:0% +is a testimony to your you know your +talent back then in a sense the the + + align:start position:0% +talent back then in a sense the the + + + align:start position:0% +talent back then in a sense the the +power of what you showed us today was a + + align:start position:0% +power of what you showed us today was a + + + align:start position:0% +power of what you showed us today was a +movement back and + + align:start position:0% +movement back and + + + align:start position:0% +movement back and +forth um between the black and white and + + align:start position:0% +forth um between the black and white and + + + align:start position:0% +forth um between the black and white and +the public + + align:start position:0% +the public + + + align:start position:0% +the public +photographs um I guess a question that I + + align:start position:0% +photographs um I guess a question that I + + + align:start position:0% +photographs um I guess a question that I +have for you as a + + align:start position:0% +have for you as a + + + align:start position:0% +have for you as a +phographer is uh how did this experience + + align:start position:0% +phographer is uh how did this experience + + + align:start position:0% +phographer is uh how did this experience +um of coming back how did it change your + + align:start position:0% +um of coming back how did it change your + + + align:start position:0% +um of coming back how did it change your +your eye you know how did it change you + + align:start position:0% +your eye you know how did it change you + + + align:start position:0% +your eye you know how did it change you +as a photographer did it change you as a + + align:start position:0% +as a photographer did it change you as a + + + align:start position:0% +as a photographer did it change you as a +photographer how did you feel coming + + align:start position:0% +photographer how did you feel coming + + + align:start position:0% +photographer how did you feel coming +back that you had developed as a + + align:start position:0% +back that you had developed as a + + + align:start position:0% +back that you had developed as a +photographer in the me + + align:start position:0% +photographer in the me + + + align:start position:0% +photographer in the me +time well before I answer your question + + align:start position:0% +time well before I answer your question + + + align:start position:0% +time well before I answer your question +I want to go to the first thing which + + align:start position:0% +I want to go to the first thing which + + + align:start position:0% +I want to go to the first thing which +because you're you and spner very soon + + align:start position:0% +because you're you and spner very soon + + + align:start position:0% +because you're you and spner very soon +to be putting out a book that looks at + + align:start position:0% +to be putting out a book that looks at + + + align:start position:0% +to be putting out a book that looks at +dorothia Lang's work I have to give all + + align:start position:0% +dorothia Lang's work I have to give all + + + align:start position:0% +dorothia Lang's work I have to give all +the credit to my 1970 photographs to the + + align:start position:0% +the credit to my 1970 photographs to the + + + align:start position:0% +the credit to my 1970 photographs to the +fact that dorothia Lang was the person I + + align:start position:0% +fact that dorothia Lang was the person I + + + align:start position:0% +fact that dorothia Lang was the person I +considered the one I wanted to become + + align:start position:0% +considered the one I wanted to become + + + align:start position:0% +considered the one I wanted to become +you know that that I I imitated her I + + align:start position:0% +you know that that I I imitated her I + + + align:start position:0% +you know that that I I imitated her I +tried to be like her um and it was um in + + align:start position:0% +tried to be like her um and it was um in + + + align:start position:0% +tried to be like her um and it was um in +terms of how did the photography change + + align:start position:0% + + + + align:start position:0% + +um I went back with a an automatic + + align:start position:0% +um I went back with a an automatic + + + align:start position:0% +um I went back with a an automatic +camera with a Flash and shot color and + + align:start position:0% +camera with a Flash and shot color and + + + align:start position:0% +camera with a Flash and shot color and +um I think I've come to feel that that + + align:start position:0% +um I think I've come to feel that that + + + align:start position:0% +um I think I've come to feel that that +isn't my preferred way of shooting but + + align:start position:0% +isn't my preferred way of shooting but + + + align:start position:0% +isn't my preferred way of shooting but +that I had to do that then I I I felt I + + align:start position:0% +that I had to do that then I I I felt I + + + align:start position:0% +that I had to do that then I I I felt I +needed to get the information I needed + + align:start position:0% +needed to get the information I needed + + + align:start position:0% +needed to get the information I needed +to use a flash to get inside I needed + + align:start position:0% +to use a flash to get inside I needed + + + align:start position:0% +to use a flash to get inside I needed +and um it's a quandry to me now because + + align:start position:0% +and um it's a quandry to me now because + + + align:start position:0% +and um it's a quandry to me now because +I do have this um there are certain + + align:start position:0% +I do have this um there are certain + + + align:start position:0% +I do have this um there are certain +aspects of the black and white + + align:start position:0% +aspects of the black and white + + + align:start position:0% +aspects of the black and white +photography which are still very strong + + align:start position:0% +photography which are still very strong + + + align:start position:0% +photography which are still very strong +to me and and I'm kind of curious about + + align:start position:0% +to me and and I'm kind of curious about + + + align:start position:0% +to me and and I'm kind of curious about +what it would be like to now go back and + + align:start position:0% +what it would be like to now go back and + + + align:start position:0% +what it would be like to now go back and +do some black and white photography with + + align:start position:0% +do some black and white photography with + + + align:start position:0% +do some black and white photography with +the um quality of life but for the + + align:start position:0% +the um quality of life but for the + + + align:start position:0% +the um quality of life but for the +purpose of of this um the garishness of + + align:start position:0% +purpose of of this um the garishness of + + + align:start position:0% +purpose of of this um the garishness of +the color is a part of the message you + + align:start position:0% +the color is a part of the message you + + + align:start position:0% +the color is a part of the message you +know the that I mean it truly does carry + + align:start position:0% +know the that I mean it truly does carry + + + align:start position:0% +know the that I mean it truly does carry +some of the the um information that um + + align:start position:0% +some of the the um information that um + + + align:start position:0% +some of the the um information that um +so uh it's it set me up to + + align:start position:0% +so uh it's it set me up to + + + align:start position:0% +so uh it's it set me up to +be I think I'll have to be more + + align:start position:0% +be I think I'll have to be more + + + align:start position:0% +be I think I'll have to be more +experimental in the future about which + + align:start position:0% +experimental in the future about which + + + align:start position:0% +experimental in the future about which +which way I go and how I use it but I'm + + align:start position:0% +which way I go and how I use it but I'm + + + align:start position:0% +which way I go and how I use it but I'm +certainly far more aware now of the + + align:start position:0% +certainly far more aware now of the + + + align:start position:0% +certainly far more aware now of the +impact of those bright lit + + align:start position:0% + + + + align:start position:0% + +colors yes just a small comment Turkish + + align:start position:0% +colors yes just a small comment Turkish + + + align:start position:0% +colors yes just a small comment Turkish +woman teachers role acting as role model + + align:start position:0% +woman teachers role acting as role model + + + align:start position:0% +woman teachers role acting as role model +goes all the way back to + + align:start position:0% +goes all the way back to + + + align:start position:0% +goes all the way back to +30s alphabet uh Revolution no I'm aware + + align:start position:0% +30s alphabet uh Revolution no I'm aware + + + align:start position:0% +30s alphabet uh Revolution no I'm aware +of that there were sort of Village + + align:start position:0% +of that there were sort of Village + + + align:start position:0% +of that there were sort of Village +School teachers that got sent out I had + + align:start position:0% +School teachers that got sent out I had + + + align:start position:0% +School teachers that got sent out I had +a friend who's grew up in all of those + + align:start position:0% +a friend who's grew up in all of those + + + align:start position:0% +a friend who's grew up in all of those +little Village Schools cuz his his + + align:start position:0% +little Village Schools cuz his his + + + align:start position:0% +little Village Schools cuz his his +father was one of those teachers in the + + align:start position:0% +father was one of those teachers in the + + + align:start position:0% +father was one of those teachers in the +my mother was admired by all the women + + align:start position:0% +my mother was admired by all the women + + + align:start position:0% +my mother was admired by all the women +in the little town she was a + + align:start position:0% +in the little town she was a + + + align:start position:0% +in the little town she was a +teacher well I think one of the things + + align:start position:0% +teacher well I think one of the things + + + align:start position:0% +teacher well I think one of the things +that people also don't realize about + + align:start position:0% +that people also don't realize about + + + align:start position:0% +that people also don't realize about +turkey is that you know in 1975 things + + align:start position:0% +turkey is that you know in 1975 things + + + align:start position:0% +turkey is that you know in 1975 things +like there were more larger percentage + + align:start position:0% +like there were more larger percentage + + + align:start position:0% +like there were more larger percentage +of women doctors and lawyers in Turkey + + align:start position:0% +of women doctors and lawyers in Turkey + + + align:start position:0% +of women doctors and lawyers in Turkey +than there were in the United States I + + align:start position:0% +than there were in the United States I + + + align:start position:0% +than there were in the United States I +mean that there are different aspects to + + align:start position:0% +mean that there are different aspects to + + + align:start position:0% +mean that there are different aspects to +which you know maybe starting with a + + align:start position:0% +which you know maybe starting with a + + + align:start position:0% +which you know maybe starting with a +Turk the society started to change + + align:start position:0% +Turk the society started to change + + + align:start position:0% +Turk the society started to change +didn't take exactly the same rots that + + align:start position:0% +didn't take exactly the same rots that + + + align:start position:0% +didn't take exactly the same rots that +uh you know we in the west think are the + + align:start position:0% +uh you know we in the west think are the + + + align:start position:0% +uh you know we in the west think are the +ones that you ought to take there were + + align:start position:0% +ones that you ought to take there were + + + align:start position:0% +ones that you ought to take there were +Innovations then but still the Kurds + + align:start position:0% +Innovations then but still the Kurds + + + align:start position:0% +Innovations then but still the Kurds +maintain a separate identity and I + + align:start position:0% +maintain a separate identity and I + + + align:start position:0% +maintain a separate identity and I +wonder especially now with Northern Iraq + + align:start position:0% +wonder especially now with Northern Iraq + + + align:start position:0% +wonder especially now with Northern Iraq +and the possibility of Kurdish state did + + align:start position:0% +and the possibility of Kurdish state did + + + align:start position:0% +and the possibility of Kurdish state did +you sense some antagonism uh toward the + + align:start position:0% +you sense some antagonism uh toward the + + + align:start position:0% +you sense some antagonism uh toward the +Turks toward the kurur because of this + + align:start position:0% +Turks toward the kurur because of this + + + align:start position:0% +Turks toward the kurur because of this +separate + + align:start position:0% +separate + + + align:start position:0% +separate +identity well when I visit in Turkey I'm + + align:start position:0% +identity well when I visit in Turkey I'm + + + align:start position:0% +identity well when I visit in Turkey I'm +visiting with friends so we can talk + + align:start position:0% +visiting with friends so we can talk + + + align:start position:0% +visiting with friends so we can talk +openly and as you can tell some of my + + align:start position:0% +openly and as you can tell some of my + + + align:start position:0% +openly and as you can tell some of my +best friends are Kurdish so um their + + align:start position:0% +best friends are Kurdish so um their + + + align:start position:0% +best friends are Kurdish so um their +experiences are often different from + + align:start position:0% +experiences are often different from + + + align:start position:0% +experiences are often different from +people who from farther west in Turkey + + align:start position:0% +people who from farther west in Turkey + + + align:start position:0% +people who from farther west in Turkey +who have not lived in the East or been + + align:start position:0% +who have not lived in the East or been + + + align:start position:0% +who have not lived in the East or been +in the East and + + align:start position:0% +in the East and + + + align:start position:0% +in the East and +um it's a it's such a sensitive subject + + align:start position:0% +um it's a it's such a sensitive subject + + + align:start position:0% +um it's a it's such a sensitive subject +I don't even discuss Kurds with some of + + align:start position:0% +I don't even discuss Kurds with some of + + + align:start position:0% +I don't even discuss Kurds with some of +my Turkish friends because um their + + align:start position:0% +my Turkish friends because um their + + + align:start position:0% +my Turkish friends because um their +experiences are so different and their + + align:start position:0% +experiences are so different and their + + + align:start position:0% +experiences are so different and their +education is so different and it's uh I + + align:start position:0% +education is so different and it's uh I + + + align:start position:0% +education is so different and it's uh I +think just as say racism is a really + + align:start position:0% +think just as say racism is a really + + + align:start position:0% +think just as say racism is a really +hard topic to discuss in in our country + + align:start position:0% +hard topic to discuss in in our country + + + align:start position:0% +hard topic to discuss in in our country +you know the Kurdish issue is equally + + align:start position:0% +you know the Kurdish issue is equally + + + align:start position:0% +you know the Kurdish issue is equally +explosive and it all depends upon who + + align:start position:0% +explosive and it all depends upon who + + + align:start position:0% +explosive and it all depends upon who +living you rumor you in and what their + + align:start position:0% +living you rumor you in and what their + + + align:start position:0% +living you rumor you in and what their +family experiences were I mean the there + + align:start position:0% +family experiences were I mean the there + + + align:start position:0% +family experiences were I mean the there +also um you + + align:start position:0% +also um you + + + align:start position:0% +also um you +know certain things people won't talk + + align:start position:0% +know certain things people won't talk + + + align:start position:0% +know certain things people won't talk +about with me because I'm a foreigner + + align:start position:0% +about with me because I'm a foreigner + + + align:start position:0% +about with me because I'm a foreigner +and because people's political histories + + align:start position:0% +and because people's political histories + + + align:start position:0% +and because people's political histories +um they don't want to be known so um + + align:start position:0% +um they don't want to be known so um + + + align:start position:0% +um they don't want to be known so um +it's it's very complicated and it's very + + align:start position:0% +it's it's very complicated and it's very + + + align:start position:0% +it's it's very complicated and it's very +hard but they're certainly a lot of you + + align:start position:0% +hard but they're certainly a lot of you + + + align:start position:0% +hard but they're certainly a lot of you +know it's going to be a long time before + + align:start position:0% +know it's going to be a long time before + + + align:start position:0% +know it's going to be a long time before +all those things are easily spoken about + + align:start position:0% +all those things are easily spoken about + + + align:start position:0% +all those things are easily spoken about +among different + + align:start position:0% +among different + + + align:start position:0% +among different +people Mara I just want to thank you + + align:start position:0% +people Mara I just want to thank you + + + align:start position:0% +people Mara I just want to thank you +seeing these photographs in this way um + + align:start position:0% +seeing these photographs in this way um + + + align:start position:0% +seeing these photographs in this way um +for and the stories for because I think + + align:start position:0% +for and the stories for because I think + + + align:start position:0% +for and the stories for because I think +in the storytelling and in the personal + + align:start position:0% +in the storytelling and in the personal + + + align:start position:0% +in the storytelling and in the personal +aspect of photojournalism it gives an + + align:start position:0% +aspect of photojournalism it gives an + + + align:start position:0% +aspect of photojournalism it gives an +emotional impact of what these changes + + align:start position:0% +emotional impact of what these changes + + + align:start position:0% +emotional impact of what these changes +mean to a person to family in a way that + + align:start position:0% +mean to a person to family in a way that + + + align:start position:0% +mean to a person to family in a way that +you can't necessarily get in just + + align:start position:0% +you can't necessarily get in just + + + align:start position:0% +you can't necessarily get in just +straight drive scholarship because it + + align:start position:0% +straight drive scholarship because it + + + align:start position:0% +straight drive scholarship because it +allows you to sort of feel and project + + align:start position:0% +allows you to sort of feel and project + + + align:start position:0% +allows you to sort of feel and project +into their lives and imagine what those + + align:start position:0% +into their lives and imagine what those + + + align:start position:0% +into their lives and imagine what those +changes viscerally mean so I think I + + align:start position:0% +changes viscerally mean so I think I + + + align:start position:0% +changes viscerally mean so I think I +think it's especially for a non-s + + align:start position:0% +think it's especially for a non-s + + + align:start position:0% +think it's especially for a non-s +scholar like myself very valuable to + + align:start position:0% +scholar like myself very valuable to + + + align:start position:0% +scholar like myself very valuable to +prompt questions about what does + + align:start position:0% +prompt questions about what does + + + align:start position:0% +prompt questions about what does +immigration un and the sadness that you + + align:start position:0% +immigration un and the sadness that you + + + align:start position:0% +immigration un and the sadness that you +can't go back you can't go home again + + align:start position:0% +can't go back you can't go home again + + + align:start position:0% +can't go back you can't go home again +and when you do about those losses and + + align:start position:0% +and when you do about those losses and + + + align:start position:0% +and when you do about those losses and +how how will her children maintain their + + align:start position:0% +how how will her children maintain their + + + align:start position:0% +how how will her children maintain their +cultural identity as they have their + + align:start position:0% + + + + align:start position:0% + +children I have two + + align:start position:0% +children I have two + + + align:start position:0% +children I have two +questions the first one is the Turkish + + align:start position:0% +questions the first one is the Turkish + + + align:start position:0% +questions the first one is the Turkish +State this publicly is secular and I'm + + align:start position:0% +State this publicly is secular and I'm + + + align:start position:0% +State this publicly is secular and I'm +wondering what the impact of that + + align:start position:0% +wondering what the impact of that + + + align:start position:0% +wondering what the impact of that +secularism is on women's emancipation in + + align:start position:0% +secularism is on women's emancipation in + + + align:start position:0% +secularism is on women's emancipation in +turkey and the second question different + + align:start position:0% +turkey and the second question different + + + align:start position:0% +turkey and the second question different +but what is the effect of this + + align:start position:0% +but what is the effect of this + + + align:start position:0% +but what is the effect of this +emancipation on + + align:start position:0% +emancipation on + + + align:start position:0% +emancipation on +men and how how have men changeed then + + align:start position:0% +men and how how have men changeed then + + + align:start position:0% +men and how how have men changeed then +how do you see women being different as + + align:start position:0% +how do you see women being different as + + + align:start position:0% +how do you see women being different as +same mothers because that has a lot to + + align:start position:0% +same mothers because that has a lot to + + + align:start position:0% +same mothers because that has a lot to +do with how patriarchal + + align:start position:0% +do with how patriarchal + + + align:start position:0% +do with how patriarchal +society well I don't think I'm + + align:start position:0% +society well I don't think I'm + + + align:start position:0% +society well I don't think I'm +necessarily qualified to comment on all + + align:start position:0% +necessarily qualified to comment on all + + + align:start position:0% +necessarily qualified to comment on all +of that that's a pretty big questions I + + align:start position:0% +of that that's a pretty big questions I + + + align:start position:0% +of that that's a pretty big questions I +think what is what it what separates + + align:start position:0% +think what is what it what separates + + + align:start position:0% +think what is what it what separates +turkey from some or distinguishes turkey + + align:start position:0% +turkey from some or distinguishes turkey + + + align:start position:0% +turkey from some or distinguishes turkey +I would say from some of the other + + align:start position:0% +I would say from some of the other + + + align:start position:0% +I would say from some of the other +Middle Eastern countries as you have + + align:start position:0% +Middle Eastern countries as you have + + + align:start position:0% +Middle Eastern countries as you have +pointed out is that this secularism was + + align:start position:0% +pointed out is that this secularism was + + + align:start position:0% +pointed out is that this secularism was +established in 1923 when the Republic + + align:start position:0% +established in 1923 when the Republic + + + align:start position:0% +established in 1923 when the Republic +was established and that you know it + + align:start position:0% +was established and that you know it + + + align:start position:0% +was established and that you know it +radically altered the course of history + + align:start position:0% +radically altered the course of history + + + align:start position:0% +radically altered the course of history +there and some of the edicts that were + + align:start position:0% +there and some of the edicts that were + + + align:start position:0% +there and some of the edicts that were +put forward in the 20s and 30s you know + + align:start position:0% +put forward in the 20s and 30s you know + + + align:start position:0% +put forward in the 20s and 30s you know +that women shouldn't wear veils and + + align:start position:0% +that women shouldn't wear veils and + + + align:start position:0% +that women shouldn't wear veils and +people had the vote I mean it didn't + + align:start position:0% +people had the vote I mean it didn't + + + align:start position:0% +people had the vote I mean it didn't +happen overnight even though that was in + + align:start position:0% +happen overnight even though that was in + + + align:start position:0% +happen overnight even though that was in +the law I mean there's much of the + + align:start position:0% +the law I mean there's much of the + + + align:start position:0% +the law I mean there's much of the +change has taken place has moved mov + + align:start position:0% +change has taken place has moved mov + + + align:start position:0% +change has taken place has moved mov +along slowly or in bodily but the fact + + align:start position:0% +along slowly or in bodily but the fact + + + align:start position:0% +along slowly or in bodily but the fact +that you start with a foundation of you + + align:start position:0% +that you start with a foundation of you + + + align:start position:0% +that you start with a foundation of you +know voting rights and legal rights is + + align:start position:0% +know voting rights and legal rights is + + + align:start position:0% +know voting rights and legal rights is +just a huge I mean that's what you have + + align:start position:0% +just a huge I mean that's what you have + + + align:start position:0% +just a huge I mean that's what you have +to turn back to when you're trying to + + align:start position:0% +to turn back to when you're trying to + + + align:start position:0% +to turn back to when you're trying to +make these changes um I mean I I I I + + align:start position:0% +make these changes um I mean I I I I + + + align:start position:0% +make these changes um I mean I I I I +couldn't + + align:start position:0% +couldn't + + + align:start position:0% +couldn't +um I think it would be foolish of me to + + align:start position:0% +um I think it would be foolish of me to + + + align:start position:0% +um I think it would be foolish of me to +to make some sort of gross + + align:start position:0% +to make some sort of gross + + + align:start position:0% +to make some sort of gross +generalizations about men as well I + + align:start position:0% +generalizations about men as well I + + + align:start position:0% +generalizations about men as well I +mean I mean I I'd be happy to to talk + + align:start position:0% +mean I mean I I'd be happy to to talk + + + align:start position:0% +mean I mean I I'd be happy to to talk +about it with you but it's um it's a + + align:start position:0% +about it with you but it's um it's a + + + align:start position:0% +about it with you but it's um it's a +huge + + align:start position:0% +huge + + + align:start position:0% +huge +topic and how has turkey changed in the + + align:start position:0% +topic and how has turkey changed in the + + + align:start position:0% +topic and how has turkey changed in the +last 75 years for men and women and + + align:start position:0% +last 75 years for men and women and + + + align:start position:0% +last 75 years for men and women and +um instances from your stories I don't + + align:start position:0% +um instances from your stories I don't + + + align:start position:0% +um instances from your stories I don't +expain well I mean the wonderful thing + + align:start position:0% +expain well I mean the wonderful thing + + + align:start position:0% +expain well I mean the wonderful thing +is that you you + + align:start position:0% +is that you you + + + align:start position:0% +is that you you +um you see with the the women pushing + + align:start position:0% +um you see with the the women pushing + + + align:start position:0% +um you see with the the women pushing +either very subtly or more openly for + + align:start position:0% +either very subtly or more openly for + + + align:start position:0% +either very subtly or more openly for +their their rights their econom + + align:start position:0% +their their rights their econom + + + align:start position:0% +their their rights their econom +freedoms and so forth you know yes in 30 + + align:start position:0% +freedoms and so forth you know yes in 30 + + + align:start position:0% +freedoms and so forth you know yes in 30 +years what's you know the men gets + + align:start position:0% +years what's you know the men gets + + + align:start position:0% +years what's you know the men gets +pushed along as well and um in some + + align:start position:0% +pushed along as well and um in some + + + align:start position:0% +pushed along as well and um in some +families that causes great friction and + + align:start position:0% +families that causes great friction and + + + align:start position:0% +families that causes great friction and +some families it just everyone benefits + + align:start position:0% +some families it just everyone benefits + + + align:start position:0% +some families it just everyone benefits +so + + align:start position:0% +so + + + align:start position:0% +so +um it depends a lot on class about what + + align:start position:0% +um it depends a lot on class about what + + + align:start position:0% +um it depends a lot on class about what +your you know where your education level + + align:start position:0% +your you know where your education level + + + align:start position:0% +your you know where your education level +is you know there there's so many + + align:start position:0% + + + + align:start position:0% + +variables and Estelle I want I wanted to + + align:start position:0% +variables and Estelle I want I wanted to + + + align:start position:0% +variables and Estelle I want I wanted to +go back to you asked you about the + + align:start position:0% +go back to you asked you about the + + + align:start position:0% +go back to you asked you about the +Northern Kurds there's there's not um + + align:start position:0% +Northern Kurds there's there's not um + + + align:start position:0% +Northern Kurds there's there's not um +there's not much there's not much + + align:start position:0% +there's not much there's not much + + + align:start position:0% +there's not much there's not much +support in in for separation I mean no I + + align:start position:0% +support in in for separation I mean no I + + + align:start position:0% +support in in for separation I mean no I +I I don't hear support in my own + + align:start position:0% +I I don't hear support in my own + + + align:start position:0% +I I don't hear support in my own +experience for um a separatist movement + + align:start position:0% +experience for um a separatist movement + + + align:start position:0% +experience for um a separatist movement +that the separatist movement was a + + align:start position:0% +that the separatist movement was a + + + align:start position:0% +that the separatist movement was a +fairly + + align:start position:0% +fairly + + + align:start position:0% +fairly +narrow um movement and that's + + align:start position:0% +narrow um movement and that's + + + align:start position:0% +narrow um movement and that's +Ian + + align:start position:0% + + + + align:start position:0% + +so well thank you thank you for coming + + align:start position:0% +so well thank you thank you for coming + + + align:start position:0% +so well thank you thank you for coming +thank you for coming + + align:start position:0% +thank you for coming + + + align:start position:0% +thank you for coming +[Applause] \ No newline at end of file diff --git a/_TdJBLu6hPc.txt b/_TdJBLu6hPc.txt new file mode 100644 index 0000000000000000000000000000000000000000..b223e4b85883ddec0cf48609565ac823211cea24 --- /dev/null +++ b/_TdJBLu6hPc.txt @@ -0,0 +1,1299 @@ +Good morning. So, I see we have a lot of parents here. + +How many parents have we got here? + +Welcome to the parents. How many of the parents have done + +the reading for today? [LAUGHTER] Good, because we'll call + +the parents too, right? We'll see what happens. + +All right, so, where are we? We've talked about this diagram that I + +keep coming back to. If you want to + +study biological function the two traditional ways to do that were to + +look at genetics or to look at biochemistry: genetics, the + +study of an organism with one broken component, those components being + +genes; biochemistry: the study of the purification of + +individual components from an organism away from the organism, + +particularly the most important such components being proteins. + +What do they have to do to each other? + +The unification in molecular biology that occurred in the middle + +of the century from the 1950s into the ‘60s and really + +up to 1970 or so, we came to a conceptual understand + + that genes encode proteins, + +and therefore these two different ways of looking at the organism: + +organism minus a component, components + +minus an organism were complementary points of view, + +and in theory, you could go from a gene sequence to a protein + +Sequence, a protein sequence back to a gene sequence, + +to go for a gene sequence to its function, its function + +to a protein, except for one to a tiny detail. This was all just + +conceptual. Conceptually we understood by about 1970 + +that the DNA made the RNA made the protein. The protein carried + +out the function but as of then, + +you couldn't individually work with or purify the DNA corresponding to + +any particular gene. All of the inferences had been + +indirect inferences: indirect inferences from bacterial genetics, + +bacterial regulation or Meselson-Stahl experiments, + +and all sorts of interesting indirect ways + +working out the genetic code, but it didn't let you read anything. + +This was a problem. Some people in the + +late 1960s said, great, molecular biology is over. + +We understand in principle how life works. Now let's go understand + +how the brain works. And there was an exodus of some + +people from molecular biology into neurobiology to now go + +nail the brain, figured that would be worth another + +ten years or so. But in fact, remarkably, + +people began to focus on how you could get to + +work with individual specific genes. Now, what's so hard about that? I + +mean, it's not very hard to crack open a + +red blood cell and purify different proteins. You can purify hemoglobin. + +You can purify different enzymes. Biochemistry allows you to purify + +different components from each other. I want to purify an enzyme: let's + +crack open a yeast cell, separate the + +proteins over some column that separates them based on their size + +or their charge, and I'll get purer and purer + +fractions. I'll assay each fraction to see + +which one has the enzymatic activity. But basically I use the + +physical chemical properties of the proteins to + +separate them into different buckets. Why not do that with, + +say, the human DNA and purify out the gene for beta + +globin, that encodes the beta component of hemoglobin? + +What would be the problem of just using physical chemical purification + +to purify one human gene from another? Well, I mean, it's one + +very big molecule. Well, I could sheer it up. + +Maybe I'll just break it up. Now, let's purify the beta + +globin containing part. It all looks the same. It's just + +DNA. It's one chemical polymer with pretty boring properties, + +and they're not very different. + +Any particular DNA sequence in any other DNA sequence basically about + +the same molecular weight, same charges, + +there's nothing to separate them by. How are you going to purify beta + +globin? That was the problem. That's where + +recombinant DNA came in was recombinant DNA was a remarkable + +and totally different way of purifying individual + +components. And the basis of it was this notion of cloning. + +If I want to purify out from the human + +genome, how big is the human genome? The human genome is about three + +billion bases long. If I want to purify a particular + +gene, let's say beta globin or some other gene, + +typical gene, might be on the order of 30,000 letters long. + +This is one part in 105 purification I've got to achieve. + +Any given gene is only one part in + +105 of the human genome. And then, what about a typical + +mutation? Maybe the mutation that causes + +sickle cell anemia by changing a single nucleotide and beta globe, + +well, that's one base pair. So that means I'm trying to identify + +something that's on the order of one part in 109 actually, + +a little less than one part in 109 of the whole genome. + +Carrying out purifications like: really kind of hard + +to imagine. But the way it was done was by the invention of cloning. + +Let me briefly overview of the idea + +of cloning, and then we'll dive into the details. The idea of cloning + +was, the way to purify individual molecules would just be + +to take the molecules and just dilute them so that there + +was only one of each model. That's very pure, + +isn't it? The problem is it's not very much, so you need + +a way to take a single copy of a molecule, + +and then make many copies of it. So purification's not hard. You + +just dilute it down so you work with + +single molecules but then you need to copy it back again + +and again and again, and no biochemical technique + +involves, say, fractionating a cell and replicating + +some enzyme, you know, copying some enzyme. + +You can't copy enzymes, but you can copy DNA, and that was + +the basis of it. So here's the way it goes. The + +basic overview we'll look at is take your DNA and cut your DNA + +of interest, maybe the human genome, + +into pieces at defined sites Then, paste your DNA, which is more + +technically ligate, the word we use. + +Paste your DNA to some other DNA called a vector. So, + +cut your DNA and paste your DNA. Each piece of your, say, human DNA + +gets stuck to some piece of vector. + +Insert this DNA into vectors that can replicate in bacteria. + +So, I'm going to actually take my piece of human DNA + +and not just ligate it to any piece of DNA. + +I'm going to take my human DNA, and I'm going to ligate it to a + +vector that has all of the machinery, + +all of the ability to be copied in a bacteria. Then what + +I'm going to do is I'm going to transform my DNA into a + +host cell, a host bacterial cell. Transform means introduce. When we + + talk about transforming DNA, + +we're not talking about changing it. It's the word that's used for + +taking my DNA, stuck into a vector, + +and introducing it into bacterial cells. Ideally, + +each bacterial cell would carry one such + +DNA molecule, and then what I want to do is I want to plate my cells, + +and select those that carry human DNA, my DNA; DNA I've put on + +it. So, I'm going to put them on a Petri plate and I want only the + +bacteria that happen to have picked an individual piece of human DNA + +to grow. So, that's the trick. It's a very simple trick. Take + +total human DNA, cut it up into pieces, glue + +it to a vector that's able to be copied so that it's able to be + +replicated in bacteria, put the vectors into bacterial + +cells; every bacterial cell picks up no more than one vector. + +You plate it out, and you simply arrange so that the + +only cells that grow are those that picked up the piece of human DNA. + +And then, every one of these colonies + +is the descendent of a single bacterial cell that picked up a + +single human molecule, but is obligingly + +copying that molecule for you again and again and again and again. + +And thus, you have what we refer + +to; this whole collection here is called a library of clones. + +This is called a recombinant library because + +every piece of the human genome is somewhere in here. + +You know, this one here probably is active, and maybe + +this one here maybe is collagen-11 and that one there might, + +ah, there's beta globin. OK, actually + +when you look at the plate there's no way to tell but in principle + +they're all there. So, there will be this question of, + +how do we look at a library and pull out what the right one + +is? But somewhere in there should be a bacterial + +colony that has pure beta globin gene, the DNA for beta globin. + +The next lecture will be about how you actually find it. + +But today let's just build this library. So our + +goal is to be able to build a library like this. + +So, we have to figure out how to cut DNA, + +paste, DNA, vectors, etc., etc. So that's what our + +subject will be today. Let's dive in. First, + +cutting DNA, how do you cut DNA? Restriction enzymes, + +etc. It turns out that the way you could cut + +DNA at particular places is as follows. Let me take a piece of DNA. + +Here's a double-stranded piece of DNA. We'll go A, + +G, C, T, A, G, A, A, T, T, C, T, T, A, C, C, + +hydroxyl there, three primad. Let's go back on the + +other strand. What do we have? G, + +G, T, A, A, G, A, A, T, T, C, T, A, G, C, T, + +hydroxyl there, three prime. There's my double + +stranded piece of DNA. It turns out that there exists an + +enzyme that recognizes that exact sequence: G, A, + +A, T, T, C. The enzyme goes by the name Eco R1. + +This protein, this enzyme, scans along the the DNA, and it + +finds this sequence: G, A, A, T, T, C. + +Actually it's on this strand. What about on the other strand does + +it say? Same thing. But it's a reverse palindrome. + +It's symmetric. That's very good. + +And it turns out most restriction enzymes do that. OK, + +so what it does when it finds that, + +with the benefit of colored chalk that has just shown up here + +is it cleaves the DNA fragment like that. + +And what it gives you then is a broken double strand with + +an overhang, T, T, A, A, five prime, + +three prime, three prime, five prime. This has a hydroxyl + +here this. This has a phosphate there. And then this other fragment + +here is A, A, T, T, C, T, T, A, C, C, G, G, T, + +A. So, what happens is, and this has a hydroxyl five + +prime, three prime, three prime, five prime I get into + + two fragments of DNA that have been + +broken there and have it over. The overhang is complementary. + +Those two sequences match each other. There's what's called a five prime + +overhang and they're complementary So, we have complementary, + +that is matching, five prime over X. This is called Eco R1 because it's + +purified, this particular enzyme, + +from E coli strain R and it's the number one such enzyme that + +was purified from it. So, it is very simple nomenclature + +here. Now, here's a question. Why do bacteria have an enzyme like + +this? There are some people who feel that the reason + +is that this enzyme is here precisely to allow molecular + +biologists to cut and paste DNA, and this represents + +impressions likely, me among them. + +How did anybody find this stuff? Well, shaggy dog story, I have to + +tell you the following shaggy dog story. + +So, this is a fun shaggy dog story, and it's an MIT shaggy dog story + +because it comes from the work of Salvador + +Luria, who is a very famous biologist who worked + +here at MIT. So, Salvador Luria was studying + +bacteriophage. Remember, bacteriophage are the + +viruses that infect bacteria. So, he was studying bacteriophage, + +and he took his bacteriophage and used it to infect a strain of + +bacteria, strain A, and he also used it to infect a strain of + +bacteria, strain B. So when he did that, + +what you do is you plate a lawn of bacterial cells. + +You kind of have a slush of bacterial cells that you + +plate here with virus mixed in, and wherever there's a + +virus, the virus grows, replicates, and either kills or + +slows down the growth of the cells so that bacterial cells grow + +everywhere else, but where a viral particle landed + +there's an absence of bacterial cells and that hole in the lawn, + +this whole thing is called a lawn of + +bacteria, and the holes in the lawn are called plaques. + +So, when he did this, he found that when he did it on + +strain A he got a bunch of plaques and when he did it + +on strain B, he didn't, no plaques. So what what's the + +simplest explanation for this? + +Strain B is different somehow. It's resistant to the virus. I + +don't know, the virus has to come in and do + +various things, and strain b isn't compatible with + +the virus or something like that. No big deal. So it's a resistant + +strain. But, occasionally you'd get a plaque. + +Very occasionally, you'd have an occasional plaque. + +So now, how would this be? I said the strain was + +resistant. How could there be an occasional plaque? + +Mutation in, could it be imitation in the bacteria? + +Sorry. Well, if it was a mutation in the bacteria + +there would be one bacteria that had the mutation. It was now + +susceptible, and it would die. But, the lawn would + +kind of grow because the cells around it wouldn't have a mutation. + +So it's probably not a mutation in the bacteria + +but what could be? Maybe a mutation of the virus: what + +if it was a mutation in the virus that was able to overcome + +the resistance? Ah, so that's OK. + +So, what this must be is the existence of a resistant + +virus that is a virus that can overcome the resistance of + +the bacteria. So far: perfectly normal, no problem. Now, let's + +do the following experiment. Let's take this resistant virus, + +and grow it, again, on strain A and grow it on + +strain b. What do you think is going to happen when I grow it on + +strain A? It'll grow lots of plaques. It still grows + +on strain A, and now what's going to happen when I grow + +it on strain B? If this was really a mutation that + +made it able to grow on strain b then it gets lots of plaques because + +it's now gained the ability to grow on strain B, and sure + +enough, that's what happens. So, + +there's nothing funky yet. But now, suppose I take one of + +these resistant viruses that I isolated here on strain B, + +I grow it again here on strain A. It grows. I grow it on strain B. + +It grows. If I take it again from strain B and + +I repeat this, it'll still grow on strain A and + +still grow on strain B. Let's take one, + +though, from strain A. It's the resistant one which we have just now + +happened to have grown on strain A. And now, + +let's grow it again on strain A versus on strain B. And sure + +enough, it continues to grow on strain A, no problem. + +And we grow it now on strain B. And, what shall we + +get? Well, it should grow on strain B, right, because it was a mutant + +virus, and it gained the ability to grow on either. + +We passage it through B, it grows. We passage it through A. + +But the answer was nothing, no growth. How can that be? + +We had a virus. We agreed that was a mutant virus that + +had picked up the ability to grow on strain B, and we demonstrated + +it has now on either A or B. + +We then reached in, and grabbed a copy of it here from + +strain A, having grown on strain A, and we try it again and it now + +won't grow on strain B. If this was a mutation, + +I mean, maybe the mutation reverted, right? + +It was a reversion of the mutation. It mutated back. Is that plausible? + +No, come on. The chance that all of the copies there would mutate + +back, come on. I mean, you could repeat this + +several times and this is always what happens. + +What does that tell you about this mutation in the virus? + +It can't be a mutation of the virus because + +if it was a mutation, it would be transmitted through. + +But, passing through strain A makes it lose + +its ability to grow on strain B. But as long as you keep passing it + +through strain B, it can grow on strain B. This is + +not your typical genetics. So, Salvador Luria loved this. + +And, he really worked out what was going on. And somehow, + +well, so anyway, they referred to this as strain B + +having the ability to restrict the growth of the + +virus. Strain B can restrict the growth of the virus. + +That's where this word restriction enzyme + +comes from. What's really, truly going on here underneath the + +shaggy dog story? It took a long time before + +the shaggy dog story that Salvador Luria was the one to really + +demonstrate is fully worked out. But, what turns out to + +be the case is that strain B has a restriction enzyme. + +That's how it restricts the growth. It has one of + +these enzymes that can cut DNA at a specific place. + +When the virus comes into strain B, it injects its DNA, + +and the enzyme comes along and cuts the virus's DNA, protecting the + +bacteria. It's got its own little defense mechanism: pretty cool, + +pretty cool. So, any DNA that's introduced, + +if it has the sequence here, it'll take G, A, A, T, T, C, the + +bacteria cuts it. Wait a second, + +the bacteria has its own DNA. Why doesn't it chop up its own + +chromosome? Well, I mean, so one simple possibility would be + +that if this thing is looking for the sequence, G, A, A, T, T, C + +in the genome, maybe it's the case that the + +bacteria has arranged that its own DNA + +never has a G, A, A, T, T, C. That would be a + +simple solution, right? But is it a plausible + +solution? Why not? But just statistically, + +how often do I expect to encounter a G, A, A, T, T, C? What's + +the frequency of any given six letter word in a four letter + +alphabet? It's about one in 46. So, about one in 46 positions will + +be a G, A, A, T, T, C, and that's about 4,000 + +letters. So, every 4, 00 letters, I expect to encounter a + +G, A, A, T, T, C. How big is the E coli genome? + +4 million letters. So, how many G, A, A, + +T, T, Cs will there be? About 1,000 + +of them. It's just not plausible to imagine that it doesn't have the + +sites. So, your idea is that if it has these sites, + +it's got to arrange to protect its own sites. So, how is + +it going to protect its own sites? + +Covers it or something. You could imagine something covers + +it or something, but you want to alter your own, + +so it turns out you're exactly right. What happens is there is + +an enzyme that comes along, and at this position, + +attaches a methyl group. It modifies the DNA + +by attaching a methyl group. It turns out that that methyl group + +is enough to prevent the restriction enzyme from binding. + +So, this blocks the restriction enzyme. So, that way the bacteria + +is able to distinguish between its own DNA, + +which is methylated, and the viral DNA. So, wait a second, how does + +that explain my virus that manage to grow? How did my virus manage to + +grow? It would need to have gotten itself modified also to be protected. + +Could that happen by chance? What if the methylation enzyme, + +the methylase, which is floating around in the cell, + +“accidentally” methylated the virus's DNA? What would + +happen then? The virus would become immune. + +So, suppose the bacteria was pretty clever, and had a + +lot more restriction enzyme, and only a little bit of methylase? + +Well, you'd imagine that most of the + +time the restriction enzyme would cut up the viral DNA first. + +But every once in a while, the methylase + +would get there first and protect the virus's DNA. + +That becomes an immune virus because it can't + +be cut by the enzyme anymore. And, if I take that, and I grow it + +again on strain B, it'll now produce lots of plaques because + +it was methylated. And, if I grow it + +again on strain B, it remains methylated because once + +it's methylated and comes into the cell, it's not + +cut. And so, its descendants will get methylated. + +But, what happens if I ever grow that methylated virus + +on strain A? Strain A doesn't have the restriction enzyme, + +and it doesn't have the methylase. So, the + +progeny phage that grew up on strain A aren't methylated. + +They're no longer protected. The protection that the + +virus has is the protection that comes from this methylation enzyme. + +It's not the sequence of the DNA. It's + +the attachment to these methyl groups. And so, + +it turns out that if you ever pass this virus through strain A, + +passage through strain A, the resulting DNA loses is + +unmethylated. And now, it can be cut. + +And it can be cut. Well, this explained the weird + +results of Luria, that somehow bacteria had a complex + +defense mechanism of a restriction enzyme + +and a cognate methylase. The restriction enzyme would cut + +the sequence. The chromosome would be protected by + +methylating that site, and usually it would work fine. + +Occasionally the bacterial virus would get methylated. + +It would be protected as long as it continues to go through strains that + +have this restricted methylation system. That was it. Now, this + +shaggy dog story took a couple of decades to work out, + +and eventually led to Nobel prizes for the discovery + +of restriction enzymes. They're extremely important because + +although bacteria do this to protect themselves, they have also + +given us the perfect tool to now cut DNA where we want to + +cut DNA. Now, what if you wanted to cut at a G, + +A, A, T, T, C? You've got Eco R1. + +But what if you wanted to cut it cut it in another sequence? + +Well, it turns out that if you want to cut it at G, G, A, T, C, C + +there's an enzyme called Bam H1. If you want to cut it at + +A, A, G, C, T, T or A, A, G, C, + +T, T, there's an enzyme called Hmd 3. If you + +want to cut it at just G, A, T, C like this, C, T, A, + +G, an enzyme called Mbo 1. And, there are enzymes that + +cut it this way, enzymes that cut it this way, + +enzymes that cut it this way, enzymes that recognize four bases, + +six bases. There are even enzymes that recognize eight bases. + +It turns out that bacteria have elaborated zillions of different + +restriction enzymes that recognize different sequences. This + +perfect for molecular biologists. Bacteria, + +of course, are much smarter than we are, having been out this much + +longer, have developed all of these tools for engineering. + +All we have to do is borrow them. So how do you get Eco R1? + +We grow out that strain of E coli; you purify Wco R1. + +And how do you get Hmd 3? You grow up + +strain of haemophilus influenza. You purify the enzyme. At least, + +that's how primitive molecular biologists did it. If you + +wanted to work with a restriction enzyme, you'd grow up the bacteria. + +You'd purify the enzyme yourself, and you would just use + +it in your laboratory. Of course today what does a modern + +molecular biologist do if he or she should want Hmd 3? + +It's in the catalog. So the catalog has 200 restriction + +enzymes. Yup, PSI-1 is new, on sale, 500 units for $400. + +Let's see what Eco R1 is going for. + +Eco R1: look at this, 50,000 units $200. That's a good + +price for Eco R1 because it's a very famous + +enzyme here. So all you have to do is you give them your credit card + +number and you have it tomorrow by FedEx. So that's how restriction + +enzymes are obtained today. So, next up, we can cut DNA any + +place we want to. We now need to glue DNA together. + +Suppose I cut DNA, human DNA, and I'm + +going to cut it. I'll just take human DNA, + +your DNA, which I've purified, and I'm going to cut + +it at all its Eco R1 sites. I can take any other DNA I want. + +I don't know, I could take zebra DNA. I could take anything and I could + +also cut it at Eco R1 sites. I could mix them together, + +and after mixing them together the fragments will float around and + +remember this down here has T, T, + +A, A. This fragment over here from some other piece + +T, T, A, A, this could be human DNA. This could be zebra DNA if you want + +to. It doesn't matter. It could be bacterial DNA. + +These fragments overlap. They'll hydrogen bond a little bit, + +but that of course won't introduce a covalent bond here. + +I'd really like to make a covalent bond. I would like to attach the + +piece of DNA from one source to the piece of DNA from the + +other source by doing the opposite of the + +restriction enzyme. The restriction enzyme cut at these + +locations. I would now like to catalyze + +the rejoining of the sugar phosphate backbone here. + +So I would like to rejoin the sugar phosphate backbone. I + +have a hydroxyl here. I have a phosphate here, + +and I would like to ligate them together. So + +how I manage to ligate? What kind of fancy chemistry do I + +do to ligate these pieces of DNA together? I don't do any fancy + +chemistry. I again sit at the feet of bacteria who have solved all + +these problems before. And I ask bacteria, how do you do + +this? And they say, well, we have an enzyme called + +ligase. So, you purify ligase from bacteria, + +you add that, and ligase ligates the fragments together. Why + +do bacteria have an enzyme ligase? + +For a pair of their own DNA. Things go wrong this is part of the + +DNA maintenance scheme of bacteria. They have an enzyme + +ligase to appear their own breaks in DNA and, obligingly, you + +can purify DNA ligase. So you add ligase, today, + +of course, if you need a ligase, + +how do you get it? It's in the catalog, + +absolutely. So, you can glue together any of those things you + +want. All right, next up, what DNA do I want to stick + +together? I mean, here I made a silly example. + +I'm going to stick some human DNA to some zebra + +DNA. Why do that? I mean, just to show you that I can + +doing it, right? I'm just demonstrating that I could stick any + +DNA to any DNA. Remember, once I've + +got a piece of DNA it doesn't know whether it came from a human or a + +zebra. It's just the molecule. You can stick the molecules together, + +right? But what do I really want to attach my human DNA to? + +I want to attach it to attach it to some other DNA that + +has the ability to grow on its own within bacteria. Vectors: I need + +to make, here's what I would really like. I would like to have + +a piece of DNA that has some sequences that contain the + +recognition sites for replication. I'd like to have some replication + +initiation sites here. So, a piece of DNA that, + +remember, because the bacterial chromosome itself, + +here's my bacteria, bacteria'chromosome replicates + +itself, and it has the ability to start DNA replication at multiple + +sites called origins of replication. But, what I + +would really like is to be able to construct in the laboratory a + +synthetic piece of DNA that also would function as an + +origin of replication because then what I could do is in vitro take + +my piece of DNA, attach it to this vector, + +and it would now have the ability to grow + +the bacteria. How am I going to make a piece of DNA? + +What kind of engineering tricks can we do to create + +a small piece of DNA that has all the machinery needed to + +be able to be copied and replicated just like bacterial + +chromosomes? That's a pretty fancy feat of engineering. + +How are you going to do that? Sorry? OK, + +so who are you going to ask? If you wanted to do this, you're + +going to ask the experts. Who are the experts? Viruses or + +bacteria, or basically, if you want to do anything, + +the place to ask is the folks who have the most + +experience. And, the folks who have the most + +experience are almost always prokaryotic organisms because they + +are by far the most evolved things on + +this planet. Anything that can replicate itself and grow every 20 + +minutes or something like that has had a lot more + +generations of evolution than you have. And therefore, + +they are much more optimized than we are. And so you go ask and say, + +has any bacteria worked out how to do this? Turns out bacteria have + +worked out how to do this just fine. In + +fact, most bacteria, at least many bacteria, + +contain within them, in addition to their own chromosome, + +small circles of DNA. These are called episomes. + +This is the chromosome. Epi means on top of + +or in addition to. So in addition to the chromosome, + +there's an episome. The episome is in fact an autonomously replicating + +piece of DNA that has an origin. And it replicates. Why do bacteria + +have episomes? It turns out episomes + +often contain genes. One fo the genes they contain, + +or some of the types of genes they contain, are resistance + +genes. There might be, for example, a penicillin resistance + +gene contained on an episome, or a streptomycin resistance gene. + +It turns out the bacteria have these + +episomes containing resistance genes, and they're not in the chromosome. + +They're separate. Now, why would they do that? + +It turns out when a bacterium dies and a cell cracks open, the + +DNA spills out. The next door neibhored bacteria has + +mechanismis to suck up DNA from the environment. You never + +know. It might find something interesting out there. + +So, it turns out that bacteria are rather promiscuously exchanging + +pieces of DNA all the time. And so, + +a bacteria that has an episome that has a penicillin resistance gene + +can spread it to other bacteria, and it's very nice. It's compact. + +It's on its own little episome, autonomously replicating + +piece of DNA. This is great for bacteria wanting to spread drug + +resistance. It's not good for human populations, + +for example, because this is how drug resistance spread through + +populations. This is why we have spreads of + +penicillin resistance. Now, of course, wait a second, + +this whole mechanism of spreading drug resistance, we've only had + +antibiotics since the 1940s. How did bacteria devise this so + +quickly? Sorry? Many generations since 1945? + +That would be very impressive. + +Yeah, but, I mean, why do they have this episome mechanism, the + +ability to spread DNA and all that? That's an awful lot + +to evolve in 50 years? Yeah? Something natural like + +penicillin. It turns out, we didn't + +think of penicillin. Who thought of penicillin? + +Fungi. Right, again, we learn from the lower organisms. Penicillin + +comes from fungi. Bacteria have been fighting + +off penicillin for millions and tens of millions of years. So, + +we may be very proud of our penicillin and all that. + +But, they've been at this for a very long time. + +This is about war between bacteria and fungi. + +That's what this is, OK? So, that's why these things are + +here. They're here so that bacteria can have these + +resistance genes against fungi and things like that that make + +antibiotics. Antibiotics are natural. We've made a few + +new ones, but most of the antibiotics have been made by nature. + +And so, if I wanted to replicate DNA, + +if I wanted to attach my human DNA to a piece of DNA that's + +capable of autonomous replication, autonomously replicating circles of + +DNA, these autonomously replicating circles of DNA are also called + +plasmids. And that's the word we'll mostly use for them, + +plasmids. All I need to do is purify a plasmid from + +a bacteria. So, I find a bacteria that has plasmids. + +I purify the plasmid, and then I can cut open the plasmid + +at the Eco R1 site, OK? So, this plasmid will have an + +ORI, an origin of replication. I'll cut + +it open at the Eco R1 sight. I'll take human DNA fragments that + +I've cut with Eco R1. I'll mix them with plasmid DNA that has + +been opened up, has an origin. Ligase will come + +along, join this up, and now I have a circle of DNA that + +has all the machinery to autonomously replicate, + +plus my human DNA. Now, if I wanted to get a vector, or an + +honest to goodness plasmid, I can go to a bacteria, + +grow it up, purify the plasmid, and cut it. Or alternatively, + +if I needed the plasmid, say, tomorrow, + +it's in the catalog. The next section of the catalog has + +a long list of plasmids here. There's + +a plasmid there, right? It's a nice plasmid. + +Oh yes, let's see, puck is a very good plasmid. + +PBR 322 is a good plasmid. The whole section, all this purple + +stuff are the plasmids. So, you can get the plasmids too. + +You place one order, you get the restriction enzymes, + +you get the ligases, you get the plasmids, no + +problem. So, I can then take total human DNA, cut up, cut + +up, cut up, cut up, add in plasmid, + +and I'm going to ligate together. And then, having ligated my human + +DNA to my plasmids, I'm going to mix with + +bacteria. I take some bacterial cells. I add my mixture of these + +plasmids containing human DNA. And now all I have to do is + +persuade the bacteria to suck up my plasmids containin human DNA. + +How do I teach bacteria to suck up DNA? They do that for + +a living. That's what they do. They're always spreading material. + +They have that ability. All we're doing is we're using + +their ability. So you get the sense that the kind + +of engineering that really works in biology is engineering that + +exploits what nature has been doing for a very long time. + +Rather than butting your head up against the problem, usually + +somebody has solved it, and it's almost always + +bacteria. So, you've transformed the bacteria. + +Now, there are a few tricks you can + +use to make them a little more transformable. + +You can add calcium phosphate, and blah, blah, blah, + +but you can sort of persuade them to take up the DNA. And then + +all you have to do is plate them out on a plate. + +Plate them out fairly dilutely so there are a lot of single bacterial + +cells that land on the plate, and wait for them to grow up. Each + +one of these had a single plasmid, a different plasmid than + +the next guy over. Wait a second, each one? + +How do I guarantee that every bacteria in my test + +tube took up a plasma? Is that plausible? I mean, + +I can't guarantee that every bacteria is going to take up a + +plasmid. Maybe I'll add so much plasmid that every bacteria will + +take one up. Oh, but that's a bad idea + +because why? Because then a lot of them will take up more than one. + +You don't want to do that. You really only + +want to have at most one. So, if you were going to arrange so + +that at random you only have about one, you've got to + +have a lot that are zero. So, this is a problem. I mean, + +it's a real waste. My library is going to have large numbers of + +bacteria that don't have any plasmid. In fact, this transformation + +process is not so efficient. It's not so efficient. So, we + +have a little bit of a problem here is + +that some of these guys will have human DNA. + +But, most of them won't. So, what can I do to arrange that + +any bacteria that did not pick up a plasmid + +was incapable of growing? Add a resistance gene to the + +plasmid. Suppose I were so clever as + +to add to that plasmid, penicillin resistance. So, + +not just an origin of replication, but suppose I also had a + +resistance gene here, say, for penicillin resistance or + +streptomycin resistance, or ampicillin tends to be a very big + +favorite, ampicillin resistance. Then, + +my plasmid would have ampicillin resistance gene encoded on it, + +an enzyme that can, say, break down ampicillin, + +so on and one way to to my perch you plate I just said ampa cell + +and now i'll even though most of the bacteria have not + +picked up a plasmid, only those bacteria that have picked + +up a plasmid have the ampicillin + +resistance gene and can grow on an ampicillin containing plate. + +Now, how do I get a plasmid with an ampicillin + +resistance gene? It's in the catalog. It's + +all there, right? In fact, these occur naturally. + +You can, with restriction enzymes, move the ampicillin resistance + +gene to your favorite plasmid. If you don't like that, you can put + +in kanamycin resistance, etc., etc., + +etc. So, that's how you do it. So, we've got the big picture here. + +We have now gotten a library, the Library of Human + +Fragments contained in E coli. The library is a big Petri plate or + +many Petri plates, each one of which is a colony. + +Each colony has a single vector with an origin, + +a resistance marker, and a distinct piece of + +human DNA. In this library lives somewhere the gene for Huntington's + +disease. Over here is a gene for cystic fibrosis, + +over here a gene for Duchenne muscular dystrophy, + +over here a gene for diastrophic dysplasia, + +over here a gene for etc. etc. The only detail, now, + +you've got a library. You've managed to purify each + +piece of human DNA away from every other piece of human DNA. + +The only question now is how do you use the library? + +How do you go to the library and withdraw the correct + +volume from the shelf? How do you find the one + +you're looking for? So, we have converted the problem + +of purification, which in every other form of biochemistry starts by + +saying, I'm going to purify something based on its distinctive + +properties, to I'm going to randomly purify everything. + +Everything would be purified in its own bacteria, and I've now converted + +to the problem of finding the one that I want in my + +library. Next time, we'll talk about how you go to the + +library and find what you want. + +See you then. \ No newline at end of file diff --git a/_bjy6AMn5aY.txt b/_bjy6AMn5aY.txt new file mode 100644 index 0000000000000000000000000000000000000000..24273f49f6ba0db5234a649e0d3cbfde2e37deaa --- /dev/null +++ b/_bjy6AMn5aY.txt @@ -0,0 +1,5163 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license + + align:start position:0% +a Creative Commons license + + + align:start position:0% +a Creative Commons license +your support will help MIT + + align:start position:0% +your support will help MIT + + + align:start position:0% +your support will help MIT +OpenCourseWare continue to offer high + + align:start position:0% +OpenCourseWare continue to offer high + + + align:start position:0% +OpenCourseWare continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +again some of this might be familiar to + + align:start position:0% +again some of this might be familiar to + + + align:start position:0% +again some of this might be familiar to +folks who have taken CMS 6:11 but but + + align:start position:0% +folks who have taken CMS 6:11 but but + + + align:start position:0% +folks who have taken CMS 6:11 but but +it's sort of revised this so that I can + + align:start position:0% +it's sort of revised this so that I can + + + align:start position:0% +it's sort of revised this so that I can +give you more board game examples and I + + align:start position:0% +give you more board game examples and I + + + align:start position:0% +give you more board game examples and I +just want to go a little bit on the kind + + align:start position:0% +just want to go a little bit on the kind + + + align:start position:0% +just want to go a little bit on the kind +of aesthetic thing that we're talking + + align:start position:0% +of aesthetic thing that we're talking + + + align:start position:0% +of aesthetic thing that we're talking +about in in assignment 2 but go more + + align:start position:0% +about in in assignment 2 but go more + + + align:start position:0% +about in in assignment 2 but go more +into things about a user experience over + + align:start position:0% +into things about a user experience over + + + align:start position:0% +into things about a user experience over +the next couple of weeks but so far + + align:start position:0% +the next couple of weeks but so far + + + align:start position:0% +the next couple of weeks but so far +we've been talking about this kind of + + align:start position:0% +we've been talking about this kind of + + + align:start position:0% +we've been talking about this kind of +aesthetic and came up in the MDA paper + + align:start position:0% +aesthetic and came up in the MDA paper + + + align:start position:0% +aesthetic and came up in the MDA paper +where we've been talking about mechanics + + align:start position:0% +where we've been talking about mechanics + + + align:start position:0% +where we've been talking about mechanics +we're talking about about strategies + + align:start position:0% +we're talking about about strategies + + + align:start position:0% +we're talking about about strategies +that come out from the dynamics of a + + align:start position:0% +that come out from the dynamics of a + + + align:start position:0% +that come out from the dynamics of a +game coming up the way how your rules + + align:start position:0% +game coming up the way how your rules + + + align:start position:0% +game coming up the way how your rules +play out to be able to give you a sense + + align:start position:0% +play out to be able to give you a sense + + + align:start position:0% +play out to be able to give you a sense +that some games are about subterfuge and + + align:start position:0% +that some games are about subterfuge and + + + align:start position:0% +that some games are about subterfuge and +some games are about pressing your luck + + align:start position:0% +some games are about pressing your luck + + + align:start position:0% +some games are about pressing your luck +there are some that there are some games + + align:start position:0% +there are some that there are some games + + + align:start position:0% +there are some that there are some games +about just dealing up dealing with + + align:start position:0% +about just dealing up dealing with + + + align:start position:0% +about just dealing up dealing with +random things that happen to you + + align:start position:0% +random things that happen to you + + + align:start position:0% +random things that happen to you +and some games about sort of dethroning + + align:start position:0% +and some games about sort of dethroning + + + align:start position:0% +and some games about sort of dethroning +the king right these are what a lot of + + align:start position:0% +the king right these are what a lot of + + + align:start position:0% +the king right these are what a lot of +your games have been about some games + + align:start position:0% +your games have been about some games + + + align:start position:0% +your games have been about some games +have been about feeling smart you know + + align:start position:0% +have been about feeling smart you know + + + align:start position:0% +have been about feeling smart you know +it's like when you make set it's like oh + + align:start position:0% +it's like when you make set it's like oh + + + align:start position:0% +it's like when you make set it's like oh +I feel really really smart about that + + align:start position:0% +I feel really really smart about that + + + align:start position:0% +I feel really really smart about that +and those come out from the designer + + align:start position:0% +and those come out from the designer + + + align:start position:0% +and those come out from the designer +from your rules that's what assignment + + align:start position:0% +from your rules that's what assignment + + + align:start position:0% +from your rules that's what assignment +was all about you you you you you've + + align:start position:0% +was all about you you you you you've + + + align:start position:0% +was all about you you you you you've +done a great job put that but of course + + align:start position:0% +done a great job put that but of course + + + align:start position:0% +done a great job put that but of course +that's not the only thing that there's + + align:start position:0% +that's not the only thing that there's + + + align:start position:0% +that's not the only thing that there's +involved in the aesthetic of the game + + align:start position:0% +involved in the aesthetic of the game + + + align:start position:0% +involved in the aesthetic of the game +we're talking about these things as well + + align:start position:0% +we're talking about these things as well + + + align:start position:0% +we're talking about these things as well +I already talked a little bit about game + + align:start position:0% +I already talked a little bit about game + + + align:start position:0% +I already talked a little bit about game +bits with the Donald Norman discussion + + align:start position:0% +bits with the Donald Norman discussion + + + align:start position:0% +bits with the Donald Norman discussion +but also things like the tone of the + + align:start position:0% +but also things like the tone of the + + + align:start position:0% +but also things like the tone of the +writing in your rules you know in this + + align:start position:0% +writing in your rules you know in this + + + align:start position:0% +writing in your rules you know in this +part in a Simon one it was fairly + + align:start position:0% +part in a Simon one it was fairly + + + align:start position:0% +part in a Simon one it was fairly +straightforward but you could imagine + + align:start position:0% +straightforward but you could imagine + + + align:start position:0% +straightforward but you could imagine +writing everything in ye olde English + + align:start position:0% +writing everything in ye olde English + + + align:start position:0% +writing everything in ye olde English +you know you know I think space alert + + align:start position:0% +you know you know I think space alert + + + align:start position:0% +you know you know I think space alert +has it's a game play the rules are + + align:start position:0% +has it's a game play the rules are + + + align:start position:0% +has it's a game play the rules are +written as if it was a cadet manual only + + align:start position:0% +written as if it was a cadet manual only + + + align:start position:0% +written as if it was a cadet manual only +a cadet manual that setting you up for + + align:start position:0% +a cadet manual that setting you up for + + + align:start position:0% +a cadet manual that setting you up for +mission for that is doomed to failure + + align:start position:0% +mission for that is doomed to failure + + + align:start position:0% +mission for that is doomed to failure +space affairs actually a really good + + align:start position:0% +space affairs actually a really good + + + align:start position:0% +space affairs actually a really good +example of sound as well and and and and + + align:start position:0% +example of sound as well and and and and + + + align:start position:0% +example of sound as well and and and and +I'll I'll play some tracks from it is a + + align:start position:0% +I'll I'll play some tracks from it is a + + + align:start position:0% +I'll I'll play some tracks from it is a +game that had the cut that has an + + align:start position:0% +game that had the cut that has an + + + align:start position:0% +game that had the cut that has an +accompanying CD but one of the games + + align:start position:0% +accompanying CD but one of the games + + + align:start position:0% +accompanying CD but one of the games +have really distinctive sounds like + + align:start position:0% +have really distinctive sounds like + + + align:start position:0% +have really distinctive sounds like +board games card games casino games like + + align:start position:0% +board games card games casino games like + + + align:start position:0% +board games card games casino games like +what what are some things that you know + + align:start position:0% +what what are some things that you know + + + align:start position:0% +what what are some things that you know +operation yeah yeah sorry because you + + align:start position:0% +operation yeah yeah sorry because you + + + align:start position:0% +operation yeah yeah sorry because you +say sorry taboo has a buzzer but also a + + align:start position:0% +say sorry taboo has a buzzer but also a + + + align:start position:0% +say sorry taboo has a buzzer but also a +lot of its dialogue game so there's also + + align:start position:0% +lot of its dialogue game so there's also + + + align:start position:0% +lot of its dialogue game so there's also +the accompanying sound around you know + + align:start position:0% +the accompanying sound around you know + + + align:start position:0% +the accompanying sound around you know +that's coming out of everybody's mouth + + align:start position:0% +that's coming out of everybody's mouth + + + align:start position:0% +that's coming out of everybody's mouth +jester's oh so it picks down so you can + + align:start position:0% +jester's oh so it picks down so you can + + + align:start position:0% +jester's oh so it picks down so you can +hear it running out of time jeopardy oh + + align:start position:0% +hear it running out of time jeopardy oh + + + align:start position:0% +hear it running out of time jeopardy oh +yeah yeah the little tinkle of the chips + + align:start position:0% +yeah yeah the little tinkle of the chips + + + align:start position:0% +yeah yeah the little tinkle of the chips +and slot machines of course yeah you + + align:start position:0% +and slot machines of course yeah you + + + align:start position:0% +and slot machines of course yeah you +know in that the all rather a whole Bank + + align:start position:0% +know in that the all rather a whole Bank + + + align:start position:0% +know in that the all rather a whole Bank +of slot machines you very rarely hear a + + align:start position:0% +of slot machines you very rarely hear a + + + align:start position:0% +of slot machines you very rarely hear a +single slot but machine operating by + + align:start position:0% +single slot but machine operating by + + + align:start position:0% +single slot but machine operating by +itself electronic stop machines + + align:start position:0% +itself electronic stop machines + + + align:start position:0% +itself electronic stop machines +obviously have a slightly different tone + + align:start position:0% +obviously have a slightly different tone + + + align:start position:0% +obviously have a slightly different tone +to to it than mechanical style machines + + align:start position:0% +to to it than mechanical style machines + + + align:start position:0% +to to it than mechanical style machines +roulette I find this very very + + align:start position:0% +roulette I find this very very + + + align:start position:0% +roulette I find this very very +distinctive sound of just the little + + align:start position:0% +distinctive sound of just the little + + + align:start position:0% +distinctive sound of just the little +ball bouncing all over the bumps so so + + align:start position:0% +ball bouncing all over the bumps so so + + + align:start position:0% +ball bouncing all over the bumps so so +definitely think a little bit about that + + align:start position:0% +definitely think a little bit about that + + + align:start position:0% +definitely think a little bit about that +you know the about the sound of your + + align:start position:0% +you know the about the sound of your + + + align:start position:0% +you know the about the sound of your +game especially if I'm making a game + + align:start position:0% +game especially if I'm making a game + + + align:start position:0% +game especially if I'm making a game +that it's about conversation or about + + align:start position:0% +that it's about conversation or about + + + align:start position:0% +that it's about conversation or about +over the table exchange + + align:start position:0% +over the table exchange + + + align:start position:0% +over the table exchange +taboo is a game that is punctuated with + + align:start position:0% +taboo is a game that is punctuated with + + + align:start position:0% +taboo is a game that is punctuated with +you know whereas something like charades + + align:start position:0% +you know whereas something like charades + + + align:start position:0% +you know whereas something like charades +the sound of that is a lot of shouting + + align:start position:0% +the sound of that is a lot of shouting + + + align:start position:0% +the sound of that is a lot of shouting +usually right you know if I everyone + + align:start position:0% +usually right you know if I everyone + + + align:start position:0% +usually right you know if I everyone +just like saying random things the first + + align:start position:0% +just like saying random things the first + + + align:start position:0% +just like saying random things the first +thing that comes to their mind is it's + + align:start position:0% +thing that comes to their mind is it's + + + align:start position:0% +thing that comes to their mind is it's +almost a free association game and of + + align:start position:0% +almost a free association game and of + + + align:start position:0% +almost a free association game and of +course the look of your game I mean that + + align:start position:0% +course the look of your game I mean that + + + align:start position:0% +course the look of your game I mean that +that should be taken for granted right + + align:start position:0% +that should be taken for granted right + + + align:start position:0% +that should be taken for granted right +and we've got a couple of examples of + + align:start position:0% +and we've got a couple of examples of + + + align:start position:0% +and we've got a couple of examples of +various bond slits that you can take a + + align:start position:0% +various bond slits that you can take a + + + align:start position:0% +various bond slits that you can take a +look at and of course that's what people + + align:start position:0% +look at and of course that's what people + + + align:start position:0% +look at and of course that's what people +normally associate with storytelling in + + align:start position:0% +normally associate with storytelling in + + + align:start position:0% +normally associate with storytelling in +games but could also be thought of as + + align:start position:0% +games but could also be thought of as + + + align:start position:0% +games but could also be thought of as +world building in games what's the theme + + align:start position:0% +world building in games what's the theme + + + align:start position:0% +world building in games what's the theme +of your game what's the plot and a + + align:start position:0% +of your game what's the plot and a + + + align:start position:0% +of your game what's the plot and a +character to be game are you making the + + align:start position:0% +character to be game are you making the + + + align:start position:0% +character to be game are you making the +you know instead of the Trivial Pursuit + + align:start position:0% +you know instead of the Trivial Pursuit + + + align:start position:0% +you know instead of the Trivial Pursuit +gave the Twilight Trivial Pursuit game + + align:start position:0% +gave the Twilight Trivial Pursuit game + + + align:start position:0% +gave the Twilight Trivial Pursuit game +or something like that and you've got a + + align:start position:0% +or something like that and you've got a + + + align:start position:0% +or something like that and you've got a +setting you've got characters even + + align:start position:0% +setting you've got characters even + + + align:start position:0% +setting you've got characters even +though the game mechanics all the same + + align:start position:0% +though the game mechanics all the same + + + align:start position:0% +though the game mechanics all the same +but there are games that integrate that + + align:start position:0% +but there are games that integrate that + + + align:start position:0% +but there are games that integrate that +better with game mechanics and and rules + + align:start position:0% +better with game mechanics and and rules + + + align:start position:0% +better with game mechanics and and rules +in your art direction that games that do + + align:start position:0% +in your art direction that games that do + + + align:start position:0% +in your art direction that games that do +a poor job because some examples of that + + align:start position:0% +a poor job because some examples of that + + + align:start position:0% +a poor job because some examples of that +so let me see let me talk about a few of + + align:start position:0% +so let me see let me talk about a few of + + + align:start position:0% +so let me see let me talk about a few of +these games come on you played Forbidden + + align:start position:0% +these games come on you played Forbidden + + + align:start position:0% +these games come on you played Forbidden +Island how might you play pandemic + + align:start position:0% +Island how might you play pandemic + + + align:start position:0% +Island how might you play pandemic +okay so forbidden I did this kind of by + + align:start position:0% +okay so forbidden I did this kind of by + + + align:start position:0% +okay so forbidden I did this kind of by +the same designer I still has that a lot + + align:start position:0% +the same designer I still has that a lot + + + align:start position:0% +the same designer I still has that a lot +of the same cooperative feel and if you + + align:start position:0% +of the same cooperative feel and if you + + + align:start position:0% +of the same cooperative feel and if you +you know first of all you have this + + align:start position:0% +you know first of all you have this + + + align:start position:0% +you know first of all you have this +metal tin that sort of make you think + + align:start position:0% +metal tin that sort of make you think + + + align:start position:0% +metal tin that sort of make you think +that this game is worth more + + align:start position:0% +that this game is worth more + + + align:start position:0% +that this game is worth more +and usually paying more for it but you + + align:start position:0% +and usually paying more for it but you + + + align:start position:0% +and usually paying more for it but you +know you've got this like nice little + + align:start position:0% +know you've got this like nice little + + + align:start position:0% +know you've got this like nice little +art that sort of it that that and + + align:start position:0% +art that sort of it that that and + + + align:start position:0% +art that sort of it that that and +because you have to open up this metal + + align:start position:0% +because you have to open up this metal + + + align:start position:0% +because you have to open up this metal +tin makes you think a little bit about + + align:start position:0% +tin makes you think a little bit about + + + align:start position:0% +tin makes you think a little bit about +you know opening up a treasure chest + + align:start position:0% +you know opening up a treasure chest + + + align:start position:0% +you know opening up a treasure chest +inside you've actually got these nice + + align:start position:0% +inside you've actually got these nice + + + align:start position:0% +inside you've actually got these nice +little treasure pieces a goblet this + + align:start position:0% +little treasure pieces a goblet this + + + align:start position:0% +little treasure pieces a goblet this +kind of like translucent crystal yeah + + align:start position:0% +kind of like translucent crystal yeah + + + align:start position:0% +kind of like translucent crystal yeah +they're all plastic kind of rubberized + + align:start position:0% +they're all plastic kind of rubberized + + + align:start position:0% +they're all plastic kind of rubberized +plastic so that they'll last a little + + align:start position:0% +plastic so that they'll last a little + + + align:start position:0% +plastic so that they'll last a little +bit longer but you know you can sort of + + align:start position:0% +bit longer but you know you can sort of + + + align:start position:0% +bit longer but you know you can sort of +see that this is got chair rule lion I + + align:start position:0% +see that this is got chair rule lion I + + + align:start position:0% +see that this is got chair rule lion I +don't know a Griffin or something you + + align:start position:0% +don't know a Griffin or something you + + + align:start position:0% +don't know a Griffin or something you +know it's got time off my old world + + align:start position:0% +know it's got time off my old world + + + align:start position:0% +know it's got time off my old world +here's some sort of mystic civilization + + align:start position:0% +here's some sort of mystic civilization + + + align:start position:0% +here's some sort of mystic civilization +and when you look at the cards you know + + align:start position:0% +and when you look at the cards you know + + + align:start position:0% +and when you look at the cards you know +you've got the choice of the fonts + + align:start position:0% +you've got the choice of the fonts + + + align:start position:0% +you've got the choice of the fonts +you've got these kinds of light very + + align:start position:0% +you've got these kinds of light very + + + align:start position:0% +you've got these kinds of light very +serif and a little bit like broken up + + align:start position:0% +serif and a little bit like broken up + + + align:start position:0% +serif and a little bit like broken up +text that looks like it might be all all + + align:start position:0% +text that looks like it might be all all + + + align:start position:0% +text that looks like it might be all all +kind of letterpress and of course all + + align:start position:0% +kind of letterpress and of course all + + + align:start position:0% +kind of letterpress and of course all +the art gets on every single card the + + align:start position:0% +the art gets on every single card the + + + align:start position:0% +the art gets on every single card the +game mechanics of this game are about + + align:start position:0% +game mechanics of this game are about + + + align:start position:0% +game mechanics of this game are about +various parts of an island turning into + + align:start position:0% +various parts of an island turning into + + + align:start position:0% +various parts of an island turning into +water and they don't actually have + + align:start position:0% +water and they don't actually have + + + align:start position:0% +water and they don't actually have +different illustrations when they get + + align:start position:0% +different illustrations when they get + + + align:start position:0% +different illustrations when they get +flooded they just have the state picture + + align:start position:0% +flooded they just have the state picture + + + align:start position:0% +flooded they just have the state picture +only in bluish so you know it's cheap to + + align:start position:0% +only in bluish so you know it's cheap to + + + align:start position:0% +only in bluish so you know it's cheap to +create this right because it's + + align:start position:0% +create this right because it's + + + align:start position:0% +create this right because it's +monochromatic I guess that I guess it's + + align:start position:0% +monochromatic I guess that I guess it's + + + align:start position:0% +monochromatic I guess that I guess it's +not really monochromatic because they + + align:start position:0% +not really monochromatic because they + + + align:start position:0% +not really monochromatic because they +have a color token at the bottom but it + + align:start position:0% +have a color token at the bottom but it + + + align:start position:0% +have a color token at the bottom but it +sort of gives you the idea that when you + + align:start position:0% +sort of gives you the idea that when you + + + align:start position:0% +sort of gives you the idea that when you +play this game everything kind of looks + + align:start position:0% +play this game everything kind of looks + + + align:start position:0% +play this game everything kind of looks +nice and colorful and then as the game + + align:start position:0% +nice and colorful and then as the game + + + align:start position:0% +nice and colorful and then as the game +goes on things are turning bluer and + + align:start position:0% +goes on things are turning bluer and + + + align:start position:0% +goes on things are turning bluer and +bluer so just give you the sense that + + align:start position:0% +bluer so just give you the sense that + + + align:start position:0% +bluer so just give you the sense that +there's more and more water surrounding + + align:start position:0% +there's more and more water surrounding + + + align:start position:0% +there's more and more water surrounding +this island as it keeps flooding and you + + align:start position:0% +this island as it keeps flooding and you + + + align:start position:0% +this island as it keeps flooding and you +know all these pieces which represents + + align:start position:0% +know all these pieces which represents + + + align:start position:0% +know all these pieces which represents +each one is different players talking + + align:start position:0% +each one is different players talking + + + align:start position:0% +each one is different players talking +could you know doesn't necessarily need + + align:start position:0% +could you know doesn't necessarily need + + + align:start position:0% +could you know doesn't necessarily need +to be shaped human but it kind of like + + align:start position:0% +to be shaped human but it kind of like + + + align:start position:0% +to be shaped human but it kind of like +makes you think that there is a human + + align:start position:0% +makes you think that there is a human + + + align:start position:0% +makes you think that there is a human +head and there's a piece it's all this + + align:start position:0% +head and there's a piece it's all this + + + align:start position:0% +head and there's a piece it's all this +adds cost to the to the production of + + align:start position:0% +adds cost to the to the production of + + + align:start position:0% +adds cost to the to the production of +this across the metal tea and also I had + + align:start position:0% +this across the metal tea and also I had + + + align:start position:0% +this across the metal tea and also I had +a cost to the production of a game like + + align:start position:0% +a cost to the production of a game like + + + align:start position:0% +a cost to the production of a game like +this but it goes a long way to making + + align:start position:0% +this but it goes a long way to making + + + align:start position:0% +this but it goes a long way to making +you feel like I'm not just moving pieces + + align:start position:0% +you feel like I'm not just moving pieces + + + align:start position:0% +you feel like I'm not just moving pieces +on a board and I'm actually exploring an + + align:start position:0% +on a board and I'm actually exploring an + + + align:start position:0% +on a board and I'm actually exploring an +island in and robbing it of his + + align:start position:0% +island in and robbing it of his + + + align:start position:0% +island in and robbing it of his +treasures but it's you know but it's + + align:start position:0% +treasures but it's you know but it's + + + align:start position:0% +treasures but it's you know but it's +trying to get us this is actually a + + align:start position:0% +trying to get us this is actually a + + + align:start position:0% +trying to get us this is actually a +counter of a kind of like that + + align:start position:0% +counter of a kind of like that + + + align:start position:0% +counter of a kind of like that +the flood levels and if they got game + + align:start position:0% +the flood levels and if they got game + + + align:start position:0% +the flood levels and if they got game +mechanic stuff these lobbyists normal + + align:start position:0% +mechanic stuff these lobbyists normal + + + align:start position:0% +mechanic stuff these lobbyists normal +elite and legendary so instead of sets + + align:start position:0% +elite and legendary so instead of sets + + + align:start position:0% +elite and legendary so instead of sets +you are with a difficulty level when the + + align:start position:0% +you are with a difficulty level when the + + + align:start position:0% +you are with a difficulty level when the +game starts but you know you have a + + align:start position:0% +game starts but you know you have a + + + align:start position:0% +game starts but you know you have a +water level that goes from bottom to top + + align:start position:0% +water level that goes from bottom to top + + + align:start position:0% +water level that goes from bottom to top +as opposed to top to bottom you can + + align:start position:0% +as opposed to top to bottom you can + + + align:start position:0% +as opposed to top to bottom you can +imagine this counter working just as + + align:start position:0% +imagine this counter working just as + + + align:start position:0% +imagine this counter working just as +well going downwards or upwards but + + align:start position:0% +well going downwards or upwards but + + + align:start position:0% +well going downwards or upwards but +since it's about flooding it goes from + + align:start position:0% +since it's about flooding it goes from + + + align:start position:0% +since it's about flooding it goes from +bottom and then the water level rises + + align:start position:0% +bottom and then the water level rises + + + align:start position:0% +bottom and then the water level rises +and Rises and Rises and of course on top + + align:start position:0% +and Rises and Rises and of course on top + + + align:start position:0% +and Rises and Rises and of course on top +they have a skull right no it's like + + align:start position:0% +they have a skull right no it's like + + + align:start position:0% +they have a skull right no it's like +it's not just that the game ends it's + + align:start position:0% +it's not just that the game ends it's + + + align:start position:0% +it's not just that the game ends it's +the game ends and everyone dies because + + align:start position:0% +the game ends and everyone dies because + + + align:start position:0% +the game ends and everyone dies because +let's just be clear about that so it + + align:start position:0% +let's just be clear about that so it + + + align:start position:0% +let's just be clear about that so it +doesn't nice a nice job of getting off + + align:start position:0% +doesn't nice a nice job of getting off + + + align:start position:0% +doesn't nice a nice job of getting off +getting that across it's actually a + + align:start position:0% +getting that across it's actually a + + + align:start position:0% +getting that across it's actually a +cooperative game and does a pretty good + + align:start position:0% +cooperative game and does a pretty good + + + align:start position:0% +cooperative game and does a pretty good +job of sort of taking all of these ideas + + align:start position:0% +job of sort of taking all of these ideas + + + align:start position:0% +job of sort of taking all of these ideas +the setting of the of the waterlogged + + align:start position:0% +the setting of the of the waterlogged + + + align:start position:0% +the setting of the of the waterlogged +island the art direction of what happens + + align:start position:0% +island the art direction of what happens + + + align:start position:0% +island the art direction of what happens +to the pieces as you flip them over and + + align:start position:0% +to the pieces as you flip them over and + + + align:start position:0% +to the pieces as you flip them over and +then across the rules that determine + + align:start position:0% +then across the rules that determine + + + align:start position:0% +then across the rules that determine +when the water level rises and how much + + align:start position:0% +when the water level rises and how much + + + align:start position:0% +when the water level rises and how much +space you've got to now begin and how + + align:start position:0% +space you've got to now begin and how + + + align:start position:0% +space you've got to now begin and how +you deal with those problems I like to + + align:start position:0% +you deal with those problems I like to + + + align:start position:0% +you deal with those problems I like to +describe all of the stuff that we've + + align:start position:0% +describe all of the stuff that we've + + + align:start position:0% +describe all of the stuff that we've +been talking so far as systemic + + align:start position:0% +been talking so far as systemic + + + align:start position:0% +been talking so far as systemic +aesthetics so these are the as statics + + align:start position:0% +aesthetics so these are the as statics + + + align:start position:0% +aesthetics so these are the as statics +that the system is creating all the + + align:start position:0% +that the system is creating all the + + + align:start position:0% +that the system is creating all the +things that would then have to do with + + align:start position:0% +things that would then have to do with + + + align:start position:0% +things that would then have to do with +art style writing tone the sound the + + align:start position:0% +art style writing tone the sound the + + + align:start position:0% +art style writing tone the sound the +pieces that you're holding walrus + + align:start position:0% +pieces that you're holding walrus + + + align:start position:0% +pieces that you're holding walrus +stylistic aesthetics and then there's + + align:start position:0% +stylistic aesthetics and then there's + + + align:start position:0% +stylistic aesthetics and then there's +the fiction the fictional me the story + + align:start position:0% +the fiction the fictional me the story + + + align:start position:0% +the fiction the fictional me the story +will be the characters will be the + + align:start position:0% +will be the characters will be the + + + align:start position:0% +will be the characters will be the +setting of the game but because this is + + align:start position:0% +setting of the game but because this is + + + align:start position:0% +setting of the game but because this is +kind of a blurry Venn diagram because + + align:start position:0% +kind of a blurry Venn diagram because + + + align:start position:0% +kind of a blurry Venn diagram because +there's a lot of things that come in + + align:start position:0% +there's a lot of things that come in + + + align:start position:0% +there's a lot of things that come in +between so for instance the way how your + + align:start position:0% +between so for instance the way how your + + + align:start position:0% +between so for instance the way how your +board looks is it's obviously a + + align:start position:0% +board looks is it's obviously a + + + align:start position:0% +board looks is it's obviously a +combination of the mechanics that + + align:start position:0% +combination of the mechanics that + + + align:start position:0% +combination of the mechanics that +specify the information that you need to + + align:start position:0% +specify the information that you need to + + + align:start position:0% +specify the information that you need to +be able to put on the board but also the + + align:start position:0% +be able to put on the board but also the + + + align:start position:0% +be able to put on the board but also the +style of how you display that + + align:start position:0% +style of how you display that + + + align:start position:0% +style of how you display that +information and how that's all + + align:start position:0% +information and how that's all + + + align:start position:0% +information and how that's all +reinforces the the setting that you want + + align:start position:0% +reinforces the the setting that you want + + + align:start position:0% +reinforces the the setting that you want +you're used to + + align:start position:0% +you're used to + + + align:start position:0% +you're used to +to be in the kind of feedback that you + + align:start position:0% +to be in the kind of feedback that you + + + align:start position:0% +to be in the kind of feedback that you +give people like the taboo buzz for + + align:start position:0% +give people like the taboo buzz for + + + align:start position:0% +give people like the taboo buzz for +instance you know the sound of that buzz + + align:start position:0% +instance you know the sound of that buzz + + + align:start position:0% +instance you know the sound of that buzz +is isn't here + + align:start position:0% +is isn't here + + + align:start position:0% +is isn't here +but obviously the rules are set up so + + align:start position:0% +but obviously the rules are set up so + + + align:start position:0% +but obviously the rules are set up so +that it's + + align:start position:0% +that it's + + + align:start position:0% +that it's +you know the more when you hear that + + align:start position:0% +you know the more when you hear that + + + align:start position:0% +you know the more when you hear that +buzz is kind of like as jarring and + + align:start position:0% +buzz is kind of like as jarring and + + + align:start position:0% +buzz is kind of like as jarring and +nerve-wracking as possible right because + + align:start position:0% +nerve-wracking as possible right because + + + align:start position:0% +nerve-wracking as possible right because +they're trying to concentrate + + align:start position:0% +they're trying to concentrate + + + align:start position:0% +they're trying to concentrate +I'm not saying the right the the wrong + + align:start position:0% +I'm not saying the right the the wrong + + + align:start position:0% +I'm not saying the right the the wrong +thing and then when you moment you you + + align:start position:0% +thing and then when you moment you you + + + align:start position:0% +thing and then when you moment you you +you you use slip up another player will + + align:start position:0% +you you use slip up another player will + + + align:start position:0% +you you use slip up another player will +buzz it and you know you get a shock of + + align:start position:0% +buzz it and you know you get a shock of + + + align:start position:0% +buzz it and you know you get a shock of +your life + + align:start position:0% +your life + + + align:start position:0% +your life +that's all attentional for our direction + + align:start position:0% +that's all attentional for our direction + + + align:start position:0% +that's all attentional for our direction +and for style and fiction those tend to + + align:start position:0% +and for style and fiction those tend to + + + align:start position:0% +and for style and fiction those tend to +be things that look that the people are + + align:start position:0% +be things that look that the people are + + + align:start position:0% +be things that look that the people are +less trouble thinking about how how + + align:start position:0% +less trouble thinking about how how + + + align:start position:0% +less trouble thinking about how how +realistic do you want your studying to + + align:start position:0% +realistic do you want your studying to + + + align:start position:0% +realistic do you want your studying to +be this is a game called king of Tokyo + + align:start position:0% +be this is a game called king of Tokyo + + + align:start position:0% +be this is a game called king of Tokyo +which is really my Mac mechanically it's + + align:start position:0% +which is really my Mac mechanically it's + + + align:start position:0% +which is really my Mac mechanically it's +every one going up on the leader and + + align:start position:0% +every one going up on the leader and + + + align:start position:0% +every one going up on the leader and +there's you know this is this is a game + + align:start position:0% +there's you know this is this is a game + + + align:start position:0% +there's you know this is this is a game +where if you're trying to be a monster + + align:start position:0% +where if you're trying to be a monster + + + align:start position:0% +where if you're trying to be a monster +taking over Tokyo and there's a lot of + + align:start position:0% +taking over Tokyo and there's a lot of + + + align:start position:0% +taking over Tokyo and there's a lot of +other monsters who want your spot and + + align:start position:0% +other monsters who want your spot and + + + align:start position:0% +other monsters who want your spot and +once you are on top of that mountain + + align:start position:0% +once you are on top of that mountain + + + align:start position:0% +once you are on top of that mountain +everyone's trying to take you down + + align:start position:0% +everyone's trying to take you down + + + align:start position:0% +everyone's trying to take you down +that's what this game is about but you + + align:start position:0% +that's what this game is about but you + + + align:start position:0% +that's what this game is about but you +can see it's kind of got this goofy not + + align:start position:0% +can see it's kind of got this goofy not + + + align:start position:0% +can see it's kind of got this goofy not +quite anime style you know but slowly + + align:start position:0% +quite anime style you know but slowly + + + align:start position:0% +quite anime style you know but slowly +pocketed four whole Japanese movies + + align:start position:0% +pocketed four whole Japanese movies + + + align:start position:0% +pocketed four whole Japanese movies +we've got a little picture of Tokyo be + + align:start position:0% +we've got a little picture of Tokyo be + + + align:start position:0% +we've got a little picture of Tokyo be +on fire here you can actually see the + + align:start position:0% +on fire here you can actually see the + + + align:start position:0% +on fire here you can actually see the +monsters and you just see a lot of like + + align:start position:0% +monsters and you just see a lot of like + + + align:start position:0% +monsters and you just see a lot of like +how they coughing this is all c2 + + align:start position:0% +how they coughing this is all c2 + + + align:start position:0% +how they coughing this is all c2 +collateral damage anyway but I believe + + align:start position:0% +collateral damage anyway but I believe + + + align:start position:0% +collateral damage anyway but I believe +this but mostly a dice rolling game + + align:start position:0% +this but mostly a dice rolling game + + + align:start position:0% +this but mostly a dice rolling game +yes Yahtzee so so the mechanics are all + + align:start position:0% +yes Yahtzee so so the mechanics are all + + + align:start position:0% +yes Yahtzee so so the mechanics are all +about you know you roll the dice a and + + align:start position:0% +about you know you roll the dice a and + + + align:start position:0% +about you know you roll the dice a and +and and and you try to roll well so so + + align:start position:0% +and and and you try to roll well so so + + + align:start position:0% +and and and you try to roll well so so +they put in a lot of effort to try to + + align:start position:0% +they put in a lot of effort to try to + + + align:start position:0% +they put in a lot of effort to try to +paint that mechanic in stylistic and in + + align:start position:0% +paint that mechanic in stylistic and in + + + align:start position:0% +paint that mechanic in stylistic and in +fictional elements to make it a little + + align:start position:0% +fictional elements to make it a little + + + align:start position:0% +fictional elements to make it a little +bit more engaging and frankly a lot more + + align:start position:0% +bit more engaging and frankly a lot more + + + align:start position:0% +bit more engaging and frankly a lot more +saleable this is Bridgette carpet yeah + + align:start position:0% +saleable this is Bridgette carpet yeah + + + align:start position:0% +saleable this is Bridgette carpet yeah +this is Richard Garfield who is also the + + align:start position:0% +this is Richard Garfield who is also the + + + align:start position:0% +this is Richard Garfield who is also the +designer of Magic the Gathering the + + align:start position:0% +designer of Magic the Gathering the + + + align:start position:0% +designer of Magic the Gathering the +original designer metric gathering so + + align:start position:0% +original designer metric gathering so + + + align:start position:0% +original designer metric gathering so +it's got a good palette with good + + align:start position:0% +it's got a good palette with good + + + align:start position:0% +it's got a good palette with good +pedigree in between the systemic and the + + align:start position:0% +pedigree in between the systemic and the + + + align:start position:0% +pedigree in between the systemic and the +fictional elements you can do things + + align:start position:0% +fictional elements you can do things + + + align:start position:0% +fictional elements you can do things +like events planets struggle another + + align:start position:0% +like events planets struggle another + + + align:start position:0% +like events planets struggle another +excellent game is about the Cold War + + align:start position:0% +excellent game is about the Cold War + + + align:start position:0% +excellent game is about the Cold War +basically and you've got cards in here + + align:start position:0% +basically and you've got cards in here + + + align:start position:0% +basically and you've got cards in here +that remind people of real things that + + align:start position:0% +that remind people of real things that + + + align:start position:0% +that remind people of real things that +actually + + align:start position:0% +actually + + + align:start position:0% +actually +happened they don't necessarily happen + + align:start position:0% +happened they don't necessarily happen + + + align:start position:0% +happened they don't necessarily happen +in the order that that that day that it + + align:start position:0% +in the order that that that day that it + + + align:start position:0% +in the order that that that day that it +happened in real life + + align:start position:0% +happened in real life + + + align:start position:0% +happened in real life +there is there are things like the space + + align:start position:0% +there is there are things like the space + + + align:start position:0% +there is there are things like the space +race as things like various presidents + + align:start position:0% +race as things like various presidents + + + align:start position:0% +race as things like various presidents +and various will various Soviet and US + + align:start position:0% +and various will various Soviet and US + + + align:start position:0% +and various will various Soviet and US +leaders from from from the Cold War this + + align:start position:0% +leaders from from from the Cold War this + + + align:start position:0% +leaders from from from the Cold War this +one specifically since 1945 to 1989 and + + align:start position:0% +one specifically since 1945 to 1989 and + + + align:start position:0% +one specifically since 1945 to 1989 and +so while we are playing this game yeah + + align:start position:0% +so while we are playing this game yeah + + + align:start position:0% +so while we are playing this game yeah +there are mechanical results for all + + align:start position:0% +there are mechanical results for all + + + align:start position:0% +there are mechanical results for all +those cars that you are flipping over + + align:start position:0% +those cars that you are flipping over + + + align:start position:0% +those cars that you are flipping over +but because they also have pictures and + + align:start position:0% +but because they also have pictures and + + + align:start position:0% +but because they also have pictures and +names of the actual events that + + align:start position:0% +names of the actual events that + + + align:start position:0% +names of the actual events that +hopefully you know this is this is + + align:start position:0% +hopefully you know this is this is + + + align:start position:0% +hopefully you know this is this is +largely targeted at people who have + + align:start position:0% +largely targeted at people who have + + + align:start position:0% +largely targeted at people who have +lived through this Europe or at least + + align:start position:0% +lived through this Europe or at least + + + align:start position:0% +lived through this Europe or at least +remember things that are occurring from + + align:start position:0% +remember things that are occurring from + + + align:start position:0% +remember things that are occurring from +the era and and is trying to be + + align:start position:0% +the era and and is trying to be + + + align:start position:0% +the era and and is trying to be +evocative of that whereas you know it's + + align:start position:0% +evocative of that whereas you know it's + + + align:start position:0% +evocative of that whereas you know it's +a fairly my chemical I guess is you it's + + align:start position:0% +a fairly my chemical I guess is you it's + + + align:start position:0% +a fairly my chemical I guess is you it's +not quite a war game it's more like a + + align:start position:0% +not quite a war game it's more like a + + + align:start position:0% +not quite a war game it's more like a +political scheme that's apology but the + + align:start position:0% +political scheme that's apology but the + + + align:start position:0% +political scheme that's apology but the +use events to sort of remind you of what + + align:start position:0% +use events to sort of remind you of what + + + align:start position:0% +use events to sort of remind you of what +the setting of this game is you know I + + align:start position:0% +the setting of this game is you know I + + + align:start position:0% +the setting of this game is you know I +call it fiction but of course this is + + align:start position:0% +call it fiction but of course this is + + + align:start position:0% +call it fiction but of course this is +not fiction this is based on what + + align:start position:0% +not fiction this is based on what + + + align:start position:0% +not fiction this is based on what +actually happened it's still a setting + + align:start position:0% +actually happened it's still a setting + + + align:start position:0% +actually happened it's still a setting +right roles and abilities back to back + + align:start position:0% +right roles and abilities back to back + + + align:start position:0% +right roles and abilities back to back +to Forbidden Island every single + + align:start position:0% +to Forbidden Island every single + + + align:start position:0% +to Forbidden Island every single +character that you play in Forbidden + + align:start position:0% +character that you play in Forbidden + + + align:start position:0% +character that you play in Forbidden +Island has a different set of abilities + + align:start position:0% +Island has a different set of abilities + + + align:start position:0% +Island has a different set of abilities +but you've got your taking on a + + align:start position:0% +but you've got your taking on a + + + align:start position:0% +but you've got your taking on a +different role like an explorer or a + + align:start position:0% +different role like an explorer or a + + + align:start position:0% +different role like an explorer or a +diver like remember what all the roles + + align:start position:0% +diver like remember what all the roles + + + align:start position:0% +diver like remember what all the roles +are yeah there's no indication on the + + align:start position:0% +are yeah there's no indication on the + + + align:start position:0% +are yeah there's no indication on the +Box on on on what you can be but every + + align:start position:0% +Box on on on what you can be but every + + + align:start position:0% +Box on on on what you can be but every +says everybody has different abilities + + align:start position:0% +says everybody has different abilities + + + align:start position:0% +says everybody has different abilities +that sort of reminder that sort of + + align:start position:0% +that sort of reminder that sort of + + + align:start position:0% +that sort of reminder that sort of +harkens back to you know what are the + + align:start position:0% +harkens back to you know what are the + + + align:start position:0% +harkens back to you know what are the +unique defining things of the character + + align:start position:0% +unique defining things of the character + + + align:start position:0% +unique defining things of the character +that you're playing and you try to think + + align:start position:0% +that you're playing and you try to think + + + align:start position:0% +that you're playing and you try to think +of you trying to think in that role if + + align:start position:0% +of you trying to think in that role if + + + align:start position:0% +of you trying to think in that role if +you are a pilot or something like that + + align:start position:0% +you are a pilot or something like that + + + align:start position:0% +you are a pilot or something like that +you try to think about rescuing people + + align:start position:0% +you try to think about rescuing people + + + align:start position:0% +you try to think about rescuing people +if a diver you're sort of trying to like + + align:start position:0% +if a diver you're sort of trying to like + + + align:start position:0% +if a diver you're sort of trying to like +forge ahead and going and and + + align:start position:0% +forge ahead and going and and + + + align:start position:0% +forge ahead and going and and +and you can stay close to the water + + align:start position:0% +and you can stay close to the water + + + align:start position:0% +and you can stay close to the water +mechanically but also you know puts you + + align:start position:0% +mechanically but also you know puts you + + + align:start position:0% +mechanically but also you know puts you +in a fictional position in your team to + + align:start position:0% +in a fictional position in your team to + + + align:start position:0% +in a fictional position in your team to +be able to be closer to risk because you + + align:start position:0% +be able to be closer to risk because you + + + align:start position:0% +be able to be closer to risk because you +know other people will just drown if + + align:start position:0% +know other people will just drown if + + + align:start position:0% +know other people will just drown if +they're too close to water + + align:start position:0% +they're too close to water + + + align:start position:0% +they're too close to water +I think that's held that that's how the + + align:start position:0% +I think that's held that that's how the + + + align:start position:0% +I think that's held that that's how the +game was if I recall + + align:start position:0% +game was if I recall + + + align:start position:0% +game was if I recall +so for assignment two we want you to be + + align:start position:0% +so for assignment two we want you to be + + + align:start position:0% +so for assignment two we want you to be +thinking about all of these things + + align:start position:0% +thinking about all of these things + + + align:start position:0% +thinking about all of these things +try obviously it's difficult to do this + + align:start position:0% +try obviously it's difficult to do this + + + align:start position:0% +try obviously it's difficult to do this +on the amount of time and the budget + + align:start position:0% +on the amount of time and the budget + + + align:start position:0% +on the amount of time and the budget +that you're working with but we want you + + align:start position:0% +that you're working with but we want you + + + align:start position:0% +that you're working with but we want you +to consider how your game looks how your + + align:start position:0% +to consider how your game looks how your + + + align:start position:0% +to consider how your game looks how your +game sounds how what is the setting that + + align:start position:0% +game sounds how what is the setting that + + + align:start position:0% +game sounds how what is the setting that +your game is in we we've already had a + + align:start position:0% +your game is in we we've already had a + + + align:start position:0% +your game is in we we've already had a +couple of things like like the spice + + align:start position:0% +couple of things like like the spice + + + align:start position:0% +couple of things like like the spice +game for instance now could just have + + align:start position:0% +game for instance now could just have + + + align:start position:0% +game for instance now could just have +been an information a game about sort of + + align:start position:0% +been an information a game about sort of + + + align:start position:0% +been an information a game about sort of +hidden variables but then you kind of + + align:start position:0% +hidden variables but then you kind of + + + align:start position:0% +hidden variables but then you kind of +have this layer of being a agent of an + + align:start position:0% +have this layer of being a agent of an + + + align:start position:0% +have this layer of being a agent of an +unknown country and sometimes the + + align:start position:0% +unknown country and sometimes the + + + align:start position:0% +unknown country and sometimes the +fiction can actually help people better + + align:start position:0% +fiction can actually help people better + + + align:start position:0% +fiction can actually help people better +understand underlying rules that you've + + align:start position:0% +understand underlying rules that you've + + + align:start position:0% +understand underlying rules that you've +got I know that this this game does + + align:start position:0% +got I know that this this game does + + + align:start position:0% +got I know that this this game does +limit the level game started off as a + + align:start position:0% +limit the level game started off as a + + + align:start position:0% +limit the level game started off as a +building construction game right so so + + align:start position:0% +building construction game right so so + + + align:start position:0% +building construction game right so so +and to a certain extent some version of + + align:start position:0% +and to a certain extent some version of + + + align:start position:0% +and to a certain extent some version of +those rules + + align:start position:0% +those rules + + + align:start position:0% +those rules +I might actually help people understand + + align:start position:0% +I might actually help people understand + + + align:start position:0% +I might actually help people understand +your rules + + align:start position:0% +your rules + + + align:start position:0% +your rules +easier but I know cause sometimes it + + align:start position:0% +easier but I know cause sometimes it + + + align:start position:0% +easier but I know cause sometimes it +gets in a way because your fiction may + + align:start position:0% +gets in a way because your fiction may + + + align:start position:0% +gets in a way because your fiction may +not necessarily match up with your with + + align:start position:0% +not necessarily match up with your with + + + align:start position:0% +not necessarily match up with your with +the way that your rules are evolving I + + align:start position:0% +the way that your rules are evolving I + + + align:start position:0% +the way that your rules are evolving I +just thought I'm not saying that you + + align:start position:0% +just thought I'm not saying that you + + + align:start position:0% +just thought I'm not saying that you +should let aesthetics necessarily + + align:start position:0% +should let aesthetics necessarily + + + align:start position:0% +should let aesthetics necessarily +constrain what you can do it rules but + + align:start position:0% +constrain what you can do it rules but + + + align:start position:0% +constrain what you can do it rules but +if you're going to change your rules and + + align:start position:0% +if you're going to change your rules and + + + align:start position:0% +if you're going to change your rules and +you're gonna have to iterate on your + + align:start position:0% +you're gonna have to iterate on your + + + align:start position:0% +you're gonna have to iterate on your +rules to make your game playable and do + + align:start position:0% +rules to make your game playable and do + + + align:start position:0% +rules to make your game playable and do +everything that you've done with + + align:start position:0% +everything that you've done with + + + align:start position:0% +everything that you've done with +assignment one you want to make sure + + align:start position:0% +assignment one you want to make sure + + + align:start position:0% +assignment one you want to make sure +that your aesthetic is coherent with + + align:start position:0% +that your aesthetic is coherent with + + + align:start position:0% +that your aesthetic is coherent with +that so that you don't have things in + + align:start position:0% +that so that you don't have things in + + + align:start position:0% +that so that you don't have things in +your storyline or your character design + + align:start position:0% +your storyline or your character design + + + align:start position:0% +your storyline or your character design +on your art style that are out like + + align:start position:0% +on your art style that are out like + + + align:start position:0% +on your art style that are out like +contradicting what your rules are trying + + align:start position:0% +contradicting what your rules are trying + + + align:start position:0% +contradicting what your rules are trying +to tell you like this is a game about + + align:start position:0% +to tell you like this is a game about + + + align:start position:0% +to tell you like this is a game about +friendly cooperation and then you're you + + align:start position:0% +friendly cooperation and then you're you + + + align:start position:0% +friendly cooperation and then you're you +know and you're saying all of you are on + + align:start position:0% +know and you're saying all of you are on + + + align:start position:0% +know and you're saying all of you are on +this island together and trying to save + + align:start position:0% +this island together and trying to save + + + align:start position:0% +this island together and trying to save +yourselves but really you're the way how + + align:start position:0% +yourselves but really you're the way how + + + align:start position:0% +yourselves but really you're the way how +your rules work does every man for + + align:start position:0% +your rules work does every man for + + + align:start position:0% +your rules work does every man for +themselves you know that would be a + + align:start position:0% +themselves you know that would be a + + + align:start position:0% +themselves you know that would be a +contradiction here this is an + + align:start position:0% +contradiction here this is an + + + align:start position:0% +contradiction here this is an +interesting game let's go check it right + + align:start position:0% +interesting game let's go check it right + + + align:start position:0% +interesting game let's go check it right +okay bus design and and title can play a + + align:start position:0% +okay bus design and and title can play a + + + align:start position:0% +okay bus design and and title can play a +very very large part in setting their + + align:start position:0% +very very large part in setting their + + + align:start position:0% +very very large part in setting their +expectations so it wasn't solve + + align:start position:0% +expectations so it wasn't solve + + + align:start position:0% +expectations so it wasn't solve +something I suppressed so much in the + + align:start position:0% +something I suppressed so much in the + + + align:start position:0% +something I suppressed so much in the +first assignment what you titled your + + align:start position:0% +first assignment what you titled your + + + align:start position:0% +first assignment what you titled your +game but in the second assignment this + + align:start position:0% +game but in the second assignment this + + + align:start position:0% +game but in the second assignment this +is wrong the title of your game have + + align:start position:0% +is wrong the title of your game have + + + align:start position:0% +is wrong the title of your game have +sine I'd be the first to of what your + + align:start position:0% +sine I'd be the first to of what your + + + align:start position:0% +sine I'd be the first to of what your +games all about it's a way of building + + align:start position:0% +games all about it's a way of building + + + align:start position:0% +games all about it's a way of building +game you can see from the back a picture + + align:start position:0% +game you can see from the back a picture + + + align:start position:0% +game you can see from the back a picture +of the board and you're sort of building + + align:start position:0% +of the board and you're sort of building + + + align:start position:0% +of the board and you're sort of building +these tracks but if you actually read + + align:start position:0% +these tracks but if you actually read + + + align:start position:0% +these tracks but if you actually read +the box it says October 2nd 1928 years + + align:start position:0% +the box it says October 2nd 1928 years + + + align:start position:0% +the box it says October 2nd 1928 years +to the day that noted London is centric + + align:start position:0% +to the day that noted London is centric + + + align:start position:0% +to the day that noted London is centric +Phileas Fogg accepted and won a twenty + + align:start position:0% +Phileas Fogg accepted and won a twenty + + + align:start position:0% +Phileas Fogg accepted and won a twenty +thousand dollar bet that he could travel + + align:start position:0% +thousand dollar bet that he could travel + + + align:start position:0% +thousand dollar bet that he could travel +around the world ad base now at the dawn + + align:start position:0% +around the world ad base now at the dawn + + + align:start position:0% +around the world ad base now at the dawn +of the century it is time for a new + + align:start position:0% +of the century it is time for a new + + + align:start position:0% +of the century it is time for a new +impossible journey travel across the + + align:start position:0% +impossible journey travel across the + + + align:start position:0% +impossible journey travel across the +United States the impossible journey and + + align:start position:0% +United States the impossible journey and + + + align:start position:0% +United States the impossible journey and +now at the dawn of said so some old + + align:start position:0% +now at the dawn of said so some old + + + align:start position:0% +now at the dawn of said so some old +friends have gathered to celebrate Fox + + align:start position:0% +friends have gathered to celebrate Fox + + + align:start position:0% +friends have gathered to celebrate Fox +impetuous and lucrative temple and to + + align:start position:0% +impetuous and lucrative temple and to + + + align:start position:0% +impetuous and lucrative temple and to +propose a new wager on their own the + + align:start position:0% +propose a new wager on their own the + + + align:start position:0% +propose a new wager on their own the +stakes 1 million in a winner-takes-all + + align:start position:0% +stakes 1 million in a winner-takes-all + + + align:start position:0% +stakes 1 million in a winner-takes-all +competition the objective to see which + + align:start position:0% +competition the objective to see which + + + align:start position:0% +competition the objective to see which +of them can travel by rail to the most + + align:start position:0% +of them can travel by rail to the most + + + align:start position:0% +of them can travel by rail to the most +cities in North America in just seven + + align:start position:0% +cities in North America in just seven + + + align:start position:0% +cities in North America in just seven +days it's interesting because at first + + align:start position:0% +days it's interesting because at first + + + align:start position:0% +days it's interesting because at first +glance you look at the game mechanics + + align:start position:0% +glance you look at the game mechanics + + + align:start position:0% +glance you look at the game mechanics +and the game I can actually feel more + + align:start position:0% +and the game I can actually feel more + + + align:start position:0% +and the game I can actually feel more +like you're sort of building building + + align:start position:0% +like you're sort of building building + + + align:start position:0% +like you're sort of building building +railway connections rather than riding + + align:start position:0% +railway connections rather than riding + + + align:start position:0% +railway connections rather than riding +the rails but if you look a little bit + + align:start position:0% +the rails but if you look a little bit + + + align:start position:0% +the rails but if you look a little bit +closer at the strategies of this game + + align:start position:0% +closer at the strategies of this game + + + align:start position:0% +closer at the strategies of this game +one what this game really comes down to + + align:start position:0% +one what this game really comes down to + + + align:start position:0% +one what this game really comes down to +is blocking other people from completing + + align:start position:0% +is blocking other people from completing + + + align:start position:0% +is blocking other people from completing +your routes are also America which I + + align:start position:0% +your routes are also America which I + + + align:start position:0% +your routes are also America which I +think is closer to I think the theme + + align:start position:0% +think is closer to I think the theme + + + align:start position:0% +think is closer to I think the theme +that the suggesting right it's not about + + align:start position:0% +that the suggesting right it's not about + + + align:start position:0% +that the suggesting right it's not about +who who can complete it's not about you + + align:start position:0% +who who can complete it's not about you + + + align:start position:0% +who who can complete it's not about you +know is it possible for you to complete + + align:start position:0% +know is it possible for you to complete + + + align:start position:0% +know is it possible for you to complete +a route around America in seven days + + align:start position:0% +a route around America in seven days + + + align:start position:0% +a route around America in seven days +no it's who can do it fastest which + + align:start position:0% +no it's who can do it fastest which + + + align:start position:0% +no it's who can do it fastest which +means how do I slow down everybody else + + align:start position:0% +means how do I slow down everybody else + + + align:start position:0% +means how do I slow down everybody else +and that's actually what high levels + + align:start position:0% +and that's actually what high levels + + + align:start position:0% +and that's actually what high levels +value in this case turns out to be so + + align:start position:0% +value in this case turns out to be so + + + align:start position:0% +value in this case turns out to be so +it's about all these tickets that you're + + align:start position:0% +it's about all these tickets that you're + + + align:start position:0% +it's about all these tickets that you're +picking like that they are picking up + + align:start position:0% +picking like that they are picking up + + + align:start position:0% +picking like that they are picking up +and and you're going from place to place + + align:start position:0% +and and you're going from place to place + + + align:start position:0% +and and you're going from place to place +you're trying to complete routes and + + align:start position:0% +you're trying to complete routes and + + + align:start position:0% +you're trying to complete routes and +you're trying to prevent other people + + align:start position:0% +you're trying to prevent other people + + + align:start position:0% +you're trying to prevent other people +from completing their routes one of the + + align:start position:0% +from completing their routes one of the + + + align:start position:0% +from completing their routes one of the +interesting things about this game is + + align:start position:0% +interesting things about this game is + + + align:start position:0% +interesting things about this game is +that you've got all these + + align:start position:0% +that you've got all these + + + align:start position:0% +that you've got all these +people that are on the box and I thought + + align:start position:0% +people that are on the box and I thought + + + align:start position:0% +people that are on the box and I thought +the assumption is that you are one of + + align:start position:0% +the assumption is that you are one of + + + align:start position:0% +the assumption is that you are one of +these people and that's deliberate the + + align:start position:0% +these people and that's deliberate the + + + align:start position:0% +these people and that's deliberate the +the board game designers wanted you to + + align:start position:0% +the board game designers wanted you to + + + align:start position:0% +the board game designers wanted you to +slap who wanted to slap someone on this + + align:start position:0% +slap who wanted to slap someone on this + + + align:start position:0% +slap who wanted to slap someone on this +box that you could personally identify + + align:start position:0% +box that you could personally identify + + + align:start position:0% +box that you could personally identify +with it says I want to be this you know + + align:start position:0% +with it says I want to be this you know + + + align:start position:0% +with it says I want to be this you know +this this this person that we looks like + + align:start position:0% +this this this person that we looks like + + + align:start position:0% +this this this person that we looks like +across the party you know and III oh + + align:start position:0% +across the party you know and III oh + + + align:start position:0% +across the party you know and III oh +this person who looks like Phineas Bogg + + align:start position:0% +this person who looks like Phineas Bogg + + + align:start position:0% +this person who looks like Phineas Bogg +because I like those books but then when + + align:start position:0% +because I like those books but then when + + + align:start position:0% +because I like those books but then when +you actually play the game there is no + + align:start position:0% +you actually play the game there is no + + + align:start position:0% +you actually play the game there is no +real and body mind off of any of these + + align:start position:0% +real and body mind off of any of these + + + align:start position:0% +real and body mind off of any of these +characters that's all like peace that + + align:start position:0% +characters that's all like peace that + + + align:start position:0% +characters that's all like peace that +you place down there says I am this + + align:start position:0% +you place down there says I am this + + + align:start position:0% +you place down there says I am this +person and and you only the only sort of + + align:start position:0% +person and and you only the only sort of + + + align:start position:0% +person and and you only the only sort of +level of a fiction that sort of + + align:start position:0% +level of a fiction that sort of + + + align:start position:0% +level of a fiction that sort of +represented in the rules it are the + + align:start position:0% +represented in the rules it are the + + + align:start position:0% +represented in the rules it are the +tickets and and and and and the routes + + align:start position:0% +tickets and and and and and the routes + + + align:start position:0% +tickets and and and and and the routes +that you're taking not the people so + + align:start position:0% +that you're taking not the people so + + + align:start position:0% +that you're taking not the people so +they've gone to it is very very large + + align:start position:0% +they've gone to it is very very large + + + align:start position:0% +they've gone to it is very very large +effort to make you think that this is + + align:start position:0% +effort to make you think that this is + + + align:start position:0% +effort to make you think that this is +that the to to make you think and this + + align:start position:0% +that the to to make you think and this + + + align:start position:0% +that the to to make you think and this +is a game about people and guess because + + align:start position:0% +is a game about people and guess because + + + align:start position:0% +is a game about people and guess because +they thought that games about people + + align:start position:0% +they thought that games about people + + + align:start position:0% +they thought that games about people +tend to sell better than games about + + align:start position:0% +tend to sell better than games about + + + align:start position:0% +tend to sell better than games about +trains but the games really about trains + + align:start position:0% +trains but the games really about trains + + + align:start position:0% +trains but the games really about trains +so I guess just I'm trying trainer um + + align:start position:0% +so I guess just I'm trying trainer um + + + align:start position:0% +so I guess just I'm trying trainer um +let's see + + align:start position:0% +let's see + + + align:start position:0% +let's see +can't talk about this at the games so + + align:start position:0% +can't talk about this at the games so + + + align:start position:0% +can't talk about this at the games so +alien frontiers a anybody know the term + + align:start position:0% +alien frontiers a anybody know the term + + + align:start position:0% +alien frontiers a anybody know the term +work replacement welcome place this game + + align:start position:0% +work replacement welcome place this game + + + align:start position:0% +work replacement welcome place this game +where you have a limited number of + + align:start position:0% +where you have a limited number of + + + align:start position:0% +where you have a limited number of +resources that you're just basically + + align:start position:0% +resources that you're just basically + + + align:start position:0% +resources that you're just basically +applying to different sections on the + + align:start position:0% +applying to different sections on the + + + align:start position:0% +applying to different sections on the +board which give you points or do things + + align:start position:0% +board which give you points or do things + + + align:start position:0% +board which give you points or do things +for you so it's a great game about + + align:start position:0% +for you so it's a great game about + + + align:start position:0% +for you so it's a great game about +colonizing this world so a lot of really + + align:start position:0% +colonizing this world so a lot of really + + + align:start position:0% +colonizing this world so a lot of really +good like old style fifties and sixties + + align:start position:0% +good like old style fifties and sixties + + + align:start position:0% +good like old style fifties and sixties +style like science fiction part lots of + + align:start position:0% +style like science fiction part lots of + + + align:start position:0% +style like science fiction part lots of +rockets spaceships things like that and + + align:start position:0% +rockets spaceships things like that and + + + align:start position:0% +rockets spaceships things like that and +your actual bits + + align:start position:0% +your actual bits + + + align:start position:0% +your actual bits +and the reason I'm using this one is + + align:start position:0% +and the reason I'm using this one is + + + align:start position:0% +and the reason I'm using this one is +because this is a game to start off with + + align:start position:0% +because this is a game to start off with + + + align:start position:0% +because this is a game to start off with +kind of like a plasticy euro style so + + align:start position:0% +kind of like a plasticy euro style so + + + align:start position:0% +kind of like a plasticy euro style so +cubes and things like that represent + + align:start position:0% +cubes and things like that represent + + + align:start position:0% +cubes and things like that represent +really represent any things your bits + + align:start position:0% +really represent any things your bits + + + align:start position:0% +really represent any things your bits +your ships or these dice you buy you buy + + align:start position:0% +your ships or these dice you buy you buy + + + align:start position:0% +your ships or these dice you buy you buy +a rocket you roll the rocket it gives + + align:start position:0% +a rocket you roll the rocket it gives + + + align:start position:0% +a rocket you roll the rocket it gives +you a number and then using those + + align:start position:0% +you a number and then using those + + + align:start position:0% +you a number and then using those +numbers you can apply it to various + + align:start position:0% +numbers you can apply it to various + + + align:start position:0% +numbers you can apply it to various +different places on the board so state + + align:start position:0% +different places on the board so state + + + align:start position:0% +different places on the board so state +savings actually pretty good because you + + align:start position:0% +savings actually pretty good because you + + + align:start position:0% +savings actually pretty good because you +can put the piece down it stays there if + + align:start position:0% +can put the piece down it stays there if + + + align:start position:0% +can put the piece down it stays there if +it gets moved around it doesn't really + + align:start position:0% +it gets moved around it doesn't really + + + align:start position:0% +it gets moved around it doesn't really +matter if it changes a number because if + + align:start position:0% +matter if it changes a number because if + + + align:start position:0% +matter if it changes a number because if +you use the number just when you're + + align:start position:0% +you use the number just when you're + + + align:start position:0% +you use the number just when you're +placing down the piece the number is no + + align:start position:0% +placing down the piece the number is no + + + align:start position:0% +placing down the piece the number is no +longer relevant anymore one thing we see + + align:start position:0% +longer relevant anymore one thing we see + + + align:start position:0% +longer relevant anymore one thing we see +in a lot of student games people using + + align:start position:0% +in a lot of student games people using + + + align:start position:0% +in a lot of student games people using +dice as counters a little bit easier + + align:start position:0% +dice as counters a little bit easier + + + align:start position:0% +dice as counters a little bit easier +with with die six because it's squared + + align:start position:0% +with with die six because it's squared + + + align:start position:0% +with with die six because it's squared +but once you start using like the D 20s + + align:start position:0% +but once you start using like the D 20s + + + align:start position:0% +but once you start using like the D 20s +as a counter they've got really small + + align:start position:0% +as a counter they've got really small + + + align:start position:0% +as a counter they've got really small +facets and they're gonna roll and you're + + align:start position:0% +facets and they're gonna roll and you're + + + align:start position:0% +facets and they're gonna roll and you're +gonna lose your place also the amount of + + align:start position:0% +gonna lose your place also the amount of + + + align:start position:0% +gonna lose your place also the amount of +time it takes to go from one number to + + align:start position:0% +time it takes to go from one number to + + + align:start position:0% +time it takes to go from one number to +the other number I'm really increases + + align:start position:0% +the other number I'm really increases + + + align:start position:0% +the other number I'm really increases +the penetration so play the game but one + + align:start position:0% +the penetration so play the game but one + + + align:start position:0% +the penetration so play the game but one +thing they join it start off with these + + align:start position:0% +thing they join it start off with these + + + align:start position:0% +thing they join it start off with these +little chips now they've added more + + align:start position:0% +little chips now they've added more + + + align:start position:0% +little chips now they've added more +plastic bits special powers you can get + + align:start position:0% +plastic bits special powers you can get + + + align:start position:0% +plastic bits special powers you can get +to move around that look + + align:start position:0% +to move around that look + + + align:start position:0% +to move around that look +Zini full alien pieces of technology and + + align:start position:0% +Zini full alien pieces of technology and + + + align:start position:0% +Zini full alien pieces of technology and +colonies you can place that kind of look + + align:start position:0% +colonies you can place that kind of look + + + align:start position:0% +colonies you can place that kind of look +like colonies now I don't have it here + + align:start position:0% +like colonies now I don't have it here + + + align:start position:0% +like colonies now I don't have it here +it's not released yet but it's on order + + align:start position:0% +it's not released yet but it's on order + + + align:start position:0% +it's not released yet but it's on order +they actually made the Rockets dice so + + align:start position:0% +they actually made the Rockets dice so + + + align:start position:0% +they actually made the Rockets dice so +dice in the shape of rockets so imagine + + align:start position:0% +dice in the shape of rockets so imagine + + + align:start position:0% +dice in the shape of rockets so imagine +this has an oblong shape that's kind of + + align:start position:0% +this has an oblong shape that's kind of + + + align:start position:0% +this has an oblong shape that's kind of +curved with cut faces on it one thing + + align:start position:0% +curved with cut faces on it one thing + + + align:start position:0% +curved with cut faces on it one thing +I'm curious is how is that going to roll + + align:start position:0% +I'm curious is how is that going to roll + + + align:start position:0% +I'm curious is how is that going to roll +how is it gonna like they've they've + + align:start position:0% +how is it gonna like they've they've + + + align:start position:0% +how is it gonna like they've they've +made it so that it feels more + + align:start position:0% +made it so that it feels more + + + align:start position:0% +made it so that it feels more +representation like it feels more like + + align:start position:0% +representation like it feels more like + + + align:start position:0% +representation like it feels more like +part of the theme but it might actually + + align:start position:0% +part of the theme but it might actually + + + align:start position:0% +part of the theme but it might actually +take away from the actual feel of + + align:start position:0% +take away from the actual feel of + + + align:start position:0% +take away from the actual feel of +rolling dice all the instant seeing how + + align:start position:0% +rolling dice all the instant seeing how + + + align:start position:0% +rolling dice all the instant seeing how +that plays out when I play that + + align:start position:0% + + + + align:start position:0% + +and the other one game about trucking + + align:start position:0% +and the other one game about trucking + + + align:start position:0% +and the other one game about trucking +the great heartland hauling company so + + align:start position:0% +the great heartland hauling company so + + + align:start position:0% +the great heartland hauling company so +on the Box you see semi truck carrying + + align:start position:0% +on the Box you see semi truck carrying + + + align:start position:0% +on the Box you see semi truck carrying +little squares on the back you see semi + + align:start position:0% +little squares on the back you see semi + + + align:start position:0% +little squares on the back you see semi +trucks and squares but the squares are + + align:start position:0% +trucks and squares but the squares are + + + align:start position:0% +trucks and squares but the squares are +on a map but the squares don't really + + align:start position:0% +on a map but the squares don't really + + + align:start position:0% +on a map but the squares don't really +fit on the trucks um so I actually + + align:start position:0% +fit on the trucks um so I actually + + + align:start position:0% +fit on the trucks um so I actually +brought this out thinking that's it + + align:start position:0% +brought this out thinking that's it + + + align:start position:0% +brought this out thinking that's it +that's a great way of saying it's it's + + align:start position:0% +that's a great way of saying it's it's + + + align:start position:0% +that's a great way of saying it's it's +not kind of like the other one they're + + align:start position:0% +not kind of like the other one they're + + + align:start position:0% +not kind of like the other one they're +showing something on the box it doesn't + + align:start position:0% +showing something on the box it doesn't + + + align:start position:0% +showing something on the box it doesn't +actually exist in the game but I found + + align:start position:0% +actually exist in the game but I found + + + align:start position:0% +actually exist in the game but I found +out when I actually took it out and + + align:start position:0% +out when I actually took it out and + + + align:start position:0% +out when I actually took it out and +opened it they have cards where you put + + align:start position:0% +opened it they have cards where you put + + + align:start position:0% +opened it they have cards where you put +your where you put your own your bits on + + align:start position:0% +your where you put your own your bits on + + + align:start position:0% +your where you put your own your bits on +so you are kind of carrying things + + align:start position:0% +so you are kind of carrying things + + + align:start position:0% +so you are kind of carrying things +around but as a disconnect between the + + align:start position:0% +around but as a disconnect between the + + + align:start position:0% +around but as a disconnect between the +map where things are on the map and + + align:start position:0% +map where things are on the map and + + + align:start position:0% +map where things are on the map and +where things are on your truck and then + + align:start position:0% +where things are on your truck and then + + + align:start position:0% +where things are on your truck and then +where your truck is actually placed on + + align:start position:0% +where your truck is actually placed on + + + align:start position:0% +where your truck is actually placed on +the map so your eyes are kind of going + + align:start position:0% +the map so your eyes are kind of going + + + align:start position:0% +the map so your eyes are kind of going +to different places when you're actually + + align:start position:0% +to different places when you're actually + + + align:start position:0% +to different places when you're actually +playing playing out the game largely + + align:start position:0% +playing playing out the game largely + + + align:start position:0% +playing playing out the game largely +done because of the it's the commercial + + align:start position:0% +done because of the it's the commercial + + + align:start position:0% +done because of the it's the commercial +manufacturing constraints of it as you + + align:start position:0% +manufacturing constraints of it as you + + + align:start position:0% +manufacturing constraints of it as you +can see it's basically just two decks in + + align:start position:0% +can see it's basically just two decks in + + + align:start position:0% +can see it's basically just two decks in +a small box you see a lot of these games + + align:start position:0% +a small box you see a lot of these games + + + align:start position:0% +a small box you see a lot of these games +they want if it's a game that they want + + align:start position:0% +they want if it's a game that they want + + + align:start position:0% +they want if it's a game that they want +you to play in a short period of time to + + align:start position:0% +you to play in a short period of time to + + + align:start position:0% +you to play in a short period of time to +likely gonna have a smaller box than a + + align:start position:0% +likely gonna have a smaller box than a + + + align:start position:0% +likely gonna have a smaller box than a +game that's gonna play longer it's kind + + align:start position:0% +game that's gonna play longer it's kind + + + align:start position:0% +game that's gonna play longer it's kind +of a code for how complicated the game + + align:start position:0% +of a code for how complicated the game + + + align:start position:0% +of a code for how complicated the game +is really how much how much you time the + + align:start position:0% +is really how much how much you time the + + + align:start position:0% +is really how much how much you time the +games gonna take + + align:start position:0% +games gonna take + + + align:start position:0% +games gonna take +definitely pay attention to how your + + align:start position:0% +definitely pay attention to how your + + + align:start position:0% +definitely pay attention to how your +pieces feel again we're not asking you + + align:start position:0% +pieces feel again we're not asking you + + + align:start position:0% +pieces feel again we're not asking you +to go you know completely to town and + + align:start position:0% +to go you know completely to town and + + + align:start position:0% +to go you know completely to town and +like laser cutting pieces or anything + + align:start position:0% +like laser cutting pieces or anything + + + align:start position:0% +like laser cutting pieces or anything +like that that's not necessary just that + + align:start position:0% +like that that's not necessary just that + + + align:start position:0% +like that that's not necessary just that +every time you like think of a harvest + + align:start position:0% +every time you like think of a harvest + + + align:start position:0% +every time you like think of a harvest +piece in our box or we decide to glue + + align:start position:0% +piece in our box or we decide to glue + + + align:start position:0% +piece in our box or we decide to glue +two pieces together or find a sense to + + align:start position:0% +two pieces together or find a sense to + + + align:start position:0% +two pieces together or find a sense to +be able to make it a different shape or + + align:start position:0% +be able to make it a different shape or + + + align:start position:0% +be able to make it a different shape or +something think about what that's + + align:start position:0% +something think about what that's + + + align:start position:0% +something think about what that's +communicating over to the players think + + align:start position:0% +communicating over to the players think + + + align:start position:0% +communicating over to the players think +about what the box may be or what what + + align:start position:0% +about what the box may be or what what + + + align:start position:0% +about what the box may be or what what +what the art in your rules is conveying + + align:start position:0% +what the art in your rules is conveying + + + align:start position:0% +what the art in your rules is conveying +about what the how the game is supposed + + align:start position:0% +about what the how the game is supposed + + + align:start position:0% +about what the how the game is supposed +to be played and and try not to mislead + + align:start position:0% +to be played and and try not to mislead + + + align:start position:0% +to be played and and try not to mislead +your players into thinking you know that + + align:start position:0% +your players into thinking you know that + + + align:start position:0% +your players into thinking you know that +this game is really about stacking + + align:start position:0% +this game is really about stacking + + + align:start position:0% +this game is really about stacking +things on little plastic trucks well it + + align:start position:0% +things on little plastic trucks well it + + + align:start position:0% +things on little plastic trucks well it +really isn't there's about putting + + align:start position:0% +really isn't there's about putting + + + align:start position:0% +really isn't there's about putting +stacking things on cards that sort of + + align:start position:0% +stacking things on cards that sort of + + + align:start position:0% +stacking things on cards that sort of +thing so yeah + + align:start position:0% +thing so yeah + + + align:start position:0% +thing so yeah +any questions materials it's still short + + align:start position:0% +any questions materials it's still short + + + align:start position:0% +any questions materials it's still short +assignment so don't think about that + + align:start position:0% +assignment so don't think about that + + + align:start position:0% +assignment so don't think about that +part yeah more about the which pieces + + align:start position:0% +part yeah more about the which pieces + + + align:start position:0% +part yeah more about the which pieces +you really think about like that the + + align:start position:0% +you really think about like that the + + + align:start position:0% +you really think about like that the +title is really really yeah the title is + + align:start position:0% +title is really really yeah the title is + + + align:start position:0% +title is really really yeah the title is +something writing you know it's + + align:start position:0% +something writing you know it's + + + align:start position:0% +something writing you know it's +something that you can spend you you you + + align:start position:0% +something that you can spend you you you + + + align:start position:0% +something that you can spend you you you +you can get a lot out of a little bit + + align:start position:0% +you can get a lot out of a little bit + + + align:start position:0% +you can get a lot out of a little bit +more time investment you can you the + + align:start position:0% +more time investment you can you the + + + align:start position:0% +more time investment you can you the +tone of your writing and your rules can + + align:start position:0% +tone of your writing and your rules can + + + align:start position:0% +tone of your writing and your rules can +go a long way but still not looking for + + align:start position:0% +go a long way but still not looking for + + + align:start position:0% +go a long way but still not looking for +rules that are easy to read so you know + + align:start position:0% +rules that are easy to read so you know + + + align:start position:0% +rules that are easy to read so you know +don't use like a Shakespearean spelling + + align:start position:0% +don't use like a Shakespearean spelling + + + align:start position:0% +don't use like a Shakespearean spelling +or something like that you know that + + align:start position:0% +or something like that you know that + + + align:start position:0% +or something like that you know that +might make things a little bit tricky + + align:start position:0% +might make things a little bit tricky + + + align:start position:0% +might make things a little bit tricky +yeah unless you're very very consistent + + align:start position:0% +yeah unless you're very very consistent + + + align:start position:0% +yeah unless you're very very consistent +with it or rather you're only using it + + align:start position:0% +with it or rather you're only using it + + + align:start position:0% +with it or rather you're only using it +for nouns or something I wish we could + + align:start position:0% +for nouns or something I wish we could + + + align:start position:0% +for nouns or something I wish we could +work pretty well + + align:start position:0% +work pretty well + + + align:start position:0% +work pretty well +sketchy art is fine you know just like + + align:start position:0% +sketchy art is fine you know just like + + + align:start position:0% +sketchy art is fine you know just like +this a hint of what you are trying to + + align:start position:0% +this a hint of what you are trying to + + + align:start position:0% +this a hint of what you are trying to +get across with your way to art you know + + align:start position:0% +get across with your way to art you know + + + align:start position:0% +get across with your way to art you know +we're not judging anybody on your + + align:start position:0% +we're not judging anybody on your + + + align:start position:0% +we're not judging anybody on your +ability to draw but we are we are + + align:start position:0% +ability to draw but we are we are + + + align:start position:0% +ability to draw but we are we are +interested in your thought process and + + align:start position:0% +interested in your thought process and + + + align:start position:0% +interested in your thought process and +in how you consider how + + align:start position:0% +in how you consider how + + + align:start position:0% +in how you consider how +all right that and that comes down back + + align:start position:0% +all right that and that comes down back + + + align:start position:0% +all right that and that comes down back +to you know the overall aesthetic right + + align:start position:0% +to you know the overall aesthetic right + + + align:start position:0% +to you know the overall aesthetic right +all of these things are working together + + align:start position:0% +all of these things are working together + + + align:start position:0% +all of these things are working together +to sort of generate a player experience + + align:start position:0% +to sort of generate a player experience + + + align:start position:0% +to sort of generate a player experience +that will be going through some examples + + align:start position:0% +that will be going through some examples + + + align:start position:0% +that will be going through some examples +of other games that generate you know + + align:start position:0% +of other games that generate you know + + + align:start position:0% +of other games that generate you know +the user experience of panic experience + + align:start position:0% +the user experience of panic experience + + + align:start position:0% +the user experience of panic experience +of you know close shave cooperation + + align:start position:0% +of you know close shave cooperation + + + align:start position:0% +of you know close shave cooperation +right again yeah + + align:start position:0% +right again yeah + + + align:start position:0% +right again yeah +remember mechanics dynamics aesthetics + + align:start position:0% +remember mechanics dynamics aesthetics + + + align:start position:0% +remember mechanics dynamics aesthetics +the aesthetic thing is the player that + + align:start position:0% +the aesthetic thing is the player that + + + align:start position:0% +the aesthetic thing is the player that +actually experiences and that's true for + + align:start position:0% +actually experiences and that's true for + + + align:start position:0% +actually experiences and that's true for +all for any definition of a study the + + align:start position:0% +all for any definition of a study the + + + align:start position:0% +all for any definition of a study the +the question is what are all the things + + align:start position:0% +the question is what are all the things + + + align:start position:0% +the question is what are all the things +that you can do to hopefully generate + + align:start position:0% +that you can do to hopefully generate + + + align:start position:0% +that you can do to hopefully generate +that now of course you only know whether + + align:start position:0% +that now of course you only know whether + + + align:start position:0% +that now of course you only know whether +you're hitting that with retesting do we + + align:start position:0% + + + + align:start position:0% + +quit 20 minutes yeah + + align:start position:0% +quit 20 minutes yeah + + + align:start position:0% +quit 20 minutes yeah +okay so aim for that it's a little + + align:start position:0% +okay so aim for that it's a little + + + align:start position:0% +okay so aim for that it's a little +longer than the last one yeah but yeah + + align:start position:0% +longer than the last one yeah but yeah + + + align:start position:0% +longer than the last one yeah but yeah +so yeah and the reason for that is + + align:start position:0% +so yeah and the reason for that is + + + align:start position:0% +so yeah and the reason for that is +largely we want to be able to grade + + align:start position:0% +largely we want to be able to grade + + + align:start position:0% +largely we want to be able to grade +these things and get your your grades + + align:start position:0% +these things and get your your grades + + + align:start position:0% +these things and get your your grades +back to you so if you made a two-hour + + align:start position:0% +back to you so if you made a two-hour + + + align:start position:0% +back to you so if you made a two-hour +long game and everybody makes a two-hour + + align:start position:0% +long game and everybody makes a two-hour + + + align:start position:0% +long game and everybody makes a two-hour +long game we're never gonna finish + + align:start position:0% +long game we're never gonna finish + + + align:start position:0% +long game we're never gonna finish +creating this dish so short kids help + + align:start position:0% +creating this dish so short kids help + + + align:start position:0% +creating this dish so short kids help +and talking about you + + align:start position:0% + + + + align:start position:0% + +cool all right I guess bear anything a + + align:start position:0% +cool all right I guess bear anything a + + + align:start position:0% +cool all right I guess bear anything a +little early today + + align:start position:0% +little early today + + + align:start position:0% +little early today +all right thanks very much don't forget + + align:start position:0% +all right thanks very much don't forget + + + align:start position:0% +all right thanks very much don't forget +to sign in if you haven't already + + align:start position:0% + + + + align:start position:0% + +just whatever oh yeah + + align:start position:0% +just whatever oh yeah + + + align:start position:0% +just whatever oh yeah +please find in your home + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/_naTiUQOq34.txt b/_naTiUQOq34.txt new file mode 100644 index 0000000000000000000000000000000000000000..bfc765400a03aa5bcb6e4af916625f51094f8038 --- /dev/null +++ b/_naTiUQOq34.txt @@ -0,0 +1,1403 @@ +align:start position:0% + +welcome back to a20 special relativity + + align:start position:0% +welcome back to a20 special relativity + + + align:start position:0% +welcome back to a20 special relativity +in this section we want to discuss + + align:start position:0% +in this section we want to discuss + + + align:start position:0% +in this section we want to discuss +lawrence transformation or in other + + align:start position:0% +lawrence transformation or in other + + + align:start position:0% +lawrence transformation or in other +words + + align:start position:0% +words + + + align:start position:0% +words +given an event observed by bob you want + + align:start position:0% +given an event observed by bob you want + + + align:start position:0% +given an event observed by bob you want +to express that event as observed by + + align:start position:0% +to express that event as observed by + + + align:start position:0% +to express that event as observed by +alice you want to find the translation + + align:start position:0% +alice you want to find the translation + + + align:start position:0% +alice you want to find the translation +between the observations and bob + + align:start position:0% +between the observations and bob + + + align:start position:0% +between the observations and bob +reference frames to the observation in + + align:start position:0% +reference frames to the observation in + + + align:start position:0% +reference frames to the observation in +alice's reference + + align:start position:0% +alice's reference + + + align:start position:0% +alice's reference +they have already done this for the + + align:start position:0% +they have already done this for the + + + align:start position:0% +they have already done this for the +classical case + + align:start position:0% +classical case + + + align:start position:0% +classical case +as galilean transformation now we want + + align:start position:0% +as galilean transformation now we want + + + align:start position:0% +as galilean transformation now we want +to do this in the framework of special + + align:start position:0% +to do this in the framework of special + + + align:start position:0% +to do this in the framework of special +relativity + + align:start position:0% +relativity + + + align:start position:0% +relativity +in order to simplify the discussion + + align:start position:0% +in order to simplify the discussion + + + align:start position:0% +in order to simplify the discussion +uh we don't worry about the y and z + + align:start position:0% +uh we don't worry about the y and z + + + align:start position:0% +uh we don't worry about the y and z +component here those dimensions can be + + align:start position:0% +component here those dimensions can be + + + align:start position:0% +component here those dimensions can be +neglected if we assume + + align:start position:0% +neglected if we assume + + + align:start position:0% +neglected if we assume +that + + align:start position:0% +that + + + align:start position:0% +that +the relative motion between the two + + align:start position:0% +the relative motion between the two + + + align:start position:0% +the relative motion between the two +reference frames only in x direction + + align:start position:0% +reference frames only in x direction + + + align:start position:0% +reference frames only in x direction +we also know from the previous + + align:start position:0% +we also know from the previous + + + align:start position:0% +we also know from the previous +discussion that you can use the + + align:start position:0% +discussion that you can use the + + + align:start position:0% +discussion that you can use the +invariant interval + + align:start position:0% +invariant interval + + + align:start position:0% +invariant interval +see t square minus x square is the same + + align:start position:0% +see t square minus x square is the same + + + align:start position:0% +see t square minus x square is the same +observed in bobs and in alice's + + align:start position:0% +observed in bobs and in alice's + + + align:start position:0% +observed in bobs and in alice's +reference frame we'll make use of this + + align:start position:0% +reference frame we'll make use of this + + + align:start position:0% +reference frame we'll make use of this +fact + + align:start position:0% +fact + + + align:start position:0% +fact +and lastly we can assume that this + + align:start position:0% +and lastly we can assume that this + + + align:start position:0% +and lastly we can assume that this +transformation has to be linear why + + align:start position:0% +transformation has to be linear why + + + align:start position:0% +transformation has to be linear why +because + + align:start position:0% +because + + + align:start position:0% +because +we transform something like a + + align:start position:0% +we transform something like a + + + align:start position:0% +we transform something like a +measurement of distance into a + + align:start position:0% +measurement of distance into a + + + align:start position:0% +measurement of distance into a +measurement of distance + + align:start position:0% +measurement of distance + + + align:start position:0% +measurement of distance +it has to be linear if not we find + + align:start position:0% +it has to be linear if not we find + + + align:start position:0% +it has to be linear if not we find +something like a length squared or the + + align:start position:0% +something like a length squared or the + + + align:start position:0% +something like a length squared or the +same for time and we might end up on + + align:start position:0% +same for time and we might end up on + + + align:start position:0% +same for time and we might end up on +time square if we don't do this + + align:start position:0% +time square if we don't do this + + + align:start position:0% +time square if we don't do this +correctly + + align:start position:0% +correctly + + + align:start position:0% +correctly +all right so we can write this down as a + + align:start position:0% +all right so we can write this down as a + + + align:start position:0% +all right so we can write this down as a +linear equation which is a + + align:start position:0% +linear equation which is a + + + align:start position:0% +linear equation which is a +multiplication of a matrix with a vector + + align:start position:0% +multiplication of a matrix with a vector + + + align:start position:0% +multiplication of a matrix with a vector +c t x + + align:start position:0% +c t x + + + align:start position:0% +c t x +into a vector ctx prime x prime + + align:start position:0% +into a vector ctx prime x prime + + + align:start position:0% +into a vector ctx prime x prime +okay so the goal here now is to find + + align:start position:0% + + + + align:start position:0% + +the parameters or the the coefficients + + align:start position:0% +the parameters or the the coefficients + + + align:start position:0% +the parameters or the the coefficients +of this matrix + + align:start position:0% +of this matrix + + + align:start position:0% +of this matrix +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um i invite you to stop the video here + + align:start position:0% +um i invite you to stop the video here + + + align:start position:0% +um i invite you to stop the video here +and try to work it out um it's an + + align:start position:0% +and try to work it out um it's an + + + align:start position:0% +and try to work it out um it's an +interesting exercise test your algebra + + align:start position:0% +interesting exercise test your algebra + + + align:start position:0% +interesting exercise test your algebra +knowledge um there's not much physics in + + align:start position:0% +knowledge um there's not much physics in + + + align:start position:0% +knowledge um there's not much physics in +here but it's still useful to go along + + align:start position:0% +here but it's still useful to go along + + + align:start position:0% +here but it's still useful to go along +and try to to work this + + align:start position:0% +and try to to work this + + + align:start position:0% +and try to to work this +out so the first thing we want to do + + align:start position:0% +out so the first thing we want to do + + + align:start position:0% +out so the first thing we want to do +is assume that + + align:start position:0% +is assume that + + + align:start position:0% +is assume that +the origins coincide at t equals zero + + align:start position:0% +the origins coincide at t equals zero + + + align:start position:0% +the origins coincide at t equals zero +and then we can follow along the + + align:start position:0% +and then we can follow along the + + + align:start position:0% +and then we can follow along the +trajectory of the origin of s prime in + + align:start position:0% +trajectory of the origin of s prime in + + + align:start position:0% +trajectory of the origin of s prime in +the s frame + + align:start position:0% +the s frame + + + align:start position:0% +the s frame +so this is just t t v t + + align:start position:0% +so this is just t t v t + + + align:start position:0% +so this is just t t v t +okay great this already gives us + + align:start position:0% +okay great this already gives us + + + align:start position:0% +okay great this already gives us +a constraint on the coefficients a 1 0 + + align:start position:0% +a constraint on the coefficients a 1 0 + + + align:start position:0% +a constraint on the coefficients a 1 0 +over a 1 1 which is equal to minus b c + + align:start position:0% +over a 1 1 which is equal to minus b c + + + align:start position:0% +over a 1 1 which is equal to minus b c +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then we can use the invariant + + align:start position:0% +and then we can use the invariant + + + align:start position:0% +and then we can use the invariant +interval + + align:start position:0% +interval + + + align:start position:0% +interval +which is another constraint and we can + + align:start position:0% +which is another constraint and we can + + + align:start position:0% +which is another constraint and we can +use this to obtain + + align:start position:0% +use this to obtain + + + align:start position:0% +use this to obtain +the set of equations here we'll not read + + align:start position:0% +the set of equations here we'll not read + + + align:start position:0% +the set of equations here we'll not read +this for you + + align:start position:0% +this for you + + + align:start position:0% +this for you +and that's already enough in order to + + align:start position:0% +and that's already enough in order to + + + align:start position:0% +and that's already enough in order to +solve the set of equations so if you do + + align:start position:0% +solve the set of equations so if you do + + + align:start position:0% +solve the set of equations so if you do +this and follow along + + align:start position:0% +this and follow along + + + align:start position:0% +this and follow along +you find + + align:start position:0% +you find + + + align:start position:0% +you find +answers for all four coefficients + + align:start position:0% +answers for all four coefficients + + + align:start position:0% +answers for all four coefficients +um you know given uh gamma and beta as + + align:start position:0% +um you know given uh gamma and beta as + + + align:start position:0% +um you know given uh gamma and beta as +we defined them before this then + + align:start position:0% +we defined them before this then + + + align:start position:0% +we defined them before this then +simplifies to our loans transformation + + align:start position:0% +simplifies to our loans transformation + + + align:start position:0% +simplifies to our loans transformation +so the only thing we did here is you + + align:start position:0% +so the only thing we did here is you + + + align:start position:0% +so the only thing we did here is you +know we simplified a little bit we + + align:start position:0% +know we simplified a little bit we + + + align:start position:0% +know we simplified a little bit we +assumed that this is a linear + + align:start position:0% +assumed that this is a linear + + + align:start position:0% +assumed that this is a linear +transformation we use the invariant + + align:start position:0% +transformation we use the invariant + + + align:start position:0% +transformation we use the invariant +interval in order to + + align:start position:0% +interval in order to + + + align:start position:0% +interval in order to +set the constraints and we find lauren's + + align:start position:0% +set the constraints and we find lauren's + + + align:start position:0% +set the constraints and we find lauren's +transformation if i summarize this we + + align:start position:0% +transformation if i summarize this we + + + align:start position:0% +transformation if i summarize this we +find this matrix here with coefficients + + align:start position:0% +find this matrix here with coefficients + + + align:start position:0% +find this matrix here with coefficients +gamma minus gamma beta minus gamma beta + + align:start position:0% +gamma minus gamma beta minus gamma beta + + + align:start position:0% +gamma minus gamma beta minus gamma beta +and gamma + + align:start position:0% +and gamma + + + align:start position:0% +and gamma +great + + align:start position:0% +great + + + align:start position:0% +great +or if you want you can + + align:start position:0% +or if you want you can + + + align:start position:0% +or if you want you can +write this as an equation for the + + align:start position:0% +write this as an equation for the + + + align:start position:0% +write this as an equation for the +spatial component and the time component + + align:start position:0% +spatial component and the time component + + + align:start position:0% +spatial component and the time component +so does this make sense there's always a + + align:start position:0% +so does this make sense there's always a + + + align:start position:0% +so does this make sense there's always a +chance that we make a mistake in this + + align:start position:0% +chance that we make a mistake in this + + + align:start position:0% +chance that we make a mistake in this +kind of calculation so we want to make + + align:start position:0% +kind of calculation so we want to make + + + align:start position:0% +kind of calculation so we want to make +sure that + + align:start position:0% +sure that + + + align:start position:0% +sure that +the answers we developed in previous + + align:start position:0% +the answers we developed in previous + + + align:start position:0% +the answers we developed in previous +sections actually are reflected by this + + align:start position:0% +sections actually are reflected by this + + + align:start position:0% +sections actually are reflected by this +transformation so let's go one by one + + align:start position:0% +transformation so let's go one by one + + + align:start position:0% +transformation so let's go one by one +the first thing we can do is check units + + align:start position:0% +the first thing we can do is check units + + + align:start position:0% +the first thing we can do is check units +if we do that we see + + align:start position:0% +if we do that we see + + + align:start position:0% +if we do that we see +that this first equation here + + align:start position:0% +that this first equation here + + + align:start position:0% +that this first equation here +is of unit meter and then we can analyze + + align:start position:0% +is of unit meter and then we can analyze + + + align:start position:0% +is of unit meter and then we can analyze +the the second part of the equation okay + + align:start position:0% +the the second part of the equation okay + + + align:start position:0% +the the second part of the equation okay +so gamma is of its unit list + + align:start position:0% +so gamma is of its unit list + + + align:start position:0% +so gamma is of its unit list +x is a unit meter and then we have + + align:start position:0% +x is a unit meter and then we have + + + align:start position:0% +x is a unit meter and then we have +better c t + + align:start position:0% +better c t + + + align:start position:0% +better c t +better is unitless c is meter per second + + align:start position:0% +better is unitless c is meter per second + + + align:start position:0% +better is unitless c is meter per second +times second also of unit meter so this + + align:start position:0% +times second also of unit meter so this + + + align:start position:0% +times second also of unit meter so this +checks out + + align:start position:0% +checks out + + + align:start position:0% +checks out +the second equation is very similar c + + align:start position:0% +the second equation is very similar c + + + align:start position:0% +the second equation is very similar c +times t is of unit meter + + align:start position:0% +times t is of unit meter + + + align:start position:0% +times t is of unit meter +meter per second times seconds of unit + + align:start position:0% +meter per second times seconds of unit + + + align:start position:0% +meter per second times seconds of unit +meter + + align:start position:0% +meter + + + align:start position:0% +meter +gamma is unitless beta is unit less and + + align:start position:0% +gamma is unitless beta is unit less and + + + align:start position:0% +gamma is unitless beta is unit less and +then we have an x unit meter + + align:start position:0% +then we have an x unit meter + + + align:start position:0% +then we have an x unit meter +plus c t + + align:start position:0% +plus c t + + + align:start position:0% +plus c t +c meter per second times second also + + align:start position:0% +c meter per second times second also + + + align:start position:0% +c meter per second times second also +meter so this checks out so this is + + align:start position:0% +meter so this checks out so this is + + + align:start position:0% +meter so this checks out so this is +great + + align:start position:0% + + + + align:start position:0% + +at least you find that we have a linear + + align:start position:0% +at least you find that we have a linear + + + align:start position:0% +at least you find that we have a linear +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +by design and the units work out + + align:start position:0% +by design and the units work out + + + align:start position:0% +by design and the units work out +so now we can see what happens now if we + + align:start position:0% +so now we can see what happens now if we + + + align:start position:0% +so now we can see what happens now if we +use this for velocities which are much + + align:start position:0% +use this for velocities which are much + + + align:start position:0% +use this for velocities which are much +much smaller than the speed of light + + align:start position:0% +much smaller than the speed of light + + + align:start position:0% +much smaller than the speed of light +in this case gamma is equal to zero and + + align:start position:0% +in this case gamma is equal to zero and + + + align:start position:0% +in this case gamma is equal to zero and +beta is very close to zero + + align:start position:0% +beta is very close to zero + + + align:start position:0% +beta is very close to zero +if we put this in our equations you find + + align:start position:0% +if we put this in our equations you find + + + align:start position:0% +if we put this in our equations you find +x + + align:start position:0% +x + + + align:start position:0% +x +prime is equal x minus vt and t prime is + + align:start position:0% +prime is equal x minus vt and t prime is + + + align:start position:0% +prime is equal x minus vt and t prime is +equal to t + + align:start position:0% +equal to t + + + align:start position:0% +equal to t +okay this checks out because this is our + + align:start position:0% +okay this checks out because this is our + + + align:start position:0% +okay this checks out because this is our +galilean transformation so for systems + + align:start position:0% +galilean transformation so for systems + + + align:start position:0% +galilean transformation so for systems +which move relative with very low + + align:start position:0% +which move relative with very low + + + align:start position:0% +which move relative with very low +difference in velocities you can use + + align:start position:0% +difference in velocities you can use + + + align:start position:0% +difference in velocities you can use +galilean transformation as an + + align:start position:0% +galilean transformation as an + + + align:start position:0% +galilean transformation as an +approximation of launch transformation + + align:start position:0% +approximation of launch transformation + + + align:start position:0% +approximation of launch transformation +okay at the third part now we can + + align:start position:0% +okay at the third part now we can + + + align:start position:0% +okay at the third part now we can +investigate a little bit further + + align:start position:0% +investigate a little bit further + + + align:start position:0% +investigate a little bit further +for example what happens now to a + + align:start position:0% +for example what happens now to a + + + align:start position:0% +for example what happens now to a +distance + + align:start position:0% +distance + + + align:start position:0% +distance +just a measure of distance or measure of + + align:start position:0% +just a measure of distance or measure of + + + align:start position:0% +just a measure of distance or measure of +length which we obtain by making this + + align:start position:0% +length which we obtain by making this + + + align:start position:0% +length which we obtain by making this +measurement + + align:start position:0% +measurement + + + align:start position:0% +measurement +at + + align:start position:0% +at + + + align:start position:0% +at +simultaneously at t1 equal to t2 we find + + align:start position:0% +simultaneously at t1 equal to t2 we find + + + align:start position:0% +simultaneously at t1 equal to t2 we find +delta x prime is equal to gamma delta x + + align:start position:0% +delta x prime is equal to gamma delta x + + + align:start position:0% +delta x prime is equal to gamma delta x +all right that's length contraction + + align:start position:0% +all right that's length contraction + + + align:start position:0% +all right that's length contraction +if we do the same thing for delta t for + + align:start position:0% +if we do the same thing for delta t for + + + align:start position:0% +if we do the same thing for delta t for +measure doing the measurement of time at + + align:start position:0% +measure doing the measurement of time at + + + align:start position:0% +measure doing the measurement of time at +x equal x2 equal x1 we find time + + align:start position:0% +x equal x2 equal x1 we find time + + + align:start position:0% +x equal x2 equal x1 we find time +relation + + align:start position:0% +relation + + + align:start position:0% +relation +all right is exactly what we expect + + align:start position:0% +all right is exactly what we expect + + + align:start position:0% +all right is exactly what we expect +and then we can look at two events which + + align:start position:0% +and then we can look at two events which + + + align:start position:0% +and then we can look at two events which +happen at the same time in frame s + + align:start position:0% +happen at the same time in frame s + + + align:start position:0% +happen at the same time in frame s +um and see what happens to the time as + + align:start position:0% +um and see what happens to the time as + + + align:start position:0% +um and see what happens to the time as +measured in system s prime + + align:start position:0% +measured in system s prime + + + align:start position:0% +measured in system s prime +delta t t prime is equal to gamma delta + + align:start position:0% +delta t t prime is equal to gamma delta + + + align:start position:0% +delta t t prime is equal to gamma delta +t well in this example we set this to + + align:start position:0% +t well in this example we set this to + + + align:start position:0% +t well in this example we set this to +zero and then we have the second term + + align:start position:0% +zero and then we have the second term + + + align:start position:0% +zero and then we have the second term +which is minus beta over c gamma delta x + + align:start position:0% +which is minus beta over c gamma delta x + + + align:start position:0% +which is minus beta over c gamma delta x +so we find that + + align:start position:0% +so we find that + + + align:start position:0% +so we find that +while this event happens simultaneously + + align:start position:0% +while this event happens simultaneously + + + align:start position:0% +while this event happens simultaneously +in our frame as s1 and s + + align:start position:0% +in our frame as s1 and s + + + align:start position:0% +in our frame as s1 and s +it does not happen simultaneously in our + + align:start position:0% +it does not happen simultaneously in our + + + align:start position:0% +it does not happen simultaneously in our +frame as prime + + align:start position:0% +frame as prime + + + align:start position:0% +frame as prime +um there's an extra term which is uh not + + align:start position:0% +um there's an extra term which is uh not + + + align:start position:0% +um there's an extra term which is uh not +zero unless you actually measure at the + + align:start position:0% +zero unless you actually measure at the + + + align:start position:0% +zero unless you actually measure at the +very same point + + align:start position:0% +very same point + + + align:start position:0% +very same point +um if l is equal to zero so this is the + + align:start position:0% +um if l is equal to zero so this is the + + + align:start position:0% +um if l is equal to zero so this is the +relativity of simultaneous 80. again + + align:start position:0% +relativity of simultaneous 80. again + + + align:start position:0% +relativity of simultaneous 80. again +this checks out and i think we're good + + align:start position:0% +this checks out and i think we're good + + + align:start position:0% +this checks out and i think we're good +with our launch transformation \ No newline at end of file diff --git a/_p3NpyfNp78.txt b/_p3NpyfNp78.txt new file mode 100644 index 0000000000000000000000000000000000000000..da06316188ce73c043252d9aa363c353048e94b1 --- /dev/null +++ b/_p3NpyfNp78.txt @@ -0,0 +1,2515 @@ +align:start position:0% + +good morning we're gonna continue doing + + align:start position:0% +good morning we're gonna continue doing + + + align:start position:0% +good morning we're gonna continue doing +perturbation theory today we'll finish + + align:start position:0% +perturbation theory today we'll finish + + + align:start position:0% +perturbation theory today we'll finish +doing non-degenerate perturbation theory + + align:start position:0% +doing non-degenerate perturbation theory + + + align:start position:0% +doing non-degenerate perturbation theory +and then turn to the generate + + align:start position:0% +and then turn to the generate + + + align:start position:0% +and then turn to the generate +perturbation theory as well we had + + align:start position:0% +perturbation theory as well we had + + + align:start position:0% +perturbation theory as well we had +computed already the first order + + align:start position:0% +computed already the first order + + + align:start position:0% +computed already the first order +corrections to the state first-order + + align:start position:0% +corrections to the state first-order + + + align:start position:0% +corrections to the state first-order +corrections to the energy and second + + align:start position:0% +corrections to the energy and second + + + align:start position:0% +corrections to the energy and second +order correction to the energy so here + + align:start position:0% +order correction to the energy so here + + + align:start position:0% +order correction to the energy so here +in this formula that I've written are + + align:start position:0% +in this formula that I've written are + + + align:start position:0% +in this formula that I've written are +all the results we have so far and the + + align:start position:0% +all the results we have so far and the + + + align:start position:0% +all the results we have so far and the +useful thing is to ask yourself whether + + align:start position:0% +useful thing is to ask yourself whether + + + align:start position:0% +useful thing is to ask yourself whether +you know what every symbol here means + + align:start position:0% +you know what every symbol here means + + + align:start position:0% +you know what every symbol here means +this is the state which is the + + align:start position:0% +this is the state which is the + + + align:start position:0% +this is the state which is the +deformation of the original state and + + align:start position:0% +deformation of the original state and + + + align:start position:0% +deformation of the original state and +zero of the hamiltonian h0 with a + + align:start position:0% +zero of the hamiltonian h0 with a + + + align:start position:0% +zero of the hamiltonian h0 with a +hamiltonian h of lamda which was equal + + align:start position:0% +hamiltonian h of lamda which was equal + + + align:start position:0% +hamiltonian h of lamda which was equal +to H 0 plus lambda Delta H and M 0 was + + align:start position:0% +to H 0 plus lambda Delta H and M 0 was + + + align:start position:0% +to H 0 plus lambda Delta H and M 0 was +an eigenstate of H 0 with energy E and 0 + + align:start position:0% +an eigenstate of H 0 with energy E and 0 + + + align:start position:0% +an eigenstate of H 0 with energy E and 0 +and we found that as you turn on lambda + + align:start position:0% +and we found that as you turn on lambda + + + align:start position:0% +and we found that as you turn on lambda +lambda becomes nonzero the energies + + align:start position:0% +lambda becomes nonzero the energies + + + align:start position:0% +lambda becomes nonzero the energies +change the state the eigenstate changes + + align:start position:0% +change the state the eigenstate changes + + + align:start position:0% +change the state the eigenstate changes +and here is lambda or first order in + + align:start position:0% +and here is lambda or first order in + + + align:start position:0% +and here is lambda or first order in +lambda second order in lambda we didn't + + align:start position:0% +lambda second order in lambda we didn't + + + align:start position:0% +lambda second order in lambda we didn't +compute the state to second order in + + align:start position:0% +compute the state to second order in + + + align:start position:0% +compute the state to second order in +lambda moreover we have this symbol + + align:start position:0% +lambda moreover we have this symbol + + + align:start position:0% +lambda moreover we have this symbol +Delta H K and that was defined to be the + + align:start position:0% +Delta H K and that was defined to be the + + + align:start position:0% +Delta H K and that was defined to be the +matrix element on the unperturbed + + align:start position:0% +matrix element on the unperturbed + + + align:start position:0% +matrix element on the unperturbed +eigenstate of the operator Delta H so + + align:start position:0% +eigenstate of the operator Delta H so + + + align:start position:0% +eigenstate of the operator Delta H so +that's another symbol in here we're + + align:start position:0% +that's another symbol in here we're + + + align:start position:0% +that's another symbol in here we're +summing over all states in the spectrum + + align:start position:0% +summing over all states in the spectrum + + + align:start position:0% +summing over all states in the spectrum +except for the state n here because the + + align:start position:0% +except for the state n here because the + + + align:start position:0% +except for the state n here because the +denominator here would give you a 0 and + + align:start position:0% +denominator here would give you a 0 and + + + align:start position:0% +denominator here would give you a 0 and +this would be problematic in general so + + align:start position:0% +this would be problematic in general so + + + align:start position:0% +this would be problematic in general so +that was what we derived and this are + + align:start position:0% +that was what we derived and this are + + + align:start position:0% +that was what we derived and this are +the formulas we have + + align:start position:0% +the formulas we have + + + align:start position:0% +the formulas we have +it's worth making a few remarks as to + + align:start position:0% +it's worth making a few remarks as to + + + align:start position:0% +it's worth making a few remarks as to +what we see from this firm is because + + align:start position:0% +what we see from this firm is because + + + align:start position:0% +what we see from this firm is because +they're a little complicated and you may + + align:start position:0% +they're a little complicated and you may + + + align:start position:0% +they're a little complicated and you may +not have a immediate intuition about it + + align:start position:0% +not have a immediate intuition about it + + + align:start position:0% +not have a immediate intuition about it +so a few remarks marks and the first one + + align:start position:0% +so a few remarks marks and the first one + + + align:start position:0% +so a few remarks marks and the first one +concern in fact both remarks that I'm + + align:start position:0% +concern in fact both remarks that I'm + + + align:start position:0% +concern in fact both remarks that I'm +gonna make concern the behavior of the + + align:start position:0% +gonna make concern the behavior of the + + + align:start position:0% +gonna make concern the behavior of the +energy as represented by this formula + + align:start position:0% +energy as represented by this formula + + + align:start position:0% +energy as represented by this formula +first remark is that if you were to look + + align:start position:0% +first remark is that if you were to look + + + align:start position:0% +first remark is that if you were to look +at the ground state energy of the system + + align:start position:0% +at the ground state energy of the system + + + align:start position:0% +at the ground state energy of the system +the first two terms here so for N equals + + align:start position:0% +the first two terms here so for N equals + + + align:start position:0% +the first two terms here so for N equals +zero if we call the ground state by the + + align:start position:0% +zero if we call the ground state by the + + + align:start position:0% +zero if we call the ground state by the +label N equals zero for the state N + + align:start position:0% +label N equals zero for the state N + + + align:start position:0% +label N equals zero for the state N +equals zero this first two terms on the + + align:start position:0% +equals zero this first two terms on the + + + align:start position:0% +equals zero this first two terms on the +energy overestimate the ground state + + align:start position:0% +energy overestimate the ground state + + + align:start position:0% +energy overestimate the ground state +energy they always give you more than + + align:start position:0% +energy they always give you more than + + + align:start position:0% +energy they always give you more than +what the true ground state energy is for + + align:start position:0% +what the true ground state energy is for + + + align:start position:0% +what the true ground state energy is for +any value of lambda that is kind of + + align:start position:0% +any value of lambda that is kind of + + + align:start position:0% +any value of lambda that is kind of +plausible given that you see here that + + align:start position:0% +plausible given that you see here that + + + align:start position:0% +plausible given that you see here that +for the ground state energy when n is + + align:start position:0% +for the ground state energy when n is + + + align:start position:0% +for the ground state energy when n is +equal to zero and it's the lowest energy + + align:start position:0% +equal to zero and it's the lowest energy + + + align:start position:0% +equal to zero and it's the lowest energy +State these differences are all positive + + align:start position:0% +State these differences are all positive + + + align:start position:0% +State these differences are all positive +all these states have more energy + + align:start position:0% +all these states have more energy + + + align:start position:0% +all these states have more energy +therefore this term is negative and the + + align:start position:0% +therefore this term is negative and the + + + align:start position:0% +therefore this term is negative and the +next correction to order lambda square + + align:start position:0% +next correction to order lambda square + + + align:start position:0% +next correction to order lambda square +tends to lower the energy of the ground + + align:start position:0% +tends to lower the energy of the ground + + + align:start position:0% +tends to lower the energy of the ground +state so so the claim is that the first + + align:start position:0% +state so so the claim is that the first + + + align:start position:0% +state so so the claim is that the first +the order lambda result not the order of + + align:start position:0% +the order lambda result not the order of + + + align:start position:0% +the order lambda result not the order of +lambda N or ground state energy + + align:start position:0% + + + + align:start position:0% + +overestimate the true ground state + + align:start position:0% +overestimate the true ground state + + + align:start position:0% +overestimate the true ground state +energy and so how do we see that + + align:start position:0% +energy and so how do we see that + + + align:start position:0% +energy and so how do we see that +so we consider e0 because we're doing N + + align:start position:0% +so we consider e0 because we're doing N + + + align:start position:0% +so we consider e0 because we're doing N +equals 0 this is the ground state we + + align:start position:0% +equals 0 this is the ground state we + + + align:start position:0% +equals 0 this is the ground state we +start labeled with N equals 0 some times + + align:start position:0% +start labeled with N equals 0 some times + + + align:start position:0% +start labeled with N equals 0 some times +0 plus lambda H 0 0 that is the order + + align:start position:0% +0 plus lambda H 0 0 that is the order + + + align:start position:0% +0 plus lambda H 0 0 that is the order +lambda estimate for the ground state + + align:start position:0% +lambda estimate for the ground state + + + align:start position:0% +lambda estimate for the ground state +energy the first term can be viewed as + + align:start position:0% +energy the first term can be viewed as + + + align:start position:0% +energy the first term can be viewed as +the expectation value of the original + + align:start position:0% +the expectation value of the original + + + align:start position:0% +the expectation value of the original +Hamiltonian on the ground state that is + + align:start position:0% +Hamiltonian on the ground state that is + + + align:start position:0% +Hamiltonian on the ground state that is +e 0 because this H 0 on 0 is e 0 0 so + + align:start position:0% +e 0 because this H 0 on 0 is e 0 0 so + + + align:start position:0% +e 0 because this H 0 on 0 is e 0 0 so +this is e 0 0 plus lambda and we also + + align:start position:0% +this is e 0 0 plus lambda and we also + + + align:start position:0% +this is e 0 0 plus lambda and we also +know that I'm I'm sorry here I made a + + align:start position:0% +know that I'm I'm sorry here I made a + + + align:start position:0% +know that I'm I'm sorry here I made a +little mistake that should be Delta H + + align:start position:0% + + + + align:start position:0% + +Delta H 0 plus lambda the expectation + + align:start position:0% +Delta H 0 plus lambda the expectation + + + align:start position:0% +Delta H 0 plus lambda the expectation +value of Delta H on the same state so + + align:start position:0% +value of Delta H on the same state so + + + align:start position:0% +value of Delta H on the same state so +these two things together are nothing + + align:start position:0% +these two things together are nothing + + + align:start position:0% +these two things together are nothing +but the expectation value on the ground + + align:start position:0% +but the expectation value on the ground + + + align:start position:0% +but the expectation value on the ground +state of H 0 plus lambda Delta H that's + + align:start position:0% +state of H 0 plus lambda Delta H that's + + + align:start position:0% +state of H 0 plus lambda Delta H that's +kind of nice isn't it that these two + + align:start position:0% +kind of nice isn't it that these two + + + align:start position:0% +kind of nice isn't it that these two +terms really are nothing else but the + + align:start position:0% +terms really are nothing else but the + + + align:start position:0% +terms really are nothing else but the +expectation value on the ground state + + align:start position:0% +expectation value on the ground state + + + align:start position:0% +expectation value on the ground state +of this thing that we called H of lambda + + align:start position:0% + + + + align:start position:0% + +and now comes the variational principle + + align:start position:0% +and now comes the variational principle + + + align:start position:0% +and now comes the variational principle +that says that if you evaluate the + + align:start position:0% +that says that if you evaluate the + + + align:start position:0% +that says that if you evaluate the +Hamiltonian on an arbitrary state + + align:start position:0% +Hamiltonian on an arbitrary state + + + align:start position:0% +Hamiltonian on an arbitrary state +expectation value of the Hamilton in an + + align:start position:0% +expectation value of the Hamilton in an + + + align:start position:0% +expectation value of the Hamilton in an +arbitrary state you get more energy than + + align:start position:0% +arbitrary state you get more energy than + + + align:start position:0% +arbitrary state you get more energy than +the ground state energy of the system + + align:start position:0% +the ground state energy of the system + + + align:start position:0% +the ground state energy of the system +you always get more when you hit the + + align:start position:0% +you always get more when you hit the + + + align:start position:0% +you always get more when you hit the +grounds that you get the lowest value so + + align:start position:0% +grounds that you get the lowest value so + + + align:start position:0% +grounds that you get the lowest value so +look at that this is the Hamiltonian and + + align:start position:0% +look at that this is the Hamiltonian and + + + align:start position:0% +look at that this is the Hamiltonian and +this is the unperturbed ground state + + align:start position:0% +this is the unperturbed ground state + + + align:start position:0% +this is the unperturbed ground state +this is not the real ground state the + + align:start position:0% +this is not the real ground state the + + + align:start position:0% +this is not the real ground state the +real branch is what we're trying to find + + align:start position:0% +real branch is what we're trying to find + + + align:start position:0% +real branch is what we're trying to find +so this is like saying okay you're + + align:start position:0% +so this is like saying okay you're + + + align:start position:0% +so this is like saying okay you're +evaluating the exact Hamiltonian on some + + align:start position:0% +evaluating the exact Hamiltonian on some + + + align:start position:0% +evaluating the exact Hamiltonian on some +arbitrary state therefore this is + + align:start position:0% +arbitrary state therefore this is + + + align:start position:0% +arbitrary state therefore this is +greater than or equal to the true ground + + align:start position:0% +greater than or equal to the true ground + + + align:start position:0% +greater than or equal to the true ground +state energy that we would call a 0 + + align:start position:0% +state energy that we would call a 0 + + + align:start position:0% +state energy that we would call a 0 +lambda true ground state energy which in + + align:start position:0% +lambda true ground state energy which in + + + align:start position:0% +lambda true ground state energy which in +that notation indeed is e 0 lambda so + + align:start position:0% +that notation indeed is e 0 lambda so + + + align:start position:0% +that notation indeed is e 0 lambda so +that's a nice result and it matches with + + align:start position:0% +that's a nice result and it matches with + + + align:start position:0% +that's a nice result and it matches with +the idea that for the ground state + + align:start position:0% + + + + align:start position:0% + +ground state the order lambda squared + + align:start position:0% +ground state the order lambda squared + + + align:start position:0% +ground state the order lambda squared +correction is minus lambda squared the + + align:start position:0% +correction is minus lambda squared the + + + align:start position:0% +correction is minus lambda squared the +sum over K different from 0 delta h k0 + + align:start position:0% +sum over K different from 0 delta h k0 + + + align:start position:0% +sum over K different from 0 delta h k0 +squared over EK minus e0 0 and this + + align:start position:0% +squared over EK minus e0 0 and this + + + align:start position:0% +squared over EK minus e0 0 and this +thing as we mentioned the numerator is + + align:start position:0% +thing as we mentioned the numerator is + + + align:start position:0% +thing as we mentioned the numerator is +positive the denominator is positive + + align:start position:0% +positive the denominator is positive + + + align:start position:0% +positive the denominator is positive +because this was the ground shake and + + align:start position:0% +because this was the ground shake and + + + align:start position:0% +because this was the ground shake and +this is a non degenerate ground state + + align:start position:0% +this is a non degenerate ground state + + + align:start position:0% +this is a non degenerate ground state +and K therefore has more energy here + + align:start position:0% +and K therefore has more energy here + + + align:start position:0% +and K therefore has more energy here +zero so everything is positive so this + + align:start position:0% +zero so everything is positive so this + + + align:start position:0% +zero so everything is positive so this +is negative and it is negative so + + align:start position:0% +is negative and it is negative so + + + align:start position:0% +is negative and it is negative so +actually here there is a generalization + + align:start position:0% +actually here there is a generalization + + + align:start position:0% +actually here there is a generalization +of this observation and you can imagine + + align:start position:0% +of this observation and you can imagine + + + align:start position:0% +of this observation and you can imagine +that you have now a particular state and + + align:start position:0% +that you have now a particular state and + + + align:start position:0% +that you have now a particular state and +here then you have all these states that + + align:start position:0% +here then you have all these states that + + + align:start position:0% +here then you have all these states that +are above and all these days that are + + align:start position:0% +are above and all these days that are + + + align:start position:0% +are above and all these days that are +below so let's look at the second order + + align:start position:0% +below so let's look at the second order + + + align:start position:0% +below so let's look at the second order +correction to the energy of the state e + + align:start position:0% +correction to the energy of the state e + + + align:start position:0% +correction to the energy of the state e +n the second order correction the first + + align:start position:0% +n the second order correction the first + + + align:start position:0% +n the second order correction the first +order correction shifts the energies + + align:start position:0% +order correction shifts the energies + + + align:start position:0% +order correction shifts the energies +proportional to Delta H and n but the + + align:start position:0% +proportional to Delta H and n but the + + + align:start position:0% +proportional to Delta H and n but the +second order correction is minus lambda + + align:start position:0% +second order correction is minus lambda + + + align:start position:0% +second order correction is minus lambda +squared the sum over K different from n + + align:start position:0% +squared the sum over K different from n + + + align:start position:0% +squared the sum over K different from n +so let's split it K greater than N and + + align:start position:0% +so let's split it K greater than N and + + + align:start position:0% +so let's split it K greater than N and +we'll write the same thing H K N squared + + align:start position:0% +we'll write the same thing H K N squared + + + align:start position:0% +we'll write the same thing H K N squared +over e K 0 minus e and 0 and then I want + + align:start position:0% +over e K 0 minus e and 0 and then I want + + + align:start position:0% +over e K 0 minus e and 0 and then I want +to write the other states the states + + align:start position:0% +to write the other states the states + + + align:start position:0% +to write the other states the states +where K is less than n but let me do one + + align:start position:0% +where K is less than n but let me do one + + + align:start position:0% +where K is less than n but let me do one +thing here on those states I'll switch + + align:start position:0% +thing here on those states I'll switch + + + align:start position:0% +thing here on those states I'll switch +the order of the some output II end 0 + + align:start position:0% +the order of the some output II end 0 + + + align:start position:0% +the order of the some output II end 0 +the order of the sign in the denominator + + align:start position:0% +the order of the sign in the denominator + + + align:start position:0% +the order of the sign in the denominator +EK 0 and change the sign here so this + + align:start position:0% +EK 0 and change the sign here so this + + + align:start position:0% +EK 0 and change the sign here so this +two changes of sign are correlated I + + align:start position:0% +two changes of sign are correlated I + + + align:start position:0% +two changes of sign are correlated I +change the sign in the denominator and I + + align:start position:0% +change the sign in the denominator and I + + + align:start position:0% +change the sign in the denominator and I +change the sign in front and now we see + + align:start position:0% +change the sign in front and now we see + + + align:start position:0% +change the sign in front and now we see +the following all these states that are + + align:start position:0% +the following all these states that are + + + align:start position:0% +the following all these states that are +above n + + align:start position:0% +above n + + + align:start position:0% +above n +cabe is greater than end this difference + + align:start position:0% +cabe is greater than end this difference + + + align:start position:0% +cabe is greater than end this difference +is positive this is manifestly positive + + align:start position:0% +is positive this is manifestly positive + + + align:start position:0% +is positive this is manifestly positive +this is negative so this state are kind + + align:start position:0% +this is negative so this state are kind + + + align:start position:0% +this is negative so this state are kind +of pushing your state down the fact of + + align:start position:0% +of pushing your state down the fact of + + + align:start position:0% +of pushing your state down the fact of +this states on top is a negative + + align:start position:0% +this states on top is a negative + + + align:start position:0% +this states on top is a negative +correction or pushing the states down on + + align:start position:0% +correction or pushing the states down on + + + align:start position:0% +correction or pushing the states down on +the other hand the lower states the + + align:start position:0% +the other hand the lower states the + + + align:start position:0% +the other hand the lower states the +states with K less than and again I've + + align:start position:0% +states with K less than and again I've + + + align:start position:0% +states with K less than and again I've +ordered it now conveniently all the + + align:start position:0% +ordered it now conveniently all the + + + align:start position:0% +ordered it now conveniently all the +states K now have less energy so this is + + align:start position:0% +states K now have less energy so this is + + + align:start position:0% +states K now have less energy so this is +positive this is positive this is + + align:start position:0% +positive this is positive this is + + + align:start position:0% +positive this is positive this is +positive so this states over here are + + align:start position:0% +positive so this states over here are + + + align:start position:0% +positive so this states over here are +actually pushing that state up so the + + align:start position:0% +actually pushing that state up so the + + + align:start position:0% +actually pushing that state up so the +upper states are pushing it down the + + align:start position:0% +upper states are pushing it down the + + + align:start position:0% +upper states are pushing it down the +lowers are pushing it up this is usually + + align:start position:0% +lowers are pushing it up this is usually + + + align:start position:0% +lowers are pushing it up this is usually +referred to as level repulsion the + + align:start position:0% +referred to as level repulsion the + + + align:start position:0% +referred to as level repulsion the +levels repel each other the upper states + + align:start position:0% +levels repel each other the upper states + + + align:start position:0% +levels repel each other the upper states +don't want the state end to go close to + + align:start position:0% +don't want the state end to go close to + + + align:start position:0% +don't want the state end to go close to +them the lower states don't want them to + + align:start position:0% +them the lower states don't want them to + + + align:start position:0% +them the lower states don't want them to +go close to them either so it's a nice + + align:start position:0% +go close to them either so it's a nice + + + align:start position:0% +go close to them either so it's a nice +dynamic that helps you understand what's + + align:start position:0% +dynamic that helps you understand what's + + + align:start position:0% +dynamic that helps you understand what's +going on here another point we want to + + align:start position:0% +going on here another point we want to + + + align:start position:0% +going on here another point we want to +make has to do with the validity of this + + align:start position:0% +make has to do with the validity of this + + + align:start position:0% +make has to do with the validity of this +expansion so when in general when you + + align:start position:0% +expansion so when in general when you + + + align:start position:0% +expansion so when in general when you +have serious expansions the issues of + + align:start position:0% +have serious expansions the issues of + + + align:start position:0% +have serious expansions the issues of +convergence are delicate so we we can + + align:start position:0% +convergence are delicate so we we can + + + align:start position:0% +convergence are delicate so we we can +get a lot of insight just by doing an + + align:start position:0% +get a lot of insight just by doing an + + + align:start position:0% +get a lot of insight just by doing an +example so let me talk about the + + align:start position:0% +example so let me talk about the + + + align:start position:0% +example so let me talk about the +validity of the perturbation series this + + align:start position:0% +validity of the perturbation series this + + + align:start position:0% +validity of the perturbation series this +is supposed to give us some insight one + + align:start position:0% +is supposed to give us some insight one + + + align:start position:0% +is supposed to give us some insight one +thing we've said is that we think delt + + align:start position:0% +thing we've said is that we think delt + + + align:start position:0% +thing we've said is that we think delt +gamma lambda sorry Delta EIJ is supposed + + align:start position:0% +gamma lambda sorry Delta EIJ is supposed + + + align:start position:0% +gamma lambda sorry Delta EIJ is supposed +to be smaller than h0 now these are + + align:start position:0% +to be smaller than h0 now these are + + + align:start position:0% +to be smaller than h0 now these are +operators so the statement that they're + + align:start position:0% +operators so the statement that they're + + + align:start position:0% +operators so the statement that they're +smaller has to be made more + + align:start position:0% +smaller has to be made more + + + align:start position:0% +smaller has to be made more +what is the size of an operator and you + + align:start position:0% +what is the size of an operator and you + + + align:start position:0% +what is the size of an operator and you +could think well we could say the + + align:start position:0% +could think well we could say the + + + align:start position:0% +could think well we could say the +entries of the matrix elements should be + + align:start position:0% +entries of the matrix elements should be + + + align:start position:0% +entries of the matrix elements should be +much smaller and that is true but it's + + align:start position:0% +much smaller and that is true but it's + + + align:start position:0% +much smaller and that is true but it's +not enough for that let's consider an + + align:start position:0% +not enough for that let's consider an + + + align:start position:0% +not enough for that let's consider an +example so this will be a two by two + + align:start position:0% +example so this will be a two by two + + + align:start position:0% +example so this will be a two by two +matrix from Antonio in which H of lambda + + align:start position:0% +matrix from Antonio in which H of lambda + + + align:start position:0% +matrix from Antonio in which H of lambda +will be given by some H zero plus lambda + + align:start position:0% +will be given by some H zero plus lambda + + + align:start position:0% +will be given by some H zero plus lambda +V hat which will be e 1 0 e 2 0 plus + + align:start position:0% +V hat which will be e 1 0 e 2 0 plus + + + align:start position:0% +V hat which will be e 1 0 e 2 0 plus +lambda that V hat matrix will be of the + + align:start position:0% +lambda that V hat matrix will be of the + + + align:start position:0% +lambda that V hat matrix will be of the +form V V star it must be hermitian so V + + align:start position:0% +form V V star it must be hermitian so V + + + align:start position:0% +form V V star it must be hermitian so V +is a number V stars the complex + + align:start position:0% +is a number V stars the complex + + + align:start position:0% +is a number V stars the complex +conjugate these are the two energies + + align:start position:0% +conjugate these are the two energies + + + align:start position:0% +conjugate these are the two energies +those because the Hamiltonian is known + + align:start position:0% +those because the Hamiltonian is known + + + align:start position:0% +those because the Hamiltonian is known +each time we talk about the Hamiltonian + + align:start position:0% +each time we talk about the Hamiltonian + + + align:start position:0% +each time we talk about the Hamiltonian +that is known we write it as a diagonal + + align:start position:0% +that is known we write it as a diagonal + + + align:start position:0% +that is known we write it as a diagonal +matrix where we're saying yes that is + + align:start position:0% +matrix where we're saying yes that is + + + align:start position:0% +matrix where we're saying yes that is +the matrix elements of the Hamiltonian + + align:start position:0% +the matrix elements of the Hamiltonian + + + align:start position:0% +the matrix elements of the Hamiltonian +in the basis of eigenstates which we + + align:start position:0% +in the basis of eigenstates which we + + + align:start position:0% +in the basis of eigenstates which we +know so unknown Hamiltonian you can + + align:start position:0% +know so unknown Hamiltonian you can + + + align:start position:0% +know so unknown Hamiltonian you can +represent by a diagonal matrix so here + + align:start position:0% +represent by a diagonal matrix so here + + + align:start position:0% +represent by a diagonal matrix so here +is our whole matrix H of lambda + + align:start position:0% + + + + align:start position:0% + +and you could say all right our + + align:start position:0% +and you could say all right our + + + align:start position:0% +and you could say all right our +perturbation theory practically speaking + + align:start position:0% +perturbation theory practically speaking + + + align:start position:0% +perturbation theory practically speaking +is this formulas that allow us to + + align:start position:0% +is this formulas that allow us to + + + align:start position:0% +is this formulas that allow us to +compute the eigenvalues of this matrices + + align:start position:0% +compute the eigenvalues of this matrices + + + align:start position:0% +compute the eigenvalues of this matrices +which are of this matrix which is the + + align:start position:0% +which are of this matrix which is the + + + align:start position:0% +which are of this matrix which is the +energies of the system of the + + align:start position:0% +energies of the system of the + + + align:start position:0% +energies of the system of the +eigenstates and compute the eigenstates + + align:start position:0% +eigenstates and compute the eigenstates + + + align:start position:0% +eigenstates and compute the eigenstates +for H 0 these are the eigen values and + + align:start position:0% +for H 0 these are the eigen values and + + + align:start position:0% +for H 0 these are the eigen values and +the eigen states are 1 0 and 0 1 so + + align:start position:0% +the eigen states are 1 0 and 0 1 so + + + align:start position:0% +the eigen states are 1 0 and 0 1 so +perturbation theory is really you can + + align:start position:0% +perturbation theory is really you can + + + align:start position:0% +perturbation theory is really you can +think in terms of hamiltonians but also + + align:start position:0% +think in terms of hamiltonians but also + + + align:start position:0% +think in terms of hamiltonians but also +you can think of it in terms of matrices + + align:start position:0% +you can think of it in terms of matrices + + + align:start position:0% +you can think of it in terms of matrices +is allowing you to find the eigenvalues + + align:start position:0% +is allowing you to find the eigenvalues + + + align:start position:0% +is allowing you to find the eigenvalues +and eigenvectors of these matrices so + + align:start position:0% +and eigenvectors of these matrices so + + + align:start position:0% +and eigenvectors of these matrices so +let's this is a 2 by 2 matrix with + + align:start position:0% +let's this is a 2 by 2 matrix with + + + align:start position:0% +let's this is a 2 by 2 matrix with +numbers you know how to compute the + + align:start position:0% +numbers you know how to compute the + + + align:start position:0% +numbers you know how to compute the +eigenvalues so I'll give you the answer + + align:start position:0% +eigenvalues so I'll give you the answer + + + align:start position:0% +eigenvalues so I'll give you the answer +the eigenvalues a plus minus are e 1 + + align:start position:0% +the eigenvalues a plus minus are e 1 + + + align:start position:0% +the eigenvalues a plus minus are e 1 +plus e 2 over 2 plus minus e1 minus e2 + + align:start position:0% +plus e 2 over 2 plus minus e1 minus e2 + + + align:start position:0% +plus e 2 over 2 plus minus e1 minus e2 +over 2 times the square root of 1 plus + + align:start position:0% +over 2 times the square root of 1 plus + + + align:start position:0% +over 2 times the square root of 1 plus +lambda squared absolute value of v2 + + align:start position:0% +lambda squared absolute value of v2 + + + align:start position:0% +lambda squared absolute value of v2 +squared e 1 minus e 2 over 2 squared + + align:start position:0% +squared e 1 minus e 2 over 2 squared + + + align:start position:0% +squared e 1 minus e 2 over 2 squared +long formula that's it those are the + + align:start position:0% +long formula that's it those are the + + + align:start position:0% +long formula that's it those are the +exact things if + + align:start position:0% +exact things if + + + align:start position:0% +exact things if +you wanted to see this as a result in + + align:start position:0% +you wanted to see this as a result in + + + align:start position:0% +you wanted to see this as a result in +perturbation theory you would say well + + align:start position:0% +perturbation theory you would say well + + + align:start position:0% +perturbation theory you would say well +lambda squared V squared or lambda V is + + align:start position:0% +lambda squared V squared or lambda V is + + + align:start position:0% +lambda squared V squared or lambda V is +small and I'm gonna think of this term + + align:start position:0% +small and I'm gonna think of this term + + + align:start position:0% +small and I'm gonna think of this term +as small and I'm gonna expand this + + align:start position:0% +as small and I'm gonna expand this + + + align:start position:0% +as small and I'm gonna expand this +square root and if I expand the square + + align:start position:0% +square root and if I expand the square + + + align:start position:0% +square root and if I expand the square +root I'm gonna get all kinds of terms + + align:start position:0% +root I'm gonna get all kinds of terms + + + align:start position:0% +root I'm gonna get all kinds of terms +with different powers of lambda you can + + align:start position:0% +with different powers of lambda you can + + + align:start position:0% +with different powers of lambda you can +also see there that there's no energy + + align:start position:0% +also see there that there's no energy + + + align:start position:0% +also see there that there's no energy +correction linear in lambda because when + + align:start position:0% +correction linear in lambda because when + + + align:start position:0% +correction linear in lambda because when +you expand one plus epsilon square root + + align:start position:0% +you expand one plus epsilon square root + + + align:start position:0% +you expand one plus epsilon square root +it's roughly 1 plus epsilon over 2 plus + + align:start position:0% +it's roughly 1 plus epsilon over 2 plus + + + align:start position:0% +it's roughly 1 plus epsilon over 2 plus +dot and therefore when you span the + + align:start position:0% +dot and therefore when you span the + + + align:start position:0% +dot and therefore when you span the +square root the first correction is + + align:start position:0% +square root the first correction is + + + align:start position:0% +square root the first correction is +going to be proportional to lambda + + align:start position:0% +going to be proportional to lambda + + + align:start position:0% +going to be proportional to lambda +squared and that actually conforms to + + align:start position:0% +squared and that actually conforms to + + + align:start position:0% +squared and that actually conforms to +that because the matrix elements of the + + align:start position:0% +that because the matrix elements of the + + + align:start position:0% +that because the matrix elements of the +Hamiltonian Delta H and n along the + + align:start position:0% +Hamiltonian Delta H and n along the + + + align:start position:0% +Hamiltonian Delta H and n along the +diagonals for the perturbation are 0 so + + align:start position:0% +diagonals for the perturbation are 0 so + + + align:start position:0% +diagonals for the perturbation are 0 so +there is no order lambda correction so + + align:start position:0% +there is no order lambda correction so + + + align:start position:0% +there is no order lambda correction so +what do you do here then you must do + + align:start position:0% +what do you do here then you must do + + + align:start position:0% +what do you do here then you must do +this expansion and here I write the + + align:start position:0% +this expansion and here I write the + + + align:start position:0% +this expansion and here I write the +relevant series f of Z if you define it + + align:start position:0% +relevant series f of Z if you define it + + + align:start position:0% +relevant series f of Z if you define it +as 1 plus Z squared is equal 1 plus Z + + align:start position:0% +as 1 plus Z squared is equal 1 plus Z + + + align:start position:0% +as 1 plus Z squared is equal 1 plus Z +squared over 2 minus Z fourth over 8 + + align:start position:0% +squared over 2 minus Z fourth over 8 + + + align:start position:0% +squared over 2 minus Z fourth over 8 +plus Z 6 over 6 and it's not that simple + + align:start position:0% +plus Z 6 over 6 and it's not that simple + + + align:start position:0% +plus Z 6 over 6 and it's not that simple +after that minus 5 over 128 Z to the + + align:start position:0% +after that minus 5 over 128 Z to the + + + align:start position:0% +after that minus 5 over 128 Z to the +eighth plus order Z to the 10 so that's + + align:start position:0% +eighth plus order Z to the 10 so that's + + + align:start position:0% +eighth plus order Z to the 10 so that's +this perturbative series expansion that + + align:start position:0% +this perturbative series expansion that + + + align:start position:0% +this perturbative series expansion that +you would use here and how good is the + + align:start position:0% +you would use here and how good is the + + + align:start position:0% +you would use here and how good is the +convergence of this series well it it's + + align:start position:0% +convergence of this series well it it's + + + align:start position:0% +convergence of this series well it it's +okay it it's something that when you + + align:start position:0% +okay it it's something that when you + + + align:start position:0% +okay it it's something that when you +study complex analysis you see this + + align:start position:0% +study complex analysis you see this + + + align:start position:0% +study complex analysis you see this +function 1 plus square root of Z square + + align:start position:0% +function 1 plus square root of Z square + + + align:start position:0% +function 1 plus square root of Z square +it has branch cuts at I and that - I in + + align:start position:0% +it has branch cuts at I and that - I in + + + align:start position:0% +it has branch cuts at I and that - I in +the complex plane in the Z complex plane + + align:start position:0% +the complex plane in the Z complex plane + + + align:start position:0% +the complex plane in the Z complex plane +those are the branch cuts these are the + + align:start position:0% +those are the branch cuts these are the + + + align:start position:0% +those are the branch cuts these are the +places where this square root becomes + + align:start position:0% +places where this square root becomes + + + align:start position:0% +places where this square root becomes +zero and you have to deal with them and + + align:start position:0% +zero and you have to deal with them and + + + align:start position:0% +zero and you have to deal with them and +the function is convergent only up to + + align:start position:0% +the function is convergent only up to + + + align:start position:0% +the function is convergent only up to +here there is a radius of convergence + + align:start position:0% +here there is a radius of convergence + + + align:start position:0% +here there is a radius of convergence +the radius of convergence is one you can + + align:start position:0% +the radius of convergence is one you can + + + align:start position:0% +the radius of convergence is one you can +try it with a mathematical or with a + + align:start position:0% +try it with a mathematical or with a + + + align:start position:0% +try it with a mathematical or with a +program and see take 30 terms for the + + align:start position:0% +program and see take 30 terms for the + + + align:start position:0% +program and see take 30 terms for the +terms and you will see that as long as + + align:start position:0% +terms and you will see that as long as + + + align:start position:0% +terms and you will see that as long as +you take a point Z here it converges you + + align:start position:0% +you take a point Z here it converges you + + + align:start position:0% +you take a point Z here it converges you +take a point a little bit out it blows + + align:start position:0% +take a point a little bit out it blows + + + align:start position:0% +take a point a little bit out it blows +up the series so it has a radius of + + align:start position:0% +up the series so it has a radius of + + + align:start position:0% +up the series so it has a radius of +convergence that's not so bad + + align:start position:0% +convergence that's not so bad + + + align:start position:0% +convergence that's not so bad +radius of convergence is okay but + + align:start position:0% +radius of convergence is okay but + + + align:start position:0% +radius of convergence is okay but +basically we need Z to be small which + + align:start position:0% +basically we need Z to be small which + + + align:start position:0% +basically we need Z to be small which +corresponds here to the statement that + + align:start position:0% +corresponds here to the statement that + + + align:start position:0% +corresponds here to the statement that +lambda V Z small for a fast convergence + + align:start position:0% +lambda V Z small for a fast convergence + + + align:start position:0% +lambda V Z small for a fast convergence +corresponds to lambda V absolute value + + align:start position:0% +corresponds to lambda V absolute value + + + align:start position:0% +corresponds to lambda V absolute value +being smaller than e 1 0 minus e to 0 + + align:start position:0% +being smaller than e 1 0 minus e to 0 + + + align:start position:0% +being smaller than e 1 0 minus e to 0 +absolute value over to roughly smaller + + align:start position:0% +absolute value over to roughly smaller + + + align:start position:0% +absolute value over to roughly smaller +and now we see that the thing that + + align:start position:0% +and now we see that the thing that + + + align:start position:0% +and now we see that the thing that +matters for a perturbation series to be + + align:start position:0% +matters for a perturbation series to be + + + align:start position:0% +matters for a perturbation series to be +good is also that the perturbation be + + align:start position:0% +good is also that the perturbation be + + + align:start position:0% +good is also that the perturbation be +small compared with the energy + + align:start position:0% +small compared with the energy + + + align:start position:0% +small compared with the energy +differences not just it should be small + + align:start position:0% +differences not just it should be small + + + align:start position:0% +differences not just it should be small +the perturbation it should be small + + align:start position:0% +the perturbation it should be small + + + align:start position:0% +the perturbation it should be small +compared with the energy difference so + + align:start position:0% +compared with the energy difference so + + + align:start position:0% +compared with the energy difference so +if you have a Hamiltonian with a state + + align:start position:0% +if you have a Hamiltonian with a state + + + align:start position:0% +if you have a Hamiltonian with a state +of energy 100 and a state of energy 101 + + align:start position:0% +of energy 100 and a state of energy 101 + + + align:start position:0% +of energy 100 and a state of energy 101 +you might say well if I take a + + align:start position:0% +you might say well if I take a + + + align:start position:0% +you might say well if I take a +perturbation of size 2 or 3 that's very + + align:start position:0% +perturbation of size 2 or 3 that's very + + + align:start position:0% +perturbation of size 2 or 3 that's very +small compared to the energy + + align:start position:0% +small compared to the energy + + + align:start position:0% +small compared to the energy +but it's not kamal compared to the + + align:start position:0% +but it's not kamal compared to the + + + align:start position:0% +but it's not kamal compared to the +difference of energies and that can + + align:start position:0% +difference of energies and that can + + + align:start position:0% +difference of energies and that can +cause the perturbation expansion to go + + align:start position:0% +cause the perturbation expansion to go + + + align:start position:0% +cause the perturbation expansion to go +wrong so this gives you extra insight + + align:start position:0% +wrong so this gives you extra insight + + + align:start position:0% +wrong so this gives you extra insight +that in fact being a small perturbation + + align:start position:0% +that in fact being a small perturbation + + + align:start position:0% +that in fact being a small perturbation +not only means small compared to the + + align:start position:0% +not only means small compared to the + + + align:start position:0% +not only means small compared to the +energies because but also small compared + + align:start position:0% +energies because but also small compared + + + align:start position:0% +energies because but also small compared +with the energy differences something + + align:start position:0% +with the energy differences something + + + align:start position:0% +with the energy differences something +that you see here as well energy + + align:start position:0% +that you see here as well energy + + + align:start position:0% +that you see here as well energy +differences are controlling things and + + align:start position:0% +differences are controlling things and + + + align:start position:0% +differences are controlling things and +if the energy differences are if the + + align:start position:0% +if the energy differences are if the + + + align:start position:0% +if the energy differences are if the +perturbation is not small compared to + + align:start position:0% +perturbation is not small compared to + + + align:start position:0% +perturbation is not small compared to +energy differences then this ratios can + + align:start position:0% +energy differences then this ratios can + + + align:start position:0% +energy differences then this ratios can +be loud rather large and the + + align:start position:0% +be loud rather large and the + + + align:start position:0% +be loud rather large and the +perturbation terms are very large and + + align:start position:0% +perturbation terms are very large and + + + align:start position:0% +perturbation terms are very large and +nothing is very simple so that's what I + + align:start position:0% +nothing is very simple so that's what I + + + align:start position:0% +nothing is very simple so that's what I +wanted to say about the convergence of a + + align:start position:0% +wanted to say about the convergence of a + + + align:start position:0% +wanted to say about the convergence of a +perturbation expansion more rigorous + + align:start position:0% +perturbation expansion more rigorous + + + align:start position:0% +perturbation expansion more rigorous +statements can be made but we're not + + align:start position:0% +statements can be made but we're not + + + align:start position:0% +statements can be made but we're not +going to try to make them here \ No newline at end of file diff --git a/a-w4F0c57nE.txt b/a-w4F0c57nE.txt new file mode 100644 index 0000000000000000000000000000000000000000..f1d09ea4064951b45a7c8552b1baaf84aa1754de --- /dev/null +++ b/a-w4F0c57nE.txt @@ -0,0 +1,4747 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% +of MIT courses visit mitop courseware at + + + align:start position:0% +of MIT courses visit mitop courseware at +ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +hi in today's lesson hopefully we will + + align:start position:0% +hi in today's lesson hopefully we will + + + align:start position:0% +hi in today's lesson hopefully we will +begin to reap the rewards of our + + align:start position:0% +begin to reap the rewards of our + + + align:start position:0% +begin to reap the rewards of our +digression into the subject of linear + + align:start position:0% +digression into the subject of linear + + + align:start position:0% +digression into the subject of linear +algebra recall that in the last few + + align:start position:0% +algebra recall that in the last few + + + align:start position:0% +algebra recall that in the last few +lectures what we have been dealing with + + align:start position:0% +lectures what we have been dealing with + + + align:start position:0% +lectures what we have been dealing with +is the problem of inverting systems of + + align:start position:0% +is the problem of inverting systems of + + + align:start position:0% +is the problem of inverting systems of +linear equations and what we would like + + align:start position:0% +linear equations and what we would like + + + align:start position:0% +linear equations and what we would like +to do today is to tackle the more + + align:start position:0% +to do today is to tackle the more + + + align:start position:0% +to do today is to tackle the more +General problem of inverting systems of + + align:start position:0% +General problem of inverting systems of + + + align:start position:0% +General problem of inverting systems of +equations even if the equations are not + + align:start position:0% +equations even if the equations are not + + + align:start position:0% +equations even if the equations are not +linear + + align:start position:0% +linear + + + align:start position:0% +linear +and with this in mind I simply entitled + + align:start position:0% +and with this in mind I simply entitled + + + align:start position:0% +and with this in mind I simply entitled +today's lesson inverting More General + + align:start position:0% +today's lesson inverting More General + + + align:start position:0% +today's lesson inverting More General +systems of equations and by way of a + + align:start position:0% +systems of equations and by way of a + + + align:start position:0% +systems of equations and by way of a +very brief review recall that given the + + align:start position:0% +very brief review recall that given the + + + align:start position:0% +very brief review recall that given the +linear system y1 equal a11 X1 plus Etc + + align:start position:0% +linear system y1 equal a11 X1 plus Etc + + + align:start position:0% +linear system y1 equal a11 X1 plus Etc +a1n xn up to ynal a N1 X1 plus Etc a NN + + align:start position:0% +a1n xn up to ynal a N1 X1 plus Etc a NN + + + align:start position:0% +a1n xn up to ynal a N1 X1 plus Etc a NN +xn we saw that that system was + + align:start position:0% +xn we saw that that system was + + + align:start position:0% +xn we saw that that system was +invertible meaning what that we could + + align:start position:0% +invertible meaning what that we could + + + align:start position:0% +invertible meaning what that we could +solve this system for the X's as linear + + align:start position:0% +solve this system for the X's as linear + + + align:start position:0% +solve this system for the X's as linear +combination a of the Y's if and only if + + align:start position:0% +combination a of the Y's if and only if + + + align:start position:0% +combination a of the Y's if and only if +the inverse of the Matrix of + + align:start position:0% +the inverse of the Matrix of + + + align:start position:0% +the inverse of the Matrix of +coefficients of this system exists and + + align:start position:0% +coefficients of this system exists and + + + align:start position:0% +coefficients of this system exists and +in terms of determinants recall that + + align:start position:0% +in terms of determinants recall that + + + align:start position:0% +in terms of determinants recall that +that means if and only if the + + align:start position:0% +that means if and only if the + + + align:start position:0% +that means if and only if the +determinant of the Matrix of + + align:start position:0% +determinant of the Matrix of + + + align:start position:0% +determinant of the Matrix of +coefficients is not zero if the + + align:start position:0% +coefficients is not zero if the + + + align:start position:0% +coefficients is not zero if the +determinant of the Matrix of + + align:start position:0% +determinant of the Matrix of + + + align:start position:0% +determinant of the Matrix of +coefficients was Zero then we saw that + + align:start position:0% +coefficients was Zero then we saw that + + + align:start position:0% +coefficients was Zero then we saw that +y1 up to YN are not independent in fact + + align:start position:0% +y1 up to YN are not independent in fact + + + align:start position:0% +y1 up to YN are not independent in fact +in that context that's where we came to + + align:start position:0% +in that context that's where we came to + + + align:start position:0% +in that context that's where we came to +grips with the concept of a + + align:start position:0% +grips with the concept of a + + + align:start position:0% +grips with the concept of a +constraint that the constraint actually + + align:start position:0% +constraint that the constraint actually + + + align:start position:0% +constraint that the constraint actually +turned out to be what the fact that the + + align:start position:0% +turned out to be what the fact that the + + + align:start position:0% +turned out to be what the fact that the +Y's were not independent meaning that we + + align:start position:0% +Y's were not independent meaning that we + + + align:start position:0% +Y's were not independent meaning that we +could express a linear combination of + + align:start position:0% +could express a linear combination of + + + align:start position:0% +could express a linear combination of +the Y's equal to zero so what situation + + align:start position:0% +the Y's equal to zero so what situation + + + align:start position:0% +the Y's equal to zero so what situation +were we at then given a linear system if + + align:start position:0% +were we at then given a linear system if + + + align:start position:0% +were we at then given a linear system if +the Matrix of coefficients does not have + + align:start position:0% +the Matrix of coefficients does not have + + + align:start position:0% +the Matrix of coefficients does not have +its determinant equal to zero the system + + align:start position:0% +its determinant equal to zero the system + + + align:start position:0% +its determinant equal to zero the system +is invertible we can solve for the x's + + align:start position:0% +is invertible we can solve for the x's + + + align:start position:0% +is invertible we can solve for the x's +in terms of the Y's if the determinant + + align:start position:0% +in terms of the Y's if the determinant + + + align:start position:0% +in terms of the Y's if the determinant +of the Matrix of coefficients is zeros + + align:start position:0% +of the Matrix of coefficients is zeros + + + align:start position:0% +of the Matrix of coefficients is zeros +the Y's are not linearly independent in + + align:start position:0% +the Y's are not linearly independent in + + + align:start position:0% +the Y's are not linearly independent in +other words the system is not invertible + + align:start position:0% +other words the system is not invertible + + + align:start position:0% +other words the system is not invertible +and now what we would like to do is to + + align:start position:0% +and now what we would like to do is to + + + align:start position:0% +and now what we would like to do is to +tackle the more General problem of + + align:start position:0% +tackle the more General problem of + + + align:start position:0% +tackle the more General problem of +inverting any system of equations and by + + align:start position:0% +inverting any system of equations and by + + + align:start position:0% +inverting any system of equations and by +any I mean what now we have y1 is f sub1 + + align:start position:0% +any I mean what now we have y1 is f sub1 + + + align:start position:0% +any I mean what now we have y1 is f sub1 +of X1 up to xn Etc Y subn is f sub + + align:start position:0% +of X1 up to xn Etc Y subn is f sub + + + align:start position:0% +of X1 up to xn Etc Y subn is f sub +of X1 up to xn and now what we're saying + + align:start position:0% +of X1 up to xn and now what we're saying + + + align:start position:0% +of X1 up to xn and now what we're saying +is we do not know whether the fs are + + align:start position:0% +is we do not know whether the fs are + + + align:start position:0% +is we do not know whether the fs are +linear or not in fact if they are linear + + align:start position:0% +linear or not in fact if they are linear + + + align:start position:0% +linear or not in fact if they are linear +we're back to as a special case what + + align:start position:0% +we're back to as a special case what + + + align:start position:0% +we're back to as a special case what +we've tackled before but now we're + + align:start position:0% +we've tackled before but now we're + + + align:start position:0% +we've tackled before but now we're +assuming that these need not be linear + + align:start position:0% +assuming that these need not be linear + + + align:start position:0% +assuming that these need not be linear +and what we would like to do is to + + align:start position:0% +and what we would like to do is to + + + align:start position:0% +and what we would like to do is to +invert this system assuming of course + + align:start position:0% +invert this system assuming of course + + + align:start position:0% +invert this system assuming of course +that such an inversion is possible again + + align:start position:0% +that such an inversion is possible again + + + align:start position:0% +that such an inversion is possible again +what do we mean by the inversion we mean + + align:start position:0% +what do we mean by the inversion we mean + + + align:start position:0% +what do we mean by the inversion we mean +somehow we would like to know that given + + align:start position:0% +somehow we would like to know that given + + + align:start position:0% +somehow we would like to know that given +this system of n equations in N unknowns + + align:start position:0% +this system of n equations in N unknowns + + + align:start position:0% +this system of n equations in N unknowns +where the Y's are expressed explicitly + + align:start position:0% +where the Y's are expressed explicitly + + + align:start position:0% +where the Y's are expressed explicitly +in terms of the X's can we invert this + + align:start position:0% +in terms of the X's can we invert this + + + align:start position:0% +in terms of the X's can we invert this +and express the x's in terms of the Y's + + align:start position:0% +and express the x's in terms of the Y's + + + align:start position:0% +and express the x's in terms of the Y's +either explicitly or implicitly that's + + align:start position:0% +either explicitly or implicitly that's + + + align:start position:0% +either explicitly or implicitly that's +the problem that we'd like to tackle and + + align:start position:0% +the problem that we'd like to tackle and + + + align:start position:0% +the problem that we'd like to tackle and +what we're going to use to tackle this + + align:start position:0% +what we're going to use to tackle this + + + align:start position:0% +what we're going to use to tackle this +is our old friendly differential the + + align:start position:0% +is our old friendly differential the + + + align:start position:0% +is our old friendly differential the +linear approximation again that + + align:start position:0% +linear approximation again that + + + align:start position:0% +linear approximation again that +motivated our whole study of linear + + align:start position:0% +motivated our whole study of linear + + + align:start position:0% +motivated our whole study of linear +systems in the first place remember we + + align:start position:0% +systems in the first place remember we + + + align:start position:0% +systems in the first place remember we +already know that if y1 is a + + align:start position:0% +already know that if y1 is a + + + align:start position:0% +already know that if y1 is a +differentiable function of X1 up to xn + + align:start position:0% +differentiable function of X1 up to xn + + + align:start position:0% +differentiable function of X1 up to xn +that Delta y1 sub 10an is exactly equal + + align:start position:0% +that Delta y1 sub 10an is exactly equal + + + align:start position:0% +that Delta y1 sub 10an is exactly equal +to the partial of FS1 with respect to X1 + + align:start position:0% +to the partial of FS1 with respect to X1 + + + align:start position:0% +to the partial of FS1 with respect to X1 +* Delta X1 plus Etc the partial of fub1 + + align:start position:0% +* Delta X1 plus Etc the partial of fub1 + + + align:start position:0% +* Delta X1 plus Etc the partial of fub1 +with respect to xn * Delta xn and in + + align:start position:0% +with respect to xn * Delta xn and in + + + align:start position:0% +with respect to xn * Delta xn and in +terms of reviewing the notation because + + align:start position:0% +terms of reviewing the notation because + + + align:start position:0% +terms of reviewing the notation because +we will use it later in the lecture + + align:start position:0% +we will use it later in the lecture + + + align:start position:0% +we will use it later in the lecture +notice that Delta y110 was what we + + align:start position:0% +notice that Delta y110 was what we + + + align:start position:0% +notice that Delta y110 was what we +abbreviated to be + + align:start position:0% +abbreviated to be + + + align:start position:0% +abbreviated to be +dy1 and that Delta X1 up to Delta xn are + + align:start position:0% +dy1 and that Delta X1 up to Delta xn are + + + align:start position:0% +dy1 and that Delta X1 up to Delta xn are +abbreviated respectively as dx1 up to + + align:start position:0% +abbreviated respectively as dx1 up to + + + align:start position:0% +abbreviated respectively as dx1 up to +dxn generalization of what we did for + + align:start position:0% +dxn generalization of what we did for + + + align:start position:0% +dxn generalization of what we did for +the differential in the case of one + + align:start position:0% +the differential in the case of one + + + align:start position:0% +the differential in the case of one +independent variable and we went through + + align:start position:0% +independent variable and we went through + + + align:start position:0% +independent variable and we went through +this discussion when we talked about + + align:start position:0% +this discussion when we talked about + + + align:start position:0% +this discussion when we talked about +exact differentials in block three and + + align:start position:0% +exact differentials in block three and + + + align:start position:0% +exact differentials in block three and +in a similar way we can of course + + align:start position:0% +in a similar way we can of course + + + align:start position:0% +in a similar way we can of course +Express deltay 2 tan Etc and we can talk + + align:start position:0% +Express deltay 2 tan Etc and we can talk + + + align:start position:0% +Express deltay 2 tan Etc and we can talk +about the linear approximations all + + align:start position:0% +about the linear approximations all + + + align:start position:0% +about the linear approximations all +right not the true Delta y's now but the + + align:start position:0% +right not the true Delta y's now but the + + + align:start position:0% +right not the true Delta y's now but the +linear part of the Delta y the Delta y1 + + align:start position:0% +linear part of the Delta y the Delta y1 + + + align:start position:0% +linear part of the Delta y the Delta y1 +sub tan or if you prefer Delta y1 suin l + + align:start position:0% +sub tan or if you prefer Delta y1 suin l + + + align:start position:0% +sub tan or if you prefer Delta y1 suin l +i n all right and the key point now is + + align:start position:0% +i n all right and the key point now is + + + align:start position:0% +i n all right and the key point now is +what if the Y's happen to be + + align:start position:0% +what if the Y's happen to be + + + align:start position:0% +what if the Y's happen to be +continuously differentiable functions of + + align:start position:0% +continuously differentiable functions of + + + align:start position:0% +continuously differentiable functions of +the x's in a neighborhood of the point + + align:start position:0% +the x's in a neighborhood of the point + + + align:start position:0% +the x's in a neighborhood of the point +xar equals a bar in other words X1 up to + + align:start position:0% +xar equals a bar in other words X1 up to + + + align:start position:0% +xar equals a bar in other words X1 up to +xn is equal to A1 comma Etc up to a n X1 + + align:start position:0% +xn is equal to A1 comma Etc up to a n X1 + + + align:start position:0% +xn is equal to A1 comma Etc up to a n X1 += A1 X2 A2 Etc then near that point what + + align:start position:0% += A1 X2 A2 Etc then near that point what + + + align:start position:0% += A1 X2 A2 Etc then near that point what +we're saying is what that the error term + + align:start position:0% +we're saying is what that the error term + + + align:start position:0% +we're saying is what that the error term +goes to zero very rapidly and as long as + + align:start position:0% +goes to zero very rapidly and as long as + + + align:start position:0% +goes to zero very rapidly and as long as +the functions are continuously + + align:start position:0% +the functions are continuously + + + align:start position:0% +the functions are continuously +differentiable it means what that the + + align:start position:0% +differentiable it means what that the + + + align:start position:0% +differentiable it means what that the +change in + + align:start position:0% +change in + + + align:start position:0% +change in +y is approximately equal to the change + + align:start position:0% +y is approximately equal to the change + + + align:start position:0% +y is approximately equal to the change +in y sub 10 so that what we're saying is + + align:start position:0% +in y sub 10 so that what we're saying is + + + align:start position:0% +in y sub 10 so that what we're saying is +and remember this is what motivated our + + align:start position:0% +and remember this is what motivated our + + + align:start position:0% +and remember this is what motivated our +linear systems in the first place that + + align:start position:0% +linear systems in the first place that + + + align:start position:0% +linear systems in the first place that +Delta y1 is approximately the partial of + + align:start position:0% +Delta y1 is approximately the partial of + + + align:start position:0% +Delta y1 is approximately the partial of +y1 with respect to X1 evaluated when xar + + align:start position:0% +y1 with respect to X1 evaluated when xar + + + align:start position:0% +y1 with respect to X1 evaluated when xar +is a bar time Delta X1 plus Etc the + + align:start position:0% +is a bar time Delta X1 plus Etc the + + + align:start position:0% +is a bar time Delta X1 plus Etc the +partial of y1 with respect to xn also + + align:start position:0% +partial of y1 with respect to xn also + + + align:start position:0% +partial of y1 with respect to xn also +evaluated when xar equal a bar time + + align:start position:0% +evaluated when xar equal a bar time + + + align:start position:0% +evaluated when xar equal a bar time +Delta X subn Etc down to Delta Y subn is + + align:start position:0% +Delta X subn Etc down to Delta Y subn is + + + align:start position:0% +Delta X subn Etc down to Delta Y subn is +approximately equal to the partial of Y + + align:start position:0% +approximately equal to the partial of Y + + + align:start position:0% +approximately equal to the partial of Y +subn with respect to X1 * Delta X1 plus + + align:start position:0% +subn with respect to X1 * Delta X1 plus + + + align:start position:0% +subn with respect to X1 * Delta X1 plus +Etc the partial of Y subn with respect + + align:start position:0% +Etc the partial of Y subn with respect + + + align:start position:0% +Etc the partial of Y subn with respect +to x subn * Delta xn where all of these + + align:start position:0% +to x subn * Delta xn where all of these + + + align:start position:0% +to x subn * Delta xn where all of these +partials are evaluated specifically at + + align:start position:0% +partials are evaluated specifically at + + + align:start position:0% +partials are evaluated specifically at +the point xar equals a bar the point + + align:start position:0% +the point xar equals a bar the point + + + align:start position:0% +the point xar equals a bar the point +being what that since we're evaluating + + align:start position:0% +being what that since we're evaluating + + + align:start position:0% +being what that since we're evaluating +all these partials at a particular point + + align:start position:0% +all these partials at a particular point + + + align:start position:0% +all these partials at a particular point +every one of these coefficients is a + + align:start position:0% +every one of these coefficients is a + + + align:start position:0% +every one of these coefficients is a +constant you see in general these + + align:start position:0% +constant you see in general these + + + align:start position:0% +constant you see in general these +partial derivatives are functions but as + + align:start position:0% +partial derivatives are functions but as + + + align:start position:0% +partial derivatives are functions but as +soon as we evaluate them at a given + + align:start position:0% +soon as we evaluate them at a given + + + align:start position:0% +soon as we evaluate them at a given +value they become specific numbers so + + align:start position:0% +value they become specific numbers so + + + align:start position:0% +value they become specific numbers so +this is now what on the right hand side + + align:start position:0% +this is now what on the right hand side + + + align:start position:0% +this is now what on the right hand side +we have a linear system and the point is + + align:start position:0% +we have a linear system and the point is + + + align:start position:0% +we have a linear system and the point is +that we are using the fundamental result + + align:start position:0% +that we are using the fundamental result + + + align:start position:0% +that we are using the fundamental result +that we can use the linear approximation + + align:start position:0% +that we can use the linear approximation + + + align:start position:0% +that we can use the linear approximation +as being very nearly equal to the true + + align:start position:0% +as being very nearly equal to the true + + + align:start position:0% +as being very nearly equal to the true +change in y and it's in that sense that + + align:start position:0% +change in y and it's in that sense that + + + align:start position:0% +change in y and it's in that sense that +we have derived our system of n linear + + align:start position:0% +we have derived our system of n linear + + + align:start position:0% +we have derived our system of n linear +equations in N unknowns you see this is + + align:start position:0% +equations in N unknowns you see this is + + + align:start position:0% +equations in N unknowns you see this is +a linear system the approximation again + + align:start position:0% +a linear system the approximation again + + + align:start position:0% +a linear system the approximation again +let me emphasize that because it's very + + align:start position:0% +let me emphasize that because it's very + + + align:start position:0% +let me emphasize that because it's very +important the approximation hinges on + + align:start position:0% +important the approximation hinges on + + + align:start position:0% +important the approximation hinges on +the fact that what this is exactly equal + + align:start position:0% +the fact that what this is exactly equal + + + align:start position:0% +the fact that what this is exactly equal +to would be Delta y1 tan Etc Delta y + + align:start position:0% +to would be Delta y1 tan Etc Delta y + + + align:start position:0% +to would be Delta y1 tan Etc Delta y +subn but we're assuming that these are + + align:start position:0% +subn but we're assuming that these are + + + align:start position:0% +subn but we're assuming that these are +close enough in a small enough + + align:start position:0% +close enough in a small enough + + + align:start position:0% +close enough in a small enough +neighborhood of xar equals a bar so that + + align:start position:0% +neighborhood of xar equals a bar so that + + + align:start position:0% +neighborhood of xar equals a bar so that +we can make this this particular + + align:start position:0% +we can make this this particular + + + align:start position:0% +we can make this this particular +statement so this is a linear system and + + align:start position:0% +statement so this is a linear system and + + + align:start position:0% +statement so this is a linear system and +because it is a linear system we're back + + align:start position:0% +because it is a linear system we're back + + + align:start position:0% +because it is a linear system we're back +to our special case that this system is + + align:start position:0% +to our special case that this system is + + + align:start position:0% +to our special case that this system is +invertible if and only if the + + align:start position:0% +invertible if and only if the + + + align:start position:0% +invertible if and only if the +determinant of the + + align:start position:0% +determinant of the + + + align:start position:0% +determinant of the +coefficients Matrix coefficients is not + + align:start position:0% +coefficients Matrix coefficients is not + + + align:start position:0% +coefficients Matrix coefficients is not +zero and what is that Matrix coefficient + + align:start position:0% +zero and what is that Matrix coefficient + + + align:start position:0% +zero and what is that Matrix coefficient +it consists of n rows and N columns and + + align:start position:0% +it consists of n rows and N columns and + + + align:start position:0% +it consists of n rows and N columns and +the row is determined by the subscript + + align:start position:0% +the row is determined by the subscript + + + align:start position:0% +the row is determined by the subscript +on the Y and the column is determined by + + align:start position:0% +on the Y and the column is determined by + + + align:start position:0% +on the Y and the column is determined by +the subscript on the X so we write that + + align:start position:0% +the subscript on the X so we write that + + + align:start position:0% +the subscript on the X so we write that +Matrix as the partial of Y sub I with + + align:start position:0% +Matrix as the partial of Y sub I with + + + align:start position:0% +Matrix as the partial of Y sub I with +respect to X subj in other words the I + + align:start position:0% +respect to X subj in other words the I + + + align:start position:0% +respect to X subj in other words the I +row involves the Y's and the jth column + + align:start position:0% +row involves the Y's and the jth column + + + align:start position:0% +row involves the Y's and the jth column +the X right and that's exactly then how + + align:start position:0% +the X right and that's exactly then how + + + align:start position:0% +the X right and that's exactly then how +we handle this particular system okay + + align:start position:0% +we handle this particular system okay + + + align:start position:0% +we handle this particular system okay +quite mechanically and let's just + + align:start position:0% +quite mechanically and let's just + + + align:start position:0% +quite mechanically and let's just +summarize that then very quickly if F + + align:start position:0% +summarize that then very quickly if F + + + align:start position:0% +summarize that then very quickly if F +sub1 Etc and F subn are continuously + + align:start position:0% +sub1 Etc and F subn are continuously + + + align:start position:0% +sub1 Etc and F subn are continuously +differentiable functions of X1 up to xn + + align:start position:0% +differentiable functions of X1 up to xn + + + align:start position:0% +differentiable functions of X1 up to xn +near xar = a bar then the system y1 = + + align:start position:0% +near xar = a bar then the system y1 = + + + align:start position:0% +near xar = a bar then the system y1 = +fub1 of X1 up to xn Etc ynal F sub subn + + align:start position:0% +fub1 of X1 up to xn Etc ynal F sub subn + + + align:start position:0% +fub1 of X1 up to xn Etc ynal F sub subn +of X1 up to xn that system is invertible + + align:start position:0% +of X1 up to xn that system is invertible + + + align:start position:0% +of X1 up to xn that system is invertible +if and only if the + + align:start position:0% +if and only if the + + + align:start position:0% +if and only if the +determinant the N byn determinant whose + + align:start position:0% +determinant the N byn determinant whose + + + align:start position:0% +determinant the N byn determinant whose +entry in the I row J column is the + + align:start position:0% +entry in the I row J column is the + + + align:start position:0% +entry in the I row J column is the +partial of Y subi with respect to X subj + + align:start position:0% +partial of Y subi with respect to X subj + + + align:start position:0% +partial of Y subi with respect to X subj +if and only if that determinant is not + + align:start position:0% +if and only if that determinant is not + + + align:start position:0% +if and only if that determinant is not +zero now what does that mean to say this + + align:start position:0% +zero now what does that mean to say this + + + align:start position:0% +zero now what does that mean to say this +invertible it means that we can solve + + align:start position:0% +invertible it means that we can solve + + + align:start position:0% +invertible it means that we can solve +for the x's in terms of the Y's now we + + align:start position:0% +for the x's in terms of the Y's now we + + + align:start position:0% +for the x's in terms of the Y's now we +may not be able to do that explicitly + + align:start position:0% +may not be able to do that explicitly + + + align:start position:0% +may not be able to do that explicitly +the best we may be able to do is to do + + align:start position:0% +the best we may be able to do is to do + + + align:start position:0% +the best we may be able to do is to do +that implicitly meaning this let me just + + align:start position:0% +that implicitly meaning this let me just + + + align:start position:0% +that implicitly meaning this let me just +come back to something I said before to + + align:start position:0% +come back to something I said before to + + + align:start position:0% +come back to something I said before to +make sure that there's no misunder + + align:start position:0% +make sure that there's no misunder + + + align:start position:0% +make sure that there's no misunder +understanding about this what we're + + align:start position:0% +understanding about this what we're + + + align:start position:0% +understanding about this what we're +saying is that in this particular linear + + align:start position:0% +saying is that in this particular linear + + + align:start position:0% +saying is that in this particular linear +system of equations as long as this + + align:start position:0% +system of equations as long as this + + + align:start position:0% +system of equations as long as this +determinant of coefficients is not zero + + align:start position:0% +determinant of coefficients is not zero + + + align:start position:0% +determinant of coefficients is not zero +we can explicitly solve for Delta X1 up + + align:start position:0% +we can explicitly solve for Delta X1 up + + + align:start position:0% +we can explicitly solve for Delta X1 up +to Delta xn if in terms of Delta y1 up + + align:start position:0% +to Delta xn if in terms of Delta y1 up + + + align:start position:0% +to Delta xn if in terms of Delta y1 up +to Delta YN even if we may not be able + + align:start position:0% +to Delta YN even if we may not be able + + + align:start position:0% +to Delta YN even if we may not be able +to solve explicitly for the x's in terms + + align:start position:0% +to solve explicitly for the x's in terms + + + align:start position:0% +to solve explicitly for the x's in terms +of the Y's in other words The crucial + + align:start position:0% +of the Y's in other words The crucial + + + align:start position:0% +of the Y's in other words The crucial +point is we can solve for the changes in + + align:start position:0% +point is we can solve for the changes in + + + align:start position:0% +point is we can solve for the changes in +X in terms of the changes in y and that + + align:start position:0% +X in terms of the changes in y and that + + + align:start position:0% +X in terms of the changes in y and that +is implicitly enough to see what the X's + + align:start position:0% +is implicitly enough to see what the X's + + + align:start position:0% +is implicitly enough to see what the X's +look like in terms of the Y's once we + + align:start position:0% +look like in terms of the Y's once we + + + align:start position:0% +look like in terms of the Y's once we +know what the change of X looks like in + + align:start position:0% +know what the change of X looks like in + + + align:start position:0% +know what the change of X looks like in +terms of the change in y then we really + + align:start position:0% +terms of the change in y then we really + + + align:start position:0% +terms of the change in y then we really +know what the change in what x itself + + align:start position:0% +know what the change in what x itself + + + align:start position:0% +know what the change in what x itself +looks like in terms of the Y's even as I + + align:start position:0% +looks like in terms of the Y's even as I + + + align:start position:0% +looks like in terms of the Y's even as I +say it may be implicitly rather than + + align:start position:0% +say it may be implicitly rather than + + + align:start position:0% +say it may be implicitly rather than +explicitly at any rate this Matrix is so + + align:start position:0% +explicitly at any rate this Matrix is so + + + align:start position:0% +explicitly at any rate this Matrix is so +important that it's given a very special + + align:start position:0% +important that it's given a very special + + + align:start position:0% +important that it's given a very special +name definition The Matrix whose entry + + align:start position:0% +name definition The Matrix whose entry + + + align:start position:0% +name definition The Matrix whose entry +in the I row jth column is the partial + + align:start position:0% +in the I row jth column is the partial + + + align:start position:0% +in the I row jth column is the partial +of Y subi with respect to X subj is + + align:start position:0% +of Y subi with respect to X subj is + + + align:start position:0% +of Y subi with respect to X subj is +called the Jacobian I put Matrix in + + align:start position:0% +called the Jacobian I put Matrix in + + + align:start position:0% +called the Jacobian I put Matrix in +quotation marks here because some people + + align:start position:0% +quotation marks here because some people + + + align:start position:0% +quotation marks here because some people +refer to the Jacobian meaning a matrix + + align:start position:0% +refer to the Jacobian meaning a matrix + + + align:start position:0% +refer to the Jacobian meaning a matrix +other people call the Jacobian the deter + + align:start position:0% +other people call the Jacobian the deter + + + align:start position:0% +other people call the Jacobian the deter +of the Jacobian matrix I'm not going to + + align:start position:0% +of the Jacobian matrix I'm not going to + + + align:start position:0% +of the Jacobian matrix I'm not going to +make any distinction this way it'll be + + align:start position:0% +make any distinction this way it'll be + + + align:start position:0% +make any distinction this way it'll be +clear from Context usually when I say + + align:start position:0% +clear from Context usually when I say + + + align:start position:0% +clear from Context usually when I say +the Jacobian I will mean the Jacobian + + align:start position:0% +the Jacobian I will mean the Jacobian + + + align:start position:0% +the Jacobian I will mean the Jacobian +matrix uh I might sometimes mean the + + align:start position:0% +matrix uh I might sometimes mean the + + + align:start position:0% +matrix uh I might sometimes mean the +Jacobian determinant and So to avoid + + align:start position:0% +Jacobian determinant and So to avoid + + + align:start position:0% +Jacobian determinant and So to avoid +ambiguity I will hopefully say Jacobian + + align:start position:0% +ambiguity I will hopefully say Jacobian + + + align:start position:0% +ambiguity I will hopefully say Jacobian +matrix when I mean the Matrix and + + align:start position:0% +matrix when I mean the Matrix and + + + align:start position:0% +matrix when I mean the Matrix and +Jacobian determinant when I mean the + + align:start position:0% +Jacobian determinant when I mean the + + + align:start position:0% +Jacobian determinant when I mean the +determinant but should I forget to do + + align:start position:0% +determinant but should I forget to do + + + align:start position:0% +determinant but should I forget to do +this or should you read a textbook where + + align:start position:0% +this or should you read a textbook where + + + align:start position:0% +this or should you read a textbook where +the word Jacobian is used without the + + align:start position:0% +the word Jacobian is used without the + + + align:start position:0% +the word Jacobian is used without the +proper noun after it it should be clear + + align:start position:0% +proper noun after it it should be clear + + + align:start position:0% +proper noun after it it should be clear +from Context which is meant but at any + + align:start position:0% +from Context which is meant but at any + + + align:start position:0% +from Context which is meant but at any +rate that's what we mean by the Jacobian + + align:start position:0% +rate that's what we mean by the Jacobian + + + align:start position:0% +rate that's what we mean by the Jacobian +of y1 up to YN with respect to X1 up to + + align:start position:0% +of y1 up to YN with respect to X1 up to + + + align:start position:0% +of y1 up to YN with respect to X1 up to +xn and this Jacobian matrix is often + + align:start position:0% +xn and this Jacobian matrix is often + + + align:start position:0% +xn and this Jacobian matrix is often +abbreviated by you either write J for + + align:start position:0% +abbreviated by you either write J for + + + align:start position:0% +abbreviated by you either write J for +Jacobian of y1 up to YN over X1 up to xn + + align:start position:0% +Jacobian of y1 up to YN over X1 up to xn + + + align:start position:0% +Jacobian of y1 up to YN over X1 up to xn +or else you use a modification of the + + align:start position:0% +or else you use a modification of the + + + align:start position:0% +or else you use a modification of the +partial derivative notation and you you + + align:start position:0% +partial derivative notation and you you + + + align:start position:0% +partial derivative notation and you you +sort of read this as if it said the + + align:start position:0% +sort of read this as if it said the + + + align:start position:0% +sort of read this as if it said the +partial + + align:start position:0% +partial + + + align:start position:0% +partial +of y1 up to YN divided by the partial of + + align:start position:0% +of y1 up to YN divided by the partial of + + + align:start position:0% +of y1 up to YN divided by the partial of +X1 up to xn and again there is the same + + align:start position:0% +X1 up to xn and again there is the same + + + align:start position:0% +X1 up to xn and again there is the same +analogy between why this notation was + + align:start position:0% +analogy between why this notation was + + + align:start position:0% +analogy between why this notation was +invented and why the notation Dy / DX + + align:start position:0% +invented and why the notation Dy / DX + + + align:start position:0% +invented and why the notation Dy / DX +was invented but in terms of giving you + + align:start position:0% +was invented but in terms of giving you + + + align:start position:0% +was invented but in terms of giving you +a general overview of what we're + + align:start position:0% +a general overview of what we're + + + align:start position:0% +a general overview of what we're +interested in I think I would like to + + align:start position:0% +interested in I think I would like to + + + align:start position:0% +interested in I think I would like to +leave the discussion of why we write + + align:start position:0% +leave the discussion of why we write + + + align:start position:0% +leave the discussion of why we write +this in a fractional form to the + + align:start position:0% +this in a fractional form to the + + + align:start position:0% +this in a fractional form to the +homework in other words be as either a + + align:start position:0% +homework in other words be as either a + + + align:start position:0% +homework in other words be as either a +supplement to the learning exercises or + + align:start position:0% +supplement to the learning exercises or + + + align:start position:0% +supplement to the learning exercises or +else as part of the supplementary notes + + align:start position:0% +else as part of the supplementary notes + + + align:start position:0% +else as part of the supplementary notes +in one form or another we will take care + + align:start position:0% +in one form or another we will take care + + + align:start position:0% +in one form or another we will take care +of all of the computational aspects of + + align:start position:0% +of all of the computational aspects of + + + align:start position:0% +of all of the computational aspects of +how one handles the Jacobian but what I + + align:start position:0% +how one handles the Jacobian but what I + + + align:start position:0% +how one handles the Jacobian but what I +wanted to do now was to emphasize how + + align:start position:0% +wanted to do now was to emphasize how + + + align:start position:0% +wanted to do now was to emphasize how +one uses the Jacobian matrix and + + align:start position:0% +one uses the Jacobian matrix and + + + align:start position:0% +one uses the Jacobian matrix and +differentials to invert systems of n + + align:start position:0% +differentials to invert systems of n + + + align:start position:0% +differentials to invert systems of n +equations and N unknowns and I will use + + align:start position:0% +equations and N unknowns and I will use + + + align:start position:0% +equations and N unknowns and I will use +the technique that's used right in the + + align:start position:0% +the technique that's used right in the + + + align:start position:0% +the technique that's used right in the +textbook and which is part of the + + align:start position:0% +textbook and which is part of the + + + align:start position:0% +textbook and which is part of the +assignment for today's unit the example + + align:start position:0% +assignment for today's unit the example + + + align:start position:0% +assignment for today's unit the example +that I have in mind I'll simply pick the + + align:start position:0% +that I have in mind I'll simply pick the + + + align:start position:0% +that I have in mind I'll simply pick the +usual case n equals 2 so that things + + align:start position:0% +usual case n equals 2 so that things + + + align:start position:0% +usual case n equals 2 so that things +don't get that messy uh using again the + + align:start position:0% +don't get that messy uh using again the + + + align:start position:0% +don't get that messy uh using again the +standard notation when one deals with + + align:start position:0% +standard notation when one deals with + + + align:start position:0% +standard notation when one deals with +two independent variables let U = x^2 - + + align:start position:0% +two independent variables let U = x^2 - + + + align:start position:0% +two independent variables let U = x^2 - +y^2 let V = 2xy Let's suppose now that I + + align:start position:0% +y^2 let V = 2xy Let's suppose now that I + + + align:start position:0% +y^2 let V = 2xy Let's suppose now that I +would like to find the partial of X with + + align:start position:0% +would like to find the partial of X with + + + align:start position:0% +would like to find the partial of X with +respect to U treating v as the other + + align:start position:0% +respect to U treating v as the other + + + align:start position:0% +respect to U treating v as the other +independent variable you see again I + + align:start position:0% +independent variable you see again I + + + align:start position:0% +independent variable you see again I +want to review this thing when I say + + align:start position:0% +want to review this thing when I say + + + align:start position:0% +want to review this thing when I say +find the partial of X with respect to U + + align:start position:0% +find the partial of X with respect to U + + + align:start position:0% +find the partial of X with respect to U +holding V constant it is not the same as + + align:start position:0% +holding V constant it is not the same as + + + align:start position:0% +holding V constant it is not the same as +finding the partial of U respect to X + + align:start position:0% +finding the partial of U respect to X + + + align:start position:0% +finding the partial of U respect to X +from here and then just inverting it + + align:start position:0% +from here and then just inverting it + + + align:start position:0% +from here and then just inverting it +namely the partial of U respect to X + + align:start position:0% +namely the partial of U respect to X + + + align:start position:0% +namely the partial of U respect to X +here assumes that Y is being held + + align:start position:0% +here assumes that Y is being held + + + align:start position:0% +here assumes that Y is being held +constant and if you then invert that + + align:start position:0% +constant and if you then invert that + + + align:start position:0% +constant and if you then invert that +recall that what you're finding is the + + align:start position:0% +recall that what you're finding is the + + + align:start position:0% +recall that what you're finding is the +partial of X with respect to you + + align:start position:0% +partial of X with respect to you + + + align:start position:0% +partial of X with respect to you +treating y as the other variable we want + + align:start position:0% +treating y as the other variable we want + + + align:start position:0% +treating y as the other variable we want +the partial of X with respect to you + + align:start position:0% +the partial of X with respect to you + + + align:start position:0% +the partial of X with respect to you +treating u and v as the pair of + + align:start position:0% +treating u and v as the pair of + + + align:start position:0% +treating u and v as the pair of +independent variables why because that's + + align:start position:0% +independent variables why because that's + + + align:start position:0% +independent variables why because that's +exactly what you mean by inverting this + + align:start position:0% +exactly what you mean by inverting this + + + align:start position:0% +exactly what you mean by inverting this +system this system as given expresses u + + align:start position:0% +system this system as given expresses u + + + align:start position:0% +system this system as given expresses u +and v in terms of the pair of + + align:start position:0% +and v in terms of the pair of + + + align:start position:0% +and v in terms of the pair of +independent variables X and Y and now + + align:start position:0% +independent variables X and Y and now + + + align:start position:0% +independent variables X and Y and now +what you'd like to do is Express the + + align:start position:0% +what you'd like to do is Express the + + + align:start position:0% +what you'd like to do is Express the +pair of variables X and Y in terms of + + align:start position:0% +pair of variables X and Y in terms of + + + align:start position:0% +pair of variables X and Y in terms of +the independent variables u and v + + align:start position:0% +the independent variables u and v + + + align:start position:0% +the independent variables u and v +assuming of course that u and v are + + align:start position:0% +assuming of course that u and v are + + + align:start position:0% +assuming of course that u and v are +indeed independent variables the + + align:start position:0% +indeed independent variables the + + + align:start position:0% +indeed independent variables the +mechanical solution is simply this using + + align:start position:0% +mechanical solution is simply this using + + + align:start position:0% +mechanical solution is simply this using +the language of differentials we write + + align:start position:0% +the language of differentials we write + + + align:start position:0% +the language of differentials we write +down d U and DV namely du is what the + + align:start position:0% +down d U and DV namely du is what the + + + align:start position:0% +down d U and DV namely du is what the +partial of U respect to x * DX plus the + + align:start position:0% +partial of U respect to x * DX plus the + + + align:start position:0% +partial of U respect to x * DX plus the +partial of U respect to y * Dy and from + + align:start position:0% +partial of U respect to y * Dy and from + + + align:start position:0% +partial of U respect to y * Dy and from +the relationship that U = x^2 - y^2 we + + align:start position:0% +the relationship that U = x^2 - y^2 we + + + align:start position:0% +the relationship that U = x^2 - y^2 we +see that du is 2x DX - 2 y Dy similarly + + align:start position:0% +see that du is 2x DX - 2 y Dy similarly + + + align:start position:0% +see that du is 2x DX - 2 y Dy similarly +since the partial of V with respect to X + + align:start position:0% +since the partial of V with respect to X + + + align:start position:0% +since the partial of V with respect to X +is 2 Y and the partial of V with respect + + align:start position:0% +is 2 Y and the partial of V with respect + + + align:start position:0% +is 2 Y and the partial of V with respect +to Y is 2x we see that DV is 2 ydx x + + + align:start position:0% +to Y is 2x we see that DV is 2 ydx x + + + + align:start position:0% +to Y is 2x we see that DV is 2 ydx x + +2x Dy if we now assume that this is + + align:start position:0% +2x Dy if we now assume that this is + + + align:start position:0% +2x Dy if we now assume that this is +evaluated at some point x0 + + align:start position:0% +evaluated at some point x0 + + + align:start position:0% +evaluated at some point x0 +y0 what do we have over here once we've + + align:start position:0% +y0 what do we have over here once we've + + + align:start position:0% +y0 what do we have over here once we've +picked out a point x0 y0 to evaluate + + align:start position:0% +picked out a point x0 y0 to evaluate + + + align:start position:0% +picked out a point x0 y0 to evaluate +this at and I left out that because it + + align:start position:0% +this at and I left out that because it + + + align:start position:0% +this at and I left out that because it +simply would make the notation too long + + align:start position:0% +simply would make the notation too long + + + align:start position:0% +simply would make the notation too long +but I'll talk about that more later + + align:start position:0% +but I'll talk about that more later + + + align:start position:0% +but I'll talk about that more later +assuming that we've evaluated this at a + + align:start position:0% +assuming that we've evaluated this at a + + + align:start position:0% +assuming that we've evaluated this at a +particular fixed value of X and Y we + + align:start position:0% +particular fixed value of X and Y we + + + align:start position:0% +particular fixed value of X and Y we +have what du is some constant time DX + + align:start position:0% +have what du is some constant time DX + + + align:start position:0% +have what du is some constant time DX +plus some constant time d d y DV is some + + align:start position:0% +plus some constant time d d y DV is some + + + align:start position:0% +plus some constant time d d y DV is some +constant * DX plus some constant time Dy + + align:start position:0% +constant * DX plus some constant time Dy + + + align:start position:0% +constant * DX plus some constant time Dy +in other words du and DV are expressed + + align:start position:0% +in other words du and DV are expressed + + + align:start position:0% +in other words du and DV are expressed +as linear combinations of DX and Dy we + + align:start position:0% +as linear combinations of DX and Dy we + + + align:start position:0% +as linear combinations of DX and Dy we +know how to invert this type of a system + + align:start position:0% +know how to invert this type of a system + + + align:start position:0% +know how to invert this type of a system +assuming that it's invertible sparing + + align:start position:0% +assuming that it's invertible sparing + + + align:start position:0% +assuming that it's invertible sparing +you the details what I'm saying is what + + align:start position:0% +you the details what I'm saying is what + + + align:start position:0% +you the details what I'm saying is what +I could multiply say the top equation by + + align:start position:0% +I could multiply say the top equation by + + + align:start position:0% +I could multiply say the top equation by +X the bottom equation by Y and when I + + align:start position:0% +X the bottom equation by Y and when I + + + align:start position:0% +X the bottom equation by Y and when I +add them the terms involving Dy will + + align:start position:0% +add them the terms involving Dy will + + + align:start position:0% +add them the terms involving Dy will +drop out and I will get xdu + ydv is 2x + + align:start position:0% +drop out and I will get xdu + ydv is 2x + + + align:start position:0% +drop out and I will get xdu + ydv is 2x +DX + 2 y DX in other words twice it's + + align:start position:0% +DX + 2 y DX in other words twice it's + + + align:start position:0% +DX + 2 y DX in other words twice it's +2x^2 I'm multiplying the top equation by + + align:start position:0% +2x^2 I'm multiplying the top equation by + + + align:start position:0% +2x^2 I'm multiplying the top equation by +X the bottom equation by y so the right + + align:start position:0% +X the bottom equation by y so the right + + + align:start position:0% +X the bottom equation by y so the right +hand side here becomes 2x^2 DX + 2 y^2 + + align:start position:0% +hand side here becomes 2x^2 DX + 2 y^2 + + + align:start position:0% +hand side here becomes 2x^2 DX + 2 y^2 +DX which is T x^2 + y^2 DX I now divide + + align:start position:0% +DX which is T x^2 + y^2 DX I now divide + + + align:start position:0% +DX which is T x^2 + y^2 DX I now divide +both sides of the equation through by T + + align:start position:0% +both sides of the equation through by T + + + align:start position:0% +both sides of the equation through by T +x^2 + y² I wind up with the fact that DX + + align:start position:0% +x^2 + y² I wind up with the fact that DX + + + align:start position:0% +x^2 + y² I wind up with the fact that DX +is X over tce the quantity X + y^2 du + + align:start position:0% +is X over tce the quantity X + y^2 du + + + align:start position:0% +is X over tce the quantity X + y^2 du +plus the quantity y /x^2 + y^2 DV recall + + align:start position:0% +plus the quantity y /x^2 + y^2 DV recall + + + align:start position:0% +plus the quantity y /x^2 + y^2 DV recall +that I also know by definition that DX + + align:start position:0% +that I also know by definition that DX + + + align:start position:0% +that I also know by definition that DX +is the partial of X with respect to U * + + align:start position:0% +is the partial of X with respect to U * + + + align:start position:0% +is the partial of X with respect to U * +du plus the partial of X with respect to + + align:start position:0% +du plus the partial of X with respect to + + + align:start position:0% +du plus the partial of X with respect to +V time DV recalling from our lecture on + + align:start position:0% +V time DV recalling from our lecture on + + + align:start position:0% +V time DV recalling from our lecture on +exact differentials that the only way + + align:start position:0% +exact differentials that the only way + + + align:start position:0% +exact differentials that the only way +two differentials in terms of du and DV + + align:start position:0% +two differentials in terms of du and DV + + + align:start position:0% +two differentials in terms of du and DV +can be equal is if they're equal + + align:start position:0% +can be equal is if they're equal + + + align:start position:0% +can be equal is if they're equal +coefficient by coefficient I can + + align:start position:0% +coefficient by coefficient I can + + + align:start position:0% +coefficient by coefficient I can +therefore equate the two coefficients of + + align:start position:0% +therefore equate the two coefficients of + + + align:start position:0% +therefore equate the two coefficients of +du to conclude that the partial of X + + align:start position:0% +du to conclude that the partial of X + + + align:start position:0% +du to conclude that the partial of X +with respect to U is X over 2times the + + align:start position:0% +with respect to U is X over 2times the + + + align:start position:0% +with respect to U is X over 2times the +quantity x^2 + y^2 in fact I can get the + + align:start position:0% +quantity x^2 + y^2 in fact I can get the + + + align:start position:0% +quantity x^2 + y^2 in fact I can get the +extra piece of information even though I + + align:start position:0% +extra piece of information even though I + + + align:start position:0% +extra piece of information even though I +wasn't asked for that in this problem + + align:start position:0% +wasn't asked for that in this problem + + + align:start position:0% +wasn't asked for that in this problem +that the partial of X with respect to V + + align:start position:0% +that the partial of X with respect to V + + + align:start position:0% +that the partial of X with respect to V +is y over tce the quantity x^2 + y^2 by + + align:start position:0% +is y over tce the quantity x^2 + y^2 by + + + align:start position:0% +is y over tce the quantity x^2 + y^2 by +the way observe purely algebraically + + align:start position:0% +the way observe purely algebraically + + + align:start position:0% +the way observe purely algebraically +that the only time I would be in any + + align:start position:0% +that the only time I would be in any + + + align:start position:0% +that the only time I would be in any +difficulty with this procedure is if x^2 + + align:start position:0% +difficulty with this procedure is if x^2 + + + align:start position:0% +difficulty with this procedure is if x^2 ++ y^2 happened to equal 0 in other words + + align:start position:0% ++ y^2 happened to equal 0 in other words + + + align:start position:0% ++ y^2 happened to equal 0 in other words +if x^2 + y^2 happened to equal 0 then to + + align:start position:0% +if x^2 + y^2 happened to equal 0 then to + + + align:start position:0% +if x^2 + y^2 happened to equal 0 then to +divide through by T x^2 + y^2 is + + align:start position:0% +divide through by T x^2 + y^2 is + + + align:start position:0% +divide through by T x^2 + y^2 is +equivalent to dividing through by zero + + align:start position:0% +equivalent to dividing through by zero + + + align:start position:0% +equivalent to dividing through by zero +and division by 0er is not permissible + + align:start position:0% +and division by 0er is not permissible + + + align:start position:0% +and division by 0er is not permissible +in other words somehow or other I must + + align:start position:0% +in other words somehow or other I must + + + align:start position:0% +in other words somehow or other I must +take into consideration that I am in + + align:start position:0% +take into consideration that I am in + + + align:start position:0% +take into consideration that I am in +trouble if x^2 + Y2 is zero notice by + + align:start position:0% +trouble if x^2 + Y2 is zero notice by + + + align:start position:0% +trouble if x^2 + Y2 is zero notice by +the way that the only time that x^2 + + + align:start position:0% +the way that the only time that x^2 + + + + align:start position:0% +the way that the only time that x^2 + +y^2 can be zero is if both X and Y is + + align:start position:0% +y^2 can be zero is if both X and Y is + + + align:start position:0% +y^2 can be zero is if both X and Y is +zero and that means again that somehow + + align:start position:0% +zero and that means again that somehow + + + align:start position:0% +zero and that means again that somehow +or other at the point 0 comma 0 in a + + align:start position:0% +or other at the point 0 comma 0 in a + + + align:start position:0% +or other at the point 0 comma 0 in a +neighborhood of the point Z over of the + + align:start position:0% +neighborhood of the point Z over of the + + + align:start position:0% +neighborhood of the point Z over of the +point 0 comma 0 in a neighborhood of the + + align:start position:0% +point 0 comma 0 in a neighborhood of the + + + align:start position:0% +point 0 comma 0 in a neighborhood of the +origin I can expect to have a little bit + + align:start position:0% +origin I can expect to have a little bit + + + align:start position:0% +origin I can expect to have a little bit +of trouble now again the main aim of the + + align:start position:0% +of trouble now again the main aim of the + + + align:start position:0% +of trouble now again the main aim of the +lecture is to give you an overview the + + align:start position:0% +lecture is to give you an overview the + + + align:start position:0% +lecture is to give you an overview the +trouble that comes in at the origin will + + align:start position:0% +trouble that comes in at the origin will + + + align:start position:0% +trouble that comes in at the origin will +again be left for the exercises in a + + align:start position:0% +again be left for the exercises in a + + + align:start position:0% +again be left for the exercises in a +learning exercise we will discuss just + + align:start position:0% +learning exercise we will discuss just + + + align:start position:0% +learning exercise we will discuss just +what goes wrong if you take a + + align:start position:0% +what goes wrong if you take a + + + align:start position:0% +what goes wrong if you take a +neighborhood of the origin to discuss + + align:start position:0% +neighborhood of the origin to discuss + + + align:start position:0% +neighborhood of the origin to discuss +the change of variables U = x^2 - y^2 V + + align:start position:0% +the change of variables U = x^2 - y^2 V + + + align:start position:0% +the change of variables U = x^2 - y^2 V += 2xy suffice it to say for the time + + align:start position:0% += 2xy suffice it to say for the time + + + align:start position:0% += 2xy suffice it to say for the time +being that the system of equations u = + + align:start position:0% +being that the system of equations u = + + + align:start position:0% +being that the system of equations u = +x^2 - y^2 V = 2xy is invertible in any + + align:start position:0% +x^2 - y^2 V = 2xy is invertible in any + + + align:start position:0% +x^2 - y^2 V = 2xy is invertible in any +neighborhood of a point x0 comma y0 + + align:start position:0% +neighborhood of a point x0 comma y0 + + + align:start position:0% +neighborhood of a point x0 comma y0 +except in that one possible case when + + align:start position:0% +except in that one possible case when + + + align:start position:0% +except in that one possible case when +you have chosen as the point x0 y0 the + + align:start position:0% +you have chosen as the point x0 y0 the + + + align:start position:0% +you have chosen as the point x0 y0 the +origin at any rate to take this problem + + align:start position:0% +origin at any rate to take this problem + + + align:start position:0% +origin at any rate to take this problem +away from a the specific concrete + + align:start position:0% +away from a the specific concrete + + + align:start position:0% +away from a the specific concrete +example that we've been talking about + + align:start position:0% +example that we've been talking about + + + align:start position:0% +example that we've been talking about +and to put this in terms of a more + + align:start position:0% +and to put this in terms of a more + + + align:start position:0% +and to put this in terms of a more +General perspective let's go back more + + align:start position:0% +General perspective let's go back more + + + align:start position:0% +General perspective let's go back more +abstractly to the more General system + + align:start position:0% +abstractly to the more General system + + + align:start position:0% +abstractly to the more General system +system let's suppose now that you and V + + align:start position:0% +system let's suppose now that you and V + + + align:start position:0% +system let's suppose now that you and V +are any two continuously differentiable + + align:start position:0% +are any two continuously differentiable + + + align:start position:0% +are any two continuously differentiable +functions of X and Y let U be F of XY + + align:start position:0% +functions of X and Y let U be F of XY + + + align:start position:0% +functions of X and Y let U be F of XY +let V equal G of XY and what we're + + align:start position:0% +let V equal G of XY and what we're + + + align:start position:0% +let V equal G of XY and what we're +saying is if you pick a particular Point + + align:start position:0% +saying is if you pick a particular Point + + + align:start position:0% +saying is if you pick a particular Point +x0 comma y0 then by mechanically using + + align:start position:0% +x0 comma y0 then by mechanically using + + + align:start position:0% +x0 comma y0 then by mechanically using +the total differential we have that du + + align:start position:0% +the total differential we have that du + + + align:start position:0% +the total differential we have that du +is the partial of f with respect to X + + align:start position:0% +is the partial of f with respect to X + + + align:start position:0% +is the partial of f with respect to X +evaluated x0 y0 * DX plus the partial of + + align:start position:0% +evaluated x0 y0 * DX plus the partial of + + + align:start position:0% +evaluated x0 y0 * DX plus the partial of +effort respect to Y evaluated x0 y0 * Dy + + align:start position:0% +effort respect to Y evaluated x0 y0 * Dy + + + align:start position:0% +effort respect to Y evaluated x0 y0 * Dy +we have that DV is the partial of G with + + align:start position:0% +we have that DV is the partial of G with + + + align:start position:0% +we have that DV is the partial of G with +respect to X evaluated x0 y0 * DX plus + + align:start position:0% +respect to X evaluated x0 y0 * DX plus + + + align:start position:0% +respect to X evaluated x0 y0 * DX plus +the partial of G respect to Y evaluated + + align:start position:0% +the partial of G respect to Y evaluated + + + align:start position:0% +the partial of G respect to Y evaluated +x0 y0 * Dy what is this now this is a + + align:start position:0% +x0 y0 * Dy what is this now this is a + + + align:start position:0% +x0 y0 * Dy what is this now this is a +linear system of two equations in two + + align:start position:0% +linear system of two equations in two + + + align:start position:0% +linear system of two equations in two +unknowns du and DV are linear + + align:start position:0% +unknowns du and DV are linear + + + align:start position:0% +unknowns du and DV are linear +combinations of DX and Dy the key point + + align:start position:0% +combinations of DX and Dy the key point + + + align:start position:0% +combinations of DX and Dy the key point +being again that's why I put this in + + align:start position:0% +being again that's why I put this in + + + align:start position:0% +being again that's why I put this in +here specifically with the X subz and + + align:start position:0% +here specifically with the X subz and + + + align:start position:0% +here specifically with the X subz and +the Y sub Z the key point is that as + + align:start position:0% +the Y sub Z the key point is that as + + + align:start position:0% +the Y sub Z the key point is that as +soon as you evaluate a partial + + align:start position:0% +soon as you evaluate a partial + + + align:start position:0% +soon as you evaluate a partial +derivative at a fixed point the value is + + align:start position:0% +derivative at a fixed point the value is + + + align:start position:0% +derivative at a fixed point the value is +a constant not a variable so this is + + align:start position:0% +a constant not a variable so this is + + + align:start position:0% +a constant not a variable so this is +what a linear system we have du is a + + align:start position:0% +what a linear system we have du is a + + + align:start position:0% +what a linear system we have du is a +constant time DX plus a con constant + + align:start position:0% +constant time DX plus a con constant + + + align:start position:0% +constant time DX plus a con constant +time d y DV is a constant time DX plus a + + align:start position:0% +time d y DV is a constant time DX plus a + + + align:start position:0% +time d y DV is a constant time DX plus a +constant time Dy again to make a long + + align:start position:0% +constant time Dy again to make a long + + + align:start position:0% +constant time Dy again to make a long +story short I can solve for DX in terms + + align:start position:0% +story short I can solve for DX in terms + + + align:start position:0% +story short I can solve for DX in terms +of du and DV I can solve for Dy in terms + + align:start position:0% +of du and DV I can solve for Dy in terms + + + align:start position:0% +of du and DV I can solve for Dy in terms +of du and + + align:start position:0% +of du and + + + align:start position:0% +of du and +DV provided what that my Matrix of + + align:start position:0% +DV provided what that my Matrix of + + + align:start position:0% +DV provided what that my Matrix of +coefficients does not have its + + align:start position:0% +coefficients does not have its + + + align:start position:0% +coefficients does not have its +determinant equal to zero and to review + + align:start position:0% +determinant equal to zero and to review + + + align:start position:0% +determinant equal to zero and to review +this more explicitly so you see the + + align:start position:0% +this more explicitly so you see the + + + align:start position:0% +this more explicitly so you see the +mechanics all I'm saying is to solve for + + align:start position:0% +mechanics all I'm saying is to solve for + + + align:start position:0% +mechanics all I'm saying is to solve for +DX I can multiply the top equation by + + align:start position:0% +DX I can multiply the top equation by + + + align:start position:0% +DX I can multiply the top equation by +the partial of G with respect to Y + + align:start position:0% +the partial of G with respect to Y + + + align:start position:0% +the partial of G with respect to Y +evaluated x0 y0 I can multiply the + + align:start position:0% +evaluated x0 y0 I can multiply the + + + align:start position:0% +evaluated x0 y0 I can multiply the +bottom equation by minus the partial of + + align:start position:0% +bottom equation by minus the partial of + + + align:start position:0% +bottom equation by minus the partial of +f respect to Y evaluated x0 y0 and then + + align:start position:0% +f respect to Y evaluated x0 y0 and then + + + align:start position:0% +f respect to Y evaluated x0 y0 and then +when I add these two equations the Dy + + align:start position:0% +when I add these two equations the Dy + + + align:start position:0% +when I add these two equations the Dy +term will drop out again leaving the + + align:start position:0% +term will drop out again leaving the + + + align:start position:0% +term will drop out again leaving the +details for you it turns out that DX is + + align:start position:0% +details for you it turns out that DX is + + + align:start position:0% +details for you it turns out that DX is +what the partial of G with respect to Y + + align:start position:0% +what the partial of G with respect to Y + + + align:start position:0% +what the partial of G with respect to Y +and I've abbreviated this again this + + align:start position:0% +and I've abbreviated this again this + + + align:start position:0% +and I've abbreviated this again this +means what evaluated x0 y0 * d U minus + + align:start position:0% +means what evaluated x0 y0 * d U minus + + + align:start position:0% +means what evaluated x0 y0 * d U minus +the partial of f respect to Y at x0 y0 * + + align:start position:0% +the partial of f respect to Y at x0 y0 * + + + align:start position:0% +the partial of f respect to Y at x0 y0 * +DV over the partial of f respect to x + + align:start position:0% +DV over the partial of f respect to x + + + align:start position:0% +DV over the partial of f respect to x +times the partial of G with respect to Y + + align:start position:0% +times the partial of G with respect to Y + + + align:start position:0% +times the partial of G with respect to Y +minus the partial of f with respect to Y + + align:start position:0% +minus the partial of f with respect to Y + + + align:start position:0% +minus the partial of f with respect to Y +times the partial of G with respect to X + + align:start position:0% +times the partial of G with respect to X + + + align:start position:0% +times the partial of G with respect to X +and notice of course that this + + align:start position:0% +and notice of course that this + + + align:start position:0% +and notice of course that this +denominator is precisely our Matrix of + + align:start position:0% +denominator is precisely our Matrix of + + + align:start position:0% +denominator is precisely our Matrix of +coefficients f subx f suby g subx g suby + + align:start position:0% +coefficients f subx f suby g subx g suby + + + align:start position:0% +coefficients f subx f suby g subx g suby +and the only place I've taken the + + align:start position:0% +and the only place I've taken the + + + align:start position:0% +and the only place I've taken the +Liberty here is to use the abbreviation + + align:start position:0% +Liberty here is to use the abbreviation + + + align:start position:0% +Liberty here is to use the abbreviation +of leaving out the x0 y0 and the key + + align:start position:0% +of leaving out the x0 y0 and the key + + + align:start position:0% +of leaving out the x0 y0 and the key +point is what the only place I am going + + align:start position:0% +point is what the only place I am going + + + align:start position:0% +point is what the only place I am going +to get in trouble is if this denominator + + align:start position:0% +to get in trouble is if this denominator + + + align:start position:0% +to get in trouble is if this denominator +happens to be zero in the two by two + + align:start position:0% +happens to be zero in the two by two + + + align:start position:0% +happens to be zero in the two by two +case another words in the case of two + + align:start position:0% +case another words in the case of two + + + align:start position:0% +case another words in the case of two +equations and two unknowns notice that + + align:start position:0% +equations and two unknowns notice that + + + align:start position:0% +equations and two unknowns notice that +we can see explicitly what goes wrong + + align:start position:0% +we can see explicitly what goes wrong + + + align:start position:0% +we can see explicitly what goes wrong +when the determinant of coefficients is + + align:start position:0% +when the determinant of coefficients is + + + align:start position:0% +when the determinant of coefficients is +zero the determinant of coefficients is + + align:start position:0% +zero the determinant of coefficients is + + + align:start position:0% +zero the determinant of coefficients is +just this denominator and when that + + align:start position:0% +just this denominator and when that + + + align:start position:0% +just this denominator and when that +denominator is zero we're in trouble in + + align:start position:0% +denominator is zero we're in trouble in + + + align:start position:0% +denominator is zero we're in trouble in +other words the only time we cannot + + align:start position:0% +other words the only time we cannot + + + align:start position:0% +other words the only time we cannot +invert this system the only time we + + align:start position:0% +invert this system the only time we + + + align:start position:0% +invert this system the only time we +cannot find Delta X and Delta Y in terms + + align:start position:0% +cannot find Delta X and Delta Y in terms + + + align:start position:0% +cannot find Delta X and Delta Y in terms +of du and DV is when this determinant is + + align:start position:0% +of du and DV is when this determinant is + + + align:start position:0% +of du and DV is when this determinant is +zero now you see I think this is pretty + + align:start position:0% +zero now you see I think this is pretty + + + align:start position:0% +zero now you see I think this is pretty +straightforward stuff the textbook has a + + align:start position:0% +straightforward stuff the textbook has a + + + align:start position:0% +straightforward stuff the textbook has a +section on this as you will be reading + + align:start position:0% +section on this as you will be reading + + + align:start position:0% +section on this as you will be reading +shortly it is not hard to work this + + align:start position:0% +shortly it is not hard to work this + + + align:start position:0% +shortly it is not hard to work this +mechanically and then the question that + + align:start position:0% +mechanically and then the question that + + + align:start position:0% +mechanically and then the question that +comes up is how come when you pick up a + + align:start position:0% +comes up is how come when you pick up a + + + align:start position:0% +comes up is how come when you pick up a +book in advanced calculus there's + + align:start position:0% +book in advanced calculus there's + + + align:start position:0% +book in advanced calculus there's +usually a huge chapter on jacobians and + + align:start position:0% +usually a huge chapter on jacobians and + + + align:start position:0% +usually a huge chapter on jacobians and +inversion why isn't it this simple in + + align:start position:0% +inversion why isn't it this simple in + + + align:start position:0% +inversion why isn't it this simple in +the advanced text books why can we have + + align:start position:0% +the advanced text books why can we have + + + align:start position:0% +the advanced text books why can we have +it in our book this simply but yet in + + align:start position:0% +it in our book this simply but yet in + + + align:start position:0% +it in our book this simply but yet in +the advanced book why is there so much + + align:start position:0% +the advanced book why is there so much + + + align:start position:0% +the advanced book why is there so much +more to this beneath the surface the + + align:start position:0% +more to this beneath the surface the + + + align:start position:0% +more to this beneath the surface the +answer behind all of this is quite + + align:start position:0% +answer behind all of this is quite + + + align:start position:0% +answer behind all of this is quite +subtle in fact the major subtlety is + + align:start position:0% +subtle in fact the major subtlety is + + + align:start position:0% +subtle in fact the major subtlety is +this that is that the notation du and + + align:start position:0% +this that is that the notation du and + + + align:start position:0% +this that is that the notation du and +for that matter DV or DX or Dy or dx1 + + align:start position:0% +for that matter DV or DX or Dy or dx1 + + + align:start position:0% +for that matter DV or DX or Dy or dx1 +dx2 whatever you're using here is + + align:start position:0% +dx2 whatever you're using here is + + + align:start position:0% +dx2 whatever you're using here is +ambiguous and it's ambiguous for the + + align:start position:0% +ambiguous and it's ambiguous for the + + + align:start position:0% +ambiguous and it's ambiguous for the +following reason recall how we Define + + align:start position:0% +following reason recall how we Define + + + align:start position:0% +following reason recall how we Define +the meaning of the symbol du If U is + + align:start position:0% +the meaning of the symbol du If U is + + + align:start position:0% +the meaning of the symbol du If U is +equal if we're assuming that U is + + align:start position:0% +equal if we're assuming that U is + + + align:start position:0% +equal if we're assuming that U is +expressed as a function of the + + align:start position:0% +expressed as a function of the + + + align:start position:0% +expressed as a function of the +independent variables X and Y then by du + + align:start position:0% +independent variables X and Y then by du + + + align:start position:0% +independent variables X and Y then by du +we mean Delta U Tan on the other hand if + + align:start position:0% +we mean Delta U Tan on the other hand if + + + align:start position:0% +we mean Delta U Tan on the other hand if +we inverted this du you now in other + + align:start position:0% +we inverted this du you now in other + + + align:start position:0% +we inverted this du you now in other +words what I mean by inverted this what + + align:start position:0% +words what I mean by inverted this what + + + align:start position:0% +words what I mean by inverted this what +I mean first of all is if we assume now + + align:start position:0% +I mean first of all is if we assume now + + + align:start position:0% +I mean first of all is if we assume now +that X and Y are expressed in terms of u + + align:start position:0% +that X and Y are expressed in terms of u + + + align:start position:0% +that X and Y are expressed in terms of u +and v for example suppose X is some + + align:start position:0% +and v for example suppose X is some + + + align:start position:0% +and v for example suppose X is some +function h of u and v what does du mean + + align:start position:0% +function h of u and v what does du mean + + + align:start position:0% +function h of u and v what does du mean +now notice that now U is playing the + + align:start position:0% +now notice that now U is playing the + + + align:start position:0% +now notice that now U is playing the +role of an independent variable for the + + align:start position:0% +role of an independent variable for the + + + align:start position:0% +role of an independent variable for the +independent variable du just means Delta + + align:start position:0% +independent variable du just means Delta + + + align:start position:0% +independent variable du just means Delta +u in other words by way of a very quick + + align:start position:0% +u in other words by way of a very quick + + + align:start position:0% +u in other words by way of a very quick +review notice that if we're viewing U as + + align:start position:0% +review notice that if we're viewing U as + + + align:start position:0% +review notice that if we're viewing U as +being a dependent variable then du means + + align:start position:0% +being a dependent variable then du means + + + align:start position:0% +being a dependent variable then du means +Delta U + + align:start position:0% +Delta U + + + align:start position:0% +Delta U +Tan but if we're VI viewing U as being + + align:start position:0% +Tan but if we're VI viewing U as being + + + align:start position:0% +Tan but if we're VI viewing U as being +an independent variable then du means + + align:start position:0% +an independent variable then du means + + + align:start position:0% +an independent variable then du means +Delta U and + + align:start position:0% +Delta U and + + + align:start position:0% +Delta U and +consequently the results that we're + + align:start position:0% +consequently the results that we're + + + align:start position:0% +consequently the results that we're +using hinge very strongly then in other + + align:start position:0% +using hinge very strongly then in other + + + align:start position:0% +using hinge very strongly then in other +words the inversion that we're using + + align:start position:0% +words the inversion that we're using + + + align:start position:0% +words the inversion that we're using +hinges very strongly on the requirement + + align:start position:0% +hinges very strongly on the requirement + + + align:start position:0% +hinges very strongly on the requirement +in other words the inversion requires + + align:start position:0% +in other words the inversion requires + + + align:start position:0% +in other words the inversion requires +the validity of interchanging Delta U + + align:start position:0% +the validity of interchanging Delta U + + + align:start position:0% +the validity of interchanging Delta U +and Delta U10 Etc now let me show you + + align:start position:0% +and Delta U10 Etc now let me show you + + + align:start position:0% +and Delta U10 Etc now let me show you +what that means more explicitly let's + + align:start position:0% +what that means more explicitly let's + + + align:start position:0% +what that means more explicitly let's +come back to something that we were + + align:start position:0% +come back to something that we were + + + align:start position:0% +come back to something that we were +talking about just a few moments ago + + align:start position:0% +talking about just a few moments ago + + + align:start position:0% +talking about just a few moments ago +from a completely mechanical point of + + align:start position:0% +from a completely mechanical point of + + + align:start position:0% +from a completely mechanical point of +view given that U equal F of XY and v g + + align:start position:0% +view given that U equal F of XY and v g + + + align:start position:0% +view given that U equal F of XY and v g +of XY we very mechanically wrote down + + align:start position:0% +of XY we very mechanically wrote down + + + align:start position:0% +of XY we very mechanically wrote down +that du was F subx DX plus F suby Dy DV + + align:start position:0% +that du was F subx DX plus F suby Dy DV + + + align:start position:0% +that du was F subx DX plus F suby Dy DV +was G subx DX plus G suby Dy and then we + + align:start position:0% +was G subx DX plus G suby Dy and then we + + + align:start position:0% +was G subx DX plus G suby Dy and then we +just mechanically solved for DX in terms + + align:start position:0% +just mechanically solved for DX in terms + + + align:start position:0% +just mechanically solved for DX in terms +of du and DV my claim is is that if we + + align:start position:0% +of du and DV my claim is is that if we + + + align:start position:0% +of du and DV my claim is is that if we +translate this thing if we Translate + + align:start position:0% +translate this thing if we Translate + + + align:start position:0% +translate this thing if we Translate +this thing into the language of Delta + + align:start position:0% +this thing into the language of Delta + + + align:start position:0% +this thing into the language of Delta +U's Delta X's Delta U Tans Delta X Tans + + align:start position:0% +U's Delta X's Delta U Tans Delta X Tans + + + align:start position:0% +U's Delta X's Delta U Tans Delta X Tans +Etc what we really said was what that + + align:start position:0% +Etc what we really said was what that + + + align:start position:0% +Etc what we really said was what that +Delta U Tan was the partial of f respect + + align:start position:0% +Delta U Tan was the partial of f respect + + + align:start position:0% +Delta U Tan was the partial of f respect +to x * Delta X plus the partial of f + + align:start position:0% +to x * Delta X plus the partial of f + + + align:start position:0% +to x * Delta X plus the partial of f +respect to y * Delta Y and Delta V tan + + align:start position:0% +respect to y * Delta Y and Delta V tan + + + align:start position:0% +respect to y * Delta Y and Delta V tan +was the partial of G respect to x * + + align:start position:0% +was the partial of G respect to x * + + + align:start position:0% +was the partial of G respect to x * +Delta X plus the partial of G respect to + + align:start position:0% +Delta X plus the partial of G respect to + + + align:start position:0% +Delta X plus the partial of G respect to +y * Delta Y and then when we eliminate a + + align:start position:0% +y * Delta Y and then when we eliminate a + + + align:start position:0% +y * Delta Y and then when we eliminate a +Delta y by multiplying the top equation + + align:start position:0% +Delta y by multiplying the top equation + + + align:start position:0% +Delta y by multiplying the top equation +by G suby and the bottom equation by + + align:start position:0% +by G suby and the bottom equation by + + + align:start position:0% +by G suby and the bottom equation by +minus F suby and adding what we found + + align:start position:0% +minus F suby and adding what we found + + + align:start position:0% +minus F suby and adding what we found +was how to express Delta X and catch + + align:start position:0% +was how to express Delta X and catch + + + align:start position:0% +was how to express Delta X and catch +this this is the key Point what we did + + align:start position:0% +this this is the key Point what we did + + + align:start position:0% +this this is the key Point what we did +was is we expressed Delta + + align:start position:0% + + + + align:start position:0% + +X as a linear combination not of Delta U + + align:start position:0% +X as a linear combination not of Delta U + + + align:start position:0% +X as a linear combination not of Delta U +and Delta V but of Delta U1 and Delta + + align:start position:0% +and Delta V but of Delta U1 and Delta + + + align:start position:0% +and Delta V but of Delta U1 and Delta +V1 you see notice that the result that + + align:start position:0% +V1 you see notice that the result that + + + align:start position:0% +V1 you see notice that the result that +we needed to have to be able to use + + align:start position:0% +we needed to have to be able to use + + + align:start position:0% +we needed to have to be able to use +differentials was not this but this see + + align:start position:0% +differentials was not this but this see + + + align:start position:0% +differentials was not this but this see +we found this not Delta X tan equals gy + + align:start position:0% +we found this not Delta X tan equals gy + + + align:start position:0% +we found this not Delta X tan equals gy +Delta uus F suby Delta V over f subx g + + align:start position:0% +Delta uus F suby Delta V over f subx g + + + align:start position:0% +Delta uus F suby Delta V over f subx g +suby minus f suby g subx to be able to + + align:start position:0% +suby minus f suby g subx to be able to + + + align:start position:0% +suby minus f suby g subx to be able to +say to invert this required that this + + align:start position:0% +say to invert this required that this + + + align:start position:0% +say to invert this required that this +was the expression that we + + align:start position:0% + + + + align:start position:0% + +had yet the expression that we were + + align:start position:0% +had yet the expression that we were + + + align:start position:0% +had yet the expression that we were +really evaluating was this one in fact + + align:start position:0% +really evaluating was this one in fact + + + align:start position:0% +really evaluating was this one in fact +let me come back for one moment and make + + align:start position:0% +let me come back for one moment and make + + + align:start position:0% +let me come back for one moment and make +sure that we see this you see notice + + align:start position:0% +sure that we see this you see notice + + + align:start position:0% +sure that we see this you see notice +again that the subtlety of going from + + align:start position:0% +again that the subtlety of going from + + + align:start position:0% +again that the subtlety of going from +here to here and inverting never shows + + align:start position:0% +here to here and inverting never shows + + + align:start position:0% +here to here and inverting never shows +us that we've interchanged the roles of + + align:start position:0% +us that we've interchanged the roles of + + + align:start position:0% +us that we've interchanged the roles of +u and v from being the dependent + + align:start position:0% +u and v from being the dependent + + + align:start position:0% +u and v from being the dependent +variables to the independent variables + + align:start position:0% +variables to the independent variables + + + align:start position:0% +variables to the independent variables +so the reason that there is so much work + + align:start position:0% +so the reason that there is so much work + + + align:start position:0% +so the reason that there is so much work +done in advanced textbooks Under The + + align:start position:0% +done in advanced textbooks Under The + + + align:start position:0% +done in advanced textbooks Under The +Heading of inverting systems of + + align:start position:0% +Heading of inverting systems of + + + align:start position:0% +Heading of inverting systems of +equations is to justify that being able + + align:start position:0% +equations is to justify that being able + + + align:start position:0% +equations is to justify that being able +to switch from Delta X to Delta X tan or + + align:start position:0% +to switch from Delta X to Delta X tan or + + + align:start position:0% +to switch from Delta X to Delta X tan or +from Delta U Tan to Delta U as we see + + align:start position:0% +from Delta U Tan to Delta U as we see + + + align:start position:0% +from Delta U Tan to Delta U as we see +fit whenever it serves our purposes the + + align:start position:0% +fit whenever it serves our purposes the + + + align:start position:0% +fit whenever it serves our purposes the +validity of being able to do that hinges + + align:start position:0% +validity of being able to do that hinges + + + align:start position:0% +validity of being able to do that hinges +on this more subtle type of proof that + + align:start position:0% +on this more subtle type of proof that + + + align:start position:0% +on this more subtle type of proof that +as far as I'm concerned goes beyond the + + align:start position:0% +as far as I'm concerned goes beyond the + + + align:start position:0% +as far as I'm concerned goes beyond the +scope of our text other than for the + + align:start position:0% +scope of our text other than for the + + + align:start position:0% +scope of our text other than for the +fact that in the learning exercises I + + align:start position:0% +fact that in the learning exercises I + + + align:start position:0% +fact that in the learning exercises I +will find excuses to bring up all of the + + align:start position:0% +will find excuses to bring up all of the + + + align:start position:0% +will find excuses to bring up all of the +situations that bring out where the + + align:start position:0% +situations that bring out where the + + + align:start position:0% +situations that bring out where the +theory is important in other words there + + align:start position:0% +theory is important in other words there + + + align:start position:0% +theory is important in other words there +will not be proofs of these more + + align:start position:0% +will not be proofs of these more + + + align:start position:0% +will not be proofs of these more +difficult things not because the proofs + + align:start position:0% +difficult things not because the proofs + + + align:start position:0% +difficult things not because the proofs +aren't important but from the point of + + align:start position:0% +aren't important but from the point of + + + align:start position:0% +aren't important but from the point of +view of what we're trying to do in our + + align:start position:0% +view of what we're trying to do in our + + + align:start position:0% +view of what we're trying to do in our +course these proofs tend to obscure the + + align:start position:0% +course these proofs tend to obscure the + + + align:start position:0% +course these proofs tend to obscure the +mainstream of things so what I will do + + align:start position:0% +mainstream of things so what I will do + + + align:start position:0% +mainstream of things so what I will do +in the learning exercises is bring up + + align:start position:0% +in the learning exercises is bring up + + + align:start position:0% +in the learning exercises is bring up +places that will show you why the theory + + align:start position:0% +places that will show you why the theory + + + align:start position:0% +places that will show you why the theory +is important at which point I will + + align:start position:0% +is important at which point I will + + + align:start position:0% +is important at which point I will +emphasize what the result of the theory + + align:start position:0% +emphasize what the result of the theory + + + align:start position:0% +emphasize what the result of the theory +is without belaboring you and be + + align:start position:0% +is without belaboring you and be + + + align:start position:0% +is without belaboring you and be +leaguing you with the proofs of these + + align:start position:0% +leaguing you with the proofs of these + + + align:start position:0% +leaguing you with the proofs of these +things at any rate what I'd like to do + + align:start position:0% +things at any rate what I'd like to do + + + align:start position:0% +things at any rate what I'd like to do +now next time time is to give you an + + align:start position:0% +now next time time is to give you an + + + align:start position:0% +now next time time is to give you an +example where all of the material of the + + align:start position:0% +example where all of the material of the + + + align:start position:0% +example where all of the material of the +blocks of material that we've done now + + align:start position:0% +blocks of material that we've done now + + + align:start position:0% +blocks of material that we've done now +on partial derivatives are sort of + + align:start position:0% +on partial derivatives are sort of + + + align:start position:0% +on partial derivatives are sort of +pulled together very nicely but at any + + align:start position:0% +pulled together very nicely but at any + + + align:start position:0% +pulled together very nicely but at any +rate we'll talk about that more next + + align:start position:0% +rate we'll talk about that more next + + + align:start position:0% +rate we'll talk about that more next +time and until next time + + align:start position:0% + + + + align:start position:0% + +goodbye funding for the publication of + + align:start position:0% +goodbye funding for the publication of + + + align:start position:0% +goodbye funding for the publication of +this video was provided by the Gabriella + + align:start position:0% +this video was provided by the Gabriella + + + align:start position:0% +this video was provided by the Gabriella +and Paul rosenbom + + align:start position:0% +and Paul rosenbom + + + align:start position:0% +and Paul rosenbom +foundation help ocw continue to provide + + align:start position:0% +foundation help ocw continue to provide + + + align:start position:0% +foundation help ocw continue to provide +free and open access to MIT courses by + + align:start position:0% +free and open access to MIT courses by + + + align:start position:0% +free and open access to MIT courses by +making a donation at ocw.mit.edu/donate \ No newline at end of file diff --git a/a2pU4XBIaWI.txt b/a2pU4XBIaWI.txt new file mode 100644 index 0000000000000000000000000000000000000000..53ef4911f1d4b44c30223cbef38e3c710f670936 --- /dev/null +++ b/a2pU4XBIaWI.txt @@ -0,0 +1,17603 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +so uh for today we're going to kind of + + align:start position:0% +so uh for today we're going to kind of + + + align:start position:0% +so uh for today we're going to kind of +continue this story of uh of this unit + + align:start position:0% +continue this story of uh of this unit + + + align:start position:0% +continue this story of uh of this unit +of what I what we began thinking about + + align:start position:0% +of what I what we began thinking about + + + align:start position:0% +of what I what we began thinking about +together last time uh a body of of uh of + + align:start position:0% +together last time uh a body of of uh of + + + align:start position:0% +together last time uh a body of of uh of +work a set of ideas it came to be + + align:start position:0% +work a set of ideas it came to be + + + align:start position:0% +work a set of ideas it came to be +grouped together under this title old + + align:start position:0% +grouped together under this title old + + + align:start position:0% +grouped together under this title old +quantum theory and as I mentioned last + + align:start position:0% +quantum theory and as I mentioned last + + + align:start position:0% +quantum theory and as I mentioned last +time that only makes sense once there's + + align:start position:0% +time that only makes sense once there's + + + align:start position:0% +time that only makes sense once there's +a new quantum theory uh to contrast it + + align:start position:0% +a new quantum theory uh to contrast it + + + align:start position:0% +a new quantum theory uh to contrast it +with so this is a term not only made up + + align:start position:0% +with so this is a term not only made up + + + align:start position:0% +with so this is a term not only made up +many many years after the fact this was + + align:start position:0% +many many years after the fact this was + + + align:start position:0% +many many years after the fact this was +introduced even by many leading + + align:start position:0% +introduced even by many leading + + + align:start position:0% +introduced even by many leading +physicists right around the years that + + align:start position:0% +physicists right around the years that + + + align:start position:0% +physicists right around the years that +we're describing so by the later years + + align:start position:0% +we're describing so by the later years + + + align:start position:0% +we're describing so by the later years +of the 1920s it already had become + + align:start position:0% +of the 1920s it already had become + + + align:start position:0% +of the 1920s it already had become +common to to make this kind of marker to + + align:start position:0% +common to to make this kind of marker to + + + align:start position:0% +common to to make this kind of marker to +distinguish between + + align:start position:0% +distinguish between + + + align:start position:0% +distinguish between +the kind of scatter shot developments + + align:start position:0% +the kind of scatter shot developments + + + align:start position:0% +the kind of scatter shot developments +that had been unfolding uh between + + align:start position:0% +that had been unfolding uh between + + + align:start position:0% +that had been unfolding uh between +roughly 1900 and 1924 or 25 or so and to + + align:start position:0% +roughly 1900 and 1924 or 25 or so and to + + + align:start position:0% +roughly 1900 and 1924 or 25 or so and to +bracket those together under these + + align:start position:0% +bracket those together under these + + + align:start position:0% +bracket those together under these +umbrella term old quantum theory because + + align:start position:0% +umbrella term old quantum theory because + + + align:start position:0% +umbrella term old quantum theory because +as we'll see starting actually in the + + align:start position:0% +as we'll see starting actually in the + + + align:start position:0% +as we'll see starting actually in the +next class by the mid 1920s there had + + align:start position:0% +next class by the mid 1920s there had + + + align:start position:0% +next class by the mid 1920s there had +been some uh some uh kind of uh some new + + align:start position:0% +been some uh some uh kind of uh some new + + + align:start position:0% +been some uh some uh kind of uh some new +bodies of work put forward that looked + + align:start position:0% +bodies of work put forward that looked + + + align:start position:0% +bodies of work put forward that looked +like this could really become the new + + align:start position:0% +like this could really become the new + + + align:start position:0% +like this could really become the new +quantum mechanics and not only a kind of + + align:start position:0% +quantum mechanics and not only a kind of + + + align:start position:0% +quantum mechanics and not only a kind of +hodgepodge of suggestive ideas within + + align:start position:0% +hodgepodge of suggestive ideas within + + + align:start position:0% +hodgepodge of suggestive ideas within +what then became known as old quantum + + align:start position:0% +what then became known as old quantum + + + align:start position:0% +what then became known as old quantum +theory so as last time I just want to + + align:start position:0% +theory so as last time I just want to + + + align:start position:0% +theory so as last time I just want to +remind you these dates uh that I include + + align:start position:0% +remind you these dates uh that I include + + + align:start position:0% +remind you these dates uh that I include +here are kind of convenient and limited + + align:start position:0% +here are kind of convenient and limited + + + align:start position:0% +here are kind of convenient and limited +so it as as we've seen throughout the + + align:start position:0% +so it as as we've seen throughout the + + + align:start position:0% +so it as as we've seen throughout the +entire term so far we'll keep seeing + + align:start position:0% +entire term so far we'll keep seeing + + + align:start position:0% +entire term so far we'll keep seeing +examples of this well beyond + + align:start position:0% +examples of this well beyond + + + align:start position:0% +examples of this well beyond +even our quantum theory unit the dates + + align:start position:0% +even our quantum theory unit the dates + + + align:start position:0% +even our quantum theory unit the dates +that we assigned in these things have to + + align:start position:0% +that we assigned in these things have to + + + align:start position:0% +that we assigned in these things have to +be taken you know with some with some + + align:start position:0% +be taken you know with some with some + + + align:start position:0% +be taken you know with some with some +grains of salt we have to kind of squint + + align:start position:0% +grains of salt we have to kind of squint + + + align:start position:0% +grains of salt we have to kind of squint +at them a bit they're helpful by giving + + align:start position:0% +at them a bit they're helpful by giving + + + align:start position:0% +at them a bit they're helpful by giving +us a rough sense of the flow and where + + align:start position:0% +us a rough sense of the flow and where + + + align:start position:0% +us a rough sense of the flow and where +within this evolving body of work + + align:start position:0% +within this evolving body of work + + + align:start position:0% +within this evolving body of work +um do these particular developments fit + + align:start position:0% +um do these particular developments fit + + + align:start position:0% +um do these particular developments fit +in but remember that it's not like + + align:start position:0% +in but remember that it's not like + + + align:start position:0% +in but remember that it's not like +someone you know conducted a single + + align:start position:0% +someone you know conducted a single + + + align:start position:0% +someone you know conducted a single +experiment or published a single paper + + align:start position:0% +experiment or published a single paper + + + align:start position:0% +experiment or published a single paper +with a kind of date and then afterwards + + align:start position:0% +with a kind of date and then afterwards + + + align:start position:0% +with a kind of date and then afterwards +everyone agreed and moved on and that's + + align:start position:0% +everyone agreed and moved on and that's + + + align:start position:0% +everyone agreed and moved on and that's +again we'll find that to be true for + + align:start position:0% +again we'll find that to be true for + + + align:start position:0% +again we'll find that to be true for +these examples today we've certainly + + align:start position:0% +these examples today we've certainly + + + align:start position:0% +these examples today we've certainly +seen it through uh in previous + + align:start position:0% +seen it through uh in previous + + + align:start position:0% +seen it through uh in previous +discussions + + align:start position:0% +discussions + + + align:start position:0% +discussions +so with those caveats today we're going + + align:start position:0% +so with those caveats today we're going + + + align:start position:0% +so with those caveats today we're going +to look at this this kind of more + + align:start position:0% +to look at this this kind of more + + + align:start position:0% +to look at this this kind of more +purplish rectangle to contrast it with + + align:start position:0% +purplish rectangle to contrast it with + + + align:start position:0% +purplish rectangle to contrast it with +this reddish pinkish one so last time we + + align:start position:0% +this reddish pinkish one so last time we + + + align:start position:0% +this reddish pinkish one so last time we +looked at some of these moments of + + align:start position:0% +looked at some of these moments of + + + align:start position:0% +looked at some of these moments of +physicists sometimes very + + align:start position:0% +physicists sometimes very + + + align:start position:0% +physicists sometimes very +um + + align:start position:0% +um + + + align:start position:0% +um +begrudgingly rethinking the nature of + + align:start position:0% +begrudgingly rethinking the nature of + + + align:start position:0% +begrudgingly rethinking the nature of +light not always going into it with that + + align:start position:0% +light not always going into it with that + + + align:start position:0% +light not always going into it with that +as their plan but coming out uh having + + align:start position:0% +as their plan but coming out uh having + + + align:start position:0% +as their plan but coming out uh having +rethought what how physicists should + + align:start position:0% +rethought what how physicists should + + + align:start position:0% +rethought what how physicists should +describe light we saw instances of more + + align:start position:0% +describe light we saw instances of more + + + align:start position:0% +describe light we saw instances of more +and more attention to to quantization + + align:start position:0% +and more attention to to quantization + + + align:start position:0% +and more attention to to quantization +discreteness maybe light even had a kind + + align:start position:0% +discreteness maybe light even had a kind + + + align:start position:0% +discreteness maybe light even had a kind +of specific particulate or particle-like + + align:start position:0% +of specific particulate or particle-like + + + align:start position:0% +of specific particulate or particle-like +behavior and today we're going to look + + align:start position:0% +behavior and today we're going to look + + + align:start position:0% +behavior and today we're going to look +at a kind of inverse or uh the the sort + + align:start position:0% +at a kind of inverse or uh the the sort + + + align:start position:0% +at a kind of inverse or uh the the sort +of the other half of those discussions + + align:start position:0% +of the other half of those discussions + + + align:start position:0% +of the other half of those discussions +as physicists uh began rethinking the + + align:start position:0% +as physicists uh began rethinking the + + + align:start position:0% +as physicists uh began rethinking the +nature of matter again not always going + + align:start position:0% +nature of matter again not always going + + + align:start position:0% +nature of matter again not always going +into that with that in mind but that's + + align:start position:0% +into that with that in mind but that's + + + align:start position:0% +into that with that in mind but that's +how these sort of developments uh really + + align:start position:0% +how these sort of developments uh really + + + align:start position:0% +how these sort of developments uh really +began to add up so today we'll look at + + align:start position:0% +began to add up so today we'll look at + + + align:start position:0% +began to add up so today we'll look at +this the second half a mirror half of + + align:start position:0% +this the second half a mirror half of + + + align:start position:0% +this the second half a mirror half of +the old quantum theory rethinking matter + + align:start position:0% +the old quantum theory rethinking matter + + + align:start position:0% +the old quantum theory rethinking matter +so + + align:start position:0% +so + + + align:start position:0% +so +by the closing years of the 19th century + + align:start position:0% +by the closing years of the 19th century + + + align:start position:0% +by the closing years of the 19th century +really in the last say two were or most + + align:start position:0% +really in the last say two were or most + + + align:start position:0% +really in the last say two were or most +three decades of uh the 19th century + + align:start position:0% +three decades of uh the 19th century + + + align:start position:0% +three decades of uh the 19th century +there really seemed to be a coalesce + + align:start position:0% +there really seemed to be a coalesce + + + align:start position:0% +there really seemed to be a coalesce +it's a pretty amazing achievement uh + + align:start position:0% +it's a pretty amazing achievement uh + + + align:start position:0% +it's a pretty amazing achievement uh +among uh physicists and Chemists in many + + align:start position:0% +among uh physicists and Chemists in many + + + align:start position:0% +among uh physicists and Chemists in many +many parts of the world it looked like + + align:start position:0% +many parts of the world it looked like + + + align:start position:0% +many parts of the world it looked like +physicists at and campus natural + + align:start position:0% +physicists at and campus natural + + + align:start position:0% +physicists at and campus natural +scientists more broadly had figured out + + align:start position:0% +scientists more broadly had figured out + + + align:start position:0% +scientists more broadly had figured out +a really deep kind of regularity to the + + align:start position:0% +a really deep kind of regularity to the + + + align:start position:0% +a really deep kind of regularity to the +stuff of which the world has made you + + align:start position:0% +stuff of which the world has made you + + + align:start position:0% +stuff of which the world has made you +think about here's an illustration of + + align:start position:0% +think about here's an illustration of + + + align:start position:0% +think about here's an illustration of +one of the very first published versions + + align:start position:0% +one of the very first published versions + + + align:start position:0% +one of the very first published versions +of Dimitri mendeleev's periodic table + + align:start position:0% +of Dimitri mendeleev's periodic table + + + align:start position:0% +of Dimitri mendeleev's periodic table +doesn't look quite the way we'd expect + + align:start position:0% +doesn't look quite the way we'd expect + + + align:start position:0% +doesn't look quite the way we'd expect +it today it's it's actually oriented in + + align:start position:0% +it today it's it's actually oriented in + + + align:start position:0% +it today it's it's actually oriented in +the obvious opposite orientation that + + align:start position:0% +the obvious opposite orientation that + + + align:start position:0% +the obvious opposite orientation that +we're used to but this was a remarkable + + align:start position:0% +we're used to but this was a remarkable + + + align:start position:0% +we're used to but this was a remarkable +effort at ordering ordering the stuff + + align:start position:0% +effort at ordering ordering the stuff + + + align:start position:0% +effort at ordering ordering the stuff +from which all other things seems to be + + align:start position:0% +from which all other things seems to be + + + align:start position:0% +from which all other things seems to be +made + + align:start position:0% +made + + + align:start position:0% +made +and uh on the strength of work like + + align:start position:0% +and uh on the strength of work like + + + align:start position:0% +and uh on the strength of work like +mendeleevs and many others uh by the + + align:start position:0% +mendeleevs and many others uh by the + + + align:start position:0% +mendeleevs and many others uh by the +late 19th century it seemed clear that + + align:start position:0% +late 19th century it seemed clear that + + + align:start position:0% +late 19th century it seemed clear that +matter consisted of chemical elements + + align:start position:0% +matter consisted of chemical elements + + + align:start position:0% +matter consisted of chemical elements +that would behave certain ways in + + align:start position:0% +that would behave certain ways in + + + align:start position:0% +that would behave certain ways in +chemical reactions and a given chemical + + align:start position:0% +chemical reactions and a given chemical + + + align:start position:0% +chemical reactions and a given chemical +element hydrogen beryllium iron uranium + + align:start position:0% +element hydrogen beryllium iron uranium + + + align:start position:0% +element hydrogen beryllium iron uranium +consisted of physical atoms so there was + + align:start position:0% +consisted of physical atoms so there was + + + align:start position:0% +consisted of physical atoms so there was +a kind of a two-part way of making + + align:start position:0% +a kind of a two-part way of making + + + align:start position:0% +a kind of a two-part way of making +trying to make sense of the world + + align:start position:0% +trying to make sense of the world + + + align:start position:0% +trying to make sense of the world +and that seemed really great until + + align:start position:0% +and that seemed really great until + + + align:start position:0% +and that seemed really great until +suddenly more complications began to + + align:start position:0% +suddenly more complications began to + + + align:start position:0% +suddenly more complications began to +really crowd in so not too long after + + align:start position:0% +really crowd in so not too long after + + + align:start position:0% +really crowd in so not too long after +this really kind of amazing synthetic + + align:start position:0% +this really kind of amazing synthetic + + + align:start position:0% +this really kind of amazing synthetic +achievement to bring together lots and + + align:start position:0% +achievement to bring together lots and + + + align:start position:0% +achievement to bring together lots and +lots of disparate phenomena in in things + + align:start position:0% +lots of disparate phenomena in in things + + + align:start position:0% +lots of disparate phenomena in in things +like the periodic table and this + + align:start position:0% +like the periodic table and this + + + align:start position:0% +like the periodic table and this +association between chemical elements + + align:start position:0% +association between chemical elements + + + align:start position:0% +association between chemical elements +and physical atoms pretty soon there + + align:start position:0% +and physical atoms pretty soon there + + + align:start position:0% +and physical atoms pretty soon there +were some new challenges to that to that + + align:start position:0% +were some new challenges to that to that + + + align:start position:0% +were some new challenges to that to that +whole scheme + + align:start position:0% +whole scheme + + + align:start position:0% +whole scheme +starting really uh in the mid-1890s and + + align:start position:0% +starting really uh in the mid-1890s and + + + align:start position:0% +starting really uh in the mid-1890s and +moving sometimes very quickly this + + align:start position:0% +moving sometimes very quickly this + + + align:start position:0% +moving sometimes very quickly this +caught a lot of people by surprise + + align:start position:0% +caught a lot of people by surprise + + + align:start position:0% +caught a lot of people by surprise +some of this was was accelerated by new + + align:start position:0% +some of this was was accelerated by new + + + align:start position:0% +some of this was was accelerated by new +types of instruments there are whole new + + align:start position:0% +types of instruments there are whole new + + + align:start position:0% +types of instruments there are whole new +kinds of ways of trying to probe the + + align:start position:0% +kinds of ways of trying to probe the + + + align:start position:0% +kinds of ways of trying to probe the +behavior of matter and radiation Cloud + + align:start position:0% +behavior of matter and radiation Cloud + + + align:start position:0% +behavior of matter and radiation Cloud +Chambers fluorescent screens that would + + align:start position:0% +Chambers fluorescent screens that would + + + align:start position:0% +Chambers fluorescent screens that would +kind of glow and they interacted with + + align:start position:0% +kind of glow and they interacted with + + + align:start position:0% +kind of glow and they interacted with +certain kinds of matter or energy + + align:start position:0% +certain kinds of matter or energy + + + align:start position:0% +certain kinds of matter or energy +photographic techniques remember + + align:start position:0% +photographic techniques remember + + + align:start position:0% +photographic techniques remember +photography of any kind was still pretty + + align:start position:0% +photography of any kind was still pretty + + + align:start position:0% +photography of any kind was still pretty +new in the middle Decades of the 19th + + align:start position:0% +new in the middle Decades of the 19th + + + align:start position:0% +new in the middle Decades of the 19th +century so trying to make reliable + + align:start position:0% +century so trying to make reliable + + + align:start position:0% +century so trying to make reliable +repeatable use of photographic plates + + align:start position:0% +repeatable use of photographic plates + + + align:start position:0% +repeatable use of photographic plates +that was still pretty new even by the + + align:start position:0% +that was still pretty new even by the + + + align:start position:0% +that was still pretty new even by the +1880s and 90s so through this kind of + + align:start position:0% +1880s and 90s so through this kind of + + + align:start position:0% +1880s and 90s so through this kind of +constellation of new techniques + + align:start position:0% +constellation of new techniques + + + align:start position:0% +constellation of new techniques +some sort of accidental uh incidents in + + align:start position:0% +some sort of accidental uh incidents in + + + align:start position:0% +some sort of accidental uh incidents in +various laboratories on unexpected + + align:start position:0% +various laboratories on unexpected + + + align:start position:0% +various laboratories on unexpected +researchers uh in many parts of the + + align:start position:0% +researchers uh in many parts of the + + + align:start position:0% +researchers uh in many parts of the +world in the 1890s in particular began + + align:start position:0% +world in the 1890s in particular began + + + align:start position:0% +world in the 1890s in particular began +to identify several different kinds of + + align:start position:0% +to identify several different kinds of + + + align:start position:0% +to identify several different kinds of +radiations or kind of emanations things + + align:start position:0% +radiations or kind of emanations things + + + align:start position:0% +radiations or kind of emanations things +that some kind of energy that could be + + align:start position:0% +that some kind of energy that could be + + + align:start position:0% +that some kind of energy that could be +flowing out of what had once seemed like + + align:start position:0% +flowing out of what had once seemed like + + + align:start position:0% +flowing out of what had once seemed like +stable + + align:start position:0% +stable + + + align:start position:0% +stable +um kind of boring matter + + align:start position:0% +um kind of boring matter + + + align:start position:0% +um kind of boring matter +and so there are a couple of these kind + + align:start position:0% +and so there are a couple of these kind + + + align:start position:0% +and so there are a couple of these kind +of points along the way that became + + align:start position:0% +of points along the way that became + + + align:start position:0% +of points along the way that became +worldwide Sensations in real time not + + align:start position:0% +worldwide Sensations in real time not + + + align:start position:0% +worldwide Sensations in real time not +only did we look back and say oh that + + align:start position:0% +only did we look back and say oh that + + + align:start position:0% +only did we look back and say oh that +was exciting but even at the day at the + + align:start position:0% +was exciting but even at the day at the + + + align:start position:0% +was exciting but even at the day at the +time this became literally headline news + + align:start position:0% +time this became literally headline news + + + align:start position:0% +time this became literally headline news +in many many parts of the world I mean + + align:start position:0% +in many many parts of the world I mean + + + align:start position:0% +in many many parts of the world I mean +throughout multiple continents and so we + + align:start position:0% +throughout multiple continents and so we + + + align:start position:0% +throughout multiple continents and so we +can again kind of attach kind of names + + align:start position:0% +can again kind of attach kind of names + + + align:start position:0% +can again kind of attach kind of names +and dates and understand these these + + align:start position:0% +and dates and understand these these + + + align:start position:0% +and dates and understand these these +were kind of extended activities + + align:start position:0% +were kind of extended activities + + + align:start position:0% +were kind of extended activities +uh one of those had to do with what + + align:start position:0% +uh one of those had to do with what + + + align:start position:0% +uh one of those had to do with what +became known as radioactivity and though + + align:start position:0% +became known as radioactivity and though + + + align:start position:0% +became known as radioactivity and though +there were many people involved in this + + align:start position:0% +there were many people involved in this + + + align:start position:0% +there were many people involved in this +very quickly among the most prominent + + align:start position:0% +very quickly among the most prominent + + + align:start position:0% +very quickly among the most prominent +the most famous + + align:start position:0% +the most famous + + + align:start position:0% +the most famous +uh researchers on this area included + + align:start position:0% +uh researchers on this area included + + + align:start position:0% +uh researchers on this area included +Pierre and Marie Curie shown here uh + + align:start position:0% +Pierre and Marie Curie shown here uh + + + align:start position:0% +Pierre and Marie Curie shown here uh +Marie Curie originally uh Maurice + + align:start position:0% +Marie Curie originally uh Maurice + + + align:start position:0% +Marie Curie originally uh Maurice +gladovska from a young student from + + align:start position:0% +gladovska from a young student from + + + align:start position:0% +gladovska from a young student from +Poland she'd made her way to study in + + align:start position:0% +Poland she'd made her way to study in + + + align:start position:0% +Poland she'd made her way to study in +Paris she met Pierre was quite a bit + + align:start position:0% +Paris she met Pierre was quite a bit + + + align:start position:0% +Paris she met Pierre was quite a bit +older they they got married they teamed + + align:start position:0% +older they they got married they teamed + + + align:start position:0% +older they they got married they teamed +up they became a remarkable research + + align:start position:0% +up they became a remarkable research + + + align:start position:0% +up they became a remarkable research +team investigating some of these kind of + + align:start position:0% +team investigating some of these kind of + + + align:start position:0% +team investigating some of these kind of +radiations or radioactive uh behaviors + + align:start position:0% +radiations or radioactive uh behaviors + + + align:start position:0% +radiations or radioactive uh behaviors +of a range of elements in fact + + align:start position:0% +of a range of elements in fact + + + align:start position:0% +of a range of elements in fact +identifying a whole new uh forms of of + + align:start position:0% +identifying a whole new uh forms of of + + + align:start position:0% +identifying a whole new uh forms of of +matter and radiation interaction right + + align:start position:0% +matter and radiation interaction right + + + align:start position:0% +matter and radiation interaction right +around that time roughly you know a year + + align:start position:0% +around that time roughly you know a year + + + align:start position:0% +around that time roughly you know a year +later there was a distinct set of + + align:start position:0% +later there was a distinct set of + + + align:start position:0% +later there was a distinct set of +developments coming in this case out of + + align:start position:0% +developments coming in this case out of + + + align:start position:0% +developments coming in this case out of +Cambridge University + + align:start position:0% +Cambridge University + + + align:start position:0% +Cambridge University +associated with J.J Thompson who's shown + + align:start position:0% +associated with J.J Thompson who's shown + + + align:start position:0% +associated with J.J Thompson who's shown +here he was experimenting uh with + + align:start position:0% +here he was experimenting uh with + + + align:start position:0% +here he was experimenting uh with +different kinds of stuff and different + + align:start position:0% +different kinds of stuff and different + + + align:start position:0% +different kinds of stuff and different +instruments and different techniques he + + align:start position:0% +instruments and different techniques he + + + align:start position:0% +instruments and different techniques he +began identifying what became known as + + align:start position:0% +began identifying what became known as + + + align:start position:0% +began identifying what became known as +cathode rays we would Now call those + + align:start position:0% +cathode rays we would Now call those + + + align:start position:0% +cathode rays we would Now call those +electrons uh a different sort of kind of + + align:start position:0% +electrons uh a different sort of kind of + + + align:start position:0% +electrons uh a different sort of kind of +energetic beam that could come out of + + align:start position:0% +energetic beam that could come out of + + + align:start position:0% +energetic beam that could come out of +one form of matter and cause effects on + + align:start position:0% +one form of matter and cause effects on + + + align:start position:0% +one form of matter and cause effects on +other forms of matter so all these these + + align:start position:0% +other forms of matter so all these these + + + align:start position:0% +other forms of matter so all these these +activities which were often quite + + align:start position:0% +activities which were often quite + + + align:start position:0% +activities which were often quite +surprising when first identified + + align:start position:0% +surprising when first identified + + + align:start position:0% +surprising when first identified +they suggested that atoms could fall + + align:start position:0% +they suggested that atoms could fall + + + align:start position:0% +they suggested that atoms could fall +apart and that they have internal + + align:start position:0% +apart and that they have internal + + + align:start position:0% +apart and that they have internal +structure and this was a big deal + + align:start position:0% +structure and this was a big deal + + + align:start position:0% +structure and this was a big deal +because as you may know the word Adam + + align:start position:0% +because as you may know the word Adam + + + align:start position:0% +because as you may know the word Adam +itself was derived from an ancient Greek + + align:start position:0% +itself was derived from an ancient Greek + + + align:start position:0% +itself was derived from an ancient Greek +word that means indivisible or + + align:start position:0% +word that means indivisible or + + + align:start position:0% +word that means indivisible or +unbreakable and so all this effort from + + align:start position:0% +unbreakable and so all this effort from + + + align:start position:0% +unbreakable and so all this effort from +uh you know Lavoisier through Mendeleev + + align:start position:0% +uh you know Lavoisier through Mendeleev + + + align:start position:0% +uh you know Lavoisier through Mendeleev +to understand the regularity of chemical + + align:start position:0% +to understand the regularity of chemical + + + align:start position:0% +to understand the regularity of chemical +elements associated with physical atoms + + align:start position:0% +elements associated with physical atoms + + + align:start position:0% +elements associated with physical atoms +that was really under some new strain of + + align:start position:0% +that was really under some new strain of + + + align:start position:0% +that was really under some new strain of +atoms themselves were actually not + + align:start position:0% +atoms themselves were actually not + + + align:start position:0% +atoms themselves were actually not +Atomic if they really could be broken + + align:start position:0% +Atomic if they really could be broken + + + align:start position:0% +Atomic if they really could be broken +apart if they have some internal + + align:start position:0% +apart if they have some internal + + + align:start position:0% +apart if they have some internal +structure + + align:start position:0% +structure + + + align:start position:0% +structure +and so by 1900 with this kind of + + align:start position:0% +and so by 1900 with this kind of + + + align:start position:0% +and so by 1900 with this kind of +remarkable series of developments + + align:start position:0% +remarkable series of developments + + + align:start position:0% +remarkable series of developments +throughout the 1890s + + align:start position:0% +throughout the 1890s + + + align:start position:0% +throughout the 1890s +researchers had begun to identify + + align:start position:0% +researchers had begun to identify + + + align:start position:0% +researchers had begun to identify +different kinds of stuff that flew out + + align:start position:0% +different kinds of stuff that flew out + + + align:start position:0% +different kinds of stuff that flew out +that they could fly out of matter + + align:start position:0% +that they could fly out of matter + + + align:start position:0% +that they could fly out of matter +different kinds of radiations and they + + align:start position:0% +different kinds of radiations and they + + + align:start position:0% +different kinds of radiations and they +had different properties so for example + + align:start position:0% +had different properties so for example + + + align:start position:0% +had different properties so for example +some of these emanations or radiations + + align:start position:0% +some of these emanations or radiations + + + align:start position:0% +some of these emanations or radiations +were easily deflected by an external + + align:start position:0% +were easily deflected by an external + + + align:start position:0% +were easily deflected by an external +magnetic field you could actually watch + + align:start position:0% +magnetic field you could actually watch + + + align:start position:0% +magnetic field you could actually watch +you know see the bending path others + + align:start position:0% +you know see the bending path others + + + align:start position:0% +you know see the bending path others +seems not to be deflected At All by + + align:start position:0% +seems not to be deflected At All by + + + align:start position:0% +seems not to be deflected At All by +magnets some of these could fog could + + align:start position:0% +magnets some of these could fog could + + + align:start position:0% +magnets some of these could fog could +begin to kind of um expose a + + align:start position:0% +begin to kind of um expose a + + + align:start position:0% +begin to kind of um expose a +photographic plate leave a kind of + + align:start position:0% +photographic plate leave a kind of + + + align:start position:0% +photographic plate leave a kind of +smudge either the plates were protected + + align:start position:0% +smudge either the plates were protected + + + align:start position:0% +smudge either the plates were protected +you know wrapped up in dark paper uh in + + align:start position:0% +you know wrapped up in dark paper uh in + + + align:start position:0% +you know wrapped up in dark paper uh in +in some desk drawer not in the direct + + align:start position:0% +in some desk drawer not in the direct + + + align:start position:0% +in some desk drawer not in the direct +line of uh fire so they had different + + align:start position:0% +line of uh fire so they had different + + + align:start position:0% +line of uh fire so they had different +properties so what what researchers + + align:start position:0% +properties so what what researchers + + + align:start position:0% +properties so what what researchers +began to do is just try to classify them + + align:start position:0% +began to do is just try to classify them + + + align:start position:0% +began to do is just try to classify them +by different kind of neutral sounding + + align:start position:0% +by different kind of neutral sounding + + + align:start position:0% +by different kind of neutral sounding +names they just began at the start of + + align:start position:0% +names they just began at the start of + + + align:start position:0% +names they just began at the start of +the Greek alphabet and named one kind + + align:start position:0% +the Greek alphabet and named one kind + + + align:start position:0% +the Greek alphabet and named one kind +Alpha Rays Another Kind beta Rays a + + align:start position:0% +Alpha Rays Another Kind beta Rays a + + + align:start position:0% +Alpha Rays Another Kind beta Rays a +third type gamma and they figured they'd + + align:start position:0% +third type gamma and they figured they'd + + + align:start position:0% +third type gamma and they figured they'd +just keep going as many letters as + + align:start position:0% +just keep going as many letters as + + + align:start position:0% +just keep going as many letters as +needed they didn't know what caused + + align:start position:0% +needed they didn't know what caused + + + align:start position:0% +needed they didn't know what caused +these emanations or radiations but they + + align:start position:0% +these emanations or radiations but they + + + align:start position:0% +these emanations or radiations but they +could at least begin to classify or + + align:start position:0% +could at least begin to classify or + + + align:start position:0% +could at least begin to classify or +distinguish among them because the the + + align:start position:0% +distinguish among them because the the + + + align:start position:0% +distinguish among them because the the +radiations themselves really did seem to + + align:start position:0% +radiations themselves really did seem to + + + align:start position:0% +radiations themselves really did seem to +have some different properties + + align:start position:0% +have some different properties + + + align:start position:0% +have some different properties +and again this was remarkably + + align:start position:0% +and again this was remarkably + + + align:start position:0% +and again this was remarkably +interesting news at the time uh the + + align:start position:0% +interesting news at the time uh the + + + align:start position:0% +interesting news at the time uh the +curies in particular were became really + + align:start position:0% +curies in particular were became really + + + align:start position:0% +curies in particular were became really +kind of media Sensations especially + + align:start position:0% +kind of media Sensations especially + + + align:start position:0% +kind of media Sensations especially +Marie Curie it was as you may know or + + align:start position:0% +Marie Curie it was as you may know or + + + align:start position:0% +Marie Curie it was as you may know or +can imagine this was really really + + align:start position:0% +can imagine this was really really + + + align:start position:0% +can imagine this was really really +unusual to have a world-class leading + + align:start position:0% +unusual to have a world-class leading + + + align:start position:0% +unusual to have a world-class leading +researcher in The Sciences who happen to + + align:start position:0% +researcher in The Sciences who happen to + + + align:start position:0% +researcher in The Sciences who happen to +be a woman and there was tremendous + + align:start position:0% +be a woman and there was tremendous + + + align:start position:0% +be a woman and there was tremendous +speculation about was she just like + + align:start position:0% +speculation about was she just like + + + align:start position:0% +speculation about was she just like +other women was she a caring mother or + + align:start position:0% +other women was she a caring mother or + + + align:start position:0% +other women was she a caring mother or +not really in from today's one of your + + align:start position:0% +not really in from today's one of your + + + align:start position:0% +not really in from today's one of your +horribly horribly gender stereotyped + + align:start position:0% +horribly horribly gender stereotyped + + + align:start position:0% +horribly horribly gender stereotyped +often very unfair attributes uh + + align:start position:0% +often very unfair attributes uh + + + align:start position:0% +often very unfair attributes uh +attributed to her in the in the wide + + align:start position:0% +attributed to her in the in the wide + + + align:start position:0% +attributed to her in the in the wide +press when she when her when Pierre + + align:start position:0% +press when she when her when Pierre + + + align:start position:0% +press when she when her when Pierre +passed away she had a relationship with + + align:start position:0% +passed away she had a relationship with + + + align:start position:0% +passed away she had a relationship with +another researcher it was uh French + + align:start position:0% +another researcher it was uh French + + + align:start position:0% +another researcher it was uh French +Scandal and and people wanted to know + + align:start position:0% +Scandal and and people wanted to know + + + align:start position:0% +Scandal and and people wanted to know +these kind of scurlish details of her + + align:start position:0% +these kind of scurlish details of her + + + align:start position:0% +these kind of scurlish details of her +private life + + align:start position:0% +private life + + + align:start position:0% +private life +on the other hand she was sort of + + align:start position:0% +on the other hand she was sort of + + + align:start position:0% +on the other hand she was sort of +constantly uh in the news and people + + align:start position:0% +constantly uh in the news and people + + + align:start position:0% +constantly uh in the news and people +were really curious uh and she was of + + align:start position:0% +were really curious uh and she was of + + + align:start position:0% +were really curious uh and she was of +course the first person to win two Nobel + + align:start position:0% +course the first person to win two Nobel + + + align:start position:0% +course the first person to win two Nobel +prizes one in chemistry and one of + + align:start position:0% +prizes one in chemistry and one of + + + align:start position:0% +prizes one in chemistry and one of +physics and I just find this remarkable + + align:start position:0% +physics and I just find this remarkable + + + align:start position:0% +physics and I just find this remarkable +this wasn't only true at turn of the + + align:start position:0% +this wasn't only true at turn of the + + + align:start position:0% +this wasn't only true at turn of the +century Paris but as recently as last + + align:start position:0% +century Paris but as recently as last + + + align:start position:0% +century Paris but as recently as last +year there was a major + + align:start position:0% +year there was a major + + + align:start position:0% +year there was a major +film some of you might have seen + + align:start position:0% +film some of you might have seen + + + align:start position:0% +film some of you might have seen +starring a major film star Roseman Pike + + align:start position:0% +starring a major film star Roseman Pike + + + align:start position:0% +starring a major film star Roseman Pike +playing yet again yet another film + + align:start position:0% +playing yet again yet another film + + + align:start position:0% +playing yet again yet another film +adaptation of the life of mariki + + align:start position:0% +adaptation of the life of mariki + + + align:start position:0% +adaptation of the life of mariki +research her personal story continues to + + align:start position:0% +research her personal story continues to + + + align:start position:0% +research her personal story continues to +Fascinate as well uh and that was true + + align:start position:0% +Fascinate as well uh and that was true + + + align:start position:0% +Fascinate as well uh and that was true +really from the beginning in real time + + align:start position:0% +really from the beginning in real time + + + align:start position:0% +really from the beginning in real time +she was already a kind of media + + align:start position:0% +she was already a kind of media + + + align:start position:0% +she was already a kind of media +sensation as were these findings things + + align:start position:0% +sensation as were these findings things + + + align:start position:0% +sensation as were these findings things +like these mysterious ghost-like rays + + align:start position:0% +like these mysterious ghost-like rays + + + align:start position:0% +like these mysterious ghost-like rays +that often people's eyes couldn't + + align:start position:0% +that often people's eyes couldn't + + + align:start position:0% +that often people's eyes couldn't +register but could have effects across + + align:start position:0% +register but could have effects across + + + align:start position:0% +register but could have effects across +the room it was a really remarkable + + align:start position:0% +the room it was a really remarkable + + + align:start position:0% +the room it was a really remarkable +conjunction + + align:start position:0% +conjunction + + + align:start position:0% +conjunction +so one of the younger folks who got + + align:start position:0% +so one of the younger folks who got + + + align:start position:0% +so one of the younger folks who got +really excited about this uh was Ernest + + align:start position:0% +really excited about this uh was Ernest + + + align:start position:0% +really excited about this uh was Ernest +Rutherford he was a bit younger than the + + align:start position:0% +Rutherford he was a bit younger than the + + + align:start position:0% +Rutherford he was a bit younger than the +curies he was a um kind of the Next + + align:start position:0% +curies he was a um kind of the Next + + + align:start position:0% +curies he was a um kind of the Next +Generation coming up he grew up in New + + align:start position:0% +Generation coming up he grew up in New + + + align:start position:0% +Generation coming up he grew up in New +Zealand but he was a very promising + + align:start position:0% +Zealand but he was a very promising + + + align:start position:0% +Zealand but he was a very promising +young student and he received a + + align:start position:0% +young student and he received a + + + align:start position:0% +young student and he received a +fellowship to come to England to to + + align:start position:0% +fellowship to come to England to to + + + align:start position:0% +fellowship to come to England to to +Cambridge to study to finish his studies + + align:start position:0% +Cambridge to study to finish his studies + + + align:start position:0% +Cambridge to study to finish his studies +there he actually studied under JJ + + align:start position:0% +there he actually studied under JJ + + + align:start position:0% +there he actually studied under JJ +Thompson the person who in 1897 was + + align:start position:0% +Thompson the person who in 1897 was + + + align:start position:0% +Thompson the person who in 1897 was +experimenting with these cathode rays + + align:start position:0% +experimenting with these cathode rays + + + align:start position:0% +experimenting with these cathode rays +that I I mentioned briefly before he + + align:start position:0% +that I I mentioned briefly before he + + + align:start position:0% +that I I mentioned briefly before he +joined uh Thompson's group of the + + align:start position:0% +joined uh Thompson's group of the + + + align:start position:0% +joined uh Thompson's group of the +Cavendish really right at that time + + align:start position:0% +Cavendish really right at that time + + + align:start position:0% +Cavendish really right at that time +Rutherford was there just in the midst + + align:start position:0% +Rutherford was there just in the midst + + + align:start position:0% +Rutherford was there just in the midst +of this tremendous excitement over some + + align:start position:0% +of this tremendous excitement over some + + + align:start position:0% +of this tremendous excitement over some +of these new Rays like like Thompson's + + align:start position:0% +of these new Rays like like Thompson's + + + align:start position:0% +of these new Rays like like Thompson's +um cathode rays + + align:start position:0% +um cathode rays + + + align:start position:0% +um cathode rays +Rutherford became fascinated by this + + align:start position:0% +Rutherford became fascinated by this + + + align:start position:0% +Rutherford became fascinated by this +topic of radioactivity it was all the + + align:start position:0% +topic of radioactivity it was all the + + + align:start position:0% +topic of radioactivity it was all the +news at the Cavendish in Paris and + + align:start position:0% +news at the Cavendish in Paris and + + + align:start position:0% +news at the Cavendish in Paris and +Beyond and he began identifying new + + align:start position:0% +Beyond and he began identifying new + + + align:start position:0% +Beyond and he began identifying new +sources that could emit by now familiar + + align:start position:0% +sources that could emit by now familiar + + + align:start position:0% +sources that could emit by now familiar +Rays meaning the alpha Rays had been + + align:start position:0% +Rays meaning the alpha Rays had been + + + align:start position:0% +Rays meaning the alpha Rays had been +identified people now knew they had + + align:start position:0% +identified people now knew they had + + + align:start position:0% +identified people now knew they had +different properties than the beta rays + + align:start position:0% +different properties than the beta rays + + + align:start position:0% +different properties than the beta rays +and so on but Rutherford found new + + align:start position:0% +and so on but Rutherford found new + + + align:start position:0% +and so on but Rutherford found new +sources that could um that could give + + align:start position:0% +sources that could um that could give + + + align:start position:0% +sources that could um that could give +off that kind of radiation + + align:start position:0% +off that kind of radiation + + + align:start position:0% +off that kind of radiation +and he also began trying to systematize + + align:start position:0% +and he also began trying to systematize + + + align:start position:0% +and he also began trying to systematize +the study of radioactivity more + + align:start position:0% +the study of radioactivity more + + + align:start position:0% +the study of radioactivity more +generally it's to Rutherford whom we owe + + align:start position:0% +generally it's to Rutherford whom we owe + + + align:start position:0% +generally it's to Rutherford whom we owe +the concept of a half-life the curies + + align:start position:0% +the concept of a half-life the curies + + + align:start position:0% +the concept of a half-life the curies +were very much involved with this rather + + align:start position:0% +were very much involved with this rather + + + align:start position:0% +were very much involved with this rather +it helps to formalize it the half-life + + align:start position:0% +it helps to formalize it the half-life + + + align:start position:0% +it helps to formalize it the half-life +being a term that's probably quite + + align:start position:0% +being a term that's probably quite + + + align:start position:0% +being a term that's probably quite +familiar to us today uh the time during + + align:start position:0% +familiar to us today uh the time during + + + align:start position:0% +familiar to us today uh the time during +which the radioactivity of a sample was + + align:start position:0% +which the radioactivity of a sample was + + + align:start position:0% +which the radioactivity of a sample was +measured by Geiger counters or other + + align:start position:0% +measured by Geiger counters or other + + + align:start position:0% +measured by Geiger counters or other +things would fall by half + + align:start position:0% +things would fall by half + + + align:start position:0% +things would fall by half +so what's the the the characteristic + + align:start position:0% +so what's the the the characteristic + + + align:start position:0% +so what's the the the characteristic +time uh during which you would measure + + align:start position:0% +time uh during which you would measure + + + align:start position:0% +time uh during which you would measure +these kinds of emanations coming out + + align:start position:0% +these kinds of emanations coming out + + + align:start position:0% +these kinds of emanations coming out +and Rutherford in particular became + + align:start position:0% +and Rutherford in particular became + + + align:start position:0% +and Rutherford in particular became +fascinated by these what we now call + + align:start position:0% +fascinated by these what we now call + + + align:start position:0% +fascinated by these what we now call +Decay chains so he could start much as + + align:start position:0% +Decay chains so he could start much as + + + align:start position:0% +Decay chains so he could start much as +the queries would do with a certain uh + + align:start position:0% +the queries would do with a certain uh + + + align:start position:0% +the queries would do with a certain uh +material and then watch that material + + align:start position:0% +material and then watch that material + + + align:start position:0% +material and then watch that material +Decay for example by emitting um Alpha + + align:start position:0% +Decay for example by emitting um Alpha + + + align:start position:0% +Decay for example by emitting um Alpha +rays and then that original substance + + align:start position:0% +rays and then that original substance + + + align:start position:0% +rays and then that original substance +would transmute or transform to a new + + align:start position:0% +would transmute or transform to a new + + + align:start position:0% +would transmute or transform to a new +kind of substance that would later be + + align:start position:0% +kind of substance that would later be + + + align:start position:0% +kind of substance that would later be +called radon if you began with radium + + align:start position:0% +called radon if you began with radium + + + align:start position:0% +called radon if you began with radium +one of the elements first scrutinized uh + + align:start position:0% +one of the elements first scrutinized uh + + + align:start position:0% +one of the elements first scrutinized uh +by the curies uh what would happen to a + + align:start position:0% +by the curies uh what would happen to a + + + align:start position:0% +by the curies uh what would happen to a +sample of radium after a bunch of alpha + + align:start position:0% +sample of radium after a bunch of alpha + + + align:start position:0% +sample of radium after a bunch of alpha +particles come out and that was the kind + + align:start position:0% +particles come out and that was the kind + + + align:start position:0% +particles come out and that was the kind +of thing Rutherford wanted to study and + + align:start position:0% +of thing Rutherford wanted to study and + + + align:start position:0% +of thing Rutherford wanted to study and +systematize so the Decay products from + + align:start position:0% +systematize so the Decay products from + + + align:start position:0% +systematize so the Decay products from +alpha decay of radium would be + + align:start position:0% +alpha decay of radium would be + + + align:start position:0% +alpha decay of radium would be +identified eventually as radon the chain + + align:start position:0% +identified eventually as radon the chain + + + align:start position:0% +identified eventually as radon the chain +would keep going radon with the + + align:start position:0% +would keep going radon with the + + + align:start position:0% +would keep going radon with the +mid-alpha particles become radium a but + + align:start position:0% +mid-alpha particles become radium a but + + + align:start position:0% +mid-alpha particles become radium a but +now it's called polonium actually in + + align:start position:0% +now it's called polonium actually in + + + align:start position:0% +now it's called polonium actually in +honor of Marie curie's homeland of + + align:start position:0% +honor of Marie curie's homeland of + + + align:start position:0% +honor of Marie curie's homeland of +Poland and so on + + align:start position:0% +Poland and so on + + + align:start position:0% +Poland and so on +so Rutherford got very quickly into this + + align:start position:0% +so Rutherford got very quickly into this + + + align:start position:0% +so Rutherford got very quickly into this +into this game into the study of + + align:start position:0% +into this game into the study of + + + align:start position:0% +into this game into the study of +radioactivity one of the things he did + + align:start position:0% +radioactivity one of the things he did + + + align:start position:0% +radioactivity one of the things he did +then uh when he was only a little bit + + align:start position:0% +then uh when he was only a little bit + + + align:start position:0% +then uh when he was only a little bit +further along was to team up with + + align:start position:0% +further along was to team up with + + + align:start position:0% +further along was to team up with +another colleague Hans Geiger originally + + align:start position:0% +another colleague Hans Geiger originally + + + align:start position:0% +another colleague Hans Geiger originally +from Germany but at this point working + + align:start position:0% +from Germany but at this point working + + + align:start position:0% +from Germany but at this point working +uh in the UK we now refer to Geiger + + align:start position:0% +uh in the UK we now refer to Geiger + + + align:start position:0% +uh in the UK we now refer to Geiger +counters they were actually developed in + + align:start position:0% +counters they were actually developed in + + + align:start position:0% +counters they were actually developed in +Partnership between Rutherford and + + align:start position:0% +Partnership between Rutherford and + + + align:start position:0% +Partnership between Rutherford and +Geiger in this first decade of the 20th + + align:start position:0% +Geiger in this first decade of the 20th + + + align:start position:0% +Geiger in this first decade of the 20th +century here's one of their earliest + + align:start position:0% +century here's one of their earliest + + + align:start position:0% +century here's one of their earliest +their own illustrations of how this + + align:start position:0% +their own illustrations of how this + + + align:start position:0% +their own illustrations of how this +would work this is of course a more + + align:start position:0% +would work this is of course a more + + + align:start position:0% +would work this is of course a more +modern version of kind of Wikipedia + + align:start position:0% +modern version of kind of Wikipedia + + + align:start position:0% +modern version of kind of Wikipedia +version + + align:start position:0% +version + + + align:start position:0% +version +and the idea was that this was a device + + align:start position:0% +and the idea was that this was a device + + + align:start position:0% +and the idea was that this was a device +with which to measure these sort of + + align:start position:0% +with which to measure these sort of + + + align:start position:0% +with which to measure these sort of +emanations especially electrically + + align:start position:0% +emanations especially electrically + + + align:start position:0% +emanations especially electrically +charged radiations coming out of these + + align:start position:0% +charged radiations coming out of these + + + align:start position:0% +charged radiations coming out of these +radioactive materials very clever and + + align:start position:0% +radioactive materials very clever and + + + align:start position:0% +radioactive materials very clever and +actually very inexpensive and robust + + align:start position:0% +actually very inexpensive and robust + + + align:start position:0% +actually very inexpensive and robust +that's partly why these things are still + + align:start position:0% +that's partly why these things are still + + + align:start position:0% +that's partly why these things are still +in such widespread use to this day again + + align:start position:0% +in such widespread use to this day again + + + align:start position:0% +in such widespread use to this day again +in the modern version you have two + + align:start position:0% +in the modern version you have two + + + align:start position:0% +in the modern version you have two +um uh two conducting uh + + align:start position:0% +um uh two conducting uh + + + align:start position:0% +um uh two conducting uh +coils or or beams the anode and the + + align:start position:0% +coils or or beams the anode and the + + + align:start position:0% +coils or or beams the anode and the +cathode uh and you have a voltage + + align:start position:0% +cathode uh and you have a voltage + + + align:start position:0% +cathode uh and you have a voltage +difference between them inside the + + align:start position:0% +difference between them inside the + + + align:start position:0% +difference between them inside the +chamber you have + + align:start position:0% +chamber you have + + + align:start position:0% +chamber you have +um inert gas that could be a kind of + + align:start position:0% +um inert gas that could be a kind of + + + align:start position:0% +um inert gas that could be a kind of +noble gas if ionizing radiations one of + + align:start position:0% +noble gas if ionizing radiations one of + + + align:start position:0% +noble gas if ionizing radiations one of +these emanations from some radioactive + + align:start position:0% +these emanations from some radioactive + + + align:start position:0% +these emanations from some radioactive +Source enters the chamber it can + + align:start position:0% +Source enters the chamber it can + + + align:start position:0% +Source enters the chamber it can +actually ionize those otherwise neutral + + align:start position:0% +actually ionize those otherwise neutral + + + align:start position:0% +actually ionize those otherwise neutral +and fairly inert atoms it can as we now + + align:start position:0% +and fairly inert atoms it can as we now + + + align:start position:0% +and fairly inert atoms it can as we now +know kind of rip off an electron or + + align:start position:0% +know kind of rip off an electron or + + + align:start position:0% +know kind of rip off an electron or +something like that so now you have a + + align:start position:0% +something like that so now you have a + + + align:start position:0% +something like that so now you have a +Charged ion running around in this + + align:start position:0% +Charged ion running around in this + + + align:start position:0% +Charged ion running around in this +chamber it will be attracted to either + + align:start position:0% +chamber it will be attracted to either + + + align:start position:0% +chamber it will be attracted to either +anode or cathode you'll complete a + + align:start position:0% +anode or cathode you'll complete a + + + align:start position:0% +anode or cathode you'll complete a +circuit you'll have a readout so you can + + align:start position:0% +circuit you'll have a readout so you can + + + align:start position:0% +circuit you'll have a readout so you can +convert + + align:start position:0% +convert + + + align:start position:0% +convert +certain kinds of physical interactions + + align:start position:0% +certain kinds of physical interactions + + + align:start position:0% +certain kinds of physical interactions +within the chamber into into measurable + + align:start position:0% +within the chamber into into measurable + + + align:start position:0% +within the chamber into into measurable +electric outputs uh from this otherwise + + align:start position:0% +electric outputs uh from this otherwise + + + align:start position:0% +electric outputs uh from this otherwise +very simple closed device so by by 1908 + + align:start position:0% +very simple closed device so by by 1908 + + + align:start position:0% +very simple closed device so by by 1908 +this has now become a new kind of tool + + align:start position:0% +this has now become a new kind of tool + + + align:start position:0% +this has now become a new kind of tool +uh in many many Laboratories because it + + align:start position:0% +uh in many many Laboratories because it + + + align:start position:0% +uh in many many Laboratories because it +was both cheap and reliable and the idea + + align:start position:0% +was both cheap and reliable and the idea + + + align:start position:0% +was both cheap and reliable and the idea +behind it was pretty easy to convey + + align:start position:0% +behind it was pretty easy to convey + + + align:start position:0% +behind it was pretty easy to convey +using these kinds of tools rather for it + + align:start position:0% +using these kinds of tools rather for it + + + align:start position:0% +using these kinds of tools rather for it +in Geiger in their immediate circle uh + + align:start position:0% +in Geiger in their immediate circle uh + + + align:start position:0% +in Geiger in their immediate circle uh +in and around the Cavendish we're able + + align:start position:0% +in and around the Cavendish we're able + + + align:start position:0% +in and around the Cavendish we're able +to determine that alpha particles + + align:start position:0% +to determine that alpha particles + + + align:start position:0% +to determine that alpha particles +actually carry twice the electric charge + + align:start position:0% +actually carry twice the electric charge + + + align:start position:0% +actually carry twice the electric charge +of Thompson's still pretty new beta + + align:start position:0% +of Thompson's still pretty new beta + + + align:start position:0% +of Thompson's still pretty new beta +particles but of the opposite side + + align:start position:0% +particles but of the opposite side + + + align:start position:0% +particles but of the opposite side +basically they would go to the anode not + + align:start position:0% +basically they would go to the anode not + + + align:start position:0% +basically they would go to the anode not +the cathode and vice versa so you can + + align:start position:0% +the cathode and vice versa so you can + + + align:start position:0% +the cathode and vice versa so you can +begin measuring more and more properties + + align:start position:0% +begin measuring more and more properties + + + align:start position:0% +begin measuring more and more properties +of these different kinds of radiations + + align:start position:0% +of these different kinds of radiations + + + align:start position:0% +of these different kinds of radiations +or emanations + + align:start position:0% +or emanations + + + align:start position:0% +or emanations +so very soon after there was a reliable + + align:start position:0% +so very soon after there was a reliable + + + align:start position:0% +so very soon after there was a reliable +way to characterize these new Rays these + + align:start position:0% +way to characterize these new Rays these + + + align:start position:0% +way to characterize these new Rays these +alpha particles in particular Rutherford + + align:start position:0% +alpha particles in particular Rutherford + + + align:start position:0% +alpha particles in particular Rutherford +got a new job he was now a young + + align:start position:0% +got a new job he was now a young + + + align:start position:0% +got a new job he was now a young +Professor at Manchester University in + + align:start position:0% +Professor at Manchester University in + + + align:start position:0% +Professor at Manchester University in +northern England he built up a big big + + align:start position:0% +northern England he built up a big big + + + align:start position:0% +northern England he built up a big big +flourishing research group and the idea + + align:start position:0% +flourishing research group and the idea + + + align:start position:0% +flourishing research group and the idea +now is not only to study alpha particles + + align:start position:0% +now is not only to study alpha particles + + + align:start position:0% +now is not only to study alpha particles +as the kind of subject of research as + + align:start position:0% +as the kind of subject of research as + + + align:start position:0% +as the kind of subject of research as +he'd been doing since his student days + + align:start position:0% +he'd been doing since his student days + + + align:start position:0% +he'd been doing since his student days +but to Flip Flip it around and use alpha + + align:start position:0% +but to Flip Flip it around and use alpha + + + align:start position:0% +but to Flip Flip it around and use alpha +particles as a tool to learn new stuff + + align:start position:0% +particles as a tool to learn new stuff + + + align:start position:0% +particles as a tool to learn new stuff +about other things so the alpha + + align:start position:0% +about other things so the alpha + + + align:start position:0% +about other things so the alpha +particles were kind of domesticated I + + align:start position:0% +particles were kind of domesticated I + + + align:start position:0% +particles were kind of domesticated I +think really remarkably quickly from + + align:start position:0% +think really remarkably quickly from + + + align:start position:0% +think really remarkably quickly from +being the the kind of topic you'd + + align:start position:0% +being the the kind of topic you'd + + + align:start position:0% +being the the kind of topic you'd +scrutinize to being just another tool on + + align:start position:0% +scrutinize to being just another tool on + + + align:start position:0% +scrutinize to being just another tool on +your kind of lab bench to learn about + + align:start position:0% +your kind of lab bench to learn about + + + align:start position:0% +your kind of lab bench to learn about +other things the Rutherford was very + + align:start position:0% +other things the Rutherford was very + + + align:start position:0% +other things the Rutherford was very +proactive as others were but Rutherford + + align:start position:0% +proactive as others were but Rutherford + + + align:start position:0% +proactive as others were but Rutherford +was really very creative in that + + align:start position:0% +was really very creative in that + + + align:start position:0% +was really very creative in that +transition + + align:start position:0% +transition + + + align:start position:0% +transition +so beginning as early as 1909 his group + + align:start position:0% +so beginning as early as 1909 his group + + + align:start position:0% +so beginning as early as 1909 his group +began directing alpha particles it would + + align:start position:0% +began directing alpha particles it would + + + align:start position:0% +began directing alpha particles it would +have a radon source of the kind he'd + + align:start position:0% +have a radon source of the kind he'd + + + align:start position:0% +have a radon source of the kind he'd +been studying for years it would be + + align:start position:0% +been studying for years it would be + + + align:start position:0% +been studying for years it would be +what's called now an alpha emitter so + + align:start position:0% +what's called now an alpha emitter so + + + align:start position:0% +what's called now an alpha emitter so +the natural form of radioactive decay of + + align:start position:0% +the natural form of radioactive decay of + + + align:start position:0% +the natural form of radioactive decay of +a radon source is to shoot out beams of + + align:start position:0% +a radon source is to shoot out beams of + + + align:start position:0% +a radon source is to shoot out beams of +alpha particles so that was in this + + align:start position:0% +alpha particles so that was in this + + + align:start position:0% +alpha particles so that was in this +block here and they could kind of + + align:start position:0% +block here and they could kind of + + + align:start position:0% +block here and they could kind of +collimate the beam they could encase the + + align:start position:0% +collimate the beam they could encase the + + + align:start position:0% +collimate the beam they could encase the +radon Source in a in kind of lead + + align:start position:0% +radon Source in a in kind of lead + + + align:start position:0% +radon Source in a in kind of lead +shielding with a very narrow opening to + + align:start position:0% +shielding with a very narrow opening to + + + align:start position:0% +shielding with a very narrow opening to +have the alpha particles shoot out in + + align:start position:0% +have the alpha particles shoot out in + + + align:start position:0% +have the alpha particles shoot out in +One Direction + + align:start position:0% +One Direction + + + align:start position:0% +One Direction +they would shoot them towards a target + + align:start position:0% +they would shoot them towards a target + + + align:start position:0% +they would shoot them towards a target +of a very very thin metallic foil often + + align:start position:0% +of a very very thin metallic foil often + + + align:start position:0% +of a very very thin metallic foil often +gold foil very very thin and then + + align:start position:0% +gold foil very very thin and then + + + align:start position:0% +gold foil very very thin and then +surround almost an entire foil by this + + align:start position:0% +surround almost an entire foil by this + + + align:start position:0% +surround almost an entire foil by this +new fluorescent screen so uh when the + + align:start position:0% +new fluorescent screen so uh when the + + + align:start position:0% +new fluorescent screen so uh when the +alpha particles would kind of Ricochet + + align:start position:0% +alpha particles would kind of Ricochet + + + align:start position:0% +alpha particles would kind of Ricochet +off that foil they would light up this + + align:start position:0% +off that foil they would light up this + + + align:start position:0% +off that foil they would light up this +fluorescent screen this was incredibly + + align:start position:0% +fluorescent screen this was incredibly + + + align:start position:0% +fluorescent screen this was incredibly +that's very easy to describe we have a + + align:start position:0% +that's very easy to describe we have a + + + align:start position:0% +that's very easy to describe we have a +nice again a nice kind of Wikipedia + + align:start position:0% +nice again a nice kind of Wikipedia + + + align:start position:0% +nice again a nice kind of Wikipedia +level cartoon makes it look so + + align:start position:0% +level cartoon makes it look so + + + align:start position:0% +level cartoon makes it look so +straightforward this was incredibly + + align:start position:0% +straightforward this was incredibly + + + align:start position:0% +straightforward this was incredibly +painstaking work the researchers had to + + align:start position:0% +painstaking work the researchers had to + + + align:start position:0% +painstaking work the researchers had to +sit in a darkened room for like a + + align:start position:0% +sit in a darkened room for like a + + + align:start position:0% +sit in a darkened room for like a +minimum half an hour just let their eyes + + align:start position:0% +minimum half an hour just let their eyes + + + align:start position:0% +minimum half an hour just let their eyes +adjust imagine sitting basically in an + + align:start position:0% +adjust imagine sitting basically in an + + + align:start position:0% +adjust imagine sitting basically in an +entirely blackened room + + align:start position:0% +entirely blackened room + + + align:start position:0% +entirely blackened room +your mind starts playing tricks on you + + align:start position:0% +your mind starts playing tricks on you + + + align:start position:0% +your mind starts playing tricks on you +you start seeing flashes where that + + align:start position:0% +you start seeing flashes where that + + + align:start position:0% +you start seeing flashes where that +might not be any just so that their eyes + + align:start position:0% +might not be any just so that their eyes + + + align:start position:0% +might not be any just so that their eyes +would be sensitive to these very very + + align:start position:0% +would be sensitive to these very very + + + align:start position:0% +would be sensitive to these very very +modest little flickers from the + + align:start position:0% +modest little flickers from the + + + align:start position:0% +modest little flickers from the +fluorescent screen and you basically sit + + align:start position:0% +fluorescent screen and you basically sit + + + align:start position:0% +fluorescent screen and you basically sit +there alone in the dark and count not + + align:start position:0% +there alone in the dark and count not + + + align:start position:0% +there alone in the dark and count not +just how many flickers but as I'll say + + align:start position:0% +just how many flickers but as I'll say + + + align:start position:0% +just how many flickers but as I'll say +in a moment where along this circle what + + align:start position:0% +in a moment where along this circle what + + + align:start position:0% +in a moment where along this circle what +angle did you see most of these little + + align:start position:0% +angle did you see most of these little + + + align:start position:0% +angle did you see most of these little +tiny short um flashes of light appear + + align:start position:0% +tiny short um flashes of light appear + + + align:start position:0% +tiny short um flashes of light appear +so what they began to find is that most + + align:start position:0% +so what they began to find is that most + + + align:start position:0% +so what they began to find is that most +of these alpha particles would pass + + align:start position:0% +of these alpha particles would pass + + + align:start position:0% +of these alpha particles would pass +right through the foil so meaning most + + align:start position:0% +right through the foil so meaning most + + + align:start position:0% +right through the foil so meaning most +of the little flashes of light would + + align:start position:0% +of the little flashes of light would + + + align:start position:0% +of the little flashes of light would +line up directly behind the target they + + align:start position:0% +line up directly behind the target they + + + align:start position:0% +line up directly behind the target they +would be like a straight line and they + + align:start position:0% +would be like a straight line and they + + + align:start position:0% +would be like a straight line and they +began to reason Rutherford and his team + + align:start position:0% +began to reason Rutherford and his team + + + align:start position:0% +began to reason Rutherford and his team +that these alpha particles were probably + + align:start position:0% +that these alpha particles were probably + + + align:start position:0% +that these alpha particles were probably +considerably smaller than the target + + align:start position:0% +considerably smaller than the target + + + align:start position:0% +considerably smaller than the target +atoms within that foil if that was gold + + align:start position:0% +atoms within that foil if that was gold + + + align:start position:0% +atoms within that foil if that was gold +foil they would assume these gold atoms + + align:start position:0% +foil they would assume these gold atoms + + + align:start position:0% +foil they would assume these gold atoms +are really big on the scale of alpha + + align:start position:0% +are really big on the scale of alpha + + + align:start position:0% +are really big on the scale of alpha +particles and kind of spread out on the + + align:start position:0% +particles and kind of spread out on the + + + align:start position:0% +particles and kind of spread out on the +scale of alpha particles so most of the + + align:start position:0% +scale of alpha particles so most of the + + + align:start position:0% +scale of alpha particles so most of the +time these little emanations these alpha + + align:start position:0% +time these little emanations these alpha + + + align:start position:0% +time these little emanations these alpha +particles could zoom right through that + + align:start position:0% +particles could zoom right through that + + + align:start position:0% +particles could zoom right through that +thin metal foil and never get deflected + + align:start position:0% +thin metal foil and never get deflected + + + align:start position:0% +thin metal foil and never get deflected +or scattered at all so in that case + + align:start position:0% +or scattered at all so in that case + + + align:start position:0% +or scattered at all so in that case +you'd expect most of the very faint + + align:start position:0% +you'd expect most of the very faint + + + align:start position:0% +you'd expect most of the very faint +short flashes on the fluorescent screen + + align:start position:0% +short flashes on the fluorescent screen + + + align:start position:0% +short flashes on the fluorescent screen +to line up directly behind the source if + + align:start position:0% +to line up directly behind the source if + + + align:start position:0% +to line up directly behind the source if +there's no deflection sometimes it'd be + + align:start position:0% +there's no deflection sometimes it'd be + + + align:start position:0% +there's no deflection sometimes it'd be +a kind of glancing scatter a small angle + + align:start position:0% +a kind of glancing scatter a small angle + + + align:start position:0% +a kind of glancing scatter a small angle +scatter a few of them over here and that + + align:start position:0% +scatter a few of them over here and that + + + align:start position:0% +scatter a few of them over here and that +doesn't indeed what they found most of + + align:start position:0% +doesn't indeed what they found most of + + + align:start position:0% +doesn't indeed what they found most of +the time but every now and then in a way + + align:start position:0% +the time but every now and then in a way + + + align:start position:0% +the time but every now and then in a way +that by doing this over and over and + + align:start position:0% +that by doing this over and over and + + + align:start position:0% +that by doing this over and over and +over again over months in the darkened + + align:start position:0% +over again over months in the darkened + + + align:start position:0% +over again over months in the darkened +room painstakingly they could quantify + + align:start position:0% +room painstakingly they could quantify + + + align:start position:0% +room painstakingly they could quantify +was roughly one out of every hundred + + align:start position:0% +was roughly one out of every hundred + + + align:start position:0% +was roughly one out of every hundred +thousand scattering events the an alpha + + align:start position:0% +thousand scattering events the an alpha + + + align:start position:0% +thousand scattering events the an alpha +particle would actually scatter by very + + align:start position:0% +particle would actually scatter by very + + + align:start position:0% +particle would actually scatter by very +large angles being known as back scatter + + align:start position:0% +large angles being known as back scatter + + + align:start position:0% +large angles being known as back scatter +it would scattered almost 180 degrees + + align:start position:0% +it would scattered almost 180 degrees + + + align:start position:0% +it would scattered almost 180 degrees +coming back almost towards its own + + align:start position:0% +coming back almost towards its own + + + align:start position:0% +coming back almost towards its own +source so most of the time there was + + align:start position:0% +source so most of the time there was + + + align:start position:0% +source so most of the time there was +either no deflection or very minimal + + align:start position:0% +either no deflection or very minimal + + + align:start position:0% +either no deflection or very minimal +deflection + + align:start position:0% +deflection + + + align:start position:0% +deflection +but some small number of times maybe a + + align:start position:0% +but some small number of times maybe a + + + align:start position:0% +but some small number of times maybe a +large angle scatter insteads they began + + align:start position:0% +large angle scatter insteads they began + + + align:start position:0% +large angle scatter insteads they began +making essentially these kinds of + + align:start position:0% +making essentially these kinds of + + + align:start position:0% +making essentially these kinds of +histograms of the number of scatting or + + align:start position:0% +histograms of the number of scatting or + + + align:start position:0% +histograms of the number of scatting or +scattering events as a function of the + + align:start position:0% +scattering events as a function of the + + + align:start position:0% +scattering events as a function of the +scattering angle and as you can see + + align:start position:0% +scattering angle and as you can see + + + align:start position:0% +scattering angle and as you can see +small angles is where almost sorry + + align:start position:0% +small angles is where almost sorry + + + align:start position:0% +small angles is where almost sorry +almost all the events would cluster and + + align:start position:0% +almost all the events would cluster and + + + align:start position:0% +almost all the events would cluster and +very rarely about one out of every + + align:start position:0% +very rarely about one out of every + + + align:start position:0% +very rarely about one out of every +hundred thousand approximately you'd + + align:start position:0% +hundred thousand approximately you'd + + + align:start position:0% +hundred thousand approximately you'd +find a very large angle scatter event + + align:start position:0% +find a very large angle scatter event + + + align:start position:0% +find a very large angle scatter event +that was not at all what they expected + + align:start position:0% +that was not at all what they expected + + + align:start position:0% +that was not at all what they expected +to find Rutherford very famously + + align:start position:0% +to find Rutherford very famously + + + align:start position:0% +to find Rutherford very famously +recalled I love this quotation + + align:start position:0% +recalled I love this quotation + + + align:start position:0% +recalled I love this quotation +referring to these experiments he said + + align:start position:0% +referring to these experiments he said + + + align:start position:0% +referring to these experiments he said +it was quite the most incredible event + + align:start position:0% +it was quite the most incredible event + + + align:start position:0% +it was quite the most incredible event +that has ever happened to me in my life + + align:start position:0% +that has ever happened to me in my life + + + align:start position:0% +that has ever happened to me in my life +it was almost as incredible as if you + + align:start position:0% +it was almost as incredible as if you + + + align:start position:0% +it was almost as incredible as if you +had fired a 15-inch artillery shell + + align:start position:0% +had fired a 15-inch artillery shell + + + align:start position:0% +had fired a 15-inch artillery shell +think about like from a cannon I fired + + align:start position:0% +think about like from a cannon I fired + + + align:start position:0% +think about like from a cannon I fired +that huge Shell at a piece of tissue + + align:start position:0% +that huge Shell at a piece of tissue + + + align:start position:0% +that huge Shell at a piece of tissue +paper and it came back and hit you + + align:start position:0% +paper and it came back and hit you + + + align:start position:0% +paper and it came back and hit you +that's what it seemed like to have these + + align:start position:0% +that's what it seemed like to have these + + + align:start position:0% +that's what it seemed like to have these +little tiny alpha particles Ricochet all + + align:start position:0% +little tiny alpha particles Ricochet all + + + align:start position:0% +little tiny alpha particles Ricochet all +the way back for a very large angle + + align:start position:0% +the way back for a very large angle + + + align:start position:0% +the way back for a very large angle +scatter + + align:start position:0% +scatter + + + align:start position:0% +scatter +so they were collecting that data + + align:start position:0% +so they were collecting that data + + + align:start position:0% +so they were collecting that data +starting around 1909 or so over months + + align:start position:0% +starting around 1909 or so over months + + + align:start position:0% +starting around 1909 or so over months +and months ultimately over about two + + align:start position:0% +and months ultimately over about two + + + align:start position:0% +and months ultimately over about two +years to really build up lots and lots + + align:start position:0% +years to really build up lots and lots + + + align:start position:0% +years to really build up lots and lots +of data and statistics + + align:start position:0% +of data and statistics + + + align:start position:0% +of data and statistics +during which Rutherford then worked hard + + align:start position:0% +during which Rutherford then worked hard + + + align:start position:0% +during which Rutherford then worked hard +to make sense of the pattern + + align:start position:0% +to make sense of the pattern + + + align:start position:0% +to make sense of the pattern +quantitatively + + align:start position:0% +quantitatively + + + align:start position:0% +quantitatively +to work out why it might be that you + + align:start position:0% +to work out why it might be that you + + + align:start position:0% +to work out why it might be that you +have not just rare scattering events at + + align:start position:0% +have not just rare scattering events at + + + align:start position:0% +have not just rare scattering events at +large angle most scattering events at + + align:start position:0% +large angle most scattering events at + + + align:start position:0% +large angle most scattering events at +small angle but really to retrace this + + align:start position:0% +small angle but really to retrace this + + + align:start position:0% +small angle but really to retrace this +particular shape of that curve that + + align:start position:0% +particular shape of that curve that + + + align:start position:0% +particular shape of that curve that +particular kind of exponential decay of + + align:start position:0% +particular kind of exponential decay of + + + align:start position:0% +particular kind of exponential decay of +the of the of the scattering rates with + + align:start position:0% +the of the of the scattering rates with + + + align:start position:0% +the of the of the scattering rates with +angle + + align:start position:0% +angle + + + align:start position:0% +angle +and he finally convinced himself with a + + align:start position:0% +and he finally convinced himself with a + + + align:start position:0% +and he finally convinced himself with a +pretty short derivation that this kind + + align:start position:0% +pretty short derivation that this kind + + + align:start position:0% +pretty short derivation that this kind +of scattering pattern would only make + + align:start position:0% +of scattering pattern would only make + + + align:start position:0% +of scattering pattern would only make +sense if most of the mass of those + + align:start position:0% +sense if most of the mass of those + + + align:start position:0% +sense if most of the mass of those +Target atoms the little gold atoms in + + align:start position:0% +Target atoms the little gold atoms in + + + align:start position:0% +Target atoms the little gold atoms in +the thin gold foil were concentrated in + + align:start position:0% +the thin gold foil were concentrated in + + + align:start position:0% +the thin gold foil were concentrated in +a very dense nucleus in the center of + + align:start position:0% +a very dense nucleus in the center of + + + align:start position:0% +a very dense nucleus in the center of +those atoms that most of the mass of the + + align:start position:0% +those atoms that most of the mass of the + + + align:start position:0% +those atoms that most of the mass of the +atom was actually in the very very + + align:start position:0% +atom was actually in the very very + + + align:start position:0% +atom was actually in the very very +center and otherwise most of the of the + + align:start position:0% +center and otherwise most of the of the + + + align:start position:0% +center and otherwise most of the of the +rest of the volume the atom might uh + + align:start position:0% +rest of the volume the atom might uh + + + align:start position:0% +rest of the volume the atom might uh +take up was empty atoms were mostly + + align:start position:0% +take up was empty atoms were mostly + + + align:start position:0% +take up was empty atoms were mostly +empty space in fact about one part in a + + align:start position:0% +empty space in fact about one part in a + + + align:start position:0% +empty space in fact about one part in a +hundred thousand was a ratio between the + + align:start position:0% +hundred thousand was a ratio between the + + + align:start position:0% +hundred thousand was a ratio between the +kind of size we might attribute to an + + align:start position:0% +kind of size we might attribute to an + + + align:start position:0% +kind of size we might attribute to an +atom and the size we would attribute to + + align:start position:0% +atom and the size we would attribute to + + + align:start position:0% +atom and the size we would attribute to +this massive inner core of the nucleus + + align:start position:0% +this massive inner core of the nucleus + + + align:start position:0% +this massive inner core of the nucleus +the nucleus much like the alpha + + align:start position:0% +the nucleus much like the alpha + + + align:start position:0% +the nucleus much like the alpha +particles e goes on must have a positive + + align:start position:0% +particles e goes on must have a positive + + + align:start position:0% +particles e goes on must have a positive +charge they were repelling each other he + + align:start position:0% +charge they were repelling each other he + + + align:start position:0% +charge they were repelling each other he +concluded uh whereas these lightweight + + align:start position:0% +concluded uh whereas these lightweight + + + align:start position:0% +concluded uh whereas these lightweight +electrons which at this point were what + + align:start position:0% +electrons which at this point were what + + + align:start position:0% +electrons which at this point were what +Thompson's cathode rays or beta + + align:start position:0% +Thompson's cathode rays or beta + + + align:start position:0% +Thompson's cathode rays or beta +particles have been identified with + + align:start position:0% +particles have been identified with + + + align:start position:0% +particles have been identified with +those must have the opposite charge and + + align:start position:0% +those must have the opposite charge and + + + align:start position:0% +those must have the opposite charge and +again you could get a sense of the sign + + align:start position:0% +again you could get a sense of the sign + + + align:start position:0% +again you could get a sense of the sign +of the charge for things like Geiger + + align:start position:0% +of the charge for things like Geiger + + + align:start position:0% +of the charge for things like Geiger +counters + + align:start position:0% +counters + + + align:start position:0% +counters +so the model that Rutherford begins to + + align:start position:0% +so the model that Rutherford begins to + + + align:start position:0% +so the model that Rutherford begins to +piece together building on these sort of + + align:start position:0% +piece together building on these sort of + + + align:start position:0% +piece together building on these sort of +multiple years of data collection is a + + align:start position:0% +multiple years of data collection is a + + + align:start position:0% +multiple years of data collection is a +kind of solar system picture of the atom + + align:start position:0% +kind of solar system picture of the atom + + + align:start position:0% +kind of solar system picture of the atom +there's a very + + align:start position:0% +there's a very + + + align:start position:0% +there's a very +um very tiny massive core the nucleus + + align:start position:0% +um very tiny massive core the nucleus + + + align:start position:0% +um very tiny massive core the nucleus +that's kind of like the sun and lighter + + align:start position:0% +that's kind of like the sun and lighter + + + align:start position:0% +that's kind of like the sun and lighter +weight objects are going to somehow move + + align:start position:0% +weight objects are going to somehow move + + + align:start position:0% +weight objects are going to somehow move +around it and that's what makes up an + + align:start position:0% +around it and that's what makes up an + + + align:start position:0% +around it and that's what makes up an +atom + + align:start position:0% +atom + + + align:start position:0% +atom +so he just introduces this kind of Solar + + align:start position:0% +so he just introduces this kind of Solar + + + align:start position:0% +so he just introduces this kind of Solar +System model by around 1911 but of + + align:start position:0% +System model by around 1911 but of + + + align:start position:0% +System model by around 1911 but of +course that led to several new questions + + align:start position:0% +course that led to several new questions + + + align:start position:0% +course that led to several new questions +on its own + + align:start position:0% +on its own + + + align:start position:0% +on its own +so one question was these electrons he's + + align:start position:0% +so one question was these electrons he's + + + align:start position:0% +so one question was these electrons he's +JJ Thompson beta particles would be + + align:start position:0% +JJ Thompson beta particles would be + + + align:start position:0% +JJ Thompson beta particles would be +constantly accelerated as they moved + + align:start position:0% +constantly accelerated as they moved + + + align:start position:0% +constantly accelerated as they moved +around the nucleus if you thought about + + align:start position:0% +around the nucleus if you thought about + + + align:start position:0% +around the nucleus if you thought about +them like the Earth in the solar system + + align:start position:0% +them like the Earth in the solar system + + + align:start position:0% +them like the Earth in the solar system +the Earth is constantly being + + align:start position:0% +the Earth is constantly being + + + align:start position:0% +the Earth is constantly being +accelerated as it moves around the Sun + + align:start position:0% +accelerated as it moves around the Sun + + + align:start position:0% +accelerated as it moves around the Sun +its direction of travel is changing it's + + align:start position:0% +its direction of travel is changing it's + + + align:start position:0% +its direction of travel is changing it's +so its velocity in fact is changed + + align:start position:0% +so its velocity in fact is changed + + + align:start position:0% +so its velocity in fact is changed +velocity Vector is changing it's + + align:start position:0% +velocity Vector is changing it's + + + align:start position:0% +velocity Vector is changing it's +suffering constant acceleration wouldn't + + align:start position:0% +suffering constant acceleration wouldn't + + + align:start position:0% +suffering constant acceleration wouldn't +that be true of these negatively charged + + align:start position:0% +that be true of these negatively charged + + + align:start position:0% +that be true of these negatively charged +electric particles the electrons as they + + align:start position:0% +electric particles the electrons as they + + + align:start position:0% +electric particles the electrons as they +move around in any old pattern around + + align:start position:0% +move around in any old pattern around + + + align:start position:0% +move around in any old pattern around +the positively charged nucleus and then + + align:start position:0% +the positively charged nucleus and then + + + align:start position:0% +the positively charged nucleus and then +the question comes up according to + + align:start position:0% +the question comes up according to + + + align:start position:0% +the question comes up according to +Maxwell's remarkably successful work on + + align:start position:0% +Maxwell's remarkably successful work on + + + align:start position:0% +Maxwell's remarkably successful work on +electromagnetism anytime electrically + + align:start position:0% +electromagnetism anytime electrically + + + align:start position:0% +electromagnetism anytime electrically +charged objects accelerate they should + + align:start position:0% +charged objects accelerate they should + + + align:start position:0% +charged objects accelerate they should +radiate they should give off light or + + align:start position:0% +radiate they should give off light or + + + align:start position:0% +radiate they should give off light or +electromagnetic radiation so question + + align:start position:0% +electromagnetic radiation so question + + + align:start position:0% +electromagnetic radiation so question +one from this new Rutherford model was + + align:start position:0% +one from this new Rutherford model was + + + align:start position:0% +one from this new Rutherford model was +where's all that light if every atom of + + align:start position:0% +where's all that light if every atom of + + + align:start position:0% +where's all that light if every atom of +every filling every kind of bit of + + align:start position:0% +every filling every kind of bit of + + + align:start position:0% +every filling every kind of bit of +matter in the universe has its inner + + align:start position:0% +matter in the universe has its inner + + + align:start position:0% +matter in the universe has its inner +parts constantly accelerated electric + + align:start position:0% +parts constantly accelerated electric + + + align:start position:0% +parts constantly accelerated electric +charge is accelerated + + align:start position:0% +charge is accelerated + + + align:start position:0% +charge is accelerated +why don't we see everything glowing all + + align:start position:0% +why don't we see everything glowing all + + + align:start position:0% +why don't we see everything glowing all +the time and perhaps an even trickier + + align:start position:0% +the time and perhaps an even trickier + + + align:start position:0% +the time and perhaps an even trickier +question was if those electrons are + + align:start position:0% +question was if those electrons are + + + align:start position:0% +question was if those electrons are +actually emitting radiation if they're + + align:start position:0% +actually emitting radiation if they're + + + align:start position:0% +actually emitting radiation if they're +giving up some of their own energy in + + align:start position:0% +giving up some of their own energy in + + + align:start position:0% +giving up some of their own energy in +the form of light it's going to carry + + align:start position:0% +the form of light it's going to carry + + + align:start position:0% +the form of light it's going to carry +that energy away then why is why are any + + align:start position:0% +that energy away then why is why are any + + + align:start position:0% +that energy away then why is why are any +atoms ever stable wouldn't those + + align:start position:0% +atoms ever stable wouldn't those + + + align:start position:0% +atoms ever stable wouldn't those +electrons be giving up their energy as + + align:start position:0% +electrons be giving up their energy as + + + align:start position:0% +electrons be giving up their energy as +they irradiate wouldn't they basically + + align:start position:0% +they irradiate wouldn't they basically + + + align:start position:0% +they irradiate wouldn't they basically +their orbits Decay Decay Decay wouldn't + + align:start position:0% +their orbits Decay Decay Decay wouldn't + + + align:start position:0% +their orbits Decay Decay Decay wouldn't +they just crash into the nucleus why + + align:start position:0% +they just crash into the nucleus why + + + align:start position:0% +they just crash into the nucleus why +don't atoms fall apart all the time and + + align:start position:0% +don't atoms fall apart all the time and + + + align:start position:0% +don't atoms fall apart all the time and +in fact very quickly so these two + + align:start position:0% +in fact very quickly so these two + + + align:start position:0% +in fact very quickly so these two +questions became at least as challenging + + align:start position:0% +questions became at least as challenging + + + align:start position:0% +questions became at least as challenging +as the successes of Rutherford's nuclear + + align:start position:0% +as the successes of Rutherford's nuclear + + + align:start position:0% +as the successes of Rutherford's nuclear +model + + align:start position:0% +model + + + align:start position:0% +model +let me pause there and see if there are + + align:start position:0% +let me pause there and see if there are + + + align:start position:0% +let me pause there and see if there are +any questions about that + + align:start position:0% + + + + align:start position:0% + +Alex asks in the chat where all the + + align:start position:0% +Alex asks in the chat where all the + + + align:start position:0% +Alex asks in the chat where all the +detection events detected by eye yes and + + align:start position:0% +detection events detected by eye yes and + + + align:start position:0% +detection events detected by eye yes and +the very first ones they were this is + + align:start position:0% +the very first ones they were this is + + + align:start position:0% +the very first ones they were this is +again it's sort of astonishing uh there + + align:start position:0% +again it's sort of astonishing uh there + + + align:start position:0% +again it's sort of astonishing uh there +were no you know kind of um + + align:start position:0% +were no you know kind of um + + + align:start position:0% +were no you know kind of um +the fancier things we would use today + + align:start position:0% +the fancier things we would use today + + + align:start position:0% +the fancier things we would use today +with say CCD cameras and so on to ccg + + align:start position:0% +with say CCD cameras and so on to ccg + + + align:start position:0% +with say CCD cameras and so on to ccg +detectors obviously those didn't exist + + align:start position:0% +detectors obviously those didn't exist + + + align:start position:0% +detectors obviously those didn't exist +yet + + align:start position:0% +yet + + + align:start position:0% +yet +um there were early photographic methods + + align:start position:0% +um there were early photographic methods + + + align:start position:0% +um there were early photographic methods +but the but they they were not they + + align:start position:0% +but the but they they were not they + + + align:start position:0% +but the but they they were not they +didn't have the resolution that people + + align:start position:0% +didn't have the resolution that people + + + align:start position:0% +didn't have the resolution that people +would need and they didn't have the + + align:start position:0% +would need and they didn't have the + + + align:start position:0% +would need and they didn't have the +timeliness uh if you just set up the + + align:start position:0% +timeliness uh if you just set up the + + + align:start position:0% +timeliness uh if you just set up the +photographic plate and didn't have a way + + align:start position:0% +photographic plate and didn't have a way + + + align:start position:0% +photographic plate and didn't have a way +to rapidly sort of take those plates out + + align:start position:0% +to rapidly sort of take those plates out + + + align:start position:0% +to rapidly sort of take those plates out +and develop them and put new ones in + + align:start position:0% +and develop them and put new ones in + + + align:start position:0% +and develop them and put new ones in +then you would lose + + align:start position:0% +then you would lose + + + align:start position:0% +then you would lose +um + + align:start position:0% +um + + + align:start position:0% +um +the kind of information they were + + align:start position:0% +the kind of information they were + + + align:start position:0% +the kind of information they were +looking to find + + align:start position:0% +looking to find + + + align:start position:0% +looking to find +and so they really were just had to have + + align:start position:0% +and so they really were just had to have + + + align:start position:0% +and so they really were just had to have +researchers sitting in the dark counting + + align:start position:0% +researchers sitting in the dark counting + + + align:start position:0% +researchers sitting in the dark counting +like for hours locked in a dark closet + + align:start position:0% +like for hours locked in a dark closet + + + align:start position:0% +like for hours locked in a dark closet +um both because the human eye once it is + + align:start position:0% +um both because the human eye once it is + + + align:start position:0% +um both because the human eye once it is +once you you you sensitize it's it was + + align:start position:0% +once you you you sensitize it's it was + + + align:start position:0% +once you you you sensitize it's it was +in its day much more sensitive than + + align:start position:0% +in its day much more sensitive than + + + align:start position:0% +in its day much more sensitive than +these photographic techniques at the + + align:start position:0% +these photographic techniques at the + + + align:start position:0% +these photographic techniques at the +time both in terms of spatial resolution + + align:start position:0% +time both in terms of spatial resolution + + + align:start position:0% +time both in terms of spatial resolution +but also for temporal response your your + + align:start position:0% +but also for temporal response your your + + + align:start position:0% +but also for temporal response your your +retina will kind of you know uh go back + + align:start position:0% +retina will kind of you know uh go back + + + align:start position:0% +retina will kind of you know uh go back +to neutral much more quickly than these + + align:start position:0% +to neutral much more quickly than these + + + align:start position:0% +to neutral much more quickly than these +than these large photographic plates + + align:start position:0% +than these large photographic plates + + + align:start position:0% +than these large photographic plates +would so they would really do basically + + align:start position:0% +would so they would really do basically + + + align:start position:0% +would so they would really do basically +naked eye observations + + align:start position:0% +naked eye observations + + + align:start position:0% +naked eye observations +um and I just I don't know how they you + + align:start position:0% +um and I just I don't know how they you + + + align:start position:0% +um and I just I don't know how they you +know could do that for so long uh silu + + align:start position:0% +know could do that for so long uh silu + + + align:start position:0% +know could do that for so long uh silu +asks did they choose use gold foil for + + align:start position:0% +asks did they choose use gold foil for + + + align:start position:0% +asks did they choose use gold foil for +specific reason why not any other metal + + align:start position:0% +specific reason why not any other metal + + + align:start position:0% +specific reason why not any other metal +that's a good question I think partly it + + align:start position:0% +that's a good question I think partly it + + + align:start position:0% +that's a good question I think partly it +was very + + align:start position:0% +was very + + + align:start position:0% +was very +um uh pliable so it was it was they + + align:start position:0% +um uh pliable so it was it was they + + + align:start position:0% +um uh pliable so it was it was they +could make very thin gold leaf uh then + + align:start position:0% +could make very thin gold leaf uh then + + + align:start position:0% +could make very thin gold leaf uh then +as now you know Bakers could make goat + + align:start position:0% +as now you know Bakers could make goat + + + align:start position:0% +as now you know Bakers could make goat +leaf on cakes I mean you can make very + + align:start position:0% +leaf on cakes I mean you can make very + + + align:start position:0% +leaf on cakes I mean you can make very +very malleable very very thin layers of + + align:start position:0% +very malleable very very thin layers of + + + align:start position:0% +very malleable very very thin layers of +of gold leaf uh and they were already + + align:start position:0% +of gold leaf uh and they were already + + + align:start position:0% +of gold leaf uh and they were already +chemical Notions chemical measurements + + align:start position:0% +chemical Notions chemical measurements + + + align:start position:0% +chemical Notions chemical measurements +to suggest that the gold atoms should be + + align:start position:0% +to suggest that the gold atoms should be + + + align:start position:0% +to suggest that the gold atoms should be +relatively massive they wanted big + + align:start position:0% +relatively massive they wanted big + + + align:start position:0% +relatively massive they wanted big +scattering targets basically even by the + + align:start position:0% +scattering targets basically even by the + + + align:start position:0% +scattering targets basically even by the +the rough estimate of what would say one + + align:start position:0% +the rough estimate of what would say one + + + align:start position:0% +the rough estimate of what would say one +you know one mole of gold atoms how much + + align:start position:0% +you know one mole of gold atoms how much + + + align:start position:0% +you know one mole of gold atoms how much +would that weigh they knew that that had + + align:start position:0% +would that weigh they knew that that had + + + align:start position:0% +would that weigh they knew that that had +a place on on mendeleev's periodic table + + align:start position:0% +a place on on mendeleev's periodic table + + + align:start position:0% +a place on on mendeleev's periodic table +that looked pretty massive compared to + + align:start position:0% +that looked pretty massive compared to + + + align:start position:0% +that looked pretty massive compared to +um other lighter targets + + align:start position:0% +um other lighter targets + + + align:start position:0% +um other lighter targets +so um so those are those are the kinds + + align:start position:0% +so um so those are those are the kinds + + + align:start position:0% +so um so those are those are the kinds +of reasons I think they did experiment + + align:start position:0% +of reasons I think they did experiment + + + align:start position:0% +of reasons I think they did experiment +with multiple types of thin foils but + + align:start position:0% +with multiple types of thin foils but + + + align:start position:0% +with multiple types of thin foils but +they were all choosing them around that + + align:start position:0% +they were all choosing them around that + + + align:start position:0% +they were all choosing them around that +part of the periodic table uh and that + + align:start position:0% +part of the periodic table uh and that + + + align:start position:0% +part of the periodic table uh and that +were both relatively inexpensive they + + align:start position:0% +were both relatively inexpensive they + + + align:start position:0% +were both relatively inexpensive they +didn't need tons and tons of gold + + align:start position:0% +didn't need tons and tons of gold + + + align:start position:0% +didn't need tons and tons of gold +bullion they just need a little little + + align:start position:0% +bullion they just need a little little + + + align:start position:0% +bullion they just need a little little +Trace Amounts of gold that was kind of + + align:start position:0% +Trace Amounts of gold that was kind of + + + align:start position:0% +Trace Amounts of gold that was kind of +workable uh had the right kind of + + align:start position:0% +workable uh had the right kind of + + + align:start position:0% +workable uh had the right kind of +macroscopic properties uh and that also + + align:start position:0% +macroscopic properties uh and that also + + + align:start position:0% +macroscopic properties uh and that also +had a kind of placement with within + + align:start position:0% +had a kind of placement with within + + + align:start position:0% +had a kind of placement with within +mendeleev's table which already was + + align:start position:0% +mendeleev's table which already was + + + align:start position:0% +mendeleev's table which already was +ordered roughly speaking by kind of + + align:start position:0% +ordered roughly speaking by kind of + + + align:start position:0% +ordered roughly speaking by kind of +atomic weight so I think those are the + + align:start position:0% +atomic weight so I think those are the + + + align:start position:0% +atomic weight so I think those are the +kind of criteria they used those did + + align:start position:0% +kind of criteria they used those did + + + align:start position:0% +kind of criteria they used those did +they did expanded with multiple types of + + align:start position:0% +they did expanded with multiple types of + + + align:start position:0% +they did expanded with multiple types of +targets those are great questions any + + align:start position:0% +targets those are great questions any + + + align:start position:0% +targets those are great questions any +other questions + + align:start position:0% +other questions + + + align:start position:0% +other questions +it's it's I mean we all have the benefit + + align:start position:0% +it's it's I mean we all have the benefit + + + align:start position:0% +it's it's I mean we all have the benefit +of many things in 2020 uh like high + + align:start position:0% +of many things in 2020 uh like high + + + align:start position:0% +of many things in 2020 uh like high +school including like high school + + align:start position:0% +school including like high school + + + align:start position:0% +school including like high school +chemistry classes so the fact that atoms + + align:start position:0% +chemistry classes so the fact that atoms + + + align:start position:0% +chemistry classes so the fact that atoms +are made up of nuclei that have a lot of + + align:start position:0% +are made up of nuclei that have a lot of + + + align:start position:0% +are made up of nuclei that have a lot of +mass and positive charge the this the + + align:start position:0% +mass and positive charge the this the + + + align:start position:0% +mass and positive charge the this the +scales might not yet have fallen from + + align:start position:0% +scales might not yet have fallen from + + + align:start position:0% +scales might not yet have fallen from +your eyes because like you kind of come + + align:start position:0% +your eyes because like you kind of come + + + align:start position:0% +your eyes because like you kind of come +in knowing that but that was really + + align:start position:0% +in knowing that but that was really + + + align:start position:0% +in knowing that but that was really +really pretty surprising uh very + + align:start position:0% +really pretty surprising uh very + + + align:start position:0% +really pretty surprising uh very +surprising in 1911. the prevailing + + align:start position:0% +surprising in 1911. the prevailing + + + align:start position:0% +surprising in 1911. the prevailing +models until then had suggested that + + align:start position:0% +models until then had suggested that + + + align:start position:0% +models until then had suggested that +atoms really were made up of different + + align:start position:0% +atoms really were made up of different + + + align:start position:0% +atoms really were made up of different +kinds of charges uh it was clear that by + + align:start position:0% +kinds of charges uh it was clear that by + + + align:start position:0% +kinds of charges uh it was clear that by +this point that Thompson's cathode rays + + align:start position:0% +this point that Thompson's cathode rays + + + align:start position:0% +this point that Thompson's cathode rays +carried a negative electric charge it + + align:start position:0% +carried a negative electric charge it + + + align:start position:0% +carried a negative electric charge it +was clear that alpha particles carried a + + align:start position:0% +was clear that alpha particles carried a + + + align:start position:0% +was clear that alpha particles carried a +positive electric charge it was clear + + align:start position:0% +positive electric charge it was clear + + + align:start position:0% +positive electric charge it was clear +that atoms were electrically neutral so + + align:start position:0% +that atoms were electrically neutral so + + + align:start position:0% +that atoms were electrically neutral so +people figure there must be equal + + align:start position:0% +people figure there must be equal + + + align:start position:0% +people figure there must be equal +numbers of these constituent parts so + + align:start position:0% +numbers of these constituent parts so + + + align:start position:0% +numbers of these constituent parts so +the total electric charge balances out + + align:start position:0% +the total electric charge balances out + + + align:start position:0% +the total electric charge balances out +but the prevailing model actually at the + + align:start position:0% +but the prevailing model actually at the + + + align:start position:0% +but the prevailing model actually at the +time before Rutherford's experiments was + + align:start position:0% +time before Rutherford's experiments was + + + align:start position:0% +time before Rutherford's experiments was +known as The Plum Pudding model which is + + align:start position:0% +known as The Plum Pudding model which is + + + align:start position:0% +known as The Plum Pudding model which is +very British uh the idea was that atoms + + align:start position:0% +very British uh the idea was that atoms + + + align:start position:0% +very British uh the idea was that atoms +might be just like this kind of mush + + align:start position:0% +might be just like this kind of mush + + + align:start position:0% +might be just like this kind of mush +like a plum pudding which I think is + + align:start position:0% +like a plum pudding which I think is + + + align:start position:0% +like a plum pudding which I think is +actually pretty gross of this kind of + + align:start position:0% +actually pretty gross of this kind of + + + align:start position:0% +actually pretty gross of this kind of +undifferentiated goo with positive and + + align:start position:0% +undifferentiated goo with positive and + + + align:start position:0% +undifferentiated goo with positive and +negative charges just kind of + + align:start position:0% +negative charges just kind of + + + align:start position:0% +negative charges just kind of +distributed at random so they average + + align:start position:0% +distributed at random so they average + + + align:start position:0% +distributed at random so they average +out within some volume + + align:start position:0% +out within some volume + + + align:start position:0% +out within some volume +that they didn't have a kind of + + align:start position:0% +that they didn't have a kind of + + + align:start position:0% +that they didn't have a kind of +structure + + align:start position:0% +structure + + + align:start position:0% +structure +let alone that the the positive charge + + align:start position:0% +let alone that the the positive charge + + + align:start position:0% +let alone that the the positive charge +was associated with such an imbalance of + + align:start position:0% +was associated with such an imbalance of + + + align:start position:0% +was associated with such an imbalance of +the mass I mean all those things were + + align:start position:0% +the mass I mean all those things were + + + align:start position:0% +the mass I mean all those things were +really quite unexpected which is I think + + align:start position:0% +really quite unexpected which is I think + + + align:start position:0% +really quite unexpected which is I think +why someone like Rutherford says it's + + align:start position:0% +why someone like Rutherford says it's + + + align:start position:0% +why someone like Rutherford says it's +like firing you know a cat and shallot + + align:start position:0% +like firing you know a cat and shallot + + + align:start position:0% +like firing you know a cat and shallot +tissue paper and having it smash back if + + align:start position:0% +tissue paper and having it smash back if + + + align:start position:0% +tissue paper and having it smash back if +you fire a cannon Shell at you know + + align:start position:0% +you fire a cannon Shell at you know + + + align:start position:0% +you fire a cannon Shell at you know +porridge you don't expect it to come + + align:start position:0% +porridge you don't expect it to come + + + align:start position:0% +porridge you don't expect it to come +back in your face the fact that these + + align:start position:0% +back in your face the fact that these + + + align:start position:0% +back in your face the fact that these +atoms had very very hard massive + + align:start position:0% +atoms had very very hard massive + + + align:start position:0% +atoms had very very hard massive +scattering sites these very very uh + + align:start position:0% +scattering sites these very very uh + + + align:start position:0% +scattering sites these very very uh +dense nuclei in the middle that was + + align:start position:0% +dense nuclei in the middle that was + + + align:start position:0% +dense nuclei in the middle that was +genuinely unexpected even though now + + align:start position:0% +genuinely unexpected even though now + + + align:start position:0% +genuinely unexpected even though now +we're like oh yeah I grew up doing that + + align:start position:0% +we're like oh yeah I grew up doing that + + + align:start position:0% +we're like oh yeah I grew up doing that +so we you know sometimes the novelty's + + align:start position:0% +so we you know sometimes the novelty's + + + align:start position:0% +so we you know sometimes the novelty's +hard to put our heads and put our heads + + align:start position:0% +hard to put our heads and put our heads + + + align:start position:0% +hard to put our heads and put our heads +back into that moment + + align:start position:0% +back into that moment + + + align:start position:0% +back into that moment +any questions about what Rutherford was + + align:start position:0% +any questions about what Rutherford was + + + align:start position:0% +any questions about what Rutherford was +up to or the kind of broader excitement + + align:start position:0% +up to or the kind of broader excitement + + + align:start position:0% +up to or the kind of broader excitement +about radioactivity and all that stuff + + align:start position:0% + + + + align:start position:0% + +if not I think I'll press ahead as + + align:start position:0% +if not I think I'll press ahead as + + + align:start position:0% +if not I think I'll press ahead as +always of course please feel free to + + align:start position:0% +always of course please feel free to + + + align:start position:0% +always of course please feel free to +chime in in the chat we'll have another + + align:start position:0% +chime in in the chat we'll have another + + + align:start position:0% +chime in in the chat we'll have another +uh question break pretty soon + + align:start position:0% + + + + align:start position:0% + +oh yeah uh Gary asked one Rutherford + + align:start position:0% +oh yeah uh Gary asked one Rutherford + + + align:start position:0% +oh yeah uh Gary asked one Rutherford +think the alpha particle is like a + + align:start position:0% +think the alpha particle is like a + + + align:start position:0% +think the alpha particle is like a +cannonball partly very good thank you + + align:start position:0% +cannonball partly very good thank you + + + align:start position:0% +cannonball partly very good thank you +uh Gary so by this point people knew + + align:start position:0% +uh Gary so by this point people knew + + + align:start position:0% +uh Gary so by this point people knew +thanks to some of his own work + + align:start position:0% +thanks to some of his own work + + + align:start position:0% +thanks to some of his own work +that the alpha particles were + + align:start position:0% +that the alpha particles were + + + align:start position:0% +that the alpha particles were +unbelievably heavy compared to the beta + + align:start position:0% +unbelievably heavy compared to the beta + + + align:start position:0% +unbelievably heavy compared to the beta +particles + + align:start position:0% +particles + + + align:start position:0% +particles +these things were on the order of ten + + align:start position:0% +these things were on the order of ten + + + align:start position:0% +these things were on the order of ten +thousand times more massive + + align:start position:0% +thousand times more massive + + + align:start position:0% +thousand times more massive +so it is like I mean in their artillery + + align:start position:0% +so it is like I mean in their artillery + + + align:start position:0% +so it is like I mean in their artillery +mines it would be like you know a BB gun + + align:start position:0% +mines it would be like you know a BB gun + + + align:start position:0% +mines it would be like you know a BB gun +versus you know a cannon blast it really + + align:start position:0% +versus you know a cannon blast it really + + + align:start position:0% +versus you know a cannon blast it really +was in that sense a huge difference in + + align:start position:0% +was in that sense a huge difference in + + + align:start position:0% +was in that sense a huge difference in +their own um in just the heft + + align:start position:0% +their own um in just the heft + + + align:start position:0% +their own um in just the heft +uh there people would conduct um what + + align:start position:0% +uh there people would conduct um what + + + align:start position:0% +uh there people would conduct um what +soon became called + + align:start position:0% +soon became called + + + align:start position:0% +soon became called +charge to mass ratio experiments some of + + align:start position:0% +charge to mass ratio experiments some of + + + align:start position:0% +charge to mass ratio experiments some of +you might know this you might have even + + align:start position:0% +you might know this you might have even + + + align:start position:0% +you might know this you might have even +done some of these in junior lab or + + align:start position:0% +done some of these in junior lab or + + + align:start position:0% +done some of these in junior lab or +earlier uh this was building on things + + align:start position:0% +earlier uh this was building on things + + + align:start position:0% +earlier uh this was building on things +that J.J Thompson had been doing in the + + align:start position:0% +that J.J Thompson had been doing in the + + + align:start position:0% +that J.J Thompson had been doing in the +1890s that Rutherford learned as a + + align:start position:0% +1890s that Rutherford learned as a + + + align:start position:0% +1890s that Rutherford learned as a +student + + align:start position:0% +student + + + align:start position:0% +student +once it became clear that both beta + + align:start position:0% +once it became clear that both beta + + + align:start position:0% +once it became clear that both beta +particles and alpha particles carried + + align:start position:0% +particles and alpha particles carried + + + align:start position:0% +particles and alpha particles carried +some electric charge that people were + + align:start position:0% +some electric charge that people were + + + align:start position:0% +some electric charge that people were +like great let me give let me go mess + + align:start position:0% +like great let me give let me go mess + + + align:start position:0% +like great let me give let me go mess +with them one of the best ways to mess + + align:start position:0% +with them one of the best ways to mess + + + align:start position:0% +with them one of the best ways to mess +with electric charges is to use magnets + + align:start position:0% +with electric charges is to use magnets + + + align:start position:0% +with electric charges is to use magnets +right use a strong external magnetic + + align:start position:0% +right use a strong external magnetic + + + align:start position:0% +right use a strong external magnetic +field and then you can measure the ratio + + align:start position:0% +field and then you can measure the ratio + + + align:start position:0% +field and then you can measure the ratio +basically how strong an external magnet + + align:start position:0% +basically how strong an external magnet + + + align:start position:0% +basically how strong an external magnet +you need to get a certain kind of Arc in + + align:start position:0% +you need to get a certain kind of Arc in + + + align:start position:0% +you need to get a certain kind of Arc in +the trajectory of those particles and + + align:start position:0% +the trajectory of those particles and + + + align:start position:0% +the trajectory of those particles and +that will help you learn the ratio of + + align:start position:0% +that will help you learn the ratio of + + + align:start position:0% +that will help you learn the ratio of +their charge to their Mass + + align:start position:0% +their charge to their Mass + + + align:start position:0% +their charge to their Mass +then separately with things like Geiger + + align:start position:0% +then separately with things like Geiger + + + align:start position:0% +then separately with things like Geiger +counters you can start measuring the + + align:start position:0% +counters you can start measuring the + + + align:start position:0% +counters you can start measuring the +ratio of just their charges you combine + + align:start position:0% +ratio of just their charges you combine + + + align:start position:0% +ratio of just their charges you combine +all that you say oh the mass of those + + align:start position:0% +all that you say oh the mass of those + + + align:start position:0% +all that you say oh the mass of those +alpha particles was again on the order + + align:start position:0% +alpha particles was again on the order + + + align:start position:0% +alpha particles was again on the order +of 10 000 times greater or more than the + + align:start position:0% +of 10 000 times greater or more than the + + + align:start position:0% +of 10 000 times greater or more than the +mass of the beta particles so they were + + align:start position:0% +mass of the beta particles so they were + + + align:start position:0% +mass of the beta particles so they were +using each of these to fire on stuff + + align:start position:0% +using each of these to fire on stuff + + + align:start position:0% +using each of these to fire on stuff +right these quickly both became um kind + + align:start position:0% +right these quickly both became um kind + + + align:start position:0% +right these quickly both became um kind +of projectiles to shoot at new targets + + align:start position:0% +of projectiles to shoot at new targets + + + align:start position:0% +of projectiles to shoot at new targets +but one of them seemed like it really + + align:start position:0% +but one of them seemed like it really + + + align:start position:0% +but one of them seemed like it really +was just this monster of the radio of + + align:start position:0% +was just this monster of the radio of + + + align:start position:0% +was just this monster of the radio of +the radioactive realm and to have that + + align:start position:0% +the radioactive realm and to have that + + + align:start position:0% +the radioactive realm and to have that +kind of you know Cannonball shell + + align:start position:0% +kind of you know Cannonball shell + + + align:start position:0% +kind of you know Cannonball shell +artillery shell bounce back if you + + align:start position:0% +artillery shell bounce back if you + + + align:start position:0% +artillery shell bounce back if you +thought you were firing it out otherwise + + align:start position:0% +thought you were firing it out otherwise + + + align:start position:0% +thought you were firing it out otherwise +undifferentiated porridge I mean that's + + align:start position:0% +undifferentiated porridge I mean that's + + + align:start position:0% +undifferentiated porridge I mean that's +I think that's what Rutherford's + + align:start position:0% +I think that's what Rutherford's + + + align:start position:0% +I think that's what Rutherford's +surprise was coming from + + align:start position:0% +surprise was coming from + + + align:start position:0% +surprise was coming from +it's a great question + + align:start position:0% +it's a great question + + + align:start position:0% +it's a great question +any other questions on that + + align:start position:0% + + + + align:start position:0% + +okay let me let me March on now we're + + align:start position:0% +okay let me let me March on now we're + + + align:start position:0% +okay let me let me March on now we're +going to hear about some work by uh one + + align:start position:0% +going to hear about some work by uh one + + + align:start position:0% +going to hear about some work by uh one +of Rutherford's postdocs + + align:start position:0% +of Rutherford's postdocs + + + align:start position:0% +of Rutherford's postdocs +who was named Niels Bohr + + align:start position:0% +who was named Niels Bohr + + + align:start position:0% +who was named Niels Bohr +so Bohr was a young Danish physicist he + + align:start position:0% +so Bohr was a young Danish physicist he + + + align:start position:0% +so Bohr was a young Danish physicist he +had just finished his PhD in theoretical + + align:start position:0% +had just finished his PhD in theoretical + + + align:start position:0% +had just finished his PhD in theoretical +physics in his native Copenhagen he grew + + align:start position:0% +physics in his native Copenhagen he grew + + + align:start position:0% +physics in his native Copenhagen he grew +up in a actually relatively well-to-do + + align:start position:0% +up in a actually relatively well-to-do + + + align:start position:0% +up in a actually relatively well-to-do +family his father was a very prestigious + + align:start position:0% +family his father was a very prestigious + + + align:start position:0% +family his father was a very prestigious +uh professor of physiology at the + + align:start position:0% +uh professor of physiology at the + + + align:start position:0% +uh professor of physiology at the +University of Copenhagen he grew up in + + align:start position:0% +University of Copenhagen he grew up in + + + align:start position:0% +University of Copenhagen he grew up in +an academic household he remembered from + + align:start position:0% +an academic household he remembered from + + + align:start position:0% +an academic household he remembered from +his childhood having lots and lots of + + align:start position:0% +his childhood having lots and lots of + + + align:start position:0% +his childhood having lots and lots of +you know distinguished Scholars come + + align:start position:0% +you know distinguished Scholars come + + + align:start position:0% +you know distinguished Scholars come +visit for dinner all the time that kind + + align:start position:0% +visit for dinner all the time that kind + + + align:start position:0% +visit for dinner all the time that kind +of thing and he was uh Niels himself was + + align:start position:0% +of thing and he was uh Niels himself was + + + align:start position:0% +of thing and he was uh Niels himself was +a very ambitious young young physicist + + align:start position:0% +a very ambitious young young physicist + + + align:start position:0% +a very ambitious young young physicist +his younger brother went on to Harold + + align:start position:0% +his younger brother went on to Harold + + + align:start position:0% +his younger brother went on to Harold +went on to a distinguished career in + + align:start position:0% +went on to a distinguished career in + + + align:start position:0% +went on to a distinguished career in +pure mathematics a very kind of elite + + align:start position:0% +pure mathematics a very kind of elite + + + align:start position:0% +pure mathematics a very kind of elite +academic family in Copenhagen + + align:start position:0% +academic family in Copenhagen + + + align:start position:0% +academic family in Copenhagen +the place he most wanted to go after + + align:start position:0% +the place he most wanted to go after + + + align:start position:0% +the place he most wanted to go after +finishing his PhD was to join + + align:start position:0% +finishing his PhD was to join + + + align:start position:0% +finishing his PhD was to join +Rutherford's group this was right at the + + align:start position:0% +Rutherford's group this was right at the + + + align:start position:0% +Rutherford's group this was right at the +time that Rutherford was doing all these + + align:start position:0% +time that Rutherford was doing all these + + + align:start position:0% +time that Rutherford was doing all these +amazing experiments on things like the + + align:start position:0% +amazing experiments on things like the + + + align:start position:0% +amazing experiments on things like the +scattering that led to the nuclear model + + align:start position:0% +scattering that led to the nuclear model + + + align:start position:0% +scattering that led to the nuclear model +so Bohr was accepted as a young + + align:start position:0% +so Bohr was accepted as a young + + + align:start position:0% +so Bohr was accepted as a young +postdoctoral scholar with Rutherford's + + align:start position:0% +postdoctoral scholar with Rutherford's + + + align:start position:0% +postdoctoral scholar with Rutherford's +group he moved to Manchester and spent + + align:start position:0% +group he moved to Manchester and spent + + + align:start position:0% +group he moved to Manchester and spent +about two years there kind of typical + + align:start position:0% +about two years there kind of typical + + + align:start position:0% +about two years there kind of typical +postdoc time right at the time that + + align:start position:0% +postdoc time right at the time that + + + align:start position:0% +postdoc time right at the time that +these scattering results were first + + align:start position:0% +these scattering results were first + + + align:start position:0% +these scattering results were first +being shared so Bohr became really + + align:start position:0% +being shared so Bohr became really + + + align:start position:0% +being shared so Bohr became really +fascinated by this new notion partly for + + align:start position:0% +fascinated by this new notion partly for + + + align:start position:0% +fascinated by this new notion partly for +the reasons I was describing that it + + align:start position:0% +the reasons I was describing that it + + + align:start position:0% +the reasons I was describing that it +really did seem so unexpected that Adams + + align:start position:0% +really did seem so unexpected that Adams + + + align:start position:0% +really did seem so unexpected that Adams +would have such a hard dense compact + + align:start position:0% +would have such a hard dense compact + + + align:start position:0% +would have such a hard dense compact +kind of scattering Center in there deep + + align:start position:0% +kind of scattering Center in there deep + + + align:start position:0% +kind of scattering Center in there deep +in their middle and although the mostly + + align:start position:0% +in their middle and although the mostly + + + align:start position:0% +in their middle and although the mostly +empty space + + align:start position:0% +empty space + + + align:start position:0% +empty space +so that was really cool for boar but he + + align:start position:0% +so that was really cool for boar but he + + + align:start position:0% +so that was really cool for boar but he +was puzzled as many of Rutherford's + + align:start position:0% +was puzzled as many of Rutherford's + + + align:start position:0% +was puzzled as many of Rutherford's +contemporaries were but how to make + + align:start position:0% +contemporaries were but how to make + + + align:start position:0% +contemporaries were but how to make +sense of the stability of matter if + + align:start position:0% +sense of the stability of matter if + + + align:start position:0% +sense of the stability of matter if +these electric charges of how whipping + + align:start position:0% +these electric charges of how whipping + + + align:start position:0% +these electric charges of how whipping +around that Central Mass like planets + + align:start position:0% +around that Central Mass like planets + + + align:start position:0% +around that Central Mass like planets +around the Sun how come they're not + + align:start position:0% +around the Sun how come they're not + + + align:start position:0% +around the Sun how come they're not +radiating all the time how come they're + + align:start position:0% +radiating all the time how come they're + + + align:start position:0% +radiating all the time how come they're +not losing all their energy why do atoms + + align:start position:0% +not losing all their energy why do atoms + + + align:start position:0% +not losing all their energy why do atoms +not just collapse on themselves in very + + align:start position:0% +not just collapse on themselves in very + + + align:start position:0% +not just collapse on themselves in very +short times + + align:start position:0% +short times + + + align:start position:0% +short times +so Bohr maybe because he came from this + + align:start position:0% +so Bohr maybe because he came from this + + + align:start position:0% +so Bohr maybe because he came from this +very elite academic family he set + + align:start position:0% +very elite academic family he set + + + align:start position:0% +very elite academic family he set +himself a very modest goal for his + + align:start position:0% +himself a very modest goal for his + + + align:start position:0% +himself a very modest goal for his +postdoc he said I'll explain the + + align:start position:0% +postdoc he said I'll explain the + + + align:start position:0% +postdoc he said I'll explain the +stability of every single kind of atom + + align:start position:0% +stability of every single kind of atom + + + align:start position:0% +stability of every single kind of atom +forever it was remarkable he wanted to + + align:start position:0% +forever it was remarkable he wanted to + + + align:start position:0% +forever it was remarkable he wanted to +get basically solve for the stability of + + align:start position:0% +get basically solve for the stability of + + + align:start position:0% +get basically solve for the stability of +every single entry on the periodic table + + align:start position:0% +every single entry on the periodic table + + + align:start position:0% +every single entry on the periodic table +you got to feel a taste of this in the + + align:start position:0% +you got to feel a taste of this in the + + + align:start position:0% +you got to feel a taste of this in the +reading for today by historian John + + align:start position:0% +reading for today by historian John + + + align:start position:0% +reading for today by historian John +heilbrin one of the things that I think + + align:start position:0% +heilbrin one of the things that I think + + + align:start position:0% +heilbrin one of the things that I think +we often forget I didn't know when I + + align:start position:0% +we often forget I didn't know when I + + + align:start position:0% +we often forget I didn't know when I +first learned about the Bohr model and I + + align:start position:0% +first learned about the Bohr model and I + + + align:start position:0% +first learned about the Bohr model and I +think that's my favorite part about the + + align:start position:0% +think that's my favorite part about the + + + align:start position:0% +think that's my favorite part about the +piece by heilbrin is it boer's first + + align:start position:0% +piece by heilbrin is it boer's first + + + align:start position:0% +piece by heilbrin is it boer's first +attempt was actually to focus on + + align:start position:0% +attempt was actually to focus on + + + align:start position:0% +attempt was actually to focus on +multi-electron atoms and even molecules + + align:start position:0% +multi-electron atoms and even molecules + + + align:start position:0% +multi-electron atoms and even molecules +he didn't first start with hydrogen the + + align:start position:0% +he didn't first start with hydrogen the + + + align:start position:0% +he didn't first start with hydrogen the +way we now usually associate with it + + align:start position:0% +way we now usually associate with it + + + align:start position:0% +way we now usually associate with it +with his work he actually figured maybe + + align:start position:0% +with his work he actually figured maybe + + + align:start position:0% +with his work he actually figured maybe +there is some kind of what we now call + + align:start position:0% +there is some kind of what we now call + + + align:start position:0% +there is some kind of what we now call +classical kind of equilibrium a kind of + + align:start position:0% +classical kind of equilibrium a kind of + + + align:start position:0% +classical kind of equilibrium a kind of +compensation mechanism that would allow + + align:start position:0% +compensation mechanism that would allow + + + align:start position:0% +compensation mechanism that would allow +these electrons to sort of uh be uh + + align:start position:0% +these electrons to sort of uh be uh + + + align:start position:0% +these electrons to sort of uh be uh +outside of a of a nucleus but not + + align:start position:0% +outside of a of a nucleus but not + + + align:start position:0% +outside of a of a nucleus but not +constantly accelerating the constantly + + align:start position:0% +constantly accelerating the constantly + + + align:start position:0% +constantly accelerating the constantly +losing their energy due to radiation so + + align:start position:0% +losing their energy due to radiation so + + + align:start position:0% +losing their energy due to radiation so +you wanted to find some combination of + + align:start position:0% +you wanted to find some combination of + + + align:start position:0% +you wanted to find some combination of +electrostatic repulsion between the + + align:start position:0% +electrostatic repulsion between the + + + align:start position:0% +electrostatic repulsion between the +electrons repelling each other and a + + align:start position:0% +electrons repelling each other and a + + + align:start position:0% +electrons repelling each other and a +kind of magnetic effect that he thought + + align:start position:0% +kind of magnetic effect that he thought + + + align:start position:0% +kind of magnetic effect that he thought +could maybe counterbalance and make a + + align:start position:0% +could maybe counterbalance and make a + + + align:start position:0% +could maybe counterbalance and make a +kind of equilibrium and then maybe that + + align:start position:0% +kind of equilibrium and then maybe that + + + align:start position:0% +kind of equilibrium and then maybe that +would explain both the structure of + + align:start position:0% +would explain both the structure of + + + align:start position:0% +would explain both the structure of +atoms and why atoms don't uh immediately + + align:start position:0% +atoms and why atoms don't uh immediately + + + align:start position:0% +atoms and why atoms don't uh immediately +Fall Apart that's quite an ambitious + + align:start position:0% +Fall Apart that's quite an ambitious + + + align:start position:0% +Fall Apart that's quite an ambitious +postdoc project + + align:start position:0% +postdoc project + + + align:start position:0% +postdoc project +and it didn't work and and pretty soon + + align:start position:0% +and it didn't work and and pretty soon + + + align:start position:0% +and it didn't work and and pretty soon +it became clear he just could not get + + align:start position:0% +it became clear he just could not get + + + align:start position:0% +it became clear he just could not get +this kind of equilibrium + + align:start position:0% +this kind of equilibrium + + + align:start position:0% +this kind of equilibrium +compensation thing to work uh the + + align:start position:0% +compensation thing to work uh the + + + align:start position:0% +compensation thing to work uh the +multi-electron systems were very + + align:start position:0% +multi-electron systems were very + + + align:start position:0% +multi-electron systems were very +complicated mathematically anytime you + + align:start position:0% +complicated mathematically anytime you + + + align:start position:0% +complicated mathematically anytime you +have many things acting on many other + + align:start position:0% +have many things acting on many other + + + align:start position:0% +have many things acting on many other +things as as you know to this day the + + align:start position:0% +things as as you know to this day the + + + align:start position:0% +things as as you know to this day the +mathematics quickly becomes pretty + + align:start position:0% +mathematics quickly becomes pretty + + + align:start position:0% +mathematics quickly becomes pretty +pretty intense + + align:start position:0% +pretty intense + + + align:start position:0% +pretty intense +so he finally + + align:start position:0% +so he finally + + + align:start position:0% +so he finally +um agreed to try a simpler case which is + + align:start position:0% +um agreed to try a simpler case which is + + + align:start position:0% +um agreed to try a simpler case which is +always a good tip in physics don't + + align:start position:0% +always a good tip in physics don't + + + align:start position:0% +always a good tip in physics don't +tackle don't try to tackle the hardest + + align:start position:0% +tackle don't try to tackle the hardest + + + align:start position:0% +tackle don't try to tackle the hardest +most complicated case first try to + + align:start position:0% +most complicated case first try to + + + align:start position:0% +most complicated case first try to +tackle a simpler case first so in a kind + + align:start position:0% +tackle a simpler case first so in a kind + + + align:start position:0% +tackle a simpler case first so in a kind +of desperation + + align:start position:0% +of desperation + + + align:start position:0% +of desperation +for switches gears and start to think + + align:start position:0% +for switches gears and start to think + + + align:start position:0% +for switches gears and start to think +hard about the simplest of all the atoms + + align:start position:0% +hard about the simplest of all the atoms + + + align:start position:0% +hard about the simplest of all the atoms +the very first placeholder on + + align:start position:0% +the very first placeholder on + + + align:start position:0% +the very first placeholder on +mendeleev's periodic table the hydrogen + + align:start position:0% +mendeleev's periodic table the hydrogen + + + align:start position:0% +mendeleev's periodic table the hydrogen +atom which even by then was known to + + align:start position:0% +atom which even by then was known to + + + align:start position:0% +atom which even by then was known to +have one electron and therefore is + + align:start position:0% +have one electron and therefore is + + + align:start position:0% +have one electron and therefore is +assumed to have one compensating proton + + align:start position:0% +assumed to have one compensating proton + + + align:start position:0% +assumed to have one compensating proton +in that nucleus so that way you don't + + align:start position:0% +in that nucleus so that way you don't + + + align:start position:0% +in that nucleus so that way you don't +have to worry about multi-electron + + align:start position:0% +have to worry about multi-electron + + + align:start position:0% +have to worry about multi-electron +repulsion within a single atom + + align:start position:0% +repulsion within a single atom + + + align:start position:0% +repulsion within a single atom +and again for Simplicity he considered a + + align:start position:0% +and again for Simplicity he considered a + + + align:start position:0% +and again for Simplicity he considered a +circular orbit it could have been a more + + align:start position:0% +circular orbit it could have been a more + + + align:start position:0% +circular orbit it could have been a more +complicated motion but he said let me + + align:start position:0% +complicated motion but he said let me + + + align:start position:0% +complicated motion but he said let me +just get started by assuming really like + + align:start position:0% +just get started by assuming really like + + + align:start position:0% +just get started by assuming really like +a simple simplified version of the solar + + align:start position:0% +a simple simplified version of the solar + + + align:start position:0% +a simple simplified version of the solar +system that the proton the positive + + align:start position:0% +system that the proton the positive + + + align:start position:0% +system that the proton the positive +nucleus sits still in the middle and the + + align:start position:0% +nucleus sits still in the middle and the + + + align:start position:0% +nucleus sits still in the middle and the +electron orbits in A Perfect Circle uh + + align:start position:0% +electron orbits in A Perfect Circle uh + + + align:start position:0% +electron orbits in A Perfect Circle uh +in a simpler version even than uh than + + align:start position:0% +in a simpler version even than uh than + + + align:start position:0% +in a simpler version even than uh than +the planet Earth around the Sun + + align:start position:0% +the planet Earth around the Sun + + + align:start position:0% +the planet Earth around the Sun +in that case now he knew how to start + + align:start position:0% +in that case now he knew how to start + + + align:start position:0% +in that case now he knew how to start +and again this is how I think any of us + + align:start position:0% +and again this is how I think any of us + + + align:start position:0% +and again this is how I think any of us +would start he knew there was an + + align:start position:0% +would start he knew there was an + + + align:start position:0% +would start he knew there was an +attractive force between the negatively + + align:start position:0% +attractive force between the negatively + + + align:start position:0% +attractive force between the negatively +charged electron and the positively + + align:start position:0% +charged electron and the positively + + + align:start position:0% +charged electron and the positively +charged proton there'd be an + + align:start position:0% +charged proton there'd be an + + + align:start position:0% +charged proton there'd be an +electromagnet electrostatic attraction + + align:start position:0% +electromagnet electrostatic attraction + + + align:start position:0% +electromagnet electrostatic attraction +the strength of which would go like the + + align:start position:0% +the strength of which would go like the + + + align:start position:0% +the strength of which would go like the +square of their charges divided by the + + align:start position:0% +square of their charges divided by the + + + align:start position:0% +square of their charges divided by the +square of their distance between them + + align:start position:0% +square of their distance between them + + + align:start position:0% +square of their distance between them +there'd also be a kind of mechanical + + align:start position:0% +there'd also be a kind of mechanical + + + align:start position:0% +there'd also be a kind of mechanical +motion of that electron constantly + + align:start position:0% +motion of that electron constantly + + + align:start position:0% +motion of that electron constantly +moving around undergoing centrifugal + + align:start position:0% +moving around undergoing centrifugal + + + align:start position:0% +moving around undergoing centrifugal +acceleration and he could just take the + + align:start position:0% +acceleration and he could just take the + + + align:start position:0% +acceleration and he could just take the +kind of Newtonian expression for that + + align:start position:0% +kind of Newtonian expression for that + + + align:start position:0% +kind of Newtonian expression for that +you have you know the planet Earth + + align:start position:0% +you have you know the planet Earth + + + align:start position:0% +you have you know the planet Earth +moving around the Sun or a ball moving + + align:start position:0% +moving around the Sun or a ball moving + + + align:start position:0% +moving around the Sun or a ball moving +on a string or in a circle there'll be + + align:start position:0% +on a string or in a circle there'll be + + + align:start position:0% +on a string or in a circle there'll be +an outward directed uh effective Force + + align:start position:0% +an outward directed uh effective Force + + + align:start position:0% +an outward directed uh effective Force +it's a different centrifugal force and + + align:start position:0% +it's a different centrifugal force and + + + align:start position:0% +it's a different centrifugal force and +he just said there must be a stable + + align:start position:0% +he just said there must be a stable + + + align:start position:0% +he just said there must be a stable +orbit when that inward directed force of + + align:start position:0% +orbit when that inward directed force of + + + align:start position:0% +orbit when that inward directed force of +electromagnetic attraction is perfectly + + align:start position:0% +electromagnetic attraction is perfectly + + + align:start position:0% +electromagnetic attraction is perfectly +balanced by that outward tendency of the + + align:start position:0% +balanced by that outward tendency of the + + + align:start position:0% +balanced by that outward tendency of the +centrifugal force balance of forces and + + align:start position:0% +centrifugal force balance of forces and + + + align:start position:0% +centrifugal force balance of forces and +now he can solve for this speed really + + align:start position:0% +now he can solve for this speed really + + + align:start position:0% +now he can solve for this speed really +the speed squared associated with one of + + align:start position:0% +the speed squared associated with one of + + + align:start position:0% +the speed squared associated with one of +those stable orbits this is all you know + + align:start position:0% +those stable orbits this is all you know + + + align:start position:0% +those stable orbits this is all you know +Newtonian and maxwellian or even pre-max + + align:start position:0% +Newtonian and maxwellian or even pre-max + + + align:start position:0% +Newtonian and maxwellian or even pre-max +well just coulomb + + align:start position:0% +well just coulomb + + + align:start position:0% +well just coulomb +so as far as Bohr was concerned at this + + align:start position:0% +so as far as Bohr was concerned at this + + + align:start position:0% +so as far as Bohr was concerned at this +stage both the speed the magnitude of + + align:start position:0% +stage both the speed the magnitude of + + + align:start position:0% +stage both the speed the magnitude of +the Velocity V and the average radius + + align:start position:0% +the Velocity V and the average radius + + + align:start position:0% +the Velocity V and the average radius +the distance between the electron and + + align:start position:0% +the distance between the electron and + + + align:start position:0% +the distance between the electron and +the nucleus these are assumed to be + + align:start position:0% +the nucleus these are assumed to be + + + align:start position:0% +the nucleus these are assumed to be +variables they could take any one of a + + align:start position:0% +variables they could take any one of a + + + align:start position:0% +variables they could take any one of a +continuous range of values it could be + + align:start position:0% +continuous range of values it could be + + + align:start position:0% +continuous range of values it could be +at one unit or 1.003 units or 1.0035 + + align:start position:0% +at one unit or 1.003 units or 1.0035 + + + align:start position:0% +at one unit or 1.003 units or 1.0035 +units Etc uh + + align:start position:0% +units Etc uh + + + align:start position:0% +units Etc uh +then Bohr says well if we just stick + + align:start position:0% +then Bohr says well if we just stick + + + align:start position:0% +then Bohr says well if we just stick +with that we have all the challenges of + + align:start position:0% +with that we have all the challenges of + + + align:start position:0% +with that we have all the challenges of +uh Rutherford's model why are these + + align:start position:0% +uh Rutherford's model why are these + + + align:start position:0% +uh Rutherford's model why are these +atoms stable why aren't they radiating + + align:start position:0% +atoms stable why aren't they radiating + + + align:start position:0% +atoms stable why aren't they radiating +and so on so now Bohr takes inspiration + + align:start position:0% +and so on so now Bohr takes inspiration + + + align:start position:0% +and so on so now Bohr takes inspiration +partly from Mox plonk remember this is + + align:start position:0% +partly from Mox plonk remember this is + + + align:start position:0% +partly from Mox plonk remember this is +now 1911 12 13. uh this is several a + + align:start position:0% +now 1911 12 13. uh this is several a + + + align:start position:0% +now 1911 12 13. uh this is several a +decade into to Planck's work on black + + align:start position:0% +decade into to Planck's work on black + + + align:start position:0% +decade into to Planck's work on black +matter radiation + + align:start position:0% +matter radiation + + + align:start position:0% +matter radiation +but we know from Boar's writings uh and + + align:start position:0% +but we know from Boar's writings uh and + + + align:start position:0% +but we know from Boar's writings uh and +letters at the time he was even more + + align:start position:0% +letters at the time he was even more + + + align:start position:0% +letters at the time he was even more +directly inspired by Einstein it was + + align:start position:0% +directly inspired by Einstein it was + + + align:start position:0% +directly inspired by Einstein it was +just a couple years older than boar + + align:start position:0% +just a couple years older than boar + + + align:start position:0% +just a couple years older than boar +himself and by this point + + align:start position:0% +himself and by this point + + + align:start position:0% +himself and by this point +uh uh Bohr was thinking about Einstein's + + align:start position:0% +uh uh Bohr was thinking about Einstein's + + + align:start position:0% +uh uh Bohr was thinking about Einstein's +kind of re-explanations of things like + + align:start position:0% +kind of re-explanations of things like + + + align:start position:0% +kind of re-explanations of things like +black body radiation and the + + align:start position:0% +black body radiation and the + + + align:start position:0% +black body radiation and the +photoelectric effect + + align:start position:0% +photoelectric effect + + + align:start position:0% +photoelectric effect +and Einstein even more than boar have + + align:start position:0% +and Einstein even more than boar have + + + align:start position:0% +and Einstein even more than boar have +been emphasizing a kind of discreetness + + align:start position:0% +been emphasizing a kind of discreetness + + + align:start position:0% +been emphasizing a kind of discreetness +that we have to break the classical + + align:start position:0% +that we have to break the classical + + + align:start position:0% +that we have to break the classical +rules at some point and say certain + + align:start position:0% +rules at some point and say certain + + + align:start position:0% +rules at some point and say certain +quantities can only take quantized units + + align:start position:0% +quantities can only take quantized units + + + align:start position:0% +quantities can only take quantized units +like Einstein's explanation for Planck's + + align:start position:0% +like Einstein's explanation for Planck's + + + align:start position:0% +like Einstein's explanation for Planck's +work saying that light quanta could only + + align:start position:0% +work saying that light quanta could only + + + align:start position:0% +work saying that light quanta could only +take fixed amount hold fixed amounts of + + align:start position:0% +take fixed amount hold fixed amounts of + + + align:start position:0% +take fixed amount hold fixed amounts of +energy H times Nu or 2H times new but + + align:start position:0% +energy H times Nu or 2H times new but + + + align:start position:0% +energy H times Nu or 2H times new but +not any non-integer value so Bohr says + + align:start position:0% +not any non-integer value so Bohr says + + + align:start position:0% +not any non-integer value so Bohr says +let me try that trick again hey + + align:start position:0% +let me try that trick again hey + + + align:start position:0% +let me try that trick again hey +basically by now it's it's a it's a + + align:start position:0% +basically by now it's it's a it's a + + + align:start position:0% +basically by now it's it's a it's a +strategy to try + + align:start position:0% +strategy to try + + + align:start position:0% +strategy to try +so Bohr just uh gives a kind of again a + + align:start position:0% +so Bohr just uh gives a kind of again a + + + align:start position:0% +so Bohr just uh gives a kind of again a +heuristic + + align:start position:0% +heuristic + + + align:start position:0% +heuristic +um uh hypothesis he doesn't prove it he + + align:start position:0% +um uh hypothesis he doesn't prove it he + + + align:start position:0% +um uh hypothesis he doesn't prove it he +doesn't derive it much like Einstein was + + align:start position:0% +doesn't derive it much like Einstein was + + + align:start position:0% +doesn't derive it much like Einstein was +doing with his heuristic suggestion of + + align:start position:0% +doing with his heuristic suggestion of + + + align:start position:0% +doing with his heuristic suggestion of +like Quantum Bohr says what if a + + align:start position:0% +like Quantum Bohr says what if a + + + align:start position:0% +like Quantum Bohr says what if a +quantity that ordinarily we would treat + + align:start position:0% +quantity that ordinarily we would treat + + + align:start position:0% +quantity that ordinarily we would treat +as having any old value at all the + + align:start position:0% +as having any old value at all the + + + align:start position:0% +as having any old value at all the +angular momentum of that electron's + + align:start position:0% +angular momentum of that electron's + + + align:start position:0% +angular momentum of that electron's +emotion in the atom which classically + + align:start position:0% +emotion in the atom which classically + + + align:start position:0% +emotion in the atom which classically +for a perfectly circular orbit has a + + align:start position:0% +for a perfectly circular orbit has a + + + align:start position:0% +for a perfectly circular orbit has a +very simple expression the electrons + + align:start position:0% +very simple expression the electrons + + + align:start position:0% +very simple expression the electrons +mass times the magnitude of its velocity + + align:start position:0% +mass times the magnitude of its velocity + + + align:start position:0% +mass times the magnitude of its velocity +times its radius and what if we just + + align:start position:0% +times its radius and what if we just + + + align:start position:0% +times its radius and what if we just +impose now a discreetness much as + + align:start position:0% +impose now a discreetness much as + + + align:start position:0% +impose now a discreetness much as +Einstein had done in other contexts what + + align:start position:0% +Einstein had done in other contexts what + + + align:start position:0% +Einstein had done in other contexts what +if we say the angular momentum of that + + align:start position:0% +if we say the angular momentum of that + + + align:start position:0% +if we say the angular momentum of that +moving electron can only take integer + + align:start position:0% +moving electron can only take integer + + + align:start position:0% +moving electron can only take integer +values a set of a scale set by planks + + align:start position:0% +values a set of a scale set by planks + + + align:start position:0% +values a set of a scale set by planks +constant and again as many of you like + + align:start position:0% +constant and again as many of you like + + + align:start position:0% +constant and again as many of you like +we've seen already + + align:start position:0% +we've seen already + + + align:start position:0% +we've seen already +there's an abbreviation that very + + align:start position:0% +there's an abbreviation that very + + + align:start position:0% +there's an abbreviation that very +quickly becomes common this is called + + align:start position:0% +quickly becomes common this is called + + + align:start position:0% +quickly becomes common this is called +h-bar so H lowercase H had been + + align:start position:0% +h-bar so H lowercase H had been + + + align:start position:0% +h-bar so H lowercase H had been +introduced by Planck in his 1900 paper + + align:start position:0% +introduced by Planck in his 1900 paper + + + align:start position:0% +introduced by Planck in his 1900 paper +became known as plugs constant at a very + + align:start position:0% +became known as plugs constant at a very + + + align:start position:0% +became known as plugs constant at a very +particular numerical value in say ERG + + align:start position:0% +particular numerical value in say ERG + + + align:start position:0% +particular numerical value in say ERG +ERG seconds and then a very convenient + + align:start position:0% +ERG seconds and then a very convenient + + + align:start position:0% +ERG seconds and then a very convenient +shorthand is to divide that numerical + + align:start position:0% +shorthand is to divide that numerical + + + align:start position:0% +shorthand is to divide that numerical +value by 2 pi which comes up up a lot if + + align:start position:0% +value by 2 pi which comes up up a lot if + + + align:start position:0% +value by 2 pi which comes up up a lot if +you're thinking about things like + + align:start position:0% +you're thinking about things like + + + align:start position:0% +you're thinking about things like +circular orbits so Bohr says one of the + + align:start position:0% +circular orbits so Bohr says one of the + + + align:start position:0% +circular orbits so Bohr says one of the +total angular momentum of that moving + + align:start position:0% +total angular momentum of that moving + + + align:start position:0% +total angular momentum of that moving +electron could only take unit values at + + align:start position:0% +electron could only take unit values at + + + align:start position:0% +electron could only take unit values at +a scale set by Place constant + + align:start position:0% +a scale set by Place constant + + + align:start position:0% +a scale set by Place constant +he doesn't say why he says what if it's + + align:start position:0% +he doesn't say why he says what if it's + + + align:start position:0% +he doesn't say why he says what if it's +again this heuristic um kind of + + align:start position:0% +again this heuristic um kind of + + + align:start position:0% +again this heuristic um kind of +hypothetical suggestion so now Bohr has + + align:start position:0% +hypothetical suggestion so now Bohr has + + + align:start position:0% +hypothetical suggestion so now Bohr has +two expressions for V he has the kind of + + align:start position:0% +two expressions for V he has the kind of + + + align:start position:0% +two expressions for V he has the kind of +classical balance of forces expression + + align:start position:0% +classical balance of forces expression + + + align:start position:0% +classical balance of forces expression +he now has a new Quantum condition + + align:start position:0% +he now has a new Quantum condition + + + align:start position:0% +he now has a new Quantum condition +expression that's his term he can solve + + align:start position:0% +expression that's his term he can solve + + + align:start position:0% +expression that's his term he can solve +each for V and set them equal to each + + align:start position:0% +each for V and set them equal to each + + + align:start position:0% +each for V and set them equal to each +other and then it can solve the + + align:start position:0% +other and then it can solve the + + + align:start position:0% +other and then it can solve the +resulting a single equation for R so now + + align:start position:0% +resulting a single equation for R so now + + + align:start position:0% +resulting a single equation for R so now +he has basically two equations or two + + align:start position:0% +he has basically two equations or two + + + align:start position:0% +he has basically two equations or two +unknowns he wants to know both V and R + + align:start position:0% +unknowns he wants to know both V and R + + + align:start position:0% +unknowns he wants to know both V and R +he has two equations one here one here + + align:start position:0% +he has two equations one here one here + + + align:start position:0% +he has two equations one here one here +you equate them and then it can solve + + align:start position:0% +you equate them and then it can solve + + + align:start position:0% +you equate them and then it can solve +for the allowable radii distances from + + align:start position:0% +for the allowable radii distances from + + + align:start position:0% +for the allowable radii distances from +the nucleus at which an electron should + + align:start position:0% +the nucleus at which an electron should + + + align:start position:0% +the nucleus at which an electron should +be found if it's angular momentum is + + align:start position:0% +be found if it's angular momentum is + + + align:start position:0% +be found if it's angular momentum is +subject to this new Quantum condition + + align:start position:0% +subject to this new Quantum condition + + + align:start position:0% +subject to this new Quantum condition +and he finds that the radii the radius + + align:start position:0% +and he finds that the radii the radius + + + align:start position:0% +and he finds that the radii the radius +can't take any old value it no longer + + align:start position:0% +can't take any old value it no longer + + + align:start position:0% +can't take any old value it no longer +Falls within a Continuum of possible + + align:start position:0% +Falls within a Continuum of possible + + + align:start position:0% +Falls within a Continuum of possible +values it now sort of snaps into place + + align:start position:0% +values it now sort of snaps into place + + + align:start position:0% +values it now sort of snaps into place +with n being any positive integer + + align:start position:0% +with n being any positive integer + + + align:start position:0% +with n being any positive integer +so it could be 1 squared 1 times some + + align:start position:0% +so it could be 1 squared 1 times some + + + align:start position:0% +so it could be 1 squared 1 times some +basic uh shortest length it could be 2 + + align:start position:0% +basic uh shortest length it could be 2 + + + align:start position:0% +basic uh shortest length it could be 2 +squared or four times that length 9 and + + align:start position:0% +squared or four times that length 9 and + + + align:start position:0% +squared or four times that length 9 and +so on but it can't be 2.05 or 8.96 right + + align:start position:0% +so on but it can't be 2.05 or 8.96 right + + + align:start position:0% +so on but it can't be 2.05 or 8.96 right +so the radius at which one we should + + align:start position:0% +so the radius at which one we should + + + align:start position:0% +so the radius at which one we should +expect to find electrons if we impose + + align:start position:0% +expect to find electrons if we impose + + + align:start position:0% +expect to find electrons if we impose +this new discreetness this new Quantum + + align:start position:0% +this new discreetness this new Quantum + + + align:start position:0% +this new discreetness this new Quantum +condition becomes set by some new + + align:start position:0% +condition becomes set by some new + + + align:start position:0% +condition becomes set by some new +integer n which becomes known as the + + align:start position:0% +integer n which becomes known as the + + + align:start position:0% +integer n which becomes known as the +principal quantum number it's just any + + align:start position:0% +principal quantum number it's just any + + + align:start position:0% +principal quantum number it's just any +old positive integer and there's now + + align:start position:0% +old positive integer and there's now + + + align:start position:0% +old positive integer and there's now +again a scale in which Planck's constant + + align:start position:0% +again a scale in which Planck's constant + + + align:start position:0% +again a scale in which Planck's constant +plays a a central role the the the the + + align:start position:0% +plays a a central role the the the the + + + align:start position:0% +plays a a central role the the the the +combination of these constants of nature + + align:start position:0% +combination of these constants of nature + + + align:start position:0% +combination of these constants of nature +H bar squared divided by the mass of the + + align:start position:0% +H bar squared divided by the mass of the + + + align:start position:0% +H bar squared divided by the mass of the +electron times the square of its charge + + align:start position:0% +electron times the square of its charge + + + align:start position:0% +electron times the square of its charge +that has dimensions of length that's the + + align:start position:0% +that has dimensions of length that's the + + + align:start position:0% +that has dimensions of length that's the +kind of unit radius + + align:start position:0% +kind of unit radius + + + align:start position:0% +kind of unit radius +an electron should be found at one times + + align:start position:0% +an electron should be found at one times + + + align:start position:0% +an electron should be found at one times +that four times that 9 times that Etc + + align:start position:0% +that four times that 9 times that Etc + + + align:start position:0% +that four times that 9 times that Etc +the radius itself is about half an + + align:start position:0% +the radius itself is about half an + + + align:start position:0% +the radius itself is about half an +angstrom if you've heard of the units + + align:start position:0% +angstrom if you've heard of the units + + + align:start position:0% +angstrom if you've heard of the units +angstroms one angstrom is 10 to the + + align:start position:0% +angstroms one angstrom is 10 to the + + + align:start position:0% +angstroms one angstrom is 10 to the +minus 10 meters + + align:start position:0% +minus 10 meters + + + align:start position:0% +minus 10 meters +and so this is about uh half of that so + + align:start position:0% +and so this is about uh half of that so + + + align:start position:0% +and so this is about uh half of that so +roughly 0.5 angstroms is what this new + + align:start position:0% +roughly 0.5 angstroms is what this new + + + align:start position:0% +roughly 0.5 angstroms is what this new +unit of length works out to be + + align:start position:0% +unit of length works out to be + + + align:start position:0% +unit of length works out to be +so now Bohr has his picture emerging not + + align:start position:0% +so now Bohr has his picture emerging not + + + align:start position:0% +so now Bohr has his picture emerging not +just of a nuclear atom like from + + align:start position:0% +just of a nuclear atom like from + + + align:start position:0% +just of a nuclear atom like from +Rutherford where most of the mass and + + align:start position:0% +Rutherford where most of the mass and + + + align:start position:0% +Rutherford where most of the mass and +all the positive charge are concentrated + + align:start position:0% +all the positive charge are concentrated + + + align:start position:0% +all the positive charge are concentrated +in this dense central nucleus but now + + align:start position:0% +in this dense central nucleus but now + + + align:start position:0% +in this dense central nucleus but now +there's a more finely articulated + + align:start position:0% +there's a more finely articulated + + + align:start position:0% +there's a more finely articulated +structure for where one should find the + + align:start position:0% +structure for where one should find the + + + align:start position:0% +structure for where one should find the +electrons outside of the nucleus as the + + align:start position:0% +electrons outside of the nucleus as the + + + align:start position:0% +electrons outside of the nucleus as the +electrons circle around at least in a + + align:start position:0% +electrons circle around at least in a + + + align:start position:0% +electrons circle around at least in a +simple atom like hydrogen which only has + + align:start position:0% +simple atom like hydrogen which only has + + + align:start position:0% +simple atom like hydrogen which only has +one electron as I was saying a moment + + align:start position:0% +one electron as I was saying a moment + + + align:start position:0% +one electron as I was saying a moment +ago the electron could be found at one + + align:start position:0% +ago the electron could be found at one + + + align:start position:0% +ago the electron could be found at one +squared times this basic length a naught + + align:start position:0% +squared times this basic length a naught + + + align:start position:0% +squared times this basic length a naught +at 2 squared times that length 3 squared + + align:start position:0% +at 2 squared times that length 3 squared + + + align:start position:0% +at 2 squared times that length 3 squared +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +and so you have this series of discrete + + align:start position:0% +and so you have this series of discrete + + + align:start position:0% +and so you have this series of discrete +orbits so now Bohr wants to know well if + + align:start position:0% +orbits so now Bohr wants to know well if + + + align:start position:0% +orbits so now Bohr wants to know well if +we if we have this Solar System model + + align:start position:0% +we if we have this Solar System model + + + align:start position:0% +we if we have this Solar System model +where the electron can only be at + + align:start position:0% +where the electron can only be at + + + align:start position:0% +where the electron can only be at +certain distances certain radii from the + + align:start position:0% +certain distances certain radii from the + + + align:start position:0% +certain distances certain radii from the +nucleus how would the energy of such a + + align:start position:0% +nucleus how would the energy of such a + + + align:start position:0% +nucleus how would the energy of such a +system + + align:start position:0% +system + + + align:start position:0% +system +um how can we characterize the energy of + + align:start position:0% +um how can we characterize the energy of + + + align:start position:0% +um how can we characterize the energy of +such a system + + align:start position:0% + + + + align:start position:0% + +so just as he done before + + align:start position:0% +so just as he done before + + + align:start position:0% +so just as he done before +he goes back and starts with the + + align:start position:0% +he goes back and starts with the + + + align:start position:0% +he goes back and starts with the +perfectly normal kind of textbook + + align:start position:0% +perfectly normal kind of textbook + + + align:start position:0% +perfectly normal kind of textbook +expressions from both Newton and Maxwell + + align:start position:0% +expressions from both Newton and Maxwell + + + align:start position:0% +expressions from both Newton and Maxwell +you have a charge a charged object in + + align:start position:0% +you have a charge a charged object in + + + align:start position:0% +you have a charge a charged object in +motion around some other charged object + + align:start position:0% +motion around some other charged object + + + align:start position:0% +motion around some other charged object +the moving thing has some kinetic energy + + align:start position:0% +the moving thing has some kinetic energy + + + align:start position:0% +the moving thing has some kinetic energy +that's always one half MV squared + + align:start position:0% +that's always one half MV squared + + + align:start position:0% +that's always one half MV squared +there'll be some in this case potential + + align:start position:0% +there'll be some in this case potential + + + align:start position:0% +there'll be some in this case potential +energy it's an attractive energy because + + align:start position:0% +energy it's an attractive energy because + + + align:start position:0% +energy it's an attractive energy because +the charge is the electron and the + + align:start position:0% +the charge is the electron and the + + + align:start position:0% +the charge is the electron and the +proton have opposite charge that's why + + align:start position:0% +proton have opposite charge that's why + + + align:start position:0% +proton have opposite charge that's why +they attract each other so the potential + + align:start position:0% +they attract each other so the potential + + + align:start position:0% +they attract each other so the potential +energy has an overall minus sign + + align:start position:0% +energy has an overall minus sign + + + align:start position:0% +energy has an overall minus sign +now already from his previous classical + + align:start position:0% +now already from his previous classical + + + align:start position:0% +now already from his previous classical +balance of forces argument he already + + align:start position:0% +balance of forces argument he already + + + align:start position:0% +balance of forces argument he already +had an expression for V squared so now + + align:start position:0% +had an expression for V squared so now + + + align:start position:0% +had an expression for V squared so now +we can just sub into this expression for + + align:start position:0% +we can just sub into this expression for + + + align:start position:0% +we can just sub into this expression for +the energy + + align:start position:0% +the energy + + + align:start position:0% +the energy +he also had from the previous exercise + + align:start position:0% +he also had from the previous exercise + + + align:start position:0% +he also had from the previous exercise +had an expression for R right now the + + align:start position:0% +had an expression for R right now the + + + align:start position:0% +had an expression for R right now the +energy depends only on R well he knows + + align:start position:0% +energy depends only on R well he knows + + + align:start position:0% +energy depends only on R well he knows +he has an expression for R this part's + + align:start position:0% +he has an expression for R this part's + + + align:start position:0% +he has an expression for R this part's +newer once he uses that uh discrete + + align:start position:0% +newer once he uses that uh discrete + + + align:start position:0% +newer once he uses that uh discrete +Quantum condition by quantizing the + + align:start position:0% +Quantum condition by quantizing the + + + align:start position:0% +Quantum condition by quantizing the +angular momentum + + align:start position:0% +angular momentum + + + align:start position:0% +angular momentum +uh and so finally he can plug in his new + + align:start position:0% +uh and so finally he can plug in his new + + + align:start position:0% +uh and so finally he can plug in his new +basic unit of length it soon gets called + + align:start position:0% +basic unit of length it soon gets called + + + align:start position:0% +basic unit of length it soon gets called +in his honor the bore radius and now + + align:start position:0% +in his honor the bore radius and now + + + align:start position:0% +in his honor the bore radius and now +Bohr has an expression for the energy of + + align:start position:0% +Bohr has an expression for the energy of + + + align:start position:0% +Bohr has an expression for the energy of +an electron in any of these quantized + + align:start position:0% +an electron in any of these quantized + + + align:start position:0% +an electron in any of these quantized +orbits or quantized forms of motion it + + align:start position:0% +orbits or quantized forms of motion it + + + align:start position:0% +orbits or quantized forms of motion it +depends only on various constants the + + align:start position:0% +depends only on various constants the + + + align:start position:0% +depends only on various constants the +mass of the electron its charge and + + align:start position:0% +mass of the electron its charge and + + + align:start position:0% +mass of the electron its charge and +Planck's Constant and that integer n + + align:start position:0% +Planck's Constant and that integer n + + + align:start position:0% +Planck's Constant and that integer n +which marks which of these orbits or + + align:start position:0% +which marks which of these orbits or + + + align:start position:0% +which marks which of these orbits or +states of motion the electron is in + + align:start position:0% +states of motion the electron is in + + + align:start position:0% +states of motion the electron is in +so uh there this the electron now has + + align:start position:0% +so uh there this the electron now has + + + align:start position:0% +so uh there this the electron now has +very particular kinds of motion it can + + align:start position:0% +very particular kinds of motion it can + + + align:start position:0% +very particular kinds of motion it can +undertake there are quantized amounts of + + align:start position:0% +undertake there are quantized amounts of + + + align:start position:0% +undertake there are quantized amounts of +energy associated with any of those + + align:start position:0% +energy associated with any of those + + + align:start position:0% +energy associated with any of those +orbits so now that means one could take + + align:start position:0% +orbits so now that means one could take + + + align:start position:0% +orbits so now that means one could take +the difference in energies between any + + align:start position:0% +the difference in energies between any + + + align:start position:0% +the difference in energies between any +of those discrete allowable orbits + + align:start position:0% +of those discrete allowable orbits + + + align:start position:0% +of those discrete allowable orbits +what's the difference in energy between + + align:start position:0% +what's the difference in energy between + + + align:start position:0% +what's the difference in energy between +say an electron over here with n equals + + align:start position:0% +say an electron over here with n equals + + + align:start position:0% +say an electron over here with n equals +three so three squared is nine uh versus + + align:start position:0% +three so three squared is nine uh versus + + + align:start position:0% +three so three squared is nine uh versus +the energy of an electron here for n + + align:start position:0% +the energy of an electron here for n + + + align:start position:0% +the energy of an electron here for n +equals two or for any two uh discrete + + align:start position:0% +equals two or for any two uh discrete + + + align:start position:0% +equals two or for any two uh discrete +states of motion labeled by some integer + + align:start position:0% +states of motion labeled by some integer + + + align:start position:0% +states of motion labeled by some integer +n + + align:start position:0% +n + + + align:start position:0% +n +the energy difference between them this + + align:start position:0% +the energy difference between them this + + + align:start position:0% +the energy difference between them this +then this has this pretty simple kind of + + align:start position:0% +then this has this pretty simple kind of + + + align:start position:0% +then this has this pretty simple kind of +expression it'll be the difference of + + align:start position:0% +expression it'll be the difference of + + + align:start position:0% +expression it'll be the difference of +the inverse squares because the energy + + align:start position:0% +the inverse squares because the energy + + + align:start position:0% +the inverse squares because the energy +for either State alone goes like 1 over + + align:start position:0% +for either State alone goes like 1 over + + + align:start position:0% +for either State alone goes like 1 over +N squared + + align:start position:0% +N squared + + + align:start position:0% +N squared +and now boar starts to get excited in + + align:start position:0% +and now boar starts to get excited in + + + align:start position:0% +and now boar starts to get excited in +fact this is why anyone began taking him + + align:start position:0% +fact this is why anyone began taking him + + + align:start position:0% +fact this is why anyone began taking him +seriously at all much like with Einstein + + align:start position:0% +seriously at all much like with Einstein + + + align:start position:0% +seriously at all much like with Einstein +he hadn't proven that the angular + + align:start position:0% +he hadn't proven that the angular + + + align:start position:0% +he hadn't proven that the angular +momentum should be quantized and + + align:start position:0% +momentum should be quantized and + + + align:start position:0% +momentum should be quantized and +discrete he hadn't even really given + + align:start position:0% +discrete he hadn't even really given + + + align:start position:0% +discrete he hadn't even really given +very good Arguments for it but he + + align:start position:0% +very good Arguments for it but he + + + align:start position:0% +very good Arguments for it but he +basically says give me a give me a + + align:start position:0% +basically says give me a give me a + + + align:start position:0% +basically says give me a give me a +moment let me show you what we get if we + + align:start position:0% +moment let me show you what we get if we + + + align:start position:0% +moment let me show you what we get if we +if we adopt that assumption and why was + + align:start position:0% +if we adopt that assumption and why was + + + align:start position:0% +if we adopt that assumption and why was +Bohr excited because by taking on that + + align:start position:0% +Bohr excited because by taking on that + + + align:start position:0% +Bohr excited because by taking on that +simple looking but otherwise not + + align:start position:0% +simple looking but otherwise not + + + align:start position:0% +simple looking but otherwise not +well-motivated assumption this special + + align:start position:0% +well-motivated assumption this special + + + align:start position:0% +well-motivated assumption this special +Quantum condition he now found that the + + align:start position:0% +Quantum condition he now found that the + + + align:start position:0% +Quantum condition he now found that the +energy differences between these + + align:start position:0% +energy differences between these + + + align:start position:0% +energy differences between these +discrete states of motion of an electron + + align:start position:0% +discrete states of motion of an electron + + + align:start position:0% +discrete states of motion of an electron +in hydrogen should should reproduce the + + align:start position:0% +in hydrogen should should reproduce the + + + align:start position:0% +in hydrogen should should reproduce the +already well measured well-characterized + + align:start position:0% +already well measured well-characterized + + + align:start position:0% +already well measured well-characterized +behavior of the light that comes out of + + align:start position:0% +behavior of the light that comes out of + + + align:start position:0% +behavior of the light that comes out of +hydrogen atoms when we excite them if + + align:start position:0% +hydrogen atoms when we excite them if + + + align:start position:0% +hydrogen atoms when we excite them if +you add some energy external energy to + + align:start position:0% +you add some energy external energy to + + + align:start position:0% +you add some energy external energy to +uh to a gas of hydrogen atoms they will + + align:start position:0% +uh to a gas of hydrogen atoms they will + + + align:start position:0% +uh to a gas of hydrogen atoms they will +radiate at very specific colors the + + align:start position:0% +radiate at very specific colors the + + + align:start position:0% +radiate at very specific colors the +emission spectrum + + align:start position:0% +emission spectrum + + + align:start position:0% +emission spectrum +the spectral lines that will come out of + + align:start position:0% +the spectral lines that will come out of + + + align:start position:0% +the spectral lines that will come out of +excited hydrogen uh have a very specific + + align:start position:0% +excited hydrogen uh have a very specific + + + align:start position:0% +excited hydrogen uh have a very specific +pattern to the frequencies and this is + + align:start position:0% +pattern to the frequencies and this is + + + align:start position:0% +pattern to the frequencies and this is +actually a real data you can actually + + align:start position:0% +actually a real data you can actually + + + align:start position:0% +actually a real data you can actually +see these with the naked eye three of + + align:start position:0% +see these with the naked eye three of + + + align:start position:0% +see these with the naked eye three of +the lines that come out are in the the + + align:start position:0% +the lines that come out are in the the + + + align:start position:0% +the lines that come out are in the the +visible range for ordinary um you know + + align:start position:0% +visible range for ordinary um you know + + + align:start position:0% +visible range for ordinary um you know +human eyesight and they're very discreet + + align:start position:0% +human eyesight and they're very discreet + + + align:start position:0% +human eyesight and they're very discreet +emission lines and so-called spectral + + align:start position:0% +emission lines and so-called spectral + + + align:start position:0% +emission lines and so-called spectral +lines these have been measured in the + + align:start position:0% +lines these have been measured in the + + + align:start position:0% +lines these have been measured in the +1880s in fact it turns out the very year + + align:start position:0% +1880s in fact it turns out the very year + + + align:start position:0% +1880s in fact it turns out the very year +that Bohr was born these were measured + + align:start position:0% +that Bohr was born these were measured + + + align:start position:0% +that Bohr was born these were measured +by a German school teacher A German + + align:start position:0% +by a German school teacher A German + + + align:start position:0% +by a German school teacher A German +German language speaking school teacher + + align:start position:0% +German language speaking school teacher + + + align:start position:0% +German language speaking school teacher +named Johann Baumer + + align:start position:0% +named Johann Baumer + + + align:start position:0% +named Johann Baumer +these were known as the bomber series + + align:start position:0% +these were known as the bomber series + + + align:start position:0% +these were known as the bomber series +after that there are other series that + + align:start position:0% +after that there are other series that + + + align:start position:0% +after that there are other series that +that have been measured that were in + + align:start position:0% +that have been measured that were in + + + align:start position:0% +that have been measured that were in +either the infrared or the ultraviolet + + align:start position:0% +either the infrared or the ultraviolet + + + align:start position:0% +either the infrared or the ultraviolet +but the three characteristic lines to + + align:start position:0% +but the three characteristic lines to + + + align:start position:0% +but the three characteristic lines to +which our our eyes are are usually + + align:start position:0% +which our our eyes are are usually + + + align:start position:0% +which our our eyes are are usually +sensitive is a simple series of three + + align:start position:0% +sensitive is a simple series of three + + + align:start position:0% +sensitive is a simple series of three +lines and these had a a numerical + + align:start position:0% +lines and these had a a numerical + + + align:start position:0% +lines and these had a a numerical +regularity to them that have otherwise + + align:start position:0% +regularity to them that have otherwise + + + align:start position:0% +regularity to them that have otherwise +been pretty much unexamined unexplained + + align:start position:0% +been pretty much unexamined unexplained + + + align:start position:0% +been pretty much unexamined unexplained +but it became clear you could you could + + align:start position:0% +but it became clear you could you could + + + align:start position:0% +but it became clear you could you could +identify each of these parts of the + + align:start position:0% +identify each of these parts of the + + + align:start position:0% +identify each of these parts of the +bomber Spectrum as being a transition + + align:start position:0% +bomber Spectrum as being a transition + + + align:start position:0% +bomber Spectrum as being a transition +between some one integer squared and + + align:start position:0% +between some one integer squared and + + + align:start position:0% +between some one integer squared and +another and there was some overall + + align:start position:0% +another and there was some overall + + + align:start position:0% +another and there was some overall +constant called R named for a different + + align:start position:0% +constant called R named for a different + + + align:start position:0% +constant called R named for a different +researcher ridberg that said again the + + align:start position:0% +researcher ridberg that said again the + + + align:start position:0% +researcher ridberg that said again the +quantitative scale for the actual + + align:start position:0% +quantitative scale for the actual + + + align:start position:0% +quantitative scale for the actual +frequencies of that shade of purple that + + align:start position:0% +frequencies of that shade of purple that + + + align:start position:0% +frequencies of that shade of purple that +shade of blue in the shade of red + + align:start position:0% +shade of blue in the shade of red + + + align:start position:0% +shade of blue in the shade of red +and so uh the bomber series would come + + align:start position:0% +and so uh the bomber series would come + + + align:start position:0% +and so uh the bomber series would come +about if you simply said there's some + + align:start position:0% +about if you simply said there's some + + + align:start position:0% +about if you simply said there's some +overall empirical constant R the red + + align:start position:0% +overall empirical constant R the red + + + align:start position:0% +overall empirical constant R the red +book constant and the light that we see + + align:start position:0% +book constant and the light that we see + + + align:start position:0% +book constant and the light that we see +would correspond to a transition between + + align:start position:0% +would correspond to a transition between + + + align:start position:0% +would correspond to a transition between +say n equals three to n equals two that + + align:start position:0% +say n equals three to n equals two that + + + align:start position:0% +say n equals three to n equals two that +would be uh the red one + + align:start position:0% +would be uh the red one + + + align:start position:0% +would be uh the red one +relatively long wavelength low lower + + align:start position:0% +relatively long wavelength low lower + + + align:start position:0% +relatively long wavelength low lower +energy there could be a transition from + + align:start position:0% +energy there could be a transition from + + + align:start position:0% +energy there could be a transition from +n equals four to n equals two that would + + align:start position:0% +n equals four to n equals two that would + + + align:start position:0% +n equals four to n equals two that would +light up to our eyes like this uh nice + + align:start position:0% +light up to our eyes like this uh nice + + + align:start position:0% +light up to our eyes like this uh nice +turquoisey blue or from n equals five + + align:start position:0% +turquoisey blue or from n equals five + + + align:start position:0% +turquoisey blue or from n equals five +that equals two that would give us the + + align:start position:0% +that equals two that would give us the + + + align:start position:0% +that equals two that would give us the +deeper purple so now Bohr could say well + + align:start position:0% +deeper purple so now Bohr could say well + + + align:start position:0% +deeper purple so now Bohr could say well +there's an energy difference between + + align:start position:0% +there's an energy difference between + + + align:start position:0% +there's an energy difference between +these discrete states of motion when an + + align:start position:0% +these discrete states of motion when an + + + align:start position:0% +these discrete states of motion when an +electron moved made a transition from an + + align:start position:0% +electron moved made a transition from an + + + align:start position:0% +electron moved made a transition from an +excited state and we had to add external + + align:start position:0% +excited state and we had to add external + + + align:start position:0% +excited state and we had to add external +energy to these hydrogen atoms maybe + + align:start position:0% +energy to these hydrogen atoms maybe + + + align:start position:0% +energy to these hydrogen atoms maybe +Bohr says that bumps them up to excited + + align:start position:0% +Bohr says that bumps them up to excited + + + align:start position:0% +Bohr says that bumps them up to excited +state of motion n gets larger at some + + align:start position:0% +state of motion n gets larger at some + + + align:start position:0% +state of motion n gets larger at some +point the atom will relax back down to a + + align:start position:0% +point the atom will relax back down to a + + + align:start position:0% +point the atom will relax back down to a +low Lower State of energy and maybe the + + align:start position:0% +low Lower State of energy and maybe the + + + align:start position:0% +low Lower State of energy and maybe the +light that gets emitted this emission + + align:start position:0% +light that gets emitted this emission + + + align:start position:0% +light that gets emitted this emission +spectral line is simply the difference + + align:start position:0% +spectral line is simply the difference + + + align:start position:0% +spectral line is simply the difference +in energy between the excited uh state + + align:start position:0% +in energy between the excited uh state + + + align:start position:0% +in energy between the excited uh state +of the electrons motion and the lower + + align:start position:0% +of the electrons motion and the lower + + + align:start position:0% +of the electrons motion and the lower +energy state so the energy that comes + + align:start position:0% +energy state so the energy that comes + + + align:start position:0% +energy state so the energy that comes +out in the form of light the energy + + align:start position:0% +out in the form of light the energy + + + align:start position:0% +out in the form of light the energy +difference is exactly the difference + + align:start position:0% +difference is exactly the difference + + + align:start position:0% +difference is exactly the difference +between these otherwise uh stable + + align:start position:0% +between these otherwise uh stable + + + align:start position:0% +between these otherwise uh stable +Quantum stable uh states of the electron + + align:start position:0% +Quantum stable uh states of the electron + + + align:start position:0% +Quantum stable uh states of the electron +so not only did Bohr find the same form + + align:start position:0% +so not only did Bohr find the same form + + + align:start position:0% +so not only did Bohr find the same form +for the difference between the energies + + align:start position:0% +for the difference between the energies + + + align:start position:0% +for the difference between the energies +of those two states he can now calculate + + align:start position:0% +of those two states he can now calculate + + + align:start position:0% +of those two states he can now calculate +this empirical constant the red per + + align:start position:0% +this empirical constant the red per + + + align:start position:0% +this empirical constant the red per +constant from first principles and when + + align:start position:0% +constant from first principles and when + + + align:start position:0% +constant from first principles and when +he plugged in the values for the mass + + align:start position:0% +he plugged in the values for the mass + + + align:start position:0% +he plugged in the values for the mass +electron the charge and flanks constant + + align:start position:0% +electron the charge and flanks constant + + + align:start position:0% +electron the charge and flanks constant +he got a remarkable match to his + + align:start position:0% +he got a remarkable match to his + + + align:start position:0% +he got a remarkable match to his +empirical value for the red precaution + + align:start position:0% +empirical value for the red precaution + + + align:start position:0% +empirical value for the red precaution +if you have trouble keeping that in mind + + align:start position:0% +if you have trouble keeping that in mind + + + align:start position:0% +if you have trouble keeping that in mind +I recommend this historian's way to + + align:start position:0% +I recommend this historian's way to + + + align:start position:0% +I recommend this historian's way to +remember the Balmer series many many + + align:start position:0% +remember the Balmer series many many + + + align:start position:0% +remember the Balmer series many many +years later well after Boar's death uh + + align:start position:0% +years later well after Boar's death uh + + + align:start position:0% +years later well after Boar's death uh +his collections of his of his most + + align:start position:0% +his collections of his of his most + + + align:start position:0% +his collections of his of his most +important Works were republished in a + + align:start position:0% +important Works were republished in a + + + align:start position:0% +important Works were republished in a +three-volume set and the edit is very + + align:start position:0% +three-volume set and the edit is very + + + align:start position:0% +three-volume set and the edit is very +very uh amusingly colored the books to + + align:start position:0% +very uh amusingly colored the books to + + + align:start position:0% +very uh amusingly colored the books to +match the Baltimore Series so volume one + + align:start position:0% +match the Baltimore Series so volume one + + + align:start position:0% +match the Baltimore Series so volume one +is the red volume two is the turquoise + + align:start position:0% +is the red volume two is the turquoise + + + align:start position:0% +is the red volume two is the turquoise +blue and volume three is the purple + + align:start position:0% +blue and volume three is the purple + + + align:start position:0% +blue and volume three is the purple +okay so at first Bohr was actually + + align:start position:0% +okay so at first Bohr was actually + + + align:start position:0% +okay so at first Bohr was actually +reluctant to publish those results + + align:start position:0% +reluctant to publish those results + + + align:start position:0% +reluctant to publish those results +partly remember he'd only treated + + align:start position:0% +partly remember he'd only treated + + + align:start position:0% +partly remember he'd only treated +hydrogen and he set out at the start of + + align:start position:0% +hydrogen and he set out at the start of + + + align:start position:0% +hydrogen and he set out at the start of +his postdoc trying to explain every + + align:start position:0% +his postdoc trying to explain every + + + align:start position:0% +his postdoc trying to explain every +single atom on the periodic table every + + align:start position:0% +single atom on the periodic table every + + + align:start position:0% +single atom on the periodic table every +single element which is pretty + + align:start position:0% +single element which is pretty + + + align:start position:0% +single element which is pretty +um ridiculous so he had fallen + + align:start position:0% +um ridiculous so he had fallen + + + align:start position:0% +um ridiculous so he had fallen +approximately a hundred steps short of + + align:start position:0% +approximately a hundred steps short of + + + align:start position:0% +approximately a hundred steps short of +his goal 90 some odd steps short happily + + align:start position:0% +his goal 90 some odd steps short happily + + + align:start position:0% +his goal 90 some odd steps short happily +his postdoc advisor and his brother said + + align:start position:0% +his postdoc advisor and his brother said + + + align:start position:0% +his postdoc advisor and his brother said +you know explaining hydrogen is pretty + + align:start position:0% +you know explaining hydrogen is pretty + + + align:start position:0% +you know explaining hydrogen is pretty +good uh and you should publish because + + align:start position:0% +good uh and you should publish because + + + align:start position:0% +good uh and you should publish because +you have this remarkable unexpected + + align:start position:0% +you have this remarkable unexpected + + + align:start position:0% +you have this remarkable unexpected +agreement uh an accounting now for + + align:start position:0% +agreement uh an accounting now for + + + align:start position:0% +agreement uh an accounting now for +things like the Baltimore series of + + align:start position:0% +things like the Baltimore series of + + + align:start position:0% +things like the Baltimore series of +these spectral lines so Rutherford + + align:start position:0% +these spectral lines so Rutherford + + + align:start position:0% +these spectral lines so Rutherford +convinced young board to publish and + + align:start position:0% +convinced young board to publish and + + + align:start position:0% +convinced young board to publish and +board action publishes Trilogy of + + align:start position:0% +board action publishes Trilogy of + + + align:start position:0% +board action publishes Trilogy of +related articles uh in 1913. on the + + align:start position:0% +related articles uh in 1913. on the + + + align:start position:0% +related articles uh in 1913. on the +constitution of atoms and molecules + + align:start position:0% +constitution of atoms and molecules + + + align:start position:0% +constitution of atoms and molecules +so what really became Central was this + + align:start position:0% +so what really became Central was this + + + align:start position:0% +so what really became Central was this +new kind of hypothesis of this Quantum + + align:start position:0% +new kind of hypothesis of this Quantum + + + align:start position:0% +new kind of hypothesis of this Quantum +condition that for reasons it still + + align:start position:0% +condition that for reasons it still + + + align:start position:0% +condition that for reasons it still +weren't at all clear that we're not + + align:start position:0% +weren't at all clear that we're not + + + align:start position:0% +weren't at all clear that we're not +proven they weren't even really kind of + + align:start position:0% +proven they weren't even really kind of + + + align:start position:0% +proven they weren't even really kind of +derived or motivated but if if one takes + + align:start position:0% +derived or motivated but if if one takes + + + align:start position:0% +derived or motivated but if if one takes +as a kind of heuristic suggestion that + + align:start position:0% +as a kind of heuristic suggestion that + + + align:start position:0% +as a kind of heuristic suggestion that +maybe the angular momentum associated + + align:start position:0% +maybe the angular momentum associated + + + align:start position:0% +maybe the angular momentum associated +with the motion of electrons could only + + align:start position:0% +with the motion of electrons could only + + + align:start position:0% +with the motion of electrons could only +take on quantized or discrete values at + + align:start position:0% +take on quantized or discrete values at + + + align:start position:0% +take on quantized or discrete values at +h-bar then that would immediately + + align:start position:0% +h-bar then that would immediately + + + align:start position:0% +h-bar then that would immediately +restrict the locations the the distances + + align:start position:0% +restrict the locations the the distances + + + align:start position:0% +restrict the locations the the distances +between the electrons and the positive + + align:start position:0% +between the electrons and the positive + + + align:start position:0% +between the electrons and the positive +nucleus now you have a discrete series + + align:start position:0% +nucleus now you have a discrete series + + + align:start position:0% +nucleus now you have a discrete series +of states in motion only for those for + + align:start position:0% +of states in motion only for those for + + + align:start position:0% +of states in motion only for those for +some reason with the atom remains stable + + align:start position:0% +some reason with the atom remains stable + + + align:start position:0% +some reason with the atom remains stable +there's some new ingredient that had + + align:start position:0% +there's some new ingredient that had + + + align:start position:0% +there's some new ingredient that had +been missing In Rutherford's own picture + + align:start position:0% +been missing In Rutherford's own picture + + + align:start position:0% +been missing In Rutherford's own picture +that now might account for the the + + align:start position:0% +that now might account for the the + + + align:start position:0% +that now might account for the the +stability of matter + + align:start position:0% +stability of matter + + + align:start position:0% +stability of matter +when it electrons in one of these + + align:start position:0% +when it electrons in one of these + + + align:start position:0% +when it electrons in one of these +special quantized units it won't radiate + + align:start position:0% +special quantized units it won't radiate + + + align:start position:0% +special quantized units it won't radiate +will only radiate when it jumps between + + align:start position:0% +will only radiate when it jumps between + + + align:start position:0% +will only radiate when it jumps between +these levels and that will account for + + align:start position:0% +these levels and that will account for + + + align:start position:0% +these levels and that will account for +the emission spectrum + + align:start position:0% +the emission spectrum + + + align:start position:0% +the emission spectrum +now of course some questions still + + align:start position:0% +now of course some questions still + + + align:start position:0% +now of course some questions still +remained why don't we see this kind of + + align:start position:0% +remained why don't we see this kind of + + + align:start position:0% +remained why don't we see this kind of +discreten this in ordinary experience so + + align:start position:0% +discreten this in ordinary experience so + + + align:start position:0% +discreten this in ordinary experience so +one of the next things that Bohr + + align:start position:0% +one of the next things that Bohr + + + align:start position:0% +one of the next things that Bohr +occupied him so well occupied himself + + align:start position:0% +occupied him so well occupied himself + + + align:start position:0% +occupied him so well occupied himself +with and it actually went over the next + + align:start position:0% +with and it actually went over the next + + + align:start position:0% +with and it actually went over the next +sort of four or five years it was a + + align:start position:0% +sort of four or five years it was a + + + align:start position:0% +sort of four or five years it was a +non-trivial exercise + + align:start position:0% +non-trivial exercise + + + align:start position:0% +non-trivial exercise +became known as the correspondence + + align:start position:0% +became known as the correspondence + + + align:start position:0% +became known as the correspondence +principle again this was something that + + align:start position:0% +principle again this was something that + + + align:start position:0% +principle again this was something that +Bohr really championed and worked out uh + + align:start position:0% +Bohr really championed and worked out uh + + + align:start position:0% +Bohr really championed and worked out uh +and then became enormously influential + + align:start position:0% +and then became enormously influential + + + align:start position:0% +and then became enormously influential +in these kind of later years of what + + align:start position:0% +in these kind of later years of what + + + align:start position:0% +in these kind of later years of what +we'll call the old quantum theory that + + align:start position:0% +we'll call the old quantum theory that + + + align:start position:0% +we'll call the old quantum theory that +these Quantum ideas seem to impose some + + align:start position:0% +these Quantum ideas seem to impose some + + + align:start position:0% +these Quantum ideas seem to impose some +new break from experience something that + + align:start position:0% +new break from experience something that + + + align:start position:0% +new break from experience something that +we usually think of as continuous can + + align:start position:0% +we usually think of as continuous can + + + align:start position:0% +we usually think of as continuous can +only be discrete in an ordinary + + align:start position:0% +only be discrete in an ordinary + + + align:start position:0% +only be discrete in an ordinary +experience we don't see that kind of + + align:start position:0% +experience we don't see that kind of + + + align:start position:0% +experience we don't see that kind of +lock in step discreetness and so Bohr + + align:start position:0% +lock in step discreetness and so Bohr + + + align:start position:0% +lock in step discreetness and so Bohr +wanted to make sense of the two + + align:start position:0% +wanted to make sense of the two + + + align:start position:0% +wanted to make sense of the two +different regimes and and see if there + + align:start position:0% +different regimes and and see if there + + + align:start position:0% +different regimes and and see if there +was a way they could kind of one could + + align:start position:0% +was a way they could kind of one could + + + align:start position:0% +was a way they could kind of one could +slide over into the other + + align:start position:0% +slide over into the other + + + align:start position:0% +slide over into the other +uh and so that's what became known as a + + align:start position:0% +uh and so that's what became known as a + + + align:start position:0% +uh and so that's what became known as a +correspondence principle which was to + + align:start position:0% +correspondence principle which was to + + + align:start position:0% +correspondence principle which was to +say in the limit of very large quantum + + align:start position:0% +say in the limit of very large quantum + + + align:start position:0% +say in the limit of very large quantum +numbers for very highly excited atoms in + + align:start position:0% +numbers for very highly excited atoms in + + + align:start position:0% +numbers for very highly excited atoms in +this case where n is much much larger + + align:start position:0% +this case where n is much much larger + + + align:start position:0% +this case where n is much much larger +than one still an integer but much + + align:start position:0% +than one still an integer but much + + + align:start position:0% +than one still an integer but much +larger than one these Quantum systems + + align:start position:0% +larger than one these Quantum systems + + + align:start position:0% +larger than one these Quantum systems +should begin to reproduce the more + + align:start position:0% +should begin to reproduce the more + + + align:start position:0% +should begin to reproduce the more +expected continuous or classical + + align:start position:0% +expected continuous or classical + + + align:start position:0% +expected continuous or classical +Behavior + + align:start position:0% +Behavior + + + align:start position:0% +Behavior +and again if these next few steps + + align:start position:0% +and again if these next few steps + + + align:start position:0% +and again if these next few steps +um are you know don't make immediate + + align:start position:0% +um are you know don't make immediate + + + align:start position:0% +um are you know don't make immediate +sense that you're in good company don't + + align:start position:0% +sense that you're in good company don't + + + align:start position:0% +sense that you're in good company don't +worry + + align:start position:0% +worry + + + align:start position:0% +worry +um the slides are on the canvas site you + + align:start position:0% +um the slides are on the canvas site you + + + align:start position:0% +um the slides are on the canvas site you +can go through these steps um uh the + + align:start position:0% +can go through these steps um uh the + + + align:start position:0% +can go through these steps um uh the +algebra on your own I just want to make + + align:start position:0% +algebra on your own I just want to make + + + align:start position:0% +algebra on your own I just want to make +sure that we understand his sort of his + + align:start position:0% +sure that we understand his sort of his + + + align:start position:0% +sure that we understand his sort of his +reasoning here so I want to go through + + align:start position:0% +reasoning here so I want to go through + + + align:start position:0% +reasoning here so I want to go through +his his main argument for the + + align:start position:0% +his his main argument for the + + + align:start position:0% +his his main argument for the +correspondence principle + + align:start position:0% + + + + align:start position:0% + +according to Maxwell's again highly + + align:start position:0% +according to Maxwell's again highly + + + align:start position:0% +according to Maxwell's again highly +successful work on electromagnetism + + align:start position:0% +successful work on electromagnetism + + + align:start position:0% +successful work on electromagnetism +the frequency of light or of any + + align:start position:0% +the frequency of light or of any + + + align:start position:0% +the frequency of light or of any +electromagnetic wave that's emitted so + + align:start position:0% +electromagnetic wave that's emitted so + + + align:start position:0% +electromagnetic wave that's emitted so +we'll call that new radiation as the + + align:start position:0% +we'll call that new radiation as the + + + align:start position:0% +we'll call that new radiation as the +frequency of the of the electromagnetic + + align:start position:0% +frequency of the of the electromagnetic + + + align:start position:0% +frequency of the of the electromagnetic +waves that come out + + align:start position:0% +waves that come out + + + align:start position:0% +waves that come out +that should be equal to the mechanical + + align:start position:0% +that should be equal to the mechanical + + + align:start position:0% +that should be equal to the mechanical +motion the frequency of the mechanical + + align:start position:0% +motion the frequency of the mechanical + + + align:start position:0% +motion the frequency of the mechanical +motion if you think about a kind of + + align:start position:0% +motion if you think about a kind of + + + align:start position:0% +motion if you think about a kind of +dipole antenna if you shake an electric + + align:start position:0% +dipole antenna if you shake an electric + + + align:start position:0% +dipole antenna if you shake an electric +charge up and down on a conducting wire + + align:start position:0% +charge up and down on a conducting wire + + + align:start position:0% +charge up and down on a conducting wire +the electromagnetic waves that come from + + align:start position:0% +the electromagnetic waves that come from + + + align:start position:0% +the electromagnetic waves that come from +accelerating an electric charge should + + align:start position:0% +accelerating an electric charge should + + + align:start position:0% +accelerating an electric charge should +be directly related to the motion of the + + align:start position:0% +be directly related to the motion of the + + + align:start position:0% +be directly related to the motion of the +charge itself so the frequency of + + align:start position:0% +charge itself so the frequency of + + + align:start position:0% +charge itself so the frequency of +radiation should be equal to or maybe a + + align:start position:0% +radiation should be equal to or maybe a + + + align:start position:0% +radiation should be equal to or maybe a +higher uh kind of multiple + + align:start position:0% +higher uh kind of multiple + + + align:start position:0% +higher uh kind of multiple +um but it should be basically + + align:start position:0% +um but it should be basically + + + align:start position:0% +um but it should be basically +proportional to if not directly equal to + + align:start position:0% +proportional to if not directly equal to + + + align:start position:0% +proportional to if not directly equal to +the mechanical motion of the charge + + align:start position:0% +the mechanical motion of the charge + + + align:start position:0% +the mechanical motion of the charge +whose acceleration is emitting that + + align:start position:0% +whose acceleration is emitting that + + + align:start position:0% +whose acceleration is emitting that +radiation that was that comes directly + + align:start position:0% +radiation that was that comes directly + + + align:start position:0% +radiation that was that comes directly +out of Maxwell's work and we use that + + align:start position:0% +out of Maxwell's work and we use that + + + align:start position:0% +out of Maxwell's work and we use that +all the time in things like antenna + + align:start position:0% +all the time in things like antenna + + + align:start position:0% +all the time in things like antenna +Theory it still works to this day + + align:start position:0% +Theory it still works to this day + + + align:start position:0% +Theory it still works to this day +so Bohr said okay well let's figure out + + align:start position:0% +so Bohr said okay well let's figure out + + + align:start position:0% +so Bohr said okay well let's figure out +these two different quantities and see + + align:start position:0% +these two different quantities and see + + + align:start position:0% +these two different quantities and see +how they relate to each other he begins + + align:start position:0% +how they relate to each other he begins + + + align:start position:0% +how they relate to each other he begins +by thinking about the mechanical motion + + align:start position:0% +by thinking about the mechanical motion + + + align:start position:0% +by thinking about the mechanical motion +the frequency of that of that electron + + align:start position:0% +the frequency of that of that electron + + + align:start position:0% +the frequency of that of that electron +constantly whirling around the nucleus + + align:start position:0% +constantly whirling around the nucleus + + + align:start position:0% +constantly whirling around the nucleus +so the frequency would be one over the + + align:start position:0% +so the frequency would be one over the + + + align:start position:0% +so the frequency would be one over the +period how long does it take the + + align:start position:0% +period how long does it take the + + + align:start position:0% +period how long does it take the +electron to complete an orbit just like + + align:start position:0% +electron to complete an orbit just like + + + align:start position:0% +electron to complete an orbit just like +the Earth taking a year to go around the + + align:start position:0% +the Earth taking a year to go around the + + + align:start position:0% +the Earth taking a year to go around the +Sun so the the mechanical frequencies + + align:start position:0% +Sun so the the mechanical frequencies + + + align:start position:0% +Sun so the the mechanical frequencies +one over the orbital uh period and that + + align:start position:0% +one over the orbital uh period and that + + + align:start position:0% +one over the orbital uh period and that +for a perfectly circular orbit to keep + + align:start position:0% +for a perfectly circular orbit to keep + + + align:start position:0% +for a perfectly circular orbit to keep +things simple would be the orbital + + align:start position:0% +things simple would be the orbital + + + align:start position:0% +things simple would be the orbital +velocity the magnitude of velocity + + align:start position:0% +velocity the magnitude of velocity + + + align:start position:0% +velocity the magnitude of velocity +so the speed divided by the distance it + + align:start position:0% +so the speed divided by the distance it + + + align:start position:0% +so the speed divided by the distance it +has to travel has to travel one + + align:start position:0% +has to travel has to travel one + + + align:start position:0% +has to travel has to travel one +circumference 2 pi r it does so at a + + align:start position:0% +circumference 2 pi r it does so at a + + + align:start position:0% +circumference 2 pi r it does so at a +speed V that's how we determine um the + + align:start position:0% +speed V that's how we determine um the + + + align:start position:0% +speed V that's how we determine um the +inverse period or the frequency + + align:start position:0% +inverse period or the frequency + + + align:start position:0% +inverse period or the frequency +well once again from the balance of + + align:start position:0% +well once again from the balance of + + + align:start position:0% +well once again from the balance of +forces he has an expression for V right + + align:start position:0% +forces he has an expression for V right + + + align:start position:0% +forces he has an expression for V right +from balancing the classical forces with + + align:start position:0% +from balancing the classical forces with + + + align:start position:0% +from balancing the classical forces with +the quantized angular momentum + + align:start position:0% +the quantized angular momentum + + + align:start position:0% +the quantized angular momentum +so he can substitute in for v as a new + + align:start position:0% +so he can substitute in for v as a new + + + align:start position:0% +so he can substitute in for v as a new +expression for the mechanical frequency + + align:start position:0% +expression for the mechanical frequency + + + align:start position:0% +expression for the mechanical frequency +this is now of the electron in motion + + align:start position:0% +this is now of the electron in motion + + + align:start position:0% +this is now of the electron in motion +around the atom and now he wants to turn + + align:start position:0% +around the atom and now he wants to turn + + + align:start position:0% +around the atom and now he wants to turn +to that other thing he wants to compare + + align:start position:0% +to that other thing he wants to compare + + + align:start position:0% +to that other thing he wants to compare +it to the frequency of the radiation + + align:start position:0% +it to the frequency of the radiation + + + align:start position:0% +it to the frequency of the radiation +that comes out + + align:start position:0% +that comes out + + + align:start position:0% +that comes out +now in his model the radiation frequency + + align:start position:0% +now in his model the radiation frequency + + + align:start position:0% +now in his model the radiation frequency +is not given in that earlier derivation + + align:start position:0% +is not given in that earlier derivation + + + align:start position:0% +is not given in that earlier derivation +by anything having to do with the with + + align:start position:0% +by anything having to do with the with + + + align:start position:0% +by anything having to do with the with +the kind of mechanical motion around the + + align:start position:0% +the kind of mechanical motion around the + + + align:start position:0% +the kind of mechanical motion around the +nucleus of the electron it actually + + align:start position:0% +nucleus of the electron it actually + + + align:start position:0% +nucleus of the electron it actually +comes from the energy differences when + + align:start position:0% +comes from the energy differences when + + + align:start position:0% +comes from the energy differences when +an electron an excited state will emit + + align:start position:0% +an electron an excited state will emit + + + align:start position:0% +an electron an excited state will emit +some of the energy and drop down to a + + align:start position:0% +some of the energy and drop down to a + + + align:start position:0% +some of the energy and drop down to a +lower energy State rather than having + + align:start position:0% +lower energy State rather than having + + + align:start position:0% +lower energy State rather than having +anything to do with this mechanical + + align:start position:0% +anything to do with this mechanical + + + align:start position:0% +anything to do with this mechanical +motion that's why it looks like it's in + + align:start position:0% +motion that's why it looks like it's in + + + align:start position:0% +motion that's why it looks like it's in +conflict with Maxwell's electrodynamics + + align:start position:0% +conflict with Maxwell's electrodynamics + + + align:start position:0% +conflict with Maxwell's electrodynamics +so we saw a boar had derived this + + align:start position:0% +so we saw a boar had derived this + + + align:start position:0% +so we saw a boar had derived this +expression for the energy for the + + align:start position:0% +expression for the energy for the + + + align:start position:0% +expression for the energy for the +frequency of the light that comes out as + + align:start position:0% +frequency of the light that comes out as + + + align:start position:0% +frequency of the light that comes out as +radiated + + align:start position:0% +radiated + + + align:start position:0% +radiated +but again you can start plugging in + + align:start position:0% +but again you can start plugging in + + + align:start position:0% +but again you can start plugging in +things he knows he can use the + + align:start position:0% +things he knows he can use the + + + align:start position:0% +things he knows he can use the +definition of this radius the poor + + align:start position:0% +definition of this radius the poor + + + align:start position:0% +definition of this radius the poor +radius + + align:start position:0% +radius + + + align:start position:0% +radius +and now we can consider not the regime + + align:start position:0% +and now we can consider not the regime + + + align:start position:0% +and now we can consider not the regime +of n equals one or two or three of small + + align:start position:0% +of n equals one or two or three of small + + + align:start position:0% +of n equals one or two or three of small +principal quantum numbers for at for + + align:start position:0% +principal quantum numbers for at for + + + align:start position:0% +principal quantum numbers for at for +states of motion that are near the + + align:start position:0% +states of motion that are near the + + + align:start position:0% +states of motion that are near the +lowest energy state but he wants to + + align:start position:0% +lowest energy state but he wants to + + + align:start position:0% +lowest energy state but he wants to +think about large quantum numbers away + + align:start position:0% +think about large quantum numbers away + + + align:start position:0% +think about large quantum numbers away +from the most kind of quantumness of of + + align:start position:0% +from the most kind of quantumness of of + + + align:start position:0% +from the most kind of quantumness of of +the behavior of this hydrogen atom is + + align:start position:0% +the behavior of this hydrogen atom is + + + align:start position:0% +the behavior of this hydrogen atom is +there a regime is there a different era + + align:start position:0% +there a regime is there a different era + + + align:start position:0% +there a regime is there a different era +a different regime in which the behavior + + align:start position:0% +a different regime in which the behavior + + + align:start position:0% +a different regime in which the behavior +predicted by this Quantum theoretic + + align:start position:0% +predicted by this Quantum theoretic + + + align:start position:0% +predicted by this Quantum theoretic +description will carry over the behavior + + align:start position:0% +description will carry over the behavior + + + align:start position:0% +description will carry over the behavior +of the expected classical system so + + align:start position:0% +of the expected classical system so + + + align:start position:0% +of the expected classical system so +let's consider a very large principal + + align:start position:0% +let's consider a very large principal + + + align:start position:0% +let's consider a very large principal +number uh uh n a very highly excited + + align:start position:0% +number uh uh n a very highly excited + + + align:start position:0% +number uh uh n a very highly excited +state and now let's considered the + + align:start position:0% +state and now let's considered the + + + align:start position:0% +state and now let's considered the +radiation that would come out + + align:start position:0% +radiation that would come out + + + align:start position:0% +radiation that would come out +between two neighboring but very large + + align:start position:0% +between two neighboring but very large + + + align:start position:0% +between two neighboring but very large +high-end States so consider both N1 and + + align:start position:0% +high-end States so consider both N1 and + + + align:start position:0% +high-end States so consider both N1 and +N2 to be very larger than one and near + + align:start position:0% +N2 to be very larger than one and near + + + align:start position:0% +N2 to be very larger than one and near +each other let's say the difference + + align:start position:0% +each other let's say the difference + + + align:start position:0% +each other let's say the difference +between N2 and N1 is small compared to + + align:start position:0% +between N2 and N1 is small compared to + + + align:start position:0% +between N2 and N1 is small compared to +either of them alone + + align:start position:0% +either of them alone + + + align:start position:0% +either of them alone +then we can expand this one over N1 + + align:start position:0% +then we can expand this one over N1 + + + align:start position:0% +then we can expand this one over N1 +squared minus one over N2 squared just + + align:start position:0% +squared minus one over N2 squared just + + + align:start position:0% +squared minus one over N2 squared just +do a Taylor expansion to first order in + + align:start position:0% +do a Taylor expansion to first order in + + + align:start position:0% +do a Taylor expansion to first order in +this tiny difference we get an + + align:start position:0% +this tiny difference we get an + + + align:start position:0% +this tiny difference we get an +expression that looks like this + + align:start position:0% +expression that looks like this + + + align:start position:0% +expression that looks like this +now we can begin comparing the the + + align:start position:0% +now we can begin comparing the the + + + align:start position:0% +now we can begin comparing the the +frequency of the light that comes out + + align:start position:0% +frequency of the light that comes out + + + align:start position:0% +frequency of the light that comes out +the electromagnetic radiation compare + + align:start position:0% +the electromagnetic radiation compare + + + align:start position:0% +the electromagnetic radiation compare +that to indeed the mechanical motion + + align:start position:0% +that to indeed the mechanical motion + + + align:start position:0% +that to indeed the mechanical motion +motion of the electron itself in one of + + align:start position:0% +motion of the electron itself in one of + + + align:start position:0% +motion of the electron itself in one of +these very high-end large n orbits and + + align:start position:0% +these very high-end large n orbits and + + + align:start position:0% +these very high-end large n orbits and +now we just take the ratio of these + + align:start position:0% +now we just take the ratio of these + + + align:start position:0% +now we just take the ratio of these +expressions + + align:start position:0% +expressions + + + align:start position:0% +expressions +once again use other things that we've + + align:start position:0% +once again use other things that we've + + + align:start position:0% +once again use other things that we've +already worked hard to learn now you + + align:start position:0% +already worked hard to learn now you + + + align:start position:0% +already worked hard to learn now you +find that in that regime not near the + + align:start position:0% +find that in that regime not near the + + + align:start position:0% +find that in that regime not near the +kind of lowest energy State we expect + + align:start position:0% +kind of lowest energy State we expect + + + align:start position:0% +kind of lowest energy State we expect +the quantum is the discrete needs to be + + align:start position:0% +the quantum is the discrete needs to be + + + align:start position:0% +the quantum is the discrete needs to be +most + + align:start position:0% +most + + + align:start position:0% +most +um on display but it's a very highly + + align:start position:0% +um on display but it's a very highly + + + align:start position:0% +um on display but it's a very highly +excited state the ratio should in fact + + align:start position:0% +excited state the ratio should in fact + + + align:start position:0% +excited state the ratio should in fact +go back to one Maxwell said that ratio + + align:start position:0% +go back to one Maxwell said that ratio + + + align:start position:0% +go back to one Maxwell said that ratio +should be identically one and the limit + + align:start position:0% +should be identically one and the limit + + + align:start position:0% +should be identically one and the limit +of large principal quantum number that + + align:start position:0% +of large principal quantum number that + + + align:start position:0% +of large principal quantum number that +ratio once again goes back to one even + + align:start position:0% +ratio once again goes back to one even + + + align:start position:0% +ratio once again goes back to one even +though the way we account for it is + + align:start position:0% +though the way we account for it is + + + align:start position:0% +though the way we account for it is +totally different we don't say according + + align:start position:0% +totally different we don't say according + + + align:start position:0% +totally different we don't say according +to Bohr's model that the radiation comes + + align:start position:0% +to Bohr's model that the radiation comes + + + align:start position:0% +to Bohr's model that the radiation comes +out with the frequency new because + + align:start position:0% +out with the frequency new because + + + align:start position:0% +out with the frequency new because +that's the frequency at which the + + align:start position:0% +that's the frequency at which the + + + align:start position:0% +that's the frequency at which the +electron is physically spinning but it + + align:start position:0% +electron is physically spinning but it + + + align:start position:0% +electron is physically spinning but it +turns out the difference between + + align:start position:0% +turns out the difference between + + + align:start position:0% +turns out the difference between +neighboring highly excited States obeys + + align:start position:0% +neighboring highly excited States obeys + + + align:start position:0% +neighboring highly excited States obeys +uh basically the maxwellian relation + + align:start position:0% +uh basically the maxwellian relation + + + align:start position:0% +uh basically the maxwellian relation +after all this becomes known as the + + align:start position:0% +after all this becomes known as the + + + align:start position:0% +after all this becomes known as the +correspondence principle but the + + align:start position:0% +correspondence principle but the + + + align:start position:0% +correspondence principle but the +behavior should smoothly morph onto the + + align:start position:0% +behavior should smoothly morph onto the + + + align:start position:0% +behavior should smoothly morph onto the +kind of classical Newtonian maxwellian + + align:start position:0% +kind of classical Newtonian maxwellian + + + align:start position:0% +kind of classical Newtonian maxwellian +behavior in an appropriate limit it + + align:start position:0% +behavior in an appropriate limit it + + + align:start position:0% +behavior in an appropriate limit it +might break from that expectation + + align:start position:0% +might break from that expectation + + + align:start position:0% +might break from that expectation +station dramatically in a + + align:start position:0% +station dramatically in a + + + align:start position:0% +station dramatically in a +in a different regime in this case small + + align:start position:0% +in a different regime in this case small + + + align:start position:0% +in a different regime in this case small +principal quantum numbers when n is one + + align:start position:0% +principal quantum numbers when n is one + + + align:start position:0% +principal quantum numbers when n is one +two three or four but there should be + + align:start position:0% +two three or four but there should be + + + align:start position:0% +two three or four but there should be +some kind of smooth almost like an + + align:start position:0% +some kind of smooth almost like an + + + align:start position:0% +some kind of smooth almost like an +asymptotic matching because you know + + align:start position:0% +asymptotic matching because you know + + + align:start position:0% +asymptotic matching because you know +then is now Maxwell's equations work + + align:start position:0% +then is now Maxwell's equations work + + + align:start position:0% +then is now Maxwell's equations work +really well for understanding things + + align:start position:0% +really well for understanding things + + + align:start position:0% +really well for understanding things +like the radiation coming off of a + + align:start position:0% +like the radiation coming off of a + + + align:start position:0% +like the radiation coming off of a +dipole antenna so boy didn't want to + + align:start position:0% +dipole antenna so boy didn't want to + + + align:start position:0% +dipole antenna so boy didn't want to +lose all the extraordinary successes of + + align:start position:0% +lose all the extraordinary successes of + + + align:start position:0% +lose all the extraordinary successes of +Maxwell or Newton but wanted to have an + + align:start position:0% +Maxwell or Newton but wanted to have an + + + align:start position:0% +Maxwell or Newton but wanted to have an +account for why things might not always + + align:start position:0% +account for why things might not always + + + align:start position:0% +account for why things might not always +only look like that when you get really + + align:start position:0% +only look like that when you get really + + + align:start position:0% +only look like that when you get really +down to the scale of atoms + + align:start position:0% +down to the scale of atoms + + + align:start position:0% +down to the scale of atoms +so for large quantum numbers Quantum + + align:start position:0% +so for large quantum numbers Quantum + + + align:start position:0% +so for large quantum numbers Quantum +systems really do start to behave like + + align:start position:0% +systems really do start to behave like + + + align:start position:0% +systems really do start to behave like +classical ones in more modern language + + align:start position:0% +classical ones in more modern language + + + align:start position:0% +classical ones in more modern language +we'd say the emission spectrum looks + + align:start position:0% +we'd say the emission spectrum looks + + + align:start position:0% +we'd say the emission spectrum looks +basically continuous even though it + + align:start position:0% +basically continuous even though it + + + align:start position:0% +basically continuous even though it +looks highly discreet uh far away from + + align:start position:0% +looks highly discreet uh far away from + + + align:start position:0% +looks highly discreet uh far away from +that regime okay I'm going to wrap up + + align:start position:0% +that regime okay I'm going to wrap up + + + align:start position:0% +that regime okay I'm going to wrap up +the board part we'll pause for + + align:start position:0% +the board part we'll pause for + + + align:start position:0% +the board part we'll pause for +discussion just in a moment + + align:start position:0% +discussion just in a moment + + + align:start position:0% +discussion just in a moment +so Bohr uh further developed + + align:start position:0% +so Bohr uh further developed + + + align:start position:0% +so Bohr uh further developed +Rutherford's kind of solar system or + + align:start position:0% +Rutherford's kind of solar system or + + + align:start position:0% +Rutherford's kind of solar system or +nuclear model of atomic structure he uh + + align:start position:0% +nuclear model of atomic structure he uh + + + align:start position:0% +nuclear model of atomic structure he uh +kind of remarkably is able to account + + align:start position:0% +kind of remarkably is able to account + + + align:start position:0% +kind of remarkably is able to account +for empirical results like the emission + + align:start position:0% +for empirical results like the emission + + + align:start position:0% +for empirical results like the emission +inspection from hydrogen but much like + + align:start position:0% +inspection from hydrogen but much like + + + align:start position:0% +inspection from hydrogen but much like +Rutherford's work this starts raising + + align:start position:0% +Rutherford's work this starts raising + + + align:start position:0% +Rutherford's work this starts raising +several new questions even as it starts + + align:start position:0% +several new questions even as it starts + + + align:start position:0% +several new questions even as it starts +to answer some for one thing again + + align:start position:0% +to answer some for one thing again + + + align:start position:0% +to answer some for one thing again +despite Boar's remarkable ambition this + + align:start position:0% +despite Boar's remarkable ambition this + + + align:start position:0% +despite Boar's remarkable ambition this +whole scheme only seemed to work for + + align:start position:0% +whole scheme only seemed to work for + + + align:start position:0% +whole scheme only seemed to work for +single electron atoms or ions so a + + align:start position:0% +single electron atoms or ions so a + + + align:start position:0% +single electron atoms or ions so a +hydrogen atom which is electrically + + align:start position:0% +hydrogen atom which is electrically + + + align:start position:0% +hydrogen atom which is electrically +neutral or a an ionized uh atom of + + align:start position:0% +neutral or a an ionized uh atom of + + + align:start position:0% +neutral or a an ionized uh atom of +helium which one of its two electrons is + + align:start position:0% +helium which one of its two electrons is + + + align:start position:0% +helium which one of its two electrons is +Stripped Away you only have one electron + + align:start position:0% +Stripped Away you only have one electron + + + align:start position:0% +Stripped Away you only have one electron +in orbit or a doubly ionized lithium + + align:start position:0% +in orbit or a doubly ionized lithium + + + align:start position:0% +in orbit or a doubly ionized lithium +right that idea + + align:start position:0% +right that idea + + + align:start position:0% +right that idea +moreover again as I've tried to + + align:start position:0% +moreover again as I've tried to + + + align:start position:0% +moreover again as I've tried to +emphasize boar really didn't have any + + align:start position:0% +emphasize boar really didn't have any + + + align:start position:0% +emphasize boar really didn't have any +answer for why we might impose this + + align:start position:0% +answer for why we might impose this + + + align:start position:0% +answer for why we might impose this +brand new seemingly kind of ad hoc + + align:start position:0% +brand new seemingly kind of ad hoc + + + align:start position:0% +brand new seemingly kind of ad hoc +Quantum condition that the angular + + align:start position:0% +Quantum condition that the angular + + + align:start position:0% +Quantum condition that the angular +momentum should only appear in integer + + align:start position:0% +momentum should only appear in integer + + + align:start position:0% +momentum should only appear in integer +units of h-bar + + align:start position:0% +units of h-bar + + + align:start position:0% +units of h-bar +another question when people began to + + align:start position:0% +another question when people began to + + + align:start position:0% +another question when people began to +try to visualize these kind of Warring + + align:start position:0% +try to visualize these kind of Warring + + + align:start position:0% +try to visualize these kind of Warring +electrons in these discrete states of + + align:start position:0% +electrons in these discrete states of + + + align:start position:0% +electrons in these discrete states of +motion what happens to electrons between + + align:start position:0% +motion what happens to electrons between + + + align:start position:0% +motion what happens to electrons between +stable orbits are they literally falling + + align:start position:0% +stable orbits are they literally falling + + + align:start position:0% +stable orbits are they literally falling +from some large excited state towards + + align:start position:0% +from some large excited state towards + + + align:start position:0% +from some large excited state towards +another one what determine when an + + align:start position:0% +another one what determine when an + + + align:start position:0% +another one what determine when an +electron would make one of these sort of + + align:start position:0% +electron would make one of these sort of + + + align:start position:0% +electron would make one of these sort of +sudden discrete jumps + + align:start position:0% +sudden discrete jumps + + + align:start position:0% +sudden discrete jumps +how did an electron know how much energy + + align:start position:0% +how did an electron know how much energy + + + align:start position:0% +how did an electron know how much energy +to radiate it has to give up a Delta e + + align:start position:0% +to radiate it has to give up a Delta e + + + align:start position:0% +to radiate it has to give up a Delta e +exactly equal to the energy to be rated + + align:start position:0% +exactly equal to the energy to be rated + + + align:start position:0% +exactly equal to the energy to be rated +away and yet if the electron can only + + align:start position:0% +away and yet if the electron can only + + + align:start position:0% +away and yet if the electron can only +kind of land at a particular value of + + align:start position:0% +kind of land at a particular value of + + + align:start position:0% +kind of land at a particular value of +its lower energy State how does it know + + align:start position:0% +its lower energy State how does it know + + + align:start position:0% +its lower energy State how does it know +so to speak no in advance where it's + + align:start position:0% +so to speak no in advance where it's + + + align:start position:0% +so to speak no in advance where it's +going to land and therefore how much + + align:start position:0% +going to land and therefore how much + + + align:start position:0% +going to land and therefore how much +energy to radiate how can it never kind + + align:start position:0% +energy to radiate how can it never kind + + + align:start position:0% +energy to radiate how can it never kind +of messes up and radiates a different + + align:start position:0% +of messes up and radiates a different + + + align:start position:0% +of messes up and radiates a different +amount of energy for which it could no + + align:start position:0% +amount of energy for which it could no + + + align:start position:0% +amount of energy for which it could no +longer land at a stable uh orbit and + + align:start position:0% +longer land at a stable uh orbit and + + + align:start position:0% +longer land at a stable uh orbit and +then another question was + + align:start position:0% +then another question was + + + align:start position:0% +then another question was +it became clear well before Bohr's time + + align:start position:0% +it became clear well before Bohr's time + + + align:start position:0% +it became clear well before Bohr's time +that in addition to a very particular + + align:start position:0% +that in addition to a very particular + + + align:start position:0% +that in addition to a very particular +pattern of the colors the frequencies of + + align:start position:0% +pattern of the colors the frequencies of + + + align:start position:0% +pattern of the colors the frequencies of +these emitted spectral lines they also + + align:start position:0% +these emitted spectral lines they also + + + align:start position:0% +these emitted spectral lines they also +came with different brightnesses + + align:start position:0% +came with different brightnesses + + + align:start position:0% +came with different brightnesses +different intensities not every line + + align:start position:0% +different intensities not every line + + + align:start position:0% +different intensities not every line +that you could measure of these emission + + align:start position:0% +that you could measure of these emission + + + align:start position:0% +that you could measure of these emission +lines was equally bright and Bohr's + + align:start position:0% +lines was equally bright and Bohr's + + + align:start position:0% +lines was equally bright and Bohr's +model didn't seem to have any way of + + align:start position:0% +model didn't seem to have any way of + + + align:start position:0% +model didn't seem to have any way of +accounting for that other kind of + + align:start position:0% +accounting for that other kind of + + + align:start position:0% +accounting for that other kind of +equally Salient uh set of measurements + + align:start position:0% +equally Salient uh set of measurements + + + align:start position:0% +equally Salient uh set of measurements +about the spectral lines so some + + align:start position:0% +about the spectral lines so some + + + align:start position:0% +about the spectral lines so some +remarkable and surprising + + align:start position:0% +remarkable and surprising + + + align:start position:0% +remarkable and surprising +um uh kind of positive steps from this + + align:start position:0% +um uh kind of positive steps from this + + + align:start position:0% +um uh kind of positive steps from this +Bohr model but again opening up a whole + + align:start position:0% +Bohr model but again opening up a whole + + + align:start position:0% +Bohr model but again opening up a whole +new set of questions as well so I'll + + align:start position:0% +new set of questions as well so I'll + + + align:start position:0% +new set of questions as well so I'll +pause there again ask us any questions + + align:start position:0% +pause there again ask us any questions + + + align:start position:0% +pause there again ask us any questions +on that + + align:start position:0% + + + + align:start position:0% + +oh very good so the question uh as you + + align:start position:0% +oh very good so the question uh as you + + + align:start position:0% +oh very good so the question uh as you +can see in the chat uh we had this + + align:start position:0% +can see in the chat uh we had this + + + align:start position:0% +can see in the chat uh we had this +reading which I like a lot we'll talk + + align:start position:0% +reading which I like a lot we'll talk + + + align:start position:0% +reading which I like a lot we'll talk +actually a little bit more about this + + align:start position:0% +actually a little bit more about this + + + align:start position:0% +actually a little bit more about this +reading uh in the next class as well the + + align:start position:0% +reading uh in the next class as well the + + + align:start position:0% +reading uh in the next class as well the +reading by um Megan Shields from Auto + + align:start position:0% +reading by um Megan Shields from Auto + + + align:start position:0% +reading by um Megan Shields from Auto +who by the way used to TA this class so + + align:start position:0% +who by the way used to TA this class so + + + align:start position:0% +who by the way used to TA this class so +it's a nice homegrown uh body of work + + align:start position:0% +it's a nice homegrown uh body of work + + + align:start position:0% +it's a nice homegrown uh body of work +Megan uh a great colleague and when she + + align:start position:0% +Megan uh a great colleague and when she + + + align:start position:0% +Megan uh a great colleague and when she +was still a grad student she worked with + + align:start position:0% +was still a grad student she worked with + + + align:start position:0% +was still a grad student she worked with +this question and Megan has this really + + align:start position:0% +this question and Megan has this really + + + align:start position:0% +this question and Megan has this really +I think very lovely very + + align:start position:0% +I think very lovely very + + + align:start position:0% +I think very lovely very +um very kind of uh + + align:start position:0% +um very kind of uh + + + align:start position:0% +um very kind of uh +eye-opening essay about how work what + + align:start position:0% +eye-opening essay about how work what + + + align:start position:0% +eye-opening essay about how work what +kinds of work got credited then or now + + align:start position:0% +kinds of work got credited then or now + + + align:start position:0% +kinds of work got credited then or now +so we always talk about boarded this + + align:start position:0% +so we always talk about boarded this + + + align:start position:0% +so we always talk about boarded this +board did that and boy did a lot of + + align:start position:0% +board did that and boy did a lot of + + + align:start position:0% +board did that and boy did a lot of +things but he was almost never doing + + align:start position:0% +things but he was almost never doing + + + align:start position:0% +things but he was almost never doing +them on his own and we'll see a lot of + + align:start position:0% +them on his own and we'll see a lot of + + + align:start position:0% +them on his own and we'll see a lot of +examples of that again actually in the + + align:start position:0% +examples of that again actually in the + + + align:start position:0% +examples of that again actually in the +next lecture I kind of placed it in the + + align:start position:0% +next lecture I kind of placed it in the + + + align:start position:0% +next lecture I kind of placed it in the +wrong slot I think that reading works + + align:start position:0% +wrong slot I think that reading works + + + align:start position:0% +wrong slot I think that reading works +even better for for Wednesday's class + + align:start position:0% +even better for for Wednesday's class + + + align:start position:0% +even better for for Wednesday's class +but bore was not only always always + + align:start position:0% +but bore was not only always always + + + align:start position:0% +but bore was not only always always +talking with younger kind of post-docs + + align:start position:0% +talking with younger kind of post-docs + + + align:start position:0% +talking with younger kind of post-docs +and younger students of his own people + + align:start position:0% +and younger students of his own people + + + align:start position:0% +and younger students of his own people +like who would come to me like Leonardo + + align:start position:0% +like who would come to me like Leonardo + + + align:start position:0% +like who would come to me like Leonardo +Heisenberg and Wolfgang Powell in a + + align:start position:0% +Heisenberg and Wolfgang Powell in a + + + align:start position:0% +Heisenberg and Wolfgang Powell in a +whole circle he was always talking with + + align:start position:0% +whole circle he was always talking with + + + align:start position:0% +whole circle he was always talking with +his very very patient and talented wife + + align:start position:0% +his very very patient and talented wife + + + align:start position:0% +his very very patient and talented wife +margarita + + align:start position:0% +margarita + + + align:start position:0% +margarita +who did not have a formal training in + + align:start position:0% +who did not have a formal training in + + + align:start position:0% +who did not have a formal training in +physics but was could certainly follow a + + align:start position:0% +physics but was could certainly follow a + + + align:start position:0% +physics but was could certainly follow a +logical argument and she seems to have + + align:start position:0% +logical argument and she seems to have + + + align:start position:0% +logical argument and she seems to have +been a very steadying Force to to help + + align:start position:0% +been a very steadying Force to to help + + + align:start position:0% +been a very steadying Force to to help +discipline Bohr's own unfolding kind of + + align:start position:0% +discipline Bohr's own unfolding kind of + + + align:start position:0% +discipline Bohr's own unfolding kind of +syllogisms if a then B kind of thing she + + align:start position:0% +syllogisms if a then B kind of thing she + + + align:start position:0% +syllogisms if a then B kind of thing she +was his like constant sounding board and + + align:start position:0% +was his like constant sounding board and + + + align:start position:0% +was his like constant sounding board and +I kind of like not debate coach but just + + align:start position:0% +I kind of like not debate coach but just + + + align:start position:0% +I kind of like not debate coach but just +his kind of like + + align:start position:0% +his kind of like + + + align:start position:0% +his kind of like +he would try things out and they would + + align:start position:0% +he would try things out and they would + + + align:start position:0% +he would try things out and they would +talk about things very actively uh and + + align:start position:0% +talk about things very actively uh and + + + align:start position:0% +talk about things very actively uh and +and then he would write them up because + + align:start position:0% +and then he would write them up because + + + align:start position:0% +and then he would write them up because +because she had helped him crystallize + + align:start position:0% +because she had helped him crystallize + + + align:start position:0% +because she had helped him crystallize +or or clarify the order of his arguments + + align:start position:0% +or or clarify the order of his arguments + + + align:start position:0% +or or clarify the order of his arguments +and say this is a red herring this makes + + align:start position:0% +and say this is a red herring this makes + + + align:start position:0% +and say this is a red herring this makes +sense so Mariana Margarita was doing as + + align:start position:0% +sense so Mariana Margarita was doing as + + + align:start position:0% +sense so Mariana Margarita was doing as +we now know a ton of kind of unseen + + align:start position:0% +we now know a ton of kind of unseen + + + align:start position:0% +we now know a ton of kind of unseen +behind the scenes work actual conceptual + + align:start position:0% +behind the scenes work actual conceptual + + + align:start position:0% +behind the scenes work actual conceptual +work uh that for which we would then + + align:start position:0% +work uh that for which we would then + + + align:start position:0% +work uh that for which we would then +usually just credit Niels Bohr himself + + align:start position:0% +usually just credit Niels Bohr himself + + + align:start position:0% +usually just credit Niels Bohr himself +would be written up usually only with + + align:start position:0% +would be written up usually only with + + + align:start position:0% +would be written up usually only with +Bohr's name not poor and moderated not + + align:start position:0% +Bohr's name not poor and moderated not + + + align:start position:0% +Bohr's name not poor and moderated not +Neil's in Margaret abort + + align:start position:0% +Neil's in Margaret abort + + + align:start position:0% +Neil's in Margaret abort +and I think Megan's piece really draws + + align:start position:0% +and I think Megan's piece really draws + + + align:start position:0% +and I think Megan's piece really draws +it out very very evocatively with some + + align:start position:0% +it out very very evocatively with some + + + align:start position:0% +it out very very evocatively with some +pretty cool use of primary sources I + + align:start position:0% +pretty cool use of primary sources I + + + align:start position:0% +pretty cool use of primary sources I +think she's exactly right so we'll see + + align:start position:0% +think she's exactly right so we'll see + + + align:start position:0% +think she's exactly right so we'll see +that again and again especially with + + align:start position:0% +that again and again especially with + + + align:start position:0% +that again and again especially with +Bohr himself next week so the question + + align:start position:0% +Bohr himself next week so the question + + + align:start position:0% +Bohr himself next week so the question +here is did uh did Einstein have a + + align:start position:0% +here is did uh did Einstein have a + + + align:start position:0% +here is did uh did Einstein have a +similar relationship with his own uh + + align:start position:0% +similar relationship with his own uh + + + align:start position:0% +similar relationship with his own uh +Partners his first wife maleva I've + + align:start position:0% +Partners his first wife maleva I've + + + align:start position:0% +Partners his first wife maleva I've +mentioned a few times had also been + + align:start position:0% +mentioned a few times had also been + + + align:start position:0% +mentioned a few times had also been +trained uh in fact they met as + + align:start position:0% +trained uh in fact they met as + + + align:start position:0% +trained uh in fact they met as +University students uh maleva was uh + + align:start position:0% +University students uh maleva was uh + + + align:start position:0% +University students uh maleva was uh +studying physics and Mathematics at the + + align:start position:0% +studying physics and Mathematics at the + + + align:start position:0% +studying physics and Mathematics at the +eth they were classmates + + align:start position:0% +eth they were classmates + + + align:start position:0% +eth they were classmates +and here it's really complicated I won't + + align:start position:0% +and here it's really complicated I won't + + + align:start position:0% +and here it's really complicated I won't +spend too long in this because if I + + align:start position:0% +spend too long in this because if I + + + align:start position:0% +spend too long in this because if I +don't watch myself I'll talk about it + + align:start position:0% +don't watch myself I'll talk about it + + + align:start position:0% +don't watch myself I'll talk about it +for the next eight hours and you all + + align:start position:0% +for the next eight hours and you all + + + align:start position:0% +for the next eight hours and you all +have things to do with your lives but I + + align:start position:0% +have things to do with your lives but I + + + align:start position:0% +have things to do with your lives but I +would be glad to um direct you to lots + + align:start position:0% +would be glad to um direct you to lots + + + align:start position:0% +would be glad to um direct you to lots +of readings the short answer is they + + align:start position:0% +of readings the short answer is they + + + align:start position:0% +of readings the short answer is they +began talking together all the time very + + align:start position:0% +began talking together all the time very + + + align:start position:0% +began talking together all the time very +much like like we now know that Neil's + + align:start position:0% +much like like we now know that Neil's + + + align:start position:0% +much like like we now know that Neil's +and Margarita what are we doing the uh + + align:start position:0% +and Margarita what are we doing the uh + + + align:start position:0% +and Margarita what are we doing the uh +Einstein and maleva marriage were doing + + align:start position:0% +Einstein and maleva marriage were doing + + + align:start position:0% +Einstein and maleva marriage were doing +that absolutely all through college they + + align:start position:0% +that absolutely all through college they + + + align:start position:0% +that absolutely all through college they +have the Charming almost kind of sappy + + align:start position:0% +have the Charming almost kind of sappy + + + align:start position:0% +have the Charming almost kind of sappy +Sweet Love Letters between them when + + align:start position:0% +Sweet Love Letters between them when + + + align:start position:0% +Sweet Love Letters between them when +they would be apart I can't wait to talk + + align:start position:0% +they would be apart I can't wait to talk + + + align:start position:0% +they would be apart I can't wait to talk +my about my problems that with you my + + align:start position:0% +my about my problems that with you my + + + align:start position:0% +my about my problems that with you my +dear you know chera but they're very + + align:start position:0% +dear you know chera but they're very + + + align:start position:0% +dear you know chera but they're very +sweet and geeky uh in a way that might + + align:start position:0% +sweet and geeky uh in a way that might + + + align:start position:0% +sweet and geeky uh in a way that might +appeal to this group in particular they + + align:start position:0% +appeal to this group in particular they + + + align:start position:0% +appeal to this group in particular they +were they were Study Buddies as well as + + align:start position:0% +were they were Study Buddies as well as + + + align:start position:0% +were they were Study Buddies as well as +developing a real uh deep relationship + + align:start position:0% +developing a real uh deep relationship + + + align:start position:0% +developing a real uh deep relationship +and as I mentioned before Einstein was + + align:start position:0% +and as I mentioned before Einstein was + + + align:start position:0% +and as I mentioned before Einstein was +cut his classes maleva was a more + + align:start position:0% +cut his classes maleva was a more + + + align:start position:0% +cut his classes maleva was a more +diligent student she would often take + + align:start position:0% +diligent student she would often take + + + align:start position:0% +diligent student she would often take +notes and let it uh study + + align:start position:0% +notes and let it uh study + + + align:start position:0% +notes and let it uh study +and so there's plenty of evidence of + + align:start position:0% +and so there's plenty of evidence of + + + align:start position:0% +and so there's plenty of evidence of +them also actively talking through + + align:start position:0% +them also actively talking through + + + align:start position:0% +them also actively talking through +questions about for example + + align:start position:0% +questions about for example + + + align:start position:0% +questions about for example +electrodynamics through eight from like + + align:start position:0% +electrodynamics through eight from like + + + align:start position:0% +electrodynamics through eight from like +1896 through 1901 1902 then their path + + align:start position:0% +1896 through 1901 1902 then their path + + + align:start position:0% +1896 through 1901 1902 then their path +begins to be different at least from all + + align:start position:0% +begins to be different at least from all + + + align:start position:0% +begins to be different at least from all +we can reconstruct from the historical + + align:start position:0% +we can reconstruct from the historical + + + align:start position:0% +we can reconstruct from the historical +documentation different than that + + align:start position:0% +documentation different than that + + + align:start position:0% +documentation different than that +between say uh Niels and Margarita Bohr + + align:start position:0% +between say uh Niels and Margarita Bohr + + + align:start position:0% +between say uh Niels and Margarita Bohr +what happens in the Einstein and + + align:start position:0% +what happens in the Einstein and + + + align:start position:0% +what happens in the Einstein and +marriage case is that they have a young + + align:start position:0% +marriage case is that they have a young + + + align:start position:0% +marriage case is that they have a young +child in fact they have a first child + + align:start position:0% +child in fact they have a first child + + + align:start position:0% +child in fact they have a first child +out of wedlock a little girl named + + align:start position:0% +out of wedlock a little girl named + + + align:start position:0% +out of wedlock a little girl named +liseral who then was given up for + + align:start position:0% +liseral who then was given up for + + + align:start position:0% +liseral who then was given up for +adoption and no one knows what came of + + align:start position:0% +adoption and no one knows what came of + + + align:start position:0% +adoption and no one knows what came of +her so they first have a first child + + align:start position:0% +her so they first have a first child + + + align:start position:0% +her so they first have a first child +they don't raise on their own then they + + align:start position:0% +they don't raise on their own then they + + + align:start position:0% +they don't raise on their own then they +very quickly get married then they have + + align:start position:0% +very quickly get married then they have + + + align:start position:0% +very quickly get married then they have +another child and eventually two and + + align:start position:0% +another child and eventually two and + + + align:start position:0% +another child and eventually two and +then maleva starts doing what was very + + align:start position:0% +then maleva starts doing what was very + + + align:start position:0% +then maleva starts doing what was very +typical gender gender typed you know + + align:start position:0% +typical gender gender typed you know + + + align:start position:0% +typical gender gender typed you know +kind of um family responsibilities + + align:start position:0% +kind of um family responsibilities + + + align:start position:0% +kind of um family responsibilities +expected of the time and and with very + + align:start position:0% +expected of the time and and with very + + + align:start position:0% +expected of the time and and with very +little variation at the time even though + + align:start position:0% +little variation at the time even though + + + align:start position:0% +little variation at the time even though +they both consider themselves like + + align:start position:0% +they both consider themselves like + + + align:start position:0% +they both consider themselves like +radical Bohemians who cares what people + + align:start position:0% +radical Bohemians who cares what people + + + align:start position:0% +radical Bohemians who cares what people +think I don't have to live by society's + + align:start position:0% +think I don't have to live by society's + + + align:start position:0% +think I don't have to live by society's +rules pretty soon they began living by + + align:start position:0% +rules pretty soon they began living by + + + align:start position:0% +rules pretty soon they began living by +pretty typical central European rules or + + align:start position:0% +pretty typical central European rules or + + + align:start position:0% +pretty typical central European rules or +or norms and that meant maleva did not + + align:start position:0% +or norms and that meant maleva did not + + + align:start position:0% +or norms and that meant maleva did not +pursue her scientific career in fact I + + align:start position:0% +pursue her scientific career in fact I + + + align:start position:0% +pursue her scientific career in fact I +think she didn't ever complete her + + align:start position:0% +think she didn't ever complete her + + + align:start position:0% +think she didn't ever complete her +degree she dropped out uh I'm pretty + + align:start position:0% +degree she dropped out uh I'm pretty + + + align:start position:0% +degree she dropped out uh I'm pretty +sure I can look that up but she either + + align:start position:0% +sure I can look that up but she either + + + align:start position:0% +sure I can look that up but she either +barely got through with her degree after + + align:start position:0% +barely got through with her degree after + + + align:start position:0% +barely got through with her degree after +some interruptions but perhaps they had + + align:start position:0% +some interruptions but perhaps they had + + + align:start position:0% +some interruptions but perhaps they had +to interrupt her studies I can't + + align:start position:0% +to interrupt her studies I can't + + + align:start position:0% +to interrupt her studies I can't +remember oh look it up + + align:start position:0% +remember oh look it up + + + align:start position:0% +remember oh look it up +she becomes basically a full-time + + align:start position:0% +she becomes basically a full-time + + + align:start position:0% +she becomes basically a full-time +Homemaker which is what we would now say + + align:start position:0% +Homemaker which is what we would now say + + + align:start position:0% +Homemaker which is what we would now say +raising their children uh while Einstein + + align:start position:0% +raising their children uh while Einstein + + + align:start position:0% +raising their children uh while Einstein +then had the kind of full-time job at + + align:start position:0% +then had the kind of full-time job at + + + align:start position:0% +then had the kind of full-time job at +the patent office and then they they + + align:start position:0% +the patent office and then they they + + + align:start position:0% +the patent office and then they they +seem not to have talked with anything + + align:start position:0% +seem not to have talked with anything + + + align:start position:0% +seem not to have talked with anything +like the same intensity about the + + align:start position:0% +like the same intensity about the + + + align:start position:0% +like the same intensity about the +scientific work + + align:start position:0% +scientific work + + + align:start position:0% +scientific work +starting a couple years before 1905. so + + align:start position:0% +starting a couple years before 1905. so + + + align:start position:0% +starting a couple years before 1905. so +there have been all these kinds of um + + align:start position:0% +there have been all these kinds of um + + + align:start position:0% +there have been all these kinds of um +efforts to tie relativity in particular + + align:start position:0% +efforts to tie relativity in particular + + + align:start position:0% +efforts to tie relativity in particular +to a joint conversation maybe maleva was + + align:start position:0% +to a joint conversation maybe maleva was + + + align:start position:0% +to a joint conversation maybe maleva was +a a key thought partner and I would love + + align:start position:0% +a a key thought partner and I would love + + + align:start position:0% +a a key thought partner and I would love +for that story to be true I mean it + + align:start position:0% +for that story to be true I mean it + + + align:start position:0% +for that story to be true I mean it +would it would cap off this college + + align:start position:0% +would it would cap off this college + + + align:start position:0% +would it would cap off this college +romance and just be thrilling and I've + + align:start position:0% +romance and just be thrilling and I've + + + align:start position:0% +romance and just be thrilling and I've +been convinced by the work by historians + + align:start position:0% +been convinced by the work by historians + + + align:start position:0% +been convinced by the work by historians +who've looked very square like this + + align:start position:0% +who've looked very square like this + + + align:start position:0% +who've looked very square like this +including a lot of women's history + + align:start position:0% +including a lot of women's history + + + align:start position:0% +including a lot of women's history +gender and science Scholars who were + + align:start position:0% +gender and science Scholars who were + + + align:start position:0% +gender and science Scholars who were +very attuned to Partnerships that don't + + align:start position:0% +very attuned to Partnerships that don't + + + align:start position:0% +very attuned to Partnerships that don't +often get a lot of credit + + align:start position:0% +often get a lot of credit + + + align:start position:0% +often get a lot of credit +uh people uh whose work otherwise will + + align:start position:0% +uh people uh whose work otherwise will + + + align:start position:0% +uh people uh whose work otherwise will +read this term and I'm convinced by + + align:start position:0% +read this term and I'm convinced by + + + align:start position:0% +read this term and I'm convinced by +their argument that that seemed not to + + align:start position:0% +their argument that that seemed not to + + + align:start position:0% +their argument that that seemed not to +have been the nature of the Einstein + + align:start position:0% +have been the nature of the Einstein + + + align:start position:0% +have been the nature of the Einstein +marriage relationship starting in like + + align:start position:0% +marriage relationship starting in like + + + align:start position:0% +marriage relationship starting in like +1902 1903 let alone 05. they quickly + + align:start position:0% +1902 1903 let alone 05. they quickly + + + align:start position:0% +1902 1903 let alone 05. they quickly +became really embittered + + align:start position:0% +became really embittered + + + align:start position:0% +became really embittered +and so uh by by the later 19 teens they + + align:start position:0% +and so uh by by the later 19 teens they + + + align:start position:0% +and so uh by by the later 19 teens they +were basically in open Warfare + + align:start position:0% +were basically in open Warfare + + + align:start position:0% +were basically in open Warfare +and they couldn't wait to get divorced + + align:start position:0% +and they couldn't wait to get divorced + + + align:start position:0% +and they couldn't wait to get divorced +and so I think couldn't afford to + + align:start position:0% +and so I think couldn't afford to + + + align:start position:0% +and so I think couldn't afford to +divorce until he won the Nobel Prize he + + align:start position:0% +divorce until he won the Nobel Prize he + + + align:start position:0% +divorce until he won the Nobel Prize he +was so sure he'd win the Nobel Prize + + align:start position:0% +was so sure he'd win the Nobel Prize + + + align:start position:0% +was so sure he'd win the Nobel Prize +that he he promised his prize winnings + + align:start position:0% +that he he promised his prize winnings + + + align:start position:0% +that he he promised his prize winnings +to be the divorce settlement before he + + align:start position:0% +to be the divorce settlement before he + + + align:start position:0% +to be the divorce settlement before he +won the prize like four years where he + + align:start position:0% +won the prize like four years where he + + + align:start position:0% +won the prize like four years where he +won the prize + + align:start position:0% +won the prize + + + align:start position:0% +won the prize +then the prize came through + + align:start position:0% +then the prize came through + + + align:start position:0% +then the prize came through +they got divorced Einstein by that point + + align:start position:0% +they got divorced Einstein by that point + + + align:start position:0% +they got divorced Einstein by that point +was already seeing his second cousin + + align:start position:0% +was already seeing his second cousin + + + align:start position:0% +was already seeing his second cousin +Elsa who soon became his wife + + align:start position:0% +Elsa who soon became his wife + + + align:start position:0% +Elsa who soon became his wife +so the story seems actually pretty + + align:start position:0% +so the story seems actually pretty + + + align:start position:0% +so the story seems actually pretty +different than this very kind of um + + align:start position:0% +different than this very kind of um + + + align:start position:0% +different than this very kind of um +lifelong intellectual partnership + + align:start position:0% +lifelong intellectual partnership + + + align:start position:0% +lifelong intellectual partnership +between Niels and Margarita which + + align:start position:0% +between Niels and Margarita which + + + align:start position:0% +between Niels and Margarita which +nonetheless never really got credited + + align:start position:0% +nonetheless never really got credited + + + align:start position:0% +nonetheless never really got credited +the way that today we I think we would + + align:start position:0% +the way that today we I think we would + + + align:start position:0% +the way that today we I think we would +find much more um appropriate that was a + + align:start position:0% +find much more um appropriate that was a + + + align:start position:0% +find much more um appropriate that was a +long answer to a really good question + + align:start position:0% +long answer to a really good question + + + align:start position:0% +long answer to a really good question +I'd be glad to say more there's really a + + align:start position:0% +I'd be glad to say more there's really a + + + align:start position:0% +I'd be glad to say more there's really a +lot on the especially in the Einstein uh + + align:start position:0% +lot on the especially in the Einstein uh + + + align:start position:0% +lot on the especially in the Einstein uh +marriage relationship uh but I'm glad so + + align:start position:0% +marriage relationship uh but I'm glad so + + + align:start position:0% +marriage relationship uh but I'm glad so +uh that you raised the question about um + + align:start position:0% +uh that you raised the question about um + + + align:start position:0% +uh that you raised the question about um +Megan's piece about Nielsen mortgage as + + align:start position:0% +Megan's piece about Nielsen mortgage as + + + align:start position:0% +Megan's piece about Nielsen mortgage as +well it's a great Point any questions on + + align:start position:0% +well it's a great Point any questions on + + + align:start position:0% +well it's a great Point any questions on +that + + align:start position:0% +that + + + align:start position:0% +that +let me jump into the to the last part + + align:start position:0% +let me jump into the to the last part + + + align:start position:0% +let me jump into the to the last part +for today the last part's shorter we + + align:start position:0% +for today the last part's shorter we + + + align:start position:0% +for today the last part's shorter we +have plenty of time to do this last part + + align:start position:0% +have plenty of time to do this last part + + + align:start position:0% +have plenty of time to do this last part +we saw with with Bohr's work there are + + align:start position:0% +we saw with with Bohr's work there are + + + align:start position:0% +we saw with with Bohr's work there are +all these kind of dangling questions + + align:start position:0% +all these kind of dangling questions + + + align:start position:0% +all these kind of dangling questions +about the Bohr model and so we're going + + align:start position:0% +about the Bohr model and so we're going + + + align:start position:0% +about the Bohr model and so we're going +to see this last moment uh that really + + align:start position:0% +to see this last moment uh that really + + + align:start position:0% +to see this last moment uh that really +helps to kind of uh at least better + + align:start position:0% +helps to kind of uh at least better + + + align:start position:0% +helps to kind of uh at least better +motivate some of these open questions + + align:start position:0% +motivate some of these open questions + + + align:start position:0% +motivate some of these open questions +from the Bohr model comes fully 10 or 11 + + align:start position:0% +from the Bohr model comes fully 10 or 11 + + + align:start position:0% +from the Bohr model comes fully 10 or 11 +years later it's introduced by literally + + align:start position:0% +years later it's introduced by literally + + + align:start position:0% +years later it's introduced by literally +a French Prince we don't often get to + + align:start position:0% +a French Prince we don't often get to + + + align:start position:0% +a French Prince we don't often get to +talk about royalty in this class a + + align:start position:0% +talk about royalty in this class a + + + align:start position:0% +talk about royalty in this class a +French Aristocrat named Louis de broy he + + align:start position:0% +French Aristocrat named Louis de broy he + + + align:start position:0% +French Aristocrat named Louis de broy he +was actually the younger brother of + + align:start position:0% +was actually the younger brother of + + + align:start position:0% +was actually the younger brother of +Maurice de broy who also by this point + + align:start position:0% +Maurice de broy who also by this point + + + align:start position:0% +Maurice de broy who also by this point +was a very accomplished experimental + + align:start position:0% +was a very accomplished experimental + + + align:start position:0% +was a very accomplished experimental +physicist they had a laboratory in in + + align:start position:0% +physicist they had a laboratory in in + + + align:start position:0% +physicist they had a laboratory in in +the basement of their enormous Castle + + align:start position:0% +the basement of their enormous Castle + + + align:start position:0% +the basement of their enormous Castle +so Louis had first studied history like + + align:start position:0% +so Louis had first studied history like + + + align:start position:0% +so Louis had first studied history like +a good Aristocrat and all the rich + + align:start position:0% +a good Aristocrat and all the rich + + + align:start position:0% +a good Aristocrat and all the rich +Humanities and then stubbornly said that + + align:start position:0% +Humanities and then stubbornly said that + + + align:start position:0% +Humanities and then stubbornly said that +like his older brother he'd like to + + align:start position:0% +like his older brother he'd like to + + + align:start position:0% +like his older brother he'd like to +study this grubby physics stuff instead + + align:start position:0% +study this grubby physics stuff instead + + + align:start position:0% +study this grubby physics stuff instead +so he finished his PhD in 1924 as in + + align:start position:0% +so he finished his PhD in 1924 as in + + + align:start position:0% +so he finished his PhD in 1924 as in +theoretical physics I think of the + + align:start position:0% +theoretical physics I think of the + + + align:start position:0% +theoretical physics I think of the +sorbot it's a very elite Paris School + + align:start position:0% +sorbot it's a very elite Paris School + + + align:start position:0% +sorbot it's a very elite Paris School +and here he began to wonder is there a + + align:start position:0% +and here he began to wonder is there a + + + align:start position:0% +and here he began to wonder is there a +way to account for Boar's powerful yet + + align:start position:0% +way to account for Boar's powerful yet + + + align:start position:0% +way to account for Boar's powerful yet +as yet unexplained hypothesis about that + + align:start position:0% +as yet unexplained hypothesis about that + + + align:start position:0% +as yet unexplained hypothesis about that +Quantum condition that the angular + + align:start position:0% +Quantum condition that the angular + + + align:start position:0% +Quantum condition that the angular +momentum of an electron should take + + align:start position:0% +momentum of an electron should take + + + align:start position:0% +momentum of an electron should take +integer units uh set by age bar + + align:start position:0% +integer units uh set by age bar + + + align:start position:0% +integer units uh set by age bar +so Deportes tries to make an explicit + + align:start position:0% +so Deportes tries to make an explicit + + + align:start position:0% +so Deportes tries to make an explicit +symmetry he really has a kind of this + + align:start position:0% +symmetry he really has a kind of this + + + align:start position:0% +symmetry he really has a kind of this +happened here can I make the same thing + + align:start position:0% +happened here can I make the same thing + + + align:start position:0% +happened here can I make the same thing +happen here kind of framework he's very + + align:start position:0% +happen here kind of framework he's very + + + align:start position:0% +happen here kind of framework he's very +explicit about that he also returns to + + align:start position:0% +explicit about that he also returns to + + + align:start position:0% +explicit about that he also returns to +Einstein's work unlike Quantum which by + + align:start position:0% +Einstein's work unlike Quantum which by + + + align:start position:0% +Einstein's work unlike Quantum which by +this point people are now taking + + align:start position:0% +this point people are now taking + + + align:start position:0% +this point people are now taking +seriously this is now fully two years + + align:start position:0% +seriously this is now fully two years + + + align:start position:0% +seriously this is now fully two years +after Compton's uh results uh with x-ray + + align:start position:0% +after Compton's uh results uh with x-ray + + + align:start position:0% +after Compton's uh results uh with x-ray +scattering the notion of returning to + + align:start position:0% +scattering the notion of returning to + + + align:start position:0% +scattering the notion of returning to +Einstein's work in 1924 was no longer + + align:start position:0% +Einstein's work in 1924 was no longer + + + align:start position:0% +Einstein's work in 1924 was no longer +controversial the way it would have been + + align:start position:0% +controversial the way it would have been + + + align:start position:0% +controversial the way it would have been +in 1905 or 1910 and so on + + align:start position:0% +in 1905 or 1910 and so on + + + align:start position:0% +in 1905 or 1910 and so on +so for Devore that looks like a pretty + + align:start position:0% +so for Devore that looks like a pretty + + + align:start position:0% +so for Devore that looks like a pretty +sensible place to start and as we saw uh + + align:start position:0% +sensible place to start and as we saw uh + + + align:start position:0% +sensible place to start and as we saw uh +in the previous class there's a + + align:start position:0% +in the previous class there's a + + + align:start position:0% +in the previous class there's a +maxwellian expression for the momentum + + align:start position:0% +maxwellian expression for the momentum + + + align:start position:0% +maxwellian expression for the momentum +of a light wave related to its energy + + align:start position:0% +of a light wave related to its energy + + + align:start position:0% +of a light wave related to its energy +and its speed we can then take on + + align:start position:0% +and its speed we can then take on + + + align:start position:0% +and its speed we can then take on +Einstein's light Quantum hypothesis the + + align:start position:0% +Einstein's light Quantum hypothesis the + + + align:start position:0% +Einstein's light Quantum hypothesis the +energy of that light Quantum can only + + align:start position:0% +energy of that light Quantum can only + + + align:start position:0% +energy of that light Quantum can only +take certain units set by again by uh by + + align:start position:0% +take certain units set by again by uh by + + + align:start position:0% +take certain units set by again by uh by +points constant page + + align:start position:0% +points constant page + + + align:start position:0% +points constant page +and so then as we saw uh Compton himself + + align:start position:0% +and so then as we saw uh Compton himself + + + align:start position:0% +and so then as we saw uh Compton himself +use this relation + + align:start position:0% +use this relation + + + align:start position:0% +use this relation +the momentum for an individual particle + + align:start position:0% +the momentum for an individual particle + + + align:start position:0% +the momentum for an individual particle +of light a light Quantum should be + + align:start position:0% +of light a light Quantum should be + + + align:start position:0% +of light a light Quantum should be +inversely proportional to its wavelength + + align:start position:0% +inversely proportional to its wavelength + + + align:start position:0% +inversely proportional to its wavelength +with a proportionality set by Planck's + + align:start position:0% +with a proportionality set by Planck's + + + align:start position:0% +with a proportionality set by Planck's +Council that by now had become pretty + + align:start position:0% +Council that by now had become pretty + + + align:start position:0% +Council that by now had become pretty +familiar even to people who were + + align:start position:0% +familiar even to people who were + + + align:start position:0% +familiar even to people who were +grudging in that what depressed as is + + align:start position:0% +grudging in that what depressed as is + + + align:start position:0% +grudging in that what depressed as is +simply assert and doesn't derive it + + align:start position:0% +simply assert and doesn't derive it + + + align:start position:0% +simply assert and doesn't derive it +doesn't prove he simply asserts what do + + align:start position:0% +doesn't prove he simply asserts what do + + + align:start position:0% +doesn't prove he simply asserts what do +the same thing happens for particles of + + align:start position:0% +the same thing happens for particles of + + + align:start position:0% +the same thing happens for particles of +matter this is all about behavior of + + align:start position:0% +matter this is all about behavior of + + + align:start position:0% +matter this is all about behavior of +light + + align:start position:0% +light + + + align:start position:0% +light +so debris says what if we relate the + + align:start position:0% +so debris says what if we relate the + + + align:start position:0% +so debris says what if we relate the +momentum of a little electron for + + align:start position:0% +momentum of a little electron for + + + align:start position:0% +momentum of a little electron for +example moving around uh of the nucleus + + align:start position:0% +example moving around uh of the nucleus + + + align:start position:0% +example moving around uh of the nucleus +in an atom + + align:start position:0% +in an atom + + + align:start position:0% +in an atom +so there'll be some expression for the + + align:start position:0% +so there'll be some expression for the + + + align:start position:0% +so there'll be some expression for the +momentum of that particle coming to say + + align:start position:0% +momentum of that particle coming to say + + + align:start position:0% +momentum of that particle coming to say +from new from Newtonian mechanics what + + align:start position:0% +from new from Newtonian mechanics what + + + align:start position:0% +from new from Newtonian mechanics what +if we also relate that to an inverse + + align:start position:0% +if we also relate that to an inverse + + + align:start position:0% +if we also relate that to an inverse +wavelength just as as eyesight had by + + align:start position:0% +wavelength just as as eyesight had by + + + align:start position:0% +wavelength just as as eyesight had by +this point convinced many physicists to + + align:start position:0% +this point convinced many physicists to + + + align:start position:0% +this point convinced many physicists to +try for light in that case you can + + align:start position:0% +try for light in that case you can + + + align:start position:0% +try for light in that case you can +rearrange this expression saying what if + + align:start position:0% +rearrange this expression saying what if + + + align:start position:0% +rearrange this expression saying what if +there's some waviness associated in with + + align:start position:0% +there's some waviness associated in with + + + align:start position:0% +there's some waviness associated in with +chunks of matter particulate solid + + align:start position:0% +chunks of matter particulate solid + + + align:start position:0% +chunks of matter particulate solid +matter + + align:start position:0% +matter + + + align:start position:0% +matter +Dubois says what if there's an inherent + + align:start position:0% +Dubois says what if there's an inherent + + + align:start position:0% +Dubois says what if there's an inherent +waviness with of a scale set inversely + + align:start position:0% +waviness with of a scale set inversely + + + align:start position:0% +waviness with of a scale set inversely +by the momentum just like you'd expect + + align:start position:0% +by the momentum just like you'd expect + + + align:start position:0% +by the momentum just like you'd expect +here and proportional to Planck's + + align:start position:0% +here and proportional to Planck's + + + align:start position:0% +here and proportional to Planck's +constant why would anyone ever take this + + align:start position:0% +constant why would anyone ever take this + + + align:start position:0% +constant why would anyone ever take this +crazy French Prince's word for it + + align:start position:0% +crazy French Prince's word for it + + + align:start position:0% +crazy French Prince's word for it +we never see this in real life in + + align:start position:0% +we never see this in real life in + + + align:start position:0% +we never see this in real life in +ordinary life and again de broy this is + + align:start position:0% +ordinary life and again de broy this is + + + align:start position:0% +ordinary life and again de broy this is +now after things like Boris + + align:start position:0% +now after things like Boris + + + align:start position:0% +now after things like Boris +correspondence principle knows to wonder + + align:start position:0% +correspondence principle knows to wonder + + + align:start position:0% +correspondence principle knows to wonder +about the scales at which one might ever + + align:start position:0% +about the scales at which one might ever + + + align:start position:0% +about the scales at which one might ever +see such a strange sounding phenomenon + + align:start position:0% +see such a strange sounding phenomenon + + + align:start position:0% +see such a strange sounding phenomenon +so if you imagine a fastball he didn't + + align:start position:0% +so if you imagine a fastball he didn't + + + align:start position:0% +so if you imagine a fastball he didn't +use this example we can for those uh + + align:start position:0% +use this example we can for those uh + + + align:start position:0% +use this example we can for those uh +more familiar with American baseball or + + align:start position:0% +more familiar with American baseball or + + + align:start position:0% +more familiar with American baseball or +cricketer fill in your favorite you know + + align:start position:0% +cricketer fill in your favorite you know + + + align:start position:0% +cricketer fill in your favorite you know +human-sized um ball throwing game + + align:start position:0% +human-sized um ball throwing game + + + align:start position:0% +human-sized um ball throwing game +if you imagine a you know a fastball + + align:start position:0% +if you imagine a you know a fastball + + + align:start position:0% +if you imagine a you know a fastball +pitched in a baseball game and calculate + + align:start position:0% +pitched in a baseball game and calculate + + + align:start position:0% +pitched in a baseball game and calculate +you know one over its momentum scaled by + + align:start position:0% +you know one over its momentum scaled by + + + align:start position:0% +you know one over its momentum scaled by +H the waviness associated with that if + + align:start position:0% +H the waviness associated with that if + + + align:start position:0% +H the waviness associated with that if +we took to broy in his word would be + + align:start position:0% +we took to broy in his word would be + + + align:start position:0% +we took to broy in his word would be +unbelievably small 10 to the minus 32nd + + align:start position:0% +unbelievably small 10 to the minus 32nd + + + align:start position:0% +unbelievably small 10 to the minus 32nd +of a meter that's you know + + align:start position:0% +of a meter that's you know + + + align:start position:0% +of a meter that's you know +smaller than the smallest known + + align:start position:0% +smaller than the smallest known + + + align:start position:0% +smaller than the smallest known +Elementary particles so of course we + + align:start position:0% +Elementary particles so of course we + + + align:start position:0% +Elementary particles so of course we +don't see this somehow inherent waviness + + align:start position:0% +don't see this somehow inherent waviness + + + align:start position:0% +don't see this somehow inherent waviness +on kind of everyday scales but before it + + align:start position:0% +on kind of everyday scales but before it + + + align:start position:0% +on kind of everyday scales but before it +goes on it says for an electron if we + + align:start position:0% +goes on it says for an electron if we + + + align:start position:0% +goes on it says for an electron if we +plug in a typical momentum uh that we + + align:start position:0% +plug in a typical momentum uh that we + + + align:start position:0% +plug in a typical momentum uh that we +estimate for its motion say in a + + align:start position:0% +estimate for its motion say in a + + + align:start position:0% +estimate for its motion say in a +hydrogen atom the waviness the actual + + align:start position:0% +hydrogen atom the waviness the actual + + + align:start position:0% +hydrogen atom the waviness the actual +wavelength somehow associated with that + + align:start position:0% +wavelength somehow associated with that + + + align:start position:0% +wavelength somehow associated with that +electron is on the same length scale as + + align:start position:0% +electron is on the same length scale as + + + align:start position:0% +electron is on the same length scale as +its own radius as its own orbital path + + align:start position:0% +its own radius as its own orbital path + + + align:start position:0% +its own radius as its own orbital path +that bore radius a naught for an + + align:start position:0% +that bore radius a naught for an + + + align:start position:0% +that bore radius a naught for an +electron this new hypothetical Quantum + + align:start position:0% +electron this new hypothetical Quantum + + + align:start position:0% +electron this new hypothetical Quantum +waviness is on the same scale as its own + + align:start position:0% +waviness is on the same scale as its own + + + align:start position:0% +waviness is on the same scale as its own +kind of mechanical motion so maybe + + align:start position:0% +kind of mechanical motion so maybe + + + align:start position:0% +kind of mechanical motion so maybe +debroy says we shouldn't ignore it we + + align:start position:0% +debroy says we shouldn't ignore it we + + + align:start position:0% +debroy says we shouldn't ignore it we +can absolutely ignore this somehow this + + align:start position:0% +can absolutely ignore this somehow this + + + align:start position:0% +can absolutely ignore this somehow this +hypothetical Quantum waviness when + + align:start position:0% +hypothetical Quantum waviness when + + + align:start position:0% +hypothetical Quantum waviness when +playing Cricket or or baseball or any + + align:start position:0% +playing Cricket or or baseball or any + + + align:start position:0% +playing Cricket or or baseball or any +kind of sport but maybe it's actually + + align:start position:0% +kind of sport but maybe it's actually + + + align:start position:0% +kind of sport but maybe it's actually +really critical when we're talking about + + align:start position:0% +really critical when we're talking about + + + align:start position:0% +really critical when we're talking about +the behavior of atoms and parts of atoms + + align:start position:0% +the behavior of atoms and parts of atoms + + + align:start position:0% +the behavior of atoms and parts of atoms +so if we if there really were some + + align:start position:0% +so if we if there really were some + + + align:start position:0% +so if we if there really were some +inherent wave-like structure wave like a + + align:start position:0% +inherent wave-like structure wave like a + + + align:start position:0% +inherent wave-like structure wave like a +feature associated with the motion of an + + align:start position:0% +feature associated with the motion of an + + + align:start position:0% +feature associated with the motion of an +electron in an atom + + align:start position:0% +electron in an atom + + + align:start position:0% +electron in an atom +could that begin to address this biggest + + align:start position:0% +could that begin to address this biggest + + + align:start position:0% +could that begin to address this biggest +as yet unanswered question about the + + align:start position:0% +as yet unanswered question about the + + + align:start position:0% +as yet unanswered question about the +Bohr model why certain configurations or + + align:start position:0% +Bohr model why certain configurations or + + + align:start position:0% +Bohr model why certain configurations or +certain discrete uh states of motion for + + align:start position:0% +certain discrete uh states of motion for + + + align:start position:0% +certain discrete uh states of motion for +an electron would lead to stability of + + align:start position:0% +an electron would lead to stability of + + + align:start position:0% +an electron would lead to stability of +matter rather than unstable Behavior and + + align:start position:0% +matter rather than unstable Behavior and + + + align:start position:0% +matter rather than unstable Behavior and +he says there what if there's a kind of + + align:start position:0% +he says there what if there's a kind of + + + align:start position:0% +he says there what if there's a kind of +constructive interference and what if + + align:start position:0% +constructive interference and what if + + + align:start position:0% +constructive interference and what if +the only stable States for an electron + + align:start position:0% +the only stable States for an electron + + + align:start position:0% +the only stable States for an electron +are those for which the uh there's a an + + align:start position:0% +are those for which the uh there's a an + + + align:start position:0% +are those for which the uh there's a an +integer number of wavelengths that can + + align:start position:0% +integer number of wavelengths that can + + + align:start position:0% +integer number of wavelengths that can +wrap around the orbit so the wave in + + align:start position:0% +wrap around the orbit so the wave in + + + align:start position:0% +wrap around the orbit so the wave in +some sense joins back on itself and + + align:start position:0% +some sense joins back on itself and + + + align:start position:0% +some sense joins back on itself and +constructively interferes to make a + + align:start position:0% +constructively interferes to make a + + + align:start position:0% +constructively interferes to make a +stable standing wave basically standing + + align:start position:0% +stable standing wave basically standing + + + align:start position:0% +stable standing wave basically standing +wave + + align:start position:0% +wave + + + align:start position:0% +wave +whereas if the radius of that orbit were + + align:start position:0% +whereas if the radius of that orbit were + + + align:start position:0% +whereas if the radius of that orbit were +ever so slightly different you would no + + align:start position:0% +ever so slightly different you would no + + + align:start position:0% +ever so slightly different you would no +longer be able to wrap an integer number + + align:start position:0% +longer be able to wrap an integer number + + + align:start position:0% +longer be able to wrap an integer number +of wavelengths around the radius and + + align:start position:0% +of wavelengths around the radius and + + + align:start position:0% +of wavelengths around the radius and +you'd start getting the wave out of + + align:start position:0% +you'd start getting the wave out of + + + align:start position:0% +you'd start getting the wave out of +phase with itself so the crests would + + align:start position:0% +phase with itself so the crests would + + + align:start position:0% +phase with itself so the crests would +actually start meeting up with troughs + + align:start position:0% +actually start meeting up with troughs + + + align:start position:0% +actually start meeting up with troughs +and the whole wave would basically like + + align:start position:0% +and the whole wave would basically like + + + align:start position:0% +and the whole wave would basically like +Fall Apart + + align:start position:0% +Fall Apart + + + align:start position:0% +Fall Apart +so debris saying if we Grant this + + align:start position:0% +so debris saying if we Grant this + + + align:start position:0% +so debris saying if we Grant this +hypothetical as yet unseen waviness to + + align:start position:0% +hypothetical as yet unseen waviness to + + + align:start position:0% +hypothetical as yet unseen waviness to +things like electrons could we start + + align:start position:0% +things like electrons could we start + + + align:start position:0% +things like electrons could we start +accounting for that stability of matter + + align:start position:0% +accounting for that stability of matter + + + align:start position:0% +accounting for that stability of matter +what would be the Criterion then you + + align:start position:0% +what would be the Criterion then you + + + align:start position:0% +what would be the Criterion then you +have to have an integer number of these + + align:start position:0% +have to have an integer number of these + + + align:start position:0% +have to have an integer number of these +wavelengths fit around the circumference + + align:start position:0% +wavelengths fit around the circumference + + + align:start position:0% +wavelengths fit around the circumference +fit around 2 pi r of that circular orbit + + align:start position:0% +fit around 2 pi r of that circular orbit + + + align:start position:0% +fit around 2 pi r of that circular orbit +well now he has an idea for what that + + align:start position:0% +well now he has an idea for what that + + + align:start position:0% +well now he has an idea for what that +wavelength should be he's now working + + align:start position:0% +wavelength should be he's now working + + + align:start position:0% +wavelength should be he's now working +directly in analogy to Einstein's work + + align:start position:0% +directly in analogy to Einstein's work + + + align:start position:0% +directly in analogy to Einstein's work +with light conscious and plug in what he + + align:start position:0% +with light conscious and plug in what he + + + align:start position:0% +with light conscious and plug in what he +thinks Lambda would be and then Presto + + align:start position:0% +thinks Lambda would be and then Presto + + + align:start position:0% +thinks Lambda would be and then Presto +Chango he's now derived or at least + + align:start position:0% +Chango he's now derived or at least + + + align:start position:0% +Chango he's now derived or at least +found an expression that exactly matches + + align:start position:0% +found an expression that exactly matches + + + align:start position:0% +found an expression that exactly matches +the form for what Bohr had put in sort + + align:start position:0% +the form for what Bohr had put in sort + + + align:start position:0% +the form for what Bohr had put in sort +of by hand in a totally unexplained and + + align:start position:0% +of by hand in a totally unexplained and + + + align:start position:0% +of by hand in a totally unexplained and +ad hoc manner so now this might account + + align:start position:0% +ad hoc manner so now this might account + + + align:start position:0% +ad hoc manner so now this might account +for why this quantity bore had begun + + align:start position:0% +for why this quantity bore had begun + + + align:start position:0% +for why this quantity bore had begun +with the angular momentum of an electron + + align:start position:0% +with the angular momentum of an electron + + + align:start position:0% +with the angular momentum of an electron +moving in a circular orbit could only + + align:start position:0% +moving in a circular orbit could only + + + align:start position:0% +moving in a circular orbit could only +take on Integer values of h-bar that + + align:start position:0% +take on Integer values of h-bar that + + + align:start position:0% +take on Integer values of h-bar that +arises from this sort of physical + + align:start position:0% +arises from this sort of physical + + + align:start position:0% +arises from this sort of physical +Criterion of stability of constructive + + align:start position:0% +Criterion of stability of constructive + + + align:start position:0% +Criterion of stability of constructive +interference to get the waves to line up + + align:start position:0% +interference to get the waves to line up + + + align:start position:0% +interference to get the waves to line up +into a basically standing wave pattern + + align:start position:0% +into a basically standing wave pattern + + + align:start position:0% +into a basically standing wave pattern +that's pretty astonishing Einstein reads + + align:start position:0% +that's pretty astonishing Einstein reads + + + align:start position:0% +that's pretty astonishing Einstein reads +the thesis and is immediately impressed + + align:start position:0% +the thesis and is immediately impressed + + + align:start position:0% +the thesis and is immediately impressed +and helps to draw news to draw attention + + align:start position:0% +and helps to draw news to draw attention + + + align:start position:0% +and helps to draw news to draw attention +to it it's still again merely + + align:start position:0% +to it it's still again merely + + + align:start position:0% +to it it's still again merely +hypothetical sort of clever but it's not + + align:start position:0% +hypothetical sort of clever but it's not + + + align:start position:0% +hypothetical sort of clever but it's not +like it's been proven and so uh quite + + align:start position:0% +like it's been proven and so uh quite + + + align:start position:0% +like it's been proven and so uh quite +remarkably in the pace of this I find + + align:start position:0% +remarkably in the pace of this I find + + + align:start position:0% +remarkably in the pace of this I find +just astonishing just within three years + + align:start position:0% +just astonishing just within three years + + + align:start position:0% +just astonishing just within three years +of that clever suggestion in a French + + align:start position:0% +of that clever suggestion in a French + + + align:start position:0% +of that clever suggestion in a French +Aristocrats PhD thesis there was some + + align:start position:0% +Aristocrats PhD thesis there was some + + + align:start position:0% +Aristocrats PhD thesis there was some +pretty compelling new empirical evidence + + align:start position:0% +pretty compelling new empirical evidence + + + align:start position:0% +pretty compelling new empirical evidence +to start taking that seriously in this + + align:start position:0% +to start taking that seriously in this + + + align:start position:0% +to start taking that seriously in this +case coming from what would soon become + + align:start position:0% +case coming from what would soon become + + + align:start position:0% +case coming from what would soon become +Bell Labs it wasn't quite Bell labs yet + + align:start position:0% +Bell Labs it wasn't quite Bell labs yet + + + align:start position:0% +Bell Labs it wasn't quite Bell labs yet +but from an industrial research + + align:start position:0% +but from an industrial research + + + align:start position:0% +but from an industrial research +laboratory + + align:start position:0% +laboratory + + + align:start position:0% +laboratory +here in the United States a work led by + + align:start position:0% +here in the United States a work led by + + + align:start position:0% +here in the United States a work led by +uh Clinton Davison and Lester German + + align:start position:0% +uh Clinton Davison and Lester German + + + align:start position:0% +uh Clinton Davison and Lester German +germer as early as 1927. so they were + + align:start position:0% +germer as early as 1927. so they were + + + align:start position:0% +germer as early as 1927. so they were +actually firing uh electron beams in a + + align:start position:0% +actually firing uh electron beams in a + + + align:start position:0% +actually firing uh electron beams in a +souped-up version of J.J Thompson's + + align:start position:0% +souped-up version of J.J Thompson's + + + align:start position:0% +souped-up version of J.J Thompson's +experiment they had a basically a + + align:start position:0% +experiment they had a basically a + + + align:start position:0% +experiment they had a basically a +cathode ray from which they could beam + + align:start position:0% +cathode ray from which they could beam + + + align:start position:0% +cathode ray from which they could beam +electrons at a certain Crystal by other + + align:start position:0% +electrons at a certain Crystal by other + + + align:start position:0% +electrons at a certain Crystal by other +techniques they knew characteristics of + + align:start position:0% +techniques they knew characteristics of + + + align:start position:0% +techniques they knew characteristics of +the of the crystal structure of that + + align:start position:0% +the of the crystal structure of that + + + align:start position:0% +the of the crystal structure of that +nickel what was the spacing for example + + align:start position:0% +nickel what was the spacing for example + + + align:start position:0% +nickel what was the spacing for example +between layers of atoms and then they + + align:start position:0% +between layers of atoms and then they + + + align:start position:0% +between layers of atoms and then they +could measure the amount of scattered + + align:start position:0% +could measure the amount of scattered + + + align:start position:0% +could measure the amount of scattered +electrons as a as a function of angle so + + align:start position:0% +electrons as a as a function of angle so + + + align:start position:0% +electrons as a as a function of angle so +as they moved their detector to + + align:start position:0% +as they moved their detector to + + + align:start position:0% +as they moved their detector to +different angles they could measure how + + align:start position:0% +different angles they could measure how + + + align:start position:0% +different angles they could measure how +large an intensity they would measure of + + align:start position:0% +large an intensity they would measure of + + + align:start position:0% +large an intensity they would measure of +the of the re-scattered Electron Beam + + align:start position:0% +the of the re-scattered Electron Beam + + + align:start position:0% +the of the re-scattered Electron Beam +and they found exactly this wave-like + + align:start position:0% +and they found exactly this wave-like + + + align:start position:0% +and they found exactly this wave-like +interference pattern that there would be + + align:start position:0% +interference pattern that there would be + + + align:start position:0% +interference pattern that there would be +a Criterion for these two scattered + + align:start position:0% +a Criterion for these two scattered + + + align:start position:0% +a Criterion for these two scattered +waves from distinct scattering off + + align:start position:0% +waves from distinct scattering off + + + align:start position:0% +waves from distinct scattering off +distinct layers within that Crystal uh + + align:start position:0% +distinct layers within that Crystal uh + + + align:start position:0% +distinct layers within that Crystal uh +to line up with an integer number of + + align:start position:0% +to line up with an integer number of + + + align:start position:0% +to line up with an integer number of +wavelengths between them that changes + + align:start position:0% +wavelengths between them that changes + + + align:start position:0% +wavelengths between them that changes +with the scattering angle they just did + + align:start position:0% +with the scattering angle they just did + + + align:start position:0% +with the scattering angle they just did +a kind of classical wave interference + + align:start position:0% +a kind of classical wave interference + + + align:start position:0% +a kind of classical wave interference +analysis not having known things like + + align:start position:0% +analysis not having known things like + + + align:start position:0% +analysis not having known things like +the the lattice spacing for that Crystal + + align:start position:0% +the the lattice spacing for that Crystal + + + align:start position:0% +the the lattice spacing for that Crystal +and they found exactly this kind of + + align:start position:0% +and they found exactly this kind of + + + align:start position:0% +and they found exactly this kind of +waviness interference pattern on exactly + + align:start position:0% +waviness interference pattern on exactly + + + align:start position:0% +waviness interference pattern on exactly +the scale to expect given de brois uh + + align:start position:0% +the scale to expect given de brois uh + + + align:start position:0% +the scale to expect given de brois uh +kind of surprising hypothesis + + align:start position:0% +kind of surprising hypothesis + + + align:start position:0% +kind of surprising hypothesis +so let me wrap up between not roughly + + align:start position:0% +so let me wrap up between not roughly + + + align:start position:0% +so let me wrap up between not roughly +1900 1924 25 we'll see even a little bit + + align:start position:0% +1900 1924 25 we'll see even a little bit + + + align:start position:0% +1900 1924 25 we'll see even a little bit +more of this in the in the coming + + align:start position:0% +more of this in the in the coming + + + align:start position:0% +more of this in the in the coming +lecture in this period that comes to be + + align:start position:0% +lecture in this period that comes to be + + + align:start position:0% +lecture in this period that comes to be +called Old quantum theory physicists + + align:start position:0% +called Old quantum theory physicists + + + align:start position:0% +called Old quantum theory physicists +really went through a pretty dramatic + + align:start position:0% +really went through a pretty dramatic + + + align:start position:0% +really went through a pretty dramatic +series of of new ideas and assumptions + + align:start position:0% +series of of new ideas and assumptions + + + align:start position:0% +series of of new ideas and assumptions +about both light and matter almost kind + + align:start position:0% +about both light and matter almost kind + + + align:start position:0% +about both light and matter almost kind +of interwoven uh among each other + + align:start position:0% +of interwoven uh among each other + + + align:start position:0% +of interwoven uh among each other +so in contrast with these great triumphs + + align:start position:0% +so in contrast with these great triumphs + + + align:start position:0% +so in contrast with these great triumphs +of 19th century physics the wave theory + + align:start position:0% +of 19th century physics the wave theory + + + align:start position:0% +of 19th century physics the wave theory +of light that we've uh looked at in the + + align:start position:0% +of light that we've uh looked at in the + + + align:start position:0% +of light that we've uh looked at in the +beginning of the class + + align:start position:0% +beginning of the class + + + align:start position:0% +beginning of the class +several physicists for several lines of + + align:start position:0% +several physicists for several lines of + + + align:start position:0% +several physicists for several lines of +reasoning begin to explore a kind of + + align:start position:0% +reasoning begin to explore a kind of + + + align:start position:0% +reasoning begin to explore a kind of +discreetness or product-like attribute + + align:start position:0% +discreetness or product-like attribute + + + align:start position:0% +discreetness or product-like attribute +of light we saw several steps along that + + align:start position:0% +of light we saw several steps along that + + + align:start position:0% +of light we saw several steps along that +way during the last class meanwhile kind + + align:start position:0% +way during the last class meanwhile kind + + + align:start position:0% +way during the last class meanwhile kind +of in parallel there's a kind of inverse + + align:start position:0% +of in parallel there's a kind of inverse + + + align:start position:0% +of in parallel there's a kind of inverse +motion uh LED alternated by people like + + align:start position:0% +motion uh LED alternated by people like + + + align:start position:0% +motion uh LED alternated by people like +de bruy to salvage this other new form + + align:start position:0% +de bruy to salvage this other new form + + + align:start position:0% +de bruy to salvage this other new form +of discreteness for his Quantum + + align:start position:0% +of discreteness for his Quantum + + + align:start position:0% +of discreteness for his Quantum +condition by suggesting that just as + + align:start position:0% +condition by suggesting that just as + + + align:start position:0% +condition by suggesting that just as +wave like light could actually be + + align:start position:0% +wave like light could actually be + + + align:start position:0% +wave like light could actually be +thought of as particle-like what if + + align:start position:0% +thought of as particle-like what if + + + align:start position:0% +thought of as particle-like what if +particle-like matter had some wave-like + + align:start position:0% +particle-like matter had some wave-like + + + align:start position:0% +particle-like matter had some wave-like +attributes + + align:start position:0% +attributes + + + align:start position:0% +attributes +and so by the early 1920s as each of + + align:start position:0% +and so by the early 1920s as each of + + + align:start position:0% +and so by the early 1920s as each of +these sort of partial successes begins + + align:start position:0% +these sort of partial successes begins + + + align:start position:0% +these sort of partial successes begins +to draw attention many many physicists + + align:start position:0% +to draw attention many many physicists + + + align:start position:0% +to draw attention many many physicists +were convinced that something had to + + align:start position:0% +were convinced that something had to + + + align:start position:0% +were convinced that something had to +change there was some quantumness that + + align:start position:0% +change there was some quantumness that + + + align:start position:0% +change there was some quantumness that +simply was not consistent with either + + align:start position:0% +simply was not consistent with either + + + align:start position:0% +simply was not consistent with either +Newton's physics or Maximus physics in + + align:start position:0% +Newton's physics or Maximus physics in + + + align:start position:0% +Newton's physics or Maximus physics in +fact I began to use the term classical + + align:start position:0% +fact I began to use the term classical + + + align:start position:0% +fact I began to use the term classical +now to speak about what was not this new + + align:start position:0% +now to speak about what was not this new + + + align:start position:0% +now to speak about what was not this new +Quantum stuff so they would use that new + + align:start position:0% +Quantum stuff so they would use that new + + + align:start position:0% +Quantum stuff so they would use that new +label + + align:start position:0% +label + + + align:start position:0% +label +and the pattern seemed familiar start + + align:start position:0% +and the pattern seemed familiar start + + + align:start position:0% +and the pattern seemed familiar start +with the kind of textbook classical + + align:start position:0% +with the kind of textbook classical + + + align:start position:0% +with the kind of textbook classical +expressions for force or energy or + + align:start position:0% +expressions for force or energy or + + + align:start position:0% +expressions for force or energy or +distance or speed and then somehow it's + + align:start position:0% +distance or speed and then somehow it's + + + align:start position:0% +distance or speed and then somehow it's +just sort of plug it Staple in some as + + align:start position:0% +just sort of plug it Staple in some as + + + align:start position:0% +just sort of plug it Staple in some as +yet unexplained new discreetness + + align:start position:0% +yet unexplained new discreetness + + + align:start position:0% +yet unexplained new discreetness +condition either the energy or the + + align:start position:0% +condition either the energy or the + + + align:start position:0% +condition either the energy or the +agamentum or some wavelength so you have + + align:start position:0% +agamentum or some wavelength so you have + + + align:start position:0% +agamentum or some wavelength so you have +this kind of ad hoc stapling onto + + align:start position:0% +this kind of ad hoc stapling onto + + + align:start position:0% +this kind of ad hoc stapling onto +otherwise perfectly uh familiar + + align:start position:0% +otherwise perfectly uh familiar + + + align:start position:0% +otherwise perfectly uh familiar +classical Expressions that began to + + align:start position:0% +classical Expressions that began to + + + align:start position:0% +classical Expressions that began to +really upset a bunch of people there's a + + align:start position:0% +really upset a bunch of people there's a + + + align:start position:0% +really upset a bunch of people there's a +marvelous book I used to assign in this + + align:start position:0% +marvelous book I used to assign in this + + + align:start position:0% +marvelous book I used to assign in this +class I dropped it this year but I + + align:start position:0% +class I dropped it this year but I + + + align:start position:0% +class I dropped it this year but I +encourage you you might enjoy it it's a + + align:start position:0% +encourage you you might enjoy it it's a + + + align:start position:0% +encourage you you might enjoy it it's a +novel by a historian Russell McCormack + + align:start position:0% +novel by a historian Russell McCormack + + + align:start position:0% +novel by a historian Russell McCormack +shown here called night thoughts of a + + align:start position:0% +shown here called night thoughts of a + + + align:start position:0% +shown here called night thoughts of a +classical physicist what McCormack does + + align:start position:0% +classical physicist what McCormack does + + + align:start position:0% +classical physicist what McCormack does +is try to really I think very movingly + + align:start position:0% +is try to really I think very movingly + + + align:start position:0% +is try to really I think very movingly +very compellingly recreate what it felt + + align:start position:0% +very compellingly recreate what it felt + + + align:start position:0% +very compellingly recreate what it felt +like to be a physicist living through + + align:start position:0% +like to be a physicist living through + + + align:start position:0% +like to be a physicist living through +this period of conceptual um disruption + + align:start position:0% +this period of conceptual um disruption + + + align:start position:0% +this period of conceptual um disruption +when it really felt like the solidity of + + align:start position:0% +when it really felt like the solidity of + + + align:start position:0% +when it really felt like the solidity of +the world began to shake and it didn't + + align:start position:0% +the world began to shake and it didn't + + + align:start position:0% +the world began to shake and it didn't +just shake it looked ugly it looked + + align:start position:0% +just shake it looked ugly it looked + + + align:start position:0% +just shake it looked ugly it looked +piecemeal and kind of ad hoc so uh + + align:start position:0% +piecemeal and kind of ad hoc so uh + + + align:start position:0% +piecemeal and kind of ad hoc so uh +McCormack who had poured over just + + align:start position:0% +McCormack who had poured over just + + + align:start position:0% +McCormack who had poured over just +literally tens of thousands of letters + + align:start position:0% +literally tens of thousands of letters + + + align:start position:0% +literally tens of thousands of letters +and laboratory notes and Publications + + align:start position:0% +and laboratory notes and Publications + + + align:start position:0% +and laboratory notes and Publications +from a whole generation of these mostly + + align:start position:0% +from a whole generation of these mostly + + + align:start position:0% +from a whole generation of these mostly +german-based physicists during this + + align:start position:0% +german-based physicists during this + + + align:start position:0% +german-based physicists during this +period of change he distills that into a + + align:start position:0% +period of change he distills that into a + + + align:start position:0% +period of change he distills that into a +160-page novel of a composite character + + align:start position:0% +160-page novel of a composite character + + + align:start position:0% +160-page novel of a composite character +named Victor Jacob to watch yaakov react + + align:start position:0% +named Victor Jacob to watch yaakov react + + + align:start position:0% +named Victor Jacob to watch yaakov react +to this kind of like that kind of makes + + align:start position:0% +to this kind of like that kind of makes + + + align:start position:0% +to this kind of like that kind of makes +sense but it's disjointed from over + + align:start position:0% +sense but it's disjointed from over + + + align:start position:0% +sense but it's disjointed from over +there I can follow you here but this + + align:start position:0% +there I can follow you here but this + + + align:start position:0% +there I can follow you here but this +looks really weird it just starts to + + align:start position:0% +looks really weird it just starts to + + + align:start position:0% +looks really weird it just starts to +feel broken it starts to feel + + align:start position:0% +feel broken it starts to feel + + + align:start position:0% +feel broken it starts to feel +disorganized and ad hoc and so when + + align:start position:0% +disorganized and ad hoc and so when + + + align:start position:0% +disorganized and ad hoc and so when +people began calling this old quantum + + align:start position:0% +people began calling this old quantum + + + align:start position:0% +people began calling this old quantum +theory it was both to say this happened + + align:start position:0% +theory it was both to say this happened + + + align:start position:0% +theory it was both to say this happened +before something new but also to try to + + align:start position:0% +before something new but also to try to + + + align:start position:0% +before something new but also to try to +crack it saying it's old and kind of + + align:start position:0% +crack it saying it's old and kind of + + + align:start position:0% +crack it saying it's old and kind of +broken it just felt conceptually + + align:start position:0% +broken it just felt conceptually + + + align:start position:0% +broken it just felt conceptually +dissatisfying to a number of people and + + align:start position:0% +dissatisfying to a number of people and + + + align:start position:0% +dissatisfying to a number of people and +people were pretty well convinced that + + align:start position:0% +people were pretty well convinced that + + + align:start position:0% +people were pretty well convinced that +couldn't be the last way these things + + align:start position:0% +couldn't be the last way these things + + + align:start position:0% +couldn't be the last way these things +will stand + + align:start position:0% +will stand + + + align:start position:0% +will stand +so I know we're just about at time I see + + align:start position:0% +so I know we're just about at time I see + + + align:start position:0% +so I know we're just about at time I see +there's a question from Diablo how did + + align:start position:0% +there's a question from Diablo how did + + + align:start position:0% +there's a question from Diablo how did +the broy waves impact the way particle + + align:start position:0% +the broy waves impact the way particle + + + align:start position:0% +the broy waves impact the way particle +debate thank you Robin so basically it + + align:start position:0% +debate thank you Robin so basically it + + + align:start position:0% +debate thank you Robin so basically it +heightens us even further I mean the + + align:start position:0% +heightens us even further I mean the + + + align:start position:0% +heightens us even further I mean the +short answer is it made it even harder + + align:start position:0% +short answer is it made it even harder + + + align:start position:0% +short answer is it made it even harder +to ignore this kind of strange unsteady + + align:start position:0% +to ignore this kind of strange unsteady + + + align:start position:0% +to ignore this kind of strange unsteady +and unstable combination of Concepts + + align:start position:0% +and unstable combination of Concepts + + + align:start position:0% +and unstable combination of Concepts +which otherwise had seemed clear but + + align:start position:0% +which otherwise had seemed clear but + + + align:start position:0% +which otherwise had seemed clear but +separate and that's the kind of thing + + align:start position:0% +separate and that's the kind of thing + + + align:start position:0% +separate and that's the kind of thing +that that is uh that this novel I just + + align:start position:0% +that that is uh that this novel I just + + + align:start position:0% +that that is uh that this novel I just +mentioned not thoughts of the classical + + align:start position:0% +mentioned not thoughts of the classical + + + align:start position:0% +mentioned not thoughts of the classical +physicist is actually really beautifully + + align:start position:0% +physicist is actually really beautifully + + + align:start position:0% +physicist is actually really beautifully +kind of helping us appreciate that it + + align:start position:0% +kind of helping us appreciate that it + + + align:start position:0% +kind of helping us appreciate that it +looked it looked dizzying people would + + align:start position:0% +looked it looked dizzying people would + + + align:start position:0% +looked it looked dizzying people would +have like a physiological reactions like + + align:start position:0% +have like a physiological reactions like + + + align:start position:0% +have like a physiological reactions like +what's solid how you know I know what a + + align:start position:0% +what's solid how you know I know what a + + + align:start position:0% +what's solid how you know I know what a +wave is and by this point think about + + align:start position:0% +wave is and by this point think about + + + align:start position:0% +wave is and by this point think about +the Wranglers or laurents or anyone else + + align:start position:0% +the Wranglers or laurents or anyone else + + + align:start position:0% +the Wranglers or laurents or anyone else +there was a huge highly successful + + align:start position:0% +there was a huge highly successful + + + align:start position:0% +there was a huge highly successful +quantitative series of tools with which + + align:start position:0% +quantitative series of tools with which + + + align:start position:0% +quantitative series of tools with which +to characterize wave phenomena + + align:start position:0% +to characterize wave phenomena + + + align:start position:0% +to characterize wave phenomena +interference or fraction diffraction + + align:start position:0% +interference or fraction diffraction + + + align:start position:0% +interference or fraction diffraction +wave equations and all the rest and then + + align:start position:0% +wave equations and all the rest and then + + + align:start position:0% +wave equations and all the rest and then +people would say I know what particles + + align:start position:0% +people would say I know what particles + + + align:start position:0% +people would say I know what particles +are and they could use Newton's laws to + + align:start position:0% +are and they could use Newton's laws to + + + align:start position:0% +are and they could use Newton's laws to +study ballistics and so on to + + align:start position:0% +study ballistics and so on to + + + align:start position:0% +study ballistics and so on to +extraordinary accuracy and now it looked + + align:start position:0% +extraordinary accuracy and now it looked + + + align:start position:0% +extraordinary accuracy and now it looked +like they had to somehow mush these + + align:start position:0% +like they had to somehow mush these + + + align:start position:0% +like they had to somehow mush these +together in a way that didn't without + + align:start position:0% +together in a way that didn't without + + + align:start position:0% +together in a way that didn't without +any rules in a way that didn't seem to + + align:start position:0% +any rules in a way that didn't seem to + + + align:start position:0% +any rules in a way that didn't seem to +have any road back and so uh the devroy + + align:start position:0% +have any road back and so uh the devroy + + + align:start position:0% +have any road back and so uh the devroy +hypothesis especially after 1927 with + + align:start position:0% +hypothesis especially after 1927 with + + + align:start position:0% +hypothesis especially after 1927 with +his Davis and germer work and they + + align:start position:0% +his Davis and germer work and they + + + align:start position:0% +his Davis and germer work and they +received the Nobel Prize like instantly + + align:start position:0% +received the Nobel Prize like instantly + + + align:start position:0% +received the Nobel Prize like instantly +this again was seen as immediately + + align:start position:0% +this again was seen as immediately + + + align:start position:0% +this again was seen as immediately +important work when they did those + + align:start position:0% +important work when they did those + + + align:start position:0% +important work when they did those +experiments that was just heightening + + align:start position:0% +experiments that was just heightening + + + align:start position:0% +experiments that was just heightening +this clash and made the stakes in the + + align:start position:0% +this clash and made the stakes in the + + + align:start position:0% +this clash and made the stakes in the +conceptual Stakes seem even higher it's + + align:start position:0% +conceptual Stakes seem even higher it's + + + align:start position:0% +conceptual Stakes seem even higher it's +a great question and we'll see how that + + align:start position:0% +a great question and we'll see how that + + + align:start position:0% +a great question and we'll see how that +plays out actually in the next several + + align:start position:0% +plays out actually in the next several + + + align:start position:0% +plays out actually in the next several +classes it doesn't get resolved what + + align:start position:0% +classes it doesn't get resolved what + + + align:start position:0% +classes it doesn't get resolved what +happens is physicists resolve themselves + + align:start position:0% +happens is physicists resolve themselves + + + align:start position:0% +happens is physicists resolve themselves +to keep dealing with this strange + + align:start position:0% +to keep dealing with this strange + + + align:start position:0% +to keep dealing with this strange +connectedness as opposed to say now it's + + align:start position:0% +connectedness as opposed to say now it's + + + align:start position:0% +connectedness as opposed to say now it's +one or the other as as many of you + + align:start position:0% +one or the other as as many of you + + + align:start position:0% +one or the other as as many of you +likely know from other classes + + align:start position:0% +likely know from other classes + + + align:start position:0% +likely know from other classes +any other questions on that + + align:start position:0% + + + + align:start position:0% + +I don't want to keep you too long I'm + + align:start position:0% +I don't want to keep you too long I'm + + + align:start position:0% +I don't want to keep you too long I'm +sure you have a full afternoon anyways + + align:start position:0% +sure you have a full afternoon anyways + + + align:start position:0% +sure you have a full afternoon anyways +uh good to see you all uh we'll pick up + + align:start position:0% +uh good to see you all uh we'll pick up + + + align:start position:0% +uh good to see you all uh we'll pick up +uh the story again on Wednesday \ No newline at end of file diff --git a/aKTOS0Nrlug.txt b/aKTOS0Nrlug.txt new file mode 100644 index 0000000000000000000000000000000000000000..4c13e818468f993962855351871fe90b6dfb8fbd --- /dev/null +++ b/aKTOS0Nrlug.txt @@ -0,0 +1,8187 @@ +align:start position:0% + +so what I want to do today is just Barry + + align:start position:0% +so what I want to do today is just Barry + + + align:start position:0% +so what I want to do today is just Barry +I want to introduce this to you very + + align:start position:0% +I want to introduce this to you very + + + align:start position:0% +I want to introduce this to you very +quickly is and I was going to show you + + align:start position:0% +quickly is and I was going to show you + + + align:start position:0% +quickly is and I was going to show you +this at the at the end of the last class + + align:start position:0% +this at the at the end of the last class + + + align:start position:0% +this at the at the end of the last class +if we simply go to the far end of the + + align:start position:0% +if we simply go to the far end of the + + + align:start position:0% +if we simply go to the far end of the +scale the picometer scale you see carbon + + align:start position:0% +scale the picometer scale you see carbon + + + align:start position:0% +scale the picometer scale you see carbon +I'm not gonna start you with carbon that + + align:start position:0% +I'm not gonna start you with carbon that + + + align:start position:0% +I'm not gonna start you with carbon that +is a little dull but over the next few + + align:start position:0% +is a little dull but over the next few + + + align:start position:0% +is a little dull but over the next few +weeks few classes rather because we have + + align:start position:0% +weeks few classes rather because we have + + + align:start position:0% +weeks few classes rather because we have +to do this in fast order we will go from + + align:start position:0% +to do this in fast order we will go from + + + align:start position:0% +to do this in fast order we will go from +we will cover details of carbohydrates + + align:start position:0% +we will cover details of carbohydrates + + + align:start position:0% +we will cover details of carbohydrates +amino acids nucleosides and + + align:start position:0% +amino acids nucleosides and + + + align:start position:0% +amino acids nucleosides and +phospholipids and how those building + + align:start position:0% +phospholipids and how those building + + + align:start position:0% +phospholipids and how those building +blocks are put together their properties + + align:start position:0% +blocks are put together their properties + + + align:start position:0% +blocks are put together their properties +their ability to interact and engage in + + align:start position:0% +their ability to interact and engage in + + + align:start position:0% +their ability to interact and engage in +non covalent interactions with other + + align:start position:0% +non covalent interactions with other + + + align:start position:0% +non covalent interactions with other +molecules and the ability to make + + align:start position:0% +molecules and the ability to make + + + align:start position:0% +molecules and the ability to make +polymers out of some of these such as + + align:start position:0% +polymers out of some of these such as + + + align:start position:0% +polymers out of some of these such as +the nuclear sides and the amino acids + + align:start position:0% +the nuclear sides and the amino acids + + + align:start position:0% +the nuclear sides and the amino acids +and the carbohydrates which then start + + align:start position:0% +and the carbohydrates which then start + + + align:start position:0% +and the carbohydrates which then start +to create the richness of life we will + + align:start position:0% +to create the richness of life we will + + + align:start position:0% +to create the richness of life we will +also discuss today the supramolecular + + align:start position:0% +also discuss today the supramolecular + + + align:start position:0% +also discuss today the supramolecular +chemistry of phospholipids as they make + + align:start position:0% +chemistry of phospholipids as they make + + + align:start position:0% +chemistry of phospholipids as they make +micelles and lipid bilayers which are + + align:start position:0% +micelles and lipid bilayers which are + + + align:start position:0% +micelles and lipid bilayers which are +the key boundary of cells so it's very + + align:start position:0% +the key boundary of cells so it's very + + + align:start position:0% +the key boundary of cells so it's very +important and then in the following week + + align:start position:0% +important and then in the following week + + + align:start position:0% +important and then in the following week +we'll go to some of the the bigger + + align:start position:0% +we'll go to some of the the bigger + + + align:start position:0% +we'll go to some of the the bigger +things like proteins nucleic acid + + align:start position:0% +things like proteins nucleic acid + + + align:start position:0% +things like proteins nucleic acid +polymers for example hist RNA so the + + align:start position:0% +polymers for example hist RNA so the + + + align:start position:0% +polymers for example hist RNA so the +course will literally do this take you + + align:start position:0% +course will literally do this take you + + + align:start position:0% +course will literally do this take you +from one end of the scale to the other + + align:start position:0% +from one end of the scale to the other + + + align:start position:0% +from one end of the scale to the other +so I want you to get a sense of these + + align:start position:0% +so I want you to get a sense of these + + + align:start position:0% +so I want you to get a sense of these +dimensions I want to mention one sort of + + align:start position:0% +dimensions I want to mention one sort of + + + align:start position:0% +dimensions I want to mention one sort of +fairly stupid thing with respect to how + + align:start position:0% +fairly stupid thing with respect to how + + + align:start position:0% +fairly stupid thing with respect to how +chemists and biochemists talk about + + align:start position:0% +chemists and biochemists talk about + + + align:start position:0% +chemists and biochemists talk about +certain metrics certain distances that + + align:start position:0% +certain metrics certain distances that + + + align:start position:0% +certain metrics certain distances that +are pertinent that pertinence to the by + + align:start position:0% +are pertinent that pertinence to the by + + + align:start position:0% +are pertinent that pertinence to the by +a lot to biology and biochemistry + + align:start position:0% +a lot to biology and biochemistry + + + align:start position:0% +a lot to biology and biochemistry +engineers tend to talk about micrometers + + align:start position:0% +engineers tend to talk about micrometers + + + align:start position:0% +engineers tend to talk about micrometers +and nanometers there is one unit that + + align:start position:0% +and nanometers there is one unit that + + + align:start position:0% +and nanometers there is one unit that +chemists and biologists use quite a lot + + align:start position:0% +chemists and biologists use quite a lot + + + align:start position:0% +chemists and biologists use quite a lot +it's the angstrom after a finish Shastra + + align:start position:0% +it's the angstrom after a finish Shastra + + + align:start position:0% +it's the angstrom after a finish Shastra +not finished I think it was a Norwegian + + align:start position:0% +not finished I think it was a Norwegian + + + align:start position:0% +not finished I think it was a Norwegian +and that is equivalent 10 angstrom + + align:start position:0% +and that is equivalent 10 angstrom + + + align:start position:0% +and that is equivalent 10 angstrom +equals one nanometer so when you're + + align:start position:0% +equals one nanometer so when you're + + + align:start position:0% +equals one nanometer so when you're +looking at scales we tend to talk about + + align:start position:0% +looking at scales we tend to talk about + + + align:start position:0% +looking at scales we tend to talk about +Armstrong because they're a convenient + + align:start position:0% +Armstrong because they're a convenient + + + align:start position:0% +Armstrong because they're a convenient +number the + + align:start position:0% +number the + + + align:start position:0% +number the +don't don't get fooled by this it's you + + align:start position:0% +don't don't get fooled by this it's you + + + align:start position:0% +don't don't get fooled by this it's you +know it can be a little bit confusing + + align:start position:0% +know it can be a little bit confusing + + + align:start position:0% +know it can be a little bit confusing +because it's 10 to 10 to the negative 10 + + align:start position:0% +because it's 10 to 10 to the negative 10 + + + align:start position:0% +because it's 10 to 10 to the negative 10 +so nanometers 10 to the negative 9 you + + align:start position:0% +so nanometers 10 to the negative 9 you + + + align:start position:0% +so nanometers 10 to the negative 9 you +know that quite frequently picometer 10 + + align:start position:0% +know that quite frequently picometer 10 + + + align:start position:0% +know that quite frequently picometer 10 +to the negative 12 micrometer negative 6 + + align:start position:0% +to the negative 12 micrometer negative 6 + + + align:start position:0% +to the negative 12 micrometer negative 6 +but the arms strum is just a funny unit + + align:start position:0% +but the arms strum is just a funny unit + + + align:start position:0% +but the arms strum is just a funny unit +we use a lot and it's 10 to the negative + + align:start position:0% +we use a lot and it's 10 to the negative + + + align:start position:0% +we use a lot and it's 10 to the negative +10 so just to make sure there's no + + align:start position:0% +10 so just to make sure there's no + + + align:start position:0% +10 so just to make sure there's no +ambiguity about that that particular + + align:start position:0% +ambiguity about that that particular + + + align:start position:0% +ambiguity about that that particular +detail okay all right so today's lecture + + align:start position:0% +detail okay all right so today's lecture + + + align:start position:0% +detail okay all right so today's lecture +will focus on the molecules of life and + + align:start position:0% +will focus on the molecules of life and + + + align:start position:0% +will focus on the molecules of life and +in particular I'm going to through the + + align:start position:0% +in particular I'm going to through the + + + align:start position:0% +in particular I'm going to through the +next few classes introduce you to the + + align:start position:0% +next few classes introduce you to the + + + align:start position:0% +next few classes introduce you to the +various molecules of life but first of + + align:start position:0% +various molecules of life but first of + + + align:start position:0% +various molecules of life but first of +all we have to do a little bit to + + align:start position:0% +all we have to do a little bit to + + + align:start position:0% +all we have to do a little bit to +understand chemical bonding and in + + align:start position:0% +understand chemical bonding and in + + + align:start position:0% +understand chemical bonding and in +particular we want to look at both + + align:start position:0% +particular we want to look at both + + + align:start position:0% +particular we want to look at both +covalent and non covalent bonding + + align:start position:0% +covalent and non covalent bonding + + + align:start position:0% +covalent and non covalent bonding +because covalent bonding is important + + align:start position:0% +because covalent bonding is important + + + align:start position:0% +because covalent bonding is important +it's the structure it's the framework + + align:start position:0% +it's the structure it's the framework + + + align:start position:0% +it's the structure it's the framework +but non covalent bonding is what gives + + align:start position:0% +but non covalent bonding is what gives + + + align:start position:0% +but non covalent bonding is what gives +us dynamics these are much weaker forces + + align:start position:0% +us dynamics these are much weaker forces + + + align:start position:0% +us dynamics these are much weaker forces +that can be broken and remade very + + align:start position:0% +that can be broken and remade very + + + align:start position:0% +that can be broken and remade very +readily that are essential for things + + align:start position:0% +readily that are essential for things + + + align:start position:0% +readily that are essential for things +like forming the DNA duplex for folding + + align:start position:0% +like forming the DNA duplex for folding + + + align:start position:0% +like forming the DNA duplex for folding +your proteins for associating the lipid + + align:start position:0% +your proteins for associating the lipid + + + align:start position:0% +your proteins for associating the lipid +bilayer all of those are non covalent + + align:start position:0% +bilayer all of those are non covalent + + + align:start position:0% +bilayer all of those are non covalent +courses forces and they are dynamic + + align:start position:0% +courses forces and they are dynamic + + + align:start position:0% +courses forces and they are dynamic +because they're weak you can break one + + align:start position:0% +because they're weak you can break one + + + align:start position:0% +because they're weak you can break one +relatively easily as long as you're + + align:start position:0% +relatively easily as long as you're + + + align:start position:0% +relatively easily as long as you're +ready to make another one in its place + + align:start position:0% +ready to make another one in its place + + + align:start position:0% +ready to make another one in its place +so I will spend a little bit of time on + + align:start position:0% +so I will spend a little bit of time on + + + align:start position:0% +so I will spend a little bit of time on +that and then today we'll talk about + + align:start position:0% +that and then today we'll talk about + + + align:start position:0% +that and then today we'll talk about +lipids and membranes but first of all + + align:start position:0% +lipids and membranes but first of all + + + align:start position:0% +lipids and membranes but first of all +let me introduce you to some of the + + align:start position:0% +let me introduce you to some of the + + + align:start position:0% +let me introduce you to some of the +molecules of life in this rendition + + align:start position:0% +molecules of life in this rendition + + + align:start position:0% +molecules of life in this rendition +that's done by David Goodsell at Scripps + + align:start position:0% +that's done by David Goodsell at Scripps + + + align:start position:0% +that's done by David Goodsell at Scripps +so up in the top corner here you look at + + align:start position:0% +so up in the top corner here you look at + + + align:start position:0% +so up in the top corner here you look at +2.3 is the 3-dimensional structure of a + + align:start position:0% +2.3 is the 3-dimensional structure of a + + + align:start position:0% +2.3 is the 3-dimensional structure of a +protein it's folded into a globular + + align:start position:0% +protein it's folded into a globular + + + align:start position:0% +protein it's folded into a globular +state through no non covalent forces I + + align:start position:0% +state through no non covalent forces I + + + align:start position:0% +state through no non covalent forces I +brought a little 3d model of a protein + + align:start position:0% +brought a little 3d model of a protein + + + align:start position:0% +brought a little 3d model of a protein +for you to look at and take a look at + + align:start position:0% +for you to look at and take a look at + + + align:start position:0% +for you to look at and take a look at +later that was one of the suggestions I + + align:start position:0% +later that was one of the suggestions I + + + align:start position:0% +later that was one of the suggestions I +made you could coordinate printing a 3d + + align:start position:0% +made you could coordinate printing a 3d + + + align:start position:0% +made you could coordinate printing a 3d +model as your one of your later projects + + align:start position:0% +model as your one of your later projects + + + align:start position:0% +model as your one of your later projects +we will learn about the forces that hold + + align:start position:0% +we will learn about the forces that hold + + + align:start position:0% +we will learn about the forces that hold +the polymer together the covalent forces + + align:start position:0% +the polymer together the covalent forces + + + align:start position:0% +the polymer together the covalent forces +but then the non covalent forces that + + align:start position:0% +but then the non covalent forces that + + + align:start position:0% +but then the non covalent forces that +make globular structures that are very + + align:start position:0% +make globular structures that are very + + + align:start position:0% +make globular structures that are very +important for function they're not much + + align:start position:0% +important for function they're not much + + + align:start position:0% +important for function they're not much +use as unraveled spagetti they're way + + align:start position:0% +use as unraveled spagetti they're way + + + align:start position:0% +use as unraveled spagetti they're way +more useful as they're three + + align:start position:0% +more useful as they're three + + + align:start position:0% +more useful as they're three +structure down here in the corner is a + + align:start position:0% +structure down here in the corner is a + + + align:start position:0% +structure down here in the corner is a +carbohydrate it really looks pretty + + align:start position:0% +carbohydrate it really looks pretty + + + align:start position:0% +carbohydrate it really looks pretty +pathetic in this rendition + + align:start position:0% +pathetic in this rendition + + + align:start position:0% +pathetic in this rendition +but carbohydrates have a lot of value + + align:start position:0% +but carbohydrates have a lot of value + + + align:start position:0% +but carbohydrates have a lot of value +particularly in energy storage but also + + align:start position:0% +particularly in energy storage but also + + + align:start position:0% +particularly in energy storage but also +in things like the extracellular matrix + + align:start position:0% +in things like the extracellular matrix + + + align:start position:0% +in things like the extracellular matrix +and as entities that single signal + + align:start position:0% +and as entities that single signal + + + align:start position:0% +and as entities that single signal +information between cells there's a lot + + align:start position:0% +information between cells there's a lot + + + align:start position:0% +information between cells there's a lot +of communication done by cell surface + + align:start position:0% +of communication done by cell surface + + + align:start position:0% +of communication done by cell surface +carbohydrates over here you see the + + align:start position:0% +carbohydrates over here you see the + + + align:start position:0% +carbohydrates over here you see the +canonical structure of double-stranded + + align:start position:0% +canonical structure of double-stranded + + + align:start position:0% +canonical structure of double-stranded +DNA we'll look at the covalent structure + + align:start position:0% +DNA we'll look at the covalent structure + + + align:start position:0% +DNA we'll look at the covalent structure +of those single strands but then we'll + + align:start position:0% +of those single strands but then we'll + + + align:start position:0% +of those single strands but then we'll +focus in on the non covalent + + align:start position:0% +focus in on the non covalent + + + align:start position:0% +focus in on the non covalent +interactions that make the + + align:start position:0% +interactions that make the + + + align:start position:0% +interactions that make the +double-stranded DNA and store genetic + + align:start position:0% +double-stranded DNA and store genetic + + + align:start position:0% +double-stranded DNA and store genetic +information which is also central to + + align:start position:0% +information which is also central to + + + align:start position:0% +information which is also central to +life and then lastly on this but we'll + + align:start position:0% +life and then lastly on this but we'll + + + align:start position:0% +life and then lastly on this but we'll +cover this today is a lipid bilayer it's + + align:start position:0% +cover this today is a lipid bilayer it's + + + align:start position:0% +cover this today is a lipid bilayer it's +a fascinating super molecular structure + + align:start position:0% +a fascinating super molecular structure + + + align:start position:0% +a fascinating super molecular structure +that really is at the hearts of how all + + align:start position:0% +that really is at the hearts of how all + + + align:start position:0% +that really is at the hearts of how all +your cells are held in a compartment + + align:start position:0% +your cells are held in a compartment + + + align:start position:0% +your cells are held in a compartment +surrounded by a lipid bilayer so by the + + align:start position:0% +surrounded by a lipid bilayer so by the + + + align:start position:0% +surrounded by a lipid bilayer so by the +time we start talking about those you'll + + align:start position:0% +time we start talking about those you'll + + + align:start position:0% +time we start talking about those you'll +understand the forces that put in place + + align:start position:0% +understand the forces that put in place + + + align:start position:0% +understand the forces that put in place +that lipid bilayer that arguably and + + align:start position:0% +that lipid bilayer that arguably and + + + align:start position:0% +that lipid bilayer that arguably and +I've read articles that say this that is + + align:start position:0% +I've read articles that say this that is + + + align:start position:0% +I've read articles that say this that is +the evolution of lipid bilayers is as + + align:start position:0% +the evolution of lipid bilayers is as + + + align:start position:0% +the evolution of lipid bilayers is as +important as the genetic code + + align:start position:0% +important as the genetic code + + + align:start position:0% +important as the genetic code +because if cells did not have a + + align:start position:0% +because if cells did not have a + + + align:start position:0% +because if cells did not have a +surrounding did not have an inside where + + align:start position:0% +surrounding did not have an inside where + + + align:start position:0% +surrounding did not have an inside where +you could concentrate reagents and + + align:start position:0% +you could concentrate reagents and + + + align:start position:0% +you could concentrate reagents and +macromolecules and do biochemistry we + + align:start position:0% +macromolecules and do biochemistry we + + + align:start position:0% +macromolecules and do biochemistry we +wouldn't exist as we a life wouldn't + + align:start position:0% +wouldn't exist as we a life wouldn't + + + align:start position:0% +wouldn't exist as we a life wouldn't +exist in the same way okay so let's take + + align:start position:0% +exist in the same way okay so let's take + + + align:start position:0% +exist in the same way okay so let's take +a look at the composition of living + + align:start position:0% +a look at the composition of living + + + align:start position:0% +a look at the composition of living +systems and remarkably we are about 75% + + align:start position:0% +systems and remarkably we are about 75% + + + align:start position:0% +systems and remarkably we are about 75% +water so most proteins are very hydrated + + align:start position:0% +water so most proteins are very hydrated + + + align:start position:0% +water so most proteins are very hydrated +there's a lot of water in cells there's + + align:start position:0% +there's a lot of water in cells there's + + + align:start position:0% +there's a lot of water in cells there's +a lot of water outside of cells in the + + align:start position:0% +a lot of water outside of cells in the + + + align:start position:0% +a lot of water outside of cells in the +matrix and really we sort of survive + + align:start position:0% +matrix and really we sort of survive + + + align:start position:0% +matrix and really we sort of survive +weird we survive in an aqueous + + align:start position:0% +weird we survive in an aqueous + + + align:start position:0% +weird we survive in an aqueous +environment and the thing that you also + + align:start position:0% +environment and the thing that you also + + + align:start position:0% +environment and the thing that you also +want to think about is when we think + + align:start position:0% +want to think about is when we think + + + align:start position:0% +want to think about is when we think +about non covalent forces these are + + align:start position:0% +about non covalent forces these are + + + align:start position:0% +about non covalent forces these are +forces put in place in water we don't + + align:start position:0% +forces put in place in water we don't + + + align:start position:0% +forces put in place in water we don't +live in a on a far distant planet where + + align:start position:0% +live in a on a far distant planet where + + + align:start position:0% +live in a on a far distant planet where +we're in sort of liquid methane or + + align:start position:0% +we're in sort of liquid methane or + + + align:start position:0% +we're in sort of liquid methane or +anything like that so water is critical + + align:start position:0% +anything like that so water is critical + + + align:start position:0% +anything like that so water is critical +to life the establishment of the + + align:start position:0% +to life the establishment of the + + + align:start position:0% +to life the establishment of the +hydrosphere + + align:start position:0% +hydrosphere + + + align:start position:0% +hydrosphere +when Earth earth first formed the + + align:start position:0% +when Earth earth first formed the + + + align:start position:0% +when Earth earth first formed the +evolutionary events that happened after + + align:start position:0% +evolutionary events that happened after + + + align:start position:0% +evolutionary events that happened after +that were - were really in hand-in-hand + + align:start position:0% +that were - were really in hand-in-hand + + + align:start position:0% +that were - were really in hand-in-hand +with the fact that it was an aqueous + + align:start position:0% +with the fact that it was an aqueous + + + align:start position:0% +with the fact that it was an aqueous +environment because forces are different + + align:start position:0% +environment because forces are different + + + align:start position:0% +environment because forces are different +whether they are in hydrophobic + + align:start position:0% +whether they are in hydrophobic + + + align:start position:0% +whether they are in hydrophobic +environments or hydrophilic environments + + align:start position:0% +environments or hydrophilic environments + + + align:start position:0% +environments or hydrophilic environments +and really you'll start to get + + align:start position:0% +and really you'll start to get + + + align:start position:0% +and really you'll start to get +appreciation for that as we move forward + + align:start position:0% +appreciation for that as we move forward + + + align:start position:0% +appreciation for that as we move forward +so this basically suggests that if I put + + align:start position:0% +so this basically suggests that if I put + + + align:start position:0% +so this basically suggests that if I put +one of you in a giant desiccator and + + align:start position:0% +one of you in a giant desiccator and + + + align:start position:0% +one of you in a giant desiccator and +pumped out all the water I could + + align:start position:0% +pumped out all the water I could + + + align:start position:0% +pumped out all the water I could +possibly pull out there'd be about sort + + align:start position:0% +possibly pull out there'd be about sort + + + align:start position:0% +possibly pull out there'd be about sort +of depending on your weight 40 pounds of + + align:start position:0% +of depending on your weight 40 pounds of + + + align:start position:0% +of depending on your weight 40 pounds of +things left behind of what's left behind + + align:start position:0% +things left behind of what's left behind + + + align:start position:0% +things left behind of what's left behind +the majority of it is going to be + + align:start position:0% +the majority of it is going to be + + + align:start position:0% +the majority of it is going to be +biological macromolecules and then the + + align:start position:0% +biological macromolecules and then the + + + align:start position:0% +biological macromolecules and then the +rest of it that little sliver are things + + align:start position:0% +rest of it that little sliver are things + + + align:start position:0% +rest of it that little sliver are things +like ions and small molecules calcium + + align:start position:0% +like ions and small molecules calcium + + + align:start position:0% +like ions and small molecules calcium +magnesium iron manganese those are those + + align:start position:0% +magnesium iron manganese those are those + + + align:start position:0% +magnesium iron manganese those are those +small inorganic ions as well as small + + align:start position:0% +small inorganic ions as well as small + + + align:start position:0% +small inorganic ions as well as small +molecule metabolites that are involved + + align:start position:0% +molecule metabolites that are involved + + + align:start position:0% +molecule metabolites that are involved +in central metabolisms let's go now look + + align:start position:0% +in central metabolisms let's go now look + + + align:start position:0% +in central metabolisms let's go now look +at the macromolecules and they're sort + + align:start position:0% +at the macromolecules and they're sort + + + align:start position:0% +at the macromolecules and they're sort +of proportions relative to each other + + align:start position:0% +of proportions relative to each other + + + align:start position:0% +of proportions relative to each other +the smallest sliver are the lipids which + + align:start position:0% +the smallest sliver are the lipids which + + + align:start position:0% +the smallest sliver are the lipids which +we'll talk about today then you have the + + align:start position:0% +we'll talk about today then you have the + + + align:start position:0% +we'll talk about today then you have the +nucleic acids that are critical for + + align:start position:0% +nucleic acids that are critical for + + + align:start position:0% +nucleic acids that are critical for +information storage you have proteins + + align:start position:0% +information storage you have proteins + + + align:start position:0% +information storage you have proteins +which make the largest piece of the pie + + align:start position:0% +which make the largest piece of the pie + + + align:start position:0% +which make the largest piece of the pie +and the carbohydrates which are one of + + align:start position:0% +and the carbohydrates which are one of + + + align:start position:0% +and the carbohydrates which are one of +the is the 25% so you can see how + + align:start position:0% +the is the 25% so you can see how + + + align:start position:0% +the is the 25% so you can see how +important carbohydrates are because of + + align:start position:0% +important carbohydrates are because of + + + align:start position:0% +important carbohydrates are because of +their proportion being relatively large + + align:start position:0% +their proportion being relatively large + + + align:start position:0% +their proportion being relatively large +the lipid proportion though is small but + + align:start position:0% +the lipid proportion though is small but + + + align:start position:0% +the lipid proportion though is small but +absolutely critical harking back to the + + align:start position:0% +absolutely critical harking back to the + + + align:start position:0% +absolutely critical harking back to the +membrane bilayer + + align:start position:0% +membrane bilayer + + + align:start position:0% +membrane bilayer +because if we didn't have the membrane + + align:start position:0% +because if we didn't have the membrane + + + align:start position:0% +because if we didn't have the membrane +bilayer once again we wouldn't have life + + align:start position:0% +bilayer once again we wouldn't have life + + + align:start position:0% +bilayer once again we wouldn't have life +in the same way that we have it now so + + align:start position:0% +in the same way that we have it now so + + + align:start position:0% +in the same way that we have it now so +that gives you a sense of the relative + + align:start position:0% +that gives you a sense of the relative + + + align:start position:0% +that gives you a sense of the relative +proportions of things and frankly when I + + align:start position:0% +proportions of things and frankly when I + + + align:start position:0% +proportions of things and frankly when I +discuss the macromolecules I really like + + align:start position:0% +discuss the macromolecules I really like + + + align:start position:0% +discuss the macromolecules I really like +to start with lipids because of the + + align:start position:0% +to start with lipids because of the + + + align:start position:0% +to start with lipids because of the +membrane bilayer but because their + + align:start position:0% +membrane bilayer but because their + + + align:start position:0% +membrane bilayer but because their +structures are comparatively simple + + align:start position:0% +structures are comparatively simple + + + align:start position:0% +structures are comparatively simple +relative to amino acids and nucleic + + align:start position:0% +relative to amino acids and nucleic + + + align:start position:0% +relative to amino acids and nucleic +acids so we can get a few of the basics + + align:start position:0% +acids so we can get a few of the basics + + + align:start position:0% +acids so we can get a few of the basics +of the chemical structures down and how + + align:start position:0% +of the chemical structures down and how + + + align:start position:0% +of the chemical structures down and how +we render them on paper so that we can + + align:start position:0% +we render them on paper so that we can + + + align:start position:0% +we render them on paper so that we can +do that with lipids which are a little + + align:start position:0% +do that with lipids which are a little + + + align:start position:0% +do that with lipids which are a little +simpler now life to a chemist you have + + align:start position:0% +simpler now life to a chemist you have + + + align:start position:0% +simpler now life to a chemist you have +to sort of worry about this entire mess + + align:start position:0% +to sort of worry about this entire mess + + + align:start position:0% +to sort of worry about this entire mess +of the periodic table but the + + align:start position:0% +of the periodic table but the + + + align:start position:0% +of the periodic table but the +good news for you is for biological + + align:start position:0% +good news for you is for biological + + + align:start position:0% +good news for you is for biological +systems we deal with very focused + + align:start position:0% +systems we deal with very focused + + + align:start position:0% +systems we deal with very focused +components of the periodic table so + + align:start position:0% +components of the periodic table so + + + align:start position:0% +components of the periodic table so +those biological macromolecules are made + + align:start position:0% +those biological macromolecules are made + + + align:start position:0% +those biological macromolecules are made +up largely of only six elements hydrogen + + align:start position:0% +up largely of only six elements hydrogen + + + align:start position:0% +up largely of only six elements hydrogen +carbon nitrogen and oxygen phosphorus + + align:start position:0% +carbon nitrogen and oxygen phosphorus + + + align:start position:0% +carbon nitrogen and oxygen phosphorus +and sulfur so that makes your problem + + align:start position:0% +and sulfur so that makes your problem + + + align:start position:0% +and sulfur so that makes your problem +your the amount of stuff you need to + + align:start position:0% +your the amount of stuff you need to + + + align:start position:0% +your the amount of stuff you need to +know about basic covalent structures way + + align:start position:0% +know about basic covalent structures way + + + align:start position:0% +know about basic covalent structures way +more simple than it is for the average + + align:start position:0% +more simple than it is for the average + + + align:start position:0% +more simple than it is for the average +chemist who has to worry about + + align:start position:0% +chemist who has to worry about + + + align:start position:0% +chemist who has to worry about +everything down here in the nether + + align:start position:0% +everything down here in the nether + + + align:start position:0% +everything down here in the nether +regions and whoops what are you doing + + align:start position:0% +regions and whoops what are you doing + + + align:start position:0% +regions and whoops what are you doing +are the things that are things that are + + align:start position:0% +are the things that are things that are + + + align:start position:0% +are the things that are things that are +radioactive all kinds of other things + + align:start position:0% +radioactive all kinds of other things + + + align:start position:0% +radioactive all kinds of other things +you don't have to worry about any of + + align:start position:0% +you don't have to worry about any of + + + align:start position:0% +you don't have to worry about any of +that so the covalent bonding we will + + align:start position:0% +that so the covalent bonding we will + + + align:start position:0% +that so the covalent bonding we will +talk about is amongst those six + + align:start position:0% +talk about is amongst those six + + + align:start position:0% +talk about is amongst those six +different elements and they make up a + + align:start position:0% +different elements and they make up a + + + align:start position:0% +different elements and they make up a +ninety-eight percent of the cellular + + align:start position:0% +ninety-eight percent of the cellular + + + align:start position:0% +ninety-eight percent of the cellular +mass and then the other components that + + align:start position:0% +mass and then the other components that + + + align:start position:0% +mass and then the other components that +are important in cells are some metal + + align:start position:0% +are important in cells are some metal + + + align:start position:0% +are important in cells are some metal +ions the alkali and alkaline earth my + + align:start position:0% +ions the alkali and alkaline earth my + + + align:start position:0% +ions the alkali and alkaline earth my +elements so sodium magnesium potassium + + align:start position:0% +elements so sodium magnesium potassium + + + align:start position:0% +elements so sodium magnesium potassium +calcium those were all quite important + + align:start position:0% +calcium those were all quite important + + + align:start position:0% +calcium those were all quite important +in life + + align:start position:0% +in life + + + align:start position:0% +in life +and then these transition metal ions + + align:start position:0% +and then these transition metal ions + + + align:start position:0% +and then these transition metal ions +that are really important in enzyme + + align:start position:0% +that are really important in enzyme + + + align:start position:0% +that are really important in enzyme +catalysis for example but we will not + + align:start position:0% +catalysis for example but we will not + + + align:start position:0% +catalysis for example but we will not +cover very much of that but those are + + align:start position:0% +cover very much of that but those are + + + align:start position:0% +cover very much of that but those are +what are known as trace elements that + + align:start position:0% +what are known as trace elements that + + + align:start position:0% +what are known as trace elements that +are very as transition metal elements + + align:start position:0% +are very as transition metal elements + + + align:start position:0% +are very as transition metal elements +that are very important for biochemistry + + align:start position:0% +that are very important for biochemistry + + + align:start position:0% +that are very important for biochemistry +and then last of all there are some + + align:start position:0% +and then last of all there are some + + + align:start position:0% +and then last of all there are some +rogue ones that there's even smaller + + align:start position:0% +rogue ones that there's even smaller + + + align:start position:0% +rogue ones that there's even smaller +amounts in physiologic systems these are + + align:start position:0% +amounts in physiologic systems these are + + + align:start position:0% +amounts in physiologic systems these are +things like chromium molybdenum and + + align:start position:0% +things like chromium molybdenum and + + + align:start position:0% +things like chromium molybdenum and +tungsten selenium and iodine and + + align:start position:0% +tungsten selenium and iodine and + + + align:start position:0% +tungsten selenium and iodine and +although certain of these elements only + + align:start position:0% +although certain of these elements only + + + align:start position:0% +although certain of these elements only +have found in totally bizarre organisms + + align:start position:0% +have found in totally bizarre organisms + + + align:start position:0% +have found in totally bizarre organisms +so for example you and I don't have much + + align:start position:0% +so for example you and I don't have much + + + align:start position:0% +so for example you and I don't have much +molybdenum and tungsten I don't think + + align:start position:0% +molybdenum and tungsten I don't think + + + align:start position:0% +molybdenum and tungsten I don't think +unless it slipped in there by accident + + align:start position:0% +unless it slipped in there by accident + + + align:start position:0% +unless it slipped in there by accident +but you and I definitely need selenium + + align:start position:0% +but you and I definitely need selenium + + + align:start position:0% +but you and I definitely need selenium +and iodine as trace elements does anyone + + align:start position:0% +and iodine as trace elements does anyone + + + align:start position:0% +and iodine as trace elements does anyone +know where iodine comes and figures most + + align:start position:0% +know where iodine comes and figures most + + + align:start position:0% +know where iodine comes and figures most +prominently yeah high right absolutely + + align:start position:0% +prominently yeah high right absolutely + + + align:start position:0% +prominently yeah high right absolutely +so the thyroid hormone is a small + + align:start position:0% +so the thyroid hormone is a small + + + align:start position:0% +so the thyroid hormone is a small +organic molecule with several iodine's + + align:start position:0% +organic molecule with several iodine's + + + align:start position:0% +organic molecule with several iodine's +in it and we need absolutely need iodine + + align:start position:0% +in it and we need absolutely need iodine + + + align:start position:0% +in it and we need absolutely need iodine +in our diets in order to build the + + align:start position:0% +in our diets in order to build the + + + align:start position:0% +in our diets in order to build the +thyroxine hormone the pro that deals + + align:start position:0% +thyroxine hormone the pro that deals + + + align:start position:0% +thyroxine hormone the pro that deals +with a lot of aspects of metabolism + + align:start position:0% +with a lot of aspects of metabolism + + + align:start position:0% +with a lot of aspects of metabolism +we don't need a lot and if we get too + + align:start position:0% +we don't need a lot and if we get too + + + align:start position:0% +we don't need a lot and if we get too +much it's bad for you but we definitely + + align:start position:0% +much it's bad for you but we definitely + + + align:start position:0% +much it's bad for you but we definitely +need traces of these elements now I will + + align:start position:0% +need traces of these elements now I will + + + align:start position:0% +need traces of these elements now I will +spend a very small amount of time just + + align:start position:0% +spend a very small amount of time just + + + align:start position:0% +spend a very small amount of time just +laying down the basics of organic + + align:start position:0% +laying down the basics of organic + + + align:start position:0% +laying down the basics of organic +chemistry bonding now who are view of + + align:start position:0% +chemistry bonding now who are view of + + + align:start position:0% +chemistry bonding now who are view of +either taken the chemistry gir or had + + align:start position:0% +either taken the chemistry gir or had + + + align:start position:0% +either taken the chemistry gir or had +high school chemistry quite recently is + + align:start position:0% +high school chemistry quite recently is + + + align:start position:0% +high school chemistry quite recently is +that pretty much all of you and now if + + align:start position:0% +that pretty much all of you and now if + + + align:start position:0% +that pretty much all of you and now if +you didn't put your hand out don't worry + + align:start position:0% +you didn't put your hand out don't worry + + + align:start position:0% +you didn't put your hand out don't worry +we're here to bring you up to speed if + + align:start position:0% +we're here to bring you up to speed if + + + align:start position:0% +we're here to bring you up to speed if +you need it frankly if you just know + + align:start position:0% +you need it frankly if you just know + + + align:start position:0% +you need it frankly if you just know +what's on the next two or three slides + + align:start position:0% +what's on the next two or three slides + + + align:start position:0% +what's on the next two or three slides +you're in great shape all the + + align:start position:0% +you're in great shape all the + + + align:start position:0% +you're in great shape all the +information that you need has been + + align:start position:0% +information that you need has been + + + align:start position:0% +information that you need has been +condensed but if it's a little bit out + + align:start position:0% +condensed but if it's a little bit out + + + align:start position:0% +condensed but if it's a little bit out +of nowhere you could come see me in + + align:start position:0% +of nowhere you could come see me in + + + align:start position:0% +of nowhere you could come see me in +office hours and I can just run through + + align:start position:0% +office hours and I can just run through + + + align:start position:0% +office hours and I can just run through +things too for you and we can just get + + align:start position:0% +things too for you and we can just get + + + align:start position:0% +things too for you and we can just get +you up to speed there is no need for pre + + align:start position:0% +you up to speed there is no need for pre + + + align:start position:0% +you up to speed there is no need for pre +knowledge I just need an idea of how + + align:start position:0% +knowledge I just need an idea of how + + + align:start position:0% +knowledge I just need an idea of how +much pre knowledge you have so when we + + align:start position:0% +much pre knowledge you have so when we + + + align:start position:0% +much pre knowledge you have so when we +talk about covalent bonding and start to + + align:start position:0% +talk about covalent bonding and start to + + + align:start position:0% +talk about covalent bonding and start to +think about the elements that are + + align:start position:0% +think about the elements that are + + + align:start position:0% +think about the elements that are +critical for life + + align:start position:0% +critical for life + + + align:start position:0% +critical for life +it's important to consider the + + align:start position:0% +it's important to consider the + + + align:start position:0% +it's important to consider the +electronic structures of these elements + + align:start position:0% +electronic structures of these elements + + + align:start position:0% +electronic structures of these elements +and why this why they happen to be the + + align:start position:0% +and why this why they happen to be the + + + align:start position:0% +and why this why they happen to be the +chosen elements okay the most important + + align:start position:0% +chosen elements okay the most important + + + align:start position:0% +chosen elements okay the most important +thing about hydrogen carbon nitrogen + + align:start position:0% +thing about hydrogen carbon nitrogen + + + align:start position:0% +thing about hydrogen carbon nitrogen +oxygen phosphorus and sulfur is they + + align:start position:0% +oxygen phosphorus and sulfur is they + + + align:start position:0% +oxygen phosphorus and sulfur is they +love to make covalent bonds a lot of + + align:start position:0% +love to make covalent bonds a lot of + + + align:start position:0% +love to make covalent bonds a lot of +metal ions form salts + + align:start position:0% +metal ions form salts + + + align:start position:0% +metal ions form salts +you know sodium chloride or many other + + align:start position:0% +you know sodium chloride or many other + + + align:start position:0% +you know sodium chloride or many other +different salts but covalent bonds are + + align:start position:0% +different salts but covalent bonds are + + + align:start position:0% +different salts but covalent bonds are +the main structure of our macromolecules + + align:start position:0% +the main structure of our macromolecules + + + align:start position:0% +the main structure of our macromolecules +strong bonds between elements such as + + align:start position:0% +strong bonds between elements such as + + + align:start position:0% +strong bonds between elements such as +these six in particular these six where + + align:start position:0% +these six in particular these six where + + + align:start position:0% +these six in particular these six where +they share electrons in covalent bonds + + align:start position:0% +they share electrons in covalent bonds + + + align:start position:0% +they share electrons in covalent bonds +rather than form ionic interactions + + align:start position:0% +rather than form ionic interactions + + + align:start position:0% +rather than form ionic interactions +where somebody gives an electron to + + align:start position:0% +where somebody gives an electron to + + + align:start position:0% +where somebody gives an electron to +someone else and you have a plus/minus + + align:start position:0% +someone else and you have a plus/minus + + + align:start position:0% +someone else and you have a plus/minus +type interaction so these shared bonds + + align:start position:0% +type interaction so these shared bonds + + + align:start position:0% +type interaction so these shared bonds +are important for life so it's good to + + align:start position:0% +are important for life so it's good to + + + align:start position:0% +are important for life so it's good to +understand why hydrogen carbon nitrogen + + align:start position:0% +understand why hydrogen carbon nitrogen + + + align:start position:0% +understand why hydrogen carbon nitrogen +and oxygen and then phosphorous and + + align:start position:0% +and oxygen and then phosphorous and + + + align:start position:0% +and oxygen and then phosphorous and +sulfur are so important in order to + + align:start position:0% +sulfur are so important in order to + + + align:start position:0% +sulfur are so important in order to +understand the covalent bonding of these + + align:start position:0% +understand the covalent bonding of these + + + align:start position:0% +understand the covalent bonding of these +elements it's useful to know the + + align:start position:0% +elements it's useful to know the + + + align:start position:0% +elements it's useful to know the +electronic configuration but you could + + align:start position:0% +electronic configuration but you could + + + align:start position:0% +electronic configuration but you could +live without that the most important + + align:start position:0% +live without that the most important + + + align:start position:0% +live without that the most important +thing is that covalent bonds such as the + + align:start position:0% +thing is that covalent bonds such as the + + + align:start position:0% +thing is that covalent bonds such as the +one between carbon and hydrogen here Rep + + align:start position:0% +one between carbon and hydrogen here Rep + + + align:start position:0% +one between carbon and hydrogen here Rep +reflects a + + align:start position:0% +reflects a + + + align:start position:0% +reflects a +pair of electrons one from the hydrogen + + align:start position:0% +pair of electrons one from the hydrogen + + + align:start position:0% +pair of electrons one from the hydrogen +one from the carbon to make a stable + + align:start position:0% +one from the carbon to make a stable + + + align:start position:0% +one from the carbon to make a stable +covalent bond because of its electronic + + align:start position:0% +covalent bond because of its electronic + + + align:start position:0% +covalent bond because of its electronic +configuration carbon is neutral when it + + align:start position:0% +configuration carbon is neutral when it + + + align:start position:0% +configuration carbon is neutral when it +has four covalent bonds nitrogen is + + align:start position:0% +has four covalent bonds nitrogen is + + + align:start position:0% +has four covalent bonds nitrogen is +neutral when it has three covalent bonds + + align:start position:0% +neutral when it has three covalent bonds + + + align:start position:0% +neutral when it has three covalent bonds +but there's an extra lone pair of + + align:start position:0% +but there's an extra lone pair of + + + align:start position:0% +but there's an extra lone pair of +electrons that are not forming bonds in + + align:start position:0% +electrons that are not forming bonds in + + + align:start position:0% +electrons that are not forming bonds in +neutral nitrogen and oxygen is neutral + + align:start position:0% +neutral nitrogen and oxygen is neutral + + + align:start position:0% +neutral nitrogen and oxygen is neutral +when it has two covalent bonds these + + align:start position:0% +when it has two covalent bonds these + + + align:start position:0% +when it has two covalent bonds these +could be with hydrogen they could be + + align:start position:0% +could be with hydrogen they could be + + + align:start position:0% +could be with hydrogen they could be +with carbon they could be with several + + align:start position:0% +with carbon they could be with several + + + align:start position:0% +with carbon they could be with several +of the other elements for carbon we + + align:start position:0% +of the other elements for carbon we + + + align:start position:0% +of the other elements for carbon we +don't deal with charge states of carbon + + align:start position:0% +don't deal with charge states of carbon + + + align:start position:0% +don't deal with charge states of carbon +because they're pretty high energy they + + align:start position:0% +because they're pretty high energy they + + + align:start position:0% +because they're pretty high energy they +may be high energy intermediates in an + + align:start position:0% +may be high energy intermediates in an + + + align:start position:0% +may be high energy intermediates in an +enzyme catalyzed reaction but they're + + align:start position:0% +enzyme catalyzed reaction but they're + + + align:start position:0% +enzyme catalyzed reaction but they're +not sitting there as high energy + + align:start position:0% +not sitting there as high energy + + + align:start position:0% +not sitting there as high energy +intermediates in your macromolecules the + + align:start position:0% +intermediates in your macromolecules the + + + align:start position:0% +intermediates in your macromolecules the +key thing you want to notice is for all + + align:start position:0% +key thing you want to notice is for all + + + align:start position:0% +key thing you want to notice is for all +of these elements surveilance shell is + + align:start position:0% +of these elements surveilance shell is + + + align:start position:0% +of these elements surveilance shell is +complete with eight electrons but these + + align:start position:0% +complete with eight electrons but these + + + align:start position:0% +complete with eight electrons but these +lone pairs and I or bunny is as people + + align:start position:0% +lone pairs and I or bunny is as people + + + align:start position:0% +lone pairs and I or bunny is as people +like to call them really feature very + + align:start position:0% +like to call them really feature very + + + align:start position:0% +like to call them really feature very +prominently in biochemistry and biology + + align:start position:0% +prominently in biochemistry and biology + + + align:start position:0% +prominently in biochemistry and biology +because they are places for hydrogen + + align:start position:0% +because they are places for hydrogen + + + align:start position:0% +because they are places for hydrogen +bonding interactions so we run a lot on + + align:start position:0% +bonding interactions so we run a lot on + + + align:start position:0% +bonding interactions so we run a lot on +electrostatic hydrogen bonding and + + align:start position:0% +electrostatic hydrogen bonding and + + + align:start position:0% +electrostatic hydrogen bonding and +hydrophobic interactions if we know + + align:start position:0% +hydrophobic interactions if we know + + + align:start position:0% +hydrophobic interactions if we know +where the lone pair electrons are we + + align:start position:0% +where the lone pair electrons are we + + + align:start position:0% +where the lone pair electrons are we +know one part of a hydrogen bonding + + align:start position:0% +know one part of a hydrogen bonding + + + align:start position:0% +know one part of a hydrogen bonding +interaction it turns out that in biology + + align:start position:0% +interaction it turns out that in biology + + + align:start position:0% +interaction it turns out that in biology +we're mostly at pH 7 or in that range + + align:start position:0% +we're mostly at pH 7 or in that range + + + align:start position:0% +we're mostly at pH 7 or in that range +except for a few subcellular + + align:start position:0% +except for a few subcellular + + + align:start position:0% +except for a few subcellular +compartments but at pH 8 nitrogen lone + + align:start position:0% +compartments but at pH 8 nitrogen lone + + + align:start position:0% +compartments but at pH 8 nitrogen lone +pair of electrons will pick up a proton + + align:start position:0% +pair of electrons will pick up a proton + + + align:start position:0% +pair of electrons will pick up a proton +to become a positively charged nitrogen + + align:start position:0% +to become a positively charged nitrogen + + + align:start position:0% +to become a positively charged nitrogen +and you'll mostly see that as a + + align:start position:0% +and you'll mostly see that as a + + + align:start position:0% +and you'll mostly see that as a +positively charged so the sidechain of + + align:start position:0% +positively charged so the sidechain of + + + align:start position:0% +positively charged so the sidechain of +lysine which has an NH 3 an NH 2 at the + + align:start position:0% +lysine which has an NH 3 an NH 2 at the + + + align:start position:0% +lysine which has an NH 3 an NH 2 at the +very end of a carbon chain is most + + align:start position:0% +very end of a carbon chain is most + + + align:start position:0% +very end of a carbon chain is most +commonly protonated and positively + + align:start position:0% +commonly protonated and positively + + + align:start position:0% +commonly protonated and positively +charged so it could be involved in an + + align:start position:0% +charged so it could be involved in an + + + align:start position:0% +charged so it could be involved in an +interaction so we can consider both the + + align:start position:0% +interaction so we can consider both the + + + align:start position:0% +interaction so we can consider both the +neutral and the charged positively + + align:start position:0% +neutral and the charged positively + + + align:start position:0% +neutral and the charged positively +charged state of nitrogen for oxygen + + align:start position:0% +charged state of nitrogen for oxygen + + + align:start position:0% +charged state of nitrogen for oxygen +that oxygen lone pair will compete our + + align:start position:0% +that oxygen lone pair will compete our + + + align:start position:0% +that oxygen lone pair will compete our +per proton to form the hydronium ion so + + align:start position:0% +per proton to form the hydronium ion so + + + align:start position:0% +per proton to form the hydronium ion so +that's positively charged o h group so + + align:start position:0% +that's positively charged o h group so + + + align:start position:0% +that's positively charged o h group so +it would have an extra proton using up a + + align:start position:0% +it would have an extra proton using up a + + + align:start position:0% +it would have an extra proton using up a +lone + + align:start position:0% +lone + + + align:start position:0% +lone +hair or and three hydrogen's or it could + + align:start position:0% +hair or and three hydrogen's or it could + + + align:start position:0% +hair or and three hydrogen's or it could +give our per proton to form the + + align:start position:0% +give our per proton to form the + + + align:start position:0% +give our per proton to form the +hydroxide iron and those are the states + + align:start position:0% +hydroxide iron and those are the states + + + align:start position:0% +hydroxide iron and those are the states +of oxygen that are most common so in + + align:start position:0% +of oxygen that are most common so in + + + align:start position:0% +of oxygen that are most common so in +that UV we've kind of dispatched the + + align:start position:0% +that UV we've kind of dispatched the + + + align:start position:0% +that UV we've kind of dispatched the +those first four of the six elements + + align:start position:0% +those first four of the six elements + + + align:start position:0% +those first four of the six elements +phosphorus and sulfur a little tricky + + align:start position:0% +phosphorus and sulfur a little tricky + + + align:start position:0% +phosphorus and sulfur a little tricky +but there is some good news + + align:start position:0% +but there is some good news + + + align:start position:0% +but there is some good news +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +sulfur copies oxygen so you don't really + + align:start position:0% +sulfur copies oxygen so you don't really + + + align:start position:0% +sulfur copies oxygen so you don't really +have to worry too much about sulfur + + align:start position:0% +have to worry too much about sulfur + + + align:start position:0% +have to worry too much about sulfur +you'll just consider it to really be + + align:start position:0% +you'll just consider it to really be + + + align:start position:0% +you'll just consider it to really be +sort of an older sibling of oxygen where + + align:start position:0% +sort of an older sibling of oxygen where + + + align:start position:0% +sort of an older sibling of oxygen where +all the chemistry is very very similar + + align:start position:0% +all the chemistry is very very similar + + + align:start position:0% +all the chemistry is very very similar +sulfur or the negatively charged sulfur + + align:start position:0% +sulfur or the negatively charged sulfur + + + align:start position:0% +sulfur or the negatively charged sulfur +anion are both important phosphorus is + + align:start position:0% +anion are both important phosphorus is + + + align:start position:0% +anion are both important phosphorus is +difference phosphorus does not tend to + + align:start position:0% +difference phosphorus does not tend to + + + align:start position:0% +difference phosphorus does not tend to +show up in the version that copies + + align:start position:0% +show up in the version that copies + + + align:start position:0% +show up in the version that copies +nitrogen it is it is capable of adopting + + align:start position:0% +nitrogen it is it is capable of adopting + + + align:start position:0% +nitrogen it is it is capable of adopting +higher oxidation states and all of the + + align:start position:0% +higher oxidation states and all of the + + + align:start position:0% +higher oxidation states and all of the +phosphorus you meet in biochemistry for + + align:start position:0% +phosphorus you meet in biochemistry for + + + align:start position:0% +phosphorus you meet in biochemistry for +the most part there's a few odd things + + align:start position:0% +the most part there's a few odd things + + + align:start position:0% +the most part there's a few odd things +in weird organisms is going to be in the + + align:start position:0% +in weird organisms is going to be in the + + + align:start position:0% +in weird organisms is going to be in the +form of an oxidized form of phosphorus + + align:start position:0% +form of an oxidized form of phosphorus + + + align:start position:0% +form of an oxidized form of phosphorus +which generally has one two three four + + align:start position:0% +which generally has one two three four + + + align:start position:0% +which generally has one two three four +five bonds to phosphorous it can take on + + align:start position:0% +five bonds to phosphorous it can take on + + + align:start position:0% +five bonds to phosphorous it can take on +a higher oxidation state and you will + + align:start position:0% +a higher oxidation state and you will + + + align:start position:0% +a higher oxidation state and you will +see phosphorus phosphorus in the + + align:start position:0% +see phosphorus phosphorus in the + + + align:start position:0% +see phosphorus phosphorus in the +phosphate form is absolutely essential + + align:start position:0% +phosphate form is absolutely essential + + + align:start position:0% +phosphate form is absolutely essential +to life but it's the place where we + + align:start position:0% +to life but it's the place where we + + + align:start position:0% +to life but it's the place where we +store a ton of reactivity for the + + align:start position:0% +store a ton of reactivity for the + + + align:start position:0% +store a ton of reactivity for the +reactions of nucleotides adenosine + + align:start position:0% +reactions of nucleotides adenosine + + + align:start position:0% +reactions of nucleotides adenosine +triphosphate adenosine diphosphate the + + align:start position:0% +triphosphate adenosine diphosphate the + + + align:start position:0% +triphosphate adenosine diphosphate the +phosphodiester backbone in nucleic acids + + align:start position:0% +phosphodiester backbone in nucleic acids + + + align:start position:0% +phosphodiester backbone in nucleic acids +phosphorylation of amino acids to form + + align:start position:0% +phosphorylation of amino acids to form + + + align:start position:0% +phosphorylation of amino acids to form +phosphoproteins it's always in this + + align:start position:0% +phosphoproteins it's always in this + + + align:start position:0% +phosphoproteins it's always in this +state with all the XD extra oxygens and + + align:start position:0% +state with all the XD extra oxygens and + + + align:start position:0% +state with all the XD extra oxygens and +that that configuration of bonds okay if + + align:start position:0% +that that configuration of bonds okay if + + + align:start position:0% +that that configuration of bonds okay if +you know this you've got a lot of the + + align:start position:0% +you know this you've got a lot of the + + + align:start position:0% +you know this you've got a lot of the +covalent bonds under control so any + + align:start position:0% +covalent bonds under control so any + + + align:start position:0% +covalent bonds under control so any +questions about this is everyone all + + align:start position:0% +questions about this is everyone all + + + align:start position:0% +questions about this is everyone all +right I know it might be it's probably a + + align:start position:0% +right I know it might be it's probably a + + + align:start position:0% +right I know it might be it's probably a +refresher for most of you the next thing + + align:start position:0% +refresher for most of you the next thing + + + align:start position:0% +refresher for most of you the next thing +I just briefly want to mention is the + + align:start position:0% +I just briefly want to mention is the + + + align:start position:0% +I just briefly want to mention is the +most typical functional groups that + + align:start position:0% +most typical functional groups that + + + align:start position:0% +most typical functional groups that +occur in biological molecules + + align:start position:0% + + + + align:start position:0% + +and you may say well what does it mean + + align:start position:0% +and you may say well what does it mean + + + align:start position:0% +and you may say well what does it mean +functional group usually it's a place + + align:start position:0% +functional group usually it's a place + + + align:start position:0% +functional group usually it's a place +where the action happens if you have a + + align:start position:0% +where the action happens if you have a + + + align:start position:0% +where the action happens if you have a +large molecule that's a bunch of carbon + + align:start position:0% +large molecule that's a bunch of carbon + + + align:start position:0% +large molecule that's a bunch of carbon +carbon and carbon hydrogen covalent + + align:start position:0% +carbon and carbon hydrogen covalent + + + align:start position:0% +carbon and carbon hydrogen covalent +bonds there's not a lot going on unless + + align:start position:0% +bonds there's not a lot going on unless + + + align:start position:0% +bonds there's not a lot going on unless +you can really rip those bonds apart but + + align:start position:0% +you can really rip those bonds apart but + + + align:start position:0% +you can really rip those bonds apart but +they're high energy but functional + + align:start position:0% +they're high energy but functional + + + align:start position:0% +they're high energy but functional +groups are often times where chemistry + + align:start position:0% +groups are often times where chemistry + + + align:start position:0% +groups are often times where chemistry +happens or biochemistry happens so + + align:start position:0% +happens or biochemistry happens so + + + align:start position:0% +happens or biochemistry happens so +there's the Oh H hydroxyl we as chemists + + align:start position:0% +there's the Oh H hydroxyl we as chemists + + + align:start position:0% +there's the Oh H hydroxyl we as chemists +and biochemists will tend to use an R + + align:start position:0% +and biochemists will tend to use an R + + + align:start position:0% +and biochemists will tend to use an R +where we mean something else + + align:start position:0% +where we mean something else + + + align:start position:0% +where we mean something else +so we don't write out a whole structure + + align:start position:0% +so we don't write out a whole structure + + + align:start position:0% +so we don't write out a whole structure +we would just put our Ohi manage us say + + align:start position:0% +we would just put our Ohi manage us say + + + align:start position:0% +we would just put our Ohi manage us say +anything so for example if R was ch3 ch2 + + align:start position:0% +anything so for example if R was ch3 ch2 + + + align:start position:0% +anything so for example if R was ch3 ch2 +you would have ethanol so but but I'm + + align:start position:0% +you would have ethanol so but but I'm + + + align:start position:0% +you would have ethanol so but but I'm +keeping it more generic the next + + align:start position:0% +keeping it more generic the next + + + align:start position:0% +keeping it more generic the next +functional group that is important is + + align:start position:0% +functional group that is important is + + + align:start position:0% +functional group that is important is +the carboxylate group or the carboxyl + + align:start position:0% +the carboxylate group or the carboxyl + + + align:start position:0% +the carboxylate group or the carboxyl +group looks like this now when we look + + align:start position:0% +group looks like this now when we look + + + align:start position:0% +group looks like this now when we look +at these molecules you always want to + + align:start position:0% +at these molecules you always want to + + + align:start position:0% +at these molecules you always want to +sort of think where the lone pair + + align:start position:0% +sort of think where the lone pair + + + align:start position:0% +sort of think where the lone pair +electrons are there's two on oxygen - on + + align:start position:0% +electrons are there's two on oxygen - on + + + align:start position:0% +electrons are there's two on oxygen - on +oxygen - on oxygen so that actually + + align:start position:0% +oxygen - on oxygen so that actually + + + align:start position:0% +oxygen - on oxygen so that actually +shows you where the rest of the + + align:start position:0% +shows you where the rest of the + + + align:start position:0% +shows you where the rest of the +electrons are this is the carboxyl group + + align:start position:0% + + + + align:start position:0% + +but in nature in physiologic systems + + align:start position:0% +but in nature in physiologic systems + + + align:start position:0% +but in nature in physiologic systems +this shows up most commonly in its + + align:start position:0% +this shows up most commonly in its + + + align:start position:0% +this shows up most commonly in its +anionic form that's important because + + align:start position:0% +anionic form that's important because + + + align:start position:0% +anionic form that's important because +when we start to think of interactions + + align:start position:0% +when we start to think of interactions + + + align:start position:0% +when we start to think of interactions +between enzymes and their substrates or + + align:start position:0% +between enzymes and their substrates or + + + align:start position:0% +between enzymes and their substrates or +the folding of proteins were thinking of + + align:start position:0% +the folding of proteins were thinking of + + + align:start position:0% +the folding of proteins were thinking of +something with a negative charge not a + + align:start position:0% +something with a negative charge not a + + + align:start position:0% +something with a negative charge not a +neutral so this group loses a proton to + + align:start position:0% +neutral so this group loses a proton to + + + align:start position:0% +neutral so this group loses a proton to +form the carboxylate group and if you + + align:start position:0% +form the carboxylate group and if you + + + align:start position:0% +form the carboxylate group and if you +want to know where the lone pairs are + + align:start position:0% +want to know where the lone pairs are + + + align:start position:0% +want to know where the lone pairs are +now that's what they look like so those + + align:start position:0% +now that's what they look like so those + + + align:start position:0% +now that's what they look like so those +are two of the key ones let's now go to + + align:start position:0% +are two of the key ones let's now go to + + + align:start position:0% +are two of the key ones let's now go to +nitrogen + + align:start position:0% + + + + align:start position:0% + +that is the neutral Ameen but as I just + + align:start position:0% +that is the neutral Ameen but as I just + + + align:start position:0% +that is the neutral Ameen but as I just +mentioned to you that will very commonly + + align:start position:0% +mentioned to you that will very commonly + + + align:start position:0% +mentioned to you that will very commonly +pick up a proton and be in the + + align:start position:0% +pick up a proton and be in the + + + align:start position:0% +pick up a proton and be in the +positively charged date now when I show + + align:start position:0% +positively charged date now when I show + + + align:start position:0% +positively charged date now when I show +you both of those guys in the positively + + align:start position:0% +you both of those guys in the positively + + + align:start position:0% +you both of those guys in the positively +charged State what you could immediately + + align:start position:0% +charged State what you could immediately + + + align:start position:0% +charged State what you could immediately +tell me is that if I have an amino acid + + align:start position:0% +tell me is that if I have an amino acid + + + align:start position:0% +tell me is that if I have an amino acid +with one of these groups and a nearby + + align:start position:0% +with one of these groups and a nearby + + + align:start position:0% +with one of these groups and a nearby +amino acid with one of these groups they + + align:start position:0% +amino acid with one of these groups they + + + align:start position:0% +amino acid with one of these groups they +could form an electrostatic interaction + + align:start position:0% +could form an electrostatic interaction + + + align:start position:0% +could form an electrostatic interaction +between themselves plus and minus + + align:start position:0% +between themselves plus and minus + + + align:start position:0% +between themselves plus and minus +complimenting each other so if you know + + align:start position:0% +complimenting each other so if you know + + + align:start position:0% +complimenting each other so if you know +the charged States you're much better + + align:start position:0% +the charged States you're much better + + + align:start position:0% +the charged States you're much better +off because you can tell where where + + align:start position:0% +off because you can tell where where + + + align:start position:0% +off because you can tell where where +non-covalent types of ionic or + + align:start position:0% +non-covalent types of ionic or + + + align:start position:0% +non-covalent types of ionic or +electrostatic interactions occur so + + align:start position:0% +electrostatic interactions occur so + + + align:start position:0% +electrostatic interactions occur so +these are very important then there's + + align:start position:0% +these are very important then there's + + + align:start position:0% +these are very important then there's +the phosphate group it's often ionized + + align:start position:0% +the phosphate group it's often ionized + + + align:start position:0% +the phosphate group it's often ionized +and the sulfhydryl group so phosphate + + align:start position:0% + + + + align:start position:0% + +the sulfhydryl group is also called the + + align:start position:0% +the sulfhydryl group is also called the + + + align:start position:0% +the sulfhydryl group is also called the +file group and i'm sure i've spelt that + + align:start position:0% +file group and i'm sure i've spelt that + + + align:start position:0% +file group and i'm sure i've spelt that +wrong because hydral they look like that + + align:start position:0% +wrong because hydral they look like that + + + align:start position:0% +wrong because hydral they look like that +and the most common state are the South + + align:start position:0% +and the most common state are the South + + + align:start position:0% +and the most common state are the South +hydral or not the most common can also + + align:start position:0% +hydral or not the most common can also + + + align:start position:0% +hydral or not the most common can also +appear as the anionic structure so + + align:start position:0% +appear as the anionic structure so + + + align:start position:0% +appear as the anionic structure so +that's the basic functional groups now + + align:start position:0% +that's the basic functional groups now + + + align:start position:0% +that's the basic functional groups now +there are two more functional group + + align:start position:0% +there are two more functional group + + + align:start position:0% +there are two more functional group +assemblies that you will see a lot in + + align:start position:0% +assemblies that you will see a lot in + + + align:start position:0% +assemblies that you will see a lot in +physiologic systems that are basically + + align:start position:0% +physiologic systems that are basically + + + align:start position:0% +physiologic systems that are basically +composites of some of these structures + + align:start position:0% +composites of some of these structures + + + align:start position:0% +composites of some of these structures +because when we have single building + + align:start position:0% +because when we have single building + + + align:start position:0% +because when we have single building +blocks we need to join them to each + + align:start position:0% +blocks we need to join them to each + + + align:start position:0% +blocks we need to join them to each +other through different types of + + align:start position:0% +other through different types of + + + align:start position:0% +other through different types of +chemistry's so I want to show you the + + align:start position:0% +chemistry's so I want to show you the + + + align:start position:0% +chemistry's so I want to show you the +types of chemistry that you get by + + align:start position:0% +types of chemistry that you get by + + + align:start position:0% +types of chemistry that you get by +forming a composite the height of a + + align:start position:0% +forming a composite the height of a + + + align:start position:0% +forming a composite the height of a +hydroxyl and the carboxyl group and a + + align:start position:0% +hydroxyl and the carboxyl group and a + + + align:start position:0% +hydroxyl and the carboxyl group and a +composite of a carboxyl group and in the + + align:start position:0% +composite of a carboxyl group and in the + + + align:start position:0% +composite of a carboxyl group and in the +mid because the polymer that's the + + align:start position:0% +mid because the polymer that's the + + + align:start position:0% +mid because the polymer that's the +protein polymer has building + + align:start position:0% +protein polymer has building + + + align:start position:0% +protein polymer has building +blocks that have a means and carboxyls + + align:start position:0% +blocks that have a means and carboxyls + + + align:start position:0% +blocks that have a means and carboxyls +but they're all put together into a + + align:start position:0% +but they're all put together into a + + + align:start position:0% +but they're all put together into a +polymeric structure where those groups + + align:start position:0% +polymeric structure where those groups + + + align:start position:0% +polymeric structure where those groups +have been joined in a condensation + + align:start position:0% +have been joined in a condensation + + + align:start position:0% +have been joined in a condensation +polymer so let me just show you what + + align:start position:0% +polymer so let me just show you what + + + align:start position:0% +polymer so let me just show you what +those look like and then we'll be done + + align:start position:0% +those look like and then we'll be done + + + align:start position:0% +those look like and then we'll be done +with the functional groups so there are + + align:start position:0% + + + + align:start position:0% + +the first one because I've drawn them in + + align:start position:0% +the first one because I've drawn them in + + + align:start position:0% +the first one because I've drawn them in +this order okay + + align:start position:0% +this order okay + + + align:start position:0% +this order okay +it's the amide and the other one + + align:start position:0% + + + + align:start position:0% + +is the esta when you do these two + + align:start position:0% +is the esta when you do these two + + + align:start position:0% +is the esta when you do these two +reactions if you do them in the lab + + align:start position:0% +reactions if you do them in the lab + + + align:start position:0% +reactions if you do them in the lab +they're called condensation reactions + + align:start position:0% +they're called condensation reactions + + + align:start position:0% +they're called condensation reactions +because as you form that bond you pick + + align:start position:0% +because as you form that bond you pick + + + align:start position:0% +because as you form that bond you pick +out a molecule of water these are really + + align:start position:0% +out a molecule of water these are really + + + align:start position:0% +out a molecule of water these are really +important new functional groups to you + + align:start position:0% +important new functional groups to you + + + align:start position:0% +important new functional groups to you +because your proteins are held together + + align:start position:0% +because your proteins are held together + + + align:start position:0% +because your proteins are held together +by a made groups in fact they're so + + align:start position:0% +by a made groups in fact they're so + + + align:start position:0% +by a made groups in fact they're so +important in proteins we often call them + + align:start position:0% +important in proteins we often call them + + + align:start position:0% +important in proteins we often call them +peptide groups you'll see more about + + align:start position:0% +peptide groups you'll see more about + + + align:start position:0% +peptide groups you'll see more about +that on Monday and the esters are really + + align:start position:0% +that on Monday and the esters are really + + + align:start position:0% +that on Monday and the esters are really +important for example in derivatives of + + align:start position:0% +important for example in derivatives of + + + align:start position:0% +important for example in derivatives of +glycerol that make fatty acids or + + align:start position:0% +glycerol that make fatty acids or + + + align:start position:0% +glycerol that make fatty acids or +phospholipids you'll see esters + + align:start position:0% +phospholipids you'll see esters + + + align:start position:0% +phospholipids you'll see esters +occurring again and again the other + + align:start position:0% +occurring again and again the other + + + align:start position:0% +occurring again and again the other +composite group that you can also see is + + align:start position:0% +composite group that you can also see is + + + align:start position:0% +composite group that you can also see is +with the phosphate plus an alcohol and + + align:start position:0% +with the phosphate plus an alcohol and + + + align:start position:0% +with the phosphate plus an alcohol and +what that group looks like is as follows + + align:start position:0% +what that group looks like is as follows + + + align:start position:0% +what that group looks like is as follows +and you're going to see this sort of + + align:start position:0% +and you're going to see this sort of + + + align:start position:0% +and you're going to see this sort of +endlessly in nucleic acids let's keep + + align:start position:0% +endlessly in nucleic acids let's keep + + + align:start position:0% +endlessly in nucleic acids let's keep +the charges all even here and this is + + align:start position:0% +the charges all even here and this is + + + align:start position:0% +the charges all even here and this is +what's known as the phosphate ester okay + + align:start position:0% +what's known as the phosphate ester okay + + + align:start position:0% +what's known as the phosphate ester okay +and that is yet another condensation + + align:start position:0% +and that is yet another condensation + + + align:start position:0% +and that is yet another condensation +where you kick out water alright so + + align:start position:0% +where you kick out water alright so + + + align:start position:0% +where you kick out water alright so +let's just run back to this image and we + + align:start position:0% +let's just run back to this image and we + + + align:start position:0% +let's just run back to this image and we +can sum it all up those are all the + + align:start position:0% +can sum it all up those are all the + + + align:start position:0% +can sum it all up those are all the +groups that I just described to you and + + align:start position:0% +groups that I just described to you and + + + align:start position:0% +groups that I just described to you and +if you want you can go back and put lone + + align:start position:0% +if you want you can go back and put lone + + + align:start position:0% +if you want you can go back and put lone +pairs of electrons on everything and + + align:start position:0% +pairs of electrons on everything and + + + align:start position:0% +pairs of electrons on everything and +then the composite groups that I want to + + align:start position:0% +then the composite groups that I want to + + + align:start position:0% +then the composite groups that I want to +mention to you in particular are the + + align:start position:0% +mention to you in particular are the + + + align:start position:0% +mention to you in particular are the +amide and the ester and they're very + + align:start position:0% +amide and the ester and they're very + + + align:start position:0% +amide and the ester and they're very +important in physiologic systems they + + align:start position:0% +important in physiologic systems they + + + align:start position:0% +important in physiologic systems they +are the bond that holds together the + + align:start position:0% +are the bond that holds together the + + + align:start position:0% +are the bond that holds together the +biopolymer in many cases not shown him + + align:start position:0% +biopolymer in many cases not shown him + + + align:start position:0% +biopolymer in many cases not shown him +on this picture is the phosphate ester + + align:start position:0% +on this picture is the phosphate ester + + + align:start position:0% +on this picture is the phosphate ester +i've added that + + align:start position:0% +i've added that + + + align:start position:0% +i've added that +this year because it's kind of important + + align:start position:0% +this year because it's kind of important + + + align:start position:0% +this year because it's kind of important +is a similar condensation reaction + + align:start position:0% +is a similar condensation reaction + + + align:start position:0% +is a similar condensation reaction +between phosphorus and an alcohol and + + align:start position:0% +between phosphorus and an alcohol and + + + align:start position:0% +between phosphorus and an alcohol and +that in particular is what the bond + + align:start position:0% +that in particular is what the bond + + + align:start position:0% +that in particular is what the bond +you'll see that holds together nucleic + + align:start position:0% +you'll see that holds together nucleic + + + align:start position:0% +you'll see that holds together nucleic +acids and now one sort of thing that we + + align:start position:0% +acids and now one sort of thing that we + + + align:start position:0% +acids and now one sort of thing that we +won't go into a lot of detail I want you + + align:start position:0% +won't go into a lot of detail I want you + + + align:start position:0% +won't go into a lot of detail I want you +to notice that this nitrogen here has a + + align:start position:0% +to notice that this nitrogen here has a + + + align:start position:0% +to notice that this nitrogen here has a +lone pair of electrons it picks up a + + align:start position:0% +lone pair of electrons it picks up a + + + align:start position:0% +lone pair of electrons it picks up a +proton very readily the amide nitrogen + + align:start position:0% +proton very readily the amide nitrogen + + + align:start position:0% +proton very readily the amide nitrogen +is not so willing to pick up a proton + + align:start position:0% +is not so willing to pick up a proton + + + align:start position:0% +is not so willing to pick up a proton +because it messes up the rest of its + + align:start position:0% +because it messes up the rest of its + + + align:start position:0% +because it messes up the rest of its +chemistry so that nitrogen in an ami + + align:start position:0% +chemistry so that nitrogen in an ami + + + align:start position:0% +chemistry so that nitrogen in an ami +tends to be observed as a neutral + + align:start position:0% +tends to be observed as a neutral + + + align:start position:0% +tends to be observed as a neutral +however that hydrogen can be involved in + + align:start position:0% +however that hydrogen can be involved in + + + align:start position:0% +however that hydrogen can be involved in +hydrogen bonds ok any questions about + + align:start position:0% +hydrogen bonds ok any questions about + + + align:start position:0% +hydrogen bonds ok any questions about +that before we move on to non covalent + + align:start position:0% +that before we move on to non covalent + + + align:start position:0% +that before we move on to non covalent +bonds it's everything clear now I try to + + align:start position:0% +bonds it's everything clear now I try to + + + align:start position:0% +bonds it's everything clear now I try to +put everything in one place so you have + + align:start position:0% +put everything in one place so you have + + + align:start position:0% +put everything in one place so you have +it in front of you what I've put on + + align:start position:0% +it in front of you what I've put on + + + align:start position:0% +it in front of you what I've put on +those two slides is what you need to + + align:start position:0% +those two slides is what you need to + + + align:start position:0% +those two slides is what you need to +know about organic covalent bonding it + + align:start position:0% +know about organic covalent bonding it + + + align:start position:0% +know about organic covalent bonding it +doesn't go beyond it this I will say + + align:start position:0% +doesn't go beyond it this I will say + + + align:start position:0% +doesn't go beyond it this I will say +there's a tiny bit of memorization but + + align:start position:0% +there's a tiny bit of memorization but + + + align:start position:0% +there's a tiny bit of memorization but +once you commit that stuff to memory you + + align:start position:0% +once you commit that stuff to memory you + + + align:start position:0% +once you commit that stuff to memory you +know you're in a good place with respect + + align:start position:0% +know you're in a good place with respect + + + align:start position:0% +know you're in a good place with respect +to understanding how the molecules of + + align:start position:0% +to understanding how the molecules of + + + align:start position:0% +to understanding how the molecules of +life were put together ok yeah what is + + align:start position:0% +life were put together ok yeah what is + + + align:start position:0% +life were put together ok yeah what is +more important to me once we've put + + align:start position:0% +more important to me once we've put + + + align:start position:0% +more important to me once we've put +those structures in place is non + + align:start position:0% +those structures in place is non + + + align:start position:0% +those structures in place is non +covalent bonding + + align:start position:0% + + + + align:start position:0% + +because to mean on covalent bonding is + + align:start position:0% +because to mean on covalent bonding is + + + align:start position:0% +because to mean on covalent bonding is +synonymous with dynamics courses that + + align:start position:0% +synonymous with dynamics courses that + + + align:start position:0% +synonymous with dynamics courses that +can be readily broken and reassembled + + align:start position:0% +can be readily broken and reassembled + + + align:start position:0% +can be readily broken and reassembled +broken and reassembled the energy the + + align:start position:0% +broken and reassembled the energy the + + + align:start position:0% +broken and reassembled the energy the +strength of a typical bond between two + + align:start position:0% +strength of a typical bond between two + + + align:start position:0% +strength of a typical bond between two +carbons or a carbon and hydrogen is on + + align:start position:0% +carbons or a carbon and hydrogen is on + + + align:start position:0% +carbons or a carbon and hydrogen is on +the order of 90 to 100 kilocalories per + + align:start position:0% +the order of 90 to 100 kilocalories per + + + align:start position:0% +the order of 90 to 100 kilocalories per +mole it takes a lot to break those bonds + + align:start position:0% +mole it takes a lot to break those bonds + + + align:start position:0% +mole it takes a lot to break those bonds +we can't break them at will to go and do + + align:start position:0% +we can't break them at will to go and do + + + align:start position:0% +we can't break them at will to go and do +some biological activity but the range + + align:start position:0% +some biological activity but the range + + + align:start position:0% +some biological activity but the range +of energies of the non covalent bonds + + align:start position:0% +of energies of the non covalent bonds + + + align:start position:0% +of energies of the non covalent bonds +are far more modest they range from so + + align:start position:0% +are far more modest they range from so + + + align:start position:0% +are far more modest they range from so +this is covalent but the non covalent + + align:start position:0% +this is covalent but the non covalent + + + align:start position:0% +this is covalent but the non covalent +ranged from one maybe to about 10 + + align:start position:0% +ranged from one maybe to about 10 + + + align:start position:0% +ranged from one maybe to about 10 +kilocalories per mole + + align:start position:0% +kilocalories per mole + + + align:start position:0% +kilocalories per mole +so when you think about those forces + + align:start position:0% +so when you think about those forces + + + align:start position:0% +so when you think about those forces +they're readily broken and made broken + + align:start position:0% +they're readily broken and made broken + + + align:start position:0% +they're readily broken and made broken +and made and what's so amazing about + + align:start position:0% +and made and what's so amazing about + + + align:start position:0% +and made and what's so amazing about +protein and nucleic acid structure is + + align:start position:0% +protein and nucleic acid structure is + + + align:start position:0% +protein and nucleic acid structure is +that you can you can gradually break a + + align:start position:0% +that you can you can gradually break a + + + align:start position:0% +that you can you can gradually break a +bond while you're making another non + + align:start position:0% +bond while you're making another non + + + align:start position:0% +bond while you're making another non +covalent bond so you can have the + + align:start position:0% +covalent bond so you can have the + + + align:start position:0% +covalent bond so you can have the +dynamics of the structure that define a + + align:start position:0% +dynamics of the structure that define a + + + align:start position:0% +dynamics of the structure that define a +lot of its functional properties because + + align:start position:0% +lot of its functional properties because + + + align:start position:0% +lot of its functional properties because +structures are dynamic an enzyme that's + + align:start position:0% +structures are dynamic an enzyme that's + + + align:start position:0% +structures are dynamic an enzyme that's +a composite of a lot of non covalent + + align:start position:0% +a composite of a lot of non covalent + + + align:start position:0% +a composite of a lot of non covalent +interaction combined a substrate can + + align:start position:0% +interaction combined a substrate can + + + align:start position:0% +interaction combined a substrate can +gradually form a set of covalent bonds + + align:start position:0% +gradually form a set of covalent bonds + + + align:start position:0% +gradually form a set of covalent bonds +with that substrate but then can start + + align:start position:0% +with that substrate but then can start + + + align:start position:0% +with that substrate but then can start +changing in the shape of that structure + + align:start position:0% +changing in the shape of that structure + + + align:start position:0% +changing in the shape of that structure +and that shape in order to go through a + + align:start position:0% +and that shape in order to go through a + + + align:start position:0% +and that shape in order to go through a +catalytic cycle to do chemistry and then + + align:start position:0% +catalytic cycle to do chemistry and then + + + align:start position:0% +catalytic cycle to do chemistry and then +to liberate products that is all driven + + align:start position:0% +to liberate products that is all driven + + + align:start position:0% +to liberate products that is all driven +by changes in covalent bonding non + + align:start position:0% +by changes in covalent bonding non + + + align:start position:0% +by changes in covalent bonding non +covalent bonding subtle changes that + + align:start position:0% +covalent bonding subtle changes that + + + align:start position:0% +covalent bonding subtle changes that +occur without big energy barriers that + + align:start position:0% +occur without big energy barriers that + + + align:start position:0% +occur without big energy barriers that +would be necessary to break the non + + align:start position:0% +would be necessary to break the non + + + align:start position:0% +would be necessary to break the non +covalent partner covalent bonds so shown + + align:start position:0% +covalent partner covalent bonds so shown + + + align:start position:0% +covalent partner covalent bonds so shown +at the top here you see the average bond + + align:start position:0% +at the top here you see the average bond + + + align:start position:0% +at the top here you see the average bond +energy of covalent bonds the small + + align:start position:0% +energy of covalent bonds the small + + + align:start position:0% +energy of covalent bonds the small +number is something for example between + + align:start position:0% +number is something for example between + + + align:start position:0% +number is something for example between +two chlorines that's a pretty weak bond + + align:start position:0% +two chlorines that's a pretty weak bond + + + align:start position:0% +two chlorines that's a pretty weak bond +but of course we + + align:start position:0% +but of course we + + + align:start position:0% +but of course we +have a lot of them running around so + + align:start position:0% +have a lot of them running around so + + + align:start position:0% +have a lot of them running around so +really carbon hydrogen carbon carbon + + align:start position:0% +really carbon hydrogen carbon carbon + + + align:start position:0% +really carbon hydrogen carbon carbon +they're at the higher end there about a + + align:start position:0% +they're at the higher end there about a + + + align:start position:0% +they're at the higher end there about a +hundred kilocalories 80 kilocalories per + + align:start position:0% +hundred kilocalories 80 kilocalories per + + + align:start position:0% +hundred kilocalories 80 kilocalories per +mole the other important interactions + + align:start position:0% +mole the other important interactions + + + align:start position:0% +mole the other important interactions +though that make up the non covalent + + align:start position:0% +though that make up the non covalent + + + align:start position:0% +though that make up the non covalent +interactions are as follows so the first + + align:start position:0% +interactions are as follows so the first + + + align:start position:0% +interactions are as follows so the first +important one is the ionic bond it is + + align:start position:0% +important one is the ionic bond it is + + + align:start position:0% +important one is the ionic bond it is +also called a salt bridge or an + + align:start position:0% +also called a salt bridge or an + + + align:start position:0% +also called a salt bridge or an +electrostatic interaction why we give + + align:start position:0% +electrostatic interaction why we give + + + align:start position:0% +electrostatic interaction why we give +three names for this probably comes from + + align:start position:0% +three names for this probably comes from + + + align:start position:0% +three names for this probably comes from +which which type of chemists decided to + + align:start position:0% +which which type of chemists decided to + + + align:start position:0% +which which type of chemists decided to +define them they are all the same things + + align:start position:0% +define them they are all the same things + + + align:start position:0% +define them they are all the same things +they are basically interactions between + + align:start position:0% +they are basically interactions between + + + align:start position:0% +they are basically interactions between +a positively charged entity a protonated + + align:start position:0% +a positively charged entity a protonated + + + align:start position:0% +a positively charged entity a protonated +amine and a negatively charged entity a + + align:start position:0% +amine and a negatively charged entity a + + + align:start position:0% +amine and a negatively charged entity a +deprotonated carboxylate those are about + + align:start position:0% +deprotonated carboxylate those are about + + + align:start position:0% +deprotonated carboxylate those are about +the strongest of the non covalent bonds + + align:start position:0% +the strongest of the non covalent bonds + + + align:start position:0% +the strongest of the non covalent bonds +but it's very variable because it + + align:start position:0% +but it's very variable because it + + + align:start position:0% +but it's very variable because it +depends a lot on their environment + + align:start position:0% +depends a lot on their environment + + + align:start position:0% +depends a lot on their environment +if those two entities are in a + + align:start position:0% +if those two entities are in a + + + align:start position:0% +if those two entities are in a +hydrophobic environment they're gonna + + align:start position:0% +hydrophobic environment they're gonna + + + align:start position:0% +hydrophobic environment they're gonna +charge right for each other to form a + + align:start position:0% +charge right for each other to form a + + + align:start position:0% +charge right for each other to form a +strong electrostatic interaction but if + + align:start position:0% +strong electrostatic interaction but if + + + align:start position:0% +strong electrostatic interaction but if +those are out in water each of those + + align:start position:0% +those are out in water each of those + + + align:start position:0% +those are out in water each of those +groups could be solvated by water and + + align:start position:0% +groups could be solvated by water and + + + align:start position:0% +groups could be solvated by water and +they'd have to give up salvation in + + align:start position:0% +they'd have to give up salvation in + + + align:start position:0% +they'd have to give up salvation in +order to form a good electrostatic + + align:start position:0% +order to form a good electrostatic + + + align:start position:0% +order to form a good electrostatic +interaction when we talk about protein + + align:start position:0% +interaction when we talk about protein + + + align:start position:0% +interaction when we talk about protein +folding we'll go into that in a little + + align:start position:0% +folding we'll go into that in a little + + + align:start position:0% +folding we'll go into that in a little +bit more detail so the reason why this + + align:start position:0% +bit more detail so the reason why this + + + align:start position:0% +bit more detail so the reason why this +says very variable is not to drive you + + align:start position:0% +says very variable is not to drive you + + + align:start position:0% +says very variable is not to drive you +crazy it's just they're very variable + + align:start position:0% +crazy it's just they're very variable + + + align:start position:0% +crazy it's just they're very variable +and they're but they will still range I + + align:start position:0% +and they're but they will still range I + + + align:start position:0% +and they're but they will still range I +would say from 2 to 10 kilocalories so + + align:start position:0% +would say from 2 to 10 kilocalories so + + + align:start position:0% +would say from 2 to 10 kilocalories so +those are important easy to pick out the + + align:start position:0% +those are important easy to pick out the + + + align:start position:0% +those are important easy to pick out the +strongest of the set if dr. a gives you + + align:start position:0% +strongest of the set if dr. a gives you + + + align:start position:0% +strongest of the set if dr. a gives you +a problem set and starts asking you to + + align:start position:0% +a problem set and starts asking you to + + + align:start position:0% +a problem set and starts asking you to +pick out non covalent interactions + + align:start position:0% +pick out non covalent interactions + + + align:start position:0% +pick out non covalent interactions +that's the one you you take care of + + align:start position:0% +that's the one you you take care of + + + align:start position:0% +that's the one you you take care of +straight away because it is the most + + align:start position:0% +straight away because it is the most + + + align:start position:0% +straight away because it is the most +obvious the next most important though + + align:start position:0% +obvious the next most important though + + + align:start position:0% +obvious the next most important though +is the hydrogen bond now + + align:start position:0% + + + + align:start position:0% + +hydrogen bonds have been known to + + align:start position:0% +hydrogen bonds have been known to + + + align:start position:0% +hydrogen bonds have been known to +mystified people for years because + + align:start position:0% +mystified people for years because + + + align:start position:0% +mystified people for years because +people are how do I pick these things + + align:start position:0% +people are how do I pick these things + + + align:start position:0% +people are how do I pick these things +out how do I pick things things out I'm + + align:start position:0% +out how do I pick things things out I'm + + + align:start position:0% +out how do I pick things things out I'm +going to give you a foolproof way of + + align:start position:0% +going to give you a foolproof way of + + + align:start position:0% +going to give you a foolproof way of +picking out hydrogen bonds so you will + + align:start position:0% +picking out hydrogen bonds so you will + + + align:start position:0% +picking out hydrogen bonds so you will +never be at a loss for hydrogen bonds + + align:start position:0% +never be at a loss for hydrogen bonds + + + align:start position:0% +never be at a loss for hydrogen bonds +okay well how do we recognize them they + + align:start position:0% +okay well how do we recognize them they + + + align:start position:0% +okay well how do we recognize them they +are between hydrogen's that are on + + align:start position:0% +are between hydrogen's that are on + + + align:start position:0% +are between hydrogen's that are on +electronegative elements such as oxygen + + align:start position:0% + + + + align:start position:0% + +of course there's other things attached + + align:start position:0% +of course there's other things attached + + + align:start position:0% +of course there's other things attached +here or on nitrogen or on sulfur so all + + align:start position:0% +here or on nitrogen or on sulfur so all + + + align:start position:0% +here or on nitrogen or on sulfur so all +of those three functional groups can + + align:start position:0% +of those three functional groups can + + + align:start position:0% +of those three functional groups can +serve as hydrogen bond donors they can + + align:start position:0% +serve as hydrogen bond donors they can + + + align:start position:0% +serve as hydrogen bond donors they can +give a proton in a hydrogen bond and + + align:start position:0% +give a proton in a hydrogen bond and + + + align:start position:0% +give a proton in a hydrogen bond and +share that proton between a hydrogen + + align:start position:0% +share that proton between a hydrogen + + + align:start position:0% +share that proton between a hydrogen +bond acceptor okay so these are all + + align:start position:0% +bond acceptor okay so these are all + + + align:start position:0% +bond acceptor okay so these are all +gonna be known as donors so you can + + align:start position:0% +gonna be known as donors so you can + + + align:start position:0% +gonna be known as donors so you can +recognize them this company is not a + + align:start position:0% +recognize them this company is not a + + + align:start position:0% +recognize them this company is not a +hydrogen bond donor carbons got his + + align:start position:0% +hydrogen bond donor carbons got his + + + align:start position:0% +hydrogen bond donor carbons got his +hydrogen and it's not giving it away to + + align:start position:0% +hydrogen and it's not giving it away to + + + align:start position:0% +hydrogen and it's not giving it away to +anybody for love or money it's hold on + + align:start position:0% +anybody for love or money it's hold on + + + align:start position:0% +anybody for love or money it's hold on +tight so this is not a hydrogen bond + + align:start position:0% +tight so this is not a hydrogen bond + + + align:start position:0% +tight so this is not a hydrogen bond +donor okay now what are the + + align:start position:0% +donor okay now what are the + + + align:start position:0% +donor okay now what are the +hydrogen-bond acceptors are places where + + align:start position:0% +hydrogen-bond acceptors are places where + + + align:start position:0% +hydrogen-bond acceptors are places where +that hydrogen would want to sit yes + + align:start position:0% + + + + align:start position:0% + +actually they just they could be double + + align:start position:0% +actually they just they could be double + + + align:start position:0% +actually they just they could be double +or they could be single but I was just + + align:start position:0% +or they could be single but I was just + + + align:start position:0% +or they could be single but I was just +putting them so that you see that the + + align:start position:0% +putting them so that you see that the + + + align:start position:0% +putting them so that you see that the +nitrogen has one two three bonds to it + + align:start position:0% +nitrogen has one two three bonds to it + + + align:start position:0% +nitrogen has one two three bonds to it +okay yeah it could alternatively also be + + align:start position:0% +okay yeah it could alternatively also be + + + align:start position:0% +okay yeah it could alternatively also be +the form of nitrogen just to confuse you + + align:start position:0% +the form of nitrogen just to confuse you + + + align:start position:0% +the form of nitrogen just to confuse you +it has an extra proton it could be the + + align:start position:0% +it has an extra proton it could be the + + + align:start position:0% +it has an extra proton it could be the +protonated version because that can + + align:start position:0% +protonated version because that can + + + align:start position:0% +protonated version because that can +still be a hydrogen bond donor okay now + + align:start position:0% +still be a hydrogen bond donor okay now + + + align:start position:0% +still be a hydrogen bond donor okay now +what are the hydrogen-bond acceptors + + align:start position:0% +what are the hydrogen-bond acceptors + + + align:start position:0% +what are the hydrogen-bond acceptors +they are any place where you have a lone + + align:start position:0% +they are any place where you have a lone + + + align:start position:0% +they are any place where you have a lone +pair so let's just think of a carbonyl + + align:start position:0% +pair so let's just think of a carbonyl + + + align:start position:0% +pair so let's just think of a carbonyl +group two lone pairs a hydroxyl group + + align:start position:0% + + + + align:start position:0% + +two lone pairs a nitrogen that is not + + align:start position:0% +two lone pairs a nitrogen that is not + + + align:start position:0% +two lone pairs a nitrogen that is not +protonated one lone pair those are the + + align:start position:0% +protonated one lone pair those are the + + + align:start position:0% +protonated one lone pair those are the +hydrogen-bond acceptors so as long as + + align:start position:0% +hydrogen-bond acceptors so as long as + + + align:start position:0% +hydrogen-bond acceptors so as long as +you know your structures in the Cova in + + align:start position:0% +you know your structures in the Cova in + + + align:start position:0% +you know your structures in the Cova in +the in the functional groups and you + + align:start position:0% +the in the functional groups and you + + + align:start position:0% +the in the functional groups and you +know where the lone pairs are you can + + align:start position:0% +know where the lone pairs are you can + + + align:start position:0% +know where the lone pairs are you can +figure out where there could be a + + align:start position:0% +figure out where there could be a + + + align:start position:0% +figure out where there could be a +hydrogen bond so these all of these + + align:start position:0% +hydrogen bond so these all of these + + + align:start position:0% +hydrogen bond so these all of these +types are acceptors okay so in protein + + align:start position:0% +types are acceptors okay so in protein + + + align:start position:0% +types are acceptors okay so in protein +biochemistry for example those kinds of + + align:start position:0% +biochemistry for example those kinds of + + + align:start position:0% +biochemistry for example those kinds of +hydrogen bonding is very very important + + align:start position:0% +hydrogen bonding is very very important + + + align:start position:0% +hydrogen bonding is very very important +to form the three-dimensional structures + + align:start position:0% +to form the three-dimensional structures + + + align:start position:0% +to form the three-dimensional structures +of proteins and the reason why is + + align:start position:0% +of proteins and the reason why is + + + align:start position:0% +of proteins and the reason why is +because in a protein proteins are made + + align:start position:0% +because in a protein proteins are made + + + align:start position:0% +because in a protein proteins are made +up of amid bonds where this h n can be a + + align:start position:0% +up of amid bonds where this h n can be a + + + align:start position:0% +up of amid bonds where this h n can be a +donor + + align:start position:0% +donor + + + align:start position:0% +donor +this Oh can be an acceptor and you can + + align:start position:0% +this Oh can be an acceptor and you can + + + align:start position:0% +this Oh can be an acceptor and you can +get networks of hydrogen bonding + + align:start position:0% +get networks of hydrogen bonding + + + align:start position:0% +get networks of hydrogen bonding +interactions to establish structures of + + align:start position:0% +interactions to establish structures of + + + align:start position:0% +interactions to establish structures of +proteins when a small molecule binds to + + align:start position:0% +proteins when a small molecule binds to + + + align:start position:0% +proteins when a small molecule binds to +a protein it may look to fit in a place + + align:start position:0% +a protein it may look to fit in a place + + + align:start position:0% +a protein it may look to fit in a place +where it can maximize electrostatic + + align:start position:0% +where it can maximize electrostatic + + + align:start position:0% +where it can maximize electrostatic +interactions and the hydrogen bonding + + align:start position:0% +interactions and the hydrogen bonding + + + align:start position:0% +interactions and the hydrogen bonding +interactions so we'll ask you to start + + align:start position:0% +interactions so we'll ask you to start + + + align:start position:0% +interactions so we'll ask you to start +to be able to take out hydrogen bonding + + align:start position:0% +to be able to take out hydrogen bonding + + + align:start position:0% +to be able to take out hydrogen bonding +so here you saw the electrostatic + + align:start position:0% +so here you saw the electrostatic + + + align:start position:0% +so here you saw the electrostatic +interaction here is a typical hydrogen + + align:start position:0% +interaction here is a typical hydrogen + + + align:start position:0% +interaction here is a typical hydrogen +bonding interaction between a hydroxyl + + align:start position:0% +bonding interaction between a hydroxyl + + + align:start position:0% +bonding interaction between a hydroxyl +and a carbonyl group + + align:start position:0% +and a carbonyl group + + + align:start position:0% +and a carbonyl group +I couldn't spot that very readily unless + + align:start position:0% +I couldn't spot that very readily unless + + + align:start position:0% +I couldn't spot that very readily unless +I remembered that there were lone pairs + + align:start position:0% +I remembered that there were lone pairs + + + align:start position:0% +I remembered that there were lone pairs +of electrons there okay the other two - + + align:start position:0% +of electrons there okay the other two - + + + align:start position:0% +of electrons there okay the other two - +any questions about that any questions + + align:start position:0% +any questions about that any questions + + + align:start position:0% +any questions about that any questions +about hydrogen bonding are you + + align:start position:0% +about hydrogen bonding are you + + + align:start position:0% +about hydrogen bonding are you +comfortable with thinking you could + + align:start position:0% +comfortable with thinking you could + + + align:start position:0% +comfortable with thinking you could +derive your way to figuring out where + + align:start position:0% +derive your way to figuring out where + + + align:start position:0% +derive your way to figuring out where +they are you'll see them used a lot so + + align:start position:0% +they are you'll see them used a lot so + + + align:start position:0% +they are you'll see them used a lot so +they'll become more and more familiar to + + align:start position:0% +they'll become more and more familiar to + + + align:start position:0% +they'll become more and more familiar to +you as you move forward okay good the + + align:start position:0% +you as you move forward okay good the + + + align:start position:0% +you as you move forward okay good the +last two types of interactions + + align:start position:0% + + + + align:start position:0% + +are the hydrophobic interactions and + + align:start position:0% +are the hydrophobic interactions and + + + align:start position:0% +are the hydrophobic interactions and +vongavel forces I never get a spelling + + align:start position:0% +vongavel forces I never get a spelling + + + align:start position:0% +vongavel forces I never get a spelling +right but I'll get the concepts over you + + align:start position:0% +right but I'll get the concepts over you + + + align:start position:0% +right but I'll get the concepts over you +now hydrophobic interactions are + + align:start position:0% +now hydrophobic interactions are + + + align:start position:0% +now hydrophobic interactions are +incredibly important so when you think + + align:start position:0% +incredibly important so when you think + + + align:start position:0% +incredibly important so when you think +of folding a protein driven solely by + + align:start position:0% +of folding a protein driven solely by + + + align:start position:0% +of folding a protein driven solely by +electrostatic interactions and hydrogen + + align:start position:0% +electrostatic interactions and hydrogen + + + align:start position:0% +electrostatic interactions and hydrogen +bonding you have a bit of a problem + + align:start position:0% +bonding you have a bit of a problem + + + align:start position:0% +bonding you have a bit of a problem +because all of those groups are hydrogen + + align:start position:0% +because all of those groups are hydrogen + + + align:start position:0% +because all of those groups are hydrogen +bonded to water so you'd have to get rid + + align:start position:0% +bonded to water so you'd have to get rid + + + align:start position:0% +bonded to water so you'd have to get rid +of the water before they could make + + align:start position:0% +of the water before they could make + + + align:start position:0% +of the water before they could make +interactions with each other that makes + + align:start position:0% +interactions with each other that makes + + + align:start position:0% +interactions with each other that makes +sense because we're in water we're + + align:start position:0% +sense because we're in water we're + + + align:start position:0% +sense because we're in water we're +folding in water hydrophobic + + align:start position:0% +folding in water hydrophobic + + + align:start position:0% +folding in water hydrophobic +interactions are really great because + + align:start position:0% +interactions are really great because + + + align:start position:0% +interactions are really great because +they want to form in water if you're + + align:start position:0% +they want to form in water if you're + + + align:start position:0% +they want to form in water if you're +making you know a batch of salad + + align:start position:0% +making you know a batch of salad + + + align:start position:0% +making you know a batch of salad +dressing oil and vinegar and you shake + + align:start position:0% +dressing oil and vinegar and you shake + + + align:start position:0% +dressing oil and vinegar and you shake +it up what happens it separates the oil + + align:start position:0% +it up what happens it separates the oil + + + align:start position:0% +it up what happens it separates the oil +goes to top the vinegar goes to the + + align:start position:0% +goes to top the vinegar goes to the + + + align:start position:0% +goes to top the vinegar goes to the +bottom why because of hydrophobic + + align:start position:0% +bottom why because of hydrophobic + + + align:start position:0% +bottom why because of hydrophobic +interactions in the oil phase so if you + + align:start position:0% +interactions in the oil phase so if you + + + align:start position:0% +interactions in the oil phase so if you +have a large protein that has a bunch of + + align:start position:0% +have a large protein that has a bunch of + + + align:start position:0% +have a large protein that has a bunch of +hydrophobic groups they will want to + + align:start position:0% +hydrophobic groups they will want to + + + align:start position:0% +hydrophobic groups they will want to +collapse out of the water to interact + + align:start position:0% +collapse out of the water to interact + + + align:start position:0% +collapse out of the water to interact +with each other and then hydrogen + + align:start position:0% +with each other and then hydrogen + + + align:start position:0% +with each other and then hydrogen +bonding and electrostatic will fall into + + align:start position:0% +bonding and electrostatic will fall into + + + align:start position:0% +bonding and electrostatic will fall into +place + + align:start position:0% +place + + + align:start position:0% +place +so hydrophobic interactions are a very + + align:start position:0% +so hydrophobic interactions are a very + + + align:start position:0% +so hydrophobic interactions are a very +important and vital force in nature in + + align:start position:0% +important and vital force in nature in + + + align:start position:0% +important and vital force in nature in +the non covalent bonding so that's those + + align:start position:0% +the non covalent bonding so that's those + + + align:start position:0% +the non covalent bonding so that's those +of 'literally interactions amongst + + align:start position:0% +of 'literally interactions amongst + + + align:start position:0% +of 'literally interactions amongst +molecules that have a lot of ch and CC + + align:start position:0% +molecules that have a lot of ch and CC + + + align:start position:0% +molecules that have a lot of ch and CC +bonds the final force that's shown up + + align:start position:0% +bonds the final force that's shown up + + + align:start position:0% +bonds the final force that's shown up +there is the band of ARs force and we + + align:start position:0% +there is the band of ARs force and we + + + align:start position:0% +there is the band of ARs force and we +don't worry too much about that but it + + align:start position:0% +don't worry too much about that but it + + + align:start position:0% +don't worry too much about that but it +is simply the interaction between very + + align:start position:0% +is simply the interaction between very + + + align:start position:0% +is simply the interaction between very +weakly polarized hydrogen carbon + + align:start position:0% +weakly polarized hydrogen carbon + + + align:start position:0% +weakly polarized hydrogen carbon +hydrogen or other types of bonds where + + align:start position:0% +hydrogen or other types of bonds where + + + align:start position:0% +hydrogen or other types of bonds where +there's a little bit of difference + + align:start position:0% +there's a little bit of difference + + + align:start position:0% +there's a little bit of difference +between the little bit of a dipole + + align:start position:0% +between the little bit of a dipole + + + align:start position:0% +between the little bit of a dipole +between the bond and they form little + + align:start position:0% +between the bond and they form little + + + align:start position:0% +between the bond and they form little +dipolar interactions but mostly I think + + align:start position:0% +dipolar interactions but mostly I think + + + align:start position:0% +dipolar interactions but mostly I think +you really want to focus on the + + align:start position:0% +you really want to focus on the + + + align:start position:0% +you really want to focus on the +electrostatic the hydrogen bond and the + + align:start position:0% +electrostatic the hydrogen bond and the + + + align:start position:0% +electrostatic the hydrogen bond and the +hydrophobic these are more minor and + + align:start position:0% +hydrophobic these are more minor and + + + align:start position:0% +hydrophobic these are more minor and +it's a little bit of a subtlety so let's + + align:start position:0% +it's a little bit of a subtlety so let's + + + align:start position:0% +it's a little bit of a subtlety so let's +focus on those three all right + + align:start position:0% +focus on those three all right + + + align:start position:0% +focus on those three all right +so with that said the key thing for you + + align:start position:0% +so with that said the key thing for you + + + align:start position:0% +so with that said the key thing for you +what do you need to be able to do is + + align:start position:0% +what do you need to be able to do is + + + align:start position:0% +what do you need to be able to do is +understand them and recognize them in + + align:start position:0% +understand them and recognize them in + + + align:start position:0% +understand them and recognize them in +complex systems + + align:start position:0% +complex systems + + + align:start position:0% +complex systems +lastly I'm just going to leave this it's + + align:start position:0% +lastly I'm just going to leave this it's + + + align:start position:0% +lastly I'm just going to leave this it's +going to stay in your notes we you know + + align:start position:0% +going to stay in your notes we you know + + + align:start position:0% +going to stay in your notes we you know +get in biochemistry tend to use line + + align:start position:0% +get in biochemistry tend to use line + + + align:start position:0% +get in biochemistry tend to use line +angle drawings it's kind of complicated + + align:start position:0% +angle drawings it's kind of complicated + + + align:start position:0% +angle drawings it's kind of complicated +to draw these sort of great big things + + align:start position:0% +to draw these sort of great big things + + + align:start position:0% +to draw these sort of great big things +with all the hydrogen's and oxygens and + + align:start position:0% +with all the hydrogen's and oxygens and + + + align:start position:0% +with all the hydrogen's and oxygens and +stuff spelled out so we use the line + + align:start position:0% +stuff spelled out so we use the line + + + align:start position:0% +stuff spelled out so we use the line +angle drawing there's some shown here + + align:start position:0% +angle drawing there's some shown here + + + align:start position:0% +angle drawing there's some shown here +for different molecules and the rules + + align:start position:0% +for different molecules and the rules + + + align:start position:0% +for different molecules and the rules +are laid out so that you can go and just + + align:start position:0% +are laid out so that you can go and just + + + align:start position:0% +are laid out so that you can go and just +figure out through a bit of practicing + + align:start position:0% +figure out through a bit of practicing + + + align:start position:0% +figure out through a bit of practicing +and just figure out the line angle + + align:start position:0% +and just figure out the line angle + + + align:start position:0% +and just figure out the line angle +drawing them what it means basically + + align:start position:0% +drawing them what it means basically + + + align:start position:0% +drawing them what it means basically +every line represents a bond every + + align:start position:0% +every line represents a bond every + + + align:start position:0% +every line represents a bond every +vertex represents a carbon atom but what + + align:start position:0% +vertex represents a carbon atom but what + + + align:start position:0% +vertex represents a carbon atom but what +you do show on the drawings that are non + + align:start position:0% +you do show on the drawings that are non + + + align:start position:0% +you do show on the drawings that are non +carbon atoms so for example oxygen or + + align:start position:0% +carbon atoms so for example oxygen or + + + align:start position:0% +carbon atoms so for example oxygen or +nitrogen and when you show you imply the + + align:start position:0% +nitrogen and when you show you imply the + + + align:start position:0% +nitrogen and when you show you imply the +hydrogen's that are bonded to carbon but + + align:start position:0% +hydrogen's that are bonded to carbon but + + + align:start position:0% +hydrogen's that are bonded to carbon but +you have to show the hydrogen's that are + + align:start position:0% +you have to show the hydrogen's that are + + + align:start position:0% +you have to show the hydrogen's that are +on nitrogen or oxygen for example and + + align:start position:0% +on nitrogen or oxygen for example and + + + align:start position:0% +on nitrogen or oxygen for example and +you have to figure out what your charge + + align:start position:0% +you have to figure out what your charge + + + align:start position:0% +you have to figure out what your charge +state might be so I'm gonna leave you + + align:start position:0% +state might be so I'm gonna leave you + + + align:start position:0% +state might be so I'm gonna leave you +with that alright okay so what we've + + align:start position:0% +with that alright okay so what we've + + + align:start position:0% +with that alright okay so what we've +learned so far is these basic forces in + + align:start position:0% +learned so far is these basic forces in + + + align:start position:0% +learned so far is these basic forces in +biology are critical for the Assembly of + + align:start position:0% +biology are critical for the Assembly of + + + align:start position:0% +biology are critical for the Assembly of +the building blocks of biological + + align:start position:0% +the building blocks of biological + + + align:start position:0% +the building blocks of biological +macromolecules what I want to talk to + + align:start position:0% +macromolecules what I want to talk to + + + align:start position:0% +macromolecules what I want to talk to +you about now and well probably because + + align:start position:0% +you about now and well probably because + + + align:start position:0% +you about now and well probably because +I've spent a little bit of time on that + + align:start position:0% +I've spent a little bit of time on that + + + align:start position:0% +I've spent a little bit of time on that +spill over a little more to next week + + align:start position:0% +spill over a little more to next week + + + align:start position:0% +spill over a little more to next week +but I'm going to talk to you about the + + align:start position:0% +but I'm going to talk to you about the + + + align:start position:0% +but I'm going to talk to you about the +first class of macromolecules which are + + align:start position:0% +first class of macromolecules which are + + + align:start position:0% +first class of macromolecules which are +the lipids so what makes something a + + align:start position:0% +the lipids so what makes something a + + + align:start position:0% +the lipids so what makes something a +lipid these are the most sort of + + align:start position:0% +lipid these are the most sort of + + + align:start position:0% +lipid these are the most sort of +complicated mixture of biological + + align:start position:0% +complicated mixture of biological + + + align:start position:0% +complicated mixture of biological +molecules and formally they're not + + align:start position:0% +molecules and formally they're not + + + align:start position:0% +molecules and formally they're not +really macromolecules they're small + + align:start position:0% +really macromolecules they're small + + + align:start position:0% +really macromolecules they're small +molecules but what's common to all of + + align:start position:0% +molecules but what's common to all of + + + align:start position:0% +molecules but what's common to all of +them is that they are very rich in + + align:start position:0% +them is that they are very rich in + + + align:start position:0% +them is that they are very rich in +carbon carbon and carbon hydrogen bonds + + align:start position:0% +carbon carbon and carbon hydrogen bonds + + + align:start position:0% +carbon carbon and carbon hydrogen bonds +because all of these the line angle + + align:start position:0% +because all of these the line angle + + + align:start position:0% +because all of these the line angle +drawings of all of these would suggest + + align:start position:0% +drawings of all of these would suggest + + + align:start position:0% +drawings of all of these would suggest +to you that the dominant feature of all + + align:start position:0% +to you that the dominant feature of all + + + align:start position:0% +to you that the dominant feature of all +these molecules is a bunch of C C and CH + + align:start position:0% +these molecules is a bunch of C C and CH + + + align:start position:0% +these molecules is a bunch of C C and CH +bonds which makes the molecules quite + + align:start position:0% +bonds which makes the molecules quite + + + align:start position:0% +bonds which makes the molecules quite +hydrophobic there are no functional + + align:start position:0% +hydrophobic there are no functional + + + align:start position:0% +hydrophobic there are no functional +groups there and and they behave very + + align:start position:0% +groups there and and they behave very + + + align:start position:0% +groups there and and they behave very +differently for example they would have + + align:start position:0% +differently for example they would have + + + align:start position:0% +differently for example they would have +a tough time dissolving in water + + align:start position:0% +a tough time dissolving in water + + + align:start position:0% +a tough time dissolving in water +in some cases and so this complicated + + align:start position:0% +in some cases and so this complicated + + + align:start position:0% +in some cases and so this complicated +looking set of molecules can be + + align:start position:0% +looking set of molecules can be + + + align:start position:0% +looking set of molecules can be +distilled out as being very rich in + + align:start position:0% +distilled out as being very rich in + + + align:start position:0% +distilled out as being very rich in +carbon hydrogen and carbon carbon bonds + + align:start position:0% +carbon hydrogen and carbon carbon bonds + + + align:start position:0% +carbon hydrogen and carbon carbon bonds +and we call those collectively lipids + + align:start position:0% +and we call those collectively lipids + + + align:start position:0% +and we call those collectively lipids +now in they have a lot of different + + align:start position:0% +now in they have a lot of different + + + align:start position:0% +now in they have a lot of different +functions so for example triglycerides + + align:start position:0% +functions so for example triglycerides + + + align:start position:0% +functions so for example triglycerides +such as shown here with 3 ester bonds a + + align:start position:0% +such as shown here with 3 ester bonds a + + + align:start position:0% +such as shown here with 3 ester bonds a +storage for energy things like estradiol + + align:start position:0% +storage for energy things like estradiol + + + align:start position:0% +storage for energy things like estradiol +things like steroids they have this 6 6 + + align:start position:0% +things like steroids they have this 6 6 + + + align:start position:0% +things like steroids they have this 6 6 +5 6 5 arrangement of rings all your + + align:start position:0% +5 6 5 arrangement of rings all your + + + align:start position:0% +5 6 5 arrangement of rings all your +steroid hormones kind of look like that + + align:start position:0% +steroid hormones kind of look like that + + + align:start position:0% +steroid hormones kind of look like that +a lot of Ch bonds there are some + + align:start position:0% +a lot of Ch bonds there are some + + + align:start position:0% +a lot of Ch bonds there are some +vitamins so for example retinol is a + + align:start position:0% +vitamins so for example retinol is a + + + align:start position:0% +vitamins so for example retinol is a +vitamin it's also a lipid and then there + + align:start position:0% +vitamin it's also a lipid and then there + + + align:start position:0% +vitamin it's also a lipid and then there +are the phospholipids shown down here I + + align:start position:0% +are the phospholipids shown down here I + + + align:start position:0% +are the phospholipids shown down here I +just briefly want to mention a little + + align:start position:0% +just briefly want to mention a little + + + align:start position:0% +just briefly want to mention a little +bit about retinol and retinol which have + + align:start position:0% +bit about retinol and retinol which have + + + align:start position:0% +bit about retinol and retinol which have +crucial retinol is a critical vitamin it + + align:start position:0% +crucial retinol is a critical vitamin it + + + align:start position:0% +crucial retinol is a critical vitamin it +comes actually from carotene which is a + + align:start position:0% +comes actually from carotene which is a + + + align:start position:0% +comes actually from carotene which is a +molecule that you find in a lot of + + align:start position:0% +molecule that you find in a lot of + + + align:start position:0% +molecule that you find in a lot of +orange and yellow fruits such as carrots + + align:start position:0% +orange and yellow fruits such as carrots + + + align:start position:0% +orange and yellow fruits such as carrots +but the oxidized products of retinol is + + align:start position:0% +but the oxidized products of retinol is + + + align:start position:0% +but the oxidized products of retinol is +this lipid called retinol which is + + align:start position:0% +this lipid called retinol which is + + + align:start position:0% +this lipid called retinol which is +central to the process of vision so + + align:start position:0% +central to the process of vision so + + + align:start position:0% +central to the process of vision so +retinol binds to proteins that sit in + + align:start position:0% +retinol binds to proteins that sit in + + + align:start position:0% +retinol binds to proteins that sit in +the membrane when light shines on them + + align:start position:0% +the membrane when light shines on them + + + align:start position:0% +the membrane when light shines on them +the shape of the retinol changes it goes + + align:start position:0% +the shape of the retinol changes it goes + + + align:start position:0% +the shape of the retinol changes it goes +from a particular configuration of the + + align:start position:0% +from a particular configuration of the + + + align:start position:0% +from a particular configuration of the +double bond to a different one the shape + + align:start position:0% +double bond to a different one the shape + + + align:start position:0% +double bond to a different one the shape +just changes and that sends a signal to + + align:start position:0% +just changes and that sends a signal to + + + align:start position:0% +just changes and that sends a signal to +your brain so lipids are important + + align:start position:0% +your brain so lipids are important + + + align:start position:0% +your brain so lipids are important +absolutely essential in vision and sight + + align:start position:0% +absolutely essential in vision and sight + + + align:start position:0% +absolutely essential in vision and sight +because they're involved in the + + align:start position:0% +because they're involved in the + + + align:start position:0% +because they're involved in the +signaling process because their shapes + + align:start position:0% +signaling process because their shapes + + + align:start position:0% +signaling process because their shapes +change and send signals other types of + + align:start position:0% +change and send signals other types of + + + align:start position:0% +change and send signals other types of +lipids are these things and we call them + + align:start position:0% +lipids are these things and we call them + + + align:start position:0% +lipids are these things and we call them +fatty acids mostly because they're + + align:start position:0% +fatty acids mostly because they're + + + align:start position:0% +fatty acids mostly because they're +greasy long-chain acids with a long + + align:start position:0% +greasy long-chain acids with a long + + + align:start position:0% +greasy long-chain acids with a long +hydrophobic tail and the hydrophilic end + + align:start position:0% +hydrophobic tail and the hydrophilic end + + + align:start position:0% +hydrophobic tail and the hydrophilic end +group here these molecules are also what + + align:start position:0% +group here these molecules are also what + + + align:start position:0% +group here these molecules are also what +are known as antha Pathak because they + + align:start position:0% +are known as antha Pathak because they + + + align:start position:0% +are known as antha Pathak because they +have a sort of split personality they + + align:start position:0% +have a sort of split personality they + + + align:start position:0% +have a sort of split personality they +have a hydrophobic moiety and a + + align:start position:0% +have a hydrophobic moiety and a + + + align:start position:0% +have a hydrophobic moiety and a +hydrophilic moiety whenever you see + + align:start position:0% +hydrophilic moiety whenever you see + + + align:start position:0% +hydrophilic moiety whenever you see +see at the beginning of a word it means + + align:start position:0% +see at the beginning of a word it means + + + align:start position:0% +see at the beginning of a word it means +in both so both hydrophilic and and and + + align:start position:0% +in both so both hydrophilic and and and + + + align:start position:0% +in both so both hydrophilic and and and +lipophilic so these are important and + + align:start position:0% +lipophilic so these are important and + + + align:start position:0% +lipophilic so these are important and +these are very important components + + align:start position:0% +these are very important components + + + align:start position:0% +these are very important components +you've probably heard a lot of press + + align:start position:0% +you've probably heard a lot of press + + + align:start position:0% +you've probably heard a lot of press +about some of the fatty acids and how + + align:start position:0% +about some of the fatty acids and how + + + align:start position:0% +about some of the fatty acids and how +bad trans fats are you for you and how + + align:start position:0% +bad trans fats are you for you and how + + + align:start position:0% +bad trans fats are you for you and how +you should be careful to make sure your + + align:start position:0% +you should be careful to make sure your + + + align:start position:0% +you should be careful to make sure your +diet is rich in sis fats or rather than + + align:start position:0% +diet is rich in sis fats or rather than + + + align:start position:0% +diet is rich in sis fats or rather than +trans fats because the trans fats are + + align:start position:0% +trans fats because the trans fats are + + + align:start position:0% +trans fats because the trans fats are +contributors to coronary heart disease + + align:start position:0% +contributors to coronary heart disease + + + align:start position:0% +contributors to coronary heart disease +so you may wonder what's the + + align:start position:0% +so you may wonder what's the + + + align:start position:0% +so you may wonder what's the +relationship between heart disease and + + align:start position:0% +relationship between heart disease and + + + align:start position:0% +relationship between heart disease and +these two types of lip affiliate + + align:start position:0% +these two types of lip affiliate + + + align:start position:0% +these two types of lip affiliate +components which are in the body so let + + align:start position:0% +components which are in the body so let + + + align:start position:0% +components which are in the body so let +me describe to you that relationship + + align:start position:0% +me describe to you that relationship + + + align:start position:0% +me describe to you that relationship +remember the cysts are rich in things + + align:start position:0% +remember the cysts are rich in things + + + align:start position:0% +remember the cysts are rich in things +like the the nut oils and fruit oils + + align:start position:0% +like the the nut oils and fruit oils + + + align:start position:0% +like the the nut oils and fruit oils +such as olive oil so coronary heart + + align:start position:0% +such as olive oil so coronary heart + + + align:start position:0% +such as olive oil so coronary heart +disease is associated with trans fats + + align:start position:0% +disease is associated with trans fats + + + align:start position:0% +disease is associated with trans fats +what's the linkage what's the biology in + + align:start position:0% +what's the linkage what's the biology in + + + align:start position:0% +what's the linkage what's the biology in +that so clicking it comes the story is + + align:start position:0% +that so clicking it comes the story is + + + align:start position:0% +that so clicking it comes the story is +related to cholesterol cholesterol is a + + align:start position:0% +related to cholesterol cholesterol is a + + + align:start position:0% +related to cholesterol cholesterol is a +critical component in our membranes the + + align:start position:0% +critical component in our membranes the + + + align:start position:0% +critical component in our membranes the +trouble is we have to be able to move + + align:start position:0% +trouble is we have to be able to move + + + align:start position:0% +trouble is we have to be able to move +cholesterol around but it's so + + align:start position:0% +cholesterol around but it's so + + + align:start position:0% +cholesterol around but it's so +hydrophobic it doesn't dissolve in water + + align:start position:0% +hydrophobic it doesn't dissolve in water + + + align:start position:0% +hydrophobic it doesn't dissolve in water +okay so in the body your cholesterol is + + align:start position:0% +okay so in the body your cholesterol is + + + align:start position:0% +okay so in the body your cholesterol is +moved around in the form of lipoproteins + + align:start position:0% +moved around in the form of lipoproteins + + + align:start position:0% +moved around in the form of lipoproteins +the bind to the cholesterol and take it + + align:start position:0% +the bind to the cholesterol and take it + + + align:start position:0% +the bind to the cholesterol and take it +to the different organs where it is + + align:start position:0% +to the different organs where it is + + + align:start position:0% +to the different organs where it is +needed all right and so the lipoproteins + + align:start position:0% +needed all right and so the lipoproteins + + + align:start position:0% +needed all right and so the lipoproteins +can either be low-density and associate + + align:start position:0% +can either be low-density and associate + + + align:start position:0% +can either be low-density and associate +with cholesterol or they can be + + align:start position:0% +with cholesterol or they can be + + + align:start position:0% +with cholesterol or they can be +high-density and those also associate + + align:start position:0% +high-density and those also associate + + + align:start position:0% +high-density and those also associate +with cholesterol the high-density + + align:start position:0% +with cholesterol the high-density + + + align:start position:0% +with cholesterol the high-density +lipoproteins are kind of large the in + + align:start position:0% +lipoproteins are kind of large the in + + + align:start position:0% +lipoproteins are kind of large the in +fact they're fairly agile they don't + + align:start position:0% +fact they're fairly agile they don't + + + align:start position:0% +fact they're fairly agile they don't +stick the arteries and vesicles vessels + + align:start position:0% +stick the arteries and vesicles vessels + + + align:start position:0% +stick the arteries and vesicles vessels +and they can be excreted in the liver or + + align:start position:0% +and they can be excreted in the liver or + + + align:start position:0% +and they can be excreted in the liver or +move around the bloodstream without any + + align:start position:0% +move around the bloodstream without any + + + align:start position:0% +move around the bloodstream without any +problem + + align:start position:0% +problem + + + align:start position:0% +problem +it's the low-density ones that are + + align:start position:0% +it's the low-density ones that are + + + align:start position:0% +it's the low-density ones that are +problems because they're low-density and + + align:start position:0% +problems because they're low-density and + + + align:start position:0% +problems because they're low-density and +they kind of stick to the walls of your + + align:start position:0% +they kind of stick to the walls of your + + + align:start position:0% +they kind of stick to the walls of your +arteries and start making build ups and + + align:start position:0% +arteries and start making build ups and + + + align:start position:0% +arteries and start making build ups and +then plaques which contribute to heart + + align:start position:0% +then plaques which contribute to heart + + + align:start position:0% +then plaques which contribute to heart +disease + + align:start position:0% +disease + + + align:start position:0% +disease +so the low-density ones have cholesterol + + align:start position:0% +so the low-density ones have cholesterol + + + align:start position:0% +so the low-density ones have cholesterol +but they're very small sticky and it's a + + align:start position:0% +but they're very small sticky and it's a + + + align:start position:0% +but they're very small sticky and it's a +physical interaction with your blood + + align:start position:0% +physical interaction with your blood + + + align:start position:0% +physical interaction with your blood +vessels and they start to clog your + + align:start position:0% +vessels and they start to clog your + + + align:start position:0% +vessels and they start to clog your +arteries what's the relationship to + + align:start position:0% +arteries what's the relationship to + + + align:start position:0% +arteries what's the relationship to +saturated and + + align:start position:0% +saturated and + + + align:start position:0% +saturated and +spats is that they increase for + + align:start position:0% +spats is that they increase for + + + align:start position:0% +spats is that they increase for +low-density lipoprotein in preference to + + align:start position:0% +low-density lipoprotein in preference to + + + align:start position:0% +low-density lipoprotein in preference to +the high-density so if you have a lot of + + align:start position:0% +the high-density so if you have a lot of + + + align:start position:0% +the high-density so if you have a lot of +trans fats you make a lot of low-density + + align:start position:0% +trans fats you make a lot of low-density + + + align:start position:0% +trans fats you make a lot of low-density +lipoproteins it's trying to carry + + align:start position:0% +lipoproteins it's trying to carry + + + align:start position:0% +lipoproteins it's trying to carry +cholesterol around but it gets stuck to + + align:start position:0% +cholesterol around but it gets stuck to + + + align:start position:0% +cholesterol around but it gets stuck to +your blood vessels and you start to clog + + align:start position:0% +your blood vessels and you start to clog + + + align:start position:0% +your blood vessels and you start to clog +your blood vessels for heart that + + align:start position:0% +your blood vessels for heart that + + + align:start position:0% +your blood vessels for heart that +contributes to heart disease + + align:start position:0% +contributes to heart disease + + + align:start position:0% +contributes to heart disease +so these lipophilic molecules are + + align:start position:0% +so these lipophilic molecules are + + + align:start position:0% +so these lipophilic molecules are +important they have places to store + + align:start position:0% +important they have places to store + + + align:start position:0% +important they have places to store +energy they are critical to hormones and + + align:start position:0% +energy they are critical to hormones and + + + align:start position:0% +energy they are critical to hormones and +signaling for example but there are some + + align:start position:0% +signaling for example but there are some + + + align:start position:0% +signaling for example but there are some +complications with disease because + + align:start position:0% +complications with disease because + + + align:start position:0% +complications with disease because +certain types of fatty acids contribute + + align:start position:0% +certain types of fatty acids contribute + + + align:start position:0% +certain types of fatty acids contribute +to heart disease + + align:start position:0% +to heart disease + + + align:start position:0% +to heart disease +yeah no no it's it's the the density is + + align:start position:0% +yeah no no it's it's the the density is + + + align:start position:0% +yeah no no it's it's the the density is +in the of the entire physical particle + + align:start position:0% +in the of the entire physical particle + + + align:start position:0% +in the of the entire physical particle +it's a nanoparticle that would be more + + align:start position:0% +it's a nanoparticle that would be more + + + align:start position:0% +it's a nanoparticle that would be more +float would show a different density + + align:start position:0% +float would show a different density + + + align:start position:0% +float would show a different density +respect to how it floats in water so the + + align:start position:0% +respect to how it floats in water so the + + + align:start position:0% +respect to how it floats in water so the +density is really the physical metric of + + align:start position:0% +density is really the physical metric of + + + align:start position:0% +density is really the physical metric of +the entire particle as opposed to just + + align:start position:0% +the entire particle as opposed to just + + + align:start position:0% +the entire particle as opposed to just +the molecule it might be different + + align:start position:0% +the molecule it might be different + + + align:start position:0% +the molecule it might be different +because of the way it compact but it + + align:start position:0% +because of the way it compact but it + + + align:start position:0% +because of the way it compact but it +that the important thing about the trans + + align:start position:0% +that the important thing about the trans + + + align:start position:0% +that the important thing about the trans +fats is that they really contribute to + + align:start position:0% +fats is that they really contribute to + + + align:start position:0% +fats is that they really contribute to +making the protein the forms are low + + align:start position:0% +making the protein the forms are low + + + align:start position:0% +making the protein the forms are low +density particles okay all right so I'm + + align:start position:0% +density particles okay all right so I'm + + + align:start position:0% +density particles okay all right so I'm +just going to introduce these not + + align:start position:0% +just going to introduce these not + + + align:start position:0% +just going to introduce these not +quickly but I'll show you some cool + + align:start position:0% +quickly but I'll show you some cool + + + align:start position:0% +quickly but I'll show you some cool +images in a at the beginning of the next + + align:start position:0% +images in a at the beginning of the next + + + align:start position:0% +images in a at the beginning of the next +class this is the last group of lipid ik + + align:start position:0% +class this is the last group of lipid ik + + + align:start position:0% +class this is the last group of lipid ik +molecules and they are actually oops + + align:start position:0% +molecules and they are actually oops + + + align:start position:0% +molecules and they are actually oops +esters and phospho esters of fatty acids + + align:start position:0% +esters and phospho esters of fatty acids + + + align:start position:0% +esters and phospho esters of fatty acids +with glycerol this is a small molecule + + align:start position:0% +with glycerol this is a small molecule + + + align:start position:0% +with glycerol this is a small molecule +that forms esters through its oxygens to + + align:start position:0% +that forms esters through its oxygens to + + + align:start position:0% +that forms esters through its oxygens to +these long chains and also to phosphate + + align:start position:0% +these long chains and also to phosphate + + + align:start position:0% +these long chains and also to phosphate +and these contribute to really important + + align:start position:0% +and these contribute to really important + + + align:start position:0% +and these contribute to really important +functions in the body + + align:start position:0% +functions in the body + + + align:start position:0% +functions in the body +they are also amphipathic because they + + align:start position:0% +they are also amphipathic because they + + + align:start position:0% +they are also amphipathic because they +have a hydrophobic component and a + + align:start position:0% +have a hydrophobic component and a + + + align:start position:0% +have a hydrophobic component and a +hydrophilic component and we often draw + + align:start position:0% +hydrophilic component and we often draw + + + align:start position:0% +hydrophilic component and we often draw +them in a shorthand form like this that + + align:start position:0% +them in a shorthand form like this that + + + align:start position:0% +them in a shorthand form like this that +represents this head group and these + + align:start position:0% +represents this head group and these + + + align:start position:0% +represents this head group and these +tails and I want to just leave you with + + align:start position:0% +tails and I want to just leave you with + + + align:start position:0% +tails and I want to just leave you with +this wonderful image of the sorts of + + align:start position:0% +this wonderful image of the sorts of + + + align:start position:0% +this wonderful image of the sorts of +supera molecular structures that these + + align:start position:0% +supera molecular structures that these + + + align:start position:0% +supera molecular structures that these +kinds of phospholipids come for + + align:start position:0% +kinds of phospholipids come for + + + align:start position:0% +kinds of phospholipids come for +so super molecular molecular it's a very + + align:start position:0% +so super molecular molecular it's a very + + + align:start position:0% +so super molecular molecular it's a very +important term in biology as it is in + + align:start position:0% +important term in biology as it is in + + + align:start position:0% +important term in biology as it is in +engineering super molecular it means + + align:start position:0% +engineering super molecular it means + + + align:start position:0% +engineering super molecular it means +it's a structure that's above the + + align:start position:0% +it's a structure that's above the + + + align:start position:0% +it's a structure that's above the +molecular level it's a an aggregation of + + align:start position:0% +molecular level it's a an aggregation of + + + align:start position:0% +molecular level it's a an aggregation of +different molecules to make a super + + align:start position:0% +different molecules to make a super + + + align:start position:0% +different molecules to make a super +molecule with different properties from + + align:start position:0% +molecule with different properties from + + + align:start position:0% +molecule with different properties from +the individual components phospholipids + + align:start position:0% +the individual components phospholipids + + + align:start position:0% +the individual components phospholipids +self-assemble that's another important + + align:start position:0% +self-assemble that's another important + + + align:start position:0% +self-assemble that's another important +into supra molecular structures that are + + align:start position:0% +into supra molecular structures that are + + + align:start position:0% +into supra molecular structures that are +very very important in living systems + + align:start position:0% +very very important in living systems + + + align:start position:0% +very very important in living systems +some of them are just useful in other + + align:start position:0% +some of them are just useful in other + + + align:start position:0% +some of them are just useful in other +sorts of engineering approaches such as + + align:start position:0% +sorts of engineering approaches such as + + + align:start position:0% +sorts of engineering approaches such as +lipice ohms and micelles but the most + + align:start position:0% +lipice ohms and micelles but the most + + + align:start position:0% +lipice ohms and micelles but the most +important super molecular structure of a + + align:start position:0% +important super molecular structure of a + + + align:start position:0% +important super molecular structure of a +phospholipid is the lipid bilayer + + align:start position:0% +phospholipid is the lipid bilayer + + + align:start position:0% +phospholipid is the lipid bilayer +that surrounds your cells and what + + align:start position:0% +that surrounds your cells and what + + + align:start position:0% +that surrounds your cells and what +happens is you simply put those + + align:start position:0% +happens is you simply put those + + + align:start position:0% +happens is you simply put those +molecules the phospholipids in water and + + align:start position:0% +molecules the phospholipids in water and + + + align:start position:0% +molecules the phospholipids in water and +they will sell assemble on their own + + align:start position:0% +they will sell assemble on their own + + + align:start position:0% +they will sell assemble on their own +into these super molecular structures + + align:start position:0% +into these super molecular structures + + + align:start position:0% +into these super molecular structures +whether they form micelles or lipice + + align:start position:0% +whether they form micelles or lipice + + + align:start position:0% +whether they form micelles or lipice +ohms or bilayers is dependent very much + + align:start position:0% +ohms or bilayers is dependent very much + + + align:start position:0% +ohms or bilayers is dependent very much +on the tails of the lipids what sorts of + + align:start position:0% +on the tails of the lipids what sorts of + + + align:start position:0% +on the tails of the lipids what sorts of +shapes and structures you get but in + + align:start position:0% +shapes and structures you get but in + + + align:start position:0% +shapes and structures you get but in +physiology and human physiology the + + align:start position:0% +physiology and human physiology the + + + align:start position:0% +physiology and human physiology the +phospholipids that we have want to form + + align:start position:0% +phospholipids that we have want to form + + + align:start position:0% +phospholipids that we have want to form +these bilayer structures that have + + align:start position:0% +these bilayer structures that have + + + align:start position:0% +these bilayer structures that have +incredibly important properties most + + align:start position:0% +incredibly important properties most + + + align:start position:0% +incredibly important properties most +importantly that they are semi permeable + + align:start position:0% +importantly that they are semi permeable + + + align:start position:0% +importantly that they are semi permeable +and they can wrap form the boundary to + + align:start position:0% +and they can wrap form the boundary to + + + align:start position:0% +and they can wrap form the boundary to +certain cells so I will continue with + + align:start position:0% +certain cells so I will continue with + + + align:start position:0% +certain cells so I will continue with +the final discussion of this on Monday + + align:start position:0% +the final discussion of this on Monday + + + align:start position:0% +the final discussion of this on Monday +before we move forward to the amino + + align:start position:0% +before we move forward to the amino + + + align:start position:0% +before we move forward to the amino +acids peptides and proteins and I just + + align:start position:0% +acids peptides and proteins and I just + + + align:start position:0% +acids peptides and proteins and I just +quickly want to move you to ask you for + + align:start position:0% +quickly want to move you to ask you for + + + align:start position:0% +quickly want to move you to ask you for +Monday to try to catch a read of the + + align:start position:0% +Monday to try to catch a read of the + + + align:start position:0% +Monday to try to catch a read of the +section 3.2 in the text if you have a + + align:start position:0% +section 3.2 in the text if you have a + + + align:start position:0% +section 3.2 in the text if you have a +chance it'll give you a nice preview + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/bHOpK1yQ9tI.txt b/bHOpK1yQ9tI.txt new file mode 100644 index 0000000000000000000000000000000000000000..fcb89995e42ddc7a7bce6df38f4ac660f1e4dc7f --- /dev/null +++ b/bHOpK1yQ9tI.txt @@ -0,0 +1,659 @@ +align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and each team on first step you have to + + align:start position:0% +and each team on first step you have to + + + align:start position:0% +and each team on first step you have to +decide the name of the team and it has + + align:start position:0% +decide the name of the team and it has + + + align:start position:0% +decide the name of the team and it has +to be an italian word + + align:start position:0% +to be an italian word + + + align:start position:0% +to be an italian word +so first step first step i need each + + align:start position:0% +so first step first step i need each + + + align:start position:0% +so first step first step i need each +team + + align:start position:0% +team + + + align:start position:0% +team +stand up what's happening one at a time + + align:start position:0% +stand up what's happening one at a time + + + align:start position:0% +stand up what's happening one at a time +one team at the time + + align:start position:0% +one team at the time + + + align:start position:0% +one team at the time +stand up and and + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +it's a great family through the history + + align:start position:0% +it's a great family through the history + + + align:start position:0% +it's a great family through the history +of + + align:start position:0% +of + + + align:start position:0% +of +uh + + align:start position:0% + + + + align:start position:0% + +very famous + + align:start position:0% +very famous + + + align:start position:0% +very famous +in the movie yes + + align:start position:0% + + + + align:start position:0% + +next team + + align:start position:0% + + + + align:start position:0% + +is that you have to discuss the right + + align:start position:0% +is that you have to discuss the right + + + align:start position:0% +is that you have to discuss the right +answer with your team and then + + align:start position:0% + + + + align:start position:0% + +and then take turns and round to the + + align:start position:0% +and then take turns and round to the + + + align:start position:0% +and then take turns and round to the +blackboard because you want to be the + + align:start position:0% +blackboard because you want to be the + + + align:start position:0% +blackboard because you want to be the +first one to write the correct answer + + align:start position:0% +first one to write the correct answer + + + align:start position:0% +first one to write the correct answer +i remember right + + align:start position:0% + + + + align:start position:0% + +the first part of the game + + align:start position:0% +the first part of the game + + + align:start position:0% +the first part of the game +it's a spelling competition + + align:start position:0% +it's a spelling competition + + + align:start position:0% +it's a spelling competition +if i say something it can be a word it + + align:start position:0% +if i say something it can be a word it + + + align:start position:0% +if i say something it can be a word it +can be a letter it can be anything + + align:start position:0% +can be a letter it can be anything + + + align:start position:0% +can be a letter it can be anything +and to learn you have to discuss and run + + align:start position:0% +and to learn you have to discuss and run + + + align:start position:0% +and to learn you have to discuss and run +or your branding discuss whatever + + align:start position:0% +or your branding discuss whatever + + + align:start position:0% +or your branding discuss whatever +you just write + + align:start position:0% +you just write + + + align:start position:0% +you just write +so i first say + + align:start position:0% +so i first say + + + align:start position:0% +so i first say +the word and then when i do this it + + align:start position:0% +the word and then when i do this it + + + align:start position:0% +the word and then when i do this it +means that you can + + align:start position:0% +means that you can + + + align:start position:0% +means that you can +okay so what's that actually + + align:start position:0% +okay so what's that actually + + + align:start position:0% +okay so what's that actually +your book + + align:start position:0% +your book + + + align:start position:0% +your book +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so first thing is + + align:start position:0% +so first thing is + + + align:start position:0% +so first thing is +ah + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +next one you're ready + + align:start position:0% + + + + align:start position:0% + +wait the + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +this is bad i let us + + align:start position:0% + + + + align:start position:0% + +i'm thirsty + + align:start position:0% + + + + align:start position:0% + +nice + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +and we use + + align:start position:0% + + + + align:start position:0% + +well maybe the trains aren't working + + align:start position:0% +well maybe the trains aren't working + + + align:start position:0% +well maybe the trains aren't working +today and that's because we're shopping + + align:start position:0% + + + + align:start position:0% + +etc + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% + + + + align:start position:0% + +a translation challenge + + align:start position:0% +a translation challenge + + + align:start position:0% +a translation challenge +i'm gonna say a sentence either in + + align:start position:0% +i'm gonna say a sentence either in + + + align:start position:0% +i'm gonna say a sentence either in +italian or in english + + align:start position:0% +italian or in english + + + align:start position:0% +italian or in english +and then you have to write it + + align:start position:0% +and then you have to write it + + + align:start position:0% +and then you have to write it +in the other language + + align:start position:0% +in the other language + + + align:start position:0% +in the other language +and again wait for the signal the + + align:start position:0% +and again wait for the signal the + + + align:start position:0% +and again wait for the signal the +sentence is this + + align:start position:0% + + + + align:start position:0% + +trainee + + align:start position:0% + + + + align:start position:0% + +be sure to discuss and take turns with + + align:start position:0% +be sure to discuss and take turns with + + + align:start position:0% +be sure to discuss and take turns with +the chalk and just + + align:start position:0% +the chalk and just + + + align:start position:0% +the chalk and just +the sentence is i need help please + + align:start position:0% +the sentence is i need help please + + + align:start position:0% +the sentence is i need help please +okay okay i need help whoa + + align:start position:0% +okay okay i need help whoa + + + align:start position:0% +okay okay i need help whoa +get it get it full you know it + + align:start position:0% + + + + align:start position:0% + +go go go + + align:start position:0% + + + + align:start position:0% + +okay we got it + + align:start position:0% + + + + align:start position:0% + +i said please + + align:start position:0% +i said please + + + align:start position:0% +i said please +he comes + + align:start position:0% +he comes + + + align:start position:0% +he comes +that you + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% +oh + + + align:start position:0% +oh +no like gnocchi + + align:start position:0% + + + + align:start position:0% + +i'm gonna repeat the game + + align:start position:0% + + + + align:start position:0% + +the grammar has to be perfect + + align:start position:0% + + + + align:start position:0% + +we don't have a winner yet + + align:start position:0% + + + + align:start position:0% + +then the subject is plural the verb is + + align:start position:0% + + + + align:start position:0% + +so we said that paul patina and + + align:start position:0% +so we said that paul patina and + + + align:start position:0% +so we said that paul patina and +pomodoroni won so they won this + + align:start position:0% +pomodoroni won so they won this + + + align:start position:0% +pomodoroni won so they won this +challenge + + align:start position:0% +challenge + + + align:start position:0% +challenge +but the challenge doesn't believe here + + align:start position:0% +but the challenge doesn't believe here + + + align:start position:0% +but the challenge doesn't believe here +what + + align:start position:0% + + + + align:start position:0% + +episode \ No newline at end of file diff --git a/bMnpf0s-mAk.txt b/bMnpf0s-mAk.txt new file mode 100644 index 0000000000000000000000000000000000000000..b15516b6ffeba808fe051549e0daac000b3c142e --- /dev/null +++ b/bMnpf0s-mAk.txt @@ -0,0 +1,3019 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high-quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: OK, let's start. + +So it's good to +remind ourselves why + +we are doing what +we are doing today. + +So we've seen that +in a number of cases, + +we look at something like +the coexistence line of gas + +and liquid that terminates +at the critical point. + +And that in the vicinity +of this critical point, + +we see various thermodynamic +quantities and correlation + +functions that have +properties that + +are independent of the +materials that are considered. + +So this led to this +concept of universality, + +and we were able to justify +that by looking at properties + +of this statistical field. + +And we ended up with +[INAUDIBLE] normalization + +group procedure, +which classified + +the different universality +classes according + +to the number of components +of the order parameter, + +the thing that categorizes +the coexisting phases, + +and the dimensionality of space. + +And that, in +particular something + +like a liquid-gas system, would +correspond to n equals to 1. + +Another example that +would correspond to that + +would be, for example, +a mixture of two metals + +in a binary alloy. + +You can have the +different components mixed + +or phase separated +from each other. + +So the normalization group +method gave us the reason + +for there is this +universality, but we + +found that calculating +the exponent + +was a hard task coming +from four dimensions. + +So the question is, given that +these models or these numbers, + +the singularities +here are universal, + +can we obtain them from +a different perspective? + +And so let's say we are +focused on this kind + +of liquid-gas system, +which belong to this n + +equals to 1 universality class. + +So we can try to imagine +the simplest model + +that we can try to +solve that belongs + +to that universality class. + +And again, maybe thinking +in terms of a binary alloy, + +something that has +two possible values. + +In the liquid-gas, +it could be cells + +that are either empty or +filled with a particle. + +And so this binary model +is this Ising model, + +where, at each +side of a lattice, + +we put a variable +that is minus plus 1. + +And so the idea is, again, if +I take any one of these Ising + +models and I +coarse-grain them, I + +will end up with the +same statistical field, + +and it would have the +same universality class. + +But if I make a sufficiently +simple version of these models, + +maybe I can do something else +and solve them in a manner + +that these critical +behaviors can come up + +in an easier fashion. + +So let's say we are interested +in two dimensions or three + +dimensions. + +I can draw two +dimensions better. + +We draw a square lattice. + +On each side of it, we put +one of these variables. + +And in order to +capture this tendency + +that there is a possibility +of coexistence where + +you have patches that are +made of liquid or gas, + +or made of copper or +zinc in our binary alloy, + +we need to have a tendency for +things that are close to each + +other to be in the same +state so that we can capture + +by a Hamiltonian, which is a +sum over nearest neighbors, that + +gives an enhanced weight +if they are parallel. + +And whatever that +coupling is, once it + +is rescaled by kT, this +combination, the energy divided + +by kT, we can parametrize +by a dimensionless number k. + +And calculating the +behavior of the system + +as a function of +temperature, as the strength + +of the coupling in +this simplified model, + +amounts to calculating +the partition function + +as a function of a parameter +k, which is a sum over, + +if I'm in a system that +has n sites all to the n + +configurations, of a weight that +tries to make variables that + +are next to each other +to be in the same state. + +So clearly, what +is captured here + +is a competition +between energy-- energy + +would like everybody to +be in the same state-- + +versus entropy. + +Entropy wants to have +different states at each site. + +So you'll have a factor +of 2 per site as opposed + +to everybody being aligned, +which is essentially one state. + +And so that +competition potentially + +could lead you to a phase +transition between something + +that has coexistent at low +temperature and something that + +is disordered at +high temperatures. + +So now we have just +recast the problem. + +Rather than having a partition +function which was a functional + +integral over all configurations +of the statistical field, + +I have to do this +partition function, which + +is finite number +of configurations, + +but it's still an +interacting theory. + +I cannot independently move +the variable at each site. + +So the question is, +are there approaches + +by which I can calculate this? + +And one set of approaches +is to start with a limit + +that I can solve and +start expanding on that. + +And these expansions that are +analogous to the perturbation + +expansions that we +learned in 8.333 + +about interacting +systems, in this case + +are usually called +series expansions. + +One would perform +them on a lattice. + +Now, I kind of hinted at +two limits of the problem + +that we know exactly +what is happening, + +and those lead to two +different series expansions. + +One of them is the +low-temperature expansions. + +And here the idea +is that I know what + +the system is doing +at T equals to 0. + +At T equals to 0, I have to +find the configuration that + +minimizes the energy. + +T equals to 0 is also equivalent +to k going to infinity. + +I have to find a state +that maximizes this weight, + +and that's obviously the +case where all of the spins + +are either plus or minus. + +So all sigma i equals to +plus 1 or all sigma i equals + +to minus 1. + +But for the sake of +doing one or the other, + +let's imagine that +they are all plus + +and that I am solving the +problem for the generalization + +of square cube to +d-dimensional lattice. + +After all, we were doing +d dimensions in general. + +So in d dimensions, each +spin will have d neighbors. + +And so if I ask, what +is the weight that I + +will get at 0 temperature, +essentially each spin + +would have d factors of k. + +So the weight that I would get +at T equals to 0-- let's call + +that Z of T equals to 0-- +is simply e to the dNk. + +There are N sites. + +Each one of them has d +neighbors in d dimensions. + +Of course, each one of +them has 2d neighbours, + +but then I have to count the +number of neighbors per site. + +So basically, this bond is +shared by two neighbors, + +so half of it +contributes to this site. + +And there are two possibilities. + +So the partition function at +T equals to 0 is simply this. + +It's just the contribution +of the two ground states. + +Now, we are interested in +the limit where T goes to 0. + +So at T equals to 0, I +know what is happening. + +Now, what I will get +as I allow temperature + +to be larger, at some +cost I am able to flip + +some of these spins from, +say, the plus to minus. + +And I will get, in this case, +islands of negative spin + +in sea of plus. + +And these islands will +give a contribution + +that is going to be +exponentially small in k + +and something to do with the +bonds that I have broken. + +And by broken, I mean gone +from the high energy, well, + +highly satisfied plus-plus state +to the unsatisfied plus-minus + +state, in fact, 2k times +number of broken bonds. + +So we can very easily write the +first few terms in this series. + +So let's make a list of +the excitation, or island + +that I can make, +how many ways I can + +make this, which I +will call degeneracy, + +and the number of broken bonds. + +So clearly, the +simplest thing that I + +can do in a sea of pluses +is to make one island, which + +is simply a site that +has been previously plus + +and now has gone +to become a minus. + +And this particular excitation +can occur any one of N places + +if I have a lattice +of size N. And I'm + +going to ignore any corrections +that I may have from the edges. + +If you want you can do that, +and that'd be more precise. + +But let's focus, +essentially, on things + +that are proportional to N. + +Then how many bonds +have I broken? + +You can see that +in two dimensions, + +I have broken four bonds. + +In three dimensions, +it would have been six. + +So essentially, it +is twice the number + +of dimensions that +is taking place. + +And so the +contribution to energy + +is going to be e +to the minus 2d. + +And I went from +plus k to minus k, + +so in fact, I would +have to multiply by 2k. + +Now, the next thing +that I can do, + +the lowest energy excitation +is to put two minuses that + +are next to each other +in this sea of pluses. + +OK? + +Now, you can see that +in two dimension, + +I can orient this pair +along the x-direction + +or along the y-direction. + +And in general, there would be d +directions, so I would have dN. + +Roughly, you would say +that the number of bonds + +that you have +broken is twice what + +you had before if the +two were separate. + +But there is this +thing in between + +that is now actually +a satisfied bond. + +So you can convince +yourself that, actually, + +if the two of them +were separate, + +these two minus excitations, +I would have 4d. + +But because I joined them, +essentially I have 2d minus 1 + +from each one of them, +and there's two of those. + +And of course, the +next lowest excitation + +would indeed be to +have two minuses that + +have no site, are totally +separate from each other. + +And the contribution-- +the number of these, + +well, this is +something to count. + +The first one can +any one of N places. + +The next one can be in any one +of N minus 2d minus 1 places. + +It cannot be on the same +one, and it cannot be in any + +of the 2d neighbors. + +And I should have +double counting, + +so there is a factor of 2 here. + +And the cost of this is simply +twice that, so this is 4d. + +So if I want to start writing +a partition function expanded + +beyond what I have +at 0 temperature, + +what I would have +would be 2e to the dNk. + +There's zero temperature +contribution. + +I would have 1 plus N e +to the minus 4dk plus dN + +e to the minus 4 2d minus 1 k. + +And then from the other +one that I have written, + +N N minus 2d minus 1 +over 2e to the minus 8dk. + +And I can keep going and +adding higher and higher order + +terms of the series. + +OK? + +OK. + +Once I have the +partition function, + +I can start calculating +the energy, which + +would be minus d log Z +with respect to d beta. + +What is beta? + +Well, I said that this +factor is something like 1 + +over kT, which is beta and J. + +So assuming that I +have a fixed energy + +and I'm changing temperature, +and the variations of k + +are reflecting the +inverse temperature beta, + +then I can certainly +multiply here a J and a J, + +which is a constant. + +And all I need to +do is to take a J d + +by dk of log of the expression +that I have above there. + +OK? + +So let's take the log +of that expression. + +I have log of 2 +plus dNk from here. + +And then I have log of +1 plus terms in a series + +that I have +calculated perturbity. + +Now, log of 1 plus +a small quantity I + +can always expand +as a small quantity + +minus x squared over 2. + +You may worry whether or +not, with N ultimately + +going to infinity, this +is a small quantity. + +Neglecting that +for the time being, + +if I look at this as log +of 1 plus a small quantity, + +from here I would get N e +to the minus 4dk plus dN + +e to the minus 4 2d minus +1 k plus N N minus 1 + +minus 2d over 2e to the +minus 8dk, and so forth. + +But then remember +that log of 1 plus x + +is x minus x squared over 2 plus +x cubed over 3, and so forth. + +So if x is my small +quantity, I will + +have a correction, which +is minus x squared over 2. + +Let's just do it +for this first term. + +I will get minus N squared +over 2e to the minus 8dk, + +and there will be a whole +bunch of higher-order terms. + +OK? + +Now, where am I going with this? + +Ultimately, I want to calculate +various quantities that + +are extensive in the sense that +they are proportional to N, + +and when I divide by +N I will get something + +like energy per site. + +So if I do that, I have to +divide this whole thing by N, + +I can see that here +I have a term that + +is log T divided by N. In +the N goes to infinity limit, + +it's a term that has order +of 1 over N I can neglect. + +But all of these other +terms are proportional to N. + +And when I divide by N, I +can drop these factors of N. + +Well, except that I +have a couple of terms + +that, if I had +left by themselves, + +potentially could have +been order of N squared. + +I have N squared over +2, but fortunately, you + +can see that it +cancels out over there. + +Now, the reason this +happens, and also + +the reason this +series is legitimate, + +is because we already did +something very similar to that + +in 8.333 when we were doing +these cumulant expansions. + +And when we were doing +these cumulant expansions, + +we obtained the series for, +then, the grand partition + +function, which was a +whole bunch of terms. + +But when we took the log, only +the connected terms survived. + +And the connected +terms were the things + +that, because they +had a center of mass, + +were giving you a factor that +was proportional to volume. + +And here you expect that +ultimately everything + +that I will get here, if I +calculate, let's say, log Z + +properly and then +divide by N, it + +should be something +that is order of 1. + +It shouldn't be order +of N, or N cubed, + +or any of these other terms. + +So essentially, the purpose of +all of these higher-order terms + +is really to subtract +off things such as this + +that would arise in +the counting when + +we look at islands +and excitations that + +are disconnected. + +So I could have something right +here, something right here. + +So this would be, +essentially, a product + +of the contributions of +these different islands. + +As long as they are disconnected +from some term in the series, + +there would be a subtraction +that would get rid of that + +and would ensure that these +additional factors of N, + +because I can move each island +over the entire lattice, + +would disappear. + +So I have this series, +and now I can basically + +take the derivatives. + +So I have minus J, +and I take d by dk + +of the various terms +that have survived. + +The first one is d. + +So dJ is essentially +the energy pair site + +that I would have +at 0 temperature. + +I have strength J, deeper site. + +And then the +excitations will start + +to reduce that and correct that. + +And so from here, I would get +minus 4d e to the minus 4dk. + +From here, I would get +minus 4 2d minus 1 d + +e to the minus 4 2d minus 1 k. + +The N-squared terms disappeared. + +So I would have +2d plus 1 over 2. + +But then it gets multiplied by +8d when I take a derivative. + +So I will get plus 4d 2d +plus 1 e to the minus 8dk, + +and so forth in the series. + +OK? + +So these terms that +are subtraction, + +you can see that you +can really easily + +connect to these +primary excitations. + +If you like, this +term corresponds + +to taking two of these and +colliding them with each other. + +They cannot be on +top of each other. + +They cannot be +next to each other. + +And so there is a +subtraction because a number + +of configurations +are not allowed. + +So this is, in +some sense, a kind + +of expansion in +these excitations + +and the interactions +among these excitations. + +OK? + +Now presumably, +what is happening + +is that at very low +temperature, you + +are going to get these +individual simple excitations + +with a little bit of +interaction between them. + +As you increase the temperature, +the size of these islands + +will get bigger and bigger. + +They start to merge +into each other. + +Configurations +that you would see + +will be big islands in a sea. + +And presumably, the +size of these islands + +is some measure of +the correlation length + +that you have in this +low temperature state. + +Eventually, this +correlation length + +will hit the size of the system. + +And then the starting point, +that you had a sea of pluses + +and you're exciting around +it, it is no longer valid. + +If you like, that vacuum +state has become unstable, + +and this series, the way +that we are constructing it, + +ceases to go beyond that point. + +OK? + +So let's take another step. + +If I've calculated the +energy, I could also + +calculate the heat +capacity, which is d by dT. + +Actually, I expect the heat +capacity to be extensive also, + +so I'll divide by +N. So I will look + +at the heat capacity per site. + +I know that the natural +units of heat capacity + +are kB, which has dimensions of +energy divided by temperature. + +So I divide by kB. + +So here I will have kBT. + +But then I notice that kBT, +these are related inversely + +to K, capital K. It is J over +K. So I can write this as J + +over K, and d by d-- 1 over K +will give me a minus K squared. + +I will have a factor of 1 +over J, and the 1 over J + +actually cancels this +factor of J here. + +So all I need to do-- well, +actually, let me write + +it, J d by dK of this E over N. + +So the expression +that I have above, I + +have to take another +derivative with respect + +to K multiplied by +minus K squared over J. + +The J's cancel +out, and so I will + +have a series that will be +proportional to K squared. + +Good, I made everything +dimensionless. + +And then the first term +that will contribute + +will be 16 d squared e to +the minus 4dK, from here. + +And from here, I will +get 16 2d minus 1 + +squared d e to the +minus 4 2d minus 1 K. + +And from here, I would +get minus 32d 2d plus 1 e + +to the minus 8dK, +and then so forth. + +OK? + +So you can see that +this is something + +that is a kind of +mechanical process, + +that in the '40s and +'50s, without even + +the need for any computers, +people could sit down and draw + +excitations, +provide these terms, + +and go to higher and higher +order terms in the series. + +Now, the reason that they +were going to do this + +is that the +expectation that if I + +look at this heat capacity +as a function of something + +like temperature, which is e +to the 1 over k, for example, + +then it starts at 0. + +And if we get corrections from +these higher and higher order + +terms in the +series-- I calculated + +the first few-- +I don't know what + +will happen if I were to include +higher and higher order terms. + +But my expectation is that, +say, at least at some point + +when this expansion from +low temperature breaks down, + +I will have a divergence, let's +say, of the heat capacity. + +Or maybe I calculated +susceptibility + +or some other +quantity, and I expect + +to have some singularity. + +And maybe by looking and fitting +more terms in the series, + +one can guess what the +exponent and the location + +of the singularity is. + +So you can see that, +actually in this case, + +the natural variable that +I am expanding is not K, + +but e to the minus 2dK-- +sorry, e to the minus 2K + +because each excitation will +have a number of broken bonds + +that I have to calculate. + +Each one of them makes a +contribution like this. + +So maybe we can call +this our new variable. + +And we have a series that +has a function of this + +or some other variable, +has a singularity. + +Actually, you should be +able to, first of all, + +convince yourself that the +nature of the singularity + +is not modified by any +mapping that is analytical + +at the point of the singularity. + +So if the heat capacity +as a function of k + +has a particular divergence, +as a function of u + +it will have exactly +the same divergence. + +In particular, we expect +that as u approaches + +some critical value, +the kinds of functions + +that we are interested have a +behavior, a singular behavior, + +that is something like +1 minus u over uC. + +Let's say for the +heat capacity, I + +would expect some kind of +a singularity such as this. + +If I had a pure +function such as this + +and I constructed an +expansion in u, what do I get? + +I will get 1 plus +alpha u over uC + +plus alpha alpha plus 1 +over 2 uC squared u squared, + +and so forth. + +It's just a binary +series expanded. + +The l term in the series would +be alpha alpha plus 1 alpha + +plus l minus 1 divided by l +factorial-- that's actually + +2 factorial-- uC to the power +of l u to the l and so forth. + +OK? + +Now, typically, one of the +ways that you look at series + +and decide whether it's a +singular convergent series + +or what the behavior +is is to look + +at the ratio of +subsequent terms. + +So let's say that when +I calculated my function + +C as a function of +u, I constructed + +a series whose terms +had coefficients + +that I will call al. + +OK? + +So here, if you had +exactly this series, + +you would say that the ratio +al divided by al minus 1 + +is essentially the ratio of +one of these factors compared + +to the previous one. + +And every time you add +one of these factors, + +you add a term that is like +this alpha plus l minus 1, + +l factorial compared to l minus +1 factorial has a factor of l, + +and then you have uC. + +And I can rewrite this as uC +inverse, l divided by l is 1, + +and then I have minus 1 +minus alpha divided by l. + +OK? + +So a pure divergence of the +form that I have over here + +would predict that the +ratio of subsequent terms + +would be something like this. + +And presumably, if +you go sufficiently + +high in the series, in order +to reproduce this divergence + +you must have that form. + +So what you could do +as a test is to plot, + +for your actual series, what +the ratio of these terms + +is as a function of 1 over l. + +So you can start with the ratio +of the second to first term. + +You would be at 1/2. + +Then you would go 1/3, +then you would go 1/4, + +you would have +1/5, and basically + +you would have a set of points. + +And you would plot +what the location + +is for the first term in +the series, the next term + +in the series, the next term +in the series, and so forth. + +And if you are +lucky, you would be + +able to then pass +a straight line + +at large distances +in the series. + +And the intercept of +that extrapolated line + +would be your inverse +of the singular point. + +And the slope of +this line would give + +you 1 minus alpha or +minus 1 minus alpha. + +OK? + +So there is really, a +priori, not much reason + +to hope that that will +happen because you + +can say that if I look at the +series that is A 1 minus u + +over uC to the minus alpha, plus +I add an analytic part, which + +is sum p equals 1 to, +say, 52 of bl u to the l. + +For any bl in this function has +exactly the same singularity + +as the original one. + +And yet the first 52 +terms in the series, + +because of this additional +analytical form, + +have nothing to do with +the eventual singularity. + +They're going to +be massing that. + +So there is no reason for you +to expect that this should work. + +But when people do this, and +they find that, let's say, + +for d equals to 2 up to +some jumping up and down, + +they get a reasonable +straight line. + +And the exponent that they get +would correspond very closely + +to the alpha of 0, which is the +logarithmic divergence that one + +gets. + +So this is, for d equals to +2, and then they repeat it, + +let's say, for d +equals to 3, they + +get a different set of points. + +OK? + +Maybe not perfectly +on a straight line, + +but you can still extrapolate +and conclude from that + +that you'll have an alpha +which is roughly 0.11 when + +d equals to 3, +which is quite good. + +So for some reason or +other, these lattice models + +are kind of sufficiently +simple that, + +in an appropriate +expansion, they + +don't seem to give you +that much of a problem. + +And so people have gone +and calculated series, + +let's say, this was +in '50s and '60s, + +just by drawing things on hand. + +And maybe some +primitive computers, + +you can go to order of +20 terms in this series, + +and then extrapolate exponents +for various quantities. + +OK? + +But it's not as simple as that. + +And the reason I calculated +the first three terms for you + +was to show you that what I +told you here was clearly a lie. + +Why is that? + +Because of the three terms that +I explicitly calculated for you + +in that series, the +third one is negative. + +Right? + +So clearly, if I +were to plot that, + +I will get something over here. + +Right? + +So what's going gone there +is a different issue. + +And people have developed +kind of methodologies and ways + +to look at series and +guess what is going on + +and yet continue to +extract exponents. + +So one potential origin +for alternating signs-- + +and any series that has a +divergence such as the one + +that I have indicated for you +will have, eventually, signs + +that need to be positive-- +has to do with the following. + +Let's say if I take a series, +which is 1 over 1 minus z/2. + +OK? + +This is a very nice series. + +It's 1 plus 0/2 z +squared/4, z cubed/8. + +You could apply this +ratio test to this series + +and conclude that you +have a linear divergence. + +Now, suppose I multiply +that by 1 over 1 + +plus z squared, which +is a function that's + +perfectly well-behaved +as a function of z. + +Yet if I multiply it here, I +will get 1 minus z squared plus + +z to the fourth +minus z to the sixth. + +And what it does is +it kind of distorts + +what is happening over here. + +Actually, in this +series you can see + +it kind of becomes ill-defined +when z is of order of 1. + +It changes the signs, et cetera. + +But the function itself has a +perfectly good singularity that + +appears at z equals to 2. + +And starting from +an expansion from 0, + +there should be no +problems along the line + +until you hit z of 2. + +What is the reason for +these alternating signs? + +It is because you should be +looking at the complex z plane. + +And in the complex z plane, you +have poles at plus and minus i + +which are located closer to +the origin than you have at 2. + +So basically, your +series will start + +to have problems by +the time you hit here, + +and that problem is reflected +in the alternating behavior. + +It's also showing up over there. + +Yet it has nothing to do with +going along the real axis + +and encountering the +singularity that you are after. + +OK? + +So one thing that you +can do is to say, well, + +who said I should +use z as my variable? + +Maybe I can choose some +other function v of z. + +OK? + +And then when I choose +the appropriate thing, + +the singularity on the real +axis will be pushed to v of 2. + +But maybe I chose appropriate +function of v of z + +such that the +other singularities + +are pushed very far away so that +the first singularity that I + +encounter is over here. + +OK? + +And it turns out that +if you take this series + +over here and rather than +working with e to the minus k, + +we recast things in terms +of tanh K-- let's call + +that v-- which is e to +the K plus e to the minus + +K-- well actually, tanh +K I can also write as e + +to the 2K minus 1 +e to the 2K plus 1. + +I mean, it's just +a transformation. + +So I can replace +e to the minus 2K + +with some function v, +substitute for u in that series, + +and I will have a +different function + +as an expansion in powers of v. + +And once people do that, +same thing happens as here. + +You'll find a function that +all of its terms are, in fact, + +positive, and the things that +I mentioned to you over here + +were applied. + +After such transformation, +you get very nice behaviors. + +OK? + +So there seems to +be some guesswork + +into finding the +appropriate transformation. + +There are other methods +for dealing with series + +and extracting +singularities called + +Pade approximants, et cetera, +which I won't go into. + +But there are kind of, again, +clever mathematical tricks + +for extracting singularity +out of series such as this. + +OK? + +So I'll tell you shortly +why this tanh K is really + +a good expansion factor. + +It turns out that +for Ising models, + +it's actually the +right expansion factor + +if we go to the other +limit of high temperatures. + +OK? + +So basically, now at +T going to infinity, + +you would say that sigma +i is minus or plus 1 + +with equal probability. + +As T goes to +infinity, this factor + +that encodes the tendency of +spins to be next to each other + +has been scaled to 0, +so I know exactly what + +is going on at +infinite temperature. + +Basically, at each site, I +have an independent variable + +that is decoupled +from everything else. + +So I can start expanding around +that for, say, the partition + +function. + +Let's think of it for +a general spin system. + +So I will write it +as a trace over, + +let's say, if I have Potts +model rather than two values, + +I would have K values +of something like e + +to the minus beta +H, again, trying + +to be reasonably general. + +And the idea is that as you +go to infinite temperature, + +beta goes to 0, +and this function + +you can expand in a series 1 +minus beta H plus beta squared + +H squared over 2, and so forth. + +Now, the trace of +1 is essentially + +summing over all +possible states. + +Let's say the two +states that you + +would have for the Ising +model or however many + +that you have for Potts models +at each site independently. + +So that can give me +some partition function + +that I will call Z0. + +It is simply 2 to the +n for the Ising model. + +But once I factor +that, you can see + +that the rest of the +terms in the series + +can be regarded as expectation +values of this Hamiltonian + +with respect to this +weight in which all + +of the degrees of +freedom are treated + +as independent, +unconstrained variables. + +And of course, the thing +that I'm interested + +is log of the +partition function. + +And so that will +give me log of Z0, + +and then I have the +log of this series. + +And then you can see that that +series is a generating function + +for the moments of +the Hamiltonian. + +So its log will be the +generating function + +for the cumulant, so H +to the l 0, the cumulant. + +So the variance at +the second order + +and appropriate cumulant +at higher orders. + +OK? + +So let's try to calculate this +for the Ising model, where + +my minus beta H is K sum +over i, j sigma i sigma j. + +OK? + +Then at the lowest +order, what do I get? + +The average of beta +H is K sum over i, + +j average of sigma i sigma +j with this zeroed weight. + +But as I emphasized, +at zeroed weight, + +every site independently +can be plus or minus. + +Because of the +independence, I can do this. + +And then since each site +has equal probability to be + +plus or minus, its average is 0. + +So basically, this will be 0. + +OK? + +So the first thing that +can happen in that series-- + +if I go to the next order. + +So at next order, beta H +squared would involve K + +squared sum over i, j K, l +sigma i sigma j sigma K sigma l. + +And I have to take +an average of this, + +which means that I have to +take an average of something + +like this. + +OK. + +And you would say, well, +again, everything is 0. + +Well, there is one case +where it won't be 0-- + +if these two pairs +are identical. + +Right? + +So this is going to give me +K squared sum over pair i, + +j being the same as K, l. + +Then I will get, +essentially, sigma i + +squared sigma j squared. + +Sigma i squared is 1. + +Sigma j squared is 1. + +So basically, I will get 1. + +And this is going +to give me K squared + +times the number of bonds. + +OK? + +So you can see that +I can start thinking + +of this already graphically. + +Because what I did over here, +I said that on my lattice + +this sum says you pick +one sigma i sigma j. + +If I were to pick the other +sigma i sigma j over here, + +the average would be 0. + +I am forced to put two of +them on top of each other. + +If I go to three, +there is no way + +that I can draw a +diagram that involves + +three pairs in which every +single site occurs twice, + +which is what I need. + +Because a single site appearing +by itself or three times + +will give me sigma i cubed +is the same as sigma i. + +It will average to 0. + +So the next thing that I can +do is to go to level four. + +At the level of +four, I can certainly + +do something like this. + +I can put all four of +them on top of each other, + +and then I get a K to +the fourth contribution. + +Or I could put a pair +here, and if they're here, + +for log Z that would be +unacceptable because that will + +get subtracted out when +I calculate the variance. + +It's not a connected piece. + +It's a disconnected piece. + +But I could have +something like this, + +two of them turned like this. + +So that's four. + +But really, the one that is +nontrivial and interesting + +is when I do something +like this, like a square. + +So I go here sigma 1 +sigma 2, sigma 2 sigma 3. + +That sigma 2 has been +repeated twice and becomes + +sigma 2 squared and goes away. + +Sigma 3 sigma 4, sigma +3 repeated twice, + +sigma 4 repeated twice, sigma +1 repeated twice, [INAUDIBLE]. + +OK? + +So you can see that +this kind of expansion + +will naturally lead you +into an expansion in terms + +of loops on a lattice. + +So the natural form of +high temperature expansions + +are these closed +strings or loops, + +if you like, that you have +to draw on the lattice. + +Now, it's also clear +that the thing that + +goes between two sites, that I'm +indicating by K, in all cases + +is likely to be +repeated by putting + +more and more things +on top of each other + +without modifying the effect. + +So I can go here to 4 and things +like actually 3 and things + +like that. + +So basically, you can +see that I should really + +do a summation over the +contribution of 2, 4, et + +cetera all on top of +each other, or 1, 3, + +5 on top of each other, and +call them new variables. + +So when we were doing the +cluster expansion for particles + +interacting, we +encountered this thing + +that we thought v was a +good variable to expand it. + +But then because +of these repeats, + +we decided that e to +the minus beta v minus 1 + +was a good variable +to expand it. + +So a similar thing happens here. + +And for the Ising model, +it is a very natural thing + +to recast this series in +a slightly different way. + +You see that the contribution +of each bond to the partition + +function, and by a bond I mean +a pair of neighboring sites, + +is a factor e to the +K sigma i sigma j. + +OK? + +Now, since we are dealing +with binary variables, + +this product, sigma i sigma +j, can only take two values. + +It's either plus K +or minus K depending + +on where things are +aligned or misaligned. + +So I can indicate +the binary nature + +of this in the +following fashion. + +I can write this as e to the +K plus e to the minus K over 2 + +plus sigma i sigma j e to the K +minus e to the minus K over 2. + +So that when I'm dealing +with sigma sigma being plus, + +I add those two factors. + +e to the minus K's disappear. + +I will get e to the +K. When I'm dealing + +with this thing to the minus, +the e to the K's disappear, + +and I will get e to +the minus K. So it's + +correct rewriting +of that factor. + +The first term you, +of course, recognize + +as the hyperbolic cosine +of K, the second one + +as the hyperbolic +sine of K. And so I + +can write the whole thing +as hyperbolic cosine + +1 plus hyperbolic tanh +of K sigma i sigma j. + +OK? + +So this tanh is really +same thing as here. + +It's the high-temperature +expansion variable. + +As K goes to 0 at +high temperature, + +tanh K also goes to 0. + +And it turns out that a much +nicer variable to expand + +is this quantity tanh K. And so +that I don't have to repeat it + +throughout, I will +give it the symbol t. + +So small t stands not for +reduced temperature anymore, + +but for hyperbolic tanh of K. + +So my partition function +now, Z-- maybe I'll + +go to another page. + +So my partition function is a +sum over the 2 to the N binary + +variables e to the K sigma i +sigma j sum over all bonds. + +I can write that as a product of +these exponential factors over + +[INAUDIBLE]. + +Each of these exponential +factors I can write as cosh K 1 + +plus t sigma i sigma j. + +All the factors of cosh K +I will take to the outside. + +So I will get cosh K +raised to the power + +of the number of bonds +that I have in my lattice + +because each bond +will contribute + +one of these factors. + +And then I have this sum over +sigma i product over bonds. + +So this is the product +of 1 plus t factors. + +So for each-- maybe +I'll do it over here. + +So for each i, j, I have to +pick one of these factors. + +I can either pick +1, nothing, or I + +can pick a factor of +t sigma i sigma j. + +OK? + +So the first term +in this series-- + +since it's a series in powers of +t, the first term in the series + +is to pick 1 everywhere. + +The next term is to pick +one factor at some point. + +But then when I +pick that factor, + +that term in the series, I +have to sum over sigma i. + +And when I sum over sigma +i, since this sigma i can + +be plus or minus with equal +probability, it will give me 0. + +OK? + +So I cannot leave this +sigma i by itself. + +So maybe I will pick +another higher-order term + +in the series that has a t, a +sigma i that would make this + +into a sigma i squared, and +then I will have a sigma K here. + +OK? + +Now, note it was kind of similar +to what I was doing here. + +But here I could +pick as many bonds + +as I like on as many factors of +K. Now what has happened here + +is, effectively, I +have only two choices. + +One choice is having +gone many, many times, + +so summing all of the terms +that had 2, 4, et cetera. + +That's what gives you the +cosh K. Or including something + +like this, sum of +1, 3, 5, et cetera. + +That's what gives you +tanh K. But the good thing + +is that it's really +now a binary choice. + +You either draw one line, +or you don't draw anything. + +OK? + +So again, your first choice is +to somehow complete the series + +by drawing something like this. + +And quite generically-- OK, +so after that has happened, + +then this is sigma i squared. + +This is sigma j squared. + +These are all-- +they have gone to 1. + +And then you do the +sum over sigma i, + +you will get a factor of 2. + +So the answer is going to +be 2 to the number of sites, + +N, cosh K to the power +of the number of bonds. + +And then I would +have a series, which + +is the sum over all graphs +with even number of bonds + +per site like here. + +So I either have 0 bond going +here, or I can have two bonds. + +I could very well have +something like this, four bonds. + +That doesn't violate anything. + +So all I need to ensure +in order that sigma i does + +not average to 0 is that I +have an even number per site. + +And then the +contribution of the graph + +is t to the number of +bonds in the graph. + +And at this stage when I'm +calculating a partition + +function, there is no +reason why I could not + +have disconnected graphs. + +For the partition function, +there is no problem. + +Presumably, when I take the +log, the disconnected pieces + +will go away. + +OK? + +Yes? + +AUDIENCE: Where does the 2 +to the N come from again? + +PROFESSOR: OK. + +So at each site, I have +to sum over sigma i. + +So sigma i is either +minus 1 or plus 1. + +What I'm doing is sum over +sigma i sigma i to some power. + +And this is either +going to give me 2 or 0 + +depending on whether +P is even or P is odd. + +All right? + +OK? + +So you can try to calculate +general terms for this series. + +Let's say we go to +hypercubic lattice, which + +is what we were doing before. + +The number of bonds +per site is d. + +So this, for the hypercubic +lattice, the number of bonds + +will be dN. + +You could do this calculation +for a triangular lattice. + +You don't have to +stick with FCC lattice. + +You don't have to stick with +these hypercubic lattices. + +The first diagram that you can +create is always the square. + +OK? + +And in d dimensions, one leg +has a choice of d direction. + +The next one would be d minus 1. + +So this would be d d minus +1 over 2 t to the fourth. + +But you could start it from +any site on the lattice + +so you would have +something like this. + +The next term that you +would have in the series + +is something that involves, +let's say, six bonds. + +So the next term +will be N t to the 6. + +And I think I sometimes +convince myself + +that the numerical factor +was something like this, + +but doesn't matter. + +You could calculate out of this. + +Yes? + +AUDIENCE: What if +we have diagrams + +of order of t squared, just +[INAUDIBLE] there and back? + +PROFESSOR: OK. + +Where would I get the +t squared from here? + +OK? + +So from this bond, +I have this factor, + +1 plus t sigma i sigma j. + +There is no t squared. + +I would have had K squared, +K to the fourth, et cetera. + +But I re-summed all of +them into hyperbolic cosine + +and the hyperbolic sine. + +So this-- + +AUDIENCE: So [INAUDIBLE] +taking this product + +along all the bonds, you can +kind of go along the same bond. + +PROFESSOR: We already +summed all of those things + +together into this factor t. + +AUDIENCE: OK. + +PROFESSOR: Yeah? + +OK? + +Yeah, it's good. + +And that's why this tanh +is such a nice variable. + +OK? + +So there is actually +the nicer series + +to work with in terms of +trying to extract exponent + +is this high-temperature +series in terms + +of these new +diagrams, et cetera. + +But I'm not going to +be doing diagrammatics. + +What I will be using this +high-temperature series + +is the following. + +One, to show that +in a few minutes + +we can use it to exactly solve +the one-dimensional Ising model + +and gain a physical +understanding of what's + +happening, and 2, to +re-derive Gaussian model. + +Turns out that there is a +close connection between all + +of these loops that you +can draw on a lattice + +through some kind of a path +integral way of thinking + +about it with the +Gaussian model. + +And that we actually will use as +a stepping stone towards where + +we are really headed, +which is the exact solution + +of the 2D Ising model. + +OK? + +So the 1D Ising model. + +And actually, the method +is sufficiently powerful + +that we can compare and +contrast two cases, one + +when you have open chain. + +So this is a system that is +composed of sites 1, 2, 3, 4, + +N minus 1, N. On each one of +them I have an Ising variable. + +And if I follow my nose, it's +a Z is 2 to the number of sites + +cosh K to the power of +the number of bonds. + +Actually, clearly with open +systems, the number of bonds + +is 1 less than the +number of sites. + +So I can be extremely precise. + +It is N minus 1. + +And then I have +to draw all graphs + +that I can on this lattice that +have an even number of bonds + +emanating from each site. + +Find one. + +[LAUGHTER] + +OK. + +Since you won't have +one, that stands. + +So you can take the log of that. + +You have this free +energy, whatever you like. + +We can't. + +1 is essentially not the zeroth +order term in this series. + +Yes? + +That was the question. + +OK. + +All right? + +You can use the same +thing, same technology, + +to calculate +spin-spin correlation. + +So I pick spins m +and n on this chain. + +Let's say this is spin m +here, and somewhere here I + +put spin n. + +And I want to know the +average of that quantity. + +What am I supposed to do? + +I'm supposed to sum over all +configurations with the weight + +sigma i sigma i plus 1 product +over all-- well, actually, + +we can be general with this. + +Let's call it product over all +bonds, which, in this case, + +are near neighbors, +sigma i sigma j. + +That weight I have to +multiply by sigma m sigma n. + +And then I have to divide +by the partition function + +so that this is +appropriately weighted. + +OK? + +So I can do precisely the +same decomposition over here. + +So I will have 2 to the N +cosh K to the number of bonds. + +In fact, this I can +do in any dimensions. + +It's not really what I would +have only in one dimension. + +And the partition +function, you have seen, + +is the sum over +all graphs, where + +t to the number of bonds +in graph is called g. + +Now I can do the same kind of +expansion that I did over here. + +If I multiply with an +additional sigma m sigma n, + +it is just like I +have already a sigma m + +and a sigma n somewhere. + +And when I sum +over sigmas, I have + +to make sure that these +things don't average to 0. + +So what I need to +do is to draw graphs + +that have an even +number at all sites + +and an odd number +at these two sites. + +All right? + +So this is sum over g with +even number except on m and n, + +where you have to +have an odd number, + +and t is subset of graphs. + +OK? + +So if I do this +for the 1D model, + +sigma m sigma n, I have to draw +graphs that have, essentially, + +an odd number. + +Essentially, sigma +m and sigma n should + +be the origins or ends of lines. + +And clearly, I can draw a +graph that connects these two. + +And so what I will get is +t to the number of steps + +that I have to make +between the two of them. + +The rest of the it is going to +be the same, 2 to the N cosh K + +to the N minus 1 in the +numerator and denominator, + +they cancel each other. + +OK? + +So you can see +explicitly that this + +is a function that decays +since t is less than 1 + +as I go further and further out. + +And that it is a +pure exponential. + +So you remember that we said in +general you would have a power + +law line in front that would +have an exponent [? theta. ?] + +And when we did r of +g, I told you, well, + +[? theta ?] came out to be +1 such that you have pure + +exponential. + +Well, here is the proof. + +And furthermore, from this +we see that c is minus 1 + +over log of the +hyperbolic tanh of K. + +And if you expand +that, you will find + +that as K goes to +infinity, it has + +precisely that e to +the 2K divergence + +that we had calculated. + +So you can see that +calculating things + +using this graphical +method is very simple. + +And essentially, the +interpretation of t + +is that it is the fidelity +with which information + +goes from one site +to the next site. + +And so the further +away you go every time, + +you lose a factor +of t in how sure + +you are about the nature +of where you started with. + +And so as you go further, you +have this exponential decay. + +OK? + +And the other thing that +we can do at no cost + +is periodic boundary conditions. + +So we take, again, +our spins 1, 2, 3, + +except that we then bend it +such that the last one comes + +and gets connected +to the first one. + +OK? + +So what's the partition +function in this case? + +It is 2 to the N. + +The number of +bonds, in this case, + +is exactly the same as +the number of sites. + +It's one more than +before, so I get + +to cosh K raised to the power +of N. And then is it just one? + +There is one thing that +goes all the way around, + +so I have 1 plus t to the N. So +this is an exponentially small + +correction as we go +further and further out. + +You can kind of regard that as +some finite-size interaction. + +I can similarly calculate sigma +m sigma n, the expectation + +value. + +OK? + +And in the denominator +from the partition + +function, I have this factor +of 1 to the t to the N. + +In the numerator, +again, you should + +be able to see two graphs. + +We can either connect this way +or we can connect that way. + +So you'll have t to +the power of n minus m, + +but you don't know which angle +is the smaller one, so you'll + +have to also include +the other one. + +OK? + +So again, if we take N +to infinity and these two + +sufficiently close, +you can see that all + +of these finite-size +effects, boundary effects, + +et cetera disappear. + +But this is, again, +a toy model in which + +to think about what the effects +of boundaries is, et cetera. + +You can see how nicely +this graphical method + +can enable you to calculate +things very rapidly. + +We'll see that, again, it +provides the right tools + +conceptually to think about what +happens in higher dimensions. \ No newline at end of file diff --git a/dT3WhWLi2wI.txt b/dT3WhWLi2wI.txt new file mode 100644 index 0000000000000000000000000000000000000000..aaa1ec3a092cd6096db950d8a2b0e53b792bce3f --- /dev/null +++ b/dT3WhWLi2wI.txt @@ -0,0 +1,13651 @@ +align:start position:0% + +the following content is provided by mit + + align:start position:0% +the following content is provided by mit + + + align:start position:0% +the following content is provided by mit +opencourseware under a creative commons + + align:start position:0% +opencourseware under a creative commons + + + align:start position:0% +opencourseware under a creative commons +license + + align:start position:0% +license + + + align:start position:0% +license +additional information about our license + + align:start position:0% +additional information about our license + + + align:start position:0% +additional information about our license +and mit opencourseware in general is + + align:start position:0% +and mit opencourseware in general is + + + align:start position:0% +and mit opencourseware in general is +available at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +what i have in mind for today is uh + + align:start position:0% +what i have in mind for today is uh + + + align:start position:0% +what i have in mind for today is uh +mainly but believe it or not + + align:start position:0% + + + + align:start position:0% + +go through + + align:start position:0% + + + + align:start position:0% + +some vocabulary strengthening + + align:start position:0% + + + + align:start position:0% + +we've gotten to a point now where + + align:start position:0% + + + + align:start position:0% + +i think the rest of the semester is + + align:start position:0% +i think the rest of the semester is + + + align:start position:0% +i think the rest of the semester is +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +much on what you all want to do but next + + align:start position:0% +much on what you all want to do but next + + + align:start position:0% +much on what you all want to do but next +week is narrative ethics + + align:start position:0% + + + + align:start position:0% + +but so i'd like to make sure we we're + + align:start position:0% +but so i'd like to make sure we we're + + + align:start position:0% +but so i'd like to make sure we we're +getting a good vocabulary build up + + align:start position:0% +getting a good vocabulary build up + + + align:start position:0% +getting a good vocabulary build up +and there'll be time for anything else i + + align:start position:0% +and there'll be time for anything else i + + + align:start position:0% +and there'll be time for anything else i +brought this in here in case i need it + + align:start position:0% +brought this in here in case i need it + + + align:start position:0% +brought this in here in case i need it +it's like a um what do you call it um + + align:start position:0% + + + + align:start position:0% + +coaches have these blankets security + + align:start position:0% +coaches have these blankets security + + + align:start position:0% +coaches have these blankets security +blankets + + align:start position:0% +blankets + + + align:start position:0% +blankets +like a security plate but i don't intend + + align:start position:0% +like a security plate but i don't intend + + + align:start position:0% +like a security plate but i don't intend +to use it + + align:start position:0% +to use it + + + align:start position:0% +to use it +but + + align:start position:0% +but + + + align:start position:0% +but +if something comes up then i got my + + align:start position:0% +if something comes up then i got my + + + align:start position:0% +if something comes up then i got my +security points + + align:start position:0% +security points + + + align:start position:0% +security points +uh but i'd like to go through some + + align:start position:0% +uh but i'd like to go through some + + + align:start position:0% +uh but i'd like to go through some +definitions + + align:start position:0% +definitions + + + align:start position:0% +definitions +okay now uh + + align:start position:0% + + + + align:start position:0% + +first of all i'd like to talk about + + align:start position:0% + + + + align:start position:0% + +some kinds of definitions + + align:start position:0% + + + + align:start position:0% + +some kinds of definitions of words + + align:start position:0% +some kinds of definitions of words + + + align:start position:0% +some kinds of definitions of words +one is called plain language + + align:start position:0% + + + + align:start position:0% + +and the opposite + + align:start position:0% +and the opposite + + + align:start position:0% +and the opposite +not the opposite but the but the uh + + align:start position:0% +not the opposite but the but the uh + + + align:start position:0% +not the opposite but the but the uh +contrast + + align:start position:0% +contrast + + + align:start position:0% +contrast +contrasting term is term of art + + align:start position:0% + + + + align:start position:0% + +we can use the word for example stress + + align:start position:0% +we can use the word for example stress + + + align:start position:0% +we can use the word for example stress +in plain language + + align:start position:0% + + + + align:start position:0% + +i got stressed out + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh we can use the term stress in + + align:start position:0% +uh we can use the term stress in + + + align:start position:0% +uh we can use the term stress in +uh at least + + align:start position:0% +uh at least + + + align:start position:0% +uh at least +uh + + align:start position:0% +uh + + + align:start position:0% +uh +two terms of art + + align:start position:0% +two terms of art + + + align:start position:0% +two terms of art +uh one is if you are + + align:start position:0% +uh one is if you are + + + align:start position:0% +uh one is if you are +a + + align:start position:0% +a + + + align:start position:0% +a +physician + + align:start position:0% +physician + + + align:start position:0% +physician +stress has a specific meaning + + align:start position:0% +stress has a specific meaning + + + align:start position:0% +stress has a specific meaning +next if you are a + + align:start position:0% +next if you are a + + + align:start position:0% +next if you are a +civil engineer + + align:start position:0% +civil engineer + + + align:start position:0% +civil engineer +stress has a specific meaning + + align:start position:0% +stress has a specific meaning + + + align:start position:0% +stress has a specific meaning +and specific those are terms of art + + align:start position:0% +and specific those are terms of art + + + align:start position:0% +and specific those are terms of art +okay + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% + + + + align:start position:0% + +in engineering + + align:start position:0% +in engineering + + + align:start position:0% +in engineering +and i would think that it is so the same + + align:start position:0% +and i would think that it is so the same + + + align:start position:0% +and i would think that it is so the same +is true in medicine + + align:start position:0% +is true in medicine + + + align:start position:0% +is true in medicine +and the same is true in law + + align:start position:0% +and the same is true in law + + + align:start position:0% +and the same is true in law +that + + align:start position:0% +that + + + align:start position:0% +that +when you encounter a term of art + + align:start position:0% + + + + align:start position:0% + +there is a standard meaning + + align:start position:0% + + + + align:start position:0% + +so if you're a lawyer or if you're not a + + align:start position:0% +so if you're a lawyer or if you're not a + + + align:start position:0% +so if you're a lawyer or if you're not a +lawyer believe it or not i got a copy of + + align:start position:0% +lawyer believe it or not i got a copy of + + + align:start position:0% +lawyer believe it or not i got a copy of +black's law + + align:start position:0% +black's law + + + align:start position:0% +black's law +dictionary + + align:start position:0% +dictionary + + + align:start position:0% +dictionary +that thick + + align:start position:0% +that thick + + + align:start position:0% +that thick +i can read it + + align:start position:0% +i can read it + + + align:start position:0% +i can read it +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now some of the terms are tedious + + align:start position:0% +now some of the terms are tedious + + + align:start position:0% +now some of the terms are tedious +because they cross-reference a whole lot + + align:start position:0% +because they cross-reference a whole lot + + + align:start position:0% +because they cross-reference a whole lot +of other terms + + align:start position:0% +of other terms + + + align:start position:0% +of other terms +and when i say tedious it becomes too + + align:start position:0% +and when i say tedious it becomes too + + + align:start position:0% +and when i say tedious it becomes too +tedious for me to get through + + align:start position:0% +tedious for me to get through + + + align:start position:0% +tedious for me to get through +but um + + align:start position:0% +but um + + + align:start position:0% +but um +i would say that of the terms that i've + + align:start position:0% +i would say that of the terms that i've + + + align:start position:0% +i would say that of the terms that i've +looked up in there and i don't know how + + align:start position:0% +looked up in there and i don't know how + + + align:start position:0% +looked up in there and i don't know how +many terms i've looked up in there maybe + + align:start position:0% +many terms i've looked up in there maybe + + + align:start position:0% +many terms i've looked up in there maybe +30 over the years i guess but just + + align:start position:0% +30 over the years i guess but just + + + align:start position:0% +30 over the years i guess but just +thumbing through it too + + align:start position:0% +thumbing through it too + + + align:start position:0% +thumbing through it too +uh a lot i can learn + + align:start position:0% +uh a lot i can learn + + + align:start position:0% +uh a lot i can learn +because in blacks they give examples + + align:start position:0% +because in blacks they give examples + + + align:start position:0% +because in blacks they give examples +of the usage + + align:start position:0% +of the usage + + + align:start position:0% +of the usage +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +i don't think that having + + align:start position:0% +i don't think that having + + + align:start position:0% +i don't think that having +is an interesting thing about learning i + + align:start position:0% +is an interesting thing about learning i + + + align:start position:0% +is an interesting thing about learning i +don't think that having + + align:start position:0% +don't think that having + + + align:start position:0% +don't think that having +understood those terms that i could re + + align:start position:0% +understood those terms that i could re + + + align:start position:0% +understood those terms that i could re +use them + + align:start position:0% + + + + align:start position:0% + +properly + + align:start position:0% + + + + align:start position:0% + +but i had to do this + + align:start position:0% + + + + align:start position:0% + +when i was chair faculty senate + + align:start position:0% +when i was chair faculty senate + + + align:start position:0% +when i was chair faculty senate +howard has a law school + + align:start position:0% +howard has a law school + + + align:start position:0% +howard has a law school +and the lawyers and the political + + align:start position:0% +and the lawyers and the political + + + align:start position:0% +and the lawyers and the political +scientists + + align:start position:0% +scientists + + + align:start position:0% +scientists +can + + align:start position:0% +can + + + align:start position:0% +can +use their specialty skills + + align:start position:0% +use their specialty skills + + + align:start position:0% +use their specialty skills +in a faculty meeting the engineers come + + align:start position:0% +in a faculty meeting the engineers come + + + align:start position:0% +in a faculty meeting the engineers come +in there with those skills + + align:start position:0% +in there with those skills + + + align:start position:0% +in there with those skills +so it was helpful to to at least learn + + align:start position:0% +so it was helpful to to at least learn + + + align:start position:0% +so it was helpful to to at least learn +that there's some differences + + align:start position:0% + + + + align:start position:0% + +i also had an experience once where + + align:start position:0% + + + + align:start position:0% + +i was in a meeting + + align:start position:0% +i was in a meeting + + + align:start position:0% +i was in a meeting +and somebody asked me to define + + align:start position:0% +and somebody asked me to define + + + align:start position:0% +and somebody asked me to define +engineering ethics + + align:start position:0% +engineering ethics + + + align:start position:0% +engineering ethics +so i defined it + + align:start position:0% +so i defined it + + + align:start position:0% +so i defined it +and this person was a physician + + align:start position:0% + + + + align:start position:0% + +and she looked in this book this um + + align:start position:0% +and she looked in this book this um + + + align:start position:0% +and she looked in this book this um +encyclopedia of + + align:start position:0% +encyclopedia of + + + align:start position:0% +encyclopedia of +of ethics found engineering ethics and + + align:start position:0% +of ethics found engineering ethics and + + + align:start position:0% +of ethics found engineering ethics and +it says something different + + align:start position:0% +it says something different + + + align:start position:0% +it says something different +he said holy + + align:start position:0% +he said holy + + + align:start position:0% +he said holy +something different + + align:start position:0% +something different + + + align:start position:0% +something different +term of art + + align:start position:0% +term of art + + + align:start position:0% +term of art +it just so happened that she looked in + + align:start position:0% +it just so happened that she looked in + + + align:start position:0% +it just so happened that she looked in +the particular encyclopedia of ethics + + align:start position:0% +the particular encyclopedia of ethics + + + align:start position:0% +the particular encyclopedia of ethics +where i wrote + + align:start position:0% +where i wrote + + + align:start position:0% +where i wrote +the engineering ethics citation + + align:start position:0% + + + + align:start position:0% + +but i told her something different + + align:start position:0% +but i told her something different + + + align:start position:0% +but i told her something different +and she said and then she saw my name + + align:start position:0% +and she said and then she saw my name + + + align:start position:0% +and she said and then she saw my name +down there and she says what's going on + + align:start position:0% +down there and she says what's going on + + + align:start position:0% +down there and she says what's going on +here + + align:start position:0% +here + + + align:start position:0% +here +i said well when you go to some other + + align:start position:0% +i said well when you go to some other + + + align:start position:0% +i said well when you go to some other +disciplines like philosophy + + align:start position:0% +disciplines like philosophy + + + align:start position:0% +disciplines like philosophy +a + + align:start position:0% +a + + + align:start position:0% +a +term of art has + + align:start position:0% +term of art has + + + align:start position:0% +term of art has +a definition that's usually located + + align:start position:0% +a definition that's usually located + + + align:start position:0% +a definition that's usually located +in a particular scholar + + align:start position:0% +in a particular scholar + + + align:start position:0% +in a particular scholar +like plato or aristotle + + align:start position:0% +like plato or aristotle + + + align:start position:0% +like plato or aristotle +and that when you write a paper + + align:start position:0% +and that when you write a paper + + + align:start position:0% +and that when you write a paper +you reference two or three usages + + align:start position:0% +you reference two or three usages + + + align:start position:0% +you reference two or three usages +by certain scholars and then you decide + + align:start position:0% +by certain scholars and then you decide + + + align:start position:0% +by certain scholars and then you decide +tell people how you are going to use it + + align:start position:0% +tell people how you are going to use it + + + align:start position:0% +tell people how you are going to use it +in that context today + + align:start position:0% +in that context today + + + align:start position:0% +in that context today +an engineer doesn't do that with the + + align:start position:0% +an engineer doesn't do that with the + + + align:start position:0% +an engineer doesn't do that with the +word stress + + align:start position:0% +word stress + + + align:start position:0% +word stress +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so what i'm going to do what + + align:start position:0% +all right so what i'm going to do what + + + align:start position:0% +all right so what i'm going to do what +what i'm going what i'm going to do is + + align:start position:0% +what i'm going what i'm going to do is + + + align:start position:0% +what i'm going what i'm going to do is +to conduct a class where we're going to + + align:start position:0% +to conduct a class where we're going to + + + align:start position:0% +to conduct a class where we're going to +experience all three levels + + align:start position:0% +experience all three levels + + + align:start position:0% +experience all three levels +and we just have to be clear on which + + align:start position:0% +and we just have to be clear on which + + + align:start position:0% +and we just have to be clear on which +ones we're talking about + + align:start position:0% +ones we're talking about + + + align:start position:0% +ones we're talking about +so when it comes to certain things i + + align:start position:0% +so when it comes to certain things i + + + align:start position:0% +so when it comes to certain things i +feel authorized to give a definition + + align:start position:0% +feel authorized to give a definition + + + align:start position:0% +feel authorized to give a definition +just like anybody else + + align:start position:0% +just like anybody else + + + align:start position:0% +just like anybody else +you look in the encyclopedia of + + align:start position:0% +you look in the encyclopedia of + + + align:start position:0% +you look in the encyclopedia of +philosophy you'll find something else + + align:start position:0% +philosophy you'll find something else + + + align:start position:0% +philosophy you'll find something else +okay i've got to justify my usage + + align:start position:0% +okay i've got to justify my usage + + + align:start position:0% +okay i've got to justify my usage +you've got to decide which one you're + + align:start position:0% +you've got to decide which one you're + + + align:start position:0% +you've got to decide which one you're +going to use + + align:start position:0% +going to use + + + align:start position:0% +going to use +my ins my experience tells me + + align:start position:0% +my ins my experience tells me + + + align:start position:0% +my ins my experience tells me +that over time you'll be doing the same + + align:start position:0% +that over time you'll be doing the same + + + align:start position:0% +that over time you'll be doing the same +thing + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so you just have to have one that's + + align:start position:0% +so you just have to have one that's + + + align:start position:0% +so you just have to have one that's +defensible in the end + + align:start position:0% +defensible in the end + + + align:start position:0% +defensible in the end +so we'll mix them up + + align:start position:0% +so we'll mix them up + + + align:start position:0% +so we'll mix them up +when you say all three levels + + align:start position:0% + + + + align:start position:0% + +uh one level is + + align:start position:0% +uh one level is + + + align:start position:0% +uh one level is +plain language + + align:start position:0% +plain language + + + align:start position:0% +plain language +one level is + + align:start position:0% +one level is + + + align:start position:0% +one level is +standardized + + align:start position:0% +standardized + + + align:start position:0% +standardized +term of art + + align:start position:0% +term of art + + + align:start position:0% +term of art +and the other one is i don't have a name + + align:start position:0% +and the other one is i don't have a name + + + align:start position:0% +and the other one is i don't have a name +for it + + align:start position:0% +for it + + + align:start position:0% +for it +but it's what you're talking about + + align:start position:0% +but it's what you're talking about + + + align:start position:0% +but it's what you're talking about +the last example + + align:start position:0% + + + + align:start position:0% + +that you can in other words a it's sort + + align:start position:0% +that you can in other words a it's sort + + + align:start position:0% +that you can in other words a it's sort +of individual justified individually + + align:start position:0% +of individual justified individually + + + align:start position:0% +of individual justified individually +justifiable + + align:start position:0% +justifiable + + + align:start position:0% +justifiable +so you give a name to it maybe you can + + align:start position:0% +so you give a name to it maybe you can + + + align:start position:0% +so you give a name to it maybe you can +find a name for it i haven't got yeah + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +uh if if a philosopher is talking it's + + align:start position:0% +uh if if a philosopher is talking it's + + + align:start position:0% +uh if if a philosopher is talking it's +legitimate to say well what do you mean + + align:start position:0% + + + + align:start position:0% + +uh by the word ethics + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +chances are the philosopher will not + + align:start position:0% +chances are the philosopher will not + + + align:start position:0% +chances are the philosopher will not +give you a dictionary or an encyclopedia + + align:start position:0% +give you a dictionary or an encyclopedia + + + align:start position:0% +give you a dictionary or an encyclopedia +definition chances are they will + + align:start position:0% +definition chances are they will + + + align:start position:0% +definition chances are they will +reference what some scholars said was + + align:start position:0% +reference what some scholars said was + + + align:start position:0% +reference what some scholars said was +how some scholar used it in certain + + align:start position:0% +how some scholar used it in certain + + + align:start position:0% +how some scholar used it in certain +works + + align:start position:0% +works + + + align:start position:0% +works +and say that i will use it much the same + + align:start position:0% +and say that i will use it much the same + + + align:start position:0% +and say that i will use it much the same +way but change it a little bit + + align:start position:0% +way but change it a little bit + + + align:start position:0% +way but change it a little bit +they'll have to change it a little bit + + align:start position:0% +they'll have to change it a little bit + + + align:start position:0% +they'll have to change it a little bit +because most of those scholars lived two + + align:start position:0% +because most of those scholars lived two + + + align:start position:0% +because most of those scholars lived two +thousand years ago + + align:start position:0% +thousand years ago + + + align:start position:0% +thousand years ago +you know to make it apply to the day you + + align:start position:0% +you know to make it apply to the day you + + + align:start position:0% +you know to make it apply to the day you +have to + + align:start position:0% +have to + + + align:start position:0% +have to +all right not only that but their + + align:start position:0% +all right not only that but their + + + align:start position:0% +all right not only that but their +translation + + align:start position:0% +translation + + + align:start position:0% +translation +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh so um + + align:start position:0% +uh so um + + + align:start position:0% +uh so um +let's let's go through some of that um + + align:start position:0% +let's let's go through some of that um + + + align:start position:0% +let's let's go through some of that um +let's see + + align:start position:0% +let's see + + + align:start position:0% +let's see +do i have + + align:start position:0% +do i have + + + align:start position:0% +do i have +i do um + + align:start position:0% +i do um + + + align:start position:0% +i do um +i've got an airport car but some reason + + align:start position:0% +i've got an airport car but some reason + + + align:start position:0% +i've got an airport car but some reason +or another + + align:start position:0% +or another + + + align:start position:0% +or another +i have not been able to get it to work + + align:start position:0% +i have not been able to get it to work + + + align:start position:0% +i have not been able to get it to work +in here + + align:start position:0% + + + + align:start position:0% + +in this room + + align:start position:0% + + + + align:start position:0% + +yeah why don't you get it out and + + align:start position:0% +yeah why don't you get it out and + + + align:start position:0% +yeah why don't you get it out and +uh whenever we um + + align:start position:0% +uh whenever we um + + + align:start position:0% +uh whenever we um +want to we can just look something up we + + align:start position:0% +want to we can just look something up we + + + align:start position:0% +want to we can just look something up we +can um + + align:start position:0% +can um + + + align:start position:0% +can um +i think uh the best one for them for the + + align:start position:0% +i think uh the best one for them for the + + + align:start position:0% +i think uh the best one for them for the +terms we're going to look at is uh how + + align:start position:0% +terms we're going to look at is uh how + + + align:start position:0% +terms we're going to look at is uh how +do you pronounce wikipedia + + align:start position:0% + + + + align:start position:0% + +okay let me erase this board and let's + + align:start position:0% +okay let me erase this board and let's + + + align:start position:0% +okay let me erase this board and let's +go through a couple of them you bring up + + align:start position:0% +go through a couple of them you bring up + + + align:start position:0% +go through a couple of them you bring up +some + + align:start position:0% +some + + + align:start position:0% +some +you can bring bring up some that you + + align:start position:0% +you can bring bring up some that you + + + align:start position:0% +you can bring bring up some that you +want to ask me about bring up something + + align:start position:0% +want to ask me about bring up something + + + align:start position:0% +want to ask me about bring up something +that you want to say tell + + align:start position:0% +that you want to say tell + + + align:start position:0% +that you want to say tell +it's + + align:start position:0% + + + + align:start position:0% + +words that we that we've used terms of + + align:start position:0% +words that we that we've used terms of + + + align:start position:0% +words that we that we've used terms of +art + + align:start position:0% +art + + + align:start position:0% +art +words that we've used in this class + + align:start position:0% + + + + align:start position:0% + +words that you think that if you're + + align:start position:0% +words that you think that if you're + + + align:start position:0% +words that you think that if you're +talking to anybody about engineering + + align:start position:0% +talking to anybody about engineering + + + align:start position:0% +talking to anybody about engineering +ethics may come up in the conversation + + align:start position:0% +ethics may come up in the conversation + + + align:start position:0% +ethics may come up in the conversation +and you would want to know + + align:start position:0% +and you would want to know + + + align:start position:0% +and you would want to know +what they + + align:start position:0% + + + + align:start position:0% + +one word that mean + + align:start position:0% + + + + align:start position:0% + +you used in the last class + + align:start position:0% +you used in the last class + + + align:start position:0% +you used in the last class +was accountability + + align:start position:0% + + + + align:start position:0% + +well let's do it now + + align:start position:0% +well let's do it now + + + align:start position:0% +well let's do it now +let's go back over + + align:start position:0% +let's go back over + + + align:start position:0% +let's go back over +um + + align:start position:0% +um + + + align:start position:0% +um +i will give you the term as i understood + + align:start position:0% +i will give you the term as i understood + + + align:start position:0% +i will give you the term as i understood +it in my military experience + + align:start position:0% +it in my military experience + + + align:start position:0% +it in my military experience +and the term goes with two other terms + + align:start position:0% + + + + align:start position:0% + +responsibility + + align:start position:0% +responsibility + + + align:start position:0% +responsibility +authority and accountability they all go + + align:start position:0% +authority and accountability they all go + + + align:start position:0% +authority and accountability they all go +together + + align:start position:0% +together + + + align:start position:0% +together +okay + + align:start position:0% + + + + align:start position:0% + +accountability is + + align:start position:0% + + + + align:start position:0% + +the requirement to be able to explain + + align:start position:0% +the requirement to be able to explain + + + align:start position:0% +the requirement to be able to explain +the situation yes with facts + + align:start position:0% + + + + align:start position:0% + +i feel like in ethics + + align:start position:0% +i feel like in ethics + + + align:start position:0% +i feel like in ethics +writing and ethics + + align:start position:0% + + + + align:start position:0% + +you know you don't hear + + align:start position:0% +you know you don't hear + + + align:start position:0% +you know you don't hear +right you don't hear a whole lot of that + + align:start position:0% +right you don't hear a whole lot of that + + + align:start position:0% +right you don't hear a whole lot of that +word used unless they're using it + + align:start position:0% +word used unless they're using it + + + align:start position:0% +word used unless they're using it +like uh a person in a case would use it + + align:start position:0% +like uh a person in a case would use it + + + align:start position:0% +like uh a person in a case would use it +but um + + align:start position:0% + + + + align:start position:0% + +no it's not used a whole lot + + align:start position:0% + + + + align:start position:0% + +but it it but i think that is impo the + + align:start position:0% +but it it but i think that is impo the + + + align:start position:0% +but it it but i think that is impo the +importance of it is to distinguish + + align:start position:0% +importance of it is to distinguish + + + align:start position:0% +importance of it is to distinguish +accountability from responsibility + + align:start position:0% + + + + align:start position:0% + +issues + + align:start position:0% +issues + + + align:start position:0% +issues +and that is you are answerable + + align:start position:0% + + + + align:start position:0% + +and sanctionable + + align:start position:0% +and sanctionable + + + align:start position:0% +and sanctionable +for some + + align:start position:0% +for some + + + align:start position:0% +for some +event + + align:start position:0% +event + + + align:start position:0% +event +or for something or something + + align:start position:0% +or for something or something + + + align:start position:0% +or for something or something +so uh you um + + align:start position:0% +so uh you um + + + align:start position:0% +so uh you um +and in order to answer you have to have + + align:start position:0% +and in order to answer you have to have + + + align:start position:0% +and in order to answer you have to have +authority + + align:start position:0% +authority + + + align:start position:0% +authority +so uh you have to have power + + align:start position:0% +so uh you have to have power + + + align:start position:0% +so uh you have to have power +and power is given to uh + + align:start position:0% +and power is given to uh + + + align:start position:0% +and power is given to uh +the person in order to carry out + + align:start position:0% +the person in order to carry out + + + align:start position:0% +the person in order to carry out +one's responsibility + + align:start position:0% +one's responsibility + + + align:start position:0% +one's responsibility +you're not giving any more + + align:start position:0% +you're not giving any more + + + align:start position:0% +you're not giving any more +and you're really not giving any less + + align:start position:0% +and you're really not giving any less + + + align:start position:0% +and you're really not giving any less +given what somebody what somebody above + + align:start position:0% +given what somebody what somebody above + + + align:start position:0% +given what somebody what somebody above +you an authority in the chain of command + + align:start position:0% +you an authority in the chain of command + + + align:start position:0% +you an authority in the chain of command +thinks this is + + align:start position:0% +thinks this is + + + align:start position:0% +thinks this is +what you need + + align:start position:0% +what you need + + + align:start position:0% +what you need +carry out your responsibility + + align:start position:0% +carry out your responsibility + + + align:start position:0% +carry out your responsibility +all right so uh + + align:start position:0% +all right so uh + + + align:start position:0% +all right so uh +one very important thing about all of + + align:start position:0% +one very important thing about all of + + + align:start position:0% +one very important thing about all of +that + + align:start position:0% +that + + + align:start position:0% +that +in life professional life + + align:start position:0% +in life professional life + + + align:start position:0% +in life professional life +is that you can delegate + + align:start position:0% +is that you can delegate + + + align:start position:0% +is that you can delegate +authority + + align:start position:0% + + + + align:start position:0% + +the bigger the organization + + align:start position:0% +the bigger the organization + + + align:start position:0% +the bigger the organization +the higher up you are in it the only way + + align:start position:0% +the higher up you are in it the only way + + + align:start position:0% +the higher up you are in it the only way +you can operate is to + + align:start position:0% +you can operate is to + + + align:start position:0% +you can operate is to +delegate authority + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +if you look at the charter + + align:start position:0% +if you look at the charter + + + align:start position:0% +if you look at the charter +of the charters of some universities + + align:start position:0% +of the charters of some universities + + + align:start position:0% +of the charters of some universities +and i've looked at some + + align:start position:0% + + + + align:start position:0% + +the trustees have all of this authority + + align:start position:0% +the trustees have all of this authority + + + align:start position:0% +the trustees have all of this authority +that they cannot possibly + + align:start position:0% +that they cannot possibly + + + align:start position:0% +that they cannot possibly +use + + align:start position:0% +use + + + align:start position:0% +use +right + + align:start position:0% +right + + + align:start position:0% +right +if you look at the + + align:start position:0% +if you look at the + + + align:start position:0% +if you look at the +original versions of the charters that + + align:start position:0% +original versions of the charters that + + + align:start position:0% +original versions of the charters that +go back into the 19th century + + align:start position:0% +go back into the 19th century + + + align:start position:0% +go back into the 19th century +they will give the trustees the + + align:start position:0% +they will give the trustees the + + + align:start position:0% +they will give the trustees the +authority to prescribe textbooks for + + align:start position:0% +authority to prescribe textbooks for + + + align:start position:0% +authority to prescribe textbooks for +classes now you know even in the last + + align:start position:0% +classes now you know even in the last + + + align:start position:0% +classes now you know even in the last +century trustees couldn't do that they + + align:start position:0% +century trustees couldn't do that they + + + align:start position:0% +century trustees couldn't do that they +had to delegate the authority to right + + align:start position:0% +had to delegate the authority to right + + + align:start position:0% +had to delegate the authority to right +but what the trustee cannot do is + + align:start position:0% +but what the trustee cannot do is + + + align:start position:0% +but what the trustee cannot do is +delegate + + align:start position:0% +delegate + + + align:start position:0% +delegate +the responsibility + + align:start position:0% +the responsibility + + + align:start position:0% +the responsibility +because if the students aren't taught + + align:start position:0% +because if the students aren't taught + + + align:start position:0% +because if the students aren't taught +and they and the charter which is a + + align:start position:0% +and they and the charter which is a + + + align:start position:0% +and they and the charter which is a +contract between the organization and + + align:start position:0% +contract between the organization and + + + align:start position:0% +contract between the organization and +society + + align:start position:0% +society + + + align:start position:0% +society +uh if the charter says that you have to + + align:start position:0% +uh if the charter says that you have to + + + align:start position:0% +uh if the charter says that you have to +teach students + + align:start position:0% +teach students + + + align:start position:0% +teach students +and if the higher body that is the + + align:start position:0% +and if the higher body that is the + + + align:start position:0% +and if the higher body that is the +the the legal body of no no let's call + + align:start position:0% +the the legal body of no no let's call + + + align:start position:0% +the the legal body of no no let's call +it the body politic + + align:start position:0% +it the body politic + + + align:start position:0% +it the body politic +of society says that we're going to + + align:start position:0% +of society says that we're going to + + + align:start position:0% +of society says that we're going to +sanction somebody for that then you're + + align:start position:0% +sanction somebody for that then you're + + + align:start position:0% +sanction somebody for that then you're +the one + + align:start position:0% +the one + + + align:start position:0% +the one +not the others + + align:start position:0% +not the others + + + align:start position:0% +not the others +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and + + align:start position:0% +and + + + align:start position:0% +and +accountability the judge is going to say + + align:start position:0% +accountability the judge is going to say + + + align:start position:0% +accountability the judge is going to say +well look before we get started let's + + align:start position:0% +well look before we get started let's + + + align:start position:0% +well look before we get started let's +put some facts on the table + + align:start position:0% +put some facts on the table + + + align:start position:0% +put some facts on the table +who should know the facts okay + + align:start position:0% +who should know the facts okay + + + align:start position:0% +who should know the facts okay +that's accountability + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% + + + + align:start position:0% + +so you see how + + align:start position:0% +so you see how + + + align:start position:0% +so you see how +these issues can come up + + align:start position:0% +these issues can come up + + + align:start position:0% +these issues can come up +when they do come up they come up uh in + + align:start position:0% +when they do come up they come up uh in + + + align:start position:0% +when they do come up they come up uh in +in what uh is a term of art now + + align:start position:0% +in what uh is a term of art now + + + align:start position:0% +in what uh is a term of art now +sensational + + align:start position:0% +sensational + + + align:start position:0% +sensational +uh cases + + align:start position:0% + + + + align:start position:0% + +kneeling + + align:start position:0% +kneeling + + + align:start position:0% +kneeling +in all of them + + align:start position:0% +in all of them + + + align:start position:0% +in all of them +okay + + align:start position:0% + + + + align:start position:0% + +and um + + align:start position:0% + + + + align:start position:0% + +okay so in the military as you say you + + align:start position:0% +okay so in the military as you say you + + + align:start position:0% +okay so in the military as you say you +are you're sanctionable + + align:start position:0% + + + + align:start position:0% + +i feel like i've i've read that in + + align:start position:0% +i feel like i've i've read that in + + + align:start position:0% +i feel like i've i've read that in +ethical cases + + align:start position:0% +ethical cases + + + align:start position:0% +ethical cases +i've read the word responsibility and it + + align:start position:0% +i've read the word responsibility and it + + + align:start position:0% +i've read the word responsibility and it +implies + + align:start position:0% +implies + + + align:start position:0% +implies +the requirement to take action like + + align:start position:0% +the requirement to take action like + + + align:start position:0% +the requirement to take action like +so-and-so has the responsibility + + align:start position:0% +so-and-so has the responsibility + + + align:start position:0% +so-and-so has the responsibility +to do this + + align:start position:0% +to do this + + + align:start position:0% +to do this +but is that a correct usage of it or an + + align:start position:0% +but is that a correct usage of it or an + + + align:start position:0% +but is that a correct usage of it or an +ethic should + + align:start position:0% + + + + align:start position:0% + +i use the word event okay also + + align:start position:0% +i use the word event okay also + + + align:start position:0% +i use the word event okay also +okay + + align:start position:0% +okay + + + align:start position:0% +okay +which means action + + align:start position:0% +which means action + + + align:start position:0% +which means action +right + + align:start position:0% +right + + + align:start position:0% +right +so uh yeah it's proactive but well i + + align:start position:0% +so uh yeah it's proactive but well i + + + align:start position:0% +so uh yeah it's proactive but well i +can't i'm trying to think now can i + + align:start position:0% +can't i'm trying to think now can i + + + align:start position:0% +can't i'm trying to think now can i +think of something passive + + align:start position:0% +think of something passive + + + align:start position:0% +think of something passive +can i say i am responsible to prevent + + align:start position:0% + + + + align:start position:0% + +maybe the better word is obligated + + align:start position:0% +maybe the better word is obligated + + + align:start position:0% +maybe the better word is obligated +like + + align:start position:0% +like + + + align:start position:0% +like +you're morally obligated to do something + + align:start position:0% +you're morally obligated to do something + + + align:start position:0% +you're morally obligated to do something +all right + + align:start position:0% +all right + + + align:start position:0% +all right +now + + align:start position:0% +now + + + align:start position:0% +now +maybe there is maybe + + align:start position:0% + + + + align:start position:0% + +now you're getting into + + align:start position:0% +now you're getting into + + + align:start position:0% +now you're getting into +an ethical or a term of art in ethics + + align:start position:0% +an ethical or a term of art in ethics + + + align:start position:0% +an ethical or a term of art in ethics +because immanuel kant has some specific + + align:start position:0% +because immanuel kant has some specific + + + align:start position:0% +because immanuel kant has some specific +definitions for + + align:start position:0% +definitions for + + + align:start position:0% +definitions for +duty + + align:start position:0% +duty + + + align:start position:0% +duty +and obligation + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so if you substitute the word duty for + + align:start position:0% +so if you substitute the word duty for + + + align:start position:0% +so if you substitute the word duty for +obligation then you get a term of art in + + align:start position:0% +obligation then you get a term of art in + + + align:start position:0% +obligation then you get a term of art in +ethics + + align:start position:0% +ethics + + + align:start position:0% +ethics +and as a matter of fact many people call + + align:start position:0% +and as a matter of fact many people call + + + align:start position:0% +and as a matter of fact many people call +kant's + + align:start position:0% +kant's + + + align:start position:0% +kant's +ethics + + align:start position:0% +ethics + + + align:start position:0% +ethics +duty ethics + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +duty ethics + + align:start position:0% +duty ethics + + + align:start position:0% +duty ethics +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% + + + + align:start position:0% + +and that's a very powerful word uh + + align:start position:0% +and that's a very powerful word uh + + + align:start position:0% +and that's a very powerful word uh +in some + + align:start position:0% +in some + + + align:start position:0% +in some +cultures because your duty + + align:start position:0% + + + + align:start position:0% + +your duty + + align:start position:0% +your duty + + + align:start position:0% +your duty +uh not only has military kind of + + align:start position:0% +uh not only has military kind of + + + align:start position:0% +uh not only has military kind of +connotations + + align:start position:0% +connotations + + + align:start position:0% +connotations +that are passed on in business + + align:start position:0% +that are passed on in business + + + align:start position:0% +that are passed on in business +but it also has moral connotations + + align:start position:0% +but it also has moral connotations + + + align:start position:0% +but it also has moral connotations +that come from emmanuel kant + + align:start position:0% +that come from emmanuel kant + + + align:start position:0% +that come from emmanuel kant +okay so put us put an asterisk beside + + align:start position:0% +okay so put us put an asterisk beside + + + align:start position:0% +okay so put us put an asterisk beside +that do some reading on that please uh a + + align:start position:0% +that do some reading on that please uh a + + + align:start position:0% +that do some reading on that please uh a +simple definition not gonna be good + + align:start position:0% +simple definition not gonna be good + + + align:start position:0% +simple definition not gonna be good +enough + + align:start position:0% +enough + + + align:start position:0% +enough +but but + + align:start position:0% +but but + + + align:start position:0% +but but +khan's ethics are often called duty + + align:start position:0% +khan's ethics are often called duty + + + align:start position:0% +khan's ethics are often called duty +ethics + + align:start position:0% + + + + align:start position:0% + +and as you know his style is to state + + align:start position:0% +and as you know his style is to state + + + align:start position:0% +and as you know his style is to state +the categorical imperative in more than + + align:start position:0% +the categorical imperative in more than + + + align:start position:0% +the categorical imperative in more than +one way + + align:start position:0% +one way + + + align:start position:0% +one way +he says they mean the same thing they're + + align:start position:0% +he says they mean the same thing they're + + + align:start position:0% +he says they mean the same thing they're +just different statements of the same + + align:start position:0% +just different statements of the same + + + align:start position:0% +just different statements of the same +thing + + align:start position:0% +thing + + + align:start position:0% +thing +but i but they but they're but if they + + align:start position:0% +but i but they but they're but if they + + + align:start position:0% +but i but they but they're but if they +were the same thing why i state them + + align:start position:0% +were the same thing why i state them + + + align:start position:0% +were the same thing why i state them +differently so there's some + + align:start position:0% +differently so there's some + + + align:start position:0% +differently so there's some +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +connotation + + align:start position:0% +connotation + + + align:start position:0% +connotation +that's different you know you have to + + align:start position:0% +that's different you know you have to + + + align:start position:0% +that's different you know you have to +read a little bit about that + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +they also have another excuse me + + align:start position:0% +they also have another excuse me + + + align:start position:0% +they also have another excuse me +political + + align:start position:0% +political + + + align:start position:0% +political +on my honor i'll do my duty + + align:start position:0% + + + + align:start position:0% + +duty on our country + + align:start position:0% + + + + align:start position:0% + +that's a good question that's a good + + align:start position:0% +that's a good question that's a good + + + align:start position:0% +that's a good question that's a good +point since the 60s it has been + + align:start position:0% +point since the 60s it has been + + + align:start position:0% +point since the 60s it has been +uh i don't know if that's going to pass + + align:start position:0% + + + + align:start position:0% + +but up until the 60s + + align:start position:0% +but up until the 60s + + + align:start position:0% +but up until the 60s +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +people would say you have a duty + + align:start position:0% +people would say you have a duty + + + align:start position:0% +people would say you have a duty +and someone just stands back and says + + align:start position:0% +and someone just stands back and says + + + align:start position:0% +and someone just stands back and says +yes i have a duty + + align:start position:0% +yes i have a duty + + + align:start position:0% +yes i have a duty +and in the 60s + + align:start position:0% + + + + align:start position:0% + +that wasn't that was an adverse term + + align:start position:0% + + + + align:start position:0% + +well partly part of the 60s was + + align:start position:0% +well partly part of the 60s was + + + align:start position:0% +well partly part of the 60s was +anti-vietnam + + align:start position:0% +anti-vietnam + + + align:start position:0% +anti-vietnam +and part of that was anti-war + + align:start position:0% +and part of that was anti-war + + + align:start position:0% +and part of that was anti-war +in general + + align:start position:0% +in general + + + align:start position:0% +in general +and a lot of that was anti-military + + align:start position:0% + + + + align:start position:0% + +i wore + + align:start position:0% +i wore + + + align:start position:0% +i wore +my military uniform + + align:start position:0% +my military uniform + + + align:start position:0% +my military uniform +in georgetown on a saturday night + + align:start position:0% + + + + align:start position:0% + +in the 60s just to see what would happen + + align:start position:0% +in the 60s just to see what would happen + + + align:start position:0% +in the 60s just to see what would happen +and + + align:start position:0% + + + + align:start position:0% + +it was crowded + + align:start position:0% +it was crowded + + + align:start position:0% +it was crowded +and all of the anti you know all of the + + align:start position:0% +and all of the anti you know all of the + + + align:start position:0% +and all of the anti you know all of the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +anti-war people were there + + align:start position:0% +anti-war people were there + + + align:start position:0% +anti-war people were there +and i walked three blocks and i remember + + align:start position:0% +and i walked three blocks and i remember + + + align:start position:0% +and i walked three blocks and i remember +the number six + + align:start position:0% +the number six + + + align:start position:0% +the number six +i was invited to six fisticuffs + + align:start position:0% + + + + align:start position:0% + +just on account notice the word i was + + align:start position:0% +just on account notice the word i was + + + align:start position:0% +just on account notice the word i was +invited i did not accept the invitation + + align:start position:0% +invited i did not accept the invitation + + + align:start position:0% +invited i did not accept the invitation +no it was the invitation for foisted on + + align:start position:0% +no it was the invitation for foisted on + + + align:start position:0% +no it was the invitation for foisted on +me + + align:start position:0% +me + + + align:start position:0% +me +nobody took the first punch + + align:start position:0% +nobody took the first punch + + + align:start position:0% +nobody took the first punch +but yeah it came to that + + align:start position:0% +but yeah it came to that + + + align:start position:0% +but yeah it came to that +i just want to see i mean + + align:start position:0% +i just want to see i mean + + + align:start position:0% +i just want to see i mean +i i + + align:start position:0% +i i + + + align:start position:0% +i i +i just want to see what would really + + align:start position:0% +i just want to see what would really + + + align:start position:0% +i just want to see what would really +happen + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +and so and i i i was uh an objection uh + + align:start position:0% +and so and i i i was uh an objection uh + + + align:start position:0% +and so and i i i was uh an objection uh +i objected to + + align:start position:0% +i objected to + + + align:start position:0% +i objected to +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the war + + align:start position:0% +the war + + + align:start position:0% +the war +when i was in the army + + align:start position:0% +when i was in the army + + + align:start position:0% +when i was in the army +uh i had a talk with my commander + + align:start position:0% +uh i had a talk with my commander + + + align:start position:0% +uh i had a talk with my commander +my commander said you plan to object to + + align:start position:0% +my commander said you plan to object to + + + align:start position:0% +my commander said you plan to object to +the war when you're in uniform i said no + + align:start position:0% + + + + align:start position:0% + +he said do you plan to object to the war + + align:start position:0% +he said do you plan to object to the war + + + align:start position:0% +he said do you plan to object to the war +when you're on duty + + align:start position:0% +when you're on duty + + + align:start position:0% +when you're on duty +i said no + + align:start position:0% +i said no + + + align:start position:0% +i said no +he said well what you do with your other + + align:start position:0% +he said well what you do with your other + + + align:start position:0% +he said well what you do with your other +time is none of my business + + align:start position:0% + + + + align:start position:0% + +so i did not object to the military + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so and i and i did not object to war + + align:start position:0% +so and i and i did not object to war + + + align:start position:0% +so and i and i did not object to war +i thought that there was such a thing as + + align:start position:0% +i thought that there was such a thing as + + + align:start position:0% +i thought that there was such a thing as +a defensive war + + align:start position:0% + + + + align:start position:0% + +um but um + + align:start position:0% +um but um + + + align:start position:0% +um but um +i just wanted to see what what would + + align:start position:0% +i just wanted to see what what would + + + align:start position:0% +i just wanted to see what what would +happen and that was and that's what + + align:start position:0% +happen and that was and that's what + + + align:start position:0% +happen and that was and that's what +happened + + align:start position:0% +happened + + + align:start position:0% +happened +so the word duty uh did fall in disfavor + + align:start position:0% +so the word duty uh did fall in disfavor + + + align:start position:0% +so the word duty uh did fall in disfavor +i think for many of those reasons + + align:start position:0% +i think for many of those reasons + + + align:start position:0% +i think for many of those reasons +in the 60s and as long as my generation + + align:start position:0% +in the 60s and as long as my generation + + + align:start position:0% +in the 60s and as long as my generation +is around it will probably have those + + align:start position:0% +is around it will probably have those + + + align:start position:0% +is around it will probably have those +connotations + + align:start position:0% +connotations + + + align:start position:0% +connotations +but we're + + align:start position:0% +but we're + + + align:start position:0% +but we're +being uh we're going out of the system + + align:start position:0% +being uh we're going out of the system + + + align:start position:0% +being uh we're going out of the system +now + + align:start position:0% +now + + + align:start position:0% +now +and i suspect that duty will return and + + align:start position:0% +and i suspect that duty will return and + + + align:start position:0% +and i suspect that duty will return and +have its uh original force here in the + + align:start position:0% +have its uh original force here in the + + + align:start position:0% +have its uh original force here in the +united states + + align:start position:0% + + + + align:start position:0% + +what about ethics what's the difference + + align:start position:0% +what about ethics what's the difference + + + align:start position:0% +what about ethics what's the difference +between ethics and morals + + align:start position:0% + + + + align:start position:0% + +did i ever cover that + + align:start position:0% + + + + align:start position:0% + +okay well let's let's deal with ethics + + align:start position:0% +okay well let's let's deal with ethics + + + align:start position:0% +okay well let's let's deal with ethics +and morals because i'll tell you there's + + align:start position:0% +and morals because i'll tell you there's + + + align:start position:0% +and morals because i'll tell you there's +one thing that's for sure + + align:start position:0% +one thing that's for sure + + + align:start position:0% +one thing that's for sure +and that is that if you ever start + + align:start position:0% +and that is that if you ever start + + + align:start position:0% +and that is that if you ever start +talking + + align:start position:0% +talking + + + align:start position:0% +talking +about engineering ethics + + align:start position:0% +about engineering ethics + + + align:start position:0% +about engineering ethics +and there and there's anybody in there + + align:start position:0% +and there and there's anybody in there + + + align:start position:0% +and there and there's anybody in there +who's not a philosopher somebody's going + + align:start position:0% +who's not a philosopher somebody's going + + + align:start position:0% +who's not a philosopher somebody's going +to say hold up what's the difference + + align:start position:0% +to say hold up what's the difference + + + align:start position:0% +to say hold up what's the difference +between ethics and moral + + align:start position:0% +between ethics and moral + + + align:start position:0% +between ethics and moral +and they're going to say it because + + align:start position:0% +and they're going to say it because + + + align:start position:0% +and they're going to say it because +they + + align:start position:0% +they + + + align:start position:0% +they +will have different responses to your + + align:start position:0% +will have different responses to your + + + align:start position:0% +will have different responses to your +calling them unethical as opposed to + + align:start position:0% +calling them unethical as opposed to + + + align:start position:0% +calling them unethical as opposed to +immoral + + align:start position:0% +immoral + + + align:start position:0% +immoral +and they want to set this up right at + + align:start position:0% +and they want to set this up right at + + + align:start position:0% +and they want to set this up right at +the beginning + + align:start position:0% +the beginning + + + align:start position:0% +the beginning +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and um + + align:start position:0% + + + + align:start position:0% + +and so i've had experiences and i'll + + align:start position:0% +and so i've had experiences and i'll + + + align:start position:0% +and so i've had experiences and i'll +tell you an experience that since the + + align:start position:0% +tell you an experience that since the + + + align:start position:0% +tell you an experience that since the +work and that is to say well + + align:start position:0% +work and that is to say well + + + align:start position:0% +work and that is to say well +let's start with a word called etymology + + align:start position:0% + + + + align:start position:0% + +that's the study of the origins of words + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +now here's this story + + align:start position:0% +now here's this story + + + align:start position:0% +now here's this story +um + + align:start position:0% +um + + + align:start position:0% +um +there's a piece of it and i'm not sure + + align:start position:0% +there's a piece of it and i'm not sure + + + align:start position:0% +there's a piece of it and i'm not sure +what it is that's anecdotal but i'd like + + align:start position:0% +what it is that's anecdotal but i'd like + + + align:start position:0% +what it is that's anecdotal but i'd like +you to see if you can work this out and + + align:start position:0% +you to see if you can work this out and + + + align:start position:0% +you to see if you can work this out and +give me um + + align:start position:0% + + + + align:start position:0% + +give me a um + + align:start position:0% +give me a um + + + align:start position:0% +give me a um +cogent etymological + + align:start position:0% +cogent etymological + + + align:start position:0% +cogent etymological +answer it seems as though + + align:start position:0% +answer it seems as though + + + align:start position:0% +answer it seems as though +aristotle + + align:start position:0% + + + + align:start position:0% + +had + + align:start position:0% + + + + align:start position:0% + +to his advantage the greek word ethos + + align:start position:0% +to his advantage the greek word ethos + + + align:start position:0% +to his advantage the greek word ethos +we still use that word + + align:start position:0% + + + + align:start position:0% + +and depending on who's translating the + + align:start position:0% +and depending on who's translating the + + + align:start position:0% +and depending on who's translating the +word + + align:start position:0% +word + + + align:start position:0% +word +it might have slightly different + + align:start position:0% +it might have slightly different + + + align:start position:0% +it might have slightly different +meanings + + align:start position:0% + + + + align:start position:0% + +uh because uh this word uh seems to uh + + align:start position:0% +uh because uh this word uh seems to uh + + + align:start position:0% +uh because uh this word uh seems to uh +give translators into english a little + + align:start position:0% +give translators into english a little + + + align:start position:0% +give translators into english a little +bit of a problem + + align:start position:0% +bit of a problem + + + align:start position:0% +bit of a problem +let me pause there for a second + + align:start position:0% + + + + align:start position:0% + +no i'll come back + + align:start position:0% +no i'll come back + + + align:start position:0% +no i'll come back +i'll come back + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +ethos had all of these meetings about + + align:start position:0% +ethos had all of these meetings about + + + align:start position:0% +ethos had all of these meetings about +what people thought + + align:start position:0% +what people thought + + + align:start position:0% +what people thought +were + + align:start position:0% + + + + align:start position:0% + +behaviors + + align:start position:0% +behaviors + + + align:start position:0% +behaviors +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and values + + align:start position:0% +and values + + + align:start position:0% +and values +that + + align:start position:0% +that + + + align:start position:0% +that +were used in a particular community + + align:start position:0% +were used in a particular community + + + align:start position:0% +were used in a particular community +so this community and we're talking + + align:start position:0% +so this community and we're talking + + + align:start position:0% +so this community and we're talking +about cities city-states now we're not + + align:start position:0% +about cities city-states now we're not + + + align:start position:0% +about cities city-states now we're not +going to talk + + align:start position:0% +going to talk + + + align:start position:0% +going to talk +before nations so when you talk about a + + align:start position:0% +before nations so when you talk about a + + + align:start position:0% +before nations so when you talk about a +community you're talking about a city + + align:start position:0% +community you're talking about a city + + + align:start position:0% +community you're talking about a city +state which was their equivalent to a + + align:start position:0% +state which was their equivalent to a + + + align:start position:0% +state which was their equivalent to a +nation + + align:start position:0% +nation + + + align:start position:0% +nation +because city states would go to war with + + align:start position:0% +because city states would go to war with + + + align:start position:0% +because city states would go to war with +one another if you don't believe it look + + align:start position:0% +one another if you don't believe it look + + + align:start position:0% +one another if you don't believe it look +at athens and uh + + align:start position:0% +at athens and uh + + + align:start position:0% +at athens and uh +sparta + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +are you saying that there weren't a + + align:start position:0% +are you saying that there weren't a + + + align:start position:0% +are you saying that there weren't a +whole lot of riots + + align:start position:0% +whole lot of riots + + + align:start position:0% +whole lot of riots +no i'm just saying + + align:start position:0% +no i'm just saying + + + align:start position:0% +no i'm just saying +they're smaller + + align:start position:0% + + + + align:start position:0% + +no they weren't no no no no they weren't + + align:start position:0% +no they weren't no no no no they weren't + + + align:start position:0% +no they weren't no no no no they weren't +but + + align:start position:0% +but + + + align:start position:0% +but +um + + align:start position:0% + + + + align:start position:0% + +uh no + + align:start position:0% +uh no + + + align:start position:0% +uh no +okay + + align:start position:0% +okay + + + align:start position:0% +okay +it was the best thing they had to a + + align:start position:0% +it was the best thing they had to a + + + align:start position:0% +it was the best thing they had to a +nation then + + align:start position:0% +nation then + + + align:start position:0% +nation then +all right + + align:start position:0% +all right + + + align:start position:0% +all right +um is that right in in greece that was + + align:start position:0% +um is that right in in greece that was + + + align:start position:0% +um is that right in in greece that was +right + + align:start position:0% +right + + + align:start position:0% +right +it wasn't right in egypt + + align:start position:0% + + + + align:start position:0% + +no they had + + align:start position:0% +no they had + + + align:start position:0% +no they had +empires yeah okay + + align:start position:0% +empires yeah okay + + + align:start position:0% +empires yeah okay +all right so you're talking about ethos + + align:start position:0% +all right so you're talking about ethos + + + align:start position:0% +all right so you're talking about ethos +and aristotle wanted to talk about + + align:start position:0% +and aristotle wanted to talk about + + + align:start position:0% +and aristotle wanted to talk about +uh the study of ethos to determine good + + align:start position:0% +uh the study of ethos to determine good + + + align:start position:0% +uh the study of ethos to determine good +and bad right wrong + + align:start position:0% +and bad right wrong + + + align:start position:0% +and bad right wrong +and he didn't have a word for it + + align:start position:0% +and he didn't have a word for it + + + align:start position:0% +and he didn't have a word for it +so + + align:start position:0% +so + + + align:start position:0% +so +he came up with this word ethicos + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +that word + + align:start position:0% +that word + + + align:start position:0% +that word +finally gets itself into the english + + align:start position:0% +finally gets itself into the english + + + align:start position:0% +finally gets itself into the english +language as + + align:start position:0% + + + + align:start position:0% + +ethics + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +wait so why what what does ethos means + + align:start position:0% +wait so why what what does ethos means + + + align:start position:0% +wait so why what what does ethos means +uh the + + align:start position:0% +uh the + + + align:start position:0% +uh the +habits and values that people had in + + align:start position:0% +habits and values that people had in + + + align:start position:0% +habits and values that people had in +particular + + align:start position:0% + + + + align:start position:0% + +the rational study of it + + align:start position:0% +the rational study of it + + + align:start position:0% +the rational study of it +so uh the way i look at the difference + + align:start position:0% +so uh the way i look at the difference + + + align:start position:0% +so uh the way i look at the difference +is that the first one is um + + align:start position:0% +is that the first one is um + + + align:start position:0% +is that the first one is um +empirical + + align:start position:0% +empirical + + + align:start position:0% +empirical +and the second one is rational + + align:start position:0% +and the second one is rational + + + align:start position:0% +and the second one is rational +that's where i look at it + + align:start position:0% +that's where i look at it + + + align:start position:0% +that's where i look at it +i don't know if i can defend it but + + align:start position:0% +i don't know if i can defend it but + + + align:start position:0% +i don't know if i can defend it but +that's the way i look at it + + align:start position:0% +that's the way i look at it + + + align:start position:0% +that's the way i look at it +that the second one really is is + + align:start position:0% +that the second one really is is + + + align:start position:0% +that the second one really is is +analyzing the first + + align:start position:0% +analyzing the first + + + align:start position:0% +analyzing the first +talking about it + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so all of this is in greek is greek + + align:start position:0% + + + + align:start position:0% + +cicero who was a roman comes along + + align:start position:0% +cicero who was a roman comes along + + + align:start position:0% +cicero who was a roman comes along +and + + align:start position:0% + + + + align:start position:0% + +he was a roman he was a roman they + + align:start position:0% +he was a roman he was a roman they + + + align:start position:0% +he was a roman he was a roman they +called him an orator but he was a lawyer + + align:start position:0% +called him an orator but he was a lawyer + + + align:start position:0% +called him an orator but he was a lawyer +he was trained in um + + align:start position:0% +he was trained in um + + + align:start position:0% +he was trained in um +greek philosophy + + align:start position:0% + + + + align:start position:0% + +uh he left rome when he was young his + + align:start position:0% +uh he left rome when he was young his + + + align:start position:0% +uh he left rome when he was young his +father sent him over there to + + align:start position:0% +father sent him over there to + + + align:start position:0% +father sent him over there to +one of the academies i think it was uh + + align:start position:0% +one of the academies i think it was uh + + + align:start position:0% +one of the academies i think it was uh +aristotle's + + align:start position:0% +aristotle's + + + align:start position:0% +aristotle's +academy that was still alive in those + + align:start position:0% +academy that was still alive in those + + + align:start position:0% +academy that was still alive in those +days + + align:start position:0% +days + + + align:start position:0% +days +and he studied over there and + + align:start position:0% +and he studied over there and + + + align:start position:0% +and he studied over there and +he translated some words + + align:start position:0% +he translated some words + + + align:start position:0% +he translated some words +uh there was already an equivalent in + + align:start position:0% +uh there was already an equivalent in + + + align:start position:0% +uh there was already an equivalent in +latin for + + align:start position:0% + + + + align:start position:0% + +ethos and it was maurice + + align:start position:0% +ethos and it was maurice + + + align:start position:0% +ethos and it was maurice +we still use that word + + align:start position:0% +we still use that word + + + align:start position:0% +we still use that word +ways and morays and all of that + + align:start position:0% +ways and morays and all of that + + + align:start position:0% +ways and morays and all of that +we might take a pause + + align:start position:0% +we might take a pause + + + align:start position:0% +we might take a pause +in a few minutes to + + align:start position:0% +in a few minutes to + + + align:start position:0% +in a few minutes to +get on wikipedia and see what some of + + align:start position:0% +get on wikipedia and see what some of + + + align:start position:0% +get on wikipedia and see what some of +this + + align:start position:0% +this + + + align:start position:0% +this +some some of what they say + + align:start position:0% + + + + align:start position:0% + +and when he got to ethicos there was no + + align:start position:0% +and when he got to ethicos there was no + + + align:start position:0% +and when he got to ethicos there was no +latin equivalent + + align:start position:0% +latin equivalent + + + align:start position:0% +latin equivalent +so + + align:start position:0% +so + + + align:start position:0% +so +[Music] + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +my sources are not unimpeachable but it + + align:start position:0% +my sources are not unimpeachable but it + + + align:start position:0% +my sources are not unimpeachable but it +seems to but it seems that but i've got + + align:start position:0% +seems to but it seems that but i've got + + + align:start position:0% +seems to but it seems that but i've got +sources i've got references + + align:start position:0% +sources i've got references + + + align:start position:0% +sources i've got references +that say that central came up with this + + align:start position:0% +that say that central came up with this + + + align:start position:0% +that say that central came up with this +word morales morales as the latin + + align:start position:0% +word morales morales as the latin + + + align:start position:0% +word morales morales as the latin +equivalent of ethical + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +that works its way into the english + + align:start position:0% +that works its way into the english + + + align:start position:0% +that works its way into the english +language + + align:start position:0% + + + + align:start position:0% + +as morals + + align:start position:0% + + + + align:start position:0% + +now let's talk about usage in the + + align:start position:0% +now let's talk about usage in the + + + align:start position:0% +now let's talk about usage in the +english language + + align:start position:0% +english language + + + align:start position:0% +english language +some usages + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +there is a branch of philosophy a major + + align:start position:0% +there is a branch of philosophy a major + + + align:start position:0% +there is a branch of philosophy a major +division of philosophy called ethics + + align:start position:0% + + + + align:start position:0% + +there is an equivalent term for ethics + + align:start position:0% +there is an equivalent term for ethics + + + align:start position:0% +there is an equivalent term for ethics +moral philosophy + + align:start position:0% + + + + align:start position:0% + +it's improper to say ethical philosophy + + align:start position:0% + + + + align:start position:0% + +uh a great deal + + align:start position:0% +uh a great deal + + + align:start position:0% +uh a great deal +of uh + + align:start position:0% +of uh + + + align:start position:0% +of uh +work + + align:start position:0% +work + + + align:start position:0% +work +in the area of ethics + + align:start position:0% +in the area of ethics + + + align:start position:0% +in the area of ethics +as you know because we covered it + + align:start position:0% +as you know because we covered it + + + align:start position:0% +as you know because we covered it +earlier was done + + align:start position:0% +earlier was done + + + align:start position:0% +earlier was done +by + + align:start position:0% +by + + + align:start position:0% +by +theologians + + align:start position:0% +theologians + + + align:start position:0% +theologians +not just christian theologians but + + align:start position:0% +not just christian theologians but + + + align:start position:0% +not just christian theologians but +obviously all theologians + + align:start position:0% +obviously all theologians + + + align:start position:0% +obviously all theologians +deal with ethics in one way or another + + align:start position:0% +deal with ethics in one way or another + + + align:start position:0% +deal with ethics in one way or another +and the western world it was done in + + align:start position:0% +and the western world it was done in + + + align:start position:0% +and the western world it was done in +guess what + + align:start position:0% +guess what + + + align:start position:0% +guess what +latin + + align:start position:0% + + + + align:start position:0% + +now uh some uh there were some great + + align:start position:0% +now uh some uh there were some great + + + align:start position:0% +now uh some uh there were some great +scholars referred to uh greek + + align:start position:0% +scholars referred to uh greek + + + align:start position:0% +scholars referred to uh greek +writings + + align:start position:0% +writings + + + align:start position:0% +writings +too but there were periods long periods + + align:start position:0% +too but there were periods long periods + + + align:start position:0% +too but there were periods long periods +where when uh + + align:start position:0% +where when uh + + + align:start position:0% +where when uh +christianity was hostile to greek + + align:start position:0% +christianity was hostile to greek + + + align:start position:0% +christianity was hostile to greek +learning + + align:start position:0% + + + + align:start position:0% + +so uh what happens when somebody says + + align:start position:0% +so uh what happens when somebody says + + + align:start position:0% +so uh what happens when somebody says +that you are immoral + + align:start position:0% +that you are immoral + + + align:start position:0% +that you are immoral +is that they are probably talking about + + align:start position:0% +is that they are probably talking about + + + align:start position:0% +is that they are probably talking about +the latin treatment + + align:start position:0% +the latin treatment + + + align:start position:0% +the latin treatment +in the context of religion + + align:start position:0% + + + + align:start position:0% + +that's bad okay + + align:start position:0% +that's bad okay + + + align:start position:0% +that's bad okay +all right + + align:start position:0% +all right + + + align:start position:0% +all right +there is such a thing called um + + align:start position:0% +there is such a thing called um + + + align:start position:0% +there is such a thing called um +professional there's a term called + + align:start position:0% +professional there's a term called + + + align:start position:0% +professional there's a term called +professional ethics + + align:start position:0% +professional ethics + + + align:start position:0% +professional ethics +as you know term of art + + align:start position:0% +as you know term of art + + + align:start position:0% +as you know term of art +and engineering ethics + + align:start position:0% +and engineering ethics + + + align:start position:0% +and engineering ethics +um includes professional ethics when + + align:start position:0% +um includes professional ethics when + + + align:start position:0% +um includes professional ethics when +they talk about professional ethics + + align:start position:0% +they talk about professional ethics + + + align:start position:0% +they talk about professional ethics +they're usually talking about + + align:start position:0% +they're usually talking about + + + align:start position:0% +they're usually talking about +or in the main they're talking about + + align:start position:0% +or in the main they're talking about + + + align:start position:0% +or in the main they're talking about +codes of ethics + + align:start position:0% +codes of ethics + + + align:start position:0% +codes of ethics +and the discussions that are + + align:start position:0% +and the discussions that are + + + align:start position:0% +and the discussions that are +in ethical discussions around codes of + + align:start position:0% +in ethical discussions around codes of + + + align:start position:0% +in ethical discussions around codes of +ethics + + align:start position:0% +ethics + + + align:start position:0% +ethics +to include cases + + align:start position:0% +to include cases + + + align:start position:0% +to include cases +all right + + align:start position:0% +all right + + + align:start position:0% +all right +but + + align:start position:0% + + + + align:start position:0% + +there is a term called professional + + align:start position:0% +there is a term called professional + + + align:start position:0% +there is a term called professional +ethics but there is no term + + align:start position:0% +ethics but there is no term + + + align:start position:0% +ethics but there is no term +called professional morals + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +so when somebody says you're unethical + + align:start position:0% +so when somebody says you're unethical + + + align:start position:0% +so when somebody says you're unethical +what that means + + align:start position:0% +what that means + + + align:start position:0% +what that means +is that is + + align:start position:0% +is that is + + + align:start position:0% +is that is +this one is an assault on your character + + align:start position:0% +this one is an assault on your character + + + align:start position:0% +this one is an assault on your character +in terms of religion this was an assault + + align:start position:0% +in terms of religion this was an assault + + + align:start position:0% +in terms of religion this was an assault +on your behavior in terms of your + + align:start position:0% +on your behavior in terms of your + + + align:start position:0% +on your behavior in terms of your +working environment + + align:start position:0% + + + + align:start position:0% + +all right so all of this has to do with + + align:start position:0% +all right so all of this has to do with + + + align:start position:0% +all right so all of this has to do with +usage how does a word get its meaning + + align:start position:0% +usage how does a word get its meaning + + + align:start position:0% +usage how does a word get its meaning +just simply by people using it a certain + + align:start position:0% +just simply by people using it a certain + + + align:start position:0% +just simply by people using it a certain +way and not using it another way got + + align:start position:0% +way and not using it another way got + + + align:start position:0% +way and not using it another way got +nothing to do with logic + + align:start position:0% +nothing to do with logic + + + align:start position:0% +nothing to do with logic +it's entirely empirical + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +okay so if you are in some kind of a + + align:start position:0% +okay so if you are in some kind of a + + + align:start position:0% +okay so if you are in some kind of a +meeting + + align:start position:0% +meeting + + + align:start position:0% +meeting +let's say or you're some kind of + + align:start position:0% +let's say or you're some kind of + + + align:start position:0% +let's say or you're some kind of +committee + + align:start position:0% +committee + + + align:start position:0% +committee +um + + align:start position:0% + + + + align:start position:0% + +and you have to deal with an issue like + + align:start position:0% +and you have to deal with an issue like + + + align:start position:0% +and you have to deal with an issue like +this let's say uh i don't know the pta + + align:start position:0% +this let's say uh i don't know the pta + + + align:start position:0% +this let's say uh i don't know the pta +okay and some students got caught + + align:start position:0% +okay and some students got caught + + + align:start position:0% +okay and some students got caught +cheating + + align:start position:0% +cheating + + + align:start position:0% +cheating +they + + align:start position:0% +they + + + align:start position:0% +they +the principal sets up what a + + align:start position:0% +the principal sets up what a + + + align:start position:0% +the principal sets up what a +president of pta sets up an ethics + + align:start position:0% +president of pta sets up an ethics + + + align:start position:0% +president of pta sets up an ethics +committee + + align:start position:0% +committee + + + align:start position:0% +committee +i said oh you studied ethics in college + + align:start position:0% +i said oh you studied ethics in college + + + align:start position:0% +i said oh you studied ethics in college +you'd be the chair of the committee + + align:start position:0% +you'd be the chair of the committee + + + align:start position:0% +you'd be the chair of the committee +where you got + + align:start position:0% +where you got + + + align:start position:0% +where you got +500 people sitting in the audience and + + align:start position:0% +500 people sitting in the audience and + + + align:start position:0% +500 people sitting in the audience and +the first thing they want to know is + + align:start position:0% +the first thing they want to know is + + + align:start position:0% +the first thing they want to know is +what's the difference between ethics and + + align:start position:0% +what's the difference between ethics and + + + align:start position:0% +what's the difference between ethics and +moral + + align:start position:0% +moral + + + align:start position:0% +moral +all right + + align:start position:0% +all right + + + align:start position:0% +all right +uh today in philosophy + + align:start position:0% +uh today in philosophy + + + align:start position:0% +uh today in philosophy +or among philosophers + + align:start position:0% + + + + align:start position:0% + +they + + align:start position:0% +they + + + align:start position:0% +they +and this is a popular thing but no one + + align:start position:0% +and this is a popular thing but no one + + + align:start position:0% +and this is a popular thing but no one +philosophy is constrained to do it but + + align:start position:0% +philosophy is constrained to do it but + + + align:start position:0% +philosophy is constrained to do it but +it's most popular to talk about morals + + align:start position:0% + + + + align:start position:0% + +very much like we talk about mores + + align:start position:0% +very much like we talk about mores + + + align:start position:0% +very much like we talk about mores +what do people say + + align:start position:0% +what do people say + + + align:start position:0% +what do people say +is good and right what do they say is + + align:start position:0% +is good and right what do they say is + + + align:start position:0% +is good and right what do they say is +bad and wrong + + align:start position:0% +bad and wrong + + + align:start position:0% +bad and wrong +like normative yeah right + + align:start position:0% +like normative yeah right + + + align:start position:0% +like normative yeah right +now i'm going to get into something so + + align:start position:0% +now i'm going to get into something so + + + align:start position:0% +now i'm going to get into something so +let's not get confused with normative + + align:start position:0% +let's not get confused with normative + + + align:start position:0% +let's not get confused with normative +ethics + + align:start position:0% +ethics + + + align:start position:0% +ethics +all right + + align:start position:0% +all right + + + align:start position:0% +all right +all right + + align:start position:0% +all right + + + align:start position:0% +all right +right + + align:start position:0% +right + + + align:start position:0% +right +and + + align:start position:0% +and + + + align:start position:0% +and +i'll tell you one problem i had with + + align:start position:0% +i'll tell you one problem i had with + + + align:start position:0% +i'll tell you one problem i had with +this word normative word normative when + + align:start position:0% +this word normative word normative when + + + align:start position:0% +this word normative word normative when +i first uh heard it + + align:start position:0% +i first uh heard it + + + align:start position:0% +i first uh heard it +and that was normal + + align:start position:0% + + + + align:start position:0% + +i don't know i'll come back yeah let's + + align:start position:0% +i don't know i'll come back yeah let's + + + align:start position:0% +i don't know i'll come back yeah let's +go i'll come back to that + + align:start position:0% +go i'll come back to that + + + align:start position:0% +go i'll come back to that +all right remind me to come back if i + + align:start position:0% +all right remind me to come back if i + + + align:start position:0% +all right remind me to come back if i +don't very soon all right so what was i + + align:start position:0% +don't very soon all right so what was i + + + align:start position:0% +don't very soon all right so what was i +saying + + align:start position:0% + + + + align:start position:0% + +right today in philosophy + + align:start position:0% + + + + align:start position:0% + +morals have to do with all of those + + align:start position:0% +morals have to do with all of those + + + align:start position:0% +morals have to do with all of those +issues and ethics has to do with the + + align:start position:0% +issues and ethics has to do with the + + + align:start position:0% +issues and ethics has to do with the +systematic study of them + + align:start position:0% +systematic study of them + + + align:start position:0% +systematic study of them +okay so uh + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +is um + + align:start position:0% + + + + align:start position:0% + +if a per of a person wants to use the + + align:start position:0% +if a per of a person wants to use the + + + align:start position:0% +if a per of a person wants to use the +difference + + align:start position:0% +difference + + + align:start position:0% +difference +if you get a research paper + + align:start position:0% +if you get a research paper + + + align:start position:0% +if you get a research paper +you may find something altogether + + align:start position:0% +you may find something altogether + + + align:start position:0% +you may find something altogether +different + + align:start position:0% +different + + + align:start position:0% +different +the good news is if they use something + + align:start position:0% +the good news is if they use something + + + align:start position:0% +the good news is if they use something +different they'll say it + + align:start position:0% +different they'll say it + + + align:start position:0% +different they'll say it +they'll tell you exactly what their + + align:start position:0% +they'll tell you exactly what their + + + align:start position:0% +they'll tell you exactly what their +meanings are + + align:start position:0% +meanings are + + + align:start position:0% +meanings are +okay so if you look up a journal you + + align:start position:0% +okay so if you look up a journal you + + + align:start position:0% +okay so if you look up a journal you +know ethics + + align:start position:0% +know ethics + + + align:start position:0% +know ethics +okay um + + align:start position:0% + + + + align:start position:0% + +now let's talk about + + align:start position:0% +now let's talk about + + + align:start position:0% +now let's talk about +when i use the word ethics unless + + align:start position:0% +when i use the word ethics unless + + + align:start position:0% +when i use the word ethics unless +unless it's clear about the context or i + + align:start position:0% +unless it's clear about the context or i + + + align:start position:0% +unless it's clear about the context or i +unless you ask me i am talking about a + + align:start position:0% +unless you ask me i am talking about a + + + align:start position:0% +unless you ask me i am talking about a +branch of philosophy called ethics and i + + align:start position:0% +branch of philosophy called ethics and i + + + align:start position:0% +branch of philosophy called ethics and i +could very well be talking about moral + + align:start position:0% +could very well be talking about moral + + + align:start position:0% +could very well be talking about moral +philosophy + + align:start position:0% +philosophy + + + align:start position:0% +philosophy +this course is called engineering ethics + + align:start position:0% +this course is called engineering ethics + + + align:start position:0% +this course is called engineering ethics +so i would choose more to use ethics + + align:start position:0% + + + + align:start position:0% + +but they mean the same thing + + align:start position:0% +but they mean the same thing + + + align:start position:0% +but they mean the same thing +now + + align:start position:0% + + + + align:start position:0% + +philosophy depending on who you talk to + + align:start position:0% +philosophy depending on who you talk to + + + align:start position:0% +philosophy depending on who you talk to +has + + align:start position:0% +has + + + align:start position:0% +has +three or depending on who you talk to + + align:start position:0% +three or depending on who you talk to + + + align:start position:0% +three or depending on who you talk to +may have four major divisions big + + align:start position:0% +may have four major divisions big + + + align:start position:0% +may have four major divisions big +divisions of philosophy and then we'll + + align:start position:0% +divisions of philosophy and then we'll + + + align:start position:0% +divisions of philosophy and then we'll +talk about and if and and here's the way + + align:start position:0% +talk about and if and and here's the way + + + align:start position:0% +talk about and if and and here's the way +it goes + + align:start position:0% + + + + align:start position:0% + +i want to keep this down i want to keep + + align:start position:0% +i want to keep this down i want to keep + + + align:start position:0% +i want to keep this down i want to keep +that on the board over there we can't + + align:start position:0% +that on the board over there we can't + + + align:start position:0% +that on the board over there we can't +see this + + align:start position:0% +see this + + + align:start position:0% +see this +so what am i going to do + + align:start position:0% +so what am i going to do + + + align:start position:0% +so what am i going to do +uh i'll erase this + + align:start position:0% + + + + align:start position:0% + +okay philosophy + + align:start position:0% + + + + align:start position:0% + +all right now one of your great + + align:start position:0% +all right now one of your great + + + align:start position:0% +all right now one of your great +divisions + + align:start position:0% + + + + align:start position:0% + +and i think i gave a short lecture on + + align:start position:0% +and i think i gave a short lecture on + + + align:start position:0% +and i think i gave a short lecture on +this + + align:start position:0% + + + + align:start position:0% + +called metaphysics + + align:start position:0% + + + + align:start position:0% + +and metaphysics is is about uh saying + + align:start position:0% +and metaphysics is is about uh saying + + + align:start position:0% +and metaphysics is is about uh saying +what a thing is + + align:start position:0% +what a thing is + + + align:start position:0% +what a thing is +and what sort of thing it is + + align:start position:0% +and what sort of thing it is + + + align:start position:0% +and what sort of thing it is +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it talks about the rational world as + + align:start position:0% +it talks about the rational world as + + + align:start position:0% +it talks about the rational world as +opposed to the + + align:start position:0% + + + + align:start position:0% + +real world + + align:start position:0% +real world + + + align:start position:0% +real world +and the real world as opposed to the + + align:start position:0% +and the real world as opposed to the + + + align:start position:0% +and the real world as opposed to the +hyper real world or hyperspace + + align:start position:0% +hyper real world or hyperspace + + + align:start position:0% +hyper real world or hyperspace +okay when you talk about all of those + + align:start position:0% +okay when you talk about all of those + + + align:start position:0% +okay when you talk about all of those +kinds of discussions you're in the realm + + align:start position:0% +kinds of discussions you're in the realm + + + align:start position:0% +kinds of discussions you're in the realm +of metaphysics + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the next one is epistemology + + align:start position:0% + + + + align:start position:0% + +and epistemology + + align:start position:0% +and epistemology + + + align:start position:0% +and epistemology +has another name + + align:start position:0% +has another name + + + align:start position:0% +has another name +theory of knowledge + + align:start position:0% + + + + align:start position:0% + +what do you know + + align:start position:0% +what do you know + + + align:start position:0% +what do you know +and how do you know it + + align:start position:0% + + + + align:start position:0% + +all right um + + align:start position:0% + + + + align:start position:0% + +the next one + + align:start position:0% +the next one + + + align:start position:0% +the next one +is called + + align:start position:0% + + + + align:start position:0% + +axiology + + align:start position:0% + + + + align:start position:0% + +and the best way to define axiology is + + align:start position:0% +and the best way to define axiology is + + + align:start position:0% +and the best way to define axiology is +to say it has that that is a word that + + align:start position:0% +to say it has that that is a word that + + + align:start position:0% +to say it has that that is a word that +has to reference one of the words is + + align:start position:0% +has to reference one of the words is + + + align:start position:0% +has to reference one of the words is +ethics and the other one is aesthetics + + align:start position:0% + + + + align:start position:0% + +okay so when we study ethics + + align:start position:0% + + + + align:start position:0% + +i think + + align:start position:0% +i think + + + align:start position:0% +i think +that + + align:start position:0% + + + + align:start position:0% + +it's fair to say that we're discussing a + + align:start position:0% +it's fair to say that we're discussing a + + + align:start position:0% +it's fair to say that we're discussing a +very large division + + align:start position:0% +very large division + + + align:start position:0% +very large division +of philosophy + + align:start position:0% + + + + align:start position:0% + +now i am going to put in + + align:start position:0% +now i am going to put in + + + align:start position:0% +now i am going to put in +dotted lines + + align:start position:0% + + + + align:start position:0% + +another division + + align:start position:0% + + + + align:start position:0% + +and um this other this dotted line is + + align:start position:0% +and um this other this dotted line is + + + align:start position:0% +and um this other this dotted line is +not so much debated + + align:start position:0% + + + + align:start position:0% + +as it is + + align:start position:0% +as it is + + + align:start position:0% +as it is +that when you start looking at all the + + align:start position:0% +that when you start looking at all the + + + align:start position:0% +that when you start looking at all the +various areas of philosophy some of them + + align:start position:0% +various areas of philosophy some of them + + + align:start position:0% +various areas of philosophy some of them +don't fit into these categories + + align:start position:0% +don't fit into these categories + + + align:start position:0% +don't fit into these categories +now when you now you can imagine most of + + align:start position:0% +now when you now you can imagine most of + + + align:start position:0% +now when you now you can imagine most of +them fit + + align:start position:0% +them fit + + + align:start position:0% +them fit +somewhere overlapping + + align:start position:0% +somewhere overlapping + + + align:start position:0% +somewhere overlapping +none of them very few of them fit + + align:start position:0% +none of them very few of them fit + + + align:start position:0% +none of them very few of them fit +directly under + + align:start position:0% +directly under + + + align:start position:0% +directly under +you know you know you're not going to + + align:start position:0% +you know you know you're not going to + + + align:start position:0% +you know you know you're not going to +get an organizational chart out of this + + align:start position:0% +get an organizational chart out of this + + + align:start position:0% +get an organizational chart out of this +you're going to get a venn diagram + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +um but there's another one over there + + align:start position:0% +um but there's another one over there + + + align:start position:0% +um but there's another one over there +that deserves a name + + align:start position:0% +that deserves a name + + + align:start position:0% +that deserves a name +uh some people have proposed names + + align:start position:0% +uh some people have proposed names + + + align:start position:0% +uh some people have proposed names +nobody likes them + + align:start position:0% + + + + align:start position:0% + +oh but i will give you a name + + align:start position:0% +oh but i will give you a name + + + align:start position:0% +oh but i will give you a name +that if that you can use and everybody + + align:start position:0% +that if that you can use and everybody + + + align:start position:0% +that if that you can use and everybody +will know what you're talking about + + align:start position:0% + + + + align:start position:0% + +they will argue with you about using + + align:start position:0% +they will argue with you about using + + + align:start position:0% +they will argue with you about using +this word but they but they won't have + + align:start position:0% +this word but they but they won't have + + + align:start position:0% +this word but they but they won't have +another word + + align:start position:0% +another word + + + align:start position:0% +another word +okay + + align:start position:0% + + + + align:start position:0% + +i want you to know that word praxis + + align:start position:0% + + + + align:start position:0% + +now uh uh + + align:start position:0% +now uh uh + + + align:start position:0% +now uh uh +i'll tell you uh + + align:start position:0% +i'll tell you uh + + + align:start position:0% +i'll tell you uh +what praxis means why it's an unpopular + + align:start position:0% +what praxis means why it's an unpopular + + + align:start position:0% +what praxis means why it's an unpopular +term + + align:start position:0% +term + + + align:start position:0% +term +in the united states + + align:start position:0% +in the united states + + + align:start position:0% +in the united states +and some of the other areas about under + + align:start position:0% +and some of the other areas about under + + + align:start position:0% +and some of the other areas about under +it + + align:start position:0% + + + + align:start position:0% + +praxis is a word + + align:start position:0% +praxis is a word + + + align:start position:0% +praxis is a word +that was i don't think + + align:start position:0% +that was i don't think + + + align:start position:0% +that was i don't think +karl marx invented the word + + align:start position:0% + + + + align:start position:0% + +but he popularized + + align:start position:0% + + + + align:start position:0% + +so you see + + align:start position:0% +so you see + + + align:start position:0% +so you see +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +that + + align:start position:0% +that + + + align:start position:0% +that +if you use the word praxis + + align:start position:0% +if you use the word praxis + + + align:start position:0% +if you use the word praxis +then some + + align:start position:0% +then some + + + align:start position:0% +then some +body who + + align:start position:0% +body who + + + align:start position:0% +body who +uh + + align:start position:0% +uh + + + align:start position:0% +uh +really has an emotional + + align:start position:0% +really has an emotional + + + align:start position:0% +really has an emotional +um + + align:start position:0% +um + + + align:start position:0% +um +aversion + + align:start position:0% +aversion + + + align:start position:0% +aversion +to communism + + align:start position:0% +to communism + + + align:start position:0% +to communism +is going to ask you if you're a comic + + align:start position:0% + + + + align:start position:0% + +i use the word + + align:start position:0% +i use the word + + + align:start position:0% +i use the word +frequently + + align:start position:0% + + + + align:start position:0% + +they don't like it okay let me give you + + align:start position:0% +they don't like it okay let me give you + + + align:start position:0% +they don't like it okay let me give you +some other words there is a a + + align:start position:0% +some other words there is a a + + + align:start position:0% +some other words there is a a +branch of philosophy called + + align:start position:0% + + + + align:start position:0% + +and you can use it e o l o g y and you + + align:start position:0% +and you can use it e o l o g y and you + + + align:start position:0% +and you can use it e o l o g y and you +can use it i o l o g y praxeology + + align:start position:0% + + + + align:start position:0% + +now first let me see what praxis means + + align:start position:0% + + + + align:start position:0% + +praxis means + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +theory + + align:start position:0% + + + + align:start position:0% + +about + + align:start position:0% + + + + align:start position:0% + +the theory that just precedes action + + align:start position:0% + + + + align:start position:0% + +in other words you got an abstract + + align:start position:0% +in other words you got an abstract + + + align:start position:0% +in other words you got an abstract +concept + + align:start position:0% +concept + + + align:start position:0% +concept +like newton's second law + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you've got a airplane that has lost this + + align:start position:0% +you've got a airplane that has lost this + + + align:start position:0% +you've got a airplane that has lost this +propulsion it's power it's getting ready + + align:start position:0% +propulsion it's power it's getting ready + + + align:start position:0% +propulsion it's power it's getting ready +to fall out of the sky + + align:start position:0% +to fall out of the sky + + + align:start position:0% +to fall out of the sky +and you want to + + align:start position:0% +and you want to + + + align:start position:0% +and you want to +figure out how long it's going to take + + align:start position:0% +figure out how long it's going to take + + + align:start position:0% +figure out how long it's going to take +the argument is that you don't go + + align:start position:0% +the argument is that you don't go + + + align:start position:0% +the argument is that you don't go +directly the mind does not go directly + + align:start position:0% +directly the mind does not go directly + + + align:start position:0% +directly the mind does not go directly +from the abstract theory to the + + align:start position:0% +from the abstract theory to the + + + align:start position:0% +from the abstract theory to the +practical application something happens + + align:start position:0% +practical application something happens + + + align:start position:0% +practical application something happens +in the middle + + align:start position:0% + + + + align:start position:0% + +theory into action i've never heard that + + align:start position:0% +theory into action i've never heard that + + + align:start position:0% +theory into action i've never heard that +term but i can use that + + align:start position:0% +term but i can use that + + + align:start position:0% +term but i can use that +theory into action + + align:start position:0% + + + + align:start position:0% + +now in philosophy there is a + + align:start position:0% +now in philosophy there is a + + + align:start position:0% +now in philosophy there is a +a + + align:start position:0% +a + + + align:start position:0% +a +robust body + + align:start position:0% + + + + align:start position:0% + +or a robust category of philosophy + + align:start position:0% +or a robust category of philosophy + + + align:start position:0% +or a robust category of philosophy +called action theory or theory of action + + align:start position:0% + + + + align:start position:0% + +you can write a dissertation on theory + + align:start position:0% +you can write a dissertation on theory + + + align:start position:0% +you can write a dissertation on theory +of action in most any big university + + align:start position:0% +of action in most any big university + + + align:start position:0% +of action in most any big university +when i say big university any university + + align:start position:0% +when i say big university any university + + + align:start position:0% +when i say big university any university +that has a philosophy department that + + align:start position:0% +that has a philosophy department that + + + align:start position:0% +that has a philosophy department that +has enough faculty + + align:start position:0% +has enough faculty + + + align:start position:0% +has enough faculty +to cover the others + + align:start position:0% + + + + align:start position:0% + +theory of action is not ethics + + align:start position:0% +theory of action is not ethics + + + align:start position:0% +theory of action is not ethics +it overlaps + + align:start position:0% + + + + align:start position:0% + +this is the term of art theory of action + + align:start position:0% + + + + align:start position:0% + +ah + + align:start position:0% +ah + + + align:start position:0% +ah +venn diagram + + align:start position:0% +venn diagram + + + align:start position:0% +venn diagram +it falls closer into practice than any + + align:start position:0% +it falls closer into practice than any + + + align:start position:0% +it falls closer into practice than any +of the rest of them + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +praxis + + align:start position:0% +praxis + + + align:start position:0% +praxis +is really talking about + + align:start position:0% +is really talking about + + + align:start position:0% +is really talking about +theory just before you act + + align:start position:0% +theory just before you act + + + align:start position:0% +theory just before you act +theory of action is talking about + + align:start position:0% +theory of action is talking about + + + align:start position:0% +theory of action is talking about +practice and action + + align:start position:0% + + + + align:start position:0% + +but if you want to write your + + align:start position:0% +but if you want to write your + + + align:start position:0% +but if you want to write your +dissertation on action theory + + align:start position:0% +dissertation on action theory + + + align:start position:0% +dissertation on action theory +you go to any department where they can + + align:start position:0% +you go to any department where they can + + + align:start position:0% +you go to any department where they can +cover + + align:start position:0% +cover + + + align:start position:0% +cover +these three and have faculty left over + + align:start position:0% +these three and have faculty left over + + + align:start position:0% +these three and have faculty left over +you will be able to do this + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +all right so theory of action is big + + align:start position:0% +all right so theory of action is big + + + align:start position:0% +all right so theory of action is big +hi tony + + align:start position:0% +hi tony + + + align:start position:0% +hi tony +we're doing um + + align:start position:0% +we're doing um + + + align:start position:0% +we're doing um +definitions + + align:start position:0% +definitions + + + align:start position:0% +definitions +vocabulary + + align:start position:0% + + + + align:start position:0% + +not a structured + + align:start position:0% +not a structured + + + align:start position:0% +not a structured +approach oh + + align:start position:0% +approach oh + + + align:start position:0% +approach oh +now + + align:start position:0% + + + + align:start position:0% + +people who talk about + + align:start position:0% + + + + align:start position:0% + +oh let's keep on let's keep going + + align:start position:0% +oh let's keep on let's keep going + + + align:start position:0% +oh let's keep on let's keep going +there is there is a uh + + align:start position:0% +there is there is a uh + + + align:start position:0% +there is there is a uh +very interesting word here praxeology + + align:start position:0% +very interesting word here praxeology + + + align:start position:0% +very interesting word here praxeology +that is a translation + + align:start position:0% +that is a translation + + + align:start position:0% +that is a translation +of a polish term + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +interesting background i want to + + align:start position:0% +interesting background i want to + + + align:start position:0% +interesting background i want to +elaborate + + align:start position:0% +elaborate + + + align:start position:0% +elaborate +i have a confession as to why i want to + + align:start position:0% +i have a confession as to why i want to + + + align:start position:0% +i have a confession as to why i want to +elaborate + + align:start position:0% + + + + align:start position:0% + +macmillan has a new uh encyclopedia of + + align:start position:0% +macmillan has a new uh encyclopedia of + + + align:start position:0% +macmillan has a new uh encyclopedia of +philosophy coming out + + align:start position:0% + + + + align:start position:0% + +and the most interesting citation in it + + align:start position:0% +and the most interesting citation in it + + + align:start position:0% +and the most interesting citation in it +is one on praxeology + + align:start position:0% + + + + align:start position:0% + +this rap is beginning to get suspicious + + align:start position:0% +this rap is beginning to get suspicious + + + align:start position:0% +this rap is beginning to get suspicious +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +why did i say most interesting that's a + + align:start position:0% +why did i say most interesting that's a + + + align:start position:0% +why did i say most interesting that's a +very loaded term + + align:start position:0% +very loaded term + + + align:start position:0% +very loaded term +for a class like no i wrote it + + align:start position:0% + + + + align:start position:0% + +well i mean that was uh that was a label + + align:start position:0% +well i mean that was uh that was a label + + + align:start position:0% +well i mean that was uh that was a label +we're not talking about a whole lot of + + align:start position:0% +we're not talking about a whole lot of + + + align:start position:0% +we're not talking about a whole lot of +words + + align:start position:0% +words + + + align:start position:0% +words +i can't remember how many words it was + + align:start position:0% +i can't remember how many words it was + + + align:start position:0% +i can't remember how many words it was +i think i gave him about 10 pages + + align:start position:0% +i think i gave him about 10 pages + + + align:start position:0% +i think i gave him about 10 pages +that was a lot of research + + align:start position:0% +that was a lot of research + + + align:start position:0% +that was a lot of research +uh what happens is is that praxeology + + align:start position:0% + + + + align:start position:0% + +got its start + + align:start position:0% + + + + align:start position:0% + +by a man named codarbinsky + + align:start position:0% +by a man named codarbinsky + + + align:start position:0% +by a man named codarbinsky +he's polish now this being polish is + + align:start position:0% +he's polish now this being polish is + + + align:start position:0% +he's polish now this being polish is +very significant + + align:start position:0% +very significant + + + align:start position:0% +very significant +okay + + align:start position:0% +okay + + + align:start position:0% +okay +because all of the development of + + align:start position:0% +because all of the development of + + + align:start position:0% +because all of the development of +praxeology it's it reached it developed + + align:start position:0% +praxeology it's it reached it developed + + + align:start position:0% +praxeology it's it reached it developed +from cold warning and got its rich + + align:start position:0% +from cold warning and got its rich + + + align:start position:0% +from cold warning and got its rich +maturity + + align:start position:0% +maturity + + + align:start position:0% +maturity +during a time when poland was + + align:start position:0% +during a time when poland was + + + align:start position:0% +during a time when poland was +politically cut off from the west + + align:start position:0% +politically cut off from the west + + + align:start position:0% +politically cut off from the west +we could not get the papers + + align:start position:0% +we could not get the papers + + + align:start position:0% +we could not get the papers +out + + align:start position:0% +out + + + align:start position:0% +out +and we could not get papers in + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so we became aware of when i say we most + + align:start position:0% +so we became aware of when i say we most + + + align:start position:0% +so we became aware of when i say we most +scholars most of us there were some who + + align:start position:0% +scholars most of us there were some who + + + align:start position:0% +scholars most of us there were some who +traveled in poland during those days + + align:start position:0% +traveled in poland during those days + + + align:start position:0% +traveled in poland during those days +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and talked about + + align:start position:0% +and talked about + + + align:start position:0% +and talked about +uh + + align:start position:0% +uh + + + align:start position:0% +uh +philosophy + + align:start position:0% +philosophy + + + align:start position:0% +philosophy +talk about well i think john dewey + + align:start position:0% +talk about well i think john dewey + + + align:start position:0% +talk about well i think john dewey +somebody traveled in there and came back + + align:start position:0% +somebody traveled in there and came back + + + align:start position:0% +somebody traveled in there and came back +talking about pragmatism + + align:start position:0% +talking about pragmatism + + + align:start position:0% +talking about pragmatism +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +praxeology + + align:start position:0% +praxeology + + + align:start position:0% +praxeology +um + + align:start position:0% + + + + align:start position:0% + +came out + + align:start position:0% +came out + + + align:start position:0% +came out +when + + align:start position:0% +when + + + align:start position:0% +when +uh let me see if i can pronounce his + + align:start position:0% +uh let me see if i can pronounce his + + + align:start position:0% +uh let me see if i can pronounce his +name correctly if i cannot pronounce his + + align:start position:0% +name correctly if i cannot pronounce his + + + align:start position:0% +name correctly if i cannot pronounce his +name correctly + + align:start position:0% +name correctly + + + align:start position:0% +name correctly +his first name is carol k-a-r-o-l + + align:start position:0% + + + + align:start position:0% + +w-o-l-t and then more it's hard + + align:start position:0% +w-o-l-t and then more it's hard + + + align:start position:0% +w-o-l-t and then more it's hard +now uh incidentally um now i qualified + + align:start position:0% +now uh incidentally um now i qualified + + + align:start position:0% +now uh incidentally um now i qualified +in russia + + align:start position:0% +in russia + + + align:start position:0% +in russia +qualified in russian and french + + align:start position:0% + + + + align:start position:0% + +i can still + + align:start position:0% +i can still + + + align:start position:0% +i can still +read russian i don't mean read it with + + align:start position:0% +read russian i don't mean read it with + + + align:start position:0% +read russian i don't mean read it with +understanding but i can pronounce the + + align:start position:0% +understanding but i can pronounce the + + + align:start position:0% +understanding but i can pronounce the +words correctly + + align:start position:0% +words correctly + + + align:start position:0% +words correctly +polish is different + + align:start position:0% +polish is different + + + align:start position:0% +polish is different +but + + align:start position:0% +but + + + align:start position:0% +but +unless they throw one of those + + align:start position:0% +unless they throw one of those + + + align:start position:0% +unless they throw one of those +accents in there on top of the + + align:start position:0% +accents in there on top of the + + + align:start position:0% +accents in there on top of the +letter and they've got a lot of them in + + align:start position:0% +letter and they've got a lot of them in + + + align:start position:0% +letter and they've got a lot of them in +polish + + align:start position:0% +polish + + + align:start position:0% +polish +i could pronounce his name + + align:start position:0% +i could pronounce his name + + + align:start position:0% +i could pronounce his name +would you hoets think it's + + align:start position:0% +would you hoets think it's + + + align:start position:0% +would you hoets think it's +pretty is let's say that's about 70 80 + + align:start position:0% +pretty is let's say that's about 70 80 + + + align:start position:0% +pretty is let's say that's about 70 80 +percent right + + align:start position:0% +percent right + + + align:start position:0% +percent right +but if they wrote it in polish i could + + align:start position:0% +but if they wrote it in polish i could + + + align:start position:0% +but if they wrote it in polish i could +probably get it about 95 percent right + + align:start position:0% + + + + align:start position:0% + +when he became pope + + align:start position:0% +when he became pope + + + align:start position:0% +when he became pope +that opened up all of this scholarship + + align:start position:0% +that opened up all of this scholarship + + + align:start position:0% +that opened up all of this scholarship +from poland to the west + + align:start position:0% +from poland to the west + + + align:start position:0% +from poland to the west +and it was around that time + + align:start position:0% +and it was around that time + + + align:start position:0% +and it was around that time +that praxeology got into uh + + align:start position:0% +that praxeology got into uh + + + align:start position:0% +that praxeology got into uh +philosophy + + align:start position:0% +philosophy + + + align:start position:0% +philosophy +and + + align:start position:0% +and + + + align:start position:0% +and +there and what they are doing what i + + align:start position:0% +there and what they are doing what i + + + align:start position:0% +there and what they are doing what i +said that they were doing it with + + align:start position:0% +said that they were doing it with + + + align:start position:0% +said that they were doing it with +praxeology + + align:start position:0% +praxeology + + + align:start position:0% +praxeology +was writing a general theory + + align:start position:0% + + + + align:start position:0% + +for the learned disciplines that we call + + align:start position:0% +for the learned disciplines that we call + + + align:start position:0% +for the learned disciplines that we call +the practical learning disciplines law + + align:start position:0% +the practical learning disciplines law + + + align:start position:0% +the practical learning disciplines law +medicine engineering + + align:start position:0% +medicine engineering + + + align:start position:0% +medicine engineering +social work but not sociology + + align:start position:0% + + + + align:start position:0% + +business but not economics + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +and that they would they would they were + + align:start position:0% +and that they would they would they were + + + align:start position:0% +and that they would they would they were +trying to develop a + + align:start position:0% +trying to develop a + + + align:start position:0% +trying to develop a +a branch of philosophy + + align:start position:0% +a branch of philosophy + + + align:start position:0% +a branch of philosophy +that would guide those to that + + align:start position:0% +that would guide those to that + + + align:start position:0% +that would guide those to that +discussion + + align:start position:0% + + + + align:start position:0% + +okay so what they were trying to do was + + align:start position:0% +okay so what they were trying to do was + + + align:start position:0% +okay so what they were trying to do was +to get open up this whole new category + + align:start position:0% + + + + align:start position:0% + +and they did pretty good at it i think + + align:start position:0% +and they did pretty good at it i think + + + align:start position:0% +and they did pretty good at it i think +uh they suffered because they did not + + align:start position:0% +uh they suffered because they did not + + + align:start position:0% +uh they suffered because they did not +have wider wider scope of debate + + align:start position:0% +have wider wider scope of debate + + + align:start position:0% +have wider wider scope of debate +they only had themselves and they were + + align:start position:0% +they only had themselves and they were + + + align:start position:0% +they only had themselves and they were +pretty much sold on uh + + align:start position:0% +pretty much sold on uh + + + align:start position:0% +pretty much sold on uh +well you know how that is + + align:start position:0% +well you know how that is + + + align:start position:0% +well you know how that is +the four of us get together and say + + align:start position:0% +the four of us get together and say + + + align:start position:0% +the four of us get together and say +we're going to invent a whole new + + align:start position:0% +we're going to invent a whole new + + + align:start position:0% +we're going to invent a whole new +category of philosophy + + align:start position:0% +category of philosophy + + + align:start position:0% +category of philosophy +we're pretty much of one mind from the + + align:start position:0% +we're pretty much of one mind from the + + + align:start position:0% +we're pretty much of one mind from the +start + + align:start position:0% +start + + + align:start position:0% +start +it really to mature this thing + + align:start position:0% +it really to mature this thing + + + align:start position:0% +it really to mature this thing +somebody's got to come in from left + + align:start position:0% +somebody's got to come in from left + + + align:start position:0% +somebody's got to come in from left +field you know + + align:start position:0% +field you know + + + align:start position:0% +field you know +so they were cut off politically cut off + + align:start position:0% +so they were cut off politically cut off + + + align:start position:0% +so they were cut off politically cut off +from the western world + + align:start position:0% +from the western world + + + align:start position:0% +from the western world +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so um + + align:start position:0% +so um + + + align:start position:0% +so um +but i think that whatever you do with + + align:start position:0% +but i think that whatever you do with + + + align:start position:0% +but i think that whatever you do with +this uh chart + + align:start position:0% +this uh chart + + + align:start position:0% +this uh chart +remember that when the definitions come + + align:start position:0% +remember that when the definitions come + + + align:start position:0% +remember that when the definitions come +up we're talking about a venn diagram + + align:start position:0% +up we're talking about a venn diagram + + + align:start position:0% +up we're talking about a venn diagram +not an organizational chart + + align:start position:0% +not an organizational chart + + + align:start position:0% +not an organizational chart +because things don't fit neatly into + + align:start position:0% +because things don't fit neatly into + + + align:start position:0% +because things don't fit neatly into +these categories but almost everybody + + align:start position:0% +these categories but almost everybody + + + align:start position:0% +these categories but almost everybody +will agree + + align:start position:0% +will agree + + + align:start position:0% +will agree +that the that these three i'm sorry + + align:start position:0% +that the that these three i'm sorry + + + align:start position:0% +that the that these three i'm sorry +there's one other one there is one other + + align:start position:0% +there's one other one there is one other + + + align:start position:0% +there's one other one there is one other +one + + align:start position:0% +one + + + align:start position:0% +one +that actually fits in this category + + align:start position:0% + + + + align:start position:0% + +and philosophers want to include it + + align:start position:0% +and philosophers want to include it + + + align:start position:0% +and philosophers want to include it +let's talk about some others that fit + + align:start position:0% +let's talk about some others that fit + + + align:start position:0% +let's talk about some others that fit +into this category + + align:start position:0% +into this category + + + align:start position:0% +into this category +uh and sometimes they'll include it one + + align:start position:0% +uh and sometimes they'll include it one + + + align:start position:0% +uh and sometimes they'll include it one +of them is + + align:start position:0% +of them is + + + align:start position:0% +of them is +philosophy of education + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% + + + + align:start position:0% + +there is such a thing called educational + + align:start position:0% +there is such a thing called educational + + + align:start position:0% +there is such a thing called educational +psychology which is a science and fits + + align:start position:0% +psychology which is a science and fits + + + align:start position:0% +psychology which is a science and fits +very closely under epistemology notice + + align:start position:0% +very closely under epistemology notice + + + align:start position:0% +very closely under epistemology notice +this science we're gonna + + align:start position:0% +this science we're gonna + + + align:start position:0% +this science we're gonna +i'm getting excited about it just now + + align:start position:0% +i'm getting excited about it just now + + + align:start position:0% +i'm getting excited about it just now +let me organize my thoughts i want to go + + align:start position:0% +let me organize my thoughts i want to go + + + align:start position:0% +let me organize my thoughts i want to go +back + + align:start position:0% + + + + align:start position:0% + +let's talk about where some + + align:start position:0% +let's talk about where some + + + align:start position:0% +let's talk about where some +learner disciplines fit into these + + align:start position:0% +learner disciplines fit into these + + + align:start position:0% +learner disciplines fit into these +categories fit in categories okay + + align:start position:0% +categories fit in categories okay + + + align:start position:0% +categories fit in categories okay +science + + align:start position:0% + + + + align:start position:0% + +a fair + + align:start position:0% +a fair + + + align:start position:0% +a fair +the fair the the the most accurate + + align:start position:0% +the fair the the the most accurate + + + align:start position:0% +the fair the the the most accurate +short statement about what science is + + align:start position:0% +short statement about what science is + + + align:start position:0% +short statement about what science is +is that is a learning discipline + + align:start position:0% + + + + align:start position:0% + +for the production + + align:start position:0% +for the production + + + align:start position:0% +for the production +of knowledge + + align:start position:0% +of knowledge + + + align:start position:0% +of knowledge +about the physical world + + align:start position:0% +about the physical world + + + align:start position:0% +about the physical world +in pursuit of the truth + + align:start position:0% +in pursuit of the truth + + + align:start position:0% +in pursuit of the truth +about the physical world + + align:start position:0% + + + + align:start position:0% + +so therefore + + align:start position:0% +so therefore + + + align:start position:0% +so therefore +science would be closer to epistemology + + align:start position:0% +science would be closer to epistemology + + + align:start position:0% +science would be closer to epistemology +with a good enough overlap with + + align:start position:0% +with a good enough overlap with + + + align:start position:0% +with a good enough overlap with +metaphysics + + align:start position:0% + + + + align:start position:0% + +than in axiology + + align:start position:0% + + + + align:start position:0% + +ethics clearly is in axiology by + + align:start position:0% +ethics clearly is in axiology by + + + align:start position:0% +ethics clearly is in axiology by +definition + + align:start position:0% +definition + + + align:start position:0% +definition +but that but any theory of values + + align:start position:0% + + + + align:start position:0% + +close fits closer to axiology than + + align:start position:0% +close fits closer to axiology than + + + align:start position:0% +close fits closer to axiology than +anything else + + align:start position:0% +anything else + + + align:start position:0% +anything else +so if you want to talk about art + + align:start position:0% + + + + align:start position:0% + +that would fit closer to + + align:start position:0% +that would fit closer to + + + align:start position:0% +that would fit closer to +to axiology than anything else theory of + + align:start position:0% +to axiology than anything else theory of + + + align:start position:0% +to axiology than anything else theory of +beauty + + align:start position:0% +beauty + + + align:start position:0% +beauty +if you want to talk about art that's not + + align:start position:0% +if you want to talk about art that's not + + + align:start position:0% +if you want to talk about art that's not +the only way to talk about art but + + align:start position:0% +the only way to talk about art but + + + align:start position:0% +the only way to talk about art but +that's one way to talk about art + + align:start position:0% +that's one way to talk about art + + + align:start position:0% +that's one way to talk about art +aesthetics + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +aesthetics can you how many of them do + + align:start position:0% +aesthetics can you how many of them do + + + align:start position:0% +aesthetics can you how many of them do +we have + + align:start position:0% + + + + align:start position:0% + +well think of your senses + + align:start position:0% + + + + align:start position:0% + +beauty in the eye is called it's that + + align:start position:0% +beauty in the eye is called it's that + + + align:start position:0% +beauty in the eye is called it's that +it's called aesthetics + + align:start position:0% + + + + align:start position:0% + +there's such a thing as gustatory + + align:start position:0% +there's such a thing as gustatory + + + align:start position:0% +there's such a thing as gustatory +uh + + align:start position:0% +uh + + + align:start position:0% +uh +values + + align:start position:0% + + + + align:start position:0% + +oh yes + + align:start position:0% +oh yes + + + align:start position:0% +oh yes +oh yes + + align:start position:0% +oh yes + + + align:start position:0% +oh yes +oh yes and guess where they work + + align:start position:0% +oh yes and guess where they work + + + align:start position:0% +oh yes and guess where they work +in art departments + + align:start position:0% + + + + align:start position:0% + +oh yes + + align:start position:0% + + + + align:start position:0% + +food yeah + + align:start position:0% +food yeah + + + align:start position:0% +food yeah +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +you'll have to go to france to get a phd + + align:start position:0% +you'll have to go to france to get a phd + + + align:start position:0% +you'll have to go to france to get a phd +in + + align:start position:0% + + + + align:start position:0% + +you're not going to get a phd in + + align:start position:0% +you're not going to get a phd in + + + align:start position:0% +you're not going to get a phd in +gustatory philosophy over here + + align:start position:0% +gustatory philosophy over here + + + align:start position:0% +gustatory philosophy over here +but no gustatory uh + + align:start position:0% +but no gustatory uh + + + align:start position:0% +but no gustatory uh +you know + + align:start position:0% +you know + + + align:start position:0% +you know +what's another one um + + align:start position:0% + + + + align:start position:0% + +music we can do that over here + + align:start position:0% +music we can do that over here + + + align:start position:0% +music we can do that over here +yes music + + align:start position:0% +yes music + + + align:start position:0% +yes music +um + + align:start position:0% +um + + + align:start position:0% +um +tactile + + align:start position:0% +tactile + + + align:start position:0% +tactile +that's the formal term t-a-c-t-i-l-e has + + align:start position:0% +that's the formal term t-a-c-t-i-l-e has + + + align:start position:0% +that's the formal term t-a-c-t-i-l-e has +to do with not feelings but with feel + + align:start position:0% + + + + align:start position:0% + +not the passions but with the sense of + + align:start position:0% +not the passions but with the sense of + + + align:start position:0% +not the passions but with the sense of +feeling + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +here's another one + + align:start position:0% +here's another one + + + align:start position:0% +here's another one +probably + + align:start position:0% +probably + + + align:start position:0% +probably +the most important one is + + align:start position:0% +the most important one is + + + align:start position:0% +the most important one is +has to do with sight + + align:start position:0% +has to do with sight + + + align:start position:0% +has to do with sight +that's our most important thing but + + align:start position:0% +that's our most important thing but + + + align:start position:0% +that's our most important thing but +there's another one that is very it is + + align:start position:0% +there's another one that is very it is + + + align:start position:0% +there's another one that is very it is +very it's coming along now and something + + align:start position:0% +very it's coming along now and something + + + align:start position:0% +very it's coming along now and something +is going to happen + + align:start position:0% +is going to happen + + + align:start position:0% +is going to happen +in your lifetimes + + align:start position:0% +in your lifetimes + + + align:start position:0% +in your lifetimes +your uh yours too sorry + + align:start position:0% +your uh yours too sorry + + + align:start position:0% +your uh yours too sorry +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +it's only going to happen + + align:start position:0% +it's only going to happen + + + align:start position:0% +it's only going to happen +to me you know when i'm in full + + align:start position:0% +to me you know when i'm in full + + + align:start position:0% +to me you know when i'm in full +retirement + + align:start position:0% + + + + align:start position:0% + +and that's in the area + + align:start position:0% +and that's in the area + + + align:start position:0% +and that's in the area +of + + align:start position:0% + + + + align:start position:0% + +old factory + + align:start position:0% + + + + align:start position:0% + +philosophy and + + align:start position:0% +philosophy and + + + align:start position:0% +philosophy and +praxis and all of that + + align:start position:0% +praxis and all of that + + + align:start position:0% +praxis and all of that +you know what they've just done + + align:start position:0% +you know what they've just done + + + align:start position:0% +you know what they've just done +i got this i'll get this from i've been + + align:start position:0% +i got this i'll get this from i've been + + + align:start position:0% +i got this i'll get this from i've been +following well first of all the old + + align:start position:0% +following well first of all the old + + + align:start position:0% +following well first of all the old +factory + + align:start position:0% +factory + + + align:start position:0% +factory +the old factory was intriguing to me + + align:start position:0% +the old factory was intriguing to me + + + align:start position:0% +the old factory was intriguing to me +when i learned that + + align:start position:0% +when i learned that + + + align:start position:0% +when i learned that +the olfactory sense that uh the sense + + align:start position:0% +the olfactory sense that uh the sense + + + align:start position:0% +the olfactory sense that uh the sense +the sense of smell + + align:start position:0% +the sense of smell + + + align:start position:0% +the sense of smell +is the only one + + align:start position:0% + + + + align:start position:0% + +uh that + + align:start position:0% +uh that + + + align:start position:0% +uh that +does not go through the cognitive area + + align:start position:0% +does not go through the cognitive area + + + align:start position:0% +does not go through the cognitive area +of the mind for processing before + + align:start position:0% +of the mind for processing before + + + align:start position:0% +of the mind for processing before +it goes other places in the body and + + align:start position:0% +it goes other places in the body and + + + align:start position:0% +it goes other places in the body and +that uh everything else requires some + + align:start position:0% +that uh everything else requires some + + + align:start position:0% +that uh everything else requires some +processing first some reason reason and + + align:start position:0% +processing first some reason reason and + + + align:start position:0% +processing first some reason reason and +all of that well it's like you put the + + align:start position:0% +all of that well it's like you put the + + + align:start position:0% +all of that well it's like you put the +neck or cube up there it's on a flat + + align:start position:0% +neck or cube up there it's on a flat + + + align:start position:0% +neck or cube up there it's on a flat +surface but we see + + align:start position:0% +surface but we see + + + align:start position:0% +surface but we see +three dimensional the brain did that + + align:start position:0% +three dimensional the brain did that + + + align:start position:0% +three dimensional the brain did that +okay olfactory go straight to the + + align:start position:0% + + + + align:start position:0% + +to the um + + align:start position:0% +to the um + + + align:start position:0% +to the um +cycle motor + + align:start position:0% + + + + align:start position:0% + +uh and it's supposed to be the only one + + align:start position:0% +uh and it's supposed to be the only one + + + align:start position:0% +uh and it's supposed to be the only one +i'm talking at the level of the best uh + + align:start position:0% +i'm talking at the level of the best uh + + + align:start position:0% +i'm talking at the level of the best uh +documentaries on television + + align:start position:0% +documentaries on television + + + align:start position:0% +documentaries on television +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right + + align:start position:0% +all right + + + align:start position:0% +all right +i can go a little bit further + + align:start position:0% +i can go a little bit further + + + align:start position:0% +i can go a little bit further +i hang out with a lot of + + align:start position:0% + + + + align:start position:0% + +psychiatrists + + align:start position:0% + + + + align:start position:0% + +on on a you know friendly basis + + align:start position:0% + + + + align:start position:0% + +uh but uh we we talk about these things + + align:start position:0% +uh but uh we we talk about these things + + + align:start position:0% +uh but uh we we talk about these things +we saw that too but they but something + + align:start position:0% +we saw that too but they but something + + + align:start position:0% +we saw that too but they but something +has happened um + + align:start position:0% +has happened um + + + align:start position:0% +has happened um +they have now been able to + + align:start position:0% + + + + align:start position:0% + +okay let me back up a minute it's + + align:start position:0% +okay let me back up a minute it's + + + align:start position:0% +okay let me back up a minute it's +something that we engineers understand + + align:start position:0% +something that we engineers understand + + + align:start position:0% +something that we engineers understand +very well + + align:start position:0% + + + + align:start position:0% + +and that is uh in mathematics + + align:start position:0% +and that is uh in mathematics + + + align:start position:0% +and that is uh in mathematics +we understand what it means to talk + + align:start position:0% +we understand what it means to talk + + + align:start position:0% +we understand what it means to talk +about a basis set + + align:start position:0% + + + + align:start position:0% + +we can talk about three space xyz and + + align:start position:0% +we can talk about three space xyz and + + + align:start position:0% +we can talk about three space xyz and +everything + + align:start position:0% +everything + + + align:start position:0% +everything +is either on one of the axes + + align:start position:0% +is either on one of the axes + + + align:start position:0% +is either on one of the axes +in a plane i mean everything can be + + align:start position:0% +in a plane i mean everything can be + + + align:start position:0% +in a plane i mean everything can be +described in terms of that basic three + + align:start position:0% +described in terms of that basic three + + + align:start position:0% +described in terms of that basic three +categories + + align:start position:0% +categories + + + align:start position:0% +categories +color + + align:start position:0% + + + + align:start position:0% + +basic + + align:start position:0% +basic + + + align:start position:0% +basic +colors everything else is a mixture of + + align:start position:0% +colors everything else is a mixture of + + + align:start position:0% +colors everything else is a mixture of +them okay + + align:start position:0% +them okay + + + align:start position:0% +them okay +they got the old factory down to a basis + + align:start position:0% +they got the old factory down to a basis + + + align:start position:0% +they got the old factory down to a basis +set + + align:start position:0% + + + + align:start position:0% + +they've got it and so now and now + + align:start position:0% +they've got it and so now and now + + + align:start position:0% +they've got it and so now and now +they're going to be able to do a lot of + + align:start position:0% +they're going to be able to do a lot of + + + align:start position:0% +they're going to be able to do a lot of +different things with it + + align:start position:0% +different things with it + + + align:start position:0% +different things with it +um i went to a movie theater + + align:start position:0% +um i went to a movie theater + + + align:start position:0% +um i went to a movie theater +it was a special movie theater over in + + align:start position:0% +it was a special movie theater over in + + + align:start position:0% +it was a special movie theater over in +baltimore i don't know if they still + + align:start position:0% +baltimore i don't know if they still + + + align:start position:0% +baltimore i don't know if they still +have it + + align:start position:0% +have it + + + align:start position:0% +have it +but + + align:start position:0% +but + + + align:start position:0% +but +it was a movie theater but the movies + + align:start position:0% +it was a movie theater but the movies + + + align:start position:0% +it was a movie theater but the movies +they played in there didn't last but + + align:start position:0% +they played in there didn't last but + + + align:start position:0% +they played in there didn't last but +five minutes and they had maybe two or + + align:start position:0% +five minutes and they had maybe two or + + + align:start position:0% +five minutes and they had maybe two or +three movies that was all it was part of + + align:start position:0% +three movies that was all it was part of + + + align:start position:0% +three movies that was all it was part of +something else you go in there and it + + align:start position:0% +something else you go in there and it + + + align:start position:0% +something else you go in there and it +was all set up like a movie theater but + + align:start position:0% +was all set up like a movie theater but + + + align:start position:0% +was all set up like a movie theater but +they only had these moments + + align:start position:0% +they only had these moments + + + align:start position:0% +they only had these moments +it was a movie theater that had these + + align:start position:0% +it was a movie theater that had these + + + align:start position:0% +it was a movie theater that had these +little spouts right by your seat that + + align:start position:0% +little spouts right by your seat that + + + align:start position:0% +little spouts right by your seat that +gave out smells + + align:start position:0% +gave out smells + + + align:start position:0% +gave out smells +so when somebody cut an apple pie you + + align:start position:0% +so when somebody cut an apple pie you + + + align:start position:0% +so when somebody cut an apple pie you +could smell it i mean + + align:start position:0% +could smell it i mean + + + align:start position:0% +could smell it i mean +god + + align:start position:0% +god + + + align:start position:0% +god +yeah and + + align:start position:0% +yeah and + + + align:start position:0% +yeah and +um + + align:start position:0% +um + + + align:start position:0% +um +and and it so + + align:start position:0% +and and it so + + + align:start position:0% +and and it so +but there was there's this fear + + align:start position:0% +but there was there's this fear + + + align:start position:0% +but there was there's this fear +of what would happen to people + + align:start position:0% +of what would happen to people + + + align:start position:0% +of what would happen to people +if you tried to control the old factory + + align:start position:0% +if you tried to control the old factory + + + align:start position:0% +if you tried to control the old factory +now you do it with the the sound you + + align:start position:0% +now you do it with the the sound you + + + align:start position:0% +now you do it with the the sound you +hear tiger in the movies + + align:start position:0% +hear tiger in the movies + + + align:start position:0% +hear tiger in the movies +3d + + align:start position:0% +3d + + + align:start position:0% +3d +uh you'd clearly do with the eye + + align:start position:0% +uh you'd clearly do with the eye + + + align:start position:0% +uh you'd clearly do with the eye +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +there have been some theaters + + align:start position:0% +there have been some theaters + + + align:start position:0% +there have been some theaters +that have had uh + + align:start position:0% +that have had uh + + + align:start position:0% +that have had uh +that where movies had the tactile + + align:start position:0% +that where movies had the tactile + + + align:start position:0% +that where movies had the tactile +worked in i'll tell you two of them + + align:start position:0% + + + + align:start position:0% + +in some movie theaters + + align:start position:0% +in some movie theaters + + + align:start position:0% +in some movie theaters +this movie earthquake + + align:start position:0% + + + + align:start position:0% + +actually had + + align:start position:0% + + + + align:start position:0% + +thrown into the movie below the auditory + + align:start position:0% +thrown into the movie below the auditory + + + align:start position:0% +thrown into the movie below the auditory +level but made you feel like that you + + align:start position:0% +level but made you feel like that you + + + align:start position:0% +level but made you feel like that you +were moving + + align:start position:0% +were moving + + + align:start position:0% +were moving +okay + + align:start position:0% +okay + + + align:start position:0% +okay +there was another one down in north + + align:start position:0% +there was another one down in north + + + align:start position:0% +there was another one down in north +carolina when i was a kid where they had + + align:start position:0% +carolina when i was a kid where they had + + + align:start position:0% +carolina when i was a kid where they had +another sound below the auditory level + + align:start position:0% +another sound below the auditory level + + + align:start position:0% +another sound below the auditory level +and + + align:start position:0% +and + + + align:start position:0% +and +they played it when the monster was + + align:start position:0% +they played it when the monster was + + + align:start position:0% +they played it when the monster was +creeping up behind this lady + + align:start position:0% +creeping up behind this lady + + + align:start position:0% +creeping up behind this lady +and just as the monster was putting his + + align:start position:0% +and just as the monster was putting his + + + align:start position:0% +and just as the monster was putting his +hands they blew that sound in you could + + align:start position:0% +hands they blew that sound in you could + + + align:start position:0% +hands they blew that sound in you could +feel it + + align:start position:0% +feel it + + + align:start position:0% +feel it +people ran out of people well that's + + align:start position:0% +people ran out of people well that's + + + align:start position:0% +people ran out of people well that's +what they said well anyway uh + + align:start position:0% +what they said well anyway uh + + + align:start position:0% +what they said well anyway uh +that that they + + align:start position:0% +that that they + + + align:start position:0% +that that they +the the old factory may very well get + + align:start position:0% +the the old factory may very well get + + + align:start position:0% +the the old factory may very well get +into the movies + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +hello you joining us are you just early + + align:start position:0% +hello you joining us are you just early + + + align:start position:0% +hello you joining us are you just early +for the other one yeah + + align:start position:0% +for the other one yeah + + + align:start position:0% +for the other one yeah +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you can join us though + + align:start position:0% +you can join us though + + + align:start position:0% +you can join us though +um + + align:start position:0% +um + + + align:start position:0% +um +so olfactory may be in the movies + + align:start position:0% +so olfactory may be in the movies + + + align:start position:0% +so olfactory may be in the movies +my instincts + + align:start position:0% +my instincts + + + align:start position:0% +my instincts +no instincts i like to use the word + + align:start position:0% +no instincts i like to use the word + + + align:start position:0% +no instincts i like to use the word +instinct because i believe in instincts + + align:start position:0% +instinct because i believe in instincts + + + align:start position:0% +instinct because i believe in instincts +but + + align:start position:0% +but + + + align:start position:0% +but +i think history will tell that it's + + align:start position:0% +i think history will tell that it's + + + align:start position:0% +i think history will tell that it's +going to take a little while + + align:start position:0% +going to take a little while + + + align:start position:0% +going to take a little while +first of all um + + align:start position:0% + + + + align:start position:0% + +the wizard of oz was not the first film + + align:start position:0% +the wizard of oz was not the first film + + + align:start position:0% +the wizard of oz was not the first film +to use color + + align:start position:0% + + + + align:start position:0% + +a number of others came out before + + align:start position:0% +a number of others came out before + + + align:start position:0% +a number of others came out before +people didn't like + + align:start position:0% + + + + align:start position:0% + +so my my guess is that + + align:start position:0% +so my my guess is that + + + align:start position:0% +so my my guess is that +the first they start really making films + + align:start position:0% +the first they start really making films + + + align:start position:0% +the first they start really making films +with the old factory and now they can do + + align:start position:0% +with the old factory and now they can do + + + align:start position:0% +with the old factory and now they can do +it because um + + align:start position:0% +it because um + + + align:start position:0% +it because um +they can put it on the tape and they can + + align:start position:0% +they can put it on the tape and they can + + + align:start position:0% +they can put it on the tape and they can +have the instruments there and for every + + align:start position:0% +have the instruments there and for every + + + align:start position:0% +have the instruments there and for every +smell you don't need a different + + align:start position:0% +smell you don't need a different + + + align:start position:0% +smell you don't need a different +pipe org + + align:start position:0% +pipe org + + + align:start position:0% +pipe org +like they had in this theater for every + + align:start position:0% +like they had in this theater for every + + + align:start position:0% +like they had in this theater for every +smell they had a different + + align:start position:0% +smell they had a different + + + align:start position:0% +smell they had a different +tube + + align:start position:0% +tube + + + align:start position:0% +tube +here you all they have to do is have the + + align:start position:0% +here you all they have to do is have the + + + align:start position:0% +here you all they have to do is have the +basic set bases set + + align:start position:0% +basic set bases set + + + align:start position:0% +basic set bases set +and mix them properly + + align:start position:0% +and mix them properly + + + align:start position:0% +and mix them properly +get any smell you want + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +they're going to have to work out + + align:start position:0% +they're going to have to work out + + + align:start position:0% +they're going to have to work out +uh the danger levels of all that + + align:start position:0% +uh the danger levels of all that + + + align:start position:0% +uh the danger levels of all that +because some of our smells operate below + + align:start position:0% +because some of our smells operate below + + + align:start position:0% +because some of our smells operate below +the level of consciousness + + align:start position:0% +the level of consciousness + + + align:start position:0% +the level of consciousness +and they tell us who we like and who we + + align:start position:0% +and they tell us who we like and who we + + + align:start position:0% +and they tell us who we like and who we +don't like + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um + + align:start position:0% +um + + + align:start position:0% +um +and all these other things uh perfume + + align:start position:0% +and all these other things uh perfume + + + align:start position:0% +and all these other things uh perfume +oh they're gonna be there's gonna be + + align:start position:0% +oh they're gonna be there's gonna be + + + align:start position:0% +oh they're gonna be there's gonna be +some those are gonna be some real ethics + + align:start position:0% +some those are gonna be some real ethics + + + align:start position:0% +some those are gonna be some real ethics +problems uh perfumes you know + + align:start position:0% +problems uh perfumes you know + + + align:start position:0% +problems uh perfumes you know +they come from these glands from these + + align:start position:0% +they come from these glands from these + + + align:start position:0% +they come from these glands from these +animals a lot of them + + align:start position:0% +animals a lot of them + + + align:start position:0% +animals a lot of them +so the animals are using the perfumes on + + align:start position:0% +so the animals are using the perfumes on + + + align:start position:0% +so the animals are using the perfumes on +each other + + align:start position:0% +each other + + + align:start position:0% +each other +and then we put we turn it into perfume + + align:start position:0% +and then we put we turn it into perfume + + + align:start position:0% +and then we put we turn it into perfume +and perfume operates at below the level + + align:start position:0% +and perfume operates at below the level + + + align:start position:0% +and perfume operates at below the level +of consciousness + + align:start position:0% + + + + align:start position:0% + +it's not just uh a kind of um + + align:start position:0% +it's not just uh a kind of um + + + align:start position:0% +it's not just uh a kind of um +olfactory + + align:start position:0% +olfactory + + + align:start position:0% +olfactory +well it's olfactory but it's not purely + + align:start position:0% +well it's olfactory but it's not purely + + + align:start position:0% +well it's olfactory but it's not purely +smell something is working at the + + align:start position:0% +smell something is working at the + + + align:start position:0% +smell something is working at the +lower levels that's telling us + + align:start position:0% +lower levels that's telling us + + + align:start position:0% +lower levels that's telling us +about persons and and it's that's going + + align:start position:0% +about persons and and it's that's going + + + align:start position:0% +about persons and and it's that's going +to be really interesting when the old + + align:start position:0% +to be really interesting when the old + + + align:start position:0% +to be really interesting when the old +factory becomes a part of everybody's + + align:start position:0% +factory becomes a part of everybody's + + + align:start position:0% +factory becomes a part of everybody's +life consciously becomes a part of + + align:start position:0% +life consciously becomes a part of + + + align:start position:0% +life consciously becomes a part of +everybody like particularly in the + + align:start position:0% +everybody like particularly in the + + + align:start position:0% +everybody like particularly in the +movies + + align:start position:0% +movies + + + align:start position:0% +movies +so look out for that one + + align:start position:0% +so look out for that one + + + align:start position:0% +so look out for that one +people are going to be writing + + align:start position:0% +people are going to be writing + + + align:start position:0% +people are going to be writing +dissertations on that + + align:start position:0% + + + + align:start position:0% + +i right now i'm going to tell you how + + align:start position:0% +i right now i'm going to tell you how + + + align:start position:0% +i right now i'm going to tell you how +what mythology can do + + align:start position:0% + + + + align:start position:0% + +i read a science fiction book + + align:start position:0% +i read a science fiction book + + + align:start position:0% +i read a science fiction book +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i got it at home + + align:start position:0% + + + + align:start position:0% + +uh this guy + + align:start position:0% +uh this guy + + + align:start position:0% +uh this guy +goes to this no no + + align:start position:0% +goes to this no no + + + align:start position:0% +goes to this no no +these beings from another planet come to + + align:start position:0% +these beings from another planet come to + + + align:start position:0% +these beings from another planet come to +earth and for some reason want to take + + align:start position:0% +earth and for some reason want to take + + + align:start position:0% +earth and for some reason want to take +this guy back with them + + align:start position:0% +this guy back with them + + + align:start position:0% +this guy back with them +to their planet + + align:start position:0% +to their planet + + + align:start position:0% +to their planet +i think a crime has been committed on + + align:start position:0% +i think a crime has been committed on + + + align:start position:0% +i think a crime has been committed on +their planet + + align:start position:0% +their planet + + + align:start position:0% +their planet +and they don't have they don't have a + + align:start position:0% +and they don't have they don't have a + + + align:start position:0% +and they don't have they don't have a +history of crime + + align:start position:0% +history of crime + + + align:start position:0% +history of crime +so they come down here to get a + + align:start position:0% +so they come down here to get a + + + align:start position:0% +so they come down here to get a +detective sherlock holmes + + align:start position:0% +detective sherlock holmes + + + align:start position:0% +detective sherlock holmes +and take the person back to help him + + align:start position:0% +and take the person back to help him + + + align:start position:0% +and take the person back to help him +find this crime + + align:start position:0% +find this crime + + + align:start position:0% +find this crime +but these + + align:start position:0% +but these + + + align:start position:0% +but these +beings the sentient beings on this other + + align:start position:0% +beings the sentient beings on this other + + + align:start position:0% +beings the sentient beings on this other +planet + + align:start position:0% +planet + + + align:start position:0% +planet +evolved from lizards + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +uh the main character + + align:start position:0% +uh the main character + + + align:start position:0% +uh the main character +is the equivalent of um + + align:start position:0% +is the equivalent of um + + + align:start position:0% +is the equivalent of um +of uh michael jackson or uh now i don't + + align:start position:0% +of uh michael jackson or uh now i don't + + + align:start position:0% +of uh michael jackson or uh now i don't +want to use michael jackson uh is uh + + align:start position:0% +want to use michael jackson uh is uh + + + align:start position:0% +want to use michael jackson uh is uh +no + + align:start position:0% +no + + + align:start position:0% +no +he's a big rock star + + align:start position:0% +he's a big rock star + + + align:start position:0% +he's a big rock star +but his instrument is not music it's old + + align:start position:0% +but his instrument is not music it's old + + + align:start position:0% +but his instrument is not music it's old +factory + + align:start position:0% +factory + + + align:start position:0% +factory +[Music] + + align:start position:0% + + + + align:start position:0% + +and and he's able to mix these sounds + + align:start position:0% +and and he's able to mix these sounds + + + align:start position:0% +and and he's able to mix these sounds +and everybody's oh my this guy's a great + + align:start position:0% +and everybody's oh my this guy's a great + + + align:start position:0% +and everybody's oh my this guy's a great +artist + + align:start position:0% +artist + + + align:start position:0% +artist +and the human being can't get it + + align:start position:0% +and the human being can't get it + + + align:start position:0% +and the human being can't get it +right + + align:start position:0% + + + + align:start position:0% + +yeah so he's mixing these old factory + + align:start position:0% +yeah so he's mixing these old factory + + + align:start position:0% +yeah so he's mixing these old factory +cords + + align:start position:0% +cords + + + align:start position:0% +cords +and playing + + align:start position:0% +and playing + + + align:start position:0% +and playing +and uh that's how science fiction + + align:start position:0% +and uh that's how science fiction + + + align:start position:0% +and uh that's how science fiction +can can develop a mythology that gets + + align:start position:0% +can can develop a mythology that gets + + + align:start position:0% +can can develop a mythology that gets +gets us ready for stuff + + align:start position:0% +gets us ready for stuff + + + align:start position:0% +gets us ready for stuff +so now i think i have a basis for sort + + align:start position:0% +so now i think i have a basis for sort + + + align:start position:0% +so now i think i have a basis for sort +of thinking about what life would be + + align:start position:0% +of thinking about what life would be + + + align:start position:0% +of thinking about what life would be +like + + align:start position:0% +like + + + align:start position:0% +like +if the old factory got in there + + align:start position:0% +if the old factory got in there + + + align:start position:0% +if the old factory got in there +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so um + + align:start position:0% +so um + + + align:start position:0% +so um +i believe that philosophy of engineering + + align:start position:0% +i believe that philosophy of engineering + + + align:start position:0% +i believe that philosophy of engineering +fits over here in this category + + align:start position:0% +fits over here in this category + + + align:start position:0% +fits over here in this category +now we have something we can we + + align:start position:0% +now we have something we can we + + + align:start position:0% +now we have something we can we +we can start with + + align:start position:0% +we can start with + + + align:start position:0% +we can start with +and then i'm done on this piece and we + + align:start position:0% +and then i'm done on this piece and we + + + align:start position:0% +and then i'm done on this piece and we +go to some others we got we got um + + align:start position:0% +go to some others we got we got um + + + align:start position:0% +go to some others we got we got um +nine minutes + + align:start position:0% +nine minutes + + + align:start position:0% +nine minutes +no we have fourteen + + align:start position:0% + + + + align:start position:0% + +um which is good time + + align:start position:0% +um which is good time + + + align:start position:0% +um which is good time +now um + + align:start position:0% + + + + align:start position:0% + +there is + + align:start position:0% +there is + + + align:start position:0% +there is +there exists + + align:start position:0% + + + + align:start position:0% + +two branches of philosophy that go + + align:start position:0% +two branches of philosophy that go + + + align:start position:0% +two branches of philosophy that go +together + + align:start position:0% +together + + + align:start position:0% +together +the differences are subtle + + align:start position:0% +the differences are subtle + + + align:start position:0% +the differences are subtle +one is called theory + + align:start position:0% + + + + align:start position:0% + +of law + + align:start position:0% + + + + align:start position:0% + +and the other one is called + + align:start position:0% +and the other one is called + + + align:start position:0% +and the other one is called +jurisprudence + + align:start position:0% + + + + align:start position:0% + +and depending on what + + align:start position:0% +and depending on what + + + align:start position:0% +and depending on what +um encyclopedia you get or what + + align:start position:0% +um encyclopedia you get or what + + + align:start position:0% +um encyclopedia you get or what +dictionary you're looking at + + align:start position:0% +dictionary you're looking at + + + align:start position:0% +dictionary you're looking at +they will either equate theory of law to + + align:start position:0% +they will either equate theory of law to + + + align:start position:0% +they will either equate theory of law to +jurisprudence + + align:start position:0% +jurisprudence + + + align:start position:0% +jurisprudence +or they'll go off in a long dissertation + + align:start position:0% +or they'll go off in a long dissertation + + + align:start position:0% +or they'll go off in a long dissertation +about how they're different + + align:start position:0% + + + + align:start position:0% + +and uh + + align:start position:0% + + + + align:start position:0% + +and um + + align:start position:0% +and um + + + align:start position:0% +and um +you will think that they're splitting + + align:start position:0% +you will think that they're splitting + + + align:start position:0% +you will think that they're splitting +hairs + + align:start position:0% + + + + align:start position:0% + +i i anticipate you'll think that they're + + align:start position:0% +i i anticipate you'll think that they're + + + align:start position:0% +i i anticipate you'll think that they're +splitting hairs + + align:start position:0% +splitting hairs + + + align:start position:0% +splitting hairs +here's what i think the difference is + + align:start position:0% +here's what i think the difference is + + + align:start position:0% +here's what i think the difference is +when i say i think no here's my learned + + align:start position:0% +when i say i think no here's my learned + + + align:start position:0% +when i say i think no here's my learned +judgment about the difference there's a + + align:start position:0% +judgment about the difference there's a + + + align:start position:0% +judgment about the difference there's a +difference + + align:start position:0% +difference + + + align:start position:0% +difference +okay + + align:start position:0% +okay + + + align:start position:0% +okay +theory of law is when you look at i've + + align:start position:0% +theory of law is when you look at i've + + + align:start position:0% +theory of law is when you look at i've +looked at the journals + + align:start position:0% +looked at the journals + + + align:start position:0% +looked at the journals +written mainly by philosophers + + align:start position:0% +written mainly by philosophers + + + align:start position:0% +written mainly by philosophers +jurisprudence written mainly by lawyers + + align:start position:0% + + + + align:start position:0% + +you can say that they're the same thing + + align:start position:0% +you can say that they're the same thing + + + align:start position:0% +you can say that they're the same thing +but they will be + + align:start position:0% +but they will be + + + align:start position:0% +but they will be +the lawyers will be interested in + + align:start position:0% +the lawyers will be interested in + + + align:start position:0% +the lawyers will be interested in +different topics + + align:start position:0% +different topics + + + align:start position:0% +different topics +than the philosophers + + align:start position:0% +than the philosophers + + + align:start position:0% +than the philosophers +and the lawyers will write in + + align:start position:0% +and the lawyers will write in + + + align:start position:0% +and the lawyers will write in +an almost legalistic style + + align:start position:0% +an almost legalistic style + + + align:start position:0% +an almost legalistic style +whereas the philosophers will write in a + + align:start position:0% +whereas the philosophers will write in a + + + align:start position:0% +whereas the philosophers will write in a +philosophical style + + align:start position:0% +philosophical style + + + align:start position:0% +philosophical style +so um + + align:start position:0% + + + + align:start position:0% + +when you go to a law school + + align:start position:0% +when you go to a law school + + + align:start position:0% +when you go to a law school +any lawyer with a jd can teach + + align:start position:0% +any lawyer with a jd can teach + + + align:start position:0% +any lawyer with a jd can teach +jurisprudence + + align:start position:0% + + + + align:start position:0% + +but not every lawyer can teach theory of + + align:start position:0% +but not every lawyer can teach theory of + + + align:start position:0% +but not every lawyer can teach theory of +law and certainly not every philosopher + + align:start position:0% +law and certainly not every philosopher + + + align:start position:0% +law and certainly not every philosopher +can teach theory of law + + align:start position:0% +can teach theory of law + + + align:start position:0% +can teach theory of law +and i would say that none of them + + align:start position:0% +and i would say that none of them + + + align:start position:0% +and i would say that none of them +can teach jurisprudence + + align:start position:0% +can teach jurisprudence + + + align:start position:0% +can teach jurisprudence +because they don't practice law + + align:start position:0% + + + + align:start position:0% + +so it's practitioners of law that do it + + align:start position:0% +so it's practitioners of law that do it + + + align:start position:0% +so it's practitioners of law that do it +right now this statement is very + + align:start position:0% +right now this statement is very + + + align:start position:0% +right now this statement is very +important because i think that + + align:start position:0% +important because i think that + + + align:start position:0% +important because i think that +all of this is going to break down + + align:start position:0% + + + + align:start position:0% + +into categories like this when it comes + + align:start position:0% +into categories like this when it comes + + + align:start position:0% +into categories like this when it comes +to the practical disciplines once we + + align:start position:0% +to the practical disciplines once we + + + align:start position:0% +to the practical disciplines once we +start doing + + align:start position:0% +start doing + + + align:start position:0% +start doing +more work in the practical discipline + + align:start position:0% +more work in the practical discipline + + + align:start position:0% +more work in the practical discipline +that what you're going to what you see + + align:start position:0% +that what you're going to what you see + + + align:start position:0% +that what you're going to what you see +already is that in philosophy of + + align:start position:0% +already is that in philosophy of + + + align:start position:0% +already is that in philosophy of +education + + align:start position:0% +education + + + align:start position:0% +education +there are people whose dissertations + + align:start position:0% +there are people whose dissertations + + + align:start position:0% +there are people whose dissertations +were in philosophy of education and + + align:start position:0% +were in philosophy of education and + + + align:start position:0% +were in philosophy of education and +nobody else teaches philosophy of + + align:start position:0% +nobody else teaches philosophy of + + + align:start position:0% +nobody else teaches philosophy of +education + + align:start position:0% +education + + + align:start position:0% +education +but then there are journals that talk + + align:start position:0% +but then there are journals that talk + + + align:start position:0% +but then there are journals that talk +about philosophical issues in education + + align:start position:0% +about philosophical issues in education + + + align:start position:0% +about philosophical issues in education +written by educators + + align:start position:0% +written by educators + + + align:start position:0% +written by educators +who've never taken a course in + + align:start position:0% +who've never taken a course in + + + align:start position:0% +who've never taken a course in +philosophy but who are talking to each + + align:start position:0% +philosophy but who are talking to each + + + align:start position:0% +philosophy but who are talking to each +other about what their discipline + + align:start position:0% +other about what their discipline + + + align:start position:0% +other about what their discipline +constitutes + + align:start position:0% +constitutes + + + align:start position:0% +constitutes +so and please anticipate in your + + align:start position:0% +so and please anticipate in your + + + align:start position:0% +so and please anticipate in your +lifetime + + align:start position:0% +lifetime + + + align:start position:0% +lifetime +that much more discussion is going to + + align:start position:0% +that much more discussion is going to + + + align:start position:0% +that much more discussion is going to +take place in this category + + align:start position:0% +take place in this category + + + align:start position:0% +take place in this category +and when it does it will break out + + align:start position:0% +and when it does it will break out + + + align:start position:0% +and when it does it will break out +into these two categories + + align:start position:0% +into these two categories + + + align:start position:0% +into these two categories +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +that philosophy of engineering will + + align:start position:0% +that philosophy of engineering will + + + align:start position:0% +that philosophy of engineering will +essentially break out like i think it is + + align:start position:0% +essentially break out like i think it is + + + align:start position:0% +essentially break out like i think it is +already + + align:start position:0% +already + + + align:start position:0% +already +between philosophical issues that + + align:start position:0% +between philosophical issues that + + + align:start position:0% +between philosophical issues that +practicing engineers talk to each other + + align:start position:0% +practicing engineers talk to each other + + + align:start position:0% +practicing engineers talk to each other +about + + align:start position:0% +about + + + align:start position:0% +about +and philosophical issues that + + align:start position:0% +and philosophical issues that + + + align:start position:0% +and philosophical issues that +philosophers + + align:start position:0% +philosophers + + + align:start position:0% +philosophers +or philosophers slash engineer like + + align:start position:0% +or philosophers slash engineer like + + + align:start position:0% +or philosophers slash engineer like +myself + + align:start position:0% +myself + + + align:start position:0% +myself +uh + + align:start position:0% +uh + + + align:start position:0% +uh +want to talk to + + align:start position:0% +want to talk to + + + align:start position:0% +want to talk to +mainly the general public about + + align:start position:0% +mainly the general public about + + + align:start position:0% +mainly the general public about +not so much each other + + align:start position:0% + + + + align:start position:0% + +now there was a term i said i was going + + align:start position:0% +now there was a term i said i was going + + + align:start position:0% +now there was a term i said i was going +to get to + + align:start position:0% +to get to + + + align:start position:0% +to get to +i ask you all to remind me + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +maybe i got to it + + align:start position:0% + + + + align:start position:0% + +i think you said that there was a + + align:start position:0% + + + + align:start position:0% + +it was education education exists out + + align:start position:0% +it was education education exists out + + + align:start position:0% +it was education education exists out +there + + align:start position:0% +there + + + align:start position:0% +there +only because + + align:start position:0% +only because + + + align:start position:0% +only because +there's been a whole lot of + + align:start position:0% +there's been a whole lot of + + + align:start position:0% +there's been a whole lot of +philosophical + + align:start position:0% +philosophical + + + align:start position:0% +philosophical +discussion devote oh i know what it was + + align:start position:0% + + + + align:start position:0% + +it was um + + align:start position:0% + + + + align:start position:0% + +normative ethics + + align:start position:0% + + + + align:start position:0% + +but i think that education + + align:start position:0% +but i think that education + + + align:start position:0% +but i think that education +really belongs in this practice category + + align:start position:0% + + + + align:start position:0% + +they don't know what to do with it + + align:start position:0% +they don't know what to do with it + + + align:start position:0% +they don't know what to do with it +they just know that there's a lot of + + align:start position:0% +they just know that there's a lot of + + + align:start position:0% +they just know that there's a lot of +work that's been done by a lot of great + + align:start position:0% +work that's been done by a lot of great + + + align:start position:0% +work that's been done by a lot of great +thinkers who've used the tools and + + align:start position:0% +thinkers who've used the tools and + + + align:start position:0% +thinkers who've used the tools and +methods of philosophy to discuss + + align:start position:0% +methods of philosophy to discuss + + + align:start position:0% +methods of philosophy to discuss +education but they don't know where to + + align:start position:0% +education but they don't know where to + + + align:start position:0% +education but they don't know where to +put it + + align:start position:0% +put it + + + align:start position:0% +put it +because most of it is still + + align:start position:0% +because most of it is still + + + align:start position:0% +because most of it is still +not + + align:start position:0% +not + + + align:start position:0% +not +knowledge you just don't come into a + + align:start position:0% +knowledge you just don't come into a + + + align:start position:0% +knowledge you just don't come into a +classroom + + align:start position:0% +classroom + + + align:start position:0% +classroom +with 30 + + align:start position:0% +with 30 + + + align:start position:0% +with 30 +12 year olds and start using a + + align:start position:0% +12 year olds and start using a + + + align:start position:0% +12 year olds and start using a +systematic approach to teach them + + align:start position:0% +systematic approach to teach them + + + align:start position:0% +systematic approach to teach them +mathematics there's something else + + align:start position:0% +mathematics there's something else + + + align:start position:0% +mathematics there's something else +involved + + align:start position:0% +involved + + + align:start position:0% +involved +it's an art form + + align:start position:0% + + + + align:start position:0% + +it's like engineering there's something + + align:start position:0% +it's like engineering there's something + + + align:start position:0% +it's like engineering there's something +that is not + + align:start position:0% + + + + align:start position:0% + +parts of that + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so they don't really know where to put + + align:start position:0% +so they don't really know where to put + + + align:start position:0% +so they don't really know where to put +it uh like i said there's so much of it + + align:start position:0% +it uh like i said there's so much of it + + + align:start position:0% +it uh like i said there's so much of it +and so many great minds have been put + + align:start position:0% +and so many great minds have been put + + + align:start position:0% +and so many great minds have been put +put to the task on it + + align:start position:0% +put to the task on it + + + align:start position:0% +put to the task on it +that they can't ignore it + + align:start position:0% +that they can't ignore it + + + align:start position:0% +that they can't ignore it +and in a school of education + + align:start position:0% +and in a school of education + + + align:start position:0% +and in a school of education +in a big state university + + align:start position:0% +in a big state university + + + align:start position:0% +in a big state university +you will find at least one faculty + + align:start position:0% +you will find at least one faculty + + + align:start position:0% +you will find at least one faculty +member + + align:start position:0% +member + + + align:start position:0% +member +who does philosophy of education + + align:start position:0% +who does philosophy of education + + + align:start position:0% +who does philosophy of education +i think that's a fair statement i don't + + align:start position:0% +i think that's a fair statement i don't + + + align:start position:0% +i think that's a fair statement i don't +know of any of the dough + + align:start position:0% + + + + align:start position:0% + +okay you got to take a course in it if + + align:start position:0% +okay you got to take a course in it if + + + align:start position:0% +okay you got to take a course in it if +you're going to get a graduate degree + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% +now + + + align:start position:0% +now +when we go to ethics + + align:start position:0% + + + + align:start position:0% + +ethics breaks out into + + align:start position:0% +ethics breaks out into + + + align:start position:0% +ethics breaks out into +two divisions + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% +oh + + + align:start position:0% +oh +i'm gonna use some terms this is what + + align:start position:0% +i'm gonna use some terms this is what + + + align:start position:0% +i'm gonna use some terms this is what +this class is all about terms + + align:start position:0% + + + + align:start position:0% + +terminology okay + + align:start position:0% +terminology okay + + + align:start position:0% +terminology okay +um + + align:start position:0% + + + + align:start position:0% + +i'm going to use three terms + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +one is called normative ethics + + align:start position:0% + + + + align:start position:0% + +the other one is called descriptive + + align:start position:0% +the other one is called descriptive + + + align:start position:0% +the other one is called descriptive +ethics + + align:start position:0% + + + + align:start position:0% + +normative ethics + + align:start position:0% +normative ethics + + + align:start position:0% +normative ethics +has as its goal to + + align:start position:0% +has as its goal to + + + align:start position:0% +has as its goal to +um + + align:start position:0% +um + + + align:start position:0% +um +say what you should do + + align:start position:0% +say what you should do + + + align:start position:0% +say what you should do +or should not do + + align:start position:0% + + + + align:start position:0% + +descriptive ethics says what you did and + + align:start position:0% +descriptive ethics says what you did and + + + align:start position:0% +descriptive ethics says what you did and +whether it was right or wrong + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so beaujolais blew the whistle was that + + align:start position:0% +so beaujolais blew the whistle was that + + + align:start position:0% +so beaujolais blew the whistle was that +right or wrong + + align:start position:0% +right or wrong + + + align:start position:0% +right or wrong +what should he have done you see there + + align:start position:0% +what should he have done you see there + + + align:start position:0% +what should he have done you see there +are two different questions + + align:start position:0% + + + + align:start position:0% + +most + + align:start position:0% +most + + + align:start position:0% +most +ethics + + align:start position:0% +ethics + + + align:start position:0% +ethics +done by philosophers + + align:start position:0% + + + + align:start position:0% + +is called theoretical ethics + + align:start position:0% +is called theoretical ethics + + + align:start position:0% +is called theoretical ethics +and they do + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +normative ethics + + align:start position:0% + + + + align:start position:0% + +most applied ethics that is applying + + align:start position:0% +most applied ethics that is applying + + + align:start position:0% +most applied ethics that is applying +ethics to specific kinds of cases + + align:start position:0% +ethics to specific kinds of cases + + + align:start position:0% +ethics to specific kinds of cases +which constitutes the greater part of + + align:start position:0% +which constitutes the greater part of + + + align:start position:0% +which constitutes the greater part of +engineering ethics + + align:start position:0% +engineering ethics + + + align:start position:0% +engineering ethics +is descriptive you get a case + + align:start position:0% +is descriptive you get a case + + + align:start position:0% +is descriptive you get a case +and you say what somebody did + + align:start position:0% +and you say what somebody did + + + align:start position:0% +and you say what somebody did +and you ask whether they did the right + + align:start position:0% +and you ask whether they did the right + + + align:start position:0% +and you ask whether they did the right +thing or the wrong thing + + align:start position:0% +thing or the wrong thing + + + align:start position:0% +thing or the wrong thing +i have given equal weight to both in + + align:start position:0% +i have given equal weight to both in + + + align:start position:0% +i have given equal weight to both in +this class + + align:start position:0% +this class + + + align:start position:0% +this class +because i want you to know i want you to + + align:start position:0% +because i want you to know i want you to + + + align:start position:0% +because i want you to know i want you to +be able to do + + align:start position:0% +be able to do + + + align:start position:0% +be able to do +normative ethics i want you to be able + + align:start position:0% +normative ethics i want you to be able + + + align:start position:0% +normative ethics i want you to be able +to say what they should have done + + align:start position:0% + + + + align:start position:0% + +now i've said what science is let's talk + + align:start position:0% +now i've said what science is let's talk + + + align:start position:0% +now i've said what science is let's talk +about science + + align:start position:0% +about science + + + align:start position:0% +about science +let's talk about we've talked about + + align:start position:0% +let's talk about we've talked about + + + align:start position:0% +let's talk about we've talked about +ethics + + align:start position:0% +ethics + + + align:start position:0% +ethics +science philosophy let's see if we can + + align:start position:0% +science philosophy let's see if we can + + + align:start position:0% +science philosophy let's see if we can +define some learning disciplines + + align:start position:0% +define some learning disciplines + + + align:start position:0% +define some learning disciplines +with the next four minutes that we have + + align:start position:0% +with the next four minutes that we have + + + align:start position:0% +with the next four minutes that we have +science a learned discipline for the on + + align:start position:0% +science a learned discipline for the on + + + align:start position:0% +science a learned discipline for the on +the production of knowledge + + align:start position:0% +the production of knowledge + + + align:start position:0% +the production of knowledge +about the physical world + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +ethics and + + align:start position:0% +ethics and + + + align:start position:0% +ethics and +its most general statement + + align:start position:0% +its most general statement + + + align:start position:0% +its most general statement +learning discipline + + align:start position:0% + + + + align:start position:0% + +on the production of values + + align:start position:0% + + + + align:start position:0% + +we can get more specific + + align:start position:0% +we can get more specific + + + align:start position:0% +we can get more specific +and we should get more specific but if + + align:start position:0% +and we should get more specific but if + + + align:start position:0% +and we should get more specific but if +you take that + + align:start position:0% +you take that + + + align:start position:0% +you take that +definition + + align:start position:0% + + + + align:start position:0% + +however so um + + align:start position:0% + + + + align:start position:0% + +cursory it may be + + align:start position:0% +cursory it may be + + + align:start position:0% +cursory it may be +it does make a distinction between + + align:start position:0% +it does make a distinction between + + + align:start position:0% +it does make a distinction between +ethics and science + + align:start position:0% +ethics and science + + + align:start position:0% +ethics and science +one studies the facts and the other one + + align:start position:0% +one studies the facts and the other one + + + align:start position:0% +one studies the facts and the other one +studies the valuables + + align:start position:0% + + + + align:start position:0% + +over in this category we're going to be + + align:start position:0% +over in this category we're going to be + + + align:start position:0% +over in this category we're going to be +talking about engineering and and law + + align:start position:0% +talking about engineering and and law + + + align:start position:0% +talking about engineering and and law +and others + + align:start position:0% +and others + + + align:start position:0% +and others +all of them have to do with changing the + + align:start position:0% +all of them have to do with changing the + + + align:start position:0% +all of them have to do with changing the +world + + align:start position:0% +world + + + align:start position:0% +world +or controlling it + + align:start position:0% +or controlling it + + + align:start position:0% +or controlling it +more precisely to intervene into it + + align:start position:0% +more precisely to intervene into it + + + align:start position:0% +more precisely to intervene into it +with an end in mind + + align:start position:0% + + + + align:start position:0% + +so we're not about creating knowledge + + align:start position:0% +so we're not about creating knowledge + + + align:start position:0% +so we're not about creating knowledge +about the world + + align:start position:0% +about the world + + + align:start position:0% +about the world +we're not about our specialty is not + + align:start position:0% +we're not about our specialty is not + + + align:start position:0% +we're not about our specialty is not +about creating knowledge about the world + + align:start position:0% +about creating knowledge about the world + + + align:start position:0% +about creating knowledge about the world +we may create knowledge as we go but + + align:start position:0% +we may create knowledge as we go but + + + align:start position:0% +we may create knowledge as we go but +that's not our specialty + + align:start position:0% +that's not our specialty + + + align:start position:0% +that's not our specialty +our specialty is not about valuing the + + align:start position:0% +our specialty is not about valuing the + + + align:start position:0% +our specialty is not about valuing the +world + + align:start position:0% +world + + + align:start position:0% +world +we have to include values in it but + + align:start position:0% +we have to include values in it but + + + align:start position:0% +we have to include values in it but +that's not our specialty our specialty + + align:start position:0% +that's not our specialty our specialty + + + align:start position:0% +that's not our specialty our specialty +has to do with changing it + + align:start position:0% +has to do with changing it + + + align:start position:0% +has to do with changing it +now here's the subtlety in changing it a + + align:start position:0% +now here's the subtlety in changing it a + + + align:start position:0% +now here's the subtlety in changing it a +scientist say we change the world too + + align:start position:0% + + + + align:start position:0% + +well we have to change the world in + + align:start position:0% +well we have to change the world in + + + align:start position:0% +well we have to change the world in +response to + + align:start position:0% +response to + + + align:start position:0% +response to +certain kinds of imperatives + + align:start position:0% +certain kinds of imperatives + + + align:start position:0% +certain kinds of imperatives +you got to do it now + + align:start position:0% +you got to do it now + + + align:start position:0% +you got to do it now +the military the enemy is coming over + + align:start position:0% +the military the enemy is coming over + + + align:start position:0% +the military the enemy is coming over +the hill + + align:start position:0% +the hill + + + align:start position:0% +the hill +engineering we got to go to the moon + + align:start position:0% + + + + align:start position:0% + +uh in medicine you're sick i can't go in + + align:start position:0% +uh in medicine you're sick i can't go in + + + align:start position:0% +uh in medicine you're sick i can't go in +the laboratory and do some more + + align:start position:0% +the laboratory and do some more + + + align:start position:0% +the laboratory and do some more +experiments + + align:start position:0% + + + + align:start position:0% + +okay so we have a systematic approach + + align:start position:0% +okay so we have a systematic approach + + + align:start position:0% +okay so we have a systematic approach +to dealing with uh situations that are + + align:start position:0% +to dealing with uh situations that are + + + align:start position:0% +to dealing with uh situations that are +knowledge deficient + + align:start position:0% +knowledge deficient + + + align:start position:0% +knowledge deficient +as well as values deficient + + align:start position:0% +as well as values deficient + + + align:start position:0% +as well as values deficient +that's what makes the engineering + + align:start position:0% +that's what makes the engineering + + + align:start position:0% +that's what makes the engineering +medicine + + align:start position:0% +medicine + + + align:start position:0% +medicine +law enough these other + + align:start position:0% +law enough these other + + + align:start position:0% +law enough these other +learning disciplines what they are + + align:start position:0% +learning disciplines what they are + + + align:start position:0% +learning disciplines what they are +is when we're able to take that leap + + align:start position:0% +is when we're able to take that leap + + + align:start position:0% +is when we're able to take that leap +in a systematic way + + align:start position:0% +in a systematic way + + + align:start position:0% +in a systematic way +we'll talk more about it i think we've + + align:start position:0% +we'll talk more about it i think we've + + + align:start position:0% +we'll talk more about it i think we've +just about gotten to the end + + align:start position:0% +just about gotten to the end + + + align:start position:0% +just about gotten to the end +um + + align:start position:0% +um + + + align:start position:0% +um +this is a continuing saga we'll always + + align:start position:0% +this is a continuing saga we'll always + + + align:start position:0% +this is a continuing saga we'll always +talk about terminology from here out + + align:start position:0% +talk about terminology from here out + + + align:start position:0% +talk about terminology from here out +but i think i've gotten some of the main + + align:start position:0% +but i think i've gotten some of the main + + + align:start position:0% +but i think i've gotten some of the main +ones \ No newline at end of file diff --git a/dx98pqJvZVk.txt b/dx98pqJvZVk.txt new file mode 100644 index 0000000000000000000000000000000000000000..9aa85db379ba82a3c5a93a5e27243bed083dfdd8 --- /dev/null +++ b/dx98pqJvZVk.txt @@ -0,0 +1,12120 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +today we're gonna talk about multi-core + + align:start position:0% +today we're gonna talk about multi-core + + + align:start position:0% +today we're gonna talk about multi-core +programming and I as I was just informed + + align:start position:0% +programming and I as I was just informed + + + align:start position:0% +programming and I as I was just informed +by Charles it's 2018 + + align:start position:0% +by Charles it's 2018 + + + align:start position:0% +by Charles it's 2018 +I had 2017 on the slide okay so first + + align:start position:0% +I had 2017 on the slide okay so first + + + align:start position:0% +I had 2017 on the slide okay so first +congratulations to all of you you turned + + align:start position:0% +congratulations to all of you you turned + + + align:start position:0% +congratulations to all of you you turned +in the first projects beta here's a + + align:start position:0% +in the first projects beta here's a + + + align:start position:0% +in the first projects beta here's a +here's a plot showing the tiers that + + align:start position:0% +here's a plot showing the tiers that + + + align:start position:0% +here's a plot showing the tiers that +different groups reach for the beta and + + align:start position:0% +different groups reach for the beta and + + + align:start position:0% +different groups reach for the beta and +this is in sorted order and we set the + + align:start position:0% +this is in sorted order and we set the + + + align:start position:0% +this is in sorted order and we set the +beta caught off to be tier 45 the final + + align:start position:0% +beta caught off to be tier 45 the final + + + align:start position:0% +beta caught off to be tier 45 the final +cut off is tier 48 so the final cut off + + align:start position:0% +cut off is tier 48 so the final cut off + + + align:start position:0% +cut off is tier 48 so the final cut off +we did set a little bit aggressively but + + align:start position:0% +we did set a little bit aggressively but + + + align:start position:0% +we did set a little bit aggressively but +keep in mind that you don't necessarily + + align:start position:0% +keep in mind that you don't necessarily + + + align:start position:0% +keep in mind that you don't necessarily +have to get to the final cut off in + + align:start position:0% +have to get to the final cut off in + + + align:start position:0% +have to get to the final cut off in +order to get an A on this project okay + + align:start position:0% +order to get an A on this project okay + + + align:start position:0% +order to get an A on this project okay +so we're going to talk about multi-core + + align:start position:0% +so we're going to talk about multi-core + + + align:start position:0% +so we're going to talk about multi-core +processing today that's gonna be a topic + + align:start position:0% +processing today that's gonna be a topic + + + align:start position:0% +processing today that's gonna be a topic +of the next project after you finish the + + align:start position:0% +of the next project after you finish the + + + align:start position:0% +of the next project after you finish the +first project so so in a multi-core + + align:start position:0% +first project so so in a multi-core + + + align:start position:0% +first project so so in a multi-core +processor we have a whole bunch of cores + + align:start position:0% +processor we have a whole bunch of cores + + + align:start position:0% +processor we have a whole bunch of cores +that are all placed on the same chip and + + align:start position:0% +that are all placed on the same chip and + + + align:start position:0% +that are all placed on the same chip and +they have access to shared memory they + + align:start position:0% +they have access to shared memory they + + + align:start position:0% +they have access to shared memory they +usually also have some sort of private + + align:start position:0% +usually also have some sort of private + + + align:start position:0% +usually also have some sort of private +cache and then a shared last level cache + + align:start position:0% +cache and then a shared last level cache + + + align:start position:0% +cache and then a shared last level cache +so l3 in this case and then they they + + align:start position:0% +so l3 in this case and then they they + + + align:start position:0% +so l3 in this case and then they they +all have access the same memory + + align:start position:0% +all have access the same memory + + + align:start position:0% +all have access the same memory +controller which goes out to main memory + + align:start position:0% +controller which goes out to main memory + + + align:start position:0% +controller which goes out to main memory +and then they also have access to IO but + + align:start position:0% +and then they also have access to IO but + + + align:start position:0% +and then they also have access to IO but +for a very long time + + align:start position:0% +for a very long time + + + align:start position:0% +for a very long time +chips only had a single core on them so + + align:start position:0% +chips only had a single core on them so + + + align:start position:0% +chips only had a single core on them so +why do we have multi-core processors + + align:start position:0% +why do we have multi-core processors + + + align:start position:0% +why do we have multi-core processors +nowadays why did semiconductor vendors + + align:start position:0% +nowadays why did semiconductor vendors + + + align:start position:0% +nowadays why did semiconductor vendors +start producing chips that had multiple + + align:start position:0% +start producing chips that had multiple + + + align:start position:0% +start producing chips that had multiple +processor cores on them so the answer is + + align:start position:0% +processor cores on them so the answer is + + + align:start position:0% +processor cores on them so the answer is +because of two things so first there's + + align:start position:0% +because of two things so first there's + + + align:start position:0% +because of two things so first there's +Moore's law which says that we get more + + align:start position:0% +Moore's law which says that we get more + + + align:start position:0% +Moore's law which says that we get more +trans + + align:start position:0% +trans + + + align:start position:0% +trans +sisters every year so the number of + + align:start position:0% +sisters every year so the number of + + + align:start position:0% +sisters every year so the number of +transistors that you can fit on a chip + + align:start position:0% +transistors that you can fit on a chip + + + align:start position:0% +transistors that you can fit on a chip +doubles approximately every two years + + align:start position:0% +doubles approximately every two years + + + align:start position:0% +doubles approximately every two years +and secondly there's an end of scaling + + align:start position:0% +and secondly there's an end of scaling + + + align:start position:0% +and secondly there's an end of scaling +of clock frequencies so for a very long + + align:start position:0% +of clock frequencies so for a very long + + + align:start position:0% +of clock frequencies so for a very long +time we could just keep increasing the + + align:start position:0% +time we could just keep increasing the + + + align:start position:0% +time we could just keep increasing the +frequency of the single core on the chip + + align:start position:0% +frequency of the single core on the chip + + + align:start position:0% +frequency of the single core on the chip +but at around 2004 to 2005 that was no + + align:start position:0% +but at around 2004 to 2005 that was no + + + align:start position:0% +but at around 2004 to 2005 that was no +longer the case + + align:start position:0% +longer the case + + + align:start position:0% +longer the case +we couldn't scale the clock frequency + + align:start position:0% +we couldn't scale the clock frequency + + + align:start position:0% +we couldn't scale the clock frequency +anymore so here's a plot showing both + + align:start position:0% +anymore so here's a plot showing both + + + align:start position:0% +anymore so here's a plot showing both +the number of transistors you can fit on + + align:start position:0% +the number of transistors you can fit on + + + align:start position:0% +the number of transistors you can fit on +the chip over time as well as a clock + + align:start position:0% +the chip over time as well as a clock + + + align:start position:0% +the chip over time as well as a clock +frequency of the processors over time + + align:start position:0% +frequency of the processors over time + + + align:start position:0% +frequency of the processors over time +and notice that the y-axis is in log + + align:start position:0% +and notice that the y-axis is in log + + + align:start position:0% +and notice that the y-axis is in log +scale here and the blue line is + + align:start position:0% +scale here and the blue line is + + + align:start position:0% +scale here and the blue line is +basically Moore's law which says that + + align:start position:0% +basically Moore's law which says that + + + align:start position:0% +basically Moore's law which says that +the number of transistors you can fit on + + align:start position:0% +the number of transistors you can fit on + + + align:start position:0% +the number of transistors you can fit on +the chip doubles approximately every two + + align:start position:0% +the chip doubles approximately every two + + + align:start position:0% +the chip doubles approximately every two +years and that's been growing pretty + + align:start position:0% +years and that's been growing pretty + + + align:start position:0% +years and that's been growing pretty +steadily so this plot goes up to 2010 + + align:start position:0% +steadily so this plot goes up to 2010 + + + align:start position:0% +steadily so this plot goes up to 2010 +but in fact it's been growing even up + + align:start position:0% +but in fact it's been growing even up + + + align:start position:0% +but in fact it's been growing even up +until the president it will continue to + + align:start position:0% +until the president it will continue to + + + align:start position:0% +until the president it will continue to +grow for a couple more years before + + align:start position:0% +grow for a couple more years before + + + align:start position:0% +grow for a couple more years before +Moore's law ends however if you look at + + align:start position:0% +Moore's law ends however if you look at + + + align:start position:0% +Moore's law ends however if you look at +the clock frequency line you see that it + + align:start position:0% +the clock frequency line you see that it + + + align:start position:0% +the clock frequency line you see that it +was growing quite steadily until about + + align:start position:0% +was growing quite steadily until about + + + align:start position:0% +was growing quite steadily until about +the early 2000s and then at that point + + align:start position:0% +the early 2000s and then at that point + + + align:start position:0% +the early 2000s and then at that point +is sort of flattened out so at that + + align:start position:0% +is sort of flattened out so at that + + + align:start position:0% +is sort of flattened out so at that +point we couldn't increase the clock + + align:start position:0% +point we couldn't increase the clock + + + align:start position:0% +point we couldn't increase the clock +frequencies anymore and the clock speed + + align:start position:0% +frequencies anymore and the clock speed + + + align:start position:0% +frequencies anymore and the clock speed +was bounded at about 4 gigahertz so + + align:start position:0% +was bounded at about 4 gigahertz so + + + align:start position:0% +was bounded at about 4 gigahertz so +nowadays if you go buy a processor is + + align:start position:0% +nowadays if you go buy a processor is + + + align:start position:0% +nowadays if you go buy a processor is +usually still bounded by around 4 + + align:start position:0% +usually still bounded by around 4 + + + align:start position:0% +usually still bounded by around 4 +gigahertz it's usually a little bit less + + align:start position:0% +gigahertz it's usually a little bit less + + + align:start position:0% +gigahertz it's usually a little bit less +than 4 gig Hertz because it doesn't + + align:start position:0% +than 4 gig Hertz because it doesn't + + + align:start position:0% +than 4 gig Hertz because it doesn't +really make sense to push it all the way + + align:start position:0% +really make sense to push it all the way + + + align:start position:0% +really make sense to push it all the way +but you might find some processors that + + align:start position:0% +but you might find some processors that + + + align:start position:0% +but you might find some processors that +are around 4 gigahertz nowadays so so + + align:start position:0% +are around 4 gigahertz nowadays so so + + + align:start position:0% +are around 4 gigahertz nowadays so so +what happened at around 2004 to 2005 + + align:start position:0% +what happened at around 2004 to 2005 + + + align:start position:0% +what happened at around 2004 to 2005 +does anyone know + + align:start position:0% + + + + align:start position:0% + +okay so so Moore's law basically says + + align:start position:0% +okay so so Moore's law basically says + + + align:start position:0% +okay so so Moore's law basically says +that we can fit more transistors on a + + align:start position:0% +that we can fit more transistors on a + + + align:start position:0% +that we can fit more transistors on a +chip because the transistors become + + align:start position:0% +chip because the transistors become + + + align:start position:0% +chip because the transistors become +smaller and when the transistors become + + align:start position:0% +smaller and when the transistors become + + + align:start position:0% +smaller and when the transistors become +smaller you can reduce the voltage + + align:start position:0% +smaller you can reduce the voltage + + + align:start position:0% +smaller you can reduce the voltage +that's needed to operate the transistors + + align:start position:0% +that's needed to operate the transistors + + + align:start position:0% +that's needed to operate the transistors +and as a result you could increase the + + align:start position:0% +and as a result you could increase the + + + align:start position:0% +and as a result you could increase the +clock frequency while maintaining the + + align:start position:0% +clock frequency while maintaining the + + + align:start position:0% +clock frequency while maintaining the +same power density and that's what + + align:start position:0% +same power density and that's what + + + align:start position:0% +same power density and that's what +manufacturers did until about 2004 to + + align:start position:0% +manufacturers did until about 2004 to + + + align:start position:0% +manufacturers did until about 2004 to +2005 they just kept increasing the clock + + align:start position:0% +2005 they just kept increasing the clock + + + align:start position:0% +2005 they just kept increasing the clock +frequency to take advantage of Moore's + + align:start position:0% +frequency to take advantage of Moore's + + + align:start position:0% +frequency to take advantage of Moore's +law but turns out that once transistors + + align:start position:0% +law but turns out that once transistors + + + align:start position:0% +law but turns out that once transistors +become small enough in the voltage used + + align:start position:0% +become small enough in the voltage used + + + align:start position:0% +become small enough in the voltage used +to operate them becomes small enough + + align:start position:0% +to operate them becomes small enough + + + align:start position:0% +to operate them becomes small enough +there's something called leakage current + + align:start position:0% +there's something called leakage current + + + align:start position:0% +there's something called leakage current +so there's current that leaks and we're + + align:start position:0% +so there's current that leaks and we're + + + align:start position:0% +so there's current that leaks and we're +unable to keep reducing the voltage + + align:start position:0% +unable to keep reducing the voltage + + + align:start position:0% +unable to keep reducing the voltage +while still having reliable switching + + align:start position:0% +while still having reliable switching + + + align:start position:0% +while still having reliable switching +and if you can't reduce a voltage + + align:start position:0% +and if you can't reduce a voltage + + + align:start position:0% +and if you can't reduce a voltage +anymore then you can't increase the + + align:start position:0% +anymore then you can't increase the + + + align:start position:0% +anymore then you can't increase the +frequency the clock frequency if you + + align:start position:0% +frequency the clock frequency if you + + + align:start position:0% +frequency the clock frequency if you +want to keep the same power density so + + align:start position:0% +want to keep the same power density so + + + align:start position:0% +want to keep the same power density so +here's a plot from Intel back in 2004 + + align:start position:0% +here's a plot from Intel back in 2004 + + + align:start position:0% +here's a plot from Intel back in 2004 +when they first started producing + + align:start position:0% +when they first started producing + + + align:start position:0% +when they first started producing +multi-core processors and this is + + align:start position:0% +multi-core processors and this is + + + align:start position:0% +multi-core processors and this is +plotting the power density versus time + + align:start position:0% +plotting the power density versus time + + + align:start position:0% +plotting the power density versus time +and again the y-axis is in log scale + + align:start position:0% +and again the y-axis is in log scale + + + align:start position:0% +and again the y-axis is in log scale +here so the green data points are actual + + align:start position:0% +here so the green data points are actual + + + align:start position:0% +here so the green data points are actual +data points and the orange ones are + + align:start position:0% +data points and the orange ones are + + + align:start position:0% +data points and the orange ones are +projected and they projected what the + + align:start position:0% +projected and they projected what the + + + align:start position:0% +projected and they projected what the +power density would be if we kept + + align:start position:0% +power density would be if we kept + + + align:start position:0% +power density would be if we kept +increasing the clock frequency at a + + align:start position:0% +increasing the clock frequency at a + + + align:start position:0% +increasing the clock frequency at a +trend of about 25 to 30 percent per year + + align:start position:0% +trend of about 25 to 30 percent per year + + + align:start position:0% +trend of about 25 to 30 percent per year +which is what happened up until around + + align:start position:0% +which is what happened up until around + + + align:start position:0% +which is what happened up until around +2004 and because we couldn't reduce the + + align:start position:0% +2004 and because we couldn't reduce the + + + align:start position:0% +2004 and because we couldn't reduce the +voltage anymore the power density will + + align:start position:0% +voltage anymore the power density will + + + align:start position:0% +voltage anymore the power density will +go up and you can see that eventually it + + align:start position:0% +go up and you can see that eventually it + + + align:start position:0% +go up and you can see that eventually it +reaches the power density of a nuclear + + align:start position:0% +reaches the power density of a nuclear + + + align:start position:0% +reaches the power density of a nuclear +reactor which is pretty hot and then and + + align:start position:0% +reactor which is pretty hot and then and + + + align:start position:0% +reactor which is pretty hot and then and +then it reaches the power density of a + + align:start position:0% +then it reaches the power density of a + + + align:start position:0% +then it reaches the power density of a +rocket nozzle and eventually you get to + + align:start position:0% +rocket nozzle and eventually you get to + + + align:start position:0% +rocket nozzle and eventually you get to +the power density of a of the sun's + + align:start position:0% +the power density of a of the sun's + + + align:start position:0% +the power density of a of the sun's +surface so if you have a chip that's + + align:start position:0% +surface so if you have a chip that's + + + align:start position:0% +surface so if you have a chip that's +that has a power density equal to the + + align:start position:0% +that has a power density equal to the + + + align:start position:0% +that has a power density equal to the +Sun surface well you don't actually + + align:start position:0% +Sun surface well you don't actually + + + align:start position:0% +Sun surface well you don't actually +really have a chip anymore + + align:start position:0% +really have a chip anymore + + + align:start position:0% +really have a chip anymore +you right and so basically if you get + + align:start position:0% +you right and so basically if you get + + + align:start position:0% +you right and so basically if you get +into this orange region you basically + + align:start position:0% +into this orange region you basically + + + align:start position:0% +into this orange region you basically +have a fire and you can't really do + + align:start position:0% +have a fire and you can't really do + + + align:start position:0% +have a fire and you can't really do +anything interesting in terms of + + align:start position:0% +anything interesting in terms of + + + align:start position:0% +anything interesting in terms of +performance engineering at that point so + + align:start position:0% +performance engineering at that point so + + + align:start position:0% +performance engineering at that point so +to solve this problem semiconductor vet + + align:start position:0% +to solve this problem semiconductor vet + + + align:start position:0% +to solve this problem semiconductor vet +semiconductor vendors they didn't + + align:start position:0% +semiconductor vendors they didn't + + + align:start position:0% +semiconductor vendors they didn't +include increase the clock frequency + + align:start position:0% +include increase the clock frequency + + + align:start position:0% +include increase the clock frequency +anymore but we still had Moore's Law + + align:start position:0% +anymore but we still had Moore's Law + + + align:start position:0% +anymore but we still had Moore's Law +giving us more and more transistors + + align:start position:0% +giving us more and more transistors + + + align:start position:0% +giving us more and more transistors +every year so what they decided to do + + align:start position:0% +every year so what they decided to do + + + align:start position:0% +every year so what they decided to do +with these extra transistors was to put + + align:start position:0% +with these extra transistors was to put + + + align:start position:0% +with these extra transistors was to put +put them into multiple cores and then + + align:start position:0% +put them into multiple cores and then + + + align:start position:0% +put them into multiple cores and then +put multiple cores on the same chip so + + align:start position:0% +put multiple cores on the same chip so + + + align:start position:0% +put multiple cores on the same chip so +we can see that starting at around 2004 + + align:start position:0% +we can see that starting at around 2004 + + + align:start position:0% +we can see that starting at around 2004 +the number of cores per chip becomes + + align:start position:0% +the number of cores per chip becomes + + + align:start position:0% +the number of cores per chip becomes +more than one and and each generation of + + align:start position:0% +more than one and and each generation of + + + align:start position:0% +more than one and and each generation of +Moore's Law will potentially double the + + align:start position:0% +Moore's Law will potentially double the + + + align:start position:0% +Moore's Law will potentially double the +number of cores that you can fit on a + + align:start position:0% +number of cores that you can fit on a + + + align:start position:0% +number of cores that you can fit on a +chip because it's doubling the number of + + align:start position:0% +chip because it's doubling the number of + + + align:start position:0% +chip because it's doubling the number of +transistors and we we've seen this trend + + align:start position:0% +transistors and we we've seen this trend + + + align:start position:0% +transistors and we we've seen this trend +up until about today and again it's + + align:start position:0% +up until about today and again it's + + + align:start position:0% +up until about today and again it's +going to continue for a couple more + + align:start position:0% +going to continue for a couple more + + + align:start position:0% +going to continue for a couple more +years before Moore's law ends so that's + + align:start position:0% +years before Moore's law ends so that's + + + align:start position:0% +years before Moore's law ends so that's +why we have chips with multiple cores + + align:start position:0% +why we have chips with multiple cores + + + align:start position:0% +why we have chips with multiple cores +today so today we're going to look at + + align:start position:0% +today so today we're going to look at + + + align:start position:0% +today so today we're going to look at +multi-core processing so I first want to + + align:start position:0% +multi-core processing so I first want to + + + align:start position:0% +multi-core processing so I first want to +introduce the abstract multi-core + + align:start position:0% +introduce the abstract multi-core + + + align:start position:0% +introduce the abstract multi-core +architecture so this is a very + + align:start position:0% +architecture so this is a very + + + align:start position:0% +architecture so this is a very +simplified version but I can fit it on + + align:start position:0% +simplified version but I can fit it on + + + align:start position:0% +simplified version but I can fit it on +this slide and it's a good example for + + align:start position:0% +this slide and it's a good example for + + + align:start position:0% +this slide and it's a good example for +illustration so here we have a whole + + align:start position:0% +illustration so here we have a whole + + + align:start position:0% +illustration so here we have a whole +bunch of processors they each have a + + align:start position:0% +bunch of processors they each have a + + + align:start position:0% +bunch of processors they each have a +cache so that's indicated with the + + align:start position:0% +cache so that's indicated with the + + + align:start position:0% +cache so that's indicated with the +dollar sign and usually they they have a + + align:start position:0% +dollar sign and usually they they have a + + + align:start position:0% +dollar sign and usually they they have a +private cache as well as a shared cache + + align:start position:0% +private cache as well as a shared cache + + + align:start position:0% +private cache as well as a shared cache +so I shared last level cache like the l3 + + align:start position:0% +so I shared last level cache like the l3 + + + align:start position:0% +so I shared last level cache like the l3 +cache and then they're all connected to + + align:start position:0% +cache and then they're all connected to + + + align:start position:0% +cache and then they're all connected to +the network and then throughout through + + align:start position:0% +the network and then throughout through + + + align:start position:0% +the network and then throughout through +the network they can connect to the main + + align:start position:0% +the network they can connect to the main + + + align:start position:0% +the network they can connect to the main +memory they can all access the same + + align:start position:0% +memory they can all access the same + + + align:start position:0% +memory they can all access the same +shared memory and then usually there's a + + align:start position:0% +shared memory and then usually there's a + + + align:start position:0% +shared memory and then usually there's a +separate network for the i/o as well + + align:start position:0% +separate network for the i/o as well + + + align:start position:0% +separate network for the i/o as well +even though I've drawn them as a single + + align:start position:0% +even though I've drawn them as a single + + + align:start position:0% +even though I've drawn them as a single +network here so they can access the i/o + + align:start position:0% +network here so they can access the i/o + + + align:start position:0% +network here so they can access the i/o +interface and potentially the network + + align:start position:0% +interface and potentially the network + + + align:start position:0% +interface and potentially the network +will also connect to other multi + + align:start position:0% +will also connect to other multi + + + align:start position:0% +will also connect to other multi +processors on the same system + + align:start position:0% +processors on the same system + + + align:start position:0% +processors on the same system +and this abstract multi-core + + align:start position:0% +and this abstract multi-core + + + align:start position:0% +and this abstract multi-core +architecture is known as a chip + + align:start position:0% +architecture is known as a chip + + + align:start position:0% +architecture is known as a chip +multiprocessor or cmp so that's the + + align:start position:0% +multiprocessor or cmp so that's the + + + align:start position:0% +multiprocessor or cmp so that's the +architecture that we'll be looking at + + align:start position:0% +architecture that we'll be looking at + + + align:start position:0% +architecture that we'll be looking at +today so here's an outline of today's + + align:start position:0% +today so here's an outline of today's + + + align:start position:0% +today so here's an outline of today's +lectures so first I'm gonna go over some + + align:start position:0% +lectures so first I'm gonna go over some + + + align:start position:0% +lectures so first I'm gonna go over some +hardware challenges with shared memory + + align:start position:0% +hardware challenges with shared memory + + + align:start position:0% +hardware challenges with shared memory +multi-core machines so we're gonna look + + align:start position:0% +multi-core machines so we're gonna look + + + align:start position:0% +multi-core machines so we're gonna look +at the cache coherence protocol and then + + align:start position:0% +at the cache coherence protocol and then + + + align:start position:0% +at the cache coherence protocol and then +after looking at hardware we're going to + + align:start position:0% +after looking at hardware we're going to + + + align:start position:0% +after looking at hardware we're going to +look at some software solutions to + + align:start position:0% +look at some software solutions to + + + align:start position:0% +look at some software solutions to +program to write parallel programs on + + align:start position:0% +program to write parallel programs on + + + align:start position:0% +program to write parallel programs on +these multi-core machines to take + + align:start position:0% +these multi-core machines to take + + + align:start position:0% +these multi-core machines to take +advantage of the extra cores and we're + + align:start position:0% +advantage of the extra cores and we're + + + align:start position:0% +advantage of the extra cores and we're +gonna look at several concurrency + + align:start position:0% +gonna look at several concurrency + + + align:start position:0% +gonna look at several concurrency +platforms listed here we're gonna look + + align:start position:0% +platforms listed here we're gonna look + + + align:start position:0% +platforms listed here we're gonna look +at P threads this is basically a + + align:start position:0% +at P threads this is basically a + + + align:start position:0% +at P threads this is basically a +low-level API for accessing or for + + align:start position:0% +low-level API for accessing or for + + + align:start position:0% +low-level API for accessing or for +running your code in parallel and if you + + align:start position:0% +running your code in parallel and if you + + + align:start position:0% +running your code in parallel and if you +program on Microsoft products the win + + align:start position:0% +program on Microsoft products the win + + + align:start position:0% +program on Microsoft products the win +API threads is pretty similar + + align:start position:0% +API threads is pretty similar + + + align:start position:0% +API threads is pretty similar +then there's Intel threading building + + align:start position:0% +then there's Intel threading building + + + align:start position:0% +then there's Intel threading building +blocks which is a library solution to + + align:start position:0% +blocks which is a library solution to + + + align:start position:0% +blocks which is a library solution to +concurrency and then there are two + + align:start position:0% +concurrency and then there are two + + + align:start position:0% +concurrency and then there are two +linguistic solutions that we'll be + + align:start position:0% +linguistic solutions that we'll be + + + align:start position:0% +linguistic solutions that we'll be +looking at openmp and so plus and so + + align:start position:0% +looking at openmp and so plus and so + + + align:start position:0% +looking at openmp and so plus and so +plus is actually the concurrency + + align:start position:0% +plus is actually the concurrency + + + align:start position:0% +plus is actually the concurrency +platform that will be using for most of + + align:start position:0% +platform that will be using for most of + + + align:start position:0% +platform that will be using for most of +this class okay + + align:start position:0% + + + + align:start position:0% + +all right so let's look at how caches + + align:start position:0% +all right so let's look at how caches + + + align:start position:0% +all right so let's look at how caches +work so so let's say that we have a + + align:start position:0% +work so so let's say that we have a + + + align:start position:0% +work so so let's say that we have a +value in memory at some location and + + align:start position:0% +value in memory at some location and + + + align:start position:0% +value in memory at some location and +that value is let's say that value is x + + align:start position:0% +that value is let's say that value is x + + + align:start position:0% +that value is let's say that value is x +equals 3 + + align:start position:0% +equals 3 + + + align:start position:0% +equals 3 +if one processor says we want to load X + + align:start position:0% +if one processor says we want to load X + + + align:start position:0% +if one processor says we want to load X +what happens is that processor reads + + align:start position:0% +what happens is that processor reads + + + align:start position:0% +what happens is that processor reads +this value from a main memory brings it + + align:start position:0% +this value from a main memory brings it + + + align:start position:0% +this value from a main memory brings it +into its own cache and then it also + + align:start position:0% +into its own cache and then it also + + + align:start position:0% +into its own cache and then it also +reads a value loads it into one of those + + align:start position:0% +reads a value loads it into one of those + + + align:start position:0% +reads a value loads it into one of those +registers and it keeps this value in + + align:start position:0% +registers and it keeps this value in + + + align:start position:0% +registers and it keeps this value in +cache so that if it wants to access this + + align:start position:0% +cache so that if it wants to access this + + + align:start position:0% +cache so that if it wants to access this +value again in the near future it + + align:start position:0% +value again in the near future it + + + align:start position:0% +value again in the near future it +doesn't have to go all the way out to + + align:start position:0% +doesn't have to go all the way out to + + + align:start position:0% +doesn't have to go all the way out to +main memory you can just look at the + + align:start position:0% +main memory you can just look at the + + + align:start position:0% +main memory you can just look at the +value in its cache now what happens if + + align:start position:0% +value in its cache now what happens if + + + align:start position:0% +value in its cache now what happens if +another processor wants to load X what + + align:start position:0% +another processor wants to load X what + + + align:start position:0% +another processor wants to load X what +just does the same thing it reads the + + align:start position:0% +just does the same thing it reads the + + + align:start position:0% +just does the same thing it reads the +value from main memory brings it in + + align:start position:0% +value from main memory brings it in + + + align:start position:0% +value from main memory brings it in +addiction is cache and then also loads + + align:start position:0% +addiction is cache and then also loads + + + align:start position:0% +addiction is cache and then also loads +it into one of the registers and then + + align:start position:0% +it into one of the registers and then + + + align:start position:0% +it into one of the registers and then +same thing with another processor turns + + align:start position:0% +same thing with another processor turns + + + align:start position:0% +same thing with another processor turns +out that you don't actually always have + + align:start position:0% +out that you don't actually always have + + + align:start position:0% +out that you don't actually always have +to go out to main memory to get the + + align:start position:0% +to go out to main memory to get the + + + align:start position:0% +to go out to main memory to get the +value of the value resides in one of the + + align:start position:0% +value of the value resides in one of the + + + align:start position:0% +value of the value resides in one of the +other processors caches you can also get + + align:start position:0% +other processors caches you can also get + + + align:start position:0% +other processors caches you can also get +the value through the other processors + + align:start position:0% +the value through the other processors + + + align:start position:0% +the value through the other processors +cache and sometimes ask cheaper than + + align:start position:0% +cache and sometimes ask cheaper than + + + align:start position:0% +cache and sometimes ask cheaper than +going all the way out to main memory + + align:start position:0% + + + + align:start position:0% + +okay so now okay so the second processor + + align:start position:0% +okay so now okay so the second processor + + + align:start position:0% +okay so now okay so the second processor +now loads acts again and it's in cache + + align:start position:0% +now loads acts again and it's in cache + + + align:start position:0% +now loads acts again and it's in cache +so it doesn't have to go to main memory + + align:start position:0% +so it doesn't have to go to main memory + + + align:start position:0% +so it doesn't have to go to main memory +or anybody else's cache so what happens + + align:start position:0% +or anybody else's cache so what happens + + + align:start position:0% +or anybody else's cache so what happens +now if we want to store X if we want to + + align:start position:0% +now if we want to store X if we want to + + + align:start position:0% +now if we want to store X if we want to +set the value of X to something else + + align:start position:0% +set the value of X to something else + + + align:start position:0% +set the value of X to something else +okay so let's say this processor wants + + align:start position:0% +okay so let's say this processor wants + + + align:start position:0% +okay so let's say this processor wants +to set X equal to five so it's going to + + align:start position:0% +to set X equal to five so it's going to + + + align:start position:0% +to set X equal to five so it's going to +write x equals five and store that + + align:start position:0% +write x equals five and store that + + + align:start position:0% +write x equals five and store that +result in its own cache so that's all + + align:start position:0% +result in its own cache so that's all + + + align:start position:0% +result in its own cache so that's all +well and good now what what happens when + + align:start position:0% +well and good now what what happens when + + + align:start position:0% +well and good now what what happens when +the first processor wants to load X well + + align:start position:0% +the first processor wants to load X well + + + align:start position:0% +the first processor wants to load X well +it sees that the value of X is is it is + + align:start position:0% +it sees that the value of X is is it is + + + align:start position:0% +it sees that the value of X is is it is +in its own cache so it's just gonna read + + align:start position:0% +in its own cache so it's just gonna read + + + align:start position:0% +in its own cache so it's just gonna read +the value of x there and it gets a value + + align:start position:0% +the value of x there and it gets a value + + + align:start position:0% +the value of x there and it gets a value +of + + align:start position:0% +of + + + align:start position:0% +of +three so what's the problem there yes + + align:start position:0% +three so what's the problem there yes + + + align:start position:0% +three so what's the problem there yes +yes so the problem is that the value of + + align:start position:0% +yes so the problem is that the value of + + + align:start position:0% +yes so the problem is that the value of +x in the first processors cache is stale + + align:start position:0% +x in the first processors cache is stale + + + align:start position:0% +x in the first processors cache is stale +because another processor updated it so + + align:start position:0% +because another processor updated it so + + + align:start position:0% +because another processor updated it so +now we can't this value of x in the + + align:start position:0% +now we can't this value of x in the + + + align:start position:0% +now we can't this value of x in the +first processors cache is invalid okay + + align:start position:0% +first processors cache is invalid okay + + + align:start position:0% +first processors cache is invalid okay +so so that's the problem and one of the + + align:start position:0% +so so that's the problem and one of the + + + align:start position:0% +so so that's the problem and one of the +main challenges of multi-core hardware + + align:start position:0% +main challenges of multi-core hardware + + + align:start position:0% +main challenges of multi-core hardware +is to try to solve this problem of cache + + align:start position:0% +is to try to solve this problem of cache + + + align:start position:0% +is to try to solve this problem of cache +coherence making sure that the values in + + align:start position:0% +coherence making sure that the values in + + + align:start position:0% +coherence making sure that the values in +different processors caches are + + align:start position:0% +different processors caches are + + + align:start position:0% +different processors caches are +consistent across updates okay so one + + align:start position:0% +consistent across updates okay so one + + + align:start position:0% +consistent across updates okay so one +basic protocol for solving this problem + + align:start position:0% +basic protocol for solving this problem + + + align:start position:0% +basic protocol for solving this problem +is known as the MSI protocol and in this + + align:start position:0% +is known as the MSI protocol and in this + + + align:start position:0% +is known as the MSI protocol and in this +protocol each cache line is labeled with + + align:start position:0% +protocol each cache line is labeled with + + + align:start position:0% +protocol each cache line is labeled with +a state so there are three possible + + align:start position:0% +a state so there are three possible + + + align:start position:0% +a state so there are three possible +states M s and I and this is done on the + + align:start position:0% +states M s and I and this is done on the + + + align:start position:0% +states M s and I and this is done on the +granularity of cache lines because it + + align:start position:0% +granularity of cache lines because it + + + align:start position:0% +granularity of cache lines because it +turns out that storing this information + + align:start position:0% +turns out that storing this information + + + align:start position:0% +turns out that storing this information +is relatively expensive so you don't + + align:start position:0% +is relatively expensive so you don't + + + align:start position:0% +is relatively expensive so you don't +want to store it for every memory + + align:start position:0% +want to store it for every memory + + + align:start position:0% +want to store it for every memory +location so they do it on a per cache + + align:start position:0% +location so they do it on a per cache + + + align:start position:0% +location so they do it on a per cache +line basis so anyone know what the size + + align:start position:0% +line basis so anyone know what the size + + + align:start position:0% +line basis so anyone know what the size +of a cache line is on the machines that + + align:start position:0% +of a cache line is on the machines that + + + align:start position:0% +of a cache line is on the machines that +we're using + + align:start position:0% + + + + align:start position:0% + +yeah yeah so it's 64 bytes and that's + + align:start position:0% +yeah yeah so it's 64 bytes and that's + + + align:start position:0% +yeah yeah so it's 64 bytes and that's +typically what you see today on most + + align:start position:0% +typically what you see today on most + + + align:start position:0% +typically what you see today on most +intel and AMD machines there are some + + align:start position:0% +intel and AMD machines there are some + + + align:start position:0% +intel and AMD machines there are some +architectures that have different cache + + align:start position:0% +architectures that have different cache + + + align:start position:0% +architectures that have different cache +lines like 128 bytes but for our class + + align:start position:0% +lines like 128 bytes but for our class + + + align:start position:0% +lines like 128 bytes but for our class +the machines that were using will have + + align:start position:0% +the machines that were using will have + + + align:start position:0% +the machines that were using will have +64 byte cache lines is important to + + align:start position:0% +64 byte cache lines is important to + + + align:start position:0% +64 byte cache lines is important to +remember that so that when you're doing + + align:start position:0% +remember that so that when you're doing + + + align:start position:0% +remember that so that when you're doing +back at the envelope calculations you + + align:start position:0% +back at the envelope calculations you + + + align:start position:0% +back at the envelope calculations you +can get accurate estimates so three + + align:start position:0% +can get accurate estimates so three + + + align:start position:0% +can get accurate estimates so three +states in the MSI protocol or ms and iso + + align:start position:0% +states in the MSI protocol or ms and iso + + + align:start position:0% +states in the MSI protocol or ms and iso +M stands for modified and when a cache + + align:start position:0% +M stands for modified and when a cache + + + align:start position:0% +M stands for modified and when a cache +block is in the modified state that + + align:start position:0% +block is in the modified state that + + + align:start position:0% +block is in the modified state that +means no other caches can contain this + + align:start position:0% +means no other caches can contain this + + + align:start position:0% +means no other caches can contain this +block in the M or the a States the S + + align:start position:0% +block in the M or the a States the S + + + align:start position:0% +block in the M or the a States the S +state means that the block is shared so + + align:start position:0% +state means that the block is shared so + + + align:start position:0% +state means that the block is shared so +other caches can also have this block in + + align:start position:0% +other caches can also have this block in + + + align:start position:0% +other caches can also have this block in +shared state and if finally I means the + + align:start position:0% +shared state and if finally I means the + + + align:start position:0% +shared state and if finally I means the +cache block is invalid so that's + + align:start position:0% +cache block is invalid so that's + + + align:start position:0% +cache block is invalid so that's +essentially the same as the cache block + + align:start position:0% +essentially the same as the cache block + + + align:start position:0% +essentially the same as the cache block +not being in the cache and to solve the + + align:start position:0% +not being in the cache and to solve the + + + align:start position:0% +not being in the cache and to solve the +problem of cache coherency when one + + align:start position:0% +problem of cache coherency when one + + + align:start position:0% +problem of cache coherency when one +cache modifies a location it has to + + align:start position:0% +cache modifies a location it has to + + + align:start position:0% +cache modifies a location it has to +inform all the other caches that their + + align:start position:0% +inform all the other caches that their + + + align:start position:0% +inform all the other caches that their +values are now stale because because + + align:start position:0% +values are now stale because because + + + align:start position:0% +values are now stale because because +this cache modified the value so it's + + align:start position:0% +this cache modified the value so it's + + + align:start position:0% +this cache modified the value so it's +going to invalidate all of the other + + align:start position:0% +going to invalidate all of the other + + + align:start position:0% +going to invalidate all of the other +copies of that cache line in other + + align:start position:0% +copies of that cache line in other + + + align:start position:0% +copies of that cache line in other +caches by changing their state from s to + + align:start position:0% +caches by changing their state from s to + + + align:start position:0% +caches by changing their state from s to +I so let's see how this works so let's + + align:start position:0% +I so let's see how this works so let's + + + align:start position:0% +I so let's see how this works so let's +say that the second processor wants to + + align:start position:0% +say that the second processor wants to + + + align:start position:0% +say that the second processor wants to +store y equals 5 so previously a value + + align:start position:0% +store y equals 5 so previously a value + + + align:start position:0% +store y equals 5 so previously a value +of y was 17 and it was in shared State + + align:start position:0% +of y was 17 and it was in shared State + + + align:start position:0% +of y was 17 and it was in shared State +the cache line containing y equals 17 + + align:start position:0% +the cache line containing y equals 17 + + + align:start position:0% +the cache line containing y equals 17 +was in shared State so now when I do y + + align:start position:0% +was in shared State so now when I do y + + + align:start position:0% +was in shared State so now when I do y +equals 5 I'm gonna set the second + + align:start position:0% +equals 5 I'm gonna set the second + + + align:start position:0% +equals 5 I'm gonna set the second +processors cache that cache line to + + align:start position:0% +processors cache that cache line to + + + align:start position:0% +processors cache that cache line to +modified State and then I'm going to + + align:start position:0% +modified State and then I'm going to + + + align:start position:0% +modified State and then I'm going to +invalidate the cache line in all of the + + align:start position:0% +invalidate the cache line in all of the + + + align:start position:0% +invalidate the cache line in all of the +other caches that contain that cache + + align:start position:0% +other caches that contain that cache + + + align:start position:0% +other caches that contain that cache +line so now the first cache in the + + align:start position:0% +line so now the first cache in the + + + align:start position:0% +line so now the first cache in the +fourth cache each have a state of I 4 y + + align:start position:0% +fourth cache each have a state of I 4 y + + + align:start position:0% +fourth cache each have a state of I 4 y +equals 17 because that value is still + + align:start position:0% +equals 17 because that value is still + + + align:start position:0% +equals 17 because that value is still +there any questions yes + + align:start position:0% +there any questions yes + + + align:start position:0% +there any questions yes +we already other yeah so there are + + align:start position:0% +we already other yeah so there are + + + align:start position:0% +we already other yeah so there are +actually some protocols that do that so + + align:start position:0% +actually some protocols that do that so + + + align:start position:0% +actually some protocols that do that so +this is just a most basic protocol so + + align:start position:0% +this is just a most basic protocol so + + + align:start position:0% +this is just a most basic protocol so +this protocol doesn't do it but there + + align:start position:0% +this protocol doesn't do it but there + + + align:start position:0% +this protocol doesn't do it but there +are some that are used in practice that + + align:start position:0% +are some that are used in practice that + + + align:start position:0% +are some that are used in practice that +actually do do that so it's a good point + + align:start position:0% +actually do do that so it's a good point + + + align:start position:0% +actually do do that so it's a good point +yeah but I just want to present the most + + align:start position:0% +yeah but I just want to present the most + + + align:start position:0% +yeah but I just want to present the most +basic protocol for now sorry okay and + + align:start position:0% +basic protocol for now sorry okay and + + + align:start position:0% +basic protocol for now sorry okay and +then when you load a value you can first + + align:start position:0% +then when you load a value you can first + + + align:start position:0% +then when you load a value you can first +check whether whether your cache line is + + align:start position:0% +check whether whether your cache line is + + + align:start position:0% +check whether whether your cache line is +it is an M or a state and if it is an M + + align:start position:0% +it is an M or a state and if it is an M + + + align:start position:0% +it is an M or a state and if it is an M +or S state then you can just read that + + align:start position:0% +or S state then you can just read that + + + align:start position:0% +or S state then you can just read that +value directly but if it's in the eye + + align:start position:0% +value directly but if it's in the eye + + + align:start position:0% +value directly but if it's in the eye +state orbs or if it's not there then you + + align:start position:0% +state orbs or if it's not there then you + + + align:start position:0% +state orbs or if it's not there then you +have to fetch that block from either + + align:start position:0% +have to fetch that block from either + + + align:start position:0% +have to fetch that block from either +another processors cache or fetch it + + align:start position:0% +another processors cache or fetch it + + + align:start position:0% +another processors cache or fetch it +from main memory so turns out that there + + align:start position:0% +from main memory so turns out that there + + + align:start position:0% +from main memory so turns out that there +are many other protocols out there + + align:start position:0% +are many other protocols out there + + + align:start position:0% +are many other protocols out there +there's something known as mes I the + + align:start position:0% +there's something known as mes I the + + + align:start position:0% +there's something known as mes I the +Massey protocol + + align:start position:0% +Massey protocol + + + align:start position:0% +Massey protocol +there's also m OE si and many other + + align:start position:0% +there's also m OE si and many other + + + align:start position:0% +there's also m OE si and many other +different protocols and some of them are + + align:start position:0% +different protocols and some of them are + + + align:start position:0% +different protocols and some of them are +proprietary and they all do different + + align:start position:0% +proprietary and they all do different + + + align:start position:0% +proprietary and they all do different +things and it turns out that all of + + align:start position:0% +things and it turns out that all of + + + align:start position:0% +things and it turns out that all of +these protocols are quite complicated + + align:start position:0% +these protocols are quite complicated + + + align:start position:0% +these protocols are quite complicated +and it's very hard to get these + + align:start position:0% +and it's very hard to get these + + + align:start position:0% +and it's very hard to get these +protocols right and in fact one of the + + align:start position:0% +protocols right and in fact one of the + + + align:start position:0% +protocols right and in fact one of the +most earliest successes of formal + + align:start position:0% +most earliest successes of formal + + + align:start position:0% +most earliest successes of formal +verification was improving some of these + + align:start position:0% +verification was improving some of these + + + align:start position:0% +verification was improving some of these +cache coherence protocols to be correct + + align:start position:0% +cache coherence protocols to be correct + + + align:start position:0% +cache coherence protocols to be correct +yes question + + align:start position:0% + + + + align:start position:0% + +yeah so if two processors try to modify + + align:start position:0% +yeah so if two processors try to modify + + + align:start position:0% +yeah so if two processors try to modify +the value one of them has to happen + + align:start position:0% +the value one of them has to happen + + + align:start position:0% +the value one of them has to happen +first so the hardware is going to take + + align:start position:0% +first so the hardware is going to take + + + align:start position:0% +first so the hardware is going to take +care of that so the first one that + + align:start position:0% +care of that so the first one that + + + align:start position:0% +care of that so the first one that +actually modifies it will invalidate all + + align:start position:0% +actually modifies it will invalidate all + + + align:start position:0% +actually modifies it will invalidate all +the other copies and then the second one + + align:start position:0% +the other copies and then the second one + + + align:start position:0% +the other copies and then the second one +that modifies the value will again + + align:start position:0% +that modifies the value will again + + + align:start position:0% +that modifies the value will again +invalidate all the other copies and when + + align:start position:0% +invalidate all the other copies and when + + + align:start position:0% +invalidate all the other copies and when +you do that when a lot of processors try + + align:start position:0% +you do that when a lot of processors try + + + align:start position:0% +you do that when a lot of processors try +to modify the same value you get + + align:start position:0% +to modify the same value you get + + + align:start position:0% +to modify the same value you get +something known as an invalidation storm + + align:start position:0% +something known as an invalidation storm + + + align:start position:0% +something known as an invalidation storm +so you have a bunch of invalidation + + align:start position:0% +so you have a bunch of invalidation + + + align:start position:0% +so you have a bunch of invalidation +messages going through throughout the + + align:start position:0% +messages going through throughout the + + + align:start position:0% +messages going through throughout the +hardware and that can lead to a big + + align:start position:0% +hardware and that can lead to a big + + + align:start position:0% +hardware and that can lead to a big +performance bottleneck because each + + align:start position:0% +performance bottleneck because each + + + align:start position:0% +performance bottleneck because each +processor when it modifies it's about + + align:start position:0% +processor when it modifies it's about + + + align:start position:0% +processor when it modifies it's about +yes inform all the other processors and + + align:start position:0% +yes inform all the other processors and + + + align:start position:0% +yes inform all the other processors and +if all the processors are modifying the + + align:start position:0% +if all the processors are modifying the + + + align:start position:0% +if all the processors are modifying the +same value get the sort of quadratic + + align:start position:0% +same value get the sort of quadratic + + + align:start position:0% +same value get the sort of quadratic +behavior the hardware is still going to + + align:start position:0% +behavior the hardware is still going to + + + align:start position:0% +behavior the hardware is still going to +guarantee that one of the processor is + + align:start position:0% +guarantee that one of the processor is + + + align:start position:0% +guarantee that one of the processor is +going to end up writing the value there + + align:start position:0% +going to end up writing the value there + + + align:start position:0% +going to end up writing the value there +but you should be aware of this + + align:start position:0% +but you should be aware of this + + + align:start position:0% +but you should be aware of this +performance issue when you're writing a + + align:start position:0% +performance issue when you're writing a + + + align:start position:0% +performance issue when you're writing a +parallel code yes yes so this is all + + align:start position:0% +parallel code yes yes so this is all + + + align:start position:0% +parallel code yes yes so this is all +implemented in hardware so if we take a + + align:start position:0% +implemented in hardware so if we take a + + + align:start position:0% +implemented in hardware so if we take a +computer architecture class you'll learn + + align:start position:0% +computer architecture class you'll learn + + + align:start position:0% +computer architecture class you'll learn +much more about these protocols and all + + align:start position:0% +much more about these protocols and all + + + align:start position:0% +much more about these protocols and all +of their variants so for our purposes we + + align:start position:0% +of their variants so for our purposes we + + + align:start position:0% +of their variants so for our purposes we +don't actually need to understand all + + align:start position:0% +don't actually need to understand all + + + align:start position:0% +don't actually need to understand all +the details of the hardware we just need + + align:start position:0% +the details of the hardware we just need + + + align:start position:0% +the details of the hardware we just need +to understand what it's doing at a high + + align:start position:0% +to understand what it's doing at a high + + + align:start position:0% +to understand what it's doing at a high +level so we can understand when we have + + align:start position:0% +level so we can understand when we have + + + align:start position:0% +level so we can understand when we have +a performance bottleneck and why we have + + align:start position:0% +a performance bottleneck and why we have + + + align:start position:0% +a performance bottleneck and why we have +a performance bottleneck so that's why + + align:start position:0% +a performance bottleneck so that's why + + + align:start position:0% +a performance bottleneck so that's why +I'm just introducing the most basic + + align:start position:0% +I'm just introducing the most basic + + + align:start position:0% +I'm just introducing the most basic +protocol here any other questions + + align:start position:0% + + + + align:start position:0% + +all right so so I talked a little bit + + align:start position:0% +all right so so I talked a little bit + + + align:start position:0% +all right so so I talked a little bit +about the shared memory hardware let's + + align:start position:0% +about the shared memory hardware let's + + + align:start position:0% +about the shared memory hardware let's +now look at some concurrency platforms + + align:start position:0% +now look at some concurrency platforms + + + align:start position:0% +now look at some concurrency platforms +so these are the four platforms that + + align:start position:0% +so these are the four platforms that + + + align:start position:0% +so these are the four platforms that +we'll be looking at today so first what + + align:start position:0% +we'll be looking at today so first what + + + align:start position:0% +we'll be looking at today so first what +is a concurrency platform both writing + + align:start position:0% +is a concurrency platform both writing + + + align:start position:0% +is a concurrency platform both writing +parallel programs is very difficult it's + + align:start position:0% +parallel programs is very difficult it's + + + align:start position:0% +parallel programs is very difficult it's +very hard to get these programs to be + + align:start position:0% +very hard to get these programs to be + + + align:start position:0% +very hard to get these programs to be +correct and if you want to optimize + + align:start position:0% +correct and if you want to optimize + + + align:start position:0% +correct and if you want to optimize +their performance it becomes even harder + + align:start position:0% +their performance it becomes even harder + + + align:start position:0% +their performance it becomes even harder +so it's very painful and error-prone and + + align:start position:0% +so it's very painful and error-prone and + + + align:start position:0% +so it's very painful and error-prone and +a concurrency platform abstracts + + align:start position:0% +a concurrency platform abstracts + + + align:start position:0% +a concurrency platform abstracts +processor cores and handles + + align:start position:0% +processor cores and handles + + + align:start position:0% +processor cores and handles +synchronization and communication + + align:start position:0% +synchronization and communication + + + align:start position:0% +synchronization and communication +protocols and it also performs load + + align:start position:0% +protocols and it also performs load + + + align:start position:0% +protocols and it also performs load +balancing for you so it makes your lives + + align:start position:0% +balancing for you so it makes your lives + + + align:start position:0% +balancing for you so it makes your lives +much easier and so today we're gonna + + align:start position:0% +much easier and so today we're gonna + + + align:start position:0% +much easier and so today we're gonna +talk about some of these different + + align:start position:0% +talk about some of these different + + + align:start position:0% +talk about some of these different +concurrency platforms so to illustrate + + align:start position:0% +concurrency platforms so to illustrate + + + align:start position:0% +concurrency platforms so to illustrate +these concurrency platforms I'm gonna do + + align:start position:0% +these concurrency platforms I'm gonna do + + + align:start position:0% +these concurrency platforms I'm gonna do +the Fibonacci numbers example so does + + align:start position:0% +the Fibonacci numbers example so does + + + align:start position:0% +the Fibonacci numbers example so does +anybody not know what Fibonacci is so + + align:start position:0% +anybody not know what Fibonacci is so + + + align:start position:0% +anybody not know what Fibonacci is so +good everybody knows what Fibonacci is + + align:start position:0% +good everybody knows what Fibonacci is + + + align:start position:0% +good everybody knows what Fibonacci is +okay so so it's a sequence where each + + align:start position:0% +okay so so it's a sequence where each + + + align:start position:0% +okay so so it's a sequence where each +numbers are sum of the previous two + + align:start position:0% +numbers are sum of the previous two + + + align:start position:0% +numbers are sum of the previous two +numbers and the recurrence here is the + + align:start position:0% +numbers and the recurrence here is the + + + align:start position:0% +numbers and the recurrence here is the +recurrence is shown in this brown box + + align:start position:0% +recurrence is shown in this brown box + + + align:start position:0% +recurrence is shown in this brown box +here the sequence is named after + + align:start position:0% +here the sequence is named after + + + align:start position:0% +here the sequence is named after +Leonardo di Pisa who was also known as + + align:start position:0% +Leonardo di Pisa who was also known as + + + align:start position:0% +Leonardo di Pisa who was also known as +Fibonacci which is a contraction of + + align:start position:0% +Fibonacci which is a contraction of + + + align:start position:0% +Fibonacci which is a contraction of +filius Bonacci son of Bonacci oh so + + align:start position:0% +filius Bonacci son of Bonacci oh so + + + align:start position:0% +filius Bonacci son of Bonacci oh so +that's where the name Fibonacci came + + align:start position:0% +that's where the name Fibonacci came + + + align:start position:0% +that's where the name Fibonacci came +from and in Fibonacci's 1202 book libra + + align:start position:0% +from and in Fibonacci's 1202 book libra + + + align:start position:0% +from and in Fibonacci's 1202 book libra +bocce he introduced the sequence the + + align:start position:0% +bocce he introduced the sequence the + + + align:start position:0% +bocce he introduced the sequence the +Fibonacci sequence to Western + + align:start position:0% +Fibonacci sequence to Western + + + align:start position:0% +Fibonacci sequence to Western +mathematics although it had been + + align:start position:0% +mathematics although it had been + + + align:start position:0% +mathematics although it had been +previously known to India and + + align:start position:0% +previously known to India and + + + align:start position:0% +previously known to India and +mathematicians for several centuries but + + align:start position:0% +mathematicians for several centuries but + + + align:start position:0% +mathematicians for several centuries but +this is what we call the the sequence + + align:start position:0% +this is what we call the the sequence + + + align:start position:0% +this is what we call the the sequence +nowadays Fibonacci numbers + + align:start position:0% +nowadays Fibonacci numbers + + + align:start position:0% +nowadays Fibonacci numbers +all right so here's a Fibonacci program + + align:start position:0% +all right so here's a Fibonacci program + + + align:start position:0% +all right so here's a Fibonacci program +has anyone seen this out algorithm + + align:start position:0% +has anyone seen this out algorithm + + + align:start position:0% +has anyone seen this out algorithm +before a couple people probably more but + + align:start position:0% +before a couple people probably more but + + + align:start position:0% +before a couple people probably more but +people didn't raise their hands okay so + + align:start position:0% +people didn't raise their hands okay so + + + align:start position:0% +people didn't raise their hands okay so +all right so it's a recursive program so + + align:start position:0% +all right so it's a recursive program so + + + align:start position:0% +all right so it's a recursive program so +it basically implements the recurrence + + align:start position:0% +it basically implements the recurrence + + + align:start position:0% +it basically implements the recurrence +from the previous slide so if n is less + + align:start position:0% +from the previous slide so if n is less + + + align:start position:0% +from the previous slide so if n is less +than 2 we just return n otherwise we + + align:start position:0% +than 2 we just return n otherwise we + + + align:start position:0% +than 2 we just return n otherwise we +compute fib of n minus 1 store that + + align:start position:0% +compute fib of n minus 1 store that + + + align:start position:0% +compute fib of n minus 1 store that +value in X filled with n minus 2 store + + align:start position:0% +value in X filled with n minus 2 store + + + align:start position:0% +value in X filled with n minus 2 store +that value in Y and then return the sum + + align:start position:0% +that value in Y and then return the sum + + + align:start position:0% +that value in Y and then return the sum +of x and y so I do want to make a + + align:start position:0% +of x and y so I do want to make a + + + align:start position:0% +of x and y so I do want to make a +disclaimer to the algorithms police that + + align:start position:0% +disclaimer to the algorithms police that + + + align:start position:0% +disclaimer to the algorithms police that +this is actually a very bad algorithm so + + align:start position:0% +this is actually a very bad algorithm so + + + align:start position:0% +this is actually a very bad algorithm so +this algorithm takes exponential time + + align:start position:0% +this algorithm takes exponential time + + + align:start position:0% +this algorithm takes exponential time +and there's actually much better ways to + + align:start position:0% +and there's actually much better ways to + + + align:start position:0% +and there's actually much better ways to +compute the Fibonacci thence the Bonacci + + align:start position:0% +compute the Fibonacci thence the Bonacci + + + align:start position:0% +compute the Fibonacci thence the Bonacci +number there's a linear time algorithm + + align:start position:0% +number there's a linear time algorithm + + + align:start position:0% +number there's a linear time algorithm +which just computes the Fibonacci + + align:start position:0% +which just computes the Fibonacci + + + align:start position:0% +which just computes the Fibonacci +numbers from bottom up this algorithm + + align:start position:0% +numbers from bottom up this algorithm + + + align:start position:0% +numbers from bottom up this algorithm +here is actually redoing a lot of the + + align:start position:0% +here is actually redoing a lot of the + + + align:start position:0% +here is actually redoing a lot of the +work because it's computing Fibonacci + + align:start position:0% +work because it's computing Fibonacci + + + align:start position:0% +work because it's computing Fibonacci +numbers multiple times whereas if you do + + align:start position:0% +numbers multiple times whereas if you do + + + align:start position:0% +numbers multiple times whereas if you do +a linear scan from the smallest numbers + + align:start position:0% +a linear scan from the smallest numbers + + + align:start position:0% +a linear scan from the smallest numbers +up you only have to compute each one + + align:start position:0% +up you only have to compute each one + + + align:start position:0% +up you only have to compute each one +once and there's actually an even better + + align:start position:0% +once and there's actually an even better + + + align:start position:0% +once and there's actually an even better +algorithm that takes logarithmic time + + align:start position:0% +algorithm that takes logarithmic time + + + align:start position:0% +algorithm that takes logarithmic time +and it's based on squaring matrices so + + align:start position:0% +and it's based on squaring matrices so + + + align:start position:0% +and it's based on squaring matrices so +has anyone seen that algorithm before + + align:start position:0% +has anyone seen that algorithm before + + + align:start position:0% +has anyone seen that algorithm before +yeah so a couple people so if you're + + align:start position:0% +yeah so a couple people so if you're + + + align:start position:0% +yeah so a couple people so if you're +interested in learning more about this + + align:start position:0% +interested in learning more about this + + + align:start position:0% +interested in learning more about this +algorithm I encourage you to look at + + align:start position:0% +algorithm I encourage you to look at + + + align:start position:0% +algorithm I encourage you to look at +your favorite textbook introduction + + align:start position:0% +your favorite textbook introduction + + + align:start position:0% +your favorite textbook introduction +algorithms by cormen leiserson rivest + + align:start position:0% +algorithms by cormen leiserson rivest + + + align:start position:0% +algorithms by cormen leiserson rivest +and stein so even though this is a yes + + align:start position:0% +and stein so even though this is a yes + + + align:start position:0% +and stein so even though this is a yes +so even though this is a pretty bad + + align:start position:0% +so even though this is a pretty bad + + + align:start position:0% +so even though this is a pretty bad +algorithm it's still a good educational + + align:start position:0% +algorithm it's still a good educational + + + align:start position:0% +algorithm it's still a good educational +example because I can fit it on on one + + align:start position:0% +example because I can fit it on on one + + + align:start position:0% +example because I can fit it on on one +slide and illustrate all the concepts of + + align:start position:0% +slide and illustrate all the concepts of + + + align:start position:0% +slide and illustrate all the concepts of +parallelism that we want to cover today + + align:start position:0% +parallelism that we want to cover today + + + align:start position:0% +parallelism that we want to cover today +so here's the execution tree for fib of + + align:start position:0% +so here's the execution tree for fib of + + + align:start position:0% +so here's the execution tree for fib of + + align:start position:0% + + + align:start position:0% +so we see that fair before is going to + + align:start position:0% +so we see that fair before is going to + + + align:start position:0% +so we see that fair before is going to +call fib of 3 in favor of to fib of 3 is + + align:start position:0% +call fib of 3 in favor of to fib of 3 is + + + align:start position:0% +call fib of 3 in favor of to fib of 3 is +gonna call fib of 2 fib of 1 and so on + + align:start position:0% +gonna call fib of 2 fib of 1 and so on + + + align:start position:0% +gonna call fib of 2 fib of 1 and so on +and you can see that repeated + + align:start position:0% +and you can see that repeated + + + align:start position:0% +and you can see that repeated +computations here it's a fib of 2 is + + align:start position:0% +computations here it's a fib of 2 is + + + align:start position:0% +computations here it's a fib of 2 is +being computed twice and so on and if + + align:start position:0% +being computed twice and so on and if + + + align:start position:0% +being computed twice and so on and if +you have a much larger tree say you ran + + align:start position:0% +you have a much larger tree say you ran + + + align:start position:0% +you have a much larger tree say you ran +it ran this on fit before T then you'll + + align:start position:0% +it ran this on fit before T then you'll + + + align:start position:0% +it ran this on fit before T then you'll +have many more overlapping computations + + align:start position:0% + + + + align:start position:0% + +it turns out that the two recursive + + align:start position:0% +it turns out that the two recursive + + + align:start position:0% +it turns out that the two recursive +calls can actually be paralyzed because + + align:start position:0% +calls can actually be paralyzed because + + + align:start position:0% +calls can actually be paralyzed because +they're completely independent + + align:start position:0% +they're completely independent + + + align:start position:0% +they're completely independent +calculations so the key idea for + + align:start position:0% +calculations so the key idea for + + + align:start position:0% +calculations so the key idea for +parallelization is to simultaneously + + align:start position:0% +parallelization is to simultaneously + + + align:start position:0% +parallelization is to simultaneously +execute the two recursive sub calls to + + align:start position:0% +execute the two recursive sub calls to + + + align:start position:0% +execute the two recursive sub calls to +fib and in fact you can do this + + align:start position:0% +fib and in fact you can do this + + + align:start position:0% +fib and in fact you can do this +recursively so the two sob calls to Fela + + align:start position:0% +recursively so the two sob calls to Fela + + + align:start position:0% +recursively so the two sob calls to Fela +3 can also be executed in parallel and + + align:start position:0% +3 can also be executed in parallel and + + + align:start position:0% +3 can also be executed in parallel and +the two sub calls a fiblet 2 can also be + + align:start position:0% +the two sub calls a fiblet 2 can also be + + + align:start position:0% +the two sub calls a fiblet 2 can also be +executed in parallel on so on so you + + align:start position:0% +executed in parallel on so on so you + + + align:start position:0% +executed in parallel on so on so you +have all of these calls that can be + + align:start position:0% +have all of these calls that can be + + + align:start position:0% +have all of these calls that can be +executed in parallel so that's a key + + align:start position:0% +executed in parallel so that's a key + + + align:start position:0% +executed in parallel so that's a key +idea for extracting parallelism from + + align:start position:0% +idea for extracting parallelism from + + + align:start position:0% +idea for extracting parallelism from +this algorithm okay so let's now look at + + align:start position:0% +this algorithm okay so let's now look at + + + align:start position:0% +this algorithm okay so let's now look at +how we can use P threads to implement + + align:start position:0% +how we can use P threads to implement + + + align:start position:0% +how we can use P threads to implement +this simple Fibonacci algorithm so P + + align:start position:0% +this simple Fibonacci algorithm so P + + + align:start position:0% +this simple Fibonacci algorithm so P +threads is a standard API for threading + + align:start position:0% +threads is a standard API for threading + + + align:start position:0% +threads is a standard API for threading +and it's supported on all UNIX based + + align:start position:0% +and it's supported on all UNIX based + + + align:start position:0% +and it's supported on all UNIX based +machines and if you're programming using + + align:start position:0% +machines and if you're programming using + + + align:start position:0% +machines and if you're programming using +Microsoft products then then the + + align:start position:0% +Microsoft products then then the + + + align:start position:0% +Microsoft products then then the +equivalent is when API threads and this + + align:start position:0% +equivalent is when API threads and this + + + align:start position:0% +equivalent is when API threads and this +is actually a P threads is actually + + align:start position:0% +is actually a P threads is actually + + + align:start position:0% +is actually a P threads is actually +standard and ANSI I Triple E so there's + + align:start position:0% +standard and ANSI I Triple E so there's + + + align:start position:0% +standard and ANSI I Triple E so there's +this number here that specifies a + + align:start position:0% +this number here that specifies a + + + align:start position:0% +this number here that specifies a +standard but nowadays we just call it P + + align:start position:0% +standard but nowadays we just call it P + + + align:start position:0% +standard but nowadays we just call it P +threads and it's basically a + + align:start position:0% +threads and it's basically a + + + align:start position:0% +threads and it's basically a +do-it-yourself concurrency platforms so + + align:start position:0% +do-it-yourself concurrency platforms so + + + align:start position:0% +do-it-yourself concurrency platforms so +it's like the assembly language of + + align:start position:0% +it's like the assembly language of + + + align:start position:0% +it's like the assembly language of +parallel programming it's built as a + + align:start position:0% +parallel programming it's built as a + + + align:start position:0% +parallel programming it's built as a +library of functions with special non C + + align:start position:0% +library of functions with special non C + + + align:start position:0% +library of functions with special non C +semantics because if you're just writing + + align:start position:0% +semantics because if you're just writing + + + align:start position:0% +semantics because if you're just writing +code in C you can't really say which + + align:start position:0% +code in C you can't really say which + + + align:start position:0% +code in C you can't really say which +parts of the code should be executed in + + align:start position:0% +parts of the code should be executed in + + + align:start position:0% +parts of the code should be executed in +parallel so P threads provides you a + + align:start position:0% +parallel so P threads provides you a + + + align:start position:0% +parallel so P threads provides you a +library of functions that allow you to + + align:start position:0% +library of functions that allow you to + + + align:start position:0% +library of functions that allow you to +specify concurrency + + align:start position:0% +specify concurrency + + + align:start position:0% +specify concurrency +your program and each thread implements + + align:start position:0% +your program and each thread implements + + + align:start position:0% +your program and each thread implements +an abstraction of a processor and these + + align:start position:0% +an abstraction of a processor and these + + + align:start position:0% +an abstraction of a processor and these +threads are then multiplex onto the + + align:start position:0% +threads are then multiplex onto the + + + align:start position:0% +threads are then multiplex onto the +actual machine resources so the number + + align:start position:0% +actual machine resources so the number + + + align:start position:0% +actual machine resources so the number +of threads that you create doesn't + + align:start position:0% +of threads that you create doesn't + + + align:start position:0% +of threads that you create doesn't +necessarily have to match the number of + + align:start position:0% +necessarily have to match the number of + + + align:start position:0% +necessarily have to match the number of +processors you have on your machine so + + align:start position:0% +processors you have on your machine so + + + align:start position:0% +processors you have on your machine so +if you have more threads than the number + + align:start position:0% +if you have more threads than the number + + + align:start position:0% +if you have more threads than the number +of processors you have then they'll just + + align:start position:0% +of processors you have then they'll just + + + align:start position:0% +of processors you have then they'll just +be multiplexing so you can actually run + + align:start position:0% +be multiplexing so you can actually run + + + align:start position:0% +be multiplexing so you can actually run +a pthreads program on a single single + + align:start position:0% +a pthreads program on a single single + + + align:start position:0% +a pthreads program on a single single +core even though you have multiple + + align:start position:0% +core even though you have multiple + + + align:start position:0% +core even though you have multiple +threads in the program they would just + + align:start position:0% +threads in the program they would just + + + align:start position:0% +threads in the program they would just +be time sharing all the threads + + align:start position:0% +be time sharing all the threads + + + align:start position:0% +be time sharing all the threads +communicate through shared memory so + + align:start position:0% +communicate through shared memory so + + + align:start position:0% +communicate through shared memory so +they all have access to the same view of + + align:start position:0% +they all have access to the same view of + + + align:start position:0% +they all have access to the same view of +the memory and the library functions + + align:start position:0% +the memory and the library functions + + + align:start position:0% +the memory and the library functions +that pthreads provides mask the + + align:start position:0% +that pthreads provides mask the + + + align:start position:0% +that pthreads provides mask the +protocols involved in inner thread + + align:start position:0% +protocols involved in inner thread + + + align:start position:0% +protocols involved in inner thread +coordination so you don't have to do it + + align:start position:0% +coordination so you don't have to do it + + + align:start position:0% +coordination so you don't have to do it +yourself because it turns out that this + + align:start position:0% +yourself because it turns out that this + + + align:start position:0% +yourself because it turns out that this +is quite difficult to do correctly by + + align:start position:0% +is quite difficult to do correctly by + + + align:start position:0% +is quite difficult to do correctly by +hand so now I want to look at the key P + + align:start position:0% +hand so now I want to look at the key P + + + align:start position:0% +hand so now I want to look at the key P +thread functions so the first P thread + + align:start position:0% +thread functions so the first P thread + + + align:start position:0% +thread functions so the first P thread +function is pthread create and this + + align:start position:0% +function is pthread create and this + + + align:start position:0% +function is pthread create and this +takes four arguments so the first + + align:start position:0% +takes four arguments so the first + + + align:start position:0% +takes four arguments so the first +argument is this a P thread underscore T + + align:start position:0% +argument is this a P thread underscore T + + + align:start position:0% +argument is this a P thread underscore T +type this is this is basically going to + + align:start position:0% +type this is this is basically going to + + + align:start position:0% +type this is this is basically going to +store and identify for the new thread + + align:start position:0% +store and identify for the new thread + + + align:start position:0% +store and identify for the new thread +that pthread create will create so that + + align:start position:0% +that pthread create will create so that + + + align:start position:0% +that pthread create will create so that +we can use that thread in our + + align:start position:0% +we can use that thread in our + + + align:start position:0% +we can use that thread in our +computations P thread attribute T decide + + align:start position:0% +computations P thread attribute T decide + + + align:start position:0% +computations P thread attribute T decide +some thread attributes and for our + + align:start position:0% +some thread attributes and for our + + + align:start position:0% +some thread attributes and for our +purposes we can just set it to null and + + align:start position:0% +purposes we can just set it to null and + + + align:start position:0% +purposes we can just set it to null and +use the default attributes the third + + align:start position:0% +use the default attributes the third + + + align:start position:0% +use the default attributes the third +argument is this function that's going + + align:start position:0% +argument is this function that's going + + + align:start position:0% +argument is this function that's going +to be executed after we create the + + align:start position:0% +to be executed after we create the + + + align:start position:0% +to be executed after we create the +thread so we're going to need to define + + align:start position:0% +thread so we're going to need to define + + + align:start position:0% +thread so we're going to need to define +this function that we want the thread to + + align:start position:0% +this function that we want the thread to + + + align:start position:0% +this function that we want the thread to +execute and then finally we have this + + align:start position:0% +execute and then finally we have this + + + align:start position:0% +execute and then finally we have this +void star argue arg argument which + + align:start position:0% +void star argue arg argument which + + + align:start position:0% +void star argue arg argument which +stores the arguments that are going to + + align:start position:0% +stores the arguments that are going to + + + align:start position:0% +stores the arguments that are going to +be passed to the function that we're + + align:start position:0% +be passed to the function that we're + + + align:start position:0% +be passed to the function that we're +going to be executing and then pthread + + align:start position:0% +going to be executing and then pthread + + + align:start position:0% +going to be executing and then pthread +create also returns an error status + + align:start position:0% +create also returns an error status + + + align:start position:0% +create also returns an error status +returns an integer specifying whether + + align:start position:0% +returns an integer specifying whether + + + align:start position:0% +returns an integer specifying whether +the thread creation was successful or + + align:start position:0% +the thread creation was successful or + + + align:start position:0% +the thread creation was successful or +not and then there's another + + align:start position:0% +not and then there's another + + + align:start position:0% +not and then there's another +function called pthread join pthread + + align:start position:0% +function called pthread join pthread + + + align:start position:0% +function called pthread join pthread +join basically says that we want to + + align:start position:0% +join basically says that we want to + + + align:start position:0% +join basically says that we want to +block at this part of our code until all + + align:start position:0% +block at this part of our code until all + + + align:start position:0% +block at this part of our code until all +the until so until this specified thread + + align:start position:0% +the until so until this specified thread + + + align:start position:0% +the until so until this specified thread +finishes so it takes us argument + + align:start position:0% +finishes so it takes us argument + + + align:start position:0% +finishes so it takes us argument +pthread underscore t so this thread + + align:start position:0% +pthread underscore t so this thread + + + align:start position:0% +pthread underscore t so this thread +identifier and these thread identifiers + + align:start position:0% +identifier and these thread identifiers + + + align:start position:0% +identifier and these thread identifiers +were created when we call p thread + + align:start position:0% +were created when we call p thread + + + align:start position:0% +were created when we call p thread +pthread create also has the second + + align:start position:0% +pthread create also has the second + + + align:start position:0% +pthread create also has the second +argument status which is going to store + + align:start position:0% +argument status which is going to store + + + align:start position:0% +argument status which is going to store +the status of the terminating thread and + + align:start position:0% +the status of the terminating thread and + + + align:start position:0% +the status of the terminating thread and +that p thread join also returns an error + + align:start position:0% +that p thread join also returns an error + + + align:start position:0% +that p thread join also returns an error +status so essentially what this does is + + align:start position:0% +status so essentially what this does is + + + align:start position:0% +status so essentially what this does is +says to wait until there's threat + + align:start position:0% +says to wait until there's threat + + + align:start position:0% +says to wait until there's threat +finishes before we continue on in our + + align:start position:0% +finishes before we continue on in our + + + align:start position:0% +finishes before we continue on in our +program so any any questions so far + + align:start position:0% + + + + align:start position:0% + +ok so here's what the implementation of + + align:start position:0% +ok so here's what the implementation of + + + align:start position:0% +ok so here's what the implementation of +Fibonacci looks like using P threads so + + align:start position:0% +Fibonacci looks like using P threads so + + + align:start position:0% +Fibonacci looks like using P threads so +on the Left we see the original program + + align:start position:0% +on the Left we see the original program + + + align:start position:0% +on the Left we see the original program +that we had the fib function there + + align:start position:0% +that we had the fib function there + + + align:start position:0% +that we had the fib function there +that's just the sequential code and then + + align:start position:0% +that's just the sequential code and then + + + align:start position:0% +that's just the sequential code and then +we have all this other stuff to enable + + align:start position:0% +we have all this other stuff to enable + + + align:start position:0% +we have all this other stuff to enable +it to run in parallel so first we have + + align:start position:0% +it to run in parallel so first we have + + + align:start position:0% +it to run in parallel so first we have +this struct on the left thread args this + + align:start position:0% +this struct on the left thread args this + + + align:start position:0% +this struct on the left thread args this +struct here is used to store the + + align:start position:0% +struct here is used to store the + + + align:start position:0% +struct here is used to store the +arguments that are passed to the + + align:start position:0% +arguments that are passed to the + + + align:start position:0% +arguments that are passed to the +function that the thread is going to + + align:start position:0% +function that the thread is going to + + + align:start position:0% +function that the thread is going to +execute and then we have this thread + + align:start position:0% +execute and then we have this thread + + + align:start position:0% +execute and then we have this thread +func what that does is it it reads the + + align:start position:0% +func what that does is it it reads the + + + align:start position:0% +func what that does is it it reads the +input argument from this thread args + + align:start position:0% +input argument from this thread args + + + align:start position:0% +input argument from this thread args +struct and then it sets that to I and + + align:start position:0% +struct and then it sets that to I and + + + align:start position:0% +struct and then it sets that to I and +then it calls fib of I and that gives + + align:start position:0% +then it calls fib of I and that gives + + + align:start position:0% +then it calls fib of I and that gives +you the output and then we store the + + align:start position:0% +you the output and then we store the + + + align:start position:0% +you the output and then we store the +result into the output of the struct and + + align:start position:0% +result into the output of the struct and + + + align:start position:0% +result into the output of the struct and +then that also just returns null and + + align:start position:0% +then that also just returns null and + + + align:start position:0% +then that also just returns null and +then over on the right hand side we have + + align:start position:0% +then over on the right hand side we have + + + align:start position:0% +then over on the right hand side we have +the main function that will actually + + align:start position:0% +the main function that will actually + + + align:start position:0% +the main function that will actually +call the fib function on the left so we + + align:start position:0% +call the fib function on the left so we + + + align:start position:0% +call the fib function on the left so we +initialize a whole bunch of variables + + align:start position:0% +initialize a whole bunch of variables + + + align:start position:0% +initialize a whole bunch of variables +that we need for + + align:start position:0% +that we need for + + + align:start position:0% +that we need for +to execute these threads and then we + + align:start position:0% +to execute these threads and then we + + + align:start position:0% +to execute these threads and then we +first check if n is less than 30 if n is + + align:start position:0% +first check if n is less than 30 if n is + + + align:start position:0% +first check if n is less than 30 if n is +less than 30 it turns out that it's + + align:start position:0% +less than 30 it turns out that it's + + + align:start position:0% +less than 30 it turns out that it's +actually not worse + + align:start position:0% +actually not worse + + + align:start position:0% +actually not worse +creating threats to execute this program + + align:start position:0% +creating threats to execute this program + + + align:start position:0% +creating threats to execute this program +in parallel because of the overhead of + + align:start position:0% +in parallel because of the overhead of + + + align:start position:0% +in parallel because of the overhead of +thread creation so if n is less than 30 + + align:start position:0% +thread creation so if n is less than 30 + + + align:start position:0% +thread creation so if n is less than 30 +we'll just execute the program + + align:start position:0% +we'll just execute the program + + + align:start position:0% +we'll just execute the program +sequentially and this idea is known as + + align:start position:0% +sequentially and this idea is known as + + + align:start position:0% +sequentially and this idea is known as +coarsening so you saw a similar example + + align:start position:0% +coarsening so you saw a similar example + + + align:start position:0% +coarsening so you saw a similar example +couple lectures ago when we did + + align:start position:0% +couple lectures ago when we did + + + align:start position:0% +couple lectures ago when we did +coarsening for sorting but this is in + + align:start position:0% +coarsening for sorting but this is in + + + align:start position:0% +coarsening for sorting but this is in +the context of parallel program so here + + align:start position:0% +the context of parallel program so here + + + align:start position:0% +the context of parallel program so here +because there are some overheads to + + align:start position:0% +because there are some overheads to + + + align:start position:0% +because there are some overheads to +running function parallel if the input + + align:start position:0% +running function parallel if the input + + + align:start position:0% +running function parallel if the input +size is small enough sometimes you want + + align:start position:0% +size is small enough sometimes you want + + + align:start position:0% +size is small enough sometimes you want +to just execute it sequentially and then + + align:start position:0% +to just execute it sequentially and then + + + align:start position:0% +to just execute it sequentially and then +we're going to okay so let me just walk + + align:start position:0% +we're going to okay so let me just walk + + + align:start position:0% +we're going to okay so let me just walk +through this code since have an + + align:start position:0% +through this code since have an + + + align:start position:0% +through this code since have an +animation okay so the next thing it's + + align:start position:0% +animation okay so the next thing it's + + + align:start position:0% +animation okay so the next thing it's +going to do is it's going to marshal the + + align:start position:0% +going to do is it's going to marshal the + + + align:start position:0% +going to do is it's going to marshal the +input argument to the threat so it's + + align:start position:0% +input argument to the threat so it's + + + align:start position:0% +input argument to the threat so it's +going to store the input argument n + + align:start position:0% +going to store the input argument n + + + align:start position:0% +going to store the input argument n +minus 1 in this args struct and then + + align:start position:0% +minus 1 in this args struct and then + + + align:start position:0% +minus 1 in this args struct and then +we're gonna call pthread create with a + + align:start position:0% +we're gonna call pthread create with a + + + align:start position:0% +we're gonna call pthread create with a +thread variable for thread arts we're + + align:start position:0% +thread variable for thread arts we're + + + align:start position:0% +thread variable for thread arts we're +just gonna use null and then we're gonna + + align:start position:0% +just gonna use null and then we're gonna + + + align:start position:0% +just gonna use null and then we're gonna +pass the thread func that we defined on + + align:start position:0% +pass the thread func that we defined on + + + align:start position:0% +pass the thread func that we defined on +the left and then we're going to pass + + align:start position:0% +the left and then we're going to pass + + + align:start position:0% +the left and then we're going to pass +the args structure and in inside this + + align:start position:0% +the args structure and in inside this + + + align:start position:0% +the args structure and in inside this +arc structure the input is set to n + + align:start position:0% +arc structure the input is set to n + + + align:start position:0% +arc structure the input is set to n +minus 1 which we did on the previous + + align:start position:0% +minus 1 which we did on the previous + + + align:start position:0% +minus 1 which we did on the previous +line okay and then pthread create is + + align:start position:0% +line okay and then pthread create is + + + align:start position:0% +line okay and then pthread create is +going to it's going to give a return + + align:start position:0% +going to it's going to give a return + + + align:start position:0% +going to it's going to give a return +value so if if the P thread creation was + + align:start position:0% +value so if if the P thread creation was + + + align:start position:0% +value so if if the P thread creation was +successful then the status is going to + + align:start position:0% +successful then the status is going to + + + align:start position:0% +successful then the status is going to +be no and we can continue and if that + + align:start position:0% +be no and we can continue and if that + + + align:start position:0% +be no and we can continue and if that +and when we continue we're going to + + align:start position:0% +and when we continue we're going to + + + align:start position:0% +and when we continue we're going to +execute now fib of n minus 2 and store + + align:start position:0% +execute now fib of n minus 2 and store + + + align:start position:0% +execute now fib of n minus 2 and store +the result of that into our result + + align:start position:0% +the result of that into our result + + + align:start position:0% +the result of that into our result +variable and this is done at the same + + align:start position:0% +variable and this is done at the same + + + align:start position:0% +variable and this is done at the same +time that fib of n minus 1 is executing + + align:start position:0% +time that fib of n minus 1 is executing + + + align:start position:0% +time that fib of n minus 1 is executing +because we created this P thread and we + + align:start position:0% +because we created this P thread and we + + + align:start position:0% +because we created this P thread and we +told it to call this thread func + + align:start position:0% +told it to call this thread func + + + align:start position:0% +told it to call this thread func +function that we defined on the left so + + align:start position:0% +function that we defined on the left so + + + align:start position:0% +function that we defined on the left so +fib of n minus 1 and fib of n minus 2 + + align:start position:0% +fib of n minus 1 and fib of n minus 2 + + + align:start position:0% +fib of n minus 1 and fib of n minus 2 +are executing in parallel now and then + + align:start position:0% +are executing in parallel now and then + + + align:start position:0% +are executing in parallel now and then +we have this pthread join which says + + align:start position:0% +we have this pthread join which says + + + align:start position:0% +we have this pthread join which says +we're going to wait until the thread + + align:start position:0% +we're going to wait until the thread + + + align:start position:0% +we're going to wait until the thread +that we created finishes before we move + + align:start position:0% +that we created finishes before we move + + + align:start position:0% +that we created finishes before we move +on because we need to know the result of + + align:start position:0% +on because we need to know the result of + + + align:start position:0% +on because we need to know the result of +both of the sub calls before we can + + align:start position:0% +both of the sub calls before we can + + + align:start position:0% +both of the sub calls before we can +finish this function and once that's + + align:start position:0% +finish this function and once that's + + + align:start position:0% +finish this function and once that's +done well we first check the status to + + align:start position:0% +done well we first check the status to + + + align:start position:0% +done well we first check the status to +see if it was successful and if so then + + align:start position:0% +see if it was successful and if so then + + + align:start position:0% +see if it was successful and if so then +we add the outputs of the arguments + + align:start position:0% +we add the outputs of the arguments + + + align:start position:0% +we add the outputs of the arguments +truck to the results so arg star output + + align:start position:0% +truck to the results so arg star output + + + align:start position:0% +truck to the results so arg star output +will store the output of fib of n minus + + align:start position:0% +will store the output of fib of n minus + + + align:start position:0% +will store the output of fib of n minus +1 so that's the that's the pthreads code + + align:start position:0% +1 so that's the that's the pthreads code + + + align:start position:0% +1 so that's the that's the pthreads code +any questions on how this works yeah + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +yeah so this is because the pthread + + align:start position:0% +yeah so this is because the pthread + + + align:start position:0% +yeah so this is because the pthread +create function takes as input void star + + align:start position:0% +create function takes as input void star + + + align:start position:0% +create function takes as input void star +pointer because it's actually a generic + + align:start position:0% +pointer because it's actually a generic + + + align:start position:0% +pointer because it's actually a generic +function so it doesn't know what the + + align:start position:0% +function so it doesn't know what the + + + align:start position:0% +function so it doesn't know what the +data type is it has to work for all data + + align:start position:0% +data type is it has to work for all data + + + align:start position:0% +data type is it has to work for all data +types and that's why we need to cast it + + align:start position:0% +types and that's why we need to cast it + + + align:start position:0% +types and that's why we need to cast it +to void star when we pass it the pthread + + align:start position:0% +to void star when we pass it the pthread + + + align:start position:0% +to void star when we pass it the pthread +create and then inside the thread func + + align:start position:0% +create and then inside the thread func + + + align:start position:0% +create and then inside the thread func +we actually do know what type of pointer + + align:start position:0% +we actually do know what type of pointer + + + align:start position:0% +we actually do know what type of pointer +that is so then we cast it yeah so does + + align:start position:0% +that is so then we cast it yeah so does + + + align:start position:0% +that is so then we cast it yeah so does +this code seem very parallel so how many + + align:start position:0% +this code seem very parallel so how many + + + align:start position:0% +this code seem very parallel so how many +parallel calls am i doing here yeah + + align:start position:0% + + + + align:start position:0% + +yeah so I'm only creating one threat so + + align:start position:0% +yeah so I'm only creating one threat so + + + align:start position:0% +yeah so I'm only creating one threat so +I'm executing two things in parallel so + + align:start position:0% +I'm executing two things in parallel so + + + align:start position:0% +I'm executing two things in parallel so +if I ran this code on four processors + + align:start position:0% +if I ran this code on four processors + + + align:start position:0% +if I ran this code on four processors +what's the maximum speed-up I could get + + align:start position:0% +what's the maximum speed-up I could get + + + align:start position:0% +what's the maximum speed-up I could get +so maximum speed-up I can get is just + + align:start position:0% +so maximum speed-up I can get is just + + + align:start position:0% +so maximum speed-up I can get is just +two because I'm only creating I'm only + + align:start position:0% +two because I'm only creating I'm only + + + align:start position:0% +two because I'm only creating I'm only +running two things in parallel so this + + align:start position:0% +running two things in parallel so this + + + align:start position:0% +running two things in parallel so this +doesn't recursively create threads only + + align:start position:0% +doesn't recursively create threads only + + + align:start position:0% +doesn't recursively create threads only +creates threads at the it only creates + + align:start position:0% +creates threads at the it only creates + + + align:start position:0% +creates threads at the it only creates +one thread at the top level and if you + + align:start position:0% +one thread at the top level and if you + + + align:start position:0% +one thread at the top level and if you +wanted to make make it so that this code + + align:start position:0% +wanted to make make it so that this code + + + align:start position:0% +wanted to make make it so that this code +actually recursively created threads it + + align:start position:0% +actually recursively created threads it + + + align:start position:0% +actually recursively created threads it +would actually become much more + + align:start position:0% +would actually become much more + + + align:start position:0% +would actually become much more +complicated and that's one of the + + align:start position:0% +complicated and that's one of the + + + align:start position:0% +complicated and that's one of the +disadvantages of implementing this code + + align:start position:0% +disadvantages of implementing this code + + + align:start position:0% +disadvantages of implementing this code +in P threads so we'll look at other + + align:start position:0% +in P threads so we'll look at other + + + align:start position:0% +in P threads so we'll look at other +solutions that will make this task much + + align:start position:0% +solutions that will make this task much + + + align:start position:0% +solutions that will make this task much +easier so some of the issues with P + + align:start position:0% +easier so some of the issues with P + + + align:start position:0% +easier so some of the issues with P +threads are shown on this slide here so + + align:start position:0% +threads are shown on this slide here so + + + align:start position:0% +threads are shown on this slide here so +there's a high overhead to creating a + + align:start position:0% +there's a high overhead to creating a + + + align:start position:0% +there's a high overhead to creating a +thread so creating a thread typically + + align:start position:0% +thread so creating a thread typically + + + align:start position:0% +thread so creating a thread typically +takes over 10 to the 4/4 cycles and this + + align:start position:0% +takes over 10 to the 4/4 cycles and this + + + align:start position:0% +takes over 10 to the 4/4 cycles and this +leads to very coarse-grained concurrency + + align:start position:0% +leads to very coarse-grained concurrency + + + align:start position:0% +leads to very coarse-grained concurrency +because your tasks have to do a lot of + + align:start position:0% +because your tasks have to do a lot of + + + align:start position:0% +because your tasks have to do a lot of +work in order to amortize the cost of + + align:start position:0% +work in order to amortize the cost of + + + align:start position:0% +work in order to amortize the cost of +creating that thread there are something + + align:start position:0% +creating that thread there are something + + + align:start position:0% +creating that thread there are something +called thread pools which can help and + + align:start position:0% +called thread pools which can help and + + + align:start position:0% +called thread pools which can help and +the idea here is to create a whole bunch + + align:start position:0% +the idea here is to create a whole bunch + + + align:start position:0% +the idea here is to create a whole bunch +of threads at the same time to amortize + + align:start position:0% +of threads at the same time to amortize + + + align:start position:0% +of threads at the same time to amortize +the cost of thread creation and then + + align:start position:0% +the cost of thread creation and then + + + align:start position:0% +the cost of thread creation and then +when you need a thread you just take one + + align:start position:0% +when you need a thread you just take one + + + align:start position:0% +when you need a thread you just take one +from the thread pool so the thread pool + + align:start position:0% +from the thread pool so the thread pool + + + align:start position:0% +from the thread pool so the thread pool +contains threads that are just waiting + + align:start position:0% +contains threads that are just waiting + + + align:start position:0% +contains threads that are just waiting +to do work there's also a scalability + + align:start position:0% +to do work there's also a scalability + + + align:start position:0% +to do work there's also a scalability +issue with this code that I showed on + + align:start position:0% +issue with this code that I showed on + + + align:start position:0% +issue with this code that I showed on +the previous slide the Fibonacci code + + align:start position:0% +the previous slide the Fibonacci code + + + align:start position:0% +the previous slide the Fibonacci code +gets at most one point five x speed-up + + align:start position:0% +gets at most one point five x speed-up + + + align:start position:0% +gets at most one point five x speed-up +for two cores why is it one point five + + align:start position:0% +for two cores why is it one point five + + + align:start position:0% +for two cores why is it one point five +here does anyone know yeah + + align:start position:0% +here does anyone know yeah + + + align:start position:0% + +yeah so it turns out that the two the + + align:start position:0% +yeah so it turns out that the two the + + + align:start position:0% +yeah so it turns out that the two the +two calls and I'm executing in parallel + + align:start position:0% +two calls and I'm executing in parallel + + + align:start position:0% +two calls and I'm executing in parallel +they're not doing the same amount of + + align:start position:0% +they're not doing the same amount of + + + align:start position:0% +they're not doing the same amount of +work so one is computing fib of n minus + + align:start position:0% +work so one is computing fib of n minus + + + align:start position:0% +work so one is computing fib of n minus +one one is computing fib of n minus twos + + align:start position:0% +one one is computing fib of n minus twos + + + align:start position:0% +one one is computing fib of n minus twos +and does anyone know what the ratio + + align:start position:0% +and does anyone know what the ratio + + + align:start position:0% +and does anyone know what the ratio +between these two values is yeah so it's + + align:start position:0% +between these two values is yeah so it's + + + align:start position:0% +between these two values is yeah so it's +the golden ratio it's about 1.6 it turns + + align:start position:0% +the golden ratio it's about 1.6 it turns + + + align:start position:0% +the golden ratio it's about 1.6 it turns +out that if you can get a speed-up of + + align:start position:0% +out that if you can get a speed-up of + + + align:start position:0% +out that if you can get a speed-up of +1.6 and that's great but there are some + + align:start position:0% +1.6 and that's great but there are some + + + align:start position:0% +1.6 and that's great but there are some +overheads so this code will get about a + + align:start position:0% +overheads so this code will get about a + + + align:start position:0% +overheads so this code will get about a +1.5 speed-up and if you want to run this + + align:start position:0% +1.5 speed-up and if you want to run this + + + align:start position:0% +1.5 speed-up and if you want to run this +to take at the edge of more course and + + align:start position:0% +to take at the edge of more course and + + + align:start position:0% +to take at the edge of more course and +you need to rewrite this code and it + + align:start position:0% +you need to rewrite this code and it + + + align:start position:0% +you need to rewrite this code and it +becomes more complicated third there's + + align:start position:0% +becomes more complicated third there's + + + align:start position:0% +becomes more complicated third there's +the issue of modularity so if you look + + align:start position:0% +the issue of modularity so if you look + + + align:start position:0% +the issue of modularity so if you look +at this code here you see that the + + align:start position:0% +at this code here you see that the + + + align:start position:0% +at this code here you see that the +Fibonacci logic is not nicely + + align:start position:0% +Fibonacci logic is not nicely + + + align:start position:0% +Fibonacci logic is not nicely +encapsulated within one function we have + + align:start position:0% +encapsulated within one function we have + + + align:start position:0% +encapsulated within one function we have +that logic in the function on the left + + align:start position:0% +that logic in the function on the left + + + align:start position:0% +that logic in the function on the left +but then we also have some of the fib + + align:start position:0% +but then we also have some of the fib + + + align:start position:0% +but then we also have some of the fib +logic on the right in our main function + + align:start position:0% +logic on the right in our main function + + + align:start position:0% +logic on the right in our main function +and this makes it this makes this code + + align:start position:0% +and this makes it this makes this code + + + align:start position:0% +and this makes it this makes this code +not modular and if we if we want to + + align:start position:0% +not modular and if we if we want to + + + align:start position:0% +not modular and if we if we want to +build programs on top of this it makes + + align:start position:0% +build programs on top of this it makes + + + align:start position:0% +build programs on top of this it makes +it very hard to maintain if we want to + + align:start position:0% +it very hard to maintain if we want to + + + align:start position:0% +it very hard to maintain if we want to +just change the logic of the Fibonacci + + align:start position:0% +just change the logic of the Fibonacci + + + align:start position:0% +just change the logic of the Fibonacci +function a little bit because now we + + align:start position:0% +function a little bit because now we + + + align:start position:0% +function a little bit because now we +have to change it in multiple places + + align:start position:0% +have to change it in multiple places + + + align:start position:0% +have to change it in multiple places +instead of just having everything in one + + align:start position:0% +instead of just having everything in one + + + align:start position:0% +instead of just having everything in one +place so it's not a good idea to write + + align:start position:0% +place so it's not a good idea to write + + + align:start position:0% +place so it's not a good idea to write +code that's not modular so please don't + + align:start position:0% +code that's not modular so please don't + + + align:start position:0% +code that's not modular so please don't +do it do that in your projects okay and + + align:start position:0% +do it do that in your projects okay and + + + align:start position:0% +do it do that in your projects okay and +then finally the code becomes + + align:start position:0% +then finally the code becomes + + + align:start position:0% +then finally the code becomes +complicated because you have to actually + + align:start position:0% +complicated because you have to actually + + + align:start position:0% +complicated because you have to actually +move these arguments around that's known + + align:start position:0% +move these arguments around that's known + + + align:start position:0% +move these arguments around that's known +as argument marshalling and then you + + align:start position:0% +as argument marshalling and then you + + + align:start position:0% +as argument marshalling and then you +have to engage in error-prone protocols + + align:start position:0% +have to engage in error-prone protocols + + + align:start position:0% +have to engage in error-prone protocols +in order to do load balancing so if you + + align:start position:0% +in order to do load balancing so if you + + + align:start position:0% +in order to do load balancing so if you +recall here we have to actually place + + align:start position:0% +recall here we have to actually place + + + align:start position:0% +recall here we have to actually place +the argument n minus 1 into into our dot + + align:start position:0% +the argument n minus 1 into into our dot + + + align:start position:0% +the argument n minus 1 into into our dot +input and we have to extract the value + + align:start position:0% +input and we have to extract the value + + + align:start position:0% +input and we have to extract the value +out of Arts dot output so that makes the + + align:start position:0% +out of Arts dot output so that makes the + + + align:start position:0% +out of Arts dot output so that makes the +code very messy + + align:start position:0% + + + + align:start position:0% + +so why do I say shades of 1958 here + + align:start position:0% +so why do I say shades of 1958 here + + + align:start position:0% +so why do I say shades of 1958 here +suddenly one no what what happened in + + align:start position:0% +suddenly one no what what happened in + + + align:start position:0% +suddenly one no what what happened in +1958 who is around in 1958 Jess Charles + + align:start position:0% + + + + align:start position:0% + +so there is a first something in 1958 + + align:start position:0% +so there is a first something in 1958 + + + align:start position:0% +so there is a first something in 1958 +what was it so turns out in 1958 we had + + align:start position:0% +what was it so turns out in 1958 we had + + + align:start position:0% +what was it so turns out in 1958 we had +the first compiler and this was the + + align:start position:0% +the first compiler and this was the + + + align:start position:0% +the first compiler and this was the +Fortran compiler and before we had the + + align:start position:0% +Fortran compiler and before we had the + + + align:start position:0% +Fortran compiler and before we had the +fortune compiler programmers were + + align:start position:0% +fortune compiler programmers were + + + align:start position:0% +fortune compiler programmers were +writing things in assembly and when you + + align:start position:0% +writing things in assembly and when you + + + align:start position:0% +writing things in assembly and when you +write things in assembly you have to do + + align:start position:0% +write things in assembly you have to do + + + align:start position:0% +write things in assembly you have to do +argument argument marshalling because + + align:start position:0% +argument argument marshalling because + + + align:start position:0% +argument argument marshalling because +you have to place things into the + + align:start position:0% +you have to place things into the + + + align:start position:0% +you have to place things into the +appropriate registers before calling a + + align:start position:0% +appropriate registers before calling a + + + align:start position:0% +appropriate registers before calling a +function and also move things around + + align:start position:0% +function and also move things around + + + align:start position:0% +function and also move things around +when you return from a function and the + + align:start position:0% +when you return from a function and the + + + align:start position:0% +when you return from a function and the +nice thing about the first compiler is + + align:start position:0% +nice thing about the first compiler is + + + align:start position:0% +nice thing about the first compiler is +that it actually did all of this + + align:start position:0% +that it actually did all of this + + + align:start position:0% +that it actually did all of this +argument marshalling for you so now you + + align:start position:0% +argument marshalling for you so now you + + + align:start position:0% +argument marshalling for you so now you +can just pass arguments to a function + + align:start position:0% +can just pass arguments to a function + + + align:start position:0% +can just pass arguments to a function +and the compiler will generate code that + + align:start position:0% +and the compiler will generate code that + + + align:start position:0% +and the compiler will generate code that +will do the argument marshalling for for + + align:start position:0% +will do the argument marshalling for for + + + align:start position:0% +will do the argument marshalling for for +us so having you do this in P threads is + + align:start position:0% +us so having you do this in P threads is + + + align:start position:0% +us so having you do this in P threads is +similar to having to write code in + + align:start position:0% +similar to having to write code in + + + align:start position:0% +similar to having to write code in +assembly because you have to actually + + align:start position:0% +assembly because you have to actually + + + align:start position:0% +assembly because you have to actually +manually marshal these arguments so + + align:start position:0% +manually marshal these arguments so + + + align:start position:0% +manually marshal these arguments so +hopefully there are better ways to do + + align:start position:0% +hopefully there are better ways to do + + + align:start position:0% +hopefully there are better ways to do +this and indeed we'll look at some other + + align:start position:0% +this and indeed we'll look at some other + + + align:start position:0% +this and indeed we'll look at some other +solutions that will make it easier on + + align:start position:0% +solutions that will make it easier on + + + align:start position:0% +solutions that will make it easier on +the programmer any questions before I + + align:start position:0% +the programmer any questions before I + + + align:start position:0% +the programmer any questions before I +continue + + align:start position:0% + + + + align:start position:0% + +all right so we looked at pthreads next + + align:start position:0% +all right so we looked at pthreads next + + + align:start position:0% +all right so we looked at pthreads next +let's look at threading building blocks + + align:start position:0% + + + + align:start position:0% + +so threading building blocks is a + + align:start position:0% +so threading building blocks is a + + + align:start position:0% +so threading building blocks is a +library solution + + align:start position:0% +library solution + + + align:start position:0% +library solution +it was developed by Intel and it's + + align:start position:0% +it was developed by Intel and it's + + + align:start position:0% +it was developed by Intel and it's +implemented as a C++ library that runs + + align:start position:0% +implemented as a C++ library that runs + + + align:start position:0% +implemented as a C++ library that runs +on top of native threads so the + + align:start position:0% +on top of native threads so the + + + align:start position:0% +on top of native threads so the +underlying implementation uses threads + + align:start position:0% +underlying implementation uses threads + + + align:start position:0% +underlying implementation uses threads +but the programmer doesn't deal with + + align:start position:0% +but the programmer doesn't deal with + + + align:start position:0% +but the programmer doesn't deal with +threads instead the programmer specifies + + align:start position:0% +threads instead the programmer specifies + + + align:start position:0% +threads instead the programmer specifies +tasks and these tasks are automatically + + align:start position:0% +tasks and these tasks are automatically + + + align:start position:0% +tasks and these tasks are automatically +load balanced across the threads using a + + align:start position:0% +load balanced across the threads using a + + + align:start position:0% +load balanced across the threads using a +work-stealing algorithm inspired by + + align:start position:0% +work-stealing algorithm inspired by + + + align:start position:0% +work-stealing algorithm inspired by +research at MIT charles license research + + align:start position:0% +research at MIT charles license research + + + align:start position:0% +research at MIT charles license research +in the focus of Intel TBB is on + + align:start position:0% +in the focus of Intel TBB is on + + + align:start position:0% +in the focus of Intel TBB is on +performance and as we'll see the code + + align:start position:0% +performance and as we'll see the code + + + align:start position:0% +performance and as we'll see the code +written using TBB is simpler than what + + align:start position:0% +written using TBB is simpler than what + + + align:start position:0% +written using TBB is simpler than what +you would have to write if you used P + + align:start position:0% +you would have to write if you used P + + + align:start position:0% +you would have to write if you used P +threads so let's look at how we can + + align:start position:0% +threads so let's look at how we can + + + align:start position:0% +threads so let's look at how we can +implement Fibonacci using TBB okay so in + + align:start position:0% +implement Fibonacci using TBB okay so in + + + align:start position:0% +implement Fibonacci using TBB okay so in +TBB we have to create these tasks so in + + align:start position:0% +TBB we have to create these tasks so in + + + align:start position:0% +TBB we have to create these tasks so in +the Fibonacci code we create this v as + + align:start position:0% +the Fibonacci code we create this v as + + + align:start position:0% +the Fibonacci code we create this v as +class and inside the task we have to + + align:start position:0% +class and inside the task we have to + + + align:start position:0% +class and inside the task we have to +define this execute function so the xq + + align:start position:0% +define this execute function so the xq + + + align:start position:0% +define this execute function so the xq +function is a function that performs the + + align:start position:0% +function is a function that performs the + + + align:start position:0% +function is a function that performs the +computation when we start the task and + + align:start position:0% +computation when we start the task and + + + align:start position:0% +computation when we start the task and +this is where we define the Fibonacci + + align:start position:0% +this is where we define the Fibonacci + + + align:start position:0% +this is where we define the Fibonacci +logic this task also takes as input + + align:start position:0% +logic this task also takes as input + + + align:start position:0% +logic this task also takes as input +these arguments parameter and in sum so + + align:start position:0% +these arguments parameter and in sum so + + + align:start position:0% +these arguments parameter and in sum so +and as they input here in sum is the + + align:start position:0% +and as they input here in sum is the + + + align:start position:0% +and as they input here in sum is the +output okay and in T bbbb we can easily + + align:start position:0% +output okay and in T bbbb we can easily + + + align:start position:0% +output okay and in T bbbb we can easily +create a recursive program that extracts + + align:start position:0% +create a recursive program that extracts + + + align:start position:0% +create a recursive program that extracts +more parallelism and here what we're + + align:start position:0% +more parallelism and here what we're + + + align:start position:0% +more parallelism and here what we're +doing is we're recursively creating two + + align:start position:0% +doing is we're recursively creating two + + + align:start position:0% +doing is we're recursively creating two +child tasks a and B that's a syntax for + + align:start position:0% +child tasks a and B that's a syntax for + + + align:start position:0% +child tasks a and B that's a syntax for +creating the task and here we can just + + align:start position:0% +creating the task and here we can just + + + align:start position:0% +creating the task and here we can just +pass two arguments to fib tasks instead + + align:start position:0% +pass two arguments to fib tasks instead + + + align:start position:0% +pass two arguments to fib tasks instead +of marshaling the arguments ourselves + + align:start position:0% +of marshaling the arguments ourselves + + + align:start position:0% +of marshaling the arguments ourselves +and and then what we have here is a set + + align:start position:0% +and and then what we have here is a set + + + align:start position:0% +and and then what we have here is a set +ref count + + align:start position:0% +ref count + + + align:start position:0% +ref count +and this basically is the number of + + align:start position:0% +and this basically is the number of + + + align:start position:0% +and this basically is the number of +casts that we have to wait for plus 1 so + + align:start position:0% +casts that we have to wait for plus 1 so + + + align:start position:0% +casts that we have to wait for plus 1 so +plus one for ourselves and in this case + + align:start position:0% +plus one for ourselves and in this case + + + align:start position:0% +plus one for ourselves and in this case +we create a two children task and we + + align:start position:0% +we create a two children task and we + + + align:start position:0% +we create a two children task and we +have ourselves so that's 2 plus 1 and + + align:start position:0% +have ourselves so that's 2 plus 1 and + + + align:start position:0% +have ourselves so that's 2 plus 1 and +then after that we start has be using + + align:start position:0% +then after that we start has be using + + + align:start position:0% +then after that we start has be using +the spawn be call and then we do spawn + + align:start position:0% +the spawn be call and then we do spawn + + + align:start position:0% +the spawn be call and then we do spawn +and wait for all with a as the argument + + align:start position:0% +and wait for all with a as the argument + + + align:start position:0% +and wait for all with a as the argument +in this place he says we're going to run + + align:start position:0% +in this place he says we're going to run + + + align:start position:0% +in this place he says we're going to run +a start task a and then also wait for + + align:start position:0% +a start task a and then also wait for + + + align:start position:0% +a start task a and then also wait for +both a and B to finish before we proceed + + align:start position:0% +both a and B to finish before we proceed + + + align:start position:0% +both a and B to finish before we proceed +so this spawn and wait for all call is + + align:start position:0% +so this spawn and wait for all call is + + + align:start position:0% +so this spawn and wait for all call is +going to look at the raft count that we + + align:start position:0% +going to look at the raft count that we + + + align:start position:0% +going to look at the raft count that we +set above and wait for that many tasks + + align:start position:0% +set above and wait for that many tasks + + + align:start position:0% +set above and wait for that many tasks +to finish before it continues and then + + align:start position:0% +to finish before it continues and then + + + align:start position:0% +to finish before it continues and then +after after both a and B have completed + + align:start position:0% +after after both a and B have completed + + + align:start position:0% +after after both a and B have completed +then we can just sum up the results and + + align:start position:0% +then we can just sum up the results and + + + align:start position:0% +then we can just sum up the results and +store that in the sum variable and here + + align:start position:0% +store that in the sum variable and here + + + align:start position:0% +store that in the sum variable and here +these tasks are created recursively so + + align:start position:0% +these tasks are created recursively so + + + align:start position:0% +these tasks are created recursively so +unlike the pthreads implementation that + + align:start position:0% +unlike the pthreads implementation that + + + align:start position:0% +unlike the pthreads implementation that +was only creating one thread at the top + + align:start position:0% +was only creating one thread at the top + + + align:start position:0% +was only creating one thread at the top +level here we're actually recursively + + align:start position:0% +level here we're actually recursively + + + align:start position:0% +level here we're actually recursively +creating more and more tasks so we can + + align:start position:0% +creating more and more tasks so we can + + + align:start position:0% +creating more and more tasks so we can +actually get more parallelism from this + + align:start position:0% +actually get more parallelism from this + + + align:start position:0% +actually get more parallelism from this +code and scale to more processors we + + align:start position:0% +code and scale to more processors we + + + align:start position:0% +code and scale to more processors we +also need this main function just to + + align:start position:0% +also need this main function just to + + + align:start position:0% +also need this main function just to +start up the program so what we do here + + align:start position:0% +start up the program so what we do here + + + align:start position:0% +start up the program so what we do here +is we create a root task which just + + align:start position:0% +is we create a root task which just + + + align:start position:0% +is we create a root task which just +computes fib of n and that we call spawn + + align:start position:0% +computes fib of n and that we call spawn + + + align:start position:0% +computes fib of n and that we call spawn +root and weight of a so a is it has for + + align:start position:0% +root and weight of a so a is it has for + + + align:start position:0% +root and weight of a so a is it has for +the root and then it will just run the + + align:start position:0% +the root and then it will just run the + + + align:start position:0% +the root and then it will just run the +root task so that's what T Fibonacci + + align:start position:0% +root task so that's what T Fibonacci + + + align:start position:0% +root task so that's what T Fibonacci +looks like in TBB so this is much + + align:start position:0% +looks like in TBB so this is much + + + align:start position:0% +looks like in TBB so this is much +simpler than the pthreads implementation + + align:start position:0% +simpler than the pthreads implementation + + + align:start position:0% +simpler than the pthreads implementation +and it also gets better performance + + align:start position:0% +and it also gets better performance + + + align:start position:0% +and it also gets better performance +because we can extract more parallelism + + align:start position:0% +because we can extract more parallelism + + + align:start position:0% +because we can extract more parallelism +from from the computation any questions + + align:start position:0% + + + + align:start position:0% + +okay so TBB also has many other features + + align:start position:0% +okay so TBB also has many other features + + + align:start position:0% +okay so TBB also has many other features +in addition to tasks + + align:start position:0% +in addition to tasks + + + align:start position:0% +in addition to tasks +so TBB provides many C++ templates to + + align:start position:0% +so TBB provides many C++ templates to + + + align:start position:0% +so TBB provides many C++ templates to +express common patterns and you can use + + align:start position:0% +express common patterns and you can use + + + align:start position:0% +express common patterns and you can use +these templates on different data types + + align:start position:0% +these templates on different data types + + + align:start position:0% +these templates on different data types +so they have a parallel for which is + + align:start position:0% +so they have a parallel for which is + + + align:start position:0% +so they have a parallel for which is +used to express loop parallelism so you + + align:start position:0% +used to express loop parallelism so you + + + align:start position:0% +used to express loop parallelism so you +can loop over a bunch of iterations in + + align:start position:0% +can loop over a bunch of iterations in + + + align:start position:0% +can loop over a bunch of iterations in +parallel they also have a parallel + + align:start position:0% +parallel they also have a parallel + + + align:start position:0% +parallel they also have a parallel +reduce for data aggregation for example + + align:start position:0% +reduce for data aggregation for example + + + align:start position:0% +reduce for data aggregation for example +if you if you want to sum together a + + align:start position:0% +if you if you want to sum together a + + + align:start position:0% +if you if you want to sum together a +whole bunch of values you can use a + + align:start position:0% +whole bunch of values you can use a + + + align:start position:0% +whole bunch of values you can use a +parallel reduce to do that in parallel + + align:start position:0% +parallel reduce to do that in parallel + + + align:start position:0% +parallel reduce to do that in parallel +they also have a pipeline and filter + + align:start position:0% +they also have a pipeline and filter + + + align:start position:0% +they also have a pipeline and filter +that's used for software pipelining TBB + + align:start position:0% +that's used for software pipelining TBB + + + align:start position:0% +that's used for software pipelining TBB +provides many concurrent container + + align:start position:0% +provides many concurrent container + + + align:start position:0% +provides many concurrent container +classes which allow multiple threats is + + align:start position:0% +classes which allow multiple threats is + + + align:start position:0% +classes which allow multiple threats is +safely access and update the items in + + align:start position:0% +safely access and update the items in + + + align:start position:0% +safely access and update the items in +the container concurrently so for + + align:start position:0% +the container concurrently so for + + + align:start position:0% +the container concurrently so for +example they have hash tables trees + + align:start position:0% +example they have hash tables trees + + + align:start position:0% +example they have hash tables trees +priority queues and so on and you can + + align:start position:0% +priority queues and so on and you can + + + align:start position:0% +priority queues and so on and you can +just use these out-of-the-box and don't + + align:start position:0% +just use these out-of-the-box and don't + + + align:start position:0% +just use these out-of-the-box and don't +work in parallel you can do concurrent + + align:start position:0% +work in parallel you can do concurrent + + + align:start position:0% +work in parallel you can do concurrent +updates and reads to these data + + align:start position:0% +updates and reads to these data + + + align:start position:0% +updates and reads to these data +structures + + align:start position:0% +structures + + + align:start position:0% +structures +TPB also has a variety of mutual + + align:start position:0% +TPB also has a variety of mutual + + + align:start position:0% +TPB also has a variety of mutual +exclusion library functions such as + + align:start position:0% +exclusion library functions such as + + + align:start position:0% +exclusion library functions such as +locks and atomic operations so there are + + align:start position:0% +locks and atomic operations so there are + + + align:start position:0% +locks and atomic operations so there are +a lot of features of TBB which is why is + + align:start position:0% +a lot of features of TBB which is why is + + + align:start position:0% +a lot of features of TBB which is why is +one of the more popular concurrency + + align:start position:0% +one of the more popular concurrency + + + align:start position:0% +one of the more popular concurrency +platforms and because of all of these + + align:start position:0% +platforms and because of all of these + + + align:start position:0% +platforms and because of all of these +features you don't have to implement + + align:start position:0% +features you don't have to implement + + + align:start position:0% +features you don't have to implement +many of these things by yourself and + + align:start position:0% +many of these things by yourself and + + + align:start position:0% +many of these things by yourself and +still get pretty good performance so TBB + + align:start position:0% +still get pretty good performance so TBB + + + align:start position:0% +still get pretty good performance so TBB +was a library solution to the + + align:start position:0% +was a library solution to the + + + align:start position:0% +was a library solution to the +concurrency problem now we're gonna look + + align:start position:0% +concurrency problem now we're gonna look + + + align:start position:0% +concurrency problem now we're gonna look +at two linguistics solutions OpenMP and + + align:start position:0% +at two linguistics solutions OpenMP and + + + align:start position:0% +at two linguistics solutions OpenMP and +silk so start with OpenMP so OpenMP is a + + align:start position:0% +silk so start with OpenMP so OpenMP is a + + + align:start position:0% +silk so start with OpenMP so OpenMP is a +specification by an industry consortium + + align:start position:0% +specification by an industry consortium + + + align:start position:0% +specification by an industry consortium +and there are several compilers + + align:start position:0% +and there are several compilers + + + align:start position:0% +and there are several compilers +available that support OpenMP both open + + align:start position:0% +available that support OpenMP both open + + + align:start position:0% +available that support OpenMP both open +source and proprietary so nowadays GCC + + align:start position:0% +source and proprietary so nowadays GCC + + + align:start position:0% +source and proprietary so nowadays GCC +icc and clang all support OpenMP as well + + align:start position:0% +icc and clang all support OpenMP as well + + + align:start position:0% +icc and clang all support OpenMP as well +as visual studio and openmp is it + + align:start position:0% +as visual studio and openmp is it + + + align:start position:0% +as visual studio and openmp is it +provides linguistic extensions to C and + + align:start position:0% +provides linguistic extensions to C and + + + align:start position:0% +provides linguistic extensions to C and +C++ as well as Fortran and + + align:start position:0% +C++ as well as Fortran and + + + align:start position:0% +C++ as well as Fortran and +form of compiler pragmas so you use + + align:start position:0% +form of compiler pragmas so you use + + + align:start position:0% +form of compiler pragmas so you use +these compiler pragmas in your code to + + align:start position:0% +these compiler pragmas in your code to + + + align:start position:0% +these compiler pragmas in your code to +specify which pieces of code should run + + align:start position:0% +specify which pieces of code should run + + + align:start position:0% +specify which pieces of code should run +in parallel and OpenMP also runs on top + + align:start position:0% +in parallel and OpenMP also runs on top + + + align:start position:0% +in parallel and OpenMP also runs on top +of native threads but the programmer + + align:start position:0% +of native threads but the programmer + + + align:start position:0% +of native threads but the programmer +isn't exposed to these threads OpenMP + + align:start position:0% +isn't exposed to these threads OpenMP + + + align:start position:0% +isn't exposed to these threads OpenMP +supports loop parallelism so you can do + + align:start position:0% +supports loop parallelism so you can do + + + align:start position:0% +supports loop parallelism so you can do +parallel for loops + + align:start position:0% +parallel for loops + + + align:start position:0% +parallel for loops +they have task parallelism as well as + + align:start position:0% +they have task parallelism as well as + + + align:start position:0% +they have task parallelism as well as +pipeline parallelism so let's look at + + align:start position:0% +pipeline parallelism so let's look at + + + align:start position:0% +pipeline parallelism so let's look at +how we can implement fibonacci in OpenMP + + align:start position:0% +how we can implement fibonacci in OpenMP + + + align:start position:0% +how we can implement fibonacci in OpenMP +so this is the entire code so I want you + + align:start position:0% +so this is the entire code so I want you + + + align:start position:0% +so this is the entire code so I want you +to compare this to the P threads + + align:start position:0% +to compare this to the P threads + + + align:start position:0% +to compare this to the P threads +implementation that we saw 10 minutes + + align:start position:0% +implementation that we saw 10 minutes + + + align:start position:0% +implementation that we saw 10 minutes +ago so so this code is much cleaner than + + align:start position:0% +ago so so this code is much cleaner than + + + align:start position:0% +ago so so this code is much cleaner than +the P threads implementation it it also + + align:start position:0% +the P threads implementation it it also + + + align:start position:0% +the P threads implementation it it also +performs better so let's see how this + + align:start position:0% +performs better so let's see how this + + + align:start position:0% +performs better so let's see how this +code works so we have these compiler + + align:start position:0% +code works so we have these compiler + + + align:start position:0% +code works so we have these compiler +pragmas or compiler directives and the + + align:start position:0% +pragmas or compiler directives and the + + + align:start position:0% +pragmas or compiler directives and the +compiler pragma for creating a parallel + + align:start position:0% +compiler pragma for creating a parallel + + + align:start position:0% +compiler pragma for creating a parallel +task is a OMP task so we're gonna create + + align:start position:0% +task is a OMP task so we're gonna create + + + align:start position:0% +task is a OMP task so we're gonna create +a openmp task for faileth n minus 1 as + + align:start position:0% +a openmp task for faileth n minus 1 as + + + align:start position:0% +a openmp task for faileth n minus 1 as +well it's a Fablab n minus 2 there's + + align:start position:0% +well it's a Fablab n minus 2 there's + + + align:start position:0% +well it's a Fablab n minus 2 there's +also this yeah there's also this shared + + align:start position:0% +also this yeah there's also this shared + + + align:start position:0% +also this yeah there's also this shared +pragma which specifies that the two + + align:start position:0% +pragma which specifies that the two + + + align:start position:0% +pragma which specifies that the two +variables in the arguments are shared + + align:start position:0% +variables in the arguments are shared + + + align:start position:0% +variables in the arguments are shared +across different threads so you also + + align:start position:0% +across different threads so you also + + + align:start position:0% +across different threads so you also +have to specify whether variables are + + align:start position:0% +have to specify whether variables are + + + align:start position:0% +have to specify whether variables are +private or shared and then the pragma + + align:start position:0% +private or shared and then the pragma + + + align:start position:0% +private or shared and then the pragma +OMP weight just says we're gonna wait + + align:start position:0% +OMP weight just says we're gonna wait + + + align:start position:0% +OMP weight just says we're gonna wait +for the preceding task to complete + + align:start position:0% +for the preceding task to complete + + + align:start position:0% +for the preceding task to complete +before we continue so here is going to + + align:start position:0% +before we continue so here is going to + + + align:start position:0% +before we continue so here is going to +wait for fib of n minus 1 and fib of n + + align:start position:0% +wait for fib of n minus 1 and fib of n + + + align:start position:0% +wait for fib of n minus 1 and fib of n +minus 2 to finish before we return the + + align:start position:0% +minus 2 to finish before we return the + + + align:start position:0% +minus 2 to finish before we return the +result which is what we want and then + + align:start position:0% +result which is what we want and then + + + align:start position:0% +result which is what we want and then +after that we just returned X plus y so + + align:start position:0% +after that we just returned X plus y so + + + align:start position:0% +after that we just returned X plus y so +that's the entire code + + align:start position:0% + + + + align:start position:0% + +and OpenMP also provides many other + + align:start position:0% +and OpenMP also provides many other + + + align:start position:0% +and OpenMP also provides many other +pragma directives in addition to tasks + + align:start position:0% +pragma directives in addition to tasks + + + align:start position:0% +pragma directives in addition to tasks +so we can use a parallel for to do loop + + align:start position:0% +so we can use a parallel for to do loop + + + align:start position:0% +so we can use a parallel for to do loop +parallelism + + align:start position:0% +parallelism + + + align:start position:0% +parallelism +there's reduction there's also + + align:start position:0% +there's reduction there's also + + + align:start position:0% +there's reduction there's also +directives for scheduling and data + + align:start position:0% +directives for scheduling and data + + + align:start position:0% +directives for scheduling and data +sharing so you can specify how you want + + align:start position:0% +sharing so you can specify how you want + + + align:start position:0% +sharing so you can specify how you want +a particular loop to be scheduled OpenMP + + align:start position:0% +a particular loop to be scheduled OpenMP + + + align:start position:0% +a particular loop to be scheduled OpenMP +has many different scheduling policies + + align:start position:0% +has many different scheduling policies + + + align:start position:0% +has many different scheduling policies +they have static parallelism dynamic + + align:start position:0% +they have static parallelism dynamic + + + align:start position:0% +they have static parallelism dynamic +parallelism and so on and then these + + align:start position:0% +parallelism and so on and then these + + + align:start position:0% +parallelism and so on and then these +scheduling directives also have + + align:start position:0% +scheduling directives also have + + + align:start position:0% +scheduling directives also have +different grain sizes the data sharing + + align:start position:0% +different grain sizes the data sharing + + + align:start position:0% +different grain sizes the data sharing +directives are specifying whether a + + align:start position:0% +directives are specifying whether a + + + align:start position:0% +directives are specifying whether a +variables are private or shared OpenMP + + align:start position:0% +variables are private or shared OpenMP + + + align:start position:0% +variables are private or shared OpenMP +also supplies a variety of + + align:start position:0% +also supplies a variety of + + + align:start position:0% +also supplies a variety of +synchronization constructs such as + + align:start position:0% +synchronization constructs such as + + + align:start position:0% +synchronization constructs such as +barriers atomic updates mutual exclusion + + align:start position:0% +barriers atomic updates mutual exclusion + + + align:start position:0% +barriers atomic updates mutual exclusion +or mutex locks so openmp also has many + + align:start position:0% +or mutex locks so openmp also has many + + + align:start position:0% +or mutex locks so openmp also has many +features and it's also one of the more + + align:start position:0% +features and it's also one of the more + + + align:start position:0% +features and it's also one of the more +popular solutions to writing parallel + + align:start position:0% +popular solutions to writing parallel + + + align:start position:0% +popular solutions to writing parallel +programs and as you saw in the previous + + align:start position:0% +programs and as you saw in the previous + + + align:start position:0% +programs and as you saw in the previous +example the code is much simpler than if + + align:start position:0% +example the code is much simpler than if + + + align:start position:0% +example the code is much simpler than if +you were to write something using + + align:start position:0% +you were to write something using + + + align:start position:0% +you were to write something using +pthreads or even a TVB this is a much + + align:start position:0% +pthreads or even a TVB this is a much + + + align:start position:0% +pthreads or even a TVB this is a much +simpler solution any questions + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +so so this code here is actually + + align:start position:0% +so so this code here is actually + + + align:start position:0% +so so this code here is actually +independent of the number of processors + + align:start position:0% +independent of the number of processors + + + align:start position:0% +independent of the number of processors +so there is actually a scheduling + + align:start position:0% +so there is actually a scheduling + + + align:start position:0% +so there is actually a scheduling +algorithm that will determine how the + + align:start position:0% +algorithm that will determine how the + + + align:start position:0% +algorithm that will determine how the +casket map to different processors so if + + align:start position:0% +casket map to different processors so if + + + align:start position:0% +casket map to different processors so if +you spawned in you test it doesn't + + align:start position:0% +you spawned in you test it doesn't + + + align:start position:0% +you spawned in you test it doesn't +necessarily put it on the different + + align:start position:0% +necessarily put it on the different + + + align:start position:0% +necessarily put it on the different +processor and you can have more tasks + + align:start position:0% +processor and you can have more tasks + + + align:start position:0% +processor and you can have more tasks +than the number of processes available + + align:start position:0% +than the number of processes available + + + align:start position:0% +than the number of processes available +so there's a scheduling algorithm that + + align:start position:0% +so there's a scheduling algorithm that + + + align:start position:0% +so there's a scheduling algorithm that +will take care of how these tasks get + + align:start position:0% +will take care of how these tasks get + + + align:start position:0% +will take care of how these tasks get +mapped to different processors and + + align:start position:0% +mapped to different processors and + + + align:start position:0% +mapped to different processors and +that's hidden from the programmer + + align:start position:0% +that's hidden from the programmer + + + align:start position:0% +that's hidden from the programmer +although you can't use these scheduling + + align:start position:0% +although you can't use these scheduling + + + align:start position:0% +although you can't use these scheduling +pragmas to give hints the compiler how + + align:start position:0% +pragmas to give hints the compiler how + + + align:start position:0% +pragmas to give hints the compiler how +it should schedule it yeah us so I mean + + align:start position:0% +it should schedule it yeah us so I mean + + + align:start position:0% +it should schedule it yeah us so I mean +underneath this is implemented using P + + align:start position:0% +underneath this is implemented using P + + + align:start position:0% +underneath this is implemented using P +threads which has to make operating + + align:start position:0% +threads which has to make operating + + + align:start position:0% +threads which has to make operating +system calls to basically directly talk + + align:start position:0% +system calls to basically directly talk + + + align:start position:0% +system calls to basically directly talk +to the processor cores and do + + align:start position:0% +to the processor cores and do + + + align:start position:0% +to the processor cores and do +multiplexing and so forth so it's the + + align:start position:0% +multiplexing and so forth so it's the + + + align:start position:0% +multiplexing and so forth so it's the +operating system is involved at a very + + align:start position:0% +operating system is involved at a very + + + align:start position:0% +operating system is involved at a very +low level + + align:start position:0% + + + + align:start position:0% + +okay so the last concurrency platform + + align:start position:0% +okay so the last concurrency platform + + + align:start position:0% +okay so the last concurrency platform +that we'll be looking at today is silk + + align:start position:0% + + + + align:start position:0% + +okay so or we're gonna look at so plus + + align:start position:0% +okay so or we're gonna look at so plus + + + align:start position:0% +okay so or we're gonna look at so plus +actually in the silk part of silk plus + + align:start position:0% +actually in the silk part of silk plus + + + align:start position:0% +actually in the silk part of silk plus +is a small set of linguistic extensions + + align:start position:0% +is a small set of linguistic extensions + + + align:start position:0% +is a small set of linguistic extensions +to C and C++ that support for joint + + align:start position:0% +to C and C++ that support for joint + + + align:start position:0% +to C and C++ that support for joint +parallelism so for example the Fibonacci + + align:start position:0% +parallelism so for example the Fibonacci + + + align:start position:0% +parallelism so for example the Fibonacci +example uses fork/join parallelism so + + align:start position:0% +example uses fork/join parallelism so + + + align:start position:0% +example uses fork/join parallelism so +you can use soap to implement that and + + align:start position:0% +you can use soap to implement that and + + + align:start position:0% +you can use soap to implement that and +the plus part of soap Plus supports + + align:start position:0% +the plus part of soap Plus supports + + + align:start position:0% +the plus part of soap Plus supports +vector parallelism which you had + + align:start position:0% +vector parallelism which you had + + + align:start position:0% +vector parallelism which you had +experience working with in your + + align:start position:0% +experience working with in your + + + align:start position:0% +experience working with in your +homeworks so silk was so plus was + + align:start position:0% +homeworks so silk was so plus was + + + align:start position:0% +homeworks so silk was so plus was +initially devolved by silk arts which + + align:start position:0% +initially devolved by silk arts which + + + align:start position:0% +initially devolved by silk arts which +was an MIT spin-off and silk arts was + + align:start position:0% +was an MIT spin-off and silk arts was + + + align:start position:0% +was an MIT spin-off and silk arts was +acquired by Intel in July 2009 and the + + align:start position:0% +acquired by Intel in July 2009 and the + + + align:start position:0% +acquired by Intel in July 2009 and the +so plus implementation is based on award + + align:start position:0% +so plus implementation is based on award + + + align:start position:0% +so plus implementation is based on award +winning based on the award-winning silk + + align:start position:0% +winning based on the award-winning silk + + + align:start position:0% +winning based on the award-winning silk +multi-threaded languished I was + + align:start position:0% +multi-threaded languished I was + + + align:start position:0% +multi-threaded languished I was +developed two decades ago here at MIT by + + align:start position:0% +developed two decades ago here at MIT by + + + align:start position:0% +developed two decades ago here at MIT by +Charles artisans research group and it + + align:start position:0% +Charles artisans research group and it + + + align:start position:0% +Charles artisans research group and it +features a provably efficient work + + align:start position:0% +features a provably efficient work + + + align:start position:0% +features a provably efficient work +stealing scheduler so this schedule is + + align:start position:0% +stealing scheduler so this schedule is + + + align:start position:0% +stealing scheduler so this schedule is +provably efficient you can actually + + align:start position:0% +provably efficient you can actually + + + align:start position:0% +provably efficient you can actually +prove theoretical bounds on it and this + + align:start position:0% +prove theoretical bounds on it and this + + + align:start position:0% +prove theoretical bounds on it and this +allows you to implement theoretically + + align:start position:0% +allows you to implement theoretically + + + align:start position:0% +allows you to implement theoretically +efficient algorithms which we'll talk + + align:start position:0% +efficient algorithms which we'll talk + + + align:start position:0% +efficient algorithms which we'll talk +more about in another lecture algorithm + + align:start position:0% +more about in another lecture algorithm + + + align:start position:0% +more about in another lecture algorithm +design but it provides a provably + + align:start position:0% +design but it provides a provably + + + align:start position:0% +design but it provides a provably +efficient work stealing scheduler and + + align:start position:0% +efficient work stealing scheduler and + + + align:start position:0% +efficient work stealing scheduler and +Charles Larsen has a very famous paper + + align:start position:0% +Charles Larsen has a very famous paper + + + align:start position:0% +Charles Larsen has a very famous paper +that has a proof of that this scheduler + + align:start position:0% +that has a proof of that this scheduler + + + align:start position:0% +that has a proof of that this scheduler +is optimal so if you're interested in + + align:start position:0% +is optimal so if you're interested in + + + align:start position:0% +is optimal so if you're interested in +reading about this you can talk to us + + align:start position:0% +reading about this you can talk to us + + + align:start position:0% +reading about this you can talk to us +offline so plus also provides a hyper + + align:start position:0% +offline so plus also provides a hyper + + + align:start position:0% +offline so plus also provides a hyper +object library for paralyzing code with + + align:start position:0% +object library for paralyzing code with + + + align:start position:0% +object library for paralyzing code with +global variables and you'll have a + + align:start position:0% +global variables and you'll have a + + + align:start position:0% +global variables and you'll have a +chance to play around with hyper objects + + align:start position:0% +chance to play around with hyper objects + + + align:start position:0% +chance to play around with hyper objects +in homework for the so plus ecosystem + + align:start position:0% +in homework for the so plus ecosystem + + + align:start position:0% +in homework for the so plus ecosystem +also includes useful programming tools + + align:start position:0% +also includes useful programming tools + + + align:start position:0% +also includes useful programming tools +such as a silk screen race detectors so + + align:start position:0% +such as a silk screen race detectors so + + + align:start position:0% +such as a silk screen race detectors so +this allows you to detect determinacy + + align:start position:0% +this allows you to detect determinacy + + + align:start position:0% +this allows you to detect determinacy +races in your program to help you + + align:start position:0% +races in your program to help you + + + align:start position:0% +races in your program to help you +isolate bugs and performance bottlenecks + + align:start position:0% +isolate bugs and performance bottlenecks + + + align:start position:0% +isolate bugs and performance bottlenecks +it also has a scalability analyzer + + align:start position:0% +it also has a scalability analyzer + + + align:start position:0% +it also has a scalability analyzer +called silk view and silk view will base + + align:start position:0% +called silk view and silk view will base + + + align:start position:0% +called silk view and silk view will base +analyze the amount of work that your + + align:start position:0% +analyze the amount of work that your + + + align:start position:0% +analyze the amount of work that your +program is doing as well as the maximum + + align:start position:0% +program is doing as well as the maximum + + + align:start position:0% +program is doing as well as the maximum +amount of parallelism that your code + + align:start position:0% +amount of parallelism that your code + + + align:start position:0% +amount of parallelism that your code +could possibly extract from the hardware + + align:start position:0% +could possibly extract from the hardware + + + align:start position:0% +could possibly extract from the hardware +so that's in Tulsa plus but it turns out + + align:start position:0% +so that's in Tulsa plus but it turns out + + + align:start position:0% +so that's in Tulsa plus but it turns out +that we're not actually going to be + + align:start position:0% +that we're not actually going to be + + + align:start position:0% +that we're not actually going to be +using in Tulsa plus in this class we're + + align:start position:0% +using in Tulsa plus in this class we're + + + align:start position:0% +using in Tulsa plus in this class we're +gonna be using a better compiler and + + align:start position:0% +gonna be using a better compiler and + + + align:start position:0% +gonna be using a better compiler and +this compiler is based on taper LLVM and + + align:start position:0% +this compiler is based on taper LLVM and + + + align:start position:0% +this compiler is based on taper LLVM and +it supports the silk subset of silk plus + + align:start position:0% +it supports the silk subset of silk plus + + + align:start position:0% +it supports the silk subset of silk plus +and taper LLVM was actually recently + + align:start position:0% +and taper LLVM was actually recently + + + align:start position:0% +and taper LLVM was actually recently +developed at MIT by TB charnel who gave + + align:start position:0% +developed at MIT by TB charnel who gave + + + align:start position:0% +developed at MIT by TB charnel who gave +a lecture last week + + align:start position:0% +a lecture last week + + + align:start position:0% +a lecture last week +William Moses who's a grad student + + align:start position:0% +William Moses who's a grad student + + + align:start position:0% +William Moses who's a grad student +working with Charles as well as charles + + align:start position:0% +working with Charles as well as charles + + + align:start position:0% +working with Charles as well as charles +leiserson and so talking a lot about + + align:start position:0% +leiserson and so talking a lot about + + + align:start position:0% +leiserson and so talking a lot about +Charles's work today and taper LVM + + align:start position:0% +Charles's work today and taper LVM + + + align:start position:0% +Charles's work today and taper LVM +generally produces better code relative + + align:start position:0% +generally produces better code relative + + + align:start position:0% +generally produces better code relative +to its base compiler than all other + + align:start position:0% +to its base compiler than all other + + + align:start position:0% +to its base compiler than all other +implementations of silk out there so + + align:start position:0% +implementations of silk out there so + + + align:start position:0% +implementations of silk out there so +it's the best cell compiler that's + + align:start position:0% +it's the best cell compiler that's + + + align:start position:0% +it's the best cell compiler that's +available today and they actually wrote + + align:start position:0% +available today and they actually wrote + + + align:start position:0% +available today and they actually wrote +a very nice paper on this last year + + align:start position:0% +a very nice paper on this last year + + + align:start position:0% +a very nice paper on this last year +Charles lisen in this group and that + + align:start position:0% +Charles lisen in this group and that + + + align:start position:0% +Charles lisen in this group and that +paper received the best paper award at + + align:start position:0% +paper received the best paper award at + + + align:start position:0% +paper received the best paper award at +the annual symposium on principles and + + align:start position:0% +the annual symposium on principles and + + + align:start position:0% +the annual symposium on principles and +practices of parallel programming or + + align:start position:0% +practices of parallel programming or + + + align:start position:0% +practices of parallel programming or +p-pop so you should look at that paper + + align:start position:0% +p-pop so you should look at that paper + + + align:start position:0% +p-pop so you should look at that paper +as well + + align:start position:0% + + + + align:start position:0% + +so right now taper LVM uses the Intel + + align:start position:0% +so right now taper LVM uses the Intel + + + align:start position:0% +so right now taper LVM uses the Intel +so plus runtime system by I believe + + align:start position:0% +so plus runtime system by I believe + + + align:start position:0% +so plus runtime system by I believe +Charles's group has plans to implement a + + align:start position:0% +Charles's group has plans to implement a + + + align:start position:0% +Charles's group has plans to implement a +better runtime system and tabor LVM also + + align:start position:0% +better runtime system and tabor LVM also + + + align:start position:0% +better runtime system and tabor LVM also +supports more general features than + + align:start position:0% +supports more general features than + + + align:start position:0% +supports more general features than +existing sole compilers so in addition + + align:start position:0% +existing sole compilers so in addition + + + align:start position:0% +existing sole compilers so in addition +to spawning functions you can also spawn + + align:start position:0% +to spawning functions you can also spawn + + + align:start position:0% +to spawning functions you can also spawn +code blocks that are not separate + + align:start position:0% +code blocks that are not separate + + + align:start position:0% +code blocks that are not separate +functions and this makes your this right + + align:start position:0% +functions and this makes your this right + + + align:start position:0% +functions and this makes your this right +makes writing programs more flexible you + + align:start position:0% +makes writing programs more flexible you + + + align:start position:0% +makes writing programs more flexible you +don't have to actually create a separate + + align:start position:0% +don't have to actually create a separate + + + align:start position:0% +don't have to actually create a separate +function if you want to execute a code + + align:start position:0% +function if you want to execute a code + + + align:start position:0% +function if you want to execute a code +block in parallel + + align:start position:0% +block in parallel + + + align:start position:0% +block in parallel +any questions + + align:start position:0% + + + + align:start position:0% + +so this is the salt coat for Fibonacci + + align:start position:0% +so this is the salt coat for Fibonacci + + + align:start position:0% +so this is the salt coat for Fibonacci +so it's also pretty simple it looks very + + align:start position:0% +so it's also pretty simple it looks very + + + align:start position:0% +so it's also pretty simple it looks very +similar to the sequential program except + + align:start position:0% +similar to the sequential program except + + + align:start position:0% +similar to the sequential program except +we have these silk spawn and silk stink + + align:start position:0% +we have these silk spawn and silk stink + + + align:start position:0% +we have these silk spawn and silk stink +statements in the code so what do these + + align:start position:0% +statements in the code so what do these + + + align:start position:0% +statements in the code so what do these +statements do so + + align:start position:0% +statements do so + + + align:start position:0% +statements do so +silk spawn says that the named child + + align:start position:0% +silk spawn says that the named child + + + align:start position:0% +silk spawn says that the named child +function which is the function that is + + align:start position:0% +function which is the function that is + + + align:start position:0% +function which is the function that is +right after the silk spawn statement may + + align:start position:0% +right after the silk spawn statement may + + + align:start position:0% +right after the silk spawn statement may +execute in parallel with the parent + + align:start position:0% +execute in parallel with the parent + + + align:start position:0% +execute in parallel with the parent +caller the parent caller is the function + + align:start position:0% +caller the parent caller is the function + + + align:start position:0% +caller the parent caller is the function +that is calling soaked spawn so this + + align:start position:0% +that is calling soaked spawn so this + + + align:start position:0% +that is calling soaked spawn so this +says that fib of n minus 1 can execute + + align:start position:0% +says that fib of n minus 1 can execute + + + align:start position:0% +says that fib of n minus 1 can execute +in parallel with the function that + + align:start position:0% +in parallel with the function that + + + align:start position:0% +in parallel with the function that +called it and then this function is then + + align:start position:0% +called it and then this function is then + + + align:start position:0% +called it and then this function is then +gonna call fib of n minus 2 and fib of n + + align:start position:0% +gonna call fib of n minus 2 and fib of n + + + align:start position:0% +gonna call fib of n minus 2 and fib of n +minus 2 and fib of n minus 1 now can be + + align:start position:0% +minus 2 and fib of n minus 1 now can be + + + align:start position:0% +minus 2 and fib of n minus 1 now can be +executing in parallel and then silk sync + + align:start position:0% +executing in parallel and then silk sync + + + align:start position:0% +executing in parallel and then silk sync +says that control cannot pass this point + + align:start position:0% +says that control cannot pass this point + + + align:start position:0% +says that control cannot pass this point +until all of the spawn children have + + align:start position:0% +until all of the spawn children have + + + align:start position:0% +until all of the spawn children have +returned since it's going to wait for + + align:start position:0% +returned since it's going to wait for + + + align:start position:0% +returned since it's going to wait for +fifth of N minus 1 to return before we + + align:start position:0% +fifth of N minus 1 to return before we + + + align:start position:0% +fifth of N minus 1 to return before we +go to the return statement where we add + + align:start position:0% +go to the return statement where we add + + + align:start position:0% +go to the return statement where we add +up X&Y so one important thing to note is + + align:start position:0% +up X&Y so one important thing to note is + + + align:start position:0% +up X&Y so one important thing to note is +that the so key where it's grant + + align:start position:0% +that the so key where it's grant + + + align:start position:0% +that the so key where it's grant +permission for parallel execution but + + align:start position:0% +permission for parallel execution but + + + align:start position:0% +permission for parallel execution but +they don't actually force or command + + align:start position:0% +they don't actually force or command + + + align:start position:0% +they don't actually force or command +parallel execution so even though I said + + align:start position:0% +parallel execution so even though I said + + + align:start position:0% +parallel execution so even though I said +soak spawn here the the runtime system + + align:start position:0% +soak spawn here the the runtime system + + + align:start position:0% +soak spawn here the the runtime system +doesn't necessarily have to run fib of n + + align:start position:0% +doesn't necessarily have to run fib of n + + + align:start position:0% +doesn't necessarily have to run fib of n +minus 1 in parallel with fib of n minus + + align:start position:0% +minus 1 in parallel with fib of n minus + + + align:start position:0% +minus 1 in parallel with fib of n minus +2 I'm just saying that I could run these + + align:start position:0% +2 I'm just saying that I could run these + + + align:start position:0% +2 I'm just saying that I could run these +two things in parallel and it's up to + + align:start position:0% +two things in parallel and it's up to + + + align:start position:0% +two things in parallel and it's up to +the runtime system to decide whether or + + align:start position:0% +the runtime system to decide whether or + + + align:start position:0% +the runtime system to decide whether or +not to run these things in parallel + + align:start position:0% +not to run these things in parallel + + + align:start position:0% +not to run these things in parallel +based on its scheduling policy so let's + + align:start position:0% +based on its scheduling policy so let's + + + align:start position:0% +based on its scheduling policy so let's +look at another example of silk so let's + + align:start position:0% +look at another example of silk so let's + + + align:start position:0% +look at another example of silk so let's +look at loop parallelism so here we want + + align:start position:0% +look at loop parallelism so here we want + + + align:start position:0% +look at loop parallelism so here we want +to do a matrix transpose and we want to + + align:start position:0% +to do a matrix transpose and we want to + + + align:start position:0% +to do a matrix transpose and we want to +do this in place so the idea here is we + + align:start position:0% +do this in place so the idea here is we + + + align:start position:0% +do this in place so the idea here is we +want to basically swap the elements + + align:start position:0% +want to basically swap the elements + + + align:start position:0% +want to basically swap the elements +below the diagonal to the + + align:start position:0% +below the diagonal to the + + + align:start position:0% +below the diagonal to the +- its mirror mirror image above the + + align:start position:0% +- its mirror mirror image above the + + + align:start position:0% +- its mirror mirror image above the +diagonal and here's some code to do this + + align:start position:0% +diagonal and here's some code to do this + + + align:start position:0% +diagonal and here's some code to do this +so we have a silk for so this is + + align:start position:0% +so we have a silk for so this is + + + align:start position:0% +so we have a silk for so this is +basically a parallel for loop it goes + + align:start position:0% +basically a parallel for loop it goes + + + align:start position:0% +basically a parallel for loop it goes +from I equals 1 to n minus 1 and then + + align:start position:0% +from I equals 1 to n minus 1 and then + + + align:start position:0% +from I equals 1 to n minus 1 and then +the inner for loop goes from J equals 0 + + align:start position:0% +the inner for loop goes from J equals 0 + + + align:start position:0% +the inner for loop goes from J equals 0 +up to I minus 1 and then we just swap a + + align:start position:0% +up to I minus 1 and then we just swap a + + + align:start position:0% +up to I minus 1 and then we just swap a +of IJ with a of ji using these three + + align:start position:0% +of IJ with a of ji using these three + + + align:start position:0% +of IJ with a of ji using these three +statements inside the body of the for + + align:start position:0% +statements inside the body of the for + + + align:start position:0% +statements inside the body of the for +loop so so to execute a for loop in + + align:start position:0% +loop so so to execute a for loop in + + + align:start position:0% +loop so so to execute a for loop in +parallel you just have to add silk + + align:start position:0% +parallel you just have to add silk + + + align:start position:0% +parallel you just have to add silk +underscore to the to the for keyword and + + align:start position:0% +underscore to the to the for keyword and + + + align:start position:0% +underscore to the to the for keyword and +that's as simple as it gets + + align:start position:0% +that's as simple as it gets + + + align:start position:0% +that's as simple as it gets +so this code is actually going to run in + + align:start position:0% +so this code is actually going to run in + + + align:start position:0% +so this code is actually going to run in +parallel and get a pretty good speed up + + align:start position:0% +parallel and get a pretty good speed up + + + align:start position:0% +parallel and get a pretty good speed up +on this for this particular problem and + + align:start position:0% +on this for this particular problem and + + + align:start position:0% +on this for this particular problem and +internally silk for loops are + + align:start position:0% +internally silk for loops are + + + align:start position:0% +internally silk for loops are +transformed into nested silks spawn in + + align:start position:0% +transformed into nested silks spawn in + + + align:start position:0% +transformed into nested silks spawn in +silks Inc calls so the compiler is going + + align:start position:0% +silks Inc calls so the compiler is going + + + align:start position:0% +silks Inc calls so the compiler is going +to get rid of the silk for and change it + + align:start position:0% +to get rid of the silk for and change it + + + align:start position:0% +to get rid of the silk for and change it +into silks spawn and silks Inc so it's + + align:start position:0% +into silks spawn and silks Inc so it's + + + align:start position:0% +into silks spawn and silks Inc so it's +going to recursively divide the + + align:start position:0% +going to recursively divide the + + + align:start position:0% +going to recursively divide the +iteration space into half and then it's + + align:start position:0% +iteration space into half and then it's + + + align:start position:0% +iteration space into half and then it's +going to spawn off one half in the next + + align:start position:0% +going to spawn off one half in the next + + + align:start position:0% +going to spawn off one half in the next +acute the other half in parallel with + + align:start position:0% +acute the other half in parallel with + + + align:start position:0% +acute the other half in parallel with +that and then recursively do that until + + align:start position:0% +that and then recursively do that until + + + align:start position:0% +that and then recursively do that until +the iteration range becomes small enough + + align:start position:0% +the iteration range becomes small enough + + + align:start position:0% +the iteration range becomes small enough +at which point doesn't make sense to + + align:start position:0% +at which point doesn't make sense to + + + align:start position:0% +at which point doesn't make sense to +execute it in parallel anymore so we + + align:start position:0% +execute it in parallel anymore so we + + + align:start position:0% +execute it in parallel anymore so we +just execute that range sequentially + + align:start position:0% +just execute that range sequentially + + + align:start position:0% +just execute that range sequentially +okay so that's loop parallelism in silk + + align:start position:0% +okay so that's loop parallelism in silk + + + align:start position:0% +okay so that's loop parallelism in silk +any questions yes + + align:start position:0% + + + + align:start position:0% + +there's something weird can I still do + + align:start position:0% +there's something weird can I still do + + + align:start position:0% +there's something weird can I still do +that yeah so the compiler can actually + + align:start position:0% +that yeah so the compiler can actually + + + align:start position:0% +that yeah so the compiler can actually +figure out what the iteration space is + + align:start position:0% +figure out what the iteration space is + + + align:start position:0% +figure out what the iteration space is +so you don't necessarily have to be + + align:start position:0% +so you don't necessarily have to be + + + align:start position:0% +so you don't necessarily have to be +incrementing by one you can do something + + align:start position:0% +incrementing by one you can do something + + + align:start position:0% +incrementing by one you can do something +else you just have to guarantee that all + + align:start position:0% +else you just have to guarantee that all + + + align:start position:0% +else you just have to guarantee that all +of the iterations are independent so if + + align:start position:0% +of the iterations are independent so if + + + align:start position:0% +of the iterations are independent so if +if you act if you have a determinacy + + align:start position:0% +if you act if you have a determinacy + + + align:start position:0% +if you act if you have a determinacy +race across the different iterations of + + align:start position:0% +race across the different iterations of + + + align:start position:0% +race across the different iterations of +your cell for loop then your result + + align:start position:0% +your cell for loop then your result + + + align:start position:0% +your cell for loop then your result +might not necessarily be correct so you + + align:start position:0% +might not necessarily be correct so you + + + align:start position:0% +might not necessarily be correct so you +have to make sure that the iterations + + align:start position:0% +have to make sure that the iterations + + + align:start position:0% +have to make sure that the iterations +are indeed independent yes yeah so you + + align:start position:0% +are indeed independent yes yeah so you + + + align:start position:0% +are indeed independent yes yeah so you +can that's silk force it turns out that + + align:start position:0% +can that's silk force it turns out that + + + align:start position:0% +can that's silk force it turns out that +for this example usually you already + + align:start position:0% +for this example usually you already + + + align:start position:0% +for this example usually you already +have enough parallelism in the outer + + align:start position:0% +have enough parallelism in the outer + + + align:start position:0% +have enough parallelism in the outer +loop for large enough values of n so it + + align:start position:0% +loop for large enough values of n so it + + + align:start position:0% +loop for large enough values of n so it +doesn't make sense to put a slope for + + align:start position:0% +doesn't make sense to put a slope for + + + align:start position:0% +doesn't make sense to put a slope for +loop inside because using a silk for + + align:start position:0% +loop inside because using a silk for + + + align:start position:0% +loop inside because using a silk for +loop adds some additional overheads + + align:start position:0% +loop adds some additional overheads + + + align:start position:0% +loop adds some additional overheads +but you can actually do nested silk for + + align:start position:0% +but you can actually do nested silk for + + + align:start position:0% +but you can actually do nested silk for +loops and in some cases it does make + + align:start position:0% +loops and in some cases it does make + + + align:start position:0% +loops and in some cases it does make +sense especially if the if there's not + + align:start position:0% +sense especially if the if there's not + + + align:start position:0% +sense especially if the if there's not +enough parallelism in that outermost for + + align:start position:0% +enough parallelism in that outermost for + + + align:start position:0% +enough parallelism in that outermost for +loop it's a good question yes + + align:start position:0% + + + + align:start position:0% + +so I mean it it it has a bunch of calls + + align:start position:0% +so I mean it it it has a bunch of calls + + + align:start position:0% +so I mean it it it has a bunch of calls +to the silk run time system I don't + + align:start position:0% +to the silk run time system I don't + + + align:start position:0% +to the silk run time system I don't +actually I don't I mean I don't know all + + align:start position:0% +actually I don't I mean I don't know all + + + align:start position:0% +actually I don't I mean I don't know all +the details because I haven't looked at + + align:start position:0% +the details because I haven't looked at + + + align:start position:0% +the details because I haven't looked at +this recently but I think you can + + align:start position:0% +this recently but I think you can + + + align:start position:0% +this recently but I think you can +actually generate the assembly code + + align:start position:0% +actually generate the assembly code + + + align:start position:0% +actually generate the assembly code +using a flag in the clang compiler so + + align:start position:0% +using a flag in the clang compiler so + + + align:start position:0% +using a flag in the clang compiler so +that's a good exercise yeah you probably + + align:start position:0% +that's a good exercise yeah you probably + + + align:start position:0% +that's a good exercise yeah you probably +want to look at the LLVM ir rather than + + align:start position:0% +want to look at the LLVM ir rather than + + + align:start position:0% +want to look at the LLVM ir rather than +the assembly to begin with to understand + + align:start position:0% +the assembly to begin with to understand + + + align:start position:0% +the assembly to begin with to understand +what's going on it has three + + align:start position:0% +what's going on it has three + + + align:start position:0% +what's going on it has three +instructions that are not in the + + align:start position:0% +instructions that are not in the + + + align:start position:0% +instructions that are not in the +standard LLVM which which were added to + + align:start position:0% +standard LLVM which which were added to + + + align:start position:0% +standard LLVM which which were added to +support parallelism those things when + + align:start position:0% +support parallelism those things when + + + align:start position:0% +support parallelism those things when +it's lowered into the assembler into + + align:start position:0% +it's lowered into the assembler into + + + align:start position:0% +it's lowered into the assembler into +assembly each of those instructions + + align:start position:0% +assembly each of those instructions + + + align:start position:0% +assembly each of those instructions +becomes a bunch of assembly language + + align:start position:0% +becomes a bunch of assembly language + + + align:start position:0% +becomes a bunch of assembly language +instructions so you don't want to mess + + align:start position:0% +instructions so you don't want to mess + + + align:start position:0% +instructions so you don't want to mess +with with looking at it in the assembler + + align:start position:0% +with with looking at it in the assembler + + + align:start position:0% +with with looking at it in the assembler +until you see what it looks like in the + + align:start position:0% +until you see what it looks like in the + + + align:start position:0% +until you see what it looks like in the +LLVM first yes a good question any other + + align:start position:0% +LLVM first yes a good question any other + + + align:start position:0% +LLVM first yes a good question any other +questions about this this code here + + align:start position:0% + + + + align:start position:0% + +okay so let's look at another example so + + align:start position:0% +okay so let's look at another example so + + + align:start position:0% +okay so let's look at another example so +let's say we had this floral loop where + + align:start position:0% +let's say we had this floral loop where + + + align:start position:0% +let's say we had this floral loop where +on each iteration I were just + + align:start position:0% +on each iteration I were just + + + align:start position:0% +on each iteration I were just +incrementing a variable sum by I so this + + align:start position:0% +incrementing a variable sum by I so this + + + align:start position:0% +incrementing a variable sum by I so this +is essentially going to commute compute + + align:start position:0% +is essentially going to commute compute + + + align:start position:0% +is essentially going to commute compute +the summation of everything from I + + align:start position:0% +the summation of everything from I + + + align:start position:0% +the summation of everything from I +equals 0 up to n minus 1 and then print + + align:start position:0% +equals 0 up to n minus 1 and then print + + + align:start position:0% +equals 0 up to n minus 1 and then print +out the result so one straightforward + + align:start position:0% +out the result so one straightforward + + + align:start position:0% +out the result so one straightforward +way to try to paralyze this code is to + + align:start position:0% +way to try to paralyze this code is to + + + align:start position:0% +way to try to paralyze this code is to +just change the 4 to a soap 4 so does + + align:start position:0% +just change the 4 to a soap 4 so does + + + align:start position:0% +just change the 4 to a soap 4 so does +this code work who thinks that this code + + align:start position:0% +this code work who thinks that this code + + + align:start position:0% +this code work who thinks that this code +doesn't work or doesn't compute the + + align:start position:0% +doesn't work or doesn't compute the + + + align:start position:0% +doesn't work or doesn't compute the +correct result so about half of you and + + align:start position:0% +correct result so about half of you and + + + align:start position:0% +correct result so about half of you and +who thinks this code does work so couple + + align:start position:0% +who thinks this code does work so couple + + + align:start position:0% +who thinks this code does work so couple +people in guess the rest of the people + + align:start position:0% +people in guess the rest of the people + + + align:start position:0% +people in guess the rest of the people +don't care so it turns out that it's not + + align:start position:0% +don't care so it turns out that it's not + + + align:start position:0% +don't care so it turns out that it's not +actually necessarily going to give you + + align:start position:0% +actually necessarily going to give you + + + align:start position:0% +actually necessarily going to give you +the right answer because the silk for + + align:start position:0% +the right answer because the silk for + + + align:start position:0% +the right answer because the silk for +loop says you can execute these + + align:start position:0% +loop says you can execute these + + + align:start position:0% +loop says you can execute these +iterations in parallel but they're all + + align:start position:0% +iterations in parallel but they're all + + + align:start position:0% +iterations in parallel but they're all +updating the same shared variable sum + + align:start position:0% +updating the same shared variable sum + + + align:start position:0% +updating the same shared variable sum +here so you have a what's called a + + align:start position:0% +here so you have a what's called a + + + align:start position:0% +here so you have a what's called a +determinacy race where multiple + + align:start position:0% +determinacy race where multiple + + + align:start position:0% +determinacy race where multiple +processors can be writing to the same + + align:start position:0% +processors can be writing to the same + + + align:start position:0% +processors can be writing to the same +memory location we'll talk much more + + align:start position:0% +memory location we'll talk much more + + + align:start position:0% +memory location we'll talk much more +about determinacy races in the next + + align:start position:0% +about determinacy races in the next + + + align:start position:0% +about determinacy races in the next +lecture but for this example it's not + + align:start position:0% +lecture but for this example it's not + + + align:start position:0% +lecture but for this example it's not +necessarily going to work if you run it + + align:start position:0% +necessarily going to work if you run it + + + align:start position:0% +necessarily going to work if you run it +on more than one processor and silk + + align:start position:0% +on more than one processor and silk + + + align:start position:0% +on more than one processor and silk +actually has a nice way to deal with + + align:start position:0% +actually has a nice way to deal with + + + align:start position:0% +actually has a nice way to deal with +this + + align:start position:0% +this + + + align:start position:0% +this +so in silk we have something known as a + + align:start position:0% +so in silk we have something known as a + + + align:start position:0% +so in silk we have something known as a +reducer this is one example of a hyper + + align:start position:0% +reducer this is one example of a hyper + + + align:start position:0% +reducer this is one example of a hyper +object which I mentioned earlier and + + align:start position:0% +object which I mentioned earlier and + + + align:start position:0% +object which I mentioned earlier and +with a reducer what you have to do is + + align:start position:0% +with a reducer what you have to do is + + + align:start position:0% +with a reducer what you have to do is +instead of declaring this some variable + + align:start position:0% +instead of declaring this some variable + + + align:start position:0% +instead of declaring this some variable +just has an unsigned long data type what + + align:start position:0% +just has an unsigned long data type what + + + align:start position:0% +just has an unsigned long data type what +you do is use this macro called silk see + + align:start position:0% +you do is use this macro called silk see + + + align:start position:0% +you do is use this macro called silk see +reducer op ad which specifies we want to + + align:start position:0% +reducer op ad which specifies we want to + + + align:start position:0% +reducer op ad which specifies we want to +create a reducer with the addition + + align:start position:0% +create a reducer with the addition + + + align:start position:0% +create a reducer with the addition +function then we have the variable name + + align:start position:0% +function then we have the variable name + + + align:start position:0% +function then we have the variable name +sum the data + + align:start position:0% +sum the data + + + align:start position:0% +sum the data +type unsigned long and then the initial + + align:start position:0% +type unsigned long and then the initial + + + align:start position:0% +type unsigned long and then the initial +value zero and then we have a macro to + + align:start position:0% +value zero and then we have a macro to + + + align:start position:0% +value zero and then we have a macro to +register this reducer so a silk see + + align:start position:0% +register this reducer so a silk see + + + align:start position:0% +register this reducer so a silk see +register reducer and then now inside + + align:start position:0% +register reducer and then now inside + + + align:start position:0% +register reducer and then now inside +this soap for loop we can increment the + + align:start position:0% +this soap for loop we can increment the + + + align:start position:0% +this soap for loop we can increment the +sum or reducer view of sum which is + + align:start position:0% +sum or reducer view of sum which is + + + align:start position:0% +sum or reducer view of sum which is +another macro by I and you can actually + + align:start position:0% +another macro by I and you can actually + + + align:start position:0% +another macro by I and you can actually +execute this in parallel and it will + + align:start position:0% +execute this in parallel and it will + + + align:start position:0% +execute this in parallel and it will +give you the same answer that you would + + align:start position:0% +give you the same answer that you would + + + align:start position:0% +give you the same answer that you would +get if you ran this sequentially so the + + align:start position:0% +get if you ran this sequentially so the + + + align:start position:0% +get if you ran this sequentially so the +reducer will take care of this + + align:start position:0% +reducer will take care of this + + + align:start position:0% +reducer will take care of this +determinacy race for you and at the end + + align:start position:0% +determinacy race for you and at the end + + + align:start position:0% +determinacy race for you and at the end +when you print out this result you'll + + align:start position:0% +when you print out this result you'll + + + align:start position:0% +when you print out this result you'll +see that the sum is equal to the sum + + align:start position:0% +see that the sum is equal to the sum + + + align:start position:0% +see that the sum is equal to the sum +that you expect and then after you + + align:start position:0% +that you expect and then after you + + + align:start position:0% +that you expect and then after you +finish using the reducer use this other + + align:start position:0% +finish using the reducer use this other + + + align:start position:0% +finish using the reducer use this other +macro called silky an unregistered + + align:start position:0% +macro called silky an unregistered + + + align:start position:0% +macro called silky an unregistered +reducer of sum that tells the system + + align:start position:0% +reducer of sum that tells the system + + + align:start position:0% +reducer of sum that tells the system +that you're done using this reducer so + + align:start position:0% +that you're done using this reducer so + + + align:start position:0% +that you're done using this reducer so +this is one way to deal with this + + align:start position:0% +this is one way to deal with this + + + align:start position:0% +this is one way to deal with this +problem when you're when you want to do + + align:start position:0% +problem when you're when you want to do + + + align:start position:0% +problem when you're when you want to do +a reduction and it turns out that there + + align:start position:0% +a reduction and it turns out that there + + + align:start position:0% +a reduction and it turns out that there +are many other interesting reduction + + align:start position:0% +are many other interesting reduction + + + align:start position:0% +are many other interesting reduction +operators that you might want to use and + + align:start position:0% +operators that you might want to use and + + + align:start position:0% +operators that you might want to use and +in general you can create reducers for + + align:start position:0% +in general you can create reducers for + + + align:start position:0% +in general you can create reducers for +Mahanoy Chand ma nodes or algebraic + + align:start position:0% +Mahanoy Chand ma nodes or algebraic + + + align:start position:0% +Mahanoy Chand ma nodes or algebraic +structures that have an associative + + align:start position:0% +structures that have an associative + + + align:start position:0% +structures that have an associative +binary operation as well as an identity + + align:start position:0% +binary operation as well as an identity + + + align:start position:0% +binary operation as well as an identity +element so the addition operator is a + + align:start position:0% +element so the addition operator is a + + + align:start position:0% +element so the addition operator is a +mono it because it's associative it's + + align:start position:0% +mono it because it's associative it's + + + align:start position:0% +mono it because it's associative it's +binary and the identity element is 0 + + align:start position:0% +binary and the identity element is 0 + + + align:start position:0% +binary and the identity element is 0 +silk also has several other predefined + + align:start position:0% +silk also has several other predefined + + + align:start position:0% +silk also has several other predefined +reducers including multiplication min + + align:start position:0% +reducers including multiplication min + + + align:start position:0% +reducers including multiplication min +Max and or XOR etc so these are all more + + align:start position:0% +Max and or XOR etc so these are all more + + + align:start position:0% +Max and or XOR etc so these are all more +mono it's and you can also define your + + align:start position:0% +mono it's and you can also define your + + + align:start position:0% +mono it's and you can also define your +own reducer so in fact in the next + + align:start position:0% +own reducer so in fact in the next + + + align:start position:0% +own reducer so in fact in the next +homework you'll have the opportunity to + + align:start position:0% +homework you'll have the opportunity to + + + align:start position:0% +homework you'll have the opportunity to +play around with reducers and write a + + align:start position:0% +play around with reducers and write a + + + align:start position:0% +play around with reducers and write a +reducer for lists so that's reducers + + align:start position:0% + + + + align:start position:0% + +another nice thing about silk is that + + align:start position:0% +another nice thing about silk is that + + + align:start position:0% +another nice thing about silk is that +there's always a valid serial + + align:start position:0% +there's always a valid serial + + + align:start position:0% +there's always a valid serial +interpretation of the program so the + + align:start position:0% +interpretation of the program so the + + + align:start position:0% +interpretation of the program so the +serial elision of a silk program is + + align:start position:0% +serial elision of a silk program is + + + align:start position:0% +serial elision of a silk program is +always a legal interpretation and for + + align:start position:0% +always a legal interpretation and for + + + align:start position:0% +always a legal interpretation and for +the silk source code on the left the + + align:start position:0% +the silk source code on the left the + + + align:start position:0% +the silk source code on the left the +serial elision is basically the code you + + align:start position:0% +serial elision is basically the code you + + + align:start position:0% +serial elision is basically the code you +get if you get rid of the silk spawn and + + align:start position:0% +get if you get rid of the silk spawn and + + + align:start position:0% +get if you get rid of the silk spawn and +soak sync statements + + align:start position:0% +soak sync statements + + + align:start position:0% +soak sync statements +this looks just like the sequential code + + align:start position:0% + + + + align:start position:0% + +remember that the sole keywords grant + + align:start position:0% +remember that the sole keywords grant + + + align:start position:0% +remember that the sole keywords grant +permission for parallel execution but + + align:start position:0% +permission for parallel execution but + + + align:start position:0% +permission for parallel execution but +they don't necessarily command parallel + + align:start position:0% +they don't necessarily command parallel + + + align:start position:0% +they don't necessarily command parallel +executions if you ran this if you ran + + align:start position:0% +executions if you ran this if you ran + + + align:start position:0% +executions if you ran this if you ran +this SIL code using a single core it + + align:start position:0% +this SIL code using a single core it + + + align:start position:0% +this SIL code using a single core it +wouldn't actually create these parallel + + align:start position:0% +wouldn't actually create these parallel + + + align:start position:0% +wouldn't actually create these parallel +tasks and you would get the same answer + + align:start position:0% +tasks and you would get the same answer + + + align:start position:0% +tasks and you would get the same answer +as the sequential program and this is in + + align:start position:0% +as the sequential program and this is in + + + align:start position:0% +as the sequential program and this is in +the serial illusion is also a correct + + align:start position:0% +the serial illusion is also a correct + + + align:start position:0% +the serial illusion is also a correct +interpretation so unlike other solutions + + align:start position:0% +interpretation so unlike other solutions + + + align:start position:0% +interpretation so unlike other solutions +such as TBB and P threads it's actually + + align:start position:0% +such as TBB and P threads it's actually + + + align:start position:0% +such as TBB and P threads it's actually +difficult in those environments to get a + + align:start position:0% +difficult in those environments to get a + + + align:start position:0% +difficult in those environments to get a +program that does what the sequential + + align:start position:0% +program that does what the sequential + + + align:start position:0% +program that does what the sequential +program does because they're actually + + align:start position:0% +program does because they're actually + + + align:start position:0% +program does because they're actually +doing a lot of additional work to set up + + align:start position:0% +doing a lot of additional work to set up + + + align:start position:0% +doing a lot of additional work to set up +these parallel calls and create these + + align:start position:0% +these parallel calls and create these + + + align:start position:0% +these parallel calls and create these +argument structures and other scheduling + + align:start position:0% +argument structures and other scheduling + + + align:start position:0% +argument structures and other scheduling +constructs whereas in silk it's very + + align:start position:0% +constructs whereas in silk it's very + + + align:start position:0% +constructs whereas in silk it's very +easy just to get the serial illusion you + + align:start position:0% +easy just to get the serial illusion you + + + align:start position:0% +easy just to get the serial illusion you +just define silks pawn and silks Inc to + + align:start position:0% +just define silks pawn and silks Inc to + + + align:start position:0% +just define silks pawn and silks Inc to +be null you also define silk for to be + + align:start position:0% +be null you also define silk for to be + + + align:start position:0% +be null you also define silk for to be +for and then this gives you a valid + + align:start position:0% +for and then this gives you a valid + + + align:start position:0% +for and then this gives you a valid +sequential program so when you're + + align:start position:0% +sequential program so when you're + + + align:start position:0% +sequential program so when you're +debugging code and you might first want + + align:start position:0% +debugging code and you might first want + + + align:start position:0% +debugging code and you might first want +to check if your if the sequential + + align:start position:0% +to check if your if the sequential + + + align:start position:0% +to check if your if the sequential +elision of your silk program is correct + + align:start position:0% +elision of your silk program is correct + + + align:start position:0% +elision of your silk program is correct +and you can easily do that by using + + align:start position:0% +and you can easily do that by using + + + align:start position:0% +and you can easily do that by using +these macros or actually there's + + align:start position:0% +these macros or actually there's + + + align:start position:0% +these macros or actually there's +actually a compiler flag that will do + + align:start position:0% +actually a compiler flag that will do + + + align:start position:0% +actually a compiler flag that will do +that for you and give you the equivalent + + align:start position:0% +that for you and give you the equivalent + + + align:start position:0% +that for you and give you the equivalent +C program so this is a nice way to debug + + align:start position:0% +C program so this is a nice way to debug + + + align:start position:0% +C program so this is a nice way to debug +because you don't have to start with the + + align:start position:0% +because you don't have to start with the + + + align:start position:0% +because you don't have to start with the +parallel program you can first check if + + align:start position:0% +parallel program you can first check if + + + align:start position:0% +parallel program you can first check if +this serial program is correct before + + align:start position:0% +this serial program is correct before + + + align:start position:0% +this serial program is correct before +you go on to debug the parallel program + + align:start position:0% + + + + align:start position:0% + +questions yes + + align:start position:0% + + + + align:start position:0% + +so it turns out that by default it it + + align:start position:0% +so it turns out that by default it it + + + align:start position:0% +so it turns out that by default it it +groups a bunch of iterations together + + align:start position:0% +groups a bunch of iterations together + + + align:start position:0% +groups a bunch of iterations together +into a single task because it doesn't + + align:start position:0% +into a single task because it doesn't + + + align:start position:0% +into a single task because it doesn't +make sense to break it down into such + + align:start position:0% +make sense to break it down into such + + + align:start position:0% +make sense to break it down into such +small chunks do that overhead so + + align:start position:0% +small chunks do that overhead so + + + align:start position:0% +small chunks do that overhead so +parallelism but there's actually a + + align:start position:0% +parallelism but there's actually a + + + align:start position:0% +parallelism but there's actually a +setting you can do to change the grain + + align:start position:0% +setting you can do to change the grain + + + align:start position:0% +setting you can do to change the grain +size of the for loop so you could + + align:start position:0% +size of the for loop so you could + + + align:start position:0% +size of the for loop so you could +actually make it so that each iteration + + align:start position:0% +actually make it so that each iteration + + + align:start position:0% +actually make it so that each iteration +it's its own task and then and then as + + align:start position:0% +it's its own task and then and then as + + + align:start position:0% +it's its own task and then and then as +you said the scheduler scheduler will + + align:start position:0% +you said the scheduler scheduler will + + + align:start position:0% +you said the scheduler scheduler will +decide how to map these different tasks + + align:start position:0% +decide how to map these different tasks + + + align:start position:0% +decide how to map these different tasks +onto different processors or even if it + + align:start position:0% +onto different processors or even if it + + + align:start position:0% +onto different processors or even if it +wants to execute any of these tasks in + + align:start position:0% +wants to execute any of these tasks in + + + align:start position:0% +wants to execute any of these tasks in +parallel it's a good question okay so + + align:start position:0% +parallel it's a good question okay so + + + align:start position:0% +parallel it's a good question okay so +the idea in seok is to allow the + + align:start position:0% +the idea in seok is to allow the + + + align:start position:0% +the idea in seok is to allow the +programmer to express logical + + align:start position:0% +programmer to express logical + + + align:start position:0% +programmer to express logical +parallelism in an application so the + + align:start position:0% +parallelism in an application so the + + + align:start position:0% +parallelism in an application so the +programmer just has to identify which + + align:start position:0% +programmer just has to identify which + + + align:start position:0% +programmer just has to identify which +pieces of the code could be executed in + + align:start position:0% +pieces of the code could be executed in + + + align:start position:0% +pieces of the code could be executed in +parallel but doesn't necessarily have to + + align:start position:0% +parallel but doesn't necessarily have to + + + align:start position:0% +parallel but doesn't necessarily have to +determine which of the piece which + + align:start position:0% +determine which of the piece which + + + align:start position:0% +determine which of the piece which +pieces of code should be executed in + + align:start position:0% +pieces of code should be executed in + + + align:start position:0% +pieces of code should be executed in +parallel and then silk has a runtime + + align:start position:0% +parallel and then silk has a runtime + + + align:start position:0% +parallel and then silk has a runtime +scheduler that will monitor matically + + align:start position:0% +scheduler that will monitor matically + + + align:start position:0% +scheduler that will monitor matically +map the executing program on to the + + align:start position:0% +map the executing program on to the + + + align:start position:0% +map the executing program on to the +available processor cores runtime and it + + align:start position:0% +available processor cores runtime and it + + + align:start position:0% +available processor cores runtime and it +does this dynamically using + + align:start position:0% +does this dynamically using + + + align:start position:0% +does this dynamically using +work-stealing scheduling algorithm and + + align:start position:0% +work-stealing scheduling algorithm and + + + align:start position:0% +work-stealing scheduling algorithm and +the work stealing scheduler is used to + + align:start position:0% +the work stealing scheduler is used to + + + align:start position:0% +the work stealing scheduler is used to +balance the tasks evenly across the + + align:start position:0% +balance the tasks evenly across the + + + align:start position:0% +balance the tasks evenly across the +different processors and we'll talk more + + align:start position:0% +different processors and we'll talk more + + + align:start position:0% +different processors and we'll talk more +about the work stealing scheduler in a + + align:start position:0% +about the work stealing scheduler in a + + + align:start position:0% +about the work stealing scheduler in a +future lecture but I want to emphasize + + align:start position:0% +future lecture but I want to emphasize + + + align:start position:0% +future lecture but I want to emphasize +that unlike unlike the other concurrency + + align:start position:0% +that unlike unlike the other concurrency + + + align:start position:0% +that unlike unlike the other concurrency +platforms that we looked at today + + align:start position:0% +platforms that we looked at today + + + align:start position:0% +platforms that we looked at today +silks works the only scheduling + + align:start position:0% +silks works the only scheduling + + + align:start position:0% +silks works the only scheduling +algorithm is theoretically efficient + + align:start position:0% +algorithm is theoretically efficient + + + align:start position:0% +algorithm is theoretically efficient +whereas the OpenMP and TBB schedulers + + align:start position:0% +whereas the OpenMP and TBB schedulers + + + align:start position:0% +whereas the OpenMP and TBB schedulers +are not theoretically efficient so this + + align:start position:0% +are not theoretically efficient so this + + + align:start position:0% +are not theoretically efficient so this +is a nice property because it will + + align:start position:0% +is a nice property because it will + + + align:start position:0% +is a nice property because it will +guarantee you that + + align:start position:0% +guarantee you that + + + align:start position:0% +guarantee you that +the algorithms you write on top of silk + + align:start position:0% +the algorithms you write on top of silk + + + align:start position:0% +the algorithms you write on top of silk +will also be theoretically efficient + + align:start position:0% + + + + align:start position:0% + +okay so here's a high-level illustration + + align:start position:0% +okay so here's a high-level illustration + + + align:start position:0% +okay so here's a high-level illustration +of the silk ecosystem it's a very + + align:start position:0% +of the silk ecosystem it's a very + + + align:start position:0% +of the silk ecosystem it's a very +simplified view but I did this to fit it + + align:start position:0% +simplified view but I did this to fit it + + + align:start position:0% +simplified view but I did this to fit it +on a single slide so so what you do is + + align:start position:0% +on a single slide so so what you do is + + + align:start position:0% +on a single slide so so what you do is +you take the silk source code you pass + + align:start position:0% +you take the silk source code you pass + + + align:start position:0% +you take the silk source code you pass +it to your favorite silk compiler the + + align:start position:0% +it to your favorite silk compiler the + + + align:start position:0% +it to your favorite silk compiler the +taper LLVM compiler and this gives you a + + align:start position:0% +taper LLVM compiler and this gives you a + + + align:start position:0% +taper LLVM compiler and this gives you a +binary that you can run on multiple + + align:start position:0% +binary that you can run on multiple + + + align:start position:0% +binary that you can run on multiple +processors and then you pass a program + + align:start position:0% +processors and then you pass a program + + + align:start position:0% +processors and then you pass a program +input to the binary you run it on + + align:start position:0% +input to the binary you run it on + + + align:start position:0% +input to the binary you run it on +however many processors you you have and + + align:start position:0% +however many processors you you have and + + + align:start position:0% +however many processors you you have and +then this allows you to benchmark the + + align:start position:0% +then this allows you to benchmark the + + + align:start position:0% +then this allows you to benchmark the +parallel performance of your program you + + align:start position:0% +parallel performance of your program you + + + align:start position:0% +parallel performance of your program you +can also do serial testing and to do + + align:start position:0% +can also do serial testing and to do + + + align:start position:0% +can also do serial testing and to do +this you just obtain a serial illusion + + align:start position:0% +this you just obtain a serial illusion + + + align:start position:0% +this you just obtain a serial illusion +of the Silk program and you pass it to + + align:start position:0% +of the Silk program and you pass it to + + + align:start position:0% +of the Silk program and you pass it to +an ordinary C or C++ compiler generates + + align:start position:0% +an ordinary C or C++ compiler generates + + + align:start position:0% +an ordinary C or C++ compiler generates +a binary that can only run on a single + + align:start position:0% +a binary that can only run on a single + + + align:start position:0% +a binary that can only run on a single +processor and you run your suite of + + align:start position:0% +processor and you run your suite of + + + align:start position:0% +processor and you run your suite of +serial regression tests on this single + + align:start position:0% +serial regression tests on this single + + + align:start position:0% +serial regression tests on this single +threaded binary and this will allow you + + align:start position:0% +threaded binary and this will allow you + + + align:start position:0% +threaded binary and this will allow you +to benchmark to performance of your + + align:start position:0% +to benchmark to performance of your + + + align:start position:0% +to benchmark to performance of your +serial code and also debug any issues + + align:start position:0% +serial code and also debug any issues + + + align:start position:0% +serial code and also debug any issues +that might have arised when you are + + align:start position:0% +that might have arised when you are + + + align:start position:0% +that might have arised when you are +running this program sequentially + + align:start position:0% + + + + align:start position:0% + +another way to do this is you can + + align:start position:0% +another way to do this is you can + + + align:start position:0% +another way to do this is you can +actually just compile the original silk + + align:start position:0% +actually just compile the original silk + + + align:start position:0% +actually just compile the original silk +code but run it on a single processor so + + align:start position:0% +code but run it on a single processor so + + + align:start position:0% +code but run it on a single processor so +there's a command-line argument that + + align:start position:0% +there's a command-line argument that + + + align:start position:0% +there's a command-line argument that +tells the runtime system how many + + align:start position:0% +tells the runtime system how many + + + align:start position:0% +tells the runtime system how many +processors you want to use any of you + + align:start position:0% +processors you want to use any of you + + + align:start position:0% +processors you want to use any of you +set that parameter to 1 then it will + + align:start position:0% +set that parameter to 1 then it will + + + align:start position:0% +set that parameter to 1 then it will +only use a single processor and this + + align:start position:0% +only use a single processor and this + + + align:start position:0% +only use a single processor and this +allows you to benchmark the + + align:start position:0% +allows you to benchmark the + + + align:start position:0% +allows you to benchmark the +single-threaded performance of your code + + align:start position:0% +single-threaded performance of your code + + + align:start position:0% +single-threaded performance of your code +as well and the parallel program + + align:start position:0% +as well and the parallel program + + + align:start position:0% +as well and the parallel program +executing on a single course should + + align:start position:0% +executing on a single course should + + + align:start position:0% +executing on a single course should +behave exactly the same way as the + + align:start position:0% +behave exactly the same way as the + + + align:start position:0% +behave exactly the same way as the +execution of this serial Alishan so + + align:start position:0% +execution of this serial Alishan so + + + align:start position:0% +execution of this serial Alishan so +that's one of the advantages of using + + align:start position:0% +that's one of the advantages of using + + + align:start position:0% +that's one of the advantages of using +silk and because because you can easily + + align:start position:0% +silk and because because you can easily + + + align:start position:0% +silk and because because you can easily +do serial testing using the silk + + align:start position:0% +do serial testing using the silk + + + align:start position:0% +do serial testing using the silk +platform this allows you to separate out + + align:start position:0% +platform this allows you to separate out + + + align:start position:0% +platform this allows you to separate out +the serial correctness from the parallel + + align:start position:0% +the serial correctness from the parallel + + + align:start position:0% +the serial correctness from the parallel +correctness as I said earlier you can + + align:start position:0% +correctness as I said earlier you can + + + align:start position:0% +correctness as I said earlier you can +first debug the serial correctness as + + align:start position:0% +first debug the serial correctness as + + + align:start position:0% +first debug the serial correctness as +well as any performance issues before + + align:start position:0% +well as any performance issues before + + + align:start position:0% +well as any performance issues before +moving on to the parallel version and + + align:start position:0% +moving on to the parallel version and + + + align:start position:0% +moving on to the parallel version and +another point I want to make is that + + align:start position:0% +another point I want to make is that + + + align:start position:0% +another point I want to make is that +because the because Silk actually uses + + align:start position:0% +because the because Silk actually uses + + + align:start position:0% +because the because Silk actually uses +the serial program inside his tasks it's + + align:start position:0% +the serial program inside his tasks it's + + + align:start position:0% +the serial program inside his tasks it's +actually good to optimize a serial + + align:start position:0% +actually good to optimize a serial + + + align:start position:0% +actually good to optimize a serial +program even when you're writing a + + align:start position:0% +program even when you're writing a + + + align:start position:0% +program even when you're writing a +parallel program because optimizing the + + align:start position:0% +parallel program because optimizing the + + + align:start position:0% +parallel program because optimizing the +serial program for performance will also + + align:start position:0% +serial program for performance will also + + + align:start position:0% +serial program for performance will also +translate to better parallel performance + + align:start position:0% + + + + align:start position:0% + +another nice feature of seok is that it + + align:start position:0% +another nice feature of seok is that it + + + align:start position:0% +another nice feature of seok is that it +has this tool called silks and which + + align:start position:0% +has this tool called silks and which + + + align:start position:0% +has this tool called silks and which +stands for silk sanitizer and the silk + + align:start position:0% +stands for silk sanitizer and the silk + + + align:start position:0% +stands for silk sanitizer and the silk +silks and will detect any determinacy + + align:start position:0% +silks and will detect any determinacy + + + align:start position:0% +silks and will detect any determinacy +races that you have in your code which + + align:start position:0% +races that you have in your code which + + + align:start position:0% +races that you have in your code which +will significantly help you with + + align:start position:0% +will significantly help you with + + + align:start position:0% +will significantly help you with +debugging the correctness and as well as + + align:start position:0% +debugging the correctness and as well as + + + align:start position:0% +debugging the correctness and as well as +the performance of your code so silks + + align:start position:0% +the performance of your code so silks + + + align:start position:0% +the performance of your code so silks +and wool if you compile the silk code + + align:start position:0% +and wool if you compile the silk code + + + align:start position:0% +and wool if you compile the silk code +using the silks and flag it will + + align:start position:0% +using the silks and flag it will + + + align:start position:0% +using the silks and flag it will +generate an instrumented binary that + + align:start position:0% +generate an instrumented binary that + + + align:start position:0% +generate an instrumented binary that +when you run it will find and localize + + align:start position:0% +when you run it will find and localize + + + align:start position:0% +when you run it will find and localize +all of the determinacy races in your + + align:start position:0% +all of the determinacy races in your + + + align:start position:0% +all of the determinacy races in your +programs it will tell you where the + + align:start position:0% +programs it will tell you where the + + + align:start position:0% +programs it will tell you where the +determinacy races occur so that you can + + align:start position:0% +determinacy races occur so that you can + + + align:start position:0% +determinacy races occur so that you can +go inspect that part of your code and + + align:start position:0% +go inspect that part of your code and + + + align:start position:0% +go inspect that part of your code and +fix it if necessary so this is a very + + align:start position:0% +fix it if necessary so this is a very + + + align:start position:0% +fix it if necessary so this is a very +useful tool for benchmarking your + + align:start position:0% +useful tool for benchmarking your + + + align:start position:0% +useful tool for benchmarking your +parallel programs silk also has another + + align:start position:0% +parallel programs silk also has another + + + align:start position:0% +parallel programs silk also has another +nice tool called silk scale silk scale + + align:start position:0% +nice tool called silk scale silk scale + + + align:start position:0% +nice tool called silk scale silk scale +it's a performance analyzer it will + + align:start position:0% +it's a performance analyzer it will + + + align:start position:0% +it's a performance analyzer it will +analyze how much parallelism is + + align:start position:0% +analyze how much parallelism is + + + align:start position:0% +analyze how much parallelism is +available in your program as well as the + + align:start position:0% +available in your program as well as the + + + align:start position:0% +available in your program as well as the +total amount of work that it's doing so + + align:start position:0% +total amount of work that it's doing so + + + align:start position:0% +total amount of work that it's doing so +again you pass a flag to the compiler + + align:start position:0% +again you pass a flag to the compiler + + + align:start position:0% +again you pass a flag to the compiler +that will turn on silk silk scale and it + + align:start position:0% +that will turn on silk silk scale and it + + + align:start position:0% +that will turn on silk silk scale and it +will generate a binary that is + + align:start position:0% +will generate a binary that is + + + align:start position:0% +will generate a binary that is +instrumented and then when you run run + + align:start position:0% +instrumented and then when you run run + + + align:start position:0% +instrumented and then when you run run +this code it will give you a scalability + + align:start position:0% +this code it will give you a scalability + + + align:start position:0% +this code it will give you a scalability +report so you'll find these tools very + + align:start position:0% +report so you'll find these tools very + + + align:start position:0% +report so you'll find these tools very +useful when you're doing the next + + align:start position:0% +useful when you're doing the next + + + align:start position:0% +useful when you're doing the next +project and we'll talk a little bit more + + align:start position:0% +project and we'll talk a little bit more + + + align:start position:0% +project and we'll talk a little bit more +about these two tools in the next + + align:start position:0% +about these two tools in the next + + + align:start position:0% +about these two tools in the next +lecture + + align:start position:0% + + + + align:start position:0% + +right as I said silk skill will analyze + + align:start position:0% +right as I said silk skill will analyze + + + align:start position:0% +right as I said silk skill will analyze +how well your program will scale to + + align:start position:0% +how well your program will scale to + + + align:start position:0% +how well your program will scale to +larger machines so as it will basically + + align:start position:0% +larger machines so as it will basically + + + align:start position:0% +larger machines so as it will basically +tell you the + + align:start position:0% +tell you the + + + align:start position:0% +tell you the +maximum number of processors that your + + align:start position:0% +maximum number of processors that your + + + align:start position:0% +maximum number of processors that your +code could possibly take advantage of + + align:start position:0% + + + + align:start position:0% + +any questions yes so I mean the + + align:start position:0% +any questions yes so I mean the + + + align:start position:0% +any questions yes so I mean the +scheduler the silk runtime scheduler + + align:start position:0% +scheduler the silk runtime scheduler + + + align:start position:0% +scheduler the silk runtime scheduler +does scheduling that different tasks + + align:start position:0% +does scheduling that different tasks + + + align:start position:0% +does scheduling that different tasks +when you're running the program so it's + + align:start position:0% +when you're running the program so it's + + + align:start position:0% +when you're running the program so it's +linked from the binary it's not stored + + align:start position:0% +linked from the binary it's not stored + + + align:start position:0% +linked from the binary it's not stored +in the same place it's linked other + + align:start position:0% +in the same place it's linked other + + + align:start position:0% +in the same place it's linked other +questions all right so let me summarize + + align:start position:0% +questions all right so let me summarize + + + align:start position:0% +questions all right so let me summarize +what we looked at today so first we saw + + align:start position:0% +what we looked at today so first we saw + + + align:start position:0% +what we looked at today so first we saw +that most processors today have multiple + + align:start position:0% +that most processors today have multiple + + + align:start position:0% +that most processors today have multiple +cores and probably all of your laptops + + align:start position:0% +cores and probably all of your laptops + + + align:start position:0% +cores and probably all of your laptops +have more than one core on it who has a + + align:start position:0% +have more than one core on it who has a + + + align:start position:0% +have more than one core on it who has a +laptop that only has one core ok when + + align:start position:0% +laptop that only has one core ok when + + + align:start position:0% +laptop that only has one core ok when +did you buy it + + align:start position:0% +did you buy it + + + align:start position:0% +did you buy it +yeah probably a long time ago I see so + + align:start position:0% +yeah probably a long time ago I see so + + + align:start position:0% +yeah probably a long time ago I see so +so nowadays obtaining high performance + + align:start position:0% +so nowadays obtaining high performance + + + align:start position:0% +so nowadays obtaining high performance +on your machines requires you to write + + align:start position:0% +on your machines requires you to write + + + align:start position:0% +on your machines requires you to write +parallel programs but parallel + + align:start position:0% +parallel programs but parallel + + + align:start position:0% +parallel programs but parallel +programming can be very hard especially + + align:start position:0% +programming can be very hard especially + + + align:start position:0% +programming can be very hard especially +if you have to program directly on the + + align:start position:0% +if you have to program directly on the + + + align:start position:0% +if you have to program directly on the +processor cores and interact with the + + align:start position:0% +processor cores and interact with the + + + align:start position:0% +processor cores and interact with the +operating system yourself so silk is + + align:start position:0% +operating system yourself so silk is + + + align:start position:0% +operating system yourself so silk is +very nice because it abstracts the + + align:start position:0% +very nice because it abstracts the + + + align:start position:0% +very nice because it abstracts the +processor cores from the programmer a + + align:start position:0% +processor cores from the programmer a + + + align:start position:0% +processor cores from the programmer a +handle synchronization and communication + + align:start position:0% +handle synchronization and communication + + + align:start position:0% +handle synchronization and communication +protocols and it also performs provably + + align:start position:0% +protocols and it also performs provably + + + align:start position:0% +protocols and it also performs provably +good load balancing and in the next + + align:start position:0% +good load balancing and in the next + + + align:start position:0% +good load balancing and in the next +project you'll have a chance to play + + align:start position:0% +project you'll have a chance to play + + + align:start position:0% +project you'll have a chance to play +around with silk you'll be implementing + + align:start position:0% +around with silk you'll be implementing + + + align:start position:0% +around with silk you'll be implementing +your own parallel screensaver so that's + + align:start position:0% +your own parallel screensaver so that's + + + align:start position:0% +your own parallel screensaver so that's +a very fun project to do and possibly in + + align:start position:0% +a very fun project to do and possibly in + + + align:start position:0% +a very fun project to do and possibly in +one of the future lectures we'll post + + align:start position:0% +one of the future lectures we'll post + + + align:start position:0% +one of the future lectures we'll post +some of the nicest screen savers that + + align:start position:0% +some of the nicest screen savers that + + + align:start position:0% +some of the nicest screen savers that +students developed for everyone to see + + align:start position:0% +students developed for everyone to see + + + align:start position:0% +students developed for everyone to see +ok so that's all + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/dxR06Mi8ExI.txt b/dxR06Mi8ExI.txt new file mode 100644 index 0000000000000000000000000000000000000000..10cb01e74d58adbecd55b58de088b28d10f7e2a5 --- /dev/null +++ b/dxR06Mi8ExI.txt @@ -0,0 +1,1645 @@ +The following content is +provided by MIT OpenCourseWare + +under a Creative Commons +license. + +Additional information about +our license and MIT + +OpenCourseWare in general is +available at ocw.mit.edu. + +What I am going to do today is +I am going to start talking + +about the development of atomic +theory. + +I am going to whiz through what +the evidence is for the + +existence of atoms. +And then, we are going to talk + +about how the atom is not the +most basic constituent of + +matter, how the atom can be +divided into at least an + +electron and a nucleus. +And then, what we are going to + +see is how the existing +classical way of thinking, + +Newtonian mechanics, +cannot explain how that + +electron and that nucleus hangs +together. + +And later on in the course, +we are going to see how that + +existing classical physics is +not going to be able to explain + +how two atoms hang together. +We are going to look at the + +fundamental principles, +here, of chemical bonding. + +I am going to get going on this +subject. + +Then, about three-quarters of +the way through, + +I am going to stop. +And then I will do some + +introductions of our teaching +team this semester. + +And then also we will talk +about the mechanics of the + +course and some expectations of +the course. + +Let's get going. +Certainly, the Ancient Greeks + +were known to have pondered +whether matter can be divided ad + +infinitum into smaller and +smaller pieces, + +chopped up into smaller and +smaller pieces, + +or whether there was a point at +which you couldn't chop up + +matter any further. +Aristotle over here was one of + +those philosophers who believed +that matter was infinitely + +divisible. +You could chop it up ad + +infinitum. +This is called the continuum + +theory of matter. +It is a continuum. + +There is no discreteness to +matter. + +That was his view of the +structure of matter, + +but there was a minority +opinion. + +An opinion actually held by +Democritus who was 100 years + +older than Aristotle. +And Democritus believed that + +matter was composed of discrete +particles called, + +in Greek, "atomos," "a" meaning +not, "tomos" meaning divisible, + +not divisible particles. +Well, for whatever reason, + +Aristotle's continuum theory of +matter prevailed all the way up + +to the 17th century. +And here he is depicted by + +Raphael, the frescos on the +walls in the Vatican holding + +court on the continuum theory of +matter. + +But at the same time that +Raphael actually painted this + +picture, there were beginning to +accumulate some observations + +about how matter behaved and how +it reacted that did not quite + +jive with this continuum theory +of matter. + +And what were those +observations? + +Well, one of those observations +was by this gentleman, + +Robert Boyle. +Guess what his profession was. + +Chemist? +Good guess. + +He was actually a theologian, +as most chemists were at that + +time. +You know him largely for the + +empirical observation that if +you take the pressure times the + +volume of a gas, +it is always a constant. + +At least when the temperature +is constant. + +But Robert Boyle also put forth +probably the first idea of an + +element. +And he called elements certain + +primitive unmingled bodies. +And he also put forth the idea + +that these unmingled bodies were +the ingredients of perfectly + +mixed bodies. +Just a pseudonym for molecules, + +for compounds. +And then there is the work of + +this gentleman, +Joseph Priestley. + +Guess what his occupation was. +Right, he was a priest. + +And what he did was he carried +out some reactions of + +dephlogisticated air with +various materials. + +And what he found was that +materials reacted more + +vigorously in dephlogisticated +air than they did in + +undephlogisticated air. +And, of course, + +dephlogisticated air is nothing +other than oxygen. + +It is the air with the nitrogen +removed from it. + +But it really took this +gentleman, Lavoisier, + +to understand what Priestley's +experiments were all about. + +And what Lavoisier realized is +that when materials were + +reacting with this +dephlogisticated air, + +this dephlogisticated air was +kind of adding to the material. + +And he came to that conclusion +because he did some very careful + +measurements of the mass of the +dephlogisticated air plus the + +material before the reaction and +some careful measurements after. + +And found that they were indeed +equal. + +There was a conservation of +mass. + +And from that Lavoisier was +really the first person to + +realize that a chemical reaction +was analogous to an algebraic + +equation. +He also went on to isolate 17 + +different metals and identified +them as elements and nine + +different nonmetals and +identified them as elements. + +But for all of his efforts, +well, we all know what happened + +to him. +He was advisor to the French + +Monarchy. +The judge at his trial + +proclaimed the Republic has no +use for Savants. + +LaGrange, who was a +mathematician at that time, + +said, "It took but a moment to +cut off that head, + +though 100 years will be +required to produce another like + +it." Well, here we have some +observations and we have some + +observations -- +Oh, I forgot one other person + +here. +That's this guy, + +J. +L. + +Proust. +J. + +L. +Proust was also a French + +scientist at that time, +but he was a little more + +politically savvy. +And so he high-tailed it out of + +France and lived a long and +productive life as a professor + +in Madrid. +And what he did were + +experiments. +He recognized from the results + +that when two elements combine +to form a given compound, + +they always did so in definite +proportions by weight, + +regardless of what kind of +method of preparation he used to + +make that particular compound. +Here is an example where matter + +didn't quite behave as a +continuum. + +There was a discreteness of +some sense to matter. + +And it really took John Dalton, +an English schoolteacher with + +broad interests, +to realize, or to recognize + +these observations of Priestley, +of Lavoisier, + +of Proust that he could +understand all of these + +observations if he resurrected +the idea of Democritus, + +the idea of atomos, +or atoms. + +And so he forth some +postulates. + +Well, those postulates are now +known as Dalton's Atomic Theory, + +but they were postulates at the +time. + +And those postulates say each +element is composed of atoms, + +atoms of a given element are +identical and that compounds + +form when atoms of more than one +element combine. + +And, of course, +that atoms are not created or + +destroyed. +And then, just an aside, + +Dalton, with his very broad +range of interest, + +was also really the first +person to document + +colorblindness in humans. +Colorblindness is also called + +Daltonism. +You see, we are getting you set + +for medical school already. +But I want you to recognize + +here that Dalton didn't actually +do any of these experiments + +himself. +I think he could have, + +but he didn't. +Instead he just said that if + +Lavoisier was right and Proust's +observations are right, + +well, then I can understand +those observations in terms of + +this framework of postulates. +And I point this out because + +this is a powerful method in +science, a powerful way in which + +science works in that there are +often some observations + +seemingly disparate. +And then somebody comes along + +and recognizes a unifying +factor. + +In this case, +the presence of atoms or + +discrete particles. +Now, of course, + +Dalton's Atomic Theory here was +not immediately accepted. + +And rightfully so. +It needed further + +substantiation. +And that further substantiation + +came in the form of work by this +gentleman, Joseph Gay-Lussac, + +the Law of Combining Volumes. +It came in the form of work by + +Lorenzo Romano Amedeo Carlo +Avogadro's hypothesis. + +And here I want you to realize +that, even though you didn't + +know it, you indeed can read +Italian. + +It says "equal volumes of gases +under the same conditions of + +temperature yield the same +number of molecules or atoms." + +There you go. +That is from an Italian stamp. + +You can read Italian. +And that further substantiation + +came from the work of this +gentleman, Ludwig Boltzmann, + +gas kinetic theory, +who recognized - you know - the + +pressure of a gas that must be +due to individual particles that + +are moving and that are ramming +into the walls of some vessel. + +That must be what gives rise to +pressure. + +And then, finally, +it took a statesman, + +Cannizzaro. +And what Cannizzaro did was he + +got the scientific establishment +at that time, + +and the scientific +establishment at that time for + +sure was a small group of pale +males, to listen to Dalton's + +Atomic Theory and to the +supporting data from Avogadro + +and company. +And ultimately got them to say, + +yes, there is something to it +here. + +And so by the late 1800s, +the idea of atoms was pretty + +strongly ingrained in the +scientific community. + +Now, of course nowadays we can +actually see individual atoms + +for molecules. +And so here is a picture of 28 + +individual CO molecules arranged +in the form of a little man or a + +little woman, +I don't know which. + +And each one of these CO +molecules is an orange ball. + +And what you are looking at are +these CO molecules bound to a + +platinum surface. +They are bound to a platinum + +surface such that the carbon end +is down and the oxygen end is + +up. +And there is a really good + +reason why the carbon end is +down and the oxygen end is up. + +And Professor Cummins, +whom I am going to introduce to + +you in a few minutes, +is going to talk to you about + +what that really good reason is +in the second half of the + +course. +We know why this is case. + +What you are looking at here is +really looking at the oxygen end + +of the CO molecule, +because we are looking at a top + +view. +All right. + +How is this image made? +Well, this image was made by a + +technique called scanning +tunneling microscopy that was + +invented before you were born, +I am sorry to say. + +I am sorry for myself to say. +It was worked on by Ruska and + +then perfected by Binnig and +Rohrer. + +And they earned themselves a +Nobel Prize for this work. + +And the way this techniques +works is the following. + +What you are going to do is +take a thin tungsten wire. + +It might be 0.01 inches in +diameter. + +And you etch it down to a fine +tip. + +You stick it in some potassium +hydroxide, do a little + +electrochemistry and etch it +down to as fine a tip as you can + +make it. +Then you attach that tungsten + +wire to something called a +piezoelectric crystal. + +And a piezoelectric material is +one in which, + +if you put a voltage across it, +you can make it expand a little + +bit, 10, 20 angstroms or so. +And if you can make it expand a + +little bit like that, +well, then you've got control + +on an angstrom-type level. +You attach it to some + +piezoelectric crystal here then +it allows you to move that + +tungsten tip by a very, +very small amount. + +You bring that tungsten tip +close to the top of this CO + +molecule sitting on this +platinum surface. + +And say you bring it to within, +oh, I don't know, + +5 angstroms or so from the +oxygen atom. + +Now, the tungsten has +electrons. + +And since this is a bulk metal, +some of those electrons are not + +firmly attached to a particular +nuclei. + +There is a sea of electrons. +And what we are going to do is + +put a negative potential on that +tungsten tip. + +And we are going to ground here +this platinum surface. + +Now, these electrons on the +tungsten, they are in this + +environment of a negative +potential. + +And that is a high-energy state +for them because they are + +negatively charged particles. +If I were to draw here an + +energy level diagram, +I am going to represent then + +the energy level of the +electrons here in this tungsten, + +around this tungsten tip as +some high energy over here. + +There are electrons on the +tungsten. + +Whereas, the electrons +associated with the platinum and + +the CO here, all of which are in +contact with each other, + +well, they are at ground. +That is a lower energy state + +for these negatively charged +particles. + +We are going to represent it by +this. + +This is the electrons on +platinum. + +And so this axis here is kind +of a distance access. + +These are the electrons on the +tip. + +These are the electrons on the +platinum. + +We are measuring kind of +distance here, + +from here to here, +in the vertical direction + +there. +There is a thermodynamic + +driving force for the electrons +on the tungsten tip to want to + +be here on the platinum, +but the problem is that this + +tungsten is not in contact with +this oxygen end here. + +There is a gap. +And if this is in a vacuum, + +we call this a vacuum gap. +And so for an electron to be + +inside of this vacuum gap, +well, that is a very high + +energy state for those +electrons. + +And so, if we were to look at +an energy level diagram here, + +that energy actually goes up +pretty high before it comes back + +down. +There is a barrier to getting + +the electrons from the tip to +the platinum surface. + +Well, you have seen this kind +of reaction coordinate before. + +You have, I am sure. +If you look at an energy level + +diagram here for some reactions, +sometimes you have reactants + +here at a high energy and +products here at a lower energy. + +And, in order to get from +reactants to products, + +there is a barrier, +an activation energy barrier. + +You called it E(act) or +something like that. + +And you know that in chemical +reactions typically what you + +have got to do is put energy +into the system in order to get + +over this barrier before you get +any energy out, + +before the reaction can +proceed. + +And that is what happens in a +lot of chemical reactions. + +There is a barrier and you have +got to supply that energy to get + +over it before you can make the +reaction go. + +But over here, +in the case of electrons, + +those electrons don't act like +atoms and molecules do, + +for the most part. +These electrons, + +what do they do? +They ignore this barrier and + +tunnel right through the +barrier, go right through that + +brick wall. +How can they do that? + +Well, they can do that because +they are quantum mechanical + +particles. +We cannot treat those electrons + +like we treat atoms and +molecules which, + +for the most part, +behave as classical particles. + +And, actually, +this is going to be the subject + +of the first few lectures here, +the need for this new kind of + +mechanics to explain phenomenon +like this and to explain + +chemical bonding. +All right. + +So, these electrons tunnel +right through. + +What does that mean? +Well, what that means here, + +for this experiment, +is that if I then take and + +attach a wire to the tungsten +tip and a wire to the platinum + +surface and I put an ammeter in +between, I will see a + +measurement of a current. +There are electrons going from + +this tungsten tip to this +platinum surface. + +I measure a current. +Well, that is nice. + +But now, from that, +how do I get this image of + +these 28 CO molecules? +Well, what I do is I also have + +this tungsten tip mounted not +only on a piezoelectric crystal + +that allows me to go up and +down. + +But another piezoelectric +crystal, which allows me to move + +it from side to side with +control on the order of an + +angstrom. +I can take the tungsten tip and + +I am going to move it over by a +certain amount. + +And exactly I am going to know +that certain amount is because I + +calibrated my piezoelectric +crystal. + +But now, when I move that +tungsten tip over, + +what is going to happen to this +current here? + +Pardon? +It is going to go down. + +It is going to plummet. +It is going to go to zero. + +Why? +Because when I move this tip + +over, I increase the distance +between the end of the tip and + +the oxygen onto the molecule. +And when I increase the + +distance, what I do is make this +barrier wider. + +And the wider the barrier is, +the more difficult it is for + +those electrons to tunnel +through. + +And so the current actually +goes down. + +To compensate for that, +I am now going to take the + +tungsten tip and move it down by +just enough such that I + +reestablish the current that I +originally have. + +And, of course, +I know exactly by how much I + +moved it down because, +again, I have my tip + +calibrated. +I've got two points now. + +I need a third point. +I am going to take that + +tungsten tip and I am going to +move it over again. + +Again, the current is going to +go down. + +But, in order to reestablish +the original current I had, + +I am going to move this down +further. + +And, again, I will know how +much I move the tip over and I + +will know exactly how much I +move the tip down. + +To get that image, +I am going to provide a color + +code. +I am going to say that when the + +tungsten tip is the largest +distance away from the surface, + +well, then that is going to +show up here on this picture and + +it is going to show up as a very +light color. + +That is the highest points. +When the tungsten tip is a + +little bit closer to the +surface, well, + +that is going to show up as the +darker colors. + +And, as it gets lower and lower +and lower, it is going to be + +deeper and deeper orangey. +Finally, when I am actually + +tunneling to the platinum +surface, instead of a CO + +molecule, I am going to make +that a blue color. + +That is how we get the image of +this molecular man. + +Now, you do see that these CO +molecules are in the form of a + +little person. +This does not represent, + +in the most au courant +language, intelligent design. + +Rather, this represents the +work of a very patient + +experimentalist, +i.e., graduate student, + +who spent 24 hours, +and I know this to be the case, + +moving these CO molecules into +this particular arrangement. + +How did he do that? +Well, how he did that is the + +following. +What he did was took this + +platinum surface and then opened +up a bottle of CO in the vacuum + +chamber, or let some CO into the +vacuum chamber, + +and the molecules just absorbed +anywhere they wanted to, + +well, sort of anywhere they +wanted to on this platinum + +surface. +First of all, + +he had to figure out where the +molecules were. + +The soccer balls are the CO +molecules and the tungsten tip + +here is my leg and my foot. +And so the first thing he did + +was scan the surface in order to +figure out where the CO + +molecules are and goes, +okay, I know where they are. + +Then he brought this tip down +right next to one of the CO + +molecules. +Then he gave that piezoelectric + +crystal a pulse of voltage which +jerked it and the CO molecule + +went flying away. +Well, that is nice, + +but now where is it? +Again, you have got to go scan + +along the whole surface to find +it. + +Well, he pushed it over too +far. + +Now we have got to come over +here, put the tip down, + +give another voltage pulse +before his tip breaks. + +Well, you get the idea. +24 hours later, + +you've got it. +This is the beginnings of + +nanotechnology. +You can see that it is going to + +be a long time before +manipulation of individual atoms + +and molecules like this, +one at a time, + +before that competes +effectively with synthesis in a + +beaker where you get the +molecules right where you want + +them because of chemistry +instead of this mechanical + +manipulation. +Well, even though 100 years ago + +these direct observations of +atoms and molecules was not + +possible, it was by the late +1800s pretty well accepted, + +or the evidence for the atomic +structure of matter, + +atoms as the most basic +constituent of matter, + +that evidence was really pretty +compelling. + +And, in fact, +by the late 1800s, + +it was basically believed that +the theoretical structure of the + +universe was complete. +Nature was understood. + +There were no big discoveries +to be made yet. + +And, in fact, +there was some justification + +for that attitude, +because certainly by the late + +1800s Newtonian mechanics, +the mechanics that described + +how bodies all around us moved, +including astronomical bodies, + +well, that had already been +known for over 200 years. + +Thermodynamics was formulated +already by that time. + +Statistical mechanics was also +formulated by that time. + +Statistical mechanics is a +field that relates the + +microscopic description of +matter to the macroscopic + +behavior of matter. +And, very importantly, + +there were experiments by +Young, Fresnel and Hertz that + +seemed to put to rest the notion +that light was a particle. + +Those experiments really +nailed, or seemed to nail the + +idea of light as a wave, +light has wavelike particles. + +They verified Maxwell's +equations that unified the + +fields of optics and +electromagnetism. + +All of these accomplishments +surely did justify a very proud + +feeling amongst the scientific +community. + +And, at that time, +the feeling was that the work + +that remained was largely to +investigate the next decimal + +place and that is it. +Well, if you look really + +carefully, though, +at the evidence, + +even with all of these +accomplishments, + +there were beginning to be, +in the late 1800s, + +some experiments that were +suggesting that, + +one, maybe the atom was not the +most basic constituent of + +matter. +That was the first set of + +measurements that indicated +something was amiss, + +the fact that the atom wasn't +the most elementary particle. + +And we are going to look at +these sets of measurements. + +Second, the other observation +that hinted that this classical + +thinking as amiss was the +observation of the photoelectric + +effect. +Because the photoelectric + +effect, what it did was it +showed that light was behaving + +like a particle and not a wave, +and that sent a lot of + +consternation throughout the +scientific community. + +We are going to look at these +two tracks. + +And we are going to start by +talking about the fact that the + +atom is not the most basic +constituent of matter. + +That at least you can divide +the atom up into an electron and + +a nucleus. +We are going to start here with + +this gentleman, +J.J. + +Thompson. +Remember that name. + +It is going to come back. +Discovery of the electron. + +This is 1897. +What J.J. + +Thompson was interested in +doing was understanding what a + +discharge was, +or what made up a discharge. + +For example, +if you have a glass vessel that + +you evacuate and then you have a +cathode in that glass vessel and + +you have an anode in that glass +vessel, and you also put some + +molecular hydrogen in it, +fill it up with molecular + +hydrogen. +But now what you do is put a + +negative voltage on the cathode +and a positive voltage on the + +anode. +And you crank up the potential + +energy difference, +the voltage difference between + +the cathode and the anode. +And you keep cranking it up. + +You have to get really pretty +high, but at some point all of a + +sudden what happens is that the +gas here begins to blow. + +And you get the establishment +of this discharge, + +this plasma. +And J.J. + +Thompson was just interested in +finding out what was in this + +plasma. +What he did to investigate it + +is he punched a hole in this +anode right here and let out a + +little bit of this plasma. +He let it impinge on a kind of + +phosphor screen here. +Even though the plasma leaking + +out was kind of glowing in the +dark, well, it also was glowing + +when it hit the phosphor screen. +That lit up. + +But then he took a pair of +parallel metal plates above and + +below this luminous beam and put +a potential difference on them, + +some delta V. +And this delta V is just a + +fraction of what this delta V +is, so it is very small. + +But what he noticed is that +some of this luminous beam was + +actually attracted toward that +positively charged plate. + +And so, if you have got +something that is attracted to + +this positively charged plate, +what does it mean about this + +particle? +It is negatively charged. + +It is just Coulomb's +interaction. + +And he could measure right here +the amount of deflection from + +the center line. +I am going to call that amount + +of deflection delta X sub minus +to indicate that + +this looks like a negatively +charged particle. + +Now, Thompson also knew enough +electromagnetism at that time to + +realize that the amount of that +deflection has to be directly + +proportional to the charge on +that particle. + +In other words, +the greater the charge the + +larger the deflection. +I am going to represent that + +charge by E sub minus. +He also recognized that the + +heavier that particle, +the more difficult it is going + +to be to deflect the particle to +the positively charged plate. + +That amount of deflection is +going to be inversely + +proportional to the mass of that +negatively charged particle. + +But then Thompson did a further +experiment. + +He increased delta V even more. +And here, I am taking a little + +liberty with the story. +It is a little bit more + +complicated, but I am just +trying to get the essence here + +across. +He cranked this up some more. + +And then, if you looked really, +really carefully, + +what happened is he also saw +some of this being deflected + +toward the negatively charged +plate. + +Indicating that, +lo and behold, + +there must also be some +positively charged particles in + +this luminous beam. +And he called that deflection + +delta X sub plus. +Again, the amount of deflection + +for the positively charged +particles has to be proportional + +to the charge on that positively +charged particle and inversely + +proportional to the mass of that +positively charged particle. + +But the other critical +observation that he made was + +that the amount of deflection +for a given voltage, + +for that negatively charged +particle was much, + +much larger that the amount of +deflection for the positively + +charged particle. +That is the evidence. + +Now we have to think. +Now we have to make some + +guesses. +What he guessed is that the + +positively charged particles +here were H plus. + +How did he know that? +Well, what he did know is that + +in this plasma there were some +neutral hydrogen atoms. + +He knew that. +How he knew that I am going to + +tell you, or we are going to +talk about in a few days. + +But he knew that this plasma +takes the H two molecule + +and tears it apart and makes +hydrogen atoms. + +And he knew it was neutral. +And so he reasoned that what + +must be happening is that +something has to be coming off + +of this hydrogen atom to make it +a positively charged particle. + +He said, okay, +this is going to be H plus. + +But then, because this was + +neutral to begin with, +whatever came off of the + +hydrogen has to be that +negatively charged particle so + +that when they come together +they are neutral, + +because a hydrogen atom is +neutral. + +And, of course, +ultimately that negatively + +charged particle was called an +electron. + +But the key point is that he +said, well, it must be then, + +when these two particles come +together, you are going to have + +a neutral particle. +It must be that the absolute + +magnitude of the charge on that +negatively charged particle, + +the electron, +that has to equal the magnitude + +of the charge on that positively +charged particle, + +this hydrogen plus ion. +That was the conjecture. + +Well, if that is the case, +if I then take a ratio of delta + +X minus the delta X plus, +what I am going to get here is + +just that it will be equal to +the mass of the hydrogen ion + +divided by the mass of this +negatively charged particle, + +the electron. +But the observation here is + +that this deflection, +for the negatively charged + +particle, is much larger than it +was for the positively charged + +particle. +That must mean, + +if this is an equality, +that the mass of this hydrogen + +ion is much, much greater than +the mass of this negatively + +charged particle, +the electron. + +And this is the stunning +result. + +It is stunning because, +at the time, + +it was already known that a +hydrogen atom is the least + +massive atom. +There wasn't evidence for any + +other atom less massive than a +hydrogen atom. + +And so here, +in this experiment, + +what we are finding is that +there is a particle that is less + +massive than the hydrogen atom. +You can chop the hydrogen atom + +up. +The atom is not the most basic + +constituent of matter. +There is some other particle + +here, which we are going to call +an electron, that is less + +massive than a hydrogen atom. +That was the first piece of + +evidence for being able to split +that hydrogen atom, + +or that atom up into smaller +particles. + +The first evidence that the +atom was not the most basic + +constituent of matter. +Now, it took another ten years, + +the Millikan oil-drop +experiment, for this ratio to + +actually be measured accurately +and for the mass of the electron + +to actually be measured +accurately. + +And what we now know is that it +takes 1,836 masses of the + +electron to equal the mass of a +hydrogen atom. \ No newline at end of file diff --git a/eGKpOd_0oSY.txt b/eGKpOd_0oSY.txt new file mode 100644 index 0000000000000000000000000000000000000000..4e4298b804af36aa4f4d1a9bd6a3c1bc7749314d --- /dev/null +++ b/eGKpOd_0oSY.txt @@ -0,0 +1,11195 @@ +align:start position:0% + +just begin with. + + align:start position:0% +just begin with. + + + align:start position:0% +just begin with. +So uh if we have a + + align:start position:0% +So uh if we have a + + + align:start position:0% +So uh if we have a +a metric space here + + align:start position:0% + + + + align:start position:0% + +uh then uh a cover of + + align:start position:0% + + + + align:start position:0% + +of x uh is a collection + + align:start position:0% + + + + align:start position:0% + +uh of subsets + + align:start position:0% + + + + align:start position:0% + +u alpha so that the + + align:start position:0% +u alpha so that the + + + align:start position:0% +u alpha so that the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh x is contained in the union of u + + align:start position:0% +uh x is contained in the union of u + + + align:start position:0% +uh x is contained in the union of u +alpha. So that's a cover of x. And + + align:start position:0% +alpha. So that's a cover of x. And + + + align:start position:0% +alpha. So that's a cover of x. And +likewise + + align:start position:0% +likewise + + + align:start position:0% +likewise +uh likewise + + align:start position:0% + + + + align:start position:0% + +if a here is a subset of x then + + align:start position:0% +if a here is a subset of x then + + + align:start position:0% +if a here is a subset of x then +uh u alpha is a cover + + align:start position:0% + + + + align:start position:0% + +of a if a here is in the union of the u + + align:start position:0% +of a if a here is in the union of the u + + + align:start position:0% +of a if a here is in the union of the u +alpha. + + align:start position:0% +alpha. + + + align:start position:0% +alpha. +So that's what it needs to cover as the + + align:start position:0% +So that's what it needs to cover as the + + + align:start position:0% +So that's what it needs to cover as the +whole set or just a subset. + + align:start position:0% +whole set or just a subset. + + + align:start position:0% +whole set or just a subset. +Then uh there are some covers that are + + align:start position:0% +Then uh there are some covers that are + + + align:start position:0% +Then uh there are some covers that are +particularly important and those are the + + align:start position:0% +particularly important and those are the + + + align:start position:0% +particularly important and those are the +open covers. So a open cover + + align:start position:0% + + + + align:start position:0% + +is a cover + + align:start position:0% +is a cover + + + align:start position:0% +is a cover +uh that consists + + align:start position:0% + + + + align:start position:0% + +of uh open subsets. + + align:start position:0% + + + + align:start position:0% + +And then finally we have uh that so if + + align:start position:0% +And then finally we have uh that so if + + + align:start position:0% +And then finally we have uh that so if +again x comma d is a metric space a here + + align:start position:0% +again x comma d is a metric space a here + + + align:start position:0% +again x comma d is a metric space a here +is a subset of x then we say that + + align:start position:0% + + + + align:start position:0% + +that uh that a is compact + + align:start position:0% + + + + align:start position:0% + +uh if every + + align:start position:0% + + + + align:start position:0% + +A open copper + + align:start position:0% + + + + align:start position:0% + +of a has a finite + + align:start position:0% + + + + align:start position:0% + +uh subco. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And one thing we proved last time was + + align:start position:0% +And one thing we proved last time was + + + align:start position:0% +And one thing we proved last time was +that if you have + + align:start position:0% +that if you have + + + align:start position:0% +that if you have +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +if you have a so proved last time that + + align:start position:0% +if you have a so proved last time that + + + align:start position:0% +if you have a so proved last time that +if if you have a if a here is compact + + align:start position:0% + + + + align:start position:0% + +then uh + + align:start position:0% +then uh + + + align:start position:0% +then uh +then uh a is + + align:start position:0% + + + + align:start position:0% + +is bound + + align:start position:0% + + + + align:start position:0% + +and closed. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +right. So it's a is a closed subset + + align:start position:0% +right. So it's a is a closed subset + + + align:start position:0% +right. So it's a is a closed subset +meaning that the complement is is um is + + align:start position:0% +meaning that the complement is is um is + + + align:start position:0% +meaning that the complement is is um is +open and uh a itself is contained in + + align:start position:0% +open and uh a itself is contained in + + + align:start position:0% +open and uh a itself is contained in +some large ball centered at some point + + align:start position:0% +some large ball centered at some point + + + align:start position:0% +some large ball centered at some point +in x. + + align:start position:0% +in x. + + + align:start position:0% +in x. +Okay. Now the the converse is not the + + align:start position:0% +Okay. Now the the converse is not the + + + align:start position:0% +Okay. Now the the converse is not the +case always. So uh so + + align:start position:0% +case always. So uh so + + + align:start position:0% +case always. So uh so +in RN + + align:start position:0% +in RN + + + align:start position:0% +in RN +uh with + + align:start position:0% +uh with + + + align:start position:0% +uh with +the usual metric + + align:start position:0% + + + + align:start position:0% + +you cleaning metric + + align:start position:0% + + + + align:start position:0% + +the converse is the + + align:start position:0% + + + + align:start position:0% + +But in general, not + + align:start position:0% +But in general, not + + + align:start position:0% +But in general, not +but not in general. + + align:start position:0% + + + + align:start position:0% + +Okay. And so we looked at one example + + align:start position:0% +Okay. And so we looked at one example + + + align:start position:0% +Okay. And so we looked at one example +on this uh last time. + + align:start position:0% +on this uh last time. + + + align:start position:0% +on this uh last time. +So we looked at the following example + + align:start position:0% +So we looked at the following example + + + align:start position:0% +So we looked at the following example +but it was a rather trivial example that + + align:start position:0% +but it was a rather trivial example that + + + align:start position:0% +but it was a rather trivial example that +if you take x here if you take the space + + align:start position:0% +if you take x here if you take the space + + + align:start position:0% +if you take x here if you take the space +x to be say the interval from 0 to one + + align:start position:0% +x to be say the interval from 0 to one + + + align:start position:0% +x to be say the interval from 0 to one +uh and uh the metric here this here is + + align:start position:0% +uh and uh the metric here this here is + + + align:start position:0% +uh and uh the metric here this here is +the usual metric. + + align:start position:0% +the usual metric. + + + align:start position:0% +the usual metric. +So the distance between two uh elements + + align:start position:0% +So the distance between two uh elements + + + align:start position:0% +So the distance between two uh elements +here is is just the norm of the + + align:start position:0% +here is is just the norm of the + + + align:start position:0% +here is is just the norm of the +difference + + align:start position:0% +difference + + + align:start position:0% +difference +and then well x is the whole set. So x + + align:start position:0% +and then well x is the whole set. So x + + + align:start position:0% +and then well x is the whole set. So x +so with this here x is the whole set. So + + align:start position:0% +so with this here x is the whole set. So + + + align:start position:0% +so with this here x is the whole set. So +x here if you think if this here is the + + align:start position:0% +x here if you think if this here is the + + + align:start position:0% +x here if you think if this here is the +metric space then x is by definition + + align:start position:0% +metric space then x is by definition + + + align:start position:0% +metric space then x is by definition +closed because the whole set is closed + + align:start position:0% +closed because the whole set is closed + + + align:start position:0% +closed because the whole set is closed +right. It's not closed as a subset of R. + + align:start position:0% +right. It's not closed as a subset of R. + + + align:start position:0% +right. It's not closed as a subset of R. +But if it's if if the matrix space just + + align:start position:0% +But if it's if if the matrix space just + + + align:start position:0% +But if it's if if the matrix space just +is X, you know, then then it is closed + + align:start position:0% +is X, you know, then then it is closed + + + align:start position:0% +is X, you know, then then it is closed +and it's it's bounded + + align:start position:0% +and it's it's bounded + + + align:start position:0% +and it's it's bounded +and bounded. + + align:start position:0% +and bounded. + + + align:start position:0% +and bounded. +In particular, this interval here is + + align:start position:0% +In particular, this interval here is + + + align:start position:0% +In particular, this interval here is +contained in the ball of radius 1/2 + + align:start position:0% +contained in the ball of radius 1/2 + + + align:start position:0% +contained in the ball of radius 1/2 +around 1/2, but it's actually equal to + + align:start position:0% +around 1/2, but it's actually equal to + + + align:start position:0% +around 1/2, but it's actually equal to +that ball, if you will. Right? + + align:start position:0% +that ball, if you will. Right? + + + align:start position:0% +that ball, if you will. Right? +So it's definitely bounded + + align:start position:0% +So it's definitely bounded + + + align:start position:0% +So it's definitely bounded +but it's not compact. Right? So it not + + align:start position:0% +but it's not compact. Right? So it not + + + align:start position:0% +but it's not compact. Right? So it not +compact + + align:start position:0% + + + + align:start position:0% + +because you can write x here as the + + align:start position:0% +because you can write x here as the + + + align:start position:0% +because you can write x here as the +union of + + align:start position:0% +union of + + + align:start position:0% +union of +1 / n + + align:start position:0% +1 / n + + + align:start position:0% +1 / n +to one and now you take the union over + + align:start position:0% +to one and now you take the union over + + + align:start position:0% +to one and now you take the union over +all inte positive integers right and but + + align:start position:0% +all inte positive integers right and but + + + align:start position:0% +all inte positive integers right and but +if you only take finitely many of them + + align:start position:0% +if you only take finitely many of them + + + align:start position:0% +if you only take finitely many of them +then you don't get all the way down to + + align:start position:0% +then you don't get all the way down to + + + align:start position:0% +then you don't get all the way down to +zero Right? So it's it's not a union. + + align:start position:0% +zero Right? So it's it's not a union. + + + align:start position:0% +zero Right? So it's it's not a union. +It's union of all of these. The each of + + align:start position:0% +It's union of all of these. The each of + + + align:start position:0% +It's union of all of these. The each of +these are is open + + align:start position:0% +these are is open + + + align:start position:0% +these are is open +but you but there's no finite union of + + align:start position:0% +but you but there's no finite union of + + + align:start position:0% +but you but there's no finite union of +those sets that cover X. + + align:start position:0% +those sets that cover X. + + + align:start position:0% +those sets that cover X. +A more interesting example + + align:start position:0% +A more interesting example + + + align:start position:0% +A more interesting example +um is that suppose you take + + align:start position:0% +um is that suppose you take + + + align:start position:0% +um is that suppose you take +suppose you take um so here's another + + align:start position:0% +suppose you take um so here's another + + + align:start position:0% +suppose you take um so here's another +example + + align:start position:0% +example + + + align:start position:0% +example +that we didn't get to last time. that if + + align:start position:0% +that we didn't get to last time. that if + + + align:start position:0% +that we didn't get to last time. that if +you take the continuous function on the + + align:start position:0% +you take the continuous function on the + + + align:start position:0% +you take the continuous function on the +unit interval. + + align:start position:0% +unit interval. + + + align:start position:0% +unit interval. +Uh and so if you take and now we use + + align:start position:0% +Uh and so if you take and now we use + + + align:start position:0% +Uh and so if you take and now we use +this metric that we have looked at + + align:start position:0% +this metric that we have looked at + + + align:start position:0% +this metric that we have looked at +before + + align:start position:0% + + + + align:start position:0% + +where the + + align:start position:0% +where the + + + align:start position:0% +where the +uh distance between two functions + + align:start position:0% +uh distance between two functions + + + align:start position:0% +uh distance between two functions +is the max + + align:start position:0% +is the max + + + align:start position:0% +is the max +uh over x in this interval here + + align:start position:0% + + + + align:start position:0% + +uh of the norm of f ofx minus g ofx. X + + align:start position:0% +uh of the norm of f ofx minus g ofx. X + + + align:start position:0% +uh of the norm of f ofx minus g ofx. X +right we've already seen that this here + + align:start position:0% +right we've already seen that this here + + + align:start position:0% +right we've already seen that this here +is a nice metric right + + align:start position:0% +is a nice metric right + + + align:start position:0% +is a nice metric right +uh and and if I now look at in this + + align:start position:0% +uh and and if I now look at in this + + + align:start position:0% +uh and and if I now look at in this +metric I look at the the unit ball so + + align:start position:0% +metric I look at the the unit ball so + + + align:start position:0% +metric I look at the the unit ball so +I'm looking at the closed unit ball so + + align:start position:0% +I'm looking at the closed unit ball so + + + align:start position:0% +I'm looking at the closed unit ball so +uh which means that I'm looking at the + + align:start position:0% +uh which means that I'm looking at the + + + align:start position:0% +uh which means that I'm looking at the +set + + align:start position:0% +set + + + align:start position:0% +set +the set uh of functions there + + align:start position:0% +the set uh of functions there + + + align:start position:0% +the set uh of functions there +so that the distance + + align:start position:0% +so that the distance + + + align:start position:0% +so that the distance +of f to the function that is constant + + align:start position:0% +of f to the function that is constant + + + align:start position:0% +of f to the function that is constant +equal to zero this distance here + + align:start position:0% +equal to zero this distance here + + + align:start position:0% +equal to zero this distance here +is sorry is uh less or equal to one + + align:start position:0% +is sorry is uh less or equal to one + + + align:start position:0% +is sorry is uh less or equal to one +so I'm looking here + + align:start position:0% +so I'm looking here + + + align:start position:0% +so I'm looking here +at the subset of the continuous function + + align:start position:0% +at the subset of the continuous function + + + align:start position:0% +at the subset of the continuous function +on this interval + + align:start position:0% + + + + align:start position:0% + +So that the distance to the zero + + align:start position:0% +So that the distance to the zero + + + align:start position:0% +So that the distance to the zero +function is at most one. So let me just + + align:start position:0% +function is at most one. So let me just + + + align:start position:0% +function is at most one. So let me just +write this out. Right? So this means + + align:start position:0% +write this out. Right? So this means + + + align:start position:0% +write this out. Right? So this means +that uh this is the function f in this + + align:start position:0% +that uh this is the function f in this + + + align:start position:0% +that uh this is the function f in this +continuous function here. So that + + align:start position:0% +continuous function here. So that + + + align:start position:0% +continuous function here. So that +um the max + + align:start position:0% +um the max + + + align:start position:0% +um the max +of f ofx minus zero. So I don't really + + align:start position:0% +of f ofx minus zero. So I don't really + + + align:start position:0% +of f ofx minus zero. So I don't really +have to write zero is + + align:start position:0% +have to write zero is + + + align:start position:0% +have to write zero is +is is less or equal to one. + + align:start position:0% +is is less or equal to one. + + + align:start position:0% +is is less or equal to one. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +Now this set again this set here is what + + align:start position:0% +Now this set again this set here is what + + + align:start position:0% +Now this set again this set here is what +we denote by the this is like the closed + + align:start position:0% +we denote by the this is like the closed + + + align:start position:0% +we denote by the this is like the closed +unit ball because you have lesser equal + + align:start position:0% +unit ball because you have lesser equal + + + align:start position:0% +unit ball because you have lesser equal +to here right. So and the closed unit + + align:start position:0% +to here right. So and the closed unit + + + align:start position:0% +to here right. So and the closed unit +ball the open unit ball we have written + + align:start position:0% +ball the open unit ball we have written + + + align:start position:0% +ball the open unit ball we have written +and this is now the the function that is + + align:start position:0% +and this is now the the function that is + + + align:start position:0% +and this is now the the function that is +identically equal to zero + + align:start position:0% +identically equal to zero + + + align:start position:0% +identically equal to zero +the open unit ball we wrote like this + + align:start position:0% +the open unit ball we wrote like this + + + align:start position:0% +the open unit ball we wrote like this +right this is if you have strict + + align:start position:0% +right this is if you have strict + + + align:start position:0% +right this is if you have strict +inequality and to to to denote that is + + align:start position:0% +inequality and to to to denote that is + + + align:start position:0% +inequality and to to to denote that is +lesser equal to I'm just putting a bar + + align:start position:0% +lesser equal to I'm just putting a bar + + + align:start position:0% +lesser equal to I'm just putting a bar +here + + align:start position:0% +here + + + align:start position:0% +here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so we already know that this thing + + align:start position:0% +and so we already know that this thing + + + align:start position:0% +and so we already know that this thing +Here if you take a metric space and + + align:start position:0% +Here if you take a metric space and + + + align:start position:0% +Here if you take a metric space and +you're looking at a closed unit ball + + align:start position:0% +you're looking at a closed unit ball + + + align:start position:0% +you're looking at a closed unit ball +like this we already proved that this + + align:start position:0% +like this we already proved that this + + + align:start position:0% +like this we already proved that this +here is closed right because you prove + + align:start position:0% +here is closed right because you prove + + + align:start position:0% +here is closed right because you prove +directly using the triangle inequality + + align:start position:0% +directly using the triangle inequality + + + align:start position:0% +directly using the triangle inequality +that the complement is open right + + align:start position:0% +that the complement is open right + + + align:start position:0% +that the complement is open right +okay so that's if so this is a closed + + align:start position:0% +okay so that's if so this is a closed + + + align:start position:0% +okay so that's if so this is a closed +subset it's obviously bounded right + + align:start position:0% +subset it's obviously bounded right + + + align:start position:0% +subset it's obviously bounded right +because it's actually even just a ball + + align:start position:0% +because it's actually even just a ball + + + align:start position:0% +because it's actually even just a ball +right + + align:start position:0% +right + + + align:start position:0% +right +um now + + align:start position:0% +um now + + + align:start position:0% +um now +so how but I claim that it's so it's + + align:start position:0% +so how but I claim that it's so it's + + + align:start position:0% +so how but I claim that it's so it's +it's closed it's bounded + + align:start position:0% +it's closed it's bounded + + + align:start position:0% +it's closed it's bounded +but it doesn't it's not compact and and + + align:start position:0% +but it doesn't it's not compact and and + + + align:start position:0% +but it doesn't it's not compact and and +here's a sort of interesting example uh + + align:start position:0% +here's a sort of interesting example uh + + + align:start position:0% +here's a sort of interesting example uh +of a sequence of element in this form so + + align:start position:0% +of a sequence of element in this form so + + + align:start position:0% +of a sequence of element in this form so +I will now construct for each + + align:start position:0% + + + + align:start position:0% + +for each n which is a natural number + + align:start position:0% +for each n which is a natural number + + + align:start position:0% +for each n which is a natural number +uh we construct a function + + align:start position:0% +uh we construct a function + + + align:start position:0% +uh we construct a function +uh fn + + align:start position:0% +uh fn + + + align:start position:0% +uh fn +in this + + align:start position:0% + + + + align:start position:0% + +that is a continuous function on this + + align:start position:0% +that is a continuous function on this + + + align:start position:0% +that is a continuous function on this +unit interval and the function f um will + + align:start position:0% +unit interval and the function f um will + + + align:start position:0% +unit interval and the function f um will +be given as follows. + + align:start position:0% +be given as follows. + + + align:start position:0% +be given as follows. +It's will be + + align:start position:0% + + + + align:start position:0% + +it will be uh one + + align:start position:0% +it will be uh one + + + align:start position:0% +it will be uh one +uh from + + align:start position:0% + + + + align:start position:0% + +uh from + + align:start position:0% +uh from + + + align:start position:0% +uh from +uh when + + align:start position:0% + + + + align:start position:0% + +uh see let me make it uh zero. + + align:start position:0% + + + + align:start position:0% + +Uh I guess doesn't matter. I I make it + + align:start position:0% +Uh I guess doesn't matter. I I make it + + + align:start position:0% +Uh I guess doesn't matter. I I make it +one uh when uh x here is between um 1 / + + align:start position:0% +one uh when uh x here is between um 1 / + + + align:start position:0% +one uh when uh x here is between um 1 / +n + one. No + + align:start position:0% +n + one. No + + + align:start position:0% +n + one. No +when zero is I would make it equal to + + align:start position:0% +when zero is I would make it equal to + + + align:start position:0% +when zero is I would make it equal to +one when x here is bigger equal to zero + + align:start position:0% +one when x here is bigger equal to zero + + + align:start position:0% +one when x here is bigger equal to zero +and lesser equal to 1 / n + one. + + align:start position:0% + + + + align:start position:0% + +Then I'll make it um when when x here is + + align:start position:0% +Then I'll make it um when when x here is + + + align:start position:0% +Then I'll make it um when when x here is +bigger than or equal to 1 / n but lesser + + align:start position:0% +bigger than or equal to 1 / n but lesser + + + align:start position:0% +bigger than or equal to 1 / n but lesser +equal to one then I'll set it equal to + + align:start position:0% +equal to one then I'll set it equal to + + + align:start position:0% +equal to one then I'll set it equal to +uh to to zero + + align:start position:0% +uh to to zero + + + align:start position:0% +uh to to zero +and then you see now I want it to be so + + align:start position:0% +and then you see now I want it to be so + + + align:start position:0% +and then you see now I want it to be so +so let me just so let's look at it. So + + align:start position:0% +so let me just so let's look at it. So + + + align:start position:0% +so let me just so let's look at it. So +this function here is + + align:start position:0% +this function here is + + + align:start position:0% +this function here is +um + + align:start position:0% + + + + align:start position:0% + +so so this function here is if you draw + + align:start position:0% +so so this function here is if you draw + + + align:start position:0% +so so this function here is if you draw +this function so + + align:start position:0% +this function so + + + align:start position:0% +this function so +I have here one here I have zero + + align:start position:0% +I have here one here I have zero + + + align:start position:0% +I have here one here I have zero +and this function is one um up to uh 1 / + + align:start position:0% +and this function is one um up to uh 1 / + + + align:start position:0% +and this function is one um up to uh 1 / +n +1. Maybe I'll draw it a little bit + + align:start position:0% +n +1. Maybe I'll draw it a little bit + + + align:start position:0% +n +1. Maybe I'll draw it a little bit +further out. Uh actually make the + + align:start position:0% +further out. Uh actually make the + + + align:start position:0% +further out. Uh actually make the +picture bigger. + + align:start position:0% +picture bigger. + + + align:start position:0% +picture bigger. +So like that. Here I have one. + + align:start position:0% +So like that. Here I have one. + + + align:start position:0% +So like that. Here I have one. +Here I have uh 1 / + + align:start position:0% +Here I have uh 1 / + + + align:start position:0% +Here I have uh 1 / +n + one and here I have 1 / n. + + align:start position:0% +n + one and here I have 1 / n. + + + align:start position:0% +n + one and here I have 1 / n. +And the function is supposed to be one + + align:start position:0% +And the function is supposed to be one + + + align:start position:0% +And the function is supposed to be one +here. + + align:start position:0% + + + + align:start position:0% + +And then it's supposed to uh die off + + align:start position:0% + + + + align:start position:0% + +between here + + align:start position:0% +between here + + + align:start position:0% +between here +and here. And I will I choose it to die + + align:start position:0% +and here. And I will I choose it to die + + + align:start position:0% +and here. And I will I choose it to die +off linearly and then a zero here. + + align:start position:0% +off linearly and then a zero here. + + + align:start position:0% +off linearly and then a zero here. +So if it's going down linearly this + + align:start position:0% +So if it's going down linearly this + + + align:start position:0% +So if it's going down linearly this +means that I have right what is the + + align:start position:0% +means that I have right what is the + + + align:start position:0% +means that I have right what is the +difference between two these two it's 1 + + align:start position:0% +difference between two these two it's 1 + + + align:start position:0% +difference between two these two it's 1 +/ n minus 1 / n + one this is this + + align:start position:0% +/ n minus 1 / n + one this is this + + + align:start position:0% +/ n minus 1 / n + one this is this +distance here and so this here putting + + align:start position:0% +distance here and so this here putting + + + align:start position:0% +distance here and so this here putting +it on a common denominator n +1 / n * n + + align:start position:0% +it on a common denominator n +1 / n * n + + + align:start position:0% +it on a common denominator n +1 / n * n ++1 this is what you get from this and if + + align:start position:0% ++1 this is what you get from this and if + + + align:start position:0% ++1 this is what you get from this and if +you put it on the common denominator for + + align:start position:0% +you put it on the common denominator for + + + align:start position:0% +you put it on the common denominator for +the second one this is what you get here + + align:start position:0% +the second one this is what you get here + + + align:start position:0% +the second one this is what you get here +and so this is just one over n + + align:start position:0% +and so this is just one over n + + + align:start position:0% +and so this is just one over n +like this right + + align:start position:0% +like this right + + + align:start position:0% +like this right +and so this is this distance here + + align:start position:0% +and so this is this distance here + + + align:start position:0% +and so this is this distance here +and so if I define the function to be + + align:start position:0% +and so if I define the function to be + + + align:start position:0% +and so if I define the function to be +uh right so I'm setting it equal to + + align:start position:0% + + + + align:start position:0% + +to this and now in between when x here + + align:start position:0% +to this and now in between when x here + + + align:start position:0% +to this and now in between when x here +is bigger equal to 1 / n +1 and lesser + + align:start position:0% +is bigger equal to 1 / n +1 and lesser + + + align:start position:0% +is bigger equal to 1 / n +1 and lesser +equal to 1 / n. I will set it equal to 1 + + align:start position:0% +equal to 1 / n. I will set it equal to 1 + + + align:start position:0% +equal to 1 / n. I will set it equal to 1 +minus + + align:start position:0% +minus + + + align:start position:0% +minus +um n * n + + + align:start position:0% +um n * n + + + + align:start position:0% +um n * n + +uh 1 + + align:start position:0% + + + + align:start position:0% + +um times sorry let me make more space. + + align:start position:0% + + + + align:start position:0% + +Yeah, let me make more space. + + align:start position:0% +Yeah, let me make more space. + + + align:start position:0% +Yeah, let me make more space. +So here this here was when zero is less + + align:start position:0% +So here this here was when zero is less + + + align:start position:0% +So here this here was when zero is less +or equal to x less or equal to 1 / n + + + align:start position:0% +or equal to x less or equal to 1 / n + + + + align:start position:0% +or equal to x less or equal to 1 / n + +1. + + align:start position:0% +1. + + + align:start position:0% +1. +This is when uh x here is between + + align:start position:0% + + + + align:start position:0% + +these two numbers and this here is when + + align:start position:0% +these two numbers and this here is when + + + align:start position:0% +these two numbers and this here is when +x is larger than one / n and it's + + align:start position:0% +x is larger than one / n and it's + + + align:start position:0% +x is larger than one / n and it's +x is always in the interval between zero + + align:start position:0% +x is always in the interval between zero + + + align:start position:0% +x is always in the interval between zero +and one. And here I'm I'm choosing it's + + align:start position:0% +and one. And here I'm I'm choosing it's + + + align:start position:0% +and one. And here I'm I'm choosing it's +x minus + + align:start position:0% +x minus + + + align:start position:0% +x minus +uh and then 1 / + + align:start position:0% +uh and then 1 / + + + align:start position:0% +uh and then 1 / +um u n + one + + align:start position:0% +um u n + one + + + align:start position:0% +um u n + one +right. So you see that if you take + + align:start position:0% +right. So you see that if you take + + + align:start position:0% +right. So you see that if you take +x to be 1 / n + one then this here + + align:start position:0% +x to be 1 / n + one then this here + + + align:start position:0% +x to be 1 / n + one then this here +contribute zero. So at this left point + + align:start position:0% +contribute zero. So at this left point + + + align:start position:0% +contribute zero. So at this left point +this here is equal it's the function is + + align:start position:0% +this here is equal it's the function is + + + align:start position:0% +this here is equal it's the function is +equal to one as it should be. And when x + + align:start position:0% +equal to one as it should be. And when x + + + align:start position:0% +equal to one as it should be. And when x +here is at the other end point then this + + align:start position:0% +here is at the other end point then this + + + align:start position:0% +here is at the other end point then this +here becomes exactly one over this. So + + align:start position:0% +here becomes exactly one over this. So + + + align:start position:0% +here becomes exactly one over this. So +this whole thing becomes zero. + + align:start position:0% +this whole thing becomes zero. + + + align:start position:0% +this whole thing becomes zero. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +So if I so this function here I drew is + + align:start position:0% +So if I so this function here I drew is + + + align:start position:0% +So if I so this function here I drew is +is uh is if you write it down precisely + + align:start position:0% +is uh is if you write it down precisely + + + align:start position:0% +is uh is if you write it down precisely +this is what the function is right + + align:start position:0% + + + + align:start position:0% + +and now um now if I'm looking at + + align:start position:0% +and now um now if I'm looking at + + + align:start position:0% +and now um now if I'm looking at +um if I'm looking at the difference + + align:start position:0% +um if I'm looking at the difference + + + align:start position:0% +um if I'm looking at the difference +between uh two such such functions. So + + align:start position:0% +between uh two such such functions. So + + + align:start position:0% +between uh two such such functions. So +for the next one you see the next one + + align:start position:0% +for the next one you see the next one + + + align:start position:0% +for the next one you see the next one +here the next one here is so this here + + align:start position:0% +here the next one here is so this here + + + align:start position:0% +here the next one here is so this here +is fn right this is how fn look like if + + align:start position:0% +is fn right this is how fn look like if + + + align:start position:0% +is fn right this is how fn look like if +I now look at fn + one right this start + + align:start position:0% +I now look at fn + one right this start + + + align:start position:0% +I now look at fn + one right this start +off being it's zero to the right of this + + align:start position:0% +off being it's zero to the right of this + + + align:start position:0% +off being it's zero to the right of this +thing here and then it's it's one once + + align:start position:0% +thing here and then it's it's one once + + + align:start position:0% +thing here and then it's it's one once +you get to + + align:start position:0% +you get to + + + align:start position:0% +you get to +n plus2 True. So the next function + + align:start position:0% +n plus2 True. So the next function + + + align:start position:0% +n plus2 True. So the next function +looks like this. I don't know if there's + + align:start position:0% +looks like this. I don't know if there's + + + align:start position:0% +looks like this. I don't know if there's +any color chalk, but this thing here + + align:start position:0% +any color chalk, but this thing here + + + align:start position:0% +any color chalk, but this thing here +uh is + + align:start position:0% +uh is + + + align:start position:0% +uh is +uh that's the next function, right? So + + align:start position:0% +uh that's the next function, right? So + + + align:start position:0% +uh that's the next function, right? So +so the the the first function is this + + align:start position:0% +so the the the first function is this + + + align:start position:0% +so the the the first function is this +function here. That's a graph of the + + align:start position:0% +function here. That's a graph of the + + + align:start position:0% +function here. That's a graph of the +first function. The next one is like + + align:start position:0% +first function. The next one is like + + + align:start position:0% +first function. The next one is like +this one here, right? + + align:start position:0% +this one here, right? + + + align:start position:0% +this one here, right? +And so if you're now looking at the + + align:start position:0% +And so if you're now looking at the + + + align:start position:0% +And so if you're now looking at the +distance between FN and FN + one, + + align:start position:0% +distance between FN and FN + one, + + + align:start position:0% +distance between FN and FN + one, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +The distance here was the soup of the + + align:start position:0% +The distance here was the soup of the + + + align:start position:0% +The distance here was the soup of the +difference of the two, right? This here + + align:start position:0% +difference of the two, right? This here + + + align:start position:0% +difference of the two, right? This here +was just the max + + align:start position:0% +was just the max + + + align:start position:0% +was just the max +of uh f of + + align:start position:0% +of uh f of + + + align:start position:0% +of uh f of +like this. + + align:start position:0% + + + + align:start position:0% + +it was just the max of this right and + + align:start position:0% +it was just the max of this right and + + + align:start position:0% +it was just the max of this right and +now I know that these two numbers is + + align:start position:0% +now I know that these two numbers is + + + align:start position:0% +now I know that these two numbers is +always between zero and one so this max + + align:start position:0% +always between zero and one so this max + + + align:start position:0% +always between zero and one so this max +here is at most one right but if I now + + align:start position:0% +here is at most one right but if I now + + + align:start position:0% +here is at most one right but if I now +evaluate it if I now looking at if I now + + align:start position:0% +evaluate it if I now looking at if I now + + + align:start position:0% +evaluate it if I now looking at if I now +just evaluate if I'm looking at fn and + + align:start position:0% +just evaluate if I'm looking at fn and + + + align:start position:0% +just evaluate if I'm looking at fn and +now I just evaluate it in in this point + + align:start position:0% +now I just evaluate it in in this point + + + align:start position:0% +now I just evaluate it in in this point +here + + align:start position:0% +here + + + align:start position:0% +here +in this point 1 / n + one. So if I'm + + align:start position:0% +in this point 1 / n + one. So if I'm + + + align:start position:0% +in this point 1 / n + one. So if I'm +looking at this thing here, + + align:start position:0% +looking at this thing here, + + + align:start position:0% +looking at this thing here, +f(n) + one 1 / n + one, + + align:start position:0% +f(n) + one 1 / n + one, + + + align:start position:0% +f(n) + one 1 / n + one, +you see this value here, this was this + + align:start position:0% +you see this value here, this was this + + + align:start position:0% +you see this value here, this was this +first function here and at this point is + + align:start position:0% +first function here and at this point is + + + align:start position:0% +first function here and at this point is +one, right? This here is one, + + align:start position:0% +one, right? This here is one, + + + align:start position:0% +one, right? This here is one, +but for the next one, you see at that + + align:start position:0% +but for the next one, you see at that + + + align:start position:0% +but for the next one, you see at that +point it's zero, right? + + align:start position:0% +point it's zero, right? + + + align:start position:0% +point it's zero, right? +So this means that this max here is for + + align:start position:0% +So this means that this max here is for + + + align:start position:0% +So this means that this max here is for +all n and n + one + + align:start position:0% +all n and n + one + + + align:start position:0% +all n and n + one +is actually equal to to one, right? + + align:start position:0% +is actually equal to to one, right? + + + align:start position:0% +is actually equal to to one, right? +And so + + align:start position:0% +And so + + + align:start position:0% +And so +so now + + align:start position:0% +so now + + + align:start position:0% +so now +if you look at + + align:start position:0% +if you look at + + + align:start position:0% +if you look at +at um if you look at at the balls + + align:start position:0% + + + + align:start position:0% + +So now in particular + + align:start position:0% +So now in particular + + + align:start position:0% +So now in particular +if I'm looking at the balls of radius + + align:start position:0% +if I'm looking at the balls of radius + + + align:start position:0% +if I'm looking at the balls of radius +1/2 + + align:start position:0% +1/2 + + + align:start position:0% +1/2 +suppose I'm looking at the ball of + + align:start position:0% +suppose I'm looking at the ball of + + + align:start position:0% +suppose I'm looking at the ball of +radius 1/2 + + align:start position:0% +radius 1/2 + + + align:start position:0% +radius 1/2 +around so this is an open ball so around + + align:start position:0% +around so this is an open ball so around + + + align:start position:0% +around so this is an open ball so around +fn right because this here is an open + + align:start position:0% +fn right because this here is an open + + + align:start position:0% +fn right because this here is an open +ball so it means that's strictly less + + align:start position:0% +ball so it means that's strictly less + + + align:start position:0% +ball so it means that's strictly less +than a half so this means that fn plus + + align:start position:0% +than a half so this means that fn plus + + + align:start position:0% +than a half so this means that fn plus +one + + align:start position:0% +one + + + align:start position:0% +one +is not in that ball. Right? + + align:start position:0% +is not in that ball. Right? + + + align:start position:0% +is not in that ball. Right? +So it's not in sorry it's not in that. + + align:start position:0% +So it's not in sorry it's not in that. + + + align:start position:0% +So it's not in sorry it's not in that. +Right? And and so now it's easy to see + + align:start position:0% +Right? And and so now it's easy to see + + + align:start position:0% +Right? And and so now it's easy to see +that all of these balls here are + + align:start position:0% +that all of these balls here are + + + align:start position:0% +that all of these balls here are +disjoint. + + align:start position:0% +disjoint. + + + align:start position:0% +disjoint. +So all of these balls here will be + + align:start position:0% +So all of these balls here will be + + + align:start position:0% +So all of these balls here will be +disjoint. They're all disjoint. And so + + align:start position:0% +disjoint. They're all disjoint. And so + + + align:start position:0% +disjoint. They're all disjoint. And so +if you're looking at if you you can + + align:start position:0% +if you're looking at if you you can + + + align:start position:0% +if you're looking at if you you can +write uh this initial ball this ball + + align:start position:0% +write uh this initial ball this ball + + + align:start position:0% +write uh this initial ball this ball +here this was this close ball that we + + align:start position:0% +here this was this close ball that we + + + align:start position:0% +here this was this close ball that we +started with in beginning + + align:start position:0% +started with in beginning + + + align:start position:0% +started with in beginning +you can write it as uh as a union + + align:start position:0% +you can write it as uh as a union + + + align:start position:0% +you can write it as uh as a union +suppose you write it you can write it of + + align:start position:0% +suppose you write it you can write it of + + + align:start position:0% +suppose you write it you can write it of +course as a union of half balls + + align:start position:0% +course as a union of half balls + + + align:start position:0% +course as a union of half balls +where you take the union over all + + align:start position:0% +where you take the union over all + + + align:start position:0% +where you take the union over all +centers. plus + + align:start position:0% + + + + align:start position:0% + +all possible centers like this, right? + + align:start position:0% +all possible centers like this, right? + + + align:start position:0% +all possible centers like this, right? +Because you know this clearly cover this + + align:start position:0% +Because you know this clearly cover this + + + align:start position:0% +Because you know this clearly cover this +set because it contains all the centers, + + align:start position:0% +set because it contains all the centers, + + + align:start position:0% +set because it contains all the centers, +right? But that's already the whole set, + + align:start position:0% +right? But that's already the whole set, + + + align:start position:0% +right? But that's already the whole set, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +But using this here, you can see that + + align:start position:0% +But using this here, you can see that + + + align:start position:0% +But using this here, you can see that +there is not that you can't have finite + + align:start position:0% +there is not that you can't have finite + + + align:start position:0% +there is not that you can't have finite +many of these half balls that cover the + + align:start position:0% +many of these half balls that cover the + + + align:start position:0% +many of these half balls that cover the +whole set. Okay. So using + + align:start position:0% +whole set. Okay. So using + + + align:start position:0% +whole set. Okay. So using +the functions + + align:start position:0% + + + + align:start position:0% + +fn + + align:start position:0% +fn + + + align:start position:0% +fn +uh it follow follows easily + + align:start position:0% + + + + align:start position:0% + +uh that finite in many + + align:start position:0% + + + + align:start position:0% + +many + + align:start position:0% +many + + + align:start position:0% +many +of these balls. + + align:start position:0% + + + + align:start position:0% + +does not cover + + align:start position:0% + + + + align:start position:0% + +uh and it's uh let me just cover this + + align:start position:0% +uh and it's uh let me just cover this + + + align:start position:0% +uh and it's uh let me just cover this +here. Why why is this the case actually + + align:start position:0% +here. Why why is this the case actually + + + align:start position:0% +here. Why why is this the case actually +sometime you you you put it uh the bar + + align:start position:0% +sometime you you you put it uh the bar + + + align:start position:0% +sometime you you you put it uh the bar +all the way across uh but but I haven't + + align:start position:0% +all the way across uh but but I haven't + + + align:start position:0% +all the way across uh but but I haven't +done that. Okay. Why is suppose that + + align:start position:0% +done that. Okay. Why is suppose that + + + align:start position:0% +done that. Okay. Why is suppose that +Suppose for a second + + align:start position:0% +Suppose for a second + + + align:start position:0% +Suppose for a second +that you have + + align:start position:0% + + + + align:start position:0% + +suppose that you have a ball here + + align:start position:0% + + + + align:start position:0% + +uh of a radius a half around some point + + align:start position:0% +uh of a radius a half around some point + + + align:start position:0% +uh of a radius a half around some point +then and suppose that you have a + + align:start position:0% +then and suppose that you have a + + + align:start position:0% +then and suppose that you have a +function + + align:start position:0% +function + + + align:start position:0% +function +g two functions g and h that are in that + + align:start position:0% +g two functions g and h that are in that + + + align:start position:0% +g two functions g and h that are in that +bone just ucing that it's a metric + + align:start position:0% +bone just ucing that it's a metric + + + align:start position:0% +bone just ucing that it's a metric +space. So now we have that this thing + + align:start position:0% +space. So now we have that this thing + + + align:start position:0% +space. So now we have that this thing +here + + align:start position:0% + + + + align:start position:0% + +g is strictly less than a half and the + + align:start position:0% +g is strictly less than a half and the + + + align:start position:0% +g is strictly less than a half and the +distance from uh f to h is strictly less + + align:start position:0% +distance from uh f to h is strictly less + + + align:start position:0% +distance from uh f to h is strictly less +than a half. So now using the triangle + + align:start position:0% +than a half. So now using the triangle + + + align:start position:0% +than a half. So now using the triangle +inequality, we conclude that the + + align:start position:0% +inequality, we conclude that the + + + align:start position:0% +inequality, we conclude that the +distance between this pair here G and H + + align:start position:0% +distance between this pair here G and H + + + align:start position:0% +distance between this pair here G and H +is less or equal to the distance where + + align:start position:0% +is less or equal to the distance where + + + align:start position:0% +is less or equal to the distance where +you go over F. + + align:start position:0% + + + + align:start position:0% + +And so this here is less strictly less + + align:start position:0% +And so this here is less strictly less + + + align:start position:0% +And so this here is less strictly less +than a half plus a half. So this is + + align:start position:0% +than a half plus a half. So this is + + + align:start position:0% +than a half plus a half. So this is +strictly less than one. + + align:start position:0% +strictly less than one. + + + align:start position:0% +strictly less than one. +So you see from this in particular that + + align:start position:0% +So you see from this in particular that + + + align:start position:0% +So you see from this in particular that +if you take such a ball here + + align:start position:0% + + + + align:start position:0% + +then you can't so it's impossible + + align:start position:0% + + + + align:start position:0% + +to have + + align:start position:0% +to have + + + align:start position:0% +to have +that + + align:start position:0% +that + + + align:start position:0% +that +fn + + align:start position:0% + + + + align:start position:0% + +and fn plus one. + + align:start position:0% +and fn plus one. + + + align:start position:0% +and fn plus one. +It's impossible to have that they both + + align:start position:0% +It's impossible to have that they both + + + align:start position:0% +It's impossible to have that they both +are in that ball, + + align:start position:0% +are in that ball, + + + align:start position:0% +are in that ball, +right? Because if they were both in this + + align:start position:0% +right? Because if they were both in this + + + align:start position:0% +right? Because if they were both in this +ball, then the distance would be + + align:start position:0% +ball, then the distance would be + + + align:start position:0% +ball, then the distance would be +strictly less than one. And we've + + align:start position:0% +strictly less than one. And we've + + + align:start position:0% +strictly less than one. And we've +already seen the distance is is one, + + align:start position:0% +already seen the distance is is one, + + + align:start position:0% +already seen the distance is is one, +right? And this holds not just from for + + align:start position:0% +right? And this holds not just from for + + + align:start position:0% +right? And this holds not just from for +fn and the next one, but it holds for + + align:start position:0% +fn and the next one, but it holds for + + + align:start position:0% +fn and the next one, but it holds for +like fn. The same argument give that + + align:start position:0% +like fn. The same argument give that + + + align:start position:0% +like fn. The same argument give that +from fn and any m larger than n. this + + align:start position:0% +from fn and any m larger than n. this + + + align:start position:0% +from fn and any m larger than n. this +this here would be impossible, right? + + align:start position:0% +this here would be impossible, right? + + + align:start position:0% +this here would be impossible, right? +And so from this it follows that you + + align:start position:0% +And so from this it follows that you + + + align:start position:0% +And so from this it follows that you +can't have finitely many that cover the + + align:start position:0% +can't have finitely many that cover the + + + align:start position:0% +can't have finitely many that cover the +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +>> or how do we know that the union of all + + align:start position:0% +>> or how do we know that the union of all + + + align:start position:0% +>> or how do we know that the union of all +of those + + align:start position:0% +of those + + + align:start position:0% +of those +functions and like the one + + align:start position:0% +functions and like the one + + + align:start position:0% +functions and like the one +>> Yeah. Yeah. So, so, so this is just and + + align:start position:0% +>> Yeah. Yeah. So, so, so this is just and + + + align:start position:0% +>> Yeah. Yeah. So, so, so this is just and +and this is important because we're + + align:start position:0% +and this is important because we're + + + align:start position:0% +and this is important because we're +going to use this in a minute anyway. So + + align:start position:0% +going to use this in a minute anyway. So + + + align:start position:0% +going to use this in a minute anyway. So +again if you take if you take a set here + + align:start position:0% +again if you take if you take a set here + + + align:start position:0% +again if you take if you take a set here +so if you take a metric space + + align:start position:0% +so if you take a metric space + + + align:start position:0% +so if you take a metric space +and suppose you take a set subset of X + + align:start position:0% +and suppose you take a set subset of X + + + align:start position:0% +and suppose you take a set subset of X +then there's always you know you can + + align:start position:0% +then there's always you know you can + + + align:start position:0% +then there's always you know you can +always find a cover even an open copper + + align:start position:0% +always find a cover even an open copper + + + align:start position:0% +always find a cover even an open copper +um and in particular in a minute we will + + align:start position:0% +um and in particular in a minute we will + + + align:start position:0% +um and in particular in a minute we will +look at so if you take a here so one + + align:start position:0% +look at so if you take a here so one + + + align:start position:0% +look at so if you take a here so one +example of an open cover of A is that + + align:start position:0% +example of an open cover of A is that + + + align:start position:0% +example of an open cover of A is that +you're looking at at the family of + + align:start position:0% +you're looking at at the family of + + + align:start position:0% +you're looking at at the family of +balls. + + align:start position:0% +balls. + + + align:start position:0% +balls. +You just pick some radius. R is positive + + align:start position:0% +You just pick some radius. R is positive + + + align:start position:0% +You just pick some radius. R is positive +and then you pick centers, + + align:start position:0% +and then you pick centers, + + + align:start position:0% +and then you pick centers, +right? But the centers, right? You you + + align:start position:0% +right? But the centers, right? You you + + + align:start position:0% +right? But the centers, right? You you +you take the centers, you know, X here + + align:start position:0% +you take the centers, you know, X here + + + align:start position:0% +you take the centers, you know, X here +is now anything in A, right? If you're + + align:start position:0% +is now anything in A, right? If you're + + + align:start position:0% +is now anything in A, right? If you're +looking at R is fixed, it's positive. + + align:start position:0% +looking at R is fixed, it's positive. + + + align:start position:0% +looking at R is fixed, it's positive. +X is anything in A. Well, the union of + + align:start position:0% +X is anything in A. Well, the union of + + + align:start position:0% +X is anything in A. Well, the union of +these guys, the union certainly contains + + align:start position:0% +these guys, the union certainly contains + + + align:start position:0% +these guys, the union certainly contains +the centers, right? So this here already + + align:start position:0% +the centers, right? So this here already + + + align:start position:0% +the centers, right? So this here already +cover a right and so and we will use + + align:start position:0% +cover a right and so and we will use + + + align:start position:0% +cover a right and so and we will use +this in just this is like a standard + + align:start position:0% +this in just this is like a standard + + + align:start position:0% +this in just this is like a standard +array to get a cover and then if it's + + align:start position:0% +array to get a cover and then if it's + + + align:start position:0% +array to get a cover and then if it's +compact then finally many of those + + align:start position:0% +compact then finally many of those + + + align:start position:0% +compact then finally many of those +should cover right okay so in fact let's + + align:start position:0% +should cover right okay so in fact let's + + + align:start position:0% +should cover right okay so in fact let's +get to that um + + align:start position:0% +get to that um + + + align:start position:0% +get to that um +so um right so the next thing I want to + + align:start position:0% +so um right so the next thing I want to + + + align:start position:0% +so um right so the next thing I want to +prove is um + + align:start position:0% + + + + align:start position:0% + +uh is um is is this volano bias version + + align:start position:0% +uh is um is is this volano bias version + + + align:start position:0% +uh is um is is this volano bias version +for a metric space. + + align:start position:0% + + + + align:start position:0% + +So you prove a banal bias theorem for + + align:start position:0% +So you prove a banal bias theorem for + + + align:start position:0% +So you prove a banal bias theorem for +metric space. Remember that the banana + + align:start position:0% +metric space. Remember that the banana + + + align:start position:0% +metric space. Remember that the banana +basis does not hold for every metric + + align:start position:0% +basis does not hold for every metric + + + align:start position:0% +basis does not hold for every metric +space. + + align:start position:0% + + + + align:start position:0% + +for a metric space. So, so now it the + + align:start position:0% +for a metric space. So, so now it the + + + align:start position:0% +for a metric space. So, so now it the +bulan visor does not hold for every + + align:start position:0% +bulan visor does not hold for every + + + align:start position:0% +bulan visor does not hold for every +metric space but it holds. So uh when + + align:start position:0% +metric space but it holds. So uh when + + + align:start position:0% +metric space but it holds. So uh when +when this space here is compact, + + align:start position:0% + + + + align:start position:0% + +right? + + align:start position:0% + + + + align:start position:0% + +Okay. So that's what I want to prove and + + align:start position:0% +Okay. So that's what I want to prove and + + + align:start position:0% +Okay. So that's what I want to prove and +that's like one of the motivations here + + align:start position:0% +that's like one of the motivations here + + + align:start position:0% +that's like one of the motivations here +and for for the for the definition of + + align:start position:0% +and for for the for the definition of + + + align:start position:0% +and for for the for the definition of +being compact. And so + + align:start position:0% +being compact. And so + + + align:start position:0% +being compact. And so +uh let me just remind you. So on RN + + align:start position:0% +uh let me just remind you. So on RN + + + align:start position:0% +uh let me just remind you. So on RN +on R say uh what is the bulani? So on r + + align:start position:0% +on R say uh what is the bulani? So on r + + + align:start position:0% +on R say uh what is the bulani? So on r +the balsano + + align:start position:0% +the balsano + + + align:start position:0% +the balsano +why the what did that say? + + align:start position:0% +why the what did that say? + + + align:start position:0% +why the what did that say? +So this is that any + + align:start position:0% +So this is that any + + + align:start position:0% +So this is that any +bounded sequence + + align:start position:0% + + + + align:start position:0% + +has a convergent + + align:start position:0% + + + + align:start position:0% + +subsequence, + + align:start position:0% + + + + align:start position:0% + +right? That was the banana bias assume + + align:start position:0% + + + + align:start position:0% + +and and so uh what we want to show here + + align:start position:0% +and and so uh what we want to show here + + + align:start position:0% +and and so uh what we want to show here +is the following theorem for a for a + + align:start position:0% +is the following theorem for a for a + + + align:start position:0% +is the following theorem for a for a +general metric space. + + align:start position:0% + + + + align:start position:0% + +So we want to prove the following + + align:start position:0% +So we want to prove the following + + + align:start position:0% +So we want to prove the following +theorem + + align:start position:0% +theorem + + + align:start position:0% +theorem +that if x comma d is a matrix space + + align:start position:0% + + + + align:start position:0% + +uh a here + + align:start position:0% +uh a here + + + align:start position:0% +uh a here +is subset is compact + + align:start position:0% + + + + align:start position:0% + +then any + + align:start position:0% + + + + align:start position:0% + +Then any + + align:start position:0% +Then any + + + align:start position:0% +Then any +sequence + + align:start position:0% + + + + align:start position:0% + +in uh A has + + align:start position:0% +in uh A has + + + align:start position:0% +in uh A has +a convergent + + align:start position:0% + + + + align:start position:0% + +subsequence. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +now let me try to divide it into the poo + + align:start position:0% +now let me try to divide it into the poo + + + align:start position:0% +now let me try to divide it into the poo +and let me try to divide it in into some + + align:start position:0% +and let me try to divide it in into some + + + align:start position:0% +and let me try to divide it in into some +sub pieces. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +I begin + + align:start position:0% +I begin + + + align:start position:0% +I begin +with a lema. + + align:start position:0% +with a lema. + + + align:start position:0% +with a lema. +So, + + align:start position:0% +So, + + + align:start position:0% +So, +so the lema, + + align:start position:0% +so the lema, + + + align:start position:0% +so the lema, +so I want to begin with a lema that is + + align:start position:0% +so I want to begin with a lema that is + + + align:start position:0% +so I want to begin with a lema that is +the following. + + align:start position:0% +the following. + + + align:start position:0% +the following. +So, I have uh + + align:start position:0% + + + + align:start position:0% + +so I have my metric space. + + align:start position:0% + + + + align:start position:0% + +I have um a here is this subset that is + + align:start position:0% +I have um a here is this subset that is + + + align:start position:0% +I have um a here is this subset that is +uh compact. + + align:start position:0% + + + + align:start position:0% + +And then I have as a a family of nested + + align:start position:0% +And then I have as a a family of nested + + + align:start position:0% +And then I have as a a family of nested +subsets. So let me just talk about + + align:start position:0% +subsets. So let me just talk about + + + align:start position:0% +subsets. So let me just talk about +nested subsets for a second. + + align:start position:0% + + + + align:start position:0% + +So I do this on this board. And so what + + align:start position:0% +So I do this on this board. And so what + + + align:start position:0% +So I do this on this board. And so what +do I mean by nested subsets? + + align:start position:0% + + + + align:start position:0% + +So, so again I have some set and then I + + align:start position:0% +So, so again I have some set and then I + + + align:start position:0% +So, so again I have some set and then I +have some subsets. + + align:start position:0% +have some subsets. + + + align:start position:0% +have some subsets. +Um, see + + align:start position:0% +Um, see + + + align:start position:0% +Um, see +it's a it's a it's a family but it's now + + align:start position:0% +it's a it's a it's a family but it's now + + + align:start position:0% +it's a it's a it's a family but it's now +a family that is uh indexed by the + + align:start position:0% +a family that is uh indexed by the + + + align:start position:0% +a family that is uh indexed by the +integers. Right? So CI here is subsets. + + align:start position:0% +integers. Right? So CI here is subsets. + + + align:start position:0% +integers. Right? So CI here is subsets. +So this is I uh equal to one two so on + + align:start position:0% +So this is I uh equal to one two so on + + + align:start position:0% +So this is I uh equal to one two so on +and next + + align:start position:0% +and next + + + align:start position:0% +and next +I mean in this case here uh I am + + align:start position:0% +I mean in this case here uh I am + + + align:start position:0% +I mean in this case here uh I am +thinking about that the next subset is + + align:start position:0% +thinking about that the next subset is + + + align:start position:0% +thinking about that the next subset is +smaller than the previous smaller or at + + align:start position:0% +smaller than the previous smaller or at + + + align:start position:0% +smaller than the previous smaller or at +most equal to the previous. So I have + + align:start position:0% +most equal to the previous. So I have + + + align:start position:0% +most equal to the previous. So I have +this + + align:start position:0% +this + + + align:start position:0% +this +I could also have looked at where they + + align:start position:0% +I could also have looked at where they + + + align:start position:0% +I could also have looked at where they +were kind of increasing the subsets but + + align:start position:0% +were kind of increasing the subsets but + + + align:start position:0% +were kind of increasing the subsets but +uh but this is what I have in mind. + + align:start position:0% + + + + align:start position:0% + +Okay. So the sets as as I become larger + + align:start position:0% +Okay. So the sets as as I become larger + + + align:start position:0% +Okay. So the sets as as I become larger +the set becomes smaller. + + align:start position:0% +the set becomes smaller. + + + align:start position:0% +the set becomes smaller. +So I have so now back to the lema. Um I + + align:start position:0% +So I have so now back to the lema. Um I + + + align:start position:0% +So I have so now back to the lema. Um I +have this metric space. I have a compact + + align:start position:0% +have this metric space. I have a compact + + + align:start position:0% +have this metric space. I have a compact +subset and then I have a sequence here + + align:start position:0% +subset and then I have a sequence here + + + align:start position:0% +subset and then I have a sequence here +of CIS + + align:start position:0% +of CIS + + + align:start position:0% +of CIS +is a sequence. + + align:start position:0% +is a sequence. + + + align:start position:0% +is a sequence. +It's a nested sequence + + align:start position:0% + + + + align:start position:0% + +sequence + + align:start position:0% +sequence + + + align:start position:0% +sequence +of subsets. + + align:start position:0% +of subsets. + + + align:start position:0% +of subsets. +So again this means that the next + + align:start position:0% +So again this means that the next + + + align:start position:0% +So again this means that the next +element is contained in the previous + + align:start position:0% +element is contained in the previous + + + align:start position:0% +element is contained in the previous +one. Right? And this nested sequence of + + align:start position:0% +one. Right? And this nested sequence of + + + align:start position:0% +one. Right? And this nested sequence of +subsets, it's actually a nested sequence + + align:start position:0% +subsets, it's actually a nested sequence + + + align:start position:0% +subsets, it's actually a nested sequence +of closed subsets. + + align:start position:0% + + + + align:start position:0% + +Closed subsets of + + align:start position:0% +Closed subsets of + + + align:start position:0% +Closed subsets of +A. Okay, so they're closed + + align:start position:0% +A. Okay, so they're closed + + + align:start position:0% +A. Okay, so they're closed +in X and they're contained in + + align:start position:0% +in X and they're contained in + + + align:start position:0% +in X and they're contained in +in A. + + align:start position:0% +in A. + + + align:start position:0% +in A. +And then I assuming that uh and assume + + align:start position:0% + + + + align:start position:0% + +also + + align:start position:0% + + + + align:start position:0% + +that the CIS that none of the CIS are + + align:start position:0% +that the CIS that none of the CIS are + + + align:start position:0% +that the CIS that none of the CIS are +the empty sets. Right? + + align:start position:0% +the empty sets. Right? + + + align:start position:0% +the empty sets. Right? +So I I don't want any of them to be + + align:start position:0% +So I I don't want any of them to be + + + align:start position:0% +So I I don't want any of them to be +trivial. + + align:start position:0% +trivial. + + + align:start position:0% +trivial. +uh then the claim is so the claim is + + align:start position:0% +uh then the claim is so the claim is + + + align:start position:0% +uh then the claim is so the claim is +that + + align:start position:0% +that + + + align:start position:0% +that +is that if that's the case then actually + + align:start position:0% +is that if that's the case then actually + + + align:start position:0% +is that if that's the case then actually +if you take the intersection of all of + + align:start position:0% +if you take the intersection of all of + + + align:start position:0% +if you take the intersection of all of +these + + align:start position:0% +these + + + align:start position:0% +these +this here is is is is non empty so there + + align:start position:0% +this here is is is is non empty so there + + + align:start position:0% +this here is is is is non empty so there +is something that is in all of the CIS + + align:start position:0% +is something that is in all of the CIS + + + align:start position:0% +is something that is in all of the CIS +right okay that's what I want to prove + + align:start position:0% +right okay that's what I want to prove + + + align:start position:0% +right okay that's what I want to prove +um and in fact this is + + align:start position:0% +um and in fact this is + + + align:start position:0% +um and in fact this is +quite straightforward Okay. + + align:start position:0% +quite straightforward Okay. + + + align:start position:0% +quite straightforward Okay. +Um + + align:start position:0% + + + + align:start position:0% + +and because + + align:start position:0% +and because + + + align:start position:0% +and because +since the so the proof here + + align:start position:0% + + + + align:start position:0% + +since + + align:start position:0% +since + + + align:start position:0% +since +CI is closed + + align:start position:0% + + + + align:start position:0% + +this means that the complement here + + align:start position:0% +this means that the complement here + + + align:start position:0% +this means that the complement here +is open. + + align:start position:0% + + + + align:start position:0% + +Right. And now for the complements here. + + align:start position:0% +Right. And now for the complements here. + + + align:start position:0% +Right. And now for the complements here. +So the complement let's call it + + align:start position:0% +So the complement let's call it + + + align:start position:0% +So the complement let's call it +complements let's call it uh bi. + + align:start position:0% +complements let's call it uh bi. + + + align:start position:0% +complements let's call it uh bi. +So BI is open again and BI + + align:start position:0% +So BI is open again and BI + + + align:start position:0% +So BI is open again and BI +um + one they actually have this + + align:start position:0% +um + one they actually have this + + + align:start position:0% +um + one they actually have this +property that they are because the + + align:start position:0% +property that they are because the + + + align:start position:0% +property that they are because the +previous ones was nested where they + + align:start position:0% +previous ones was nested where they + + + align:start position:0% +previous ones was nested where they +became smaller then when you're looking + + align:start position:0% +became smaller then when you're looking + + + align:start position:0% +became smaller then when you're looking +at the complements then they become + + align:start position:0% +at the complements then they become + + + align:start position:0% +at the complements then they become +larger + + align:start position:0% + + + + align:start position:0% + +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +but uh so since this is closed then we + + align:start position:0% +but uh so since this is closed then we + + + align:start position:0% +but uh so since this is closed then we +have is uh if + + align:start position:0% +have is uh if + + + align:start position:0% +have is uh if +the intersection of these CR if there + + align:start position:0% +the intersection of these CR if there + + + align:start position:0% +the intersection of these CR if there +was nothing in the intersection of all + + align:start position:0% +was nothing in the intersection of all + + + align:start position:0% +was nothing in the intersection of all +of them if this here was the empty set + + align:start position:0% +of them if this here was the empty set + + + align:start position:0% +of them if this here was the empty set +but then it means that + + align:start position:0% +but then it means that + + + align:start position:0% +but then it means that +that the complement of these guys would + + align:start position:0% +that the complement of these guys would + + + align:start position:0% +that the complement of these guys would +then cover a right it would actually + + align:start position:0% +then cover a right it would actually + + + align:start position:0% +then cover a right it would actually +right the cover right because there's + + align:start position:0% +right the cover right because there's + + + align:start position:0% +right the cover right because there's +nothing the union of the complement so + + align:start position:0% +nothing the union of the complement so + + + align:start position:0% +nothing the union of the complement so +the union of the complement here + + align:start position:0% + + + + align:start position:0% + +it would actually cover X but it would + + align:start position:0% +it would actually cover X but it would + + + align:start position:0% +it would actually cover X but it would +in particular cover + + align:start position:0% +in particular cover + + + align:start position:0% +in particular cover +A right. So yeah this here called BI. + + align:start position:0% +A right. So yeah this here called BI. + + + align:start position:0% +A right. So yeah this here called BI. +So you have that. + + align:start position:0% +So you have that. + + + align:start position:0% +So you have that. +So this mean and again this here is this + + align:start position:0% +So this mean and again this here is this + + + align:start position:0% +So this mean and again this here is this +here is the same as BI. + + align:start position:0% +here is the same as BI. + + + align:start position:0% +here is the same as BI. +So now since uh A is compact + + align:start position:0% + + + + align:start position:0% + +since uh A is compact + + align:start position:0% + + + + align:start position:0% + +this means that uh A here + + align:start position:0% +this means that uh A here + + + align:start position:0% +this means that uh A here +A here is contained in finitely many + + align:start position:0% +A here is contained in finitely many + + + align:start position:0% +A here is contained in finitely many +of these let's call them + + align:start position:0% + + + + align:start position:0% + +So you have finally many like this + + align:start position:0% +So you have finally many like this + + + align:start position:0% +So you have finally many like this +of the bees and I just you know I'm not + + align:start position:0% +of the bees and I just you know I'm not + + + align:start position:0% +of the bees and I just you know I'm not +sure whether it's the first but but but + + align:start position:0% +sure whether it's the first but but but + + + align:start position:0% +sure whether it's the first but but but +there are finitely many of these that + + align:start position:0% +there are finitely many of these that + + + align:start position:0% +there are finitely many of these that +cover it + + align:start position:0% + + + + align:start position:0% + +and so in particular but one of these + + align:start position:0% +and so in particular but one of these + + + align:start position:0% +and so in particular but one of these +is like right one of the indices here is + + align:start position:0% +is like right one of the indices here is + + + align:start position:0% +is like right one of the indices here is +the largest one of those right and so + + align:start position:0% +the largest one of those right and so + + + align:start position:0% +the largest one of those right and so +this means that it's actually contained + + align:start position:0% +this means that it's actually contained + + + align:start position:0% +this means that it's actually contained +in the largest of these Let's say that + + align:start position:0% +in the largest of these Let's say that + + + align:start position:0% +in the largest of these Let's say that +that the largest of these is b right. So + + align:start position:0% +that the largest of these is b right. So + + + align:start position:0% +that the largest of these is b right. So +you have this for some n right? + + align:start position:0% +you have this for some n right? + + + align:start position:0% +you have this for some n right? +But this say but this here remember that + + align:start position:0% +But this say but this here remember that + + + align:start position:0% +But this say but this here remember that +this here was the complement of + + align:start position:0% +this here was the complement of + + + align:start position:0% +this here was the complement of +CN like this right. So this means that a + + align:start position:0% +CN like this right. So this means that a + + + align:start position:0% +CN like this right. So this means that a +have nothing in CN right. So this mean + + align:start position:0% +have nothing in CN right. So this mean + + + align:start position:0% +have nothing in CN right. So this mean +but A was a sub C was so CN intersected + + align:start position:0% +but A was a sub C was so CN intersected + + + align:start position:0% +but A was a sub C was so CN intersected +with A + + align:start position:0% +with A + + + align:start position:0% +with A +is empty but CN was contained in A. So + + align:start position:0% +is empty but CN was contained in A. So + + + align:start position:0% +is empty but CN was contained in A. So +this means that since + + align:start position:0% +this means that since + + + align:start position:0% +this means that since +cn was assumed to be + + align:start position:0% +cn was assumed to be + + + align:start position:0% +cn was assumed to be +uh contained in a right this was subsets + + align:start position:0% +uh contained in a right this was subsets + + + align:start position:0% +uh contained in a right this was subsets +of a + + align:start position:0% +of a + + + align:start position:0% +of a +then this means that cn. So this here is + + align:start position:0% +then this means that cn. So this here is + + + align:start position:0% +then this means that cn. So this here is +this means that this here then implies + + align:start position:0% +this means that this here then implies + + + align:start position:0% +this means that this here then implies +that that this thing here is is cn. + + align:start position:0% +that that this thing here is is cn. + + + align:start position:0% +that that this thing here is is cn. +Right? So you have that one of them was + + align:start position:0% +Right? So you have that one of them was + + + align:start position:0% +Right? So you have that one of them was +empty but that we assume that none of + + align:start position:0% +empty but that we assume that none of + + + align:start position:0% +empty but that we assume that none of +the sets CN was empty. Fine. + + align:start position:0% + + + + align:start position:0% + +Okay. Was that clear? Sorry. Yep. + + align:start position:0% + + + + align:start position:0% + +>> Okay. So that's right. So So I'm I'm + + align:start position:0% +>> Okay. So that's right. So So I'm I'm + + + align:start position:0% +>> Okay. So that's right. So So I'm I'm +trying to prove uh this theorem here, + + align:start position:0% +trying to prove uh this theorem here, + + + align:start position:0% +trying to prove uh this theorem here, +right? And it it's uh it's not super + + align:start position:0% +right? And it it's uh it's not super + + + align:start position:0% +right? And it it's uh it's not super +complicated, but it's a little bit + + align:start position:0% +complicated, but it's a little bit + + + align:start position:0% +complicated, but it's a little bit +involved. And so I'm trying to of course + + align:start position:0% +involved. And so I'm trying to of course + + + align:start position:0% +involved. And so I'm trying to of course +this is always a great idea if and it's + + align:start position:0% +this is always a great idea if and it's + + + align:start position:0% +this is always a great idea if and it's +kind of like important thing in this + + align:start position:0% +kind of like important thing in this + + + align:start position:0% +kind of like important thing in this +class + + align:start position:0% +class + + + align:start position:0% +class +and and and and also if you take other + + align:start position:0% +and and and and also if you take other + + + align:start position:0% +and and and and also if you take other +math, you know, more advanced math + + align:start position:0% +math, you know, more advanced math + + + align:start position:0% +math, you know, more advanced math +classes is that when you're trying to + + align:start position:0% +classes is that when you're trying to + + + align:start position:0% +classes is that when you're trying to +prove something, + + align:start position:0% +prove something, + + + align:start position:0% +prove something, +it's, you know, there's things that are + + align:start position:0% +it's, you know, there's things that are + + + align:start position:0% +it's, you know, there's things that are +really easy to prove, but then there are + + align:start position:0% +really easy to prove, but then there are + + + align:start position:0% +really easy to prove, but then there are +things that are much more complicated, + + align:start position:0% +things that are much more complicated, + + + align:start position:0% +things that are much more complicated, +right? So one thing is that you try to + + align:start position:0% +right? So one thing is that you try to + + + align:start position:0% +right? So one thing is that you try to +prove it. Another thing is that you try + + align:start position:0% +prove it. Another thing is that you try + + + align:start position:0% +prove it. Another thing is that you try +to explain to other the proof right and + + align:start position:0% +to explain to other the proof right and + + + align:start position:0% +to explain to other the proof right and +so in either case if you can divide it + + align:start position:0% +so in either case if you can divide it + + + align:start position:0% +so in either case if you can divide it +into substeps right and so this here is + + align:start position:0% +into substeps right and so this here is + + + align:start position:0% +into substeps right and so this here is +a substep + + align:start position:0% +a substep + + + align:start position:0% +a substep +uh in the proof + + align:start position:0% +uh in the proof + + + align:start position:0% +uh in the proof +and uh and so in a minute we will see + + align:start position:0% +and uh and so in a minute we will see + + + align:start position:0% +and uh and so in a minute we will see +why this here is relevant and so this + + align:start position:0% +why this here is relevant and so this + + + align:start position:0% +why this here is relevant and so this +sort of answer your question right I + + align:start position:0% +sort of answer your question right I + + + align:start position:0% +sort of answer your question right I +mean how does how does this come up + + align:start position:0% +mean how does how does this come up + + + align:start position:0% +mean how does how does this come up +right and and in a minute you'll see how + + align:start position:0% +right and and in a minute you'll see how + + + align:start position:0% +right and and in a minute you'll see how +it comes up so So, so let me get back to + + align:start position:0% +it comes up so So, so let me get back to + + + align:start position:0% +it comes up so So, so let me get back to +that question just a minute. + + align:start position:0% +that question just a minute. + + + align:start position:0% +that question just a minute. +>> Are you able to explain the last remark + + align:start position:0% +>> Are you able to explain the last remark + + + align:start position:0% +>> Are you able to explain the last remark +again? + + align:start position:0% +again? + + + align:start position:0% +again? +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> So, so here so so again the BIS are open + + align:start position:0% +>> So, so here so so again the BIS are open + + + align:start position:0% +>> So, so here so so again the BIS are open +and using compactness because all of the + + align:start position:0% +and using compactness because all of the + + + align:start position:0% +and using compactness because all of the +BIS cover a then finally many must cover + + align:start position:0% +BIS cover a then finally many must cover + + + align:start position:0% +BIS cover a then finally many must cover +it. + + align:start position:0% +it. + + + align:start position:0% +it. +But the bis are nested in in this way + + align:start position:0% +But the bis are nested in in this way + + + align:start position:0% +But the bis are nested in in this way +that they are increasing as subsets. So + + align:start position:0% +that they are increasing as subsets. So + + + align:start position:0% +that they are increasing as subsets. So +if I'm thinking about maybe this here is + + align:start position:0% +if I'm thinking about maybe this here is + + + align:start position:0% +if I'm thinking about maybe this here is +the one where the index is large this + + align:start position:0% +the one where the index is large this + + + align:start position:0% +the one where the index is large this +then contain all the other. So this is + + align:start position:0% +then contain all the other. So this is + + + align:start position:0% +then contain all the other. So this is +it's actually equal to in that case it + + align:start position:0% +it's actually equal to in that case it + + + align:start position:0% +it's actually equal to in that case it +would be equal you know this really is + + align:start position:0% +would be equal you know this really is + + + align:start position:0% +would be equal you know this really is +equal to like this. + + align:start position:0% +equal to like this. + + + align:start position:0% +equal to like this. +So again, so this means that A is + + align:start position:0% +So again, so this means that A is + + + align:start position:0% +So again, so this means that A is +contained in in the complement of CN. So + + align:start position:0% +contained in in the complement of CN. So + + + align:start position:0% +contained in in the complement of CN. So +in other words, there is no elements + + align:start position:0% +in other words, there is no elements + + + align:start position:0% +in other words, there is no elements +in uh in A that are in CN. Right? That's + + align:start position:0% +in uh in A that are in CN. Right? That's + + + align:start position:0% +in uh in A that are in CN. Right? That's +what it means. So there is no elements + + align:start position:0% +what it means. So there is no elements + + + align:start position:0% +what it means. So there is no elements +in A that has a CN. This is that this + + align:start position:0% +in A that has a CN. This is that this + + + align:start position:0% +in A that has a CN. This is that this +thing here is empty. + + align:start position:0% +thing here is empty. + + + align:start position:0% +thing here is empty. +But the CN remember that the CN was + + align:start position:0% +But the CN remember that the CN was + + + align:start position:0% +But the CN remember that the CN was +assumed to be subsets of A. Right? So + + align:start position:0% +assumed to be subsets of A. Right? So + + + align:start position:0% +assumed to be subsets of A. Right? So +this means that that there is nothing in + + align:start position:0% +this means that that there is nothing in + + + align:start position:0% +this means that that there is nothing in +CN that is not in A. So this is really + + align:start position:0% +CN that is not in A. So this is really + + + align:start position:0% +CN that is not in A. So this is really +just equal to CN + + align:start position:0% +just equal to CN + + + align:start position:0% +just equal to CN +>> and so is that essentially just creating + + align:start position:0% +>> and so is that essentially just creating + + + align:start position:0% +>> and so is that essentially just creating +a contradiction. Uh and so that's why + + align:start position:0% +a contradiction. Uh and so that's why + + + align:start position:0% +a contradiction. Uh and so that's why +and that's a contradiction because now + + align:start position:0% +and that's a contradiction because now + + + align:start position:0% +and that's a contradiction because now +this show that this one here this CN is + + align:start position:0% +this show that this one here this CN is + + + align:start position:0% +this show that this one here this CN is +empty but they were all assumed to be + + align:start position:0% +empty but they were all assumed to be + + + align:start position:0% +empty but they were all assumed to be +non empty right yeah okay + + align:start position:0% +non empty right yeah okay + + + align:start position:0% +non empty right yeah okay +so so this is this is like uh yeah Sorry + + align:start position:0% +so so this is this is like uh yeah Sorry + + + align:start position:0% +so so this is this is like uh yeah Sorry +question. + + align:start position:0% + + + + align:start position:0% + +>> Right. Right. Okay. So if + + align:start position:0% +>> Right. Right. Okay. So if + + + align:start position:0% +>> Right. Right. Okay. So if +so if the intersection of the CI + + align:start position:0% +so if the intersection of the CI + + + align:start position:0% +so if the intersection of the CI +right so here sorry if they inter so I + + align:start position:0% +right so here sorry if they inter so I + + + align:start position:0% +right so here sorry if they inter so I +want to prove this. So I'm assuming that + + align:start position:0% +want to prove this. So I'm assuming that + + + align:start position:0% +want to prove this. So I'm assuming that +this is the case and I define the BIS to + + align:start position:0% +this is the case and I define the BIS to + + + align:start position:0% +this is the case and I define the BIS to +be the complement of the CIS. So if + + align:start position:0% +be the complement of the CIS. So if + + + align:start position:0% +be the complement of the CIS. So if +there is nothing + + align:start position:0% +there is nothing + + + align:start position:0% +there is nothing +in the intersection of all of the CIS + + align:start position:0% +in the intersection of all of the CIS + + + align:start position:0% +in the intersection of all of the CIS +then it means that the union of the + + align:start position:0% +then it means that the union of the + + + align:start position:0% +then it means that the union of the +complements must cover the whole set + + align:start position:0% +complements must cover the whole set + + + align:start position:0% +complements must cover the whole set +right because you know right so if you + + align:start position:0% +right because you know right so if you + + + align:start position:0% +right because you know right so if you +takes anything in even in X if you take + + align:start position:0% +takes anything in even in X if you take + + + align:start position:0% +takes anything in even in X if you take +anything in X it's not in all of the CIS + + align:start position:0% +anything in X it's not in all of the CIS + + + align:start position:0% +anything in X it's not in all of the CIS +so this means that there is some I so + + align:start position:0% +so this means that there is some I so + + + align:start position:0% +so this means that there is some I so +that it's in complement of that CI right + + align:start position:0% +that it's in complement of that CI right + + + align:start position:0% +that it's in complement of that CI right +but that's that's exactly this + + align:start position:0% + + + + align:start position:0% + +um okay so now so you're asking why is + + align:start position:0% +um okay so now so you're asking why is + + + align:start position:0% +um okay so now so you're asking why is +this relevance right and and that's a + + align:start position:0% +this relevance right and and that's a + + + align:start position:0% +this relevance right and and that's a +good question and uh and I'm not I'm I + + align:start position:0% +good question and uh and I'm not I'm I + + + align:start position:0% +good question and uh and I'm not I'm I +will answer it in a minute but I will uh + + align:start position:0% +will answer it in a minute but I will uh + + + align:start position:0% +will answer it in a minute but I will uh +kind of elaborate I will give you an + + align:start position:0% +kind of elaborate I will give you an + + + align:start position:0% +kind of elaborate I will give you an +example where I have it and then we will + + align:start position:0% +example where I have it and then we will + + + align:start position:0% +example where I have it and then we will +eventually see how to get to that + + align:start position:0% +eventually see how to get to that + + + align:start position:0% +eventually see how to get to that +example okay so the next thing is + + align:start position:0% +example okay so the next thing is + + + align:start position:0% +example okay so the next thing is +that suppose I take a + + align:start position:0% +that suppose I take a + + + align:start position:0% +that suppose I take a +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +suppose I have the same setup + + align:start position:0% +suppose I have the same setup + + + align:start position:0% +suppose I have the same setup +but now my sets are you know the the + + align:start position:0% +but now my sets are you know the the + + + align:start position:0% +but now my sets are you know the the +then close sets so I have this setup + + align:start position:0% +then close sets so I have this setup + + + align:start position:0% +then close sets so I have this setup +again so this is like a corner + + align:start position:0% + + + + align:start position:0% + +of of the lema that we just pruned + + align:start position:0% +of of the lema that we just pruned + + + align:start position:0% +of of the lema that we just pruned +so we We have x comma d. This is matrix + + align:start position:0% +so we We have x comma d. This is matrix + + + align:start position:0% +so we We have x comma d. This is matrix +space. + + align:start position:0% + + + + align:start position:0% + +And we have uh a here is a subset of x + + align:start position:0% +And we have uh a here is a subset of x + + + align:start position:0% +And we have uh a here is a subset of x +uh is compact. + + align:start position:0% + + + + align:start position:0% + +And now now my sets CIS + + align:start position:0% +And now now my sets CIS + + + align:start position:0% +And now now my sets CIS +is going to be so CIS here these are + + align:start position:0% +is going to be so CIS here these are + + + align:start position:0% +is going to be so CIS here these are +going to be balls + + align:start position:0% +going to be balls + + + align:start position:0% +going to be balls +of radius R I + + align:start position:0% +of radius R I + + + align:start position:0% +of radius R I +and center X I + + align:start position:0% +and center X I + + + align:start position:0% +and center X I +and U there would be balls like this + + align:start position:0% +and U there would be balls like this + + + align:start position:0% +and U there would be balls like this +and I'm assuming that they are nested + + align:start position:0% +and I'm assuming that they are nested + + + align:start position:0% +and I'm assuming that they are nested +so in the Same way I'm assuming that + + align:start position:0% +so in the Same way I'm assuming that + + + align:start position:0% +so in the Same way I'm assuming that +this thing here + + align:start position:0% +this thing here + + + align:start position:0% +this thing here +the centers change the radi and the + + align:start position:0% +the centers change the radi and the + + + align:start position:0% +the centers change the radi and the +center change is depending on I they're + + align:start position:0% +center change is depending on I they're + + + align:start position:0% +center change is depending on I they're +all this close ball where it's like + + align:start position:0% +all this close ball where it's like + + + align:start position:0% +all this close ball where it's like +lesser equal to the eye. So I'm assuming + + align:start position:0% +lesser equal to the eye. So I'm assuming + + + align:start position:0% +lesser equal to the eye. So I'm assuming +that the next one is contained in the + + align:start position:0% +that the next one is contained in the + + + align:start position:0% +that the next one is contained in the +previous one. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And then I'm making one more assumption + + align:start position:0% +And then I'm making one more assumption + + + align:start position:0% +And then I'm making one more assumption +is that the RA I + + align:start position:0% +is that the RA I + + + align:start position:0% +is that the RA I +goes to zero. + + align:start position:0% +goes to zero. + + + align:start position:0% +goes to zero. +Okay. So I have that. So so just let's + + align:start position:0% +Okay. So I have that. So so just let's + + + align:start position:0% +Okay. So I have that. So so just let's +observe that these sets here they are + + align:start position:0% +observe that these sets here they are + + + align:start position:0% +observe that these sets here they are +nested by assumption. They're closed, + + align:start position:0% +nested by assumption. They're closed, + + + align:start position:0% +nested by assumption. They're closed, +right? Because it's it's it's it's this + + align:start position:0% +right? Because it's it's it's it's this + + + align:start position:0% +right? Because it's it's it's it's this +closed ball. So they're closed subsets. + + align:start position:0% +closed ball. So they're closed subsets. + + + align:start position:0% +closed ball. So they're closed subsets. +Also observe that each of these balls + + align:start position:0% +Also observe that each of these balls + + + align:start position:0% +Also observe that each of these balls +contain the center. So right so this + + align:start position:0% +contain the center. So right so this + + + align:start position:0% +contain the center. So right so this +means that each of these balls is not + + align:start position:0% +means that each of these balls is not + + + align:start position:0% +means that each of these balls is not +empty. Right? So it's automatic that + + align:start position:0% +empty. Right? So it's automatic that + + + align:start position:0% +empty. Right? So it's automatic that +they're not empty. Right? + + align:start position:0% +they're not empty. Right? + + + align:start position:0% +they're not empty. Right? +Okay. So now I claim that + + align:start position:0% +Okay. So now I claim that + + + align:start position:0% +Okay. So now I claim that +I claim that the intersection of all of + + align:start position:0% +I claim that the intersection of all of + + + align:start position:0% +I claim that the intersection of all of +these balls + + align:start position:0% +these balls + + + align:start position:0% +these balls +is is just one point. + + align:start position:0% + + + + align:start position:0% + +So now + + align:start position:0% +So now + + + align:start position:0% +So now +uh so now the claim here + + align:start position:0% + + + + align:start position:0% + +that the uh intersection of these balls + + align:start position:0% +that the uh intersection of these balls + + + align:start position:0% +that the uh intersection of these balls +here, + + align:start position:0% + + + + align:start position:0% + +these closed balls here + + align:start position:0% +these closed balls here + + + align:start position:0% +these closed balls here +is uh is a single point. + + align:start position:0% + + + + align:start position:0% + +Okay. Yeah. How do we know that each of + + align:start position:0% +Okay. Yeah. How do we know that each of + + + align:start position:0% +Okay. Yeah. How do we know that each of +balls contain the center? + + align:start position:0% +balls contain the center? + + + align:start position:0% +balls contain the center? +>> Uh because you know but if you take um + + align:start position:0% +>> Uh because you know but if you take um + + + align:start position:0% +>> Uh because you know but if you take um +if you take a ball + + align:start position:0% + + + + align:start position:0% + +so if you take a ball here in any metric + + align:start position:0% +so if you take a ball here in any metric + + + align:start position:0% +so if you take a ball here in any metric +space this is the y in the space in this + + align:start position:0% +space this is the y in the space in this + + + align:start position:0% +space this is the y in the space in this +set. So that the distance from X to now + + align:start position:0% +set. So that the distance from X to now + + + align:start position:0% +set. So that the distance from X to now +I take the open one but similarly with + + align:start position:0% +I take the open one but similarly with + + + align:start position:0% +I take the open one but similarly with +the closed this thing here is less than + + align:start position:0% +the closed this thing here is less than + + + align:start position:0% +the closed this thing here is less than +sorry this here is why saying + + align:start position:0% +sorry this here is why saying + + + align:start position:0% +sorry this here is why saying +>> it contains its own center but not like + + align:start position:0% +>> it contains its own center but not like + + + align:start position:0% +>> it contains its own center but not like +one single point across all + + align:start position:0% +one single point across all + + + align:start position:0% +one single point across all +>> yeah so that's right so so I'm just + + align:start position:0% +>> yeah so that's right so so I'm just + + + align:start position:0% +>> yeah so that's right so so I'm just +saying that so so if you plug in y x for + + align:start position:0% +saying that so so if you plug in y x for + + + align:start position:0% +saying that so so if you plug in y x for +y right you get zero right so this is + + align:start position:0% +y right you get zero right so this is + + + align:start position:0% +y right you get zero right so this is +definitely so so this here x definitely + + align:start position:0% +definitely so so this here x definitely + + + align:start position:0% +definitely so so this here x definitely +is in here right and I'm just saying + + align:start position:0% +is in here right and I'm just saying + + + align:start position:0% +is in here right and I'm just saying +that each of these guys is not empty + + align:start position:0% +that each of these guys is not empty + + + align:start position:0% +that each of these guys is not empty +right + + align:start position:0% +right + + + align:start position:0% +right +okay so now but and then I want to claim + + align:start position:0% +okay so now but and then I want to claim + + + align:start position:0% +okay so now but and then I want to claim +that actually there's something in the + + align:start position:0% +that actually there's something in the + + + align:start position:0% +that actually there's something in the +intersection of all of these balls and I + + align:start position:0% +intersection of all of these balls and I + + + align:start position:0% +intersection of all of these balls and I +want to claim that there's only one + + align:start position:0% +want to claim that there's only one + + + align:start position:0% +want to claim that there's only one +thing such thing there's a unique thing + + align:start position:0% +thing such thing there's a unique thing + + + align:start position:0% +thing such thing there's a unique thing +that is in intersection of all these + + align:start position:0% +that is in intersection of all these + + + align:start position:0% +that is in intersection of all these +balls right okay so now First, + + align:start position:0% + + + + align:start position:0% + +first I want to prove that this thing + + align:start position:0% +first I want to prove that this thing + + + align:start position:0% +first I want to prove that this thing +here + + align:start position:0% + + + + align:start position:0% + +is non right + + align:start position:0% +is non right + + + align:start position:0% +is non right +and sorry and this here should have been + + align:start position:0% +and sorry and this here should have been + + + align:start position:0% +and sorry and this here should have been +the closed balls like this but you see + + align:start position:0% +the closed balls like this but you see + + + align:start position:0% +the closed balls like this but you see +uh this just follows from + + align:start position:0% + + + + align:start position:0% + +from the lema + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% + + + + align:start position:0% + +each each + + align:start position:0% +each each + + + align:start position:0% +each each +uh B, you know, because each B R I + + align:start position:0% +uh B, you know, because each B R I + + + align:start position:0% +uh B, you know, because each B R I +XI is closed + + align:start position:0% + + + + align:start position:0% + +and non- empty + + align:start position:0% + + + + align:start position:0% + +is each is closed non- empty. + + align:start position:0% +is each is closed non- empty. + + + align:start position:0% +is each is closed non- empty. +Um and and and + + align:start position:0% +Um and and and + + + align:start position:0% +Um and and and +the family + + align:start position:0% +the family + + + align:start position:0% +the family +or sequence + + align:start position:0% +or sequence + + + align:start position:0% +or sequence +of of walls + + align:start position:0% + + + + align:start position:0% + +is nested. + + align:start position:0% + + + + align:start position:0% + +Right? By assumption, right? By + + align:start position:0% +Right? By assumption, right? By + + + align:start position:0% +Right? By assumption, right? By +assumption, we assume that this thing + + align:start position:0% +assumption, we assume that this thing + + + align:start position:0% +assumption, we assume that this thing +here is our i + 1 x i + 1 that this + + align:start position:0% +here is our i + 1 x i + 1 that this + + + align:start position:0% +here is our i + 1 x i + 1 that this +thing here is contained in the previous + + align:start position:0% +thing here is contained in the previous + + + align:start position:0% +thing here is contained in the previous +right. So by assumption by assumption so + + align:start position:0% +right. So by assumption by assumption so + + + align:start position:0% +right. So by assumption by assumption so +we again we use the lema and this is the + + align:start position:0% +we again we use the lema and this is the + + + align:start position:0% +we again we use the lema and this is the +CIS right and the CIS are closed and + + align:start position:0% +CIS right and the CIS are closed and + + + align:start position:0% +CIS right and the CIS are closed and +they are indeed nested as they should be + + align:start position:0% +they are indeed nested as they should be + + + align:start position:0% +they are indeed nested as they should be +and they are all non- empty just because + + align:start position:0% +and they are all non- empty just because + + + align:start position:0% +and they are all non- empty just because +they each contain their own centers + + align:start position:0% +they each contain their own centers + + + align:start position:0% +they each contain their own centers +right I you know yeah + + align:start position:0% + + + + align:start position:0% + +>> we're making some assumption. That's + + align:start position:0% +>> we're making some assumption. That's + + + align:start position:0% +>> we're making some assumption. That's +right. We're making some assumption + + align:start position:0% +right. We're making some assumption + + + align:start position:0% +right. We're making some assumption +about um right so + + align:start position:0% +about um right so + + + align:start position:0% +about um right so +we're you know and uh uh right we're + + align:start position:0% +we're you know and uh uh right we're + + + align:start position:0% +we're you know and uh uh right we're +making some assumption about that we the + + align:start position:0% +making some assumption about that we the + + + align:start position:0% +making some assumption about that we the +when you when you make this assumption + + align:start position:0% +when you when you make this assumption + + + align:start position:0% +when you when you make this assumption +about nested there's some assumption + + align:start position:0% +about nested there's some assumption + + + align:start position:0% +about nested there's some assumption +about the centers the the distance + + align:start position:0% +about the centers the the distance + + + align:start position:0% +about the centers the the distance +between centers and there's also + + align:start position:0% +between centers and there's also + + + align:start position:0% +between centers and there's also +something about the radi that you know + + align:start position:0% +something about the radi that you know + + + align:start position:0% +something about the radi that you know +how large is one radio relative itude to + + align:start position:0% +how large is one radio relative itude to + + + align:start position:0% +how large is one radio relative itude to +the other, right? Because if you have if + + align:start position:0% +the other, right? Because if you have if + + + align:start position:0% +the other, right? Because if you have if +you imagine that this here is BR I + + align:start position:0% +you imagine that this here is BR I + + + align:start position:0% +you imagine that this here is BR I +like this. This is this. So in the + + align:start position:0% +like this. This is this. So in the + + + align:start position:0% +like this. This is this. So in the +picture it would be kind of contain the + + align:start position:0% +picture it would be kind of contain the + + + align:start position:0% +picture it would be kind of contain the +boundary and then the next one but the + + align:start position:0% +boundary and then the next one but the + + + align:start position:0% +boundary and then the next one but the +next one may be out here on the side but + + align:start position:0% +next one may be out here on the side but + + + align:start position:0% +next one may be out here on the side but +it's supposed to be + + align:start position:0% +it's supposed to be + + + align:start position:0% +it's supposed to be +contained in it. + + align:start position:0% +contained in it. + + + align:start position:0% +contained in it. +Right? So you see that the center the + + align:start position:0% +Right? So you see that the center the + + + align:start position:0% +Right? So you see that the center the +sender may have moved. This here was the + + align:start position:0% +sender may have moved. This here was the + + + align:start position:0% +sender may have moved. This here was the +XI and the next center may have moved. + + align:start position:0% +XI and the next center may have moved. + + + align:start position:0% +XI and the next center may have moved. +It may have shifted quite a bit, right? + + align:start position:0% +It may have shifted quite a bit, right? + + + align:start position:0% +It may have shifted quite a bit, right? +But of course, you know, this here is + + align:start position:0% +But of course, you know, this here is + + + align:start position:0% +But of course, you know, this here is +the RA I radius and this here is the RA + + align:start position:0% +the RA I radius and this here is the RA + + + align:start position:0% +the RA I radius and this here is the RA +I + one radius, right? So you see that + + align:start position:0% +I + one radius, right? So you see that + + + align:start position:0% +I + one radius, right? So you see that +there's u there's some sort of relation, + + align:start position:0% +there's u there's some sort of relation, + + + align:start position:0% +there's u there's some sort of relation, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +But okay so so the so we have that the + + align:start position:0% +But okay so so the so we have that the + + + align:start position:0% +But okay so so the so we have that the +it just follows from the lema that the + + align:start position:0% +it just follows from the lema that the + + + align:start position:0% +it just follows from the lema that the +intersection of all these closed balls + + align:start position:0% +intersection of all these closed balls + + + align:start position:0% +intersection of all these closed balls +is non empty right yeah + + align:start position:0% +is non empty right yeah + + + align:start position:0% +is non empty right yeah +>> it just follows + + align:start position:0% +>> it just follows + + + align:start position:0% +>> it just follows +you + + align:start position:0% +you + + + align:start position:0% +you +>> yeah that's right so it follows now from + + align:start position:0% +>> yeah that's right so it follows now from + + + align:start position:0% +>> yeah that's right so it follows now from +that I that's why we're using the r= to + + align:start position:0% +that I that's why we're using the r= to + + + align:start position:0% +that I that's why we're using the r= to +zero because suppose that you have two + + align:start position:0% +zero because suppose that you have two + + + align:start position:0% +zero because suppose that you have two +elements, right? Suppose that you have X + + align:start position:0% +elements, right? Suppose that you have X + + + align:start position:0% +elements, right? Suppose that you have X +here and Y. Suppose that they are in the + + align:start position:0% +here and Y. Suppose that they are in the + + + align:start position:0% +here and Y. Suppose that they are in the +intersection of these guys here. + + align:start position:0% + + + + align:start position:0% + +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +Now look at the distance between X and + + align:start position:0% +Now look at the distance between X and + + + align:start position:0% +Now look at the distance between X and +Y. + + align:start position:0% +Y. + + + align:start position:0% +Y. +Well, they are into intersection. So + + align:start position:0% +Well, they are into intersection. So + + + align:start position:0% +Well, they are into intersection. So +this means that for each I for each I + + align:start position:0% +this means that for each I for each I + + + align:start position:0% +this means that for each I for each I +so for each + + align:start position:0% +so for each + + + align:start position:0% +so for each +each eye we have that X here and Y + + align:start position:0% +each eye we have that X here and Y + + + align:start position:0% +each eye we have that X here and Y +is in this guy here. + + align:start position:0% +is in this guy here. + + + align:start position:0% +is in this guy here. +Right? So if it's in in this ball here + + align:start position:0% +Right? So if it's in in this ball here + + + align:start position:0% +Right? So if it's in in this ball here +for for a a I then you can use the + + align:start position:0% +for for a a I then you can use the + + + align:start position:0% +for for a a I then you can use the +triangle inequality, + + align:start position:0% + + + + align:start position:0% + +right? And this thing here is bounded by + + align:start position:0% +right? And this thing here is bounded by + + + align:start position:0% +right? And this thing here is bounded by +this here should have been a RA. + + align:start position:0% +this here should have been a RA. + + + align:start position:0% +this here should have been a RA. +This here is bounded by less or equal to + + align:start position:0% +This here is bounded by less or equal to + + + align:start position:0% +This here is bounded by less or equal to +because I have this bar RA I plus RA I + + align:start position:0% +because I have this bar RA I plus RA I + + + align:start position:0% +because I have this bar RA I plus RA I +so 2 R I but it this here holds for all + + align:start position:0% +so 2 R I but it this here holds for all + + + align:start position:0% +so 2 R I but it this here holds for all +I this here goes to zero. So this means + + align:start position:0% +I this here goes to zero. So this means + + + align:start position:0% +I this here goes to zero. So this means +that this here implies as you say this + + align:start position:0% +that this here implies as you say this + + + align:start position:0% +that this here implies as you say this +here implies that the distance + + align:start position:0% +here implies that the distance + + + align:start position:0% +here implies that the distance +had to be zero but this is part of what + + align:start position:0% +had to be zero but this is part of what + + + align:start position:0% +had to be zero but this is part of what +it is means to be a metric space that if + + align:start position:0% +it is means to be a metric space that if + + + align:start position:0% +it is means to be a metric space that if +the distance is zero then the two points + + align:start position:0% +the distance is zero then the two points + + + align:start position:0% +the distance is zero then the two points +are the same. + + align:start position:0% +are the same. + + + align:start position:0% +are the same. +Okay so that was actually so the whole + + align:start position:0% +Okay so that was actually so the whole + + + align:start position:0% +Okay so that was actually so the whole +core was really quite easy from the + + align:start position:0% +core was really quite easy from the + + + align:start position:0% +core was really quite easy from the +demo. Okay. + + align:start position:0% +demo. Okay. + + + align:start position:0% +demo. Okay. +And so now the question is so this is + + align:start position:0% +And so now the question is so this is + + + align:start position:0% +And so now the question is so this is +your question is why is this relevant in + + align:start position:0% +your question is why is this relevant in + + + align:start position:0% +your question is why is this relevant in +in the in this balsano vast stress right + + align:start position:0% +in the in this balsano vast stress right + + + align:start position:0% +in the in this balsano vast stress right +I mean there may be not so interesting I + + align:start position:0% +I mean there may be not so interesting I + + + align:start position:0% +I mean there may be not so interesting I +mean the lema and color on its own but + + align:start position:0% +mean the lema and color on its own but + + + align:start position:0% +mean the lema and color on its own but +but it's but there are tools to prove + + align:start position:0% +but it's but there are tools to prove + + + align:start position:0% +but it's but there are tools to prove +the banana bio + + align:start position:0% + + + + align:start position:0% + +okay so let me try to first + + align:start position:0% + + + + align:start position:0% + +explain the idea and then then we go to + + align:start position:0% +explain the idea and then then we go to + + + align:start position:0% +explain the idea and then then we go to +the proof. + + align:start position:0% +the proof. + + + align:start position:0% +the proof. +So we have + + align:start position:0% +So we have + + + align:start position:0% +So we have +we have this matrix space + + align:start position:0% +we have this matrix space + + + align:start position:0% +we have this matrix space +and we have a subset + + align:start position:0% +and we have a subset + + + align:start position:0% +and we have a subset +and the subset here is compact. + + align:start position:0% +and the subset here is compact. + + + align:start position:0% +and the subset here is compact. +subset is assumed to be compact. + + align:start position:0% + + + + align:start position:0% + +Then we have a sequence + + align:start position:0% +Then we have a sequence + + + align:start position:0% +Then we have a sequence +XN + + align:start position:0% +XN + + + align:start position:0% +XN +and this sequence here. So this is a + + align:start position:0% +and this sequence here. So this is a + + + align:start position:0% +and this sequence here. So this is a +sequence + + align:start position:0% + + + + align:start position:0% + +contained in + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% +in + + + align:start position:0% +in +And we want to prove that there exist. + + align:start position:0% +And we want to prove that there exist. + + + align:start position:0% +And we want to prove that there exist. +So want to show one to + + align:start position:0% +So want to show one to + + + align:start position:0% +So want to show one to +to find + + align:start position:0% +to find + + + align:start position:0% +to find +a convergent + + align:start position:0% + + + + align:start position:0% + +subsequent + + align:start position:0% + + + + align:start position:0% + +remember that here I mean you know just + + align:start position:0% +remember that here I mean you know just + + + align:start position:0% +remember that here I mean you know just +that there's no assumption you know I'm + + align:start position:0% +that there's no assumption you know I'm + + + align:start position:0% +that there's no assumption you know I'm +not talking about some cushy complete + + align:start position:0% +not talking about some cushy complete + + + align:start position:0% +not talking about some cushy complete +set space or something like that right + + align:start position:0% +set space or something like that right + + + align:start position:0% +set space or something like that right +so in this case I really have to + + align:start position:0% +so in this case I really have to + + + align:start position:0% +so in this case I really have to +construct the you So I have to construct + + align:start position:0% +construct the you So I have to construct + + + align:start position:0% +construct the you So I have to construct +the convergence sequence but I also have + + align:start position:0% +the convergence sequence but I also have + + + align:start position:0% +the convergence sequence but I also have +to kind of construct the limits right + + align:start position:0% +to kind of construct the limits right + + + align:start position:0% +to kind of construct the limits right +and so this is where or you know like in + + align:start position:0% +and so this is where or you know like in + + + align:start position:0% +and so this is where or you know like in +particular like the limit this is why we + + align:start position:0% +particular like the limit this is why we + + + align:start position:0% +particular like the limit this is why we +want this thing here to have a unique + + align:start position:0% +want this thing here to have a unique + + + align:start position:0% +want this thing here to have a unique +intersection + + align:start position:0% + + + + align:start position:0% + +okay so that's what I want to do right + + align:start position:0% +okay so that's what I want to do right + + + align:start position:0% +okay so that's what I want to do right +so you you have this uh space you have + + align:start position:0% +so you you have this uh space you have + + + align:start position:0% +so you you have this uh space you have +the subset that's compact and and you + + align:start position:0% +the subset that's compact and and you + + + align:start position:0% +the subset that's compact and and you +are given a sequence + + align:start position:0% +are given a sequence + + + align:start position:0% +are given a sequence +So now I start with um so so and and and + + align:start position:0% +So now I start with um so so and and and + + + align:start position:0% +So now I start with um so so and and and +before I actually get to the proof let + + align:start position:0% +before I actually get to the proof let + + + align:start position:0% +before I actually get to the proof let +me just try to explain the idea. + + align:start position:0% + + + + align:start position:0% + +So this is this is again this is sort of + + align:start position:0% +So this is this is again this is sort of + + + align:start position:0% +So this is this is again this is sort of +uh before the proof + + align:start position:0% + + + + align:start position:0% + +So I want to make an observation. So if + + align:start position:0% +So I want to make an observation. So if + + + align:start position:0% +So I want to make an observation. So if +I am in this s iteration and suppose now + + align:start position:0% +I am in this s iteration and suppose now + + + align:start position:0% +I am in this s iteration and suppose now +that I take so I have a here and I take + + align:start position:0% +that I take so I have a here and I take + + + align:start position:0% +that I take so I have a here and I take +some r think of r as being really small + + align:start position:0% +some r think of r as being really small + + + align:start position:0% +some r think of r as being really small +and then do what we did just did a + + align:start position:0% +and then do what we did just did a + + + align:start position:0% +and then do what we did just did a +little while ago. We cover we cover + + align:start position:0% +little while ago. We cover we cover + + + align:start position:0% +little while ago. We cover we cover +we're looking at A here is covered by A. + + align:start position:0% +we're looking at A here is covered by A. + + + align:start position:0% +we're looking at A here is covered by A. +You can write A as a union of these + + align:start position:0% +You can write A as a union of these + + + align:start position:0% +You can write A as a union of these +balls here where the center is anything + + align:start position:0% +balls here where the center is anything + + + align:start position:0% +balls here where the center is anything +in A. Right? So again that cover + + align:start position:0% +in A. Right? So again that cover + + + align:start position:0% +in A. Right? So again that cover +A and so this means that finally many + + align:start position:0% +A and so this means that finally many + + + align:start position:0% +A and so this means that finally many +that's finally many + + align:start position:0% + + + + align:start position:0% + +many + + align:start position:0% +many + + + align:start position:0% +many +cover + + align:start position:0% +cover + + + align:start position:0% +cover +a + + align:start position:0% +a + + + align:start position:0% +a +since + + align:start position:0% +since + + + align:start position:0% +since +a is compact. + + align:start position:0% + + + + align:start position:0% + +So I can write a here + + align:start position:0% +So I can write a here + + + align:start position:0% +So I can write a here +as the as uh contained in and then r + + align:start position:0% +as the as uh contained in and then r + + + align:start position:0% +as the as uh contained in and then r +uh now I had to be careful because this + + align:start position:0% +uh now I had to be careful because this + + + align:start position:0% +uh now I had to be careful because this +is not the x probably I should use a y + + align:start position:0% +is not the x probably I should use a y + + + align:start position:0% +is not the x probably I should use a y +here. Sorry, just to to not confuse it + + align:start position:0% +here. Sorry, just to to not confuse it + + + align:start position:0% +here. Sorry, just to to not confuse it +with the sequence that I have. Okay. + + align:start position:0% +with the sequence that I have. Okay. + + + align:start position:0% +with the sequence that I have. Okay. +And so I can I can it's contained in the + + align:start position:0% +And so I can I can it's contained in the + + + align:start position:0% +And so I can I can it's contained in the +union of balls like this. + + align:start position:0% + + + + align:start position:0% + +YM right is contained in the union of + + align:start position:0% +YM right is contained in the union of + + + align:start position:0% +YM right is contained in the union of +finitely many balls like this. + + align:start position:0% +finitely many balls like this. + + + align:start position:0% +finitely many balls like this. +Okay. So far we haven't used our + + align:start position:0% +Okay. So far we haven't used our + + + align:start position:0% +Okay. So far we haven't used our +sequence, right? But now of course I can + + align:start position:0% +sequence, right? But now of course I can + + + align:start position:0% +sequence, right? But now of course I can +say that we we we were given a sequence + + align:start position:0% +say that we we we were given a sequence + + + align:start position:0% +say that we we we were given a sequence +right we now have finally many balls + + align:start position:0% +right we now have finally many balls + + + align:start position:0% +right we now have finally many balls +right so and there are like infinite + + align:start position:0% +right so and there are like infinite + + + align:start position:0% +right so and there are like infinite +many elements in the sequence so it + + align:start position:0% +many elements in the sequence so it + + + align:start position:0% +many elements in the sequence so it +means that there is one of these balls + + align:start position:0% +means that there is one of these balls + + + align:start position:0% +means that there is one of these balls +finite many balls so for one of them + + align:start position:0% + + + + align:start position:0% + +for one maybe more more than one maybe + + align:start position:0% +for one maybe more more than one maybe + + + align:start position:0% +for one maybe more more than one maybe +all of them but for at least for one + + align:start position:0% +all of them but for at least for one + + + align:start position:0% +all of them but for at least for one +of these sports. + + align:start position:0% + + + + align:start position:0% + +There are + + align:start position:0% +There are + + + align:start position:0% +There are +infinite many + + align:start position:0% + + + + align:start position:0% + +elements + + align:start position:0% + + + + align:start position:0% + +in the sequence. + + align:start position:0% + + + + align:start position:0% + +Let me be very precise what I mean by + + align:start position:0% +Let me be very precise what I mean by + + + align:start position:0% +Let me be very precise what I mean by +that. + + align:start position:0% +that. + + + align:start position:0% +that. +So by that I mean of course this + + align:start position:0% +So by that I mean of course this + + + align:start position:0% +So by that I mean of course this +sequence could be like a constant + + align:start position:0% +sequence could be like a constant + + + align:start position:0% +sequence could be like a constant +sequence. What I mean that for + + align:start position:0% +sequence. What I mean that for + + + align:start position:0% +sequence. What I mean that for +infinitely many ns xn is in one of these + + align:start position:0% +infinitely many ns xn is in one of these + + + align:start position:0% +infinitely many ns xn is in one of these +balls right. So let me just write that + + align:start position:0% +balls right. So let me just write that + + + align:start position:0% +balls right. So let me just write that +out just to be totally clear. So meaning + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% +for + + + align:start position:0% +for +one of these balls. + + align:start position:0% + + + + align:start position:0% + +There are + + align:start position:0% +There are + + + align:start position:0% +There are +infinitely many + + align:start position:0% + + + + align:start position:0% + +many ends such that + + align:start position:0% + + + + align:start position:0% + +XN + + align:start position:0% +XN + + + align:start position:0% +XN +is in in that ball + + align:start position:0% +is in in that ball + + + align:start position:0% +is in in that ball +and let's say that this is uh Y3 + + align:start position:0% +and let's say that this is uh Y3 + + + align:start position:0% +and let's say that this is uh Y3 +whatever right so there's infin many n + + align:start position:0% +whatever right so there's infin many n + + + align:start position:0% +whatever right so there's infin many n +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now + + align:start position:0% +so now + + + align:start position:0% +so now +I can just think about that one ball + + align:start position:0% +I can just think about that one ball + + + align:start position:0% +I can just think about that one ball +right and I can just think about the + + align:start position:0% +right and I can just think about the + + + align:start position:0% +right and I can just think about the +sequence instead of the original + + align:start position:0% +sequence instead of the original + + + align:start position:0% +sequence instead of the original +sequence I think about a subsequence + + align:start position:0% +sequence I think about a subsequence + + + align:start position:0% +sequence I think about a subsequence +that is contained in it. Right? So + + align:start position:0% +that is contained in it. Right? So + + + align:start position:0% +that is contained in it. Right? So +meaning this means that there is a + + align:start position:0% +meaning this means that there is a + + + align:start position:0% +meaning this means that there is a +therefore + + align:start position:0% + + + + align:start position:0% + +there is a subsequence + + align:start position:0% + + + + align:start position:0% + +a subsequent + + align:start position:0% + + + + align:start position:0% + +of the given sequence + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +is contained in this + + align:start position:0% + + + + align:start position:0% + +in this form. + + align:start position:0% +in this form. + + + align:start position:0% +in this form. +Okay. + + align:start position:0% + + + + align:start position:0% + +Now, + + align:start position:0% +Now, + + + align:start position:0% +Now, +um, + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +okay. Now, I want to somehow repeat this + + align:start position:0% +okay. Now, I want to somehow repeat this + + + align:start position:0% +okay. Now, I want to somehow repeat this +process. + + align:start position:0% +process. + + + align:start position:0% +process. +I want to repeat this process and again + + align:start position:0% +I want to repeat this process and again + + + align:start position:0% +I want to repeat this process and again +I'm I I haven't quite started the proof + + align:start position:0% +I'm I I haven't quite started the proof + + + align:start position:0% +I'm I I haven't quite started the proof +here but I'm just trying to explain the + + align:start position:0% +here but I'm just trying to explain the + + + align:start position:0% +here but I'm just trying to explain the +idea right so this is like this this is + + align:start position:0% +idea right so this is like this this is + + + align:start position:0% +idea right so this is like this this is +like a step in the proof that you then + + align:start position:0% +like a step in the proof that you then + + + align:start position:0% +like a step in the proof that you then +for the right sort of has to use over + + align:start position:0% +for the right sort of has to use over + + + align:start position:0% +for the right sort of has to use over +and over again right + + align:start position:0% +and over again right + + + align:start position:0% +and over again right +and so now + + align:start position:0% +and so now + + + align:start position:0% +and so now +um so I want to repeat this process and + + align:start position:0% +um so I want to repeat this process and + + + align:start position:0% +um so I want to repeat this process and +for that I I need to remind you that if + + align:start position:0% +for that I I need to remind you that if + + + align:start position:0% +for that I I need to remind you that if +you take um metric space, if you have a + + align:start position:0% +you take um metric space, if you have a + + + align:start position:0% +you take um metric space, if you have a +metric space, so the coin + + align:start position:0% + + + + align:start position:0% + +that if um + + align:start position:0% +that if um + + + align:start position:0% +that if um +if um x here is a metric space + + align:start position:0% + + + + align:start position:0% + +uh a here is a substance + + align:start position:0% +uh a here is a substance + + + align:start position:0% +uh a here is a substance +a compact subset. + + align:start position:0% + + + + align:start position:0% + +A is a compact subset + + align:start position:0% +A is a compact subset + + + align:start position:0% +A is a compact subset +and B here is a closed + + align:start position:0% + + + + align:start position:0% + +set and is a closed subset + + align:start position:0% + + + + align:start position:0% + +of X. Well, then A intersected with B, + + align:start position:0% +of X. Well, then A intersected with B, + + + align:start position:0% +of X. Well, then A intersected with B, +right? The intersection of if it's + + align:start position:0% +right? The intersection of if it's + + + align:start position:0% +right? The intersection of if it's +compact, it's also it's also closed, + + align:start position:0% +compact, it's also it's also closed, + + + align:start position:0% +compact, it's also it's also closed, +right? We proved that. And so this is + + align:start position:0% +right? We proved that. And so this is + + + align:start position:0% +right? We proved that. And so this is +the intersection of two closed sets. So + + align:start position:0% +the intersection of two closed sets. So + + + align:start position:0% +the intersection of two closed sets. So +this is closed. This is contained in A. + + align:start position:0% +this is closed. This is contained in A. + + + align:start position:0% +this is closed. This is contained in A. +And now we proved last time that if you + + align:start position:0% +And now we proved last time that if you + + + align:start position:0% +And now we proved last time that if you +take H. So this here is a closed subset. + + align:start position:0% +take H. So this here is a closed subset. + + + align:start position:0% +take H. So this here is a closed subset. +This is closed + + align:start position:0% + + + + align:start position:0% + +and is contained in A. + + align:start position:0% +and is contained in A. + + + align:start position:0% +and is contained in A. +Since A is compact, if you take a closed + + align:start position:0% +Since A is compact, if you take a closed + + + align:start position:0% +Since A is compact, if you take a closed +subset of A, then this is also compact. + + align:start position:0% +subset of A, then this is also compact. + + + align:start position:0% +subset of A, then this is also compact. +So this is also compact. + + align:start position:0% + + + + align:start position:0% + +Okay. So now + + align:start position:0% +Okay. So now + + + align:start position:0% +Okay. So now +now let's continue + + align:start position:0% +now let's continue + + + align:start position:0% +now let's continue +that uh string of thoughts from over + + align:start position:0% +that uh string of thoughts from over + + + align:start position:0% +that uh string of thoughts from over +there. So how do we + + align:start position:0% +there. So how do we + + + align:start position:0% +there. So how do we +now we + + align:start position:0% +now we + + + align:start position:0% +now we +repeat this? + + align:start position:0% + + + + align:start position:0% + +So it's have I have a set I have here + + align:start position:0% +So it's have I have a set I have here + + + align:start position:0% +So it's have I have a set I have here +maybe even bigger. I have here uh this + + align:start position:0% +maybe even bigger. I have here uh this + + + align:start position:0% +maybe even bigger. I have here uh this +here is my space x. Then I have some + + align:start position:0% +here is my space x. Then I have some + + + align:start position:0% +here is my space x. Then I have some +subset. This here is a + + align:start position:0% +subset. This here is a + + + align:start position:0% +subset. This here is a +a is compact. + + align:start position:0% +a is compact. + + + align:start position:0% +a is compact. +I cover it with balls here + + align:start position:0% +I cover it with balls here + + + align:start position:0% +I cover it with balls here +of radius uh and I now have that + + align:start position:0% +of radius uh and I now have that + + + align:start position:0% +of radius uh and I now have that +finitely many. These are balls of radius + + align:start position:0% +finitely many. These are balls of radius + + + align:start position:0% +finitely many. These are balls of radius +r around some some y's, + + align:start position:0% +r around some some y's, + + + align:start position:0% +r around some some y's, +right? Finitely many. as fin as many of + + align:start position:0% +right? Finitely many. as fin as many of + + + align:start position:0% +right? Finitely many. as fin as many of +these balls and the copper eight right + + align:start position:0% +these balls and the copper eight right + + + align:start position:0% +these balls and the copper eight right +then + + align:start position:0% +then + + + align:start position:0% +then +these sets here are of course not closed + + align:start position:0% +these sets here are of course not closed + + + align:start position:0% +these sets here are of course not closed +and so I'm looking at + + align:start position:0% +and so I'm looking at + + + align:start position:0% +and so I'm looking at +this + + align:start position:0% +this + + + align:start position:0% +this +ball here these finally many and I just + + align:start position:0% +ball here these finally many and I just + + + align:start position:0% +ball here these finally many and I just +take the closed balls + + align:start position:0% + + + + align:start position:0% + +now I want to cover right and and and I + + align:start position:0% +now I want to cover right and and and I + + + align:start position:0% +now I want to cover right and and and I +found that for one of + + align:start position:0% +found that for one of + + + align:start position:0% +found that for one of +there was a subsequence that was + + align:start position:0% +there was a subsequence that was + + + align:start position:0% +there was a subsequence that was +contained in fact in the open ball so + + align:start position:0% +contained in fact in the open ball so + + + align:start position:0% +contained in fact in the open ball so +even you know so therefore also in the + + align:start position:0% +even you know so therefore also in the + + + align:start position:0% +even you know so therefore also in the +closed ball right there was a + + align:start position:0% +closed ball right there was a + + + align:start position:0% +closed ball right there was a +subsequence of the original sequence + + align:start position:0% +subsequence of the original sequence + + + align:start position:0% +subsequence of the original sequence +that's a ball I'm focusing on right + + align:start position:0% +that's a ball I'm focusing on right + + + align:start position:0% +that's a ball I'm focusing on right +now this ball I can then cover by balls + + align:start position:0% +now this ball I can then cover by balls + + + align:start position:0% +now this ball I can then cover by balls +of radius so I'm covering this so cover + + align:start position:0% +of radius so I'm covering this so cover + + + align:start position:0% +of radius so I'm covering this so cover +this + + align:start position:0% + + + + align:start position:0% + +by balls + + align:start position:0% + + + + align:start position:0% + +of radius + + align:start position:0% + + + + align:start position:0% + +uh r over 4. + + align:start position:0% +uh r over 4. + + + align:start position:0% +uh r over 4. +So I'm going to write this thing here in + + align:start position:0% +So I'm going to write this thing here in + + + align:start position:0% +So I'm going to write this thing here in +the same way. I'm going to write this + + align:start position:0% +the same way. I'm going to write this + + + align:start position:0% +the same way. I'm going to write this +this here I now know + + align:start position:0% +this here I now know + + + align:start position:0% +this here I now know +um + + align:start position:0% +um + + + align:start position:0% +um +this thing here + + align:start position:0% +this thing here + + + align:start position:0% +this thing here +this thing here I'm only interested in + + align:start position:0% +this thing here I'm only interested in + + + align:start position:0% +this thing here I'm only interested in +syncs that are contained in a. So I know + + align:start position:0% +syncs that are contained in a. So I know + + + align:start position:0% +syncs that are contained in a. So I know +that if I intersect it with A + + align:start position:0% +that if I intersect it with A + + + align:start position:0% +that if I intersect it with A +then this here is is compact, right? I + + align:start position:0% +then this here is is compact, right? I + + + align:start position:0% +then this here is is compact, right? I +know that this is compact. That was + + align:start position:0% +know that this is compact. That was + + + align:start position:0% +know that this is compact. That was +because this here was closed, right? And + + align:start position:0% +because this here was closed, right? And + + + align:start position:0% +because this here was closed, right? And +and Na was compact, right? So this here + + align:start position:0% +and Na was compact, right? So this here + + + align:start position:0% +and Na was compact, right? So this here +is compact. + + align:start position:0% + + + + align:start position:0% + +So this means that that if I can write + + align:start position:0% +So this means that that if I can write + + + align:start position:0% +So this means that that if I can write +that set here, + + align:start position:0% +that set here, + + + align:start position:0% +that set here, +I can write that set + + align:start position:0% +I can write that set + + + align:start position:0% +I can write that set +uh as so I can write this set here. + + align:start position:0% + + + + align:start position:0% + +So, so I have so + + align:start position:0% +So, so I have so + + + align:start position:0% +So, so I have so +I have + + align:start position:0% +I have + + + align:start position:0% +I have +so I start with a that is compact then I + + align:start position:0% +so I start with a that is compact then I + + + align:start position:0% +so I start with a that is compact then I +find a ball + + align:start position:0% +find a ball + + + align:start position:0% +find a ball +so that a subsequence is contained in + + align:start position:0% +so that a subsequence is contained in + + + align:start position:0% +so that a subsequence is contained in +that ball right this is was that ball + + align:start position:0% +that ball right this is was that ball + + + align:start position:0% +that ball right this is was that ball +then I'm looking at so this is like the + + align:start position:0% +then I'm looking at so this is like the + + + align:start position:0% +then I'm looking at so this is like the +process I start with here this is step + + align:start position:0% +process I start with here this is step + + + align:start position:0% +process I start with here this is step +one step two I looking at this set three + + align:start position:0% +one step two I looking at this set three + + + align:start position:0% +one step two I looking at this set three +I'm Looking at now the closure of this + + align:start position:0% +I'm Looking at now the closure of this + + + align:start position:0% +I'm Looking at now the closure of this +ball + + align:start position:0% + + + + align:start position:0% + +intersected with a this here is here is + + align:start position:0% +intersected with a this here is here is + + + align:start position:0% +intersected with a this here is here is +compact. + + align:start position:0% +compact. + + + align:start position:0% +compact. +This here contains a subsequence + + align:start position:0% + + + + align:start position:0% + +a subsequence + + align:start position:0% + + + + align:start position:0% + +of xn. + + align:start position:0% +of xn. + + + align:start position:0% +of xn. +This thing here is compact. + + align:start position:0% + + + + align:start position:0% + +This means that I can cover it by balls + + align:start position:0% +This means that I can cover it by balls + + + align:start position:0% +This means that I can cover it by balls +of radius. So cover it + + align:start position:0% + + + + align:start position:0% + +by balls + + align:start position:0% + + + + align:start position:0% + +of radius + + align:start position:0% + + + + align:start position:0% + +um r over four. I want smaller radius as + + align:start position:0% +um r over four. I want smaller radius as + + + align:start position:0% +um r over four. I want smaller radius as +I'm going along. Okay. So I'm covering + + align:start position:0% +I'm going along. Okay. So I'm covering + + + align:start position:0% +I'm going along. Okay. So I'm covering +it with and in fact I can cover it by + + align:start position:0% +it with and in fact I can cover it by + + + align:start position:0% +it with and in fact I can cover it by +finitely many balls. + + align:start position:0% + + + + align:start position:0% + +Right? Why finite many? This is because + + align:start position:0% +Right? Why finite many? This is because + + + align:start position:0% +Right? Why finite many? This is because +this here is compact. I'm writing this + + align:start position:0% +this here is compact. I'm writing this + + + align:start position:0% +this here is compact. I'm writing this +here as the union of balls of this + + align:start position:0% +here as the union of balls of this + + + align:start position:0% +here as the union of balls of this +radius where anything in this set is a + + align:start position:0% +radius where anything in this set is a + + + align:start position:0% +radius where anything in this set is a +center. And so I have the finite many of + + align:start position:0% +center. And so I have the finite many of + + + align:start position:0% +center. And so I have the finite many of +those cover it right by compactness. + + align:start position:0% +those cover it right by compactness. + + + align:start position:0% +those cover it right by compactness. +Right? + + align:start position:0% + + + + align:start position:0% + +And so now what I observe is that if I + + align:start position:0% +And so now what I observe is that if I + + + align:start position:0% +And so now what I observe is that if I +take and now I just had to be a little + + align:start position:0% +take and now I just had to be a little + + + align:start position:0% +take and now I just had to be a little +bit careful. So now I'm observing that + + align:start position:0% +bit careful. So now I'm observing that + + + align:start position:0% +bit careful. So now I'm observing that +if I take the ball of radius + + align:start position:0% +if I take the ball of radius + + + align:start position:0% +if I take the ball of radius +the double ball + + align:start position:0% +the double ball + + + align:start position:0% +the double ball +suppose I'm taking this ball here. So I + + align:start position:0% +suppose I'm taking this ball here. So I + + + align:start position:0% +suppose I'm taking this ball here. So I +get finite sorry no before that. So I + + align:start position:0% +get finite sorry no before that. So I + + + align:start position:0% +get finite sorry no before that. So I +have that it's now finitely many balls + + align:start position:0% +have that it's now finitely many balls + + + align:start position:0% +have that it's now finitely many balls +cover this. So this means that a + + align:start position:0% +cover this. So this means that a + + + align:start position:0% +cover this. So this means that a +subsequence + + align:start position:0% +subsequence + + + align:start position:0% +subsequence +must lie in one of these balls. Right? + + align:start position:0% +must lie in one of these balls. Right? + + + align:start position:0% +must lie in one of these balls. Right? +So therefore, so this is the fifth step. + + align:start position:0% +So therefore, so this is the fifth step. + + + align:start position:0% +So therefore, so this is the fifth step. +A subsequence + + align:start position:0% + + + + align:start position:0% + +of the subsequence + + align:start position:0% + + + + align:start position:0% + +lies + + align:start position:0% +lies + + + align:start position:0% +lies +in one of these these + + align:start position:0% +in one of these these + + + align:start position:0% +in one of these these +these finite many balls. + + align:start position:0% + + + + align:start position:0% + +of radius + + align:start position:0% + + + + align:start position:0% + +uh r + + align:start position:0% +uh r + + + align:start position:0% +uh r +over four, right? + + align:start position:0% + + + + align:start position:0% + +And now + + align:start position:0% + + + + align:start position:0% + +now I take so the next thing is I do and + + align:start position:0% +now I take so the next thing is I do and + + + align:start position:0% +now I take so the next thing is I do and +now I want to I want to apply the color + + align:start position:0% +now I want to I want to apply the color + + + align:start position:0% +now I want to I want to apply the color +from before. Right. So I started with my + + align:start position:0% +from before. Right. So I started with my + + + align:start position:0% +from before. Right. So I started with my +space X. I got this ball here of radius + + align:start position:0% +space X. I got this ball here of radius + + + align:start position:0% +space X. I got this ball here of radius +R and then there was some center. + + align:start position:0% +R and then there was some center. + + + align:start position:0% +R and then there was some center. +Then then the next thing is that I get a + + align:start position:0% +Then then the next thing is that I get a + + + align:start position:0% +Then then the next thing is that I get a +ball of radius + + align:start position:0% +ball of radius + + + align:start position:0% +ball of radius +uh one + + align:start position:0% +uh one + + + align:start position:0% +uh one +quarter + + align:start position:0% +quarter + + + align:start position:0% +quarter +ah and now this is with you know one of + + align:start position:0% +ah and now this is with you know one of + + + align:start position:0% +ah and now this is with you know one of +these other finite many balls where a + + align:start position:0% +these other finite many balls where a + + + align:start position:0% +these other finite many balls where a +subsequence is called it like this uh + + align:start position:0% +subsequence is called it like this uh + + + align:start position:0% +subsequence is called it like this uh +maybe like one or something like that + + align:start position:0% +maybe like one or something like that + + + align:start position:0% +maybe like one or something like that +right so I get that so so + + align:start position:0% +right so I get that so so + + + align:start position:0% +right so I get that so so +The balls of radius R over four they + + align:start position:0% +The balls of radius R over four they + + + align:start position:0% +The balls of radius R over four they +cover this. So a subsequence actually + + align:start position:0% +cover this. So a subsequence actually + + + align:start position:0% +cover this. So a subsequence actually +would have to lie here. + + align:start position:0% +would have to lie here. + + + align:start position:0% +would have to lie here. +Right? And so now but now I want to use + + align:start position:0% +Right? And so now but now I want to use + + + align:start position:0% +Right? And so now but now I want to use +the corner. If I need the to use the + + align:start position:0% +the corner. If I need the to use the + + + align:start position:0% +the corner. If I need the to use the +corner I need to have nested and I need + + align:start position:0% +corner I need to have nested and I need + + + align:start position:0% +corner I need to have nested and I need +to have closed sets. Right? And so in + + align:start position:0% +to have closed sets. Right? And so in + + + align:start position:0% +to have closed sets. Right? And so in +order to make them nested then I double + + align:start position:0% +order to make them nested then I double + + + align:start position:0% +order to make them nested then I double +I'm I'm going to double this ball. Why + + align:start position:0% +I'm I'm going to double this ball. Why + + + align:start position:0% +I'm I'm going to double this ball. Why +do I double this ball? Well, I double + + align:start position:0% +do I double this ball? Well, I double + + + align:start position:0% +do I double this ball? Well, I double +this ball here because these guys here + + align:start position:0% +this ball here because these guys here + + + align:start position:0% +this ball here because these guys here +cover this, right? But it means of + + align:start position:0% +cover this, right? But it means of + + + align:start position:0% +cover this, right? But it means of +course that there could be something + + align:start position:0% +course that there could be something + + + align:start position:0% +course that there could be something +outside, right? There could be. So this + + align:start position:0% +outside, right? There could be. So this + + + align:start position:0% +outside, right? There could be. So this +is like a ball of radius R. + + align:start position:0% +is like a ball of radius R. + + + align:start position:0% +is like a ball of radius R. +And so then you have this ball of radius + + align:start position:0% +And so then you have this ball of radius + + + align:start position:0% +And so then you have this ball of radius +a quarter R but the quarter balls they + + align:start position:0% +a quarter R but the quarter balls they + + + align:start position:0% +a quarter R but the quarter balls they +may have some part outside and some part + + align:start position:0% +may have some part outside and some part + + + align:start position:0% +may have some part outside and some part +inside right so so it's not this ball + + align:start position:0% +inside right so so it's not this ball + + + align:start position:0% +inside right so so it's not this ball +here is not contained in that ball right + + align:start position:0% +here is not contained in that ball right + + + align:start position:0% +here is not contained in that ball right +but if you went to the double ball + + align:start position:0% +but if you went to the double ball + + + align:start position:0% +but if you went to the double ball +if you went to this ball of radius 2 R + + align:start position:0% +if you went to this ball of radius 2 R + + + align:start position:0% +if you went to this ball of radius 2 R +you see this this point here the center + + align:start position:0% +you see this this point here the center + + + align:start position:0% +you see this this point here the center +the the the center here It would lie + + align:start position:0% +the the the center here It would lie + + + align:start position:0% +the the the center here It would lie +right there would be some points in this + + align:start position:0% +right there would be some points in this + + + align:start position:0% +right there would be some points in this +ball here that would be within it may + + align:start position:0% +ball here that would be within it may + + + align:start position:0% +ball here that would be within it may +not be the center but there's some point + + align:start position:0% +not be the center but there's some point + + + align:start position:0% +not be the center but there's some point +here that's within R of the center and + + align:start position:0% +here that's within R of the center and + + + align:start position:0% +here that's within R of the center and +then by the triangle inequality any + + align:start position:0% +then by the triangle inequality any + + + align:start position:0% +then by the triangle inequality any +other points is actually within R2 R + + align:start position:0% +other points is actually within R2 R + + + align:start position:0% +other points is actually within R2 R +over two of that point. So everything is + + align:start position:0% +over two of that point. So everything is + + + align:start position:0% +over two of that point. So everything is +comfortably. So this thing here and even + + align:start position:0% +comfortably. So this thing here and even + + + align:start position:0% +comfortably. So this thing here and even +the half ball. So I I can + + align:start position:0% +the half ball. So I I can + + + align:start position:0% +the half ball. So I I can +conclude that even the ball of radius r + + align:start position:0% +conclude that even the ball of radius r + + + align:start position:0% +conclude that even the ball of radius r +over two. Even this one here + + align:start position:0% + + + + align:start position:0% + +is contained + + align:start position:0% +is contained + + + align:start position:0% +is contained +in the double ball + + align:start position:0% + + + + align:start position:0% + +like that. Okay. + + align:start position:0% + + + + align:start position:0% + +And and in fact if you make things less + + align:start position:0% +And and in fact if you make things less + + + align:start position:0% +And and in fact if you make things less +or equal to on both things then you have + + align:start position:0% +or equal to on both things then you have + + + align:start position:0% +or equal to on both things then you have +that. + + align:start position:0% +that. + + + align:start position:0% +that. +Okay. Now what I have is at least here + + align:start position:0% +Okay. Now what I have is at least here + + + align:start position:0% +Okay. Now what I have is at least here +you have + + align:start position:0% +you have + + + align:start position:0% +you have +something that is nested. Right. And you + + align:start position:0% +something that is nested. Right. And you + + + align:start position:0% +something that is nested. Right. And you +see that the radius went down. Right. + + align:start position:0% +see that the radius went down. Right. + + + align:start position:0% +see that the radius went down. Right. +Right. So these are nested and they're + + align:start position:0% +Right. So these are nested and they're + + + align:start position:0% +Right. So these are nested and they're +closed. Okay. And so now what we do is + + align:start position:0% +closed. Okay. And so now what we do is + + + align:start position:0% +closed. Okay. And so now what we do is +so now we want to do this for a + + align:start position:0% +so now we want to do this for a + + + align:start position:0% +so now we want to do this for a +sequence, right? And then of course we + + align:start position:0% +sequence, right? And then of course we + + + align:start position:0% +sequence, right? And then of course we +want so now we want to construct a + + align:start position:0% +want so now we want to construct a + + + align:start position:0% +want so now we want to construct a +sequence of closed balls like this, + + align:start position:0% +sequence of closed balls like this, + + + align:start position:0% +sequence of closed balls like this, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +And so and now when you pick your + + align:start position:0% +And so and now when you pick your + + + align:start position:0% +And so and now when you pick your +subsequence, you have to you can't wait + + align:start position:0% +subsequence, you have to you can't wait + + + align:start position:0% +subsequence, you have to you can't wait +with picking the first element in a + + align:start position:0% +with picking the first element in a + + + align:start position:0% +with picking the first element in a +subsequence. Right? Remember if you keep + + align:start position:0% +subsequence. Right? Remember if you keep + + + align:start position:0% +subsequence. Right? Remember if you keep +waiting then you will end up getting + + align:start position:0% +waiting then you will end up getting + + + align:start position:0% +waiting then you will end up getting +nothing right? So you pick at each stage + + align:start position:0% +nothing right? So you pick at each stage + + + align:start position:0% +nothing right? So you pick at each stage +you pick one element in a subsequence + + align:start position:0% +you pick one element in a subsequence + + + align:start position:0% +you pick one element in a subsequence +and then when you have the next ball you + + align:start position:0% +and then when you have the next ball you + + + align:start position:0% +and then when you have the next ball you +pick the next element in a subsequence + + align:start position:0% +pick the next element in a subsequence + + + align:start position:0% +pick the next element in a subsequence +and so on right and so + + align:start position:0% +and so on right and so + + + align:start position:0% +and so on right and so +so we will do this with + + align:start position:0% +so we will do this with + + + align:start position:0% +so we will do this with +so we're going to do this procedure here + + align:start position:0% +so we're going to do this procedure here + + + align:start position:0% +so we're going to do this procedure here +so now we're getting back to the the + + align:start position:0% +so now we're getting back to the the + + + align:start position:0% +so now we're getting back to the the +proof of the theorem right and again + + align:start position:0% +proof of the theorem right and again + + + align:start position:0% +proof of the theorem right and again +remember the theorem was this maybe I + + align:start position:0% +remember the theorem was this maybe I + + + align:start position:0% +remember the theorem was this maybe I +erased it now mistake but the the serum + + align:start position:0% +erased it now mistake but the the serum + + + align:start position:0% +erased it now mistake but the the serum +was this bosano V theorem for a metric + + align:start position:0% +was this bosano V theorem for a metric + + + align:start position:0% +was this bosano V theorem for a metric +space that you have a metric space you + + align:start position:0% +space that you have a metric space you + + + align:start position:0% +space that you have a metric space you +have a compact subset and you have a + + align:start position:0% +have a compact subset and you have a + + + align:start position:0% +have a compact subset and you have a +sequence in this compact subset and you + + align:start position:0% +sequence in this compact subset and you + + + align:start position:0% +sequence in this compact subset and you +want to construct a convergent + + align:start position:0% +want to construct a convergent + + + align:start position:0% +want to construct a convergent +subsequence. + + align:start position:0% +subsequence. + + + align:start position:0% +subsequence. +So, so what you do is there's a proof + + align:start position:0% +So, so what you do is there's a proof + + + align:start position:0% +So, so what you do is there's a proof +of the bulan visor + + align:start position:0% + + + + align:start position:0% + +for metric spaces. + + align:start position:0% + + + + align:start position:0% + +So, so what you do is so you have this + + align:start position:0% +So, so what you do is so you have this + + + align:start position:0% +So, so what you do is so you have this +again a here is compact and you have a + + align:start position:0% +again a here is compact and you have a + + + align:start position:0% +again a here is compact and you have a +sequence xn this is a sequence that is + + align:start position:0% +sequence xn this is a sequence that is + + + align:start position:0% +sequence xn this is a sequence that is +contained in a + + align:start position:0% +contained in a + + + align:start position:0% +contained in a +What you do is that first you can just + + align:start position:0% +What you do is that first you can just + + + align:start position:0% +What you do is that first you can just +let r be equal to one + + align:start position:0% +let r be equal to one + + + align:start position:0% +let r be equal to one +and then and then you do this you you + + align:start position:0% +and then and then you do this you you + + + align:start position:0% +and then and then you do this you you +cover it + + align:start position:0% +cover it + + + align:start position:0% +cover it +uh by you cover it you have here a and + + align:start position:0% +uh by you cover it you have here a and + + + align:start position:0% +uh by you cover it you have here a and +you cover it by finitely many balls of + + align:start position:0% +you cover it by finitely many balls of + + + align:start position:0% +you cover it by finitely many balls of +radius one + + align:start position:0% +radius one + + + align:start position:0% +radius one +and for one of these balls you have that + + align:start position:0% +and for one of these balls you have that + + + align:start position:0% +and for one of these balls you have that +there's infinite many element in the + + align:start position:0% +there's infinite many element in the + + + align:start position:0% +there's infinite many element in the +sequence. So you're going to focus on + + align:start position:0% +sequence. So you're going to focus on + + + align:start position:0% +sequence. So you're going to focus on +that ball from here on and out. And you + + align:start position:0% +that ball from here on and out. And you + + + align:start position:0% +that ball from here on and out. And you +just pick in your subsequence. You now + + align:start position:0% +just pick in your subsequence. You now + + + align:start position:0% +just pick in your subsequence. You now +pick your first element in the + + align:start position:0% +pick your first element in the + + + align:start position:0% +pick your first element in the +subsequence to be some element in that + + align:start position:0% +subsequence to be some element in that + + + align:start position:0% +subsequence to be some element in that +ball. + + align:start position:0% +ball. + + + align:start position:0% +ball. +Then so now the picture is that you just + + align:start position:0% +Then so now the picture is that you just + + + align:start position:0% +Then so now the picture is that you just +look at that ball, right? Forget about + + align:start position:0% +look at that ball, right? Forget about + + + align:start position:0% +look at that ball, right? Forget about +the other ball and everything else. + + align:start position:0% +the other ball and everything else. + + + align:start position:0% +the other ball and everything else. +You now cover it by uh balls of radius a + + align:start position:0% +You now cover it by uh balls of radius a + + + align:start position:0% +You now cover it by uh balls of radius a +quarter, + + align:start position:0% +quarter, + + + align:start position:0% +quarter, +right? And you have that again that's + + align:start position:0% +right? And you have that again that's + + + align:start position:0% +right? And you have that again that's +finally many cover + + align:start position:0% +finally many cover + + + align:start position:0% +finally many cover +the this this ball intersected with a + + align:start position:0% +the this this ball intersected with a + + + align:start position:0% +the this this ball intersected with a +finally many cover it + + align:start position:0% +finally many cover it + + + align:start position:0% +finally many cover it +right and so one of them has infinitely + + align:start position:0% +right and so one of them has infinitely + + + align:start position:0% +right and so one of them has infinitely +many elements + + align:start position:0% +many elements + + + align:start position:0% +many elements +in this in in in this sort of + + align:start position:0% +in this in in in this sort of + + + align:start position:0% +in this in in in this sort of +subsequence I consider and so you just + + align:start position:0% +subsequence I consider and so you just + + + align:start position:0% +subsequence I consider and so you just +pick one element in that right that's + + align:start position:0% +pick one element in that right that's + + + align:start position:0% +pick one element in that right that's +the next one + + align:start position:0% +the next one + + + align:start position:0% +the next one +and now you Repeat this process, right? + + align:start position:0% +and now you Repeat this process, right? + + + align:start position:0% +and now you Repeat this process, right? +And so you see that for these balls, but + + align:start position:0% +And so you see that for these balls, but + + + align:start position:0% +And so you see that for these balls, but +remember that. So you're starting with + + align:start position:0% +remember that. So you're starting with + + + align:start position:0% +remember that. So you're starting with +radius one, but you have to double + + align:start position:0% +radius one, but you have to double + + + align:start position:0% +radius one, but you have to double +syncs, right? So the sequence of closed + + align:start position:0% +syncs, right? So the sequence of closed + + + align:start position:0% +syncs, right? So the sequence of closed +sets, the initial closed set will have + + align:start position:0% +sets, the initial closed set will have + + + align:start position:0% +sets, the initial closed set will have +radius two, right? And the next one + + align:start position:0% +radius two, right? And the next one + + + align:start position:0% +radius two, right? And the next one +won't have radius a quarter, but it will + + align:start position:0% +won't have radius a quarter, but it will + + + align:start position:0% +won't have radius a quarter, but it will +have radius two times a quarter. So a + + align:start position:0% +have radius two times a quarter. So a + + + align:start position:0% +have radius two times a quarter. So a +half, right? And the next one will then + + align:start position:0% +half, right? And the next one will then + + + align:start position:0% +half, right? And the next one will then +be a ball. It will have a different + + align:start position:0% +be a ball. It will have a different + + + align:start position:0% +be a ball. It will have a different +center and it will have a radius of + + align:start position:0% +center and it will have a radius of + + + align:start position:0% +center and it will have a radius of +half. And then the next one you see at + + align:start position:0% +half. And then the next one you see at + + + align:start position:0% +half. And then the next one you see at +each stage when I do it like this then + + align:start position:0% +each stage when I do it like this then + + + align:start position:0% +each stage when I do it like this then +it go down with a factor of four at each + + align:start position:0% +it go down with a factor of four at each + + + align:start position:0% +it go down with a factor of four at each +stage. Right? So this here would be 1 / + + align:start position:0% +stage. Right? So this here would be 1 / + + + align:start position:0% +stage. Right? So this here would be 1 / +8 and so on. Right? And so you see that + + align:start position:0% +8 and so on. Right? And so you see that + + + align:start position:0% +8 and so on. Right? And so you see that +this sequence these are are these closed + + align:start position:0% +this sequence these are are these closed + + + align:start position:0% +this sequence these are are these closed +balls. they are nested as they should be + + align:start position:0% +balls. they are nested as they should be + + + align:start position:0% +balls. they are nested as they should be +and the rad goes to zero. Right? So this + + align:start position:0% +and the rad goes to zero. Right? So this + + + align:start position:0% +and the rad goes to zero. Right? So this +means that there is an element that lies + + align:start position:0% +means that there is an element that lies + + + align:start position:0% +means that there is an element that lies +in all of these and that is now the + + align:start position:0% +in all of these and that is now the + + + align:start position:0% +in all of these and that is now the +limit because of the subsequence if you + + align:start position:0% +limit because of the subsequence if you + + + align:start position:0% +limit because of the subsequence if you +are from here on and out it will be like + + align:start position:0% +are from here on and out it will be like + + + align:start position:0% +are from here on and out it will be like +in that ball and from later on and out + + align:start position:0% +in that ball and from later on and out + + + align:start position:0% +in that ball and from later on and out +it will be in the next ball. Right? So + + align:start position:0% +it will be in the next ball. Right? So + + + align:start position:0% +it will be in the next ball. Right? So +that intersection of all of these balls + + align:start position:0% +that intersection of all of these balls + + + align:start position:0% +that intersection of all of these balls +will be your limit. Yeah. + + align:start position:0% + + + + align:start position:0% + +So, right. So, really what you're + + align:start position:0% +So, right. So, really what you're + + + align:start position:0% +So, right. So, really what you're +looking at that this thing here + + align:start position:0% +looking at that this thing here + + + align:start position:0% +looking at that this thing here +intersected with a + + align:start position:0% +intersected with a + + + align:start position:0% +intersected with a +right. So, it's just that these balls + + align:start position:0% +right. So, it's just that these balls + + + align:start position:0% +right. So, it's just that these balls +here. So, the intersection here that + + align:start position:0% +here. So, the intersection here that + + + align:start position:0% +here. So, the intersection here that +these are the the closed sets. + + align:start position:0% +these are the the closed sets. + + + align:start position:0% +these are the the closed sets. +These are the compacts. they are each of + + align:start position:0% +These are the compacts. they are each of + + + align:start position:0% +These are the compacts. they are each of +them are non- empty and and they are the + + align:start position:0% +them are non- empty and and they are the + + + align:start position:0% +them are non- empty and and they are the +uh the closed subsets of a right so + + align:start position:0% +uh the closed subsets of a right so + + + align:start position:0% +uh the closed subsets of a right so +you're really arguing on these guys here + + align:start position:0% +you're really arguing on these guys here + + + align:start position:0% +you're really arguing on these guys here +you see what I mean + + align:start position:0% +you see what I mean + + + align:start position:0% +you see what I mean +I know I stated it for balls in the call + + align:start position:0% +I know I stated it for balls in the call + + + align:start position:0% +I know I stated it for balls in the call +length right but if you just think about + + align:start position:0% +length right but if you just think about + + + align:start position:0% +length right but if you just think about +it right the balls play no particular + + align:start position:0% +it right the balls play no particular + + + align:start position:0% +it right the balls play no particular +role except for saying that the + + align:start position:0% +role except for saying that the + + + align:start position:0% +role except for saying that the +intersection of all of them contained + + align:start position:0% +intersection of all of them contained + + + align:start position:0% +intersection of all of them contained +just one point and that was because the + + align:start position:0% +just one point and that was because the + + + align:start position:0% +just one point and that was because the +rad went to zero right the important + + align:start position:0% +rad went to zero right the important + + + align:start position:0% +rad went to zero right the important +points were that the sets were closed + + align:start position:0% +points were that the sets were closed + + + align:start position:0% +points were that the sets were closed +subsets, right? Because then there was + + align:start position:0% +subsets, right? Because then there was + + + align:start position:0% +subsets, right? Because then there was +the lema was just all about closed + + align:start position:0% +the lema was just all about closed + + + align:start position:0% +the lema was just all about closed +subset. It had nothing to do with and so + + align:start position:0% +subset. It had nothing to do with and so + + + align:start position:0% +subset. It had nothing to do with and so +you see that + + align:start position:0% + + + + align:start position:0% + +that these guys here are closed subsets + + align:start position:0% +that these guys here are closed subsets + + + align:start position:0% +that these guys here are closed subsets +of a, right? And so yeah, + + align:start position:0% + + + + align:start position:0% + +it + + align:start position:0% + + + + align:start position:0% + +You mean why why I went to double the + + align:start position:0% +You mean why why I went to double the + + + align:start position:0% +You mean why why I went to double the +ball? No. + + align:start position:0% +ball? No. + + + align:start position:0% +ball? No. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Okay. So I So the reason I go to the + + align:start position:0% +>> Okay. So I So the reason I go to the + + + align:start position:0% +>> Okay. So I So the reason I go to the +double ball is that I want to make sure + + align:start position:0% +double ball is that I want to make sure + + + align:start position:0% +double ball is that I want to make sure +that things are nested, right? And and + + align:start position:0% +that things are nested, right? And and + + + align:start position:0% +that things are nested, right? And and +if I I just did this procedure. Suppose + + align:start position:0% +if I I just did this procedure. Suppose + + + align:start position:0% +if I I just did this procedure. Suppose +so again I take this ball here. This is + + align:start position:0% +so again I take this ball here. This is + + + align:start position:0% +so again I take this ball here. This is +the first step. I have these balls of + + align:start position:0% +the first step. I have these balls of + + + align:start position:0% +the first step. I have these balls of +radius one and I find one of them so + + align:start position:0% +radius one and I find one of them so + + + align:start position:0% +radius one and I find one of them so +that there's infinite many in sequence. + + align:start position:0% +that there's infinite many in sequence. + + + align:start position:0% +that there's infinite many in sequence. +Then I want to have something finer, + + align:start position:0% +Then I want to have something finer, + + + align:start position:0% +Then I want to have something finer, +right? And so I go to + + align:start position:0% +right? And so I go to + + + align:start position:0% +right? And so I go to +I chose because I think you didn't quite + + align:start position:0% +I chose because I think you didn't quite + + + align:start position:0% +I chose because I think you didn't quite +have to do a quarter. You could actually + + align:start position:0% +have to do a quarter. You could actually + + + align:start position:0% +have to do a quarter. You could actually +have gotten away with a half, but I + + align:start position:0% +have gotten away with a half, but I + + + align:start position:0% +have gotten away with a half, but I +thought it wasn't as clear if I I did + + align:start position:0% +thought it wasn't as clear if I I did + + + align:start position:0% +thought it wasn't as clear if I I did +it. So I did it with a quarter because + + align:start position:0% +it. So I did it with a quarter because + + + align:start position:0% +it. So I did it with a quarter because +then I thought it was it looked more + + align:start position:0% +then I thought it was it looked more + + + align:start position:0% +then I thought it was it looked more +obvious. So if you now take this ball + + align:start position:0% +obvious. So if you now take this ball + + + align:start position:0% +obvious. So if you now take this ball +here and and as you say you always have + + align:start position:0% +here and and as you say you always have + + + align:start position:0% +here and and as you say you always have +to intersect with a right uh but just to + + align:start position:0% +to intersect with a right uh but just to + + + align:start position:0% +to intersect with a right uh but just to +make things compact but so I cover it + + align:start position:0% +make things compact but so I cover it + + + align:start position:0% +make things compact but so I cover it +with balls of radius + + align:start position:0% +with balls of radius + + + align:start position:0% +with balls of radius +a quarter right but some of these balls + + align:start position:0% +a quarter right but some of these balls + + + align:start position:0% +a quarter right but some of these balls +part of it may lie outside this ball + + align:start position:0% +part of it may lie outside this ball + + + align:start position:0% +part of it may lie outside this ball +here right because you know I couldn't + + align:start position:0% +here right because you know I couldn't + + + align:start position:0% +here right because you know I couldn't +cover you see if I take a ball here I + + align:start position:0% +cover you see if I take a ball here I + + + align:start position:0% +cover you see if I take a ball here I +can't cover it by finally many balls if + + align:start position:0% +can't cover it by finally many balls if + + + align:start position:0% +can't cover it by finally many balls if +I insist you know just if it was like + + align:start position:0% +I insist you know just if it was like + + + align:start position:0% +I insist you know just if it was like +you clean if I insist that the balls had + + align:start position:0% +you clean if I insist that the balls had + + + align:start position:0% +you clean if I insist that the balls had +to be these smaller ball had to be + + align:start position:0% +to be these smaller ball had to be + + + align:start position:0% +to be these smaller ball had to be +inside this ball then there wouldn't be + + align:start position:0% +inside this ball then there wouldn't be + + + align:start position:0% +inside this ball then there wouldn't be +finite many so I have to kind of look at + + align:start position:0% +finite many so I have to kind of look at + + + align:start position:0% +finite many so I have to kind of look at +balls that where some of these balls is + + align:start position:0% +balls that where some of these balls is + + + align:start position:0% +balls that where some of these balls is +kind of outside the surface right but + + align:start position:0% +kind of outside the surface right but + + + align:start position:0% +kind of outside the surface right but +now of course you know so that wouldn't + + align:start position:0% +now of course you know so that wouldn't + + + align:start position:0% +now of course you know so that wouldn't +really work because it's not like this + + align:start position:0% +really work because it's not like this + + + align:start position:0% +really work because it's not like this +ball here let alone the double of this + + align:start position:0% +ball here let alone the double of this + + + align:start position:0% +ball here let alone the double of this +ball is not contained in this So that's + + align:start position:0% +ball is not contained in this So that's + + + align:start position:0% +ball is not contained in this So that's +why I doubled that ball. Then everything + + align:start position:0% +why I doubled that ball. Then everything + + + align:start position:0% +why I doubled that ball. Then everything +is comfortably contained to each other. + + align:start position:0% +is comfortably contained to each other. + + + align:start position:0% +is comfortably contained to each other. +Any other questions? + + align:start position:0% +Any other questions? + + + align:start position:0% +Any other questions? +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Isn't there since they're all closed + + align:start position:0% +>> Isn't there since they're all closed + + + align:start position:0% +>> Isn't there since they're all closed +ball or wait no these are open balls? + + align:start position:0% +ball or wait no these are open balls? + + + align:start position:0% +ball or wait no these are open balls? +>> When I cover things they are open + + align:start position:0% +>> When I cover things they are open + + + align:start position:0% +>> When I cover things they are open +because I have to have when I have a + + align:start position:0% +because I have to have when I have a + + + align:start position:0% +because I have to have when I have a +compact set I have to cover it by open + + align:start position:0% +compact set I have to cover it by open + + + align:start position:0% +compact set I have to cover it by open +subsets. But then once I'm looking at + + align:start position:0% +subsets. But then once I'm looking at + + + align:start position:0% +subsets. But then once I'm looking at +the nested things, I have to go to the + + align:start position:0% +the nested things, I have to go to the + + + align:start position:0% +the nested things, I have to go to the +closure because otherwise the lema in + + align:start position:0% +closure because otherwise the lema in + + + align:start position:0% +closure because otherwise the lema in +the corner would not apply. + + align:start position:0% +the corner would not apply. + + + align:start position:0% +the corner would not apply. +>> Okay. + + align:start position:0% +>> Okay. + + + align:start position:0% +>> Okay. +>> And if hypothetically though, if they + + align:start position:0% +>> And if hypothetically though, if they + + + align:start position:0% +>> And if hypothetically though, if they +were closed though, you would be able to + + align:start position:0% +were closed though, you would be able to + + + align:start position:0% +were closed though, you would be able to +cover like E1 with a + + align:start position:0% +cover like E1 with a + + + align:start position:0% +cover like E1 with a +>> and and and I and I'm just saying that + + align:start position:0% +>> and and and I and I'm just saying that + + + align:start position:0% +>> and and and I and I'm just saying that +if the the open balls cover it, then of + + align:start position:0% +if the the open balls cover it, then of + + + align:start position:0% +if the the open balls cover it, then of +course their closure also cover it + + align:start position:0% +course their closure also cover it + + + align:start position:0% +course their closure also cover it +because the closure is a larger set, + + align:start position:0% +because the closure is a larger set, + + + align:start position:0% +because the closure is a larger set, +>> right? But you know it wouldn't be + + align:start position:0% +>> right? But you know it wouldn't be + + + align:start position:0% +>> right? But you know it wouldn't be +approic clear that you know with you + + align:start position:0% +approic clear that you know with you + + + align:start position:0% +approic clear that you know with you +know like it's not like you know they're + + align:start position:0% +know like it's not like you know they're + + + align:start position:0% +know like it's not like you know they're +closed set so that it's not working the + + align:start position:0% +closed set so that it's not working the + + + align:start position:0% +closed set so that it's not working the +definition. Yeah. + + align:start position:0% +definition. Yeah. + + + align:start position:0% +definition. Yeah. +>> I'm not sure if we prove that like up + + align:start position:0% +>> I'm not sure if we prove that like up + + + align:start position:0% +>> I'm not sure if we prove that like up +there we have like you have a compact + + align:start position:0% +there we have like you have a compact + + + align:start position:0% +there we have like you have a compact +subset + + align:start position:0% +subset + + + align:start position:0% +subset +and take the intersection with subset. + + align:start position:0% +and take the intersection with subset. + + + align:start position:0% +and take the intersection with subset. +Yeah we prove that it's closed. We prove + + align:start position:0% +Yeah we prove that it's closed. We prove + + + align:start position:0% +Yeah we prove that it's closed. We prove +it's compact. + + align:start position:0% +it's compact. + + + align:start position:0% +it's compact. +>> We prove that it's compact and I can + + align:start position:0% +>> We prove that it's compact and I can + + + align:start position:0% +>> We prove that it's compact and I can +prove it again because it's very easy. + + align:start position:0% +prove it again because it's very easy. + + + align:start position:0% +prove it again because it's very easy. +So uh so if you take um if you take a + + align:start position:0% +So uh so if you take um if you take a + + + align:start position:0% +So uh so if you take um if you take a +if you have a + + align:start position:0% +if you have a + + + align:start position:0% +if you have a +if you have + + align:start position:0% +if you have + + + align:start position:0% +if you have +you have a metric space this here is + + align:start position:0% +you have a metric space this here is + + + align:start position:0% +you have a metric space this here is +compact + + align:start position:0% +compact + + + align:start position:0% +compact +and now you take a subset here of this + + align:start position:0% +and now you take a subset here of this + + + align:start position:0% +and now you take a subset here of this +here and this here is is closed. It's a + + align:start position:0% +here and this here is is closed. It's a + + + align:start position:0% +here and this here is is closed. It's a +closed subset of X. + + align:start position:0% +closed subset of X. + + + align:start position:0% +closed subset of X. +Then you look at X take away B. You take + + align:start position:0% +Then you look at X take away B. You take + + + align:start position:0% +Then you look at X take away B. You take +any copper of this together with this + + align:start position:0% +any copper of this together with this + + + align:start position:0% +any copper of this together with this +they cover A. But then finally many but + + align:start position:0% +they cover A. But then finally many but + + + align:start position:0% +they cover A. But then finally many but +this here have nothing in B. So actually + + align:start position:0% +this here have nothing in B. So actually + + + align:start position:0% +this here have nothing in B. So actually +finally many of the other one cover. + + align:start position:0% +finally many of the other one cover. + + + align:start position:0% +finally many of the other one cover. +Any other questions? + + align:start position:0% +Any other questions? + + + align:start position:0% +Any other questions? +Okay. Okay. Great. Thanks. \ No newline at end of file diff --git a/ekWxanQrsz4.txt b/ekWxanQrsz4.txt new file mode 100644 index 0000000000000000000000000000000000000000..d427a0348c4afb3bbad078bf5960e24767f63020 --- /dev/null +++ b/ekWxanQrsz4.txt @@ -0,0 +1,3964 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high-quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: So today is the +fourth and last lecture + +on the sort of +microfounded macro models. + +And then next +class, we will turn + +to a section on measurement, +which is like a halfway point, + +or not really, in terms of +total number of lectures. + +But we'll get into them-- +to the micro evidence. + +I must say, this is sometime-- + +I said this last time-- in +reverse of what I sometimes do. + +I often start with the +micro stuff and build it up. + +But this isn't a bad +idea, because you'll + +get to see this way how +different assumptions matter + +within each of these +models as you compare + +the predicted solutions. + +So it hopefully heightens your +sensitivity to assumptions. + +And then we'll get +into the microdata + +and really scrutinize +what we see there. + +This paper, in particular, +is part of that conversation. + +The way it's organized +in terms of the lectures + +is this paper features +mostly something + +other than limited commitment. + +Almost every single model has +had sort of very limited credit + +or financing constraints, +collateral constraints, + +basically putting a damper +on sudden transitions + +and generating growth paths. + +And here, we're going to +be looking at transition + +somewhat-- also, steady states. + +The main thing is +we're going to be + +featuring on other alternative +underpinnings of the models-- + +costly state verification, +adverse selection, + +moral hazard. + +Again, the irony, for +those of you coming down + +from the advanced +macro class, is + +that Alp was featuring costly +state verification up there + +early in a lecture. + +And these things +are somehow related, + +in the sense that the dynamics +that are created with the debt + +contracts and so on have +to do with what you assume + +about the information structure, +as well as adverse selection + +and so on. + +So you'll be perhaps +a little relieved + +to know there isn't +as much material + +on the front end of this +lecture as there was last time. + +That's kind of a sad +comment on the literature. + +Almost everybody assumes +limited commitment, + +so there really wasn't +much to choose from. + +We sort of scoured the earth +to find some relevant papers + +in this genre. + +So there's three, +and the third one + +is what I'm going to focus +my attention on, the tree, so + +to speak, of the lecture. + +And now we'll look +at several trees. + +The first two are +a bit different. + +This one is Greenwood, +Sanchez, and Wang-- + +Jeremy Greenwood, as of +Greenwood and Jovanavic, + +which was a key feature of +one of the first two models + +we talked about in lecture 2. + +And he's going to focus +on Levine's comment. + +It's kind of cool the way +these things come together. + +Levine worried that the +finance causes growth. + +Empirical literature +doesn't have + +a microfounded view of what +really impedes intermediation. + +So that's what this +paper is about. + +And it's going to be sort of +a costly state verification + +point of view with diminishing +returns and exogenous, + +technological progress. + +There's a telling sentence. + +In the paper, Uganda +could more than + +double its output if +it would adopt best + +practice in the financial +sector, which is something + +like the US or Luxembourg. + +Although, there are other +things in the model, + +so that that's not +enough to get it up to, + +quote unquote, "its +total potential output." + +Again, you see this +language of gaps + +here that we focused +on earlier in one + +of those financial +possibilities frontier. + +So this is very +much trying to get + +at gaps in terms of +the underlying model. + +AUDIENCE: What are +these other factors? + +PROFESSOR: Hmm? + +AUDIENCE: What are +these other factors? + +PROFESSOR: There's going to +be some technological progress + +that varies across countries, +which is pretty standard stuff. + +And then this is +kind of layered in, + +or it's actually more of +the heart of the model, + +given that other. + +Well, we've seen that was done +in the China paper as well. + +So another interesting +thing, 29% of US growth + +is due to improvements in +financial intermediation. + +So this paper both has +transition paths in it, + +as well as steady states. + +This is a comment +about steady state. + +There's exogenous technological +progress going on, + +not at the level of +the sort of TFP shocks + +that are in front of +the production function, + +but in terms of the +monitoring technologies which + +intermediaries can use to +verify some private information. + +And that's where the +technological progress + +is that's driving, say, steady +state US growth rate according + +to their calibrated +version of the model. + +Now, there are two key variables +here that they focus a lot + +on-- the interest rate spread +and the capital output ratio. + +So let's look at them. + +These slides are +interest rate spreads. + +This is the US. + +That's Taiwan. + +This is the spread +in the US, maybe 3%, + +maybe declining, +but not so clear-- + +modestly so. + +And this is sort of the +capital to GDP ratio. + +And it's paired to Taiwan, +where it's a bit more-- + +at first at least-- + +easier to interpret. + +This spread is +high and declining. + +So this is the transition part. + +This is Taiwan experiencing +technological progress that's + +lowering, or even I guess +it was in the steady state, + +at different levels of +technological progress + +in monitoring output. + +And as that happens, as the +intermediation system becomes + +more efficient, +capital is increasing. + +You can make better +use of capital + +because banks have +better information, + +and they can lend +more appropriately + +and adjust for risk +more appropriately. + +Now, even then, this +diagram is kind of striking. + +Because you can see that this +is steadily rising as the spread + +is coming down. + +But relative to US, the capital +to GDP ratio is quite high. + +So you know, just be mindful. + +There's two variables here, +and one of them is GDP. + +So low levels of GDP kind +of make that ratio high, + +and that's going on and +also moving these variables + +as you compare over +time and over countries. + +So the idea is that +firms, banks, really + +monitor cash flows. + +The efficiency depends on +the amount of resources + +you devote to monitoring +and to the productivity + +of that monitoring technology. + +And as well, firms have +differences ex ante + +in the structure of +returns that they face. + +So they get the +usual sort of why + +money doesn't flow from +low productive firms + +to high productive firms. + +And the answer is +this monitoring. + +At any moment in +time, there are firms + +with high expected returns. + +They tend to be underfunded. + +But it's underfunded +relative to this world + +with complete information. + +Whereas, we're in the +constrained second best world. + +Others have low returns +and they're overfunded. + +So these are the sort of not +so talented wealthier firms. + +That theme keeps coming +up in all the lectures. + +In China, it was the +state-owned sector. + +And last time it was +firms drawing talent, + +and some people having +low talent which + +is persisting and so on, which +is sort of what's true here. + +And of course, as +efficiency increases, + +funds are reallocated +from less productive + +to more productive firms, +and the interest rate spread + +goes down. + +There's going to be perfect +competition in the banking + +sector. + +So the cost of +borrowing is going + +to fall because these firms +are going to be kind of less + +able to walk away with the +money in terms of the monitoring + +technology. + +So here is a picture of +the interest rate spread. + +And it kind of goes the +way you would think. + +The low interest +rate spread countries + +are these highly +industrialized countries, + +and they tend to have low +capital to GDP ratios, + +in part, because +they have high GDP. + +And here's a +cross-section of countries + +that vary with respect to the +level of income and the capital + +output ratio. + +And this is, again, +very similar, + +except this is TFP over here. + +So you can see that interest +rate spread is a bad thing, + +and the higher the spread, +the worse the system. + +So as the interest rate spread +goes down, TFP is going up. + +So TFP is a function of this +sort of financial efficiency. + +Yeah, Matt. + +AUDIENCE: What data do they use +for the interest rate spreads? + +PROFESSOR: Oh-- + +AUDIENCE: [INAUDIBLE] the +interest rate [INAUDIBLE].. + +PROFESSOR: I don't know if they +grabbed some IMF statistics. + +I think IMF financial statistics +[INAUDIBLE] have that. + +I'm not sure if +that's what they used. + +But basically, yeah, +it's some measure + +of the difference between the +lending rate and the borrowing + +rate. + +And then that sounds +good at first, + +until you start thinking about +all the many ways you could + +get at the borrowing rate. + +Often, these things ignore +the informal sector entirely, + +for example. + +This is-- which this paper is +doing as well in the theory. + +And this is the usual +growth accounting stuff. + +OK? + +I don't know that we should have +had this on the earlier slide. + +You want to predict a +country's per capita income. + +It's efficient countries +with higher TFP. + +So this is sort of behind +the Lucas thing, which + +is why isn't money +flowing very quickly + +from low-income countries +to high-income countries, + +since high TFP tends to +mean high marginal product + +of capital and so on. + +But it's amazing. + +They almost all lie on the line. + +AUDIENCE: Is there +a TFP solo residual? + +PROFESSOR: Yeah. + +It's just a solo residual. + +And that's a good comment, +because this paper + +is about the different ways +to decompose at the firm level + +the sort of coefficient +that's hanging + +outside the front of +the production function. + +And then add it up the way +[INAUDIBLE] were doing. + +So they also do this sort of +Rajan/Zingales thing, which + +is to try to calibrate +against the US economy, + +they look at the firm +size distributions + +and the interest rate +spreads in the US + +to get some of their +parameters, and then take it + +to these cross-country data. + +AUDIENCE: Sir. + +PROFESSOR: Yeah. + +AUDIENCE: Actually, +are [INAUDIBLE] + +distributions similar? + +Or is it developed +[INAUDIBLE] country? + +PROFESSOR: No. + +So what they're saying is the +US would be a more or less + +efficient financial system. + +So you could sort of +think about grabbing + +the relative technology +parameters from that, + +and then take those +sort of what are + +counterfactual-- +those parameters are + +put in the context of +a developed country + +with lots of other restrictions. + +So the idea is to get +the technology right, + +and then somehow figure out what +difference the financial system + +makes. + +Yeah? + +AUDIENCE: What are +the main assumptions + +you have to make +in your own model + +to get that [INAUDIBLE] +distribution [INAUDIBLE].. + +Because I mean, +[INAUDIBLE] then it + +seems to be about the +distribution of talent + +or distribution of [INAUDIBLE]. + +PROFESSOR: Yeah. + +Each one of these models tries +to be really careful about how + +to map the data into the +notation and assumptions + +they're making. + +And that's-- here, I can +give you a hint of that, + +although I can't get to it in +as much detail as I would like. + +So here's this +production function. + +There is some aggregate shock +that hits all the firms. + +There is some theta, which +is an idiosyncratic-specific + +firm-level shock. + +And then we have the usual-- + +Cobb-Douglas actually just +noting constant returns + +to scale. + +Different papers differ on that. + +And where do these +idiosyncratic shocks come from? + +They're drawn at random from-- + +in this case, some simple +two-point distribution. + +It could be high or low. + +But here is over and +above that, another source + +of the heterogeneity +that different firms + +have different sets of thetas. + +So the whole sort +of range domain + +can be different, depending +on, quote, "the tau type" + +that these firms are. + +Intermediaries are competitive. + +So they're going to sort of not +get any surplus out of this. + +They raise funds from consumers +and lend them to firms. + +That's typical +intermediation structure. + +And the intermediary +knows the firm's type tau. + +However, it doesn't know output. + +It doesn't know the +idiosyncratic shock theta. + +And it doesn't know +the labor supply. + +So all he's doing here +is being careful to throw + +in enough sources of unknown +that you can't basically + +back out from the output +the unknown things + +on the right-hand side. + +And he probably could have gone +with different assumptions, + +but that's certainly +the spirit of it. + +Or at least, doesn't observe +these things costlessly. + +But there is this +monitoring technology. + +The firms experience their true +productivity, say, high or low, + +call it for the theta +i for a given firm. + +And suppose the firm lies +about it and says theta j. + +Theta's not observed +nor inferred + +from any of the other +ex ante or ex post. + +Then the intermediary devotes +labor to monitoring the claim. + +So this technology +of verification + +is actually resource using. + +It's another +production function. + +And then the size of +the loan is determined. + +That's the capitalization +of the firm. + +They don't have any +wealth on their own. + +That's kind of the +scale of the project. + +The level of productivity +and monitoring is z. + +So that's kind of like whether +it's a completely noisy signal, + +or an extremely accurate signal +of the actual true state theta + +i. + +So this object, Pij is-- + +that's the probability +that if the firm + +made a counterfactual +report of theta j + +and really were a theta i, +with this amount of labor + +devoted to monitoring, +given this loan size, + +and given this index of the +productivity of the technology, + +this is the probability +of finding out + +what the truth of it really is. + +And so-- and then +this mapping here + +is to provide +between productivity + +and financial sector z, +which, say, we don't see. + +And the things that +we do see, at least + +we, as econometricians, see +output and interest rate + +spreads. + +Now, let me pause for a +second because you might well + +think of the obvious +thing is, wait a minute. + +Didn't you just say +output was unobserved? + +Well, this model and +others make a distinction + +between the exposed +data that we have + +as analysts about +firm output, as + +opposed to what the intermediary +is seeing along the way. + +So we're imagining +we do see output + +and these interest rate spreads. + +Those were the slides +I just showed you. + +And then this is +where I'm going to-- + +Matt-- going to be a bit vague. + +If you looked at the +equations in the notation, + +they can basically invert +those equations to get x and z. + +And you can do it at a point +in time for a given country, + +or you can do it at two +different points in time. + +If you're getting +z, you're getting + +a measure of this productivity +of the monitoring technology. + +And that's why, +for example, they + +are able to make statements +about Taiwan's productivity + +increased over whatever +it was, 10, 15 years, + +along with the drop in the +intermediation spreads. + +They infer that from the drop +in the intermediation spreads + +and the capital output ratio. + +AUDIENCE: Question. + +PROFESSOR: Yep. + +AUDIENCE: So the assumption +that the probability of getting + +[INAUDIBLE] is decreasing. + +PROFESSOR: Yeah. + +So this is a scale effect. + +This came up in Alp's +lecture the other day + +as well, which is if you have +a fixed cost of monitoring + +or something, and then the +country gets richer and richer, + +and credit is going +up and up, then + +basically, the cost +of verification + +is going down and down. + +But here, a country's +getting richer and richer, + +and you don't want this sort +of information imperfection + +to go away other than +through investment + +in improved technology. + +So it allows that-- + +I guess that conceptually, +it's like bunch of little firms + +all spread out. + +And the bigger the loan +size, the more plants + +you got to go to see- +something like that. + +AUDIENCE: And is +the result partially + +depending on this assumption? + +Because it might be +the direction is-- + +PROFESSOR: Yeah. + +Yeah. + +It matters quite a bit. + +Now, this is kind of linear. + +If it's diminishing, the +effect eventually goes away. + +If it's convex, then I +don't know what happens. + +But it matters. + +All right. + +So that's the spirit +of that paper. + +Again, hopefully, it +whets your appetite and-- + +or at least you can get +some sense of what people + +are doing in the literature. + +And there's one +other that I want + +to talk about before we get to +the main paper of this lecture. + +And this I discovered +recently, actually-- + +"International Capital +Flows and Credit Markets-- + +A Tale of Two Frictions." + +Somehow everyone's got +taken with Dickens. + +The one we looked at last time +was "A Tale of Two Sectors." + +I don't know whether you +thought that was clever or not. + +This paper was +written after that. + +So it's kind of +intriguing, and I'm not + +quite sure I totally believe it. + +But let me try to +walk you through it. + +So the idea is we +see a lot of capital + +moving around the world, +and we see boom/bust cycles. + +And they're going to try +to get both of those things + +in into one model. + +So it's ambitious. + +Global imbalances, large +and persistent capital + +flows coming out +of Asia to the US-- + +we talked about that +last time in the-- + +last time in the China paper. + +And there the idea is it's +hard to make good use of it + +within China for the reasons +that that model and others + +postulate, namely, +financial friction. + +So then it should +go somewhere else. + +But you could also think about +it on the other side of it. + +This is the tricky part. + +Namely, that that money is +going to unproductive investment + +in the US. + +So at least that's +ex post the judgment. + +So then you have to +model sort of what's + +going on with the US interest +rate that would allow + +the existence of bad +projects and the coexistence + +of bad projects +with good projects. + +So they try to do both. + +So again, there's +credit market which + +intermediates the money +that comes from savers + +and goes to investors. + +Individuals are endowed +with some resources + +and with an investment project. + +And they have to decide +whether to do the project + +and become an +entrepreneur, in which case + +they're going to want +some credit to fund it, + +or to forego their project and +become savers, in which case + +they supply resources +to the credit market. + +Now, this building block is the +same on almost all the papers + +that we've looked at. + +It's an occupation +choice model of-- + +that's used to address +financial issues. + +To give adverse +selection a crucial role, + +we assume individual +productivity + +is private information and +unobservable by the lenders. + +That kind of sounds like the +previous Greenwood paper. + +So there is some +cross-subsidization + +between high and low +productivity entrepreneurs. + +A key assumption-- there's +only one interest rate. + +So there's no menu of contracts. + +There's no other ways to +separate good from bad. + +And the thing, to +say it intuitively, + +about adverse selection +is, who wants to borrow + +at a given interest rate? + +Well, that's really +attractive for people who + +expect never to repay loans. + +So the lender is going to +have to somehow break even + +on those bad types that +are indistinguishable + +from the good types. + +And that is a force +determining the interest rate. + +Now, the question is whether +that kind of perverse dynamics + +would move around +with wealth and so on. + +Yes. + +AUDIENCE: Are the lenders +endowed with mechanisms + +to prevent that? + +Is there physical +collateral, or is there + +some sort of reputation-- + +PROFESSOR: Not here. + +Not here. + +But there is a big +literature that argues-- + +AUDIENCE: OK. + +So in this-- this +environment has + +the potential for the sort of +adverse selection [INAUDIBLE] + +type things. + +PROFESSOR: Yeah. + +There is always an issue in +papers and as researchers + +at what-- how much-- how +many substantive things you + +want going on at the same time. + +I would say this is among +the simpler adverse selection + +thing. + +Personally, I would always +think menus of contracts + +could select-- + +allow selection or +sort of truth-telling. + +And that's just shut down. + +But Rothschild/Stiglitz +shut that down. + +So maybe that's off to +a tradition of sorts. + +So what are the implications +of this adverse selection? + +The interest rate has +to be higher than it + +would have been otherwise. + +But on the other +hand, there's a lot + +of borrowing and investment. + +Now, be careful here, because +these low productivity + +guys are happy to be borrowers. + +So not all borrowing +is a good thing. + +And that's kind of the seeds +of the bust getting created. + +Because of adverse +selection we have + +this wedge between the +equilibrium interest rate + +and the marginal +return to investment. + +Again, it's a common wedge. + +We just did an +interest rate spread. + +Here's another way to +think about that spread. + +That doesn't mean +it doesn't matter. + +The underlying +assumptions do matter. + +But this phenomenon is pervasive +across countries in the data, + +and is a big part of +almost all these models. + +So adverse selection +means that the economy + +can attract more +capital, and boost in + +that capital flows seems +odd just to say it there. + +You can see it written. + +But again, the idea is that +somehow the interest rate + +is higher than it would have +been in the full information + +economy, and outside investors +seek the higher interest. + +So that's kind of what +they mean by that. + +But the true marginal return +lies below the interest rate. + +So something bad is happening. + +And the way it comes out in +the bath here is the capital-- + +there's lower aggregate +consumption because you've + +used resources inefficiently. + +And then they claim this +adverse selection actually + +is a force for volatility. + +This is kind of key. + +The incentives of less +productive individuals + +to become entrepreneurs +are strongest-- + +there's bad types borrow and +don't expect to repay much. + +That force is strongest, +ironically, when the capital + +stock is low and income is low. + +And what's that all about? + +Well, basically this +debt overhang problem + +is more severe when the +capital stock is low, + +because you have to borrow more +than you would if the capital + +stock were high, and you +could almost self-finance. + +And there's a lot of +untalented firms borrowing + +when the total income and +capital stock of the economy + +is low. + +Or conversely, as capital +and income increases, + +that cross-subsidization +is decreasing. + +There's more self-financing, +and entrepreneurship + +loses its appeal for less +productive individuals. + +Well, I mean, it's actually +kind of interesting. + +Because you can see the +dynamics of occupation choice + +that we've had in +the other papers. + +Who's going to be a firm +as opposed to a wage earner + +depends on what happens +if you were a firm + +and decided to borrow. + +And then they actually +get a boom/bust cycle. + +They claim to show that capital +inflows are going to fuel + +this accumulation period. + +And then you'll +get a contraction. + +Actually, toward the end, the +tale of two obstacles or two + +frictions, is they throw +pledgeability on top of it. + +So the more traditional sort +of collateral constraint + +reduces investment and +lowers the interest rate. + +We've seen that, right? + +You can't borrow as much, +so there's less pressure + +on the interest rate. + +So the interest +rate would be lower. + +Ironically, that low +interest rate, though, + +decreases the +returns to savings. + +And why be a wage earner and get +a lower return on your savings + +when you can be a not +so good entrepreneur + +and borrow money +at low interest? + +So you get this +sort of, they claim, + +a kind of accelerator +or exacerbating feature, + +that the adverse +selection is interacting + +with the limited +collateral constraint. + +And that should whet your +appetite for that paper. + +Now again, I apologize in a way, +although it wasn't my intention + +to go through all the +details of that paper. + +And it is on the +Stellar website. + +And we can study +it in more detail. + +But I offered it +here just to show + +you the kinds of +phenomenon that people + +are trying to address +with the interplay + +of financial frictions. + +And then we come to the +paper I wish to focus on, + +which is, again, a +tale of two frictions. + +But we can't use that title. + +But we're doing it +in a different way. + +We allow moral hazard and +also limited commitment. + +So on the one hand, +we're going to take + +the traditional limited +commitment constraint + +and remove it, and +insert a moral hazard + +constraint explicitly. + +And this time, I can +show you the equations. + +But we also allow-- + +we don't get rid of the +capital constraint entirely. + +And then you say, well, +what are the rules here + +for making this stuff up? + +And my answer is the data. + +And in particular-- this is +the reverse order coming here-- + +you will see a paper +that I've written + +with Alex Karaivanov, where +we have consumption, output, + +investment, and +capital stock data, + +and we actually estimate a +variety of financial regimes. + +And it turns out that the +so-called limited commitment + +regime fits the data best in +the rural data that I have + +and in the Northeast, and +the moral hazard regime + +fits better in the urban +areas and in the areas + +in and around Bangkok. + +So that's the way to think +about these two frictions. + +They're, for us, going +to be microfounded. + +Although here, we're just +borrowing that and putting it + +in. + +So-- + +AUDIENCE: Sir. + +PROFESSOR: Yep. + +AUDIENCE: So +basically, are you-- + +you're going to sort of let +these two things interplay, + +and you're going to +have them be differently + +important in different places. + +PROFESSOR: Yeah. + +So that's where we end up. + +And where we start is +we have an economy, + +and I'll tell you all +about the environment. + +And then I'll describe what goes +on with the limited commitment + +constraint as if it +were the whole economy. + +I'll do the same for moral +hazard, the whole economy. + +Then I'll have like 50-50, and +use the general equilibrium. + +And the punch line is going +to be the general equilibrium + +with the two +frictions is not just + +a simple convex combination +of the two extremes. + +And the reason that +that's going on + +has to do with the +general equilibrium. + +So you're going to get-- + +roughly, you're going to get +interest rates and wages that + +are somewhat between +the two extremes. + +But then given +that, the question + +about who is to be a firm or a +worker depends on the obstacles + +that you face. + +And actually, what +turns out to be + +cool at the parameters we have, +which we think are reasonable + +and are largely similar +to what Alex and I had, + +that in the places +with moral hazard, + +output is substantially higher. + +There are slightly +more firms there. + +They're larger. + +Those firms are renting more +capital or borrowing more. + +The ratio of credit to GDP, +the financing ratio, is higher. + +And they employ more labor. + +Without any geography +somehow, we've created these-- + +replicated these stylized +facts of development + +when you think about rural +areas versus urban areas. + +Money is flowing from +savings in rural areas + +to the urbanizing cities. + +Now, I'm not going to claim that +we've captured everything going + +on in all these countries. + +But this simple +sort of combination + +of financial +frictions allows that. + +In that sense, this is very +different from the other paper. + +Yes. + +AUDIENCE: And so do you have +something that endogenously + +makes these two regimes being +relevant in those areas? + +PROFESSOR: That's a good +question, and it's-- + +at this point, it's +hard to answer. + +I mean, it looks +as if either there + +is a legal restriction +on collateral, + +or the set of financial +institutions that are operating + +in the rural areas is +different from what's + +going on in the urban areas. + +And if we were going to +follow Jeremy's path, + +we would ask your question. + +We are asking, and we just +don't have answers yet, + +as to what is the configuration +of the financial service + +providers? + +You'll see there is a +heavy distinction-- we've + +already seen, actually, where +the commercial banks are + +operating and where this +government agricultural bank is + +operating. + +And I think that's +probably part of the story. + +But in this paper, we do +not take a stand on it. + +We take as given just +this sort of difference + +in the financial +information regime. + +OK. + +So this, we've already said. + +This, we've already +talked about. + +So we get to the model. + +So a household that could +decide to be either a wage + +earner or a firm will maximize +discounted expected utility. + +Beta is the discount rate. +u is the common utility + +function, the +arguments of which are + +consumption of this household i, +and effort of this household i. + +We'll parameterize this when +we need to compute something. + +At this level, +it's quite general. + +You can-- if x is equal-- +this is like a binary choice. + +You can be a worker or a firm. + +By convention, when x +is 1, you're a firm, + +and when x is zero, +you're a worker. + +And that's going +to be endogenous. + +If you do become a firm, you +have this productivity draw z, + +and it evolves over +time according to sort + +of a standard Markov process. + +I was rushing toward the end +of the lecture last time, + +but this was the thing +that was in the [INAUDIBLE] + +paper toward the +end, and I guess + +in some of the other papers. + +And finally, we have wealth. + +So at the beginning +of the period, + +everyone has some +predetermined level of wealth, + +and it's in the +bank essentially. + +And so an individual +is characterized + +by their initial wealth +and their current talent. + +Here is the production function. + +It's diminishing returns +to scale in capital + +and hired labor. + +And then we have these sort +of things out front here. + +The notation varies from +one paper to the next. + +But epsilon is here, +an idiosyncratic shock. + +iid over households, and z +is that level of productivity + +we already talked about +that's evolving over time. + +Now, there's +actually-- the effort + +of the entrepreneur is +another factor of production. + +And that's basically little e. + +So the way that the effort of +the entrepreneur is modeled + +is through this. + +The epsilon, the +idiosyncratic productivity, + +depends on how hard the +entrepreneur is, quote, + +"working," or +thinking, you know, + +staying up at night worrying-- +basically, due diligence. + +This is not measured. + +You do see the epsilon, +but you don't see the e. + +And that's if-- well, at least +in the moral hazard model, + +you don't see the e. + +But I should qualify +that we're going + +through the standard +environment, + +and there's going to +be a full information + +environment with limited +commitment in which everything + +is seen and full +insurance is possible, + +versus the moral hazard +environment which + +is going to be the source +of limited insurance, + +and it's going to interact-- + +both frictions interact +with productivity. + +So there are banks or +financial intermediaries, + +and you should think of them +as basically risk syndicates. + +Because not only do they sort +of lend out of the wealth + +that households have been +depositing with them, + +they can also smooth over +idiosyncratic shocks. + +So there's a state +contingent payment + +that the banks can make-- + +it could be negative-- + +say, to the households +as a function + +of their realized +and observed epsilon. + +Now, in some +respects, it's still-- + +we're not solving a +massive programming problem + +and then capturing +the interest rates + +and wages off some +first order conditions. + +Instead, we're going to +imagine that these risk + +syndicates, these banks, and +the firms and the households + +all take as given economy-wide +interest rates and wages. + +And like many of +the other papers, + +we're going to have to determine +those by supply and demand + +mechanically. + +So that's a +computational burden, + +but it is one that other +papers have faced as well. + +Now, what to do about talent-- + +is it insurable or not? + +Well, we kind of decided +to try to be realistic + +and to not let it be insured. + +We could go the other way. + +In some sense, we know +exactly how to do it. + +And there's some duals +which would be satisfied + +if we had allowed it. + +But we thought it was just +on the side of realism + +to say don't worry +about your job market. + +We're going to cover that. + +NYT is going to +fully insure you. + +Well, of course, we could put +moral hazard on the z thing. + +But anyway, we +didn't get into that. + +So you're going assign the +occupation, induce effort-- + +where did I say-- + +I guess I didn't say it. + +It'll come up in a +second, hopefully. + +Yeah. + +It was right here. + +We actually also +allow there to be + +some insurance and moral hazard +issues on the worker side. + +Now, for simplicity, we give +them this same p of e function. + +We could have allowed +it to be different. + +What is this? + +Well, the idea is you can +sort of put a lot of effort + +into working, and +the firm is going + +to observe your total +sort of productivity. + +But the firm doesn't +see your effort. + +It's like piece +rate in some sense. + +So we just got tired +of being asymmetric, + +as so many papers are about-- +you know, there's an insurance + +problem for intermediaries +and wage earners don't + +suffer from things like that. + +So here's the timeline. + +The household comes in with-- + +a certain household i comes +in with a certain amount + +of wealth and talent. + +There's going to be an +assignment, if you will, + +of who's a worker or a firm. + +Then if a firm-- + +well, if a worker or firm ever +gets determined, if a firm-- + +the capitalization and +labor hiring of the firm + +gets determined, then +the epsilon hits. + +Effort comes first. + +Epsilon comes after that and +gets in the way, so to speak, + +especially if effort +is not observed. + +So this is like idiosyncratic +risk subject to moral hazard + +potentially. + +Then consumption and the +level of your savings + +that you're carrying +over putting + +into the bank for +tomorrow, those things + +are functions potentially +of those epsilons. + +So the point is, you do +bear the consequences + +in the moral hazard +model of shirking. + +If you shirked and +your productivity + +were low as a +consequence of that, + +you're going to have +to take a hit in terms + +of lower consumption and lower +savings from tomorrow on. + +So here's the optimization +problem really of the bank, + +but it's more like an +equilibrium outcome. + +The banks are +basically competitive. + +There's free entry. + +And for any sort of cohort +fully observed, by the way, + +az sort of people out there-- + +there's a lot of them in +every little cubbyhole-- + +the banks compete to +offer them contracts. + +In effect, they +would bid down things + +until utility is maximized. + +So it's as if they're maximizing +the utility of this cohort + +by choice of all these +things I just went through. + +And this is the +resource constraint + +that the risk syndicate faces. + +Partly it's familiar +and partly not. + +Namely, you've got +uses and sources. + +The uses of money or resources +is in consumption and how much + +you save for next time. + +And the sources +comes from if you're + +a firm in this syndicate, +your net profits, + +after subtracting off the +cost of labor and capital + +and depreciating the capital, +and from the other guys + +who are wage earners. + +And as is standard +in many models, + +you begin the period with +basically the savings + +that you had as a bank. + +But now they've sort +of accrued interest. + +So you have principal +and interest + +at the beginning of the period. + +Now, it looks like a standard +sort of incomplete markets + +model, where you have the +choices between saving + +and, quote, "borrowing/lending." + +The difference here and-- well, +and some profit maximization + +embedded. + +But the difference really +is the summing over epsilon. + +So this is the total sort +of assigned consumption + +and savings throughout +the whole syndicate, + +the average per capita number. + +And this is the +per capita sources. + +The intermediaries in trying +to break even on every epsilon + +type in the population-- + +that's the risk-sharing +part of it, + +that some people could +have higher output + +than other people. + +but subject to +incentives or insurance. + +The intermediary will smooth +that by assigning, say, + +higher consumption than output +for the low epsilon guys, + +and conversely for +the high epsilon guys. + +Yes. + +AUDIENCE: So the financial +intermediary, they + +can control the distribution +between consumption and asset? + +PROFESSOR: Yeah. + +That's all observed. + +AUDIENCE: So household +can't bypass that + +by saving themselves. + +PROFESSOR: They don't. + +Yeah. + +We assume not. + +But you could +assume that they get + +their sort of +assignment of assets, + +and then they act on their own. + +But they would +put it in the bank + +because they accrue interest. + +So there's really no loss in +letting it sit in the bank. + +Now, we can have banks +competing with one another. + +That's a bit more subtle. + +AUDIENCE: [INAUDIBLE] the +other way around though, right? + +PROFESSOR: Hmm? + +AUDIENCE: You +can't like really-- + +OK. + +Like, the household +can choose to save, + +but household can +choose to consume too? + +I don't know. + +I feel that here, bank has +more control over household, + +and they can say exactly +how much you can-- + +PROFESSOR: Well, that's +probably a better way + +to think about it anyway. + +Because as you'll see, +these information frictions + +and collateral +restrictions create + +pressures that make savings more +or less than what households + +might want to do if they were +just following their Euler + +equation. + +So in the end, I agree with you. + +What's going to be +actually interesting + +is that it's going-- + +and you'll see this-- + +it's going to go +a different way. + +In the collateral +constraint model, + +you would like to +borrow more, actually, + +in order to have more +assets in the future. + +That's not allowed to happen. + +So they're going to be +borrowing-constrained + +in terms of looking at their +intertemporal consumption path. + +The guy subject to this sort +of incentive moral hazard + +constraint, they're +actually going to end up + +being savings-constrained. + +They would like to save more. + +So it's already a hint that +the dynamics of the household + +decision problems +are very different, + +not just of the firm, +but the households. + +So what do we mean by +the incentive constraint? + +Well, when effort +is unobserved, you + +want to induce the +assigned effort. + +So these are the good boys. + +They were recommended to do +e, and they actually do it. + +So this is the distribution +of output, epsilon, + +that results from it. + +And they go into tomorrow +with the assigned levels + +of savings and draw talent. + +But effort is not seen. + +So they actually +contemplate some + +out of equilibrium +behavior, like doing + +e hat, which is other than e. + +Now, what are the +consequences of that? + +Well, first of all, there's +a direct consequence + +in the utility function, +because shirking + +might be good in terms +of higher utility. + +But also, there is +a direct consequence + +in terms of the +distribution of output. + +So this is sort of the +moral hazard induced + +productivity consequence. + +And if you do some typical +monotonicity or something, + +then higher effort is +associated with likely + +getting higher epsilons. + +So that's a standard-looking +incentive constraint. + +The-- yes. + +AUDIENCE: So probably +we could introduce + +some costs associated +with changing jobs + +between [INAUDIBLE]. + +Does it change the +analysis at all? + +PROFESSOR: Well, +you get to choose. + +But yeah. + +There's no extra cost. + +It would increase the +dimensionality of the state + +space rather enormously, +because then you'd not only + +have to worry about the +current distribution of wealth + +and talent, you'd have to worry +about what these guys were + +doing last period. + +And it's actually hard enough +to get any kind of solutions, + +analytic or numeric. + +So I think that's the constraint +here is keeping the state. + +I mean, there is-- you'll +see that there's already + +a huge distribution +of wealth, and we're + +going to have to keep track of +how that histogram is evolving + +the population jointly with +the talent distribution. + +So hopefully, good +enough for starters. + +Oh. + +I'm going to skip this slide. + +I'll tell you what was on it, +and then we'll come back to it + +when we get to the microdata. + +Basically, instead +of solving directly + +for consumption as a function of +epsilon and all of that stuff, + +we trick it into a linear +programming problem. + +And we do that by keeping +track of histograms of things, + +basically, the joint +distribution of consumption, + +epsilon, recommended effort and +so on, respecting the timing. + +So in words, hopefully, +you would think + +that's kind of equivalent. + +Anyway. + +Now, what's the gain? + +The gain is it literally +is a linear program. + +So that little module can be +solved as a linear programming + +problem, and that's +how we're computing + +the solutions to that part. + +But this isn't the right +context to go into the notation. + +We'll do it in a very simple +convex cost or a fixed cost + +problem first, and then +build up to it later. + +So I'm missing something. + +Oh, yeah. + +This thing. + +So this is the other constraint, +that the capitalization + +of the firm is just some +proportion of your wealth. + +Lambda could be greater than +1, but it's not infinity. + +So this is the +constraint that we had + +on so many of the other papers. + +And you can tell +stories and model + +this about running away +with a capital and so on. + +But this is the essence of it. + +We could do both. + +We're going to imagine +that it's one or the other. + +I mean, both simultaneously +for a given firm. + +But we're going to put people +in one sector or the other. + +So then we're going to solve for +the factors occupation choice, + +labor, hiring, capitalization. + +And you want to think +about labor supply-- + +it's just only slightly tricky. + +X means entrepreneur. + +1 minus x means wage earner. + +What's the total labor supply +coming from wage earners? + +Well, epsilon is +units of labor supply. + +It's induced by the effort. + +There's a histogram. + +So we basically add up +overall the epsilons + +at the fractions with which +they exist in the population. + +And this is total labor supply. + +And so then the rest +is pretty less daunting + +in terms of notation. + +We have-- we're going to equate +labor supply to labor demand. + +This is the l being +employed within the firms. + +The firms vary in +terms of their a and z. + +And everyone's facing +these economy-wide wage + +and interest rates. + +But this does depend +on the az argument, + +so we have to add up over-- + +or integrate up over-- all the +az people in the population. + +So again, in +practice, we're going + +to have a large finite +number of wealths, + +a finite number of +talents, and this is going + +to be some kind of summation. + +This is also the capital +clearing constraint. + +All that wealth sitting +there-- forget the d. + +Don't know why that's there. + +You have all that wealth +sitting in the bank, + +and it's going to be lent out +at interest to the firms that + +are renting the capital. + +So we grab some parameters +and some functional forms. + +These are pretty traditional. + +I guess we didn't want to +do anything unconventional, + +because we want to show what +difference the obstacles make + +rather than force you +into a utility function + +you don't believe. + +Also, we can grab from the +literature values for these + +that people believe. + +I don't mean to belittling +calibration all the time. + +Beta is realistic here. + +It's about basically 5%, or +95% of the future is valued. + +Sigma's the degree +of risk aversion. + +It's 1.5. + +People have values well +within that range-- + +just utility is a bit tricky +to parameterize of effort, + +but the power function +is the Frisch elasticity. + +People have estimated that. + +This is a simple transition +which we made up. + +But in other papers, people talk +about entry and exit of firms, + +and we could imagine doing that. + +And they are also +similar to the parameters + +that Alex and I estimate would +likely [INAUDIBLE] functions. + +So here is the-- + +with the Euler equation, +it's at the household side. + +Borrowing-constrained households +have a Lagrange multiplier + +on that limited +commitment constraint. + +It turns out to be tomorrow, +but in expectation, it + +leads to this same phenomenon +that the marginal utility + +of consumption is high today and +lower in expectation tomorrow. + +So these guys are +borrowing-constrained. + +Yes. + +AUDIENCE: Question, sir-- +going back to [INAUDIBLE].. + +So when you +described it earlier, + +so something that entrepreneur +can do to [INAUDIBLE] + +to make productivity high. + +If it was mainly +labor monitoring, + +I guess it would maybe sort of +really only scale with labor. + +Would that-- how much +would that change + +what goes on in the model. + +PROFESSOR: Oh, that's a +bit like in the spirit + +of Jeremy's model, and +we're not doing that. + +But yes, you could put-- + +it's very much like +what Jeremy is doing. + +You could put the technology +for monitoring effort + +to create a signal +at least of effort, + +and that would mitigate-- +that would move us + +more toward the full +insurance solution. + +And this is the weird one. + +And I'm not sure if you've +seen this yet or not + +in public finance. + +But-- so I'm just going +to basically assert + +that the first order +condition, when + +you're subject to moral +hazard, looks like this. + +And for obvious reasons, +this is sometimes + +called the inverse +Euler equation, + +because this is 1 over u prime. + +The point here is +Jensen's inequality. + +You know, if you replace-- + +if you pull the expectation +operator outside of it, + +you'd have 1 over u +prime, but the inverse + +would take it back to u prime. + +But when you move that +expectation operator outside, + +you're taking an average +over the interior object. + +I'm sorry. + +This is an average over the +interior object as opposed + +to an integration +from the outside. + +So it is basically a classical +example of Jensen's inequality, + +and it makes the +right-hand side higher. + +That's mechanical, +but hopefully-- + +we've already talked about this. + +You can see that in +the limited commitment, + +people cannot borrow +as much as they want. + +That's going to make the +demand for funds less, + +and the interest +rate is going to be + +less when all the economy +is subject from that limited + +commitment +constraint, as opposed + +to the moral hazard economy +where households and firms are + +savings-constrained. + +So they would like to save more. + +Savings is less. + +It's scarce. + +You have a higher interest rate. + +So these interest rate +numbers kind of make sense. + +Don't be too spooked by +the negative interest rate. + +You know, we have a depreciation +rate in this economy. + +So it's still sort of on net-- + +it's positive. + +And then you can see, comparing +these two different countries, + +GDP, TFP-- + +the TFP dynamics +are very different, + +although the numbers, +though different, + +are not radically different. + +TFP is dragged down in the +limited commitment economy, + +because high productivity firms +cannot borrow as much as they + +want. + +They can't exploit their z. + +Whereas, in the +moral hazard economy, + +you have to induce effort, +and that's kind of a drag. + +I mean, if you were draconian +and you had no insurance, + +then yes, people would +be working very hard. + +But that's actually not optimal. + +The right thing to do is to have +this blend between insurance + +and productivity. + +So partially, it's-- this +language people use about moral + +hazard in the banking +system and in the press + +and the policymakers, +pick that up like, + +let's get rid of moral hazard. + +That's not the right +way to think about it. + +Moral hazard is an +information problem. + +You want incentives +to do as best you can, + +given the moral hazard problem. + +But it's like-- eliminate +moral hazard is like, let's + +just shut down +all the insurance, + +then you don't have a problem. + +But yeah, well, you +got other problems. + +Wages are a bit different. + +They're higher in +the moral-- these + +are economy-wide wages and +interest rates, of course. + +But you can also see +a bigger difference + +in the financing ratio. + +Actually, labor here tends +to compensate for the more + +restricted capital, and +the drag makes labor lower + +in the moral hazard economy. + +External finance is more limited +in the limited commitment + +economy. + +Why? + +Because you can't borrow. + +You run into that +lambda constraint. + +There's nothing like that +in the moral hazard economy. + +So the external finance +to GDP ratio is higher. + +AUDIENCE: So why is the +interest rate negative? + +PROFESSOR: That's, +again, because there's + +an interest rate going on here. + +I mean capital gets +utilized, and it gets-- + +it's depreciating. + +And you've got to basically +pay for that somehow. + +So it lowers the net yield. + +And here's +interesting-- you know, + +I didn't get to say much at +all about Joaquin Blaum's paper + +on inequality. + +But I get to be reminded +to say something now, + +because here the wealth +inequality curve's generated + +by the different constraints. + +And you can see there's +actually more inequality + +in the limited +commitment economy + +than there is in the +moral hazard economy. + +But again, that has to do with +this dispersion of the capital. + +Capital tends to be more-- + +not identical, but +more compressed + +in the moral hazard economy. + +And capital is very limited. + +You can't take advantage of your +productivity in the other one. + +So the wealth dispersion +is playing a bigger role, + +and feeding back in turn to-- + +it's like you can't +get the convergences. + +And then we take 50-50. + +Same economy-- now we have the +urban/rural of the same size, + +and-- + +AUDIENCE: Question. + +PROFESSOR: Yep. + +AUDIENCE: So in the slides +with the parameters, + +you don't talk about lambda. + +How much do you +think that to be? + +The-- so the-- how +much is the constraint? + +PROFESSOR: I'm not sure +I remember the number. + +AUDIENCE: But-- I mean, do you +remember how you configured it? + +PROFESSOR: It should have been +on that list of parameters? + +It wasn't on that page? + +No. + +I don't remember. + +We probably-- it was +probably something like 1.3, + +because that's-- + +but that's right off +the top of my head. + +AUDIENCE: How do you-- + +[INAUDIBLE] in the same way? + +Because that's +how-- like, that's + +something you estimated +somewhere else? + +PROFESSOR: Hopefully, +we just drew it + +from this literature, +the [INAUDIBLE] paper + +that you've seen before. + +I don't think we +matched it with data. + +That's actually hard to +pin down in the data. + +AUDIENCE: Would +it be particularly + +sensitive to the +choice of lambda? + +PROFESSOR: Oh, yeah. + +Yeah. + +Remember the [INAUDIBLE] +thing, where lambda goes from-- + +I think it was 1.3 to infinity. + +And at infinity, there's +no constraint at all. + +You're back to the full +insurance, full productivity + +solution. + +AUDIENCE: So some +of the things about + +like the wealth +inequality and [INAUDIBLE] + +expect those [INAUDIBLE]. + +PROFESSOR: Oh, yeah. + +Now what-- so what +you're not seeing here, + +although we have +recently done this, + +is run a whole suite of +computations for all kinds + +of-- we put sort of error +bands or confidence intervals + +on these just to make sure that +none of the things that we want + +to emphasize are-- + +either they're +always true, or we're + +going to say they're +not always true, + +and they depend on +these parameters. + +But you're absolutely +right, that just showing + +some simulations looks a +bit arbitrary, especially + +for things like lambda, +which I'm not even + +remembering in the moment, so-- + +But different things would +matter for the moral hazard + +economy too. + +You know, the curvature of +the labor supply utility + +that generates labor supply-- + +that's going to be +that Frisch elasticity. + +We'll see that again when we +get to the sort of microdata. + +And the chi that sits in +front of labor disutility-- + +that's a huge number, +important number. + +So what are these slides? + +Well, this is a +bit like generating + +many, many, many simulations. + +We have many economies, +and we vary this fraction + +from zero to one. + +I just showed you +the 50-50 economy. + +But this allows everyone to be +in limited commitment, everyone + +to be in moral hazard, +or anywhere in between. + +And so you can see how +GDP, TFP, and so on, + +how these things move +around with the fraction + +of the population that are +subject to moral hazard. + +And partly, this mirrors what +I said before in labor supply. + +But on other things, you can +see things aren't monotone. + +So those are surprises. + +It actually goes up, and +then it comes down again. + +GDP climbs pretty fast, +and then it kind of + +wobbles around a bit. + +We've tried to get rid of +as many wobbles as possible + +for worries that they're +just computational. + +But some of them-- some +of the wobbles remain. + +So I've kind of learned to +not pay too much attention. + +But this is not numerical error. + +This is systematic, this drop. + +And you can see what the +wages and the interest rates + +are doing, and the fraction +of firms for that matter. + +Now, here is back to 1/2, 1/2. + +But within that economy, we have +the limited commitment sector + +and the moral hazard sector. + +Obviously, there is +economy-wide wages + +and interest rates are the same. + +It's one economy clearing. + +But other things vary +across these two columns. + +Probably the most +exciting part is + +this, which is let's look +at labor, for example. + +Labor employed in +the sector 0.38; + +labor supplied by +the sector 0.53. + +So they're exporters +of labor, if you allow + +me to use that terminology. + +Or people are +costlessly migrating + +from the limited commitment +sector to the moral hazard. + +And indeed, you'll pick up +the other side of this thing, + +basically, labor supplied, +0.46; labor demanded, 0.61. + +Now, you say, why isn't +it all zero and one. + +No, no, no, no, no. + +Remember the z's. + +Remember the productivity. + +Every sector has some +really inefficient people + +who shouldn't be running firms. + +They're going to supply +labor no matter what, + +or at least at these +equilibrium wages. + +And the same thing is true +with the flow of funds + +if we had the geographic +decomposition-- + +and we got Mexico to +do this, by the way. + +It's really cool-- +through their CNBV, + +their financial regulator. + +And the question +there, is money flowing + +to Mexico City from +the outlying areas + +as they improve intermediation? + +And what consequences does that +have for the outlying areas? + +Well, here, money's flowing from +the limited commitments sector + +to the moral hazard sector. + +So this is where the +action is, so to speak. + +We don't get a lot of +difference in terms + +of the numbers of firms, +but you're clearly + +seeing differences in +terms of employment size. + +And remember the China paper +was like this, where labor-- + +the allocation of labor +was playing a huge role. + +So-- sorry. + +We had more results +over the weekend. + +We've been trying to get these. + +This, we've had for +a long time, but I'll + +show you something else +that's quite exciting. + +First of all, speed +of transitions-- + +you remember that where a paper +was all about the puzzle, which + +is, why don't miracle +Asian economies grow + +even faster if you believe +they were in a solo world? + +But of course, there is-- + +and then they assume +this financial friction, + +which slowed things down. + +The friction you assume is +going to make a big difference + +to the speed of transitions. + +Actually, here, even +in the steady state, + +you can ask how fast do +people go from an az state + +to an a prime z prime state? + +This is some big Markov matrix. + +It's sort of steady +state, but it's + +transition from +the household level + +from one state to another. + +So you may remember, you +can multiply those matrices + +over and over times each +other, or you can basically + +do an eigenvalue, +eigenvector decomposition. + +And the closer this eigenvalue +is to 1, the slower things are. + +Things are moving. + +The next multiplication +of the matrix + +is kind of very similar-- + +that times the +control [INAUDIBLE] + +very similar to what is +in the previous period. + +It's 0.93. + +That's a very-- sorry. + +0.93 for one; 0.98 +for the other. + +So there's roughly three +more times difference + +in the speed of sort of within +steady state transitions going + +on. + +Now, there's a technical +reason for this, basically. + +On the limited +commitment thing we + +have this forward-looking +savings behavior. + +So people are going +to save their way out + +of these constraints. + +And they can do +it pretty quickly. + +In fact, you're going +to see some homework + +and so on motivated by thinking +through [INAUDIBLE] papers + +and job market papers +and so on, that kind of + +get at this thing, which is-- +the twist is, why doesn't money + +flow from the US to India? + +The answer is, why doesn't India +save its way out of constraints + +more quickly than they seem to? + +So there's discussion in +the literature about that. + +But here we do have constraints. + +It's just that +they're different. + +And essentially +what's going on here + +is you don't want to-- +you don't want that wealth + +to move very fast. + +You're going to balance +off the incentives + +of today's consumption +versus tomorrow's wealth. + +Wealth moves a little bit, +depending on whether epsilon + +is high or low. + +But you don't want it +to move a whole lot. + +Because if it did, that's +the bulk of your utility. + +That's kind of very-- + +that is actually +algebraically in the dual, + +equivalent with discounted +expected utility. + +And so if you move +that quickly, there's + +a big welfare loss +because of the concavity. + +So you don't want +it to move fast. + +So that's-- OK. + +And then if you look +at growth rates, + +the distribution of growth +rates looks like it's all zero. + +Actually, what the point +is, the growth rates + +are all very similar +to each other, + +because there isn't this big +dispersion in the moral hazard + +economy because they +don't move that fast. + +But a limited +commitment-- there's + +a huge dispersion +and growth rate. + +And you can imagine going to +data with this kind of stuff. + +We didn't look at +this in the data. + +But if you have Panel, +you can actually + +look not only at static +firm size distributions + +but the growth rates, and +get some evidence one way + +or the other for one friction. + +Then finally, the weekend-- + +we've had a devil of +a time doing this. + +We start with the +whole economy subject + +to a limited +commitment constraint. + +And then we move it after 10 +periods to a moral hazard. + +Now, this is meant to mimic +some kind of financial reform. + +If you want to be +generous with me, + +think of there being +two constraints, + +and then we managed +to get rid of one. + +Well, that's not quite +what we're doing. + +We kind of substitute limited +commitment for moral hazard. + +Basically, they get rid of +a constraining legal system, + +but it turns out that created +an information problem. + +Anyway, what's +really important is + +that you can actually look +at the transition dynamics. + +Well, let me just +show you the pictures. + +So here, you're +in a steady state, + +and then you do a +financial reform. + +But it's not like-- + +Kaboski, they did-- they left +the financial structure intact, + +and they did real reforms. + +We're leaving everything in +the environment and everything + +intact and doing a +financial reform, hopefully + +in the spirit of what +Levine might have wanted. + +And then we see the implications +of that for deeper levels + +of capitalization. + +And look at the wage rate. + +It's no wonder we had +trouble finding it-- + +pops up like that +instantaneously. + +Now, let me just say, these +things are not easy to compute. + +Because-- and [INAUDIBLE] +going to say something + +about that on Friday. + +Essentially, when you're +out of the steady state, + +you have to figure out +where you're going to go + +and how long it's going +to take to get there. + +And then you've got +to sort of guess + +about the paths of the +interest rates and the wages. + +And of course, any arbitrary +guess about how long it takes + +and how they're going to +move is quite arbitrary. + +So then you need +a systematic way + +to adjust period by period +to get in new guesses + +and then to try to iterate. + +[INAUDIBLE] managed to do it. + +We have their code. + +I've shared it +with many students + +working on related problems. + +It turned out that +their code, which + +is getting better and better +because they're playing around + +with it too, works for this +limited commitment better-- + +much, much better than +it ever worked for us + +with moral hazard. + +We were quite +despondent about being + +able to compute the transitions. + +But evidently, now we're +in business on that. + +So the summary, back +to the big picture, + +is these obstacles matter. + +Ideally, I think, +if you can manage, + +use the microdata to try +to take a stand on what + +the frictions are. + +And through the dynamics +of Euler equations and debt + +overhang and so on, you'll +generate these dynamic paths. + +And they're going to +be general equilibrium + +consequences of the reforms. + +So it's like doing an +experiment on these economies + +to see what would happen. + +And this allows us to begin to +answer those questions I went + +over in the introductory lecture +about finance causes growth, + +but then what? + +What do we do? + +And how do we engineer it? + +And what would we +expect to happen? + +And are there winners +and losers, and so on? \ No newline at end of file diff --git a/fRD43u-pY4A.txt b/fRD43u-pY4A.txt new file mode 100644 index 0000000000000000000000000000000000000000..48bee1853a630e5896083670ce72146185f894a1 --- /dev/null +++ b/fRD43u-pY4A.txt @@ -0,0 +1,16381 @@ +align:start position:0% + +okay so I'm going to start with um you + + align:start position:0% +okay so I'm going to start with um you + + + align:start position:0% +okay so I'm going to start with um you +know something I I also cover in 122 + + align:start position:0% +know something I I also cover in 122 + + + align:start position:0% +know something I I also cover in 122 +which is uh collusion with perfect sort + + align:start position:0% +which is uh collusion with perfect sort + + + align:start position:0% +which is uh collusion with perfect sort +of simplest model of dynamic collusion + + align:start position:0% +of simplest model of dynamic collusion + + + align:start position:0% +of simplest model of dynamic collusion +so you me sort of say the I guess reason + + align:start position:0% +so you me sort of say the I guess reason + + + align:start position:0% +so you me sort of say the I guess reason +for thinking about Dynamic competition + + align:start position:0% +for thinking about Dynamic competition + + + align:start position:0% +for thinking about Dynamic competition +is in part because we think Dynamic + + align:start position:0% +is in part because we think Dynamic + + + align:start position:0% +is in part because we think Dynamic +competition is a very good model for how + + align:start position:0% +competition is a very good model for how + + + align:start position:0% +competition is a very good model for how +many Industries work you know it's + + align:start position:0% +many Industries work you know it's + + + align:start position:0% +many Industries work you know it's +T-Mobile and Verizon and whatever you + + align:start position:0% +T-Mobile and Verizon and whatever you + + + align:start position:0% +T-Mobile and Verizon and whatever you +know competing against each other period + + align:start position:0% +know competing against each other period + + + align:start position:0% +know competing against each other period +after period after period it's the same + + align:start position:0% +after period after period it's the same + + + align:start position:0% +after period after period it's the same +cable companies competing it's the same + + align:start position:0% +cable companies competing it's the same + + + align:start position:0% +cable companies competing it's the same +auto companies competing and many + + align:start position:0% +auto companies competing and many + + + align:start position:0% +auto companies competing and many +Industries with a small number of + + align:start position:0% +Industries with a small number of + + + align:start position:0% +Industries with a small number of +firms the small number of firms reflect + + align:start position:0% +firms the small number of firms reflect + + + align:start position:0% +firms the small number of firms reflect +that it's hard to enter and you have + + align:start position:0% +that it's hard to enter and you have + + + align:start position:0% +that it's hard to enter and you have +those same firms for over and over and + + align:start position:0% +those same firms for over and over and + + + align:start position:0% +those same firms for over and over and +over again um and then this second + + align:start position:0% +over again um and then this second + + + align:start position:0% +over again um and then this second +reason for covering this is you know a + + align:start position:0% +reason for covering this is you know a + + + align:start position:0% +reason for covering this is you know a +lot of this course is about markups and + + align:start position:0% +lot of this course is about markups and + + + align:start position:0% +lot of this course is about markups and +think about where markups come from I've + + align:start position:0% +think about where markups come from I've + + + align:start position:0% +think about where markups come from I've +talked about differentiation as a source + + align:start position:0% +talked about differentiation as a source + + + align:start position:0% +talked about differentiation as a source +of markups and I've talked about search + + align:start position:0% +of markups and I've talked about search + + + align:start position:0% +of markups and I've talked about search +as a source of markups I think we also + + align:start position:0% +as a source of markups I think we also + + + align:start position:0% +as a source of markups I think we also +think that uh Dynamic collusion is + + align:start position:0% +think that uh Dynamic collusion is + + + align:start position:0% +think that uh Dynamic collusion is +another potential source of markups and + + align:start position:0% +another potential source of markups and + + + align:start position:0% +another potential source of markups and +I did do the um R Miller and Weinberg + + align:start position:0% +I did do the um R Miller and Weinberg + + + align:start position:0% +I did do the um R Miller and Weinberg +had that sort of conclusion that it + + align:start position:0% +had that sort of conclusion that it + + + align:start position:0% +had that sort of conclusion that it +looks like when you look at sort of the + + align:start position:0% +looks like when you look at sort of the + + + align:start position:0% +looks like when you look at sort of the +Miller Coors merger part of the effect + + align:start position:0% +Miller Coors merger part of the effect + + + align:start position:0% +Miller Coors merger part of the effect +was Miller and K is no longer pricing in + + align:start position:0% +was Miller and K is no longer pricing in + + + align:start position:0% +was Miller and K is no longer pricing in +static Nash form as they had before uh + + align:start position:0% +static Nash form as they had before uh + + + align:start position:0% +static Nash form as they had before uh +and and ab and Bev as they had before + + align:start position:0% +and and ab and Bev as they had before + + + align:start position:0% +and and ab and Bev as they had before +the merger you know theory of dyamic + + align:start position:0% +the merger you know theory of dyamic + + + align:start position:0% +the merger you know theory of dyamic +collusion is thinking about like how it + + align:start position:0% +collusion is thinking about like how it + + + align:start position:0% +collusion is thinking about like how it +is that we can think about when firms + + align:start position:0% +is that we can think about when firms + + + align:start position:0% +is that we can think about when firms +are going to have markups and or when + + align:start position:0% +are going to have markups and or when + + + align:start position:0% +are going to have markups and or when +they're going to do something other than + + align:start position:0% +they're going to do something other than + + + align:start position:0% +they're going to do something other than +static Mash okay so simplest + + align:start position:0% +static Mash okay so simplest + + + align:start position:0% +static Mash okay so simplest +model I've got n identical firms they + + align:start position:0% +model I've got n identical firms they + + + align:start position:0% +model I've got n identical firms they +have a constant marginal cost of C they + + align:start position:0% +have a constant marginal cost of C they + + + align:start position:0% +have a constant marginal cost of C they +all a discount factor of + + align:start position:0% +all a discount factor of + + + align:start position:0% +all a discount factor of +Delta we're going to have them play the + + align:start position:0% +Delta we're going to have them play the + + + align:start position:0% +Delta we're going to have them play the +simplest betrand pricing game where + + align:start position:0% +simplest betrand pricing game where + + + align:start position:0% +simplest betrand pricing game where +there's some market demand function Q + + align:start position:0% +there's some market demand function Q + + + align:start position:0% +there's some market demand function Q +ofp so that means all of the demand goes + + align:start position:0% +ofp so that means all of the demand goes + + + align:start position:0% +ofp so that means all of the demand goes +to whichever firm charges the lowest + + align:start position:0% +to whichever firm charges the lowest + + + align:start position:0% +to whichever firm charges the lowest +price uh the other firms uh sell zero if + + align:start position:0% +price uh the other firms uh sell zero if + + + align:start position:0% +price uh the other firms uh sell zero if +firms charge equal prices I'll assume + + align:start position:0% +firms charge equal prices I'll assume + + + align:start position:0% +firms charge equal prices I'll assume +they split the + + align:start position:0% +they split the + + + align:start position:0% +they split the +demand um firms all observe prices at + + align:start position:0% +demand um firms all observe prices at + + + align:start position:0% +demand um firms all observe prices at +the end of every period so you know the + + align:start position:0% +the end of every period so you know the + + + align:start position:0% +the end of every period so you know the +history um at the history at time T is + + align:start position:0% +history um at the history at time T is + + + align:start position:0% +history um at the history at time T is +HT minus one it's all the prices charged + + align:start position:0% +HT minus one it's all the prices charged + + + align:start position:0% +HT minus one it's all the prices charged +by all the firms in every period to less + + align:start position:0% +by all the firms in every period to less + + + align:start position:0% +by all the firms in every period to less +than T minus one and a strategy in a + + align:start position:0% +than T minus one and a strategy in a + + + align:start position:0% +than T minus one and a strategy in a +repeated game is a function from I sets + + align:start position:0% +repeated game is a function from I sets + + + align:start position:0% +repeated game is a function from I sets +its time T price as a function of + + align:start position:0% +its time T price as a function of + + + align:start position:0% +its time T price as a function of +everything that it's observed in all + + align:start position:0% +everything that it's observed in all + + + align:start position:0% +everything that it's observed in all +previous + + align:start position:0% +previous + + + align:start position:0% +previous +periods uh and when I teach this model + + align:start position:0% +periods uh and when I teach this model + + + align:start position:0% +periods uh and when I teach this model +in 122 I note that um this model has a + + align:start position:0% +in 122 I note that um this model has a + + + align:start position:0% +in 122 I note that um this model has a +subgame perfect dealm that looks like + + align:start position:0% +subgame perfect dealm that looks like + + + align:start position:0% +subgame perfect dealm that looks like +perfect competition the static Nash + + align:start position:0% +perfect competition the static Nash + + + align:start position:0% +perfect competition the static Nash +equilibrium which is just everybody + + align:start position:0% +equilibrium which is just everybody + + + align:start position:0% +equilibrium which is just everybody +plays price equal to cost in every + + align:start position:0% +plays price equal to cost in every + + + align:start position:0% +plays price equal to cost in every +period um but if Delta is at least 1 - + + align:start position:0% +period um but if Delta is at least 1 - + + + align:start position:0% +period um but if Delta is at least 1 - +one /n this model also has a subgame + + align:start position:0% +one /n this model also has a subgame + + + align:start position:0% +one /n this model also has a subgame +perfect that looks like perfect + + align:start position:0% +perfect that looks like perfect + + + align:start position:0% +perfect that looks like perfect +collusion and what that is is the firms + + align:start position:0% +collusion and what that is is the firms + + + align:start position:0% +collusion and what that is is the firms +charge the Monopoly price as long as + + align:start position:0% +charge the Monopoly price as long as + + + align:start position:0% +charge the Monopoly price as long as +everyone has charged the Monopoly price + + align:start position:0% +everyone has charged the Monopoly price + + + align:start position:0% +everyone has charged the Monopoly price +in every previous period And if anyone + + align:start position:0% +in every previous period And if anyone + + + align:start position:0% +in every previous period And if anyone +ever deviates they set price equal to C + + align:start position:0% +ever deviates they set price equal to C + + + align:start position:0% +ever deviates they set price equal to C +in all future periods you know that + + align:start position:0% +in all future periods you know that + + + align:start position:0% +in all future periods you know that +price War punishment as we would call it + + align:start position:0% +price War punishment as we would call it + + + align:start position:0% +price War punishment as we would call it +that price War punishment is going to + + align:start position:0% +that price War punishment is going to + + + align:start position:0% +that price War punishment is going to +deter people from deviating and Lead + + align:start position:0% +deter people from deviating and Lead + + + align:start position:0% +deter people from deviating and Lead +everyone to want the coordinate on the + + align:start position:0% +everyone to want the coordinate on the + + + align:start position:0% +everyone to want the coordinate on the +Monopoly price if they're patient and + + align:start position:0% +Monopoly price if they're patient and + + + align:start position:0% +Monopoly price if they're patient and +this is how patient they have to + + align:start position:0% +this is how patient they have to + + + align:start position:0% +this is how patient they have to +be um so some comments you know this + + align:start position:0% +be um so some comments you know this + + + align:start position:0% +be um so some comments you know this +model identifies another factor that can + + align:start position:0% +model identifies another factor that can + + + align:start position:0% +model identifies another factor that can +determine markups uh in particular just + + align:start position:0% +determine markups uh in particular just + + + align:start position:0% +determine markups uh in particular just +repeated competition can lead to markups + + align:start position:0% +repeated competition can lead to markups + + + align:start position:0% +repeated competition can lead to markups +with you know no product differentiation + + align:start position:0% +with you know no product differentiation + + + align:start position:0% +with you know no product differentiation +no search cost nothing else um it has + + align:start position:0% +no search cost nothing else um it has + + + align:start position:0% +no search cost nothing else um it has +you know a lot of natural comparative + + align:start position:0% +you know a lot of natural comparative + + + align:start position:0% +you know a lot of natural comparative +Statics so it's easier to stay sustain + + align:start position:0% +Statics so it's easier to stay sustain + + + align:start position:0% +Statics so it's easier to stay sustain +collusion when Delta's larger so when + + align:start position:0% +collusion when Delta's larger so when + + + align:start position:0% +collusion when Delta's larger so when +Delta's above this number you can + + align:start position:0% +Delta's above this number you can + + + align:start position:0% +Delta's above this number you can +collude when Delta's below that number + + align:start position:0% +collude when Delta's below that number + + + align:start position:0% +collude when Delta's below that number +you cannot um so you know what could + + align:start position:0% +you cannot um so you know what could + + + align:start position:0% +you cannot um so you know what could +delta mean you if you think about Delta + + align:start position:0% +delta mean you if you think about Delta + + + align:start position:0% +delta mean you if you think about Delta +in this model Delta is the time the disc + + align:start position:0% +in this model Delta is the time the disc + + + align:start position:0% +in this model Delta is the time the disc +account you apply in between you see + + align:start position:0% +account you apply in between you see + + + align:start position:0% +account you apply in between you see +someone cheat on the agreement and then + + align:start position:0% +someone cheat on the agreement and then + + + align:start position:0% +someone cheat on the agreement and then +you start punishing them and so Delta is + + align:start position:0% +you start punishing them and so Delta is + + + align:start position:0% +you start punishing them and so Delta is +your sort of time rate of discounting + + align:start position:0% +your sort of time rate of discounting + + + align:start position:0% +your sort of time rate of discounting +between those two events someone cheats + + align:start position:0% +between those two events someone cheats + + + align:start position:0% +between those two events someone cheats +I start punishing so what makes + + align:start position:0% +I start punishing so what makes + + + align:start position:0% +I start punishing so what makes +collusion harder um one would be + + align:start position:0% +collusion harder um one would be + + + align:start position:0% +collusion harder um one would be +detection lags if people cheat on the + + align:start position:0% +detection lags if people cheat on the + + + align:start position:0% +detection lags if people cheat on the +agreement you see you know you don't see + + align:start position:0% +agreement you see you know you don't see + + + align:start position:0% +agreement you see you know you don't see +them cheat for a while that makes it + + align:start position:0% +them cheat for a while that makes it + + + align:start position:0% +them cheat for a while that makes it +harder to + + align:start position:0% +harder to + + + align:start position:0% +harder to +collude um lumpy demands you know in + + align:start position:0% +collude um lumpy demands you know in + + + align:start position:0% +collude um lumpy demands you know in +some Industries firms are selling Goods + + align:start position:0% +some Industries firms are selling Goods + + + align:start position:0% +some Industries firms are selling Goods +over over and over again and see their + + align:start position:0% +over over and over again and see their + + + align:start position:0% +over over and over again and see their +demand coming in in real time you know + + align:start position:0% +demand coming in in real time you know + + + align:start position:0% +demand coming in in real time you know +other demand like if you think + + align:start position:0% +other demand like if you think + + + align:start position:0% +other demand like if you think +about uh you know rathon competing with + + align:start position:0% +about uh you know rathon competing with + + + align:start position:0% +about uh you know rathon competing with +flock heat if they're still separate + + align:start position:0% +flock heat if they're still separate + + + align:start position:0% +flock heat if they're still separate +companies to produce you know fighter + + align:start position:0% +companies to produce you know fighter + + + align:start position:0% +companies to produce you know fighter +Next Generation fighter jets for US + + align:start position:0% +Next Generation fighter jets for US + + + align:start position:0% +Next Generation fighter jets for US +Government if those orders for new F + + align:start position:0% +Government if those orders for new F + + + align:start position:0% +Government if those orders for new F +generation fighter Dre come along once + + align:start position:0% +generation fighter Dre come along once + + + align:start position:0% +generation fighter Dre come along once +every 15 years if someone cheats on the + + align:start position:0% +every 15 years if someone cheats on the + + + align:start position:0% +every 15 years if someone cheats on the +agreement to collude on prices and you + + align:start position:0% +agreement to collude on prices and you + + + align:start position:0% +agreement to collude on prices and you +can't do anything about it for 15 years + + align:start position:0% +can't do anything about it for 15 years + + + align:start position:0% +can't do anything about it for 15 years +Delta is going to be very small so the + + align:start position:0% +Delta is going to be very small so the + + + align:start position:0% +Delta is going to be very small so the +you know whether demand is sort of + + align:start position:0% +you know whether demand is sort of + + + align:start position:0% +you know whether demand is sort of +coming in continuously or Lumpy matters + + align:start position:0% +coming in continuously or Lumpy matters + + + align:start position:0% +coming in continuously or Lumpy matters +um it's easier to collude in uh growing + + align:start position:0% +um it's easier to collude in uh growing + + + align:start position:0% +um it's easier to collude in uh growing +markets it's easier to collude in + + align:start position:0% +markets it's easier to collude in + + + align:start position:0% +markets it's easier to collude in +growing markets because again the basic + + align:start position:0% +growing markets because again the basic + + + align:start position:0% +growing markets because again the basic +consideration here is how much do you + + align:start position:0% +consideration here is how much do you + + + align:start position:0% +consideration here is how much do you +hate how much do you dislike this + + align:start position:0% +hate how much do you dislike this + + + align:start position:0% +hate how much do you dislike this +punishment of switching to pricing at + + align:start position:0% +punishment of switching to pricing at + + + align:start position:0% +punishment of switching to pricing at +marginal cost and losing the collusive + + align:start position:0% +marginal cost and losing the collusive + + + align:start position:0% +marginal cost and losing the collusive +profits and how much does that deter you + + align:start position:0% +profits and how much does that deter you + + + align:start position:0% +profits and how much does that deter you +from deviating if the future is more + + align:start position:0% +from deviating if the future is more + + + align:start position:0% +from deviating if the future is more +important than the present then that's + + align:start position:0% +important than the present then that's + + + align:start position:0% +important than the present then that's +like um Delta is large that makes + + align:start position:0% +like um Delta is large that makes + + + align:start position:0% +like um Delta is large that makes +collusion easy uh and on the other hand + + align:start position:0% +collusion easy uh and on the other hand + + + align:start position:0% +collusion easy uh and on the other hand +like techn IAL change like if this is a + + align:start position:0% +like techn IAL change like if this is a + + + align:start position:0% +like techn IAL change like if this is a +market that's going to be replaced by + + align:start position:0% +market that's going to be replaced by + + + align:start position:0% +market that's going to be replaced by +some other product then the future + + align:start position:0% +some other product then the future + + + align:start position:0% +some other product then the future +doesn't matter if the future doesn't + + align:start position:0% +doesn't matter if the future doesn't + + + align:start position:0% +doesn't matter if the future doesn't +matter then it's hard to collude and so + + align:start position:0% +matter then it's hard to collude and so + + + align:start position:0% +matter then it's hard to collude and so +you might see collusion breaking down + + align:start position:0% +you might see collusion breaking down + + + align:start position:0% +you might see collusion breaking down +just because on when the market is on + + align:start position:0% +just because on when the market is on + + + align:start position:0% +just because on when the market is on +its way out collusion could break + + align:start position:0% +its way out collusion could break + + + align:start position:0% +its way out collusion could break +down okay um model also has a nice + + align:start position:0% +down okay um model also has a nice + + + align:start position:0% +down okay um model also has a nice +comparative static that it's easier to + + align:start position:0% +comparative static that it's easier to + + + align:start position:0% +comparative static that it's easier to +sustain collusion when n is small um + + align:start position:0% +sustain collusion when n is small um + + + align:start position:0% +sustain collusion when n is small um +because again when n is small one minus + + align:start position:0% +because again when n is small one minus + + + align:start position:0% +because again when n is small one minus +one over N is a smaller number so more + + align:start position:0% +one over N is a smaller number so more + + + align:start position:0% +one over N is a smaller number so more +markets where you could + + align:start position:0% +markets where you could + + + align:start position:0% +markets where you could +collude um + + align:start position:0% +collude um + + + align:start position:0% +collude um +you another Con on this is that this + + align:start position:0% +you another Con on this is that this + + + align:start position:0% +you another Con on this is that this +Theory also in some ways suggests that + + align:start position:0% +Theory also in some ways suggests that + + + align:start position:0% +Theory also in some ways suggests that +everything we've done in the entire + + align:start position:0% +everything we've done in the entire + + + align:start position:0% +everything we've done in the entire +semester is almost worthless because + + align:start position:0% +semester is almost worthless because + + + align:start position:0% +semester is almost worthless because +anytime you have a market with a small + + align:start position:0% +anytime you have a market with a small + + + align:start position:0% +anytime you have a market with a small +number of firms how much differentiation + + align:start position:0% +number of firms how much differentiation + + + align:start position:0% +number of firms how much differentiation +there is how much search costs there are + + align:start position:0% +there is how much search costs there are + + + align:start position:0% +there is how much search costs there are +how much of you know multi you know + + align:start position:0% +how much of you know multi you know + + + align:start position:0% +how much of you know multi you know +whatever you know how much multi-product + + align:start position:0% +whatever you know how much multi-product + + + align:start position:0% +whatever you know how much multi-product +competition all of that sort of stuff in + + align:start position:0% +competition all of that sort of stuff in + + + align:start position:0% +competition all of that sort of stuff in +some sense is irrelevant because the + + align:start position:0% +some sense is irrelevant because the + + + align:start position:0% +some sense is irrelevant because the +firms could collude on anything and so + + align:start position:0% +firms could collude on anything and so + + + align:start position:0% +firms could collude on anything and so +you know maybe one suggestion is that + + align:start position:0% +you know maybe one suggestion is that + + + align:start position:0% +you know maybe one suggestion is that +you know we either have to sort of think + + align:start position:0% +you know we either have to sort of think + + + align:start position:0% +you know we either have to sort of think +about which equilibrium in this repeated + + align:start position:0% +about which equilibrium in this repeated + + + align:start position:0% +about which equilibrium in this repeated +game we think is going to happen or we + + align:start position:0% +game we think is going to happen or we + + + align:start position:0% +game we think is going to happen or we +have to just accept that we can't always + + align:start position:0% +have to just accept that we can't always + + + align:start position:0% +have to just accept that we can't always +forecast what's going on and we're + + align:start position:0% +forecast what's going on and we're + + + align:start position:0% +forecast what's going on and we're +always we may always be surprised about + + align:start position:0% +always we may always be surprised about + + + align:start position:0% +always we may always be surprised about +how things are + + align:start position:0% +how things are + + + align:start position:0% +how things are +happening the other thing I'd like to + + align:start position:0% +happening the other thing I'd like to + + + align:start position:0% +happening the other thing I'd like to +say about this model is that numerically + + align:start position:0% +say about this model is that numerically + + + align:start position:0% +say about this model is that numerically +it's it's just giving a wrong answer you + + align:start position:0% +it's it's just giving a wrong answer you + + + align:start position:0% +it's it's just giving a wrong answer you +know it's saying that with Delta at + + align:start position:0% +know it's saying that with Delta at + + + align:start position:0% +know it's saying that with Delta at +least 1 minus one over n we can conclude + + align:start position:0% +least 1 minus one over n we can conclude + + + align:start position:0% +least 1 minus one over n we can conclude +we can collude and if you think about it + + align:start position:0% +we can collude and if you think about it + + + align:start position:0% +we can collude and if you think about it +you know like if you think about an + + align:start position:0% +you know like if you think about an + + + align:start position:0% +you know like if you think about an +typical industry with you know like + + align:start position:0% +typical industry with you know like + + + align:start position:0% +typical industry with you know like +prices are posted on the Internet or + + align:start position:0% +prices are posted on the Internet or + + + align:start position:0% +prices are posted on the Internet or +whatever how long does it take you to + + align:start position:0% +whatever how long does it take you to + + + align:start position:0% +whatever how long does it take you to +observe that your rival has colluded um + + align:start position:0% +observe that your rival has colluded um + + + align:start position:0% +observe that your rival has colluded um +you know like if you're T-Mobile and you + + align:start position:0% +you know like if you're T-Mobile and you + + + align:start position:0% +you know like if you're T-Mobile and you +see Verizon changing their prices they + + align:start position:0% +see Verizon changing their prices they + + + align:start position:0% +see Verizon changing their prices they +put a big TV ad campaign saying they've + + align:start position:0% +put a big TV ad campaign saying they've + + + align:start position:0% +put a big TV ad campaign saying they've +changed their prices within a week or + + align:start position:0% +changed their prices within a week or + + + align:start position:0% +changed their prices within a week or +within a day you know what they've done + + align:start position:0% +within a day you know what they've done + + + align:start position:0% +within a day you know what they've done +what's the discount Factor over a day + + align:start position:0% +what's the discount Factor over a day + + + align:start position:0% +what's the discount Factor over a day +you know discount factor of a day is you + + align:start position:0% +you know discount factor of a day is you + + + align:start position:0% +you know discount factor of a day is you +know 0.00 you know or Delta should be + + align:start position:0% +know 0.00 you know or Delta should be + + + align:start position:0% +know 0.00 you know or Delta should be +9999 or 59 or whatever ever you know you + + align:start position:0% +9999 or 59 or whatever ever you know you + + + align:start position:0% +9999 or 59 or whatever ever you know you +could compete collude with thousands of + + align:start position:0% +could compete collude with thousands of + + + align:start position:0% +could compete collude with thousands of +firms and and so I think that you know + + align:start position:0% +firms and and so I think that you know + + + align:start position:0% +firms and and so I think that you know +while you know even you put n equals 100 + + align:start position:0% +while you know even you put n equals 100 + + + align:start position:0% +while you know even you put n equals 100 +Delta's 0.99 .99 is a good discount + + align:start position:0% +Delta's 0.99 .99 is a good discount + + + align:start position:0% +Delta's 0.99 .99 is a good discount +factor for a month or less than a month + + align:start position:0% +factor for a month or less than a month + + + align:start position:0% +factor for a month or less than a month +so this would say you know the hundred + + align:start position:0% +so this would say you know the hundred + + + align:start position:0% +so this would say you know the hundred +firms even if it takes you a month to + + align:start position:0% +firms even if it takes you a month to + + + align:start position:0% +firms even if it takes you a month to +realize your Rivals have changed their + + align:start position:0% +realize your Rivals have changed their + + + align:start position:0% +realize your Rivals have changed their +prices you could collude perfectly and I + + align:start position:0% +prices you could collude perfectly and I + + + align:start position:0% +prices you could collude perfectly and I +think we don't think that collusion + + align:start position:0% +think we don't think that collusion + + + align:start position:0% +think we don't think that collusion +typically happens with 100 firms when + + align:start position:0% +typically happens with 100 firms when + + + align:start position:0% +typically happens with 100 firms when +you have month-long delays so there's + + align:start position:0% +you have month-long delays so there's + + + align:start position:0% +you have month-long delays so there's +something about collusion is just harder + + align:start position:0% +something about collusion is just harder + + + align:start position:0% +something about collusion is just harder +than this model suggests it should be + + align:start position:0% +than this model suggests it should be + + + align:start position:0% +than this model suggests it should be +okay and so you know one thing you find + + align:start position:0% +okay and so you know one thing you find + + + align:start position:0% +okay and so you know one thing you find +the io literature is uh bunch of factors + + align:start position:0% +the io literature is uh bunch of factors + + + align:start position:0% +the io literature is uh bunch of factors +that all may make collusion harder than + + align:start position:0% +that all may make collusion harder than + + + align:start position:0% +that all may make collusion harder than +it would be in this model so I I thought + + align:start position:0% +it would be in this model so I I thought + + + align:start position:0% +it would be in this model so I I thought +you know I would do is I'm just going to + + align:start position:0% +you know I would do is I'm just going to + + + align:start position:0% +you know I would do is I'm just going to +um it's an old fairly old literature and + + align:start position:0% +um it's an old fairly old literature and + + + align:start position:0% +um it's an old fairly old literature and +it's all well covered into roll's book + + align:start position:0% +it's all well covered into roll's book + + + align:start position:0% +it's all well covered into roll's book +so I'll do a few of those models but + + align:start position:0% +so I'll do a few of those models but + + + align:start position:0% +so I'll do a few of those models but +maybe I'll go through some of them kind + + align:start position:0% +maybe I'll go through some of them kind + + + align:start position:0% +maybe I'll go through some of them kind +of quickly so the one I did want to do + + align:start position:0% +of quickly so the one I did want to do + + + align:start position:0% +of quickly so the one I did want to do +in more detail was this sort of + + align:start position:0% +in more detail was this sort of + + + align:start position:0% +in more detail was this sort of +literature on collusion with imperfect + + align:start position:0% +literature on collusion with imperfect + + + align:start position:0% +literature on collusion with imperfect +monitoring and I I think this is I think + + align:start position:0% +monitoring and I I think this is I think + + + align:start position:0% +monitoring and I I think this is I think +what we think of as probably the most + + align:start position:0% +what we think of as probably the most + + + align:start position:0% +what we think of as probably the most +important reason why + + align:start position:0% +important reason why + + + align:start position:0% +important reason why +uh collusion is hard which is that you + + align:start position:0% +uh collusion is hard which is that you + + + align:start position:0% +uh collusion is hard which is that you +know + + align:start position:0% +know + + + align:start position:0% +know +it's often hard to know when your Rivals + + align:start position:0% +it's often hard to know when your Rivals + + + align:start position:0% +it's often hard to know when your Rivals +Have Cheated you know it's easy to know + + align:start position:0% +Have Cheated you know it's easy to know + + + align:start position:0% +Have Cheated you know it's easy to know +when your Rivals are cheated if your + + align:start position:0% +when your Rivals are cheated if your + + + align:start position:0% +when your Rivals are cheated if your +Rivals are consumer facing businesses + + align:start position:0% +Rivals are consumer facing businesses + + + align:start position:0% +Rivals are consumer facing businesses +that have to post prices that are + + align:start position:0% +that have to post prices that are + + + align:start position:0% +that have to post prices that are +visible but in many Industries where + + align:start position:0% +visible but in many Industries where + + + align:start position:0% +visible but in many Industries where +you're sort of selling to businesses or + + align:start position:0% +you're sort of selling to businesses or + + + align:start position:0% +you're sort of selling to businesses or +selling elsewhere or selling with + + align:start position:0% +selling elsewhere or selling with + + + align:start position:0% +selling elsewhere or selling with +negotiated prices it can be much harder + + align:start position:0% +negotiated prices it can be much harder + + + align:start position:0% +negotiated prices it can be much harder +to know if your Rivals are cheating on + + align:start position:0% +to know if your Rivals are cheating on + + + align:start position:0% +to know if your Rivals are cheating on +an agreement so I'm going to discuss + + align:start position:0% +an agreement so I'm going to discuss + + + align:start position:0% +an agreement so I'm going to discuss +this as you know ideas due to green and + + align:start position:0% +this as you know ideas due to green and + + + align:start position:0% +this as you know ideas due to green and +Porter this this version of the model + + align:start position:0% +Porter this this version of the model + + + align:start position:0% +Porter this this version of the model +I'm giving you here is the one that's + + align:start position:0% +I'm giving you here is the one that's + + + align:start position:0% +I'm giving you here is the one that's +just out of terr's textbook where + + align:start position:0% +just out of terr's textbook where + + + align:start position:0% +just out of terr's textbook where +terroll sort of reconfigured it to be a + + align:start position:0% +terroll sort of reconfigured it to be a + + + align:start position:0% +terroll sort of reconfigured it to be a +easier model to solve but you know not + + align:start position:0% +easier model to solve but you know not + + + align:start position:0% +easier model to solve but you know not +obviously not as realistic but so in + + align:start position:0% +obviously not as realistic but so in + + + align:start position:0% +obviously not as realistic but so in +this story uh I've got two firms they + + align:start position:0% +this story uh I've got two firms they + + + align:start position:0% +this story uh I've got two firms they +have a constant marginal cost of c and + + align:start position:0% +have a constant marginal cost of c and + + + align:start position:0% +have a constant marginal cost of c and +they're engaged in brand + + align:start position:0% +they're engaged in brand + + + align:start position:0% +they're engaged in brand +competition and market demand is noisy + + align:start position:0% +competition and market demand is noisy + + + align:start position:0% +competition and market demand is noisy +um so market demand is either Q of p + + align:start position:0% +um so market demand is either Q of p + + + align:start position:0% +um so market demand is either Q of p +with some probability 1 minus alpha or + + align:start position:0% +with some probability 1 minus alpha or + + + align:start position:0% +with some probability 1 minus alpha or +it's zero with probability Alpha so you + + align:start position:0% +it's zero with probability Alpha so you + + + align:start position:0% +it's zero with probability Alpha so you +know where that might make sense is you + + align:start position:0% +know where that might make sense is you + + + align:start position:0% +know where that might make sense is you +know you could have two firms that are + + align:start position:0% +know you could have two firms that are + + + align:start position:0% +know you could have two firms that are +competing to supply computer equipment + + align:start position:0% +competing to supply computer equipment + + + align:start position:0% +competing to supply computer equipment +to some large business and many months + + align:start position:0% +to some large business and many months + + + align:start position:0% +to some large business and many months +that business calls them up and says I + + align:start position:0% +that business calls them up and says I + + + align:start position:0% +that business calls them up and says I +need 132 new computers or I need 147 new + + align:start position:0% +need 132 new computers or I need 147 new + + + align:start position:0% +need 132 new computers or I need 147 new +desk chairs or whatever um but then some + + align:start position:0% +desk chairs or whatever um but then some + + + align:start position:0% +desk chairs or whatever um but then some +months it doesn't call so you know if + + align:start position:0% +months it doesn't call so you know if + + + align:start position:0% +months it doesn't call so you know if +there's sort of these two levels of + + align:start position:0% +there's sort of these two levels of + + + align:start position:0% +there's sort of these two levels of +demand either there's demand Q of P + + align:start position:0% +demand either there's demand Q of P + + + align:start position:0% +demand either there's demand Q of P +because the firm places a large order + + align:start position:0% +because the firm places a large order + + + align:start position:0% +because the firm places a large order +with one of you and it's + + align:start position:0% +with one of you and it's + + + align:start position:0% +with one of you and it's +zero um I'm going to assume that demand + + align:start position:0% +zero um I'm going to assume that demand + + + align:start position:0% +zero um I'm going to assume that demand +goes to the lower priced firm uh or + + align:start position:0% +goes to the lower priced firm uh or + + + align:start position:0% +goes to the lower priced firm uh or +splits 50/50 if the prices are equal and + + align:start position:0% +splits 50/50 if the prices are equal and + + + align:start position:0% +splits 50/50 if the prices are equal and +I'm going to assume there's imperfect + + align:start position:0% +I'm going to assume there's imperfect + + + align:start position:0% +I'm going to assume there's imperfect +observability in that firms see whether + + align:start position:0% +observability in that firms see whether + + + align:start position:0% +observability in that firms see whether +they've made a delivery to the to the + + align:start position:0% +they've made a delivery to the to the + + + align:start position:0% +they've made a delivery to the to the +customer uh but they don't know what + + align:start position:0% +customer uh but they don't know what + + + align:start position:0% +customer uh but they don't know what +their Rivals price is or what the Rival + + align:start position:0% +their Rivals price is or what the Rival + + + align:start position:0% +their Rivals price is or what the Rival +sales are so you know you both have + + align:start position:0% +sales are so you know you both have + + + align:start position:0% +sales are so you know you both have +websites websites give your official + + align:start position:0% +websites websites give your official + + + align:start position:0% +websites websites give your official +price + + align:start position:0% +price + + + align:start position:0% +price +but you don't know whether the firm + + align:start position:0% +but you don't know whether the firm + + + align:start position:0% +but you don't know whether the firm +called your rival and said can you give + + align:start position:0% +called your rival and said can you give + + + align:start position:0% +called your rival and said can you give +me a 10% discount and I'll buy all my + + align:start position:0% +me a 10% discount and I'll buy all my + + + align:start position:0% +me a 10% discount and I'll buy all my +stuff from you this month and then they + + align:start position:0% +stuff from you this month and then they + + + align:start position:0% +stuff from you this month and then they +did and then they shipped it to them all + + align:start position:0% +did and then they shipped it to them all + + + align:start position:0% +did and then they shipped it to them all +you can observe is your own demand so + + align:start position:0% +you can observe is your own demand so + + + align:start position:0% +you can observe is your own demand so +the you know difficulty when that + + align:start position:0% +the you know difficulty when that + + + align:start position:0% +the you know difficulty when that +happens is we get this imperfect + + align:start position:0% +happens is we get this imperfect + + + align:start position:0% +happens is we get this imperfect +observability suppose there's some month + + align:start position:0% +observability suppose there's some month + + + align:start position:0% +observability suppose there's some month +where I get zero + + align:start position:0% +where I get zero + + + align:start position:0% +where I get zero +demand there one of two things happened + + align:start position:0% +demand there one of two things happened + + + align:start position:0% +demand there one of two things happened +one thing that could have happened is + + align:start position:0% +one thing that could have happened is + + + align:start position:0% +one thing that could have happened is +we're just in a low demand month and the + + align:start position:0% +we're just in a low demand month and the + + + align:start position:0% +we're just in a low demand month and the +firm didn't take place any orders the + + align:start position:0% +firm didn't take place any orders the + + + align:start position:0% +firm didn't take place any orders the +other thing that could have happened is + + align:start position:0% +other thing that could have happened is + + + align:start position:0% +other thing that could have happened is +the fir my rival is Che in on the + + align:start position:0% +the fir my rival is Che in on the + + + align:start position:0% +the fir my rival is Che in on the +agreement and the firm did make an order + + align:start position:0% +agreement and the firm did make an order + + + align:start position:0% +agreement and the firm did make an order +and all the the entire order went to my + + align:start position:0% +and all the the entire order went to my + + + align:start position:0% +and all the the entire order went to my +arrival okay um and you know obviously + + align:start position:0% +arrival okay um and you know obviously + + + align:start position:0% +arrival okay um and you know obviously +you could call your rival and say oh you + + align:start position:0% +you could call your rival and say oh you + + + align:start position:0% +you could call your rival and say oh you +know I got zero demand how about you and + + align:start position:0% +know I got zero demand how about you and + + + align:start position:0% +know I got zero demand how about you and +then they can be like yeah zero demand + + align:start position:0% +then they can be like yeah zero demand + + + align:start position:0% +then they can be like yeah zero demand +me too or whatever and you just don't + + align:start position:0% +me too or whatever and you just don't + + + align:start position:0% +me too or whatever and you just don't +know are they lying to you or is this + + align:start position:0% +know are they lying to you or is this + + + align:start position:0% +know are they lying to you or is this +really a you know what happened um so + + align:start position:0% +really a you know what happened um so + + + align:start position:0% +really a you know what happened um so +immediate + + align:start position:0% +immediate + + + align:start position:0% +immediate +conclusion no matter what the discount + + align:start position:0% +conclusion no matter what the discount + + + align:start position:0% +conclusion no matter what the discount +factor is this model can't have an + + align:start position:0% +factor is this model can't have an + + + align:start position:0% +factor is this model can't have an +equilibrium in which both firms always + + align:start position:0% +equilibrium in which both firms always + + + align:start position:0% +equilibrium in which both firms always +charge the Monopoly price on the + + align:start position:0% +charge the Monopoly price on the + + + align:start position:0% +charge the Monopoly price on the +equilibrium path + + align:start position:0% +equilibrium path + + + align:start position:0% +equilibrium path +because if you had an equilibrium where + + align:start position:0% +because if you had an equilibrium where + + + align:start position:0% +because if you had an equilibrium where +both firms were always charging the + + align:start position:0% +both firms were always charging the + + + align:start position:0% +both firms were always charging the +Monopoly price you know there would be + + align:start position:0% +Monopoly price you know there would be + + + align:start position:0% +Monopoly price you know there would be +some chance given that these are IID + + align:start position:0% +some chance given that these are IID + + + align:start position:0% +some chance given that these are IID +that you'd have like a million periods + + align:start position:0% +that you'd have like a million periods + + + align:start position:0% +that you'd have like a million periods +in a row where there's no demand and if + + align:start position:0% +in a row where there's no demand and if + + + align:start position:0% +in a row where there's no demand and if +it was in every period on the + + align:start position:0% +it was in every period on the + + + align:start position:0% +it was in every period on the +equilibrium path you always charge + + align:start position:0% +equilibrium path you always charge + + + align:start position:0% +equilibrium path you always charge +Monopoly price then after that million + + align:start position:0% +Monopoly price then after that million + + + align:start position:0% +Monopoly price then after that million +periods of Z million zeros in a row you + + align:start position:0% +periods of Z million zeros in a row you + + + align:start position:0% +periods of Z million zeros in a row you +still have to have both firms charged a + + align:start position:0% +still have to have both firms charged a + + + align:start position:0% +still have to have both firms charged a +Monopoly price but then if that was + + align:start position:0% +Monopoly price but then if that was + + + align:start position:0% +Monopoly price but then if that was +going to happen you know obviously it's + + align:start position:0% +going to happen you know obviously it's + + + align:start position:0% +going to happen you know obviously it's +better for you to cheat in the first + + align:start position:0% +better for you to cheat in the first + + + align:start position:0% +better for you to cheat in the first +million periods in a row and sell it + + align:start position:0% +million periods in a row and sell it + + + align:start position:0% +million periods in a row and sell it +sell the entire Market instead of half + + align:start position:0% +sell the entire Market instead of half + + + align:start position:0% +sell the entire Market instead of half +the market and leave your rival with + + align:start position:0% +the market and leave your rival with + + + align:start position:0% +the market and leave your rival with +nothing then to follow the equilibrium + + align:start position:0% +nothing then to follow the equilibrium + + + align:start position:0% +nothing then to follow the equilibrium +so the fact that we've got that + + align:start position:0% +so the fact that we've got that + + + align:start position:0% +so the fact that we've got that +fundamental unobservability means + + align:start position:0% +fundamental unobservability means + + + align:start position:0% +fundamental unobservability means +there's no perfect collusions just + + align:start position:0% +there's no perfect collusions just + + + align:start position:0% +there's no perfect collusions just +impossible no matter how patient firms + + align:start position:0% +impossible no matter how patient firms + + + align:start position:0% +impossible no matter how patient firms +are okay um and then you know I think + + align:start position:0% +are okay um and then you know I think + + + align:start position:0% +are okay um and then you know I think +the key Insight of green importer is + + align:start position:0% +the key Insight of green importer is + + + align:start position:0% +the key Insight of green importer is +that while perfect collusion is + + align:start position:0% +that while perfect collusion is + + + align:start position:0% +that while perfect collusion is +impossible you can get partial ction in + + align:start position:0% +impossible you can get partial ction in + + + align:start position:0% +impossible you can get partial ction in +a model like this so + + align:start position:0% +a model like this so + + + align:start position:0% +a model like this so +um uh proposition if Alpha is less than + + align:start position:0% +um uh proposition if Alpha is less than + + + align:start position:0% +um uh proposition if Alpha is less than +a half which you should think of as the + + align:start position:0% +a half which you should think of as the + + + align:start position:0% +a half which you should think of as the +sort of noise is not too large and Delta + + align:start position:0% +sort of noise is not too large and Delta + + + align:start position:0% +sort of noise is not too large and Delta +sufficiently close to one the model has + + align:start position:0% +sufficiently close to one the model has + + + align:start position:0% +sufficiently close to one the model has +a partially clusive equilibrium and what + + align:start position:0% +a partially clusive equilibrium and what + + + align:start position:0% +a partially clusive equilibrium and what +happens in this partially clusive + + align:start position:0% +happens in this partially clusive + + + align:start position:0% +happens in this partially clusive +equilibrium is the firms initially set + + align:start position:0% +equilibrium is the firms initially set + + + align:start position:0% +equilibrium is the firms initially set +the Monopoly + + align:start position:0% +the Monopoly + + + align:start position:0% +the Monopoly +price and then if they ever get zero + + align:start position:0% +price and then if they ever get zero + + + align:start position:0% +price and then if they ever get zero +demand they switch to C for capital T + + align:start position:0% +demand they switch to C for capital T + + + align:start position:0% +demand they switch to C for capital T +periods and then they go back to the + + align:start position:0% +periods and then they go back to the + + + align:start position:0% +periods and then they go back to the +Monopoly price so what we would + + align:start position:0% +Monopoly price so what we would + + + align:start position:0% +Monopoly price so what we would +see you know what we would observe in + + align:start position:0% +see you know what we would observe in + + + align:start position:0% +see you know what we would observe in +this model + + align:start position:0% +this model + + + align:start position:0% +this model +is we would observe the firms going + + align:start position:0% +is we would observe the firms going + + + align:start position:0% +is we would observe the firms going +along charging Monopoly price they would + + align:start position:0% +along charging Monopoly price they would + + + align:start position:0% +along charging Monopoly price they would +do that for some period of time and then + + align:start position:0% +do that for some period of time and then + + + align:start position:0% +do that for some period of time and then +when there's one of these bad demand + + align:start position:0% +when there's one of these bad demand + + + align:start position:0% +when there's one of these bad demand +periods where the customer doesn't order + + align:start position:0% +periods where the customer doesn't order + + + align:start position:0% +periods where the customer doesn't order +from them they would switch and they + + align:start position:0% +from them they would switch and they + + + align:start position:0% +from them they would switch and they +would charge C for capital T + + align:start position:0% +would charge C for capital T + + + align:start position:0% +would charge C for capital T +periods and then price would go back up + + align:start position:0% +periods and then price would go back up + + + align:start position:0% +periods and then price would go back up +and then they continue to collude for a + + align:start position:0% +and then they continue to collude for a + + + align:start position:0% +and then they continue to collude for a +while another price + + align:start position:0% +while another price + + + align:start position:0% +while another price +war and so in the SQL we get this sort + + align:start position:0% +war and so in the SQL we get this sort + + + align:start position:0% +war and so in the SQL we get this sort +of funny price pattern that looks like + + align:start position:0% +of funny price pattern that looks like + + + align:start position:0% +of funny price pattern that looks like +that where the firms go along charging + + align:start position:0% +that where the firms go along charging + + + align:start position:0% +that where the firms go along charging +Monopoly price they jump down they have + + align:start position:0% +Monopoly price they jump down they have + + + align:start position:0% +Monopoly price they jump down they have +a price war and then they go on like + + align:start position:0% +a price war and then they go on like + + + align:start position:0% +a price war and then they go on like +that and so + + align:start position:0% + + + + align:start position:0% + +on so then the theorem is that you know + + align:start position:0% +on so then the theorem is that you know + + + align:start position:0% +on so then the theorem is that you know +that that is an equilibrium of this + + align:start position:0% +that that is an equilibrium of this + + + align:start position:0% +that that is an equilibrium of this +model and intuitively you know why don't + + align:start position:0% +model and intuitively you know why don't + + + align:start position:0% +model and intuitively you know why don't +you want to deviate from such an + + align:start position:0% +you want to deviate from such an + + + align:start position:0% +you want to deviate from such an +equilibrium you know if you cheat in + + align:start position:0% +equilibrium you know if you cheat in + + + align:start position:0% +equilibrium you know if you cheat in +this model the you know the other firm's + + align:start position:0% +this model the you know the other firm's + + + align:start position:0% +this model the you know the other firm's +charging PM you charge PM minus Epsilon + + align:start position:0% +charging PM you charge PM minus Epsilon + + + align:start position:0% +charging PM you charge PM minus Epsilon +to try to get all the demand you do get + + align:start position:0% +to try to get all the demand you do get + + + align:start position:0% +to try to get all the demand you do get +some extra profit today from getting the + + align:start position:0% +some extra profit today from getting the + + + align:start position:0% +some extra profit today from getting the +Serv getting the whole Market instead of + + align:start position:0% +Serv getting the whole Market instead of + + + align:start position:0% +Serv getting the whole Market instead of +half the market but then you immediately + + align:start position:0% +half the market but then you immediately + + + align:start position:0% +half the market but then you immediately +trigger this t period price War um the + + align:start position:0% +trigger this t period price War um the + + + align:start position:0% +trigger this t period price War um the +money you lose in these T periods of a + + align:start position:0% +money you lose in these T periods of a + + + align:start position:0% +money you lose in these T periods of a +price war is going to offset the gain + + align:start position:0% +price war is going to offset the gain + + + align:start position:0% +price war is going to offset the gain +you get in the one period in which you + + align:start position:0% +you get in the one period in which you + + + align:start position:0% +you get in the one period in which you +succeeded um you know and T sometimes + + align:start position:0% +succeeded um you know and T sometimes + + + align:start position:0% +succeeded um you know and T sometimes +doesn't need bigger than two or three to + + align:start position:0% +doesn't need bigger than two or three to + + + align:start position:0% +doesn't need bigger than two or three to +make that + + align:start position:0% + + + + align:start position:0% + +true um + + align:start position:0% +true um + + + align:start position:0% +true um +um okay so how am I going to prove + + align:start position:0% +um okay so how am I going to prove + + + align:start position:0% +um okay so how am I going to prove +that the way I'm going is I'm just going + + align:start position:0% +that the way I'm going is I'm just going + + + align:start position:0% +that the way I'm going is I'm just going +to + + align:start position:0% +to + + + align:start position:0% +to +do lights on the + + align:start position:0% + + + + align:start position:0% + +board okay the way I'm going to do is + + align:start position:0% +board okay the way I'm going to do is + + + align:start position:0% +board okay the way I'm going to do is +it's just going to be a simple sort of + + align:start position:0% +it's just going to be a simple sort of + + + align:start position:0% +it's just going to be a simple sort of +uh dynamic programming kind of + + align:start position:0% +uh dynamic programming kind of + + + align:start position:0% +uh dynamic programming kind of +calculation I make these two definitions + + align:start position:0% +calculation I make these two definitions + + + align:start position:0% +calculation I make these two definitions +VM is the present discounted value of + + align:start position:0% +VM is the present discounted value of + + + align:start position:0% +VM is the present discounted value of +payoffs at t equal + + align:start position:0% + + + + align:start position:0% + +zero and VP is the present Discounter + + align:start position:0% +zero and VP is the present Discounter + + + align:start position:0% +zero and VP is the present Discounter +value of payoffs if we're at the start + + align:start position:0% +value of payoffs if we're at the start + + + align:start position:0% +value of payoffs if we're at the start +of the punishment phase and the + + align:start position:0% +of the punishment phase and the + + + align:start position:0% +of the punishment phase and the +strategies are symmetric so these things + + align:start position:0% +strategies are symmetric so these things + + + align:start position:0% +strategies are symmetric so these things +don't need an index for the players on + + align:start position:0% +don't need an index for the players on + + + align:start position:0% +don't need an index for the players on +them uh and I just need to show there's + + align:start position:0% +them uh and I just need to show there's + + + align:start position:0% +them uh and I just need to show there's +no profitable + + align:start position:0% +no profitable + + + align:start position:0% +no profitable +deviation uh showing that there's no + + align:start position:0% +deviation uh showing that there's no + + + align:start position:0% +deviation uh showing that there's no +profitable deviation during the + + align:start position:0% +profitable deviation during the + + + align:start position:0% +profitable deviation during the +punishment phase is + + align:start position:0% +punishment phase is + + + align:start position:0% +punishment phase is +easy you know if you if we're down + + align:start position:0% +easy you know if you if we're down + + + align:start position:0% +easy you know if you if we're down +here and I decide that I'm supposed to + + align:start position:0% +here and I decide that I'm supposed to + + + align:start position:0% +here and I decide that I'm supposed to +charge C and I'm going to charge some + + align:start position:0% +charge C and I'm going to charge some + + + align:start position:0% +charge C and I'm going to charge some +other price well if I deviate and I + + align:start position:0% +other price well if I deviate and I + + + align:start position:0% +other price well if I deviate and I +charge a price that's less than C all I + + align:start position:0% +charge a price that's less than C all I + + + align:start position:0% +charge a price that's less than C all I +do is sell at a loss and I don't affect + + align:start position:0% +do is sell at a loss and I don't affect + + + align:start position:0% +do is sell at a loss and I don't affect +the future at all and if I deviate and + + align:start position:0% +the future at all and if I deviate and + + + align:start position:0% +the future at all and if I deviate and +raise my price I sell nothing which is + + align:start position:0% +raise my price I sell nothing which is + + + align:start position:0% +raise my price I sell nothing which is +the same and again I don't affect the + + align:start position:0% +the same and again I don't affect the + + + align:start position:0% +the same and again I don't affect the +future as I've described the strategies + + align:start position:0% +future as I've described the strategies + + + align:start position:0% +future as I've described the strategies +so in the punishment phase you're never + + align:start position:0% +so in the punishment phase you're never + + + align:start position:0% +so in the punishment phase you're never +going to want to deviate you're never + + align:start position:0% +going to want to deviate you're never + + + align:start position:0% +going to want to deviate you're never +going to gain from deviating because all + + align:start position:0% +going to gain from deviating because all + + + align:start position:0% +going to gain from deviating because all +you do is lose or weekly lose in the + + align:start position:0% +you do is lose or weekly lose in the + + + align:start position:0% +you do is lose or weekly lose in the +current period and have no effect on the + + align:start position:0% +current period and have no effect on the + + + align:start position:0% +current period and have no effect on the +Future Okay so it just remains to show + + align:start position:0% +Future Okay so it just remains to show + + + align:start position:0% +Future Okay so it just remains to show +that when you're at some point like this + + align:start position:0% +that when you're at some point like this + + + align:start position:0% +that when you're at some point like this +then you don't also want to deviate from + + align:start position:0% +then you don't also want to deviate from + + + align:start position:0% +then you don't also want to deviate from +the + + align:start position:0% + + + + align:start position:0% + +equilibrium okay so to do that what I + + align:start position:0% +equilibrium okay so to do that what I + + + align:start position:0% +equilibrium okay so to do that what I +need to show is if I follow the + + align:start position:0% +need to show is if I follow the + + + align:start position:0% +need to show is if I follow the +equilibrium I'm going to get dis present + + align:start position:0% +equilibrium I'm going to get dis present + + + align:start position:0% +equilibrium I'm going to get dis present +discounted value P + + align:start position:0% +discounted value P + + + align:start position:0% +discounted value P +VM if I do + + align:start position:0% +VM if I do + + + align:start position:0% +VM if I do +deviate uh if there is we're in one of + + align:start position:0% +deviate uh if there is we're in one of + + + align:start position:0% +deviate uh if there is we're in one of +the positive demand periods I'm going to + + align:start position:0% +the positive demand periods I'm going to + + + align:start position:0% +the positive demand periods I'm going to +get the full Monopoly profit instead of + + align:start position:0% +get the full Monopoly profit instead of + + + align:start position:0% +get the full Monopoly profit instead of +one half the Monopoly + + align:start position:0% +one half the Monopoly + + + align:start position:0% +one half the Monopoly +profit uh but then one period later + + align:start position:0% +profit uh but then one period later + + + align:start position:0% +profit uh but then one period later +we're going to be starting a punishment + + align:start position:0% +we're going to be starting a punishment + + + align:start position:0% +we're going to be starting a punishment +phase so I'm going to get Delta time VP + + align:start position:0% +phase so I'm going to get Delta time VP + + + align:start position:0% +phase so I'm going to get Delta time VP +so I need to show that VM is at least + + align:start position:0% +so I need to show that VM is at least + + + align:start position:0% +so I need to show that VM is at least +the right hand side of that + + align:start position:0% +the right hand side of that + + + align:start position:0% +the right hand side of that +expression um so to show that I just + + align:start position:0% +expression um so to show that I just + + + align:start position:0% +expression um so to show that I just +need to find VM and VP and to do that I + + align:start position:0% +need to find VM and VP and to do that I + + + align:start position:0% +need to find VM and VP and to do that I +just solve two equations and two + + align:start position:0% +just solve two equations and two + + + align:start position:0% +just solve two equations and two +unknowns you know one recursive equation + + align:start position:0% +unknowns you know one recursive equation + + + align:start position:0% +unknowns you know one recursive equation +for VM is the profit I get uh at the + + align:start position:0% +for VM is the profit I get uh at the + + + align:start position:0% +for VM is the profit I get uh at the +start of the game is with probability 1 + + align:start position:0% +start of the game is with probability 1 + + + align:start position:0% +start of the game is with probability 1 +minus Alpha I get Pi m/ 2 and then next + + align:start position:0% +minus Alpha I get Pi m/ 2 and then next + + + align:start position:0% +minus Alpha I get Pi m/ 2 and then next +period we remain in the Cooperative + + align:start position:0% +period we remain in the Cooperative + + + align:start position:0% +period we remain in the Cooperative +phase and with probability alpha one + + align:start position:0% +phase and with probability alpha one + + + align:start position:0% +phase and with probability alpha one +period later we end up in the punishment + + align:start position:0% +period later we end up in the punishment + + + align:start position:0% +period later we end up in the punishment +phase so this is sort of one equation + + align:start position:0% +phase so this is sort of one equation + + + align:start position:0% +phase so this is sort of one equation +for you know VM is 1 - Alpha + + align:start position:0% +for you know VM is 1 - Alpha + + + align:start position:0% +for you know VM is 1 - Alpha +time Pi m/ 2 + + align:start position:0% +time Pi m/ 2 + + + align:start position:0% +time Pi m/ 2 +plus uh Delta + + align:start position:0% +plus uh Delta + + + align:start position:0% +plus uh Delta +VM plus Alpha Delta + + align:start position:0% +VM plus Alpha Delta + + + align:start position:0% +VM plus Alpha Delta +VP and then VP is Delta to the T + + align:start position:0% +VP and then VP is Delta to the T + + + align:start position:0% +VP and then VP is Delta to the T +V time + + align:start position:0% +V time + + + align:start position:0% +V time +VM + + align:start position:0% +VM + + + align:start position:0% +VM +okay so if you look at what's going on + + align:start position:0% +okay so if you look at what's going on + + + align:start position:0% +okay so if you look at what's going on +here these are just you know I you can + + align:start position:0% +here these are just you know I you can + + + align:start position:0% +here these are just you know I you can +think about bringing all of the VMS and + + align:start position:0% +think about bringing all of the VMS and + + + align:start position:0% +think about bringing all of the VMS and +VPS over to one side of the equation so + + align:start position:0% +VPS over to one side of the equation so + + + align:start position:0% +VPS over to one side of the equation so +for instance this first one looks like + + align:start position:0% +for instance this first one looks like + + + align:start position:0% +for instance this first one looks like +VM + + align:start position:0% +VM + + + align:start position:0% +VM +minus 1us Alpha Delta + + align:start position:0% +minus 1us Alpha Delta + + + align:start position:0% +minus 1us Alpha Delta +VM and then VP is Delta to the + + align:start position:0% +VM and then VP is Delta to the + + + align:start position:0% +VM and then VP is Delta to the +TVM so this is really minus Alpha Delta + + align:start position:0% +TVM so this is really minus Alpha Delta + + + align:start position:0% +TVM so this is really minus Alpha Delta +to the t + 1 + + align:start position:0% +to the t + 1 + + + align:start position:0% +to the t + 1 +VM uh + + align:start position:0% +VM uh + + + align:start position:0% +VM uh +equals 1 - Alpha * pi M over two so just + + align:start position:0% +equals 1 - Alpha * pi M over two so just + + + align:start position:0% +equals 1 - Alpha * pi M over two so just +by substituting in for this one I just + + align:start position:0% +by substituting in for this one I just + + + align:start position:0% +by substituting in for this one I just +get an equation in one unknown I can + + align:start position:0% +get an equation in one unknown I can + + + align:start position:0% +get an equation in one unknown I can +solve that for what VM + + align:start position:0% +solve that for what VM + + + align:start position:0% +solve that for what VM +is + + align:start position:0% +is + + + align:start position:0% +is +okay but it's it's just a two equation + + align:start position:0% +okay but it's it's just a two equation + + + align:start position:0% +okay but it's it's just a two equation +into a known problem anyway so so this + + align:start position:0% +into a known problem anyway so so this + + + align:start position:0% +into a known problem anyway so so this +is what I get so this is the expression + + align:start position:0% +is what I get so this is the expression + + + align:start position:0% +is what I get so this is the expression +for what VM is and this is an expression + + align:start position:0% +for what VM is and this is an expression + + + align:start position:0% +for what VM is and this is an expression +for what VP + + align:start position:0% +for what VP + + + align:start position:0% +for what VP +is so then what we're trying to show is + + align:start position:0% +is so then what we're trying to show is + + + align:start position:0% +is so then what we're trying to show is +that um this is + + align:start position:0% +that um this is + + + align:start position:0% +that um this is +true + + align:start position:0% +true + + + align:start position:0% +true +okay again I bring this term over to + + align:start position:0% +okay again I bring this term over to + + + align:start position:0% +okay again I bring this term over to +that side so what I need to show is + + align:start position:0% +that side so what I need to show is + + + align:start position:0% +that side so what I need to show is +that + + align:start position:0% +that + + + align:start position:0% +that +uh v m minus Delta to the t + + + align:start position:0% +uh v m minus Delta to the t + + + + align:start position:0% +uh v m minus Delta to the t + + + align:start position:0% + + + align:start position:0% +VM uh is at least Pi M * 1 minus + + align:start position:0% + + + + align:start position:0% + +Alpha okay so that's what I wrote + + align:start position:0% +Alpha okay so that's what I wrote + + + align:start position:0% +Alpha okay so that's what I wrote +here uh the VM has a one minus Alpha in + + align:start position:0% +here uh the VM has a one minus Alpha in + + + align:start position:0% +here uh the VM has a one minus Alpha in +it I cancel the one minus + + align:start position:0% +it I cancel the one minus + + + align:start position:0% +it I cancel the one minus +Alphas uh this term also has a piim in + + align:start position:0% +Alphas uh this term also has a piim in + + + align:start position:0% +Alphas uh this term also has a piim in +it uh as does this term so I cancel the + + align:start position:0% +it uh as does this term so I cancel the + + + align:start position:0% +it uh as does this term so I cancel the +PM's I multiply out anyway way I + + align:start position:0% +PM's I multiply out anyway way I + + + align:start position:0% +PM's I multiply out anyway way I +get bunch of Algebra I get this + + align:start position:0% +get bunch of Algebra I get this + + + align:start position:0% +get bunch of Algebra I get this +expression 2 1 - Alpha Delta plus 2 + + align:start position:0% +expression 2 1 - Alpha Delta plus 2 + + + align:start position:0% +expression 2 1 - Alpha Delta plus 2 +alpha- 1 Delta t + 1 is greater than one + + align:start position:0% +alpha- 1 Delta t + 1 is greater than one + + + align:start position:0% +alpha- 1 Delta t + 1 is greater than one +so if you look at this + + align:start position:0% +so if you look at this + + + align:start position:0% +so if you look at this +expression if Alpha is less than a half + + align:start position:0% +expression if Alpha is less than a half + + + align:start position:0% +expression if Alpha is less than a half +2 * 1us Alpha is bigger than one so I + + align:start position:0% +2 * 1us Alpha is bigger than one so I + + + align:start position:0% +2 * 1us Alpha is bigger than one so I +have a number bigger than one time Delta + + align:start position:0% +have a number bigger than one time Delta + + + align:start position:0% +have a number bigger than one time Delta +plus something with a Delta to the t + 1 + + align:start position:0% +plus something with a Delta to the t + 1 + + + align:start position:0% +plus something with a Delta to the t + 1 +has to be bigger than one so if 2 1us + + align:start position:0% +has to be bigger than one so if 2 1us + + + align:start position:0% +has to be bigger than one so if 2 1us +Alpha is bigger than one and I choose + + align:start position:0% +Alpha is bigger than one and I choose + + + align:start position:0% +Alpha is bigger than one and I choose +Delta close to one + + align:start position:0% +Delta close to one + + + align:start position:0% +Delta close to one +this is bigger than one and then I can + + align:start position:0% +this is bigger than one and then I can + + + align:start position:0% +this is bigger than one and then I can +choose capital T large enough to make + + align:start position:0% +choose capital T large enough to make + + + align:start position:0% +choose capital T large enough to make +this thing approximately zero so I've + + align:start position:0% +this thing approximately zero so I've + + + align:start position:0% +this thing approximately zero so I've +got something bigger than one plus + + align:start position:0% +got something bigger than one plus + + + align:start position:0% +got something bigger than one plus +something that I can make as close to + + align:start position:0% +something that I can make as close to + + + align:start position:0% +something that I can make as close to +zero as I want that's going to be um + + align:start position:0% +zero as I want that's going to be um + + + align:start position:0% +zero as I want that's going to be um +that is going to be greater than one so + + align:start position:0% +that is going to be greater than one so + + + align:start position:0% +that is going to be greater than one so +just the intuition is just make Delta + + align:start position:0% +just the intuition is just make Delta + + + align:start position:0% +just the intuition is just make Delta +big make Delta large so people care + + align:start position:0% +big make Delta large so people care + + + align:start position:0% +big make Delta large so people care +about the punishments about the future + + align:start position:0% +about the punishments about the future + + + align:start position:0% +about the punishments about the future +and then make targe which is just making + + align:start position:0% +and then make targe which is just making + + + align:start position:0% +and then make targe which is just making +the punishment as severe as you need it + + align:start position:0% +the punishment as severe as you need it + + + align:start position:0% +the punishment as severe as you need it +to be you + + align:start position:0% +to be you + + + align:start position:0% +to be you +make so if Delta is close to one and T + + align:start position:0% +make so if Delta is close to one and T + + + align:start position:0% +make so if Delta is close to one and T +is large this is going to work + + align:start position:0% +is large this is going to work + + + align:start position:0% +is large this is going to work +okay and I I described that as you know + + align:start position:0% +okay and I I described that as you know + + + align:start position:0% +okay and I I described that as you know +T going to Infinity but if if you think + + align:start position:0% +T going to Infinity but if if you think + + + align:start position:0% +T going to Infinity but if if you think +about the math of it you know if I gain + + align:start position:0% +about the math of it you know if I gain + + + align:start position:0% +about the math of it you know if I gain +I gain in one period I gain half the + + align:start position:0% +I gain in one period I gain half the + + + align:start position:0% +I gain in one period I gain half the +Monopoly profits and then in every + + align:start position:0% +Monopoly profits and then in every + + + align:start position:0% +Monopoly profits and then in every +future period I'm losing half the + + align:start position:0% +future period I'm losing half the + + + align:start position:0% +future period I'm losing half the +Monopoly profits so even losing half the + + align:start position:0% +Monopoly profits so even losing half the + + + align:start position:0% +Monopoly profits so even losing half the +Monopoly profits twice may be enough to + + align:start position:0% +Monopoly profits twice may be enough to + + + align:start position:0% +Monopoly profits twice may be enough to +make me not want to get half the + + align:start position:0% +make me not want to get half the + + + align:start position:0% +make me not want to get half the +Monopoly profits once so you know + + align:start position:0% +Monopoly profits once so you know + + + align:start position:0% +Monopoly profits once so you know +capital T equals 2 will often work for + + align:start position:0% +capital T equals 2 will often work for + + + align:start position:0% +capital T equals 2 will often work for +this capital T equals 3 you know will + + align:start position:0% +this capital T equals 3 you know will + + + align:start position:0% +this capital T equals 3 you know will +almost always work you know there is + + align:start position:0% +almost always work you know there is + + + align:start position:0% +almost always work you know there is +this sort of problem with the one minus + + align:start position:0% +this sort of problem with the one minus + + + align:start position:0% +this sort of problem with the one minus +Alphas in there that it you may not + + align:start position:0% +Alphas in there that it you may not + + + align:start position:0% +Alphas in there that it you may not +actually get punished here because it + + align:start position:0% +actually get punished here because it + + + align:start position:0% +actually get punished here because it +may be that there's no demand but you + + align:start position:0% +may be that there's no demand but you + + + align:start position:0% +may be that there's no demand but you +know if if Alpha's small so that the + + align:start position:0% +know if if Alpha's small so that the + + + align:start position:0% +know if if Alpha's small so that the +punishment really does occur you just + + align:start position:0% +punishment really does occur you just + + + align:start position:0% +punishment really does occur you just +don't need T very big to get this thing + + align:start position:0% +don't need T very big to get this thing + + + align:start position:0% +don't need T very big to get this thing +to + + align:start position:0% + + + + align:start position:0% + +work okay so you know while it's a very + + align:start position:0% +work okay so you know while it's a very + + + align:start position:0% +work okay so you know while it's a very +artificial model I I think it's a very + + align:start position:0% +artificial model I I think it's a very + + + align:start position:0% +artificial model I I think it's a very +insightful one because it makes several + + align:start position:0% +insightful one because it makes several + + + align:start position:0% +insightful one because it makes several +uh important predictions so first one is + + align:start position:0% +uh important predictions so first one is + + + align:start position:0% +uh important predictions so first one is +you know maybe unintuitive price Wars + + align:start position:0% +you know maybe unintuitive price Wars + + + align:start position:0% +you know maybe unintuitive price Wars +should be observed in equilibrium you + + align:start position:0% +should be observed in equilibrium you + + + align:start position:0% +should be observed in equilibrium you +know I think there was a there was if + + align:start position:0% +know I think there was a there was if + + + align:start position:0% +know I think there was a there was if +you read the old Literature Like There's + + align:start position:0% +you read the old Literature Like There's + + + align:start position:0% +you read the old Literature Like There's +this um you know very nice book by you + + align:start position:0% +this um you know very nice book by you + + + align:start position:0% +this um you know very nice book by you +know Tom Ulan about railroad + + align:start position:0% +know Tom Ulan about railroad + + + align:start position:0% +know Tom Ulan about railroad +cartels you know written in the 1970s + + align:start position:0% +cartels you know written in the 1970s + + + align:start position:0% +cartels you know written in the 1970s +that's thinking about you know these + + align:start position:0% +that's thinking about you know these + + + align:start position:0% +that's thinking about you know these +cartels tried to organize collusion the + + align:start position:0% +cartels tried to organize collusion the + + + align:start position:0% +cartels tried to organize collusion the +collusion kept breaking down and they + + align:start position:0% +collusion kept breaking down and they + + + align:start position:0% +collusion kept breaking down and they +kept having price Wars because they + + align:start position:0% +kept having price Wars because they + + + align:start position:0% +kept having price Wars because they +couldn't collude with each other you + + align:start position:0% +couldn't collude with each other you + + + align:start position:0% +couldn't collude with each other you +know Green importer makes a point that + + align:start position:0% +know Green importer makes a point that + + + align:start position:0% +know Green importer makes a point that +no price Wars are not something that's + + align:start position:0% +no price Wars are not something that's + + + align:start position:0% +no price Wars are not something that's +sort of a sign that the cartel has + + align:start position:0% +sort of a sign that the cartel has + + + align:start position:0% +sort of a sign that the cartel has +broken down if you have a well-designed + + align:start position:0% +broken down if you have a well-designed + + + align:start position:0% +broken down if you have a well-designed +cartel it has to have these price Wars + + align:start position:0% +cartel it has to have these price Wars + + + align:start position:0% +cartel it has to have these price Wars +in it because if it didn't have the + + align:start position:0% +in it because if it didn't have the + + + align:start position:0% +in it because if it didn't have the +price Wars in it people would be + + align:start position:0% +price Wars in it people would be + + + align:start position:0% +price Wars in it people would be +cheating and so when we see price Wars + + align:start position:0% +cheating and so when we see price Wars + + + align:start position:0% +cheating and so when we see price Wars +we can think well- functioning cartel + + align:start position:0% +we can think well- functioning cartel + + + align:start position:0% +we can think well- functioning cartel +rather than poorly functioning cartel + + align:start position:0% +rather than poorly functioning cartel + + + align:start position:0% +rather than poorly functioning cartel +that keeps breaking down okay um you the + + align:start position:0% +that keeps breaking down okay um you the + + + align:start position:0% +that keeps breaking down okay um you the +optimal collusion in this model can have + + align:start position:0% +optimal collusion in this model can have + + + align:start position:0% +optimal collusion in this model can have +T finite why is that you know certainly + + align:start position:0% +T finite why is that you know certainly + + + align:start position:0% +T finite why is that you know certainly +making T infinite makes it the biggest + + align:start position:0% +making T infinite makes it the biggest + + + align:start position:0% +making T infinite makes it the biggest +punishment and makes people not want to + + align:start position:0% +punishment and makes people not want to + + + align:start position:0% +punishment and makes people not want to +deviate but if you make t infinite and + + align:start position:0% +deviate but if you make t infinite and + + + align:start position:0% +deviate but if you make t infinite and +Alpha's not super small then just + + align:start position:0% +Alpha's not super small then just + + + align:start position:0% +Alpha's not super small then just +basically only clude at the very + + align:start position:0% +basically only clude at the very + + + align:start position:0% +basically only clude at the very +beginning of the game and so what you + + align:start position:0% +beginning of the game and so what you + + + align:start position:0% +beginning of the game and so what you +want to do is have the a punishment that + + align:start position:0% +want to do is have the a punishment that + + + align:start position:0% +want to do is have the a punishment that +keep people from deviating but not so + + align:start position:0% +keep people from deviating but not so + + + align:start position:0% +keep people from deviating but not so +long that you lose a lot of Revenue + + align:start position:0% +long that you lose a lot of Revenue + + + align:start position:0% +long that you lose a lot of Revenue +while you're in the punishment so the + + align:start position:0% +while you're in the punishment so the + + + align:start position:0% +while you're in the punishment so the +best equilibrium of this point is going + + align:start position:0% +best equilibrium of this point is going + + + align:start position:0% +best equilibrium of this point is going +to be the one that has the shortest T + + align:start position:0% +to be the one that has the shortest T + + + align:start position:0% +to be the one that has the shortest T +possible that deters collusion so we + + align:start position:0% +possible that deters collusion so we + + + align:start position:0% +possible that deters collusion so we +should have these short finite price + + align:start position:0% +should have these short finite price + + + align:start position:0% +should have these short finite price +Wars okay um what causes price Wars uh + + align:start position:0% +Wars okay um what causes price Wars uh + + + align:start position:0% +Wars okay um what causes price Wars uh +in this model the Insight is price Wars + + align:start position:0% +in this model the Insight is price Wars + + + align:start position:0% +in this model the Insight is price Wars +are caused by demand patterns that make + + align:start position:0% +are caused by demand patterns that make + + + align:start position:0% +are caused by demand patterns that make +the participants think someone has + + align:start position:0% +the participants think someone has + + + align:start position:0% +the participants think someone has +cheated in equilibrium no one ever + + align:start position:0% +cheated in equilibrium no one ever + + + align:start position:0% +cheated in equilibrium no one ever +cheats it's not people cheat price Wars + + align:start position:0% +cheats it's not people cheat price Wars + + + align:start position:0% +cheats it's not people cheat price Wars +start it's always suspicious demand + + align:start position:0% +start it's always suspicious demand + + + align:start position:0% +start it's always suspicious demand +patterns arise people start price Wars + + align:start position:0% +patterns arise people start price Wars + + + align:start position:0% +patterns arise people start price Wars +knowing that it was a with probability + + align:start position:0% +knowing that it was a with probability + + + align:start position:0% +knowing that it was a with probability +one in equilibrium it was a suspicious + + align:start position:0% +one in equilibrium it was a suspicious + + + align:start position:0% +one in equilibrium it was a suspicious +demand pattern but it's suspicious + + align:start position:0% +demand pattern but it's suspicious + + + align:start position:0% +demand pattern but it's suspicious +demand patterns that trigger price Wars + + align:start position:0% +demand patterns that trigger price Wars + + + align:start position:0% +demand patterns that trigger price Wars +among + + align:start position:0% +among + + + align:start position:0% +among +firms okay and you might think well if + + align:start position:0% +firms okay and you might think well if + + + align:start position:0% +firms okay and you might think well if +the firms all know that it's a + + align:start position:0% +the firms all know that it's a + + + align:start position:0% +the firms all know that it's a +suspicious demand pattern that triggered + + align:start position:0% +suspicious demand pattern that triggered + + + align:start position:0% +suspicious demand pattern that triggered +it can't they just renegotiate out of it + + align:start position:0% +it can't they just renegotiate out of it + + + align:start position:0% +it can't they just renegotiate out of it +and say okay look let's go back and + + align:start position:0% +and say okay look let's go back and + + + align:start position:0% +and say okay look let's go back and +ignore that one because we all know just + + align:start position:0% +ignore that one because we all know just + + + align:start position:0% +ignore that one because we all know just +the firm made no orders this week you + + align:start position:0% +the firm made no orders this week you + + + align:start position:0% +the firm made no orders this week you +know once you do that it doesn't work + + align:start position:0% +know once you do that it doesn't work + + + align:start position:0% +know once you do that it doesn't work +you you know the firms have to commit + + align:start position:0% +you you know the firms have to commit + + + align:start position:0% +you you know the firms have to commit +that we're going to have these price + + align:start position:0% +that we're going to have these price + + + align:start position:0% +that we're going to have these price +Wars when these suspicious demand + + align:start position:0% +Wars when these suspicious demand + + + align:start position:0% +Wars when these suspicious demand +patterns arise because it's the + + align:start position:0% +patterns arise because it's the + + + align:start position:0% +patterns arise because it's the +suspicious man patterns that resemble + + align:start position:0% +suspicious man patterns that resemble + + + align:start position:0% +suspicious man patterns that resemble +someone + + align:start position:0% +someone + + + align:start position:0% +someone +cheating okay um + + align:start position:0% +cheating okay um + + + align:start position:0% +cheating okay um +yes are cases we know about where um we + + align:start position:0% +yes are cases we know about where um we + + + align:start position:0% +yes are cases we know about where um we +know it was like the price were due to + + align:start position:0% +know it was like the price were due to + + + align:start position:0% +know it was like the price were due to +the cartel functioning and not just Dem + + align:start position:0% +the cartel functioning and not just Dem + + + align:start position:0% +the cartel functioning and not just Dem +yeah so I will um um you know I I'm I'm + + align:start position:0% +yeah so I will um um you know I I'm I'm + + + align:start position:0% +yeah so I will um um you know I I'm I'm +in Wednesday's lecture I'm going to talk + + align:start position:0% +in Wednesday's lecture I'm going to talk + + + align:start position:0% +in Wednesday's lecture I'm going to talk +about like Rob Porter has this paper + + align:start position:0% +about like Rob Porter has this paper + + + align:start position:0% +about like Rob Porter has this paper +reexamining a railroad cartel from the + + align:start position:0% +reexamining a railroad cartel from the + + + align:start position:0% +reexamining a railroad cartel from the +19th century and they um I don't know I + + align:start position:0% +19th century and they um I don't know I + + + align:start position:0% +19th century and they um I don't know I +guess he at least he argues very much + + align:start position:0% +guess he at least he argues very much + + + align:start position:0% +guess he at least he argues very much +that this model looks like it's + + align:start position:0% +that this model looks like it's + + + align:start position:0% +that this model looks like it's +describing what's going on I I think it + + align:start position:0% +describing what's going on I I think it + + + align:start position:0% +describing what's going on I I think it +is an open question in that example + + align:start position:0% +is an open question in that example + + + align:start position:0% +is an open question in that example +whether whether it's whether it's + + align:start position:0% +whether whether it's whether it's + + + align:start position:0% +whether whether it's whether it's +cheating or whether it's suspicious + + align:start position:0% +cheating or whether it's suspicious + + + align:start position:0% +cheating or whether it's suspicious +demand shocks or whatever you know there + + align:start position:0% +demand shocks or whatever you know there + + + align:start position:0% +demand shocks or whatever you know there +are plenty of cartels where we know that + + align:start position:0% +are plenty of cartels where we know that + + + align:start position:0% +are plenty of cartels where we know that +someone cheated and that someone cheated + + align:start position:0% +someone cheated and that someone cheated + + + align:start position:0% +someone cheated and that someone cheated +in that triggered price Wars um the no + + align:start position:0% +in that triggered price Wars um the no + + + align:start position:0% +in that triggered price Wars um the no +one cheated is often harder to know + + align:start position:0% +one cheated is often harder to know + + + align:start position:0% +one cheated is often harder to know +empirically because you know the whole + + align:start position:0% +empirically because you know the whole + + + align:start position:0% +empirically because you know the whole +point is that these things are + + align:start position:0% +point is that these things are + + + align:start position:0% +point is that these things are +unobservable and so how do you prove + + align:start position:0% +unobservable and so how do you prove + + + align:start position:0% +unobservable and so how do you prove +that no one did cheat and cause that + + align:start position:0% +that no one did cheat and cause that + + + align:start position:0% +that no one did cheat and cause that +shock that made people Everyone start to + + align:start position:0% +shock that made people Everyone start to + + + align:start position:0% +shock that made people Everyone start to +price Wars + + align:start position:0% +price Wars + + + align:start position:0% +price Wars +um + + align:start position:0% +um + + + align:start position:0% +um +so but actually you know it's I will + + align:start position:0% +so but actually you know it's I will + + + align:start position:0% +so but actually you know it's I will +talk about this next time but you know + + align:start position:0% +talk about this next time but you know + + + align:start position:0% +talk about this next time but you know +in the um uh you know collusion wasn't + + align:start position:0% +in the um uh you know collusion wasn't + + + align:start position:0% +in the um uh you know collusion wasn't +illegal in the United States until + + align:start position:0% +illegal in the United States until + + + align:start position:0% +illegal in the United States until +1887 and so in the 1880s there were + + align:start position:0% +1887 and so in the 1880s there were + + + align:start position:0% +1887 and so in the 1880s there were +collusion Consultants so just like you + + align:start position:0% +collusion Consultants so just like you + + + align:start position:0% +collusion Consultants so just like you +can go like firms can go out and hire + + align:start position:0% +can go like firms can go out and hire + + + align:start position:0% +can go like firms can go out and hire +McKenzie today in the 1880s you go and + + align:start position:0% +McKenzie today in the 1880s you go and + + + align:start position:0% +McKenzie today in the 1880s you go and +hire a collusion consultant and say we + + align:start position:0% +hire a collusion consultant and say we + + + align:start position:0% +hire a collusion consultant and say we +have our industry we're having competing + + align:start position:0% +have our industry we're having competing + + + align:start position:0% +have our industry we're having competing +to too much we're not making you know + + align:start position:0% +to too much we're not making you know + + + align:start position:0% +to too much we're not making you know +like this was like the you know area of + + align:start position:0% +like this was like the you know area of + + + align:start position:0% +like this was like the you know area of +the Vander builts and whatever we're not + + align:start position:0% +the Vander builts and whatever we're not + + + align:start position:0% +the Vander builts and whatever we're not +making enough money you know my mansion + + align:start position:0% +making enough money you know my mansion + + + align:start position:0% +making enough money you know my mansion +in Newport only has 137 rooms I need + + align:start position:0% +in Newport only has 137 rooms I need + + + align:start position:0% +in Newport only has 137 rooms I need +more you know like I need higher prices + + align:start position:0% +more you know like I need higher prices + + + align:start position:0% +more you know like I need higher prices +and you would hire like there were like + + align:start position:0% +and you would hire like there were like + + + align:start position:0% +and you would hire like there were like +MacKenzie like firms you would hire and + + align:start position:0% +MacKenzie like firms you would hire and + + + align:start position:0% +MacKenzie like firms you would hire and +those firms would con consult with you + + align:start position:0% +those firms would con consult with you + + + align:start position:0% +those firms would con consult with you +on how to set up your collusive + + align:start position:0% +on how to set up your collusive + + + align:start position:0% +on how to set up your collusive +agreement so that you know you would be + + align:start position:0% +agreement so that you know you would be + + + align:start position:0% +agreement so that you know you would be +able to keep prices up or whatever um + + align:start position:0% +able to keep prices up or whatever um + + + align:start position:0% +able to keep prices up or whatever um +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um this model is very Stark that you get + + align:start position:0% +um this model is very Stark that you get + + + align:start position:0% +um this model is very Stark that you get +these sort of Random that like no one + + align:start position:0% +these sort of Random that like no one + + + align:start position:0% +these sort of Random that like no one +ever gets away with cheating in this + + align:start position:0% +ever gets away with cheating in this + + + align:start position:0% +ever gets away with cheating in this +model in a model with continuous demand + + align:start position:0% +model in a model with continuous demand + + + align:start position:0% +model in a model with continuous demand +shocks you would get away with + + align:start position:0% +shocks you would get away with + + + align:start position:0% +shocks you would get away with +cheating okay so um you know like so let + + align:start position:0% +cheating okay so um you know like so let + + + align:start position:0% +cheating okay so um you know like so let +me say green and Porter do a different + + align:start position:0% +me say green and Porter do a different + + + align:start position:0% +me say green and Porter do a different +vers do a better version of this model + + align:start position:0% +vers do a better version of this model + + + align:start position:0% +vers do a better version of this model +you know green and Porter do they do + + align:start position:0% +you know green and Porter do they do + + + align:start position:0% +you know green and Porter do they do +like a Corno version of this model where + + align:start position:0% +like a Corno version of this model where + + + align:start position:0% +like a Corno version of this model where +the + + align:start position:0% +the + + + align:start position:0% +the +firms uh + + align:start position:0% +firms uh + + + align:start position:0% +firms uh +choose uh + + align:start position:0% +choose uh + + + align:start position:0% +choose uh +q1t and q2t + + align:start position:0% +q1t and q2t + + + align:start position:0% +q1t and q2t +and then you have price at time T equals + + align:start position:0% +and then you have price at time T equals + + + align:start position:0% +and then you have price at time T equals +P of + + align:start position:0% +P of + + + align:start position:0% +P of +q1t plus + + align:start position:0% +q1t plus + + + align:start position:0% +q1t plus +q2t plus Epsilon it so you know you have + + align:start position:0% +q2t plus Epsilon it so you know you have + + + align:start position:0% +q2t plus Epsilon it so you know you have +something that looks like real demand + + align:start position:0% +something that looks like real demand + + + align:start position:0% +something that looks like real demand +shocks the firms choose + + align:start position:0% +shocks the firms choose + + + align:start position:0% +shocks the firms choose +quantities there's some then you know + + align:start position:0% +quantities there's some then you know + + + align:start position:0% +quantities there's some then you know +downward sloping demand curve but then + + align:start position:0% +downward sloping demand curve but then + + + align:start position:0% +downward sloping demand curve but then +demand is also just random in every + + align:start position:0% +demand is also just random in every + + + align:start position:0% +demand is also just random in every +period the market clearing price is + + align:start position:0% +period the market clearing price is + + + align:start position:0% +period the market clearing price is +random if you think about this you know + + align:start position:0% +random if you think about this you know + + + align:start position:0% +random if you think about this you know +there's sort of some price they're + + align:start position:0% +there's sort of some price they're + + + align:start position:0% +there's sort of some price they're +trying to coordinate on the Monopoly + + align:start position:0% +trying to coordinate on the Monopoly + + + align:start position:0% +trying to coordinate on the Monopoly +price as the outcome + + align:start position:0% +price as the outcome + + + align:start position:0% +price as the outcome +but you're going to get this + + align:start position:0% +but you're going to get this + + + align:start position:0% +but you're going to get this +distribution of prices even in + + align:start position:0% +distribution of prices even in + + + align:start position:0% +distribution of prices even in +equilibrium and so what would you do if + + align:start position:0% +equilibrium and so what would you do if + + + align:start position:0% +equilibrium and so what would you do if +like if every period you're going to get + + align:start position:0% +like if every period you're going to get + + + align:start position:0% +like if every period you're going to get +a price drawn from this normal + + align:start position:0% +a price drawn from this normal + + + align:start position:0% +a price drawn from this normal +distribution around PM if everyone's + + align:start position:0% +distribution around PM if everyone's + + + align:start position:0% +distribution around PM if everyone's +behaving properly you know you can't say + + align:start position:0% +behaving properly you know you can't say + + + align:start position:0% +behaving properly you know you can't say +okay if price isn't PM we start a price + + align:start position:0% +okay if price isn't PM we start a price + + + align:start position:0% +okay if price isn't PM we start a price +War because that would happen all the + + align:start position:0% +War because that would happen all the + + + align:start position:0% +War because that would happen all the +time so what you do is you you know you + + align:start position:0% +time so what you do is you you know you + + + align:start position:0% +time so what you do is you you know you +do some cut off here like P hat and if + + align:start position:0% +do some cut off here like P hat and if + + + align:start position:0% +do some cut off here like P hat and if +price is greater than P hat we keep + + align:start position:0% +price is greater than P hat we keep + + + align:start position:0% +price is greater than P hat we keep +colluding if price is less than P hat we + + align:start position:0% +colluding if price is less than P hat we + + + align:start position:0% +colluding if price is less than P hat we +think it's likely enough that someone + + align:start position:0% +think it's likely enough that someone + + + align:start position:0% +think it's likely enough that someone +cheated that we start a price war in a + + align:start position:0% +cheated that we start a price war in a + + + align:start position:0% +cheated that we start a price war in a +model like this right I I can I can + + align:start position:0% +model like this right I I can I can + + + align:start position:0% +model like this right I I can I can +cheat and not and not get caught right + + align:start position:0% +cheat and not and not get caught right + + + align:start position:0% +cheat and not and not get caught right +if I cheat I'm sort of pushing the price + + align:start position:0% +if I cheat I'm sort of pushing the price + + + align:start position:0% +if I cheat I'm sort of pushing the price +distribution down but pushing the price + + align:start position:0% +distribution down but pushing the price + + + align:start position:0% +distribution down but pushing the price +distribution down there's still this + + align:start position:0% +distribution down there's still this + + + align:start position:0% +distribution down there's still this +large probability that we don't start a + + align:start position:0% +large probability that we don't start a + + + align:start position:0% +large probability that we don't start a +price War but I do you know I do + + align:start position:0% +price War but I do you know I do + + + align:start position:0% +price War but I do you know I do +increase the probability of the price + + align:start position:0% +increase the probability of the price + + + align:start position:0% +increase the probability of the price +war and you have to hope that the it's + + align:start position:0% +war and you have to hope that the it's + + + align:start position:0% +war and you have to hope that the it's +got a said the increased probability of + + align:start position:0% +got a said the increased probability of + + + align:start position:0% +got a said the increased probability of +a price war from a small deviation + + align:start position:0% +a price war from a small deviation + + + align:start position:0% +a price war from a small deviation +is enough to get you to not make that + + align:start position:0% +is enough to get you to not make that + + + align:start position:0% +is enough to get you to not make that +small deviation but so you know + + align:start position:0% +small deviation but so you know + + + align:start position:0% +small deviation but so you know +it's in a more realistic model you know + + align:start position:0% +it's in a more realistic model you know + + + align:start position:0% +it's in a more realistic model you know +firms will firms could cheat and get + + align:start position:0% +firms will firms could cheat and get + + + align:start position:0% +firms will firms could cheat and get +away with cheating and only get caught + + align:start position:0% +away with cheating and only get caught + + + align:start position:0% +away with cheating and only get caught +probabilistically this this is parts of + + align:start position:0% +probabilistically this this is parts of + + + align:start position:0% +probabilistically this this is parts of +what also makes it harder for us to know + + align:start position:0% +what also makes it harder for us to know + + + align:start position:0% +what also makes it harder for us to know +was there really cheating there because + + align:start position:0% +was there really cheating there because + + + align:start position:0% +was there really cheating there because +if you do Epsilon cheating there's only + + align:start position:0% +if you do Epsilon cheating there's only + + + align:start position:0% +if you do Epsilon cheating there's only +an you know if you an EP order Epsilon + + align:start position:0% +an you know if you an EP order Epsilon + + + align:start position:0% +an you know if you an EP order Epsilon +cheat you get an order Epsilon increase + + align:start position:0% +cheat you get an order Epsilon increase + + + align:start position:0% +cheat you get an order Epsilon increase +in profit and an order Epsilon increase + + align:start position:0% +in profit and an order Epsilon increase + + + align:start position:0% +in profit and an order Epsilon increase +in causing the price War hard to know if + + align:start position:0% +in causing the price War hard to know if + + + align:start position:0% +in causing the price War hard to know if +that's happening or + + align:start position:0% +that's happening or + + + align:start position:0% +that's happening or +not okay um yeah sometimes in this model + + align:start position:0% +not okay um yeah sometimes in this model + + + align:start position:0% +not okay um yeah sometimes in this model +uh you will get G do you mean in the + + align:start position:0% +uh you will get G do you mean in the + + + align:start position:0% +uh you will get G do you mean in the +sense that like the there's like a mix + + align:start position:0% +sense that like the there's like a mix + + + align:start position:0% +sense that like the there's like a mix +strategy in which you cheat sometimes or + + align:start position:0% +strategy in which you cheat sometimes or + + + align:start position:0% +strategy in which you cheat sometimes or +in that equ no so the the equilibrium + + align:start position:0% +in that equ no so the the equilibrium + + + align:start position:0% +in that equ no so the the equilibrium +we're going to look for is an equ with + + align:start position:0% +we're going to look for is an equ with + + + align:start position:0% +we're going to look for is an equ with +no cheating it's an equilibri where + + align:start position:0% +no cheating it's an equilibri where + + + align:start position:0% +no cheating it's an equilibri where +firms always charge exactly these prices + + align:start position:0% +firms always charge exactly these prices + + + align:start position:0% +firms always charge exactly these prices +but if you did go to you know q1 P minus + + align:start position:0% +but if you did go to you know q1 P minus + + + align:start position:0% +but if you did go to you know q1 P minus +Epsilon then you just raise the + + align:start position:0% +Epsilon then you just raise the + + + align:start position:0% +Epsilon then you just raise the +probability of a price War by Epsilon so + + align:start position:0% +probability of a price War by Epsilon so + + + align:start position:0% +probability of a price War by Epsilon so +there's some you know probab you know + + align:start position:0% +there's some you know probab you know + + + align:start position:0% +there's some you know probab you know +probability you know X star that we + + align:start position:0% +probability you know X star that we + + + align:start position:0% +probability you know X star that we +should start price Wars and now Pro + + align:start position:0% +should start price Wars and now Pro + + + align:start position:0% +should start price Wars and now Pro +price Wars start with probability X Star + + align:start position:0% +price Wars start with probability X Star + + + align:start position:0% +price Wars start with probability X Star +Plus Epsilon or + + align:start position:0% +Plus Epsilon or + + + align:start position:0% +Plus Epsilon or +something yeah + + align:start position:0% + + + + align:start position:0% + +um okay and sustaining collusion is more + + align:start position:0% +um okay and sustaining collusion is more + + + align:start position:0% +um okay and sustaining collusion is more +difficult when demands are noisier here + + align:start position:0% +difficult when demands are noisier here + + + align:start position:0% +difficult when demands are noisier here +you know in this model when Alpha gets + + align:start position:0% +you know in this model when Alpha gets + + + align:start position:0% +you know in this model when Alpha gets +large you can't cud you know like you + + align:start position:0% +large you can't cud you know like you + + + align:start position:0% +large you can't cud you know like you +need Alpha less than a half to make this + + align:start position:0% +need Alpha less than a half to make this + + + align:start position:0% +need Alpha less than a half to make this +work in this + + align:start position:0% +work in this + + + align:start position:0% +work in this +model you know the the if the price + + align:start position:0% +model you know the the if the price + + + align:start position:0% +model you know the the if the price +distribution looks like this it's + + align:start position:0% +distribution looks like this it's + + + align:start position:0% +distribution looks like this it's +relatively easy to collude because you + + align:start position:0% +relatively easy to collude because you + + + align:start position:0% +relatively easy to collude because you +just sort of put a threshold here and no + + align:start position:0% +just sort of put a threshold here and no + + + align:start position:0% +just sort of put a threshold here and no +one wants to shift demand down below + + align:start position:0% +one wants to shift demand down below + + + align:start position:0% +one wants to shift demand down below +that but if if prices look like this it + + align:start position:0% +that but if if prices look like this it + + + align:start position:0% +that but if if prices look like this it +could be that no matter where you draw + + align:start position:0% +could be that no matter where you draw + + + align:start position:0% +could be that no matter where you draw +the cut off the increase in probability + + align:start position:0% +the cut off the increase in probability + + + align:start position:0% +the cut off the increase in probability +of a price war from cheating is so small + + align:start position:0% +of a price war from cheating is so small + + + align:start position:0% +of a price war from cheating is so small +that you know you're not pushing much + + align:start position:0% +that you know you're not pushing much + + + align:start position:0% +that you know you're not pushing much +mass Beyond any one of these points it's + + align:start position:0% +mass Beyond any one of these points it's + + + align:start position:0% +mass Beyond any one of these points it's +hard to stop collusion it's hard to + + align:start position:0% +hard to stop collusion it's hard to + + + align:start position:0% +hard to stop collusion it's hard to +collude so the you know the closer we + + align:start position:0% +collude so the you know the closer we + + + align:start position:0% +collude so the you know the closer we +get to that sort of first model example + + align:start position:0% +get to that sort of first model example + + + align:start position:0% +get to that sort of first model example +of you see someone cheat you know they + + align:start position:0% +of you see someone cheat you know they + + + align:start position:0% +of you see someone cheat you know they +cheated the easier it is to sustain + + align:start position:0% +cheated the easier it is to sustain + + + align:start position:0% +cheated the easier it is to sustain +collusion and the more there's noise in + + align:start position:0% +collusion and the more there's noise in + + + align:start position:0% +collusion and the more there's noise in +that the harder it + + align:start position:0% + + + + align:start position:0% + +is okay + + align:start position:0% +is okay + + + align:start position:0% +is okay +questions okay so you know obviously you + + align:start position:0% +questions okay so you know obviously you + + + align:start position:0% +questions okay so you know obviously you +know this was a very beautiful 1984 + + align:start position:0% +know this was a very beautiful 1984 + + + align:start position:0% +know this was a very beautiful 1984 +paper that first did this um as I said + + align:start position:0% +paper that first did this um as I said + + + align:start position:0% +paper that first did this um as I said +this is how green and Porter actually + + align:start position:0% +this is how green and Porter actually + + + align:start position:0% +this is how green and Porter actually +did the model it's harder to solve but + + align:start position:0% +did the model it's harder to solve but + + + align:start position:0% +did the model it's harder to solve but +it more economically + + align:start position:0% +it more economically + + + align:start position:0% +it more economically +sensible + + align:start position:0% +sensible + + + align:start position:0% +sensible +um there's a big subsequent Game Theory + + align:start position:0% +um there's a big subsequent Game Theory + + + align:start position:0% +um there's a big subsequent Game Theory +literature if you take 126 they cover + + align:start position:0% +literature if you take 126 they cover + + + align:start position:0% +literature if you take 126 they cover +many of these models um + + align:start position:0% +many of these models um + + + align:start position:0% +many of these models um +one you know very nice paper in this AB + + align:start position:0% +one you know very nice paper in this AB + + + align:start position:0% +one you know very nice paper in this AB +brw Pierce stiti econometric a + + align:start position:0% +brw Pierce stiti econometric a + + + align:start position:0% +brw Pierce stiti econometric a +1990 discusses more General strongly + + align:start position:0% +1990 discusses more General strongly + + + align:start position:0% +1990 discusses more General strongly +symmetric models like + + align:start position:0% +symmetric models like + + + align:start position:0% +symmetric models like +this um what you know a brew Pearson + + align:start position:0% +this um what you know a brew Pearson + + + align:start position:0% +this um what you know a brew Pearson +stiti show is that in a like the more + + align:start position:0% +stiti show is that in a like the more + + + align:start position:0% +stiti show is that in a like the more +General version like green and porters + + align:start position:0% +General version like green and porters + + + align:start position:0% +General version like green and porters +um you actually want to have you know + + align:start position:0% +um you actually want to have you know + + + align:start position:0% +um you actually want to have you know +they sort of give us dynamic programming + + align:start position:0% +they sort of give us dynamic programming + + + align:start position:0% +they sort of give us dynamic programming +thing where what there it it is + + align:start position:0% +thing where what there it it is + + + align:start position:0% +thing where what there it it is +basically always a + + align:start position:0% + + + + align:start position:0% + +two it's always a a two + + align:start position:0% +two it's always a a two + + + align:start position:0% +two it's always a a two +um uh always a sort of a two-phase thing + + align:start position:0% +um uh always a sort of a two-phase thing + + + align:start position:0% +um uh always a sort of a two-phase thing +but you actually what you end up doing + + align:start position:0% +but you actually what you end up doing + + + align:start position:0% +but you actually what you end up doing +is you do punishment you do incentives + + align:start position:0% +is you do punishment you do incentives + + + align:start position:0% +is you do punishment you do incentives +on both sides like here firms don't want + + align:start position:0% +on both sides like here firms don't want + + + align:start position:0% +on both sides like here firms don't want +to cheat from the high price because if + + align:start position:0% +to cheat from the high price because if + + + align:start position:0% +to cheat from the high price because if +they cheat we start a price War but in + + align:start position:0% +they cheat we start a price War but in + + + align:start position:0% +they cheat we start a price War but in +the price War Phase what gets firms to + + align:start position:0% +the price War Phase what gets firms to + + + align:start position:0% +the price War Phase what gets firms to +charge these really low prices is the + + align:start position:0% +charge these really low prices is the + + + align:start position:0% +charge these really low prices is the +lower is the resulting price you only + + align:start position:0% +lower is the resulting price you only + + + align:start position:0% +lower is the resulting price you only +switch back you switch back to the top + + align:start position:0% +switch back you switch back to the top + + + align:start position:0% +switch back you switch back to the top +not + + align:start position:0% +not + + + align:start position:0% +not +when um not after T periods but when + + align:start position:0% +when um not after T periods but when + + + align:start position:0% +when um not after T periods but when +price ends up low enough and so it's + + align:start position:0% +price ends up low enough and so it's + + + align:start position:0% +price ends up low enough and so it's +like the firms are trying to drive price + + align:start position:0% +like the firms are trying to drive price + + + align:start position:0% +like the firms are trying to drive price +low enough to get back to a price get + + align:start position:0% +low enough to get back to a price get + + + align:start position:0% +low enough to get back to a price get +back to a a colluding again and so in + + align:start position:0% +back to a a colluding again and so in + + + align:start position:0% +back to a a colluding again and so in +some sense you use the incentives on + + align:start position:0% +some sense you use the incentives on + + + align:start position:0% +some sense you use the incentives on +both sides here they have an incentive + + align:start position:0% +both sides here they have an incentive + + + align:start position:0% +both sides here they have an incentive +not to cheat because it causes this here + + align:start position:0% +not to cheat because it causes this here + + + align:start position:0% +not to cheat because it causes this here +they have an incentive to price low + + align:start position:0% +they have an incentive to price low + + + align:start position:0% +they have an incentive to price low +because the lower they price the more + + align:start position:0% +because the lower they price the more + + + align:start position:0% +because the lower they price the more +likely it is to jump back up and so you + + align:start position:0% +likely it is to jump back up and so you + + + align:start position:0% +likely it is to jump back up and so you +still get this sort of two-phase um + + align:start position:0% +still get this sort of two-phase um + + + align:start position:0% +still get this sort of two-phase um +thing going on but you get this sort of + + align:start position:0% +thing going on but you get this sort of + + + align:start position:0% +thing going on but you get this sort of +two-phase thing where you have + + align:start position:0% +two-phase thing where you have + + + align:start position:0% +two-phase thing where you have +incentives incentives cause a you know + + align:start position:0% +incentives incentives cause a you know + + + align:start position:0% +incentives incentives cause a you know +rare events cause us to jump down and + + align:start position:0% +rare events cause us to jump down and + + + align:start position:0% +rare events cause us to jump down and +then rare events cause us to jump back + + align:start position:0% +then rare events cause us to jump back + + + align:start position:0% +then rare events cause us to jump back +up and that's the optimal collusive + + align:start position:0% +up and that's the optimal collusive + + + align:start position:0% +up and that's the optimal collusive +agreement um yeah is the reason why + + align:start position:0% +agreement um yeah is the reason why + + + align:start position:0% +agreement um yeah is the reason why +they're pushing the price even below + + align:start position:0% +they're pushing the price even below + + + align:start position:0% +they're pushing the price even below +cost to make the punishment painful + + align:start position:0% +cost to make the punishment painful + + + align:start position:0% +cost to make the punishment painful +enough that go back up why would that + + align:start position:0% +enough that go back up why would that + + + align:start position:0% +enough that go back up why would that +happen yeah well if you think about it + + align:start position:0% +happen yeah well if you think about it + + + align:start position:0% +happen yeah well if you think about it +um you know um punishments are + + align:start position:0% +um you know um punishments are + + + align:start position:0% +um you know um punishments are +wasteful right pun you're in a + + align:start position:0% +wasteful right pun you're in a + + + align:start position:0% +wasteful right pun you're in a +punishment phase you had a period where + + align:start position:0% +punishment phase you had a period where + + + align:start position:0% +punishment phase you had a period where +there was demand and you served it at + + align:start position:0% +there was demand and you served it at + + + align:start position:0% +there was demand and you served it at +profit zero so wouldn't it be better to + + align:start position:0% +profit zero so wouldn't it be better to + + + align:start position:0% +profit zero so wouldn't it be better to +lose a little bit more money + + align:start position:0% +lose a little bit more money + + + align:start position:0% +lose a little bit more money +today you know because you're DP DP + + align:start position:0% +today you know because you're DP DP + + + align:start position:0% +today you know because you're DP DP +evaluated at C is like is small or + + align:start position:0% +evaluated at C is like is small or + + + align:start position:0% +evaluated at C is like is small or +whatever so you lose more money today + + align:start position:0% +whatever so you lose more money today + + + align:start position:0% +whatever so you lose more money today +and then you can get more money back in + + align:start position:0% +and then you can get more money back in + + + align:start position:0% +and then you can get more money back in +the future or something like that so it + + align:start position:0% +the future or something like that so it + + + align:start position:0% +the future or something like that so it +it's just in general you want + + align:start position:0% +it's just in general you want + + + align:start position:0% +it's just in general you want +to you know you want to give firms as + + align:start position:0% +to you know you want to give firms as + + + align:start position:0% +to you know you want to give firms as +much incentive as you can to make them + + align:start position:0% +much incentive as you can to make them + + + align:start position:0% +much incentive as you can to make them +low and a sort of a good incentive to + + align:start position:0% +low and a sort of a good incentive to + + + align:start position:0% +low and a sort of a good incentive to +price low is that things will get better + + align:start position:0% +price low is that things will get better + + + align:start position:0% +price low is that things will get better +in the future if you PR the lower you + + align:start position:0% +in the future if you PR the lower you + + + align:start position:0% +in the future if you PR the lower you +price today the more likely it is things + + align:start position:0% +price today the more likely it is things + + + align:start position:0% +price today the more likely it is things +will get better in the future is an + + align:start position:0% +will get better in the future is an + + + align:start position:0% +will get better in the future is an +extra incentive to get them to carry out + + align:start position:0% +extra incentive to get them to carry out + + + align:start position:0% +extra incentive to get them to carry out +the pricing low um + + align:start position:0% +the pricing low um + + + align:start position:0% +the pricing low um +yeah in this + + align:start position:0% + + + + align:start position:0% + +um I'm not sure if we need it in that P + + align:start position:0% +um I'm not sure if we need it in that P + + + align:start position:0% +um I'm not sure if we need it in that P +equal C example with pure Bertrand + + align:start position:0% +equal C example with pure Bertrand + + + align:start position:0% +equal C example with pure Bertrand +competition but in general you want the + + align:start position:0% +competition but in general you want the + + + align:start position:0% +competition but in general you want the +incentives on both sides um and it's you + + align:start position:0% +incentives on both sides um and it's you + + + align:start position:0% +incentives on both sides um and it's you +know I I guess thing about a br also + + align:start position:0% +know I I guess thing about a br also + + + align:start position:0% +know I I guess thing about a br also +wres that like in some sense the what + + align:start position:0% +wres that like in some sense the what + + + align:start position:0% +wres that like in some sense the what +they'll show you is that it's wrong like + + align:start position:0% +they'll show you is that it's wrong like + + + align:start position:0% +they'll show you is that it's wrong like +if you're trying to think about what are + + align:start position:0% +if you're trying to think about what are + + + align:start position:0% +if you're trying to think about what are +all the possible strategies you can use + + align:start position:0% +all the possible strategies you can use + + + align:start position:0% +all the possible strategies you can use +it's generally a bad idea to focus on + + align:start position:0% +it's generally a bad idea to focus on + + + align:start position:0% +it's generally a bad idea to focus on +strategy space because strategy space is + + align:start position:0% +strategy space because strategy space is + + + align:start position:0% +strategy space because strategy space is +very very complicated what you want to + + align:start position:0% +very very complicated what you want to + + + align:start position:0% +very very complicated what you want to +do is focus on payoff space where these + + align:start position:0% +do is focus on payoff space where these + + + align:start position:0% +do is focus on payoff space where these +things are just numbers and think about + + align:start position:0% +things are just numbers and think about + + + align:start position:0% +things are just numbers and think about +what num what what's the highest VM we + + align:start position:0% +what num what what's the highest VM we + + + align:start position:0% +what num what what's the highest VM we +can use and to support the highest VM + + align:start position:0% +can use and to support the highest VM + + + align:start position:0% +can use and to support the highest VM +possible we want to use the lowest VP + + align:start position:0% +possible we want to use the lowest VP + + + align:start position:0% +possible we want to use the lowest VP +possible and to just think about what + + align:start position:0% +possible and to just think about what + + + align:start position:0% +possible and to just think about what +constraints the VM and VP have to solve + + align:start position:0% +constraints the VM and VP have to solve + + + align:start position:0% +constraints the VM and VP have to solve +and think about that from a dynamic + + align:start position:0% +and think about that from a dynamic + + + align:start position:0% +and think about that from a dynamic +programming perspective just what's the + + align:start position:0% +programming perspective just what's the + + + align:start position:0% +programming perspective just what's the +highest VM what's the lowest VP what + + align:start position:0% +highest VM what's the lowest VP what + + + align:start position:0% +highest VM what's the lowest VP what +constraint would VP have to satisfy what + + align:start position:0% +constraint would VP have to satisfy what + + + align:start position:0% +constraint would VP have to satisfy what +constraint would VM have to satisfy from + + align:start position:0% +constraint would VM have to satisfy from + + + align:start position:0% +constraint would VM have to satisfy from +not wanting to deviate and then use that + + align:start position:0% +not wanting to deviate and then use that + + + align:start position:0% +not wanting to deviate and then use that +to I don't know it's focusing I was to + + align:start position:0% +to I don't know it's focusing I was to + + + align:start position:0% +to I don't know it's focusing I was to +say that's a big Insight from roup here + + align:start position:0% +say that's a big Insight from roup here + + + align:start position:0% +say that's a big Insight from roup here +SK we want to focus on this payoff space + + align:start position:0% +SK we want to focus on this payoff space + + + align:start position:0% +SK we want to focus on this payoff space +rather than on strategy space because + + align:start position:0% +rather than on strategy space because + + + align:start position:0% +rather than on strategy space because +payoff space can be like just + + align:start position:0% +payoff space can be like just + + + align:start position:0% +payoff space can be like just +two-dimensional whereas strategy space + + align:start position:0% +two-dimensional whereas strategy space + + + align:start position:0% +two-dimensional whereas strategy space +is infinite + + align:start position:0% +is infinite + + + align:start position:0% +is infinite +dimensional yeah okay then U fudenberg + + align:start position:0% +dimensional yeah okay then U fudenberg + + + align:start position:0% +dimensional yeah okay then U fudenberg +LaVine masin a few years later have this + + align:start position:0% +LaVine masin a few years later have this + + + align:start position:0% +LaVine masin a few years later have this +sort of paper showing that in many + + align:start position:0% +sort of paper showing that in many + + + align:start position:0% +sort of paper showing that in many +models we can avoid the inefficiency + + align:start position:0% +models we can avoid the inefficiency + + + align:start position:0% +models we can avoid the inefficiency +that's in green Porter and a Brer stiti + + align:start position:0% +that's in green Porter and a Brer stiti + + + align:start position:0% +that's in green Porter and a Brer stiti +by using asym + + align:start position:0% +by using asym + + + align:start position:0% +by using asym +strategies um the idea here is that + + align:start position:0% +strategies um the idea here is that + + + align:start position:0% +strategies um the idea here is that +let's suppose that you actually get a + + align:start position:0% +let's suppose that you actually get a + + + align:start position:0% +let's suppose that you actually get a +signal not only of that someone cheated + + align:start position:0% +signal not only of that someone cheated + + + align:start position:0% +signal not only of that someone cheated +but who cheated now the green Porter + + align:start position:0% +but who cheated now the green Porter + + + align:start position:0% +but who cheated now the green Porter +model you can't tell who cheated like if + + align:start position:0% +model you can't tell who cheated like if + + + align:start position:0% +model you can't tell who cheated like if +this is firms are supposed to be + + align:start position:0% +this is firms are supposed to be + + + align:start position:0% +this is firms are supposed to be +choosing these quantities price is too + + align:start position:0% +choosing these quantities price is too + + + align:start position:0% +choosing these quantities price is too +low there's no common signal of who + + align:start position:0% +low there's no common signal of who + + + align:start position:0% +low there's no common signal of who +cheated there's just that someone + + align:start position:0% +cheated there's just that someone + + + align:start position:0% +cheated there's just that someone +cheated but in other you know if the + + align:start position:0% +cheated but in other you know if the + + + align:start position:0% +cheated but in other you know if the +demand was at all + + align:start position:0% +demand was at all + + + align:start position:0% +demand was at all +asymmetric with regard to firm One's + + align:start position:0% +asymmetric with regard to firm One's + + + align:start position:0% +asymmetric with regard to firm One's +price and firm two's price or firm one + + align:start position:0% +price and firm two's price or firm one + + + align:start position:0% +price and firm two's price or firm one +quantity from two's quantity then you + + align:start position:0% +quantity from two's quantity then you + + + align:start position:0% +quantity from two's quantity then you +would get a signal about who cheated and + + align:start position:0% +would get a signal about who cheated and + + + align:start position:0% +would get a signal about who cheated and +so what fudenberg L Mas can say is that + + align:start position:0% +so what fudenberg L Mas can say is that + + + align:start position:0% +so what fudenberg L Mas can say is that +well if if you actually had a signal + + align:start position:0% +well if if you actually had a signal + + + align:start position:0% +well if if you actually had a signal +about who's cheated you should get rid + + align:start position:0% +about who's cheated you should get rid + + + align:start position:0% +about who's cheated you should get rid +of the price Wars and you should just do + + align:start position:0% +of the price Wars and you should just do + + + align:start position:0% +of the price Wars and you should just do +say a market share adjustment um if firm + + align:start position:0% +say a market share adjustment um if firm + + + align:start position:0% +say a market share adjustment um if firm +One prices if it looks like the demand + + align:start position:0% +One prices if it looks like the demand + + + align:start position:0% +One prices if it looks like the demand +makes me think firm one cheated then uh + + align:start position:0% +makes me think firm one cheated then uh + + + align:start position:0% +makes me think firm one cheated then uh +I should have instead of punishing firm + + align:start position:0% +I should have instead of punishing firm + + + align:start position:0% +I should have instead of punishing firm +instead of having a price War we should + + align:start position:0% +instead of having a price War we should + + + align:start position:0% +instead of having a price War we should +just have a market share reallocation + + align:start position:0% +just have a market share reallocation + + + align:start position:0% +just have a market share reallocation +where in the next period firm one gets a + + align:start position:0% +where in the next period firm one gets a + + + align:start position:0% +where in the next period firm one gets a +smaller market share and from two gets a + + align:start position:0% +smaller market share and from two gets a + + + align:start position:0% +smaller market share and from two gets a +larger market share uh and by doing + + align:start position:0% +larger market share uh and by doing + + + align:start position:0% +larger market share uh and by doing +market share reallocations we avoid all + + align:start position:0% +market share reallocations we avoid all + + + align:start position:0% +market share reallocations we avoid all +the inefficiency of the price war and we + + align:start position:0% +the inefficiency of the price war and we + + + align:start position:0% +the inefficiency of the price war and we +still punish people you know so for + + align:start position:0% +still punish people you know so for + + + align:start position:0% +still punish people you know so for +instance if you assumed like there were + + align:start position:0% +instance if you assumed like there were + + + align:start position:0% +instance if you assumed like there were +these two + + align:start position:0% +these two + + + align:start position:0% +these two +firms you know one of them had larger + + align:start position:0% +firms you know one of them had larger + + + align:start position:0% +firms you know one of them had larger +Demand on the Eastern us and one had + + align:start position:0% +Demand on the Eastern us and one had + + + align:start position:0% +Demand on the Eastern us and one had +larger demand in the western us then if + + align:start position:0% +larger demand in the western us then if + + + align:start position:0% +larger demand in the western us then if +you saw prices go down more in the East + + align:start position:0% +you saw prices go down more in the East + + + align:start position:0% +you saw prices go down more in the East +than in the west you'd be like okay the + + align:start position:0% +than in the west you'd be like okay the + + + align:start position:0% +than in the west you'd be like okay the +East Coast firm cheated therefore Next + + align:start position:0% +East Coast firm cheated therefore Next + + + align:start position:0% +East Coast firm cheated therefore Next +Period East Coast firm has to charge + + align:start position:0% +Period East Coast firm has to charge + + + align:start position:0% +Period East Coast firm has to charge +price you know Monopoly price plus + + align:start position:0% +price you know Monopoly price plus + + + align:start position:0% +price you know Monopoly price plus +something and the West Coast firm + + align:start position:0% +something and the West Coast firm + + + align:start position:0% +something and the West Coast firm +charges Monopoly price minus something + + align:start position:0% +charges Monopoly price minus something + + + align:start position:0% +charges Monopoly price minus something +and we reallocate market shares so that + + align:start position:0% +and we reallocate market shares so that + + + align:start position:0% +and we reallocate market shares so that +the East Coast firm is relatively + + align:start position:0% +the East Coast firm is relatively + + + align:start position:0% +the East Coast firm is relatively +disadvantaged but where there's no first + + align:start position:0% +disadvantaged but where there's no first + + + align:start position:0% +disadvantaged but where there's no first +order loss in in + + align:start position:0% +order loss in in + + + align:start position:0% +order loss in in +profits um so in general that's the sort + + align:start position:0% +profits um so in general that's the sort + + + align:start position:0% +profits um so in general that's the sort +of fudenberg L mask and ideaas if there + + align:start position:0% +of fudenberg L mask and ideaas if there + + + align:start position:0% +of fudenberg L mask and ideaas if there +is an asymmetry you know Green Porter is + + align:start position:0% +is an asymmetry you know Green Porter is + + + align:start position:0% +is an asymmetry you know Green Porter is +unusual in not having any asymmetry but + + align:start position:0% +unusual in not having any asymmetry but + + + align:start position:0% +unusual in not having any asymmetry but +if there is an asymmetry you just want + + align:start position:0% +if there is an asymmetry you just want + + + align:start position:0% +if there is an asymmetry you just want +to reallocate market shares between the + + align:start position:0% +to reallocate market shares between the + + + align:start position:0% +to reallocate market shares between the +firms rather than uh doing that okay uh + + align:start position:0% +firms rather than uh doing that okay uh + + + align:start position:0% +firms rather than uh doing that okay uh +anyway so there's sort of one place here + + align:start position:0% +anyway so there's sort of one place here + + + align:start position:0% +anyway so there's sort of one place here +where there's recent literature is + + align:start position:0% +where there's recent literature is + + + align:start position:0% +where there's recent literature is +the private monitoring where um you know + + align:start position:0% +the private monitoring where um you know + + + align:start position:0% +the private monitoring where um you know +uh all these papers are sort of focusing + + align:start position:0% +uh all these papers are sort of focusing + + + align:start position:0% +uh all these papers are sort of focusing +on this public monitoring where everyone + + align:start position:0% +on this public monitoring where everyone + + + align:start position:0% +on this public monitoring where everyone +observes the same + + align:start position:0% +observes the same + + + align:start position:0% +observes the same +signal everyone observes the same signal + + align:start position:0% +signal everyone observes the same signal + + + align:start position:0% +signal everyone observes the same signal +of what happened um if you imagine like + + align:start position:0% +of what happened um if you imagine like + + + align:start position:0% +of what happened um if you imagine like +if you had a model where the firm set + + align:start position:0% +if you had a model where the firm set + + + align:start position:0% +if you had a model where the firm set +p1t so you know we have these sort of + + align:start position:0% +p1t so you know we have these sort of + + + align:start position:0% +p1t so you know we have these sort of +firm set p1t and then you get demands + + align:start position:0% +firm set p1t and then you get demands + + + align:start position:0% +firm set p1t and then you get demands +q1t equals some function Q of p1t + + align:start position:0% +q1t equals some function Q of p1t + + + align:start position:0% +q1t equals some function Q of p1t +p2t uh plus Epsilon 1T and + + align:start position:0% +p2t uh plus Epsilon 1T and + + + align:start position:0% +p2t uh plus Epsilon 1T and +q2t Q2 of + + align:start position:0% +q2t Q2 of + + + align:start position:0% +q2t Q2 of +p1t + + align:start position:0% +p1t + + + align:start position:0% +p1t +p2t plus Epsilon 2T this would be what + + align:start position:0% +p2t plus Epsilon 2T this would be what + + + align:start position:0% +p2t plus Epsilon 2T this would be what +we would call a private monitoring model + + align:start position:0% +we would call a private monitoring model + + + align:start position:0% +we would call a private monitoring model +where each firm gets a s different + + align:start position:0% +where each firm gets a s different + + + align:start position:0% +where each firm gets a s different +signal so firm one observes its demand + + align:start position:0% +signal so firm one observes its demand + + + align:start position:0% +signal so firm one observes its demand +firm two its demands and the they have + + align:start position:0% +firm two its demands and the they have + + + align:start position:0% +firm two its demands and the they have +different signals because they have + + align:start position:0% +different signals because they have + + + align:start position:0% +different signals because they have +different epsilons this would be a + + align:start position:0% +different epsilons this would be a + + + align:start position:0% +different epsilons this would be a +private monitoring model where I don't + + align:start position:0% +private monitoring model where I don't + + + align:start position:0% +private monitoring model where I don't +know what you I don't know what signal + + align:start position:0% +know what you I don't know what signal + + + align:start position:0% +know what you I don't know what signal +you got you don't know what signal I got + + align:start position:0% +you got you don't know what signal I got + + + align:start position:0% +you got you don't know what signal I got +anyway it it's you know harder to solve + + align:start position:0% +anyway it it's you know harder to solve + + + align:start position:0% +anyway it it's you know harder to solve +models once you have that sort of + + align:start position:0% +models once you have that sort of + + + align:start position:0% +models once you have that sort of +private uncertainty instead of the + + align:start position:0% +private uncertainty instead of the + + + align:start position:0% +private uncertainty instead of the +public uncertainty there's a literature + + align:start position:0% +public uncertainty there's a literature + + + align:start position:0% +public uncertainty there's a literature +on that um actually Alex has a very nice + + align:start position:0% +on that um actually Alex has a very nice + + + align:start position:0% +on that um actually Alex has a very nice +recent paper arguing that sometimes + + align:start position:0% +recent paper arguing that sometimes + + + align:start position:0% +recent paper arguing that sometimes +actually private monitoring will makes + + align:start position:0% +actually private monitoring will makes + + + align:start position:0% +actually private monitoring will makes +more complicated could even make + + align:start position:0% +more complicated could even make + + + align:start position:0% +more complicated could even make +collusion easy easier um although + + align:start position:0% +collusion easy easier um although + + + align:start position:0% +collusion easy easier um although +obviously sometimes the normal case + + align:start position:0% +obviously sometimes the normal case + + + align:start position:0% +obviously sometimes the normal case +would makes collusion harder but some + + align:start position:0% +would makes collusion harder but some + + + align:start position:0% +would makes collusion harder but some +case where that can even make collusion + + align:start position:0% +case where that can even make collusion + + + align:start position:0% +case where that can even make collusion +easier + + align:start position:0% +easier + + + align:start position:0% +easier +okay okay and any + + align:start position:0% + + + + align:start position:0% + +questions okay the next set of things I + + align:start position:0% +questions okay the next set of things I + + + align:start position:0% +questions okay the next set of things I +wanted to just I'm going to go through + + align:start position:0% +wanted to just I'm going to go through + + + align:start position:0% +wanted to just I'm going to go through +and highlight them quickly maybe I'd + + align:start position:0% +and highlight them quickly maybe I'd + + + align:start position:0% +and highlight them quickly maybe I'd +come back to them at the end but I + + align:start position:0% +come back to them at the end but I + + + align:start position:0% +come back to them at the end but I +wanted to get to sort of more recent + + align:start position:0% +wanted to get to sort of more recent + + + align:start position:0% +wanted to get to sort of more recent +material at the end so just some + + align:start position:0% +material at the end so just some + + + align:start position:0% +material at the end so just some +Classics uh rber and saloner 1986 + + align:start position:0% +Classics uh rber and saloner 1986 + + + align:start position:0% +Classics uh rber and saloner 1986 +uh argues + + align:start position:0% +uh argues + + + align:start position:0% +uh argues +that variable demand can make collusion + + align:start position:0% +that variable demand can make collusion + + + align:start position:0% +that variable demand can make collusion +harder uh let me just say the basic + + align:start position:0% +harder uh let me just say the basic + + + align:start position:0% +harder uh let me just say the basic +argument here is as I said it's harder + + align:start position:0% +argument here is as I said it's harder + + + align:start position:0% +argument here is as I said it's harder +to collude when the present is more + + align:start position:0% +to collude when the present is more + + + align:start position:0% +to collude when the present is more +important than the future and when the + + align:start position:0% +important than the future and when the + + + align:start position:0% +important than the future and when the +future is more important it's easy to + + align:start position:0% +future is more important it's easy to + + + align:start position:0% +future is more important it's easy to +collude when the future's less important + + align:start position:0% +collude when the future's less important + + + align:start position:0% +collude when the future's less important +it's hard to collude and so the basic + + align:start position:0% +it's hard to collude and so the basic + + + align:start position:0% +it's hard to collude and so the basic +intuition for rodenberg and Sol owner + + align:start position:0% +intuition for rodenberg and Sol owner + + + align:start position:0% +intuition for rodenberg and Sol owner +was that imagine we just + + align:start position:0% +was that imagine we just + + + align:start position:0% +was that imagine we just +have firms competing + + align:start position:0% +have firms competing + + + align:start position:0% +have firms competing +and you know they're just facing sort of + + align:start position:0% +and you know they're just facing sort of + + + align:start position:0% +and you know they're just facing sort of +a macroeconomy that has ups and downs to + + align:start position:0% +a macroeconomy that has ups and downs to + + + align:start position:0% +a macroeconomy that has ups and downs to +it so if you just have you know business + + align:start position:0% +it so if you just have you know business + + + align:start position:0% +it so if you just have you know business +Cycles like this where this is um this + + align:start position:0% +Cycles like this where this is um this + + + align:start position:0% +Cycles like this where this is um this +is T and this is QT of P star so imagine + + align:start position:0% +is T and this is QT of P star so imagine + + + align:start position:0% +is T and this is QT of P star so imagine +you have firms are trying to collude + + align:start position:0% +you have firms are trying to collude + + + align:start position:0% +you have firms are trying to collude +with their business cycles and so there + + align:start position:0% +with their business cycles and so there + + + align:start position:0% +with their business cycles and so there +are times when they're selling 1955 + + align:start position:0% +are times when they're selling 1955 + + + align:start position:0% +are times when they're selling 1955 +they're selling a lot of cars 1957 + + align:start position:0% +they're selling a lot of cars 1957 + + + align:start position:0% +they're selling a lot of cars 1957 +they're not selling as many cars um + + align:start position:0% + + + + align:start position:0% + +you know R against the owner note that + + align:start position:0% +you know R against the owner note that + + + align:start position:0% +you know R against the owner note that +in an economy like this it's harder to + + align:start position:0% +in an economy like this it's harder to + + + align:start position:0% +in an economy like this it's harder to +collude when when demand is variable + + align:start position:0% +collude when when demand is variable + + + align:start position:0% +collude when when demand is variable +because here the present matters a lot + + align:start position:0% +because here the present matters a lot + + + align:start position:0% +because here the present matters a lot +rela to the Future whereas here the + + align:start position:0% +rela to the Future whereas here the + + + align:start position:0% +rela to the Future whereas here the +present future would matter more so here + + align:start position:0% +present future would matter more so here + + + align:start position:0% +present future would matter more so here +it's relatively easy to collude here + + align:start position:0% +it's relatively easy to collude here + + + align:start position:0% +it's relatively easy to collude here +it's hard to + + align:start position:0% +it's hard to + + + align:start position:0% +it's hard to +collude and so then what renberg and + + align:start position:0% +collude and so then what renberg and + + + align:start position:0% +collude and so then what renberg and +owner ask is well you know what would + + align:start position:0% +owner ask is well you know what would + + + align:start position:0% +owner ask is well you know what would +firms do if they were colluding in a + + align:start position:0% +firms do if they were colluding in a + + + align:start position:0% +firms do if they were colluding in a +market like + + align:start position:0% +market like + + + align:start position:0% +market like +this + + align:start position:0% +this + + + align:start position:0% +this +and imagine the Delta is such that you + + align:start position:0% +and imagine the Delta is such that you + + + align:start position:0% +and imagine the Delta is such that you +can't collude on the Monopoly price here + + align:start position:0% +can't collude on the Monopoly price here + + + align:start position:0% +can't collude on the Monopoly price here +but you can collude on the Monopoly + + align:start position:0% +but you can collude on the Monopoly + + + align:start position:0% +but you can collude on the Monopoly +price here so what do you + + align:start position:0% +price here so what do you + + + align:start position:0% +price here so what do you +do in these periods um so if there was + + align:start position:0% +do in these periods um so if there was + + + align:start position:0% +do in these periods um so if there was +some you + + align:start position:0% + + + + align:start position:0% + +know you know imagine this is just a + + align:start position:0% +know you know imagine this is just a + + + align:start position:0% +know you know imagine this is just a +multiplicative shock to demand so what + + align:start position:0% +multiplicative shock to demand so what + + + align:start position:0% +multiplicative shock to demand so what +I'd like to do is have the same Monopoly + + align:start position:0% +I'd like to do is have the same Monopoly + + + align:start position:0% +I'd like to do is have the same Monopoly +price in every period um I'd like to + + align:start position:0% +price in every period um I'd like to + + + align:start position:0% +price in every period um I'd like to +have the same Monopoly price in every + + align:start position:0% +have the same Monopoly price in every + + + align:start position:0% +have the same Monopoly price in every +period but what I'm going to need to do + + align:start position:0% +period but what I'm going to need to do + + + align:start position:0% +period but what I'm going to need to do +is when we're in these value of the high + + align:start position:0% +is when we're in these value of the high + + + align:start position:0% +is when we're in these value of the high +demand shocks I'm going to have to sort + + align:start position:0% +demand shocks I'm going to have to sort + + + align:start position:0% +demand shocks I'm going to have to sort +of drag down my price and price it less + + align:start position:0% +of drag down my price and price it less + + + align:start position:0% +of drag down my price and price it less +than the Monopoly + + align:start position:0% +than the Monopoly + + + align:start position:0% +than the Monopoly +price and I'm going to have to price it + + align:start position:0% +price and I'm going to have to price it + + + align:start position:0% +price and I'm going to have to price it +less than Monopoly price because I just + + align:start position:0% +less than Monopoly price because I just + + + align:start position:0% +less than Monopoly price because I just +pull my price down to reduce the + + align:start position:0% +pull my price down to reduce the + + + align:start position:0% +pull my price down to reduce the +incentive to temptation to + + align:start position:0% +incentive to temptation to + + + align:start position:0% +incentive to temptation to +deviate and so what + + align:start position:0% +deviate and so what + + + align:start position:0% +deviate and so what +uh you know road to marget owner argue + + align:start position:0% +uh you know road to marget owner argue + + + align:start position:0% +uh you know road to marget owner argue +is that if you have a + + align:start position:0% +is that if you have a + + + align:start position:0% +is that if you have a +cartel um it's harder to clude during + + align:start position:0% +cartel um it's harder to clude during + + + align:start position:0% +cartel um it's harder to clude during +the Booms that doesn't mean you should + + align:start position:0% +the Booms that doesn't mean you should + + + align:start position:0% +the Booms that doesn't mean you should +have price Wars that inclusion should + + align:start position:0% +have price Wars that inclusion should + + + align:start position:0% +have price Wars that inclusion should +break down but what you should have is + + align:start position:0% +break down but what you should have is + + + align:start position:0% +break down but what you should have is +like counter cyclical pricing where + + align:start position:0% +like counter cyclical pricing where + + + align:start position:0% +like counter cyclical pricing where +because demand is high we drop our price + + align:start position:0% +because demand is high we drop our price + + + align:start position:0% +because demand is high we drop our price +down and we could actually see lower + + align:start position:0% +down and we could actually see lower + + + align:start position:0% +down and we could actually see lower +prices here uh than we see + + align:start position:0% +prices here uh than we see + + + align:start position:0% +prices here uh than we see +here now obviously you know depending on + + align:start position:0% +here now obviously you know depending on + + + align:start position:0% +here now obviously you know depending on +what demand specification you make if if + + align:start position:0% +what demand specification you make if if + + + align:start position:0% +what demand specification you make if if +I I do linear demands you know in linear + + align:start position:0% +I I do linear demands you know in linear + + + align:start position:0% +I I do linear demands you know in linear +demands price goes up when demand goes + + align:start position:0% +demands price goes up when demand goes + + + align:start position:0% +demands price goes up when demand goes +up so it could be that the Monopoly + + align:start position:0% +up so it could be that the Monopoly + + + align:start position:0% +up so it could be that the Monopoly +price isn't a flatline it could be the + + align:start position:0% +price isn't a flatline it could be the + + + align:start position:0% +price isn't a flatline it could be the +Monopoly price is would also be + + align:start position:0% +Monopoly price is would also be + + + align:start position:0% +Monopoly price is would also be +something that mirrors the + + align:start position:0% +something that mirrors the + + + align:start position:0% +something that mirrors the +demand then what what we going to own + + align:start position:0% +demand then what what we going to own + + + align:start position:0% +demand then what what we going to own +say is okay you're going to pull down + + align:start position:0% +say is okay you're going to pull down + + + align:start position:0% +say is okay you're going to pull down +your price here but pulling down your + + align:start position:0% +your price here but pulling down your + + + align:start position:0% +your price here but pulling down your +price here it could still be you know + + align:start position:0% +price here it could still be you know + + + align:start position:0% +price here it could still be you know +the it it could still be higher than the + + align:start position:0% +the it it could still be higher than the + + + align:start position:0% +the it it could still be higher than the +price here because it's uh i' I've + + align:start position:0% +price here because it's uh i' I've + + + align:start position:0% +price here because it's uh i' I've +pulled down my price but I pulled it + + align:start position:0% +pulled down my price but I pulled it + + + align:start position:0% +pulled down my price but I pulled it +down from something that was starting + + align:start position:0% +down from something that was starting + + + align:start position:0% +down from something that was starting +even higher um but anyway the basic idea + + align:start position:0% +even higher um but anyway the basic idea + + + align:start position:0% +even higher um but anyway the basic idea +of ronberg against loner is that you can + + align:start position:0% +of ronberg against loner is that you can + + + align:start position:0% +of ronberg against loner is that you can +get this counter cyclical pricing that + + align:start position:0% +get this counter cyclical pricing that + + + align:start position:0% +get this counter cyclical pricing that +comes from a counter cyclical incentive + + align:start position:0% +comes from a counter cyclical incentive + + + align:start position:0% +comes from a counter cyclical incentive +to deviate on a cartel + + align:start position:0% +to deviate on a cartel + + + align:start position:0% +to deviate on a cartel +agreement uh anyway on the slide + + align:start position:0% +agreement uh anyway on the slide + + + align:start position:0% +agreement uh anyway on the slide +I've worked out an example in a + + align:start position:0% +I've worked out an example in a + + + align:start position:0% +I've worked out an example in a +two-state model where demand is just IID + + align:start position:0% +two-state model where demand is just IID + + + align:start position:0% +two-state model where demand is just IID +high or + + align:start position:0% +high or + + + align:start position:0% +high or +low uh and when it's demand is IID high + + align:start position:0% +low uh and when it's demand is IID high + + + align:start position:0% +low uh and when it's demand is IID high +or low the algebra is easy and you can + + align:start position:0% +or low the algebra is easy and you can + + + align:start position:0% +or low the algebra is easy and you can +work out what you do um but you can look + + align:start position:0% +work out what you do um but you can look + + + align:start position:0% +work out what you do um but you can look +at that on slides if you like + + align:start position:0% + + + + align:start position:0% + +um see which of these things do I want + + align:start position:0% +um see which of these things do I want + + + align:start position:0% +um see which of these things do I want +to say yeah so for intermediate do + + align:start position:0% +to say yeah so for intermediate do + + + align:start position:0% +to say yeah so for intermediate do +markups or counter + + align:start position:0% +markups or counter + + + align:start position:0% +markups or counter +cyclical um yeah if you add imperfect + + align:start position:0% +cyclical um yeah if you add imperfect + + + align:start position:0% +cyclical um yeah if you add imperfect +observation to this um you know the + + align:start position:0% +observation to this um you know the + + + align:start position:0% +observation to this um you know the +intuition is still that collusion is + + align:start position:0% +intuition is still that collusion is + + + align:start position:0% +intuition is still that collusion is +harder when demand is high than when + + align:start position:0% +harder when demand is high than when + + + align:start position:0% +harder when demand is high than when +demand is low um and so what are you + + align:start position:0% +demand is low um and so what are you + + + align:start position:0% +demand is low um and so what are you +going to have to do you know one of two + + align:start position:0% +going to have to do you know one of two + + + align:start position:0% +going to have to do you know one of two +things has to happen + + align:start position:0% +things has to happen + + + align:start position:0% +things has to happen +either um either you have to reduce the + + align:start position:0% +either um either you have to reduce the + + + align:start position:0% +either um either you have to reduce the +prices and reduce the markups or + + align:start position:0% +prices and reduce the markups or + + + align:start position:0% +prices and reduce the markups or +breakdowns of collusion become more + + align:start position:0% +breakdowns of collusion become more + + + align:start position:0% +breakdowns of collusion become more +likely or both uh but in general you + + align:start position:0% +likely or both uh but in general you + + + align:start position:0% +likely or both uh but in general you +could do adjust one either of two ways + + align:start position:0% +could do adjust one either of two ways + + + align:start position:0% +could do adjust one either of two ways +you know you could either drop the + + align:start position:0% +you know you could either drop the + + + align:start position:0% +you know you could either drop the +prices or you could keep the prices up + + align:start position:0% +prices or you could keep the prices up + + + align:start position:0% +prices or you could keep the prices up +and just have more frequent breakdowns + + align:start position:0% +and just have more frequent breakdowns + + + align:start position:0% +and just have more frequent breakdowns +of collusion or um you know you could do + + align:start position:0% +of collusion or um you know you could do + + + align:start position:0% +of collusion or um you know you could do +a combination of the two of them or you + + align:start position:0% +a combination of the two of them or you + + + align:start position:0% +a combination of the two of them or you +could do one but not the other possibly + + align:start position:0% +could do one but not the other possibly + + + align:start position:0% +could do one but not the other possibly +depending on the specification but it + + align:start position:0% +depending on the specification but it + + + align:start position:0% +depending on the specification but it +it's just sort of the general idea + + align:start position:0% +it's just sort of the general idea + + + align:start position:0% +it's just sort of the general idea +should be that collusion is harder and + + align:start position:0% +should be that collusion is harder and + + + align:start position:0% +should be that collusion is harder and +something has to work + + align:start position:0% +something has to work + + + align:start position:0% +something has to work +worse + + align:start position:0% + + + + align:start position:0% + +okay okay + + align:start position:0% +okay okay + + + align:start position:0% +okay okay +um second idea I'll do kind of quickly + + align:start position:0% +um second idea I'll do kind of quickly + + + align:start position:0% +um second idea I'll do kind of quickly +um private cost + + align:start position:0% +um private cost + + + align:start position:0% +um private cost +shocks um so you know aan Bagwell note + + align:start position:0% +shocks um so you know aan Bagwell note + + + align:start position:0% +shocks um so you know aan Bagwell note +that sort of efficient collusion you can + + align:start position:0% +that sort of efficient collusion you can + + + align:start position:0% +that sort of efficient collusion you can +think of as having two components to it + + align:start position:0% +think of as having two components to it + + + align:start position:0% +think of as having two components to it +one is that + + align:start position:0% +one is that + + + align:start position:0% +one is that +um one is that firms want to charge the + + align:start position:0% +um one is that firms want to charge the + + + align:start position:0% +um one is that firms want to charge the +Monopoly price the other is that the + + align:start position:0% +Monopoly price the other is that the + + + align:start position:0% +Monopoly price the other is that the +colluding firms want to produce + + align:start position:0% +colluding firms want to produce + + + align:start position:0% +colluding firms want to produce +efficiently and in some cases the firms + + align:start position:0% +efficiently and in some cases the firms + + + align:start position:0% +efficiently and in some cases the firms +are going to have cost shocks and make + + align:start position:0% +are going to have cost shocks and make + + + align:start position:0% +are going to have cost shocks and make +it efficient for one of the two of them + + align:start position:0% +it efficient for one of the two of them + + + align:start position:0% +it efficient for one of the two of them +to to serve so for instance for this one + + align:start position:0% +to to serve so for instance for this one + + + align:start position:0% +to to serve so for instance for this one +for an example think about you know + + align:start position:0% +for an example think about you know + + + align:start position:0% +for an example think about you know +let's imagine this may not be sort of so + + align:start position:0% +let's imagine this may not be sort of so + + + align:start position:0% +let's imagine this may not be sort of so +unrealistic that in a city like + + align:start position:0% +unrealistic that in a city like + + + align:start position:0% +unrealistic that in a city like +Cambridge if there's a giant Paving job + + align:start position:0% +Cambridge if there's a giant Paving job + + + align:start position:0% +Cambridge if there's a giant Paving job +that needs to be done like you need to + + align:start position:0% +that needs to be done like you need to + + + align:start position:0% +that needs to be done like you need to +repave Memorial Drive or whatever + + align:start position:0% +repave Memorial Drive or whatever + + + align:start position:0% +repave Memorial Drive or whatever +there's a very small number of firms + + align:start position:0% +there's a very small number of firms + + + align:start position:0% +there's a very small number of firms +that could do that job okay and so what + + align:start position:0% +that could do that job okay and so what + + + align:start position:0% +that could do that job okay and so what +the city of Cambridge is going to do is + + align:start position:0% +the city of Cambridge is going to do is + + + align:start position:0% +the city of Cambridge is going to do is +sort of put out for bids like we need + + align:start position:0% +sort of put out for bids like we need + + + align:start position:0% +sort of put out for bids like we need +someone to repay two miles of Memorial + + align:start position:0% +someone to repay two miles of Memorial + + + align:start position:0% +someone to repay two miles of Memorial +Drive there's a very limited number of + + align:start position:0% +Drive there's a very limited number of + + + align:start position:0% +Drive there's a very limited number of +firms who could do that job um those two + + align:start position:0% +firms who could do that job um those two + + + align:start position:0% +firms who could do that job um those two +firms are going to have different costs + + align:start position:0% +firms are going to have different costs + + + align:start position:0% +firms are going to have different costs +of doing the job in each period because + + align:start position:0% +of doing the job in each period because + + + align:start position:0% +of doing the job in each period because +their equipment may be in use elsewhere + + align:start position:0% +their equipment may be in use elsewhere + + + align:start position:0% +their equipment may be in use elsewhere +it may be that I've got a job in Riv + + align:start position:0% +it may be that I've got a job in Riv + + + align:start position:0% +it may be that I've got a job in Riv +where I'm Paving some big road and it + + align:start position:0% +where I'm Paving some big road and it + + + align:start position:0% +where I'm Paving some big road and it +would be costly for me to also get extra + + align:start position:0% +would be costly for me to also get extra + + + align:start position:0% +would be costly for me to also get extra +Manpower and equipment to get to + + align:start position:0% +Manpower and equipment to get to + + + align:start position:0% +Manpower and equipment to get to +Cambridge or could be that I don't have + + align:start position:0% +Cambridge or could be that I don't have + + + align:start position:0% +Cambridge or could be that I don't have +any other jobs and so this will be a + + align:start position:0% +any other jobs and so this will be a + + + align:start position:0% +any other jobs and so this will be a +good time for me to serve Cambridge um + + align:start position:0% +good time for me to serve Cambridge um + + + align:start position:0% +good time for me to serve Cambridge um +so what they assume is that you know we + + align:start position:0% +so what they assume is that you know we + + + align:start position:0% +so what they assume is that you know we +have these two firms they're serving + + align:start position:0% +have these two firms they're serving + + + align:start position:0% +have these two firms they're serving +some demand and the firms have random + + align:start position:0% +some demand and the firms have random + + + align:start position:0% +some demand and the firms have random +cost shocks again to make it simple they + + align:start position:0% +cost shocks again to make it simple they + + + align:start position:0% +cost shocks again to make it simple they +just go with two different levels of + + align:start position:0% +just go with two different levels of + + + align:start position:0% +just go with two different levels of +cost CL or ch and what the firms would + + align:start position:0% +cost CL or ch and what the firms would + + + align:start position:0% +cost CL or ch and what the firms would +like to do is collude on charging + + align:start position:0% +like to do is collude on charging + + + align:start position:0% +like to do is collude on charging +Monopoly price and collude on whichever + + align:start position:0% +Monopoly price and collude on whichever + + + align:start position:0% +Monopoly price and collude on whichever +of us has low + + align:start position:0% +of us has low + + + align:start position:0% +of us has low +cost uh wins the job and whoever has + + align:start position:0% +cost uh wins the job and whoever has + + + align:start position:0% +cost uh wins the job and whoever has +high cost doesn't win the job so in some + + align:start position:0% +high cost doesn't win the job so in some + + + align:start position:0% +high cost doesn't win the job so in some +sense what we should do every period is + + align:start position:0% +sense what we should do every period is + + + align:start position:0% +sense what we should do every period is +you know if + + align:start position:0% + + + + align:start position:0% + +um yeah so the city of Cambridge is just + + align:start position:0% +um yeah so the city of Cambridge is just + + + align:start position:0% +um yeah so the city of Cambridge is just +repeatedly issuing these requests for + + align:start position:0% +repeatedly issuing these requests for + + + align:start position:0% +repeatedly issuing these requests for +bids if our costs Are CL C what we + + align:start position:0% +bids if our costs Are CL C what we + + + align:start position:0% +bids if our costs Are CL C what we +should do is I bid the Monopoly price + + align:start position:0% +should do is I bid the Monopoly price + + + align:start position:0% +should do is I bid the Monopoly price +and you bid the Monopoly price plus + + align:start position:0% +and you bid the Monopoly price plus + + + align:start position:0% +and you bid the Monopoly price plus +Epsilon and if the costs are + + align:start position:0% +Epsilon and if the costs are + + + align:start position:0% +Epsilon and if the costs are +chcl uh then we can bid you know + + align:start position:0% +chcl uh then we can bid you know + + + align:start position:0% +chcl uh then we can bid you know +Monopoly price plus Epsilon Monopoly + + align:start position:0% +Monopoly price plus Epsilon Monopoly + + + align:start position:0% +Monopoly price plus Epsilon Monopoly +price and you know the costs are ch + + align:start position:0% +price and you know the costs are ch + + + align:start position:0% +price and you know the costs are ch +ch you know we can just go ahead and bid + + align:start position:0% +ch you know we can just go ahead and bid + + + align:start position:0% +ch you know we can just go ahead and bid +Monopoly price Monopoly price and just + + align:start position:0% +Monopoly price Monopoly price and just + + + align:start position:0% +Monopoly price Monopoly price and just +one of us has chosen at random to win + + align:start position:0% +one of us has chosen at random to win + + + align:start position:0% +one of us has chosen at random to win +that auction so this is what we would + + align:start position:0% +that auction so this is what we would + + + align:start position:0% +that auction so this is what we would +like to + + align:start position:0% +like to + + + align:start position:0% +like to +do + + align:start position:0% + + + + align:start position:0% + +um you know how do you do that well the + + align:start position:0% +um you know how do you do that well the + + + align:start position:0% +um you know how do you do that well the +firms have this other problem now like + + align:start position:0% +firms have this other problem now like + + + align:start position:0% +firms have this other problem now like +the problem is like this communication + + align:start position:0% +the problem is like this communication + + + align:start position:0% +the problem is like this communication +between them like the question is who + + align:start position:0% +between them like the question is who + + + align:start position:0% +between them like the question is who +gets to bid the Monopoly price and who's + + align:start position:0% +gets to bid the Monopoly price and who's + + + align:start position:0% +gets to bid the Monopoly price and who's +supposed to bid the higher price and let + + align:start position:0% +supposed to bid the higher price and let + + + align:start position:0% +supposed to bid the higher price and let +the other firm thing you know in some + + align:start position:0% +the other firm thing you know in some + + + align:start position:0% +the other firm thing you know in some +sense every period like the firms can + + align:start position:0% +sense every period like the firms can + + + align:start position:0% +sense every period like the firms can +get together and be like okay who wins + + align:start position:0% +get together and be like okay who wins + + + align:start position:0% +get together and be like okay who wins +this who wins this job who has the CL + + align:start position:0% +this who wins this job who has the CL + + + align:start position:0% +this who wins this job who has the CL +cost and like everyone's going raise + + align:start position:0% +cost and like everyone's going raise + + + align:start position:0% +cost and like everyone's going raise +hand oh yeah my cost is CL this period I + + align:start position:0% +hand oh yeah my cost is CL this period I + + + align:start position:0% +hand oh yeah my cost is CL this period I +should get this job you know bad luck + + align:start position:0% +should get this job you know bad luck + + + align:start position:0% +should get this job you know bad luck +for you but I guess you bid price plus + + align:start position:0% +for you but I guess you bid price plus + + + align:start position:0% +for you but I guess you bid price plus +Epsilon or whatever and then you know + + align:start position:0% +Epsilon or whatever and then you know + + + align:start position:0% +Epsilon or whatever and then you know +again you have this temptation over and + + align:start position:0% +again you have this temptation over and + + + align:start position:0% +again you have this temptation over and +over and over again the FR raise the + + align:start position:0% +over and over again the FR raise the + + + align:start position:0% +over and over again the FR raise the +hands be like oh yep me just happen to + + align:start position:0% +hands be like oh yep me just happen to + + + align:start position:0% +hands be like oh yep me just happen to +have all my equipment spare a bunch of + + align:start position:0% +have all my equipment spare a bunch of + + + align:start position:0% +have all my equipment spare a bunch of +spare labor I need to win this job again + + align:start position:0% +spare labor I need to win this job again + + + align:start position:0% +spare labor I need to win this job again +this + + align:start position:0% +this + + + align:start position:0% +this +month + + align:start position:0% +month + + + align:start position:0% +month +um what a b shows you know that's an + + align:start position:0% +um what a b shows you know that's an + + + align:start position:0% +um what a b shows you know that's an +additional obstacle to collusion this + + align:start position:0% +additional obstacle to collusion this + + + align:start position:0% +additional obstacle to collusion this +desire to sort of that having sort of + + align:start position:0% +desire to sort of that having sort of + + + align:start position:0% +desire to sort of that having sort of +the need to shift the market shares + + align:start position:0% +the need to shift the market shares + + + align:start position:0% +the need to shift the market shares +across firms is an extra problem + + align:start position:0% +across firms is an extra problem + + + align:start position:0% +across firms is an extra problem +uh one thing they show is if Delta's + + align:start position:0% +uh one thing they show is if Delta's + + + align:start position:0% +uh one thing they show is if Delta's +close to one um the firms can still + + align:start position:0% +close to one um the firms can still + + + align:start position:0% +close to one um the firms can still +achieve full collusion and this isn't a + + align:start position:0% +achieve full collusion and this isn't a + + + align:start position:0% +achieve full collusion and this isn't a +problem uh the way they can do this is + + align:start position:0% +problem uh the way they can do this is + + + align:start position:0% +problem uh the way they can do this is +with this sort of uh Dynamic allocation + + align:start position:0% +with this sort of uh Dynamic allocation + + + align:start position:0% +with this sort of uh Dynamic allocation +of market share so the rule could be you + + align:start position:0% +of market share so the rule could be you + + + align:start position:0% +of market share so the rule could be you +know if my costs are really low and your + + align:start position:0% +know if my costs are really low and your + + + align:start position:0% +know if my costs are really low and your +costs are high I go ahead and bid pm and + + align:start position:0% +costs are high I go ahead and bid pm and + + + align:start position:0% +costs are high I go ahead and bid pm and +I win but then the next time cl cl + + align:start position:0% +I win but then the next time cl cl + + + align:start position:0% +I win but then the next time cl cl +happens + + align:start position:0% + + + + align:start position:0% + +if you said your cost was low and you + + align:start position:0% +if you said your cost was low and you + + + align:start position:0% +if you said your cost was low and you +wanted to be the the winner of this + + align:start position:0% +wanted to be the the winner of this + + + align:start position:0% +wanted to be the the winner of this +auction then the next time an auction + + align:start position:0% +auction then the next time an auction + + + align:start position:0% +auction then the next time an auction +comes around where we both raise our + + align:start position:0% + + + + align:start position:0% + +hands you have to set the high price and + + align:start position:0% +hands you have to set the high price and + + + align:start position:0% +hands you have to set the high price and +the other firm gets to set the low price + + align:start position:0% +the other firm gets to set the low price + + + align:start position:0% +the other firm gets to set the low price +so it's like you dynamically make up for + + align:start position:0% +so it's like you dynamically make up for + + + align:start position:0% +so it's like you dynamically make up for +the market share that gains that firms + + align:start position:0% +the market share that gains that firms + + + align:start position:0% +the market share that gains that firms +got from claiming their cost was low by + + align:start position:0% +got from claiming their cost was low by + + + align:start position:0% +got from claiming their cost was low by +saying okay if you claim your cost is + + align:start position:0% +saying okay if you claim your cost is + + + align:start position:0% +saying okay if you claim your cost is +low today then the next time we both + + align:start position:0% +low today then the next time we both + + + align:start position:0% +low today then the next time we both +claim our cost or low I get the demand + + align:start position:0% +claim our cost or low I get the demand + + + align:start position:0% +claim our cost or low I get the demand +and you don't get the demand + + align:start position:0% +and you don't get the demand + + + align:start position:0% +and you don't get the demand +and so the idea is that by dynamically + + align:start position:0% +and so the idea is that by dynamically + + + align:start position:0% +and so the idea is that by dynamically +reallocating market share um we can + + align:start position:0% +reallocating market share um we can + + + align:start position:0% +reallocating market share um we can +sometimes collude optimally um when + + align:start position:0% +sometimes collude optimally um when + + + align:start position:0% +sometimes collude optimally um when +Delta's not as close to one however this + + align:start position:0% +Delta's not as close to one however this + + + align:start position:0% +Delta's not as close to one however this +stops working and the problem is you can + + align:start position:0% +stops working and the problem is you can + + + align:start position:0% +stops working and the problem is you can +get this sort of same problem I + + align:start position:0% +get this sort of same problem I + + + align:start position:0% +get this sort of same problem I +discussed before if just some firm over + + align:start position:0% +discussed before if just some firm over + + + align:start position:0% +discussed before if just some firm over +and over again says yeah my costs are + + align:start position:0% +and over again says yeah my costs are + + + align:start position:0% +and over again says yeah my costs are +low my costs are low my costs are low + + align:start position:0% +low my costs are low my costs are low + + + align:start position:0% +low my costs are low my costs are low +there's got you know like you can't keep + + align:start position:0% +there's got you know like you can't keep + + + align:start position:0% +there's got you know like you can't keep +promising okay next time your cost next + + align:start position:0% +promising okay next time your cost next + + + align:start position:0% +promising okay next time your cost next +time both costs are like you you sort of + + align:start position:0% +time both costs are like you you sort of + + + align:start position:0% +time both costs are like you you sort of +in some sense you're accumulating debts + + align:start position:0% +in some sense you're accumulating debts + + + align:start position:0% +in some sense you're accumulating debts +to the other firm and you can't + + align:start position:0% +to the other firm and you can't + + + align:start position:0% +to the other firm and you can't +accumulate too many debts before the + + align:start position:0% +accumulate too many debts before the + + + align:start position:0% +accumulate too many debts before the +thing stops working so at some point + + align:start position:0% +thing stops working so at some point + + + align:start position:0% +thing stops working so at some point +you'd have to get to an agreement where + + align:start position:0% +you'd have to get to an agreement where + + + align:start position:0% +you'd have to get to an agreement where +okay if you've done too many times in a + + align:start position:0% +okay if you've done too many times in a + + + align:start position:0% +okay if you've done too many times in a +row even if your costs are low and my + + align:start position:0% +row even if your costs are low and my + + + align:start position:0% +row even if your costs are low and my +costs are high you still have to back + + align:start position:0% +costs are high you still have to back + + + align:start position:0% +costs are high you still have to back +out and do this um or we can stop you + + align:start position:0% +out and do this um or we can stop you + + + align:start position:0% +out and do this um or we can stop you +from deviating stop you from doing that + + align:start position:0% +from deviating stop you from doing that + + + align:start position:0% +from deviating stop you from doing that +by saying you've done it too many times + + align:start position:0% +by saying you've done it too many times + + + align:start position:0% +by saying you've done it too many times +in a row if you claim your costs are low + + align:start position:0% +in a row if you claim your costs are low + + + align:start position:0% +in a row if you claim your costs are low +you have to cut your price below the + + align:start position:0% +you have to cut your price below the + + + align:start position:0% +you have to cut your price below the +Monopoly price instead of charging the + + align:start position:0% +Monopoly price instead of charging the + + + align:start position:0% +Monopoly price instead of charging the +Monopoly price price because we need + + align:start position:0% +Monopoly price price because we need + + + align:start position:0% +Monopoly price price because we need +some extra disincentive to you know once + + align:start position:0% +some extra disincentive to you know once + + + align:start position:0% +some extra disincentive to you know once +you've already sort of saying in the + + align:start position:0% +you've already sort of saying in the + + + align:start position:0% +you've already sort of saying in the +year 2045 I'll give you market share + + align:start position:0% +year 2045 I'll give you market share + + + align:start position:0% +year 2045 I'll give you market share +that doesn't work so you have to sort of + + align:start position:0% +that doesn't work so you have to sort of + + + align:start position:0% +that doesn't work so you have to sort of +forth firm if you're going to say your + + align:start position:0% +forth firm if you're going to say your + + + align:start position:0% +forth firm if you're going to say your +costs are low we're going to make you + + align:start position:0% +costs are low we're going to make you + + + align:start position:0% +costs are low we're going to make you +cut your + + align:start position:0% +cut your + + + align:start position:0% +cut your +price um so anyway I I think message of + + align:start position:0% +price um so anyway I I think message of + + + align:start position:0% +price um so anyway I I think message of +a Bagwell is it's like the cost shocks + + align:start position:0% +a Bagwell is it's like the cost shocks + + + align:start position:0% +a Bagwell is it's like the cost shocks +are a problem but they're if firms are + + align:start position:0% +are a problem but they're if firms are + + + align:start position:0% +are a problem but they're if firms are +clever and have can do these dynamic + + align:start position:0% +clever and have can do these dynamic + + + align:start position:0% +clever and have can do these dynamic +reallocations because it's frequent + + align:start position:0% +reallocations because it's frequent + + + align:start position:0% +reallocations because it's frequent +things that may not be such an obstacle + + align:start position:0% +things that may not be such an obstacle + + + align:start position:0% +things that may not be such an obstacle +after + + align:start position:0% +after + + + align:start position:0% +after +all um + + align:start position:0% +all um + + + align:start position:0% +all um +uh Harrington has this paper about + + align:start position:0% +uh Harrington has this paper about + + + align:start position:0% +uh Harrington has this paper about +antitrust authorities obviously in + + align:start position:0% +antitrust authorities obviously in + + + align:start position:0% +antitrust authorities obviously in +practice one of we do think that one of + + align:start position:0% +practice one of we do think that one of + + + align:start position:0% +practice one of we do think that one of +the reasons firms don't collude is + + align:start position:0% +the reasons firms don't collude is + + + align:start position:0% +the reasons firms don't collude is +because it's illegal and you can go to + + align:start position:0% +because it's illegal and you can go to + + + align:start position:0% +because it's illegal and you can go to +jail um and you know business Executives + + align:start position:0% +jail um and you know business Executives + + + align:start position:0% +jail um and you know business Executives +who make millions of dollars don't like + + align:start position:0% +who make millions of dollars don't like + + + align:start position:0% +who make millions of dollars don't like +spending time in federal prison it's + + align:start position:0% +spending time in federal prison it's + + + align:start position:0% +spending time in federal prison it's +it's unpleasant um so um you know + + align:start position:0% +it's unpleasant um so um you know + + + align:start position:0% +it's unpleasant um so um you know +obviously so that is a constraint on any + + align:start position:0% +obviously so that is a constraint on any + + + align:start position:0% +obviously so that is a constraint on any +on on any Trust on on collusion is that + + align:start position:0% +on on any Trust on on collusion is that + + + align:start position:0% +on on any Trust on on collusion is that +people can go to jail um and firms can + + align:start position:0% +people can go to jail um and firms can + + + align:start position:0% +people can go to jail um and firms can +pay very large fines um you know one + + align:start position:0% +pay very large fines um you know one + + + align:start position:0% +pay very large fines um you know one +thing that Harrington notes is that that + + align:start position:0% +thing that Harrington notes is that that + + + align:start position:0% +thing that Harrington notes is that that +is true but you can imagine reasons that + + align:start position:0% +is true but you can imagine reasons that + + + align:start position:0% +is true but you can imagine reasons that +doesn't work so well so for instance you + + align:start position:0% +doesn't work so well so for instance you + + + align:start position:0% +doesn't work so well so for instance you +know once you have those penalties there + + align:start position:0% +know once you have those penalties there + + + align:start position:0% +know once you have those penalties there +firms really don't want the penalties to + + align:start position:0% +firms really don't want the penalties to + + + align:start position:0% +firms really don't want the penalties to +get triggered and it may be that + + align:start position:0% +get triggered and it may be that + + + align:start position:0% +get triggered and it may be that +something that triggers a penalty is + + align:start position:0% +something that triggers a penalty is + + + align:start position:0% +something that triggers a penalty is +like a breakdown of the cartel agreement + + align:start position:0% +like a breakdown of the cartel agreement + + + align:start position:0% +like a breakdown of the cartel agreement +so like if we have a price War and the + + align:start position:0% +so like if we have a price War and the + + + align:start position:0% +so like if we have a price War and the +price drops from 100 to 60 and then goes + + align:start position:0% +price drops from 100 to 60 and then goes + + + align:start position:0% +price drops from 100 to 60 and then goes +back up + + align:start position:0% +back up + + + align:start position:0% +back up +again like that's a clear sign to anti + + align:start position:0% +again like that's a clear sign to anti + + + align:start position:0% +again like that's a clear sign to anti +trust authorities that maybe we should + + align:start position:0% +trust authorities that maybe we should + + + align:start position:0% +trust authorities that maybe we should +look into what's going on here and are + + align:start position:0% +look into what's going on here and are + + + align:start position:0% +look into what's going on here and are +they colluding with each other therefore + + align:start position:0% +they colluding with each other therefore + + + align:start position:0% +they colluding with each other therefore +you may not want to cut price and cheat + + align:start position:0% +you may not want to cut price and cheat + + + align:start position:0% +you may not want to cut price and cheat +from the agreement in the first place + + align:start position:0% +from the agreement in the first place + + + align:start position:0% +from the agreement in the first place +and therefore you may some sense you can + + align:start position:0% +and therefore you may some sense you can + + + align:start position:0% +and therefore you may some sense you can +like drift into collusion and get even + + align:start position:0% +like drift into collusion and get even + + + align:start position:0% +like drift into collusion and get even +more collusion with the anti trust + + align:start position:0% +more collusion with the anti trust + + + align:start position:0% +more collusion with the anti trust +Authority than you get without because + + align:start position:0% +Authority than you get without because + + + align:start position:0% +Authority than you get without because +no one wants to risk starting the price + + align:start position:0% +no one wants to risk starting the price + + + align:start position:0% +no one wants to risk starting the price +war that then makes people notice that + + align:start position:0% +war that then makes people notice that + + + align:start position:0% +war that then makes people notice that +there was a a cartel agreement going on + + align:start position:0% +there was a a cartel agreement going on + + + align:start position:0% +there was a a cartel agreement going on +so it's you know I think while I do + + align:start position:0% +so it's you know I think while I do + + + align:start position:0% +so it's you know I think while I do +think the + + align:start position:0% +think the + + + align:start position:0% +think the +main version of that is certainly true + + align:start position:0% +main version of that is certainly true + + + align:start position:0% +main version of that is certainly true +that collusion being illegal is a + + align:start position:0% +that collusion being illegal is a + + + align:start position:0% +that collusion being illegal is a +deterrent it can also be you know not + + align:start position:0% +deterrent it can also be you know not + + + align:start position:0% +deterrent it can also be you know not +well-designed collusion policies can + + align:start position:0% +well-designed collusion policies can + + + align:start position:0% +well-designed collusion policies can +also then sort of in some sense lock + + align:start position:0% +also then sort of in some sense lock + + + align:start position:0% +also then sort of in some sense lock +people into cartels um something you + + align:start position:0% +people into cartels um something you + + + align:start position:0% +people into cartels um something you +often see in practice reflecting this is + + align:start position:0% +often see in practice reflecting this is + + + align:start position:0% +often see in practice reflecting this is +that you know sometimes these um things + + align:start position:0% +that you know sometimes these um things + + + align:start position:0% +that you know sometimes these um things +have like whistleblower protections that + + align:start position:0% +have like whistleblower protections that + + + align:start position:0% +have like whistleblower protections that +if you go to the government and say hey + + align:start position:0% +if you go to the government and say hey + + + align:start position:0% +if you go to the government and say hey +I've been colluding with these guys for + + align:start position:0% +I've been colluding with these guys for + + + align:start position:0% +I've been colluding with these guys for +the past 5 years you get off with a much + + align:start position:0% +the past 5 years you get off with a much + + + align:start position:0% +the past 5 years you get off with a much +lighter punishment than everyone that + + align:start position:0% +lighter punishment than everyone that + + + align:start position:0% +lighter punishment than everyone that +you were colluding with and that can be + + align:start position:0% +you were colluding with and that can be + + + align:start position:0% +you were colluding with and that can be +a way to try to sort of get rid of this + + align:start position:0% +a way to try to sort of get rid of this + + + align:start position:0% +a way to try to sort of get rid of this +problem + + align:start position:0% +problem + + + align:start position:0% +problem +okay okay uh multimarket contact limited + + align:start position:0% +okay okay uh multimarket contact limited + + + align:start position:0% +okay okay uh multimarket contact limited +time I will leave that for you to read + + align:start position:0% +time I will leave that for you to read + + + align:start position:0% +time I will leave that for you to read +also okay so things I wanted to do + + align:start position:0% + + + + align:start position:0% + +um you know how do people in IO get away + + align:start position:0% +um you know how do people in IO get away + + + align:start position:0% +um you know how do people in IO get away +from this indeterminacy and and not just + + align:start position:0% +from this indeterminacy and and not just + + + align:start position:0% +from this indeterminacy and and not just +always have this conclusion that we + + align:start position:0% +always have this conclusion that we + + + align:start position:0% +always have this conclusion that we +can't do empirical work we can't do + + align:start position:0% +can't do empirical work we can't do + + + align:start position:0% +can't do empirical work we can't do +other things because we can't tell + + align:start position:0% +other things because we can't tell + + + align:start position:0% +other things because we can't tell +what's going on + + align:start position:0% +what's going on + + + align:start position:0% +what's going on +um you know one thing we do is we adopt + + align:start position:0% +um you know one thing we do is we adopt + + + align:start position:0% +um you know one thing we do is we adopt +this sort of static Nash framework of + + align:start position:0% +this sort of static Nash framework of + + + align:start position:0% +this sort of static Nash framework of +just like okay we're just going to + + align:start position:0% +just like okay we're just going to + + + align:start position:0% +just like okay we're just going to +assume static Nash describe what goes on + + align:start position:0% +assume static Nash describe what goes on + + + align:start position:0% +assume static Nash describe what goes on +in a lot of models you can't just assume + + align:start position:0% +in a lot of models you can't just assume + + + align:start position:0% +in a lot of models you can't just assume +static Nash is what goes on + + align:start position:0% +static Nash is what goes on + + + align:start position:0% +static Nash is what goes on +because there is some variable that's + + align:start position:0% +because there is some variable that's + + + align:start position:0% +because there is some variable that's +changing over time like firms are + + align:start position:0% +changing over time like firms are + + + align:start position:0% +changing over time like firms are +investing in their equality or in + + align:start position:0% +investing in their equality or in + + + align:start position:0% +investing in their equality or in +reducing costs or there's you know firms + + align:start position:0% +reducing costs or there's you know firms + + + align:start position:0% +reducing costs or there's you know firms +are setting prices and it's costly to + + align:start position:0% +are setting prices and it's costly to + + + align:start position:0% +are setting prices and it's costly to +change their prices so whatever price + + align:start position:0% +change their prices so whatever price + + + align:start position:0% +change their prices so whatever price +they set today are locked in for the + + align:start position:0% +they set today are locked in for the + + + align:start position:0% +they set today are locked in for the +future we need some model where firms + + align:start position:0% +future we need some model where firms + + + align:start position:0% +future we need some model where firms +change we need some you know there needs + + align:start position:0% +change we need some you know there needs + + + align:start position:0% +change we need some you know there needs +to be some trade today in the future to + + align:start position:0% +to be some trade today in the future to + + + align:start position:0% +to be some trade today in the future to +think about staggered price setting or + + align:start position:0% +think about staggered price setting or + + + align:start position:0% +think about staggered price setting or +to think about cost quality Investments + + align:start position:0% +to think about cost quality Investments + + + align:start position:0% +to think about cost quality Investments +or whatever um what people often do is + + align:start position:0% +or whatever um what people often do is + + + align:start position:0% +or whatever um what people often do is +to sort of um use this concept called + + align:start position:0% +to sort of um use this concept called + + + align:start position:0% +to sort of um use this concept called +Markov perfect equilibrium you know in a + + align:start position:0% +Markov perfect equilibrium you know in a + + + align:start position:0% +Markov perfect equilibrium you know in a +Markov perfect equilibrium player + + align:start position:0% +Markov perfect equilibrium player + + + align:start position:0% +Markov perfect equilibrium player +strategies are assumed to depend only on + + align:start position:0% +strategies are assumed to depend only on + + + align:start position:0% +strategies are assumed to depend only on +payoff relevant variables so for + + align:start position:0% +payoff relevant variables so for + + + align:start position:0% +payoff relevant variables so for +instance you know you can price + + align:start position:0% +instance you know you can price + + + align:start position:0% +instance you know you can price +on you know my price PR at time T is a + + align:start position:0% +on you know my price PR at time T is a + + + align:start position:0% +on you know my price PR at time T is a +function of my cost and your costs you + + align:start position:0% +function of my cost and your costs you + + + align:start position:0% +function of my cost and your costs you +know these things are relevant to the + + align:start position:0% +know these things are relevant to the + + + align:start position:0% +know these things are relevant to the +payoffs in the game and therefore if + + align:start position:0% +payoffs in the game and therefore if + + + align:start position:0% +payoffs in the game and therefore if +these things are changing the payoffs in + + align:start position:0% +these things are changing the payoffs in + + + align:start position:0% +these things are changing the payoffs in +the game uh I'm allowed to price based + + align:start position:0% +the game uh I'm allowed to price based + + + align:start position:0% +the game uh I'm allowed to price based +on this but I can't be doing I'm pricing + + align:start position:0% +on this but I can't be doing I'm pricing + + + align:start position:0% +on this but I can't be doing I'm pricing +today based on the price I set at T + + align:start position:0% +today based on the price I set at T + + + align:start position:0% +today based on the price I set at T +minus one and the price you set at T + + align:start position:0% +minus one and the price you set at T + + + align:start position:0% +minus one and the price you set at T +minus one because those prices are + + align:start position:0% +minus one because those prices are + + + align:start position:0% +minus one because those prices are +completely irrelevant today so mark off + + align:start position:0% +completely irrelevant today so mark off + + + align:start position:0% +completely irrelevant today so mark off +perfect equal what we want to do is + + align:start position:0% +perfect equal what we want to do is + + + align:start position:0% +perfect equal what we want to do is +assume that firms can set their + + align:start position:0% +assume that firms can set their + + + align:start position:0% +assume that firms can set their +strategies based on payoff relevant + + align:start position:0% +strategies based on payoff relevant + + + align:start position:0% +strategies based on payoff relevant +variables but assume that they can't set + + align:start position:0% +variables but assume that they can't set + + + align:start position:0% +variables but assume that they can't set +their price based on payoff irrelevant + + align:start position:0% +their price based on payoff irrelevant + + + align:start position:0% +their price based on payoff irrelevant +variables and this so saying that can't + + align:start position:0% +variables and this so saying that can't + + + align:start position:0% +variables and this so saying that can't +happen this is what rules out like the + + align:start position:0% +happen this is what rules out like the + + + align:start position:0% +happen this is what rules out like the +um like those sort of grim trigger + + align:start position:0% +um like those sort of grim trigger + + + align:start position:0% +um like those sort of grim trigger +punishments in the in the repeated + + align:start position:0% +punishments in the in the repeated + + + align:start position:0% +punishments in the in the repeated +betran game you can't say if you said + + align:start position:0% +betran game you can't say if you said + + + align:start position:0% +betran game you can't say if you said +price PM minus Epsilon yesterday instead + + align:start position:0% +price PM minus Epsilon yesterday instead + + + align:start position:0% +price PM minus Epsilon yesterday instead +of PM yesterday then we go to a price + + align:start position:0% +of PM yesterday then we go to a price + + + align:start position:0% +of PM yesterday then we go to a price +War forever I'm I'm basically trying to + + align:start position:0% +War forever I'm I'm basically trying to + + + align:start position:0% +War forever I'm I'm basically trying to +sort of recreate get as close as I can + + align:start position:0% +sort of recreate get as close as I can + + + align:start position:0% +sort of recreate get as close as I can +to static Nash by saying you can only + + align:start position:0% +to static Nash by saying you can only + + + align:start position:0% +to static Nash by saying you can only +price based on things that are payoff + + align:start position:0% +price based on things that are payoff + + + align:start position:0% +price based on things that are payoff +relevant not based on things that are + + align:start position:0% +relevant not based on things that are + + + align:start position:0% +relevant not based on things that are +payoff irrelevant + + align:start position:0% +payoff irrelevant + + + align:start position:0% +payoff irrelevant +um and you know people often think of + + align:start position:0% +um and you know people often think of + + + align:start position:0% +um and you know people often think of +this as a way to get back + + align:start position:0% +this as a way to get back + + + align:start position:0% +this as a way to get back +to um obtaining unique + + align:start position:0% +to um obtaining unique + + + align:start position:0% +to um obtaining unique +equilibrium um we say interesting + + align:start position:0% +equilibrium um we say interesting + + + align:start position:0% +equilibrium um we say interesting +observation is that people often think + + align:start position:0% +observation is that people often think + + + align:start position:0% +observation is that people often think +of Markoff perfect equilibrium as doing + + align:start position:0% +of Markoff perfect equilibrium as doing + + + align:start position:0% +of Markoff perfect equilibrium as doing +that but in practice it doesn't always + + align:start position:0% +that but in practice it doesn't always + + + align:start position:0% +that but in practice it doesn't always +do that um and so there's this you know + + align:start position:0% +do that um and so there's this you know + + + align:start position:0% +do that um and so there's this you know +I talk about this interesting beautiful + + align:start position:0% +I talk about this interesting beautiful + + + align:start position:0% +I talk about this interesting beautiful +paper by mask and tooll that just sort + + align:start position:0% +paper by mask and tooll that just sort + + + align:start position:0% +paper by mask and tooll that just sort +of give examples of what kind of Markoff + + align:start position:0% +of give examples of what kind of Markoff + + + align:start position:0% +of give examples of what kind of Markoff +perfect equilibrium could we have in an + + align:start position:0% +perfect equilibrium could we have in an + + + align:start position:0% +perfect equilibrium could we have in an +alternating move price game so in mask + + align:start position:0% +alternating move price game so in mask + + + align:start position:0% +alternating move price game so in mask +and and terr's game it's just this + + align:start position:0% +and and terr's game it's just this + + + align:start position:0% +and and terr's game it's just this +um it's this alternating move G we have + + align:start position:0% +um it's this alternating move G we have + + + align:start position:0% +um it's this alternating move G we have +two move Players let's say player one + + align:start position:0% +two move Players let's say player one + + + align:start position:0% +two move Players let's say player one +and player + + align:start position:0% +and player + + + align:start position:0% +and player +two and you know player one pick some + + align:start position:0% +two and you know player one pick some + + + align:start position:0% +two and you know player one pick some +price um at say Tal + + align:start position:0% +price um at say Tal + + + align:start position:0% +price um at say Tal +one and set some price that's going to + + align:start position:0% +one and set some price that's going to + + + align:start position:0% +one and set some price that's going to +have to hold for two + + align:start position:0% +have to hold for two + + + align:start position:0% +have to hold for two +periods and then player two gets to pick + + align:start position:0% +periods and then player two gets to pick + + + align:start position:0% +periods and then player two gets to pick +a price in Period T equals 2 and that + + align:start position:0% +a price in Period T equals 2 and that + + + align:start position:0% +a price in Period T equals 2 and that +has to be there for two periods and then + + align:start position:0% +has to be there for two periods and then + + + align:start position:0% +has to be there for two periods and then +player one choose a new price at three + + align:start position:0% +player one choose a new price at three + + + align:start position:0% +player one choose a new price at three +that holds for three and + + align:start position:0% +that holds for three and + + + align:start position:0% +that holds for three and +four and player two choose a price that + + align:start position:0% +four and player two choose a price that + + + align:start position:0% +four and player two choose a price that +holds for four and five but you know the + + align:start position:0% +holds for four and five but you know the + + + align:start position:0% +holds for four and five but you know the +idea they were trying to get at is in + + align:start position:0% +idea they were trying to get at is in + + + align:start position:0% +idea they were trying to get at is in +reality price changing is asynchronous + + align:start position:0% +reality price changing is asynchronous + + + align:start position:0% +reality price changing is asynchronous +like if you look at two gas stations + + align:start position:0% +like if you look at two gas stations + + + align:start position:0% +like if you look at two gas stations +across the street from each other it's + + align:start position:0% +across the street from each other it's + + + align:start position:0% +across the street from each other it's +not like the guys climb on the signs and + + align:start position:0% +not like the guys climb on the signs and + + + align:start position:0% +not like the guys climb on the signs and +change the price listings at exactly the + + align:start position:0% +change the price listings at exactly the + + + align:start position:0% +change the price listings at exactly the +same time and change the pumps at + + align:start position:0% +same time and change the pumps at + + + align:start position:0% +same time and change the pumps at +exactly the same time you know it's like + + align:start position:0% +exactly the same time you know it's like + + + align:start position:0% +exactly the same time you know it's like +somebody changes their price and then + + align:start position:0% +somebody changes their price and then + + + align:start position:0% +somebody changes their price and then +the other guy sees the first one's price + + align:start position:0% +the other guy sees the first one's price + + + align:start position:0% +the other guy sees the first one's price +and changes his price and they will tend + + align:start position:0% +and changes his price and they will tend + + + align:start position:0% +and changes his price and they will tend +to go back and forth like that you know + + align:start position:0% +to go back and forth like that you know + + + align:start position:0% +to go back and forth like that you know +each one observing you needing some time + + align:start position:0% +each one observing you needing some time + + + align:start position:0% +each one observing you needing some time +to observe One's price do something R + + align:start position:0% +to observe One's price do something R + + + align:start position:0% +to observe One's price do something R +and then change their price so they + + align:start position:0% +and then change their price so they + + + align:start position:0% +and then change their price so they +consider this sort of stylized game + + align:start position:0% +consider this sort of stylized game + + + align:start position:0% +consider this sort of stylized game +where firm one chooses prices that keep + + align:start position:0% +where firm one chooses prices that keep + + + align:start position:0% +where firm one chooses prices that keep += 1 T = 3 T = 5 and from two chooses + + align:start position:0% += 1 T = 3 T = 5 and from two chooses + + + align:start position:0% += 1 T = 3 T = 5 and from two chooses +prices it tal 2 T = 4 tal + + align:start position:0% +prices it tal 2 T = 4 tal + + + align:start position:0% +prices it tal 2 T = 4 tal + + align:start position:0% + + + align:start position:0% +um and then besides that they do + + align:start position:0% +um and then besides that they do + + + align:start position:0% +um and then besides that they do +repeated Bertrand competition so just + + align:start position:0% +repeated Bertrand competition so just + + + align:start position:0% +repeated Bertrand competition so just +repeated brand competition D of p is 1 + + align:start position:0% +repeated brand competition D of p is 1 + + + align:start position:0% +repeated brand competition D of p is 1 +minus p and to make a simple example + + align:start position:0% +minus p and to make a simple example + + + align:start position:0% +minus p and to make a simple example +they restrict prices to this sort of + + align:start position:0% +they restrict prices to this sort of + + + align:start position:0% +they restrict prices to this sort of +simple grid 01626 36 46 + + align:start position:0% +simple grid 01626 36 46 + + + align:start position:0% +simple grid 01626 36 46 +56 um one observation is that in this + + align:start position:0% +56 um one observation is that in this + + + align:start position:0% +56 um one observation is that in this +model + + align:start position:0% +model + + + align:start position:0% +model +there's no Mark of equilibrium in which + + align:start position:0% +there's no Mark of equilibrium in which + + + align:start position:0% +there's no Mark of equilibrium in which +the firm's price it cost so the betrand + + align:start position:0% +the firm's price it cost so the betrand + + + align:start position:0% +the firm's price it cost so the betrand +equilibrium of just pricing at C goes + + align:start position:0% +equilibrium of just pricing at C goes + + + align:start position:0% +equilibrium of just pricing at C goes +away and why is that well because + + align:start position:0% +away and why is that well because + + + align:start position:0% +away and why is that well because +imagine you had an equilibrium where the + + align:start position:0% +imagine you had an equilibrium where the + + + align:start position:0% +imagine you had an equilibrium where the +firms were supposed to price at cost in + + align:start position:0% +firms were supposed to price at cost in + + + align:start position:0% +firms were supposed to price at cost in +all periods what firm one could do is + + align:start position:0% +all periods what firm one could do is + + + align:start position:0% +all periods what firm one could do is +just in the first period instead of + + align:start position:0% +just in the first period instead of + + + align:start position:0% +just in the first period instead of +pricing at C I raise my price and I + + align:start position:0% +pricing at C I raise my price and I + + + align:start position:0% +pricing at C I raise my price and I +charge like so suppos C was zero right + + align:start position:0% +charge like so suppos C was zero right + + + align:start position:0% +charge like so suppos C was zero right +instead of price zero uh I raised my + + align:start position:0% +instead of price zero uh I raised my + + + align:start position:0% +instead of price zero uh I raised my +price to 46 I said a really high price + + align:start position:0% +price to 46 I said a really high price + + + align:start position:0% +price to 46 I said a really high price +then in Period two is firm two going to + + align:start position:0% +then in Period two is firm two going to + + + align:start position:0% +then in Period two is firm two going to +continue pricing at Cost well if it + + align:start position:0% +continue pricing at Cost well if it + + + align:start position:0% +continue pricing at Cost well if it +continues pricing it at zero it earns + + align:start position:0% +continues pricing it at zero it earns + + + align:start position:0% +continues pricing it at zero it earns +zero profits it has this you've given it + + align:start position:0% +zero profits it has this you've given it + + + align:start position:0% +zero profits it has this you've given it +this opportunity it knows you're locked + + align:start position:0% +this opportunity it knows you're locked + + + align:start position:0% +this opportunity it knows you're locked +in at this really high price it could + + align:start position:0% +in at this really high price it could + + + align:start position:0% +in at this really high price it could +raise its price uh to 36 and charge them + + align:start position:0% +raise its price uh to 36 and charge them + + + align:start position:0% +raise its price uh to 36 and charge them +which is the Monopoly price in this + + align:start position:0% +which is the Monopoly price in this + + + align:start position:0% +which is the Monopoly price in this +model and earn the Monopoly price for + + align:start position:0% +model and earn the Monopoly price for + + + align:start position:0% +model and earn the Monopoly price for +two periods if it does that then here + + align:start position:0% +two periods if it does that then here + + + align:start position:0% +two periods if it does that then here +you know I can price at 26 and earn some + + align:start position:0% +you know I can price at 26 and earn some + + + align:start position:0% +you know I can price at 26 and earn some +money and I'm earning zero in + + align:start position:0% +money and I'm earning zero in + + + align:start position:0% +money and I'm earning zero in +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +so we can't have a zero profit + + align:start position:0% +so we can't have a zero profit + + + align:start position:0% +so we can't have a zero profit +equilibrium here because firms could + + align:start position:0% +equilibrium here because firms could + + + align:start position:0% +equilibrium here because firms could +always raise their prices tempt the + + align:start position:0% +always raise their prices tempt the + + + align:start position:0% +always raise their prices tempt the +other firm to raise their prices then + + align:start position:0% +other firm to raise their prices then + + + align:start position:0% +other firm to raise their prices then +undercut that other firm and earn + + align:start position:0% +undercut that other firm and earn + + + align:start position:0% +undercut that other firm and earn +something positive so zero profit + + align:start position:0% +something positive so zero profit + + + align:start position:0% +something positive so zero profit +equilibria go away in this model they + + align:start position:0% +equilibria go away in this model they + + + align:start position:0% +equilibria go away in this model they +don't exist um what does exist um one + + align:start position:0% +don't exist um what does exist um one + + + align:start position:0% +don't exist um what does exist um one +thing that still exists here is um + + align:start position:0% +thing that still exists here is um + + + align:start position:0% +thing that still exists here is um +collusive agreement collusive equilibria + + align:start position:0% +collusive agreement collusive equilibria + + + align:start position:0% +collusive agreement collusive equilibria +like the ones that Markov equilibrium is + + align:start position:0% +like the ones that Markov equilibrium is + + + align:start position:0% +like the ones that Markov equilibrium is +in some sense designed to get rid of so + + align:start position:0% +in some sense designed to get rid of so + + + align:start position:0% +in some sense designed to get rid of so +consider this clusive of equilibrium + + align:start position:0% +consider this clusive of equilibrium + + + align:start position:0% +consider this clusive of equilibrium +where basically you know we always + + align:start position:0% +where basically you know we always + + + align:start position:0% +where basically you know we always +whatever the you know the other firm is + + align:start position:0% +whatever the you know the other firm is + + + align:start position:0% +whatever the you know the other firm is +charging if it's high we charge the + + align:start position:0% +charging if it's high we charge the + + + align:start position:0% +charging if it's high we charge the +Monopoly price of a + + align:start position:0% +Monopoly price of a + + + align:start position:0% +Monopoly price of a +half and then if someone undercuts the + + align:start position:0% +half and then if someone undercuts the + + + align:start position:0% +half and then if someone undercuts the +other firm and goes to 2 six then you + + align:start position:0% +other firm and goes to 2 six then you + + + align:start position:0% +other firm and goes to 2 six then you +undercut them and go to one six and then + + align:start position:0% +undercut them and go to one six and then + + + align:start position:0% +undercut them and go to one six and then +if the other firm's charging one six you + + align:start position:0% +if the other firm's charging one six you + + + align:start position:0% +if the other firm's charging one six you +either under stick at one six or you go + + align:start position:0% +either under stick at one six or you go + + + align:start position:0% +either under stick at one six or you go +back to the Monopoly price so this is + + align:start position:0% +back to the Monopoly price so this is + + + align:start position:0% +back to the Monopoly price so this is +like a you can think of this as a + + align:start position:0% +like a you can think of this as a + + + align:start position:0% +like a you can think of this as a +probabilistic price War right so like + + align:start position:0% +probabilistic price War right so like + + + align:start position:0% +probabilistic price War right so like +we're going along we're supposed to be + + align:start position:0% +we're going along we're supposed to be + + + align:start position:0% +we're going along we're supposed to be +charging this P PT we're supposed to be + + align:start position:0% +charging this P PT we're supposed to be + + + align:start position:0% +charging this P PT we're supposed to be +charging this price of 1/2 in every + + align:start position:0% + + + + align:start position:0% + +period if someone deviates and instead + + align:start position:0% +period if someone deviates and instead + + + align:start position:0% +period if someone deviates and instead +goes here then the next firm the P firm + + align:start position:0% +goes here then the next firm the P firm + + + align:start position:0% +goes here then the next firm the P firm +goes there and then then they have the + + align:start position:0% +goes there and then then they have the + + + align:start position:0% +goes there and then then they have the +sort of randomization between do that + + align:start position:0% +sort of randomization between do that + + + align:start position:0% +sort of randomization between do that +and then somebody gives up and goes back + + align:start position:0% +and then somebody gives up and goes back + + + align:start position:0% +and then somebody gives up and goes back +to2 and then we continue so what they've + + align:start position:0% +to2 and then we continue so what they've + + + align:start position:0% +to2 and then we continue so what they've +basically been a do in this Markov + + align:start position:0% +basically been a do in this Markov + + + align:start position:0% +basically been a do in this Markov +framework is you know because the other + + align:start position:0% +framework is you know because the other + + + align:start position:0% +framework is you know because the other +firm's previous period price is payoff + + align:start position:0% +firm's previous period price is payoff + + + align:start position:0% +firm's previous period price is payoff +relevant you have to include it in the + + align:start position:0% +relevant you have to include it in the + + + align:start position:0% +relevant you have to include it in the +Markov State space that you price on and + + align:start position:0% +Markov State space that you price on and + + + align:start position:0% +Markov State space that you price on and +so we can get these price probabilistic + + align:start position:0% +so we can get these price probabilistic + + + align:start position:0% +so we can get these price probabilistic +price War looking just like green Porter + + align:start position:0% +price War looking just like green Porter + + + align:start position:0% +price War looking just like green Porter +then jump back + + align:start position:0% + + + + align:start position:0% + +up but you know this is also a paper + + align:start position:0% +up but you know this is also a paper + + + align:start position:0% +up but you know this is also a paper +like a folk theem paper there's also + + align:start position:0% +like a folk theem paper there's also + + + align:start position:0% +like a folk theem paper there's also +equilibrium multiplicity here and we get + + align:start position:0% +equilibrium multiplicity here and we get + + + align:start position:0% +equilibrium multiplicity here and we get +these other equilibria to so interest + + align:start position:0% +these other equilibria to so interest + + + align:start position:0% +these other equilibria to so interest +one interesting one they point out are + + align:start position:0% +one interesting one they point out are + + + align:start position:0% +one interesting one they point out are +these things called Edgeworth Cycles Ed + + align:start position:0% +these things called Edgeworth Cycles Ed + + + align:start position:0% +these things called Edgeworth Cycles Ed +Ed War Cycles we never settle down on + + align:start position:0% +Ed War Cycles we never settle down on + + + align:start position:0% +Ed War Cycles we never settle down on +pricing and what the firms just do is + + align:start position:0% +pricing and what the firms just do is + + + align:start position:0% +pricing and what the firms just do is +forever undercut each + + align:start position:0% +forever undercut each + + + align:start position:0% +forever undercut each +other so the firms just do this they + + align:start position:0% +other so the firms just do this they + + + align:start position:0% +other so the firms just do this they +start out at a high price uh + + align:start position:0% +start out at a high price uh + + + align:start position:0% +start out at a high price uh +of uh four + + align:start position:0% +of uh four + + + align:start position:0% +of uh four +six and then they just undercut each + + align:start position:0% +six and then they just undercut each + + + align:start position:0% +six and then they just undercut each +other they get down to the bottom + + align:start position:0% +other they get down to the bottom + + + align:start position:0% +other they get down to the bottom +there's some mixing and then somebody + + align:start position:0% +there's some mixing and then somebody + + + align:start position:0% +there's some mixing and then somebody +wants to end again this is like you know + + align:start position:0% +wants to end again this is like you know + + + align:start position:0% +wants to end again this is like you know +incentive to end you have this incentive + + align:start position:0% +incentive to end you have this incentive + + + align:start position:0% +incentive to end you have this incentive +to end the punishment where it's like + + align:start position:0% +to end the punishment where it's like + + + align:start position:0% +to end the punishment where it's like +each one wants the other guy to end the + + align:start position:0% +each one wants the other guy to end the + + + align:start position:0% +each one wants the other guy to end the +punishment but then someone jumps up to + + align:start position:0% +punishment but then someone jumps up to + + + align:start position:0% +punishment but then someone jumps up to +56 and lets the other one undercut him + + align:start position:0% +56 and lets the other one undercut him + + + align:start position:0% +56 and lets the other one undercut him +in the next period to 46 and then we + + align:start position:0% +in the next period to 46 and then we + + + align:start position:0% +in the next period to 46 and then we +just continue like + + align:start position:0% + + + + align:start position:0% + +this so we can get these sort of um Edge + + align:start position:0% +this so we can get these sort of um Edge + + + align:start position:0% +this so we can get these sort of um Edge +worth cycle equilibria where the firms + + align:start position:0% +worth cycle equilibria where the firms + + + align:start position:0% +worth cycle equilibria where the firms +just continually undercut each other + + align:start position:0% +just continually undercut each other + + + align:start position:0% +just continually undercut each other +over and over and over again and then at + + align:start position:0% +over and over and over again and then at + + + align:start position:0% +over and over and over again and then at +the bottom of the cycle you know you've + + align:start position:0% +the bottom of the cycle you know you've + + + align:start position:0% +the bottom of the cycle you know you've +driven the price all the way to zero + + align:start position:0% +driven the price all the way to zero + + + align:start position:0% +driven the price all the way to zero +what do you do at some point you give up + + align:start position:0% +what do you do at some point you give up + + + align:start position:0% +what do you do at some point you give up +and say okay we've been at zero for long + + align:start position:0% +and say okay we've been at zero for long + + + align:start position:0% +and say okay we've been at zero for long +enough I'm going to go ahead and price + + align:start position:0% +enough I'm going to go ahead and price + + + align:start position:0% +enough I'm going to go ahead and price +at 56 also earning nothing but then lit + + align:start position:0% +at 56 also earning nothing but then lit + + + align:start position:0% +at 56 also earning nothing but then lit +you undercut me to get to 46 and then + + align:start position:0% +you undercut me to get to 46 and then + + + align:start position:0% +you undercut me to get to 46 and then +I'll get to 36 two periods from now um + + align:start position:0% +I'll get to 36 two periods from now um + + + align:start position:0% +I'll get to 36 two periods from now um +so we also have these Edgeworth cycle + + align:start position:0% +so we also have these Edgeworth cycle + + + align:start position:0% +so we also have these Edgeworth cycle +equilibria and so I think you know + + align:start position:0% +equilibria and so I think you know + + + align:start position:0% +equilibria and so I think you know +lesson here of this paper was that we + + align:start position:0% +lesson here of this paper was that we + + + align:start position:0% +lesson here of this paper was that we +may think of Markov equilibrium as + + align:start position:0% +may think of Markov equilibrium as + + + align:start position:0% +may think of Markov equilibrium as +eliminating multiplicity but if you know + + align:start position:0% +eliminating multiplicity but if you know + + + align:start position:0% +eliminating multiplicity but if you know +in you know here it it's because the + + align:start position:0% +in you know here it it's because the + + + align:start position:0% +in you know here it it's because the +previous periods price is is payoff + + align:start position:0% +previous periods price is is payoff + + + align:start position:0% +previous periods price is is payoff +relevant and that would happen in any + + align:start position:0% +relevant and that would happen in any + + + align:start position:0% +relevant and that would happen in any +staggered price setting game or you + + align:start position:0% +staggered price setting game or you + + + align:start position:0% +staggered price setting game or you +could also do this based on other things + + align:start position:0% +could also do this based on other things + + + align:start position:0% +could also do this based on other things +that are payoff relevant like if costs + + align:start position:0% +that are payoff relevant like if costs + + + align:start position:0% +that are payoff relevant like if costs +are there we can also sort of bootstrap + + align:start position:0% +are there we can also sort of bootstrap + + + align:start position:0% +are there we can also sort of bootstrap +on the costs but so what we can get is + + align:start position:0% +on the costs but so what we can get is + + + align:start position:0% +on the costs but so what we can get is +multiplicity and we can actually get + + align:start position:0% +multiplicity and we can actually get + + + align:start position:0% +multiplicity and we can actually get +multiple interesting patterns we can get + + align:start position:0% +multiple interesting patterns we can get + + + align:start position:0% +multiple interesting patterns we can get +the collusive pattern we've seen before + + align:start position:0% +the collusive pattern we've seen before + + + align:start position:0% +the collusive pattern we've seen before +you could also get this kind of pattern + + align:start position:0% +you could also get this kind of pattern + + + align:start position:0% +you could also get this kind of pattern +as an equilibrium and what the one thing + + align:start position:0% +as an equilibrium and what the one thing + + + align:start position:0% +as an equilibrium and what the one thing +you can't get in that model + + align:start position:0% +you can't get in that model + + + align:start position:0% +you can't get in that model +interestingly enough is competitive + + align:start position:0% +interestingly enough is competitive + + + align:start position:0% +interestingly enough is competitive +pricing so competitive doesn't work but + + align:start position:0% +pricing so competitive doesn't work but + + + align:start position:0% +pricing so competitive doesn't work but +this is possible sometimes it's sort of + + align:start position:0% +this is possible sometimes it's sort of + + + align:start position:0% +this is possible sometimes it's sort of +that Perpetual cycling of prices makes + + align:start position:0% +that Perpetual cycling of prices makes + + + align:start position:0% +that Perpetual cycling of prices makes +more economic sense than just static + + align:start position:0% +more economic sense than just static + + + align:start position:0% +more economic sense than just static +Nash pricing in this + + align:start position:0% + + + + align:start position:0% + +model okay any questions on that + + align:start position:0% +model okay any questions on that + + + align:start position:0% +model okay any questions on that +obviously you know this is a simple + + align:start position:0% +obviously you know this is a simple + + + align:start position:0% +obviously you know this is a simple +numerical example but if you know things + + align:start position:0% +numerical example but if you know things + + + align:start position:0% +numerical example but if you know things +happen in this numerical + + align:start position:0% +happen in this numerical + + + align:start position:0% +happen in this numerical +example similar things are going to + + align:start position:0% +example similar things are going to + + + align:start position:0% +example similar things are going to +happen in lots of more complicated + + align:start position:0% +happen in lots of more complicated + + + align:start position:0% +happen in lots of more complicated +models that you can get these sort of + + align:start position:0% +models that you can get these sort of + + + align:start position:0% +models that you can get these sort of +multiple kind types of Markov equilibria + + align:start position:0% + + + + align:start position:0% + +okay so then final thing I was going to + + align:start position:0% +okay so then final thing I was going to + + + align:start position:0% +okay so then final thing I was going to +talk about today is a more recent paper + + align:start position:0% +talk about today is a more recent paper + + + align:start position:0% +talk about today is a more recent paper +calano calari Den Colo pastorello um + + align:start position:0% +calano calari Den Colo pastorello um + + + align:start position:0% +calano calari Den Colo pastorello um +this is a 2020 AER paper motivated by + + align:start position:0% +this is a 2020 AER paper motivated by + + + align:start position:0% +this is a 2020 AER paper motivated by +thinking about online + + align:start position:0% +thinking about online + + + align:start position:0% +thinking about online +businesses and you know they note that + + align:start position:0% +businesses and you know they note that + + + align:start position:0% +businesses and you know they note that +in many online + + align:start position:0% +in many online + + + align:start position:0% +in many online +businesses firms are setting prices + + align:start position:0% +businesses firms are setting prices + + + align:start position:0% +businesses firms are setting prices +repeatedly and we really are in a case + + align:start position:0% +repeatedly and we really are in a case + + + align:start position:0% +repeatedly and we really are in a case +where Delta is very very close to one if + + align:start position:0% +where Delta is very very close to one if + + + align:start position:0% +where Delta is very very close to one if +you think about like you know Herz + + align:start position:0% +you think about like you know Herz + + + align:start position:0% +you think about like you know Herz +competing with Avis competing with + + align:start position:0% +competing with Avis competing with + + + align:start position:0% +competing with Avis competing with +Budget on selling rental cars through + + align:start position:0% +Budget on selling rental cars through + + + align:start position:0% +Budget on selling rental cars through +orbits they can change their price every + + align:start position:0% +orbits they can change their price every + + + align:start position:0% +orbits they can change their price every +second they have a computer monitoring + + align:start position:0% +second they have a computer monitoring + + + align:start position:0% +second they have a computer monitoring +the other prices and changing prices you + + align:start position:0% +the other prices and changing prices you + + + align:start position:0% +the other prices and changing prices you +think about competing sellers selling + + align:start position:0% +think about competing sellers selling + + + align:start position:0% +think about competing sellers selling +through Amazon many firms are trying to + + align:start position:0% +through Amazon many firms are trying to + + + align:start position:0% +through Amazon many firms are trying to +sell umbrellas through Amazon they're + + align:start position:0% +sell umbrellas through Amazon they're + + + align:start position:0% +sell umbrellas through Amazon they're +competing with all the other firms + + align:start position:0% +competing with all the other firms + + + align:start position:0% +competing with all the other firms +trying to sell exactly the same umbrella + + align:start position:0% +trying to sell exactly the same umbrella + + + align:start position:0% +trying to sell exactly the same umbrella +or the same Nike shoes through Amazon + + align:start position:0% +or the same Nike shoes through Amazon + + + align:start position:0% +or the same Nike shoes through Amazon +you can also think about you know Amazon + + align:start position:0% +you can also think about you know Amazon + + + align:start position:0% +you can also think about you know Amazon +competing with Target there like the + + align:start position:0% +competing with Target there like the + + + align:start position:0% +competing with Target there like the +prices are not appearing side by side + + align:start position:0% +prices are not appearing side by side + + + align:start position:0% +prices are not appearing side by side +but it's still Amazon choosing the price + + align:start position:0% +but it's still Amazon choosing the price + + + align:start position:0% +but it's still Amazon choosing the price +of which it's going to sell something + + align:start position:0% +of which it's going to sell something + + + align:start position:0% +of which it's going to sell something +Target and Walmart choosing the price of + + align:start position:0% +Target and Walmart choosing the price of + + + align:start position:0% +Target and Walmart choosing the price of +which they're going to sell it and the + + align:start position:0% +which they're going to sell it and the + + + align:start position:0% +which they're going to sell it and the +demand is a function of all those prices + + align:start position:0% +demand is a function of all those prices + + + align:start position:0% +demand is a function of all those prices +and again Amazon is not having a guy + + align:start position:0% +and again Amazon is not having a guy + + + align:start position:0% +and again Amazon is not having a guy +decide what's the price at which you + + align:start position:0% +decide what's the price at which you + + + align:start position:0% +decide what's the price at which you +know I'm going to sell this pen Amazon + + align:start position:0% +know I'm going to sell this pen Amazon + + + align:start position:0% +know I'm going to sell this pen Amazon +has got you know a computer that's + + align:start position:0% +has got you know a computer that's + + + align:start position:0% +has got you know a computer that's +monitoring the internet and changing + + align:start position:0% +monitoring the internet and changing + + + align:start position:0% +monitoring the internet and changing +prices continuously and trying to figure + + align:start position:0% +prices continuously and trying to figure + + + align:start position:0% +prices continuously and trying to figure +out what a good price is um and so what + + align:start position:0% +out what a good price is um and so what + + + align:start position:0% +out what a good price is um and so what +the paper's asking is you know what what + + align:start position:0% +the paper's asking is you know what what + + + align:start position:0% +the paper's asking is you know what what +do we think is going to happen in that + + align:start position:0% +do we think is going to happen in that + + + align:start position:0% +do we think is going to happen in that +situation where you have computers + + align:start position:0% +situation where you have computers + + + align:start position:0% +situation where you have computers +setting price is competing against other + + align:start position:0% +setting price is competing against other + + + align:start position:0% +setting price is competing against other +computers in a repeated game setting you + + align:start position:0% +computers in a repeated game setting you + + + align:start position:0% +computers in a repeated game setting you +know we know that there should be many + + align:start position:0% +know we know that there should be many + + + align:start position:0% +know we know that there should be many +many equilibrius and sometimes the + + align:start position:0% +many equilibrius and sometimes the + + + align:start position:0% +many equilibrius and sometimes the +question is which equilibrium will the + + align:start position:0% +question is which equilibrium will the + + + align:start position:0% +question is which equilibrium will the +computers find of the many repeated game + + align:start position:0% +computers find of the many repeated game + + + align:start position:0% +computers find of the many repeated game +equilibria that exist and they notice + + align:start position:0% +equilibria that exist and they notice + + + align:start position:0% +equilibria that exist and they notice +that you know we should when we think + + align:start position:0% +that you know we should when we think + + + align:start position:0% +that you know we should when we think +about what the computers are going to be + + align:start position:0% +about what the computers are going to be + + + align:start position:0% +about what the computers are going to be +doing the computers are going to be + + align:start position:0% +doing the computers are going to be + + + align:start position:0% +doing the computers are going to be +trying to learn what's happening you + + align:start position:0% +trying to learn what's happening you + + + align:start position:0% +trying to learn what's happening you +know the computers are not born knowing + + align:start position:0% +know the computers are not born knowing + + + align:start position:0% +know the computers are not born knowing +what's my demand when my price is 39 and + + align:start position:0% +what's my demand when my price is 39 and + + + align:start position:0% +what's my demand when my price is 39 and +your price is 38 the computers have to + + align:start position:0% +your price is 38 the computers have to + + + align:start position:0% +your price is 38 the computers have to +figure that out and the computers also + + align:start position:0% +figure that out and the computers also + + + align:start position:0% +figure that out and the computers also +have to figure out what's your strategy + + align:start position:0% +have to figure out what's your strategy + + + align:start position:0% +have to figure out what's your strategy +if you at 39 and I undercut to 38 do you + + align:start position:0% +if you at 39 and I undercut to 38 do you + + + align:start position:0% +if you at 39 and I undercut to 38 do you +undercut to 37 or do you stick with 38 + + align:start position:0% +undercut to 37 or do you stick with 38 + + + align:start position:0% +undercut to 37 or do you stick with 38 +or you know the computers in some sense + + align:start position:0% +or you know the computers in some sense + + + align:start position:0% +or you know the computers in some sense +have to figure out what should we be + + align:start position:0% +have to figure out what should we be + + + align:start position:0% +have to figure out what should we be +doing to profit maximize and so they try + + align:start position:0% +doing to profit maximize and so they try + + + align:start position:0% +doing to profit maximize and so they try +to think about what would happen when + + align:start position:0% +to think about what would happen when + + + align:start position:0% +to think about what would happen when +you have agents were trying to learn uh + + align:start position:0% +you have agents were trying to learn uh + + + align:start position:0% +you have agents were trying to learn uh +competing with each other and in some + + align:start position:0% +competing with each other and in some + + + align:start position:0% +competing with each other and in some +sense you know this is sort of + + align:start position:0% +sense you know this is sort of + + + align:start position:0% +sense you know this is sort of +resurrecting there was a large Theory + + align:start position:0% +resurrecting there was a large Theory + + + align:start position:0% +resurrecting there was a large Theory +literature on this in the 1990s you know + + align:start position:0% +literature on this in the 1990s you know + + + align:start position:0% +literature on this in the 1990s you know +Drew has this very nice book from with + + align:start position:0% +Drew has this very nice book from with + + + align:start position:0% +Drew has this very nice book from with +David LaVine from 1998 discussing lots + + align:start position:0% +David LaVine from 1998 discussing lots + + + align:start position:0% +David LaVine from 1998 discussing lots +of theoretical results about what + + align:start position:0% +of theoretical results about what + + + align:start position:0% +of theoretical results about what +happens if people are naively trying to + + align:start position:0% +happens if people are naively trying to + + + align:start position:0% +happens if people are naively trying to +learn and you know at the time you know + + align:start position:0% +learn and you know at the time you know + + + align:start position:0% +learn and you know at the time you know +the theorists were arguing that this is + + align:start position:0% +the theorists were arguing that this is + + + align:start position:0% +the theorists were arguing that this is +a very interesting question because you + + align:start position:0% +a very interesting question because you + + + align:start position:0% +a very interesting question because you +know if people are naively trying to + + align:start position:0% +know if people are naively trying to + + + align:start position:0% +know if people are naively trying to +learn do they learn an equilibrium or + + align:start position:0% +learn do they learn an equilibrium or + + + align:start position:0% +learn do they learn an equilibrium or +not to believe in equilibrium we need to + + align:start position:0% +not to believe in equilibrium we need to + + + align:start position:0% +not to believe in equilibrium we need to +think that that process converges and if + + align:start position:0% +think that that process converges and if + + + align:start position:0% +think that that process converges and if +that process does converge then the + + align:start position:0% +that process does converge then the + + + align:start position:0% +that process does converge then the +question is well if we have a game with + + align:start position:0% +question is well if we have a game with + + + align:start position:0% +question is well if we have a game with +multiple equilibria are there some + + align:start position:0% +multiple equilibria are there some + + + align:start position:0% +multiple equilibria are there some +equilibria that are more likely to + + align:start position:0% +equilibria that are more likely to + + + align:start position:0% +equilibria that are more likely to +emerge from that learning than others + + align:start position:0% +emerge from that learning than others + + + align:start position:0% +emerge from that learning than others +and so that some sense that's what uh + + align:start position:0% +and so that some sense that's what uh + + + align:start position:0% +and so that some sense that's what uh +kanano all are trying to do + + align:start position:0% +kanano all are trying to do + + + align:start position:0% +kanano all are trying to do +here so they bring in sort of a more + + align:start position:0% +here so they bring in sort of a more + + + align:start position:0% +here so they bring in sort of a more +complicated learning model than exists + + align:start position:0% +complicated learning model than exists + + + align:start position:0% +complicated learning model than exists +in the 1990s Theory literature um but + + align:start position:0% +in the 1990s Theory literature um but + + + align:start position:0% +in the 1990s Theory literature um but +it's a learning literature you know + + align:start position:0% +it's a learning literature you know + + + align:start position:0% +it's a learning literature you know +thinking of how you know operations + + align:start position:0% +thinking of how you know operations + + + align:start position:0% +thinking of how you know operations +research or computer scientists would + + align:start position:0% +research or computer scientists would + + + align:start position:0% +research or computer scientists would +say you should design a pricing + + align:start position:0% +say you should design a pricing + + + align:start position:0% +say you should design a pricing +algorithm for your website so we have + + align:start position:0% +algorithm for your website so we have + + + align:start position:0% +algorithm for your website so we have +situation where profit + + align:start position:0% +situation where profit + + + align:start position:0% +situation where profit +Pi depend on S a state of the world + + align:start position:0% +Pi depend on S a state of the world + + + align:start position:0% +Pi depend on S a state of the world +that's observable to the firms in their + + align:start position:0% +that's observable to the firms in their + + + align:start position:0% +that's observable to the firms in their +setting prices and a an action that they + + align:start position:0% +setting prices and a an action that they + + + align:start position:0% +setting prices and a an action that they +take which you can think of as their + + align:start position:0% +take which you can think of as their + + + align:start position:0% +take which you can think of as their +price okay and the profits depend on + + align:start position:0% +price okay and the profits depend on + + + align:start position:0% +price okay and the profits depend on +this observable State this action but + + align:start position:0% +this observable State this action but + + + align:start position:0% +this observable State this action but +it's also depends on a random shock so + + align:start position:0% +it's also depends on a random shock so + + + align:start position:0% +it's also depends on a random shock so +like I set my my rental car price at $39 + + align:start position:0% +like I set my my rental car price at $39 + + + align:start position:0% +like I set my my rental car price at $39 +someone else sets it at + + align:start position:0% +someone else sets it at + + + align:start position:0% +someone else sets it at +38 and then you know look at demand over + + align:start position:0% +38 and then you know look at demand over + + + align:start position:0% +38 and then you know look at demand over +the next day there's some random number + + align:start position:0% +the next day there's some random number + + + align:start position:0% +the next day there's some random number +of people who reserve a car at LAX on + + align:start position:0% +of people who reserve a car at LAX on + + + align:start position:0% +of people who reserve a car at LAX on +that date at that given those prices um + + align:start position:0% +that date at that given those prices um + + + align:start position:0% +that date at that given those prices um +and then there's some State transition + + align:start position:0% +and then there's some State transition + + + align:start position:0% +and then there's some State transition +process probability that state goes to S + + align:start position:0% +process probability that state goes to S + + + align:start position:0% +process probability that state goes to S +Prime given sna that's also unknown so + + align:start position:0% +Prime given sna that's also unknown so + + + align:start position:0% +Prime given sna that's also unknown so +like in the staggered price setting game + + align:start position:0% +like in the staggered price setting game + + + align:start position:0% +like in the staggered price setting game +you can think of the S the state of the + + align:start position:0% +you can think of the S the state of the + + + align:start position:0% +you can think of the S the state of the +world as everybody's price on that + + align:start position:0% +world as everybody's price on that + + + align:start position:0% +world as everybody's price on that +rental car website like the current + + align:start position:0% +rental car website like the current + + + align:start position:0% +rental car website like the current +prices today out of Lex are 4140 40 + + align:start position:0% +prices today out of Lex are 4140 40 + + + align:start position:0% +prices today out of Lex are 4140 40 +something like that that's today's State + + align:start position:0% +something like that that's today's State + + + align:start position:0% +something like that that's today's State +I observe the prices are 4140 40 where + + align:start position:0% +I observe the prices are 4140 40 where + + + align:start position:0% +I observe the prices are 4140 40 where +I'm the third of those prices I choose + + align:start position:0% +I'm the third of those prices I choose + + + align:start position:0% +I'm the third of those prices I choose +what price do I charge and then + + align:start position:0% +what price do I charge and then + + + align:start position:0% +what price do I charge and then +I'm going to get some profit over the + + align:start position:0% +I'm going to get some profit over the + + + align:start position:0% +I'm going to get some profit over the +course of the next day and then the next + + align:start position:0% +course of the next day and then the next + + + align:start position:0% +course of the next day and then the next +day when I go back to check the website + + align:start position:0% +day when I go back to check the website + + + align:start position:0% +day when I go back to check the website +again all the prices are going to be + + align:start position:0% +again all the prices are going to be + + + align:start position:0% +again all the prices are going to be +different it may be 35 38 39 and then + + align:start position:0% +different it may be 35 38 39 and then + + + align:start position:0% +different it may be 35 38 39 and then +you know I'm going to try I'm try some + + align:start position:0% +you know I'm going to try I'm try some + + + align:start position:0% +you know I'm going to try I'm try some +sometimes I don't know what that state + + align:start position:0% +sometimes I don't know what that state + + + align:start position:0% +sometimes I don't know what that state +transition process is because I don't + + align:start position:0% +transition process is because I don't + + + align:start position:0% +transition process is because I don't +know what my rivals are doing and I also + + align:start position:0% +know what my rivals are doing and I also + + + align:start position:0% +know what my rivals are doing and I also +don't know my profits are because I + + align:start position:0% +don't know my profits are because I + + + align:start position:0% +don't know my profits are because I +don't know the demand + + align:start position:0% +don't know the demand + + + align:start position:0% +don't know the demand +curve okay so what would you do well + + align:start position:0% +curve okay so what would you do well + + + align:start position:0% +curve okay so what would you do well +Dynamic program suggests that a good + + align:start position:0% +Dynamic program suggests that a good + + + align:start position:0% +Dynamic program suggests that a good +thing to do is to try to learn this + + align:start position:0% +thing to do is to try to learn this + + + align:start position:0% +thing to do is to try to learn this +function Q of of sa you know often we + + align:start position:0% +function Q of of sa you know often we + + + align:start position:0% +function Q of of sa you know often we +talk about the sort of value function + + align:start position:0% +talk about the sort of value function + + + align:start position:0% +talk about the sort of value function +the value that you get being in state + + align:start position:0% +the value that you get being in state + + + align:start position:0% +the value that you get being in state +but they're s going to find V of sa is + + align:start position:0% +but they're s going to find V of sa is + + + align:start position:0% +but they're s going to find V of sa is +going to be the max over a q of SAA + + align:start position:0% +going to be the max over a q of SAA + + + align:start position:0% +going to be the max over a q of SAA +sorry that's behind the board um so Q of + + align:start position:0% +sorry that's behind the board um so Q of + + + align:start position:0% +sorry that's behind the board um so Q of +s comma a is the profit you get if + + align:start position:0% +s comma a is the profit you get if + + + align:start position:0% +s comma a is the profit you get if +you're in state s and you play a today + + align:start position:0% +you're in state s and you play a today + + + align:start position:0% +you're in state s and you play a today +and then you play optimally in all + + align:start position:0% +and then you play optimally in all + + + align:start position:0% +and then you play optimally in all +future + + align:start position:0% +future + + + align:start position:0% +future +periods so Q ofsa the the sort of + + align:start position:0% +periods so Q ofsa the the sort of + + + align:start position:0% +periods so Q ofsa the the sort of +recursive definition of it is Q of a is + + align:start position:0% +recursive definition of it is Q of a is + + + align:start position:0% +recursive definition of it is Q of a is +the expected profit you get from taking + + align:start position:0% +the expected profit you get from taking + + + align:start position:0% +the expected profit you get from taking +action a When You observe State + + align:start position:0% +action a When You observe State + + + align:start position:0% +action a When You observe State +S Plus Delta times the expectation over + + align:start position:0% +S Plus Delta times the expectation over + + + align:start position:0% +S Plus Delta times the expectation over +what tomorrow's state is going to be + + align:start position:0% +what tomorrow's state is going to be + + + align:start position:0% +what tomorrow's state is going to be +given that state was s and you took a of + + align:start position:0% +given that state was s and you took a of + + + align:start position:0% +given that state was s and you took a of +the maximum over all few actions you're + + align:start position:0% +the maximum over all few actions you're + + + align:start position:0% +the maximum over all few actions you're +going to take Next Period Q of S Prime a + + align:start position:0% +going to take Next Period Q of S Prime a + + + align:start position:0% +going to take Next Period Q of S Prime a +prime so I'm going to take action a and + + align:start position:0% +prime so I'm going to take action a and + + + align:start position:0% +prime so I'm going to take action a and +then next period I'm going to see some + + align:start position:0% +then next period I'm going to see some + + + align:start position:0% +then next period I'm going to see some +new state S Prime and therefore I'm + + align:start position:0% +new state S Prime and therefore I'm + + + align:start position:0% +new state S Prime and therefore I'm +going to choose some new action a prime + + align:start position:0% +going to choose some new action a prime + + + align:start position:0% +going to choose some new action a prime +and then I'm going to get this + + align:start position:0% +and then I'm going to get this + + + align:start position:0% +and then I'm going to get this +discounted + + align:start position:0% +discounted + + + align:start position:0% +discounted +present value of profits Q of S Prime a + + align:start position:0% +present value of profits Q of S Prime a + + + align:start position:0% +present value of profits Q of S Prime a +prime so you know if I knew this object + + align:start position:0% +prime so you know if I knew this object + + + align:start position:0% +prime so you know if I knew this object +Q of sa then I can behave optimally + + align:start position:0% +Q of sa then I can behave optimally + + + align:start position:0% +Q of sa then I can behave optimally +right I just do the argmax overall I + + align:start position:0% +right I just do the argmax overall I + + + align:start position:0% +right I just do the argmax overall I +observe a state I just choose the a that + + align:start position:0% +observe a state I just choose the a that + + + align:start position:0% +observe a state I just choose the a that +maximizes Q of + + align:start position:0% +maximizes Q of + + + align:start position:0% +maximizes Q of +sa um so if you think about it you know + + align:start position:0% +sa um so if you think about it you know + + + align:start position:0% +sa um so if you think about it you know +Q is just a matrix of numbers that I + + align:start position:0% +Q is just a matrix of numbers that I + + + align:start position:0% +Q is just a matrix of numbers that I +need to + + align:start position:0% +need to + + + align:start position:0% +need to +know right I have all the + + align:start position:0% +know right I have all the + + + align:start position:0% +know right I have all the +possible I have all the possible States + + align:start position:0% +possible I have all the possible States + + + align:start position:0% +possible I have all the possible States +s s Prime s double Prime SLE Prime and + + align:start position:0% +s s Prime s double Prime SLE Prime and + + + align:start position:0% +s s Prime s double Prime SLE Prime and +there all the possible actions I can + + align:start position:0% +there all the possible actions I can + + + align:start position:0% +there all the possible actions I can +take a a prime a double prime a triple + + align:start position:0% +take a a prime a double prime a triple + + + align:start position:0% +take a a prime a double prime a triple +prime I just need to know what's my + + align:start position:0% +prime I just need to know what's my + + + align:start position:0% +prime I just need to know what's my +discounted present value in each of + + align:start position:0% +discounted present value in each of + + + align:start position:0% +discounted present value in each of +these in all of these things if I know + + align:start position:0% +these in all of these things if I know + + + align:start position:0% +these in all of these things if I know +the numbers in this Matrix I just + + align:start position:0% +the numbers in this Matrix I just + + + align:start position:0% +the numbers in this Matrix I just +whatever state I'm in I just maximize + + align:start position:0% +whatever state I'm in I just maximize + + + align:start position:0% +whatever state I'm in I just maximize +the numbers in that column and that's + + align:start position:0% +the numbers in that column and that's + + + align:start position:0% +the numbers in that column and that's +how I + + align:start position:0% +how I + + + align:start position:0% +how I +behave so here's a sort of standard + + align:start position:0% +behave so here's a sort of standard + + + align:start position:0% +behave so here's a sort of standard +learning algorithm for how you might + + align:start position:0% +learning algorithm for how you might + + + align:start position:0% +learning algorithm for how you might +program a computer to behave in this + + align:start position:0% +program a computer to behave in this + + + align:start position:0% +program a computer to behave in this +situation you conjecture some initial + + align:start position:0% +situation you conjecture some initial + + + align:start position:0% +situation you conjecture some initial +Matrix Q so maybe you have sort of some + + align:start position:0% +Matrix Q so maybe you have sort of some + + + align:start position:0% +Matrix Q so maybe you have sort of some +initial conjectured demand curve and + + align:start position:0% +initial conjectured demand curve and + + + align:start position:0% +initial conjectured demand curve and +maybe you assume just sort of some flat + + align:start position:0% +maybe you assume just sort of some flat + + + align:start position:0% +maybe you assume just sort of some flat +conjecture about how your Rivals are + + align:start position:0% +conjecture about how your Rivals are + + + align:start position:0% +conjecture about how your Rivals are +going to price and figure out you know + + align:start position:0% +going to price and figure out you know + + + align:start position:0% +going to price and figure out you know +what profit do I think I'm going to get + + align:start position:0% +what profit do I think I'm going to get + + + align:start position:0% +what profit do I think I'm going to get +if there's no + + align:start position:0% +if there's no + + + align:start position:0% +if there's no +Dynamics I just guess what the demand + + align:start position:0% +Dynamics I just guess what the demand + + + align:start position:0% +Dynamics I just guess what the demand +curve is I just initialize Q to some I + + align:start position:0% +curve is I just initialize Q to some I + + + align:start position:0% +curve is I just initialize Q to some I +initialize Q to something like so I sort + + align:start position:0% +initialize Q to something like so I sort + + + align:start position:0% +initialize Q to something like so I sort +of assume that this is the profit + + align:start position:0% +of assume that this is the profit + + + align:start position:0% +of assume that this is the profit +maximizing things my profit is + + align:start position:0% +maximizing things my profit is + + + align:start position:0% +maximizing things my profit is +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +22222 1.9 1.9 1 .9 1.9 1.8 I just + + align:start position:0% +22222 1.9 1.9 1 .9 1.9 1.8 I just + + + align:start position:0% +22222 1.9 1.9 1 .9 1.9 1.8 I just +initialize this Matrix to something + + align:start position:0% +initialize this Matrix to something + + + align:start position:0% +initialize this Matrix to something +guessing that I think this is the best + + align:start position:0% +guessing that I think this is the best + + + align:start position:0% +guessing that I think this is the best +and I think my profits stayed + + align:start position:0% +and I think my profits stayed + + + align:start position:0% +and I think my profits stayed +independent okay um then at every Point + + align:start position:0% +independent okay um then at every Point + + + align:start position:0% +independent okay um then at every Point +T I figure out okay if this is the state + + align:start position:0% +T I figure out okay if this is the state + + + align:start position:0% +T I figure out okay if this is the state +at time zero that's my optimal action so + + align:start position:0% +at time zero that's my optimal action so + + + align:start position:0% +at time zero that's my optimal action so +I take + + align:start position:0% +I take + + + align:start position:0% +I take +it uh so I choose the profit maximizing + + align:start position:0% +it uh so I choose the profit maximizing + + + align:start position:0% +it uh so I choose the profit maximizing +action given my current knowledge of the + + align:start position:0% +action given my current knowledge of the + + + align:start position:0% +action given my current knowledge of the +Q Matrix and my current observation of + + align:start position:0% +Q Matrix and my current observation of + + + align:start position:0% +Q Matrix and my current observation of +the + + align:start position:0% +the + + + align:start position:0% +the +State well I choose that with large + + align:start position:0% +State well I choose that with large + + + align:start position:0% +State well I choose that with large +probability but with Epsilon probability + + align:start position:0% +probability but with Epsilon probability + + + align:start position:0% +probability but with Epsilon probability +I experiment because I don't know right + + align:start position:0% +I experiment because I don't know right + + + align:start position:0% +I experiment because I don't know right +that maybe that this price is not good + + align:start position:0% +that maybe that this price is not good + + + align:start position:0% +that maybe that this price is not good +so I usually choose this but with some + + align:start position:0% +so I usually choose this but with some + + + align:start position:0% +so I usually choose this but with some +probability I experiment and choose a + + align:start position:0% +probability I experiment and choose a + + + align:start position:0% +probability I experiment and choose a +different action + + align:start position:0% +different action + + + align:start position:0% +different action +instead and then when I choose this + + align:start position:0% +instead and then when I choose this + + + align:start position:0% +instead and then when I choose this +action I update the number in this cell + + align:start position:0% +action I update the number in this cell + + + align:start position:0% +action I update the number in this cell +by saying I'm going to take a weighted + + align:start position:0% +by saying I'm going to take a weighted + + + align:start position:0% +by saying I'm going to take a weighted +average of what I thought the number was + + align:start position:0% +average of what I thought the number was + + + align:start position:0% +average of what I thought the number was +so I thought the number was two so I + + align:start position:0% +so I thought the number was two so I + + + align:start position:0% +so I thought the number was two so I +take a weighted average of two and + + align:start position:0% +take a weighted average of two and + + + align:start position:0% +take a weighted average of two and +what I now what my current period + + align:start position:0% +what I now what my current period + + + align:start position:0% +what I now what my current period +experience is which is I got profit Pi T + + align:start position:0% +experience is which is I got profit Pi T + + + align:start position:0% +experience is which is I got profit Pi T +and then I got profit Pi T and then I + + align:start position:0% +and then I got profit Pi T and then I + + + align:start position:0% +and then I got profit Pi T and then I +end up in this state and I think what's + + align:start position:0% +end up in this state and I think what's + + + align:start position:0% +end up in this state and I think what's +the best I'm going to do in this state + + align:start position:0% +the best I'm going to do in this state + + + align:start position:0% +the best I'm going to do in this state +and so I do I know that I got profit Pi + + align:start position:0% +and so I do I know that I got profit Pi + + + align:start position:0% +and so I do I know that I got profit Pi +T and I know that I ended up in state + + align:start position:0% +T and I know that I ended up in state + + + align:start position:0% +T and I know that I ended up in state +st+ one so I do this plus what I expect + + align:start position:0% +st+ one so I do this plus what I expect + + + align:start position:0% +st+ one so I do this plus what I expect +from optimal play in that state still + + align:start position:0% +from optimal play in that state still + + + align:start position:0% +from optimal play in that state still +using my my Q Matrix that I started with + + align:start position:0% +using my my Q Matrix that I started with + + + align:start position:0% +using my my Q Matrix that I started with +so here actually I think I'm still going + + align:start position:0% +so here actually I think I'm still going + + + align:start position:0% +so here actually I think I'm still going +to get two even though the state has + + align:start position:0% +to get two even though the state has + + + align:start position:0% +to get two even though the state has +changed + + align:start position:0% +changed + + + align:start position:0% +changed +changed + + align:start position:0% +changed + + + align:start position:0% +changed +um anyway so theorem you know from from + + align:start position:0% +um anyway so theorem you know from from + + + align:start position:0% +um anyway so theorem you know from from +uh people who study these kinds of + + align:start position:0% +uh people who study these kinds of + + + align:start position:0% +uh people who study these kinds of +learning algorithms is that if I'm + + align:start position:0% +learning algorithms is that if I'm + + + align:start position:0% +learning algorithms is that if I'm +playing against the stationary + + align:start position:0% +playing against the stationary + + + align:start position:0% +playing against the stationary +environment there really is just some + + align:start position:0% +environment there really is just some + + + align:start position:0% +environment there really is just some +exogenous process by which states + + align:start position:0% +exogenous process by which states + + + align:start position:0% +exogenous process by which states +transition which can depend on my action + + align:start position:0% +transition which can depend on my action + + + align:start position:0% +transition which can depend on my action +and depends on the current state but if + + align:start position:0% +and depends on the current state but if + + + align:start position:0% +and depends on the current state but if +there's some Markoff State transitions + + align:start position:0% +there's some Markoff State transitions + + + align:start position:0% +there's some Markoff State transitions +like this and there's some profit + + align:start position:0% +like this and there's some profit + + + align:start position:0% +like this and there's some profit +function I don't even know what it is + + align:start position:0% +function I don't even know what it is + + + align:start position:0% +function I don't even know what it is +this Q learning algorithm finds the best + + align:start position:0% +this Q learning algorithm finds the best + + + align:start position:0% +this Q learning algorithm finds the best +thing to do in the long + + align:start position:0% +thing to do in the long + + + align:start position:0% +thing to do in the long +run okay again you need some sort of + + align:start position:0% +run okay again you need some sort of + + + align:start position:0% +run okay again you need some sort of +ability of of full support of the markof + + align:start position:0% +ability of of full support of the markof + + + align:start position:0% +ability of of full support of the markof +process so you don't get stuck like + + align:start position:0% +process so you don't get stuck like + + + align:start position:0% +process so you don't get stuck like +there was some great thing to do but + + align:start position:0% +there was some great thing to do but + + + align:start position:0% +there was some great thing to do but +once you leave that you can never get + + align:start position:0% +once you leave that you can never get + + + align:start position:0% +once you leave that you can never get +back to that state but if there's a a + + align:start position:0% +back to that state but if there's a a + + + align:start position:0% +back to that state but if there's a a +you know if the markof processor is + + align:start position:0% +you know if the markof processor is + + + align:start position:0% +you know if the markof processor is +going to cover all states this thing + + align:start position:0% +going to cover all states this thing + + + align:start position:0% +going to cover all states this thing +will eventually find it because you're + + align:start position:0% +will eventually find it because you're + + + align:start position:0% +will eventually find it because you're +just sort of updating you know every + + align:start position:0% +just sort of updating you know every + + + align:start position:0% +just sort of updating you know every +period you're just updating one element + + align:start position:0% +period you're just updating one element + + + align:start position:0% +period you're just updating one element +in this to reflect the profit you get in + + align:start position:0% +in this to reflect the profit you get in + + + align:start position:0% +in this to reflect the profit you get in +this state and then the profit you get + + align:start position:0% +this state and then the profit you get + + + align:start position:0% +this state and then the profit you get +in the next state and then if you're in + + align:start position:0% +in the next state and then if you're in + + + align:start position:0% +in the next state and then if you're in +this state you update the profit here to + + align:start position:0% +this state you update the profit here to + + + align:start position:0% +this state you update the profit here to +reflect where you end up up there you + + align:start position:0% +reflect where you end up up there you + + + align:start position:0% +reflect where you end up up there you +just keep updating the profits taking a + + align:start position:0% +just keep updating the profits taking a + + + align:start position:0% +just keep updating the profits taking a +weighted average what you thought they + + align:start position:0% +weighted average what you thought they + + + align:start position:0% +weighted average what you thought they +were and the um current thing so at some + + align:start position:0% +were and the um current thing so at some + + + align:start position:0% +were and the um current thing so at some +point the right the current the actual + + align:start position:0% +point the right the current the actual + + + align:start position:0% +point the right the current the actual +experience starts to overwhelm the past + + align:start position:0% +experience starts to overwhelm the past + + + align:start position:0% +experience starts to overwhelm the past +experience this thing + + align:start position:0% + + + + align:start position:0% + +converges and so you know calano at all + + align:start position:0% +converges and so you know calano at all + + + align:start position:0% +converges and so you know calano at all +sort of conjectured that this would be a + + align:start position:0% +sort of conjectured that this would be a + + + align:start position:0% +sort of conjectured that this would be a +reasonable thing for firms to do if + + align:start position:0% +reasonable thing for firms to do if + + + align:start position:0% +reasonable thing for firms to do if +they're pricing against another firm on + + align:start position:0% +they're pricing against another firm on + + + align:start position:0% +they're pricing against another firm on +a travel website if you know if I were + + align:start position:0% +a travel website if you know if I were + + + align:start position:0% +a travel website if you know if I were +to assign you like here I want you to + + align:start position:0% +to assign you like here I want you to + + + align:start position:0% +to assign you like here I want you to +design a pricing algorithm + + align:start position:0% +design a pricing algorithm + + + align:start position:0% +design a pricing algorithm +for Herz to use you you might have come + + align:start position:0% +for Herz to use you you might have come + + + align:start position:0% +for Herz to use you you might have come +up with this + + align:start position:0% +up with this + + + align:start position:0% +up with this +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um okay so what they do is then they + + align:start position:0% +um okay so what they do is then they + + + align:start position:0% +um okay so what they do is then they +sort of study what would happen here in + + align:start position:0% +sort of study what would happen here in + + + align:start position:0% +sort of study what would happen here in +the repeated competition games they go + + align:start position:0% +the repeated competition games they go + + + align:start position:0% +the repeated competition games they go +to things that look very much like we're + + align:start position:0% +to things that look very much like we're + + + align:start position:0% +to things that look very much like we're +used to so they go to like a lit uh + + align:start position:0% +used to so they go to like a lit uh + + + align:start position:0% +used to so they go to like a lit uh +price competition game where consumers + + align:start position:0% +price competition game where consumers + + + align:start position:0% +price competition game where consumers +have these V minus P plus Epsilon + + align:start position:0% +have these V minus P plus Epsilon + + + align:start position:0% +have these V minus P plus Epsilon +preferences and the epsilons are loog at + + align:start position:0% +preferences and the epsilons are loog at + + + align:start position:0% +preferences and the epsilons are loog at +distributed errors + + align:start position:0% +distributed errors + + + align:start position:0% +distributed errors +their base model has two firms in + + align:start position:0% +their base model has two firms in + + + align:start position:0% +their base model has two firms in +it the two firms have identical + + align:start position:0% +it the two firms have identical + + + align:start position:0% +it the two firms have identical +costs they have a grid that has 15 + + align:start position:0% +costs they have a grid that has 15 + + + align:start position:0% +costs they have a grid that has 15 +possible prices they have a discount + + align:start position:0% +possible prices they have a discount + + + align:start position:0% +possible prices they have a discount +factor of + + align:start position:0% +factor of + + + align:start position:0% +factor of +0.95 + + align:start position:0% +0.95 + + + align:start position:0% +0.95 +um they don't know what parameters firms + + align:start position:0% +um they don't know what parameters firms + + + align:start position:0% +um they don't know what parameters firms +would use Alpha if you remember was the + + align:start position:0% +would use Alpha if you remember was the + + + align:start position:0% +would use Alpha if you remember was the +weight on current profits how fast you + + align:start position:0% +weight on current profits how fast you + + + align:start position:0% +weight on current profits how fast you +update the numbers in the Q Matrix when + + align:start position:0% +update the numbers in the Q Matrix when + + + align:start position:0% +update the numbers in the Q Matrix when +when you get profits in each period and + + align:start position:0% +when you get profits in each period and + + + align:start position:0% +when you get profits in each period and +again you know here profit are random + + align:start position:0% +again you know here profit are random + + + align:start position:0% +again you know here profit are random +because the fir Customer because the + + align:start position:0% +because the fir Customer because the + + + align:start position:0% +because the fir Customer because the +epsilons might buy from you might not + + align:start position:0% +epsilons might buy from you might not + + + align:start position:0% +epsilons might buy from you might not +buy from you um and again you know you + + align:start position:0% +buy from you um and again you know you + + + align:start position:0% +buy from you um and again you know you +don't know the low jit parameter but you + + align:start position:0% +don't know the low jit parameter but you + + + align:start position:0% +don't know the low jit parameter but you +just sort of know that higher price less + + align:start position:0% +just sort of know that higher price less + + + align:start position:0% +just sort of know that higher price less +likely but I don't know the elasticity + + align:start position:0% +likely but I don't know the elasticity + + + align:start position:0% +likely but I don't know the elasticity +and then they have a second parameter + + align:start position:0% +and then they have a second parameter + + + align:start position:0% +and then they have a second parameter +beta which governs how fast the + + align:start position:0% +beta which governs how fast the + + + align:start position:0% +beta which governs how fast the +experimentation rate goes to zero um as + + align:start position:0% +experimentation rate goes to zero um as + + + align:start position:0% +experimentation rate goes to zero um as +I said you know you're going to want the + + align:start position:0% +I said you know you're going to want the + + + align:start position:0% +I said you know you're going to want the +early in the game you're going to want + + align:start position:0% +early in the game you're going to want + + + align:start position:0% +early in the game you're going to want +to experiment a lot after you've been + + align:start position:0% +to experiment a lot after you've been + + + align:start position:0% +to experiment a lot after you've been +playing this thing for a million periods + + align:start position:0% +playing this thing for a million periods + + + align:start position:0% +playing this thing for a million periods +you want to stop experimenting and just + + align:start position:0% +you want to stop experimenting and just + + + align:start position:0% +you want to stop experimenting and just +start picking the best thing and so + + align:start position:0% +start picking the best thing and so + + + align:start position:0% +start picking the best thing and so +these two parameters Alpha is how fast + + align:start position:0% +these two parameters Alpha is how fast + + + align:start position:0% +these two parameters Alpha is how fast +you adjust your Q Matrix and beta is how + + align:start position:0% +you adjust your Q Matrix and beta is how + + + align:start position:0% +you adjust your Q Matrix and beta is how +quickly you aband how how long you aband + + align:start position:0% +quickly you aband how how long you aband + + + align:start position:0% +quickly you aband how how long you aband +how slowly you abandon + + align:start position:0% +how slowly you abandon + + + align:start position:0% +how slowly you abandon +experimenting okay um anyway they + + align:start position:0% +experimenting okay um anyway they + + + align:start position:0% +experimenting okay um anyway they +declare learning to have converged when + + align:start position:0% +declare learning to have converged when + + + align:start position:0% +declare learning to have converged when +optimal play is unchanged in their model + + align:start position:0% +optimal play is unchanged in their model + + + align:start position:0% +optimal play is unchanged in their model +for 100,000 periods in a row obviously + + align:start position:0% +for 100,000 periods in a row obviously + + + align:start position:0% +for 100,000 periods in a row obviously +they had a big computer uh and they also + + align:start position:0% +they had a big computer uh and they also + + + align:start position:0% +they had a big computer uh and they also +actually considered 10,000 different + + align:start position:0% +actually considered 10,000 different + + + align:start position:0% +actually considered 10,000 different +parameter combinations Alpha and beta to + + align:start position:0% +parameter combinations Alpha and beta to + + + align:start position:0% +parameter combinations Alpha and beta to +sort of be able to talk about what + + align:start position:0% +sort of be able to talk about what + + + align:start position:0% +sort of be able to talk about what +happens here based on what Alpha and + + align:start position:0% +happens here based on what Alpha and + + + align:start position:0% +happens here based on what Alpha and +beta did the firms use um main results + + align:start position:0% +beta did the firms use um main results + + + align:start position:0% +beta did the firms use um main results +they have are that really it turns out + + align:start position:0% +they have are that really it turns out + + + align:start position:0% +they have are that really it turns out +that for a wide range of Alpha and beta + + align:start position:0% +that for a wide range of Alpha and beta + + + align:start position:0% +that for a wide range of Alpha and beta +pretty much the same things happen what + + align:start position:0% +pretty much the same things happen what + + + align:start position:0% +pretty much the same things happen what +what happens um first profits are + + align:start position:0% +what happens um first profits are + + + align:start position:0% +what happens um first profits are +usually 70 to 90% of the way from from + + align:start position:0% +usually 70 to 90% of the way from from + + + align:start position:0% +usually 70 to 90% of the way from from +static nashed Monopoly so what we find + + align:start position:0% +static nashed Monopoly so what we find + + + align:start position:0% +static nashed Monopoly so what we find +the computers learning is to collude + + align:start position:0% +the computers learning is to collude + + + align:start position:0% +the computers learning is to collude +with each other uh and so they end up + + align:start position:0% +with each other uh and so they end up + + + align:start position:0% +with each other uh and so they end up +with these sort of collusive pricing + + align:start position:0% +with these sort of collusive pricing + + + align:start position:0% +with these sort of collusive pricing +that's you know pretty far towards pure + + align:start position:0% +that's you know pretty far towards pure + + + align:start position:0% +that's you know pretty far towards pure +Monopoly from static Nash + + align:start position:0% + + + + align:start position:0% + +um where do the computers end up the + + align:start position:0% +um where do the computers end up the + + + align:start position:0% +um where do the computers end up the +computers end up playing things that are + + align:start position:0% +computers end up playing things that are + + + align:start position:0% +computers end up playing things that are +Epsilon Nash equilibrium some sense the + + align:start position:0% +Epsilon Nash equilibrium some sense the + + + align:start position:0% +Epsilon Nash equilibrium some sense the +computers invent punishments with finite + + align:start position:0% +computers invent punishments with finite + + + align:start position:0% +computers invent punishments with finite +price Wars so the computers sort of + + align:start position:0% +price Wars so the computers sort of + + + align:start position:0% +price Wars so the computers sort of +develop these beliefs about what's going + + align:start position:0% +develop these beliefs about what's going + + + align:start position:0% +develop these beliefs about what's going +to happen that means that we all charge + + align:start position:0% +to happen that means that we all charge + + + align:start position:0% +to happen that means that we all charge +this Monopoly price and then if you know + + align:start position:0% +this Monopoly price and then if you know + + + align:start position:0% +this Monopoly price and then if you know +so let's suppose this is the state where + + align:start position:0% +so let's suppose this is the state where + + + align:start position:0% +so let's suppose this is the state where +we're both charging price + + align:start position:0% +we're both charging price + + + align:start position:0% +we're both charging price +two and then what the computers think is + + align:start position:0% +two and then what the computers think is + + + align:start position:0% +two and then what the computers think is +that if they deviate + + align:start position:0% +that if they deviate + + + align:start position:0% +that if they deviate +uh to 1.92 and we're in this state S + + align:start position:0% +uh to 1.92 and we're in this state S + + + align:start position:0% +uh to 1.92 and we're in this state S +Prime then in the state + + align:start position:0% +Prime then in the state + + + align:start position:0% +Prime then in the state +1.92 um profits are lower and profits + + align:start position:0% +1.92 um profits are lower and profits + + + align:start position:0% +1.92 um profits are lower and profits +are lower in a way that's going to make + + align:start position:0% +are lower in a way that's going to make + + + align:start position:0% +are lower in a way that's going to make +the + + align:start position:0% +the + + + align:start position:0% +the +state the other firm underc cut and + + align:start position:0% +state the other firm underc cut and + + + align:start position:0% +state the other firm underc cut and +we're going to transition and follow + + align:start position:0% +we're going to transition and follow + + + align:start position:0% +we're going to transition and follow +this arrow in the mat some sense the + + align:start position:0% +this arrow in the mat some sense the + + + align:start position:0% +this arrow in the mat some sense the +computers learn that from here profits + + align:start position:0% +computers learn that from here profits + + + align:start position:0% +computers learn that from here profits +are going to be such that I want to I + + align:start position:0% +are going to be such that I want to I + + + align:start position:0% +are going to be such that I want to I +want to undercut and charge an even + + align:start position:0% +want to undercut and charge an even + + + align:start position:0% +want to undercut and charge an even +lower price PR and then the next time + + align:start position:0% +lower price PR and then the next time + + + align:start position:0% +lower price PR and then the next time +he's going to want to undercut and + + align:start position:0% +he's going to want to undercut and + + + align:start position:0% +he's going to want to undercut and +charge an even lower price and the + + align:start position:0% +charge an even lower price and the + + + align:start position:0% +charge an even lower price and the +computers in some sense learn that the + + align:start position:0% +computers in some sense learn that the + + + align:start position:0% +computers in some sense learn that the +payoffs are such that you want to do + + align:start position:0% +payoffs are such that you want to do + + + align:start position:0% +payoffs are such that you want to do +something not so different from one of + + align:start position:0% +something not so different from one of + + + align:start position:0% +something not so different from one of +these Mass skoll Cycles off the + + align:start position:0% +these Mass skoll Cycles off the + + + align:start position:0% +these Mass skoll Cycles off the +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +path + + align:start position:0% +path + + + align:start position:0% +path +um so even when you set Delta + + align:start position:0% +um so even when you set Delta + + + align:start position:0% +um so even when you set Delta +approximately equal to zero um the + + align:start position:0% +approximately equal to zero um the + + + align:start position:0% +approximately equal to zero um the +computers still learn that they should + + align:start position:0% +computers still learn that they should + + + align:start position:0% +computers still learn that they should +you know like you know Delta's positive + + align:start position:0% +you know like you know Delta's positive + + + align:start position:0% +you know like you know Delta's positive +but nonzero the computers still learn + + align:start position:0% +but nonzero the computers still learn + + + align:start position:0% +but nonzero the computers still learn +they should collude they don't collude + + align:start position:0% +they should collude they don't collude + + + align:start position:0% +they should collude they don't collude +much when Delta small they like collude + + align:start position:0% +much when Delta small they like collude + + + align:start position:0% +much when Delta small they like collude +with like 20% of the way the Monopoly + + align:start position:0% +with like 20% of the way the Monopoly + + + align:start position:0% +with like 20% of the way the Monopoly +price but it seems that whatever you + + align:start position:0% +price but it seems that whatever you + + + align:start position:0% +price but it seems that whatever you +pick the computers are colluding that + + align:start position:0% +pick the computers are colluding that + + + align:start position:0% +pick the computers are colluding that +way um and then as you increase the + + align:start position:0% +way um and then as you increase the + + + align:start position:0% +way um and then as you increase the +number of firms it does decrease the + + align:start position:0% +number of firms it does decrease the + + + align:start position:0% +number of firms it does decrease the +collusive level of prices so if we want + + align:start position:0% +collusive level of prices so if we want + + + align:start position:0% +collusive level of prices so if we want +to ask you know what causes prices to go + + align:start position:0% +to ask you know what causes prices to go + + + align:start position:0% +to ask you know what causes prices to go +down as as Delta increases like I said + + align:start position:0% +down as as Delta increases like I said + + + align:start position:0% +down as as Delta increases like I said +that the pure Theory version has a very + + align:start position:0% +that the pure Theory version has a very + + + align:start position:0% +that the pure Theory version has a very +hard time with that because one minus + + align:start position:0% +hard time with that because one minus + + + align:start position:0% +hard time with that because one minus +one over a quarter is not a big number + + align:start position:0% +one over a quarter is not a big number + + + align:start position:0% +one over a quarter is not a big number +but this says that prices do seem to + + align:start position:0% +but this says that prices do seem to + + + align:start position:0% +but this says that prices do seem to +decline the number of firms and they + + align:start position:0% +decline the number of firms and they + + + align:start position:0% +decline the number of firms and they +learn less clu of equal IA when the + + align:start position:0% +learn less clu of equal IA when the + + + align:start position:0% +learn less clu of equal IA when the +number of firms is larger but still high + + align:start position:0% +number of firms is larger but still high + + + align:start position:0% +number of firms is larger but still high +with four firms and let me say you know + + align:start position:0% +with four firms and let me say you know + + + align:start position:0% +with four firms and let me say you know +it's hard to write papers like this + + align:start position:0% +it's hard to write papers like this + + + align:start position:0% +it's hard to write papers like this +because you're sort of used to in a + + align:start position:0% +because you're sort of used to in a + + + align:start position:0% +because you're sort of used to in a +theory paper people want to see theorems + + align:start position:0% +theory paper people want to see theorems + + + align:start position:0% +theory paper people want to see theorems +and you can sort of read this as an + + align:start position:0% +and you can sort of read this as an + + + align:start position:0% +and you can sort of read this as an +example for how do I present results + + align:start position:0% +example for how do I present results + + + align:start position:0% +example for how do I present results +from a paper that has lots of + + align:start position:0% +from a paper that has lots of + + + align:start position:0% +from a paper that has lots of +simulations instead of theories and they + + align:start position:0% +simulations instead of theories and they + + + align:start position:0% +simulations instead of theories and they +have a lot of nice pretty graphs in it I + + align:start position:0% +have a lot of nice pretty graphs in it I + + + align:start position:0% +have a lot of nice pretty graphs in it I +think that helps it's like so this is + + align:start position:0% +think that helps it's like so this is + + + align:start position:0% +think that helps it's like so this is +their profit gain as a function of the + + align:start position:0% +their profit gain as a function of the + + + align:start position:0% +their profit gain as a function of the +two parameters Alpha and beta where this + + align:start position:0% +two parameters Alpha and beta where this + + + align:start position:0% +two parameters Alpha and beta where this +color here is like 90% of the way there + + align:start position:0% +color here is like 90% of the way there + + + align:start position:0% +color here is like 90% of the way there +this color here is 60 or 70% of the way + + align:start position:0% +this color here is 60 or 70% of the way + + + align:start position:0% +this color here is 60 or 70% of the way +there but they're showing you that for + + align:start position:0% +there but they're showing you that for + + + align:start position:0% +there but they're showing you that for +many things it looks like 70 to 90% of + + align:start position:0% +many things it looks like 70 to 90% of + + + align:start position:0% +many things it looks like 70 to 90% of +the way there here's their graph of + + align:start position:0% +the way there here's their graph of + + + align:start position:0% +the way there here's their graph of +profits versus the discount Factor so + + align:start position:0% +profits versus the discount Factor so + + + align:start position:0% +profits versus the discount Factor so +when discount factors are anything below + + align:start position:0% +when discount factors are anything below + + + align:start position:0% +when discount factors are anything below +04.5 we're roughly getting 20% of the + + align:start position:0% +04.5 we're roughly getting 20% of the + + + align:start position:0% +04.5 we're roughly getting 20% of the +way of the Monopoly profits on average + + align:start position:0% +way of the Monopoly profits on average + + + align:start position:0% +way of the Monopoly profits on average +uh but then as people become more + + align:start position:0% +uh but then as people become more + + + align:start position:0% +uh but then as people become more +patient the computers the more patient + + align:start position:0% +patient the computers the more patient + + + align:start position:0% +patient the computers the more patient +computers learn more and more to collude + + align:start position:0% +computers learn more and more to collude + + + align:start position:0% +computers learn more and more to collude +with each other and when the computers + + align:start position:0% +with each other and when the computers + + + align:start position:0% +with each other and when the computers +are very patient they're learning 90 + + align:start position:0% +are very patient they're learning 90 + + + align:start position:0% +are very patient they're learning 90 +something per of the way to the Monopoly + + align:start position:0% +something per of the way to the Monopoly + + + align:start position:0% +something per of the way to the Monopoly +price okay um they have illustrations of + + align:start position:0% +price okay um they have illustrations of + + + align:start position:0% +price okay um they have illustrations of +what the price Wars look like so this + + align:start position:0% +what the price Wars look like so this + + + align:start position:0% +what the price Wars look like so this +was just an example take a final + + align:start position:0% +was just an example take a final + + + align:start position:0% +was just an example take a final +strategy someone undercuts the other + + align:start position:0% +strategy someone undercuts the other + + + align:start position:0% +strategy someone undercuts the other +firm then does undercut them and it + + align:start position:0% +firm then does undercut them and it + + + align:start position:0% +firm then does undercut them and it +takes them a while to get back to the + + align:start position:0% +takes them a while to get back to the + + + align:start position:0% +takes them a while to get back to the +Monopoly price so the computers have + + align:start position:0% +Monopoly price so the computers have + + + align:start position:0% +Monopoly price so the computers have +learned to follow some pattern like this + + align:start position:0% +learned to follow some pattern like this + + + align:start position:0% +learned to follow some pattern like this +that has finite price Wars um and this + + align:start position:0% +that has finite price Wars um and this + + + align:start position:0% +that has finite price Wars um and this +is sort of their illustration of what + + align:start position:0% +is sort of their illustration of what + + + align:start position:0% +is sort of their illustration of what +one of the equipment strategies looks + + align:start position:0% +one of the equipment strategies looks + + + align:start position:0% +one of the equipment strategies looks +like where this is the sort of absorbing + + align:start position:0% +like where this is the sort of absorbing + + + align:start position:0% +like where this is the sort of absorbing +state where we charge the Monopoly price + + align:start position:0% +state where we charge the Monopoly price + + + align:start position:0% +state where we charge the Monopoly price +and if you deviate you follow one of + + align:start position:0% +and if you deviate you follow one of + + + align:start position:0% +and if you deviate you follow one of +these paths like this and then + + align:start position:0% +these paths like this and then + + + align:start position:0% +these paths like this and then +eventually come back there or six or + + align:start position:0% +eventually come back there or six or + + + align:start position:0% +eventually come back there or six or +eight or whatever periods later but the + + align:start position:0% +eight or whatever periods later but the + + + align:start position:0% +eight or whatever periods later but the +computers in some sense created this + + align:start position:0% +computers in some sense created this + + + align:start position:0% +computers in some sense created this +network of ways that you Traverse this + + align:start position:0% +network of ways that you Traverse this + + + align:start position:0% +network of ways that you Traverse this +thing that eventually gets you back to + + align:start position:0% +thing that eventually gets you back to + + + align:start position:0% +thing that eventually gets you back to +the clusive + + align:start position:0% +the clusive + + + align:start position:0% +the clusive +price um and just you cute illustration + + align:start position:0% +price um and just you cute illustration + + + align:start position:0% +price um and just you cute illustration +of what happens in these things you know + + align:start position:0% +of what happens in these things you know + + + align:start position:0% +of what happens in these things you know +you do see a lot of Stories on this of + + align:start position:0% +you do see a lot of Stories on this of + + + align:start position:0% +you do see a lot of Stories on this of +this happens on Amazon that firms have + + align:start position:0% +this happens on Amazon that firms have + + + align:start position:0% +this happens on Amazon that firms have +these automatic pricing algorithms and + + align:start position:0% +these automatic pricing algorithms and + + + align:start position:0% +these automatic pricing algorithms and +you go to like buy something on Amazon + + align:start position:0% +you go to like buy something on Amazon + + + align:start position:0% +you go to like buy something on Amazon +you see these crazy prices + + align:start position:0% +you see these crazy prices + + + align:start position:0% +you see these crazy prices +this is sort of just some illustration I + + align:start position:0% +this is sort of just some illustration I + + + align:start position:0% +this is sort of just some illustration I +found of like you know this pillow was + + align:start position:0% +found of like you know this pillow was + + + align:start position:0% +found of like you know this pillow was +being sold on Amazon for + + align:start position:0% +being sold on Amazon for + + + align:start position:0% +being sold on Amazon for +$1,235 and it clearly it was there were + + align:start position:0% +$1,235 and it clearly it was there were + + + align:start position:0% +$1,235 and it clearly it was there were +two firms selling this particular + + align:start position:0% +two firms selling this particular + + + align:start position:0% +two firms selling this particular +downright Ider down 434 thread count + + align:start position:0% +downright Ider down 434 thread count + + + align:start position:0% +downright Ider down 434 thread count +silk pillow and the computers were + + align:start position:0% +silk pillow and the computers were + + + align:start position:0% +silk pillow and the computers were +playing against each other and somehow + + align:start position:0% +playing against each other and somehow + + + align:start position:0% +playing against each other and somehow +they went off into a part of the space + + align:start position:0% +they went off into a part of the space + + + align:start position:0% +they went off into a part of the space +where each one thought I you know if I'm + + align:start position:0% +where each one thought I you know if I'm + + + align:start position:0% +where each one thought I you know if I'm +a little more expensive than him I'm a + + align:start position:0% +a little more expensive than him I'm a + + + align:start position:0% +a little more expensive than him I'm a +little more expensive than him something + + align:start position:0% +little more expensive than him something + + + align:start position:0% +little more expensive than him something +great is going to happen and they ended + + align:start position:0% +great is going to happen and they ended + + + align:start position:0% +great is going to happen and they ended +up with like you know they competed + + align:start position:0% +up with like you know they competed + + + align:start position:0% +up with like you know they competed +themselves off to $110,000 pillow and + + align:start position:0% +themselves off to $110,000 pillow and + + + align:start position:0% +themselves off to $110,000 pillow and +you maybe the pillow doesn't you know + + align:start position:0% +you maybe the pillow doesn't you know + + + align:start position:0% +you maybe the pillow doesn't you know +like once you get out here you try + + align:start position:0% +like once you get out here you try + + + align:start position:0% +like once you get out here you try +undercutting from 10,000 to 9,000 it + + align:start position:0% +undercutting from 10,000 to 9,000 it + + + align:start position:0% +undercutting from 10,000 to 9,000 it +makes no difference you don't notice + + align:start position:0% +makes no difference you don't notice + + + align:start position:0% +makes no difference you don't notice +your way back to a pillow should be $30 + + align:start position:0% +your way back to a pillow should be $30 + + + align:start position:0% +your way back to a pillow should be $30 +or whatever um so it is you know I think + + align:start position:0% +or whatever um so it is you know I think + + + align:start position:0% +or whatever um so it is you know I think +but you can get lots of things like to + + align:start position:0% +but you can get lots of things like to + + + align:start position:0% +but you can get lots of things like to +make it clear evidence that it does seem + + align:start position:0% +make it clear evidence that it does seem + + + align:start position:0% +make it clear evidence that it does seem +like on a lot of products there are + + align:start position:0% +like on a lot of products there are + + + align:start position:0% +like on a lot of products there are +algorithms competing and the algorithms + + align:start position:0% +algorithms competing and the algorithms + + + align:start position:0% +algorithms competing and the algorithms +work sometimes and not others + + align:start position:0% +work sometimes and not others + + + align:start position:0% +work sometimes and not others +so okay any questions so anyway if + + align:start position:0% +so okay any questions so anyway if + + + align:start position:0% +so okay any questions so anyway if +that's it I uh so um next class I'm I'm + + align:start position:0% +that's it I uh so um next class I'm I'm + + + align:start position:0% +that's it I uh so um next class I'm I'm +sort of doing empirical stuff so it's um + + align:start position:0% +sort of doing empirical stuff so it's um + + + align:start position:0% +sort of doing empirical stuff so it's um +Rob Porter's paper if you want to pick + + align:start position:0% +Rob Porter's paper if you want to pick + + + align:start position:0% +Rob Porter's paper if you want to pick +one thing to read Rob Porter's paper on + + align:start position:0% +one thing to read Rob Porter's paper on + + + align:start position:0% +one thing to read Rob Porter's paper on +Railroad cartels I have a paper building + + align:start position:0% +Railroad cartels I have a paper building + + + align:start position:0% +Railroad cartels I have a paper building +on Rob's paper and then also a paper + + align:start position:0% +on Rob's paper and then also a paper + + + align:start position:0% +on Rob's paper and then also a paper +about uh uh talk about paper about + + align:start position:0% +about uh uh talk about paper about + + + align:start position:0% +about uh uh talk about paper about +Edgeworth price Cycles in practice so \ No newline at end of file diff --git a/fW4JKL0AFxA.txt b/fW4JKL0AFxA.txt new file mode 100644 index 0000000000000000000000000000000000000000..195fac05e9a0b303b80ac9cecf1119d9145098b4 --- /dev/null +++ b/fW4JKL0AFxA.txt @@ -0,0 +1,6859 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +let me say a little bit about the course + + align:start position:0% +let me say a little bit about the course + + + align:start position:0% +let me say a little bit about the course +we all have views of evolution you've + + align:start position:0% +we all have views of evolution you've + + + align:start position:0% +we all have views of evolution you've +all taken high school biology you you + + align:start position:0% +all taken high school biology you you + + + align:start position:0% +all taken high school biology you you +know you've all been exposed to the set + + align:start position:0% +know you've all been exposed to the set + + + align:start position:0% +know you've all been exposed to the set +of concepts it's a very broad set of + + align:start position:0% +of concepts it's a very broad set of + + + align:start position:0% +of concepts it's a very broad set of +concepts it connects in many many + + align:start position:0% +concepts it connects in many many + + + align:start position:0% +concepts it connects in many many +different ways across the culture but + + align:start position:0% +different ways across the culture but + + + align:start position:0% +different ways across the culture but +fundamentally evolution is a scientific + + align:start position:0% +fundamentally evolution is a scientific + + + align:start position:0% +fundamentally evolution is a scientific +subject and you know people who work in + + align:start position:0% +subject and you know people who work in + + + align:start position:0% +subject and you know people who work in +evolution sometimes are amazed at all + + align:start position:0% +evolution sometimes are amazed at all + + + align:start position:0% +evolution sometimes are amazed at all +the religious controversy because it's + + align:start position:0% +the religious controversy because it's + + + align:start position:0% +the religious controversy because it's +basically a scientific topic and so + + align:start position:0% +basically a scientific topic and so + + + align:start position:0% +basically a scientific topic and so +we'll talk about some of these questions + + align:start position:0% +we'll talk about some of these questions + + + align:start position:0% +we'll talk about some of these questions +but it should be an area that you're all + + align:start position:0% +but it should be an area that you're all + + + align:start position:0% +but it should be an area that you're all +coming to MIT we all should have + + align:start position:0% +coming to MIT we all should have + + + align:start position:0% +coming to MIT we all should have +opinions and you all should have some + + align:start position:0% +opinions and you all should have some + + + align:start position:0% +opinions and you all should have some +exposure to the set of ideas of + + align:start position:0% +exposure to the set of ideas of + + + align:start position:0% +exposure to the set of ideas of +evolution all right so a little bit + + align:start position:0% +evolution all right so a little bit + + + align:start position:0% +evolution all right so a little bit +about the course concept Darwin is a key + + align:start position:0% +about the course concept Darwin is a key + + + align:start position:0% +about the course concept Darwin is a key +figure and as you all know he's + + align:start position:0% +figure and as you all know he's + + + align:start position:0% +figure and as you all know he's +associated with evolution and sometimes + + align:start position:0% +associated with evolution and sometimes + + + align:start position:0% +associated with evolution and sometimes +people think oh evolution is Darwin but + + align:start position:0% +people think oh evolution is Darwin but + + + align:start position:0% +people think oh evolution is Darwin but +that is not my view Darwin was one of + + align:start position:0% +that is not my view Darwin was one of + + + align:start position:0% +that is not my view Darwin was one of +the most important exponents of a + + align:start position:0% +the most important exponents of a + + + align:start position:0% +the most important exponents of a +approach to evolution that was developed + + align:start position:0% +approach to evolution that was developed + + + align:start position:0% +approach to evolution that was developed +in the 19th century tremendously + + align:start position:0% +in the 19th century tremendously + + + align:start position:0% +in the 19th century tremendously +important figure but evolution as a + + align:start position:0% +important figure but evolution as a + + + align:start position:0% +important figure but evolution as a +topic has been around for centuries and + + align:start position:0% +topic has been around for centuries and + + + align:start position:0% +topic has been around for centuries and +evolution connects to many many + + align:start position:0% +evolution connects to many many + + + align:start position:0% +evolution connects to many many +different science fields and so Darwin + + align:start position:0% +different science fields and so Darwin + + + align:start position:0% +different science fields and so Darwin +was the chief exponent of natural + + align:start position:0% +was the chief exponent of natural + + + align:start position:0% +was the chief exponent of natural +selection in the 19th century but + + align:start position:0% +selection in the 19th century but + + + align:start position:0% +selection in the 19th century but +evolutionary thought can be traced all + + align:start position:0% +evolutionary thought can be traced all + + + align:start position:0% +evolutionary thought can be traced all +the way back to Aristotle many many + + align:start position:0% +the way back to Aristotle many many + + + align:start position:0% +the way back to Aristotle many many +figures from the past so what we will do + + align:start position:0% +figures from the past so what we will do + + + align:start position:0% +figures from the past so what we will do +in this class is we're gonna trace some + + align:start position:0% +in this class is we're gonna trace some + + + align:start position:0% +in this class is we're gonna trace some +of these ideas with the notion of trying + + align:start position:0% +of these ideas with the notion of trying + + + align:start position:0% +of these ideas with the notion of trying +to see how the basis of evolution was + + align:start position:0% +to see how the basis of evolution was + + + align:start position:0% +to see how the basis of evolution was +established through various speculators + + align:start position:0% +established through various speculators + + + align:start position:0% +established through various speculators +in the history of ideas my bias in this + + align:start position:0% +in the history of ideas my bias in this + + + align:start position:0% +in the history of ideas my bias in this +course is a little more history of ideas + + align:start position:0% +course is a little more history of ideas + + + align:start position:0% +course is a little more history of ideas +maybe perhaps than literary history I + + align:start position:0% +maybe perhaps than literary history I + + + align:start position:0% +maybe perhaps than literary history I +mean + + align:start position:0% +mean + + + align:start position:0% +mean +literary history is one of my areas of + + align:start position:0% +literary history is one of my areas of + + + align:start position:0% +literary history is one of my areas of +expertise but I'm particularly + + align:start position:0% +expertise but I'm particularly + + + align:start position:0% +expertise but I'm particularly +interested in looking at this topic + + align:start position:0% +interested in looking at this topic + + + align:start position:0% +interested in looking at this topic +through the history of ideas because + + align:start position:0% +through the history of ideas because + + + align:start position:0% +through the history of ideas because +there have been many speculators who + + align:start position:0% +there have been many speculators who + + + align:start position:0% +there have been many speculators who +have talked about things related to + + align:start position:0% +have talked about things related to + + + align:start position:0% +have talked about things related to +evolution and so those are the figures I + + align:start position:0% +evolution and so those are the figures I + + + align:start position:0% +evolution and so those are the figures I +will be examining and the way the course + + align:start position:0% +will be examining and the way the course + + + align:start position:0% +will be examining and the way the course +of design is we'll look at some pre + + align:start position:0% +of design is we'll look at some pre + + + align:start position:0% +of design is we'll look at some pre +Darwin thinkers for example David Hume + + align:start position:0% +Darwin thinkers for example David Hume + + + align:start position:0% +Darwin thinkers for example David Hume +very very important philosopher of the + + align:start position:0% +very very important philosopher of the + + + align:start position:0% +very very important philosopher of the +18th century and him was speculator + + align:start position:0% +18th century and him was speculator + + + align:start position:0% +18th century and him was speculator +about miracles and a whole range of + + align:start position:0% +about miracles and a whole range of + + + align:start position:0% +about miracles and a whole range of +topics related to the way in which the + + align:start position:0% +topics related to the way in which the + + + align:start position:0% +topics related to the way in which the +world may have come into existence + + align:start position:0% +world may have come into existence + + + align:start position:0% +world may have come into existence +humans sometimes seen as a skeptic but + + align:start position:0% +humans sometimes seen as a skeptic but + + + align:start position:0% +humans sometimes seen as a skeptic but +he actually the book of his that we will + + align:start position:0% +he actually the book of his that we will + + + align:start position:0% +he actually the book of his that we will +read will provide three different + + align:start position:0% +read will provide three different + + + align:start position:0% +read will provide three different +perspectives on how the world came into + + align:start position:0% +perspectives on how the world came into + + + align:start position:0% +perspectives on how the world came into +existence it's a wonderful dialogue a + + align:start position:0% +existence it's a wonderful dialogue a + + + align:start position:0% +existence it's a wonderful dialogue a +set of dialogues so we'll also we'll + + align:start position:0% +set of dialogues so we'll also we'll + + + align:start position:0% +set of dialogues so we'll also we'll +also read Thomas Malthus his essay in + + align:start position:0% +also read Thomas Malthus his essay in + + + align:start position:0% +also read Thomas Malthus his essay in +population and that's a tremendously + + align:start position:0% +population and that's a tremendously + + + align:start position:0% +population and that's a tremendously +important work one of the first big + + align:start position:0% +important work one of the first big + + + align:start position:0% +important work one of the first big +works that put together a sort of a + + align:start position:0% +works that put together a sort of a + + + align:start position:0% +works that put together a sort of a +statistical approach to thinking with + + align:start position:0% +statistical approach to thinking with + + + align:start position:0% +statistical approach to thinking with +the cycles of life itself and came up + + align:start position:0% +the cycles of life itself and came up + + + align:start position:0% +the cycles of life itself and came up +with a theory about the difference + + align:start position:0% +with a theory about the difference + + + align:start position:0% +with a theory about the difference +between the way in which production + + align:start position:0% +between the way in which production + + + align:start position:0% +between the way in which production +could be increased and the way in which + + align:start position:0% +could be increased and the way in which + + + align:start position:0% +could be increased and the way in which +populations increase in the fact that + + align:start position:0% +populations increase in the fact that + + + align:start position:0% +populations increase in the fact that +there was a differential so we'll look + + align:start position:0% +there was a differential so we'll look + + + align:start position:0% +there was a differential so we'll look +at these are pre Darwin Darwinian + + align:start position:0% +at these are pre Darwin Darwinian + + + align:start position:0% +at these are pre Darwin Darwinian +thinkers so we will look at some of + + align:start position:0% +thinkers so we will look at some of + + + align:start position:0% +thinkers so we will look at some of +those people we will then we will have a + + align:start position:0% +those people we will then we will have a + + + align:start position:0% +those people we will then we will have a +big unit on Darwin and we will read a + + align:start position:0% +big unit on Darwin and we will read a + + + align:start position:0% +big unit on Darwin and we will read a +pretty big chunk of the origin that's + + align:start position:0% +pretty big chunk of the origin that's + + + align:start position:0% +pretty big chunk of the origin that's +it's a great book it's it's a bit of a + + align:start position:0% +it's a great book it's it's a bit of a + + + align:start position:0% +it's a great book it's it's a bit of a +challenge to to read for modern people + + align:start position:0% +challenge to to read for modern people + + + align:start position:0% +challenge to to read for modern people +because this it's it's a scientific work + + align:start position:0% +because this it's it's a scientific work + + + align:start position:0% +because this it's it's a scientific work +but it's not written the way sign + + align:start position:0% +but it's not written the way sign + + + align:start position:0% +but it's not written the way sign +science has not done this way today + + align:start position:0% +science has not done this way today + + + align:start position:0% +science has not done this way today +science has done and you know papers and + + align:start position:0% +science has done and you know papers and + + + align:start position:0% +science has done and you know papers and +shorter presentations so it'll be there + + align:start position:0% +shorter presentations so it'll be there + + + align:start position:0% +shorter presentations so it'll be there +will be a bit of a challenge but I have + + align:start position:0% +will be a bit of a challenge but I have + + + align:start position:0% +will be a bit of a challenge but I have +lots and lots of material on it and we + + align:start position:0% +lots and lots of material on it and we + + + align:start position:0% +lots and lots of material on it and we +will really get into the into the core + + align:start position:0% +will really get into the into the core + + + align:start position:0% +will really get into the into the core +of Darwin's Origin of Species really try + + align:start position:0% +of Darwin's Origin of Species really try + + + align:start position:0% +of Darwin's Origin of Species really try +to understand it as a book and what + + align:start position:0% +to understand it as a book and what + + + align:start position:0% +to understand it as a book and what +Darwin was up to then we were then we + + align:start position:0% +Darwin was up to then we were then we + + + align:start position:0% +Darwin was up to then we were then we +will read a bunch of post Iranian + + align:start position:0% +will read a bunch of post Iranian + + + align:start position:0% +will read a bunch of post Iranian +figures people who were influenced by + + align:start position:0% +figures people who were influenced by + + + align:start position:0% +figures people who were influenced by +the Darwinian view of the world and + + align:start position:0% +the Darwinian view of the world and + + + align:start position:0% +the Darwinian view of the world and +wrote works of literature speculation + + align:start position:0% +wrote works of literature speculation + + + align:start position:0% +wrote works of literature speculation +all sorts of interesting science fiction + + align:start position:0% +all sorts of interesting science fiction + + + align:start position:0% +all sorts of interesting science fiction +all sorts of interesting material that + + align:start position:0% +all sorts of interesting material that + + + align:start position:0% +all sorts of interesting material that +flowed out of Darwin's thinking or not + + align:start position:0% +flowed out of Darwin's thinking or not + + + align:start position:0% +flowed out of Darwin's thinking or not +necessarily flowed out of his thinking + + align:start position:0% +necessarily flowed out of his thinking + + + align:start position:0% +necessarily flowed out of his thinking +but was influenced by his thinking so + + align:start position:0% +but was influenced by his thinking so + + + align:start position:0% +but was influenced by his thinking so +we'll look at dr. Jekyll and mr. Hyde + + align:start position:0% +we'll look at dr. Jekyll and mr. Hyde + + + align:start position:0% +we'll look at dr. Jekyll and mr. Hyde +which is a very famous work and try to + + align:start position:0% +which is a very famous work and try to + + + align:start position:0% +which is a very famous work and try to +understand that from a Darwinian point + + align:start position:0% +understand that from a Darwinian point + + + align:start position:0% +understand that from a Darwinian point +of view what what was Stevenson how is + + align:start position:0% +of view what what was Stevenson how is + + + align:start position:0% +of view what what was Stevenson how is +Darwin Darwin Ian thinking influencing + + align:start position:0% +Darwin Darwin Ian thinking influencing + + + align:start position:0% +Darwin Darwin Ian thinking influencing +that work and then we'll finish with a + + align:start position:0% +that work and then we'll finish with a + + + align:start position:0% +that work and then we'll finish with a +unit actually on feedback theory and in + + align:start position:0% +unit actually on feedback theory and in + + + align:start position:0% +unit actually on feedback theory and in +modern views of machines and machine + + align:start position:0% +modern views of machines and machine + + + align:start position:0% +modern views of machines and machine +thought one of the questions we will + + align:start position:0% +thought one of the questions we will + + + align:start position:0% +thought one of the questions we will +explore in this class is can machines be + + align:start position:0% +explore in this class is can machines be + + + align:start position:0% +explore in this class is can machines be +made to think could machines think so we + + align:start position:0% +made to think could machines think so we + + + align:start position:0% +made to think could machines think so we +will look at a number of controversies + + align:start position:0% +will look at a number of controversies + + + align:start position:0% +will look at a number of controversies +that emerged out of out of the in the + + align:start position:0% +that emerged out of out of the in the + + + align:start position:0% +that emerged out of out of the in the +20th century but we're based in + + align:start position:0% +20th century but we're based in + + + align:start position:0% +20th century but we're based in +evolutionary thinking and we're gonna + + align:start position:0% +evolutionary thinking and we're gonna + + + align:start position:0% +evolutionary thinking and we're gonna +look at one of the key figures we'll + + align:start position:0% +look at one of the key figures we'll + + + align:start position:0% +look at one of the key figures we'll +look at is Norbert Wiener and we'll read + + align:start position:0% +look at is Norbert Wiener and we'll read + + + align:start position:0% +look at is Norbert Wiener and we'll read +one of his works and he was a very + + align:start position:0% +one of his works and he was a very + + + align:start position:0% +one of his works and he was a very +important thinker on contemporary + + align:start position:0% +important thinker on contemporary + + + align:start position:0% +important thinker on contemporary +feedback theory use he was an MIT + + align:start position:0% +feedback theory use he was an MIT + + + align:start position:0% +feedback theory use he was an MIT +professor actually very colorful and + + align:start position:0% +professor actually very colorful and + + + align:start position:0% +professor actually very colorful and +important thinker so we'll read his work + + align:start position:0% +important thinker so we'll read his work + + + align:start position:0% +important thinker so we'll read his work +and we'll look at Turing Summit Turing's + + align:start position:0% +and we'll look at Turing Summit Turing's + + + align:start position:0% +and we'll look at Turing Summit Turing's +papers on the Turing test and machine + + align:start position:0% +papers on the Turing test and machine + + + align:start position:0% +papers on the Turing test and machine +intelligence so at the end of the course + + align:start position:0% +intelligence so at the end of the course + + + align:start position:0% +intelligence so at the end of the course +my hope is you will see how all these + + align:start position:0% +my hope is you will see how all these + + + align:start position:0% +my hope is you will see how all these +different topics are connected + + align:start position:0% +different topics are connected + + + align:start position:0% +different topics are connected +organically together into a whole set of + + align:start position:0% +organically together into a whole set of + + + align:start position:0% +organically together into a whole set of +questions + + align:start position:0% + + + + align:start position:0% + +this is a class as many humanities + + align:start position:0% +this is a class as many humanities + + + align:start position:0% +this is a class as many humanities +classes are about questions it's not + + align:start position:0% +classes are about questions it's not + + + align:start position:0% +classes are about questions it's not +necessarily class about answers I don't + + align:start position:0% +necessarily class about answers I don't + + + align:start position:0% +necessarily class about answers I don't +have specific answers I'm not here to + + align:start position:0% +have specific answers I'm not here to + + + align:start position:0% +have specific answers I'm not here to +promote one view of evolution or + + align:start position:0% +promote one view of evolution or + + + align:start position:0% +promote one view of evolution or +religion or anything like that I'm here + + align:start position:0% +religion or anything like that I'm here + + + align:start position:0% +religion or anything like that I'm here +to ask the questions and to get you + + align:start position:0% +to ask the questions and to get you + + + align:start position:0% +to ask the questions and to get you +thinking and you know I really don't + + align:start position:0% +thinking and you know I really don't + + + align:start position:0% +thinking and you know I really don't +care what your ultimate view of the + + align:start position:0% +care what your ultimate view of the + + + align:start position:0% +care what your ultimate view of the +world + + align:start position:0% +world + + + align:start position:0% +world +Emer it what it emerges as or what it is + + align:start position:0% +Emer it what it emerges as or what it is + + + align:start position:0% +Emer it what it emerges as or what it is +I'm not here to change that but what I + + align:start position:0% +I'm not here to change that but what I + + + align:start position:0% +I'm not here to change that but what I +am here to do is talk about evolution + + align:start position:0% +am here to do is talk about evolution + + + align:start position:0% +am here to do is talk about evolution +and sort of think about it as a whole + + align:start position:0% +and sort of think about it as a whole + + + align:start position:0% +and sort of think about it as a whole +system and ask interesting questions + + align:start position:0% +system and ask interesting questions + + + align:start position:0% +system and ask interesting questions +about it so okay any any questions here + + align:start position:0% +about it so okay any any questions here + + + align:start position:0% +about it so okay any any questions here +let's talk a little bit about some of + + align:start position:0% +let's talk a little bit about some of + + + align:start position:0% +let's talk a little bit about some of +these early early questions so this is a + + align:start position:0% +these early early questions so this is a + + + align:start position:0% +these early early questions so this is a +class that has design in the title what + + align:start position:0% +class that has design in the title what + + + align:start position:0% +class that has design in the title what +do we mean by design what is designed + + align:start position:0% +do we mean by design what is designed + + + align:start position:0% +do we mean by design what is designed +now mighty is a place that design is all + + align:start position:0% +now mighty is a place that design is all + + + align:start position:0% +now mighty is a place that design is all +over the place it's like everybody talks + + align:start position:0% +over the place it's like everybody talks + + + align:start position:0% +over the place it's like everybody talks +about design so what does the word mean + + align:start position:0% + + + + align:start position:0% + +because anybody can anybody come up with + + align:start position:0% +because anybody can anybody come up with + + + align:start position:0% +because anybody can anybody come up with +a definition of design or or or describe + + align:start position:0% +a definition of design or or or describe + + + align:start position:0% +a definition of design or or or describe +something about design yes + + align:start position:0% + + + + align:start position:0% + +are the way they are because + + align:start position:0% + + + + align:start position:0% + +the idea of God okay + + align:start position:0% +the idea of God okay + + + align:start position:0% +the idea of God okay +okay that's one concept of design a sort + + align:start position:0% +okay that's one concept of design a sort + + + align:start position:0% +okay that's one concept of design a sort +of theological concept of design + + align:start position:0% +of theological concept of design + + + align:start position:0% +of theological concept of design +absolutely true that's one way in which + + align:start position:0% +absolutely true that's one way in which + + + align:start position:0% +absolutely true that's one way in which +people use that word what about the word + + align:start position:0% +people use that word what about the word + + + align:start position:0% +people use that word what about the word +itself what does what do we mean when we + + align:start position:0% +itself what does what do we mean when we + + + align:start position:0% +itself what does what do we mean when we +say design yeah okay and what about how + + align:start position:0% +say design yeah okay and what about how + + + align:start position:0% +say design yeah okay and what about how +does that how is that consistent with + + align:start position:0% +does that how is that consistent with + + + align:start position:0% +does that how is that consistent with +design over in course to mechanical + + align:start position:0% +design over in course to mechanical + + + align:start position:0% +design over in course to mechanical +engineering okay so there's some kind of + + align:start position:0% +engineering okay so there's some kind of + + + align:start position:0% +engineering okay so there's some kind of +intention involved some kind of planning + + align:start position:0% +intention involved some kind of planning + + + align:start position:0% +intention involved some kind of planning +ahead of time anything else okay + + align:start position:0% +ahead of time anything else okay + + + align:start position:0% +ahead of time anything else okay +so implementing something any other yes + + align:start position:0% + + + + align:start position:0% + +okay yeah those are some keywords that + + align:start position:0% +okay yeah those are some keywords that + + + align:start position:0% +okay yeah those are some keywords that +there yeah there's a purpose so purpose + + align:start position:0% +there yeah there's a purpose so purpose + + + align:start position:0% +there yeah there's a purpose so purpose +is usually associated with the concept + + align:start position:0% +is usually associated with the concept + + + align:start position:0% +is usually associated with the concept +of design isn't it the classic + + align:start position:0% +of design isn't it the classic + + + align:start position:0% +of design isn't it the classic +definition or one classic definition + + align:start position:0% +definition or one classic definition + + + align:start position:0% +definition or one classic definition +design is just adaptation of means to + + align:start position:0% +design is just adaptation of means to + + + align:start position:0% +design is just adaptation of means to +ends so an end is something that you're + + align:start position:0% +ends so an end is something that you're + + + align:start position:0% +ends so an end is something that you're +trying to accomplish you have a set of + + align:start position:0% +trying to accomplish you have a set of + + + align:start position:0% +trying to accomplish you have a set of +means I mean what about all the contests + + align:start position:0% +means I mean what about all the contests + + + align:start position:0% +means I mean what about all the contests +that get done in over in course to you + + align:start position:0% +that get done in over in course to you + + + align:start position:0% +that get done in over in course to you +know where people design you know they + + align:start position:0% +know where people design you know they + + + align:start position:0% +know where people design you know they +they're given a certain amount of + + align:start position:0% +they're given a certain amount of + + + align:start position:0% +they're given a certain amount of +material and they have to carry out a + + align:start position:0% +material and they have to carry out a + + + align:start position:0% +material and they have to carry out a +certain task that's a classic design + + align:start position:0% +certain task that's a classic design + + + align:start position:0% +certain task that's a classic design +situation where there is a goal and you + + align:start position:0% +situation where there is a goal and you + + + align:start position:0% +situation where there is a goal and you +have a certain set of means and you + + align:start position:0% +have a certain set of means and you + + + align:start position:0% +have a certain set of means and you +adapt those means to the goal + + align:start position:0% +adapt those means to the goal + + + align:start position:0% +adapt those means to the goal +so in design we have this concept of + + align:start position:0% +so in design we have this concept of + + + align:start position:0% +so in design we have this concept of +purpose and it's it's very very + + align:start position:0% +purpose and it's it's very very + + + align:start position:0% +purpose and it's it's very very +important part so how does this relate + + align:start position:0% +important part so how does this relate + + + align:start position:0% +important part so how does this relate +to these two figures here the left one + + align:start position:0% +to these two figures here the left one + + + align:start position:0% +to these two figures here the left one +is a deity creating + + align:start position:0% +is a deity creating + + + align:start position:0% +is a deity creating +the world it's from william blake's one + + align:start position:0% +the world it's from william blake's one + + + align:start position:0% +the world it's from william blake's one +of william blake's works and right we + + align:start position:0% +of william blake's works and right we + + + align:start position:0% +of william blake's works and right we +have darwin sitting here as a young man + + align:start position:0% +have darwin sitting here as a young man + + + align:start position:0% +have darwin sitting here as a young man +very quiet and looking out and staring + + align:start position:0% +very quiet and looking out and staring + + + align:start position:0% +very quiet and looking out and staring +at us so how are these two figures + + align:start position:0% +at us so how are these two figures + + + align:start position:0% +at us so how are these two figures +related to concepts of design couple of + + align:start position:0% +related to concepts of design couple of + + + align:start position:0% +related to concepts of design couple of +people said already creation of the + + align:start position:0% +people said already creation of the + + + align:start position:0% +people said already creation of the +world why is a world associated with + + align:start position:0% +world why is a world associated with + + + align:start position:0% +world why is a world associated with +design and the concept of creation with + + align:start position:0% +design and the concept of creation with + + + align:start position:0% +design and the concept of creation with +a purpose what is it about the world + + align:start position:0% +a purpose what is it about the world + + + align:start position:0% +a purpose what is it about the world +that leads to that sort of thinking + + align:start position:0% + + + + align:start position:0% + +whether you believe in creation or the + + align:start position:0% +whether you believe in creation or the + + + align:start position:0% +whether you believe in creation or the +world is constantly adapting to what's + + align:start position:0% +world is constantly adapting to what's + + + align:start position:0% +world is constantly adapting to what's +happening around + + align:start position:0% + + + + align:start position:0% + +well okay so the world shows the ability + + align:start position:0% +well okay so the world shows the ability + + + align:start position:0% +well okay so the world shows the ability +to change or things in the world change + + align:start position:0% +to change or things in the world change + + + align:start position:0% +to change or things in the world change +and what's what's peculiar about the + + align:start position:0% +and what's what's peculiar about the + + + align:start position:0% +and what's what's peculiar about the +change what is it about to change okay + + align:start position:0% +change what is it about to change okay + + + align:start position:0% +change what is it about to change okay +so there seems to be some kind of goal + + align:start position:0% +so there seems to be some kind of goal + + + align:start position:0% +so there seems to be some kind of goal +that is being achieved in these changes + + align:start position:0% +that is being achieved in these changes + + + align:start position:0% +that is being achieved in these changes +is there not so what else about the + + align:start position:0% +is there not so what else about the + + + align:start position:0% +is there not so what else about the +world leads to these notions of a grand + + align:start position:0% +world leads to these notions of a grand + + + align:start position:0% +world leads to these notions of a grand +designer yeah I mean the more we learn + + align:start position:0% +designer yeah I mean the more we learn + + + align:start position:0% +designer yeah I mean the more we learn +about the world the more incredible it + + align:start position:0% +about the world the more incredible it + + + align:start position:0% +about the world the more incredible it +is isn't it I mean when we really study + + align:start position:0% +is isn't it I mean when we really study + + + align:start position:0% +is isn't it I mean when we really study +closely the phenomena of the world we + + align:start position:0% +closely the phenomena of the world we + + + align:start position:0% +closely the phenomena of the world we +see patterns and you know adaptations + + align:start position:0% +see patterns and you know adaptations + + + align:start position:0% +see patterns and you know adaptations +that are just kind of incredible I mean + + align:start position:0% +that are just kind of incredible I mean + + + align:start position:0% +that are just kind of incredible I mean +you find insects that are perfectly + + align:start position:0% +you find insects that are perfectly + + + align:start position:0% +you find insects that are perfectly +adapted to the other organisms they feed + + align:start position:0% +adapted to the other organisms they feed + + + align:start position:0% +adapted to the other organisms they feed +on their their limbs and everything I + + align:start position:0% +on their their limbs and everything I + + + align:start position:0% +on their their limbs and everything I +mean you find this this constant process + + align:start position:0% +mean you find this this constant process + + + align:start position:0% +mean you find this this constant process +of in fact of adaptation in the world so + + align:start position:0% +of in fact of adaptation in the world so + + + align:start position:0% +of in fact of adaptation in the world so +when you step back and you look at the + + align:start position:0% +when you step back and you look at the + + + align:start position:0% +when you step back and you look at the +world it's a fairly complicated but + + align:start position:0% +world it's a fairly complicated but + + + align:start position:0% +world it's a fairly complicated but +nevertheless it's full of purpose isn't + + align:start position:0% +nevertheless it's full of purpose isn't + + + align:start position:0% +nevertheless it's full of purpose isn't +it I mean it seems so it certainly is + + align:start position:0% +it I mean it seems so it certainly is + + + align:start position:0% +it I mean it seems so it certainly is +full of adaptation and of course + + align:start position:0% +full of adaptation and of course + + + align:start position:0% +full of adaptation and of course +adaptation is one of the big topics of + + align:start position:0% +adaptation is one of the big topics of + + + align:start position:0% +adaptation is one of the big topics of +evolution things get adapted and + + align:start position:0% +evolution things get adapted and + + + align:start position:0% +evolution things get adapted and +amazingly well worker bees + + align:start position:0% +amazingly well worker bees + + + align:start position:0% +amazingly well worker bees +I mean think of them they don't even + + align:start position:0% +I mean think of them they don't even + + + align:start position:0% +I mean think of them they don't even +reproduce and there they are their + + align:start position:0% +reproduce and there they are their + + + align:start position:0% +reproduce and there they are their +creation they work together collectively + + align:start position:0% +creation they work together collectively + + + align:start position:0% +creation they work together collectively +to support the hive and how did that all + + align:start position:0% +to support the hive and how did that all + + + align:start position:0% +to support the hive and how did that all +happen that kind of complexity in human + + align:start position:0% +happen that kind of complexity in human + + + align:start position:0% +happen that kind of complexity in human +behavior + + align:start position:0% + + + + align:start position:0% + +this concept + + align:start position:0% +this concept + + + align:start position:0% +this concept +if you look at the past the history of + + align:start position:0% +if you look at the past the history of + + + align:start position:0% +if you look at the past the history of +man all technological progression is + + align:start position:0% +man all technological progression is + + + align:start position:0% +man all technological progression is +very intentional with the purpose but so + + align:start position:0% +very intentional with the purpose but so + + + align:start position:0% +very intentional with the purpose but so +once again it seems improbable + + align:start position:0% + + + + align:start position:0% + +okay so you're you're really making an + + align:start position:0% +okay so you're you're really making an + + + align:start position:0% +okay so you're you're really making an +interesting distinction here and one is + + align:start position:0% +interesting distinction here and one is + + + align:start position:0% +interesting distinction here and one is +humans seem to definitely have this kind + + align:start position:0% +humans seem to definitely have this kind + + + align:start position:0% +humans seem to definitely have this kind +of purpose of process where they have + + align:start position:0% +of purpose of process where they have + + + align:start position:0% +of purpose of process where they have +needs and they develop tools and + + align:start position:0% +needs and they develop tools and + + + align:start position:0% +needs and they develop tools and +implements + + align:start position:0% +implements + + + align:start position:0% +implements +I mean who who can fail to be impressed + + align:start position:0% +I mean who who can fail to be impressed + + + align:start position:0% +I mean who who can fail to be impressed +with you know the the early implements + + align:start position:0% +with you know the the early implements + + + align:start position:0% +with you know the the early implements +of early humans you know how ingenious + + align:start position:0% +of early humans you know how ingenious + + + align:start position:0% +of early humans you know how ingenious +they were you know + + align:start position:0% +they were you know + + + align:start position:0% +they were you know +capturing fire and doing all sorts of + + align:start position:0% +capturing fire and doing all sorts of + + + align:start position:0% +capturing fire and doing all sorts of +things with the primitive tools they had + + align:start position:0% +things with the primitive tools they had + + + align:start position:0% +things with the primitive tools they had +in learning how to interact with their + + align:start position:0% +in learning how to interact with their + + + align:start position:0% +in learning how to interact with their +environments who and that's very + + align:start position:0% +environments who and that's very + + + align:start position:0% +environments who and that's very +impressive the the record of humans just + + align:start position:0% +impressive the the record of humans just + + + align:start position:0% +impressive the the record of humans just +the in their ability to design but then + + align:start position:0% +the in their ability to design but then + + + align:start position:0% +the in their ability to design but then +you mentioned the outside world itself + + align:start position:0% +you mentioned the outside world itself + + + align:start position:0% +you mentioned the outside world itself +humans didn't design and yet it also + + align:start position:0% +humans didn't design and yet it also + + + align:start position:0% +humans didn't design and yet it also +shows patterns and designs + + align:start position:0% + + + + align:start position:0% + +okay so any further comments on the + + align:start position:0% +okay so any further comments on the + + + align:start position:0% +okay so any further comments on the +outside world and design what was + + align:start position:0% +outside world and design what was + + + align:start position:0% +outside world and design what was +Darwin's contribution to design I mean + + align:start position:0% +Darwin's contribution to design I mean + + + align:start position:0% +Darwin's contribution to design I mean +how did Darwin get how did his work + + align:start position:0% +how did Darwin get how did his work + + + align:start position:0% +how did Darwin get how did his work +approach what what what realm was he + + align:start position:0% +approach what what what realm was he + + + align:start position:0% +approach what what what realm was he +primarily interested in and how did he + + align:start position:0% +primarily interested in and how did he + + + align:start position:0% +primarily interested in and how did he +approach this concept of design + + align:start position:0% + + + + align:start position:0% + +why is evolution at the center of the + + align:start position:0% +why is evolution at the center of the + + + align:start position:0% +why is evolution at the center of the +discussion of design + + align:start position:0% + + + + align:start position:0% + +we design at the current rule + + align:start position:0% + + + + align:start position:0% + +Darwin came up with some new approaches + + align:start position:0% +Darwin came up with some new approaches + + + align:start position:0% +Darwin came up with some new approaches +to the concept of how design might take + + align:start position:0% +to the concept of how design might take + + + align:start position:0% +to the concept of how design might take +place in natural in organisms in in in + + align:start position:0% +place in natural in organisms in in in + + + align:start position:0% +place in natural in organisms in in in +the organic world Darwin came up with + + align:start position:0% +the organic world Darwin came up with + + + align:start position:0% +the organic world Darwin came up with +some new approaches that in which a + + align:start position:0% +some new approaches that in which a + + + align:start position:0% +some new approaches that in which a +designer was not necessarily the agent + + align:start position:0% +designer was not necessarily the agent + + + align:start position:0% +designer was not necessarily the agent +of the design and this threw a big + + align:start position:0% +of the design and this threw a big + + + align:start position:0% +of the design and this threw a big +wrench into the whole discussion the + + align:start position:0% +wrench into the whole discussion the + + + align:start position:0% +wrench into the whole discussion the +sort of conflict of terms in Darwinian + + align:start position:0% +sort of conflict of terms in Darwinian + + + align:start position:0% +sort of conflict of terms in Darwinian +language which we'll find but where a + + align:start position:0% +language which we'll find but where a + + + align:start position:0% +language which we'll find but where a +lot of the a lot of the original work in + + align:start position:0% +lot of the a lot of the original work in + + + align:start position:0% +lot of the a lot of the original work in +in in Darwin + + align:start position:0% +in in Darwin + + + align:start position:0% +in in Darwin +Darwinian thinking was around this + + align:start position:0% +Darwinian thinking was around this + + + align:start position:0% +Darwinian thinking was around this +concept of how could these patterns and + + align:start position:0% +concept of how could these patterns and + + + align:start position:0% +concept of how could these patterns and +adaptations emerge in the world without + + align:start position:0% +adaptations emerge in the world without + + + align:start position:0% +adaptations emerge in the world without +being put there by some individual + + align:start position:0% +being put there by some individual + + + align:start position:0% +being put there by some individual +intentionally but through a natural + + align:start position:0% +intentionally but through a natural + + + align:start position:0% +intentionally but through a natural +process of interaction with the + + align:start position:0% +process of interaction with the + + + align:start position:0% +process of interaction with the +surroundings of the world so this was a + + align:start position:0% +surroundings of the world so this was a + + + align:start position:0% +surroundings of the world so this was a +this is a very great problem and Darwin + + align:start position:0% +this is a very great problem and Darwin + + + align:start position:0% +this is a very great problem and Darwin +came up with some approaches to thinking + + align:start position:0% +came up with some approaches to thinking + + + align:start position:0% +came up with some approaches to thinking +about design that really changed the way + + align:start position:0% +about design that really changed the way + + + align:start position:0% +about design that really changed the way +in which we used the term in the natural + + align:start position:0% +in which we used the term in the natural + + + align:start position:0% +in which we used the term in the natural +world and thus humans and they're very + + align:start position:0% +world and thus humans and they're very + + + align:start position:0% +world and thus humans and they're very +direct purpose of way of designing was + + align:start position:0% +direct purpose of way of designing was + + + align:start position:0% +direct purpose of way of designing was +seen as somewhat separate from the + + align:start position:0% +seen as somewhat separate from the + + + align:start position:0% +seen as somewhat separate from the +natural world in the way in which design + + align:start position:0% +natural world in the way in which design + + + align:start position:0% +natural world in the way in which design +emerged in the natural world but let's + + align:start position:0% +emerged in the natural world but let's + + + align:start position:0% +emerged in the natural world but let's +have a look okay okay so this the one of + + align:start position:0% +have a look okay okay so this the one of + + + align:start position:0% +have a look okay okay so this the one of +the key questions and in Darwinian + + align:start position:0% +the key questions and in Darwinian + + + align:start position:0% +the key questions and in Darwinian +thinking emerged around the question of + + align:start position:0% +thinking emerged around the question of + + + align:start position:0% +thinking emerged around the question of +can there be design without a designer + + align:start position:0% +can there be design without a designer + + + align:start position:0% +can there be design without a designer +and here you see some very natural + + align:start position:0% +and here you see some very natural + + + align:start position:0% +and here you see some very natural +implements you see work from Leonardo's + + align:start position:0% +implements you see work from Leonardo's + + + align:start position:0% +implements you see work from Leonardo's +great sketchbook gears and cogs and + + align:start position:0% +great sketchbook gears and cogs and + + + align:start position:0% +great sketchbook gears and cogs and +and then and then you see a simple shelf + + align:start position:0% +and then and then you see a simple shelf + + + align:start position:0% +and then and then you see a simple shelf +design you see two patterns of two + + align:start position:0% +design you see two patterns of two + + + align:start position:0% +design you see two patterns of two +approaches two kinds of design here + + align:start position:0% + + + + align:start position:0% + +what's the difference okay so we have a + + align:start position:0% +what's the difference okay so we have a + + + align:start position:0% +what's the difference okay so we have a +type of design and emerges from the + + align:start position:0% +type of design and emerges from the + + + align:start position:0% +type of design and emerges from the +natural world and we have a human + + align:start position:0% +natural world and we have a human + + + align:start position:0% +natural world and we have a human +thinking human coming up with concepts + + align:start position:0% +thinking human coming up with concepts + + + align:start position:0% +thinking human coming up with concepts +of designs and patterns yes + + align:start position:0% + + + + align:start position:0% + +yeah that's uh that's a fair question + + align:start position:0% +yeah that's uh that's a fair question + + + align:start position:0% +yeah that's uh that's a fair question +that's a I mean certainly if if what we + + align:start position:0% +that's a I mean certainly if if what we + + + align:start position:0% +that's a I mean certainly if if what we +say if humans are product of the natural + + align:start position:0% +say if humans are product of the natural + + + align:start position:0% +say if humans are product of the natural +world then whatever they do is is in + + align:start position:0% +world then whatever they do is is in + + + align:start position:0% +world then whatever they do is is in +some sense a natural product is it not + + align:start position:0% +some sense a natural product is it not + + + align:start position:0% +some sense a natural product is it not +so are there differences how do how do + + align:start position:0% +so are there differences how do how do + + + align:start position:0% +so are there differences how do how do +humans change the formula do they change + + align:start position:0% +humans change the formula do they change + + + align:start position:0% +humans change the formula do they change +the formula at all I mean we don't have + + align:start position:0% +the formula at all I mean we don't have + + + align:start position:0% +the formula at all I mean we don't have +to say it's unnatural to design a chair + + align:start position:0% +to say it's unnatural to design a chair + + + align:start position:0% +to say it's unnatural to design a chair +to sit in because we can say well this + + align:start position:0% +to sit in because we can say well this + + + align:start position:0% +to sit in because we can say well this +is uh do humans know anything different + + align:start position:0% +is uh do humans know anything different + + + align:start position:0% +is uh do humans know anything different +why do humans bring to the to the whole + + align:start position:0% +why do humans bring to the to the whole + + + align:start position:0% +why do humans bring to the to the whole +process okay + + align:start position:0% +process okay + + + align:start position:0% +process okay +a purpose what is the purpose in the + + align:start position:0% +a purpose what is the purpose in the + + + align:start position:0% +a purpose what is the purpose in the +design of the shelf okay all right so + + align:start position:0% +design of the shelf okay all right so + + + align:start position:0% +design of the shelf okay all right so +did the creature design it or so you see + + align:start position:0% +did the creature design it or so you see + + + align:start position:0% +did the creature design it or so you see +we come up into some in this area we + + align:start position:0% +we come up into some in this area we + + + align:start position:0% +we come up into some in this area we +come up into a big ambiguity and that is + + align:start position:0% +come up into a big ambiguity and that is + + + align:start position:0% +come up into a big ambiguity and that is +we have natural designs but we don't + + align:start position:0% +we have natural designs but we don't + + + align:start position:0% +we have natural designs but we don't +necessarily have an author for them who + + align:start position:0% +necessarily have an author for them who + + + align:start position:0% +necessarily have an author for them who +actually built a thing just like it was + + align:start position:0% +actually built a thing just like it was + + + align:start position:0% +actually built a thing just like it was +we can refer to a process and say while + + align:start position:0% +we can refer to a process and say while + + + align:start position:0% +we can refer to a process and say while +these emerge through you know the + + align:start position:0% +these emerge through you know the + + + align:start position:0% +these emerge through you know the +interaction of millions of years of + + align:start position:0% +interaction of millions of years of + + + align:start position:0% +interaction of millions of years of +development and so on and so forth but + + align:start position:0% +development and so on and so forth but + + + align:start position:0% +development and so on and so forth but +so whereas in the human we have a as you + + align:start position:0% +so whereas in the human we have a as you + + + align:start position:0% +so whereas in the human we have a as you +say self conscious intentional purpose + + align:start position:0% +say self conscious intentional purpose + + + align:start position:0% +say self conscious intentional purpose +and to build something with a certain + + align:start position:0% +and to build something with a certain + + + align:start position:0% +and to build something with a certain +effect now the point of whether one's + + align:start position:0% +effect now the point of whether one's + + + align:start position:0% +effect now the point of whether one's +natural or one's artificial may be you + + align:start position:0% +natural or one's artificial may be you + + + align:start position:0% +natural or one's artificial may be you +know not that important but the process + + align:start position:0% +know not that important but the process + + + align:start position:0% +know not that important but the process +said humans humans kind of speed up + + align:start position:0% +said humans humans kind of speed up + + + align:start position:0% +said humans humans kind of speed up +design don't they I mean think how fast + + align:start position:0% +design don't they I mean think how fast + + + align:start position:0% +design don't they I mean think how fast +humans I mean just think of the the rise + + align:start position:0% +humans I mean just think of the the rise + + + align:start position:0% +humans I mean just think of the the rise +of the car the automobile how fast that + + align:start position:0% +of the car the automobile how fast that + + + align:start position:0% +of the car the automobile how fast that +all took place period of a couple + + align:start position:0% +all took place period of a couple + + + align:start position:0% +all took place period of a couple +hundred years so human design + + align:start position:0% +hundred years so human design + + + align:start position:0% +hundred years so human design +to iterate does it not very quickly and + + align:start position:0% +to iterate does it not very quickly and + + + align:start position:0% +to iterate does it not very quickly and +reproduce itself and improve itself and + + align:start position:0% +reproduce itself and improve itself and + + + align:start position:0% +reproduce itself and improve itself and +so on and so forth so there's a very + + align:start position:0% +so on and so forth so there's a very + + + align:start position:0% +so on and so forth so there's a very +definite design process that you're all + + align:start position:0% +definite design process that you're all + + + align:start position:0% +definite design process that you're all +here to study whatever your respective + + align:start position:0% +here to study whatever your respective + + + align:start position:0% +here to study whatever your respective +field is you're probably involved in + + align:start position:0% +field is you're probably involved in + + + align:start position:0% +field is you're probably involved in +some aspect of design whether you're you + + align:start position:0% +some aspect of design whether you're you + + + align:start position:0% +some aspect of design whether you're you +know designing a polymer or you're + + align:start position:0% +know designing a polymer or you're + + + align:start position:0% +know designing a polymer or you're +designing a new kind of material or + + align:start position:0% +designing a new kind of material or + + + align:start position:0% +designing a new kind of material or +you're you know we we designed MIT as a + + align:start position:0% +you're you know we we designed MIT as a + + + align:start position:0% +you're you know we we designed MIT as a +Center for design but it's this very + + align:start position:0% +Center for design but it's this very + + + align:start position:0% +Center for design but it's this very +intentional deeply informed type of + + align:start position:0% +intentional deeply informed type of + + + align:start position:0% +intentional deeply informed type of +design in the natural world how does + + align:start position:0% +design in the natural world how does + + + align:start position:0% +design in the natural world how does +design take place what is the scale of + + align:start position:0% +design take place what is the scale of + + + align:start position:0% +design take place what is the scale of +it sorry well that's one of the we'll + + align:start position:0% +it sorry well that's one of the we'll + + + align:start position:0% +it sorry well that's one of the we'll +explore that later in the term will come + + align:start position:0% +explore that later in the term will come + + + align:start position:0% +explore that later in the term will come +yeah but I'm sort of thinking just in in + + align:start position:0% +yeah but I'm sort of thinking just in in + + + align:start position:0% +yeah but I'm sort of thinking just in in +terms of the time scale for designs to + + align:start position:0% +terms of the time scale for designs to + + + align:start position:0% +terms of the time scale for designs to +emerge in the natural world + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah so part of what happened in + + align:start position:0% +yeah so part of what happened in + + + align:start position:0% +yeah so part of what happened in +Darwin's time was it became clear that + + align:start position:0% +Darwin's time was it became clear that + + + align:start position:0% +Darwin's time was it became clear that +from geological study that the earth was + + align:start position:0% +from geological study that the earth was + + + align:start position:0% +from geological study that the earth was +really very very old and not just a few + + align:start position:0% +really very very old and not just a few + + + align:start position:0% +really very very old and not just a few +thousand years old as some of the + + align:start position:0% +thousand years old as some of the + + + align:start position:0% +thousand years old as some of the +earlier speculators had thought so + + align:start position:0% +earlier speculators had thought so + + + align:start position:0% +earlier speculators had thought so +Darwin had millions of years to work + + align:start position:0% +Darwin had millions of years to work + + + align:start position:0% +Darwin had millions of years to work +with when he began to think about his + + align:start position:0% +with when he began to think about his + + + align:start position:0% +with when he began to think about his +system and of course with millions of + + align:start position:0% +system and of course with millions of + + + align:start position:0% +system and of course with millions of +years and many many different changes + + align:start position:0% +years and many many different changes + + + align:start position:0% +years and many many different changes +many many different generations very + + align:start position:0% +many many different generations very + + + align:start position:0% +many many different generations very +tiny shifts in one direction could add + + align:start position:0% +tiny shifts in one direction could add + + + align:start position:0% +tiny shifts in one direction could add +up to huge changes over a couple of + + align:start position:0% +up to huge changes over a couple of + + + align:start position:0% +up to huge changes over a couple of +hundred thousand years so Darwin began + + align:start position:0% +hundred thousand years so Darwin began + + + align:start position:0% +hundred thousand years so Darwin began +to expand into this huge time scale that + + align:start position:0% +to expand into this huge time scale that + + + align:start position:0% +to expand into this huge time scale that +geology had given him and we'll look at + + align:start position:0% +geology had given him and we'll look at + + + align:start position:0% +geology had given him and we'll look at +that a little more closely when I get to + + align:start position:0% +that a little more closely when I get to + + + align:start position:0% +that a little more closely when I get to +the Darwin unit because geology was + + align:start position:0% +the Darwin unit because geology was + + + align:start position:0% +the Darwin unit because geology was +really one of Darwin's first areas of + + align:start position:0% +really one of Darwin's first areas of + + + align:start position:0% +really one of Darwin's first areas of +interest but now he had millions of + + align:start position:0% +interest but now he had millions of + + + align:start position:0% +interest but now he had millions of +years to work with then he could begin + + align:start position:0% +years to work with then he could begin + + + align:start position:0% +years to work with then he could begin +to think of incremental changes that + + align:start position:0% +to think of incremental changes that + + + align:start position:0% +to think of incremental changes that +would add up to tremendous adaptations + + align:start position:0% +would add up to tremendous adaptations + + + align:start position:0% +would add up to tremendous adaptations +so human design as always we always + + align:start position:0% +so human design as always we always + + + align:start position:0% +so human design as always we always +think of it in a very collapsed tight + + align:start position:0% +think of it in a very collapsed tight + + + align:start position:0% +think of it in a very collapsed tight +time scale whereas natural design we + + align:start position:0% +time scale whereas natural design we + + + align:start position:0% +time scale whereas natural design we +think of in the terms of emerging + + align:start position:0% +think of in the terms of emerging + + + align:start position:0% +think of in the terms of emerging +through Ian's thousands millions of + + align:start position:0% +through Ian's thousands millions of + + + align:start position:0% +through Ian's thousands millions of +years okay so those are a couple of + + align:start position:0% +years okay so those are a couple of + + + align:start position:0% +years okay so those are a couple of +things we can say one of the problems of + + align:start position:0% +things we can say one of the problems of + + + align:start position:0% +things we can say one of the problems of +using the word design is can we really + + align:start position:0% +using the word design is can we really + + + align:start position:0% +using the word design is can we really +use design for these shelves I mean in + + align:start position:0% +use design for these shelves I mean in + + + align:start position:0% +use design for these shelves I mean in +what sense is designed the right word is + + align:start position:0% +what sense is designed the right word is + + + align:start position:0% +what sense is designed the right word is +this snowflake can we say a snowflake is + + align:start position:0% +this snowflake can we say a snowflake is + + + align:start position:0% +this snowflake can we say a snowflake is +is design so this word design is gives + + align:start position:0% +is design so this word design is gives + + + align:start position:0% +is design so this word design is gives +us a lot of a lot of difficulty which is + + align:start position:0% +us a lot of a lot of difficulty which is + + + align:start position:0% +us a lot of a lot of difficulty which is +good because it makes us think about the + + align:start position:0% +good because it makes us think about the + + + align:start position:0% +good because it makes us think about the +question but what about the app applying + + align:start position:0% +question but what about the app applying + + + align:start position:0% +question but what about the app applying +this word designed to snowflakes or or + + align:start position:0% +this word designed to snowflakes or or + + + align:start position:0% +this word designed to snowflakes or or +natural yeah + + align:start position:0% + + + + align:start position:0% + +something towards the purpose you said + + align:start position:0% +something towards the purpose you said + + + align:start position:0% +something towards the purpose you said +about to the animal doesn't design the + + align:start position:0% +about to the animal doesn't design the + + + align:start position:0% +about to the animal doesn't design the +show the purpose is more so okay the + + align:start position:0% +show the purpose is more so okay the + + + align:start position:0% +show the purpose is more so okay the +purpose of the show okay I think I'm + + align:start position:0% +purpose of the show okay I think I'm + + + align:start position:0% +purpose of the show okay I think I'm +getting that yeah so what you're saying + + align:start position:0% +getting that yeah so what you're saying + + + align:start position:0% +getting that yeah so what you're saying +is purpose really are you saying purpose + + align:start position:0% +is purpose really are you saying purpose + + + align:start position:0% +is purpose really are you saying purpose +is just an individual thing and these + + align:start position:0% +is just an individual thing and these + + + align:start position:0% +is just an individual thing and these +are that it doesn't exist + + align:start position:0% + + + + align:start position:0% + +like cognizant like animals and users + + align:start position:0% +like cognizant like animals and users + + + align:start position:0% +like cognizant like animals and users +who've been just like something like a + + align:start position:0% +who've been just like something like a + + + align:start position:0% +who've been just like something like a +shell it's like no this is just like a + + align:start position:0% +shell it's like no this is just like a + + + align:start position:0% +shell it's like no this is just like a +pattern so is there a difference between + + align:start position:0% +pattern so is there a difference between + + + align:start position:0% +pattern so is there a difference between +designs and patterns + + align:start position:0% + + + + align:start position:0% + +I think so I mean patterns are certain + + align:start position:0% +I think so I mean patterns are certain + + + align:start position:0% +I think so I mean patterns are certain +they're regularities and patterns and so + + align:start position:0% +they're regularities and patterns and so + + + align:start position:0% +they're regularities and patterns and so +forth but we don't necessarily assign an + + align:start position:0% +forth but we don't necessarily assign an + + + align:start position:0% +forth but we don't necessarily assign an +intention to them nobody intended yes so + + align:start position:0% +intention to them nobody intended yes so + + + align:start position:0% +intention to them nobody intended yes so +that's that's in a case where something + + align:start position:0% +that's that's in a case where something + + + align:start position:0% +that's that's in a case where something +acquires but if if the shell is the + + align:start position:0% +acquires but if if the shell is the + + + align:start position:0% +acquires but if if the shell is the +object is the ant is the organism we + + align:start position:0% +object is the ant is the organism we + + + align:start position:0% +object is the ant is the organism we +wouldn't assign purpose to that organism + + align:start position:0% +wouldn't assign purpose to that organism + + + align:start position:0% +wouldn't assign purpose to that organism +in creating its own shell because it + + align:start position:0% +in creating its own shell because it + + + align:start position:0% +in creating its own shell because it +didn't do anything intentionally the the + + align:start position:0% +didn't do anything intentionally the the + + + align:start position:0% +didn't do anything intentionally the the +shell simply exists and so this is a + + align:start position:0% +shell simply exists and so this is a + + + align:start position:0% +shell simply exists and so this is a +this is an ambiguity we often time + + align:start position:0% +this is an ambiguity we often time + + + align:start position:0% +this is an ambiguity we often time +assign purpose to patterns when we don't + + align:start position:0% +assign purpose to patterns when we don't + + + align:start position:0% +assign purpose to patterns when we don't +really mean it I mean we say you know + + align:start position:0% +really mean it I mean we say you know + + + align:start position:0% +really mean it I mean we say you know +Mike my computer is giving me a lot of + + align:start position:0% +Mike my computer is giving me a lot of + + + align:start position:0% +Mike my computer is giving me a lot of +trouble or my computer is you know we + + align:start position:0% +trouble or my computer is you know we + + + align:start position:0% +trouble or my computer is you know we +don't really mean that the computer is + + align:start position:0% +don't really mean that the computer is + + + align:start position:0% +don't really mean that the computer is +doing something intentionally so there + + align:start position:0% +doing something intentionally so there + + + align:start position:0% +doing something intentionally so there +is a there is a way in which humans + + align:start position:0% +is a there is a way in which humans + + + align:start position:0% +is a there is a way in which humans +assign the word purpose the concept of + + align:start position:0% +assign the word purpose the concept of + + + align:start position:0% +assign the word purpose the concept of +purpose to designs were just for kind of + + align:start position:0% +purpose to designs were just for kind of + + + align:start position:0% +purpose to designs were just for kind of +a shorthand we're gonna explore this + + align:start position:0% +a shorthand we're gonna explore this + + + align:start position:0% +a shorthand we're gonna explore this +problem and so this is a very very big + + align:start position:0% +problem and so this is a very very big + + + align:start position:0% +problem and so this is a very very big +problem and nobody's ever really solved + + align:start position:0% +problem and nobody's ever really solved + + + align:start position:0% +problem and nobody's ever really solved +this you know made a really clear way of + + align:start position:0% +this you know made a really clear way of + + + align:start position:0% +this you know made a really clear way of +coming up with this concept of applying + + align:start position:0% +coming up with this concept of applying + + + align:start position:0% +coming up with this concept of applying +design to natural objects + + align:start position:0% + + + + align:start position:0% + +like nonliving + + align:start position:0% +like nonliving + + + align:start position:0% +like nonliving +nonliving things there have been some + + align:start position:0% +nonliving things there have been some + + + align:start position:0% +nonliving things there have been some +special cases but generally not + + align:start position:0% +special cases but generally not + + + align:start position:0% +special cases but generally not +evolution has seen primarily as a + + align:start position:0% +evolution has seen primarily as a + + + align:start position:0% +evolution has seen primarily as a +phenomenon of life and it's a remarkable + + align:start position:0% +phenomenon of life and it's a remarkable + + + align:start position:0% +phenomenon of life and it's a remarkable +phenomenon because when humans + + align:start position:0% +phenomenon because when humans + + + align:start position:0% +phenomenon because when humans +discovered that life forms changed this + + align:start position:0% +discovered that life forms changed this + + + align:start position:0% +discovered that life forms changed this +was this was really big news I mean this + + align:start position:0% +was this was really big news I mean this + + + align:start position:0% +was this was really big news I mean this +was kind of astounding because people + + align:start position:0% +was kind of astounding because people + + + align:start position:0% +was kind of astounding because people +thought basically the forms have been + + align:start position:0% +thought basically the forms have been + + + align:start position:0% +thought basically the forms have been +put on the earth and they were that way + + align:start position:0% +put on the earth and they were that way + + + align:start position:0% +put on the earth and they were that way +forever what happened to make people + + align:start position:0% +forever what happened to make people + + + align:start position:0% +forever what happened to make people +think forms changed + + align:start position:0% + + + + align:start position:0% + +well that was certainly a classic + + align:start position:0% +well that was certainly a classic + + + align:start position:0% +well that was certainly a classic +example of it you know people people + + align:start position:0% +example of it you know people people + + + align:start position:0% +example of it you know people people +began to discover I mean there were lots + + align:start position:0% +began to discover I mean there were lots + + + align:start position:0% +began to discover I mean there were lots +of speculation about changing forms and + + align:start position:0% +of speculation about changing forms and + + + align:start position:0% +of speculation about changing forms and +certain early thinkers actually detected + + align:start position:0% +certain early thinkers actually detected + + + align:start position:0% +certain early thinkers actually detected +certain types of changes in living forms + + align:start position:0% +certain types of changes in living forms + + + align:start position:0% +certain types of changes in living forms +but the discovery of fossils and older + + align:start position:0% +but the discovery of fossils and older + + + align:start position:0% +but the discovery of fossils and older +forms began to really change people's + + align:start position:0% +forms began to really change people's + + + align:start position:0% +forms began to really change people's +concepts of what existed when when + + align:start position:0% +concepts of what existed when when + + + align:start position:0% +concepts of what existed when when +Darwin traveled to South South America I + + align:start position:0% +Darwin traveled to South South America I + + + align:start position:0% +Darwin traveled to South South America I +mean he he found fossils in a lot of the + + align:start position:0% +mean he he found fossils in a lot of the + + + align:start position:0% +mean he he found fossils in a lot of the +geological areas he studied and you know + + align:start position:0% +geological areas he studied and you know + + + align:start position:0% +geological areas he studied and you know +these were of organisms that didn't + + align:start position:0% +these were of organisms that didn't + + + align:start position:0% +these were of organisms that didn't +exist anymore so you know people had to + + align:start position:0% +exist anymore so you know people had to + + + align:start position:0% +exist anymore so you know people had to +come up with some kind of explanation + + align:start position:0% +come up with some kind of explanation + + + align:start position:0% +come up with some kind of explanation +some people thought they were monsters + + align:start position:0% +some people thought they were monsters + + + align:start position:0% +some people thought they were monsters +from some ancient time or something like + + align:start position:0% +from some ancient time or something like + + + align:start position:0% +from some ancient time or something like +that there were all kinds of theories + + align:start position:0% +that there were all kinds of theories + + + align:start position:0% +that there were all kinds of theories +about how to explain the fossil remains + + align:start position:0% +about how to explain the fossil remains + + + align:start position:0% +about how to explain the fossil remains +of the earth and that was just one area + + align:start position:0% +of the earth and that was just one area + + + align:start position:0% +of the earth and that was just one area +but there were a number of areas that + + align:start position:0% +but there were a number of areas that + + + align:start position:0% +but there were a number of areas that +began to change people's way of thinking + + align:start position:0% +began to change people's way of thinking + + + align:start position:0% +began to change people's way of thinking +about life forms and their change okay + + align:start position:0% +about life forms and their change okay + + + align:start position:0% +about life forms and their change okay +so well we're going to come back to the + + align:start position:0% +so well we're going to come back to the + + + align:start position:0% +so well we're going to come back to the +concept of design but it's really + + align:start position:0% +concept of design but it's really + + + align:start position:0% +concept of design but it's really +central to what we're trying to explore + + align:start position:0% +central to what we're trying to explore + + + align:start position:0% +central to what we're trying to explore +in this course and the ambiguity is what + + align:start position:0% +in this course and the ambiguity is what + + + align:start position:0% +in this course and the ambiguity is what +I'm interested in because we have this + + align:start position:0% +I'm interested in because we have this + + + align:start position:0% +I'm interested in because we have this +kind of play of the word design and we + + align:start position:0% +kind of play of the word design and we + + + align:start position:0% +kind of play of the word design and we +apply the word design to natural objects + + align:start position:0% +apply the word design to natural objects + + + align:start position:0% +apply the word design to natural objects +but we don't fully mean that they were + + align:start position:0% +but we don't fully mean that they were + + + align:start position:0% +but we don't fully mean that they were +that individual object was intended to + + align:start position:0% +that individual object was intended to + + + align:start position:0% +that individual object was intended to +be exactly as it is by some maker + + align:start position:0% +be exactly as it is by some maker + + + align:start position:0% +be exactly as it is by some maker +now we have a lot of ways of thinking + + align:start position:0% +now we have a lot of ways of thinking + + + align:start position:0% +now we have a lot of ways of thinking +about that but we'll explore some of + + align:start position:0% +about that but we'll explore some of + + + align:start position:0% +about that but we'll explore some of +those and Darwin of course had to deal + + align:start position:0% +those and Darwin of course had to deal + + + align:start position:0% +those and Darwin of course had to deal +with that okay so one of the things that + + align:start position:0% +with that okay so one of the things that + + + align:start position:0% +with that okay so one of the things that +I think is important for our study is is + + align:start position:0% +I think is important for our study is is + + + align:start position:0% +I think is important for our study is is +just sort of the understanding a little + + align:start position:0% +just sort of the understanding a little + + + align:start position:0% +just sort of the understanding a little +bit about the concept of nature itself + + align:start position:0% +bit about the concept of nature itself + + + align:start position:0% +bit about the concept of nature itself +how we talk about nature and what nature + + align:start position:0% +how we talk about nature and what nature + + + align:start position:0% +how we talk about nature and what nature +is and the environment in which we live + + align:start position:0% +is and the environment in which we live + + + align:start position:0% +is and the environment in which we live +in and so many of the works were going + + align:start position:0% +in and so many of the works were going + + + align:start position:0% +in and so many of the works were going +to be reading explore these the + + align:start position:0% +to be reading explore these the + + + align:start position:0% +to be reading explore these the +reflect different concepts of the + + align:start position:0% +reflect different concepts of the + + + align:start position:0% +reflect different concepts of the +natural world and in Darwin's time + + align:start position:0% +natural world and in Darwin's time + + + align:start position:0% +natural world and in Darwin's time +probably the leading view of the world + + align:start position:0% +probably the leading view of the world + + + align:start position:0% +probably the leading view of the world +or one of the leading views because you + + align:start position:0% +or one of the leading views because you + + + align:start position:0% +or one of the leading views because you +know there are many different elements + + align:start position:0% +know there are many different elements + + + align:start position:0% +know there are many different elements +and aspects to every culture but one of + + align:start position:0% +and aspects to every culture but one of + + + align:start position:0% +and aspects to every culture but one of +the one of the dominant views certainly + + align:start position:0% +the one of the dominant views certainly + + + align:start position:0% +the one of the dominant views certainly +in educated circles was the sort of + + align:start position:0% +in educated circles was the sort of + + + align:start position:0% +in educated circles was the sort of +romantic view of the world as the + + align:start position:0% +romantic view of the world as the + + + align:start position:0% +romantic view of the world as the +romantic image of nature itself and I + + align:start position:0% +romantic image of nature itself and I + + + align:start position:0% +romantic image of nature itself and I +mean ask you to read a short poem in a + + align:start position:0% +mean ask you to read a short poem in a + + + align:start position:0% +mean ask you to read a short poem in a +minute but this was one of the famous + + align:start position:0% +minute but this was one of the famous + + + align:start position:0% +minute but this was one of the famous +and it's set at this location this is an + + align:start position:0% +and it's set at this location this is an + + + align:start position:0% +and it's set at this location this is an +abbey and it was a Abbey in England that + + align:start position:0% +abbey and it was a Abbey in England that + + + align:start position:0% +abbey and it was a Abbey in England that +William Wordsworth visited and on the + + align:start position:0% +William Wordsworth visited and on the + + + align:start position:0% +William Wordsworth visited and on the +occasion of his visit in 1798 he + + align:start position:0% +occasion of his visit in 1798 he + + + align:start position:0% +occasion of his visit in 1798 he +actually wrote a very famous poem that + + align:start position:0% +actually wrote a very famous poem that + + + align:start position:0% +actually wrote a very famous poem that +reflected some of his concepts of of the + + align:start position:0% +reflected some of his concepts of of the + + + align:start position:0% +reflected some of his concepts of of the +natural world and memory and some other + + align:start position:0% +natural world and memory and some other + + + align:start position:0% +natural world and memory and some other +elements that we'll talk about it in a + + align:start position:0% +elements that we'll talk about it in a + + + align:start position:0% +elements that we'll talk about it in a +minute but I just want you to think + + align:start position:0% +minute but I just want you to think + + + align:start position:0% +minute but I just want you to think +about this this relation of design here + + align:start position:0% +about this this relation of design here + + + align:start position:0% +about this this relation of design here +in this picture look at these what's + + align:start position:0% +in this picture look at these what's + + + align:start position:0% +in this picture look at these what's +happening in this picture was painting + + align:start position:0% +happening in this picture was painting + + + align:start position:0% +happening in this picture was painting +this is a painting by Edward days and it + + align:start position:0% +this is a painting by Edward days and it + + + align:start position:0% +this is a painting by Edward days and it +was painted a little bit before the time + + align:start position:0% +was painted a little bit before the time + + + align:start position:0% +was painted a little bit before the time +that Wordsworth visited but what do you + + align:start position:0% +that Wordsworth visited but what do you + + + align:start position:0% +that Wordsworth visited but what do you +see in this picture that says something + + align:start position:0% +see in this picture that says something + + + align:start position:0% +see in this picture that says something +about design what kind of design do we + + align:start position:0% +about design what kind of design do we + + + align:start position:0% +about design what kind of design do we +have here + + align:start position:0% + + + + align:start position:0% + +we've been talking about artificial and + + align:start position:0% +we've been talking about artificial and + + + align:start position:0% +we've been talking about artificial and +natural designs + + align:start position:0% + + + + align:start position:0% + +okay yeah there's there's something + + align:start position:0% +okay yeah there's there's something + + + align:start position:0% +okay yeah there's there's something +going on here isn't there it's a I + + align:start position:0% +going on here isn't there it's a I + + + align:start position:0% +going on here isn't there it's a I +suppose an architect or an engineer + + align:start position:0% +suppose an architect or an engineer + + + align:start position:0% +suppose an architect or an engineer +would say well that's a serious case of + + align:start position:0% +would say well that's a serious case of + + + align:start position:0% +would say well that's a serious case of +where this is this ancient Abbi that was + + align:start position:0% +where this is this ancient Abbi that was + + + align:start position:0% +where this is this ancient Abbi that was +designed by some masterful architect and + + align:start position:0% +designed by some masterful architect and + + + align:start position:0% +designed by some masterful architect and +bilk is falling apart so it's it's it's + + align:start position:0% +bilk is falling apart so it's it's it's + + + align:start position:0% +bilk is falling apart so it's it's it's +it's a sort of it's a it's a ruined + + align:start position:0% +it's a sort of it's a it's a ruined + + + align:start position:0% +it's a sort of it's a it's a ruined +Abbey it's a it's a it's a church + + align:start position:0% +Abbey it's a it's a it's a church + + + align:start position:0% +Abbey it's a it's a it's a church +structure a structure designed to you + + align:start position:0% +structure a structure designed to you + + + align:start position:0% +structure a structure designed to you +know give shelter to make a statement + + align:start position:0% +know give shelter to make a statement + + + align:start position:0% +know give shelter to make a statement +about views of religious views it's it's + + align:start position:0% +about views of religious views it's it's + + + align:start position:0% +about views of religious views it's it's +and it's put on the earth and yet over + + align:start position:0% +and it's put on the earth and yet over + + + align:start position:0% +and it's put on the earth and yet over +time the earth gradually is taking it + + align:start position:0% +time the earth gradually is taking it + + + align:start position:0% +time the earth gradually is taking it +back and you know eventually there won't + + align:start position:0% +back and you know eventually there won't + + + align:start position:0% +back and you know eventually there won't +be anything left so we see the + + align:start position:0% +be anything left so we see the + + + align:start position:0% +be anything left so we see the +intersection of and we could say the + + align:start position:0% +intersection of and we could say the + + + align:start position:0% +intersection of and we could say the +natural world is also a world that + + align:start position:0% +natural world is also a world that + + + align:start position:0% +natural world is also a world that +reflects design so this comes back to + + align:start position:0% +reflects design so this comes back to + + + align:start position:0% +reflects design so this comes back to +this kind of ambiguity between human + + align:start position:0% +this kind of ambiguity between human + + + align:start position:0% +this kind of ambiguity between human +design your point and you know if we're + + align:start position:0% +design your point and you know if we're + + + align:start position:0% +design your point and you know if we're +humans we're part of the natural world + + align:start position:0% +humans we're part of the natural world + + + align:start position:0% +humans we're part of the natural world +and the fact that everything that gets + + align:start position:0% +and the fact that everything that gets + + + align:start position:0% +and the fact that everything that gets +designed ultimately wears down + + align:start position:0% +designed ultimately wears down + + + align:start position:0% +designed ultimately wears down +eventually collapses so humans are in + + align:start position:0% +eventually collapses so humans are in + + + align:start position:0% +eventually collapses so humans are in +this constant kind of tension with the + + align:start position:0% +this constant kind of tension with the + + + align:start position:0% +this constant kind of tension with the +natural world as are all individuals in + + align:start position:0% +natural world as are all individuals in + + + align:start position:0% +natural world as are all individuals in +the natural world reclaims itself yeah + + align:start position:0% + + + + align:start position:0% + +this design design we don't use anymore + + align:start position:0% + + + + align:start position:0% + +so you're talking about sort of human + + align:start position:0% +so you're talking about sort of human + + + align:start position:0% +so you're talking about sort of human +artificial objects yeah I mean there + + align:start position:0% +artificial objects yeah I mean there + + + align:start position:0% +artificial objects yeah I mean there +many cases where old Abbie's were taken + + align:start position:0% +many cases where old Abbie's were taken + + + align:start position:0% +many cases where old Abbie's were taken +the stones were taken from them to build + + align:start position:0% +the stones were taken from them to build + + + align:start position:0% +the stones were taken from them to build +new structures and so and space is + + align:start position:0% +new structures and so and space is + + + align:start position:0% +new structures and so and space is +always something that you know people + + align:start position:0% +always something that you know people + + + align:start position:0% +always something that you know people +build something on it and then somebody + + align:start position:0% +build something on it and then somebody + + + align:start position:0% +build something on it and then somebody +else comes along and wants to build + + align:start position:0% +else comes along and wants to build + + + align:start position:0% +else comes along and wants to build +something different or something bigger + + align:start position:0% +something different or something bigger + + + align:start position:0% +something different or something bigger +or something newer or something so yeah + + align:start position:0% +or something newer or something so yeah + + + align:start position:0% +or something newer or something so yeah +we're we're constantly sort of in some + + align:start position:0% +we're we're constantly sort of in some + + + align:start position:0% +we're we're constantly sort of in some +kind of conflict even with our own + + align:start position:0% +kind of conflict even with our own + + + align:start position:0% +kind of conflict even with our own +designs but all of our designs are also + + align:start position:0% +designs but all of our designs are also + + + align:start position:0% +designs but all of our designs are also +in conflict with some natural process + + align:start position:0% +in conflict with some natural process + + + align:start position:0% +in conflict with some natural process +out there we have a few minutes and I'd + + align:start position:0% +out there we have a few minutes and I'd + + + align:start position:0% +out there we have a few minutes and I'd +like to pass out William Wordsworth's + + align:start position:0% +like to pass out William Wordsworth's + + + align:start position:0% +like to pass out William Wordsworth's +poem and have you read it over and maybe + + align:start position:0% +poem and have you read it over and maybe + + + align:start position:0% +poem and have you read it over and maybe +we'll get a few minutes to talk about it + + align:start position:0% +we'll get a few minutes to talk about it + + + align:start position:0% +we'll get a few minutes to talk about it +a little bit here in class - this is a + + align:start position:0% +a little bit here in class - this is a + + + align:start position:0% +a little bit here in class - this is a +very important poem of William + + align:start position:0% +very important poem of William + + + align:start position:0% +very important poem of William +Wordsworth's its title is tintern abbey + + align:start position:0% + + + + align:start position:0% + +in which he it's a wonderful poem it's a + + align:start position:0% +in which he it's a wonderful poem it's a + + + align:start position:0% +in which he it's a wonderful poem it's a +beautiful poem is written by Wordsworth + + align:start position:0% +beautiful poem is written by Wordsworth + + + align:start position:0% +beautiful poem is written by Wordsworth +it's in on a tour to this location of + + align:start position:0% +it's in on a tour to this location of + + + align:start position:0% +it's in on a tour to this location of +tintern abbey and it's a poem of memory + + align:start position:0% +tintern abbey and it's a poem of memory + + + align:start position:0% +tintern abbey and it's a poem of memory +about his sister door + + align:start position:0% +about his sister door + + + align:start position:0% +about his sister door +but also about just his relationship + + align:start position:0% +but also about just his relationship + + + align:start position:0% +but also about just his relationship +with nature and how he viewed nature and + + align:start position:0% +with nature and how he viewed nature and + + + align:start position:0% +with nature and how he viewed nature and +the human relationship to nature so if + + align:start position:0% +the human relationship to nature so if + + + align:start position:0% +the human relationship to nature so if +you take let's take ten minutes and see + + align:start position:0% +you take let's take ten minutes and see + + + align:start position:0% +you take let's take ten minutes and see +if you see how far you get in this poem + + align:start position:0% +if you see how far you get in this poem + + + align:start position:0% +if you see how far you get in this poem +and we can start talking about it and + + align:start position:0% +and we can start talking about it and + + + align:start position:0% +and we can start talking about it and +then we'll come back to it next class + + align:start position:0% +then we'll come back to it next class + + + align:start position:0% +then we'll come back to it next class +okay you can I mean you can't read a + + align:start position:0% +okay you can I mean you can't read a + + + align:start position:0% +okay you can I mean you can't read a +poem like this in ten minutes but I'd + + align:start position:0% +poem like this in ten minutes but I'd + + + align:start position:0% +poem like this in ten minutes but I'd +like you to read it over over the + + align:start position:0% +like you to read it over over the + + + align:start position:0% +like you to read it over over the +weekend here but what can we say about + + align:start position:0% +weekend here but what can we say about + + + align:start position:0% +weekend here but what can we say about +this view that Wordsworth is expressing + + align:start position:0% +this view that Wordsworth is expressing + + + align:start position:0% +this view that Wordsworth is expressing +in here his view of nature and what is + + align:start position:0% +in here his view of nature and what is + + + align:start position:0% +in here his view of nature and what is +his view of nature have to do with + + align:start position:0% +his view of nature have to do with + + + align:start position:0% +his view of nature have to do with +Tintern Abbey he doesn't really talk + + align:start position:0% +Tintern Abbey he doesn't really talk + + + align:start position:0% +Tintern Abbey he doesn't really talk +about the Abbey too much does he what's + + align:start position:0% +about the Abbey too much does he what's + + + align:start position:0% +about the Abbey too much does he what's +Wordsworth interested in here what's he + + align:start position:0% +Wordsworth interested in here what's he + + + align:start position:0% +Wordsworth interested in here what's he +talking about + + align:start position:0% + + + + align:start position:0% + +sorry okay so his client has his + + align:start position:0% +sorry okay so his client has his + + + align:start position:0% +sorry okay so his client has his +response to nature is what Wow + + align:start position:0% +response to nature is what Wow + + + align:start position:0% +response to nature is what Wow +obviously he's he's a deep admirer of + + align:start position:0% +obviously he's he's a deep admirer of + + + align:start position:0% +obviously he's he's a deep admirer of +natural the natural world and nature + + align:start position:0% +natural the natural world and nature + + + align:start position:0% +natural the natural world and nature +itself + + align:start position:0% +itself + + + align:start position:0% +itself +what are some what are some other things + + align:start position:0% +what are some what are some other things + + + align:start position:0% +what are some what are some other things +that he what are some things he says + + align:start position:0% +that he what are some things he says + + + align:start position:0% +that he what are some things he says +about it that captured your attention + + align:start position:0% + + + + align:start position:0% + +yeah loyal judging from that + + align:start position:0% + + + + align:start position:0% + +Oh + + align:start position:0% + + + + align:start position:0% + +okay he feels his relationship to nature + + align:start position:0% +okay he feels his relationship to nature + + + align:start position:0% +okay he feels his relationship to nature +is a kind of a very spiritual and + + align:start position:0% +is a kind of a very spiritual and + + + align:start position:0% +is a kind of a very spiritual and +trusting and sort of a sense of the + + align:start position:0% +trusting and sort of a sense of the + + + align:start position:0% +trusting and sort of a sense of the +incredible sense of well-being he feels + + align:start position:0% +incredible sense of well-being he feels + + + align:start position:0% +incredible sense of well-being he feels +in natural environments so that you know + + align:start position:0% +in natural environments so that you know + + + align:start position:0% +in natural environments so that you know +there's this very very powerful mood in + + align:start position:0% +there's this very very powerful mood in + + + align:start position:0% +there's this very very powerful mood in +the poem itself is there not about just + + align:start position:0% +the poem itself is there not about just + + + align:start position:0% +the poem itself is there not about just +being in nature I mean you must do any + + align:start position:0% +being in nature I mean you must do any + + + align:start position:0% +being in nature I mean you must do any +of you have I mean what sure I mean do + + align:start position:0% +of you have I mean what sure I mean do + + + align:start position:0% +of you have I mean what sure I mean do +you have similar types of responses some + + align:start position:0% +you have similar types of responses some + + + align:start position:0% +you have similar types of responses some +of you go hiking or go out into the + + align:start position:0% +of you go hiking or go out into the + + + align:start position:0% +of you go hiking or go out into the +world do you how do you feel about being + + align:start position:0% +world do you how do you feel about being + + + align:start position:0% +world do you how do you feel about being +in nature and is that similar to what + + align:start position:0% +in nature and is that similar to what + + + align:start position:0% +in nature and is that similar to what +Wordsworth feels + + align:start position:0% + + + + align:start position:0% + +and he feels like he certainly his his + + align:start position:0% +and he feels like he certainly his his + + + align:start position:0% +and he feels like he certainly his his +he has a very beautiful gor capacious + + align:start position:0% +he has a very beautiful gor capacious + + + align:start position:0% +he has a very beautiful gor capacious +sense of nature itself as being a place + + align:start position:0% +sense of nature itself as being a place + + + align:start position:0% +sense of nature itself as being a place +to that is his humans are intimately + + align:start position:0% +to that is his humans are intimately + + + align:start position:0% +to that is his humans are intimately +related to and you know in some sense + + align:start position:0% +related to and you know in some sense + + + align:start position:0% +related to and you know in some sense +humans are of nature they come from + + align:start position:0% +humans are of nature they come from + + + align:start position:0% +humans are of nature they come from +nature and there is a there's a sort of + + align:start position:0% +nature and there is a there's a sort of + + + align:start position:0% +nature and there is a there's a sort of +sense of the b9s and support of natural + + align:start position:0% +sense of the b9s and support of natural + + + align:start position:0% +sense of the b9s and support of natural +forms he distinguishes between his youth + + align:start position:0% +forms he distinguishes between his youth + + + align:start position:0% +forms he distinguishes between his youth +and his older later years yes + + align:start position:0% + + + + align:start position:0% + +it's sort of it evolves in his sense yes + + align:start position:0% +it's sort of it evolves in his sense yes + + + align:start position:0% +it's sort of it evolves in his sense yes +so he he speaks of you know he says in + + align:start position:0% +so he he speaks of you know he says in + + + align:start position:0% +so he he speaks of you know he says in +in line 65 down here or just start at + + align:start position:0% +in line 65 down here or just start at + + + align:start position:0% +in line 65 down here or just start at +about line 60 and now with gleams of + + align:start position:0% +about line 60 and now with gleams of + + + align:start position:0% +about line 60 and now with gleams of +half-extinguished thought and with many + + align:start position:0% +half-extinguished thought and with many + + + align:start position:0% +half-extinguished thought and with many +recognitions dim and faint in somewhat + + align:start position:0% +recognitions dim and faint in somewhat + + + align:start position:0% +recognitions dim and faint in somewhat +of a sad perplexity the picture of the + + align:start position:0% +of a sad perplexity the picture of the + + + align:start position:0% +of a sad perplexity the picture of the +mind revives again so his mental process + + align:start position:0% +mind revives again so his mental process + + + align:start position:0% +mind revives again so his mental process +is really important here this is a this + + align:start position:0% +is really important here this is a this + + + align:start position:0% +is really important here this is a this +is a poem partly about the mental + + align:start position:0% +is a poem partly about the mental + + + align:start position:0% +is a poem partly about the mental +process of interaction and the spiritual + + align:start position:0% +process of interaction and the spiritual + + + align:start position:0% +process of interaction and the spiritual +process and then in the mind being in + + align:start position:0% +process and then in the mind being in + + + align:start position:0% +process and then in the mind being in +the mind the life of the mind the + + align:start position:0% +the mind the life of the mind the + + + align:start position:0% +the mind the life of the mind the +picture of the mind revives again well + + align:start position:0% +picture of the mind revives again well + + + align:start position:0% +picture of the mind revives again well +here I stand not only with the sense of + + align:start position:0% +here I stand not only with the sense of + + + align:start position:0% +here I stand not only with the sense of +present pleasure but with pleasing + + align:start position:0% +present pleasure but with pleasing + + + align:start position:0% +present pleasure but with pleasing +thoughts that in this moment there is + + align:start position:0% +thoughts that in this moment there is + + + align:start position:0% +thoughts that in this moment there is +life and food for future years and so I + + align:start position:0% +life and food for future years and so I + + + align:start position:0% +life and food for future years and so I +dare to hope though change no doubt from + + align:start position:0% +dare to hope though change no doubt from + + + align:start position:0% +dare to hope though change no doubt from +what I was at first I came among these + + align:start position:0% +what I was at first I came among these + + + align:start position:0% +what I was at first I came among these +hills when like a row i bounded order + + align:start position:0% +hills when like a row i bounded order + + + align:start position:0% +hills when like a row i bounded order +the mountains by the sides of the deep + + align:start position:0% +the mountains by the sides of the deep + + + align:start position:0% +the mountains by the sides of the deep +rivers and the lonely streams wherever + + align:start position:0% +rivers and the lonely streams wherever + + + align:start position:0% +rivers and the lonely streams wherever +nature led more like a man flying from + + align:start position:0% +nature led more like a man flying from + + + align:start position:0% +nature led more like a man flying from +something that he dreads then one who + + align:start position:0% +something that he dreads then one who + + + align:start position:0% +something that he dreads then one who +sought the thing he loved for nature + + align:start position:0% +sought the thing he loved for nature + + + align:start position:0% +sought the thing he loved for nature +then the coarser pleasures of my boy + + align:start position:0% +then the coarser pleasures of my boy + + + align:start position:0% +then the coarser pleasures of my boy +days and they're glad animal moments all + + align:start position:0% +days and they're glad animal moments all + + + align:start position:0% +days and they're glad animal moments all +gone by to me was all in all I cannot + + align:start position:0% +gone by to me was all in all I cannot + + + align:start position:0% +gone by to me was all in all I cannot +paint what I was the sounding cataract + + align:start position:0% +paint what I was the sounding cataract + + + align:start position:0% +paint what I was the sounding cataract +haunted me like a passion the tall rock + + align:start position:0% +haunted me like a passion the tall rock + + + align:start position:0% +haunted me like a passion the tall rock +the mountain the deep and gloomy wood + + align:start position:0% +the mountain the deep and gloomy wood + + + align:start position:0% +the mountain the deep and gloomy wood +their colours and their forms were then + + align:start position:0% +their colours and their forms were then + + + align:start position:0% +their colours and their forms were then +to me an appetite a feeling and a love + + align:start position:0% +to me an appetite a feeling and a love + + + align:start position:0% +to me an appetite a feeling and a love +that had no need of a remoter charm of a + + align:start position:0% +that had no need of a remoter charm of a + + + align:start position:0% +that had no need of a remoter charm of a +remoter charm by thought supplied nor + + align:start position:0% +remoter charm by thought supplied nor + + + align:start position:0% +remoter charm by thought supplied nor +any interest unborrowed from the eye + + align:start position:0% +any interest unborrowed from the eye + + + align:start position:0% +any interest unborrowed from the eye +that time is past this is the shift that + + align:start position:0% +that time is past this is the shift that + + + align:start position:0% +that time is past this is the shift that +time has passed and all its aching joys + + align:start position:0% +time has passed and all its aching joys + + + align:start position:0% +time has passed and all its aching joys +are now no more in all its dizzy + + align:start position:0% +are now no more in all its dizzy + + + align:start position:0% +are now no more in all its dizzy +raptures not for this faint eye nor + + align:start position:0% +raptures not for this faint eye nor + + + align:start position:0% +raptures not for this faint eye nor +mourn normal other gifts have followed + + align:start position:0% +mourn normal other gifts have followed + + + align:start position:0% +mourn normal other gifts have followed +for such loss I would believe abundant + + align:start position:0% +for such loss I would believe abundant + + + align:start position:0% +for such loss I would believe abundant +recompense for I have learned to look on + + align:start position:0% +recompense for I have learned to look on + + + align:start position:0% +recompense for I have learned to look on +nature not as in the hour of thoughtless + + align:start position:0% +nature not as in the hour of thoughtless + + + align:start position:0% +nature not as in the hour of thoughtless +youth but hearing oftentimes the still + + align:start position:0% +youth but hearing oftentimes the still + + + align:start position:0% +youth but hearing oftentimes the still +sad music of human + + align:start position:0% +sad music of human + + + align:start position:0% +sad music of human +nor harsh nor grading though of ample + + align:start position:0% +nor harsh nor grading though of ample + + + align:start position:0% +nor harsh nor grading though of ample +power to chasten and subdue and I have + + align:start position:0% +power to chasten and subdue and I have + + + align:start position:0% +power to chasten and subdue and I have +felt the presence that disturbs me with + + align:start position:0% +felt the presence that disturbs me with + + + align:start position:0% +felt the presence that disturbs me with +the joy of elevated thoughts a sense + + align:start position:0% +the joy of elevated thoughts a sense + + + align:start position:0% +the joy of elevated thoughts a sense +sublime of something far more deeply + + align:start position:0% +sublime of something far more deeply + + + align:start position:0% +sublime of something far more deeply +interfused whose dwelling is the light + + align:start position:0% +interfused whose dwelling is the light + + + align:start position:0% +interfused whose dwelling is the light +of setting Suns in the round ocean in + + align:start position:0% +of setting Suns in the round ocean in + + + align:start position:0% +of setting Suns in the round ocean in +the living error in the blue sky in the + + align:start position:0% +the living error in the blue sky in the + + + align:start position:0% +the living error in the blue sky in the +mind of man emotion and the spirit that + + align:start position:0% +mind of man emotion and the spirit that + + + align:start position:0% +mind of man emotion and the spirit that +impels all thinking things all objects + + align:start position:0% +impels all thinking things all objects + + + align:start position:0% +impels all thinking things all objects +of all thought and rolls through all + + align:start position:0% +of all thought and rolls through all + + + align:start position:0% +of all thought and rolls through all +things so what's what's he talking about + + align:start position:0% +things so what's what's he talking about + + + align:start position:0% +things so what's what's he talking about +here + + align:start position:0% + + + + align:start position:0% + +what does he find in nature you know + + align:start position:0% + + + + align:start position:0% + +yeah it's it's capacious it's it's the + + align:start position:0% +yeah it's it's capacious it's it's the + + + align:start position:0% +yeah it's it's capacious it's it's the +source it's it's the ultimate source of + + align:start position:0% +source it's it's the ultimate source of + + + align:start position:0% +source it's it's the ultimate source of +what we are I mean we can't divorce + + align:start position:0% +what we are I mean we can't divorce + + + align:start position:0% +what we are I mean we can't divorce +ourselves from nature or we shouldn't + + align:start position:0% +ourselves from nature or we shouldn't + + + align:start position:0% +ourselves from nature or we shouldn't +there's Wordsworth feel that sometimes + + align:start position:0% +there's Wordsworth feel that sometimes + + + align:start position:0% +there's Wordsworth feel that sometimes +humans do divorce elsewhere in the poem + + align:start position:0% + + + + align:start position:0% + +he sees that there there's a kind of + + align:start position:0% +he sees that there there's a kind of + + + align:start position:0% +he sees that there there's a kind of +conflict in the minister or not between + + align:start position:0% +conflict in the minister or not between + + + align:start position:0% +conflict in the minister or not between +being in nature and what he calls the + + align:start position:0% +being in nature and what he calls the + + + align:start position:0% +being in nature and what he calls the +the sort of the the tediousness of urban + + align:start position:0% +the sort of the the tediousness of urban + + + align:start position:0% +the sort of the the tediousness of urban +living he sort of sees the the country + + align:start position:0% +living he sort of sees the the country + + + align:start position:0% +living he sort of sees the the country +versus the city the urban versus the + + align:start position:0% +versus the city the urban versus the + + + align:start position:0% +versus the city the urban versus the +wild is definitely something that + + align:start position:0% +wild is definitely something that + + + align:start position:0% +wild is definitely something that +there's a conflict that emerges in this + + align:start position:0% +there's a conflict that emerges in this + + + align:start position:0% +there's a conflict that emerges in this +this work but he sees in nature what + + align:start position:0% +this work but he sees in nature what + + + align:start position:0% +this work but he sees in nature what +else + + align:start position:0% +else + + + align:start position:0% +else +not just the source of our existence in + + align:start position:0% +not just the source of our existence in + + + align:start position:0% +not just the source of our existence in +our being what else is infused in nature + + align:start position:0% + + + + align:start position:0% + +but being + + align:start position:0% +but being + + + align:start position:0% +but being +triangles in mind + + align:start position:0% +triangles in mind + + + align:start position:0% +triangles in mind +you're carving a ball rather than + + align:start position:0% + + + + align:start position:0% + +certainly that certainly that + + align:start position:0% +certainly that certainly that + + + align:start position:0% +certainly that certainly that +tranquility this he sees a scene he's + + align:start position:0% +tranquility this he sees a scene he's + + + align:start position:0% +tranquility this he sees a scene he's +looking down on the scene from above not + + align:start position:0% +looking down on the scene from above not + + + align:start position:0% +looking down on the scene from above not +not this perspective but from above but + + align:start position:0% +not this perspective but from above but + + + align:start position:0% +not this perspective but from above but +he sees this strength tranquil setting + + align:start position:0% +he sees this strength tranquil setting + + + align:start position:0% +he sees this strength tranquil setting +little smoke puffs coming from the trees + + align:start position:0% +little smoke puffs coming from the trees + + + align:start position:0% +little smoke puffs coming from the trees +way down below he's on some cliffs above + + align:start position:0% +way down below he's on some cliffs above + + + align:start position:0% +way down below he's on some cliffs above +but he sees he sees even more than that + + align:start position:0% +but he sees he sees even more than that + + + align:start position:0% +but he sees he sees even more than that +nature yes and now it seems that he's + + align:start position:0% +nature yes and now it seems that he's + + + align:start position:0% +nature yes and now it seems that he's +more comparing things and seeing how + + align:start position:0% +more comparing things and seeing how + + + align:start position:0% +more comparing things and seeing how +everything + + align:start position:0% +everything + + + align:start position:0% +everything +yeah yeah he sees the texture the + + align:start position:0% +yeah yeah he sees the texture the + + + align:start position:0% +yeah yeah he sees the texture the +organic quality of the + + align:start position:0% +organic quality of the + + + align:start position:0% +organic quality of the +interconnectedness of things in nature + + align:start position:0% +interconnectedness of things in nature + + + align:start position:0% +interconnectedness of things in nature +and he identifies him as part of that + + align:start position:0% +and he identifies him as part of that + + + align:start position:0% +and he identifies him as part of that +himself as part of that he feels akin to + + align:start position:0% +himself as part of that he feels akin to + + + align:start position:0% +himself as part of that he feels akin to +that he feels embraced by that but he + + align:start position:0% +that he feels embraced by that but he + + + align:start position:0% +that he feels embraced by that but he +also sees in nature some kind of a force + + align:start position:0% +also sees in nature some kind of a force + + + align:start position:0% +also sees in nature some kind of a force +does he not I mean what's he talking + + align:start position:0% +does he not I mean what's he talking + + + align:start position:0% +does he not I mean what's he talking +about here who's who's he says whose + + align:start position:0% +about here who's who's he says whose + + + align:start position:0% +about here who's who's he says whose +dwelling is the light of setting Suns + + align:start position:0% + + + + align:start position:0% + +what's he talking about here I mean what + + align:start position:0% +what's he talking about here I mean what + + + align:start position:0% +what's he talking about here I mean what +is the argument for the spiritual + + align:start position:0% +is the argument for the spiritual + + + align:start position:0% +is the argument for the spiritual +quality of nature this is our argument + + align:start position:0% +quality of nature this is our argument + + + align:start position:0% +quality of nature this is our argument +what is the you know what is how does + + align:start position:0% +what is the you know what is how does + + + align:start position:0% +what is the you know what is how does +this emerge and Wordsworth poem Nature + + align:start position:0% +this emerge and Wordsworth poem Nature + + + align:start position:0% +this emerge and Wordsworth poem Nature +is not just a set of objects in which he + + align:start position:0% +is not just a set of objects in which he + + + align:start position:0% +is not just a set of objects in which he +relates to beauteous forms but it has + + align:start position:0% +relates to beauteous forms but it has + + + align:start position:0% +relates to beauteous forms but it has +martyrs or not yes + + align:start position:0% + + + + align:start position:0% + +well probably yeah I mean designer is + + align:start position:0% +well probably yeah I mean designer is + + + align:start position:0% +well probably yeah I mean designer is +probably not what he has in mind but + + align:start position:0% +probably not what he has in mind but + + + align:start position:0% +probably not what he has in mind but +certainly a spiritual force the + + align:start position:0% +certainly a spiritual force the + + + align:start position:0% +certainly a spiritual force the +spiritual essence in nature itself that + + align:start position:0% +spiritual essence in nature itself that + + + align:start position:0% +spiritual essence in nature itself that +he identifies with and he doesn't have a + + align:start position:0% +he identifies with and he doesn't have a + + + align:start position:0% +he identifies with and he doesn't have a +name for it you know you could say well + + align:start position:0% +name for it you know you could say well + + + align:start position:0% +name for it you know you could say well +maybe he's a pantheist or maybe he you + + align:start position:0% +maybe he's a pantheist or maybe he you + + + align:start position:0% +maybe he's a pantheist or maybe he you +know we could put labels on Wordsworth + + align:start position:0% +know we could put labels on Wordsworth + + + align:start position:0% +know we could put labels on Wordsworth +but that would be missing the point of + + align:start position:0% +but that would be missing the point of + + + align:start position:0% +but that would be missing the point of +the poem it's it's a sense of that + + align:start position:0% +the poem it's it's a sense of that + + + align:start position:0% +the poem it's it's a sense of that +there's a that there's a larger force in + + align:start position:0% +there's a that there's a larger force in + + + align:start position:0% +there's a that there's a larger force in +the natural surroundings that humans + + align:start position:0% +the natural surroundings that humans + + + align:start position:0% +the natural surroundings that humans +have come from that can be discerned or + + align:start position:0% +have come from that can be discerned or + + + align:start position:0% +have come from that can be discerned or +detected or felt if you allow yourself + + align:start position:0% +detected or felt if you allow yourself + + + align:start position:0% +detected or felt if you allow yourself +to become part of it so this is and this + + align:start position:0% +to become part of it so this is and this + + + align:start position:0% +to become part of it so this is and this +is a this is a tremendous source of sort + + align:start position:0% +is a this is a tremendous source of sort + + + align:start position:0% +is a this is a tremendous source of sort +of I mean many many romantics explored + + align:start position:0% +of I mean many many romantics explored + + + align:start position:0% +of I mean many many romantics explored +these ideas of you know where word is + + align:start position:0% +these ideas of you know where word is + + + align:start position:0% +these ideas of you know where word is +the spiritual center of the human + + align:start position:0% +the spiritual center of the human + + + align:start position:0% +the spiritual center of the human +existence well where is it where how can + + align:start position:0% +existence well where is it where how can + + + align:start position:0% +existence well where is it where how can +it be found how can it be touched how + + align:start position:0% +it be found how can it be touched how + + + align:start position:0% +it be found how can it be touched how +can it be seen how can be felt and + + align:start position:0% +can it be seen how can be felt and + + + align:start position:0% +can it be seen how can be felt and +Wordsworth is a poet and chief on this I + + align:start position:0% +Wordsworth is a poet and chief on this I + + + align:start position:0% +Wordsworth is a poet and chief on this I +mean he's a tremendous he's a tremendous + + align:start position:0% +mean he's a tremendous he's a tremendous + + + align:start position:0% +mean he's a tremendous he's a tremendous +sense of the powers of nature it is true + + align:start position:0% +sense of the powers of nature it is true + + + align:start position:0% +sense of the powers of nature it is true +the view of nature he has well what what + + align:start position:0% +the view of nature he has well what what + + + align:start position:0% +the view of nature he has well what what +kinds of Nate I mean what nature is he + + align:start position:0% +kinds of Nate I mean what nature is he + + + align:start position:0% +kinds of Nate I mean what nature is he +talking about where is he seeing his + + align:start position:0% +talking about where is he seeing his + + + align:start position:0% +talking about where is he seeing his +where is his nature + + align:start position:0% + + + + align:start position:0% + +one of the Huxley's rota rota sa once + + align:start position:0% +one of the Huxley's rota rota sa once + + + align:start position:0% +one of the Huxley's rota rota sa once +called Wordsworth in the tropics well + + align:start position:0% +called Wordsworth in the tropics well + + + align:start position:0% +called Wordsworth in the tropics well +you know in essence you know the + + align:start position:0% +you know in essence you know the + + + align:start position:0% +you know in essence you know the +tropical nature is is also beautiful and + + align:start position:0% +tropical nature is is also beautiful and + + + align:start position:0% +tropical nature is is also beautiful and +and Darwin had the same phenomenal + + align:start position:0% +and Darwin had the same phenomenal + + + align:start position:0% +and Darwin had the same phenomenal +experience when he first visited the + + align:start position:0% +experience when he first visited the + + + align:start position:0% +experience when he first visited the +tropics he just on his voyage of the + + align:start position:0% +tropics he just on his voyage of the + + + align:start position:0% +tropics he just on his voyage of the +Beagle he wrote about how he was just + + align:start position:0% +Beagle he wrote about how he was just + + + align:start position:0% +Beagle he wrote about how he was just +kind of drunk with the beauty of being + + align:start position:0% +kind of drunk with the beauty of being + + + align:start position:0% +kind of drunk with the beauty of being +in these dense tropical force and + + align:start position:0% +in these dense tropical force and + + + align:start position:0% +in these dense tropical force and +butterflies and things you know however + + align:start position:0% +butterflies and things you know however + + + align:start position:0% +butterflies and things you know however +there are things that eat you to where + + align:start position:0% +there are things that eat you to where + + + align:start position:0% +there are things that eat you to where +they're either there negative forces out + + align:start position:0% +they're either there negative forces out + + + align:start position:0% +they're either there negative forces out +there so it's not always not always + + align:start position:0% +there so it's not always not always + + + align:start position:0% +there so it's not always not always +benign and Wordsworth is of course + + align:start position:0% +benign and Wordsworth is of course + + + align:start position:0% +benign and Wordsworth is of course +writing really not so much about a + + align:start position:0% +writing really not so much about a + + + align:start position:0% +writing really not so much about a +wilderness concept of nature is more + + align:start position:0% +wilderness concept of nature is more + + + align:start position:0% +wilderness concept of nature is more +pastoral nature in the pastoral sense + + align:start position:0% +pastoral nature in the pastoral sense + + + align:start position:0% +pastoral nature in the pastoral sense +and this is a nature that's you know + + align:start position:0% +and this is a nature that's you know + + + align:start position:0% +and this is a nature that's you know +more or less inhabited by humans they're + + align:start position:0% +more or less inhabited by humans they're + + + align:start position:0% +more or less inhabited by humans they're +little puffs of smoke coming up through + + align:start position:0% +little puffs of smoke coming up through + + + align:start position:0% +little puffs of smoke coming up through +the trees and so forth whereas you know + + align:start position:0% +the trees and so forth whereas you know + + + align:start position:0% +the trees and so forth whereas you know +there are many places and spaces in the + + align:start position:0% +there are many places and spaces in the + + + align:start position:0% +there are many places and spaces in the +in the world where what we would call + + align:start position:0% +in the world where what we would call + + + align:start position:0% +in the world where what we would call +nature is tremendously hostile and you + + align:start position:0% +nature is tremendously hostile and you + + + align:start position:0% +nature is tremendously hostile and you +know foreboding so it's it's it's it's + + align:start position:0% +know foreboding so it's it's it's it's + + + align:start position:0% +know foreboding so it's it's it's it's +not necessarily a place that you can + + align:start position:0% +not necessarily a place that you can + + + align:start position:0% +not necessarily a place that you can +assume is going to be in a place of + + align:start position:0% +assume is going to be in a place of + + + align:start position:0% +assume is going to be in a place of +comfort and solace and spiritual reward + + align:start position:0% +comfort and solace and spiritual reward + + + align:start position:0% +comfort and solace and spiritual reward +and of course we're you know we're now + + align:start position:0% +and of course we're you know we're now + + + align:start position:0% +and of course we're you know we're now +just this was written almost just before + + align:start position:0% +just this was written almost just before + + + align:start position:0% +just this was written almost just before +1800 1798 and we're only sixty years out + + align:start position:0% +1800 1798 and we're only sixty years out + + + align:start position:0% +1800 1798 and we're only sixty years out +from Darwin's Origin and Darwin's Origin + + align:start position:0% +from Darwin's Origin and Darwin's Origin + + + align:start position:0% +from Darwin's Origin and Darwin's Origin +is going to bring a rather different + + align:start position:0% +is going to bring a rather different + + + align:start position:0% +is going to bring a rather different +view of nature but I wouldn't say it's + + align:start position:0% +view of nature but I wouldn't say it's + + + align:start position:0% +view of nature but I wouldn't say it's +opposed + + align:start position:0% +opposed + + + align:start position:0% +opposed +view I mean Darwin himself felt in many + + align:start position:0% +view I mean Darwin himself felt in many + + + align:start position:0% +view I mean Darwin himself felt in many +ways the way Wordsworth felt about being + + align:start position:0% +ways the way Wordsworth felt about being + + + align:start position:0% +ways the way Wordsworth felt about being +out in natural world and his voyage of + + align:start position:0% +out in natural world and his voyage of + + + align:start position:0% +out in natural world and his voyage of +the Beagle was one of the great + + align:start position:0% +the Beagle was one of the great + + + align:start position:0% +the Beagle was one of the great +experiences of his life and he spent + + align:start position:0% +experiences of his life and he spent + + + align:start position:0% +experiences of his life and he spent +lots and lots of time and you know very + + align:start position:0% +lots and lots of time and you know very + + + align:start position:0% +lots and lots of time and you know very +challenging and foreboding landscapes + + align:start position:0% +challenging and foreboding landscapes + + + align:start position:0% +challenging and foreboding landscapes +there but he still carried with him this + + align:start position:0% +there but he still carried with him this + + + align:start position:0% +there but he still carried with him this +sense of you know nature as a as a as a + + align:start position:0% +sense of you know nature as a as a as a + + + align:start position:0% +sense of you know nature as a as a as a +spiritually powerful source of + + align:start position:0% +spiritually powerful source of + + + align:start position:0% +spiritually powerful source of +well-being and sense of beauty and I + + align:start position:0% +well-being and sense of beauty and I + + + align:start position:0% +well-being and sense of beauty and I +don't think Darwin ever lost that in + + align:start position:0% +don't think Darwin ever lost that in + + + align:start position:0% +don't think Darwin ever lost that in +this entire life and yet and in science + + align:start position:0% +this entire life and yet and in science + + + align:start position:0% +this entire life and yet and in science +he he did something quite different he + + align:start position:0% +he he did something quite different he + + + align:start position:0% +he he did something quite different he +was he was not trying to create quote + + align:start position:0% +was he was not trying to create quote + + + align:start position:0% +was he was not trying to create quote +nature but he was trying to understand + + align:start position:0% +nature but he was trying to understand + + + align:start position:0% +nature but he was trying to understand +living forms and how these forms and the + + align:start position:0% +living forms and how these forms and the + + + align:start position:0% +living forms and how these forms and the +patterns of their existence led to + + align:start position:0% +patterns of their existence led to + + + align:start position:0% +patterns of their existence led to +adaptations in the constant change and + + align:start position:0% +adaptations in the constant change and + + + align:start position:0% +adaptations in the constant change and +growth of the evolutionary evolutionary + + align:start position:0% +growth of the evolutionary evolutionary + + + align:start position:0% +growth of the evolutionary evolutionary +experience or phenomenon and that led in + + align:start position:0% +experience or phenomenon and that led in + + + align:start position:0% +experience or phenomenon and that led in +quite a different view in quite a + + align:start position:0% +quite a different view in quite a + + + align:start position:0% +quite a different view in quite a +different direction + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/fZKrUgm9R1o.txt b/fZKrUgm9R1o.txt new file mode 100644 index 0000000000000000000000000000000000000000..5c2ca8fa031c19e27209381c24bb3c04a619902d --- /dev/null +++ b/fZKrUgm9R1o.txt @@ -0,0 +1,5259 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so what's been important the last couple + + align:start position:0% +so what's been important the last couple + + + align:start position:0% +so what's been important the last couple +of lectures + + align:start position:0% + + + + align:start position:0% + +Christina transfer function all right + + align:start position:0% + + + + align:start position:0% + +how about something else + + align:start position:0% +how about something else + + + align:start position:0% +how about something else +modal coordinates and I'll expand that + + align:start position:0% +modal coordinates and I'll expand that + + + align:start position:0% +modal coordinates and I'll expand that +to call this modal analysis in general + + align:start position:0% +to call this modal analysis in general + + + align:start position:0% +to call this modal analysis in general +anything else + + align:start position:0% + + + + align:start position:0% + +anything while I think more about that + + align:start position:0% +anything while I think more about that + + + align:start position:0% +anything while I think more about that +and are there any questions for the week + + align:start position:0% +and are there any questions for the week + + + align:start position:0% +and are there any questions for the week +no what are anything muddy fuzzy not + + align:start position:0% +no what are anything muddy fuzzy not + + + align:start position:0% +no what are anything muddy fuzzy not +quite clear to you that if I have time + + align:start position:0% +quite clear to you that if I have time + + + align:start position:0% +quite clear to you that if I have time +to say a few words about today you'd + + align:start position:0% +to say a few words about today you'd + + + align:start position:0% +to say a few words about today you'd +like me to talk about is that just like + + align:start position:0% +like me to talk about is that just like + + + align:start position:0% +like me to talk about is that just like +so we did originally + + align:start position:0% + + + + align:start position:0% + +his model analysis a an alternative way + + align:start position:0% +his model analysis a an alternative way + + + align:start position:0% +his model analysis a an alternative way +of if the analogy isn't too helpful but + + align:start position:0% +of if the analogy isn't too helpful but + + + align:start position:0% +of if the analogy isn't too helpful but +modal analysis is one way of attacking + + align:start position:0% +modal analysis is one way of attacking + + + align:start position:0% +modal analysis is one way of attacking +the equations of motion that describe + + align:start position:0% +the equations of motion that describe + + + align:start position:0% +the equations of motion that describe +vibration of linear systems you can work + + align:start position:0% +vibration of linear systems you can work + + + align:start position:0% +vibration of linear systems you can work +through the entire analysis and figure + + align:start position:0% +through the entire analysis and figure + + + align:start position:0% +through the entire analysis and figure +out the solution to the equations of + + align:start position:0% +out the solution to the equations of + + + align:start position:0% +out the solution to the equations of +motion the unusual with these multiple + + align:start position:0% +motion the unusual with these multiple + + + align:start position:0% +motion the unusual with these multiple +degree freedom vibration problems you + + align:start position:0% +degree freedom vibration problems you + + + align:start position:0% +degree freedom vibration problems you +can cast them as a mass matrix times an + + align:start position:0% +can cast them as a mass matrix times an + + + align:start position:0% +can cast them as a mass matrix times an +acceleration vector plus a stiffness + + align:start position:0% +acceleration vector plus a stiffness + + + align:start position:0% +acceleration vector plus a stiffness +matrix times the displacement vector + + align:start position:0% +matrix times the displacement vector + + + align:start position:0% +matrix times the displacement vector +equals some forcing function right so + + align:start position:0% +equals some forcing function right so + + + align:start position:0% +equals some forcing function right so +these are and we linearize them and we + + align:start position:0% +these are and we linearize them and we + + + align:start position:0% +these are and we linearize them and we +know they're for vibration problems we + + align:start position:0% +know they're for vibration problems we + + + align:start position:0% +know they're for vibration problems we +can solve these equations using modal + + align:start position:0% +can solve these equations using modal + + + align:start position:0% +can solve these equations using modal +analysis or we can solve them brute + + align:start position:0% +analysis or we can solve them brute + + + align:start position:0% +analysis or we can solve them brute +force directly without breaking the the + + align:start position:0% +force directly without breaking the the + + + align:start position:0% +force directly without breaking the the +results into their modal contributions + + align:start position:0% +results into their modal contributions + + + align:start position:0% +results into their modal contributions +and so there really are two kind of + + align:start position:0% +and so there really are two kind of + + + align:start position:0% +and so there really are two kind of +approaches that you can use to doing it + + align:start position:0% +approaches that you can use to doing it + + + align:start position:0% +approaches that you can use to doing it +so they any other kind of questions yeah + + align:start position:0% + + + + align:start position:0% + +just the ratio + + align:start position:0% +just the ratio + + + align:start position:0% +just the ratio +the case is a two degree of freedom + + align:start position:0% +the case is a two degree of freedom + + + align:start position:0% +the case is a two degree of freedom +system so mode shapes for mode n of an N + + align:start position:0% +system so mode shapes for mode n of an N + + + align:start position:0% +system so mode shapes for mode n of an N +degree of freedom system like let's say + + align:start position:0% +degree of freedom system like let's say + + + align:start position:0% +degree of freedom system like let's say +N equals three here so for mode in the + + align:start position:0% +N equals three here so for mode in the + + + align:start position:0% +N equals three here so for mode in the +mode shape and we you have to you always + + align:start position:0% +mode shape and we you have to you always + + + align:start position:0% +mode shape and we you have to you always +have to present some normalization I do + + align:start position:0% +have to present some normalization I do + + + align:start position:0% +have to present some normalization I do +the normalization oftentimes by just + + align:start position:0% +the normalization oftentimes by just + + + align:start position:0% +the normalization oftentimes by just +saying okay I'm going to make the top + + align:start position:0% +saying okay I'm going to make the top + + + align:start position:0% +saying okay I'm going to make the top +cordon that I get to give it unit + + align:start position:0% +cordon that I get to give it unit + + + align:start position:0% +cordon that I get to give it unit +amplitude so that's I'm going to take a + + align:start position:0% +amplitude so that's I'm going to take a + + + align:start position:0% +amplitude so that's I'm going to take a +1 and divide it by itself and that will + + align:start position:0% +1 and divide it by itself and that will + + + align:start position:0% +1 and divide it by itself and that will +give me a 1 and then every other ones + + align:start position:0% +give me a 1 and then every other ones + + + align:start position:0% +give me a 1 and then every other ones +becomes a2 over a1 a3 over a1 the mode + + align:start position:0% +becomes a2 over a1 a3 over a1 the mode + + + align:start position:0% +becomes a2 over a1 a3 over a1 the mode +shape says if this is then 1 minus 1/2 + + align:start position:0% +shape says if this is then 1 minus 1/2 + + + align:start position:0% +shape says if this is then 1 minus 1/2 +and 1/4 it says that if mo if coordinate + + align:start position:0% +and 1/4 it says that if mo if coordinate + + + align:start position:0% +and 1/4 it says that if mo if coordinate +generalized coordinate 1 moves a unit + + align:start position:0% +generalized coordinate 1 moves a unit + + + align:start position:0% +generalized coordinate 1 moves a unit +amount generalized coordinate 2 will + + align:start position:0% +amount generalized coordinate 2 will + + + align:start position:0% +amount generalized coordinate 2 will +move half of that in its in the opposite + + align:start position:0% +move half of that in its in the opposite + + + align:start position:0% +move half of that in its in the opposite +and it's negative in its negative + + align:start position:0% +and it's negative in its negative + + + align:start position:0% +and it's negative in its negative +direction this could be an exodus + + align:start position:0% +direction this could be an exodus + + + align:start position:0% +direction this could be an exodus +placement and that could be a rotation + + align:start position:0% +placement and that could be a rotation + + + align:start position:0% +placement and that could be a rotation +but they all have positively defined + + align:start position:0% +but they all have positively defined + + + align:start position:0% +but they all have positively defined +directions right so if there's a + + align:start position:0% +directions right so if there's a + + + align:start position:0% +directions right so if there's a +positive one at x1 + + align:start position:0% +positive one at x1 + + + align:start position:0% +positive one at x1 +there's a minus 1/2 at generalized + + align:start position:0% +there's a minus 1/2 at generalized + + + align:start position:0% +there's a minus 1/2 at generalized +coordinate 2 and there's no plus 1/4 + + align:start position:0% +coordinate 2 and there's no plus 1/4 + + + align:start position:0% +coordinate 2 and there's no plus 1/4 +generalized coordinate 3 and that ratio + + align:start position:0% +generalized coordinate 3 and that ratio + + + align:start position:0% +generalized coordinate 3 and that ratio +stays constant for the mode and if so if + + align:start position:0% +stays constant for the mode and if so if + + + align:start position:0% +stays constant for the mode and if so if +you have if it's an initial condition + + align:start position:0% +you have if it's an initial condition + + + align:start position:0% +you have if it's an initial condition +problem have you set it up so that it + + align:start position:0% +problem have you set it up so that it + + + align:start position:0% +problem have you set it up so that it +you actually give it an exhibit just an + + align:start position:0% +you actually give it an exhibit just an + + + align:start position:0% +you actually give it an exhibit just an +initial displacement of exactly that + + align:start position:0% +initial displacement of exactly that + + + align:start position:0% +initial displacement of exactly that +shape it will sit there and vibrate only + + align:start position:0% +shape it will sit there and vibrate only + + + align:start position:0% +shape it will sit there and vibrate only +in that mode and you'll notice that it + + align:start position:0% +in that mode and you'll notice that it + + + align:start position:0% +in that mode and you'll notice that it +will enact amping the proportion of the + + align:start position:0% +will enact amping the proportion of the + + + align:start position:0% +will enact amping the proportion of the +first two the other two stays exactly + + align:start position:0% +first two the other two stays exactly + + + align:start position:0% +first two the other two stays exactly +constant that's what a mode is and it's + + align:start position:0% +constant that's what a mode is and it's + + + align:start position:0% +constant that's what a mode is and it's +a character it's a property of the + + align:start position:0% +a character it's a property of the + + + align:start position:0% +a character it's a property of the +system the natural frequencies of + + align:start position:0% +system the natural frequencies of + + + align:start position:0% +system the natural frequencies of +property and the Shea + + align:start position:0% +property and the Shea + + + align:start position:0% +property and the Shea +type of every mode is a property of that + + align:start position:0% +type of every mode is a property of that + + + align:start position:0% +type of every mode is a property of that +system okay anything else questions next + + align:start position:0% +system okay anything else questions next + + + align:start position:0% +system okay anything else questions next +lecture we'll do more modal analysis we + + align:start position:0% +lecture we'll do more modal analysis we + + + align:start position:0% +lecture we'll do more modal analysis we +did the response to initial conditions + + align:start position:0% +did the response to initial conditions + + + align:start position:0% +did the response to initial conditions +yesterday Tuesday we'll talk about the + + align:start position:0% +yesterday Tuesday we'll talk about the + + + align:start position:0% +yesterday Tuesday we'll talk about the +response to external forces and then we + + align:start position:0% +response to external forces and then we + + + align:start position:0% +response to external forces and then we +give us a chance to review it and post + + align:start position:0% +give us a chance to review it and post + + + align:start position:0% +give us a chance to review it and post +it on stellar last night I put up a + + align:start position:0% +it on stellar last night I put up a + + + align:start position:0% +it on stellar last night I put up a +little two-page sheet that is a cookbook + + align:start position:0% +little two-page sheet that is a cookbook + + + align:start position:0% +little two-page sheet that is a cookbook +how to do the procedure of modal + + align:start position:0% +how to do the procedure of modal + + + align:start position:0% +how to do the procedure of modal +analysis it's a very cookbook you know + + align:start position:0% +analysis it's a very cookbook you know + + + align:start position:0% +analysis it's a very cookbook you know +just step by step bang bang bang and + + align:start position:0% +just step by step bang bang bang and + + + align:start position:0% +just step by step bang bang bang and +everything get everything falls out any + + align:start position:0% +everything get everything falls out any + + + align:start position:0% +everything get everything falls out any +other questions yeah is that where you + + align:start position:0% +other questions yeah is that where you + + + align:start position:0% +other questions yeah is that where you +get the mode shape by solving the + + align:start position:0% +get the mode shape by solving the + + + align:start position:0% +get the mode shape by solving the +characteristic you're doing it by hand + + align:start position:0% +characteristic you're doing it by hand + + + align:start position:0% +characteristic you're doing it by hand +by solving the characteristic equation + + align:start position:0% +by solving the characteristic equation + + + align:start position:0% +by solving the characteristic equation +which we're going to get some practice + + align:start position:0% +which we're going to get some practice + + + align:start position:0% +which we're going to get some practice +at today so I think this is the exercise + + align:start position:0% +at today so I think this is the exercise + + + align:start position:0% +at today so I think this is the exercise +of today's how to get natural + + align:start position:0% +of today's how to get natural + + + align:start position:0% +of today's how to get natural +frequencies and mode shapes as in a + + align:start position:0% +frequencies and mode shapes as in a + + + align:start position:0% +frequencies and mode shapes as in a +graph it shows the displacement of it or + + align:start position:0% +graph it shows the displacement of it or + + + align:start position:0% +graph it shows the displacement of it or +it shows the time history well sometimes + + align:start position:0% +it shows the time history well sometimes + + + align:start position:0% +it shows the time history well sometimes +to do if it's easy you know like for a + + align:start position:0% +to do if it's easy you know like for a + + + align:start position:0% +to do if it's easy you know like for a +vibrating string it's easy to draw the + + align:start position:0% +vibrating string it's easy to draw the + + + align:start position:0% +vibrating string it's easy to draw the +mode shape and it is yeah went into a + + align:start position:0% +mode shape and it is yeah went into a + + + align:start position:0% +mode shape and it is yeah went into a +vibrating string if first mode vibration + + align:start position:0% +vibrating string if first mode vibration + + + align:start position:0% +vibrating string if first mode vibration +looks like half a sine wave the mode + + align:start position:0% +looks like half a sine wave the mode + + + align:start position:0% +looks like half a sine wave the mode +shape is just half the sine way going up + + align:start position:0% +shape is just half the sine way going up + + + align:start position:0% +shape is just half the sine way going up +and down in space for this system the + + align:start position:0% +and down in space for this system the + + + align:start position:0% +and down in space for this system the +mode shape is to amp to different + + align:start position:0% +mode shape is to amp to different + + + align:start position:0% +mode shape is to amp to different +amplitudes of these two bobs and their + + align:start position:0% +amplitudes of these two bobs and their + + + align:start position:0% +amplitudes of these two bobs and their +relative motion we're going to figure + + align:start position:0% +relative motion we're going to figure + + + align:start position:0% +relative motion we're going to figure +that out today okay we better get the + + align:start position:0% +that out today okay we better get the + + + align:start position:0% +that out today okay we better get the +owner you won't finish so the good + + align:start position:0% +owner you won't finish so the good + + + align:start position:0% +owner you won't finish so the good +questions and + + align:start position:0% + + + + align:start position:0% + +here's the here's the system simplified + + align:start position:0% +here's the here's the system simplified + + + align:start position:0% +here's the here's the system simplified +just into two Bob's and Masel strings + + align:start position:0% +just into two Bob's and Masel strings + + + align:start position:0% +just into two Bob's and Masel strings +here's the equations of motion for that + + align:start position:0% +here's the equations of motion for that + + + align:start position:0% +here's the equations of motion for that +linear they've been linearized already + + align:start position:0% +linear they've been linearized already + + + align:start position:0% +linear they've been linearized already +there's no sine Thetas or anything and + + align:start position:0% +there's no sine Thetas or anything and + + + align:start position:0% +there's no sine Thetas or anything and +if part of the linearization so you + + align:start position:0% +if part of the linearization so you + + + align:start position:0% +if part of the linearization so you +enters this assumes then small + + align:start position:0% +enters this assumes then small + + + align:start position:0% +enters this assumes then small +amplitudes right it not only did the + + align:start position:0% +amplitudes right it not only did the + + + align:start position:0% +amplitudes right it not only did the +sine you know the torque for a pendulum + + align:start position:0% +sine you know the torque for a pendulum + + + align:start position:0% +sine you know the torque for a pendulum +you get this MGL sine theta term and so + + align:start position:0% +you get this MGL sine theta term and so + + + align:start position:0% +you get this MGL sine theta term and so +the linearization you say small angles + + align:start position:0% +the linearization you say small angles + + + align:start position:0% +the linearization you say small angles +sine theta becomes theta so that gives + + align:start position:0% +sine theta becomes theta so that gives + + + align:start position:0% +sine theta becomes theta so that gives +that's where this G over L sine theta is + + align:start position:0% +that's where this G over L sine theta is + + + align:start position:0% +that's where this G over L sine theta is +become theta term there's another + + align:start position:0% +become theta term there's another + + + align:start position:0% +become theta term there's another +assumption that's been made to model + + align:start position:0% +assumption that's been made to model + + + align:start position:0% +assumption that's been made to model +this system we're essentially modeling + + align:start position:0% +this system we're essentially modeling + + + align:start position:0% +this system we're essentially modeling +the system and that is for small angles + + align:start position:0% +the system and that is for small angles + + + align:start position:0% +the system and that is for small angles +are assuming the spring rains horizontal + + align:start position:0% +are assuming the spring rains horizontal + + + align:start position:0% +are assuming the spring rains horizontal +because if it the spring puts a force on + + align:start position:0% +because if it the spring puts a force on + + + align:start position:0% +because if it the spring puts a force on +the rod right and what you wants the + + align:start position:0% +the rod right and what you wants the + + + align:start position:0% +the rod right and what you wants the +torque about that point these two + + align:start position:0% +torque about that point these two + + + align:start position:0% +torque about that point these two +equations are the equations for torque + + align:start position:0% +equations are the equations for torque + + + align:start position:0% +equations are the equations for torque +about that point about that point and if + + align:start position:0% +about that point about that point and if + + + align:start position:0% +about that point about that point and if +the the torque is the spring force times + + align:start position:0% +the the torque is the spring force times + + + align:start position:0% +the the torque is the spring force times +that distance and if they're + + align:start position:0% +that distance and if they're + + + align:start position:0% +that distance and if they're +perpendicular it's just that's just one + + align:start position:0% +perpendicular it's just that's just one + + + align:start position:0% +perpendicular it's just that's just one +times the other but if it doesn't remain + + align:start position:0% +times the other but if it doesn't remain + + + align:start position:0% +times the other but if it doesn't remain +perpendicular they need have to take a + + align:start position:0% +perpendicular they need have to take a + + + align:start position:0% +perpendicular they need have to take a +cosine right and it gets really messy so + + align:start position:0% +cosine right and it gets really messy so + + + align:start position:0% +cosine right and it gets really messy so +another part of this small angle + + align:start position:0% +another part of this small angle + + + align:start position:0% +another part of this small angle +approximation is that spring stays + + align:start position:0% +approximation is that spring stays + + + align:start position:0% +approximation is that spring stays +horizontal all right there's your + + align:start position:0% +horizontal all right there's your + + + align:start position:0% +horizontal all right there's your +equation of motion and you can see + + align:start position:0% +equation of motion and you can see + + + align:start position:0% +equation of motion and you can see +what's happened here is that this used + + align:start position:0% +what's happened here is that this used + + + align:start position:0% +what's happened here is that this used +to have an m1 l1 squared that's the this + + align:start position:0% +to have an m1 l1 squared that's the this + + + align:start position:0% +to have an m1 l1 squared that's the this +is the mass moment of inertia of that + + align:start position:0% +is the mass moment of inertia of that + + + align:start position:0% +is the mass moment of inertia of that +mass we've divided through the equation + + align:start position:0% +mass we've divided through the equation + + + align:start position:0% +mass we've divided through the equation +by m1 l1 squared and that's put things + + align:start position:0% +by m1 l1 squared and that's put things + + + align:start position:0% +by m1 l1 squared and that's put things +in the bottom here like that then it + + align:start position:0% +in the bottom here like that then it + + + align:start position:0% +in the bottom here like that then it +just makes this actually a little easier + + align:start position:0% +just makes this actually a little easier + + + align:start position:0% +just makes this actually a little easier +to work with the mass matrix turns out + + align:start position:0% +to work with the mass matrix turns out + + + align:start position:0% +to work with the mass matrix turns out +to be 1:1 when you do this but it's + + align:start position:0% +to be 1:1 when you do this but it's + + + align:start position:0% +to be 1:1 when you do this but it's +still the same two equations of motion + + align:start position:0% +still the same two equations of motion + + + align:start position:0% +still the same two equations of motion +I've just divided through by m1 l + + align:start position:0% +I've just divided through by m1 l + + + align:start position:0% +I've just divided through by m1 l +squared and this one by m2 l squared so + + align:start position:0% +squared and this one by m2 l squared so + + + align:start position:0% +squared and this one by m2 l squared so +these are your equations of motion and + + align:start position:0% +these are your equations of motion and + + + align:start position:0% +these are your equations of motion and +your job is to come up first of all + + align:start position:0% +your job is to come up first of all + + + align:start position:0% +your job is to come up first of all +let's just put them in matrix form and + + align:start position:0% +let's just put them in matrix form and + + + align:start position:0% +let's just put them in matrix form and +you're going to do this in groups today + + align:start position:0% +you're going to do this in groups today + + + align:start position:0% +you're going to do this in groups today +we've got + + align:start position:0% +we've got + + + align:start position:0% +we've got +five 10 and 18 people so that's probably + + align:start position:0% +five 10 and 18 people so that's probably + + + align:start position:0% +five 10 and 18 people so that's probably +four groups of four work together in + + align:start position:0% +four groups of four work together in + + + align:start position:0% +four groups of four work together in +groups quickly let's put up the + + align:start position:0% +groups quickly let's put up the + + + align:start position:0% +groups quickly let's put up the +equations of motion from this in matrix + + align:start position:0% +equations of motion from this in matrix + + + align:start position:0% +equations of motion from this in matrix +form + + align:start position:0% + + + + align:start position:0% + +yeah and then walk out to one piece + + align:start position:0% + + + + align:start position:0% + +in your look in your lower left yeah + + align:start position:0% +in your look in your lower left yeah + + + align:start position:0% +in your look in your lower left yeah +matrix is is the oh the cake what I'm + + align:start position:0% +matrix is is the oh the cake what I'm + + + align:start position:0% +matrix is is the oh the cake what I'm +worried about the M oh there you go yeah + + align:start position:0% +worried about the M oh there you go yeah + + + align:start position:0% +worried about the M oh there you go yeah +just one there's a single kick the only + + align:start position:0% +just one there's a single kick the only + + + align:start position:0% +just one there's a single kick the only +one spring so we just call it cake okay + + align:start position:0% + + + + align:start position:0% + +alright you're all looking pretty good + + align:start position:0% +alright you're all looking pretty good + + + align:start position:0% +alright you're all looking pretty good +to me and the last hour we did this and + + align:start position:0% +to me and the last hour we did this and + + + align:start position:0% +to me and the last hour we did this and +it went up and I looked at it and I just + + align:start position:0% +it went up and I looked at it and I just + + + align:start position:0% +it went up and I looked at it and I just +had one of these moments of just Oh + + align:start position:0% +had one of these moments of just Oh + + + align:start position:0% +had one of these moments of just Oh +cognitive dissonance it just says how + + align:start position:0% +cognitive dissonance it just says how + + + align:start position:0% +cognitive dissonance it just says how +can that possibly be and the reason was + + align:start position:0% + + + + align:start position:0% + +this stiffness matrix this matrix is not + + align:start position:0% +this stiffness matrix this matrix is not + + + align:start position:0% +this stiffness matrix this matrix is not +diagonal not die scuse me I'm and wrong + + align:start position:0% +diagonal not die scuse me I'm and wrong + + + align:start position:0% +diagonal not die scuse me I'm and wrong +word this matrix is not symmetric and + + align:start position:0% +word this matrix is not symmetric and + + + align:start position:0% +word this matrix is not symmetric and +linear stiffness matrices are always + + align:start position:0% +linear stiffness matrices are always + + + align:start position:0% +linear stiffness matrices are always +symmetric so I saw this as is what has + + align:start position:0% +symmetric so I saw this as is what has + + + align:start position:0% +symmetric so I saw this as is what has +gone wrong every one of you had the same + + align:start position:0% +gone wrong every one of you had the same + + + align:start position:0% +gone wrong every one of you had the same +answer every one of you the resistance + + align:start position:0% +answer every one of you the resistance + + + align:start position:0% +answer every one of you the resistance +matrices are not symmetric it's minus K + + align:start position:0% +matrices are not symmetric it's minus K + + + align:start position:0% +matrices are not symmetric it's minus K +1 over m 1 and minus K minus K over m 1 + + align:start position:0% +1 over m 1 and minus K minus K over m 1 + + + align:start position:0% +1 over m 1 and minus K minus K over m 1 +minus K over m 2 in it I did by had a + + align:start position:0% +minus K over m 2 in it I did by had a + + + align:start position:0% +minus K over m 2 in it I did by had a +heart failure I've been doing this for + + align:start position:0% +heart failure I've been doing this for + + + align:start position:0% +heart failure I've been doing this for +you know 40 years and it's always been + + align:start position:0% +you know 40 years and it's always been + + + align:start position:0% +you know 40 years and it's always been +symmetric and almost said you guys + + align:start position:0% +symmetric and almost said you guys + + + align:start position:0% +symmetric and almost said you guys +unanimously get asymmetric so I figured + + align:start position:0% +unanimously get asymmetric so I figured + + + align:start position:0% +unanimously get asymmetric so I figured +it out + + align:start position:0% +it out + + + align:start position:0% +it out +a great relief we divided through by m1 + + align:start position:0% +a great relief we divided through by m1 + + + align:start position:0% +a great relief we divided through by m1 +l1 squared in the first + + align:start position:0% +l1 squared in the first + + + align:start position:0% +l1 squared in the first +and m2 l2 squared in the second equation + + align:start position:0% +and m2 l2 squared in the second equation + + + align:start position:0% +and m2 l2 squared in the second equation +the stiffness matrix by just the true + + align:start position:0% +the stiffness matrix by just the true + + + align:start position:0% +the stiffness matrix by just the true +stiffness matrix hasn't been divided + + align:start position:0% +stiffness matrix hasn't been divided + + + align:start position:0% +stiffness matrix hasn't been divided +through by the ML Squared's and it is + + align:start position:0% +through by the ML Squared's and it is + + + align:start position:0% +through by the ML Squared's and it is +indeed symmetric okay it's one of the + + align:start position:0% +indeed symmetric okay it's one of the + + + align:start position:0% +indeed symmetric okay it's one of the +things that's really helpful to know + + align:start position:0% +things that's really helpful to know + + + align:start position:0% +things that's really helpful to know +because when you're working these things + + align:start position:0% +because when you're working these things + + + align:start position:0% +because when you're working these things +out if there's something you know the + + align:start position:0% +out if there's something you know the + + + align:start position:0% +out if there's something you know the +symmetric you don't have to evaluate all + + align:start position:0% +symmetric you don't have to evaluate all + + + align:start position:0% +symmetric you don't have to evaluate all +the terms you only have to do the + + align:start position:0% +the terms you only have to do the + + + align:start position:0% +the terms you only have to do the +diagonals and a half of the ones the + + align:start position:0% +diagonals and a half of the ones the + + + align:start position:0% +diagonals and a half of the ones the +mass matrices you use these symmetric to + + align:start position:0% +mass matrices you use these symmetric to + + + align:start position:0% +mass matrices you use these symmetric to +there's maybe some exceptions if you + + align:start position:0% +there's maybe some exceptions if you + + + align:start position:0% +there's maybe some exceptions if you +start putting in gyroscopes and stuff + + align:start position:0% +start putting in gyroscopes and stuff + + + align:start position:0% +start putting in gyroscopes and stuff +like that but then it's not very linear + + align:start position:0% +like that but then it's not very linear + + + align:start position:0% +like that but then it's not very linear +okay so your next task is to the way we + + align:start position:0% +okay so your next task is to the way we + + + align:start position:0% +okay so your next task is to the way we +find we find natural frequencies mode + + align:start position:0% +find we find natural frequencies mode + + + align:start position:0% +find we find natural frequencies mode +shapes kind of the hard way doing use + + align:start position:0% +shapes kind of the hard way doing use + + + align:start position:0% +shapes kind of the hard way doing use +and algebra is to find the caret what we + + align:start position:0% +and algebra is to find the caret what we + + + align:start position:0% +and algebra is to find the caret what we +call the characteristic equation alright + + align:start position:0% +call the characteristic equation alright + + + align:start position:0% +call the characteristic equation alright +it turns out to be a fourth order + + align:start position:0% +it turns out to be a fourth order + + + align:start position:0% +it turns out to be a fourth order +equation and make it to the fourth find + + align:start position:0% +equation and make it to the fourth find + + + align:start position:0% +equation and make it to the fourth find +it don't solve it just write down the + + align:start position:0% +it don't solve it just write down the + + + align:start position:0% +it don't solve it just write down the +acoustic equation for this thing that's + + align:start position:0% +acoustic equation for this thing that's + + + align:start position:0% +acoustic equation for this thing that's +you're up then as soon as you have that + + align:start position:0% +you're up then as soon as you have that + + + align:start position:0% +you're up then as soon as you have that +come up write it down to remember you + + align:start position:0% +come up write it down to remember you + + + align:start position:0% +come up write it down to remember you +basically have matrices this is the what + + align:start position:0% +basically have matrices this is the what + + + align:start position:0% +basically have matrices this is the what +you're working with you've got something + + align:start position:0% +you're working with you've got something + + + align:start position:0% +you're working with you've got something +of this form we've normally divided + + align:start position:0% +of this form we've normally divided + + + align:start position:0% +of this form we've normally divided +through by some stuff to collect terms + + align:start position:0% +through by some stuff to collect terms + + + align:start position:0% +through by some stuff to collect terms +but how do you go about going from the + + align:start position:0% +but how do you go about going from the + + + align:start position:0% +but how do you go about going from the +equations of motion to your algebraic + + align:start position:0% +equations of motion to your algebraic + + + align:start position:0% +equations of motion to your algebraic +equation you know make it to the fourth + + align:start position:0% + + + + align:start position:0% + +I want you to write up the edges want + + align:start position:0% +I want you to write up the edges want + + + align:start position:0% +I want you to write up the edges want +you right up the characteristic equation + + align:start position:0% +you right up the characteristic equation + + + align:start position:0% +you right up the characteristic equation +you're going to get a quadratic and + + align:start position:0% +you're going to get a quadratic and + + + align:start position:0% +you're going to get a quadratic and +Omega to the fourth just we're open + + align:start position:0% +Omega to the fourth just we're open + + + align:start position:0% +Omega to the fourth just we're open +write down the equation I expand what do + + align:start position:0% +write down the equation I expand what do + + + align:start position:0% +write down the equation I expand what do +you mean well you send if I want an + + align:start position:0% +you mean well you send if I want an + + + align:start position:0% +you mean well you send if I want an +equation a negative fourth just write it + + align:start position:0% +equation a negative fourth just write it + + + align:start position:0% +equation a negative fourth just write it +just write one up there and if you want + + align:start position:0% +just write one up there and if you want + + + align:start position:0% +just write one up there and if you want +to simplify the writing you can let H + + align:start position:0% +to simplify the writing you can let H + + + align:start position:0% +to simplify the writing you can let H +equal oh and buy let's see you know I + + align:start position:0% +equal oh and buy let's see you know I + + + align:start position:0% +equal oh and buy let's see you know I +forgot to tell you something the key + + align:start position:0% +forgot to tell you something the key + + + align:start position:0% +forgot to tell you something the key +assumption here key thing is going to + + align:start position:0% +assumption here key thing is going to + + + align:start position:0% +assumption here key thing is going to +make it easier for you let ya sorry my + + align:start position:0% +make it easier for you let ya sorry my + + + align:start position:0% +make it easier for you let ya sorry my +mistake + + align:start position:0% +mistake + + + align:start position:0% +mistake +let the m2 be equal then it makes it a + + align:start position:0% +let the m2 be equal then it makes it a + + + align:start position:0% +let the m2 be equal then it makes it a +lot easier and then you can say call H G + + align:start position:0% +lot easier and then you can say call H G + + + align:start position:0% +lot easier and then you can say call H G +over L plus K over m and it'll kind of + + align:start position:0% +over L plus K over m and it'll kind of + + + align:start position:0% +over L plus K over m and it'll kind of +make the quote make the equation a whole + + align:start position:0% +make the quote make the equation a whole + + + align:start position:0% +make the quote make the equation a whole +lot easier to write + + align:start position:0% + + + + align:start position:0% + +right okay people are getting all the + + align:start position:0% +right okay people are getting all the + + + align:start position:0% +right okay people are getting all the +same answers here that's so good okay so + + align:start position:0% +same answers here that's so good okay so + + + align:start position:0% +same answers here that's so good okay so +the next step is I will give you you + + align:start position:0% +the next step is I will give you you + + + align:start position:0% +the next step is I will give you you +solve this you get omega 1.is G over L + + align:start position:0% +solve this you get omega 1.is G over L + + + align:start position:0% +solve this you get omega 1.is G over L +like 1 squared is G over L and a mega 2 + + align:start position:0% +like 1 squared is G over L and a mega 2 + + + align:start position:0% +like 1 squared is G over L and a mega 2 +squared is G over L plus 2 K over m + + align:start position:0% +squared is G over L plus 2 K over m + + + align:start position:0% +squared is G over L plus 2 K over m +those are two natural frequencies so now + + align:start position:0% +those are two natural frequencies so now + + + align:start position:0% +those are two natural frequencies so now +find the mode shapes find the mode + + align:start position:0% +find the mode shapes find the mode + + + align:start position:0% +find the mode shapes find the mode +shapes if you know the natural + + align:start position:0% +shapes if you know the natural + + + align:start position:0% +shapes if you know the natural +frequencies now you go back in and you + + align:start position:0% +frequencies now you go back in and you + + + align:start position:0% +frequencies now you go back in and you +get a lift + + align:start position:0% +get a lift + + + align:start position:0% +get a lift +pardon yeah keep H if I think H will + + align:start position:0% +pardon yeah keep H if I think H will + + + align:start position:0% +pardon yeah keep H if I think H will +things will fall out rather quickly well + + align:start position:0% +things will fall out rather quickly well + + + align:start position:0% +things will fall out rather quickly well +I like to zoo I like to normalize the + + align:start position:0% +I like to zoo I like to normalize the + + + align:start position:0% +I like to zoo I like to normalize the +mode shapes so the top one is 1 and so + + align:start position:0% +mode shapes so the top one is 1 and so + + + align:start position:0% +mode shapes so the top one is 1 and so +the top with the top element of the mode + + align:start position:0% +the top with the top element of the mode + + + align:start position:0% +the top with the top element of the mode +shape vector I call a 1 or u1 down + + align:start position:0% +shape vector I call a 1 or u1 down + + + align:start position:0% +shape vector I call a 1 or u1 down +through u N and so if you divide out + + align:start position:0% +through u N and so if you divide out + + + align:start position:0% +through u N and so if you divide out +each one by the top one the top one + + align:start position:0% +each one by the top one the top one + + + align:start position:0% +each one by the top one the top one +becomes 1 the second one becomes a2 over + + align:start position:0% +becomes 1 the second one becomes a2 over + + + align:start position:0% +becomes 1 the second one becomes a2 over +a1 the third one of its three degree + + align:start position:0% +a1 the third one of its three degree + + + align:start position:0% +a1 the third one of its three degree +freedom be a 3 over a1 when the fact + + align:start position:0% +freedom be a 3 over a1 when the fact + + + align:start position:0% +freedom be a 3 over a1 when the fact +that this equal you know you just solve + + align:start position:0% +that this equal you know you just solve + + + align:start position:0% +that this equal you know you just solve +this equation to get to get that + + align:start position:0% +this equation to get to get that + + + align:start position:0% +this equation to get to get that +characteristic determinant you said this + + align:start position:0% +characteristic determinant you said this + + + align:start position:0% +characteristic determinant you said this +was true and when that's a particular + + align:start position:0% +was true and when that's a particular + + + align:start position:0% +was true and when that's a particular +kind of situation where you have linear + + align:start position:0% +kind of situation where you have linear + + + align:start position:0% +kind of situation where you have linear +a set of linear homogeneous equations + + align:start position:0% +a set of linear homogeneous equations + + + align:start position:0% +a set of linear homogeneous equations +equal to 0 they're not independent + + align:start position:0% +equal to 0 they're not independent + + + align:start position:0% +equal to 0 they're not independent +remember from algebra when you have a + + align:start position:0% +remember from algebra when you have a + + + align:start position:0% +remember from algebra when you have a +equations with constant coefficients and + + align:start position:0% +equations with constant coefficients and + + + align:start position:0% +equations with constant coefficients and +you have no the they're equal to a + + align:start position:0% +you have no the they're equal to a + + + align:start position:0% +you have no the they're equal to a +constant in the constants are all 0 + + align:start position:0% +constant in the constants are all 0 + + + align:start position:0% +constant in the constants are all 0 +means if they are not independent + + align:start position:0% +means if they are not independent + + + align:start position:0% +means if they are not independent +equations so this is two equations and + + align:start position:0% +equations so this is two equations and + + + align:start position:0% +equations so this is two equations and +two unknowns and they're not independent + + align:start position:0% +two unknowns and they're not independent + + + align:start position:0% +two unknowns and they're not independent +you won't be able to solve for unique + + align:start position:0% +you won't be able to solve for unique + + + align:start position:0% +you won't be able to solve for unique +values of a1 u1 and u2 you only be able + + align:start position:0% +values of a1 u1 and u2 you only be able + + + align:start position:0% +values of a1 u1 and u2 you only be able +to get the ratio so you're solved + + align:start position:0% +to get the ratio so you're solved + + + align:start position:0% +to get the ratio so you're solved +basically you found this value you're + + align:start position:0% +basically you found this value you're + + + align:start position:0% +basically you found this value you're +going to plug in a value for Omega + + align:start position:0% +going to plug in a value for Omega + + + align:start position:0% +going to plug in a value for Omega +squared and find out the values of a1 + + align:start position:0% +squared and find out the values of a1 + + + align:start position:0% +squared and find out the values of a1 +a tooth at work that's what the mode + + align:start position:0% +a tooth at work that's what the mode + + + align:start position:0% +a tooth at work that's what the mode +shapes are let's let me pull you back + + align:start position:0% +shapes are let's let me pull you back + + + align:start position:0% +shapes are let's let me pull you back +together here and let's run through this + + align:start position:0% +together here and let's run through this + + + align:start position:0% +together here and let's run through this +kind of quickly you've basically solved + + align:start position:0% +kind of quickly you've basically solved + + + align:start position:0% +kind of quickly you've basically solved +this equation you said I'm going to + + align:start position:0% +this equation you said I'm going to + + + align:start position:0% +this equation you said I'm going to +assume this thing it has a mode shape + + align:start position:0% +assume this thing it has a mode shape + + + align:start position:0% +assume this thing it has a mode shape +and a frequency you know a harmonic it's + + align:start position:0% +and a frequency you know a harmonic it's + + + align:start position:0% +and a frequency you know a harmonic it's +going to vibrate son damn so it's either + + align:start position:0% +going to vibrate son damn so it's either + + + align:start position:0% +going to vibrate son damn so it's either +you could write this as cosine Omega T + + align:start position:0% +you could write this as cosine Omega T + + + align:start position:0% +you could write this as cosine Omega T +sine Omega T e to the I Omega T but it + + align:start position:0% +sine Omega T e to the I Omega T but it + + + align:start position:0% +sine Omega T e to the I Omega T but it +has some constants out here called the + + align:start position:0% +has some constants out here called the + + + align:start position:0% +has some constants out here called the +shape you plug it in to the you plug + + align:start position:0% +shape you plug it in to the you plug + + + align:start position:0% +shape you plug it in to the you plug +that into the equations of motion you're + + align:start position:0% +that into the equations of motion you're + + + align:start position:0% +that into the equations of motion you're +going to get big that you get back this + + align:start position:0% +going to get big that you get back this + + + align:start position:0% +going to get big that you get back this +expression the two derivatives the theta + + align:start position:0% +expression the two derivatives the theta + + + align:start position:0% +expression the two derivatives the theta +double dot to give you the minus Omega + + align:start position:0% +double dot to give you the minus Omega + + + align:start position:0% +double dot to give you the minus Omega +square it's right you can write it like + + align:start position:0% +square it's right you can write it like + + + align:start position:0% +square it's right you can write it like +that you can throw away the e to the I + + align:start position:0% +that you can throw away the e to the I + + + align:start position:0% +that you can throw away the e to the I +Omega T in this case I've expanded this + + align:start position:0% +Omega T in this case I've expanded this + + + align:start position:0% +Omega T in this case I've expanded this +mm is just that one one matrix so this + + align:start position:0% +mm is just that one one matrix so this + + + align:start position:0% +mm is just that one one matrix so this +part looks like this the K matrix looks + + align:start position:0% +part looks like this the K matrix looks + + + align:start position:0% +part looks like this the K matrix looks +like this you can add them element by + + align:start position:0% +like this you can add them element by + + + align:start position:0% +like this you can add them element by +element so this is minus Omega squared + + align:start position:0% +element so this is minus Omega squared + + + align:start position:0% +element so this is minus Omega squared +plus h minus K over m this one is minus + + align:start position:0% +plus h minus K over m this one is minus + + + align:start position:0% +plus h minus K over m this one is minus +K over m and this term is minus Omega + + align:start position:0% +K over m and this term is minus Omega + + + align:start position:0% +K over m and this term is minus Omega +squared plus h again right times u1 or + + align:start position:0% +squared plus h again right times u1 or + + + align:start position:0% +squared plus h again right times u1 or +u2 the two elements that we're looking + + align:start position:0% +u2 the two elements that we're looking + + + align:start position:0% +u2 the two elements that we're looking +for that's two equations into this is + + align:start position:0% +for that's two equations into this is + + + align:start position:0% +for that's two equations into this is +just now an algebraic equation to + + align:start position:0% +just now an algebraic equation to + + + align:start position:0% +just now an algebraic equation to +algebraic equations this times u1 minus + + align:start position:0% +algebraic equations this times u1 minus + + + align:start position:0% +algebraic equations this times u1 minus +K over m times u2 and the second + + align:start position:0% +K over m times u2 and the second + + + align:start position:0% +K over m times u2 and the second +equation is phat now we know there + + align:start position:0% +equation is phat now we know there + + + align:start position:0% +equation is phat now we know there +there's only two equations and not + + align:start position:0% +there's only two equations and not + + + align:start position:0% +there's only two equations and not +linearly independent so you actually + + align:start position:0% +linearly independent so you actually + + + align:start position:0% +linearly independent so you actually +only have one useful equation if it's a + + align:start position:0% +only have one useful equation if it's a + + + align:start position:0% +only have one useful equation if it's a +three by three you'd have they're not + + align:start position:0% +three by three you'd have they're not + + + align:start position:0% +three by three you'd have they're not +independent but you need to use two out + + align:start position:0% +independent but you need to use two out + + + align:start position:0% +independent but you need to use two out +of the three yeah + + align:start position:0% +of the three yeah + + + align:start position:0% +of the three yeah +second one I take the first one and I + + align:start position:0% +second one I take the first one and I + + + align:start position:0% +second one I take the first one and I +multiply it up here and that gives me an + + align:start position:0% +multiply it up here and that gives me an + + + align:start position:0% +multiply it up here and that gives me an +equation this times u1 plus this times + + align:start position:0% +equation this times u1 plus this times + + + align:start position:0% +equation this times u1 plus this times +u2 that's equation one I take this and I + + align:start position:0% +u2 that's equation one I take this and I + + + align:start position:0% +u2 that's equation one I take this and I +multiply by that and I get minus K over + + align:start position:0% +multiply by that and I get minus K over + + + align:start position:0% +multiply by that and I get minus K over +m u2 and this is u1 + + align:start position:0% +m u2 and this is u1 + + + align:start position:0% +m u2 and this is u1 +this is the Omega squared I plugged in + + align:start position:0% +this is the Omega squared I plugged in + + + align:start position:0% +this is the Omega squared I plugged in +the natural frequencies that we saw for + + align:start position:0% +the natural frequencies that we saw for + + + align:start position:0% +the natural frequencies that we saw for +right Oh minus Omega squared okay I'm + + align:start position:0% +right Oh minus Omega squared okay I'm + + + align:start position:0% +right Oh minus Omega squared okay I'm +picking one of the natural frequencies G + + align:start position:0% +picking one of the natural frequencies G + + + align:start position:0% +picking one of the natural frequencies G +over L so this is up here is G over L + + align:start position:0% +over L so this is up here is G over L + + + align:start position:0% +over L so this is up here is G over L +plus h u1 my that one down here it's G + + align:start position:0% +plus h u1 my that one down here it's G + + + align:start position:0% +plus h u1 my that one down here it's G +over L hu - and you see these two + + align:start position:0% +over L hu - and you see these two + + + align:start position:0% +over L hu - and you see these two +equations turn out to be this year you + + align:start position:0% +equations turn out to be this year you + + + align:start position:0% +equations turn out to be this year you +want to do it one at a time you just + + align:start position:0% +want to do it one at a time you just + + + align:start position:0% +want to do it one at a time you just +plug in one of the natural frequencies + + align:start position:0% +plug in one of the natural frequencies + + + align:start position:0% +plug in one of the natural frequencies +and you get two equations in two + + align:start position:0% +and you get two equations in two + + + align:start position:0% +and you get two equations in two +unknowns and they're going to each give + + align:start position:0% +unknowns and they're going to each give + + + align:start position:0% +unknowns and they're going to each give +you exactly the same information they're + + align:start position:0% +you exactly the same information they're + + + align:start position:0% +you exactly the same information they're +not independent any longer so you solve + + align:start position:0% +not independent any longer so you solve + + + align:start position:0% +not independent any longer so you solve +this one H it has what in it a plus G + + align:start position:0% +this one H it has what in it a plus G + + + align:start position:0% +this one H it has what in it a plus G +over L and a plus K over m right + + align:start position:0% +over L and a plus K over m right + + + align:start position:0% +over L and a plus K over m right +the G over L p-- is cancelled and you're + + align:start position:0% +the G over L p-- is cancelled and you're + + + align:start position:0% +the G over L p-- is cancelled and you're +left with K over m u1 minus K over m u2 + + align:start position:0% +left with K over m u1 minus K over m u2 + + + align:start position:0% +left with K over m u1 minus K over m u2 +equals zero if this implies that u1 + + align:start position:0% +equals zero if this implies that u1 + + + align:start position:0% +equals zero if this implies that u1 +equals u - right + + align:start position:0% + + + + align:start position:0% + +this is the G over L in this I'm going + + align:start position:0% +this is the G over L in this I'm going + + + align:start position:0% +this is the G over L in this I'm going +to plug in the that is H I just put it + + align:start position:0% +to plug in the that is H I just put it + + + align:start position:0% +to plug in the that is H I just put it +in here I've plugged in one of the + + align:start position:0% +in here I've plugged in one of the + + + align:start position:0% +in here I've plugged in one of the +natural frequency squared the G over L + + align:start position:0% +natural frequency squared the G over L + + + align:start position:0% +natural frequency squared the G over L +ports cancel this is plus K over mu 1 + + align:start position:0% +ports cancel this is plus K over mu 1 + + + align:start position:0% +ports cancel this is plus K over mu 1 +minus K over mu 2 that means K over m u + + align:start position:0% +minus K over mu 2 that means K over m u + + + align:start position:0% +minus K over mu 2 that means K over m u +1 equals K over mu to cancel out the K + + align:start position:0% +1 equals K over mu to cancel out the K + + + align:start position:0% +1 equals K over mu to cancel out the K +over m I get that it just tells me that + + align:start position:0% +over m I get that it just tells me that + + + align:start position:0% +over m I get that it just tells me that +that's the answer and I'm if that's the + + align:start position:0% +that's the answer and I'm if that's the + + + align:start position:0% +that's the answer and I'm if that's the +answer the vector looks like u1 u2 + + align:start position:0% +answer the vector looks like u1 u2 + + + align:start position:0% +answer the vector looks like u1 u2 +that's also equal to factor out of U 1 u + + align:start position:0% +that's also equal to factor out of U 1 u + + + align:start position:0% +that's also equal to factor out of U 1 u +1 times 1 + u2 over u1 that's that's the + + align:start position:0% +1 times 1 + u2 over u1 that's that's the + + + align:start position:0% +1 times 1 + u2 over u1 that's that's the +mode shape there 1 + u2 over u1 that's + + align:start position:0% +mode shape there 1 + u2 over u1 that's + + + align:start position:0% +mode shape there 1 + u2 over u1 that's +how you factor it out to put it in the + + align:start position:0% +how you factor it out to put it in the + + + align:start position:0% +how you factor it out to put it in the +normalized form you just take whatever's + + align:start position:0% +normalized form you just take whatever's + + + align:start position:0% +normalized form you just take whatever's +in the top one and divide everything in + + align:start position:0% +in the top one and divide everything in + + + align:start position:0% +in the top one and divide everything in +the column by it so to do the second + + align:start position:0% +the column by it so to do the second + + + align:start position:0% +the column by it so to do the second +equation you just now go back to this + + align:start position:0% +equation you just now go back to this + + + align:start position:0% +equation you just now go back to this +plug in for Omega 2 squared the second + + align:start position:0% +plug in for Omega 2 squared the second + + + align:start position:0% +plug in for Omega 2 squared the second +natural frequency is G over L plus 2 K + + align:start position:0% +natural frequency is G over L plus 2 K + + + align:start position:0% +natural frequency is G over L plus 2 K +over m this is G over L minus K over m + + align:start position:0% +over m this is G over L minus K over m + + + align:start position:0% +over m this is G over L minus K over m +the K over m s cancel and you just left + + align:start position:0% +the K over m s cancel and you just left + + + align:start position:0% +the K over m s cancel and you just left +with G over L you work this through + + align:start position:0% +with G over L you work this through + + + align:start position:0% +with G over L you work this through +you're going to find out that u 2 equals + + align:start position:0% +you're going to find out that u 2 equals + + + align:start position:0% +you're going to find out that u 2 equals +minus u1 if you put in the second one + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +so we have a 1 over 80 group you want to + + align:start position:0% +so we have a 1 over 80 group you want to + + + align:start position:0% +so we have a 1 over 80 group you want to +be so obviously + + align:start position:0% + + + + align:start position:0% + +but I don't understand you just like + + align:start position:0% +but I don't understand you just like + + + align:start position:0% +but I don't understand you just like +plug back into you then you sit like you + + align:start position:0% +plug back into you then you sit like you + + + align:start position:0% +plug back into you then you sit like you +want over you do people do whatever you + + align:start position:0% +want over you do people do whatever you + + + align:start position:0% +want over you do people do whatever you +do well when you solve this you find + + align:start position:0% +do well when you solve this you find + + + align:start position:0% +do well when you solve this you find +that K over m u1 equals K over m u2 + + align:start position:0% +that K over m u1 equals K over m u2 + + + align:start position:0% +that K over m u1 equals K over m u2 +right that's just saying in this case + + align:start position:0% +right that's just saying in this case + + + align:start position:0% +right that's just saying in this case +they are equal period that's and that's + + align:start position:0% +they are equal period that's and that's + + + align:start position:0% +they are equal period that's and that's +all you learn you only have two + + align:start position:0% +all you learn you only have two + + + align:start position:0% +all you learn you only have two +equations and they're not independence + + align:start position:0% +equations and they're not independence + + + align:start position:0% +equations and they're not independence +of means you only have one equation and + + align:start position:0% +of means you only have one equation and + + + align:start position:0% +of means you only have one equation and +you don't learn you're not able to solve + + align:start position:0% +you don't learn you're not able to solve + + + align:start position:0% +you don't learn you're not able to solve +for numeric values of u1 and u2 at best + + align:start position:0% +for numeric values of u1 and u2 at best + + + align:start position:0% +for numeric values of u1 and u2 at best +you can get u 1 over u 2 right so you + + align:start position:0% +you can get u 1 over u 2 right so you + + + align:start position:0% +you can get u 1 over u 2 right so you +can in fact you can just solve this for + + align:start position:0% +can in fact you can just solve this for + + + align:start position:0% +can in fact you can just solve this for +u u2 over u1 and it would be 1 ok well + + align:start position:0% +u u2 over u1 and it would be 1 ok well + + + align:start position:0% +u u2 over u1 and it would be 1 ok well +that's my back in my vector format I + + align:start position:0% +that's my back in my vector format I + + + align:start position:0% +that's my back in my vector format I +want to write the mode shape as a vector + + align:start position:0% +want to write the mode shape as a vector + + + align:start position:0% +want to write the mode shape as a vector +you've solved for you one for you one so + + align:start position:0% +you've solved for you one for you one so + + + align:start position:0% +you've solved for you one for you one so +you could actually do this you can take + + align:start position:0% +you could actually do this you can take + + + align:start position:0% +you could actually do this you can take +you know that that's true you say well + + align:start position:0% +you know that that's true you say well + + + align:start position:0% +you know that that's true you say well +top ones one and the bottom one is the + + align:start position:0% +top ones one and the bottom one is the + + + align:start position:0% +top ones one and the bottom one is the +same as that so the mode shape remote + + align:start position:0% +same as that so the mode shape remote + + + align:start position:0% +same as that so the mode shape remote +one is that if you want to do one + + align:start position:0% +one is that if you want to do one + + + align:start position:0% +one is that if you want to do one +the ratio of two more days there's a I'm + + align:start position:0% +the ratio of two more days there's a I'm + + + align:start position:0% +the ratio of two more days there's a I'm +using use and some of their use days + + align:start position:0% +using use and some of their use days + + + align:start position:0% +using use and some of their use days +they're the elements of the mochit + + align:start position:0% +they're the elements of the mochit + + + align:start position:0% +they're the elements of the mochit +vector okay so we had put in the other + + align:start position:0% +vector okay so we had put in the other + + + align:start position:0% +vector okay so we had put in the other +natural frequency instead of I'm am just + + align:start position:0% +natural frequency instead of I'm am just + + + align:start position:0% +natural frequency instead of I'm am just +drawn too many steps here at once to so + + align:start position:0% +drawn too many steps here at once to so + + + align:start position:0% +drawn too many steps here at once to so +our first equation looks like minus + + align:start position:0% +our first equation looks like minus + + + align:start position:0% +our first equation looks like minus +Omega squared plus h minus K K over m + + align:start position:0% +Omega squared plus h minus K K over m + + + align:start position:0% +Omega squared plus h minus K K over m +and the second equation is minus K over + + align:start position:0% +and the second equation is minus K over + + + align:start position:0% +and the second equation is minus K over +m and over here is minus Omega squared + + align:start position:0% +m and over here is minus Omega squared + + + align:start position:0% +m and over here is minus Omega squared +plus h again that's our matrix when we + + align:start position:0% +plus h again that's our matrix when we + + + align:start position:0% +plus h again that's our matrix when we +add these two matrices together the + + align:start position:0% +add these two matrices together the + + + align:start position:0% +add these two matrices together the +minus Omega squared M plus K that's what + + align:start position:0% +minus Omega squared M plus K that's what + + + align:start position:0% +minus Omega squared M plus K that's what +it looks like when you add the elements + + align:start position:0% +it looks like when you add the elements + + + align:start position:0% +it looks like when you add the elements +together right + + align:start position:0% +together right + + + align:start position:0% +together right +and we're looking these are two + + align:start position:0% +and we're looking these are two + + + align:start position:0% +and we're looking these are two +equations and two unknowns we're looking + + align:start position:0% +equations and two unknowns we're looking + + + align:start position:0% +equations and two unknowns we're looking +for the answer for some u1 u2 multiplied + + align:start position:0% +for the answer for some u1 u2 multiplied + + + align:start position:0% +for the answer for some u1 u2 multiplied +by this so you multiply this out you get + + align:start position:0% +by this so you multiply this out you get + + + align:start position:0% +by this so you multiply this out you get +minus Omega squared plus h u1 minus K + + align:start position:0% +minus Omega squared plus h u1 minus K + + + align:start position:0% +minus Omega squared plus h u1 minus K +over m u2 and now let's plug in the + + align:start position:0% +over m u2 and now let's plug in the + + + align:start position:0% +over m u2 and now let's plug in the +second natural frequency so mega two + + align:start position:0% +second natural frequency so mega two + + + align:start position:0% +second natural frequency so mega two +squared is that and solve for the second + + align:start position:0% +squared is that and solve for the second + + + align:start position:0% +squared is that and solve for the second +mode now plug it in here we get minus G + + align:start position:0% +mode now plug it in here we get minus G + + + align:start position:0% +mode now plug it in here we get minus G +over L minus two K over m plus h which + + align:start position:0% +over L minus two K over m plus h which + + + align:start position:0% +over L minus two K over m plus h which +is G over L plus K over m plus and + + align:start position:0% +is G over L plus K over m plus and + + + align:start position:0% +is G over L plus K over m plus and +that's times u1 plus K over m u2 right + + align:start position:0% +that's times u1 plus K over m u2 right + + + align:start position:0% +that's times u1 plus K over m u2 right +all that's equal to zero + + align:start position:0% +all that's equal to zero + + + align:start position:0% +all that's equal to zero +this cancels this this this plus one + + align:start position:0% +this cancels this this this plus one + + + align:start position:0% +this cancels this this this plus one +minus two I get a minus K over m out of + + align:start position:0% +minus two I get a minus K over m out of + + + align:start position:0% +minus two I get a minus K over m out of +this so I have this whole thing gives me + + align:start position:0% +this so I have this whole thing gives me + + + align:start position:0% +this so I have this whole thing gives me +minus K over mu 1 plus K over m u 2 + + align:start position:0% + + + + align:start position:0% + +which should i agree with you where did + + align:start position:0% +which should i agree with you where did + + + align:start position:0% +which should i agree with you where did +I make the mistake oh good all right and + + align:start position:0% +I make the mistake oh good all right and + + + align:start position:0% +I make the mistake oh good all right and +this is equal to 0 k over m is cancel + + align:start position:0% +this is equal to 0 k over m is cancel + + + align:start position:0% +this is equal to 0 k over m is cancel +out and you find that this implies that + + align:start position:0% +out and you find that this implies that + + + align:start position:0% +out and you find that this implies that +u 1 equals minus u 2 and so the mode + + align:start position:0% +u 1 equals minus u 2 and so the mode + + + align:start position:0% +u 1 equals minus u 2 and so the mode +shape for two for mode two you could + + align:start position:0% +shape for two for mode two you could + + + align:start position:0% +shape for two for mode two you could +write as u 1 and u 2 is minus u 1 if you + + align:start position:0% +write as u 1 and u 2 is minus u 1 if you + + + align:start position:0% +write as u 1 and u 2 is minus u 1 if you +will and it's obvious if you factor out + + align:start position:0% +will and it's obvious if you factor out + + + align:start position:0% +will and it's obvious if you factor out +u 1 you get u 1 and a 1 minus 1 right so + + align:start position:0% +u 1 you get u 1 and a 1 minus 1 right so + + + align:start position:0% +u 1 you get u 1 and a 1 minus 1 right so +now you've solved through the second + + align:start position:0% +now you've solved through the second + + + align:start position:0% +now you've solved through the second +mode shape if this had been more than a + + align:start position:0% +mode shape if this had been more than a + + + align:start position:0% +mode shape if this had been more than a +two by two like a three by three degree + + align:start position:0% +two by two like a three by three degree + + + align:start position:0% +two by two like a three by three degree +freedom system you would get 2 you'd + + align:start position:0% +freedom system you would get 2 you'd + + + align:start position:0% +freedom system you would get 2 you'd +have to use two of the three equations + + align:start position:0% +have to use two of the three equations + + + align:start position:0% +have to use two of the three equations +to get the ratio you'd get two equations + + align:start position:0% +to get the ratio you'd get two equations + + + align:start position:0% +to get the ratio you'd get two equations +in three unknowns and at best you can + + align:start position:0% +in three unknowns and at best you can + + + align:start position:0% +in three unknowns and at best you can +find the two of them in terms of the + + align:start position:0% +find the two of them in terms of the + + + align:start position:0% +find the two of them in terms of the +third and the third one would be u 1 you + + align:start position:0% +third and the third one would be u 1 you + + + align:start position:0% +third and the third one would be u 1 you +just divide out all the others by u 1 so + + align:start position:0% +just divide out all the others by u 1 so + + + align:start position:0% +just divide out all the others by u 1 so +you want to get their ratios okay so + + align:start position:0% +you want to get their ratios okay so + + + align:start position:0% +you want to get their ratios okay so +those are the those are the natural + + align:start position:0% +those are the those are the natural + + + align:start position:0% +those are the those are the natural +frequencies those are the mode shapes + + align:start position:0% +frequencies those are the mode shapes + + + align:start position:0% +frequencies those are the mode shapes +let's demonstrate it let's look at it + + align:start position:0% +let's demonstrate it let's look at it + + + align:start position:0% +let's demonstrate it let's look at it +this is basically the system and you now + + align:start position:0% +this is basically the system and you now + + + align:start position:0% +this is basically the system and you now +know that mode shapes are 1 & 2 mode + + align:start position:0% +know that mode shapes are 1 & 2 mode + + + align:start position:0% +know that mode shapes are 1 & 2 mode +shapes of this thing are 1 1 for the + + align:start position:0% +shapes of this thing are 1 1 for the + + + align:start position:0% +shapes of this thing are 1 1 for the +first mode and 1 minus 1 for the second + + align:start position:0% +first mode and 1 minus 1 for the second + + + align:start position:0% +first mode and 1 minus 1 for the second +mode + + align:start position:0% +mode + + + align:start position:0% +mode +and the modal expansion theorem depends + + align:start position:0% +and the modal expansion theorem depends + + + align:start position:0% +and the modal expansion theorem depends +on this this fact that the mode shapes + + align:start position:0% +on this this fact that the mode shapes + + + align:start position:0% +on this this fact that the mode shapes +form a complete independent set of + + align:start position:0% +form a complete independent set of + + + align:start position:0% +form a complete independent set of +vectors that are orthogonal to one + + align:start position:0% +vectors that are orthogonal to one + + + align:start position:0% +vectors that are orthogonal to one +another a weighted sum of all the mode + + align:start position:0% +another a weighted sum of all the mode + + + align:start position:0% +another a weighted sum of all the mode +shapes of the system can represent any + + align:start position:0% +shapes of the system can represent any + + + align:start position:0% +shapes of the system can represent any +allowable motion of the system any + + align:start position:0% +allowable motion of the system any + + + align:start position:0% +allowable motion of the system any +possible motion system can be written as + + align:start position:0% +possible motion system can be written as + + + align:start position:0% +possible motion system can be written as +a weight of so anyway I can displace + + align:start position:0% +a weight of so anyway I can displace + + + align:start position:0% +a weight of so anyway I can displace +this thing these things a little bit + + align:start position:0% +this thing these things a little bit + + + align:start position:0% +this thing these things a little bit +here a little bit there I can write that + + align:start position:0% +here a little bit there I can write that + + + align:start position:0% +here a little bit there I can write that +position as a weighted sum of those two + + align:start position:0% +position as a weighted sum of those two + + + align:start position:0% +position as a weighted sum of those two +mode shapes so that lets say I want to + + align:start position:0% +mode shapes so that lets say I want to + + + align:start position:0% +mode shapes so that lets say I want to +have initial conditions on displacement + + align:start position:0% +have initial conditions on displacement + + + align:start position:0% +have initial conditions on displacement +our theta 1 0 and theta 2 0 no initial + + align:start position:0% +our theta 1 0 and theta 2 0 no initial + + + align:start position:0% +our theta 1 0 and theta 2 0 no initial +velocity is just initial angles and I + + align:start position:0% +velocity is just initial angles and I + + + align:start position:0% +velocity is just initial angles and I +want that initial condition vector to be + + align:start position:0% +want that initial condition vector to be + + + align:start position:0% +want that initial condition vector to be +1 0 I'm claiming I can write that as a + + align:start position:0% +1 0 I'm claiming I can write that as a + + + align:start position:0% +1 0 I'm claiming I can write that as a +sum of something 1 1 plus another or + + align:start position:0% +sum of something 1 1 plus another or + + + align:start position:0% +sum of something 1 1 plus another or +something 1 minus 1 so what does c1 and + + align:start position:0% +something 1 minus 1 so what does c1 and + + + align:start position:0% +something 1 minus 1 so what does c1 and +c2 have to be to give me that you ought + + align:start position:0% +c2 have to be to give me that you ought + + + align:start position:0% +c2 have to be to give me that you ought +to be able to kind of do that by + + align:start position:0% +to be able to kind of do that by + + + align:start position:0% +to be able to kind of do that by +inspection almost + + align:start position:0% +inspection almost + + + align:start position:0% +inspection almost +like for example just try them equal in + + align:start position:0% +like for example just try them equal in + + + align:start position:0% +like for example just try them equal in +what happens + + align:start position:0% + + + + align:start position:0% + +so happening here right great so this to + + align:start position:0% +so happening here right great so this to + + + align:start position:0% +so happening here right great so this to +satisfy this it's a half 1 1 plus a half + + align:start position:0% +satisfy this it's a half 1 1 plus a half + + + align:start position:0% +satisfy this it's a half 1 1 plus a half +1 minus 1 and they're just illustrated + + align:start position:0% +1 minus 1 and they're just illustrated + + + align:start position:0% +1 minus 1 and they're just illustrated +the fact that you can represent an + + align:start position:0% +the fact that you can represent an + + + align:start position:0% +the fact that you can represent an +arbitrary deflection allowable + + align:start position:0% +arbitrary deflection allowable + + + align:start position:0% +arbitrary deflection allowable +deflection of the system as a weighted + + align:start position:0% +deflection of the system as a weighted + + + align:start position:0% +deflection of the system as a weighted +sum of the two mode shapes all right so + + align:start position:0% +sum of the two mode shapes all right so + + + align:start position:0% +sum of the two mode shapes all right so +that says if we if I make the initial + + align:start position:0% +that says if we if I make the initial + + + align:start position:0% +that says if we if I make the initial +now this says that theta 1 is 1 and + + align:start position:0% +now this says that theta 1 is 1 and + + + align:start position:0% +now this says that theta 1 is 1 and +theta 2 is 0 what is telling us is by + + align:start position:0% +theta 2 is 0 what is telling us is by + + + align:start position:0% +theta 2 is 0 what is telling us is by +modal analysis that means the resulting + + align:start position:0% +modal analysis that means the resulting + + + align:start position:0% +modal analysis that means the resulting +motion should look like the response to + + align:start position:0% +motion should look like the response to + + + align:start position:0% +motion should look like the response to +initial conditions where I have equal + + align:start position:0% +initial conditions where I have equal + + + align:start position:0% +initial conditions where I have equal +amounts of each of those two modes so + + align:start position:0% +amounts of each of those two modes so + + + align:start position:0% +amounts of each of those two modes so +there ought to be some vibration at + + align:start position:0% +there ought to be some vibration at + + + align:start position:0% +there ought to be some vibration at +Omega 1 now out of these equal amount of + + align:start position:0% +Omega 1 now out of these equal amount of + + + align:start position:0% +Omega 1 now out of these equal amount of +vibration at Omega 2 agreed ok let's try + + align:start position:0% +vibration at Omega 2 agreed ok let's try + + + align:start position:0% +vibration at Omega 2 agreed ok let's try +it + + align:start position:0% +it + + + align:start position:0% +it +I'll hold one of these in place I'll + + align:start position:0% +I'll hold one of these in place I'll + + + align:start position:0% +I'll hold one of these in place I'll +deflect the other one and let go + + align:start position:0% + + + + align:start position:0% + +now that one's stationary and this one's + + align:start position:0% +now that one's stationary and this one's + + + align:start position:0% +now that one's stationary and this one's +moving and a few cycles later this one + + align:start position:0% +moving and a few cycles later this one + + + align:start position:0% +moving and a few cycles later this one +will be stationary and that one will be + + align:start position:0% +will be stationary and that one will be + + + align:start position:0% +will be stationary and that one will be +moving so are what you observing could + + align:start position:0% +moving so are what you observing could + + + align:start position:0% +moving so are what you observing could +that motion what you're seeing possibly + + align:start position:0% +that motion what you're seeing possibly + + + align:start position:0% +that motion what you're seeing possibly +be a mode a natural mode by itself no + + align:start position:0% +be a mode a natural mode by itself no + + + align:start position:0% +be a mode a natural mode by itself no +because the different proportions are + + align:start position:0% +because the different proportions are + + + align:start position:0% +because the different proportions are +changing right this is the sum of two + + align:start position:0% +changing right this is the sum of two + + + align:start position:0% +changing right this is the sum of two +modes exactly as you said equal amounts + + align:start position:0% +modes exactly as you said equal amounts + + + align:start position:0% +modes exactly as you said equal amounts +of each and when you do that you have + + align:start position:0% +of each and when you do that you have + + + align:start position:0% +of each and when you do that you have +two things + + align:start position:0% +two things + + + align:start position:0% +two things +each two things of equal amplitude - + + align:start position:0% +each two things of equal amplitude - + + + align:start position:0% +each two things of equal amplitude - +cosine Omega T like terms of equal + + align:start position:0% +cosine Omega T like terms of equal + + + align:start position:0% +cosine Omega T like terms of equal +amplitude and different frequencies you + + align:start position:0% +amplitude and different frequencies you + + + align:start position:0% +amplitude and different frequencies you +get a phenomena known as beating that's + + align:start position:0% +get a phenomena known as beating that's + + + align:start position:0% +get a phenomena known as beating that's +what this is beating means it one + + align:start position:0% +what this is beating means it one + + + align:start position:0% +what this is beating means it one +vibrates and then will get small and + + align:start position:0% +vibrates and then will get small and + + + align:start position:0% +vibrates and then will get small and +then you'll see it build up again and it + + align:start position:0% +then you'll see it build up again and it + + + align:start position:0% +then you'll see it build up again and it +gets small so if you watch eating one of + + align:start position:0% +gets small so if you watch eating one of + + + align:start position:0% +gets small so if you watch eating one of +these it's doing large and stopping and + + align:start position:0% +these it's doing large and stopping and + + + align:start position:0% +these it's doing large and stopping and +the other one is doing the same thing + + align:start position:0% +the other one is doing the same thing + + + align:start position:0% +the other one is doing the same thing +but actually ninety degrees out of phase + + align:start position:0% +but actually ninety degrees out of phase + + + align:start position:0% +but actually ninety degrees out of phase +so what we're really saying is that the + + align:start position:0% +so what we're really saying is that the + + + align:start position:0% +so what we're really saying is that the +motion of this system this is one one + + align:start position:0% +motion of this system this is one one + + + align:start position:0% +motion of this system this is one one +half and one one cosine Omega 1 T plus + + align:start position:0% +half and one one cosine Omega 1 T plus + + + align:start position:0% +half and one one cosine Omega 1 T plus +1/2 one minus 1 cosine Omega 2 T that's + + align:start position:0% +1/2 one minus 1 cosine Omega 2 T that's + + + align:start position:0% +1/2 one minus 1 cosine Omega 2 T that's +the total responsibility let's look at + + align:start position:0% +the total responsibility let's look at + + + align:start position:0% +the total responsibility let's look at +the first line of this this says 1/2 + + align:start position:0% +the first line of this this says 1/2 + + + align:start position:0% +the first line of this this says 1/2 +cosine Omega 1 T plus 1/2 cosine Omega 2 + + align:start position:0% +cosine Omega 1 T plus 1/2 cosine Omega 2 + + + align:start position:0% +cosine Omega 1 T plus 1/2 cosine Omega 2 +T should be equal to the motion we call + + align:start position:0% +T should be equal to the motion we call + + + align:start position:0% +T should be equal to the motion we call +theta 1 of T that's the first row here + + align:start position:0% +theta 1 of T that's the first row here + + + align:start position:0% +theta 1 of T that's the first row here +this is theta 1 theta 2 so the first row + + align:start position:0% +this is theta 1 theta 2 so the first row + + + align:start position:0% +this is theta 1 theta 2 so the first row +of this the first equation is that and + + align:start position:0% +of this the first equation is that and + + + align:start position:0% +of this the first equation is that and +to equal amplitude cosines of different + + align:start position:0% +to equal amplitude cosines of different + + + align:start position:0% +to equal amplitude cosines of different +frequencies you can write as cosine + + align:start position:0% +frequencies you can write as cosine + + + align:start position:0% +frequencies you can write as cosine +Omega 2 minus Omega 1 + + align:start position:0% +Omega 2 minus Omega 1 + + + align:start position:0% +Omega 2 minus Omega 1 +over two times T times cosine Omega 1 + + align:start position:0% +over two times T times cosine Omega 1 + + + align:start position:0% +over two times T times cosine Omega 1 +plus Omega 2 over 2t this beat phenomena + + align:start position:0% +plus Omega 2 over 2t this beat phenomena + + + align:start position:0% +plus Omega 2 over 2t this beat phenomena +that you're seeing when you when you'd + + align:start position:0% +that you're seeing when you when you'd + + + align:start position:0% +that you're seeing when you when you'd +plot this and you this is now for theta + + align:start position:0% +plot this and you this is now for theta + + + align:start position:0% +plot this and you this is now for theta +1 it'd start us off at some amplitude + + align:start position:0% + + + + align:start position:0% + +and the actual motion you see if you + + align:start position:0% +and the actual motion you see if you + + + align:start position:0% +and the actual motion you see if you +will if you watch it it does what my + + align:start position:0% +will if you watch it it does what my + + + align:start position:0% +will if you watch it it does what my +going what I'm drawing right now this + + align:start position:0% +going what I'm drawing right now this + + + align:start position:0% +going what I'm drawing right now this +envelope is this term the difference + + align:start position:0% +envelope is this term the difference + + + align:start position:0% +envelope is this term the difference +frequency you divided by 2 + + align:start position:0% +frequency you divided by 2 + + + align:start position:0% +frequency you divided by 2 +what's inside is that term and this is + + align:start position:0% +what's inside is that term and this is + + + align:start position:0% +what's inside is that term and this is +called this is called beating this is + + align:start position:0% +called this is called beating this is + + + align:start position:0% +called this is called beating this is +the equation for beating when you add to + + align:start position:0% +the equation for beating when you add to + + + align:start position:0% +the equation for beating when you add to +equal amplitude cosines together they + + align:start position:0% +equal amplitude cosines together they + + + align:start position:0% +equal amplitude cosines together they +give you something looks like that in + + align:start position:0% +give you something looks like that in + + + align:start position:0% +give you something looks like that in +one period of the beat is how long it + + align:start position:0% +one period of the beat is how long it + + + align:start position:0% +one period of the beat is how long it +takes to go through one full cycle from + + align:start position:0% +takes to go through one full cycle from + + + align:start position:0% +takes to go through one full cycle from +here to here that's one period of the + + align:start position:0% +here to here that's one period of the + + + align:start position:0% +here to here that's one period of the +beat yeah + + align:start position:0% + + + + align:start position:0% + +wow that's just trig identity you add + + align:start position:0% +wow that's just trig identity you add + + + align:start position:0% +wow that's just trig identity you add +you just go back to your trig take + + align:start position:0% +you just go back to your trig take + + + align:start position:0% +you just go back to your trig take +cosine of a plus cosine of B you'll find + + align:start position:0% +cosine of a plus cosine of B you'll find + + + align:start position:0% +cosine of a plus cosine of B you'll find +out you can do that I'm not going to + + align:start position:0% +out you can do that I'm not going to + + + align:start position:0% +out you can do that I'm not going to +don't have time to grunt to go through + + align:start position:0% +don't have time to grunt to go through + + + align:start position:0% +don't have time to grunt to go through +that and the other one is 1/2 cosine + + align:start position:0% +that and the other one is 1/2 cosine + + + align:start position:0% +that and the other one is 1/2 cosine +Omega 1t minus 1/2 cosine Omega 2t and + + align:start position:0% +Omega 1t minus 1/2 cosine Omega 2t and + + + align:start position:0% +Omega 1t minus 1/2 cosine Omega 2t and +that turns out to be sine Omega 2 minus + + align:start position:0% +that turns out to be sine Omega 2 minus + + + align:start position:0% +that turns out to be sine Omega 2 minus +Omega 1 over 2t times sine Omega 1 plus + + align:start position:0% +Omega 1 over 2t times sine Omega 1 plus + + + align:start position:0% +Omega 1 over 2t times sine Omega 1 plus +Omega 2 over 2 quantity times time and + + align:start position:0% +Omega 2 over 2 quantity times time and + + + align:start position:0% +Omega 2 over 2 quantity times time and +that means that the theta 2 coordinate + + align:start position:0% +that means that the theta 2 coordinate + + + align:start position:0% +that means that the theta 2 coordinate +what it looks like when you draw it is + + align:start position:0% +what it looks like when you draw it is + + + align:start position:0% +what it looks like when you draw it is +90 degrees how to face it's the same + + align:start position:0% +90 degrees how to face it's the same + + + align:start position:0% +90 degrees how to face it's the same +thing but it starts at 0 here and beats + + align:start position:0% +thing but it starts at 0 here and beats + + + align:start position:0% +thing but it starts at 0 here and beats +but it starts 0 where that one started + + align:start position:0% +but it starts 0 where that one started + + + align:start position:0% +but it starts 0 where that one started +here and that's what you look at 1 so + + align:start position:0% +here and that's what you look at 1 so + + + align:start position:0% +here and that's what you look at 1 so +that's theta 1 and this is Theta 2 when + + align:start position:0% +that's theta 1 and this is Theta 2 when + + + align:start position:0% +that's theta 1 and this is Theta 2 when +one of them stops and that's one of + + align:start position:0% +one of them stops and that's one of + + + align:start position:0% +one of them stops and that's one of +these lines one of these equations and + + align:start position:0% +these lines one of these equations and + + + align:start position:0% +these lines one of these equations and +the other equation is 90 degrees so that + + align:start position:0% +the other equation is 90 degrees so that + + + align:start position:0% +the other equation is 90 degrees so that +one's stopped right now 90 if PI over 2 + + align:start position:0% +one's stopped right now 90 if PI over 2 + + + align:start position:0% +one's stopped right now 90 if PI over 2 +later this one will be stopped so the + + align:start position:0% +later this one will be stopped so the + + + align:start position:0% +later this one will be stopped so the +beat it's behaves like sine in one case + + align:start position:0% +beat it's behaves like sine in one case + + + align:start position:0% +beat it's behaves like sine in one case +and behaves like cosine in the other + + align:start position:0% +and behaves like cosine in the other + + + align:start position:0% +and behaves like cosine in the other +case one of these needs a minus sign + + align:start position:0% +case one of these needs a minus sign + + + align:start position:0% +case one of these needs a minus sign +that's plus minus and plus minus and + + align:start position:0% +that's plus minus and plus minus and + + + align:start position:0% +that's plus minus and plus minus and +plus + + align:start position:0% +plus + + + align:start position:0% +plus +that's what if you have unequal amounts + + align:start position:0% +that's what if you have unequal amounts + + + align:start position:0% +that's what if you have unequal amounts +if you we have exactly equal amounts of + + align:start position:0% +if you we have exactly equal amounts of + + + align:start position:0% +if you we have exactly equal amounts of +of the two modes if you have unequal + + align:start position:0% +of the two modes if you have unequal + + + align:start position:0% +of the two modes if you have unequal +amounts of the two modes then it's not + + align:start position:0% +amounts of the two modes then it's not + + + align:start position:0% +amounts of the two modes then it's not +going to be a half and a half whatever + + align:start position:0% +going to be a half and a half whatever + + + align:start position:0% +going to be a half and a half whatever +it's like one and point one then do you + + align:start position:0% +it's like one and point one then do you + + + align:start position:0% +it's like one and point one then do you +see full beats does one come to a stop + + align:start position:0% +see full beats does one come to a stop + + + align:start position:0% +see full beats does one come to a stop +if they're not equal you'll find that + + align:start position:0% +if they're not equal you'll find that + + + align:start position:0% +if they're not equal you'll find that +the two sums of the two motions will + + align:start position:0% +the two sums of the two motions will + + + align:start position:0% +the two sums of the two motions will +look the envelope will look like this + + align:start position:0% + + + + align:start position:0% + +it'll be modulated each one's motion to + + align:start position:0% +it'll be modulated each one's motion to + + + align:start position:0% +it'll be modulated each one's motion to +look like that it'll never go to 0 coy + + align:start position:0% +look like that it'll never go to 0 coy + + + align:start position:0% +look like that it'll never go to 0 coy +okay that's beating no time we're good + + align:start position:0% +okay that's beating no time we're good + + + align:start position:0% +okay that's beating no time we're good +and let's see did we do if we said the + + align:start position:0% +and let's see did we do if we said the + + + align:start position:0% +and let's see did we do if we said the +one natural one natural mode is the two + + align:start position:0% +one natural one natural mode is the two + + + align:start position:0% +one natural one natural mode is the two +opposite one another so if I start go + + align:start position:0% +opposite one another so if I start go + + + align:start position:0% +opposite one another so if I start go +equal amounts in opposite directions and + + align:start position:0% +equal amounts in opposite directions and + + + align:start position:0% +equal amounts in opposite directions and +let go it ought to just sit there and + + align:start position:0% +let go it ought to just sit there and + + + align:start position:0% +let go it ought to just sit there and +vibrate all day like that + + align:start position:0% +vibrate all day like that + + + align:start position:0% +vibrate all day like that +no beats because it's it is the one zero + + align:start position:0% +no beats because it's it is the one zero + + + align:start position:0% +no beats because it's it is the one zero +case over there so this is a zero one + + align:start position:0% +case over there so this is a zero one + + + align:start position:0% +case over there so this is a zero one +case this is one minus one I gave an + + align:start position:0% +case this is one minus one I gave an + + + align:start position:0% +case this is one minus one I gave an +initial displacement in exactly the + + align:start position:0% +initial displacement in exactly the + + + align:start position:0% +initial displacement in exactly the +shape of the second mode and that means + + align:start position:0% +shape of the second mode and that means + + + align:start position:0% +shape of the second mode and that means +the two contributions are that one of + + align:start position:0% +the two contributions are that one of + + + align:start position:0% +the two contributions are that one of +those constants is zero it's there's no + + align:start position:0% +those constants is zero it's there's no + + + align:start position:0% +those constants is zero it's there's no +mode one in this it's only mode two and + + align:start position:0% +mode one in this it's only mode two and + + + align:start position:0% +mode one in this it's only mode two and +they'll sit here all day long and by + + align:start position:0% +they'll sit here all day long and by + + + align:start position:0% +they'll sit here all day long and by +right just in the mode two and if i + + align:start position:0% +right just in the mode two and if i + + + align:start position:0% +right just in the mode two and if i +displace it in the shape of mode one + + align:start position:0% +displace it in the shape of mode one + + + align:start position:0% +displace it in the shape of mode one +only it will vibrate and that's hard to + + align:start position:0% +only it will vibrate and that's hard to + + + align:start position:0% +only it will vibrate and that's hard to +do because i have to ask to have to move + + align:start position:0% +do because i have to ask to have to move + + + align:start position:0% +do because i have to ask to have to move +exactly the same amount that's mode one + + align:start position:0% +exactly the same amount that's mode one + + + align:start position:0% +exactly the same amount that's mode one +and it should by rate all day long and + + align:start position:0% +and it should by rate all day long and + + + align:start position:0% +and it should by rate all day long and +mode one because now there's no mode two + + align:start position:0% +mode one because now there's no mode two + + + align:start position:0% +mode one because now there's no mode two +involved in that one you can see it's + + align:start position:0% +involved in that one you can see it's + + + align:start position:0% +involved in that one you can see it's +already getting a little out of phase + + align:start position:0% +already getting a little out of phase + + + align:start position:0% +already getting a little out of phase +like it's hard to get it for me to move + + align:start position:0% +like it's hard to get it for me to move + + + align:start position:0% +like it's hard to get it for me to move +my hands exactly the same amount so I + + align:start position:0% +my hands exactly the same amount so I + + + align:start position:0% +my hands exactly the same amount so I +have a little bit of both the other mode + + align:start position:0% +have a little bit of both the other mode + + + align:start position:0% +have a little bit of both the other mode +in there but you'll never see either one + + align:start position:0% +in there but you'll never see either one + + + align:start position:0% +in there but you'll never see either one +of these come to a full stop it's + + align:start position:0% +of these come to a full stop it's + + + align:start position:0% +of these come to a full stop it's +actually doing that + + align:start position:0% + + + + align:start position:0% + +when you get a little contamination to + + align:start position:0% +when you get a little contamination to + + + align:start position:0% +when you get a little contamination to +the second mode in there all right + + align:start position:0% + + + + align:start position:0% + +okay so I've posted on stellar a little + + align:start position:0% +okay so I've posted on stellar a little + + + align:start position:0% +okay so I've posted on stellar a little +two-page sheet that just gives you step + + align:start position:0% +two-page sheet that just gives you step + + + align:start position:0% +two-page sheet that just gives you step +by step how to do a modal analysis it's + + align:start position:0% +by step how to do a modal analysis it's + + + align:start position:0% +by step how to do a modal analysis it's +just cookbook modal houses is easy you + + align:start position:0% +just cookbook modal houses is easy you + + + align:start position:0% +just cookbook modal houses is easy you +do it all on the computer just put in + + align:start position:0% +do it all on the computer just put in + + + align:start position:0% +do it all on the computer just put in +your M matrix and your K matrix and you + + align:start position:0% +your M matrix and your K matrix and you + + + align:start position:0% +your M matrix and your K matrix and you +crank stuff out next Tuesday we did + + align:start position:0% +crank stuff out next Tuesday we did + + + align:start position:0% +crank stuff out next Tuesday we did +modal analysis yesterday just from + + align:start position:0% +modal analysis yesterday just from + + + align:start position:0% +modal analysis yesterday just from +initial conditions next Tuesday would do + + align:start position:0% +initial conditions next Tuesday would do + + + align:start position:0% +initial conditions next Tuesday would do +modal analysis assuming you've got + + align:start position:0% +modal analysis assuming you've got + + + align:start position:0% +modal analysis assuming you've got +harmonic excitation and steady-state + + align:start position:0% +harmonic excitation and steady-state + + + align:start position:0% +harmonic excitation and steady-state +vibration and do that kind of thing \ No newline at end of file diff --git a/fkGAF5jHjdY.txt b/fkGAF5jHjdY.txt new file mode 100644 index 0000000000000000000000000000000000000000..045571769205dc03374fd0e6685d4b95cd4dcfe8 --- /dev/null +++ b/fkGAF5jHjdY.txt @@ -0,0 +1,2107 @@ +align:start position:0% + +welcome back so in this session we're + + align:start position:0% +welcome back so in this session we're + + + align:start position:0% +welcome back so in this session we're +going to look at Cold inputs for + + align:start position:0% +going to look at Cold inputs for + + + align:start position:0% +going to look at Cold inputs for +ordinary differential equations of order + + align:start position:0% +ordinary differential equations of order + + + align:start position:0% +ordinary differential equations of order +one so here in question one you're used + + align:start position:0% +one so here in question one you're used + + + align:start position:0% +one so here in question one you're used +to use you're asked to use complex + + align:start position:0% +to use you're asked to use complex + + + align:start position:0% +to use you're asked to use complex +techniques to solve x dot plus KX equal + + align:start position:0% +techniques to solve x dot plus KX equal + + + align:start position:0% +techniques to solve x dot plus KX equal +cosine of Omega T here K and Omega are + + align:start position:0% +cosine of Omega T here K and Omega are + + + align:start position:0% +cosine of Omega T here K and Omega are +constants this is a OD of first order uh + + align:start position:0% +constants this is a OD of first order uh + + + align:start position:0% +constants this is a OD of first order uh +and the cidal input is referring to the + + align:start position:0% +and the cidal input is referring to the + + + align:start position:0% +and the cidal input is referring to the +right hand side of the OD where + + align:start position:0% +right hand side of the OD where + + + align:start position:0% +right hand side of the OD where +basically the we are forcing a system + + align:start position:0% +basically the we are forcing a system + + + align:start position:0% +basically the we are forcing a system +with a function and its sinusoidal of + + align:start position:0% +with a function and its sinusoidal of + + + align:start position:0% +with a function and its sinusoidal of +angular frequency Omega which means + + align:start position:0% +angular frequency Omega which means + + + align:start position:0% +angular frequency Omega which means +basically a period of 2 pi over Omega so + + align:start position:0% +basically a period of 2 pi over Omega so + + + align:start position:0% +basically a period of 2 pi over Omega so +you're used to you're asked to use + + align:start position:0% +you're used to you're asked to use + + + align:start position:0% +you're used to you're asked to use +complex techniques to solve + + align:start position:0% +complex techniques to solve + + + align:start position:0% +complex techniques to solve +this in question a in question B we're + + align:start position:0% +this in question a in question B we're + + + align:start position:0% +this in question a in question B we're +asked to use what we had in question a + + align:start position:0% +asked to use what we had in question a + + + align:start position:0% +asked to use what we had in question a +to solve this modified function where + + align:start position:0% +to solve this modified function where + + + align:start position:0% +to solve this modified function where +again we have a cidal input on the right + + align:start position:0% +again we have a cidal input on the right + + + align:start position:0% +again we have a cidal input on the right +hand side with an additional amp ude F + + align:start position:0% +hand side with an additional amp ude F + + + align:start position:0% +hand side with an additional amp ude F +which is now constant in the third part + + align:start position:0% +which is now constant in the third part + + + align:start position:0% +which is now constant in the third part +we're asked to use superposition + + align:start position:0% +we're asked to use superposition + + + align:start position:0% +we're asked to use superposition +principle to solve this combined + + align:start position:0% +principle to solve this combined + + + align:start position:0% +principle to solve this combined +equation where now we're introducing a + + align:start position:0% +equation where now we're introducing a + + + align:start position:0% +equation where now we're introducing a +value for example for f which is three + + align:start position:0% +value for example for f which is three + + + align:start position:0% +value for example for f which is three +and you can see also that the right hand + + align:start position:0% +and you can see also that the right hand + + + align:start position:0% +and you can see also that the right hand +side is also a cidal input because it's + + align:start position:0% +side is also a cidal input because it's + + + align:start position:0% +side is also a cidal input because it's +a linear combination of Cal functions + + align:start position:0% +a linear combination of Cal functions + + + align:start position:0% +a linear combination of Cal functions +all these equations are linear with + + align:start position:0% +all these equations are linear with + + + align:start position:0% +all these equations are linear with +constant + + align:start position:0% +constant + + + align:start position:0% +constant +coefficients and hence superposition + + align:start position:0% +coefficients and hence superposition + + + align:start position:0% +coefficients and hence superposition +principle would hold so why don't you + + align:start position:0% +principle would hold so why don't you + + + align:start position:0% +principle would hold so why don't you +stop the video take a few minutes and + + align:start position:0% +stop the video take a few minutes and + + + align:start position:0% +stop the video take a few minutes and +work through the problems and we'll be + + align:start position:0% +work through the problems and we'll be + + + align:start position:0% +work through the problems and we'll be +back + + align:start position:0% + + + + align:start position:0% + +welcome back so what is it that we're + + align:start position:0% +welcome back so what is it that we're + + + align:start position:0% +welcome back so what is it that we're +asked to do here we're asked to solve + + align:start position:0% +asked to do here we're asked to solve + + + align:start position:0% +asked to do here we're asked to solve +this using a trick that you learn in + + align:start position:0% +this using a trick that you learn in + + + align:start position:0% +this using a trick that you learn in +class to basically convert a real valued + + align:start position:0% +class to basically convert a real valued + + + align:start position:0% +class to basically convert a real valued +OD into complex form so in the + + align:start position:0% +OD into complex form so in the + + + align:start position:0% +OD into complex form so in the +first first thing to do is to realize + + align:start position:0% +first first thing to do is to realize + + + align:start position:0% +first first thing to do is to realize +that + + align:start position:0% + + + + align:start position:0% + +the first thing to do is to realize that + + align:start position:0% +the first thing to do is to realize that + + + align:start position:0% +the first thing to do is to realize that +the cosine of Omega + + align:start position:0% +the cosine of Omega + + + align:start position:0% +the cosine of Omega +T is simply the real part of the + + align:start position:0% +T is simply the real part of the + + + align:start position:0% +T is simply the real part of the +imaginary complex exponential I Omega T + + align:start position:0% +imaginary complex exponential I Omega T + + + align:start position:0% +imaginary complex exponential I Omega T +so when when we realize that and we see + + align:start position:0% +so when when we realize that and we see + + + align:start position:0% +so when when we realize that and we see +that the OD is real valued linear we + + align:start position:0% + + + + align:start position:0% + +can convert this real value + + align:start position:0% + + + + align:start position:0% + +OD into this complex + + align:start position:0% + + + + align:start position:0% + +value + + align:start position:0% + + + + align:start position:0% + +complex so from this point and we're + + align:start position:0% +complex so from this point and we're + + + align:start position:0% +complex so from this point and we're +going to label this equation + + align:start position:0% +going to label this equation + + + align:start position:0% +going to label this equation +star from this this point we can go back + + align:start position:0% +star from this this point we can go back + + + align:start position:0% +star from this this point we can go back +to the techniques that we learned in + + align:start position:0% +to the techniques that we learned in + + + align:start position:0% +to the techniques that we learned in +class namely the integrating factor to + + align:start position:0% +class namely the integrating factor to + + + align:start position:0% +class namely the integrating factor to +realize that we can rewrite the right + + align:start position:0% +realize that we can rewrite the right + + + align:start position:0% +realize that we can rewrite the right +hand + + align:start position:0% +hand + + + align:start position:0% +hand +side in this form introducing a new + + align:start position:0% +side in this form introducing a new + + + align:start position:0% +side in this form introducing a new +function U so + + align:start position:0% +function U so + + + align:start position:0% +function U so +that we need to seek a function U that + + align:start position:0% +that we need to seek a function U that + + + align:start position:0% +that we need to seek a function U that +will then recover this function this + + align:start position:0% +will then recover this function this + + + align:start position:0% +will then recover this function this +equation and from + + align:start position:0% +equation and from + + + align:start position:0% +equation and from +previous recitations and problem we saw + + align:start position:0% +previous recitations and problem we saw + + + align:start position:0% +previous recitations and problem we saw +that clearly the U that we would need to + + align:start position:0% +that clearly the U that we would need to + + + align:start position:0% +that clearly the U that we would need to +pick is just exponential of KT okay so + + align:start position:0% +pick is just exponential of KT okay so + + + align:start position:0% +pick is just exponential of KT okay so +now from this we basically have we're + + align:start position:0% +now from this we basically have we're + + + align:start position:0% +now from this we basically have we're +back + + align:start position:0% + + + + align:start position:0% + +to I Omega plus K the whole thing t on + + align:start position:0% +to I Omega plus K the whole thing t on + + + align:start position:0% +to I Omega plus K the whole thing t on +the right hand side and + + align:start position:0% +the right hand side and + + + align:start position:0% +the right hand side and +here z u Prime that we just need to + + align:start position:0% +here z u Prime that we just need to + + + align:start position:0% +here z u Prime that we just need to +integrate on both sides so this is + + align:start position:0% +integrate on both sides so this is + + + align:start position:0% +integrate on both sides so this is +simply KT Z on the left hand side + + align:start position:0% +simply KT Z on the left hand side + + + align:start position:0% +simply KT Z on the left hand side +and on the right hand side we're + + align:start position:0% +and on the right hand side we're + + + align:start position:0% +and on the right hand side we're +integrating again it's just still an + + align:start position:0% +integrating again it's just still an + + + align:start position:0% +integrating again it's just still an +exponential even though it's + + align:start position:0% + + + + align:start position:0% + +complex and we need to introduce of + + align:start position:0% +complex and we need to introduce of + + + align:start position:0% +complex and we need to introduce of +course constant of + + align:start position:0% + + + + align:start position:0% + +integration so the solution for the + + align:start position:0% +integration so the solution for the + + + align:start position:0% +integration so the solution for the +equation + + align:start position:0% +equation + + + align:start position:0% +equation +star is then I'm going to write it up + + align:start position:0% +star is then I'm going to write it up + + + align:start position:0% +star is then I'm going to write it up +here so that we keep that for the rest + + align:start position:0% +here so that we keep that for the rest + + + align:start position:0% +here so that we keep that for the rest +of the problem + + align:start position:0% + + + + align:start position:0% + +minus t minus + + align:start position:0% +minus t minus + + + align:start position:0% +minus t minus +KT when I divide by this and here the + + align:start position:0% +KT when I divide by this and here the + + + align:start position:0% +KT when I divide by this and here the +minus KT of this exponential is going to + + align:start position:0% +minus KT of this exponential is going to + + + align:start position:0% +minus KT of this exponential is going to +be canceled out by the integrating + + align:start position:0% + + + + align:start position:0% + +Factor okay so we're going to keep that + + align:start position:0% +Factor okay so we're going to keep that + + + align:start position:0% +Factor okay so we're going to keep that +here so here I gave the general solution + + align:start position:0% +here so here I gave the general solution + + + align:start position:0% +here so here I gave the general solution +with the solution that would come from + + align:start position:0% +with the solution that would come from + + + align:start position:0% +with the solution that would come from +the homogeneous equation which we could + + align:start position:0% +the homogeneous equation which we could + + + align:start position:0% +the homogeneous equation which we could +refer to also as a transient here + + align:start position:0% +refer to also as a transient here + + + align:start position:0% +refer to also as a transient here +because basically after a long time T + + align:start position:0% +because basically after a long time T + + + align:start position:0% +because basically after a long time T +this exponential if K is positive would + + align:start position:0% +this exponential if K is positive would + + + align:start position:0% +this exponential if K is positive would +Decay and the solute the part of the + + align:start position:0% +Decay and the solute the part of the + + + align:start position:0% +Decay and the solute the part of the +solution that comes from the Cal input + + align:start position:0% +solution that comes from the Cal input + + + align:start position:0% +solution that comes from the Cal input +or the forcing which would be a + + align:start position:0% +or the forcing which would be a + + + align:start position:0% +or the forcing which would be a +particular + + align:start position:0% +particular + + + align:start position:0% +particular +solution so to go back to the original + + align:start position:0% +solution so to go back to the original + + + align:start position:0% +solution so to go back to the original +question we were asked to solve this + + align:start position:0% +question we were asked to solve this + + + align:start position:0% +question we were asked to solve this +real valued equation so from what we + + align:start position:0% +real valued equation so from what we + + + align:start position:0% +real valued equation so from what we +know noticed above we saw that the right + + align:start position:0% +know noticed above we saw that the right + + + align:start position:0% +know noticed above we saw that the right +hand side is just a real part of the + + align:start position:0% +hand side is just a real part of the + + + align:start position:0% +hand side is just a real part of the +right hand side of the complex value + + align:start position:0% +right hand side of the complex value + + + align:start position:0% +right hand side of the complex value +equation star and similarly then we + + align:start position:0% + + + + align:start position:0% + +can do the same for the actual Solutions + + align:start position:0% +can do the same for the actual Solutions + + + align:start position:0% +can do the same for the actual Solutions +themselves X is also just a real value + + align:start position:0% +themselves X is also just a real value + + + align:start position:0% +themselves X is also just a real value +of this complex number so here for this + + align:start position:0% +of this complex number so here for this + + + align:start position:0% +of this complex number so here for this +General solution I'm going to just use c + + align:start position:0% +General solution I'm going to just use c + + + align:start position:0% +General solution I'm going to just use c +bar for General complex constant here uh + + align:start position:0% +bar for General complex constant here uh + + + align:start position:0% +bar for General complex constant here uh +and in this case we will take the real + + align:start position:0% +and in this case we will take the real + + + align:start position:0% +and in this case we will take the real +value so at this point we don't really + + align:start position:0% +value so at this point we don't really + + + align:start position:0% +value so at this point we don't really +doesn't really matter matter what C is + + align:start position:0% +doesn't really matter matter what C is + + + align:start position:0% +doesn't really matter matter what C is +is just we're going to keep it as a + + align:start position:0% +is just we're going to keep it as a + + + align:start position:0% +is just we're going to keep it as a +constant and now it's just real + + align:start position:0% +constant and now it's just real + + + align:start position:0% +constant and now it's just real +valued that's for the one part and then + + align:start position:0% +valued that's for the one part and then + + + align:start position:0% +valued that's for the one part and then +we need to + + align:start position:0% +we need to + + + align:start position:0% +we need to +take the real part of this + + align:start position:0% +take the real part of this + + + align:start position:0% +take the real part of this +expression come back to the line here so + + align:start position:0% +expression come back to the line here so + + + align:start position:0% +expression come back to the line here so +to take the real part of this + + align:start position:0% + + + + align:start position:0% + +expression you learn that basically you + + align:start position:0% +expression you learn that basically you + + + align:start position:0% +expression you learn that basically you +just need to multiply the denominator + + align:start position:0% +just need to multiply the denominator + + + align:start position:0% +just need to multiply the denominator +the numerator by the complex conjugate + + align:start position:0% +the numerator by the complex conjugate + + + align:start position:0% +the numerator by the complex conjugate +for + + align:start position:0% + + + + align:start position:0% + +and that will only give + + align:start position:0% + + + + align:start position:0% + +us so we have K minus I Omega over the + + align:start position:0% +us so we have K minus I Omega over the + + + align:start position:0% +us so we have K minus I Omega over the +squares + + align:start position:0% +squares + + + align:start position:0% +squares +and and then again earlier formula that + + align:start position:0% +and and then again earlier formula that + + + align:start position:0% +and and then again earlier formula that +we saw in the previous recitation so X + + align:start position:0% +we saw in the previous recitation so X + + + align:start position:0% +we saw in the previous recitation so X +from this expression is just the real + + align:start position:0% +from this expression is just the real + + + align:start position:0% +from this expression is just the real +part of all of this so it's going to be + + align:start position:0% +part of all of this so it's going to be + + + align:start position:0% +part of all of this so it's going to be +this + + align:start position:0% + + + + align:start position:0% + +term actually let me + + align:start position:0% +term actually let me + + + align:start position:0% +term actually let me +factorize + + align:start position:0% + + + + align:start position:0% + +denominator and then the result of + + align:start position:0% +denominator and then the result of + + + align:start position:0% +denominator and then the result of +multiplying the two complex Parts as + + align:start position:0% +multiplying the two complex Parts as + + + align:start position:0% +multiplying the two complex Parts as +well I do I minus + + align:start position:0% + + + + align:start position:0% + +one and so that + + align:start position:0% +one and so that + + + align:start position:0% +one and so that +ansers the part A of the + + align:start position:0% +ansers the part A of the + + + align:start position:0% +ansers the part A of the +question the part A of the the problem + + align:start position:0% +question the part A of the the problem + + + align:start position:0% +question the part A of the the problem +so if we look at Part B I'm just going + + align:start position:0% +so if we look at Part B I'm just going + + + align:start position:0% +so if we look at Part B I'm just going +to do it + + align:start position:0% +to do it + + + align:start position:0% +to do it +here Part B we're asked to to solve a + + align:start position:0% +here Part B we're asked to to solve a + + + align:start position:0% +here Part B we're asked to to solve a +very very similar + + align:start position:0% + + + + align:start position:0% + +equation and I'm just going to + + align:start position:0% +equation and I'm just going to + + + align:start position:0% +equation and I'm just going to +leave the F out for + + align:start position:0% +leave the F out for + + + align:start position:0% +leave the F out for +now it's basically the same equation + + align:start position:0% +now it's basically the same equation + + + align:start position:0% +now it's basically the same equation +except that the input now is a sign + + align:start position:0% +except that the input now is a sign + + + align:start position:0% +except that the input now is a sign +instead of a cosine so we can use the + + align:start position:0% +instead of a cosine so we can use the + + + align:start position:0% +instead of a cosine so we can use the +same trick as we used for question a by + + align:start position:0% +same trick as we used for question a by + + + align:start position:0% +same trick as we used for question a by +realizing that now the sign is just the + + align:start position:0% +realizing that now the sign is just the + + + align:start position:0% +realizing that now the sign is just the +imaginary part of the + + align:start position:0% + + + + align:start position:0% + +exponential the complex + + align:start position:0% +exponential the complex + + + align:start position:0% +exponential the complex +exponential so we don't need to redo all + + align:start position:0% +exponential so we don't need to redo all + + + align:start position:0% +exponential so we don't need to redo all +the work we only need to if we were + + align:start position:0% +the work we only need to if we were + + + align:start position:0% +the work we only need to if we were +considering this equation to just take + + align:start position:0% +considering this equation to just take + + + align:start position:0% +considering this equation to just take +the imaginary part of the solution that + + align:start position:0% +the imaginary part of the solution that + + + align:start position:0% +the imaginary part of the solution that +we just found here and we can just read + + align:start position:0% +we just found here and we can just read + + + align:start position:0% +we just found here and we can just read +off the solution from this from this + + align:start position:0% +off the solution from this from this + + + align:start position:0% +off the solution from this from this +line um + + align:start position:0% +line um + + + align:start position:0% +line um +note that in this expression I left out + + align:start position:0% +note that in this expression I left out + + + align:start position:0% +note that in this expression I left out +the homogeneous part which I should add + + align:start position:0% + + + + align:start position:0% + +here from here and this was just a + + align:start position:0% +here from here and this was just a + + + align:start position:0% +here from here and this was just a +complex part so to come back to what I + + align:start position:0% +complex part so to come back to what I + + + align:start position:0% +complex part so to come back to what I +was saying the sign is just the + + align:start position:0% +was saying the sign is just the + + + align:start position:0% +was saying the sign is just the +imaginary part of the complex + + align:start position:0% +imaginary part of the complex + + + align:start position:0% +imaginary part of the complex +exponential so we just going to just + + align:start position:0% +exponential so we just going to just + + + align:start position:0% +exponential so we just going to just +write + + align:start position:0% +write + + + align:start position:0% +write +down the solution by reading off here so + + align:start position:0% +down the solution by reading off here so + + + align:start position:0% +down the solution by reading off here so +again we have the homogeneous + + align:start position:0% +again we have the homogeneous + + + align:start position:0% +again we have the homogeneous +part which would be another + + align:start position:0% +part which would be another + + + align:start position:0% +part which would be another +real valued constant and then the real + + align:start position:0% +real valued constant and then the real + + + align:start position:0% +real valued constant and then the real +part of this + + align:start position:0% + + + + align:start position:0% + +expression 1 / k sare + Omega + + align:start position:0% +expression 1 / k sare + Omega + + + align:start position:0% +expression 1 / k sare + Omega +square and its imaginary part then would + + align:start position:0% +square and its imaginary part then would + + + align:start position:0% +square and its imaginary part then would +give us a + + align:start position:0% +give us a + + + align:start position:0% +give us a +k sin Omega + + align:start position:0% +k sin Omega + + + align:start position:0% +k sin Omega +T and A + + align:start position:0% +T and A + + + align:start position:0% +T and A +minus Omega + + align:start position:0% +minus Omega + + + align:start position:0% +minus Omega +plus Omega + + align:start position:0% +plus Omega + + + align:start position:0% +plus Omega +T so this would be the solution for Part + + align:start position:0% +T so this would be the solution for Part + + + align:start position:0% +T so this would be the solution for Part +B if we had this equation but we + + align:start position:0% +B if we had this equation but we + + + align:start position:0% +B if we had this equation but we +actually have an equation with an + + align:start position:0% +actually have an equation with an + + + align:start position:0% +actually have an equation with an +additional amplitude F and what this + + align:start position:0% +additional amplitude F and what this + + + align:start position:0% +additional amplitude F and what this +leads to is just an additional constant + + align:start position:0% +leads to is just an additional constant + + + align:start position:0% +leads to is just an additional constant +that would appear then for this solution + + align:start position:0% +that would appear then for this solution + + + align:start position:0% +that would appear then for this solution +and we could see that if we rewinded the + + align:start position:0% +and we could see that if we rewinded the + + + align:start position:0% +and we could see that if we rewinded the +way we solved in part A and saw that + + align:start position:0% +way we solved in part A and saw that + + + align:start position:0% +way we solved in part A and saw that +introducing constant constant F to the + + align:start position:0% +introducing constant constant F to the + + + align:start position:0% +introducing constant constant F to the +equation is equivalent to just + + align:start position:0% +equation is equivalent to just + + + align:start position:0% +equation is equivalent to just +multiplying the full equation with f and + + align:start position:0% +multiplying the full equation with f and + + + align:start position:0% +multiplying the full equation with f and +then the integrating Factor uh part we + + align:start position:0% +then the integrating Factor uh part we + + + align:start position:0% +then the integrating Factor uh part we +would end up with an F in front of our + + align:start position:0% +would end up with an F in front of our + + + align:start position:0% +would end up with an F in front of our +solution when we are doing the + + align:start position:0% +solution when we are doing the + + + align:start position:0% +solution when we are doing the +integration and so basically that + + align:start position:0% +integration and so basically that + + + align:start position:0% +integration and so basically that +amplitude could be absorbed in the + + align:start position:0% +amplitude could be absorbed in the + + + align:start position:0% +amplitude could be absorbed in the +constant of integration for the uh + + align:start position:0% +constant of integration for the uh + + + align:start position:0% +constant of integration for the uh +homogeneous part and the F would just + + align:start position:0% +homogeneous part and the F would just + + + align:start position:0% +homogeneous part and the F would just +remains in the particular + + align:start position:0% +remains in the particular + + + align:start position:0% +remains in the particular +solution + + align:start position:0% + + + + align:start position:0% + +here so for the last part of the problem + + align:start position:0% +here so for the last part of the problem + + + align:start position:0% +here so for the last part of the problem +we were now used + + align:start position:0% +we were now used + + + align:start position:0% +we were now used +we're now you asked to use the + + align:start position:0% +we're now you asked to use the + + + align:start position:0% +we're now you asked to use the +superposition principle to + + align:start position:0% +superposition principle to + + + align:start position:0% +superposition principle to +combine to combine Solutions + + align:start position:0% +combine to combine Solutions + + + align:start position:0% +combine to combine Solutions +of two previous Odes that we + + align:start position:0% + + + + align:start position:0% + +could split from this + + align:start position:0% +could split from this + + + align:start position:0% +could split from this +equation and what was it + + align:start position:0% +equation and what was it + + + align:start position:0% +equation and what was it +cosine Oma t + 3 + + align:start position:0% +cosine Oma t + 3 + + + align:start position:0% +cosine Oma t + 3 +sin Omega T so you saw from previous + + align:start position:0% +sin Omega T so you saw from previous + + + align:start position:0% +sin Omega T so you saw from previous +recitations that superposition principle + + align:start position:0% +recitations that superposition principle + + + align:start position:0% +recitations that superposition principle +applies for linear equations this is + + align:start position:0% +applies for linear equations this is + + + align:start position:0% +applies for linear equations this is +clearly a linear equation and here on + + align:start position:0% +clearly a linear equation and here on + + + align:start position:0% +clearly a linear equation and here on +the right hand side we have two + + align:start position:0% +the right hand side we have two + + + align:start position:0% +the right hand side we have two +sinusoidal functions because it's linear + + align:start position:0% +sinusoidal functions because it's linear + + + align:start position:0% +sinusoidal functions because it's linear +we + + align:start position:0% +we + + + align:start position:0% +we +can look at this by splitting + + align:start position:0% +can look at this by splitting + + + align:start position:0% +can look at this by splitting +it into two + + align:start position:0% +it into two + + + align:start position:0% +it into two +equations and I'm just introducing X1 X2 + + align:start position:0% +equations and I'm just introducing X1 X2 + + + align:start position:0% +equations and I'm just introducing X1 X2 +as notation to distinguish between the + + align:start position:0% + + + + align:start position:0% + +two and here we can recognize that we + + align:start position:0% +two and here we can recognize that we + + + align:start position:0% +two and here we can recognize that we +already did this work that was in part A + + align:start position:0% +already did this work that was in part A + + + align:start position:0% +already did this work that was in part A +and we already did this work in Part B + + align:start position:0% +and we already did this work in Part B + + + align:start position:0% +and we already did this work in Part B +where F now has a value of three and so + + align:start position:0% +where F now has a value of three and so + + + align:start position:0% +where F now has a value of three and so +what this is telling us because it's a + + align:start position:0% +what this is telling us because it's a + + + align:start position:0% +what this is telling us because it's a +linear equation we can use superposition + + align:start position:0% +linear equation we can use superposition + + + align:start position:0% +linear equation we can use superposition +principle the solution if you were to + + align:start position:0% + + + + align:start position:0% + +do the addition of these two + + align:start position:0% + + + + align:start position:0% + +equations would just be the the sum of + + align:start position:0% +equations would just be the the sum of + + + align:start position:0% +equations would just be the the sum of +the two previous solutions that we found + + align:start position:0% +the two previous solutions that we found + + + align:start position:0% +the two previous solutions that we found +so this would be our + + align:start position:0% + + + + align:start position:0% + +X3 if I had labeled this with a three + + align:start position:0% +X3 if I had labeled this with a three + + + align:start position:0% +X3 if I had labeled this with a three +and so basically the solution is simply + + align:start position:0% +and so basically the solution is simply + + + align:start position:0% +and so basically the solution is simply +the sum of the two previous forms and so + + align:start position:0% +the sum of the two previous forms and so + + + align:start position:0% +the sum of the two previous forms and so +we would end up still with our C minus + + align:start position:0% +we would end up still with our C minus + + + align:start position:0% +we would end up still with our C minus +KT which is basically the homogeneous + + align:start position:0% +KT which is basically the homogeneous + + + align:start position:0% +KT which is basically the homogeneous +part that we obtained in the two + + align:start position:0% +part that we obtained in the two + + + align:start position:0% +part that we obtained in the two +previous part which is common and then + + align:start position:0% +previous part which is common and then + + + align:start position:0% +previous part which is common and then +we just need to + + align:start position:0% +we just need to + + + align:start position:0% +we just need to +add to add each particular solution + + align:start position:0% +add to add each particular solution + + + align:start position:0% +add to add each particular solution +introduced by in part A and Part B so if + + align:start position:0% +introduced by in part A and Part B so if + + + align:start position:0% +introduced by in part A and Part B so if +I have room I will write it + + align:start position:0% + + + + align:start position:0% + +Alla so we would have + + align:start position:0% +Alla so we would have + + + align:start position:0% +Alla so we would have +K count Omega t plus Omega + + align:start position:0% +K count Omega t plus Omega + + + align:start position:0% +K count Omega t plus Omega +s Omega T from the first part of the + + align:start position:0% +s Omega T from the first part of the + + + align:start position:0% +s Omega T from the first part of the +cosine and then we're introducing a + + align:start position:0% +cosine and then we're introducing a + + + align:start position:0% +cosine and then we're introducing a +three k sin Omega t + + align:start position:0% + + + + align:start position:0% + +plus minus a 3 omega cosine Omega + + align:start position:0% + + + + align:start position:0% + +T and that would be then the solution of + + align:start position:0% +T and that would be then the solution of + + + align:start position:0% +T and that would be then the solution of +the combined two equations and so you + + align:start position:0% +the combined two equations and so you + + + align:start position:0% +the combined two equations and so you +don't need to redo the full work by + + align:start position:0% +don't need to redo the full work by + + + align:start position:0% +don't need to redo the full work by +using the superposition principle so + + align:start position:0% +using the superposition principle so + + + align:start position:0% +using the superposition principle so +here the key was just to recognize that + + align:start position:0% +here the key was just to recognize that + + + align:start position:0% +here the key was just to recognize that +the cosiness and the signs are basically + + align:start position:0% +the cosiness and the signs are basically + + + align:start position:0% +the cosiness and the signs are basically +real part and imaginary parts of the + + align:start position:0% +real part and imaginary parts of the + + + align:start position:0% +real part and imaginary parts of the +complex number of exponential of I Omega + + align:start position:0% +complex number of exponential of I Omega + + + align:start position:0% +complex number of exponential of I Omega +T again it's just cular formula and + + align:start position:0% +T again it's just cular formula and + + + align:start position:0% +T again it's just cular formula and +using that as a shortcut to be able to + + align:start position:0% +using that as a shortcut to be able to + + + align:start position:0% +using that as a shortcut to be able to +kill two birds with one stone and solve + + align:start position:0% +kill two birds with one stone and solve + + + align:start position:0% +kill two birds with one stone and solve +the two equations by using only really + + align:start position:0% +the two equations by using only really + + + align:start position:0% +the two equations by using only really +one approach which is just the + + align:start position:0% +one approach which is just the + + + align:start position:0% +one approach which is just the +integrating factor and this ends the + + align:start position:0% +integrating factor and this ends the + + + align:start position:0% +integrating factor and this ends the +session for today \ No newline at end of file diff --git a/flAwb1TmOkQ.txt b/flAwb1TmOkQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..f3f4982823bdf23978dd39f62ab74578de46acff --- /dev/null +++ b/flAwb1TmOkQ.txt @@ -0,0 +1,3044 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +DAVID THORBURN: There +are various kinds + +of neorealisms, flavors of +neorealism-- an Italian flavor, + +a French flavor. + +There is a kind of +tonal difference + +that's worth paying +attention to. + +And I maybe I can capture +it over-simply in two + +short clips for you. + +So the first clip +I want to show you + +is from an Italian neorealist +film, the last really + +powerful fully neorealist film +that De Sica himself directed, + +a film called Umberto +D, made in 1952. + +[VIDEO PLAYBACK] + +-[SPEAKING ITALIAN] + +DAVID THORBURN: And this +is our hero, of course. + +-[SPEAKING ITALIAN] + +- + +[MUSIC PLAYING] + +DAVID THORBURN: And compare +this-- think about this scene + +and then compare t-- to the +opening scene of The 400 Blows + +and you'll feel a +difference in mood, I think. + +Even the music is a part of it. + +So he's in great despair +here, and we in the audience + +know that. + +[MUSIC PLAYING] + +-[SPEAKING ITALIAN] + +- + +DAVID THORBURN: +Random dialogue-- + +we don't even know +who said that. + +[MUSIC PLAYING] + +Did you see how Umberto +looked at the man who + +sat down next to him? + +I think the purpose +of that close look + +was to make the audience look at +him too, pay attention to him, + +even though he +never says a word. + +It's possible that +these scenes might + +make some members +of the audience + +think that he's thinking +about jumping off a building. + +All right, freeze it, James. + +Back it up two seconds. + +This is the last moment in the +scene that I want you to see. + +Look what happened here. + +Why are you smiling? + +AUDIENCE: It's because +he was facing-- + +DAVID THORBURN: Speak +up so everyone can hear. + +AUDIENCE: It's +because he was facing + +towards the middle of the bus. + +And then, Umberto, he got up-- + +[END PLAYBACK] + +--and he turned right forward. + +DAVID THORBURN: Yes, as +if he had more space. + +AUDIENCE: Yes. + +DAVID THORBURN: +But then what else? + +What about the gesture? + +What do we feel about this man? + +Never says a word. + +Sits down next to him Umberto. + +When he goes like this, +what do we feel about him? + +He has some horrible story too. + +He maybe is in much +despair as Umberto. + +The point, of +course, is remember + +I talked quite a bit +in earlier lectures + +about what I called +the retarding + +impulse in certain +neorealist films + +and also in certain films of +Renoir-- the extent to which + +what suddenly happens, as the +camera is looking at the world, + +it finds a locus of +interest that may + +be distracting in some sense. + +Now it doesn't truly +distract in the sense + +that it takes you off completely +on a digressive course. + +But what it reminds you of is +the complexity of the world. + +What it reminds you of-- +this particular scene + +especially-- is there's plenty +of despair to go around. + +What it reminds you of is +that the story that has not + +been told about this man-- +this silent, suffering, + +working man who sat down next +to old Umberto-- probably + +has a story, just as +poignant, just as terrible + +as Umberto himself. + +And it's one of the +ways that the film + +has of enlarging +the implications + +of the individuated +story that it tells. + +But the most significant +thing about this moment-- + +so it's a moment in which the +camera doesn't actually swerve, + +but even though our hero, the +protagonist, moves off the bus, + +the camera stays briefly +on that man with the hat. + +Can we watch it-- just the very +end, James-- one more time, + +just to get another look at it? + +[VIDEO PLAYBACK] + +See, that's a gesture +of, what, despair? + +[END PLAYBACK] + +Misery? + +Sadness? + +Sorrow? + +Reflection over what terrible +things are about to happen? + +And the idea that that +story has not been told + +is as significant for our +understanding of the film + +as the story that is told. + +So there's a +similar-- I don't want + +to call it a digressive +impulse, but let's call it + +an impulse toward +noticing what is not + +at the center of the story. + +We might call it an impulse +toward a partial kind + +of abstraction, an attentiveness +to the world that is always + +threatened or challenged +by new options + +that it might want to look at. + +And not all of these impulses +lead to misery or despair, + +even in the +neorealist tradition. + +But the point I want +to make is that I + +think the neorealist +tradition lays more emphasis + +on social problems. + +Its stories are often parables +of impoverishment or parables + +about disempowerment. + +Now the film you're going to +see tonight, The 400 Blows, + +could in many ways be said +to fit that description. + +But there's a lightness, +a lyricism in it, + +that doesn't sustain the heavy +mood, the mood of disturbance, + +the mood of-- if not tragedy-- +of misery, or at least + +of very alert social +awareness that + +permeates neorealist films. + +So here's a moment from the film +you're going to see tonight. + +But it's a very +distracting moment. + +You won't forget +it, when you see it. + +And I'm doing a little harm +to your experience of the film + +by calling your attention +to it, because it's + +such a strange +moment in the film. + +The hero is one of these two +boys, the boy on the left. + +And the guy on the +right-- if you're + +facing the film-- to your left +is the hero, the protagonist. + +And the boy on the right +is his best friend. + +The girl in the +middle is a sister. + +And they're accompanying +this girl-- this + +is in the middle of the film. + +We're not even told where +they're going when it happens, + +but they're going to the +park to watch a puppet show. + +And watch what happens. + +We're in the middle of the film. + +We already know a +lot about the boys. + +The boys have played +hooky, neither of them + +get along very well +with their parents. + +[VIDEO PLAYBACK] + +[MUSIC PLAYING] + +-[SPEAKING FRENCH] + +[YELLING] + +- + +- + +DAVID THORBURN: +Freeze it second. + +They're talking about stealing a +typewriter to get money, right. + +So all right, continue. + +-[SPEAKING FRENCH] + +[YELLING] + +- + +[YELLING] + +- + +[END PLAYBACK] + +DAVID THORBURN: One +thing I should say + +immediately is that it is that +this scene alone would give you + +a very false sense of +the film, if this was + +all you ever saw of the film. + +And the fact is it comes +as a tremendous shock + +when you're watching it. + +Although you enjoy it +when you're watching it, + +you're wondering, +why has Truffaut + +spent so much time +on these faces, + +so much time on these children? + +We never go back +to such a scene. + +None of the little +children's faces + +that we see there do we +ever see again in the film. + +Something happens +to the movie here. + +It's almost as if +it gets sidetracked. + +It's interested in the +boy and in his friend. + +And when we're +watching this scene, + +it certainly occurs to us +in the film, my goodness, + +the scene might be useful, but +why has it gone on so long. + +And I think the simple answer +is that Truffaut, the camera, + +became preoccupied by +the astonishing variety + +and vivid individuating +complexity of those children's + +faces, that the +drama of that became + +so interesting to the +camera, to the filmmaker, + +that he couldn't quite +desert it without giving it + +its just due, even +though from a narrative + +standpoint it doesn't really +advance the story very well. + +But that moment, +when we do cut back + +to the two older boys +sitting in the back, + +talking about +stealing something, + +does justify this scene. + +Why? + +What does it show? + +That they're separated +from innocence. + +That they're too old for this. + +They're sitting there, +everybody else in the audience + +is absolutely rapt. + +Now they're a little younger. + +The implication is these +boys can't participate + +in the joy of innocence any +longer, that they're already + +too old for it in +some sense, and almost + +because of their own behavior, +the choices they've made. + +So the scene does further a +central element in the film, + +clarifying our sense that +especially the protagonist + +of the film is being wrenched +too quickly out of childhood, + +is being forced out of +childlike circumstances + +into circumstances +that no child should + +have to should have to face. + +So it does in some +sense dramatize that. + +But it dramatizes that +in a very imperfect way + +if that were its +primary purpose. + +And what we have to say is, no, +that's not its only purpose. + +The film is stopping +here and watching + +this joy in these children +for the same reason + +that Jean Renoir +stopped to watch + +Boudu do his tricks +in the water-- + +not because it was +furthering any plot, + +but because the spectacle +of Boudu's pleasure + +became what was interesting +that the film, to the filmmaker, + +and to the camera. + +And so one way to understand the +difference between these forms + +of new realism, these kinds +of neorealism-- the Italian + +and the French-- is to +say that the French is + +more open to this lyrical joy, +that there's a lighter tone, + +that the social and political +dimensions of the story + +are not obliterated in +Nouvelle Vague films. + +But they play a lesser +role, they're less central. + +There is no programmatic +social message + +in most of the +Nouvelle Vague films, + +even though there +is by implication-- + +as you'll see in The 400 Blows-- +certainly a powerful critique + +of adult society and the ways +in which disempowered creatures + +like children are treated +in modern society. + +And that theme is there, +it's at the center of it, + +and there's no question +that it's significant. + +But it is surrounded by +other complicating attitudes + +and things that make the +version of new realism + +that the French develop +in the decade beginning + +around 1959 different in +tone from its origins. + +Well, let me very quickly say +a little bit about the origins + +of the Nouvelle Vague. + +You're prepared for this. + +And if I showed you this +film without any background, + +and I said, where +does this come from, + +my hope is that most +of you would say, + +oh, I can see Italian +neorealist elements here, + +I can see Renoirish +elements here. + +A really acute and +perceptive student + +might even see that this +line goes back to Chaplin. + +And Chaplin's +films are committed + +to forms of realistic +representation + +that is in a line, I think, +with these later, more complex + +films, more visually +complex films. + +And in fact, there's an allusion +to Chaplin in tonight's film. + +I hope you'll watch for it. + +One of the teachers actually +plays a Chaplin-like role + +at a certain point. + +And there's no +question that the film + +intends to invoke the joy +and pleasure of the Chaplin + +character in the +memory of its audience + +when those allusions occur. + +So the origins of the Nouvelle +Vague-- first in Jean Vigo + +and in French poetic realism, +in the practices that + +are developed by John Renoir +and other directors of the time, + +that kind of lyrical, +improvisatory open camera + +of Renoir, and then +the way in which those + +are adapted by the +Italians, very much + +influenced by the French. + +So those traditions are at the +center of the Nouvelle Vague. + +And the primary practitioners +of the Nouvelle Vague, + +directors like Truffaut +and Jean-Luc Godard, + +and Alain Resnais, +and Jacques Rivette, + +and a number of other +directors-- Louis Malle, + +a little older, one who +would make magnificent films. + +It's a wonderful, wonderful +group of really significant + +directors. + +Most of them still alive, but +in their dotage now-- even older + +than I am, if you +can believe that-- + +and with magnificent +careers behind them, + +all starting in this moment of +the late '50s when French film + +took a new energy from +the critical discourses + +of the critics who were working +for Cahiers du Cinema, which + +I'll talk about in a second. + +So one central source +for the Nouvelle Vague + +are these earlier +film traditions. + +And the directors who made +the Nouvelle Vague were quite + +self-conscious about +this-- many of them + +had spent a decade before +they became directors writing + +for Cahiers du Cinema, +the great magazine founded + +in 1951 by Andre Bazin, +the critic I've talked + +about earlier in the course. + +And probably Truffaut +was the most well-known + +of the critics who +worked for the magazine. + +Truffaut spent at least +seven or eight years + +working for Cahiers du Cinema +before he made his first film. + +And in their time working +for Cahiers du Cinema, + +they actually articulated +certain theories + +of movie making. + +One of the theories +that they articulated, + +or an aspect of their +overriding theory, + +was articulated in an article-- +a very famous article-- written + +by Truffaut himself before he +became a director, before he + +became an actual director. + +And the title translated went +something like this-- A Certain + +Tendency of French Cinema. + +He published this essay in +Cahiers du Cinema in 1954. + +And it was an attack +on what he called + +the tradition of quality, +in quotes the "tradition + +of quality" in French movies. + +It attacked contemporary +French movies for being stiff, + +for being too literary, +for being too much + +of the establishment. + +And the other +thing that article, + +and many other articles in +Cahiers du Cinema did, was they + +began to write very favorably +about American studio + +directors, the directors who +worked under the Hollywood + +system most effectively, among +them especially Hitchcock. + +And in fact Truffaut did +a series of interviews + +with Hitchcock later +published as a book, Truffaut + +on Hitchcock, or +Truffaut/Hitchcock. + +I forgot the exact +title in English. + +It has a different +title in French. + +It's a very interesting +series of interviews. + +And those of you who +are interested in this + +might want to look at it. + +Because one of the +comical things that + +happens in the interviews +is you constantly see + +Truffaut, who's much more +articulate and theoretically + +subtle than Hitchcock +is-- abstractly, + +I don't mean Hitchcock's +not a great theorist, + +but he's a practicing +theorist-- and you constantly + +see Truffaut trying +to turn Hitchcock + +into an intellectual and +Hitchcock refusing, Hitchcock + +saying, no, no. + +It's almost as if +Truffaut is disappointed + +that Hitchcock can't articulate +the theories that Truffaut + +wants him to articulate. + +So Truffaut is constantly +trying to make Hitchcock + +into a great director, +and Hitchcock + +is often in the interview +saying, I make genre movies, + +leave me alone, I just +want to entertain people. + +So it's comical. + +And in fact I do think that +the French inflated-- Truffaut + +especially-- inflated +Hitchcock's reputation, maybe + +even beyond what it +actually deserved. + +But in any case, it was +subversive of the Cahiers du + +Cinema critics to write about +American directors, studio + +directors-- because +the American studios + +were held to be the essence of +commercial popular art, nothing + +artistic in it at all. + +And in fact it was +these French critics + +who first began to write +about American directors + +in a way that showed respect, +recognized their complexity. + +It's a great irony that +the French recognized + +the artistic value +of American movies + +before the Americans did. + +And at the very time that +the Americans were swooning + +over European art cinema, +this is the period + +when the Nouvelle +Vague appears, when + +I was in college-- in the +late '50s and early '60s. + +And it was an extraordinarily +exciting time in the United + +States for people +interested in movies, + +not because of the American +movies that were being made, + +but because there was +this astonishing-- what + +seemed like an astonishing-- +flower of European + +and Asian cinema. + +It's also the +moment of Kurasawa, + +as I'll mention next week +when we talk about Rashomon, + +and Kurosawa's intervention in +world cinema occurring earlier + +in the 1950s, at the same time +as the Italian neorealists. + +So it was an incredibly +exciting time. + +And educated Americans +for the first time + +began to realize that +the movies weren't just + +popular entertainment, but +were serious works of art. + +The irony is they recognized +this about European films + +but not about their own films. + +And it took another +generation really + +before a serious attention +to American movies + +was paid by American scholars +and American critics. + +Interesting irony. + +A further articulation +of some of + +the theoretical underpinnings +of the Nouvelle Vague + +came from the +director and theorist + +Alexandre Astruc, born in 1923. + +He was good director, +admired director. + +But he's most well-known +as a critic, a theorist. + +And his central theory, +then elaborated and embraced + +by generations later +including Bazin + +and the writers for +Cahiers du Cinema, + +was focused on the +term camera-stylo, + +camera-style, camera hyphen +pen, as if what he imagined + +was that the camera +should be wielded + +by the director with +the same subtlety + +as the writer wields his pen. + +And It was an idea that +the visual style of a film + +could have the +suggestiveness and subtlety + +of a literary work. + +And when Astruc +articulated this, + +it was rather a +revolutionary idea. + +And it was elaborated, +further picked up. + +And the directors +of Cahiers du Cinema + +were very powerfully +in favor of what + +came to be called the auteur +theory-- author, that's + +French for author. + +And the auteur +theory essentially + +is that the director +of the film is + +an author who +leaves his signature + +in every frame of the film. + +It's a radical +over-simplification of course, + +because films are such +collaborative enterprises. + +But it is still nonetheless true +that it grants to the director + +a kind of respected +authority that is certainly + +justified in the case +of many, many films, + +where the director is +the dominant and central + +creative energy. + +And this of course has been +especially true in Europe, + +and even more especially +true in France, + +perhaps, than in +any other society. + +So auteur was a very important +underpinning, encouragement + +to the Nouvelle Vague. + +So when these +critics-turned-movie makers + +began to make movies, +they had already + +made theory for why they were +doing what they were doing. + +They were hostile to certain +forms of pretentiousness + +in contemporary +French films, they + +wanted some of the +energy and power + +to entertain that they +associated with the most + +gifted American +directors, but they also + +wanted films that expressed +a signature individuality. + +They thought films +ought to be and were + +the expression of the +sensibility of their director. + +And the film you're going +to see tonight certainly + +embodies those values. + +One way to think about the +moment at which the Nouvelle + +Vague emerges in both +French and in global culture + +is to think of the year +1955-60-- I used to say just + +'59, but there's some dispute +about when Jean-Luc Godard's + +film actually first +appeared, whether it was + +'59 or '60, so I've added 1960. + +But these three films appeared +within a very short time + +of each other in 1959-60. + +And all three of +them are thought + +to be sort of the origins of the +Nouvelle Vague, the moment when + +the Nouvelle Vague declared +itself as a major film + +movement. + +But Hiroshima, Mon Amour was +a dramatically important film + +when it first appeared. + +In the foreground of the +film is a story of a love + +affair between a Japanese +architect and a French woman. + +And the love affair +is in the foreground. + +But in the background is +Hiroshima and the dropping + +of the bomb on Hiroshima. + +And the story of the lovers-- +I don't mean that it takes + +place while Hiroshima +is going on. + +Hiroshima is +remembered and invoked + +in the course of the film. + +So the foreground of +the film are the lovers. + +The background of the film +is this horrific event, + +the atomic bombing of Hiroshima. + +And the film plays +with our sense of time. + +Its sense of the passage of +time is confused in some sense. + +It's not linear in +the traditional sense + +of an ordinary well-made film. + +And there's not exactly +a surreal quality in it, + +but there's a +quality in it that we + +might say that one of +the things that happens + +is that time is sometimes +treated subjectively + +rather than objectively +in the film. + +And so the time frames you're +in are often mixed or unclear + +in the film. + +The film was also much more +explicit with its nudity + +than American +audiences were used to, + +and it caused quite +a scandal when + +it came to the United States. + +I remember the people who were +in college with me at the time + +were very excited to see +it, partly for that reason. + +Nudity was much rarer +in the popular culture + +when I was your age +than it is today. + +An even more dramatic +and radical movie + +was Jean-Luc +Godard's Breathless, + +which tells the story of a +third-rate criminal played + +with astonishing +panache by Jean-Paul + +Belmondo with a cigarette +stuck in his lips + +through most of the film. + +And there's one moment in the +film where Belmondo walks up + +to a movie marquee, I think, +outside a movie theater. + +And he sees a poster advertising +a film with Humphrey Bogart. + +And he looks at the +film and he tries + +to imitate a Bogart move-- he +goes like goes, puts his arm, + +Bogart had a move like this. + +And he says something +like this, Bogie + +he says in his French accent. + +And you can see in a certain +way that he's patterning himself + +on Bogart, the Bogart who played +ambiguous, sometimes criminal, + +characters in the movies. + +And it's one of the earliest +examples of something + +that becomes really +common in America, + +for example in the +great television series + +The Sopranos, where all the +gangsters are constantly + +invoking The Godfather and +other fictional gangsters, + +and modeling themselves on them, +or quoting scenes from them. + +Well, Belmondo's +character in Breathless + +is one of the first gangsters +to pattern himself on gangsters + +out of popular culture, instead +of being a real gangster. + +And there's a moral ambiguity +in the film that is never + +fully resolved, because +the protagonist of the film + +is this-- we're not going to +show that, James, we don't have + +time for it. + +I was going to show you a +clip, but there's no time. + +It's quite a remarkable film. + +Some of you might +want to look at it-- + +it's available from +the film office. + +And the central ambiguity +is that we identify + +in some degree with the +protagonist-- we follow him + +all the way through the film. + +Very early in the +film he actually + +commits a murder-- it's an +accident, he doesn't intend it, + +it just sort of happens. + +But he still is a murderer. + +He steals a car in the +very opening scene. + +And then he ends up +murdering someone. + +He's on the run-- and +for the rest of the film, + +he's on the run. + +He takes up with +an American girl + +played by Jean Seberg who ends +up betraying him to the cops. + +And in the very final +scene in the film, + +he's shot down by the police. + +And we see him +running down a street + +with a wound in +his back, finally + +falling in a very dramatic +way with his girlfriend + +coming and looking over him. + +And the ending of the +ending of the film + +is very strange, +because it leaves + +the audience uncertain about +what its attitudes toward what + +has happened ought to be. + +Should we resent this betraying +girlfriend as an evil character + +because she's sold her +boyfriend out to the cop? + +On the other hand, her boyfriend +is an amoral murderer and thief + +who doesn't seem to care +about anyone, much less her. + +And yet there's a kind of +charm and an erotic energy + +about the Belmondo character. + +So the film's moral and +psychological grounding + +is unclear. + +And so it was very powerful and +significant for that reason. + +And then finally The 400 Blows, +even more successful film + +in a popular sense than +either of those two, + +appears in the same time frame. + +And it won the best director's +prize at the Cannes Film + +Festival in 1960. + +And it put Truffaut on the map. + +It made Truffaut +a famous director. + +And he never really +looked back after that. + +He went on to have quite +a remarkable career. + +Let me say a couple of +things about the style + +and tone of the Nouvelle Vague. + +Most of it applies to what we've +already said about neorealism + +and about French poetic realism. + +So there's no reason to +go through a lot of it. + +But let's jump to the +bottom, to the items + +at the end of the list. + +First, the improvisatory +aspect of, let's say, + +Renoir's practice +becomes even more pointed + +and central in many of +the Nouvelle Vague films. + +And there really is a +sense in which they often + +would begin filming without +having a full script, letting + +the story itself play +out, discover itself + +as they were filming. + +Tremendous amount +of collaboration + +between performer and director. + +So both plot and +dialogue are often + +the result of a kind of +inspired improvisation. + +Even more significant is the +commitment in the Nouvelle + +Vague-- even more powerful, +much more powerfully + +then than in the earlier +realisms-- toward use + +of a style we might call +a discontinuous style, + +a jumpy style, an edgy style. + +What's a jump cut? + +A jump cut is an +edit that takes place + +in the middle of an action. + +A normal cut, or what we +might call a classic cut. + +If a character is +speaking and making + +a gesture-- say the camera's +on me-- and he says, + +I insist on this +idea more powerfully + +than any other-- +like this, right. + +Well in a classic +sense, you would + +wait until my fist came +down before you cut. + +But if you did a jump cut, +it would say something + +like, I insist on this +idea more than any other. + +Or maybe not even let me +get the word "other" out + +and it would cut +to another scene. + +It creates a sense of +discontinuity or of jaggedness + +that reminds you that life +itself is not so smooth. + +And the other thing that +the jump cut reminds you of + +is something else-- +it reminds you + +of the presence of the editor. + +It reminds you that you +are watching a film. + +It's a very quiet +way of doing this, + +And these films have other, more +explicit, ways of reminding you + +that you're watching a film. + +But there is in +these films not only + +the use of discontinuous +editing and what + +David Cook in his A +History of Narrative Film + +calls elliptical +editing, in which things + +are much more compressed, +much more elliptical. + +Things are not always +perfectly worked out. + +Remember I've talked +about this earlier, how + +in classical Hollywood style if +I were walking toward the door + +they would show me walking. + +When I got here, +they might cut it, + +and then they might pick up the +scene as I reached the door. + +But in a Nouvelle +Vague film, they + +might show me going +like this, and the next + +cut I'd be in the next room +or in bed with my girlfriend. + +They wouldn't bother +to show-- in my case, + +it would be my wife, +please, important. + +But they wouldn't bother +to show that progress, + +because it's silly, +it's unnecessary. + +That's what is meant +by elliptical editing. + +And it makes a greater +demand on the audience. + +But it also has the +effect of creating + +a continuous, quiet sense of +what I call self-reflexiveness + +or self-awareness in the film. + +That is to say, you are +aware at almost every moment + +of these Nouvelle +Vague films that it + +is an artifact, that the film +has been made by human hands, + +that various strategies +and gestures have + +created these effects. + +And that distances you from +the material in some sense. + +But it opens out a new topic. + +And that new topic +is film itself. + +And many of the +Nouvelle Vague films-- + +and especially the films that +come after the Nouvelle Vague, + +but influenced by it-- +turn out to be films + +that one of their topics is the +making of movies themselves, + +films about film. + +And there are a couple of +wonderful examples of this + +in Truffaut's own corpus +of work, including + +a very lovely, gentle film +called-- a light film, not + +as profound as his +most powerful films, + +but a beautiful, beautiful +film-- the French title + +is La Nuit Americaine. + +But it was translated in the +English-speaking world as Day + +for Night. + +If you want to +create the illusion + +that you're filming +at night, you + +can put a filter on the camera. + +And even though you're +filming during the day, + +it will look nighty, +it will look dark. + +It's a strategy of +directors of photography. + +And it's an allusion to that. + +It's called The American +Night because this + +was a strategy that was +especially associated + +with American movies, thought +by the French-- especially + +by the Nouvelle +Vague directors-- + +to be shocking and +ridiculous, because you should + +film on location. + +You should minimize +the falsity that + +is involved in setting up +filters for your film-- faking + +that it's night when +it's really not, + +or faking that it's day when +it's right, that kind of thing. + +But the film, La Nuit Americaine +Is about the making of a film. + +And in it Truffaut +himself I think appears. + +He plays the director who is +having trouble making a film. + +And is the film is +interesting about character. + +It studies the +psychological circumstances + +of its central characters with +great subtlety and interest. + +It says powerful and +interesting things + +about the erotic and +personal connections + +among serious adults. + +And it also says something +about what is involved + +in the making of a film. + +It's about making movies. + +Its subject matter is +the making of a film. + +That level of self-reflexiveness +or self-consciousness + +is always present in at least +some degree in these films. + +And sometimes it can become +an explicit central topic. + +These films, as I've +already indicated, + +are full of allusions and +references to earlier films. + +And I mentioned the +references to Chaplin-- + +you'll see other references +like this, I think, in the film. + +And one thing that happens +in this film, for example, + +is that the characters +go to the movies. + +There's a moment when the +family goes to the movies. + +And the film that's +playing is the title + +of a film by a friend of +Truffaut's, Jacques Rivette, + +a film called Paris +Belongs to Us. + +And it's a real film. + +So it's a kind of allusion +in a way, to another film, + +to a friend. + +But again, there's a level +of self-reflexiveness + +in which that +sequence in the film + +is also a meditation on the +role of movies in social life. + +I'll come back to +that in a second + +when I talk a little bit +about The 400 Blows itself. + +So let me say a word +about Francois Truffaut. + +I hope you'll read +more deeply about him + +in Wikipedia and +in other places. + +His biography is very +rich and interesting. + +One decisive thing to say +about it is that in some sense + +The 400 Blows is a deeply +autobiographical film. + +That is to say, Truffaut +himself was born out-of-wedlock, + +lived with his grandmother. + +Not all the details are +exactly the same in the film, + +but these details I'm +giving you will show you + +how closely the film mirrors the +reality of Truffaut's own life. + +He was raised by his grandmother +until he was eight years old. + +Then he lived with his +mother and his stepfather, + +who gave him his name. + +And you'll see that that's +an issue in this film too. + +The father of Antoine Doinel, +the central character, + +is his stepfather, +not his real father. + +Lived with his mother and his +stepfather until he was 14. + +Was constantly +truant from school. + +His father ended +up turning him in, + +and he spent time +in a reformatory. + +To escape his parents +and other miseries, + +he joined the army at the age +of 18, but he hated the army. + +He was constantly looking +for a chance to desert. + +He finally did desert the +army, and he was arrested. + +He spent time in +prison for desertion. + +And he was really +in big trouble. + +But he had always loved +film, even as a kid. + +And as a 14-year-old in +Paris, he had found his way. + +You'll see that this is +replicated in The 400 Blows, + +because the attraction +of Parisian movies + +is one of the great escapes +for this boy and his friend. + +So in his real life +he loved movies, + +and he went to the French +bibliotheque to watch films. + +And there he met Andre +Bazin, who was already + +an eminent critic and +was the co-founder + +of Cahiers du Cinema. + +Bazin intervened in his case, +apparently used his influence + +to get him either released from +prisoner or have his sentence + +reduced-- I don't know +the exact details. + +He went to work for +Cahiers du Cinema. + +And the rest is history. + +He worked for something +like eight years + +as a critic for +Cahiers du Cinema + +and then began to +make his own films. + +And one of the most +significant things + +about his life as +a critic is that he + +was famous for being +a nasty, incredibly + +unsympathetic critic. + +He was famous for the +viciousness and unforgiving + +quality of his reviews. + +And think what it means that +such a person should then, + +after eight years of doing +this and making enemies + +all over the French +film world, should + +take the risk of beginning +to make a film on his own. + +In many ways very bold of him. + +But it's also true that +the Cahiers du Cinema + +crew, as we might call it, +including the great eminence + +of Bazin himself +and a whole bunch + +of other ambitious young +critics would-be directors, + +they constituted a kind +of critical mass of folks + +with shared ambitions. + +So I don't want +to make it appear + +that what Truffaut was +doing was shockingly brave, + +or courageous, or +self-destructive. + +But it was a dangerous thing, +because he was certainly + +opening himself to revenge +reviews by other people. + +And he was really infamous for +being nasty to other directors, + +especially to French directors. + +You'll see on the outline +that I've listed some + +of his most significant films. + +And the films that +have asterisks next + +to them, those five films, are +all about the same character + +that you're going to +see in tonight's film. + +They're all about +Antoine Doinel. + +And it's a unique film record. + +It's a series of +autobiographical films, played + +by the same actor, who is a +kind of Truffaut stand-in. + +And the second film that I +have on the list, or rather + +the third film, +Antoine and Colette, + +I have it in quotations because +it's not a feature-length film. + +It's an episode from +an anthology film + +that appeared in 1962 +called Love at Twenty. + +It was a very flattering +thing for the young director + +to be asked to +contribute to that. + +And so that's +another installment + +of the story of Antoine Doinel. + +And then the next +one takes place + +in 1968, Stolen Kisses, again +in 1970-- Bread and Board. + +And then finally, nine years +later, the final Doinel film, + +Love on the Run. + +It ends in an ambiguous +way, like all of the films. + +And one of the wonderful things, +Jean-Pierre Leaud-- L-E-A-U-D, + +I don't know how to +say it, Leaud, Leaud-- + +who plays Doinel, you can see +him aging through these films. + +It's a wonderful sequence. + +And if you like +The 400 Blows, you + +might want to watch +the other films. + +The 400 Blows is probably +the best of all of them, + +but they're beautiful films. + +And what they show +is, in some sense, + +Truffaut returning to this +autobiographical theme + +at different stages in his life. + +There are even some scholars +who have suggested that there's + +a kind of analogy, or +a mirror relationship, + +between the young +Jean-Pierre Leaud, + +the 14-year-old who plays the +central character in The 400 + +Blows, that there's an analogy +between his relationship + +to Truffaut and Truffaut's +relationship to Bazin, + +as if what's happened +is that Truffaut + +with his new young actor +is re-enacting-- but now + +on the other side-- the +mentor-mentee relationship + +that Bazin and Truffaut +apparently enjoyed as well. + +I don't have time to talk about +this remarkable list of films. + +The only film on this +list that isn't wonderful, + +I think-- certainly +worth looking at closely, + +maybe two that are not +absolutely first-rate-- + +is the one in 1966, +Fahrenheit 451. + +I mention it to you because it's +such an interesting example. + +Based on the Ray Bradbury. + +And it is his worst film. + +It's his first +film in English, he + +didn't know English very +well when he made it. + +It's an oddly heavy-handed +and wooden film. + +But I still have some +kind of affection for it, + +even though it's not a +very good adaptation. + +Because he was attentive +to Ray Bradbury, + +attentive to the ambitions. + +It's a film that's theoretically +much more interesting than it + +is in practice. + +But all the other films +are very remarkable films + +and among the most significant +films of their day. + +And let me just say one final +word about the last film I've + +listed there, The Last Metro, +which starred Catherine + +Deneuve and Gerard Depardieu. + +In a way it's a +World War II film. + +It tells the story of +a Jewish director who + +has to hide in the hidden +basement of his theater + +while his wife, +who is not Jewish, + +is able to run the +theater above ground. + +And it tells the story of +the importance of theater + +even during the war +years, when Paris + +was occupied by the Germans. + +It's a very powerful and +moving love story, as well as + +a story that celebrates +the power of theater + +and the power of +art in hard times. + +And it's a lovely, +poignant, powerful film. + +I want to say a few words +about the film itself. + +It's fairly +straightforward, and I think + +you'll absolutely enjoy it. + +First the title, weird +title, The 400 Blows. + +It comes from a French idiom. + +And the idiom means +something like + +to sow your wild +oats, to raise hell. + +[SPEAKING FRENCH] + +To do or to make +the 400 blows means + +essentially to raise hell, +to do a walkabout, something + +that young people do. + +And of course the +title is very resonant. + +You end without any +certainty about what + +the resolution of this wild +behavior is going to be. + +The second important thing +to say about the film, + +something I've implied +earlier, is that it's + +a film that loves Paris. + +And in a certain sense the +boy's odyssey through the film + +is an exploration of Paris +and of Parisian delights. + +And again, think of what it +says about the city, about + +this great city, in the +time that the film was made, + +that boys of this age could +wander around so safely + +and engage in so many remarkable +adventures in the course + +of an ordinary day in Paris. + +So the film is attentive +to the feel, the texture, + +of Paris, in +something of the way + +that some of the +Italian neorealist films + +were attentive to the +physical texture of Rome, + +or of other Italian +environments. + +The family romance at +the heart of this film + +is one of Truffaut's +subtlest achievements. + +And I just want to +call your attention + +to how subtle it actually is. + +Watch how the story +unfolds, and how + +in a very brief +and elliptical way + +we come to understand +the motivations + +and the unhappinesses of each +of the major characters-- + +the mother, the +father, and the son. + +What we discover fairly early +is that the mother isn't + +that happy with her husband. + +She feels that she's +losing her beauty, + +she feels trapped in +an unhappy marriage. + +The husband is to her a +kind of boring character. + +He's the boy's stepfather. + +Early in the film, we +get a wonderful sequence. + +Remember, watch for the +principle of multiplicity + +there, because so many things +are going on simultaneously. + +The physical, and social, +and economic environment + +within which the family +lives is dramatized + +in those opening scenes. + +The boy's relation to +his family is dramatized + +in those opening scenes. + +And the father's +relation to the mother + +is dramatized in those +opening scenes as well. + +And what we discover, +of course, is + +that the father is +actually-- even though he's + +the stepfather-- actually feels +great affection for the boy. + +And they get along +very well, much better + +than the boy gets along +with his mother, who + +is actually his blood relative. + +And the mother's resentment +partly has to do with the fact + +that she must feel that +the boy has trapped her. + +And she's entering +middle age, she + +thinks she's losing +her beauty, she + +thinks she's chained to a +child and to a marriage. + +And you can feel this. + +And there are certain +moments in the film when + +the mother, for various reasons, +is embarrassed over the fact + +that she seems to have +been a bad mother. + +And she uses various strategies +to reach out to her son. + +And some of them are kind of +creepy, as you'll discover. + +She's a very complex character, +and the least sympathetic + +character in the +film, because she + +behaves in many ways so +shockingly toward her son. + +But even she, the least +sympathetic character + +in the film, is treated in the +film with a kind of complexity + +that we expect from adults. + +In other words, we +don't think that she's + +an evil villainess +who would like + +to suck the blood of her child. + +Not at all, not at all. + +What you feel is +that she's driven + +to her hostilities +and her unhappinesses + +by the confined and unhappy +circumstances of her life. + +Not that she's totally +forgiven, but she's + +understood by the film. + +Something of the +same kind of thing + +is true for the husband, +who loves his wife + +and knows that his wife is +probably dissatisfied with him, + +may be unfaithful to him. + +And that colors his +relation to his son, + +with whom he often feels +a great connection. + +So there's a great +poignant sense + +that this dysfunctional +family is less happy + +than it needs to +be, if only it could + +understand its circumstances. + +There's one wonderful moment +in the film where some + +of the hostility disappears. + +And it comes at a moment +that I mentioned earlier + +where the husband and the +wife go off to the movies + +together, taking +their son with them. + +It's like a family outing. + +That's when they go to see +the Jacques Rivette film. + +And it's the one moment +in the film where + +all three of the central +characters in the film + +are happy together. + +And you might ask, why? + +Well, the father is +happy because the wife + +is paying attention to +him and is doing something + +with the family. + +And the boy is happy because the +family, the father and mother, + +aren't squabbling +with each other + +and they're including him. + +And the mother is at +least partly happy + +because she can +see both of the men + +are delighted by what's going +on and because she likes movies + +too. + +So one of the things that +the film dramatizes is + +the importance of +film in human life, + +is how film is a kind of +escape or a respite from misery + +in certain ways. + +And so it's a kind of +commentary on the centrality + +of the movies as a source +of information, insight, + +and consolation. + +Pay attention to the way +the film is structured. + +It's not unlike what I've +said about the organic form + +of certain earlier +Italian and French movies. + +The structure unfolds +in a natural way. + +We don't feel that plot +is driving the story, + +we feel that what +happens in the film + +happens out of a kind of +natural unfolding that + +is a function of both the +environment and the characters. + +There's so much that +I've left out here + +that I feel guilty about +not having mentioned. + +I should mention one +parenthetic remark, + +just because it's +such a vivid detail. + +The film was made for a +relatively small amount + +of money, even in those days. + +It cost $75,000 to +make this movie. + +And in the United +States alone it + +earned over $500,000, a gigantic +amount of money in those days. + +So it was an astonishing +success in that way. + +Let me end by saying +one final word + +about the astonishing +conclusion of the movie. + +The ending is beautiful +in its own right. + +I mean there's a +kind of visual beauty + +that's constantly competing for +your attention as you watch. + +The boy, as you'll +see in the story, + +ends up in a kind +of reform school. + +His crimes are so +modest and that's + +part of what makes +the film so poignant. + +He's actually caught stealing-- +not stealing-- the typewriter + +that he was talking about +stealing in that scene you saw. + +He's caught when he's trying +to return the typewriter. + +He has an attack of +conscience, and he + +thinks I shouldn't do this. + +And he's caught +returning the typewriter, + +and that's his big crime. + +And you'll see, one of the +things that happens to him when + +he's kicked out-- he runs +away from his family at one + +point-- he spends +nights in Paris + +on his own, this +14-year-old child, boy. + +Very interesting +again, about the way + +the film celebrates +the city of Paris + +as a nurturing, adventurous, +exciting, not really dangerous + +place. + +But let me say one final +word about the ending. + +At the end very end of the +movie, he kind of escapes. + +He makes a kind of escape +from this reform school + +that he's in. + +And it's an immensely +beautiful sequence, + +in which we see him running +through a countryside. + +And it's a tracking shot, an +immense long tracking shot. + +And the camera follows him +as he's running-- running, + +running, running. + +And it goes on, in some sense, +something like the scene + +that I showed you, where +the puppet show seems + +to be going on forever. + +When you're watching +the film, you'll + +see that it's strange, because +the puppet show intervenes + +in the movie without explanation +and disappears from the movie + +without explanation. + +Something of the +same kind of thing + +is true here, where the +beauty of the countryside + +starts to compete +for your attention. + +But in any case, finally +at the end of his run + +he comes he comes to +a verge, to an end. + +He comes to the water, +he comes to the sea. + +He always said he +wanted to see the sea, + +but this is a very disappointing +version of the sea. + +And he runs up against it. + +Watch how the music works. + +There's a beautiful use +of a stringed instrumen-- + +I'm not sure what +instrument, maybe a guitar. + +But anyway, a beautiful +stringed instrument + +plays a melody that you've +heard earlier in the film. + +And we see him running +up to this verge. + +And then there's an +astonishing moment + +in which he comes to a stop. + +And he's looking at the water. + +And the camera freezes on him. + +There's a freeze +frame at the very end. + +It's the most famous freeze +frame in the history of movies. + +And after this film, the freeze +frame became a cheapo trick. + +You began to find it in +television commercials. + +But at the time that he +used this frieze frame, + +it was an immensely +dramatic effect. + +I don't mean nobody had ever +used such strategies before. + +But it is one of the +subtlest uses of a freeze + +frame in the history of movies. + +And one of the reasons I +want you to watch for it + +and pay attention to it, +is listen to the music + +as it's going on. + +Because the tune is finally +unfinished at the end. + +In other words, where one +final note that isn't played. + +But you've heard +the note before, + +so you keep expecting it. + +And that's part of the power of +that freeze frame at the end. + +I think he's looking at us +when the freeze frame occurred. + +But the point is, where is +he going, what comes next? + +The film doesn't +really have an answer. + +We don't know where +the film is going. + +We don't know what's going +to happen to this boy. + +So it ends on a note of +open-endedness and ambiguity + +that's powerful and profound. + +But what we also know +is that this has not + +been an apocalyptic ending. + +It's not a catastrophic ending. + +The boy is isolated, +the boy is alone, + +he doesn't know what's +going to happen to him, + +he doesn't know whether +he'll be recaptured, + +he doesn't know where +he's going to go. + +But I don't think we have any +sense that he's going to die. + +We don't have any sense that +this is the end of his life. + +We have a sense, +maybe, that this + +is the beginning of his life. + +So that there's a +profound uncertainty, + +a kind of beautiful uncertainty, +a beautiful ambiguity + +at the end of the +movie, that is partly + +captured in the complex +relation between sound and image + +at the end of this movie. + +Those of you who have +never seen The 400 Blows + +are in for a really great treat. + +The final films in this course +are among the greatest films + +ever made. + +I hope you enjoy it +as much as I did. + +I still remember +the place in which + +I saw this film and the +exhilaration I felt when + +I came out of watching it, with +the recognition that movies + +could be what great +novels had been. \ No newline at end of file diff --git a/g2ISFplW5zQ.txt b/g2ISFplW5zQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..57fd5ed95ff7c6b6d868de1500344c6d3154691d --- /dev/null +++ b/g2ISFplW5zQ.txt @@ -0,0 +1,7851 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so how many of you have exposure or have + + align:start position:0% +so how many of you have exposure or have + + + align:start position:0% +so how many of you have exposure or have +taken any uh heat transfer classes + + align:start position:0% +taken any uh heat transfer classes + + + align:start position:0% +taken any uh heat transfer classes +here okay it's about half of you cool + + align:start position:0% +here okay it's about half of you cool + + + align:start position:0% +here okay it's about half of you cool +uh so can you start + + align:start position:0% +uh so can you start + + + align:start position:0% +uh so can you start +by telling me what heat + + align:start position:0% + + + + align:start position:0% + +is it's like pretty B + + align:start position:0% +is it's like pretty B + + + align:start position:0% +is it's like pretty B +Bic yeah okay it's a form of + + align:start position:0% +Bic yeah okay it's a form of + + + align:start position:0% +Bic yeah okay it's a form of +energy + + align:start position:0% + + + + align:start position:0% + +uh what are the units of + + align:start position:0% +uh what are the units of + + + align:start position:0% +uh what are the units of +that + + align:start position:0% +that + + + align:start position:0% +that +cool + + align:start position:0% +cool + + + align:start position:0% +cool +um and what about heat transfer what + + align:start position:0% +um and what about heat transfer what + + + align:start position:0% +um and what about heat transfer what +what + + align:start position:0% + + + + align:start position:0% + +are I guess that's pretty + + align:start position:0% +are I guess that's pretty + + + align:start position:0% +are I guess that's pretty +self-explanatory just transferring heat + + align:start position:0% +self-explanatory just transferring heat + + + align:start position:0% +self-explanatory just transferring heat +uh what are the units of heat + + align:start position:0% + + + + align:start position:0% + +transfer + + align:start position:0% +transfer + + + align:start position:0% +transfer +uh generally you're trying to figure out + + align:start position:0% +uh generally you're trying to figure out + + + align:start position:0% +uh generally you're trying to figure out +how much uh energy is being transferred + + align:start position:0% +how much uh energy is being transferred + + + align:start position:0% +how much uh energy is being transferred +per second so you're going to have a + + align:start position:0% +per second so you're going to have a + + + align:start position:0% +per second so you're going to have a +jewel per second or Watts + + align:start position:0% +jewel per second or Watts + + + align:start position:0% +jewel per second or Watts +yeah uh so what are + + align:start position:0% +yeah uh so what are + + + align:start position:0% +yeah uh so what are +what are like what are three major modes + + align:start position:0% +what are like what are three major modes + + + align:start position:0% +what are like what are three major modes +of heat + + align:start position:0% +of heat + + + align:start position:0% +of heat +transfer as well if do you + + align:start position:0% +transfer as well if do you + + + align:start position:0% +transfer as well if do you +remember right + + align:start position:0% + + + + align:start position:0% + +awesome um + + align:start position:0% + + + + align:start position:0% + +and tell for people who haven't seen + + align:start position:0% +and tell for people who haven't seen + + + align:start position:0% +and tell for people who haven't seen +this material before tell me if I'm + + align:start position:0% +this material before tell me if I'm + + + align:start position:0% +this material before tell me if I'm +going through it too quickly uh when I + + align:start position:0% +going through it too quickly uh when I + + + align:start position:0% +going through it too quickly uh when I +started talking about + + align:start position:0% +started talking about + + + align:start position:0% +started talking about +it + + align:start position:0% + + + + align:start position:0% + +but um Can someone + + align:start position:0% +but um Can someone + + + align:start position:0% +but um Can someone +can Okay can people explain what the + + align:start position:0% +can Okay can people explain what the + + + align:start position:0% +can Okay can people explain what the +difference between the three types of + + align:start position:0% +difference between the three types of + + + align:start position:0% +difference between the three types of +heat + + align:start position:0% + + + + align:start position:0% + +transfer + + align:start position:0% +transfer + + + align:start position:0% +transfer +what + + align:start position:0% + + + + align:start position:0% + +else + + align:start position:0% + + + + align:start position:0% + +yes okay + + align:start position:0% + + + + align:start position:0% + +convection Bally conduction ex + + align:start position:0% +convection Bally conduction ex + + + align:start position:0% +convection Bally conduction ex +fluid + + align:start position:0% + + + + align:start position:0% + +cool um in radiation + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um I think this is more generally just + + align:start position:0% +um I think this is more generally just + + + align:start position:0% +um I think this is more generally just +heating through electromagnetic waves + + align:start position:0% +heating through electromagnetic waves + + + align:start position:0% +heating through electromagnetic waves +uh but yeah so that's kind of the three + + align:start position:0% +uh but yeah so that's kind of the three + + + align:start position:0% +uh but yeah so that's kind of the three +the three sort of big modes of heat + + align:start position:0% +the three sort of big modes of heat + + + align:start position:0% +the three sort of big modes of heat +transfer uh you have we'll be talking + + align:start position:0% +transfer uh you have we'll be talking + + + align:start position:0% +transfer uh you have we'll be talking +about convection and conduction a lot + + align:start position:0% +about convection and conduction a lot + + + align:start position:0% +about convection and conduction a lot +more later when we're doing say cooking + + align:start position:0% +more later when we're doing say cooking + + + align:start position:0% +more later when we're doing say cooking +and stoves because that plays into that + + align:start position:0% +and stoves because that plays into that + + + align:start position:0% +and stoves because that plays into that +a lot more like when you're putting a + + align:start position:0% +a lot more like when you're putting a + + + align:start position:0% +a lot more like when you're putting a +pot on a fire like um but when we're + + align:start position:0% +pot on a fire like um but when we're + + + align:start position:0% +pot on a fire like um but when we're +dealing with solar uh solar stuff we're + + align:start position:0% +dealing with solar uh solar stuff we're + + + align:start position:0% +dealing with solar uh solar stuff we're +going to be dealing mostly with + + align:start position:0% +going to be dealing mostly with + + + align:start position:0% +going to be dealing mostly with +radiation + + align:start position:0% +radiation + + + align:start position:0% +radiation +um but while we're on the topic of heat + + align:start position:0% +um but while we're on the topic of heat + + + align:start position:0% +um but while we're on the topic of heat +or while we're on the topic of heat + + align:start position:0% +or while we're on the topic of heat + + + align:start position:0% +or while we're on the topic of heat +transfer I might as well give you the + + align:start position:0% +transfer I might as well give you the + + + align:start position:0% +transfer I might as well give you the +equations for the other two but we'll + + align:start position:0% +equations for the other two but we'll + + + align:start position:0% +equations for the other two but we'll +start by talking about ation + + align:start position:0% + + + + align:start position:0% + +um so when we're dealing + + align:start position:0% +um so when we're dealing + + + align:start position:0% +um so when we're dealing +with when we're dealing with radiation + + align:start position:0% +with when we're dealing with radiation + + + align:start position:0% +with when we're dealing with radiation +we're + + align:start position:0% + + + + align:start position:0% + +uh cool uh when we're dealing with + + align:start position:0% +uh cool uh when we're dealing with + + + align:start position:0% +uh cool uh when we're dealing with +radiation we're thinking of objects + + align:start position:0% +radiation we're thinking of objects + + + align:start position:0% +radiation we're thinking of objects +giving off energy in electromagnetic + + align:start position:0% +giving off energy in electromagnetic + + + align:start position:0% +giving off energy in electromagnetic +waves um the only thing that it really + + align:start position:0% +waves um the only thing that it really + + + align:start position:0% +waves um the only thing that it really +matters when you're dealing with this is + + align:start position:0% +matters when you're dealing with this is + + + align:start position:0% +matters when you're dealing with this is +is what the temperature of the object is + + align:start position:0% +is what the temperature of the object is + + + align:start position:0% +is what the temperature of the object is +um so you can approximate things as or + + align:start position:0% +um so you can approximate things as or + + + align:start position:0% +um so you can approximate things as or +there's an equation for it + + align:start position:0% +there's an equation for it + + + align:start position:0% +there's an equation for it +um which + + align:start position:0% + + + + align:start position:0% + +is um which is the heat transfer from + + align:start position:0% +is um which is the heat transfer from + + + align:start position:0% +is um which is the heat transfer from +due to radiation is the Stefan boltzman + + align:start position:0% +due to radiation is the Stefan boltzman + + + align:start position:0% +due to radiation is the Stefan boltzman +constant times the area of the surface + + align:start position:0% +constant times the area of the surface + + + align:start position:0% +constant times the area of the surface +area of the object times the temperature + + align:start position:0% +area of the object times the temperature + + + align:start position:0% +area of the object times the temperature +to the 4th which is an important + + align:start position:0% +to the 4th which is an important + + + align:start position:0% +to the 4th which is an important +equation to know uh + + align:start position:0% +equation to know uh + + + align:start position:0% +equation to know uh +for convective heat transfer you have a + + align:start position:0% +for convective heat transfer you have a + + + align:start position:0% +for convective heat transfer you have a +different equation but again like this + + align:start position:0% +different equation but again like this + + + align:start position:0% +different equation but again like this +isn't that relevant so I'm going to move + + align:start position:0% +isn't that relevant so I'm going to move + + + align:start position:0% +isn't that relevant so I'm going to move +on to talking to you guys + + align:start position:0% +on to talking to you guys + + + align:start position:0% +on to talking to you guys +about + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +about solar different types of Solar + + align:start position:0% +about solar different types of Solar + + + align:start position:0% +about solar different types of Solar +Technologies now uh so the first one we + + align:start position:0% +Technologies now uh so the first one we + + + align:start position:0% +Technologies now uh so the first one we +GNA talk about is Sodis do you guys have + + align:start position:0% +GNA talk about is Sodis do you guys have + + + align:start position:0% +GNA talk about is Sodis do you guys have +you do you have any okay so you have + + align:start position:0% +you do you have any okay so you have + + + align:start position:0% +you do you have any okay so you have +Sodis you have solar thermal um so solar + + align:start position:0% +Sodis you have solar thermal um so solar + + + align:start position:0% +Sodis you have solar thermal um so solar +thermal is when you're there are + + align:start position:0% +thermal is when you're there are + + + align:start position:0% +thermal is when you're there are +different types of Technologies it's + + align:start position:0% +different types of Technologies it's + + + align:start position:0% +different types of Technologies it's +where you're using heat from uh you're + + align:start position:0% +where you're using heat from uh you're + + + align:start position:0% +where you're using heat from uh you're +using heat from the sunlight directly so + + align:start position:0% +using heat from the sunlight directly so + + + align:start position:0% +using heat from the sunlight directly so +you're using solar radiation to heat + + align:start position:0% +you're using solar radiation to heat + + + align:start position:0% +you're using solar radiation to heat +things and there are three different + + align:start position:0% +things and there are three different + + + align:start position:0% +things and there are three different +sorts of big ways you can do this you + + align:start position:0% +sorts of big ways you can do this you + + + align:start position:0% +sorts of big ways you can do this you +can do use it for cooking and drying you + + align:start position:0% +can do use it for cooking and drying you + + + align:start position:0% +can do use it for cooking and drying you +can use it for heating of water and you + + align:start position:0% +can use it for heating of water and you + + + align:start position:0% +can use it for heating of water and you +can use it for generating electricity + + align:start position:0% +can use it for generating electricity + + + align:start position:0% +can use it for generating electricity +and you also have photov voltaics um + + align:start position:0% +and you also have photov voltaics um + + + align:start position:0% +and you also have photov voltaics um +which we worked with last time for + + align:start position:0% +which we worked with last time for + + + align:start position:0% +which we worked with last time for +generating electricity + + align:start position:0% +generating electricity + + + align:start position:0% +generating electricity +um do you so Sodus the way Sodus works + + align:start position:0% +um do you so Sodus the way Sodus works + + + align:start position:0% +um do you so Sodus the way Sodus works +is you fill bottles with water and you + + align:start position:0% +is you fill bottles with water and you + + + align:start position:0% +is you fill bottles with water and you +close the cap then you leave these + + align:start position:0% +close the cap then you leave these + + + align:start position:0% +close the cap then you leave these +bottles out on a rooftop and you expose + + align:start position:0% +bottles out on a rooftop and you expose + + + align:start position:0% +bottles out on a rooftop and you expose +them to sunlight for about 6 hours and + + align:start position:0% +them to sunlight for about 6 hours and + + + align:start position:0% +them to sunlight for about 6 hours and +you uh you can St like and the UV light + + align:start position:0% +you uh you can St like and the UV light + + + align:start position:0% +you uh you can St like and the UV light +from the sun plus the heat from the Sun + + align:start position:0% +from the sun plus the heat from the Sun + + + align:start position:0% +from the sun plus the heat from the Sun +Also kills the pathogens and bacteria + + align:start position:0% +Also kills the pathogens and bacteria + + + align:start position:0% +Also kills the pathogens and bacteria +inside the water if you remember do you + + align:start position:0% +inside the water if you remember do you + + + align:start position:0% +inside the water if you remember do you +guys remember from last week when we + + align:start position:0% +guys remember from last week when we + + + align:start position:0% +guys remember from last week when we +were build like playing with the bags + + align:start position:0% +were build like playing with the bags + + + align:start position:0% +were build like playing with the bags +there was a Sodus bag does that sound + + align:start position:0% +there was a Sodus bag does that sound + + + align:start position:0% +there was a Sodus bag does that sound +familiar at all with the plastic + + align:start position:0% +familiar at all with the plastic + + + align:start position:0% +familiar at all with the plastic +sealer yeah why you why you laughing I + + align:start position:0% +sealer yeah why you why you laughing I + + + align:start position:0% +sealer yeah why you why you laughing I +spent like two hours trying to make + + align:start position:0% +spent like two hours trying to make + + + align:start position:0% +spent like two hours trying to make +one yeah um so so Sodus is a really cool + + align:start position:0% +one yeah um so so Sodus is a really cool + + + align:start position:0% +one yeah um so so Sodus is a really cool +technology um it's an example of how you + + align:start position:0% +technology um it's an example of how you + + + align:start position:0% +technology um it's an example of how you +can use solar energy to purify water + + align:start position:0% +can use solar energy to purify water + + + align:start position:0% +can use solar energy to purify water +there other like there are other ways + + align:start position:0% +there other like there are other ways + + + align:start position:0% +there other like there are other ways +you can use solar energy to purify water + + align:start position:0% +you can use solar energy to purify water + + + align:start position:0% +you can use solar energy to purify water +too but this is supposed to be one of + + align:start position:0% +too but this is supposed to be one of + + + align:start position:0% +too but this is supposed to be one of +the better ones + + align:start position:0% +the better ones + + + align:start position:0% +the better ones +um so I guess we kind of jumped ahead by + + align:start position:0% +um so I guess we kind of jumped ahead by + + + align:start position:0% +um so I guess we kind of jumped ahead by +showing you a really good Sodus + + align:start position:0% +showing you a really good Sodus + + + align:start position:0% +showing you a really good Sodus +technology last week before talking to + + align:start position:0% +technology last week before talking to + + + align:start position:0% +technology last week before talking to +you about Sodus as as like a technology + + align:start position:0% +you about Sodus as as like a technology + + + align:start position:0% +you about Sodus as as like a technology +but in most of the developing world the + + align:start position:0% +but in most of the developing world the + + + align:start position:0% +but in most of the developing world the +companies that are promoting Sodus what + + align:start position:0% +companies that are promoting Sodus what + + + align:start position:0% +companies that are promoting Sodus what +they do is they tell people to use 2 lit + + align:start position:0% +they do is they tell people to use 2 lit + + + align:start position:0% +they do is they tell people to use 2 lit +bottles um which are available in a lot + + align:start position:0% +bottles um which are available in a lot + + + align:start position:0% +bottles um which are available in a lot +of the developing world and uh fill them + + align:start position:0% +of the developing world and uh fill them + + + align:start position:0% +of the developing world and uh fill them +with water and leave them out on your + + align:start position:0% +with water and leave them out on your + + + align:start position:0% +with water and leave them out on your +rooftops can you guys think of any ideas + + align:start position:0% +rooftops can you guys think of any ideas + + + align:start position:0% +rooftops can you guys think of any ideas +or any reasons why this is not a good + + align:start position:0% +or any reasons why this is not a good + + + align:start position:0% +or any reasons why this is not a good +idea or what's or what isn't the best + + align:start position:0% +idea or what's or what isn't the best + + + align:start position:0% +idea or what's or what isn't the best +okay why this isn't the best solution to + + align:start position:0% +okay why this isn't the best solution to + + + align:start position:0% +okay why this isn't the best solution to +using this technology or best implement + + align:start position:0% +using this technology or best implement + + + align:start position:0% +using this technology or best implement +mentation of this technology and why I + + align:start position:0% +mentation of this technology and why I + + + align:start position:0% +mentation of this technology and why I +say a bag would be + + align:start position:0% +say a bag would be + + + align:start position:0% +say a bag would be +better um so what are some of the + + align:start position:0% +better um so what are some of the + + + align:start position:0% +better um so what are some of the +problems with with a a plastic bottle so + + align:start position:0% +problems with with a a plastic bottle so + + + align:start position:0% +problems with with a a plastic bottle so +you have this plastic bottle looks kind + + align:start position:0% +you have this plastic bottle looks kind + + + align:start position:0% +you have this plastic bottle looks kind +of + + align:start position:0% +of + + + align:start position:0% +of +like + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +um + + align:start position:0% + + + + align:start position:0% + +yeah over fall + + align:start position:0% +yeah over fall + + + align:start position:0% +yeah over fall +off sit whereas the bag at Le class was + + align:start position:0% +off sit whereas the bag at Le class was + + + align:start position:0% +off sit whereas the bag at Le class was +like + + align:start position:0% +like + + + align:start position:0% +like +more just floppy yeah uh I actually + + align:start position:0% +more just floppy yeah uh I actually + + + align:start position:0% +more just floppy yeah uh I actually +haven't seen uh that particular issue + + align:start position:0% +haven't seen uh that particular issue + + + align:start position:0% +haven't seen uh that particular issue +before but that's a good point + + align:start position:0% +before but that's a good point + + + align:start position:0% +before but that's a good point +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um what about in terms of + + align:start position:0% +um what about in terms of + + + align:start position:0% +um what about in terms of +Transportation how easy is it to get a + + align:start position:0% +Transportation how easy is it to get a + + + align:start position:0% +Transportation how easy is it to get a +plastic bottle that's shaped like this + + align:start position:0% +plastic bottle that's shaped like this + + + align:start position:0% +plastic bottle that's shaped like this +what if I if I wanted to provide an + + align:start position:0% +what if I if I wanted to provide an + + + align:start position:0% +what if I if I wanted to provide an +entire Community with these how would I + + align:start position:0% +entire Community with these how would I + + + align:start position:0% +entire Community with these how would I +send it to them + + align:start position:0% +send it to them + + + align:start position:0% +send it to them +I would have to like I would have to + + align:start position:0% +I would have to like I would have to + + + align:start position:0% +I would have to like I would have to +ship a giant container with 2 L bottles + + align:start position:0% +ship a giant container with 2 L bottles + + + align:start position:0% +ship a giant container with 2 L bottles +and they don't really pack well at all + + align:start position:0% +and they don't really pack well at all + + + align:start position:0% +and they don't really pack well at all +right you need to fill like a crate of + + align:start position:0% +right you need to fill like a crate of + + + align:start position:0% +right you need to fill like a crate of +uh 2 L bottles and it just seems really + + align:start position:0% +uh 2 L bottles and it just seems really + + + align:start position:0% +uh 2 L bottles and it just seems really +silly to ship an empty contain or a + + align:start position:0% +silly to ship an empty contain or a + + + align:start position:0% +silly to ship an empty contain or a +container of empty water bottles um in + + align:start position:0% +container of empty water bottles um in + + + align:start position:0% +container of empty water bottles um in +places where they have 2 L bottles it's + + align:start position:0% +places where they have 2 L bottles it's + + + align:start position:0% +places where they have 2 L bottles it's +a really good technology because I mean + + align:start position:0% +a really good technology because I mean + + + align:start position:0% +a really good technology because I mean +if they're just taking existing things + + align:start position:0% +if they're just taking existing things + + + align:start position:0% +if they're just taking existing things +that they already have and they're using + + align:start position:0% +that they already have and they're using + + + align:start position:0% +that they already have and they're using +them repurposing them for this then it's + + align:start position:0% +them repurposing them for this then it's + + + align:start position:0% +them repurposing them for this then it's +great but otherwise it's not it doesn't + + align:start position:0% +great but otherwise it's not it doesn't + + + align:start position:0% +great but otherwise it's not it doesn't +seem to make that much sense to try to + + align:start position:0% +seem to make that much sense to try to + + + align:start position:0% +seem to make that much sense to try to +fly them in and that's what some of like + + align:start position:0% +fly them in and that's what some of like + + + align:start position:0% +fly them in and that's what some of like +the companies that were really promoting + + align:start position:0% +the companies that were really promoting + + + align:start position:0% +the companies that were really promoting +so just heavily in the beginning were + + align:start position:0% +so just heavily in the beginning were + + + align:start position:0% +so just heavily in the beginning were +doing they were trying to like ship 2 L + + align:start position:0% +doing they were trying to like ship 2 L + + + align:start position:0% +doing they were trying to like ship 2 L +bottles in bulk to uh communities to get + + align:start position:0% +bottles in bulk to uh communities to get + + + align:start position:0% +bottles in bulk to uh communities to get +them to use them + + align:start position:0% +them to use them + + + align:start position:0% +them to use them +um can you guys think of any other + + align:start position:0% +um can you guys think of any other + + + align:start position:0% +um can you guys think of any other +disadvantages to + + align:start position:0% + + + + align:start position:0% + +using uh using these water bottles what + + align:start position:0% +using uh using these water bottles what + + + align:start position:0% +using uh using these water bottles what +about so how does how does okay maybe + + align:start position:0% +about so how does how does okay maybe + + + align:start position:0% +about so how does how does okay maybe +I'll I'll go a little bit more into how + + align:start position:0% +I'll I'll go a little bit more into how + + + align:start position:0% +I'll I'll go a little bit more into how +the technology works so you have your + + align:start position:0% +the technology works so you have your + + + align:start position:0% +the technology works so you have your +water bottle like this I guess that's + + align:start position:0% +water bottle like this I guess that's + + + align:start position:0% +water bottle like this I guess that's +not how it + + align:start position:0% + + + + align:start position:0% + +looks + + align:start position:0% + + + + align:start position:0% + +um um with your your capped water bottle + + align:start position:0% +um um with your your capped water bottle + + + align:start position:0% +um um with your your capped water bottle +it's filled with water like say this is + + align:start position:0% +it's filled with water like say this is + + + align:start position:0% +it's filled with water like say this is +all + + align:start position:0% +all + + + align:start position:0% +all +water so so what happens is you have + + align:start position:0% +water so so what happens is you have + + + align:start position:0% +water so so what happens is you have +sunlight coming from here it's heating + + align:start position:0% +sunlight coming from here it's heating + + + align:start position:0% +sunlight coming from here it's heating +up the water it + + align:start position:0% + + + + align:start position:0% + +yes so + + align:start position:0% +yes so + + + align:start position:0% +yes so +the water bottom half of the bottle we + + align:start position:0% +the water bottom half of the bottle we + + + align:start position:0% +the water bottom half of the bottle we +get as much long + + align:start position:0% + + + + align:start position:0% + +yeah um so because because water and + + align:start position:0% +yeah um so because because water and + + + align:start position:0% +yeah um so because because water and +your plastic both absorb some of the + + align:start position:0% +your plastic both absorb some of the + + + align:start position:0% +your plastic both absorb some of the +sunlight um you have you have a lot of + + align:start position:0% +sunlight um you have you have a lot of + + + align:start position:0% +sunlight um you have you have a lot of +it being absorbed by this fluid and what + + align:start position:0% +it being absorbed by this fluid and what + + + align:start position:0% +it being absorbed by this fluid and what +what they say is if you have like if + + align:start position:0% +what they say is if you have like if + + + align:start position:0% +what they say is if you have like if +this depth is more than 4 + + align:start position:0% +this depth is more than 4 + + + align:start position:0% +this depth is more than 4 +in + + align:start position:0% +in + + + align:start position:0% +in +uh that Sis's Effectiveness is droing by + + align:start position:0% +uh that Sis's Effectiveness is droing by + + + align:start position:0% +uh that Sis's Effectiveness is droing by +maybe uh 50% I think is what they say so + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +um yeah so that's another problem I + + align:start position:0% +um yeah so that's another problem I + + + align:start position:0% +um yeah so that's another problem I +think I think a 2 L bottle is right is + + align:start position:0% +think I think a 2 L bottle is right is + + + align:start position:0% +think I think a 2 L bottle is right is +about the right size so it's not it's + + align:start position:0% +about the right size so it's not it's + + + align:start position:0% +about the right size so it's not it's +still like in the range of the right + + align:start position:0% +still like in the range of the right + + + align:start position:0% +still like in the range of the right +size so you're not going to have over or + + align:start position:0% +size so you're not going to have over or + + + align:start position:0% +size so you're not going to have over or +you're not going to have more than 4 in + + align:start position:0% +you're not going to have more than 4 in + + + align:start position:0% +you're not going to have more than 4 in +there uh but + + align:start position:0% +there uh but + + + align:start position:0% +there uh but +that's definitely something to take into + + align:start position:0% +that's definitely something to take into + + + align:start position:0% +that's definitely something to take into +consideration what about what about + + align:start position:0% +consideration what about what about + + + align:start position:0% +consideration what about what about +place so what about the cap can you guys + + align:start position:0% +place so what about the cap can you guys + + + align:start position:0% +place so what about the cap can you guys +think of why the cap might be a + + align:start position:0% + + + + align:start position:0% + +problem it's + + align:start position:0% + + + + align:start position:0% + +not yeah that's exactly like one of the + + align:start position:0% +not yeah that's exactly like one of the + + + align:start position:0% +not yeah that's exactly like one of the +biggest problems with uh Sodus with + + align:start position:0% +biggest problems with uh Sodus with + + + align:start position:0% +biggest problems with uh Sodus with +using a water bottle is just because the + + align:start position:0% +using a water bottle is just because the + + + align:start position:0% +using a water bottle is just because the +region in this area where the cap is + + align:start position:0% +region in this area where the cap is + + + align:start position:0% +region in this area where the cap is +just doesn't like doesn't I mean it's + + align:start position:0% +just doesn't like doesn't I mean it's + + + align:start position:0% +just doesn't like doesn't I mean it's +opaque plastic so your UV arays are + + align:start position:0% +opaque plastic so your UV arays are + + + align:start position:0% +opaque plastic so your UV arays are +getting most of them are getting blocked + + align:start position:0% +getting most of them are getting blocked + + + align:start position:0% +getting most of them are getting blocked +by the plastic and so your bacteria + + align:start position:0% +by the plastic and so your bacteria + + + align:start position:0% +by the plastic and so your bacteria +don't die necessarily over there so + + align:start position:0% +don't die necessarily over there so + + + align:start position:0% +don't die necessarily over there so +that's why that's why the bag that Sean + + align:start position:0% +that's why that's why the bag that Sean + + + align:start position:0% +that's why that's why the bag that Sean +FR uh came up with the Sodus bag that + + align:start position:0% +FR uh came up with the Sodus bag that + + + align:start position:0% +FR uh came up with the Sodus bag that +you guys saw the other time that used + + align:start position:0% +you guys saw the other time that used + + + align:start position:0% +you guys saw the other time that used +two oneway valves works a lot better + + align:start position:0% +two oneway valves works a lot better + + + align:start position:0% +two oneway valves works a lot better +because the entire thing is transparent + + align:start position:0% +because the entire thing is transparent + + + align:start position:0% +because the entire thing is transparent +uh there were like there were + + align:start position:0% +uh there were like there were + + + align:start position:0% +uh there were like there were +a lot of work trying to be that people + + align:start position:0% +a lot of work trying to be that people + + + align:start position:0% +a lot of work trying to be that people +were trying to do trying to redesign + + align:start position:0% +were trying to do trying to redesign + + + align:start position:0% +were trying to do trying to redesign +this into a better system so like they + + align:start position:0% +this into a better system so like they + + + align:start position:0% +this into a better system so like they +they looked at uh they looked at the + + align:start position:0% +they looked at uh they looked at the + + + align:start position:0% +they looked at uh they looked at the +problems with the with Transportation + + align:start position:0% +problems with the with Transportation + + + align:start position:0% +problems with the with Transportation +with the 2 L bottle and then they came + + align:start position:0% +with the 2 L bottle and then they came + + + align:start position:0% +with the 2 L bottle and then they came +up with another black bag that was kind + + align:start position:0% +up with another black bag that was kind + + + align:start position:0% +up with another black bag that was kind +of like just a bag that had a handle + + align:start position:0% +of like just a bag that had a handle + + + align:start position:0% +of like just a bag that had a handle +here and then it had uh the same sort of + + align:start position:0% +here and then it had uh the same sort of + + + align:start position:0% +here and then it had uh the same sort of +like twiston cap over here that a 2 L + + align:start position:0% +like twiston cap over here that a 2 L + + + align:start position:0% +like twiston cap over here that a 2 L +bottle does like that + + align:start position:0% +bottle does like that + + + align:start position:0% +bottle does like that +um and then they made the back of the + + align:start position:0% +um and then they made the back of the + + + align:start position:0% +um and then they made the back of the +black or the back of the bag black so + + align:start position:0% +black or the back of the bag black so + + + align:start position:0% +black or the back of the bag black so +that it would heat up more which was a + + align:start position:0% +that it would heat up more which was a + + + align:start position:0% +that it would heat up more which was a +pretty cool design but then we still had + + align:start position:0% +pretty cool design but then we still had + + + align:start position:0% +pretty cool design but then we still had +problems with well for one + + align:start position:0% +problems with well for one + + + align:start position:0% +problems with well for one +having um having like expensive molded + + align:start position:0% +having um having like expensive molded + + + align:start position:0% +having um having like expensive molded +Parts is also really expensive because + + align:start position:0% +Parts is also really expensive because + + + align:start position:0% +Parts is also really expensive because +you and you can't really fabricate that + + align:start position:0% +you and you can't really fabricate that + + + align:start position:0% +you and you can't really fabricate that +everywhere like you can't go into a + + align:start position:0% +everywhere like you can't go into a + + + align:start position:0% +everywhere like you can't go into a +village + + align:start position:0% +village + + + align:start position:0% +village +and expect and try to create something + + align:start position:0% +and expect and try to create something + + + align:start position:0% +and expect and try to create something +that looks like this or even something + + align:start position:0% +that looks like this or even something + + + align:start position:0% +that looks like this or even something +that looks like this whereas if you have + + align:start position:0% +that looks like this whereas if you have + + + align:start position:0% +that looks like this whereas if you have +a simple plastic sealer you could make + + align:start position:0% +a simple plastic sealer you could make + + + align:start position:0% +a simple plastic sealer you could make +one of the sodas bags that we were + + align:start position:0% +one of the sodas bags that we were + + + align:start position:0% +one of the sodas bags that we were +working on or that we saw last week um + + align:start position:0% +working on or that we saw last week um + + + align:start position:0% +working on or that we saw last week um +does anyone has anyone not seen these + + align:start position:0% +does anyone has anyone not seen these + + + align:start position:0% +does anyone has anyone not seen these +Sodus bags from last week or have no + + align:start position:0% +Sodus bags from last week or have no + + + align:start position:0% +Sodus bags from last week or have no +idea what I'm talking + + align:start position:0% +idea what I'm talking + + + align:start position:0% +idea what I'm talking +about + + align:start position:0% +about + + + align:start position:0% +about +okay and how many of you have heard of + + align:start position:0% +okay and how many of you have heard of + + + align:start position:0% +okay and how many of you have heard of +Sodus + + align:start position:0% + + + + align:start position:0% + +before okay uh + + align:start position:0% +before okay uh + + + align:start position:0% +before okay uh +so yeah so this design sort of went from + + align:start position:0% +so yeah so this design sort of went from + + + align:start position:0% +so yeah so this design sort of went from +this iteration to this iteration and + + align:start position:0% +this iteration to this iteration and + + + align:start position:0% +this iteration to this iteration and +then Sean FR came along and worked on it + + align:start position:0% +then Sean FR came along and worked on it + + + align:start position:0% +then Sean FR came along and worked on it +a little bit and came up with the next + + align:start position:0% +a little bit and came up with the next + + + align:start position:0% +a little bit and came up with the next +iteration of or came up with his + + align:start position:0% +iteration of or came up with his + + + align:start position:0% +iteration of or came up with his +technology which is like really really + + align:start position:0% +technology which is like really really + + + align:start position:0% +technology which is like really really +good technology + + align:start position:0% +good technology + + + align:start position:0% +good technology +um in terms of usage because I want you + + align:start position:0% +um in terms of usage because I want you + + + align:start position:0% +um in terms of usage because I want you +guys to start thinking about these + + align:start position:0% +guys to start thinking about these + + + align:start position:0% +guys to start thinking about these +Technologies and how you would use them + + align:start position:0% +Technologies and how you would use them + + + align:start position:0% +Technologies and how you would use them +too what's another problem that is uh + + align:start position:0% +too what's another problem that is uh + + + align:start position:0% +too what's another problem that is uh +with this you're supposed to take this + + align:start position:0% +with this you're supposed to take this + + + align:start position:0% +with this you're supposed to take this +you're supposed to leave it out + + align:start position:0% +you're supposed to leave it out + + + align:start position:0% +you're supposed to leave it out +in uh the Sun for six hours and then + + align:start position:0% +in uh the Sun for six hours and then + + + align:start position:0% +in uh the Sun for six hours and then +it um or six hours to two days depending + + align:start position:0% +it um or six hours to two days depending + + + align:start position:0% +it um or six hours to two days depending +on the weather conditions and then it's + + align:start position:0% +on the weather conditions and then it's + + + align:start position:0% +on the weather conditions and then it's +supposed to clean your water and you're + + align:start position:0% +supposed to clean your water and you're + + + align:start position:0% +supposed to clean your water and you're +supposed to drink + + align:start position:0% + + + + align:start position:0% + +it yeah a question how like what is it + + align:start position:0% +it yeah a question how like what is it + + + align:start position:0% +it yeah a question how like what is it +chemical inside the water to purify it + + align:start position:0% +chemical inside the water to purify it + + + align:start position:0% +chemical inside the water to purify it +no no you just you just take water right + + align:start position:0% +no no you just you just take water right + + + align:start position:0% +no no you just you just take water right +uh and you leave it out in the sun and + + align:start position:0% +uh and you leave it out in the sun and + + + align:start position:0% +uh and you leave it out in the sun and +the UV raay from the Sun kill the + + align:start position:0% +the UV raay from the Sun kill the + + + align:start position:0% +the UV raay from the Sun kill the +bacteria it breaks down the bacteria so + + align:start position:0% +bacteria it breaks down the bacteria so + + + align:start position:0% +bacteria it breaks down the bacteria so +any container any container as long as + + align:start position:0% +any container any container as long as + + + align:start position:0% +any container any container as long as +it's clear Nu UV transparent or + + align:start position:0% +it's clear Nu UV transparent or + + + align:start position:0% +it's clear Nu UV transparent or +transmissive what is s uh solar + + align:start position:0% +transmissive what is s uh solar + + + align:start position:0% +transmissive what is s uh solar +disinfection I should have explained + + align:start position:0% +disinfection I should have explained + + + align:start position:0% +disinfection I should have explained +that yeah sorry I guess Sodis is stands + + align:start position:0% +that yeah sorry I guess Sodis is stands + + + align:start position:0% +that yeah sorry I guess Sodis is stands +for solar disinfection so you're + + align:start position:0% +for solar disinfection so you're + + + align:start position:0% +for solar disinfection so you're +purifying water just using + + align:start position:0% + + + + align:start position:0% + +sunlight it's a + + align:start position:0% + + + + align:start position:0% + +technique so then like I know that BPA + + align:start position:0% +technique so then like I know that BPA + + + align:start position:0% +technique so then like I know that BPA +free water bottles are in the news right + + align:start position:0% +free water bottles are in the news right + + + align:start position:0% +free water bottles are in the news right +because of all the toxins + + align:start position:0% +because of all the toxins + + + align:start position:0% +because of all the toxins +an extreme heat like an extreme low or + + align:start position:0% +an extreme heat like an extreme low or + + + align:start position:0% +an extreme heat like an extreme low or +extrem high temperature is that + + align:start position:0% +extrem high temperature is that + + + align:start position:0% +extrem high temperature is that +consideration + + align:start position:0% + + + + align:start position:0% + +IDE + + align:start position:0% +IDE + + + align:start position:0% +IDE +uh so generally leeching from plastic is + + align:start position:0% +uh so generally leeching from plastic is + + + align:start position:0% +uh so generally leeching from plastic is +a much like it's a problem that's on a + + align:start position:0% +a much like it's a problem that's on a + + + align:start position:0% +a much like it's a problem that's on a +much smaller scale than uh having unsafe + + align:start position:0% +much smaller scale than uh having unsafe + + + align:start position:0% +much smaller scale than uh having unsafe +drinking water and so if you had to + + align:start position:0% +drinking water and so if you had to + + + align:start position:0% +drinking water and so if you had to +choose the trade-off between having some + + align:start position:0% +choose the trade-off between having some + + + align:start position:0% +choose the trade-off between having some +plastic potentially leech into your + + align:start position:0% +plastic potentially leech into your + + + align:start position:0% +plastic potentially leech into your +water and drink it and over like dozens + + align:start position:0% +water and drink it and over like dozens + + + align:start position:0% +water and drink it and over like dozens +of years that might cause some health + + align:start position:0% +of years that might cause some health + + + align:start position:0% +of years that might cause some health +problems uh versus having unsafe + + align:start position:0% +problems uh versus having unsafe + + + align:start position:0% +problems uh versus having unsafe +drinking water like you would choose you + + align:start position:0% +drinking water like you would choose you + + + align:start position:0% +drinking water like you would choose you +would definitely choose the unsafe or + + align:start position:0% +would definitely choose the unsafe or + + + align:start position:0% +would definitely choose the unsafe or +you definitely choose the drinking using + + align:start position:0% +you definitely choose the drinking using + + + align:start position:0% +you definitely choose the drinking using +Sodus to drink your water but yeah that + + align:start position:0% +Sodus to drink your water but yeah that + + + align:start position:0% +Sodus to drink your water but yeah that +is some of like that is one of the + + align:start position:0% +is some of like that is one of the + + + align:start position:0% +is some of like that is one of the +bigger concerns with + + align:start position:0% + + + + align:start position:0% + +Sodis um + + align:start position:0% + + + + align:start position:0% + +cool are there any other questions about + + align:start position:0% + + + + align:start position:0% + +Sodis all right uh then I'm going to go + + align:start position:0% +Sodis all right uh then I'm going to go + + + align:start position:0% +Sodis all right uh then I'm going to go +into solar + + align:start position:0% +into solar + + + align:start position:0% +into solar +drying + + align:start position:0% +drying + + + align:start position:0% +drying +uh so solar drying is another technology + + align:start position:0% +uh so solar drying is another technology + + + align:start position:0% +uh so solar drying is another technology +that is used in a lot of places in the + + align:start position:0% +that is used in a lot of places in the + + + align:start position:0% +that is used in a lot of places in the +world uh and the idea is + + align:start position:0% +world uh and the idea is + + + align:start position:0% +world uh and the idea is +basically um that you you take fruits or + + align:start position:0% +basically um that you you take fruits or + + + align:start position:0% +basically um that you you take fruits or +whatever and you you drve them so that + + align:start position:0% +whatever and you you drve them so that + + + align:start position:0% +whatever and you you drve them so that +you can preserve them and the thing is + + align:start position:0% +you can preserve them and the thing is + + + align:start position:0% +you can preserve them and the thing is +like a lot in a lot of places you'll + + align:start position:0% +like a lot in a lot of places you'll + + + align:start position:0% +like a lot in a lot of places you'll +have uh you'll have farmers who are + + align:start position:0% +have uh you'll have farmers who are + + + align:start position:0% +have uh you'll have farmers who are +growing something and they'll all have + + align:start position:0% +growing something and they'll all have + + + align:start position:0% +growing something and they'll all have +crops that grow at the same time and so + + align:start position:0% +crops that grow at the same time and so + + + align:start position:0% +crops that grow at the same time and so +they'll Harvest and then they'll go take + + align:start position:0% +they'll Harvest and then they'll go take + + + align:start position:0% +they'll Harvest and then they'll go take +them to the market and because there's + + align:start position:0% +them to the market and because there's + + + align:start position:0% +them to the market and because there's +an overabundance of these uh fruits or + + align:start position:0% +an overabundance of these uh fruits or + + + align:start position:0% +an overabundance of these uh fruits or +something people aren't getting their + + align:start position:0% +something people aren't getting their + + + align:start position:0% +something people aren't getting their +Peak like they're not getting as much as + + align:start position:0% +Peak like they're not getting as much as + + + align:start position:0% +Peak like they're not getting as much as +money as they can for these um for their + + align:start position:0% +money as they can for these um for their + + + align:start position:0% +money as they can for these um for their +fruits because um because there's way + + align:start position:0% +fruits because um because there's way + + + align:start position:0% +fruits because um because there's way +too much of like there's way more Supply + + align:start position:0% +too much of like there's way more Supply + + + align:start position:0% +too much of like there's way more Supply +than people there's a demand for it + + align:start position:0% +than people there's a demand for it + + + align:start position:0% +than people there's a demand for it +so so and if they they they don't have a + + align:start position:0% +so so and if they they they don't have a + + + align:start position:0% +so so and if they they they don't have a +very good way of preserving food + + align:start position:0% +very good way of preserving food + + + align:start position:0% +very good way of preserving food +otherwise so they can't like refrigerate + + align:start position:0% +otherwise so they can't like refrigerate + + + align:start position:0% +otherwise so they can't like refrigerate +these fruits so if they don't if they + + align:start position:0% +these fruits so if they don't if they + + + align:start position:0% +these fruits so if they don't if they +don't keep them refrigerated then + + align:start position:0% +don't keep them refrigerated then + + + align:start position:0% +don't keep them refrigerated then +they're just going to spoil so it's + + align:start position:0% +they're just going to spoil so it's + + + align:start position:0% +they're just going to spoil so it's +either sell at a low cost or um don't + + align:start position:0% +either sell at a low cost or um don't + + + align:start position:0% +either sell at a low cost or um don't +get anything for them and so their food + + align:start position:0% +get anything for them and so their food + + + align:start position:0% +get anything for them and so their food +preservation is a pretty big deal as + + align:start position:0% +preservation is a pretty big deal as + + + align:start position:0% +preservation is a pretty big deal as +well and so you can use solar energy to + + align:start position:0% +well and so you can use solar energy to + + + align:start position:0% +well and so you can use solar energy to +also dry fruits and + + align:start position:0% +also dry fruits and + + + align:start position:0% +also dry fruits and +uh this is a project called fruits of + + align:start position:0% +uh this is a project called fruits of + + + align:start position:0% +uh this is a project called fruits of +the Nile that works in Uganda where they + + align:start position:0% +the Nile that works in Uganda where they + + + align:start position:0% +the Nile that works in Uganda where they +do + + align:start position:0% +do + + + align:start position:0% +do +that and then I'm going to go to talking + + align:start position:0% +that and then I'm going to go to talking + + + align:start position:0% +that and then I'm going to go to talking +about solar thermal panels for water + + align:start position:0% +about solar thermal panels for water + + + align:start position:0% +about solar thermal panels for water +heating + + align:start position:0% +heating + + + align:start position:0% +heating +um I don't know if you guys have seen + + align:start position:0% +um I don't know if you guys have seen + + + align:start position:0% +um I don't know if you guys have seen +these These are taken from the US these + + align:start position:0% +these These are taken from the US these + + + align:start position:0% +these These are taken from the US these +pictures um but have have any uh do any + + align:start position:0% +pictures um but have have any uh do any + + + align:start position:0% +pictures um but have have any uh do any +of you have exposure to solar + + align:start position:0% +of you have exposure to solar + + + align:start position:0% +of you have exposure to solar +thermal Okay so basically what you're + + align:start position:0% +thermal Okay so basically what you're + + + align:start position:0% +thermal Okay so basically what you're +basically doing here is you + + align:start position:0% +basically doing here is you + + + align:start position:0% +basically doing here is you +have well there two types of systems + + align:start position:0% +have well there two types of systems + + + align:start position:0% +have well there two types of systems +which I'll I guess are on the next slide + + align:start position:0% +which I'll I guess are on the next slide + + + align:start position:0% +which I'll I guess are on the next slide +but uh so you have you have two + + align:start position:0% +but uh so you have you have two + + + align:start position:0% +but uh so you have you have two +different types of systems but this is a + + align:start position:0% +different types of systems but this is a + + + align:start position:0% +different types of systems but this is a +little bit more complicated than it + + align:start position:0% +little bit more complicated than it + + + align:start position:0% +little bit more complicated than it +needs to be so basically the idea is + + align:start position:0% +needs to be so basically the idea is + + + align:start position:0% +needs to be so basically the idea is +you're taking in sunlight and using the + + align:start position:0% +you're taking in sunlight and using the + + + align:start position:0% +you're taking in sunlight and using the +sunlight you're heating water or some + + align:start position:0% +sunlight you're heating water or some + + + align:start position:0% +sunlight you're heating water or some +sort of fluid and so you have sort of + + align:start position:0% +sort of fluid and so you have sort of + + + align:start position:0% +sort of fluid and so you have sort of +this container that's shaped like this + + align:start position:0% +this container that's shaped like this + + + align:start position:0% +this container that's shaped like this +or you have two + + align:start position:0% +or you have two + + + align:start position:0% +or you have two +that have water some container or + + align:start position:0% +that have water some container or + + + align:start position:0% +that have water some container or +something running through it sunlight + + align:start position:0% +something running through it sunlight + + + align:start position:0% +something running through it sunlight +hits this container heats up the water + + align:start position:0% +hits this container heats up the water + + + align:start position:0% +hits this container heats up the water +inside these tubes and then you get + + align:start position:0% +inside these tubes and then you get + + + align:start position:0% +inside these tubes and then you get +uh and then you store the hot water in a + + align:start position:0% +uh and then you store the hot water in a + + + align:start position:0% +uh and then you store the hot water in a +tank um so that's a direct solar thermal + + align:start position:0% +tank um so that's a direct solar thermal + + + align:start position:0% +tank um so that's a direct solar thermal +system there's also indirect solar + + align:start position:0% +system there's also indirect solar + + + align:start position:0% +system there's also indirect solar +thermal systems where instead of now + + align:start position:0% +thermal systems where instead of now + + + align:start position:0% +thermal systems where instead of now +instead of + + align:start position:0% +instead of + + + align:start position:0% +instead of +having um your water being heated + + align:start position:0% +having um your water being heated + + + align:start position:0% +having um your water being heated +directly your + + align:start position:0% +directly your + + + align:start position:0% +directly your +you have a heat exchanger + + align:start position:0% +you have a heat exchanger + + + align:start position:0% +you have a heat exchanger +here and then you have some sort of + + align:start position:0% +here and then you have some sort of + + + align:start position:0% +here and then you have some sort of +fluid that goes through the system and + + align:start position:0% +fluid that goes through the system and + + + align:start position:0% +fluid that goes through the system and +then you have + + align:start position:0% +then you have + + + align:start position:0% +then you have +your Reservoir or something and um + + align:start position:0% +your Reservoir or something and um + + + align:start position:0% +your Reservoir or something and um +what's heating the water + + align:start position:0% +what's heating the water + + + align:start position:0% +what's heating the water +is um this like hot fluid like the heat + + align:start position:0% +is um this like hot fluid like the heat + + + align:start position:0% +is um this like hot fluid like the heat +exchanger is what's heating the + + align:start position:0% +exchanger is what's heating the + + + align:start position:0% +exchanger is what's heating the +water um a heat exchanger is just + + align:start position:0% +water um a heat exchanger is just + + + align:start position:0% +water um a heat exchanger is just +something that transfers heat from one + + align:start position:0% +something that transfers heat from one + + + align:start position:0% +something that transfers heat from one +thing to another if you were wondering + + align:start position:0% +thing to another if you were wondering + + + align:start position:0% +thing to another if you were wondering +and so there's a lot of solar thermal is + + align:start position:0% +and so there's a lot of solar thermal is + + + align:start position:0% +and so there's a lot of solar thermal is +way less efficient than solar PV photov + + align:start position:0% +way less efficient than solar PV photov + + + align:start position:0% +way less efficient than solar PV photov +voltaics but it's also significantly + + align:start position:0% +voltaics but it's also significantly + + + align:start position:0% +voltaics but it's also significantly +cheaper I I don't have numbers for you + + align:start position:0% +cheaper I I don't have numbers for you + + + align:start position:0% +cheaper I I don't have numbers for you +for that if but uh but you you don't + + align:start position:0% +for that if but uh but you you don't + + + align:start position:0% +for that if but uh but you you don't +like you don't want to think of solar + + align:start position:0% +like you don't want to think of solar + + + align:start position:0% +like you don't want to think of solar +thermal as only being a small scale + + align:start position:0% +thermal as only being a small scale + + + align:start position:0% +thermal as only being a small scale +technology because there are large scale + + align:start position:0% +technology because there are large scale + + + align:start position:0% +technology because there are large scale +applications of it as well uh this is + + align:start position:0% +applications of it as well uh this is + + + align:start position:0% +applications of it as well uh this is +sort of like the smallest case you can + + align:start position:0% +sort of like the smallest case you can + + + align:start position:0% +sort of like the smallest case you can +think of it would be like having one of + + align:start position:0% +think of it would be like having one of + + + align:start position:0% +think of it would be like having one of +these for your household in + + align:start position:0% +these for your household in + + + align:start position:0% +these for your household in +um like for your household to heat water + + align:start position:0% +um like for your household to heat water + + + align:start position:0% +um like for your household to heat water +for showering or something like that um + + align:start position:0% +for showering or something like that um + + + align:start position:0% +for showering or something like that um +and then you have larger scale versions + + align:start position:0% +and then you have larger scale versions + + + align:start position:0% +and then you have larger scale versions +of this too which + + align:start position:0% +of this too which + + + align:start position:0% +of this too which +is um the loose project in the Mojave + + align:start position:0% +is um the loose project in the Mojave + + + align:start position:0% +is um the loose project in the Mojave +Desert and it's the largest solar + + align:start position:0% +Desert and it's the largest solar + + + align:start position:0% +Desert and it's the largest solar +Thermal electric installation in the + + align:start position:0% +Thermal electric installation in the + + + align:start position:0% +Thermal electric installation in the +world it has uh 350 megawatt Peak output + + align:start position:0% +world it has uh 350 megawatt Peak output + + + align:start position:0% +world it has uh 350 megawatt Peak output +and if you can see like this + + align:start position:0% +and if you can see like this + + + align:start position:0% +and if you can see like this +picture uh those are three people + + align:start position:0% +picture uh those are three people + + + align:start position:0% +picture uh those are three people +standing next to it so this thing is + + align:start position:0% +standing next to it so this thing is + + + align:start position:0% +standing next to it so this thing is +massive + + align:start position:0% +massive + + + align:start position:0% +massive +it's it's on the order of + + align:start position:0% +it's it's on the order of + + + align:start position:0% +it's it's on the order of +kilometers + + align:start position:0% +kilometers + + + align:start position:0% +kilometers +um yeah and the way this works is it's + + align:start position:0% +um yeah and the way this works is it's + + + align:start position:0% +um yeah and the way this works is it's +similar to this except uh you have you + + align:start position:0% +similar to this except uh you have you + + + align:start position:0% +similar to this except uh you have you +have your pipes that have you have your + + align:start position:0% +have your pipes that have you have your + + + align:start position:0% +have your pipes that have you have your +pipes that have water in them but then + + align:start position:0% +pipes that have water in them but then + + + align:start position:0% +pipes that have water in them but then +you have these concentrating troughs + + align:start position:0% +you have these concentrating troughs + + + align:start position:0% +you have these concentrating troughs +that are focusing all of + + align:start position:0% +that are focusing all of + + + align:start position:0% +that are focusing all of +the all of the sunlight + + align:start position:0% +the all of the sunlight + + + align:start position:0% +the all of the sunlight +onto + + align:start position:0% +onto + + + align:start position:0% +onto +the the pipes and so you get with the + + align:start position:0% +the the pipes and so you get with the + + + align:start position:0% +the the pipes and so you get with the +way this normally works is you have um + + align:start position:0% +way this normally works is you have um + + + align:start position:0% +way this normally works is you have um +this technology works is you have you + + align:start position:0% +this technology works is you have you + + + align:start position:0% +this technology works is you have you +heat up water to the point where it + + align:start position:0% +heat up water to the point where it + + + align:start position:0% +heat up water to the point where it +turns into steam and then you have the + + align:start position:0% +turns into steam and then you have the + + + align:start position:0% +turns into steam and then you have the +steam power turbine and then uh you + + align:start position:0% +steam power turbine and then uh you + + + align:start position:0% +steam power turbine and then uh you +produce electricity using + + align:start position:0% +produce electricity using + + + align:start position:0% +produce electricity using +that um + + align:start position:0% + + + + align:start position:0% + +yeah what KN they use + + align:start position:0% +yeah what KN they use + + + align:start position:0% +yeah what KN they use +oil to + + align:start position:0% + + + + align:start position:0% + +upol did you do research yeah I did um I + + align:start position:0% +upol did you do research yeah I did um I + + + align:start position:0% +upol did you do research yeah I did um I +did energ uh solar energy Consulting + + align:start position:0% +did energ uh solar energy Consulting + + + align:start position:0% +did energ uh solar energy Consulting +this past summer do so like we looked at + + align:start position:0% +this past summer do so like we looked at + + + align:start position:0% +this past summer do so like we looked at +the new energy uh CSP um Power PLS to us + + align:start position:0% +the new energy uh CSP um Power PLS to us + + + align:start position:0% +the new energy uh CSP um Power PLS to us +cool what what does it say Thermal + + align:start position:0% +cool what what does it say Thermal + + + align:start position:0% +cool what what does it say Thermal +electric like the thermal part yet what + + align:start position:0% +electric like the thermal part yet what + + + align:start position:0% +electric like the thermal part yet what +about + + align:start position:0% +about + + + align:start position:0% +about +the those power plants are used for oh + + align:start position:0% +the those power plants are used for oh + + + align:start position:0% +the those power plants are used for oh +they used for energy generation so oh so + + align:start position:0% +they used for energy generation so oh so + + + align:start position:0% +they used for energy generation so oh so +these yeah these generate + + align:start position:0% +these yeah these generate + + + align:start position:0% +these yeah these generate +electricity uh + + align:start position:0% +electricity uh + + + align:start position:0% +electricity uh +yeah does that make + + align:start position:0% + + + + align:start position:0% + +sense so you have steam which Powers a + + align:start position:0% +sense so you have steam which Powers a + + + align:start position:0% +sense so you have steam which Powers a +turbine and that turbine generates + + align:start position:0% +turbine and that turbine generates + + + align:start position:0% +turbine and that turbine generates +electricity and so you like not only do + + align:start position:0% +electricity and so you like not only do + + + align:start position:0% +electricity and so you like not only do +you have + + align:start position:0% +you have + + + align:start position:0% +you have +um do you have yeah like you're not just + + align:start position:0% +um do you have yeah like you're not just + + + align:start position:0% +um do you have yeah like you're not just +taking you're not doing something simple + + align:start position:0% +taking you're not doing something simple + + + align:start position:0% +taking you're not doing something simple +like heating water anymore you you're + + align:start position:0% +like heating water anymore you you're + + + align:start position:0% +like heating water anymore you you're +also using the same technology but now + + align:start position:0% +also using the same technology but now + + + align:start position:0% +also using the same technology but now +you're generating electricity from it + + align:start position:0% +you're generating electricity from it + + + align:start position:0% +you're generating electricity from it +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um and I thought I would throw this just + + align:start position:0% +um and I thought I would throw this just + + + align:start position:0% +um and I thought I would throw this just +for fun uh this was another cool type + + align:start position:0% +for fun uh this was another cool type + + + align:start position:0% +for fun uh this was another cool type +like this is a project that I was + + align:start position:0% +like this is a project that I was + + + align:start position:0% +like this is a project that I was +working on last year in Brazil um and + + align:start position:0% +working on last year in Brazil um and + + + align:start position:0% +working on last year in Brazil um and +it's a really lowcost solar water heater + + align:start position:0% +it's a really lowcost solar water heater + + + align:start position:0% +it's a really lowcost solar water heater +um but the reason I threw this in was + + align:start position:0% +um but the reason I threw this in was + + + align:start position:0% +um but the reason I threw this in was +because a way a lot of these lower cost + + align:start position:0% +because a way a lot of these lower cost + + + align:start position:0% +because a way a lot of these lower cost +cheaper ones work is they they work + + align:start position:0% +cheaper ones work is they they work + + + align:start position:0% +cheaper ones work is they they work +based off of a thermos siphon and + + align:start position:0% + + + + align:start position:0% + +um so basically what happens is when you + + align:start position:0% +um so basically what happens is when you + + + align:start position:0% +um so basically what happens is when you +have + + align:start position:0% + + + + align:start position:0% + +what happens is in a system like + + align:start position:0% +what happens is in a system like + + + align:start position:0% +what happens is in a system like +this uh you'll have a system like this + + align:start position:0% +this uh you'll have a system like this + + + align:start position:0% +this uh you'll have a system like this +that's + + align:start position:0% + + + + align:start position:0% + +connected to a + + align:start position:0% + + + + align:start position:0% + +tank + + align:start position:0% +tank + + + align:start position:0% +tank +um and so water heats up in this and as + + align:start position:0% +um and so water heats up in this and as + + + align:start position:0% +um and so water heats up in this and as +water heats up you mean like um if you + + align:start position:0% +water heats up you mean like um if you + + + align:start position:0% +water heats up you mean like um if you +remember from I guess I guess you + + align:start position:0% +remember from I guess I guess you + + + align:start position:0% +remember from I guess I guess you +learned this in Middle School hot air + + align:start position:0% +learned this in Middle School hot air + + + align:start position:0% +learned this in Middle School hot air +rises like things like that so hot water + + align:start position:0% +rises like things like that so hot water + + + align:start position:0% +rises like things like that so hot water +Also Rises you got uh you got a flow of + + align:start position:0% +Also Rises you got uh you got a flow of + + + align:start position:0% +Also Rises you got uh you got a flow of +water towards the top of this thing so + + align:start position:0% +water towards the top of this thing so + + + align:start position:0% +water towards the top of this thing so +what happens is if you connect this to a + + align:start position:0% +what happens is if you connect this to a + + + align:start position:0% +what happens is if you connect this to a +reservoir you'll get + + align:start position:0% +reservoir you'll get + + + align:start position:0% +reservoir you'll get +um + + align:start position:0% +um + + + align:start position:0% +um +and you basically get a flow caused just + + align:start position:0% +and you basically get a flow caused just + + + align:start position:0% +and you basically get a flow caused just +by the temperature differential in the + + align:start position:0% +by the temperature differential in the + + + align:start position:0% +by the temperature differential in the +water so hot water will rise flow into + + align:start position:0% +water so hot water will rise flow into + + + align:start position:0% +water so hot water will rise flow into +this Reservoir and it'll get displaced + + align:start position:0% +this Reservoir and it'll get displaced + + + align:start position:0% +this Reservoir and it'll get displaced +by cold water and so you're you're + + align:start position:0% +by cold water and so you're you're + + + align:start position:0% +by cold water and so you're you're +regulating the temperature and heating + + align:start position:0% +regulating the temperature and heating + + + align:start position:0% +regulating the temperature and heating +all of the water consistently which is + + align:start position:0% +all of the water consistently which is + + + align:start position:0% +all of the water consistently which is +pretty cool because with a system that's + + align:start position:0% +pretty cool because with a system that's + + + align:start position:0% +pretty cool because with a system that's +based off of the thermosyphon you don't + + align:start position:0% +based off of the thermosyphon you don't + + + align:start position:0% +based off of the thermosyphon you don't +need to throw in a pump or something + + align:start position:0% +need to throw in a pump or something + + + align:start position:0% +need to throw in a pump or something +like that to extract the water from your + + align:start position:0% + + + + align:start position:0% + +yes yeah just a + + align:start position:0% +yes yeah just a + + + align:start position:0% +yes yeah just a +e + + align:start position:0% +e + + + align:start position:0% +e +uh um but yeah so it's like it's just a + + align:start position:0% +uh um but yeah so it's like it's just a + + + align:start position:0% +uh um but yeah so it's like it's just a +passive way of doing the same sort of + + align:start position:0% +passive way of doing the same sort of + + + align:start position:0% +passive way of doing the same sort of +flow + + align:start position:0% +flow + + + align:start position:0% +flow +um now I'm going to go into are there + + align:start position:0% +um now I'm going to go into are there + + + align:start position:0% +um now I'm going to go into are there +any questions on any of what I've talked + + align:start position:0% +any questions on any of what I've talked + + + align:start position:0% +any questions on any of what I've talked +about I know I did a like a really + + align:start position:0% +about I know I did a like a really + + + align:start position:0% +about I know I did a like a really +really cursory job of heat transfer + + align:start position:0% +really cursory job of heat transfer + + + align:start position:0% +really cursory job of heat transfer +earlier but that's because we're going + + align:start position:0% +earlier but that's because we're going + + + align:start position:0% +earlier but that's because we're going +to go more into it when we're talking + + align:start position:0% +to go more into it when we're talking + + + align:start position:0% +to go more into it when we're talking +about photo voltic + + align:start position:0% +about photo voltic + + + align:start position:0% +about photo voltic +um but and more next week when you're + + align:start position:0% +um but and more next week when you're + + + align:start position:0% +um but and more next week when you're +going into + + align:start position:0% +going into + + + align:start position:0% +going into +conductance and convection for cooking + + align:start position:0% +conductance and convection for cooking + + + align:start position:0% +conductance and convection for cooking +but are there any other questions that + + align:start position:0% +but are there any other questions that + + + align:start position:0% +but are there any other questions that +you guys have + + align:start position:0% +you guys have + + + align:start position:0% +you guys have +about what we just talked + + align:start position:0% +about what we just talked + + + align:start position:0% +about what we just talked +about okay so we're going to move on to + + align:start position:0% +about okay so we're going to move on to + + + align:start position:0% +about okay so we're going to move on to +photo voltaics um I'm going to try to + + align:start position:0% +photo voltaics um I'm going to try to + + + align:start position:0% +photo voltaics um I'm going to try to +explain to you how solar cells work um I + + align:start position:0% +explain to you how solar cells work um I + + + align:start position:0% +explain to you how solar cells work um I +got a lot of this information was taken + + align:start position:0% +got a lot of this information was taken + + + align:start position:0% +got a lot of this information was taken +from this website called PVE education + + align:start position:0% +from this website called PVE education + + + align:start position:0% +from this website called PVE education +it's actually used to be called pvcd ROM + + align:start position:0% +it's actually used to be called pvcd ROM + + + align:start position:0% +it's actually used to be called pvcd ROM +which I thought was pretty funny because + + align:start position:0% +which I thought was pretty funny because + + + align:start position:0% +which I thought was pretty funny because +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it's a website now uh so I guess it's + + align:start position:0% +it's a website now uh so I guess it's + + + align:start position:0% +it's a website now uh so I guess it's +been around for a while how many of are + + align:start position:0% +been around for a while how many of are + + + align:start position:0% +been around for a while how many of are +you familiar with this yeah okay um it's + + align:start position:0% +you familiar with this yeah okay um it's + + + align:start position:0% +you familiar with this yeah okay um it's +a great resource for a lot of + + align:start position:0% +a great resource for a lot of + + + align:start position:0% +a great resource for a lot of +information that you might and it'll + + align:start position:0% +information that you might and it'll + + + align:start position:0% +information that you might and it'll +answer a lot of the questions you have + + align:start position:0% +answer a lot of the questions you have + + + align:start position:0% +answer a lot of the questions you have +and it does a pretty good job of keeping + + align:start position:0% +and it does a pretty good job of keeping + + + align:start position:0% +and it does a pretty good job of keeping +its level like basic enough for you to + + align:start position:0% +its level like basic enough for you to + + + align:start position:0% +its level like basic enough for you to +understand plus being mathy enough for + + align:start position:0% +understand plus being mathy enough for + + + align:start position:0% +understand plus being mathy enough for +you to actually understand what's going + + align:start position:0% +you to actually understand what's going + + + align:start position:0% +you to actually understand what's going +on to if you're interested in that + + align:start position:0% +on to if you're interested in that + + + align:start position:0% +on to if you're interested in that +um so so let's start by so yeah you + + align:start position:0% +um so so let's start by so yeah you + + + align:start position:0% +um so so let's start by so yeah you +should you should go on that and read up + + align:start position:0% +should you should go on that and read up + + + align:start position:0% +should you should go on that and read up +on more of it if you want if you have + + align:start position:0% +on more of it if you want if you have + + + align:start position:0% +on more of it if you want if you have +time and you are inclined to learn more + + align:start position:0% +time and you are inclined to learn more + + + align:start position:0% +time and you are inclined to learn more +about how photov voltaic story but + + align:start position:0% +about how photov voltaic story but + + + align:start position:0% +about how photov voltaic story but +anyway um the temperature of the sun + + align:start position:0% +anyway um the temperature of the sun + + + align:start position:0% +anyway um the temperature of the sun +does anyone know what the temperature of + + align:start position:0% +does anyone know what the temperature of + + + align:start position:0% +does anyone know what the temperature of +the Sun is + + align:start position:0% + + + + align:start position:0% + +about little that's a little high + + align:start position:0% +about little that's a little high + + + align:start position:0% +about little that's a little high +like that's a + + align:start position:0% +like that's a + + + align:start position:0% +like that's a +little + + align:start position:0% +little + + + align:start position:0% +little +higher uh it's less than that's it's + + align:start position:0% +higher uh it's less than that's it's + + + align:start position:0% +higher uh it's less than that's it's +about it's about 6,000 + + align:start position:0% +about it's about 6,000 + + + align:start position:0% +about it's about 6,000 +Kelvin + + align:start position:0% + + + + align:start position:0% + +6,000 well so so to be fair when you + + align:start position:0% +6,000 well so so to be fair when you + + + align:start position:0% +6,000 well so so to be fair when you +when you have the so you have the Sun + + align:start position:0% +when you have the so you have the Sun + + + align:start position:0% +when you have the so you have the Sun +and it's kind of like that you have you + + align:start position:0% +and it's kind of like that you have you + + + align:start position:0% +and it's kind of like that you have you +have the core where there's Fusion going + + align:start position:0% +have the core where there's Fusion going + + + align:start position:0% +have the core where there's Fusion going +on and I think the the core temperature + + align:start position:0% +on and I think the the core temperature + + + align:start position:0% +on and I think the the core temperature +is maybe like 20 million Kelvin or + + align:start position:0% +is maybe like 20 million Kelvin or + + + align:start position:0% +is maybe like 20 million Kelvin or +something like that + + align:start position:0% +something like that + + + align:start position:0% +something like that +uh so something like that it's something + + align:start position:0% +uh so something like that it's something + + + align:start position:0% +uh so something like that it's something +ridiculously high I might be off by an + + align:start position:0% +ridiculously high I might be off by an + + + align:start position:0% +ridiculously high I might be off by an +order or two of magnitude in some + + align:start position:0% +order or two of magnitude in some + + + align:start position:0% +order or two of magnitude in some +Direction but it's it's not really that + + align:start position:0% +Direction but it's it's not really that + + + align:start position:0% +Direction but it's it's not really that +important uh but what happens is most of + + align:start position:0% +important uh but what happens is most of + + + align:start position:0% +important uh but what happens is most of +that energy is blocked off by like the + + align:start position:0% +that energy is blocked off by like the + + + align:start position:0% +that energy is blocked off by like the +sort of dense hydrogen around here and + + align:start position:0% +sort of dense hydrogen around here and + + + align:start position:0% +sort of dense hydrogen around here and +then you have the very like end of uh + + align:start position:0% +then you have the very like end of uh + + + align:start position:0% +then you have the very like end of uh +you have like the outer rim of the sun + + align:start position:0% +you have like the outer rim of the sun + + + align:start position:0% +you have like the outer rim of the sun +which is at about 6,000 Kelvin which is + + align:start position:0% +which is at about 6,000 Kelvin which is + + + align:start position:0% +which is at about 6,000 Kelvin which is +what's radiating most of the heat um to + + align:start position:0% +what's radiating most of the heat um to + + + align:start position:0% +what's radiating most of the heat um to +the Earth and so that's where we get all + + align:start position:0% +the Earth and so that's where we get all + + + align:start position:0% +the Earth and so that's where we get all +of our energy from + + align:start position:0% +of our energy from + + + align:start position:0% +of our energy from +um it's kind of cool to look at a graph + + align:start position:0% +um it's kind of cool to look at a graph + + + align:start position:0% +um it's kind of cool to look at a graph +of what the energy of of what + + align:start position:0% +of what the energy of of what + + + align:start position:0% +of what the energy of of what +the radiance looks like um so this is + + align:start position:0% +the radiance looks like um so this is + + + align:start position:0% +the radiance looks like um so this is +what this is what wavelength so this is + + align:start position:0% +what this is what wavelength so this is + + + align:start position:0% +what this is what wavelength so this is +a weird graph of um the red green and + + align:start position:0% +a weird graph of um the red green and + + + align:start position:0% +a weird graph of um the red green and +blue are three different types of + + align:start position:0% +blue are three different types of + + + align:start position:0% +blue are three different types of +lighting and the purple is what the sun + + align:start position:0% +lighting and the purple is what the sun + + + align:start position:0% +lighting and the purple is what the sun +is so you can ignore the other three but + + align:start position:0% +is so you can ignore the other three but + + + align:start position:0% +is so you can ignore the other three but +you should look at the purple to see + + align:start position:0% +you should look at the purple to see + + + align:start position:0% +you should look at the purple to see +what wavelengths of light the the sun + + align:start position:0% +what wavelengths of light the the sun + + + align:start position:0% +what wavelengths of light the the sun +outputs + + align:start position:0% +outputs + + + align:start position:0% +outputs +at + + align:start position:0% +at + + + align:start position:0% +at +um it's it's interesting because you can + + align:start position:0% +um it's it's interesting because you can + + + align:start position:0% +um it's it's interesting because you can +see that this is also on + + align:start position:0% +see that this is also on + + + align:start position:0% +see that this is also on +a on a log scale so it's you can see + + align:start position:0% +a on a log scale so it's you can see + + + align:start position:0% +a on a log scale so it's you can see +that um the bulk of the light is in the + + align:start position:0% +that um the bulk of the light is in the + + + align:start position:0% +that um the bulk of the light is in the +visible + + align:start position:0% +visible + + + align:start position:0% +visible +spectrum which is cool + + align:start position:0% +spectrum which is cool + + + align:start position:0% +spectrum which is cool +because + + align:start position:0% +because + + + align:start position:0% +because +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um + + align:start position:0% +um + + + align:start position:0% +um +but to and to measure how much out + + align:start position:0% +but to and to measure how much out + + + align:start position:0% +but to and to measure how much out +energy is being outputed by + + align:start position:0% +energy is being outputed by + + + align:start position:0% +energy is being outputed by +um + + align:start position:0% + + + + align:start position:0% + +by um Sorry by the sun you can just + + align:start position:0% +by um Sorry by the sun you can just + + + align:start position:0% +by um Sorry by the sun you can just +integrate under this curve to find out + + align:start position:0% +integrate under this curve to find out + + + align:start position:0% +integrate under this curve to find out +to measure the entire thing + + align:start position:0% +to measure the entire thing + + + align:start position:0% +to measure the entire thing +um do you guys know what the the energy + + align:start position:0% +um do you guys know what the the energy + + + align:start position:0% +um do you guys know what the the energy +from a + + align:start position:0% +from a + + + align:start position:0% +from a +single um photon is based off of the + + align:start position:0% +single um photon is based off of the + + + align:start position:0% +single um photon is based off of the +wavelength do you remember the equations + + align:start position:0% +wavelength do you remember the equations + + + align:start position:0% +wavelength do you remember the equations +for that so you can calculate you can + + align:start position:0% +for that so you can calculate you can + + + align:start position:0% +for that so you can calculate you can +calculate someone + + align:start position:0% +calculate someone + + + align:start position:0% +calculate someone +say yeah L it's uh it's plank constant + + align:start position:0% +say yeah L it's uh it's plank constant + + + align:start position:0% +say yeah L it's uh it's plank constant +times C over Lambda so you have this um + + align:start position:0% +times C over Lambda so you have this um + + + align:start position:0% +times C over Lambda so you have this um +like you don't need to know this + + align:start position:0% +like you don't need to know this + + + align:start position:0% +like you don't need to know this +equation but it'll give you a good sense + + align:start position:0% +equation but it'll give you a good sense + + + align:start position:0% +equation but it'll give you a good sense +of how you can derive how much energy is + + align:start position:0% +of how you can derive how much energy is + + + align:start position:0% +of how you can derive how much energy is +coming from uh a photon or a wave so so + + align:start position:0% +coming from uh a photon or a wave so so + + + align:start position:0% +coming from uh a photon or a wave so so +this is Plank's constant uh this is the + + align:start position:0% +this is Plank's constant uh this is the + + + align:start position:0% +this is Plank's constant uh this is the +speed of light and this is the + + align:start position:0% +speed of light and this is the + + + align:start position:0% +speed of light and this is the +wavelength um and so what's important + + align:start position:0% +wavelength um and so what's important + + + align:start position:0% +wavelength um and so what's important +from this is that lower the lower the + + align:start position:0% +from this is that lower the lower the + + + align:start position:0% +from this is that lower the lower the +wavelength the more energy you + + align:start position:0% +wavelength the more energy you + + + align:start position:0% +wavelength the more energy you +have um so yeah your your blue light is + + align:start position:0% +have um so yeah your your blue light is + + + align:start position:0% +have um so yeah your your blue light is +going to have more energy than your red + + align:start position:0% +going to have more energy than your red + + + align:start position:0% +going to have more energy than your red +light um + + align:start position:0% +light um + + + align:start position:0% +light um +does that make + + align:start position:0% + + + + align:start position:0% + +sense + + align:start position:0% +sense + + + align:start position:0% +sense +cool so so you have + + align:start position:0% +cool so so you have + + + align:start position:0% +cool so so you have +this so you have your sun it's + + align:start position:0% + + + + align:start position:0% + +outputting so you have the sun which + + align:start position:0% +outputting so you have the sun which + + + align:start position:0% +outputting so you have the sun which +you're looking at um is radiating a + + align:start position:0% +you're looking at um is radiating a + + + align:start position:0% +you're looking at um is radiating a +bunch of electromagnetic waves in the + + align:start position:0% +bunch of electromagnetic waves in the + + + align:start position:0% +bunch of electromagnetic waves in the +form of I guess photons um to the Earth + + align:start position:0% +form of I guess photons um to the Earth + + + align:start position:0% +form of I guess photons um to the Earth +which is here + + align:start position:0% +which is here + + + align:start position:0% +which is here +um what's + + align:start position:0% + + + + align:start position:0% + +um and then we're trying to look at what + + align:start position:0% +um and then we're trying to look at what + + + align:start position:0% +um and then we're trying to look at what +happens like if we if we're trying to + + align:start position:0% +happens like if we if we're trying to + + + align:start position:0% +happens like if we if we're trying to +follow the path of this radiation um we + + align:start position:0% +follow the path of this radiation um we + + + align:start position:0% +follow the path of this radiation um we +can see that not all of it reaches the + + align:start position:0% +can see that not all of it reaches the + + + align:start position:0% +can see that not all of it reaches the +Earth um or not all of it that reaches + + align:start position:0% +Earth um or not all of it that reaches + + + align:start position:0% +Earth um or not all of it that reaches +the earth makes it to the surface of the + + align:start position:0% +the earth makes it to the surface of the + + + align:start position:0% +the earth makes it to the surface of the +Earth because a lot of it is absorbed by + + align:start position:0% +Earth because a lot of it is absorbed by + + + align:start position:0% +Earth because a lot of it is absorbed by +our atmosphere um and so this is a kind + + align:start position:0% +our atmosphere um and so this is a kind + + + align:start position:0% +our atmosphere um and so this is a kind +of graphic that'll uh show you where a + + align:start position:0% +of graphic that'll uh show you where a + + + align:start position:0% +of graphic that'll uh show you where a +lot of energy is lost + + align:start position:0% +lot of energy is lost + + + align:start position:0% +lot of energy is lost +or so only only about 70% of it is + + align:start position:0% +or so only only about 70% of it is + + + align:start position:0% +or so only only about 70% of it is +actually directed to the + + align:start position:0% +actually directed to the + + + align:start position:0% +actually directed to the +Earth + + align:start position:0% +Earth + + + align:start position:0% +Earth +um 3% is scattered to space and 18% is + + align:start position:0% +um 3% is scattered to space and 18% is + + + align:start position:0% +um 3% is scattered to space and 18% is +absorbed by the + + align:start position:0% + + + + align:start position:0% + +atmosphere um now we're going to go into + + align:start position:0% +atmosphere um now we're going to go into + + + align:start position:0% +atmosphere um now we're going to go into +how a solar cell + + align:start position:0% +how a solar cell + + + align:start position:0% +how a solar cell +works + + align:start position:0% +works + + + align:start position:0% +works +um + + align:start position:0% +um + + + align:start position:0% +um +so yeah + + align:start position:0% + + + + align:start position:0% + +okay so this is like also a little bit + + align:start position:0% +okay so this is like also a little bit + + + align:start position:0% +okay so this is like also a little bit +complicated + + align:start position:0% + + + + align:start position:0% + +um so you have you have a solar cell + + align:start position:0% +um so you have you have a solar cell + + + align:start position:0% +um so you have you have a solar cell +which looks like this if you haven't + + align:start position:0% +which looks like this if you haven't + + + align:start position:0% +which looks like this if you haven't +seen one before they're super fragile we + + align:start position:0% +seen one before they're super fragile we + + + align:start position:0% +seen one before they're super fragile we +can pass them + + align:start position:0% +can pass them + + + align:start position:0% +can pass them +around these are broken + + align:start position:0% +around these are broken + + + align:start position:0% +around these are broken +ones + + align:start position:0% +ones + + + align:start position:0% +ones +uh Evergreen solar was like was kind + + align:start position:0% +uh Evergreen solar was like was kind + + + align:start position:0% +uh Evergreen solar was like was kind +enough to donate 200 of these tests for + + align:start position:0% +enough to donate 200 of these tests for + + + align:start position:0% +enough to donate 200 of these tests for +this lab + + align:start position:0% +this lab + + + align:start position:0% +this lab +uh and for our projects so we'll be + + align:start position:0% +uh and for our projects so we'll be + + + align:start position:0% +uh and for our projects so we'll be +playing with them and wiring them up + + align:start position:0% +playing with them and wiring them up + + + align:start position:0% +playing with them and wiring them up +today + + align:start position:0% +today + + + align:start position:0% +today +um + + align:start position:0% +um + + + align:start position:0% +um +so are + + align:start position:0% +so are + + + align:start position:0% +so are +you what + + align:start position:0% +you what + + + align:start position:0% +you what +happened I want to my Thum on it and I + + align:start position:0% +happened I want to my Thum on it and I + + + align:start position:0% +happened I want to my Thum on it and I +yeah they're they're super fragile you + + align:start position:0% +yeah they're they're super fragile you + + + align:start position:0% +yeah they're they're super fragile you +can see why like it's one of the reasons + + align:start position:0% +can see why like it's one of the reasons + + + align:start position:0% +can see why like it's one of the reasons +why working with solar cells is such a + + align:start position:0% +why working with solar cells is such a + + + align:start position:0% +why working with solar cells is such a +pain because they're so easy to break + + align:start position:0% +pain because they're so easy to break + + + align:start position:0% +pain because they're so easy to break +like when you try like you have to + + align:start position:0% +like when you try like you have to + + + align:start position:0% +like when you try like you have to +solder them together to make them work + + align:start position:0% +solder them together to make them work + + + align:start position:0% +solder them together to make them work +so it's kind of difficult but we'll get + + align:start position:0% +so it's kind of difficult but we'll get + + + align:start position:0% +so it's kind of difficult but we'll get +into that later uh so how do they + + align:start position:0% +into that later uh so how do they + + + align:start position:0% +into that later uh so how do they +work so you basically have two layers in + + align:start position:0% +work so you basically have two layers in + + + align:start position:0% +work so you basically have two layers in +your solar like in your solar cell + + align:start position:0% + + + + align:start position:0% + +um as is described in this drawing and + + align:start position:0% +um as is described in this drawing and + + + align:start position:0% +um as is described in this drawing and +what happens is you have a photon coming + + align:start position:0% +what happens is you have a photon coming + + + align:start position:0% +what happens is you have a photon coming +in and for + + align:start position:0% +in and for + + + align:start position:0% +in and for +one um + + align:start position:0% +one um + + + align:start position:0% +one um +they're they're + + align:start position:0% +they're they're + + + align:start position:0% +they're they're +semiconductor + + align:start position:0% +semiconductor + + + align:start position:0% +semiconductor +um so you can tell me what a + + align:start position:0% +um so you can tell me what a + + + align:start position:0% +um so you can tell me what a +semiconductor + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yes you have a f band you have a condu + + align:start position:0% +yes you have a f band you have a condu + + + align:start position:0% +yes you have a f band you have a condu +and you have to have exactly the right + + align:start position:0% +and you have to have exactly the right + + + align:start position:0% +and you have to have exactly the right +band Gap um in between the two so that + + align:start position:0% +band Gap um in between the two so that + + + align:start position:0% +band Gap um in between the two so that +when you when the phon hits it when the + + align:start position:0% +when you when the phon hits it when the + + + align:start position:0% +when you when the phon hits it when the +phon is incident on it it like activates + + align:start position:0% +phon is incident on it it like activates + + + align:start position:0% +phon is incident on it it like activates +exactly + + align:start position:0% + + + + align:start position:0% + +that's correct yeah that's uh did + + align:start position:0% +that's correct yeah that's uh did + + + align:start position:0% +that's correct yeah that's uh did +everyone understand + + align:start position:0% +everyone understand + + + align:start position:0% +everyone understand +that okay so so basically what happens + + align:start position:0% +that okay so so basically what happens + + + align:start position:0% +that okay so so basically what happens +is uh you have in a semiconductor you + + align:start position:0% +is uh you have in a semiconductor you + + + align:start position:0% +is uh you have in a semiconductor you +have things in a pretty like ordered + + align:start position:0% +have things in a pretty like ordered + + + align:start position:0% +have things in a pretty like ordered +pattern so you'll have like + + align:start position:0% + + + + align:start position:0% + +atam something like that um and so + + align:start position:0% +atam something like that um and so + + + align:start position:0% +atam something like that um and so +they're all B like Bound in this lattice + + align:start position:0% +they're all B like Bound in this lattice + + + align:start position:0% +they're all B like Bound in this lattice +and so what happens is they don't have + + align:start position:0% +and so what happens is they don't have + + + align:start position:0% +and so what happens is they don't have +free electrons right now but you can get + + align:start position:0% +free electrons right now but you can get + + + align:start position:0% +free electrons right now but you can get +a free electron from them if you excite + + align:start position:0% +a free electron from them if you excite + + + align:start position:0% +a free electron from them if you excite +the electron with enough energy + + align:start position:0% +the electron with enough energy + + + align:start position:0% +the electron with enough energy +um and so if you have a photon coming in + + align:start position:0% +um and so if you have a photon coming in + + + align:start position:0% +um and so if you have a photon coming in +and it has the right amount of energy to + + align:start position:0% +and it has the right amount of energy to + + + align:start position:0% +and it has the right amount of energy to +excite an electron out of one of these + + align:start position:0% +excite an electron out of one of these + + + align:start position:0% +excite an electron out of one of these +bonds then the the electron or the + + align:start position:0% +bonds then the the electron or the + + + align:start position:0% +bonds then the the electron or the +veence electron or out of the lattice + + align:start position:0% +veence electron or out of the lattice + + + align:start position:0% +veence electron or out of the lattice +the + + align:start position:0% +the + + + align:start position:0% +the +electron uh the electon + + align:start position:0% +electron uh the electon + + + align:start position:0% +electron uh the electon +becomes excited and you then get an + + align:start position:0% +becomes excited and you then get an + + + align:start position:0% +becomes excited and you then get an +electron whole pair and this is all a + + align:start position:0% +electron whole pair and this is all a + + + align:start position:0% +electron whole pair and this is all a +gross simplification of how this works + + align:start position:0% +gross simplification of how this works + + + align:start position:0% +gross simplification of how this works +because um a lot of this is like I mean + + align:start position:0% +because um a lot of this is like I mean + + + align:start position:0% +because um a lot of this is like I mean +you can't really just think of you can't + + align:start position:0% +you can't really just think of you can't + + + align:start position:0% +you can't really just think of you can't +you can think of electrons as particles + + align:start position:0% +you can think of electrons as particles + + + align:start position:0% +you can think of electrons as particles +that are moving across uh a circuit but + + align:start position:0% +that are moving across uh a circuit but + + + align:start position:0% +that are moving across uh a circuit but +that's not actually how it works but for + + align:start position:0% +that's not actually how it works but for + + + align:start position:0% +that's not actually how it works but for +this we going to like assume this + + align:start position:0% +this we going to like assume this + + + align:start position:0% +this we going to like assume this +simplification makes sense to try to + + align:start position:0% +simplification makes sense to try to + + + align:start position:0% +simplification makes sense to try to +like conceptually understand how it + + align:start position:0% +like conceptually understand how it + + + align:start position:0% +like conceptually understand how it +works so what happens is you have like a + + align:start position:0% +works so what happens is you have like a + + + align:start position:0% +works so what happens is you have like a +photon hitting this uh so you get this + + align:start position:0% +photon hitting this uh so you get this + + + align:start position:0% +photon hitting this uh so you get this +electron hole pair um and you can think + + align:start position:0% +electron hole pair um and you can think + + + align:start position:0% +electron hole pair um and you can think +of a hole is where the electron was + + align:start position:0% +of a hole is where the electron was + + + align:start position:0% +of a hole is where the electron was +before and so now there's this space + + align:start position:0% +before and so now there's this space + + + align:start position:0% +before and so now there's this space +where this electron was and so it's kind + + align:start position:0% +where this electron was and so it's kind + + + align:start position:0% +where this electron was and so it's kind +of positive area because + + align:start position:0% +of positive area because + + + align:start position:0% +of positive area because +um + + align:start position:0% +um + + + align:start position:0% +um +because there like there's less electron + + align:start position:0% +because there like there's less electron + + + align:start position:0% +because there like there's less electron +like there's no electron there anymore U + + align:start position:0% +like there's no electron there anymore U + + + align:start position:0% +like there's no electron there anymore U +so you can think of it kind of like a + + align:start position:0% +so you can think of it kind of like a + + + align:start position:0% +so you can think of it kind of like a +bubble in a fluid almost and so this + + align:start position:0% +bubble in a fluid almost and so this + + + align:start position:0% +bubble in a fluid almost and so this +electron wants to go back into this + + align:start position:0% +electron wants to go back into this + + + align:start position:0% +electron wants to go back into this +bubble + + align:start position:0% +bubble + + + align:start position:0% +bubble +um and this bubble is free to move as + + align:start position:0% +um and this bubble is free to move as + + + align:start position:0% +um and this bubble is free to move as +well just like the electron is free to + + align:start position:0% +well just like the electron is free to + + + align:start position:0% +well just like the electron is free to +move through the structure now because + + align:start position:0% +move through the structure now because + + + align:start position:0% +move through the structure now because +uh it can trans it can go through it and + + align:start position:0% +uh it can trans it can go through it and + + + align:start position:0% +uh it can trans it can go through it and +so what happens is if you but the thing + + align:start position:0% +so what happens is if you but the thing + + + align:start position:0% +so what happens is if you but the thing +is that you're using two different types + + align:start position:0% +is that you're using two different types + + + align:start position:0% +is that you're using two different types +of um silicon and one of them is an N + + align:start position:0% +of um silicon and one of them is an N + + + align:start position:0% +of um silicon and one of them is an N +type and one of them is a p type and the + + align:start position:0% +type and one of them is a p type and the + + + align:start position:0% +type and one of them is a p type and the +n and p just stand for negative and + + align:start position:0% +n and p just stand for negative and + + + align:start position:0% +n and p just stand for negative and +positive and so other thing is you can + + align:start position:0% +positive and so other thing is you can + + + align:start position:0% +positive and so other thing is you can +you can dopee silicon and what that does + + align:start position:0% +you can dopee silicon and what that does + + + align:start position:0% +you can dopee silicon and what that does +means is you put impurities in it and + + align:start position:0% +means is you put impurities in it and + + + align:start position:0% +means is you put impurities in it and +that creates a permanent uh electric + + align:start position:0% +that creates a permanent uh electric + + + align:start position:0% +that creates a permanent uh electric +field inside the silicon and so so one + + align:start position:0% +field inside the silicon and so so one + + + align:start position:0% +field inside the silicon and so so one +of your sides is more positive and one + + align:start position:0% +of your sides is more positive and one + + + align:start position:0% +of your sides is more positive and one +of them is more negative um so when you + + align:start position:0% +of them is more negative um so when you + + + align:start position:0% +of them is more negative um so when you +create + + align:start position:0% +create + + + align:start position:0% +create +this uh when you create this + + align:start position:0% +this uh when you create this + + + align:start position:0% +this uh when you create this +electron whole pair here um they're + + align:start position:0% +electron whole pair here um they're + + + align:start position:0% +electron whole pair here um they're +going to want to be pulled towards + + align:start position:0% +going to want to be pulled towards + + + align:start position:0% +going to want to be pulled towards +opposite directions just based off of + + align:start position:0% +opposite directions just based off of + + + align:start position:0% +opposite directions just based off of +like based off of what + + align:start position:0% +like based off of what + + + align:start position:0% +like based off of what +uh based off of drift um and so once it + + align:start position:0% +uh based off of drift um and so once it + + + align:start position:0% +uh based off of drift um and so once it +get pulled to either + + align:start position:0% +get pulled to either + + + align:start position:0% +get pulled to either +side uh you can if you create a circuit + + align:start position:0% +side uh you can if you create a circuit + + + align:start position:0% +side uh you can if you create a circuit +and you put a load on this thing then + + align:start position:0% +and you put a load on this thing then + + + align:start position:0% +and you put a load on this thing then +you can have the electron flow through + + align:start position:0% +you can have the electron flow through + + + align:start position:0% +you can have the electron flow through +here and go back and if the hole is here + + align:start position:0% +here and go back and if the hole is here + + + align:start position:0% +here and go back and if the hole is here +then it'll close the circuit again and + + align:start position:0% +then it'll close the circuit again and + + + align:start position:0% +then it'll close the circuit again and +combine with the um + + align:start position:0% +combine with the um + + + align:start position:0% +combine with the um +yeah so that's that's a very + + align:start position:0% +yeah so that's that's a very + + + align:start position:0% +yeah so that's that's a very +like simplified way of how photov + + align:start position:0% +like simplified way of how photov + + + align:start position:0% +like simplified way of how photov +voltaics Works work does that make sense + + align:start position:0% +voltaics Works work does that make sense + + + align:start position:0% +voltaics Works work does that make sense +to people are there any questions about + + align:start position:0% +to people are there any questions about + + + align:start position:0% +to people are there any questions about +that + + align:start position:0% + + + + align:start position:0% + +uh no the end type should be the + + align:start position:0% +uh no the end type should be the + + + align:start position:0% +uh no the end type should be the +negative huh the end type is negative a + + align:start position:0% +negative huh the end type is negative a + + + align:start position:0% +negative huh the end type is negative a +really good animation of Education that + + align:start position:0% +really good animation of Education that + + + align:start position:0% +really good animation of Education that +shows two sides + + align:start position:0% +shows two sides + + + align:start position:0% +shows two sides +of that's true we could actually just + + align:start position:0% +of that's true we could actually just + + + align:start position:0% +of that's true we could actually just +watch it + + align:start position:0% + + + + align:start position:0% + +I had it + + align:start position:0% + + + + align:start position:0% + +open okay uh yeah + + align:start position:0% + + + + align:start position:0% + +anyway + + align:start position:0% + + + + align:start position:0% + +um so so we + + align:start position:0% +um so so we + + + align:start position:0% +um so so we +can so that that's basically how photov + + align:start position:0% +can so that that's basically how photov + + + align:start position:0% +can so that that's basically how photov +voltaics work you get yes um doesn't + + align:start position:0% +voltaics work you get yes um doesn't + + + align:start position:0% +voltaics work you get yes um doesn't +sunlight hit the junction though isn't + + align:start position:0% +sunlight hit the junction though isn't + + + align:start position:0% +sunlight hit the junction though isn't +that how um I mean because you have like + + align:start position:0% +that how um I mean because you have like + + + align:start position:0% +that how um I mean because you have like +the hold and then the electrons on the + + align:start position:0% +the hold and then the electrons on the + + + align:start position:0% +the hold and then the electrons on the +side creating the um the you know the + + align:start position:0% +side creating the um the you know the + + + align:start position:0% +side creating the um the you know the +opposite uh electric field doesn't the + + align:start position:0% +opposite uh electric field doesn't the + + + align:start position:0% +opposite uh electric field doesn't the +light hit the middle I mean that that + + align:start position:0% +light hit the middle I mean that that + + + align:start position:0% +light hit the middle I mean that that +that's that was my understanding could + + align:start position:0% +that's that was my understanding could + + + align:start position:0% +that's that was my understanding could +be wrong but I thought it hit the mid I + + align:start position:0% +be wrong but I thought it hit the mid I + + + align:start position:0% +be wrong but I thought it hit the mid I +don't I'm not sure I that's not how I + + align:start position:0% +don't I'm not sure I that's not how I + + + align:start position:0% +don't I'm not sure I that's not how I +understood I don't think I feel + + align:start position:0% +understood I don't think I feel + + + align:start position:0% +understood I don't think I feel +like so the reason + + align:start position:0% +like so the reason + + + align:start position:0% +like so the reason +so the ab like the absorption + + align:start position:0% +so the ab like the absorption + + + align:start position:0% +so the ab like the absorption +coefficient of silicon is really uh low + + align:start position:0% +coefficient of silicon is really uh low + + + align:start position:0% +coefficient of silicon is really uh low +so so you have like you have a lot of + + align:start position:0% +so so you have like you have a lot of + + + align:start position:0% +so so you have like you have a lot of +different solar cells right you have uh + + align:start position:0% +different solar cells right you have uh + + + align:start position:0% +different solar cells right you have uh +amorph of silicon you have like multi + + align:start position:0% +amorph of silicon you have like multi + + + align:start position:0% +amorph of silicon you have like multi +Crystal and silicon um and stuff and the + + align:start position:0% +Crystal and silicon um and stuff and the + + + align:start position:0% +Crystal and silicon um and stuff and the +reason why and you have like thin film + + align:start position:0% +reason why and you have like thin film + + + align:start position:0% +reason why and you have like thin film +cells as well but the reason why silicon + + align:start position:0% +cells as well but the reason why silicon + + + align:start position:0% +cells as well but the reason why silicon +cells are so thick is because the + + align:start position:0% +cells are so thick is because the + + + align:start position:0% +cells are so thick is because the +absorption coefficient is so low that + + align:start position:0% +absorption coefficient is so low that + + + align:start position:0% +absorption coefficient is so low that +you basically need a thicker area to be + + align:start position:0% +you basically need a thicker area to be + + + align:start position:0% +you basically need a thicker area to be +able to absorb most of the + + align:start position:0% +able to absorb most of the + + + align:start position:0% +able to absorb most of the +the light um I'm not answering your + + align:start position:0% +the light um I'm not answering your + + + align:start position:0% +the light um I'm not answering your +question am I you thought you think that + + align:start position:0% +question am I you thought you think that + + + align:start position:0% +question am I you thought you think that +so understanding middle like not not + + align:start position:0% +so understanding middle like not not + + + align:start position:0% +so understanding middle like not not +exactly the middle but you know how like + + align:start position:0% +exactly the middle but you know how like + + + align:start position:0% +exactly the middle but you know how like +in the middle you have the opposite + + align:start position:0% +in the middle you have the opposite + + + align:start position:0% +in the middle you have the opposite +electric field because of the holes and + + align:start position:0% +electric field because of the holes and + + + align:start position:0% +electric field because of the holes and +the electrons uh on the sides right so + + align:start position:0% +the electrons uh on the sides right so + + + align:start position:0% +the electrons uh on the sides right so +like if this is your n and your P then + + align:start position:0% +like if this is your n and your P then + + + align:start position:0% +like if this is your n and your P then +you'd have holds here and you have + + align:start position:0% +you'd have holds here and you have + + + align:start position:0% +you'd have holds here and you have +electrons here for the opposite field um + + align:start position:0% +electrons here for the opposite field um + + + align:start position:0% +electrons here for the opposite field um +and minor understanding was that it + + align:start position:0% +and minor understanding was that it + + + align:start position:0% +and minor understanding was that it +would hit the middle and the field would + + align:start position:0% +would hit the middle and the field would + + + align:start position:0% +would hit the middle and the field would +force the electrons to go uh in One + + align:start position:0% +force the electrons to go uh in One + + + align:start position:0% +force the electrons to go uh in One +Direction which would then be used to + + align:start position:0% +Direction which would then be used to + + + align:start position:0% +Direction which would then be used to +then we we helped by an external circuit + + align:start position:0% +then we we helped by an external circuit + + + align:start position:0% +then we we helped by an external circuit +well there there few like factors in + + align:start position:0% +well there there few like factors in + + + align:start position:0% +well there there few like factors in +place so you have + + align:start position:0% +place so you have + + + align:start position:0% +place so you have +a so you have one side that's more that + + align:start position:0% +a so you have one side that's more that + + + align:start position:0% +a so you have one side that's more that +has here I can show you a a video + + align:start position:0% +has here I can show you a a video + + + align:start position:0% +has here I can show you a a video +on on + + align:start position:0% + + + + align:start position:0% + +how okay I don't know this will work so + + align:start position:0% +how okay I don't know this will work so + + + align:start position:0% +how okay I don't know this will work so +this is + + align:start position:0% +this is + + + align:start position:0% +this is +from this is from the this PV CD ROM + + align:start position:0% +from this is from the this PV CD ROM + + + align:start position:0% +from this is from the this PV CD ROM +website and so it's an animation saying + + align:start position:0% +website and so it's an animation saying + + + align:start position:0% +website and so it's an animation saying +how things work and so if you have + + align:start position:0% +how things work and so if you have + + + align:start position:0% +how things work and so if you have +a if you have a moderate field you have + + align:start position:0% +a if you have a moderate field you have + + + align:start position:0% +a if you have a moderate field you have +so you have two things that work you + + align:start position:0% +so you have two things that work you + + + align:start position:0% +so you have two things that work you +have uh diffusion and the thing is in + + align:start position:0% +have uh diffusion and the thing is in + + + align:start position:0% +have uh diffusion and the thing is in +diffusion the way diffusion works is if + + align:start position:0% +diffusion the way diffusion works is if + + + align:start position:0% +diffusion the way diffusion works is if +you have a a lot of I mean it just if + + align:start position:0% +you have a a lot of I mean it just if + + + align:start position:0% +you have a a lot of I mean it just if +you have a lot of holes on one side and + + align:start position:0% +you have a lot of holes on one side and + + + align:start position:0% +you have a lot of holes on one side and +electrons on the other the electrons + + align:start position:0% +electrons on the other the electrons + + + align:start position:0% +electrons on the other the electrons +want to tend to go to the side where + + align:start position:0% +want to tend to go to the side where + + + align:start position:0% +want to tend to go to the side where +there aren't electrons and the holes + + align:start position:0% +there aren't electrons and the holes + + + align:start position:0% +there aren't electrons and the holes +want to go tend to go to the side where + + align:start position:0% +want to go tend to go to the side where + + + align:start position:0% +want to go tend to go to the side where +there aren't um holes and so you have + + align:start position:0% +there aren't um holes and so you have + + + align:start position:0% +there aren't um holes and so you have +that but that's working against the the + + align:start position:0% +that but that's working against the the + + + align:start position:0% +that but that's working against the the +positive and negative factor of like or + + align:start position:0% +positive and negative factor of like or + + + align:start position:0% +positive and negative factor of like or +the positive and negative charges of the + + align:start position:0% +the positive and negative charges of the + + + align:start position:0% +the positive and negative charges of the +two sides as well + + align:start position:0% +two sides as well + + + align:start position:0% +two sides as well +um so you have those two kind of + + align:start position:0% +um so you have those two kind of + + + align:start position:0% +um so you have those two kind of +balancing each other out in some + + align:start position:0% +balancing each other out in some + + + align:start position:0% +balancing each other out in some +way um so + + align:start position:0% +way um so + + + align:start position:0% +way um so +I'm really confused by this + + align:start position:0% + + + + align:start position:0% + +um so once you + + align:start position:0% + + + + align:start position:0% + +have um hold + + align:start position:0% + + + + align:start position:0% + +on okay yeah so once you have uh once + + align:start position:0% +on okay yeah so once you have uh once + + + align:start position:0% +on okay yeah so once you have uh once +you're connecting this to a load you + + align:start position:0% +you're connecting this to a load you + + + align:start position:0% +you're connecting this to a load you +you're now + + align:start position:0% +you're now + + + align:start position:0% +you're now +enabling the holes and electrons to + + align:start position:0% +enabling the holes and electrons to + + + align:start position:0% +enabling the holes and electrons to +travel across this conductive region uh + + align:start position:0% +travel across this conductive region uh + + + align:start position:0% +travel across this conductive region uh +to um and so they're not only like now + + align:start position:0% +to um and so they're not only like now + + + align:start position:0% +to um and so they're not only like now +they're not just diffusing and drifting + + align:start position:0% +they're not just diffusing and drifting + + + align:start position:0% +they're not just diffusing and drifting +through here they're also like traveling + + align:start position:0% +through here they're also like traveling + + + align:start position:0% +through here they're also like traveling +through does that not that's still not + + align:start position:0% +through does that not that's still not + + + align:start position:0% +through does that not that's still not +answering your question I mean um so + + align:start position:0% +answering your question I mean um so + + + align:start position:0% +answering your question I mean um so +basically I understand um I understand + + align:start position:0% +basically I understand um I understand + + + align:start position:0% +basically I understand um I understand +the concept uh I was just curious + + align:start position:0% +the concept uh I was just curious + + + align:start position:0% +the concept uh I was just curious +whether like uh in the diagram you know + + align:start position:0% +whether like uh in the diagram you know + + + align:start position:0% +whether like uh in the diagram you know +how there's a you know the middle region + + align:start position:0% +how there's a you know the middle region + + + align:start position:0% +how there's a you know the middle region +the depletion there um my understanding + + align:start position:0% +the depletion there um my understanding + + + align:start position:0% +the depletion there um my understanding +was that's where the electrons were uh + + align:start position:0% +was that's where the electrons were uh + + + align:start position:0% +was that's where the electrons were uh +you know I mean that's where the light + + align:start position:0% +you know I mean that's where the light + + + align:start position:0% +you know I mean that's where the light +hit and that's where the electrons were + + align:start position:0% +hit and that's where the electrons were + + + align:start position:0% +hit and that's where the electrons were +uh ejected and then they would move + + align:start position:0% +uh ejected and then they would move + + + align:start position:0% +uh ejected and then they would move +around um but I mean this diagr doesn't + + align:start position:0% +around um but I mean this diagr doesn't + + + align:start position:0% +around um but I mean this diagr doesn't +seem to be doing yeah I'm pretty I'm + + align:start position:0% +seem to be doing yeah I'm pretty I'm + + + align:start position:0% +seem to be doing yeah I'm pretty I'm +pretty sure that um I'm pretty sure that + + align:start position:0% +pretty sure that um I'm pretty sure that + + + align:start position:0% +pretty sure that um I'm pretty sure that +like the light excites El or creates + + align:start position:0% +like the light excites El or creates + + + align:start position:0% +like the light excites El or creates +electron whole pairs anywhere inside the + + align:start position:0% +electron whole pairs anywhere inside the + + + align:start position:0% +electron whole pairs anywhere inside the +entire soell but I can double check with + + align:start position:0% +entire soell but I can double check with + + + align:start position:0% +entire soell but I can double check with +the fall on that as well um + + align:start position:0% + + + + align:start position:0% + +cool so now we're going to go + + align:start position:0% +cool so now we're going to go + + + align:start position:0% +cool so now we're going to go +into some practical considerations for + + align:start position:0% +into some practical considerations for + + + align:start position:0% +into some practical considerations for +developing world work in solar um yes so + + align:start position:0% +developing world work in solar um yes so + + + align:start position:0% +developing world work in solar um yes so +um solar + + align:start position:0% +um solar + + + align:start position:0% +um solar +panels past like certain 15 years right + + align:start position:0% +panels past like certain 15 years right + + + align:start position:0% +panels past like certain 15 years right +or something what exactly is breaking + + align:start position:0% +or something what exactly is breaking + + + align:start position:0% +or something what exactly is breaking +down in + + align:start position:0% +down in + + + align:start position:0% +down in +this to cause + + align:start position:0% +this to cause + + + align:start position:0% +this to cause +that uh not sure they they often + + align:start position:0% +that uh not sure they they often + + + align:start position:0% +that uh not sure they they often +function a lot more than 15 years + + align:start position:0% +function a lot more than 15 years + + + align:start position:0% +function a lot more than 15 years +I think most of it has to do like + + align:start position:0% +I think most of it has to do like + + + align:start position:0% +I think most of it has to do like +actually not the + + align:start position:0% +actually not the + + + align:start position:0% +actually not the +cells the glass matal breaking down + + align:start position:0% +cells the glass matal breaking down + + + align:start position:0% +cells the glass matal breaking down +getting scratches and + + align:start position:0% +getting scratches and + + + align:start position:0% +getting scratches and +dirty I think a lot of the a lot of the + + align:start position:0% +dirty I think a lot of the a lot of the + + + align:start position:0% +dirty I think a lot of the a lot of the +pedals are actually like + + align:start position:0% + + + + align:start position:0% + +outlasting have like 25 year + + align:start position:0% +outlasting have like 25 year + + + align:start position:0% +outlasting have like 25 year +80% 25 years should still be + + align:start position:0% + + + + align:start position:0% + +making I think some of the earlier + + align:start position:0% +making I think some of the earlier + + + align:start position:0% +making I think some of the earlier +coming to that time they're still well + + align:start position:0% +coming to that time they're still well + + + align:start position:0% +coming to that time they're still well +that + + align:start position:0% +that + + + align:start position:0% +that +there's there might be a little bit but + + align:start position:0% +there's there might be a little bit but + + + align:start position:0% +there's there might be a little bit but +that's not really the biggest most + + align:start position:0% + + + + align:start position:0% + +yeah I can also look that up and get + + align:start position:0% +yeah I can also look that up and get + + + align:start position:0% +yeah I can also look that up and get +back to that + + align:start position:0% +back to that + + + align:start position:0% +back to that +um yeah um so let's let's look at some + + align:start position:0% +um yeah um so let's let's look at some + + + align:start position:0% +um yeah um so let's let's look at some +of the financial tools that are + + align:start position:0% +of the financial tools that are + + + align:start position:0% +of the financial tools that are +available in order to + + align:start position:0% +available in order to + + + align:start position:0% +available in order to +finance um solar so you you can do the + + align:start position:0% +finance um solar so you you can do the + + + align:start position:0% +finance um solar so you you can do the +four sort + + align:start position:0% +four sort + + + align:start position:0% +four sort +of big ones are uh micro finance a fee + + align:start position:0% +of big ones are uh micro finance a fee + + + align:start position:0% +of big ones are uh micro finance a fee +for service income generation or smaller + + align:start position:0% +for service income generation or smaller + + + align:start position:0% +for service income generation or smaller +systems + + align:start position:0% +systems + + + align:start position:0% +systems +um and then so you have for micr finance + + align:start position:0% +um and then so you have for micr finance + + + align:start position:0% +um and then so you have for micr finance +you have smaller payments over a longer + + align:start position:0% +you have smaller payments over a longer + + + align:start position:0% +you have smaller payments over a longer +period of time for fee for service you + + align:start position:0% +period of time for fee for service you + + + align:start position:0% +period of time for fee for service you +have a company that owns a PV system and + + align:start position:0% +have a company that owns a PV system and + + + align:start position:0% +have a company that owns a PV system and +a household that pays the electric bill + + align:start position:0% +a household that pays the electric bill + + + align:start position:0% +a household that pays the electric bill +for it uh for income generation which we + + align:start position:0% +for it uh for income generation which we + + + align:start position:0% +for it uh for income generation which we +saw I think in the lighting lecture last + + align:start position:0% +saw I think in the lighting lecture last + + + align:start position:0% +saw I think in the lighting lecture last +week we saw how people were using solar + + align:start position:0% +week we saw how people were using solar + + + align:start position:0% +week we saw how people were using solar +panels to generate income you use a a + + align:start position:0% +panels to generate income you use a a + + + align:start position:0% +panels to generate income you use a a +system to improve your income stream so + + align:start position:0% +system to improve your income stream so + + + align:start position:0% +system to improve your income stream so +you can + + align:start position:0% +you can + + + align:start position:0% +you can +um with something like this you'll have + + align:start position:0% +um with something like this you'll have + + + align:start position:0% +um with something like this you'll have +one person with a lot of solar panels + + align:start position:0% +one person with a lot of solar panels + + + align:start position:0% +one person with a lot of solar panels +who will charge a lot of batteries and + + align:start position:0% +who will charge a lot of batteries and + + + align:start position:0% +who will charge a lot of batteries and +uh rent them out as electricity and then + + align:start position:0% +uh rent them out as electricity and then + + + align:start position:0% +uh rent them out as electricity and then +uh for smaller systems you can like you + + align:start position:0% +uh for smaller systems you can like you + + + align:start position:0% +uh for smaller systems you can like you +can scale the technology down so you're + + align:start position:0% +can scale the technology down so you're + + + align:start position:0% +can scale the technology down so you're +not using giant solar panels anymore but + + align:start position:0% +not using giant solar panels anymore but + + + align:start position:0% +not using giant solar panels anymore but +you're using smaller sort of panels to + + align:start position:0% +you're using smaller sort of panels to + + + align:start position:0% +you're using smaller sort of panels to +uh Power a lantern or something like + + align:start position:0% +uh Power a lantern or something like + + + align:start position:0% +uh Power a lantern or something like +that for + + align:start position:0% +that for + + + align:start position:0% +that for +example + + align:start position:0% +example + + + align:start position:0% +example +um yeah and so that was the bulk of what + + align:start position:0% +um yeah and so that was the bulk of what + + + align:start position:0% +um yeah and so that was the bulk of what +I wanted to talk about today + + align:start position:0% +I wanted to talk about today + + + align:start position:0% +I wanted to talk about today +um about solar cells um I guess one of + + align:start position:0% +um about solar cells um I guess one of + + + align:start position:0% +um about solar cells um I guess one of +the interesting things though to note + + align:start position:0% +the interesting things though to note + + + align:start position:0% +the interesting things though to note +about them is that it's weird because + + align:start position:0% +about them is that it's weird because + + + align:start position:0% +about them is that it's weird because +they they're a technology that's very + + align:start position:0% +they they're a technology that's very + + + align:start position:0% +they they're a technology that's very +much + + align:start position:0% +much + + + align:start position:0% +much +um there's a quote from Harish Hundai + + align:start position:0% +um there's a quote from Harish Hundai + + + align:start position:0% +um there's a quote from Harish Hundai +who is a founder of celo that's solar is + + align:start position:0% +who is a founder of celo that's solar is + + + align:start position:0% +who is a founder of celo that's solar is +expensive for the rich and affordable + + align:start position:0% +expensive for the rich and affordable + + + align:start position:0% +expensive for the rich and affordable +for the poor it's the rich who need + + align:start position:0% +for the poor it's the rich who need + + + align:start position:0% +for the poor it's the rich who need +subsidies um and it's sort of this weird + + align:start position:0% +subsidies um and it's sort of this weird + + + align:start position:0% +subsidies um and it's sort of this weird +thing because + + align:start position:0% +thing because + + + align:start position:0% +thing because +electricity for the amount that people + + align:start position:0% +electricity for the amount that people + + + align:start position:0% +electricity for the amount that people +need um in the developing world + + align:start position:0% +need um in the developing world + + + align:start position:0% +need um in the developing world +for like the amount like the amount of + + align:start position:0% +for like the amount like the amount of + + + align:start position:0% +for like the amount like the amount of +energy that they need there solar is a + + align:start position:0% +energy that they need there solar is a + + + align:start position:0% +energy that they need there solar is a +very cheap solution for that whereas + + align:start position:0% +very cheap solution for that whereas + + + align:start position:0% +very cheap solution for that whereas +um the amount of electricity that we're + + align:start position:0% +um the amount of electricity that we're + + + align:start position:0% +um the amount of electricity that we're +using like at the scales we're looking + + align:start position:0% +using like at the scales we're looking + + + align:start position:0% +using like at the scales we're looking +at solar is a very expensive option + + align:start position:0% +at solar is a very expensive option + + + align:start position:0% +at solar is a very expensive option +compared to other sorts of electricity + + align:start position:0% +compared to other sorts of electricity + + + align:start position:0% +compared to other sorts of electricity +so it's it's pretty important like it's + + align:start position:0% +so it's it's pretty important like it's + + + align:start position:0% +so it's it's pretty important like it's +pretty important to think about or it's + + align:start position:0% +pretty important to think about or it's + + + align:start position:0% +pretty important to think about or it's +like important to think of solar is not + + align:start position:0% +like important to think of solar is not + + + align:start position:0% +like important to think of solar is not +an expensive technology per se because + + align:start position:0% +an expensive technology per se because + + + align:start position:0% +an expensive technology per se because +uh because I think in in the US at least + + align:start position:0% +uh because I think in in the US at least + + + align:start position:0% +uh because I think in in the US at least +we have that bias as solar being + + align:start position:0% +we have that bias as solar being + + + align:start position:0% +we have that bias as solar being +expensive um and celco makes profit + + align:start position:0% +expensive um and celco makes profit + + + align:start position:0% +expensive um and celco makes profit +because they sell all of their solar + + align:start position:0% +because they sell all of their solar + + + align:start position:0% +because they sell all of their solar +panels without subsidies at all so I + + align:start position:0% +panels without subsidies at all so I + + + align:start position:0% +panels without subsidies at all so I +thought that was pretty cool \ No newline at end of file diff --git a/g6Ksr5sJ0sM.txt b/g6Ksr5sJ0sM.txt new file mode 100644 index 0000000000000000000000000000000000000000..88bfe8db829f52537e7de9fc1cbfcc4f282ed799 --- /dev/null +++ b/g6Ksr5sJ0sM.txt @@ -0,0 +1,4211 @@ +align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +hi everyone my name is Brandon Lewinsky + + align:start position:0% +hi everyone my name is Brandon Lewinsky + + + align:start position:0% +hi everyone my name is Brandon Lewinsky +and I'm a graduate student here at MIT + + align:start position:0% +and I'm a graduate student here at MIT + + + align:start position:0% +and I'm a graduate student here at MIT +now the presentation that you're + + align:start position:0% +now the presentation that you're + + + align:start position:0% +now the presentation that you're +watching was created by an organization + + align:start position:0% +watching was created by an organization + + + align:start position:0% +watching was created by an organization +here at MIT called earth DNA but it's + + align:start position:0% +here at MIT called earth DNA but it's + + + align:start position:0% +here at MIT called earth DNA but it's +gonna be shared with high school + + align:start position:0% +gonna be shared with high school + + + align:start position:0% +gonna be shared with high school +students all around the country and so + + align:start position:0% +students all around the country and so + + + align:start position:0% +students all around the country and so +I'm really excited to be sharing it with + + align:start position:0% +I'm really excited to be sharing it with + + + align:start position:0% +I'm really excited to be sharing it with +you guys welcome this talk is gonna have + + align:start position:0% +you guys welcome this talk is gonna have + + + align:start position:0% +you guys welcome this talk is gonna have +some audience interaction so to get + + align:start position:0% +some audience interaction so to get + + + align:start position:0% +some audience interaction so to get +everybody warmed up please just yell out + + align:start position:0% +everybody warmed up please just yell out + + + align:start position:0% +everybody warmed up please just yell out +your own name on three ready one two + + align:start position:0% +your own name on three ready one two + + + align:start position:0% +your own name on three ready one two +three + + align:start position:0% +three + + + align:start position:0% +three +nice to meet you like I said I'm Brandon + + align:start position:0% +nice to meet you like I said I'm Brandon + + + align:start position:0% +nice to meet you like I said I'm Brandon +now in this talk we're gonna cover four + + align:start position:0% +now in this talk we're gonna cover four + + + align:start position:0% +now in this talk we're gonna cover four +things the truth the consequences the + + align:start position:0% +things the truth the consequences the + + + align:start position:0% +things the truth the consequences the +myths in the future and I want to start + + align:start position:0% +myths in the future and I want to start + + + align:start position:0% +myths in the future and I want to start +with a truth in particular let's review + + align:start position:0% +with a truth in particular let's review + + + align:start position:0% +with a truth in particular let's review +the science of what's happening we'll go + + align:start position:0% +the science of what's happening we'll go + + + align:start position:0% +the science of what's happening we'll go +through it slowly in 1896 a scientist + + align:start position:0% +through it slowly in 1896 a scientist + + + align:start position:0% +through it slowly in 1896 a scientist +discovered the greenhouse effect can + + align:start position:0% +discovered the greenhouse effect can + + + align:start position:0% +discovered the greenhouse effect can +somebody here tell me what the + + align:start position:0% +somebody here tell me what the + + + align:start position:0% +somebody here tell me what the +greenhouse effect is does anybody here + + align:start position:0% +greenhouse effect is does anybody here + + + align:start position:0% +greenhouse effect is does anybody here +know yes + + align:start position:0% + + + + align:start position:0% + +they're cool it's part of the songs as + + align:start position:0% +they're cool it's part of the songs as + + + align:start position:0% +they're cool it's part of the songs as +part of the Earth's atmosphere that + + align:start position:0% +part of the Earth's atmosphere that + + + align:start position:0% +part of the Earth's atmosphere that +keeps our temperature warm and normal + + align:start position:0% +keeps our temperature warm and normal + + + align:start position:0% +keeps our temperature warm and normal +okay anybody else + + align:start position:0% +okay anybody else + + + align:start position:0% +okay anybody else +what is the greenhouse effect yes go + + align:start position:0% +what is the greenhouse effect yes go + + + align:start position:0% +what is the greenhouse effect yes go +ahead + + align:start position:0% + + + + align:start position:0% + +after it's retracted something called + + align:start position:0% +after it's retracted something called + + + align:start position:0% +after it's retracted something called +radiative forcing and so some for a lot + + align:start position:0% +radiative forcing and so some for a lot + + + align:start position:0% +radiative forcing and so some for a lot +of gases in the atmosphere like nitrogen + + align:start position:0% +of gases in the atmosphere like nitrogen + + + align:start position:0% +of gases in the atmosphere like nitrogen +the sunrays just pass right through but + + align:start position:0% +the sunrays just pass right through but + + + align:start position:0% +the sunrays just pass right through but +bird a select few like water and carbon + + align:start position:0% +bird a select few like water and carbon + + + align:start position:0% +bird a select few like water and carbon +dioxide that absorb infrared light and + + align:start position:0% +dioxide that absorb infrared light and + + + align:start position:0% +dioxide that absorb infrared light and +then for red spectrum and then that + + align:start position:0% +then for red spectrum and then that + + + align:start position:0% +then for red spectrum and then that +drops eat the answer fantastic you must + + align:start position:0% +drops eat the answer fantastic you must + + + align:start position:0% +drops eat the answer fantastic you must +know your climate science but that's + + align:start position:0% +know your climate science but that's + + + align:start position:0% +know your climate science but that's +exactly right and the basic idea is that + + align:start position:0% +exactly right and the basic idea is that + + + align:start position:0% +exactly right and the basic idea is that +some gases in our atmosphere trap heat + + align:start position:0% +some gases in our atmosphere trap heat + + + align:start position:0% +some gases in our atmosphere trap heat +and you can see here how light from the + + align:start position:0% +and you can see here how light from the + + + align:start position:0% +and you can see here how light from the +Sun hits the earth it gets converted + + align:start position:0% +Sun hits the earth it gets converted + + + align:start position:0% +Sun hits the earth it gets converted +into heat and it gets trapped underneath + + align:start position:0% +into heat and it gets trapped underneath + + + align:start position:0% +into heat and it gets trapped underneath +this atmospheric blanket we emit these + + align:start position:0% +this atmospheric blanket we emit these + + + align:start position:0% +this atmospheric blanket we emit these +greenhouse gases by burning fossil fuels + + align:start position:0% +greenhouse gases by burning fossil fuels + + + align:start position:0% +greenhouse gases by burning fossil fuels +for transportation and electricity + + align:start position:0% +for transportation and electricity + + + align:start position:0% +for transportation and electricity +things like driving flying air + + align:start position:0% +things like driving flying air + + + align:start position:0% +things like driving flying air +conditioning these all emit greenhouse + + align:start position:0% +conditioning these all emit greenhouse + + + align:start position:0% +conditioning these all emit greenhouse +gases into the atmosphere as we burn + + align:start position:0% +gases into the atmosphere as we burn + + + align:start position:0% +gases into the atmosphere as we burn +fossil fuels like oil gas and coal + + align:start position:0% +fossil fuels like oil gas and coal + + + align:start position:0% +fossil fuels like oil gas and coal +greenhouse gas concentrations rise you + + align:start position:0% +greenhouse gas concentrations rise you + + + align:start position:0% +greenhouse gas concentrations rise you +can see here that since 2005 the amount + + align:start position:0% +can see here that since 2005 the amount + + + align:start position:0% +can see here that since 2005 the amount +of carbon dioxide one of the main + + align:start position:0% +of carbon dioxide one of the main + + + align:start position:0% +of carbon dioxide one of the main +greenhouse gases has increased steadily + + align:start position:0% +greenhouse gases has increased steadily + + + align:start position:0% +greenhouse gases has increased steadily +here's that same graph since 1700 you + + align:start position:0% +here's that same graph since 1700 you + + + align:start position:0% +here's that same graph since 1700 you +can see the industrial revolution + + align:start position:0% +can see the industrial revolution + + + align:start position:0% +can see the industrial revolution +happening in 1760 and shortly thereafter + + align:start position:0% +happening in 1760 and shortly thereafter + + + align:start position:0% +happening in 1760 and shortly thereafter +we start to see this increase in the + + align:start position:0% +we start to see this increase in the + + + align:start position:0% +we start to see this increase in the +amount of carbon dioxide in the + + align:start position:0% +amount of carbon dioxide in the + + + align:start position:0% +amount of carbon dioxide in the +atmosphere here's the last 800,000 years + + align:start position:0% +atmosphere here's the last 800,000 years + + + align:start position:0% +atmosphere here's the last 800,000 years +now notice in the last 800,000 years the + + align:start position:0% +now notice in the last 800,000 years the + + + align:start position:0% +now notice in the last 800,000 years the +maximum carbon dioxide level has been + + align:start position:0% +maximum carbon dioxide level has been + + + align:start position:0% +maximum carbon dioxide level has been +300 parts per million three hundred + + align:start position:0% +300 parts per million three hundred + + + align:start position:0% +300 parts per million three hundred +thousand years ago is the oldest Homo + + align:start position:0% +thousand years ago is the oldest Homo + + + align:start position:0% +thousand years ago is the oldest Homo +sapiens fossil that's us the Industrial + + align:start position:0% +sapiens fossil that's us the Industrial + + + align:start position:0% +sapiens fossil that's us the Industrial +Revolution happened in 1760 a little + + align:start position:0% +Revolution happened in 1760 a little + + + align:start position:0% +Revolution happened in 1760 a little +under 300 years ago and here's where we + + align:start position:0% +under 300 years ago and here's where we + + + align:start position:0% +under 300 years ago and here's where we +are now atmospheric greenhouse gases + + align:start position:0% +are now atmospheric greenhouse gases + + + align:start position:0% +are now atmospheric greenhouse gases +have spiked + + align:start position:0% + + + + align:start position:0% + +as humans emit more greenhouse gases our + + align:start position:0% +as humans emit more greenhouse gases our + + + align:start position:0% +as humans emit more greenhouse gases our +atmosphere traps more heat and the earth + + align:start position:0% +atmosphere traps more heat and the earth + + + align:start position:0% +atmosphere traps more heat and the earth +gets warmer you can see here the global + + align:start position:0% +gets warmer you can see here the global + + + align:start position:0% +gets warmer you can see here the global +temperature anomaly from NASA over time + + align:start position:0% +temperature anomaly from NASA over time + + + align:start position:0% +temperature anomaly from NASA over time +it starts with lots of blues and reds + + align:start position:0% +it starts with lots of blues and reds + + + align:start position:0% +it starts with lots of blues and reds +meaning things are pretty normal but as + + align:start position:0% +meaning things are pretty normal but as + + + align:start position:0% +meaning things are pretty normal but as +time goes on from 1950 to today it gets + + align:start position:0% +time goes on from 1950 to today it gets + + + align:start position:0% +time goes on from 1950 to today it gets +redder and redder and redder that's + + align:start position:0% +redder and redder and redder that's + + + align:start position:0% +redder and redder and redder that's +that's Earth warming to 0.82 degrees + + align:start position:0% +that's Earth warming to 0.82 degrees + + + align:start position:0% +that's Earth warming to 0.82 degrees +Celsius above normal or 1.5 degrees + + align:start position:0% +Celsius above normal or 1.5 degrees + + + align:start position:0% +Celsius above normal or 1.5 degrees +Fahrenheit now I know what you're + + align:start position:0% +Fahrenheit now I know what you're + + + align:start position:0% +Fahrenheit now I know what you're +thinking I know what you're thinking who + + align:start position:0% +thinking I know what you're thinking who + + + align:start position:0% +thinking I know what you're thinking who +cares about 1.5 degrees Fahrenheit + + align:start position:0% +cares about 1.5 degrees Fahrenheit + + + align:start position:0% +cares about 1.5 degrees Fahrenheit +that's like nothing and I can barely + + align:start position:0% +that's like nothing and I can barely + + + align:start position:0% +that's like nothing and I can barely +even feel it well to answer this + + align:start position:0% +even feel it well to answer this + + + align:start position:0% +even feel it well to answer this +question we have to talk about the + + align:start position:0% +question we have to talk about the + + + align:start position:0% +question we have to talk about the +consequences climate change already + + align:start position:0% +consequences climate change already + + + align:start position:0% +consequences climate change already +affects us whether it's through + + align:start position:0% +affects us whether it's through + + + align:start position:0% +affects us whether it's through +wildfires in California or flooding in + + align:start position:0% +wildfires in California or flooding in + + + align:start position:0% +wildfires in California or flooding in +the Midwest or hurricanes on the East + + align:start position:0% +the Midwest or hurricanes on the East + + + align:start position:0% +the Midwest or hurricanes on the East +Coast the effects of climate change are + + align:start position:0% +Coast the effects of climate change are + + + align:start position:0% +Coast the effects of climate change are +already here heat waves floods and other + + align:start position:0% +already here heat waves floods and other + + + align:start position:0% +already here heat waves floods and other +disasters are becoming more frequent you + + align:start position:0% +disasters are becoming more frequent you + + + align:start position:0% +disasters are becoming more frequent you +can see the recorded natural disasters + + align:start position:0% +can see the recorded natural disasters + + + align:start position:0% +can see the recorded natural disasters +per year has skyrocketed since the 1960s + + align:start position:0% +per year has skyrocketed since the 1960s + + + align:start position:0% +per year has skyrocketed since the 1960s +in Boston the city is already planning + + align:start position:0% +in Boston the city is already planning + + + align:start position:0% +in Boston the city is already planning +sea walls because of more intense and + + align:start position:0% +sea walls because of more intense and + + + align:start position:0% +sea walls because of more intense and +frequent flooding we are already doing + + align:start position:0% +frequent flooding we are already doing + + + align:start position:0% +frequent flooding we are already doing +these things in other words cities must + + align:start position:0% +these things in other words cities must + + + align:start position:0% +these things in other words cities must +spend your parents tax money on climate + + align:start position:0% +spend your parents tax money on climate + + + align:start position:0% +spend your parents tax money on climate +adaptations instead of schools transit + + align:start position:0% +adaptations instead of schools transit + + + align:start position:0% +adaptations instead of schools transit +and hospitals unusual weather also + + align:start position:0% +and hospitals unusual weather also + + + align:start position:0% +and hospitals unusual weather also +affects food by 2030 a drought could + + align:start position:0% +affects food by 2030 a drought could + + + align:start position:0% +affects food by 2030 a drought could +double the price of corn and maybe you + + align:start position:0% +double the price of corn and maybe you + + + align:start position:0% +double the price of corn and maybe you +don't like corn but I bet you like + + align:start position:0% +don't like corn but I bet you like + + + align:start position:0% +don't like corn but I bet you like +chicken or fish which are both raised on + + align:start position:0% +chicken or fish which are both raised on + + + align:start position:0% +chicken or fish which are both raised on +corn feed or maybe you like high + + align:start position:0% +corn feed or maybe you like high + + + align:start position:0% +corn feed or maybe you like high +fructose corn syrup in cereal or bread + + align:start position:0% +fructose corn syrup in cereal or bread + + + align:start position:0% +fructose corn syrup in cereal or bread +the point is corn isn't a lot of foods + + align:start position:0% +the point is corn isn't a lot of foods + + + align:start position:0% +the point is corn isn't a lot of foods +and bicycling crop growth climate change + + align:start position:0% +and bicycling crop growth climate change + + + align:start position:0% +and bicycling crop growth climate change +limits food access of course it's not + + align:start position:0% +limits food access of course it's not + + + align:start position:0% +limits food access of course it's not +just corn either but at any rate climate + + align:start position:0% +just corn either but at any rate climate + + + align:start position:0% +just corn either but at any rate climate +change also effects water this woman + + align:start position:0% +change also effects water this woman + + + align:start position:0% +change also effects water this woman +migrated over 150 miles because of a + + align:start position:0% +migrated over 150 miles because of a + + + align:start position:0% +migrated over 150 miles because of a +drought by 2050 the UN projects 200 + + align:start position:0% +drought by 2050 the UN projects 200 + + + align:start position:0% +drought by 2050 the UN projects 200 +million environmental migrants these are + + align:start position:0% +million environmental migrants these are + + + align:start position:0% +million environmental migrants these are +people who leave their homes because of + + align:start position:0% +people who leave their homes because of + + + align:start position:0% +people who leave their homes because of +changes in the environment and my + + align:start position:0% +changes in the environment and my + + + align:start position:0% +changes in the environment and my +question to you is this + + align:start position:0% +question to you is this + + + align:start position:0% +question to you is this +in recent migrant crises thousands of + + align:start position:0% +in recent migrant crises thousands of + + + align:start position:0% +in recent migrant crises thousands of +refugees created turmoil in Europe and + + align:start position:0% +refugees created turmoil in Europe and + + + align:start position:0% +refugees created turmoil in Europe and +America what happens when millions of + + align:start position:0% +America what happens when millions of + + + align:start position:0% +America what happens when millions of +people move north in search of food + + align:start position:0% +people move north in search of food + + + align:start position:0% +people move north in search of food +water and safety + + align:start position:0% +water and safety + + + align:start position:0% +water and safety +can we handle that I'm not sure even the + + align:start position:0% +can we handle that I'm not sure even the + + + align:start position:0% +can we handle that I'm not sure even the +US military refers to climate change as + + align:start position:0% +US military refers to climate change as + + + align:start position:0% +US military refers to climate change as +a threat multiplier because it makes + + align:start position:0% +a threat multiplier because it makes + + + align:start position:0% +a threat multiplier because it makes +every bad situation worse and by the way + + align:start position:0% +every bad situation worse and by the way + + + align:start position:0% +every bad situation worse and by the way +the Pentagon has released reports about + + align:start position:0% +the Pentagon has released reports about + + + align:start position:0% +the Pentagon has released reports about +climate change under both Democratic and + + align:start position:0% +climate change under both Democratic and + + + align:start position:0% +climate change under both Democratic and +Republican administrations this is not a + + align:start position:0% +Republican administrations this is not a + + + align:start position:0% +Republican administrations this is not a +partisan issue these problems are not + + align:start position:0% +partisan issue these problems are not + + + align:start position:0% +partisan issue these problems are not +just in the future either they're + + align:start position:0% +just in the future either they're + + + align:start position:0% +just in the future either they're +happening right now the current species + + align:start position:0% +happening right now the current species + + + align:start position:0% +happening right now the current species +extinction rate is 1,000 times higher + + align:start position:0% +extinction rate is 1,000 times higher + + + align:start position:0% +extinction rate is 1,000 times higher +than normal if pollinators go so do we + + align:start position:0% +than normal if pollinators go so do we + + + align:start position:0% +than normal if pollinators go so do we +there's no more crops left we're on + + align:start position:0% +there's no more crops left we're on + + + align:start position:0% +there's no more crops left we're on +track for 1 million species extinctions + + align:start position:0% +track for 1 million species extinctions + + + align:start position:0% +track for 1 million species extinctions +and here's what just one of those looks + + align:start position:0% +and here's what just one of those looks + + + align:start position:0% +and here's what just one of those looks +like + + align:start position:0% + + + + align:start position:0% + +we could live more sustainably so why + + align:start position:0% +we could live more sustainably so why + + + align:start position:0% +we could live more sustainably so why +don't we to really understand this we + + align:start position:0% +don't we to really understand this we + + + align:start position:0% +don't we to really understand this we +have to talk about the myths and I want + + align:start position:0% +have to talk about the myths and I want + + + align:start position:0% +have to talk about the myths and I want +to set the stage with a game called + + align:start position:0% +to set the stage with a game called + + + align:start position:0% +to set the stage with a game called +Commons so at this point I want + + align:start position:0% +Commons so at this point I want + + + align:start position:0% +Commons so at this point I want +everybody to form groups of five and + + align:start position:0% +everybody to form groups of five and + + + align:start position:0% +everybody to form groups of five and +count off from one to five go ahead and + + align:start position:0% +count off from one to five go ahead and + + + align:start position:0% +count off from one to five go ahead and +sit in a circle you guys can stand up + + align:start position:0% +sit in a circle you guys can stand up + + + align:start position:0% +sit in a circle you guys can stand up +form groups I'll give you a second to to + + align:start position:0% +form groups I'll give you a second to to + + + align:start position:0% +form groups I'll give you a second to to +make this happen it might be easier for + + align:start position:0% +make this happen it might be easier for + + + align:start position:0% +make this happen it might be easier for +people in the front row to kind of move + + align:start position:0% +people in the front row to kind of move + + + align:start position:0% +people in the front row to kind of move +to turn your chairs to face the back + + align:start position:0% +to turn your chairs to face the back + + + align:start position:0% +to turn your chairs to face the back +because we're gonna be sitting in a + + align:start position:0% +because we're gonna be sitting in a + + + align:start position:0% +because we're gonna be sitting in a +circle cool okay and everybody count off + + align:start position:0% +circle cool okay and everybody count off + + + align:start position:0% +circle cool okay and everybody count off +from one to five within your groups + + align:start position:0% + + + + align:start position:0% + +there's everybody count it off we get to + + align:start position:0% +there's everybody count it off we get to + + + align:start position:0% +there's everybody count it off we get to +go okay so you're gonna all start a pond + + align:start position:0% +go okay so you're gonna all start a pond + + + align:start position:0% +go okay so you're gonna all start a pond +with twenty fish this is your ponds + + align:start position:0% +with twenty fish this is your ponds + + + align:start position:0% +with twenty fish this is your ponds +carrying capacity your goal at the end + + align:start position:0% +carrying capacity your goal at the end + + + align:start position:0% +carrying capacity your goal at the end +of the game the winner is the person in + + align:start position:0% +of the game the winner is the person in + + + align:start position:0% +of the game the winner is the person in +the room with the most fish and remember + + align:start position:0% +the room with the most fish and remember + + + align:start position:0% +the room with the most fish and remember +you win as an individual not as a group + + align:start position:0% +you win as an individual not as a group + + + align:start position:0% +you win as an individual not as a group +here's how the game actually works each + + align:start position:0% +here's how the game actually works each + + + align:start position:0% +here's how the game actually works each +round every person in your group will + + align:start position:0% +round every person in your group will + + + align:start position:0% +round every person in your group will +take between one and four fish you have + + align:start position:0% +take between one and four fish you have + + + align:start position:0% +take between one and four fish you have +to take at least one but you can't take + + align:start position:0% +to take at least one but you can't take + + + align:start position:0% +to take at least one but you can't take +more than four after each round your + + align:start position:0% +more than four after each round your + + + align:start position:0% +more than four after each round your +pond will be restocked by doubling the + + align:start position:0% +pond will be restocked by doubling the + + + align:start position:0% +pond will be restocked by doubling the +number of fish without exceeding 20 so + + align:start position:0% +number of fish without exceeding 20 so + + + align:start position:0% +number of fish without exceeding 20 so +four fish becomes eight nine fish + + align:start position:0% +four fish becomes eight nine fish + + + align:start position:0% +four fish becomes eight nine fish +becomes 18 10 fish or more brings the + + align:start position:0% +becomes 18 10 fish or more brings the + + + align:start position:0% +becomes 18 10 fish or more brings the +pond back to 20 does that make sense for + + align:start position:0% +pond back to 20 does that make sense for + + + align:start position:0% +pond back to 20 does that make sense for +the group of four in the back your + + align:start position:0% +the group of four in the back your + + + align:start position:0% +the group of four in the back your +carrying capacity is actually gonna be + + align:start position:0% +carrying capacity is actually gonna be + + + align:start position:0% +carrying capacity is actually gonna be +four times the number of people in your + + align:start position:0% +four times the number of people in your + + + align:start position:0% +four times the number of people in your +group so you're gonna have 16 and so all + + align:start position:0% +group so you're gonna have 16 and so all + + + align:start position:0% +group so you're gonna have 16 and so all +the same rules apply where if you double + + align:start position:0% +the same rules apply where if you double + + + align:start position:0% +the same rules apply where if you double +the number of fish at 8 or higher you'll + + align:start position:0% +the number of fish at 8 or higher you'll + + + align:start position:0% +the number of fish at 8 or higher you'll +go back to 16 you will never have a pond + + align:start position:0% +go back to 16 you will never have a pond + + + align:start position:0% +go back to 16 you will never have a pond +with 20 fish in it does that make sense + + align:start position:0% +with 20 fish in it does that make sense + + + align:start position:0% +with 20 fish in it does that make sense +to the group before great don't eat the + + align:start position:0% +to the group before great don't eat the + + + align:start position:0% +to the group before great don't eat the +goldfish yet and if you have allergies + + align:start position:0% +goldfish yet and if you have allergies + + + align:start position:0% +goldfish yet and if you have allergies +don't eat the goldfish at all so if + + align:start position:0% +don't eat the goldfish at all so if + + + align:start position:0% +don't eat the goldfish at all so if +everybody could send person number one + + align:start position:0% +everybody could send person number one + + + align:start position:0% +everybody could send person number one +up to the front I can hand you guys + + align:start position:0% +up to the front I can hand you guys + + + align:start position:0% +up to the front I can hand you guys +goldfish + + align:start position:0% + + + + align:start position:0% + +great so everybody should have a pond + + align:start position:0% +great so everybody should have a pond + + + align:start position:0% +great so everybody should have a pond +and a restock supply and can everybody + + align:start position:0% +and a restock supply and can everybody + + + align:start position:0% +and a restock supply and can everybody +just make sure that you have the right + + align:start position:0% +just make sure that you have the right + + + align:start position:0% +just make sure that you have the right +number of fish in your pond so it's four + + align:start position:0% +number of fish in your pond so it's four + + + align:start position:0% +number of fish in your pond so it's four +times the number of people in your group + + align:start position:0% +times the number of people in your group + + + align:start position:0% +times the number of people in your group +everybody just make sure everybody good + + align:start position:0% +everybody just make sure everybody good + + + align:start position:0% +everybody just make sure everybody good +okay you guys have 30 seconds to discuss + + align:start position:0% +okay you guys have 30 seconds to discuss + + + align:start position:0% +okay you guys have 30 seconds to discuss +strategy starting now + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +round one take turns going clockwise + + align:start position:0% +round one take turns going clockwise + + + align:start position:0% +round one take turns going clockwise +starting with player three you have 60 + + align:start position:0% +starting with player three you have 60 + + + align:start position:0% +starting with player three you have 60 +seconds + + align:start position:0% + + + + align:start position:0% + +go ahead and restock your pawns you have + + align:start position:0% +go ahead and restock your pawns you have + + + align:start position:0% +go ahead and restock your pawns you have +30 seconds to do this each time you'll + + align:start position:0% +30 seconds to do this each time you'll + + + align:start position:0% +30 seconds to do this each time you'll +play four rounds everybody good I'm + + align:start position:0% +play four rounds everybody good I'm + + + align:start position:0% +play four rounds everybody good I'm +gonna go ahead and skip round two + + align:start position:0% +gonna go ahead and skip round two + + + align:start position:0% +gonna go ahead and skip round two +starting with player two + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +round three take turns + + align:start position:0% +round three take turns + + + align:start position:0% +round three take turns +starting with player four + + align:start position:0% + + + + align:start position:0% + +[Laughter] + + align:start position:0% + + + + align:start position:0% + +does anybody need more time I'm gonna go + + align:start position:0% +does anybody need more time I'm gonna go + + + align:start position:0% +does anybody need more time I'm gonna go +ahead and skip again go ahead and + + align:start position:0% +ahead and skip again go ahead and + + + align:start position:0% +ahead and skip again go ahead and +restock everybody good final round + + align:start position:0% +restock everybody good final round + + + align:start position:0% +restock everybody good final round +start with player 3 + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +everybody said anybody need more time + + align:start position:0% +everybody said anybody need more time + + + align:start position:0% +everybody said anybody need more time +cool let's do one last round just for + + align:start position:0% +cool let's do one last round just for + + + align:start position:0% +cool let's do one last round just for +fun so who still has fish in their pond + + align:start position:0% +fun so who still has fish in their pond + + + align:start position:0% +fun so who still has fish in their pond +cool okay so we're actually doing this + + align:start position:0% +cool okay so we're actually doing this + + + align:start position:0% +cool okay so we're actually doing this +sometimes we don't go ahead and restock + + align:start position:0% +sometimes we don't go ahead and restock + + + align:start position:0% +sometimes we don't go ahead and restock +your ponds you guys have 30 seconds + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +are you guys all set so you guys are + + align:start position:0% +are you guys all set so you guys are + + + align:start position:0% +are you guys all set so you guys are +restocked cool all right I'm just gonna + + align:start position:0% +restocked cool all right I'm just gonna + + + align:start position:0% +restocked cool all right I'm just gonna +go ahead and skip ahead final round for + + align:start position:0% +go ahead and skip ahead final round for + + + align:start position:0% +go ahead and skip ahead final round for +real this time take turns going + + align:start position:0% +real this time take turns going + + + align:start position:0% +real this time take turns going +clockwise starting with player number + + align:start position:0% +clockwise starting with player number + + + align:start position:0% +clockwise starting with player number +one all right is everybody good cool all + + align:start position:0% +one all right is everybody good cool all + + + align:start position:0% +one all right is everybody good cool all +right + + align:start position:0% +right + + + align:start position:0% +right +so who won raise your hand if you have + + align:start position:0% +so who won raise your hand if you have + + + align:start position:0% +so who won raise your hand if you have +more than 10 fish I'm sorry go ahead and + + align:start position:0% +more than 10 fish I'm sorry go ahead and + + + align:start position:0% +more than 10 fish I'm sorry go ahead and +count your fish first and then raise + + align:start position:0% +count your fish first and then raise + + + align:start position:0% +count your fish first and then raise +your hand if you have more than 10 cool + + align:start position:0% +your hand if you have more than 10 cool + + + align:start position:0% +your hand if you have more than 10 cool +yeah okay only two people have more than + + align:start position:0% +yeah okay only two people have more than + + + align:start position:0% +yeah okay only two people have more than +10 three people okay more than 11 fish + + align:start position:0% +10 three people okay more than 11 fish + + + align:start position:0% +10 three people okay more than 11 fish +okay so you guys each have 12 or more do + + align:start position:0% +okay so you guys each have 12 or more do + + + align:start position:0% +okay so you guys each have 12 or more do +have 13 or more fish 14 or more fish 15 + + align:start position:0% +have 13 or more fish 14 or more fish 15 + + + align:start position:0% +have 13 or more fish 14 or more fish 15 +or more fish how many do you have 15 + + align:start position:0% +or more fish how many do you have 15 + + + align:start position:0% +or more fish how many do you have 15 +congratulations to the winner great + + align:start position:0% +congratulations to the winner great + + + align:start position:0% +congratulations to the winner great +okay awesome okay so so talk to me + + align:start position:0% +okay awesome okay so so talk to me + + + align:start position:0% +okay awesome okay so so talk to me +why was Commons hard what was hard about + + align:start position:0% +why was Commons hard what was hard about + + + align:start position:0% +why was Commons hard what was hard about +this game you guys can go ahead and yell + + align:start position:0% +this game you guys can go ahead and yell + + + align:start position:0% +this game you guys can go ahead and yell +it out or raise your hands as you wish + + align:start position:0% + + + + align:start position:0% + +you have to have a strategy that + + align:start position:0% +you have to have a strategy that + + + align:start position:0% +you have to have a strategy that +everyone agrees upon okay anybody else + + align:start position:0% +everyone agrees upon okay anybody else + + + align:start position:0% +everyone agrees upon okay anybody else +what was hard about this game go ahead + + align:start position:0% + + + + align:start position:0% + +the thing that was best for the Commons + + align:start position:0% +the thing that was best for the Commons + + + align:start position:0% +the thing that was best for the Commons +was the most damaging personally anybody + + align:start position:0% +was the most damaging personally anybody + + + align:start position:0% +was the most damaging personally anybody +else yes cool + + align:start position:0% +else yes cool + + + align:start position:0% +else yes cool +so you weren't quite sure how long we + + align:start position:0% +so you weren't quite sure how long we + + + align:start position:0% +so you weren't quite sure how long we +were gonna keep going great these are + + align:start position:0% +were gonna keep going great these are + + + align:start position:0% +were gonna keep going great these are +all good answers and really the core of + + align:start position:0% +all good answers and really the core of + + + align:start position:0% +all good answers and really the core of +this is if everyone acts in their own + + align:start position:0% +this is if everyone acts in their own + + + align:start position:0% +this is if everyone acts in their own +interest the pond the Commons dies this + + align:start position:0% +interest the pond the Commons dies this + + + align:start position:0% +interest the pond the Commons dies this +is called the tragedy of the Commons + + align:start position:0% +is called the tragedy of the Commons + + + align:start position:0% +is called the tragedy of the Commons +when anyone can access a limited + + align:start position:0% +when anyone can access a limited + + + align:start position:0% +when anyone can access a limited +resource it runs out roads are another + + align:start position:0% +resource it runs out roads are another + + + align:start position:0% +resource it runs out roads are another +really good example anybody with a car + + align:start position:0% +really good example anybody with a car + + + align:start position:0% +really good example anybody with a car +can access a road and soon enough + + align:start position:0% +can access a road and soon enough + + + align:start position:0% +can access a road and soon enough +everybody is thinking if these idiots + + align:start position:0% +everybody is thinking if these idiots + + + align:start position:0% +everybody is thinking if these idiots +would just take the bus I could be home + + align:start position:0% +would just take the bus I could be home + + + align:start position:0% +would just take the bus I could be home +by now can somebody or can anybody else + + align:start position:0% +by now can somebody or can anybody else + + + align:start position:0% +by now can somebody or can anybody else +name some other real-life examples of + + align:start position:0% +name some other real-life examples of + + + align:start position:0% +name some other real-life examples of +Commons think about limited resources + + align:start position:0% +Commons think about limited resources + + + align:start position:0% +Commons think about limited resources +that anyone can access yes go ahead air + + align:start position:0% +that anyone can access yes go ahead air + + + align:start position:0% +that anyone can access yes go ahead air +say more can you say more about air + + align:start position:0% +say more can you say more about air + + + align:start position:0% +say more can you say more about air +pollution yes so anybody can access the + + align:start position:0% +pollution yes so anybody can access the + + + align:start position:0% +pollution yes so anybody can access the +air and therefore anybody can pollute it + + align:start position:0% +air and therefore anybody can pollute it + + + align:start position:0% +air and therefore anybody can pollute it +great + + align:start position:0% +great + + + align:start position:0% +great +anybody else why okay wireless internet + + align:start position:0% +anybody else why okay wireless internet + + + align:start position:0% +anybody else why okay wireless internet +say more so if everybody watches Memphis + + align:start position:0% +say more so if everybody watches Memphis + + + align:start position:0% +say more so if everybody watches Memphis +in HD at the same time nobody so if + + align:start position:0% +in HD at the same time nobody so if + + + align:start position:0% +in HD at the same time nobody so if +everybody watches Netflix in HD then + + align:start position:0% +everybody watches Netflix in HD then + + + align:start position:0% +everybody watches Netflix in HD then +nobody gets to watch Netflix in HD cuz + + align:start position:0% +nobody gets to watch Netflix in HD cuz + + + align:start position:0% +nobody gets to watch Netflix in HD cuz +you don't have enough bandwidth great + + align:start position:0% +you don't have enough bandwidth great + + + align:start position:0% +you don't have enough bandwidth great +any others let's do one last one any any + + align:start position:0% +any others let's do one last one any any + + + align:start position:0% +any others let's do one last one any any +takers + + align:start position:0% +takers + + + align:start position:0% +takers +yes go ahead office mugs tell me more + + align:start position:0% +yes go ahead office mugs tell me more + + + align:start position:0% +yes go ahead office mugs tell me more +about office mugs + + align:start position:0% + + + + align:start position:0% + +great so office mugs are something that + + align:start position:0% +great so office mugs are something that + + + align:start position:0% +great so office mugs are something that +anybody in the office can access but + + align:start position:0% +anybody in the office can access but + + + align:start position:0% +anybody in the office can access but +nobody's incentivized to actually take + + align:start position:0% +nobody's incentivized to actually take + + + align:start position:0% +nobody's incentivized to actually take +care of them great what about this one + + align:start position:0% +care of them great what about this one + + + align:start position:0% +care of them great what about this one +earth is a Commons we can all access + + align:start position:0% +earth is a Commons we can all access + + + align:start position:0% +earth is a Commons we can all access +earth we're all on it and certainly it's + + align:start position:0% +earth we're all on it and certainly it's + + + align:start position:0% +earth we're all on it and certainly it's +limited so how do we solve Commons + + align:start position:0% +limited so how do we solve Commons + + + align:start position:0% +limited so how do we solve Commons +problems either in the game or in real + + align:start position:0% +problems either in the game or in real + + + align:start position:0% +problems either in the game or in real +life does anybody have any ideas how did + + align:start position:0% +life does anybody have any ideas how did + + + align:start position:0% +life does anybody have any ideas how did +you guys solve it in the game let's + + align:start position:0% +you guys solve it in the game let's + + + align:start position:0% +you guys solve it in the game let's +start there + + align:start position:0% + + + + align:start position:0% + +strategize together cool can you be more + + align:start position:0% +strategize together cool can you be more + + + align:start position:0% +strategize together cool can you be more +specific we talked about how we would be + + align:start position:0% +specific we talked about how we would be + + + align:start position:0% +specific we talked about how we would be +able to keep the most fish on our plate + + align:start position:0% +able to keep the most fish on our plate + + + align:start position:0% +able to keep the most fish on our plate +earner climb by each just taking two so + + align:start position:0% +earner climb by each just taking two so + + + align:start position:0% +earner climb by each just taking two so +you guys you guys all ended up each + + align:start position:0% +you guys you guys all ended up each + + + align:start position:0% +you guys you guys all ended up each +taking two not the entire time okay + + align:start position:0% +taking two not the entire time okay + + + align:start position:0% +taking two not the entire time okay +anybody else why how do we solve Commons + + align:start position:0% +anybody else why how do we solve Commons + + + align:start position:0% +anybody else why how do we solve Commons +problems either in the game or in real + + align:start position:0% +problems either in the game or in real + + + align:start position:0% +problems either in the game or in real +life what do you guys think + + align:start position:0% + + + + align:start position:0% + +yes God so if some people if some people + + align:start position:0% +yes God so if some people if some people + + + align:start position:0% +yes God so if some people if some people +took more others would take less great + + align:start position:0% +took more others would take less great + + + align:start position:0% +took more others would take less great +how did that work not well okay + + align:start position:0% +how did that work not well okay + + + align:start position:0% +how did that work not well okay +so it didn't work very well well the + + align:start position:0% +so it didn't work very well well the + + + align:start position:0% +so it didn't work very well well the +answer is and when we kind of came upon + + align:start position:0% +answer is and when we kind of came upon + + + align:start position:0% +answer is and when we kind of came upon +it already + + align:start position:0% +it already + + + align:start position:0% +it already +collective action we have to set rules + + align:start position:0% +collective action we have to set rules + + + align:start position:0% +collective action we have to set rules +in order to solve Commons problems one + + align:start position:0% +in order to solve Commons problems one + + + align:start position:0% +in order to solve Commons problems one +example was let's all take two but we + + align:start position:0% +example was let's all take two but we + + + align:start position:0% +example was let's all take two but we +saw in your case that sometimes those + + align:start position:0% +saw in your case that sometimes those + + + align:start position:0% +saw in your case that sometimes those +rules get broken that's why climate + + align:start position:0% +rules get broken that's why climate + + + align:start position:0% +rules get broken that's why climate +change is really hard but at any rate + + align:start position:0% +change is really hard but at any rate + + + align:start position:0% +change is really hard but at any rate +setting rules for everyone is called + + align:start position:0% +setting rules for everyone is called + + + align:start position:0% +setting rules for everyone is called +politics setting rules for everyone is + + align:start position:0% +politics setting rules for everyone is + + + align:start position:0% +politics setting rules for everyone is +called politics and therefore protecting + + align:start position:0% +called politics and therefore protecting + + + align:start position:0% +called politics and therefore protecting +the most important comments and + + align:start position:0% +the most important comments and + + + align:start position:0% +the most important comments and +inhabitable earth is political we need + + align:start position:0% +inhabitable earth is political we need + + + align:start position:0% +inhabitable earth is political we need +rules there's an issue rules cost money + + align:start position:0% +rules there's an issue rules cost money + + + align:start position:0% +rules there's an issue rules cost money +for example if I can't sell my products + + align:start position:0% +for example if I can't sell my products + + + align:start position:0% +for example if I can't sell my products +because I emit carbon to make them I + + align:start position:0% +because I emit carbon to make them I + + + align:start position:0% +because I emit carbon to make them I +lose money and that's not acceptable to + + align:start position:0% +lose money and that's not acceptable to + + + align:start position:0% +lose money and that's not acceptable to +me so now we can answer the question why + + align:start position:0% +me so now we can answer the question why + + + align:start position:0% +me so now we can answer the question why +haven't we done anything and the answer + + align:start position:0% +haven't we done anything and the answer + + + align:start position:0% +haven't we done anything and the answer +is no one wants rules limiting carbon + + align:start position:0% +is no one wants rules limiting carbon + + + align:start position:0% +is no one wants rules limiting carbon +but especially not fossil fuel groups + + align:start position:0% +but especially not fossil fuel groups + + + align:start position:0% +but especially not fossil fuel groups +who emit more than anyone you can see + + align:start position:0% +who emit more than anyone you can see + + + align:start position:0% +who emit more than anyone you can see +here carbon dioxide emissions by sector + + align:start position:0% +here carbon dioxide emissions by sector + + + align:start position:0% +here carbon dioxide emissions by sector +residential and commercial industry + + align:start position:0% +residential and commercial industry + + + align:start position:0% +residential and commercial industry +transportation agriculture and land use + + align:start position:0% +transportation agriculture and land use + + + align:start position:0% +transportation agriculture and land use +anybody want to guess what that big blue + + align:start position:0% +anybody want to guess what that big blue + + + align:start position:0% +anybody want to guess what that big blue +one is fossil fuels energy oil gas and + + align:start position:0% +one is fossil fuels energy oil gas and + + + align:start position:0% +one is fossil fuels energy oil gas and +coal yeah + + align:start position:0% +coal yeah + + + align:start position:0% +coal yeah +the fossil fuel industry has actually + + align:start position:0% +the fossil fuel industry has actually + + + align:start position:0% +the fossil fuel industry has actually +known about climate change for decades + + align:start position:0% +known about climate change for decades + + + align:start position:0% +known about climate change for decades +in 1978 more than 40 years ago Exxon's + + align:start position:0% +in 1978 more than 40 years ago Exxon's + + + align:start position:0% +in 1978 more than 40 years ago Exxon's +senior scientists had this to say + + align:start position:0% +senior scientists had this to say + + + align:start position:0% +senior scientists had this to say +present thinking holds but man has a + + align:start position:0% +present thinking holds but man has a + + + align:start position:0% +present thinking holds but man has a +time window of five to ten years before + + align:start position:0% +time window of five to ten years before + + + align:start position:0% +time window of five to ten years before +the need for hard decisions regarding + + align:start position:0% +the need for hard decisions regarding + + + align:start position:0% +the need for hard decisions regarding +changes and energy strategies might + + align:start position:0% +changes and energy strategies might + + + align:start position:0% +changes and energy strategies might +become critical in other words we have 5 + + align:start position:0% +become critical in other words we have 5 + + + align:start position:0% +become critical in other words we have 5 +to 10 years to figure out how to get + + align:start position:0% +to 10 years to figure out how to get + + + align:start position:0% +to 10 years to figure out how to get +energy a different way he said that + + align:start position:0% +energy a different way he said that + + + align:start position:0% +energy a different way he said that +40 years ago but fossil fuel companies + + align:start position:0% +40 years ago but fossil fuel companies + + + align:start position:0% +40 years ago but fossil fuel companies +spread climate myths to the public + + align:start position:0% +spread climate myths to the public + + + align:start position:0% +spread climate myths to the public +including schools + + align:start position:0% + + + + align:start position:0% + +from 2003 to 2010 Koch family + + align:start position:0% +from 2003 to 2010 Koch family + + + align:start position:0% +from 2003 to 2010 Koch family +foundations and other fossil fuel groups + + align:start position:0% +foundations and other fossil fuel groups + + + align:start position:0% +foundations and other fossil fuel groups +gave 558 million dollars to climate + + align:start position:0% +gave 558 million dollars to climate + + + align:start position:0% +gave 558 million dollars to climate +denial organizations and I wish that I + + align:start position:0% +denial organizations and I wish that I + + + align:start position:0% +denial organizations and I wish that I +could share more financial data with you + + align:start position:0% +could share more financial data with you + + + align:start position:0% +could share more financial data with you +but these groups are secretive and hard + + align:start position:0% +but these groups are secretive and hard + + + align:start position:0% +but these groups are secretive and hard +to study in any case the point is this + + align:start position:0% +to study in any case the point is this + + + align:start position:0% +to study in any case the point is this +fossil fuel companies know that rules + + align:start position:0% +fossil fuel companies know that rules + + + align:start position:0% +fossil fuel companies know that rules +will hurt their profits so they spread + + align:start position:0% +will hurt their profits so they spread + + + align:start position:0% +will hurt their profits so they spread +myths to the public about climate change + + align:start position:0% +myths to the public about climate change + + + align:start position:0% +myths to the public about climate change +but now you know the truth you know that + + align:start position:0% +but now you know the truth you know that + + + align:start position:0% +but now you know the truth you know that +climate change is real it's happening + + align:start position:0% +climate change is real it's happening + + + align:start position:0% +climate change is real it's happening +because of us it already affects you it + + align:start position:0% +because of us it already affects you it + + + align:start position:0% +because of us it already affects you it +will only get worse and we haven't done + + align:start position:0% +will only get worse and we haven't done + + + align:start position:0% +will only get worse and we haven't done +anything because fossil fuel companies + + align:start position:0% +anything because fossil fuel companies + + + align:start position:0% +anything because fossil fuel companies +have lied to us for decades that leaves + + align:start position:0% +have lied to us for decades that leaves + + + align:start position:0% +have lied to us for decades that leaves +us with one final question how do we + + align:start position:0% +us with one final question how do we + + + align:start position:0% +us with one final question how do we +shape our future + + align:start position:0% + + + + align:start position:0% + +We Need to Talk and I know that words + + align:start position:0% +We Need to Talk and I know that words + + + align:start position:0% +We Need to Talk and I know that words +may seem inconsequential given some of + + align:start position:0% +may seem inconsequential given some of + + + align:start position:0% +may seem inconsequential given some of +the other information I've shared but + + align:start position:0% +the other information I've shared but + + + align:start position:0% +the other information I've shared but +words give life to ideas and ideas lead + + align:start position:0% +words give life to ideas and ideas lead + + + align:start position:0% +words give life to ideas and ideas lead +to change in other words your words + + align:start position:0% +to change in other words your words + + + align:start position:0% +to change in other words your words +matter I know it may feel awkward but + + align:start position:0% +matter I know it may feel awkward but + + + align:start position:0% +matter I know it may feel awkward but +studies show that teens are actually + + align:start position:0% +studies show that teens are actually + + + align:start position:0% +studies show that teens are actually +great at making parents care about + + align:start position:0% +great at making parents care about + + + align:start position:0% +great at making parents care about +climate change + + align:start position:0% +climate change + + + align:start position:0% +climate change +be open be gentle be honest you can try + + align:start position:0% +be open be gentle be honest you can try + + + align:start position:0% +be open be gentle be honest you can try +starting with how do you feel about + + align:start position:0% +starting with how do you feel about + + + align:start position:0% +starting with how do you feel about +climate change in fact on the count of + + align:start position:0% +climate change in fact on the count of + + + align:start position:0% +climate change in fact on the count of +three I want everybody to practice so on + + align:start position:0% +three I want everybody to practice so on + + + align:start position:0% +three I want everybody to practice so on +the count of three let's all say how do + + align:start position:0% +the count of three let's all say how do + + + align:start position:0% +the count of three let's all say how do +you feel about climate change ready one + + align:start position:0% +you feel about climate change ready one + + + align:start position:0% +you feel about climate change ready one +two three + + align:start position:0% +two three + + + align:start position:0% +two three +how do you feel about climate change + + align:start position:0% +how do you feel about climate change + + + align:start position:0% +how do you feel about climate change +it's easy and it works I want to share + + align:start position:0% +it's easy and it works I want to share + + + align:start position:0% +it's easy and it works I want to share +one last perspective on why we need to + + align:start position:0% +one last perspective on why we need to + + + align:start position:0% +one last perspective on why we need to +talk + + align:start position:0% + + + + align:start position:0% + +it's not too late to keep our paradise + + align:start position:0% +it's not too late to keep our paradise + + + align:start position:0% +it's not too late to keep our paradise +but we can't do it without you + + align:start position:0% + + + + align:start position:0% + +I'm gonna leave you guys with a five day + + align:start position:0% +I'm gonna leave you guys with a five day + + + align:start position:0% +I'm gonna leave you guys with a five day +challenge so go ahead and write down the + + align:start position:0% +challenge so go ahead and write down the + + + align:start position:0% +challenge so go ahead and write down the +names of five people you can talk to + + align:start position:0% +names of five people you can talk to + + + align:start position:0% +names of five people you can talk to +about climate change you can do it on + + align:start position:0% +about climate change you can do it on + + + align:start position:0% +about climate change you can do it on +your phones you can do it + + align:start position:0% +your phones you can do it + + + align:start position:0% +your phones you can do it +on a piece of paper but go ahead and + + align:start position:0% +on a piece of paper but go ahead and + + + align:start position:0% +on a piece of paper but go ahead and +write down five names of people you can + + align:start position:0% +write down five names of people you can + + + align:start position:0% +write down five names of people you can +talk to about climate change each day + + align:start position:0% +talk to about climate change each day + + + align:start position:0% +talk to about climate change each day +each day for the next five days talk + + align:start position:0% +each day for the next five days talk + + + align:start position:0% +each day for the next five days talk +about climate change with someone on + + align:start position:0% +about climate change with someone on + + + align:start position:0% +about climate change with someone on +your list and remember time is of the + + align:start position:0% +your list and remember time is of the + + + align:start position:0% +your list and remember time is of the +essence thank you questions + + align:start position:0% + + + + align:start position:0% + +I notice the station in reforestation + + align:start position:0% +I notice the station in reforestation + + + align:start position:0% +I notice the station in reforestation +for the large solution to a lot of the + + align:start position:0% +for the large solution to a lot of the + + + align:start position:0% +for the large solution to a lot of the +solutions our collective based and by + + align:start position:0% +solutions our collective based and by + + + align:start position:0% +solutions our collective based and by +the way I'll be sending out a handout to + + align:start position:0% +the way I'll be sending out a handout to + + + align:start position:0% +the way I'll be sending out a handout to +all of you guys for things you can do + + align:start position:0% +all of you guys for things you can do + + + align:start position:0% +all of you guys for things you can do +and informational resources that you can + + align:start position:0% +and informational resources that you can + + + align:start position:0% +and informational resources that you can +use for after this talk but to answer + + align:start position:0% +use for after this talk but to answer + + + align:start position:0% +use for after this talk but to answer +your question the main thing that you + + align:start position:0% +your question the main thing that you + + + align:start position:0% +your question the main thing that you +can do in your life is actually stop + + align:start position:0% +can do in your life is actually stop + + + align:start position:0% +can do in your life is actually stop +eating beef cattle have a huge impact on + + align:start position:0% +eating beef cattle have a huge impact on + + + align:start position:0% +eating beef cattle have a huge impact on +greenhouse gases because of the methane + + align:start position:0% +greenhouse gases because of the methane + + + align:start position:0% +greenhouse gases because of the methane +they produce and so if you stop eating + + align:start position:0% +they produce and so if you stop eating + + + align:start position:0% +they produce and so if you stop eating +beef that's actually the single biggest + + align:start position:0% +beef that's actually the single biggest + + + align:start position:0% +beef that's actually the single biggest +contribution you can make within your + + align:start position:0% +contribution you can make within your + + + align:start position:0% +contribution you can make within your +personal life obviously if you are able + + align:start position:0% +personal life obviously if you are able + + + align:start position:0% +personal life obviously if you are able +to drive less fly less that's another + + align:start position:0% +to drive less fly less that's another + + + align:start position:0% +to drive less fly less that's another +huge one these are all ways that you can + + align:start position:0% +huge one these are all ways that you can + + + align:start position:0% +huge one these are all ways that you can +contribute but as we saw a part of the + + align:start position:0% +contribute but as we saw a part of the + + + align:start position:0% +contribute but as we saw a part of the +reason that climate change is such a + + align:start position:0% +reason that climate change is such a + + + align:start position:0% +reason that climate change is such a +tricky problems because we need + + align:start position:0% +tricky problems because we need + + + align:start position:0% +tricky problems because we need +everybody to come together we need wind + + align:start position:0% +everybody to come together we need wind + + + align:start position:0% +everybody to come together we need wind +farms we need afforestation as you + + align:start position:0% +farms we need afforestation as you + + + align:start position:0% +farms we need afforestation as you +mentioned we need other kinds of + + align:start position:0% +mentioned we need other kinds of + + + align:start position:0% +mentioned we need other kinds of +renewable energy resources but in your + + align:start position:0% +renewable energy resources but in your + + + align:start position:0% +renewable energy resources but in your +personal life don't eat beef talk about + + align:start position:0% +personal life don't eat beef talk about + + + align:start position:0% +personal life don't eat beef talk about +climate change and fly less are the top + + align:start position:0% +climate change and fly less are the top + + + align:start position:0% +climate change and fly less are the top +three + + align:start position:0% +three + + + align:start position:0% +three +yes go ahead we talk a lot about fossil + + align:start position:0% +yes go ahead we talk a lot about fossil + + + align:start position:0% +yes go ahead we talk a lot about fossil +fuels and transportation and flying and + + align:start position:0% +fuels and transportation and flying and + + + align:start position:0% +fuels and transportation and flying and +things like that and same with beef we + + align:start position:0% +things like that and same with beef we + + + align:start position:0% +things like that and same with beef we +care a lot about that and now people are + + align:start position:0% +care a lot about that and now people are + + + align:start position:0% +care a lot about that and now people are +starting to hear more about plastics + + align:start position:0% +starting to hear more about plastics + + + align:start position:0% +starting to hear more about plastics +which is a use of fossil fuels but + + align:start position:0% +which is a use of fossil fuels but + + + align:start position:0% +which is a use of fossil fuels but +there's a lot of fossil fuel uses that + + align:start position:0% +there's a lot of fossil fuel uses that + + + align:start position:0% +there's a lot of fossil fuel uses that +are huge like in manufacturing processes + + align:start position:0% +are huge like in manufacturing processes + + + align:start position:0% +are huge like in manufacturing processes +and things where we could buy from + + align:start position:0% +and things where we could buy from + + + align:start position:0% +and things where we could buy from +companies who use less fossil fuels but + + align:start position:0% +companies who use less fossil fuels but + + + align:start position:0% +companies who use less fossil fuels but +it's really hard for us to find + + align:start position:0% +it's really hard for us to find + + + align:start position:0% +it's really hard for us to find +information about that is there + + align:start position:0% +information about that is there + + + align:start position:0% +information about that is there +for the resource for that I haven't seen + + align:start position:0% +for the resource for that I haven't seen + + + align:start position:0% +for the resource for that I haven't seen +any but I can follow up with you so I + + align:start position:0% +any but I can follow up with you so I + + + align:start position:0% +any but I can follow up with you so I +can send you something after along with + + align:start position:0% +can send you something after along with + + + align:start position:0% +can send you something after along with +the handouts I'll do the best I can + + align:start position:0% + + + + align:start position:0% + +paradise he must protect nature or the + + align:start position:0% +paradise he must protect nature or the + + + align:start position:0% +paradise he must protect nature or the +Celtic let's talk how do you think you + + align:start position:0% +Celtic let's talk how do you think you + + + align:start position:0% +Celtic let's talk how do you think you +should be that's a good question so the + + align:start position:0% +should be that's a good question so the + + + align:start position:0% +should be that's a good question so the +question is how should we talk to our + + align:start position:0% +question is how should we talk to our + + + align:start position:0% +question is how should we talk to our +parents about climate change you know + + align:start position:0% +parents about climate change you know + + + align:start position:0% +parents about climate change you know +your parents better than I do and that's + + align:start position:0% +your parents better than I do and that's + + + align:start position:0% +your parents better than I do and that's +part of why it turns out that teenagers + + align:start position:0% +part of why it turns out that teenagers + + + align:start position:0% +part of why it turns out that teenagers +and kids are actually so good at this + + align:start position:0% +and kids are actually so good at this + + + align:start position:0% +and kids are actually so good at this +messenger matter is much more than + + align:start position:0% +messenger matter is much more than + + + align:start position:0% +messenger matter is much more than +message when it comes to climate change + + align:start position:0% +message when it comes to climate change + + + align:start position:0% +message when it comes to climate change +and so if you come to your parents and + + align:start position:0% +and so if you come to your parents and + + + align:start position:0% +and so if you come to your parents and +say this is important to you I think + + align:start position:0% +say this is important to you I think + + + align:start position:0% +say this is important to you I think +that's enough to start a conversation + + align:start position:0% +that's enough to start a conversation + + + align:start position:0% +that's enough to start a conversation +don't attack people including your + + align:start position:0% +don't attack people including your + + + align:start position:0% +don't attack people including your +parents that tends not to be super + + align:start position:0% +parents that tends not to be super + + + align:start position:0% +parents that tends not to be super +helpful to quote one of the professor's + + align:start position:0% +helpful to quote one of the professor's + + + align:start position:0% +helpful to quote one of the professor's +here at MIT research shows that showing + + align:start position:0% +here at MIT research shows that showing + + + align:start position:0% +here at MIT research shows that showing +research to people doesn't work and so + + align:start position:0% +research to people doesn't work and so + + + align:start position:0% +research to people doesn't work and so +if you can if you can talk to your + + align:start position:0% +if you can if you can talk to your + + + align:start position:0% +if you can if you can talk to your +parents from a personal perspective and + + align:start position:0% +parents from a personal perspective and + + + align:start position:0% +parents from a personal perspective and +what it means to you that I think is the + + align:start position:0% +what it means to you that I think is the + + + align:start position:0% +what it means to you that I think is the +best way to start these conversations + + align:start position:0% +best way to start these conversations + + + align:start position:0% +best way to start these conversations +stories and personal impacts work a lot + + align:start position:0% +stories and personal impacts work a lot + + + align:start position:0% +stories and personal impacts work a lot +better than graphs and data yeah does + + align:start position:0% +better than graphs and data yeah does + + + align:start position:0% +better than graphs and data yeah does +that answer your question yeah cool + + align:start position:0% +that answer your question yeah cool + + + align:start position:0% +that answer your question yeah cool +thanks anybody else + + align:start position:0% + + + + align:start position:0% + +awesome oh yes one more so what did you + + align:start position:0% +awesome oh yes one more so what did you + + + align:start position:0% +awesome oh yes one more so what did you +come up against someone who it's not I + + align:start position:0% + + + + align:start position:0% + +that's a really hard question the + + align:start position:0% +that's a really hard question the + + + align:start position:0% +that's a really hard question the +question is how do we talk to people who + + align:start position:0% +question is how do we talk to people who + + + align:start position:0% +question is how do we talk to people who +are truly convinced that climate change + + align:start position:0% +are truly convinced that climate change + + + align:start position:0% +are truly convinced that climate change +is not real if it's a stranger honestly + + align:start position:0% +is not real if it's a stranger honestly + + + align:start position:0% +is not real if it's a stranger honestly +you're probably not gonna have much of a + + align:start position:0% +you're probably not gonna have much of a + + + align:start position:0% +you're probably not gonna have much of a +shot at convincing them as I said + + align:start position:0% +shot at convincing them as I said + + + align:start position:0% +shot at convincing them as I said +messenger matters more than message and + + align:start position:0% +messenger matters more than message and + + + align:start position:0% +messenger matters more than message and +there's not you don't really have the + + align:start position:0% +there's not you don't really have the + + + align:start position:0% +there's not you don't really have the +credibility with that person to sway + + align:start position:0% +credibility with that person to sway + + + align:start position:0% +credibility with that person to sway +their opinion on something that they + + align:start position:0% +their opinion on something that they + + + align:start position:0% +their opinion on something that they +hold so dearly but again if it's a + + align:start position:0% +hold so dearly but again if it's a + + + align:start position:0% +hold so dearly but again if it's a +relative start the conversation with + + align:start position:0% +relative start the conversation with + + + align:start position:0% +relative start the conversation with +what climate change means for you and as + + align:start position:0% +what climate change means for you and as + + + align:start position:0% +what climate change means for you and as +I said I'll send out resources from NASA + + align:start position:0% +I said I'll send out resources from NASA + + + align:start position:0% +I said I'll send out resources from NASA +and from NOAA and from a bunch of other + + align:start position:0% +and from NOAA and from a bunch of other + + + align:start position:0% +and from NOAA and from a bunch of other +very credible institutions that you can + + align:start position:0% +very credible institutions that you can + + + align:start position:0% +very credible institutions that you can +look at to see more information and and + + align:start position:0% +look at to see more information and and + + + align:start position:0% +look at to see more information and and +why our models work and how we know all + + align:start position:0% +why our models work and how we know all + + + align:start position:0% +why our models work and how we know all +of the things that we know about climate + + align:start position:0% +of the things that we know about climate + + + align:start position:0% +of the things that we know about climate +change and of course you're more than + + align:start position:0% +change and of course you're more than + + + align:start position:0% +change and of course you're more than +welcome + + align:start position:0% +welcome + + + align:start position:0% +welcome +in fact encouraged to share that with + + align:start position:0% +in fact encouraged to share that with + + + align:start position:0% +in fact encouraged to share that with +your relatives and friends and so on + + align:start position:0% +your relatives and friends and so on + + + align:start position:0% +your relatives and friends and so on +does that answer your question thank you + + align:start position:0% +does that answer your question thank you + + + align:start position:0% +does that answer your question thank you +do we have no yes in the back + + align:start position:0% + + + + align:start position:0% + +my question is really more formed than + + align:start position:0% +my question is really more formed than + + + align:start position:0% +my question is really more formed than +anything whenever whenever you ask the + + align:start position:0% +anything whenever whenever you ask the + + + align:start position:0% +anything whenever whenever you ask the +question about greenhouse gas effect is + + align:start position:0% +question about greenhouse gas effect is + + + align:start position:0% +question about greenhouse gas effect is +there like a number in your head that + + align:start position:0% +there like a number in your head that + + + align:start position:0% +there like a number in your head that +you have before like you'll ask a + + align:start position:0% +you have before like you'll ask a + + + align:start position:0% +you have before like you'll ask a +certain number of people before you just + + align:start position:0% +certain number of people before you just + + + align:start position:0% +certain number of people before you just +move on for the sake of time cool I want + + align:start position:0% +move on for the sake of time cool I want + + + align:start position:0% +move on for the sake of time cool I want +to hold with just two questions for + + align:start position:0% +to hold with just two questions for + + + align:start position:0% +to hold with just two questions for +afterwards but does anybody have any + + align:start position:0% +afterwards but does anybody have any + + + align:start position:0% +afterwards but does anybody have any +questions within the scope of the + + align:start position:0% +questions within the scope of the + + + align:start position:0% +questions within the scope of the +presentation anybody else + + align:start position:0% + + + + align:start position:0% + +like saying like the data are you + + align:start position:0% +like saying like the data are you + + + align:start position:0% +like saying like the data are you +kidding like where you're getting this + + align:start position:0% +kidding like where you're getting this + + + align:start position:0% +kidding like where you're getting this +information from this bias if you look + + align:start position:0% +information from this bias if you look + + + align:start position:0% +information from this bias if you look +elsewhere you'll see different data and + + align:start position:0% +elsewhere you'll see different data and + + + align:start position:0% +elsewhere you'll see different data and +then I just leave it and over time they + + align:start position:0% +then I just leave it and over time they + + + align:start position:0% +then I just leave it and over time they +start to see that and like I've started + + align:start position:0% +start to see that and like I've started + + + align:start position:0% +start to see that and like I've started +to change their minds about it that's a + + align:start position:0% +to change their minds about it that's a + + + align:start position:0% +to change their minds about it that's a +really good point so don't expect for a + + align:start position:0% +really good point so don't expect for a + + + align:start position:0% +really good point so don't expect for a +single conversation to completely change + + align:start position:0% +single conversation to completely change + + + align:start position:0% +single conversation to completely change +somebody's mind that's really hard and + + align:start position:0% +somebody's mind that's really hard and + + + align:start position:0% +somebody's mind that's really hard and +unlikely but over the course of of these + + align:start position:0% +unlikely but over the course of of these + + + align:start position:0% +unlikely but over the course of of these +conversations I think you'll be + + align:start position:0% +conversations I think you'll be + + + align:start position:0% +conversations I think you'll be +surprised and pleased at how successful + + align:start position:0% +surprised and pleased at how successful + + + align:start position:0% +surprised and pleased at how successful +you'll be at at changing the minds of + + align:start position:0% +you'll be at at changing the minds of + + + align:start position:0% +you'll be at at changing the minds of +people that are close to you cool thank + + align:start position:0% +people that are close to you cool thank + + + align:start position:0% +people that are close to you cool thank +you guys so much for coming I really + + align:start position:0% +you guys so much for coming I really + + + align:start position:0% +you guys so much for coming I really +appreciate it and we can answer some + + align:start position:0% +appreciate it and we can answer some + + + align:start position:0% +appreciate it and we can answer some +logistical questions but we don't need + + align:start position:0% +logistical questions but we don't need + + + align:start position:0% +logistical questions but we don't need +to record that + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/gSfc4GhlZ44.txt b/gSfc4GhlZ44.txt new file mode 100644 index 0000000000000000000000000000000000000000..d854d542b515e91499e47e6b440f07fd96c8b90e --- /dev/null +++ b/gSfc4GhlZ44.txt @@ -0,0 +1,555 @@ +align:start position:0% + +we are super excited that we've got over + + align:start position:0% +we are super excited that we've got over + + + align:start position:0% +we are super excited that we've got over +2 million subscribers now to the OCW + + align:start position:0% +2 million subscribers now to the OCW + + + align:start position:0% +2 million subscribers now to the OCW +youtube channel it's 2 million it's like + + align:start position:0% +youtube channel it's 2 million it's like + + + align:start position:0% +youtube channel it's 2 million it's like +the biggest educational thing on YouTube + + align:start position:0% +the biggest educational thing on YouTube + + + align:start position:0% +the biggest educational thing on YouTube +it's awesome it's ridiculous it's + + align:start position:0% +it's awesome it's ridiculous it's + + + align:start position:0% +it's awesome it's ridiculous it's +ridiculous you know I have a hard time + + align:start position:0% +ridiculous you know I have a hard time + + + align:start position:0% +ridiculous you know I have a hard time +understanding how big 2 million is 2 + + align:start position:0% +understanding how big 2 million is 2 + + + align:start position:0% +understanding how big 2 million is 2 +million people cared about watching I'm + + align:start position:0% +million people cared about watching I'm + + + align:start position:0% +million people cared about watching I'm +really glad that that many people have + + align:start position:0% +really glad that that many people have + + + align:start position:0% +really glad that that many people have +found us I think it could be more I also + + align:start position:0% +found us I think it could be more I also + + + align:start position:0% +found us I think it could be more I also +wonder why did it take so long + + align:start position:0% +wonder why did it take so long + + + align:start position:0% +wonder why did it take so long +everything we have is so amazing and so + + align:start position:0% +everything we have is so amazing and so + + + align:start position:0% +everything we have is so amazing and so +useful for people I'm not satisfied you + + align:start position:0% +useful for people I'm not satisfied you + + + align:start position:0% +useful for people I'm not satisfied you +know what my favorite million + + align:start position:0% +know what my favorite million + + + align:start position:0% +know what my favorite million +subscribers is the next million + + align:start position:0% +subscribers is the next million + + + align:start position:0% +subscribers is the next million +subscribers it's a Tom Brady thing + + align:start position:0% +subscribers it's a Tom Brady thing + + + align:start position:0% +subscribers it's a Tom Brady thing +you've come from all over the world + + align:start position:0% +you've come from all over the world + + + align:start position:0% +you've come from all over the world +watching OCW videos over 187 million + + align:start position:0% +watching OCW videos over 187 million + + + align:start position:0% +watching OCW videos over 187 million +times for over 1 billion minutes and + + align:start position:0% +times for over 1 billion minutes and + + + align:start position:0% +times for over 1 billion minutes and +it's all thanks to the generosity of the + + align:start position:0% +it's all thanks to the generosity of the + + + align:start position:0% +it's all thanks to the generosity of the +MIT faculty I think it's really a + + align:start position:0% +MIT faculty I think it's really a + + + align:start position:0% +MIT faculty I think it's really a +testament to how hungry the whole world + + align:start position:0% +testament to how hungry the whole world + + + align:start position:0% +testament to how hungry the whole world +is for the kind of openly shared + + align:start position:0% +is for the kind of openly shared + + + align:start position:0% +is for the kind of openly shared +knowledge that MIT OpenCourseWare is + + align:start position:0% +knowledge that MIT OpenCourseWare is + + + align:start position:0% +knowledge that MIT OpenCourseWare is +providing here's some of the things that + + align:start position:0% +providing here's some of the things that + + + align:start position:0% +providing here's some of the things that +we've enjoyed working on so I worked on + + align:start position:0% +we've enjoyed working on so I worked on + + + align:start position:0% +we've enjoyed working on so I worked on +classical mechanics vibrations and waves + + align:start position:0% +classical mechanics vibrations and waves + + + align:start position:0% +classical mechanics vibrations and waves +girls who built these are some pretty + + align:start position:0% +girls who built these are some pretty + + + align:start position:0% +girls who built these are some pretty +kick-ass girls in stem and they're + + align:start position:0% +kick-ass girls in stem and they're + + + align:start position:0% +kick-ass girls in stem and they're +building wearables I recently published + + align:start position:0% +building wearables I recently published + + + align:start position:0% +building wearables I recently published +a music course that was all about the + + align:start position:0% +a music course that was all about the + + + align:start position:0% +a music course that was all about the +Beatles single variable calculus + + align:start position:0% +Beatles single variable calculus + + + align:start position:0% +Beatles single variable calculus +multivariable calculus differential + + align:start position:0% +multivariable calculus differential + + + align:start position:0% +multivariable calculus differential +equations conlangs it's about + + align:start position:0% +equations conlangs it's about + + + align:start position:0% +equations conlangs it's about +constructed languages like Elvis and + + align:start position:0% +constructed languages like Elvis and + + + align:start position:0% +constructed languages like Elvis and +Esperanto and Dothraki quantum mechanics + + align:start position:0% +Esperanto and Dothraki quantum mechanics + + + align:start position:0% +Esperanto and Dothraki quantum mechanics +one quantum mechanics two quantum + + align:start position:0% +one quantum mechanics two quantum + + + align:start position:0% +one quantum mechanics two quantum +mechanics three speak Italian with your + + align:start position:0% +mechanics three speak Italian with your + + + align:start position:0% +mechanics three speak Italian with your +mouth full + + align:start position:0% +mouth full + + + align:start position:0% +mouth full +they spent half the time in the + + align:start position:0% +they spent half the time in the + + + align:start position:0% +they spent half the time in the +classroom learning Italian and then the + + align:start position:0% +classroom learning Italian and then the + + + align:start position:0% +classroom learning Italian and then the +second half in the kitchen cooking and + + align:start position:0% +second half in the kitchen cooking and + + + align:start position:0% +second half in the kitchen cooking and +using the language that they learned I + + align:start position:0% +using the language that they learned I + + + align:start position:0% +using the language that they learned I +did not get to eat the food Go Go + + align:start position:0% +did not get to eat the food Go Go + + + align:start position:0% +did not get to eat the food Go Go +studies and language courses I think you + + align:start position:0% +studies and language courses I think you + + + align:start position:0% +studies and language courses I think you +know to be able to have a global view of + + align:start position:0% +know to be able to have a global view of + + + align:start position:0% +know to be able to have a global view of +the world can make people understand the + + align:start position:0% +the world can make people understand the + + + align:start position:0% +the world can make people understand the +world better atomic and optical physics + + align:start position:0% +world better atomic and optical physics + + + align:start position:0% +world better atomic and optical physics +1 atomic and optical physics 2 + + align:start position:0% +1 atomic and optical physics 2 + + + align:start position:0% +1 atomic and optical physics 2 +experimental physics which is junior lab + + align:start position:0% +experimental physics which is junior lab + + + align:start position:0% +experimental physics which is junior lab +one and two of course called creating + + align:start position:0% +one and two of course called creating + + + align:start position:0% +one and two of course called creating +video games he's really cool the + + align:start position:0% +video games he's really cool the + + + align:start position:0% +video games he's really cool the +students created games of their own for + + align:start position:0% +students created games of their own for + + + align:start position:0% +students created games of their own for +their final projects and we actually + + align:start position:0% +their final projects and we actually + + + align:start position:0% +their final projects and we actually +have those playable on our website be + + align:start position:0% +have those playable on our website be + + + align:start position:0% +have those playable on our website be +sure to check out our interviews also + + align:start position:0% +sure to check out our interviews also + + + align:start position:0% +sure to check out our interviews also +with MIT faculty talking about how they + + align:start position:0% +with MIT faculty talking about how they + + + align:start position:0% +with MIT faculty talking about how they +teach and their passion for teaching and + + align:start position:0% +teach and their passion for teaching and + + + align:start position:0% +teach and their passion for teaching and +be sure to check out all the other + + align:start position:0% +be sure to check out all the other + + + align:start position:0% +be sure to check out all the other +course materials from thousands of MIT + + align:start position:0% +course materials from thousands of MIT + + + align:start position:0% +course materials from thousands of MIT +courses on the OCW website keep + + align:start position:0% +courses on the OCW website keep + + + align:start position:0% +courses on the OCW website keep +exploring discovering new topics sharing + + align:start position:0% +exploring discovering new topics sharing + + + align:start position:0% +exploring discovering new topics sharing +with your friends we're really glad + + align:start position:0% +with your friends we're really glad + + + align:start position:0% +with your friends we're really glad +you've joined us on this journey and + + align:start position:0% +you've joined us on this journey and + + + align:start position:0% +you've joined us on this journey and +stick with us we are nowhere near done + + align:start position:0% +stick with us we are nowhere near done + + + align:start position:0% +stick with us we are nowhere near done +thank you thank you + + align:start position:0% +thank you thank you + + + align:start position:0% +thank you thank you +thank you Marcel Egon sure you and + + align:start position:0% +thank you Marcel Egon sure you and + + + align:start position:0% +thank you Marcel Egon sure you and +Shanshan - Curtin can mean the + + align:start position:0% +Shanshan - Curtin can mean the + + + align:start position:0% +Shanshan - Curtin can mean the +thing you can't see she's just a woman + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/gbOyppJ9OK4.txt b/gbOyppJ9OK4.txt new file mode 100644 index 0000000000000000000000000000000000000000..c12791e598d1594752466f50a494303d82fc0f30 --- /dev/null +++ b/gbOyppJ9OK4.txt @@ -0,0 +1,5587 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu hello and welcome to 507 + + align:start position:0% +ocw.mit.edu hello and welcome to 507 + + + align:start position:0% +ocw.mit.edu hello and welcome to 507 +biochemistry online I'm Dr bdan + + align:start position:0% + + + + align:start position:0% + +fideles despite the Staggering + + align:start position:0% +fideles despite the Staggering + + + align:start position:0% +fideles despite the Staggering +biodiversity we see in nature the types + + align:start position:0% +biodiversity we see in nature the types + + + align:start position:0% +biodiversity we see in nature the types +of chemical reactions employed are only + + align:start position:0% +of chemical reactions employed are only + + + align:start position:0% +of chemical reactions employed are only +but a couple of handfuls and these are + + align:start position:0% +but a couple of handfuls and these are + + + align:start position:0% +but a couple of handfuls and these are +used over and over again very + + align:start position:0% +used over and over again very + + + align:start position:0% +used over and over again very +efficiently and with conserved + + align:start position:0% +efficiently and with conserved + + + align:start position:0% +efficiently and with conserved +mechanisms as you might recall from + + align:start position:0% +mechanisms as you might recall from + + + align:start position:0% +mechanisms as you might recall from +organic chemistry one of the most + + align:start position:0% +organic chemistry one of the most + + + align:start position:0% +organic chemistry one of the most +versatile chemical groups is the + + align:start position:0% +versatile chemical groups is the + + + align:start position:0% +versatile chemical groups is the +carbonal cbond O not surprisingly + + align:start position:0% +carbonal cbond O not surprisingly + + + align:start position:0% +carbonal cbond O not surprisingly +carbonal chemistry is well represented + + align:start position:0% +carbonal chemistry is well represented + + + align:start position:0% +carbonal chemistry is well represented +in + + align:start position:0% +in + + + align:start position:0% +in +Biochemistry in fact the carbon + + align:start position:0% +Biochemistry in fact the carbon + + + align:start position:0% +Biochemistry in fact the carbon +chemistry allows formation of carbon + + align:start position:0% +chemistry allows formation of carbon + + + align:start position:0% +chemistry allows formation of carbon +carbon bonds is one of the very few ways + + align:start position:0% +carbon bonds is one of the very few ways + + + align:start position:0% +carbon bonds is one of the very few ways +in which enzymes can start with small + + align:start position:0% +in which enzymes can start with small + + + align:start position:0% +in which enzymes can start with small +molecules and put them together into a + + align:start position:0% +molecules and put them together into a + + + align:start position:0% +molecules and put them together into a +Macro Molecule or start with a Macro + + align:start position:0% +Macro Molecule or start with a Macro + + + align:start position:0% +Macro Molecule or start with a Macro +Molecule and break it down into smaller + + align:start position:0% +Molecule and break it down into smaller + + + align:start position:0% +Molecule and break it down into smaller +pieces during + + align:start position:0% +pieces during + + + align:start position:0% +pieces during +metabolism this video summarizes some of + + align:start position:0% +metabolism this video summarizes some of + + + align:start position:0% +metabolism this video summarizes some of +the most important carbonal reactions + + align:start position:0% +the most important carbonal reactions + + + align:start position:0% +the most important carbonal reactions +you will encounter in 507 in this video + + align:start position:0% +you will encounter in 507 in this video + + + align:start position:0% +you will encounter in 507 in this video +we're going to be talking about carbonal + + align:start position:0% +we're going to be talking about carbonal + + + align:start position:0% +we're going to be talking about carbonal +chemistry and as as we will see carbonal + + align:start position:0% +chemistry and as as we will see carbonal + + + align:start position:0% +chemistry and as as we will see carbonal +chemistry is fundamental for some of the + + align:start position:0% +chemistry is fundamental for some of the + + + align:start position:0% +chemistry is fundamental for some of the +carbon carbon Bond formation and + + align:start position:0% +carbon carbon Bond formation and + + + align:start position:0% +carbon carbon Bond formation and +cleavage + + align:start position:0% +cleavage + + + align:start position:0% +cleavage +reactions as you recall from organic + + align:start position:0% +reactions as you recall from organic + + + align:start position:0% +reactions as you recall from organic +chemistry a carbonal contains a cble + + align:start position:0% +chemistry a carbonal contains a cble + + + align:start position:0% +chemistry a carbonal contains a cble +bond o and all the properties of the + + align:start position:0% +bond o and all the properties of the + + + align:start position:0% +bond o and all the properties of the +carbonal derive from its ability to + + align:start position:0% +carbonal derive from its ability to + + + align:start position:0% +carbonal derive from its ability to +polarize this + + align:start position:0% +polarize this + + + align:start position:0% +polarize this +Bond so that we can draw a resonance + + align:start position:0% +Bond so that we can draw a resonance + + + align:start position:0% +Bond so that we can draw a resonance +structure where the carbon has a + + align:start position:0% +structure where the carbon has a + + + align:start position:0% +structure where the carbon has a +positive charge and a oxygen a negative + + align:start position:0% +positive charge and a oxygen a negative + + + align:start position:0% +positive charge and a oxygen a negative +charge as you recall there are simple + + align:start position:0% +charge as you recall there are simple + + + align:start position:0% +charge as you recall there are simple +carbonal such as alahh + + align:start position:0% +carbonal such as alahh + + + align:start position:0% +carbonal such as alahh +tides and + + align:start position:0% + + + + align:start position:0% + +ketones also we have asil + + align:start position:0% +ketones also we have asil + + + align:start position:0% +ketones also we have asil +derivatives compounds in which the + + align:start position:0% +derivatives compounds in which the + + + align:start position:0% +derivatives compounds in which the +carbonal is attached to a hetero atom X + + align:start position:0% +carbonal is attached to a hetero atom X + + + align:start position:0% +carbonal is attached to a hetero atom X +can be oxygen nitrogen sulfur so here + + align:start position:0% +can be oxygen nitrogen sulfur so here + + + align:start position:0% +can be oxygen nitrogen sulfur so here +respectively we have Esters amides + + align:start position:0% +respectively we have Esters amides + + + align:start position:0% +respectively we have Esters amides +thesters and of course if we have an O + + align:start position:0% +thesters and of course if we have an O + + + align:start position:0% +thesters and of course if we have an O +group here carboxilic + + align:start position:0% +group here carboxilic + + + align:start position:0% +group here carboxilic +acid here is a summary of the reactions + + align:start position:0% +acid here is a summary of the reactions + + + align:start position:0% +acid here is a summary of the reactions +that we're going to be talking about + + align:start position:0% +that we're going to be talking about + + + align:start position:0% +that we're going to be talking about +first I'm going to be discussing + + align:start position:0% +first I'm going to be discussing + + + align:start position:0% +first I'm going to be discussing +nucleophilic + + align:start position:0% +nucleophilic + + + align:start position:0% +nucleophilic +addition here a good nucleophile react + + align:start position:0% +addition here a good nucleophile react + + + align:start position:0% +addition here a good nucleophile react +with the carbonal adding to the carbon + + align:start position:0% +with the carbonal adding to the carbon + + + align:start position:0% +with the carbonal adding to the carbon +of the carbonal and + + align:start position:0% + + + + align:start position:0% + +generate this tetrahedral + + align:start position:0% +generate this tetrahedral + + + align:start position:0% +generate this tetrahedral +compound next we're going to be talking + + align:start position:0% +compound next we're going to be talking + + + align:start position:0% +compound next we're going to be talking +about + + align:start position:0% +about + + + align:start position:0% +about +enolization this is the property of + + align:start position:0% +enolization this is the property of + + + align:start position:0% +enolization this is the property of +carbonal that contain an alpha hydrogen + + align:start position:0% +carbonal that contain an alpha hydrogen + + + align:start position:0% +carbonal that contain an alpha hydrogen +which can rearrange to form + + align:start position:0% + + + + align:start position:0% + +enol next we're going to introduce the + + align:start position:0% +enol next we're going to introduce the + + + align:start position:0% +enol next we're going to introduce the +alol + + align:start position:0% +alol + + + align:start position:0% +alol +reaction this is the reaction in which a + + align:start position:0% +reaction this is the reaction in which a + + + align:start position:0% +reaction this is the reaction in which a +carbon carbon bond is formed and occurs + + align:start position:0% +carbon carbon bond is formed and occurs + + + align:start position:0% +carbon carbon bond is formed and occurs +between a carbonal that acts as + + align:start position:0% +between a carbonal that acts as + + + align:start position:0% +between a carbonal that acts as +electrophile and an enolizable carbonal + + align:start position:0% +electrophile and an enolizable carbonal + + + align:start position:0% +electrophile and an enolizable carbonal +which acts as a + + align:start position:0% +which acts as a + + + align:start position:0% +which acts as a +nucleophile in the Alo reaction a bond + + align:start position:0% +nucleophile in the Alo reaction a bond + + + align:start position:0% +nucleophile in the Alo reaction a bond +is formed between these two carbons + + align:start position:0% +is formed between these two carbons + + + align:start position:0% +is formed between these two carbons +generating an + + align:start position:0% +generating an + + + align:start position:0% +generating an +alol we're also going to see that the + + align:start position:0% +alol we're also going to see that the + + + align:start position:0% +alol we're also going to see that the +aldols can + + align:start position:0% +aldols can + + + align:start position:0% +aldols can +dehydrate the aldol we saw + + align:start position:0% +dehydrate the aldol we saw + + + align:start position:0% +dehydrate the aldol we saw +above can lose a water + + align:start position:0% +above can lose a water + + + align:start position:0% +above can lose a water +molecule to form an alpha beta + + align:start position:0% +molecule to form an alpha beta + + + align:start position:0% +molecule to form an alpha beta +unsaturated + + align:start position:0% +unsaturated + + + align:start position:0% +unsaturated +carbonal now about asil derivatives + + align:start position:0% +carbonal now about asil derivatives + + + align:start position:0% +carbonal now about asil derivatives +we're going to be talking about asil + + align:start position:0% +we're going to be talking about asil + + + align:start position:0% +we're going to be talking about asil +transfer + + align:start position:0% +transfer + + + align:start position:0% +transfer +Reactions where an asil + + align:start position:0% +Reactions where an asil + + + align:start position:0% +Reactions where an asil +derivative can convert into a different + + align:start position:0% +derivative can convert into a different + + + align:start position:0% +derivative can convert into a different +ail derivative with the appropriate + + align:start position:0% +ail derivative with the appropriate + + + align:start position:0% +ail derivative with the appropriate +nucleophile and a variation of this + + align:start position:0% +nucleophile and a variation of this + + + align:start position:0% +nucleophile and a variation of this +reaction is cazin + + align:start position:0% +reaction is cazin + + + align:start position:0% +reaction is cazin +reaction where similarly to the aldol + + align:start position:0% +reaction where similarly to the aldol + + + align:start position:0% +reaction where similarly to the aldol +reaction we have an enolizable + + align:start position:0% +reaction we have an enolizable + + + align:start position:0% +reaction we have an enolizable +carbonal reacting with an ASO + + align:start position:0% + + + + align:start position:0% + +derivative and generating a beta keto + + align:start position:0% +derivative and generating a beta keto + + + align:start position:0% +derivative and generating a beta keto +carbonal this + + align:start position:0% +carbonal this + + + align:start position:0% +carbonal this +reaction also forms a carbon carbon bond + + align:start position:0% +reaction also forms a carbon carbon bond + + + align:start position:0% +reaction also forms a carbon carbon bond +which is right + + align:start position:0% + + + + align:start position:0% + +here let's talk in more detail about the + + align:start position:0% +here let's talk in more detail about the + + + align:start position:0% +here let's talk in more detail about the +nucleophilic + + align:start position:0% +nucleophilic + + + align:start position:0% +nucleophilic +addition the general reaction scheme is + + align:start position:0% +addition the general reaction scheme is + + + align:start position:0% +addition the general reaction scheme is +as we saw before here is a carbonal + + align:start position:0% +as we saw before here is a carbonal + + + align:start position:0% +as we saw before here is a carbonal +compound reacting with a + + align:start position:0% + + + + align:start position:0% + +nucleophile and forming a tetrahedr + + align:start position:0% +nucleophile and forming a tetrahedr + + + align:start position:0% +nucleophile and forming a tetrahedr +intermediate that contains an Alco oxide + + align:start position:0% +intermediate that contains an Alco oxide + + + align:start position:0% +intermediate that contains an Alco oxide +or an alcohol now let's take a look at + + align:start position:0% +or an alcohol now let's take a look at + + + align:start position:0% +or an alcohol now let's take a look at +two different reactions one is the + + align:start position:0% +two different reactions one is the + + + align:start position:0% +two different reactions one is the +reaction of alcohols with carbonal + + align:start position:0% +reaction of alcohols with carbonal + + + align:start position:0% +reaction of alcohols with carbonal +compounds where we + + align:start position:0% +compounds where we + + + align:start position:0% +compounds where we +form a compound that looks like this + + align:start position:0% +form a compound that looks like this + + + align:start position:0% +form a compound that looks like this +this is called a h acety + + align:start position:0% +this is called a h acety + + + align:start position:0% +this is called a h acety +now this reaction is + + align:start position:0% +now this reaction is + + + align:start position:0% +now this reaction is +reversible and in fact it reaches + + align:start position:0% +reversible and in fact it reaches + + + align:start position:0% +reversible and in fact it reaches +equilibrium because Delta G KN is + + align:start position:0% +equilibrium because Delta G KN is + + + align:start position:0% +equilibrium because Delta G KN is +approximately + + align:start position:0% +approximately + + + align:start position:0% +approximately +zero this reaction can be both acid or + + align:start position:0% +zero this reaction can be both acid or + + + align:start position:0% +zero this reaction can be both acid or +base + + align:start position:0% + + + + align:start position:0% + +catalyzed let's take a quick look at the + + align:start position:0% +catalyzed let's take a quick look at the + + + align:start position:0% +catalyzed let's take a quick look at the +mechanism if it's base + + align:start position:0% + + + + align:start position:0% + +catalyzed the base will first + + align:start position:0% +catalyzed the base will first + + + align:start position:0% +catalyzed the base will first +deprotonate the alcohol + + align:start position:0% +deprotonate the alcohol + + + align:start position:0% +deprotonate the alcohol +which will form the AL oxide which is + + align:start position:0% +which will form the AL oxide which is + + + align:start position:0% +which will form the AL oxide which is +then a very good nucleophile to attack + + align:start position:0% +then a very good nucleophile to attack + + + align:start position:0% +then a very good nucleophile to attack +the + + align:start position:0% +the + + + align:start position:0% +the +carbonal which forms this alkoxide + + align:start position:0% +carbonal which forms this alkoxide + + + align:start position:0% +carbonal which forms this alkoxide +version of the H acety which can be then + + align:start position:0% + + + + align:start position:0% + +protonated in acid catalyze mechanism we + + align:start position:0% +protonated in acid catalyze mechanism we + + + align:start position:0% +protonated in acid catalyze mechanism we +have to activate the carbonal first so + + align:start position:0% +have to activate the carbonal first so + + + align:start position:0% +have to activate the carbonal first so +the pronation of the carbonal is the + + align:start position:0% +the pronation of the carbonal is the + + + align:start position:0% +the pronation of the carbonal is the +first step + + align:start position:0% + + + + align:start position:0% + +all right so this activated carbonal can + + align:start position:0% +all right so this activated carbonal can + + + align:start position:0% +all right so this activated carbonal can +then be attacked by our + + align:start position:0% + + + + align:start position:0% + +alcohol which this product is just one + + align:start position:0% +alcohol which this product is just one + + + align:start position:0% +alcohol which this product is just one +proton transfer away from our H acid + + align:start position:0% +proton transfer away from our H acid + + + align:start position:0% +proton transfer away from our H acid +tow all right the second reaction uh I + + align:start position:0% +tow all right the second reaction uh I + + + align:start position:0% +tow all right the second reaction uh I +want to include here is the formation of + + align:start position:0% +want to include here is the formation of + + + align:start position:0% +want to include here is the formation of +shift bases which is the reaction of an + + align:start position:0% +shift bases which is the reaction of an + + + align:start position:0% +shift bases which is the reaction of an +carbonal with an + + align:start position:0% +carbonal with an + + + align:start position:0% +carbonal with an +amine similarly to the hastal formation + + align:start position:0% +amine similarly to the hastal formation + + + align:start position:0% +amine similarly to the hastal formation +this reaction generates first a + + align:start position:0% +this reaction generates first a + + + align:start position:0% +this reaction generates first a +tetrahedral + + align:start position:0% +tetrahedral + + + align:start position:0% +tetrahedral +intermediate which is however unstable + + align:start position:0% +intermediate which is however unstable + + + align:start position:0% +intermediate which is however unstable +and loses water to generate the em or + + align:start position:0% +and loses water to generate the em or + + + align:start position:0% +and loses water to generate the em or +the shift + + align:start position:0% + + + + align:start position:0% + +base let's take a look at the + + align:start position:0% +base let's take a look at the + + + align:start position:0% +base let's take a look at the +mechanism as you + + align:start position:0% +mechanism as you + + + align:start position:0% +mechanism as you +notice the reaction because the amine + + align:start position:0% +notice the reaction because the amine + + + align:start position:0% +notice the reaction because the amine +group is a good nucleophile the reaction + + align:start position:0% +group is a good nucleophile the reaction + + + align:start position:0% +group is a good nucleophile the reaction +could occur even in neutral conditions + + align:start position:0% +could occur even in neutral conditions + + + align:start position:0% +could occur even in neutral conditions +so we don't need necessarily acid or + + align:start position:0% +so we don't need necessarily acid or + + + align:start position:0% +so we don't need necessarily acid or +base + + align:start position:0% + + + + align:start position:0% + +catalysis the first step the Aman + + align:start position:0% +catalysis the first step the Aman + + + align:start position:0% +catalysis the first step the Aman +attacks the + + align:start position:0% + + + + align:start position:0% + +carbonal forming this compound with + + align:start position:0% +carbonal forming this compound with + + + align:start position:0% +carbonal forming this compound with +split + + align:start position:0% + + + + align:start position:0% + +charges now proton transfer happens + + align:start position:0% +charges now proton transfer happens + + + align:start position:0% +charges now proton transfer happens +generate our intermediate then water is + + align:start position:0% + + + + align:start position:0% + +eliminated and this is the E now notice + + align:start position:0% +eliminated and this is the E now notice + + + align:start position:0% +eliminated and this is the E now notice +the E nitrogen can also be + + align:start position:0% + + + + align:start position:0% + +protonated to generate this aminium + + align:start position:0% +protonated to generate this aminium + + + align:start position:0% +protonated to generate this aminium +ion which as we will see in uh in other + + align:start position:0% +ion which as we will see in uh in other + + + align:start position:0% +ion which as we will see in uh in other +situations it's + + align:start position:0% +situations it's + + + align:start position:0% +situations it's +an activated version of the carbonal + + align:start position:0% +an activated version of the carbonal + + + align:start position:0% +an activated version of the carbonal +group from these two examples we can get + + align:start position:0% +group from these two examples we can get + + + align:start position:0% +group from these two examples we can get +some idea how the nucleophilic addition + + align:start position:0% +some idea how the nucleophilic addition + + + align:start position:0% +some idea how the nucleophilic addition +occurs so let's take a look at what kind + + align:start position:0% +occurs so let's take a look at what kind + + + align:start position:0% +occurs so let's take a look at what kind +of nucleophiles we can add to the + + align:start position:0% +of nucleophiles we can add to the + + + align:start position:0% +of nucleophiles we can add to the +carbonal group we have some good + + align:start position:0% +carbonal group we have some good + + + align:start position:0% +carbonal group we have some good +nucleophiles and here we have things + + align:start position:0% +nucleophiles and here we have things + + + align:start position:0% +nucleophiles and here we have things +with negative charges such as Al coxide + + align:start position:0% +with negative charges such as Al coxide + + + align:start position:0% +with negative charges such as Al coxide +or hydroxide we have the + + align:start position:0% +or hydroxide we have the + + + align:start position:0% +or hydroxide we have the +Tates and other things such as am means + + align:start position:0% +Tates and other things such as am means + + + align:start position:0% +Tates and other things such as am means +and we also have some okay + + align:start position:0% +and we also have some okay + + + align:start position:0% +and we also have some okay +nucleophiles and here we have alcohols + + align:start position:0% +nucleophiles and here we have alcohols + + + align:start position:0% +nucleophiles and here we have alcohols +even water and + + align:start position:0% +even water and + + + align:start position:0% +even water and +thol as you saw in this couple of + + align:start position:0% +thol as you saw in this couple of + + + align:start position:0% +thol as you saw in this couple of +mechanisms the OK nucleophiles don't + + align:start position:0% +mechanisms the OK nucleophiles don't + + + align:start position:0% +mechanisms the OK nucleophiles don't +react very well unless they either + + align:start position:0% +react very well unless they either + + + align:start position:0% +react very well unless they either +deprotonated to form good nucleophiles + + align:start position:0% +deprotonated to form good nucleophiles + + + align:start position:0% +deprotonated to form good nucleophiles +such as the alcohols or the carbonal + + align:start position:0% +such as the alcohols or the carbonal + + + align:start position:0% +such as the alcohols or the carbonal +gets activated either by protonation in + + align:start position:0% +gets activated either by protonation in + + + align:start position:0% +gets activated either by protonation in +a strong acid as we saw here or it's + + align:start position:0% +a strong acid as we saw here or it's + + + align:start position:0% +a strong acid as we saw here or it's +becomes an activated carbonal for examp + + align:start position:0% +becomes an activated carbonal for examp + + + align:start position:0% +becomes an activated carbonal for examp +example in an aminium + + align:start position:0% +example in an aminium + + + align:start position:0% +example in an aminium +ion another important nucleophiles that + + align:start position:0% +ion another important nucleophiles that + + + align:start position:0% +ion another important nucleophiles that +we're going to see is + + align:start position:0% +we're going to see is + + + align:start position:0% +we're going to see is +the what we going to call a c minus + + align:start position:0% +the what we going to call a c minus + + + align:start position:0% +the what we going to call a c minus +basically a + + align:start position:0% +basically a + + + align:start position:0% +basically a +carbanion in our case it's going to be + + align:start position:0% +carbanion in our case it's going to be + + + align:start position:0% +carbanion in our case it's going to be +enolates which can also add to the + + align:start position:0% +enolates which can also add to the + + + align:start position:0% +enolates which can also add to the +carbonal and these will form the basis + + align:start position:0% +carbonal and these will form the basis + + + align:start position:0% +carbonal and these will form the basis +for the alol + + align:start position:0% + + + + align:start position:0% + +reaction the second reaction we're going + + align:start position:0% +reaction the second reaction we're going + + + align:start position:0% +reaction the second reaction we're going +to be talking about is + + align:start position:0% +to be talking about is + + + align:start position:0% +to be talking about is +enolization here a + + align:start position:0% +enolization here a + + + align:start position:0% +enolization here a +carbonal that contains an alpha + + align:start position:0% +carbonal that contains an alpha + + + align:start position:0% +carbonal that contains an alpha +hydrogen can rearrange to form an enol + + align:start position:0% +hydrogen can rearrange to form an enol + + + align:start position:0% +hydrogen can rearrange to form an enol +we're going to call this the keto form + + align:start position:0% +we're going to call this the keto form + + + align:start position:0% +we're going to call this the keto form +and this the enol + + align:start position:0% +and this the enol + + + align:start position:0% +and this the enol +form an equilibrium between a keto and + + align:start position:0% +form an equilibrium between a keto and + + + align:start position:0% +form an equilibrium between a keto and +an enol form is called + + align:start position:0% +an enol form is called + + + align:start position:0% +an enol form is called +talization and this is a very important + + align:start position:0% +talization and this is a very important + + + align:start position:0% +talization and this is a very important +reaction in many biochemical systems + + align:start position:0% +reaction in many biochemical systems + + + align:start position:0% +reaction in many biochemical systems +turns out the Delta G for the reaction + + align:start position:0% +turns out the Delta G for the reaction + + + align:start position:0% +turns out the Delta G for the reaction +as written it's very high 30 to 50 KJ + + align:start position:0% +as written it's very high 30 to 50 KJ + + + align:start position:0% +as written it's very high 30 to 50 KJ +per + + align:start position:0% +per + + + align:start position:0% +per +mole that means the equilibrium strongly + + align:start position:0% +mole that means the equilibrium strongly + + + align:start position:0% +mole that means the equilibrium strongly +favors the keto + + align:start position:0% +favors the keto + + + align:start position:0% +favors the keto +form however in certain cases the enol + + align:start position:0% +form however in certain cases the enol + + + align:start position:0% +form however in certain cases the enol +can form and get + + align:start position:0% +can form and get + + + align:start position:0% +can form and get +stabilized the mechanism of enolization + + align:start position:0% +stabilized the mechanism of enolization + + + align:start position:0% +stabilized the mechanism of enolization +it's very + + align:start position:0% +it's very + + + align:start position:0% +it's very +straightforward all we need is a decent + + align:start position:0% +straightforward all we need is a decent + + + align:start position:0% +straightforward all we need is a decent +base that can remove the alpha proton + + align:start position:0% + + + + align:start position:0% + +and it will form this + + align:start position:0% +and it will form this + + + align:start position:0% +and it will form this +enolate now enolate is able to form + + align:start position:0% +enolate now enolate is able to form + + + align:start position:0% +enolate now enolate is able to form +because it has resonance stabilization + + align:start position:0% +because it has resonance stabilization + + + align:start position:0% +because it has resonance stabilization +we can draw another resonance structure + + align:start position:0% +we can draw another resonance structure + + + align:start position:0% +we can draw another resonance structure +as + + align:start position:0% +as + + + align:start position:0% +as +such but we see the negative charge is + + align:start position:0% +such but we see the negative charge is + + + align:start position:0% +such but we see the negative charge is +on the carbon so is in fact a carbanion + + align:start position:0% +on the carbon so is in fact a carbanion + + + align:start position:0% +on the carbon so is in fact a carbanion +we're going to call it a disguised + + align:start position:0% +we're going to call it a disguised + + + align:start position:0% +we're going to call it a disguised +carban as the carbon is not very Electro + + align:start position:0% +carban as the carbon is not very Electro + + + align:start position:0% +carban as the carbon is not very Electro +negative having s such a High electron + + align:start position:0% +negative having s such a High electron + + + align:start position:0% +negative having s such a High electron +density on the carbon would make it a + + align:start position:0% +density on the carbon would make it a + + + align:start position:0% +density on the carbon would make it a +very good + + align:start position:0% +very good + + + align:start position:0% +very good +nucleophile and in fact this enolate is + + align:start position:0% +nucleophile and in fact this enolate is + + + align:start position:0% +nucleophile and in fact this enolate is +the nucleophile that executes reactions + + align:start position:0% +the nucleophile that executes reactions + + + align:start position:0% +the nucleophile that executes reactions +such as the aldol reaction and the cazin + + align:start position:0% +such as the aldol reaction and the cazin + + + align:start position:0% +such as the aldol reaction and the cazin +reaction something to keep in mind well + + align:start position:0% +reaction something to keep in mind well + + + align:start position:0% +reaction something to keep in mind well +how acidic is this Alpha + + align:start position:0% +how acidic is this Alpha + + + align:start position:0% +how acidic is this Alpha +hydrogen so we can compare it with a + + align:start position:0% +hydrogen so we can compare it with a + + + align:start position:0% +hydrogen so we can compare it with a +hydrogen in an an alkane the pka of such + + align:start position:0% +hydrogen in an an alkane the pka of such + + + align:start position:0% +hydrogen in an an alkane the pka of such +a hydrogen is close to 50 it's + + align:start position:0% +a hydrogen is close to 50 it's + + + align:start position:0% +a hydrogen is close to 50 it's +extremely hard to remove a + + align:start position:0% +extremely hard to remove a + + + align:start position:0% +extremely hard to remove a +proton now if you looking the alpha + + align:start position:0% +proton now if you looking the alpha + + + align:start position:0% +proton now if you looking the alpha +hydrogen next to a carbonal the pka is + + align:start position:0% +hydrogen next to a carbonal the pka is + + + align:start position:0% +hydrogen next to a carbonal the pka is +18 to 20 so it's 30 orders of magnitude + + align:start position:0% +18 to 20 so it's 30 orders of magnitude + + + align:start position:0% +18 to 20 so it's 30 orders of magnitude +more + + align:start position:0% +more + + + align:start position:0% +more +acidic and this is because as we saw + + align:start position:0% +acidic and this is because as we saw + + + align:start position:0% +acidic and this is because as we saw +when we remove this hydrogen we formed + + align:start position:0% +when we remove this hydrogen we formed + + + align:start position:0% +when we remove this hydrogen we formed +the + + align:start position:0% +the + + + align:start position:0% +the +enolate anion which is resonance + + align:start position:0% +enolate anion which is resonance + + + align:start position:0% +enolate anion which is resonance +stabilized a more extreme case of this + + align:start position:0% +stabilized a more extreme case of this + + + align:start position:0% +stabilized a more extreme case of this +if we have two carbon + + align:start position:0% + + + + align:start position:0% + +Alpha to the same proton the pka drops + + align:start position:0% +Alpha to the same proton the pka drops + + + align:start position:0% +Alpha to the same proton the pka drops +even + + align:start position:0% +even + + + align:start position:0% +even +further around 9 to + + align:start position:0% +further around 9 to + + + align:start position:0% +further around 9 to +11 this is because we can draw even more + + align:start position:0% +11 this is because we can draw even more + + + align:start position:0% +11 this is because we can draw even more +resonance uh structures to the inate + + align:start position:0% +resonance uh structures to the inate + + + align:start position:0% +resonance uh structures to the inate +that's + + align:start position:0% +that's + + + align:start position:0% +that's +formed this is + + align:start position:0% + + + + align:start position:0% + +one this is another + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +another as we saw before the charge here + + align:start position:0% +another as we saw before the charge here + + + align:start position:0% +another as we saw before the charge here +is delocalized between the oxygen and + + align:start position:0% +is delocalized between the oxygen and + + + align:start position:0% +is delocalized between the oxygen and +the alpha carbon so it + + align:start position:0% +the alpha carbon so it + + + align:start position:0% +the alpha carbon so it +is this beta keto carbonal in its + + align:start position:0% +is this beta keto carbonal in its + + + align:start position:0% +is this beta keto carbonal in its +enolate form will behave as a carbanion + + align:start position:0% +enolate form will behave as a carbanion + + + align:start position:0% +enolate form will behave as a carbanion +and it + + align:start position:0% +and it + + + align:start position:0% +and it +can act as a good + + align:start position:0% + + + + align:start position:0% + +nucleophile the alal + + align:start position:0% +nucleophile the alal + + + align:start position:0% +nucleophile the alal +reaction this is a very important + + align:start position:0% +reaction this is a very important + + + align:start position:0% +reaction this is a very important +reaction biochemistry because allows + + align:start position:0% +reaction biochemistry because allows + + + align:start position:0% +reaction biochemistry because allows +formation of carbon carbon + + align:start position:0% +formation of carbon carbon + + + align:start position:0% +formation of carbon carbon +bonds or if the reaction run in Reverse + + align:start position:0% +bonds or if the reaction run in Reverse + + + align:start position:0% +bonds or if the reaction run in Reverse +cleavage of the carbon carbon + + align:start position:0% +cleavage of the carbon carbon + + + align:start position:0% +cleavage of the carbon carbon +bonds the Alo + + align:start position:0% +bonds the Alo + + + align:start position:0% +bonds the Alo +reaction is the reaction between an + + align:start position:0% +reaction is the reaction between an + + + align:start position:0% +reaction is the reaction between an +enolizable + + align:start position:0% +enolizable + + + align:start position:0% +enolizable +carbonal as we show here a carbonal that + + align:start position:0% +carbonal as we show here a carbonal that + + + align:start position:0% +carbonal as we show here a carbonal that +has an alpha hydrogen and another + + align:start position:0% +has an alpha hydrogen and another + + + align:start position:0% +has an alpha hydrogen and another +carbonal and what happens is a new + + align:start position:0% +carbonal and what happens is a new + + + align:start position:0% +carbonal and what happens is a new +carbon carbon bond forms between the + + align:start position:0% +carbon carbon bond forms between the + + + align:start position:0% +carbon carbon bond forms between the +alpha + + align:start position:0% + + + + align:start position:0% + +carbon and the carbonal + + align:start position:0% + + + + align:start position:0% + +carbon the product of the aldol reaction + + align:start position:0% +carbon the product of the aldol reaction + + + align:start position:0% +carbon the product of the aldol reaction +it's called aldol has a contraction + + align:start position:0% +it's called aldol has a contraction + + + align:start position:0% +it's called aldol has a contraction +between alahh and + + align:start position:0% +between alahh and + + + align:start position:0% +between alahh and +alcohol as in some cases this carbonal + + align:start position:0% +alcohol as in some cases this carbonal + + + align:start position:0% +alcohol as in some cases this carbonal +will be an alahh and this will be an + + align:start position:0% +will be an alahh and this will be an + + + align:start position:0% +will be an alahh and this will be an +aldol it's essentially a beta + + align:start position:0% +aldol it's essentially a beta + + + align:start position:0% +aldol it's essentially a beta +hydroxy + + align:start position:0% +hydroxy + + + align:start position:0% +hydroxy +carbonal now + + align:start position:0% +carbonal now + + + align:start position:0% +carbonal now +this reaction has a Delta G knot close + + align:start position:0% +this reaction has a Delta G knot close + + + align:start position:0% +this reaction has a Delta G knot close +to zero that is it reaches a very uh + + align:start position:0% +to zero that is it reaches a very uh + + + align:start position:0% +to zero that is it reaches a very uh +reaches equilibrium and it can be + + align:start position:0% +reaches equilibrium and it can be + + + align:start position:0% +reaches equilibrium and it can be +catalyzed by acid or by + + align:start position:0% +catalyzed by acid or by + + + align:start position:0% +catalyzed by acid or by +base let's take a quick look at the + + align:start position:0% +base let's take a quick look at the + + + align:start position:0% +base let's take a quick look at the +mechanism given the previous mechanistic + + align:start position:0% +mechanism given the previous mechanistic + + + align:start position:0% +mechanism given the previous mechanistic +insights we looked at at the + + align:start position:0% +insights we looked at at the + + + align:start position:0% +insights we looked at at the +nucleophilic addition and enol formation + + align:start position:0% +nucleophilic addition and enol formation + + + align:start position:0% +nucleophilic addition and enol formation +then the mechanism of the Aldo reaction + + align:start position:0% +then the mechanism of the Aldo reaction + + + align:start position:0% +then the mechanism of the Aldo reaction +should be fairly straight p if it's base + + align:start position:0% +should be fairly straight p if it's base + + + align:start position:0% +should be fairly straight p if it's base +catalyze the base is going to help us + + align:start position:0% +catalyze the base is going to help us + + + align:start position:0% +catalyze the base is going to help us +form the + + align:start position:0% + + + + align:start position:0% + +enolate as such and as we discussed + + align:start position:0% +enolate as such and as we discussed + + + align:start position:0% +enolate as such and as we discussed +previously the enolate is a good + + align:start position:0% +previously the enolate is a good + + + align:start position:0% +previously the enolate is a good +nucleophile and can react via + + align:start position:0% +nucleophile and can react via + + + align:start position:0% +nucleophile and can react via +nucleophilic addition with the the other + + align:start position:0% +nucleophilic addition with the the other + + + align:start position:0% +nucleophilic addition with the the other +carbonal + + align:start position:0% + + + + align:start position:0% + +and one proton transfer to + + align:start position:0% +and one proton transfer to + + + align:start position:0% +and one proton transfer to +generate the alal + + align:start position:0% + + + + align:start position:0% + +product the reaction can also be acid + + align:start position:0% +product the reaction can also be acid + + + align:start position:0% +product the reaction can also be acid +catalyzed again formation of the enol in + + align:start position:0% +catalyzed again formation of the enol in + + + align:start position:0% +catalyzed again formation of the enol in +acid catalysis involves first + + align:start position:0% +acid catalysis involves first + + + align:start position:0% +acid catalysis involves first +protonation of the + + align:start position:0% + + + + align:start position:0% + +carbonal now this activated carbonal + + align:start position:0% +carbonal now this activated carbonal + + + align:start position:0% +carbonal now this activated carbonal +it's much better electrons Sy and + + align:start position:0% +it's much better electrons Sy and + + + align:start position:0% +it's much better electrons Sy and +stabilizes the enol + + align:start position:0% + + + + align:start position:0% + +formation now in the Second Step the + + align:start position:0% +formation now in the Second Step the + + + align:start position:0% +formation now in the Second Step the +enol can react with the other + + align:start position:0% + + + + align:start position:0% + +carbonal to generate prary version of + + align:start position:0% +carbonal to generate prary version of + + + align:start position:0% +carbonal to generate prary version of +the aldol which is one proton transfer + + align:start position:0% +the aldol which is one proton transfer + + + align:start position:0% +the aldol which is one proton transfer +away + + align:start position:0% +away + + + align:start position:0% +away +from the alol + + align:start position:0% +from the alol + + + align:start position:0% +from the alol +product in biochemical systems the + + align:start position:0% +product in biochemical systems the + + + align:start position:0% +product in biochemical systems the +enzyme that catalyzes the alal reaction + + align:start position:0% +enzyme that catalyzes the alal reaction + + + align:start position:0% +enzyme that catalyzes the alal reaction +is is called + + align:start position:0% +is is called + + + align:start position:0% +is is called +alalas and there are actually two kinds + + align:start position:0% +alalas and there are actually two kinds + + + align:start position:0% +alalas and there are actually two kinds +of + + align:start position:0% +of + + + align:start position:0% +of +aldolases class one and class two the + + align:start position:0% +aldolases class one and class two the + + + align:start position:0% +aldolases class one and class two the +distinctive feature of these enzymes is + + align:start position:0% +distinctive feature of these enzymes is + + + align:start position:0% +distinctive feature of these enzymes is +the way they catalyze the reaction class + + align:start position:0% +the way they catalyze the reaction class + + + align:start position:0% +the way they catalyze the reaction class +one uses an active site lysine to to + + align:start position:0% +one uses an active site lysine to to + + + align:start position:0% +one uses an active site lysine to to +form a shift base with the carbonal + + align:start position:0% +form a shift base with the carbonal + + + align:start position:0% +form a shift base with the carbonal +which activates the carbonal and allows + + align:start position:0% +which activates the carbonal and allows + + + align:start position:0% +which activates the carbonal and allows +for the enol formation class two uses a + + align:start position:0% +for the enol formation class two uses a + + + align:start position:0% +for the enol formation class two uses a +metal ion such as zinc to accomplish the + + align:start position:0% +metal ion such as zinc to accomplish the + + + align:start position:0% +metal ion such as zinc to accomplish the +same + + align:start position:0% +same + + + align:start position:0% +same +thing so here is how the mechanism for + + align:start position:0% +thing so here is how the mechanism for + + + align:start position:0% +thing so here is how the mechanism for +the class one Alay would look + + align:start position:0% + + + + align:start position:0% + +like so here is our enolizable + + align:start position:0% + + + + align:start position:0% + +carbonal and here is our active side + + align:start position:0% +carbonal and here is our active side + + + align:start position:0% +carbonal and here is our active side +lysine and as we saw before an Aman rea + + align:start position:0% +lysine and as we saw before an Aman rea + + + align:start position:0% +lysine and as we saw before an Aman rea +ING with a carbonal will give us a shift + + align:start position:0% +ING with a carbonal will give us a shift + + + align:start position:0% +ING with a carbonal will give us a shift +bace the reaction goes via tetraedro + + align:start position:0% +bace the reaction goes via tetraedro + + + align:start position:0% +bace the reaction goes via tetraedro +intermediate which we're not going to + + align:start position:0% +intermediate which we're not going to + + + align:start position:0% +intermediate which we're not going to +draw + + align:start position:0% +draw + + + align:start position:0% +draw +here but what we form is this + + align:start position:0% +here but what we form is this + + + align:start position:0% +here but what we form is this +aminium + + align:start position:0% +aminium + + + align:start position:0% +aminium +ion now the carbonal is activated enough + + align:start position:0% +ion now the carbonal is activated enough + + + align:start position:0% +ion now the carbonal is activated enough +that an active side base can remove the + + align:start position:0% +that an active side base can remove the + + + align:start position:0% +that an active side base can remove the +alpha hydrogen to form the enol + + align:start position:0% + + + + align:start position:0% + +which is now well positioned to attack + + align:start position:0% +which is now well positioned to attack + + + align:start position:0% +which is now well positioned to attack +the other + + align:start position:0% + + + + align:start position:0% + +carbonal this generates the alal product + + align:start position:0% +carbonal this generates the alal product + + + align:start position:0% +carbonal this generates the alal product +in its em form still attached to the + + align:start position:0% +in its em form still attached to the + + + align:start position:0% +in its em form still attached to the +enzyme and now the hydrolysis of em is + + align:start position:0% +enzyme and now the hydrolysis of em is + + + align:start position:0% +enzyme and now the hydrolysis of em is +going to release the + + align:start position:0% + + + + align:start position:0% + +alol now class two enzymes + + align:start position:0% +alol now class two enzymes + + + align:start position:0% +alol now class two enzymes +use a + + align:start position:0% +use a + + + align:start position:0% +use a +zinc + + align:start position:0% +zinc + + + align:start position:0% +zinc +ion as the ion uh approaches the + + align:start position:0% +ion as the ion uh approaches the + + + align:start position:0% +ion as the ion uh approaches the +carbonal it's going to draw some of the + + align:start position:0% +carbonal it's going to draw some of the + + + align:start position:0% +carbonal it's going to draw some of the +electrons from the + + align:start position:0% +electrons from the + + + align:start position:0% +electrons from the +carbonal and make the proton in the + + align:start position:0% +carbonal and make the proton in the + + + align:start position:0% +carbonal and make the proton in the +alpha position a lot more + + align:start position:0% + + + + align:start position:0% + +acidic so we can imagine some of these + + align:start position:0% +acidic so we can imagine some of these + + + align:start position:0% +acidic so we can imagine some of these +electrons get delocalized + + align:start position:0% + + + + align:start position:0% + +so that a + + align:start position:0% +so that a + + + align:start position:0% +so that a +base can remove the proton and form the + + align:start position:0% + + + + align:start position:0% + +enolate which in the second step it + + align:start position:0% +enolate which in the second step it + + + align:start position:0% +enolate which in the second step it +reacts with the + + align:start position:0% + + + + align:start position:0% + +carbonal which will generate the alal + + align:start position:0% +carbonal which will generate the alal + + + align:start position:0% +carbonal which will generate the alal +product in the active side of the + + align:start position:0% + + + + align:start position:0% + +enzyme still bound to the zinc and now + + align:start position:0% +enzyme still bound to the zinc and now + + + align:start position:0% +enzyme still bound to the zinc and now +which can dissociate and generate the + + align:start position:0% +which can dissociate and generate the + + + align:start position:0% +which can dissociate and generate the +final and release the + + align:start position:0% +final and release the + + + align:start position:0% +final and release the +product now very important consideration + + align:start position:0% +product now very important consideration + + + align:start position:0% +product now very important consideration +for the Alo reaction is this they going + + align:start position:0% +for the Alo reaction is this they going + + + align:start position:0% +for the Alo reaction is this they going +occur in the reverse fashion for example + + align:start position:0% +occur in the reverse fashion for example + + + align:start position:0% +occur in the reverse fashion for example +to cleave a carbon carbon + + align:start position:0% +to cleave a carbon carbon + + + align:start position:0% +to cleave a carbon carbon +Bond so the bond that will be cleaved as + + align:start position:0% +Bond so the bond that will be cleaved as + + + align:start position:0% +Bond so the bond that will be cleaved as +we see here is the bond that got formed + + align:start position:0% +we see here is the bond that got formed + + + align:start position:0% +we see here is the bond that got formed +which is the bond + + align:start position:0% +which is the bond + + + align:start position:0% +which is the bond +between the Alpha and the beta carbons + + align:start position:0% +between the Alpha and the beta carbons + + + align:start position:0% +between the Alpha and the beta carbons +alalay is one of the key enzyme and + + align:start position:0% +alalay is one of the key enzyme and + + + align:start position:0% +alalay is one of the key enzyme and +glycolysis that allows us to break a six + + align:start position:0% +glycolysis that allows us to break a six + + + align:start position:0% +glycolysis that allows us to break a six +carbon sugar into three two three carbon + + align:start position:0% +carbon sugar into three two three carbon + + + align:start position:0% +carbon sugar into three two three carbon +sugars by cleaving a carbon carbon Bond + + align:start position:0% +sugars by cleaving a carbon carbon Bond + + + align:start position:0% +sugars by cleaving a carbon carbon Bond +via the aldol + + align:start position:0% +via the aldol + + + align:start position:0% +via the aldol +reaction as the mechanism catalyzed by + + align:start position:0% +reaction as the mechanism catalyzed by + + + align:start position:0% +reaction as the mechanism catalyzed by +the alas you we can see that the reverse + + align:start position:0% +the alas you we can see that the reverse + + + align:start position:0% +the alas you we can see that the reverse +pathway it's pretty straightforward + + align:start position:0% +pathway it's pretty straightforward + + + align:start position:0% +pathway it's pretty straightforward +where the alol binds to the enzyme say + + align:start position:0% +where the alol binds to the enzyme say + + + align:start position:0% +where the alol binds to the enzyme say +in class one forms an active side Co + + align:start position:0% +in class one forms an active side Co + + + align:start position:0% +in class one forms an active side Co +valent interaction a shift base with the + + align:start position:0% +valent interaction a shift base with the + + + align:start position:0% +valent interaction a shift base with the +lysine from which the chemistry URS to + + align:start position:0% +lysine from which the chemistry URS to + + + align:start position:0% +lysine from which the chemistry URS to +break the carbon carbon Bond and leads + + align:start position:0% +break the carbon carbon Bond and leads + + + align:start position:0% +break the carbon carbon Bond and leads +to the release of one carbonal molecule + + align:start position:0% +to the release of one carbonal molecule + + + align:start position:0% +to the release of one carbonal molecule +and then the other one will be still + + align:start position:0% +and then the other one will be still + + + align:start position:0% +and then the other one will be still +bound to the enzyme as a shift base and + + align:start position:0% +bound to the enzyme as a shift base and + + + align:start position:0% +bound to the enzyme as a shift base and +hydrolized for the class two the aldol + + align:start position:0% +hydrolized for the class two the aldol + + + align:start position:0% +hydrolized for the class two the aldol +will interact with the enzyme by forming + + align:start position:0% +will interact with the enzyme by forming + + + align:start position:0% +will interact with the enzyme by forming +a uh interaction with the zinc and this + + align:start position:0% +a uh interaction with the zinc and this + + + align:start position:0% +a uh interaction with the zinc and this +activates the carbonal allows the + + align:start position:0% +activates the carbonal allows the + + + align:start position:0% +activates the carbonal allows the +chemistry to + + align:start position:0% +chemistry to + + + align:start position:0% +chemistry to +occur uh exactly in the reverse manner + + align:start position:0% +occur uh exactly in the reverse manner + + + align:start position:0% +occur uh exactly in the reverse manner +as shown here + + align:start position:0% + + + + align:start position:0% + +one other reaction involving ald dolls + + align:start position:0% +one other reaction involving ald dolls + + + align:start position:0% +one other reaction involving ald dolls +is aldol + + align:start position:0% + + + + align:start position:0% + +dehydration here's an aldol beta hydroxy + + align:start position:0% +dehydration here's an aldol beta hydroxy + + + align:start position:0% +dehydration here's an aldol beta hydroxy +carbonal now if an Aldon has an + + align:start position:0% +carbonal now if an Aldon has an + + + align:start position:0% +carbonal now if an Aldon has an +additional Alpha + + align:start position:0% +additional Alpha + + + align:start position:0% +additional Alpha +hydrogen it can lose a water + + align:start position:0% +hydrogen it can lose a water + + + align:start position:0% +hydrogen it can lose a water +molecule to + + align:start position:0% +molecule to + + + align:start position:0% +molecule to +form an alpha beta + + align:start position:0% +form an alpha beta + + + align:start position:0% +form an alpha beta +unsaturated + + align:start position:0% +unsaturated + + + align:start position:0% +unsaturated +carbonal now this reaction is favorable + + align:start position:0% +carbonal now this reaction is favorable + + + align:start position:0% +carbonal now this reaction is favorable +thermodynamically the Delta G KN is + + align:start position:0% +thermodynamically the Delta G KN is + + + align:start position:0% +thermodynamically the Delta G KN is +approximately zero and this is a + + align:start position:0% +approximately zero and this is a + + + align:start position:0% +approximately zero and this is a +reaction we're going to see in in a lot + + align:start position:0% +reaction we're going to see in in a lot + + + align:start position:0% +reaction we're going to see in in a lot +of biochemical Pathways for example in + + align:start position:0% +of biochemical Pathways for example in + + + align:start position:0% +of biochemical Pathways for example in +the biosynthesis of fatty acids going + + align:start position:0% +the biosynthesis of fatty acids going + + + align:start position:0% +the biosynthesis of fatty acids going +left to right or in the catabolism of + + align:start position:0% +left to right or in the catabolism of + + + align:start position:0% +left to right or in the catabolism of +fatty acids going right to + + align:start position:0% +fatty acids going right to + + + align:start position:0% +fatty acids going right to +left here is a quick Insight on the + + align:start position:0% +left here is a quick Insight on the + + + align:start position:0% +left here is a quick Insight on the +mechanism when once again it can be base + + align:start position:0% +mechanism when once again it can be base + + + align:start position:0% +mechanism when once again it can be base +or acid + + align:start position:0% + + + + align:start position:0% + +catalyze this reaction works because the + + align:start position:0% +catalyze this reaction works because the + + + align:start position:0% +catalyze this reaction works because the +alpha hydrogen here is next to a + + align:start position:0% +alpha hydrogen here is next to a + + + align:start position:0% +alpha hydrogen here is next to a +carbonal and therefore can form an + + align:start position:0% + + + + align:start position:0% + +enol so if a base can remove this + + align:start position:0% +enol so if a base can remove this + + + align:start position:0% +enol so if a base can remove this +hydrogen to form the + + align:start position:0% + + + + align:start position:0% + +enolate then we can Envision + + align:start position:0% +enolate then we can Envision + + + align:start position:0% +enolate then we can Envision +how this Electronic Movement will + + align:start position:0% +how this Electronic Movement will + + + align:start position:0% +how this Electronic Movement will +allow for for the water molecule to be + + align:start position:0% +allow for for the water molecule to be + + + align:start position:0% +allow for for the water molecule to be +eliminated forming our Alpha Beta + + align:start position:0% +eliminated forming our Alpha Beta + + + align:start position:0% +eliminated forming our Alpha Beta +unsaturated + + align:start position:0% +unsaturated + + + align:start position:0% +unsaturated +carbonal the acid catalyze mechanism + + align:start position:0% +carbonal the acid catalyze mechanism + + + align:start position:0% +carbonal the acid catalyze mechanism +goes along the + + align:start position:0% +goes along the + + + align:start position:0% +goes along the +same + + align:start position:0% +same + + + align:start position:0% +same +lines as you remember in order to form + + align:start position:0% +lines as you remember in order to form + + + align:start position:0% +lines as you remember in order to form +the enol in an acid catalyzed the + + align:start position:0% +the enol in an acid catalyzed the + + + align:start position:0% +the enol in an acid catalyzed the +context first we have to pronate the + + align:start position:0% + + + + align:start position:0% + +carbonal all right now a base can remove + + align:start position:0% +carbonal all right now a base can remove + + + align:start position:0% +carbonal all right now a base can remove +our Alpha + + align:start position:0% + + + + align:start position:0% + +hydrogen forming the + + align:start position:0% + + + + align:start position:0% + +enol which can kick off water + + align:start position:0% + + + + align:start position:0% + +molecule generating this pieces which is + + align:start position:0% +molecule generating this pieces which is + + + align:start position:0% +molecule generating this pieces which is +just one proton transfer + + align:start position:0% +just one proton transfer + + + align:start position:0% +just one proton transfer +away from our final + + align:start position:0% + + + + align:start position:0% + +product so let's talk now about asil + + align:start position:0% +product so let's talk now about asil + + + align:start position:0% +product so let's talk now about asil +derivatives and asil + + align:start position:0% + + + + align:start position:0% + +transfer as we mentioned asil + + align:start position:0% +transfer as we mentioned asil + + + align:start position:0% +transfer as we mentioned asil +derivatives have a carbonal attached to + + align:start position:0% +derivatives have a carbonal attached to + + + align:start position:0% +derivatives have a carbonal attached to +a heter + + align:start position:0% +a heter + + + align:start position:0% +a heter +atom and this heter atom can be oxygen + + align:start position:0% +atom and this heter atom can be oxygen + + + align:start position:0% +atom and this heter atom can be oxygen +nitrogen + + align:start position:0% +nitrogen + + + align:start position:0% +nitrogen +sulfur as all these heter atoms contain + + align:start position:0% +sulfur as all these heter atoms contain + + + align:start position:0% +sulfur as all these heter atoms contain +a lone pair of electrons one of the key + + align:start position:0% +a lone pair of electrons one of the key + + + align:start position:0% +a lone pair of electrons one of the key +property of the asil derivatives would + + align:start position:0% +property of the asil derivatives would + + + align:start position:0% +property of the asil derivatives would +be + + align:start position:0% + + + + align:start position:0% + +resonance between the heter atom and the + + align:start position:0% + + + + align:start position:0% + +oxygen now the properties of the asil + + align:start position:0% +oxygen now the properties of the asil + + + align:start position:0% +oxygen now the properties of the asil +derivatives would be dictated by how + + align:start position:0% +derivatives would be dictated by how + + + align:start position:0% +derivatives would be dictated by how +easy or how difficult it is to adopt + + align:start position:0% +easy or how difficult it is to adopt + + + align:start position:0% +easy or how difficult it is to adopt +this minor resonance structure in other + + align:start position:0% +this minor resonance structure in other + + + align:start position:0% +this minor resonance structure in other +words How likely is for the heter atom + + align:start position:0% +words How likely is for the heter atom + + + align:start position:0% +words How likely is for the heter atom +to + + align:start position:0% +to + + + align:start position:0% +to +participate in in these electron + + align:start position:0% +participate in in these electron + + + align:start position:0% +participate in in these electron +conjugation let's take a look at a + + align:start position:0% +conjugation let's take a look at a + + + align:start position:0% +conjugation let's take a look at a +couple of asil + + align:start position:0% +couple of asil + + + align:start position:0% +couple of asil +derivatives this is a + + align:start position:0% +derivatives this is a + + + align:start position:0% +derivatives this is a +carboxilate if the Hader atom is in + + align:start position:0% +carboxilate if the Hader atom is in + + + align:start position:0% +carboxilate if the Hader atom is in +nitrogen we have + + align:start position:0% + + + + align:start position:0% + +Amite if the header + + align:start position:0% +Amite if the header + + + align:start position:0% +Amite if the header +atom is oxygen we also + + align:start position:0% +atom is oxygen we also + + + align:start position:0% +atom is oxygen we also +have + + align:start position:0% +have + + + align:start position:0% +have +Esters or carboxylic acids + + align:start position:0% +Esters or carboxylic acids + + + align:start position:0% +Esters or carboxylic acids +and when the H atom is + + align:start position:0% +and when the H atom is + + + align:start position:0% +and when the H atom is +sulfur we have + + align:start position:0% +sulfur we have + + + align:start position:0% +sulfur we have +testers the order in which I wrote them + + align:start position:0% +testers the order in which I wrote them + + + align:start position:0% +testers the order in which I wrote them +here is not actually random it turns out + + align:start position:0% +here is not actually random it turns out + + + align:start position:0% +here is not actually random it turns out +for the carboxilate because it has + + align:start position:0% +for the carboxilate because it has + + + align:start position:0% +for the carboxilate because it has +already a negative charge the ability to + + align:start position:0% +already a negative charge the ability to + + + align:start position:0% +already a negative charge the ability to +adopt this resonance is greatly + + align:start position:0% +adopt this resonance is greatly + + + align:start position:0% +adopt this resonance is greatly +increased so it's very well resonance + + align:start position:0% +increased so it's very well resonance + + + align:start position:0% +increased so it's very well resonance +stabilized the ability to to form these + + align:start position:0% +stabilized the ability to to form these + + + align:start position:0% +stabilized the ability to to form these +resonance structures it's also great for + + align:start position:0% +resonance structures it's also great for + + + align:start position:0% +resonance structures it's also great for +amides and this dictates the the + + align:start position:0% +amides and this dictates the the + + + align:start position:0% +amides and this dictates the the +chemistry and biochemistry of the Ami + + align:start position:0% +chemistry and biochemistry of the Ami + + + align:start position:0% +chemistry and biochemistry of the Ami +bond which is explored in more greater + + align:start position:0% +bond which is explored in more greater + + + align:start position:0% +bond which is explored in more greater +detail when we talk about + + align:start position:0% +detail when we talk about + + + align:start position:0% +detail when we talk about +protein Esters can also + + align:start position:0% +protein Esters can also + + + align:start position:0% +protein Esters can also +do and adopt this resonance + + align:start position:0% +do and adopt this resonance + + + align:start position:0% +do and adopt this resonance +structures however thioesters because + + align:start position:0% +structures however thioesters because + + + align:start position:0% +structures however thioesters because +the sulfur is a third row element so the + + align:start position:0% +the sulfur is a third row element so the + + + align:start position:0% +the sulfur is a third row element so the +P orbitals of sufur are much bigger they + + align:start position:0% +P orbitals of sufur are much bigger they + + + align:start position:0% +P orbitals of sufur are much bigger they +don't overlap very well with the p + + align:start position:0% +don't overlap very well with the p + + + align:start position:0% +don't overlap very well with the p +orbitals of the carbon + + align:start position:0% +orbitals of the carbon + + + align:start position:0% +orbitals of the carbon +ability to to adopt these resonance + + align:start position:0% +ability to to adopt these resonance + + + align:start position:0% +ability to to adopt these resonance +structures is greatly diminished + + align:start position:0% +structures is greatly diminished + + + align:start position:0% +structures is greatly diminished +therefore + + align:start position:0% +therefore + + + align:start position:0% +therefore +pesters uh behave a lot more like + + align:start position:0% +pesters uh behave a lot more like + + + align:start position:0% +pesters uh behave a lot more like +ketones where the electrons of the + + align:start position:0% +ketones where the electrons of the + + + align:start position:0% +ketones where the electrons of the +carbonal bond are localized between the + + align:start position:0% +carbonal bond are localized between the + + + align:start position:0% +carbonal bond are localized between the +carbon oxygen and not so + + align:start position:0% +carbon oxygen and not so + + + align:start position:0% +carbon oxygen and not so +much between the carbon and sulfur so + + align:start position:0% +much between the carbon and sulfur so + + + align:start position:0% +much between the carbon and sulfur so +therefore thesters are the + + align:start position:0% +therefore thesters are the + + + align:start position:0% +therefore thesters are the +least + + align:start position:0% + + + + align:start position:0% + +resonance and this is the + + align:start position:0% +resonance and this is the + + + align:start position:0% +resonance and this is the +trend and this and inversely correlates + + align:start position:0% +trend and this and inversely correlates + + + align:start position:0% +trend and this and inversely correlates +with the + + align:start position:0% +with the + + + align:start position:0% +with the +reactivity carboxilate are least + + align:start position:0% +reactivity carboxilate are least + + + align:start position:0% +reactivity carboxilate are least +reactive whereas testers are the most + + align:start position:0% + + + + align:start position:0% + +reactive now when we talk about ASO + + align:start position:0% + + + + align:start position:0% + +transfer we talk about the reaction + + align:start position:0% +transfer we talk about the reaction + + + align:start position:0% +transfer we talk about the reaction +between an asil derivative with another + + align:start position:0% +between an asil derivative with another + + + align:start position:0% +between an asil derivative with another +nucleophile which will replace the X + + align:start position:0% +nucleophile which will replace the X + + + align:start position:0% +nucleophile which will replace the X +header atom with the Y heter atom so + + align:start position:0% +header atom with the Y heter atom so + + + align:start position:0% +header atom with the Y heter atom so +this + + align:start position:0% +this + + + align:start position:0% +this +reaction always occurs via a tetrahedral + + align:start position:0% +reaction always occurs via a tetrahedral + + + align:start position:0% +reaction always occurs via a tetrahedral +intermediate when both + + align:start position:0% +intermediate when both + + + align:start position:0% +intermediate when both +substituents are attached to the + + align:start position:0% +substituents are attached to the + + + align:start position:0% +substituents are attached to the +carbon now from here this tetri + + align:start position:0% +carbon now from here this tetri + + + align:start position:0% +carbon now from here this tetri +intermediate can fall apart by kicking + + align:start position:0% +intermediate can fall apart by kicking + + + align:start position:0% +intermediate can fall apart by kicking +off the yr to regenerate the starting + + align:start position:0% +off the yr to regenerate the starting + + + align:start position:0% +off the yr to regenerate the starting +material or it can kick off the XR group + + align:start position:0% +material or it can kick off the XR group + + + align:start position:0% +material or it can kick off the XR group +to generate a new a + + align:start position:0% + + + + align:start position:0% + +derivative let's now talk about the Clon + + align:start position:0% +derivative let's now talk about the Clon + + + align:start position:0% +derivative let's now talk about the Clon +reaction this is a very important + + align:start position:0% +reaction this is a very important + + + align:start position:0% +reaction this is a very important +reaction in Biochemistry related to the + + align:start position:0% +reaction in Biochemistry related to the + + + align:start position:0% +reaction in Biochemistry related to the +alal reaction in which we form or cleave + + align:start position:0% +alal reaction in which we form or cleave + + + align:start position:0% +alal reaction in which we form or cleave +carbon carbon + + align:start position:0% +carbon carbon + + + align:start position:0% +carbon carbon +bonds the Cleon reaction happens between + + align:start position:0% +bonds the Cleon reaction happens between + + + align:start position:0% +bonds the Cleon reaction happens between +an enolizable + + align:start position:0% +an enolizable + + + align:start position:0% +an enolizable +carbonal and an asil + + align:start position:0% +carbonal and an asil + + + align:start position:0% +carbonal and an asil +derivative let's pick in this case an + + align:start position:0% +derivative let's pick in this case an + + + align:start position:0% +derivative let's pick in this case an +Esther + + align:start position:0% +Esther + + + align:start position:0% +Esther +and during this reaction a carbon carbon + + align:start position:0% +and during this reaction a carbon carbon + + + align:start position:0% +and during this reaction a carbon carbon +bond is formed + + align:start position:0% +bond is formed + + + align:start position:0% +bond is formed +between the alpha carbon of the + + align:start position:0% +between the alpha carbon of the + + + align:start position:0% +between the alpha carbon of the +enolizable carbonal and the keto carbon + + align:start position:0% +enolizable carbonal and the keto carbon + + + align:start position:0% +enolizable carbonal and the keto carbon +of the acil + + align:start position:0% +of the acil + + + align:start position:0% +of the acil +derivative the product of the cazin + + align:start position:0% +derivative the product of the cazin + + + align:start position:0% +derivative the product of the cazin +reaction + + align:start position:0% +reaction + + + align:start position:0% +reaction +is a beta keto + + align:start position:0% +is a beta keto + + + align:start position:0% +is a beta keto +carbonal let's look at the + + align:start position:0% +carbonal let's look at the + + + align:start position:0% +carbonal let's look at the +mechanism as with all carbonal reactions + + align:start position:0% +mechanism as with all carbonal reactions + + + align:start position:0% +mechanism as with all carbonal reactions +when we form a carbon carbon Bond we + + align:start position:0% +when we form a carbon carbon Bond we + + + align:start position:0% +when we form a carbon carbon Bond we +need to form an + + align:start position:0% +need to form an + + + align:start position:0% +need to form an +enolate so this is the first + + align:start position:0% + + + + align:start position:0% + +step a base or form remove the alpha + + align:start position:0% +step a base or form remove the alpha + + + align:start position:0% +step a base or form remove the alpha +proton and form the + + align:start position:0% +proton and form the + + + align:start position:0% +proton and form the +enolate which is now poised to add to + + align:start position:0% +enolate which is now poised to add to + + + align:start position:0% +enolate which is now poised to add to +the asil derivative in an asil transfer + + align:start position:0% + + + + align:start position:0% + +reaction forming first a tedral + + align:start position:0% +reaction forming first a tedral + + + align:start position:0% +reaction forming first a tedral +intermediate + + align:start position:0% + + + + align:start position:0% + +which can spontaneously fall apart by + + align:start position:0% +which can spontaneously fall apart by + + + align:start position:0% +which can spontaneously fall apart by +eliminating the hetero atom group to + + align:start position:0% +eliminating the hetero atom group to + + + align:start position:0% +eliminating the hetero atom group to +form our beta keto carbonal + + align:start position:0% + + + + align:start position:0% + +product now in Biochemistry a preferred + + align:start position:0% +product now in Biochemistry a preferred + + + align:start position:0% +product now in Biochemistry a preferred +substrate for cazin reaction is a + + align:start position:0% +substrate for cazin reaction is a + + + align:start position:0% +substrate for cazin reaction is a +thioester one of the most common testers + + align:start position:0% +thioester one of the most common testers + + + align:start position:0% +thioester one of the most common testers +we're going to encounter in this course + + align:start position:0% +we're going to encounter in this course + + + align:start position:0% +we're going to encounter in this course +is atil COA COA or coenzyme a it's a + + align:start position:0% +is atil COA COA or coenzyme a it's a + + + align:start position:0% +is atil COA COA or coenzyme a it's a +thle that can form thesters with a lot + + align:start position:0% +thle that can form thesters with a lot + + + align:start position:0% +thle that can form thesters with a lot +of acids for example acetic acid here + + align:start position:0% +of acids for example acetic acid here + + + align:start position:0% +of acids for example acetic acid here +aetl COA can undergo a c reaction with + + align:start position:0% +aetl COA can undergo a c reaction with + + + align:start position:0% +aetl COA can undergo a c reaction with +itself and therefore acts both as a + + align:start position:0% +itself and therefore acts both as a + + + align:start position:0% +itself and therefore acts both as a +enolizable carbonal and as an asil + + align:start position:0% +enolizable carbonal and as an asil + + + align:start position:0% +enolizable carbonal and as an asil +derivative from when we were talking + + align:start position:0% +derivative from when we were talking + + + align:start position:0% +derivative from when we were talking +about testers because their limited + + align:start position:0% +about testers because their limited + + + align:start position:0% +about testers because their limited +conjugation with a + + align:start position:0% +conjugation with a + + + align:start position:0% +conjugation with a +carbonal they are very reactive and they + + align:start position:0% +carbonal they are very reactive and they + + + align:start position:0% +carbonal they are very reactive and they +allow the formation of the + + align:start position:0% + + + + align:start position:0% + +enolate here is the atil COA enolate + + align:start position:0% +enolate here is the atil COA enolate + + + align:start position:0% +enolate here is the atil COA enolate +which can react with + + align:start position:0% +which can react with + + + align:start position:0% +which can react with +another atil COA + + align:start position:0% +another atil COA + + + align:start position:0% +another atil COA +molecule and will generate a tetrahedral + + align:start position:0% +molecule and will generate a tetrahedral + + + align:start position:0% +molecule and will generate a tetrahedral +intermediate let's draw this molecule + + align:start position:0% + + + + align:start position:0% + +first which can lose one of the COA + + align:start position:0% +first which can lose one of the COA + + + align:start position:0% +first which can lose one of the COA +molecules to generate + + align:start position:0% +molecules to generate + + + align:start position:0% +molecules to generate +this beta keto + + align:start position:0% +this beta keto + + + align:start position:0% +this beta keto +thester aceto + + align:start position:0% +thester aceto + + + align:start position:0% +thester aceto +atil + + align:start position:0% +atil + + + align:start position:0% +atil +COA as we will see later in the course + + align:start position:0% +COA as we will see later in the course + + + align:start position:0% +COA as we will see later in the course +this is + + align:start position:0% +this is + + + align:start position:0% +this is +a precursor to formation of Ketone + + align:start position:0% +a precursor to formation of Ketone + + + align:start position:0% +a precursor to formation of Ketone +bodies one of the ways in which atil COA + + align:start position:0% +bodies one of the ways in which atil COA + + + align:start position:0% +bodies one of the ways in which atil COA +can be used to store energy now what is + + align:start position:0% +can be used to store energy now what is + + + align:start position:0% +can be used to store energy now what is +coenzyme + + align:start position:0% +coenzyme + + + align:start position:0% +coenzyme +a often abbreviated COA + + align:start position:0% +a often abbreviated COA + + + align:start position:0% +a often abbreviated COA +we mentioned it's a tile it's a + + align:start position:0% +we mentioned it's a tile it's a + + + align:start position:0% +we mentioned it's a tile it's a +tile that means it has an sh + + align:start position:0% +tile that means it has an sh + + + align:start position:0% +tile that means it has an sh +Group which it turns + + align:start position:0% +Group which it turns + + + align:start position:0% +Group which it turns +out is on a very long + + align:start position:0% + + + + align:start position:0% + +Linker there we go this is coenzyme a + + align:start position:0% +Linker there we go this is coenzyme a + + + align:start position:0% +Linker there we go this is coenzyme a +you might recognize this part of the + + align:start position:0% +you might recognize this part of the + + + align:start position:0% +you might recognize this part of the +molecule as being Adine bound to a ribos + + align:start position:0% +molecule as being Adine bound to a ribos + + + align:start position:0% +molecule as being Adine bound to a ribos +bound to two phosphates it's essentially + + align:start position:0% +bound to two phosphates it's essentially + + + align:start position:0% +bound to two phosphates it's essentially +ADP and but notice there's another + + align:start position:0% +ADP and but notice there's another + + + align:start position:0% +ADP and but notice there's another +phosphate at a three prime + + align:start position:0% +phosphate at a three prime + + + align:start position:0% +phosphate at a three prime +position so it's an ADP with a three + + align:start position:0% +position so it's an ADP with a three + + + align:start position:0% +position so it's an ADP with a three +prime + + align:start position:0% +prime + + + align:start position:0% +prime +phosphate this portion of the + + align:start position:0% +phosphate this portion of the + + + align:start position:0% +phosphate this portion of the +molecule if squint resembles the amino + + align:start position:0% +molecule if squint resembles the amino + + + align:start position:0% +molecule if squint resembles the amino +acid + + align:start position:0% + + + + align:start position:0% + +cysteine but without the carboxy + + align:start position:0% +cysteine but without the carboxy + + + align:start position:0% +cysteine but without the carboxy +group and this middle portion of the + + align:start position:0% +group and this middle portion of the + + + align:start position:0% +group and this middle portion of the +molecule it's something that + + align:start position:0% +molecule it's something that + + + align:start position:0% +molecule it's something that +looks uh very difficult to synthesize + + align:start position:0% +looks uh very difficult to synthesize + + + align:start position:0% +looks uh very difficult to synthesize +notice this carbon that has two methyl + + align:start position:0% +notice this carbon that has two methyl + + + align:start position:0% +notice this carbon that has two methyl +group attached and two other carbons + + align:start position:0% +group attached and two other carbons + + + align:start position:0% +group attached and two other carbons +attached to it so it's like a Tetra uh + + align:start position:0% +attached to it so it's like a Tetra uh + + + align:start position:0% +attached to it so it's like a Tetra uh +veence a carbon attached to four other + + align:start position:0% +veence a carbon attached to four other + + + align:start position:0% +veence a carbon attached to four other +carbons that's a fairly rare site in + + align:start position:0% +carbons that's a fairly rare site in + + + align:start position:0% +carbons that's a fairly rare site in +Biochemistry this portion of the + + align:start position:0% +Biochemistry this portion of the + + + align:start position:0% +Biochemistry this portion of the +molecule is called penic acid Panic acid + + align:start position:0% +molecule is called penic acid Panic acid + + + align:start position:0% +molecule is called penic acid Panic acid +is an essential + + align:start position:0% +is an essential + + + align:start position:0% +is an essential +nutrient also known as vitamin B + + align:start position:0% + + + + align:start position:0% + +5 in this video we talked about carbonal + + align:start position:0% +5 in this video we talked about carbonal + + + align:start position:0% +5 in this video we talked about carbonal +chemistry carbonal is the cble bond o + + align:start position:0% +chemistry carbonal is the cble bond o + + + align:start position:0% +chemistry carbonal is the cble bond o +and a lot of its properties are due + + align:start position:0% +and a lot of its properties are due + + + align:start position:0% +and a lot of its properties are due +to the polarizability of this Bond where + + align:start position:0% +to the polarizability of this Bond where + + + align:start position:0% +to the polarizability of this Bond where +the carbon has a partial positive charge + + align:start position:0% +the carbon has a partial positive charge + + + align:start position:0% +the carbon has a partial positive charge +and oxygen partial negative charge we + + align:start position:0% +and oxygen partial negative charge we + + + align:start position:0% +and oxygen partial negative charge we +talked about reactions symbol carbonal + + align:start position:0% +talked about reactions symbol carbonal + + + align:start position:0% +talked about reactions symbol carbonal +such as nucleophilic addition + + align:start position:0% +such as nucleophilic addition + + + align:start position:0% +such as nucleophilic addition +enolization Aldo reaction and the Alo + + align:start position:0% +enolization Aldo reaction and the Alo + + + align:start position:0% +enolization Aldo reaction and the Alo +dehydration + + align:start position:0% +dehydration + + + align:start position:0% +dehydration +and asil derivatives where the carbonat + + align:start position:0% +and asil derivatives where the carbonat + + + align:start position:0% +and asil derivatives where the carbonat +is next to a Herer atom such as oxygen + + align:start position:0% +is next to a Herer atom such as oxygen + + + align:start position:0% +is next to a Herer atom such as oxygen +nitrogen or + + align:start position:0% +nitrogen or + + + align:start position:0% +nitrogen or +sulfur and we mentioned the asil + + align:start position:0% +sulfur and we mentioned the asil + + + align:start position:0% +sulfur and we mentioned the asil +transfer reaction and the cazin + + align:start position:0% +transfer reaction and the cazin + + + align:start position:0% +transfer reaction and the cazin +reaction we saw in this video the + + align:start position:0% +reaction we saw in this video the + + + align:start position:0% +reaction we saw in this video the +nucleophilic addition where a + + align:start position:0% +nucleophilic addition where a + + + align:start position:0% +nucleophilic addition where a +nucleophile attacks the carbon of the + + align:start position:0% +nucleophile attacks the carbon of the + + + align:start position:0% +nucleophile attacks the carbon of the +carbonal to add and form a + + align:start position:0% +carbonal to add and form a + + + align:start position:0% +carbonal to add and form a +tedral + + align:start position:0% +tedral + + + align:start position:0% +tedral +product for example alcohols can add to + + align:start position:0% +product for example alcohols can add to + + + align:start position:0% +product for example alcohols can add to +carbonal to form Hemi acidil and amines + + align:start position:0% +carbonal to form Hemi acidil and amines + + + align:start position:0% +carbonal to form Hemi acidil and amines +can add to carbon to form e or shift + + align:start position:0% +can add to carbon to form e or shift + + + align:start position:0% +can add to carbon to form e or shift +bases and we reviewed that good + + align:start position:0% +bases and we reviewed that good + + + align:start position:0% +bases and we reviewed that good +nucleophiles are the ones like Alco + + align:start position:0% +nucleophiles are the ones like Alco + + + align:start position:0% +nucleophiles are the ones like Alco +oxides uh Tates amines or C minus + + align:start position:0% +oxides uh Tates amines or C minus + + + align:start position:0% +oxides uh Tates amines or C minus +enolates whereas okay nucleophiles like + + align:start position:0% +enolates whereas okay nucleophiles like + + + align:start position:0% +enolates whereas okay nucleophiles like +alcohols and thol they need to be + + align:start position:0% +alcohols and thol they need to be + + + align:start position:0% +alcohols and thol they need to be +activated first to undergo nucle + + align:start position:0% +activated first to undergo nucle + + + align:start position:0% +activated first to undergo nucle +addition we also talked about + + align:start position:0% +addition we also talked about + + + align:start position:0% +addition we also talked about +enolization the ability of a carbonal + + align:start position:0% +enolization the ability of a carbonal + + + align:start position:0% +enolization the ability of a carbonal +with an alpha hydrogen to rearrange into + + align:start position:0% +with an alpha hydrogen to rearrange into + + + align:start position:0% +with an alpha hydrogen to rearrange into +an hyd oxil uh bound to a double bond + + align:start position:0% +an hyd oxil uh bound to a double bond + + + align:start position:0% +an hyd oxil uh bound to a double bond +which we call an enol now this + + align:start position:0% +which we call an enol now this + + + align:start position:0% +which we call an enol now this +equilibrium colorization favors strongly + + align:start position:0% +equilibrium colorization favors strongly + + + align:start position:0% +equilibrium colorization favors strongly +the keto form however it does uh form to + + align:start position:0% +the keto form however it does uh form to + + + align:start position:0% +the keto form however it does uh form to +a sufficient extent to allow chemistry + + align:start position:0% +a sufficient extent to allow chemistry + + + align:start position:0% +a sufficient extent to allow chemistry +to happen for example when we remove the + + align:start position:0% +to happen for example when we remove the + + + align:start position:0% +to happen for example when we remove the +alpha hydrogen we form an annion called + + align:start position:0% +alpha hydrogen we form an annion called + + + align:start position:0% +alpha hydrogen we form an annion called +enolate which is a disguised carbon + + align:start position:0% +enolate which is a disguised carbon + + + align:start position:0% +enolate which is a disguised carbon +which is a very good + + align:start position:0% +which is a very good + + + align:start position:0% +which is a very good +nucleophile next we discuss the aldar + + align:start position:0% +nucleophile next we discuss the aldar + + + align:start position:0% +nucleophile next we discuss the aldar +reaction a very important carbon carbon + + align:start position:0% +reaction a very important carbon carbon + + + align:start position:0% +reaction a very important carbon carbon +bone Bond formation or clear reaction in + + align:start position:0% +bone Bond formation or clear reaction in + + + align:start position:0% +bone Bond formation or clear reaction in +Biochemistry this reaction happens + + align:start position:0% +Biochemistry this reaction happens + + + align:start position:0% +Biochemistry this reaction happens +between an enolizable carbonal and a + + align:start position:0% +between an enolizable carbonal and a + + + align:start position:0% +between an enolizable carbonal and a +regular + + align:start position:0% +regular + + + align:start position:0% +regular +carbonal and a new carbon carbon bond is + + align:start position:0% +carbonal and a new carbon carbon bond is + + + align:start position:0% +carbonal and a new carbon carbon bond is +formed between the alpha carbon and the + + align:start position:0% +formed between the alpha carbon and the + + + align:start position:0% +formed between the alpha carbon and the +keto carbon as shown here the mechanism + + align:start position:0% +keto carbon as shown here the mechanism + + + align:start position:0% +keto carbon as shown here the mechanism +can be both base catalyzed and acid + + align:start position:0% +can be both base catalyzed and acid + + + align:start position:0% +can be both base catalyzed and acid +catalyzed and the enzymes that catalyze + + align:start position:0% +catalyzed and the enzymes that catalyze + + + align:start position:0% +catalyzed and the enzymes that catalyze +this called + + align:start position:0% +this called + + + align:start position:0% +this called +aldolases use either a lysine and the + + align:start position:0% +aldolases use either a lysine and the + + + align:start position:0% +aldolases use either a lysine and the +active side to form first a shift base + + align:start position:0% +active side to form first a shift base + + + align:start position:0% +active side to form first a shift base +or they use a zinc in the active site to + + align:start position:0% +or they use a zinc in the active site to + + + align:start position:0% +or they use a zinc in the active site to +polarize the carbonal and allow for the + + align:start position:0% +polarize the carbonal and allow for the + + + align:start position:0% +polarize the carbonal and allow for the +enol + + align:start position:0% +enol + + + align:start position:0% +enol +formation we also saw that aldol + + align:start position:0% +formation we also saw that aldol + + + align:start position:0% +formation we also saw that aldol +products can dehydrate to form Alpha + + align:start position:0% +products can dehydrate to form Alpha + + + align:start position:0% +products can dehydrate to form Alpha +Beta and saturated carbonal the + + align:start position:0% +Beta and saturated carbonal the + + + align:start position:0% +Beta and saturated carbonal the +mechanism could be both acid and base + + align:start position:0% +mechanism could be both acid and base + + + align:start position:0% +mechanism could be both acid and base +catalyzed and involves in both cases + + align:start position:0% +catalyzed and involves in both cases + + + align:start position:0% +catalyzed and involves in both cases +formation of an + + align:start position:0% +formation of an + + + align:start position:0% +formation of an +enol next we also talked about asil + + align:start position:0% +enol next we also talked about asil + + + align:start position:0% +enol next we also talked about asil +derivatives and asil transfer as we show + + align:start position:0% +derivatives and asil transfer as we show + + + align:start position:0% +derivatives and asil transfer as we show +here the resonance + + align:start position:0% +here the resonance + + + align:start position:0% +here the resonance +in the asil derivative is is + + align:start position:0% +in the asil derivative is is + + + align:start position:0% +in the asil derivative is is +the dictates there how + + align:start position:0% +the dictates there how + + + align:start position:0% +the dictates there how +well uh they + + align:start position:0% +well uh they + + + align:start position:0% +well uh they +react carboxilate and M the most + + align:start position:0% +react carboxilate and M the most + + + align:start position:0% +react carboxilate and M the most +resonant stabilized therefore are the + + align:start position:0% +resonant stabilized therefore are the + + + align:start position:0% +resonant stabilized therefore are the +least reactive whereas Esters but + + align:start position:0% +least reactive whereas Esters but + + + align:start position:0% +least reactive whereas Esters but +especially tho Esters are the least + + align:start position:0% +especially tho Esters are the least + + + align:start position:0% +especially tho Esters are the least +resonance stabilized and therefore most + + align:start position:0% +resonance stabilized and therefore most + + + align:start position:0% +resonance stabilized and therefore most +reactive finally we discussed the cing + + align:start position:0% +reactive finally we discussed the cing + + + align:start position:0% +reactive finally we discussed the cing +reaction a reaction similar to the aldol + + align:start position:0% +reaction a reaction similar to the aldol + + + align:start position:0% +reaction a reaction similar to the aldol +between an enolizable carbonal and asil + + align:start position:0% +between an enolizable carbonal and asil + + + align:start position:0% +between an enolizable carbonal and asil +derivative which generates a beta keto + + align:start position:0% +derivative which generates a beta keto + + + align:start position:0% +derivative which generates a beta keto +carbonal we introduced estil COA a very + + align:start position:0% +carbonal we introduced estil COA a very + + + align:start position:0% +carbonal we introduced estil COA a very +important tester that can undergo cion + + align:start position:0% +important tester that can undergo cion + + + align:start position:0% +important tester that can undergo cion +reaction was itself to form aeto ail KOA + + align:start position:0% +reaction was itself to form aeto ail KOA + + + align:start position:0% +reaction was itself to form aeto ail KOA +and we also introduced the structure of + + align:start position:0% +and we also introduced the structure of + + + align:start position:0% +and we also introduced the structure of +KOA which is built uh around vitamin B5 + + align:start position:0% +KOA which is built uh around vitamin B5 + + + align:start position:0% +KOA which is built uh around vitamin B5 +an essential nutrient \ No newline at end of file diff --git a/gxU2Eo3oBPg.txt b/gxU2Eo3oBPg.txt new file mode 100644 index 0000000000000000000000000000000000000000..4d68e1aa332c4aba240e789bf897d66b9ef0e95e --- /dev/null +++ b/gxU2Eo3oBPg.txt @@ -0,0 +1,455 @@ +We are going to compare the behavior of 3 +different cache configurations on a benchmark + +program to better understand the impact of +the cache configuration on the performance + +of the benchmark. + +The first cache we will consider is a 64-line +direct mapped cache. + +The second is a 2-way set associative cache +that uses the LRU, or least recently used, + +replacement strategy, and has a total of 64 +lines. + +The third is a 4-way set associative cache +that uses the LRU replacement strategy, and + +also has a total of 64 lines. + +Note that all three caches have the same capacity +in that they can store a total of 64 words + +of data. + +In a direct mapped cache any particular memory +address maps to exactly one line in the cache. + +Let's assume that our data is 32 bits, or +4 bytes wide. + +This means that consecutive addresses are +4 bytes apart, so we treat the bottom two + +address bits as always being 00 so that our +address is on a data word boundary. + +Next, we want to determine which cache line +this particular address maps to. + +Since there are 64 lines in this cache, we +need 6 bits to select one of the 64 lines. + +These 6 bits are called the index. + +In this example, the index is 000011, so this +particular address maps to line 3 of the cache. + +The data that gets stored in the cache is +the tag portion of the address of the line + +plus the 32 bits of data. + +The tag is used for comparison when checking +if a particular address is in the cache or + +not. + +It uniquely identifies the particular memory +address. + +In addition, each cache line has a valid bit +that lets you know whether the data in the + +cache is currently valid or not. + +This is important upon startup because without +this bit there is no way to know whether the + +data in the cache is garbage or real data. + +In a 2-way set associative cache, the cache +is divided into 2 sets each with half the + +number of lines. + +So we have two sets with 32 lines each. + +Since there are only 32 lines, we now only +need a 5 bit index to select the line. + +However, any given index can map to two distinct +locations, one in each set. + +This also means that when the tag comparisons +are done, two comparisons are required, one + +per set. + +In a 4-way set associative cache, the cache +is divided into 4 sets each with 16 lines. + +The width of the index is now 4 bits to select +the cache line. + +Here, selecting a line identifies one of 4 +words as possible locations for reading or + +writing the associated data. + +This also implies that 4 tags need to be compared +when trying to read from the cache to determine + +if the desired address is stored in the cache +or not. + +The test program begins by defining a few +constants, J, A, B, and N. + +J specifies the address where the program +lives. + +A is the starting address of data region 1, +and B is the starting address of data region + +2. + +Finally, N specifies the size of the data +regions. + +Since one word consists of 4 bytes, 16 bytes +of data mean that there are 4 data elements + +per region. + +Next the assembler is told that the beginning +of the program is at address 0x1000. + +The green rectangle identifies the outer loop, +and the yellow rectangle identifies the inner + +loop of the code. + +Before entering the outer loop, a loop counter, +which is stored in register R6 is initialized + +to 1,000. + +Then each time through the outer loop, R6 +is decremented by 1 and the loop is repeated + +as long as R6 is not equal to 0. + +The outer loop also resets R0 to N each time +through the loop. + +R0 is used to hold the desired array offset. + +Since the last element of the array is stored +at location N – 4, the first step of the + +inner loop, is to decrement R0 by 4. + +R1 is then loaded with the value at address +A + N – 4 which is the address of A[3] because + +array indeces begin at 0. + +R2 is loaded with B[3]. + +As long as R0 is not equal to 0, the loop +repeats itself, each time accessing the previous + +element of each array until the first element +(index 0) is loaded. + +Then the outer loop decrements R6 and repeats +the entire thing 1000 times. + +Now that we understand the configuration of +our three caches and the behavior of our test + +benchmark, we can begin comparing the behavior +of this benchmark on the three caches. + +The first thing we want to ask ourselves is +which of the three cache configurations gets + +the highest hit ratio. + +Here we are not asked to calculate an actual +hit ratio, instead we just need to realize + +that there are 3 distinct regions of data +in this benchmark. + +The first holds the instructions, the second +holds array A, and the third holds array B. + +If we think about the addresses of each of +these regions in memory, we see that the first + +instruction is at address 0x1000. + +This will result in an index of 0 regardless +of which cache you consider, so for all three + +caches the first instruction would map to +the first line of the cache. + +Similarly the first element of arrays A and +B are at address 0x2000 and 0x3000. + +These addresses will also result in an index +of 0 regardless of which of the three caches + +you consider. + +So we see that the 1st CMOVE, A[0], and B[0] +would all map to line 0 of the cache. + +Similarly, the 2nd CMOVE whose address is +0x1004 would map to line 1 of the cache as + +would array elements A[1] and B[1]. + +This tells us that if we use the direct mapped +cache, or a 2-way set associative cache, then + +we will have cache collisions between the +instructions, and the array elements. + +Collisions in the cache imply cache misses +as we replace one piece of data with another + +in the cache. + +However, if we use a 4-way set associative +cache then each region of memory can go in + +a distinct set in the cache thus avoiding +collisions and resulting in 100% hit rate + +after the first time through the loop. + +Note that the first time through the loop +each instruction and data access will result + +in a cache miss because the data needs to +initially be brought into the cache. + +But when the loop is repeated, the data is +already there and results in cache hits. + +Now suppose that we make a minor modification +to our test program by changing B from 0x3000 + +to 0x2000. + +This means that array A and array B now refer +to same locations in memory. + +We want to determine, which of the cache's +hit rate will show a noticeable improvement + +as a result of this change. + +The difference between our original benchmark +and this modified one is that we now have + +two distinct regions of memory to access, +one for the instructions, and one for the + +data. + +This means that the 2-way set associative +cache will no longer experience collisions + +in its cache, so its hit rate will be significantly +better than with the original benchmark. + +Now suppose that we change our benchmark once +again, this time making J, A and B all equal + +to 0, and changing N to be 64. + +This means that we now have 16 elements in +our arrays instead of 4. + +It also means that the array values that we +are loading for arrays A and B are actually + +the same as the instructions of the program. + +Another way of thinking about this is that +we now only have one distinct region of memory + +being accessed. + +What we want to determine now, is the total +number of cache misses that will occur for + +each of the cache configurations. + +Let's begin by considering the direct mapped +cache. + +In the direct mapped cache, we would want +to first access the first CMOVE instruction. + +Since this instruction is not yet in the cache, +our first access is a cache miss. + +We now bring the binary equivalent of this +instruction into line 0 of our cache. + +Next, we want to access the second CMOVE instruction. + +Once again the instruction is not in our cache +so we get another cache miss. + +This results in our loading the 2nd CMOVE +instruction to line 1 of our cache. + +We continue in the same manner with the SUBC +instruction and the first LD instruction. + +Again we get cache misses for each of those +instructions and that in turn causes us to + +load those instructions into our cache. + +Now, we are ready to execute our first load +operation. + +This operation wants to load A[15] into R1. + +Because the beginning of array A is at address +0, then A[15] maps to line 15 of our cache. + +Since we have not yet loaded anything into +line 15 of our cache, this means that our + +first data access is a miss. + +We continue with the second load instruction. + +This instruction is not yet in the cache, +so we get a cache miss and then load it into + +line 4 of our cache. + +We then try to access B[15]. + +B[15] corresponds to the same piece of data +as A[15], so this data access is already in + +the cache thus resulting in a data hit for +B[15]. + +So far we have gotten 5 instruction misses, +1 data miss and 1 data hit. + +Next we need to access the BNE instruction. + +Once again we get a cache miss which results +in loading the BNE instruction into line 5 + +of our cache. + +The inner loop is now repeated with R0 = 60 +which corresponds to element 14 of the arrays. + +This time through the loop, all the instructions +are already in the cache and result in instruction + +hits. + +A[14] which maps to line 14 of our cache results +in a data miss because it is not yet present + +in our cache. + +So we bring A[14] into the cache. + +Then as before, when we try to access B[14], +we get a data hit because it corresponds to + +the same piece of data as A[14]. + +So in total, we have now seen 6 instruction +misses and 2 data misses. + +The rest of the accesses have all been hits. + +This process repeats itself with a data miss +for array element A[i], and a data hit for + +array element B[i] until we get to A[5] which +actually results in a hit because it corresponds + +to the location in memory that holds the BNE(R0, +R) instruction which is already in the cache + +at line 5. + +From then on the remaining data accesses all +result in hits. + +At this point we have completed the inner +loop and proceed to the remaining instructions + +in the outer loop. + +These instructions are the second SUBC and +the second BNE instructions. + +These correspond to the data that is in lines +6 and 7 of the cache thus resulting in hits. + +The loop then repeats itself 1000 times but +each time through all the instructions and + +all the data is in the cache so they all result +in hits. + +So the total number of misses that we get +when executing this benchmark on a direct + +mapped cache is 16. + +These are known as compulsory misses which +are misses that occur when you are first loading + +the data into your cache. + +Recall that the direct mapped cache has one +set of 64 lines in the cache. + +The 2-way set associative has 2 sets of 32 +lines each, and the 4-way set associative + +has 4 sets of 16 lines each. + +Since only 16 lines are required to fit all +the instructions and data associated with + +this benchmark, this means that effectively, +only one set will be used in the set associative + +caches, and because even in the 4-way set +associative cache there are 16 lines, that + +means that once the data is loaded into the +cache it does not need to be replaced with + +other data so after the first miss per line, +the remaining accesses in the entire benchmark + +will be hits. + +So the total number of misses in the 2-way +and 4-way set associative caches is also 16. \ No newline at end of file diff --git a/hP9FIMolHEA.txt b/hP9FIMolHEA.txt new file mode 100644 index 0000000000000000000000000000000000000000..e751410a6675a78afe1ba7b53a0139bec5c65daa --- /dev/null +++ b/hP9FIMolHEA.txt @@ -0,0 +1,531 @@ +[MUSIC PLAYING] + +REAZUL AHSAN: I am +Dr. Reazul Ahsan, + +a visiting scholar of MIT UTM +Malaysian sustainable city + +program. + +I am presenting two stories +of development induced + +displacement in Malaysia. + +One follows up with communities +affected by a hydroelectric dam + +in East Malaysia. + +The other addresses an ongoing +housing development project + +on the southern tip +of peninsula Malaysia. + +Malaysia is one of the world's +fastest developing nations. + +Under its own militia program, +the government [INAUDIBLE] + +be a developed country by 2025. + +Accordingly, federal +and state governments + +are intensively investing in +infrastructure development, + +especially in housing, energy, +and manufacturing sectors. + +However, many national +infrastructure development + +programs fail to +consider indigenous + +poor and marginalized +communities, who + +have very limited voice in +planning these mega projects. + +From 1980 to 1990, +almost 10 million people + +were displaced in South Asia +due to development projects, + +like hydroelectric dams. + +The process known as +development induced displacement + +remains a global challenge +for socially sustainable + +development planning. + +Sarawak, one of two +Malaysian estates + +on the island of Borneo, +is a real example + +of development +induced displacement + +due to hydroelectric dams. + +Sarawak is home to +2.37 million people, + +and its 27 indigenous +ethnic communities + +speak 45 different languages. + +In Malaya, these indigenous +groups are known as Orang Asli. + +Beginning IN the year 1994, +the Sarawak's government + +initiated the second largest +hydroelectric dam in Asia. + +In the name of region +wide economic development, + +the dam inundated +1,700 hectares of land + +in the interior zone +of Bakun, and displaced + +more than 10,000 Orang Asli +from their home and their land. + +To learn more about those +displaced communities, + +I journeyed to Bakun. + +These displaced +indigenous communities + +have been relocated +next to the Bintulu City + +on land allocated by the +government, which is now + +known as Village [INAUDIBLE] +Before the resettlement, + +indigenous communities +harvested their everyday needs + +from river and forest in Bakun. + +But this new location +is far from their source + +of livelihood. + +Every week many +displaced villagers + +make a long journey +to Bakun to fish + +and get their food +from the forest. + +Their government appointed +village leader, Mr. [INAUDIBLE] + +said, that it was a +completely new life for them + +after displacement. + +To him, the new home was a +jungle far away from the river + +essential to their livelihood. + +SPEAKER: It's very +totally new to our people. + +It's totally new. + +Because they are used +to the way of life. + +They're used to the +way of-- how they + +do living in the old place. + +So when we moved +to this new place, + +so can see that all the +area here is jungle. + +REAZUL AHSAN: As a +part of the relocation, + +they also claimed compensation +from the government. + +SPEAKER: There is Bakun +Development Committee, BDC. + +So we have a thick book that +we pass to the government + +so that they can study about +our land, how much do they + +compensate for +land, and how much + +do they compensate for +the garden, rubber, paper, + +and so on. + +And what about our house? + +And how are you going +to compensate the house? + +REAZUL AHSAN: However, +the compensation + +wasn't enough to start fresh +in their resettlement location. + +SPEAKER: It's [INAUDIBLE] +for this, because they + +are using the government rate. + +REAZUL AHSAN: I helped +team group discussions + +with men and women in +the indigenous community + +to understand the +challenges they + +faced since their relocation. + +[INAUDIBLE] interviews +say the greatest challenge + +at the relocation site +was, insufficient access + +to land to sustain them. + +At least one member +of every family + +travels back to the dam areas +for the daily intake needs, + +two hours there from +the new location. + +This travel is costly, and also +raises their daily living cost. + +To compensate, some have +started living semi-permanently + +in the dam area, collecting +food under compromised living + +condition, while their families +remain in the new settlement + +areas. + +[INAUDIBLE] is one of +the indigenous people who + +moved to the dam area to +minimize her family's living + +costs, and harvest the +food from the rivers. + +SPEAKER: Half an hour +from here to their house. + +REAZUL AHSAN: Back in +the settlement area, + +some elders feel +isolated and have + +no bond with the community +since becoming displaced. + +[INAUDIBLE] Is one of them. + +SPEAKER: [NON-ENGLISH SPEECH] + +REAZUL AHSAN: After being +displaced for 16 years, + +the villagers now settle +into normal daily routines, + +but they're still struggling to +subsist only on the new lands, + +and improve condition +for the next generations. + +On the southernmost tip +of peninsula Malaysia, + +and ongoing story of +development induced displacement + +is unfolding. + +Iskander Malaysia, it is an +old development authority + +in the state of Johor, is aiming +to house three million people + +by 2025. + +One of the region's +largest new housing + +projects Country +Garden in Danga Bay + +is being built in a variety +of [INAUDIBLE] coastal areas + +between two rivers. + +Within an aim to accommodate +about 9000 new residents, + +Country Garden is +an eviction threat + +for the indigenous people +living in Danga Bay area + +for hundreds of years. + +The project pushed them to +the edge of the developing + +boundary, and left no +other options for them + +but to displace. + +Mr. [INAUDIBLE], director +of Iskander Malaysia, + +knows about the indigenous +history of Danga Bay. + +SPEAKER: [INAUDIBLE] is also +where we have the fisherman + +relation and we have the +indigenous group, which call + +[INAUDIBLE]. + +The British used +call them sea gypsy. + +REAZUL AHSAN: In the +questions of land right, + +[INAUDIBLE] says. + +SPEAKER: It's not enough to +get [INAUDIBLE] So whether they + +like it or not, it's +just a matter of time. + +This will have to relocated +to [INAUDIBLE] the area. + +REAZUL AHSAN: I asked him what +alternatives are available. + +SPEAKER: The land there itself, +is belong to third parties. + +So we only got two choice, +is that [INAUDIBLE] the area, + +or we have to relocate +them to other area. + +Is not that easy for us to +[INAUDIBLE] It's a growing + +community, and maybe +for start, 100 , + +150 families is sufficient +for to say there. + +But not as the community +grow double or triple, + +we still have the [INAUDIBLE]. + +We also need to be realistic. + +We're not talking about +50 years ago, [INAUDIBLE] + +ago, where we have abundant +of land on seafront. + +REAZUL AHSAN: Indigenous +community leader [INAUDIBLE] + +also says land right +and displacement + +are longstanding issues. + +SPEAKER: [NON-ENGLISH SPEECH] + +REAZUL AHSAN: To his community, +the Country Garden project + +was unexpected. + +SPEAKER: [NON-ENGLSIH] + +REAZUL AHSAN: They protested, +and reported the land + +occupation to the police. + +SPEAKER: [NON-ENGLISH SPEECH] + +REAZUL AHSAN: Mr. +[INAUDIBLE] a leader + +among local fishermen, +also suffered + +due to the reclamation process. + +SPEAKER: [NON-ENGLISH SPEECH] + +REAZUL AHSAN: According to Dr. +Colin G. Nicholas, director + +of Center for Orang Asli +Concern, in Malaysia, + +resettlement or +relocation can never + +be a solution for displaced +indigenous communities. + +COLIN NICHOLAS: This +first thing that + +happens in the resettlement +scheme is you break down + +the social structure. + +Indigenous peoples are +not interested in land, + +they are interested in +their traditional land + +and their culture. + +REAZUL AHSAN: Across the +river from Danga Bay, + +Iskander Development Authority +has produced an ecotourism + +development plan for +Kompang [? Sona ?] + +Melayu, a village for +traditional Malay people, + +known as Bumiputras. + +However, the authority has no +corresponding development plan + +for the indigenous +village in Danga Bay. + +Incorporating this community +into Kompang [? Sona ?] Melayu + +plan, could prevent +its displacement, + +and protect its indigenous +culture and tradition. + +The village currently operates +a Cultural Heritage Center, + +which villagers believe could +be a launchpad for a similarly + +ecotourism development strategy. + +Recognizing the inevitability +of development and displacement, + +communities often +have generated ideas + +about how to mitigate +the social impacts. + +Engaging in +participatory planning + +with the indigenous +community could + +sustain the land, +livelihood, and culture + +for them, and for the +following generations. + +Thank you. + +[MUSIC PLAYING] \ No newline at end of file diff --git a/hWtSvemuN0Y.txt b/hWtSvemuN0Y.txt new file mode 100644 index 0000000000000000000000000000000000000000..44dbcee1b06a04f992e85037065edf3d95e0dddf --- /dev/null +++ b/hWtSvemuN0Y.txt @@ -0,0 +1,13328 @@ +align:start position:0% + +the following content is provided by mit + + align:start position:0% +the following content is provided by mit + + + align:start position:0% +the following content is provided by mit +opencourseware under a creative commons + + align:start position:0% +opencourseware under a creative commons + + + align:start position:0% +opencourseware under a creative commons +license + + align:start position:0% +license + + + align:start position:0% +license +additional information about our license + + align:start position:0% +additional information about our license + + + align:start position:0% +additional information about our license +and mit opencourseware in general is + + align:start position:0% +and mit opencourseware in general is + + + align:start position:0% +and mit opencourseware in general is +available at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay we're getting ready and let's go + + align:start position:0% +okay we're getting ready and let's go + + + align:start position:0% +okay we're getting ready and let's go +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +welcome to the first class of + + align:start position:0% +welcome to the first class of + + + align:start position:0% +welcome to the first class of +bio e101 or biophysics 101 or hst 508 or + + align:start position:0% +bio e101 or biophysics 101 or hst 508 or + + + align:start position:0% +bio e101 or biophysics 101 or hst 508 or +genetics 224 + + align:start position:0% +genetics 224 + + + align:start position:0% +genetics 224 +you you can see that this is a + + align:start position:0% +you you can see that this is a + + + align:start position:0% +you you can see that this is a +truly interdisciplinary class and i hope + + align:start position:0% +truly interdisciplinary class and i hope + + + align:start position:0% +truly interdisciplinary class and i hope +that's going to be one of its + + align:start position:0% +that's going to be one of its + + + 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align:start position:0% +going at uh noon +over in the cannon room or you have the + + align:start position:0% +over in the cannon room or you have the + + + align:start position:0% +over in the cannon room or you have the +option of tuning into the video which is + + align:start position:0% +option of tuning into the video which is + + + align:start position:0% +option of tuning into the video which is +which is intended mainly for the + + align:start position:0% +which is intended mainly for the + + + align:start position:0% +which is intended mainly for the +distance education students but it also + + align:start position:0% +distance education students but it also + + + align:start position:0% +distance education students but it also +serves as a backup in case one of you + + align:start position:0% +serves as a backup in case one of you + + + align:start position:0% +serves as a backup in case one of you +gets sick or out of town or something + + align:start position:0% +gets sick 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align:start position:0% +she was a teaching fellow last year and + + + align:start position:0% +she was a teaching fellow last year and +many of these + + align:start position:0% +many of these + + + align:start position:0% +many of these +almost all of these teaching fellows + + align:start position:0% +almost all of these teaching fellows + + + align:start position:0% +almost all of these teaching fellows +have taken this course + + align:start position:0% +have taken this course + + + align:start position:0% +have taken this course +last year + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that's most of the + + align:start position:0% +that's most of the + + + align:start position:0% +that's most of the +bureaucratic uh aspects of it unless + + align:start position:0% +bureaucratic uh aspects of it unless + + + align:start position:0% +bureaucratic uh aspects of it unless +there are some questions + + align:start position:0% +there are some questions + + + align:start position:0% +there are some questions +please feel free to interrupt at any + + align:start position:0% +please feel free to interrupt at any + + + align:start position:0% +please feel free to interrupt at any +time this + + align:start position:0% +time this + + + align:start position:0% +time this +can be + + align:start position:0% +can be + + + align:start position:0% +can be +interactive if you if you want it to be + + align:start position:0% +interactive if you if you want it to be + + + align:start position:0% +interactive if you if you want it to be +i can set aside enough time for that + + align:start position:0% +i can set aside enough time for that + + + align:start position:0% +i can set aside enough time for that +uh you're certainly also welcome to come + + align:start position:0% +uh you're certainly also welcome to come + + + align:start position:0% +uh you're certainly also welcome to 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will be a schedule of all + + align:start position:0% +sessions there will be a schedule of all + + + align:start position:0% +sessions there will be a schedule of all +the sections + + align:start position:0% +the sections + + + align:start position:0% +the sections +um + + align:start position:0% +um + + + align:start position:0% +um +evolving on the on the website within + + align:start position:0% +evolving on the on the website within + + + align:start position:0% +evolving on the on the website within +the next day or two depending on what + + align:start position:0% +the next day or two depending on what + + + align:start position:0% +the next day or two depending on what +your questionnaires show up uh there + + align:start position:0% +your questionnaires show up uh there + + + align:start position:0% +your questionnaires show up uh there +will probably be three or four extra + + align:start position:0% +will probably be three or four extra + + + align:start position:0% +will probably be three or four extra +sections within the first couple of + + align:start position:0% +sections within the first couple of + + + align:start position:0% +sections within the first couple of +weeks + + align:start position:0% + + + + align:start position:0% + +you will sign through your your uh + + align:start position:0% +you will sign through your your uh + + + align:start position:0% +you will sign through your your uh +section head if you put your your email + + align:start position:0% +section head if you put your your email + + + align:start position:0% +section head if you put your your email +address uh will allow the section head + + align:start position:0% +address uh will allow the section head + + + align:start position:0% +address uh will allow the section head +teaching fellow to contact you + + align:start position:0% +teaching fellow to contact you + + + align:start position:0% +teaching fellow to contact you +uh or you can contact any of them if you + + align:start position:0% +uh or you can contact any of them if you + + + align:start position:0% +uh or you can contact any of them if you +don't if no one contacts you + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the overview for the course + + align:start position:0% +so the overview for the course + + + align:start position:0% +so the overview for the course +this is + + align:start position:0% + + + + align:start position:0% + +constrained to fit into the calendar of + + align:start position:0% +constrained to fit into the calendar of + + + align:start position:0% +constrained to fit into the calendar of +both harvard and mit + + align:start position:0% +both harvard and mit + + + align:start position:0% +both harvard and mit +it also tries to achieve the goal of + + align:start position:0% +it also tries to achieve the goal of + + + align:start position:0% +it also tries to achieve the goal of +keeping the division of continuing + + align:start position:0% +keeping the division of continuing + + + align:start position:0% +keeping the division of continuing +education students so they only have to + + align:start position:0% +education students so they only have to + + + align:start position:0% +education students so they only have to +come in + + align:start position:0% +come in + + + align:start position:0% +come in +for one day a week + + align:start position:0% +for one day a week + + + align:start position:0% +for one day a week +which is a considerable + + align:start position:0% +which is a considerable + + + align:start position:0% +which is a considerable +plus section some of them choose to have + + align:start position:0% +plus section some of them choose to have + + + align:start position:0% +plus section some of them choose to have +section on same day + + align:start position:0% +section on same day + + + align:start position:0% +section on same day +and so some of them have commun + + align:start position:0% +and so some of them have commun + + + align:start position:0% +and so some of them have commun +considerable commute so that's basic + + align:start position:0% +considerable commute so that's basic + + + align:start position:0% +considerable commute so that's basic +determines the the timing of this + + align:start position:0% +determines the the timing of this + + + align:start position:0% +determines the the timing of this +the topics will have two introductory + + align:start position:0% +the topics will have two introductory + + + align:start position:0% +the topics will have two introductory +lectures which actually cover pretty + + align:start position:0% +lectures which actually cover pretty + + + align:start position:0% +lectures which actually cover pretty +pretty interesting topics for + + align:start position:0% +pretty interesting topics for + + + align:start position:0% +pretty interesting topics for +introductory uh + + align:start position:0% +introductory uh + + + align:start position:0% +introductory uh +thematically one on computing followed + + align:start position:0% +thematically one on computing followed + + + align:start position:0% +thematically one on computing followed +by one on biology although both of them + + align:start position:0% +by one on biology although both of them + + + align:start position:0% +by one on biology although both of them +and the whole course is on computational + + align:start position:0% +and the whole course is on computational + + + align:start position:0% +and the whole course is on computational +biology and systems biology + + align:start position:0% +biology and systems biology + + + align:start position:0% +biology and systems biology +then as just a sort of another way of + + align:start position:0% +then as just a sort of another way of + + + align:start position:0% +then as just a sort of another way of +focusing we'll have a series of six + + align:start position:0% +focusing we'll have a series of six + + + align:start position:0% +focusing we'll have a series of six +lectures two on dna two on rna and two + + align:start position:0% +lectures two on dna two on rna and two + + + align:start position:0% +lectures two on dna two on rna and two +on proteins or proteomics + + align:start position:0% +on proteins or proteomics + + + align:start position:0% +on proteins or proteomics +which reflects the central dogma like + + align:start position:0% +which reflects the central dogma like + + + align:start position:0% +which reflects the central dogma like +the biology where dna encodes rna which + + align:start position:0% +the biology where dna encodes rna which + + + align:start position:0% +the biology where dna encodes rna which +encodes proteins but much more so it's + + align:start position:0% +encodes proteins but much more so it's + + + align:start position:0% +encodes proteins but much more so it's +telling us about the 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which are on +everyone's + + align:start position:0% +everyone's + + + align:start position:0% +everyone's +attention right now + + align:start position:0% +attention right now + + + align:start position:0% +attention right now +then finally three + + align:start position:0% +then finally three + + + align:start position:0% +then finally three +topics + + align:start position:0% +topics + + + align:start position:0% +topics +on the which which really focus on the + + align:start position:0% +on the which which really focus on the + + + align:start position:0% +on the which which really focus on the +overarching theme of the whole course + + align:start position:0% +overarching theme of the whole course + + + align:start position:0% +overarching theme of the whole course +which is on networks and systems biology + + align:start position:0% +which is on networks and systems biology + + + align:start position:0% +which is on networks and systems biology +uh + + align:start position:0% +uh 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align:start position:0% +uh material problem sets and so forth + + + align:start position:0% +uh material problem sets and so forth +and incorporate it into your uh + + align:start position:0% +and incorporate it into your uh + + + align:start position:0% +and incorporate it into your uh +view of what's exciting and pres and + + align:start position:0% +view of what's exciting and pres and + + + align:start position:0% +view of what's exciting and pres and +then present to all of us + + align:start position:0% +then present to all of us + + + align:start position:0% +then present to all of us +that information as team or individual + + align:start position:0% +that information as team or individual + + + align:start position:0% +that information as team or individual +presentations + + align:start position:0% +presentations + + + align:start position:0% +presentations +okay that's the overview for the whole + + align:start position:0% +okay that's the overview for the whole + + + align:start position:0% +okay that's the overview for the whole +course + + align:start position:0% + + + + align:start position:0% + +today's + + align:start position:0% +today's + + + align:start position:0% +today's +story i try to make this somewhat + + align:start position:0% + + + + align:start position:0% + +narrative and and with themes + + align:start position:0% +narrative and and with themes + + + align:start position:0% +narrative and and with themes +so + + align:start position:0% +so + + + align:start position:0% +so +we're going to + + align:start position:0% +we're going to + + + align:start position:0% +we're going to +toggle back and forth throughout the + + align:start position:0% +toggle back and forth throughout the + + + align:start position:0% +toggle back and forth throughout the +lecture + + align:start position:0% +lecture + + + align:start position:0% +lecture +on + + align:start position:0% +on + + + align:start position:0% +on +living systems and computational systems + + align:start position:0% +living systems and computational systems + + + align:start position:0% +living systems and computational systems +similarities differences how we can use + + align:start position:0% +similarities differences how we can use + + + align:start position:0% +similarities differences how we can use +one to tell us something about the other + + align:start position:0% +one to tell us something about the other + + + align:start position:0% +one to tell us something about the other +in particular we'll focus in on an + + align:start position:0% +in particular we'll focus in on an + + + align:start position:0% +in particular we'll focus in on an +aspect of of living systems which is + + align:start position:0% +aspect of of living systems which is + + + align:start position:0% +aspect of of living systems which is +fairly unique + + align:start position:0% +fairly unique + + + align:start position:0% +fairly unique +which is self-assembly and replication + + align:start position:0% +which is self-assembly and replication + + + align:start position:0% +which is self-assembly and replication +these are + + align:start position:0% +these are + + + align:start position:0% +these are +put in the context of another theme for + + align:start position:0% +put in the context of another theme for + + + align:start position:0% +put in the context of another theme for +today which is discrete versus + + align:start position:0% +today which is discrete versus + + + align:start position:0% +today which is discrete versus +continuous data discrete versus + + align:start position:0% +continuous data discrete versus + + + align:start position:0% +continuous data discrete versus +continuous modeling of data + + align:start position:0% +continuous modeling of data + + + align:start position:0% +continuous modeling of data +since this is an introductory lecture + + align:start position:0% +since this is an introductory lecture + + + align:start position:0% +since this is an introductory lecture +and we want to get you warmed up i'm + + align:start position:0% +and we want to get you warmed up i'm + + + align:start position:0% +and we want to get you warmed up i'm +going to try to illustrate as much as + + align:start position:0% +going to try to illustrate as much as + + + align:start position:0% +going to try to illustrate as much as +possible with minimal examples small + + align:start position:0% +possible with minimal examples small + + + align:start position:0% +possible with minimal examples small +exam small examples so you can kind of + + align:start position:0% +exam small examples so you can kind of + + + align:start position:0% +exam small examples so you can kind of +see it all on one page or all in one + + align:start position:0% +see it all on one page or all in one + + + align:start position:0% +see it all on one page or all in one +line even + + align:start position:0% +line even + + + align:start position:0% +line even +examples of minimal life + + align:start position:0% +examples of minimal life + + + align:start position:0% +examples of minimal life +things that illustrate the minimal + + align:start position:0% +things that illustrate the minimal + + + align:start position:0% +things that illustrate the minimal +aspects of life replication mainly and + + align:start position:0% +aspects of life replication mainly and + + + align:start position:0% +aspects of life replication mainly and +minimal programs which allow us to + + align:start position:0% +minimal programs which allow us to + + + align:start position:0% +minimal programs which allow us to +analyze some key aspects of modeling + + align:start position:0% +analyze some key aspects of modeling + + + align:start position:0% +analyze some key aspects of modeling +living systems + + align:start position:0% +living systems + + + align:start position:0% +living systems +some of those key aspects are catalysis + + align:start position:0% +some of those key aspects are catalysis + + + align:start position:0% +some of those key aspects are catalysis +and replication + + align:start position:0% +and replication + + + align:start position:0% +and replication +and + + align:start position:0% +and + + + align:start position:0% +and +here we'll use differential equations + + align:start position:0% +here we'll use differential equations + + + align:start position:0% +here we'll use differential equations +this will be + + align:start position:0% +this will be + + + align:start position:0% +this will be +quite + + align:start position:0% +quite + + + align:start position:0% +quite +i think an interesting approach to it + + align:start position:0% +i think an interesting approach to it + + + align:start position:0% +i think an interesting approach to it +painless + + align:start position:0% +painless + + + align:start position:0% +painless +and + + align:start position:0% +and + + + align:start position:0% +and +exciting the way it connects to biology + + align:start position:0% +exciting the way it connects to biology + + + align:start position:0% +exciting the way it connects to biology +and then after + + align:start position:0% +and then after + + + align:start position:0% +and then after +talking about that + + align:start position:0% + + + + align:start position:0% + +replication in the context of + + align:start position:0% +replication in the context of + + + align:start position:0% +replication in the context of +differential equations we'll introduce + + align:start position:0% +differential equations we'll introduce + + + align:start position:0% +differential equations we'll introduce +directed graphs which indicate how + + align:start position:0% +directed graphs which indicate how + + + align:start position:0% +directed graphs which indicate how +growth occurs in a pedigree not just + + align:start position:0% +growth occurs in a pedigree not just + + + align:start position:0% +growth occurs in a pedigree not just +growth in exponential mode + + align:start position:0% +growth in exponential mode + + + align:start position:0% +growth in exponential mode +and then uh + + align:start position:0% +and then uh + + + align:start position:0% +and then uh +finally we'll connect this to + + align:start position:0% +finally we'll connect this to + + + align:start position:0% +finally we'll connect this to +the the issues that surround single + + align:start position:0% +the the issues that surround single + + + align:start position:0% +the the issues that surround single +molecules which are actually very + + align:start position:0% +molecules which are actually very + + + align:start position:0% +molecules which are actually very +significant + + align:start position:0% +significant + + + align:start position:0% +significant +in biological systems and involve a + + align:start position:0% +in biological systems and involve a + + + align:start position:0% +in biological systems and involve a +different type of analysis than this + + align:start position:0% +different type of analysis than this + + + align:start position:0% +different type of analysis than this +sort of continuous functions that we + + align:start position:0% +sort of continuous functions that we + + + align:start position:0% +sort of continuous functions that we +will use in ordinary differential + + align:start position:0% +will use in ordinary differential + + + align:start position:0% +will use in ordinary differential +equations + + align:start position:0% + + + + align:start position:0% + +when we analyze errors + + align:start position:0% +when we analyze errors + + + align:start position:0% +when we analyze errors +either in data + + align:start position:0% +either in data + + + align:start position:0% +either in data +or + + align:start position:0% +or + + + align:start position:0% +or +or variants in biological populations we + + align:start position:0% +or variants in biological populations we + + + align:start position:0% +or variants in biological populations we +use statistics broadly speaking that + + align:start position:0% +use statistics broadly speaking that + + + align:start position:0% +use statistics broadly speaking that +fall under velcro statistics actually + + align:start position:0% +fall under velcro statistics actually + + + align:start position:0% +fall under velcro statistics actually +more than that and overall the entire + + align:start position:0% +more than that and overall the entire + + + align:start position:0% +more than that and overall the entire +uh final the theme that unites + + align:start position:0% +uh final the theme that unites + + + align:start position:0% +uh final the theme that unites +all of biology and most of the course in + + align:start position:0% +all of biology and most of the course in + + + align:start position:0% +all of biology and most of the course in +this lecture in particular + + align:start position:0% +this lecture in particular + + + align:start position:0% +this lecture in particular +is uh the idea that many of these + + align:start position:0% + + + + align:start position:0% + +functions in biological systems can be + + align:start position:0% +functions in biological systems can be + + + align:start position:0% +functions in biological systems can be +under selection + + align:start position:0% +under selection + + + align:start position:0% +under selection +experimental selection in the laboratory + + align:start position:0% +experimental selection in the laboratory + + + align:start position:0% +experimental selection in the laboratory +in order to obtain + + align:start position:0% +in order to obtain + + + align:start position:0% +in order to obtain +an optimal + + align:start position:0% +an optimal + + + align:start position:0% +an optimal +growth rate or some other aspect of + + align:start position:0% +growth rate or some other aspect of + + + align:start position:0% +growth rate or some other aspect of +optimality you generally will will do + + align:start position:0% +optimality you generally will will do + + + align:start position:0% +optimality you generally will will do +well in betting that a biological system + + align:start position:0% +well in betting that a biological system + + + align:start position:0% +well in betting that a biological system +either is optimal or can be made optimal + + align:start position:0% +either is optimal or can be made optimal + + + align:start position:0% +either is optimal or can be made optimal +for a particular task + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% +now + + + align:start position:0% +now +i'm just poking fun at the at the + + align:start position:0% +i'm just poking fun at the at the + + + align:start position:0% +i'm just poking fun at the at the +number for this course it is also + + align:start position:0% +number for this course it is also + + + align:start position:0% +number for this course it is also +an intrinsically uh important symbol for + + align:start position:0% +an intrinsically uh important symbol for + + + align:start position:0% +an intrinsically uh important symbol for +the zeros and ones that occur in all of + + align:start position:0% +the zeros and ones that occur in all of + + + align:start position:0% +the zeros and ones that occur in all of +our computers and under underlie + + align:start position:0% +our computers and under underlie + + + align:start position:0% +our computers and under underlie +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +the way we just we either deal with + + align:start position:0% +the way we just we either deal with + + + align:start position:0% +the way we just we either deal with +discrete data or make continuous data + + align:start position:0% +discrete data or make continuous data + + + align:start position:0% +discrete data or make continuous data +appear to be discrete we'll start with + + align:start position:0% +appear to be discrete we'll start with + + + align:start position:0% +appear to be discrete we'll start with +the most + + align:start position:0% +the most + + + align:start position:0% +the most +the biological + + align:start position:0% +the biological + + + align:start position:0% +the biological +entities most similar to the zeros and + + align:start position:0% +entities most similar to the zeros and + + + align:start position:0% +entities most similar to the zeros and +ones that make the + + align:start position:0% +ones that make the + + + align:start position:0% +ones that make the +your computer's hum + + align:start position:0% +your computer's hum + + + align:start position:0% +your computer's hum +and these are the + + align:start position:0% +and these are the + + + align:start position:0% +and these are the +nucleotides of dna and rna ac g and t or + + align:start position:0% +nucleotides of dna and rna ac g and t or + + + align:start position:0% +nucleotides of dna and rna ac g and t or +acg and u in the case of rna and you can + + align:start position:0% +acg and u in the case of rna and you can + + + align:start position:0% +acg and u in the case of rna and you can +even these are of course all of this is + + align:start position:0% +even these are of course all of this is + + + align:start position:0% +even these are of course all of this is +symbols right the the a's stand for + + align:start position:0% +symbols right the the a's stand for + + + align:start position:0% +symbols right the the a's stand for +adenine and adenine of course doesn't + + align:start position:0% +adenine and adenine of course doesn't + + + align:start position:0% +adenine and adenine of course doesn't +look like an a it looks like some + + align:start position:0% +look like an a it looks like some + + + align:start position:0% +look like an a it looks like some +electron density and we often represent + + align:start position:0% +electron density and we often represent + + + align:start position:0% +electron density and we often represent +it with chemical formula you'll see in + + align:start position:0% +it with chemical formula you'll see in + + + align:start position:0% +it with chemical formula you'll see in +subsequent slides + + align:start position:0% +subsequent slides + + + align:start position:0% +subsequent slides +but here in slide five we're talking + + align:start position:0% +but here in slide five we're talking + + + align:start position:0% +but here in slide five we're talking +about + + align:start position:0% + + + + align:start position:0% + +schematically + + align:start position:0% +schematically + + + align:start position:0% +schematically +a c g and t being rep a being + + align:start position:0% +a c g and t being rep a being + + + align:start position:0% +a c g and t being rep a being +represented by the two digit + + align:start position:0% +represented by the two digit + + + align:start position:0% +represented by the two digit +binary number zero zero and c zero one + + align:start position:0% +binary number zero zero and c zero one + + + align:start position:0% +binary number zero zero and c zero one +and one zero and one one + + align:start position:0% +and one zero and one one + + + align:start position:0% +and one zero and one one +so you can see that two bits + + align:start position:0% +so you can see that two bits + + + align:start position:0% +so you can see that two bits +two digits and + + align:start position:0% +two digits and + + + align:start position:0% +two digits and +isn't quite enough to encode + + align:start position:0% +isn't quite enough to encode + + + align:start position:0% +isn't quite enough to encode +the four + + align:start position:0% +the four + + + align:start position:0% +the four +nucleotides which are strung together or + + align:start position:0% +nucleotides which are strung together or + + + align:start position:0% +nucleotides which are strung together or +you might have + + align:start position:0% +you might have + + + align:start position:0% +you might have +three billion such nucleotides making up + + align:start position:0% +three billion such nucleotides making up + + + align:start position:0% +three billion such nucleotides making up +one of your two human genomes + + align:start position:0% +one of your two human genomes + + + align:start position:0% +one of your two human genomes +now things get a little bit more + + align:start position:0% +now things get a little bit more + + + align:start position:0% +now things get a little bit more +complicated once this + + align:start position:0% +complicated once this + + + align:start position:0% +complicated once this +digital + + align:start position:0% +digital + + + align:start position:0% +digital +uh three billion nucleotides in your + + align:start position:0% +uh three billion nucleotides in your + + + align:start position:0% +uh three billion nucleotides in your +genome + + align:start position:0% +genome + + + align:start position:0% +genome +starts uh + + align:start position:0% +starts uh + + + align:start position:0% +starts uh +being turned into molecules that + + align:start position:0% +being turned into molecules that + + + align:start position:0% +being turned into molecules that +actually do the work of the cell the + + align:start position:0% +actually do the work of the cell the + + + align:start position:0% +actually do the work of the cell the +work of your body which is rna and + + align:start position:0% +work of your body which is rna and + + + align:start position:0% +work of your body which is rna and +proteins this is an example of one of + + align:start position:0% +proteins this is an example of one of + + + align:start position:0% +proteins this is an example of one of +the primary transcripts here + + align:start position:0% +the primary transcripts here + + + align:start position:0% +the primary transcripts here +common to all living organisms that we + + align:start position:0% +common to all living organisms that we + + + align:start position:0% +common to all living organisms that we +know of this is a transfer rna + + align:start position:0% +know of this is a transfer rna + + + align:start position:0% +know of this is a transfer rna +i actually participated in this in + + align:start position:0% +i actually participated in this in + + + align:start position:0% +i actually participated in this in +solving this complicated structure + + align:start position:0% +solving this complicated structure + + + align:start position:0% +solving this complicated structure +and the 70s + + align:start position:0% +and the 70s + + + align:start position:0% +and the 70s +and this is color-coded the dna sequence + + align:start position:0% +and this is color-coded the dna sequence + + + align:start position:0% +and this is color-coded the dna sequence +that encodes + + align:start position:0% +that encodes + + + align:start position:0% +that encodes +this particular rna + + align:start position:0% +this particular rna + + + align:start position:0% +this particular rna +and when the rna is made it folds up + + align:start position:0% +and when the rna is made it folds up + + + align:start position:0% +and when the rna is made it folds up +into this three-dimensional structure + + align:start position:0% +into this three-dimensional structure + + + align:start position:0% +into this three-dimensional structure +which you see rotating here this is + + align:start position:0% +which you see rotating here this is + + + align:start position:0% +which you see rotating here this is +actually a stereo image which if you + + align:start position:0% +actually a stereo image which if you + + + align:start position:0% +actually a stereo image which if you +cross your eyes in the right way will + + align:start position:0% +cross your eyes in the right way will + + + align:start position:0% +cross your eyes in the right way will +appear to be even more three-dimensional + + align:start position:0% +appear to be even more three-dimensional + + + align:start position:0% +appear to be even more three-dimensional +than it is there + + align:start position:0% +than it is there + + + align:start position:0% +than it is there +you will learn more about this later in + + align:start position:0% +you will learn more about this later in + + + align:start position:0% +you will learn more about this later in +the course + + align:start position:0% +the course + + + align:start position:0% +the course +if you don't know already but the point + + align:start position:0% +if you don't know already but the point + + + align:start position:0% +if you don't know already but the point +is that the + + align:start position:0% +is that the + + + align:start position:0% +is that the +this goes from a five prime ended blue + + align:start position:0% +this goes from a five prime ended blue + + + align:start position:0% +this goes from a five prime ended blue +all the way out to the three prime end + + align:start position:0% +all the way out to the three prime end + + + align:start position:0% +all the way out to the three prime end +in red + + align:start position:0% +in red + + + align:start position:0% +in red +and it has to fold in this manner it + + align:start position:0% +and it has to fold in this manner it + + + align:start position:0% +and it has to fold in this manner it +reproducibly folds in this manner and + + align:start position:0% +reproducibly folds in this manner and + + + align:start position:0% +reproducibly folds in this manner and +has to stay + + align:start position:0% + + + + align:start position:0% + +in order to perform its function which + + align:start position:0% +in order to perform its function which + + + align:start position:0% +in order to perform its function which +is which is actually translating from + + align:start position:0% +is which is actually translating from + + + align:start position:0% +is which is actually translating from +dna sorry from rna sequences into + + align:start position:0% +dna sorry from rna sequences into + + + align:start position:0% +dna sorry from rna sequences into +protein + + align:start position:0% +protein + + + align:start position:0% +protein +but what we're illustrating here is the + + align:start position:0% +but what we're illustrating here is the + + + align:start position:0% +but what we're illustrating here is the +relationship between this discrete + + align:start position:0% +relationship between this discrete + + + align:start position:0% +relationship between this discrete +binary binary uh + + align:start position:0% +binary binary uh + + + align:start position:0% +binary binary uh +sort of digital code and dna and the + + align:start position:0% +sort of digital code and dna and the + + + align:start position:0% +sort of digital code and dna and the +more uh + + align:start position:0% +more uh + + + align:start position:0% +more uh +continuous + + align:start position:0% +continuous + + + align:start position:0% +continuous +uh + + align:start position:0% + + + + align:start position:0% + +code that you have which is the x y and + + align:start position:0% +code that you have which is the x y and + + + align:start position:0% +code that you have which is the x y and +z coordinates of the atoms the + + align:start position:0% +z coordinates of the atoms the + + + align:start position:0% +z coordinates of the atoms the +continuous nature of the probability + + align:start position:0% +continuous nature of the probability + + + align:start position:0% +continuous nature of the probability +distribution of electrons in each around + + align:start position:0% +distribution of electrons in each around + + + align:start position:0% +distribution of electrons in each around +each of those atoms + + align:start position:0% +each of those atoms + + + align:start position:0% +each of those atoms +and + + align:start position:0% +and + + + align:start position:0% +and +the continuous nature of its position in + + align:start position:0% +the continuous nature of its position in + + + align:start position:0% +the continuous nature of its position in +space and its various uh binding + + align:start position:0% +space and its various uh binding + + + align:start position:0% +space and its various uh binding +constants + + align:start position:0% +constants + + + align:start position:0% +constants +affinities for other molecules in the + + align:start position:0% +affinities for other molecules in the + + + align:start position:0% +affinities for other molecules in the +cell and let me just take those two + + align:start position:0% +cell and let me just take those two + + + align:start position:0% +cell and let me just take those two +examples the dna sequence and the + + align:start position:0% +examples the dna sequence and the + + + align:start position:0% +examples the dna sequence and the +three-dimensional structure for the + + align:start position:0% +three-dimensional structure for the + + + align:start position:0% +three-dimensional structure for the +transfer rna that it encodes + + align:start position:0% +transfer rna that it encodes + + + align:start position:0% +transfer rna that it encodes +and expand upon them a little bit + + align:start position:0% +and expand upon them a little bit + + + align:start position:0% +and expand upon them a little bit +or + + align:start position:0% +or + + + align:start position:0% +or +give other examples we have + + align:start position:0% +give other examples we have + + + align:start position:0% +give other examples we have +a sequence + + align:start position:0% +a sequence + + + align:start position:0% +a sequence +the previous slide showed a sequence of + + align:start position:0% +the previous slide showed a sequence of + + + align:start position:0% +the previous slide showed a sequence of +76 nucleotides + + align:start position:0% +76 nucleotides + + + align:start position:0% +76 nucleotides +what on the left hand side are examples + + align:start position:0% +what on the left hand side are examples + + + align:start position:0% +what on the left hand side are examples +of discrete concepts concepts which are + + align:start position:0% +of discrete concepts concepts which are + + + align:start position:0% +of discrete concepts concepts which are +very naturally encoded in in a discrete + + align:start position:0% +very naturally encoded in in a discrete + + + align:start position:0% +very naturally encoded in in a discrete +digital way and then + + align:start position:0% +digital way and then + + + align:start position:0% +digital way and then +as close as we can get to the continuous + + align:start position:0% +as close as we can get to the continuous + + + align:start position:0% +as close as we can get to the continuous +version of that + + align:start position:0% +version of that + + + align:start position:0% +version of that +so a continuous version of a sequence + + align:start position:0% +so a continuous version of a sequence + + + align:start position:0% +so a continuous version of a sequence +might be + + align:start position:0% +might be + + + align:start position:0% +might be +a probability + + align:start position:0% +a probability + + + align:start position:0% +a probability +of a sequence in other words at the + + align:start position:0% +of a sequence in other words at the + + + align:start position:0% +of a sequence in other words at the +first position if you look at a + + align:start position:0% +first position if you look at a + + + align:start position:0% +first position if you look at a +population of sequences a number of + + align:start position:0% +population of sequences a number of + + + align:start position:0% +population of sequences a number of +different trnas a number of different + + align:start position:0% +different trnas a number of different + + + align:start position:0% +different trnas a number of different +people in this room it may not be that + + align:start position:0% +people in this room it may not be that + + + align:start position:0% +people in this room it may not be that +there's always an a at position one it + + align:start position:0% +there's always an a at position one it + + + align:start position:0% +there's always an a at position one it +could be that it's uh got a different + + align:start position:0% +could be that it's uh got a different + + + align:start position:0% +could be that it's uh got a different +probability in different people so you + + align:start position:0% +probability in different people so you + + + align:start position:0% +probability in different people so you +represent that as a + + align:start position:0% +represent that as a + + + align:start position:0% +represent that as a +a probability a c g and t + + align:start position:0% +a probability a c g and t + + + align:start position:0% +a probability a c g and t +it's a vector with four uh numbers in it + + align:start position:0% +it's a vector with four uh numbers in it + + + align:start position:0% +it's a vector with four uh numbers in it +that's more continuous + + align:start position:0% +that's more continuous + + + align:start position:0% +that's more continuous +the + + align:start position:0% +the + + + align:start position:0% +the +similar we have digital analog devices + + align:start position:0% +similar we have digital analog devices + + + align:start position:0% +similar we have digital analog devices +in the instruments you will be that + + align:start position:0% +in the instruments you will be that + + + align:start position:0% +in the instruments you will be that +collect the data that you'll be working + + align:start position:0% +collect the data that you'll be working + + + align:start position:0% +collect the data that you'll be working +with in this course + + align:start position:0% +with in this course + + + align:start position:0% +with in this course +we have integration can be represented + + align:start position:0% +we have integration can be represented + + + align:start position:0% +we have integration can be represented +as practically speaking as a sum of + + align:start position:0% +as practically speaking as a sum of + + + align:start position:0% +as practically speaking as a sum of +little of small steps + + align:start position:0% +little of small steps + + + align:start position:0% +little of small steps +when we're talking about + + align:start position:0% + + + + align:start position:0% + +say a + + align:start position:0% +say a + + + align:start position:0% +say a +neural network that's responsible for + + align:start position:0% +neural network that's responsible for + + + align:start position:0% +neural network that's responsible for +some of your thoughts + + align:start position:0% +some of your thoughts + + + align:start position:0% +some of your thoughts +and uh or regulatory network that causes + + align:start position:0% +and uh or regulatory network that causes + + + align:start position:0% +and uh or regulatory network that causes +homeostasis in your body + + align:start position:0% +homeostasis in your body + + + align:start position:0% +homeostasis in your body +we ca biologists casually often reflect + + align:start position:0% +we ca biologists casually often reflect + + + align:start position:0% +we ca biologists casually often reflect +on these as being on and off it's a good + + align:start position:0% +on these as being on and off it's a good + + + align:start position:0% +on these as being on and off it's a good +approximation it allows you to make very + + align:start position:0% +approximation it allows you to make very + + + align:start position:0% +approximation it allows you to make very +simple diagrams but you must remember + + align:start position:0% +simple diagrams but you must remember + + + align:start position:0% +simple diagrams but you must remember +that many of these + + align:start position:0% +that many of these + + + align:start position:0% +that many of these +actually composed of gradients or graded + + align:start position:0% +actually composed of gradients or graded + + + align:start position:0% +actually composed of gradients or graded +responses + + align:start position:0% +responses + + + align:start position:0% +responses +not necessarily all or on off some of + + align:start position:0% +not necessarily all or on off some of + + + align:start position:0% +not necessarily all or on off some of +these gradients or graded responses have + + align:start position:0% +these gradients or graded responses have + + + align:start position:0% +these gradients or graded responses have +this sort of sigmoid shape that i've + + align:start position:0% +this sort of sigmoid shape that i've + + + align:start position:0% +this sort of sigmoid shape that i've +drawn as an icon down the middle of this + + align:start position:0% +drawn as an icon down the middle of this + + + align:start position:0% +drawn as an icon down the middle of this +separating the discrete from the + + align:start position:0% +separating the discrete from the + + + align:start position:0% +separating the discrete from the +continuous + + align:start position:0% +continuous + + + align:start position:0% +continuous +and so for all intensive purposes things + + align:start position:0% +and so for all intensive purposes things + + + align:start position:0% +and so for all intensive purposes things +tend to hang out either off here at the + + align:start position:0% +tend to hang out either off here at the + + + align:start position:0% +tend to hang out either off here at the +bottom or on at the top of the + + align:start position:0% +bottom or on at the top of the + + + align:start position:0% +bottom or on at the top of the +concentration + + align:start position:0% + + + + align:start position:0% + +limits or the signal limits if the + + align:start position:0% +limits or the signal limits if the + + + align:start position:0% +limits or the signal limits if the +signal was a + + align:start position:0% +signal was a + + + align:start position:0% +signal was a +electrical or so forth + + align:start position:0% +electrical or so forth + + + align:start position:0% +electrical or so forth +similarly we'll have examples where some + + align:start position:0% +similarly we'll have examples where some + + + align:start position:0% +similarly we'll have examples where some +cells will be they'll be have a field of + + align:start position:0% +cells will be they'll be have a field of + + + align:start position:0% +cells will be they'll be have a field of +cells which are either + + align:start position:0% +cells which are either + + + align:start position:0% +cells which are either +on or off effectively very extreme ends + + align:start position:0% +on or off effectively very extreme ends + + + align:start position:0% +on or off effectively very extreme ends +of this but because there's a mixture of + + align:start position:0% +of this but because there's a mixture of + + + align:start position:0% +of this but because there's a mixture of +them if you were to mush them up and + + align:start position:0% +them if you were to mush them up and + + + align:start position:0% +them if you were to mush them up and +measure + + align:start position:0% +measure + + + align:start position:0% +measure +some property of them it would appear to + + align:start position:0% +some property of them it would appear to + + + align:start position:0% +some property of them it would appear to +be somewhere intermediate so this is an + + align:start position:0% +be somewhere intermediate so this is an + + + align:start position:0% +be somewhere intermediate so this is an +alarm that should be going off every + + align:start position:0% +alarm that should be going off every + + + align:start position:0% +alarm that should be going off every +time you see mixtures that they may be + + align:start position:0% +time you see mixtures that they may be + + + align:start position:0% +time you see mixtures that they may be +composed of + + align:start position:0% +composed of + + + align:start position:0% +composed of +you may need to model it you may have to + + align:start position:0% +you may need to model it you may have to + + + align:start position:0% +you may need to model it you may have to +model it as a + + align:start position:0% +model it as a + + + align:start position:0% +model it as a +population + + align:start position:0% +population + + + align:start position:0% +population +each individual behaving either as uh as + + align:start position:0% +each individual behaving either as uh as + + + align:start position:0% +each individual behaving either as uh as +more extreme than the average + + align:start position:0% +more extreme than the average + + + align:start position:0% +more extreme than the average +with very few in the middle + + align:start position:0% +with very few in the middle + + + align:start position:0% +with very few in the middle +similarly with mutations so you might + + align:start position:0% +similarly with mutations so you might + + + align:start position:0% +similarly with mutations so you might +say that certain mutations are essential + + align:start position:0% +say that certain mutations are essential + + + align:start position:0% +say that certain mutations are essential +for life others are neutral they have no + + align:start position:0% +for life others are neutral they have no + + + align:start position:0% +for life others are neutral they have no +effect + + align:start position:0% +effect + + + align:start position:0% +effect +others + + align:start position:0% +others + + + align:start position:0% +others +more sort of moral gray zone are + + align:start position:0% +more sort of moral gray zone are + + + align:start position:0% +more sort of moral gray zone are +conditional + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +just a point of orientation + + align:start position:0% +just a point of orientation + + + align:start position:0% +just a point of orientation +for how we can describe not only the the + + align:start position:0% +for how we can describe not only the the + + + align:start position:0% +for how we can describe not only the the +bits the discrete or digital components + + align:start position:0% +bits the discrete or digital components + + + align:start position:0% +bits the discrete or digital components +of this course + + align:start position:0% +of this course + + + align:start position:0% +of this course +but uh but also many of these prefixes + + align:start position:0% +but uh but also many of these prefixes + + + align:start position:0% +but uh but also many of these prefixes +are useful for describing the continuous + + align:start position:0% +are useful for describing the continuous + + + align:start position:0% +are useful for describing the continuous +uh as well + + align:start position:0% +uh as well + + + align:start position:0% +uh as well +but you can see there's there's a this + + align:start position:0% +but you can see there's there's a this + + + align:start position:0% +but you can see there's there's a this +is a + + align:start position:0% +is a + + + align:start position:0% +is a +many of you will be familiar with these + + align:start position:0% +many of you will be familiar with these + + + align:start position:0% +many of you will be familiar with these +that all of you i'm sure have + + align:start position:0% +that all of you i'm sure have + + + align:start position:0% +that all of you i'm sure have +access to computers and so you've used + + align:start position:0% +access to computers and so you've used + + + align:start position:0% +access to computers and so you've used +terms like kilobyte megabyte and + + align:start position:0% +terms like kilobyte megabyte and + + + align:start position:0% +terms like kilobyte megabyte and +gigabyte um + + align:start position:0% +gigabyte um + + + align:start position:0% +gigabyte um +technically uh + + align:start position:0% +technically uh + + + align:start position:0% +technically uh +ten uh two to the tenth power is a + + align:start position:0% +ten uh two to the tenth power is a + + + align:start position:0% +ten uh two to the tenth power is a +thousand and twenty four not a thousand + + align:start position:0% +thousand and twenty four not a thousand + + + align:start position:0% +thousand and twenty four not a thousand +and so it shouldn't be referred to as + + align:start position:0% +and so it shouldn't be referred to as + + + align:start position:0% +and so it shouldn't be referred to as +kilo but for most intensive purposes + + align:start position:0% +kilo but for most intensive purposes + + + align:start position:0% +kilo but for most intensive purposes +these are so close + + align:start position:0% +these are so close + + + align:start position:0% +these are so close +to a thousand or a million or a billion + + align:start position:0% +to a thousand or a million or a billion + + + align:start position:0% +to a thousand or a million or a billion +that it's uh they're used + + align:start position:0% +that it's uh they're used + + + align:start position:0% +that it's uh they're used +interchangeably but this is the official + + align:start position:0% +interchangeably but this is the official + + + align:start position:0% +interchangeably but this is the official +standard here + + align:start position:0% +standard here + + + align:start position:0% +standard here +and for certainly for the continuous + + align:start position:0% + + + + align:start position:0% + +numbers that we'll be talking about + + align:start position:0% + + + + align:start position:0% + +this is the the order we'll have is is + + align:start position:0% +this is the the order we'll have is is + + + align:start position:0% +this is the the order we'll have is is +ten to the plus three would be kilo ten + + align:start position:0% +ten to the plus three would be kilo ten + + + align:start position:0% +ten to the plus three would be kilo ten +to the minus three will be milli like + + align:start position:0% +to the minus three will be milli like + + + align:start position:0% +to the minus three will be milli like +milliliter milliliters um mega micro + + align:start position:0% +milliliter milliliters um mega micro + + + align:start position:0% +milliliter milliliters um mega micro +giga nano + + align:start position:0% +giga nano + + + align:start position:0% +giga nano +and so on all the way up uh sort of + + align:start position:0% +and so on all the way up uh sort of + + + align:start position:0% +and so on all the way up uh sort of +numbers at atomol is getting uh zepta + + align:start position:0% +numbers at atomol is getting uh zepta + + + align:start position:0% +numbers at atomol is getting uh zepta +moles getting close to the limit of + + align:start position:0% +moles getting close to the limit of + + + align:start position:0% +moles getting close to the limit of +where you're getting close to single + + align:start position:0% +where you're getting close to single + + + align:start position:0% +where you're getting close to single +molecules + + align:start position:0% +molecules + + + align:start position:0% +molecules +petabyte is getting close to the limit + + align:start position:0% +petabyte is getting close to the limit + + + align:start position:0% +petabyte is getting close to the limit +of where your computers can go right now + + align:start position:0% + + + + align:start position:0% + +why is it important to have defined + + align:start position:0% +why is it important to have defined + + + align:start position:0% +why is it important to have defined +quantitative measures why can't we just + + align:start position:0% +quantitative measures why can't we just + + + align:start position:0% +quantitative measures why can't we just +kind of casually say oh yeah it's a long + + align:start position:0% +kind of casually say oh yeah it's a long + + + align:start position:0% +kind of casually say oh yeah it's a long +time + + align:start position:0% +time + + + align:start position:0% +time +rather than seconds or it's really a + + align:start position:0% +rather than seconds or it's really a + + + align:start position:0% +rather than seconds or it's really a +long distance to + + align:start position:0% +long distance to + + + align:start position:0% +long distance to +harvard square in meters why do we have + + align:start position:0% +harvard square in meters why do we have + + + align:start position:0% +harvard square in meters why do we have +to use meters kilograms moles + + align:start position:0% +to use meters kilograms moles + + + align:start position:0% +to use meters kilograms moles +degrees kelvin candela and amperes these + + align:start position:0% +degrees kelvin candela and amperes these + + + align:start position:0% +degrees kelvin candela and amperes these +are the seven basic + + align:start position:0% +are the seven basic + + + align:start position:0% +are the seven basic +international system units + + align:start position:0% +international system units + + + align:start position:0% +international system units +from which + + align:start position:0% +from which + + + align:start position:0% +from which +most of the other units that you use in + + align:start position:0% +most of the other units that you use in + + + align:start position:0% +most of the other units that you use in +science are derived in a certain sense + + align:start position:0% +science are derived in a certain sense + + + align:start position:0% +science are derived in a certain sense +these are + + align:start position:0% +these are + + + align:start position:0% +these are +there is some interconvertibility even + + align:start position:0% +there is some interconvertibility even + + + align:start position:0% +there is some interconvertibility even +within these + + align:start position:0% +within these + + + align:start position:0% +within these +we will be talking about precision a + + align:start position:0% +we will be talking about precision a + + + align:start position:0% +we will be talking about precision a +little bit at the end of today's class + + align:start position:0% +little bit at the end of today's class + + + align:start position:0% +little bit at the end of today's class +and throughout the course + + align:start position:0% +and throughout the course + + + align:start position:0% +and throughout the course +in fact a theme today is that even + + align:start position:0% +in fact a theme today is that even + + + align:start position:0% +in fact a theme today is that even +things that are represented digitally + + align:start position:0% +things that are represented digitally + + + align:start position:0% +things that are represented digitally +are not uh + + align:start position:0% +are not uh + + + align:start position:0% +are not uh +in order to represent things digitally + + align:start position:0% +in order to represent things digitally + + + align:start position:0% +in order to represent things digitally +there are approximations that are made + + align:start position:0% +there are approximations that are made + + + align:start position:0% +there are approximations that are made +and + + align:start position:0% +and + + + align:start position:0% +and +you should always question what what + + align:start position:0% +you should always question what what + + + align:start position:0% +you should always question what what +those assumptions are that when you make + + align:start position:0% +those assumptions are that when you make + + + align:start position:0% +those assumptions are that when you make +an approximation the precision for some + + align:start position:0% +an approximation the precision for some + + + align:start position:0% +an approximation the precision for some +of these units of measure for example + + align:start position:0% +of these units of measure for example + + + align:start position:0% +of these units of measure for example +the time scale measured in seconds + + align:start position:0% +the time scale measured in seconds + + + align:start position:0% +the time scale measured in seconds +can be + + align:start position:0% +can be + + + align:start position:0% +can be +as precise as + + align:start position:0% +as precise as + + + align:start position:0% +as precise as +14 significant decimal digits + + align:start position:0% +14 significant decimal digits + + + align:start position:0% +14 significant decimal digits +now + + align:start position:0% +now + + + align:start position:0% +now +you may wonder from time to time in the + + align:start position:0% +you may wonder from time to time in the + + + align:start position:0% +you may wonder from time to time in the +course why biology doesn't have 14 + + align:start position:0% +course why biology doesn't have 14 + + + align:start position:0% +course why biology doesn't have 14 +significant figures + + align:start position:0% +significant figures + + + align:start position:0% +significant figures +i will leave that up + + align:start position:0% +i will leave that up + + + align:start position:0% +i will leave that up +as an exercise for one of your projects + + align:start position:0% +as an exercise for one of your projects + + + align:start position:0% +as an exercise for one of your projects +maybe + + align:start position:0% +maybe + + + align:start position:0% +maybe +to figure out how to get that but for + + align:start position:0% +to figure out how to get that but for + + + align:start position:0% +to figure out how to get that but for +all practical purposes most of biology + + align:start position:0% +all practical purposes most of biology + + + align:start position:0% +all practical purposes most of biology +is + + align:start position:0% +is + + + align:start position:0% +is +three or four significant + + align:start position:0% +three or four significant + + + align:start position:0% +three or four significant +figures there are quant quantum + + align:start position:0% +figures there are quant quantum + + + align:start position:0% +figures there are quant quantum +uh limits to time and length which + + align:start position:0% +uh limits to time and length which + + + align:start position:0% +uh limits to time and length which +are so short that we don't need to + + align:start position:0% +are so short that we don't need to + + + align:start position:0% +are so short that we don't need to +concern ourselves + + align:start position:0% +concern ourselves + + + align:start position:0% +concern ourselves +but the interest the quantum unit for + + align:start position:0% +but the interest the quantum unit for + + + align:start position:0% +but the interest the quantum unit for +the mole + + align:start position:0% +the mole + + + align:start position:0% +the mole +is actually of great importance to this + + align:start position:0% +is actually of great importance to this + + + align:start position:0% +is actually of great importance to this +course + + align:start position:0% +course + + + align:start position:0% +course +a mole is + + align:start position:0% +a mole is + + + align:start position:0% +a mole is +6 times 10 to the 23rd entities these + + align:start position:0% +6 times 10 to the 23rd entities these + + + align:start position:0% +6 times 10 to the 23rd entities these +entities can be photons or molecules or + + align:start position:0% +entities can be photons or molecules or + + + align:start position:0% +entities can be photons or molecules or +we even have over six times twenty to + + align:start position:0% +we even have over six times twenty to + + + align:start position:0% +we even have over six times twenty to +ten to the twenty third + + align:start position:0% +ten to the twenty third + + + align:start position:0% +ten to the twenty third +uh + + align:start position:0% +uh + + + align:start position:0% +uh +of the + + align:start position:0% +of the + + + align:start position:0% +of the +bacteria in uh in an ocean + + align:start position:0% +bacteria in uh in an ocean + + + align:start position:0% +bacteria in uh in an ocean +so + + align:start position:0% +so + + + align:start position:0% +so +what's important here is that the the + + align:start position:0% +what's important here is that the the + + + align:start position:0% +what's important here is that the the +quantum of this is the molecule and many + + align:start position:0% +quantum of this is the molecule and many + + + align:start position:0% +quantum of this is the molecule and many +of the things we'll be dealing with are + + align:start position:0% +of the things we'll be dealing with are + + + align:start position:0% +of the things we'll be dealing with are +single molecules and that'll be the + + align:start position:0% +single molecules and that'll be the + + + align:start position:0% +single molecules and that'll be the +the last topic of today's lecture will + + align:start position:0% +the last topic of today's lecture will + + + align:start position:0% +the last topic of today's lecture will +be + + align:start position:0% +be + + + align:start position:0% +be +how one uh deals with single molecules + + align:start position:0% +how one uh deals with single molecules + + + align:start position:0% +how one uh deals with single molecules +as opposed to large buckets of molecules + + align:start position:0% +as opposed to large buckets of molecules + + + align:start position:0% +as opposed to large buckets of molecules +now we have all those great + + align:start position:0% +now we have all those great + + + align:start position:0% +now we have all those great +quantitative + + align:start position:0% +quantitative + + + align:start position:0% +quantitative +definitions for all those + + align:start position:0% +definitions for all those + + + align:start position:0% +definitions for all those +standard + + align:start position:0% +standard + + + align:start position:0% +standard +units used in physics and chemistry + + align:start position:0% +units used in physics and chemistry + + + align:start position:0% +units used in physics and chemistry +and even in biology but what about the + + align:start position:0% +and even in biology but what about the + + + align:start position:0% +and even in biology but what about the +definition of biology itself + + align:start position:0% +definition of biology itself + + + align:start position:0% +definition of biology itself +many most uh biology books start with + + align:start position:0% +many most uh biology books start with + + + align:start position:0% +many most uh biology books start with +this their entire books dedicated to + + align:start position:0% +this their entire books dedicated to + + + align:start position:0% +this their entire books dedicated to +this question of what is life + + align:start position:0% +this question of what is life + + + align:start position:0% +this question of what is life +i think that + + align:start position:0% +i think that + + + align:start position:0% +i think that +rather than + + align:start position:0% +rather than + + + align:start position:0% +rather than +in this session ask what is + + align:start position:0% +in this session ask what is + + + align:start position:0% +in this session ask what is +alive or not + + align:start position:0% +alive or not + + + align:start position:0% +alive or not +rather than make it a dichotomy + + align:start position:0% +rather than make it a dichotomy + + + align:start position:0% +rather than make it a dichotomy +i'd prefer to say + + align:start position:0% +i'd prefer to say + + + align:start position:0% +i'd prefer to say +you know how alive is something what is + + align:start position:0% +you know how alive is something what is + + + align:start position:0% +you know how alive is something what is +the probability that a given entity will + + align:start position:0% +the probability that a given entity will + + + align:start position:0% +the probability that a given entity will +replicate + + align:start position:0% +replicate + + + align:start position:0% +replicate +we have here on slide 10 + + align:start position:0% +we have here on slide 10 + + + align:start position:0% +we have here on slide 10 +the probability of replication + + align:start position:0% +the probability of replication + + + align:start position:0% +the probability of replication +and not just + + align:start position:0% +and not just + + + align:start position:0% +and not just +how likely is it for + + align:start position:0% +how likely is it for + + + align:start position:0% +how likely is it for +the whole thing to replicate or some + + align:start position:0% +the whole thing to replicate or some + + + align:start position:0% +the whole thing to replicate or some +part of it to replicate but + + align:start position:0% +part of it to replicate but + + + align:start position:0% +part of it to replicate but +is it doing so using simple uh parts + + align:start position:0% +is it doing so using simple uh parts + + + align:start position:0% +is it doing so using simple uh parts +simple environmental components and + + align:start position:0% +simple environmental components and + + + align:start position:0% +simple environmental components and +creating creating great complexity from + + align:start position:0% +creating creating great complexity from + + + align:start position:0% +creating creating great complexity from +that how faithful is the replication + + align:start position:0% +that how faithful is the replication + + + align:start position:0% +that how faithful is the replication +now this probability of replication + + align:start position:0% +now this probability of replication + + + align:start position:0% +now this probability of replication +from simplicity to complexity + + align:start position:0% +from simplicity to complexity + + + align:start position:0% +from simplicity to complexity +can be defined for a specific + + align:start position:0% +can be defined for a specific + + + align:start position:0% +can be defined for a specific +environment sometimes the environment + + align:start position:0% +environment sometimes the environment + + + align:start position:0% +environment sometimes the environment +required for replication + + align:start position:0% +required for replication + + + align:start position:0% +required for replication +is of necessity very specific certain + + align:start position:0% +is of necessity very specific certain + + + align:start position:0% +is of necessity very specific certain +organisms + + align:start position:0% +organisms + + + align:start position:0% +organisms +do not do well + + align:start position:0% +do not do well + + + align:start position:0% +do not do well +except in their native environments + + align:start position:0% +except in their native environments + + + align:start position:0% +except in their native environments +zoos discover this and we keep killing + + align:start position:0% +zoos discover this and we keep killing + + + align:start position:0% +zoos discover this and we keep killing +off species for a variety of reasons one + + align:start position:0% +off species for a variety of reasons one + + + align:start position:0% +off species for a variety of reasons one +of them being this + + align:start position:0% +of them being this + + + align:start position:0% +of them being this +specificity + + align:start position:0% +specificity + + + align:start position:0% +specificity +so when we talk about so another aspect + + align:start position:0% +so when we talk about so another aspect + + + align:start position:0% +so when we talk about so another aspect +of life um + + align:start position:0% +of life um + + + align:start position:0% +of life um +which + + align:start position:0% +which + + + align:start position:0% +which +each of these in principle can be + + align:start position:0% +each of these in principle can be + + + align:start position:0% +each of these in principle can be +quantitated is how robust is it how many + + align:start position:0% +quantitated is how robust is it how many + + + align:start position:0% +quantitated is how robust is it how many +environments can it handle uh + + align:start position:0% +environments can it handle uh + + + align:start position:0% +environments can it handle uh +inevitably there are environments that + + align:start position:0% +inevitably there are environments that + + + align:start position:0% +inevitably there are environments that +cannot be handled but the the more + + align:start position:0% +cannot be handled but the the more + + + align:start position:0% +cannot be handled but the the more +robust and adaptable it is in a certain + + align:start position:0% +robust and adaptable it is in a certain + + + align:start position:0% +robust and adaptable it is in a certain +sense the more + + align:start position:0% +sense the more + + + align:start position:0% +sense the more +alive it is or the more alive it will be + + align:start position:0% +alive it is or the more alive it will be + + + align:start position:0% +alive it is or the more alive it will be +uh its descendants will be + + align:start position:0% +uh its descendants will be + + + align:start position:0% +uh its descendants will be +millions of years from now probably now + + align:start position:0% +millions of years from now probably now + + + align:start position:0% +millions of years from now probably now +some very challenging examples i list + + align:start position:0% +some very challenging examples i list + + + align:start position:0% +some very challenging examples i list +here i'm not going to walk through all + + align:start position:0% +here i'm not going to walk through all + + + align:start position:0% +here i'm not going to walk through all +of them but + + align:start position:0% +of them but + + + align:start position:0% +of them but +just + + align:start position:0% +just + + + align:start position:0% +just +the things that have challenged people's + + align:start position:0% +the things that have challenged people's + + + align:start position:0% +the things that have challenged people's +definitions of life before are mules + + align:start position:0% +definitions of life before are mules + + + align:start position:0% +definitions of life before are mules +that is to say sterile hybrids + + align:start position:0% +that is to say sterile hybrids + + + align:start position:0% +that is to say sterile hybrids +uh which will not leave behind progeny + + align:start position:0% +uh which will not leave behind progeny + + + align:start position:0% +uh which will not leave behind progeny +but or seem quite as alive as their + + align:start position:0% +but or seem quite as alive as their + + + align:start position:0% +but or seem quite as alive as their +parents were + + align:start position:0% +parents were + + + align:start position:0% +parents were +fire but will not replicate + + align:start position:0% +fire but will not replicate + + + align:start position:0% +fire but will not replicate +generally so the probability of + + align:start position:0% +generally so the probability of + + + align:start position:0% +generally so the probability of +replication is low for the entire + + align:start position:0% +replication is low for the entire + + + align:start position:0% +replication is low for the entire +organism but maybe for individual cells + + align:start position:0% +organism but maybe for individual cells + + + align:start position:0% +organism but maybe for individual cells +fires replicate quite well + + align:start position:0% +fires replicate quite well + + + align:start position:0% +fires replicate quite well +but most people would like to exclude + + align:start position:0% +but most people would like to exclude + + + align:start position:0% +but most people would like to exclude +them from this definition + + align:start position:0% +them from this definition + + + align:start position:0% +them from this definition +or perhaps + + align:start position:0% +or perhaps + + + align:start position:0% +or perhaps +if we're in the mode of not excluding + + align:start position:0% +if we're in the mode of not excluding + + + align:start position:0% +if we're in the mode of not excluding +things from life but the probability of + + align:start position:0% +things from life but the probability of + + + align:start position:0% +things from life but the probability of +replication complexity versus simplicity + + align:start position:0% +replication complexity versus simplicity + + + align:start position:0% +replication complexity versus simplicity +might impinge upon fires crystals and + + align:start position:0% +might impinge upon fires crystals and + + + align:start position:0% +might impinge upon fires crystals and +if you nucleate a super saturated + + align:start position:0% +if you nucleate a super saturated + + + align:start position:0% +if you nucleate a super saturated +solution with a crystal it will make in + + align:start position:0% +solution with a crystal it will make in + + + align:start position:0% +solution with a crystal it will make in +certain sense copies of itself how + + align:start position:0% +certain sense copies of itself how + + + align:start position:0% +certain sense copies of itself how +faithful is that + + align:start position:0% +faithful is that + + + align:start position:0% +faithful is that +how simple is it + + align:start position:0% + + + + align:start position:0% + +flowers viruses predators these require + + align:start position:0% +flowers viruses predators these require + + + align:start position:0% +flowers viruses predators these require +very complex environments they require + + align:start position:0% +very complex environments they require + + + align:start position:0% +very complex environments they require +environments often more complex than + + align:start position:0% +environments often more complex than + + + align:start position:0% +environments often more complex than +themselves in order to replicate + + align:start position:0% +themselves in order to replicate + + + align:start position:0% +themselves in order to replicate +does that make them less alive + + align:start position:0% + + + + align:start position:0% + +we will i'll show an example of + + align:start position:0% +we will i'll show an example of + + + align:start position:0% +we will i'll show an example of +molecular ligation as the simplest case + + align:start position:0% +molecular ligation as the simplest case + + + align:start position:0% +molecular ligation as the simplest case +just to get us warmed up for this + + align:start position:0% +just to get us warmed up for this + + + align:start position:0% +just to get us warmed up for this +introductory + + align:start position:0% +introductory + + + align:start position:0% +introductory +class + + align:start position:0% + + + + align:start position:0% + +we can since we're in the topic here + + align:start position:0% +we can since we're in the topic here + + + align:start position:0% +we can since we're in the topic here +briefly of general biology not just the + + align:start position:0% +briefly of general biology not just the + + + align:start position:0% +briefly of general biology not just the +historical terrestrial biology from + + align:start position:0% +historical terrestrial biology from + + + align:start position:0% +historical terrestrial biology from +which all of us feel particular affinity + + align:start position:0% +which all of us feel particular affinity + + + align:start position:0% +which all of us feel particular affinity +if we had + + align:start position:0% +if we had + + + align:start position:0% +if we had +uh visitors + + align:start position:0% +uh visitors + + + align:start position:0% +uh visitors +from uh + + align:start position:0% +from uh + + + align:start position:0% +from uh +some you know another planet or if we + + align:start position:0% +some you know another planet or if we + + + align:start position:0% +some you know another planet or if we +started making our own self-assembling + + align:start position:0% +started making our own self-assembling + + + align:start position:0% +started making our own self-assembling +machines and to some extent we have + + align:start position:0% +machines and to some extent we have + + + align:start position:0% +machines and to some extent we have +already have we already are making + + align:start position:0% +already have we already are making + + + align:start position:0% +already have we already are making +uh self-assembling machines in factories + + align:start position:0% +uh self-assembling machines in factories + + + align:start position:0% +uh self-assembling machines in factories +uh they require a very complex + + align:start position:0% +uh they require a very complex + + + align:start position:0% +uh they require a very complex +environment which includes humans but + + align:start position:0% +environment which includes humans but + + + align:start position:0% +environment which includes humans but +you know how do we define these things + + align:start position:0% +you know how do we define these things + + + align:start position:0% +you know how do we define these things +now in order to define + + align:start position:0% +now in order to define + + + align:start position:0% +now in order to define +to get at that complexity versus + + align:start position:0% +to get at that complexity versus + + + align:start position:0% +to get at that complexity versus +simplicity issue + + align:start position:0% + + + + align:start position:0% + +and faithfulness or replication we need + + align:start position:0% +and faithfulness or replication we need + + + align:start position:0% +and faithfulness or replication we need +to define both replication and + + align:start position:0% +to define both replication and + + + align:start position:0% +to define both replication and +complexity + + align:start position:0% +complexity + + + align:start position:0% +complexity +replication + + align:start position:0% +replication + + + align:start position:0% +replication +is not + + align:start position:0% + + + + align:start position:0% + +perfectly faithful in many of the things + + align:start position:0% +perfectly faithful in many of the things + + + align:start position:0% +perfectly faithful in many of the things +that you consider + + align:start position:0% +that you consider + + + align:start position:0% +that you consider +alive + + align:start position:0% +alive + + + align:start position:0% +alive +simple bacterium even though it will + + align:start position:0% +simple bacterium even though it will + + + align:start position:0% +simple bacterium even though it will +make a copy that does many of the same + + align:start position:0% +make a copy that does many of the same + + + align:start position:0% +make a copy that does many of the same +things + + align:start position:0% +things + + + align:start position:0% +things +uh we know it when we see it it looks + + align:start position:0% +uh we know it when we see it it looks + + + align:start position:0% +uh we know it when we see it it looks +like it's the same thing if you actually + + align:start position:0% +like it's the same thing if you actually + + + align:start position:0% +like it's the same thing if you actually +counted the molecules no two bacteria + + align:start position:0% +counted the molecules no two bacteria + + + align:start position:0% +counted the molecules no two bacteria +would be alike no two humans certainly + + align:start position:0% +would be alike no two humans certainly + + + align:start position:0% +would be alike no two humans certainly +are alike but even even supposedly + + align:start position:0% +are alike but even even supposedly + + + align:start position:0% +are alike but even even supposedly +genetically identical bacteria will have + + align:start position:0% +genetically identical bacteria will have + + + align:start position:0% +genetically identical bacteria will have +different numbers of proteins and small + + align:start position:0% +different numbers of proteins and small + + + align:start position:0% +different numbers of proteins and small +molecules + + align:start position:0% +molecules + + + align:start position:0% +molecules +complexity + + align:start position:0% +complexity + + + align:start position:0% +complexity +has at least four definitions we will + + align:start position:0% +has at least four definitions we will + + + align:start position:0% +has at least four definitions we will +use in this course + + align:start position:0% +use in this course + + + align:start position:0% +use in this course +there is computational complexity which + + align:start position:0% +there is computational complexity which + + + align:start position:0% +there is computational complexity which +is a practical significance in + + align:start position:0% +is a practical significance in + + + align:start position:0% +is a practical significance in +computational biology as the computer + + align:start position:0% +computational biology as the computer + + + align:start position:0% +computational biology as the computer +scientists in the room will know + + align:start position:0% +scientists in the room will know + + + align:start position:0% +scientists in the room will know +in that this tells us the speed and + + align:start position:0% +in that this tells us the speed and + + + align:start position:0% +in that this tells us the speed and +memory tradeoffs that we have in scaling + + align:start position:0% +memory tradeoffs that we have in scaling + + + align:start position:0% +memory tradeoffs that we have in scaling +up any problem does a problem + + align:start position:0% +up any problem does a problem + + + align:start position:0% +up any problem does a problem +scale up + + align:start position:0% +scale up + + + align:start position:0% +scale up +as a simple linear function of the + + align:start position:0% +as a simple linear function of the + + + align:start position:0% +as a simple linear function of the +number of inputs that you give to the + + align:start position:0% +number of inputs that you give to the + + + align:start position:0% +number of inputs that you give to the +computer does it scale up as a simple + + align:start position:0% +computer does it scale up as a simple + + + align:start position:0% +computer does it scale up as a simple +polynomial or is it worse than that is + + align:start position:0% +polynomial or is it worse than that is + + + align:start position:0% +polynomial or is it worse than that is +it exponential in behavior is it + + align:start position:0% +it exponential in behavior is it + + + align:start position:0% +it exponential in behavior is it +something that you can + + align:start position:0% +something that you can + + + align:start position:0% +something that you can +prove you got the right answer in + + align:start position:0% +prove you got the right answer in + + + align:start position:0% +prove you got the right answer in +polynomial time and so on we'll get to + + align:start position:0% +polynomial time and so on we'll get to + + + align:start position:0% +polynomial time and so on we'll get to +this later on but the i just want to + + align:start position:0% +this later on but the i just want to + + + align:start position:0% +this later on but the i just want to +introduce it as something that where the + + align:start position:0% +introduce it as something that where the + + + align:start position:0% +introduce it as something that where the +word complexity is used + + align:start position:0% +word complexity is used + + + align:start position:0% +word complexity is used +number two sounds similar but is + + align:start position:0% +number two sounds similar but is + + + align:start position:0% +number two sounds similar but is +actually some quite a bit different + + align:start position:0% +actually some quite a bit different + + + align:start position:0% +actually some quite a bit different +it's algorithmic complexity or + + align:start position:0% +it's algorithmic complexity or + + + align:start position:0% +it's algorithmic complexity or +algorithmic randomness + + align:start position:0% +algorithmic randomness + + + align:start position:0% +algorithmic randomness +and this is basically any string not + + align:start position:0% +and this is basically any string not + + + align:start position:0% +and this is basically any string not +just a computer program but a computer + + align:start position:0% +just a computer program but a computer + + + align:start position:0% +just a computer program but a computer +program will be represented as a string + + align:start position:0% +program will be represented as a string + + + align:start position:0% +program will be represented as a string +can be reduced down + + align:start position:0% +can be reduced down + + + align:start position:0% +can be reduced down +where you get rid of + + align:start position:0% +where you get rid of + + + align:start position:0% +where you get rid of +obvious redundancy and what's left is + + align:start position:0% +obvious redundancy and what's left is + + + align:start position:0% +obvious redundancy and what's left is +the randomness and the number of bits it + + align:start position:0% +the randomness and the number of bits it + + + align:start position:0% +the randomness and the number of bits it +takes to encode that algorithm is a + + align:start position:0% +takes to encode that algorithm is a + + + align:start position:0% +takes to encode that algorithm is a +reflection of the + + align:start position:0% +reflection of the + + + align:start position:0% +reflection of the +complexity uh that doesn't necessarily + + align:start position:0% +complexity uh that doesn't necessarily + + + align:start position:0% +complexity uh that doesn't necessarily +give you any predictions about how long + + align:start position:0% +give you any predictions about how long + + + align:start position:0% +give you any predictions about how long +it will run or how much memory it will + + align:start position:0% +it will run or how much memory it will + + + align:start position:0% +it will run or how much memory it will +require during computation + + align:start position:0% +require during computation + + + align:start position:0% +require during computation +entropy and information is related + + align:start position:0% +entropy and information is related + + + align:start position:0% +entropy and information is related +number three is related to item number + + align:start position:0% +number three is related to item number + + + align:start position:0% +number three is related to item number +two uh + + align:start position:0% +two uh + + + align:start position:0% +two uh +in that the more complex the string a + + align:start position:0% +in that the more complex the string a + + + align:start position:0% +in that the more complex the string a +string is just a series of symbols like + + align:start position:0% +string is just a series of symbols like + + + align:start position:0% +string is just a series of symbols like +this and we that was what we were + + align:start position:0% +this and we that was what we were + + + align:start position:0% +this and we that was what we were +talking about with a randomness the more + + align:start position:0% +talking about with a randomness the more + + + align:start position:0% +talking about with a randomness the more +complex the string or the an image can + + align:start position:0% +complex the string or the an image can + + + align:start position:0% +complex the string or the an image can +be turned into a string these are three + + align:start position:0% +be turned into a string these are three + + + align:start position:0% +be turned into a string these are three +images here + + align:start position:0% +images here + + + align:start position:0% +images here +then the more bits you need to encode it + + align:start position:0% +then the more bits you need to encode it + + + align:start position:0% +then the more bits you need to encode it +in order to say make a file you might + + align:start position:0% +in order to say make a file you might + + + align:start position:0% +in order to say make a file you might +compress the data but ultimately that + + align:start position:0% +compress the data but ultimately that + + + align:start position:0% +compress the data but ultimately that +after it's fully compressed that's the + + align:start position:0% +after it's fully compressed that's the + + + align:start position:0% +after it's fully compressed that's the +amount of information you need + + align:start position:0% +amount of information you need + + + align:start position:0% +amount of information you need +entropy is a chemical term + + align:start position:0% +entropy is a chemical term + + + align:start position:0% +entropy is a chemical term +information was chant this information + + align:start position:0% +information was chant this information + + + align:start position:0% +information was chant this information +definition was championed by uh + + align:start position:0% +definition was championed by uh + + + align:start position:0% +definition was championed by uh +shannon will come back to it and entropy + + align:start position:0% +shannon will come back to it and entropy + + + align:start position:0% +shannon will come back to it and entropy +by boltzmann and others and the fusion + + align:start position:0% +by boltzmann and others and the fusion + + + align:start position:0% +by boltzmann and others and the fusion +of these two into a a unified theme is + + align:start position:0% +of these two into a a unified theme is + + + align:start position:0% +of these two into a a unified theme is +extremely important in both chemistry + + align:start position:0% +extremely important in both chemistry + + + align:start position:0% +extremely important in both chemistry +and information theory + + align:start position:0% + + + + align:start position:0% + +nevertheless these none of these above + + align:start position:0% +nevertheless these none of these above + + + align:start position:0% +nevertheless these none of these above +reflect our intuitive feeling for when + + align:start position:0% +reflect our intuitive feeling for when + + + align:start position:0% +reflect our intuitive feeling for when +we look at these three panels + + align:start position:0% +we look at these three panels + + + align:start position:0% +we look at these three panels +we have a highly ordered + + align:start position:0% +we have a highly ordered + + + align:start position:0% +we have a highly ordered +which would be a very low entropy + + align:start position:0% +which would be a very low entropy + + + align:start position:0% +which would be a very low entropy +array + + align:start position:0% +array + + + align:start position:0% +array +on the left hand side we have on the far + + align:start position:0% +on the left hand side we have on the far + + + align:start position:0% +on the left hand side we have on the far +right hand side something highly + + align:start position:0% +right hand side something highly + + + align:start position:0% +right hand side something highly +disordered essentially random you could + + align:start position:0% +disordered essentially random you could + + + align:start position:0% +disordered essentially random you could +have this may have been generated by a + + align:start position:0% +have this may have been generated by a + + + align:start position:0% +have this may have been generated by a +coin toss where as you fill up the array + + align:start position:0% +coin toss where as you fill up the array + + + align:start position:0% +coin toss where as you fill up the array +you just say black or white + + align:start position:0% +you just say black or white + + + align:start position:0% +you just say black or white +um toss a coin + + align:start position:0% +um toss a coin + + + align:start position:0% +um toss a coin +the one in the middle + + align:start position:0% +the one in the middle + + + align:start position:0% +the one in the middle +and so in the one on the the with the + + align:start position:0% +and so in the one on the the with the + + + align:start position:0% +and so in the one on the the with the +low entropy on the left could be easily + + align:start position:0% +low entropy on the left could be easily + + + align:start position:0% +low entropy on the left could be easily +represented as 0 1 0 1 0 1 in a simple + + align:start position:0% +represented as 0 1 0 1 0 1 in a simple + + + align:start position:0% +represented as 0 1 0 1 0 1 in a simple +array very little + + align:start position:0% +array very little + + + align:start position:0% +array very little +information very little entropy + + align:start position:0% +information very little entropy + + + align:start position:0% +information very little entropy +algorithmically not very random + + align:start position:0% +algorithmically not very random + + + align:start position:0% +algorithmically not very random +at the other end though you it is it has + + align:start position:0% +at the other end though you it is it has + + + align:start position:0% +at the other end though you it is it has +high entropy high information content it + + align:start position:0% +high entropy high information content it + + + align:start position:0% +high entropy high information content it +takes a lot of bits to represent it even + + align:start position:0% +takes a lot of bits to represent it even + + + align:start position:0% +takes a lot of bits to represent it even +though you know you got it just by a + + align:start position:0% +though you know you got it just by a + + + align:start position:0% +though you know you got it just by a +coin toss + + align:start position:0% +coin toss + + + align:start position:0% +coin toss +and uh it has high algorithmic + + align:start position:0% +and uh it has high algorithmic + + + align:start position:0% +and uh it has high algorithmic +randomness + + align:start position:0% +randomness + + + align:start position:0% +randomness +you can get uh + + align:start position:0% + + + + align:start position:0% + +but if you allow a coin toss to be part + + align:start position:0% +but if you allow a coin toss to be part + + + align:start position:0% +but if you allow a coin toss to be part +of your description of the physical + + align:start position:0% +of your description of the physical + + + align:start position:0% +of your description of the physical +complexity of this uh pattern on the far + + align:start position:0% +complexity of this uh pattern on the far + + + align:start position:0% +complexity of this uh pattern on the far +right + + align:start position:0% +right + + + align:start position:0% +right +say you know a gas or something that + + align:start position:0% +say you know a gas or something that + + + align:start position:0% +say you know a gas or something that +like this generated by coin toss + + align:start position:0% +like this generated by coin toss + + + align:start position:0% +like this generated by coin toss +then you can then you can represent it + + align:start position:0% +then you can then you can represent it + + + align:start position:0% +then you can then you can represent it +uh as a + + align:start position:0% +uh as a + + + align:start position:0% +uh as a +particular kind of uh random description + + align:start position:0% +particular kind of uh random description + + + align:start position:0% +particular kind of uh random description +which so this is almost as this is about + + align:start position:0% +which so this is almost as this is about + + + align:start position:0% +which so this is almost as this is about +as easy to describe as the highly + + align:start position:0% +as easy to describe as the highly + + + align:start position:0% +as easy to describe as the highly +ordered system so even as high entropy + + align:start position:0% +ordered system so even as high entropy + + + align:start position:0% +ordered system so even as high entropy +it has low complexity and complexity + + align:start position:0% +it has low complexity and complexity + + + align:start position:0% +it has low complexity and complexity +lies somewhere in between we have lots + + align:start position:0% +lies somewhere in between we have lots + + + align:start position:0% +lies somewhere in between we have lots +of different kinds of symmetries + + align:start position:0% +of different kinds of symmetries + + + align:start position:0% +of different kinds of symmetries +lots of different uh + + align:start position:0% +lots of different uh + + + align:start position:0% +lots of different uh +scales of structures and it's very hard + + align:start position:0% +scales of structures and it's very hard + + + align:start position:0% +scales of structures and it's very hard +to represent it either as a random coin + + align:start position:0% +to represent it either as a random coin + + + align:start position:0% +to represent it either as a random coin +toss or as + + align:start position:0% +toss or as + + + align:start position:0% +toss or as +a highly ordered system + + align:start position:0% +a highly ordered system + + + align:start position:0% +a highly ordered system +how do we quantitate this + + align:start position:0% +how do we quantitate this + + + align:start position:0% +how do we quantitate this +we're really trying to + + align:start position:0% +we're really trying to + + + align:start position:0% +we're really trying to +move from the vegar definitions to + + align:start position:0% +move from the vegar definitions to + + + align:start position:0% +move from the vegar definitions to +something + + align:start position:0% +something + + + align:start position:0% +something +that really + + align:start position:0% +that really + + + align:start position:0% +that really +encompasses what we intuitively feel + + align:start position:0% +encompasses what we intuitively feel + + + align:start position:0% +encompasses what we intuitively feel +about complexity + + align:start position:0% +about complexity + + + align:start position:0% +about complexity +here's a is an example i happen to like + + align:start position:0% +here's a is an example i happen to like + + + align:start position:0% +here's a is an example i happen to like +this is i would say that this is not + + align:start position:0% +this is i would say that this is not + + + align:start position:0% +this is i would say that this is not +something that's broadly adapted but i + + align:start position:0% +something that's broadly adapted but i + + + align:start position:0% +something that's broadly adapted but i +want to expose you to it + + align:start position:0% +want to expose you to it + + + align:start position:0% +want to expose you to it +here we have entropy + + align:start position:0% +here we have entropy + + + align:start position:0% +here we have entropy +or the randomness the sort of the + + align:start position:0% +or the randomness the sort of the + + + align:start position:0% +or the randomness the sort of the +information uh shannon information on + + align:start position:0% +information uh shannon information on + + + align:start position:0% +information uh shannon information on +the horizontal axis of slide 12 + + align:start position:0% +the horizontal axis of slide 12 + + + align:start position:0% +the horizontal axis of slide 12 +where the low entropy is highly ordered + + align:start position:0% +where the low entropy is highly ordered + + + align:start position:0% +where the low entropy is highly ordered +is on the left-hand side it's zero + + align:start position:0% +is on the left-hand side it's zero + + + align:start position:0% +is on the left-hand side it's zero +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +the highly disordered + + align:start position:0% +the highly disordered + + + align:start position:0% +the highly disordered +random high entropy of one + + align:start position:0% +random high entropy of one + + + align:start position:0% +random high entropy of one +on this + + align:start position:0% +on this + + + align:start position:0% +on this +type of scale + + align:start position:0% +type of scale + + + align:start position:0% +type of scale +is on the right hand side + + align:start position:0% +is on the right hand side + + + align:start position:0% +is on the right hand side +and complexity + + align:start position:0% +and complexity + + + align:start position:0% +and complexity +uh as we said we expect does not + + align:start position:0% +uh as we said we expect does not + + + align:start position:0% +uh as we said we expect does not +correlate perfectly + + align:start position:0% +correlate perfectly + + + align:start position:0% +correlate perfectly +with + + align:start position:0% +with + + + align:start position:0% +with +information or entropy + + align:start position:0% +information or entropy + + + align:start position:0% +information or entropy +in that we can + + align:start position:0% +in that we can + + + align:start position:0% +in that we can +that this highly disordered structure on + + align:start position:0% +that this highly disordered structure on + + + align:start position:0% +that this highly disordered structure on +the right hand side is actually has very + + align:start position:0% +the right hand side is actually has very + + + align:start position:0% +the right hand side is actually has very +low complexity and complexity is not + + align:start position:0% +low complexity and complexity is not + + + align:start position:0% +low complexity and complexity is not +even a single valued function of + + align:start position:0% +even a single valued function of + + + align:start position:0% +even a single valued function of +uh entropy or + + align:start position:0% +uh entropy or + + + align:start position:0% +uh entropy or +information + + align:start position:0% +information + + + align:start position:0% +information +because you can have multiple different + + align:start position:0% +because you can have multiple different + + + align:start position:0% +because you can have multiple different +structures that have the same entropy + + align:start position:0% +structures that have the same entropy + + + align:start position:0% +structures that have the same entropy +but have different complexities that's + + align:start position:0% +but have different complexities that's + + + align:start position:0% +but have different complexities that's +what we see here when you take + + align:start position:0% +what we see here when you take + + + align:start position:0% +what we see here when you take +a slice or a line up from the horizontal + + align:start position:0% +a slice or a line up from the horizontal + + + align:start position:0% +a slice or a line up from the horizontal +axis up through the complexity + + align:start position:0% +axis up through the complexity + + + align:start position:0% +axis up through the complexity +you can have multiple + + align:start position:0% +you can have multiple + + + align:start position:0% +you can have multiple +different values in here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +that was an example of a model + + align:start position:0% + + + + align:start position:0% + +what definition + + align:start position:0% +what definition + + + align:start position:0% +what definition +the the the you you'll really have to + + align:start position:0% +the the the you you'll really have to + + + align:start position:0% +the the the you you'll really have to +refer to this article it's a fairly + + align:start position:0% +refer to this article it's a fairly + + + align:start position:0% +refer to this article it's a fairly +complicated one but the the idea here + + align:start position:0% +complicated one but the the idea here + + + align:start position:0% +complicated one but the the idea here +was you take + + align:start position:0% +was you take + + + align:start position:0% +was you take +a uh + + align:start position:0% +a uh + + + align:start position:0% +a uh +a complicate a complicated + + align:start position:0% +a complicate a complicated + + + align:start position:0% +a complicate a complicated +um + + align:start position:0% + + + + align:start position:0% + +set of data generated by a logistic map + + align:start position:0% +set of data generated by a logistic map + + + align:start position:0% +set of data generated by a logistic map +that we'll come to in just a few slides + + align:start position:0% +that we'll come to in just a few slides + + + align:start position:0% +that we'll come to in just a few slides +and you ask as you increase the + + align:start position:0% +and you ask as you increase the + + + align:start position:0% +and you ask as you increase the +complexity of the map + + align:start position:0% + + + + align:start position:0% + +in a way that + + align:start position:0% +in a way that + + + align:start position:0% +in a way that +you know appeals to the intuitive + + align:start position:0% +you know appeals to the intuitive + + + align:start position:0% +you know appeals to the intuitive +definition of complex we had in the + + align:start position:0% +definition of complex we had in the + + + align:start position:0% +definition of complex we had in the +previous one you can you you uh + + align:start position:0% +previous one you can you you uh + + + align:start position:0% +previous one you can you you uh +you calculate the the number of + + align:start position:0% +you calculate the the number of + + + align:start position:0% +you calculate the the number of +symmetries the physical symmetry that it + + align:start position:0% +symmetries the physical symmetry that it + + + align:start position:0% +symmetries the physical symmetry that it +would take to represent this allowing + + align:start position:0% +would take to represent this allowing + + + align:start position:0% +would take to represent this allowing +coin tosses as part of the algorithm for + + align:start position:0% +coin tosses as part of the algorithm for + + + align:start position:0% +coin tosses as part of the algorithm for +uh simplifying it just barred from all + + align:start position:0% +uh simplifying it just barred from all + + + align:start position:0% +uh simplifying it just barred from all +the previous definitions + + align:start position:0% +the previous definitions + + + align:start position:0% +the previous definitions +uh + + align:start position:0% +uh + + + align:start position:0% +uh +crutchfield and co-workers have have + + align:start position:0% +crutchfield and co-workers have have + + + align:start position:0% +crutchfield and co-workers have have +championed this and i would say it's not + + align:start position:0% +championed this and i would say it's not + + + align:start position:0% +championed this and i would say it's not +widely accepted but it's certainly not + + align:start position:0% +widely accepted but it's certainly not + + + align:start position:0% +widely accepted but it's certainly not +rejected either i i find it appealing + + align:start position:0% + + + + align:start position:0% + +so why do we model + + align:start position:0% +so why do we model + + + align:start position:0% +so why do we model +that was an example of modeling + + align:start position:0% +that was an example of modeling + + + align:start position:0% +that was an example of modeling +complexity we'll have uh i + + align:start position:0% +complexity we'll have uh i + + + align:start position:0% +complexity we'll have uh i +pointed out earlier that + + align:start position:0% +pointed out earlier that + + + align:start position:0% +pointed out earlier that +the models that we had for a + + align:start position:0% +the models that we had for a + + + align:start position:0% +the models that we had for a +three-dimensional structure + + align:start position:0% +three-dimensional structure + + + align:start position:0% +three-dimensional structure +this course is mainly about measurements + + align:start position:0% +this course is mainly about measurements + + + align:start position:0% +this course is mainly about measurements +so why model i would argue that most of + + align:start position:0% +so why model i would argue that most of + + + align:start position:0% +so why model i would argue that most of +the + + align:start position:0% +the + + + align:start position:0% +the +when we measure we actually must model + + align:start position:0% +when we measure we actually must model + + + align:start position:0% +when we measure we actually must model +and we need to do that not merely to + + align:start position:0% +and we need to do that not merely to + + + align:start position:0% +and we need to do that not merely to +understand the biological chemical data + + align:start position:0% +understand the biological chemical data + + + align:start position:0% +understand the biological chemical data +that we are collecting + + align:start position:0% +that we are collecting + + + align:start position:0% +that we are collecting +if i understand our we can have various + + align:start position:0% +if i understand our we can have various + + + align:start position:0% +if i understand our we can have various +tests for our understanding + + align:start position:0% +tests for our understanding + + + align:start position:0% +tests for our understanding +tests might include but not be limited + + align:start position:0% +tests might include but not be limited + + + align:start position:0% +tests might include but not be limited +to + + align:start position:0% +to + + + align:start position:0% +to +designing useful modifications of a of a + + align:start position:0% +designing useful modifications of a of a + + + align:start position:0% +designing useful modifications of a of a +system + + align:start position:0% +system + + + align:start position:0% +system +this course is mainly about systems and + + align:start position:0% +this course is mainly about systems and + + + align:start position:0% +this course is mainly about systems and +by + + align:start position:0% +by + + + align:start position:0% +by +using our models to design a new ver + + align:start position:0% +using our models to design a new ver + + + align:start position:0% +using our models to design a new ver +a new variation on the system and then + + align:start position:0% +a new variation on the system and then + + + align:start position:0% +a new variation on the system and then +obtaining additional data and modeling + + align:start position:0% +obtaining additional data and modeling + + + align:start position:0% +obtaining additional data and modeling +that new data we get a better uh + + align:start position:0% +that new data we get a better uh + + + align:start position:0% +that new data we get a better uh +successive approximation to what is what + + align:start position:0% +successive approximation to what is what + + + align:start position:0% +successive approximation to what is what +the underlying data mean + + align:start position:0% +the underlying data mean + + + align:start position:0% +the underlying data mean +and we prove it + + align:start position:0% +and we prove it + + + align:start position:0% +and we prove it +often with useful modifications that can + + align:start position:0% +often with useful modifications that can + + + align:start position:0% +often with useful modifications that can +be of have impact on society + + align:start position:0% +be of have impact on society + + + align:start position:0% +be of have impact on society +or impact on other research agenda + + align:start position:0% +or impact on other research agenda + + + align:start position:0% +or impact on other research agenda +another reason why we model is in order + + align:start position:0% +another reason why we model is in order + + + align:start position:0% +another reason why we model is in order +to share data typically when you look in + + align:start position:0% +to share data typically when you look in + + + align:start position:0% +to share data typically when you look in +a database + + align:start position:0% +a database + + + align:start position:0% +a database +those of you have looked at biological + + align:start position:0% +those of you have looked at biological + + + align:start position:0% +those of you have looked at biological +data or chemical databases that is not + + align:start position:0% +data or chemical databases that is not + + + align:start position:0% +data or chemical databases that is not +data in the database + + align:start position:0% +data in the database + + + align:start position:0% +data in the database +generally speaking it is + + align:start position:0% + + + + align:start position:0% + +there are models in there + + align:start position:0% +there are models in there + + + align:start position:0% +there are models in there +and the things that you download are + + align:start position:0% +and the things that you download are + + + align:start position:0% +and the things that you download are +models so for example the sequence that + + align:start position:0% +models so for example the sequence that + + + align:start position:0% +models so for example the sequence that +i showed at the beginning the 76 + + align:start position:0% +i showed at the beginning the 76 + + + align:start position:0% +i showed at the beginning the 76 +nucleotides of ac's g's and keys that's + + align:start position:0% +nucleotides of ac's g's and keys that's + + + align:start position:0% +nucleotides of ac's g's and keys that's +a model that represents our + + align:start position:0% +a model that represents our + + + align:start position:0% +a model that represents our +interpretation of some kind of + + align:start position:0% +interpretation of some kind of + + + align:start position:0% +interpretation of some kind of +fluorescent patterns that we see + + align:start position:0% +fluorescent patterns that we see + + + align:start position:0% +fluorescent patterns that we see +when we run our instruments on amplified + + align:start position:0% +when we run our instruments on amplified + + + align:start position:0% +when we run our instruments on amplified +dna taken from a variety of organisms + + align:start position:0% +dna taken from a variety of organisms + + + align:start position:0% +dna taken from a variety of organisms +that's + + align:start position:0% +that's + + + align:start position:0% +that's +the model + + align:start position:0% + + + + align:start position:0% + +similarly the three-dimensional rotating + + align:start position:0% +similarly the three-dimensional rotating + + + align:start position:0% +similarly the three-dimensional rotating +transfer rna that we saw was probably + + align:start position:0% +transfer rna that we saw was probably + + + align:start position:0% +transfer rna that we saw was probably +more obviously a model there + + align:start position:0% +more obviously a model there + + + align:start position:0% +more obviously a model there +the + + align:start position:0% + + + + align:start position:0% + +we integrate + + align:start position:0% +we integrate + + + align:start position:0% +we integrate +the chemistry of molecular mechanics + + align:start position:0% +the chemistry of molecular mechanics + + + align:start position:0% +the chemistry of molecular mechanics +and the + + align:start position:0% +and the + + + align:start position:0% +and the +the physics of the diffraction data + + align:start position:0% +the physics of the diffraction data + + + align:start position:0% +the physics of the diffraction data +where where the + + align:start position:0% +where where the + + + align:start position:0% +where where the +atoms the electron density and a crystal + + align:start position:0% +atoms the electron density and a crystal + + + align:start position:0% +atoms the electron density and a crystal +lattice diffract and make a pattern we + + align:start position:0% +lattice diffract and make a pattern we + + + align:start position:0% +lattice diffract and make a pattern we +integrate those models uh + + align:start position:0% +integrate those models uh + + + align:start position:0% +integrate those models uh +and and that's what's shared in + + align:start position:0% +and and that's what's shared in + + + align:start position:0% +and and that's what's shared in +databases + + align:start position:0% +databases + + + align:start position:0% +databases +not only does it allow us to share data + + align:start position:0% +not only does it allow us to share data + + + align:start position:0% +not only does it allow us to share data +but the way we share it is by searching + + align:start position:0% +but the way we share it is by searching + + + align:start position:0% +but the way we share it is by searching +those of you who have searched either + + align:start position:0% +those of you who have searched either + + + align:start position:0% +those of you who have searched either +biological databases or the internet + + align:start position:0% +biological databases or the internet + + + align:start position:0% +biological databases or the internet +with google or something like that know + + align:start position:0% +with google or something like that know + + + align:start position:0% +with google or something like that know +how powerful a search can be + + align:start position:0% +how powerful a search can be + + + align:start position:0% +how powerful a search can be +in order to typically it is easier to + + align:start position:0% +in order to typically it is easier to + + + align:start position:0% +in order to typically it is easier to +search with a model + + align:start position:0% +search with a model + + + align:start position:0% +search with a model +and more powerful and more accurate to + + align:start position:0% +and more powerful and more accurate to + + + align:start position:0% +and more powerful and more accurate to +search for the model than to search + + align:start position:0% +search for the model than to search + + + align:start position:0% +search for the model than to search +through raw data + + align:start position:0% +through raw data + + + align:start position:0% +through raw data +when we merge data sets + + align:start position:0% +when we merge data sets + + + align:start position:0% +when we merge data sets +we will align them we will + + align:start position:0% +we will align them we will + + + align:start position:0% +we will align them we will +find redundancies we will + + align:start position:0% + + + + align:start position:0% + +merge them + + align:start position:0% +merge them + + + align:start position:0% +merge them +integrate different concepts that + + align:start position:0% +integrate different concepts that + + + align:start position:0% +integrate different concepts that +requires modeling and finally checking + + align:start position:0% +requires modeling and finally checking + + + align:start position:0% +requires modeling and finally checking +data one of the themes of this course + + align:start position:0% +data one of the themes of this course + + + align:start position:0% +data one of the themes of this course +will be to + + align:start position:0% +will be to + + + align:start position:0% +will be to +embrace your outliers when you when you + + align:start position:0% +embrace your outliers when you when you + + + align:start position:0% +embrace your outliers when you when you +model your raw data or and you find uh + + align:start position:0% +model your raw data or and you find uh + + + align:start position:0% +model your raw data or and you find uh +data that are very far away from + + align:start position:0% +data that are very far away from + + + align:start position:0% +data that are very far away from +expectation this is a good thing + + align:start position:0% +expectation this is a good thing + + + align:start position:0% +expectation this is a good thing +it allows you to find errors in your + + align:start position:0% +it allows you to find errors in your + + + align:start position:0% +it allows you to find errors in your +model or errors in your data or + + align:start position:0% +model or errors in your data or + + + align:start position:0% +model or errors in your data or +discoveries + + align:start position:0% +discoveries + + + align:start position:0% +discoveries +so checking is another + + align:start position:0% +so checking is another + + + align:start position:0% +so checking is another +finally integrating as i said this + + align:start position:0% +finally integrating as i said this + + + align:start position:0% +finally integrating as i said this +course is about measures and models and + + align:start position:0% +course is about measures and models and + + + align:start position:0% +course is about measures and models and +it's not just a survey of all the things + + align:start position:0% +it's not just a survey of all the things + + + align:start position:0% +it's not just a survey of all the things +that you can do with computation and + + align:start position:0% +that you can do with computation and + + + align:start position:0% +that you can do with computation and +biology and computational biology but + + align:start position:0% +biology and computational biology but + + + align:start position:0% +biology and computational biology but +most importantly it's about integration + + align:start position:0% + + + + align:start position:0% + +how + + align:start position:0% + + + + align:start position:0% + +we need more than one data type to make + + align:start position:0% +we need more than one data type to make + + + align:start position:0% +we need more than one data type to make +progress in biology and medicine + + align:start position:0% +progress in biology and medicine + + + align:start position:0% +progress in biology and medicine +agriculture + + align:start position:0% +agriculture + + + align:start position:0% +agriculture +and integration is one of the biggest + + align:start position:0% +and integration is one of the biggest + + + align:start position:0% +and integration is one of the biggest +challenges that we have right now it's + + align:start position:0% +challenges that we have right now it's + + + align:start position:0% +challenges that we have right now it's +relatively easy to collect a single + + align:start position:0% +relatively easy to collect a single + + + align:start position:0% +relatively easy to collect a single +homogeneous data set but then to connect + + align:start position:0% +homogeneous data set but then to connect + + + align:start position:0% +homogeneous data set but then to connect +that to the rest of the world is the big + + align:start position:0% +that to the rest of the world is the big + + + align:start position:0% +that to the rest of the world is the big +challenge that all of you will have + + align:start position:0% + + + + align:start position:0% + +a theme that will go throughout the + + align:start position:0% +a theme that will go throughout the + + + align:start position:0% +a theme that will go throughout the +course + + align:start position:0% +course + + + align:start position:0% +course +will be + + align:start position:0% +will be + + + align:start position:0% +will be +this business about errors two types of + + align:start position:0% +this business about errors two types of + + + align:start position:0% +this business about errors two types of +errors random and systematic + + align:start position:0% + + + + align:start position:0% + +and every time that somebody hands you + + align:start position:0% +and every time that somebody hands you + + + align:start position:0% +and every time that somebody hands you +some data or you collect your own data + + align:start position:0% +some data or you collect your own data + + + align:start position:0% +some data or you collect your own data +or you're dealing with something from + + align:start position:0% +or you're dealing with something from + + + align:start position:0% +or you're dealing with something from +the literature you should know you + + align:start position:0% +the literature you should know you + + + align:start position:0% +the literature you should know you +should immediately assume there are both + + align:start position:0% +should immediately assume there are both + + + align:start position:0% +should immediately assume there are both +random and systematic errors you should + + align:start position:0% +random and systematic errors you should + + + align:start position:0% +random and systematic errors you should +know which is which and how much there + + align:start position:0% +know which is which and how much there + + + align:start position:0% +know which is which and how much there +is you should not accept anything + + align:start position:0% +is you should not accept anything + + + align:start position:0% +is you should not accept anything +as being true without qualification + + align:start position:0% + + + + align:start position:0% + +random errors mean that if you repeat + + align:start position:0% +random errors mean that if you repeat + + + align:start position:0% +random errors mean that if you repeat +the experiment again and again + + align:start position:0% +the experiment again and again + + + align:start position:0% +the experiment again and again +you will get complete you'll get + + align:start position:0% +you will get complete you'll get + + + align:start position:0% +you will get complete you'll get +slightly different variations on that on + + align:start position:0% +slightly different variations on that on + + + align:start position:0% +slightly different variations on that on +the error types and to a certain extent + + align:start position:0% +the error types and to a certain extent + + + align:start position:0% +the error types and to a certain extent +they will average out over enough + + align:start position:0% +they will average out over enough + + + align:start position:0% +they will average out over enough +determination systematic errors on the + + align:start position:0% +determination systematic errors on the + + + align:start position:0% +determination systematic errors on the +other hand you have a high probability + + align:start position:0% +other hand you have a high probability + + + align:start position:0% +other hand you have a high probability +of getting almost exactly the same error + + align:start position:0% +of getting almost exactly the same error + + + align:start position:0% +of getting almost exactly the same error +again and again or a very small subset + + align:start position:0% +again and again or a very small subset + + + align:start position:0% +again and again or a very small subset +of a certain class of errors + + align:start position:0% +of a certain class of errors + + + align:start position:0% +of a certain class of errors +which means that just doing it over and + + align:start position:0% +which means that just doing it over and + + + align:start position:0% +which means that just doing it over and +over will not improve your statistics or + + align:start position:0% +over will not improve your statistics or + + + align:start position:0% +over will not improve your statistics or +improve your + + align:start position:0% +improve your + + + align:start position:0% +improve your +accuracy you need to change uh paradigms + + align:start position:0% +accuracy you need to change uh paradigms + + + align:start position:0% +accuracy you need to change uh paradigms +altogether + + align:start position:0% +altogether + + + align:start position:0% +altogether +collecting data by more than one method + + align:start position:0% +collecting data by more than one method + + + align:start position:0% +collecting data by more than one method +so + + align:start position:0% +so + + + align:start position:0% +so +so those are the + + align:start position:0% +so those are the + + + align:start position:0% +so those are the +types of + + align:start position:0% +types of + + + align:start position:0% +types of +reasons that we model and now we should + + align:start position:0% +reasons that we model and now we should + + + align:start position:0% +reasons that we model and now we should +go through the kinds of models that + + align:start position:0% +go through the kinds of models that + + + align:start position:0% +go through the kinds of models that +we'll do + + align:start position:0% +we'll do + + + align:start position:0% +we'll do +this is of course it's basically on + + align:start position:0% +this is of course it's basically on + + + align:start position:0% +this is of course it's basically on +sequence how sequence leads to + + align:start position:0% +sequence how sequence leads to + + + align:start position:0% +sequence how sequence leads to +three-dimensional or even + + align:start position:0% +three-dimensional or even + + + align:start position:0% +three-dimensional or even +four-dimensional structures with time + + align:start position:0% +four-dimensional structures with time + + + align:start position:0% +four-dimensional structures with time +how three-dimensional structures lead to + + align:start position:0% +how three-dimensional structures lead to + + + align:start position:0% +how three-dimensional structures lead to +to function how function + + align:start position:0% +to function how function + + + align:start position:0% +to function how function +is embedded in system complicated + + align:start position:0% +is embedded in system complicated + + + align:start position:0% +is embedded in system complicated +systems + + align:start position:0% +systems + + + align:start position:0% +systems +so + + align:start position:0% +so + + + align:start position:0% +so +which models we will be searching + + align:start position:0% +which models we will be searching + + + align:start position:0% +which models we will be searching +merging and checking + + align:start position:0% +merging and checking + + + align:start position:0% +merging and checking +as as we said in the previous slide + + align:start position:0% +as as we said in the previous slide + + + align:start position:0% +as as we said in the previous slide +which models will sequence we will be + + align:start position:0% +which models will sequence we will be + + + align:start position:0% +which models will sequence we will be +making + + align:start position:0% +making + + + align:start position:0% +making +the assumption in dynamic programming + + align:start position:0% +the assumption in dynamic programming + + + align:start position:0% +the assumption in dynamic programming +which is just a fancy way of saying + + align:start position:0% +which is just a fancy way of saying + + + align:start position:0% +which is just a fancy way of saying +searching and aligning + + align:start position:0% +searching and aligning + + + align:start position:0% +searching and aligning +dynamic programming will make the + + align:start position:0% +dynamic programming will make the + + + align:start position:0% +dynamic programming will make the +assumption that sequences are related to + + align:start position:0% +assumption that sequences are related to + + + align:start position:0% +assumption that sequences are related to +one another they can be they may make + + align:start position:0% +one another they can be they may make + + + align:start position:0% +one another they can be they may make +the further assumption they are related + + align:start position:0% +the further assumption they are related + + + align:start position:0% +the further assumption they are related +by ancestry that is to say you mutated + + align:start position:0% +by ancestry that is to say you mutated + + + align:start position:0% +by ancestry that is to say you mutated +them in the laboratory + + align:start position:0% +them in the laboratory + + + align:start position:0% +them in the laboratory +or + + align:start position:0% +or + + + align:start position:0% +or +perhaps they were mutated before you + + align:start position:0% +perhaps they were mutated before you + + + align:start position:0% +perhaps they were mutated before you +came to the laboratory + + align:start position:0% +came to the laboratory + + + align:start position:0% +came to the laboratory +that's dynamic programming a lot can + + align:start position:0% +that's dynamic programming a lot can + + + align:start position:0% +that's dynamic programming a lot can +align + + align:start position:0% +align + + + align:start position:0% +align +sequences or three-dimensional + + align:start position:0% +sequences or three-dimensional + + + align:start position:0% +sequences or three-dimensional +structures which are quite different + + align:start position:0% +structures which are quite different + + + align:start position:0% +structures which are quite different +from one another + + align:start position:0% +from one another + + + align:start position:0% +from one another +a few slides back when we talk about + + align:start position:0% +a few slides back when we talk about + + + align:start position:0% +a few slides back when we talk about +replication if two things are replicated + + align:start position:0% +replication if two things are replicated + + + align:start position:0% +replication if two things are replicated +showing common ancestry say + + align:start position:0% +showing common ancestry say + + + align:start position:0% +showing common ancestry say +the faithfulness of that replication is + + align:start position:0% +the faithfulness of that replication is + + + align:start position:0% +the faithfulness of that replication is +key to the dynamic programming is key to + + align:start position:0% +key to the dynamic programming is key to + + + align:start position:0% +key to the dynamic programming is key to +your to your accepting that something is + + align:start position:0% +your to your accepting that something is + + + align:start position:0% +your to your accepting that something is +actually replicated if it if it changes + + align:start position:0% +actually replicated if it if it changes + + + align:start position:0% +actually replicated if it if it changes +into something completely new + + align:start position:0% +into something completely new + + + align:start position:0% +into something completely new +in the process of replication then then + + align:start position:0% +in the process of replication then then + + + align:start position:0% +in the process of replication then then +you've + + align:start position:0% +you've + + + align:start position:0% +you've +it's unlikely it will be able to + + align:start position:0% +it's unlikely it will be able to + + + align:start position:0% +it's unlikely it will be able to +maintain that + + align:start position:0% + + + + align:start position:0% + +three-dimensional structure we will be + + align:start position:0% +three-dimensional structure we will be + + + align:start position:0% +three-dimensional structure we will be +talking about motifs catalysis + + align:start position:0% +talking about motifs catalysis + + + align:start position:0% +talking about motifs catalysis +complementary surfaces i'll give you a + + align:start position:0% +complementary surfaces i'll give you a + + + align:start position:0% +complementary surfaces i'll give you a +beautiful example of complementary + + align:start position:0% +beautiful example of complementary + + + align:start position:0% +beautiful example of complementary +surface in a few slides and all of this + + align:start position:0% +surface in a few slides and all of this + + + align:start position:0% +surface in a few slides and all of this +is dealing with the continuous functions + + align:start position:0% +is dealing with the continuous functions + + + align:start position:0% +is dealing with the continuous functions +of energy + + align:start position:0% +of energy + + + align:start position:0% +of energy +and kinetics + + align:start position:0% +and kinetics + + + align:start position:0% +and kinetics +where + + align:start position:0% +where + + + align:start position:0% +where +different complementary surfaces will + + align:start position:0% +different complementary surfaces will + + + align:start position:0% +different complementary surfaces will +bind to one another + + align:start position:0% +bind to one another + + + align:start position:0% +bind to one another +with very specific rate constants + + align:start position:0% +with very specific rate constants + + + align:start position:0% +with very specific rate constants +covering many + + align:start position:0% +covering many + + + align:start position:0% +covering many +orders of magnitude + + align:start position:0% +orders of magnitude + + + align:start position:0% +orders of magnitude +these + + align:start position:0% +these + + + align:start position:0% +these +energetic and + + align:start position:0% +energetic and + + + align:start position:0% +energetic and +kinetic phenomenon is what underlies the + + align:start position:0% +kinetic phenomenon is what underlies the + + + align:start position:0% +kinetic phenomenon is what underlies the +functional genomics we collect + + align:start position:0% +functional genomics we collect + + + align:start position:0% +functional genomics we collect +functional genomic data one of the ways + + align:start position:0% +functional genomic data one of the ways + + + align:start position:0% +functional genomic data one of the ways +we model it is we ask whether + + align:start position:0% +we model it is we ask whether + + + align:start position:0% +we model it is we ask whether +uh + + align:start position:0% + + + + align:start position:0% + +phenomena that we're studying inside our + + align:start position:0% +phenomena that we're studying inside our + + + align:start position:0% +phenomena that we're studying inside our +bodies or inside of microorganisms and + + align:start position:0% +bodies or inside of microorganisms and + + + align:start position:0% +bodies or inside of microorganisms and +so forth + + align:start position:0% +so forth + + + align:start position:0% +so forth +the the protein levels the rna levels + + align:start position:0% +the the protein levels the rna levels + + + align:start position:0% +the the protein levels the rna levels +and so forth whether they go up and down + + align:start position:0% +and so forth whether they go up and down + + + align:start position:0% +and so forth whether they go up and down +together + + align:start position:0% +together + + + align:start position:0% +together +means they're a cluster they have common + + align:start position:0% +means they're a cluster they have common + + + align:start position:0% +means they're a cluster they have common +properties do those common properties + + align:start position:0% +properties do those common properties + + + align:start position:0% +properties do those common properties +reflect + + align:start position:0% +reflect + + + align:start position:0% +reflect +yet another aspect of them like their + + align:start position:0% +yet another aspect of them like their + + + align:start position:0% +yet another aspect of them like their +common + + align:start position:0% +common + + + align:start position:0% +common +functions or their common mechanisms for + + align:start position:0% +functions or their common mechanisms for + + + align:start position:0% +functions or their common mechanisms for +being co-regulated in systems biology we + + align:start position:0% +being co-regulated in systems biology we + + + align:start position:0% +being co-regulated in systems biology we +have we have these qualitative + + align:start position:0% +have we have these qualitative + + + align:start position:0% +have we have these qualitative +diagrams + + align:start position:0% +diagrams + + + align:start position:0% +diagrams +that tell us about sort of the all or + + align:start position:0% +that tell us about sort of the all or + + + align:start position:0% +that tell us about sort of the all or +none + + align:start position:0% +none + + + align:start position:0% +none +or boolean which means logical + + align:start position:0% +or boolean which means logical + + + align:start position:0% +or boolean which means logical +zeros and ones + + align:start position:0% +zeros and ones + + + align:start position:0% +zeros and ones +or we can + + align:start position:0% +or we can + + + align:start position:0% +or we can +treat them as continuous + + align:start position:0% +treat them as continuous + + + align:start position:0% +treat them as continuous +differential equations + + align:start position:0% +differential equations + + + align:start position:0% +differential equations +or for stochastic where you have some of + + align:start position:0% +or for stochastic where you have some of + + + align:start position:0% +or for stochastic where you have some of +the power of the differential equations + + align:start position:0% +the power of the differential equations + + + align:start position:0% +the power of the differential equations +but you deal with individual molecules + + align:start position:0% +but you deal with individual molecules + + + align:start position:0% +but you deal with individual molecules +or individual + + align:start position:0% + + + + align:start position:0% + +organisms and populations organisms can + + align:start position:0% +organisms and populations organisms can + + + align:start position:0% +organisms and populations organisms can +be sarcastic models can be + + align:start position:0% +be sarcastic models can be + + + align:start position:0% +be sarcastic models can be +molecules to be stochastic + + align:start position:0% +molecules to be stochastic + + + align:start position:0% +molecules to be stochastic +and another thing again this theme of + + align:start position:0% +and another thing again this theme of + + + align:start position:0% +and another thing again this theme of +optimization we can we can ask whether a + + align:start position:0% +optimization we can we can ask whether a + + + align:start position:0% +optimization we can we can ask whether a +network or a network component is + + align:start position:0% +network or a network component is + + + align:start position:0% +network or a network component is +optimal we can make if it it is it + + align:start position:0% +optimal we can make if it it is it + + + align:start position:0% +optimal we can make if it it is it +optimal due to + + align:start position:0% +optimal due to + + + align:start position:0% +optimal due to +the past history of the organism or is + + align:start position:0% +the past history of the organism or is + + + align:start position:0% +the past history of the organism or is +it something we can set a goal of a + + align:start position:0% +it something we can set a goal of a + + + align:start position:0% +it something we can set a goal of a +biotech process to optimize it for a new + + align:start position:0% +biotech process to optimize it for a new + + + align:start position:0% +biotech process to optimize it for a new +function + + align:start position:0% +function + + + align:start position:0% +function +linear programming is the mathematical + + align:start position:0% +linear programming is the mathematical + + + align:start position:0% +linear programming is the mathematical +tool + + align:start position:0% +tool + + + align:start position:0% +tool +that one can use for studying this it's + + align:start position:0% +that one can use for studying this it's + + + align:start position:0% +that one can use for studying this it's +common in economic + + align:start position:0% + + + + align:start position:0% + +algorithms so + + align:start position:0% +algorithms so + + + align:start position:0% +algorithms so +so we were talking about modeling in + + align:start position:0% +so we were talking about modeling in + + + align:start position:0% +so we were talking about modeling in +this uh + + align:start position:0% +this uh + + + align:start position:0% +this uh +this + + align:start position:0% +this + + + align:start position:0% +this +whole realm going from sort of minimal + + align:start position:0% +whole realm going from sort of minimal + + + align:start position:0% +whole realm going from sort of minimal +life + + align:start position:0% +life + + + align:start position:0% +life +sequences + + align:start position:0% +sequences + + + align:start position:0% +sequences +through the catalysis that involves + + align:start position:0% +through the catalysis that involves + + + align:start position:0% +through the catalysis that involves +interactions of three-dimensional + + align:start position:0% +interactions of three-dimensional + + + align:start position:0% +interactions of three-dimensional +structures functional genomics + + align:start position:0% +structures functional genomics + + + align:start position:0% +structures functional genomics +and this + + align:start position:0% +and this + + + align:start position:0% +and this +and the optimality that we + + align:start position:0% +and the optimality that we + + + align:start position:0% +and the optimality that we +that we get that's required as we will + + align:start position:0% +that we get that's required as we will + + + align:start position:0% +that we get that's required as we will +see momentarily for getting single + + align:start position:0% +see momentarily for getting single + + + align:start position:0% +see momentarily for getting single +molecules to work + + align:start position:0% + + + + align:start position:0% + +what's our parts list we're going to try + + align:start position:0% +what's our parts list we're going to try + + + align:start position:0% +what's our parts list we're going to try +to start simple + + align:start position:0% +to start simple + + + align:start position:0% +to start simple +uh + + align:start position:0% +uh + + + align:start position:0% +uh +but put the simplicity in the context of + + align:start position:0% +but put the simplicity in the context of + + + align:start position:0% +but put the simplicity in the context of +the big picture the big picture for + + align:start position:0% +the big picture the big picture for + + + align:start position:0% +the big picture the big picture for +the the atoms is the periodic table of + + align:start position:0% +the the atoms is the periodic table of + + + align:start position:0% +the the atoms is the periodic table of +the more than 100 + + align:start position:0% + + + + align:start position:0% + +elements we have a very short list here + + align:start position:0% +elements we have a very short list here + + + align:start position:0% +elements we have a very short list here +sodium potassium iron chlorine + + align:start position:0% +sodium potassium iron chlorine + + + align:start position:0% +sodium potassium iron chlorine +calcium magnesium molybdenum manganese + + align:start position:0% +calcium magnesium molybdenum manganese + + + align:start position:0% +calcium magnesium molybdenum manganese +sulfur selenium copper nickel cobalt and + + align:start position:0% +sulfur selenium copper nickel cobalt and + + + align:start position:0% +sulfur selenium copper nickel cobalt and +silicon + + align:start position:0% +silicon + + + align:start position:0% +silicon +which are useful in many species + + align:start position:0% +which are useful in many species + + + align:start position:0% +which are useful in many species +if you have to + + align:start position:0% +if you have to + + + align:start position:0% +if you have to +pick a + + align:start position:0% +pick a + + + align:start position:0% +pick a +something that's + + align:start position:0% +something that's + + + align:start position:0% +something that's +related to us + + align:start position:0% + + + + align:start position:0% + +as a just a minimal kind of biochemical + + align:start position:0% +as a just a minimal kind of biochemical + + + align:start position:0% +as a just a minimal kind of biochemical +system that shows some of the + + align:start position:0% +system that shows some of the + + + align:start position:0% +system that shows some of the +replicative properties and and + + align:start position:0% +replicative properties and and + + + align:start position:0% +replicative properties and and +evolutionary properties of life you + + align:start position:0% +evolutionary properties of life you + + + align:start position:0% +evolutionary properties of life you +would say rna baselife so one of the + + align:start position:0% +would say rna baselife so one of the + + + align:start position:0% +would say rna baselife so one of the +breakthroughs uh + + align:start position:0% +breakthroughs uh + + + align:start position:0% +breakthroughs uh +in experimental science over the last + + align:start position:0% +in experimental science over the last + + + align:start position:0% +in experimental science over the last +couple decades is is recognizing that + + align:start position:0% +couple decades is is recognizing that + + + align:start position:0% +couple decades is is recognizing that +rna like proteins has catalytic + + align:start position:0% +rna like proteins has catalytic + + + align:start position:0% +rna like proteins has catalytic +capabilities it has the it has the + + align:start position:0% +capabilities it has the it has the + + + align:start position:0% +capabilities it has the it has the +potential to have been one of the early + + align:start position:0% +potential to have been one of the early + + + align:start position:0% +potential to have been one of the early +replicating units just just for the sake + + align:start position:0% +replicating units just just for the sake + + + align:start position:0% +replicating units just just for the sake +of + + align:start position:0% +of + + + align:start position:0% +of +describing a simple system let's look at + + align:start position:0% +describing a simple system let's look at + + + align:start position:0% +describing a simple system let's look at +something made up of five elements + + align:start position:0% +something made up of five elements + + + align:start position:0% +something made up of five elements +it's not necessarily the simplest but + + align:start position:0% +it's not necessarily the simplest but + + + align:start position:0% +it's not necessarily the simplest but +it's just something to think about + + align:start position:0% +it's just something to think about + + + align:start position:0% +it's just something to think about +these five elements + + align:start position:0% + + + + align:start position:0% + +can be + + align:start position:0% +can be + + + align:start position:0% +can be +in the presence of an environment which + + align:start position:0% +in the presence of an environment which + + + align:start position:0% +in the presence of an environment which +uh be composed of various of the same + + align:start position:0% +uh be composed of various of the same + + + align:start position:0% +uh be composed of various of the same +five elements the environment would be + + align:start position:0% +five elements the environment would be + + + align:start position:0% +five elements the environment would be +very simple + + align:start position:0% +very simple + + + align:start position:0% +very simple +you know that complexity versus + + align:start position:0% +you know that complexity versus + + + align:start position:0% +you know that complexity versus +simplicity would be water + + align:start position:0% +simplicity would be water + + + align:start position:0% +simplicity would be water +uh + + align:start position:0% +uh + + + align:start position:0% +uh +ammonium + + align:start position:0% +ammonium + + + align:start position:0% +ammonium +positively charged ions nucleotide + + align:start position:0% +positively charged ions nucleotide + + + align:start position:0% +positively charged ions nucleotide +triphosphates negatively charged ions + + align:start position:0% +triphosphates negatively charged ions + + + align:start position:0% +triphosphates negatively charged ions +which are precursors to the making + + align:start position:0% +which are precursors to the making + + + align:start position:0% +which are precursors to the making +polymers + + align:start position:0% +polymers + + + align:start position:0% +polymers +and then possibly lipids to fatty + + align:start position:0% +and then possibly lipids to fatty + + + align:start position:0% +and then possibly lipids to fatty +substances that bound membranes + + align:start position:0% +substances that bound membranes + + + align:start position:0% +substances that bound membranes +an example of rna catalyzed rna + + align:start position:0% +an example of rna catalyzed rna + + + align:start position:0% +an example of rna catalyzed rna +polymerization + + align:start position:0% +polymerization + + + align:start position:0% +polymerization +is in this article and then i'll deal + + align:start position:0% +is in this article and then i'll deal + + + align:start position:0% +is in this article and then i'll deal +with + + align:start position:0% +with + + + align:start position:0% +with +another one + + align:start position:0% +another one + + + align:start position:0% +another one +that rather than using nucleotide + + align:start position:0% +that rather than using nucleotide + + + align:start position:0% +that rather than using nucleotide +triphosphates uses slightly larger rna + + align:start position:0% +triphosphates uses slightly larger rna + + + align:start position:0% +triphosphates uses slightly larger rna +precursors + + align:start position:0% +precursors + + + align:start position:0% +precursors +now let's start doing this toggling back + + align:start position:0% +now let's start doing this toggling back + + + align:start position:0% +now let's start doing this toggling back +and forth between living systems and + + align:start position:0% +and forth between living systems and + + + align:start position:0% +and forth between living systems and +computational systems so that + + align:start position:0% +computational systems so that + + + align:start position:0% +computational systems so that +whether you're from a computational + + align:start position:0% +whether you're from a computational + + + align:start position:0% +whether you're from a computational +background or biological or both you'll + + align:start position:0% +background or biological or both you'll + + + align:start position:0% +background or biological or both you'll +see some interesting relationships + + align:start position:0% +see some interesting relationships + + + align:start position:0% +see some interesting relationships +here we talked about a minimal + + align:start position:0% +here we talked about a minimal + + + align:start position:0% +here we talked about a minimal +biological system with five elements + + align:start position:0% +biological system with five elements + + + align:start position:0% +biological system with five elements +here we're going to talk about some + + align:start position:0% +here we're going to talk about some + + + align:start position:0% +here we're going to talk about some +minimal programs with a very small + + align:start position:0% +minimal programs with a very small + + + align:start position:0% +minimal programs with a very small +number of elements basically they're + + align:start position:0% +number of elements basically they're + + + align:start position:0% +number of elements basically they're +limited to a single line of code each + + align:start position:0% +limited to a single line of code each + + + align:start position:0% +limited to a single line of code each +and they do something which is related + + align:start position:0% +and they do something which is related + + + align:start position:0% +and they do something which is related +to the the topic here replication is an + + align:start position:0% +to the the topic here replication is an + + + align:start position:0% +to the the topic here replication is an +exponential + + align:start position:0% +exponential + + + align:start position:0% +exponential +uh process exponentially growing + + align:start position:0% +uh process exponentially growing + + + align:start position:0% +uh process exponentially growing +if something + + align:start position:0% +if something + + + align:start position:0% +if something +is auto catalytic is another way of + + align:start position:0% +is auto catalytic is another way of + + + align:start position:0% +is auto catalytic is another way of +describing it so we we've used that as + + align:start position:0% +describing it so we we've used that as + + + align:start position:0% +describing it so we we've used that as +the theme for our minimal programs the + + align:start position:0% +the theme for our minimal programs the + + + align:start position:0% +the theme for our minimal programs the +what is the + + align:start position:0% +what is the + + + align:start position:0% +what is the +this exponential function we give it a + + align:start position:0% +this exponential function we give it a + + + align:start position:0% +this exponential function we give it a +very specific argument the argument is + + align:start position:0% +very specific argument the argument is + + + align:start position:0% +very specific argument the argument is +one so this is + + align:start position:0% +one so this is + + + align:start position:0% +one so this is +e to the one power or e e being this + + align:start position:0% +e to the one power or e e being this + + + align:start position:0% +e to the one power or e e being this +number here that's represented number of + + align:start position:0% +number here that's represented number of + + + align:start position:0% +number here that's represented number of +times okay about 2.7 + + align:start position:0% +times okay about 2.7 + + + align:start position:0% +times okay about 2.7 +the four languages that we're that we're + + align:start position:0% +the four languages that we're that we're + + + align:start position:0% +the four languages that we're that we're +demonstrating here is pearl excel + + align:start position:0% +demonstrating here is pearl excel + + + align:start position:0% +demonstrating here is pearl excel +fortran 77 + + align:start position:0% +fortran 77 + + + align:start position:0% +fortran 77 +and mathematica + + align:start position:0% +and mathematica + + + align:start position:0% +and mathematica +this course will mainly use pearl and + + align:start position:0% +this course will mainly use pearl and + + + align:start position:0% +this course will mainly use pearl and +mathematica for reasons that will be + + align:start position:0% +mathematica for reasons that will be + + + align:start position:0% +mathematica for reasons that will be +evident in the next couple of slides + + align:start position:0% +evident in the next couple of slides + + + align:start position:0% +evident in the next couple of slides +but i just want to show you these + + align:start position:0% +but i just want to show you these + + + align:start position:0% +but i just want to show you these +different what ones and + + align:start position:0% +different what ones and + + + align:start position:0% +different what ones and +sort of in in the theme of accuracy of + + align:start position:0% +sort of in in the theme of accuracy of + + + align:start position:0% +sort of in in the theme of accuracy of +replication how faithfully is a + + align:start position:0% +replication how faithfully is a + + + align:start position:0% +replication how faithfully is a +particular + + align:start position:0% +particular + + + align:start position:0% +particular +string handled + + align:start position:0% +string handled + + + align:start position:0% +string handled +either the string of nucleotides in a + + align:start position:0% +either the string of nucleotides in a + + + align:start position:0% +either the string of nucleotides in a +simple + + align:start position:0% +simple + + + align:start position:0% +simple +life form or the string of digits in a + + align:start position:0% +life form or the string of digits in a + + + align:start position:0% +life form or the string of digits in a +number and you can see that the internal + + align:start position:0% +number and you can see that the internal + + + align:start position:0% +number and you can see that the internal +representation of the the math that goes + + align:start position:0% +representation of the the math that goes + + + align:start position:0% +representation of the the math that goes +on inside the computer has to be done + + align:start position:0% +on inside the computer has to be done + + + align:start position:0% +on inside the computer has to be done +digitally even though these are + + align:start position:0% +digitally even though these are + + + align:start position:0% +digitally even though these are +transcendental numbers which have an + + align:start position:0% +transcendental numbers which have an + + + align:start position:0% +transcendental numbers which have an +arbitrary number of + + align:start position:0% +arbitrary number of + + + align:start position:0% +arbitrary number of +digits and you can see that some + + align:start position:0% +digits and you can see that some + + + align:start position:0% +digits and you can see that some +programs are are + + align:start position:0% +programs are are + + + align:start position:0% +programs are are +you know typically limited and you can + + align:start position:0% +you know typically limited and you can + + + align:start position:0% +you know typically limited and you can +even guess the number of bits + + align:start position:0% +even guess the number of bits + + + align:start position:0% +even guess the number of bits +representing it internally here down at + + align:start position:0% +representing it internally here down at + + + align:start position:0% +representing it internally here down at +the bottom of slide 17 you can see some + + align:start position:0% +the bottom of slide 17 you can see some + + + align:start position:0% +the bottom of slide 17 you can see some +of the + + align:start position:0% + + + + align:start position:0% + +nitty gritty detail of how these things + + align:start position:0% +nitty gritty detail of how these things + + + align:start position:0% +nitty gritty detail of how these things +are represented as zeros and ones + + align:start position:0% +are represented as zeros and ones + + + align:start position:0% +are represented as zeros and ones +representing the mantissa + + align:start position:0% +representing the mantissa + + + align:start position:0% +representing the mantissa +the exponent + + align:start position:0% +the exponent + + + align:start position:0% +the exponent +and so on but you can see some of these + + align:start position:0% +and so on but you can see some of these + + + align:start position:0% +and so on but you can see some of these +programs when they print + + align:start position:0% +programs when they print + + + align:start position:0% +programs when they print +when they actually print + + align:start position:0% +when they actually print + + + align:start position:0% +when they actually print +they don't that the program is not aware + + align:start position:0% +they don't that the program is not aware + + + align:start position:0% +they don't that the program is not aware +of or the programmer was not + + align:start position:0% +of or the programmer was not + + + align:start position:0% +of or the programmer was not +aware of + + align:start position:0% +aware of + + + align:start position:0% +aware of +exactly what the internal representation + + align:start position:0% +exactly what the internal representation + + + align:start position:0% +exactly what the internal representation +was and so all these trailing zeros are + + align:start position:0% +was and so all these trailing zeros are + + + align:start position:0% +was and so all these trailing zeros are +incorrect + + align:start position:0% + + + + align:start position:0% + +the winner in this of course is + + align:start position:0% +the winner in this of course is + + + align:start position:0% +the winner in this of course is +mathematica uh here to ask for the e to + + align:start position:0% +mathematica uh here to ask for the e to + + + align:start position:0% +mathematica uh here to ask for the e to +the one power you say let's give it uh + + align:start position:0% +the one power you say let's give it uh + + + align:start position:0% +the one power you say let's give it uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +this in bracket says let's start giving + + align:start position:0% +this in bracket says let's start giving + + + align:start position:0% +this in bracket says let's start giving +arbitrary precision + + align:start position:0% +arbitrary precision + + + align:start position:0% +arbitrary precision +um where the precision + + align:start position:0% +um where the precision + + + align:start position:0% +um where the precision +the numeric the end numeric is a hundred + + align:start position:0% +the numeric the end numeric is a hundred + + + align:start position:0% +the numeric the end numeric is a hundred +digits + + align:start position:0% +digits + + + align:start position:0% +digits +and this seems like a stunt in this + + align:start position:0% +and this seems like a stunt in this + + + align:start position:0% +and this seems like a stunt in this +particular case but actually when you + + align:start position:0% +particular case but actually when you + + + align:start position:0% +particular case but actually when you +start doing a series of calculations + + align:start position:0% +start doing a series of calculations + + + align:start position:0% +start doing a series of calculations +where errors can accumulate um the + + align:start position:0% +where errors can accumulate um the + + + align:start position:0% +where errors can accumulate um the +ability to go into sort of arbitrary + + align:start position:0% +ability to go into sort of arbitrary + + + align:start position:0% +ability to go into sort of arbitrary +precision will allow you to prevent uh + + align:start position:0% +precision will allow you to prevent uh + + + align:start position:0% +precision will allow you to prevent uh +sort of catastrophic imprecision + + align:start position:0% +sort of catastrophic imprecision + + + align:start position:0% +sort of catastrophic imprecision +and what happens is in a mathematical + + align:start position:0% +and what happens is in a mathematical + + + align:start position:0% +and what happens is in a mathematical +calculation if it needs a little more + + align:start position:0% +calculation if it needs a little more + + + align:start position:0% +calculation if it needs a little more +precision than you initially anticipated + + align:start position:0% +precision than you initially anticipated + + + align:start position:0% +precision than you initially anticipated +it will go out and get it um + + align:start position:0% +it will go out and get it um + + + align:start position:0% +it will go out and get it um +on its own which is quite remarkable try + + align:start position:0% +on its own which is quite remarkable try + + + align:start position:0% +on its own which is quite remarkable try +to do that in any of these other + + align:start position:0% +to do that in any of these other + + + align:start position:0% +to do that in any of these other +languages + + align:start position:0% +languages + + + align:start position:0% +languages +they will typically give you what's + + align:start position:0% +they will typically give you what's + + + align:start position:0% +they will typically give you what's +called an underflow or an overflow error + + align:start position:0% +called an underflow or an overflow error + + + align:start position:0% +called an underflow or an overflow error +and + + align:start position:0% +and + + + align:start position:0% +and +either stop or just make mistakes + + align:start position:0% +either stop or just make mistakes + + + align:start position:0% +either stop or just make mistakes +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that's my first advertisement for + + align:start position:0% +that's my first advertisement for + + + align:start position:0% +that's my first advertisement for +mathematica + + align:start position:0% +mathematica + + + align:start position:0% +mathematica +you can see all of these are very simple + + align:start position:0% +you can see all of these are very simple + + + align:start position:0% +you can see all of these are very simple +very simple programs uh that be lie and + + align:start position:0% +very simple programs uh that be lie and + + + align:start position:0% +very simple programs uh that be lie and +hide underneath the very complicated + + align:start position:0% +hide underneath the very complicated + + + align:start position:0% +hide underneath the very complicated +electronics and algorithms that are + + align:start position:0% +electronics and algorithms that are + + + align:start position:0% +electronics and algorithms that are +built in + + align:start position:0% +built in + + + align:start position:0% +built in +to accomplish this i'll give you a + + align:start position:0% +to accomplish this i'll give you a + + + align:start position:0% +to accomplish this i'll give you a +feeling for what that is in just a + + align:start position:0% +feeling for what that is in just a + + + align:start position:0% +feeling for what that is in just a +couple of slides + + align:start position:0% +couple of slides + + + align:start position:0% +couple of slides +so back to self-replication we're + + align:start position:0% +so back to self-replication we're + + + align:start position:0% +so back to self-replication we're +tolerant back and forth between simple + + align:start position:0% +tolerant back and forth between simple + + + align:start position:0% +tolerant back and forth between simple +biological and computational systems + + align:start position:0% +biological and computational systems + + + align:start position:0% +biological and computational systems +we have uh + + align:start position:0% +we have uh + + + align:start position:0% +we have uh +here we've represented + + align:start position:0% +here we've represented + + + align:start position:0% +here we've represented +tri and hexanucleotides three + + align:start position:0% +tri and hexanucleotides three + + + align:start position:0% +tri and hexanucleotides three +nucleotides and and six again remember + + align:start position:0% +nucleotides and and six again remember + + + align:start position:0% +nucleotides and and six again remember +these letters are + + align:start position:0% +these letters are + + + align:start position:0% +these letters are +crude or i should say simple + + align:start position:0% +crude or i should say simple + + + align:start position:0% +crude or i should say simple +representations of electron density + + align:start position:0% +representations of electron density + + + align:start position:0% +representations of electron density +involving dozens of atoms in the shape + + align:start position:0% +involving dozens of atoms in the shape + + + align:start position:0% +involving dozens of atoms in the shape +of a cytosine or c or guanine or a g + + align:start position:0% +of a cytosine or c or guanine or a g + + + align:start position:0% +of a cytosine or c or guanine or a g +it's important that you know that there + + align:start position:0% +it's important that you know that there + + + align:start position:0% +it's important that you know that there +are two strands in dna typically + + align:start position:0% +are two strands in dna typically + + + align:start position:0% +are two strands in dna typically +or even many rnas in this particular + + align:start position:0% +or even many rnas in this particular + + + align:start position:0% +or even many rnas in this particular +example whether it's rna or dna + + align:start position:0% +example whether it's rna or dna + + + align:start position:0% +example whether it's rna or dna +and in order to indicate the orientation + + align:start position:0% +and in order to indicate the orientation + + + align:start position:0% +and in order to indicate the orientation +of the strand it has a directionality + + align:start position:0% +of the strand it has a directionality + + + align:start position:0% +of the strand it has a directionality +we indicate five prime which is the name + + align:start position:0% +we indicate five prime which is the name + + + align:start position:0% +we indicate five prime which is the name +of a + + align:start position:0% +of a + + + align:start position:0% +of a +at the atom + + align:start position:0% +at the atom + + + align:start position:0% +at the atom +in the ribose but the the details are + + align:start position:0% +in the ribose but the the details are + + + align:start position:0% +in the ribose but the the details are +not important from a from a + + align:start position:0% +not important from a from a + + + align:start position:0% +not important from a from a +computational standpoint it's just a way + + align:start position:0% +computational standpoint it's just a way + + + align:start position:0% +computational standpoint it's just a way +of indicating this is one end of the rna + + align:start position:0% +of indicating this is one end of the rna + + + align:start position:0% +of indicating this is one end of the rna +and a ccg is not the same as a gcc + + align:start position:0% +and a ccg is not the same as a gcc + + + align:start position:0% +and a ccg is not the same as a gcc +the five prime indicates the five prime + + align:start position:0% +the five prime indicates the five prime + + + align:start position:0% +the five prime indicates the five prime +end of that + + align:start position:0% +end of that + + + align:start position:0% +end of that +we take two of these which are basically + + align:start position:0% +we take two of these which are basically + + + align:start position:0% +we take two of these which are basically +identical + + align:start position:0% +identical + + + align:start position:0% +identical +and we can like it they will likely + + align:start position:0% +and we can like it they will likely + + + align:start position:0% +and we can like it they will likely +together spontaneously if you set up the + + align:start position:0% +together spontaneously if you set up the + + + align:start position:0% +together spontaneously if you set up the +chemistry right + + align:start position:0% +chemistry right + + + align:start position:0% +chemistry right +to make this + + align:start position:0% +to make this + + + align:start position:0% +to make this +these two trinucleotides into a + + align:start position:0% +these two trinucleotides into a + + + align:start position:0% +these two trinucleotides into a +hexanucleotide ccg ccg + + align:start position:0% +hexanucleotide ccg ccg + + + align:start position:0% +hexanucleotide ccg ccg +in the presence of a complement here + + align:start position:0% +in the presence of a complement here + + + align:start position:0% +in the presence of a complement here +which is cgg cgg a different sequence + + align:start position:0% +which is cgg cgg a different sequence + + + align:start position:0% +which is cgg cgg a different sequence +i've tried to emphasize that by making + + align:start position:0% +i've tried to emphasize that by making + + + align:start position:0% +i've tried to emphasize that by making +it capital in green that + + align:start position:0% +it capital in green that + + + align:start position:0% +it capital in green that +uh would bind to these two these these + + align:start position:0% +uh would bind to these two these these + + + align:start position:0% +uh would bind to these two these these +tr two trinucleotides would bind to this + + align:start position:0% +tr two trinucleotides would bind to this + + + align:start position:0% +tr two trinucleotides would bind to this +aligned by watson quick base pairs the + + align:start position:0% +aligned by watson quick base pairs the + + + align:start position:0% +aligned by watson quick base pairs the +rules for watson quick base pairs hope + + align:start position:0% +rules for watson quick base pairs hope + + + align:start position:0% +rules for watson quick base pairs hope +many of you may know a pairs with t and + + align:start position:0% +many of you may know a pairs with t and + + + align:start position:0% +many of you may know a pairs with t and +c pairs with g + + align:start position:0% +c pairs with g + + + align:start position:0% +c pairs with g +and that will catalyze this process it + + align:start position:0% +and that will catalyze this process it + + + align:start position:0% +and that will catalyze this process it +will it will + + align:start position:0% +will it will + + + align:start position:0% +will it will +speed up the kinetics in which these + + align:start position:0% +speed up the kinetics in which these + + + align:start position:0% +speed up the kinetics in which these +trinucleotides turn to hexanucleotides + + align:start position:0% +trinucleotides turn to hexanucleotides + + + align:start position:0% +trinucleotides turn to hexanucleotides +now here it gets interesting this + + align:start position:0% +now here it gets interesting this + + + align:start position:0% +now here it gets interesting this +hexanucleotide now drops down here and + + align:start position:0% +hexanucleotide now drops down here and + + + align:start position:0% +hexanucleotide now drops down here and +speeds up the process of this different + + align:start position:0% +speeds up the process of this different + + + align:start position:0% +speeds up the process of this different +trinucleotide dimerizing and forming + + align:start position:0% +trinucleotide dimerizing and forming + + + align:start position:0% +trinucleotide dimerizing and forming +the original one that catalyzed the + + align:start position:0% +the original one that catalyzed the + + + align:start position:0% +the original one that catalyzed the +first reaction so this catalog this + + align:start position:0% +first reaction so this catalog this + + + align:start position:0% +first reaction so this catalog this +catalyzes speeds up + + align:start position:0% +catalyzes speeds up + + + align:start position:0% +catalyzes speeds up +the first reaction which produces a + + align:start position:0% +the first reaction which produces a + + + align:start position:0% +the first reaction which produces a +product that speeds up the second which + + align:start position:0% +product that speeds up the second which + + + align:start position:0% +product that speeds up the second which +produces the first catalyst and so on + + align:start position:0% +produces the first catalyst and so on + + + align:start position:0% +produces the first catalyst and so on +this is called a hypercycle + + align:start position:0% +this is called a hypercycle + + + align:start position:0% +this is called a hypercycle +championed by eigen and schuster + + align:start position:0% +championed by eigen and schuster + + + align:start position:0% +championed by eigen and schuster +and this is probably one of the simplest + + align:start position:0% +and this is probably one of the simplest + + + align:start position:0% +and this is probably one of the simplest +examples of it and i think gives you a + + align:start position:0% +examples of it and i think gives you a + + + align:start position:0% +examples of it and i think gives you a +feeling for how a variety of + + align:start position:0% +feeling for how a variety of + + + align:start position:0% +feeling for how a variety of +interdependent biochemical processes can + + align:start position:0% +interdependent biochemical processes can + + + align:start position:0% +interdependent biochemical processes can +result in auto catalysis where you get + + align:start position:0% +result in auto catalysis where you get + + + align:start position:0% +result in auto catalysis where you get +these exponential cycles which we + + align:start position:0% +these exponential cycles which we + + + align:start position:0% +these exponential cycles which we +recognize as something very similar to + + align:start position:0% +recognize as something very similar to + + + align:start position:0% +recognize as something very similar to +replication this would have a very + + align:start position:0% +replication this would have a very + + + align:start position:0% +replication this would have a very +high this could have a very high + + align:start position:0% +high this could have a very high + + + align:start position:0% +high this could have a very high +probability of replication it could be + + align:start position:0% +probability of replication it could be + + + align:start position:0% +probability of replication it could be +very faithful + + align:start position:0% +very faithful + + + align:start position:0% +very faithful +but its complexity is low the input + + align:start position:0% +but its complexity is low the input + + + align:start position:0% +but its complexity is low the input +complexity is low and the output + + align:start position:0% +complexity is low and the output + + + align:start position:0% +complexity is low and the output +complexity is low that's how we would + + align:start position:0% +complexity is low that's how we would + + + align:start position:0% +complexity is low that's how we would +qualify it + + align:start position:0% + + + + align:start position:0% + +toggling back to + + align:start position:0% + + + + align:start position:0% + +computing and simple examples + + align:start position:0% +computing and simple examples + + + align:start position:0% +computing and simple examples +i've given some simple examples already + + align:start position:0% +i've given some simple examples already + + + align:start position:0% +i've given some simple examples already +of pearl and mathematica but in order to + + align:start position:0% +of pearl and mathematica but in order to + + + align:start position:0% +of pearl and mathematica but in order to +give a few more here on slide 19 + + align:start position:0% +give a few more here on slide 19 + + + align:start position:0% +give a few more here on slide 19 +why did we choose these two for this + + align:start position:0% +why did we choose these two for this + + + align:start position:0% +why did we choose these two for this +course it's been my experience both in + + align:start position:0% +course it's been my experience both in + + + align:start position:0% +course it's been my experience both in +the in our laboratory and + + align:start position:0% +the in our laboratory and + + + align:start position:0% +the in our laboratory and +research environment and also in this + + align:start position:0% +research environment and also in this + + + align:start position:0% +research environment and also in this +class that these are two of the easiest + + align:start position:0% +class that these are two of the easiest + + + align:start position:0% +class that these are two of the easiest +languages to learn that doesn't mean + + align:start position:0% +languages to learn that doesn't mean + + + align:start position:0% +languages to learn that doesn't mean +that they're + + align:start position:0% +that they're + + + align:start position:0% +that they're +absolutely easy but they're but their + + align:start position:0% +absolutely easy but they're but their + + + align:start position:0% +absolutely easy but they're but their +their learning curve is very simple uh + + align:start position:0% +their learning curve is very simple uh + + + align:start position:0% +their learning curve is very simple uh +it's very fast + + align:start position:0% +it's very fast + + + align:start position:0% +it's very fast +and you can + + align:start position:0% +and you can + + + align:start position:0% +and you can +by example + + align:start position:0% +by example + + + align:start position:0% +by example +uh + + align:start position:0% +uh + + + align:start position:0% +uh +change programs that are working into + + align:start position:0% +change programs that are working into + + + align:start position:0% +change programs that are working into +things that do what you want very + + align:start position:0% +things that do what you want very + + + align:start position:0% +things that do what you want very +quickly + + align:start position:0% +quickly + + + align:start position:0% +quickly +it's a high level language in a sense + + align:start position:0% +it's a high level language in a sense + + + align:start position:0% +it's a high level language in a sense +it's if the higher the level of language + + align:start position:0% +it's if the higher the level of language + + + align:start position:0% +it's if the higher the level of language +the closer you are to english + + align:start position:0% +the closer you are to english + + + align:start position:0% +the closer you are to english +conversation the lower level language + + align:start position:0% +conversation the lower level language + + + align:start position:0% +conversation the lower level language +you are the closer you are to um + + align:start position:0% +you are the closer you are to um + + + align:start position:0% +you are the closer you are to um +bits zeros and ones or + + align:start position:0% +bits zeros and ones or + + + align:start position:0% +bits zeros and ones or +or the actual electronics inside of + + align:start position:0% +or the actual electronics inside of + + + align:start position:0% +or the actual electronics inside of +computers + + align:start position:0% +computers + + + align:start position:0% +computers +so in the hierarchy pearl and + + align:start position:0% +so in the hierarchy pearl and + + + align:start position:0% +so in the hierarchy pearl and +mathematics are very high up there + + align:start position:0% + + + + align:start position:0% + +you will get that from your section + + align:start position:0% +you will get that from your section + + + align:start position:0% +you will get that from your section +teaching fellow um + + align:start position:0% +teaching fellow um + + + align:start position:0% +teaching fellow um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so the question is where do you get the + + align:start position:0% +so the question is where do you get the + + + align:start position:0% +so the question is where do you get the +password from for mathematica for this + + align:start position:0% +password from for mathematica for this + + + align:start position:0% +password from for mathematica for this +course and the teaching fellows are + + align:start position:0% +course and the teaching fellows are + + + align:start position:0% +course and the teaching fellows are +responsible for that and that's been + + align:start position:0% +responsible for that and that's been + + + align:start position:0% +responsible for that and that's been +tested i think that works + + align:start position:0% +tested i think that works + + + align:start position:0% +tested i think that works +uh + + align:start position:0% + + + + align:start position:0% + +mathematic up so so perl is is freely + + align:start position:0% +mathematic up so so perl is is freely + + + align:start position:0% +mathematic up so so perl is is freely +it's open source it's interesting in + + align:start position:0% +it's open source it's interesting in + + + align:start position:0% +it's open source it's interesting in +that regard i think many of you sh + + align:start position:0% +that regard i think many of you sh + + + align:start position:0% +that regard i think many of you sh +will find the concept of open source + + align:start position:0% +will find the concept of open source + + + align:start position:0% +will find the concept of open source +where anyone can uh + + align:start position:0% +where anyone can uh + + + align:start position:0% +where anyone can uh +when when software breaks or needs to be + + align:start position:0% +when when software breaks or needs to be + + + align:start position:0% +when when software breaks or needs to be +expanded or needs to be understood it's + + align:start position:0% +expanded or needs to be understood it's + + + align:start position:0% +expanded or needs to be understood it's +there for your inspection rather than + + align:start position:0% +there for your inspection rather than + + + align:start position:0% +there for your inspection rather than +hidden behind some corporate doors very + + align:start position:0% +hidden behind some corporate doors very + + + align:start position:0% +hidden behind some corporate doors very +interesting aspect of pearl mathematica + + align:start position:0% +interesting aspect of pearl mathematica + + + align:start position:0% +interesting aspect of pearl mathematica +is not open source + + align:start position:0% +is not open source + + + align:start position:0% +is not open source +as far as i know uh it has some + + align:start position:0% +as far as i know uh it has some + + + align:start position:0% +as far as i know uh it has some +interesting redeeming features though + + align:start position:0% +interesting redeeming features though + + + align:start position:0% +interesting redeeming features though +it's very strong on math uh as no + + align:start position:0% +it's very strong on math uh as no + + + align:start position:0% +it's very strong on math uh as no +surprise given its name + + align:start position:0% + + + + align:start position:0% + +in particular it's it both symbolic and + + align:start position:0% +in particular it's it both symbolic and + + + align:start position:0% +in particular it's it both symbolic and +numeric and in graphics and we'll have + + align:start position:0% +numeric and in graphics and we'll have + + + align:start position:0% +numeric and in graphics and we'll have +some examples that in just a moment you + + align:start position:0% +some examples that in just a moment you + + + align:start position:0% +some examples that in just a moment you +can do things that are hard to do in in + + align:start position:0% +can do things that are hard to do in in + + + align:start position:0% +can do things that are hard to do in in +pearl and other languages + + align:start position:0% +pearl and other languages + + + align:start position:0% +pearl and other languages +pearl is also very strong for web + + align:start position:0% +pearl is also very strong for web + + + align:start position:0% +pearl is also very strong for web +applications many of the most amazing + + align:start position:0% +applications many of the most amazing + + + align:start position:0% +applications many of the most amazing +things which are done on the web + + align:start position:0% +things which are done on the web + + + align:start position:0% +things which are done on the web +have pearl + + align:start position:0% +have pearl + + + align:start position:0% +have pearl +behind the scenes + + align:start position:0% +behind the scenes + + + align:start position:0% +behind the scenes +now when we + + align:start position:0% +now when we + + + align:start position:0% +now when we +uh + + align:start position:0% + + + + align:start position:0% + +further comparison of comp this is the + + align:start position:0% +further comparison of comp this is the + + + align:start position:0% +further comparison of comp this is the +dark side of computation and biology + + align:start position:0% +dark side of computation and biology + + + align:start position:0% +dark side of computation and biology +showing another analogy + + align:start position:0% +showing another analogy + + + align:start position:0% +showing another analogy +which is + + align:start position:0% +which is + + + align:start position:0% +which is +parasites we have parasitic uh computer + + align:start position:0% +parasites we have parasitic uh computer + + + align:start position:0% +parasites we have parasitic uh computer +and viral + + align:start position:0% +and viral + + + align:start position:0% +and viral +biological viruses + + align:start position:0% +biological viruses + + + align:start position:0% +biological viruses +this one uh + + align:start position:0% +this one uh + + + align:start position:0% +this one uh +in past years i had this uh + + align:start position:0% +in past years i had this uh + + + align:start position:0% +in past years i had this uh +little bit of a computer virus uh just + + align:start position:0% +little bit of a computer virus uh just + + + align:start position:0% +little bit of a computer virus uh just +this is not the whole thing it's just a + + align:start position:0% +this is not the whole thing it's just a + + + align:start position:0% +this is not the whole thing it's just a +little piece of it it's fairly short + + align:start position:0% +little piece of it it's fairly short + + + align:start position:0% +little piece of it it's fairly short +code and this was a + + align:start position:0% +code and this was a + + + align:start position:0% +code and this was a +a very nasty one at the time quite a + + align:start position:0% +a very nasty one at the time quite a + + + align:start position:0% +a very nasty one at the time quite a +while ago + + align:start position:0% +while ago + + + align:start position:0% +while ago +and + + align:start position:0% +and + + + align:start position:0% +and +i had it in the powerpoint presentation + + align:start position:0% +i had it in the powerpoint presentation + + + align:start position:0% +i had it in the powerpoint presentation +when people would download it they would + + align:start position:0% +when people would download it they would + + + align:start position:0% +when people would download it they would +then send me an email + + align:start position:0% +then send me an email + + + align:start position:0% +then send me an email +uh + + align:start position:0% + + + + align:start position:0% + +i'm sorry to inform you you have a + + align:start position:0% +i'm sorry to inform you you have a + + + align:start position:0% +i'm sorry to inform you you have a +virus in your powerpoint + + align:start position:0% +virus in your powerpoint + + + align:start position:0% +virus in your powerpoint +and so this year i've upgraded + + align:start position:0% +and so this year i've upgraded + + + align:start position:0% +and so this year i've upgraded +powerpoint so this is actually an image + + align:start position:0% +powerpoint so this is actually an image + + + align:start position:0% +powerpoint so this is actually an image +rather than the actual text + + align:start position:0% +rather than the actual text + + + align:start position:0% +rather than the actual text +and so your viral detectors will not + + align:start position:0% +and so your viral detectors will not + + + align:start position:0% +and so your viral detectors will not +detect this unless they're a lot smarter + + align:start position:0% +detect this unless they're a lot smarter + + + align:start position:0% +detect this unless they're a lot smarter +than i think they are + + align:start position:0% +than i think they are + + + align:start position:0% +than i think they are +this on the other hand + + align:start position:0% +this on the other hand + + + align:start position:0% +this on the other hand +uh is the cost of these viruses this is + + align:start position:0% +uh is the cost of these viruses this is + + + align:start position:0% +uh is the cost of these viruses this is +not a laughing matter + + align:start position:0% +not a laughing matter + + + align:start position:0% +not a laughing matter +this is four times the cost of the + + align:start position:0% +this is four times the cost of the + + + align:start position:0% +this is four times the cost of the +entire human genome project + + align:start position:0% +entire human genome project + + + align:start position:0% +entire human genome project +per year the genome project took us + + align:start position:0% +per year the genome project took us + + + align:start position:0% +per year the genome project took us +about 20 years to get going every year + + align:start position:0% +about 20 years to get going every year + + + align:start position:0% +about 20 years to get going every year +we spend four times that amount on + + align:start position:0% +we spend four times that amount on + + + align:start position:0% +we spend four times that amount on +computer viruses which are as far as i + + align:start position:0% +computer viruses which are as far as i + + + align:start position:0% +computer viruses which are as far as i +can tell completely frivolous + + align:start position:0% +can tell completely frivolous + + + align:start position:0% +can tell completely frivolous +uh even more serious + + align:start position:0% +uh even more serious + + + align:start position:0% +uh even more serious +is this now this is real text this is + + align:start position:0% +is this now this is real text this is + + + align:start position:0% +is this now this is real text this is +not an image they look like an image to + + align:start position:0% +not an image they look like an image to + + + align:start position:0% +not an image they look like an image to +you uh + + align:start position:0% +you uh + + + align:start position:0% +you uh +it's it's very serious and i i sincerely + + align:start position:0% +it's it's very serious and i i sincerely + + + align:start position:0% +it's it's very serious and i i sincerely +hope that some of the people in this + + align:start position:0% +hope that some of the people in this + + + align:start position:0% +hope that some of the people in this +class + + align:start position:0% +class + + + align:start position:0% +class +make a contribution to + + align:start position:0% +make a contribution to + + + align:start position:0% +make a contribution to +the intellectual + + align:start position:0% +the intellectual + + + align:start position:0% +the intellectual +avenues which will ultimately lead to + + align:start position:0% +avenues which will ultimately lead to + + + align:start position:0% +avenues which will ultimately lead to +the defeat of the aids virus and various + + align:start position:0% +the defeat of the aids virus and various + + + align:start position:0% +the defeat of the aids virus and various +other + + align:start position:0% +other + + + align:start position:0% +other +viruses and bacteria like them that + + align:start position:0% +viruses and bacteria like them that + + + align:start position:0% +viruses and bacteria like them that +cause so much + + align:start position:0% + + + + align:start position:0% + +suffering in the world 20 million have + + align:start position:0% +suffering in the world 20 million have + + + align:start position:0% +suffering in the world 20 million have +died this is worse than the black plague + + align:start position:0% +died this is worse than the black plague + + + align:start position:0% +died this is worse than the black plague +in in the + + align:start position:0% +in in the + + + align:start position:0% +in in the +1918 influenza epidemic + + align:start position:0% +1918 influenza epidemic + + + align:start position:0% +1918 influenza epidemic +and the analogy here between this part + + align:start position:0% +and the analogy here between this part + + + align:start position:0% +and the analogy here between this part +of the virus just like this is a little + + align:start position:0% +of the virus just like this is a little + + + align:start position:0% +of the virus just like this is a little +piece of the viral code in symbols of + + align:start position:0% +piece of the viral code in symbols of + + + align:start position:0% +piece of the viral code in symbols of +the 20 amino acid single letter code + + align:start position:0% +the 20 amino acid single letter code + + + align:start position:0% +the 20 amino acid single letter code +this is a little piece of the + + align:start position:0% +this is a little piece of the + + + align:start position:0% +this is a little piece of the +computer virus + + align:start position:0% +computer virus + + + align:start position:0% +computer virus +and i've highlighted here the command + + align:start position:0% +and i've highlighted here the command + + + align:start position:0% +and i've highlighted here the command +copy in the computer virus this is just + + align:start position:0% +copy in the computer virus this is just + + + align:start position:0% +copy in the computer virus this is just +part of what it does to get this + + align:start position:0% +part of what it does to get this + + + align:start position:0% +part of what it does to get this +particular vbs script the thing you're + + align:start position:0% +particular vbs script the thing you're + + + align:start position:0% +particular vbs script the thing you're +seeing here into some other part of your + + align:start position:0% +seeing here into some other part of your + + + align:start position:0% +seeing here into some other part of your +directory + + align:start position:0% +directory + + + align:start position:0% +directory +and this + + align:start position:0% +and this + + + align:start position:0% +and this +in essentially is part of the copy + + align:start position:0% +in essentially is part of the copy + + + align:start position:0% +in essentially is part of the copy +command uh in the in the aids virus this + + align:start position:0% +command uh in the in the aids virus this + + + align:start position:0% +command uh in the in the aids virus this +is the polymerase the protein that's + + align:start position:0% +is the polymerase the protein that's + + + align:start position:0% +is the polymerase the protein that's +responsible for making copies of + + align:start position:0% +responsible for making copies of + + + align:start position:0% +responsible for making copies of +the + + align:start position:0% +the + + + align:start position:0% +the +code for the virus and highlighted in + + align:start position:0% +code for the virus and highlighted in + + + align:start position:0% +code for the virus and highlighted in +red here are some of the mutations that + + align:start position:0% +red here are some of the mutations that + + + align:start position:0% +red here are some of the mutations that +make this particular aids virus + + align:start position:0% +make this particular aids virus + + + align:start position:0% +make this particular aids virus +resistant to the drugs which have been + + align:start position:0% +resistant to the drugs which have been + + + align:start position:0% +resistant to the drugs which have been +instrumental in some cases in + + align:start position:0% +instrumental in some cases in + + + align:start position:0% +instrumental in some cases in +taming aids temporarily and at great + + align:start position:0% +taming aids temporarily and at great + + + align:start position:0% +taming aids temporarily and at great +cost + + align:start position:0% +cost + + + align:start position:0% +cost +clearly + + align:start position:0% +clearly + + + align:start position:0% +clearly +vaccines and hopefully other + + align:start position:0% +vaccines and hopefully other + + + align:start position:0% +vaccines and hopefully other +public health measures will be the + + align:start position:0% +public health measures will be the + + + align:start position:0% +public health measures will be the +answer + + align:start position:0% +answer + + + align:start position:0% +answer +here are some other conceptual + + align:start position:0% +here are some other conceptual + + + align:start position:0% +here are some other conceptual +connections these are not meant to be + + align:start position:0% +connections these are not meant to be + + + align:start position:0% +connections these are not meant to be +dogma or to limit you anyway but + + align:start position:0% +dogma or to limit you anyway but + + + align:start position:0% +dogma or to limit you anyway but +hopefully to expand the way you think + + align:start position:0% +hopefully to expand the way you think + + + align:start position:0% +hopefully to expand the way you think +about these things + + align:start position:0% +about these things + + + align:start position:0% +about these things +obviously as with other analogies they + + align:start position:0% +obviously as with other analogies they + + + align:start position:0% +obviously as with other analogies they +will break down but let's just follow + + align:start position:0% +will break down but let's just follow + + + align:start position:0% +will break down but let's just follow +for a moment + + align:start position:0% +for a moment + + + align:start position:0% +for a moment +what we're calling the instruction set + + align:start position:0% +what we're calling the instruction set + + + align:start position:0% +what we're calling the instruction set +the concept of the construction set + + align:start position:0% +the concept of the construction set + + + align:start position:0% +the concept of the construction set +in computers as a program + + align:start position:0% +in computers as a program + + + align:start position:0% +in computers as a program +in organisms as a genome + + align:start position:0% +in organisms as a genome + + + align:start position:0% +in organisms as a genome +we've already said bits are zeros and + + align:start position:0% +we've already said bits are zeros and + + + align:start position:0% +we've already said bits are zeros and +ones a c g and t + + align:start position:0% +ones a c g and t + + + align:start position:0% +ones a c g and t +the stable memory the thing that you can + + align:start position:0% +the stable memory the thing that you can + + + align:start position:0% +the stable memory the thing that you can +depend on but is a little bit slow for + + align:start position:0% +depend on but is a little bit slow for + + + align:start position:0% +depend on but is a little bit slow for +access are disks and tapes and computers + + align:start position:0% +access are disks and tapes and computers + + + align:start position:0% +access are disks and tapes and computers +and their dna + + align:start position:0% +and their dna + + + align:start position:0% +and their dna +or in some cases rna genomes + + align:start position:0% +or in some cases rna genomes + + + align:start position:0% +or in some cases rna genomes +that then you take it out of the slow + + align:start position:0% +that then you take it out of the slow + + + align:start position:0% +that then you take it out of the slow +memory stable memory and move it into + + align:start position:0% +memory stable memory and move it into + + + align:start position:0% +memory stable memory and move it into +something that's more active more + + align:start position:0% +something that's more active more + + + align:start position:0% +something that's more active more +volatile which is random access memory + + align:start position:0% +volatile which is random access memory + + + align:start position:0% +volatile which is random access memory +and computers + + align:start position:0% +and computers + + + align:start position:0% +and computers +and the rna + + align:start position:0% +and the rna + + + align:start position:0% +and the rna +in + + align:start position:0% +in + + + align:start position:0% +in +in organisms + + align:start position:0% +in organisms + + + align:start position:0% +in organisms +the environment for computers is tends + + align:start position:0% +the environment for computers is tends + + + align:start position:0% +the environment for computers is tends +to be complex + + align:start position:0% +to be complex + + + align:start position:0% +to be complex +it's the internet sockets and people + + align:start position:0% +it's the internet sockets and people + + + align:start position:0% +it's the internet sockets and people +banging on the keyboard while organisms + + align:start position:0% +banging on the keyboard while organisms + + + align:start position:0% +banging on the keyboard while organisms +can be very simple i gave some examples + + align:start position:0% +can be very simple i gave some examples + + + align:start position:0% +can be very simple i gave some examples +earlier where it's complex but it can be + + align:start position:0% +earlier where it's complex but it can be + + + align:start position:0% +earlier where it's complex but it can be +as simple as water and salts in which + + align:start position:0% +as simple as water and salts in which + + + align:start position:0% +as simple as water and salts in which +they can replicate very complicated + + align:start position:0% +they can replicate very complicated + + + align:start position:0% +they can replicate very complicated +structures + + align:start position:0% +structures + + + align:start position:0% +structures +the input and + + align:start position:0% +the input and + + + align:start position:0% +the input and +output can be + + align:start position:0% +output can be + + + align:start position:0% +output can be +the input can be analog and converted to + + align:start position:0% +the input can be analog and converted to + + + align:start position:0% +the input can be analog and converted to +digital and is processed digitally + + align:start position:0% +digital and is processed digitally + + + align:start position:0% +digital and is processed digitally +digital + + align:start position:0% +digital + + + align:start position:0% +digital +analog for output + + align:start position:0% +analog for output + + + align:start position:0% +analog for output +the analog say of your screens + + align:start position:0% +the analog say of your screens + + + align:start position:0% +the analog say of your screens +and the input output is governed by + + align:start position:0% +and the input output is governed by + + + align:start position:0% +and the input output is governed by +these proteins at the end of the central + + align:start position:0% +these proteins at the end of the central + + + align:start position:0% +these proteins at the end of the central +dogma + + align:start position:0% +dogma + + + align:start position:0% +dogma +in + + align:start position:0% +in + + + align:start position:0% +in +organisms + + align:start position:0% + + + + align:start position:0% + +when we put these uh + + align:start position:0% +when we put these uh + + + align:start position:0% +when we put these uh +when we make these complicated systems + + align:start position:0% +when we make these complicated systems + + + align:start position:0% +when we make these complicated systems +from simple things they go from monomer + + align:start position:0% +from simple things they go from monomer + + + align:start position:0% +from simple things they go from monomer +so-called monomers which really + + align:start position:0% +so-called monomers which really + + + align:start position:0% +so-called monomers which really +uh + + align:start position:0% + + + + align:start position:0% + +combine into polymers which need not be + + align:start position:0% +combine into polymers which need not be + + + align:start position:0% +combine into polymers which need not be +linear polymers all they often are in + + align:start position:0% +linear polymers all they often are in + + + align:start position:0% +linear polymers all they often are in +biological systems basically go from + + align:start position:0% +biological systems basically go from + + + align:start position:0% +biological systems basically go from +minerals to chips + + align:start position:0% +minerals to chips + + + align:start position:0% +minerals to chips +and computers these are replicated at + + align:start position:0% +and computers these are replicated at + + + align:start position:0% +and computers these are replicated at +factories the factories their cells can + + align:start position:0% +factories the factories their cells can + + + align:start position:0% +factories the factories their cells can +be as small as symptom leader remember + + align:start position:0% +be as small as symptom leader remember + + + align:start position:0% +be as small as symptom leader remember +this prefix is femto is 10 to the minus + + align:start position:0% +this prefix is femto is 10 to the minus + + + align:start position:0% +this prefix is femto is 10 to the minus + + align:start position:0% + + + align:start position:0% +that's about one cubic micron + + align:start position:0% +that's about one cubic micron + + + align:start position:0% +that's about one cubic micron +very small factories very + + align:start position:0% +very small factories very + + + align:start position:0% +very small factories very +amazing productivity and complexity + + align:start position:0% +amazing productivity and complexity + + + align:start position:0% +amazing productivity and complexity +again input output as above and + + align:start position:0% +again input output as above and + + + align:start position:0% +again input output as above and +communication is extremely fast and + + align:start position:0% +communication is extremely fast and + + + align:start position:0% +communication is extremely fast and +computers + + align:start position:0% +computers + + + align:start position:0% +computers +are slower but very rich in organisms + + align:start position:0% +are slower but very rich in organisms + + + align:start position:0% +are slower but very rich in organisms +after a very short break + + align:start position:0% +after a very short break + + + align:start position:0% +after a very short break +we can stretch we'll come back + + align:start position:0% +we can stretch we'll come back + + + align:start position:0% +we can stretch we'll come back +and talk in more detail about how + + align:start position:0% +and talk in more detail about how + + + align:start position:0% +and talk in more detail about how +computers actually are made and how + + align:start position:0% +computers actually are made and how + + + align:start position:0% +computers actually are made and how +biological systems are made + + align:start position:0% +biological systems are made + + + align:start position:0% +biological systems are made +thank you + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/hvcYz4yzS0w.txt b/hvcYz4yzS0w.txt new file mode 100644 index 0000000000000000000000000000000000000000..1f4e4e14c9a6772db7110bf26a7fc2921b5571df --- /dev/null +++ b/hvcYz4yzS0w.txt @@ -0,0 +1,339 @@ +align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +hello + + align:start position:0% +hello + + + align:start position:0% +hello +i'm dan fry and i'm the faculty research + + align:start position:0% +i'm dan fry and i'm the faculty research + + + align:start position:0% +i'm dan fry and i'm the faculty research +director at mit's d-lab + + align:start position:0% +director at mit's d-lab + + + align:start position:0% +director at mit's d-lab +i'm also principal investigator for the + + align:start position:0% +i'm also principal investigator for the + + + align:start position:0% +i'm also principal investigator for the +comprehensive initiative on technology + + align:start position:0% +comprehensive initiative on technology + + + align:start position:0% +comprehensive initiative on technology +evaluation + + align:start position:0% +evaluation + + + align:start position:0% +evaluation +which we refer to by the acronym site + + align:start position:0% +which we refer to by the acronym site + + + align:start position:0% +which we refer to by the acronym site +the site program was established in + + align:start position:0% +the site program was established in + + + align:start position:0% +the site program was established in +order to assess + + align:start position:0% +order to assess + + + align:start position:0% +order to assess +and evaluate technologies and products + + align:start position:0% +and evaluate technologies and products + + + align:start position:0% +and evaluate technologies and products +so that we can better understand + + align:start position:0% +so that we can better understand + + + align:start position:0% +so that we can better understand +which ones perform the best and also + + align:start position:0% +which ones perform the best and also + + + align:start position:0% +which ones perform the best and also +which ones provide the best value + + align:start position:0% +which ones provide the best value + + + align:start position:0% +which ones provide the best value +given the context and better information + + align:start position:0% +given the context and better information + + + align:start position:0% +given the context and better information +about products and technologies + + align:start position:0% +about products and technologies + + + align:start position:0% +about products and technologies +also helps us to best implement + + align:start position:0% +also helps us to best implement + + + align:start position:0% +also helps us to best implement +those technologies in an international + + align:start position:0% +those technologies in an international + + + align:start position:0% +those technologies in an international +development setting + + align:start position:0% +development setting + + + align:start position:0% +development setting +now this topic is especially important + + align:start position:0% +now this topic is especially important + + + align:start position:0% +now this topic is especially important +in machine learning + + align:start position:0% +in machine learning + + + align:start position:0% +in machine learning +we understand that these exciting new + + align:start position:0% +we understand that these exciting new + + + align:start position:0% +we understand that these exciting new +technologies + + align:start position:0% +technologies + + + align:start position:0% +technologies +can sometimes cause or else + + align:start position:0% +can sometimes cause or else + + + align:start position:0% +can sometimes cause or else +propagate certain inequities or biases + + align:start position:0% +propagate certain inequities or biases + + + align:start position:0% +propagate certain inequities or biases +and there are a number of techniques + + align:start position:0% +and there are a number of techniques + + + align:start position:0% +and there are a number of techniques +that are now emerging from the research + + align:start position:0% +that are now emerging from the research + + + align:start position:0% +that are now emerging from the research +community + + align:start position:0% +community + + + align:start position:0% +community +that can help us to mitigate those + + align:start position:0% +that can help us to mitigate those + + + align:start position:0% +that can help us to mitigate those +problems + + align:start position:0% +problems + + + align:start position:0% +problems +by adjusting the algorithms or else + + align:start position:0% +by adjusting the algorithms or else + + + align:start position:0% +by adjusting the algorithms or else +modifying data sets + + align:start position:0% +modifying data sets + + + align:start position:0% +modifying data sets +in order to provide better more + + align:start position:0% +in order to provide better more + + + align:start position:0% +in order to provide better more +equitable and more + + align:start position:0% +equitable and more + + + align:start position:0% +equitable and more +fair outcomes now we hope that you'll + + align:start position:0% +fair outcomes now we hope that you'll + + + align:start position:0% +fair outcomes now we hope that you'll +engage with us + + align:start position:0% +engage with us + + + align:start position:0% +engage with us +very deeply in this course and that + + align:start position:0% +very deeply in this course and that + + + align:start position:0% +very deeply in this course and that +we'll be able to provide knowledge that + + align:start position:0% +we'll be able to provide knowledge that + + + align:start position:0% +we'll be able to provide knowledge that +can help you to + + align:start position:0% +can help you to + + + align:start position:0% +can help you to +better implement these techniques in + + align:start position:0% +better implement these techniques in + + + align:start position:0% +better implement these techniques in +your own professional endeavors + + align:start position:0% +your own professional endeavors + + + align:start position:0% +your own professional endeavors +thanks for joining us in this course + + align:start position:0% + + + + align:start position:0% + +[Music] \ No newline at end of file diff --git a/i5lpHaGpeaI.txt b/i5lpHaGpeaI.txt new file mode 100644 index 0000000000000000000000000000000000000000..ada1638c4803140aff98b9d156ab7d47664fd51e --- /dev/null +++ b/i5lpHaGpeaI.txt @@ -0,0 +1,10539 @@ +align:start position:0% + +Okay. So, um so the topic of today is uh + + align:start position:0% +Okay. So, um so the topic of today is uh + + + align:start position:0% +Okay. So, um so the topic of today is uh +civ theory and the the large civ um + + align:start position:0% +civ theory and the the large civ um + + + align:start position:0% +civ theory and the the large civ um +which was the first place that I know of + + align:start position:0% +which was the first place that I know of + + + align:start position:0% +which was the first place that I know of +where proofs like the proof that proofs + + align:start position:0% +where proofs like the proof that proofs + + + align:start position:0% +where proofs like the proof that proofs +that we've been talking about appeared + + align:start position:0% +that we've been talking about appeared + + + align:start position:0% +that we've been talking about appeared +and it appeared in the context of of + + align:start position:0% +and it appeared in the context of of + + + align:start position:0% +and it appeared in the context of of +analytic number theory. Um, we'll talk + + align:start position:0% +analytic number theory. Um, we'll talk + + + align:start position:0% +analytic number theory. Um, we'll talk +about that and then if there's time I'll + + align:start position:0% +about that and then if there's time I'll + + + align:start position:0% +about that and then if there's time I'll +try to show you like a really very + + align:start position:0% +try to show you like a really very + + + align:start position:0% +try to show you like a really very +closely analogous thing in the context + + align:start position:0% +closely analogous thing in the context + + + align:start position:0% +closely analogous thing in the context +of real analysis. Um, and we'll compare + + align:start position:0% +of real analysis. Um, and we'll compare + + + align:start position:0% +of real analysis. Um, and we'll compare +it. + + align:start position:0% +it. + + + align:start position:0% +it. +Okay. Um, + + align:start position:0% + + + + align:start position:0% + +all right. So the setting of the large + + align:start position:0% +all right. So the setting of the large + + + align:start position:0% +all right. So the setting of the large +civ is that we have a function on the + + align:start position:0% +civ is that we have a function on the + + + align:start position:0% +civ is that we have a function on the +numbers from one up to n. So remember + + align:start position:0% +numbers from one up to n. So remember + + + align:start position:0% +numbers from one up to n. So remember +that that notation is the integers from + + align:start position:0% +that that notation is the integers from + + + align:start position:0% +that that notation is the integers from +one up to n and I have a function. + + align:start position:0% + + + + align:start position:0% + +Okay. And then I'm going to think about + + align:start position:0% +Okay. And then I'm going to think about + + + align:start position:0% +Okay. And then I'm going to think about +what happens when I + + align:start position:0% +what happens when I + + + align:start position:0% +what happens when I +reduce these integers mod p. + + align:start position:0% +reduce these integers mod p. + + + align:start position:0% +reduce these integers mod p. +So um + + align:start position:0% +So um + + + align:start position:0% +So um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so I'll have pi p of f that's a function + + align:start position:0% +so I'll have pi p of f that's a function + + + align:start position:0% +so I'll have pi p of f that's a function +from z mod p to c and the definition is + + align:start position:0% +from z mod p to c and the definition is + + + align:start position:0% +from z mod p to c and the definition is +like this pi pf of a is defined to be + + align:start position:0% +like this pi pf of a is defined to be + + + align:start position:0% +like this pi pf of a is defined to be +the sum over all the n= to a mod p of f + + align:start position:0% +the sum over all the n= to a mod p of f + + + align:start position:0% +the sum over all the n= to a mod p of f +of a. + + align:start position:0% + + + + align:start position:0% + +Okay. Um the setting of the large civ is + + align:start position:0% +Okay. Um the setting of the large civ is + + + align:start position:0% +Okay. Um the setting of the large civ is +I have I have one function f but then I + + align:start position:0% +I have I have one function f but then I + + + align:start position:0% +I have I have one function f but then I +consider this is sort of a projection of + + align:start position:0% +consider this is sort of a projection of + + + align:start position:0% +consider this is sort of a projection of +f and I consider pi p of f for many + + align:start position:0% +f and I consider pi p of f for many + + + align:start position:0% +f and I consider pi p of f for many +different ps and see what sort of the + + align:start position:0% +different ps and see what sort of the + + + align:start position:0% +different ps and see what sort of the +typical behavior and how the different + + align:start position:0% +typical behavior and how the different + + + align:start position:0% +typical behavior and how the different +the different ps are related to each + + align:start position:0% +the different ps are related to each + + + align:start position:0% +the different ps are related to each +other. + + align:start position:0% +other. + + + align:start position:0% +other. +Okay. Um + + align:start position:0% + + + + align:start position:0% + +okay. Now, as before, we've seen it's + + align:start position:0% +okay. Now, as before, we've seen it's + + + align:start position:0% +okay. Now, as before, we've seen it's +sometimes helpful to separate a function + + align:start position:0% +sometimes helpful to separate a function + + + align:start position:0% +sometimes helpful to separate a function +out into its constant part and its mean + + align:start position:0% +out into its constant part and its mean + + + align:start position:0% +out into its constant part and its mean +zero part. + + align:start position:0% +zero part. + + + align:start position:0% +zero part. +So, + + align:start position:0% +So, + + + align:start position:0% +So, +f0 would be so the take the average + + align:start position:0% +f0 would be so the take the average + + + align:start position:0% +f0 would be so the take the average +value. So, 1 / n= + + align:start position:0% +value. So, 1 / n= + + + align:start position:0% +value. So, 1 / n= +1 to n. + + align:start position:0% +1 to n. + + + align:start position:0% +1 to n. +So, that's the average value. + + align:start position:0% +So, that's the average value. + + + align:start position:0% +So, that's the average value. +And then maybe still + + align:start position:0% +And then maybe still + + + align:start position:0% +And then maybe still +I still have a function on on numbers + + align:start position:0% +I still have a function on on numbers + + + align:start position:0% +I still have a function on on numbers +from one to n. + + align:start position:0% +from one to n. + + + align:start position:0% +from one to n. +Okay. And then the high part of f is f + + align:start position:0% +Okay. And then the high part of f is f + + + align:start position:0% +Okay. And then the high part of f is f +minus the constant part. So subn + + align:start position:0% +minus the constant part. So subn + + + align:start position:0% +minus the constant part. So subn +f high of f is zero. + + align:start position:0% +f high of f is zero. + + + align:start position:0% +f high of f is zero. +So this is the dangerous notation with + + align:start position:0% +So this is the dangerous notation with + + + align:start position:0% +So this is the dangerous notation with +the I'll make it a capital h. + + align:start position:0% + + + + align:start position:0% + +Okay. And you can do the same thing with + + align:start position:0% +Okay. And you can do the same thing with + + + align:start position:0% +Okay. And you can do the same thing with +the with the projections. + + align:start position:0% +the with the projections. + + + align:start position:0% +the with the projections. +So if I take the projection of f zero, + + align:start position:0% +So if I take the projection of f zero, + + + align:start position:0% +So if I take the projection of f zero, +it's 1 / p + + align:start position:0% +it's 1 / p + + + align:start position:0% +it's 1 / p +sub a and z by pi + + align:start position:0% +sub a and z by pi + + + align:start position:0% +sub a and z by pi +p f of a. It's a constant function + + align:start position:0% + + + + align:start position:0% + +and pi p of f pi is pi p of f minus pi p + + align:start position:0% +and pi p of f pi is pi p of f minus pi p + + + align:start position:0% +and pi p of f pi is pi p of f minus pi p +of f. + + align:start position:0% + + + + align:start position:0% + +Okay, a little tiny remark is I was sort + + align:start position:0% +Okay, a little tiny remark is I was sort + + + align:start position:0% +Okay, a little tiny remark is I was sort +of careful about where to put the + + align:start position:0% +of careful about where to put the + + + align:start position:0% +of careful about where to put the +parenthesis, but it doesn't actually + + align:start position:0% +parenthesis, but it doesn't actually + + + align:start position:0% +parenthesis, but it doesn't actually +matter. So, + + align:start position:0% +matter. So, + + + align:start position:0% +matter. So, +um, pi p of f high is the same thing as + + align:start position:0% +um, pi p of f high is the same thing as + + + align:start position:0% +um, pi p of f high is the same thing as +pi p of f high and + + align:start position:0% +pi p of f high and + + + align:start position:0% +pi p of f high and +pi p of f zero is the same thing as pi p + + align:start position:0% +pi p of f zero is the same thing as pi p + + + align:start position:0% +pi p of f zero is the same thing as pi p +of x. + + align:start position:0% +of x. + + + align:start position:0% +of x. +>> Sorry, could you just explain what the + + align:start position:0% +>> Sorry, could you just explain what the + + + align:start position:0% +>> Sorry, could you just explain what the +bracket means on the definition of zero + + align:start position:0% +bracket means on the definition of zero + + + align:start position:0% +bracket means on the definition of zero +again? + + align:start position:0% +again? + + + align:start position:0% +again? +this one here. + + align:start position:0% +this one here. + + + align:start position:0% +this one here. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Um so f0 is a function of let's say m + + align:start position:0% +>> Um so f0 is a function of let's say m + + + align:start position:0% +>> Um so f0 is a function of let's say m +and + + align:start position:0% +and + + + align:start position:0% +and +inside the large bracket is a number + + align:start position:0% +inside the large bracket is a number + + + align:start position:0% +inside the large bracket is a number +which is like the the average value of + + align:start position:0% +which is like the the average value of + + + align:start position:0% +which is like the the average value of +f. + + align:start position:0% +f. + + + align:start position:0% +f. +>> Oh those are just parentheses here. + + align:start position:0% +>> Oh those are just parentheses here. + + + align:start position:0% +>> Oh those are just parentheses here. +>> Those are just parenthesis. + + align:start position:0% +>> Those are just parenthesis. + + + align:start position:0% +>> Those are just parenthesis. +>> Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. So the the theme of the large civ + + align:start position:0% +Okay. So the the theme of the large civ + + + align:start position:0% +Okay. So the the theme of the large civ +is that if you take a almost arbitrary + + align:start position:0% +is that if you take a almost arbitrary + + + align:start position:0% +is that if you take a almost arbitrary +function here and you look at many + + align:start position:0% +function here and you look at many + + + align:start position:0% +function here and you look at many +different projections then the um + + align:start position:0% +different projections then the um + + + align:start position:0% +different projections then the um +uh the oscillating part of the high + + align:start position:0% +uh the oscillating part of the high + + + align:start position:0% +uh the oscillating part of the high +frequency part of the projections will + + align:start position:0% +frequency part of the projections will + + + align:start position:0% +frequency part of the projections will +on average be pretty small whereas the + + align:start position:0% +on average be pretty small whereas the + + + align:start position:0% +on average be pretty small whereas the +um the constant part um well it only + + align:start position:0% +um the constant part um well it only + + + align:start position:0% +um the constant part um well it only +depends on the constant part of f but it + + align:start position:0% +depends on the constant part of f but it + + + align:start position:0% +depends on the constant part of f but it +will be it could be typically bigger. Um + + align:start position:0% +will be it could be typically bigger. Um + + + align:start position:0% +will be it could be typically bigger. Um +okay so let me write a theorem which is + + align:start position:0% +okay so let me write a theorem which is + + + align:start position:0% +okay so let me write a theorem which is +makes that sense + + align:start position:0% + + + + align:start position:0% + +I might need just a little more notation + + align:start position:0% +I might need just a little more notation + + + align:start position:0% +I might need just a little more notation +to state our theorem. + + align:start position:0% + + + + align:start position:0% + +Okay. So let's say capital P M is the + + align:start position:0% +Okay. So let's say capital P M is the + + + align:start position:0% +Okay. So let's say capital P M is the +set of prime numbers P prime in the + + align:start position:0% +set of prime numbers P prime in the + + + align:start position:0% +set of prime numbers P prime in the +range M / 2 less than P less than. + + align:start position:0% + + + + align:start position:0% + +Okay. So here is the main theorem which + + align:start position:0% +Okay. So here is the main theorem which + + + align:start position:0% +Okay. So here is the main theorem which +was proven by Linu + + align:start position:0% +was proven by Linu + + + align:start position:0% +was proven by Linu +says that if you have a function + + align:start position:0% +says that if you have a function + + + align:start position:0% +says that if you have a function +n goes to c um and we have an m which + + align:start position:0% +n goes to c um and we have an m which + + + align:start position:0% +n goes to c um and we have an m which +goes up to square root of n. + + align:start position:0% + + + + align:start position:0% + +Then if I take um + + align:start position:0% +Then if I take um + + + align:start position:0% +Then if I take um +the the sum + + align:start position:0% +the the sum + + + align:start position:0% +the the sum +p and pm + + align:start position:0% +p and pm + + + align:start position:0% +p and pm +of pi p of fi + + align:start position:0% +of pi p of fi + + + align:start position:0% +of pi p of fi +l2 + + align:start position:0% +l2 + + + align:start position:0% +l2 +and that is bounded by + + align:start position:0% +and that is bounded by + + + align:start position:0% +and that is bounded by +n / m times the sum on n of f of n^2. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% + + + + align:start position:0% + +so it takes a little bit of work to uh + + align:start position:0% +so it takes a little bit of work to uh + + + align:start position:0% +so it takes a little bit of work to uh +digest the statement of this theorem and + + align:start position:0% +digest the statement of this theorem and + + + align:start position:0% +digest the statement of this theorem and +like what kind of a bound this is giving + + align:start position:0% +like what kind of a bound this is giving + + + align:start position:0% +like what kind of a bound this is giving +us. So let's digest it together and and + + align:start position:0% +us. So let's digest it together and and + + + align:start position:0% +us. So let's digest it together and and +by doing we'll digest it by doing some + + align:start position:0% +by doing we'll digest it by doing some + + + align:start position:0% +by doing we'll digest it by doing some +applications and then after that we'll + + align:start position:0% +applications and then after that we'll + + + align:start position:0% +applications and then after that we'll +come back and we'll prove this theorem. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So, + + align:start position:0% +So, + + + align:start position:0% +So, +so there are the character in our story + + align:start position:0% +so there are the character in our story + + + align:start position:0% +so there are the character in our story +is the primes of size about M and it's + + align:start position:0% +is the primes of size about M and it's + + + align:start position:0% +is the primes of size about M and it's +useful to know about how many there are. + + align:start position:0% +useful to know about how many there are. + + + align:start position:0% +useful to know about how many there are. +So, a background fact from analytic + + align:start position:0% +So, a background fact from analytic + + + align:start position:0% +So, a background fact from analytic +number theory is that the number of + + align:start position:0% +number theory is that the number of + + + align:start position:0% +number theory is that the number of +primes about M is around M over log M + + align:start position:0% +primes about M is around M over log M + + + align:start position:0% +primes about M is around M over log M +which very roughly I'm just going to say + + align:start position:0% +which very roughly I'm just going to say + + + align:start position:0% +which very roughly I'm just going to say +is about M. + + align:start position:0% +is about M. + + + align:start position:0% +is about M. +Uh, okay. So, there are about M terms in + + align:start position:0% +Uh, okay. So, there are about M terms in + + + align:start position:0% +Uh, okay. So, there are about M terms in +this sum and it sometimes is helpful to + + align:start position:0% +this sum and it sometimes is helpful to + + + align:start position:0% +this sum and it sometimes is helpful to +replace the sum by an average. + + align:start position:0% +replace the sum by an average. + + + align:start position:0% +replace the sum by an average. +Um so correlary + + align:start position:0% +Um so correlary + + + align:start position:0% +Um so correlary +is that the average + + align:start position:0% + + + + align:start position:0% + +P and PM + + align:start position:0% +P and PM + + + align:start position:0% +P and PM +of pi P of FI + + align:start position:0% +of pi P of FI + + + align:start position:0% +of pi P of FI +L2 + + align:start position:0% +L2 + + + align:start position:0% +L2 +is less than N / M^2 + + align:start position:0% +is less than N / M^2 + + + align:start position:0% +is less than N / M^2 +times the sum on M of FI N + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So as a first application of this, let's + + align:start position:0% +So as a first application of this, let's + + + align:start position:0% +So as a first application of this, let's +um prove an estimate about uh so so we + + align:start position:0% +um prove an estimate about uh so so we + + + align:start position:0% +um prove an estimate about uh so so we +so last time I gave the example of the + + align:start position:0% +so last time I gave the example of the + + + align:start position:0% +so last time I gave the example of the +square numbers. Square numbers have the + + align:start position:0% +square numbers. Square numbers have the + + + align:start position:0% +square numbers. Square numbers have the +interesting property that if you reduce + + align:start position:0% +interesting property that if you reduce + + + align:start position:0% +interesting property that if you reduce +them mod p for any p you get the + + align:start position:0% +them mod p for any p you get the + + + align:start position:0% +them mod p for any p you get the +quadratic residues and they're only p+ + + align:start position:0% +quadratic residues and they're only p+ + + + align:start position:0% +quadratic residues and they're only p+ +one over two of them. Um so let's think + + align:start position:0% +one over two of them. Um so let's think + + + align:start position:0% +one over two of them. Um so let's think +about a situation like that. Suppose you + + align:start position:0% +about a situation like that. Suppose you + + + align:start position:0% +about a situation like that. Suppose you +have a set and when you reduce it modulo + + align:start position:0% +have a set and when you reduce it modulo + + + align:start position:0% +have a set and when you reduce it modulo +P, you get significantly less than all P + + align:start position:0% +P, you get significantly less than all P + + + align:start position:0% +P, you get significantly less than all P +of the of the residue classes. What does + + align:start position:0% +of the of the residue classes. What does + + + align:start position:0% +of the of the residue classes. What does +that tell us about the set? + + align:start position:0% + + + + align:start position:0% + +So there is a corlary + + align:start position:0% +So there is a corlary + + + align:start position:0% +So there is a corlary +if a is a subset of 1 to n + + align:start position:0% +if a is a subset of 1 to n + + + align:start position:0% +if a is a subset of 1 to n +and pi p of a is significantly smaller + + align:start position:0% +and pi p of a is significantly smaller + + + align:start position:0% +and pi p of a is significantly smaller +than p. So I'm going to say it's less + + align:start position:0% +than p. So I'm going to say it's less + + + align:start position:0% +than p. So I'm going to say it's less +than.99 + + align:start position:0% +than.99 + + + align:start position:0% +than.99 +* p just some constant that's less than + + align:start position:0% +* p just some constant that's less than + + + align:start position:0% +* p just some constant that's less than +one. Um, and + + align:start position:0% +one. Um, and + + + align:start position:0% +one. Um, and +for all P would be interesting, but but + + align:start position:0% +for all P would be interesting, but but + + + align:start position:0% +for all P would be interesting, but but +I'm going to say for all the P in P n to + + align:start position:0% +I'm going to say for all the P in P n to + + + align:start position:0% +I'm going to say for all the P in P n to +the 1/2. So we only actually are going + + align:start position:0% +the 1/2. So we only actually are going + + + align:start position:0% +the 1/2. So we only actually are going +to use the primes of size about n^ the + + align:start position:0% +to use the primes of size about n^ the + + + align:start position:0% +to use the primes of size about n^ the +1/2. + + align:start position:0% +1/2. + + + align:start position:0% +1/2. +Um, then the conclusion is that the size + + align:start position:0% +Um, then the conclusion is that the size + + + align:start position:0% +Um, then the conclusion is that the size +of a is bounded by around n to the 12. + + align:start position:0% +of a is bounded by around n to the 12. + + + align:start position:0% +of a is bounded by around n to the 12. +So this would be the this would be the + + align:start position:0% +So this would be the this would be the + + + align:start position:0% +So this would be the this would be the +case if a was the set of square numbers. + + align:start position:0% +case if a was the set of square numbers. + + + align:start position:0% +case if a was the set of square numbers. +A was the set of square numbers. would + + align:start position:0% +A was the set of square numbers. would + + + align:start position:0% +A was the set of square numbers. would +be basically half of P. This would be + + align:start position:0% +be basically half of P. This would be + + + align:start position:0% +be basically half of P. This would be +all the primes. So in particular all of + + align:start position:0% +all the primes. So in particular all of + + + align:start position:0% +all the primes. So in particular all of +those primes and this set of square + + align:start position:0% +those primes and this set of square + + + align:start position:0% +those primes and this set of square +numbers would have cardality n to the + + align:start position:0% +numbers would have cardality n to the + + + align:start position:0% +numbers would have cardality n to the +1/2. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So let's make our function a + + align:start position:0% +So let's make our function a + + + align:start position:0% +So let's make our function a +characteristic function of a. + + align:start position:0% +characteristic function of a. + + + align:start position:0% +characteristic function of a. +All right. Um + + align:start position:0% + + + + align:start position:0% + +okay. So + + align:start position:0% +okay. So + + + align:start position:0% +okay. So +if I look at the sum uh a and z mod p of + + align:start position:0% +if I look at the sum uh a and z mod p of + + + align:start position:0% +if I look at the sum uh a and z mod p of +pi p + + align:start position:0% +pi p + + + align:start position:0% +pi p +f of a squared let's so let's say that p + + align:start position:0% +f of a squared let's so let's say that p + + + align:start position:0% +f of a squared let's so let's say that p +is in this pn to the 12 + + align:start position:0% +is in this pn to the 12 + + + align:start position:0% +is in this pn to the 12 +okay so how big would this be well if + + align:start position:0% +okay so how big would this be well if + + + align:start position:0% +okay so how big would this be well if +each of these entries if each of these + + align:start position:0% +each of these entries if each of these + + + align:start position:0% +each of these entries if each of these +guys were the same as each other then + + align:start position:0% +guys were the same as each other then + + + align:start position:0% +guys were the same as each other then +the size of this thing would be a / p + + align:start position:0% +the size of this thing would be a / p + + + align:start position:0% +the size of this thing would be a / p +and it would be squared and I'd be + + align:start position:0% +and it would be squared and I'd be + + + align:start position:0% +and it would be squared and I'd be +summing over p terms. + + align:start position:0% +summing over p terms. + + + align:start position:0% +summing over p terms. +Right? So if all these values pi pf of a + + align:start position:0% +Right? So if all these values pi pf of a + + + align:start position:0% +Right? So if all these values pi pf of a +they were all equal to each other they + + align:start position:0% +they were all equal to each other they + + + align:start position:0% +they were all equal to each other they +would each have size size of a over pum + + align:start position:0% +would each have size size of a over pum + + + align:start position:0% +would each have size size of a over pum +and then the sum would be like this. + + align:start position:0% +and then the sum would be like this. + + + align:start position:0% +and then the sum would be like this. +They could be unequal to each other and + + align:start position:0% +They could be unequal to each other and + + + align:start position:0% +They could be unequal to each other and +then by koshi schwarz argument they + + align:start position:0% +then by koshi schwarz argument they + + + align:start position:0% +then by koshi schwarz argument they +would this would be even bigger. Okay. + + align:start position:0% +would this would be even bigger. Okay. + + + align:start position:0% +would this would be even bigger. Okay. +And then simplifying this a little bit, + + align:start position:0% +And then simplifying this a little bit, + + + align:start position:0% +And then simplifying this a little bit, +it's + + align:start position:0% +it's + + + align:start position:0% +it's +it's around a^2 n to the minus a half + + align:start position:0% + + + + align:start position:0% + +because p is around n^ the half. + + align:start position:0% + + + + align:start position:0% + +Okay. Now what happens if we take the + + align:start position:0% +Okay. Now what happens if we take the + + + align:start position:0% +Okay. Now what happens if we take the +high part? + + align:start position:0% +high part? + + + align:start position:0% +high part? +Um well + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% + + + + align:start position:0% + +pi p so the support + + align:start position:0% +pi p so the support + + + align:start position:0% +pi p so the support +of pi p of f that's contained in pi p of + + align:start position:0% +of pi p of f that's contained in pi p of + + + align:start position:0% +of pi p of f that's contained in pi p of +a + + align:start position:0% +a + + + align:start position:0% +a +um so the size of the support + + align:start position:0% +um so the size of the support + + + align:start position:0% +um so the size of the support +pi p of f is less than.99 + + align:start position:0% +pi p of f is less than.99 + + + align:start position:0% +pi p of f is less than.99 +* + + align:start position:0% + + + + align:start position:0% + +That's enough to say that this function + + align:start position:0% +That's enough to say that this function + + + align:start position:0% +That's enough to say that this function +is not super close to a constant + + align:start position:0% +is not super close to a constant + + + align:start position:0% +is not super close to a constant +function in L2. + + align:start position:0% + + + + align:start position:0% + +So that implies + + align:start position:0% +So that implies + + + align:start position:0% +So that implies +that um the sum and cp + + align:start position:0% +that um the sum and cp + + + align:start position:0% +that um the sum and cp +pi p of f high + + align:start position:0% +pi p of f high + + + align:start position:0% +pi p of f high +squared is around the sum without the + + align:start position:0% +squared is around the sum without the + + + align:start position:0% +squared is around the sum without the +high. + + align:start position:0% +high. + + + align:start position:0% +high. +[Applause] + + align:start position:0% + + + + align:start position:0% + +So, so all of these L2 norms they're + + align:start position:0% +So, so all of these L2 norms they're + + + align:start position:0% +So, so all of these L2 norms they're +they're all big. + + align:start position:0% + + + + align:start position:0% + +Does that feel intuitive to people? + + align:start position:0% +Does that feel intuitive to people? + + + align:start position:0% +Does that feel intuitive to people? +Should we talk about that more? + + align:start position:0% + + + + align:start position:0% + +>> Yeah. Okay. So, let's call let's call it + + align:start position:0% +>> Yeah. Okay. So, let's call let's call it + + + align:start position:0% +>> Yeah. Okay. So, let's call let's call it +a lema. + + align:start position:0% + + + + align:start position:0% + +So, lema is that if I have a function G + + align:start position:0% +So, lema is that if I have a function G + + + align:start position:0% +So, lema is that if I have a function G +um CP to C, it's not really important + + align:start position:0% +um CP to C, it's not really important + + + align:start position:0% +um CP to C, it's not really important +that this is CP. It's just a finite set. + + align:start position:0% +that this is CP. It's just a finite set. + + + align:start position:0% +that this is CP. It's just a finite set. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +and um + + align:start position:0% +and um + + + align:start position:0% +and um +uh and the support of G has size + + align:start position:0% +uh and the support of G has size + + + align:start position:0% +uh and the support of G has size +significantly less than P. + + align:start position:0% + + + + align:start position:0% + +Then the conclusion is that the high + + align:start position:0% +Then the conclusion is that the high + + + align:start position:0% +Then the conclusion is that the high +part of G L2 is around the same as GL2. + + align:start position:0% + + + + align:start position:0% + +Um okay. So, um, + + align:start position:0% + + + + align:start position:0% + +okay. So, G is G knot plus G high. And G + + align:start position:0% +okay. So, G is G knot plus G high. And G + + + align:start position:0% +okay. So, G is G knot plus G high. And G +knot and G high are always perpendicular + + align:start position:0% +knot and G high are always perpendicular + + + align:start position:0% +knot and G high are always perpendicular +to each other. + + align:start position:0% + + + + align:start position:0% + +Um + + align:start position:0% +Um + + + align:start position:0% +Um +so + + align:start position:0% +so + + + align:start position:0% +so +so the sum + + align:start position:0% +so the sum + + + align:start position:0% +so the sum +so gl 2 + + align:start position:0% +so gl 2 + + + align:start position:0% +so gl 2 +is around + + align:start position:0% +is around + + + align:start position:0% +is around +g2 + + align:start position:0% + + + + align:start position:0% + +is equal to g l2 2 plus g high l2. + + align:start position:0% + + + + align:start position:0% + +Um okay. + + align:start position:0% + + + + align:start position:0% + +Um + + align:start position:0% + + + + align:start position:0% + +um so okay if if GL L2 squared was much + + align:start position:0% +um so okay if if GL L2 squared was much + + + align:start position:0% +um so okay if if GL L2 squared was much +smaller than G L2 + + align:start position:0% +smaller than G L2 + + + align:start position:0% +smaller than G L2 +then clearly G high L2 squ would be + + align:start position:0% +then clearly G high L2 squ would be + + + align:start position:0% +then clearly G high L2 squ would be +bigger. + + align:start position:0% +bigger. + + + align:start position:0% +bigger. +So + + align:start position:0% +So + + + align:start position:0% +So +if G knot + + align:start position:0% +if G knot + + + align:start position:0% +if G knot +L2 2 um is less than half of G L2. + + align:start position:0% +L2 2 um is less than half of G L2. + + + align:start position:0% +L2 2 um is less than half of G L2. +We're done. + + align:start position:0% + + + + align:start position:0% + +Otherwise, we go the other way. + + align:start position:0% +Otherwise, we go the other way. + + + align:start position:0% +Otherwise, we go the other way. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +and um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% +so um + + + align:start position:0% +so um +let's say S is the support of G + + align:start position:0% +let's say S is the support of G + + + align:start position:0% +let's say S is the support of G +complement and notice that S is at least + + align:start position:0% +complement and notice that S is at least + + + align:start position:0% +complement and notice that S is at least +some definite fraction of P + + align:start position:0% +some definite fraction of P + + + align:start position:0% +some definite fraction of P +and on S + + align:start position:0% +and on S + + + align:start position:0% +and on S +uh G high is equal to I guess negative g + + align:start position:0% +uh G high is equal to I guess negative g + + + align:start position:0% +uh G high is equal to I guess negative g +because they have to add up to to zero. + + align:start position:0% +because they have to add up to to zero. + + + align:start position:0% +because they have to add up to to zero. +G vanishes on on on s. + + align:start position:0% +G vanishes on on on s. + + + align:start position:0% +G vanishes on on on s. +Um so we get + + align:start position:0% +Um so we get + + + align:start position:0% +Um so we get +g high l2 + + align:start position:0% +g high l2 + + + align:start position:0% +g high l2 +is at least um the sum the sum in s of + + align:start position:0% +is at least um the sum the sum in s of + + + align:start position:0% +is at least um the sum the sum in s of +of g + + align:start position:0% +of g + + + align:start position:0% +of g +squ. + + align:start position:0% +squ. + + + align:start position:0% +squ. +But since g is constant + + align:start position:0% +But since g is constant + + + align:start position:0% +But since g is constant +um this is at least s over p times + + align:start position:0% +um this is at least s over p times + + + align:start position:0% +um this is at least s over p times +g l2 + + align:start position:0% +g l2 + + + align:start position:0% +g l2 +which is then at least uh + + align:start position:0% +which is then at least uh + + + align:start position:0% +which is then at least uh +so s over p is on the order of 1 and g + + align:start position:0% +so s over p is on the order of 1 and g + + + align:start position:0% +so s over p is on the order of 1 and g +l2 is on the order of gl2. + + align:start position:0% +l2 is on the order of gl2. + + + align:start position:0% +l2 is on the order of gl2. +So that's + + align:start position:0% + + + + align:start position:0% + +okay. + + align:start position:0% + + + + align:start position:0% + +Okay. So the high part of this + + align:start position:0% +Okay. So the high part of this + + + align:start position:0% +Okay. So the high part of this +projection has an L2 norm that's + + align:start position:0% +projection has an L2 norm that's + + + align:start position:0% +projection has an L2 norm that's +comparable to the L2 norm of the whole + + align:start position:0% +comparable to the L2 norm of the whole + + + align:start position:0% +comparable to the L2 norm of the whole +projection which is at least this big in + + align:start position:0% +projection which is at least this big in + + + align:start position:0% +projection which is at least this big in +terms of the size of A. + + align:start position:0% +terms of the size of A. + + + align:start position:0% +terms of the size of A. +But the L2 norm of the projection high + + align:start position:0% +But the L2 norm of the projection high + + + align:start position:0% +But the L2 norm of the projection high +pride of the projection shouldn't be too + + align:start position:0% +pride of the projection shouldn't be too + + + align:start position:0% +pride of the projection shouldn't be too +big by our theorem. + + align:start position:0% +big by our theorem. + + + align:start position:0% +big by our theorem. +So the theorem + + align:start position:0% +So the theorem + + + align:start position:0% +So the theorem +implies that the average over p^ + + align:start position:0% +implies that the average over p^ + + + align:start position:0% +implies that the average over p^ +12 of this same thing is bounded above + + align:start position:0% +12 of this same thing is bounded above + + + align:start position:0% +12 of this same thing is bounded above +by + + align:start position:0% +by + + + align:start position:0% +by +n / m^2. My m is the square root of n. + + align:start position:0% +n / m^2. My m is the square root of n. + + + align:start position:0% +n / m^2. My m is the square root of n. +So this just cancels and then I get the + + align:start position:0% +So this just cancels and then I get the + + + align:start position:0% +So this just cancels and then I get the +sum of f of n^2. + + align:start position:0% +sum of f of n^2. + + + align:start position:0% +sum of f of n^2. +So this would be bounded above by the + + align:start position:0% +So this would be bounded above by the + + + align:start position:0% +So this would be bounded above by the +size of A. + + align:start position:0% + + + + align:start position:0% + +Okay. So to summarize this is bounded by + + align:start position:0% +Okay. So to summarize this is bounded by + + + align:start position:0% +Okay. So to summarize this is bounded by +this is bounded by this a^2 n^ the minus + + align:start position:0% +this is bounded by this a^2 n^ the minus + + + align:start position:0% +this is bounded by this a^2 n^ the minus +a half bounded by a a is bounded by n^ + + align:start position:0% +a half bounded by a a is bounded by n^ + + + align:start position:0% +a half bounded by a a is bounded by n^ +the 1 + + align:start position:0% + + + + align:start position:0% + +Any questions or comments about it? + + align:start position:0% + + + + align:start position:0% + +Okay. Okay. So, um, so I feel like it's, + + align:start position:0% +Okay. Okay. So, um, so I feel like it's, + + + align:start position:0% +Okay. Okay. So, um, so I feel like it's, +you know, it's interesting that it + + align:start position:0% +you know, it's interesting that it + + + align:start position:0% +you know, it's interesting that it +matches the examples of of the square + + align:start position:0% +matches the examples of of the square + + + align:start position:0% +matches the examples of of the square +numbers. So, it's sort of sharp in that + + align:start position:0% +numbers. So, it's sort of sharp in that + + + align:start position:0% +numbers. So, it's sort of sharp in that +context. Um + + align:start position:0% +context. Um + + + align:start position:0% +context. Um +uh but also it would be nice to discuss + + align:start position:0% +uh but also it would be nice to discuss + + + align:start position:0% +uh but also it would be nice to discuss +more and look at more examples to try to + + align:start position:0% +more and look at more examples to try to + + + align:start position:0% +more and look at more examples to try to +get a feel for sort of the numerology of + + align:start position:0% +get a feel for sort of the numerology of + + + align:start position:0% +get a feel for sort of the numerology of +the equations. And a helpful reference + + align:start position:0% +the equations. And a helpful reference + + + align:start position:0% +the equations. And a helpful reference +point for me is to look at a random set. + + align:start position:0% +point for me is to look at a random set. + + + align:start position:0% +point for me is to look at a random set. +So reference point + + align:start position:0% + + + + align:start position:0% + +be a random set. + + align:start position:0% + + + + align:start position:0% + +Okay. So here we're going to take a + + align:start position:0% +Okay. So here we're going to take a + + + align:start position:0% +Okay. So here we're going to take a +subset of the numbers from 1 to n and we + + align:start position:0% +subset of the numbers from 1 to n and we + + + align:start position:0% +subset of the numbers from 1 to n and we +include + + align:start position:0% +include + + + align:start position:0% +include +each number in a + + align:start position:0% +each number in a + + + align:start position:0% +each number in a +with probability 1/2. + + align:start position:0% +with probability 1/2. + + + align:start position:0% +with probability 1/2. +You could also as an exercise play with + + align:start position:0% +You could also as an exercise play with + + + align:start position:0% +You could also as an exercise play with +this probability but let's just talk + + align:start position:0% +this probability but let's just talk + + + align:start position:0% +this probability but let's just talk +about 1/2 and you know independently. + + align:start position:0% +about 1/2 and you know independently. + + + align:start position:0% +about 1/2 and you know independently. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So um + + align:start position:0% +So um + + + align:start position:0% +So um +so + + align:start position:0% +so + + + align:start position:0% +so +what would we expect + + align:start position:0% + + + + align:start position:0% + +pi p characteristic function at a what + + align:start position:0% +pi p characteristic function at a what + + + align:start position:0% +pi p characteristic function at a what +would we how would we expect this to + + align:start position:0% +would we how would we expect this to + + + align:start position:0% +would we how would we expect this to +behave? + + align:start position:0% + + + + align:start position:0% + +So this is the number of n uh from one + + align:start position:0% +So this is the number of n uh from one + + + align:start position:0% +So this is the number of n uh from one +up to n. So that n= a mod p and n is in + + align:start position:0% +up to n. So that n= a mod p and n is in + + + align:start position:0% +up to n. So that n= a mod p and n is in +capital a + + align:start position:0% +capital a + + + align:start position:0% +capital a +and each one of those candidates was + + align:start position:0% +and each one of those candidates was + + + align:start position:0% +and each one of those candidates was +chosen with probability a half. + + align:start position:0% + + + + align:start position:0% + +Okay. So, + + align:start position:0% + + + + align:start position:0% + +so the expected value over our choice of + + align:start position:0% +so the expected value over our choice of + + + align:start position:0% +so the expected value over our choice of +a so over the random choice of this set + + align:start position:0% +a so over the random choice of this set + + + align:start position:0% +a so over the random choice of this set +a of pi p1 a little a would be half of + + align:start position:0% +a of pi p1 a little a would be half of + + + align:start position:0% +a of pi p1 a little a would be half of +the number of guys here. + + align:start position:0% + + + + align:start position:0% + +So that's essentially um half of n over + + align:start position:0% +So that's essentially um half of n over + + + align:start position:0% +So that's essentially um half of n over +p. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +But um well you you wouldn't necessarily + + align:start position:0% +But um well you you wouldn't necessarily + + + align:start position:0% +But um well you you wouldn't necessarily +expect this number to be exactly n over + + align:start position:0% +expect this number to be exactly n over + + + align:start position:0% +expect this number to be exactly n over +2p every time. If we choose randomly + + align:start position:0% +2p every time. If we choose randomly + + + align:start position:0% +2p every time. If we choose randomly +you'll see some ups and downs. Um and um + + align:start position:0% +you'll see some ups and downs. Um and um + + + align:start position:0% +you'll see some ups and downs. Um and um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um so the standard deviation of the + + align:start position:0% +um so the standard deviation of the + + + align:start position:0% +um so the standard deviation of the +number that gets picked here would be + + align:start position:0% +number that gets picked here would be + + + align:start position:0% +number that gets picked here would be +the square root of the size of this. + + align:start position:0% +the square root of the size of this. + + + align:start position:0% +the square root of the size of this. +We also would see + + align:start position:0% +We also would see + + + align:start position:0% +We also would see +that with high probability + + align:start position:0% + + + + align:start position:0% + +the size of the actual size of the + + align:start position:0% +the size of the actual size of the + + + align:start position:0% +the size of the actual size of the +projection minus + + align:start position:0% +projection minus + + + align:start position:0% +projection minus +the approximate size + + align:start position:0% +the approximate size + + + align:start position:0% +the approximate size +would be bounded by like the square root + + align:start position:0% +would be bounded by like the square root + + + align:start position:0% +would be bounded by like the square root +of the um of of this + + align:start position:0% + + + + align:start position:0% + +um and it typ typically would have size + + align:start position:0% +um and it typ typically would have size + + + align:start position:0% +um and it typ typically would have size +around this square root. + + align:start position:0% + + + + align:start position:0% + +Okay. So for example + + align:start position:0% +Okay. So for example + + + align:start position:0% +Okay. So for example +uh if if p is in capital p n to the 12 + + align:start position:0% +uh if if p is in capital p n to the 12 + + + align:start position:0% +uh if if p is in capital p n to the 12 +then the actual size of the projection + + align:start position:0% +then the actual size of the projection + + + align:start position:0% +then the actual size of the projection +minus its expected size would be around + + align:start position:0% +minus its expected size would be around + + + align:start position:0% +minus its expected size would be around +n to the + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So let's compare this with what our what + + align:start position:0% +So let's compare this with what our what + + + align:start position:0% +So let's compare this with what our what +our what our theorem says about an + + align:start position:0% +our what our theorem says about an + + + align:start position:0% +our what our theorem says about an +arbitrary set. + + align:start position:0% +arbitrary set. + + + align:start position:0% +arbitrary set. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +so so what we concluded is for every P + + align:start position:0% +so so what we concluded is for every P + + + align:start position:0% +so so what we concluded is for every P +in here and for every A in C mod P + + align:start position:0% +in here and for every A in C mod P + + + align:start position:0% +in here and for every A in C mod P +we would have this. So if we took a + + align:start position:0% +we would have this. So if we took a + + + align:start position:0% +we would have this. So if we took a +random set um and then for every P and + + align:start position:0% +random set um and then for every P and + + + align:start position:0% +random set um and then for every P and +every A + + align:start position:0% +every A + + + align:start position:0% +every A +the difference between the actual size + + align:start position:0% +the difference between the actual size + + + align:start position:0% +the difference between the actual size +of the projection and its expected size + + align:start position:0% +of the projection and its expected size + + + align:start position:0% +of the projection and its expected size +would be a square root of the of the + + align:start position:0% +would be a square root of the of the + + + align:start position:0% +would be a square root of the of the +number of choices which would work out + + align:start position:0% +number of choices which would work out + + + align:start position:0% +number of choices which would work out +to n^ the 1/4. + + align:start position:0% +to n^ the 1/4. + + + align:start position:0% +to n^ the 1/4. +We're going to compare this to um what + + align:start position:0% +We're going to compare this to um what + + + align:start position:0% +We're going to compare this to um what +what our large civ tells us about an + + align:start position:0% +what our large civ tells us about an + + + align:start position:0% +what our large civ tells us about an +arbitrary set. + + align:start position:0% + + + + align:start position:0% + +Any questions or comments about the + + align:start position:0% +Any questions or comments about the + + + align:start position:0% +Any questions or comments about the +reference setup? + + align:start position:0% + + + + align:start position:0% + +So corollary three. So a is any um a is + + align:start position:0% +So corollary three. So a is any um a is + + + align:start position:0% +So corollary three. So a is any um a is +any subset of numbers up to n. + + align:start position:0% + + + + align:start position:0% + +Then um + + align:start position:0% +Then um + + + align:start position:0% +Then um +if I take the average + + align:start position:0% +if I take the average + + + align:start position:0% +if I take the average +over primes of size around n to the half + + align:start position:0% +over primes of size around n to the half + + + align:start position:0% +over primes of size around n to the half +um and then I take the average over a z + + align:start position:0% +um and then I take the average over a z + + + align:start position:0% +um and then I take the average over a z +mod p. I take the actual size pi p 1 a + + align:start position:0% +mod p. I take the actual size pi p 1 a + + + align:start position:0% +mod p. I take the actual size pi p 1 a +and I subtract off the expected size. um + + align:start position:0% +and I subtract off the expected size. um + + + align:start position:0% +and I subtract off the expected size. um +a over a over p. + + align:start position:0% +a over a over p. + + + align:start position:0% +a over a over p. +So this is this is what so we have this + + align:start position:0% +So this is this is what so we have this + + + align:start position:0% +So this is this is what so we have this +many elements and we reduce them all mod + + align:start position:0% +many elements and we reduce them all mod + + + align:start position:0% +many elements and we reduce them all mod +p. I would expect on average that this + + align:start position:0% +p. I would expect on average that this + + + align:start position:0% +p. I would expect on average that this +number of them would be congruent to + + align:start position:0% +number of them would be congruent to + + + align:start position:0% +number of them would be congruent to +little a mod b. + + align:start position:0% +little a mod b. + + + align:start position:0% +little a mod b. +So then this is bounded by n to the one + + align:start position:0% +So then this is bounded by n to the one + + + align:start position:0% +So then this is bounded by n to the one +and this matches this + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Um, so + + align:start position:0% + + + + align:start position:0% + +so the proof is uh coropy down what + + align:start position:0% +so the proof is uh coropy down what + + + align:start position:0% +so the proof is uh coropy down what +corlary one tells us and it basically + + align:start position:0% +corlary one tells us and it basically + + + align:start position:0% +corlary one tells us and it basically +tells us this. + + align:start position:0% +tells us this. + + + align:start position:0% +tells us this. +So we're going to plug in corlary one + + align:start position:0% +So we're going to plug in corlary one + + + align:start position:0% +So we're going to plug in corlary one +where um p is pn + + align:start position:0% +where um p is pn + + + align:start position:0% +where um p is pn +um where where m is n to the 12. that + + align:start position:0% +um where where m is n to the 12. that + + + align:start position:0% +um where where m is n to the 12. that +will make this disappear. + + align:start position:0% +will make this disappear. + + + align:start position:0% +will make this disappear. +and cor so corlary one tells us that the + + align:start position:0% +and cor so corlary one tells us that the + + + align:start position:0% +and cor so corlary one tells us that the +average + + align:start position:0% +average + + + align:start position:0% +average +p and pn to the half sum a and z mod p + + align:start position:0% +p and pn to the half sum a and z mod p + + + align:start position:0% +p and pn to the half sum a and z mod p +of pi p1 a of a minus a over p^ 2 um is + + align:start position:0% +of pi p1 a of a minus a over p^ 2 um is + + + align:start position:0% +of pi p1 a of a minus a over p^ 2 um is +bounded by the l2 norm of f which would + + align:start position:0% +bounded by the l2 norm of f which would + + + align:start position:0% +bounded by the l2 norm of f which would +be the size of a + + align:start position:0% + + + + align:start position:0% + +Okay. Um, and that's smaller than n. + + align:start position:0% +Okay. Um, and that's smaller than n. + + + align:start position:0% +Okay. Um, and that's smaller than n. +Then if I want to replace this average, + + align:start position:0% +Then if I want to replace this average, + + + align:start position:0% +Then if I want to replace this average, +this sum by an average, + + align:start position:0% + + + + align:start position:0% + +then I'm going to divide by p, which has + + align:start position:0% +then I'm going to divide by p, which has + + + align:start position:0% +then I'm going to divide by p, which has +size around n^ the 1/2. So I replace the + + align:start position:0% +size around n^ the 1/2. So I replace the + + + align:start position:0% +size around n^ the 1/2. So I replace the +sum by the average. Then this is bounded + + align:start position:0% +sum by the average. Then this is bounded + + + align:start position:0% +sum by the average. Then this is bounded +by n^ the 1/2. + + align:start position:0% +by n^ the 1/2. + + + align:start position:0% +by n^ the 1/2. +And there's a square here. So I want to + + align:start position:0% +And there's a square here. So I want to + + + align:start position:0% +And there's a square here. So I want to +get rid of the square. I would use Koshy + + align:start position:0% +get rid of the square. I would use Koshy + + + align:start position:0% +get rid of the square. I would use Koshy +Schwarz. Get the average on P, average + + align:start position:0% +Schwarz. Get the average on P, average + + + align:start position:0% +Schwarz. Get the average on P, average +on A. + + align:start position:0% + + + + align:start position:0% + +Get rid of this. + + align:start position:0% + + + + align:start position:0% + +So that's the proof of the coral. + + align:start position:0% + + + + align:start position:0% + +Okay. Um + + align:start position:0% + + + + align:start position:0% + +so so the large civ is telling us that + + align:start position:0% +so so the large civ is telling us that + + + align:start position:0% +so so the large civ is telling us that +if you look at a residue class with a + + align:start position:0% +if you look at a residue class with a + + + align:start position:0% +if you look at a residue class with a +random P and a random A + + align:start position:0% +random P and a random A + + + align:start position:0% +random P and a random A +then it behaves a so you take an + + align:start position:0% +then it behaves a so you take an + + + align:start position:0% +then it behaves a so you take an +arbitrary set a worst case complicated + + align:start position:0% +arbitrary set a worst case complicated + + + align:start position:0% +arbitrary set a worst case complicated +any set at all but then you look at a + + align:start position:0% +any set at all but then you look at a + + + align:start position:0% +any set at all but then you look at a +random residue class with a random P and + + align:start position:0% +random residue class with a random P and + + + align:start position:0% +random residue class with a random P and +a random A then it behaves a lot like + + align:start position:0% +a random A then it behaves a lot like + + + align:start position:0% +a random A then it behaves a lot like +you had taken a random set. + + align:start position:0% + + + + align:start position:0% + +Um, okay. So, a cute application of this + + align:start position:0% +Um, okay. So, a cute application of this + + + align:start position:0% +Um, okay. So, a cute application of this +is if a is the set of primes and there's + + align:start position:0% +is if a is the set of primes and there's + + + align:start position:0% +is if a is the set of primes and there's +a fun question as a interesting question + + align:start position:0% +a fun question as a interesting question + + + align:start position:0% +a fun question as a interesting question +in number theory. How many primes are + + align:start position:0% +in number theory. How many primes are + + + align:start position:0% +in number theory. How many primes are +there in some arithmetic progression? + + align:start position:0% +there in some arithmetic progression? + + + align:start position:0% +there in some arithmetic progression? +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +so that that's exactly this thing. A is + + align:start position:0% +so that that's exactly this thing. A is + + + align:start position:0% +so that that's exactly this thing. A is +the set of primes and this is telling us + + align:start position:0% +the set of primes and this is telling us + + + align:start position:0% +the set of primes and this is telling us +how many primes there are that are + + align:start position:0% +how many primes there are that are + + + align:start position:0% +how many primes there are that are +congruent to A modulo little B. + + align:start position:0% +congruent to A modulo little B. + + + align:start position:0% +congruent to A modulo little B. +Um and um + + align:start position:0% +Um and um + + + align:start position:0% +Um and um +and + + align:start position:0% +and + + + align:start position:0% +and +so the question is how evenly + + align:start position:0% +so the question is how evenly + + + align:start position:0% +so the question is how evenly +distributed are the primes among these + + align:start position:0% +distributed are the primes among these + + + align:start position:0% +distributed are the primes among these +different arithmetic progressions? And + + align:start position:0% +different arithmetic progressions? And + + + align:start position:0% +different arithmetic progressions? And +the conjecture would be that for every + + align:start position:0% +the conjecture would be that for every + + + align:start position:0% +the conjecture would be that for every +little p and every little a that's not + + align:start position:0% +little p and every little a that's not + + + align:start position:0% +little p and every little a that's not +zero, this is always true. + + align:start position:0% +zero, this is always true. + + + align:start position:0% +zero, this is always true. +Um, and this corlary actually makes some + + align:start position:0% +Um, and this corlary actually makes some + + + align:start position:0% +Um, and this corlary actually makes some +progress towards that. It says we don't + + align:start position:0% +progress towards that. It says we don't + + + align:start position:0% +progress towards that. It says we don't +know that it's true for all the little + + align:start position:0% +know that it's true for all the little + + + align:start position:0% +know that it's true for all the little +P's and all the little A's, but we know + + align:start position:0% +P's and all the little A's, but we know + + + align:start position:0% +P's and all the little A's, but we know +it's true for most of them. + + align:start position:0% +it's true for most of them. + + + align:start position:0% +it's true for most of them. +Now, it's a little bit silly to call + + align:start position:0% +Now, it's a little bit silly to call + + + align:start position:0% +Now, it's a little bit silly to call +that a correlary about about the primes + + align:start position:0% +that a correlary about about the primes + + + align:start position:0% +that a correlary about about the primes +because it uses nothing about the + + align:start position:0% +because it uses nothing about the + + + align:start position:0% +because it uses nothing about the +primes. It just uses the fact that the + + align:start position:0% +primes. It just uses the fact that the + + + align:start position:0% +primes. It just uses the fact that the +primes are a set of numbers. Um but um + + align:start position:0% +primes are a set of numbers. Um but um + + + align:start position:0% +primes are a set of numbers. Um but um +uh okay but but that line of reasoning + + align:start position:0% +uh okay but but that line of reasoning + + + align:start position:0% +uh okay but but that line of reasoning +is actually important in some of the + + align:start position:0% +is actually important in some of the + + + align:start position:0% +is actually important in some of the +some of the things we know about the + + align:start position:0% +some of the things we know about the + + + align:start position:0% +some of the things we know about the +questions how well are primes + + align:start position:0% +questions how well are primes + + + align:start position:0% +questions how well are primes +distributed modulo p okay okay so next + + align:start position:0% +distributed modulo p okay okay so next + + + align:start position:0% +distributed modulo p okay okay so next +class we'll come back to the question um + + align:start position:0% +class we'll come back to the question um + + + align:start position:0% +class we'll come back to the question um +how much do we know about uh about this + + align:start position:0% +how much do we know about uh about this + + + align:start position:0% +how much do we know about uh about this +function when a is the set of primes um + + align:start position:0% +function when a is the set of primes um + + + align:start position:0% +function when a is the set of primes um +and we'll do the the bombiier venogradov + + align:start position:0% +and we'll do the the bombiier venogradov + + + align:start position:0% +and we'll do the the bombiier venogradov +theorem which is not quite the + + align:start position:0% +theorem which is not quite the + + + align:start position:0% +theorem which is not quite the +state-of-the-art but for many many years + + align:start position:0% +state-of-the-art but for many many years + + + align:start position:0% +state-of-the-art but for many many years +was the state-of-the-art about about + + align:start position:0% +was the state-of-the-art about about + + + align:start position:0% +was the state-of-the-art about about +this question. Um + + align:start position:0% +this question. Um + + + align:start position:0% +this question. Um +and well yeah any it uses these ideas in + + align:start position:0% +and well yeah any it uses these ideas in + + + align:start position:0% +and well yeah any it uses these ideas in +a crucial way. + + align:start position:0% + + + + align:start position:0% + +Okay. So that was my survey of some + + align:start position:0% +Okay. So that was my survey of some + + + align:start position:0% +Okay. So that was my survey of some +applications of this large civ + + align:start position:0% +applications of this large civ + + + align:start position:0% +applications of this large civ +inequality and next we'll prove the + + align:start position:0% +inequality and next we'll prove the + + + align:start position:0% +inequality and next we'll prove the +large civ inequality itself. + + align:start position:0% + + + + align:start position:0% + +Oh, there's actually there was one other + + align:start position:0% +Oh, there's actually there was one other + + + align:start position:0% +Oh, there's actually there was one other +thing I wanted to say. So, okay. So, + + align:start position:0% +thing I wanted to say. So, okay. So, + + + align:start position:0% +thing I wanted to say. So, okay. So, +imagine that a was a set of size n /2. + + align:start position:0% + + + + align:start position:0% + +Then, + + align:start position:0% +Then, + + + align:start position:0% +Then, +um this thing here + + align:start position:0% +um this thing here + + + align:start position:0% +um this thing here +would have size about n over p which + + align:start position:0% +would have size about n over p which + + + align:start position:0% +would have size about n over p which +works out to about n^ the 1/2 and this + + align:start position:0% +works out to about n^ the 1/2 and this + + + align:start position:0% +works out to about n^ the 1/2 and this +thing has size about n to the one half + + align:start position:0% +thing has size about n to the one half + + + align:start position:0% +thing has size about n to the one half +and the error is about n to the one + + align:start position:0% +and the error is about n to the one + + + align:start position:0% +and the error is about n to the one +quarter. So this thing here is the pi pi + + align:start position:0% +quarter. So this thing here is the pi pi + + + align:start position:0% +quarter. So this thing here is the pi pi +p of f sub0. + + align:start position:0% +p of f sub0. + + + align:start position:0% +p of f sub0. +And so what what we're seeing here is + + align:start position:0% +And so what what we're seeing here is + + + align:start position:0% +And so what what we're seeing here is +that the um the pi p of f0 + + align:start position:0% +that the um the pi p of f0 + + + align:start position:0% +that the um the pi p of f0 +is much larger than pi p of f high at + + align:start position:0% +is much larger than pi p of f high at + + + align:start position:0% +is much larger than pi p of f high at +most of the points. So say in L2. + + align:start position:0% +most of the points. So say in L2. + + + align:start position:0% +most of the points. So say in L2. +So when we we take a set of size n /2 + + align:start position:0% +So when we we take a set of size n /2 + + + align:start position:0% +So when we we take a set of size n /2 +and we look at all these different + + align:start position:0% +and we look at all these different + + + align:start position:0% +and we look at all these different +projections, a typical projection looks + + align:start position:0% +projections, a typical projection looks + + + align:start position:0% +projections, a typical projection looks +almost constant. it's a constant + + align:start position:0% +almost constant. it's a constant + + + align:start position:0% +almost constant. it's a constant +function plus something that's much + + align:start position:0% +function plus something that's much + + + align:start position:0% +function plus something that's much +smaller. + + align:start position:0% +smaller. + + + align:start position:0% +smaller. +Um, so this process of taking a random + + align:start position:0% +Um, so this process of taking a random + + + align:start position:0% +Um, so this process of taking a random +function takes a set with with no + + align:start position:0% +function takes a set with with no + + + align:start position:0% +function takes a set with with no +structure and it produces something + + align:start position:0% +structure and it produces something + + + align:start position:0% +structure and it produces something +that's almost constant. And people + + align:start position:0% +that's almost constant. And people + + + align:start position:0% +that's almost constant. And people +sometimes use the word that the + + align:start position:0% +sometimes use the word that the + + + align:start position:0% +sometimes use the word that the +projections are getting uh smoother. And + + align:start position:0% +projections are getting uh smoother. And + + + align:start position:0% +projections are getting uh smoother. And +when we do the real analysis version a + + align:start position:0% +when we do the real analysis version a + + + align:start position:0% +when we do the real analysis version a +little bit later in class, we'll see + + align:start position:0% +little bit later in class, we'll see + + + align:start position:0% +little bit later in class, we'll see +that smoother is is exactly the the + + align:start position:0% +that smoother is is exactly the the + + + align:start position:0% +that smoother is is exactly the the +right word. + + align:start position:0% + + + + align:start position:0% + +Cool. Okay. Um yeah so I think that's a + + align:start position:0% +Cool. Okay. Um yeah so I think that's a + + + align:start position:0% +Cool. Okay. Um yeah so I think that's a +good way to summarize what the largest + + align:start position:0% +good way to summarize what the largest + + + align:start position:0% +good way to summarize what the largest +div is telling us it says if we take a + + align:start position:0% +div is telling us it says if we take a + + + align:start position:0% +div is telling us it says if we take a +set A which is a pretty decent fraction + + align:start position:0% +set A which is a pretty decent fraction + + + align:start position:0% +set A which is a pretty decent fraction +of the numbers from one to n and then + + align:start position:0% +of the numbers from one to n and then + + + align:start position:0% +of the numbers from one to n and then +when we look at all the projections of + + align:start position:0% +when we look at all the projections of + + + align:start position:0% +when we look at all the projections of +it most of those projections are almost + + align:start position:0% +it most of those projections are almost + + + align:start position:0% +it most of those projections are almost +constant + + align:start position:0% +constant + + + align:start position:0% +constant +and that's relevant for this question up + + align:start position:0% +and that's relevant for this question up + + + align:start position:0% +and that's relevant for this question up +here because um you know if we + + align:start position:0% +here because um you know if we + + + align:start position:0% +here because um you know if we +hypothesize that pi subp of a is has + + align:start position:0% +hypothesize that pi subp of a is has + + + align:start position:0% +hypothesize that pi subp of a is has +size smaller than.99 of p that's telling + + align:start position:0% +size smaller than.99 of p that's telling + + + align:start position:0% +size smaller than.99 of p that's telling +us the projection is really not very + + align:start position:0% +us the projection is really not very + + + align:start position:0% +us the projection is really not very +constant + + align:start position:0% +constant + + + align:start position:0% +constant +And that's only possible for small sets. + + align:start position:0% +And that's only possible for small sets. + + + align:start position:0% +And that's only possible for small sets. +So that's where we get that upper bound + + align:start position:0% +So that's where we get that upper bound + + + align:start position:0% +So that's where we get that upper bound +on the size of a. If a was bigger than + + align:start position:0% +on the size of a. If a was bigger than + + + align:start position:0% +on the size of a. If a was bigger than +that, then it would start to be the case + + align:start position:0% +that, then it would start to be the case + + + align:start position:0% +that, then it would start to be the case +that the projections of A would have + + align:start position:0% +that the projections of A would have + + + align:start position:0% +that the projections of A would have +pretty would would look pretty constant + + align:start position:0% +pretty would would look pretty constant + + + align:start position:0% +pretty would would look pretty constant +and it would then it would be impossible + + align:start position:0% +and it would then it would be impossible + + + align:start position:0% +and it would then it would be impossible +that the support would be that small. + + align:start position:0% +that the support would be that small. + + + align:start position:0% +that the support would be that small. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> What does P tell the capital P to the 12 + + align:start position:0% +>> What does P tell the capital P to the 12 + + + align:start position:0% +>> What does P tell the capital P to the 12 +mean? + + align:start position:0% +mean? + + + align:start position:0% +mean? +What does + + align:start position:0% +What does + + + align:start position:0% +What does +>> under the average + + align:start position:0% +>> under the average + + + align:start position:0% +>> under the average +>> this one + + align:start position:0% +>> this one + + + align:start position:0% +>> this one +>> oh sorry that's P in so capital P n to + + align:start position:0% +>> oh sorry that's P in so capital P n to + + + align:start position:0% +>> oh sorry that's P in so capital P n to +the half is the set of primes of size + + align:start position:0% +the half is the set of primes of size + + + align:start position:0% +the half is the set of primes of size +about n to the half and this is this + + align:start position:0% +about n to the half and this is this + + + align:start position:0% +about n to the half and this is this +prime is one of them yeah thanks for + + align:start position:0% +prime is one of them yeah thanks for + + + align:start position:0% +prime is one of them yeah thanks for +thanks + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so next um let's prove Linux theorem + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Um so the proof of Linux theorem is + + align:start position:0% +Um so the proof of Linux theorem is + + + align:start position:0% +Um so the proof of Linux theorem is +based on the forier transform. So we're + + align:start position:0% +based on the forier transform. So we're + + + align:start position:0% +based on the forier transform. So we're +going to take the fora transform of all + + align:start position:0% +going to take the fora transform of all + + + align:start position:0% +going to take the fora transform of all +of these characters and then we're going + + align:start position:0% +of these characters and then we're going + + + align:start position:0% +of these characters and then we're going +to see how the different fora transforms + + align:start position:0% +to see how the different fora transforms + + + align:start position:0% +to see how the different fora transforms +are related to each other. + + align:start position:0% +are related to each other. + + + align:start position:0% +are related to each other. +Um so first let me remind you how the + + align:start position:0% +Um so first let me remind you how the + + + align:start position:0% +Um so first let me remind you how the +for a transform works for uh functions + + align:start position:0% +for a transform works for uh functions + + + align:start position:0% +for a transform works for uh functions +on the integers and functions on z mod + + align:start position:0% +on the integers and functions on z mod + + + align:start position:0% +on the integers and functions on z mod +p. + + align:start position:0% +p. + + + align:start position:0% +p. +So f is going to be a think of it as a + + align:start position:0% +So f is going to be a think of it as a + + + align:start position:0% +So f is going to be a think of it as a +function on the integers which is + + align:start position:0% +function on the integers which is + + + align:start position:0% +function on the integers which is +supported in in this set one of tan + + align:start position:0% +supported in in this set one of tan + + + align:start position:0% +supported in in this set one of tan +and so if I take its fora transform what + + align:start position:0% +and so if I take its fora transform what + + + align:start position:0% +and so if I take its fora transform what +does that mean the for transform is + + align:start position:0% +does that mean the for transform is + + + align:start position:0% +does that mean the for transform is +going to be a function on r mod z and + + align:start position:0% +going to be a function on r mod z and + + + align:start position:0% +going to be a function on r mod z and +it's defined by f of c is the sum on n f + + align:start position:0% +it's defined by f of c is the sum on n f + + + align:start position:0% +it's defined by f of c is the sum on n f +of n eus 2 pi i c do n c that's the for + + align:start position:0% +of n eus 2 pi i c do n c that's the for + + + align:start position:0% +of n eus 2 pi i c do n c that's the for +transform + + align:start position:0% +transform + + + align:start position:0% +transform +And it has a forier inversion and it has + + align:start position:0% +And it has a forier inversion and it has + + + align:start position:0% +And it has a forier inversion and it has +a planter route. And they go like this. + + align:start position:0% +a planter route. And they go like this. + + + align:start position:0% +a planter route. And they go like this. +Forier inversion. + + align:start position:0% +Forier inversion. + + + align:start position:0% +Forier inversion. +It tells us that + + align:start position:0% +It tells us that + + + align:start position:0% +It tells us that +f of n is the integral from 0 to 1 f of + + align:start position:0% +f of n is the integral from 0 to 1 f of + + + align:start position:0% +f of n is the integral from 0 to 1 f of +c e 2 pi i cn dx. + + align:start position:0% +c e 2 pi i cn dx. + + + align:start position:0% +c e 2 pi i cn dx. +And there's a planer. + + align:start position:0% +And there's a planer. + + + align:start position:0% +And there's a planer. +And it tells us that the sum on n of f + + align:start position:0% +And it tells us that the sum on n of f + + + align:start position:0% +And it tells us that the sum on n of f +of n^2 is the integral from 0 to 1 norm + + align:start position:0% +of n^2 is the integral from 0 to 1 norm + + + align:start position:0% +of n^2 is the integral from 0 to 1 norm +of fat x c^2 dx. + + align:start position:0% + + + + align:start position:0% + +Okay. So this is probably most familiar + + align:start position:0% +Okay. So this is probably most familiar + + + align:start position:0% +Okay. So this is probably most familiar +backwards from the way I've written it. + + align:start position:0% +backwards from the way I've written it. + + + align:start position:0% +backwards from the way I've written it. +If you started with a function on r modz + + align:start position:0% +If you started with a function on r modz + + + align:start position:0% +If you started with a function on r modz +z a periodic function you would take its + + align:start position:0% +z a periodic function you would take its + + + align:start position:0% +z a periodic function you would take its +forier series and if you sum the forier + + align:start position:0% +forier series and if you sum the forier + + + align:start position:0% +forier series and if you sum the forier +series you get the function. This is the + + align:start position:0% +series you get the function. This is the + + + align:start position:0% +series you get the function. This is the +same thing. We've just chosen to label + + align:start position:0% +same thing. We've just chosen to label + + + align:start position:0% +same thing. We've just chosen to label +the for a series by f and the uh + + align:start position:0% +the for a series by f and the uh + + + align:start position:0% +the for a series by f and the uh +function on the circle by fhat. + + align:start position:0% +function on the circle by fhat. + + + align:start position:0% +function on the circle by fhat. +Okay. And then + + align:start position:0% + + + + align:start position:0% + +we will also have a function on z mod p. + + align:start position:0% +we will also have a function on z mod p. + + + align:start position:0% +we will also have a function on z mod p. +So suppose I have a function z mod p + + align:start position:0% +So suppose I have a function z mod p + + + align:start position:0% +So suppose I have a function z mod p +goes to c. Then its fora transform will + + align:start position:0% +goes to c. Then its fora transform will + + + align:start position:0% +goes to c. Then its fora transform will +also be a function z mod p goes to c. + + align:start position:0% +also be a function z mod p goes to c. + + + align:start position:0% +also be a function z mod p goes to c. +And the definition is ghat of uh alpha. + + align:start position:0% +And the definition is ghat of uh alpha. + + + align:start position:0% +And the definition is ghat of uh alpha. +So I'll say that this variable is called + + align:start position:0% +So I'll say that this variable is called + + + align:start position:0% +So I'll say that this variable is called +a and this variable is called alpha. So + + align:start position:0% +a and this variable is called alpha. So + + + align:start position:0% +a and this variable is called alpha. So +ghat of alpha will be the sum a and z + + align:start position:0% +ghat of alpha will be the sum a and z + + + align:start position:0% +ghat of alpha will be the sum a and z +mod p g of a eus 2 pi i a alpha over p. + + align:start position:0% +mod p g of a eus 2 pi i a alpha over p. + + + align:start position:0% +mod p g of a eus 2 pi i a alpha over p. +And then we have fora inversion + + align:start position:0% +And then we have fora inversion + + + align:start position:0% +And then we have fora inversion +which tells us that g of a can be + + align:start position:0% +which tells us that g of a can be + + + align:start position:0% +which tells us that g of a can be +recovered as 1 / p sum alpha and z mod p + + align:start position:0% +recovered as 1 / p sum alpha and z mod p + + + align:start position:0% +recovered as 1 / p sum alpha and z mod p +ghat of alpha e to the 2 pi i a alpha + + align:start position:0% +ghat of alpha e to the 2 pi i a alpha + + + align:start position:0% +ghat of alpha e to the 2 pi i a alpha +over p + + align:start position:0% +over p + + + align:start position:0% +over p +and uh and planer + + align:start position:0% +and uh and planer + + + align:start position:0% +and uh and planer +that tells us that the sum on a norm of + + align:start position:0% +that tells us that the sum on a norm of + + + align:start position:0% +that tells us that the sum on a norm of +g of a^ 2 is 1 / p * the sum on alpha + + align:start position:0% +g of a^ 2 is 1 / p * the sum on alpha + + + align:start position:0% +g of a^ 2 is 1 / p * the sum on alpha +norm of g of alpha square. + + align:start position:0% + + + + align:start position:0% + +Okay, so that's how the for transforms + + align:start position:0% +Okay, so that's how the for transforms + + + align:start position:0% +Okay, so that's how the for transforms +works for each of these worlds. + + align:start position:0% +works for each of these worlds. + + + align:start position:0% +works for each of these worlds. +And now we're going to put it together. + + align:start position:0% +And now we're going to put it together. + + + align:start position:0% +And now we're going to put it together. +So if I start with a function on the + + align:start position:0% +So if I start with a function on the + + + align:start position:0% +So if I start with a function on the +integers, I reduce it mod p to get a + + align:start position:0% +integers, I reduce it mod p to get a + + + align:start position:0% +integers, I reduce it mod p to get a +function on z mod p. How does this for a + + align:start position:0% +function on z mod p. How does this for a + + + align:start position:0% +function on z mod p. How does this for a +transform relate to this for a + + align:start position:0% +transform relate to this for a + + + align:start position:0% +transform relate to this for a +transform? Okay. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So, lama I'll call this lama dictionary. + + align:start position:0% + + + + align:start position:0% + +This is a dictionary between the integer + + align:start position:0% +This is a dictionary between the integer + + + align:start position:0% +This is a dictionary between the integer +world and the mod p world. And it says + + align:start position:0% +world and the mod p world. And it says + + + align:start position:0% +world and the mod p world. And it says +that if I take pi p of f hat of alpha + + align:start position:0% +that if I take pi p of f hat of alpha + + + align:start position:0% +that if I take pi p of f hat of alpha +that is fhat of alpha and vp. + + align:start position:0% + + + + align:start position:0% + +Okay the proof is just unwinding the + + align:start position:0% +Okay the proof is just unwinding the + + + align:start position:0% +Okay the proof is just unwinding the +definitions of what all these for + + align:start position:0% +definitions of what all these for + + + align:start position:0% +definitions of what all these for +transforms mean. So what does it mean pi + + align:start position:0% +transforms mean. So what does it mean pi + + + align:start position:0% +transforms mean. So what does it mean pi +pfhat of alpha? Pi PF hat of alpha + + align:start position:0% +pfhat of alpha? Pi PF hat of alpha + + + align:start position:0% +pfhat of alpha? Pi PF hat of alpha +that's the sum a and z mod pi + + align:start position:0% +that's the sum a and z mod pi + + + align:start position:0% +that's the sum a and z mod pi +pf of a e - 2<unk>i i a alpha over p + + align:start position:0% +pf of a e - 2<unk>i i a alpha over p + + + align:start position:0% +pf of a e - 2<unk>i i a alpha over p +okay now who is pi pf of a + + align:start position:0% + + + + align:start position:0% + +sum a and z mod p open parenthesis sum + + align:start position:0% +sum a and z mod p open parenthesis sum + + + align:start position:0% +sum a and z mod p open parenthesis sum +n= a mod p of f of n + + align:start position:0% +n= a mod p of f of n + + + align:start position:0% +n= a mod p of f of n +e - 2<unk>i i a alpha. + + align:start position:0% + + + + align:start position:0% + +All right. Now, if you look at this + + align:start position:0% +All right. Now, if you look at this + + + align:start position:0% +All right. Now, if you look at this +double sum, + + align:start position:0% +double sum, + + + align:start position:0% +double sum, +we're just summing over all the x. + + align:start position:0% + + + + align:start position:0% + +And now let's look at the thing that + + align:start position:0% +And now let's look at the thing that + + + align:start position:0% +And now let's look at the thing that +we're summing. + + align:start position:0% +we're summing. + + + align:start position:0% +we're summing. +So + + align:start position:0% +So + + + align:start position:0% +So +uh n= a mod p that tells us that e to + + align:start position:0% +uh n= a mod p that tells us that e to + + + align:start position:0% +uh n= a mod p that tells us that e to +the - 2<unk>i i n alpha / p is the same + + align:start position:0% +the - 2<unk>i i n alpha / p is the same + + + align:start position:0% +the - 2<unk>i i n alpha / p is the same +as e - 2 pi i a alpha p. + + align:start position:0% +as e - 2 pi i a alpha p. + + + align:start position:0% +as e - 2 pi i a alpha p. +Why? I have different ns that are + + align:start position:0% +Why? I have different ns that are + + + align:start position:0% +Why? I have different ns that are +congruent to a mod p. So I think of + + align:start position:0% +congruent to a mod p. So I think of + + + align:start position:0% +congruent to a mod p. So I think of +adding a multiple of p to this n. that + + align:start position:0% +adding a multiple of p to this n. that + + + align:start position:0% +adding a multiple of p to this n. that +multiple of P the P cancels with that P. + + align:start position:0% +multiple of P the P cancels with that P. + + + align:start position:0% +multiple of P the P cancels with that P. +So we're changing this by an integer and + + align:start position:0% +So we're changing this by an integer and + + + align:start position:0% +So we're changing this by an integer and +it doesn't change the value of of it. + + align:start position:0% +it doesn't change the value of of it. + + + align:start position:0% +it doesn't change the value of of it. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +so this is just the sum over n f of n e + + align:start position:0% +so this is just the sum over n f of n e + + + align:start position:0% +so this is just the sum over n f of n e +to the - 2 pi i n alpha p. + + align:start position:0% + + + + align:start position:0% + +Cool. + + align:start position:0% + + + + align:start position:0% + +Um, another little remark, this is + + align:start position:0% +Um, another little remark, this is + + + align:start position:0% +Um, another little remark, this is +something we basically saw last time + + align:start position:0% +something we basically saw last time + + + align:start position:0% +something we basically saw last time +that if you take the high part of pi p + + align:start position:0% +that if you take the high part of pi p + + + align:start position:0% +that if you take the high part of pi p +of f and it's l2 norm squared. If you + + align:start position:0% +of f and it's l2 norm squared. If you + + + align:start position:0% +of f and it's l2 norm squared. If you +take the high part of it, what it means + + align:start position:0% +take the high part of it, what it means + + + align:start position:0% +take the high part of it, what it means +is that we removed the zero frequency. + + align:start position:0% +is that we removed the zero frequency. + + + align:start position:0% +is that we removed the zero frequency. +So I guess I'll also call this a lema, + + align:start position:0% +So I guess I'll also call this a lema, + + + align:start position:0% +So I guess I'll also call this a lema, +but it's very similar to things we've + + align:start position:0% +but it's very similar to things we've + + + align:start position:0% +but it's very similar to things we've +already proved. + + align:start position:0% + + + + align:start position:0% + +So pi pfi + + align:start position:0% +So pi pfi + + + align:start position:0% +So pi pfi +L2 squared is the sum on the nonzero + + align:start position:0% +L2 squared is the sum on the nonzero + + + align:start position:0% +L2 squared is the sum on the nonzero +alphas. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um, so, + + align:start position:0% +Um, so, + + + align:start position:0% +Um, so, +so now we have a way of writing. So, + + align:start position:0% +so now we have a way of writing. So, + + + align:start position:0% +so now we have a way of writing. So, +let's look at the theorem we want to + + align:start position:0% +let's look at the theorem we want to + + + align:start position:0% +let's look at the theorem we want to +prove. We're going to take a sum over + + align:start position:0% +prove. We're going to take a sum over + + + align:start position:0% +prove. We're going to take a sum over +different ps of the L2 norms of the high + + align:start position:0% +different ps of the L2 norms of the high + + + align:start position:0% +different ps of the L2 norms of the high +parts of pi p of f. + + align:start position:0% +parts of pi p of f. + + + align:start position:0% +parts of pi p of f. +These lemas give us a way of writing + + align:start position:0% +These lemas give us a way of writing + + + align:start position:0% +These lemas give us a way of writing +that and translating it into a sum that + + align:start position:0% +that and translating it into a sum that + + + align:start position:0% +that and translating it into a sum that +involves the for transform of f. + + align:start position:0% + + + + align:start position:0% + +Yeah, I guess one last remark is um + + align:start position:0% + + + + align:start position:0% + +so so pi p of f hat of alpha is fhat of + + align:start position:0% +so so pi p of f hat of alpha is fhat of + + + align:start position:0% +so so pi p of f hat of alpha is fhat of +alpha over p that's for any function f + + align:start position:0% +alpha over p that's for any function f + + + align:start position:0% +alpha over p that's for any function f +and so if I were to take pi p of f high + + align:start position:0% +and so if I were to take pi p of f high + + + align:start position:0% +and so if I were to take pi p of f high +hat of alpha that would be fi hat alpha + + align:start position:0% + + + + align:start position:0% + +Okay. So now let's let's write out the + + align:start position:0% +Okay. So now let's let's write out the + + + align:start position:0% +Okay. So now let's let's write out the +left hand side of Linux theorem using 4A + + align:start position:0% +left hand side of Linux theorem using 4A + + + align:start position:0% +left hand side of Linux theorem using 4A +using the 4A transform. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um, so the left hand side of our + + align:start position:0% +Um, so the left hand side of our + + + align:start position:0% +Um, so the left hand side of our +theorem, I'll just copy it. The sum p in + + align:start position:0% +theorem, I'll just copy it. The sum p in + + + align:start position:0% +theorem, I'll just copy it. The sum p in +primes of size m + + align:start position:0% +primes of size m + + + align:start position:0% +primes of size m +pi p of f high part l2 squ. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So that's now some pinp + + align:start position:0% + + + + align:start position:0% + +on the nonzero alpha n cp + + align:start position:0% +on the nonzero alpha n cp + + + align:start position:0% +on the nonzero alpha n cp +um + + align:start position:0% +um + + + align:start position:0% +um +pi p of fi hat of alpha squared + + align:start position:0% + + + + align:start position:0% + +which is equal to some p of pm + + align:start position:0% +which is equal to some p of pm + + + align:start position:0% +which is equal to some p of pm +some alpha not equal to zero np + + align:start position:0% +some alpha not equal to zero np + + + align:start position:0% +some alpha not equal to zero np +of fi fi hat of alpha over p + + align:start position:0% + + + + align:start position:0% + +norm + + align:start position:0% + + + + align:start position:0% + +cool. Okay, so we're taking the 4A + + align:start position:0% +cool. Okay, so we're taking the 4A + + + align:start position:0% +cool. Okay, so we're taking the 4A +transform of the high part of f and + + align:start position:0% +transform of the high part of f and + + + align:start position:0% +transform of the high part of f and +evaluating it at a set of points norm + + align:start position:0% +evaluating it at a set of points norm + + + align:start position:0% +evaluating it at a set of points norm +squared and adding them all up. Uh let's + + align:start position:0% +squared and adding them all up. Uh let's + + + align:start position:0% +squared and adding them all up. Uh let's +visualize that set of points. + + align:start position:0% +visualize that set of points. + + + align:start position:0% +visualize that set of points. +So let's say qm is the set of uh alpha + + align:start position:0% +So let's say qm is the set of uh alpha + + + align:start position:0% +So let's say qm is the set of uh alpha +over p where p is a prime of size around + + align:start position:0% +over p where p is a prime of size around + + + align:start position:0% +over p where p is a prime of size around +m and alpha + + align:start position:0% +m and alpha + + + align:start position:0% +m and alpha +is strictly positive and less than or + + align:start position:0% +is strictly positive and less than or + + + align:start position:0% +is strictly positive and less than or +equal to p minus one. + + align:start position:0% + + + + align:start position:0% + +Okay, so um the size of qm is roughly m + + align:start position:0% +Okay, so um the size of qm is roughly m + + + align:start position:0% +Okay, so um the size of qm is roughly m +squ. So we mentioned before how many + + align:start position:0% +squ. So we mentioned before how many + + + align:start position:0% +squ. So we mentioned before how many +choices are there for this prime p? It's + + align:start position:0% +choices are there for this prime p? It's + + + align:start position:0% +choices are there for this prime p? It's +about m over log m which is roughly m. + + align:start position:0% +about m over log m which is roughly m. + + + align:start position:0% +about m over log m which is roughly m. +And then for each prime there are + + align:start position:0% +And then for each prime there are + + + align:start position:0% +And then for each prime there are +basically p choices of alpha which is + + align:start position:0% +basically p choices of alpha which is + + + align:start position:0% +basically p choices of alpha which is +also around m. They're roughly m squ of + + align:start position:0% +also around m. They're roughly m squ of + + + align:start position:0% +also around m. They're roughly m squ of +these um quotients. + + align:start position:0% +these um quotients. + + + align:start position:0% +these um quotients. +Um and an important fact about these + + align:start position:0% +Um and an important fact about these + + + align:start position:0% +Um and an important fact about these +quotients is that they're distributed + + align:start position:0% +quotients is that they're distributed + + + align:start position:0% +quotients is that they're distributed +quite evenly on the real line. So + + align:start position:0% +quite evenly on the real line. So + + + align:start position:0% +quite evenly on the real line. So +they're about m^ squ of them and the + + align:start position:0% +they're about m^ squ of them and the + + + align:start position:0% +they're about m^ squ of them and the +distance between any two of them is at + + align:start position:0% +distance between any two of them is at + + + align:start position:0% +distance between any two of them is at +least m^2. + + align:start position:0% +least m^2. + + + align:start position:0% +least m^2. +So here's a lema. + + align:start position:0% +So here's a lema. + + + align:start position:0% +So here's a lema. +Um, if alpha 1 over p1 and alpha 2 over + + align:start position:0% +Um, if alpha 1 over p1 and alpha 2 over + + + align:start position:0% +Um, if alpha 1 over p1 and alpha 2 over +p2 are in qm and they're not equal to + + align:start position:0% +p2 are in qm and they're not equal to + + + align:start position:0% +p2 are in qm and they're not equal to +each other, + + align:start position:0% +each other, + + + align:start position:0% +each other, +then the distance between them + + align:start position:0% +then the distance between them + + + align:start position:0% +then the distance between them +is at least 1 / m^2. + + align:start position:0% + + + + align:start position:0% + +Okay, proof. Um, we're just going to put + + align:start position:0% +Okay, proof. Um, we're just going to put + + + align:start position:0% +Okay, proof. Um, we're just going to put +it over a common denominator. + + align:start position:0% +it over a common denominator. + + + align:start position:0% +it over a common denominator. +Alpha 1 P1 Alpha 1 over P1 + + align:start position:0% +Alpha 1 P1 Alpha 1 over P1 + + + align:start position:0% +Alpha 1 P1 Alpha 1 over P1 +minus Alpha 2 over P2 + + align:start position:0% +minus Alpha 2 over P2 + + + align:start position:0% +minus Alpha 2 over P2 +is alpha 1 P2 minus alpha 2 P1 over P1 + + align:start position:0% +is alpha 1 P2 minus alpha 2 P1 over P1 + + + align:start position:0% +is alpha 1 P2 minus alpha 2 P1 over P1 +P2 + + align:start position:0% + + + + align:start position:0% + +by assumption there the difference is + + align:start position:0% +by assumption there the difference is + + + align:start position:0% +by assumption there the difference is +not zero um and so this numerator is not + + align:start position:0% +not zero um and so this numerator is not + + + align:start position:0% +not zero um and so this numerator is not +zero um and so this it's an integer so + + align:start position:0% +zero um and so this it's an integer so + + + align:start position:0% +zero um and so this it's an integer so +it has norm at least + + align:start position:0% + + + + align:start position:0% + +some say at least that big. + + align:start position:0% + + + + align:start position:0% + +Okay. Um I guess to be careful I should + + align:start position:0% +Okay. Um I guess to be careful I should + + + align:start position:0% +Okay. Um I guess to be careful I should +also say that if you know if P1 is + + align:start position:0% +also say that if you know if P1 is + + + align:start position:0% +also say that if you know if P1 is +different from P2 then these two are + + align:start position:0% +different from P2 then these two are + + + align:start position:0% +different from P2 then these two are +never equal to each other. + + align:start position:0% +never equal to each other. + + + align:start position:0% +never equal to each other. +So we never so the importance of making + + align:start position:0% +So we never so the importance of making + + + align:start position:0% +So we never so the importance of making +these primes is that um we never have + + align:start position:0% +these primes is that um we never have + + + align:start position:0% +these primes is that um we never have +the same number written as a fraction in + + align:start position:0% +the same number written as a fraction in + + + align:start position:0% +the same number written as a fraction in +two different ways here. + + align:start position:0% +two different ways here. + + + align:start position:0% +two different ways here. +So let's also make the remark + + align:start position:0% +So let's also make the remark + + + align:start position:0% +So let's also make the remark +that um + + align:start position:0% +that um + + + align:start position:0% +that um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +if alpha 1 over p1 equals alpha 2 over + + align:start position:0% +if alpha 1 over p1 equals alpha 2 over + + + align:start position:0% +if alpha 1 over p1 equals alpha 2 over +p2 um in qm + + align:start position:0% +p2 um in qm + + + align:start position:0% +p2 um in qm +then it must be that alpha 1 equals + + align:start position:0% +then it must be that alpha 1 equals + + + align:start position:0% +then it must be that alpha 1 equals +alpha 2 and p1 equals p2. + + align:start position:0% + + + + align:start position:0% + +Okay. Um, + + align:start position:0% +Okay. Um, + + + align:start position:0% +Okay. Um, +cool. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +So, I'm going to erase the dictionary + + align:start position:0% +So, I'm going to erase the dictionary + + + align:start position:0% +So, I'm going to erase the dictionary +lema and I'll make a picture of this set + + align:start position:0% +lema and I'll make a picture of this set + + + align:start position:0% +lema and I'll make a picture of this set +and of what we're what we're doing. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +here's a picture. + + align:start position:0% + + + + align:start position:0% + +So, here's the line from 0 to one. And + + align:start position:0% +So, here's the line from 0 to one. And + + + align:start position:0% +So, here's the line from 0 to one. And +on this line we have this set Q subm + + align:start position:0% +on this line we have this set Q subm + + + align:start position:0% +on this line we have this set Q subm +which is maybe not quite that evenly + + align:start position:0% +which is maybe not quite that evenly + + + align:start position:0% +which is maybe not quite that evenly +spaced but it's it's quite evenly + + align:start position:0% +spaced but it's it's quite evenly + + + align:start position:0% +spaced but it's it's quite evenly +spaced. So that's Q sub. + + align:start position:0% +spaced. So that's Q sub. + + + align:start position:0% +spaced. So that's Q sub. +Okay. And then we have we're interested + + align:start position:0% +Okay. And then we have we're interested + + + align:start position:0% +Okay. And then we have we're interested +in the uh our formula involves the the + + align:start position:0% +in the uh our formula involves the the + + + align:start position:0% +in the uh our formula involves the the +norm of squared of the 4A transform of + + align:start position:0% +norm of squared of the 4A transform of + + + align:start position:0% +norm of squared of the 4A transform of +f. + + align:start position:0% + + + + align:start position:0% + +Let me put that on this axis. + + align:start position:0% + + + + align:start position:0% + +Okay. So, um, so this will look however + + align:start position:0% +Okay. So, um, so this will look however + + + align:start position:0% +Okay. So, um, so this will look however +it looks. + + align:start position:0% +it looks. + + + align:start position:0% +it looks. +Okay. We'll talk about this a little bit + + align:start position:0% +Okay. We'll talk about this a little bit + + + align:start position:0% +Okay. We'll talk about this a little bit +more. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +So what what we're taking in that sum is + + align:start position:0% +So what what we're taking in that sum is + + + align:start position:0% +So what what we're taking in that sum is +we're finding the actual values at these + + align:start position:0% +we're finding the actual values at these + + + align:start position:0% +we're finding the actual values at these +points and we're adding them up. + + align:start position:0% + + + + align:start position:0% + +And this sum might remind you a little + + align:start position:0% +And this sum might remind you a little + + + align:start position:0% +And this sum might remind you a little +bit of a remon sum that would help to + + align:start position:0% +bit of a remon sum that would help to + + + align:start position:0% +bit of a remon sum that would help to +give an approximation of this integral. + + align:start position:0% +give an approximation of this integral. + + + align:start position:0% +give an approximation of this integral. +And indeed we're going to compare this + + align:start position:0% +And indeed we're going to compare this + + + align:start position:0% +And indeed we're going to compare this +sum to this integral. + + align:start position:0% +sum to this integral. + + + align:start position:0% +sum to this integral. +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +okay. Now, there is a way that the sum + + align:start position:0% +okay. Now, there is a way that the sum + + + align:start position:0% +okay. Now, there is a way that the sum +could be a lot bigger than the integral, + + align:start position:0% +could be a lot bigger than the integral, + + + align:start position:0% +could be a lot bigger than the integral, +which is a narrow peak like this. You + + align:start position:0% +which is a narrow peak like this. You + + + align:start position:0% +which is a narrow peak like this. You +know, if if the function is very big at + + align:start position:0% +know, if if the function is very big at + + + align:start position:0% +know, if if the function is very big at +this one point, but the peak is + + align:start position:0% +this one point, but the peak is + + + align:start position:0% +this one point, but the peak is +extremely narrow, then it wouldn't + + align:start position:0% +extremely narrow, then it wouldn't + + + align:start position:0% +extremely narrow, then it wouldn't +contribute much to the integral, but + + align:start position:0% +contribute much to the integral, but + + + align:start position:0% +contribute much to the integral, but +it's still there as part of our sum. So, + + align:start position:0% +it's still there as part of our sum. So, + + + align:start position:0% +it's still there as part of our sum. So, +it's important to know sort of how + + align:start position:0% +it's important to know sort of how + + + align:start position:0% +it's important to know sort of how +narrow a peak like this can be. And the + + align:start position:0% +narrow a peak like this can be. And the + + + align:start position:0% +narrow a peak like this can be. And the +heristic + + align:start position:0% +heristic + + + align:start position:0% +heristic +which is similar to heristic we've + + align:start position:0% +which is similar to heristic we've + + + align:start position:0% +which is similar to heristic we've +talked about before is that the function + + align:start position:0% +talked about before is that the function + + + align:start position:0% +talked about before is that the function +fi hat of c is roughly constant + + align:start position:0% +fi hat of c is roughly constant + + + align:start position:0% +fi hat of c is roughly constant +on intervals of length 1 / n + + align:start position:0% + + + + align:start position:0% + +because remember that f is supported on + + align:start position:0% +because remember that f is supported on + + + align:start position:0% +because remember that f is supported on +the numbers from 1 to n. + + align:start position:0% +the numbers from 1 to n. + + + align:start position:0% +the numbers from 1 to n. +Okay. So we'll make this precise in a + + align:start position:0% +Okay. So we'll make this precise in a + + + align:start position:0% +Okay. So we'll make this precise in a +moment. Uh so I'll draw in what it means + + align:start position:0% +moment. Uh so I'll draw in what it means + + + align:start position:0% +moment. Uh so I'll draw in what it means +that this peak here should have width at + + align:start position:0% +that this peak here should have width at + + + align:start position:0% +that this peak here should have width at +least 1 / n. + + align:start position:0% +least 1 / n. + + + align:start position:0% +least 1 / n. +Okay. And I'll also make a remark that + + align:start position:0% +Okay. And I'll also make a remark that + + + align:start position:0% +Okay. And I'll also make a remark that +um m is less than or equal to n^ the 12. + + align:start position:0% +um m is less than or equal to n^ the 12. + + + align:start position:0% +um m is less than or equal to n^ the 12. +That's one of the hypotheses in in Linux + + align:start position:0% +That's one of the hypotheses in in Linux + + + align:start position:0% +That's one of the hypotheses in in Linux +theorem. + + align:start position:0% +theorem. + + + align:start position:0% +theorem. +And so that guarantees + + align:start position:0% +And so that guarantees + + + align:start position:0% +And so that guarantees +that the spacing between consecutive + + align:start position:0% +that the spacing between consecutive + + + align:start position:0% +that the spacing between consecutive +points of QM + + align:start position:0% +points of QM + + + align:start position:0% +points of QM +is smaller than this one overn. + + align:start position:0% +is smaller than this one overn. + + + align:start position:0% +is smaller than this one overn. +So the picture is sort of right that you + + align:start position:0% +So the picture is sort of right that you + + + align:start position:0% +So the picture is sort of right that you +know this 1 / n is smaller than the + + align:start position:0% +know this 1 / n is smaller than the + + + align:start position:0% +know this 1 / n is smaller than the +distance between the different points of + + align:start position:0% +distance between the different points of + + + align:start position:0% +distance between the different points of +Q. + + align:start position:0% + + + + align:start position:0% + +Okay. So this is just a heristic but + + align:start position:0% +Okay. So this is just a heristic but + + + align:start position:0% +Okay. So this is just a heristic but +let's follow it for now and we'll see + + align:start position:0% +let's follow it for now and we'll see + + + align:start position:0% +let's follow it for now and we'll see +that it basically gives the inequality + + align:start position:0% +that it basically gives the inequality + + + align:start position:0% +that it basically gives the inequality +that we want and then we can come back + + align:start position:0% +that we want and then we can come back + + + align:start position:0% +that we want and then we can come back +and prove things rigorously. + + align:start position:0% +and prove things rigorously. + + + align:start position:0% +and prove things rigorously. +Okay. So the heristic tells us + + align:start position:0% + + + + align:start position:0% + +that um + + align:start position:0% +that um + + + align:start position:0% +that um +the sum + + align:start position:0% +the sum + + + align:start position:0% +the sum +c and qm + + align:start position:0% +c and qm + + + align:start position:0% +c and qm +fi hat of c^ squared + + align:start position:0% +fi hat of c^ squared + + + align:start position:0% +fi hat of c^ squared +um + + align:start position:0% + + + + align:start position:0% + +is bounded by + + align:start position:0% +is bounded by + + + align:start position:0% +is bounded by +n times the integral from 0 to 1 + + align:start position:0% +n times the integral from 0 to 1 + + + align:start position:0% +n times the integral from 0 to 1 +fat high x^2 + + align:start position:0% + + + + align:start position:0% + +y. So take a one term of this sum say + + align:start position:0% +y. So take a one term of this sum say + + + align:start position:0% +y. So take a one term of this sum say +from this point that one term is bounded + + align:start position:0% +from this point that one term is bounded + + + align:start position:0% +from this point that one term is bounded +by n times the integral on this um + + align:start position:0% +by n times the integral on this um + + + align:start position:0% +by n times the integral on this um +interval around here of of side with 1 / + + align:start position:0% +interval around here of of side with 1 / + + + align:start position:0% +interval around here of of side with 1 / +n + + align:start position:0% +n + + + align:start position:0% +n +which is a piece of this integral. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. Okay. So, the rest is just + + align:start position:0% +Okay. Okay. So, the rest is just + + + align:start position:0% +Okay. Okay. So, the rest is just +algebra. And it's a little bit um + + align:start position:0% +algebra. And it's a little bit um + + + align:start position:0% +algebra. And it's a little bit um +annoying to get all of the constants + + align:start position:0% +annoying to get all of the constants + + + align:start position:0% +annoying to get all of the constants +right in the algebra, all the exponents + + align:start position:0% +right in the algebra, all the exponents + + + align:start position:0% +right in the algebra, all the exponents +right. And in fact, I have already + + align:start position:0% +right. And in fact, I have already + + + align:start position:0% +right. And in fact, I have already +messed it up a little bit. + + align:start position:0% + + + + align:start position:0% + +So if we go back here, um the left hand + + align:start position:0% +So if we go back here, um the left hand + + + align:start position:0% +So if we go back here, um the left hand +side of the theorem is indeed this sum. + + align:start position:0% +side of the theorem is indeed this sum. + + + align:start position:0% +side of the theorem is indeed this sum. +I would just copied that correctly. Um + + align:start position:0% +I would just copied that correctly. Um + + + align:start position:0% +I would just copied that correctly. Um +and then for the sum, I did planer. But + + align:start position:0% +and then for the sum, I did planer. But + + + align:start position:0% +and then for the sum, I did planer. But +when you do planer mod p there's this + + align:start position:0% +when you do planer mod p there's this + + + align:start position:0% +when you do planer mod p there's this +factor of one over p that I forget + + align:start position:0% +factor of one over p that I forget + + + align:start position:0% +factor of one over p that I forget +frequently. So there's a one over p + + align:start position:0% +frequently. So there's a one over p + + + align:start position:0% +frequently. So there's a one over p +there. Now the one over p the p has size + + align:start position:0% +there. Now the one over p the p has size + + + align:start position:0% +there. Now the one over p the p has size +about m. This is around 1 / m * + + align:start position:0% + + + + align:start position:0% + +all right. So the left hand side of the + + align:start position:0% +all right. So the left hand side of the + + + align:start position:0% +all right. So the left hand side of the +theorem is actually around 1 / m * this + + align:start position:0% +theorem is actually around 1 / m * this + + + align:start position:0% +theorem is actually around 1 / m * this +sum over here. So that would be bounded + + align:start position:0% +sum over here. So that would be bounded + + + align:start position:0% +sum over here. So that would be bounded +by n / m * this integral + + align:start position:0% + + + + align:start position:0% + +and then we use plan again and this time + + align:start position:0% +and then we use plan again and this time + + + align:start position:0% +and then we use plan again and this time +there's no factor that I have trouble + + align:start position:0% +there's no factor that I have trouble + + + align:start position:0% +there's no factor that I have trouble +remembering. So that's n / m sum n f of + + align:start position:0% +remembering. So that's n / m sum n f of + + + align:start position:0% +remembering. So that's n / m sum n f of +n^2. + + align:start position:0% + + + + align:start position:0% + +Okay. So this is the lin theorem. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Yeah, let me mention in this picture uh + + align:start position:0% +Yeah, let me mention in this picture uh + + + align:start position:0% +Yeah, let me mention in this picture uh +so we had this theme that if you you + + align:start position:0% +so we had this theme that if you you + + + align:start position:0% +so we had this theme that if you you +take one function and you reduce it mod + + align:start position:0% +take one function and you reduce it mod + + + align:start position:0% +take one function and you reduce it mod +p for many different ps most of them are + + align:start position:0% +p for many different ps most of them are + + + align:start position:0% +p for many different ps most of them are +almost constant. + + align:start position:0% +almost constant. + + + align:start position:0% +almost constant. +So why the constant frequency is special + + align:start position:0% +So why the constant frequency is special + + + align:start position:0% +So why the constant frequency is special +compared to all the other frequencies in + + align:start position:0% +compared to all the other frequencies in + + + align:start position:0% +compared to all the other frequencies in +this story? + + align:start position:0% + + + + align:start position:0% + +Okay. Um so + + align:start position:0% + + + + align:start position:0% + +um so let me shade in for one particular + + align:start position:0% +um so let me shade in for one particular + + + align:start position:0% +um so let me shade in for one particular +prime the frequencies alpha over p. + + align:start position:0% +prime the frequencies alpha over p. + + + align:start position:0% +prime the frequencies alpha over p. +So that would be frequencies alpha over + + align:start position:0% +So that would be frequencies alpha over + + + align:start position:0% +So that would be frequencies alpha over +p1 alpha and zp1. + + align:start position:0% + + + + align:start position:0% + +Let me do it for another prime. + + align:start position:0% + + + + align:start position:0% + +So, and the color blue, I'll draw alpha + + align:start position:0% +So, and the color blue, I'll draw alpha + + + align:start position:0% +So, and the color blue, I'll draw alpha +over P2. + + align:start position:0% +over P2. + + + align:start position:0% +over P2. +Alpha and Z mod P2. + + align:start position:0% +Alpha and Z mod P2. + + + align:start position:0% +Alpha and Z mod P2. +What would that look like? Well, + + align:start position:0% +What would that look like? Well, + + + align:start position:0% +What would that look like? Well, +crucially, it would still have zero, + + align:start position:0% +crucially, it would still have zero, + + + align:start position:0% +crucially, it would still have zero, +but all the other ones would be + + align:start position:0% +but all the other ones would be + + + align:start position:0% +but all the other ones would be +different. + + align:start position:0% + + + + align:start position:0% + +Okay. So now imagine doing this with all + + align:start position:0% +Okay. So now imagine doing this with all + + + align:start position:0% +Okay. So now imagine doing this with all +the different primes in our set of + + align:start position:0% +the different primes in our set of + + + align:start position:0% +the different primes in our set of +primes. P subm I would get a whole + + align:start position:0% +primes. P subm I would get a whole + + + align:start position:0% +primes. P subm I would get a whole +rainbow of different stuff. Zero would + + align:start position:0% +rainbow of different stuff. Zero would + + + align:start position:0% +rainbow of different stuff. Zero would +be in every color. But other than that + + align:start position:0% +be in every color. But other than that + + + align:start position:0% +be in every color. But other than that +each point is only one color. There are + + align:start position:0% +each point is only one color. There are + + + align:start position:0% +each point is only one color. There are +no other overlaps. + + align:start position:0% + + + + align:start position:0% + +Okay. Now fhat can be distributed + + align:start position:0% +Okay. Now fhat can be distributed + + + align:start position:0% +Okay. Now fhat can be distributed +anyway. We've assumed nothing about the + + align:start position:0% +anyway. We've assumed nothing about the + + + align:start position:0% +anyway. We've assumed nothing about the +function f except that it's supported + + align:start position:0% +function f except that it's supported + + + align:start position:0% +function f except that it's supported +from one to n. So we know nothing about + + align:start position:0% +from one to n. So we know nothing about + + + align:start position:0% +from one to n. So we know nothing about +its fora transform except for this + + align:start position:0% +its fora transform except for this + + + align:start position:0% +its fora transform except for this +heristic. + + align:start position:0% +heristic. + + + align:start position:0% +heristic. +So fhat could look like anything + + align:start position:0% +So fhat could look like anything + + + align:start position:0% +So fhat could look like anything +but um + + align:start position:0% +but um + + + align:start position:0% +but um +well most of the places that you put + + align:start position:0% +well most of the places that you put + + + align:start position:0% +well most of the places that you put +fhat. So okay so one thing we do know is + + align:start position:0% +fhat. So okay so one thing we do know is + + + align:start position:0% +fhat. So okay so one thing we do know is +let's say we know the sum of f the L2 + + align:start position:0% +let's say we know the sum of f the L2 + + + align:start position:0% +let's say we know the sum of f the L2 +norm of f. So we know the L2 norm of + + align:start position:0% +norm of f. So we know the L2 norm of + + + align:start position:0% +norm of f. So we know the L2 norm of +fhat. + + align:start position:0% +fhat. + + + align:start position:0% +fhat. +If you stick some mass of L2 norm of + + align:start position:0% +If you stick some mass of L2 norm of + + + align:start position:0% +If you stick some mass of L2 norm of +fhat over this point, it will contribute + + align:start position:0% +fhat over this point, it will contribute + + + align:start position:0% +fhat over this point, it will contribute +to this one prime but none of the + + align:start position:0% +to this one prime but none of the + + + align:start position:0% +to this one prime but none of the +others. + + align:start position:0% +others. + + + align:start position:0% +others. +But if you stick some mass over zero, it + + align:start position:0% +But if you stick some mass over zero, it + + + align:start position:0% +But if you stick some mass over zero, it +will contribute to everybody. + + align:start position:0% +will contribute to everybody. + + + align:start position:0% +will contribute to everybody. +So zero frequency is being counted very + + align:start position:0% +So zero frequency is being counted very + + + align:start position:0% +So zero frequency is being counted very +differently from any other frequency. + + align:start position:0% +differently from any other frequency. + + + align:start position:0% +differently from any other frequency. +Every other frequency only contributes + + align:start position:0% +Every other frequency only contributes + + + align:start position:0% +Every other frequency only contributes +to one prime, but the zero frequency + + align:start position:0% +to one prime, but the zero frequency + + + align:start position:0% +to one prime, but the zero frequency +contributes to all primes. + + align:start position:0% + + + + align:start position:0% + +Okay. So therefore, if you if I start + + align:start position:0% +Okay. So therefore, if you if I start + + + align:start position:0% +Okay. So therefore, if you if I start +with my function f, if it has a decent + + align:start position:0% +with my function f, if it has a decent + + + align:start position:0% +with my function f, if it has a decent +amount in the zero frequency, then all + + align:start position:0% +amount in the zero frequency, then all + + + align:start position:0% +amount in the zero frequency, then all +the different ps also will see a decent + + align:start position:0% +the different ps also will see a decent + + + align:start position:0% +the different ps also will see a decent +amount in the zero frequency. + + align:start position:0% +amount in the zero frequency. + + + align:start position:0% +amount in the zero frequency. +And then my function may have a bunch of + + align:start position:0% +And then my function may have a bunch of + + + align:start position:0% +And then my function may have a bunch of +other frequencies, but each one of them + + align:start position:0% +other frequencies, but each one of them + + + align:start position:0% +other frequencies, but each one of them +is only contributing to one prime. So + + align:start position:0% +is only contributing to one prime. So + + + align:start position:0% +is only contributing to one prime. So +kind of uh if I average over all the + + align:start position:0% +kind of uh if I average over all the + + + align:start position:0% +kind of uh if I average over all the +primes, those get damped down a lot + + align:start position:0% +primes, those get damped down a lot + + + align:start position:0% +primes, those get damped down a lot +compared to the zero frequency. + + align:start position:0% +compared to the zero frequency. + + + align:start position:0% +compared to the zero frequency. +So that's what's go that's a + + align:start position:0% +So that's what's go that's a + + + align:start position:0% +So that's what's go that's a +possible a possible intuition about + + align:start position:0% +possible a possible intuition about + + + align:start position:0% +possible a possible intuition about +what's going on in the large s. + + align:start position:0% + + + + align:start position:0% + +Okay. So the last thing to uh to round + + align:start position:0% +Okay. So the last thing to uh to round + + + align:start position:0% +Okay. So the last thing to uh to round +out our proof of the large s is we'll + + align:start position:0% +out our proof of the large s is we'll + + + align:start position:0% +out our proof of the large s is we'll +actually rigorously prove this heristic. + + align:start position:0% +actually rigorously prove this heristic. + + + align:start position:0% +actually rigorously prove this heristic. +Um any questions or comments before we + + align:start position:0% +Um any questions or comments before we + + + align:start position:0% +Um any questions or comments before we +do that? + + align:start position:0% + + + + align:start position:0% + +Well, it seems like we have more freedom + + align:start position:0% +Well, it seems like we have more freedom + + + align:start position:0% +Well, it seems like we have more freedom +to choose f here than in the like + + align:start position:0% +to choose f here than in the like + + + align:start position:0% +to choose f here than in the like +reality. + + align:start position:0% +reality. + + + align:start position:0% +reality. +We always just choose fing. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. So the question is um do we do we + + align:start position:0% +>> Yeah. So the question is um do we do we + + + align:start position:0% +>> Yeah. So the question is um do we do we +choose f? So here f doesn't have to be + + align:start position:0% +choose f? So here f doesn't have to be + + + align:start position:0% +choose f? So here f doesn't have to be +the characteristic function of a set. + + align:start position:0% +the characteristic function of a set. + + + align:start position:0% +the characteristic function of a set. +We've often talked about f being the + + align:start position:0% +We've often talked about f being the + + + align:start position:0% +We've often talked about f being the +characteristic function of a set. What's + + align:start position:0% +characteristic function of a set. What's + + + align:start position:0% +characteristic function of a set. What's +up with that? Um + + align:start position:0% +up with that? Um + + + align:start position:0% +up with that? Um +uh we'll also do something at the end of + + align:start position:0% +uh we'll also do something at the end of + + + align:start position:0% +uh we'll also do something at the end of +class we'll mention something in the + + align:start position:0% +class we'll mention something in the + + + align:start position:0% +class we'll mention something in the +real setting where f doesn't have to be + + align:start position:0% +real setting where f doesn't have to be + + + align:start position:0% +real setting where f doesn't have to be +a characteristic function. Um so + + align:start position:0% + + + + align:start position:0% + +yeah so there so there are there are + + align:start position:0% +yeah so there so there are there are + + + align:start position:0% +yeah so there so there are there are +some theorems that become interesting + + align:start position:0% +some theorems that become interesting + + + align:start position:0% +some theorems that become interesting +where f is a is a characteristic + + align:start position:0% +where f is a is a characteristic + + + align:start position:0% +where f is a is a characteristic +function of kind of a sparse set and + + align:start position:0% +function of kind of a sparse set and + + + align:start position:0% +function of kind of a sparse set and +that sparity comes into play. Um and + + align:start position:0% +that sparity comes into play. Um and + + + align:start position:0% +that sparity comes into play. Um and +there are others where f could just be + + align:start position:0% +there are others where f could just be + + + align:start position:0% +there are others where f could just be +anything there. + + align:start position:0% +anything there. + + + align:start position:0% +anything there. +They're both they're all part of the + + align:start position:0% +They're both they're all part of the + + + align:start position:0% +They're both they're all part of the +theory. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Um + + align:start position:0% + + + + align:start position:0% + +So this heristic, this locally constant + + align:start position:0% +So this heristic, this locally constant + + + align:start position:0% +So this heristic, this locally constant +heristic is similar to the one that's on + + align:start position:0% +heristic is similar to the one that's on + + + align:start position:0% +heristic is similar to the one that's on +the homework that you're thinking + + align:start position:0% +the homework that you're thinking + + + align:start position:0% +the homework that you're thinking +through that's due tonight. And by the + + align:start position:0% +through that's due tonight. And by the + + + align:start position:0% +through that's due tonight. And by the +way, there are office hours after the + + align:start position:0% +way, there are office hours after the + + + align:start position:0% +way, there are office hours after the +class for anybody who would like to talk + + align:start position:0% +class for anybody who would like to talk + + + align:start position:0% +class for anybody who would like to talk +about that or anything else. Um so yeah. + + align:start position:0% +about that or anything else. Um so yeah. + + + align:start position:0% +about that or anything else. Um so yeah. +Okay. So I'll also prove this in class. + + align:start position:0% +Okay. So I'll also prove this in class. + + + align:start position:0% +Okay. So I'll also prove this in class. +Um and um yeah. All right. + + align:start position:0% +Um and um yeah. All right. + + + align:start position:0% +Um and um yeah. All right. +So how does it work? + + align:start position:0% +So how does it work? + + + align:start position:0% +So how does it work? +I'm gonna choose a function CN. It's a + + align:start position:0% +I'm gonna choose a function CN. It's a + + + align:start position:0% +I'm gonna choose a function CN. It's a +function Z to C. So that CN of little N + + align:start position:0% +function Z to C. So that CN of little N + + + align:start position:0% +function Z to C. So that CN of little N +is one if N is an integer from 1 to N. + + align:start position:0% +is one if N is an integer from 1 to N. + + + align:start position:0% +is one if N is an integer from 1 to N. +And CN is also um smooth and rapidly + + align:start position:0% +And CN is also um smooth and rapidly + + + align:start position:0% +And CN is also um smooth and rapidly +decaying. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um so then when I take the fora + + align:start position:0% +Um so then when I take the fora + + + align:start position:0% +Um so then when I take the fora +transform of CN behaves like this + + align:start position:0% +transform of CN behaves like this + + + align:start position:0% +transform of CN behaves like this +so it's around n if the frequency c has + + align:start position:0% +so it's around n if the frequency c has + + + align:start position:0% +so it's around n if the frequency c has +size less than 1 / n and then it's + + align:start position:0% +size less than 1 / n and then it's + + + align:start position:0% +size less than 1 / n and then it's +rapidly decaying. + + align:start position:0% + + + + align:start position:0% + +So in pictures, so C is only well + + align:start position:0% +So in pictures, so C is only well + + + align:start position:0% +So in pictures, so C is only well +defined modulo one. And in this context, + + align:start position:0% +defined modulo one. And in this context, + + + align:start position:0% +defined modulo one. And in this context, +it's nice to draw the modulo one as + + align:start position:0% +it's nice to draw the modulo one as + + + align:start position:0% +it's nice to draw the modulo one as +going from negative a half to positive a + + align:start position:0% +going from negative a half to positive a + + + align:start position:0% +going from negative a half to positive a +half. Here's zero. + + align:start position:0% + + + + align:start position:0% + +So this axis has the norm of CN C. This + + align:start position:0% +So this axis has the norm of CN C. This + + + align:start position:0% +So this axis has the norm of CN C. This +is N. And this distance here is one N. + + align:start position:0% +is N. And this distance here is one N. + + + align:start position:0% +is N. And this distance here is one N. +That's what it looks like. + + align:start position:0% +That's what it looks like. + + + align:start position:0% +That's what it looks like. +Okay. And rapidly decaying could mean + + align:start position:0% +Okay. And rapidly decaying could mean + + + align:start position:0% +Okay. And rapidly decaying could mean +rigorously + + align:start position:0% +rigorously + + + align:start position:0% +rigorously +n* + + align:start position:0% + + + + align:start position:0% + +c * n. So once c is bigger than 1 / n, + + align:start position:0% +c * n. So once c is bigger than 1 / n, + + + align:start position:0% +c * n. So once c is bigger than 1 / n, +this thing starts to be bigger than one + + align:start position:0% +this thing starts to be bigger than one + + + align:start position:0% +this thing starts to be bigger than one +and kick in. And we could throw in that. + + align:start position:0% +and kick in. And we could throw in that. + + + align:start position:0% +and kick in. And we could throw in that. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> What does smoothness mean for a map from + + align:start position:0% +>> What does smoothness mean for a map from + + + align:start position:0% +>> What does smoothness mean for a map from +the integers? + + align:start position:0% +the integers? + + + align:start position:0% +the integers? +>> Yeah. What does smoothness mean? Um, + + align:start position:0% + + + + align:start position:0% + +>> right. Um you you could think of C as a + + align:start position:0% +>> right. Um you you could think of C as a + + + align:start position:0% +>> right. Um you you could think of C as a +map that's defined on the whole real + + align:start position:0% +map that's defined on the whole real + + + align:start position:0% +map that's defined on the whole real +line and it's smooth on the whole real + + align:start position:0% +line and it's smooth on the whole real + + + align:start position:0% +line and it's smooth on the whole real +line and then we happen to be evaluating + + align:start position:0% +line and then we happen to be evaluating + + + align:start position:0% +line and then we happen to be evaluating +it at the integers. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Um okay. Now this is helpful because + + align:start position:0% +Um okay. Now this is helpful because + + + align:start position:0% +Um okay. Now this is helpful because +f is equal to f * cn. + + align:start position:0% +f is equal to f * cn. + + + align:start position:0% +f is equal to f * cn. +If so, if the support of f is contained + + align:start position:0% +If so, if the support of f is contained + + + align:start position:0% +If so, if the support of f is contained +in integers up to n. + + align:start position:0% +in integers up to n. + + + align:start position:0% +in integers up to n. +Um and then when we take the for + + align:start position:0% +Um and then when we take the for + + + align:start position:0% +Um and then when we take the for +transform we get that f hat is f hat + + align:start position:0% +transform we get that f hat is f hat + + + align:start position:0% +transform we get that f hat is f hat +convolved with cn hat. + + align:start position:0% +convolved with cn hat. + + + align:start position:0% +convolved with cn hat. +And so in particular um so fhat at a + + align:start position:0% +And so in particular um so fhat at a + + + align:start position:0% +And so in particular um so fhat at a +particular frequency of v is c is fhat + + align:start position:0% +particular frequency of v is c is fhat + + + align:start position:0% +particular frequency of v is c is fhat +convolved with cn + + align:start position:0% +convolved with cn + + + align:start position:0% +convolved with cn +c. Chat looks like that. + + align:start position:0% +c. Chat looks like that. + + + align:start position:0% +c. Chat looks like that. +And so the norm of fhat is bounded by + + align:start position:0% +And so the norm of fhat is bounded by + + + align:start position:0% +And so the norm of fhat is bounded by +the norm of fhat convolved with cn hat. + + align:start position:0% +the norm of fhat convolved with cn hat. + + + align:start position:0% +the norm of fhat convolved with cn hat. +And also the norm of fhat squared is + + align:start position:0% +And also the norm of fhat squared is + + + align:start position:0% +And also the norm of fhat squared is +bounded by the norm of fhat squared + + align:start position:0% +bounded by the norm of fhat squared + + + align:start position:0% +bounded by the norm of fhat squared +convolved with cn hat by koshi schwarz. + + align:start position:0% +convolved with cn hat by koshi schwarz. + + + align:start position:0% +convolved with cn hat by koshi schwarz. +So what actually one feature of this + + align:start position:0% +So what actually one feature of this + + + align:start position:0% +So what actually one feature of this +formula is that the integral of cn hat + + align:start position:0% +formula is that the integral of cn hat + + + align:start position:0% +formula is that the integral of cn hat +xc dx c is bounded by one. + + align:start position:0% + + + + align:start position:0% + +It has height one and it has width + + align:start position:0% +It has height one and it has width + + + align:start position:0% +It has height one and it has width +height n and width one n. + + align:start position:0% + + + + align:start position:0% + +>> Sorry. So head is the for transform of S + + align:start position:0% +>> Sorry. So head is the for transform of S + + + align:start position:0% +>> Sorry. So head is the for transform of S +in the sense of real function and + + align:start position:0% +in the sense of real function and + + + align:start position:0% +in the sense of real function and +or is the form in the sense of + + align:start position:0% + + + + align:start position:0% + +>> okay yeah there's a good question + + align:start position:0% +>> okay yeah there's a good question + + + align:start position:0% +>> okay yeah there's a good question +there's a good question okay so um + + align:start position:0% +there's a good question okay so um + + + align:start position:0% +there's a good question okay so um +all right so there's so I originally + + align:start position:0% +all right so there's so I originally + + + align:start position:0% +all right so there's so I originally +said is a function on the integers But + + align:start position:0% +said is a function on the integers But + + + align:start position:0% +said is a function on the integers But +in answer to the question, what does it + + align:start position:0% +in answer to the question, what does it + + + align:start position:0% +in answer to the question, what does it +mean to be smooth? I said we should also + + align:start position:0% +mean to be smooth? I said we should also + + + align:start position:0% +mean to be smooth? I said we should also +think of it as a function on the real + + align:start position:0% +think of it as a function on the real + + + align:start position:0% +think of it as a function on the real +line. So I'll call them SN integers + + align:start position:0% +line. So I'll call them SN integers + + + align:start position:0% +line. So I'll call them SN integers +that's our function on the integers and + + align:start position:0% +that's our function on the integers and + + + align:start position:0% +that's our function on the integers and +P n real line that's a function on the + + align:start position:0% +P n real line that's a function on the + + + align:start position:0% +P n real line that's a function on the +real + + align:start position:0% +real + + + align:start position:0% +real +and they each have a fora transform + + align:start position:0% +and they each have a fora transform + + + align:start position:0% +and they each have a fora transform +s on the integers hat of c is the sum + + align:start position:0% +s on the integers hat of c is the sum + + + align:start position:0% +s on the integers hat of c is the sum +over integers s n of n eus 2 pi i n c + + align:start position:0% +over integers s n of n eus 2 pi i n c + + + align:start position:0% +over integers s n of n eus 2 pi i n c +and s n if you think of it as a real + + align:start position:0% +and s n if you think of it as a real + + + align:start position:0% +and s n if you think of it as a real +valued function It has a 4A transform + + align:start position:0% +valued function It has a 4A transform + + + align:start position:0% +valued function It has a 4A transform +and XC that's defined to be the integral + + align:start position:0% +and XC that's defined to be the integral + + + align:start position:0% +and XC that's defined to be the integral +over the real line s of x e - 2<unk> iix + + align:start position:0% +over the real line s of x e - 2<unk> iix + + + align:start position:0% +over the real line s of x e - 2<unk> iix +xc dx + + align:start position:0% + + + + align:start position:0% + +okay so the question was um when I write + + align:start position:0% +okay so the question was um when I write + + + align:start position:0% +okay so the question was um when I write +n hat which one of these two things do I + + align:start position:0% +n hat which one of these two things do I + + + align:start position:0% +n hat which one of these two things do I +mean + + align:start position:0% +mean + + + align:start position:0% +mean +okay so I mean this one but they're + + align:start position:0% +okay so I mean this one but they're + + + align:start position:0% +okay so I mean this one but they're +equal to each other so the + + align:start position:0% +equal to each other so the + + + align:start position:0% +equal to each other so the +summation theorem + + align:start position:0% + + + + align:start position:0% + +says that + + align:start position:0% +says that + + + align:start position:0% +says that +C and Z hat is equal to of C + + align:start position:0% +C and Z hat is equal to of C + + + align:start position:0% +C and Z hat is equal to of C +is equal to + + align:start position:0% + + + + align:start position:0% + +right is that right + + align:start position:0% + + + + align:start position:0% + +wait + + align:start position:0% +wait + + + align:start position:0% +wait +so these are closely related + + align:start position:0% +so these are closely related + + + align:start position:0% +so these are closely related +for a + + align:start position:0% + + + + align:start position:0% + +Yeah. So this guy is the sum uh Z and Z + + align:start position:0% +Yeah. So this guy is the sum uh Z and Z + + + align:start position:0% +Yeah. So this guy is the sum uh Z and Z +of C and R hat of C plus Z. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um, so we should make two pictures + + align:start position:0% + + + + align:start position:0% + +in yellow. I will draw C and R hat. + + align:start position:0% +in yellow. I will draw C and R hat. + + + align:start position:0% +in yellow. I will draw C and R hat. +Let's extend this. + + align:start position:0% + + + + align:start position:0% + +It looks basically the same. + + align:start position:0% +It looks basically the same. + + + align:start position:0% +It looks basically the same. +And then it gets really small + + align:start position:0% +And then it gets really small + + + align:start position:0% +And then it gets really small +and it stays really small. + + align:start position:0% + + + + align:start position:0% + +And + + align:start position:0% + + + + align:start position:0% + +what does so in blue I'll do at z hat. + + align:start position:0% + + + + align:start position:0% + +It looks really almost the same + + align:start position:0% +It looks really almost the same + + + align:start position:0% +It looks really almost the same +except + + align:start position:0% +except + + + align:start position:0% +except +this one is periodic. This 4A transform + + align:start position:0% +this one is periodic. This 4A transform + + + align:start position:0% +this one is periodic. This 4A transform +is defined on R modulo Z. So it's going + + align:start position:0% +is defined on R modulo Z. So it's going + + + align:start position:0% +is defined on R modulo Z. So it's going +to be periodic Z periodic. So then here + + align:start position:0% +to be periodic Z periodic. So then here + + + align:start position:0% +to be periodic Z periodic. So then here +at minus one, + + align:start position:0% +at minus one, + + + align:start position:0% +at minus one, +it's going to go up again. So there's + + align:start position:0% +it's going to go up again. So there's + + + align:start position:0% +it's going to go up again. So there's +going to be an identical copy. The blue + + align:start position:0% +going to be an identical copy. The blue + + + align:start position:0% +going to be an identical copy. The blue +one is Z periodic. + + align:start position:0% + + + + align:start position:0% + +Okay. Um so if you compare so then if + + align:start position:0% +Okay. Um so if you compare so then if + + + align:start position:0% +Okay. Um so if you compare so then if +you know if you look at this formula it + + align:start position:0% +you know if you look at this formula it + + + align:start position:0% +you know if you look at this formula it +is also it's taking this function and + + align:start position:0% +is also it's taking this function and + + + align:start position:0% +is also it's taking this function and +turning it into a z periodic function by + + align:start position:0% +turning it into a z periodic function by + + + align:start position:0% +turning it into a z periodic function by +periodizing it and since this function + + align:start position:0% +periodizing it and since this function + + + align:start position:0% +periodizing it and since this function +originally was extremely localized to + + align:start position:0% +originally was extremely localized to + + + align:start position:0% +originally was extremely localized to +between minus a half and a half. It + + align:start position:0% +between minus a half and a half. It + + + align:start position:0% +between minus a half and a half. It +almost looks like I took the yellow + + align:start position:0% +almost looks like I took the yellow + + + align:start position:0% +almost looks like I took the yellow +function and I just took copies of it + + align:start position:0% +function and I just took copies of it + + + align:start position:0% +function and I just took copies of it +and put them here. + + align:start position:0% +and put them here. + + + align:start position:0% +and put them here. +Um so the you know the the the copy over + + align:start position:0% +Um so the you know the the the copy over + + + align:start position:0% +Um so the you know the the the copy over +here can + + align:start position:0% +here can + + + align:start position:0% +here can +Yeah. Sorry. Okay. + + align:start position:0% +Yeah. Sorry. Okay. + + + align:start position:0% +Yeah. Sorry. Okay. +Anyway, so that's what that's what this + + align:start position:0% +Anyway, so that's what that's what this + + + align:start position:0% +Anyway, so that's what that's what this +one that's what this one looks like and + + align:start position:0% +one that's what this one looks like and + + + align:start position:0% +one that's what this one looks like and +what this one looks like. + + align:start position:0% + + + + align:start position:0% + +Okay. Um so to prove this estimate first + + align:start position:0% +Okay. Um so to prove this estimate first + + + align:start position:0% +Okay. Um so to prove this estimate first +you prove it for C and R and you can do + + align:start position:0% +you prove it for C and R and you can do + + + align:start position:0% +you prove it for C and R and you can do +that using rate for analysis over R and + + align:start position:0% +that using rate for analysis over R and + + + align:start position:0% +that using rate for analysis over R and +you use the smoothness and you integrate + + align:start position:0% +you use the smoothness and you integrate + + + align:start position:0% +you use the smoothness and you integrate +by parts many times + + align:start position:0% +by parts many times + + + align:start position:0% +by parts many times +and then to study the one over Z you use + + align:start position:0% +and then to study the one over Z you use + + + align:start position:0% +and then to study the one over Z you use +this formula and because this guy is + + align:start position:0% +this formula and because this guy is + + + align:start position:0% +this formula and because this guy is +decaying so rapidly the contribution + + align:start position:0% +decaying so rapidly the contribution + + + align:start position:0% +decaying so rapidly the contribution +from the so if C if if if this C is + + align:start position:0% +from the so if C if if if this C is + + + align:start position:0% +from the so if C if if if this C is +between minus a half and a half then the + + align:start position:0% +between minus a half and a half then the + + + align:start position:0% +between minus a half and a half then the +contribution coming from integer Z other + + align:start position:0% +contribution coming from integer Z other + + + align:start position:0% +contribution coming from integer Z other +than zero is incredibly small. + + align:start position:0% +than zero is incredibly small. + + + align:start position:0% +than zero is incredibly small. +Anyway, so so the bounds for this one + + align:start position:0% +Anyway, so so the bounds for this one + + + align:start position:0% +Anyway, so so the bounds for this one +you use to give bounds for this one. + + align:start position:0% + + + + align:start position:0% + +Okay, thanks for those questions + + align:start position:0% +Okay, thanks for those questions + + + align:start position:0% +Okay, thanks for those questions +everybody. That was helpful. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So now we're going to do a slightly more + + align:start position:0% +So now we're going to do a slightly more + + + align:start position:0% +So now we're going to do a slightly more +rigorous version of this argument. + + align:start position:0% + + + + align:start position:0% + +So rigorous proof. + + align:start position:0% + + + + align:start position:0% + +So the left hand side we decided was + + align:start position:0% +So the left hand side we decided was + + + align:start position:0% +So the left hand side we decided was +around 1 / m times the sum over the + + align:start position:0% +around 1 / m times the sum over the + + + align:start position:0% +around 1 / m times the sum over the +frequencies in qm + + align:start position:0% +frequencies in qm + + + align:start position:0% +frequencies in qm +of + + align:start position:0% +of + + + align:start position:0% +of +f fi of c norm squ. That part was + + align:start position:0% +f fi of c norm squ. That part was + + + align:start position:0% +f fi of c norm squ. That part was +rigorous before. We didn't need to make + + align:start position:0% +rigorous before. We didn't need to make + + + align:start position:0% +rigorous before. We didn't need to make +it rigorous. But now we need to relate + + align:start position:0% +it rigorous. But now we need to relate + + + align:start position:0% +it rigorous. But now we need to relate +this sum to an integral + + align:start position:0% +this sum to an integral + + + align:start position:0% +this sum to an integral +and we use this fact here. This fact + + align:start position:0% +and we use this fact here. This fact + + + align:start position:0% +and we use this fact here. This fact +encodes the idea that this quantity is + + align:start position:0% +encodes the idea that this quantity is + + + align:start position:0% +encodes the idea that this quantity is +locally constant at the scale 1 / n. + + align:start position:0% + + + + align:start position:0% + +So this is bounded by 1 / m + + align:start position:0% +So this is bounded by 1 / m + + + align:start position:0% +So this is bounded by 1 / m +sum c and qm of the integral + + align:start position:0% +sum c and qm of the integral + + + align:start position:0% +sum c and qm of the integral +f^ 2 of um + + align:start position:0% +f^ 2 of um + + + align:start position:0% +f^ 2 of um +omega time cnhat + + align:start position:0% +omega time cnhat + + + align:start position:0% +omega time cnhat +of c minus omega. + + align:start position:0% + + + + align:start position:0% + +So this is just writing out the + + align:start position:0% +So this is just writing out the + + + align:start position:0% +So this is just writing out the +convolution as an integral. + + align:start position:0% +convolution as an integral. + + + align:start position:0% +convolution as an integral. +Now we can bring this sum inside. + + align:start position:0% +Now we can bring this sum inside. + + + align:start position:0% +Now we can bring this sum inside. +So this is 1 / m integral + + align:start position:0% +So this is 1 / m integral + + + align:start position:0% +So this is 1 / m integral +fi hat of omega^ 2 times the sum over c + + align:start position:0% +fi hat of omega^ 2 times the sum over c + + + align:start position:0% +fi hat of omega^ 2 times the sum over c +in qm + + align:start position:0% +in qm + + + align:start position:0% +in qm +of + + align:start position:0% +of + + + align:start position:0% +of +cn hat of c minus omega omega. + + align:start position:0% + + + + align:start position:0% + +Okay. And this sum we can bound by n. + + align:start position:0% +Okay. And this sum we can bound by n. + + + align:start position:0% +Okay. And this sum we can bound by n. +Why? Because each each term in the sum + + align:start position:0% +Why? Because each each term in the sum + + + align:start position:0% +Why? Because each each term in the sum +has size at least around n. This term is + + align:start position:0% +has size at least around n. This term is + + + align:start position:0% +has size at least around n. This term is +a bump essentially a bump of height n + + align:start position:0% +a bump essentially a bump of height n + + + align:start position:0% +a bump essentially a bump of height n +and width 1 /n around c. And the + + align:start position:0% +and width 1 /n around c. And the + + + align:start position:0% +and width 1 /n around c. And the +distance between any two different is at + + align:start position:0% +distance between any two different is at + + + align:start position:0% +distance between any two different is at +least one overn. So those bumps don't + + align:start position:0% +least one overn. So those bumps don't + + + align:start position:0% +least one overn. So those bumps don't +overlap with each other. + + align:start position:0% +overlap with each other. + + + align:start position:0% +overlap with each other. +Now the bumps aren't quite compactly + + align:start position:0% +Now the bumps aren't quite compactly + + + align:start position:0% +Now the bumps aren't quite compactly +supported. They have the the tails that + + align:start position:0% +supported. They have the the tails that + + + align:start position:0% +supported. They have the the tails that +you can see in the picture, but the + + align:start position:0% +you can see in the picture, but the + + + align:start position:0% +you can see in the picture, but the +tails are incredibly tiny. And so if you + + align:start position:0% +tails are incredibly tiny. And so if you + + + align:start position:0% +tails are incredibly tiny. And so if you +just plug in the rapidly decaying bound, + + align:start position:0% +just plug in the rapidly decaying bound, + + + align:start position:0% +just plug in the rapidly decaying bound, +the tails don't contribute anything and + + align:start position:0% +the tails don't contribute anything and + + + align:start position:0% +the tails don't contribute anything and +you get this bound. + + align:start position:0% + + + + align:start position:0% + +Okay. Then if you take out this n, you + + align:start position:0% +Okay. Then if you take out this n, you + + + align:start position:0% +Okay. Then if you take out this n, you +have what we had before. + + align:start position:0% +have what we had before. + + + align:start position:0% +have what we had before. +n / m integral from 0 to 1 f^ 2 c + + align:start position:0% +n / m integral from 0 to 1 f^ 2 c + + + align:start position:0% +n / m integral from 0 to 1 f^ 2 c +uh + + align:start position:0% +uh + + + align:start position:0% +uh +n / m + + align:start position:0% +n / m + + + align:start position:0% +n / m +sum f of n squ + + align:start position:0% +sum f of n squ + + + align:start position:0% +sum f of n squ +and that's the proof of of linux Good + + align:start position:0% +and that's the proof of of linux Good + + + align:start position:0% +and that's the proof of of linux Good +stuff. + + align:start position:0% + + + + align:start position:0% + +So, we only have a little bit of time + + align:start position:0% +So, we only have a little bit of time + + + align:start position:0% +So, we only have a little bit of time +left, about five minutes. Um + + align:start position:0% +left, about five minutes. Um + + + align:start position:0% +left, about five minutes. Um +in + + align:start position:0% +in + + + align:start position:0% +in +e we could either if people have things + + align:start position:0% +e we could either if people have things + + + align:start position:0% +e we could either if people have things +you want to talk about we could just + + align:start position:0% +you want to talk about we could just + + + align:start position:0% +you want to talk about we could just +talk for five minutes + + align:start position:0% +talk for five minutes + + + align:start position:0% +talk for five minutes +or I could set up the next thing and try + + align:start position:0% +or I could set up the next thing and try + + + align:start position:0% +or I could set up the next thing and try +to try to give a feeling of how + + align:start position:0% +to try to give a feeling of how + + + align:start position:0% +to try to give a feeling of how +something in real real variable setting + + align:start position:0% +something in real real variable setting + + + align:start position:0% +something in real real variable setting +is analogous to this thing in a kind of + + align:start position:0% +is analogous to this thing in a kind of + + + align:start position:0% +is analogous to this thing in a kind of +number theoretic + + align:start position:0% + + + + align:start position:0% + +Okay. So, I I give a little try to give + + align:start position:0% +Okay. So, I I give a little try to give + + + align:start position:0% +Okay. So, I I give a little try to give +a little teaser preview foreshadowing of + + align:start position:0% +a little teaser preview foreshadowing of + + + align:start position:0% +a little teaser preview foreshadowing of +how the same idea occurs in real + + align:start position:0% +how the same idea occurs in real + + + align:start position:0% +how the same idea occurs in real +analysis. I want to keep this picture + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay. So the the um the thing that we + + align:start position:0% +Okay. So the the um the thing that we + + + align:start position:0% +Okay. So the the um the thing that we +proved is if you have a function on the + + align:start position:0% +proved is if you have a function on the + + + align:start position:0% +proved is if you have a function on the +integers from one to n then when you + + align:start position:0% +integers from one to n then when you + + + align:start position:0% +integers from one to n then when you +project it mod p most of the projections + + align:start position:0% +project it mod p most of the projections + + + align:start position:0% +project it mod p most of the projections +look almost constant. They look smoother + + align:start position:0% +look almost constant. They look smoother + + + align:start position:0% +look almost constant. They look smoother +than the original function. And there's + + align:start position:0% +than the original function. And there's + + + align:start position:0% +than the original function. And there's +a totally analogous phenomenon in R to + + align:start position:0% +a totally analogous phenomenon in R to + + + align:start position:0% +a totally analogous phenomenon in R to +the D. If you have a function on R to + + align:start position:0% +the D. If you have a function on R to + + + align:start position:0% +the D. If you have a function on R to +the D and you consider projections onto + + align:start position:0% +the D and you consider projections onto + + + align:start position:0% +the D and you consider projections onto +lower dimensional subspaces, then almost + + align:start position:0% +lower dimensional subspaces, then almost + + + align:start position:0% +lower dimensional subspaces, then almost +all of them look smoother than the + + align:start position:0% +all of them look smoother than the + + + align:start position:0% +all of them look smoother than the +original function. And like we mentioned + + align:start position:0% +original function. And like we mentioned + + + align:start position:0% +original function. And like we mentioned +on the first day, if you're in high + + align:start position:0% +on the first day, if you're in high + + + align:start position:0% +on the first day, if you're in high +enough dimension, if you take a a + + align:start position:0% +enough dimension, if you take a a + + + align:start position:0% +enough dimension, if you take a a +function and you project it onto a + + align:start position:0% +function and you project it onto a + + + align:start position:0% +function and you project it onto a +typical line, even if the initial + + align:start position:0% +typical line, even if the initial + + + align:start position:0% +typical line, even if the initial +function is only in L2 and is nowhere + + align:start position:0% +function is only in L2 and is nowhere + + + align:start position:0% +function is only in L2 and is nowhere +continuous, the on a typical line, the + + align:start position:0% +continuous, the on a typical line, the + + + align:start position:0% +continuous, the on a typical line, the +projection will be continuous and even + + align:start position:0% +projection will be continuous and even + + + align:start position:0% +projection will be continuous and even +C1 and even C2, right? So the + + align:start position:0% +C1 and even C2, right? So the + + + align:start position:0% +C1 and even C2, right? So the +projections are much smoother than the + + align:start position:0% +projections are much smoother than the + + + align:start position:0% +projections are much smoother than the +original function. + + align:start position:0% +original function. + + + align:start position:0% +original function. +Okay, so uh here is a setup for this + + align:start position:0% +Okay, so uh here is a setup for this + + + align:start position:0% +Okay, so uh here is a setup for this +that's kind of analogous to the large + + align:start position:0% +that's kind of analogous to the large + + + align:start position:0% +that's kind of analogous to the large +sip. we have a function on R to the D + + align:start position:0% +sip. we have a function on R to the D + + + align:start position:0% +sip. we have a function on R to the D +and then we'll have V contained in R to + + align:start position:0% +and then we'll have V contained in R to + + + align:start position:0% +and then we'll have V contained in R to +the D which is a subspace. + + align:start position:0% + + + + align:start position:0% + +Um and if if you have a function so so + + align:start position:0% +Um and if if you have a function so so + + + align:start position:0% +Um and if if you have a function so so +pi V of F is the projection of F onto + + align:start position:0% +pi V of F is the projection of F onto + + + align:start position:0% +pi V of F is the projection of F onto +this plane. So that's a function from V + + align:start position:0% +this plane. So that's a function from V + + + align:start position:0% +this plane. So that's a function from V +to C. + + align:start position:0% + + + + align:start position:0% + +Okay. So now I have a remark that if you + + align:start position:0% +Okay. So now I have a remark that if you + + + align:start position:0% +Okay. So now I have a remark that if you +have any function of this vector space V + + align:start position:0% +have any function of this vector space V + + + align:start position:0% +have any function of this vector space V +then it's for a transform is also + + align:start position:0% +then it's for a transform is also + + + align:start position:0% +then it's for a transform is also +defined on the vector space V. + + align:start position:0% +defined on the vector space V. + + + align:start position:0% +defined on the vector space V. +Okay. And there's a dictionary lama. + + align:start position:0% + + + + align:start position:0% + +How is the 4A transform of the + + align:start position:0% +How is the 4A transform of the + + + align:start position:0% +How is the 4A transform of the +projection related to the 4A transform + + align:start position:0% +projection related to the 4A transform + + + align:start position:0% +projection related to the 4A transform +of the original function? And it says + + align:start position:0% +of the original function? And it says + + + align:start position:0% +of the original function? And it says +that um + + align:start position:0% +that um + + + align:start position:0% +that um +pi v of f hat + + align:start position:0% +pi v of f hat + + + align:start position:0% +pi v of f hat +uh is just fhat restricted to v. + + align:start position:0% + + + + align:start position:0% + +So this is a function on the vector + + align:start position:0% +So this is a function on the vector + + + align:start position:0% +So this is a function on the vector +space v. It's for a transform is + + align:start position:0% +space v. It's for a transform is + + + align:start position:0% +space v. It's for a transform is +supposed to be a function on the vector + + align:start position:0% +supposed to be a function on the vector + + + align:start position:0% +supposed to be a function on the vector +space v. + + align:start position:0% +space v. + + + align:start position:0% +space v. +fhat is a function on r to the d. But + + align:start position:0% +fhat is a function on r to the d. But + + + align:start position:0% +fhat is a function on r to the d. But +this for transform is just fhat + + align:start position:0% +this for transform is just fhat + + + align:start position:0% +this for transform is just fhat +restricted to that to v. + + align:start position:0% +restricted to that to v. + + + align:start position:0% +restricted to that to v. +Okay. So now make a picture. Um + + align:start position:0% + + + + align:start position:0% + +uh so here is r to the d and inside of + + align:start position:0% +uh so here is r to the d and inside of + + + align:start position:0% +uh so here is r to the d and inside of +there + + align:start position:0% +there + + + align:start position:0% +there +there's a space v1 and there's another + + align:start position:0% +there's a space v1 and there's another + + + align:start position:0% +there's a space v1 and there's another +space + + align:start position:0% +space + + + align:start position:0% +space +uh v2. + + align:start position:0% +uh v2. + + + align:start position:0% +uh v2. +Whoops. And okay. And I let you imagine + + align:start position:0% +Whoops. And okay. And I let you imagine + + + align:start position:0% +Whoops. And okay. And I let you imagine +other ones. They're all subspaces. So + + align:start position:0% +other ones. They're all subspaces. So + + + align:start position:0% +other ones. They're all subspaces. So +they all go through zero. Although my + + align:start position:0% +they all go through zero. Although my + + + align:start position:0% +they all go through zero. Although my +picture was not perfect. + + align:start position:0% + + + + align:start position:0% + +And I want you to imagine this as 4A + + align:start position:0% +And I want you to imagine this as 4A + + + align:start position:0% +And I want you to imagine this as 4A +space. + + align:start position:0% + + + + align:start position:0% + +So we have a function f. F is just an + + align:start position:0% +So we have a function f. F is just an + + + align:start position:0% +So we have a function f. F is just an +L2. + + align:start position:0% +L2. + + + align:start position:0% +L2. +Uh say it's an L2 function on the unit + + align:start position:0% +Uh say it's an L2 function on the unit + + + align:start position:0% +Uh say it's an L2 function on the unit +ball. So its 4A transform could be + + align:start position:0% +ball. So its 4A transform could be + + + align:start position:0% +ball. So its 4A transform could be +anywhere here. + + align:start position:0% +anywhere here. + + + align:start position:0% +anywhere here. +Um and all we know about it is say say + + align:start position:0% +Um and all we know about it is say say + + + align:start position:0% +Um and all we know about it is say say +we know the L2 norm of f. So we know the + + align:start position:0% +we know the L2 norm of f. So we know the + + + align:start position:0% +we know the L2 norm of f. So we know the +L2 norm of fhat could be anywhere. If + + align:start position:0% +L2 norm of fhat could be anywhere. If + + + align:start position:0% +L2 norm of fhat could be anywhere. If +you happen to put some L2 norm of fhat + + align:start position:0% +you happen to put some L2 norm of fhat + + + align:start position:0% +you happen to put some L2 norm of fhat +near zero then that will be part of the + + align:start position:0% +near zero then that will be part of the + + + align:start position:0% +near zero then that will be part of the +for transform of pi v for all the + + align:start position:0% +for transform of pi v for all the + + + align:start position:0% +for transform of pi v for all the +different v's. + + align:start position:0% +different v's. + + + align:start position:0% +different v's. +But if you put some of the l2 mass of + + align:start position:0% +But if you put some of the l2 mass of + + + align:start position:0% +But if you put some of the l2 mass of +fhat over here that will contribute to + + align:start position:0% +fhat over here that will contribute to + + + align:start position:0% +fhat over here that will contribute to +pi v1 but it won't contribute to most of + + align:start position:0% +pi v1 but it won't contribute to most of + + + align:start position:0% +pi v1 but it won't contribute to most of +the other pi vs. + + align:start position:0% + + + + align:start position:0% + +Um so therefore uh when you take a + + align:start position:0% +Um so therefore uh when you take a + + + align:start position:0% +Um so therefore uh when you take a +random projection the part of the for + + align:start position:0% +random projection the part of the for + + + align:start position:0% +random projection the part of the for +transform at low frequencies is uh kind + + align:start position:0% +transform at low frequencies is uh kind + + + align:start position:0% +transform at low frequencies is uh kind +of more highly represented and the part + + align:start position:0% +of more highly represented and the part + + + align:start position:0% +of more highly represented and the part +at high frequencies is less highly + + align:start position:0% +at high frequencies is less highly + + + align:start position:0% +at high frequencies is less highly +represented. + + align:start position:0% +represented. + + + align:start position:0% +represented. +So a typical projection so initially the + + align:start position:0% +So a typical projection so initially the + + + align:start position:0% +So a typical projection so initially the +for transform could have been anywhere + + align:start position:0% +for transform could have been anywhere + + + align:start position:0% +for transform could have been anywhere +but then a typical projection will now + + align:start position:0% +but then a typical projection will now + + + align:start position:0% +but then a typical projection will now +have its fora transform concentrated at + + align:start position:0% +have its fora transform concentrated at + + + align:start position:0% +have its fora transform concentrated at +low frequencies which makes it look + + align:start position:0% +low frequencies which makes it look + + + align:start position:0% +low frequencies which makes it look +smooth. + + align:start position:0% + + + + align:start position:0% + +Okay. So here's a statement like that + + align:start position:0% +Okay. So here's a statement like that + + + align:start position:0% +Okay. So here's a statement like that +that we will prove next time by the + + align:start position:0% +that we will prove next time by the + + + align:start position:0% +that we will prove next time by the +analogous reasoning. + + align:start position:0% +analogous reasoning. + + + align:start position:0% +analogous reasoning. +theorem. + + align:start position:0% +theorem. + + + align:start position:0% +theorem. +If f is an L2 function on R to the D + + align:start position:0% +If f is an L2 function on R to the D + + + align:start position:0% +If f is an L2 function on R to the D +supported in the unit ball + + align:start position:0% +supported in the unit ball + + + align:start position:0% +supported in the unit ball +and if D is big enough + + align:start position:0% + + + + align:start position:0% + +um then + + align:start position:0% +um then + + + align:start position:0% +um then +for almost every so then um if I take + + align:start position:0% +for almost every so then um if I take + + + align:start position:0% +for almost every so then um if I take +the average over theta in the d minus + + align:start position:0% +the average over theta in the d minus + + + align:start position:0% +the average over theta in the d minus +one sphere + + align:start position:0% +one sphere + + + align:start position:0% +one sphere +of um pi theta of f. So this means I + + align:start position:0% +of um pi theta of f. So this means I + + + align:start position:0% +of um pi theta of f. So this means I +take f and I project it onto the line in + + align:start position:0% +take f and I project it onto the line in + + + align:start position:0% +take f and I project it onto the line in +the theta direction. + + align:start position:0% +the theta direction. + + + align:start position:0% +the theta direction. +The ck norm of that is bounded by the L2 + + align:start position:0% +The ck norm of that is bounded by the L2 + + + align:start position:0% +The ck norm of that is bounded by the L2 +norm of fition. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay. And so the to so we'll prove that + + align:start position:0% +Okay. And so the to so we'll prove that + + + align:start position:0% +Okay. And so the to so we'll prove that +next time but to end I just wanted to + + align:start position:0% +next time but to end I just wanted to + + + align:start position:0% +next time but to end I just wanted to +have everyone look at the analogy + + align:start position:0% +have everyone look at the analogy + + + align:start position:0% +have everyone look at the analogy +between these two pictures. So in fora + + align:start position:0% +between these two pictures. So in fora + + + align:start position:0% +between these two pictures. So in fora +space when we project our function onto + + align:start position:0% +space when we project our function onto + + + align:start position:0% +space when we project our function onto +different um subspaces then that we have + + align:start position:0% +different um subspaces then that we have + + + align:start position:0% +different um subspaces then that we have +these different uh pieces of the fora + + align:start position:0% +these different uh pieces of the fora + + + align:start position:0% +these different uh pieces of the fora +transform that we're seeing and in for a + + align:start position:0% +transform that we're seeing and in for a + + + align:start position:0% +transform that we're seeing and in for a +space in the large civ when we take our + + align:start position:0% +space in the large civ when we take our + + + align:start position:0% +space in the large civ when we take our +function and we project it mod p for + + align:start position:0% +function and we project it mod p for + + + align:start position:0% +function and we project it mod p for +different p we have these different + + align:start position:0% +different p we have these different + + + align:start position:0% +different p we have these different +color pieces of the 4 a space that we're + + align:start position:0% +color pieces of the 4 a space that we're + + + align:start position:0% +color pieces of the 4 a space that we're +seeing and the different color pieces + + align:start position:0% +seeing and the different color pieces + + + align:start position:0% +seeing and the different color pieces +intersect at zero + + align:start position:0% +intersect at zero + + + align:start position:0% +intersect at zero +and they don't intersect anywhere + + align:start position:0% + + + + align:start position:0% + +or they don't intersect very much + + align:start position:0% +or they don't intersect very much + + + align:start position:0% +or they don't intersect very much +anywhere else. + + align:start position:0% +anywhere else. + + + align:start position:0% +anywhere else. +And that has the effect that when you + + align:start position:0% +And that has the effect that when you + + + align:start position:0% +And that has the effect that when you +take the projections, it emphasizes the + + align:start position:0% +take the projections, it emphasizes the + + + align:start position:0% +take the projections, it emphasizes the +zero frequency or the low frequency. + + align:start position:0% +zero frequency or the low frequency. + + + align:start position:0% +zero frequency or the low frequency. +And and that plays out slight in + + align:start position:0% +And and that plays out slight in + + + align:start position:0% +And and that plays out slight in +slightly different ways in the different + + align:start position:0% +slightly different ways in the different + + + align:start position:0% +slightly different ways in the different +settings, but but morally very similar. + + align:start position:0% + + + + align:start position:0% + +Okay, cool. So, let's stop there for + + align:start position:0% +Okay, cool. So, let's stop there for + + + align:start position:0% +Okay, cool. So, let's stop there for +today. I will hang out afterwards and + + align:start position:0% +today. I will hang out afterwards and + + + align:start position:0% +today. I will hang out afterwards and +office hour, make office hours talk. Um, + + align:start position:0% +office hour, make office hours talk. Um, + + + align:start position:0% +office hour, make office hours talk. Um, +and I will see you next week. \ No newline at end of file diff --git a/iinr4-0C0Yc.txt b/iinr4-0C0Yc.txt new file mode 100644 index 0000000000000000000000000000000000000000..8e61b4ba2574477a444b290d50b223b83b07496a --- /dev/null +++ b/iinr4-0C0Yc.txt @@ -0,0 +1,1995 @@ +align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +throughout your laboratory experiences + + align:start position:0% +throughout your laboratory experiences + + + align:start position:0% +throughout your laboratory experiences +you will frequently need to assess the + + align:start position:0% +you will frequently need to assess the + + + align:start position:0% +you will frequently need to assess the +Purity or identity of a crystallin solid + + align:start position:0% +Purity or identity of a crystallin solid + + + align:start position:0% +Purity or identity of a crystallin solid +both of these goals can be accomplished + + align:start position:0% +both of these goals can be accomplished + + + align:start position:0% +both of these goals can be accomplished +by determining a compound's melting + + align:start position:0% +by determining a compound's melting + + + align:start position:0% +by determining a compound's melting +point + + align:start position:0% +point + + + align:start position:0% +point +when a compound is in a crystallin solid + + align:start position:0% +when a compound is in a crystallin solid + + + align:start position:0% +when a compound is in a crystallin solid +state the intermolecular forces that are + + align:start position:0% +state the intermolecular forces that are + + + align:start position:0% +state the intermolecular forces that are +holding the molecules together greatly + + align:start position:0% +holding the molecules together greatly + + + align:start position:0% +holding the molecules together greatly +outweigh the kinetic energy that is + + align:start position:0% +outweigh the kinetic energy that is + + + align:start position:0% +outweigh the kinetic energy that is +trying to pull them apart therefore the + + align:start position:0% +trying to pull them apart therefore the + + + align:start position:0% +trying to pull them apart therefore the +molecules appear to vibrate in a fixed + + align:start position:0% +molecules appear to vibrate in a fixed + + + align:start position:0% +molecules appear to vibrate in a fixed +location If energy is introduced into + + align:start position:0% +location If energy is introduced into + + + align:start position:0% +location If energy is introduced into +the system in the form of heat the + + align:start position:0% +the system in the form of heat the + + + align:start position:0% +the system in the form of heat the +kinetic energy of the molecules and thus + + align:start position:0% +kinetic energy of the molecules and thus + + + align:start position:0% +kinetic energy of the molecules and thus +the temperature of the system is + + align:start position:0% +the temperature of the system is + + + align:start position:0% +the temperature of the system is +increased at a certain point the + + align:start position:0% +increased at a certain point the + + + align:start position:0% +increased at a certain point the +molecular kinetic energy is high enough + + align:start position:0% +molecular kinetic energy is high enough + + + align:start position:0% +molecular kinetic energy is high enough +to overcome the attractive forces that + + align:start position:0% +to overcome the attractive forces that + + + align:start position:0% +to overcome the attractive forces that +are holding the molecules together as a + + align:start position:0% +are holding the molecules together as a + + + align:start position:0% +are holding the molecules together as a +result the crystal lattice breaks down + + align:start position:0% +result the crystal lattice breaks down + + + align:start position:0% +result the crystal lattice breaks down +and the molecules enter a liquid state + + align:start position:0% +and the molecules enter a liquid state + + + align:start position:0% +and the molecules enter a liquid state +the temperature at which the solid and + + align:start position:0% +the temperature at which the solid and + + + align:start position:0% +the temperature at which the solid and +liquid phases of a compound are in + + align:start position:0% +liquid phases of a compound are in + + + align:start position:0% +liquid phases of a compound are in +equilibrium at a certain pressure is + + align:start position:0% +equilibrium at a certain pressure is + + + align:start position:0% +equilibrium at a certain pressure is +called the melting + + align:start position:0% +called the melting + + + align:start position:0% +called the melting +point in reality a solid melts over a + + align:start position:0% +point in reality a solid melts over a + + + align:start position:0% +point in reality a solid melts over a +temperature range instead of at a + + align:start position:0% +temperature range instead of at a + + + align:start position:0% +temperature range instead of at a +specific + + align:start position:0% +specific + + + align:start position:0% +specific +temperature because this range is a the + + align:start position:0% +temperature because this range is a the + + + align:start position:0% +temperature because this range is a the +physical characteristic it is + + align:start position:0% +physical characteristic it is + + + align:start position:0% +physical characteristic it is +reproducible for a pure compound for + + align:start position:0% +reproducible for a pure compound for + + + align:start position:0% +reproducible for a pure compound for +example n feny acetamin melts between 11 + + align:start position:0% +example n feny acetamin melts between 11 + + + align:start position:0% +example n feny acetamin melts between 11 +14.2 and 11 14.9 de C therefore the term + + align:start position:0% +14.2 and 11 14.9 de C therefore the term + + + align:start position:0% +14.2 and 11 14.9 de C therefore the term +melting point really implies a melting + + align:start position:0% +melting point really implies a melting + + + align:start position:0% +melting point really implies a melting +range although a variety of melting + + align:start position:0% +range although a variety of melting + + + align:start position:0% +range although a variety of melting +point apparatuses are commercially + + align:start position:0% +point apparatuses are commercially + + + align:start position:0% +point apparatuses are commercially +available this video will demonstrate + + align:start position:0% +available this video will demonstrate + + + align:start position:0% +available this video will demonstrate +the determination of melting point by + + align:start position:0% +the determination of melting point by + + + align:start position:0% +the determination of melting point by +using the + + align:start position:0% +using the + + + align:start position:0% +using the +meltemp the meltemp appar Rus consists + + align:start position:0% +meltemp the meltemp appar Rus consists + + + align:start position:0% +meltemp the meltemp appar Rus consists +of an onoff switch a sample holder a + + align:start position:0% +of an onoff switch a sample holder a + + + align:start position:0% +of an onoff switch a sample holder a +light source that illuminates the sample + + align:start position:0% +light source that illuminates the sample + + + align:start position:0% +light source that illuminates the sample +an eyepiece that magnifies the sample a + + align:start position:0% +an eyepiece that magnifies the sample a + + + align:start position:0% +an eyepiece that magnifies the sample a +digital thermometer which indicates the + + align:start position:0% +digital thermometer which indicates the + + + align:start position:0% +digital thermometer which indicates the +temperature of the system and a voltage + + align:start position:0% +temperature of the system and a voltage + + + align:start position:0% +temperature of the system and a voltage +control the voltage control dictates the + + align:start position:0% +control the voltage control dictates the + + + align:start position:0% +control the voltage control dictates the +rate of heating with a higher setting + + align:start position:0% +rate of heating with a higher setting + + + align:start position:0% +rate of heating with a higher setting +corresponding to a faster rate the + + align:start position:0% +corresponding to a faster rate the + + + align:start position:0% +corresponding to a faster rate the +voltage control does not control the + + align:start position:0% +voltage control does not control the + + + align:start position:0% +voltage control does not control the +temperature of the system use caution + + align:start position:0% +temperature of the system use caution + + + align:start position:0% +temperature of the system use caution +when touching the Melt Temp and always + + align:start position:0% +when touching the Melt Temp and always + + + align:start position:0% +when touching the Melt Temp and always +assume that the apparatus is hot espe + + align:start position:0% +assume that the apparatus is hot espe + + + align:start position:0% +assume that the apparatus is hot espe +especially the part that is labeled + + align:start position:0% +especially the part that is labeled + + + align:start position:0% +especially the part that is labeled +caution unit + + align:start position:0% +caution unit + + + align:start position:0% +caution unit +hot the first step in determining a + + align:start position:0% +hot the first step in determining a + + + align:start position:0% +hot the first step in determining a +melting point is the preparation of the + + align:start position:0% +melting point is the preparation of the + + + align:start position:0% +melting point is the preparation of the +crystallin solid to prepare the sample + + align:start position:0% +crystallin solid to prepare the sample + + + align:start position:0% +crystallin solid to prepare the sample +you will need a spatula a watch glass a + + align:start position:0% +you will need a spatula a watch glass a + + + align:start position:0% +you will need a spatula a watch glass a +mortar and pestal capillary tubes that + + align:start position:0% +mortar and pestal capillary tubes that + + + align:start position:0% +mortar and pestal capillary tubes that +are sealed at one end and a long piece + + align:start position:0% +are sealed at one end and a long piece + + + align:start position:0% +are sealed at one end and a long piece +of glass tubing such as a long stem + + align:start position:0% +of glass tubing such as a long stem + + + align:start position:0% +of glass tubing such as a long stem +funnel before proceeding ensure that the + + align:start position:0% +funnel before proceeding ensure that the + + + align:start position:0% +funnel before proceeding ensure that the +crystallin solid is clean and dry if the + + align:start position:0% +crystallin solid is clean and dry if the + + + align:start position:0% +crystallin solid is clean and dry if the +solid is wet you can try to Pat it dry + + align:start position:0% +solid is wet you can try to Pat it dry + + + align:start position:0% +solid is wet you can try to Pat it dry +with Filter paper do not place the + + align:start position:0% +with Filter paper do not place the + + + align:start position:0% +with Filter paper do not place the +sample in the oven where it may melt or + + align:start position:0% +sample in the oven where it may melt or + + + align:start position:0% +sample in the oven where it may melt or +decompose if your sample consists of + + align:start position:0% +decompose if your sample consists of + + + align:start position:0% +decompose if your sample consists of +large crystals you must first crush them + + align:start position:0% +large crystals you must first crush them + + + align:start position:0% +large crystals you must first crush them +into smaller crystals with a mortar and + + align:start position:0% +into smaller crystals with a mortar and + + + align:start position:0% +into smaller crystals with a mortar and +pestal large crystals cannot pack + + align:start position:0% +pestal large crystals cannot pack + + + align:start position:0% +pestal large crystals cannot pack +together well which creates air pockets + + align:start position:0% +together well which creates air pockets + + + align:start position:0% +together well which creates air pockets +if air pockets are present in your + + align:start position:0% +if air pockets are present in your + + + align:start position:0% +if air pockets are present in your +sample then a time lag for heat transfer + + align:start position:0% +sample then a time lag for heat transfer + + + align:start position:0% +sample then a time lag for heat transfer +will exist causing the crystals to heat + + align:start position:0% +will exist causing the crystals to heat + + + align:start position:0% +will exist causing the crystals to heat +unevenly if you do not have a mortar and + + align:start position:0% +unevenly if you do not have a mortar and + + + align:start position:0% +unevenly if you do not have a mortar and +pestl you can use the flat end of a + + align:start position:0% +pestl you can use the flat end of a + + + align:start position:0% +pestl you can use the flat end of a +spatula to grind the sample + + align:start position:0% +spatula to grind the sample + + + align:start position:0% +spatula to grind the sample +instead after crushing the crystals + + align:start position:0% +instead after crushing the crystals + + + align:start position:0% +instead after crushing the crystals +place them on a watch glass turn the + + align:start position:0% +place them on a watch glass turn the + + + align:start position:0% +place them on a watch glass turn the +capillary tube upside down and thrust + + align:start position:0% +capillary tube upside down and thrust + + + align:start position:0% +capillary tube upside down and thrust +the open end over the crystals a small + + align:start position:0% +the open end over the crystals a small + + + align:start position:0% +the open end over the crystals a small +amount of crystals should be trapped + + align:start position:0% +amount of crystals should be trapped + + + align:start position:0% +amount of crystals should be trapped +inside the capillary invert the tube to + + align:start position:0% +inside the capillary invert the tube to + + + align:start position:0% +inside the capillary invert the tube to +its correct orientation and pack the + + align:start position:0% +its correct orientation and pack the + + + align:start position:0% +its correct orientation and pack the +crystals down to the bottom by gently + + align:start position:0% +crystals down to the bottom by gently + + + align:start position:0% +crystals down to the bottom by gently +stroking the tube or by taing it on your + + align:start position:0% +stroking the tube or by taing it on your + + + align:start position:0% +stroking the tube or by taing it on your +bench top if the crystals fail to fall + + align:start position:0% +bench top if the crystals fail to fall + + + align:start position:0% +bench top if the crystals fail to fall +to the bottom of the capillary then drop + + align:start position:0% +to the bottom of the capillary then drop + + + align:start position:0% +to the bottom of the capillary then drop +the capillary through a length of glass + + align:start position:0% +the capillary through a length of glass + + + align:start position:0% +the capillary through a length of glass +tubing a long stem funnel works well for + + align:start position:0% +tubing a long stem funnel works well for + + + align:start position:0% +tubing a long stem funnel works well for +this application you may have to repeat + + align:start position:0% +this application you may have to repeat + + + align:start position:0% +this application you may have to repeat +this action several times to ensure that + + align:start position:0% +this action several times to ensure that + + + align:start position:0% +this action several times to ensure that +the crystals are effectively packed down + + align:start position:0% +the crystals are effectively packed down + + + align:start position:0% +the crystals are effectively packed down +loose material contains air pockets + + align:start position:0% +loose material contains air pockets + + + align:start position:0% +loose material contains air pockets +which cause the sample to heat unevenly + + align:start position:0% +which cause the sample to heat unevenly + + + align:start position:0% +which cause the sample to heat unevenly +ideally the smallest manageable amount + + align:start position:0% +ideally the smallest manageable amount + + + align:start position:0% +ideally the smallest manageable amount +of material should be used which + + align:start position:0% +of material should be used which + + + align:start position:0% +of material should be used which +correlates to a depth of approximately 1 + + align:start position:0% +correlates to a depth of approximately 1 + + + align:start position:0% +correlates to a depth of approximately 1 +mm of packed material if the depth + + align:start position:0% +mm of packed material if the depth + + + align:start position:0% +mm of packed material if the depth +exceeds 2 mm inaccuracies may result due + + align:start position:0% +exceeds 2 mm inaccuracies may result due + + + align:start position:0% +exceeds 2 mm inaccuracies may result due +to uneven + + align:start position:0% +to uneven + + + align:start position:0% +to uneven +heating prepare four capillary tubes of + + align:start position:0% +heating prepare four capillary tubes of + + + align:start position:0% +heating prepare four capillary tubes of +your sample one filled capillary tube + + align:start position:0% +your sample one filled capillary tube + + + align:start position:0% +your sample one filled capillary tube +will be used to determine a crude + + align:start position:0% +will be used to determine a crude + + + align:start position:0% +will be used to determine a crude +melting point and the other three will + + align:start position:0% +melting point and the other three will + + + align:start position:0% +melting point and the other three will +be used to determine your actual melting + + align:start position:0% +be used to determine your actual melting + + + align:start position:0% +be used to determine your actual melting +point in + + align:start position:0% +point in + + + align:start position:0% +point in +triplicate if you do not know the + + align:start position:0% +triplicate if you do not know the + + + align:start position:0% +triplicate if you do not know the +expected melting point of your compound + + align:start position:0% +expected melting point of your compound + + + align:start position:0% +expected melting point of your compound +you must first determine a crude melting + + align:start position:0% +you must first determine a crude melting + + + align:start position:0% +you must first determine a crude melting +point finding the approximate melting + + align:start position:0% +point finding the approximate melting + + + align:start position:0% +point finding the approximate melting +point of a sample will save a lot of + + align:start position:0% +point of a sample will save a lot of + + + align:start position:0% +point of a sample will save a lot of +time when performing the actual + + align:start position:0% +time when performing the actual + + + align:start position:0% +time when performing the actual +measurement to determine the crude + + align:start position:0% +measurement to determine the crude + + + align:start position:0% +measurement to determine the crude +melting point set the voltage on the + + align:start position:0% +melting point set the voltage on the + + + align:start position:0% +melting point set the voltage on the +Melt temp to zero and wait until the + + align:start position:0% +Melt temp to zero and wait until the + + + align:start position:0% +Melt temp to zero and wait until the +apparatus has cooled to room temperature + + align:start position:0% +apparatus has cooled to room temperature + + + align:start position:0% +apparatus has cooled to room temperature +insert a sample increase the temperature + + align:start position:0% +insert a sample increase the temperature + + + align:start position:0% +insert a sample increase the temperature +at a rate of 10 to 20° Celsius per + + align:start position:0% +at a rate of 10 to 20° Celsius per + + + align:start position:0% +at a rate of 10 to 20° Celsius per +minute and record a rough temperature + + align:start position:0% +minute and record a rough temperature + + + align:start position:0% +minute and record a rough temperature +when the sample + + align:start position:0% +when the sample + + + align:start position:0% +when the sample +melts to determine the melting point of + + align:start position:0% +melts to determine the melting point of + + + align:start position:0% +melts to determine the melting point of +a crystall in solid set the voltage on + + align:start position:0% +a crystall in solid set the voltage on + + + align:start position:0% +a crystall in solid set the voltage on +the meltemp to zero turn on the power in + + align:start position:0% +the meltemp to zero turn on the power in + + + align:start position:0% +the meltemp to zero turn on the power in +the digital thermometer and then insert + + align:start position:0% +the digital thermometer and then insert + + + align:start position:0% +the digital thermometer and then insert +a filled capillary tube into the sample + + align:start position:0% +a filled capillary tube into the sample + + + align:start position:0% +a filled capillary tube into the sample +holder if the temperature is lower than + + align:start position:0% +holder if the temperature is lower than + + + align:start position:0% +holder if the temperature is lower than +20° C below the expected melting point + + align:start position:0% +20° C below the expected melting point + + + align:start position:0% +20° C below the expected melting point +then dial the voltage to a setting that + + align:start position:0% +then dial the voltage to a setting that + + + align:start position:0% +then dial the voltage to a setting that +enables the temperature to increase at a + + align:start position:0% +enables the temperature to increase at a + + + align:start position:0% +enables the temperature to increase at a +rate of 10 to 20° cus per minute after + + align:start position:0% +rate of 10 to 20° cus per minute after + + + align:start position:0% +rate of 10 to 20° cus per minute after +the temperature is within 20° C of the + + align:start position:0% +the temperature is within 20° C of the + + + align:start position:0% +the temperature is within 20° C of the +expected melting point dial down the + + align:start position:0% +expected melting point dial down the + + + align:start position:0% +expected melting point dial down the +voltage so that the temperature + + align:start position:0% +voltage so that the temperature + + + align:start position:0% +voltage so that the temperature +increases at a rate of 1 to 2° C per + + align:start position:0% +increases at a rate of 1 to 2° C per + + + align:start position:0% +increases at a rate of 1 to 2° C per +minute while watch the sample through + + align:start position:0% +minute while watch the sample through + + + align:start position:0% +minute while watch the sample through +the eyepiece and record the temperature + + align:start position:0% +the eyepiece and record the temperature + + + align:start position:0% +the eyepiece and record the temperature +when the first Crystal starts to melt + + align:start position:0% +when the first Crystal starts to melt + + + align:start position:0% +when the first Crystal starts to melt +which means when the first droplet of + + align:start position:0% +which means when the first droplet of + + + align:start position:0% +which means when the first droplet of +liquid appears finally record the + + align:start position:0% +liquid appears finally record the + + + align:start position:0% +liquid appears finally record the +temperature when the last Crystal + + align:start position:0% +temperature when the last Crystal + + + align:start position:0% +temperature when the last Crystal +disappears turn down the voltage remove + + align:start position:0% +disappears turn down the voltage remove + + + align:start position:0% +disappears turn down the voltage remove +the melted sample and throw it into the + + align:start position:0% +the melted sample and throw it into the + + + align:start position:0% +the melted sample and throw it into the +proper waste receptacle allow the Melt + + align:start position:0% +proper waste receptacle allow the Melt + + + align:start position:0% +proper waste receptacle allow the Melt +tump apparatus to cool to 20° below the + + align:start position:0% +tump apparatus to cool to 20° below the + + + align:start position:0% +tump apparatus to cool to 20° below the +melting point of the compound and repeat + + align:start position:0% +melting point of the compound and repeat + + + align:start position:0% +melting point of the compound and repeat +the process two more times with the + + align:start position:0% +the process two more times with the + + + align:start position:0% +the process two more times with the +remaining samples to ensure + + align:start position:0% +remaining samples to ensure + + + align:start position:0% +remaining samples to ensure +reproducibility never remelt a compound + + align:start position:0% +reproducibility never remelt a compound + + + align:start position:0% +reproducibility never remelt a compound +because it may have undergone a chemical + + align:start position:0% +because it may have undergone a chemical + + + align:start position:0% +because it may have undergone a chemical +change while heating such as oxidation + + align:start position:0% +change while heating such as oxidation + + + align:start position:0% +change while heating such as oxidation +decomposition or + + align:start position:0% +decomposition or + + + align:start position:0% +decomposition or +rearrangement the point where the first + + align:start position:0% +rearrangement the point where the first + + + align:start position:0% +rearrangement the point where the first +Crystal starts to melt can seem + + align:start position:0% +Crystal starts to melt can seem + + + align:start position:0% +Crystal starts to melt can seem +ambiguous to someone taking a melting + + align:start position:0% +ambiguous to someone taking a melting + + + align:start position:0% +ambiguous to someone taking a melting +point for the first time as stated + + align:start position:0% +point for the first time as stated + + + align:start position:0% +point for the first time as stated +earlier this is the point where the + + align:start position:0% +earlier this is the point where the + + + align:start position:0% +earlier this is the point where the +first droplet of liquid forms it is not + + align:start position:0% +first droplet of liquid forms it is not + + + align:start position:0% +first droplet of liquid forms it is not +when the material begins to settle + + align:start position:0% +when the material begins to settle + + + align:start position:0% +when the material begins to settle +soften or Shrink only the appearance of + + align:start position:0% +soften or Shrink only the appearance of + + + align:start position:0% +soften or Shrink only the appearance of +a liquid droplet indicates the beginning + + align:start position:0% +a liquid droplet indicates the beginning + + + align:start position:0% +a liquid droplet indicates the beginning +of + + align:start position:0% +of + + + align:start position:0% +of +melting one common use for melting point + + align:start position:0% +melting one common use for melting point + + + align:start position:0% +melting one common use for melting point +is to assess the purity of a known + + align:start position:0% +is to assess the purity of a known + + + align:start position:0% +is to assess the purity of a known +compound if an impurity is present in a + + align:start position:0% +compound if an impurity is present in a + + + align:start position:0% +compound if an impurity is present in a +sample it will interrupt the crystal + + align:start position:0% +sample it will interrupt the crystal + + + align:start position:0% +sample it will interrupt the crystal +lattice and weaken the forces of + + align:start position:0% +lattice and weaken the forces of + + + align:start position:0% +lattice and weaken the forces of +attraction that are holding the + + align:start position:0% +attraction that are holding the + + + align:start position:0% +attraction that are holding the +molecules together therefore the sample + + align:start position:0% +molecules together therefore the sample + + + align:start position:0% +molecules together therefore the sample +will melt at a temperature that is lower + + align:start position:0% +will melt at a temperature that is lower + + + align:start position:0% +will melt at a temperature that is lower +than expected the sample will also melt + + align:start position:0% +than expected the sample will also melt + + + align:start position:0% +than expected the sample will also melt +over a wide temperature range as a + + align:start position:0% +over a wide temperature range as a + + + align:start position:0% +over a wide temperature range as a +general guideline if a the compound + + align:start position:0% +general guideline if a the compound + + + align:start position:0% +general guideline if a the compound +melts over a range greater than 2 to 3° + + align:start position:0% +melts over a range greater than 2 to 3° + + + align:start position:0% +melts over a range greater than 2 to 3° +C it is most likely + + align:start position:0% +C it is most likely + + + align:start position:0% +C it is most likely +impure another common application of + + align:start position:0% +impure another common application of + + + align:start position:0% +impure another common application of +melting point is the identification of + + align:start position:0% +melting point is the identification of + + + align:start position:0% +melting point is the identification of +an unknown crystallin solid to identify + + align:start position:0% +an unknown crystallin solid to identify + + + align:start position:0% +an unknown crystallin solid to identify +a solid simply compare the melting point + + align:start position:0% +a solid simply compare the melting point + + + align:start position:0% +a solid simply compare the melting point +of the unknown with the melting points + + align:start position:0% +of the unknown with the melting points + + + align:start position:0% +of the unknown with the melting points +of known compounds that are listed in a + + align:start position:0% +of known compounds that are listed in a + + + align:start position:0% +of known compounds that are listed in a +reference book typically just the upper + + align:start position:0% +reference book typically just the upper + + + align:start position:0% +reference book typically just the upper +limit is reported in these reference + + align:start position:0% +limit is reported in these reference + + + align:start position:0% +limit is reported in these reference +books when combined with other + + align:start position:0% +books when combined with other + + + align:start position:0% +books when combined with other +spectroscopic data you may be able to + + align:start position:0% +spectroscopic data you may be able to + + + align:start position:0% +spectroscopic data you may be able to +identify your compound to confirm that + + align:start position:0% +identify your compound to confirm that + + + align:start position:0% +identify your compound to confirm that +your compound is indeed what you think + + align:start position:0% +your compound is indeed what you think + + + align:start position:0% +your compound is indeed what you think +prepare three samples containing + + align:start position:0% +prepare three samples containing + + + align:start position:0% +prepare three samples containing +mixtures of your unknown compound and + + align:start position:0% +mixtures of your unknown compound and + + + align:start position:0% +mixtures of your unknown compound and +the proposed compound 20 to 80 5050 and + + align:start position:0% +the proposed compound 20 to 80 5050 and + + + align:start position:0% +the proposed compound 20 to 80 5050 and +80 to 20 are good ratios to start with + + align:start position:0% +80 to 20 are good ratios to start with + + + align:start position:0% +80 to 20 are good ratios to start with +determine the melting point of each + + align:start position:0% +determine the melting point of each + + + align:start position:0% +determine the melting point of each +mixture if all the mixtures melt at the + + align:start position:0% +mixture if all the mixtures melt at the + + + align:start position:0% +mixture if all the mixtures melt at the +same temperature and within the same + + align:start position:0% +same temperature and within the same + + + align:start position:0% +same temperature and within the same +range you may have correctly identified + + align:start position:0% +range you may have correctly identified + + + align:start position:0% +range you may have correctly identified +your compound if they do not + + align:start position:0% +your compound if they do not + + + align:start position:0% +your compound if they do not +then you definitely have not identified + + align:start position:0% +then you definitely have not identified + + + align:start position:0% +then you definitely have not identified +your + + align:start position:0% +your + + + align:start position:0% +your +compound there are several ways to + + align:start position:0% +compound there are several ways to + + + align:start position:0% +compound there are several ways to +obtain inaccurate melting point readings + + align:start position:0% +obtain inaccurate melting point readings + + + align:start position:0% +obtain inaccurate melting point readings +the most common mistake is increasing + + align:start position:0% +the most common mistake is increasing + + + align:start position:0% +the most common mistake is increasing +the temperature too rapidly in this + + align:start position:0% +the temperature too rapidly in this + + + align:start position:0% +the temperature too rapidly in this +situation the capillary will not have + + align:start position:0% +situation the capillary will not have + + + align:start position:0% +situation the capillary will not have +enough time to equilibrate with the + + align:start position:0% +enough time to equilibrate with the + + + align:start position:0% +enough time to equilibrate with the +heated block as a result the melting + + align:start position:0% +heated block as a result the melting + + + align:start position:0% +heated block as a result the melting +range will appear narrower than it + + align:start position:0% +range will appear narrower than it + + + align:start position:0% +range will appear narrower than it +actually is and the melting temperature + + align:start position:0% +actually is and the melting temperature + + + align:start position:0% +actually is and the melting temperature +will appear + + align:start position:0% +will appear + + + align:start position:0% +will appear +higher a sample that disappears upon + + align:start position:0% +higher a sample that disappears upon + + + align:start position:0% +higher a sample that disappears upon +heating indicates that if it is + + align:start position:0% +heating indicates that if it is + + + align:start position:0% +heating indicates that if it is +subliming instead of melting to remedy + + align:start position:0% +subliming instead of melting to remedy + + + align:start position:0% +subliming instead of melting to remedy +this problem seal the open end of the + + align:start position:0% +this problem seal the open end of the + + + align:start position:0% +this problem seal the open end of the +filled capillary with a bunson burner + + align:start position:0% +filled capillary with a bunson burner + + + align:start position:0% +filled capillary with a bunson burner +before placing it in the sample holder a + + align:start position:0% +before placing it in the sample holder a + + + align:start position:0% +before placing it in the sample holder a +sample that changes color upon heating + + align:start position:0% +sample that changes color upon heating + + + align:start position:0% +sample that changes color upon heating +is probably undergoing + + align:start position:0% +is probably undergoing + + + align:start position:0% +is probably undergoing +decomposition decomposition must be + + align:start position:0% +decomposition decomposition must be + + + align:start position:0% +decomposition decomposition must be +reported along with the melting point of + + align:start position:0% +reported along with the melting point of + + + align:start position:0% +reported along with the melting point of +the + + align:start position:0% +the + + + align:start position:0% +the +compound if the melting point is still + + align:start position:0% +compound if the melting point is still + + + align:start position:0% +compound if the melting point is still +incorrect after troubleshooting or if + + align:start position:0% +incorrect after troubleshooting or if + + + align:start position:0% +incorrect after troubleshooting or if +you need to confirm the accuracy of your + + align:start position:0% +you need to confirm the accuracy of your + + + align:start position:0% +you need to confirm the accuracy of your +result you must calibrate the Melt temp + + align:start position:0% +result you must calibrate the Melt temp + + + align:start position:0% +result you must calibrate the Melt temp +Apper Rus to do this find pure compounds + + align:start position:0% +Apper Rus to do this find pure compounds + + + align:start position:0% +Apper Rus to do this find pure compounds +with known but dissimilar melting points + + align:start position:0% +with known but dissimilar melting points + + + align:start position:0% +with known but dissimilar melting points +this video we'll use napthine neny + + align:start position:0% +this video we'll use napthine neny + + + align:start position:0% +this video we'll use napthine neny +acetamide salicylic acid and succinic + + align:start position:0% +acetamide salicylic acid and succinic + + + align:start position:0% +acetamide salicylic acid and succinic +acid determine the melting point of each + + align:start position:0% +acid determine the melting point of each + + + align:start position:0% +acid determine the melting point of each +pure compound and compare the value you + + align:start position:0% +pure compound and compare the value you + + + align:start position:0% +pure compound and compare the value you +received with what is expected plot the + + align:start position:0% +received with what is expected plot the + + + align:start position:0% +received with what is expected plot the +actual melting point of each compound + + align:start position:0% +actual melting point of each compound + + + align:start position:0% +actual melting point of each compound +against its observed melting point use + + align:start position:0% +against its observed melting point use + + + align:start position:0% +against its observed melting point use +the resulting calibration curve to + + align:start position:0% +the resulting calibration curve to + + + align:start position:0% +the resulting calibration curve to +determine the expected melting point of + + align:start position:0% +determine the expected melting point of + + + align:start position:0% +determine the expected melting point of +your + + align:start position:0% +your + + + align:start position:0% +your +compound determining the correct melting + + align:start position:0% +compound determining the correct melting + + + align:start position:0% +compound determining the correct melting +point of a crystal in solid involves + + align:start position:0% +point of a crystal in solid involves + + + align:start position:0% +point of a crystal in solid involves +good technique in both sample + + align:start position:0% +good technique in both sample + + + align:start position:0% +good technique in both sample +preparation and in taking the melting + + align:start position:0% +preparation and in taking the melting + + + align:start position:0% +preparation and in taking the melting +point to ensure accurate results use a + + align:start position:0% +point to ensure accurate results use a + + + align:start position:0% +point to ensure accurate results use a +minimal amount of solid pack the + + align:start position:0% +minimal amount of solid pack the + + + align:start position:0% +minimal amount of solid pack the +crystals tightly together and increase + + align:start position:0% +crystals tightly together and increase + + + align:start position:0% +crystals tightly together and increase +the temperature + + align:start position:0% +the temperature + + + align:start position:0% +the temperature +slowly determining the melting point of + + align:start position:0% +slowly determining the melting point of + + + align:start position:0% +slowly determining the melting point of +a crystal in solid is the best way to + + align:start position:0% +a crystal in solid is the best way to + + + align:start position:0% +a crystal in solid is the best way to +assess its Purity or establish its + + align:start position:0% +assess its Purity or establish its + + + align:start position:0% +assess its Purity or establish its +identity + + align:start position:0% + + + + align:start position:0% + +[Music] \ No newline at end of file diff --git a/isycxGdK-1Q.txt b/isycxGdK-1Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..e76d16d75aee7f884d73f929760e7e1bbc9b386c --- /dev/null +++ b/isycxGdK-1Q.txt @@ -0,0 +1,15851 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +so let's start with so I want to try to + + align:start position:0% +so let's start with so I want to try to + + + align:start position:0% +so let's start with so I want to try to +do two two things today + + align:start position:0% +do two two things today + + + align:start position:0% +do two two things today +start with the neoclassical model and + + align:start position:0% +start with the neoclassical model and + + + align:start position:0% +start with the neoclassical model and +its implication + + align:start position:0% +its implication + + + align:start position:0% +its implication +and then move from the new classical + + align:start position:0% +and then move from the new classical + + + align:start position:0% +and then move from the new classical +model and its implication + + align:start position:0% +model and its implication + + + align:start position:0% +model and its implication +to a more behavioral more behavioral + + align:start position:0% +to a more behavioral more behavioral + + + align:start position:0% +to a more behavioral more behavioral +models which both because this is pretty + + align:start position:0% +models which both because this is pretty + + + align:start position:0% +models which both because this is pretty +essential to understand savings as we + + align:start position:0% +essential to understand savings as we + + + align:start position:0% +essential to understand savings as we +will see the new classical model fails + + align:start position:0% +will see the new classical model fails + + + align:start position:0% +will see the new classical model fails +to fit the empirical facts in a pretty + + align:start position:0% +to fit the empirical facts in a pretty + + + align:start position:0% +to fit the empirical facts in a pretty +obvious way + + align:start position:0% +obvious way + + + align:start position:0% +obvious way +and second because the the model that is + + align:start position:0% +and second because the the model that is + + + align:start position:0% +and second because the the model that is +useful to think about savings is the + + align:start position:0% +useful to think about savings is the + + + align:start position:0% +useful to think about savings is the +model that is useful to think about many + + align:start position:0% +model that is useful to think about many + + + align:start position:0% +model that is useful to think about many +problems in development that have some + + align:start position:0% +problems in development that have some + + + align:start position:0% +problems in development that have some +inter temporal + + align:start position:0% +inter temporal + + + align:start position:0% +inter temporal +um + + align:start position:0% +um + + + align:start position:0% +um +flavor to them including for example + + align:start position:0% +flavor to them including for example + + + align:start position:0% +flavor to them including for example +Health which is also an important topic + + align:start position:0% +Health which is also an important topic + + + align:start position:0% +Health which is also an important topic +we're going to see soon + + align:start position:0% +we're going to see soon + + + align:start position:0% +we're going to see soon +so let's start with the uh with how in + + align:start position:0% +so let's start with the uh with how in + + + align:start position:0% +so let's start with the uh with how in +macro uh I I hoped you would have been + + align:start position:0% +macro uh I I hoped you would have been + + + align:start position:0% +macro uh I I hoped you would have been +taught savings already or will be told + + align:start position:0% +taught savings already or will be told + + + align:start position:0% +taught savings already or will be told +savings already certainly I was told + + align:start position:0% +savings already certainly I was told + + + align:start position:0% +savings already certainly I was told +savings when I told macro uh which is + + align:start position:0% +savings when I told macro uh which is + + + align:start position:0% +savings when I told macro uh which is +the the basic inter-temporal + + align:start position:0% +the the basic inter-temporal + + + align:start position:0% +the the basic inter-temporal +optimization model so I'm gonna go + + align:start position:0% +optimization model so I'm gonna go + + + align:start position:0% +optimization model so I'm gonna go +quickly because I'm gonna assume you've + + align:start position:0% +quickly because I'm gonna assume you've + + + align:start position:0% +quickly because I'm gonna assume you've +seen it but it is worth kind of having + + align:start position:0% +seen it but it is worth kind of having + + + align:start position:0% +seen it but it is worth kind of having +making sure we're on the same pages and + + align:start position:0% +making sure we're on the same pages and + + + align:start position:0% +making sure we're on the same pages and +if it goes too quickly you have the + + align:start position:0% +if it goes too quickly you have the + + + align:start position:0% +if it goes too quickly you have the +slides for easy reference + + align:start position:0% +slides for easy reference + + + align:start position:0% +slides for easy reference +so suppose that an individual follow a + + align:start position:0% +so suppose that an individual follow a + + + align:start position:0% +so suppose that an individual follow a +variable income process and an interest + + align:start position:0% +variable income process and an interest + + + align:start position:0% +variable income process and an interest +rate + + align:start position:0% +rate + + + align:start position:0% +rate +uh how much the question of uh + + align:start position:0% +uh how much the question of uh + + + align:start position:0% +uh how much the question of uh +inter-temporal maximization issue is how + + align:start position:0% +inter-temporal maximization issue is how + + + align:start position:0% +inter-temporal maximization issue is how +much they should + + align:start position:0% +much they should + + + align:start position:0% +much they should +how much they should save + + align:start position:0% +how much they should save + + + align:start position:0% +how much they should save +and both if they can vote + + align:start position:0% +and both if they can vote + + + align:start position:0% +and both if they can vote +so we start with the uh the utility + + align:start position:0% +so we start with the uh the utility + + + align:start position:0% +so we start with the uh the utility +attempty defined as the expected value + + align:start position:0% +attempty defined as the expected value + + + align:start position:0% +attempty defined as the expected value +of over your lifetime + + align:start position:0% +of over your lifetime + + + align:start position:0% +of over your lifetime +of all the instant intense tenuous + + align:start position:0% +of all the instant intense tenuous + + + align:start position:0% +of all the instant intense tenuous +utility of consumption in all period as + + align:start position:0% +utility of consumption in all period as + + + align:start position:0% +utility of consumption in all period as +viewed from period T we can be very + + align:start position:0% +viewed from period T we can be very + + + align:start position:0% +viewed from period T we can be very +generous but of course Very quickly we + + align:start position:0% +generous but of course Very quickly we + + + align:start position:0% +generous but of course Very quickly we +can we simplify it in some way or we + + align:start position:0% +can we simplify it in some way or we + + + align:start position:0% +can we simplify it in some way or we +parametrize it in some way otherwise + + align:start position:0% +parametrize it in some way otherwise + + + align:start position:0% +parametrize it in some way otherwise +it's getting difficult to say anything + + align:start position:0% +it's getting difficult to say anything + + + align:start position:0% +it's getting difficult to say anything +so for example you could say that you're + + align:start position:0% +so for example you could say that you're + + + align:start position:0% +so for example you could say that you're +discounting the future you're at summary + + align:start position:0% +discounting the future you're at summary + + + align:start position:0% +discounting the future you're at summary +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +so a common example becomes uh this one + + align:start position:0% +so a common example becomes uh this one + + + align:start position:0% +so a common example becomes uh this one +that your discontinentary Delta so + + align:start position:0% +that your discontinentary Delta so + + + align:start position:0% +that your discontinentary Delta so +viewed from period T it's the discount + + align:start position:0% +viewed from period T it's the discount + + + align:start position:0% +viewed from period T it's the discount +rate of view of City for some utility + + align:start position:0% +rate of view of City for some utility + + + align:start position:0% +rate of view of City for some utility +function that we assume constant so + + align:start position:0% +function that we assume constant so + + + align:start position:0% +function that we assume constant so +there is of course a lot nested in that + + align:start position:0% +there is of course a lot nested in that + + + align:start position:0% +there is of course a lot nested in that +model + + align:start position:0% +model + + + align:start position:0% +model +uh in particular uh the the idea that is + + align:start position:0% +uh in particular uh the the idea that is + + + align:start position:0% +uh in particular uh the the idea that is +inter inter + + align:start position:0% +inter inter + + + align:start position:0% +inter inter +temporally consistent + + align:start position:0% +temporally consistent + + + align:start position:0% +temporally consistent +so you're valuing tomorrow's consumption + + align:start position:0% +so you're valuing tomorrow's consumption + + + align:start position:0% +so you're valuing tomorrow's consumption +uh exactly like today's except with some + + align:start position:0% +uh exactly like today's except with some + + + align:start position:0% +uh exactly like today's except with some +discount rate that is constant over time + + align:start position:0% +discount rate that is constant over time + + + align:start position:0% +discount rate that is constant over time +uh so this is a lot of what we're gonna + + align:start position:0% +uh so this is a lot of what we're gonna + + + align:start position:0% +uh so this is a lot of what we're gonna +today is going to basically said this is + + align:start position:0% +today is going to basically said this is + + + align:start position:0% +today is going to basically said this is +actually not very accurate or maybe not + + align:start position:0% +actually not very accurate or maybe not + + + align:start position:0% +actually not very accurate or maybe not +the best representation of how people + + align:start position:0% +the best representation of how people + + + align:start position:0% +the best representation of how people +think about the future and that's what + + align:start position:0% +think about the future and that's what + + + align:start position:0% +think about the future and that's what +we're gonna change + + align:start position:0% +we're gonna change + + + align:start position:0% +we're gonna change +now + + align:start position:0% +now + + + align:start position:0% +now +assuming that it's the case for the + + align:start position:0% +assuming that it's the case for the + + + align:start position:0% +assuming that it's the case for the +movement uh then you the individual face + + align:start position:0% +movement uh then you the individual face + + + align:start position:0% +movement uh then you the individual face +a terminal condition so uh in finite + + align:start position:0% +a terminal condition so uh in finite + + + align:start position:0% +a terminal condition so uh in finite +time it means they cannot borrow you die + + align:start position:0% +time it means they cannot borrow you die + + + align:start position:0% +time it means they cannot borrow you die +with debt and they also don't want to + + align:start position:0% +with debt and they also don't want to + + + align:start position:0% +with debt and they also don't want to +leave any money at the end of their life + + align:start position:0% +leave any money at the end of their life + + + align:start position:0% +leave any money at the end of their life +and there is an equivalent of that in + + align:start position:0% +and there is an equivalent of that in + + + align:start position:0% +and there is an equivalent of that in +infinite time + + align:start position:0% +infinite time + + + align:start position:0% +infinite time +and then there is otherwise another + + align:start position:0% +and then there is otherwise another + + + align:start position:0% +and then there is otherwise another +accumulative accumulation equation which + + align:start position:0% +accumulative accumulation equation which + + + align:start position:0% +accumulative accumulation equation which +we already saw when we discussed + + align:start position:0% +we already saw when we discussed + + + align:start position:0% +we already saw when we discussed +education which is that your assets is + + align:start position:0% +education which is that your assets is + + + align:start position:0% +education which is that your assets is +uh what you had minus what you uh plus + + align:start position:0% +uh what you had minus what you uh plus + + + align:start position:0% +uh what you had minus what you uh plus +what you earned minus what you consumed + + align:start position:0% +what you earned minus what you consumed + + + align:start position:0% +what you earned minus what you consumed +multiplied by the growth interest rate + + align:start position:0% +multiplied by the growth interest rate + + + align:start position:0% +multiplied by the growth interest rate +to solve this problem we use the + + align:start position:0% +to solve this problem we use the + + + align:start position:0% +to solve this problem we use the +standard dynamic programming tool so we + + align:start position:0% +standard dynamic programming tool so we + + + align:start position:0% +standard dynamic programming tool so we +write the value function of the problem + + align:start position:0% +write the value function of the problem + + + align:start position:0% +write the value function of the problem +which is the expected utility of an + + align:start position:0% +which is the expected utility of an + + + align:start position:0% +which is the expected utility of an +individual who makes the optimal choice + + align:start position:0% +individual who makes the optimal choice + + + align:start position:0% +individual who makes the optimal choice +of savings today given a certain level + + align:start position:0% +of savings today given a certain level + + + align:start position:0% +of savings today given a certain level +of a city has so that's the belt money + + align:start position:0% +of a city has so that's the belt money + + + align:start position:0% +of a city has so that's the belt money +question so if the value of your asset + + align:start position:0% +question so if the value of your asset + + + align:start position:0% +question so if the value of your asset +is the maximum over you know the best + + align:start position:0% +is the maximum over you know the best + + + align:start position:0% +is the maximum over you know the best +the maximum value over the all any + + align:start position:0% +the maximum value over the all any + + + align:start position:0% +the maximum value over the all any +possible value of Omega-3 you're saving + + align:start position:0% +possible value of Omega-3 you're saving + + + align:start position:0% +possible value of Omega-3 you're saving +of the instantaneous utility of + + align:start position:0% +of the instantaneous utility of + + + align:start position:0% +of the instantaneous utility of +consuming a certain amount plus the + + align:start position:0% +consuming a certain amount plus the + + + align:start position:0% +consuming a certain amount plus the +expected value at t plus one of the + + align:start position:0% +expected value at t plus one of the + + + align:start position:0% +expected value at t plus one of the +assets you're going to be left with if + + align:start position:0% +assets you're going to be left with if + + + align:start position:0% +assets you're going to be left with if +that's what if if that's your choice of + + align:start position:0% +that's what if if that's your choice of + + + align:start position:0% +that's what if if that's your choice of +saving and borrowing right + + align:start position:0% +saving and borrowing right + + + align:start position:0% +saving and borrowing right +so at this point we are making no + + align:start position:0% +so at this point we are making no + + + align:start position:0% +so at this point we are making no +assumption about whether I'm talking + + align:start position:0% +assumption about whether I'm talking + + + align:start position:0% +assumption about whether I'm talking +about savings but it could be negative + + align:start position:0% +about savings but it could be negative + + + align:start position:0% +about savings but it could be negative +saving that which would be borrowing so + + align:start position:0% +saving that which would be borrowing so + + + align:start position:0% +saving that which would be borrowing so +that's the Batman equation + + align:start position:0% +that's the Batman equation + + + align:start position:0% +that's the Batman equation +once you have the bandman equation all + + align:start position:0% +once you have the bandman equation all + + + align:start position:0% +once you have the bandman equation all +we need to do is to derive it in order + + align:start position:0% +we need to do is to derive it in order + + + align:start position:0% +we need to do is to derive it in order +to get the optimal the optimal decisions + + align:start position:0% +to get the optimal the optimal decisions + + + align:start position:0% +to get the optimal the optimal decisions +we take the first order condition + + align:start position:0% +we take the first order condition + + + align:start position:0% +we take the first order condition +and we get that the marginal utility of + + align:start position:0% +and we get that the marginal utility of + + + align:start position:0% +and we get that the marginal utility of +consumption must be equal to the uh to + + align:start position:0% +consumption must be equal to the uh to + + + align:start position:0% +consumption must be equal to the uh to +to this term the expected value at empty + + align:start position:0% +to this term the expected value at empty + + + align:start position:0% +to this term the expected value at empty +of the value function the derivative of + + align:start position:0% +of the value function the derivative of + + + align:start position:0% +of the value function the derivative of +the value function at t plus 1 + + align:start position:0% +the value function at t plus 1 + + + align:start position:0% +the value function at t plus 1 +multiplied by the interest rate now + + align:start position:0% +multiplied by the interest rate now + + + align:start position:0% +multiplied by the interest rate now +that's not yet very helpful because we + + align:start position:0% +that's not yet very helpful because we + + + align:start position:0% +that's not yet very helpful because we +don't know what this guy is + + align:start position:0% +don't know what this guy is + + + align:start position:0% +don't know what this guy is +so we need to do take one more step we + + align:start position:0% +so we need to do take one more step we + + + align:start position:0% +so we need to do take one more step we +need to express this guy as a function + + align:start position:0% +need to express this guy as a function + + + align:start position:0% +need to express this guy as a function +of quantity we know + + align:start position:0% +of quantity we know + + + align:start position:0% +of quantity we know +and for this well we derive the Bellman + + align:start position:0% +and for this well we derive the Bellman + + + align:start position:0% +and for this well we derive the Bellman +equation with respect to assets a at the + + align:start position:0% +equation with respect to assets a at the + + + align:start position:0% +equation with respect to assets a at the +optimal uh saving rate + + align:start position:0% +optimal uh saving rate + + + align:start position:0% +optimal uh saving rate +Omega + + align:start position:0% +Omega + + + align:start position:0% +Omega +and the result is that uh the the + + align:start position:0% +and the result is that uh the the + + + align:start position:0% +and the result is that uh the the +derivative of the of the value function + + align:start position:0% +derivative of the of the value function + + + align:start position:0% +derivative of the of the value function +with respect to asset at the optimum is + + align:start position:0% +with respect to asset at the optimum is + + + align:start position:0% +with respect to asset at the optimum is +simply the derivative of the utility + + align:start position:0% +simply the derivative of the utility + + + align:start position:0% +simply the derivative of the utility +function of consumption why that's two + + align:start position:0% +function of consumption why that's two + + + align:start position:0% +function of consumption why that's two +where is that too what to make why don't + + align:start position:0% +where is that too what to make why don't + + + align:start position:0% +where is that too what to make why don't +we have like that thing to uh + + align:start position:0% +we have like that thing to uh + + + align:start position:0% +we have like that thing to uh +to mess this up when we derive with + + align:start position:0% +to mess this up when we derive with + + + align:start position:0% +to mess this up when we derive with +respect to our sets + + align:start position:0% + + + + align:start position:0% + +yeah Vision you look like him + + align:start position:0% +yeah Vision you look like him + + + align:start position:0% +yeah Vision you look like him +that's the envelope tour which is uh at + + align:start position:0% +that's the envelope tour which is uh at + + + align:start position:0% +that's the envelope tour which is uh at +the optimum then uh this is uh + + align:start position:0% +the optimum then uh this is uh + + + align:start position:0% +the optimum then uh this is uh +the derivative of the of this disrespect + + align:start position:0% +the derivative of the of this disrespect + + + align:start position:0% +the derivative of the of this disrespect +to a0 that's the envelope theorem + + align:start position:0% +to a0 that's the envelope theorem + + + align:start position:0% +to a0 that's the envelope theorem +so we are great we're happy it becomes + + align:start position:0% +so we are great we're happy it becomes + + + align:start position:0% +so we are great we're happy it becomes +very simple + + align:start position:0% +very simple + + + align:start position:0% +very simple +we can combine equation two and three + + align:start position:0% +we can combine equation two and three + + + align:start position:0% +we can combine equation two and three +the first order condition and the + + align:start position:0% +the first order condition and the + + + align:start position:0% +the first order condition and the +derivative of the Bell mining question + + align:start position:0% +derivative of the Bell mining question + + + align:start position:0% +derivative of the Bell mining question +with respect to assets to get uh the + + align:start position:0% +with respect to assets to get uh the + + + align:start position:0% +with respect to assets to get uh the +Lambda of C or the marginal utility of + + align:start position:0% +Lambda of C or the marginal utility of + + + align:start position:0% +Lambda of C or the marginal utility of +consumption is the expected value of the + + align:start position:0% +consumption is the expected value of the + + + align:start position:0% +consumption is the expected value of the +marginal utility of consumption in the + + align:start position:0% +marginal utility of consumption in the + + + align:start position:0% +marginal utility of consumption in the +next period uh + + align:start position:0% +next period uh + + + align:start position:0% +next period uh +times the the interest rate so that's + + align:start position:0% +times the the interest rate so that's + + + align:start position:0% +times the the interest rate so that's +the euleric question which is a pretty + + align:start position:0% +the euleric question which is a pretty + + + align:start position:0% +the euleric question which is a pretty +Central value of Economics so it must it + + align:start position:0% +Central value of Economics so it must it + + + align:start position:0% +Central value of Economics so it must it +it says that the marginal utility of + + align:start position:0% +it says that the marginal utility of + + + align:start position:0% +it says that the marginal utility of +consumption today must be the marginal + + align:start position:0% +consumption today must be the marginal + + + align:start position:0% +consumption today must be the marginal +consumption of a majority of consumption + + align:start position:0% +consumption of a majority of consumption + + + align:start position:0% +consumption of a majority of consumption +tomorrow up to a discount Factor + + align:start position:0% +tomorrow up to a discount Factor + + + align:start position:0% +tomorrow up to a discount Factor +now if the the we have some special keys + + align:start position:0% +now if the the we have some special keys + + + align:start position:0% +now if the the we have some special keys +that are well known uh if we have + + align:start position:0% +that are well known uh if we have + + + align:start position:0% +that are well known uh if we have +exponential utility and a constant + + align:start position:0% +exponential utility and a constant + + + align:start position:0% +exponential utility and a constant +interest rate the Euler equation becomes + + align:start position:0% +interest rate the Euler equation becomes + + + align:start position:0% +interest rate the Euler equation becomes +simplifies very nicely and what's the + + align:start position:0% +simplifies very nicely and what's the + + + align:start position:0% +simplifies very nicely and what's the +results there before I put it on the + + align:start position:0% +results there before I put it on the + + + align:start position:0% +results there before I put it on the +board + + align:start position:0% + + + + align:start position:0% + +this you probably saw even in + + align:start position:0% +this you probably saw even in + + + align:start position:0% +this you probably saw even in +undergraduate + + align:start position:0% +undergraduate + + + align:start position:0% +undergraduate +macro if you've taken a valued Markov + + align:start position:0% + + + + align:start position:0% + +or you can recalculate it in your head + + align:start position:0% + + + + align:start position:0% + +that's how it simplifies + + align:start position:0% + + + + align:start position:0% + +and if in addition it's actually + + align:start position:0% +and if in addition it's actually + + + align:start position:0% +and if in addition it's actually +quadratic so it's even simpler than it + + align:start position:0% +quadratic so it's even simpler than it + + + align:start position:0% +quadratic so it's even simpler than it +and if r equal to Delta which it should + + align:start position:0% +and if r equal to Delta which it should + + + align:start position:0% +and if r equal to Delta which it should +be in equilibrium and the equation + + align:start position:0% +be in equilibrium and the equation + + + align:start position:0% +be in equilibrium and the equation +further simplifies to the consumption is + + align:start position:0% +further simplifies to the consumption is + + + align:start position:0% +further simplifies to the consumption is +equal to the expected value of + + align:start position:0% +equal to the expected value of + + + align:start position:0% +equal to the expected value of +consumption tomorrow so consumption is a + + align:start position:0% +consumption tomorrow so consumption is a + + + align:start position:0% +consumption tomorrow so consumption is a +Martingale that's the whole result + + align:start position:0% + + + + align:start position:0% + +so it's make sense + + align:start position:0% + + + + align:start position:0% + +now if of consumption has uh of course + + align:start position:0% +now if of consumption has uh of course + + + align:start position:0% +now if of consumption has uh of course +the smarting algor result will not hold + + align:start position:0% +the smarting algor result will not hold + + + align:start position:0% +the smarting algor result will not hold +for + + align:start position:0% +for + + + align:start position:0% +for +measures so for different utility + + align:start position:0% +measures so for different utility + + + align:start position:0% +measures so for different utility +function + + align:start position:0% +function + + + align:start position:0% +function +in particular if the utility function is + + align:start position:0% +in particular if the utility function is + + + align:start position:0% +in particular if the utility function is +not quadratic the derivative of it will + + align:start position:0% +not quadratic the derivative of it will + + + align:start position:0% +not quadratic the derivative of it will +be a little more complicated so it will + + align:start position:0% +be a little more complicated so it will + + + align:start position:0% +be a little more complicated so it will +not simplify to this very simple + + align:start position:0% +not simplify to this very simple + + + align:start position:0% +not simplify to this very simple +formula and there is a cases that's + + align:start position:0% +formula and there is a cases that's + + + align:start position:0% +formula and there is a cases that's +particularly interesting which is one + + align:start position:0% +particularly interesting which is one + + + align:start position:0% +particularly interesting which is one +where the utility function of course is + + align:start position:0% +where the utility function of course is + + + align:start position:0% +where the utility function of course is +the the derivative is positive that is + + align:start position:0% +the the derivative is positive that is + + + align:start position:0% +the the derivative is positive that is +more is better + + align:start position:0% +more is better + + + align:start position:0% +more is better +the secondary derivative is negative + + align:start position:0% +the secondary derivative is negative + + + align:start position:0% +the secondary derivative is negative +that is your risk of us + + align:start position:0% +that is your risk of us + + + align:start position:0% +that is your risk of us +and the third derivative is positive + + align:start position:0% +and the third derivative is positive + + + align:start position:0% +and the third derivative is positive +which is called precaution + + align:start position:0% +which is called precaution + + + align:start position:0% +which is called precaution +so what does this that becomes hard to + + align:start position:0% +so what does this that becomes hard to + + + align:start position:0% +so what does this that becomes hard to +think about third derivative of utility + + align:start position:0% +think about third derivative of utility + + + align:start position:0% +think about third derivative of utility +function so if you were to express it + + align:start position:0% +function so if you were to express it + + + align:start position:0% +function so if you were to express it +the third derivative being positive what + + align:start position:0% +the third derivative being positive what + + + align:start position:0% +the third derivative being positive what +in words what might that what might that + + align:start position:0% +in words what might that what might that + + + align:start position:0% +in words what might that what might that +reflect + + align:start position:0% + + + + align:start position:0% + +I get less risk the verses + + align:start position:0% +I get less risk the verses + + + align:start position:0% +I get less risk the verses +you get less work as you get wealthier + + align:start position:0% +you get less work as you get wealthier + + + align:start position:0% +you get less work as you get wealthier +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +so that's why it's precaution to the + + align:start position:0% +so that's why it's precaution to the + + + align:start position:0% +so that's why it's precaution to the +poor particularly dislike changes and + + align:start position:0% +poor particularly dislike changes and + + + align:start position:0% +poor particularly dislike changes and +changes in their income + + align:start position:0% +changes in their income + + + align:start position:0% +changes in their income +uh there is a and therefore they are + + align:start position:0% +uh there is a and therefore they are + + + align:start position:0% +uh there is a and therefore they are +going to want to to the poor you are the + + align:start position:0% +going to want to to the poor you are the + + + align:start position:0% +going to want to to the poor you are the +more they are going to want to build the + + align:start position:0% +more they are going to want to build the + + + align:start position:0% +more they are going to want to build the +buffer stocks of savings or ought to be + + align:start position:0% +buffer stocks of savings or ought to be + + + align:start position:0% +buffer stocks of savings or ought to be +if they ought to be able to borrow in + + align:start position:0% +if they ought to be able to borrow in + + + align:start position:0% +if they ought to be able to borrow in +other company compensate a lost income + + align:start position:0% +other company compensate a lost income + + + align:start position:0% +other company compensate a lost income +if they can + + align:start position:0% +if they can + + + align:start position:0% +if they can +I do think there is a something on the + + align:start position:0% +I do think there is a something on the + + + align:start position:0% +I do think there is a something on the +fourth derivative being negative which + + align:start position:0% +fourth derivative being negative which + + + align:start position:0% +fourth derivative being negative which +is called temperance but I forget + + align:start position:0% +is called temperance but I forget + + + align:start position:0% +is called temperance but I forget +exactly how it interprets in world but I + + align:start position:0% +exactly how it interprets in world but I + + + align:start position:0% +exactly how it interprets in world but I +do think there is one more that we can + + align:start position:0% +do think there is one more that we can + + + align:start position:0% +do think there is one more that we can +that people have been thinking about + + align:start position:0% +that people have been thinking about + + + align:start position:0% +that people have been thinking about +so uh exactly like uh okay let's set + + align:start position:0% +so uh exactly like uh okay let's set + + + align:start position:0% +so uh exactly like uh okay let's set +positive uh uh third derivative means + + align:start position:0% +positive uh uh third derivative means + + + align:start position:0% +positive uh uh third derivative means +that at low value of consumption the + + align:start position:0% +that at low value of consumption the + + + align:start position:0% +that at low value of consumption the +variation are more painful than if you + + align:start position:0% +variation are more painful than if you + + + align:start position:0% +variation are more painful than if you +are starting at high value of + + align:start position:0% +are starting at high value of + + + align:start position:0% +are starting at high value of +consumption + + align:start position:0% + + + + align:start position:0% + +that means that uh an increase the + + align:start position:0% +that means that uh an increase the + + + align:start position:0% +that means that uh an increase the +consequence of the third derivative why + + align:start position:0% +consequence of the third derivative why + + + align:start position:0% +consequence of the third derivative why +are we interested in the third + + align:start position:0% +are we interested in the third + + + align:start position:0% +are we interested in the third +derivative well it's because our Euler + + align:start position:0% +derivative well it's because our Euler + + + align:start position:0% +derivative well it's because our Euler +equation is expressed in terms of second + + align:start position:0% +equation is expressed in terms of second + + + align:start position:0% +equation is expressed in terms of second +derivative so if we want to say + + align:start position:0% +derivative so if we want to say + + + align:start position:0% +derivative so if we want to say +something about it using the arc you + + align:start position:0% +something about it using the arc you + + + align:start position:0% +something about it using the arc you +know using our famous looking at things + + align:start position:0% +know using our famous looking at things + + + align:start position:0% +know using our famous looking at things +we we need to we need to say something + + align:start position:0% +we we need to we need to say something + + + align:start position:0% +we we need to we need to say something +about it but it's it's the second + + align:start position:0% +about it but it's it's the second + + + align:start position:0% +about it but it's it's the second +derivative of the Euler equation + + align:start position:0% +derivative of the Euler equation + + + align:start position:0% +derivative of the Euler equation +so the the to use the to use the the + + align:start position:0% +so the the to use the to use the the + + + align:start position:0% +so the the to use the to use the the +inequality the Euler inequality so this + + align:start position:0% +inequality the Euler inequality so this + + + align:start position:0% +inequality the Euler inequality so this +the consequence of the cell derivative + + align:start position:0% +the consequence of the cell derivative + + + align:start position:0% +the consequence of the cell derivative +being positive is that an increase in + + align:start position:0% +being positive is that an increase in + + + align:start position:0% +being positive is that an increase in +the variability of consumption will + + align:start position:0% +the variability of consumption will + + + align:start position:0% +the variability of consumption will +increase the height and size of the + + align:start position:0% +increase the height and size of the + + + align:start position:0% +increase the height and size of the +Euler equation + + align:start position:0% +Euler equation + + + align:start position:0% +Euler equation +that means that uh consumption must + + align:start position:0% +that means that uh consumption must + + + align:start position:0% +that means that uh consumption must +decline uh to and savings must increase + + align:start position:0% +decline uh to and savings must increase + + + align:start position:0% +decline uh to and savings must increase +if we parent able to borrow to + + align:start position:0% +if we parent able to borrow to + + + align:start position:0% +if we parent able to borrow to +compensate in piety to compensate for an + + align:start position:0% +compensate in piety to compensate for an + + + align:start position:0% +compensate in piety to compensate for an +increase in the viability of consumption + + align:start position:0% +increase in the viability of consumption + + + align:start position:0% +increase in the viability of consumption +that's just restating uh what you told + + align:start position:0% +that's just restating uh what you told + + + align:start position:0% +that's just restating uh what you told +us + + align:start position:0% +us + + + align:start position:0% +us +uh so that's kind of a testable + + align:start position:0% +uh so that's kind of a testable + + + align:start position:0% +uh so that's kind of a testable +prediction of this model which is there + + align:start position:0% +prediction of this model which is there + + + align:start position:0% +prediction of this model which is there +should be a precaution what's called + + align:start position:0% +should be a precaution what's called + + + align:start position:0% +should be a precaution what's called +precautionary savings so if you think + + align:start position:0% +precautionary savings so if you think + + + align:start position:0% +precautionary savings so if you think +that the the income tomorrow is going to + + align:start position:0% +that the the income tomorrow is going to + + + align:start position:0% +that the the income tomorrow is going to +be very variable you should start + + align:start position:0% +be very variable you should start + + + align:start position:0% +be very variable you should start +putting some aside + + align:start position:0% +putting some aside + + + align:start position:0% +putting some aside +right + + align:start position:0% +right + + + align:start position:0% +right +uh so there is a test very a classic + + align:start position:0% +uh so there is a test very a classic + + + align:start position:0% +uh so there is a test very a classic +paper by Kristina Paxton is a test of + + align:start position:0% +paper by Kristina Paxton is a test of + + + align:start position:0% +paper by Kristina Paxton is a test of +this of this hypothesis uh uh the the + + align:start position:0% +this of this hypothesis uh uh the the + + + align:start position:0% +this of this hypothesis uh uh the the +ili question implies that the the change + + align:start position:0% +ili question implies that the the change + + + align:start position:0% +ili question implies that the the change +in permanent and considerate income + + align:start position:0% +in permanent and considerate income + + + align:start position:0% +in permanent and considerate income +should have different consequences and + + align:start position:0% +should have different consequences and + + + align:start position:0% +should have different consequences and +consumption + + align:start position:0% +consumption + + + align:start position:0% +consumption +so if you take a change in permanent + + align:start position:0% +so if you take a change in permanent + + + align:start position:0% +so if you take a change in permanent +income what you should what should you + + align:start position:0% +income what you should what should you + + + align:start position:0% +income what you should what should you +do what should you do with it + + align:start position:0% +do what should you do with it + + + align:start position:0% +do what should you do with it +uh say uh just just uh got the Nobel + + align:start position:0% +uh say uh just just uh got the Nobel + + + align:start position:0% +uh say uh just just uh got the Nobel +Prize there is a transitory component + + align:start position:0% +Prize there is a transitory component + + + align:start position:0% +Prize there is a transitory component +it's gonna get some + + align:start position:0% +it's gonna get some + + + align:start position:0% +it's gonna get some +big check + + align:start position:0% +big check + + + align:start position:0% +big check +and there is a a permanent component and + + align:start position:0% +and there is a a permanent component and + + + align:start position:0% +and there is a a permanent component and +this is going to be invited to give + + align:start position:0% +this is going to be invited to give + + + align:start position:0% +this is going to be invited to give +talks that uh you know where they're + + align:start position:0% +talks that uh you know where they're + + + align:start position:0% +talks that uh you know where they're +going to pay him enough money to do it + + align:start position:0% +going to pay him enough money to do it + + + align:start position:0% +going to pay him enough money to do it +if he wants to so and then he can also + + align:start position:0% +if he wants to so and then he can also + + + align:start position:0% +if he wants to so and then he can also +bag it with MIT to get some increase in + + align:start position:0% +bag it with MIT to get some increase in + + + align:start position:0% +bag it with MIT to get some increase in +his wages so that's so he has both he + + align:start position:0% +his wages so that's so he has both he + + + align:start position:0% +his wages so that's so he has both he +just experienced on Monday + + align:start position:0% +just experienced on Monday + + + align:start position:0% +just experienced on Monday +a transitory income stock and a + + align:start position:0% +a transitory income stock and a + + + align:start position:0% +a transitory income stock and a +permanent income shock + + align:start position:0% +permanent income shock + + + align:start position:0% +permanent income shock +so what should you do with the permanent + + align:start position:0% +so what should you do with the permanent + + + align:start position:0% +so what should you do with the permanent +part of the what what should we see on + + align:start position:0% +part of the what what should we see on + + + align:start position:0% +part of the what what should we see on +consumption + + align:start position:0% +consumption + + + align:start position:0% +consumption +what should we do with the permanent + + align:start position:0% +what should we do with the permanent + + + align:start position:0% +what should we do with the permanent +part of his of his uh when + + align:start position:0% + + + + align:start position:0% + +yeah I should go ahead and increase + + align:start position:0% +yeah I should go ahead and increase + + + align:start position:0% +yeah I should go ahead and increase +consumption to that extent how about the + + align:start position:0% +consumption to that extent how about the + + + align:start position:0% +consumption to that extent how about the +transitory part + + align:start position:0% + + + + align:start position:0% + +yeah that should be saved that should be + + align:start position:0% +yeah that should be saved that should be + + + align:start position:0% +yeah that should be saved that should be +saved and uh maybe it should be saved a + + align:start position:0% +saved and uh maybe it should be saved a + + + align:start position:0% +saved and uh maybe it should be saved a +little less because this temp is common + + align:start position:0% +little less because this temp is common + + + align:start position:0% +little less because this temp is common +income increase so therefore he becomes + + align:start position:0% +income increase so therefore he becomes + + + align:start position:0% +income increase so therefore he becomes +less risk over so he needs to save a + + align:start position:0% +less risk over so he needs to save a + + + align:start position:0% +less risk over so he needs to save a +little less for it + + align:start position:0% +little less for it + + + align:start position:0% +little less for it +so that's an empirical test not just of + + align:start position:0% +so that's an empirical test not just of + + + align:start position:0% +so that's an empirical test not just of +precurrency precautionary saving by the + + align:start position:0% +precurrency precautionary saving by the + + + align:start position:0% +precurrency precautionary saving by the +way but any the Euler equation itself uh + + align:start position:0% +way but any the Euler equation itself uh + + + align:start position:0% +way but any the Euler equation itself uh +pretty much with with most form of the + + align:start position:0% +pretty much with with most form of the + + + align:start position:0% +pretty much with with most form of the +utility function in the simplest case a + + align:start position:0% +utility function in the simplest case a + + + align:start position:0% +utility function in the simplest case a +permanent change income should be + + align:start position:0% +permanent change income should be + + + align:start position:0% +permanent change income should be +entirely consumed and transitory change + + align:start position:0% +entirely consumed and transitory change + + + align:start position:0% +entirely consumed and transitory change +in income should be entirely saved + + align:start position:0% + + + + align:start position:0% + +because that's going to go away it's + + align:start position:0% +because that's going to go away it's + + + align:start position:0% +because that's going to go away it's +going to you know it needs to be smooth + + align:start position:0% +going to you know it needs to be smooth + + + align:start position:0% +going to you know it needs to be smooth +over infinite number of periods so it's + + align:start position:0% +over infinite number of periods so it's + + + align:start position:0% +over infinite number of periods so it's +really nothing + + align:start position:0% +really nothing + + + align:start position:0% +really nothing +so what does this correspond to what we + + align:start position:0% +so what does this correspond to what we + + + align:start position:0% +so what does this correspond to what we +see so Pakistan so Pakistan test is + + align:start position:0% +see so Pakistan so Pakistan test is + + + align:start position:0% +see so Pakistan so Pakistan test is +going to test this using data from Rice + + align:start position:0% +going to test this using data from Rice + + + align:start position:0% +going to test this using data from Rice +farmer in Thailand + + align:start position:0% +farmer in Thailand + + + align:start position:0% +farmer in Thailand +and her key idea which was then used in + + align:start position:0% +and her key idea which was then used in + + + align:start position:0% +and her key idea which was then used in +some form of another in in many other + + align:start position:0% +some form of another in in many other + + + align:start position:0% +some form of another in in many other +papers + + align:start position:0% +papers + + + align:start position:0% +papers +is that if you use rainfall variation + + align:start position:0% +is that if you use rainfall variation + + + align:start position:0% +is that if you use rainfall variation +the year-to-year variation in rainfall + + align:start position:0% +the year-to-year variation in rainfall + + + align:start position:0% +the year-to-year variation in rainfall +uh change transito evaluation in income + + align:start position:0% +uh change transito evaluation in income + + + align:start position:0% +uh change transito evaluation in income +a permanent change for example acquiring + + align:start position:0% +a permanent change for example acquiring + + + align:start position:0% +a permanent change for example acquiring +irrigation + + align:start position:0% +irrigation + + + align:start position:0% +irrigation +would make a farmer permanently richer + + align:start position:0% +would make a farmer permanently richer + + + align:start position:0% +would make a farmer permanently richer +that should be consumed away but the + + align:start position:0% +that should be consumed away but the + + + align:start position:0% +that should be consumed away but the +fact that the rain happens to be good or + + align:start position:0% +fact that the rain happens to be good or + + + align:start position:0% +fact that the rain happens to be good or +bad this year shouldn't really affect + + align:start position:0% +bad this year shouldn't really affect + + + align:start position:0% +bad this year shouldn't really affect +consumption at all because it should be + + align:start position:0% +consumption at all because it should be + + + align:start position:0% +consumption at all because it should be +smoothed away either by savings or by by + + align:start position:0% +smoothed away either by savings or by by + + + align:start position:0% +smoothed away either by savings or by by +borrowing + + align:start position:0% +borrowing + + + align:start position:0% +borrowing +so the test becomes whether that + + align:start position:0% +so the test becomes whether that + + + align:start position:0% +so the test becomes whether that +translates into larger variation savings + + align:start position:0% +translates into larger variation savings + + + align:start position:0% +translates into larger variation savings +then a permanent source of variation + + align:start position:0% +then a permanent source of variation + + + align:start position:0% +then a permanent source of variation +income such that individual ownership of + + align:start position:0% +income such that individual ownership of + + + align:start position:0% +income such that individual ownership of +land or whether people have irrigation + + align:start position:0% +land or whether people have irrigation + + + align:start position:0% +land or whether people have irrigation +or whether it's Goodland Badland and so + + align:start position:0% +or whether it's Goodland Badland and so + + + align:start position:0% +or whether it's Goodland Badland and so +on and so forth + + align:start position:0% +on and so forth + + + align:start position:0% +on and so forth +so if you write your estimating equation + + align:start position:0% +so if you write your estimating equation + + + align:start position:0% +so if you write your estimating equation +as saving is a function of permanent + + align:start position:0% +as saving is a function of permanent + + + align:start position:0% +as saving is a function of permanent +income transit or income you would like + + align:start position:0% +income transit or income you would like + + + align:start position:0% +income transit or income you would like +to to see a one here and a zero here and + + align:start position:0% +to to see a one here and a zero here and + + + align:start position:0% +to to see a one here and a zero here and +the two being uh oh sorry a zero here + + align:start position:0% +the two being uh oh sorry a zero here + + + align:start position:0% +the two being uh oh sorry a zero here +and a one here because this is saving uh + + align:start position:0% +and a one here because this is saving uh + + + align:start position:0% +and a one here because this is saving uh +with the uh you know and then + + align:start position:0% +with the uh you know and then + + + align:start position:0% +with the uh you know and then +potentially and then the variance of + + align:start position:0% +potentially and then the variance of + + + align:start position:0% +potentially and then the variance of +income you people who have income that + + align:start position:0% +income you people who have income that + + + align:start position:0% +income you people who have income that +are more variable irrespective of the + + align:start position:0% +are more variable irrespective of the + + + align:start position:0% +are more variable irrespective of the +realization this year might want to save + + align:start position:0% +realization this year might want to save + + + align:start position:0% +realization this year might want to save +more + + align:start position:0% +more + + + align:start position:0% +more +uh then we might in principle interact + + align:start position:0% +uh then we might in principle interact + + + align:start position:0% +uh then we might in principle interact +variation with permanent income because + + align:start position:0% +variation with permanent income because + + + align:start position:0% +variation with permanent income because +the poorer would want to save more + + align:start position:0% +the poorer would want to save more + + + align:start position:0% +the poorer would want to save more +traditionally + + align:start position:0% +traditionally + + + align:start position:0% +traditionally +what people were thinking about is oh + + align:start position:0% +what people were thinking about is oh + + + align:start position:0% +what people were thinking about is oh +let's treat the transitory income as uh + + align:start position:0% +let's treat the transitory income as uh + + + align:start position:0% +let's treat the transitory income as uh +as a nuisance + + align:start position:0% +as a nuisance + + + align:start position:0% +as a nuisance +uh because it's you know it's just it's + + align:start position:0% +uh because it's you know it's just it's + + + align:start position:0% +uh because it's you know it's just it's +it's noise in the income process let's + + align:start position:0% +it's noise in the income process let's + + + align:start position:0% +it's noise in the income process let's +try to uh predict the part of the income + + align:start position:0% +try to uh predict the part of the income + + + align:start position:0% +try to uh predict the part of the income +that is permanent and see whether people + + align:start position:0% +that is permanent and see whether people + + + align:start position:0% +that is permanent and see whether people +respond to permanent uh changes in it so + + align:start position:0% +respond to permanent uh changes in it so + + + align:start position:0% +respond to permanent uh changes in it so +things that affect permanent income + + align:start position:0% +things that affect permanent income + + + align:start position:0% +things that affect permanent income +uh so people run this type of regression + + align:start position:0% +uh so people run this type of regression + + + align:start position:0% +uh so people run this type of regression +of savings on our income obviously that + + align:start position:0% +of savings on our income obviously that + + + align:start position:0% +of savings on our income obviously that +should be why so the Y could be savings + + align:start position:0% +should be why so the Y could be savings + + + align:start position:0% +should be why so the Y could be savings +or consumption on a set of household + + align:start position:0% +or consumption on a set of household + + + align:start position:0% +or consumption on a set of household +characteristics + + align:start position:0% +characteristics + + + align:start position:0% +characteristics +uh that would be uh that would predict + + align:start position:0% +uh that would be uh that would predict + + + align:start position:0% +uh that would be uh that would predict +more money so your whether people had a + + align:start position:0% +more money so your whether people had a + + + align:start position:0% +more money so your whether people had a +job or something like that + + align:start position:0% +job or something like that + + + align:start position:0% +job or something like that +now it has a bunch of problems of course + + align:start position:0% +now it has a bunch of problems of course + + + align:start position:0% +now it has a bunch of problems of course +because people who have you know + + align:start position:0% +because people who have you know + + + align:start position:0% +because people who have you know +occupation education for example which + + align:start position:0% +occupation education for example which + + + align:start position:0% +occupation education for example which +was a thing that people put here on the + + align:start position:0% +was a thing that people put here on the + + + align:start position:0% +was a thing that people put here on the +right hand side to predict permanent + + align:start position:0% +right hand side to predict permanent + + + align:start position:0% +right hand side to predict permanent +income they also predict a million other + + align:start position:0% +income they also predict a million other + + + align:start position:0% +income they also predict a million other +things so it's pretty bad + + align:start position:0% +things so it's pretty bad + + + align:start position:0% +things so it's pretty bad +and so the idea is that well that's + + align:start position:0% +and so the idea is that well that's + + + align:start position:0% +and so the idea is that well that's +actually + + align:start position:0% +actually + + + align:start position:0% +actually +easier to make the case that we might + + align:start position:0% +easier to make the case that we might + + + align:start position:0% +easier to make the case that we might +have a a random or quasi-random form of + + align:start position:0% +have a a random or quasi-random form of + + + align:start position:0% +have a a random or quasi-random form of +transitory income than a random request + + align:start position:0% +transitory income than a random request + + + align:start position:0% +transitory income than a random request +random form of permanent income so maybe + + align:start position:0% +random form of permanent income so maybe + + + align:start position:0% +random form of permanent income so maybe +the identification of uh of that of of + + align:start position:0% +the identification of uh of that of of + + + align:start position:0% +the identification of uh of that of of +this coefficient is much easier because + + align:start position:0% +this coefficient is much easier because + + + align:start position:0% +this coefficient is much easier because +we can just you know forget about the + + align:start position:0% +we can just you know forget about the + + + align:start position:0% +we can just you know forget about the +permanent income or not pay my attention + + align:start position:0% +permanent income or not pay my attention + + + align:start position:0% +permanent income or not pay my attention +to the coefficient we estimate but focus + + align:start position:0% +to the coefficient we estimate but focus + + + align:start position:0% +to the coefficient we estimate but focus +on a variation in income that uh that + + align:start position:0% +on a variation in income that uh that + + + align:start position:0% +on a variation in income that uh that +can be credibly considered to be random + + align:start position:0% + + + + align:start position:0% + +if they are random they might you know + + align:start position:0% +if they are random they might you know + + + align:start position:0% +if they are random they might you know +disappear in the next year but then + + align:start position:0% +disappear in the next year but then + + + align:start position:0% +disappear in the next year but then +that's good this is precisely what we're + + align:start position:0% +that's good this is precisely what we're + + + align:start position:0% +that's good this is precisely what we're +looking for here so that was the insight + + align:start position:0% +looking for here so that was the insight + + + align:start position:0% +looking for here so that was the insight +and this was before any of this natural + + align:start position:0% +and this was before any of this natural + + + align:start position:0% +and this was before any of this natural +experiments was really developed so it + + align:start position:0% +experiments was really developed so it + + + align:start position:0% +experiments was really developed so it +was a particularly uh clever Insight + + align:start position:0% +was a particularly uh clever Insight + + + align:start position:0% +was a particularly uh clever Insight +because you know uh Pakistan + + align:start position:0% +because you know uh Pakistan + + + align:start position:0% +because you know uh Pakistan +so instead of trying to find instruments + + align:start position:0% +so instead of trying to find instruments + + + align:start position:0% +so instead of trying to find instruments +for permanent income that are + + align:start position:0% +for permanent income that are + + + align:start position:0% +for permanent income that are +uncorrelated with tests and consumption + + align:start position:0% +uncorrelated with tests and consumption + + + align:start position:0% +uncorrelated with tests and consumption +or patients which is kind of a hopeless + + align:start position:0% +or patients which is kind of a hopeless + + + align:start position:0% +or patients which is kind of a hopeless +Enterprise + + align:start position:0% +Enterprise + + + align:start position:0% +Enterprise +you can find a variation in transitory + + align:start position:0% +you can find a variation in transitory + + + align:start position:0% +you can find a variation in transitory +income that are you know much can be + + align:start position:0% +income that are you know much can be + + + align:start position:0% +income that are you know much can be +much more much more much easier to to + + align:start position:0% +much more much more much easier to to + + + align:start position:0% +much more much more much easier to to +consider than random + + align:start position:0% +consider than random + + + align:start position:0% +consider than random +so what does she do this is a very small + + align:start position:0% +so what does she do this is a very small + + + align:start position:0% +so what does she do this is a very small +table but we only need to look at the + + align:start position:0% +table but we only need to look at the + + + align:start position:0% +table but we only need to look at the +only look to look at here she's saying + + align:start position:0% +only look to look at here she's saying + + + align:start position:0% +only look to look at here she's saying +well let's look at not rainfall in a + + align:start position:0% +well let's look at not rainfall in a + + + align:start position:0% +well let's look at not rainfall in a +place but the deviation in a particular + + align:start position:0% +place but the deviation in a particular + + + align:start position:0% +place but the deviation in a particular +Year from the current + + align:start position:0% +Year from the current + + + align:start position:0% +Year from the current +that could be uh reasonably assumed to + + align:start position:0% +that could be uh reasonably assumed to + + + align:start position:0% +that could be uh reasonably assumed to +be random with respect to each + + align:start position:0% +be random with respect to each + + + align:start position:0% +be random with respect to each +individual farmer + + align:start position:0% +individual farmer + + + align:start position:0% +individual farmer +and that can and that can be reasonably + + align:start position:0% +and that can and that can be reasonably + + + align:start position:0% +and that can and that can be reasonably +assumed to be transitory and in fact + + align:start position:0% +assumed to be transitory and in fact + + + align:start position:0% +assumed to be transitory and in fact +when you look for example at A variation + + align:start position:0% +when you look for example at A variation + + + align:start position:0% +when you look for example at A variation +lagged one period so this is the this is + + align:start position:0% +lagged one period so this is the this is + + + align:start position:0% +lagged one period so this is the this is +the variation this year you can see that + + align:start position:0% +the variation this year you can see that + + + align:start position:0% +the variation this year you can see that +if the rain was good this year + + align:start position:0% +if the rain was good this year + + + align:start position:0% +if the rain was good this year +uh people make more money + + align:start position:0% +uh people make more money + + + align:start position:0% +uh people make more money +this is a t statistic so that's a t + + align:start position:0% +this is a t statistic so that's a t + + + align:start position:0% +this is a t statistic so that's a t +statistic of two + + align:start position:0% +statistic of two + + + align:start position:0% +statistic of two +and she'd like to see that well if it + + align:start position:0% +and she'd like to see that well if it + + + align:start position:0% +and she'd like to see that well if it +rained last year or the income should + + align:start position:0% +rained last year or the income should + + + align:start position:0% +rained last year or the income should +not be larger or that's actually not the + + align:start position:0% +not be larger or that's actually not the + + + align:start position:0% +not be larger or that's actually not the +case the T statistic is also high but + + align:start position:0% +case the T statistic is also high but + + + align:start position:0% +case the T statistic is also high but +for the uh you know the rainfall last + + align:start position:0% +for the uh you know the rainfall last + + + align:start position:0% +for the uh you know the rainfall last +year and the year before the the uh it + + align:start position:0% +year and the year before the the uh it + + + align:start position:0% +year and the year before the the uh it +doesn't it doesn't affect income anymore + + align:start position:0% +doesn't it doesn't affect income anymore + + + align:start position:0% +doesn't it doesn't affect income anymore +so maybe the income process is one that + + align:start position:0% +so maybe the income process is one that + + + align:start position:0% +so maybe the income process is one that +responds to this area + + align:start position:0% +responds to this area + + + align:start position:0% +responds to this area +rainfall and last year rainfall she also + + align:start position:0% +rainfall and last year rainfall she also + + + align:start position:0% +rainfall and last year rainfall she also +makes the argument that this year + + align:start position:0% +makes the argument that this year + + + align:start position:0% +makes the argument that this year +rainfall has no predictive property of + + align:start position:0% +rainfall has no predictive property of + + + align:start position:0% +rainfall has no predictive property of +next year going to follow otherwise the + + align:start position:0% +next year going to follow otherwise the + + + align:start position:0% +next year going to follow otherwise the +realization of this year would give you + + align:start position:0% +realization of this year would give you + + + align:start position:0% +realization of this year would give you +some indication of what's going to + + align:start position:0% +some indication of what's going to + + + align:start position:0% +some indication of what's going to +happen next year and therefore you need + + align:start position:0% +happen next year and therefore you need + + + align:start position:0% +happen next year and therefore you need +to take that into account in making your + + align:start position:0% +to take that into account in making your + + + align:start position:0% +to take that into account in making your +your your own suspicion about what your + + align:start position:0% +your your own suspicion about what your + + + align:start position:0% +your your own suspicion about what your +income is going to be that's going to + + align:start position:0% +income is going to be that's going to + + + align:start position:0% +income is going to be that's going to +affect your income so she shows that in + + align:start position:0% +affect your income so she shows that in + + + align:start position:0% +affect your income so she shows that in +fact incomes is not seriously correct + + align:start position:0% +fact incomes is not seriously correct + + + align:start position:0% +fact incomes is not seriously correct +those shocks are iig + + align:start position:0% +those shocks are iig + + + align:start position:0% +those shocks are iig +uh and therefore what we can do now is + + align:start position:0% +uh and therefore what we can do now is + + + align:start position:0% +uh and therefore what we can do now is +to see whether it's it appears that uh + + align:start position:0% +to see whether it's it appears that uh + + + align:start position:0% +to see whether it's it appears that uh +saving is is strongly correlated uh with + + align:start position:0% +saving is is strongly correlated uh with + + + align:start position:0% +saving is is strongly correlated uh with +uh this year's rainfall variable + + align:start position:0% +uh this year's rainfall variable + + + align:start position:0% +uh this year's rainfall variable +and she has various measures of savings + + align:start position:0% +and she has various measures of savings + + + align:start position:0% +and she has various measures of savings +that's a bit of a problem in any + + align:start position:0% +that's a bit of a problem in any + + + align:start position:0% +that's a bit of a problem in any +empirical data is to measure saving it's + + align:start position:0% +empirical data is to measure saving it's + + + align:start position:0% +empirical data is to measure saving it's +pretty bad + + align:start position:0% +pretty bad + + + align:start position:0% +pretty bad +this is no exception this is pretty bad + + align:start position:0% +this is no exception this is pretty bad + + + align:start position:0% +this is no exception this is pretty bad +but she's trying three measures uh we + + align:start position:0% +but she's trying three measures uh we + + + align:start position:0% +but she's trying three measures uh we +don't need to get into the details + + align:start position:0% +don't need to get into the details + + + align:start position:0% +don't need to get into the details +because frankly it's more about the + + align:start position:0% +because frankly it's more about the + + + align:start position:0% +because frankly it's more about the +method than about the results given that + + align:start position:0% +method than about the results given that + + + align:start position:0% +method than about the results given that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh given given the the measure of saving + + align:start position:0% +uh given given the the measure of saving + + + align:start position:0% +uh given given the the measure of saving +that she has to play with but she's + + align:start position:0% +that she has to play with but she's + + + align:start position:0% +that she has to play with but she's +finding it to be quite correlated with + + align:start position:0% +finding it to be quite correlated with + + + align:start position:0% +finding it to be quite correlated with +savings that's sort of reduced form then + + align:start position:0% +savings that's sort of reduced form then + + + align:start position:0% +savings that's sort of reduced form then +once you have that you can run an IV and + + align:start position:0% +once you have that you can run an IV and + + + align:start position:0% +once you have that you can run an IV and +you saying well what's the effect of uh + + align:start position:0% +you saying well what's the effect of uh + + + align:start position:0% +you saying well what's the effect of uh +transitory income on savings uh so this + + align:start position:0% +transitory income on savings uh so this + + + align:start position:0% +transitory income on savings uh so this +one is two steps which is just like + + align:start position:0% +one is two steps which is just like + + + align:start position:0% +one is two steps which is just like +literally constructing the IV by hand + + align:start position:0% +literally constructing the IV by hand + + + align:start position:0% +literally constructing the IV by hand +this is maximum likelihood that's closer + + align:start position:0% +this is maximum likelihood that's closer + + + align:start position:0% +this is maximum likelihood that's closer +to a to SLS estimation + + align:start position:0% +to a to SLS estimation + + + align:start position:0% +to a to SLS estimation +uh she also a instrument for permanent + + align:start position:0% +uh she also a instrument for permanent + + + align:start position:0% +uh she also a instrument for permanent +income but we can forget that for now + + align:start position:0% +income but we can forget that for now + + + align:start position:0% +income but we can forget that for now +I mean we can look at it but we know + + align:start position:0% +I mean we can look at it but we know + + + align:start position:0% +I mean we can look at it but we know +that it's pretty hard to find + + align:start position:0% +that it's pretty hard to find + + + align:start position:0% +that it's pretty hard to find +instruments for permanent income + + align:start position:0% +instruments for permanent income + + + align:start position:0% +instruments for permanent income +but focusing on this guys uh you can see + + align:start position:0% +but focusing on this guys uh you can see + + + align:start position:0% +but focusing on this guys uh you can see +now using the the rainfall entire one + + align:start position:0% +now using the the rainfall entire one + + + align:start position:0% +now using the the rainfall entire one +and two as an instrument for income + + align:start position:0% +and two as an instrument for income + + + align:start position:0% +and two as an instrument for income +uh she seemed pretty strong coefficient + + align:start position:0% +uh she seemed pretty strong coefficient + + + align:start position:0% +uh she seemed pretty strong coefficient +of this transitory + + align:start position:0% +of this transitory + + + align:start position:0% +of this transitory +component on savings which and then once + + align:start position:0% +component on savings which and then once + + + align:start position:0% +component on savings which and then once +you've done that you can try to see + + align:start position:0% +you've done that you can try to see + + + align:start position:0% +you've done that you can try to see +whether you're rejecting one + + align:start position:0% +whether you're rejecting one + + + align:start position:0% +whether you're rejecting one +and you don't really reject one so you + + align:start position:0% +and you don't really reject one so you + + + align:start position:0% +and you don't really reject one so you +know you could she cannot you cannot on + + align:start position:0% +know you could she cannot you cannot on + + + align:start position:0% +know you could she cannot you cannot on +the other hand you can reject that these + + align:start position:0% +the other hand you can reject that these + + + align:start position:0% +the other hand you can reject that these +two are the same + + align:start position:0% +two are the same + + + align:start position:0% +two are the same +so uh that would be a test + + align:start position:0% +so uh that would be a test + + + align:start position:0% +so uh that would be a test +of uh that people that of of this + + align:start position:0% +of uh that people that of of this + + + align:start position:0% +of uh that people that of of this +particular implication of the standard + + align:start position:0% +particular implication of the standard + + + align:start position:0% +particular implication of the standard +utility maximization model that people + + align:start position:0% +utility maximization model that people + + + align:start position:0% +utility maximization model that people +save most of their terms their income + + align:start position:0% +save most of their terms their income + + + align:start position:0% +save most of their terms their income +and consume most of their permanent + + align:start position:0% +and consume most of their permanent + + + align:start position:0% +and consume most of their permanent +income yeah + + align:start position:0% +income yeah + + + align:start position:0% +income yeah +so why is it hard to measure savings uh + + align:start position:0% +so why is it hard to measure savings uh + + + align:start position:0% +so why is it hard to measure savings uh +because people save in all sorts of ways + + align:start position:0% +because people save in all sorts of ways + + + align:start position:0% +because people save in all sorts of ways +so you can't uh easily so these are + + align:start position:0% +so you can't uh easily so these are + + + align:start position:0% +so you can't uh easily so these are +people and farmers in Thailand + + align:start position:0% +people and farmers in Thailand + + + align:start position:0% +people and farmers in Thailand +they don't really have bank accounts at + + align:start position:0% +they don't really have bank accounts at + + + align:start position:0% +they don't really have bank accounts at +that time they were there saving the + + align:start position:0% +that time they were there saving the + + + align:start position:0% +that time they were there saving the +money today they probably are doing it + + align:start position:0% +money today they probably are doing it + + + align:start position:0% +money today they probably are doing it +more but in the time where she collects + + align:start position:0% +more but in the time where she collects + + + align:start position:0% +more but in the time where she collects +the data or even today if you went to + + align:start position:0% +the data or even today if you went to + + + align:start position:0% +the data or even today if you went to +Indian household they are saving is like + + align:start position:0% +Indian household they are saving is like + + + align:start position:0% +Indian household they are saving is like +all over the place they have some in a + + align:start position:0% +all over the place they have some in a + + + align:start position:0% +all over the place they have some in a +bank account they have some in the form + + align:start position:0% +bank account they have some in the form + + + align:start position:0% +bank account they have some in the form +of grains that have not been eaten this + + align:start position:0% +of grains that have not been eaten this + + + align:start position:0% +of grains that have not been eaten this +year they have some another mattress + + align:start position:0% +year they have some another mattress + + + align:start position:0% +year they have some another mattress +they have some that are saved in the + + align:start position:0% +they have some that are saved in the + + + align:start position:0% +they have some that are saved in the +form of having lent them to a causing + + align:start position:0% +form of having lent them to a causing + + + align:start position:0% +form of having lent them to a causing +you know second cousin twice removed + + align:start position:0% +you know second cousin twice removed + + + align:start position:0% +you know second cousin twice removed +that might be given back + + align:start position:0% +that might be given back + + + align:start position:0% +that might be given back +and so uh accumulating like so to sum it + + align:start position:0% +and so uh accumulating like so to sum it + + + align:start position:0% +and so uh accumulating like so to sum it +up or summing it up over all the + + align:start position:0% +up or summing it up over all the + + + align:start position:0% +up or summing it up over all the +possible way that you actually can save + + align:start position:0% +possible way that you actually can save + + + align:start position:0% +possible way that you actually can save +is very difficult + + align:start position:0% +is very difficult + + + align:start position:0% +is very difficult +especially when you try to think about + + align:start position:0% +especially when you try to think about + + + align:start position:0% +especially when you try to think about +you know what's the value of that saving + + align:start position:0% +you know what's the value of that saving + + + align:start position:0% +you know what's the value of that saving +like is this someone causing twice + + align:start position:0% +like is this someone causing twice + + + align:start position:0% +like is this someone causing twice +remove going to give it back or not + + align:start position:0% +remove going to give it back or not + + + align:start position:0% +remove going to give it back or not +so that's one so the direct measurement + + align:start position:0% +so that's one so the direct measurement + + + align:start position:0% +so that's one so the direct measurement +of saving this stuff so what people then + + align:start position:0% +of saving this stuff so what people then + + + align:start position:0% +of saving this stuff so what people then +try to do is to say well let's try to do + + align:start position:0% +try to do is to say well let's try to do + + + align:start position:0% +try to do is to say well let's try to do +it by measuring income minus consumption + + align:start position:0% +it by measuring income minus consumption + + + align:start position:0% +it by measuring income minus consumption +that saving + + align:start position:0% +that saving + + + align:start position:0% +that saving +and the difficulty with that is that + + align:start position:0% +and the difficulty with that is that + + + align:start position:0% +and the difficulty with that is that +first of all income is very poorly + + align:start position:0% +first of all income is very poorly + + + align:start position:0% +first of all income is very poorly +measured + + align:start position:0% +measured + + + align:start position:0% +measured +because people have all sorts of sources + + align:start position:0% +because people have all sorts of sources + + + align:start position:0% +because people have all sorts of sources +of income many of them informal and then + + align:start position:0% +of income many of them informal and then + + + align:start position:0% +of income many of them informal and then +they don't know you know how much money + + align:start position:0% +they don't know you know how much money + + + align:start position:0% +they don't know you know how much money +they made like if they're Farmers like + + align:start position:0% +they made like if they're Farmers like + + + align:start position:0% +they made like if they're Farmers like +you need to Value everything minus the + + align:start position:0% +you need to Value everything minus the + + + align:start position:0% +you need to Value everything minus the +input it's like super + + align:start position:0% +input it's like super + + + align:start position:0% +input it's like super +painful + + align:start position:0% +painful + + + align:start position:0% +painful +uh and uh consumption is better measured + + align:start position:0% +uh and uh consumption is better measured + + + align:start position:0% +uh and uh consumption is better measured +but not + + align:start position:0% +but not + + + align:start position:0% +but not +great either + + align:start position:0% +great either + + + align:start position:0% +great either +and then you have durable expenditure + + align:start position:0% +and then you have durable expenditure + + + align:start position:0% +and then you have durable expenditure +that is a form of consumption but it's + + align:start position:0% +that is a form of consumption but it's + + + align:start position:0% +that is a form of consumption but it's +also a form of saving so you should + + align:start position:0% +also a form of saving so you should + + + align:start position:0% +also a form of saving so you should +really value the services from that + + align:start position:0% +really value the services from that + + + align:start position:0% +really value the services from that +consumption in order to have the full + + align:start position:0% +consumption in order to have the full + + + align:start position:0% +consumption in order to have the full +measure of consumption + + align:start position:0% +measure of consumption + + + align:start position:0% +measure of consumption +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and you just got me started it's pretty + + align:start position:0% +and you just got me started it's pretty + + + align:start position:0% +and you just got me started it's pretty +hard to do with your savings + + align:start position:0% +hard to do with your savings + + + align:start position:0% +hard to do with your savings +yeah I believe the last point about + + align:start position:0% +yeah I believe the last point about + + + align:start position:0% +yeah I believe the last point about +dribbles how do you think about like + + align:start position:0% +dribbles how do you think about like + + + align:start position:0% +dribbles how do you think about like +illiquid assets or like people liquid + + align:start position:0% +illiquid assets or like people liquid + + + align:start position:0% +illiquid assets or like people liquid +forms + + align:start position:0% +forms + + + align:start position:0% +forms +like suppose I'm I don't know + + align:start position:0% +like suppose I'm I don't know + + + align:start position:0% +like suppose I'm I don't know +like I buy a cow or a bullock yeah yeah + + align:start position:0% +like I buy a cow or a bullock yeah yeah + + + align:start position:0% +like I buy a cow or a bullock yeah yeah +so it's super interesting uh super + + align:start position:0% +so it's super interesting uh super + + + align:start position:0% +so it's super interesting uh super +interesting thing uh in fact there are + + align:start position:0% +interesting thing uh in fact there are + + + align:start position:0% +interesting thing uh in fact there are +interesting uh barrier there's a very + + align:start position:0% +interesting uh barrier there's a very + + + align:start position:0% +interesting uh barrier there's a very +nice people by fosterone presence effect + + align:start position:0% +nice people by fosterone presence effect + + + align:start position:0% +nice people by fosterone presence effect +or wasn't old people on bullocks + + align:start position:0% +or wasn't old people on bullocks + + + align:start position:0% +or wasn't old people on bullocks +uh showing that you know people invest + + align:start position:0% +uh showing that you know people invest + + + align:start position:0% +uh showing that you know people invest +in Bullocks and the issue with Bullocks + + align:start position:0% +in Bullocks and the issue with Bullocks + + + align:start position:0% +in Bullocks and the issue with Bullocks +is not an easy liquid but it's also a + + align:start position:0% +is not an easy liquid but it's also a + + + align:start position:0% +is not an easy liquid but it's also a +protective asset + + align:start position:0% +protective asset + + + align:start position:0% +protective asset +and so in that time you have inefficient + + align:start position:0% +and so in that time you have inefficient + + + align:start position:0% +and so in that time you have inefficient +liquidation of bullocks + + align:start position:0% +liquidation of bullocks + + + align:start position:0% +liquidation of bullocks +uh because people all are saving is in + + align:start position:0% +uh because people all are saving is in + + + align:start position:0% +uh because people all are saving is in +the Bullock and they need to to they + + align:start position:0% +the Bullock and they need to to they + + + align:start position:0% +the Bullock and they need to to they +need to sell to to to consume and then + + align:start position:0% +need to sell to to to consume and then + + + align:start position:0% +need to sell to to to consume and then +they don't have uh they don't have the + + align:start position:0% +they don't have uh they don't have the + + + align:start position:0% +they don't have uh they don't have the +Bullock to actually + + align:start position:0% +Bullock to actually + + + align:start position:0% +Bullock to actually +so that creates this kind of that + + align:start position:0% +so that creates this kind of that + + + align:start position:0% +so that creates this kind of that +creates so this is about sort of the the + + align:start position:0% +creates so this is about sort of the the + + + align:start position:0% +creates so this is about sort of the the +we'll go in a minute talk about credit + + align:start position:0% +we'll go in a minute talk about credit + + + align:start position:0% +we'll go in a minute talk about credit +constraint savings constraint it might + + align:start position:0% +constraint savings constraint it might + + + align:start position:0% +constraint savings constraint it might +be difficult it's not one of the reason + + align:start position:0% +be difficult it's not one of the reason + + + align:start position:0% +be difficult it's not one of the reason +why people don't save into bank accounts + + align:start position:0% +why people don't save into bank accounts + + + align:start position:0% +why people don't save into bank accounts +is they don't have access to bank + + align:start position:0% +is they don't have access to bank + + + align:start position:0% +is they don't have access to bank +accounts and in particular they don't + + align:start position:0% +accounts and in particular they don't + + + align:start position:0% +accounts and in particular they don't +have access to bank accounts that are + + align:start position:0% +have access to bank accounts that are + + + align:start position:0% +have access to bank accounts that are +cheap and easy to to to manage and so + + align:start position:0% +cheap and easy to to to manage and so + + + align:start position:0% +cheap and easy to to to manage and so +they're saving all sorts of ways + + align:start position:0% +they're saving all sorts of ways + + + align:start position:0% +they're saving all sorts of ways +including you know potentially in + + align:start position:0% +including you know potentially in + + + align:start position:0% +including you know potentially in +Bullocks which has this feature that + + align:start position:0% +Bullocks which has this feature that + + + align:start position:0% +Bullocks which has this feature that +it's both productive investment and + + align:start position:0% +it's both productive investment and + + + align:start position:0% +it's both productive investment and +Savings in particular Bullocks go by + + align:start position:0% +Savings in particular Bullocks go by + + + align:start position:0% +Savings in particular Bullocks go by +there + + align:start position:0% +there + + + align:start position:0% +there +so if you have to liquid one Bullock + + align:start position:0% +so if you have to liquid one Bullock + + + align:start position:0% +so if you have to liquid one Bullock +then you have your one block + + align:start position:0% +then you have your one block + + + align:start position:0% +then you have your one block +that still needs to eat but you you have + + align:start position:0% +that still needs to eat but you you have + + + align:start position:0% +that still needs to eat but you you have +a pair of Bullocks so you can't really + + align:start position:0% +a pair of Bullocks so you can't really + + + align:start position:0% +a pair of Bullocks so you can't really +use them to harvest + + align:start position:0% +use them to harvest + + + align:start position:0% +use them to harvest +so it's a party + + align:start position:0% +so it's a party + + + align:start position:0% +so it's a party +that creates one more it's a nice paper + + align:start position:0% +that creates one more it's a nice paper + + + align:start position:0% +that creates one more it's a nice paper +although it + + align:start position:0% + + + + align:start position:0% + +that's a great question + + align:start position:0% + + + + align:start position:0% + +ah so this is where we're going to + + align:start position:0% +ah so this is where we're going to + + + align:start position:0% +ah so this is where we're going to +constraint let's start by adding uh + + align:start position:0% +constraint let's start by adding uh + + + align:start position:0% +constraint let's start by adding uh +we already started to talk about savings + + align:start position:0% +we already started to talk about savings + + + align:start position:0% +we already started to talk about savings +constraint I'll talk to uh we'll go back + + align:start position:0% +constraint I'll talk to uh we'll go back + + + align:start position:0% +constraint I'll talk to uh we'll go back +to that a little bit later but there are + + align:start position:0% +to that a little bit later but there are + + + align:start position:0% +to that a little bit later but there are +also you know what my colleague should + + align:start position:0% +also you know what my colleague should + + + align:start position:0% +also you know what my colleague should +hear certainly has paid attention to is + + align:start position:0% +hear certainly has paid attention to is + + + align:start position:0% +hear certainly has paid attention to is +the possibility that you might not be + + align:start position:0% +the possibility that you might not be + + + align:start position:0% +the possibility that you might not be +able to borrow + + align:start position:0% +able to borrow + + + align:start position:0% +able to borrow +uh so then that's really adding the + + align:start position:0% +uh so then that's really adding the + + + align:start position:0% +uh so then that's really adding the +addition an additional constraint that + + align:start position:0% +addition an additional constraint that + + + align:start position:0% +addition an additional constraint that +the assets have to be positive + + align:start position:0% +the assets have to be positive + + + align:start position:0% +the assets have to be positive +at any given time or the consumption + + align:start position:0% +at any given time or the consumption + + + align:start position:0% +at any given time or the consumption +cannot exceed the sum of the asset and + + align:start position:0% +cannot exceed the sum of the asset and + + + align:start position:0% +cannot exceed the sum of the asset and +the income you're making or cash in + + align:start position:0% +the income you're making or cash in + + + align:start position:0% +the income you're making or cash in +hands + + align:start position:0% +hands + + + align:start position:0% +hands +so yeah now you have two regimes uh and + + align:start position:0% +so yeah now you have two regimes uh and + + + align:start position:0% +so yeah now you have two regimes uh and +the unconstrained uh regime uh you you + + align:start position:0% +the unconstrained uh regime uh you you + + + align:start position:0% +the unconstrained uh regime uh you you +can you have your Euler equation + + align:start position:0% +can you have your Euler equation + + + align:start position:0% +can you have your Euler equation +dissatisfied as uh you know as as usual + + align:start position:0% +dissatisfied as uh you know as as usual + + + align:start position:0% +dissatisfied as uh you know as as usual +uh your marginal utility of consumption + + align:start position:0% +uh your marginal utility of consumption + + + align:start position:0% +uh your marginal utility of consumption +is the expected utility of future + + align:start position:0% +is the expected utility of future + + + align:start position:0% +is the expected utility of future +marginal utility of consumption up to a + + align:start position:0% +marginal utility of consumption up to a + + + align:start position:0% +marginal utility of consumption up to a +discount Factor + + align:start position:0% +discount Factor + + + align:start position:0% +discount Factor +but once you're concerned you just + + align:start position:0% +but once you're concerned you just + + + align:start position:0% +but once you're concerned you just +consume everything you can + + align:start position:0% +consume everything you can + + + align:start position:0% +consume everything you can +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and therefore the marginal utility of + + align:start position:0% +and therefore the marginal utility of + + + align:start position:0% +and therefore the marginal utility of +consumption today is too high compared + + align:start position:0% +consumption today is too high compared + + + align:start position:0% +consumption today is too high compared +to Wood you know you take you make it as + + align:start position:0% +to Wood you know you take you make it as + + + align:start position:0% +to Wood you know you take you make it as +close to the desired uh + + align:start position:0% +close to the desired uh + + + align:start position:0% +close to the desired uh +utility as you want but it's too high + + align:start position:0% +utility as you want but it's too high + + + align:start position:0% +utility as you want but it's too high +that means you're not consuming enough + + align:start position:0% +that means you're not consuming enough + + + align:start position:0% +that means you're not consuming enough +right + + align:start position:0% + + + + align:start position:0% + +um so if you put the two cases together + + align:start position:0% +um so if you put the two cases together + + + align:start position:0% +um so if you put the two cases together +we have that the marginal utility of + + align:start position:0% +we have that the marginal utility of + + + align:start position:0% +we have that the marginal utility of +consumption is the maximum of the + + align:start position:0% +consumption is the maximum of the + + + align:start position:0% +consumption is the maximum of the +marginal utility of consuming everything + + align:start position:0% +marginal utility of consuming everything + + + align:start position:0% +marginal utility of consuming everything +you have today + + align:start position:0% +you have today + + + align:start position:0% +you have today +and the uh the the the product of the + + align:start position:0% +and the uh the the the product of the + + + align:start position:0% +and the uh the the the product of the +standard Euler equation the expected + + align:start position:0% +standard Euler equation the expected + + + align:start position:0% +standard Euler equation the expected +utility of tomorrow's consumption + + align:start position:0% + + + + align:start position:0% + +uh so did another a pair of plastic + + align:start position:0% +uh so did another a pair of plastic + + + align:start position:0% +uh so did another a pair of plastic +paper and a book uh showing at the the + + align:start position:0% +paper and a book uh showing at the the + + + align:start position:0% +paper and a book uh showing at the the +solution to this problem can be + + align:start position:0% +solution to this problem can be + + + align:start position:0% +solution to this problem can be +characterized by a consumption function + + align:start position:0% +characterized by a consumption function + + + align:start position:0% +characterized by a consumption function +where you uh your consumption is a is a + + align:start position:0% +where you uh your consumption is a is a + + + align:start position:0% +where you uh your consumption is a is a +consumption of what you what's your cash + + align:start position:0% +consumption of what you what's your cash + + + align:start position:0% +consumption of what you what's your cash +on hand in total + + align:start position:0% +on hand in total + + + align:start position:0% +on hand in total +uh with a c a r a production function + + align:start position:0% +uh with a c a r a production function + + + align:start position:0% +uh with a c a r a production function +that consumption utility function sorry + + align:start position:0% +that consumption utility function sorry + + + align:start position:0% +that consumption utility function sorry +uh it can be shown that it has the + + align:start position:0% +uh it can be shown that it has the + + + align:start position:0% +uh it can be shown that it has the +following form if you if you have less + + align:start position:0% +following form if you if you have less + + + align:start position:0% +following form if you if you have less +than something + + align:start position:0% +than something + + + align:start position:0% +than something +you eat or everything you have + + align:start position:0% +you eat or everything you have + + + align:start position:0% +you eat or everything you have +if you have more than that threshold + + align:start position:0% +if you have more than that threshold + + + align:start position:0% +if you have more than that threshold +you save a fraction of the difference + + align:start position:0% +you save a fraction of the difference + + + align:start position:0% +you save a fraction of the difference +between the cash you have in hand and + + align:start position:0% +between the cash you have in hand and + + + align:start position:0% +between the cash you have in hand and +that threshold + + align:start position:0% + + + + align:start position:0% + +so you uh + + align:start position:0% +so you uh + + + align:start position:0% +so you uh +you know if your income is less than + + align:start position:0% +you know if your income is less than + + + align:start position:0% +you know if your income is less than +so you can write it so basically what + + align:start position:0% +so you can write it so basically what + + + align:start position:0% +so you can write it so basically what +you do is when you can + + align:start position:0% +you do is when you can + + + align:start position:0% +you do is when you can +you uh you save a little bit to + + align:start position:0% +you uh you save a little bit to + + + align:start position:0% +you uh you save a little bit to +constitute your buffer stock + + align:start position:0% +constitute your buffer stock + + + align:start position:0% +constitute your buffer stock +and then when you have enough then you + + align:start position:0% +and then when you have enough then you + + + align:start position:0% +and then when you have enough then you +you can just consume normally + + align:start position:0% + + + + align:start position:0% + +so the the problems to consumer of your + + align:start position:0% +so the the problems to consumer of your + + + align:start position:0% +so the the problems to consumer of your +assets will be smaller + + align:start position:0% +assets will be smaller + + + align:start position:0% +assets will be smaller +and when your assets are higher than + + align:start position:0% +and when your assets are higher than + + + align:start position:0% +and when your assets are higher than +when they are low + + align:start position:0% +when they are low + + + align:start position:0% +when they are low +and when they are low the eventually you + + align:start position:0% +and when they are low the eventually you + + + align:start position:0% +and when they are low the eventually you +you're gonna when the assets are very + + align:start position:0% +you're gonna when the assets are very + + + align:start position:0% +you're gonna when the assets are very +low you're gonna deplete them completely + + align:start position:0% +low you're gonna deplete them completely + + + align:start position:0% +low you're gonna deplete them completely +if the next realization of income is low + + align:start position:0% +if the next realization of income is low + + + align:start position:0% +if the next realization of income is low +and then you're gonna end up with zero + + align:start position:0% +and then you're gonna end up with zero + + + align:start position:0% +and then you're gonna end up with zero +assets + + align:start position:0% +assets + + + align:start position:0% +assets +so what you can do is to to simulate uh + + align:start position:0% +so what you can do is to to simulate uh + + + align:start position:0% +so what you can do is to to simulate uh +simulate and to see you know how much + + align:start position:0% +simulate and to see you know how much + + + align:start position:0% +simulate and to see you know how much +you can achieve visually and that's + + align:start position:0% +you can achieve visually and that's + + + align:start position:0% +you can achieve visually and that's +something he has in his book + + align:start position:0% +something he has in his book + + + align:start position:0% +something he has in his book +understanding consumption it's actually + + align:start position:0% +understanding consumption it's actually + + + align:start position:0% +understanding consumption it's actually +a very nice book uh and uh and it has he + + align:start position:0% +a very nice book uh and uh and it has he + + + align:start position:0% +a very nice book uh and uh and it has he +has these simulations + + align:start position:0% +has these simulations + + + align:start position:0% +has these simulations +is to say well + + align:start position:0% +is to say well + + + align:start position:0% +is to say well +uh suppose that your income is ideal + + align:start position:0% +uh suppose that your income is ideal + + + align:start position:0% +uh suppose that your income is ideal +between 100 and standard deviation 10. + + align:start position:0% +between 100 and standard deviation 10. + + + align:start position:0% +between 100 and standard deviation 10. +and you uh you construct a rule of thumb + + align:start position:0% +and you uh you construct a rule of thumb + + + align:start position:0% +and you uh you construct a rule of thumb +for consumption that actually looks + + align:start position:0% +for consumption that actually looks + + + align:start position:0% +for consumption that actually looks +pretty similar to what would be the + + align:start position:0% +pretty similar to what would be the + + + align:start position:0% +pretty similar to what would be the +optimal rule + + align:start position:0% +optimal rule + + + align:start position:0% +optimal rule +uh which is uh consume everything + + align:start position:0% +uh which is uh consume everything + + + align:start position:0% +uh which is uh consume everything +if it's consume everything plus 70 + + align:start position:0% +if it's consume everything plus 70 + + + align:start position:0% +if it's consume everything plus 70 +percent of what's above the threshold + + align:start position:0% +percent of what's above the threshold + + + align:start position:0% +percent of what's above the threshold +and the threshold is uh is a hundred + + align:start position:0% +and the threshold is uh is a hundred + + + align:start position:0% +and the threshold is uh is a hundred +so for a mean of hundred + + align:start position:0% +so for a mean of hundred + + + align:start position:0% +so for a mean of hundred +so what it shows is that that rule of + + align:start position:0% +so what it shows is that that rule of + + + align:start position:0% +so what it shows is that that rule of +thumb is very very similar to the + + align:start position:0% +thumb is very very similar to the + + + align:start position:0% +thumb is very very similar to the +optimal path + + align:start position:0% +optimal path + + + align:start position:0% +optimal path +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +so we can simulate that easily + + align:start position:0% +so we can simulate that easily + + + align:start position:0% +so we can simulate that easily +so here's the consumption of someone + + align:start position:0% +so here's the consumption of someone + + + align:start position:0% +so here's the consumption of someone +with this variable the income of someone + + align:start position:0% +with this variable the income of someone + + + align:start position:0% +with this variable the income of someone +we mean 100 standard deviation what did + + align:start position:0% +we mean 100 standard deviation what did + + + align:start position:0% +we mean 100 standard deviation what did +I say 10 + + align:start position:0% +I say 10 + + + align:start position:0% +I say 10 +boom boom + + align:start position:0% +boom boom + + + align:start position:0% +boom boom +so you can see that there are a couple + + align:start position:0% +so you can see that there are a couple + + + align:start position:0% +so you can see that there are a couple +of good realization of income so people + + align:start position:0% +of good realization of income so people + + + align:start position:0% +of good realization of income so people +have so the the the person has been + + align:start position:0% +have so the the the person has been + + + align:start position:0% +have so the the the person has been +building up some some assets + + align:start position:0% +building up some some assets + + + align:start position:0% +building up some some assets +and he's like uh she or he is doing uh + + align:start position:0% +and he's like uh she or he is doing uh + + + align:start position:0% +and he's like uh she or he is doing uh +at some as a lot of assets at some point + + align:start position:0% +at some as a lot of assets at some point + + + align:start position:0% +at some as a lot of assets at some point +and then there are a few bad years and + + align:start position:0% +and then there are a few bad years and + + + align:start position:0% +and then there are a few bad years and +then his uh + + align:start position:0% +then his uh + + + align:start position:0% +then his uh +trying to keep the consumption more or + + align:start position:0% +trying to keep the consumption more or + + + align:start position:0% +trying to keep the consumption more or +less stable so the assets get depleted + + align:start position:0% +less stable so the assets get depleted + + + align:start position:0% +less stable so the assets get depleted +at some point there are so low that the + + align:start position:0% +at some point there are so low that the + + + align:start position:0% +at some point there are so low that the +next one is another low income in fact + + align:start position:0% +next one is another low income in fact + + + align:start position:0% +next one is another low income in fact +that one's very low they're eating + + align:start position:0% +that one's very low they're eating + + + align:start position:0% +that one's very low they're eating +everything and their consumption took + + align:start position:0% +everything and their consumption took + + + align:start position:0% +everything and their consumption took +takes a big fall + + align:start position:0% +takes a big fall + + + align:start position:0% +takes a big fall +and then they can they start again + + align:start position:0% +and then they can they start again + + + align:start position:0% +and then they can they start again +building the assets + + align:start position:0% +building the assets + + + align:start position:0% +building the assets +so that is someone that's uh that's uh + + align:start position:0% +so that is someone that's uh that's uh + + + align:start position:0% +so that is someone that's uh that's uh +it's a conservative saving policy that's + + align:start position:0% +it's a conservative saving policy that's + + + align:start position:0% +it's a conservative saving policy that's +a less conservative saving policy where + + align:start position:0% +a less conservative saving policy where + + + align:start position:0% +a less conservative saving policy where +they are saving a lower fraction of the + + align:start position:0% +they are saving a lower fraction of the + + + align:start position:0% +they are saving a lower fraction of the +excess and you can see that the + + align:start position:0% +excess and you can see that the + + + align:start position:0% +excess and you can see that the +consumption is that that the consumption + + align:start position:0% +consumption is that that the consumption + + + align:start position:0% +consumption is that that the consumption +is is higher on average than than in + + align:start position:0% +is is higher on average than than in + + + align:start position:0% +is is higher on average than than in +this one but it's the and the asset + + align:start position:0% +this one but it's the and the asset + + + align:start position:0% +this one but it's the and the asset +level is lower but sometimes the + + align:start position:0% +level is lower but sometimes the + + + align:start position:0% +level is lower but sometimes the +construction Tech is like huge tips + + align:start position:0% +construction Tech is like huge tips + + + align:start position:0% +construction Tech is like huge tips +so depending on someone's level of risk + + align:start position:0% +so depending on someone's level of risk + + + align:start position:0% +so depending on someone's level of risk +aversion they would she would choose + + align:start position:0% +aversion they would she would choose + + + align:start position:0% +aversion they would she would choose +between one of these two process they + + align:start position:0% +between one of these two process they + + + align:start position:0% +between one of these two process they +can choose they can choose more or less + + align:start position:0% +can choose they can choose more or less + + + align:start position:0% +can choose they can choose more or less +stable with the occasional dip or they + + align:start position:0% +stable with the occasional dip or they + + + align:start position:0% +stable with the occasional dip or they +can choose a much less stable with more + + align:start position:0% +can choose a much less stable with more + + + align:start position:0% +can choose a much less stable with more +dips but then they don't have to hold + + align:start position:0% +dips but then they don't have to hold + + + align:start position:0% +dips but then they don't have to hold +all of this cash that they are actually + + align:start position:0% +all of this cash that they are actually + + + align:start position:0% +all of this cash that they are actually +not consuming + + align:start position:0% +not consuming + + + align:start position:0% +not consuming +you don't get any value from the assets + + align:start position:0% +you don't get any value from the assets + + + align:start position:0% +you don't get any value from the assets +it does make you happy to to have all + + align:start position:0% +it does make you happy to to have all + + + align:start position:0% +it does make you happy to to have all +this all this thing in the bank + + align:start position:0% + + + + align:start position:0% + +so that's the neoclassical model for you + + align:start position:0% +so that's the neoclassical model for you + + + align:start position:0% +so that's the neoclassical model for you +that means that uh if someone has a very + + align:start position:0% +that means that uh if someone has a very + + + align:start position:0% +that means that uh if someone has a very +viable income which is the case of the + + align:start position:0% +viable income which is the case of the + + + align:start position:0% +viable income which is the case of the +poor in many developing countries + + align:start position:0% +poor in many developing countries + + + align:start position:0% +poor in many developing countries +uh and if they risk worth then they + + align:start position:0% +uh and if they risk worth then they + + + align:start position:0% +uh and if they risk worth then they +should receive a whole lot in fact even + + align:start position:0% +should receive a whole lot in fact even + + + align:start position:0% +should receive a whole lot in fact even +here where they are saving a whole lot + + align:start position:0% +here where they are saving a whole lot + + + align:start position:0% +here where they are saving a whole lot +they can't fully eliminate bad times + + align:start position:0% +they can't fully eliminate bad times + + + align:start position:0% +they can't fully eliminate bad times +sometimes the bad times arrive and then + + align:start position:0% +sometimes the bad times arrive and then + + + align:start position:0% +sometimes the bad times arrive and then +when they save less then they really + + align:start position:0% +when they save less then they really + + + align:start position:0% +when they save less then they really +have a lot of lean periods + + align:start position:0% + + + + align:start position:0% + +uh so riskaba's households should be + + align:start position:0% +uh so riskaba's households should be + + + align:start position:0% +uh so riskaba's households should be +saving a ton + + align:start position:0% +saving a ton + + + align:start position:0% +saving a ton +if they don't have access to good credit + + align:start position:0% +if they don't have access to good credit + + + align:start position:0% +if they don't have access to good credit +uh which uh + + align:start position:0% +uh which uh + + + align:start position:0% +uh which uh +you can grant grant me for a moment we + + align:start position:0% +you can grant grant me for a moment we + + + align:start position:0% +you can grant grant me for a moment we +are going to do credit for a long moment + + align:start position:0% +are going to do credit for a long moment + + + align:start position:0% +are going to do credit for a long moment +because you're going to see credit uh + + align:start position:0% +because you're going to see credit uh + + + align:start position:0% +because you're going to see credit uh +later uh with Ben but basically it's a + + align:start position:0% +later uh with Ben but basically it's a + + + align:start position:0% +later uh with Ben but basically it's a +fair approximation to say that it's + + align:start position:0% +fair approximation to say that it's + + + align:start position:0% +fair approximation to say that it's +pretty hard for households to rely on + + align:start position:0% +pretty hard for households to rely on + + + align:start position:0% +pretty hard for households to rely on +the credit Market on the + + align:start position:0% +the credit Market on the + + + align:start position:0% +the credit Market on the +well-functioning credit Market to + + align:start position:0% +well-functioning credit Market to + + + align:start position:0% +well-functioning credit Market to +finance consumption when they need it + + align:start position:0% +finance consumption when they need it + + + align:start position:0% +finance consumption when they need it +and therefore they should be saving a + + align:start position:0% +and therefore they should be saving a + + + align:start position:0% +and therefore they should be saving a +ton + + align:start position:0% +ton + + + align:start position:0% +ton +even if they don't have great savings + + align:start position:0% +even if they don't have great savings + + + align:start position:0% +even if they don't have great savings +option even if they don't like savings + + align:start position:0% +option even if they don't like savings + + + align:start position:0% +option even if they don't like savings +account but particularly if they do for + + align:start position:0% +account but particularly if they do for + + + align:start position:0% +account but particularly if they do for +example if they could invest in their + + align:start position:0% +example if they could invest in their + + + align:start position:0% +example if they could invest in their +business and get some return for it then + + align:start position:0% +business and get some return for it then + + + align:start position:0% +business and get some return for it then +they should + + align:start position:0% +they should + + + align:start position:0% +they should +uh and then in fact I'll show you in in + + align:start position:0% +uh and then in fact I'll show you in in + + + align:start position:0% +uh and then in fact I'll show you in in +a minute two papers uh one by Pascal and + + align:start position:0% +a minute two papers uh one by Pascal and + + + align:start position:0% +a minute two papers uh one by Pascal and +Japan John Robinson and one was Simon + + align:start position:0% +Japan John Robinson and one was Simon + + + align:start position:0% +Japan John Robinson and one was Simon +Shanna which shows that uh there are a + + align:start position:0% +Shanna which shows that uh there are a + + + align:start position:0% +Shanna which shows that uh there are a +huge benefit to the business + + align:start position:0% +huge benefit to the business + + + align:start position:0% +huge benefit to the business +to people for people who have small + + align:start position:0% +to people for people who have small + + + align:start position:0% +to people for people who have small +businesses there are huge benefits to + + align:start position:0% +businesses there are huge benefits to + + + align:start position:0% +businesses there are huge benefits to +the business of saving a bit + + align:start position:0% +the business of saving a bit + + + align:start position:0% +the business of saving a bit +so they basically have access to + + align:start position:0% +so they basically have access to + + + align:start position:0% +so they basically have access to +households in particular self-employed + + align:start position:0% +households in particular self-employed + + + align:start position:0% +households in particular self-employed +households have access to to saving + + align:start position:0% +households have access to to saving + + + align:start position:0% +households have access to to saving +opportunities and even if they don't + + align:start position:0% +opportunities and even if they don't + + + align:start position:0% +opportunities and even if they don't +they should just save another mattress + + align:start position:0% +they should just save another mattress + + + align:start position:0% +they should just save another mattress +or in Bullocks or in bad savings + + align:start position:0% +or in Bullocks or in bad savings + + + align:start position:0% +or in Bullocks or in bad savings +opportunity just to avoid this like huge + + align:start position:0% +opportunity just to avoid this like huge + + + align:start position:0% +opportunity just to avoid this like huge +dips that are going to happen from time + + align:start position:0% +dips that are going to happen from time + + + align:start position:0% +dips that are going to happen from time +to time if you cannot borrow + + align:start position:0% +to time if you cannot borrow + + + align:start position:0% +to time if you cannot borrow +so that's so far there is no puzzle + + align:start position:0% +so that's so far there is no puzzle + + + align:start position:0% +so that's so far there is no puzzle +that's just the prediction and where it + + align:start position:0% +that's just the prediction and where it + + + align:start position:0% +that's just the prediction and where it +becomes a puzzle is that they don't + + align:start position:0% +becomes a puzzle is that they don't + + + align:start position:0% +becomes a puzzle is that they don't +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so after this this the people that I'm + + align:start position:0% +so after this this the people that I'm + + + align:start position:0% +so after this this the people that I'm +going to show you where they found that + + align:start position:0% +going to show you where they found that + + + align:start position:0% +going to show you where they found that +when people in Kenya have access to a + + align:start position:0% +when people in Kenya have access to a + + + align:start position:0% +when people in Kenya have access to a +savings account uh that has great impact + + align:start position:0% +savings account uh that has great impact + + + align:start position:0% +savings account uh that has great impact +on their businesses and on their + + align:start position:0% +on their businesses and on their + + + align:start position:0% +on their businesses and on their +consumption and everything is great they + + align:start position:0% +consumption and everything is great they + + + align:start position:0% +consumption and everything is great they +replicated this experiment along with + + align:start position:0% +replicated this experiment along with + + + align:start position:0% +replicated this experiment along with +dinkle and indigoop but + + align:start position:0% +dinkle and indigoop but + + + align:start position:0% +dinkle and indigoop but +in uh in in Uganda Malawi and Chile and + + align:start position:0% +in uh in in Uganda Malawi and Chile and + + + align:start position:0% +in uh in in Uganda Malawi and Chile and +they found that basically very few + + align:start position:0% +they found that basically very few + + + align:start position:0% +they found that basically very few +people had any interest in this account + + align:start position:0% +people had any interest in this account + + + align:start position:0% +people had any interest in this account +uh after all the fee were waived and + + align:start position:0% +uh after all the fee were waived and + + + align:start position:0% +uh after all the fee were waived and +people were given this like basically + + align:start position:0% +people were given this like basically + + + align:start position:0% +people were given this like basically +free savings account so you would think + + align:start position:0% +free savings account so you would think + + + align:start position:0% +free savings account so you would think +if the problem was saving constraint and + + align:start position:0% +if the problem was saving constraint and + + + align:start position:0% +if the problem was saving constraint and +people should + + align:start position:0% +people should + + + align:start position:0% +people should +get hold of it and in fact basically + + align:start position:0% +get hold of it and in fact basically + + + align:start position:0% +get hold of it and in fact basically +people are on this experiment on savings + + align:start position:0% +people are on this experiment on savings + + + align:start position:0% +people are on this experiment on savings +open savings account to people and then + + align:start position:0% +open savings account to people and then + + + align:start position:0% +open savings account to people and then +people say thank you very much and they + + align:start position:0% +people say thank you very much and they + + + align:start position:0% +people say thank you very much and they +don't use them at all so in Uganda 17 + + align:start position:0% +don't use them at all so in Uganda 17 + + + align:start position:0% +don't use them at all so in Uganda 17 +percent Malawi 10 percent Chile three + + align:start position:0% +percent Malawi 10 percent Chile three + + + align:start position:0% +percent Malawi 10 percent Chile three +percent use the accounts + + align:start position:0% +percent use the accounts + + + align:start position:0% +percent use the accounts +so these models are not gonna + + align:start position:0% +so these models are not gonna + + + align:start position:0% +so these models are not gonna +and now elaborate a little bit on these + + align:start position:0% +and now elaborate a little bit on these + + + align:start position:0% +and now elaborate a little bit on these +points but these models the the basic + + align:start position:0% +points but these models the the basic + + + align:start position:0% +points but these models the the basic +model do not rationalize that savings + + align:start position:0% +model do not rationalize that savings + + + align:start position:0% +model do not rationalize that savings +Behavior + + align:start position:0% +Behavior + + + align:start position:0% +Behavior +the people should be willing to say that + + align:start position:0% +the people should be willing to say that + + + align:start position:0% +the people should be willing to say that +negative even if the returns are + + align:start position:0% +negative even if the returns are + + + align:start position:0% +negative even if the returns are +negative just to to avoid this big dips + + align:start position:0% +negative just to to avoid this big dips + + + align:start position:0% +negative just to to avoid this big dips +in consumption + + align:start position:0% +in consumption + + + align:start position:0% +in consumption +so before we + + align:start position:0% +so before we + + + align:start position:0% +so before we +we think about other models let me just + + align:start position:0% +we think about other models let me just + + + align:start position:0% +we think about other models let me just +elaborate a bit on these two to paper + + align:start position:0% +elaborate a bit on these two to paper + + + align:start position:0% +elaborate a bit on these two to paper +so what pascalin dupa and John Robinson + + align:start position:0% +so what pascalin dupa and John Robinson + + + align:start position:0% +so what pascalin dupa and John Robinson +did is that they opened a free savings + + align:start position:0% +did is that they opened a free savings + + + align:start position:0% +did is that they opened a free savings +account for small business owners at the + + align:start position:0% +account for small business owners at the + + + align:start position:0% +account for small business owners at the +local bank + + align:start position:0% +local bank + + + align:start position:0% +local bank +so we are discussing about saving in + + align:start position:0% +so we are discussing about saving in + + + align:start position:0% +so we are discussing about saving in +Bullocks or liquid as a liquid assets so + + align:start position:0% +Bullocks or liquid as a liquid assets so + + + align:start position:0% +Bullocks or liquid as a liquid assets so +why would people do that well it's + + align:start position:0% +why would people do that well it's + + + align:start position:0% +why would people do that well it's +because it's pretty hard for the poor to + + align:start position:0% +because it's pretty hard for the poor to + + + align:start position:0% +because it's pretty hard for the poor to +open savings accounts + + align:start position:0% +open savings accounts + + + align:start position:0% +open savings accounts +and you know why it's hard for the port + + align:start position:0% +and you know why it's hard for the port + + + align:start position:0% +and you know why it's hard for the port +to open savings and why is it so + + align:start position:0% +to open savings and why is it so + + + align:start position:0% +to open savings and why is it so +expensive like seven dollars to open a + + align:start position:0% +expensive like seven dollars to open a + + + align:start position:0% +expensive like seven dollars to open a +to open a savings account for people who + + align:start position:0% +to open a savings account for people who + + + align:start position:0% +to open a savings account for people who +make two dollars a day that's a lot of + + align:start position:0% +make two dollars a day that's a lot of + + + align:start position:0% +make two dollars a day that's a lot of +money proportionally + + align:start position:0% +money proportionally + + + align:start position:0% +money proportionally +so why is it so much uh so expensive to + + align:start position:0% +so why is it so much uh so expensive to + + + align:start position:0% +so why is it so much uh so expensive to +to open + + align:start position:0% +to open + + + align:start position:0% +to open +savings account + + align:start position:0% +savings account + + + align:start position:0% +savings account +why isn't just + + align:start position:0% +why isn't just + + + align:start position:0% +why isn't just +why isn't it just for you + + align:start position:0% +why isn't it just for you + + + align:start position:0% +why isn't it just for you +after all they are putting their money + + align:start position:0% +after all they are putting their money + + + align:start position:0% +after all they are putting their money +in the bank which the people can then + + align:start position:0% +in the bank which the people can then + + + align:start position:0% +in the bank which the people can then +use + + align:start position:0% +use + + + align:start position:0% +use +to invest + + align:start position:0% +to invest + + + align:start position:0% +to invest +right yep our bank is charging for + + align:start position:0% +right yep our bank is charging for + + + align:start position:0% +right yep our bank is charging for +security yes so they are in particular + + align:start position:0% +security yes so they are in particular + + + align:start position:0% +security yes so they are in particular +what's the what's the issue with savings + + align:start position:0% +what's the what's the issue with savings + + + align:start position:0% +what's the what's the issue with savings +as opposed to credit + + align:start position:0% + + + + align:start position:0% + +well yeah they beat your money somewhere + + align:start position:0% +well yeah they beat your money somewhere + + + align:start position:0% +well yeah they beat your money somewhere +but particularly they're re-lending it + + align:start position:0% +but particularly they're re-lending it + + + align:start position:0% +but particularly they're re-lending it +so it's not Security in the form of + + align:start position:0% +so it's not Security in the form of + + + align:start position:0% +so it's not Security in the form of +giving you access to a safe + + align:start position:0% +giving you access to a safe + + + align:start position:0% +giving you access to a safe +because their Banks you know they are + + align:start position:0% +because their Banks you know they are + + + align:start position:0% +because their Banks you know they are +just re-lending it and all that there is + + align:start position:0% +just re-lending it and all that there is + + + align:start position:0% +just re-lending it and all that there is +probably some security but uh I I don't + + align:start position:0% +probably some security but uh I I don't + + + align:start position:0% +probably some security but uh I I don't +think the issue is if + + align:start position:0% +think the issue is if + + + align:start position:0% +think the issue is if +because the money is you know put to use + + align:start position:0% + + + + align:start position:0% + +in fact you would think you know there + + align:start position:0% +in fact you would think you know there + + + align:start position:0% +in fact you would think you know there +is not so much capital of moving around + + align:start position:0% +is not so much capital of moving around + + + align:start position:0% +is not so much capital of moving around +people should like really like to to + + align:start position:0% +people should like really like to to + + + align:start position:0% +people should like really like to to +have liquidities + + align:start position:0% + + + + align:start position:0% + +so why is it that I need to charge so + + align:start position:0% +so why is it that I need to charge so + + + align:start position:0% +so why is it that I need to charge so +much to people to to hold the money + + align:start position:0% +much to people to to hold the money + + + align:start position:0% +much to people to to hold the money +for the privilege of holding the money + + align:start position:0% + + + + align:start position:0% + +well you might think of your money that + + align:start position:0% +well you might think of your money that + + + align:start position:0% +well you might think of your money that +you have in your bank account what + + align:start position:0% +you have in your bank account what + + + align:start position:0% +you have in your bank account what +feature does it have for being in a bank + + align:start position:0% +feature does it have for being in a bank + + + align:start position:0% +feature does it have for being in a bank +account or in savings account + + align:start position:0% + + + + align:start position:0% + +what happens if your bank fails + + align:start position:0% +what happens if your bank fails + + + align:start position:0% +what happens if your bank fails +you lose the money + + align:start position:0% + + + + align:start position:0% + +yes no you don't lose the money we send + + align:start position:0% +yes no you don't lose the money we send + + + align:start position:0% +yes no you don't lose the money we send +good news you do not if it's FDIC + + align:start position:0% +good news you do not if it's FDIC + + + align:start position:0% +good news you do not if it's FDIC +insured uh + + align:start position:0% +insured uh + + + align:start position:0% +insured uh +um up to a limit that I think is + + align:start position:0% +um up to a limit that I think is + + + align:start position:0% +um up to a limit that I think is +relevant for I hope it's irrelevant for + + align:start position:0% +relevant for I hope it's irrelevant for + + + align:start position:0% +relevant for I hope it's irrelevant for +most of them + + align:start position:0% +most of them + + + align:start position:0% +most of them +so it's it's called FDIC insured which + + align:start position:0% +so it's it's called FDIC insured which + + + align:start position:0% +so it's it's called FDIC insured which +is it's the the basically the you cannot + + align:start position:0% +is it's the the basically the you cannot + + + align:start position:0% +is it's the the basically the you cannot +lose your savings the the government + + align:start position:0% +lose your savings the the government + + + align:start position:0% +lose your savings the the government +ensures it same thing in Kenya same + + align:start position:0% +ensures it same thing in Kenya same + + + align:start position:0% +ensures it same thing in Kenya same +thing in Uganda money the money that is + + align:start position:0% +thing in Uganda money the money that is + + + align:start position:0% +thing in Uganda money the money that is +the money that is in savings account and + + align:start position:0% +the money that is in savings account and + + + align:start position:0% +the money that is in savings account and +deposit account is insured + + align:start position:0% +deposit account is insured + + + align:start position:0% +deposit account is insured +you cannot as a bank or the government + + align:start position:0% +you cannot as a bank or the government + + + align:start position:0% +you cannot as a bank or the government +run the risks that people poor people + + align:start position:0% +run the risks that people poor people + + + align:start position:0% +run the risks that people poor people +who have put their savings into your + + align:start position:0% +who have put their savings into your + + + align:start position:0% +who have put their savings into your +bank would lose it + + align:start position:0% +bank would lose it + + + align:start position:0% +bank would lose it +uh so that's why you were right with + + align:start position:0% +uh so that's why you were right with + + + align:start position:0% +uh so that's why you were right with +security although that's not like + + align:start position:0% +security although that's not like + + + align:start position:0% +security although that's not like +physical theft but it's the kind of loss + + align:start position:0% +physical theft but it's the kind of loss + + + align:start position:0% +physical theft but it's the kind of loss +bankruptcy of the bank or this that so + + align:start position:0% +bankruptcy of the bank or this that so + + + align:start position:0% +bankruptcy of the bank or this that so +the money is safe it's FDIC insured + + align:start position:0% +the money is safe it's FDIC insured + + + align:start position:0% +the money is safe it's FDIC insured +but what this means is that uh you know + + align:start position:0% +but what this means is that uh you know + + + align:start position:0% +but what this means is that uh you know +at the bank you need to do all sorts of + + align:start position:0% +at the bank you need to do all sorts of + + + align:start position:0% +at the bank you need to do all sorts of +paperwork to make sure that you know who + + align:start position:0% +paperwork to make sure that you know who + + + align:start position:0% +paperwork to make sure that you know who +has lent to whom and so there is a whole + + align:start position:0% +has lent to whom and so there is a whole + + + align:start position:0% +has lent to whom and so there is a whole +know your customer set of forms that + + align:start position:0% +know your customer set of forms that + + + align:start position:0% +know your customer set of forms that +need to be filled regardless of how much + + align:start position:0% +need to be filled regardless of how much + + + align:start position:0% +need to be filled regardless of how much +money is in the account so there are big + + align:start position:0% +money is in the account so there are big + + + align:start position:0% +money is in the account so there are big +fixed costs of operating + + align:start position:0% +fixed costs of operating + + + align:start position:0% +fixed costs of operating +a savings account so they don't really + + align:start position:0% +a savings account so they don't really + + + align:start position:0% +a savings account so they don't really +want your money in fact + + align:start position:0% +want your money in fact + + + align:start position:0% +want your money in fact +because it's too little money compared + + align:start position:0% +because it's too little money compared + + + align:start position:0% +because it's too little money compared +to the the cost of actually uh creating + + align:start position:0% +to the the cost of actually uh creating + + + align:start position:0% +to the the cost of actually uh creating +the account that is not worth it at all + + align:start position:0% +the account that is not worth it at all + + + align:start position:0% +the account that is not worth it at all +for banks to to to hold Savings of the + + align:start position:0% +for banks to to to hold Savings of the + + + align:start position:0% +for banks to to to hold Savings of the +poor + + align:start position:0% +poor + + + align:start position:0% +poor +and because it's not worth it for them + + align:start position:0% +and because it's not worth it for them + + + align:start position:0% +and because it's not worth it for them +then they don't particularly do it and + + align:start position:0% +then they don't particularly do it and + + + align:start position:0% +then they don't particularly do it and +then you know it's not really a product + + align:start position:0% +then you know it's not really a product + + + align:start position:0% +then you know it's not really a product +that's offered by the market + + align:start position:0% +that's offered by the market + + + align:start position:0% +that's offered by the market +uh in the absence of uh specific + + align:start position:0% +uh in the absence of uh specific + + + align:start position:0% +uh in the absence of uh specific +intervention by + + align:start position:0% +intervention by + + + align:start position:0% +intervention by +governments ngos or or others so in this + + align:start position:0% +governments ngos or or others so in this + + + align:start position:0% +governments ngos or or others so in this +case what they did is that they just + + align:start position:0% +case what they did is that they just + + + align:start position:0% +case what they did is that they just +paid the fee seven dollars opening fee + + align:start position:0% +paid the fee seven dollars opening fee + + + align:start position:0% +paid the fee seven dollars opening fee +once you have your money in your bathing + + align:start position:0% +once you have your money in your bathing + + + align:start position:0% +once you have your money in your bathing +income by the way they can't have no + + align:start position:0% +income by the way they can't have no + + + align:start position:0% +income by the way they can't have no +interest and they have a reasonable fee + + align:start position:0% +interest and they have a reasonable fee + + + align:start position:0% +interest and they have a reasonable fee +or 50 cents for transfer below eight + + align:start position:0% +or 50 cents for transfer below eight + + + align:start position:0% +or 50 cents for transfer below eight +dollars eighty cents between eight and + + align:start position:0% +dollars eighty cents between eight and + + + align:start position:0% +dollars eighty cents between eight and +fifteen and one point five a ball + + align:start position:0% +fifteen and one point five a ball + + + align:start position:0% +fifteen and one point five a ball +so it's very it's actually pretty + + align:start position:0% +so it's very it's actually pretty + + + align:start position:0% +so it's very it's actually pretty +expensive to have your money in the + + align:start position:0% +expensive to have your money in the + + + align:start position:0% +expensive to have your money in the +savings account + + align:start position:0% +savings account + + + align:start position:0% +savings account +and now they are because taking it away + + align:start position:0% +and now they are because taking it away + + + align:start position:0% +and now they are because taking it away +is expensive so it's not necessarily the + + align:start position:0% +is expensive so it's not necessarily the + + + align:start position:0% +is expensive so it's not necessarily the +most attractive accounts but very + + align:start position:0% +most attractive accounts but very + + + align:start position:0% +most attractive accounts but very +representative of the type of savings + + align:start position:0% +representative of the type of savings + + + align:start position:0% +representative of the type of savings +account that would be accessible to + + align:start position:0% +account that would be accessible to + + + align:start position:0% +account that would be accessible to +people + + align:start position:0% +people + + + align:start position:0% +people +uh so we were talking about saving + + align:start position:0% +uh so we were talking about saving + + + align:start position:0% +uh so we were talking about saving +constraints the first one is just this + + align:start position:0% +constraints the first one is just this + + + align:start position:0% +constraints the first one is just this +very basic one it's just like not that + + align:start position:0% +very basic one it's just like not that + + + align:start position:0% +very basic one it's just like not that +easily available and in fact at Baseline + + align:start position:0% +easily available and in fact at Baseline + + + align:start position:0% +easily available and in fact at Baseline +they're working mainly with uh with uh + + align:start position:0% +they're working mainly with uh with uh + + + align:start position:0% +they're working mainly with uh with uh +bicycle taxis + + align:start position:0% +bicycle taxis + + + align:start position:0% +bicycle taxis +called Buddha Buddha and and fruit + + align:start position:0% +called Buddha Buddha and and fruit + + + align:start position:0% +called Buddha Buddha and and fruit +seller the market sellers Etc they're + + align:start position:0% +seller the market sellers Etc they're + + + align:start position:0% +seller the market sellers Etc they're +only two percent of them had an account + + align:start position:0% +only two percent of them had an account + + + align:start position:0% +only two percent of them had an account +so what they did is that they did they + + align:start position:0% +so what they did is that they did they + + + align:start position:0% +so what they did is that they did they +took a baseline uh they opened the + + align:start position:0% +took a baseline uh they opened the + + + align:start position:0% +took a baseline uh they opened the +account to half of them and then they + + align:start position:0% +account to half of them and then they + + + align:start position:0% +account to half of them and then they +asked them to fill diaries that they + + align:start position:0% +asked them to fill diaries that they + + + align:start position:0% +asked them to fill diaries that they +were periodically checking with them uh + + align:start position:0% +were periodically checking with them uh + + + align:start position:0% +were periodically checking with them uh +once a week + + align:start position:0% +once a week + + + align:start position:0% +once a week +they were checking their daily log books + + align:start position:0% +they were checking their daily log books + + + align:start position:0% +they were checking their daily log books +for about three months and that kind of + + align:start position:0% +for about three months and that kind of + + + align:start position:0% +for about three months and that kind of +goes a little bit in trying to + + align:start position:0% +goes a little bit in trying to + + + align:start position:0% +goes a little bit in trying to +understand better their profit and + + align:start position:0% +understand better their profit and + + + align:start position:0% +understand better their profit and +business you know going back to + + align:start position:0% +business you know going back to + + + align:start position:0% +business you know going back to +discussion we had about measuring + + align:start position:0% +discussion we had about measuring + + + align:start position:0% +discussion we had about measuring +savings + + align:start position:0% +savings + + + align:start position:0% +savings +uh so here is what they they found so + + align:start position:0% +uh so here is what they they found so + + + align:start position:0% +uh so here is what they they found so +what's the main finding here + + align:start position:0% + + + + align:start position:0% + +in a sense + + align:start position:0% + + + + align:start position:0% + +yeah do you use it almost immediately + + align:start position:0% +yeah do you use it almost immediately + + + align:start position:0% +yeah do you use it almost immediately +but whatever you're going to put into it + + align:start position:0% +but whatever you're going to put into it + + + align:start position:0% +but whatever you're going to put into it +and then all right so yeah that's number + + align:start position:0% +and then all right so yeah that's number + + + align:start position:0% +and then all right so yeah that's number +of transaction in the first + + align:start position:0% +of transaction in the first + + + align:start position:0% +of transaction in the first +so this thing is not + + align:start position:0% +so this thing is not + + + align:start position:0% +so this thing is not +yet that big mess of zero is telling us + + align:start position:0% + + + + align:start position:0% + +telling us something else than what + + align:start position:0% +telling us something else than what + + + align:start position:0% +telling us something else than what +you're saying + + align:start position:0% +you're saying + + + align:start position:0% +you're saying +telling us that the 55 percent of people + + align:start position:0% +telling us that the 55 percent of people + + + align:start position:0% +telling us that the 55 percent of people +have invested exactly I've done it zero + + align:start position:0% +have invested exactly I've done it zero + + + align:start position:0% +have invested exactly I've done it zero +time I've never done anything with the + + align:start position:0% +time I've never done anything with the + + + align:start position:0% +time I've never done anything with the +account + + align:start position:0% +account + + + align:start position:0% +account +right so that's uh and then these are + + align:start position:0% +right so that's uh and then these are + + + align:start position:0% +right so that's uh and then these are +the people who used it and most of them + + align:start position:0% +the people who used it and most of them + + + align:start position:0% +the people who used it and most of them +use it very little + + align:start position:0% +use it very little + + + align:start position:0% +use it very little +are you right maybe they're putting + + align:start position:0% +are you right maybe they're putting + + + align:start position:0% +are you right maybe they're putting +everything they had in the first six + + align:start position:0% +everything they had in the first six + + + align:start position:0% +everything they had in the first six +months that applies oops and then some + + align:start position:0% +months that applies oops and then some + + + align:start position:0% +months that applies oops and then some +people use it more + + align:start position:0% +people use it more + + + align:start position:0% +people use it more +so that gives you a bank account usage + + align:start position:0% +so that gives you a bank account usage + + + align:start position:0% +so that gives you a bank account usage +of about 40 you know first stage of + + align:start position:0% +of about 40 you know first stage of + + + align:start position:0% +of about 40 you know first stage of +about a 40 percent of people I've + + align:start position:0% +about a 40 percent of people I've + + + align:start position:0% +about a 40 percent of people I've +actually I've used it at least once + + align:start position:0% +actually I've used it at least once + + + align:start position:0% +actually I've used it at least once +uh so on average including the zeros + + align:start position:0% +uh so on average including the zeros + + + align:start position:0% +uh so on average including the zeros +they have more money in the bank + + align:start position:0% +they have more money in the bank + + + align:start position:0% +they have more money in the bank +and then they look at whether they have + + align:start position:0% +and then they look at whether they have + + + align:start position:0% +and then they look at whether they have +more money in other forms so one is + + align:start position:0% +more money in other forms so one is + + + align:start position:0% +more money in other forms so one is +animals the famous Bullocks or other + + align:start position:0% +animals the famous Bullocks or other + + + align:start position:0% +animals the famous Bullocks or other +things and the other is Ross gas + + align:start position:0% +things and the other is Ross gas + + + align:start position:0% +things and the other is Ross gas +contribution those are these rotating + + align:start position:0% +contribution those are these rotating + + + align:start position:0% +contribution those are these rotating +saving and credit association where + + align:start position:0% +saving and credit association where + + + align:start position:0% +saving and credit association where +people sleep together + + align:start position:0% +people sleep together + + + align:start position:0% +people sleep together +so they don't find a substitution from + + align:start position:0% +so they don't find a substitution from + + + align:start position:0% +so they don't find a substitution from +the roskas the the they have if anything + + align:start position:0% +the roskas the the they have if anything + + + align:start position:0% +the roskas the the they have if anything +people are more likely to have animals + + align:start position:0% +people are more likely to have animals + + + align:start position:0% +people are more likely to have animals +perhaps because they accumulated enough + + align:start position:0% +perhaps because they accumulated enough + + + align:start position:0% +perhaps because they accumulated enough +money to buy an animal and have more in + + align:start position:0% +money to buy an animal and have more in + + + align:start position:0% +money to buy an animal and have more in +the bank you notice that they don't try + + align:start position:0% +the bank you notice that they don't try + + + align:start position:0% +the bank you notice that they don't try +to charge savings they don't they don't + + align:start position:0% +to charge savings they don't they don't + + + align:start position:0% +to charge savings they don't they don't +even attempt + + align:start position:0% +even attempt + + + align:start position:0% +even attempt +to measure total ceiling so this goes + + align:start position:0% +to measure total ceiling so this goes + + + align:start position:0% +to measure total ceiling so this goes +back to your question of it's hard to + + align:start position:0% +back to your question of it's hard to + + + align:start position:0% +back to your question of it's hard to +measure savings + + align:start position:0% +measure savings + + + align:start position:0% +measure savings +and then you can look at business + + align:start position:0% +and then you can look at business + + + align:start position:0% +and then you can look at business +outcomes and they found that they are + + align:start position:0% +outcomes and they found that they are + + + align:start position:0% +outcomes and they found that they are +able to invest more in a business uh + + align:start position:0% +able to invest more in a business uh + + + align:start position:0% +able to invest more in a business uh +like business investment of is Lumpy so + + align:start position:0% +like business investment of is Lumpy so + + + align:start position:0% +like business investment of is Lumpy so +they try with and without trimming a + + align:start position:0% +they try with and without trimming a + + + align:start position:0% +they try with and without trimming a +little bit but you get the same kind of + + align:start position:0% +little bit but you get the same kind of + + + align:start position:0% +little bit but you get the same kind of +results this is uh mostly the the woman + + align:start position:0% +results this is uh mostly the the woman + + + align:start position:0% +results this is uh mostly the the woman +as opposed to the men who are cycling + + align:start position:0% +as opposed to the men who are cycling + + + align:start position:0% +as opposed to the men who are cycling +driver + + align:start position:0% +driver + + + align:start position:0% +driver +maybe because they don't need much of an + + align:start position:0% +maybe because they don't need much of an + + + align:start position:0% +maybe because they don't need much of an +investment they just have their Cycles + + align:start position:0% +investment they just have their Cycles + + + align:start position:0% +investment they just have their Cycles +and then when you look at their + + align:start position:0% +and then when you look at their + + + align:start position:0% +and then when you look at their +expenditure or you find that they are + + align:start position:0% +expenditure or you find that they are + + + align:start position:0% +expenditure or you find that they are +able to invest a little more in their + + align:start position:0% +able to invest a little more in their + + + align:start position:0% +able to invest a little more in their +daily expenditure + + align:start position:0% +daily expenditure + + + align:start position:0% +daily expenditure +uh so this this coming back to this idea + + align:start position:0% +uh so this this coming back to this idea + + + align:start position:0% +uh so this this coming back to this idea +that in Saving and then allows them to + + align:start position:0% +that in Saving and then allows them to + + + align:start position:0% +that in Saving and then allows them to +invest in the business which actually + + align:start position:0% +invest in the business which actually + + + align:start position:0% +invest in the business which actually +has a as a positive return so they and + + align:start position:0% +has a as a positive return so they and + + + align:start position:0% +has a as a positive return so they and +then they have somebody down on on + + align:start position:0% +then they have somebody down on on + + + align:start position:0% +then they have somebody down on on +consumption smoothing and they show that + + align:start position:0% +consumption smoothing and they show that + + + align:start position:0% +consumption smoothing and they show that +when people have a shop for example when + + align:start position:0% +when people have a shop for example when + + + align:start position:0% +when people have a shop for example when +they get malaria they consume much more + + align:start position:0% +they get malaria they consume much more + + + align:start position:0% +they get malaria they consume much more +in periods where where they have malaria + + align:start position:0% +in periods where where they have malaria + + + align:start position:0% +in periods where where they have malaria +and they can't work because they have + + align:start position:0% +and they can't work because they have + + + align:start position:0% +and they can't work because they have +some money in the savings uh either in + + align:start position:0% +some money in the savings uh either in + + + align:start position:0% +some money in the savings uh either in +the bank or in or or from the fact that + + align:start position:0% +the bank or in or or from the fact that + + + align:start position:0% +the bank or in or or from the fact that +they are making a bit more + + align:start position:0% +they are making a bit more + + + align:start position:0% +they are making a bit more +so it seems to be that their business is + + align:start position:0% +so it seems to be that their business is + + + align:start position:0% +so it seems to be that their business is +actually a profitable saving investment + + align:start position:0% +actually a profitable saving investment + + + align:start position:0% +actually a profitable saving investment +opportunity + + align:start position:0% +opportunity + + + align:start position:0% +opportunity +but the argument they are making here is + + align:start position:0% +but the argument they are making here is + + + align:start position:0% +but the argument they are making here is +that it's somewhat lumpy so you you know + + align:start position:0% +that it's somewhat lumpy so you you know + + + align:start position:0% +that it's somewhat lumpy so you you know +if you're selling vegetable selling + + align:start position:0% +if you're selling vegetable selling + + + align:start position:0% +if you're selling vegetable selling +charcoal for example you can buy one bag + + align:start position:0% +charcoal for example you can buy one bag + + + align:start position:0% +charcoal for example you can buy one bag +of charcoal or two + + align:start position:0% +of charcoal or two + + + align:start position:0% +of charcoal or two +and then in order to get to the second + + align:start position:0% +and then in order to get to the second + + + align:start position:0% +and then in order to get to the second +one you need to put your money somewhere + + align:start position:0% +one you need to put your money somewhere + + + align:start position:0% +one you need to put your money somewhere +until you can get the second one so they + + align:start position:0% +until you can get the second one so they + + + align:start position:0% +until you can get the second one so they +are this they are return of being able + + align:start position:0% +are this they are return of being able + + + align:start position:0% +are this they are return of being able +to save from time to time in in the + + align:start position:0% +to save from time to time in in the + + + align:start position:0% +to save from time to time in in the +business itself + + align:start position:0% +business itself + + + align:start position:0% +business itself +and this is on top of the consumption + + align:start position:0% +and this is on top of the consumption + + + align:start position:0% +and this is on top of the consumption +smoothing benefits that we discussed + + align:start position:0% +smoothing benefits that we discussed + + + align:start position:0% +smoothing benefits that we discussed +before so it's suggesting that they have + + align:start position:0% +before so it's suggesting that they have + + + align:start position:0% +before so it's suggesting that they have +profitable receiving the opportunity and + + align:start position:0% +profitable receiving the opportunity and + + + align:start position:0% +profitable receiving the opportunity and +they should therefore use them yeah just + + align:start position:0% +they should therefore use them yeah just + + + align:start position:0% +they should therefore use them yeah just +a good qualification and so a little bit + + align:start position:0% +a good qualification and so a little bit + + + align:start position:0% +a good qualification and so a little bit +confused though because if the if the + + align:start position:0% +confused though because if the if the + + + align:start position:0% +confused though because if the if the +accounts paying no interest and it costs + + align:start position:0% +accounts paying no interest and it costs + + + align:start position:0% +accounts paying no interest and it costs +that money to withdraw then why is + + align:start position:0% +that money to withdraw then why is + + + align:start position:0% +that money to withdraw then why is +anyone finding this you know it is the + + align:start position:0% +anyone finding this you know it is the + + + align:start position:0% +anyone finding this you know it is the +primary value of the account just being + + align:start position:0% +primary value of the account just being + + + align:start position:0% +primary value of the account just being +able to put your money somewhere yeah + + align:start position:0% +able to put your money somewhere yeah + + + align:start position:0% +able to put your money somewhere yeah +attempted to use it on something exactly + + align:start position:0% +attempted to use it on something exactly + + + align:start position:0% +attempted to use it on something exactly +so to that C50 plus you know own + + align:start position:0% +so to that C50 plus you know own + + + align:start position:0% +so to that C50 plus you know own +internal + + align:start position:0% +internal + + + align:start position:0% +internal +saving difficulties which we can which I + + align:start position:0% +saving difficulties which we can which I + + + align:start position:0% +saving difficulties which we can which I +can which I'll get to in a minute so in + + align:start position:0% +can which I'll get to in a minute so in + + + align:start position:0% +can which I'll get to in a minute so in +fact the very feature of this money that + + align:start position:0% +fact the very feature of this money that + + + align:start position:0% +fact the very feature of this money that +is hard to withdraw + + align:start position:0% +is hard to withdraw + + + align:start position:0% +is hard to withdraw +might be an attractive feature if you go + + align:start position:0% +might be an attractive feature if you go + + + align:start position:0% +might be an attractive feature if you go +back to the Caroline Zinman Carolyn um + + align:start position:0% +back to the Caroline Zinman Carolyn um + + + align:start position:0% +back to the Caroline Zinman Carolyn um +Ashcraft uh Yin that's uh that's in the + + align:start position:0% +Ashcraft uh Yin that's uh that's in the + + + align:start position:0% +Ashcraft uh Yin that's uh that's in the +sense that's + + align:start position:0% +sense that's + + + align:start position:0% +sense that's +this serves a little bit of these + + align:start position:0% +this serves a little bit of these + + + align:start position:0% +this serves a little bit of these +features which is it's gonna be a bit + + align:start position:0% +features which is it's gonna be a bit + + + align:start position:0% +features which is it's gonna be a bit +costly to withdraw the money so you + + align:start position:0% +costly to withdraw the money so you + + + align:start position:0% +costly to withdraw the money so you +you're not going to do it until you + + align:start position:0% +you're not going to do it until you + + + align:start position:0% +you're not going to do it until you +until you really need it it's going to + + align:start position:0% +until you really need it it's going to + + + align:start position:0% +until you really need it it's going to +put some constraint on you yeah + + align:start position:0% + + + + align:start position:0% + +yeah yeah so here what I'm trying to + + align:start position:0% +yeah yeah so here what I'm trying to + + + align:start position:0% +yeah yeah so here what I'm trying to +make the point is that for household + + align:start position:0% +make the point is that for household + + + align:start position:0% +make the point is that for household +that have a small business they are + + align:start position:0% +that have a small business they are + + + align:start position:0% +that have a small business they are +invest saving is as potentially higher + + align:start position:0% +invest saving is as potentially higher + + + align:start position:0% +invest saving is as potentially higher +returns + + align:start position:0% +returns + + + align:start position:0% +returns +now for for a family that doesn't have a + + align:start position:0% +now for for a family that doesn't have a + + + align:start position:0% +now for for a family that doesn't have a +business then you might not have that + + align:start position:0% +business then you might not have that + + + align:start position:0% +business then you might not have that +uh but in effect the fact that savings + + align:start position:0% +uh but in effect the fact that savings + + + align:start position:0% +uh but in effect the fact that savings +has potentially higher return compounds + + align:start position:0% +has potentially higher return compounds + + + align:start position:0% +has potentially higher return compounds +the the puzzle that was in the first + + align:start position:0% +the the puzzle that was in the first + + + align:start position:0% +the the puzzle that was in the first +slide which is the ticket of savings + + align:start position:0% +slide which is the ticket of savings + + + align:start position:0% +slide which is the ticket of savings +account and any form of savings you can + + align:start position:0% +account and any form of savings you can + + + align:start position:0% +account and any form of savings you can +measure is pretty low + + align:start position:0% +measure is pretty low + + + align:start position:0% +measure is pretty low +so this is the that that's the point the + + align:start position:0% +so this is the that that's the point the + + + align:start position:0% +so this is the that that's the point the +point I'm trying to substantiate there + + align:start position:0% +point I'm trying to substantiate there + + + align:start position:0% +point I'm trying to substantiate there +is that a lot of these people a lot of + + align:start position:0% +is that a lot of these people a lot of + + + align:start position:0% +is that a lot of these people a lot of +the poor have some form of small + + align:start position:0% +the poor have some form of small + + + align:start position:0% +the poor have some form of small +business activities + + align:start position:0% +business activities + + + align:start position:0% +business activities +uh even if they're actually otherwise + + align:start position:0% +uh even if they're actually otherwise + + + align:start position:0% +uh even if they're actually otherwise +working and then if they do it seems to + + align:start position:0% +working and then if they do it seems to + + + align:start position:0% +working and then if they do it seems to +be from the evidence we had that it's + + align:start position:0% +be from the evidence we had that it's + + + align:start position:0% +be from the evidence we had that it's +actually beneficial for them to save in + + align:start position:0% +actually beneficial for them to save in + + + align:start position:0% +actually beneficial for them to save in +this form in the form of the + + align:start position:0% + + + + align:start position:0% + +uh then there is another paper by Simon + + align:start position:0% +uh then there is another paper by Simon + + + align:start position:0% +uh then there is another paper by Simon +Channel which I'm let I'm not going to + + align:start position:0% +Channel which I'm let I'm not going to + + + align:start position:0% +Channel which I'm let I'm not going to +show you the table in detail but it's it + + align:start position:0% +show you the table in detail but it's it + + + align:start position:0% +show you the table in detail but it's it +depends in a sense that that puzzle + + align:start position:0% +depends in a sense that that puzzle + + + align:start position:0% +depends in a sense that that puzzle +because she gives saving incentives in + + align:start position:0% +because she gives saving incentives in + + + align:start position:0% +because she gives saving incentives in +the form of high interest rate for a few + + align:start position:0% +the form of high interest rate for a few + + + align:start position:0% +the form of high interest rate for a few +months + + align:start position:0% +months + + + align:start position:0% +months +uh and then she followed them + + align:start position:0% +uh and then she followed them + + + align:start position:0% +uh and then she followed them +immediately and then 2.5 years later + + align:start position:0% +immediately and then 2.5 years later + + + align:start position:0% +immediately and then 2.5 years later +and what she finds uh is that the + + align:start position:0% +and what she finds uh is that the + + + align:start position:0% +and what she finds uh is that the +they are huge yeah there are large + + align:start position:0% +they are huge yeah there are large + + + align:start position:0% +they are huge yeah there are large +benefits to the small business 2.5 years + + align:start position:0% +benefits to the small business 2.5 years + + + align:start position:0% +benefits to the small business 2.5 years +later + + align:start position:0% +later + + + align:start position:0% +later +so it seems to be that people uh who got + + align:start position:0% +so it seems to be that people uh who got + + + align:start position:0% +so it seems to be that people uh who got +the initial saving incentives started to + + align:start position:0% +the initial saving incentives started to + + + align:start position:0% +the initial saving incentives started to +save and then kind of continued to save + + align:start position:0% +save and then kind of continued to save + + + align:start position:0% +save and then kind of continued to save +somehow and then eventually uh reach + + align:start position:0% +somehow and then eventually uh reach + + + align:start position:0% +somehow and then eventually uh reach +benefits for their businesses + + align:start position:0% +benefits for their businesses + + + align:start position:0% +benefits for their businesses +uh it's a bit of a puzzle why it could + + align:start position:0% +uh it's a bit of a puzzle why it could + + + align:start position:0% +uh it's a bit of a puzzle why it could +be because of some lumpy investment the + + align:start position:0% +be because of some lumpy investment the + + + align:start position:0% +be because of some lumpy investment the +businesses is capable of doing it could + + align:start position:0% +businesses is capable of doing it could + + + align:start position:0% +businesses is capable of doing it could +be because it creates a saving habits + + align:start position:0% +be because it creates a saving habits + + + align:start position:0% +be because it creates a saving habits +that they are continuing with we don't + + align:start position:0% +that they are continuing with we don't + + + align:start position:0% +that they are continuing with we don't +quite know + + align:start position:0% + + + + align:start position:0% + +the reason why I don't want to spend too + + align:start position:0% +the reason why I don't want to spend too + + + align:start position:0% +the reason why I don't want to spend too +much time on that is that I want to go + + align:start position:0% +much time on that is that I want to go + + + align:start position:0% +much time on that is that I want to go +to go back to our car puzzle which is + + align:start position:0% +to go back to our car puzzle which is + + + align:start position:0% +to go back to our car puzzle which is +that + + align:start position:0% +that + + + align:start position:0% +that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +households should save they don't save + + align:start position:0% +households should save they don't save + + + align:start position:0% +households should save they don't save +that much in fact not only they don't + + align:start position:0% +that much in fact not only they don't + + + align:start position:0% +that much in fact not only they don't +save that much but they borrow at very + + align:start position:0% +save that much but they borrow at very + + + align:start position:0% +save that much but they borrow at very +high rates and when they can borrow the + + align:start position:0% +high rates and when they can borrow the + + + align:start position:0% +high rates and when they can borrow the +borrowing is easy is difficult but they + + align:start position:0% +borrowing is easy is difficult but they + + + align:start position:0% +borrowing is easy is difficult but they +can borrow the board at very high rates + + align:start position:0% +can borrow the board at very high rates + + + align:start position:0% +can borrow the board at very high rates +uh and that for for for them for + + align:start position:0% +uh and that for for for them for + + + align:start position:0% +uh and that for for for them for +household to borrow at very high rates + + align:start position:0% +household to borrow at very high rates + + + align:start position:0% +household to borrow at very high rates +borrowing less is a form of uh savings + + align:start position:0% +borrowing less is a form of uh savings + + + align:start position:0% +borrowing less is a form of uh savings +right + + align:start position:0% +right + + + align:start position:0% +right +if we go back to the Euler equation it + + align:start position:0% +if we go back to the Euler equation it + + + align:start position:0% +if we go back to the Euler equation it +tells us that the the ratio of marginal + + align:start position:0% +tells us that the the ratio of marginal + + + align:start position:0% +tells us that the the ratio of marginal +utility should be at least beta r with r + + align:start position:0% +utility should be at least beta r with r + + + align:start position:0% +utility should be at least beta r with r +is now the gross interest rate because + + align:start position:0% +is now the gross interest rate because + + + align:start position:0% +is now the gross interest rate because +it's beta R in when they can and it's + + align:start position:0% +it's beta R in when they can and it's + + + align:start position:0% +it's beta R in when they can and it's +greater when the uh when they are + + align:start position:0% +greater when the uh when they are + + + align:start position:0% +greater when the uh when they are +constrained + + align:start position:0% +constrained + + + align:start position:0% +constrained +uh + + align:start position:0% +uh + + + align:start position:0% +uh +just putting some number it suggests + + align:start position:0% +just putting some number it suggests + + + align:start position:0% +just putting some number it suggests +that the ratio with the CRA preferences + + align:start position:0% +that the ratio with the CRA preferences + + + align:start position:0% +that the ratio with the CRA preferences +this simplifies to do to this that means + + align:start position:0% +this simplifies to do to this that means + + + align:start position:0% +this simplifies to do to this that means +that the consumption should raise really + + align:start position:0% +that the consumption should raise really + + + align:start position:0% +that the consumption should raise really +fast + + align:start position:0% +fast + + + align:start position:0% +fast +for the poorest because they they have + + align:start position:0% +for the poorest because they they have + + + align:start position:0% +for the poorest because they they have +interest in savings and it is beneficial + + align:start position:0% +interest in savings and it is beneficial + + + align:start position:0% +interest in savings and it is beneficial +for them to save because they are they + + align:start position:0% +for them to save because they are they + + + align:start position:0% +for them to save because they are they +are so unhappy being so poor + + align:start position:0% +are so unhappy being so poor + + + align:start position:0% +are so unhappy being so poor +so the return to saving in terms of + + align:start position:0% +so the return to saving in terms of + + + align:start position:0% +so the return to saving in terms of +their utility is very very high because + + align:start position:0% +their utility is very very high because + + + align:start position:0% +their utility is very very high because +when you're poor uh your your marginal + + align:start position:0% +when you're poor uh your your marginal + + + align:start position:0% +when you're poor uh your your marginal +utility of consumption is super high so + + align:start position:0% +utility of consumption is super high so + + + align:start position:0% +utility of consumption is super high so +people they should save and their + + align:start position:0% +people they should save and their + + + align:start position:0% +people they should save and their +consumption should increase fast and of + + align:start position:0% +consumption should increase fast and of + + + align:start position:0% +consumption should increase fast and of +course we don't see that + + align:start position:0% +course we don't see that + + + align:start position:0% +course we don't see that +so uh what could be going on uh + + align:start position:0% + + + + align:start position:0% + +one experiment is kind of more like + + align:start position:0% +one experiment is kind of more like + + + align:start position:0% +one experiment is kind of more like +deepening the puzzle in terms of what + + align:start position:0% +deepening the puzzle in terms of what + + + align:start position:0% +deepening the puzzle in terms of what +could be going on it's a experiment that + + align:start position:0% +could be going on it's a experiment that + + + align:start position:0% +could be going on it's a experiment that +was uh set up originally by Dean Carlin + + align:start position:0% +was uh set up originally by Dean Carlin + + + align:start position:0% +was uh set up originally by Dean Carlin +and Sandy mulanas and stayed idle for a + + align:start position:0% +and Sandy mulanas and stayed idle for a + + + align:start position:0% +and Sandy mulanas and stayed idle for a +long time and finally Ben Rod came and + + align:start position:0% +long time and finally Ben Rod came and + + + align:start position:0% +long time and finally Ben Rod came and +helped them take it to the finish line + + align:start position:0% +helped them take it to the finish line + + + align:start position:0% +helped them take it to the finish line +so it's a Carolina + + align:start position:0% +so it's a Carolina + + + align:start position:0% +so it's a Carolina +very nice people in the area inside + + align:start position:0% +very nice people in the area inside + + + align:start position:0% +very nice people in the area inside +and they kind of provide an Evidence of + + align:start position:0% +and they kind of provide an Evidence of + + + align:start position:0% +and they kind of provide an Evidence of +that oil or equation puzzle which is uh + + align:start position:0% +that oil or equation puzzle which is uh + + + align:start position:0% +that oil or equation puzzle which is uh +they look at vegetable vendors + + align:start position:0% +they look at vegetable vendors + + + align:start position:0% +they look at vegetable vendors +they have a very simple production + + align:start position:0% +they have a very simple production + + + align:start position:0% +they have a very simple production +function you purchase food in the + + align:start position:0% +function you purchase food in the + + + align:start position:0% +function you purchase food in the +morning you sell them through the day + + align:start position:0% +morning you sell them through the day + + + align:start position:0% +morning you sell them through the day +and you uh and then the next morning you + + align:start position:0% +and you uh and then the next morning you + + + align:start position:0% +and you uh and then the next morning you +do the same thing again + + align:start position:0% +do the same thing again + + + align:start position:0% +do the same thing again +so do you constant you constantly need + + align:start position:0% +so do you constant you constantly need + + + align:start position:0% +so do you constant you constantly need +working capital for one day + + align:start position:0% +working capital for one day + + + align:start position:0% +working capital for one day +because you said you buy in the morning + + align:start position:0% +because you said you buy in the morning + + + align:start position:0% +because you said you buy in the morning +and you so how do they finance it + + align:start position:0% +and you so how do they finance it + + + align:start position:0% +and you so how do they finance it +do you know + + align:start position:0% +do you know + + + align:start position:0% +do you know +it's daily uh + + align:start position:0% +it's daily uh + + + align:start position:0% +it's daily uh +How do they + + align:start position:0% +How do they + + + align:start position:0% +How do they +purchase the vegetable in the morning + + align:start position:0% +purchase the vegetable in the morning + + + align:start position:0% +purchase the vegetable in the morning +yeah check out like a pretty high + + align:start position:0% +yeah check out like a pretty high + + + align:start position:0% +yeah check out like a pretty high +interest daily mode they take out the + + align:start position:0% +interest daily mode they take out the + + + align:start position:0% +interest daily mode they take out the +daily loan so what they do is that they + + align:start position:0% +daily loan so what they do is that they + + + align:start position:0% +daily loan so what they do is that they +purchase it from the vendor who give + + align:start position:0% +purchase it from the vendor who give + + + align:start position:0% +purchase it from the vendor who give +from the you know wholesale grocer who + + align:start position:0% +from the you know wholesale grocer who + + + align:start position:0% +from the you know wholesale grocer who +gives them alone and these loans are + + align:start position:0% +gives them alone and these loans are + + + align:start position:0% +gives them alone and these loans are +five percent a day + + align:start position:0% +five percent a day + + + align:start position:0% +five percent a day +so basically people pay uh five percent + + align:start position:0% +so basically people pay uh five percent + + + align:start position:0% +so basically people pay uh five percent +a day so the question is + + align:start position:0% +a day so the question is + + + align:start position:0% +a day so the question is +why are they borrowing at these trades + + align:start position:0% +why are they borrowing at these trades + + + align:start position:0% +why are they borrowing at these trades +why are they not saving saving it + + align:start position:0% +why are they not saving saving it + + + align:start position:0% +why are they not saving saving it +in other way in other words they have + + align:start position:0% +in other way in other words they have + + + align:start position:0% +in other way in other words they have +access to a higher return investment + + align:start position:0% +access to a higher return investment + + + align:start position:0% +access to a higher return investment +which is uh saving a little bit + + align:start position:0% +which is uh saving a little bit + + + align:start position:0% +which is uh saving a little bit +five percent a day is really a lot + + align:start position:0% +five percent a day is really a lot + + + align:start position:0% +five percent a day is really a lot +you can you know write it in an Excel + + align:start position:0% +you can you know write it in an Excel + + + align:start position:0% +you can you know write it in an Excel +sheet and convince yourself that after + + align:start position:0% +sheet and convince yourself that after + + + align:start position:0% +sheet and convince yourself that after +30 days at five five percent a day + + align:start position:0% +30 days at five five percent a day + + + align:start position:0% +30 days at five five percent a day +you'll be quite richer + + align:start position:0% +you'll be quite richer + + + align:start position:0% +you'll be quite richer +so imagine for example that you grip you + + align:start position:0% +so imagine for example that you grip you + + + align:start position:0% +so imagine for example that you grip you +drink one last cup of tea every day + + align:start position:0% +drink one last cup of tea every day + + + align:start position:0% +drink one last cup of tea every day +so you're saving some + + align:start position:0% +so you're saving some + + + align:start position:0% +so you're saving some +small small amount of money and you + + align:start position:0% +small small amount of money and you + + + align:start position:0% +small small amount of money and you +reinvest back in the business such that + + align:start position:0% +reinvest back in the business such that + + + align:start position:0% +reinvest back in the business such that +you uh you uh have to borrow a little + + align:start position:0% +you uh you uh have to borrow a little + + + align:start position:0% +you uh you uh have to borrow a little +less + + align:start position:0% +less + + + align:start position:0% +less +uh in 30 days you would have doubled + + align:start position:0% +uh in 30 days you would have doubled + + + align:start position:0% +uh in 30 days you would have doubled +your income + + align:start position:0% +your income + + + align:start position:0% +your income +by not having to by not having to uh to + + align:start position:0% +by not having to by not having to uh to + + + align:start position:0% +by not having to by not having to uh to +borrow and then you can you know every + + align:start position:0% +borrow and then you can you know every + + + align:start position:0% +borrow and then you can you know every +time then you can take a little bit once + + align:start position:0% +time then you can take a little bit once + + + align:start position:0% +time then you can take a little bit once +you are fully paid off when you don't + + align:start position:0% +you are fully paid off when you don't + + + align:start position:0% +you are fully paid off when you don't +need any money to pay off what you take + + align:start position:0% +need any money to pay off what you take + + + align:start position:0% +need any money to pay off what you take +normally you can take a bit more + + align:start position:0% +normally you can take a bit more + + + align:start position:0% +normally you can take a bit more +so why don't they + + align:start position:0% +so why don't they + + + align:start position:0% +so why don't they +so one possibility is that the the true + + align:start position:0% +so one possibility is that the the true + + + align:start position:0% +so one possibility is that the the true +cost of the loan is different they don't + + align:start position:0% +cost of the loan is different they don't + + + align:start position:0% +cost of the loan is different they don't +want to they want this is how the money + + align:start position:0% +want to they want this is how the money + + + align:start position:0% +want to they want this is how the money +lender slash wholesaler is is working + + align:start position:0% +lender slash wholesaler is is working + + + align:start position:0% +lender slash wholesaler is is working +with them uh + + align:start position:0% +with them uh + + + align:start position:0% +with them uh +maybe you you're not allowed to borrow a + + align:start position:0% +maybe you you're not allowed to borrow a + + + align:start position:0% +maybe you you're not allowed to borrow a +little less you have to do everything on + + align:start position:0% +little less you have to do everything on + + + align:start position:0% +little less you have to do everything on +credit or everything without credit so + + align:start position:0% +credit or everything without credit so + + + align:start position:0% +credit or everything without credit so +there is some fixed thing maybe you + + align:start position:0% +there is some fixed thing maybe you + + + align:start position:0% +there is some fixed thing maybe you +can't cut your uh your consumption + + align:start position:0% +can't cut your uh your consumption + + + align:start position:0% +can't cut your uh your consumption +maybe your ex extraordinarily impatient + + align:start position:0% +maybe your ex extraordinarily impatient + + + align:start position:0% +maybe your ex extraordinarily impatient +uh maybe you don't understand + + align:start position:0% +uh maybe you don't understand + + + align:start position:0% +uh maybe you don't understand +compounding maybe you don't have access + + align:start position:0% +compounding maybe you don't have access + + + align:start position:0% +compounding maybe you don't have access +to a good savings opportunity + + align:start position:0% +to a good savings opportunity + + + align:start position:0% +to a good savings opportunity +uh or maybe the performances are not + + align:start position:0% +uh or maybe the performances are not + + + align:start position:0% +uh or maybe the performances are not +what we wrote and there is something + + align:start position:0% +what we wrote and there is something + + + align:start position:0% +what we wrote and there is something +that makes them more efficient today + + align:start position:0% +that makes them more efficient today + + + align:start position:0% +that makes them more efficient today +than in the future is there in the + + align:start position:0% +than in the future is there in the + + + align:start position:0% +than in the future is there in the +household family Dynamics or our + + align:start position:0% +household family Dynamics or our + + + align:start position:0% +household family Dynamics or our +self-control self-control issues + + align:start position:0% +self-control self-control issues + + + align:start position:0% +self-control self-control issues +so in order to learn a bit about that + + align:start position:0% +so in order to learn a bit about that + + + align:start position:0% +so in order to learn a bit about that +the uh there are two treatment + + align:start position:0% +the uh there are two treatment + + + align:start position:0% +the uh there are two treatment +one where they just paid the entire loan + + align:start position:0% +one where they just paid the entire loan + + + align:start position:0% +one where they just paid the entire loan +so that eliminates a lot of the issues + + align:start position:0% +so that eliminates a lot of the issues + + + align:start position:0% +so that eliminates a lot of the issues +about this uh the fact that the loan + + align:start position:0% +about this uh the fact that the loan + + + align:start position:0% +about this uh the fact that the loan +would have to be fixed uh and um so they + + align:start position:0% +would have to be fixed uh and um so they + + + align:start position:0% +would have to be fixed uh and um so they +just paid + + align:start position:0% +just paid + + + align:start position:0% +just paid +um + + align:start position:0% +um + + + align:start position:0% +um +for 3000 rupees walks of vegetable + + align:start position:0% +for 3000 rupees walks of vegetable + + + align:start position:0% +for 3000 rupees walks of vegetable +and then the second in order to make + + align:start position:0% +and then the second in order to make + + + align:start position:0% +and then the second in order to make +sure that this is not about + + align:start position:0% +sure that this is not about + + + align:start position:0% +sure that this is not about +misunderstanding is that they give sort + + align:start position:0% +misunderstanding is that they give sort + + + align:start position:0% +misunderstanding is that they give sort +of a cash course in financial education + + align:start position:0% +of a cash course in financial education + + + align:start position:0% +of a cash course in financial education +so they they teach this vegetable seller + + align:start position:0% +so they they teach this vegetable seller + + + align:start position:0% +so they they teach this vegetable seller +I have the class where they worked how + + align:start position:0% +I have the class where they worked how + + + align:start position:0% +I have the class where they worked how +much how much they spend in total show + + align:start position:0% +much how much they spend in total show + + + align:start position:0% +much how much they spend in total show +them the benefit of cutting down + + align:start position:0% +them the benefit of cutting down + + + align:start position:0% +them the benefit of cutting down +discussed compound interest rate discuss + + align:start position:0% +discussed compound interest rate discuss + + + align:start position:0% +discussed compound interest rate discuss +what they could have done with the money + + align:start position:0% +what they could have done with the money + + + align:start position:0% +what they could have done with the money +and brainstorm on whether they could cut + + align:start position:0% +and brainstorm on whether they could cut + + + align:start position:0% +and brainstorm on whether they could cut +down consumption so + + align:start position:0% + + + + align:start position:0% + +so the training is to pick up the effect + + align:start position:0% +so the training is to pick up the effect + + + align:start position:0% +so the training is to pick up the effect +of potentially not knowing + + align:start position:0% +of potentially not knowing + + + align:start position:0% +of potentially not knowing +if you if you can't get back consumption + + align:start position:0% +if you if you can't get back consumption + + + align:start position:0% +if you if you can't get back consumption +then because of the stone gear utility + + align:start position:0% +then because of the stone gear utility + + + align:start position:0% +then because of the stone gear utility +function then the buyout should the + + align:start position:0% +function then the buyout should the + + + align:start position:0% +function then the buyout should the +one-time buyout should should put you on + + align:start position:0% +one-time buyout should should put you on + + + align:start position:0% +one-time buyout should should put you on +a on a path to save + + align:start position:0% +a on a path to save + + + align:start position:0% +a on a path to save +and even if you can't save you should + + align:start position:0% +and even if you can't save you should + + + align:start position:0% +and even if you can't save you should +stay be able to stay where you are + + align:start position:0% +stay be able to stay where you are + + + align:start position:0% +stay be able to stay where you are +unless you get hit by a shark + + align:start position:0% +unless you get hit by a shark + + + align:start position:0% +unless you get hit by a shark +in which case you kind of + + align:start position:0% +in which case you kind of + + + align:start position:0% +in which case you kind of +restart from scratch + + align:start position:0% +restart from scratch + + + align:start position:0% +restart from scratch +if they're impeached if if they are + + align:start position:0% +if they're impeached if if they are + + + align:start position:0% +if they're impeached if if they are +impatient or if they have self-control + + align:start position:0% +impatient or if they have self-control + + + align:start position:0% +impatient or if they have self-control +issues uh then you should fall back fast + + align:start position:0% +issues uh then you should fall back fast + + + align:start position:0% +issues uh then you should fall back fast +so that's the uh that's kind of how we + + align:start position:0% +so that's the uh that's kind of how we + + + align:start position:0% +so that's the uh that's kind of how we +can interpret this to treatment + + align:start position:0% +can interpret this to treatment + + + align:start position:0% +can interpret this to treatment +they do this in India and the + + align:start position:0% +they do this in India and the + + + align:start position:0% +they do this in India and the +Philippines as I said uh in Philippines + + align:start position:0% +Philippines as I said uh in Philippines + + + align:start position:0% +Philippines as I said uh in Philippines +they they have the survey every + + align:start position:0% +they they have the survey every + + + align:start position:0% +they they have the survey every +um in two weeks six weeks 10 weeks in + + align:start position:0% +um in two weeks six weeks 10 weeks in + + + align:start position:0% +um in two weeks six weeks 10 weeks in +India three months six months 12 months + + align:start position:0% +India three months six months 12 months + + + align:start position:0% +India three months six months 12 months +um I'll just show you the result for + + align:start position:0% +um I'll just show you the result for + + + align:start position:0% +um I'll just show you the result for +India there's no impact of financial + + align:start position:0% +India there's no impact of financial + + + align:start position:0% +India there's no impact of financial +education so I didn't even put it on the + + align:start position:0% +education so I didn't even put it on the + + + align:start position:0% +education so I didn't even put it on the +on the + + align:start position:0% +on the + + + align:start position:0% +on the +on the slides it's because it's a big + + align:start position:0% +on the slides it's because it's a big + + + align:start position:0% +on the slides it's because it's a big +table uh in uh + + align:start position:0% +table uh in uh + + + align:start position:0% +table uh in uh +for the treatment of buyout and so the + + align:start position:0% +for the treatment of buyout and so the + + + align:start position:0% +for the treatment of buyout and so the +treatment of buyout only and buyout PLUS + + align:start position:0% +treatment of buyout only and buyout PLUS + + + align:start position:0% +treatment of buyout only and buyout PLUS +Financial education is the same and + + align:start position:0% +Financial education is the same and + + + align:start position:0% +Financial education is the same and +financial education has no effect so + + align:start position:0% +financial education has no effect so + + + align:start position:0% +financial education has no effect so +these are a few the first few numbers + + align:start position:0% +these are a few the first few numbers + + + align:start position:0% +these are a few the first few numbers +with buyout only + + align:start position:0% +with buyout only + + + align:start position:0% +with buyout only +where you can see that at two four + + align:start position:0% +where you can see that at two four + + + align:start position:0% +where you can see that at two four +months they have + + align:start position:0% +months they have + + + align:start position:0% +months they have +they have uh they are less likely to + + align:start position:0% +they have uh they are less likely to + + + align:start position:0% +they have uh they are less likely to +have money under that + + align:start position:0% +have money under that + + + align:start position:0% +have money under that +at five to eight months that's gone and + + align:start position:0% +at five to eight months that's gone and + + + align:start position:0% +at five to eight months that's gone and +uh and uh it's then durably gone + + align:start position:0% +uh and uh it's then durably gone + + + align:start position:0% +uh and uh it's then durably gone +so originally of course none of them has + + align:start position:0% +so originally of course none of them has + + + align:start position:0% +so originally of course none of them has +that two to four months later they still + + align:start position:0% +that two to four months later they still + + + align:start position:0% +that two to four months later they still +don't have debt but then it kind of goes + + align:start position:0% +don't have debt but then it kind of goes + + + align:start position:0% +don't have debt but then it kind of goes +away + + align:start position:0% +away + + + align:start position:0% +away +so the The Fallout is relatively quick + + align:start position:0% +so the The Fallout is relatively quick + + + align:start position:0% +so the The Fallout is relatively quick +it's not instant as in the immediately + + align:start position:0% +it's not instant as in the immediately + + + align:start position:0% +it's not instant as in the immediately +blow it in a big party the 3000 rupees + + align:start position:0% +blow it in a big party the 3000 rupees + + + align:start position:0% +blow it in a big party the 3000 rupees +they were given for the day but it's + + align:start position:0% +they were given for the day but it's + + + align:start position:0% +they were given for the day but it's +it's it's it's pretty other way fairly + + align:start position:0% +it's it's it's pretty other way fairly + + + align:start position:0% +it's it's it's pretty other way fairly +quickly + + align:start position:0% +quickly + + + align:start position:0% +quickly +uh so this is the um + + align:start position:0% +uh so this is the um + + + align:start position:0% +uh so this is the um +uh that's the main that's the main + + align:start position:0% +uh that's the main that's the main + + + align:start position:0% +uh that's the main that's the main +impact + + align:start position:0% +impact + + + align:start position:0% +impact +and that means that originally uh yeah + + align:start position:0% +and that means that originally uh yeah + + + align:start position:0% +and that means that originally uh yeah +yeah so that's the first sort of + + align:start position:0% +yeah so that's the first sort of + + + align:start position:0% +yeah so that's the first sort of +interesting fact + + align:start position:0% +interesting fact + + + align:start position:0% +interesting fact +that they seem to in a sense they are + + align:start position:0% +that they seem to in a sense they are + + + align:start position:0% +that they seem to in a sense they are +sitting under a monetary + + align:start position:0% +sitting under a monetary + + + align:start position:0% +sitting under a monetary +just by uh which is stop growing and + + align:start position:0% +just by uh which is stop growing and + + + align:start position:0% +just by uh which is stop growing and +they don't take advantage of the food + + align:start position:0% +they don't take advantage of the food + + + align:start position:0% +they don't take advantage of the food +from that monitoring + + align:start position:0% +from that monitoring + + + align:start position:0% +from that monitoring +there are many other examples + + align:start position:0% +there are many other examples + + + align:start position:0% +there are many other examples +a bunch of nice people that try to that + + align:start position:0% +a bunch of nice people that try to that + + + align:start position:0% +a bunch of nice people that try to that +makes the same effect for example John + + align:start position:0% +makes the same effect for example John + + + align:start position:0% +makes the same effect for example John +Robinson and Lori Beaman have a paper + + align:start position:0% +Robinson and Lori Beaman have a paper + + + align:start position:0% +Robinson and Lori Beaman have a paper +where they simply observe that often + + align:start position:0% +where they simply observe that often + + + align:start position:0% +where they simply observe that often +people in shops don't have a cell phone + + align:start position:0% +people in shops don't have a cell phone + + + align:start position:0% +people in shops don't have a cell phone +count + + align:start position:0% +count + + + align:start position:0% +count +and a cell phone card is what people buy + + align:start position:0% +and a cell phone card is what people buy + + + align:start position:0% +and a cell phone card is what people buy +to get prepaid money on your phone it + + align:start position:0% +to get prepaid money on your phone it + + + align:start position:0% +to get prepaid money on your phone it +doesn't spoil + + align:start position:0% +doesn't spoil + + + align:start position:0% +doesn't spoil +uh I don't think it can even be stolen + + align:start position:0% +uh I don't think it can even be stolen + + + align:start position:0% +uh I don't think it can even be stolen +because if you if they were stolen you + + align:start position:0% +because if you if they were stolen you + + + align:start position:0% +because if you if they were stolen you +could call the office and say my car to + + align:start position:0% +could call the office and say my car to + + + align:start position:0% +could call the office and say my car to +go the card got stolen it it doesn't + + align:start position:0% +go the card got stolen it it doesn't + + + align:start position:0% +go the card got stolen it it doesn't +take any space + + align:start position:0% +take any space + + + align:start position:0% +take any space +uh so and people keep coming to you and + + align:start position:0% +uh so and people keep coming to you and + + + align:start position:0% +uh so and people keep coming to you and +buying them in small increments since + + align:start position:0% +buying them in small increments since + + + align:start position:0% +buying them in small increments since +they don't have any savings they want so + + align:start position:0% +they don't have any savings they want so + + + align:start position:0% +they don't have any savings they want so +it's and on each of them you make a + + align:start position:0% +it's and on each of them you make a + + + align:start position:0% +it's and on each of them you make a +small amount of money + + align:start position:0% +small amount of money + + + align:start position:0% +small amount of money +so you think you'd always want to have + + align:start position:0% +so you think you'd always want to have + + + align:start position:0% +so you think you'd always want to have +uh this cell phone card + + align:start position:0% +uh this cell phone card + + + align:start position:0% +uh this cell phone card +and yet very frequently they just don't + + align:start position:0% +and yet very frequently they just don't + + + align:start position:0% +and yet very frequently they just don't +have them the little shops + + align:start position:0% +have them the little shops + + + align:start position:0% +have them the little shops +uh so they miss out on the cell and + + align:start position:0% +uh so they miss out on the cell and + + + align:start position:0% +uh so they miss out on the cell and +someone else is making the sale so + + align:start position:0% +someone else is making the sale so + + + align:start position:0% +someone else is making the sale so +that's kind of another kind of + + align:start position:0% +that's kind of another kind of + + + align:start position:0% +that's kind of another kind of +uh missed opportunity that comes from + + align:start position:0% +uh missed opportunity that comes from + + + align:start position:0% +uh missed opportunity that comes from +just not having the liquidity and not + + align:start position:0% +just not having the liquidity and not + + + align:start position:0% +just not having the liquidity and not +having the ability to save in money + + align:start position:0% +having the ability to save in money + + + align:start position:0% +having the ability to save in money +cards saving in Monica and it seems like + + align:start position:0% +cards saving in Monica and it seems like + + + align:start position:0% +cards saving in Monica and it seems like +a perfect investment a perfect way to + + align:start position:0% +a perfect investment a perfect way to + + + align:start position:0% +a perfect investment a perfect way to +save for a for a shop owner + + align:start position:0% +save for a for a shop owner + + + align:start position:0% +save for a for a shop owner +another example to which we'll come back + + align:start position:0% +another example to which we'll come back + + + align:start position:0% +another example to which we'll come back +to one at the very end of the lecture is + + align:start position:0% +to one at the very end of the lecture is + + + align:start position:0% +to one at the very end of the lecture is +um + + align:start position:0% +um + + + align:start position:0% +um +Michael Michael Karma John Robinson and + + align:start position:0% +Michael Michael Karma John Robinson and + + + align:start position:0% +Michael Michael Karma John Robinson and +myself have a series of paper on + + align:start position:0% +myself have a series of paper on + + + align:start position:0% +myself have a series of paper on +fertilizer and asking why people aren't + + align:start position:0% +fertilizer and asking why people aren't + + + align:start position:0% +fertilizer and asking why people aren't +investing in fertilizer in Kenya again + + align:start position:0% +investing in fertilizer in Kenya again + + + align:start position:0% +investing in fertilizer in Kenya again +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +despite the fact that through to our + + align:start position:0% +despite the fact that through to our + + + align:start position:0% +despite the fact that through to our +first hypothesis that maybe it's not + + align:start position:0% +first hypothesis that maybe it's not + + + align:start position:0% +first hypothesis that maybe it's not +profitable but we conducted a series of + + align:start position:0% +profitable but we conducted a series of + + + align:start position:0% +profitable but we conducted a series of +experiments showing that it appears to + + align:start position:0% +experiments showing that it appears to + + + align:start position:0% +experiments showing that it appears to +be quite profitable so despite the fact + + align:start position:0% +be quite profitable so despite the fact + + + align:start position:0% +be quite profitable so despite the fact +that fertilizer is profitable people + + align:start position:0% +that fertilizer is profitable people + + + align:start position:0% +that fertilizer is profitable people +don't seem to be saving in + + align:start position:0% +don't seem to be saving in + + + align:start position:0% +don't seem to be saving in +saving in + + align:start position:0% +saving in + + + align:start position:0% +saving in +in the form of fertilizer which is + + align:start position:0% +in the form of fertilizer which is + + + align:start position:0% +in the form of fertilizer which is +basically buying fertilizer at the when + + align:start position:0% +basically buying fertilizer at the when + + + align:start position:0% +basically buying fertilizer at the when +it's time to plant it + + align:start position:0% +it's time to plant it + + + align:start position:0% +it's time to plant it +then it's in the ground for a while but + + align:start position:0% +then it's in the ground for a while but + + + align:start position:0% +then it's in the ground for a while but +then you have much more much more + + align:start position:0% +then you have much more much more + + + align:start position:0% +then you have much more much more +fertilizer on people aren't able to so + + align:start position:0% +fertilizer on people aren't able to so + + + align:start position:0% +fertilizer on people aren't able to so +what they say is that they don't have + + align:start position:0% +what they say is that they don't have + + + align:start position:0% +what they say is that they don't have +the money when it comes time to planting + + align:start position:0% +the money when it comes time to planting + + + align:start position:0% +the money when it comes time to planting +which basically what it means they have + + align:start position:0% +which basically what it means they have + + + align:start position:0% +which basically what it means they have +an accumulated enough to save I also + + align:start position:0% +an accumulated enough to save I also + + + align:start position:0% +an accumulated enough to save I also +asked why people are not doing it yeah + + align:start position:0% +asked why people are not doing it yeah + + + align:start position:0% +asked why people are not doing it yeah +that's what they say is and we finally + + align:start position:0% +that's what they say is and we finally + + + align:start position:0% +that's what they say is and we finally +for frustrated that doesn't mean + + align:start position:0% +for frustrated that doesn't mean + + + align:start position:0% +for frustrated that doesn't mean +anything how can you not have the money + + align:start position:0% +anything how can you not have the money + + + align:start position:0% +anything how can you not have the money +it's divisible + + align:start position:0% +it's divisible + + + align:start position:0% +it's divisible +so if you have three cents just by three + + align:start position:0% +so if you have three cents just by three + + + align:start position:0% +so if you have three cents just by three +cents worth of fertilizer but it's like + + align:start position:0% +cents worth of fertilizer but it's like + + + align:start position:0% +cents worth of fertilizer but it's like +oh we have to go to the place to the + + align:start position:0% +oh we have to go to the place to the + + + align:start position:0% +oh we have to go to the place to the +shop and we have to buy the fertilizer + + align:start position:0% +shop and we have to buy the fertilizer + + + align:start position:0% +shop and we have to buy the fertilizer +it's not worth it if you're not gonna do + + align:start position:0% +it's not worth it if you're not gonna do + + + align:start position:0% +it's not worth it if you're not gonna do +a little bit more + + align:start position:0% +a little bit more + + + align:start position:0% +a little bit more +so I don't know whether I agree with + + align:start position:0% +so I don't know whether I agree with + + + align:start position:0% +so I don't know whether I agree with +that but it's basically they say that's + + align:start position:0% +that but it's basically they say that's + + + align:start position:0% +that but it's basically they say that's +because at the time of planting they + + align:start position:0% +because at the time of planting they + + + align:start position:0% +because at the time of planting they +don't have the money + + align:start position:0% +don't have the money + + + align:start position:0% +don't have the money +and uh uh options that are available + + align:start position:0% +and uh uh options that are available + + + align:start position:0% +and uh uh options that are available +exactly so let me go back to uh let me + + align:start position:0% +exactly so let me go back to uh let me + + + align:start position:0% +exactly so let me go back to uh let me +go back to that that's kind of what we + + align:start position:0% +go back to that that's kind of what we + + + align:start position:0% +go back to that that's kind of what we +introduced + + align:start position:0% +introduced + + + align:start position:0% +introduced +um + + align:start position:0% +um + + + align:start position:0% +um +but that seems that basically uh at + + align:start position:0% +but that seems that basically uh at + + + align:start position:0% +but that seems that basically uh at +Harvest they have lots of maize which is + + align:start position:0% +Harvest they have lots of maize which is + + + align:start position:0% +Harvest they have lots of maize which is +basically lots of money because Macy's + + align:start position:0% +basically lots of money because Macy's + + + align:start position:0% +basically lots of money because Macy's +gets sold for money and they buy and + + align:start position:0% +gets sold for money and they buy and + + + align:start position:0% +gets sold for money and they buy and +sell Maize so at Harvest they have lots + + align:start position:0% +sell Maize so at Harvest they have lots + + + align:start position:0% +sell Maize so at Harvest they have lots +of money but it's not the time to put + + align:start position:0% +of money but it's not the time to put + + + align:start position:0% +of money but it's not the time to put +the fertilizer in + + align:start position:0% +the fertilizer in + + + align:start position:0% +the fertilizer in +at that time they don't go to buy the + + align:start position:0% +at that time they don't go to buy the + + + align:start position:0% +at that time they don't go to buy the +fertilizer then + + align:start position:0% +fertilizer then + + + align:start position:0% +fertilizer then +a few you know three months later it's + + align:start position:0% +a few you know three months later it's + + + align:start position:0% +a few you know three months later it's +the time to put the fertilizer in the + + align:start position:0% +the time to put the fertilizer in the + + + align:start position:0% +the time to put the fertilizer in the +ground but they don't have money anymore + + align:start position:0% +ground but they don't have money anymore + + + align:start position:0% +ground but they don't have money anymore +they feel poor they're not sure they're + + align:start position:0% +they feel poor they're not sure they're + + + align:start position:0% +they feel poor they're not sure they're +going to be able to stretch their Mist + + align:start position:0% +going to be able to stretch their Mist + + + align:start position:0% +going to be able to stretch their Mist +till the end of the season so they don't + + align:start position:0% +till the end of the season so they don't + + + align:start position:0% +till the end of the season so they don't +want to to put money into fertilizer + + align:start position:0% +want to to put money into fertilizer + + + align:start position:0% +want to to put money into fertilizer +that's a puzzle that's another puzzle so + + align:start position:0% +that's a puzzle that's another puzzle so + + + align:start position:0% +that's a puzzle that's another puzzle so +let's hold that puzzle in mind for now + + align:start position:0% +let's hold that puzzle in mind for now + + + align:start position:0% +let's hold that puzzle in mind for now +uh and uh but that's another example of + + align:start position:0% +uh and uh but that's another example of + + + align:start position:0% +uh and uh but that's another example of +a missed opportunity you know people are + + align:start position:0% +a missed opportunity you know people are + + + align:start position:0% +a missed opportunity you know people are +not able to save enough to buy a bag of + + align:start position:0% +not able to save enough to buy a bag of + + + align:start position:0% +not able to save enough to buy a bag of +fertilizer + + align:start position:0% + + + + align:start position:0% + +so how can we explain that well one sort + + align:start position:0% +so how can we explain that well one sort + + + align:start position:0% +so how can we explain that well one sort +of + + align:start position:0% +of + + + align:start position:0% +of +way that uh + + align:start position:0% +way that uh + + + align:start position:0% +way that uh +we have already sort of circled around + + align:start position:0% +we have already sort of circled around + + + align:start position:0% +we have already sort of circled around +and hinted in in the whole class is the + + align:start position:0% +and hinted in in the whole class is the + + + align:start position:0% +and hinted in in the whole class is the +idea that uh that this concrete is + + align:start position:0% +idea that uh that this concrete is + + + align:start position:0% +idea that uh that this concrete is +really low + + align:start position:0% +really low + + + align:start position:0% +really low +or in fact uh it's uh people are of + + align:start position:0% +or in fact uh it's uh people are of + + + align:start position:0% +or in fact uh it's uh people are of +individual inconsistent time preferences + + align:start position:0% +individual inconsistent time preferences + + + align:start position:0% +individual inconsistent time preferences +so the discount rate might be different + + align:start position:0% +so the discount rate might be different + + + align:start position:0% +so the discount rate might be different +for the present and for the future + + align:start position:0% + + + + align:start position:0% + +so you can so the + + align:start position:0% +so you can so the + + + align:start position:0% +so you can so the +the standard way that this is modeled + + align:start position:0% +the standard way that this is modeled + + + align:start position:0% +the standard way that this is modeled +and I think Frank introduced it briefly + + align:start position:0% +and I think Frank introduced it briefly + + + align:start position:0% +and I think Frank introduced it briefly +when he did his lecture is the idea of + + align:start position:0% +when he did his lecture is the idea of + + + align:start position:0% +when he did his lecture is the idea of +hyperbolic time discount team where + + align:start position:0% +hyperbolic time discount team where + + + align:start position:0% +hyperbolic time discount team where +the the entire future + + align:start position:0% +the the entire future + + + align:start position:0% +the the entire future +is discounted more from viewed from + + align:start position:0% +is discounted more from viewed from + + + align:start position:0% +is discounted more from viewed from +today then tomorrow is discounted then + + align:start position:0% +today then tomorrow is discounted then + + + align:start position:0% +today then tomorrow is discounted then +Day After Tomorrow is discounted with + + align:start position:0% +Day After Tomorrow is discounted with + + + align:start position:0% +Day After Tomorrow is discounted with +respect to two more + + align:start position:0% +respect to two more + + + align:start position:0% +respect to two more +so that's the hyperbolic discounting + + align:start position:0% +so that's the hyperbolic discounting + + + align:start position:0% +so that's the hyperbolic discounting +model + + align:start position:0% +model + + + align:start position:0% +model +more generally + + align:start position:0% +more generally + + + align:start position:0% +more generally +again as you saw it in in Frank's + + align:start position:0% +again as you saw it in in Frank's + + + align:start position:0% +again as you saw it in in Frank's +lecture + + align:start position:0% +lecture + + + align:start position:0% +lecture +either and good or money people seem to + + align:start position:0% +either and good or money people seem to + + + align:start position:0% +either and good or money people seem to +think differently about the future than + + align:start position:0% +think differently about the future than + + + align:start position:0% +think differently about the future than +about today + + align:start position:0% +about today + + + align:start position:0% +about today +so for example uh there is an experiment + + align:start position:0% +so for example uh there is an experiment + + + align:start position:0% +so for example uh there is an experiment +where people are given an opportunity to + + align:start position:0% +where people are given an opportunity to + + + align:start position:0% +where people are given an opportunity to +choose a movie video from a set of + + align:start position:0% +choose a movie video from a set of + + + align:start position:0% +choose a movie video from a set of +24-hour titles + + align:start position:0% +24-hour titles + + + align:start position:0% +24-hour titles +including for example four weddings and + + align:start position:0% +including for example four weddings and + + + align:start position:0% +including for example four weddings and +a funeral + + align:start position:0% +a funeral + + + align:start position:0% +a funeral +that's that's deep to study I don't know + + align:start position:0% +that's that's deep to study I don't know + + + align:start position:0% +that's that's deep to study I don't know +probably you were you were in + + align:start position:0% +probably you were you were in + + + align:start position:0% +probably you were you were in +Bournemouth for a wedding and a funeral + + align:start position:0% +Bournemouth for a wedding and a funeral + + + align:start position:0% +Bournemouth for a wedding and a funeral +was a was shown but it's uh it's fun and + + align:start position:0% +was a was shown but it's uh it's fun and + + + align:start position:0% +was a was shown but it's uh it's fun and +it's liberal + + align:start position:0% +it's liberal + + + align:start position:0% +it's liberal +and you also had the Schindler's List + + align:start position:0% +and you also had the Schindler's List + + + align:start position:0% +and you also had the Schindler's List +which is not logo + + align:start position:0% +which is not logo + + + align:start position:0% +which is not logo +and the point is that when choosing for + + align:start position:0% +and the point is that when choosing for + + + align:start position:0% +and the point is that when choosing for +today 56 percent choose lowbrow + + align:start position:0% +today 56 percent choose lowbrow + + + align:start position:0% +today 56 percent choose lowbrow +so far wedding and a funeral versus the + + align:start position:0% +so far wedding and a funeral versus the + + + align:start position:0% +so far wedding and a funeral versus the +cinderellix but for choosing for next + + align:start position:0% +cinderellix but for choosing for next + + + align:start position:0% +cinderellix but for choosing for next +Monday 37 percent choose the logo and + + align:start position:0% +Monday 37 percent choose the logo and + + + align:start position:0% +Monday 37 percent choose the logo and +frustrating for the Monday even in two + + align:start position:0% +frustrating for the Monday even in two + + + align:start position:0% +frustrating for the Monday even in two +weeks 29 percent choose the Luma + + align:start position:0% +weeks 29 percent choose the Luma + + + align:start position:0% +weeks 29 percent choose the Luma +uh so that's that shows that so it could + + align:start position:0% +uh so that's that shows that so it could + + + align:start position:0% +uh so that's that shows that so it could +be a put in the index + + align:start position:0% +be a put in the index + + + align:start position:0% +be a put in the index +um inconsistent uh it's certainly + + align:start position:0% +um inconsistent uh it's certainly + + + align:start position:0% +um inconsistent uh it's certainly +inconsistent time preferences in terms + + align:start position:0% +inconsistent time preferences in terms + + + align:start position:0% +inconsistent time preferences in terms +of goods you seem to have your different + + align:start position:0% +of goods you seem to have your different + + + align:start position:0% +of goods you seem to have your different +preferences for today then for next + + align:start position:0% +preferences for today then for next + + + align:start position:0% +preferences for today then for next +month they are for the Monday after it + + align:start position:0% +month they are for the Monday after it + + + align:start position:0% +month they are for the Monday after it +could be caught in couch in hyperbolic + + align:start position:0% +could be caught in couch in hyperbolic + + + align:start position:0% +could be caught in couch in hyperbolic +discounting + + align:start position:0% +discounting + + + align:start position:0% +discounting +but more generally we could write it in + + align:start position:0% +but more generally we could write it in + + + align:start position:0% +but more generally we could write it in +saying well there are only two type of + + align:start position:0% +saying well there are only two type of + + + align:start position:0% +saying well there are only two type of +things that we two type of goods they + + align:start position:0% +things that we two type of goods they + + + align:start position:0% +things that we two type of goods they +are the goods that we really enjoy now + + align:start position:0% +are the goods that we really enjoy now + + + align:start position:0% +are the goods that we really enjoy now +and we enjoy in the future and they are + + align:start position:0% +and we enjoy in the future and they are + + + align:start position:0% +and we enjoy in the future and they are +the goods that we only enjoy + + align:start position:0% +the goods that we only enjoy + + + align:start position:0% +the goods that we only enjoy +we enjoy if we consume them today but we + + align:start position:0% +we enjoy if we consume them today but we + + + align:start position:0% +we enjoy if we consume them today but we +don't look forward to consuming them in + + align:start position:0% +don't look forward to consuming them in + + + align:start position:0% +don't look forward to consuming them in +the future + + align:start position:0% +the future + + + align:start position:0% +the future +so with uh watching uh for wedding and a + + align:start position:0% +so with uh watching uh for wedding and a + + + align:start position:0% +so with uh watching uh for wedding and a +funeral + + align:start position:0% +funeral + + + align:start position:0% +funeral +so let me first take the example of + + align:start position:0% +so let me first take the example of + + + align:start position:0% +so let me first take the example of +a big + + align:start position:0% +a big + + + align:start position:0% +a big +sweet double glazed Krispy Kreme donuts + + align:start position:0% +sweet double glazed Krispy Kreme donuts + + + align:start position:0% +sweet double glazed Krispy Kreme donuts +uh you if it's in front of you in the + + align:start position:0% +uh you if it's in front of you in the + + + align:start position:0% +uh you if it's in front of you in the +shop you said oh I would really like I + + align:start position:0% +shop you said oh I would really like I + + + align:start position:0% +shop you said oh I would really like I +really want it now and you'd feel quite + + align:start position:0% +really want it now and you'd feel quite + + + align:start position:0% +really want it now and you'd feel quite +happy having eating it + + align:start position:0% +happy having eating it + + + align:start position:0% +happy having eating it +but if you think about yourself tomorrow + + align:start position:0% +but if you think about yourself tomorrow + + + align:start position:0% +but if you think about yourself tomorrow +and say + + align:start position:0% +and say + + + align:start position:0% +and say +would I you know every everything taken + + align:start position:0% +would I you know every everything taken + + + align:start position:0% +would I you know every everything taken +into account would I really like uh my + + align:start position:0% +into account would I really like uh my + + + align:start position:0% +into account would I really like uh my +future yourself to eat that thing + + align:start position:0% +future yourself to eat that thing + + + align:start position:0% +future yourself to eat that thing +it's like not really + + align:start position:0% +it's like not really + + + align:start position:0% +it's like not really +so that's the donut is uh is a an + + align:start position:0% +so that's the donut is uh is a an + + + align:start position:0% +so that's the donut is uh is a an +example of a Temptation good which is + + align:start position:0% +example of a Temptation good which is + + + align:start position:0% +example of a Temptation good which is +you would enjoy it if you eat now but + + align:start position:0% +you would enjoy it if you eat now but + + + align:start position:0% +you would enjoy it if you eat now but +you don't derive any Joy from thinking + + align:start position:0% +you don't derive any Joy from thinking + + + align:start position:0% +you don't derive any Joy from thinking +about yourself eating it in the future + + align:start position:0% +about yourself eating it in the future + + + align:start position:0% +about yourself eating it in the future +in fact you might you know see the + + align:start position:0% +in fact you might you know see the + + + align:start position:0% +in fact you might you know see the +opposite you might become + + align:start position:0% +opposite you might become + + + align:start position:0% +opposite you might become +uh similarly spending time on on + + align:start position:0% +uh similarly spending time on on + + + align:start position:0% +uh similarly spending time on on +Facebook + + align:start position:0% +Facebook + + + align:start position:0% +Facebook +I + + align:start position:0% +I + + + align:start position:0% +I +um there is a nice paper + + align:start position:0% +um there is a nice paper + + + align:start position:0% +um there is a nice paper +by Matt ginskill and + + align:start position:0% +by Matt ginskill and + + + align:start position:0% +by Matt ginskill and +hunter + + align:start position:0% +hunter + + + align:start position:0% +hunter +called digital addiction + + align:start position:0% +called digital addiction + + + align:start position:0% +called digital addiction +showing that + + align:start position:0% +showing that + + + align:start position:0% +showing that +basically paying people to give up on + + align:start position:0% +basically paying people to give up on + + + align:start position:0% +basically paying people to give up on +the on internet and showing that people + + align:start position:0% +the on internet and showing that people + + + align:start position:0% +the on internet and showing that people +when they think about the Facebook + + align:start position:0% +when they think about the Facebook + + + align:start position:0% +when they think about the Facebook +Twitter and the like + + align:start position:0% +Twitter and the like + + + align:start position:0% +Twitter and the like +Instagram + + align:start position:0% +Instagram + + + align:start position:0% +Instagram +the uh they would like to consume less + + align:start position:0% +the uh they would like to consume less + + + align:start position:0% +the uh they would like to consume less +of it in the future + + align:start position:0% +of it in the future + + + align:start position:0% +of it in the future +so they do not enjoy thinking about + + align:start position:0% +so they do not enjoy thinking about + + + align:start position:0% +so they do not enjoy thinking about +themselves doing it in the future but on + + align:start position:0% +themselves doing it in the future but on + + + align:start position:0% +themselves doing it in the future but on +the other hand today they don't want to + + align:start position:0% +the other hand today they don't want to + + + align:start position:0% +the other hand today they don't want to +stop you would need to pay them a lot to + + align:start position:0% +stop you would need to pay them a lot to + + + align:start position:0% +stop you would need to pay them a lot to +stop today + + align:start position:0% +stop today + + + align:start position:0% +stop today +so that's another example of a + + align:start position:0% +so that's another example of a + + + align:start position:0% +so that's another example of a +Temptation good and similarly of course + + align:start position:0% +Temptation good and similarly of course + + + align:start position:0% +Temptation good and similarly of course +you with the example of for wedding and + + align:start position:0% +you with the example of for wedding and + + + align:start position:0% +you with the example of for wedding and +a funeral and she does this you would + + align:start position:0% +a funeral and she does this you would + + + align:start position:0% +a funeral and she does this you would +really you would it would be very fun to + + align:start position:0% +really you would it would be very fun to + + + align:start position:0% +really you would it would be very fun to +watch it now but in the future you might + + align:start position:0% +watch it now but in the future you might + + + align:start position:0% +watch it now but in the future you might +like your future self to watch the scene + + align:start position:0% +like your future self to watch the scene + + + align:start position:0% +like your future self to watch the scene +like this because that's more + + align:start position:0% +like this because that's more + + + align:start position:0% +like this because that's more +educational + + align:start position:0% +educational + + + align:start position:0% +educational +so that's the + + align:start position:0% +so that's the + + + align:start position:0% +so that's the +that's the the point uh + + align:start position:0% +that's the the point uh + + + align:start position:0% +that's the the point uh +So within so so there are two barriers + + align:start position:0% +So within so so there are two barriers + + + align:start position:0% +So within so so there are two barriers +that so and within each parallel + + align:start position:0% +that so and within each parallel + + + align:start position:0% +that so and within each parallel +potentially infinite number of period + + align:start position:0% +potentially infinite number of period + + + align:start position:0% +potentially infinite number of period +but even two is sufficient to to start + + align:start position:0% +but even two is sufficient to to start + + + align:start position:0% +but even two is sufficient to to start +creating this uh to create that + + align:start position:0% +creating this uh to create that + + + align:start position:0% +creating this uh to create that +inconsistency + + align:start position:0% +inconsistency + + + align:start position:0% +inconsistency +and within each period you maximize uh + + align:start position:0% +and within each period you maximize uh + + + align:start position:0% +and within each period you maximize uh +your utility over the non-partition good + + align:start position:0% +your utility over the non-partition good + + + align:start position:0% +your utility over the non-partition good +and the Temptation good that could be in + + align:start position:0% +and the Temptation good that could be in + + + align:start position:0% +and the Temptation good that could be in +you know you could separate the goods + + align:start position:0% +you know you could separate the goods + + + align:start position:0% +you know you could separate the goods +into two and that's kind of a reduced + + align:start position:0% +into two and that's kind of a reduced + + + align:start position:0% +into two and that's kind of a reduced +form for uh all of the Gooding that are + + align:start position:0% +form for uh all of the Gooding that are + + + align:start position:0% +form for uh all of the Gooding that are +conditioned and all the good that are + + align:start position:0% +conditioned and all the good that are + + + align:start position:0% +conditioned and all the good that are +not transition + + align:start position:0% +not transition + + + align:start position:0% +not transition +and then the interactable preferences + + align:start position:0% +and then the interactable preferences + + + align:start position:0% +and then the interactable preferences +maximize today's plus the discounted sum + + align:start position:0% +maximize today's plus the discounted sum + + + align:start position:0% +maximize today's plus the discounted sum +of the non-competition good + + align:start position:0% +of the non-competition good + + + align:start position:0% +of the non-competition good +subject to your uh to your + + align:start position:0% +subject to your uh to your + + + align:start position:0% +subject to your uh to your +usual asset + + align:start position:0% +usual asset + + + align:start position:0% +usual asset +accumulation constraint + + align:start position:0% + + + + align:start position:0% + +so as soon as you have two periods you + + align:start position:0% +so as soon as you have two periods you + + + align:start position:0% +so as soon as you have two periods you +have a commitment problem which if it's + + align:start position:0% +have a commitment problem which if it's + + + align:start position:0% +have a commitment problem which if it's +actually not the case in in hyperbolic + + align:start position:0% +actually not the case in in hyperbolic + + + align:start position:0% +actually not the case in in hyperbolic +discounting you need trade to make one + + align:start position:0% +discounting you need trade to make one + + + align:start position:0% +discounting you need trade to make one +appear here you have you have it + + align:start position:0% +appear here you have you have it + + + align:start position:0% +appear here you have you have it +initially because today itself wants uh + + align:start position:0% +initially because today itself wants uh + + + align:start position:0% +initially because today itself wants uh +even with only two per year to the cell + + align:start position:0% +even with only two per year to the cell + + + align:start position:0% +even with only two per year to the cell +phone the extension but for tomorrow + + align:start position:0% +phone the extension but for tomorrow + + + align:start position:0% +phone the extension but for tomorrow +they only want X + + align:start position:0% + + + + align:start position:0% + +this Nest hyperbolic model if the + + align:start position:0% +this Nest hyperbolic model if the + + + align:start position:0% +this Nest hyperbolic model if the +consumption is the Sierra CRA with the + + align:start position:0% +consumption is the Sierra CRA with the + + + align:start position:0% +consumption is the Sierra CRA with the +same discount rate you can see that you + + align:start position:0% +same discount rate you can see that you + + + align:start position:0% +same discount rate you can see that you +can rewrite exactly you can rewrite this + + align:start position:0% +can rewrite exactly you can rewrite this + + + align:start position:0% +can rewrite exactly you can rewrite this +model in a way that will have a higher + + align:start position:0% +model in a way that will have a higher + + + align:start position:0% +model in a way that will have a higher +discount rate for today and for the + + align:start position:0% +discount rate for today and for the + + + align:start position:0% +discount rate for today and for the +future + + align:start position:0% +future + + + align:start position:0% +future +but it's actually much easier to to work + + align:start position:0% +but it's actually much easier to to work + + + align:start position:0% +but it's actually much easier to to work +with + + align:start position:0% +with + + + align:start position:0% +with +because the key result in the paper + + align:start position:0% +because the key result in the paper + + + align:start position:0% +because the key result in the paper +is that basically it's like the Euler + + align:start position:0% +is that basically it's like the Euler + + + align:start position:0% +is that basically it's like the Euler +equation one the the when you maximize + + align:start position:0% +equation one the the when you maximize + + + align:start position:0% +equation one the the when you maximize +this problem + + align:start position:0% +this problem + + + align:start position:0% +this problem +you you can maximize this you can you + + align:start position:0% +you you can maximize this you can you + + + align:start position:0% +you you can maximize this you can you +can choose how much of x and z is going + + align:start position:0% +can choose how much of x and z is going + + + align:start position:0% +can choose how much of x and z is going +to be consumed in Period one + + align:start position:0% +to be consumed in Period one + + + align:start position:0% +to be consumed in Period one +and what you're going to get for the + + align:start position:0% +and what you're going to get for the + + + align:start position:0% +and what you're going to get for the +consumption of X is like a Euler + + align:start position:0% +consumption of X is like a Euler + + + align:start position:0% +consumption of X is like a Euler +equation except there is that term + + align:start position:0% +equation except there is that term + + + align:start position:0% +equation except there is that term +which is a sort of consumption tax + + align:start position:0% +which is a sort of consumption tax + + + align:start position:0% +which is a sort of consumption tax +which is in the future + + align:start position:0% +which is in the future + + + align:start position:0% +which is in the future +in the Temptation text or in Temptation + + align:start position:0% +in the Temptation text or in Temptation + + + align:start position:0% +in the Temptation text or in Temptation +text in the future + + align:start position:0% +text in the future + + + align:start position:0% +text in the future +if you save some money to be consumed in + + align:start position:0% +if you save some money to be consumed in + + + align:start position:0% +if you save some money to be consumed in +the future in the future some of it is + + align:start position:0% +the future in the future some of it is + + + align:start position:0% +the future in the future some of it is +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +devoted to the the Z good which you + + align:start position:0% +devoted to the the Z good which you + + + align:start position:0% +devoted to the the Z good which you +don't like + + align:start position:0% +don't like + + + align:start position:0% +don't like +so this is now Z of so this is a and + + align:start position:0% +so this is now Z of so this is a and + + + align:start position:0% +so this is now Z of so this is a and +that gives you a z of C + + align:start position:0% +that gives you a z of C + + + align:start position:0% +that gives you a z of C +um so this Z is a new function that you + + align:start position:0% +um so this Z is a new function that you + + + align:start position:0% +um so this Z is a new function that you +haven't seen yet + + align:start position:0% +haven't seen yet + + + align:start position:0% +haven't seen yet +but what they show is that basically the + + align:start position:0% +but what they show is that basically the + + + align:start position:0% +but what they show is that basically the +the this is just an invert of the X of + + align:start position:0% +the this is just an invert of the X of + + + align:start position:0% +the this is just an invert of the X of +the of the X of C uh of the of the + + align:start position:0% +the of the X of C uh of the of the + + + align:start position:0% +the of the X of C uh of the of the +U of X like this is this is an inverse + + align:start position:0% +U of X like this is this is an inverse + + + align:start position:0% +U of X like this is this is an inverse +of the uh consumption + + align:start position:0% + + + + align:start position:0% + +inverse of the marginality of + + align:start position:0% +inverse of the marginality of + + + align:start position:0% +inverse of the marginality of +consumption uh uh with respect to uh to + + align:start position:0% +consumption uh uh with respect to uh to + + + align:start position:0% +consumption uh uh with respect to uh to +x and z + + align:start position:0% +x and z + + + align:start position:0% +x and z +so you can easily rewrite the problem + + align:start position:0% +so you can easily rewrite the problem + + + align:start position:0% +so you can easily rewrite the problem +actually the hoof takes one paragraph + + align:start position:0% +actually the hoof takes one paragraph + + + align:start position:0% +actually the hoof takes one paragraph +and I have it in the same in the next + + align:start position:0% +and I have it in the same in the next + + + align:start position:0% +and I have it in the same in the next +slides but that we you can just have a + + align:start position:0% +slides but that we you can just have a + + + align:start position:0% +slides but that we you can just have a +look at the paper + + align:start position:0% +look at the paper + + + align:start position:0% +look at the paper +uh but it's very intuitive but the + + align:start position:0% +uh but it's very intuitive but the + + + align:start position:0% +uh but it's very intuitive but the +result is very intuitive it's saying + + align:start position:0% +result is very intuitive it's saying + + + align:start position:0% +result is very intuitive it's saying +that basically the person who is subject + + align:start position:0% +that basically the person who is subject + + + align:start position:0% +that basically the person who is subject +to some teacher is going to maximize + + align:start position:0% +to some teacher is going to maximize + + + align:start position:0% +to some teacher is going to maximize +their uh their utility that's going to + + align:start position:0% +their uh their utility that's going to + + + align:start position:0% +their uh their utility that's going to +give you pretty much the same result + + align:start position:0% +give you pretty much the same result + + + align:start position:0% +give you pretty much the same result +that the standard Euler equation except + + align:start position:0% +that the standard Euler equation except + + + align:start position:0% +that the standard Euler equation except +there is going to be this temptation tax + + align:start position:0% +there is going to be this temptation tax + + + align:start position:0% +there is going to be this temptation tax +already that with respect so so the this + + align:start position:0% +already that with respect so so the this + + + align:start position:0% +already that with respect so so the this +Z function is increasing so it's it's a + + align:start position:0% +Z function is increasing so it's it's a + + + align:start position:0% +Z function is increasing so it's it's a +Z Prime is is positive + + align:start position:0% +Z Prime is is positive + + + align:start position:0% +Z Prime is is positive +so 1 minus Z Prime is less than is less + + align:start position:0% +so 1 minus Z Prime is less than is less + + + align:start position:0% +so 1 minus Z Prime is less than is less +than one yeah + + align:start position:0% +than one yeah + + + align:start position:0% +than one yeah +in this model people are investigated + + align:start position:0% +in this model people are investigated + + + align:start position:0% +in this model people are investigated +enough yes people are completely + + align:start position:0% +enough yes people are completely + + + align:start position:0% +enough yes people are completely +sophisticated in this model + + align:start position:0% +sophisticated in this model + + + align:start position:0% +sophisticated in this model +and so what does that mean that means + + align:start position:0% +and so what does that mean that means + + + align:start position:0% +and so what does that mean that means +they understand to sophisticated means + + align:start position:0% +they understand to sophisticated means + + + align:start position:0% +they understand to sophisticated means +they understand exactly what model + + align:start position:0% +they understand exactly what model + + + align:start position:0% +they understand exactly what model +they're talking about so for example + + align:start position:0% +they're talking about so for example + + + align:start position:0% +they're talking about so for example +from this model you're going to get the + + align:start position:0% +from this model you're going to get the + + + align:start position:0% +from this model you're going to get the +demand for commitment that you're + + align:start position:0% +demand for commitment that you're + + + align:start position:0% +demand for commitment that you're +finding and to some extent in in + + align:start position:0% +finding and to some extent in in + + + align:start position:0% +finding and to some extent in in +um people + + align:start position:0% + + + + align:start position:0% + +which is they know what's going on they + + align:start position:0% +which is they know what's going on they + + + align:start position:0% +which is they know what's going on they +want to uh to protect their consumption + + align:start position:0% +want to uh to protect their consumption + + + align:start position:0% +want to uh to protect their consumption +against their future self + + align:start position:0% + + + + align:start position:0% + +um so that's the first result you're + + align:start position:0% +um so that's the first result you're + + + align:start position:0% +um so that's the first result you're +getting from from here is is is a demand + + align:start position:0% +getting from from here is is is a demand + + + align:start position:0% +getting from from here is is is a demand +for commitment + + align:start position:0% +for commitment + + + align:start position:0% +for commitment +you get more interesting uh even more + + align:start position:0% +you get more interesting uh even more + + + align:start position:0% +you get more interesting uh even more +interesting results in the case where + + align:start position:0% +interesting results in the case where + + + align:start position:0% +interesting results in the case where +the competition are declining that is + + align:start position:0% +the competition are declining that is + + + align:start position:0% +the competition are declining that is +the Z Prime function + + align:start position:0% +the Z Prime function + + + align:start position:0% +the Z Prime function +is uh decreasing in C so the Temptation + + align:start position:0% +is uh decreasing in C so the Temptation + + + align:start position:0% +is uh decreasing in C so the Temptation +tax is decreasing decreasing in C + + align:start position:0% +tax is decreasing decreasing in C + + + align:start position:0% +tax is decreasing decreasing in C +where what does that what does that uh + + align:start position:0% +where what does that what does that uh + + + align:start position:0% +where what does that what does that uh +intuitively what's the intuition for uh + + align:start position:0% +intuitively what's the intuition for uh + + + align:start position:0% +intuitively what's the intuition for uh +decreasing and of our Temptation tax + + align:start position:0% +decreasing and of our Temptation tax + + + align:start position:0% +decreasing and of our Temptation tax +that declines with your with your + + align:start position:0% +that declines with your with your + + + align:start position:0% +that declines with your with your +consumption levels + + align:start position:0% + + + + align:start position:0% + +what what what does this reflect + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +yes so I guess like the first uh + + align:start position:0% +yes so I guess like the first uh + + + align:start position:0% +yes so I guess like the first uh +chocolate bar it tastes really good + + align:start position:0% +chocolate bar it tastes really good + + + align:start position:0% +chocolate bar it tastes really good +within the second third + + align:start position:0% +within the second third + + + align:start position:0% +within the second third +exactly it's saying that the shape of + + align:start position:0% +exactly it's saying that the shape of + + + align:start position:0% +exactly it's saying that the shape of +competition it's exactly it can be + + align:start position:0% +competition it's exactly it can be + + + align:start position:0% +competition it's exactly it can be +mapped to the shape of competition the + + align:start position:0% +mapped to the shape of competition the + + + align:start position:0% +mapped to the shape of competition the +utility function from the from the + + align:start position:0% +utility function from the from the + + + align:start position:0% +utility function from the from the +Temptation good is concave + + align:start position:0% +Temptation good is concave + + + align:start position:0% +Temptation good is concave +that means that uh Temptations are + + align:start position:0% +that means that uh Temptations are + + + align:start position:0% +that means that uh Temptations are +larger as a fraction of your uh + + align:start position:0% +larger as a fraction of your uh + + + align:start position:0% +larger as a fraction of your uh +of your consumption when you're poor + + align:start position:0% +of your consumption when you're poor + + + align:start position:0% +of your consumption when you're poor +than when you reach so for example so if + + align:start position:0% +than when you reach so for example so if + + + align:start position:0% +than when you reach so for example so if +Plantation are mostly visceral Goods + + align:start position:0% +Plantation are mostly visceral Goods + + + align:start position:0% +Plantation are mostly visceral Goods +like chocolate crispy creams Etc that + + align:start position:0% +like chocolate crispy creams Etc that + + + align:start position:0% +like chocolate crispy creams Etc that +makes a lot of sense because in + + align:start position:0% +makes a lot of sense because in + + + align:start position:0% +makes a lot of sense because in +proportion of your income there is only + + align:start position:0% +proportion of your income there is only + + + align:start position:0% +proportion of your income there is only +so many Krispy Kreme you you you might + + align:start position:0% +so many Krispy Kreme you you you might + + + align:start position:0% +so many Krispy Kreme you you you might +want to eat so the the even if the + + align:start position:0% +want to eat so the the even if the + + + align:start position:0% +want to eat so the the even if the +number of speaker increases it increases + + align:start position:0% +number of speaker increases it increases + + + align:start position:0% +number of speaker increases it increases +less fast than the amount of money you + + align:start position:0% +less fast than the amount of money you + + + align:start position:0% +less fast than the amount of money you +have to to to give to that to the share + + align:start position:0% +have to to to give to that to the share + + + align:start position:0% +have to to to give to that to the share +of the consumption good as a function of + + align:start position:0% +of the consumption good as a function of + + + align:start position:0% +of the consumption good as a function of +your of your budget is is going to + + align:start position:0% +your of your budget is is going to + + + align:start position:0% +your of your budget is is going to +decrease so that's that's what it that's + + align:start position:0% +decrease so that's that's what it that's + + + align:start position:0% +decrease so that's that's what it that's +the that's what it uh it reflects it + + align:start position:0% +the that's what it uh it reflects it + + + align:start position:0% +the that's what it uh it reflects it +doesn't have to be true right for + + align:start position:0% +doesn't have to be true right for + + + align:start position:0% +doesn't have to be true right for +example you could say well no for a rich + + align:start position:0% +example you could say well no for a rich + + + align:start position:0% +example you could say well no for a rich +person the Temptation good is going to + + align:start position:0% +person the Temptation good is going to + + + align:start position:0% +person the Temptation good is going to +be a yacht and a youth is super + + align:start position:0% +be a yacht and a youth is super + + + align:start position:0% +be a yacht and a youth is super +expensive so you know you graduate from + + align:start position:0% +expensive so you know you graduate from + + + align:start position:0% +expensive so you know you graduate from +Krispy Kreme to home TV to yorton and + + align:start position:0% +Krispy Kreme to home TV to yorton and + + + align:start position:0% +Krispy Kreme to home TV to yorton and +find finally this is a non-decreasing or + + align:start position:0% +find finally this is a non-decreasing or + + + align:start position:0% +find finally this is a non-decreasing or +even an increasing shape + + align:start position:0% + + + + align:start position:0% + +note for example that the hyperbolic + + align:start position:0% +note for example that the hyperbolic + + + align:start position:0% +note for example that the hyperbolic +discounting function is with CRA with + + align:start position:0% +discounting function is with CRA with + + + align:start position:0% +discounting function is with CRA with +the same + + align:start position:0% +the same + + + align:start position:0% +the same +coefficient in that case it's + + align:start position:0% +coefficient in that case it's + + + align:start position:0% +coefficient in that case it's +non-decreasing because uh the the con + + align:start position:0% +non-decreasing because uh the the con + + + align:start position:0% +non-decreasing because uh the the con +the Temptation always remain a fraction + + align:start position:0% +the Temptation always remain a fraction + + + align:start position:0% +the Temptation always remain a fraction +of your income so the hyperbolic + + align:start position:0% +of your income so the hyperbolic + + + align:start position:0% +of your income so the hyperbolic +discontinent is actually your case can + + align:start position:0% +discontinent is actually your case can + + + align:start position:0% +discontinent is actually your case can +be mapped into this model with a + + align:start position:0% +be mapped into this model with a + + + align:start position:0% +be mapped into this model with a +constant with non-decreasing conditions + + align:start position:0% +constant with non-decreasing conditions + + + align:start position:0% +constant with non-decreasing conditions +yeah + + align:start position:0% + + + + align:start position:0% + +are + + align:start position:0% + + + + align:start position:0% + +more Temptation for it + + align:start position:0% +more Temptation for it + + + align:start position:0% +more Temptation for it +say YouTube yeah this can be because + + align:start position:0% +say YouTube yeah this can be because + + + align:start position:0% +say YouTube yeah this can be because +like I like as mother predicts something + + align:start position:0% +like I like as mother predicts something + + + align:start position:0% +like I like as mother predicts something +there is a subtitation but also there's + + align:start position:0% +there is a subtitation but also there's + + + align:start position:0% +there is a subtitation but also there's +the other way around which is if there + + align:start position:0% +the other way around which is if there + + + align:start position:0% +the other way around which is if there +are different people saying more patient + + align:start position:0% +are different people saying more patient + + + align:start position:0% +are different people saying more patient +and less patient people + + align:start position:0% +and less patient people + + + align:start position:0% +and less patient people +less patient people + + align:start position:0% +less patient people + + + align:start position:0% +less patient people +would end up poor + + align:start position:0% +would end up poor + + + align:start position:0% +would end up poor +yeah yeah of course so you're right + + align:start position:0% +yeah yeah of course so you're right + + + align:start position:0% +yeah yeah of course so you're right +which is in the data the model would + + align:start position:0% +which is in the data the model would + + + align:start position:0% +which is in the data the model would +predict that but that would also be + + align:start position:0% +predict that but that would also be + + + align:start position:0% +predict that but that would also be +predicted by heterogeneity so what your + + align:start position:0% +predicted by heterogeneity so what your + + + align:start position:0% +predicted by heterogeneity so what your +purpose as a prediction is not a + + align:start position:0% +purpose as a prediction is not a + + + align:start position:0% +purpose as a prediction is not a +testable implication I mean it is a test + + align:start position:0% +testable implication I mean it is a test + + + align:start position:0% +testable implication I mean it is a test +it is an implication but it's not gonna + + align:start position:0% +it is an implication but it's not gonna + + + align:start position:0% +it is an implication but it's not gonna +it's not going to make the difference + + align:start position:0% +it's not going to make the difference + + + align:start position:0% +it's not going to make the difference +between this model or another model + + align:start position:0% +between this model or another model + + + align:start position:0% +between this model or another model +based on basic heterogeneity absolutely + + align:start position:0% +based on basic heterogeneity absolutely + + + align:start position:0% +based on basic heterogeneity absolutely +um + + align:start position:0% +um + + + align:start position:0% +um +I'll give you another example where uh + + align:start position:0% +I'll give you another example where uh + + + align:start position:0% +I'll give you another example where uh +so so we should think about what this + + align:start position:0% +so so we should think about what this + + + align:start position:0% +so so we should think about what this +model predicts and then we should think + + align:start position:0% +model predicts and then we should think + + + align:start position:0% +model predicts and then we should think +about other tests for uh for uh in + + align:start position:0% +about other tests for uh for uh in + + + align:start position:0% +about other tests for uh for uh in +for whether or not we seem to have + + align:start position:0% +for whether or not we seem to have + + + align:start position:0% +for whether or not we seem to have +competition in the world and that's + + align:start position:0% +competition in the world and that's + + + align:start position:0% +competition in the world and that's +related with to some of this implication + + align:start position:0% +related with to some of this implication + + + align:start position:0% +related with to some of this implication +could be related also could be we could + + align:start position:0% +could be related also could be we could + + + align:start position:0% +could be related also could be we could +devise uh consumption + + align:start position:0% +devise uh consumption + + + align:start position:0% +devise uh consumption +we could divide tests based on the the + + align:start position:0% +we could divide tests based on the the + + + align:start position:0% +we could divide tests based on the the +shape of consumption function for some + + align:start position:0% +shape of consumption function for some + + + align:start position:0% +shape of consumption function for some +Goods + + align:start position:0% +Goods + + + align:start position:0% +Goods +before I go to the implication think of + + align:start position:0% +before I go to the implication think of + + + align:start position:0% +before I go to the implication think of +another example so one form of + + align:start position:0% +another example so one form of + + + align:start position:0% +another example so one form of +Temptation Goods that seemed to you know + + align:start position:0% +Temptation Goods that seemed to you know + + + align:start position:0% +Temptation Goods that seemed to you know +that would satisfy this declining + + align:start position:0% +that would satisfy this declining + + + align:start position:0% +that would satisfy this declining +Temptation tax is this visceral things + + align:start position:0% +Temptation tax is this visceral things + + + align:start position:0% +Temptation tax is this visceral things +another is being taxed by your relatives + + align:start position:0% +another is being taxed by your relatives + + + align:start position:0% +another is being taxed by your relatives +because you could think of this uh you + + align:start position:0% +because you could think of this uh you + + + align:start position:0% +because you could think of this uh you +know map that into a household model + + align:start position:0% +know map that into a household model + + + align:start position:0% +know map that into a household model +where part of your temptation is someone + + align:start position:0% +where part of your temptation is someone + + + align:start position:0% +where part of your temptation is someone +will come and ask you for something + + align:start position:0% +will come and ask you for something + + + align:start position:0% +will come and ask you for something +so your child wants a a toy or your + + align:start position:0% +so your child wants a a toy or your + + + align:start position:0% +so your child wants a a toy or your +cousin wants some money because they are + + align:start position:0% +cousin wants some money because they are + + + align:start position:0% +cousin wants some money because they are +starving + + align:start position:0% +starving + + + align:start position:0% +starving +so the the the non the declining + + align:start position:0% +so the the the non the declining + + + align:start position:0% +so the the the non the declining +Temptation would be that where if it's + + align:start position:0% +Temptation would be that where if it's + + + align:start position:0% +Temptation would be that where if it's +easier + + align:start position:0% +easier + + + align:start position:0% +easier +to say no to your cousin who wants a + + align:start position:0% +to say no to your cousin who wants a + + + align:start position:0% +to say no to your cousin who wants a +thousand dollars to start a business + + align:start position:0% +thousand dollars to start a business + + + align:start position:0% +thousand dollars to start a business +when you're quite rich + + align:start position:0% +when you're quite rich + + + align:start position:0% +when you're quite rich +uh then to say no to your cousin who + + align:start position:0% +uh then to say no to your cousin who + + + align:start position:0% +uh then to say no to your cousin who +wants a bowl of rice when they are quite + + align:start position:0% +wants a bowl of rice when they are quite + + + align:start position:0% +wants a bowl of rice when they are quite +one you're quite poor + + align:start position:0% +one you're quite poor + + + align:start position:0% +one you're quite poor +so this is a that's + + align:start position:0% +so this is a that's + + + align:start position:0% +so this is a that's +so I don't know whether that's the case + + align:start position:0% +so I don't know whether that's the case + + + align:start position:0% +so I don't know whether that's the case +or not but that that would be that that + + align:start position:0% +or not but that that would be that that + + + align:start position:0% +or not but that that would be that that +would be that proportionally it's uh you + + align:start position:0% +would be that proportionally it's uh you + + + align:start position:0% +would be that proportionally it's uh you +don't have to give a proportion of your + + align:start position:0% +don't have to give a proportion of your + + + align:start position:0% +don't have to give a proportion of your +income to your relatives even though you + + align:start position:0% +income to your relatives even though you + + + align:start position:0% +income to your relatives even though you +don't you have to do it at the time but + + align:start position:0% +don't you have to do it at the time but + + + align:start position:0% +don't you have to do it at the time but +you don't enjoy it that would be a form + + align:start position:0% +you don't enjoy it that would be a form + + + align:start position:0% +you don't enjoy it that would be a form +of the of competition good but uh uh so + + align:start position:0% +of the of competition good but uh uh so + + + align:start position:0% +of the of competition good but uh uh so +you um you uh maybe that's that's easier + + align:start position:0% +you um you uh maybe that's that's easier + + + align:start position:0% +you um you uh maybe that's that's easier +for the rich to give them to not give in + + align:start position:0% +for the rich to give them to not give in + + + align:start position:0% +for the rich to give them to not give in +proportion of their income or maybe not + + align:start position:0% +proportion of their income or maybe not + + + align:start position:0% +proportion of their income or maybe not +but that's the example + + align:start position:0% +but that's the example + + + align:start position:0% +but that's the example +so assuming that you do have uh this + + align:start position:0% +so assuming that you do have uh this + + + align:start position:0% +so assuming that you do have uh this +declining competition then you have uh + + align:start position:0% +declining competition then you have uh + + + align:start position:0% +declining competition then you have uh +you have extra implications that are + + align:start position:0% +you have extra implications that are + + + align:start position:0% +you have extra implications that are +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +the first one is the precautionary + + align:start position:0% +the first one is the precautionary + + + align:start position:0% +the first one is the precautionary +saving argument might not take place + + align:start position:0% +saving argument might not take place + + + align:start position:0% +saving argument might not take place +because uh for someone who is very poor + + align:start position:0% +because uh for someone who is very poor + + + align:start position:0% +because uh for someone who is very poor +if they are thinking they are also going + + align:start position:0% +if they are thinking they are also going + + + align:start position:0% +if they are thinking they are also going +to be very poor in the future + + align:start position:0% +to be very poor in the future + + + align:start position:0% +to be very poor in the future +and therefore most of their saving is + + align:start position:0% +and therefore most of their saving is + + + align:start position:0% +and therefore most of their saving is +going to be eaten by themselves in the + + align:start position:0% +going to be eaten by themselves in the + + + align:start position:0% +going to be eaten by themselves in the +form of these that they don't want so + + align:start position:0% +form of these that they don't want so + + + align:start position:0% +form of these that they don't want so +the consumption tax is going to be high + + align:start position:0% +the consumption tax is going to be high + + + align:start position:0% +the consumption tax is going to be high +uh when someone so someone and then in + + align:start position:0% +uh when someone so someone and then in + + + align:start position:0% +uh when someone so someone and then in +fact when there is more viability of + + align:start position:0% +fact when there is more viability of + + + align:start position:0% +fact when there is more viability of +when there is more variability of income + + align:start position:0% +when there is more variability of income + + + align:start position:0% +when there is more variability of income +and uh when they are practically + + align:start position:0% +and uh when they are practically + + + align:start position:0% +and uh when they are practically +employees where when the execute + + align:start position:0% +employees where when the execute + + + align:start position:0% +employees where when the execute +yourself is going to extract all of this + + align:start position:0% +yourself is going to extract all of this + + + align:start position:0% +yourself is going to extract all of this +consumption in the form of Z so they + + align:start position:0% +consumption in the form of Z so they + + + align:start position:0% +consumption in the form of Z so they +might say I might as well eat it now if + + align:start position:0% +might say I might as well eat it now if + + + align:start position:0% +might say I might as well eat it now if +I'm going to in other words if I'm going + + align:start position:0% +I'm going to in other words if I'm going + + + align:start position:0% +I'm going to in other words if I'm going +to eat some some Krispy Kreme tomorrow + + align:start position:0% +to eat some some Krispy Kreme tomorrow + + + align:start position:0% +to eat some some Krispy Kreme tomorrow +which I don't like the sort of I might + + align:start position:0% +which I don't like the sort of I might + + + align:start position:0% +which I don't like the sort of I might +as well eat it now where I'm gonna enjoy + + align:start position:0% +as well eat it now where I'm gonna enjoy + + + align:start position:0% +as well eat it now where I'm gonna enjoy +it + + align:start position:0% +it + + + align:start position:0% +it +and therefore you might not have you + + align:start position:0% +and therefore you might not have you + + + align:start position:0% +and therefore you might not have you +might not have the precautionary saving + + align:start position:0% +might not have the precautionary saving + + + align:start position:0% +might not have the precautionary saving +mode even and therefore you might have + + align:start position:0% +mode even and therefore you might have + + + align:start position:0% +mode even and therefore you might have +to pull saving less than the rich + + align:start position:0% +to pull saving less than the rich + + + align:start position:0% +to pull saving less than the rich +and you also have and what is + + align:start position:0% +and you also have and what is + + + align:start position:0% +and you also have and what is +interesting is that is the the + + align:start position:0% +interesting is that is the the + + + align:start position:0% +interesting is that is the the +perspective that you have for the future + + align:start position:0% +perspective that you have for the future + + + align:start position:0% +perspective that you have for the future +so in a precautionary saving model + + align:start position:0% +so in a precautionary saving model + + + align:start position:0% +so in a precautionary saving model +someone who anticipating getting richer + + align:start position:0% +someone who anticipating getting richer + + + align:start position:0% +someone who anticipating getting richer +can consume more today because they will + + align:start position:0% +can consume more today because they will + + + align:start position:0% +can consume more today because they will +be richer in the future so they don't + + align:start position:0% +be richer in the future so they don't + + + align:start position:0% +be richer in the future so they don't +need that saving + + align:start position:0% +need that saving + + + align:start position:0% +need that saving +someone who anticipate that times might + + align:start position:0% +someone who anticipate that times might + + + align:start position:0% +someone who anticipate that times might +become back should save a lot okay + + align:start position:0% +become back should save a lot okay + + + align:start position:0% +become back should save a lot okay +that's the third derivative of the + + align:start position:0% +that's the third derivative of the + + + align:start position:0% +that's the third derivative of the +utility function being positive + + align:start position:0% +utility function being positive + + + align:start position:0% +utility function being positive +now if you think that in the future + + align:start position:0% +now if you think that in the future + + + align:start position:0% +now if you think that in the future +you're going to be richer therefore the + + align:start position:0% +you're going to be richer therefore the + + + align:start position:0% +you're going to be richer therefore the +competition tax the the infraction of + + align:start position:0% +competition tax the the infraction of + + + align:start position:0% +competition tax the the infraction of +what's available the Temptation tax is + + align:start position:0% +what's available the Temptation tax is + + + align:start position:0% +what's available the Temptation tax is +going to be lower + + align:start position:0% +going to be lower + + + align:start position:0% +going to be lower +and therefore you might you can you can + + align:start position:0% +and therefore you might you can you can + + + align:start position:0% +and therefore you might you can you can +afford to save more today because you + + align:start position:0% +afford to save more today because you + + + align:start position:0% +afford to save more today because you +think the time will be better so you + + align:start position:0% +think the time will be better so you + + + align:start position:0% +think the time will be better so you +have the opposite of the precautionary + + align:start position:0% +have the opposite of the precautionary + + + align:start position:0% +have the opposite of the precautionary +motive where the hope for the future + + align:start position:0% +motive where the hope for the future + + + align:start position:0% +motive where the hope for the future +might actually get help people getting + + align:start position:0% +might actually get help people getting + + + align:start position:0% +might actually get help people getting +started in in in in savings + + align:start position:0% +started in in in in savings + + + align:start position:0% +started in in in in savings +so that's the first implication of of + + align:start position:0% +so that's the first implication of of + + + align:start position:0% +so that's the first implication of of +that model with the with an on uh + + align:start position:0% +that model with the with an on uh + + + align:start position:0% +that model with the with an on uh +decreasing with decreasing competition + + align:start position:0% +decreasing with decreasing competition + + + align:start position:0% +decreasing with decreasing competition +that doesn't work with non-decreasing + + align:start position:0% +that doesn't work with non-decreasing + + + align:start position:0% +that doesn't work with non-decreasing +condition another one is that you have a + + align:start position:0% +condition another one is that you have a + + + align:start position:0% +condition another one is that you have a +poverty trap even if there is no you + + align:start position:0% +poverty trap even if there is no you + + + align:start position:0% +poverty trap even if there is no you +could have poverty traps even if there + + align:start position:0% +could have poverty traps even if there + + + align:start position:0% +could have poverty traps even if there +is no other source of discontinuity why + + align:start position:0% +is no other source of discontinuity why + + + align:start position:0% +is no other source of discontinuity why +because the poor people won't save + + align:start position:0% +because the poor people won't save + + + align:start position:0% +because the poor people won't save +because they know that they are again + + align:start position:0% +because they know that they are again + + + align:start position:0% +because they know that they are again +poor tomorrow and any saving is going to + + align:start position:0% +poor tomorrow and any saving is going to + + + align:start position:0% +poor tomorrow and any saving is going to +be spent in the Z because it's a large + + align:start position:0% +be spent in the Z because it's a large + + + align:start position:0% +be spent in the Z because it's a large +fraction of zero present a large + + align:start position:0% +fraction of zero present a large + + + align:start position:0% +fraction of zero present a large +fraction of their income + + align:start position:0% +fraction of their income + + + align:start position:0% +fraction of their income +if you're sufficiently rich it is worth + + align:start position:0% +if you're sufficiently rich it is worth + + + align:start position:0% +if you're sufficiently rich it is worth +saving because you know that you are not + + align:start position:0% +saving because you know that you are not + + + align:start position:0% +saving because you know that you are not +extracting such a large fraction of your + + align:start position:0% +extracting such a large fraction of your + + + align:start position:0% +extracting such a large fraction of your +of those Savings in the form of these + + align:start position:0% +of those Savings in the form of these + + + align:start position:0% +of those Savings in the form of these +that you don't enjoy and do you so + + align:start position:0% +that you don't enjoy and do you so + + + align:start position:0% +that you don't enjoy and do you so +you're going to save more + + align:start position:0% +you're going to save more + + + align:start position:0% +you're going to save more +and so the original people are becoming + + align:start position:0% +and so the original people are becoming + + + align:start position:0% +and so the original people are becoming +richer and richer because they are + + align:start position:0% +richer and richer because they are + + + align:start position:0% +richer and richer because they are +saving saving saving money poor people + + align:start position:0% +saving saving saving money poor people + + + align:start position:0% +saving saving saving money poor people +are becoming poor because they are + + align:start position:0% +are becoming poor because they are + + + align:start position:0% +are becoming poor because they are +saving saving saving less + + align:start position:0% +saving saving saving less + + + align:start position:0% +saving saving saving less +so the the poverty itself is the source + + align:start position:0% +so the the poverty itself is the source + + + align:start position:0% +so the the poverty itself is the source +of what makes you poor which creates the + + align:start position:0% +of what makes you poor which creates the + + + align:start position:0% +of what makes you poor which creates the +potential for poverty trap in the + + align:start position:0% +potential for poverty trap in the + + + align:start position:0% +potential for poverty trap in the +absence of any other any other uh + + align:start position:0% +absence of any other any other uh + + + align:start position:0% +absence of any other any other uh +discontinuity + + align:start position:0% +discontinuity + + + align:start position:0% +discontinuity +It also says that people might prefer to + + align:start position:0% +It also says that people might prefer to + + + align:start position:0% +It also says that people might prefer to +have uh might not find it going back to + + align:start position:0% +have uh might not find it going back to + + + align:start position:0% +have uh might not find it going back to +my fertilizer thing where it is where + + align:start position:0% +my fertilizer thing where it is where + + + align:start position:0% +my fertilizer thing where it is where +when I was telling them but you could + + align:start position:0% +when I was telling them but you could + + + align:start position:0% +when I was telling them but you could +buy just so little why do you + + align:start position:0% +buy just so little why do you + + + align:start position:0% +buy just so little why do you +even if you have a tiny bit of money buy + + align:start position:0% +even if you have a tiny bit of money buy + + + align:start position:0% +even if you have a tiny bit of money buy +a tiny bit of fertilizer well a tiny + + align:start position:0% +a tiny bit of fertilizer well a tiny + + + align:start position:0% +a tiny bit of fertilizer well a tiny +project is not making you rich enough + + align:start position:0% +project is not making you rich enough + + + align:start position:0% +project is not making you rich enough +that it's going that it's really + + align:start position:0% +that it's going that it's really + + + align:start position:0% +that it's going that it's really +changing your Temptation tags so most of + + align:start position:0% +changing your Temptation tags so most of + + + align:start position:0% +changing your Temptation tags so most of +that extra money you would make from the + + align:start position:0% +that extra money you would make from the + + + align:start position:0% +that extra money you would make from the +fertilizer on a small scale is going to + + align:start position:0% +fertilizer on a small scale is going to + + + align:start position:0% +fertilizer on a small scale is going to +be frittered away and things that you + + align:start position:0% +be frittered away and things that you + + + align:start position:0% +be frittered away and things that you +don't hear from today so what's the + + align:start position:0% +don't hear from today so what's the + + + align:start position:0% +don't hear from today so what's the +point + + align:start position:0% +point + + + align:start position:0% +point +so that might explain why even if there + + align:start position:0% +so that might explain why even if there + + + align:start position:0% +so that might explain why even if there +is no really fixed cost in going to the + + align:start position:0% +is no really fixed cost in going to the + + + align:start position:0% +is no really fixed cost in going to the +shop + + align:start position:0% +shop + + + align:start position:0% +shop +there is no reason to do fertilizer + + align:start position:0% +there is no reason to do fertilizer + + + align:start position:0% +there is no reason to do fertilizer +unless you're going to do enough because + + align:start position:0% +unless you're going to do enough because + + + align:start position:0% +unless you're going to do enough because +the the extra money that is going to be + + align:start position:0% +the the extra money that is going to be + + + align:start position:0% +the the extra money that is going to be +generated from the fertilizer won't + + align:start position:0% +generated from the fertilizer won't + + + align:start position:0% +generated from the fertilizer won't +won't work + + align:start position:0% +won't work + + + align:start position:0% +won't work +uh and you you might choose a + + align:start position:0% +uh and you you might choose a + + + align:start position:0% +uh and you you might choose a +microfinance loan at a high interest + + align:start position:0% +microfinance loan at a high interest + + + align:start position:0% +microfinance loan at a high interest +rate in order to put money in uh rather + + align:start position:0% +rate in order to put money in uh rather + + + align:start position:0% +rate in order to put money in uh rather +than a credit card loan because you want + + align:start position:0% +than a credit card loan because you want + + + align:start position:0% +than a credit card loan because you want +a large project + + align:start position:0% +a large project + + + align:start position:0% +a large project +uh you might like this kind of funny + + align:start position:0% +uh you might like this kind of funny + + + align:start position:0% +uh you might like this kind of funny +account where you have to pay for + + align:start position:0% +account where you have to pay for + + + align:start position:0% +account where you have to pay for +withdrawing money + + align:start position:0% +withdrawing money + + + align:start position:0% +withdrawing money +because uh since the amount you're + + align:start position:0% +because uh since the amount you're + + + align:start position:0% +because uh since the amount you're +paying is smaller when the amount to + + align:start position:0% +paying is smaller when the amount to + + + align:start position:0% +paying is smaller when the amount to +withdraw is smaller you won't be able to + + align:start position:0% +withdraw is smaller you won't be able to + + + align:start position:0% +withdraw is smaller you won't be able to +access it it's not going to be worth it + + align:start position:0% +access it it's not going to be worth it + + + align:start position:0% +access it it's not going to be worth it +accessing until until there is enough + + align:start position:0% +accessing until until there is enough + + + align:start position:0% +accessing until until there is enough +and once there is enough in one go then + + align:start position:0% +and once there is enough in one go then + + + align:start position:0% +and once there is enough in one go then +you won't want to Fritter the whole + + align:start position:0% +you won't want to Fritter the whole + + + align:start position:0% +you won't want to Fritter the whole +thing it won't make if you were saving + + align:start position:0% +thing it won't make if you were saving + + + align:start position:0% +thing it won't make if you were saving +and you were able to withdraw two + + align:start position:0% +and you were able to withdraw two + + + align:start position:0% +and you were able to withdraw two +dollars to pay your crusty cream you + + align:start position:0% +dollars to pay your crusty cream you + + + align:start position:0% +dollars to pay your crusty cream you +might but if it's expensive to do so you + + align:start position:0% +might but if it's expensive to do so you + + + align:start position:0% +might but if it's expensive to do so you +might + + align:start position:0% +might + + + align:start position:0% +might +and wait till you have 50 which is where + + align:start position:0% +and wait till you have 50 which is where + + + align:start position:0% +and wait till you have 50 which is where +the the the withdrawal costs are smaller + + align:start position:0% +the the the withdrawal costs are smaller + + + align:start position:0% +the the the withdrawal costs are smaller +and then you can you can do something + + align:start position:0% +and then you can you can do something + + + align:start position:0% +and then you can you can do something +more meaningful with the money that you + + align:start position:0% +more meaningful with the money that you + + + align:start position:0% +more meaningful with the money that you +value from the point of view of x + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +very quickly uh you read the paper and + + align:start position:0% +very quickly uh you read the paper and + + + align:start position:0% +very quickly uh you read the paper and +it's pretty self-explanatory but it's a + + align:start position:0% +it's pretty self-explanatory but it's a + + + align:start position:0% +it's pretty self-explanatory but it's a +very it's uh nice in the you know in in + + align:start position:0% +very it's uh nice in the you know in in + + + align:start position:0% +very it's uh nice in the you know in in +the context of this model this is the + + align:start position:0% +the context of this model this is the + + + align:start position:0% +the context of this model this is the +first paper to set up an experiment for + + align:start position:0% +first paper to set up an experiment for + + + align:start position:0% +first paper to set up an experiment for +a demand for commitment + + align:start position:0% +a demand for commitment + + + align:start position:0% +a demand for commitment +uh it's a very perfect paper as many of + + align:start position:0% +uh it's a very perfect paper as many of + + + align:start position:0% +uh it's a very perfect paper as many of +you have pointed out uh starting with + + align:start position:0% +you have pointed out uh starting with + + + align:start position:0% +you have pointed out uh starting with +the fact that the results are pretty + + align:start position:0% +the fact that the results are pretty + + + align:start position:0% +the fact that the results are pretty +mushy because uh the the the the + + align:start position:0% +mushy because uh the the the the + + + align:start position:0% +mushy because uh the the the the +marketing the saving marketing is in + + align:start position:0% +marketing the saving marketing is in + + + align:start position:0% +marketing the saving marketing is in +fact almost as large the impact as the + + align:start position:0% +fact almost as large the impact as the + + + align:start position:0% +fact almost as large the impact as the +demand for commitment uh thing so it's + + align:start position:0% +demand for commitment uh thing so it's + + + align:start position:0% +demand for commitment uh thing so it's +uh and the other thing is they are + + align:start position:0% +uh and the other thing is they are + + + align:start position:0% +uh and the other thing is they are +trying to test whether people who have + + align:start position:0% +trying to test whether people who have + + + align:start position:0% +trying to test whether people who have +hyperbolic who look hyperbolic + + align:start position:0% +hyperbolic who look hyperbolic + + + align:start position:0% +hyperbolic who look hyperbolic +discounting have um in fact are more + + align:start position:0% +discounting have um in fact are more + + + align:start position:0% +discounting have um in fact are more +likely to take up + + align:start position:0% +likely to take up + + + align:start position:0% +likely to take up +but in their in their graphs there are a + + align:start position:0% +but in their in their graphs there are a + + + align:start position:0% +but in their in their graphs there are a +lot of people who seem to be confused so + + align:start position:0% +lot of people who seem to be confused so + + + align:start position:0% +lot of people who seem to be confused so +you would test high probability + + align:start position:0% +you would test high probability + + + align:start position:0% +you would test high probability +discounting by saying if you are more + + align:start position:0% +discounting by saying if you are more + + + align:start position:0% +discounting by saying if you are more +patient uh + + align:start position:0% +patient uh + + + align:start position:0% +patient uh +in the present than in the future but a + + align:start position:0% +in the present than in the future but a + + + align:start position:0% +in the present than in the future but a +lot of people are not on the diagonal on + + align:start position:0% +lot of people are not on the diagonal on + + + align:start position:0% +lot of people are not on the diagonal on +both ends and that's not predicted by + + align:start position:0% +both ends and that's not predicted by + + + align:start position:0% +both ends and that's not predicted by +any model so that's that that's + + align:start position:0% +any model so that's that that's + + + align:start position:0% +any model so that's that that's +confusion but then if that's confusion + + align:start position:0% +confusion but then if that's confusion + + + align:start position:0% +confusion but then if that's confusion +then maybe that's also confusion so + + align:start position:0% +then maybe that's also confusion so + + + align:start position:0% +then maybe that's also confusion so +since then since that paper the the the + + align:start position:0% +since then since that paper the the the + + + align:start position:0% +since then since that paper the the the +ability to measure with the work of + + align:start position:0% +ability to measure with the work of + + + align:start position:0% +ability to measure with the work of +Charlie's penga in particular we are + + align:start position:0% +Charlie's penga in particular we are + + + align:start position:0% +Charlie's penga in particular we are +much better at measuring + + align:start position:0% +much better at measuring + + + align:start position:0% +much better at measuring +women for commitment but you know this + + align:start position:0% +women for commitment but you know this + + + align:start position:0% +women for commitment but you know this +is how science progresses this paper is + + align:start position:0% +is how science progresses this paper is + + + align:start position:0% +is how science progresses this paper is +a wonderful + + align:start position:0% +a wonderful + + + align:start position:0% +a wonderful +wonderfully creative thing of going + + align:start position:0% +wonderfully creative thing of going + + + align:start position:0% +wonderfully creative thing of going +ahead and creating the thing and then + + align:start position:0% +ahead and creating the thing and then + + + align:start position:0% +ahead and creating the thing and then +you've seen a Frank's people are + + align:start position:0% +you've seen a Frank's people are + + + align:start position:0% +you've seen a Frank's people are +building building on it with uh with his + + align:start position:0% +building building on it with uh with his + + + align:start position:0% +building building on it with uh with his +alcohol paper if you're interested in + + align:start position:0% +alcohol paper if you're interested in + + + align:start position:0% +alcohol paper if you're interested in +what I think is like the the + + align:start position:0% +what I think is like the the + + + align:start position:0% +what I think is like the the +state of the art in terms of a + + align:start position:0% +state of the art in terms of a + + + align:start position:0% +state of the art in terms of a +commitment savings product it's the + + align:start position:0% +commitment savings product it's the + + + align:start position:0% +commitment savings product it's the +paper by an Afghanistan savings account + + align:start position:0% +paper by an Afghanistan savings account + + + align:start position:0% +paper by an Afghanistan savings account +by um + + align:start position:0% +by um + + + align:start position:0% +by um +uh Michael Kellen uh + + align:start position:0% +uh Michael Kellen uh + + + align:start position:0% +uh Michael Kellen uh +it has it is kind of the 2.0 of the + + align:start position:0% +it has it is kind of the 2.0 of the + + + align:start position:0% +it has it is kind of the 2.0 of the +Ashcraft Caroline using uh using the + + align:start position:0% +Ashcraft Caroline using uh using the + + + align:start position:0% +Ashcraft Caroline using uh using the +worker of a bigger + + align:start position:0% +worker of a bigger + + + align:start position:0% +worker of a bigger +big farm in Afghanistan it's excellent + + align:start position:0% +big farm in Afghanistan it's excellent + + + align:start position:0% +big farm in Afghanistan it's excellent +in fact it's Kalen and I think it has + + align:start position:0% +in fact it's Kalen and I think it has + + + align:start position:0% +in fact it's Kalen and I think it has +the son of uh ashrafgani on it as well + + align:start position:0% +the son of uh ashrafgani on it as well + + + align:start position:0% +the son of uh ashrafgani on it as well +so + + align:start position:0% +so + + + align:start position:0% +so +who is actually a economics professor + + align:start position:0% +who is actually a economics professor + + + align:start position:0% +who is actually a economics professor +and business school somewhere in the US + + align:start position:0% +and business school somewhere in the US + + + align:start position:0% +and business school somewhere in the US +so it's interesting also for that + + align:start position:0% +so it's interesting also for that + + + align:start position:0% +so it's interesting also for that +purpose and I suggest that you read it + + align:start position:0% +purpose and I suggest that you read it + + + align:start position:0% +purpose and I suggest that you read it +there is also a lot more on on savings + + align:start position:0% +there is also a lot more on on savings + + + align:start position:0% +there is also a lot more on on savings +now it is inspired by unsavings people + + align:start position:0% +now it is inspired by unsavings people + + + align:start position:0% +now it is inspired by unsavings people +more recent empirical literature + + align:start position:0% +more recent empirical literature + + + align:start position:0% +more recent empirical literature +inspired by Boost the combination of + + align:start position:0% +inspired by Boost the combination of + + + align:start position:0% +inspired by Boost the combination of +these the type of models we discussed + + align:start position:0% +these the type of models we discussed + + + align:start position:0% +these the type of models we discussed +today and this original paper + + align:start position:0% +today and this original paper + + + align:start position:0% +today and this original paper +which maybe you'll see will have a + + align:start position:0% +which maybe you'll see will have a + + + align:start position:0% +which maybe you'll see will have a +chance to see investigation + + align:start position:0% +chance to see investigation + + + align:start position:0% +chance to see investigation +great thank you so much \ No newline at end of file diff --git a/j-C6QC5ufSw.txt b/j-C6QC5ufSw.txt new file mode 100644 index 0000000000000000000000000000000000000000..ad367c6eca58eeaaa718bdd7f75dae39e7fbf4f3 --- /dev/null +++ b/j-C6QC5ufSw.txt @@ -0,0 +1,7523 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following content is provided by MIT +open courseware under a Creative Commons + + align:start position:0% +open courseware under a Creative Commons + + + align:start position:0% +open courseware under a Creative Commons +license additional information about our + + align:start position:0% +license additional information about our + + + align:start position:0% +license additional information about our +license and MIT open courseware in + + align:start position:0% +license and MIT open courseware in + + + align:start position:0% +license and MIT open courseware in +general is available at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay so we go uh great um + + align:start position:0% +ocw.mit.edu okay so we go uh great um + + + align:start position:0% +ocw.mit.edu okay so we go uh great um +well I hope you enjoyed Patriots Day and + + align:start position:0% +well I hope you enjoyed Patriots Day and + + + align:start position:0% +well I hope you enjoyed Patriots Day and +uh we'll go for the final weeks of the + + align:start position:0% +uh we'll go for the final weeks of the + + + align:start position:0% +uh we'll go for the final weeks of the +course and I wanted to start with just + + align:start position:0% +course and I wanted to start with just + + + align:start position:0% +course and I wanted to start with just +uh thought about scientific Computing + + align:start position:0% +uh thought about scientific Computing + + + align:start position:0% +uh thought about scientific Computing +and and the people who work in it and + + align:start position:0% +and and the people who work in it and + + + align:start position:0% +and and the people who work in it and +the problems um so just sort of + + align:start position:0% +the problems um so just sort of + + + align:start position:0% +the problems um so just sort of +orientation uh and and maybe my point is + + align:start position:0% +orientation uh and and maybe my point is + + + align:start position:0% +orientation uh and and maybe my point is +that in part of the + + align:start position:0% +that in part of the + + + align:start position:0% +that in part of the +subject + + align:start position:0% +subject + + + align:start position:0% +subject +uh it's the the the it begins the + + align:start position:0% +uh it's the the the it begins the + + + align:start position:0% +uh it's the the the it begins the +situation is sorted like just give me + + align:start position:0% +situation is sorted like just give me + + + align:start position:0% +situation is sorted like just give me +the Matrix tell me the equation I don't + + align:start position:0% +the Matrix tell me the equation I don't + + + align:start position:0% +the Matrix tell me the equation I don't +want to know the physics behind + + align:start position:0% +want to know the physics behind + + + align:start position:0% +want to know the physics behind +it just the form of the equation and + + align:start position:0% +it just the form of the equation and + + + align:start position:0% +it just the form of the equation and +I'll discuss how it could be + + align:start position:0% +I'll discuss how it could be + + + align:start position:0% +I'll discuss how it could be +solved and to contrast that with what + + align:start position:0% +solved and to contrast that with what + + + align:start position:0% +solved and to contrast that with what +you may often be meeting in your Theses + + align:start position:0% +you may often be meeting in your Theses + + + align:start position:0% +you may often be meeting in your Theses +even in + + align:start position:0% +even in + + + align:start position:0% +even in +projects where + + align:start position:0% +projects where + + + align:start position:0% +projects where +uh the details the the physical + + align:start position:0% +uh the details the the physical + + + align:start position:0% +uh the details the the physical +consequences the the actual detailed + + align:start position:0% +consequences the the actual detailed + + + align:start position:0% +consequences the the actual detailed +behavior of the solution is what you're + + align:start position:0% +behavior of the solution is what you're + + + align:start position:0% +behavior of the solution is what you're +looking for so somehow there those two + + align:start position:0% +looking for so somehow there those two + + + align:start position:0% +looking for so somehow there those two +two parts of the world and and people + + align:start position:0% +two parts of the world and and people + + + align:start position:0% +two parts of the world and and people +people who know understand the physical + + align:start position:0% +people who know understand the physical + + + align:start position:0% +people who know understand the physical +problem are on the second side and + + align:start position:0% +problem are on the second side and + + + align:start position:0% +problem are on the second side and +people + + align:start position:0% +people + + + align:start position:0% +people +who maybe think just about + + align:start position:0% +who maybe think just about + + + align:start position:0% +who maybe think just about +matrices like that Matrix for example + + align:start position:0% +matrices like that Matrix for example + + + align:start position:0% +matrices like that Matrix for example +that Saddle Point Matrix uh are more on + + align:start position:0% +that Saddle Point Matrix uh are more on + + + align:start position:0% +that Saddle Point Matrix uh are more on +the first side like just give me the + + align:start position:0% +the first side like just give me the + + + align:start position:0% +the first side like just give me the +Matrix and I'll figure out how to uh how + + align:start position:0% +Matrix and I'll figure out how to uh how + + + align:start position:0% +Matrix and I'll figure out how to uh how +to uh solve it if how to solve the + + align:start position:0% +to uh solve it if how to solve the + + + align:start position:0% +to uh solve it if how to solve the +linear system if it's a large linear + + align:start position:0% +linear system if it's a large linear + + + align:start position:0% +linear system if it's a large linear +system I'll I'll invent + + align:start position:0% +system I'll I'll invent + + + align:start position:0% +system I'll I'll invent +preconditioners uh study stability + + align:start position:0% +preconditioners uh study stability + + + align:start position:0% +preconditioners uh study stability +whatever you have to do uh and uh but + + align:start position:0% +whatever you have to do uh and uh but + + + align:start position:0% +whatever you have to do uh and uh but +today's lecture is kind of half and half + + align:start position:0% +today's lecture is kind of half and half + + + align:start position:0% +today's lecture is kind of half and half +because that is the framework that we're + + align:start position:0% +because that is the framework that we're + + + align:start position:0% +because that is the framework that we're +in but the problem comes from a + + align:start position:0% +in but the problem comes from a + + + align:start position:0% +in but the problem comes from a +real uh problem in + + align:start position:0% +real uh problem in + + + align:start position:0% +real uh problem in +fluids and it's called The Stokes + + align:start position:0% +fluids and it's called The Stokes + + + align:start position:0% +fluids and it's called The Stokes +problem not na + + align:start position:0% +problem not na + + + align:start position:0% +problem not na +Stokes so Stokes + + align:start position:0% +Stokes so Stokes + + + align:start position:0% +Stokes so Stokes +alone is dealing with this question when + + align:start position:0% +alone is dealing with this question when + + + align:start position:0% +alone is dealing with this question when +there is a diffusion term and I've + + align:start position:0% +there is a diffusion term and I've + + + align:start position:0% +there is a diffusion term and I've +normalized the coefficient there + + align:start position:0% +normalized the coefficient there + + + align:start position:0% +normalized the coefficient there +viscos viscosity term whatever we call + + align:start position:0% +viscos viscosity term whatever we call + + + align:start position:0% +viscos viscosity term whatever we call +it to be one and there is the constraint + + align:start position:0% +it to be one and there is the constraint + + + align:start position:0% +it to be one and there is the constraint +of incompressibility + + align:start position:0% + + + + align:start position:0% + +constant pressure Divergence P equals z + + align:start position:0% +constant pressure Divergence P equals z + + + align:start position:0% +constant pressure Divergence P equals z +i sorry not constant Divergence of P + + align:start position:0% +i sorry not constant Divergence of P + + + align:start position:0% +i sorry not constant Divergence of P +equals z is a is a + + align:start position:0% +equals z is a is a + + + align:start position:0% +equals z is a is a +constraint and + + align:start position:0% + + + + align:start position:0% + +uh H how does that first let's just + + align:start position:0% +uh H how does that first let's just + + + align:start position:0% +uh H how does that first let's just +so make some comment on the physical + + align:start position:0% +so make some comment on the physical + + + align:start position:0% +so make some comment on the physical +side of this + + align:start position:0% +side of this + + + align:start position:0% +side of this +equation what we're + + align:start position:0% +equation what we're + + + align:start position:0% +equation what we're +missing that NV Stokes would put in is a + + align:start position:0% +missing that NV Stokes would put in is a + + + align:start position:0% +missing that NV Stokes would put in is a +convection term + + align:start position:0% +convection term + + + align:start position:0% +convection term +a a term of v. grad V that takes account + + align:start position:0% +a a term of v. grad V that takes account + + + align:start position:0% +a a term of v. grad V that takes account +of the fact that + + align:start position:0% +of the fact that + + + align:start position:0% +of the fact that +the there's a flow + + align:start position:0% +the there's a flow + + + align:start position:0% +the there's a flow +here things are moving we're not in a + + align:start position:0% +here things are moving we're not in a + + + align:start position:0% +here things are moving we're not in a +stationary situation and that term has + + align:start position:0% +stationary situation and that term has + + + align:start position:0% +stationary situation and that term has +been + + align:start position:0% +been + + + align:start position:0% +been +dropped so that's telling us then we are + + align:start position:0% +dropped so that's telling us then we are + + + align:start position:0% +dropped so that's telling us then we are +in the case of very very slow + + align:start position:0% +in the case of very very slow + + + align:start position:0% +in the case of very very slow +flow where that term could be neglected + + align:start position:0% +flow where that term could be neglected + + + align:start position:0% +flow where that term could be neglected +and certainly neglecting that term makes + + align:start position:0% +and certainly neglecting that term makes + + + align:start position:0% +and certainly neglecting that term makes +our problem easier it leaves us with + + align:start position:0% +our problem easier it leaves us with + + + align:start position:0% +our problem easier it leaves us with +this + + align:start position:0% +this + + + align:start position:0% +this +symmetric + + align:start position:0% +symmetric + + + align:start position:0% +symmetric +Matrix it doesn't make it totally easy + + align:start position:0% +Matrix it doesn't make it totally easy + + + align:start position:0% +Matrix it doesn't make it totally easy +as we'll see but it it's a lot easier + + align:start position:0% +as we'll see but it it's a lot easier + + + align:start position:0% +as we'll see but it it's a lot easier +than when the the convection term that + + align:start position:0% +than when the the convection term that + + + align:start position:0% +than when the the convection term that +which by the way is not symmetric + + align:start position:0% +which by the way is not symmetric + + + align:start position:0% +which by the way is not symmetric +and pushes us outside this framework if + + align:start position:0% +and pushes us outside this framework if + + + align:start position:0% +and pushes us outside this framework if +that's present and of course in + + align:start position:0% +that's present and of course in + + + align:start position:0% +that's present and of course in +computational fluid dynamics that's the + + align:start position:0% +computational fluid dynamics that's the + + + align:start position:0% +computational fluid dynamics that's the +central problem uh you have to deal with + + align:start position:0% +central problem uh you have to deal with + + + align:start position:0% +central problem uh you have to deal with +it but so we're taking a model problem + + align:start position:0% +it but so we're taking a model problem + + + align:start position:0% +it but so we're taking a model problem +that doesn't have the convection doesn't + + align:start position:0% +that doesn't have the convection doesn't + + + align:start position:0% +that doesn't have the convection doesn't +have that unsymmetric + + align:start position:0% +have that unsymmetric + + + align:start position:0% +have that unsymmetric +complexity but actually it's become uh + + align:start position:0% +complexity but actually it's become uh + + + align:start position:0% +complexity but actually it's become uh +more and more important it's more than a + + align:start position:0% +more and more important it's more than a + + + align:start position:0% +more and more important it's more than a +model problem now because there are a + + align:start position:0% +model problem now because there are a + + + align:start position:0% +model problem now because there are a +lot of medical applications say probably + + align:start position:0% +lot of medical applications say probably + + + align:start position:0% +lot of medical applications say probably +the flow that your heart the flow of + + align:start position:0% +the flow that your heart the flow of + + + align:start position:0% +the flow that your heart the flow of +your + + align:start position:0% +your + + + align:start position:0% +your +blood pushed by the heart + + align:start position:0% +blood pushed by the heart + + + align:start position:0% +blood pushed by the heart +is you've got to account that's that's + + align:start position:0% +is you've got to account that's that's + + + align:start position:0% +is you've got to account that's that's +moving along at a decent rate but flow + + align:start position:0% +moving along at a decent rate but flow + + + align:start position:0% +moving along at a decent rate but flow +into tiny capillaries is slow and Stokes + + align:start position:0% +into tiny capillaries is slow and Stokes + + + align:start position:0% +into tiny capillaries is slow and Stokes +is a reasonable step and and then + + align:start position:0% +is a reasonable step and and then + + + align:start position:0% +is a reasonable step and and then +actually Stokes is also going to appear + + align:start position:0% +actually Stokes is also going to appear + + + align:start position:0% +actually Stokes is also going to appear +in N Stokes calculations because often + + align:start position:0% +in N Stokes calculations because often + + + align:start position:0% +in N Stokes calculations because often +when you have two difficult processes + + align:start position:0% +when you have two difficult processes + + + align:start position:0% +when you have two difficult processes +you do a kind of splitting method and + + align:start position:0% +you do a kind of splitting method and + + + align:start position:0% +you do a kind of splitting method and +you uh + + align:start position:0% +you uh + + + align:start position:0% +you uh +solve you you drop one + + align:start position:0% +solve you you drop one + + + align:start position:0% +solve you you drop one +term for half a step so you take for + + align:start position:0% +term for half a step so you take for + + + align:start position:0% +term for half a step so you take for +example a sto step and then you do + + align:start position:0% +example a sto step and then you do + + + align:start position:0% +example a sto step and then you do +what the fluid forces you to do you move + + align:start position:0% +what the fluid forces you to do you move + + + align:start position:0% +what the fluid forces you to do you move +that process with the flow okay so we're + + align:start position:0% +that process with the flow okay so we're + + + align:start position:0% +that process with the flow okay so we're +flowing slowly here + + align:start position:0% +flowing slowly here + + + align:start position:0% +flowing slowly here +okay and uh and the nice thing is that + + align:start position:0% +okay and uh and the nice thing is that + + + align:start position:0% +okay and uh and the nice thing is that +this fits + + align:start position:0% +this fits + + + align:start position:0% +this fits +our uh Saddle Point framework that's why + + align:start position:0% +our uh Saddle Point framework that's why + + + align:start position:0% +our uh Saddle Point framework that's why +I'm calling this block Matrix S and you + + align:start position:0% +I'm calling this block Matrix S and you + + + align:start position:0% +I'm calling this block Matrix S and you +see that it it really it came from the + + align:start position:0% +see that it it really it came from the + + + align:start position:0% +see that it it really it came from the +from from a + + align:start position:0% +from from a + + + align:start position:0% +from from a +minimization the minimization was the + + align:start position:0% +minimization the minimization was the + + + align:start position:0% +minimization the minimization was the +problem that leads to the lassan that + + align:start position:0% +problem that leads to the lassan that + + + align:start position:0% +problem that leads to the lassan that +that stands for the the llas operator + + align:start position:0% +that stands for the the llas operator + + + align:start position:0% +that stands for the the llas operator +with a minus sign to make it positive + + align:start position:0% +with a minus sign to make it positive + + + align:start position:0% +with a minus sign to make it positive +definite and and then this constraint + + align:start position:0% +definite and and then this constraint + + + align:start position:0% +definite and and then this constraint +gets imposed by a lon's + + align:start position:0% +gets imposed by a lon's + + + align:start position:0% +gets imposed by a lon's +multiplier P so p is the lon's + + align:start position:0% +multiplier P so p is the lon's + + + align:start position:0% +multiplier P so p is the lon's +multiplier here oh + + align:start position:0% +multiplier here oh + + + align:start position:0% +multiplier here oh +wrong Divergence V is zero + + align:start position:0% +wrong Divergence V is zero + + + align:start position:0% +wrong Divergence V is zero +incompressible + + align:start position:0% + + + + align:start position:0% + +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +please now that that's on the tape it's + + align:start position:0% +please now that that's on the tape it's + + + align:start position:0% +please now that that's on the tape it's +now on the tape right Divergence V is + + align:start position:0% +now on the tape right Divergence V is + + + align:start position:0% +now on the tape right Divergence V is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay okay so you remember that this you + + align:start position:0% +okay okay so you remember that this you + + + align:start position:0% +okay okay so you remember that this you +remember how our equations look + + align:start position:0% +remember how our equations look + + + align:start position:0% +remember how our equations look +uh let me just see if I'm going to write + + align:start position:0% +uh let me just see if I'm going to write + + + align:start position:0% +uh let me just see if I'm going to write +the the unknowns here V and P so that + + align:start position:0% +the the unknowns here V and P so that + + + align:start position:0% +the the unknowns here V and P so that +you see what everything is and it equals + + align:start position:0% +you see what everything is and it equals + + + align:start position:0% +you see what everything is and it equals +F and zero + + align:start position:0% +F and zero + + + align:start position:0% +F and zero +okay so this is now s so I chop off here + + align:start position:0% +okay so this is now s so I chop off here + + + align:start position:0% +okay so this is now s so I chop off here +so there you see the equations in the + + align:start position:0% +so there you see the equations in the + + + align:start position:0% +so there you see the equations in the +saddle point form so so a is the + + align:start position:0% +saddle point form so so a is the + + + align:start position:0% +saddle point form so so a is the +gradient + + align:start position:0% +gradient + + + align:start position:0% +gradient +and it operates on P and so p is a + + align:start position:0% +and it operates on P and so p is a + + + align:start position:0% +and it operates on P and so p is a +scalar I I better say can I if I put a + + align:start position:0% +scalar I I better say can I if I put a + + + align:start position:0% +scalar I I better say can I if I put a +little arrow here V is a vector it has + + align:start position:0% +little arrow here V is a vector it has + + + align:start position:0% +little arrow here V is a vector it has +two components say if we're in two a 2d + + align:start position:0% +two components say if we're in two a 2d + + + align:start position:0% +two components say if we're in two a 2d +problem F has two + + align:start position:0% +problem F has two + + + align:start position:0% +problem F has two +components P the lr's multiplier for + + align:start position:0% +components P the lr's multiplier for + + + align:start position:0% +components P the lr's multiplier for +this + + align:start position:0% +this + + + align:start position:0% +this +constraint the constraint is just a + + align:start position:0% +constraint the constraint is just a + + + align:start position:0% +constraint the constraint is just a +scalar constraint the Divergence is zero + + align:start position:0% +scalar constraint the Divergence is zero + + + align:start position:0% +scalar constraint the Divergence is zero +you remember what Divergence means + + align:start position:0% +you remember what Divergence means + + + align:start position:0% +you remember what Divergence means +dv1 DX + + + align:start position:0% +dv1 DX + + + + align:start position:0% +dv1 DX + +dv2 Dy so those are the two components + + align:start position:0% +dv2 Dy so those are the two components + + + align:start position:0% +dv2 Dy so those are the two components +of V the vector and its Divergence is + + align:start position:0% +of V the vector and its Divergence is + + + align:start position:0% +of V the vector and its Divergence is +zero and the and the these are well with + + align:start position:0% +zero and the and the these are well with + + + align:start position:0% +zero and the and the these are well with +the minus sign are uh adjoints of each + + align:start position:0% +the minus sign are uh adjoints of each + + + align:start position:0% +the minus sign are uh adjoints of each +other + + align:start position:0% + + + + align:start position:0% + +okay so what's new that makes this + + align:start position:0% +okay so what's new that makes this + + + align:start position:0% +okay so what's new that makes this +problem worth some + + align:start position:0% + + + + align:start position:0% + +study I guess that up to now we've taken + + align:start position:0% +study I guess that up to now we've taken + + + align:start position:0% +study I guess that up to now we've taken +problems like this and we've done + + align:start position:0% +problems like this and we've done + + + align:start position:0% +problems like this and we've done +elimination to get to a single equation + + align:start position:0% +elimination to get to a single equation + + + align:start position:0% +elimination to get to a single equation +you you remember that so that single + + align:start position:0% +you you remember that so that single + + + align:start position:0% +you you remember that so that single +equation is a transpose c + + align:start position:0% +equation is a transpose c + + + align:start position:0% +equation is a transpose c +a uh let's see what we're multiplying + + align:start position:0% +a uh let's see what we're multiplying + + + align:start position:0% +a uh let's see what we're multiplying +that row by a transpose C and + + align:start position:0% + + + + align:start position:0% + +subtracting and it right let me do the + + align:start position:0% +subtracting and it right let me do the + + + align:start position:0% +subtracting and it right let me do the +elimination on here I multiply the first + + align:start position:0% +elimination on here I multiply the first + + + align:start position:0% +elimination on here I multiply the first +equation by a transpose C you see I'm + + align:start position:0% +equation by a transpose C you see I'm + + + align:start position:0% +equation by a transpose C you see I'm +I'm doing the just give me the Matrix + + align:start position:0% +I'm doing the just give me the Matrix + + + align:start position:0% +I'm doing the just give me the Matrix +mode for now I'm multiply by a transpose + + align:start position:0% +mode for now I'm multiply by a transpose + + + align:start position:0% +mode for now I'm multiply by a transpose +C and I subtract so I the first equation + + align:start position:0% +C and I subtract so I the first equation + + + align:start position:0% +C and I subtract so I the first equation +is still there C inverse V plus a is + + align:start position:0% +is still there C inverse V plus a is + + + align:start position:0% +is still there C inverse V plus a is +f but the second equation now when I + + align:start position:0% +f but the second equation now when I + + + align:start position:0% +f but the second equation now when I +multiply by a transpose C so I just put + + align:start position:0% +multiply by a transpose C so I just put + + + align:start position:0% +multiply by a transpose C so I just put +it up there and subtract that produces a + + align:start position:0% +it up there and subtract that produces a + + + align:start position:0% +it up there and subtract that produces a +zero there it produces minus a transpose + + align:start position:0% +zero there it produces minus a transpose + + + align:start position:0% +zero there it produces minus a transpose +c a p equal minus a + + align:start position:0% +c a p equal minus a + + + align:start position:0% +c a p equal minus a +transpose + + align:start position:0% + + + + align:start position:0% + +CF it leads us to + + align:start position:0% +CF it leads us to + + + align:start position:0% +CF it leads us to +this crucial + + align:start position:0% +this crucial + + + align:start position:0% +this crucial +Matrix and in applications up to now + + align:start position:0% +Matrix and in applications up to now + + + align:start position:0% +Matrix and in applications up to now +that was the way to go that was totally + + align:start position:0% +that was the way to go that was totally + + + align:start position:0% +that was the way to go that was totally +satisfactory we eliminated V we got an + + align:start position:0% +satisfactory we eliminated V we got an + + + align:start position:0% +satisfactory we eliminated V we got an +equation for p we solved it and + + align:start position:0% +equation for p we solved it and + + + align:start position:0% +equation for p we solved it and +uh then once we knew P we went back and + + align:start position:0% +uh then once we knew P we went back and + + + align:start position:0% +uh then once we knew P we went back and +found V okay so why is this + + align:start position:0% +found V okay so why is this + + + align:start position:0% +found V okay so why is this +different why don't I want to get to a + + align:start position:0% +different why don't I want to get to a + + + align:start position:0% +different why don't I want to get to a +transpose CA the stiffness Matrix if we + + align:start position:0% +transpose CA the stiffness Matrix if we + + + align:start position:0% +transpose CA the stiffness Matrix if we +were in finite elements why do I want to + + align:start position:0% +were in finite elements why do I want to + + + align:start position:0% +were in finite elements why do I want to +stay with this two- field system these + + align:start position:0% +stay with this two- field system these + + + align:start position:0% +stay with this two- field system these +which in finite elements it's going to + + align:start position:0% +which in finite elements it's going to + + + align:start position:0% +which in finite elements it's going to +be a mixed method of finite elements I'm + + align:start position:0% +be a mixed method of finite elements I'm + + + align:start position:0% +be a mixed method of finite elements I'm +going to keep V and P in the problem for + + align:start position:0% +going to keep V and P in the problem for + + + align:start position:0% +going to keep V and P in the problem for +for a simple reason that + + align:start position:0% +for a simple reason that + + + align:start position:0% +for a simple reason that +c is a is in this problem is awkward c + + align:start position:0% +c is a is in this problem is awkward c + + + align:start position:0% +c is a is in this problem is awkward c +would be the inverse of the Lum C is the + + align:start position:0% +would be the inverse of the Lum C is the + + + align:start position:0% +would be the inverse of the Lum C is the +inverse of the Lan D2 by dx^ 2 plus D2 + + align:start position:0% +inverse of the Lan D2 by dx^ 2 plus D2 + + + align:start position:0% +inverse of the Lan D2 by dx^ 2 plus D2 +by D y^ + + align:start position:0% + + + + align:start position:0% + +2 that's what Delta stands for + + align:start position:0% +2 that's what Delta stands for + + + align:start position:0% +2 that's what Delta stands for +and that's an uncom + + align:start position:0% +and that's an uncom + + + align:start position:0% +and that's an uncom +able uh operator to work with the + + align:start position:0% +able uh operator to work with the + + + align:start position:0% +able uh operator to work with the +inverse here in Matrix language when we + + align:start position:0% +inverse here in Matrix language when we + + + align:start position:0% +inverse here in Matrix language when we +discretize it won't be sparse right the + + align:start position:0% +discretize it won't be sparse right the + + + align:start position:0% +discretize it won't be sparse right the +Lan is sparse the Lan gives us the 5 + + align:start position:0% +Lan is sparse the Lan gives us the 5 + + + align:start position:0% +Lan is sparse the Lan gives us the 5 +point Matrix The Matrix with five + + align:start position:0% +point Matrix The Matrix with five + + + align:start position:0% +point Matrix The Matrix with five +nonzeros on every row four on the + + align:start position:0% +nonzeros on every row four on the + + + align:start position:0% +nonzeros on every row four on the +diagonal and four minus ones that Matrix + + align:start position:0% +diagonal and four minus ones that Matrix + + + align:start position:0% +diagonal and four minus ones that Matrix +that we know the k2d + + align:start position:0% +that we know the k2d + + + align:start position:0% +that we know the k2d +Matrix but this is its inverse c is now + + align:start position:0% +Matrix but this is its inverse c is now + + + align:start position:0% +Matrix but this is its inverse c is now +its inverse it's the inverse of that + + align:start position:0% +its inverse it's the inverse of that + + + align:start position:0% +its inverse it's the inverse of that +Matrix k2d that we've studied and of + + align:start position:0% +Matrix k2d that we've studied and of + + + align:start position:0% +Matrix k2d that we've studied and of +course it's + + align:start position:0% +course it's + + + align:start position:0% +course it's +full so taking this + + align:start position:0% +full so taking this + + + align:start position:0% +full so taking this +step uh produces a completely full + + align:start position:0% +step uh produces a completely full + + + align:start position:0% +step uh produces a completely full +Matrix and uh all our efficient + + align:start position:0% +Matrix and uh all our efficient + + + align:start position:0% +Matrix and uh all our efficient +algorithms for large + + align:start position:0% +algorithms for large + + + align:start position:0% +algorithms for large +problems were for sparse + + align:start position:0% +problems were for sparse + + + align:start position:0% +problems were for sparse +matrices so whereas this one one is + + align:start position:0% +matrices so whereas this one one is + + + align:start position:0% +matrices so whereas this one one is +sparse I mean this is this is still this + + align:start position:0% +sparse I mean this is this is still this + + + align:start position:0% +sparse I mean this is this is still this +is the the plasan so we have the + + align:start position:0% +is the the plasan so we have the + + + align:start position:0% +is the the plasan so we have the +fivepoint Matrix sitting here here we + + align:start position:0% +fivepoint Matrix sitting here here we + + + align:start position:0% +fivepoint Matrix sitting here here we +have a discrete gradient and a discrete + + align:start position:0% +have a discrete gradient and a discrete + + + align:start position:0% +have a discrete gradient and a discrete +Divergence those are they're all + + align:start position:0% +Divergence those are they're all + + + align:start position:0% +Divergence those are they're all +derivatives and and you think of the + + align:start position:0% +derivatives and and you think of the + + + align:start position:0% +derivatives and and you think of the +derivatives as being replaced by + + align:start position:0% +derivatives as being replaced by + + + align:start position:0% +derivatives as being replaced by +differences these are all these matrices + + align:start position:0% +differences these are all these matrices + + + align:start position:0% +differences these are all these matrices +are + + align:start position:0% +are + + + align:start position:0% +are +sparse but if we take that fatal step of + + align:start position:0% +sparse but if we take that fatal step of + + + align:start position:0% +sparse but if we take that fatal step of +eliminating to get here the Matrix is + + align:start position:0% +eliminating to get here the Matrix is + + + align:start position:0% +eliminating to get here the Matrix is +full because of this this fact that the + + align:start position:0% +full because of this this fact that the + + + align:start position:0% +full because of this this fact that the +inverse of a sparse Matrix tends to be a + + align:start position:0% +inverse of a sparse Matrix tends to be a + + + align:start position:0% +inverse of a sparse Matrix tends to be a +full Matrix and you don't want to work + + align:start position:0% +full Matrix and you don't want to work + + + align:start position:0% +full Matrix and you don't want to work +with it so we don't want that's my + + align:start position:0% +with it so we don't want that's my + + + align:start position:0% +with it so we don't want that's my +message don't + + align:start position:0% +message don't + + + align:start position:0% +message don't +want a transpose a when this is not + + align:start position:0% +want a transpose a when this is not + + + align:start position:0% +want a transpose a when this is not +sparse okay + + align:start position:0% + + + + align:start position:0% + +so that's the point about this example + + align:start position:0% +so that's the point about this example + + + align:start position:0% +so that's the point about this example +which in the uh + + align:start position:0% +which in the uh + + + align:start position:0% +which in the uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh the notes on the website is uh on the + + align:start position:0% +uh the notes on the website is uh on the + + + align:start position:0% +uh the notes on the website is uh on the +is the section called the saddle point + + align:start position:0% +is the section called the saddle point + + + align:start position:0% +is the section called the saddle point +Stokes problem okay all right so now we + + align:start position:0% +Stokes problem okay all right so now we + + + align:start position:0% +Stokes problem okay all right so now we +we have both a specific example of the + + align:start position:0% +we have both a specific example of the + + + align:start position:0% +we have both a specific example of the +Stokes equations three equations really + + align:start position:0% +Stokes equations three equations really + + + align:start position:0% +Stokes equations three equations really +because this is two equations for V1 and + + align:start position:0% +because this is two equations for V1 and + + + align:start position:0% +because this is two equations for V1 and +V2 and this is the third + + align:start position:0% +V2 and this is the third + + + align:start position:0% +V2 and this is the third +equation the the + + align:start position:0% +equation the the + + + align:start position:0% +equation the the +constraint okay so we have both the + + align:start position:0% +constraint okay so we have both the + + + align:start position:0% +constraint okay so we have both the +specific example and the general case + + align:start position:0% +specific example and the general case + + + align:start position:0% +specific example and the general case +of how do + + align:start position:0% +of how do + + + align:start position:0% +of how do +you how do you so we're now going to + + align:start position:0% +you how do you so we're now going to + + + align:start position:0% +you how do you so we're now going to +work with that Matrix as a whole we're + + align:start position:0% +work with that Matrix as a whole we're + + + align:start position:0% +work with that Matrix as a whole we're +not going to reduce it to a transpose C + + align:start position:0% +not going to reduce it to a transpose C + + + align:start position:0% +not going to reduce it to a transpose C +though in principle we could and the the + + align:start position:0% +though in principle we could and the the + + + align:start position:0% +though in principle we could and the the +the question is one of + + align:start position:0% +the question is one of + + + align:start position:0% +the question is one of +stability so like stability is a + + align:start position:0% +stability so like stability is a + + + align:start position:0% +stability so like stability is a +question that didn't come up for our + + align:start position:0% +question that didn't come up for our + + + align:start position:0% +question that didn't come up for our +minimum principles when there were no + + align:start position:0% +minimum principles when there were no + + + align:start position:0% +minimum principles when there were no +constraints and maybe I'll just put a + + align:start position:0% +constraints and maybe I'll just put a + + + align:start position:0% +constraints and maybe I'll just put a +little mention why so so this is the + + align:start position:0% +little mention why so so this is the + + + align:start position:0% +little mention why so so this is the +first time we've had to face the + + align:start position:0% +first time we've had to face the + + + align:start position:0% +first time we've had to face the +question of + + align:start position:0% +question of + + + align:start position:0% +question of +stability that meaning meaning what what + + align:start position:0% +stability that meaning meaning what what + + + align:start position:0% +stability that meaning meaning what what +do I mean that the that s inverse is + + align:start position:0% +do I mean that the that s inverse is + + + align:start position:0% +do I mean that the that s inverse is +under + + align:start position:0% + + + + align:start position:0% + +control I don't mean that it's + + align:start position:0% + + + + align:start position:0% + +easy to compute that the M the inverse + + align:start position:0% +easy to compute that the M the inverse + + + align:start position:0% +easy to compute that the M the inverse +of that block Matrix but I I have to + + align:start position:0% +of that block Matrix but I I have to + + + align:start position:0% +of that block Matrix but I I have to +know that the Matrix is invertible and + + align:start position:0% +know that the Matrix is invertible and + + + align:start position:0% +know that the Matrix is invertible and +stability is always like one slight step + + align:start position:0% +stability is always like one slight step + + + align:start position:0% +stability is always like one slight step +more than just being invertible it means + + align:start position:0% +more than just being invertible it means + + + align:start position:0% +more than just being invertible it means +it's invertible and and you have some + + align:start position:0% +it's invertible and and you have some + + + align:start position:0% +it's invertible and and you have some +control of the inverse you know it's not + + align:start position:0% +control of the inverse you know it's not + + + align:start position:0% +control of the inverse you know it's not +just on the verge of disaster so + + align:start position:0% +just on the verge of disaster so + + + align:start position:0% +just on the verge of disaster so +stability we want to know about the + + align:start position:0% +stability we want to know about the + + + align:start position:0% +stability we want to know about the +inverse of that Matrix that that's + + align:start position:0% +inverse of that Matrix that that's + + + align:start position:0% +inverse of that Matrix that that's +essentially we want to know about the + + align:start position:0% +essentially we want to know about the + + + align:start position:0% +essentially we want to know about the +inverse of that Matrix and uh in the + + align:start position:0% +inverse of that Matrix and uh in the + + + align:start position:0% +inverse of that Matrix and uh in the +process we really want to know about the + + align:start position:0% +process we really want to know about the + + + align:start position:0% +process we really want to know about the +inverse of this + + align:start position:0% +inverse of this + + + align:start position:0% +inverse of this +Matrix so so we may not want to compute + + align:start position:0% +Matrix so so we may not want to compute + + + align:start position:0% +Matrix so so we may not want to compute +it that was my point but stability is is + + align:start position:0% +it that was my point but stability is is + + + align:start position:0% +it that was my point but stability is is +telling us we have here a matrix that's + + align:start position:0% +telling us we have here a matrix that's + + + align:start position:0% +telling us we have here a matrix that's +not positive definite that that's the + + align:start position:0% +not positive definite that that's the + + + align:start position:0% +not positive definite that that's the +that's the key issue here our Saddle + + align:start position:0% +that's the key issue here our Saddle + + + align:start position:0% +that's the key issue here our Saddle +Point M Matrix is not positive + + align:start position:0% +Point M Matrix is not positive + + + align:start position:0% +Point M Matrix is not positive +definite it has + + align:start position:0% +definite it has + + + align:start position:0% +definite it has +positive igen values and negative igen + + align:start position:0% +positive igen values and negative igen + + + align:start position:0% +positive igen values and negative igen +values let let me just take some example + + align:start position:0% +values let let me just take some example + + + align:start position:0% +values let let me just take some example +okay so here's here's an + + align:start position:0% +okay so here's here's an + + + align:start position:0% +okay so here's here's an +S so I have a positive thing there + + align:start position:0% +S so I have a positive thing there + + + align:start position:0% +S so I have a positive thing there +positive stuff or nonzero stuff there + + align:start position:0% +positive stuff or nonzero stuff there + + + align:start position:0% +positive stuff or nonzero stuff there +say there there's a simplest example I + + align:start position:0% +say there there's a simplest example I + + + align:start position:0% +say there there's a simplest example I +could think + + align:start position:0% + + + + align:start position:0% + +of that Matrix is not positive + + align:start position:0% + + + + align:start position:0% + +definite it's determinant as minus one + + align:start position:0% +definite it's determinant as minus one + + + align:start position:0% +definite it's determinant as minus one +actually + + align:start position:0% +actually + + + align:start position:0% +actually +but its igen values + + align:start position:0% +but its igen values + + + align:start position:0% +but its igen values +are I mean they're safely away from zero + + align:start position:0% +are I mean they're safely away from zero + + + align:start position:0% +are I mean they're safely away from zero +it's not singular or close to singular + + align:start position:0% +it's not singular or close to singular + + + align:start position:0% +it's not singular or close to singular +either now the question is uh so that 2 + + align:start position:0% +either now the question is uh so that 2 + + + align:start position:0% +either now the question is uh so that 2 +by two example no + + align:start position:0% +by two example no + + + align:start position:0% +by two example no +problem + + align:start position:0% +problem + + + align:start position:0% +problem +this + + align:start position:0% +this + + + align:start position:0% +this +equation + + align:start position:0% +equation + + + align:start position:0% +equation +uh well I could study the invertibility + + align:start position:0% +uh well I could study the invertibility + + + align:start position:0% +uh well I could study the invertibility +of that of this uh of this particular + + align:start position:0% +of that of this uh of this particular + + + align:start position:0% +of that of this uh of this particular +Matrix that would be solving + + align:start position:0% +Matrix that would be solving + + + align:start position:0% +Matrix that would be solving +differential equations in other words I + + align:start position:0% +differential equations in other words I + + + align:start position:0% +differential equations in other words I +could study the case are p and v uh + + align:start position:0% +could study the case are p and v uh + + + align:start position:0% +could study the case are p and v uh +under control if I have a bound on F + + align:start position:0% +under control if I have a bound on F + + + align:start position:0% +under control if I have a bound on F +Well they are but the the issue comes + + align:start position:0% +Well they are but the the issue comes + + + align:start position:0% +Well they are but the the issue comes +when I go to finite elements when I look + + align:start position:0% +when I go to finite elements when I look + + + align:start position:0% +when I go to finite elements when I look +at a Subspace now so I have to try to + + align:start position:0% +at a Subspace now so I have to try to + + + align:start position:0% +at a Subspace now so I have to try to +make that + + align:start position:0% +make that + + + align:start position:0% +make that +clear that that uh what I plan to do to + + align:start position:0% +clear that that uh what I plan to do to + + + align:start position:0% +clear that that uh what I plan to do to +solve a continuous problem is to + + align:start position:0% +solve a continuous problem is to + + + align:start position:0% +solve a continuous problem is to +discretize it so I'm going to this is my + + align:start position:0% +discretize it so I'm going to this is my + + + align:start position:0% +discretize it so I'm going to this is my +continuous + + align:start position:0% + + + + align:start position:0% + +Matrix block Matrix symbolic of the of + + align:start position:0% +Matrix block Matrix symbolic of the of + + + align:start position:0% +Matrix block Matrix symbolic of the of +the differential equation and it's + + align:start position:0% +the differential equation and it's + + + align:start position:0% +the differential equation and it's +okay analysis would show that but the + + align:start position:0% +okay analysis would show that but the + + + align:start position:0% +okay analysis would show that but the +question is if I approximate V by some + + align:start position:0% +question is if I approximate V by some + + + align:start position:0% +question is if I approximate V by some +finite + + align:start position:0% +finite + + + align:start position:0% +finite +element by some combination of finite + + align:start position:0% +element by some combination of finite + + + align:start position:0% +element by some combination of finite +elements let me call it + + align:start position:0% +elements let me call it + + + align:start position:0% +elements let me call it +VH if I approximate the pressure by some + + align:start position:0% +VH if I approximate the pressure by some + + + align:start position:0% +VH if I approximate the pressure by some +pressure elements + + align:start position:0% +pressure elements + + + align:start position:0% +pressure elements +pH then I'm sort of projecting the + + align:start position:0% +pH then I'm sort of projecting the + + + align:start position:0% +pH then I'm sort of projecting the +problem down into these into these + + align:start position:0% +problem down into these into these + + + align:start position:0% +problem down into these into these +finite dimensional finite element + + align:start position:0% +finite dimensional finite element + + + align:start position:0% +finite dimensional finite element +subspaces and of course F will get + + align:start position:0% +subspaces and of course F will get + + + align:start position:0% +subspaces and of course F will get +projected down to FH and the Matrix + + align:start position:0% +projected down to FH and the Matrix + + + align:start position:0% +projected down to FH and the Matrix +these these operators will turn into + + align:start position:0% +these these operators will turn into + + + align:start position:0% +these these operators will turn into +finite sparse Matrix IES and the + + align:start position:0% +finite sparse Matrix IES and the + + + align:start position:0% +finite sparse Matrix IES and the +question is that is that projection safe + + align:start position:0% +question is that is that projection safe + + + align:start position:0% +question is that is that projection safe +so that that's really it's the it's the + + align:start position:0% +so that that's really it's the it's the + + + align:start position:0% +so that that's really it's the it's the +stability s inverse is under control + + align:start position:0% +stability s inverse is under control + + + align:start position:0% +stability s inverse is under control +this is okay but is the projection of s + + align:start position:0% +this is okay but is the projection of s + + + align:start position:0% +this is okay but is the projection of s +inverse under control is the projection + + align:start position:0% +inverse under control is the projection + + + align:start position:0% +inverse under control is the projection +of s so if I project it is that is the + + align:start position:0% +of s so if I project it is that is the + + + align:start position:0% +of s so if I project it is that is the +inverse of that under + + align:start position:0% +inverse of that under + + + align:start position:0% +inverse of that under +control that's the question + + align:start position:0% +control that's the question + + + align:start position:0% +control that's the question +and and and the this projection + + align:start position:0% + + + + align:start position:0% + +is I what what comes up in applications + + align:start position:0% +is I what what comes up in applications + + + align:start position:0% +is I what what comes up in applications +this is a projection projection of the + + align:start position:0% +this is a projection projection of the + + + align:start position:0% +this is a projection projection of the +of the continuous problem the + + align:start position:0% +of the continuous problem the + + + align:start position:0% +of the continuous problem the +differential equation onto finite + + align:start position:0% +differential equation onto finite + + + align:start position:0% +differential equation onto finite +element + + align:start position:0% + + + + align:start position:0% + +spaces finite element trial functions + + align:start position:0% + + + + align:start position:0% + +Okay so we've spoken a little about + + align:start position:0% +Okay so we've spoken a little about + + + align:start position:0% +Okay so we've spoken a little about +finite elements in this course and More + + align:start position:0% +finite elements in this course and More + + + align:start position:0% +finite elements in this course and More +in + + align:start position:0% +in + + + align:start position:0% +in +18085 and you probably have seen them + + align:start position:0% +18085 and you probably have seen them + + + align:start position:0% +18085 and you probably have seen them +elsewhere you know that we can + + align:start position:0% +elsewhere you know that we can + + + align:start position:0% +elsewhere you know that we can +approximate uh + + align:start position:0% +approximate uh + + + align:start position:0% +approximate uh +velocities by well here here would be a + + align:start position:0% +velocities by well here here would be a + + + align:start position:0% +velocities by well here here would be a +here would be a for here would be a a + + align:start position:0% +here would be a for here would be a a + + + align:start position:0% +here would be a for here would be a a +really important example because it's + + align:start position:0% +really important example because it's + + + align:start position:0% +really important example because it's +especially simple finite + + align:start position:0% +especially simple finite + + + align:start position:0% +especially simple finite +elements I take my region suppose it + + align:start position:0% +elements I take my region suppose it + + + align:start position:0% +elements I take my region suppose it +happened to be that + + align:start position:0% +happened to be that + + + align:start position:0% +happened to be that +rectangle I divide that rectangle into + + align:start position:0% +rectangle I divide that rectangle into + + + align:start position:0% +rectangle I divide that rectangle into +small + + align:start position:0% +small + + + align:start position:0% +small +squares there's a small square now in + + align:start position:0% +squares there's a small square now in + + + align:start position:0% +squares there's a small square now in +I'm using squares rather than + + align:start position:0% +I'm using squares rather than + + + align:start position:0% +I'm using squares rather than +triangles and in each + + align:start position:0% +triangles and in each + + + align:start position:0% +triangles and in each +Square I make some low degree + + align:start position:0% +Square I make some low degree + + + align:start position:0% +Square I make some low degree +approximation low degree trial function + + align:start position:0% +approximation low degree trial function + + + align:start position:0% +approximation low degree trial function +for the velocities and the pressures and + + align:start position:0% +for the velocities and the pressures and + + + align:start position:0% +for the velocities and the pressures and +the question is what functions can I + + align:start position:0% +the question is what functions can I + + + align:start position:0% +the question is what functions can I +use and for example one I would love to + + align:start position:0% +use and for example one I would love to + + + align:start position:0% +use and for example one I would love to +be able to use would be so in each + + align:start position:0% +be able to use would be so in each + + + align:start position:0% +be able to use would be so in each +Square I would like to be able to use + + align:start position:0% +Square I would like to be able to use + + + align:start position:0% +Square I would like to be able to use +piecewise constant + + align:start position:0% +piecewise constant + + + align:start position:0% +piecewise constant +pressures piecewise constant pressure so + + align:start position:0% +pressures piecewise constant pressure so + + + align:start position:0% +pressures piecewise constant pressure so +pH equal constant in in this is in each + + align:start position:0% +pH equal constant in in this is in each + + + align:start position:0% +pH equal constant in in this is in each +element in each El element is is the + + align:start position:0% +element in each El element is is the + + + align:start position:0% +element in each El element is is the +square so pH a different constant in + + align:start position:0% +square so pH a different constant in + + + align:start position:0% +square so pH a different constant in +each element so that would give me my my + + align:start position:0% +each element so that would give me my my + + + align:start position:0% +each element so that would give me my my +Vector of ph's it would be one component + + align:start position:0% +Vector of ph's it would be one component + + + align:start position:0% +Vector of ph's it would be one component +for every little + + align:start position:0% +for every little + + + align:start position:0% +for every little +square and now what about + + align:start position:0% +square and now what about + + + align:start position:0% +square and now what about +VH what would what trial function would + + align:start position:0% +VH what would what trial function would + + + align:start position:0% +VH what would what trial function would +I like to use for the + + align:start position:0% +I like to use for the + + + align:start position:0% +I like to use for the +velocities constant velocities wouldn't + + align:start position:0% +velocities constant velocities wouldn't + + + align:start position:0% +velocities constant velocities wouldn't +be good that's at least that's further + + align:start position:0% +be good that's at least that's further + + + align:start position:0% +be good that's at least that's further +than I'm willing to go I I'll go + + align:start position:0% +than I'm willing to go I I'll go + + + align:start position:0% +than I'm willing to go I I'll go +piecewise linear piecewise linear in + + align:start position:0% +piecewise linear piecewise linear in + + + align:start position:0% +piecewise linear piecewise linear in +each Square now piecewise linear in each + + align:start position:0% +each Square now piecewise linear in each + + + align:start position:0% +each Square now piecewise linear in each +triangle meant that it it had the form a + + align:start position:0% +triangle meant that it it had the form a + + + align:start position:0% +triangle meant that it it had the form a ++ BX plus c + + align:start position:0% ++ BX plus c + + + align:start position:0% ++ BX plus c +y strictly speaking that's what I should + + align:start position:0% +y strictly speaking that's what I should + + + align:start position:0% +y strictly speaking that's what I should +mean by piecewise linear with a + + align:start position:0% +mean by piecewise linear with a + + + align:start position:0% +mean by piecewise linear with a +different coefficient ABC in each piece + + align:start position:0% +different coefficient ABC in each piece + + + align:start position:0% +different coefficient ABC in each piece +but because we're in squares now we've + + align:start position:0% +but because we're in squares now we've + + + align:start position:0% +but because we're in squares now we've +got + + align:start position:0% +got + + + align:start position:0% +got +four noal Valu vales and we want a + + align:start position:0% +four noal Valu vales and we want a + + + align:start position:0% +four noal Valu vales and we want a +fourth coefficient this was appropriate + + align:start position:0% +fourth coefficient this was appropriate + + + align:start position:0% +fourth coefficient this was appropriate +on triangles on a square we really + + align:start position:0% +on triangles on a square we really + + + align:start position:0% +on triangles on a square we really +include the bilary term + + align:start position:0% +include the bilary term + + + align:start position:0% +include the bilary term +dxy okay so we have + + align:start position:0% +dxy okay so we have + + + align:start position:0% +dxy okay so we have +four + + align:start position:0% +four + + + align:start position:0% +four +uh + + align:start position:0% +uh + + + align:start position:0% +uh +coefficients which we can determine from + + align:start position:0% +coefficients which we can determine from + + + align:start position:0% +coefficients which we can determine from +the which determine and can be + + align:start position:0% +the which determine and can be + + + align:start position:0% +the which determine and can be +determined from the four values of the + + align:start position:0% +determined from the four values of the + + + align:start position:0% +determined from the four values of the +nodes do you see that I'm describing the + + align:start position:0% +nodes do you see that I'm describing the + + + align:start position:0% +nodes do you see that I'm describing the +whole Space now I cut the region into + + align:start position:0% +whole Space now I cut the region into + + + align:start position:0% +whole Space now I cut the region into +more + + align:start position:0% +more + + + align:start position:0% +more +squares and uh I I've described a way of + + align:start position:0% +squares and uh I I've described a way of + + + align:start position:0% +squares and uh I I've described a way of +discretizing the differential equation + + align:start position:0% +discretizing the differential equation + + + align:start position:0% +discretizing the differential equation +of discretizing the differential + + align:start position:0% +of discretizing the differential + + + align:start position:0% +of discretizing the differential +equation the weak form of the continuous + + align:start position:0% +equation the weak form of the continuous + + + align:start position:0% +equation the weak form of the continuous +problem when I plug in these + + align:start position:0% +problem when I plug in these + + + align:start position:0% +problem when I plug in these +functions would give me a matrix problem + + align:start position:0% +functions would give me a matrix problem + + + align:start position:0% +functions would give me a matrix problem +a discrete problem that'll have this + + align:start position:0% +a discrete problem that'll have this + + + align:start position:0% +a discrete problem that'll have this +form and the question is + + align:start position:0% +form and the question is + + + align:start position:0% +form and the question is +how about do I have any control so it + + align:start position:0% +how about do I have any control so it + + + align:start position:0% +how about do I have any control so it +would give me this projected Matrix now + + align:start position:0% +would give me this projected Matrix now + + + align:start position:0% +would give me this projected Matrix now +finite dimensional instead of a + + align:start position:0% +finite dimensional instead of a + + + align:start position:0% +finite dimensional instead of a +continuous problem and the question is + + align:start position:0% +continuous problem and the question is + + + align:start position:0% +continuous problem and the question is +do I have I still got any + + align:start position:0% + + + + align:start position:0% + +control well the answer in this + + align:start position:0% +control well the answer in this + + + align:start position:0% +control well the answer in this +particular for this particular choice of + + align:start position:0% +particular for this particular choice of + + + align:start position:0% +particular for this particular choice of +pressure space and velocity space is + + align:start position:0% +pressure space and velocity space is + + + align:start position:0% +pressure space and velocity space is +no + + align:start position:0% +no + + + align:start position:0% +no +unfortunately this + + align:start position:0% +unfortunately this + + + align:start position:0% +unfortunately this +The Matrix that c that s that appears + + align:start position:0% +The Matrix that c that s that appears + + + align:start position:0% +The Matrix that c that s that appears +instead the the C + + align:start position:0% +instead the the C + + + align:start position:0% +instead the the C +inverse H shall I say the the the like + + align:start position:0% +inverse H shall I say the the the like + + + align:start position:0% +inverse H shall I say the the the like +the it would be it would be like our two + + align:start position:0% +the it would be it would be like our two + + + align:start position:0% +the it would be it would be like our two +k2d inverse that was pretty close to + + align:start position:0% +k2d inverse that was pretty close to + + + align:start position:0% +k2d inverse that was pretty close to +what it would be and the and the a h and + + align:start position:0% +what it would be and the and the a h and + + + align:start position:0% +what it would be and the and the a h and +the a transpose H and the + + align:start position:0% +the a transpose H and the + + + align:start position:0% +the a transpose H and the +zero uh that + + align:start position:0% +zero uh that + + + align:start position:0% +zero uh that +Matrix has a + + align:start position:0% +Matrix has a + + + align:start position:0% +Matrix has a +famous null Vector in this for this + + align:start position:0% +famous null Vector in this for this + + + align:start position:0% +famous null Vector in this for this +specific example I'm I'm asking you to + + align:start position:0% +specific example I'm I'm asking you to + + + align:start position:0% +specific example I'm I'm asking you to +I'm taking big jumps + + align:start position:0% + + + + align:start position:0% + +here because I'm just want to say the + + align:start position:0% +here because I'm just want to say the + + + align:start position:0% +here because I'm just want to say the +main + + align:start position:0% +main + + + align:start position:0% +main +point the main point here is that a a a + + align:start position:0% +point the main point here is that a a a + + + align:start position:0% +point the main point here is that a a a +null Vector appears in this problem s + + align:start position:0% +null Vector appears in this problem s + + + align:start position:0% +null Vector appears in this problem s +fails to be invertible and that null + + align:start position:0% +fails to be invertible and that null + + + align:start position:0% +fails to be invertible and that null +Vector is like + + align:start position:0% +Vector is like + + + align:start position:0% +Vector is like +finite element people know to know its + + align:start position:0% +finite element people know to know its + + + align:start position:0% +finite element people know to know its +name it has a couple of names actually + + align:start position:0% +name it has a couple of names actually + + + align:start position:0% +name it has a couple of names actually +maybe + + align:start position:0% +maybe + + + align:start position:0% +maybe +checkerboard it's it's the null Vector + + align:start position:0% +checkerboard it's it's the null Vector + + + align:start position:0% +checkerboard it's it's the null Vector +is a is a vector when the pressure is + + align:start position:0% +is a is a vector when the pressure is + + + align:start position:0% +is a is a vector when the pressure is +one minus one one minus one in a + + align:start position:0% +one minus one one minus one in a + + + align:start position:0% +one minus one one minus one in a +checkerboard + + align:start position:0% +checkerboard + + + align:start position:0% +checkerboard +pattern over the whole + + align:start position:0% +pattern over the whole + + + align:start position:0% +pattern over the whole +region and a corresponding + + align:start position:0% +region and a corresponding + + + align:start position:0% +region and a corresponding +velocity and well the trouble is that a + + align:start position:0% +velocity and well the trouble is that a + + + align:start position:0% +velocity and well the trouble is that a +* a * this p Ah * this p is zero that's + + align:start position:0% +* a * this p Ah * this p is zero that's + + + align:start position:0% +* a * this p Ah * this p is zero that's +that's what kills + + align:start position:0% +that's what kills + + + align:start position:0% +that's what kills +you that it turns out that a times that + + align:start position:0% +you that it turns out that a times that + + + align:start position:0% +you that it turns out that a times that +particular pressure is zero and if you + + align:start position:0% +particular pressure is zero and if you + + + align:start position:0% +particular pressure is zero and if you +lose control of a that way you've lost + + align:start position:0% +lose control of a that way you've lost + + + align:start position:0% +lose control of a that way you've lost +control of a transposed CA you've lost + + align:start position:0% +control of a transposed CA you've lost + + + align:start position:0% +control of a transposed CA you've lost +everything so uh + + align:start position:0% +everything so uh + + + align:start position:0% +everything so uh +so I guess coming back to my uh opening + + align:start position:0% +so I guess coming back to my uh opening + + + align:start position:0% +so I guess coming back to my uh opening +comments here's a case in which we have + + align:start position:0% +comments here's a case in which we have + + + align:start position:0% +comments here's a case in which we have +a physical problem but it falls into a + + align:start position:0% +a physical problem but it falls into a + + + align:start position:0% +a physical problem but it falls into a +pattern which uh where where where the + + align:start position:0% +pattern which uh where where where the + + + align:start position:0% +pattern which uh where where where the +mathematics actually decides are we able + + align:start position:0% +mathematics actually decides are we able + + + align:start position:0% +mathematics actually decides are we able +to use the trial spaces that are most + + align:start position:0% +to use the trial spaces that are most + + + align:start position:0% +to use the trial spaces that are most +convenient I say convenient rather than + + align:start position:0% +convenient I say convenient rather than + + + align:start position:0% +convenient I say convenient rather than +most accurate of course if I wanted to + + align:start position:0% +most accurate of course if I wanted to + + + align:start position:0% +most accurate of course if I wanted to +improve the accuracy I would improve I + + align:start position:0% +improve the accuracy I would improve I + + + align:start position:0% +improve the accuracy I would improve I +would go up in the degree I would take + + align:start position:0% +would go up in the degree I would take + + + align:start position:0% +would go up in the degree I would take +pressures to be peie wise linear and + + align:start position:0% +pressures to be peie wise linear and + + + align:start position:0% +pressures to be peie wise linear and +velocities to be + + align:start position:0% +velocities to be + + + align:start position:0% +velocities to be +piecewise + + align:start position:0% +piecewise + + + align:start position:0% +piecewise +quadratic with more points and I could + + align:start position:0% +quadratic with more points and I could + + + align:start position:0% +quadratic with more points and I could +check the stability or not the control + + align:start position:0% +check the stability or not the control + + + align:start position:0% +check the stability or not the control +of of the is the Matrix invertible or + + align:start position:0% +of of the is the Matrix invertible or + + + align:start position:0% +of of the is the Matrix invertible or +not and the answer might be better there + + align:start position:0% +not and the answer might be better there + + + align:start position:0% +not and the answer might be better there +in fact the notes and any book on finite + + align:start position:0% +in fact the notes and any book on finite + + + align:start position:0% +in fact the notes and any book on finite +elements has a list + + align:start position:0% +elements has a list + + + align:start position:0% +elements has a list +of and I don't plan to make that list + + align:start position:0% +of and I don't plan to make that list + + + align:start position:0% +of and I don't plan to make that list +here but it has a list of pressure + + align:start position:0% +here but it has a list of pressure + + + align:start position:0% +here but it has a list of pressure +spaces pressure + + align:start position:0% +spaces pressure + + + align:start position:0% +spaces pressure +elements and velocity + + align:start position:0% + + + + align:start position:0% + +elements on which the first guy that + + align:start position:0% +elements on which the first guy that + + + align:start position:0% +elements on which the first guy that +I've mentioned would be like q0 degree 0 + + align:start position:0% +I've mentioned would be like q0 degree 0 + + + align:start position:0% +I've mentioned would be like q0 degree 0 +and velocities q1 degree 1 and the + + align:start position:0% +and velocities q1 degree 1 and the + + + align:start position:0% +and velocities q1 degree 1 and the +letter Q being used for + + align:start position:0% +letter Q being used for + + + align:start position:0% +letter Q being used for +quadrilateral if I divided into + + align:start position:0% +quadrilateral if I divided into + + + align:start position:0% +quadrilateral if I divided into +triangles I would use the letter P for + + align:start position:0% +triangles I would use the letter P for + + + align:start position:0% +triangles I would use the letter P for +polom in that case and this is a a fail + + align:start position:0% +polom in that case and this is a a fail + + + align:start position:0% +polom in that case and this is a a fail +this one + + align:start position:0% +this one + + + align:start position:0% +this one +fails + + align:start position:0% +fails + + + align:start position:0% +fails +well and then but other lists would be + + align:start position:0% +well and then but other lists would be + + + align:start position:0% +well and then but other lists would be +how about q1 + + align:start position:0% +how about q1 + + + align:start position:0% +how about q1 +q1 I don't know I I wouldn't bet much on + + align:start position:0% +q1 I don't know I I wouldn't bet much on + + + align:start position:0% +q1 I don't know I I wouldn't bet much on +q1 q1 and of course I could look at the + + align:start position:0% +q1 q1 and of course I could look at the + + + align:start position:0% +q1 q1 and of course I could look at the +notes to see what the answer is or q1 Q2 + + align:start position:0% +notes to see what the answer is or q1 Q2 + + + align:start position:0% +notes to see what the answer is or q1 Q2 +that's probably got a better + + align:start position:0% +that's probably got a better + + + align:start position:0% +that's probably got a better +chance or many many you know people are + + align:start position:0% +chance or many many you know people are + + + align:start position:0% +chance or many many you know people are +inventing find out elements all the time + + align:start position:0% +inventing find out elements all the time + + + align:start position:0% +inventing find out elements all the time +and they're having to check the + + align:start position:0% +and they're having to check the + + + align:start position:0% +and they're having to check the +stability or not the in the uniform + + align:start position:0% +stability or not the in the uniform + + + align:start position:0% +stability or not the in the uniform +invertibility or not of s okay I I I + + align:start position:0% +invertibility or not of s okay I I I + + + align:start position:0% +invertibility or not of s okay I I I +just want to say that this one is so + + align:start position:0% +just want to say that this one is so + + + align:start position:0% +just want to say that this one is so +attractive because it's so simple that + + align:start position:0% +attractive because it's so simple that + + + align:start position:0% +attractive because it's so simple that +people don't give up on + + align:start position:0% +people don't give up on + + + align:start position:0% +people don't give up on +it they they want to go with this this + + align:start position:0% +it they they want to go with this this + + + align:start position:0% +it they they want to go with this this +is a fail + + align:start position:0% +is a fail + + + align:start position:0% +is a fail +but but so so + + align:start position:0% + + + + align:start position:0% + +stabilized that that one is so + + align:start position:0% +stabilized that that one is so + + + align:start position:0% +stabilized that that one is so +attractive and you know specifically + + align:start position:0% +attractive and you know specifically + + + align:start position:0% +attractive and you know specifically +that it's this checkerboard + + align:start position:0% +that it's this checkerboard + + + align:start position:0% +that it's this checkerboard +mode that is that's in the null space so + + align:start position:0% +mode that is that's in the null space so + + + align:start position:0% +mode that is that's in the null space so +you just think how am I going to get + + align:start position:0% +you just think how am I going to get + + + align:start position:0% +you just think how am I going to get +that mode out of the null space and the + + align:start position:0% +that mode out of the null space and the + + + align:start position:0% +that mode out of the null space and the +stabilizing method is you add in you + + align:start position:0% +stabilizing method is you add in you + + + align:start position:0% +stabilizing method is you add in you +stick a matrix here for purely numerical + + align:start position:0% +stick a matrix here for purely numerical + + + align:start position:0% +stick a matrix here for purely numerical +reasons and it'll be a matrix that's + + align:start position:0% +reasons and it'll be a matrix that's + + + align:start position:0% +reasons and it'll be a matrix that's +exactly has this checkerboard pattern so + + align:start position:0% +exactly has this checkerboard pattern so + + + align:start position:0% +exactly has this checkerboard pattern so +that it so that the checker board is not + + align:start position:0% +that it so that the checker board is not + + + align:start position:0% +that it so that the checker board is not +any longer in the null space Maybe I + + align:start position:0% +any longer in the null space Maybe I + + + align:start position:0% +any longer in the null space Maybe I +call it minus some little some small + + align:start position:0% +call it minus some little some small + + + align:start position:0% +call it minus some little some small +number times some some e matrix it's + + align:start position:0% +number times some some e matrix it's + + + align:start position:0% +number times some some e matrix it's +often written + + align:start position:0% + + + + align:start position:0% + +e and Alpha you keep as small as you + + align:start position:0% +e and Alpha you keep as small as you + + + align:start position:0% +e and Alpha you keep as small as you +dare but the effect is that it takes + + align:start position:0% +dare but the effect is that it takes + + + align:start position:0% +dare but the effect is that it takes +this + + align:start position:0% +this + + + align:start position:0% +this +checkerboard pressure out of the null + + align:start position:0% +checkerboard pressure out of the null + + + align:start position:0% +checkerboard pressure out of the null +space and and you + + align:start position:0% +space and and you + + + align:start position:0% +space and and you +uh you see the problem was that the + + align:start position:0% +uh you see the problem was that the + + + align:start position:0% +uh you see the problem was that the +without that The Columns of a were not + + align:start position:0% +without that The Columns of a were not + + + align:start position:0% +without that The Columns of a were not +independent a * P could be zero and if + + align:start position:0% +independent a * P could be zero and if + + + align:start position:0% +independent a * P could be zero and if +the if those columns are not independent + + align:start position:0% +the if those columns are not independent + + + align:start position:0% +the if those columns are not independent +you're lost let me put the zero + + align:start position:0% +you're lost let me put the zero + + + align:start position:0% +you're lost let me put the zero +back why was that a bad thing I want to + + align:start position:0% +back why was that a bad thing I want to + + + align:start position:0% +back why was that a bad thing I want to +Now sort of connect it to the Matrix + + align:start position:0% +Now sort of connect it to the Matrix + + + align:start position:0% +Now sort of connect it to the Matrix +theory if I have this particular + + align:start position:0% +theory if I have this particular + + + align:start position:0% +theory if I have this particular +pressure + + align:start position:0% +pressure + + + align:start position:0% +pressure +and ahp is zero so that that tells me + + align:start position:0% +and ahp is zero so that that tells me + + + align:start position:0% +and ahp is zero so that that tells me +that those columns of ah are + + align:start position:0% + + + + align:start position:0% + +dependent then The Columns of s are + + align:start position:0% +dependent then The Columns of s are + + + align:start position:0% +dependent then The Columns of s are +dependent right if I have something in + + align:start position:0% +dependent right if I have something in + + + align:start position:0% +dependent right if I have something in +the null space of + + align:start position:0% +the null space of + + + align:start position:0% +the null space of +ah then I just put a a pressure this + + align:start position:0% +ah then I just put a a pressure this + + + align:start position:0% +ah then I just put a a pressure this +pressure in the null space of ah then I + + align:start position:0% +pressure in the null space of ah then I + + + align:start position:0% +pressure in the null space of ah then I +just take the V to be zero then these + + align:start position:0% +just take the V to be zero then these + + + align:start position:0% +just take the V to be zero then these +guys don't do anything and the a times + + align:start position:0% +guys don't do anything and the a times + + + align:start position:0% +guys don't do anything and the a times +that bad pressure gives zero + + align:start position:0% +that bad pressure gives zero + + + align:start position:0% +that bad pressure gives zero +so I have a v p a velocity pressure + + align:start position:0% +so I have a v p a velocity pressure + + + align:start position:0% +so I have a v p a velocity pressure +that's in the null space okay so the way + + align:start position:0% +that's in the null space okay so the way + + + align:start position:0% +that's in the null space okay so the way +it gets fixed is to is toh stick in some + + align:start position:0% +it gets fixed is to is toh stick in some + + + align:start position:0% +it gets fixed is to is toh stick in some +small stabilizing Factor there okay all + + align:start position:0% +small stabilizing Factor there okay all + + + align:start position:0% +small stabilizing Factor there okay all +right now that's the specifics of this + + align:start position:0% +right now that's the specifics of this + + + align:start position:0% +right now that's the specifics of this +um particular + + align:start position:0% +um particular + + + align:start position:0% +um particular +example well I didn't give all the + + align:start position:0% +example well I didn't give all the + + + align:start position:0% +example well I didn't give all the +specifics if I were really on the ball I + + align:start position:0% +specifics if I were really on the ball I + + + align:start position:0% +specifics if I were really on the ball I +would show in + + align:start position:0% +would show in + + + align:start position:0% +would show in +detail why that + + align:start position:0% +detail why that + + + align:start position:0% +detail why that +checkerboard appears and kills this + + align:start position:0% +checkerboard appears and kills this + + + align:start position:0% +checkerboard appears and kills this +choice I would check each of these other + + align:start position:0% +choice I would check each of these other + + + align:start position:0% +choice I would check each of these other +choices and + + align:start position:0% +choices and + + + align:start position:0% +choices and +uh beside each one I would put fail or + + align:start position:0% +uh beside each one I would put fail or + + + align:start position:0% +uh beside each one I would put fail or +success and when it fails I would try to + + align:start position:0% +success and when it fails I would try to + + + align:start position:0% +success and when it fails I would try to +identify the P the the failure mode so + + align:start position:0% +identify the P the the failure mode so + + + align:start position:0% +identify the P the the failure mode so +that if if you wanted you could + + align:start position:0% +that if if you wanted you could + + + align:start position:0% +that if if you wanted you could +stabilize and get rid of that failure + + align:start position:0% +stabilize and get rid of that failure + + + align:start position:0% +stabilize and get rid of that failure +mode okay but uh + + align:start position:0% +mode okay but uh + + + align:start position:0% +mode okay but uh +maybe what I'll do instead is to look at + + align:start position:0% +maybe what I'll do instead is to look at + + + align:start position:0% +maybe what I'll do instead is to look at +is to come to the general question here + + align:start position:0% +is to come to the general question here + + + align:start position:0% +is to come to the general question here +so the general question is to deal with + + align:start position:0% +so the general question is to deal with + + + align:start position:0% +so the general question is to deal with +this Matrix S can I write it again C + + align:start position:0% +this Matrix S can I write it again C + + + align:start position:0% +this Matrix S can I write it again C +inverse a a transpose + + align:start position:0% +inverse a a transpose + + + align:start position:0% +inverse a a transpose +zero I want to look at its is it + + align:start position:0% +zero I want to look at its is it + + + align:start position:0% +zero I want to look at its is it +invertible can I get some bound on its + + align:start position:0% +invertible can I get some bound on its + + + align:start position:0% +invertible can I get some bound on its +inverse what do I have to know and again + + align:start position:0% +inverse what do I have to know and again + + + align:start position:0% +inverse what do I have to know and again +the the real I'll just emphasize here + + align:start position:0% +the the real I'll just emphasize here + + + align:start position:0% +the the real I'll just emphasize here +what's the real problem because we saw + + align:start position:0% +what's the real problem because we saw + + + align:start position:0% +what's the real problem because we saw +it right there the real problem + + align:start position:0% +it right there the real problem + + + align:start position:0% +it right there the real problem +is + + align:start position:0% +is + + + align:start position:0% +is +if The Columns of + + align:start position:0% +if The Columns of + + + align:start position:0% +if The Columns of +a are + + align:start position:0% + + + + align:start position:0% + +dependent in other + + align:start position:0% +dependent in other + + + align:start position:0% +dependent in other +words IE in other words a p equal Z has + + align:start position:0% +words IE in other words a p equal Z has + + + align:start position:0% +words IE in other words a p equal Z has +a nonzero + + align:start position:0% +a nonzero + + + align:start position:0% +a nonzero +solution then you're wiped + + align:start position:0% +solution then you're wiped + + + align:start position:0% +solution then you're wiped +out because as I'll just repeat if The + + align:start position:0% +out because as I'll just repeat if The + + + align:start position:0% +out because as I'll just repeat if The +Columns of a are + + align:start position:0% +Columns of a are + + + align:start position:0% +Columns of a are +dependent then The Columns of s are + + align:start position:0% +dependent then The Columns of s are + + + align:start position:0% +dependent then The Columns of s are +dependent The Matrix is singular and + + align:start position:0% +dependent The Matrix is singular and + + + align:start position:0% +dependent The Matrix is singular and +you're you're finished so somehow we + + align:start position:0% +you're you're finished so somehow we + + + align:start position:0% +you're you're finished so somehow we +have to get some muscle behind a but + + align:start position:0% +have to get some muscle behind a but + + + align:start position:0% +have to get some muscle behind a but +remember a is a rectangular Matrix this + + align:start position:0% +remember a is a rectangular Matrix this + + + align:start position:0% +remember a is a rectangular Matrix this +C is this C is M by m this a that comes + + align:start position:0% +C is this C is M by m this a that comes + + + align:start position:0% +C is this C is M by m this a that comes +up in the constraint this is the is is M + + align:start position:0% +up in the constraint this is the is is M + + + align:start position:0% +up in the constraint this is the is is M +byn it + + align:start position:0% +byn it + + + align:start position:0% +byn it +has we hope + + align:start position:0% +has we hope + + + align:start position:0% +has we hope +more rows than + + align:start position:0% + + + + align:start position:0% + +columns but still The Columns could be + + align:start position:0% +columns but still The Columns could be + + + align:start position:0% +columns but still The Columns could be +dependent and in this situation they are + + align:start position:0% +dependent and in this situation they are + + + align:start position:0% +dependent and in this situation they are +okay so the question is we have to get + + align:start position:0% +okay so the question is we have to get + + + align:start position:0% +okay so the question is we have to get +some muscle behind a and this is the + + align:start position:0% +some muscle behind a and this is the + + + align:start position:0% +some muscle behind a and this is the +famous + + align:start position:0% +famous + + + align:start position:0% +famous +condition so-called in soup condition + + align:start position:0% +condition so-called in soup condition + + + align:start position:0% +condition so-called in soup condition +that you would find in Professor B's + + align:start position:0% +that you would find in Professor B's + + + align:start position:0% +that you would find in Professor B's +finite element book but maybe uh these + + align:start position:0% +finite element book but maybe uh these + + + align:start position:0% +finite element book but maybe uh these +notes kind of focus on the heart of the + + align:start position:0% +notes kind of focus on the heart of the + + + align:start position:0% +notes kind of focus on the heart of the +idea + + align:start position:0% +idea + + + align:start position:0% +idea +and + + align:start position:0% +and + + + align:start position:0% +and +again it's in some way it's it's it's a + + align:start position:0% +again it's in some way it's it's it's a + + + align:start position:0% +again it's in some way it's it's it's a +condition on a + + align:start position:0% +condition on a + + + align:start position:0% +condition on a +really and on the pressure spaces and + + align:start position:0% +really and on the pressure spaces and + + + align:start position:0% +really and on the pressure spaces and +the velocity spaces that you + + align:start position:0% +the velocity spaces that you + + + align:start position:0% +the velocity spaces that you +choose okay so these you could really + + align:start position:0% +choose okay so these you could really + + + align:start position:0% +choose okay so these you could really +say are ah pH and VH but I'll skip + + align:start position:0% +say are ah pH and VH but I'll skip + + + align:start position:0% +say are ah pH and VH but I'll skip +writing hes on everything now so I'm I'm + + align:start position:0% +writing hes on everything now so I'm I'm + + + align:start position:0% +writing hes on everything now so I'm I'm +down on the discrete case uh but I have + + align:start position:0% +down on the discrete case uh but I have + + + align:start position:0% +down on the discrete case uh but I have +a sequence of discrete problems that's + + align:start position:0% +a sequence of discrete problems that's + + + align:start position:0% +a sequence of discrete problems that's +uh which are growing as h get smaller + + align:start position:0% +uh which are growing as h get smaller + + + align:start position:0% +uh which are growing as h get smaller +and the question is do I have a fixed + + align:start position:0% +and the question is do I have a fixed + + + align:start position:0% +and the question is do I have a fixed +beta that controls things and and it + + align:start position:0% +beta that controls things and and it + + + align:start position:0% +beta that controls things and and it +turns out that this is the this is the + + align:start position:0% +turns out that this is the this is the + + + align:start position:0% +turns out that this is the this is the +requirement that this in soup condition + + align:start position:0% +requirement that this in soup condition + + + align:start position:0% +requirement that this in soup condition +says that for every + + align:start position:0% +says that for every + + + align:start position:0% +says that for every +pressure there is a + + align:start position:0% +pressure there is a + + + align:start position:0% +pressure there is a +velocity every pressure every pressure + + align:start position:0% +velocity every pressure every pressure + + + align:start position:0% +velocity every pressure every pressure +every discrete pressure now there is a + + align:start position:0% +every discrete pressure now there is a + + + align:start position:0% +every discrete pressure now there is a +discrete velocity such that this holds + + align:start position:0% +discrete velocity such that this holds + + + align:start position:0% +discrete velocity such that this holds +so it's sort of forcing a to stay away + + align:start position:0% +so it's sort of forcing a to stay away + + + align:start position:0% +so it's sort of forcing a to stay away +from zero this this beta is a fixed + + align:start position:0% +from zero this this beta is a fixed + + + align:start position:0% +from zero this this beta is a fixed +number that's and and this sort of is + + align:start position:0% +number that's and and this sort of is + + + align:start position:0% +number that's and and this sort of is +the right + + align:start position:0% +the right + + + align:start position:0% +the right +normalization + + align:start position:0% +normalization + + + align:start position:0% +normalization +to that goes with this you you see why + + align:start position:0% +to that goes with this you you see why + + + align:start position:0% +to that goes with this you you see why +it's V transpose AP because + + align:start position:0% +it's V transpose AP because + + + align:start position:0% +it's V transpose AP because +a you know if I if I look at the at the + + align:start position:0% +a you know if I if I look at the at the + + + align:start position:0% +a you know if I if I look at the at the +quadratic form V transpose + + align:start position:0% +quadratic form V transpose + + + align:start position:0% +quadratic form V transpose +ppose you know the quadratic form with + + align:start position:0% +ppose you know the quadratic form with + + + align:start position:0% +ppose you know the quadratic form with +the Matrix is always multiply by a + + align:start position:0% +the Matrix is always multiply by a + + + align:start position:0% +the Matrix is always multiply by a +vector here multiply by its transpose + + align:start position:0% +vector here multiply by its transpose + + + align:start position:0% +vector here multiply by its transpose +here where does what where where is the + + align:start position:0% +here where does what where where is the + + + align:start position:0% +here where does what where where is the +a term a will multiply p and it'll be + + align:start position:0% +a term a will multiply p and it'll be + + + align:start position:0% +a term a will multiply p and it'll be +multiplied by V transpose in the in the + + align:start position:0% +multiplied by V transpose in the in the + + + align:start position:0% +multiplied by V transpose in the in the +quadratic part in the energy is this V + + align:start position:0% +quadratic part in the energy is this V + + + align:start position:0% +quadratic part in the energy is this V +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +AP and that's what we can't + + align:start position:0% +AP and that's what we can't + + + align:start position:0% +AP and that's what we can't +let go to zero because we are not + + align:start position:0% +let go to zero because we are not + + + align:start position:0% +let go to zero because we are not +because we're not if that part fails us + + align:start position:0% +because we're not if that part fails us + + + align:start position:0% +because we're not if that part fails us +then we've if we lose these and we have + + align:start position:0% +then we've if we lose these and we have + + + align:start position:0% +then we've if we lose these and we have +a zero there this part on the submatrix + + align:start position:0% +a zero there this part on the submatrix + + + align:start position:0% +a zero there this part on the submatrix +can't save us + + align:start position:0% +can't save us + + + align:start position:0% +can't save us +right so before I say anything more + + align:start position:0% +right so before I say anything more + + + align:start position:0% +right so before I say anything more +about that let me just emphasize what + + align:start position:0% +about that let me just emphasize what + + + align:start position:0% +about that let me just emphasize what +stability was in the in the + + align:start position:0% +stability was in the in the + + + align:start position:0% +stability was in the in the +uh in the in the symmetric case so + + align:start position:0% +uh in the in the symmetric case so + + + align:start position:0% +uh in the in the symmetric case so +suppose I have a symmetric positive def + + align:start position:0% +suppose I have a symmetric positive def + + + align:start position:0% +suppose I have a symmetric positive def +symmetric + + align:start position:0% + + + + align:start position:0% + +matrix it's got some + + align:start position:0% +matrix it's got some + + + align:start position:0% +matrix it's got some +values Lambda + + align:start position:0% +values Lambda + + + align:start position:0% +values Lambda +1 to Lambda n okay now so this is this + + align:start position:0% +1 to Lambda n okay now so this is this + + + align:start position:0% +1 to Lambda n okay now so this is this +is what what you see on this board is + + align:start position:0% +is what what you see on this board is + + + align:start position:0% +is what what you see on this board is +going to explain why stability is + + align:start position:0% +going to explain why stability is + + + align:start position:0% +going to explain why stability is +automatic if I'm if I'm dealing with + + align:start position:0% +automatic if I'm if I'm dealing with + + + align:start position:0% +automatic if I'm if I'm dealing with +positive definite + + align:start position:0% +positive definite + + + align:start position:0% +positive definite +things so suppose I + + align:start position:0% +things so suppose I + + + align:start position:0% +things so suppose I +project I take this m + + align:start position:0% +project I take this m + + + align:start position:0% +project I take this m +uh let me just let me project in the in + + align:start position:0% +uh let me just let me project in the in + + + align:start position:0% +uh let me just let me project in the in +the most uh direct way I'll throw away + + align:start position:0% +the most uh direct way I'll throw away + + + align:start position:0% +the most uh direct way I'll throw away +the first the last row and + + align:start position:0% +the first the last row and + + + align:start position:0% +the first the last row and +column suppose I throw away the last row + + align:start position:0% +column suppose I throw away the last row + + + align:start position:0% +column suppose I throw away the last row +and column so that that part is now gone + + align:start position:0% +and column so that that part is now gone + + + align:start position:0% +and column so that that part is now gone +so this these are the I values of + + align:start position:0% + + + + align:start position:0% + +K and of course being positive definite + + align:start position:0% +K and of course being positive definite + + + align:start position:0% +K and of course being positive definite +they're bigger than zero okay now so + + align:start position:0% +they're bigger than zero okay now so + + + align:start position:0% +they're bigger than zero okay now so +that was the whole Matrix but now what + + align:start position:0% +that was the whole Matrix but now what + + + align:start position:0% +that was the whole Matrix but now what +I'm going to do is I'm going to project + + align:start position:0% +I'm going to do is I'm going to project + + + align:start position:0% +I'm going to do is I'm going to project +on the first n minus one rows and + + align:start position:0% +on the first n minus one rows and + + + align:start position:0% +on the first n minus one rows and +columns so I'm going to look at the + + align:start position:0% +columns so I'm going to look at the + + + align:start position:0% +columns so I'm going to look at the +submatrix K sub n minus + + align:start position:0% +submatrix K sub n minus + + + align:start position:0% +submatrix K sub n minus +one and it has some igen + + align:start position:0% +one and it has some igen + + + align:start position:0% +one and it has some igen +values are they the same as those no no + + align:start position:0% +values are they the same as those no no + + + align:start position:0% +values are they the same as those no no +way the the igen values of K of this + + align:start position:0% +way the the igen values of K of this + + + align:start position:0% +way the the igen values of K of this +submatrix will be and you see I'm not in + + align:start position:0% +submatrix will be and you see I'm not in + + + align:start position:0% +submatrix will be and you see I'm not in +this situation this was not positive + + align:start position:0% +this situation this was not positive + + + align:start position:0% +this situation this was not positive +definite so I'm looking here at the + + align:start position:0% +definite so I'm looking here at the + + + align:start position:0% +definite so I'm looking here at the +positive definite case this has some IG + + align:start position:0% +positive definite case this has some IG + + + align:start position:0% +positive definite case this has some IG +values say mu1 up to Mu n minus one + + align:start position:0% +values say mu1 up to Mu n minus one + + + align:start position:0% +values say mu1 up to Mu n minus one +these will be the IG values of of the + + align:start position:0% +these will be the IG values of of the + + + align:start position:0% +these will be the IG values of of the +submatrix KNN minus + + align:start position:0% +submatrix KNN minus + + + align:start position:0% +submatrix KNN minus +one and linear algebra is just like the + + align:start position:0% +one and linear algebra is just like the + + + align:start position:0% +one and linear algebra is just like the +right place to look for some information + + align:start position:0% +right place to look for some information + + + align:start position:0% +right place to look for some information +on + + align:start position:0% +on + + + align:start position:0% +on +the connection between the M's and the + + align:start position:0% +the connection between the M's and the + + + align:start position:0% +the connection between the M's and the +lambdas they're certainly not + + align:start position:0% +lambdas they're certainly not + + + align:start position:0% +lambdas they're certainly not +equal now here's a question here's a a + + align:start position:0% +equal now here's a question here's a a + + + align:start position:0% +equal now here's a question here's a a +first question is if I take a positive + + align:start position:0% +first question is if I take a positive + + + align:start position:0% +first question is if I take a positive +definite Matrix with positive I values I + + align:start position:0% +definite Matrix with positive I values I + + + align:start position:0% +definite Matrix with positive I values I +throw away the + + align:start position:0% +throw away the + + + align:start position:0% +throw away the +last row and column do I still have a + + align:start position:0% +last row and column do I still have a + + + align:start position:0% +last row and column do I still have a +positive definite is that submatrix + + align:start position:0% +positive definite is that submatrix + + + align:start position:0% +positive definite is that submatrix +positive + + align:start position:0% +positive + + + align:start position:0% +positive +definite and the answer is yes the igen + + align:start position:0% +definite and the answer is yes the igen + + + align:start position:0% +definite and the answer is yes the igen +values are all + + align:start position:0% +values are all + + + align:start position:0% +values are all +positive and more than that + + align:start position:0% +positive and more than that + + + align:start position:0% +positive and more than that +more than that the small how about that + + align:start position:0% +more than that the small how about that + + + align:start position:0% +more than that the small how about that +smallest IG value because the smallest + + align:start position:0% +smallest IG value because the smallest + + + align:start position:0% +smallest IG value because the smallest +IG value is measuring like how close are + + align:start position:0% +IG value is measuring like how close are + + + align:start position:0% +IG value is measuring like how close are +we to disaster to singular can I say + + align:start position:0% +we to disaster to singular can I say + + + align:start position:0% +we to disaster to singular can I say +anything about that smallest I value and + + align:start position:0% +anything about that smallest I value and + + + align:start position:0% +anything about that smallest I value and +the answer is yes that the smallest Dion + + align:start position:0% +the answer is yes that the smallest Dion + + + align:start position:0% +the answer is yes that the smallest Dion +value of k n minus one is never below + + align:start position:0% +value of k n minus one is never below + + + align:start position:0% +value of k n minus one is never below +the smallest ion value of the big of the + + align:start position:0% +the smallest ion value of the big of the + + + align:start position:0% +the smallest ion value of the big of the +full Matrix so if the full Matrix is + + align:start position:0% +full Matrix so if the full Matrix is + + + align:start position:0% +full Matrix so if the full Matrix is +okay all the projections all the all the + + align:start position:0% +okay all the projections all the all the + + + align:start position:0% +okay all the projections all the all the +subspaces all the submatrices are even + + align:start position:0% +subspaces all the submatrices are even + + + align:start position:0% +subspaces all the submatrices are even +more okay that's the and up at the other + + align:start position:0% +more okay that's the and up at the other + + + align:start position:0% +more okay that's the and up at the other +end the at the top + + align:start position:0% +end the at the top + + + align:start position:0% +end the at the top +end Lambda n mu n mu the top I value in + + align:start position:0% +end Lambda n mu n mu the top I value in + + + align:start position:0% +end Lambda n mu n mu the top I value in +the + + align:start position:0% +the + + + align:start position:0% +the +submatrix never passes the top ion value + + align:start position:0% +submatrix never passes the top ion value + + + align:start position:0% +submatrix never passes the top ion value +in the big Matrix so you see at both + + align:start position:0% +in the big Matrix so you see at both + + + align:start position:0% +in the big Matrix so you see at both +ends I have what I want I have control + + align:start position:0% +ends I have what I want I have control + + + align:start position:0% +ends I have what I want I have control +the if I have some range of ion values + + align:start position:0% +the if I have some range of ion values + + + align:start position:0% +the if I have some range of ion values +for the big Matrix then all its + + align:start position:0% +for the big Matrix then all its + + + align:start position:0% +for the big Matrix then all its +projections are inside that + + align:start position:0% +projections are inside that + + + align:start position:0% +projections are inside that +range and therefore the condition number + + align:start position:0% +range and therefore the condition number + + + align:start position:0% +range and therefore the condition number +which would be the ratio of this to this + + align:start position:0% +which would be the ratio of this to this + + + align:start position:0% +which would be the ratio of this to this +is smaller than the condition number of + + align:start position:0% +is smaller than the condition number of + + + align:start position:0% +is smaller than the condition number of +the of the whole Matrix so the so the + + align:start position:0% +the of the whole Matrix so the so the + + + align:start position:0% +the of the whole Matrix so the so the +condition number + + align:start position:0% +condition number + + + align:start position:0% +condition number +of KNN minus1 is lesser equal the + + align:start position:0% +of KNN minus1 is lesser equal the + + + align:start position:0% +of KNN minus1 is lesser equal the +condition number of knen + + align:start position:0% +condition number of knen + + + align:start position:0% +condition number of knen +okay so okay and that's exactly what why + + align:start position:0% +okay so okay and that's exactly what why + + + align:start position:0% +okay so okay and that's exactly what why +working with positive definite matrices + + align:start position:0% +working with positive definite matrices + + + align:start position:0% +working with positive definite matrices +is is so comfortable it's the stability + + align:start position:0% +is is so comfortable it's the stability + + + align:start position:0% +is is so comfortable it's the stability +is just + + align:start position:0% +is just + + + align:start position:0% +is just +automatic but here we're not working + + align:start position:0% +automatic but here we're not working + + + align:start position:0% +automatic but here we're not working +with positive definite matrices the + + align:start position:0% +with positive definite matrices the + + + align:start position:0% +with positive definite matrices the +stability is not automatic and we need + + align:start position:0% +stability is not automatic and we need + + + align:start position:0% +stability is not automatic and we need +this uh in soup condition and I don't + + align:start position:0% +this uh in soup condition and I don't + + + align:start position:0% +this uh in soup condition and I don't +know whether to try maybe I'm I'm a + + align:start position:0% +know whether to try maybe I'm I'm a + + + align:start position:0% +know whether to try maybe I'm I'm a +little hesitant to go through the steps + + align:start position:0% +little hesitant to go through the steps + + + align:start position:0% +little hesitant to go through the steps +that lead from there to + + align:start position:0% +that lead from there to + + + align:start position:0% +that lead from there to +there because I've already this lecture + + align:start position:0% +there because I've already this lecture + + + align:start position:0% +there because I've already this lecture +is already uh asking you to to put a lot + + align:start position:0% +is already uh asking you to to put a lot + + + align:start position:0% +is already uh asking you to to put a lot +of things together without details and + + align:start position:0% +of things together without details and + + + align:start position:0% +of things together without details and +the notes do the best job I could do in + + align:start position:0% +the notes do the best job I could do in + + + align:start position:0% +the notes do the best job I could do in +the in in making those steps simple and + + align:start position:0% +the in in making those steps simple and + + + align:start position:0% +the in in making those steps simple and +clear that and this is what you actually + + align:start position:0% +clear that and this is what you actually + + + align:start position:0% +clear that and this is what you actually +check you you check this condition + + align:start position:0% + + + + align:start position:0% + +for any proposed finite + + align:start position:0% +for any proposed finite + + + align:start position:0% +for any proposed finite +element and uh and any different problem + + align:start position:0% +element and uh and any different problem + + + align:start position:0% +element and uh and any different problem +it wouldn't have to be the Stokes + + align:start position:0% +it wouldn't have to be the Stokes + + + align:start position:0% +it wouldn't have to be the Stokes +problem other problems would give us uh + + align:start position:0% +problem other problems would give us uh + + + align:start position:0% +problem other problems would give us uh +a constraint Matrix + + align:start position:0% +a constraint Matrix + + + align:start position:0% +a constraint Matrix +a + + align:start position:0% +a + + + align:start position:0% +a +uh a sort of stiffness submatrix C + + align:start position:0% +uh a sort of stiffness submatrix C + + + align:start position:0% +uh a sort of stiffness submatrix C +inverse and uh and we could check the + + align:start position:0% +inverse and uh and we could check the + + + align:start position:0% +inverse and uh and we could check the +the the condition again okay so maybe + + align:start position:0% +the the condition again okay so maybe + + + align:start position:0% +the the condition again okay so maybe +I'm going to leave that statement to uh + + align:start position:0% +I'm going to leave that statement to uh + + + align:start position:0% +I'm going to leave that statement to uh +for uh for um the + + align:start position:0% +for uh for um the + + + align:start position:0% +for uh for um the +notes okay so that's this in soup + + align:start position:0% +notes okay so that's this in soup + + + align:start position:0% +notes okay so that's this in soup +condition that says that and and of + + align:start position:0% +condition that says that and and of + + + align:start position:0% +condition that says that and and of +course you you see right away + + align:start position:0% +course you you see right away + + + align:start position:0% +course you you see right away +that if if a had dependent columns which + + align:start position:0% +that if if a had dependent columns which + + + align:start position:0% +that if if a had dependent columns which +is the the big risk + + align:start position:0% +is the the big risk + + + align:start position:0% +is the the big risk +if a had dependent columns that would + + align:start position:0% +if a had dependent columns that would + + + align:start position:0% +if a had dependent columns that would +mean that AP is + + align:start position:0% +mean that AP is + + + align:start position:0% +mean that AP is +zero for some p and then there would be + + align:start position:0% +zero for some p and then there would be + + + align:start position:0% +zero for some p and then there would be +no v no V could possibly be found that + + align:start position:0% +no v no V could possibly be found that + + + align:start position:0% +no v no V could possibly be found that +would save it right if if a had + + align:start position:0% +would save it right if if a had + + + align:start position:0% +would save it right if if a had +dependent columns that's that's the real + + align:start position:0% +dependent columns that's that's the real + + + align:start position:0% +dependent columns that's that's the real +that's the like the the bogey man that + + align:start position:0% +that's the like the the bogey man that + + + align:start position:0% +that's the like the the bogey man that +we're avoiding above all if a had + + align:start position:0% +we're avoiding above all if a had + + + align:start position:0% +we're avoiding above all if a had +dependent columns then there would be a + + align:start position:0% +dependent columns then there would be a + + + align:start position:0% +dependent columns then there would be a +solution to AP equals z the this left + + align:start position:0% +solution to AP equals z the this left + + + align:start position:0% +solution to AP equals z the this left +side would would be zero the right side + + align:start position:0% +side would would be zero the right side + + + align:start position:0% +side would would be zero the right side +wouldn't and + + align:start position:0% +wouldn't and + + + align:start position:0% +wouldn't and +uh um and the inp condition would fail + + align:start position:0% +uh um and the inp condition would fail + + + align:start position:0% +uh um and the inp condition would fail +but the in soup condition tells us well + + align:start position:0% +but the in soup condition tells us well + + + align:start position:0% +but the in soup condition tells us well +what about if if there's if there are + + align:start position:0% +what about if if there's if there are + + + align:start position:0% +what about if if there's if there are +pressures that where + + align:start position:0% +pressures that where + + + align:start position:0% +pressures that where +a gets smaller and smaller as as the + + align:start position:0% +a gets smaller and smaller as as the + + + align:start position:0% +a gets smaller and smaller as as the +mesh size changes then the question is + + align:start position:0% +mesh size changes then the question is + + + align:start position:0% +mesh size changes then the question is +can I find a V and so on so that this + + align:start position:0% +can I find a V and so on so that this + + + align:start position:0% +can I find a V and so on so that this +that's the the full condition but not to + + align:start position:0% +that's the the full condition but not to + + + align:start position:0% +that's the the full condition but not to +lose sight of the fact that the the uh + + align:start position:0% +lose sight of the fact that the the uh + + + align:start position:0% +lose sight of the fact that the the uh +central question the the the key + + align:start position:0% +central question the the the key + + + align:start position:0% +central question the the the key +question is this de Independence or + + align:start position:0% +question is this de Independence or + + + align:start position:0% +question is this de Independence or +dependence of The Columns of a okay good + + align:start position:0% +dependence of The Columns of a okay good + + + align:start position:0% +dependence of The Columns of a okay good +so + + align:start position:0% +so + + + align:start position:0% +so +uh let's + + align:start position:0% +uh let's + + + align:start position:0% +uh let's +see maybe that's as much as I want to + + align:start position:0% +see maybe that's as much as I want to + + + align:start position:0% +see maybe that's as much as I want to +say about the Stokes example and what it + + align:start position:0% +say about the Stokes example and what it + + + align:start position:0% +say about the Stokes example and what it +leads to in the finite element world uh + + align:start position:0% +leads to in the finite element world uh + + + align:start position:0% +leads to in the finite element world uh +I guess I'm going to + + align:start position:0% +I guess I'm going to + + + align:start position:0% +I guess I'm going to +um stay for another lecture or two with + + align:start position:0% +um stay for another lecture or two with + + + align:start position:0% +um stay for another lecture or two with +these um with these + + align:start position:0% +these um with these + + + align:start position:0% +these um with these +minimizations so maybe I just anticipate + + align:start position:0% +minimizations so maybe I just anticipate + + + align:start position:0% +minimizations so maybe I just anticipate +slightly the start of the next + + align:start position:0% + + + + align:start position:0% + +lecture because I'm quite uh pleased + + align:start position:0% +lecture because I'm quite uh pleased + + + align:start position:0% +lecture because I'm quite uh pleased +about getting this next topic into the + + align:start position:0% +about getting this next topic into the + + + align:start position:0% +about getting this next topic into the +series of + + align:start position:0% +series of + + + align:start position:0% +series of +lectures and uh I'll say right let me + + align:start position:0% +lectures and uh I'll say right let me + + + align:start position:0% +lectures and uh I'll say right let me +say what it + + align:start position:0% +say what it + + + align:start position:0% +say what it +is so it's it's going to be a + + align:start position:0% + + + + align:start position:0% + +minimization of uh an au minus B + + align:start position:0% +minimization of uh an au minus B + + + align:start position:0% +minimization of uh an au minus B +squar + + align:start position:0% +squar + + + align:start position:0% +squar +okay but I'm it's going to be now a case + + align:start position:0% +okay but I'm it's going to be now a case + + + align:start position:0% +okay but I'm it's going to be now a case +in which + + align:start position:0% +in which + + + align:start position:0% +in which +just as this lecture has + + align:start position:0% +just as this lecture has + + + align:start position:0% +just as this lecture has +seen the possibility comes that The + + align:start position:0% +seen the possibility comes that The + + + align:start position:0% +seen the possibility comes that The +Columns of a are not dependent or not + + align:start position:0% +Columns of a are not dependent or not + + + align:start position:0% +Columns of a are not dependent or not +independent that this problem is in + + align:start position:0% +independent that this problem is in + + + align:start position:0% +independent that this problem is in +trouble so I I want to I want to + + align:start position:0% +trouble so I I want to I want to + + + align:start position:0% +trouble so I I want to I want to +regularize this problem how do I save a + + align:start position:0% +regularize this problem how do I save a + + + align:start position:0% +regularize this problem how do I save a +problem in which so this is a so this is + + align:start position:0% +problem in which so this is a so this is + + + align:start position:0% +problem in which so this is a so this is +a and this is a major application in + + align:start position:0% +a and this is a major application in + + + align:start position:0% +a and this is a major application in +which a is + + align:start position:0% +which a is + + + align:start position:0% +which a is +say uh or Columns of a a maybe a + + align:start position:0% +say uh or Columns of a a maybe a + + + align:start position:0% +say uh or Columns of a a maybe a +transpose a is the easiest thing to + + align:start position:0% +transpose a is the easiest thing to + + + align:start position:0% +transpose a is the easiest thing to +say a transpose a is nearly + + align:start position:0% + + + + align:start position:0% + +singular or just Blain + + align:start position:0% +singular or just Blain + + + align:start position:0% +singular or just Blain +singular I'll say or + + align:start position:0% + + + + align:start position:0% + +singular how do + + align:start position:0% +singular how do + + + align:start position:0% +singular how do +we rescue the the problem because + + align:start position:0% +we rescue the the problem because + + + align:start position:0% +we rescue the the problem because +numerically and theor ically it's it's a + + align:start position:0% +numerically and theor ically it's it's a + + + align:start position:0% +numerically and theor ically it's it's a +disaster as it stands now okay it's ill + + align:start position:0% + + + + align:start position:0% + +posed so let me introduce that word + + align:start position:0% +posed so let me introduce that word + + + align:start position:0% +posed so let me introduce that word +illos + + align:start position:0% +illos + + + align:start position:0% +illos +problem and let me + + align:start position:0% +problem and let me + + + align:start position:0% +problem and let me +mention since I'm just using these last + + align:start position:0% +mention since I'm just using these last + + + align:start position:0% +mention since I'm just using these last +few minutes as a kind of uh getting the + + align:start position:0% +few minutes as a kind of uh getting the + + + align:start position:0% +few minutes as a kind of uh getting the +big picture where to illos problems come + + align:start position:0% +big picture where to illos problems come + + + align:start position:0% +big picture where to illos problems come +from where do these things come from + + align:start position:0% +from where do these things come from + + + align:start position:0% +from where do these things come from +they come from typically from what are + + align:start position:0% +they come from typically from what are + + + align:start position:0% +they come from typically from what are +called inverse problems so often they + + align:start position:0% +called inverse problems so often they + + + align:start position:0% +called inverse problems so often they +come from so the + + align:start position:0% + + + + align:start position:0% + +application is to inverse problems now + + align:start position:0% +application is to inverse problems now + + + align:start position:0% +application is to inverse problems now +what is a what's an inverse + + align:start position:0% + + + + align:start position:0% + +problem an inverse problem is for a + + align:start position:0% +problem an inverse problem is for a + + + align:start position:0% +problem an inverse problem is for a +differential + + align:start position:0% +differential + + + align:start position:0% +differential +equation you know some inputs and + + align:start position:0% +equation you know some inputs and + + + align:start position:0% +equation you know some inputs and +outputs you know some solutions but you + + align:start position:0% +outputs you know some solutions but you + + + align:start position:0% +outputs you know some solutions but you +don't know the equation you don't know + + align:start position:0% +don't know the equation you don't know + + + align:start position:0% +don't know the equation you don't know +the + + align:start position:0% + + + + align:start position:0% + +coefficient so you're trying to + + align:start position:0% +coefficient so you're trying to + + + align:start position:0% +coefficient so you're trying to +determine what what are the material + + align:start position:0% +determine what what are the material + + + align:start position:0% +determine what what are the material +Properties + + align:start position:0% +Properties + + + align:start position:0% +Properties +by looking to see what uh what the + + align:start position:0% +by looking to see what uh what the + + + align:start position:0% +by looking to see what uh what the +outputs are + + align:start position:0% +outputs are + + + align:start position:0% +outputs are +for uh experimental + + align:start position:0% + + + + align:start position:0% + +inputs and very frequently you don't + + align:start position:0% +inputs and very frequently you don't + + + align:start position:0% +inputs and very frequently you don't +have enough inputs to really determine + + align:start position:0% +have enough inputs to really determine + + + align:start position:0% +have enough inputs to really determine +what these so it's inverse problem to + + align:start position:0% +what these so it's inverse problem to + + + align:start position:0% +what these so it's inverse problem to +find the the + + align:start position:0% +find the the + + + align:start position:0% +find the the +coefficients of the + + align:start position:0% +coefficients of the + + + align:start position:0% +coefficients of the +equation + + align:start position:0% +equation + + + align:start position:0% +equation +given some some + + align:start position:0% +given some some + + + align:start position:0% +given some some +information on its + + align:start position:0% +information on its + + + align:start position:0% +information on its +Solutions some measurements and of + + align:start position:0% +Solutions some measurements and of + + + align:start position:0% +Solutions some measurements and of +course they're probably noisy + + align:start position:0% +course they're probably noisy + + + align:start position:0% +course they're probably noisy +measurements I mean this is an enormous + + align:start position:0% +measurements I mean this is an enormous + + + align:start position:0% +measurements I mean this is an enormous +source of + + align:start position:0% +source of + + + align:start position:0% +source of +um + + align:start position:0% +um + + + align:start position:0% +um +applications growing in + + align:start position:0% +applications growing in + + + align:start position:0% +applications growing in +importance and how do we deal with + + align:start position:0% +importance and how do we deal with + + + align:start position:0% +importance and how do we deal with +it + + align:start position:0% +it + + + align:start position:0% +it +well you regularize it so this is + + align:start position:0% +well you regularize it so this is + + + align:start position:0% +well you regularize it so this is +typical + + align:start position:0% +typical + + + align:start position:0% +typical +of + + align:start position:0% +of + + + align:start position:0% +of +uh this type of problem you add on some + + align:start position:0% +uh this type of problem you add on some + + + align:start position:0% +uh this type of problem you add on some +multiple of something that's safe like + + align:start position:0% +multiple of something that's safe like + + + align:start position:0% +multiple of something that's safe like +for example u s + + align:start position:0% + + + + align:start position:0% + +so the the + + align:start position:0% +so the the + + + align:start position:0% +so the the +uh result is + + align:start position:0% +uh result is + + + align:start position:0% +uh result is +here that this a transpose a that comes + + align:start position:0% +here that this a transpose a that comes + + + align:start position:0% +here that this a transpose a that comes +from this problem is there's an alpha + + align:start position:0% +from this problem is there's an alpha + + + align:start position:0% +from this problem is there's an alpha +times the identity coming from this + + align:start position:0% +times the identity coming from this + + + align:start position:0% +times the identity coming from this +problem I mean it's a it's an ordinary + + align:start position:0% +problem I mean it's a it's an ordinary + + + align:start position:0% +problem I mean it's a it's an ordinary +Le squares problem and it leads us to + + align:start position:0% +Le squares problem and it leads us to + + + align:start position:0% +Le squares problem and it leads us to +The Matrix a transpose + + align:start position:0% +The Matrix a transpose + + + align:start position:0% +The Matrix a transpose +a transpose a comes from the first + + align:start position:0% +a transpose a comes from the first + + + align:start position:0% +a transpose a comes from the first +part but I'm just talking about the + + align:start position:0% +part but I'm just talking about the + + + align:start position:0% +part but I'm just talking about the +standard normal equations it'll produce + + align:start position:0% +standard normal equations it'll produce + + + align:start position:0% +standard normal equations it'll produce +an a transpose a from here but from here + + align:start position:0% +an a transpose a from here but from here + + + align:start position:0% +an a transpose a from here but from here +it'll produce an alpha times the + + align:start position:0% +it'll produce an alpha times the + + + align:start position:0% +it'll produce an alpha times the +identity and of + + align:start position:0% +identity and of + + + align:start position:0% +identity and of +course just the way this minus E worked + + align:start position:0% +course just the way this minus E worked + + + align:start position:0% +course just the way this minus E worked +up there here I'm here I'm doing it even + + align:start position:0% +up there here I'm here I'm doing it even + + + align:start position:0% +up there here I'm here I'm doing it even +more directly I'm I'm pushing + + align:start position:0% +more directly I'm I'm pushing + + + align:start position:0% +more directly I'm I'm pushing +the problem away from + + align:start position:0% +the problem away from + + + align:start position:0% +the problem away from +zero this this Alpha this parameter and + + align:start position:0% +zero this this Alpha this parameter and + + + align:start position:0% +zero this this Alpha this parameter and +the choice of that parameter is the is + + align:start position:0% +the choice of that parameter is the is + + + align:start position:0% +the choice of that parameter is the is +the million dooll question in this whole + + align:start position:0% +the million dooll question in this whole + + + align:start position:0% +the million dooll question in this whole +subject uh but its purpose is to + + align:start position:0% +subject uh but its purpose is to + + + align:start position:0% +subject uh but its purpose is to +regularize the problem to take this + + align:start position:0% +regularize the problem to take this + + + align:start position:0% +regularize the problem to take this +nearly singular Matrix and push it up + + align:start position:0% +nearly singular Matrix and push it up + + + align:start position:0% +nearly singular Matrix and push it up +you see this this Matrix a transpose a + + align:start position:0% +you see this this Matrix a transpose a + + + align:start position:0% +you see this this Matrix a transpose a +never has negative igen values the + + align:start position:0% +never has negative igen values the + + + align:start position:0% +never has negative igen values the +problem is zero or very small small + + align:start position:0% +problem is zero or very small small + + + align:start position:0% +problem is zero or very small small +small positive so by adding on Alpha I I + + align:start position:0% +small positive so by adding on Alpha I I + + + align:start position:0% +small positive so by adding on Alpha I I +push those away from zero over there we + + align:start position:0% +push those away from zero over there we + + + align:start position:0% +push those away from zero over there we +had the problem of I values being + + align:start position:0% +had the problem of I values being + + + align:start position:0% +had the problem of I values being +positive or negative and by pushing in + + align:start position:0% +positive or negative and by pushing in + + + align:start position:0% +positive or negative and by pushing in +One Direction we might just bring a + + align:start position:0% +One Direction we might just bring a + + + align:start position:0% +One Direction we might just bring a +negative Igan value right on zero that's + + align:start position:0% +negative Igan value right on zero that's + + + align:start position:0% +negative Igan value right on zero that's +not our problem in this upcoming lecture + + align:start position:0% +not our problem in this upcoming lecture + + + align:start position:0% +not our problem in this upcoming lecture +in this upcoming lecture we do + + align:start position:0% +in this upcoming lecture we do + + + align:start position:0% +in this upcoming lecture we do +have we do have we know that nothing's + + align:start position:0% +have we do have we know that nothing's + + + align:start position:0% +have we do have we know that nothing's +negative but we need to make it properly + + align:start position:0% +negative but we need to make it properly + + + align:start position:0% +negative but we need to make it properly +positive okay so that's what's coming + + align:start position:0% +positive okay so that's what's coming + + + align:start position:0% +positive okay so that's what's coming +can I just say the application that I + + align:start position:0% +can I just say the application that I + + + align:start position:0% +can I just say the application that I +want to describe is the first one I've + + align:start position:0% +want to describe is the first one I've + + + align:start position:0% +want to describe is the first one I've +given in life + + align:start position:0% +given in life + + + align:start position:0% +given in life +sciences and I hope not the last I would + + align:start position:0% +sciences and I hope not the last I would + + + align:start position:0% +sciences and I hope not the last I would +be I don't know if any of you can + + align:start position:0% +be I don't know if any of you can + + + align:start position:0% +be I don't know if any of you can +suggest and if you do if you can an + + align:start position:0% +suggest and if you do if you can an + + + align:start position:0% +suggest and if you do if you can an +email be very much appreciated + + align:start position:0% +email be very much appreciated + + + align:start position:0% +email be very much appreciated +applications of this whole framework in + + align:start position:0% +applications of this whole framework in + + + align:start position:0% +applications of this whole framework in +life sciences + + align:start position:0% +life sciences + + + align:start position:0% +life sciences +so you'll see a particular application + + align:start position:0% +so you'll see a particular application + + + align:start position:0% +so you'll see a particular application +of this illos problem in trying to + + align:start position:0% +of this illos problem in trying to + + + align:start position:0% +of this illos problem in trying to +determine uh uh Gene structure from uh + + align:start position:0% +determine uh uh Gene structure from uh + + + align:start position:0% +determine uh uh Gene structure from uh +Expressions okay so that's what's coming + + align:start position:0% +Expressions okay so that's what's coming + + + align:start position:0% +Expressions okay so that's what's coming +uh Friday and + + align:start position:0% +uh Friday and + + + align:start position:0% +uh Friday and +uh I'm I realize here I'm talking about + + align:start position:0% +uh I'm I realize here I'm talking about + + + align:start position:0% +uh I'm I realize here I'm talking about +material that probably is not going to + + align:start position:0% +material that probably is not going to + + + align:start position:0% +material that probably is not going to +go in your project uh + + align:start position:0% +go in your project uh + + + align:start position:0% +go in your project uh +because of the time in um I'm I'm + + align:start position:0% +because of the time in um I'm I'm + + + align:start position:0% +because of the time in um I'm I'm +thinking that your projects will are + + align:start position:0% +thinking that your projects will are + + + align:start position:0% +thinking that your projects will are +more likely to work to build on what we + + align:start position:0% +more likely to work to build on what we + + + align:start position:0% +more likely to work to build on what we +what you had in Project one and the + + align:start position:0% +what you had in Project one and the + + + align:start position:0% +what you had in Project one and the +material about uh um the basic material + + align:start position:0% +material about uh um the basic material + + + align:start position:0% +material about uh um the basic material +about solving large systems and basic + + align:start position:0% +about solving large systems and basic + + + align:start position:0% +about solving large systems and basic +minimizations here okay thank you see + + align:start position:0% +minimizations here okay thank you see + + + align:start position:0% +minimizations here okay thank you see +you Friday \ No newline at end of file diff --git a/jcE-Ue83P7U.txt b/jcE-Ue83P7U.txt new file mode 100644 index 0000000000000000000000000000000000000000..c275908133a0fcb08ba0e7c01143c238008a61b1 --- /dev/null +++ b/jcE-Ue83P7U.txt @@ -0,0 +1,8544 @@ +align:start position:0% + +which capacitor converters which is + + align:start position:0% +which capacitor converters which is + + + align:start position:0% +which capacitor converters which is +covered in uh principles of Power + + align:start position:0% +covered in uh principles of Power + + + align:start position:0% +covered in uh principles of Power +Electronics chapter + + align:start position:0% +Electronics chapter + + + align:start position:0% +Electronics chapter +6 um + + align:start position:0% +6 um + + + align:start position:0% +6 um +and we saw some very interesting + + align:start position:0% +and we saw some very interesting + + + align:start position:0% +and we saw some very interesting +phenomena in terms of uh the effective + + align:start position:0% +phenomena in terms of uh the effective + + + align:start position:0% +phenomena in terms of uh the effective +output resistance of a switch capacitor + + align:start position:0% +output resistance of a switch capacitor + + + align:start position:0% +output resistance of a switch capacitor +converter and I'd like to take a few + + align:start position:0% +converter and I'd like to take a few + + + align:start position:0% +converter and I'd like to take a few +minutes just to talk about sort of what + + align:start position:0% +minutes just to talk about sort of what + + + align:start position:0% +minutes just to talk about sort of what +are the origins of that behavior okay so + + align:start position:0% +are the origins of that behavior okay so + + + align:start position:0% +are the origins of that behavior okay so +let's just take a really simple case + + align:start position:0% +let's just take a really simple case + + + align:start position:0% +let's just take a really simple case +suppose I have a voltage Supply that I'm + + align:start position:0% +suppose I have a voltage Supply that I'm + + + align:start position:0% +suppose I have a voltage Supply that I'm +going to call V + + align:start position:0% + + + + align:start position:0% + +subs and I'm going to use it and at T + + align:start position:0% +subs and I'm going to use it and at T + + + align:start position:0% +subs and I'm going to use it and at T +equals 0 I'm going to close a switch + + align:start position:0% +equals 0 I'm going to close a switch + + + align:start position:0% +equals 0 I'm going to close a switch +through a resistor R to charge a + + align:start position:0% +through a resistor R to charge a + + + align:start position:0% +through a resistor R to charge a +capacitor + + align:start position:0% +capacitor + + + align:start position:0% +capacitor +VC and at Tal 0us + + align:start position:0% + + + + align:start position:0% + +we're going to say that has some initial + + align:start position:0% +we're going to say that has some initial + + + align:start position:0% +we're going to say that has some initial +voltage V subi in the capacitor right so + + align:start position:0% +voltage V subi in the capacitor right so + + + align:start position:0% +voltage V subi in the capacitor right so +this capacitor you know I'm going to + + align:start position:0% +this capacitor you know I'm going to + + + align:start position:0% +this capacitor you know I'm going to +close the switch and I'm going to charge + + align:start position:0% +close the switch and I'm going to charge + + + align:start position:0% +close the switch and I'm going to charge +the capacitor up from V subi to its + + align:start position:0% +the capacitor up from V subi to its + + + align:start position:0% +the capacitor up from V subi to its +final value which is going to end up at + + align:start position:0% +final value which is going to end up at + + + align:start position:0% +final value which is going to end up at +V Subs you know and if I plotted the + + align:start position:0% +V Subs you know and if I plotted the + + + align:start position:0% +V Subs you know and if I plotted the +behavior + + align:start position:0% +behavior + + + align:start position:0% +behavior +here right I could find for example if I + + align:start position:0% +here right I could find for example if I + + + align:start position:0% +here right I could find for example if I +plotted uh I sub + + align:start position:0% +plotted uh I sub + + + align:start position:0% +plotted uh I sub +c right what would I expect to happen + + align:start position:0% +c right what would I expect to happen + + + align:start position:0% +c right what would I expect to happen +well it you know it's it's 0 before tals + + align:start position:0% +well it you know it's it's 0 before tals + + + align:start position:0% +well it you know it's it's 0 before tals +0 obviously at tals 0 it's going to be + + align:start position:0% +0 obviously at tals 0 it's going to be + + + align:start position:0% +0 obviously at tals 0 it's going to be +vs minus VC which is VI over R right so + + align:start position:0% +vs minus VC which is VI over R right so + + + align:start position:0% +vs minus VC which is VI over R right so +I'd have some initial value vs minus + + align:start position:0% +I'd have some initial value vs minus + + + align:start position:0% +I'd have some initial value vs minus +VI over + + align:start position:0% +VI over + + + align:start position:0% +VI over +R and then it will Ex exponentially + + align:start position:0% +R and then it will Ex exponentially + + + align:start position:0% +R and then it will Ex exponentially +Decay down to zero with some time + + align:start position:0% +Decay down to zero with some time + + + align:start position:0% +Decay down to zero with some time +constant to is equal to + + align:start position:0% +constant to is equal to + + + align:start position:0% +constant to is equal to +rc okay and so you know as we're + + align:start position:0% +rc okay and so you know as we're + + + align:start position:0% +rc okay and so you know as we're +charging up the capacitor we dissipate + + align:start position:0% +charging up the capacitor we dissipate + + + align:start position:0% +charging up the capacitor we dissipate +some energy in the resistor and we can + + align:start position:0% +some energy in the resistor and we can + + + align:start position:0% +some energy in the resistor and we can +calculate that okay what would happen if + + align:start position:0% +calculate that okay what would happen if + + + align:start position:0% +calculate that okay what would happen if +I changed the resistor value here + + align:start position:0% +I changed the resistor value here + + + align:start position:0% +I changed the resistor value here +suppose I used a much smaller resistor + + align:start position:0% +suppose I used a much smaller resistor + + + align:start position:0% +suppose I used a much smaller resistor +so um if I did that what would happen to + + align:start position:0% +so um if I did that what would happen to + + + align:start position:0% +so um if I did that what would happen to +the initial current well if I used a + + align:start position:0% +the initial current well if I used a + + + align:start position:0% +the initial current well if I used a +smaller resistor the initial current + + align:start position:0% +smaller resistor the initial current + + + align:start position:0% +smaller resistor the initial current +would be higher so here I'll pick you + + align:start position:0% +would be higher so here I'll pick you + + + align:start position:0% +would be higher so here I'll pick you +know this will be vs minus VI over R + + align:start position:0% +know this will be vs minus VI over R + + + align:start position:0% +know this will be vs minus VI over R +smaller and and then it will also Decay + + align:start position:0% +smaller and and then it will also Decay + + + align:start position:0% +smaller and and then it will also Decay +with the same RT RC time constant so + + align:start position:0% +with the same RT RC time constant so + + + align:start position:0% +with the same RT RC time constant so +it'll go from zero it'll jump up and + + align:start position:0% +it'll go from zero it'll jump up and + + + align:start position:0% +it'll go from zero it'll jump up and +it'll Decay now the RC time constant + + align:start position:0% +it'll Decay now the RC time constant + + + align:start position:0% +it'll Decay now the RC time constant +will be shorter so it'll do something + + align:start position:0% +will be shorter so it'll do something + + + align:start position:0% +will be shorter so it'll do something +like this so you know to is again equal + + align:start position:0% +like this so you know to is again equal + + + align:start position:0% +like this so you know to is again equal +to rc but R is smaller than yellow R is + + align:start position:0% +to rc but R is smaller than yellow R is + + + align:start position:0% +to rc but R is smaller than yellow R is +smaller than the pink R so it sort of + + align:start position:0% +smaller than the pink R so it sort of + + + align:start position:0% +smaller than the pink R so it sort of +starts with a higher current and decays + + align:start position:0% +starts with a higher current and decays + + + align:start position:0% +starts with a higher current and decays +quicker all right all right let's + + align:start position:0% +quicker all right all right let's + + + align:start position:0% +quicker all right all right let's +calculate this stuff just + + align:start position:0% +calculate this stuff just + + + align:start position:0% +calculate this stuff just +analytically okay so um + + align:start position:0% +analytically okay so um + + + align:start position:0% +analytically okay so um +um let's ask this how much charge do I + + align:start position:0% +um let's ask this how much charge do I + + + align:start position:0% +um let's ask this how much charge do I +deliver in charging this capacitor how + + align:start position:0% +deliver in charging this capacitor how + + + align:start position:0% +deliver in charging this capacitor how +much charge do I deliver from vs to VC + + align:start position:0% +much charge do I deliver from vs to VC + + + align:start position:0% +much charge do I deliver from vs to VC +or what's the equivalent the integral of + + align:start position:0% +or what's the equivalent the integral of + + + align:start position:0% +or what's the equivalent the integral of +IC here all right + + align:start position:0% + + + + align:start position:0% + +um so we could calculate that as Delta Q + + align:start position:0% +um so we could calculate that as Delta Q + + + align:start position:0% +um so we could calculate that as Delta Q +is the charge I'm going to deliver to + + align:start position:0% +is the charge I'm going to deliver to + + + align:start position:0% +is the charge I'm going to deliver to +the capacitor is the integral from 0 to + + align:start position:0% +the capacitor is the integral from 0 to + + + align:start position:0% +the capacitor is the integral from 0 to +Infinity of I DT + + align:start position:0% +Infinity of I DT + + + align:start position:0% +Infinity of I DT +right + + align:start position:0% +right + + + align:start position:0% +right +and I can calculate that in a number of + + align:start position:0% +and I can calculate that in a number of + + + align:start position:0% +and I can calculate that in a number of +ways um I could write this icdt as equal + + align:start position:0% +ways um I could write this icdt as equal + + + align:start position:0% +ways um I could write this icdt as equal +to + + align:start position:0% +to + + + align:start position:0% +to +DQ which is also equal to the integral + + align:start position:0% +DQ which is also equal to the integral + + + align:start position:0% +DQ which is also equal to the integral +of + + align:start position:0% +of + + + align:start position:0% +of +CDV where this is + + align:start position:0% +CDV where this is + + + align:start position:0% +CDV where this is +um where CDV is going from V sub I to V + + align:start position:0% +um where CDV is going from V sub I to V + + + align:start position:0% +um where CDV is going from V sub I to V +Subs which is my final charges up + + align:start position:0% +Subs which is my final charges up + + + align:start position:0% +Subs which is my final charges up +eventually to V Subs + + align:start position:0% +eventually to V Subs + + + align:start position:0% +eventually to V Subs +right so I could write this charge as + + align:start position:0% +right so I could write this charge as + + + align:start position:0% +right so I could write this charge as +just simply C * + + align:start position:0% +just simply C * + + + align:start position:0% +just simply C * +vs minus + + align:start position:0% +vs minus + + + align:start position:0% +vs minus +VI okay that's the amount of charge that + + align:start position:0% +VI okay that's the amount of charge that + + + align:start position:0% +VI okay that's the amount of charge that +flows out of the source onto the + + align:start position:0% +flows out of the source onto the + + + align:start position:0% +flows out of the source onto the +capacitor to get it from its initial + + align:start position:0% +capacitor to get it from its initial + + + align:start position:0% +capacitor to get it from its initial +voltage up to its final voltage vs okay + + align:start position:0% +voltage up to its final voltage vs okay + + + align:start position:0% +voltage up to its final voltage vs okay +any questions about + + align:start position:0% + + + + align:start position:0% + +that so let's just ask where's the + + align:start position:0% +that so let's just ask where's the + + + align:start position:0% +that so let's just ask where's the +energy going in this circuit I said + + align:start position:0% +energy going in this circuit I said + + + align:start position:0% +energy going in this circuit I said +qualitatively you know we're we're going + + align:start position:0% +qualitatively you know we're we're going + + + align:start position:0% +qualitatively you know we're we're going +to dissipate some power in the resistor + + align:start position:0% +to dissipate some power in the resistor + + + align:start position:0% +to dissipate some power in the resistor +to charge up the capacitor let's + + align:start position:0% +to charge up the capacitor let's + + + align:start position:0% +to charge up the capacitor let's +calculate that how much energy comes + + align:start position:0% +calculate that how much energy comes + + + align:start position:0% +calculate that how much energy comes +from the source Delta E + + align:start position:0% + + + + align:start position:0% + +Source and I'm talking about the energy + + align:start position:0% +Source and I'm talking about the energy + + + align:start position:0% +Source and I'm talking about the energy +out coming out of the source to charge + + align:start position:0% +out coming out of the source to charge + + + align:start position:0% +out coming out of the source to charge +everything is simply going to be vs * + + align:start position:0% +everything is simply going to be vs * + + + align:start position:0% +everything is simply going to be vs * +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +Q which is going to be uh + + align:start position:0% +Q which is going to be uh + + + align:start position:0% +Q which is going to be uh +c vs^ 2 minus C vs + + align:start position:0% +c vs^ 2 minus C vs + + + align:start position:0% +c vs^ 2 minus C vs +VI okay that's how much energy comes out + + align:start position:0% +VI okay that's how much energy comes out + + + align:start position:0% +VI okay that's how much energy comes out +of the source to charge the + + align:start position:0% +of the source to charge the + + + align:start position:0% +of the source to charge the +capacitor how much energy goes into the + + align:start position:0% +capacitor how much energy goes into the + + + align:start position:0% +capacitor how much energy goes into the +capacitor we can again use oh here we + + align:start position:0% +capacitor we can again use oh here we + + + align:start position:0% +capacitor we can again use oh here we +can use energy methods very clearly + + align:start position:0% +can use energy methods very clearly + + + align:start position:0% +can use energy methods very clearly +Delta e + + align:start position:0% +Delta e + + + align:start position:0% +Delta e +cap is well the energy that ends up on + + align:start position:0% +cap is well the energy that ends up on + + + align:start position:0% +cap is well the energy that ends up on +the cap is 12 C vs s the energy we + + align:start position:0% +the cap is 12 C vs s the energy we + + + align:start position:0% +the cap is 12 C vs s the energy we +started on the cap before you know + + align:start position:0% +started on the cap before you know + + + align:start position:0% +started on the cap before you know +before we Clos the switch was simply 12 + + align:start position:0% +before we Clos the switch was simply 12 + + + align:start position:0% +before we Clos the switch was simply 12 +C VI quantity squared and that's how + + align:start position:0% +C VI quantity squared and that's how + + + align:start position:0% +C VI quantity squared and that's how +much energy ends that's how much change + + align:start position:0% +much energy ends that's how much change + + + align:start position:0% +much energy ends that's how much change +in energy is existing on the + + align:start position:0% +in energy is existing on the + + + align:start position:0% +in energy is existing on the +C make sense + + align:start position:0% +C make sense + + + align:start position:0% +C make sense +everybody so that means that the Lost + + align:start position:0% +everybody so that means that the Lost + + + align:start position:0% +everybody so that means that the Lost +energy Delta e + + align:start position:0% +energy Delta e + + + align:start position:0% +energy Delta e +loss which of course you know if some + + align:start position:0% +loss which of course you know if some + + + align:start position:0% +loss which of course you know if some +energy is coming out of the the cap some + + align:start position:0% +energy is coming out of the the cap some + + + align:start position:0% +energy is coming out of the the cap some +energ is coming out of the source and + + align:start position:0% +energ is coming out of the source and + + + align:start position:0% +energ is coming out of the source and +some energ is ending up in the cap the + + align:start position:0% +some energ is ending up in the cap the + + + align:start position:0% +some energ is ending up in the cap the +rest obviously Delta e loss is in the + + align:start position:0% +rest obviously Delta e loss is in the + + + align:start position:0% +rest obviously Delta e loss is in the +resistor right in this model right + + align:start position:0% +resistor right in this model right + + + align:start position:0% +resistor right in this model right +there's nowhere else for it to go uh is + + align:start position:0% +there's nowhere else for it to go uh is + + + align:start position:0% +there's nowhere else for it to go uh is +going to be Delta E + + align:start position:0% + + + + align:start position:0% + +Source minus Delta e + + align:start position:0% +Source minus Delta e + + + align:start position:0% +Source minus Delta e +cap which I could write as um this minus + + align:start position:0% +cap which I could write as um this minus + + + align:start position:0% +cap which I could write as um this minus +this which is going to be C vs 2 minus C + + align:start position:0% +this which is going to be C vs 2 minus C + + + align:start position:0% +this which is going to be C vs 2 minus C +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +vsv minus 12 cv^ 2 CVS s plus 12 CV i^ 2 + + align:start position:0% +vsv minus 12 cv^ 2 CVS s plus 12 CV i^ 2 + + + align:start position:0% +vsv minus 12 cv^ 2 CVS s plus 12 CV i^ 2 +and if I Collapse this down a little bit + + align:start position:0% +and if I Collapse this down a little bit + + + align:start position:0% +and if I Collapse this down a little bit +and rearrange it what I get is 12 + + align:start position:0% +and rearrange it what I get is 12 + + + align:start position:0% +and rearrange it what I get is 12 +c times uh vs minus VI quantity + + align:start position:0% + + + + align:start position:0% + +squared + + align:start position:0% + + + + align:start position:0% + +okay and this is in the + + align:start position:0% +okay and this is in the + + + align:start position:0% +okay and this is in the +resistor okay + + align:start position:0% +resistor okay + + + align:start position:0% +resistor okay +okay any questions about + + align:start position:0% + + + + align:start position:0% + +that yeah um this model like you you + + align:start position:0% +that yeah um this model like you you + + + align:start position:0% +that yeah um this model like you you +didn't assume that the resistor was in + + align:start position:0% +didn't assume that the resistor was in + + + align:start position:0% +didn't assume that the resistor was in +the circuit no I did of course I did + + align:start position:0% +the circuit no I did of course I did + + + align:start position:0% +the circuit no I did of course I did +right I I I I mean I still have + + align:start position:0% +right I I I I mean I still have + + + align:start position:0% +right I I I I mean I still have +conservation of energy right I didn't + + align:start position:0% +conservation of energy right I didn't + + + align:start position:0% +conservation of energy right I didn't +calculate an integral like I didn't + + align:start position:0% +calculate an integral like I didn't + + + align:start position:0% +calculate an integral like I didn't +write the integral in terms of the + + align:start position:0% +write the integral in terms of the + + + align:start position:0% +write the integral in terms of the +resistor but I still I didn't it's not + + align:start position:0% +resistor but I still I didn't it's not + + + align:start position:0% +resistor but I still I didn't it's not +that I didn't assume it was there I + + align:start position:0% +that I didn't assume it was there I + + + align:start position:0% +that I didn't assume it was there I +guess I think you could have drawn the + + align:start position:0% +guess I think you could have drawn the + + + align:start position:0% +guess I think you could have drawn the +circuit and written down the same + + align:start position:0% +circuit and written down the same + + + align:start position:0% +circuit and written down the same +equations and the same + + align:start position:0% +equations and the same + + + align:start position:0% +equations and the same +result absolutely + + align:start position:0% +result absolutely + + + align:start position:0% +result absolutely +right very good observation so what's + + align:start position:0% +right very good observation so what's + + + align:start position:0% +right very good observation so what's +going on here did I cheat no I did not + + align:start position:0% +going on here did I cheat no I did not + + + align:start position:0% +going on here did I cheat no I did not +cheat I just I'm lazy and I don't like + + align:start position:0% +cheat I just I'm lazy and I don't like + + + align:start position:0% +cheat I just I'm lazy and I don't like +doing hard integrals so or even easy + + align:start position:0% +doing hard integrals so or even easy + + + align:start position:0% +doing hard integrals so or even easy +integrals for that matter what's going + + align:start position:0% +integrals for that matter what's going + + + align:start position:0% +integrals for that matter what's going +on here it's exactly the picture I + + align:start position:0% +on here it's exactly the picture I + + + align:start position:0% +on here it's exactly the picture I +drew + + align:start position:0% +drew + + + align:start position:0% +drew +okay um if I had some nominal value of + + align:start position:0% +okay um if I had some nominal value of + + + align:start position:0% +okay um if I had some nominal value of +resistor you know one + + align:start position:0% +resistor you know one + + + align:start position:0% +resistor you know one +I'd get exactly this curve and if I + + align:start position:0% +I'd get exactly this curve and if I + + + align:start position:0% +I'd get exactly this curve and if I +squared this this is a current if I + + align:start position:0% +squared this this is a current if I + + + align:start position:0% +squared this this is a current if I +squared this I could write the + + align:start position:0% +squared this I could write the + + + align:start position:0% +squared this I could write the +exponential decay and then I could + + align:start position:0% +exponential decay and then I could + + + align:start position:0% +exponential decay and then I could +integrate it and I get some loss I would + + align:start position:0% +integrate it and I get some loss I would + + + align:start position:0% +integrate it and I get some loss I would +get exactly that + + align:start position:0% +get exactly that + + + align:start position:0% +get exactly that +loss and if I change the value of + + align:start position:0% +loss and if I change the value of + + + align:start position:0% +loss and if I change the value of +resistance I'd get this curve and I'd + + align:start position:0% +resistance I'd get this curve and I'd + + + align:start position:0% +resistance I'd get this curve and I'd +get exactly the same loss so what's + + align:start position:0% +get exactly the same loss so what's + + + align:start position:0% +get exactly the same loss so what's +being noticed here is the none of these + + align:start position:0% +being noticed here is the none of these + + + align:start position:0% +being noticed here is the none of these +answers the amount of energy that comes + + align:start position:0% +answers the amount of energy that comes + + + align:start position:0% +answers the amount of energy that comes +out of the source the amount of energy + + align:start position:0% +out of the source the amount of energy + + + align:start position:0% +out of the source the amount of energy +that went on the cap and the amount of + + align:start position:0% +that went on the cap and the amount of + + + align:start position:0% +that went on the cap and the amount of +energy I lose don't depend on the + + align:start position:0% +energy I lose don't depend on the + + + align:start position:0% +energy I lose don't depend on the +resistance at all you get the same + + align:start position:0% +resistance at all you get the same + + + align:start position:0% +resistance at all you get the same +answer the waveforms are different right + + align:start position:0% +answer the waveforms are different right + + + align:start position:0% +answer the waveforms are different right +it depends you know the current waveform + + align:start position:0% +it depends you know the current waveform + + + align:start position:0% +it depends you know the current waveform +that I get depends upon the value of the + + align:start position:0% +that I get depends upon the value of the + + + align:start position:0% +that I get depends upon the value of the +resistor what happens if I keep making + + align:start position:0% +resistor what happens if I keep making + + + align:start position:0% +resistor what happens if I keep making +that resistor smaller and smaller and + + align:start position:0% +that resistor smaller and smaller and + + + align:start position:0% +that resistor smaller and smaller and +smaller what I get is currents that have + + align:start position:0% +smaller what I get is currents that have + + + align:start position:0% +smaller what I get is currents that have +higher Peaks and shorter durations until + + align:start position:0% +higher Peaks and shorter durations until + + + align:start position:0% +higher Peaks and shorter durations until +like as R approaches zero this more or + + align:start position:0% +like as R approaches zero this more or + + + align:start position:0% +like as R approaches zero this more or +less becomes a kind of + + align:start position:0% +less becomes a kind of + + + align:start position:0% +less becomes a kind of +impulse okay but it's an Impulse with an + + align:start position:0% +impulse okay but it's an Impulse with an + + + align:start position:0% +impulse okay but it's an Impulse with an +amount of charge Delta Q that's CVS + + align:start position:0% +amount of charge Delta Q that's CVS + + + align:start position:0% +amount of charge Delta Q that's CVS +minus + + align:start position:0% +minus + + + align:start position:0% +minus +VI okay and the amount of energy I lose + + align:start position:0% +VI okay and the amount of energy I lose + + + align:start position:0% +VI okay and the amount of energy I lose +in the resistor yeah I have a smaller + + align:start position:0% +in the resistor yeah I have a smaller + + + align:start position:0% +in the resistor yeah I have a smaller +resistor it's going to zero but it's + + align:start position:0% +resistor it's going to zero but it's + + + align:start position:0% +resistor it's going to zero but it's +current through it's going to infinity + + align:start position:0% +current through it's going to infinity + + + align:start position:0% +current through it's going to infinity +and it goes through it in just such a + + align:start position:0% +and it goes through it in just such a + + + align:start position:0% +and it goes through it in just such a +way that I lose the same amount of + + align:start position:0% +way that I lose the same amount of + + + align:start position:0% +way that I lose the same amount of +energy no matter what the resistance is + + align:start position:0% +energy no matter what the resistance is + + + align:start position:0% +energy no matter what the resistance is +so it's not that I'm cheating it's just + + align:start position:0% +so it's not that I'm cheating it's just + + + align:start position:0% +so it's not that I'm cheating it's just +that this is what happens when you get + + align:start position:0% +that this is what happens when you get + + + align:start position:0% +that this is what happens when you get +you take a limit of a resistance go to + + align:start position:0% +you take a limit of a resistance go to + + + align:start position:0% +you take a limit of a resistance go to +zero but you're getting a limit as a + + align:start position:0% +zero but you're getting a limit as a + + + align:start position:0% +zero but you're getting a limit as a +current goes to infinity and if I put + + align:start position:0% +current goes to infinity and if I put + + + align:start position:0% +current goes to infinity and if I put +that into the circuit and I took that + + align:start position:0% +that into the circuit and I took that + + + align:start position:0% +that into the circuit and I took that +integral and I took the limit as R goes + + align:start position:0% +integral and I took the limit as R goes + + + align:start position:0% +integral and I took the limit as R goes +to zero I'd get the same answer right so + + align:start position:0% +to zero I'd get the same answer right so + + + align:start position:0% +to zero I'd get the same answer right so +I'm just lazy and I kind of skip over + + align:start position:0% +I'm just lazy and I kind of skip over + + + align:start position:0% +I'm just lazy and I kind of skip over +the + + align:start position:0% +the + + + align:start position:0% +the +integral okay yeah s in the case that + + align:start position:0% +integral okay yeah s in the case that + + + align:start position:0% +integral okay yeah s in the case that +there is a non z r makes sense that the + + align:start position:0% +there is a non z r makes sense that the + + + align:start position:0% +there is a non z r makes sense that the +energy is lost through the resistor is + + align:start position:0% +energy is lost through the resistor is + + + align:start position:0% +energy is lost through the resistor is +where is the energy loss the energy loss + + align:start position:0% +where is the energy loss the energy loss + + + align:start position:0% +where is the energy loss the energy loss +I mean the actual distribution of the + + align:start position:0% +I mean the actual distribution of the + + + align:start position:0% +I mean the actual distribution of the +energy loss now you're asking about + + align:start position:0% +energy loss now you're asking about + + + align:start position:0% +energy loss now you're asking about +idealized situations right somewhere in + + align:start position:0% +idealized situations right somewhere in + + + align:start position:0% +idealized situations right somewhere in +this Loop + + align:start position:0% +this Loop + + + align:start position:0% +this Loop +right I've got to dissipate + + align:start position:0% +right I've got to dissipate + + + align:start position:0% +right I've got to dissipate +energy right and so there has to be some + + align:start position:0% +energy right and so there has to be some + + + align:start position:0% +energy right and so there has to be some +you know it's sort of like saying if I + + align:start position:0% +you know it's sort of like saying if I + + + align:start position:0% +you know it's sort of like saying if I +connect a voltage Source across a short + + align:start position:0% +connect a voltage Source across a short + + + align:start position:0% +connect a voltage Source across a short +circuit what happens right like well + + align:start position:0% +circuit what happens right like well + + + align:start position:0% +circuit what happens right like well +you've got to have some approximation + + align:start position:0% +you've got to have some approximation + + + align:start position:0% +you've got to have some approximation +you got to have some limiting resistance + + align:start position:0% +you got to have some limiting resistance + + + align:start position:0% +you got to have some limiting resistance +going to zero so in the real world you + + align:start position:0% +going to zero so in the real world you + + + align:start position:0% +going to zero so in the real world you +know if this switch and resistor were an + + align:start position:0% +know if this switch and resistor were an + + + align:start position:0% +know if this switch and resistor were an +ideal mosfet or something where would + + align:start position:0% +ideal mosfet or something where would + + + align:start position:0% +ideal mosfet or something where would +the energy go depend upon where the + + align:start position:0% +the energy go depend upon where the + + + align:start position:0% +the energy go depend upon where the +where the actual resistance was + + align:start position:0% +where the actual resistance was + + + align:start position:0% +where the actual resistance was +distributed in the circuit um and to the + + align:start position:0% +distributed in the circuit um and to the + + + align:start position:0% +distributed in the circuit um and to the +extent that you know the the resistances + + align:start position:0% +extent that you know the the resistances + + + align:start position:0% +extent that you know the the resistances +in the plates of the capacitor will get + + align:start position:0% +in the plates of the capacitor will get + + + align:start position:0% +in the plates of the capacitor will get +dissipated there right but you know if + + align:start position:0% +dissipated there right but you know if + + + align:start position:0% +dissipated there right but you know if +you want to if you want to force + + align:start position:0% +you want to if you want to force + + + align:start position:0% +you want to if you want to force +idealities where things are zero then + + align:start position:0% +idealities where things are zero then + + + align:start position:0% +idealities where things are zero then +you get squirly results if you don't + + align:start position:0% +you get squirly results if you don't + + + align:start position:0% +you get squirly results if you don't +like account for the fact that you have + + align:start position:0% +like account for the fact that you have + + + align:start position:0% +like account for the fact that you have +infinite + + align:start position:0% +infinite + + + align:start position:0% +infinite +currents + + align:start position:0% +currents + + + align:start position:0% +currents +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um this kind of charge or energy charge + + align:start position:0% +um this kind of charge or energy charge + + + align:start position:0% +um this kind of charge or energy charge +and energy methods are very convenient + + align:start position:0% +and energy methods are very convenient + + + align:start position:0% +and energy methods are very convenient +for working + + align:start position:0% +for working + + + align:start position:0% +for working +things results out where you don't want + + align:start position:0% +things results out where you don't want + + + align:start position:0% +things results out where you don't want +to have to integrate things and it turns + + align:start position:0% +to have to integrate things and it turns + + + align:start position:0% +to have to integrate things and it turns +out in fact it doesn't matter what this + + align:start position:0% +out in fact it doesn't matter what this + + + align:start position:0% +out in fact it doesn't matter what this +element is + + align:start position:0% +element is + + + align:start position:0% +element is +right basically I could replace this + + align:start position:0% +right basically I could replace this + + + align:start position:0% +right basically I could replace this +with a nonlinear resistor like so if the + + align:start position:0% +with a nonlinear resistor like so if the + + + align:start position:0% +with a nonlinear resistor like so if the +mosfet was + + align:start position:0% +mosfet was + + + align:start position:0% +mosfet was +nonlinear you'd get the same answer + + align:start position:0% +nonlinear you'd get the same answer + + + align:start position:0% +nonlinear you'd get the same answer +because it doesn't matter the the time + + align:start position:0% +because it doesn't matter the the time + + + align:start position:0% +because it doesn't matter the the time +wave for the fact that I drew this as a + + align:start position:0% +wave for the fact that I drew this as a + + + align:start position:0% +wave for the fact that I drew this as a +perfect exponential even if this + + align:start position:0% +perfect exponential even if this + + + align:start position:0% +perfect exponential even if this +resistor was nonlinear so long as I + + align:start position:0% +resistor was nonlinear so long as I + + + align:start position:0% +resistor was nonlinear so long as I +ended up with VC at the same voltage as + + align:start position:0% +ended up with VC at the same voltage as + + + align:start position:0% +ended up with VC at the same voltage as +VSS I'm going to get the same + + align:start position:0% +VSS I'm going to get the same + + + align:start position:0% +VSS I'm going to get the same +dissipation so in fact even if this had + + align:start position:0% +dissipation so in fact even if this had + + + align:start position:0% +dissipation so in fact even if this had +some inductance and it rang back and + + align:start position:0% +some inductance and it rang back and + + + align:start position:0% +some inductance and it rang back and +forth a little bit and then settle down + + align:start position:0% +forth a little bit and then settle down + + + align:start position:0% +forth a little bit and then settle down +I get the same total loss okay it it + + align:start position:0% +I get the same total loss okay it it + + + align:start position:0% +I get the same total loss okay it it +just doesn't + + align:start position:0% +just doesn't + + + align:start position:0% +just doesn't +matter this is just a result of the fact + + align:start position:0% +matter this is just a result of the fact + + + align:start position:0% +matter this is just a result of the fact +that + + align:start position:0% +that + + + align:start position:0% +that +this yeah is it that's right I mean + + align:start position:0% +this yeah is it that's right I mean + + + align:start position:0% +this yeah is it that's right I mean +satisfies conservation of energy and it + + align:start position:0% +satisfies conservation of energy and it + + + align:start position:0% +satisfies conservation of energy and it +satisfies the fact that the um change in + + align:start position:0% +satisfies the fact that the um change in + + + align:start position:0% +satisfies the fact that the um change in +the capacitor voltage determines the + + align:start position:0% +the capacitor voltage determines the + + + align:start position:0% +the capacitor voltage determines the +charge flow both here and + + align:start position:0% + + + + align:start position:0% + +here excellent observation + + align:start position:0% + + + + align:start position:0% + +what does this + + align:start position:0% +what does this + + + align:start position:0% +what does this +imply well what is the efficiency of + + align:start position:0% +imply well what is the efficiency of + + + align:start position:0% +imply well what is the efficiency of +charging this capacitor if I thought + + align:start position:0% +charging this capacitor if I thought + + + align:start position:0% +charging this capacitor if I thought +okay I brought this capacitor from some + + align:start position:0% +okay I brought this capacitor from some + + + align:start position:0% +okay I brought this capacitor from some +initial voltage up to + + align:start position:0% +initial voltage up to + + + align:start position:0% +initial voltage up to +vs what fraction of the energy I sourced + + align:start position:0% +vs what fraction of the energy I sourced + + + align:start position:0% +vs what fraction of the energy I sourced +got to the the load right so if I + + align:start position:0% +got to the the load right so if I + + + align:start position:0% +got to the the load right so if I +thought of the capacitor as the load so + + align:start position:0% +thought of the capacitor as the load so + + + align:start position:0% +thought of the capacitor as the load so +I could think of the charging + + align:start position:0% +I could think of the charging + + + align:start position:0% +I could think of the charging +efficiency as being equal to um the + + align:start position:0% +efficiency as being equal to um the + + + align:start position:0% +efficiency as being equal to um the +energy Delta e cap + + align:start position:0% +energy Delta e cap + + + align:start position:0% +energy Delta e cap +that's the energy that went to the + + align:start position:0% +that's the energy that went to the + + + align:start position:0% +that's the energy that went to the +capacitor over Delta E + + align:start position:0% + + + + align:start position:0% + +Source right and what is that well I + + align:start position:0% +Source right and what is that well I + + + align:start position:0% +Source right and what is that well I +could write that as uh equal to 12 cvs^2 + + align:start position:0% +could write that as uh equal to 12 cvs^2 + + + align:start position:0% +could write that as uh equal to 12 cvs^2 +- 12 + + align:start position:0% +- 12 + + + align:start position:0% +- 12 +CBI + + align:start position:0% +CBI + + + align:start position:0% +CBI +squared divided by um Delta E Source is + + align:start position:0% +squared divided by um Delta E Source is + + + align:start position:0% +squared divided by um Delta E Source is +cvs^2 minus CV svi + + align:start position:0% + + + + align:start position:0% + +right and I can divide out uh the + + align:start position:0% +right and I can divide out uh the + + + align:start position:0% +right and I can divide out uh the +capacitance here in + + align:start position:0% +capacitance here in + + + align:start position:0% +capacitance here in +this + + align:start position:0% + + + + align:start position:0% + +okay so I can write this as uh equal to + + align:start position:0% +okay so I can write this as uh equal to + + + align:start position:0% +okay so I can write this as uh equal to +if I factor out 12 vs squared or if I + + align:start position:0% +if I factor out 12 vs squared or if I + + + align:start position:0% +if I factor out 12 vs squared or if I +divide top and bottom by vs^ S I can + + align:start position:0% +divide top and bottom by vs^ S I can + + + align:start position:0% +divide top and bottom by vs^ S I can +write this as 12 + + align:start position:0% +write this as 12 + + + align:start position:0% +write this as 12 +times + + align:start position:0% +times + + + align:start position:0% +times +uh + + align:start position:0% +uh + + + align:start position:0% +uh + + align:start position:0% + + + align:start position:0% +minus VI over V s^ sared divided by 1 + + align:start position:0% +minus VI over V s^ sared divided by 1 + + + align:start position:0% +minus VI over V s^ sared divided by 1 +minus VI over + + align:start position:0% +minus VI over + + + align:start position:0% +minus VI over +vs right which I could write as 12 time + + align:start position:0% +vs right which I could write as 12 time + + + align:start position:0% +vs right which I could write as 12 time +uh 1 + VI over vs + + align:start position:0% + + + + align:start position:0% + +that make sense + + align:start position:0% +that make sense + + + align:start position:0% +that make sense +everybody and in fact actually you can + + align:start position:0% +everybody and in fact actually you can + + + align:start position:0% +everybody and in fact actually you can +write it in a slightly different way if + + align:start position:0% +write it in a slightly different way if + + + align:start position:0% +write it in a slightly different way if +I thought of Delta + + align:start position:0% + + + + align:start position:0% + +v as being equal to uh v s minus VI + + align:start position:0% +v as being equal to uh v s minus VI + + + align:start position:0% +v as being equal to uh v s minus VI +that's how much I'm charging up the cap + + align:start position:0% +that's how much I'm charging up the cap + + + align:start position:0% +that's how much I'm charging up the cap +this can also be written I won't go + + align:start position:0% +this can also be written I won't go + + + align:start position:0% +this can also be written I won't go +through the math this can also be + + align:start position:0% +through the math this can also be + + + align:start position:0% +through the math this can also be +written as + + align:start position:0% +written as + + + align:start position:0% +written as +one one m + + align:start position:0% +one one m + + + align:start position:0% +one one m +one sorry 1us 1 12 of Delta V over + + align:start position:0% +one sorry 1us 1 12 of Delta V over + + + align:start position:0% +one sorry 1us 1 12 of Delta V over +vs + + align:start position:0% +vs + + + align:start position:0% +vs +okay so why am I dragging you through + + align:start position:0% +okay so why am I dragging you through + + + align:start position:0% +okay so why am I dragging you through +this what I want to understand is how + + align:start position:0% +this what I want to understand is how + + + align:start position:0% +this what I want to understand is how +does this charging efficiency go well if + + align:start position:0% +does this charging efficiency go well if + + + align:start position:0% +does this charging efficiency go well if +I charge the capacitor from + + align:start position:0% +I charge the capacitor from + + + align:start position:0% +I charge the capacitor from +zero right what would be the charging + + align:start position:0% +zero right what would be the charging + + + align:start position:0% +zero right what would be the charging +efficiency well if VI was zero this + + align:start position:0% +efficiency well if VI was zero this + + + align:start position:0% +efficiency well if VI was zero this +would go to zero this would go to this + + align:start position:0% +would go to zero this would go to this + + + align:start position:0% +would go to zero this would go to this +the numerator would go to one the button + + align:start position:0% +the numerator would go to one the button + + + align:start position:0% +the numerator would go to one the button +denominator to go to one my charging + + align:start position:0% +denominator to go to one my charging + + + align:start position:0% +denominator to go to one my charging +efficiency would be + + align:start position:0% +efficiency would be + + + align:start position:0% +efficiency would be +50% right so if I charge the capacitor + + align:start position:0% +50% right so if I charge the capacitor + + + align:start position:0% +50% right so if I charge the capacitor +up from zero to final value I put half + + align:start position:0% +up from zero to final value I put half + + + align:start position:0% +up from zero to final value I put half +cv^ squ on the capacitor and I dissipate + + align:start position:0% +cv^ squ on the capacitor and I dissipate + + + align:start position:0% +cv^ squ on the capacitor and I dissipate +half cv^ squ in the resistor so it's not + + align:start position:0% +half cv^ squ in the resistor so it's not + + + align:start position:0% +half cv^ squ in the resistor so it's not +a very happy energy transfer right I + + align:start position:0% +a very happy energy transfer right I + + + align:start position:0% +a very happy energy transfer right I +lose half my energy in charging up that + + align:start position:0% +lose half my energy in charging up that + + + align:start position:0% +lose half my energy in charging up that +capacitor on the other + + align:start position:0% +capacitor on the other + + + align:start position:0% +capacitor on the other +hand suppose VI was suppose the initial + + align:start position:0% +hand suppose VI was suppose the initial + + + align:start position:0% +hand suppose VI was suppose the initial +voltage on the capacitor was half of + + align:start position:0% +voltage on the capacitor was half of + + + align:start position:0% +voltage on the capacitor was half of +vs okay if I do this calculation this is + + align:start position:0% +vs okay if I do this calculation this is + + + align:start position:0% +vs okay if I do this calculation this is +a half of 1 +0.5 or it becomes 75 so if + + align:start position:0% +a half of 1 +0.5 or it becomes 75 so if + + + align:start position:0% +a half of 1 +0.5 or it becomes 75 so if +I charge halfway up from VSS to + + align:start position:0% +I charge halfway up from VSS to + + + align:start position:0% +I charge halfway up from VSS to +vs I have 75% Energy Efficiency in + + align:start position:0% +vs I have 75% Energy Efficiency in + + + align:start position:0% +vs I have 75% Energy Efficiency in +charging that and the limit as VI + + align:start position:0% +charging that and the limit as VI + + + align:start position:0% +charging that and the limit as VI +approaches + + align:start position:0% +approaches + + + align:start position:0% +approaches +VSS the efficiency goes to one right so + + align:start position:0% +VSS the efficiency goes to one right so + + + align:start position:0% +VSS the efficiency goes to one right so +if I want to have high + + align:start position:0% +if I want to have high + + + align:start position:0% +if I want to have high +efficiency I only want to charge the + + align:start position:0% +efficiency I only want to charge the + + + align:start position:0% +efficiency I only want to charge the +capacitor a + + align:start position:0% +capacitor a + + + align:start position:0% +capacitor a +little and the way you could think about + + align:start position:0% +little and the way you could think about + + + align:start position:0% +little and the way you could think about +that is you know what's this happening + + align:start position:0% +that is you know what's this happening + + + align:start position:0% +that is you know what's this happening +right when I have the capacitor voltage + + align:start position:0% +right when I have the capacitor voltage + + + align:start position:0% +right when I have the capacitor voltage +is very small and the vs is very big + + align:start position:0% +is very small and the vs is very big + + + align:start position:0% +is very small and the vs is very big +I've got a big res voltage across this + + align:start position:0% +I've got a big res voltage across this + + + align:start position:0% +I've got a big res voltage across this +resistor I'm dumping a lot of energy in + + align:start position:0% +resistor I'm dumping a lot of energy in + + + align:start position:0% +resistor I'm dumping a lot of energy in +the resistor compared to the capacitor + + align:start position:0% +the resistor compared to the capacitor + + + align:start position:0% +the resistor compared to the capacitor +whereas if VC is very close to VSS I + + align:start position:0% +whereas if VC is very close to VSS I + + + align:start position:0% +whereas if VC is very close to VSS I +only have a tiny voltage across the + + align:start position:0% +only have a tiny voltage across the + + + align:start position:0% +only have a tiny voltage across the +resistor most of the energy goes into + + align:start position:0% +resistor most of the energy goes into + + + align:start position:0% +resistor most of the energy goes into +the capacitor so if I charge a capacitor + + align:start position:0% +the capacitor so if I charge a capacitor + + + align:start position:0% +the capacitor so if I charge a capacitor +only a little bit I only lose a small + + align:start position:0% +only a little bit I only lose a small + + + align:start position:0% +only a little bit I only lose a small +fraction of the + + align:start position:0% +fraction of the + + + align:start position:0% +fraction of the +energy does that make sense everybody + + align:start position:0% + + + + align:start position:0% + +I should I should have + + align:start position:0% +I should I should have + + + align:start position:0% +I should I should have +noted um by the way that + + align:start position:0% + + + + align:start position:0% + +um there is a way to make this + + align:start position:0% +um there is a way to make this + + + align:start position:0% +um there is a way to make this +circuit have greater + + align:start position:0% +circuit have greater + + + align:start position:0% +circuit have greater +efficiency and what that would be is if + + align:start position:0% +efficiency and what that would be is if + + + align:start position:0% +efficiency and what that would be is if +I put an inductor in series + + align:start position:0% +I put an inductor in series + + + align:start position:0% +I put an inductor in series +here and I SLO charge from VSS onto VC + + align:start position:0% +here and I SLO charge from VSS onto VC + + + align:start position:0% +here and I SLO charge from VSS onto VC +but let VC + + align:start position:0% +but let VC + + + align:start position:0% +but let VC +finish and then reopen the switch when + + align:start position:0% +finish and then reopen the switch when + + + align:start position:0% +finish and then reopen the switch when +VC is at some voltage greater than + + align:start position:0% +VC is at some voltage greater than + + + align:start position:0% +VC is at some voltage greater than +vs right so this limit on the efficiency + + align:start position:0% +vs right so this limit on the efficiency + + + align:start position:0% +vs right so this limit on the efficiency +that no it doesn't matter how I charge + + align:start position:0% +that no it doesn't matter how I charge + + + align:start position:0% +that no it doesn't matter how I charge +it is only true if VC ends up at VSS if + + align:start position:0% +it is only true if VC ends up at VSS if + + + align:start position:0% +it is only true if VC ends up at VSS if +I if I end make VC somehow end up + + align:start position:0% +I if I end make VC somehow end up + + + align:start position:0% +I if I end make VC somehow end up +greater than vs through for example + + align:start position:0% +greater than vs through for example + + + align:start position:0% +greater than vs through for example +through a resident lhing of energy then + + align:start position:0% +through a resident lhing of energy then + + + align:start position:0% +through a resident lhing of energy then +I can get higher efficiency okay but in + + align:start position:0% +I can get higher efficiency okay but in + + + align:start position:0% +I can get higher efficiency okay but in +a switch capacitor converter or in a + + align:start position:0% +a switch capacitor converter or in a + + + align:start position:0% +a switch capacitor converter or in a +converter where I'm going to let the fin + + align:start position:0% +converter where I'm going to let the fin + + + align:start position:0% +converter where I'm going to let the fin +value of the capacitor go to vs the + + align:start position:0% +value of the capacitor go to vs the + + + align:start position:0% +value of the capacitor go to vs the +efficiency is fixed by the charge + + align:start position:0% +efficiency is fixed by the charge + + + align:start position:0% +efficiency is fixed by the charge +transfer and the initial + + align:start position:0% +transfer and the initial + + + align:start position:0% +transfer and the initial +value any questions about + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +okay so how does this relate to what we + + align:start position:0% +okay so how does this relate to what we + + + align:start position:0% +okay so how does this relate to what we +were talking about last time let's + + align:start position:0% +were talking about last time let's + + + align:start position:0% +were talking about last time let's +remind ourselves of the circuit that we + + align:start position:0% +remind ourselves of the circuit that we + + + align:start position:0% +remind ourselves of the circuit that we +saw last time and it was a + + align:start position:0% +saw last time and it was a + + + align:start position:0% +saw last time and it was a +2:1 switch capacitor step down converter + + align:start position:0% +2:1 switch capacitor step down converter + + + align:start position:0% +2:1 switch capacitor step down converter +when we say 2 to one we're referring to + + align:start position:0% +when we say 2 to one we're referring to + + + align:start position:0% +when we say 2 to one we're referring to +voltage conversion because this just the + + align:start position:0% +voltage conversion because this just the + + + align:start position:0% +voltage conversion because this just the +way people do it um so here's the + + align:start position:0% +way people do it um so here's the + + + align:start position:0% +way people do it um so here's the +circuit we're talking + + align:start position:0% + + + + align:start position:0% + +about here's VSS I'm going to have a + + align:start position:0% +about here's VSS I'm going to have a + + + align:start position:0% +about here's VSS I'm going to have a +first switch one I'm going to have a + + align:start position:0% +first switch one I'm going to have a + + + align:start position:0% +first switch one I'm going to have a +capacitor where I'm going to have some + + align:start position:0% +capacitor where I'm going to have some + + + align:start position:0% +capacitor where I'm going to have some +voltage VC on it another switch one and + + align:start position:0% +voltage VC on it another switch one and + + + align:start position:0% +voltage VC on it another switch one and +then this is going to go to some big + + align:start position:0% +then this is going to go to some big + + + align:start position:0% +then this is going to go to some big +capacitor I'll call it c + + align:start position:0% +capacitor I'll call it c + + + align:start position:0% +capacitor I'll call it c +big that's going to hold the voltage + + align:start position:0% +big that's going to hold the voltage + + + align:start position:0% +big that's going to hold the voltage +okay and he's loaded with some current I + + align:start position:0% +okay and he's loaded with some current I + + + align:start position:0% +okay and he's loaded with some current I +out right and then this is One charging + + align:start position:0% +out right and then this is One charging + + + align:start position:0% +out right and then this is One charging +State and then the other charging State + + align:start position:0% +State and then the other charging State + + + align:start position:0% +State and then the other charging State +um is looks like this this is switch two + + align:start position:0% +um is looks like this this is switch two + + + align:start position:0% +um is looks like this this is switch two +and switch + + align:start position:0% +and switch + + + align:start position:0% +and switch +two right so what we do is in say the + + align:start position:0% +two right so what we do is in say the + + + align:start position:0% +two right so what we do is in say the +switch to + + align:start position:0% +switch to + + + align:start position:0% +switch to +state I'm sorry in the switch one state + + align:start position:0% +state I'm sorry in the switch one state + + + align:start position:0% +state I'm sorry in the switch one state +we charge from VSS + + align:start position:0% +we charge from VSS + + + align:start position:0% +we charge from VSS +charging this capacitor C up by the + + align:start position:0% +charging this capacitor C up by the + + + align:start position:0% +charging this capacitor C up by the +difference between vs and V + + align:start position:0% + + + + align:start position:0% + +out right and then in the two State we + + align:start position:0% +out right and then in the two State we + + + align:start position:0% +out right and then in the two State we +discharge C into the output so that the + + align:start position:0% +discharge C into the output so that the + + + align:start position:0% +discharge C into the output so that the +output current is going to be always + + align:start position:0% +output current is going to be always + + + align:start position:0% +output current is going to be always +twice the average input current and we + + align:start position:0% +twice the average input current and we + + + align:start position:0% +twice the average input current and we +came up with a model we derived a model + + align:start position:0% +came up with a model we derived a model + + + align:start position:0% +came up with a model we derived a model +for everything inside of this box right + + align:start position:0% +for everything inside of this box right + + + align:start position:0% +for everything inside of this box right +so I could I could take everything in + + align:start position:0% +so I could I could take everything in + + + align:start position:0% +so I could I could take everything in +here + + align:start position:0% +here + + + align:start position:0% +here +and come up with an equivalent average + + align:start position:0% +and come up with an equivalent average + + + align:start position:0% +and come up with an equivalent average +circuit model a DC average model it + + align:start position:0% +circuit model a DC average model it + + + align:start position:0% +circuit model a DC average model it +would look like this I'd have uh + + align:start position:0% +would look like this I'd have uh + + + align:start position:0% +would look like this I'd have uh +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +VN and the rest of it I can model with a + + align:start position:0% +VN and the rest of it I can model with a + + + align:start position:0% +VN and the rest of it I can model with a +2:1 + + align:start position:0% + + + + align:start position:0% + +Transformer and then a + + align:start position:0% +Transformer and then a + + + align:start position:0% +Transformer and then a +resistor + + align:start position:0% +resistor + + + align:start position:0% +resistor +req and in the slow switching + + align:start position:0% + + + + align:start position:0% + +limit this is 1 over4 FC where this is + + align:start position:0% +limit this is 1 over4 FC where this is + + + align:start position:0% +limit this is 1 over4 FC where this is +switching + + align:start position:0% +switching + + + align:start position:0% +switching +frequency okay and this is everything + + align:start position:0% +frequency okay and this is everything + + + align:start position:0% +frequency okay and this is everything +inside that + + align:start position:0% + + + + align:start position:0% + +box and then I can model the output + + align:start position:0% +box and then I can model the output + + + align:start position:0% +box and then I can model the output +resistance output current I + + align:start position:0% +resistance output current I + + + align:start position:0% +resistance output current I +out this is V + + align:start position:0% +out this is V + + + align:start position:0% +out this is V +out that make sense to everybody + + align:start position:0% +out that make sense to everybody + + + align:start position:0% +out that make sense to everybody +everybody recall this + + align:start position:0% +everybody recall this + + + align:start position:0% +everybody recall this +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so notice that this is the slow + + align:start position:0% +so notice that this is the slow + + + align:start position:0% +so notice that this is the slow +switching limit and the slow switching + + align:start position:0% +switching limit and the slow switching + + + align:start position:0% +switching limit and the slow switching +limit R + + align:start position:0% +limit R + + + align:start position:0% +limit R +EQ on the log scale versus F switch on a + + align:start position:0% +EQ on the log scale versus F switch on a + + + align:start position:0% +EQ on the log scale versus F switch on a +log scale right goes as 1 over + + align:start position:0% + + + + align:start position:0% + +4fc + + align:start position:0% +4fc + + + align:start position:0% +4fc +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and why why does it do + + align:start position:0% +and why why does it do + + + align:start position:0% +and why why does it do +that because for a given load + + align:start position:0% + + + + align:start position:0% + +current the charge the charge transfer + + align:start position:0% +current the charge the charge transfer + + + align:start position:0% +current the charge the charge transfer +on this on and off of this capacitance + + align:start position:0% +on this on and off of this capacitance + + + align:start position:0% +on this on and off of this capacitance +is exactly determined by the load + + align:start position:0% +is exactly determined by the load + + + align:start position:0% +is exactly determined by the load +current right I I transfer a certain + + align:start position:0% +current right I I transfer a certain + + + align:start position:0% +current right I I transfer a certain +amount of charge per cycle through the + + align:start position:0% +amount of charge per cycle through the + + + align:start position:0% +amount of charge per cycle through the +cap with Delta Q coming out of VSS and + + align:start position:0% +cap with Delta Q coming out of VSS and + + + align:start position:0% +cap with Delta Q coming out of VSS and +and ultimately two Delta Q going to the + + align:start position:0% +and ultimately two Delta Q going to the + + + align:start position:0% +and ultimately two Delta Q going to the +output and as + + align:start position:0% +output and as + + + align:start position:0% +output and as +I make that current bigger and bigger + + align:start position:0% +I make that current bigger and bigger + + + align:start position:0% +I make that current bigger and bigger +that capacitor + + align:start position:0% +that capacitor + + + align:start position:0% +that capacitor +if I make the current bigger and bigger + + align:start position:0% +if I make the current bigger and bigger + + + align:start position:0% +if I make the current bigger and bigger +that capacitor has to charge up and down + + align:start position:0% +that capacitor has to charge up and down + + + align:start position:0% +that capacitor has to charge up and down +more and my efficiency should droop or + + align:start position:0% +more and my efficiency should droop or + + + align:start position:0% +more and my efficiency should droop or +equivalently is I make C bigger and + + align:start position:0% +equivalently is I make C bigger and + + + align:start position:0% +equivalently is I make C bigger and +bigger for a given charge transfer his + + align:start position:0% +bigger for a given charge transfer his + + + align:start position:0% +bigger for a given charge transfer his +voltage swing + + align:start position:0% +voltage swing + + + align:start position:0% +voltage swing +shrinks right so or if I turn up + + align:start position:0% +shrinks right so or if I turn up + + + align:start position:0% +shrinks right so or if I turn up +switching frequency the amount of time I + + align:start position:0% +switching frequency the amount of time I + + + align:start position:0% +switching frequency the amount of time I +have to transfer less charge in each + + align:start position:0% +have to transfer less charge in each + + + align:start position:0% +have to transfer less charge in each +switching cycle and the capacitor + + align:start position:0% +switching cycle and the capacitor + + + align:start position:0% +switching cycle and the capacitor +voltage doesn't move as much and the + + align:start position:0% +voltage doesn't move as much and the + + + align:start position:0% +voltage doesn't move as much and the +resistance goes down the charging loss + + align:start position:0% +resistance goes down the charging loss + + + align:start position:0% +resistance goes down the charging loss +goes down why because essentially in + + align:start position:0% +goes down why because essentially in + + + align:start position:0% +goes down why because essentially in +each cycle I charge and discharge that + + align:start position:0% +each cycle I charge and discharge that + + + align:start position:0% +each cycle I charge and discharge that +capacitor less okay so this reflection + + align:start position:0% +capacitor less okay so this reflection + + + align:start position:0% +capacitor less okay so this reflection +that the output resistance or the loss + + align:start position:0% +that the output resistance or the loss + + + align:start position:0% +that the output resistance or the loss +due to charging discharging this + + align:start position:0% +due to charging discharging this + + + align:start position:0% +due to charging discharging this +resistance this capacitor through the + + align:start position:0% +resistance this capacitor through the + + + align:start position:0% +resistance this capacitor through the +switch resistances inversely varied for + + align:start position:0% +switch resistances inversely varied for + + + align:start position:0% +switch resistances inversely varied for +with + + align:start position:0% +with + + + align:start position:0% +with +frequency or uh increases with load + + align:start position:0% +frequency or uh increases with load + + + align:start position:0% +frequency or uh increases with load +current that the loss is exactly related + + align:start position:0% +current that the loss is exactly related + + + align:start position:0% +current that the loss is exactly related +to how much up and down I'm charging the + + align:start position:0% +to how much up and down I'm charging the + + + align:start position:0% +to how much up and down I'm charging the +capacitor okay does that any questions + + align:start position:0% +capacitor okay does that any questions + + + align:start position:0% +capacitor okay does that any questions +about that + + align:start position:0% + + + + align:start position:0% + +then the only thing we said last time + + align:start position:0% +then the only thing we said last time + + + align:start position:0% +then the only thing we said last time +was + + align:start position:0% +was + + + align:start position:0% +was +well this isn't the slow switching limit + + align:start position:0% +well this isn't the slow switching limit + + + align:start position:0% +well this isn't the slow switching limit +where I have this kind of charging right + + align:start position:0% +where I have this kind of charging right + + + align:start position:0% +where I have this kind of charging right +the the capacitor charges you know the + + align:start position:0% +the the capacitor charges you know the + + + align:start position:0% +the the capacitor charges you know the +capacitor current does this and gets to + + align:start position:0% +capacitor current does this and gets to + + + align:start position:0% +capacitor current does this and gets to +its final charge state right assuming + + align:start position:0% +its final charge state right assuming + + + align:start position:0% +its final charge state right assuming +that c big is so big that it's staying + + align:start position:0% +that c big is so big that it's staying + + + align:start position:0% +that c big is so big that it's staying +constant right if I turn up the + + align:start position:0% +constant right if I turn up the + + + align:start position:0% +constant right if I turn up the +switching frequency enough I get onto a + + align:start position:0% +switching frequency enough I get onto a + + + align:start position:0% +switching frequency enough I get onto a +time scale that's short compared to this + + align:start position:0% +time scale that's short compared to this + + + align:start position:0% +time scale that's short compared to this +time constant maybe you know it's it's + + align:start position:0% +time constant maybe you know it's it's + + + align:start position:0% +time constant maybe you know it's it's +only doing this the current's never + + align:start position:0% +only doing this the current's never + + + align:start position:0% +only doing this the current's never +charging or discharging the capacitor + + align:start position:0% +charging or discharging the capacitor + + + align:start position:0% +charging or discharging the capacitor +voltage very much and the capacitor + + align:start position:0% +voltage very much and the capacitor + + + align:start position:0% +voltage very much and the capacitor +voltage isn't moving around very much + + align:start position:0% +voltage isn't moving around very much + + + align:start position:0% +voltage isn't moving around very much +okay and in that case I would get to a + + align:start position:0% +okay and in that case I would get to a + + + align:start position:0% +okay and in that case I would get to a +new limit and we said the resistance in + + align:start position:0% +new limit and we said the resistance in + + + align:start position:0% +new limit and we said the resistance in +the in the fast switching limit so this + + align:start position:0% +the in the fast switching limit so this + + + align:start position:0% +the in the fast switching limit so this +is the + + align:start position:0% + + + + align:start position:0% + +SSL would look like + + align:start position:0% +SSL would look like + + + align:start position:0% +SSL would look like +this and in the + + align:start position:0% +this and in the + + + align:start position:0% +this and in the +FSL + + align:start position:0% +FSL + + + align:start position:0% +FSL +req req ends up + + align:start position:0% +req req ends up + + + align:start position:0% +req req ends up +being uh four I'm sorry to our + + align:start position:0% + + + + align:start position:0% + +switch and that makes sense because in + + align:start position:0% +switch and that makes sense because in + + + align:start position:0% +switch and that makes sense because in +the fast switching limit right I'm + + align:start position:0% +the fast switching limit right I'm + + + align:start position:0% +the fast switching limit right I'm +basically always charging the output + + align:start position:0% +basically always charging the output + + + align:start position:0% +basically always charging the output +through two + + align:start position:0% +through two + + + align:start position:0% +through two +switches and so I ought to see two + + align:start position:0% +switches and so I ought to see two + + + align:start position:0% +switches and so I ought to see two +switch resistances in the fast switching + + align:start position:0% +switch resistances in the fast switching + + + align:start position:0% +switch resistances in the fast switching +limit and if I said well what is you + + align:start position:0% +limit and if I said well what is you + + + align:start position:0% +limit and if I said well what is you +know what does it look like + + align:start position:0% +know what does it look like + + + align:start position:0% +know what does it look like +across um + + align:start position:0% +across um + + + align:start position:0% +across um +the switching frequency for a given load + + align:start position:0% +the switching frequency for a given load + + + align:start position:0% +the switching frequency for a given load +across the switching frequency it does + + align:start position:0% +across the switching frequency it does + + + align:start position:0% +across the switching frequency it does +something like + + align:start position:0% +something like + + + align:start position:0% +something like +this it's one thing in the fast + + align:start position:0% +this it's one thing in the fast + + + align:start position:0% +this it's one thing in the fast +switching slow switching limit is + + align:start position:0% +switching slow switching limit is + + + align:start position:0% +switching slow switching limit is +another thing in the fast switching + + align:start position:0% +another thing in the fast switching + + + align:start position:0% +another thing in the fast switching +limit okay any questions about + + align:start position:0% +limit okay any questions about + + + align:start position:0% +limit okay any questions about +that so if I'm going to draw more + + align:start position:0% +that so if I'm going to draw more + + + align:start position:0% +that so if I'm going to draw more +current I'm going to get more droop + + align:start position:0% +current I'm going to get more droop + + + align:start position:0% +current I'm going to get more droop +right if I draw more current there's + + align:start position:0% +right if I draw more current there's + + + align:start position:0% +right if I draw more current there's +more droop across this equivalent + + align:start position:0% +more droop across this equivalent + + + align:start position:0% +more droop across this equivalent +resistance or if I turn up + + align:start position:0% +resistance or if I turn up + + + align:start position:0% +resistance or if I turn up +frequency until I hit the switching + + align:start position:0% +frequency until I hit the switching + + + align:start position:0% +frequency until I hit the switching +limit I can make that resistance smaller + + align:start position:0% +limit I can make that resistance smaller + + + align:start position:0% +limit I can make that resistance smaller +and make the droop + + align:start position:0% +and make the droop + + + align:start position:0% +and make the droop +smaller okay let's see a demonstration + + align:start position:0% +smaller okay let's see a demonstration + + + align:start position:0% +smaller okay let's see a demonstration +of this so I'm going to pass this to + + align:start position:0% +of this so I'm going to pass this to + + + align:start position:0% +of this so I'm going to pass this to +Dave auton who's built us a really + + align:start position:0% +Dave auton who's built us a really + + + align:start position:0% +Dave auton who's built us a really +beautiful demo to illustrate this + + align:start position:0% + + + + align:start position:0% + +property okay uh so right now I'm going + + align:start position:0% +property okay uh so right now I'm going + + + align:start position:0% +property okay uh so right now I'm going +to the purple waveform which I'm about + + align:start position:0% +to the purple waveform which I'm about + + + align:start position:0% +to the purple waveform which I'm about +to turn off is my input Supply and the + + align:start position:0% +to turn off is my input Supply and the + + + align:start position:0% +to turn off is my input Supply and the +green waveform is the output of this + + align:start position:0% +green waveform is the output of this + + + align:start position:0% +green waveform is the output of this +converter and right now I have no load + + align:start position:0% +converter and right now I have no load + + + align:start position:0% +converter and right now I have no load +on it okay so let me turn off the purple + + align:start position:0% +on it okay so let me turn off the purple + + + align:start position:0% +on it okay so let me turn off the purple +so you can see it now the yellow + + align:start position:0% +so you can see it now the yellow + + + align:start position:0% +so you can see it now the yellow +waveform is the top of our flying + + align:start position:0% +waveform is the top of our flying + + + align:start position:0% +waveform is the top of our flying +capacitor so you can see that it + + align:start position:0% +capacitor so you can see that it + + + align:start position:0% +capacitor so you can see that it +sometimes is up at the supply sometimes + + align:start position:0% +sometimes is up at the supply sometimes + + + align:start position:0% +sometimes is up at the supply sometimes +it's at the output and then the uh blue + + align:start position:0% +it's at the output and then the uh blue + + + align:start position:0% +it's at the output and then the uh blue +waveform is the bottom of the flying + + align:start position:0% +waveform is the bottom of the flying + + + align:start position:0% +waveform is the bottom of the flying +capacitor sometimes it's grounded + + align:start position:0% +capacitor sometimes it's grounded + + + align:start position:0% +capacitor sometimes it's grounded +sometimes it's at the middle okay so now + + align:start position:0% +sometimes it's at the middle okay so now + + + align:start position:0% +sometimes it's at the middle okay so now +I'm going to uh + + align:start position:0% +I'm going to uh + + + align:start position:0% +I'm going to uh +make sure we can see the green and I'm + + align:start position:0% +make sure we can see the green and I'm + + + align:start position:0% +make sure we can see the green and I'm +going to turn on a small load okay and + + align:start position:0% +going to turn on a small load okay and + + + align:start position:0% +going to turn on a small load okay and +you can see that the output voltage came + + align:start position:0% +you can see that the output voltage came + + + align:start position:0% +you can see that the output voltage came +down okay as a result and if you look at + + align:start position:0% +down okay as a result and if you look at + + + align:start position:0% +down okay as a result and if you look at +the yellow waveform you know you can + + align:start position:0% +the yellow waveform you know you can + + + align:start position:0% +the yellow waveform you know you can +sort of see an RC kind of a time + + align:start position:0% +sort of see an RC kind of a time + + + align:start position:0% +sort of see an RC kind of a time +constant on it okay and it and it looks + + align:start position:0% +constant on it okay and it and it looks + + + align:start position:0% +constant on it okay and it and it looks +like you know we could switch sooner + + align:start position:0% +like you know we could switch sooner + + + align:start position:0% +like you know we could switch sooner +okay if I increase the load a little bit + + align:start position:0% +okay if I increase the load a little bit + + + align:start position:0% +okay if I increase the load a little bit +so this is twice as much okay you you + + align:start position:0% +so this is twice as much okay you you + + + align:start position:0% +so this is twice as much okay you you +can see that that r c time it might be + + align:start position:0% +can see that that r c time it might be + + + align:start position:0% +can see that that r c time it might be +faster you can also see that the output + + align:start position:0% +faster you can also see that the output + + + align:start position:0% +faster you can also see that the output +Changed by quite a bit in terms of its + + align:start position:0% +Changed by quite a bit in terms of its + + + align:start position:0% +Changed by quite a bit in terms of its +output droop okay so now I'm going to + + align:start position:0% +output droop okay so now I'm going to + + + align:start position:0% +output droop okay so now I'm going to +start turning up the frequency uh and + + align:start position:0% +start turning up the frequency uh and + + + align:start position:0% +start turning up the frequency uh and +and we can watch the uh output increase + + align:start position:0% +and we can watch the uh output increase + + + align:start position:0% +and we can watch the uh output increase +okay so there's the the frequency coming + + align:start position:0% +okay so there's the the frequency coming + + + align:start position:0% +okay so there's the the frequency coming +up let me change the time scale a little + + align:start position:0% +up let me change the time scale a little + + + align:start position:0% +up let me change the time scale a little +bit so we can see it better now it's + + align:start position:0% +bit so we can see it better now it's + + + align:start position:0% +bit so we can see it better now it's +less clear exactly what the uh RC time + + align:start position:0% +less clear exactly what the uh RC time + + + align:start position:0% +less clear exactly what the uh RC time +constant is here you know maybe it's + + align:start position:0% +constant is here you know maybe it's + + + align:start position:0% +constant is here you know maybe it's +settling in the time that we give it but + + align:start position:0% +settling in the time that we give it but + + + align:start position:0% +settling in the time that we give it but +but maybe it hasn't quite made it yet + + align:start position:0% +but maybe it hasn't quite made it yet + + + align:start position:0% +but maybe it hasn't quite made it yet +and you can see that the output voltage + + align:start position:0% +and you can see that the output voltage + + + align:start position:0% +and you can see that the output voltage +is + + align:start position:0% +is + + + align:start position:0% +is +rising oops went the wrong + + align:start position:0% +rising oops went the wrong + + + align:start position:0% +rising oops went the wrong +way so I can turn it up by quite a bit + + align:start position:0% +way so I can turn it up by quite a bit + + + align:start position:0% +way so I can turn it up by quite a bit +this is sort of so I went from 5 kerz to + + align:start position:0% +this is sort of so I went from 5 kerz to + + + align:start position:0% +this is sort of so I went from 5 kerz to +250 khz so it's whoops uh sorry I + + align:start position:0% +250 khz so it's whoops uh sorry I + + + align:start position:0% +250 khz so it's whoops uh sorry I +changed the wrong knob here we go okay + + align:start position:0% +changed the wrong knob here we go okay + + + align:start position:0% +changed the wrong knob here we go okay +so at this at this high frequency uh you + + align:start position:0% +so at this at this high frequency uh you + + + align:start position:0% +so at this at this high frequency uh you +can you can see that there really isn't + + align:start position:0% +can you can see that there really isn't + + + align:start position:0% +can you can see that there really isn't +much Ripple on the output we're doing a + + align:start position:0% +much Ripple on the output we're doing a + + + align:start position:0% +much Ripple on the output we're doing a +pretty good job of switching it fast + + align:start position:0% +pretty good job of switching it fast + + + align:start position:0% +pretty good job of switching it fast +enough so that the capacitor voltage + + align:start position:0% +enough so that the capacitor voltage + + + align:start position:0% +enough so that the capacitor voltage +doesn't change so this is the most + + align:start position:0% +doesn't change so this is the most + + + align:start position:0% +doesn't change so this is the most +efficient point for this converter + + align:start position:0% +efficient point for this converter + + + align:start position:0% +efficient point for this converter +particularly if you don't count the + + align:start position:0% +particularly if you don't count the + + + align:start position:0% +particularly if you don't count the +power that goes into the gate drives and + + align:start position:0% +power that goes into the gate drives and + + + align:start position:0% +power that goes into the gate drives and +the power that goes into switching the + + align:start position:0% +the power that goes into switching the + + + align:start position:0% +the power that goes into switching the +switches that decreases the efficiency a + + align:start position:0% +switches that decreases the efficiency a + + + align:start position:0% +switches that decreases the efficiency a +little bit but in terms of the power + + align:start position:0% +little bit but in terms of the power + + + align:start position:0% +little bit but in terms of the power +part of it this is its Best Shot + + align:start position:0% + + + + align:start position:0% + +okay so any questions about the fact + + align:start position:0% +okay so any questions about the fact + + + align:start position:0% +okay so any questions about the fact +that we can really get some benefit by + + align:start position:0% +that we can really get some benefit by + + + align:start position:0% +that we can really get some benefit by +turning up the switching frequency we + + align:start position:0% +turning up the switching frequency we + + + align:start position:0% +turning up the switching frequency we +drop the resistance which increases our + + align:start position:0% +drop the resistance which increases our + + + align:start position:0% +drop the resistance which increases our +converter efficiency neglecting gate + + align:start position:0% +converter efficiency neglecting gate + + + align:start position:0% +converter efficiency neglecting gate +charge losses and that sort of thing and + + align:start position:0% +charge losses and that sort of thing and + + + align:start position:0% +charge losses and that sort of thing and +we would keep doing that we' usually + + align:start position:0% +we would keep doing that we' usually + + + align:start position:0% +we would keep doing that we' usually +like to keep doing that until we get up + + align:start position:0% +like to keep doing that until we get up + + + align:start position:0% +like to keep doing that until we get up +here somewhere so we're at maximum + + align:start position:0% +here somewhere so we're at maximum + + + align:start position:0% +here somewhere so we're at maximum +efficiency okay we wouldn't want to go + + align:start position:0% +efficiency okay we wouldn't want to go + + + align:start position:0% +efficiency okay we wouldn't want to go +out here because there are other losses + + align:start position:0% +out here because there are other losses + + + align:start position:0% +out here because there are other losses +that I'm not counting so there's always + + align:start position:0% +that I'm not counting so there's always + + + align:start position:0% +that I'm not counting so there's always +an Optimum switching frequency and nice + + align:start position:0% +an Optimum switching frequency and nice + + + align:start position:0% +an Optimum switching frequency and nice +thing is is the load decreases we can + + align:start position:0% +thing is is the load decreases we can + + + align:start position:0% +thing is is the load decreases we can +often change the switching frequency to + + align:start position:0% +often change the switching frequency to + + + align:start position:0% +often change the switching frequency to +keep efficiency really high in these + + align:start position:0% +keep efficiency really high in these + + + align:start position:0% +keep efficiency really high in these +converters across a very wide power + + align:start position:0% +converters across a very wide power + + + align:start position:0% +converters across a very wide power +range okay any questions about + + align:start position:0% + + + + align:start position:0% + +that so let's conf consider a few other + + align:start position:0% +that so let's conf consider a few other + + + align:start position:0% +that so let's conf consider a few other +things about switch capacitor converters + + align:start position:0% +things about switch capacitor converters + + + align:start position:0% +things about switch capacitor converters +one thing I'd like to like you to notice + + align:start position:0% +one thing I'd like to like you to notice + + + align:start position:0% +one thing I'd like to like you to notice +is in fact that if you have the right + + align:start position:0% +is in fact that if you have the right + + + align:start position:0% +is in fact that if you have the right +switch implementation switch capacitor + + align:start position:0% +switch implementation switch capacitor + + + align:start position:0% +switch implementation switch capacitor +converters are are bire in their power + + align:start position:0% +converters are are bire in their power + + + align:start position:0% +converters are are bire in their power +flow capability just like other + + align:start position:0% +flow capability just like other + + + align:start position:0% +flow capability just like other +converters like remember we could run a + + align:start position:0% +converters like remember we could run a + + + align:start position:0% +converters like remember we could run a +buck converter essentially backwards and + + align:start position:0% +buck converter essentially backwards and + + + align:start position:0% +buck converter essentially backwards and +turn it into a boost converter that same + + align:start position:0% +turn it into a boost converter that same + + + align:start position:0% +turn it into a boost converter that same +trick works with switching power + + align:start position:0% +trick works with switching power + + + align:start position:0% +trick works with switching power +converter uh works with switch capacitor + + align:start position:0% +converter uh works with switch capacitor + + + align:start position:0% +converter uh works with switch capacitor +converters so let me just choose another + + align:start position:0% +converters so let me just choose another + + + align:start position:0% +converters so let me just choose another +converter and what I'm going to do is + + align:start position:0% +converter and what I'm going to do is + + + align:start position:0% +converter and what I'm going to do is +I'm going to go take the output put it + + align:start position:0% +I'm going to go take the output put it + + + align:start position:0% +I'm going to go take the output put it +over here take the source put it over + + align:start position:0% +over here take the source put it over + + + align:start position:0% +over here take the source put it over +here I'll draw it backwards and the only + + align:start position:0% +here I'll draw it backwards and the only + + + align:start position:0% +here I'll draw it backwards and the only +other thing is I'll change the voltage + + align:start position:0% +other thing is I'll change the voltage + + + align:start position:0% +other thing is I'll change the voltage +here just so you can just for clarity in + + align:start position:0% +here just so you can just for clarity in + + + align:start position:0% +here just so you can just for clarity in +the circuit and what would we get if I + + align:start position:0% +the circuit and what would we get if I + + + align:start position:0% +the circuit and what would we get if I +did that it would look something like + + align:start position:0% +did that it would look something like + + + align:start position:0% +did that it would look something like +this okay + + align:start position:0% +this okay + + + align:start position:0% +this okay +so okay let me let me draw I'll keep my + + align:start position:0% +so okay let me let me draw I'll keep my + + + align:start position:0% +so okay let me let me draw I'll keep my +source and I'll you know what I'll I'll + + align:start position:0% +source and I'll you know what I'll I'll + + + align:start position:0% +source and I'll you know what I'll I'll +keep my source on my load and I'll flip + + align:start position:0% +keep my source on my load and I'll flip + + + align:start position:0% +keep my source on my load and I'll flip +the circuit around okay so here we go + + align:start position:0% +the circuit around okay so here we go + + + align:start position:0% +the circuit around okay so here we go +here's vs okay uh I'm going to have I'm + + align:start position:0% +here's vs okay uh I'm going to have I'm + + + align:start position:0% +here's vs okay uh I'm going to have I'm +first going to go + + align:start position:0% +first going to go + + + align:start position:0% +first going to go +through with a switch in a one and then + + align:start position:0% +through with a switch in a one and then + + + align:start position:0% +through with a switch in a one and then +up switch + + align:start position:0% +up switch + + + align:start position:0% +up switch +two okay and then I'm gonna have a + + align:start position:0% +two okay and then I'm gonna have a + + + align:start position:0% +two okay and then I'm gonna have a +capacitor that I'm going to draw it as + + align:start position:0% +capacitor that I'm going to draw it as + + + align:start position:0% +capacitor that I'm going to draw it as +VC like this and then I'm going to have + + align:start position:0% +VC like this and then I'm going to have + + + align:start position:0% +VC like this and then I'm going to have +a switch that's a + + align:start position:0% +a switch that's a + + + align:start position:0% +a switch that's a +one + + align:start position:0% +one + + + align:start position:0% +one +and + + align:start position:0% +and + + + align:start position:0% +and +uh I've got to come to the output so I'm + + align:start position:0% +uh I've got to come to the output so I'm + + + align:start position:0% +uh I've got to come to the output so I'm +going to have a c big + + align:start position:0% + + + + align:start position:0% + +I'm going to have a load current on this + + align:start position:0% + + + + align:start position:0% + +side + + align:start position:0% +side + + + align:start position:0% +side +okay and now um so what am I going to + + align:start position:0% +okay and now um so what am I going to + + + align:start position:0% +okay and now um so what am I going to +get here I've got to draw my other + + align:start position:0% +get here I've got to draw my other + + + align:start position:0% +get here I've got to draw my other +switch so he's ending up on this side so + + align:start position:0% +switch so he's ending up on this side so + + + align:start position:0% +switch so he's ending up on this side so +let me get just get this right switch + + align:start position:0% +let me get just get this right switch + + + align:start position:0% +let me get just get this right switch +one switch two goes + + align:start position:0% + + + + align:start position:0% + +here switch one comes from the source + + align:start position:0% +here switch one comes from the source + + + align:start position:0% +here switch one comes from the source +and comes here yes so two and two like + + align:start position:0% +and comes here yes so two and two like + + + align:start position:0% +and comes here yes so two and two like +this okay so what am I what am I doing + + align:start position:0% +this okay so what am I what am I doing + + + align:start position:0% +this okay so what am I what am I doing +in this circuit okay one one two2 it's + + align:start position:0% +in this circuit okay one one two2 it's + + + align:start position:0% +in this circuit okay one one two2 it's +the same thing all I did was basically + + align:start position:0% +the same thing all I did was basically + + + align:start position:0% +the same thing all I did was basically +flip the internal circuit around and + + align:start position:0% +flip the internal circuit around and + + + align:start position:0% +flip the internal circuit around and +kept the the source and load in the same + + align:start position:0% +kept the the source and load in the same + + + align:start position:0% +kept the the source and load in the same +place okay so what are the two switch + + align:start position:0% +place okay so what are the two switch + + + align:start position:0% +place okay so what are the two switch +States here if I have one in one what + + align:start position:0% +States here if I have one in one what + + + align:start position:0% +States here if I have one in one what +I'm doing is + + align:start position:0% +I'm doing is + + + align:start position:0% +I'm doing is +this if if switch ones are on what I got + + align:start position:0% +this if if switch ones are on what I got + + + align:start position:0% +this if if switch ones are on what I got +is this + + align:start position:0% + + + + align:start position:0% + +and here's my C + + align:start position:0% +and here's my C + + + align:start position:0% +and here's my C +big all right and here's my eye + + align:start position:0% + + + + align:start position:0% + +out okay and if I have my switch so this + + align:start position:0% +out okay and if I have my switch so this + + + align:start position:0% +out okay and if I have my switch so this +is State + + align:start position:0% + + + + align:start position:0% + +one if I have state + + align:start position:0% + + + + align:start position:0% + +two right uh essentially I am + + align:start position:0% + + + + align:start position:0% + +doing + + align:start position:0% + + + + align:start position:0% + +this okay so what happens like what how + + align:start position:0% +this okay so what happens like what how + + + align:start position:0% +this okay so what happens like what how +might I think about the charge transfers + + align:start position:0% +might I think about the charge transfers + + + align:start position:0% +might I think about the charge transfers +here in States one and two + + align:start position:0% + + + + align:start position:0% + +in this state state two what I'm going + + align:start position:0% +in this state state two what I'm going + + + align:start position:0% +in this state state two what I'm going +to do if if I have a active load over + + align:start position:0% +to do if if I have a active load over + + + align:start position:0% +to do if if I have a active load over +here I + + align:start position:0% +here I + + + align:start position:0% +here I +out right is I'm basically in state two + + align:start position:0% +out right is I'm basically in state two + + + align:start position:0% +out right is I'm basically in state two +I'm basically just charging this + + align:start position:0% +I'm basically just charging this + + + align:start position:0% +I'm basically just charging this +capacitor from the input so this + + align:start position:0% +capacitor from the input so this + + + align:start position:0% +capacitor from the input so this +capacitor VC is going to charge up to VM + + align:start position:0% +capacitor VC is going to charge up to VM + + + align:start position:0% +capacitor VC is going to charge up to VM +or to + + align:start position:0% + + + + align:start position:0% + +vs + + align:start position:0% +vs + + + align:start position:0% +vs +okay then in state one what I'm going to + + align:start position:0% +okay then in state one what I'm going to + + + align:start position:0% +okay then in state one what I'm going to +do is I'm going to discharge him + + align:start position:0% +do is I'm going to discharge him + + + align:start position:0% +do is I'm going to discharge him +like + + align:start position:0% + + + + align:start position:0% + +this right so I'm putting something + + align:start position:0% +this right so I'm putting something + + + align:start position:0% +this right so I'm putting something +that's charged to vs and series with VSS + + align:start position:0% +that's charged to vs and series with VSS + + + align:start position:0% +that's charged to vs and series with VSS +and I'm discharging into the output so + + align:start position:0% +and I'm discharging into the output so + + + align:start position:0% +and I'm discharging into the output so +the output ideally ought to charge up if + + align:start position:0% +the output ideally ought to charge up if + + + align:start position:0% +the output ideally ought to charge up if +I had no load current what will happen + + align:start position:0% +I had no load current what will happen + + + align:start position:0% +I had no load current what will happen +is the output will charge up to 2vs or + + align:start position:0% +is the output will charge up to 2vs or + + + align:start position:0% +is the output will charge up to 2vs or +2vn let me call this VN just for + + align:start position:0% + + + + align:start position:0% + +consistency + + align:start position:0% +consistency + + + align:start position:0% +consistency +okay so this becomes a 1:2 + + align:start position:0% +okay so this becomes a 1:2 + + + align:start position:0% +okay so this becomes a 1:2 +converter all right right I could do the + + align:start position:0% +converter all right right I could do the + + + align:start position:0% +converter all right right I could do the +same kind of analysis on this converter + + align:start position:0% +same kind of analysis on this converter + + + align:start position:0% +same kind of analysis on this converter +that I did on the converter from last + + align:start position:0% +that I did on the converter from last + + + align:start position:0% +that I did on the converter from last +class and if I did that we would get + + align:start position:0% +class and if I did that we would get + + + align:start position:0% +class and if I did that we would get +this equivalent circuit model I would + + align:start position:0% +this equivalent circuit model I would + + + align:start position:0% +this equivalent circuit model I would +get + + align:start position:0% +get + + + align:start position:0% +get +BN the equivalent circuit model for this + + align:start position:0% +BN the equivalent circuit model for this + + + align:start position:0% +BN the equivalent circuit model for this +whole thing would be like + + align:start position:0% + + + + align:start position:0% + +this one to + + align:start position:0% + + + + align:start position:0% + +two and then + + align:start position:0% + + + + align:start position:0% + +I would have an + + align:start position:0% +I would have an + + + align:start position:0% +I would have an +req that would be equal to 1 over F + + align:start position:0% +req that would be equal to 1 over F + + + align:start position:0% +req that would be equal to 1 over F +switch + + align:start position:0% +switch + + + align:start position:0% +switch +C in + + align:start position:0% +C in + + + align:start position:0% +C in +SSL and then here's my load current I + + align:start position:0% + + + + align:start position:0% + +out okay it's the same kind of analysis + + align:start position:0% +out okay it's the same kind of analysis + + + align:start position:0% +out okay it's the same kind of analysis +we do the same charge transfer thing we + + align:start position:0% +we do the same charge transfer thing we + + + align:start position:0% +we do the same charge transfer thing we +get an equation we see that this circuit + + align:start position:0% +get an equation we see that this circuit + + + align:start position:0% +get an equation we see that this circuit +model right here matches what goes on in + + align:start position:0% +model right here matches what goes on in + + + align:start position:0% +model right here matches what goes on in +the slow switching + + align:start position:0% +the slow switching + + + align:start position:0% +the slow switching +limit does that make sense everybody + + align:start position:0% + + + + align:start position:0% + +the neat thing about this is that + + align:start position:0% +the neat thing about this is that + + + align:start position:0% +the neat thing about this is that +actually the model hasn't + + align:start position:0% +actually the model hasn't + + + align:start position:0% +actually the model hasn't +changed + + align:start position:0% +changed + + + align:start position:0% +changed +right if I you know I'm using idealized + + align:start position:0% +right if I you know I'm using idealized + + + align:start position:0% +right if I you know I'm using idealized +switch let's just say assume they're + + align:start position:0% +switch let's just say assume they're + + + align:start position:0% +switch let's just say assume they're +perfect switches I can block and carry + + align:start position:0% +perfect switches I can block and carry + + + align:start position:0% +perfect switches I can block and carry +bir directionally so I I have a full + + align:start position:0% +bir directionally so I I have a full + + + align:start position:0% +bir directionally so I I have a full +switch implementation full four quadrant + + align:start position:0% +switch implementation full four quadrant + + + align:start position:0% +switch implementation full four quadrant +switch + + align:start position:0% +switch + + + align:start position:0% +switch +implementation + + align:start position:0% +implementation + + + align:start position:0% +implementation +um I could take this circuit model and + + align:start position:0% +um I could take this circuit model and + + + align:start position:0% +um I could take this circuit model and +reflect this R equivalent through the + + align:start position:0% +reflect this R equivalent through the + + + align:start position:0% +reflect this R equivalent through the +trans forer right and what would I do + + align:start position:0% +trans forer right and what would I do + + + align:start position:0% +trans forer right and what would I do +when I go through the Transformer I have + + align:start position:0% +when I go through the Transformer I have + + + align:start position:0% +when I go through the Transformer I have +to scale impedances by the square of the + + align:start position:0% +to scale impedances by the square of the + + + align:start position:0% +to scale impedances by the square of the +turns ratio so another model I could + + align:start position:0% +turns ratio so another model I could + + + align:start position:0% +turns ratio so another model I could +develop for this an equivalent to this + + align:start position:0% +develop for this an equivalent to this + + + align:start position:0% +develop for this an equivalent to this +model is the following I could put a + + align:start position:0% +model is the following I could put a + + + align:start position:0% +model is the following I could put a +resistor here that would be scaled by + + align:start position:0% +resistor here that would be scaled by + + + align:start position:0% +resistor here that would be scaled by +1/4 so I'd have 1 + + align:start position:0% +1/4 so I'd have 1 + + + align:start position:0% +1/4 so I'd have 1 +over4 F switch C + + align:start position:0% + + + + align:start position:0% + +one to + + align:start position:0% +one to + + + align:start position:0% +one to +two and this would be my alternative + + align:start position:0% +two and this would be my alternative + + + align:start position:0% +two and this would be my alternative +circuit model and now here I have I + + align:start position:0% + + + + align:start position:0% + +out + + align:start position:0% +out + + + align:start position:0% +out +okay so here's my point this is this is + + align:start position:0% +okay so here's my point this is this is + + + align:start position:0% +okay so here's my point this is this is +just another way to draw the circuit + + align:start position:0% +just another way to draw the circuit + + + align:start position:0% +just another way to draw the circuit +model same circuit model I've just + + align:start position:0% +model same circuit model I've just + + + align:start position:0% +model same circuit model I've just +reflected the resistance through the + + align:start position:0% +reflected the resistance through the + + + align:start position:0% +reflected the resistance through the +Transformer and if you look at this + + align:start position:0% +Transformer and if you look at this + + + align:start position:0% +Transformer and if you look at this +you're going to see it's exactly equal + + align:start position:0% +you're going to see it's exactly equal + + + align:start position:0% +you're going to see it's exactly equal +to the one up there right it's one over4 + + align:start position:0% +to the one up there right it's one over4 + + + align:start position:0% +to the one up there right it's one over4 +F switch C + + align:start position:0% +F switch C + + + align:start position:0% +F switch C +so the energy loss doesn't really depend + + align:start position:0% +so the energy loss doesn't really depend + + + align:start position:0% +so the energy loss doesn't really depend +upon which way we're transferring power + + align:start position:0% +upon which way we're transferring power + + + align:start position:0% +upon which way we're transferring power +through the converter in other words am + + align:start position:0% +through the converter in other words am + + + align:start position:0% +through the converter in other words am +I sticking current in here and + + align:start position:0% +I sticking current in here and + + + align:start position:0% +I sticking current in here and +delivering energy to here or vice versa + + align:start position:0% +delivering energy to here or vice versa + + + align:start position:0% +delivering energy to here or vice versa +I'm going to get the same efficiency in + + align:start position:0% +I'm going to get the same efficiency in + + + align:start position:0% +I'm going to get the same efficiency in +either direction so long as my switch + + align:start position:0% +either direction so long as my switch + + + align:start position:0% +either direction so long as my switch +implementations and so forth can support + + align:start position:0% +implementations and so forth can support + + + align:start position:0% +implementations and so forth can support +that any questions about + + align:start position:0% +that any questions about + + + align:start position:0% +that any questions about +that so you know once you've analyzed + + align:start position:0% +that so you know once you've analyzed + + + align:start position:0% +that so you know once you've analyzed +the two: one you've Al analized the one + + align:start position:0% +the two: one you've Al analized the one + + + align:start position:0% +the two: one you've Al analized the one +to two you just don't know it yet we + + align:start position:0% +to two you just don't know it yet we + + + align:start position:0% +to two you just don't know it yet we +could have just like + + align:start position:0% +could have just like + + + align:start position:0% +could have just like +SWA the source and the load and been + + align:start position:0% +SWA the source and the load and been + + + align:start position:0% +SWA the source and the load and been +done and then I would have probably slid + + align:start position:0% +done and then I would have probably slid + + + align:start position:0% +done and then I would have probably slid +the resistor through the Transformer + + align:start position:0% +the resistor through the Transformer + + + align:start position:0% +the resistor through the Transformer +just to put it in its standard form we + + align:start position:0% +just to put it in its standard form we + + + align:start position:0% +just to put it in its standard form we +would have been + + align:start position:0% + + + + align:start position:0% + +done let's talk + + align:start position:0% +done let's talk + + + align:start position:0% +done let's talk +about + + align:start position:0% +about + + + align:start position:0% +about +um let's talk about challenges of this + + align:start position:0% +um let's talk about challenges of this + + + align:start position:0% +um let's talk about challenges of this +converter if I thought about building + + align:start position:0% +converter if I thought about building + + + align:start position:0% +converter if I thought about building +this + + align:start position:0% +this + + + align:start position:0% +this +converter okay um let's think about + + align:start position:0% +converter okay um let's think about + + + align:start position:0% +converter okay um let's think about +where the um physical components are big + + align:start position:0% +where the um physical components are big + + + align:start position:0% +where the um physical components are big +this capacitor + + align:start position:0% +this capacitor + + + align:start position:0% +this capacitor +here is my energy transfer + + align:start position:0% +here is my energy transfer + + + align:start position:0% +here is my energy transfer +capacitor + + align:start position:0% +capacitor + + + align:start position:0% +capacitor +right and we've already said yeah if I + + align:start position:0% +right and we've already said yeah if I + + + align:start position:0% +right and we've already said yeah if I +can make him a bigger energy transfer + + align:start position:0% +can make him a bigger energy transfer + + + align:start position:0% +can make him a bigger energy transfer +capacitor um you know the bigger C gets + + align:start position:0% +capacitor um you know the bigger C gets + + + align:start position:0% +capacitor um you know the bigger C gets +the smaller the resistance gets so it's + + align:start position:0% +the smaller the resistance gets so it's + + + align:start position:0% +the smaller the resistance gets so it's +good to have this capacitor be pretty + + align:start position:0% +good to have this capacitor be pretty + + + align:start position:0% +good to have this capacitor be pretty +big relative to the amount of power I'm + + align:start position:0% +big relative to the amount of power I'm + + + align:start position:0% +big relative to the amount of power I'm +pulling out of it so I can be close to + + align:start position:0% +pulling out of it so I can be close to + + + align:start position:0% +pulling out of it so I can be close to +the fast switching limit + + align:start position:0% +the fast switching limit + + + align:start position:0% +the fast switching limit +on the other hand I've treated this + + align:start position:0% +on the other hand I've treated this + + + align:start position:0% +on the other hand I've treated this +capacitor here as if he was infinite + + align:start position:0% +capacitor here as if he was infinite + + + align:start position:0% +capacitor here as if he was infinite +right so if I do nothing else usually + + align:start position:0% +right so if I do nothing else usually + + + align:start position:0% +right so if I do nothing else usually +this capacitor c big is Big compared to + + align:start position:0% +this capacitor c big is Big compared to + + + align:start position:0% +this capacitor c big is Big compared to +C and his job here if you notice is that + + align:start position:0% +C and his job here if you notice is that + + + align:start position:0% +C and his job here if you notice is that +he's sort of holding up the output in + + align:start position:0% +he's sort of holding up the output in + + + align:start position:0% +he's sort of holding up the output in +one of the two states in this + + align:start position:0% +one of the two states in this + + + align:start position:0% +one of the two states in this +state there really is nothing else + + align:start position:0% +state there really is nothing else + + + align:start position:0% +state there really is nothing else +making V out constant except for c big + + align:start position:0% +making V out constant except for c big + + + align:start position:0% +making V out constant except for c big +he has to be big enough so that V out's + + align:start position:0% +he has to be big enough so that V out's + + + align:start position:0% +he has to be big enough so that V out's +not going to droop while this guy is in + + align:start position:0% +not going to droop while this guy is in + + + align:start position:0% +not going to droop while this guy is in +his other + + align:start position:0% +his other + + + align:start position:0% +his other +state does that make sense to everybody + + align:start position:0% +state does that make sense to everybody + + + align:start position:0% +state does that make sense to everybody +so when you size the capacitors in this + + align:start position:0% +so when you size the capacitors in this + + + align:start position:0% +so when you size the capacitors in this +thing if I built this circuit usually c + + align:start position:0% +thing if I built this circuit usually c + + + align:start position:0% +thing if I built this circuit usually c +big would be substantially bigger than C + + align:start position:0% +big would be substantially bigger than C + + + align:start position:0% +big would be substantially bigger than C +which is in some sense a shame because + + align:start position:0% +which is in some sense a shame because + + + align:start position:0% +which is in some sense a shame because +I'm using C big only as a filter but not + + align:start position:0% +I'm using C big only as a filter but not + + + align:start position:0% +I'm using C big only as a filter but not +to transfer energy through the converter + + align:start position:0% +to transfer energy through the converter + + + align:start position:0% +to transfer energy through the converter +so the question is is there something + + align:start position:0% +so the question is is there something + + + align:start position:0% +so the question is is there something +clever I could do about this to make + + align:start position:0% +clever I could do about this to make + + + align:start position:0% +clever I could do about this to make +better use of my my capacitor energy + + align:start position:0% +better use of my my capacitor energy + + + align:start position:0% +better use of my my capacitor energy +storage and the answer is there is and + + align:start position:0% +storage and the answer is there is and + + + align:start position:0% +storage and the answer is there is and +here's the trick suppose I wish to build + + align:start position:0% +here's the trick suppose I wish to build + + + align:start position:0% +here's the trick suppose I wish to build +this + + align:start position:0% +this + + + align:start position:0% +this +circuit okay and let me just um let me + + align:start position:0% +circuit okay and let me just um let me + + + align:start position:0% +circuit okay and let me just um let me +just draw I'll redraw this circuit so + + align:start position:0% +just draw I'll redraw this circuit so + + + align:start position:0% +just draw I'll redraw this circuit so +here's + + align:start position:0% + + + + align:start position:0% + +VN and here's the here's my circuit I'm + + align:start position:0% +VN and here's the here's my circuit I'm + + + align:start position:0% +VN and here's the here's my circuit I'm +going to redraw this just up here and I + + align:start position:0% +going to redraw this just up here and I + + + align:start position:0% +going to redraw this just up here and I +get + + align:start position:0% +get + + + align:start position:0% +get +um here's + + align:start position:0% + + + + align:start position:0% + +two BC + + align:start position:0% + + + + align:start position:0% + +here's one I'm sorry here's this is + + align:start position:0% +here's one I'm sorry here's this is + + + align:start position:0% +here's one I'm sorry here's this is +switch one this is switch one I also + + align:start position:0% +switch one this is switch one I also + + + align:start position:0% +switch one this is switch one I also +have a switch + + align:start position:0% + + + + align:start position:0% + +two and I have a switch + + align:start position:0% +two and I have a switch + + + align:start position:0% +two and I have a switch +two okay and he comes down to this + + align:start position:0% +two okay and he comes down to this + + + align:start position:0% +two okay and he comes down to this +ground input right and then I have C big + + align:start position:0% +ground input right and then I have C big + + + align:start position:0% +ground input right and then I have C big +over + + align:start position:0% + + + + align:start position:0% + +here and here's my + + align:start position:0% +here and here's my + + + align:start position:0% +here and here's my +output okay okay and I'm going to + + align:start position:0% +output okay okay and I'm going to + + + align:start position:0% +output okay okay and I'm going to +deliver energy here what is this current + + align:start position:0% +deliver energy here what is this current + + + align:start position:0% +deliver energy here what is this current +what does this current look like let me + + align:start position:0% +what does this current look like let me + + + align:start position:0% +what does this current look like let me +call this I'll call this + + align:start position:0% +call this I'll call this + + + align:start position:0% +call this I'll call this +ix1 + + align:start position:0% +ix1 + + + align:start position:0% +ix1 +okay what does ix1 look like well let me + + align:start position:0% +okay what does ix1 look like well let me + + + align:start position:0% +okay what does ix1 look like well let me +think about in the fast switching + + align:start position:0% +think about in the fast switching + + + align:start position:0% +think about in the fast switching +limit okay what ix1 looks like well when + + align:start position:0% +limit okay what ix1 looks like well when + + + align:start position:0% +limit okay what ix1 looks like well when +I'm when I'm in the fast switching limit + + align:start position:0% +I'm when I'm in the fast switching limit + + + align:start position:0% +I'm when I'm in the fast switching limit +I'm dumping some charge off of VC into + + align:start position:0% +I'm dumping some charge off of VC into + + + align:start position:0% +I'm dumping some charge off of VC into +the output right and in the fast + + align:start position:0% +the output right and in the fast + + + align:start position:0% +the output right and in the fast +switching limit this capacitor is not + + align:start position:0% +switching limit this capacitor is not + + + align:start position:0% +switching limit this capacitor is not +charging or discharging much so the + + align:start position:0% +charging or discharging much so the + + + align:start position:0% +charging or discharging much so the +current flow is limited by these switch + + align:start position:0% +current flow is limited by these switch + + + align:start position:0% +current flow is limited by these switch +resistances right so in the fast + + align:start position:0% +resistances right so in the fast + + + align:start position:0% +resistances right so in the fast +switching limit ix1 looks like + + align:start position:0% + + + + align:start position:0% + +this so This Is state + + align:start position:0% + + + + align:start position:0% + +one and then in state two he's just + + align:start position:0% +one and then in state two he's just + + + align:start position:0% +one and then in state two he's just +zero because in state two this this + + align:start position:0% +zero because in state two this this + + + align:start position:0% +zero because in state two this this +switch is open okay and it's so I I dump + + align:start position:0% +switch is open okay and it's so I I dump + + + align:start position:0% +switch is open okay and it's so I I dump +a bunch of charge in C big in state one + + align:start position:0% +a bunch of charge in C big in state one + + + align:start position:0% +a bunch of charge in C big in state one +and then nothing in state two so C Big's + + align:start position:0% +and then nothing in state two so C Big's + + + align:start position:0% +and then nothing in state two so C Big's +left to sort of take this total charge + + align:start position:0% +left to sort of take this total charge + + + align:start position:0% +left to sort of take this total charge +and then deliver the average current to + + align:start position:0% +and then deliver the average current to + + + align:start position:0% +and then deliver the average current to +the + + align:start position:0% +the + + + align:start position:0% +the +output well what would happen if I came + + align:start position:0% +output well what would happen if I came + + + align:start position:0% +output well what would happen if I came +along and said you know what let me + + align:start position:0% +along and said you know what let me + + + align:start position:0% +along and said you know what let me +build a second + + align:start position:0% +build a second + + + align:start position:0% +build a second +converter okay I'm going to build the + + align:start position:0% +converter okay I'm going to build the + + + align:start position:0% +converter okay I'm going to build the +complement to the the first converter so + + align:start position:0% +complement to the the first converter so + + + align:start position:0% +complement to the the first converter so +I'm going to build somebody that looks + + align:start position:0% +I'm going to build somebody that looks + + + align:start position:0% +I'm going to build somebody that looks +like + + align:start position:0% +like + + + align:start position:0% +like +this it'll be my orange converter so + + align:start position:0% +this it'll be my orange converter so + + + align:start position:0% +this it'll be my orange converter so +maybe what I'll do is I'll build a + + align:start position:0% +maybe what I'll do is I'll build a + + + align:start position:0% +maybe what I'll do is I'll build a +second + + align:start position:0% +second + + + align:start position:0% +second +converter exactly like this and I'm + + align:start position:0% +converter exactly like this and I'm + + + align:start position:0% +converter exactly like this and I'm +going to make this turn on in state + + align:start position:0% +going to make this turn on in state + + + align:start position:0% +going to make this turn on in state +two I'm going to have another capacitor + + align:start position:0% +two I'm going to have another capacitor + + + align:start position:0% +two I'm going to have another capacitor +VC + + align:start position:0% +VC + + + align:start position:0% +VC +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +okay here's state + + align:start position:0% + + + + align:start position:0% + +two and now I'll deliver his charge to + + align:start position:0% +two and now I'll deliver his charge to + + + align:start position:0% +two and now I'll deliver his charge to +the output I'll call this + + align:start position:0% +the output I'll call this + + + align:start position:0% +the output I'll call this +ix2 okay now in state one I'm going to + + align:start position:0% +ix2 okay now in state one I'm going to + + + align:start position:0% +ix2 okay now in state one I'm going to +do the + + align:start position:0% +do the + + + align:start position:0% +do the +complement so I'm going to do this and + + align:start position:0% +complement so I'm going to do this and + + + align:start position:0% +complement so I'm going to do this and +here's I'm going to have this guy in + + align:start position:0% +here's I'm going to have this guy in + + + align:start position:0% +here's I'm going to have this guy in +state one and this guy in state + + align:start position:0% + + + + align:start position:0% + +one all right so all I've done is I've + + align:start position:0% +one all right so all I've done is I've + + + align:start position:0% +one all right so all I've done is I've +built a copy of this circuit but I've + + align:start position:0% +built a copy of this circuit but I've + + + align:start position:0% +built a copy of this circuit but I've +switched the switches exactly oppositely + + align:start position:0% +switched the switches exactly oppositely + + + align:start position:0% +switched the switches exactly oppositely +does that make sense to + + align:start position:0% +does that make sense to + + + align:start position:0% +does that make sense to +everybody so what is iix maybe I should + + align:start position:0% +everybody so what is iix maybe I should + + + align:start position:0% +everybody so what is iix maybe I should +call them iix Prime here + + align:start position:0% +call them iix Prime here + + + align:start position:0% +call them iix Prime here +what isix primee I guess I call them1 I + + align:start position:0% +what isix primee I guess I call them1 I + + + align:start position:0% +what isix primee I guess I call them1 I +guess I will call this I2 I have ix12 is + + align:start position:0% +guess I will call this I2 I have ix12 is + + + align:start position:0% +guess I will call this I2 I have ix12 is +going to be the exact compl of + + align:start position:0% +going to be the exact compl of + + + align:start position:0% +going to be the exact compl of +ix1 right because he happens in the + + align:start position:0% +ix1 right because he happens in the + + + align:start position:0% +ix1 right because he happens in the +opposite portion of the + + align:start position:0% +opposite portion of the + + + align:start position:0% +opposite portion of the +cycle right and then if I said well + + align:start position:0% +cycle right and then if I said well + + + align:start position:0% +cycle right and then if I said well +what's the total + + align:start position:0% +what's the total + + + align:start position:0% +what's the total +current coming in what is this current + + align:start position:0% +current coming in what is this current + + + align:start position:0% +current coming in what is this current +IX wellx is just now doing this he's + + align:start position:0% +IX wellx is just now doing this he's + + + align:start position:0% +IX wellx is just now doing this he's +he's following ix1 he's following + + align:start position:0% +he's following ix1 he's following + + + align:start position:0% +he's following ix1 he's following +ix2 right so he's almost a constant + + align:start position:0% +ix2 right so he's almost a constant + + + align:start position:0% +ix2 right so he's almost a constant +current into the + + align:start position:0% +current into the + + + align:start position:0% +current into the +output and so this capacitor is only + + align:start position:0% +output and so this capacitor is only + + + align:start position:0% +output and so this capacitor is only +filtering the difference between this + + align:start position:0% +filtering the difference between this + + + align:start position:0% +filtering the difference between this +and the load current the load current + + align:start position:0% +and the load current the load current + + + align:start position:0% +and the load current the load current +iil or I out is just the average of this + + align:start position:0% +iil or I out is just the average of this + + + align:start position:0% +iil or I out is just the average of this +current so I out looks like this all + + align:start position:0% + + + + align:start position:0% + +right and so this circuit really doesn't + + align:start position:0% +right and so this circuit really doesn't + + + align:start position:0% +right and so this circuit really doesn't +need c big anymore he only needs a tiny + + align:start position:0% +need c big anymore he only needs a tiny + + + align:start position:0% +need c big anymore he only needs a tiny +capacitor here so I could take this + + align:start position:0% +capacitor here so I could take this + + + align:start position:0% +capacitor here so I could take this +giant capacitor and divvy him up among + + align:start position:0% +giant capacitor and divvy him up among + + + align:start position:0% +giant capacitor and divvy him up among +you know this guy at this is C Prime and + + align:start position:0% +you know this guy at this is C Prime and + + + align:start position:0% +you know this guy at this is C Prime and +this guy is C and basically instead of + + align:start position:0% +this guy is C and basically instead of + + + align:start position:0% +this guy is C and basically instead of +having an energy transfer capacitor on a + + align:start position:0% +having an energy transfer capacitor on a + + + align:start position:0% +having an energy transfer capacitor on a +giant filter capacitor I can have two + + align:start position:0% +giant filter capacitor I can have two + + + align:start position:0% +giant filter capacitor I can have two +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +big energy transfer capacitors and a + + align:start position:0% +big energy transfer capacitors and a + + + align:start position:0% +big energy transfer capacitors and a +tiny filter capacitor and I can get the + + align:start position:0% +tiny filter capacitor and I can get the + + + align:start position:0% +tiny filter capacitor and I can get the +same behavior the same performance for + + align:start position:0% +same behavior the same performance for + + + align:start position:0% +same behavior the same performance for +much less capacitance or lower output + + align:start position:0% +much less capacitance or lower output + + + align:start position:0% +much less capacitance or lower output +resistance for the same to + + align:start position:0% +resistance for the same to + + + align:start position:0% +resistance for the same to +capacitance any questions about + + align:start position:0% +capacitance any questions about + + + align:start position:0% +capacitance any questions about +that this trick is very commonly used + + align:start position:0% +that this trick is very commonly used + + + align:start position:0% +that this trick is very commonly used +this is called + + align:start position:0% + + + + align:start position:0% + +interleaving right so this is an + + align:start position:0% +interleaving right so this is an + + + align:start position:0% +interleaving right so this is an +interleaved One to2 Step Up switch + + align:start position:0% +interleaved One to2 Step Up switch + + + align:start position:0% +interleaved One to2 Step Up switch +capacitor + + align:start position:0% +capacitor + + + align:start position:0% +capacitor +converter and it just has the benefit + + align:start position:0% +converter and it just has the benefit + + + align:start position:0% +converter and it just has the benefit +that you can get the same performance + + align:start position:0% +that you can get the same performance + + + align:start position:0% +that you can get the same performance +for much less total capacitance because + + align:start position:0% +for much less total capacitance because + + + align:start position:0% +for much less total capacitance because +I don't need to have some filtering you + + align:start position:0% +I don't need to have some filtering you + + + align:start position:0% +I don't need to have some filtering you +know any filtering going on I should say + + align:start position:0% +know any filtering going on I should say + + + align:start position:0% +know any filtering going on I should say +by the way this this is a two-phase + + align:start position:0% +by the way this this is a two-phase + + + align:start position:0% +by the way this this is a two-phase +circuit you know the states one and + + align:start position:0% +circuit you know the states one and + + + align:start position:0% +circuit you know the states one and +States two you can have more phases + + align:start position:0% +States two you can have more phases + + + align:start position:0% +States two you can have more phases +there are other games you can play but + + align:start position:0% +there are other games you can play but + + + align:start position:0% +there are other games you can play but +this is sort of the basic one what's the + + align:start position:0% +this is sort of the basic one what's the + + + align:start position:0% +this is sort of the basic one what's the +penalty you pay to do this I more or + + align:start position:0% +penalty you pay to do this I more or + + + align:start position:0% +penalty you pay to do this I more or +less have twice as many energy transfer + + align:start position:0% +less have twice as many energy transfer + + + align:start position:0% +less have twice as many energy transfer +capacitors and twice as many switches + + align:start position:0% +capacitors and twice as many switches + + + align:start position:0% +capacitors and twice as many switches +and in a world where the count of the + + align:start position:0% +and in a world where the count of the + + + align:start position:0% +and in a world where the count of the +components matters that's a pain in the + + align:start position:0% +components matters that's a pain in the + + + align:start position:0% +components matters that's a pain in the +butt on the other hand if I cared about + + align:start position:0% +butt on the other hand if I cared about + + + align:start position:0% +butt on the other hand if I cared about +the size of my energy transfer + + align:start position:0% +the size of my energy transfer + + + align:start position:0% +the size of my energy transfer +capacitors this thing's + + align:start position:0% +capacitors this thing's + + + align:start position:0% +capacitors this thing's +wonderful okay and this is a very common + + align:start position:0% +wonderful okay and this is a very common + + + align:start position:0% +wonderful okay and this is a very common +technique is interleaving your switch + + align:start position:0% +technique is interleaving your switch + + + align:start position:0% +technique is interleaving your switch +capacitor converters to uh alleviate the + + align:start position:0% +capacitor converters to uh alleviate the + + + align:start position:0% +capacitor converters to uh alleviate the +need for big either input Capa filter + + align:start position:0% +need for big either input Capa filter + + + align:start position:0% +need for big either input Capa filter +capacitors or output filter + + align:start position:0% +capacitors or output filter + + + align:start position:0% +capacitors or output filter +capacitors + + align:start position:0% + + + + align:start position:0% + +questions from a DC perspective all we + + align:start position:0% +questions from a DC perspective all we + + + align:start position:0% +questions from a DC perspective all we +do is basically put two of those + + align:start position:0% +do is basically put two of those + + + align:start position:0% +do is basically put two of those +circuits in parallel and I get half the + + align:start position:0% +circuits in parallel and I get half the + + + align:start position:0% +circuits in parallel and I get half the +output resistance essentially but what + + align:start position:0% +output resistance essentially but what + + + align:start position:0% +output resistance essentially but what +I've gotten rid of is the filter + + align:start position:0% +I've gotten rid of is the filter + + + align:start position:0% +I've gotten rid of is the filter +capacitor that's not in that DC + + align:start position:0% +capacitor that's not in that DC + + + align:start position:0% +capacitor that's not in that DC +model now I should say I've to spend all + + align:start position:0% +model now I should say I've to spend all + + + align:start position:0% +model now I should say I've to spend all +my time talking about um 2: one or 1:2 + + align:start position:0% +my time talking about um 2: one or 1:2 + + + align:start position:0% +my time talking about um 2: one or 1:2 +switch capacitor converters there are a + + align:start position:0% +switch capacitor converters there are a + + + align:start position:0% +switch capacitor converters there are a +lot of different kind of switch + + align:start position:0% +lot of different kind of switch + + + align:start position:0% +lot of different kind of switch +capacitor converters you can expand out + + align:start position:0% +capacitor converters you can expand out + + + align:start position:0% +capacitor converters you can expand out +to almost any rational conversion ratio + + align:start position:0% +to almost any rational conversion ratio + + + align:start position:0% +to almost any rational conversion ratio +and keep in mind as we said the rational + + align:start position:0% +and keep in mind as we said the rational + + + align:start position:0% +and keep in mind as we said the rational +conversion ratio gives you perfect + + align:start position:0% +conversion ratio gives you perfect + + + align:start position:0% +conversion ratio gives you perfect +conversion in current you know the this + + align:start position:0% +conversion in current you know the this + + + align:start position:0% +conversion in current you know the this +current is exactly twice this current + + align:start position:0% +current is exactly twice this current + + + align:start position:0% +current is exactly twice this current +right so you get a perfect current + + align:start position:0% +right so you get a perfect current + + + align:start position:0% +right so you get a perfect current +conversion ratio and a proximate voltage + + align:start position:0% +conversion ratio and a proximate voltage + + + align:start position:0% +conversion ratio and a proximate voltage +conversion ratio but you can almost get + + align:start position:0% +conversion ratio but you can almost get + + + align:start position:0% +conversion ratio but you can almost get +any ratio by picking the switching + + align:start position:0% +any ratio by picking the switching + + + align:start position:0% +any ratio by picking the switching +states in the capacitors you can get + + align:start position:0% +states in the capacitors you can get + + + align:start position:0% +states in the capacitors you can get +almost any ratio here that's rational + + align:start position:0% +almost any ratio here that's rational + + + align:start position:0% +almost any ratio here that's rational +like 2: 1 3: 1 4: 1 3:2 you know you + + align:start position:0% +like 2: 1 3: 1 4: 1 3:2 you know you + + + align:start position:0% +like 2: 1 3: 1 4: 1 3:2 you know you +name it + + align:start position:0% +name it + + + align:start position:0% +name it +okay there are bounds and and there's + + align:start position:0% +okay there are bounds and and there's + + + align:start position:0% +okay there are bounds and and there's +different ways to expand on this basic + + align:start position:0% +different ways to expand on this basic + + + align:start position:0% +different ways to expand on this basic +idea let me just show you a couple for + + align:start position:0% +idea let me just show you a couple for + + + align:start position:0% +idea let me just show you a couple for +out of + + align:start position:0% +out of + + + align:start position:0% +out of +many here's one idea suppose I did this + + align:start position:0% +many here's one idea suppose I did this + + + align:start position:0% +many here's one idea suppose I did this +suppose I had my input + + align:start position:0% +suppose I had my input + + + align:start position:0% +suppose I had my input +source VN and I did + + align:start position:0% +source VN and I did + + + align:start position:0% +source VN and I did +this I will + + align:start position:0% +this I will + + + align:start position:0% +this I will +um transfer energy to a capacitor + + align:start position:0% +um transfer energy to a capacitor + + + align:start position:0% +um transfer energy to a capacitor +here and then to + + align:start position:0% +here and then to + + + align:start position:0% +here and then to +here and then to + + align:start position:0% + + + + align:start position:0% + +here and then I'll have my C big + + align:start position:0% +here and then I'll have my C big + + + align:start position:0% +here and then I'll have my C big +here all right so when I close this and + + align:start position:0% +here all right so when I close this and + + + align:start position:0% +here all right so when I close this and +switch one one one one I'm going to + + align:start position:0% +switch one one one one I'm going to + + + align:start position:0% +switch one one one one I'm going to +charge these capacitors in series + + align:start position:0% +charge these capacitors in series + + + align:start position:0% +charge these capacitors in series +between the input and the output right + + align:start position:0% +between the input and the output right + + + align:start position:0% +between the input and the output right +so I'll get charge flow that sort of + + align:start position:0% +so I'll get charge flow that sort of + + + align:start position:0% +so I'll get charge flow that sort of +does + + align:start position:0% + + + + align:start position:0% + +this and I'll charge up all my + + align:start position:0% +this and I'll charge up all my + + + align:start position:0% +this and I'll charge up all my +capacitors to the + + align:start position:0% +capacitors to the + + + align:start position:0% +capacitors to the +output and then I can add another set of + + align:start position:0% +output and then I can add another set of + + + align:start position:0% +output and then I can add another set of +switches that are sort of like this + + align:start position:0% + + + + align:start position:0% + +and then maybe these guys will + + align:start position:0% + + + + align:start position:0% + +discharge in parallel to the output so + + align:start position:0% +discharge in parallel to the output so + + + align:start position:0% +discharge in parallel to the output so +I'll get charge flows that flow out of + + align:start position:0% +I'll get charge flows that flow out of + + + align:start position:0% +I'll get charge flows that flow out of +this capacitor like this out of this guy + + align:start position:0% +this capacitor like this out of this guy + + + align:start position:0% +this capacitor like this out of this guy +like this out of this guy like this + + align:start position:0% +like this out of this guy like this + + + align:start position:0% +like this out of this guy like this +right so I'll charge them in series and + + align:start position:0% +right so I'll charge them in series and + + + align:start position:0% +right so I'll charge them in series and +discharge them in parallel to the output + + align:start position:0% +discharge them in parallel to the output + + + align:start position:0% +discharge them in parallel to the output +so in the in the in the final state + + align:start position:0% +so in the in the in the final state + + + align:start position:0% +so in the in the in the final state +these capacitors will charge to V + + align:start position:0% +these capacitors will charge to V + + + align:start position:0% +these capacitors will charge to V +out and then so I would get in the state + + align:start position:0% +out and then so I would get in the state + + + align:start position:0% +out and then so I would get in the state +one I would get V out plus v out plus v + + align:start position:0% +one I would get V out plus v out plus v + + + align:start position:0% +one I would get V out plus v out plus v +out plus v out so four V + + align:start position:0% +out plus v out so four V + + + align:start position:0% +out plus v out so four V +out at the input so this is a 4:1 step + + align:start position:0% +out at the input so this is a 4:1 step + + + align:start position:0% +out at the input so this is a 4:1 step +down series parallel switch capacitor + + align:start position:0% +down series parallel switch capacitor + + + align:start position:0% +down series parallel switch capacitor +converter okay so we charge the + + align:start position:0% +converter okay so we charge the + + + align:start position:0% +converter okay so we charge the +capacitors in series we discharge them + + align:start position:0% +capacitors in series we discharge them + + + align:start position:0% +capacitors in series we discharge them +in parallel or if I turned this around + + align:start position:0% +in parallel or if I turned this around + + + align:start position:0% +in parallel or if I turned this around +and swapped where the source and load + + align:start position:0% +and swapped where the source and load + + + align:start position:0% +and swapped where the source and load +were it would a 1 to four + + align:start position:0% +were it would a 1 to four + + + align:start position:0% +were it would a 1 to four +convert + + align:start position:0% +convert + + + align:start position:0% +convert +okay that's one + + align:start position:0% +okay that's one + + + align:start position:0% +okay that's one +kind + + align:start position:0% +kind + + + align:start position:0% +kind +um there are many others and I'm kind of + + align:start position:0% +um there are many others and I'm kind of + + + align:start position:0% +um there are many others and I'm kind of +out of time so I'm not going to draw any + + align:start position:0% +out of time so I'm not going to draw any + + + align:start position:0% +out of time so I'm not going to draw any +of those there there are others listed + + align:start position:0% +of those there there are others listed + + + align:start position:0% +of those there there are others listed +in the book and I show another one I + + align:start position:0% +in the book and I show another one I + + + align:start position:0% +in the book and I show another one I +show a ladder converter in my notes what + + align:start position:0% +show a ladder converter in my notes what + + + align:start position:0% +show a ladder converter in my notes what +distinguishes these + + align:start position:0% +distinguishes these + + + align:start position:0% +distinguishes these +converters is how many switches and how + + align:start position:0% +converters is how many switches and how + + + align:start position:0% +converters is how many switches and how +many capacitors do you need to do a + + align:start position:0% +many capacitors do you need to do a + + + align:start position:0% +many capacitors do you need to do a +certain conversion function some are + + align:start position:0% +certain conversion function some are + + + align:start position:0% +certain conversion function some are +better than others what are the voltage + + align:start position:0% +better than others what are the voltage + + + align:start position:0% +better than others what are the voltage +ratings of the switches and Capac + + align:start position:0% +ratings of the switches and Capac + + + align:start position:0% +ratings of the switches and Capac +capacitors how much energy storage do + + align:start position:0% +capacitors how much energy storage do + + + align:start position:0% +capacitors how much energy storage do +you need to do a given conversion + + align:start position:0% +you need to do a given conversion + + + align:start position:0% +you need to do a given conversion +function and whether they're the same or + + align:start position:0% +function and whether they're the same or + + + align:start position:0% +function and whether they're the same or +not so in this circuit for example this + + align:start position:0% +not so in this circuit for example this + + + align:start position:0% +not so in this circuit for example this +switch has different ratings than the + + align:start position:0% +switch has different ratings than the + + + align:start position:0% +switch has different ratings than the +other switches for example so you might + + align:start position:0% +other switches for example so you might + + + align:start position:0% +other switches for example so you might +choose this one if you really cared + + align:start position:0% +choose this one if you really cared + + + align:start position:0% +choose this one if you really cared +about all the capacitors having the same + + align:start position:0% +about all the capacitors having the same + + + align:start position:0% +about all the capacitors having the same +voltage but you weren't so worried about + + align:start position:0% +voltage but you weren't so worried about + + + align:start position:0% +voltage but you weren't so worried about +the switches being different you might + + align:start position:0% +the switches being different you might + + + align:start position:0% +the switches being different you might +choose a different one if you had + + align:start position:0% +choose a different one if you had + + + align:start position:0% +choose a different one if you had +different constraints so there's a bunch + + align:start position:0% +different constraints so there's a bunch + + + align:start position:0% +different constraints so there's a bunch +of different converters that are popular + + align:start position:0% +of different converters that are popular + + + align:start position:0% +of different converters that are popular +you know ser parallel like this one + + align:start position:0% +you know ser parallel like this one + + + align:start position:0% +you know ser parallel like this one +ladder Dixon you know there there's a + + align:start position:0% +ladder Dixon you know there there's a + + + align:start position:0% +ladder Dixon you know there there's a +whole variety of them that you pick the + + align:start position:0% +whole variety of them that you pick the + + + align:start position:0% +whole variety of them that you pick the +one that sort of matches the design + + align:start position:0% +one that sort of matches the design + + + align:start position:0% +one that sort of matches the design +regime you're in if you're in an + + align:start position:0% +regime you're in if you're in an + + + align:start position:0% +regime you're in if you're in an +integrated circuit maybe you care about + + align:start position:0% +integrated circuit maybe you care about + + + align:start position:0% +integrated circuit maybe you care about +one things if you're really high voltage + + align:start position:0% +one things if you're really high voltage + + + align:start position:0% +one things if you're really high voltage +maybe you care about another + + align:start position:0% +maybe you care about another + + + align:start position:0% +maybe you care about another +thing any questions about + + align:start position:0% +thing any questions about + + + align:start position:0% +thing any questions about +that I should also + + align:start position:0% +that I should also + + + align:start position:0% +that I should also +say that while I'm showing you DC todc + + align:start position:0% +say that while I'm showing you DC todc + + + align:start position:0% +say that while I'm showing you DC todc +converters you can also make switch + + align:start position:0% +converters you can also make switch + + + align:start position:0% +converters you can also make switch +capacitor inverters or switch capacitor + + align:start position:0% +capacitor inverters or switch capacitor + + + align:start position:0% +capacitor inverters or switch capacitor +rectifiers and in fact uh I haven't + + align:start position:0% +rectifiers and in fact uh I haven't + + + align:start position:0% +rectifiers and in fact uh I haven't +drawn the right circuit I'm kind of out + + align:start position:0% +drawn the right circuit I'm kind of out + + + align:start position:0% +drawn the right circuit I'm kind of out +of time it's in the notes um but if you + + align:start position:0% +of time it's in the notes um but if you + + + align:start position:0% +of time it's in the notes um but if you +can take a circuit that has an AC driven + + align:start position:0% +can take a circuit that has an AC driven + + + align:start position:0% +can take a circuit that has an AC driven +input with diodes and sort of charges + + align:start position:0% +input with diodes and sort of charges + + + align:start position:0% +input with diodes and sort of charges +the the capacitors in one part of the + + align:start position:0% +the the capacitors in one part of the + + + align:start position:0% +the the capacitors in one part of the +cycle and then discharges them in the + + align:start position:0% +cycle and then discharges them in the + + + align:start position:0% +cycle and then discharges them in the +other in just such a manner that you + + align:start position:0% +other in just such a manner that you + + + align:start position:0% +other in just such a manner that you +Shuffle charge up and get a a rectifier + + align:start position:0% +Shuffle charge up and get a a rectifier + + + align:start position:0% +Shuffle charge up and get a a rectifier +that multiplies the voltage the + + align:start position:0% +that multiplies the voltage the + + + align:start position:0% +that multiplies the voltage the +so-called famous cockro wal and voltage + + align:start position:0% +so-called famous cockro wal and voltage + + + align:start position:0% +so-called famous cockro wal and voltage +multiplier is one example of a switch + + align:start position:0% +multiplier is one example of a switch + + + align:start position:0% +multiplier is one example of a switch +capacitor rectifier and those are very + + align:start position:0% +capacitor rectifier and those are very + + + align:start position:0% +capacitor rectifier and those are very +often used in high voltage power + + align:start position:0% +often used in high voltage power + + + align:start position:0% +often used in high voltage power +supplies where you want to generate very + + align:start position:0% +supplies where you want to generate very + + + align:start position:0% +supplies where you want to generate very +high voltages and that's why in fact Co + + align:start position:0% +high voltages and that's why in fact Co + + + align:start position:0% +high voltages and that's why in fact Co +Walton got the Nobel Prize for splitting + + align:start position:0% +Walton got the Nobel Prize for splitting + + + align:start position:0% +Walton got the Nobel Prize for splitting +the atom with really huge voltages + + align:start position:0% +the atom with really huge voltages + + + align:start position:0% +the atom with really huge voltages +generated by just such a rectifier so + + align:start position:0% +generated by just such a rectifier so + + + align:start position:0% +generated by just such a rectifier so +while I've spent my time talking about + + align:start position:0% +while I've spent my time talking about + + + align:start position:0% +while I've spent my time talking about +switch capacitor DC to conversion you + + align:start position:0% +switch capacitor DC to conversion you + + + align:start position:0% +switch capacitor DC to conversion you +can do inversion and rectification and + + align:start position:0% +can do inversion and rectification and + + + align:start position:0% +can do inversion and rectification and +they all follow the same fundamental + + align:start position:0% +they all follow the same fundamental + + + align:start position:0% +they all follow the same fundamental +principles so I'm kind of out of time to + + align:start position:0% +principles so I'm kind of out of time to + + + align:start position:0% +principles so I'm kind of out of time to +talk about this but I'd be happy to take + + align:start position:0% +talk about this but I'd be happy to take + + + align:start position:0% +talk about this but I'd be happy to take +any final + + align:start position:0% + + + + align:start position:0% + +questions okay next class we will take + + align:start position:0% +questions okay next class we will take + + + align:start position:0% +questions okay next class we will take +up uh a new topic have a great day \ No newline at end of file diff --git a/jfhdvFAplpU.txt b/jfhdvFAplpU.txt new file mode 100644 index 0000000000000000000000000000000000000000..f2125da10c327c57ff036f7b3b30109a17db5274 --- /dev/null +++ b/jfhdvFAplpU.txt @@ -0,0 +1,523 @@ +align:start position:0% + +my name is Lee Dyer I've been teaching + + align:start position:0% +my name is Lee Dyer I've been teaching + + + align:start position:0% +my name is Lee Dyer I've been teaching +human resource management at Cornell + + align:start position:0% +human resource management at Cornell + + + align:start position:0% +human resource management at Cornell +University for 45 years I've seen a lot + + align:start position:0% +University for 45 years I've seen a lot + + + align:start position:0% +University for 45 years I've seen a lot +of change in that time but none more + + align:start position:0% +of change in that time but none more + + + align:start position:0% +of change in that time but none more +profound or more important than the + + align:start position:0% +profound or more important than the + + + align:start position:0% +profound or more important than the +changes that lie ahead over the next few + + align:start position:0% +changes that lie ahead over the next few + + + align:start position:0% +changes that lie ahead over the next few +years major Transformations will be + + align:start position:0% +years major Transformations will be + + + align:start position:0% +years major Transformations will be +taking place in the nature of work and + + align:start position:0% +taking place in the nature of work and + + + align:start position:0% +taking place in the nature of work and +it will be up to each of us to decide + + align:start position:0% +it will be up to each of us to decide + + + align:start position:0% +it will be up to each of us to decide +how these will unfold and to make sure + + align:start position:0% +how these will unfold and to make sure + + + align:start position:0% +how these will unfold and to make sure +that they work out the way we want them + + align:start position:0% +that they work out the way we want them + + + align:start position:0% +that they work out the way we want them +to + + align:start position:0% +to + + + align:start position:0% +to +be as this figure shows HR professionals + + align:start position:0% +be as this figure shows HR professionals + + + align:start position:0% +be as this figure shows HR professionals +will be right Square in the middle of + + align:start position:0% +will be right Square in the middle of + + + align:start position:0% +will be right Square in the middle of +things ultimately it is the human + + align:start position:0% +things ultimately it is the human + + + align:start position:0% +things ultimately it is the human +resource strategies that organizations + + align:start position:0% +resource strategies that organizations + + + align:start position:0% +resource strategies that organizations +enact which play a major role in + + align:start position:0% +enact which play a major role in + + + align:start position:0% +enact which play a major role in +determining how many jobs are created as + + align:start position:0% +determining how many jobs are created as + + + align:start position:0% +determining how many jobs are created as +well as the quality of these jobs but if + + align:start position:0% +well as the quality of these jobs but if + + + align:start position:0% +well as the quality of these jobs but if +of course HR professionals don't operate + + align:start position:0% +of course HR professionals don't operate + + + align:start position:0% +of course HR professionals don't operate +in a vacuum a number of forces Global + + align:start position:0% +in a vacuum a number of forces Global + + + align:start position:0% +in a vacuum a number of forces Global +competition emerging technological + + align:start position:0% +competition emerging technological + + + align:start position:0% +competition emerging technological +developments societal pressures and + + align:start position:0% +developments societal pressures and + + + align:start position:0% +developments societal pressures and +labor market conditions influence firms + + align:start position:0% +labor market conditions influence firms + + + align:start position:0% +labor market conditions influence firms +business strategies and in turn their + + align:start position:0% +business strategies and in turn their + + + align:start position:0% +business strategies and in turn their +human resource + + align:start position:0% +human resource + + + align:start position:0% +human resource +strategies and there are a number of key + + align:start position:0% +strategies and there are a number of key + + + align:start position:0% +strategies and there are a number of key +players in the process as well these + + align:start position:0% +players in the process as well these + + + align:start position:0% +players in the process as well these +include labor organizations of various + + align:start position:0% +include labor organizations of various + + + align:start position:0% +include labor organizations of various +types public policy makers who make and + + align:start position:0% +types public policy makers who make and + + + align:start position:0% +types public policy makers who make and +enforce the rules of the game and + + align:start position:0% +enforce the rules of the game and + + + align:start position:0% +enforce the rules of the game and +Educators who are responsible for + + align:start position:0% +Educators who are responsible for + + + align:start position:0% +Educators who are responsible for +helping folks develop the skills they + + align:start position:0% +helping folks develop the skills they + + + align:start position:0% +helping folks develop the skills they +need to succeed the challenge for HR + + align:start position:0% +need to succeed the challenge for HR + + + align:start position:0% +need to succeed the challenge for HR +professionals is to understand the + + align:start position:0% +professionals is to understand the + + + align:start position:0% +professionals is to understand the +environmental forces at work and to work + + align:start position:0% +environmental forces at work and to work + + + align:start position:0% +environmental forces at work and to work +with the key players to develop desired + + align:start position:0% +with the key players to develop desired + + + align:start position:0% +with the key players to develop desired +results and of course this means doing + + align:start position:0% +results and of course this means doing + + + align:start position:0% +results and of course this means doing +all they can to be sure that their + + align:start position:0% +all they can to be sure that their + + + align:start position:0% +all they can to be sure that their +organizations have enough highquality + + align:start position:0% +organizations have enough highquality + + + align:start position:0% +organizations have enough highquality +people to do the work that needs doing + + align:start position:0% +people to do the work that needs doing + + + align:start position:0% +people to do the work that needs doing +but it also means striving to ensure + + align:start position:0% +but it also means striving to ensure + + + align:start position:0% +but it also means striving to ensure +that everyone who wants to work is able + + align:start position:0% +that everyone who wants to work is able + + + align:start position:0% +that everyone who wants to work is able +to get a job and not just any job but + + align:start position:0% +to get a job and not just any job but + + + align:start position:0% +to get a job and not just any job but +one that provides both a decent standard + + align:start position:0% +one that provides both a decent standard + + + align:start position:0% +one that provides both a decent standard +of living and a sense of personal + + align:start position:0% +of living and a sense of personal + + + align:start position:0% +of living and a sense of personal +fulfillment and + + align:start position:0% +fulfillment and + + + align:start position:0% +fulfillment and +accomplishment this is where our course + + align:start position:0% +accomplishment this is where our course + + + align:start position:0% +accomplishment this is where our course +comes in you will learn how the + + align:start position:0% +comes in you will learn how the + + + align:start position:0% +comes in you will learn how the +important external forces + + align:start position:0% +important external forces + + + align:start position:0% +important external forces +globalization technology and so forth + + align:start position:0% +globalization technology and so forth + + + align:start position:0% +globalization technology and so forth +have changed over time and are expected + + align:start position:0% +have changed over time and are expected + + + align:start position:0% +have changed over time and are expected +to change in the years + + align:start position:0% +to change in the years + + + align:start position:0% +to change in the years +ahead you also will learn what can be + + align:start position:0% +ahead you also will learn what can be + + + align:start position:0% +ahead you also will learn what can be +expected of key players in the process + + align:start position:0% +expected of key players in the process + + + align:start position:0% +expected of key players in the process +labor organizations public policy makers + + align:start position:0% +labor organizations public policy makers + + + align:start position:0% +labor organizations public policy makers +and so forth in the coming years and how + + align:start position:0% +and so forth in the coming years and how + + + align:start position:0% +and so forth in the coming years and how +you can work with them to forge mutually + + align:start position:0% +you can work with them to forge mutually + + + align:start position:0% +you can work with them to forge mutually +acceptable agreements on key + + align:start position:0% +acceptable agreements on key + + + align:start position:0% +acceptable agreements on key +issues in short if you are or are + + align:start position:0% +issues in short if you are or are + + + align:start position:0% +issues in short if you are or are +aspiring to be an HR professional or + + align:start position:0% +aspiring to be an HR professional or + + + align:start position:0% +aspiring to be an HR professional or +manager completion of this course will + + align:start position:0% +manager completion of this course will + + + align:start position:0% +manager completion of this course will +help position you to influence the + + align:start position:0% +help position you to influence the + + + align:start position:0% +help position you to influence the +nature of the changes that will be + + align:start position:0% +nature of the changes that will be + + + align:start position:0% +nature of the changes that will be +taking place in the years ahead both in + + align:start position:0% +taking place in the years ahead both in + + + align:start position:0% +taking place in the years ahead both in +the US and around the world \ No newline at end of file diff --git a/jl7wEsOZaU8.txt b/jl7wEsOZaU8.txt new file mode 100644 index 0000000000000000000000000000000000000000..5b028479bb7d882893bcbe1941be047e8465e30c --- /dev/null +++ b/jl7wEsOZaU8.txt @@ -0,0 +1,1315 @@ +align:start position:0% + +basically something like + + align:start position:0% +basically something like + + + align:start position:0% +basically something like +uh eight ten + + align:start position:0% +uh eight ten + + + align:start position:0% +uh eight ten +ten moves at the beginning with my pawns + + align:start position:0% +ten moves at the beginning with my pawns + + + align:start position:0% +ten moves at the beginning with my pawns +and uh my castle on my rooks i would + + align:start position:0% +and uh my castle on my rooks i would + + + align:start position:0% +and uh my castle on my rooks i would +have + + align:start position:0% +have + + + align:start position:0% +have +uh + + align:start position:0% +uh + + + align:start position:0% +uh +ten possible choices or twelve possible + + align:start position:0% +ten possible choices or twelve possible + + + align:start position:0% +ten possible choices or twelve possible +choices here + + align:start position:0% +choices here + + + align:start position:0% +choices here +and then i could have what my opponent + + align:start position:0% +and then i could have what my opponent + + + align:start position:0% +and then i could have what my opponent +does and + + align:start position:0% +does and + + + align:start position:0% +does and +uh a realistic problem can explode on + + align:start position:0% +uh a realistic problem can explode on + + + align:start position:0% +uh a realistic problem can explode on +you so one of the issues here + + align:start position:0% +you so one of the issues here + + + align:start position:0% +you so one of the issues here +again back to my + + align:start position:0% +again back to my + + + align:start position:0% +again back to my +emphasis at the beginning or my remark + + align:start position:0% +emphasis at the beginning or my remark + + + align:start position:0% +emphasis at the beginning or my remark +at the beginning is that decision + + align:start position:0% +at the beginning is that decision + + + align:start position:0% +at the beginning is that decision +analysis is good for simple problems for + + align:start position:0% +analysis is good for simple problems for + + + align:start position:0% +analysis is good for simple problems for +complicated problems it just gets too + + align:start position:0% +complicated problems it just gets too + + + align:start position:0% +complicated problems it just gets too +messy + + align:start position:0% + + + + align:start position:0% + +so i'm going to illustrate this with a + + align:start position:0% +so i'm going to illustrate this with a + + + align:start position:0% +so i'm going to illustrate this with a +simple example + + align:start position:0% +simple example + + + align:start position:0% +simple example +so the situation is as i said as i use + + align:start position:0% +so the situation is as i said as i use + + + align:start position:0% +so the situation is as i said as i use +them you you when i get get this each + + align:start position:0% +them you you when i get get this each + + + align:start position:0% +them you you when i get get this each +fall + + align:start position:0% +fall + + + align:start position:0% +fall +it's autumn at mit you can expect rain + + align:start position:0% +it's autumn at mit you can expect rain + + + align:start position:0% +it's autumn at mit you can expect rain +you're about to leave your apartment and + + align:start position:0% +you're about to leave your apartment and + + + align:start position:0% +you're about to leave your apartment and +head to campus uh + + align:start position:0% +head to campus uh + + + align:start position:0% +head to campus uh +what's the probability of + + align:start position:0% +what's the probability of + + + align:start position:0% +what's the probability of +noticeable rain during the day + + align:start position:0% +noticeable rain during the day + + + align:start position:0% +noticeable rain during the day +so + + align:start position:0% +so + + + align:start position:0% +so +again this is part of decision analysis + + align:start position:0% +again this is part of decision analysis + + + align:start position:0% +again this is part of decision analysis +it's fairly simple that + + align:start position:0% +it's fairly simple that + + + align:start position:0% +it's fairly simple that +um + + align:start position:0% +um + + + align:start position:0% +um +you could + + align:start position:0% +you could + + + align:start position:0% +you could +what's a rainy day does it rain for a + + align:start position:0% +what's a rainy day does it rain for a + + + align:start position:0% +what's a rainy day does it rain for a +few seconds does it rain for + + align:start position:0% +few seconds does it rain for + + + align:start position:0% +few seconds does it rain for +uh 10 minutes is it is it a downpour + + align:start position:0% +uh 10 minutes is it is it a downpour + + + align:start position:0% +uh 10 minutes is it is it a downpour +good many states but let's just have + + align:start position:0% +good many states but let's just have + + + align:start position:0% +good many states but let's just have +it's a yes no answer that's either going + + align:start position:0% +it's a yes no answer that's either going + + + align:start position:0% +it's a yes no answer that's either going +to rain or it's not going to rain + + align:start position:0% +to rain or it's not going to rain + + + align:start position:0% +to rain or it's not going to rain +noticeable rain + + align:start position:0% +noticeable rain + + + align:start position:0% +noticeable rain +so you have four possible outcomes you + + align:start position:0% +so you have four possible outcomes you + + + align:start position:0% +so you have four possible outcomes you +take your coat and it rains you take + + align:start position:0% +take your coat and it rains you take + + + align:start position:0% +take your coat and it rains you take +your coat and it's not raining you + + align:start position:0% +your coat and it's not raining you + + + align:start position:0% +your coat and it's not raining you +didn't take your coat and it rains you + + align:start position:0% +didn't take your coat and it rains you + + + align:start position:0% +didn't take your coat and it rains you +didn't take your coat in no rains + + align:start position:0% +didn't take your coat in no rains + + + align:start position:0% +didn't take your coat in no rains +nervous i've + + align:start position:0% +nervous i've + + + align:start position:0% +nervous i've +given values to the outcome that you + + align:start position:0% +given values to the outcome that you + + + align:start position:0% +given values to the outcome that you +might that a person might feel for this + + align:start position:0% +might that a person might feel for this + + + align:start position:0% +might that a person might feel for this +i could i have a sort of cover story for + + align:start position:0% +i could i have a sort of cover story for + + + align:start position:0% +i could i have a sort of cover story for +them as to why i invaded the numbers but + + align:start position:0% +them as to why i invaded the numbers but + + + align:start position:0% +them as to why i invaded the numbers but +they're all fake anyway it's it's more + + align:start position:0% +they're all fake anyway it's it's more + + + align:start position:0% +they're all fake anyway it's it's more +to show you + + align:start position:0% +to show you + + + align:start position:0% +to show you +uh a simple example of how you set it up + + align:start position:0% +uh a simple example of how you set it up + + + align:start position:0% +uh a simple example of how you set it up +and do the calculations so bear with me + + align:start position:0% +and do the calculations so bear with me + + + align:start position:0% +and do the calculations so bear with me +that these numbers are okay for the + + align:start position:0% +that these numbers are okay for the + + + align:start position:0% +that these numbers are okay for the +purpose of a demonstration + + align:start position:0% + + + + align:start position:0% + +so first i create the decision tree + + align:start position:0% +so first i create the decision tree + + + align:start position:0% +so first i create the decision tree +so my first decision is do i take the + + align:start position:0% +so my first decision is do i take the + + + align:start position:0% +so my first decision is do i take the +raincoat or not + + align:start position:0% +raincoat or not + + + align:start position:0% +raincoat or not +then whether it rains or doesn't rain it + + align:start position:0% +then whether it rains or doesn't rain it + + + align:start position:0% +then whether it rains or doesn't rain it +so happens that nothing to do of course + + align:start position:0% +so happens that nothing to do of course + + + align:start position:0% +so happens that nothing to do of course +nothing to do with my taking the + + align:start position:0% +nothing to do with my taking the + + + align:start position:0% +nothing to do with my taking the +raincoat affects the amount of rain + + align:start position:0% +raincoat affects the amount of rain + + + align:start position:0% +raincoat affects the amount of rain +so these are the same here + + align:start position:0% +so these are the same here + + + align:start position:0% +so these are the same here +probability of rain is on one case + + align:start position:0% +probability of rain is on one case + + + align:start position:0% +probability of rain is on one case +probably of no rain and so forth + + align:start position:0% +probably of no rain and so forth + + + align:start position:0% +probably of no rain and so forth +now as a + + align:start position:0% +now as a + + + align:start position:0% +now as a +it may well be in general that the + + align:start position:0% +it may well be in general that the + + + align:start position:0% +it may well be in general that the +decision you make + + align:start position:0% +decision you make + + + align:start position:0% +decision you make +affects the competition so their + + align:start position:0% +affects the competition so their + + + align:start position:0% +affects the competition so their +response depending on what you have so + + align:start position:0% +response depending on what you have so + + + align:start position:0% +response depending on what you have so +the + + align:start position:0% +the + + + align:start position:0% +the +probability associated with one + + align:start position:0% +probability associated with one + + + align:start position:0% +probability associated with one +choice + + align:start position:0% +choice + + + align:start position:0% +choice +is not necessarily the probability + + align:start position:0% +is not necessarily the probability + + + align:start position:0% +is not necessarily the probability +associated with another choice that is + + align:start position:0% +associated with another choice that is + + + align:start position:0% +associated with another choice that is +if you + + align:start position:0% +if you + + + align:start position:0% +if you +be aggressive in the market + + align:start position:0% +be aggressive in the market + + + align:start position:0% +be aggressive in the market +uh your competitors may respond by price + + align:start position:0% +uh your competitors may respond by price + + + align:start position:0% +uh your competitors may respond by price +cuts themselves and the whole situation + + align:start position:0% +cuts themselves and the whole situation + + + align:start position:0% +cuts themselves and the whole situation +may be different if you're not + + align:start position:0% +may be different if you're not + + + align:start position:0% +may be different if you're not +aggressive they might be not the price + + align:start position:0% +aggressive they might be not the price + + + align:start position:0% +aggressive they might be not the price +cuts and uh you have a different + + align:start position:0% +cuts and uh you have a different + + + align:start position:0% +cuts and uh you have a different +situation so but for the simple + + align:start position:0% +situation so but for the simple + + + align:start position:0% +situation so but for the simple +demonstration i have a + + align:start position:0% +demonstration i have a + + + align:start position:0% +demonstration i have a +uh + + align:start position:0% +uh + + + align:start position:0% +uh +there's no there's no dependence between + + align:start position:0% +there's no there's no dependence between + + + align:start position:0% +there's no there's no dependence between +your choices and the outcomes which is + + align:start position:0% +your choices and the outcomes which is + + + align:start position:0% +your choices and the outcomes which is +contrary to the most general case but + + align:start position:0% +contrary to the most general case but + + + align:start position:0% +contrary to the most general case but +again this is a very trying to make this + + align:start position:0% +again this is a very trying to make this + + + align:start position:0% +again this is a very trying to make this +very simple + + align:start position:0% +very simple + + + align:start position:0% +very simple +so first step + + align:start position:0% +so first step + + + align:start position:0% +so first step +set up the tree + + align:start position:0% + + + + align:start position:0% + +secondly + + align:start position:0% +secondly + + + align:start position:0% +secondly +for e you now the the process is to + + align:start position:0% +for e you now the the process is to + + + align:start position:0% +for e you now the the process is to +calculate the expected value of the + + align:start position:0% +calculate the expected value of the + + + align:start position:0% +calculate the expected value of the +outcomes + + align:start position:0% +outcomes + + + align:start position:0% +outcomes +so given the data i have for the + + align:start position:0% +so given the data i have for the + + + align:start position:0% +so given the data i have for the +probability of rain and not rain i can + + align:start position:0% +probability of rain and not rain i can + + + align:start position:0% +probability of rain and not rain i can +calculate the expected value of the + + align:start position:0% +calculate the expected value of the + + + align:start position:0% +calculate the expected value of the +raincode so it's 2 that is 0.4 times 5 + + align:start position:0% +raincode so it's 2 that is 0.4 times 5 + + + align:start position:0% +raincode so it's 2 that is 0.4 times 5 +minus 1.2 that is 0.6 times -2 and it's + + align:start position:0% +minus 1.2 that is 0.6 times -2 and it's + + + align:start position:0% +minus 1.2 that is 0.6 times -2 and it's +0.8 + + align:start position:0% +0.8 + + + align:start position:0% +0.8 +i can do the same thing for the other + + align:start position:0% +i can do the same thing for the other + + + align:start position:0% +i can do the same thing for the other +alternative + + align:start position:0% +alternative + + + align:start position:0% +alternative +it is + + align:start position:0% +it is + + + align:start position:0% +it is +0.4 times minus + + align:start position:0% +0.4 times minus + + + align:start position:0% +0.4 times minus +whoops that + + align:start position:0% +whoops that + + + align:start position:0% +whoops that +i didn't notice that it's -10 + + align:start position:0% +i didn't notice that it's -10 + + + align:start position:0% +i didn't notice that it's -10 +um + + align:start position:0% +um + + + align:start position:0% +um +somehow + + align:start position:0% +somehow + + + align:start position:0% +somehow +when i transferred it from powerpoint it + + align:start position:0% +when i transferred it from powerpoint it + + + align:start position:0% +when i transferred it from powerpoint it +got moved there + + align:start position:0% +got moved there + + + align:start position:0% +got moved there +uh + + align:start position:0% +uh + + + align:start position:0% +uh +can i change it probably not right now + + align:start position:0% +can i change it probably not right now + + + align:start position:0% +can i change it probably not right now +well i won't right now + + align:start position:0% +well i won't right now + + + align:start position:0% +well i won't right now +um and it that's the 4 and no rain which + + align:start position:0% +um and it that's the 4 and no rain which + + + align:start position:0% +um and it that's the 4 and no rain which +is 0.6 times the value of 4. it is the + + align:start position:0% +is 0.6 times the value of 4. it is the + + + align:start position:0% +is 0.6 times the value of 4. it is the +plus so + + align:start position:0% +plus so + + + align:start position:0% +plus so +here i have the two values outcome this + + align:start position:0% +here i have the two values outcome this + + + align:start position:0% +here i have the two values outcome this +says + + align:start position:0% +says + + + align:start position:0% +says +right i've done the decision tree on it + + align:start position:0% +right i've done the decision tree on it + + + align:start position:0% +right i've done the decision tree on it +with these values my better choice the + + align:start position:0% +with these values my better choice the + + + align:start position:0% +with these values my better choice the +expected value of that of the decision + + align:start position:0% +expected value of that of the decision + + + align:start position:0% +expected value of that of the decision +to take the raincoat is 0.8 it's better + + align:start position:0% +to take the raincoat is 0.8 it's better + + + align:start position:0% +to take the raincoat is 0.8 it's better +than minus 1.6 decision + + align:start position:0% +than minus 1.6 decision + + + align:start position:0% +than minus 1.6 decision +marked is to take the rating code + + align:start position:0% + + + + align:start position:0% + +now i can also do this if you're + + align:start position:0% +now i can also do this if you're + + + align:start position:0% +now i can also do this if you're +interested in i can do it not as a tree + + align:start position:0% +interested in i can do it not as a tree + + + align:start position:0% +interested in i can do it not as a tree +but in an excel layout + + align:start position:0% +but in an excel layout + + + align:start position:0% +but in an excel layout +so here's an example of it so i have the + + align:start position:0% +so here's an example of it so i have the + + + align:start position:0% +so here's an example of it so i have the +decisions and you can imagine i leave + + align:start position:0% +decisions and you can imagine i leave + + + align:start position:0% +decisions and you can imagine i leave +the space here and i haven't had the + + align:start position:0% +the space here and i haven't had the + + + align:start position:0% +the space here and i haven't had the +grid behind it to remove that + + align:start position:0% +grid behind it to remove that + + + align:start position:0% +grid behind it to remove that +i can go through i can automate i can + + align:start position:0% +i can go through i can automate i can + + + align:start position:0% +i can go through i can automate i can +accept equations so that probability + + align:start position:0% +accept equations so that probability + + + align:start position:0% +accept equations so that probability +times outcome probability times out this + + align:start position:0% +times outcome probability times out this + + + align:start position:0% +times outcome probability times out this +is the sum of the probability times + + align:start position:0% +is the sum of the probability times + + + align:start position:0% +is the sum of the probability times +outcome here plus the sum of the + + align:start position:0% +outcome here plus the sum of the + + + align:start position:0% +outcome here plus the sum of the +probability times outcome here i get 0.8 + + align:start position:0% +probability times outcome here i get 0.8 + + + align:start position:0% +probability times outcome here i get 0.8 +which i put in bold i didn't indicate + + align:start position:0% +which i put in bold i didn't indicate + + + align:start position:0% +which i put in bold i didn't indicate +that it's the + + align:start position:0% +that it's the + + + align:start position:0% +that it's the +the solution uh the better solution the + + align:start position:0% +the solution uh the better solution the + + + align:start position:0% +the solution uh the better solution the +and i do the same thing here so + + align:start position:0% +and i do the same thing here so + + + align:start position:0% +and i do the same thing here so +it can be automated and they're + + align:start position:0% +it can be automated and they're + + + align:start position:0% +it can be automated and they're +programmed to this the classroom + + align:start position:0% +programmed to this the classroom + + + align:start position:0% +programmed to this the classroom +demonstration of the model might be + + align:start position:0% +demonstration of the model might be + + + align:start position:0% +demonstration of the model might be +why tossing coins or how many do i get + + align:start position:0% +why tossing coins or how many do i get + + + align:start position:0% +why tossing coins or how many do i get +in a row or something where everything + + align:start position:0% +in a row or something where everything + + + align:start position:0% +in a row or something where everything +is discreet the real world however is + + align:start position:0% +is discreet the real world however is + + + align:start position:0% +is discreet the real world however is +quite complicated so that if you're + + align:start position:0% +quite complicated so that if you're + + + align:start position:0% +quite complicated so that if you're +thinking of using it to model + + align:start position:0% +thinking of using it to model + + + align:start position:0% +thinking of using it to model +a + + align:start position:0% +a + + + align:start position:0% +a +business expansion plan or some kind of + + align:start position:0% +business expansion plan or some kind of + + + align:start position:0% +business expansion plan or some kind of +activity + + align:start position:0% +activity + + + align:start position:0% +activity +you'd have to have some kind of way say + + align:start position:0% +you'd have to have some kind of way say + + + align:start position:0% +you'd have to have some kind of way say +okay if i did this and this if i took + + align:start position:0% +okay if i did this and this if i took + + + align:start position:0% +okay if i did this and this if i took +the raincoat or i did this action and + + align:start position:0% +the raincoat or i did this action and + + + align:start position:0% +the raincoat or i did this action and +this happened i'd have some way of + + align:start position:0% +this happened i'd have some way of + + + align:start position:0% +this happened i'd have some way of +calculating the result + + align:start position:0% +calculating the result + + + align:start position:0% +calculating the result +and i didn't want to + + align:start position:0% +and i didn't want to + + + align:start position:0% +and i didn't want to +show something like that for this simple + + align:start position:0% +show something like that for this simple + + + align:start position:0% +show something like that for this simple +example so i invented these numbers to + + align:start position:0% +example so i invented these numbers to + + + align:start position:0% +example so i invented these numbers to +um + + align:start position:0% +um + + + align:start position:0% +um +to fulfill it \ No newline at end of file diff --git a/jsJ0nR38zvo.txt b/jsJ0nR38zvo.txt new file mode 100644 index 0000000000000000000000000000000000000000..ad1de98f6d1cb37a7a42208a0f9b1ba92419cc2d --- /dev/null +++ b/jsJ0nR38zvo.txt @@ -0,0 +1,236 @@ +In order for multiple processes to be able +to run on the same computer, using a shared + +address space, we need to have an operating +system that controls which process gets to + +run at any given point in time and ensures +that the state that is currently loaded into + +the system is the state of the current process. + +Through the following example we will take +a closer look at how the operating system + +for the beta works. + +We begin by examining the code responsible +for maintaining the current processor state + +as well as scheduling which process should +run at any given point in time. + +The operating system uses a structure called +MState to keep track of the value of the 32 + +registers for each of the running processes. + +The UserMState variable holds the state of +the currently running process. + +The ProcTbl or process table, holds all the +necessary state for each of the processes + +that runs on the machine. + +For each process, it stores the value of all +of its registers in the State variable. + +Additional state may be stored per process. + +Examples of some additional state that would +go in a process table are a page map per process + +if we want to use virtual memory. + +Another example, is a keyboard identifier, +that associates hardware with a particular + +process. + +The Cur, or current variable, holds the index +of the currently running process. + +When we want to switch control from one process +to another, we call the Scheduler. + +The Scheduler first stores the state of the +currently running process into the process + +table. + +Next, it increments the current process by +1. + +If the current process was process N – 1, +then it goes back to process 0. + +Finally, it reloads the user variable with +the state for the new current process. + +In order to be able to run a diagnostic program +on one process that samples the values in + +the PC of another process, a supervisor call +named SamplePC is provided for you. + +The C portion of the SVC handler is provided +for you here. + +It is incomplete, so our first goal is to +determine what should replace the ???. + +We are told that the way SamplePC SVC works +is that it takes a process number p in R0, + +and returns in R1 the value currently in the +program counter of process p. + +The handler shown here reads register 0 from +the UserMState data structure and stores the + +value into variable p. + +This is the number of the process that is +to be monitored. + +In order to determine the value of the PC +of process p, one can look up the value of + +the XP register that was saved for process +p the last time process p was run. + +The XP register holds the value of the next +PC address. + +So reading the XP register from ProcTbl[p] +tells us the next value of the pc for process + +p. + +The pc value is to be returned in register +R1 of the current program. + +This means that the missing code is UserMState.Regs[1] +and that should be assigned the value of pc. + +Suppose you have a compute-bound process consisting +of a single 10,000 instruction loop. + +You use the SamplePC supervisor call to sample +the PC while running this loop. + +You notice many repeated values in the results +of the SamplePC code. + +You realize that the reason this is happening +is because every time your profiling process + +gets scheduled to run, it makes many SamplePC +calls but the other processes aren't running + +so you are getting the same sampled PC multiple +times. + +How can the repeated samples be avoided? + +To avoid repeated samples, we add a call to +Scheduler() in our SamplePC handler. + +This ensures that every time that the profiler +process is scheduled, it only samples a single + +PC value and then let's another process run. + +Suppose that you continue using the original +version of your SamplePC handler, which does + +not call Scheduler, and you use it to test +this code which repeatedly calls the GetKey() + +supervisor call to read a character from the +keyboard, and then calls the WrCh() supervisor + +call to write the character that was just +read. + +We want to answer the question of which PC +value will be the one reported the most often. + +Address 0x100 which is the address of the +GetKey() call is reported the most often because + +most of the time when GetKey() is called, +there is no key stroke waiting to be processed. + +This means that the GetKey() call will get +processed over and over again until there + +is finally a key to process. + +The result of this is that the PC value that +shows up the most often is 0x100. + +The last question we want to consider is what +behavior is observed when the profiler which + +is running in process 0 profiles process 0 +itself. + +Assume that the profiler code consists primarily +of one big loop which has a single call to + +the SamplePC supervisor call at instruction +0x1000. + +The rest of the loop processes the data that +was collected by the SamplePC call. + +The question we want to answer is what is +observed in the SamplePC results. + +We are given 4 choices to select from. + +The first choice to consider is whether or +not all the sampled PC values point to the + +kernel OS code. + +This choice is false because if it were true +it would mean that you somehow managed to + +interrupt kernel code which is not allowed +by the beta. + +The next choice to consider is whether the +sampled PC is always 0x1004. + +This seems like it might be a correct choice +because the SamplePC supervisor call is at + +address 0x1000, so storing PC + 4 would result +in 0x1004 being stored into the UserMState.Regs[XP]. + +However, if you look closely at the SamplePC +handler you see that the XP register is read + +from the ProcTbl. + +But the UserMState regs are only written to +ProcTbl when Scheduler() is called, so reading + +the value from ProcTbl would provide the last +value of the PC when process 0 was last interrupted. + +To get the correct value, you would need to +read UserMState.Regs[XP] instead. + +The third choice is that the SamplePC call +never returns. + +There is no reason for this to be true. + +Finally, the last choice is "None of the above". + +Since none of the other choices were correct, +this is the correct answer. \ No newline at end of file diff --git a/k95abdkdCPk.txt b/k95abdkdCPk.txt new file mode 100644 index 0000000000000000000000000000000000000000..68c792bf8f8ff7c8fc9aab8b98dc65b4132d4c86 --- /dev/null +++ b/k95abdkdCPk.txt @@ -0,0 +1,14011 @@ +align:start position:0% + +alright let's get started welcome ladies + + align:start position:0% +alright let's get started welcome ladies + + + align:start position:0% +alright let's get started welcome ladies +and gentlemen today I'm it's my pleasure + + align:start position:0% +and gentlemen today I'm it's my pleasure + + + align:start position:0% +and gentlemen today I'm it's my pleasure +to introduce two guest speakers who will + + align:start position:0% +to introduce two guest speakers who will + + + align:start position:0% +to introduce two guest speakers who will +talk about the regulation of AI and + + align:start position:0% +talk about the regulation of AI and + + + align:start position:0% +talk about the regulation of AI and +machine learning and about both the + + align:start position:0% +machine learning and about both the + + + align:start position:0% +machine learning and about both the +federal FDA level regulation and about + + align:start position:0% +federal FDA level regulation and about + + + align:start position:0% +federal FDA level regulation and about +IRB issues of regulation within + + align:start position:0% +IRB issues of regulation within + + + align:start position:0% +IRB issues of regulation within +institutions so first speaker is Andy + + align:start position:0% +institutions so first speaker is Andy + + + align:start position:0% +institutions so first speaker is Andy +Cabos Andy is the CEO and founding + + align:start position:0% +Cabos Andy is the CEO and founding + + + align:start position:0% +Cabos Andy is the CEO and founding +founder of electro labs which is a small + + align:start position:0% +founder of electro labs which is a small + + + align:start position:0% +founder of electro labs which is a small +company that's doing digital biomarkers + + align:start position:0% +company that's doing digital biomarkers + + + align:start position:0% +company that's doing digital biomarkers +for healthcare and mark is a data and + + align:start position:0% +for healthcare and mark is a data and + + + align:start position:0% +for healthcare and mark is a data and +software engineer for the Institute for + + align:start position:0% +software engineer for the Institute for + + + align:start position:0% +software engineer for the Institute for +next-generation healthcare at Mount + + align:start position:0% +next-generation healthcare at Mount + + + align:start position:0% +next-generation healthcare at Mount +Sinai in New York and it was kind enough + + align:start position:0% +Sinai in New York and it was kind enough + + + align:start position:0% +Sinai in New York and it was kind enough +to come up to speak to us today so with + + align:start position:0% +to come up to speak to us today so with + + + align:start position:0% +to come up to speak to us today so with +that I'm going to introduce them and sit + + align:start position:0% +that I'm going to introduce them and sit + + + align:start position:0% +that I'm going to introduce them and sit +back and enjoy thank you thank you thank + + align:start position:0% +back and enjoy thank you thank you thank + + + align:start position:0% +back and enjoy thank you thank you thank +you for having us + + align:start position:0% +you for having us + + + align:start position:0% +you for having us +yeah so I am working on digital + + align:start position:0% +yeah so I am working on digital + + + align:start position:0% +yeah so I am working on digital +biomarkers and I'm also research + + align:start position:0% +biomarkers and I'm also research + + + align:start position:0% +biomarkers and I'm also research +collaborator at the Harvard MIT Center + + align:start position:0% +collaborator at the Harvard MIT Center + + + align:start position:0% +collaborator at the Harvard MIT Center +for regulatory sciences so you all have + + align:start position:0% +for regulatory sciences so you all have + + + align:start position:0% +for regulatory sciences so you all have +a center that is looking just at how + + align:start position:0% +a center that is looking just at how + + + align:start position:0% +a center that is looking just at how +regulators should think about some of + + align:start position:0% +regulators should think about some of + + + align:start position:0% +regulators should think about some of +these problems and then I'm also an + + align:start position:0% +these problems and then I'm also an + + + align:start position:0% +these problems and then I'm also an +advisor at the bio hacking village at + + align:start position:0% +advisor at the bio hacking village at + + + align:start position:0% +advisor at the bio hacking village at +DEFCON which we can talk a little bit + + align:start position:0% +DEFCON which we can talk a little bit + + + align:start position:0% +DEFCON which we can talk a little bit +more about my background I'm a software + + align:start position:0% +more about my background I'm a software + + + align:start position:0% +more about my background I'm a software +engineer had worked with the FDA + + align:start position:0% +engineer had worked with the FDA + + + align:start position:0% +engineer had worked with the FDA +formerly as an entrepreneur residence in + + align:start position:0% +formerly as an entrepreneur residence in + + + align:start position:0% +formerly as an entrepreneur residence in +the digital health unit and then spent + + align:start position:0% +the digital health unit and then spent + + + align:start position:0% +the digital health unit and then spent +some time in corporate blend yep I'm + + align:start position:0% +some time in corporate blend yep I'm + + + align:start position:0% +some time in corporate blend yep I'm +mark Chevy I work at Institute for + + align:start position:0% +mark Chevy I work at Institute for + + + align:start position:0% +mark Chevy I work at Institute for +next-generation healthcare at Mount + + align:start position:0% +next-generation healthcare at Mount + + + align:start position:0% +next-generation healthcare at Mount +Sinai I've been there about three years + + align:start position:0% +Sinai I've been there about three years + + + align:start position:0% +Sinai I've been there about three years +there now my background is in software + + align:start position:0% +there now my background is in software + + + align:start position:0% +there now my background is in software +and data engineering coming mostly from + + align:start position:0% +and data engineering coming mostly from + + + align:start position:0% +and data engineering coming mostly from +banking and media this is a new spot and + + align:start position:0% +banking and media this is a new spot and + + + align:start position:0% +banking and media this is a new spot and +most of my responsibilities focus around + + align:start position:0% +most of my responsibilities focus around + + + align:start position:0% +most of my responsibilities focus around +data security and I are being ethical + + align:start position:0% +data security and I are being ethical + + + align:start position:0% +data security and I are being ethical +responsibilities we also know how much + + align:start position:0% +responsibilities we also know how much + + + align:start position:0% +responsibilities we also know how much +people generally love regulatory + + align:start position:0% +people generally love regulatory + + + align:start position:0% +people generally love regulatory +conversations so we will try to make + + align:start position:0% +conversations so we will try to make + + + align:start position:0% +conversations so we will try to make +this very fun and exciting for you if + + align:start position:0% +this very fun and exciting for you if + + + align:start position:0% +this very fun and exciting for you if +you do have questions those regulations + + align:start position:0% +you do have questions those regulations + + + align:start position:0% +you do have questions those regulations +are weird and they're constantly + + align:start position:0% +are weird and they're constantly + + + align:start position:0% +are weird and they're constantly +changing you can also shoot us a note + + align:start position:0% +changing you can also shoot us a note + + + align:start position:0% +changing you can also shoot us a note +Twitter will respond back if you have + + align:start position:0% +Twitter will respond back if you have + + + align:start position:0% +Twitter will respond back if you have +things that come up also the regulatory + + align:start position:0% +things that come up also the regulatory + + + align:start position:0% +things that come up also the regulatory +community on Twitter amazing when + + align:start position:0% +community on Twitter amazing when + + + align:start position:0% +community on Twitter amazing when +somebody comes out with like what is + + align:start position:0% +somebody comes out with like what is + + + align:start position:0% +somebody comes out with like what is +real-world data actually mean + + align:start position:0% +real-world data actually mean + + + align:start position:0% +real-world data actually mean +everybody's talking to one another so + + align:start position:0% +everybody's talking to one another so + + + align:start position:0% +everybody's talking to one another so +once you start tapping into I'm sure you + + align:start position:0% +once you start tapping into I'm sure you + + + align:start position:0% +once you start tapping into I'm sure you +have your own like Twitter communities + + align:start position:0% +have your own like Twitter communities + + + align:start position:0% +have your own like Twitter communities +but if you tap into the regulatory + + align:start position:0% +but if you tap into the regulatory + + + align:start position:0% +but if you tap into the regulatory +Twitter community it is a very good one + + align:start position:0% +Twitter community it is a very good one + + + align:start position:0% +Twitter community it is a very good one +the digital health unit tweets a lot at + + align:start position:0% +the digital health unit tweets a lot at + + + align:start position:0% +the digital health unit tweets a lot at +the FDA ok disclaimers these are our + + align:start position:0% +the FDA ok disclaimers these are our + + + align:start position:0% +the FDA ok disclaimers these are our +opinions and the information that you'll + + align:start position:0% +opinions and the information that you'll + + + align:start position:0% +opinions and the information that you'll +see here is not does not necessarily + + align:start position:0% +see here is not does not necessarily + + + align:start position:0% +see here is not does not necessarily +reflect the United States government or + + align:start position:0% +reflect the United States government or + + + align:start position:0% +reflect the United States government or +the institutions that we are affiliated + + align:start position:0% +the institutions that we are affiliated + + + align:start position:0% +the institutions that we are affiliated +with and policies and regulations are + + align:start position:0% +with and policies and regulations are + + + align:start position:0% +with and policies and regulations are +constantly changing so by the time we + + align:start position:0% +constantly changing so by the time we + + + align:start position:0% +constantly changing so by the time we +have presented this to you most likely + + align:start position:0% +have presented this to you most likely + + + align:start position:0% +have presented this to you most likely +parts of it is are wrong so you should + + align:start position:0% +parts of it is are wrong so you should + + + align:start position:0% +parts of it is are wrong so you should +definitely interact early and often with + + align:start position:0% +definitely interact early and often with + + + align:start position:0% +definitely interact early and often with +relevant regulatory institutions your + + align:start position:0% +relevant regulatory institutions your + + + align:start position:0% +relevant regulatory institutions your +lawyers might say not to do that it is + + align:start position:0% +lawyers might say not to do that it is + + + align:start position:0% +lawyers might say not to do that it is +there are definitely different ways and + + align:start position:0% +there are definitely different ways and + + + align:start position:0% +there are definitely different ways and +we can talk through like how you'd want + + align:start position:0% +we can talk through like how you'd want + + + align:start position:0% +we can talk through like how you'd want +to do that but it is especially as a + + align:start position:0% +to do that but it is especially as a + + + align:start position:0% +to do that but it is especially as a +software engineer and developing + + align:start position:0% +software engineer and developing + + + align:start position:0% +software engineer and developing +anything on the data side if you spend + + align:start position:0% +anything on the data side if you spend + + + align:start position:0% +anything on the data side if you spend +too much time developing a product that + + align:start position:0% +too much time developing a product that + + + align:start position:0% +too much time developing a product that +is never going to get through it is + + align:start position:0% +is never going to get through it is + + + align:start position:0% +is never going to get through it is +really a wasted period of time so + + align:start position:0% +really a wasted period of time so + + + align:start position:0% +really a wasted period of time so +working with the regulators and given + + align:start position:0% +working with the regulators and given + + + align:start position:0% +working with the regulators and given +how open they are right now to getting + + align:start position:0% +how open they are right now to getting + + + align:start position:0% +how open they are right now to getting +feedback as you saw with the paper that + + align:start position:0% +feedback as you saw with the paper that + + + align:start position:0% +feedback as you saw with the paper that +you read is going to be important and + + align:start position:0% +you read is going to be important and + + + align:start position:0% +you read is going to be important and +then the last thing which mark and I + + align:start position:0% +then the last thing which mark and I + + + align:start position:0% +then the last thing which mark and I +talked a lot about is many of these + + align:start position:0% +talked a lot about is many of these + + + align:start position:0% +talked a lot about is many of these +definitions and frameworks have not + + align:start position:0% +definitions and frameworks have not + + + align:start position:0% +definitions and frameworks have not +actually happened yet and so when + + align:start position:0% +actually happened yet and so when + + + align:start position:0% +actually happened yet and so when +somebody says a biomarker they might + + align:start position:0% +somebody says a biomarker they might + + + align:start position:0% +somebody says a biomarker they might +actually not mean a biomarker they might + + align:start position:0% +actually not mean a biomarker they might + + + align:start position:0% +actually not mean a biomarker they might +need a measurement I'm sure you know + + align:start position:0% +need a measurement I'm sure you know + + + align:start position:0% +need a measurement I'm sure you know +this when someone's like I work in AI + + align:start position:0% +this when someone's like I work in AI + + + align:start position:0% +this when someone's like I work in AI +and you're like what does that actually + + align:start position:0% +and you're like what does that actually + + + align:start position:0% +and you're like what does that actually +mean so you should ask us questions and + + align:start position:0% +mean so you should ask us questions and + + + align:start position:0% +mean so you should ask us questions and +you really are you think about it the + + align:start position:0% +you really are you think about it the + + + align:start position:0% +you really are you think about it the +type of knowledge that you have is a + + align:start position:0% +type of knowledge that you have is a + + + align:start position:0% +type of knowledge that you have is a +very specific rare set of knowledge + + align:start position:0% +very specific rare set of knowledge + + + align:start position:0% +very specific rare set of knowledge +compared to almost everybody else in the + + align:start position:0% +compared to almost everybody else in the + + + align:start position:0% +compared to almost everybody else in the +country and so as the FDA and other + + align:start position:0% +country and so as the FDA and other + + + align:start position:0% +country and so as the FDA and other +regulators start thinking about how to + + align:start position:0% +regulators start thinking about how to + + + align:start position:0% +regulators start thinking about how to +regulate and oversee these technologies + + align:start position:0% +regulate and oversee these technologies + + + align:start position:0% +regulate and oversee these technologies +you can have a really big amount of + + align:start position:0% +you can have a really big amount of + + + align:start position:0% +you can have a really big amount of +influence and so what we're going to do + + align:start position:0% +influence and so what we're going to do + + + align:start position:0% +influence and so what we're going to do +is a little bit of the dry stuff around + + align:start position:0% +is a little bit of the dry stuff around + + + align:start position:0% +is a little bit of the dry stuff around +regulatory and then I'm going to + + align:start position:0% +regulatory and then I'm going to + + + align:start position:0% +regulatory and then I'm going to +somewhat plead with you and also teach + + align:start position:0% +somewhat plead with you and also teach + + + align:start position:0% +somewhat plead with you and also teach +you how to submit public comments so + + align:start position:0% +you how to submit public comments so + + + align:start position:0% +you how to submit public comments so +that + + align:start position:0% +that + + + align:start position:0% +that +you can be part of this regulatory + + align:start position:0% +you can be part of this regulatory + + + align:start position:0% +you can be part of this regulatory +process and then I will speak about the + + align:start position:0% +process and then I will speak about the + + + align:start position:0% +process and then I will speak about the +insert institutional review board how + + align:start position:0% +insert institutional review board how + + + align:start position:0% +insert institutional review board how +many people in here have worked with an + + align:start position:0% +many people in here have worked with an + + + align:start position:0% +many people in here have worked with an +IRB or aware of them okay good that's a + + align:start position:0% +IRB or aware of them okay good that's a + + + align:start position:0% +IRB or aware of them okay good that's a +good mix so it's it'll be a quick thing + + align:start position:0% +good mix so it's it'll be a quick thing + + + align:start position:0% +good mix so it's it'll be a quick thing +just kind of reviewing when to involve + + align:start position:0% +just kind of reviewing when to involve + + + align:start position:0% +just kind of reviewing when to involve +the IRB how to involve the IRB things + + align:start position:0% +the IRB how to involve the IRB things + + + align:start position:0% +the IRB how to involve the IRB things +you need the IRB for and some things + + align:start position:0% +you need the IRB for and some things + + + align:start position:0% +you need the IRB for and some things +that you don't as kind of a alternative + + align:start position:0% +that you don't as kind of a alternative + + + align:start position:0% +that you don't as kind of a alternative +to taking it the FDA approach + + align:start position:0% +to taking it the FDA approach + + + align:start position:0% +to taking it the FDA approach +all right good all right and then I'll + + align:start position:0% +all right good all right and then I'll + + + align:start position:0% +all right good all right and then I'll +go first and then we'll go through IRB s + + align:start position:0% +go first and then we'll go through IRB s + + + align:start position:0% +go first and then we'll go through IRB s +and then we'll leave the last part for + + align:start position:0% +and then we'll leave the last part for + + + align:start position:0% +and then we'll leave the last part for +your impressions of the paper okay so + + align:start position:0% +your impressions of the paper okay so + + + align:start position:0% +your impressions of the paper okay so +before I start I'll ground us and some + + align:start position:0% +before I start I'll ground us and some + + + align:start position:0% +before I start I'll ground us and some +ideas around algorithmically driven + + align:start position:0% +ideas around algorithmically driven + + + align:start position:0% +ideas around algorithmically driven +healthcare products and so as you know + + align:start position:0% +healthcare products and so as you know + + + align:start position:0% +healthcare products and so as you know +these can have wide ranges of what they + + align:start position:0% +these can have wide ranges of what they + + + align:start position:0% +these can have wide ranges of what they +can do a general framework that I like + + align:start position:0% +can do a general framework that I like + + + align:start position:0% +can do a general framework that I like +to use to think about them is products + + align:start position:0% +to use to think about them is products + + + align:start position:0% +to use to think about them is products +that measure that diagnose or treat so + + align:start position:0% +that measure that diagnose or treat so + + + align:start position:0% +that measure that diagnose or treat so +measurement products might include + + align:start position:0% +measurement products might include + + + align:start position:0% +measurement products might include +things like digital biomarkers or + + align:start position:0% +things like digital biomarkers or + + + align:start position:0% +things like digital biomarkers or +clinical decision support Diagnostics + + align:start position:0% +clinical decision support Diagnostics + + + align:start position:0% +clinical decision support Diagnostics +might take that measurement and then say + + align:start position:0% +might take that measurement and then say + + + align:start position:0% +might take that measurement and then say +whether or not somebody has some sort of + + align:start position:0% +whether or not somebody has some sort of + + + align:start position:0% +whether or not somebody has some sort of +condition given those metrics and then + + align:start position:0% +condition given those metrics and then + + + align:start position:0% +condition given those metrics and then +treatment our ideas around digital + + align:start position:0% +treatment our ideas around digital + + + align:start position:0% +treatment our ideas around digital +therapeutics how many people here think + + align:start position:0% +therapeutics how many people here think + + + align:start position:0% +therapeutics how many people here think +that software can treat a person whew + + align:start position:0% +that software can treat a person whew + + + align:start position:0% +that software can treat a person whew +maybe okay and and I think one thing + + align:start position:0% +maybe okay and and I think one thing + + + align:start position:0% +maybe okay and and I think one thing +that people don't think about always + + align:start position:0% +that people don't think about always + + + align:start position:0% +that people don't think about always +when they have these sorts of tools is + + align:start position:0% +when they have these sorts of tools is + + + align:start position:0% +when they have these sorts of tools is +even something and you all probably + + align:start position:0% +even something and you all probably + + + align:start position:0% +even something and you all probably +think about this a lot more is even + + align:start position:0% +think about this a lot more is even + + + align:start position:0% +think about this a lot more is even +something as simple as a step count is + + align:start position:0% +something as simple as a step count is + + + align:start position:0% +something as simple as a step count is +an algorithm right so it takes your + + align:start position:0% +an algorithm right so it takes your + + + align:start position:0% +an algorithm right so it takes your +gyroscope accelerometer height weight + + align:start position:0% +gyroscope accelerometer height weight + + + align:start position:0% +gyroscope accelerometer height weight +and age and then it predicts whether or + + align:start position:0% +and age and then it predicts whether or + + + align:start position:0% +and age and then it predicts whether or +not you've made a step and if you think + + align:start position:0% +not you've made a step and if you think + + + align:start position:0% +not you've made a step and if you think +about the types of different steps that + + align:start position:0% +about the types of different steps that + + + align:start position:0% +about the types of different steps that +people make older people drag their feet + + align:start position:0% +people make older people drag their feet + + + align:start position:0% +people make older people drag their feet +a little bit more than younger people so + + align:start position:0% +a little bit more than younger people so + + + align:start position:0% +a little bit more than younger people so +an algorithm for step count looks very + + align:start position:0% +an algorithm for step count looks very + + + align:start position:0% +an algorithm for step count looks very +different from an algorithm for younger + + align:start position:0% +different from an algorithm for younger + + + align:start position:0% +different from an algorithm for younger +people for step count and so all of + + align:start position:0% +people for step count and so all of + + + align:start position:0% +people for step count and so all of +these tools have some level of error and + + align:start position:0% +these tools have some level of error and + + + align:start position:0% +these tools have some level of error and +they're all algorithms effectively one + + align:start position:0% +they're all algorithms effectively one + + + align:start position:0% +they're all algorithms effectively one +of my favorite frameworks as you start + + align:start position:0% +of my favorite frameworks as you start + + + align:start position:0% +of my favorite frameworks as you start +thinking about a lot of people are very + + align:start position:0% +thinking about a lot of people are very + + + align:start position:0% +thinking about a lot of people are very +interested in the measurement side + + align:start position:0% +interested in the measurement side + + + align:start position:0% +interested in the measurement side +around what's called digital biomarkers + + align:start position:0% +around what's called digital biomarkers + + + align:start position:0% +around what's called digital biomarkers +and it turns out that the FDA realized + + align:start position:0% +and it turns out that the FDA realized + + + align:start position:0% +and it turns out that the FDA realized +that many people even within their own + + align:start position:0% +that many people even within their own + + + align:start position:0% +that many people even within their own +agency didn't know + + align:start position:0% +agency didn't know + + + align:start position:0% +agency didn't know +what a biomarker was and everyone was + + align:start position:0% +what a biomarker was and everyone was + + + align:start position:0% +what a biomarker was and everyone was +using the term slightly differently + + align:start position:0% +using the term slightly differently + + + align:start position:0% +using the term slightly differently +probably how people approach you + + align:start position:0% +probably how people approach you + + + align:start position:0% +probably how people approach you +slightly differently of what machine + + align:start position:0% +slightly differently of what machine + + + align:start position:0% +slightly differently of what machine +learning actually is so there is a + + align:start position:0% +learning actually is so there is a + + + align:start position:0% +learning actually is so there is a +really good framework around the seven + + align:start position:0% +really good framework around the seven + + + align:start position:0% +really good framework around the seven +different types of biomarkers that would + + align:start position:0% +different types of biomarkers that would + + + align:start position:0% +different types of biomarkers that would +highly recommend you read if you go into + + align:start position:0% +highly recommend you read if you go into + + + align:start position:0% +highly recommend you read if you go into +this area a digital biomarker only in my + + align:start position:0% +this area a digital biomarker only in my + + + align:start position:0% +this area a digital biomarker only in my +definition and how other people have + + align:start position:0% +definition and how other people have + + + align:start position:0% +definition and how other people have +started to use this is the way that that + + align:start position:0% +started to use this is the way that that + + + align:start position:0% +started to use this is the way that that +measurement is collected and so you + + align:start position:0% +measurement is collected and so you + + + align:start position:0% +measurement is collected and so you +might have a monitoring biomarker a + + align:start position:0% +might have a monitoring biomarker a + + + align:start position:0% +might have a monitoring biomarker a +diagnostic biomarkers but it is + + align:start position:0% +diagnostic biomarkers but it is + + + align:start position:0% +diagnostic biomarkers but it is +collected in an ambulatory remote way + + align:start position:0% +collected in an ambulatory remote way + + + align:start position:0% +collected in an ambulatory remote way +that is collecting digital data and this + + align:start position:0% +that is collecting digital data and this + + + align:start position:0% +that is collecting digital data and this +type of data is very tricky and to give + + align:start position:0% +type of data is very tricky and to give + + + align:start position:0% +type of data is very tricky and to give +you an example of why this is + + align:start position:0% +you an example of why this is + + + align:start position:0% +you an example of why this is +particularly difficult to regulate so + + align:start position:0% +particularly difficult to regulate so + + + align:start position:0% +particularly difficult to regulate so +think about a couple of products that + + align:start position:0% +think about a couple of products that + + + align:start position:0% +think about a couple of products that +just look at something that would be + + align:start position:0% +just look at something that would be + + + align:start position:0% +just look at something that would be +simple like a fib so a fib is an + + align:start position:0% +simple like a fib so a fib is an + + + align:start position:0% +simple like a fib so a fib is an +abnormal heart condition you might have + + align:start position:0% +abnormal heart condition you might have + + + align:start position:0% +abnormal heart condition you might have +seen in the news that a number of + + align:start position:0% +seen in the news that a number of + + + align:start position:0% +seen in the news that a number of +different companies are coming out with + + align:start position:0% +different companies are coming out with + + + align:start position:0% +different companies are coming out with +a fib products put simply there's + + align:start position:0% +a fib products put simply there's + + + align:start position:0% +a fib products put simply there's +obviously a large stack of different + + align:start position:0% +obviously a large stack of different + + + align:start position:0% +obviously a large stack of different +types of data and one person's raw data + + align:start position:0% +types of data and one person's raw data + + + align:start position:0% +types of data and one person's raw data +is another person's processed data so + + align:start position:0% +is another person's processed data so + + + align:start position:0% +is another person's processed data so +you see on this chart is a list of five + + align:start position:0% +you see on this chart is a list of five + + + align:start position:0% +you see on this chart is a list of five +different companies that are all + + align:start position:0% +different companies that are all + + + align:start position:0% +different companies that are all +developing afib products from whether or + + align:start position:0% +developing afib products from whether or + + + align:start position:0% +developing afib products from whether or +not they develop the product internally + + align:start position:0% +not they develop the product internally + + + align:start position:0% +not they develop the product internally +which is the green part versus whether + + align:start position:0% +which is the green part versus whether + + + align:start position:0% +which is the green part versus whether +or not they might use a third-party + + align:start position:0% +or not they might use a third-party + + + align:start position:0% +or not they might use a third-party +product so developing an app on top of + + align:start position:0% +product so developing an app on top of + + + align:start position:0% +product so developing an app on top of +somebody else's product and so in a in a + + align:start position:0% +somebody else's product and so in a in a + + + align:start position:0% +somebody else's product and so in a in a +broad way thinking about going from the + + align:start position:0% +broad way thinking about going from the + + + align:start position:0% +broad way thinking about going from the +operating system to the sensor data so + + align:start position:0% +operating system to the sensor data so + + + align:start position:0% +operating system to the sensor data so +somebody might be using something like a + + align:start position:0% +somebody might be using something like a + + + align:start position:0% +somebody might be using something like a +PPG sensor and collecting the sort of + + align:start position:0% +PPG sensor and collecting the sort of + + + align:start position:0% +PPG sensor and collecting the sort of +data from their watch and then doing + + align:start position:0% +data from their watch and then doing + + + align:start position:0% +data from their watch and then doing +some sort of signal processing then + + align:start position:0% +some sort of signal processing then + + + align:start position:0% +some sort of signal processing then +making another algorithm that makes some + + align:start position:0% +making another algorithm that makes some + + + align:start position:0% +making another algorithm that makes some +sort of diagnostic and then you have + + align:start position:0% +sort of diagnostic and then you have + + + align:start position:0% +sort of diagnostic and then you have +some sort of user interface on top of + + align:start position:0% +some sort of user interface on top of + + + align:start position:0% +some sort of user interface on top of +that so if you were the FDA where would + + align:start position:0% +that so if you were the FDA where would + + + align:start position:0% +that so if you were the FDA where would +you draw the line which part of this + + align:start position:0% +you draw the line which part of this + + + align:start position:0% +you draw the line which part of this +product when somebody says my product is + + align:start position:0% +product when somebody says my product is + + + align:start position:0% +product when somebody says my product is +validated is should it be actually + + align:start position:0% +validated is should it be actually + + + align:start position:0% +validated is should it be actually +validated and then thinking about what + + align:start position:0% +validated and then thinking about what + + + align:start position:0% +validated and then thinking about what +does it actually mean if something is + + align:start position:0% +does it actually mean if something is + + + align:start position:0% +does it actually mean if something is +verified versus validated so verified + + align:start position:0% +verified versus validated so verified + + + align:start position:0% +verified versus validated so verified +being like if I walk a hundred steps + + align:start position:0% +being like if I walk a hundred steps + + + align:start position:0% +being like if I walk a hundred steps +does this thing measure a hundred steps + + align:start position:0% +does this thing measure a hundred steps + + + align:start position:0% +does this thing measure a hundred steps +and then validation being does a hundred + + align:start position:0% +and then validation being does a hundred + + + align:start position:0% +and then validation being does a hundred +steps mean something for my patient + + align:start position:0% +steps mean something for my patient + + + align:start position:0% +steps mean something for my patient +population or for my clinical use case + + align:start position:0% +population or for my clinical use case + + + align:start position:0% +population or for my clinical use case +and so one of the things that the FDA + + align:start position:0% +and so one of the things that the FDA + + + align:start position:0% +and so one of the things that the FDA +has started to think through is how + + align:start position:0% +has started to think through is how + + + align:start position:0% +has started to think through is how +might you do + + align:start position:0% +might you do + + + align:start position:0% +might you do +all the hardware components from the + + align:start position:0% +all the hardware components from the + + + align:start position:0% +all the hardware components from the +software components where you think + + align:start position:0% +software components where you think + + + align:start position:0% +software components where you think +about some of the hardware components as + + align:start position:0% +about some of the hardware components as + + + align:start position:0% +about some of the hardware components as +the ways that you would like effectively + + align:start position:0% +the ways that you would like effectively + + + align:start position:0% +the ways that you would like effectively +like the supply chain for collecting + + align:start position:0% +like the supply chain for collecting + + + align:start position:0% +like the supply chain for collecting +that data and then you would be using + + align:start position:0% +that data and then you would be using + + + align:start position:0% +that data and then you would be using +something on top and so maybe you have + + align:start position:0% +something on top and so maybe you have + + + align:start position:0% +something on top and so maybe you have +certain types of companies that might do + + align:start position:0% +certain types of companies that might do + + + align:start position:0% +certain types of companies that might do +some sort of verification or validation + + align:start position:0% +some sort of verification or validation + + + align:start position:0% +some sort of verification or validation +lower down the stack and then you can + + align:start position:0% +lower down the stack and then you can + + + align:start position:0% +lower down the stack and then you can +innovate higher up and so these and + + align:start position:0% +innovate higher up and so these and + + + align:start position:0% +innovate higher up and so these and +those these these measurements have + + align:start position:0% +those these these measurements have + + + align:start position:0% +those these these measurements have +pretty meaningful impacts so in the past + + align:start position:0% +pretty meaningful impacts so in the past + + + align:start position:0% +pretty meaningful impacts so in the past +a lot of these tools you really had to + + align:start position:0% +a lot of these tools you really had to + + + align:start position:0% +a lot of these tools you really had to +go into the clinic it was very expensive + + align:start position:0% +go into the clinic it was very expensive + + + align:start position:0% +go into the clinic it was very expensive +to get these sorts of measurements and + + align:start position:0% +to get these sorts of measurements and + + + align:start position:0% +to get these sorts of measurements and +more and more a number of different + + align:start position:0% +more and more a number of different + + + align:start position:0% +more and more a number of different +companies are getting their products + + align:start position:0% +companies are getting their products + + + align:start position:0% +companies are getting their products +cleared to use in in some care settings + + align:start position:0% +cleared to use in in some care settings + + + align:start position:0% +cleared to use in in some care settings +with a doctor or possibly to inform + + align:start position:0% +with a doctor or possibly to inform + + + align:start position:0% +with a doctor or possibly to inform +decisions at home all right and so in + + align:start position:0% +decisions at home all right and so in + + + align:start position:0% +decisions at home all right and so in +the last one of some examples is around + + align:start position:0% +the last one of some examples is around + + + align:start position:0% +the last one of some examples is around +digital therapeutics so I had worked + + align:start position:0% +digital therapeutics so I had worked + + + align:start position:0% +digital therapeutics so I had worked +with a company that was using a + + align:start position:0% +with a company that was using a + + + align:start position:0% +with a company that was using a +technology based out of UCSF that is + + align:start position:0% +technology based out of UCSF that is + + + align:start position:0% +technology based out of UCSF that is +developing effectively a video game for + + align:start position:0% +developing effectively a video game for + + + align:start position:0% +developing effectively a video game for +pediatric ADHD and so when kids play the + + align:start position:0% +pediatric ADHD and so when kids play the + + + align:start position:0% +pediatric ADHD and so when kids play the +game they reduce their ADHD symptoms and + + align:start position:0% +game they reduce their ADHD symptoms and + + + align:start position:0% +game they reduce their ADHD symptoms and +one of the things that's pretty exciting + + align:start position:0% +one of the things that's pretty exciting + + + align:start position:0% +one of the things that's pretty exciting +about this game is it as a 30-day + + align:start position:0% +about this game is it as a 30-day + + + align:start position:0% +about this game is it as a 30-day +protocol and unlike something like + + align:start position:0% +protocol and unlike something like + + + align:start position:0% +protocol and unlike something like +Ritalin or adderall where you have to + + align:start position:0% +Ritalin or adderall where you have to + + + align:start position:0% +Ritalin or adderall where you have to +take that drug every day for the rest of + + align:start position:0% +take that drug every day for the rest of + + + align:start position:0% +take that drug every day for the rest of +your life as you reduce the symptoms + + align:start position:0% +your life as you reduce the symptoms + + + align:start position:0% +your life as you reduce the symptoms +this seems to have an effect that after + + align:start position:0% +this seems to have an effect that after + + + align:start position:0% +this seems to have an effect that after +30 days is more long-term and that when + + align:start position:0% +30 days is more long-term and that when + + + align:start position:0% +30 days is more long-term and that when +you test somebody months down the line + + align:start position:0% +you test somebody months down the line + + + align:start position:0% +you test somebody months down the line +they still retain the effects of the + + align:start position:0% +they still retain the effects of the + + + align:start position:0% +they still retain the effects of the +treatment so this technology was taken + + align:start position:0% +treatment so this technology was taken + + + align:start position:0% +treatment so this technology was taken +out of UCSF and licensed to a company + + align:start position:0% +out of UCSF and licensed to a company + + + align:start position:0% +out of UCSF and licensed to a company +called Achille who decided hey we should + + align:start position:0% +called Achille who decided hey we should + + + align:start position:0% +called Achille who decided hey we should +just structure ourselves like a drug + + align:start position:0% +just structure ourselves like a drug + + + align:start position:0% +just structure ourselves like a drug +company so they raise venture capital + + align:start position:0% +company so they raise venture capital + + + align:start position:0% +company so they raise venture capital +like a drug company they look brand + + align:start position:0% +like a drug company they look brand + + + align:start position:0% +like a drug company they look brand +clinical trials like a drug company and + + align:start position:0% +clinical trials like a drug company and + + + align:start position:0% +clinical trials like a drug company and +they're now submitting to the FDA and + + align:start position:0% +they're now submitting to the FDA and + + + align:start position:0% +they're now submitting to the FDA and +might be the first prescription drug so + + align:start position:0% +might be the first prescription drug so + + + align:start position:0% +might be the first prescription drug so +anybody who was told that drugs or video + + align:start position:0% +anybody who was told that drugs or video + + + align:start position:0% +anybody who was told that drugs or video +games might rot your brain you now have + + align:start position:0% +games might rot your brain you now have + + + align:start position:0% +games might rot your brain you now have +a a like revenge maybe + + align:start position:0% + + + + align:start position:0% + +so the FDA has been looking at more and + + align:start position:0% +so the FDA has been looking at more and + + + align:start position:0% +so the FDA has been looking at more and +more of these tools I don't have to tell + + align:start position:0% +more of these tools I don't have to tell + + + align:start position:0% +more of these tools I don't have to tell +you you're probably thinking a lot about + + align:start position:0% +you you're probably thinking a lot about + + + align:start position:0% +you you're probably thinking a lot about +it and the FDA has been clearing a + + align:start position:0% +it and the FDA has been clearing a + + + align:start position:0% +it and the FDA has been clearing a +number of these different types of + + align:start position:0% +number of these different types of + + + align:start position:0% +number of these different types of +algorithms and one of the questions that + + align:start position:0% +algorithms and one of the questions that + + + align:start position:0% +algorithms and one of the questions that +has come up is what part of the agency + + align:start position:0% +has come up is what part of the agency + + + align:start position:0% +has come up is what part of the agency +should you think about what are you + + align:start position:0% +should you think about what are you + + + align:start position:0% +should you think about what are you +claiming when you use these sorts of + + align:start position:0% +claiming when you use these sorts of + + + align:start position:0% +claiming when you use these sorts of +algorithms and what one should be + + align:start position:0% +algorithms and what one should be + + + align:start position:0% +algorithms and what one should be +cleared and what's not and how should we + + align:start position:0% +cleared and what's not and how should we + + + align:start position:0% +cleared and what's not and how should we +really think about the regulatory + + align:start position:0% +really think about the regulatory + + + align:start position:0% +really think about the regulatory +oversight for them and a lot of these + + align:start position:0% +oversight for them and a lot of these + + + align:start position:0% +oversight for them and a lot of these +technologies enable things that are + + align:start position:0% +technologies enable things that are + + + align:start position:0% +technologies enable things that are +really quite exciting too so it's not + + align:start position:0% +really quite exciting too so it's not + + + align:start position:0% +really quite exciting too so it's not +just about the measurement but what you + + align:start position:0% +just about the measurement but what you + + + align:start position:0% +just about the measurement but what you +can do with them so one thing that has a + + align:start position:0% +can do with them so one thing that has a + + + align:start position:0% +can do with them so one thing that has a +lot of people really excited about is an + + align:start position:0% +lot of people really excited about is an + + + align:start position:0% +lot of people really excited about is an +idea around decentralized clinical + + align:start position:0% +idea around decentralized clinical + + + align:start position:0% +idea around decentralized clinical +trials no block chains here you might be + + align:start position:0% +trials no block chains here you might be + + + align:start position:0% +trials no block chains here you might be +able to build it with a block chain but + + align:start position:0% +able to build it with a block chain but + + + align:start position:0% +able to build it with a block chain but +not necessary so on the y-axis you can + + align:start position:0% +not necessary so on the y-axis you can + + + align:start position:0% +not necessary so on the y-axis you can +think about where are the data collected + + align:start position:0% +think about where are the data collected + + + align:start position:0% +think about where are the data collected +so is it collected at a clinical site or + + align:start position:0% +so is it collected at a clinical site or + + + align:start position:0% +so is it collected at a clinical site or +is it collected remotely and then the + + align:start position:0% +is it collected remotely and then the + + + align:start position:0% +is it collected remotely and then the +method is how its collected so do you + + align:start position:0% +method is how its collected so do you + + + align:start position:0% +method is how its collected so do you +need a human to do the interaction or is + + align:start position:0% +need a human to do the interaction or is + + + align:start position:0% +need a human to do the interaction or is +it fully virtual so at the top you can + + align:start position:0% +it fully virtual so at the top you can + + + align:start position:0% +it fully virtual so at the top you can +think about somebody doing telemedicine + + align:start position:0% +think about somebody doing telemedicine + + + align:start position:0% +think about somebody doing telemedicine +where they call in to somebody at home + + align:start position:0% +where they call in to somebody at home + + + align:start position:0% +where they call in to somebody at home +and then they might fill out ask some + + align:start position:0% +and then they might fill out ask some + + + align:start position:0% +and then they might fill out ask some +questions and fill out a survey on the + + align:start position:0% +questions and fill out a survey on the + + + align:start position:0% +questions and fill out a survey on the +bottom you can imagine in a research + + align:start position:0% +bottom you can imagine in a research + + + align:start position:0% +bottom you can imagine in a research +facility where I'm using a number of + + align:start position:0% +facility where I'm using a number of + + + align:start position:0% +facility where I'm using a number of +different instruments and perhaps them + + align:start position:0% +different instruments and perhaps them + + + align:start position:0% +different instruments and perhaps them +in a Parkinson's study and you're + + align:start position:0% +in a Parkinson's study and you're + + + align:start position:0% +in a Parkinson's study and you're +measuring my tremor with some sort of + + align:start position:0% +measuring my tremor with some sort of + + + align:start position:0% +measuring my tremor with some sort of +accelerometer and so the challenge + + align:start position:0% +accelerometer and so the challenge + + + align:start position:0% +accelerometer and so the challenge +that's happening is a lot of people use + + align:start position:0% +that's happening is a lot of people use + + + align:start position:0% +that's happening is a lot of people use +all of these terms for different things + + align:start position:0% +all of these terms for different things + + + align:start position:0% +all of these terms for different things +when they mean decentralized trials is + + align:start position:0% +when they mean decentralized trials is + + + align:start position:0% +when they mean decentralized trials is +it telemedicine is that somebody who's + + align:start position:0% +it telemedicine is that somebody who's + + + align:start position:0% +it telemedicine is that somebody who's +instrumented with a lot of wearables how + + align:start position:0% +instrumented with a lot of wearables how + + + align:start position:0% +instrumented with a lot of wearables how +do you know that the data are accurate + + align:start position:0% +do you know that the data are accurate + + + align:start position:0% +do you know that the data are accurate +and but this is I think in many + + align:start position:0% +and but this is I think in many + + + align:start position:0% +and but this is I think in many +instances really exciting because the + + align:start position:0% +instances really exciting because the + + + align:start position:0% +instances really exciting because the +number one reason why people don't want + + align:start position:0% +number one reason why people don't want + + + align:start position:0% +number one reason why people don't want +to enroll in a clinical trial is to get + + align:start position:0% +to enroll in a clinical trial is to get + + + align:start position:0% +to enroll in a clinical trial is to get +a placebo I think nobody really wants to + + align:start position:0% +a placebo I think nobody really wants to + + + align:start position:0% +a placebo I think nobody really wants to +participate in research if you're not + + align:start position:0% +participate in research if you're not + + + align:start position:0% +participate in research if you're not +getting the actual drug and then the + + align:start position:0% +getting the actual drug and then the + + + align:start position:0% +getting the actual drug and then the +other reason is location people don't + + align:start position:0% +other reason is location people don't + + + align:start position:0% +other reason is location people don't +want to have to drive in find parking + + align:start position:0% +want to have to drive in find parking + + + align:start position:0% +want to have to drive in find parking +like participate and this allows people + + align:start position:0% +like participate and this allows people + + + align:start position:0% +like participate and this allows people +to participate from home and the FDA has + + align:start position:0% +to participate from home and the FDA has + + + align:start position:0% +to participate from home and the FDA has +been doing a lot of work around how to + + align:start position:0% +been doing a lot of work around how to + + + align:start position:0% +been doing a lot of work around how to +rethink the clinical trial design + + align:start position:0% +rethink the clinical trial design + + + align:start position:0% +rethink the clinical trial design +process and incorporate some of this + + align:start position:0% +process and incorporate some of this + + + align:start position:0% +process and incorporate some of this +real-world data into decision making + + align:start position:0% +real-world data into decision making + + + align:start position:0% +real-world data into decision making +right before I jump into some of the + + align:start position:0% +right before I jump into some of the + + + align:start position:0% +right before I jump into some of the +regulatory things I wanted to set a + + align:start position:0% +regulatory things I wanted to set a + + + align:start position:0% +regulatory things I wanted to set a +framework of how to think about what + + align:start position:0% +framework of how to think about what + + + align:start position:0% +framework of how to think about what +these tools can do so + + align:start position:0% +these tools can do so + + + align:start position:0% +these tools can do so +three different scenarios of how you + + align:start position:0% +three different scenarios of how you + + + align:start position:0% +three different scenarios of how you +might use software and a piece of + + align:start position:0% +might use software and a piece of + + + align:start position:0% +might use software and a piece of +clinical research so imagine that + + align:start position:0% +clinical research so imagine that + + + align:start position:0% +clinical research so imagine that +somebody has Parkinson's and you want to + + align:start position:0% +somebody has Parkinson's and you want to + + + align:start position:0% +somebody has Parkinson's and you want to +measure how their Parkinson's is + + align:start position:0% +measure how their Parkinson's is + + + align:start position:0% +measure how their Parkinson's is +changing over time using a smartphone + + align:start position:0% +changing over time using a smartphone + + + align:start position:0% +changing over time using a smartphone +based test you have a standard + + align:start position:0% +based test you have a standard + + + align:start position:0% +based test you have a standard +Parkinson's drug that they would use and + + align:start position:0% +Parkinson's drug that they would use and + + + align:start position:0% +Parkinson's drug that they would use and +then you would collect the endpoint data + + align:start position:0% +then you would collect the endpoint data + + + align:start position:0% +then you would collect the endpoint data +which is how you see if that drugs + + align:start position:0% +which is how you see if that drugs + + + align:start position:0% +which is how you see if that drugs +performed using a piece of software + + align:start position:0% +performed using a piece of software + + + align:start position:0% +performed using a piece of software +another idea would be say you have an + + align:start position:0% +another idea would be say you have an + + + align:start position:0% +another idea would be say you have an +insulin pump and then you have a CGM + + align:start position:0% +insulin pump and then you have a CGM + + + align:start position:0% +insulin pump and then you have a CGM +that is measuring your blood sugar + + align:start position:0% +that is measuring your blood sugar + + + align:start position:0% +that is measuring your blood sugar +levels and you want to dose the insulin + + align:start position:0% +levels and you want to dose the insulin + + + align:start position:0% +levels and you want to dose the insulin +based on those readings you might have + + align:start position:0% +based on those readings you might have + + + align:start position:0% +based on those readings you might have +software both on the interventional side + + align:start position:0% +software both on the interventional side + + + align:start position:0% +software both on the interventional side +and on the endpoint side or like the + + align:start position:0% +and on the endpoint side or like the + + + align:start position:0% +and on the endpoint side or like the +company we talked about which has a + + align:start position:0% +company we talked about which has a + + + align:start position:0% +company we talked about which has a +digital product they said the only thing + + align:start position:0% +digital product they said the only thing + + + align:start position:0% +digital product they said the only thing +we want to change in the study is that + + align:start position:0% +we want to change in the study is that + + + align:start position:0% +we want to change in the study is that +the intervention is digital but we want + + align:start position:0% +the intervention is digital but we want + + + align:start position:0% +the intervention is digital but we want +you to compare us like any other + + align:start position:0% +you to compare us like any other + + + align:start position:0% +you to compare us like any other +intervention for pediatric ADHD so we + + align:start position:0% +intervention for pediatric ADHD so we + + + align:start position:0% +intervention for pediatric ADHD so we +want to use standard endpoints and not + + align:start position:0% +want to use standard endpoints and not + + + align:start position:0% +want to use standard endpoints and not +make that in innovation the challenge + + align:start position:0% +make that in innovation the challenge + + + align:start position:0% +make that in innovation the challenge +here is the first one most likely would + + align:start position:0% +here is the first one most likely would + + + align:start position:0% +here is the first one most likely would +go to the drug side of the FDA the + + align:start position:0% +go to the drug side of the FDA the + + + align:start position:0% +go to the drug side of the FDA the +second one would go to both the drug and + + align:start position:0% +second one would go to both the drug and + + + align:start position:0% +second one would go to both the drug and +the device side of the FDA as a + + align:start position:0% +the device side of the FDA as a + + + align:start position:0% +the device side of the FDA as a +combination product and the final one + + align:start position:0% +combination product and the final one + + + align:start position:0% +combination product and the final one +would just go to devices which has been + + align:start position:0% +would just go to devices which has been + + + align:start position:0% +would just go to devices which has been +generally handling software we've never + + align:start position:0% +generally handling software we've never + + + align:start position:0% +generally handling software we've never +really had products at the FDA in my + + align:start position:0% +really had products at the FDA in my + + + align:start position:0% +really had products at the FDA in my +opinion we're like we don't have drugs + + align:start position:0% +opinion we're like we don't have drugs + + + align:start position:0% +opinion we're like we don't have drugs +that can measure and diagnose and treat + + align:start position:0% +that can measure and diagnose and treat + + + align:start position:0% +that can measure and diagnose and treat +and change all the different ways and so + + align:start position:0% +and change all the different ways and so + + + align:start position:0% +and change all the different ways and so +you're now having software hitting + + align:start position:0% +you're now having software hitting + + + align:start position:0% +you're now having software hitting +multiple different parts of a system + + align:start position:0% +multiple different parts of a system + + + align:start position:0% +multiple different parts of a system +where it might even be the same product + + align:start position:0% +where it might even be the same product + + + align:start position:0% +where it might even be the same product +but in one instance it's used as an + + align:start position:0% +but in one instance it's used as an + + + align:start position:0% +but in one instance it's used as an +intervention another instance it's used + + align:start position:0% +intervention another instance it's used + + + align:start position:0% +intervention another instance it's used +as a diagnostic another it's to inform + + align:start position:0% +as a diagnostic another it's to inform + + + align:start position:0% +as a diagnostic another it's to inform +work span labeling and so the lines are + + align:start position:0% +work span labeling and so the lines are + + + align:start position:0% +work span labeling and so the lines are +like not as clean anymore about how you + + align:start position:0% +like not as clean anymore about how you + + + align:start position:0% +like not as clean anymore about how you +would manage this product so how do you + + align:start position:0% +would manage this product so how do you + + + align:start position:0% +would manage this product so how do you +manage these there's a couple agencies + + align:start position:0% +manage these there's a couple agencies + + + align:start position:0% +manage these there's a couple agencies +that are responsible for thinking + + align:start position:0% +that are responsible for thinking + + + align:start position:0% +that are responsible for thinking +through and overseeing healthcare + + align:start position:0% +through and overseeing healthcare + + + align:start position:0% +through and overseeing healthcare +software the big one that will spend + + align:start position:0% +software the big one that will spend + + + align:start position:0% +software the big one that will spend +most of our time on in is the FDA but + + align:start position:0% +most of our time on in is the FDA but + + + align:start position:0% +most of our time on in is the FDA but +it's also worth thinking about how they + + align:start position:0% +it's also worth thinking about how they + + + align:start position:0% +it's also worth thinking about how they +interact with some of the other ones + + align:start position:0% +interact with some of the other ones + + + align:start position:0% +interact with some of the other ones +including ONC FCC and FTC so the FDA is + + align:start position:0% +including ONC FCC and FTC so the FDA is + + + align:start position:0% +including ONC FCC and FTC so the FDA is +responsible for safety and effectiveness + + align:start position:0% +responsible for safety and effectiveness + + + align:start position:0% +responsible for safety and effectiveness +and for facilitating medical product + + align:start position:0% +and for facilitating medical product + + + align:start position:0% +and for facilitating medical product +innovation and ensuring that patients + + align:start position:0% +innovation and ensuring that patients + + + align:start position:0% +innovation and ensuring that patients +have access + + align:start position:0% +have access + + + align:start position:0% +have access +to high-quality products the ONC is + + align:start position:0% +to high-quality products the ONC is + + + align:start position:0% +to high-quality products the ONC is +responsible for health information + + align:start position:0% +responsible for health information + + + align:start position:0% +responsible for health information +technology and you can imagine where the + + align:start position:0% +technology and you can imagine where the + + + align:start position:0% +technology and you can imagine where the +lines between storing data and whether + + align:start position:0% +lines between storing data and whether + + + align:start position:0% +lines between storing data and whether +or not you're making a diagnosis on that + + align:start position:0% +or not you're making a diagnosis on that + + + align:start position:0% +or not you're making a diagnosis on that +data start to get really vague and it + + align:start position:0% +data start to get really vague and it + + + align:start position:0% +data start to get really vague and it +really might be the exact same product + + align:start position:0% +really might be the exact same product + + + align:start position:0% +really might be the exact same product +but just the change of what claim you're + + align:start position:0% +but just the change of what claim you're + + + align:start position:0% +but just the change of what claim you're +making on that product and most of these + + align:start position:0% +making on that product and most of these + + + align:start position:0% +making on that product and most of these +products have some level of connectivity + + align:start position:0% +products have some level of connectivity + + + align:start position:0% +products have some level of connectivity +to them so they also are working with + + align:start position:0% +to them so they also are working with + + + align:start position:0% +to them so they also are working with +FCC and have to abide by the ways that + + align:start position:0% +FCC and have to abide by the ways that + + + align:start position:0% +FCC and have to abide by the ways that +these sorts of these tools are regulated + + align:start position:0% +these sorts of these tools are regulated + + + align:start position:0% +these sorts of these tools are regulated +by this agency and then finally and + + align:start position:0% +by this agency and then finally and + + + align:start position:0% +by this agency and then finally and +probably most interesting is around the + + align:start position:0% +probably most interesting is around the + + + align:start position:0% +probably most interesting is around the +FTC which is really focused on informing + + align:start position:0% +FTC which is really focused on informing + + + align:start position:0% +FTC which is really focused on informing +consumer choice and if you think about + + align:start position:0% +consumer choice and if you think about + + + align:start position:0% +consumer choice and if you think about +FDA and FTC they're actually really + + align:start position:0% +FDA and FTC they're actually really + + + align:start position:0% +FDA and FTC they're actually really +similar so both of these agencies are + + align:start position:0% +similar so both of these agencies are + + + align:start position:0% +similar so both of these agencies are +responsible for consumer protection and + + align:start position:0% +responsible for consumer protection and + + + align:start position:0% +responsible for consumer protection and +the FDA really takes that with a public + + align:start position:0% +the FDA really takes that with a public + + + align:start position:0% +the FDA really takes that with a public +health perspective so in many instances + + align:start position:0% +health perspective so in many instances + + + align:start position:0% +health perspective so in many instances +if you've seen some of like the + + align:start position:0% +if you've seen some of like the + + + align:start position:0% +if you've seen some of like the +penalties around somebody having + + align:start position:0% +penalties around somebody having + + + align:start position:0% +penalties around somebody having +deceptive practices it actually wasn't + + align:start position:0% +deceptive practices it actually wasn't + + + align:start position:0% +deceptive practices it actually wasn't +the FDA who stepped in it was the FTC + + align:start position:0% +the FDA who stepped in it was the FTC + + + align:start position:0% +the FDA who stepped in it was the FTC +and I think some of the agencies are + + align:start position:0% +and I think some of the agencies are + + + align:start position:0% +and I think some of the agencies are +thinking about where do their lines and + + align:start position:0% +thinking about where do their lines and + + + align:start position:0% +thinking about where do their lines and +and where do others begin and in many + + align:start position:0% +and where do others begin and in many + + + align:start position:0% +and where do others begin and in many +instances as we probably seen with a lot + + align:start position:0% +instances as we probably seen with a lot + + + align:start position:0% +instances as we probably seen with a lot +of probably bad behavior that happens in + + align:start position:0% +of probably bad behavior that happens in + + + align:start position:0% +of probably bad behavior that happens in +tech there's really gaps across multiple + + align:start position:0% +tech there's really gaps across multiple + + + align:start position:0% +tech there's really gaps across multiple +places where nobody's stepping in and + + align:start position:0% +places where nobody's stepping in and + + + align:start position:0% +places where nobody's stepping in and +then there's some also non regulatory + + align:start position:0% +then there's some also non regulatory + + + align:start position:0% +then there's some also non regulatory +agencies to think about so an important + + align:start position:0% +agencies to think about so an important + + + align:start position:0% +agencies to think about so an important +one is around standards and technology + + align:start position:0% +one is around standards and technology + + + align:start position:0% +one is around standards and technology +and probably think about this all the + + align:start position:0% +and probably think about this all the + + + align:start position:0% +and probably think about this all the +time with inner and operability and + + align:start position:0% +time with inner and operability and + + + align:start position:0% +time with inner and operability and +whether or not you can actually import + + align:start position:0% +whether or not you can actually import + + + align:start position:0% +whether or not you can actually import +the data there are people who spend a + + align:start position:0% +the data there are people who spend a + + + align:start position:0% +the data there are people who spend a +lot of time thinking about standards is + + align:start position:0% +lot of time thinking about standards is + + + align:start position:0% +lot of time thinking about standards is +a very painful and very important job to + + align:start position:0% +a very painful and very important job to + + + align:start position:0% +a very painful and very important job to +promote innovation okay so the FDA has + + align:start position:0% +promote innovation okay so the FDA has + + + align:start position:0% +promote innovation okay so the FDA has +multiple centers I'm going to use a lot + + align:start position:0% +multiple centers I'm going to use a lot + + + align:start position:0% +multiple centers I'm going to use a lot +of acronyms so you might want to write + + align:start position:0% +of acronyms so you might want to write + + + align:start position:0% +of acronyms so you might want to write +this down or take picture and I'll try + + align:start position:0% +this down or take picture and I'll try + + + align:start position:0% +this down or take picture and I'll try +to minimize my acronyms but there are + + align:start position:0% +to minimize my acronyms but there are + + + align:start position:0% +to minimize my acronyms but there are +three centers that will be the most + + align:start position:0% +three centers that will be the most + + + align:start position:0% +three centers that will be the most +interesting for you so cedar is the one + + align:start position:0% +interesting for you so cedar is the one + + + align:start position:0% +interesting for you so cedar is the one +for drugs and this is the one where you + + align:start position:0% +for drugs and this is the one where you + + + align:start position:0% +for drugs and this is the one where you +would have a regular drug and possibly + + align:start position:0% +would have a regular drug and possibly + + + align:start position:0% +would have a regular drug and possibly +use a software product to see how that + + align:start position:0% +use a software product to see how that + + + align:start position:0% +use a software product to see how that +drug is performing CDRH is for devices + + align:start position:0% +drug is performing CDRH is for devices + + + align:start position:0% +drug is performing CDRH is for devices +and Sieber is for biological products I + + align:start position:0% +and Sieber is for biological products I + + + align:start position:0% +and Sieber is for biological products I +will probably use drugs and biologics in + + align:start position:0% +will probably use drugs and biologics in + + + align:start position:0% +will probably use drugs and biologics in +a very + + align:start position:0% +a very + + + align:start position:0% +a very +sort of way and the distinctions that + + align:start position:0% +sort of way and the distinctions that + + + align:start position:0% +sort of way and the distinctions that +we'll spend most of our time on are + + align:start position:0% +we'll spend most of our time on are + + + align:start position:0% +we'll spend most of our time on are +around drugs versus device there's a + + align:start position:0% +around drugs versus device there's a + + + align:start position:0% +around drugs versus device there's a +bunch of policy that is coming out that + + align:start position:0% +bunch of policy that is coming out that + + + align:start position:0% +bunch of policy that is coming out that +is both exciting and making things + + align:start position:0% +is both exciting and making things + + + align:start position:0% +is both exciting and making things +change + + align:start position:0% +change + + + align:start position:0% +change +so one of the big ones is around the + + align:start position:0% +so one of the big ones is around the + + + align:start position:0% +so one of the big ones is around the +21st century cures this has accelerated + + align:start position:0% +21st century cures this has accelerated + + + align:start position:0% +21st century cures this has accelerated +a lot of innovation in healthcare it's + + align:start position:0% +a lot of innovation in healthcare it's + + + align:start position:0% +a lot of innovation in healthcare it's +also changed the definition of what a + + align:start position:0% +also changed the definition of what a + + + align:start position:0% +also changed the definition of what a +devices which has a pretty meaningful + + align:start position:0% +devices which has a pretty meaningful + + + align:start position:0% +devices which has a pretty meaningful +impact on software and the FDA has been + + align:start position:0% +impact on software and the FDA has been + + + align:start position:0% +impact on software and the FDA has been +thinking a lot about how you would + + align:start position:0% +thinking a lot about how you would + + + align:start position:0% +thinking a lot about how you would +actually incorporate these products in I + + align:start position:0% +actually incorporate these products in I + + + align:start position:0% +actually incorporate these products in I +think there's a lot of people who are + + align:start position:0% +think there's a lot of people who are + + + align:start position:0% +think there's a lot of people who are +really excited about them there's a lot + + align:start position:0% +really excited about them there's a lot + + + align:start position:0% +really excited about them there's a lot +of innovation and so how do we create + + align:start position:0% +of innovation and so how do we create + + + align:start position:0% +of innovation and so how do we create +standards both to expand labeling be + + align:start position:0% +standards both to expand labeling be + + + align:start position:0% +standards both to expand labeling be +able to actually ingest digital data and + + align:start position:0% +able to actually ingest digital data and + + + align:start position:0% +able to actually ingest digital data and +have these sorts of digital products + + align:start position:0% +have these sorts of digital products + + + align:start position:0% +have these sorts of digital products +that are actually under FDA oversight + + align:start position:0% +that are actually under FDA oversight + + + align:start position:0% +that are actually under FDA oversight +and not just like weird snake oil on the + + align:start position:0% +and not just like weird snake oil on the + + + align:start position:0% +and not just like weird snake oil on the +App Store but what is a medical device + + align:start position:0% +App Store but what is a medical device + + + align:start position:0% +App Store but what is a medical device +pretty much a device is like anything + + align:start position:0% +pretty much a device is like anything + + + align:start position:0% +pretty much a device is like anything +that's not the other centers which has + + align:start position:0% +that's not the other centers which has + + + align:start position:0% +that's not the other centers which has +like a big catch-all for all the other + + align:start position:0% +like a big catch-all for all the other + + + align:start position:0% +like a big catch-all for all the other +components and so one of the big + + align:start position:0% +components and so one of the big + + + align:start position:0% +components and so one of the big +challenges for people is thinking about + + align:start position:0% +challenges for people is thinking about + + + align:start position:0% +challenges for people is thinking about +what a device is is it's if you think + + align:start position:0% +what a device is is it's if you think + + + align:start position:0% +what a device is is it's if you think +about generally what the FDA does it + + align:start position:0% +about generally what the FDA does it + + + align:start position:0% +about generally what the FDA does it +doesn't always make sure that your + + align:start position:0% +doesn't always make sure that your + + + align:start position:0% +doesn't always make sure that your +products are safe and effective they + + align:start position:0% +products are safe and effective they + + + align:start position:0% +products are safe and effective they +check whether or not you claim that they + + align:start position:0% +check whether or not you claim that they + + + align:start position:0% +check whether or not you claim that they +are safe and effective so it's really + + align:start position:0% +are safe and effective so it's really + + + align:start position:0% +are safe and effective so it's really +all about claims management and what + + align:start position:0% +all about claims management and what + + + align:start position:0% +all about claims management and what +you're claiming that this product can do + + align:start position:0% +you're claiming that this product can do + + + align:start position:0% +you're claiming that this product can do +and evaluating that for marketing + + align:start position:0% +and evaluating that for marketing + + + align:start position:0% +and evaluating that for marketing +obviously if your product like causes + + align:start position:0% +obviously if your product like causes + + + align:start position:0% +obviously if your product like causes +very significant harm that is an issue + + align:start position:0% +very significant harm that is an issue + + + align:start position:0% +very significant harm that is an issue +but the the challenge really happens to + + align:start position:0% +but the the challenge really happens to + + + align:start position:0% +but the the challenge really happens to +be when somebody makes like the product + + align:start position:0% +be when somebody makes like the product + + + align:start position:0% +be when somebody makes like the product +can do something that it doesn't + + align:start position:0% +can do something that it doesn't + + + align:start position:0% +can do something that it doesn't +necessarily who claimed to do but then + + align:start position:0% +necessarily who claimed to do but then + + + align:start position:0% +necessarily who claimed to do but then +you are able to like imply that it does + + align:start position:0% +you are able to like imply that it does + + + align:start position:0% +you are able to like imply that it does +other things and the most people don't + + align:start position:0% +other things and the most people don't + + + align:start position:0% +other things and the most people don't +really have a really good understanding + + align:start position:0% +really have a really good understanding + + + align:start position:0% +really have a really good understanding +of what the difference is between + + align:start position:0% +of what the difference is between + + + align:start position:0% +of what the difference is between +informing a product versus diagnosing a + + align:start position:0% +informing a product versus diagnosing a + + + align:start position:0% +informing a product versus diagnosing a +product and so I think in many instances + + align:start position:0% +product and so I think in many instances + + + align:start position:0% +product and so I think in many instances +for the public it gets a bit confusing + + align:start position:0% +for the public it gets a bit confusing + + + align:start position:0% +for the public it gets a bit confusing +so as we talked about before the FDA has + + align:start position:0% +so as we talked about before the FDA has + + + align:start position:0% +so as we talked about before the FDA has +been thinking about how do you decouple + + align:start position:0% +been thinking about how do you decouple + + + align:start position:0% +been thinking about how do you decouple +the hardware from the software and + + align:start position:0% +the hardware from the software and + + + align:start position:0% +the hardware from the software and +they've come + + align:start position:0% +they've come + + + align:start position:0% +they've come +with a concept around software as a + + align:start position:0% +with a concept around software as a + + + align:start position:0% +with a concept around software as a +medical device so the the software that + + align:start position:0% +medical device so the the software that + + + align:start position:0% +medical device so the the software that +has effectively defined as having no + + align:start position:0% +has effectively defined as having no + + + align:start position:0% +has effectively defined as having no +hardware components where you can + + align:start position:0% +hardware components where you can + + + align:start position:0% +hardware components where you can +evaluate just this product and this is + + align:start position:0% +evaluate just this product and this is + + + align:start position:0% +evaluate just this product and this is +pronounced Sam D and Sam DS are pretty + + align:start position:0% +pronounced Sam D and Sam DS are pretty + + + align:start position:0% +pronounced Sam D and Sam DS are pretty +interesting and there is this is very + + align:start position:0% +interesting and there is this is very + + + align:start position:0% +interesting and there is this is very +hard to hard to read but I pulled it + + align:start position:0% +hard to hard to read but I pulled it + + + align:start position:0% +hard to hard to read but I pulled it +straight from legal documents so you + + align:start position:0% +straight from legal documents so you + + + align:start position:0% +straight from legal documents so you +know I'm not changing it so something is + + align:start position:0% +know I'm not changing it so something is + + + align:start position:0% +know I'm not changing it so something is +interesting about Sam P so if you go all + + align:start position:0% +interesting about Sam P so if you go all + + + align:start position:0% +interesting about Sam P so if you go all +the way to the end so if you have like + + align:start position:0% +the way to the end so if you have like + + + align:start position:0% +the way to the end so if you have like +electronic healthcare data that's just + + align:start position:0% +electronic healthcare data that's just + + + align:start position:0% +electronic healthcare data that's just +storing health data that is not a Sam D + + align:start position:0% +storing health data that is not a Sam D + + + align:start position:0% +storing health data that is not a Sam D +and often can go straight to market and + + align:start position:0% +and often can go straight to market and + + + align:start position:0% +and often can go straight to market and +is not regulated by the FDA if you have + + align:start position:0% +is not regulated by the FDA if you have + + + align:start position:0% +is not regulated by the FDA if you have +a piece of software that is embedded + + align:start position:0% +a piece of software that is embedded + + + align:start position:0% +a piece of software that is embedded +into a system so something like a + + align:start position:0% +into a system so something like a + + + align:start position:0% +into a system so something like a +pacemaker a blood infusion pump then + + align:start position:0% +pacemaker a blood infusion pump then + + + align:start position:0% +pacemaker a blood infusion pump then +that is software in a medical device and + + align:start position:0% +that is software in a medical device and + + + align:start position:0% +that is software in a medical device and +that's not a Sam D so there's a line + + align:start position:0% +that's not a Sam D so there's a line + + + align:start position:0% +that's not a Sam D so there's a line +between these about what the + + align:start position:0% +between these about what the + + + align:start position:0% +between these about what the +functionality is that the product is + + align:start position:0% +functionality is that the product is + + + align:start position:0% +functionality is that the product is +doing and then how serious is it and + + align:start position:0% +doing and then how serious is it and + + + align:start position:0% +doing and then how serious is it and +that informs how you would be evaluated + + align:start position:0% +that informs how you would be evaluated + + + align:start position:0% +that informs how you would be evaluated +for that product and if you haven't + + align:start position:0% +for that product and if you haven't + + + align:start position:0% +for that product and if you haven't +noticed I try not to almost ever use the + + align:start position:0% +noticed I try not to almost ever use the + + + align:start position:0% +noticed I try not to almost ever use the +term device so when I talked about these + + align:start position:0% +term device so when I talked about these + + + align:start position:0% +term device so when I talked about these +connected wearables and other sorts of + + align:start position:0% +connected wearables and other sorts of + + + align:start position:0% +connected wearables and other sorts of +tools I will use the word tool and not + + align:start position:0% +tools I will use the word tool and not + + + align:start position:0% +tools I will use the word tool and not +device because this has a very specific + + align:start position:0% +device because this has a very specific + + + align:start position:0% +device because this has a very specific +meaning for the FDA and so if you're + + align:start position:0% +meaning for the FDA and so if you're + + + align:start position:0% +meaning for the FDA and so if you're +curious whether or not your product is a + + align:start position:0% +curious whether or not your product is a + + + align:start position:0% +curious whether or not your product is a +device or your algorithm is a device + + align:start position:0% +device or your algorithm is a device + + + align:start position:0% +device or your algorithm is a device +first you should talk to the regulators + + align:start position:0% +first you should talk to the regulators + + + align:start position:0% +first you should talk to the regulators +and talk to your lawyer and we'll play a + + align:start position:0% +and talk to your lawyer and we'll play a + + + align:start position:0% +and talk to your lawyer and we'll play a +little game so there are two products + + align:start position:0% +little game so there are two products + + + align:start position:0% +little game so there are two products +here one is an Apple product and one is + + align:start position:0% +here one is an Apple product and one is + + + align:start position:0% +here one is an Apple product and one is +a Fitbit product which one is a device + + align:start position:0% +a Fitbit product which one is a device + + + align:start position:0% +a Fitbit product which one is a device +I'm going to call in somebody randomly + + align:start position:0% +I'm going to call in somebody randomly + + + align:start position:0% +I'm going to call in somebody randomly +or you can someone can raise their hand + + align:start position:0% +or you can someone can raise their hand + + + align:start position:0% +or you can someone can raise their hand +and offer as tribute + + align:start position:0% + + + + align:start position:0% + +okay which one that's very sharp so + + align:start position:0% +okay which one that's very sharp so + + + align:start position:0% +okay which one that's very sharp so +we'll talk about this the Apple I did + + align:start position:0% +we'll talk about this the Apple I did + + + align:start position:0% +we'll talk about this the Apple I did +submit to the FDA for clearance and they + + align:start position:0% +submit to the FDA for clearance and they + + + align:start position:0% +submit to the FDA for clearance and they +submitted for de novo which is very + + align:start position:0% +submitted for de novo which is very + + + align:start position:0% +submitted for de novo which is very +similar to net of 510k and they + + align:start position:0% +similar to net of 510k and they + + + align:start position:0% +similar to net of 510k and they +submitted for two products to Sandi's + + align:start position:0% +submitted for two products to Sandi's + + + align:start position:0% +submitted for two products to Sandi's +one was based on the signal from their + + align:start position:0% +one was based on the signal from their + + + align:start position:0% +one was based on the signal from their +PPG and the second was on the app so it + + align:start position:0% +PPG and the second was on the app so it + + + align:start position:0% +PPG and the second was on the app so it +has two devices neither of which are + + align:start position:0% +has two devices neither of which are + + + align:start position:0% +has two devices neither of which are +hardware and the Fitbit has today no + + align:start position:0% +hardware and the Fitbit has today no + + + align:start position:0% +hardware and the Fitbit has today no +devices how about now is it a device or + + align:start position:0% +devices how about now is it a device or + + + align:start position:0% +devices how about now is it a device or +is it not a device sure question + + align:start position:0% +is it not a device sure question + + + align:start position:0% +is it not a device sure question +obviously because there are two devices + + align:start position:0% +obviously because there are two devices + + + align:start position:0% +obviously because there are two devices +there and then a number of things that + + align:start position:0% +there and then a number of things that + + + align:start position:0% +there and then a number of things that +are not devices so it really just + + align:start position:0% +are not devices so it really just + + + align:start position:0% +are not devices so it really just +depends on what you are claiming the + + align:start position:0% +depends on what you are claiming the + + + align:start position:0% +depends on what you are claiming the +product does and back to that set of + + align:start position:0% +product does and back to that set of + + + align:start position:0% +product does and back to that set of +modularity what is actually the product + + align:start position:0% +modularity what is actually the product + + + align:start position:0% +modularity what is actually the product +so is the product signal processing + + align:start position:0% +so is the product signal processing + + + align:start position:0% +so is the product signal processing +algorithm is the product and app is the + + align:start position:0% +algorithm is the product and app is the + + + align:start position:0% +algorithm is the product and app is the +product the the whole entire system and + + align:start position:0% +product the the whole entire system and + + + align:start position:0% +product the the whole entire system and +so people are thinking about + + align:start position:0% +so people are thinking about + + + align:start position:0% +so people are thinking about +strategically frankly like which parts + + align:start position:0% +strategically frankly like which parts + + + align:start position:0% +strategically frankly like which parts +or devices because you might have you + + align:start position:0% +or devices because you might have you + + + align:start position:0% +or devices because you might have you +might want somebody else to be building + + align:start position:0% +might want somebody else to be building + + + align:start position:0% +might want somebody else to be building +on your system so maybe you want to make + + align:start position:0% +on your system so maybe you want to make + + + align:start position:0% +on your system so maybe you want to make +your hardware device and that other + + align:start position:0% +your hardware device and that other + + + align:start position:0% +your hardware device and that other +people can build off of it and so there + + align:start position:0% +people can build off of it and so there + + + align:start position:0% +people can build off of it and so there +are strategic ways of thinking about it + + align:start position:0% +are strategic ways of thinking about it + + + align:start position:0% +are strategic ways of thinking about it +so the crazy thing here if you can + + align:start position:0% +so the crazy thing here if you can + + + align:start position:0% +so the crazy thing here if you can +imagine this is that the exact same + + align:start position:0% +imagine this is that the exact same + + + align:start position:0% +imagine this is that the exact same +product can be a device or not a device + + align:start position:0% +product can be a device or not a device + + + align:start position:0% +product can be a device or not a device +through just a change of words and no + + align:start position:0% +through just a change of words and no + + + align:start position:0% +through just a change of words and no +change in hardware or code so if you + + align:start position:0% +change in hardware or code so if you + + + align:start position:0% +change in hardware or code so if you +think about whether or not my product is + + align:start position:0% +think about whether or not my product is + + + align:start position:0% +think about whether or not my product is +a device is actually generally not the + + align:start position:0% +a device is actually generally not the + + + align:start position:0% +a device is actually generally not the +most useful question the more useful + + align:start position:0% +most useful question the more useful + + + align:start position:0% +most useful question the more useful +question is what is the intended use of + + align:start position:0% +question is what is the intended use of + + + align:start position:0% +question is what is the intended use of +the product and so are you making a + + align:start position:0% +the product and so are you making a + + + align:start position:0% +the product and so are you making a +medical device claim with what your + + align:start position:0% +medical device claim with what your + + + align:start position:0% +medical device claim with what your +product is doing obviously this is like + + align:start position:0% +product is doing obviously this is like + + + align:start position:0% +product is doing obviously this is like +a little bit overwhelming I think and + + align:start position:0% +a little bit overwhelming I think and + + + align:start position:0% +a little bit overwhelming I think and +like trying to figure out how to + + align:start position:0% +like trying to figure out how to + + + align:start position:0% +like trying to figure out how to +navigate all of this and the FDA + + align:start position:0% +navigate all of this and the FDA + + + align:start position:0% +navigate all of this and the FDA +recognizes that and their goal is to + + align:start position:0% +recognizes that and their goal is to + + + align:start position:0% +recognizes that and their goal is to +increase innovation and so particularly + + align:start position:0% +increase innovation and so particularly + + + align:start position:0% +increase innovation and so particularly +for products like software there + + align:start position:0% +for products like software there + + + align:start position:0% +for products like software there +having constant updates it seems a + + align:start position:0% +having constant updates it seems a + + + align:start position:0% +having constant updates it seems a +little bit difficult if you're + + align:start position:0% +little bit difficult if you're + + + align:start position:0% +little bit difficult if you're +constantly figuring out all the + + align:start position:0% +constantly figuring out all the + + + align:start position:0% +constantly figuring out all the +different words and how you're going to + + align:start position:0% +different words and how you're going to + + + align:start position:0% +different words and how you're going to +get these products to market so + + align:start position:0% +get these products to market so + + + align:start position:0% +get these products to market so +something that I think is really + + align:start position:0% +something that I think is really + + + align:start position:0% +something that I think is really +innovative by the FDA is piloting this + + align:start position:0% +innovative by the FDA is piloting this + + + align:start position:0% +innovative by the FDA is piloting this +is one example of a program that they're + + align:start position:0% +is one example of a program that they're + + + align:start position:0% +is one example of a program that they're +thinking through which is working with + + align:start position:0% +thinking through which is working with + + + align:start position:0% +thinking through which is working with +nine different companies and the idea is + + align:start position:0% +nine different companies and the idea is + + + align:start position:0% +nine different companies and the idea is +can you pre certify an entire company + + align:start position:0% +can you pre certify an entire company + + + align:start position:0% +can you pre certify an entire company +that is developing software as an + + align:start position:0% +that is developing software as an + + + align:start position:0% +that is developing software as an +excellent company across a series of + + align:start position:0% +excellent company across a series of + + + align:start position:0% +excellent company across a series of +objectives and then allow them to ship + + align:start position:0% +objectives and then allow them to ship + + + align:start position:0% +objectives and then allow them to ship +additional updates so today if you had + + align:start position:0% +additional updates so today if you had + + + align:start position:0% +additional updates so today if you had +an update and you wanted to make a + + align:start position:0% +an update and you wanted to make a + + + align:start position:0% +an update and you wanted to make a +change you have to go through an entire + + align:start position:0% +change you have to go through an entire + + + align:start position:0% +change you have to go through an entire +five 10k or de novo process or other + + align:start position:0% +five 10k or de novo process or other + + + align:start position:0% +five 10k or de novo process or other +type of process which is pretty wild if + + align:start position:0% +type of process which is pretty wild if + + + align:start position:0% +type of process which is pretty wild if +you imagine that like we only would let + + align:start position:0% +you imagine that like we only would let + + + align:start position:0% +you imagine that like we only would let +Facebook ship one update a year that + + align:start position:0% +Facebook ship one update a year that + + + align:start position:0% +Facebook ship one update a year that +would be crazy and we don't expect + + align:start position:0% +would be crazy and we don't expect + + + align:start position:0% +would be crazy and we don't expect +facebook to like maintain or sustain a + + align:start position:0% +facebook to like maintain or sustain a + + + align:start position:0% +facebook to like maintain or sustain a +human life and so being able to have + + align:start position:0% +human life and so being able to have + + + align:start position:0% +human life and so being able to have +updates in a more regular fashion is + + align:start position:0% +updates in a more regular fashion is + + + align:start position:0% +updates in a more regular fashion is +very important but how do you know that + + align:start position:0% +very important but how do you know that + + + align:start position:0% +very important but how do you know that +that change is going to have a big + + align:start position:0% +that change is going to have a big + + + align:start position:0% +that change is going to have a big +impact or not and I'll pause on this but + + align:start position:0% +impact or not and I'll pause on this but + + + align:start position:0% +impact or not and I'll pause on this but +you all read the document I'm actually + + align:start position:0% +you all read the document I'm actually + + + align:start position:0% +you all read the document I'm actually +very glad that you read this document + + align:start position:0% +very glad that you read this document + + + align:start position:0% +very glad that you read this document +without talking to us because you are + + align:start position:0% +without talking to us because you are + + + align:start position:0% +without talking to us because you are +the exact audience of somebody who would + + align:start position:0% +the exact audience of somebody who would + + + align:start position:0% +the exact audience of somebody who would +not necessarily have the background and + + align:start position:0% +not necessarily have the background and + + + align:start position:0% +not necessarily have the background and +so it needs to be put in a way that is + + align:start position:0% +so it needs to be put in a way that is + + + align:start position:0% +so it needs to be put in a way that is +readable for people who are developing + + align:start position:0% +readable for people who are developing + + + align:start position:0% +readable for people who are developing +these types of products to know how to + + align:start position:0% +these types of products to know how to + + + align:start position:0% +these types of products to know how to +go into them it will save some time at + + align:start position:0% +go into them it will save some time at + + + align:start position:0% +go into them it will save some time at +the end of the discussion because I'm + + align:start position:0% +the end of the discussion because I'm + + + align:start position:0% +the end of the discussion because I'm +curious of how you perceived the piece + + align:start position:0% +curious of how you perceived the piece + + + align:start position:0% +curious of how you perceived the piece +but you should definitely trust your + + align:start position:0% +but you should definitely trust your + + + align:start position:0% +but you should definitely trust your +first reading as a honest good reading + + align:start position:0% +first reading as a honest good reading + + + align:start position:0% +first reading as a honest good reading +you also probably read it way more + + align:start position:0% +you also probably read it way more + + + align:start position:0% +you also probably read it way more +intensely than any other person who is + + align:start position:0% +intensely than any other person who is + + + align:start position:0% +intensely than any other person who is +reading it and so the notes that you + + align:start position:0% +reading it and so the notes that you + + + align:start position:0% +reading it and so the notes that you +took are valid and I'm curious what you + + align:start position:0% +took are valid and I'm curious what you + + + align:start position:0% +took are valid and I'm curious what you +saw okay another thing to help you be + + align:start position:0% +saw okay another thing to help you be + + + align:start position:0% +saw okay another thing to help you be +cool at cocktail hour fda-cleared not + + align:start position:0% +cool at cocktail hour fda-cleared not + + + align:start position:0% +cool at cocktail hour fda-cleared not +the same thing as fda-approved okay so + + align:start position:0% +the same thing as fda-approved okay so + + + align:start position:0% +the same thing as fda-approved okay so +for devices there are three pathways to + + align:start position:0% +for devices there are three pathways to + + + align:start position:0% +for devices there are three pathways to +think about one is the 510k the next is + + align:start position:0% +think about one is the 510k the next is + + + align:start position:0% +think about one is the 510k the next is +de novo the next is a pre-market + + align:start position:0% +de novo the next is a pre-market + + + align:start position:0% +de novo the next is a pre-market +approval also known as a PMA they're + + align:start position:0% +approval also known as a PMA they're + + + align:start position:0% +approval also known as a PMA they're +generally stratified by whether or not + + align:start position:0% +generally stratified by whether or not + + + align:start position:0% +generally stratified by whether or not +something is risky and the type of data + + align:start position:0% +something is risky and the type of data + + + align:start position:0% +something is risky and the type of data +that you have to submit to be able to + + align:start position:0% +that you have to submit to be able to + + + align:start position:0% +that you have to submit to be able to +get one of these clearances varies so + + align:start position:0% +get one of these clearances varies so + + + align:start position:0% +get one of these clearances varies so +the more risky you are the more type of + + align:start position:0% +the more risky you are the more type of + + + align:start position:0% +the more risky you are the more type of +data that you have to have + + align:start position:0% +data that you have to have + + + align:start position:0% +data that you have to have +so de Novo's are granted but people + + align:start position:0% +so de Novo's are granted but people + + + align:start position:0% +so de Novo's are granted but people +often will say cleared 5-10 K's are + + align:start position:0% +often will say cleared 5-10 K's are + + + align:start position:0% +often will say cleared 5-10 K's are +cleared very few products that you've + + align:start position:0% +cleared very few products that you've + + + align:start position:0% +cleared very few products that you've +seen go through an PMA process tell me I + + align:start position:0% + + + + align:start position:0% + +am NOT Apple but if I had to guess once + + align:start position:0% +am NOT Apple but if I had to guess once + + + align:start position:0% +am NOT Apple but if I had to guess once +you create a de novo you can then become + + align:start position:0% +you create a de novo you can then become + + + align:start position:0% +you create a de novo you can then become +a predicate for other things and so if + + align:start position:0% +a predicate for other things and so if + + + align:start position:0% +a predicate for other things and so if +they wanted to create a new class of + + align:start position:0% +they wanted to create a new class of + + + align:start position:0% +they wanted to create a new class of +predicates that they could then build on + + align:start position:0% +predicates that they could then build on + + + align:start position:0% +predicates that they could then build on +over time and they didn't want to like + + align:start position:0% +over time and they didn't want to like + + + align:start position:0% +over time and they didn't want to like +get stuck in an old type of predicate + + align:start position:0% +get stuck in an old type of predicate + + + align:start position:0% +get stuck in an old type of predicate +system I think strategically the fact + + align:start position:0% +system I think strategically the fact + + + align:start position:0% +system I think strategically the fact +that they picked a PPG and their app I + + align:start position:0% +that they picked a PPG and their app I + + + align:start position:0% +that they picked a PPG and their app I +don't know what they'll eventually do + + align:start position:0% +don't know what they'll eventually do + + + align:start position:0% +don't know what they'll eventually do +over time but I think it's part of their + + align:start position:0% +over time but I think it's part of their + + + align:start position:0% +over time but I think it's part of their +long-term strategy + + align:start position:0% +long-term strategy + + + align:start position:0% +long-term strategy +great question okay so the tools are + + align:start position:0% +great question okay so the tools are + + + align:start position:0% +great question okay so the tools are +safe and effective perhaps depending on + + align:start position:0% +safe and effective perhaps depending on + + + align:start position:0% +safe and effective perhaps depending on +how much data is committed is submitted + + align:start position:0% +how much data is committed is submitted + + + align:start position:0% +how much data is committed is submitted +and but what about the information + + align:start position:0% +and but what about the information + + + align:start position:0% +and but what about the information +that's collected from the tools so today + + align:start position:0% +that's collected from the tools so today + + + align:start position:0% +that's collected from the tools so today +our healthcare system has pretty strong + + align:start position:0% +our healthcare system has pretty strong + + + align:start position:0% +our healthcare system has pretty strong +protections for biospecimens your blood + + align:start position:0% +protections for biospecimens your blood + + + align:start position:0% +protections for biospecimens your blood +your stool your genomic data but we + + align:start position:0% +your stool your genomic data but we + + + align:start position:0% +your stool your genomic data but we +really don't have any protections around + + align:start position:0% +really don't have any protections around + + + align:start position:0% +really don't have any protections around +digital specimens you can imagine how + + align:start position:0% +digital specimens you can imagine how + + + align:start position:0% +digital specimens you can imagine how +many data breaches we constantly have + + align:start position:0% +many data breaches we constantly have + + + align:start position:0% +many data breaches we constantly have +and what ads get served to us on + + align:start position:0% +and what ads get served to us on + + + align:start position:0% +and what ads get served to us on +Facebook a lot of this is considered + + align:start position:0% +Facebook a lot of this is considered + + + align:start position:0% +Facebook a lot of this is considered +wellness data and not actually health + + align:start position:0% +wellness data and not actually health + + + align:start position:0% +wellness data and not actually health +data but in many instances you're + + align:start position:0% +data but in many instances you're + + + align:start position:0% +data but in many instances you're +finding quite a lot of health + + align:start position:0% +finding quite a lot of health + + + align:start position:0% +finding quite a lot of health +information from somebody in that and + + align:start position:0% +information from somebody in that and + + + align:start position:0% +information from somebody in that and +and I have a lot more we can nerd about + + align:start position:0% +and I have a lot more we can nerd about + + + align:start position:0% +and I have a lot more we can nerd about +this forever but generally there's a + + align:start position:0% +this forever but generally there's a + + + align:start position:0% +this forever but generally there's a +couple things that are good to know is + + align:start position:0% +couple things that are good to know is + + + align:start position:0% +couple things that are good to know is +that with most of this data you can't + + align:start position:0% +that with most of this data you can't + + + align:start position:0% +that with most of this data you can't +really do identify it anymore who here + + align:start position:0% +really do identify it anymore who here + + + align:start position:0% +really do identify it anymore who here +thinks I could do identify my genome you + + align:start position:0% +thinks I could do identify my genome you + + + align:start position:0% +thinks I could do identify my genome you +can't write like my genomes unique to me + + align:start position:0% +can't write like my genomes unique to me + + + align:start position:0% +can't write like my genomes unique to me +maybe you can strip out like personally + + align:start position:0% +maybe you can strip out like personally + + + align:start position:0% +maybe you can strip out like personally +identifiable information but you're not + + align:start position:0% +identifiable information but you're not + + + align:start position:0% +identifiable information but you're not +really going to de identify it + + align:start position:0% +really going to de identify it + + + align:start position:0% +really going to de identify it +I am uniquely identifiable with 30 + + align:start position:0% +I am uniquely identifiable with 30 + + + align:start position:0% +I am uniquely identifiable with 30 +seconds of walk data so all of this + + align:start position:0% +seconds of walk data so all of this + + + align:start position:0% +seconds of walk data so all of this +biometric signatures is pretty specific + + align:start position:0% +biometric signatures is pretty specific + + + align:start position:0% +biometric signatures is pretty specific +and so there are some agencies today who + + align:start position:0% +and so there are some agencies today who + + + align:start position:0% +and so there are some agencies today who +are thinking about how you might handle + + align:start position:0% +are thinking about how you might handle + + + align:start position:0% +are thinking about how you might handle +these sorts of tools but in the end + + align:start position:0% +these sorts of tools but in the end + + + align:start position:0% +these sorts of tools but in the end +there is I think a pretty substantial + + align:start position:0% +there is I think a pretty substantial + + + align:start position:0% +there is I think a pretty substantial +gap so in general the FDA is really folk + + align:start position:0% +gap so in general the FDA is really folk + + + align:start position:0% +gap so in general the FDA is really folk +on safety and efficacy and safety is + + align:start position:0% +on safety and efficacy and safety is + + + align:start position:0% +on safety and efficacy and safety is +considered much more of like a body + + align:start position:0% +considered much more of like a body + + + align:start position:0% +considered much more of like a body +safety and not as like we are very + + align:start position:0% +safety and not as like we are very + + + align:start position:0% +safety and not as like we are very +programmable as humans and the type of + + align:start position:0% +programmable as humans and the type of + + + align:start position:0% +programmable as humans and the type of +information that we see or change the + + align:start position:0% +information that we see or change the + + + align:start position:0% +information that we see or change the +type of safety so the data that we + + align:start position:0% +type of safety so the data that we + + + align:start position:0% +type of safety so the data that we +collect FTC could have a lot of power + + align:start position:0% +collect FTC could have a lot of power + + + align:start position:0% +collect FTC could have a lot of power +here but they're much smaller agency + + align:start position:0% +here but they're much smaller agency + + + align:start position:0% +here but they're much smaller agency +that isn't as well resourced and there's + + align:start position:0% +that isn't as well resourced and there's + + + align:start position:0% +that isn't as well resourced and there's +a couple different organizations that + + align:start position:0% +a couple different organizations that + + + align:start position:0% +a couple different organizations that +are trying to think through how to do + + align:start position:0% +are trying to think through how to do + + + align:start position:0% +are trying to think through how to do +rulemaking for Internet of Things and + + align:start position:0% +rulemaking for Internet of Things and + + + align:start position:0% +rulemaking for Internet of Things and +how that data is being used but + + align:start position:0% +how that data is being used but + + + align:start position:0% +how that data is being used but +generally in my opinion we probably need + + align:start position:0% +generally in my opinion we probably need + + + align:start position:0% +generally in my opinion we probably need +some sort of congressional action around + + align:start position:0% +some sort of congressional action around + + + align:start position:0% +some sort of congressional action around +non-discrimination of digital specimen + + align:start position:0% +non-discrimination of digital specimen + + + align:start position:0% +non-discrimination of digital specimen +data which would require a Congress that + + align:start position:0% +data which would require a Congress that + + + align:start position:0% +data which would require a Congress that +could think through I think a really + + align:start position:0% +could think through I think a really + + + align:start position:0% +could think through I think a really +difficult problem of how you would + + align:start position:0% +difficult problem of how you would + + + align:start position:0% +difficult problem of how you would +handle data rights and management okay + + align:start position:0% +handle data rights and management okay + + + align:start position:0% +handle data rights and management okay +so I'll go through a couple examples of + + align:start position:0% +so I'll go through a couple examples of + + + align:start position:0% +so I'll go through a couple examples of +how government agencies are interacting + + align:start position:0% +how government agencies are interacting + + + align:start position:0% +how government agencies are interacting +with members of the public which I think + + align:start position:0% +with members of the public which I think + + + align:start position:0% +with members of the public which I think +you might find interesting + + align:start position:0% +you might find interesting + + + align:start position:0% +you might find interesting +so many of these companies many of the + + align:start position:0% +so many of these companies many of the + + + align:start position:0% +so many of these companies many of the +government agencies are really thinking + + align:start position:0% +government agencies are really thinking + + + align:start position:0% +government agencies are really thinking +through realizing that they are not + + align:start position:0% +through realizing that they are not + + + align:start position:0% +through realizing that they are not +necessarily the experts in their field + + align:start position:0% +necessarily the experts in their field + + + align:start position:0% +necessarily the experts in their field +and how do they get the data that they + + align:start position:0% +and how do they get the data that they + + + align:start position:0% +and how do they get the data that they +need so a couple pieces that will be + + align:start position:0% +need so a couple pieces that will be + + + align:start position:0% +need so a couple pieces that will be +interesting for you I think one is + + align:start position:0% +interesting for you I think one is + + + align:start position:0% +interesting for you I think one is +there's a joint group with the FDA and + + align:start position:0% +there's a joint group with the FDA and + + + align:start position:0% +there's a joint group with the FDA and +Duke where they're thinking through + + align:start position:0% +Duke where they're thinking through + + + align:start position:0% +Duke where they're thinking through +what's called novel endpoints so if you + + align:start position:0% +what's called novel endpoints so if you + + + align:start position:0% +what's called novel endpoints so if you +are working on a study today where you + + align:start position:0% +are working on a study today where you + + + align:start position:0% +are working on a study today where you +realize that you're measuring something + + align:start position:0% +realize that you're measuring something + + + align:start position:0% +realize that you're measuring something +better than the quote gold standard and + + align:start position:0% +better than the quote gold standard and + + + align:start position:0% +better than the quote gold standard and +the gold standard is actually quite a + + align:start position:0% +the gold standard is actually quite a + + + align:start position:0% +the gold standard is actually quite a +terrible gold standard how do you create + + align:start position:0% +terrible gold standard how do you create + + + align:start position:0% +terrible gold standard how do you create +and develop a novel metric that might + + align:start position:0% +and develop a novel metric that might + + + align:start position:0% +and develop a novel metric that might +not have a reference standard or legacy + + align:start position:0% +not have a reference standard or legacy + + + align:start position:0% +not have a reference standard or legacy +standard and this is a way of thinking + + align:start position:0% +standard and this is a way of thinking + + + align:start position:0% +standard and this is a way of thinking +through that the second is around + + align:start position:0% +through that the second is around + + + align:start position:0% +through that the second is around +selecting a mobile technology this used + + align:start position:0% +selecting a mobile technology this used + + + align:start position:0% +selecting a mobile technology this used +to be called mobile devices and they + + align:start position:0% +to be called mobile devices and they + + + align:start position:0% +to be called mobile devices and they +changed it for the same reason around + + align:start position:0% +changed it for the same reason around + + + align:start position:0% +changed it for the same reason around +not calling things a device unless it is + + align:start position:0% +not calling things a device unless it is + + + align:start position:0% +not calling things a device unless it is +a device and so these are thinking + + align:start position:0% +a device and so these are thinking + + + align:start position:0% +a device and so these are thinking +through what type of connective tech + + align:start position:0% +through what type of connective tech + + + align:start position:0% +through what type of connective tech +would you want to use to generate the + + align:start position:0% +would you want to use to generate the + + + align:start position:0% +would you want to use to generate the +patient data that you might use in your + + align:start position:0% +patient data that you might use in your + + + align:start position:0% +patient data that you might use in your +study all right who here knows what + + align:start position:0% +study all right who here knows what + + + align:start position:0% +study all right who here knows what +DEFCON is three of you okay so DEFCON is + + align:start position:0% +DEFCON is three of you okay so DEFCON is + + + align:start position:0% +DEFCON is three of you okay so DEFCON is +a hacker conference it is probably one + + align:start position:0% +a hacker conference it is probably one + + + align:start position:0% +a hacker conference it is probably one +of the biggest hacker conferences it is + + align:start position:0% +of the biggest hacker conferences it is + + + align:start position:0% +of the biggest hacker conferences it is +a conference that if you do have the joy + + align:start position:0% +a conference that if you do have the joy + + + align:start position:0% +a conference that if you do have the joy +of going to you should not bring your + + align:start position:0% +of going to you should not bring your + + + align:start position:0% +of going to you should not bring your +phone and you should not bring your + + align:start position:0% +phone and you should not bring your + + + align:start position:0% +phone and you should not bring your +computer and you should definitely not + + align:start position:0% +computer and you should definitely not + + + align:start position:0% +computer and you should definitely not +connect to the Internet + + align:start position:0% +connect to the Internet + + + align:start position:0% +connect to the Internet +because there is a group called the wall + + align:start position:0% +because there is a group called the wall + + + align:start position:0% +because there is a group called the wall +of sheep and they will just straight + + align:start position:0% +of sheep and they will just straight + + + align:start position:0% +of sheep and they will just straight +stream all your Gmail passwords + + align:start position:0% +stream all your Gmail passwords + + + align:start position:0% +stream all your Gmail passwords +plaintext and your account logins and + + align:start position:0% +plaintext and your account logins and + + + align:start position:0% +plaintext and your account logins and +anything that you are putting on the + + align:start position:0% +anything that you are putting on the + + + align:start position:0% +anything that you are putting on the +Internet + + align:start position:0% +Internet + + + align:start position:0% +Internet +this group is amazing and you may have + + align:start position:0% +this group is amazing and you may have + + + align:start position:0% +this group is amazing and you may have +also heard about them because they + + align:start position:0% +also heard about them because they + + + align:start position:0% +also heard about them because they +bought a number of voting machines last + + align:start position:0% +bought a number of voting machines last + + + align:start position:0% +bought a number of voting machines last +year hacked them found the voting + + align:start position:0% +year hacked them found the voting + + + align:start position:0% +year hacked them found the voting +records and sent them back to Congress + + align:start position:0% +records and sent them back to Congress + + + align:start position:0% +records and sent them back to Congress +and said hey you should probably fix + + align:start position:0% +and said hey you should probably fix + + + align:start position:0% +and said hey you should probably fix +this Def Con has a number of villages + + align:start position:0% +this Def Con has a number of villages + + + align:start position:0% +this Def Con has a number of villages +that sit under the Maine DEFCON one of + + align:start position:0% +that sit under the Maine DEFCON one of + + + align:start position:0% +that sit under the Maine DEFCON one of +them is called bio hacking village and + + align:start position:0% +them is called bio hacking village and + + + align:start position:0% +them is called bio hacking village and +there is some bio hacking so like doing + + align:start position:0% +there is some bio hacking so like doing + + + align:start position:0% +there is some bio hacking so like doing +the RFID chip being citizen science but + + align:start position:0% +the RFID chip being citizen science but + + + align:start position:0% +the RFID chip being citizen science but +there's also a set of people at bio + + align:start position:0% +there's also a set of people at bio + + + align:start position:0% +there's also a set of people at bio +hacking village that do what's called + + align:start position:0% +hacking village that do what's called + + + align:start position:0% +hacking village that do what's called +white hat hacking so for people who know + + align:start position:0% +white hat hacking so for people who know + + + align:start position:0% +white hat hacking so for people who know +about this there's blackhat where you + + align:start position:0% +about this there's blackhat where you + + + align:start position:0% +about this there's blackhat where you +might you know like encrypt somebody's + + align:start position:0% +might you know like encrypt somebody's + + + align:start position:0% +might you know like encrypt somebody's +website or and then like hold them for + + align:start position:0% +website or and then like hold them for + + + align:start position:0% +website or and then like hold them for +ransom and do things that are disruptive + + align:start position:0% +ransom and do things that are disruptive + + + align:start position:0% +ransom and do things that are disruptive +white hat hackers are considered ethical + + align:start position:0% +white hat hackers are considered ethical + + + align:start position:0% +white hat hackers are considered ethical +hackers where they're doing security + + align:start position:0% +hackers where they're doing security + + + align:start position:0% +hackers where they're doing security +research on a product so the hackers in + + align:start position:0% +research on a product so the hackers in + + + align:start position:0% +research on a product so the hackers in +the bio hacking village started to do a + + align:start position:0% +the bio hacking village started to do a + + + align:start position:0% +the bio hacking village started to do a +lot of work on pacemakers which are + + align:start position:0% +lot of work on pacemakers which are + + + align:start position:0% +lot of work on pacemakers which are +connected technologies a lot of + + align:start position:0% +connected technologies a lot of + + + align:start position:0% +connected technologies a lot of +pacemaker companies an easy way to think + + align:start position:0% +pacemaker companies an easy way to think + + + align:start position:0% +pacemaker companies an easy way to think +about how they're thinking about this + + align:start position:0% +about how they're thinking about this + + + align:start position:0% +about how they're thinking about this +was the pacemaker companies are + + align:start position:0% +was the pacemaker companies are + + + align:start position:0% +was the pacemaker companies are +generally trying to optimize for battery + + align:start position:0% +generally trying to optimize for battery + + + align:start position:0% +generally trying to optimize for battery +life they don't want to do anything + + align:start position:0% +life they don't want to do anything + + + align:start position:0% +life they don't want to do anything +that's computationally expensive it + + align:start position:0% +that's computationally expensive it + + + align:start position:0% +that's computationally expensive it +turns out encrypting things is + + align:start position:0% +turns out encrypting things is + + + align:start position:0% +turns out encrypting things is +computationally expensive they did a + + align:start position:0% +computationally expensive they did a + + + align:start position:0% +computationally expensive they did a +regular Tivoli trivial exploit where + + align:start position:0% +regular Tivoli trivial exploit where + + + align:start position:0% +regular Tivoli trivial exploit where +they're able to reverse-engineer the + + align:start position:0% +they're able to reverse-engineer the + + + align:start position:0% +they're able to reverse-engineer the +protocol pacemakers stay in a low-power + + align:start position:0% +protocol pacemakers stay in a low-power + + + align:start position:0% +protocol pacemakers stay in a low-power +mode as long as they can if you ping it + + align:start position:0% +mode as long as they can if you ping it + + + align:start position:0% +mode as long as they can if you ping it +it will turn into high power mode so you + + align:start position:0% +it will turn into high power mode so you + + + align:start position:0% +it will turn into high power mode so you +can drain a multiyear + + align:start position:0% +can drain a multiyear + + + align:start position:0% +can drain a multiyear +battery of a pacemaker into a couple + + align:start position:0% +battery of a pacemaker into a couple + + + align:start position:0% +battery of a pacemaker into a couple +days or weeks they're also able to + + align:start position:0% +days or weeks they're also able to + + + align:start position:0% +days or weeks they're also able to +reverse engineer the shock that a + + align:start position:0% +reverse engineer the shock that a + + + align:start position:0% +reverse engineer the shock that a +pacemaker can deliver upon a cardiac + + align:start position:0% +pacemaker can deliver upon a cardiac + + + align:start position:0% +pacemaker can deliver upon a cardiac +event and so this has pretty significant + + align:start position:0% +event and so this has pretty significant + + + align:start position:0% +event and so this has pretty significant +implications for what this exploit can + + align:start position:0% +implications for what this exploit can + + + align:start position:0% +implications for what this exploit can +do with any normal tech company when you + + align:start position:0% +do with any normal tech company when you + + + align:start position:0% +do with any normal tech company when you +have an exploit of this type you can go + + align:start position:0% +have an exploit of this type you can go + + + align:start position:0% +have an exploit of this type you can go +to Facebook you can go to Amazon there's + + align:start position:0% +to Facebook you can go to Amazon there's + + + align:start position:0% +to Facebook you can go to Amazon there's +something called a coordinated + + align:start position:0% +something called a coordinated + + + align:start position:0% +something called a coordinated +disclosure you might have a bug bounty + + align:start position:0% +disclosure you might have a bug bounty + + + align:start position:0% +disclosure you might have a bug bounty +and then you share the update you can + + align:start position:0% +and then you share the update you can + + + align:start position:0% +and then you share the update you can +submit the update and then you're done + + align:start position:0% +submit the update and then you're done + + + align:start position:0% +submit the update and then you're done +with the device companies what was + + align:start position:0% +with the device companies what was + + + align:start position:0% +with the device companies what was +generally happening is people were + + align:start position:0% +generally happening is people were + + + align:start position:0% +generally happening is people were +the researchers were going to the device + + align:start position:0% +the researchers were going to the device + + + align:start position:0% +the researchers were going to the device +companies hey we found this exploit and + + align:start position:0% +companies hey we found this exploit and + + + align:start position:0% +companies hey we found this exploit and +the device companies are saying thank + + align:start position:0% +the device companies are saying thank + + + align:start position:0% +the device companies are saying thank +you we are going to see you now and the + + align:start position:0% +you we are going to see you now and the + + + align:start position:0% +you we are going to see you now and the +security searchers like why are you + + align:start position:0% +security searchers like why are you + + + align:start position:0% +security searchers like why are you +suing us and they said you're tampering + + align:start position:0% +suing us and they said you're tampering + + + align:start position:0% +suing us and they said you're tampering +with our product we are regulated by + + align:start position:0% +with our product we are regulated by + + + align:start position:0% +with our product we are regulated by +agencies we can't just ship updates + + align:start position:0% +agencies we can't just ship updates + + + align:start position:0% +agencies we can't just ship updates +whenever we want and so we have to see + + align:start position:0% +whenever we want and so we have to see + + + align:start position:0% +whenever we want and so we have to see +you turns out that is not true and the + + align:start position:0% +you turns out that is not true and the + + + align:start position:0% +you turns out that is not true and the +FDA found out about this and they're + + align:start position:0% +FDA found out about this and they're + + + align:start position:0% +FDA found out about this and they're +like you can't just sue security + + align:start position:0% +like you can't just sue security + + + align:start position:0% +like you can't just sue security +researchers if you have a security issue + + align:start position:0% +researchers if you have a security issue + + + align:start position:0% +researchers if you have a security issue +you have to like fix that and so the FDA + + align:start position:0% +you have to like fix that and so the FDA + + + align:start position:0% +you have to like fix that and so the FDA +did something that was pretty bold which + + align:start position:0% +did something that was pretty bold which + + + align:start position:0% +did something that was pretty bold which +was three years ago they went to DEFCON + + align:start position:0% +was three years ago they went to DEFCON + + + align:start position:0% +was three years ago they went to DEFCON +and if anyone has actually gone to + + align:start position:0% +and if anyone has actually gone to + + + align:start position:0% +and if anyone has actually gone to +DEFCON you would know that you do not go + + align:start position:0% +DEFCON you would know that you do not go + + + align:start position:0% +DEFCON you would know that you do not go +to DEFCON if you are part of the + + align:start position:0% +to DEFCON if you are part of the + + + align:start position:0% +to DEFCON if you are part of the +government because there is a game + + align:start position:0% +government because there is a game + + + align:start position:0% +government because there is a game +called find the Fed and you do not want + + align:start position:0% +called find the Fed and you do not want + + + align:start position:0% +called find the Fed and you do not want +to be found and of course like you know + + align:start position:0% +to be found and of course like you know + + + align:start position:0% +to be found and of course like you know +at NSA CIA like a lot of members of the + + align:start position:0% +at NSA CIA like a lot of members of the + + + align:start position:0% +at NSA CIA like a lot of members of the +government will go to DEFCON but it is + + align:start position:0% +government will go to DEFCON but it is + + + align:start position:0% +government will go to DEFCON but it is +generally like not a particularly + + align:start position:0% +generally like not a particularly + + + align:start position:0% +generally like not a particularly +friendly environment the bio hacking + + align:start position:0% +friendly environment the bio hacking + + + align:start position:0% +friendly environment the bio hacking +village said hey we will protect you we + + align:start position:0% +village said hey we will protect you we + + + align:start position:0% +village said hey we will protect you we +will give you a speaker slot we really + + align:start position:0% +will give you a speaker slot we really + + + align:start position:0% +will give you a speaker slot we really +want to work together with you and so + + align:start position:0% +want to work together with you and so + + + align:start position:0% +want to work together with you and so +over the last three years the agency has + + align:start position:0% +over the last three years the agency has + + + align:start position:0% +over the last three years the agency has +been working closely with security + + align:start position:0% +been working closely with security + + + align:start position:0% +been working closely with security +researchers to really think through the + + align:start position:0% +researchers to really think through the + + + align:start position:0% +researchers to really think through the +best ways of doing cyber security + + align:start position:0% +best ways of doing cyber security + + + align:start position:0% +best ways of doing cyber security +particularly for connected devices and + + align:start position:0% +particularly for connected devices and + + + align:start position:0% +particularly for connected devices and +so if you look at the past couple + + align:start position:0% +so if you look at the past couple + + + align:start position:0% +so if you look at the past couple +guidances there's a pre market and post + + align:start position:0% +guidances there's a pre market and post + + + align:start position:0% +guidances there's a pre market and post +market guidance where they've been + + align:start position:0% +market guidance where they've been + + + align:start position:0% +market guidance where they've been +collaborating and they're very good and + + align:start position:0% +collaborating and they're very good and + + + align:start position:0% +collaborating and they're very good and +strong guidances so the FDA did + + align:start position:0% +strong guidances so the FDA did + + + align:start position:0% +strong guidances so the FDA did +something really interesting which was + + align:start position:0% +something really interesting which was + + + align:start position:0% +something really interesting which was +in January they announced a new + + align:start position:0% +in January they announced a new + + + align:start position:0% +in January they announced a new +initiative which i think is quite + + align:start position:0% +initiative which i think is quite + + + align:start position:0% +initiative which i think is quite +amazing called hashtag we heart hackers + + align:start position:0% +amazing called hashtag we heart hackers + + + align:start position:0% +amazing called hashtag we heart hackers +and if you go to we heart hackers org + + align:start position:0% +and if you go to we heart hackers org + + + align:start position:0% +and if you go to we heart hackers org +the FDA has been encouraging device + + align:start position:0% +the FDA has been encouraging device + + + align:start position:0% +the FDA has been encouraging device +manufacturers like Medtronic and BD in + + align:start position:0% +manufacturers like Medtronic and BD in + + + align:start position:0% +manufacturers like Medtronic and BD in +Philips and thermo Fisher Fisher and + + align:start position:0% +Philips and thermo Fisher Fisher and + + + align:start position:0% +Philips and thermo Fisher Fisher and +others to bring their devices and work + + align:start position:0% +others to bring their devices and work + + + align:start position:0% +others to bring their devices and work +together with security researchers + + align:start position:0% + + + + align:start position:0% + +another group has probably worth knowing + + align:start position:0% +another group has probably worth knowing + + + align:start position:0% +another group has probably worth knowing +is that you think about what a lot of + + align:start position:0% +is that you think about what a lot of + + + align:start position:0% +is that you think about what a lot of +these connected products do they in many + + align:start position:0% +these connected products do they in many + + + align:start position:0% +these connected products do they in many +instances might mint or change the way + + align:start position:0% +instances might mint or change the way + + + align:start position:0% +instances might mint or change the way +that a clinician does their work and so + + align:start position:0% +that a clinician does their work and so + + + align:start position:0% +that a clinician does their work and so +today if you are a clinician + + align:start position:0% +today if you are a clinician + + + align:start position:0% +today if you are a clinician +and you graduate from med school you + + align:start position:0% +and you graduate from med school you + + + align:start position:0% +and you graduate from med school you +would take something like a Hippocratic + + align:start position:0% +would take something like a Hippocratic + + + align:start position:0% +would take something like a Hippocratic +oath to do no harm should the software + + align:start position:0% +oath to do no harm should the software + + + align:start position:0% +oath to do no harm should the software +engineers and the manufacturers of these + + align:start position:0% +engineers and the manufacturers of these + + + align:start position:0% +engineers and the manufacturers of these +products also take some sort of oath to + + align:start position:0% +products also take some sort of oath to + + + align:start position:0% +products also take some sort of oath to +do no harm and would that oath look + + align:start position:0% +do no harm and would that oath look + + + align:start position:0% +do no harm and would that oath look +similar or different and that line of + + align:start position:0% +similar or different and that line of + + + align:start position:0% +similar or different and that line of +thinking helped people realize that + + align:start position:0% +thinking helped people realize that + + + align:start position:0% +thinking helped people realize that +there are entire professional + + align:start position:0% +there are entire professional + + + align:start position:0% +there are entire professional +communities and societies for people who + + align:start position:0% +communities and societies for people who + + + align:start position:0% +communities and societies for people who +do this sort of for doctors in their + + align:start position:0% +do this sort of for doctors in their + + + align:start position:0% +do this sort of for doctors in their +specialties so society for narrowing + + align:start position:0% +specialties so society for narrowing + + + align:start position:0% +specialties so society for narrowing +ecology society for geology but there's + + align:start position:0% +ecology society for geology but there's + + + align:start position:0% +ecology society for geology but there's +really no Society for people who + + align:start position:0% +really no Society for people who + + + align:start position:0% +really no Society for people who +practice digital medicine so there's a + + align:start position:0% +practice digital medicine so there's a + + + align:start position:0% +practice digital medicine so there's a +group that is starting now which you all + + align:start position:0% +group that is starting now which you all + + + align:start position:0% +group that is starting now which you all +might like to join because I think you + + align:start position:0% +might like to join because I think you + + + align:start position:0% +might like to join because I think you +would all be part of this type of + + align:start position:0% +would all be part of this type of + + + align:start position:0% +would all be part of this type of +community which is a society for it's + + align:start position:0% +community which is a society for it's + + + align:start position:0% +community which is a society for it's +called the dime society and so if you're + + align:start position:0% +called the dime society and so if you're + + + align:start position:0% +called the dime society and so if you're +thinking through how do I do inform + + align:start position:0% +thinking through how do I do inform + + + align:start position:0% +thinking through how do I do inform +consent with these sorts of digital + + align:start position:0% +consent with these sorts of digital + + + align:start position:0% +consent with these sorts of digital +products what are the new ways that I + + align:start position:0% +products what are the new ways that I + + + align:start position:0% +products what are the new ways that I +need to think through regulation how am + + align:start position:0% +need to think through regulation how am + + + align:start position:0% +need to think through regulation how am +I going to work with my IRB this society + + align:start position:0% +I going to work with my IRB this society + + + align:start position:0% +I going to work with my IRB this society +could be a resource for you all right so + + align:start position:0% +could be a resource for you all right so + + + align:start position:0% +could be a resource for you all right so +how do you participate in the rulemaking + + align:start position:0% +how do you participate in the rulemaking + + + align:start position:0% +how do you participate in the rulemaking +process one is I would highly encourage + + align:start position:0% +process one is I would highly encourage + + + align:start position:0% +process one is I would highly encourage +if you get a chance to to serve some + + align:start position:0% +if you get a chance to to serve some + + + align:start position:0% +if you get a chance to to serve some +time in government there are more + + align:start position:0% +time in government there are more + + + align:start position:0% +time in government there are more +opportunities to do that through + + align:start position:0% +opportunities to do that through + + + align:start position:0% +opportunities to do that through +organizations like the president of + + align:start position:0% +organizations like the president of + + + align:start position:0% +organizations like the president of +Asian fellow to be an entrepreneur + + align:start position:0% +Asian fellow to be an entrepreneur + + + align:start position:0% +Asian fellow to be an entrepreneur +residence somewhere to be part of the + + align:start position:0% +residence somewhere to be part of the + + + align:start position:0% +residence somewhere to be part of the +u.s. digital service the payment system + + align:start position:0% +u.s. digital service the payment system + + + align:start position:0% +u.s. digital service the payment system +of CMS is like millions of line of + + align:start position:0% +of CMS is like millions of line of + + + align:start position:0% +of CMS is like millions of line of +kobold and so that obviously needs some + + align:start position:0% +kobold and so that obviously needs some + + + align:start position:0% +kobold and so that obviously needs some +fixing and so if you are want to do a + + align:start position:0% +fixing and so if you are want to do a + + + align:start position:0% +fixing and so if you are want to do a +service I think this is a really + + align:start position:0% +service I think this is a really + + + align:start position:0% +service I think this is a really +important way another way that you can + + align:start position:0% +important way another way that you can + + + align:start position:0% +important way another way that you can +do it is submitting to a public docket + + align:start position:0% +do it is submitting to a public docket + + + align:start position:0% +do it is submitting to a public docket +and so this is something I will be + + align:start position:0% +and so this is something I will be + + + align:start position:0% +and so this is something I will be +asking you to do and we'll talk about it + + align:start position:0% +asking you to do and we'll talk about it + + + align:start position:0% +asking you to do and we'll talk about it +after is how can you take what you + + align:start position:0% +after is how can you take what you + + + align:start position:0% +after is how can you take what you +learned in that white paper and ways + + align:start position:0% +learned in that white paper and ways + + + align:start position:0% +learned in that white paper and ways +that you can share back with the agency + + align:start position:0% +that you can share back with the agency + + + align:start position:0% +that you can share back with the agency +of how you would use that product you + + align:start position:0% +of how you would use that product you + + + align:start position:0% +of how you would use that product you +would think about developing rules and + + align:start position:0% +would think about developing rules and + + + align:start position:0% +would think about developing rules and +laws around AI machine learning there's + + align:start position:0% +laws around AI machine learning there's + + + align:start position:0% +laws around AI machine learning there's +a much longer resource that you can look + + align:start position:0% +a much longer resource that you can look + + + align:start position:0% +a much longer resource that you can look +at my friend Meena wrote which is that + + align:start position:0% +at my friend Meena wrote which is that + + + align:start position:0% +at my friend Meena wrote which is that +these are a couple of things to know so + + align:start position:0% +these are a couple of things to know so + + + align:start position:0% +these are a couple of things to know so +anyone can comment you will be heard if + + align:start position:0% +anyone can comment you will be heard if + + + align:start position:0% +anyone can comment you will be heard if +you write a very long comment someone at + + align:start position:0% +you write a very long comment someone at + + + align:start position:0% +you write a very long comment someone at +the agency probably multiple will have + + align:start position:0% +the agency probably multiple will have + + + align:start position:0% +the agency probably multiple will have +to read every single thing that you + + align:start position:0% +to read every single thing that you + + + align:start position:0% +to read every single thing that you +write so please be judicious and how you + + align:start position:0% +write so please be judicious and how you + + + align:start position:0% +write so please be judicious and how you +do that but it will be you will be heard + + align:start position:0% +do that but it will be you will be heard + + + align:start position:0% +do that but it will be you will be heard +and + + align:start position:0% +and + + + align:start position:0% +and +most of the time comments come from big + + align:start position:0% +most of the time comments come from big + + + align:start position:0% +most of the time comments come from big +organizations and people who have come + + align:start position:0% +organizations and people who have come + + + align:start position:0% +organizations and people who have come +together and not from the people who are + + align:start position:0% +together and not from the people who are + + + align:start position:0% +together and not from the people who are +experiencing and using a lot of the + + align:start position:0% +experiencing and using a lot of the + + + align:start position:0% +experiencing and using a lot of the +products so in my opinion I think + + align:start position:0% +products so in my opinion I think + + + align:start position:0% +products so in my opinion I think +someone like you is a really important + + align:start position:0% +someone like you is a really important + + + align:start position:0% +someone like you is a really important +comment invoice for the agency to have + + align:start position:0% +comment invoice for the agency to have + + + align:start position:0% +comment invoice for the agency to have +and to have a technical perspective + + align:start position:0% +and to have a technical perspective + + + align:start position:0% +and to have a technical perspective +another way that you can do this which + + align:start position:0% +another way that you can do this which + + + align:start position:0% +another way that you can do this which +I'm going to put Irene on a spot is we + + align:start position:0% +I'm going to put Irene on a spot is we + + + align:start position:0% +I'm going to put Irene on a spot is we +need new regulatory paradigms and so + + align:start position:0% +need new regulatory paradigms and so + + + align:start position:0% +need new regulatory paradigms and so +when you are out at beers or ice cream + + align:start position:0% +when you are out at beers or ice cream + + + align:start position:0% +when you are out at beers or ice cream +or whatever + + align:start position:0% +or whatever + + + align:start position:0% +or whatever +you do for fun you can think through new + + align:start position:0% +you do for fun you can think through new + + + align:start position:0% +you do for fun you can think through new +models and so we were kicking around an + + align:start position:0% +models and so we were kicking around an + + + align:start position:0% +models and so we were kicking around an +idea of could you use a clinical trial + + align:start position:0% +idea of could you use a clinical trial + + + align:start position:0% +idea of could you use a clinical trial +framework to think about AI in general + + align:start position:0% +framework to think about AI in general + + + align:start position:0% +framework to think about AI in general +so algorithms perform differently on + + align:start position:0% +so algorithms perform differently on + + + align:start position:0% +so algorithms perform differently on +different patient populations and + + align:start position:0% +different patient populations and + + + align:start position:0% +different patient populations and +different groups you need inclusion + + align:start position:0% +different groups you need inclusion + + + align:start position:0% +different groups you need inclusion +exclusion criteria should this be + + align:start position:0% +exclusion criteria should this be + + + align:start position:0% +exclusion criteria should this be +something maybe we even expand beyond + + align:start position:0% +something maybe we even expand beyond + + + align:start position:0% +something maybe we even expand beyond +healthcare algorithms to how you decide + + align:start position:0% +healthcare algorithms to how you decide + + + align:start position:0% +healthcare algorithms to how you decide +whether or not someone gets bail or + + align:start position:0% +whether or not someone gets bail or + + + align:start position:0% +whether or not someone gets bail or +teacher benefits and then the fun thing + + align:start position:0% +teacher benefits and then the fun thing + + + align:start position:0% +teacher benefits and then the fun thing +about putting your ideas online if you + + align:start position:0% +about putting your ideas online if you + + + align:start position:0% +about putting your ideas online if you +do that is then people start coming to + + align:start position:0% +do that is then people start coming to + + + align:start position:0% +do that is then people start coming to +you and we realized there was a group in + + align:start position:0% +you and we realized there was a group in + + + align:start position:0% +you and we realized there was a group in +Italy who had proposed a version of FDA + + align:start position:0% +Italy who had proposed a version of FDA + + + align:start position:0% +Italy who had proposed a version of FDA +for algorithms and you start to collect + + align:start position:0% +for algorithms and you start to collect + + + align:start position:0% +for algorithms and you start to collect +people who think or thinking about + + align:start position:0% +people who think or thinking about + + + align:start position:0% +people who think or thinking about +things that you're thinking about and + + align:start position:0% +things that you're thinking about and + + + align:start position:0% +things that you're thinking about and +now we will dig into the thing that you + + align:start position:0% +now we will dig into the thing that you + + + align:start position:0% +now we will dig into the thing that you +most likely will spend more time with + + align:start position:0% +most likely will spend more time with + + + align:start position:0% +most likely will spend more time with +than the government which is your IRB + + align:start position:0% + + + + align:start position:0% + +okay I could probably not give the rest + + align:start position:0% +okay I could probably not give the rest + + + align:start position:0% +okay I could probably not give the rest +of this talk if you just follow the + + align:start position:0% +of this talk if you just follow the + + + align:start position:0% +of this talk if you just follow the +thing on the bottom if you don't know if + + align:start position:0% +thing on the bottom if you don't know if + + + align:start position:0% +thing on the bottom if you don't know if +you're doing human research human + + align:start position:0% +you're doing human research human + + + align:start position:0% +you're doing human research human +subjects research ask the IRB ask your + + align:start position:0% +subjects research ask the IRB ask your + + + align:start position:0% +subjects research ask the IRB ask your +professor ask somebody I think when most + + align:start position:0% +professor ask somebody I think when most + + + align:start position:0% +professor ask somebody I think when most +of what I'm gonna say is gonna be a lot + + align:start position:0% +of what I'm gonna say is gonna be a lot + + + align:start position:0% +of what I'm gonna say is gonna be a lot +softer squishier than what Andy went + + align:start position:0% +softer squishier than what Andy went + + + align:start position:0% +softer squishier than what Andy went +around and it's really just to try to + + align:start position:0% +around and it's really just to try to + + + align:start position:0% +around and it's really just to try to +get the thought process going through + + align:start position:0% +get the thought process going through + + + align:start position:0% +get the thought process going through +your head of you know if we're doing + + align:start position:0% +your head of you know if we're doing + + + align:start position:0% +your head of you know if we're doing +actual human research if the IRB has to + + align:start position:0% +actual human research if the IRB has to + + + align:start position:0% +actual human research if the IRB has to +be involved what actually constitutes + + align:start position:0% +be involved what actually constitutes + + + align:start position:0% +be involved what actually constitutes +human research and just to be sure that + + align:start position:0% +human research and just to be sure that + + + align:start position:0% +human research and just to be sure that +you're aware of what's going on there + + align:start position:0% +you're aware of what's going on there + + + align:start position:0% +you're aware of what's going on there +all the time we've done this so research + + align:start position:0% +all the time we've done this so research + + + align:start position:0% +all the time we've done this so research +is + + align:start position:0% +is + + + align:start position:0% +is +systematic investigation to develop or + + align:start position:0% +systematic investigation to develop or + + + align:start position:0% +systematic investigation to develop or +contribute generalizable knowledge so + + align:start position:0% +contribute generalizable knowledge so + + + align:start position:0% +contribute generalizable knowledge so +you can do that in Iraq + + align:start position:0% +you can do that in Iraq + + + align:start position:0% +you can do that in Iraq +what's important about human subjects + + align:start position:0% +what's important about human subjects + + + align:start position:0% +what's important about human subjects +research is that people's lives are on + + align:start position:0% +research is that people's lives are on + + + align:start position:0% +research is that people's lives are on +the line what generally the easiest + + align:start position:0% +the line what generally the easiest + + + align:start position:0% +the line what generally the easiest +thing to know is if there's any any sort + + align:start position:0% +thing to know is if there's any any sort + + + align:start position:0% +thing to know is if there's any any sort +of identifiable information with the + + align:start position:0% +of identifiable information with the + + + align:start position:0% +of identifiable information with the +data that you're working with that is + + align:start position:0% +data that you're working with that is + + + align:start position:0% +data that you're working with that is +going to fall under human subjects + + align:start position:0% +going to fall under human subjects + + + align:start position:0% +going to fall under human subjects +research things that won't are publicly + + align:start position:0% +research things that won't are publicly + + + align:start position:0% +research things that won't are publicly +available anonymous data there's you + + align:start position:0% +available anonymous data there's you + + + align:start position:0% +available anonymous data there's you +know there's all sorts of imaging + + align:start position:0% +know there's all sorts of imaging + + + align:start position:0% +know there's all sorts of imaging +training data sets that you can use that + + align:start position:0% +training data sets that you can use that + + + align:start position:0% +training data sets that you can use that +are anonymized to what is an acceptable + + align:start position:0% +are anonymized to what is an acceptable + + + align:start position:0% +are anonymized to what is an acceptable +level but to Andy's point there's really + + align:start position:0% +level but to Andy's point there's really + + + align:start position:0% +level but to Andy's point there's really +no way to truly D identify a data set + + align:start position:0% +no way to truly D identify a data set + + + align:start position:0% +no way to truly D identify a data set +and just kind of with the amount of data + + align:start position:0% +and just kind of with the amount of data + + + align:start position:0% +and just kind of with the amount of data +that we're working with all right now in + + align:start position:0% +that we're working with all right now in + + + align:start position:0% +that we're working with all right now in +the world it's becoming impossible to D + + align:start position:0% +the world it's becoming impossible to D + + + align:start position:0% +the world it's becoming impossible to D +identify any data set if you have any + + align:start position:0% +identify any data set if you have any + + + align:start position:0% +identify any data set if you have any +other reference data set so any time + + align:start position:0% +other reference data set so any time + + + align:start position:0% +other reference data set so any time +you're working with any people you are + + align:start position:0% +you're working with any people you are + + + align:start position:0% +you're working with any people you are +almost certainly going to have to + + align:start position:0% +almost certainly going to have to + + + align:start position:0% +almost certainly going to have to +involve the IRB again + + align:start position:0% + + + + align:start position:0% + +so why the IRB is there it's not + + align:start position:0% +so why the IRB is there it's not + + + align:start position:0% +so why the IRB is there it's not +specifically to slap you on the wrist + + align:start position:0% +specifically to slap you on the wrist + + + align:start position:0% +specifically to slap you on the wrist +you know - it's not that anything's + + align:start position:0% +you know - it's not that anything's + + + align:start position:0% +you know - it's not that anything's +expected to purposely do anything wrong + + align:start position:0% +expected to purposely do anything wrong + + + align:start position:0% +expected to purposely do anything wrong +although that has happened that's such a + + align:start position:0% +although that has happened that's such a + + + align:start position:0% +although that has happened that's such a +small amount that it's just it's + + align:start position:0% +small amount that it's just it's + + + align:start position:0% +small amount that it's just it's +unhelpful to think that everybody is + + align:start position:0% +unhelpful to think that everybody is + + + align:start position:0% +unhelpful to think that everybody is +malicious + + align:start position:0% +malicious + + + align:start position:0% +malicious +so you're not gonna do anything + + align:start position:0% +so you're not gonna do anything + + + align:start position:0% +so you're not gonna do anything +particularly wrong but there are things + + align:start position:0% +particularly wrong but there are things + + + align:start position:0% +particularly wrong but there are things +that you just may not know and this is + + align:start position:0% +that you just may not know and this is + + + align:start position:0% +that you just may not know and this is +not the IR B's thousand thousands rodeo + + align:start position:0% +not the IR B's thousand thousands rodeo + + + align:start position:0% +not the IR B's thousand thousands rodeo +so if you bring something up to them + + align:start position:0% +so if you bring something up to them + + + align:start position:0% +so if you bring something up to them +they'll know almost immediately + + align:start position:0% +they'll know almost immediately + + + align:start position:0% +they'll know almost immediately +participants are giving up their time + + align:start position:0% +participants are giving up their time + + + align:start position:0% +participants are giving up their time +and information so it's the IRB more + + align:start position:0% +and information so it's the IRB more + + + align:start position:0% +and information so it's the IRB more +than keeping the institution from harm + + align:start position:0% +than keeping the institution from harm + + + align:start position:0% +than keeping the institution from harm +is really protecting the patients first + + align:start position:0% +is really protecting the patients first + + + align:start position:0% +is really protecting the patients first +and the institution at the same time but + + align:start position:0% +and the institution at the same time but + + + align:start position:0% +and the institution at the same time but +the main role is to part protect the + + align:start position:0% +the main role is to part protect the + + + align:start position:0% +the main role is to part protect the +participants specifically here's + + align:start position:0% +participants specifically here's + + + align:start position:0% +participants specifically here's +something you that might not go through + + align:start position:0% +something you that might not go through + + + align:start position:0% +something you that might not go through +everybody's head + + align:start position:0% +everybody's head + + + align:start position:0% +everybody's head +research that may be questionable or + + align:start position:0% +research that may be questionable or + + + align:start position:0% +research that may be questionable or +overly manipulative that gets into + + align:start position:0% +overly manipulative that gets into + + + align:start position:0% +overly manipulative that gets into +compensation for studies you can imagine + + align:start position:0% +compensation for studies you can imagine + + + align:start position:0% +compensation for studies you can imagine +certain places in an impoverished nation + + align:start position:0% +certain places in an impoverished nation + + + align:start position:0% +certain places in an impoverished nation +that you say we will do will pay fifty + + align:start position:0% +that you say we will do will pay fifty + + + align:start position:0% +that you say we will do will pay fifty +thousand dollars per person to come + + align:start position:0% +thousand dollars per person to come + + + align:start position:0% +thousand dollars per person to come +participate in this study you can + + align:start position:0% +participate in this study you can + + + align:start position:0% +participate in this study you can +imagine people want to be in that study + + align:start position:0% +imagine people want to be in that study + + + align:start position:0% +imagine people want to be in that study +and it can become a problem so the IRB + + align:start position:0% +and it can become a problem so the IRB + + + align:start position:0% +and it can become a problem so the IRB +is also a huge part of making sure that + + align:start position:0% +is also a huge part of making sure that + + + align:start position:0% +is also a huge part of making sure that +the studies aren't actually affecting + + align:start position:0% +the studies aren't actually affecting + + + align:start position:0% +the studies aren't actually affecting +anybody negatively in that kind of sense + + align:start position:0% +anybody negatively in that kind of sense + + + align:start position:0% +anybody negatively in that kind of sense +now before I do this next slide gets + + align:start position:0% +now before I do this next slide gets + + + align:start position:0% +now before I do this next slide gets +dark for a second so we'll try to move + + align:start position:0% +dark for a second so we'll try to move + + + align:start position:0% +dark for a second so we'll try to move +through it but it talks about how the + + align:start position:0% +through it but it talks about how the + + + align:start position:0% +through it but it talks about how the +IRB came about so we start with the + + align:start position:0% +IRB came about so we start with the + + + align:start position:0% +IRB came about so we start with the +Nuremberg code human research conducted + + align:start position:0% +Nuremberg code human research conducted + + + align:start position:0% +Nuremberg code human research conducted +on prisoners and others not participants + + align:start position:0% +on prisoners and others not participants + + + align:start position:0% +on prisoners and others not participants +but subjects of research Tuskegee + + align:start position:0% +but subjects of research Tuskegee + + + align:start position:0% +but subjects of research Tuskegee +Experiment another thing that people + + align:start position:0% +Experiment another thing that people + + + align:start position:0% +Experiment another thing that people +were not properly consented into the + + align:start position:0% +were not properly consented into the + + + align:start position:0% +were not properly consented into the +studies so they didn't know what they + + align:start position:0% +studies so they didn't know what they + + + align:start position:0% +studies so they didn't know what they +were actually being tested for so they + + align:start position:0% +were actually being tested for so they + + + align:start position:0% +were actually being tested for so they +couldn't possibly have consented the + + align:start position:0% +couldn't possibly have consented the + + + align:start position:0% +couldn't possibly have consented the +study went for forty years instead of + + align:start position:0% +study went for forty years instead of + + + align:start position:0% +study went for forty years instead of +six months and even after a standard of + + align:start position:0% +six months and even after a standard of + + + align:start position:0% +six months and even after a standard of +care had been established the study + + align:start position:0% +care had been established the study + + + align:start position:0% +care had been established the study +continued on that essentially is what + + align:start position:0% +continued on that essentially is what + + + align:start position:0% +continued on that essentially is what +began the National Commission for + + align:start position:0% +began the National Commission for + + + align:start position:0% +began the National Commission for +protection of human subjects which led + + align:start position:0% +protection of human subjects which led + + + align:start position:0% +protection of human subjects which led +to the IRB being the requirement for + + align:start position:0% +to the IRB being the requirement for + + + align:start position:0% +to the IRB being the requirement for +research and then five years later the + + align:start position:0% +research and then five years later the + + + align:start position:0% +research and then five years later the +Belmont report came out essentially + + align:start position:0% +Belmont report came out essentially + + + align:start position:0% +Belmont report came out essentially +enumerated these three basic principles + + align:start position:0% +enumerated these three basic principles + + + align:start position:0% +enumerated these three basic principles +respect for participants beneficence as + + align:start position:0% +respect for participants beneficence as + + + align:start position:0% +respect for participants beneficence as +far as do no harm + + align:start position:0% +far as do no harm + + + align:start position:0% +far as do no harm +don't take extra blood if it just makes + + align:start position:0% +don't take extra blood if it just makes + + + align:start position:0% +don't take extra blood if it just makes +it more convenient don't add extra drug + + align:start position:0% +it more convenient don't add extra drug + + + align:start position:0% +it more convenient don't add extra drug +if you just want to see what happens + + align:start position:0% +if you just want to see what happens + + + align:start position:0% +if you just want to see what happens +and then just making sure that + + align:start position:0% +and then just making sure that + + + align:start position:0% +and then just making sure that +participants are safe outside of any + + align:start position:0% +participants are safe outside of any + + + align:start position:0% +participants are safe outside of any +other harm that you can do so we follow + + align:start position:0% +other harm that you can do so we follow + + + align:start position:0% +other harm that you can do so we follow +the Belmont report that's essentially + + align:start position:0% +the Belmont report that's essentially + + + align:start position:0% +the Belmont report that's essentially +the state of the art that we have now + + align:start position:0% +the state of the art that we have now + + + align:start position:0% +the state of the art that we have now +with modernisations moving forward this + + align:start position:0% +with modernisations moving forward this + + + align:start position:0% +with modernisations moving forward this +is not something to really worry about + + align:start position:0% +is not something to really worry about + + + align:start position:0% +is not something to really worry about +but HHS has a great site that has a flow + + align:start position:0% +but HHS has a great site that has a flow + + + align:start position:0% +but HHS has a great site that has a flow +chart for just about any circumstance + + align:start position:0% +chart for just about any circumstance + + + align:start position:0% +chart for just about any circumstance +that you can think of to decide if + + align:start position:0% +that you can think of to decide if + + + align:start position:0% +that you can think of to decide if +you're actually doing human subjects + + align:start position:0% +you're actually doing human subjects + + + align:start position:0% +you're actually doing human subjects +research or not this is pretty much the + + align:start position:0% +research or not this is pretty much the + + + align:start position:0% +research or not this is pretty much the +most basic one you can go through it on + + align:start position:0% +most basic one you can go through it on + + + align:start position:0% +most basic one you can go through it on +your own just to highlight the main + + align:start position:0% +your own just to highlight the main + + + align:start position:0% +your own just to highlight the main +thing that I think you guys will + + align:start position:0% +thing that I think you guys will + + + align:start position:0% +thing that I think you guys will +probably be worried about is you will be + + align:start position:0% +probably be worried about is you will be + + + align:start position:0% +probably be worried about is you will be +collecting identifiable data which just + + align:start position:0% +collecting identifiable data which just + + + align:start position:0% +collecting identifiable data which just +immediately puts you in IRB land so any + + align:start position:0% +immediately puts you in IRB land so any + + + align:start position:0% +immediately puts you in IRB land so any +any time you can identify that that's + + align:start position:0% +any time you can identify that that's + + + align:start position:0% +any time you can identify that that's +the thing that's happening you're just + + align:start position:0% +the thing that's happening you're just + + + align:start position:0% +the thing that's happening you're just +you're there so you don't really have to + + align:start position:0% +you're there so you don't really have to + + + align:start position:0% +you're there so you don't really have to +go through any of this what is health + + align:start position:0% +go through any of this what is health + + + align:start position:0% +go through any of this what is health +data so you have names obviously most of + + align:start position:0% +data so you have names obviously most of + + + align:start position:0% +data so you have names obviously most of +these are either identifications or you + + align:start position:0% +these are either identifications or you + + + align:start position:0% +these are either identifications or you +know some sort of identifying thing a + + align:start position:0% +know some sort of identifying thing a + + + align:start position:0% +know some sort of identifying thing a +thing that the - I guess that a lot of + + align:start position:0% +thing that the - I guess that a lot of + + + align:start position:0% +thing that the - I guess that a lot of +people maybe gloss over that aren't so + + align:start position:0% +people maybe gloss over that aren't so + + + align:start position:0% +people maybe gloss over that aren't so +obvious is zip codes you have to limit + + align:start position:0% +obvious is zip codes you have to limit + + + align:start position:0% +obvious is zip codes you have to limit +them to the first three numbers of a zip + + align:start position:0% +them to the first three numbers of a zip + + + align:start position:0% +them to the first three numbers of a zip +code which gives a generalizable area + + align:start position:0% +code which gives a generalizable area + + + align:start position:0% +code which gives a generalizable area +without actually dialing in on a + + align:start position:0% +without actually dialing in on a + + + align:start position:0% +without actually dialing in on a +person's place dates are an extremely + + align:start position:0% +person's place dates are an extremely + + + align:start position:0% +person's place dates are an extremely +sensitive topic so anytime you're + + align:start position:0% +sensitive topic so anytime you're + + + align:start position:0% +sensitive topic so anytime you're +working with actual dates which I assume + + align:start position:0% +working with actual dates which I assume + + + align:start position:0% +working with actual dates which I assume +in you know wearable technologies you're + + align:start position:0% +in you know wearable technologies you're + + + align:start position:0% +in you know wearable technologies you're +going to be dealing with time series + + align:start position:0% +going to be dealing with time series + + + align:start position:0% +going to be dealing with time series +data and that kind of stuff there are + + align:start position:0% +data and that kind of stuff there are + + + align:start position:0% +data and that kind of stuff there are +different ways of getting rid of or + + align:start position:0% +different ways of getting rid of or + + + align:start position:0% +different ways of getting rid of or +making that less sensitive but anytime + + align:start position:0% +making that less sensitive but anytime + + + align:start position:0% +making that less sensitive but anytime +you're dealing with research anytime + + align:start position:0% +you're dealing with research anytime + + + align:start position:0% +you're dealing with research anytime +we're dealing with the + + align:start position:0% +we're dealing with the + + + align:start position:0% +we're dealing with the +electronic health records we deal in + + align:start position:0% +electronic health records we deal in + + + align:start position:0% +electronic health records we deal in +years not in actual dates which can it + + align:start position:0% +years not in actual dates which can it + + + align:start position:0% +years not in actual dates which can it +creates problems if you are trying to do + + align:start position:0% +creates problems if you are trying to do + + + align:start position:0% +creates problems if you are trying to do +time series analysis for somebody's + + align:start position:0% +time series analysis for somebody's + + + align:start position:0% +time series analysis for somebody's +entire health record in which case you + + align:start position:0% +entire health record in which case you + + + align:start position:0% +entire health record in which case you +can get further clearance to work with + + align:start position:0% +can get further clearance to work with + + + align:start position:0% +can get further clearance to work with +more identical identifiable data but + + align:start position:0% +more identical identifiable data but + + + align:start position:0% +more identical identifiable data but +that is progressive as it can be there's + + align:start position:0% +that is progressive as it can be there's + + + align:start position:0% +that is progressive as it can be there's +no reason to start with that kind of + + align:start position:0% +no reason to start with that kind of + + + align:start position:0% +no reason to start with that kind of +data if you don't so it's always on a + + align:start position:0% +data if you don't so it's always on a + + + align:start position:0% +data if you don't so it's always on a +need-to-know finally if you're working + + align:start position:0% +need-to-know finally if you're working + + + align:start position:0% +need-to-know finally if you're working +with patients older than 90 90 year + + align:start position:0% +with patients older than 90 90 year + + + align:start position:0% +with patients older than 90 90 year +older they are just generalized as a + + align:start position:0% +older they are just generalized as a + + + align:start position:0% +older they are just generalized as a +category of greater than 90 the rest of + + align:start position:0% +category of greater than 90 the rest of + + + align:start position:0% +category of greater than 90 the rest of +these I think are fairly fairly + + align:start position:0% +these I think are fairly fairly + + + align:start position:0% +these I think are fairly fairly +guessable so we don't have to go through + + align:start position:0% +guessable so we don't have to go through + + + align:start position:0% +guessable so we don't have to go through +them but those are kind of the those are + + align:start position:0% +them but those are kind of the those are + + + align:start position:0% +them but those are kind of the those are +the tricky ones that some people don't + + align:start position:0% +the tricky ones that some people don't + + + align:start position:0% +the tricky ones that some people don't +catch again just limit the collection of + + align:start position:0% +catch again just limit the collection of + + + align:start position:0% +catch again just limit the collection of +pahi as strictly as possible if you + + align:start position:0% +pahi as strictly as possible if you + + + align:start position:0% +pahi as strictly as possible if you +don't need it don't get it if you're + + align:start position:0% +don't need it don't get it if you're + + + align:start position:0% +don't need it don't get it if you're +sharing the data instead of sharing an + + align:start position:0% +sharing the data instead of sharing an + + + align:start position:0% +sharing the data instead of sharing an +entire data set if you do have strong pH + + align:start position:0% +entire data set if you do have strong pH + + + align:start position:0% +entire data set if you do have strong pH +I limit what you're giving or sharing to + + align:start position:0% +I limit what you're giving or sharing to + + + align:start position:0% +I limit what you're giving or sharing to +another researcher that's just a hygiene + + align:start position:0% +another researcher that's just a hygiene + + + align:start position:0% +another researcher that's just a hygiene +issue and we'll get it's really limiting + + align:start position:0% +issue and we'll get it's really limiting + + + align:start position:0% +issue and we'll get it's really limiting +the amount of errors that can happen so + + align:start position:0% + + + + align:start position:0% + +why is it so important + + align:start position:0% +why is it so important + + + align:start position:0% +why is it so important +cirb again is particularly in interested + + align:start position:0% +cirb again is particularly in interested + + + align:start position:0% +cirb again is particularly in interested +in protecting patients and making sure + + align:start position:0% +in protecting patients and making sure + + + align:start position:0% +in protecting patients and making sure +that there's as little harm if any done + + align:start position:0% +that there's as little harm if any done + + + align:start position:0% +that there's as little harm if any done +as possible to patients just general + + align:start position:0% +as possible to patients just general + + + align:start position:0% +as possible to patients just general +human decency and respect there are + + align:start position:0% +human decency and respect there are + + + align:start position:0% +human decency and respect there are +there's institutional risk if something + + align:start position:0% +there's institutional risk if something + + + align:start position:0% +there's institutional risk if something +is done without an IRB and you can't + + align:start position:0% +is done without an IRB and you can't + + + align:start position:0% +is done without an IRB and you can't +publish if you have done human subjects + + align:start position:0% +publish if you have done human subjects + + + align:start position:0% +publish if you have done human subjects +research without an IRB those two are + + align:start position:0% +research without an IRB those two are + + + align:start position:0% +research without an IRB those two are +kind of the stick but the carrot really + + align:start position:0% +kind of the stick but the carrot really + + + align:start position:0% +kind of the stick but the carrot really +should be the top two as far as just + + align:start position:0% +should be the top two as far as just + + + align:start position:0% +should be the top two as far as just +human decency and making sure that + + align:start position:0% +human decency and making sure that + + + align:start position:0% +human decency and making sure that +you've protected any patients or any + + align:start position:0% +you've protected any patients or any + + + align:start position:0% +you've protected any patients or any +participants that you have involved + + align:start position:0% +participants that you have involved + + + align:start position:0% +participants that you have involved +in your research these are a couple + + align:start position:0% +in your research these are a couple + + + align:start position:0% +in your research these are a couple +violations we don't have to get too far + + align:start position:0% +violations we don't have to get too far + + + align:start position:0% +violations we don't have to get too far +into it but they were both allegedly + + align:start position:0% +into it but they were both allegedly + + + align:start position:0% +into it but they were both allegedly +conducted without any IRB approval + + align:start position:0% +conducted without any IRB approval + + + align:start position:0% +conducted without any IRB approval +there's possible fraud involved and it + + align:start position:0% +there's possible fraud involved and it + + + align:start position:0% +there's possible fraud involved and it +it ruined both of their careers but it + + align:start position:0% +it ruined both of their careers but it + + + align:start position:0% +it ruined both of their careers but it +put people at huge exposures to + + align:start position:0% +put people at huge exposures to + + + align:start position:0% +put people at huge exposures to +unhealthy conditions this is probably a + + align:start position:0% +unhealthy conditions this is probably a + + + align:start position:0% +unhealthy conditions this is probably a +much bigger common issue than you're + + align:start position:0% +much bigger common issue than you're + + + align:start position:0% +much bigger common issue than you're +gonna have pH I data breaches are they + + align:start position:0% +gonna have pH I data breaches are they + + + align:start position:0% +gonna have pH I data breaches are they +happen a lot they're generally not + + align:start position:0% +happen a lot they're generally not + + + align:start position:0% +happen a lot they're generally not +breaches from the outside their + + align:start position:0% +breaches from the outside their + + + align:start position:0% +breaches from the outside their +accidents somebody will set up a web + + align:start position:0% +accidents somebody will set up a web + + + align:start position:0% +accidents somebody will set up a web +server on the machine + + align:start position:0% +server on the machine + + + align:start position:0% +server on the machine +serving pH I because they found it + + align:start position:0% +serving pH I because they found it + + + align:start position:0% +serving pH I because they found it +easier to work at home one day it could + + align:start position:0% +easier to work at home one day it could + + + align:start position:0% +easier to work at home one day it could +just be they don't know how software is + + align:start position:0% +just be they don't know how software is + + + align:start position:0% +just be they don't know how software is +set up so anytime you're working with pH + + align:start position:0% +set up so anytime you're working with pH + + + align:start position:0% +set up so anytime you're working with pH +I it's you really got to overdo it on + + align:start position:0% +I it's you really got to overdo it on + + + align:start position:0% +I it's you really got to overdo it on +knowing exactly how you're working with + + align:start position:0% +knowing exactly how you're working with + + + align:start position:0% +knowing exactly how you're working with +it other breaches are losing unencrypted + + align:start position:0% +it other breaches are losing unencrypted + + + align:start position:0% +it other breaches are losing unencrypted +computers putting data on a thumb drive + + align:start position:0% +computers putting data on a thumb drive + + + align:start position:0% +computers putting data on a thumb drive +and losing it + + align:start position:0% + + + + align:start position:0% + +there's the gross amount of data + + align:start position:0% +there's the gross amount of data + + + align:start position:0% +there's the gross amount of data +breaches happen just from negligence and + + align:start position:0% +breaches happen just from negligence and + + + align:start position:0% +breaches happen just from negligence and +not being as careful as you want to be + + align:start position:0% +not being as careful as you want to be + + + align:start position:0% +not being as careful as you want to be +so it's always good to keep in mind I + + align:start position:0% +so it's always good to keep in mind I + + + align:start position:0% +so it's always good to keep in mind I +guess a new thing with dir B and digital + + align:start position:0% +guess a new thing with dir B and digital + + + align:start position:0% +guess a new thing with dir B and digital +research is things have been changing + + align:start position:0% +research is things have been changing + + + align:start position:0% +research is things have been changing +now from face-to-face recruitment and + + align:start position:0% +now from face-to-face recruitment and + + + align:start position:0% +now from face-to-face recruitment and +research into being able to consent + + align:start position:0% +research into being able to consent + + + align:start position:0% +research into being able to consent +online to be able to reach you know + + align:start position:0% +online to be able to reach you know + + + align:start position:0% +online to be able to reach you know +millions of people across the world and + + align:start position:0% +millions of people across the world and + + + align:start position:0% +millions of people across the world and +allowing them to consent on their own so + + align:start position:0% +allowing them to consent on their own so + + + align:start position:0% +allowing them to consent on their own so +this has become obviously a new thing + + align:start position:0% +this has become obviously a new thing + + + align:start position:0% +this has become obviously a new thing +since the Belmont report and it's + + align:start position:0% +since the Belmont report and it's + + + align:start position:0% +since the Belmont report and it's +something that we are working closely + + align:start position:0% +something that we are working closely + + + align:start position:0% +something that we are working closely +with our IRB to make sure that we're + + align:start position:0% +with our IRB to make sure that we're + + + align:start position:0% +with our IRB to make sure that we're +being as respectful as we can to the + + align:start position:0% +being as respectful as we can to the + + + align:start position:0% +being as respectful as we can to the +patients but also making sure that we + + align:start position:0% +patients but also making sure that we + + + align:start position:0% +patients but also making sure that we +can develop software solutions that + + align:start position:0% +can develop software solutions that + + + align:start position:0% +can develop software solutions that +are not hurting anybody and develop into + + align:start position:0% +are not hurting anybody and develop into + + + align:start position:0% +are not hurting anybody and develop into +kind of swim lanes so what we've kind of + + align:start position:0% +kind of swim lanes so what we've kind of + + + align:start position:0% +kind of swim lanes so what we've kind of +come up with a framework for is that + + align:start position:0% +come up with a framework for is that + + + align:start position:0% +come up with a framework for is that +there's a project which is you know + + align:start position:0% +there's a project which is you know + + + align:start position:0% +there's a project which is you know +we're studying all cancers so we can you + + align:start position:0% +we're studying all cancers so we can you + + + align:start position:0% +we're studying all cancers so we can you +can post reports about different + + align:start position:0% +can post reports about different + + + align:start position:0% +can post reports about different +research that's going on things that + + align:start position:0% +research that's going on things that + + + align:start position:0% +research that's going on things that +seem important a study is an actual + + align:start position:0% +seem important a study is an actual + + + align:start position:0% +seem important a study is an actual +person that's consented to a protocol + + align:start position:0% +person that's consented to a protocol + + + align:start position:0% +person that's consented to a protocol +which is human research and subject to + + align:start position:0% +which is human research and subject to + + + align:start position:0% +which is human research and subject to +IRB then we'll have a platform that the + + align:start position:0% +IRB then we'll have a platform that the + + + align:start position:0% +IRB then we'll have a platform that the +soft that the users will use and that + + align:start position:0% +soft that the users will use and that + + + align:start position:0% +soft that the users will use and that +will be like a website or an iPhone app + + align:start position:0% +will be like a website or an iPhone app + + + align:start position:0% +will be like a website or an iPhone app +that they can get you know literature + + align:start position:0% +that they can get you know literature + + + align:start position:0% +that they can get you know literature +information about what the project is + + align:start position:0% +information about what the project is + + + align:start position:0% +information about what the project is +going on and then we'll have a + + align:start position:0% +going on and then we'll have a + + + align:start position:0% +going on and then we'll have a +participant who's actually part of a + + align:start position:0% +participant who's actually part of a + + + align:start position:0% +participant who's actually part of a +study + + align:start position:0% +study + + + align:start position:0% +study +who's again covered under IRB through + + align:start position:0% +who's again covered under IRB through + + + align:start position:0% +who's again covered under IRB through +consent so in the old way why this kind + + align:start position:0% +consent so in the old way why this kind + + + align:start position:0% +consent so in the old way why this kind +of development has been important the + + align:start position:0% +of development has been important the + + + align:start position:0% +of development has been important the +old way of software development was the + + align:start position:0% +old way of software development was the + + + align:start position:0% +old way of software development was the +waterfall approach where you work for + + align:start position:0% +waterfall approach where you work for + + + align:start position:0% +waterfall approach where you work for +three weeks implement something work for + + align:start position:0% +three weeks implement something work for + + + align:start position:0% +three weeks implement something work for +three weeks implement something where we + + align:start position:0% +three weeks implement something where we + + + align:start position:0% +three weeks implement something where we +have moved to a agile approach in + + align:start position:0% +have moved to a agile approach in + + + align:start position:0% +have moved to a agile approach in +software and so while agile makes our + + align:start position:0% +software and so while agile makes our + + + align:start position:0% +software and so while agile makes our +lives a lot easier as far as development + + align:start position:0% +lives a lot easier as far as development + + + align:start position:0% +lives a lot easier as far as development +it's not we can't be sure what we're + + align:start position:0% +it's not we can't be sure what we're + + + align:start position:0% +it's not we can't be sure what we're +doing isn't going to affect patients in + + align:start position:0% +doing isn't going to affect patients in + + + align:start position:0% +doing isn't going to affect patients in +certain contexts so within a study + + align:start position:0% +certain contexts so within a study + + + align:start position:0% +certain contexts so within a study +working agile lead makes no sense or + + align:start position:0% +working agile lead makes no sense or + + + align:start position:0% +working agile lead makes no sense or +it's we have we want to work with the + + align:start position:0% +it's we have we want to work with the + + + align:start position:0% +it's we have we want to work with the +IRB to approve things but IRB approval + + align:start position:0% +IRB to approve things but IRB approval + + + align:start position:0% +IRB to approve things but IRB approval +takes you know between two and four + + align:start position:0% +takes you know between two and four + + + align:start position:0% +takes you know between two and four +weeks for expedited things when we talk + + align:start position:0% +weeks for expedited things when we talk + + + align:start position:0% +weeks for expedited things when we talk +about like projects and stuff that's + + align:start position:0% +about like projects and stuff that's + + + align:start position:0% +about like projects and stuff that's +where we want to work safely in an agile + + align:start position:0% +where we want to work safely in an agile + + + align:start position:0% +where we want to work safely in an agile +environment and try to figure out places + + align:start position:0% +environment and try to figure out places + + + align:start position:0% +environment and try to figure out places +where the IRB doesn't necessarily have + + align:start position:0% +where the IRB doesn't necessarily have + + + align:start position:0% +where the IRB doesn't necessarily have +to be involved or doesn't want to be + + align:start position:0% +to be involved or doesn't want to be + + + align:start position:0% +to be involved or doesn't want to be +involved and that there isn't any added + + align:start position:0% +involved and that there isn't any added + + + align:start position:0% +involved and that there isn't any added +patient risk whatsoever in working in + + align:start position:0% +patient risk whatsoever in working in + + + align:start position:0% +patient risk whatsoever in working in +that kind of ironmen so it's almost + + align:start position:0% +that kind of ironmen so it's almost + + + align:start position:0% +that kind of ironmen so it's almost +working it's working with software + + align:start position:0% +working it's working with software + + + align:start position:0% +working it's working with software +products versus study + + align:start position:0% +products versus study + + + align:start position:0% +products versus study +and so working with the IRB to be sure + + align:start position:0% +and so working with the IRB to be sure + + + align:start position:0% +and so working with the IRB to be sure +that we can separate those things and + + align:start position:0% +that we can separate those things and + + + align:start position:0% +that we can separate those things and +make sure that things move on as well as + + align:start position:0% +make sure that things move on as well as + + + align:start position:0% +make sure that things move on as well as +possible without any added harm so + + align:start position:0% +possible without any added harm so + + + align:start position:0% +possible without any added harm so +that's these categories again so a + + align:start position:0% +that's these categories again so a + + + align:start position:0% +that's these categories again so a +project activity would be you know + + align:start position:0% +project activity would be you know + + + align:start position:0% +project activity would be you know +social media outreach sharing content + + align:start position:0% +social media outreach sharing content + + + align:start position:0% +social media outreach sharing content +that you know is relevant to the project + + align:start position:0% +that you know is relevant to the project + + + align:start position:0% +that you know is relevant to the project +and kind of just informing about a + + align:start position:0% +and kind of just informing about a + + + align:start position:0% +and kind of just informing about a +general idea + + align:start position:0% +general idea + + + align:start position:0% +general idea +a study activity is what you would + + align:start position:0% +a study activity is what you would + + + align:start position:0% +a study activity is what you would +generally be used to with consent data + + align:start position:0% +generally be used to with consent data + + + align:start position:0% +generally be used to with consent data +sharing actually participating in the + + align:start position:0% +sharing actually participating in the + + + align:start position:0% +sharing actually participating in the +study where whether it's through wearing + + align:start position:0% +study where whether it's through wearing + + + align:start position:0% +study where whether it's through wearing +a wearable answering questions and then + + align:start position:0% +a wearable answering questions and then + + + align:start position:0% +a wearable answering questions and then +withdrawing in the process and that's + + align:start position:0% +withdrawing in the process and that's + + + align:start position:0% +withdrawing in the process and that's +the study activities are 100% IRB where + + align:start position:0% +the study activities are 100% IRB where + + + align:start position:0% +the study activities are 100% IRB where +the project activities that aren't + + align:start position:0% +the project activities that aren't + + + align:start position:0% +the project activities that aren't +directly dealing with the study can + + align:start position:0% +directly dealing with the study can + + + align:start position:0% +directly dealing with the study can +hopefully be separated in most cases so + + align:start position:0% +hopefully be separated in most cases so + + + align:start position:0% +hopefully be separated in most cases so +the three takeaways really are just if + + align:start position:0% +the three takeaways really are just if + + + align:start position:0% +the three takeaways really are just if +you don't know ask limit the collection + + align:start position:0% +you don't know ask limit the collection + + + align:start position:0% +you don't know ask limit the collection +of pH I as strictly as possible and + + align:start position:0% + + + + align:start position:0% + +working in agile developments are great + + align:start position:0% +working in agile developments are great + + + align:start position:0% +working in agile developments are great +but it is unsafe in a lot of human + + align:start position:0% +but it is unsafe in a lot of human + + + align:start position:0% +but it is unsafe in a lot of human +research so we have to focus on where + + align:start position:0% +research so we have to focus on where + + + align:start position:0% +research so we have to focus on where +that can be used and where it can't and + + align:start position:0% +that can be used and where it can't and + + + align:start position:0% +that can be used and where it can't and +that's it thank you + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so as an irony ser mei-ling share that + + align:start position:0% +so as an irony ser mei-ling share that + + + align:start position:0% +so as an irony ser mei-ling share that +the researcher + + align:start position:0% +the researcher + + + align:start position:0% +the researcher +by training + + align:start position:0% +by training + + + align:start position:0% +by training +yeah is there a third-party service + + align:start position:0% +yeah is there a third-party service + + + align:start position:0% +yeah is there a third-party service +inside yeah yeah so we we certify all of + + align:start position:0% +inside yeah yeah so we we certify all of + + + align:start position:0% +inside yeah yeah so we we certify all of +our researchers with human research and + + align:start position:0% +our researchers with human research and + + + align:start position:0% +our researchers with human research and +HIPAA compliance just just blanket and + + align:start position:0% +HIPAA compliance just just blanket and + + + align:start position:0% +HIPAA compliance just just blanket and +if you provide that and you have you + + align:start position:0% +if you provide that and you have you + + + align:start position:0% +if you provide that and you have you +know your certifications are up to date + + align:start position:0% +know your certifications are up to date + + + align:start position:0% +know your certifications are up to date +that's kind of the it's an understanding + + align:start position:0% +that's kind of the it's an understanding + + + align:start position:0% +that's kind of the it's an understanding +that the researcher knows what they + + align:start position:0% +that the researcher knows what they + + + align:start position:0% +that the researcher knows what they +should be looking out for + + align:start position:0% +should be looking out for + + + align:start position:0% +should be looking out for +and that IRB understands oh yeah yeah + + align:start position:0% +and that IRB understands oh yeah yeah + + + align:start position:0% +and that IRB understands oh yeah yeah +it's we use a third-party you can you + + align:start position:0% +it's we use a third-party you can you + + + align:start position:0% +it's we use a third-party you can you +can have I don't we we use a third-party + + align:start position:0% +can have I don't we we use a third-party + + + align:start position:0% +can have I don't we we use a third-party +so at MIT there's something called + + align:start position:0% +so at MIT there's something called + + + align:start position:0% +so at MIT there's something called +couey's the Committee on use of human + + align:start position:0% +couey's the Committee on use of human + + + align:start position:0% +couey's the Committee on use of human +subhumans as experimental subjects and + + align:start position:0% +subhumans as experimental subjects and + + + align:start position:0% +subhumans as experimental subjects and +they are our official IRB there's it + + align:start position:0% +they are our official IRB there's it + + + align:start position:0% +they are our official IRB there's it +used to be all paper now there's an + + align:start position:0% +used to be all paper now there's an + + + align:start position:0% +used to be all paper now there's an +electronic way where you can apply for a + + align:start position:0% +electronic way where you can apply for a + + + align:start position:0% +electronic way where you can apply for a +coup ease protocol and it's a reasonably + + align:start position:0% +coup ease protocol and it's a reasonably + + + align:start position:0% +coup ease protocol and it's a reasonably +long document in which you describe the + + align:start position:0% +long document in which you describe the + + + align:start position:0% +long document in which you describe the +purpose of the experiment what you're + + align:start position:0% +purpose of the experiment what you're + + + align:start position:0% +purpose of the experiment what you're +going to do what kind of people you're + + align:start position:0% +going to do what kind of people you're + + + align:start position:0% +going to do what kind of people you're +going to recruit what recruiting + + align:start position:0% +going to recruit what recruiting + + + align:start position:0% +going to recruit what recruiting +material you're going to use how you + + align:start position:0% +material you're going to use how you + + + align:start position:0% +material you're going to use how you +will handle the data what security + + align:start position:0% +will handle the data what security + + + align:start position:0% +will handle the data what security +provisions you have of course if you're + + align:start position:0% +provisions you have of course if you're + + + align:start position:0% +provisions you have of course if you're +doing something like injecting people + + align:start position:0% +doing something like injecting people + + + align:start position:0% +doing something like injecting people +with toxins then that's a much more + + align:start position:0% +with toxins then that's a much more + + + align:start position:0% +with toxins then that's a much more +serious kind of thing and you have to + + align:start position:0% +serious kind of thing and you have to + + + align:start position:0% +serious kind of thing and you have to +describe the preliminary data on why you + + align:start position:0% +describe the preliminary data on why you + + + align:start position:0% +describe the preliminary data on why you +think this is safe and so on and that + + align:start position:0% +think this is safe and so on and that + + + align:start position:0% +think this is safe and so on and that +gets reviewed at essentially one of + + align:start position:0% +gets reviewed at essentially one of + + + align:start position:0% +gets reviewed at essentially one of +three levels + + align:start position:0% +three levels + + + align:start position:0% +three levels +there's exempt review which is you can't + + align:start position:0% +there's exempt review which is you can't + + + align:start position:0% +there's exempt review which is you can't +exempt yourself but they can exempt you + + align:start position:0% +exempt yourself but they can exempt you + + + align:start position:0% +exempt yourself but they can exempt you +and what they would say is this is + + align:start position:0% +and what they would say is this is + + + align:start position:0% +and what they would say is this is +minimal risk kind of problem so let's + + align:start position:0% +minimal risk kind of problem so let's + + + align:start position:0% +minimal risk kind of problem so let's +say you're doing a data only study using + + align:start position:0% +say you're doing a data only study using + + + align:start position:0% +say you're doing a data only study using +mimic data and you've done the city + + align:start position:0% +mimic data and you've done the city + + + align:start position:0% +mimic data and you've done the city +training you've signed the data use + + align:start position:0% +training you've signed the data use + + + align:start position:0% +training you've signed the data use +agreement and the I you're supposed to + + align:start position:0% +agreement and the I you're supposed to + + + align:start position:0% +agreement and the I you're supposed to +get IRB permission for it there is an + + align:start position:0% +get IRB permission for it there is an + + + align:start position:0% +get IRB permission for it there is an +exception for students in a classroom + + align:start position:0% +exception for students in a classroom + + + align:start position:0% +exception for students in a classroom +okay in which case I'm responsible + + align:start position:0% +okay in which case I'm responsible + + + align:start position:0% +okay in which case I'm responsible +than making you responsible but if you + + align:start position:0% +than making you responsible but if you + + + align:start position:0% +than making you responsible but if you +screw it up I'm responsible the second + + align:start position:0% +screw it up I'm responsible the second + + + align:start position:0% +screw it up I'm responsible the second +level is a an expedited approval which + + align:start position:0% +level is a an expedited approval which + + + align:start position:0% +level is a an expedited approval which +is a low-risk kind of approval typically + + align:start position:0% +is a low-risk kind of approval typically + + + align:start position:0% +is a low-risk kind of approval typically +data only studies but it may involve + + align:start position:0% +data only studies but it may involve + + + align:start position:0% +data only studies but it may involve +things like using limited datasets where + + align:start position:0% +things like using limited datasets where + + + align:start position:0% +things like using limited datasets where +for example if you're trying to study + + align:start position:0% +for example if you're trying to study + + + align:start position:0% +for example if you're trying to study +the geographical distribution of disease + + align:start position:0% +the geographical distribution of disease + + + align:start position:0% +the geographical distribution of disease +then you you clearly need better + + align:start position:0% +then you you clearly need better + + + align:start position:0% +then you you clearly need better +geographical identifiers than a + + align:start position:0% +geographical identifiers than a + + + align:start position:0% +geographical identifiers than a +three-digit zip code or if you're trying + + align:start position:0% +three-digit zip code or if you're trying + + + align:start position:0% +three-digit zip code or if you're trying +to study a time series as Mark was + + align:start position:0% +to study a time series as Mark was + + + align:start position:0% +to study a time series as Mark was +talking about you need actual dates and + + align:start position:0% +talking about you need actual dates and + + + align:start position:0% +talking about you need actual dates and +so you can get approval to use that kind + + align:start position:0% +so you can get approval to use that kind + + + align:start position:0% +so you can get approval to use that kind +of data and then there's the full-on + + align:start position:0% +of data and then there's the full-on + + + align:start position:0% +of data and then there's the full-on +review which takes much longer where + + align:start position:0% +review which takes much longer where + + + align:start position:0% +review which takes much longer where +they do actually bring in people to + + align:start position:0% +they do actually bring in people to + + + align:start position:0% +they do actually bring in people to +evaluate the safety of what you're + + align:start position:0% +evaluate the safety of what you're + + + align:start position:0% +evaluate the safety of what you're +proposing to do so far my experience is + + align:start position:0% +proposing to do so far my experience is + + + align:start position:0% +proposing to do so far my experience is +that mostly with the kinds of studies + + align:start position:0% +that mostly with the kinds of studies + + + align:start position:0% +that mostly with the kinds of studies +that we do that are representative of + + align:start position:0% +that we do that are representative of + + + align:start position:0% +that we do that are representative of +the material we're studying in class we + + align:start position:0% +the material we're studying in class we + + + align:start position:0% +the material we're studying in class we +don't have to get into that third + + align:start position:0% +don't have to get into that third + + + align:start position:0% +don't have to get into that third +category because we're not actually + + align:start position:0% +category because we're not actually + + + align:start position:0% +category because we're not actually +doing anything that is likely to harm + + align:start position:0% +doing anything that is likely to harm + + + align:start position:0% +doing anything that is likely to harm +individual patients except in a kind of + + align:start position:0% +individual patients except in a kind of + + + align:start position:0% +individual patients except in a kind of +reputational or data oriented sense and + + align:start position:0% +reputational or data oriented sense and + + + align:start position:0% +reputational or data oriented sense and +that doesn't require the full-blown + + align:start position:0% +that doesn't require the full-blown + + + align:start position:0% +that doesn't require the full-blown +review so that's the local situation ok + + align:start position:0% +review so that's the local situation ok + + + align:start position:0% +review so that's the local situation ok +yeah thank you I yeah I think I + + align:start position:0% +yeah thank you I yeah I think I + + + align:start position:0% +yeah thank you I yeah I think I +misunderstood the full range of the + + align:start position:0% +misunderstood the full range of the + + + align:start position:0% +misunderstood the full range of the +question yeah and that that's roughly + + align:start position:0% +question yeah and that that's roughly + + + align:start position:0% +question yeah and that that's roughly +our same thing so we have a Eddy golden + + align:start position:0% +our same thing so we have a Eddy golden + + + align:start position:0% +our same thing so we have a Eddy golden +as our research project manager who is + + align:start position:0% +as our research project manager who is + + + align:start position:0% +as our research project manager who is +my favorite person in the office it's + + align:start position:0% +my favorite person in the office it's + + + align:start position:0% +my favorite person in the office it's +kind of stuff she keeps on top of + + align:start position:0% +kind of stuff she keeps on top of + + + align:start position:0% +kind of stuff she keeps on top of +everything and make sure that the right + + align:start position:0% +everything and make sure that the right + + + align:start position:0% +everything and make sure that the right +people are listed on research and that + + align:start position:0% +people are listed on research and that + + + align:start position:0% +people are listed on research and that +people are taken off that kind of stuff + + align:start position:0% +people are taken off that kind of stuff + + + align:start position:0% +people are taken off that kind of stuff +but it's it's a good relationship with + + align:start position:0% +but it's it's a good relationship with + + + align:start position:0% +but it's it's a good relationship with +the IRB on that kind of stuff yeah + + align:start position:0% +the IRB on that kind of stuff yeah + + + align:start position:0% +the IRB on that kind of stuff yeah +that's one was unfamiliar with agile + + align:start position:0% +that's one was unfamiliar with agile + + + align:start position:0% +that's one was unfamiliar with agile +software development practices on a high + + align:start position:0% +software development practices on a high + + + align:start position:0% +software development practices on a high +level it's just more parallelized yeah + + align:start position:0% +level it's just more parallelized yeah + + + align:start position:0% +level it's just more parallelized yeah +yeah yeah and I don't know if I took + + align:start position:0% +yeah yeah and I don't know if I took + + + align:start position:0% +yeah yeah and I don't know if I took +that slide out but there's there's + + align:start position:0% +that slide out but there's there's + + + align:start position:0% +that slide out but there's there's +something where you know Amazon will + + align:start position:0% +something where you know Amazon will + + + align:start position:0% +something where you know Amazon will +deploy 50 million updates per year or + + align:start position:0% +deploy 50 million updates per year or + + + align:start position:0% +deploy 50 million updates per year or +something like that so it's it's + + align:start position:0% +something like that so it's it's + + + align:start position:0% +something like that so it's it's +constantly on an update frequency + + align:start position:0% +constantly on an update frequency + + + align:start position:0% +constantly on an update frequency +instead of yet just do like building + + align:start position:0% +instead of yet just do like building + + + align:start position:0% +instead of yet just do like building +everything out them and dropping it and + + align:start position:0% +everything out them and dropping it and + + + align:start position:0% +everything out them and dropping it and +that's that's just been a new + + align:start position:0% +that's that's just been a new + + + align:start position:0% +that's that's just been a new +development in software can you tell us + + align:start position:0% +development in software can you tell us + + + align:start position:0% +development in software can you tell us +more about electro labs I just I + + align:start position:0% +more about electro labs I just I + + + align:start position:0% +more about electro labs I just I +couldn't fully understand like are you + + align:start position:0% +couldn't fully understand like are you + + + align:start position:0% +couldn't fully understand like are you +guys more a consultancy for like all + + align:start position:0% +guys more a consultancy for like all + + + align:start position:0% +guys more a consultancy for like all +these companies or is it more like a + + align:start position:0% +these companies or is it more like a + + + align:start position:0% +these companies or is it more like a +lobbying kind of thing and then like and + + align:start position:0% +lobbying kind of thing and then like and + + + align:start position:0% +lobbying kind of thing and then like and +the reason I ask this is also cuz I + + align:start position:0% +the reason I ask this is also cuz I + + + align:start position:0% +the reason I ask this is also cuz I +wonder what your opinion is on like a + + align:start position:0% +wonder what your opinion is on like a + + + align:start position:0% +wonder what your opinion is on like a +third-party source for like kind of + + align:start position:0% +third-party source for like kind of + + + align:start position:0% +third-party source for like kind of +determining whether these things are + + align:start position:0% +determining whether these things are + + + align:start position:0% +determining whether these things are +like good or bad kind of thing because + + align:start position:0% +like good or bad kind of thing because + + + align:start position:0% +like good or bad kind of thing because +it seems like the FDA would have trouble + + align:start position:0% +it seems like the FDA would have trouble + + + align:start position:0% +it seems like the FDA would have trouble +understand so if you had some like + + align:start position:0% +understand so if you had some like + + + align:start position:0% +understand so if you had some like +organic certified kind of thing would + + align:start position:0% +organic certified kind of thing would + + + align:start position:0% +organic certified kind of thing would +that be a useful solution or where does + + align:start position:0% +that be a useful solution or where does + + + align:start position:0% +that be a useful solution or where does +that go wrong mm-hmm yeah so what we're + + align:start position:0% +that go wrong mm-hmm yeah so what we're + + + align:start position:0% +that go wrong mm-hmm yeah so what we're +building with Elektra is effectively a + + align:start position:0% +building with Elektra is effectively a + + + align:start position:0% +building with Elektra is effectively a +pharmacy for connecting technologies so + + align:start position:0% +pharmacy for connecting technologies so + + + align:start position:0% +pharmacy for connecting technologies so +the way that more like today you have + + align:start position:0% +the way that more like today you have + + + align:start position:0% +the way that more like today you have +pharmacies that have a formulary of all + + align:start position:0% +pharmacies that have a formulary of all + + + align:start position:0% +pharmacies that have a formulary of all +the different drugs that are available + + align:start position:0% +the different drugs that are available + + + align:start position:0% +the different drugs that are available +this is effectively like a digital + + align:start position:0% +this is effectively like a digital + + + align:start position:0% +this is effectively like a digital +pharmacy like a kelly blue book of all + + align:start position:0% +pharmacy like a kelly blue book of all + + + align:start position:0% +pharmacy like a kelly blue book of all +the different tools and then we're + + align:start position:0% +the different tools and then we're + + + align:start position:0% +the different tools and then we're +building out a label for each of them + + align:start position:0% +building out a label for each of them + + + align:start position:0% +building out a label for each of them +based on as much objective data as we + + align:start position:0% +based on as much objective data as we + + + align:start position:0% +based on as much objective data as we +can so that we're not scoring whether or + + align:start position:0% +can so that we're not scoring whether or + + + align:start position:0% +can so that we're not scoring whether or +not something's good or bad because in + + align:start position:0% +not something's good or bad because in + + + align:start position:0% +not something's good or bad because in +most instances things aren't good or bad + + align:start position:0% +most instances things aren't good or bad + + + align:start position:0% +most instances things aren't good or bad +and absolute they're good or bad for a + + align:start position:0% +and absolute they're good or bad for a + + + align:start position:0% +and absolute they're good or bad for a +purpose and so you can imagine something + + align:start position:0% +purpose and so you can imagine something + + + align:start position:0% +purpose and so you can imagine something +maybe you need really high levels of + + align:start position:0% +maybe you need really high levels of + + + align:start position:0% +maybe you need really high levels of +accuracy so you need to know whether or + + align:start position:0% +accuracy so you need to know whether or + + + align:start position:0% +accuracy so you need to know whether or +not that tool has been verified and + + align:start position:0% +not that tool has been verified and + + + align:start position:0% +not that tool has been verified and +validated in certain contexts and + + align:start position:0% +validated in certain contexts and + + + align:start position:0% +validated in certain contexts and +certain patient populations even if the + + align:start position:0% +certain patient populations even if the + + + align:start position:0% +certain patient populations even if the +tools accurate if you have to recharge + + align:start position:0% +tools accurate if you have to recharge + + + align:start position:0% +tools accurate if you have to recharge +it all the time or you can't we're in + + align:start position:0% +it all the time or you can't we're in + + + align:start position:0% +it all the time or you can't we're in +the shower you won't have the usability + + align:start position:0% +the shower you won't have the usability + + + align:start position:0% +the shower you won't have the usability +or if the api's are really hard to work + + align:start position:0% +or if the api's are really hard to work + + + align:start position:0% +or if the api's are really hard to work +with and then security profile whether + + align:start position:0% +with and then security profile whether + + + align:start position:0% +with and then security profile whether +or not they have coordinated disclosure + + align:start position:0% +or not they have coordinated disclosure + + + align:start position:0% +or not they have coordinated disclosure +how they handle things like the tool + + align:start position:0% +how they handle things like the tool + + + align:start position:0% +how they handle things like the tool +companies like a software building + + align:start position:0% +companies like a software building + + + align:start position:0% +companies like a software building +materials and what kind of software is + + align:start position:0% +materials and what kind of software is + + + align:start position:0% +materials and what kind of software is +used and then even if the tools accurate + + align:start position:0% +used and then even if the tools accurate + + + align:start position:0% +used and then even if the tools accurate +even if it's relatively usable even if + + align:start position:0% +even if it's relatively usable even if + + + align:start position:0% +even if it's relatively usable even if +it's secure + + align:start position:0% +it's secure + + + align:start position:0% +it's secure +that doesn't solve the Cambridge + + align:start position:0% +that doesn't solve the Cambridge + + + align:start position:0% +that doesn't solve the Cambridge +analytical problems so like how tools + + align:start position:0% +analytical problems so like how tools + + + align:start position:0% +analytical problems so like how tools +are doing third-party transfer and so we + + align:start position:0% +are doing third-party transfer and so we + + + align:start position:0% +are doing third-party transfer and so we +when the philosophies is we don't like + + align:start position:0% +when the philosophies is we don't like + + + align:start position:0% +when the philosophies is we don't like +score but we are building out the data + + align:start position:0% +score but we are building out the data + + + align:start position:0% +score but we are building out the data +set so when you are evaluating a certain + + align:start position:0% +set so when you are evaluating a certain + + + align:start position:0% +set so when you are evaluating a certain +tool you it's it's like a nutrition + + align:start position:0% +tool you it's it's like a nutrition + + + align:start position:0% +tool you it's it's like a nutrition +label like sometimes you need more sugar + + align:start position:0% +label like sometimes you need more sugar + + + align:start position:0% +label like sometimes you need more sugar +sometimes you need more protein maybe + + align:start position:0% +sometimes you need more protein maybe + + + align:start position:0% +sometimes you need more protein maybe +you need more security maybe you really + + align:start position:0% +you need more security maybe you really + + + align:start position:0% +you need more security maybe you really +need to think about the data rates maybe + + align:start position:0% +need to think about the data rates maybe + + + align:start position:0% +need to think about the data rates maybe +you can take a leave on some of the + + align:start position:0% +you can take a leave on some of the + + + align:start position:0% +you can take a leave on some of the +accuracy levels and so we're building + + align:start position:0% +accuracy levels and so we're building + + + align:start position:0% +accuracy levels and so we're building +out this ability to evaluate the tools + + align:start position:0% +out this ability to evaluate the tools + + + align:start position:0% +out this ability to evaluate the tools +and then also to deploy them like the + + align:start position:0% +and then also to deploy them like the + + + align:start position:0% +and then also to deploy them like the +way that a pharmacy would deploy them + + align:start position:0% +way that a pharmacy would deploy them + + + align:start position:0% +way that a pharmacy would deploy them +out um one thing I would like to do with + + align:start position:0% +out um one thing I would like to do with + + + align:start position:0% +out um one thing I would like to do with +the group if you all are down for it out + + align:start position:0% +the group if you all are down for it out + + + align:start position:0% +the group if you all are down for it out +of civic duty and I'm serious though + + align:start position:0% + + + + align:start position:0% + +voting is very important and submitting + + align:start position:0% +voting is very important and submitting + + + align:start position:0% +voting is very important and submitting +your comments to the public register is + + align:start position:0% +your comments to the public register is + + + align:start position:0% +your comments to the public register is +very important and I read all your + + align:start position:0% +very important and I read all your + + + align:start position:0% +very important and I read all your +comments because Irene sent them to me + + align:start position:0% +comments because Irene sent them to me + + + align:start position:0% +comments because Irene sent them to me +and they're very good and I know + + align:start position:0% +and they're very good and I know + + + align:start position:0% +and they're very good and I know +probably people who came here want to + + align:start position:0% +probably people who came here want to + + + align:start position:0% +probably people who came here want to +like polish everything and make them + + align:start position:0% +like polish everything and make them + + + align:start position:0% +like polish everything and make them +perfect you can submit them exactly how + + align:start position:0% +perfect you can submit them exactly how + + + align:start position:0% +perfect you can submit them exactly how +they are and I am very much hoping that + + align:start position:0% +they are and I am very much hoping that + + + align:start position:0% +they are and I am very much hoping that +we get about 95% of you to submit and + + align:start position:0% +we get about 95% of you to submit and + + + align:start position:0% +we get about 95% of you to submit and +the 5% of you that didn't like your + + align:start position:0% +the 5% of you that didn't like your + + + align:start position:0% +the 5% of you that didn't like your +internet broke or something + + align:start position:0% +internet broke or something + + + align:start position:0% +internet broke or something +you can submit tonight I will email + + align:start position:0% +you can submit tonight I will email + + + align:start position:0% +you can submit tonight I will email +Irene because you already have done the + + align:start position:0% +Irene because you already have done the + + + align:start position:0% +Irene because you already have done the +work and you can submit it but I would + + align:start position:0% +work and you can submit it but I would + + + align:start position:0% +work and you can submit it but I would +like to just hear some of your thoughts + + align:start position:0% +like to just hear some of your thoughts + + + align:start position:0% +like to just hear some of your thoughts +so what I'm gonna do is I'm gonna use + + align:start position:0% +so what I'm gonna do is I'm gonna use + + + align:start position:0% +so what I'm gonna do is I'm gonna use +that same framework around what would + + align:start position:0% +that same framework around what would + + + align:start position:0% +that same framework around what would +you keep what would you change and then + + align:start position:0% +you keep what would you change and then + + + align:start position:0% +you keep what would you change and then +change can also include like what was so + + align:start position:0% +change can also include like what was so + + + align:start position:0% +change can also include like what was so +confusing and there that like it didn't + + align:start position:0% +confusing and there that like it didn't + + + align:start position:0% +confusing and there that like it didn't +even really make sense part of the + + align:start position:0% +even really make sense part of the + + + align:start position:0% +even really make sense part of the +confusion might be that it was you know + + align:start position:0% +confusion might be that it was you know + + + align:start position:0% +confusion might be that it was you know +some regulations are confusing but some + + align:start position:0% +some regulations are confusing but some + + + align:start position:0% +some regulations are confusing but some +of the confusion is that part of that + + align:start position:0% +of the confusion is that part of that + + + align:start position:0% +of the confusion is that part of that +document was not written by people who + + align:start position:0% +document was not written by people who + + + align:start position:0% +document was not written by people who +some some people have technical + + align:start position:0% +some some people have technical + + + align:start position:0% +some some people have technical +backgrounds and some do not + + align:start position:0% +backgrounds and some do not + + + align:start position:0% +backgrounds and some do not +and so sometimes some of the language + + align:start position:0% +and so sometimes some of the language + + + align:start position:0% +and so sometimes some of the language +might not actually be used in the way + + align:start position:0% +might not actually be used in the way + + + align:start position:0% +might not actually be used in the way +that industry is using it today so + + align:start position:0% +that industry is using it today so + + + align:start position:0% +that industry is using it today so +refining the language and then what did + + align:start position:0% +refining the language and then what did + + + align:start position:0% +refining the language and then what did +you see that was missing so here's what + + align:start position:0% +you see that was missing so here's what + + + align:start position:0% +you see that was missing so here's what +we're gonna do keep + + align:start position:0% + + + + align:start position:0% + +change / confusing and then like start + + align:start position:0% +change / confusing and then like start + + + align:start position:0% +change / confusing and then like start +or add and before I ask you I want you + + align:start position:0% +or add and before I ask you I want you + + + align:start position:0% +or add and before I ask you I want you +to look at the person next to you + + align:start position:0% +to look at the person next to you + + + align:start position:0% +to look at the person next to you +seriously and if there's three of you + + align:start position:0% +seriously and if there's three of you + + + align:start position:0% +seriously and if there's three of you +that's fine and I want you to tell them + + align:start position:0% +that's fine and I want you to tell them + + + align:start position:0% +that's fine and I want you to tell them +when you will be submitting the comment + + align:start position:0% +when you will be submitting the comment + + + align:start position:0% +when you will be submitting the comment +is it tonight tomorrow or you are + + align:start position:0% +is it tonight tomorrow or you are + + + align:start position:0% +is it tonight tomorrow or you are +choosing not to just look at them and + + align:start position:0% +choosing not to just look at them and + + + align:start position:0% +choosing not to just look at them and +talk there will be a link I will send + + align:start position:0% +talk there will be a link I will send + + + align:start position:0% +talk there will be a link I will send +you all links I will make this very easy + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +all right who wants to start + + align:start position:0% +all right who wants to start + + + align:start position:0% +all right who wants to start +we got three things on the board yes for + + align:start position:0% +we got three things on the board yes for + + + align:start position:0% +we got three things on the board yes for +things like quality systems and machine + + align:start position:0% +things like quality systems and machine + + + align:start position:0% +things like quality systems and machine +learning facts a sir who sets those + + align:start position:0% +learning facts a sir who sets those + + + align:start position:0% +learning facts a sir who sets those +standards and how can they be a mm-hmm I + + align:start position:0% +standards and how can they be a mm-hmm I + + + align:start position:0% +standards and how can they be a mm-hmm I +don't also know that answer and so I + + align:start position:0% +don't also know that answer and so I + + + align:start position:0% +don't also know that answer and so I +would like you to submit one of the + + align:start position:0% +would like you to submit one of the + + + align:start position:0% +would like you to submit one of the +things that is nice is then they that + + align:start position:0% +things that is nice is then they that + + + align:start position:0% +things that is nice is then they that +you have to respond yeah and I think + + align:start position:0% +you have to respond yeah and I think + + + align:start position:0% +you have to respond yeah and I think +it's also a little bit confusing even + + align:start position:0% +it's also a little bit confusing even + + + align:start position:0% +it's also a little bit confusing even +the language so people are using + + align:start position:0% +the language so people are using + + + align:start position:0% +the language so people are using +different things so it was like good + + align:start position:0% +different things so it was like good + + + align:start position:0% +different things so it was like good +people call it GXP good manufacturing + + align:start position:0% +people call it GXP good manufacturing + + + align:start position:0% +people call it GXP good manufacturing +practice good clinical practice these + + align:start position:0% +practice good clinical practice these + + + align:start position:0% +practice good clinical practice these +are maintained I think in some instances + + align:start position:0% +are maintained I think in some instances + + + align:start position:0% +are maintained I think in some instances +by different orgs I wonder if good + + align:start position:0% +by different orgs I wonder if good + + + align:start position:0% +by different orgs I wonder if good +algorithm practice gap or good machine + + align:start position:0% +algorithm practice gap or good machine + + + align:start position:0% +algorithm practice gap or good machine +learning practice like whoo yeah that's + + align:start position:0% +learning practice like whoo yeah that's + + + align:start position:0% +learning practice like whoo yeah that's +a good thing so who owns GXP okay + + align:start position:0% + + + + align:start position:0% + +yes you didn't have a question no yes + + align:start position:0% + + + + align:start position:0% + +like that examples are helpful yep we + + align:start position:0% +like that examples are helpful yep we + + + align:start position:0% +like that examples are helpful yep we +should generally adhere to guidelines as + + align:start position:0% +should generally adhere to guidelines as + + + align:start position:0% +should generally adhere to guidelines as +opposed to this is the exact not be + + align:start position:0% +opposed to this is the exact not be + + + align:start position:0% +opposed to this is the exact not be +transparent and so if those are as + + align:start position:0% +transparent and so if those are as + + + align:start position:0% +transparent and so if those are as +specific I worried it + + align:start position:0% + + + + align:start position:0% + +the analyte that I thought it was sort + + align:start position:0% +the analyte that I thought it was sort + + + align:start position:0% +the analyte that I thought it was sort +of like Quentin Facebook a smear data + + align:start position:0% +of like Quentin Facebook a smear data + + + align:start position:0% +of like Quentin Facebook a smear data +they sort of say here are the things + + align:start position:0% +they sort of say here are the things + + + align:start position:0% +they sort of say here are the things +that we need or that we're using a very + + align:start position:0% +that we need or that we're using a very + + + align:start position:0% +that we need or that we're using a very +explicit event even have a choice of + + align:start position:0% +explicit event even have a choice of + + + align:start position:0% +explicit event even have a choice of +like whether or not you actually want + + align:start position:0% +like whether or not you actually want + + + align:start position:0% +like whether or not you actually want +that mmm okay so part of it is like + + align:start position:0% +that mmm okay so part of it is like + + + align:start position:0% +that mmm okay so part of it is like +transparency but I also like user choice + + align:start position:0% +transparency but I also like user choice + + + align:start position:0% +transparency but I also like user choice +and data selection or yes yep at the + + align:start position:0% +and data selection or yes yep at the + + + align:start position:0% +and data selection or yes yep at the +very least saying this algorithm is + + align:start position:0% +very least saying this algorithm is + + + align:start position:0% +very least saying this algorithm is +using this you know and and and maybe + + align:start position:0% +using this you know and and and maybe + + + align:start position:0% +using this you know and and and maybe +some sort of choice so you can sort of + + align:start position:0% +some sort of choice so you can sort of + + + align:start position:0% +some sort of choice so you can sort of +work with someone maybe there's some + + align:start position:0% +work with someone maybe there's some + + + align:start position:0% +work with someone maybe there's some +parameters around what you would or + + align:start position:0% +parameters around what you would or + + + align:start position:0% +parameters around what you would or +would not that's okay yep yes + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah my I don't know if I slept enough + + align:start position:0% +yeah my I don't know if I slept enough + + + align:start position:0% +yeah my I don't know if I slept enough +so if I just gave this example about a + + align:start position:0% +so if I just gave this example about a + + + align:start position:0% +so if I just gave this example about a +friend of mine called me last week and + + align:start position:0% +friend of mine called me last week and + + + align:start position:0% +friend of mine called me last week and +asked for PPG's so these the the sensor + + align:start position:0% +asked for PPG's so these the the sensor + + + align:start position:0% +asked for PPG's so these the the sensor +on the back she was asking me if it + + align:start position:0% +on the back she was asking me if it + + + align:start position:0% +on the back she was asking me if it +works on all skin colors and whether or + + align:start position:0% +works on all skin colors and whether or + + + align:start position:0% +works on all skin colors and whether or +not it responds differently and if it + + align:start position:0% +not it responds differently and if it + + + align:start position:0% +not it responds differently and if it +responds differently whether or not + + align:start position:0% +responds differently whether or not + + + align:start position:0% +responds differently whether or not +somebody has a tattoo and so for some of + + align:start position:0% +somebody has a tattoo and so for some of + + + align:start position:0% +somebody has a tattoo and so for some of +the big registries that are doing + + align:start position:0% +the big registries that are doing + + + align:start position:0% +the big registries that are doing +bring-your-own-device data you can have + + align:start position:0% +bring-your-own-device data you can have + + + align:start position:0% +bring-your-own-device data you can have +unintended biases in the data sets just + + align:start position:0% +unintended biases in the data sets just + + + align:start position:0% +unintended biases in the data sets just +because of how that it's processing so + + align:start position:0% +because of how that it's processing so + + + align:start position:0% +because of how that it's processing so +yeah what do you think how do you think + + align:start position:0% +yeah what do you think how do you think + + + align:start position:0% +yeah what do you think how do you think +what are ways I mean I think Irene's + + align:start position:0% +what are ways I mean I think Irene's + + + align:start position:0% +what are ways I mean I think Irene's +worked with some of this how would how + + align:start position:0% +worked with some of this how would how + + + align:start position:0% +worked with some of this how would how +do you think about whether or not + + align:start position:0% +do you think about whether or not + + + align:start position:0% +do you think about whether or not +something is what would be a good system + + align:start position:0% +something is what would be a good system + + + align:start position:0% +something is what would be a good system +for the agency to consider around bias + + align:start position:0% + + + + align:start position:0% + +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +yeah there can also be sort of like a + + align:start position:0% +yeah there can also be sort of like a + + + align:start position:0% +yeah there can also be sort of like a +scorecard of have you seen any places + + align:start position:0% +scorecard of have you seen any places + + + align:start position:0% +scorecard of have you seen any places +that do something like that when you do + + align:start position:0% +that do something like that when you do + + + align:start position:0% +that do something like that when you do +submit your comment if you have ideas or + + align:start position:0% +submit your comment if you have ideas or + + + align:start position:0% +submit your comment if you have ideas or +links or it can be like posts or blogs + + align:start position:0% +links or it can be like posts or blogs + + + align:start position:0% +links or it can be like posts or blogs +or whatever just like link them in + + align:start position:0% +or whatever just like link them in + + + align:start position:0% +or whatever just like link them in +because one thing that you'll find is + + align:start position:0% +because one thing that you'll find is + + + align:start position:0% +because one thing that you'll find is +that you know we we read a lot of things + + align:start position:0% +that you know we we read a lot of things + + + align:start position:0% +that you know we we read a lot of things +probably the same things on Twitter but + + align:start position:0% +probably the same things on Twitter but + + + align:start position:0% +probably the same things on Twitter but +other groups don't necessarily see all + + align:start position:0% +other groups don't necessarily see all + + + align:start position:0% +other groups don't necessarily see all +of that so I think that Kathy O'Neil is + + align:start position:0% +of that so I think that Kathy O'Neil is + + + align:start position:0% +of that so I think that Kathy O'Neil is +really interesting work um but yeah just + + align:start position:0% +really interesting work um but yeah just + + + align:start position:0% +really interesting work um but yeah just +like tag stuff it doesn't have to be + + align:start position:0% +like tag stuff it doesn't have to be + + + align:start position:0% +like tag stuff it doesn't have to be +formatted amazing some of the + + align:start position:0% +formatted amazing some of the + + + align:start position:0% +formatted amazing some of the +communities that I follow not on Twitter + + align:start position:0% +communities that I follow not on Twitter + + + align:start position:0% +communities that I follow not on Twitter +but you know and and on the web there's + + align:start position:0% +but you know and and on the web there's + + + align:start position:0% +but you know and and on the web there's +been a lot of discussion about really + + align:start position:0% +been a lot of discussion about really + + + align:start position:0% +been a lot of discussion about really +terrible design of information systems + + align:start position:0% +terrible design of information systems + + + align:start position:0% +terrible design of information systems +in hospitals and how these lead to her + + align:start position:0% +in hospitals and how these lead to her + + + align:start position:0% +in hospitals and how these lead to her +now I know from your slide Andy that the + + align:start position:0% +now I know from your slide Andy that the + + + align:start position:0% +now I know from your slide Andy that the +FDA has defined those to be out of its + + align:start position:0% +FDA has defined those to be out of its + + + align:start position:0% +FDA has defined those to be out of its +purview but in it seems to me that + + align:start position:0% +purview but in it seems to me that + + + align:start position:0% +purview but in it seems to me that +there's probably at the moment more harm + + align:start position:0% +there's probably at the moment more harm + + + align:start position:0% +there's probably at the moment more harm +being done by information systems that + + align:start position:0% +being done by information systems that + + + align:start position:0% +being done by information systems that +encourage really bad practice or that + + align:start position:0% +encourage really bad practice or that + + + align:start position:0% +encourage really bad practice or that +allowed Brad practice then there is by + + align:start position:0% +allowed Brad practice then there is by + + + align:start position:0% +allowed Brad practice then there is by +you know retinopathy AI machine learning + + align:start position:0% +you know retinopathy AI machine learning + + + align:start position:0% +you know retinopathy AI machine learning +techniques that make mistakes so just + + align:start position:0% +techniques that make mistakes so just + + + align:start position:0% +techniques that make mistakes so just +this morning for example somebody posted + + align:start position:0% +this morning for example somebody posted + + + align:start position:0% +this morning for example somebody posted +a message about a patient who had a a + + align:start position:0% +a message about a patient who had a a + + + align:start position:0% +a message about a patient who had a a +heart rate of 12,000 which seems + + align:start position:0% +heart rate of 12,000 which seems + + + align:start position:0% +heart rate of 12,000 which seems +extremely oh and the problem is that + + align:start position:0% +extremely oh and the problem is that + + + align:start position:0% +extremely oh and the problem is that +that when you start automating processes + + align:start position:0% +that when you start automating processes + + + align:start position:0% +that when you start automating processes +that are based on the information that + + align:start position:0% +that are based on the information that + + + align:start position:0% +that are based on the information that +is collected in these systems things can + + align:start position:0% +is collected in these systems things can + + + align:start position:0% +is collected in these systems things can +go really screwy when you get garbage + + align:start position:0% +go really screwy when you get garbage + + + align:start position:0% +go really screwy when you get garbage +data and we cannot get good data + + align:start position:0% +data and we cannot get good data + + + align:start position:0% +data and we cannot get good data +I mean you you're not gonna get good + + align:start position:0% +I mean you you're not gonna get good + + + align:start position:0% +I mean you you're not gonna get good +data out of the system any what you're + + align:start position:0% +data out of the system any what you're + + + align:start position:0% +data out of the system any what you're +seeing is across the board and there's + + align:start position:0% +seeing is across the board and there's + + + align:start position:0% +seeing is across the board and there's +there's not much you can do about it + + align:start position:0% +there's not much you can do about it + + + align:start position:0% +there's not much you can do about it +other than validate good ranges and kind + + align:start position:0% +other than validate good ranges and kind + + + align:start position:0% +other than validate good ranges and kind +of go from there well I can think of + + align:start position:0% +of go from there well I can think of + + + align:start position:0% +of go from there well I can think of +things to do for example if if FDA were + + align:start position:0% +things to do for example if if FDA were + + + align:start position:0% +things to do for example if if FDA were +interested in regulating such devices or + + align:start position:0% +interested in regulating such devices or + + + align:start position:0% +interested in regulating such devices or +such oh sorry + + align:start position:0% +such oh sorry + + + align:start position:0% +such oh sorry +tools well they would regulate devices + + align:start position:0% +tools well they would regulate devices + + + align:start position:0% +tools well they would regulate devices +so one of the funny things with FDA is + + align:start position:0% +so one of the funny things with FDA is + + + align:start position:0% +so one of the funny things with FDA is +and I should have mentioned this is the + + align:start position:0% +and I should have mentioned this is the + + + align:start position:0% +and I should have mentioned this is the +FDA does not regulate the practice of + + align:start position:0% +FDA does not regulate the practice of + + + align:start position:0% +FDA does not regulate the practice of +medicine so doctors can do whatever they + + align:start position:0% +medicine so doctors can do whatever they + + + align:start position:0% +medicine so doctors can do whatever they +want and it is it they regulate well I + + align:start position:0% +want and it is it they regulate well I + + + align:start position:0% +want and it is it they regulate well I +mean you should look up exactly the way + + align:start position:0% +mean you should look up exactly the way + + + align:start position:0% +mean you should look up exactly the way +I interpret it is they regulate the + + align:start position:0% +I interpret it is they regulate the + + + align:start position:0% +I interpret it is they regulate the +marketing that a manufacturer would do + + align:start position:0% +marketing that a manufacturer would do + + + align:start position:0% +marketing that a manufacturer would do +so I actually wonder if the EHRs would + + align:start position:0% +so I actually wonder if the EHRs would + + + align:start position:0% +so I actually wonder if the EHRs would +be considered practice in medicine or if + + align:start position:0% +be considered practice in medicine or if + + + align:start position:0% +be considered practice in medicine or if +it would be a marketing from the EHR + + align:start position:0% +it would be a marketing from the EHR + + + align:start position:0% +it would be a marketing from the EHR +company and maybe that's how it could be + + align:start position:0% +company and maybe that's how it could be + + + align:start position:0% +company and maybe that's how it could be +under the purview yeah yeah + + align:start position:0% +under the purview yeah yeah + + + align:start position:0% +under the purview yeah yeah +that's yeah yes okay yeah + + align:start position:0% + + + + align:start position:0% + +realistically how many of you do you + + align:start position:0% +realistically how many of you do you + + + align:start position:0% +realistically how many of you do you +think you will actually submit a comment + + align:start position:0% +think you will actually submit a comment + + + align:start position:0% +think you will actually submit a comment +a couple so if you if you're thinking + + align:start position:0% +a couple so if you if you're thinking + + + align:start position:0% +a couple so if you if you're thinking +you wouldn't submit a comment what just + + align:start position:0% +you wouldn't submit a comment what just + + + align:start position:0% +you wouldn't submit a comment what just +out of curiosity I won't argue you it + + align:start position:0% +out of curiosity I won't argue you it + + + align:start position:0% +out of curiosity I won't argue you it +and I'm just curious what would hold you + + align:start position:0% +and I'm just curious what would hold you + + + align:start position:0% +and I'm just curious what would hold you +back from submitting a comment you + + align:start position:0% +back from submitting a comment you + + + align:start position:0% +back from submitting a comment you +didn't raise your hand now I get to cold + + align:start position:0% +didn't raise your hand now I get to cold + + + align:start position:0% +didn't raise your hand now I get to cold +call you yes + + align:start position:0% +call you yes + + + align:start position:0% +call you yes +[Music] + + align:start position:0% + + + + align:start position:0% + +you really want to submit + + align:start position:0% + + + + align:start position:0% + +okay okay okay so what while Andy is + + align:start position:0% +okay okay okay so what while Andy is + + + align:start position:0% +okay okay okay so what while Andy is +looking at up the I should say when the + + align:start position:0% +looking at up the I should say when the + + + align:start position:0% +looking at up the I should say when the +HIPAA regulations the privacy + + align:start position:0% +HIPAA regulations the privacy + + + align:start position:0% +HIPAA regulations the privacy +regulations were first proposed the + + align:start position:0% +regulations were first proposed the + + + align:start position:0% +regulations were first proposed the +initial version got 70,000 public + + align:start position:0% +initial version got 70,000 public + + + align:start position:0% +initial version got 70,000 public +comments about it and it is really true + + align:start position:0% +comments about it and it is really true + + + align:start position:0% +comments about it and it is really true +that the the regulatory agency in that + + align:start position:0% +that the the regulatory agency in that + + + align:start position:0% +that the the regulatory agency in that +case it was Health and Human Services + + align:start position:0% +case it was Health and Human Services + + + align:start position:0% +case it was Health and Human Services +had to respond to every one of those by + + align:start position:0% +had to respond to every one of those by + + + align:start position:0% +had to respond to every one of those by +law and so they published you know reams + + align:start position:0% +law and so they published you know reams + + + align:start position:0% +law and so they published you know reams +of paper about responding to all those + + align:start position:0% +of paper about responding to all those + + + align:start position:0% +of paper about responding to all those +requests so they will take your comments + + align:start position:0% +requests so they will take your comments + + + align:start position:0% +requests so they will take your comments +seriously because they have to + + align:start position:0% + + + + align:start position:0% + +anyway anonymously uh I don't know I + + align:start position:0% +anyway anonymously uh I don't know I + + + align:start position:0% +anyway anonymously uh I don't know I +think it's generally I think it I don't + + align:start position:0% +think it's generally I think it I don't + + + align:start position:0% +think it's generally I think it I don't +know I'd have to look at it again I + + align:start position:0% +know I'd have to look at it again I + + + align:start position:0% +know I'd have to look at it again I +think most of them are public comments I + + align:start position:0% +think most of them are public comments I + + + align:start position:0% +think most of them are public comments I +mean I guess if you wanted to maybe you + + align:start position:0% +mean I guess if you wanted to maybe you + + + align:start position:0% +mean I guess if you wanted to maybe you +could coordinate your comments and you + + align:start position:0% +could coordinate your comments and you + + + align:start position:0% +could coordinate your comments and you +could um would you yeah okay Irene is + + align:start position:0% +could um would you yeah okay Irene is + + + align:start position:0% +could um would you yeah okay Irene is +willing to group comment so you can also + + align:start position:0% +willing to group comment so you can also + + + align:start position:0% +willing to group comment so you can also +send if you'd like to do it that way and + + align:start position:0% +send if you'd like to do it that way and + + + align:start position:0% +send if you'd like to do it that way and +it can be like a set of class comments + + align:start position:0% +it can be like a set of class comments + + + align:start position:0% +it can be like a set of class comments +if you'd prefer the bitly is capital MIT + + align:start position:0% +if you'd prefer the bitly is capital MIT + + + align:start position:0% +if you'd prefer the bitly is capital MIT +all lowercase loves FDA will send you + + align:start position:0% +all lowercase loves FDA will send you + + + align:start position:0% +all lowercase loves FDA will send you +over to the docket I'm amazed that that + + align:start position:0% +over to the docket I'm amazed that that + + + align:start position:0% +over to the docket I'm amazed that that +bit we has not been taken already + + align:start position:0% + + + + align:start position:0% + +Eleazar has been asleep on the job + + align:start position:0% + + + + align:start position:0% + +what are the questions you all have yes + + align:start position:0% +what are the questions you all have yes + + + align:start position:0% +what are the questions you all have yes +what is the like line between like an HR + + align:start position:0% +what is the like line between like an HR + + + align:start position:0% +what is the like line between like an HR +and the same thing so because it's said + + align:start position:0% +and the same thing so because it's said + + + align:start position:0% +and the same thing so because it's said +earlier that HR is exempt except + + align:start position:0% +earlier that HR is exempt except + + + align:start position:0% +earlier that HR is exempt except +anything else it says Oh for example a + + align:start position:0% +anything else it says Oh for example a + + + align:start position:0% +anything else it says Oh for example a +family could be you know fizzy what + + align:start position:0% +family could be you know fizzy what + + + align:start position:0% +family could be you know fizzy what +things in the electrical signals and + + align:start position:0% +things in the electrical signals and + + + align:start position:0% +things in the electrical signals and +then they might send an audible alarm to + + align:start position:0% +then they might send an audible alarm to + + + align:start position:0% +then they might send an audible alarm to +indicate copter click and my + + align:start position:0% +indicate copter click and my + + + align:start position:0% +indicate copter click and my +understanding is some of you a charge do + + align:start position:0% +understanding is some of you a charge do + + + align:start position:0% +understanding is some of you a charge do +that and then and so when they need to + + align:start position:0% +that and then and so when they need to + + + align:start position:0% +that and then and so when they need to +be retro actively approved and partially + + align:start position:0% +be retro actively approved and partially + + + align:start position:0% +be retro actively approved and partially +you say my door yeah so I'm not a + + align:start position:0% +you say my door yeah so I'm not a + + + align:start position:0% +you say my door yeah so I'm not a +regulator so you should ask your + + align:start position:0% +regulator so you should ask your + + + align:start position:0% +regulator so you should ask your +regulator a couple resources that could + + align:start position:0% +regulator a couple resources that could + + + align:start position:0% +regulator a couple resources that could +help you decide this is again it's about + + align:start position:0% +help you decide this is again it's about + + + align:start position:0% +help you decide this is again it's about +what you're claiming the product does + + align:start position:0% +what you're claiming the product does + + + align:start position:0% +what you're claiming the product does +perhaps not what it actually does the + + align:start position:0% +perhaps not what it actually does the + + + align:start position:0% +perhaps not what it actually does the +next thing which I don't think I mean I + + align:start position:0% +next thing which I don't think I mean I + + + align:start position:0% +next thing which I don't think I mean I +think if it really does that you should + + align:start position:0% +think if it really does that you should + + + align:start position:0% +think if it really does that you should +like also claim that it does what it + + align:start position:0% +like also claim that it does what it + + + align:start position:0% +like also claim that it does what it +does especially if it's confusing for + + align:start position:0% +does especially if it's confusing for + + + align:start position:0% +does especially if it's confusing for +people + + align:start position:0% +people + + + align:start position:0% +people +the there's a couple of regulations that + + align:start position:0% +the there's a couple of regulations that + + + align:start position:0% +the there's a couple of regulations that +might be helpful one is called clinical + + align:start position:0% +might be helpful one is called clinical + + + align:start position:0% +might be helpful one is called clinical +decision support and if you read any FDA + + align:start position:0% +decision support and if you read any FDA + + + align:start position:0% +decision support and if you read any FDA +things they love their algorithms I mean + + align:start position:0% +things they love their algorithms I mean + + + align:start position:0% +things they love their algorithms I mean +they look they love their algorithms but + + align:start position:0% +they look they love their algorithms but + + + align:start position:0% +they look they love their algorithms but +they also love their acronyms so + + align:start position:0% +they also love their acronyms so + + + align:start position:0% +they also love their acronyms so +clinical decision support is C D s and + + align:start position:0% +clinical decision support is C D s and + + + align:start position:0% +clinical decision support is C D s and +then also patient decision support + + align:start position:0% +then also patient decision support + + + align:start position:0% +then also patient decision support +there's a guidance that just came out + + align:start position:0% +there's a guidance that just came out + + + align:start position:0% +there's a guidance that just came out +around the two types of decision support + + align:start position:0% +around the two types of decision support + + + align:start position:0% +around the two types of decision support +tools and I would guess maybe that is + + align:start position:0% +tools and I would guess maybe that is + + + align:start position:0% +tools and I would guess maybe that is +supporting a decision that EHR so it + + align:start position:0% +supporting a decision that EHR so it + + + align:start position:0% +supporting a decision that EHR so it +might actually be considered something + + align:start position:0% +might actually be considered something + + + align:start position:0% +might actually be considered something +that would be regulated there's also a + + align:start position:0% +that would be regulated there's also a + + + align:start position:0% +that would be regulated there's also a +lot of kind of weird that we didn't go + + align:start position:0% +lot of kind of weird that we didn't go + + + align:start position:0% +lot of kind of weird that we didn't go +into it but there are many instances + + align:start position:0% +into it but there are many instances + + + align:start position:0% +into it but there are many instances +where something might actually be a + + align:start position:0% +where something might actually be a + + + align:start position:0% +where something might actually be a +device and the FDA says it's a device + + align:start position:0% +device and the FDA says it's a device + + + align:start position:0% +device and the FDA says it's a device +but it will do something called + + align:start position:0% +but it will do something called + + + align:start position:0% +but it will do something called +enforcement discretion which says it's a + + align:start position:0% +enforcement discretion which says it's a + + + align:start position:0% +enforcement discretion which says it's a +device but we will not regulate it as + + align:start position:0% +device but we will not regulate it as + + + align:start position:0% +device but we will not regulate it as +such there's actually a little bit risky + + align:start position:0% +such there's actually a little bit risky + + + align:start position:0% +such there's actually a little bit risky +for a manufacturer because you are a + + align:start position:0% +for a manufacturer because you are a + + + align:start position:0% +for a manufacturer because you are a +device but you can now go straight to + + align:start position:0% +device but you can now go straight to + + + align:start position:0% +device but you can now go straight to +market and in some instances you still + + align:start position:0% +market and in some instances you still + + + align:start position:0% +market and in some instances you still +have to register and list the product + + align:start position:0% +have to register and list the product + + + align:start position:0% +have to register and list the product +but you don't have to necessarily get + + align:start position:0% +but you don't have to necessarily get + + + align:start position:0% +but you don't have to necessarily get +reviewed and it also could eventually be + + align:start position:0% +reviewed and it also could eventually be + + + align:start position:0% +reviewed and it also could eventually be +reviewed so the line of is a device the + + align:start position:0% +reviewed so the line of is a device the + + + align:start position:0% +reviewed so the line of is a device the +device thing you have to register is it + + align:start position:0% +device thing you have to register is it + + + align:start position:0% +device thing you have to register is it +a device you have to get cleared or + + align:start position:0% +a device you have to get cleared or + + + align:start position:0% +a device you have to get cleared or +approved is why you should early enough + + align:start position:0% +approved is why you should early enough + + + align:start position:0% +approved is why you should early enough +in yes + + align:start position:0% +in yes + + + align:start position:0% +in yes +I enjoyed your game with rejoice to + + align:start position:0% +I enjoyed your game with rejoice to + + + align:start position:0% +I enjoyed your game with rejoice to +pivot and + + align:start position:0% +pivot and + + + align:start position:0% +pivot and +I know that you're not Apple either but + + align:start position:0% +I know that you're not Apple either but + + + align:start position:0% +I know that you're not Apple either but +why do you think that + + align:start position:0% + + + + align:start position:0% + +I motivations + + align:start position:0% +I motivations + + + align:start position:0% +I motivations +would say in public documents Fitbit has + + align:start position:0% +would say in public documents Fitbit has + + + align:start position:0% +would say in public documents Fitbit has +expressed an interest in working with + + align:start position:0% +expressed an interest in working with + + + align:start position:0% +expressed an interest in working with +the FDA I don't know at what point they + + align:start position:0% +the FDA I don't know at what point they + + + align:start position:0% +the FDA I don't know at what point they +have decided what they submitted or had + + align:start position:0% +have decided what they submitted or had + + + align:start position:0% +have decided what they submitted or had +their package there they're also working + + align:start position:0% +their package there they're also working + + + align:start position:0% +their package there they're also working +with the pre cert program so I think I + + align:start position:0% +with the pre cert program so I think I + + + align:start position:0% +with the pre cert program so I think I +don't know what's happening behind the + + align:start position:0% +don't know what's happening behind the + + + align:start position:0% +don't know what's happening behind the +scenes yeah + + align:start position:0% + + + + align:start position:0% + +I cannot comment on that yeah yeah I + + align:start position:0% +I cannot comment on that yeah yeah I + + + align:start position:0% +I cannot comment on that yeah yeah I +would say generally people want to use + + align:start position:0% +would say generally people want to use + + + align:start position:0% +would say generally people want to use +tools that are trustworthy and + + align:start position:0% +tools that are trustworthy and + + + align:start position:0% +tools that are trustworthy and +developing more tools that have some + + align:start position:0% +developing more tools that have some + + + align:start position:0% +developing more tools that have some +body of evidence is a really important + + align:start position:0% +body of evidence is a really important + + + align:start position:0% +body of evidence is a really important +thing I think the FDA is one way of + + align:start position:0% +thing I think the FDA is one way of + + + align:start position:0% +thing I think the FDA is one way of +having evidence I think there are other + + align:start position:0% +having evidence I think there are other + + + align:start position:0% +having evidence I think there are other +ways that tools can contend devices can + + align:start position:0% +ways that tools can contend devices can + + + align:start position:0% +ways that tools can contend devices can +continue to build evidence my hope is + + align:start position:0% +continue to build evidence my hope is + + + align:start position:0% +continue to build evidence my hope is +over time that a lot of these things + + align:start position:0% +over time that a lot of these things + + + align:start position:0% +over time that a lot of these things +that we consider to be wellness tools + + align:start position:0% +that we consider to be wellness tools + + + align:start position:0% +that we consider to be wellness tools +also have evidence around them like + + align:start position:0% +also have evidence around them like + + + align:start position:0% +also have evidence around them like +maybe in some instances we don't always + + align:start position:0% +maybe in some instances we don't always + + + align:start position:0% +maybe in some instances we don't always +regulate vitamins but like you want to + + align:start position:0% +regulate vitamins but like you want to + + + align:start position:0% +regulate vitamins but like you want to +still trust that your vitamin doesn't + + align:start position:0% +still trust that your vitamin doesn't + + + align:start position:0% +still trust that your vitamin doesn't +have like sawdust in it right and that + + align:start position:0% +have like sawdust in it right and that + + + align:start position:0% +have like sawdust in it right and that +it's like a real product and so the more + + align:start position:0% +it's like a real product and so the more + + + align:start position:0% +it's like a real product and so the more +that we I think push companies to have + + align:start position:0% +that we I think push companies to have + + + align:start position:0% +that we I think push companies to have +evidence and that we use products that + + align:start position:0% +evidence and that we use products that + + + align:start position:0% +evidence and that we use products that +do that I hope over time this helps us + + align:start position:0% +do that I hope over time this helps us + + + align:start position:0% +do that I hope over time this helps us +does it give them any legal protection + + align:start position:0% +does it give them any legal protection + + + align:start position:0% +does it give them any legal protection +to have it be classified as an FDA + + align:start position:0% +to have it be classified as an FDA + + + align:start position:0% +to have it be classified as an FDA +device sure about that and I in + + align:start position:0% +device sure about that and I in + + + align:start position:0% +device sure about that and I in +historically it has helped with + + align:start position:0% +historically it has helped with + + + align:start position:0% +historically it has helped with +reimbursement so a class-2 product is + + align:start position:0% +reimbursement so a class-2 product is + + + align:start position:0% +reimbursement so a class-2 product is +kind of been easier to reimburse that + + align:start position:0% +kind of been easier to reimburse that + + + align:start position:0% +kind of been easier to reimburse that +also is generally changing but that + + align:start position:0% +also is generally changing but that + + + align:start position:0% +also is generally changing but that +helps with the business model around + + align:start position:0% +helps with the business model around + + + align:start position:0% +helps with the business model around +that yeah well I want to thank you both + + align:start position:0% +that yeah well I want to thank you both + + + align:start position:0% +that yeah well I want to thank you both +very much that was really interesting + + align:start position:0% +very much that was really interesting + + + align:start position:0% +very much that was really interesting +and I do encourage all of you to + + align:start position:0% +and I do encourage all of you to + + + align:start position:0% +and I do encourage all of you to +participate in this regulatory process + + align:start position:0% +participate in this regulatory process + + + align:start position:0% +participate in this regulatory process +by submitting your comments and I + + align:start position:0% +by submitting your comments and I + + + align:start position:0% +by submitting your comments and I +enjoyed the presentations thank you + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/kIl6LsJuxqI.txt b/kIl6LsJuxqI.txt new file mode 100644 index 0000000000000000000000000000000000000000..5e3bc1a87389f7d5fddd9903d7562af5f3ed5e65 --- /dev/null +++ b/kIl6LsJuxqI.txt @@ -0,0 +1,10176 @@ +align:start position:0% + +so um well last week's lecture four uh + + align:start position:0% +so um well last week's lecture four uh + + + align:start position:0% +so um well last week's lecture four uh +ended with the uh Le squares estimation + + align:start position:0% +ended with the uh Le squares estimation + + + align:start position:0% +ended with the uh Le squares estimation +and a hint of recursive Le squares and + + align:start position:0% +and a hint of recursive Le squares and + + + align:start position:0% +and a hint of recursive Le squares and +calman filter uh so those are topics + + align:start position:0% +calman filter uh so those are topics + + + align:start position:0% +calman filter uh so those are topics +we're coming back to um but the next + + align:start position:0% +we're coming back to um but the next + + + align:start position:0% +we're coming back to um but the next +step on the syllabus is to stay with the + + align:start position:0% +step on the syllabus is to stay with the + + + align:start position:0% +step on the syllabus is to stay with the +basic uh uh beginnings and in particular + + align:start position:0% +basic uh uh beginnings and in particular + + + align:start position:0% +basic uh uh beginnings and in particular +with igen Val + + align:start position:0% +with igen Val + + + align:start position:0% +with igen Val +so igen values and igen vectors and + + align:start position:0% +so igen values and igen vectors and + + + align:start position:0% +so igen values and igen vectors and +their uses in solving initial value + + align:start position:0% +their uses in solving initial value + + + align:start position:0% +their uses in solving initial value +problems so that's today's lecture and + + align:start position:0% +problems so that's today's lecture and + + + align:start position:0% +problems so that's today's lecture and +I've written on the board the sort of + + align:start position:0% +I've written on the board the sort of + + + align:start position:0% +I've written on the board the sort of +the most + + align:start position:0% +the most + + + align:start position:0% +the most +straightforward + + align:start position:0% +straightforward + + + align:start position:0% +straightforward +uh the approach to igen values uh so let + + align:start position:0% +uh the approach to igen values uh so let + + + align:start position:0% +uh the approach to igen values uh so let +me take these steps here's the key + + align:start position:0% +me take these steps here's the key + + + align:start position:0% +me take these steps here's the key +equation we're looking what does it say + + align:start position:0% +equation we're looking what does it say + + + align:start position:0% +equation we're looking what does it say +we're looking for a special Vector X + + align:start position:0% +we're looking for a special Vector X + + + align:start position:0% +we're looking for a special Vector X +so that when we multiply by a the result + + align:start position:0% +so that when we multiply by a the result + + + align:start position:0% +so that when we multiply by a the result +comes out in the same direction I mean I + + align:start position:0% +comes out in the same direction I mean I + + + align:start position:0% +comes out in the same direction I mean I +think of X as the input and ax as the + + align:start position:0% +think of X as the input and ax as the + + + align:start position:0% +think of X as the input and ax as the +output a is kind of a black box and uh + + align:start position:0% +output a is kind of a black box and uh + + + align:start position:0% +output a is kind of a black box and uh +normally uh the vector that comes out is + + align:start position:0% +normally uh the vector that comes out is + + + align:start position:0% +normally uh the vector that comes out is +head heads off in some different + + align:start position:0% +head heads off in some different + + + align:start position:0% +head heads off in some different +direction from the vector that comes in + + align:start position:0% +direction from the vector that comes in + + + align:start position:0% +direction from the vector that comes in +but for these special igen vectors ax is + + align:start position:0% +but for these special igen vectors ax is + + + align:start position:0% +but for these special igen vectors ax is +in the same direction as X just multiply + + align:start position:0% +in the same direction as X just multiply + + + align:start position:0% +in the same direction as X just multiply +IED by some Lambda and + + align:start position:0% +IED by some Lambda and + + + align:start position:0% +IED by some Lambda and +uh for example if Lambda is one then we + + align:start position:0% +uh for example if Lambda is one then we + + + align:start position:0% +uh for example if Lambda is one then we +have a steady state Vector ax equaling X + + align:start position:0% +have a steady state Vector ax equaling X + + + align:start position:0% +have a steady state Vector ax equaling X +the same Vector came out if Lambda is + + align:start position:0% +the same Vector came out if Lambda is + + + align:start position:0% +the same Vector came out if Lambda is +zero well then we still have an igen + + align:start position:0% +zero well then we still have an igen + + + align:start position:0% +zero well then we still have an igen +Vector notice Lambda equals z is a + + align:start position:0% +Vector notice Lambda equals z is a + + + align:start position:0% +Vector notice Lambda equals z is a +little bit interesting ax is then zero + + align:start position:0% +little bit interesting ax is then zero + + + align:start position:0% +little bit interesting ax is then zero +so that means an X in the null space is + + align:start position:0% +so that means an X in the null space is + + + align:start position:0% +so that means an X in the null space is +an igen Vector connected with the igen + + align:start position:0% +an igen Vector connected with the igen + + + align:start position:0% +an igen Vector connected with the igen +value zero + + align:start position:0% +value zero + + + align:start position:0% +value zero +or Lambda could be imaginary + + align:start position:0% +or Lambda could be imaginary + + + align:start position:0% +or Lambda could be imaginary +complex uh for we'll see that for + + align:start position:0% +complex uh for we'll see that for + + + align:start position:0% +complex uh for we'll see that for +symmetric matrices the igen values are + + align:start position:0% +symmetric matrices the igen values are + + + align:start position:0% +symmetric matrices the igen values are +always + + align:start position:0% +always + + + align:start position:0% +always +real and special facts too about the + + align:start position:0% +real and special facts too about the + + + align:start position:0% +real and special facts too about the +igen vectors okay so this is the the + + align:start position:0% +igen vectors okay so this is the the + + + align:start position:0% +igen vectors okay so this is the the +idea and and the reason behind it the + + align:start position:0% +idea and and the reason behind it the + + + align:start position:0% +idea and and the reason behind it the +reason it's a good thing is that for + + align:start position:0% +reason it's a good thing is that for + + + align:start position:0% +reason it's a good thing is that for +these vectors The Matrix with with all + + align:start position:0% +these vectors The Matrix with with all + + + align:start position:0% +these vectors The Matrix with with all +its n squ entries is just acting like a + + align:start position:0% +its n squ entries is just acting like a + + + align:start position:0% +its n squ entries is just acting like a +number if we if we if we can follow an + + align:start position:0% +number if we if we if we can follow an + + + align:start position:0% +number if we if we if we can follow an +igen Vector then only that single number + + align:start position:0% +igen Vector then only that single number + + + align:start position:0% +igen Vector then only that single number +Lambda is is going to come in it's + + align:start position:0% +Lambda is is going to come in it's + + + align:start position:0% +Lambda is is going to come in it's +acting like a 1 by one so it's terrific + + align:start position:0% +acting like a 1 by one so it's terrific + + + align:start position:0% +acting like a 1 by one so it's terrific +if we can find these x's and lambdas so + + align:start position:0% +if we can find these x's and lambdas so + + + align:start position:0% +if we can find these x's and lambdas so +in principle here's how to find them + + align:start position:0% +in principle here's how to find them + + + align:start position:0% +in principle here's how to find them +first just move that on to the other + + align:start position:0% +first just move that on to the other + + + align:start position:0% +first just move that on to the other +side of the + + align:start position:0% +side of the + + + align:start position:0% +side of the +equation now we + + align:start position:0% +equation now we + + + align:start position:0% +equation now we +recognize that we're asking this Matrix + + align:start position:0% +recognize that we're asking this Matrix + + + align:start position:0% +recognize that we're asking this Matrix +here to be singular this will have if if + + align:start position:0% +here to be singular this will have if if + + + align:start position:0% +here to be singular this will have if if +if there's a x that it takes to zero and + + align:start position:0% +if there's a x that it takes to zero and + + + align:start position:0% +if there's a x that it takes to zero and +of course we have no interest in the + + align:start position:0% +of course we have no interest in the + + + align:start position:0% +of course we have no interest in the +zero Vector so we're looking for a + + align:start position:0% +zero Vector so we're looking for a + + + align:start position:0% +zero Vector so we're looking for a +nonzero X then this Matrix must be + + align:start position:0% +nonzero X then this Matrix must be + + + align:start position:0% +nonzero X then this Matrix must be +singular its determinant must be zero + + align:start position:0% +singular its determinant must be zero + + + align:start position:0% +singular its determinant must be zero +and now we've got an + + align:start position:0% +and now we've got an + + + align:start position:0% +and now we've got an +equation uh this is a this determinant + + align:start position:0% +equation uh this is a this determinant + + + align:start position:0% +equation uh this is a this determinant +is a + + align:start position:0% +is a + + + align:start position:0% +is a +polom it starts out with minus Lambda to + + align:start position:0% +polom it starts out with minus Lambda to + + + align:start position:0% +polom it starts out with minus Lambda to +the N power and other terms equaling + + align:start position:0% +the N power and other terms equaling + + + align:start position:0% +the N power and other terms equaling +zero in other words it's an Nth + + align:start position:0% +zero in other words it's an Nth + + + align:start position:0% +zero in other words it's an Nth +Degree where n is the size of the + + align:start position:0% + + + + align:start position:0% + +Matrix uh you see what that determinant + + align:start position:0% +Matrix uh you see what that determinant + + + align:start position:0% +Matrix uh you see what that determinant +looks like it has minus lambdas down the + + align:start position:0% +looks like it has minus lambdas down the + + + align:start position:0% +looks like it has minus lambdas down the +diagonal so one of the the first term in + + align:start position:0% +diagonal so one of the the first term in + + + align:start position:0% +diagonal so one of the the first term in +the determinant will be minus Lambda + + align:start position:0% +the determinant will be minus Lambda + + + align:start position:0% +the determinant will be minus Lambda +time minus Lambda all the way down minus + + align:start position:0% +time minus Lambda all the way down minus + + + align:start position:0% +time minus Lambda all the way down minus +Lambda n * and then the other terms will + + align:start position:0% +Lambda n * and then the other terms will + + + align:start position:0% +Lambda n * and then the other terms will +involve lower power of Lambda but we've + + align:start position:0% +involve lower power of Lambda but we've + + + align:start position:0% +involve lower power of Lambda but we've +got a polom and it's got n Roots so + + align:start position:0% +got a polom and it's got n Roots so + + + align:start position:0% +got a polom and it's got n Roots so +these are these are the N roots and + + align:start position:0% +these are these are the N roots and + + + align:start position:0% +these are these are the N roots and +those roots are the igen values and + + align:start position:0% +those roots are the igen values and + + + align:start position:0% +those roots are the igen values and +there they + + align:start position:0% +there they + + + align:start position:0% +there they +go okay so that's the standard system I + + align:start position:0% +go okay so that's the standard system I + + + align:start position:0% +go okay so that's the standard system I +just have to say because this is a part + + align:start position:0% +just have to say because this is a part + + + align:start position:0% +just have to say because this is a part +of these course is scientific Computing + + align:start position:0% +of these course is scientific Computing + + + align:start position:0% +of these course is scientific Computing +that you would never compute the lambdas + + align:start position:0% +that you would never compute the lambdas + + + align:start position:0% +that you would never compute the lambdas +this way except maybe maybe 2x two I + + align:start position:0% +this way except maybe maybe 2x two I + + + align:start position:0% +this way except maybe maybe 2x two I +would 3x3 that would give me a cubic + + align:start position:0% +would 3x3 that would give me a cubic + + + align:start position:0% +would 3x3 that would give me a cubic +well unless I had unless it was a very + + align:start position:0% +well unless I had unless it was a very + + + align:start position:0% +well unless I had unless it was a very +nice cubic I wouldn't even want to do a + + align:start position:0% +nice cubic I wouldn't even want to do a + + + align:start position:0% +nice cubic I wouldn't even want to do a +cubic polinomial that way so uh so this + + align:start position:0% +cubic polinomial that way so uh so this + + + align:start position:0% +cubic polinomial that way so uh so this +is sort of in principle but to pack all + + align:start position:0% +is sort of in principle but to pack all + + + align:start position:0% +is sort of in principle but to pack all +this information into this determinant + + align:start position:0% +this information into this determinant + + + align:start position:0% +this information into this determinant +and then try to extract it is not the + + align:start position:0% +and then try to extract it is not the + + + align:start position:0% +and then try to extract it is not the +way to go is not the way to go in fact + + align:start position:0% +way to go is not the way to go in fact + + + align:start position:0% +way to go is not the way to go in fact +well I could maybe having started that + + align:start position:0% +well I could maybe having started that + + + align:start position:0% +well I could maybe having started that +with a notot I should say what is a + + align:start position:0% +with a notot I should say what is a + + + align:start position:0% +with a notot I should say what is a +better way to go a better way to go is + + align:start position:0% +better way to go a better way to go is + + + align:start position:0% +better way to go a better way to go is +to uh so so let me hear Let me hear a + + align:start position:0% +to uh so so let me hear Let me hear a + + + align:start position:0% +to uh so so let me hear Let me hear a +comment then on + + align:start position:0% + + + + align:start position:0% + +Computing Computing we we we we start + + align:start position:0% +Computing Computing we we we we start + + + align:start position:0% +Computing Computing we we we we start +with our Matrix a and do operations on + + align:start position:0% +with our Matrix a and do operations on + + + align:start position:0% +with our Matrix a and do operations on +it maybe I'll won't give the details on + + align:start position:0% +it maybe I'll won't give the details on + + + align:start position:0% +it maybe I'll won't give the details on +that yet but there operations that don't + + align:start position:0% +that yet but there operations that don't + + + align:start position:0% +that yet but there operations that don't +change the igen + + align:start position:0% +change the igen + + + align:start position:0% +change the igen +values just the way we did elimination + + align:start position:0% +values just the way we did elimination + + + align:start position:0% +values just the way we did elimination +steps and didn't change in ax equal B + + align:start position:0% +steps and didn't change in ax equal B + + + align:start position:0% +steps and didn't change in ax equal B +now we do what we'll have to think what + + align:start position:0% +now we do what we'll have to think what + + + align:start position:0% +now we do what we'll have to think what +are we allowed to do to a matrix that + + align:start position:0% +are we allowed to do to a matrix that + + + align:start position:0% +are we allowed to do to a matrix that +won't mess up its igen values we're not + + align:start position:0% +won't mess up its igen values we're not + + + align:start position:0% +won't mess up its igen values we're not +allowed to do elimination If I subtract + + align:start position:0% +allowed to do elimination If I subtract + + + align:start position:0% +allowed to do elimination If I subtract +the first row from the second row most + + align:start position:0% +the first row from the second row most + + + align:start position:0% +the first row from the second row most +likely I've changed all the I value but + + align:start position:0% +likely I've changed all the I value but + + + align:start position:0% +likely I've changed all the I value but +there's steps that that we can do and we + + align:start position:0% +there's steps that that we can do and we + + + align:start position:0% +there's steps that that we can do and we +try to get it to a triangular + + align:start position:0% + + + + align:start position:0% + +form or even even diagonal if if it's uh + + align:start position:0% +form or even even diagonal if if it's uh + + + align:start position:0% +form or even even diagonal if if it's uh +if it's a particularly nice Matrix now + + align:start position:0% +if it's a particularly nice Matrix now + + + align:start position:0% +if it's a particularly nice Matrix now +so you could say we did that before but + + align:start position:0% +so you could say we did that before but + + + align:start position:0% +so you could say we did that before but +now this is going to + + align:start position:0% +now this is going to + + + align:start position:0% +now this is going to +be a form that has the same igen values + + align:start position:0% +be a form that has the same igen values + + + align:start position:0% +be a form that has the same igen values +so now let me ask if I have a matrix and + + align:start position:0% +so now let me ask if I have a matrix and + + + align:start position:0% +so now let me ask if I have a matrix and +it is + + align:start position:0% +it is + + + align:start position:0% +it is +triangular suppose it has a b c on the + + align:start position:0% +triangular suppose it has a b c on the + + + align:start position:0% +triangular suppose it has a b c on the +diagonal and d e f above but Zer + + align:start position:0% +diagonal and d e f above but Zer + + + align:start position:0% +diagonal and d e f above but Zer +below what are the igen values of that + + align:start position:0% +below what are the igen values of that + + + align:start position:0% +below what are the igen values of that +Matrix I mean part of talking about IG + + align:start position:0% +Matrix I mean part of talking about IG + + + align:start position:0% +Matrix I mean part of talking about IG +values is to like get + + align:start position:0% +values is to like get + + + align:start position:0% +values is to like get +practice uh with igon values of of + + align:start position:0% +practice uh with igon values of of + + + align:start position:0% +practice uh with igon values of of +important or convenient matrices okay + + align:start position:0% +important or convenient matrices okay + + + align:start position:0% +important or convenient matrices okay +what are the I values if we get if we + + align:start position:0% +what are the I values if we get if we + + + align:start position:0% +what are the I values if we get if we +get the Matrix into this form or if we + + align:start position:0% +get the Matrix into this form or if we + + + align:start position:0% +get the Matrix into this form or if we +have this Matrix what are itson + + align:start position:0% +have this Matrix what are itson + + + align:start position:0% +have this Matrix what are itson +values they're right on the diagonal + + align:start position:0% +values they're right on the diagonal + + + align:start position:0% +values they're right on the diagonal +they're a b and c right because if I + + align:start position:0% +they're a b and c right because if I + + + align:start position:0% +they're a b and c right because if I +because if I took uh so that's an igen + + align:start position:0% +because if I took uh so that's an igen + + + align:start position:0% +because if I took uh so that's an igen +value for example because a minus that + + align:start position:0% +value for example because a minus that + + + align:start position:0% +value for example because a minus that +times the identity you see what what + + align:start position:0% +times the identity you see what what + + + align:start position:0% +times the identity you see what what +what we're doing is we're really taking + + align:start position:0% +what we're doing is we're really taking + + + align:start position:0% +what we're doing is we're really taking +our Matrix well so let me call that one + + align:start position:0% +our Matrix well so let me call that one + + + align:start position:0% +our Matrix well so let me call that one +a for the moment uh if we subtract we're + + align:start position:0% +a for the moment uh if we subtract we're + + + align:start position:0% +a for the moment uh if we subtract we're +sort of Shifting our Matrix to make it + + align:start position:0% +sort of Shifting our Matrix to make it + + + align:start position:0% +sort of Shifting our Matrix to make it +singular shifting by a multip of the + + align:start position:0% +singular shifting by a multip of the + + + align:start position:0% +singular shifting by a multip of the +identity and if I shift this one by a + + align:start position:0% +identity and if I shift this one by a + + + align:start position:0% +identity and if I shift this one by a +multiple of the identity what do I do I + + align:start position:0% +multiple of the identity what do I do I + + + align:start position:0% +multiple of the identity what do I do I +subtract a from the diagonal and what do + + align:start position:0% +subtract a from the diagonal and what do + + + align:start position:0% +subtract a from the diagonal and what do +I have left well for sure I have a zero + + align:start position:0% +I have left well for sure I have a zero + + + align:start position:0% +I have left well for sure I have a zero +there and something else B minus a and C + + align:start position:0% +there and something else B minus a and C + + + align:start position:0% +there and something else B minus a and C +minus a in other words it's singular + + align:start position:0% +minus a in other words it's singular + + + align:start position:0% +minus a in other words it's singular +there'll be an igen Vector in fact it + + align:start position:0% +there'll be an igen Vector in fact it + + + align:start position:0% +there'll be an igen Vector in fact it +would be the IG the igon vector with + + align:start position:0% +would be the IG the igon vector with + + + align:start position:0% +would be the IG the igon vector with +that looking at that column what what's + + align:start position:0% +that looking at that column what what's + + + align:start position:0% +that looking at that column what what's +in the null space of that Matrix + + align:start position:0% +in the null space of that Matrix + + + align:start position:0% +in the null space of that Matrix +can you even tell me the ion Vector one + + align:start position:0% +can you even tell me the ion Vector one + + + align:start position:0% +can you even tell me the ion Vector one +0 0 because when we multiply you + + align:start position:0% +0 0 because when we multiply you + + + align:start position:0% +0 0 because when we multiply you +remember the key when I multiply by one + + align:start position:0% +remember the key when I multiply by one + + + align:start position:0% +remember the key when I multiply by one +0 0 that just picks out the First Column + + align:start position:0% +0 0 that just picks out the First Column + + + align:start position:0% +0 0 that just picks out the First Column +which is zero so uh so there's the ion + + align:start position:0% + + + + align:start position:0% + +vector and there's the igen value or one + + align:start position:0% +vector and there's the igen value or one + + + align:start position:0% +vector and there's the igen value or one +of the three I mean there were three a + + align:start position:0% +of the three I mean there were three a + + + align:start position:0% +of the three I mean there were three a +was the first one and similarly B and + + align:start position:0% +was the first one and similarly B and + + + align:start position:0% +was the first one and similarly B and +similarly C + + align:start position:0% +similarly C + + + align:start position:0% +similarly C +so uh so so that result gave us 00 0 + + align:start position:0% +so uh so so that result gave us 00 0 + + + align:start position:0% +so uh so so that result gave us 00 0 +okay so there we found an igen value and + + align:start position:0% +okay so there we found an igen value and + + + align:start position:0% +okay so there we found an igen value and +we found an igen Vector so so Computing + + align:start position:0% +we found an igen Vector so so Computing + + + align:start position:0% +we found an igen Vector so so Computing +and this was actually how to compute + + align:start position:0% +and this was actually how to compute + + + align:start position:0% +and this was actually how to compute +igen values of matrices let's say order + + align:start position:0% +igen values of matrices let's say order + + + align:start position:0% +igen values of matrices let's say order +100 then when like when I was in + + align:start position:0% +100 then when like when I was in + + + align:start position:0% +100 then when like when I was in +graduate school it basically wouldn't + + align:start position:0% +graduate school it basically wouldn't + + + align:start position:0% +graduate school it basically wouldn't +have been possible to compute I values + + align:start position:0% +have been possible to compute I values + + + align:start position:0% +have been possible to compute I values +of of 100 by 100 matrices + + align:start position:0% +of of 100 by 100 matrices + + + align:start position:0% +of of 100 by 100 matrices +uh so this is really one of the + + align:start position:0% +uh so this is really one of the + + + align:start position:0% +uh so this is really one of the +successes of numerical linear algebra + + align:start position:0% +successes of numerical linear algebra + + + align:start position:0% +successes of numerical linear algebra +how do you H how do you actually in a + + align:start position:0% +how do you H how do you actually in a + + + align:start position:0% +how do you H how do you actually in a +stable accurate fast way uh find the + + align:start position:0% +stable accurate fast way uh find the + + + align:start position:0% +stable accurate fast way uh find the +igen values of a reasonable size Matrix + + align:start position:0% +igen values of a reasonable size Matrix + + + align:start position:0% +igen values of a reasonable size Matrix +of course the way I would find it now I + + align:start position:0% +of course the way I would find it now I + + + align:start position:0% +of course the way I would find it now I +would be on mat lab and I would typ type + + align:start position:0% +would be on mat lab and I would typ type + + + align:start position:0% +would be on mat lab and I would typ type +those magic letters and it would list + + align:start position:0% +those magic letters and it would list + + + align:start position:0% +those magic letters and it would list +100 igen values and uh if I wanted them + + align:start position:0% +100 igen values and uh if I wanted them + + + align:start position:0% +100 igen values and uh if I wanted them +in order I would do sort of vave and uh + + align:start position:0% +in order I would do sort of vave and uh + + + align:start position:0% +in order I would do sort of vave and uh +so on anyway + + align:start position:0% +so on anyway + + + align:start position:0% +so on anyway +um and the way it does it is this idea + + align:start position:0% +um and the way it does it is this idea + + + align:start position:0% +um and the way it does it is this idea +of gradually moving to a triangular form + + align:start position:0% +of gradually moving to a triangular form + + + align:start position:0% +of gradually moving to a triangular form +okay I I think to give you details about + + align:start position:0% +okay I I think to give you details about + + + align:start position:0% +okay I I think to give you details about +that should come later all right so + + align:start position:0% +that should come later all right so + + + align:start position:0% +that should come later all right so +that's some comments on the Computing + + align:start position:0% +that's some comments on the Computing + + + align:start position:0% +that's some comments on the Computing +this is comments on the basic facts now + + align:start position:0% +this is comments on the basic facts now + + + align:start position:0% +this is comments on the basic facts now +let me come back to the this is the + + align:start position:0% +let me come back to the this is the + + + align:start position:0% +let me come back to the this is the +central equation that's what we we use + + align:start position:0% +central equation that's what we we use + + + align:start position:0% +central equation that's what we we use +all the time let me use it + + align:start position:0% +all the time let me use it + + + align:start position:0% +all the time let me use it +in different ways let me uh well I have + + align:start position:0% +in different ways let me uh well I have + + + align:start position:0% +in different ways let me uh well I have +to make one comment one + + align:start position:0% +to make one comment one + + + align:start position:0% +to make one comment one +mathematical uh possibility possibility + + align:start position:0% +mathematical uh possibility possibility + + + align:start position:0% +mathematical uh possibility possibility +is that some of these igen values are + + align:start position:0% +is that some of these igen values are + + + align:start position:0% +is that some of these igen values are +repeated we've got a polinomial degree n + + align:start position:0% +repeated we've got a polinomial degree n + + + align:start position:0% +repeated we've got a polinomial degree n +you know A or B or C might be the same + + align:start position:0% +you know A or B or C might be the same + + + align:start position:0% +you know A or B or C might be the same +we might a if a equal B then a question + + align:start position:0% +we might a if a equal B then a question + + + align:start position:0% +we might a if a equal B then a question +arises if a if the a equal B in that + + align:start position:0% +arises if a if the a equal B in that + + + align:start position:0% +arises if a if the a equal B in that +case let me just go back to the to the + + align:start position:0% +case let me just go back to the to the + + + align:start position:0% +case let me just go back to the to the +Matrix as it was so if I have a + + align:start position:0% +Matrix as it was so if I have a + + + align:start position:0% +Matrix as it was so if I have a +triangular + + align:start position:0% +triangular + + + align:start position:0% +triangular +Matrix and I have so my my my polom oh + + align:start position:0% +Matrix and I have so my my my polom oh + + + align:start position:0% +Matrix and I have so my my my polom oh +well just tell me what's my polinomial + + align:start position:0% +well just tell me what's my polinomial + + + align:start position:0% +well just tell me what's my polinomial +determinant of a minus Lambda I just + + align:start position:0% +determinant of a minus Lambda I just + + + align:start position:0% +determinant of a minus Lambda I just +just let's carry on this nice case when + + align:start position:0% +just let's carry on this nice case when + + + align:start position:0% +just let's carry on this nice case when +when this is my Matrix a I'm I'm + + align:start position:0% +when this is my Matrix a I'm I'm + + + align:start position:0% +when this is my Matrix a I'm I'm +renaming uh the Triangular one a what + + align:start position:0% +renaming uh the Triangular one a what + + + align:start position:0% +renaming uh the Triangular one a what +would be the determinant what would be + + align:start position:0% +would be the determinant what would be + + + align:start position:0% +would be the determinant what would be +the + + align:start position:0% +the + + + align:start position:0% +the +determinant of a minus Lambda I for this + + align:start position:0% +determinant of a minus Lambda I for this + + + align:start position:0% +determinant of a minus Lambda I for this +for this triangular + + align:start position:0% +for this triangular + + + align:start position:0% +for this triangular +one well we subtract lambdas from the + + align:start position:0% +one well we subtract lambdas from the + + + align:start position:0% +one well we subtract lambdas from the +diagonal right that's the minus Lambda I + + align:start position:0% +diagonal right that's the minus Lambda I + + + align:start position:0% +diagonal right that's the minus Lambda I +and we take the determinant and we + + align:start position:0% +and we take the determinant and we + + + align:start position:0% +and we take the determinant and we +get well product of these three that's + + align:start position:0% +get well product of these three that's + + + align:start position:0% +get well product of these three that's +the the beauty of the Triangular part A + + align:start position:0% +the the beauty of the Triangular part A + + + align:start position:0% +the the beauty of the Triangular part A +minus Lambda B minus Lambda cus Lambda + + align:start position:0% +minus Lambda B minus Lambda cus Lambda + + + align:start position:0% +minus Lambda B minus Lambda cus Lambda +because when I take a determinant it's + + align:start position:0% +because when I take a determinant it's + + + align:start position:0% +because when I take a determinant it's +got a lot of more terms but if there + + align:start position:0% +got a lot of more terms but if there + + + align:start position:0% +got a lot of more terms but if there +they'll all be zero because of those so + + align:start position:0% +they'll all be zero because of those so + + + align:start position:0% +they'll all be zero because of those so +of course I see the three + + align:start position:0% +of course I see the three + + + align:start position:0% +of course I see the three +Roots uh no problem and uh the + + align:start position:0% +Roots uh no problem and uh the + + + align:start position:0% +Roots uh no problem and uh the +possibility is that anigen value might + + align:start position:0% +possibility is that anigen value might + + + align:start position:0% +possibility is that anigen value might +be repeated now that raises various + + align:start position:0% +be repeated now that raises various + + + align:start position:0% +be repeated now that raises various +headaches possible headaches everything + + align:start position:0% +headaches possible headaches everything + + + align:start position:0% +headaches possible headaches everything +might be just fine on the other hand it + + align:start position:0% +might be just fine on the other hand it + + + align:start position:0% +might be just fine on the other hand it +might be not so fine not by not so fine + + align:start position:0% +might be not so fine not by not so fine + + + align:start position:0% +might be not so fine not by not so fine +I mean we might have have a equal B say + + align:start position:0% +I mean we might have have a equal B say + + + align:start position:0% +I mean we might have have a equal B say +a double IG value but we might not have + + align:start position:0% +a double IG value but we might not have + + + align:start position:0% +a double IG value but we might not have +two IG + + align:start position:0% +two IG + + + align:start position:0% +two IG +vectors or we might have a and b and c a + + align:start position:0% +vectors or we might have a and b and c a + + + align:start position:0% +vectors or we might have a and b and c a +triple I value and we might have only + + align:start position:0% +triple I value and we might have only + + + align:start position:0% +triple I value and we might have only +two or possibly only one IG Vector so I + + align:start position:0% +two or possibly only one IG Vector so I + + + align:start position:0% +two or possibly only one IG Vector so I +I always have to sort of be concerned + + align:start position:0% +I always have to sort of be concerned + + + align:start position:0% +I always have to sort of be concerned +about that or or if I'm going to say + + align:start position:0% +about that or or if I'm going to say + + + align:start position:0% +about that or or if I'm going to say +something about all matrices then those + + align:start position:0% +something about all matrices then those + + + align:start position:0% +something about all matrices then those +uh sort of degenerate cases have to be + + align:start position:0% +uh sort of degenerate cases have to be + + + align:start position:0% +uh sort of degenerate cases have to be +remembered but uh for symmetric matrices + + align:start position:0% +remembered but uh for symmetric matrices + + + align:start position:0% +remembered but uh for symmetric matrices +it won't happen see for if if the Matrix + + align:start position:0% +it won't happen see for if if the Matrix + + + align:start position:0% +it won't happen see for if if the Matrix +is symmetric then these the above the + + align:start position:0% +is symmetric then these the above the + + + align:start position:0% +is symmetric then these the above the +diagonal would be 02 and we'd have a + + align:start position:0% +diagonal would be 02 and we'd have a + + + align:start position:0% +diagonal would be 02 and we'd have a +totally beautiful example so symmetric + + align:start position:0% +totally beautiful example so symmetric + + + align:start position:0% +totally beautiful example so symmetric +is good in this situation okay all right + + align:start position:0% +is good in this situation okay all right + + + align:start position:0% +is good in this situation okay all right +now back to here okay so I'm going to + + align:start position:0% +now back to here okay so I'm going to + + + align:start position:0% +now back to here okay so I'm going to +take I'm going to suppose that there are + + align:start position:0% +take I'm going to suppose that there are + + + align:start position:0% +take I'm going to suppose that there are +and different independent igen vectors + + align:start position:0% +and different independent igen vectors + + + align:start position:0% +and different independent igen vectors +and I'll make them The Columns of a + + align:start position:0% +and I'll make them The Columns of a + + + align:start position:0% +and I'll make them The Columns of a +matrix X1 + + align:start position:0% +matrix X1 + + + align:start position:0% +matrix X1 +X2 + + align:start position:0% + + + + align:start position:0% + +xn and I'm going to call that Matrix S + + align:start position:0% +xn and I'm going to call that Matrix S + + + align:start position:0% +xn and I'm going to call that Matrix S +so that's the IG Vector Matrix this can + + align:start position:0% +so that's the IG Vector Matrix this can + + + align:start position:0% +so that's the IG Vector Matrix this can +I put that in here IG Vector + + align:start position:0% +I put that in here IG Vector + + + align:start position:0% +I put that in here IG Vector +Matrix and I'm just going to do this + + align:start position:0% +Matrix and I'm just going to do this + + + align:start position:0% +Matrix and I'm just going to do this +matrix multiplication a * + + align:start position:0% +matrix multiplication a * + + + align:start position:0% +matrix multiplication a * +s and ask you what come comes + + align:start position:0% +s and ask you what come comes + + + align:start position:0% +s and ask you what come comes +out okay so what are the rules of matrix + + align:start position:0% +out okay so what are the rules of matrix + + + align:start position:0% +out okay so what are the rules of matrix +multiplication I can do it a times the + + align:start position:0% +multiplication I can do it a times the + + + align:start position:0% +multiplication I can do it a times the +First Column right that gives me the + + align:start position:0% +First Column right that gives me the + + + align:start position:0% +First Column right that gives me the +First Column of the + + align:start position:0% +First Column of the + + + align:start position:0% +First Column of the +answer and what is it Lambda 1 X1 right + + align:start position:0% +answer and what is it Lambda 1 X1 right + + + align:start position:0% +answer and what is it Lambda 1 X1 right +this X1 was an IG Vector we we're + + align:start position:0% +this X1 was an IG Vector we we're + + + align:start position:0% +this X1 was an IG Vector we we're +imagining with IG value Lambda 1 so that + + align:start position:0% +imagining with IG value Lambda 1 so that + + + align:start position:0% +imagining with IG value Lambda 1 so that +a * that is Lambda 1 X1 and then a * X2 + + align:start position:0% +a * that is Lambda 1 X1 and then a * X2 + + + align:start position:0% +a * that is Lambda 1 X1 and then a * X2 +is Lambda 2 X2 + + align:start position:0% +is Lambda 2 X2 + + + align:start position:0% +is Lambda 2 X2 +and so on Lambda n xn so The Columns of + + align:start position:0% +and so on Lambda n xn so The Columns of + + + align:start position:0% +and so on Lambda n xn so The Columns of +a s + + align:start position:0% +a s + + + align:start position:0% +a s +are very nice but now I can do even + + align:start position:0% +are very nice but now I can do even + + + align:start position:0% +are very nice but now I can do even +better do even more I can write that as + + align:start position:0% +better do even more I can write that as + + + align:start position:0% +better do even more I can write that as +X1 my S Matrix again X2 to xn times The + + align:start position:0% +X1 my S Matrix again X2 to xn times The + + + align:start position:0% +X1 my S Matrix again X2 to xn times The +Matrix diagonal guy now Lambda 1 Lambda + + align:start position:0% +Matrix diagonal guy now Lambda 1 Lambda + + + align:start position:0% +Matrix diagonal guy now Lambda 1 Lambda +2 down to Lambda n + + align:start position:0% + + + + align:start position:0% + +do you see that that + + align:start position:0% +do you see that that + + + align:start position:0% +do you see that that +works again yeah let's see that let's + + align:start position:0% +works again yeah let's see that let's + + + align:start position:0% +works again yeah let's see that let's +check the First Column that will prove + + align:start position:0% +check the First Column that will prove + + + align:start position:0% +check the First Column that will prove +everything uh so we want to get Lambda 1 + + align:start position:0% +everything uh so we want to get Lambda 1 + + + align:start position:0% +everything uh so we want to get Lambda 1 +X1 in the First Column do we get it from + + align:start position:0% +X1 in the First Column do we get it from + + + align:start position:0% +X1 in the First Column do we get it from +from this is that we do get Lambda + + align:start position:0% +from this is that we do get Lambda + + + align:start position:0% +from this is that we do get Lambda +1x1 yeah because I'm multiplying this + + align:start position:0% +1x1 yeah because I'm multiplying this + + + align:start position:0% +1x1 yeah because I'm multiplying this +times the First + + align:start position:0% +times the First + + + align:start position:0% +times the First +Column and the result is Lambda one of + + align:start position:0% +Column and the result is Lambda one of + + + align:start position:0% +Column and the result is Lambda one of +that and none of the others so it is + + align:start position:0% +that and none of the others so it is + + + align:start position:0% +that and none of the others so it is +Lambda 1 1 X1 so this is my S + + align:start position:0% +Lambda 1 1 X1 so this is my S + + + align:start position:0% +Lambda 1 1 X1 so this is my S +again and this is my igen value Matrix + + align:start position:0% +again and this is my igen value Matrix + + + align:start position:0% +again and this is my igen value Matrix +all zeros called Capital Lambda we get + + align:start position:0% +all zeros called Capital Lambda we get + + + align:start position:0% +all zeros called Capital Lambda we get +this + + align:start position:0% +this + + + align:start position:0% +this +nice this comes this is just the Matrix + + align:start position:0% +nice this comes this is just the Matrix + + + align:start position:0% +nice this comes this is just the Matrix +form of that maybe I put two box two + + align:start position:0% +form of that maybe I put two box two + + + align:start position:0% +form of that maybe I put two box two +squares around it just to emphasize that + + align:start position:0% +squares around it just to emphasize that + + + align:start position:0% +squares around it just to emphasize that +it's really the same thing doing all in + + align:start position:0% +it's really the same thing doing all in + + + align:start position:0% +it's really the same thing doing all in +at + + align:start position:0% +at + + + align:start position:0% +at +once so that's uh that's the way now let + + align:start position:0% +once so that's uh that's the way now let + + + align:start position:0% +once so that's uh that's the way now let +me just jiggle a little I could put the + + align:start position:0% +me just jiggle a little I could put the + + + align:start position:0% +me just jiggle a little I could put the +S I could multiply both sides by S + + align:start position:0% +S I could multiply both sides by S + + + align:start position:0% +S I could multiply both sides by S +inverse so I would have then a equal + + align:start position:0% +inverse so I would have then a equal + + + align:start position:0% +inverse so I would have then a equal +getting rid of that s will'll put an S + + align:start position:0% +getting rid of that s will'll put an S + + + align:start position:0% +getting rid of that s will'll put an S +inverse over + + align:start position:0% + + + + align:start position:0% + +there yeah so that's that's maybe even + + align:start position:0% +there yeah so that's that's maybe even + + + align:start position:0% +there yeah so that's that's maybe even +nicer that's + + align:start position:0% + + + + align:start position:0% + +uh that's one of the most most important + + align:start position:0% +uh that's one of the most most important + + + align:start position:0% +uh that's one of the most most important +that's the the diagonalization of a + + align:start position:0% +that's the the diagonalization of a + + + align:start position:0% +that's the the diagonalization of a +matrix this is so I I'll put that word + + align:start position:0% +matrix this is so I I'll put that word + + + align:start position:0% +matrix this is so I I'll put that word +up + + align:start position:0% + + + + align:start position:0% + +diagonalization I started with a matrix + + align:start position:0% +diagonalization I started with a matrix + + + align:start position:0% +diagonalization I started with a matrix +a and I ended with a diagonal matrix + + align:start position:0% +a and I ended with a diagonal matrix + + + align:start position:0% +a and I ended with a diagonal matrix +Lambda the igen value Matrix that's + + align:start position:0% +Lambda the igen value Matrix that's + + + align:start position:0% +Lambda the igen value Matrix that's +this and they're connected by the igen + + align:start position:0% +this and they're connected by the igen + + + align:start position:0% +this and they're connected by the igen +vector Matrix and its inverse and there + + align:start position:0% +vector Matrix and its inverse and there + + + align:start position:0% +vector Matrix and its inverse and there +is an in inverse because I said if there + + align:start position:0% +is an in inverse because I said if there + + + align:start position:0% +is an in inverse because I said if there +was an if in here if there are an + + align:start position:0% +was an if in here if there are an + + + align:start position:0% +was an if in here if there are an +independent ion vectors then then this I + + align:start position:0% +independent ion vectors then then this I + + + align:start position:0% +independent ion vectors then then this I +Vector Matrix will be invertible and I'm + + align:start position:0% +Vector Matrix will be invertible and I'm + + + align:start position:0% +Vector Matrix will be invertible and I'm +okay so this diagonalization require it + + align:start position:0% +okay so this diagonalization require it + + + align:start position:0% +okay so this diagonalization require it +needs n + + align:start position:0% +needs n + + + align:start position:0% +needs n +independent ion + + align:start position:0% +independent ion + + + align:start position:0% +independent ion +vectors and as I said that's + + align:start position:0% +vectors and as I said that's + + + align:start position:0% +vectors and as I said that's +guaranteed if the I value are distinct + + align:start position:0% +guaranteed if the I value are distinct + + + align:start position:0% +guaranteed if the I value are distinct +if the Lambda one if none of the lambdas + + align:start position:0% +if the Lambda one if none of the lambdas + + + align:start position:0% +if the Lambda one if none of the lambdas +are equal then no problem if there are + + align:start position:0% +are equal then no problem if there are + + + align:start position:0% +are equal then no problem if there are +some equal repeated lambdas then could + + align:start position:0% +some equal repeated lambdas then could + + + align:start position:0% +some equal repeated lambdas then could +be a problem or possibly not depending + + align:start position:0% +be a problem or possibly not depending + + + align:start position:0% +be a problem or possibly not depending +on the individual Matrix okay so that + + align:start position:0% +on the individual Matrix okay so that + + + align:start position:0% +on the individual Matrix okay so that +that was our goal there and uh oh now + + align:start position:0% +that was our goal there and uh oh now + + + align:start position:0% +that was our goal there and uh oh now +could we practice on some igen values + + align:start position:0% +could we practice on some igen values + + + align:start position:0% +could we practice on some igen values +just just like we first we practiced on + + align:start position:0% +just just like we first we practiced on + + + align:start position:0% +just just like we first we practiced on +a triangular + + align:start position:0% +a triangular + + + align:start position:0% +a triangular +Matrix that that's a real + + align:start position:0% +Matrix that that's a real + + + align:start position:0% +Matrix that that's a real +warmup uh how + + align:start position:0% +warmup uh how + + + align:start position:0% +warmup uh how +about a matrix uh let me let me ask you + + align:start position:0% +about a matrix uh let me let me ask you + + + align:start position:0% +about a matrix uh let me let me ask you +for the igen values and igen vectors of + + align:start position:0% +for the igen values and igen vectors of + + + align:start position:0% +for the igen values and igen vectors of +the Matrix that we saw in the um Network + + align:start position:0% +the Matrix that we saw in the um Network + + + align:start position:0% +the Matrix that we saw in the um Network +problem when there were four + + align:start position:0% +problem when there were four + + + align:start position:0% +problem when there were four +nodes and we had grounded one of them I + + align:start position:0% +nodes and we had grounded one of them I + + + align:start position:0% +nodes and we had grounded one of them I +guess it I didn't write down the the + + align:start position:0% +guess it I didn't write down the the + + + align:start position:0% +guess it I didn't write down the the +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +until uh the note so this Matrix would + + align:start position:0% +until uh the note so this Matrix would + + + align:start position:0% +until uh the note so this Matrix would +be in the notes for lecture three so + + align:start position:0% +be in the notes for lecture three so + + + align:start position:0% +be in the notes for lecture three so +that that came from lecture three that's + + align:start position:0% +that that came from lecture three that's + + + align:start position:0% +that that came from lecture three that's +the one with with four nodes and one has + + align:start position:0% +the one with with four nodes and one has + + + align:start position:0% +the one with with four nodes and one has +been already grounded and we so we have + + align:start position:0% +been already grounded and we so we have + + + align:start position:0% +been already grounded and we so we have +a 3X3 Matrix and I guess that's the LI + + align:start position:0% +a 3X3 Matrix and I guess that's the LI + + + align:start position:0% +a 3X3 Matrix and I guess that's the LI +we + + align:start position:0% +we + + + align:start position:0% +we +could compute the determinant of K minus + + align:start position:0% +could compute the determinant of K minus + + + align:start position:0% +could compute the determinant of K minus +Lambda I and expand it into a cubic + + align:start position:0% +Lambda I and expand it into a cubic + + + align:start position:0% +Lambda I and expand it into a cubic +polinomial and look for roots let's do + + align:start position:0% +polinomial and look for roots let's do + + + align:start position:0% +polinomial and look for roots let's do +it let's try to think of a better + + align:start position:0% +it let's try to think of a better + + + align:start position:0% +it let's try to think of a better +idea let me ask you what could I shift + + align:start position:0% +idea let me ask you what could I shift + + + align:start position:0% +idea let me ask you what could I shift +that matrix by so I'm I'm going to shoot + + align:start position:0% +that matrix by so I'm I'm going to shoot + + + align:start position:0% +that matrix by so I'm I'm going to shoot +for the igen values just sort of without + + align:start position:0% +for the igen values just sort of without + + + align:start position:0% +for the igen values just sort of without +just by thinking what are we looking for + + align:start position:0% +just by thinking what are we looking for + + + align:start position:0% +just by thinking what are we looking for +we're looking for uh subtracting + + align:start position:0% +we're looking for uh subtracting + + + align:start position:0% +we're looking for uh subtracting +something from the + + align:start position:0% +something from the + + + align:start position:0% +something from the +diagonal that would make that Matrix + + align:start position:0% +diagonal that would make that Matrix + + + align:start position:0% +diagonal that would make that Matrix +singular + + align:start position:0% + + + + align:start position:0% + +and I think you can tell me one number + + align:start position:0% +and I think you can tell me one number + + + align:start position:0% +and I think you can tell me one number +that I could subtract from the diagonal + + align:start position:0% +that I could subtract from the diagonal + + + align:start position:0% +that I could subtract from the diagonal +that would make the Matrix singular If I + + align:start position:0% +that would make the Matrix singular If I + + + align:start position:0% +that would make the Matrix singular If I +subtract four if I subtract four from + + align:start position:0% +subtract four if I subtract four from + + + align:start position:0% +subtract four if I subtract four from +the + + align:start position:0% +the + + + align:start position:0% +the +diagonal what so K minus 4 I would be + + align:start position:0% +diagonal what so K minus 4 I would be + + + align:start position:0% +diagonal what so K minus 4 I would be +what it would be if I took four from the + + align:start position:0% +what it would be if I took four from the + + + align:start position:0% +what it would be if I took four from the +diagonal so you see we've shifted the + + align:start position:0% +diagonal so you see we've shifted the + + + align:start position:0% +diagonal so you see we've shifted the +matrix by + + align:start position:0% +matrix by + + + align:start position:0% +matrix by +four then then the threes become minus + + align:start position:0% +four then then the threes become minus + + + align:start position:0% +four then then the threes become minus +ones and you see we have a matrix which + + align:start position:0% +ones and you see we have a matrix which + + + align:start position:0% +ones and you see we have a matrix which +is + + align:start position:0% +is + + + align:start position:0% +is +very it's quite + + align:start position:0% +very it's quite + + + align:start position:0% +very it's quite +singular so there's an igen value Lambda + + align:start position:0% +singular so there's an igen value Lambda + + + align:start position:0% +singular so there's an igen value Lambda +one and and in fact this this example + + align:start position:0% +one and and in fact this this example + + + align:start position:0% +one and and in fact this this example +brings up you know gets us really into + + align:start position:0% +brings up you know gets us really into + + + align:start position:0% +brings up you know gets us really into +it + + align:start position:0% +it + + + align:start position:0% +it +because when I say very singular what do + + align:start position:0% +because when I say very singular what do + + + align:start position:0% +because when I say very singular what do +I what's a better way to say that that's + + align:start position:0% +I what's a better way to say that that's + + + align:start position:0% +I what's a better way to say that that's +not a very mathematical way to say it + + align:start position:0% +not a very mathematical way to say it + + + align:start position:0% +not a very mathematical way to say it +what what's what kind of + + align:start position:0% +what what's what kind of + + + align:start position:0% +what what's what kind of +a what would you say about that + + align:start position:0% +a what would you say about that + + + align:start position:0% +a what would you say about that +matrix it's it's rank + + align:start position:0% +matrix it's it's rank + + + align:start position:0% +matrix it's it's rank +one meaning what about its null space + + align:start position:0% +one meaning what about its null space + + + align:start position:0% +one meaning what about its null space +because its null space is where the igen + + align:start position:0% +because its null space is where the igen + + + align:start position:0% +because its null space is where the igen +vectors are right null space + + align:start position:0% +vectors are right null space + + + align:start position:0% +vectors are right null space +is a minus Lambda I then here is the I + + align:start position:0% +is a minus Lambda I then here is the I + + + align:start position:0% +is a minus Lambda I then here is the I +Vector in the null space of this Matrix + + align:start position:0% +Vector in the null space of this Matrix + + + align:start position:0% +Vector in the null space of this Matrix +that we've shifted to become singular + + align:start position:0% +that we've shifted to become singular + + + align:start position:0% +that we've shifted to become singular +okay how big is that null + + align:start position:0% +okay how big is that null + + + align:start position:0% +okay how big is that null +space two-dimensional right because it's + + align:start position:0% +space two-dimensional right because it's + + + align:start position:0% +space two-dimensional right because it's +we're inside three dimensions but we + + align:start position:0% +we're inside three dimensions but we + + + align:start position:0% +we're inside three dimensions but we +only only really have one equation here + + align:start position:0% +only only really have one equation here + + + align:start position:0% +only only really have one equation here +so tell me a couple I we should be able + + align:start position:0% +so tell me a couple I we should be able + + + align:start position:0% +so tell me a couple I we should be able +to pin down a couple of vectors in its + + align:start position:0% +to pin down a couple of vectors in its + + + align:start position:0% +to pin down a couple of vectors in its +in its null space so so actually this is + + align:start position:0% +in its null space so so actually this is + + + align:start position:0% +in its null space so so actually this is +this is four is going to also be Lambda + + align:start position:0% +this is four is going to also be Lambda + + + align:start position:0% +this is four is going to also be Lambda +2 this is going to be a case of a + + align:start position:0% +2 this is going to be a case of a + + + align:start position:0% +2 this is going to be a case of a +repeated igon value because that ion + + align:start position:0% +repeated igon value because that ion + + + align:start position:0% +repeated igon value because that ion +value that shifting by4 produce two IG + + align:start position:0% +value that shifting by4 produce two IG + + + align:start position:0% +value that shifting by4 produce two IG +vectors A 2D a 2d space of vectors so we + + align:start position:0% +vectors A 2D a 2d space of vectors so we + + + align:start position:0% +vectors A 2D a 2d space of vectors so we +know it must have been a double I + + align:start position:0% +know it must have been a double I + + + align:start position:0% +know it must have been a double I +value not a triple I value but a double + + align:start position:0% +value not a triple I value but a double + + + align:start position:0% +value not a triple I value but a double +so tell me two I vectors that go with it + + align:start position:0% +so tell me two I vectors that go with it + + + align:start position:0% +so tell me two I vectors that go with it +maybe maybe you can + + align:start position:0% +maybe maybe you can + + + align:start position:0% +maybe maybe you can +uh one Z ne1 so so I call these X1 1 + + align:start position:0% + + + + align:start position:0% + +01 and a second might be you see you + + align:start position:0% +01 and a second might be you see you + + + align:start position:0% +01 and a second might be you see you +have quite a bit of Freedom + + align:start position:0% +have quite a bit of Freedom + + + align:start position:0% +have quite a bit of Freedom +here what would be a second igen Vector + + align:start position:0% +here what would be a second igen Vector + + + align:start position:0% +here what would be a second igen Vector +also in the null space of that + + align:start position:0% + + + + align:start position:0% + +Matrix 1 1 0 would be another one and + + align:start position:0% +Matrix 1 1 0 would be another one and + + + align:start position:0% +Matrix 1 1 0 would be another one and +you're really giving me a basis for that + + align:start position:0% +you're really giving me a basis for that + + + align:start position:0% +you're really giving me a basis for that +two-dimensional null space + + align:start position:0% +two-dimensional null space + + + align:start position:0% +two-dimensional null space +okay so we have found two sort of by + + align:start position:0% +okay so we have found two sort of by + + + align:start position:0% +okay so we have found two sort of by +inspection now what's the third what's + + align:start position:0% +inspection now what's the third what's + + + align:start position:0% +inspection now what's the third what's +the third IG value of this of this + + align:start position:0% +the third IG value of this of this + + + align:start position:0% +the third IG value of this of this +original Matrix + + align:start position:0% +original Matrix + + + align:start position:0% +original Matrix +well um + + align:start position:0% +well um + + + align:start position:0% +well um +let's see so we've Lambda 1 was 4 and + + align:start position:0% +let's see so we've Lambda 1 was 4 and + + + align:start position:0% +let's see so we've Lambda 1 was 4 and +Lambda 2 was 4 and now um let me when + + align:start position:0% +Lambda 2 was 4 and now um let me when + + + align:start position:0% +Lambda 2 was 4 and now um let me when +you only have one igen value to go + + align:start position:0% +you only have one igen value to go + + + align:start position:0% +you only have one igen value to go +you've made it uh we have now why is + + align:start position:0% +you've made it uh we have now why is + + + align:start position:0% +you've made it uh we have now why is +that because the trace the sum down the + + align:start position:0% +that because the trace the sum down the + + + align:start position:0% +that because the trace the sum down the +diagonal which is nine in this case + + align:start position:0% +diagonal which is nine in this case + + + align:start position:0% +diagonal which is nine in this case +always + + align:start position:0% +always + + + align:start position:0% +always +equals the sum of the igen values so the + + align:start position:0% +equals the sum of the igen values so the + + + align:start position:0% +equals the sum of the igen values so the +trace so the trace so the sum down the + + align:start position:0% +trace so the trace so the sum down the + + + align:start position:0% +trace so the trace so the sum down the +diagonal the sum of a i i or k II + + align:start position:0% +diagonal the sum of a i i or k II + + + align:start position:0% +diagonal the sum of a i i or k II +whatever Matrix we've got always agrees + + align:start position:0% +whatever Matrix we've got always agrees + + + align:start position:0% +whatever Matrix we've got always agrees +with the sum of the igen + + align:start position:0% +with the sum of the igen + + + align:start position:0% +with the sum of the igen +values that's the one Pleasant linear + + align:start position:0% +values that's the one Pleasant linear + + + align:start position:0% +values that's the one Pleasant linear +fact about a nonlinear problem axal + + align:start position:0% +fact about a nonlinear problem axal + + + align:start position:0% +fact about a nonlinear problem axal +Lambda X is not linear because it's got + + align:start position:0% +Lambda X is not linear because it's got + + + align:start position:0% +Lambda X is not linear because it's got +Lambda and X multiplied but one nice + + align:start position:0% +Lambda and X multiplied but one nice + + + align:start position:0% +Lambda and X multiplied but one nice +fact the sum of the I values and this is + + align:start position:0% +fact the sum of the I values and this is + + + align:start position:0% +fact the sum of the I values and this is +called the trace of the Matrix trace of + + align:start position:0% +called the trace of the Matrix trace of + + + align:start position:0% +called the trace of the Matrix trace of +okay so what's the what's the remaining + + align:start position:0% +okay so what's the what's the remaining + + + align:start position:0% +okay so what's the what's the remaining +IG + + align:start position:0% +IG + + + align:start position:0% +IG +value must be one right that the trace + + align:start position:0% +value must be one right that the trace + + + align:start position:0% +value must be one right that the trace +is nine we've already got four and four + + align:start position:0% +is nine we've already got four and four + + + align:start position:0% +is nine we've already got four and four +used up eight so there's there must be + + align:start position:0% +used up eight so there's there must be + + + align:start position:0% +used up eight so there's there must be +an IG value If I subtract what do that + + align:start position:0% +an IG value If I subtract what do that + + + align:start position:0% +an IG value If I subtract what do that +mean then the the third igon value must + + align:start position:0% +mean then the the third igon value must + + + align:start position:0% +mean then the the third igon value must +be one from the + + align:start position:0% +be one from the + + + align:start position:0% +be one from the +trace and now that means that if I + + align:start position:0% +trace and now that means that if I + + + align:start position:0% +trace and now that means that if I +subtract one from the diagonal can I do + + align:start position:0% +subtract one from the diagonal can I do + + + align:start position:0% +subtract one from the diagonal can I do +that by a moments + + align:start position:0% +that by a moments + + + align:start position:0% +that by a moments +erasing K -1 * I will change these + + align:start position:0% +erasing K -1 * I will change these + + + align:start position:0% +erasing K -1 * I will change these +threes to + + align:start position:0% +threes to + + + align:start position:0% +threes to +twos and do we have there a singular + + align:start position:0% +twos and do we have there a singular + + + align:start position:0% +twos and do we have there a singular +Matrix we're supposed to right that's if + + align:start position:0% +Matrix we're supposed to right that's if + + + align:start position:0% +Matrix we're supposed to right that's if +we that's the check always if you don't + + align:start position:0% +we that's the check always if you don't + + + align:start position:0% +we that's the check always if you don't +have a singular Matrix then you filed up + + align:start position:0% +have a singular Matrix then you filed up + + + align:start position:0% +have a singular Matrix then you filed up +somewhere okay so but that is singular + + align:start position:0% +somewhere okay so but that is singular + + + align:start position:0% +somewhere okay so but that is singular +and you can tell me something in its + + align:start position:0% +and you can tell me something in its + + + align:start position:0% +and you can tell me something in its +null + + align:start position:0% +null + + + align:start position:0% +null +space in the null space of that that + + align:start position:0% +space in the null space of that that + + + align:start position:0% +space in the null space of that that +Matrix because that's a vector we've + + align:start position:0% +Matrix because that's a vector we've + + + align:start position:0% +Matrix because that's a vector we've +seen before is a problem we've seen + + align:start position:0% +seen before is a problem we've seen + + + align:start position:0% +seen before is a problem we've seen +before or a type we've seen before tell + + align:start position:0% +before or a type we've seen before tell + + + align:start position:0% +before or a type we've seen before tell +me a vector in its null space 111 okay + + align:start position:0% +me a vector in its null space 111 okay + + + align:start position:0% +me a vector in its null space 111 okay +so we have found for that + + align:start position:0% + + + + align:start position:0% + +Matrix not in a systematic way but + + align:start position:0% +Matrix not in a systematic way but + + + align:start position:0% +Matrix not in a systematic way but +anyway successfully three ion vectors + + align:start position:0% +anyway successfully three ion vectors + + + align:start position:0% +anyway successfully three ion vectors +three igen + + align:start position:0% +three igen + + + align:start position:0% +three igen +values two of them happen to be repeated + + align:start position:0% +values two of them happen to be repeated + + + align:start position:0% +values two of them happen to be repeated +but it did not + + align:start position:0% +but it did not + + + align:start position:0% +but it did not +degenerate symmetric matrices can I tell + + align:start position:0% +degenerate symmetric matrices can I tell + + + align:start position:0% +degenerate symmetric matrices can I tell +you some important facts now about + + align:start position:0% +you some important facts now about + + + align:start position:0% +you some important facts now about +symmetric + + align:start position:0% +symmetric + + + align:start position:0% +symmetric +matrices + + align:start position:0% + + + + align:start position:0% + +yes well okay so the question is how did + + align:start position:0% +yes well okay so the question is how did + + + align:start position:0% +yes well okay so the question is how did +I know that this four was a double I + + align:start position:0% +I know that this four was a double I + + + align:start position:0% +I know that this four was a double I +value well it was to do with the fact + + align:start position:0% +value well it was to do with the fact + + + align:start position:0% +value well it was to do with the fact +that you found two IG + + align:start position:0% +that you found two IG + + + align:start position:0% +that you found two IG +vectors and if you've got two iion + + align:start position:0% +vectors and if you've got two iion + + + align:start position:0% +vectors and if you've got two iion +vectors I darn well know that that + + align:start position:0% +vectors I darn well know that that + + + align:start position:0% +vectors I darn well know that that +Lambda had to be repeated twice yeah + + align:start position:0% +Lambda had to be repeated twice yeah + + + align:start position:0% +Lambda had to be repeated twice yeah +yeah so the fact that this rank dropped + + align:start position:0% +yeah so the fact that this rank dropped + + + align:start position:0% +yeah so the fact that this rank dropped +all the way to one see what what's the + + align:start position:0% +all the way to one see what what's the + + + align:start position:0% +all the way to one see what what's the +rank of that Matrix just while we're + + align:start position:0% +rank of that Matrix just while we're + + + align:start position:0% +rank of that Matrix just while we're +practicing what's the rank of that + + align:start position:0% +practicing what's the rank of that + + + align:start position:0% +practicing what's the rank of that +Matrix two it's not rank three why + + align:start position:0% + + + + align:start position:0% + +not because it's singular right it's not + + align:start position:0% +not because it's singular right it's not + + + align:start position:0% +not because it's singular right it's not +rank + + align:start position:0% +rank + + + align:start position:0% +rank +one certainly because it was rank one + + align:start position:0% +one certainly because it was rank one + + + align:start position:0% +one certainly because it was rank one +all the rows would be multiples of the + + align:start position:0% +all the rows would be multiples of the + + + align:start position:0% +all the rows would be multiples of the +same row but that's not true so we have + + align:start position:0% +same row but that's not true so we have + + + align:start position:0% +same row but that's not true so we have +that row and that row are independent + + align:start position:0% +that row and that row are independent + + + align:start position:0% +that row and that row are independent +and that row is dependent on those + + align:start position:0% +and that row is dependent on those + + + align:start position:0% +and that row is dependent on those +because all three of the rows add up to + + align:start position:0% +because all three of the rows add up to + + + align:start position:0% +because all three of the rows add up to +the zero row right yeah it's uh okay so + + align:start position:0% +the zero row right yeah it's uh okay so + + + align:start position:0% +the zero row right yeah it's uh okay so +so what I so what was I going to + + align:start position:0% +so what I so what was I going to + + + align:start position:0% +so what I so what was I going to +say okay so K was uh We've now got K was + + align:start position:0% +say okay so K was uh We've now got K was + + + align:start position:0% +say okay so K was uh We've now got K was +a symmetric Matrix to start + + align:start position:0% +a symmetric Matrix to start + + + align:start position:0% +a symmetric Matrix to start +with and with a symmetric Matrix I + + align:start position:0% +with and with a symmetric Matrix I + + + align:start position:0% +with and with a symmetric Matrix I +wasn't worried that is I knew we would + + align:start position:0% +wasn't worried that is I knew we would + + + align:start position:0% +wasn't worried that is I knew we would +find full we would find we might have + + align:start position:0% +find full we would find we might have + + + align:start position:0% +find full we would find we might have +some repeated igen values in this for + + align:start position:0% +some repeated igen values in this for + + + align:start position:0% +some repeated igen values in this for +this symmetric Matrix but I was not + + align:start position:0% +this symmetric Matrix but I was not + + + align:start position:0% +this symmetric Matrix but I was not +worried that we wouldn't come up with + + align:start position:0% +worried that we wouldn't come up with + + + align:start position:0% +worried that we wouldn't come up with +the I vectors and we did more than that + + align:start position:0% +the I vectors and we did more than that + + + align:start position:0% +the I vectors and we did more than that +so let me go back can I go back to K you + + align:start position:0% +so let me go back can I go back to K you + + + align:start position:0% +so let me go back can I go back to K you +you this one is singular so one is an + + align:start position:0% +you this one is singular so one is an + + + align:start position:0% +you this one is singular so one is an +nigen value let me go back to the + + align:start position:0% +nigen value let me go back to the + + + align:start position:0% +nigen value let me go back to the +original + + align:start position:0% +original + + + align:start position:0% +original +K with for some more + + align:start position:0% +K with for some more + + + align:start position:0% +K with for some more +comments okay my comments then are about + + align:start position:0% +comments okay my comments then are about + + + align:start position:0% +comments okay my comments then are about +symmetric + + align:start position:0% +symmetric + + + align:start position:0% +symmetric +matrices so the symmetri + + align:start position:0% + + + + align:start position:0% + +case what's good what's great about the + + align:start position:0% +case what's good what's great about the + + + align:start position:0% +case what's good what's great about the +symmetric M case and and we see it here + + align:start position:0% +symmetric M case and and we see it here + + + align:start position:0% +symmetric M case and and we see it here +first point about symmetric matrices the + + align:start position:0% +first point about symmetric matrices the + + + align:start position:0% +first point about symmetric matrices the +lambdas are all real + + align:start position:0% +lambdas are all real + + + align:start position:0% +lambdas are all real +numbers here they were 1 four and four + + align:start position:0% +numbers here they were 1 four and four + + + align:start position:0% +numbers here they were 1 four and four +good second point and this is my new + + align:start position:0% +good second point and this is my new + + + align:start position:0% +good second point and this is my new +point the + + align:start position:0% +point the + + + align:start position:0% +point the +X's the I vectors are + + align:start position:0% + + + + align:start position:0% + +perpendicular okay so that's really + + align:start position:0% +perpendicular okay so that's really + + + align:start position:0% +perpendicular okay so that's really +terrific to be able or or I should I + + align:start position:0% +terrific to be able or or I should I + + + align:start position:0% +terrific to be able or or I should I +have to say we can choose them + + align:start position:0% +have to say we can choose them + + + align:start position:0% +have to say we can choose them +perpendicular can be can be chosen + + align:start position:0% +perpendicular can be can be chosen + + + align:start position:0% +perpendicular can be can be chosen +because we have some + + align:start position:0% +because we have some + + + align:start position:0% +because we have some +Freedom now did we what look at these + + align:start position:0% +Freedom now did we what look at these + + + align:start position:0% +Freedom now did we what look at these +three igen vectors that we picked what's + + align:start position:0% +three igen vectors that we picked what's + + + align:start position:0% +three igen vectors that we picked what's +perpendicular to what there + + align:start position:0% +perpendicular to what there + + + align:start position:0% +perpendicular to what there +X3 is perpendicular + + align:start position:0% +X3 is perpendicular + + + align:start position:0% +X3 is perpendicular +to one and two the dotproduct of that + + align:start position:0% +to one and two the dotproduct of that + + + align:start position:0% +to one and two the dotproduct of that +Vector with that one is certainly zero + + align:start position:0% +Vector with that one is certainly zero + + + align:start position:0% +Vector with that one is certainly zero +the dotproduct of that Vector which came + + align:start position:0% +the dotproduct of that Vector which came + + + align:start position:0% +the dotproduct of that Vector which came +from the igen value one and this that + + align:start position:0% +from the igen value one and this that + + + align:start position:0% +from the igen value one and this that +came from the igen value four certainly + + align:start position:0% +came from the igen value four certainly + + + align:start position:0% +came from the igen value four certainly +zero what's we didn't quite do it right + + align:start position:0% +zero what's we didn't quite do it right + + + align:start position:0% +zero what's we didn't quite do it right +though you see what we should have I + + align:start position:0% +though you see what we should have I + + + align:start position:0% +though you see what we should have I +mean if we wanted + + align:start position:0% +mean if we wanted + + + align:start position:0% +mean if we wanted +Perfection What should if we want + + align:start position:0% +Perfection What should if we want + + + align:start position:0% +Perfection What should if we want +Perfection What then these two this was + + align:start position:0% +Perfection What then these two this was + + + align:start position:0% +Perfection What then these two this was +n the perfect choice of this wasn't the + + align:start position:0% +n the perfect choice of this wasn't the + + + align:start position:0% +n the perfect choice of this wasn't the +perfect choice of + + align:start position:0% +perfect choice of + + + align:start position:0% +perfect choice of +X2 do you see that I + + align:start position:0% +X2 do you see that I + + + align:start position:0% +X2 do you see that I +could I could do I could fiddle around + + align:start position:0% +could I could do I could fiddle around + + + align:start position:0% +could I could do I could fiddle around +so because I'm me I I have a plane this + + align:start position:0% +so because I'm me I I have a plane this + + + align:start position:0% +so because I'm me I I have a plane this +this s space is a plane here this this + + align:start position:0% +this s space is a plane here this this + + + align:start position:0% +this s space is a plane here this this +is only a + + align:start position:0% + + + + align:start position:0% + +one-dimensional + + align:start position:0% + + + + align:start position:0% + +uh a rank one Matrix so it's going to + + align:start position:0% +uh a rank one Matrix so it's going to + + + align:start position:0% +uh a rank one Matrix so it's going to +have and I'm in 3D so I I'll have two as + + align:start position:0% +have and I'm in 3D so I I'll have two as + + + align:start position:0% +have and I'm in 3D so I I'll have two as +you as we did and and within this plane + + align:start position:0% +you as we did and and within this plane + + + align:start position:0% +you as we did and and within this plane +of I vectors why don't I choose a + + align:start position:0% +of I vectors why don't I choose a + + + align:start position:0% +of I vectors why don't I choose a +perpendicular pair so this guy is fine + + align:start position:0% +perpendicular pair so this guy is fine + + + align:start position:0% +perpendicular pair so this guy is fine +but let me not sure quite what to how to + + align:start position:0% +but let me not sure quite what to how to + + + align:start position:0% +but let me not sure quite what to how to +do it + + align:start position:0% +do it + + + align:start position:0% +do it +but what's the what's a good one that's + + align:start position:0% +but what's the what's a good one that's + + + align:start position:0% +but what's the what's a good one that's +also in the null space of this so it's + + align:start position:0% +also in the null space of this so it's + + + align:start position:0% +also in the null space of this so it's +also an igen Vector but I'd like it to + + align:start position:0% +also an igen Vector but I'd like it to + + + align:start position:0% +also an igen Vector but I'd like it to +be perpendicular to + + align:start position:0% + + + + align:start position:0% + +this 2 - one - one that would seem to + + align:start position:0% +this 2 - one - one that would seem to + + + align:start position:0% +this 2 - one - one that would seem to +work + + align:start position:0% +work + + + align:start position:0% +work +2 -1 -1 is that + + align:start position:0% +2 -1 -1 is that + + + align:start position:0% +2 -1 -1 is that +perpendicular no well so how fix it up + + align:start position:0% +perpendicular no well so how fix it up + + + align:start position:0% +perpendicular no well so how fix it up +for + + align:start position:0% + + + + align:start position:0% + +me + + align:start position:0% +me + + + align:start position:0% +me +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +to let's see that my equation is making + + align:start position:0% +to let's see that my equation is making + + + align:start position:0% +to let's see that my equation is making +them add up to zero which that did but + + align:start position:0% +them add up to zero which that did but + + + align:start position:0% +them add up to zero which that did but +it wasn't perpendicular okay let's try + + align:start position:0% +it wasn't perpendicular okay let's try + + + align:start position:0% +it wasn't perpendicular okay let's try +again we need three numbers that add to + + align:start position:0% +again we need three numbers that add to + + + align:start position:0% +again we need three numbers that add to +zero maybe if I put the two + + align:start position:0% +zero maybe if I put the two + + + align:start position:0% +zero maybe if I put the two +in the + + align:start position:0% +in the + + + align:start position:0% +in the +middle will that do + + align:start position:0% + + + + align:start position:0% + +it yes because now the dotproduct of + + align:start position:0% +it yes because now the dotproduct of + + + align:start position:0% +it yes because now the dotproduct of +that with that is a minus one nothing + + align:start position:0% +that with that is a minus one nothing + + + align:start position:0% +that with that is a minus one nothing +and a plus one so it is now so that's + + align:start position:0% +and a plus one so it is now so that's + + + align:start position:0% +and a plus one so it is now so that's +the great thing then that the X's are or + + align:start position:0% +the great thing then that the X's are or + + + align:start position:0% +the great thing then that the X's are or +I if I had space to write or can be + + align:start position:0% +I if I had space to write or can be + + + align:start position:0% +I if I had space to write or can be +chosen because you saw that there was a + + align:start position:0% +chosen because you saw that there was a + + + align:start position:0% +chosen because you saw that there was a +little Choice involved + + align:start position:0% +little Choice involved + + + align:start position:0% +little Choice involved +uh + + align:start position:0% +uh + + + align:start position:0% +uh +perpendicular and actually now if we + + align:start position:0% +perpendicular and actually now if we + + + align:start position:0% +perpendicular and actually now if we +really want Perfection why don't we make + + align:start position:0% +really want Perfection why don't we make + + + align:start position:0% +really want Perfection why don't we make +them unit + + align:start position:0% +them unit + + + align:start position:0% +them unit +vectors why don't I make them unit + + align:start position:0% +vectors why don't I make them unit + + + align:start position:0% +vectors why don't I make them unit +vectors then so I will divide that M + + align:start position:0% +vectors then so I will divide that M + + + align:start position:0% +vectors then so I will divide that M +that vector by square < TK of two divide + + align:start position:0% +that vector by square < TK of two divide + + + align:start position:0% +that vector by square < TK of two divide +that one by sare < TK of 6 divide that + + align:start position:0% +that one by sare < TK of 6 divide that + + + align:start position:0% +that one by sare < TK of 6 divide that +by S < TK of three those were the + + align:start position:0% +by S < TK of three those were the + + + align:start position:0% +by S < TK of three those were the +lengths of the three vectors and now + + align:start position:0% +lengths of the three vectors and now + + + align:start position:0% +lengths of the three vectors and now +they have length one so they're now unit + + align:start position:0% +they have length one so they're now unit + + + align:start position:0% +they have length one so they're now unit +vectors now I'm totally happy with those + + align:start position:0% +vectors now I'm totally happy with those + + + align:start position:0% +vectors now I'm totally happy with those +three igen vectors + + align:start position:0% +three igen vectors + + + align:start position:0% +three igen vectors +and my comment is that as soon as I had + + align:start position:0% +and my comment is that as soon as I had + + + align:start position:0% +and my comment is that as soon as I had +a 3X3 symmetric Matrix I knew we I knew + + align:start position:0% +a 3X3 symmetric Matrix I knew we I knew + + + align:start position:0% +a 3X3 symmetric Matrix I knew we I knew +it was + + align:start position:0% +it was + + + align:start position:0% +it was +possible I knew it was possible okay um + + align:start position:0% +possible I knew it was possible okay um + + + align:start position:0% +possible I knew it was possible okay um +and now I want to say what happens to + + align:start position:0% +and now I want to say what happens to + + + align:start position:0% +and now I want to say what happens to +this + + align:start position:0% +this + + + align:start position:0% +this +great this diagonalization stuff so we + + align:start position:0% +great this diagonalization stuff so we + + + align:start position:0% +great this diagonalization stuff so we +have the igen vector Matrix and I've + + align:start position:0% +have the igen vector Matrix and I've + + + align:start position:0% +have the igen vector Matrix and I've +written we've got the igen vectors we've + + align:start position:0% +written we've got the igen vectors we've + + + align:start position:0% +written we've got the igen vectors we've +got the igen values so why am I coming + + align:start position:0% +got the igen values so why am I coming + + + align:start position:0% +got the igen values so why am I coming +back to this uh + + align:start position:0% +back to this uh + + + align:start position:0% +back to this uh +result because I want to + + align:start position:0% +result because I want to + + + align:start position:0% +result because I want to +somehow identify or or point to or + + align:start position:0% +somehow identify or or point to or + + + align:start position:0% +somehow identify or or point to or +highlight the fact that these I vectors + + align:start position:0% +highlight the fact that these I vectors + + + align:start position:0% +highlight the fact that these I vectors +the three we finally chose + + align:start position:0% +the three we finally chose + + + align:start position:0% +the three we finally chose +are perpendicular in fact they're + + align:start position:0% +are perpendicular in fact they're + + + align:start position:0% +are perpendicular in fact they're +perpendicular unit vectors and there's a + + align:start position:0% +perpendicular unit vectors and there's a + + + align:start position:0% +perpendicular unit vectors and there's a +there's a single word that that that uh + + align:start position:0% +there's a single word that that that uh + + + align:start position:0% +there's a single word that that that uh +talk that says when you have a bunch of + + align:start position:0% +talk that says when you have a bunch of + + + align:start position:0% +talk that says when you have a bunch of +vectors that are perpendicular to each + + align:start position:0% +vectors that are perpendicular to each + + + align:start position:0% +vectors that are perpendicular to each +other mutually perpendicular and they're + + align:start position:0% +other mutually perpendicular and they're + + + align:start position:0% +other mutually perpendicular and they're +all unit + + align:start position:0% +all unit + + + align:start position:0% +all unit +vectors that's a well it's a basis for + + align:start position:0% +vectors that's a well it's a basis for + + + align:start position:0% +vectors that's a well it's a basis for +sure but what's the adjective + + align:start position:0% +sure but what's the adjective + + + align:start position:0% +sure but what's the adjective +orthonormal Ortho orthogonal is the same + + align:start position:0% +orthonormal Ortho orthogonal is the same + + + align:start position:0% +orthonormal Ortho orthogonal is the same +as + + align:start position:0% +as + + + align:start position:0% +as +perpendicular and then by making them + + align:start position:0% +perpendicular and then by making them + + + align:start position:0% +perpendicular and then by making them +unit vectors we normalize them so now + + align:start position:0% +unit vectors we normalize them so now + + + align:start position:0% +unit vectors we normalize them so now +these X's were orthonormal so that's the + + align:start position:0% +these X's were orthonormal so that's the + + + align:start position:0% +these X's were orthonormal so that's the +these ones I chose here so now I'll race + + align:start position:0% +these ones I chose here so now I'll race + + + align:start position:0% +these ones I chose here so now I'll race +this + + align:start position:0% +this + + + align:start position:0% +this +above we've got + + align:start position:0% + + + + align:start position:0% + +orthonormal igen + + align:start position:0% + + + + align:start position:0% + +vectors + + align:start position:0% + + + + align:start position:0% + +okay right and I'll even give them a + + align:start position:0% +okay right and I'll even give them a + + + align:start position:0% +okay right and I'll even give them a +special name a special letter that + + align:start position:0% +special name a special letter that + + + align:start position:0% +special name a special letter that +which will be Q can I call those igen + + align:start position:0% +which will be Q can I call those igen + + + align:start position:0% +which will be Q can I call those igen +vectors Q just again to highlight the + + align:start position:0% +vectors Q just again to highlight the + + + align:start position:0% +vectors Q just again to highlight the +fact + + align:start position:0% +fact + + + align:start position:0% +fact +that they're orthonormal so I'll use + + align:start position:0% +that they're orthonormal so I'll use + + + align:start position:0% +that they're orthonormal so I'll use +orthonormal the letter little Q for a + + align:start position:0% +orthonormal the letter little Q for a + + + align:start position:0% +orthonormal the letter little Q for a +bunch of vectors that's that are that + + align:start position:0% +bunch of vectors that's that are that + + + align:start position:0% +bunch of vectors that's that are that +have this special property then it + + align:start position:0% +have this special property then it + + + align:start position:0% +have this special property then it +highlights it so as a result I'll call + + align:start position:0% +highlights it so as a result I'll call + + + align:start position:0% +highlights it so as a result I'll call +my + + align:start position:0% +my + + + align:start position:0% +my +Matrix capital Q so what I'm what the + + align:start position:0% +Matrix capital Q so what I'm what the + + + align:start position:0% +Matrix capital Q so what I'm what the +the result I'm getting to is that in the + + align:start position:0% +the result I'm getting to is that in the + + + align:start position:0% +the result I'm getting to is that in the +symmetric case for a symmetric Matrix + + align:start position:0% +symmetric case for a symmetric Matrix + + + align:start position:0% +symmetric case for a symmetric Matrix +this a equal s Lambda inverse + + align:start position:0% +this a equal s Lambda inverse + + + align:start position:0% +this a equal s Lambda inverse +becomes K can I use K for the symmetric + + align:start position:0% +becomes K can I use K for the symmetric + + + align:start position:0% +becomes K can I use K for the symmetric +Matrix and the point is that s is now + + align:start position:0% +Matrix and the point is that s is now + + + align:start position:0% +Matrix and the point is that s is now +I'm going to use the letter + + align:start position:0% +I'm going to use the letter + + + align:start position:0% +I'm going to use the letter +q and then Lambda I'm staying with that + + align:start position:0% +q and then Lambda I'm staying with that + + + align:start position:0% +q and then Lambda I'm staying with that +letter Lambda and now here goes Q + + align:start position:0% +letter Lambda and now here goes Q + + + align:start position:0% +letter Lambda and now here goes Q +inverse + + align:start position:0% + + + + align:start position:0% + +right I haven't done anything except to + + align:start position:0% +right I haven't done anything except to + + + align:start position:0% +right I haven't done anything except to +introduce the letter Q as highlighting + + align:start position:0% +introduce the letter Q as highlighting + + + align:start position:0% +introduce the letter Q as highlighting +the the fact that the columns are + + align:start position:0% +the the fact that the columns are + + + align:start position:0% +the the fact that the columns are +orthonormal so I used X's when they + + align:start position:0% +orthonormal so I used X's when they + + + align:start position:0% +orthonormal so I used X's when they +weren't anything special but just + + align:start position:0% +weren't anything special but just + + + align:start position:0% +weren't anything special but just +independent now I'm using Q's to say + + align:start position:0% +independent now I'm using Q's to say + + + align:start position:0% +independent now I'm using Q's to say +they're orthonormal but now there's + + align:start position:0% +they're orthonormal but now there's + + + align:start position:0% +they're orthonormal but now there's +something about + + align:start position:0% +something about + + + align:start position:0% +something about +matrices there's something about a + + align:start position:0% +matrices there's something about a + + + align:start position:0% +matrices there's something about a +matrix whose columns are orthonormal so + + align:start position:0% +matrix whose columns are orthonormal so + + + align:start position:0% +matrix whose columns are orthonormal so +these these X's I can now call these are + + align:start position:0% +these these X's I can now call these are + + + align:start position:0% +these these X's I can now call these are +now + + align:start position:0% +now + + + align:start position:0% +now +q's and there's something special about + + align:start position:0% +q's and there's something special about + + + align:start position:0% +q's and there's something special about +a matrix who's with a The Matrix with + + align:start position:0% +a matrix who's with a The Matrix with + + + align:start position:0% +a matrix who's with a The Matrix with +those three + + align:start position:0% +those three + + + align:start position:0% +those three +columns what's special about the Matrix + + align:start position:0% +columns what's special about the Matrix + + + align:start position:0% +columns what's special about the Matrix +that has those three + + align:start position:0% +that has those three + + + align:start position:0% +that has those three +columns well oh let me say its + + align:start position:0% +columns well oh let me say its + + + align:start position:0% +columns well oh let me say its +inverse is its transpose this is like + + align:start position:0% +inverse is its transpose this is like + + + align:start position:0% +inverse is its transpose this is like +orthogonal and and and even more orthon + + align:start position:0% +orthogonal and and and even more orthon + + + align:start position:0% +orthogonal and and and even more orthon +normal has so much importance through uh + + align:start position:0% +normal has so much importance through uh + + + align:start position:0% +normal has so much importance through uh +through applied math and here we're + + align:start position:0% +through applied math and here we're + + + align:start position:0% +through applied math and here we're +meeting it for matrices so for matrices + + align:start position:0% +meeting it for matrices so for matrices + + + align:start position:0% +meeting it for matrices so for matrices +Q inverse is the same as Q + + align:start position:0% +Q inverse is the same as Q + + + align:start position:0% +Q inverse is the same as Q +transpose that's the or or I could say Q + + align:start position:0% +transpose that's the or or I could say Q + + + align:start position:0% +transpose that's the or or I could say Q +transpose Q is I that would be another + + align:start position:0% +transpose Q is I that would be another + + + align:start position:0% +transpose Q is I that would be another +way to say + + align:start position:0% +way to say + + + align:start position:0% +way to say +it maybe that's the way to think about + + align:start position:0% +it maybe that's the way to think about + + + align:start position:0% +it maybe that's the way to think about +it why is Q transposed Q equal + + align:start position:0% +it why is Q transposed Q equal + + + align:start position:0% +it why is Q transposed Q equal +I can can I'll make some space to + + align:start position:0% +I can can I'll make some space to + + + align:start position:0% +I can can I'll make some space to +multiply Q transpose by Q so that you + + align:start position:0% +multiply Q transpose by Q so that you + + + align:start position:0% +multiply Q transpose by Q so that you +see you get do get I then that's saying + + align:start position:0% +see you get do get I then that's saying + + + align:start position:0% +see you get do get I then that's saying +that here we found the inverse because + + align:start position:0% +that here we found the inverse because + + + align:start position:0% +that here we found the inverse because +we found the Matrix which multiplies Q + + align:start position:0% +we found the Matrix which multiplies Q + + + align:start position:0% +we found the Matrix which multiplies Q +to be I so the inverse must be the + + align:start position:0% +to be I so the inverse must be the + + + align:start position:0% +to be I so the inverse must be the +transpose and I'm especially + + align:start position:0% +transpose and I'm especially + + + align:start position:0% +transpose and I'm especially +happy to change that to Q transpose and + + align:start position:0% +happy to change that to Q transpose and + + + align:start position:0% +happy to change that to Q transpose and +why so this was the goal I was really + + align:start position:0% +why so this was the goal I was really + + + align:start position:0% +why so this was the goal I was really +ask I'll do that with large + + align:start position:0% +ask I'll do that with large + + + align:start position:0% +ask I'll do that with large +chart why was that of course sometime I + + align:start position:0% +chart why was that of course sometime I + + + align:start position:0% +chart why was that of course sometime I +pay the price by having to erase it uh + + align:start position:0% +pay the price by having to erase it uh + + + align:start position:0% +pay the price by having to erase it uh +why why am I why do + + align:start position:0% +why why am I why do + + + align:start position:0% +why why am I why do +I this is really a key fact here that a + + align:start position:0% +I this is really a key fact here that a + + + align:start position:0% +I this is really a key fact here that a +symmetric Matrix can be factored this + + align:start position:0% +symmetric Matrix can be factored this + + + align:start position:0% +symmetric Matrix can be factored this +way into orthogonal time diagonal time + + align:start position:0% +way into orthogonal time diagonal time + + + align:start position:0% +way into orthogonal time diagonal time +orthogonal transpose that's one of the + + align:start position:0% +orthogonal transpose that's one of the + + + align:start position:0% +orthogonal transpose that's one of the +most basic theorems of linear + + align:start position:0% +most basic theorems of linear + + + align:start position:0% +most basic theorems of linear +algebra + + align:start position:0% +algebra + + + align:start position:0% +algebra +and why why is it limited how do I know + + align:start position:0% +and why why is it limited how do I know + + + align:start position:0% +and why why is it limited how do I know +that that Matrix has to be + + align:start position:0% +that that Matrix has to be + + + align:start position:0% +that that Matrix has to be +symmetric that I could only that I + + align:start position:0% +symmetric that I could only that I + + + align:start position:0% +symmetric that I could only that I +couldn't do it with an unsymmetric + + align:start position:0% +couldn't do it with an unsymmetric + + + align:start position:0% +couldn't do it with an unsymmetric +Matrix that this is really something + + align:start position:0% +Matrix that this is really something + + + align:start position:0% +Matrix that this is really something +special for symmetric + + align:start position:0% + + + + align:start position:0% + +matrices because the right hand side is + + align:start position:0% +matrices because the right hand side is + + + align:start position:0% +matrices because the right hand side is +self-evidently symmetric right so the + + align:start position:0% +self-evidently symmetric right so the + + + align:start position:0% +self-evidently symmetric right so the +right hand side is symmetric Okay so + + align:start position:0% +right hand side is symmetric Okay so + + + align:start position:0% +right hand side is symmetric Okay so +right and then I just wanted to complete + + align:start position:0% +right and then I just wanted to complete + + + align:start position:0% +right and then I just wanted to complete +this thought by asking you to check this + + align:start position:0% +this thought by asking you to check this + + + align:start position:0% +this thought by asking you to check this +Q transpose Q equal I part so let me put + + align:start position:0% +Q transpose Q equal I part so let me put + + + align:start position:0% +Q transpose Q equal I part so let me put +that up above as the matrix + + align:start position:0% +that up above as the matrix + + + align:start position:0% +that up above as the matrix +multiplication of the year + + align:start position:0% +multiplication of the year + + + align:start position:0% +multiplication of the year +uh uh so Q transposed times Q so here + + align:start position:0% +uh uh so Q transposed times Q so here + + + align:start position:0% +uh uh so Q transposed times Q so here +comes here's + + align:start position:0% +comes here's + + + align:start position:0% +comes here's +Q so whatever it was well it was q1 and + + align:start position:0% +Q so whatever it was well it was q1 and + + + align:start position:0% +Q so whatever it was well it was q1 and +Q2 and Q3 I'll shorten my life here okay + + align:start position:0% +Q2 and Q3 I'll shorten my life here okay + + + align:start position:0% +Q2 and Q3 I'll shorten my life here okay +and the transpose will be q1 transpose + + align:start position:0% +and the transpose will be q1 transpose + + + align:start position:0% +and the transpose will be q1 transpose +along that row Q2 transpose and Q3 + + align:start position:0% +along that row Q2 transpose and Q3 + + + align:start position:0% +along that row Q2 transpose and Q3 +transpose so that's Q transpose time q + + align:start position:0% +transpose so that's Q transpose time q + + + align:start position:0% +transpose so that's Q transpose time q +and what are we hoping to + + align:start position:0% +and what are we hoping to + + + align:start position:0% +and what are we hoping to +get + + align:start position:0% +get + + + align:start position:0% +get +I and why because q1 transpose q1 + + align:start position:0% +I and why because q1 transpose q1 + + + align:start position:0% +I and why because q1 transpose q1 +is one that's the length of q1 squar so + + align:start position:0% +is one that's the length of q1 squar so + + + align:start position:0% +is one that's the length of q1 squar so +it's one and q1 transpose time Q2 is is + + align:start position:0% +it's one and q1 transpose time Q2 is is + + + align:start position:0% +it's one and q1 transpose time Q2 is is +that zero there and q1 transpose time Q3 + + align:start position:0% +that zero there and q1 transpose time Q3 + + + align:start position:0% +that zero there and q1 transpose time Q3 +they're orthogonals so that's zero so + + align:start position:0% +they're orthogonals so that's zero so + + + align:start position:0% +they're orthogonals so that's zero so +orthogonal gives us all the zeros and + + align:start position:0% +orthogonal gives us all the zeros and + + + align:start position:0% +orthogonal gives us all the zeros and +normal gives us the + + align:start position:0% +normal gives us the + + + align:start position:0% +normal gives us the +ones and then Q transpose Q is I and we + + align:start position:0% +ones and then Q transpose Q is I and we + + + align:start position:0% +ones and then Q transpose Q is I and we +have square + + align:start position:0% +have square + + + align:start position:0% +have square +Matrix so if we have a square Matrix + + align:start position:0% +Matrix so if we have a square Matrix + + + align:start position:0% +Matrix so if we have a square Matrix +we're in business we must have found the + + align:start position:0% +we're in business we must have found the + + + align:start position:0% +we're in business we must have found the +inverse Q transpose must be the same as + + align:start position:0% +inverse Q transpose must be the same as + + + align:start position:0% +inverse Q transpose must be the same as +Q inverse and + + align:start position:0% +Q inverse and + + + align:start position:0% +Q inverse and +and uh oh let me make just throw in a + + align:start position:0% +and uh oh let me make just throw in a + + + align:start position:0% +and uh oh let me make just throw in a +comment connected for example to Fier + + align:start position:0% +comment connected for example to Fier + + + align:start position:0% +comment connected for example to Fier +Series so there's a situation where we + + align:start position:0% +Series so there's a situation where we + + + align:start position:0% +Series so there's a situation where we +have orthogonal basis uh those signs and + + align:start position:0% +have orthogonal basis uh those signs and + + + align:start position:0% +have orthogonal basis uh those signs and +cosiness are orthogonal or the complex + + align:start position:0% +cosiness are orthogonal or the complex + + + align:start position:0% +cosiness are orthogonal or the complex +exponentials we'll see Fier a lot + + align:start position:0% +exponentials we'll see Fier a lot + + + align:start position:0% +exponentials we'll see Fier a lot +um do you remember the there so there's + + align:start position:0% +um do you remember the there so there's + + + align:start position:0% +um do you remember the there so there's +a formula to find forier transform and + + align:start position:0% +a formula to find forier transform and + + + align:start position:0% +a formula to find forier transform and +then there's an inverse transform + + align:start position:0% +then there's an inverse transform + + + align:start position:0% +then there's an inverse transform +formula and the point was those formulas + + align:start position:0% +formula and the point was those formulas + + + align:start position:0% +formula and the point was those formulas +are almost identical they're just like + + align:start position:0% +are almost identical they're just like + + + align:start position:0% +are almost identical they're just like +transposes of each other because there's + + align:start position:0% +transposes of each other because there's + + + align:start position:0% +transposes of each other because there's +another + + align:start position:0% +another + + + align:start position:0% +another +situation of that most desirable kind + + align:start position:0% +situation of that most desirable kind + + + align:start position:0% +situation of that most desirable kind +when we have things that are orthonormal + + align:start position:0% +when we have things that are orthonormal + + + align:start position:0% +when we have things that are orthonormal +and inverting is just + + align:start position:0% +and inverting is just + + + align:start position:0% +and inverting is just +transposing ultimately that's why we + + align:start position:0% +transposing ultimately that's why we + + + align:start position:0% +transposing ultimately that's why we +love + + align:start position:0% +love + + + align:start position:0% +love +orthonormal functions or vectors why we + + align:start position:0% +orthonormal functions or vectors why we + + + align:start position:0% +orthonormal functions or vectors why we +like to calculate with orthonormal + + align:start position:0% +like to calculate with orthonormal + + + align:start position:0% +like to calculate with orthonormal +things is that inverting is no trouble + + align:start position:0% +things is that inverting is no trouble + + + align:start position:0% +things is that inverting is no trouble +it's just + + align:start position:0% +it's just + + + align:start position:0% +it's just +transposing well from the scientific + + align:start position:0% +transposing well from the scientific + + + align:start position:0% +transposing well from the scientific +Computing point of view I think of + + align:start position:0% +Computing point of view I think of + + + align:start position:0% +Computing point of view I think of +another reason why we like orthonormal + + align:start position:0% +another reason why we like orthonormal + + + align:start position:0% +another reason why we like orthonormal +matrices and that is that they never get + + align:start position:0% +matrices and that is that they never get + + + align:start position:0% +matrices and that is that they never get +out of hand they can't if we multiply + + align:start position:0% +out of hand they can't if we multiply + + + align:start position:0% +out of hand they can't if we multiply +together a whole lot of orthonormal + + align:start position:0% +together a whole lot of orthonormal + + + align:start position:0% +together a whole lot of orthonormal +matrices Q's well that it's still + + align:start position:0% +matrices Q's well that it's still + + + align:start position:0% +matrices Q's well that it's still +orthonormal and uh never never grows so + + align:start position:0% +orthonormal and uh never never grows so + + + align:start position:0% +orthonormal and uh never never grows so +numerical numerical instability is never + + align:start position:0% +numerical numerical instability is never + + + align:start position:0% +numerical numerical instability is never +going to happen as long as we're dealing + + align:start position:0% +going to happen as long as we're dealing + + + align:start position:0% +going to happen as long as we're dealing +with q's right or or or these orthogonal + + align:start position:0% +with q's right or or or these orthogonal + + + align:start position:0% +with q's right or or or these orthogonal +matrices okay so that's completes the + + align:start position:0% +matrices okay so that's completes the + + + align:start position:0% +matrices okay so that's completes the +first part of the lecture let me for a + + align:start position:0% +first part of the lecture let me for a + + + align:start position:0% +first part of the lecture let me for a +second + + align:start position:0% +second + + + align:start position:0% +second +part give a second example and then move + + align:start position:0% +part give a second example and then move + + + align:start position:0% +part give a second example and then move +to differential equations and it may + + align:start position:0% +to differential equations and it may + + + align:start position:0% +to differential equations and it may +happen that this + + align:start position:0% +happen that this + + + align:start position:0% +happen that this +lecture the hour runs out before the + + align:start position:0% +lecture the hour runs out before the + + + align:start position:0% +lecture the hour runs out before the +lecture does and then I'll start the + + align:start position:0% +lecture does and then I'll start the + + + align:start position:0% +lecture does and then I'll start the +beginning of lecture six with the + + align:start position:0% +beginning of lecture six with the + + + align:start position:0% +beginning of lecture six with the +completing the differential equations I + + align:start position:0% +completing the differential equations I + + + align:start position:0% +completing the differential equations I +just wanted to take one of our earlier + + align:start position:0% + + + + align:start position:0% + +KS or two of them + + align:start position:0% +KS or two of them + + + align:start position:0% +KS or two of them +maybe so do you remember cuz like I my + + align:start position:0% +maybe so do you remember cuz like I my + + + align:start position:0% +maybe so do you remember cuz like I my +idea is to build this whole thing on + + align:start position:0% +idea is to build this whole thing on + + + align:start position:0% +idea is to build this whole thing on +those original matrices K so let me take + + align:start position:0% +those original matrices K so let me take + + + align:start position:0% +those original matrices K so let me take +K you remember the you remember the two + + align:start position:0% +K you remember the you remember the two + + + align:start position:0% +K you remember the you remember the two +minus one this one + + align:start position:0% + + + + align:start position:0% + +and I it would be nice to know the igen + + align:start position:0% +and I it would be nice to know the igen + + + align:start position:0% +and I it would be nice to know the igen +vectors and igen values of that one or + + align:start position:0% +vectors and igen values of that one or + + + align:start position:0% +vectors and igen values of that one or +do you remember B the one that had both + + align:start position:0% +do you remember B the one that had both + + + align:start position:0% +do you remember B the one that had both +ends switched to + + align:start position:0% + + + + align:start position:0% + +whoops 1 - one 0 -1 2 -1 0 - one one + + align:start position:0% +whoops 1 - one 0 -1 2 -1 0 - one one + + + align:start position:0% +whoops 1 - one 0 -1 2 -1 0 - one one +that was the one that had both ends + + align:start position:0% +that was the one that had both ends + + + align:start position:0% +that was the one that had both ends +changed to one I I could do the third + + align:start position:0% +changed to one I I could do the third + + + align:start position:0% +changed to one I I could do the third +one that had one end change but for a + + align:start position:0% +one that had one end change but for a + + + align:start position:0% +one that had one end change but for a +time let's okay I'd be interested in the + + align:start position:0% +time let's okay I'd be interested in the + + + align:start position:0% +time let's okay I'd be interested in the +igen values and igen + + align:start position:0% +igen values and igen + + + align:start position:0% +igen values and igen +vectors of our favorite + + align:start position:0% +vectors of our favorite + + + align:start position:0% +vectors of our favorite +matrices okay so let me leave a little + + align:start position:0% +matrices okay so let me leave a little + + + align:start position:0% +matrices okay so let me leave a little +space these these examples are so + + align:start position:0% + + + + align:start position:0% + +important and what do we hope to do + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +well we hope to uh see a pattern that's + + align:start position:0% +well we hope to uh see a pattern that's + + + align:start position:0% +well we hope to uh see a pattern that's +going to be true for all sizes right + + align:start position:0% +going to be true for all sizes right + + + align:start position:0% +going to be true for all sizes right +because the the it wasn't just the 3X3 + + align:start position:0% +because the the it wasn't just the 3X3 + + + align:start position:0% +because the the it wasn't just the 3X3 +case that interested us but n byn and + + align:start position:0% +case that interested us but n byn and + + + align:start position:0% +case that interested us but n byn and +actually the N byn example that I erased + + align:start position:0% +actually the N byn example that I erased + + + align:start position:0% +actually the N byn example that I erased +with the with the minus ones filling all + + align:start position:0% +with the with the minus ones filling all + + + align:start position:0% +with the with the minus ones filling all +the above and below the diagonal you + + align:start position:0% +the above and below the diagonal you + + + align:start position:0% +the above and below the diagonal you +could move to n byn on that one and + + align:start position:0% +could move to n byn on that one and + + + align:start position:0% +could move to n byn on that one and +maybe the Lector notes asked if you + + align:start position:0% +maybe the Lector notes asked if you + + + align:start position:0% +maybe the Lector notes asked if you +could find the I value so that would be + + align:start position:0% +could find the I value so that would be + + + align:start position:0% +could find the I value so that would be +certainly a problem and feel that you + + align:start position:0% +certainly a problem and feel that you + + + align:start position:0% +certainly a problem and feel that you +could + + align:start position:0% +could + + + align:start position:0% +could +uh put send me a number of people send + + align:start position:0% +uh put send me a number of people send + + + align:start position:0% +uh put send me a number of people send +me comments or or + + align:start position:0% +me comments or or + + + align:start position:0% +me comments or or +improvements uh and they're very very + + align:start position:0% +improvements uh and they're very very + + + align:start position:0% +improvements uh and they're very very +welcome uh or new + + align:start position:0% +welcome uh or new + + + align:start position:0% +welcome uh or new +examples uh please go ahead you could + + align:start position:0% +examples uh please go ahead you could + + + align:start position:0% +examples uh please go ahead you could +either send it just directly to me so + + align:start position:0% +either send it just directly to me so + + + align:start position:0% +either send it just directly to me so +that's discreet or U put it on the uh + + align:start position:0% +that's discreet or U put it on the uh + + + align:start position:0% +that's discreet or U put it on the uh +Tech ad uh send it to everybody uh + + align:start position:0% +Tech ad uh send it to everybody uh + + + align:start position:0% +Tech ad uh send it to everybody uh +that's uh less discreet but uh both both + + align:start position:0% +that's uh less discreet but uh both both + + + align:start position:0% +that's uh less discreet but uh both both +great so please do + + align:start position:0% +great so please do + + + align:start position:0% +great so please do +it sorry no laughing right that's right + + align:start position:0% +it sorry no laughing right that's right + + + align:start position:0% +it sorry no laughing right that's right +okay so any any igen values for these + + align:start position:0% +okay so any any igen values for these + + + align:start position:0% +okay so any any igen values for these +well tell me an IG value for this one + + align:start position:0% +well tell me an IG value for this one + + + align:start position:0% +well tell me an IG value for this one +anyway you remember about that Matrix + + align:start position:0% +anyway you remember about that Matrix + + + align:start position:0% +anyway you remember about that Matrix +now this is taking you back two weeks + + align:start position:0% +now this is taking you back two weeks + + + align:start position:0% +now this is taking you back two weeks +what was what was UN so special or maybe + + align:start position:0% +what was what was UN so special or maybe + + + align:start position:0% +what was what was UN so special or maybe +even unpleasant about that + + align:start position:0% +even unpleasant about that + + + align:start position:0% +even unpleasant about that +Matrix it was it was singular so you + + align:start position:0% +Matrix it was it was singular so you + + + align:start position:0% +Matrix it was it was singular so you +know one of its I values already + + align:start position:0% +know one of its I values already + + + align:start position:0% +know one of its I values already +zero right so the I values here are + + align:start position:0% +zero right so the I values here are + + + align:start position:0% +zero right so the I values here are +zero and two more to find okay and what + + align:start position:0% +zero and two more to find okay and what + + + align:start position:0% +zero and two more to find okay and what +what do you know about the other two + + align:start position:0% +what do you know about the other two + + + align:start position:0% +what do you know about the other two +igen values well they add to four anyway + + align:start position:0% +igen values well they add to four anyway + + + align:start position:0% +igen values well they add to four anyway +but I'm not at a glance I've sort of + + align:start position:0% +but I'm not at a glance I've sort of + + + align:start position:0% +but I'm not at a glance I've sort of +I've forgotten what they were I actually + + align:start position:0% +I've forgotten what they were I actually + + + align:start position:0% +I've forgotten what they were I actually +I'm more interested in the igen + + align:start position:0% +I'm more interested in the igen + + + align:start position:0% +I'm more interested in the igen +vectors the igen vectors of this Matrix + + align:start position:0% +vectors the igen vectors of this Matrix + + + align:start position:0% +vectors the igen vectors of this Matrix +and the I vectors of this and uh they're + + align:start position:0% +and the I vectors of this and uh they're + + + align:start position:0% +and the I vectors of this and uh they're +so important important actually they're + + align:start position:0% +so important important actually they're + + + align:start position:0% +so important important actually they're +so important let me come to let me talk + + align:start position:0% +so important let me come to let me talk + + + align:start position:0% +so important let me come to let me talk +about an igen Vector of this + + align:start position:0% +about an igen Vector of this + + + align:start position:0% +about an igen Vector of this +one this is totally special right I'm + + align:start position:0% +one this is totally special right I'm + + + align:start position:0% +one this is totally special right I'm +I'm writing up a 3X3 Matrix I could + + align:start position:0% +I'm writing up a 3X3 Matrix I could + + + align:start position:0% +I'm writing up a 3X3 Matrix I could +numerically compute the igen values of + + align:start position:0% +numerically compute the igen values of + + + align:start position:0% +numerically compute the igen values of +these + + align:start position:0% +these + + + align:start position:0% +these +matrices and the igen vectors or get mat + + align:start position:0% +matrices and the igen vectors or get mat + + + align:start position:0% +matrices and the igen vectors or get mat +lab to do it but we would miss the + + align:start position:0% +lab to do it but we would miss the + + + align:start position:0% +lab to do it but we would miss the +pattern which extends to n byn that's + + align:start position:0% +pattern which extends to n byn that's + + + align:start position:0% +pattern which extends to n byn that's +the only thing mat lab well maybe not + + align:start position:0% +the only thing mat lab well maybe not + + + align:start position:0% +the only thing mat lab well maybe not +the only thing mat lab can't do but one + + align:start position:0% +the only thing mat lab can't do but one + + + align:start position:0% +the only thing mat lab can't do but one +of its + + align:start position:0% +of its + + + align:start position:0% +of its +limitations is that if we if we give it + + align:start position:0% +limitations is that if we if we give it + + + align:start position:0% +limitations is that if we if we give it +a matrix it'll find its IG values and + + align:start position:0% +a matrix it'll find its IG values and + + + align:start position:0% +a matrix it'll find its IG values and +igen vectors but then we say ha just + + align:start position:0% +igen vectors but then we say ha just + + + align:start position:0% +igen vectors but then we say ha just +generalize and uh Matt lab says what uh + + align:start position:0% +generalize and uh Matt lab says what uh + + + align:start position:0% +generalize and uh Matt lab says what uh +and uh doesn't know what to do so let's + + align:start position:0% +and uh doesn't know what to do so let's + + + align:start position:0% +and uh doesn't know what to do so let's +do better than matlb here okay let me + + align:start position:0% +do better than matlb here okay let me + + + align:start position:0% +do better than matlb here okay let me +look at this one + + align:start position:0% +look at this one + + + align:start position:0% +look at this one +first what I see there is and you + + align:start position:0% +first what I see there is and you + + + align:start position:0% +first what I see there is and you +remember it came from that line of + + align:start position:0% +remember it came from that line of + + + align:start position:0% +remember it came from that line of +Springs I see this -1 2 -1 this second + + align:start position:0% +Springs I see this -1 2 -1 this second + + + align:start position:0% +Springs I see this -1 2 -1 this second +difference coming up and I see it's been + + align:start position:0% +difference coming up and I see it's been + + + align:start position:0% +difference coming up and I see it's been +chopped off so that the u0 and the u4 + + align:start position:0% +chopped off so that the u0 and the u4 + + + align:start position:0% +chopped off so that the u0 and the u4 +which nowhere appear here it's as if + + align:start position:0% +which nowhere appear here it's as if + + + align:start position:0% +which nowhere appear here it's as if +they were zero right the the the two + + align:start position:0% +they were zero right the the the two + + + align:start position:0% +they were zero right the the the two +ends of the spring were fixed this was a + + align:start position:0% +ends of the spring were fixed this was a + + + align:start position:0% +ends of the spring were fixed this was a +this was fixed with u equals + + align:start position:0% + + + + align:start position:0% + +0 and now I want to think of a + + align:start position:0% +0 and now I want to think of a + + + align:start position:0% +0 and now I want to think of a +vector that I see that'll be the + + align:start position:0% +vector that I see that'll be the + + + align:start position:0% +vector that I see that'll be the +pattern u0 and + + align:start position:0% +pattern u0 and + + + align:start position:0% +pattern u0 and +u4 the N one's zero and does something + + align:start position:0% +u4 the N one's zero and does something + + + align:start position:0% +u4 the N one's zero and does something +in + + align:start position:0% +in + + + align:start position:0% +in +between and in between it does something + + align:start position:0% +between and in between it does something + + + align:start position:0% +between and in between it does something +I'm I'm just like + + align:start position:0% +I'm I'm just like + + + align:start position:0% +I'm I'm just like +uh proceeding by analogy + + align:start position:0% +uh proceeding by analogy + + + align:start position:0% +uh proceeding by analogy +here suppose it was a differential + + align:start position:0% +here suppose it was a differential + + + align:start position:0% +here suppose it was a differential +equation suppose it was a differential + + align:start position:0% +equation suppose it was a differential + + + align:start position:0% +equation suppose it was a differential +equation this is sort of analogous to + + align:start position:0% +equation this is sort of analogous to + + + align:start position:0% +equation this is sort of analogous to +yeah if you're willing to to + + align:start position:0% +yeah if you're willing to to + + + align:start position:0% +yeah if you're willing to to +to give me this one this is sort of + + align:start position:0% +to give me this one this is sort of + + + align:start position:0% +to give me this one this is sort of +analogous to looking at that this is a + + align:start position:0% +analogous to looking at that this is a + + + align:start position:0% +analogous to looking at that this is a +second difference and we talk a lot + + align:start position:0% +second difference and we talk a lot + + + align:start position:0% +second difference and we talk a lot +about that it or minus a second + + align:start position:0% +about that it or minus a second + + + align:start position:0% +about that it or minus a second +difference so it's really analogous so + + align:start position:0% +difference so it's really analogous so + + + align:start position:0% +difference so it's really analogous so +this is + + align:start position:0% + + + + align:start position:0% + +analogy equals Lambda U that's what + + align:start position:0% +analogy equals Lambda U that's what + + + align:start position:0% +analogy equals Lambda U that's what +we're looking + + align:start position:0% +we're looking + + + align:start position:0% +we're looking +for here this is just by analogy we're + + align:start position:0% +for here this is just by analogy we're + + + align:start position:0% +for here this is just by analogy we're +looking for k u equal Lambda U and K is + + align:start position:0% +looking for k u equal Lambda U and K is + + + align:start position:0% +looking for k u equal Lambda U and K is +like a second derivative but it's really + + align:start position:0% +like a second derivative but it's really + + + align:start position:0% +like a second derivative but it's really +a second difference true and we're we're + + align:start position:0% +a second difference true and we're we're + + + align:start position:0% +a second difference true and we're we're +and it's as if U of 0 is zero and U at + + align:start position:0% +and it's as if U of 0 is zero and U at + + + align:start position:0% +and it's as if U of 0 is zero and U at +the other end is zero say Pi maybe or + + align:start position:0% +the other end is zero say Pi maybe or + + + align:start position:0% +the other end is zero say Pi maybe or +one or something maybe + + align:start position:0% +one or something maybe + + + align:start position:0% +one or something maybe +one could you tell me an igen Vector of + + align:start position:0% +one could you tell me an igen Vector of + + + align:start position:0% +one could you tell me an igen Vector of +the second + + align:start position:0% +the second + + + align:start position:0% +the second +derivative can you tell me a fun IG + + align:start position:0% +derivative can you tell me a fun IG + + + align:start position:0% +derivative can you tell me a fun IG +function I better say can you tell me a + + align:start position:0% +function I better say can you tell me a + + + align:start position:0% +function I better say can you tell me a +function whose second derivative is a a + + align:start position:0% +function whose second derivative is a a + + + align:start position:0% +function whose second derivative is a a +multiple of itself yeah you can do that + + align:start position:0% +multiple of itself yeah you can do that + + + align:start position:0% +multiple of itself yeah you can do that +SS and cosin SS and cosiness the second + + align:start position:0% +SS and cosin SS and cosiness the second + + + align:start position:0% +SS and cosin SS and cosiness the second +derivative comes out a multiple of + + align:start position:0% +derivative comes out a multiple of + + + align:start position:0% +derivative comes out a multiple of +itself actually a negative multiple if I + + align:start position:0% +itself actually a negative multiple if I + + + align:start position:0% +itself actually a negative multiple if I +differentiate sign twice I'll come out + + align:start position:0% +differentiate sign twice I'll come out + + + align:start position:0% +differentiate sign twice I'll come out +with a minus sign but then the minus + + align:start position:0% +with a minus sign but then the minus + + + align:start position:0% +with a minus sign but then the minus +sign would be there so the Lambda will + + align:start position:0% +sign would be there so the Lambda will + + + align:start position:0% +sign would be there so the Lambda will +be positive good and now make it now + + align:start position:0% +be positive good and now make it now + + + align:start position:0% +be positive good and now make it now +it's okay any sign and cosine now now + + align:start position:0% +it's okay any sign and cosine now now + + + align:start position:0% +it's okay any sign and cosine now now +what one would satisfy this boundary + + align:start position:0% +what one would satisfy this boundary + + + align:start position:0% +what one would satisfy this boundary +condition or tell me one that would so + + align:start position:0% +condition or tell me one that would so + + + align:start position:0% +condition or tell me one that would so +when I can vector or I function + + align:start position:0% +when I can vector or I function + + + align:start position:0% +when I can vector or I function +maybe tell me a few with signs would be + + align:start position:0% +maybe tell me a few with signs would be + + + align:start position:0% +maybe tell me a few with signs would be +good right signs would be good because + + align:start position:0% +good right signs would be good because + + + align:start position:0% +good right signs would be good because +we want them to start at zero and then + + align:start position:0% +we want them to start at zero and then + + + align:start position:0% +we want them to start at zero and then +we want them to end at zero too so s + + align:start position:0% +we want them to end at zero too so s + + + align:start position:0% +we want them to end at zero too so s +well s of T but now what shall I fix how + + align:start position:0% +well s of T but now what shall I fix how + + + align:start position:0% +well s of T but now what shall I fix how +shall I fix that there so that it comes + + align:start position:0% +shall I fix that there so that it comes + + + align:start position:0% +shall I fix that there so that it comes +back to zero say it at one Pi T Pi t + + align:start position:0% +back to zero say it at one Pi T Pi t + + + align:start position:0% +back to zero say it at one Pi T Pi t +would be good uh tell me some more tell + + align:start position:0% +would be good uh tell me some more tell + + + align:start position:0% +would be good uh tell me some more tell +me another one 2 pi t n Pi T right any + + align:start position:0% +me another one 2 pi t n Pi T right any + + + align:start position:0% +me another one 2 pi t n Pi T right any +mo any s of something Pi T so s of in + + align:start position:0% +mo any s of something Pi T so s of in + + + align:start position:0% +mo any s of something Pi T so s of in +general s of n Pi + + align:start position:0% +general s of n Pi + + + align:start position:0% +general s of n Pi +T + + align:start position:0% +T + + + align:start position:0% +T +okay yeah so that would be the most + + align:start position:0% +okay yeah so that would be the most + + + align:start position:0% +okay yeah so that would be the most +General and now I'm going to come back + + align:start position:0% +General and now I'm going to come back + + + align:start position:0% +General and now I'm going to come back +to this problem and say well maybe it + + align:start position:0% +to this problem and say well maybe it + + + align:start position:0% +to this problem and say well maybe it +works if I + + align:start position:0% +works if I + + + align:start position:0% +works if I +try UK equals s + + align:start position:0% +try UK equals s + + + align:start position:0% +try UK equals s +of + + align:start position:0% +of + + + align:start position:0% +of +Pi K or yeah + + align:start position:0% +Pi K or yeah + + + align:start position:0% +Pi K or yeah +K uh now T I can't use + + align:start position:0% +K uh now T I can't use + + + align:start position:0% +K uh now T I can't use +anymore + + align:start position:0% +anymore + + + align:start position:0% +anymore +uh so let's see T K Over + + align:start position:0% +uh so let's see T K Over + + + align:start position:0% +uh so let's see T K Over +N little n I've been using for + + align:start position:0% +N little n I've been using for + + + align:start position:0% +N little n I've been using for +the I I think that would + + align:start position:0% +the I I think that would + + + align:start position:0% +the I I think that would +work the Ki the Ki uh component of it of + + align:start position:0% +work the Ki the Ki uh component of it of + + + align:start position:0% +work the Ki the Ki uh component of it of +this this is one I Vector this is this + + align:start position:0% +this this is one I Vector this is this + + + align:start position:0% +this this is one I Vector this is this +is first igen + + align:start position:0% + + + + align:start position:0% + +Vector I have to tell you the whole + + align:start position:0% +Vector I have to tell you the whole + + + align:start position:0% +Vector I have to tell you the whole +Vector so I I'm hoping that this works + + align:start position:0% +Vector so I I'm hoping that this works + + + align:start position:0% +Vector so I I'm hoping that this works +that the case + + align:start position:0% +that the case + + + align:start position:0% +that the case +component should be this + + align:start position:0% +component should be this + + + align:start position:0% +component should be this +now first of all does that satisfy our + + align:start position:0% +now first of all does that satisfy our + + + align:start position:0% +now first of all does that satisfy our +little hope that u0 will come out zero + + align:start position:0% +little hope that u0 will come out zero + + + align:start position:0% +little hope that u0 will come out zero +yes and will u + + align:start position:0% +yes and will u + + + align:start position:0% +yes and will u +n u4 so this let me make this clear what + + align:start position:0% +n u4 so this let me make this clear what + + + align:start position:0% +n u4 so this let me make this clear what +it is it better make it a + + align:start position:0% +it is it better make it a + + + align:start position:0% +it is it better make it a +four right because then u4 will be the + + align:start position:0% +four right because then u4 will be the + + + align:start position:0% +four right because then u4 will be the +sign of Pi and we already saw that + + align:start position:0% +sign of Pi and we already saw that + + + align:start position:0% +sign of Pi and we already saw that +that's great that comes out zero this is + + align:start position:0% +that's great that comes out zero this is + + + align:start position:0% +that's great that comes out zero this is +an igen Vector well actually I could + + align:start position:0% +an igen Vector well actually I could + + + align:start position:0% +an igen Vector well actually I could +write down what it is what is that + + align:start position:0% +write down what it is what is that + + + align:start position:0% +write down what it is what is that +Vector s of pi over 4 is > of 2 over + + align:start position:0% +Vector s of pi over 4 is > of 2 over + + + align:start position:0% +Vector s of pi over 4 is > of 2 over + + align:start position:0% + + + align:start position:0% +zero what's the s of 3i over + + align:start position:0% +zero what's the s of 3i over + + + align:start position:0% +zero what's the s of 3i over +4 is it plus or minus + + align:start position:0% +4 is it plus or minus + + + align:start position:0% +4 is it plus or minus +oh it's a one oh because the S + + align:start position:0% +oh it's a one oh because the S + + + align:start position:0% +oh it's a one oh because the S +of Pi part two is one thanks right + + align:start position:0% +of Pi part two is one thanks right + + + align:start position:0% +of Pi part two is one thanks right +and and is it the same again yes it + + align:start position:0% +and and is it the same again yes it + + + align:start position:0% +and and is it the same again yes it +doesn't switch okay so that's that's an + + align:start position:0% +doesn't switch okay so that's that's an + + + align:start position:0% +doesn't switch okay so that's that's an +igen Vector I I guarantee that if I + + align:start position:0% +igen Vector I I guarantee that if I + + + align:start position:0% +igen Vector I I guarantee that if I +multipli that matrix by that Vector I it + + align:start position:0% +multipli that matrix by that Vector I it + + + align:start position:0% +multipli that matrix by that Vector I it +would come out of Lambda times that + + align:start position:0% +would come out of Lambda times that + + + align:start position:0% +would come out of Lambda times that +Vector Okay so + + align:start position:0% + + + + align:start position:0% + +am I + + align:start position:0% + + + + align:start position:0% + +okay do I need a + + align:start position:0% +okay do I need a + + + align:start position:0% +okay do I need a +negative let's see if this is my if that + + align:start position:0% +negative let's see if this is my if that + + + align:start position:0% +negative let's see if this is my if that +formula that would be one I Vector I + + align:start position:0% +formula that would be one I Vector I + + + align:start position:0% +formula that would be one I Vector I +think it might come + + align:start position:0% +think it might come + + + align:start position:0% +think it might come +out it's a little hard to do the + + align:start position:0% +out it's a little hard to do the + + + align:start position:0% +out it's a little hard to do the +multiplication of that by that but I'm + + align:start position:0% +multiplication of that by that but I'm + + + align:start position:0% +multiplication of that by that but I'm +pretty sure that will + + align:start position:0% +pretty sure that will + + + align:start position:0% +pretty sure that will +work now I guess I ought to find three + + align:start position:0% +work now I guess I ought to find three + + + align:start position:0% +work now I guess I ought to find three +igen vectors and the way to find more IG + + align:start position:0% +igen vectors and the way to find more IG + + + align:start position:0% +igen vectors and the way to find more IG +vectors was just to + + align:start position:0% +vectors was just to + + + align:start position:0% +vectors was just to +to double the frequency and triple the + + align:start position:0% +to double the frequency and triple the + + + align:start position:0% +to double the frequency and triple the +frequency so I could find a a next Dion + + align:start position:0% +frequency so I could find a a next Dion + + + align:start position:0% +frequency so I could find a a next Dion +Vector uh let + + align:start position:0% +Vector uh let + + + align:start position:0% +Vector uh let +me the next igon Vector would be uh so + + align:start position:0% +me the next igon Vector would be uh so + + + align:start position:0% +me the next igon Vector would be uh so +that was the first maybe the + + align:start position:0% +that was the first maybe the + + + align:start position:0% +that was the first maybe the +second I + + align:start position:0% + + + + align:start position:0% + +Vector will have components uh s of 2 pi + + align:start position:0% +Vector will have components uh s of 2 pi + + + align:start position:0% +Vector will have components uh s of 2 pi +K Over N so what would it it + + align:start position:0% +K Over N so what would it it + + + align:start position:0% +K Over N so what would it it +be so again k equal 0 fine we get zero + + align:start position:0% +be so again k equal 0 fine we get zero + + + align:start position:0% +be so again k equal 0 fine we get zero +then K = 1 I get oh four always I'm I'm + + align:start position:0% +then K = 1 I get oh four always I'm I'm + + + align:start position:0% +then K = 1 I get oh four always I'm I'm +doing what madlab can't do and + + align:start position:0% +doing what madlab can't do and + + + align:start position:0% +doing what madlab can't do and +generalizing uh okay the K component of + + align:start position:0% +generalizing uh okay the K component of + + + align:start position:0% +generalizing uh okay the K component of +this second ion Vector will + + align:start position:0% +this second ion Vector will + + + align:start position:0% +this second ion Vector will +be uh the so the first component is s of + + align:start position:0% +be uh the so the first component is s of + + + align:start position:0% +be uh the so the first component is s of +pi/ 2 is that a + + align:start position:0% +pi/ 2 is that a + + + align:start position:0% +pi/ 2 is that a +one and then when K is two I get the S + + align:start position:0% +one and then when K is two I get the S + + + align:start position:0% +one and then when K is two I get the S +of Pi what's the sign of Pi zero and + + align:start position:0% +of Pi what's the sign of Pi zero and + + + align:start position:0% +of Pi what's the sign of Pi zero and +when K is three I get the S of 6 piun + + align:start position:0% +when K is three I get the S of 6 piun + + + align:start position:0% +when K is three I get the S of 6 piun +over 4 3 pi over 2 which is minus one + + align:start position:0% +over 4 3 pi over 2 which is minus one + + + align:start position:0% +over 4 3 pi over 2 which is minus one +okay so I believe that's an ion Vector + + align:start position:0% +okay so I believe that's an ion Vector + + + align:start position:0% +okay so I believe that's an ion Vector +too and I believe it's perpendicular to + + align:start position:0% +too and I believe it's perpendicular to + + + align:start position:0% +too and I believe it's perpendicular to +that one why why did I why was I sure it + + align:start position:0% +that one why why did I why was I sure it + + + align:start position:0% +that one why why did I why was I sure it +would + + align:start position:0% + + + + align:start position:0% + +be because our Matrix is symmetric + + align:start position:0% +be because our Matrix is symmetric + + + align:start position:0% +be because our Matrix is symmetric +because our Matrix is symmetric I knew I + + align:start position:0% +because our Matrix is symmetric I knew I + + + align:start position:0% +because our Matrix is symmetric I knew I +would get perpendicular I vectors and + + align:start position:0% +would get perpendicular I vectors and + + + align:start position:0% +would get perpendicular I vectors and +I've got one more to go and you can + + align:start position:0% +I've got one more to go and you can + + + align:start position:0% +I've got one more to go and you can +guess that it'll be the S of 3 Pi over4 + + align:start position:0% +guess that it'll be the S of 3 Pi over4 + + + align:start position:0% +guess that it'll be the S of 3 Pi over4 +so let me 3 yeah 3 Pi K over4 and what + + align:start position:0% +so let me 3 yeah 3 Pi K over4 and what + + + align:start position:0% +so let me 3 yeah 3 Pi K over4 and what +will that give us that'll give us when K + + align:start position:0% +will that give us that'll give us when K + + + align:start position:0% +will that give us that'll give us when K +is one we get this < TK of 2 over two + + align:start position:0% +is one we get this < TK of 2 over two + + + align:start position:0% +is one we get this < TK of 2 over two +when K is two I get S of 6 piun over 4 + + align:start position:0% +when K is two I get S of 6 piun over 4 + + + align:start position:0% +when K is two I get S of 6 piun over 4 +that's 3 piun / 2 is that zero + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +it or is it minus one sorry um which is + + align:start position:0% +it or is it minus one sorry um which is + + + align:start position:0% +it or is it minus one sorry um which is +it I believe anything minus one is it + + align:start position:0% +it I believe anything minus one is it + + + align:start position:0% +it I believe anything minus one is it +minus one 6 s of 6 pi over + + align:start position:0% +minus one 6 s of 6 pi over + + + align:start position:0% +minus one 6 s of 6 pi over +4 okay and then 9 pi + + align:start position:0% + + + + align:start position:0% + +over4 what's that + + align:start position:0% +over4 what's that + + + align:start position:0% +over4 what's that +one of 2 over + + align:start position:0% +one of 2 over + + + align:start position:0% +one of 2 over +two okay H now we can just check that d + + align:start position:0% +two okay H now we can just check that d + + + align:start position:0% +two okay H now we can just check that d +come out orthogonal they really + + align:start position:0% +come out orthogonal they really + + + align:start position:0% +come out orthogonal they really +do yeah and finally should should we + + align:start position:0% +do yeah and finally should should we + + + align:start position:0% +do yeah and finally should should we +check that now I've you see what's a + + align:start position:0% +check that now I've you see what's a + + + align:start position:0% +check that now I've you see what's a +little unusual here I've guessed the + + align:start position:0% +little unusual here I've guessed the + + + align:start position:0% +little unusual here I've guessed the +vectors without stopping for the igen + + align:start position:0% +vectors without stopping for the igen + + + align:start position:0% +vectors without stopping for the igen +values I didn't do it in the usual + + align:start position:0% +values I didn't do it in the usual + + + align:start position:0% +values I didn't do it in the usual +order and uh I think these are the three + + align:start position:0% +order and uh I think these are the three + + + align:start position:0% +order and uh I think these are the three +igen vectors which I wrote in a row but + + align:start position:0% +igen vectors which I wrote in a row but + + + align:start position:0% +igen vectors which I wrote in a row but +uh previously we were writing them in + + align:start position:0% +uh previously we were writing them in + + + align:start position:0% +uh previously we were writing them in +columns can I just what's the igen value + + align:start position:0% +columns can I just what's the igen value + + + align:start position:0% +columns can I just what's the igen value +for that guy if it if it truly is an IG + + align:start position:0% +for that guy if it if it truly is an IG + + + align:start position:0% +for that guy if it if it truly is an IG +Vector then I should be able to multiply + + align:start position:0% +Vector then I should be able to multiply + + + align:start position:0% +Vector then I should be able to multiply +by K and get + + align:start position:0% +by K and get + + + align:start position:0% +by K and get +some and stay in the same direction + + align:start position:0% +some and stay in the same direction + + + align:start position:0% +some and stay in the same direction +right that's what an igen Vector would + + align:start position:0% +right that's what an igen Vector would + + + align:start position:0% +right that's what an igen Vector would +do if I multiply that matrix by that one + + align:start position:0% +do if I multiply that matrix by that one + + + align:start position:0% +do if I multiply that matrix by that one +Z minus one I could write it up here to + + align:start position:0% +Z minus one I could write it up here to + + + align:start position:0% +Z minus one I could write it up here to +make that easier 1 0 minus one this is + + align:start position:0% +make that easier 1 0 minus one this is + + + align:start position:0% +make that easier 1 0 minus one this is +our igen Vector can you do that + + align:start position:0% +our igen Vector can you do that + + + align:start position:0% +our igen Vector can you do that +multiplication what what happens if you + + align:start position:0% +multiplication what what happens if you + + + align:start position:0% +multiplication what what happens if you +do that multiplication + + align:start position:0% + + + + align:start position:0% + +what do you get two 0 minus + + align:start position:0% +what do you get two 0 minus + + + align:start position:0% +what do you get two 0 minus +two yeah two 0 minus two so the igen + + align:start position:0% +two yeah two 0 minus two so the igen + + + align:start position:0% +two yeah two 0 minus two so the igen +value is two right the igen value is two + + align:start position:0% +value is two right the igen value is two + + + align:start position:0% +value is two right the igen value is two +and and and there's this nice formula + + align:start position:0% +and and and there's this nice formula + + + align:start position:0% +and and and there's this nice formula +for the igen values as well as these + + align:start position:0% +for the igen values as well as these + + + align:start position:0% +for the igen values as well as these +nice formula for the igen + + align:start position:0% +nice formula for the igen + + + align:start position:0% +nice formula for the igen +vectors I can tell you what the ion + + align:start position:0% +vectors I can tell you what the ion + + + align:start position:0% +vectors I can tell you what the ion +values for this Matrix are they're two + + align:start position:0% +values for this Matrix are they're two + + + align:start position:0% +values for this Matrix are they're two +which we just figured there's the + + align:start position:0% +which we just figured there's the + + + align:start position:0% +which we just figured there's the +smaller one 2 minus < tk2 and there's + + align:start position:0% +smaller one 2 minus < tk2 and there's + + + align:start position:0% +smaller one 2 minus < tk2 and there's +the larger one 2+ < + + align:start position:0% +the larger one 2+ < + + + align:start position:0% +the larger one 2+ < +tk2 oh and that reminds + + align:start position:0% +tk2 oh and that reminds + + + align:start position:0% +tk2 oh and that reminds +me uh somebody in the + + align:start position:0% +me uh somebody in the + + + align:start position:0% +me uh somebody in the +class uh had the brilliant idea so you + + align:start position:0% +class uh had the brilliant idea so you + + + align:start position:0% +class uh had the brilliant idea so you +see that kind of nice right two and two + + align:start position:0% +see that kind of nice right two and two + + + align:start position:0% +see that kind of nice right two and two +minus < tk2 and 2 plus < tk2 somebody + + align:start position:0% +minus < tk2 and 2 plus < tk2 somebody + + + align:start position:0% +minus < tk2 and 2 plus < tk2 somebody +was who was using + + align:start position:0% +was who was using + + + align:start position:0% +was who was using +Mathematica which is + + align:start position:0% +Mathematica which is + + + align:start position:0% +Mathematica which is +allowed uh uh even if cleave would + + align:start position:0% +allowed uh uh even if cleave would + + + align:start position:0% +allowed uh uh even if cleave would +disapprove + + align:start position:0% +disapprove + + + align:start position:0% +disapprove +uh it turned + + align:start position:0% +uh it turned + + + align:start position:0% +uh it turned +out much highly + + align:start position:0% +out much highly + + + align:start position:0% +out much highly +interesting uh use Mathematica or or or + + align:start position:0% +interesting uh use Mathematica or or or + + + align:start position:0% +interesting uh use Mathematica or or or +Matt well mat lab you'd have to use the + + align:start position:0% +Matt well mat lab you'd have to use the + + + align:start position:0% +Matt well mat lab you'd have to use the +symbolic toolbox to to see the point um + + align:start position:0% +symbolic toolbox to to see the point um + + + align:start position:0% +symbolic toolbox to to see the point um +but I it was something completely new to + + align:start position:0% +but I it was something completely new to + + + align:start position:0% +but I it was something completely new to +me so just by chance I think uh found + + align:start position:0% +me so just by chance I think uh found + + + align:start position:0% +me so just by chance I think uh found +the igen values in the + + align:start position:0% +the igen values in the + + + align:start position:0% +the igen values in the +3X3 7 by7 15 by 15 31 by 31 one one less + + align:start position:0% +3X3 7 by7 15 by 15 31 by 31 one one less + + + align:start position:0% +3X3 7 by7 15 by 15 31 by 31 one one less +than powers of two I I don't know why it + + align:start position:0% +than powers of two I I don't know why it + + + align:start position:0% +than powers of two I I don't know why it +happened that experiment got done but + + align:start position:0% +happened that experiment got done but + + + align:start position:0% +happened that experiment got done but +the results are + + align:start position:0% +the results are + + + align:start position:0% +the results are +Sensational uh let me get those results + + align:start position:0% +Sensational uh let me get those results + + + align:start position:0% +Sensational uh let me get those results +onto the web page the the igen values of + + align:start position:0% +onto the web page the the igen values of + + + align:start position:0% +onto the web page the the igen values of +those of that subf family K3 K7 K15 k31 + + align:start position:0% +those of that subf family K3 K7 K15 k31 + + + align:start position:0% +those of that subf family K3 K7 K15 k31 +came out incred with an incredible + + align:start position:0% +came out incred with an incredible + + + align:start position:0% +came out incred with an incredible +pattern which uh I pose as a exercise to + + align:start position:0% +pattern which uh I pose as a exercise to + + + align:start position:0% +pattern which uh I pose as a exercise to +explain + + align:start position:0% +explain + + + align:start position:0% +explain +okay main point + + align:start position:0% +okay main point + + + align:start position:0% +okay main point +point this has very nice IG vectors and + + align:start position:0% +point this has very nice IG vectors and + + + align:start position:0% +point this has very nice IG vectors and +we can even guess them and check them + + align:start position:0% +we can even guess them and check them + + + align:start position:0% +we can even guess them and check them +before finding the IG values good and + + align:start position:0% +before finding the IG values good and + + + align:start position:0% +before finding the IG values good and +those IG vectors are signs discrete + + align:start position:0% +those IG vectors are signs discrete + + + align:start position:0% +those IG vectors are signs discrete +signs if they in fact they go into the + + align:start position:0% +signs if they in fact they go into the + + + align:start position:0% +signs if they in fact they go into the +discrete sign transform the DST the + + align:start position:0% +discrete sign transform the DST the + + + align:start position:0% +discrete sign transform the DST the +discrete sign transform + + align:start position:0% +discrete sign transform + + + align:start position:0% +discrete sign transform +is is is the Q column is the is this + + align:start position:0% +is is is the Q column is the is this + + + align:start position:0% +is is is the Q column is the is this +Matrix the with it the I vectors are the + + align:start position:0% +Matrix the with it the I vectors are the + + + align:start position:0% +Matrix the with it the I vectors are the +columns and they are these sign + + align:start position:0% +columns and they are these sign + + + align:start position:0% +columns and they are these sign +functions okay wonderful so that sign + + align:start position:0% +functions okay wonderful so that sign + + + align:start position:0% +functions okay wonderful so that sign +transform is quite important only + + align:start position:0% +transform is quite important only + + + align:start position:0% +transform is quite important only +exceeded by the cosine + + align:start position:0% +exceeded by the cosine + + + align:start position:0% +exceeded by the cosine +transform so the cosine the discrete + + align:start position:0% +transform so the cosine the discrete + + + align:start position:0% +transform so the cosine the discrete +cosine transform the + + align:start position:0% +cosine transform the + + + align:start position:0% +cosine transform the +DCT is of very great importance it's + + align:start position:0% +DCT is of very great importance it's + + + align:start position:0% +DCT is of very great importance it's +this it's the it has been the standard + + align:start position:0% +this it's the it has been the standard + + + align:start position:0% +this it's the it has been the standard +for image processing the jpeg standard + + align:start position:0% +for image processing the jpeg standard + + + align:start position:0% +for image processing the jpeg standard +for image processing has used the desp + + align:start position:0% +for image processing has used the desp + + + align:start position:0% +for image processing has used the desp +cosign + + align:start position:0% +cosign + + + align:start position:0% +cosign +transform that is until this very year + + align:start position:0% +transform that is until this very year + + + align:start position:0% +transform that is until this very year +uh well jpeg 2000 but they're running + + align:start position:0% +uh well jpeg 2000 but they're running + + + align:start position:0% +uh well jpeg 2000 but they're running +late uh is the new standard for image + + align:start position:0% +late uh is the new standard for image + + + align:start position:0% +late uh is the new standard for image +processing and uses wavelets so my later + + align:start position:0% +processing and uses wavelets so my later + + + align:start position:0% +processing and uses wavelets so my later +lectures on wavelets will connect + + align:start position:0% +lectures on wavelets will connect + + + align:start position:0% +lectures on wavelets will connect +directly to the itle E the new standard + + align:start position:0% +directly to the itle E the new standard + + + align:start position:0% +directly to the itle E the new standard +that's actually just voted on this week + + align:start position:0% +that's actually just voted on this week + + + align:start position:0% +that's actually just voted on this week +for um using wavelets for image + + align:start position:0% +for um using wavelets for image + + + align:start position:0% +for um using wavelets for image +processing but up to now + + align:start position:0% +processing but up to now + + + align:start position:0% +processing but up to now +the ordinary jpeg standard and we'll + + align:start position:0% +the ordinary jpeg standard and we'll + + + align:start position:0% +the ordinary jpeg standard and we'll +come back to that discussion is the + + align:start position:0% +come back to that discussion is the + + + align:start position:0% +come back to that discussion is the +cosiness and where do the cosines come + + align:start position:0% +cosiness and where do the cosines come + + + align:start position:0% +cosiness and where do the cosines come +from they come from this + + align:start position:0% +from they come from this + + + align:start position:0% +from they come from this +Matrix that + + align:start position:0% +Matrix that + + + align:start position:0% +Matrix that +Matrix because + + align:start position:0% +Matrix because + + + align:start position:0% +Matrix because +I've left the ends free remember that + + align:start position:0% +I've left the ends free remember that + + + align:start position:0% +I've left the ends free remember that +was the free free hanging + + align:start position:0% +was the free free hanging + + + align:start position:0% +was the free free hanging +spring so what's the boundary condition + + align:start position:0% +spring so what's the boundary condition + + + align:start position:0% +spring so what's the boundary condition +at a free end + + align:start position:0% +at a free end + + + align:start position:0% +at a free end +the slope is zero at the fixed + + align:start position:0% +the slope is zero at the fixed + + + align:start position:0% +the slope is zero at the fixed +end u0 is zero at the free end at a free + + align:start position:0% +end u0 is zero at the free end at a free + + + align:start position:0% +end u0 is zero at the free end at a free +end the slope is zero you remember it + + align:start position:0% +end the slope is zero you remember it + + + align:start position:0% +end the slope is zero you remember it +came from and and so what if I change + + align:start position:0% +came from and and so what if I change + + + align:start position:0% +came from and and so what if I change +this to + + align:start position:0% +this to + + + align:start position:0% +this to +slopes + + align:start position:0% + + + + align:start position:0% + +UT being + + align:start position:0% +UT being + + + align:start position:0% +UT being +zero for for this what uh what and then + + align:start position:0% +zero for for this what uh what and then + + + align:start position:0% +zero for for this what uh what and then +back in + + align:start position:0% +back in + + + align:start position:0% +back in +the uh continuous case I'll use cosiness + + align:start position:0% +the uh continuous case I'll use cosiness + + + align:start position:0% +the uh continuous case I'll use cosiness +right cosiness would be the functions + + align:start position:0% +right cosiness would be the functions + + + align:start position:0% +right cosiness would be the functions +that would would be the igen functions + + align:start position:0% +that would would be the igen functions + + + align:start position:0% +that would would be the igen functions +when we're using a zero slope boundary + + align:start position:0% +when we're using a zero slope boundary + + + align:start position:0% +when we're using a zero slope boundary +condition and do you see that maybe and + + align:start position:0% +condition and do you see that maybe and + + + align:start position:0% +condition and do you see that maybe and +this is going to be part of a lecture do + + align:start position:0% +this is going to be part of a lecture do + + + align:start position:0% +this is going to be part of a lecture do +you see that this one minus one row + + align:start position:0% +you see that this one minus one row + + + align:start position:0% +you see that this one minus one row +corresponds to saying zero + + align:start position:0% +corresponds to saying zero + + + align:start position:0% +corresponds to saying zero +slope it it somehow that one minus one + + align:start position:0% +slope it it somehow that one minus one + + + align:start position:0% +slope it it somehow that one minus one +is a first + + align:start position:0% +is a first + + + align:start position:0% +is a first +difference a first difference where in + + align:start position:0% +difference a first difference where in + + + align:start position:0% +difference a first difference where in +the middle here we have second + + align:start position:0% +the middle here we have second + + + align:start position:0% +the middle here we have second +differences and here a first difference + + align:start position:0% +differences and here a first difference + + + align:start position:0% +differences and here a first difference +again let me + + align:start position:0% +again let me + + + align:start position:0% +again let me +just capture this idea then so what do I + + align:start position:0% +just capture this idea then so what do I + + + align:start position:0% +just capture this idea then so what do I +think is what do I think is the igen + + align:start position:0% +think is what do I think is the igen + + + align:start position:0% +think is what do I think is the igen +vector for IG value all zeros oh yeah + + align:start position:0% +vector for IG value all zeros oh yeah + + + align:start position:0% +vector for IG value all zeros oh yeah +you know that one so the I Vector for + + align:start position:0% +you know that one so the I Vector for + + + align:start position:0% +you know that one so the I Vector for +the zero I value is what's the vector in + + align:start position:0% +the zero I value is what's the vector in + + + align:start position:0% +the zero I value is what's the vector in +the null space of + + align:start position:0% +the null space of + + + align:start position:0% +the null space of +B 111 so the igen vector this Lambda + + align:start position:0% +B 111 so the igen vector this Lambda + + + align:start position:0% +B 111 so the igen vector this Lambda +equals z corresponds to 11 one so that's + + align:start position:0% +equals z corresponds to 11 one so that's + + + align:start position:0% +equals z corresponds to 11 one so that's +cosine that's cosine zero I guess repeat + + align:start position:0% +cosine that's cosine zero I guess repeat + + + align:start position:0% +cosine that's cosine zero I guess repeat +it right now the other there are two + + align:start position:0% +it right now the other there are two + + + align:start position:0% +it right now the other there are two +more I vectors let me uh look up the the + + align:start position:0% +more I vectors let me uh look up the the + + + align:start position:0% +more I vectors let me uh look up the the +form of the igen vectors and I'll erase + + align:start position:0% +form of the igen vectors and I'll erase + + + align:start position:0% +form of the igen vectors and I'll erase +this one but well well I won't erase it + + align:start position:0% +this one but well well I won't erase it + + + align:start position:0% +this one but well well I won't erase it +cuz that's the most important I Vector + + align:start position:0% +cuz that's the most important I Vector + + + align:start position:0% +cuz that's the most important I Vector +in Signal processing image processing + + align:start position:0% +in Signal processing image processing + + + align:start position:0% +in Signal processing image processing +this you want to have this I Vector you + + align:start position:0% +this you want to have this I Vector you + + + align:start position:0% +this you want to have this I Vector you +want to have that basis function because + + align:start position:0% +want to have that basis function because + + + align:start position:0% +want to have that basis function because +that's the DC term that picks + + align:start position:0% +that's the DC term that picks + + + align:start position:0% +that's the DC term that picks +up uh all the like all the constant + + align:start position:0% +up uh all the like all the constant + + + align:start position:0% +up uh all the like all the constant +background is picked up by this constant + + align:start position:0% +background is picked up by this constant + + + align:start position:0% +background is picked up by this constant +Vector so we'll make sense of these + + align:start position:0% +Vector so we'll make sense of these + + + align:start position:0% +Vector so we'll make sense of these +statements when discussing image + + align:start position:0% +statements when discussing image + + + align:start position:0% +statements when discussing image +processing + + align:start position:0% +processing + + + align:start position:0% +processing +but uh it's beautiful to have that + + align:start position:0% +but uh it's beautiful to have that + + + align:start position:0% +but uh it's beautiful to have that +Vector in the basis to be able to get + + align:start position:0% +Vector in the basis to be able to get + + + align:start position:0% +Vector in the basis to be able to get +the Blackboard before I wrote on it uh + + align:start position:0% +the Blackboard before I wrote on it uh + + + align:start position:0% +the Blackboard before I wrote on it uh +the whole Blackboard in one vector where + + align:start position:0% +the whole Blackboard in one vector where + + + align:start position:0% +the whole Blackboard in one vector where +these signs are not so great because as + + align:start position:0% +these signs are not so great because as + + + align:start position:0% +these signs are not so great because as +you see they don't have the DC term okay + + align:start position:0% +you see they don't have the DC term okay + + + align:start position:0% +you see they don't have the DC term okay +so I'm using the letter the words the + + align:start position:0% +so I'm using the letter the words the + + + align:start position:0% +so I'm using the letter the words the +letters DC in two connections here + + align:start position:0% +letters DC in two connections here + + + align:start position:0% +letters DC in two connections here +discrete cosine transform is the DCT and + + align:start position:0% +discrete cosine transform is the DCT and + + + align:start position:0% +discrete cosine transform is the DCT and +then when I called said the DC term that + + align:start position:0% +then when I called said the DC term that + + + align:start position:0% +then when I called said the DC term that +was like direct current uh constant okay + + align:start position:0% +was like direct current uh constant okay + + + align:start position:0% +was like direct current uh constant okay +now so just to finish what are the igen + + align:start position:0% +now so just to finish what are the igen + + + align:start position:0% +now so just to finish what are the igen +vectors what are the what are all the + + align:start position:0% +vectors what are the what are all the + + + align:start position:0% +vectors what are the what are all the +igen vectors of this of this family this + + align:start position:0% +igen vectors of this of this family this + + + align:start position:0% +igen vectors of this of this family this +B + + align:start position:0% +B + + + align:start position:0% +B +family of + + align:start position:0% +family of + + + align:start position:0% +family of +matrices okay this was this is always + + align:start position:0% +matrices okay this was this is always + + + align:start position:0% +matrices okay this was this is always +one of them right we always have the + + align:start position:0% +one of them right we always have the + + + align:start position:0% +one of them right we always have the +every every The Columns adding to the + + align:start position:0% +every every The Columns adding to the + + + align:start position:0% +every every The Columns adding to the +zero column now I'm just need to tell + + align:start position:0% +zero column now I'm just need to tell + + + align:start position:0% +zero column now I'm just need to tell +you what are the others so that was + + align:start position:0% +you what are the others so that was + + + align:start position:0% +you what are the others so that was +Lambda equals z let me let + + align:start position:0% +Lambda equals z let me let + + + align:start position:0% +Lambda equals z let me let +me bring that over here this this gave + + align:start position:0% +me bring that over here this this gave + + + align:start position:0% +me bring that over here this this gave +us the IG Vector 11 one and + + align:start position:0% +us the IG Vector 11 one and + + + align:start position:0% +us the IG Vector 11 one and +now the the other the typical lambdas + + align:start position:0% +now the the other the typical lambdas + + + align:start position:0% +now the the other the typical lambdas +and the typical X's so I call them X's + + align:start position:0% +and the typical X's so I call them X's + + + align:start position:0% +and the typical X's so I call them X's +or oh here I call them U's okay and I + + align:start position:0% +or oh here I call them U's okay and I + + + align:start position:0% +or oh here I call them U's okay and I +could have called them + + align:start position:0% +could have called them + + + align:start position:0% +could have called them +Q's well let's let's call them Q's why + + align:start position:0% +Q's well let's let's call them Q's why + + + align:start position:0% +Q's well let's let's call them Q's why +not okay so they'll be + + align:start position:0% +not okay so they'll be + + + align:start position:0% +not okay so they'll be +cosiness so how much of this formula can + + align:start position:0% +cosiness so how much of this formula can + + + align:start position:0% +cosiness so how much of this formula can +I remember there'll be a cosine and + + align:start position:0% +I remember there'll be a cosine and + + + align:start position:0% +I remember there'll be a cosine and +they'll there be a pi of course there'll + + align:start position:0% +they'll there be a pi of course there'll + + + align:start position:0% +they'll there be a pi of course there'll +be a four in the + + align:start position:0% +be a four in the + + + align:start position:0% +be a four in the +denominator and there will + + align:start position:0% +denominator and there will + + + align:start position:0% +denominator and there will +be is it a + + align:start position:0% +be is it a + + + align:start position:0% +be is it a +okay let's see I'm looking this + + align:start position:0% +okay let's see I'm looking this + + + align:start position:0% +okay let's see I'm looking this +is do you see right there be a there'll + + align:start position:0% +is do you see right there be a there'll + + + align:start position:0% +is do you see right there be a there'll +be a one two or + + align:start position:0% +be a one two or + + + align:start position:0% +be a one two or +three so there would be a one two or + + align:start position:0% +three so there would be a one two or + + + align:start position:0% +three so there would be a one two or +three three or no 01 or two + + align:start position:0% +three three or no 01 or two + + + align:start position:0% +three three or no 01 or two +damn uh is it 01 or + + align:start position:0% +damn uh is it 01 or + + + align:start position:0% +damn uh is it 01 or +two I looked this up actually just to + + align:start position:0% +two I looked this up actually just to + + + align:start position:0% +two I looked this up actually just to +mention on this yeah this is better than + + align:start position:0% +mention on this yeah this is better than + + + align:start position:0% +mention on this yeah this is better than +trying to get it right on this little + + align:start position:0% +trying to get it right on this little + + + align:start position:0% +trying to get it right on this little +last corner of the board um I wrote a + + align:start position:0% +last corner of the board um I wrote a + + + align:start position:0% +last corner of the board um I wrote a +survey paper about the + + align:start position:0% +survey paper about the + + + align:start position:0% +survey paper about the +DCT the discret cosine transform in cam + + align:start position:0% +DCT the discret cosine transform in cam + + + align:start position:0% +DCT the discret cosine transform in cam +review and it would be on my web page + + align:start position:0% +review and it would be on my web page + + + align:start position:0% +review and it would be on my web page +page uh you could download the whole + + align:start position:0% +page uh you could download the whole + + + align:start position:0% +page uh you could download the whole +paper and it would discuss the igen + + align:start position:0% +paper and it would discuss the igen + + + align:start position:0% +paper and it would discuss the igen +values and igen vectors of whole bunch + + align:start position:0% +values and igen vectors of whole bunch + + + align:start position:0% +values and igen vectors of whole bunch +of matrices of which this is the most + + align:start position:0% +of matrices of which this is the most + + + align:start position:0% +of matrices of which this is the most +important there are + + align:start position:0% +important there are + + + align:start position:0% +important there are +actually uh several cosine + + align:start position:0% +actually uh several cosine + + + align:start position:0% +actually uh several cosine +transforms but the winner the one that + + align:start position:0% +transforms but the winner the one that + + + align:start position:0% +transforms but the winner the one that +uh people mean when they just say cosine + + align:start position:0% +uh people mean when they just say cosine + + + align:start position:0% +uh people mean when they just say cosine +transform is the is the igen vectors of + + align:start position:0% +transform is the is the igen vectors of + + + align:start position:0% +transform is the is the igen vectors of +this Matrix and the beauty is that so + + align:start position:0% +this Matrix and the beauty is that so + + + align:start position:0% +this Matrix and the beauty is that so +that Matrix is + + align:start position:0% +that Matrix is + + + align:start position:0% +that Matrix is +symmetric so what do we know about those + + align:start position:0% +symmetric so what do we know about those + + + align:start position:0% +symmetric so what do we know about those +cosine + + align:start position:0% +cosine + + + align:start position:0% +cosine +vectors they're orthogonal that we have + + align:start position:0% +vectors they're orthogonal that we have + + + align:start position:0% +vectors they're orthogonal that we have +and we can make them orthonormal right + + align:start position:0% +and we can make them orthonormal right + + + align:start position:0% +and we can make them orthonormal right +that's right so that's the point of that + + align:start position:0% +that's right so that's the point of that + + + align:start position:0% +that's right so that's the point of that +paper so that paper is the discrete + + align:start position:0% +paper so that paper is the discrete + + + align:start position:0% +paper so that paper is the discrete +cosine transform and shall I maybe uh + + align:start position:0% +cosine transform and shall I maybe uh + + + align:start position:0% +cosine transform and shall I maybe uh +put take take just a little space to to + + align:start position:0% +put take take just a little space to to + + + align:start position:0% +put take take just a little space to to +put the um so that's called the + + align:start position:0% +put the um so that's called the + + + align:start position:0% +put the um so that's called the +discrete cosign transform it's in cam + + align:start position:0% + + + + align:start position:0% + +review uh I think the year is + + align:start position:0% +review uh I think the year is + + + align:start position:0% +review uh I think the year is +99 and the web page is + + align:start position:0% +99 and the web page is + + + align:start position:0% +99 and the web page is +www uh + + align:start position:0% +www uh + + + align:start position:0% +www uh +math + + align:start position:0% +math + + + align:start position:0% +math +MIT + + align:start position:0% +MIT + + + align:start position:0% +MIT +edu Tilda + + align:start position:0% +edu Tilda + + + align:start position:0% +edu Tilda +GS and you would see it there and you + + align:start position:0% +GS and you would see it there and you + + + align:start position:0% +GS and you would see it there and you +could download it or I'd be happy if you + + align:start position:0% +could download it or I'd be happy if you + + + align:start position:0% +could download it or I'd be happy if you +review if you looked at cam + + align:start position:0% +review if you looked at cam + + + align:start position:0% +review if you looked at cam +review I'd be even happier if you joined + + align:start position:0% +review I'd be even happier if you joined + + + align:start position:0% +review I'd be even happier if you joined +cam actually uh I've just completed a + + align:start position:0% +cam actually uh I've just completed a + + + align:start position:0% +cam actually uh I've just completed a +term as president I think it's a + + align:start position:0% +term as president I think it's a + + + align:start position:0% +term as president I think it's a +wonderful society and I uh take this + + align:start position:0% +wonderful society and I uh take this + + + align:start position:0% +wonderful society and I uh take this +improper moment to to say that uh that + + align:start position:0% +improper moment to to say that uh that + + + align:start position:0% +improper moment to to say that uh that +uh it's good okay why don't we stop here + + align:start position:0% +uh it's good okay why don't we stop here + + + align:start position:0% +uh it's good okay why don't we stop here +I didn't give you the the uh the I + + align:start position:0% +I didn't give you the the uh the I + + + align:start position:0% +I didn't give you the the uh the I +didn't complete this is there's a K plus + + align:start position:0% +didn't complete this is there's a K plus + + + align:start position:0% +didn't complete this is there's a K plus +a half comes in + + align:start position:0% +a half comes in + + + align:start position:0% +a half comes in +there where a k happened to enter here + + align:start position:0% +there where a k happened to enter here + + + align:start position:0% +there where a k happened to enter here +and uh it just comes out right just + + align:start position:0% +and uh it just comes out right just + + + align:start position:0% +and uh it just comes out right just +comes out right so that's the discrete + + align:start position:0% +comes out right so that's the discrete + + + align:start position:0% +comes out right so that's the discrete +the these igen vectors are automatically + + align:start position:0% +the these igen vectors are automatically + + + align:start position:0% +the these igen vectors are automatically +orthogonal so the Q Matrix with those + + align:start position:0% +orthogonal so the Q Matrix with those + + + align:start position:0% +orthogonal so the Q Matrix with those +igen vectors is the dctt Matrix and to + + align:start position:0% +igen vectors is the dctt Matrix and to + + + align:start position:0% +igen vectors is the dctt Matrix and to +invert that transform what's the inverse + + align:start position:0% +invert that transform what's the inverse + + + align:start position:0% +invert that transform what's the inverse +of Q so this is a final question it's + + align:start position:0% +of Q so this is a final question it's + + + align:start position:0% +of Q so this is a final question it's +its transfers right so uh the the + + align:start position:0% +its transfers right so uh the the + + + align:start position:0% +its transfers right so uh the the +transform is very fast you can you you + + align:start position:0% +transform is very fast you can you you + + + align:start position:0% +transform is very fast you can you you +can use the fft to to execute it and um + + align:start position:0% +can use the fft to to execute it and um + + + align:start position:0% +can use the fft to to execute it and um +you uh get a highly useful transform + + align:start position:0% +you uh get a highly useful transform + + + align:start position:0% +you uh get a highly useful transform +it's a real version of the forier + + align:start position:0% +it's a real version of the forier + + + align:start position:0% +it's a real version of the forier +transform it's a real version with + + align:start position:0% +transform it's a real version with + + + align:start position:0% +transform it's a real version with +cosiness and the point about the + + align:start position:0% +cosiness and the point about the + + + align:start position:0% +cosiness and the point about the +cosiness is they have they correspond + + align:start position:0% +cosiness is they have they correspond + + + align:start position:0% +cosiness is they have they correspond +respond to free free boundary + + align:start position:0% +respond to free free boundary + + + align:start position:0% +respond to free free boundary +conditions the sign transform is has its + + align:start position:0% +conditions the sign transform is has its + + + align:start position:0% +conditions the sign transform is has its +uses too and it corresponds to fixed + + align:start position:0% +uses too and it corresponds to fixed + + + align:start position:0% +uses too and it corresponds to fixed +fixed boundary conditions and in between + + align:start position:0% +fixed boundary conditions and in between + + + align:start position:0% +fixed boundary conditions and in between +of course we could have our t with a + + align:start position:0% +of course we could have our t with a + + + align:start position:0% +of course we could have our t with a +fixed free pair but that's somehow not + + align:start position:0% +fixed free pair but that's somehow not + + + align:start position:0% +fixed free pair but that's somehow not +quite not as uh not as important in + + align:start position:0% +quite not as uh not as important in + + + align:start position:0% +quite not as uh not as important in +reality as these two so so now we've + + align:start position:0% +reality as these two so so now we've + + + align:start position:0% +reality as these two so so now we've +computed the cosiness the igen values + + align:start position:0% +computed the cosiness the igen values + + + align:start position:0% +computed the cosiness the igen values +and IG vectors of of of the matrices + + align:start position:0% +and IG vectors of of of the matrices + + + align:start position:0% +and IG vectors of of of the matrices +that we have have focused on and then in + + align:start position:0% +that we have have focused on and then in + + + align:start position:0% +that we have have focused on and then in +the next the first part of the next + + align:start position:0% +the next the first part of the next + + + align:start position:0% +the next the first part of the next +lecture can I use these while they're + + align:start position:0% +lecture can I use these while they're + + + align:start position:0% +lecture can I use these while they're +fresh in our mind to solve differential + + align:start position:0% +fresh in our mind to solve differential + + + align:start position:0% +fresh in our mind to solve differential +equations and then speak about other + + align:start position:0% +equations and then speak about other + + + align:start position:0% +equations and then speak about other +topics because the topic of lecture six + + align:start position:0% +topics because the topic of lecture six + + + align:start position:0% +topics because the topic of lecture six +is applied linear algebra uh other more + + align:start position:0% +is applied linear algebra uh other more + + + align:start position:0% +is applied linear algebra uh other more +widely but I'm going to be uh this is a + + align:start position:0% +widely but I'm going to be uh this is a + + + align:start position:0% +widely but I'm going to be uh this is a +highlight of that one too okay so let me + + align:start position:0% +highlight of that one too okay so let me + + + align:start position:0% +highlight of that one too okay so let me +stop here and pick up \ No newline at end of file diff --git a/kcLc4FsshO4.txt b/kcLc4FsshO4.txt new file mode 100644 index 0000000000000000000000000000000000000000..02bd6e64a8a082a7a5a385fd0ae0e2c0bd426249 --- /dev/null +++ b/kcLc4FsshO4.txt @@ -0,0 +1,2235 @@ +align:start position:0% + +okay this is my second video on the + + align:start position:0% +okay this is my second video on the + + + align:start position:0% +okay this is my second video on the +llast transform and this one will be + + align:start position:0% +llast transform and this one will be + + + align:start position:0% +llast transform and this one will be +about solving second order equations so + + align:start position:0% +about solving second order equations so + + + align:start position:0% +about solving second order equations so +let me remember the the plan uh so + + align:start position:0% +let me remember the the plan uh so + + + align:start position:0% +let me remember the the plan uh so +there's our second order equation and + + align:start position:0% +there's our second order equation and + + + align:start position:0% +there's our second order equation and +I'm taking this example first with the + + align:start position:0% +I'm taking this example first with the + + + align:start position:0% +I'm taking this example first with the +Delta function on the right hand side + + align:start position:0% +Delta function on the right hand side + + + align:start position:0% +Delta function on the right hand side +you remember that's a key example and + + align:start position:0% +you remember that's a key example and + + + align:start position:0% +you remember that's a key example and +actually we have a special letter for + + align:start position:0% +actually we have a special letter for + + + align:start position:0% +actually we have a special letter for +the Sol solution this is an impulse and + + align:start position:0% +the Sol solution this is an impulse and + + + align:start position:0% +the Sol solution this is an impulse and +the solution is the impulse response and + + align:start position:0% +the solution is the impulse response and + + + align:start position:0% +the solution is the impulse response and +I use a little G so I I should have + + align:start position:0% +I use a little G so I I should have + + + align:start position:0% +I use a little G so I I should have +turned this Y into a g so that g is the + + align:start position:0% +turned this Y into a g so that g is the + + + align:start position:0% +turned this Y into a g so that g is the +solution starting from zero initial + + align:start position:0% +solution starting from zero initial + + + align:start position:0% +solution starting from zero initial +conditions for with that Delta so what's + + align:start position:0% +conditions for with that Delta so what's + + + align:start position:0% +conditions for with that Delta so what's +the plan we want to take the transform + + align:start position:0% +the plan we want to take the transform + + + align:start position:0% +the plan we want to take the transform +of every term we have to check what is + + align:start position:0% +of every term we have to check what is + + + align:start position:0% +of every term we have to check what is +the transform the lass transform of the + + align:start position:0% +the transform the lass transform of the + + + align:start position:0% +the transform the lass transform of the +the Delta function you remember the + + align:start position:0% +the Delta function you remember the + + + align:start position:0% +the Delta function you remember the +definition of the transform it's this + + align:start position:0% +definition of the transform it's this + + + align:start position:0% +definition of the transform it's this +integral you take your function whatever + + align:start position:0% +integral you take your function whatever + + + align:start position:0% +integral you take your function whatever +it is here Delta multiply by E the minus + + align:start position:0% +it is here Delta multiply by E the minus + + + align:start position:0% +it is here Delta multiply by E the minus +St and integrate s equal 0 to Infinity + + align:start position:0% +St and integrate s equal 0 to Infinity + + + align:start position:0% +St and integrate s equal 0 to Infinity +well e easy to integrate with a Delta + + align:start position:0% +well e easy to integrate with a Delta + + + align:start position:0% +well e easy to integrate with a Delta +function there it's zero except where + + align:start position:0% +function there it's zero except where + + + align:start position:0% +function there it's zero except where +the impulse is at tal 0 at tal 0 and at + + align:start position:0% +the impulse is at tal 0 at tal 0 and at + + + align:start position:0% +the impulse is at tal 0 at tal 0 and at +T t equal 0 this is one so the answer is + + align:start position:0% +T t equal 0 this is one so the answer is + + + align:start position:0% +T t equal 0 this is one so the answer is +one that's the nice lass transform of + + align:start position:0% +one that's the nice lass transform of + + + align:start position:0% +one that's the nice lass transform of +the impulse and now I want the transform + + align:start position:0% +the impulse and now I want the transform + + + align:start position:0% +the impulse and now I want the transform +of the impulse response so the impulse + + align:start position:0% +of the impulse response so the impulse + + + align:start position:0% +of the impulse response so the impulse +response comes from this equation so now + + align:start position:0% +response comes from this equation so now + + + align:start position:0% +response comes from this equation so now +transform every + + align:start position:0% +transform every + + + align:start position:0% +transform every +term uh so the transform of G will be + + align:start position:0% +term uh so the transform of G will be + + + align:start position:0% +term uh so the transform of G will be +called capital G and the transform of + + align:start position:0% +called capital G and the transform of + + + align:start position:0% +called capital G and the transform of +the Delta function is one and the + + align:start position:0% +the Delta function is one and the + + + align:start position:0% +the Delta function is one and the +derivative you remember has an extra + + align:start position:0% +derivative you remember has an extra + + + align:start position:0% +derivative you remember has an extra +Factor + + align:start position:0% +Factor + + + align:start position:0% +Factor +s the the transform of the derivative + + align:start position:0% +s the the transform of the derivative + + + align:start position:0% +s the the transform of the derivative +from the first llas transform video was + + align:start position:0% +from the first llas transform video was + + + align:start position:0% +from the first llas transform video was +stimes G of s and the second derivative + + align:start position:0% +stimes G of s and the second derivative + + + align:start position:0% +stimes G of s and the second derivative +another s so s s * G of s we're not + + align:start position:0% +another s so s s * G of s we're not + + + align:start position:0% +another s so s s * G of s we're not +surprised to see the very familiar + + align:start position:0% +surprised to see the very familiar + + + align:start position:0% +surprised to see the very familiar +quadratic whose roots are the two + + align:start position:0% +quadratic whose roots are the two + + + align:start position:0% +quadratic whose roots are the two +exponents S1 and S2 so showing up here + + align:start position:0% +exponents S1 and S2 so showing up here + + + align:start position:0% +exponents S1 and S2 so showing up here +we've seen this every time because we + + align:start position:0% +we've seen this every time because we + + + align:start position:0% +we've seen this every time because we +have constant coefficients we always see + + align:start position:0% +have constant coefficients we always see + + + align:start position:0% +have constant coefficients we always see +this quantity and now we see that look + + align:start position:0% +this quantity and now we see that look + + + align:start position:0% +this quantity and now we see that look +the + + align:start position:0% +the + + + align:start position:0% +the +transform capital G I divide by that + + align:start position:0% +transform capital G I divide by that + + + align:start position:0% +transform capital G I divide by that +it's exactly the transfer function so + + align:start position:0% +it's exactly the transfer function so + + + align:start position:0% +it's exactly the transfer function so +that's connecting + + align:start position:0% +that's connecting + + + align:start position:0% +that's connecting +in uh the the idea of the transfer + + align:start position:0% +in uh the the idea of the transfer + + + align:start position:0% +in uh the the idea of the transfer +function to the lass transform of the + + align:start position:0% +function to the lass transform of the + + + align:start position:0% +function to the lass transform of the +impulse response because I have this in + + align:start position:0% +impulse response because I have this in + + + align:start position:0% +impulse response because I have this in +the denominator okay so I want now I've + + align:start position:0% +the denominator okay so I want now I've + + + align:start position:0% +the denominator okay so I want now I've +taken the transform of the equation I've + + align:start position:0% +taken the transform of the equation I've + + + align:start position:0% +taken the transform of the equation I've +got the transform of little G the + + align:start position:0% +got the transform of little G the + + + align:start position:0% +got the transform of little G the +impulse response so now I'm ready to + + align:start position:0% +impulse response so now I'm ready to + + + align:start position:0% +impulse response so now I'm ready to +find G the the impulse response by + + align:start position:0% +find G the the impulse response by + + + align:start position:0% +find G the the impulse response by +invert Theo transform how do I find the + + align:start position:0% +invert Theo transform how do I find the + + + align:start position:0% +invert Theo transform how do I find the +function with that La + + align:start position:0% +function with that La + + + align:start position:0% +function with that La +transform right now it's one over a + + align:start position:0% +transform right now it's one over a + + + align:start position:0% +transform right now it's one over a +quadratic the whole idea of partial + + align:start position:0% +quadratic the whole idea of partial + + + align:start position:0% +quadratic the whole idea of partial +fractions is split this so This G of s + + align:start position:0% +fractions is split this so This G of s + + + align:start position:0% +fractions is split this so This G of s +final + + align:start position:0% +final + + + align:start position:0% +final +step is G of s well you remember that + + align:start position:0% +step is G of s well you remember that + + + align:start position:0% +step is G of s well you remember that +this is the polom that has the two Roots + + align:start position:0% +this is the polom that has the two Roots + + + align:start position:0% +this is the polom that has the two Roots +S1 and + + align:start position:0% +S1 and + + + align:start position:0% +S1 and +S2 I'm going to write that as 1 over s - + + align:start position:0% +S2 I'm going to write that as 1 over s - + + + align:start position:0% +S2 I'm going to write that as 1 over s - +S1 and S - S2 + + align:start position:0% + + + + align:start position:0% + +those are the two roots from the + + align:start position:0% +those are the two roots from the + + + align:start position:0% +those are the two roots from the +quadratic formula the two poles we could + + align:start position:0% +quadratic formula the two poles we could + + + align:start position:0% +quadratic formula the two poles we could +say poles of G ofs and now I have to I + + align:start position:0% +say poles of G ofs and now I have to I + + + align:start position:0% +say poles of G ofs and now I have to I +want to use partial fractions so I want + + align:start position:0% +want to use partial fractions so I want + + + align:start position:0% +want to use partial fractions so I want +to separate this into two fractions and + + align:start position:0% +to separate this into two fractions and + + + align:start position:0% +to separate this into two fractions and +they are it turns out that they are 1 / + + align:start position:0% +they are it turns out that they are 1 / + + + align:start position:0% +they are it turns out that they are 1 / +s - + + align:start position:0% +s - + + + align:start position:0% +s - +S1 - 1 / s - S2 and it turns out that + + align:start position:0% +S1 - 1 / s - S2 and it turns out that + + + align:start position:0% +S1 - 1 / s - S2 and it turns out that +there's a there's + + align:start position:0% + + + + align:start position:0% + +a factor there to make it correct you + + align:start position:0% +a factor there to make it correct you + + + align:start position:0% +a factor there to make it correct you +could check when you put these this over + + align:start position:0% +could check when you put these this over + + + align:start position:0% +could check when you put these this over +a common denominator you get this and + + align:start position:0% +a common denominator you get this and + + + align:start position:0% +a common denominator you get this and +when you put that over a common + + align:start position:0% +when you put that over a common + + + align:start position:0% +when you put that over a common +denominator you'll get uh a numerator + + align:start position:0% +denominator you'll get uh a numerator + + + align:start position:0% +denominator you'll get uh a numerator +which you have to + + align:start position:0% +which you have to + + + align:start position:0% +which you have to +uh cancel okay so + + align:start position:0% +uh cancel okay so + + + align:start position:0% +uh cancel okay so +then now I have two + + align:start position:0% +then now I have two + + + align:start position:0% +then now I have two +simple poles and I can write here what I + + align:start position:0% +simple poles and I can write here what I + + + align:start position:0% +simple poles and I can write here what I +know what G of T + + align:start position:0% +know what G of T + + + align:start position:0% +know what G of T +is remember the transform the the + + align:start position:0% +is remember the transform the the + + + align:start position:0% +is remember the transform the the +function with that transform is just e + + align:start position:0% +function with that transform is just e + + + align:start position:0% +function with that transform is just e +to the s1t the one most important of all + + align:start position:0% +to the s1t the one most important of all + + + align:start position:0% +to the s1t the one most important of all +transforms is the transform of the + + align:start position:0% +transforms is the transform of the + + + align:start position:0% +transforms is the transform of the +exponential is that simple pole so I + + align:start position:0% +exponential is that simple pole so I + + + align:start position:0% +exponential is that simple pole so I +have simp now I'm invert the laass + + align:start position:0% +have simp now I'm invert the laass + + + align:start position:0% +have simp now I'm invert the laass +transform so this gives me an e to the + + align:start position:0% +transform so this gives me an e to the + + + align:start position:0% +transform so this gives me an e to the +S1 + + align:start position:0% +S1 + + + align:start position:0% +S1 +T minus the function with that transform + + align:start position:0% +T minus the function with that transform + + + align:start position:0% +T minus the function with that transform +is e to the + + align:start position:0% +is e to the + + + align:start position:0% +is e to the +s2t and I still have this constant S1 - + + align:start position:0% +s2t and I still have this constant S1 - + + + align:start position:0% +s2t and I still have this constant S1 - +S2 I've + + align:start position:0% +S2 I've + + + align:start position:0% +S2 I've +rediscovered the impulse + + align:start position:0% +rediscovered the impulse + + + align:start position:0% +rediscovered the impulse +response it's a solution to my equation + + align:start position:0% +response it's a solution to my equation + + + align:start position:0% +response it's a solution to my equation +with impulse + + align:start position:0% +with impulse + + + align:start position:0% +with impulse +force and it's this function that plays + + align:start position:0% +force and it's this function that plays + + + align:start position:0% +force and it's this function that plays +it's that particular function that plays + + align:start position:0% +it's that particular function that plays + + + align:start position:0% +it's that particular function that plays +such a important part in uh the + + align:start position:0% +such a important part in uh the + + + align:start position:0% +such a important part in uh the +whole subject of constant coefficient + + align:start position:0% +whole subject of constant coefficient + + + align:start position:0% +whole subject of constant coefficient +differential equations because it's it's + + align:start position:0% +differential equations because it's it's + + + align:start position:0% +differential equations because it's it's +you see it's the critical thing here + + align:start position:0% +you see it's the critical thing here + + + align:start position:0% +you see it's the critical thing here +here's the critical transfer function + + align:start position:0% +here's the critical transfer function + + + align:start position:0% +here's the critical transfer function +and here is the inverse luse transform + + align:start position:0% +and here is the inverse luse transform + + + align:start position:0% +and here is the inverse luse transform +the Laos transform of that is that good + + align:start position:0% +the Laos transform of that is that good + + + align:start position:0% +the Laos transform of that is that good +that's that example and now I just want + + align:start position:0% +that's that example and now I just want + + + align:start position:0% +that's that example and now I just want +to take another function than Delta + + align:start position:0% +to take another function than Delta + + + align:start position:0% +to take another function than Delta +okay I could go all the way to + + align:start position:0% +okay I could go all the way to + + + align:start position:0% +okay I could go all the way to +take F of T any F of T but let me stay + + align:start position:0% +take F of T any F of T but let me stay + + + align:start position:0% +take F of T any F of T but let me stay +with uh + + align:start position:0% +with uh + + + align:start position:0% +with uh +examples let me stay with examples so + + align:start position:0% +examples let me stay with examples so + + + align:start position:0% +examples let me stay with examples so +now I'm going to do y Prime and plus v y + + align:start position:0% +now I'm going to do y Prime and plus v y + + + align:start position:0% +now I'm going to do y Prime and plus v y +Prime plus c y the oh the most important + + align:start position:0% +Prime plus c y the oh the most important + + + align:start position:0% +Prime plus c y the oh the most important +example the best one we could do would + + align:start position:0% +example the best one we could do would + + + align:start position:0% +example the best one we could do would +be cosine of Omega + + align:start position:0% +be cosine of Omega + + + align:start position:0% +be cosine of Omega +T an oscillating problem with an + + align:start position:0% +T an oscillating problem with an + + + align:start position:0% +T an oscillating problem with an +oscillating Force at a frequency + + align:start position:0% +oscillating Force at a frequency + + + align:start position:0% +oscillating Force at a frequency +different from the natural frequency + + align:start position:0% +different from the natural frequency + + + align:start position:0% +different from the natural frequency +well and and we also have damping there + + align:start position:0% +well and and we also have damping there + + + align:start position:0% +well and and we also have damping there +so this is the standard spraying Mass + + align:start position:0% +so this is the standard spraying Mass + + + align:start position:0% +so this is the standard spraying Mass +dashbot problem or RLC circuit problem + + align:start position:0% +dashbot problem or RLC circuit problem + + + align:start position:0% +dashbot problem or RLC circuit problem +certainly RLC these circuits H highly + + align:start position:0% +certainly RLC these circuits H highly + + + align:start position:0% +certainly RLC these circuits H highly +important + + align:start position:0% +important + + + align:start position:0% +important +and uh you might remember the solution + + align:start position:0% +and uh you might remember the solution + + + align:start position:0% +and uh you might remember the solution +gets a little messy a solution gets a + + align:start position:0% +gets a little messy a solution gets a + + + align:start position:0% +gets a little messy a solution gets a +little messy it's highly important but I + + align:start position:0% +little messy it's highly important but I + + + align:start position:0% +little messy it's highly important but I +so I I'll carry it through to the last + + align:start position:0% +so I I'll carry it through to the last + + + align:start position:0% +so I I'll carry it through to the last +step but I probably won't take that + + align:start position:0% +step but I probably won't take that + + + align:start position:0% +step but I probably won't take that +final step just this what I want you to + + align:start position:0% +final step just this what I want you to + + + align:start position:0% +final step just this what I want you to +see is an example another example of the + + align:start position:0% +see is an example another example of the + + + align:start position:0% +see is an example another example of the +inverse l transform so what do we need + + align:start position:0% +inverse l transform so what do we need + + + align:start position:0% +inverse l transform so what do we need +we need the luse transform of that I + + align:start position:0% +we need the luse transform of that I + + + align:start position:0% +we need the luse transform of that I +plan to take the luse transform of every + + align:start position:0% +plan to take the luse transform of every + + + align:start position:0% +plan to take the luse transform of every +term s² + b s + C will multiply the I'm + + align:start position:0% +term s² + b s + C will multiply the I'm + + + align:start position:0% +term s² + b s + C will multiply the I'm +transforming everything and here I have + + align:start position:0% +transforming everything and here I have + + + align:start position:0% +transforming everything and here I have +to put the transform of + + align:start position:0% +to put the transform of + + + align:start position:0% +to put the transform of +that okay + + align:start position:0% +that okay + + + align:start position:0% +that okay +so how how will I get that and and of + + align:start position:0% +so how how will I get that and and of + + + align:start position:0% +so how how will I get that and and of +course it might be it might there might + + align:start position:0% +course it might be it might there might + + + align:start position:0% +course it might be it might there might +be a sin Omega T in there I I would + + align:start position:0% +be a sin Omega T in there I I would + + + align:start position:0% +be a sin Omega T in there I I would +really like to get them both at once so + + align:start position:0% +really like to get them both at once so + + + align:start position:0% +really like to get them both at once so +let me put down them both at once the S + + align:start position:0% +let me put down them both at once the S + + + align:start position:0% +let me put down them both at once the S +the cosine and the sign are the + + align:start position:0% +the cosine and the sign are the + + + align:start position:0% +the cosine and the sign are the +real and imaginary parts of e to the I + + align:start position:0% +real and imaginary parts of e to the I + + + align:start position:0% +real and imaginary parts of e to the I +Omega T + + align:start position:0% + + + + align:start position:0% + +right Oiler great Formula E to the I + + align:start position:0% +right Oiler great Formula E to the I + + + align:start position:0% +right Oiler great Formula E to the I +Omega T is cosine Omega T the real part + + align:start position:0% +Omega T is cosine Omega T the real part + + + align:start position:0% +Omega T is cosine Omega T the real part +plus I sin Omega T the imaginary part + + align:start position:0% +plus I sin Omega T the imaginary part + + + align:start position:0% +plus I sin Omega T the imaginary part +but now I know the transform of e to + + align:start position:0% +but now I know the transform of e to + + + align:start position:0% +but now I know the transform of e to +the a t e to the I Omega T so that + + align:start position:0% +the a t e to the I Omega T so that + + + align:start position:0% +the a t e to the I Omega T so that +transforms to one so I want the real and + + align:start position:0% +transforms to one so I want the real and + + + align:start position:0% +transforms to one so I want the real and +the imaginary parts of one over you + + align:start position:0% +the imaginary parts of one over you + + + align:start position:0% +the imaginary parts of one over you +remember what it is it's just that + + align:start position:0% +remember what it is it's just that + + + align:start position:0% +remember what it is it's just that +simple pole again s minus the exponent I + + align:start position:0% + + + + align:start position:0% + +Omega so I'm going to get the cosine and + + align:start position:0% +Omega so I'm going to get the cosine and + + + align:start position:0% +Omega so I'm going to get the cosine and +the sign at at the same time from one + + align:start position:0% +the sign at at the same time from one + + + align:start position:0% +the sign at at the same time from one +calculation finding the real and + + align:start position:0% +calculation finding the real and + + + align:start position:0% +calculation finding the real and +imaginary parts of this 1 / s + i s + + align:start position:0% +imaginary parts of this 1 / s + i s + + + align:start position:0% +imaginary parts of this 1 / s + i s +minus I + + align:start position:0% +minus I + + + align:start position:0% +minus I +Omega how do you do how do you deal with + + align:start position:0% +Omega how do you do how do you deal with + + + align:start position:0% +Omega how do you do how do you deal with +uh a a + + align:start position:0% +uh a a + + + align:start position:0% +uh a a +pole when you really if you want the + + align:start position:0% +pole when you really if you want the + + + align:start position:0% +pole when you really if you want the +real and imaginary Parts you want you + + align:start position:0% +real and imaginary Parts you want you + + + align:start position:0% +real and imaginary Parts you want you +want a a you're happy to get a real + + align:start position:0% +want a a you're happy to get a real + + + align:start position:0% +want a a you're happy to get a real +number in the denominator and and see + + align:start position:0% +number in the denominator and and see + + + align:start position:0% +number in the denominator and and see +the real and imaginary Parts up above I + + align:start position:0% +the real and imaginary Parts up above I + + + align:start position:0% +the real and imaginary Parts up above I +don't like it when it's down there so + + align:start position:0% +don't like it when it's down there so + + + align:start position:0% +don't like it when it's down there so +what I'm going to do is real and + + align:start position:0% +what I'm going to do is real and + + + align:start position:0% +what I'm going to do is real and +imaginary parts of I'll + + align:start position:0% +imaginary parts of I'll + + + align:start position:0% +imaginary parts of I'll +multiply s minus I Omega this is the key + + align:start position:0% +multiply s minus I Omega this is the key + + + align:start position:0% +multiply s minus I Omega this is the key +trick with complex numbers it comes up + + align:start position:0% +trick with complex numbers it comes up + + + align:start position:0% +trick with complex numbers it comes up +enough so it's good to learn I multiply + + align:start position:0% +enough so it's good to learn I multiply + + + align:start position:0% +enough so it's good to learn I multiply +that by its conjugate s + I Omega time + + align:start position:0% +that by its conjugate s + I Omega time + + + align:start position:0% +that by its conjugate s + I Omega time +over s + I Omega so I multiplied by one + + align:start position:0% +over s + I Omega so I multiplied by one + + + align:start position:0% +over s + I Omega so I multiplied by one +but you see what's happened now + + align:start position:0% +but you see what's happened now + + + align:start position:0% +but you see what's happened now +is real and imaginary parts of I've got + + align:start position:0% +is real and imaginary parts of I've got + + + align:start position:0% +is real and imaginary parts of I've got +what I want s + I Omega is now uh up in + + align:start position:0% +what I want s + I Omega is now uh up in + + + align:start position:0% +what I want s + I Omega is now uh up in +the numerator where it's I can see it's + + align:start position:0% +the numerator where it's I can see it's + + + align:start position:0% +the numerator where it's I can see it's +and and what do I have down below s- I + + align:start position:0% +and and what do I have down below s- I + + + align:start position:0% +and and what do I have down below s- I +Omega * s + I Omega the very important + + align:start position:0% +Omega * s + I Omega the very important + + + align:start position:0% +Omega * s + I Omega the very important +quantity s + + align:start position:0% + + + + align:start position:0% + +SAR minus I Omega S Plus I Omega s + + align:start position:0% +SAR minus I Omega S Plus I Omega s + + + align:start position:0% +SAR minus I Omega S Plus I Omega s +- i^ 2 that's + 1 Omega 2 plus Omega 2 + + align:start position:0% +- i^ 2 that's + 1 Omega 2 plus Omega 2 + + + align:start position:0% +- i^ 2 that's + 1 Omega 2 plus Omega 2 +okay we've done + + align:start position:0% +okay we've done + + + align:start position:0% +okay we've done +it I've transformed the cosine and the + + align:start position:0% +it I've transformed the cosine and the + + + align:start position:0% +it I've transformed the cosine and the +sign into s over this and Omega over + + align:start position:0% +sign into s over this and Omega over + + + align:start position:0% +sign into s over this and Omega over +this so two at once two two transforms + + align:start position:0% +this so two at once two two transforms + + + align:start position:0% +this so two at once two two transforms +and of course as always we're we're able + + align:start position:0% +and of course as always we're we're able + + + align:start position:0% +and of course as always we're we're able +to do and recognize and work with the + + align:start position:0% +to do and recognize and work with the + + + align:start position:0% +to do and recognize and work with the +transforms of a special group of nice + + align:start position:0% +transforms of a special group of nice + + + align:start position:0% +transforms of a special group of nice +functions exponentials above all signs + + align:start position:0% +functions exponentials above all signs + + + align:start position:0% +functions exponentials above all signs +and cosiness coming from exponentials + + align:start position:0% +and cosiness coming from exponentials + + + align:start position:0% +and cosiness coming from exponentials +Delta functions it's a short list we + + align:start position:0% +Delta functions it's a short list we + + + align:start position:0% +Delta functions it's a short list we +just those are the ones we can do + + align:start position:0% +just those are the ones we can do + + + align:start position:0% +just those are the ones we can do +unfortunately those are the ones that we + + align:start position:0% +unfortunately those are the ones that we + + + align:start position:0% +unfortunately those are the ones that we +need to do okay so I'm now ready to put + + align:start position:0% +need to do okay so I'm now ready to put + + + align:start position:0% +need to do okay so I'm now ready to put +in the right the right uh + + align:start position:0% +in the right the right uh + + + align:start position:0% +in the right the right uh +uh what did that turn turn out to be it + + align:start position:0% +uh what did that turn turn out to be it + + + align:start position:0% +uh what did that turn turn out to be it +turned out to be S from the cosine I'm + + align:start position:0% +turned out to be S from the cosine I'm + + + align:start position:0% +turned out to be S from the cosine I'm +not doing the sign now the cosine I'm + + align:start position:0% +not doing the sign now the cosine I'm + + + align:start position:0% +not doing the sign now the cosine I'm +taking the real part is s over that + + align:start position:0% +taking the real part is s over that + + + align:start position:0% +taking the real part is s over that +positive s^2 + Omega + + align:start position:0% +positive s^2 + Omega + + + align:start position:0% +positive s^2 + Omega +s are you with + + align:start position:0% +s are you with + + + align:start position:0% +s are you with +me left hand side all normal I'm + + align:start position:0% +me left hand side all normal I'm + + + align:start position:0% +me left hand side all normal I'm +starting from zero initial conditions + + align:start position:0% +starting from zero initial conditions + + + align:start position:0% +starting from zero initial conditions +otherwise I would see some initial I + + align:start position:0% +otherwise I would see some initial I + + + align:start position:0% +otherwise I would see some initial I +would see uh the initial values in here + + align:start position:0% +would see uh the initial values in here + + + align:start position:0% +would see uh the initial values in here +but I don't because there is zero and + + align:start position:0% +but I don't because there is zero and + + + align:start position:0% +but I don't because there is zero and +over here I've got the transform of the + + align:start position:0% +over here I've got the transform of the + + + align:start position:0% +over here I've got the transform of the +right hand side okay then I just bring + + align:start position:0% +right hand side okay then I just bring + + + align:start position:0% +right hand side okay then I just bring +that down there so finally I know y of s + + align:start position:0% +that down there so finally I know y of s + + + align:start position:0% +that down there so finally I know y of s +is s + + align:start position:0% +is s + + + align:start position:0% +is s +over + + align:start position:0% +over + + + align:start position:0% +over +this all + + align:start position:0% +this all + + + align:start position:0% +this all +important quadratic and then I have the + + align:start position:0% +important quadratic and then I have the + + + align:start position:0% +important quadratic and then I have the +s² + Omega + + align:start position:0% + + + + align:start position:0% + +squ + + align:start position:0% +squ + + + align:start position:0% +squ +okay well you see it did get + + align:start position:0% +okay well you see it did get + + + align:start position:0% +okay well you see it did get +harder we have s s from a quadratic + + align:start position:0% +harder we have s s from a quadratic + + + align:start position:0% +harder we have s s from a quadratic +there we have two quadratics we have a + + align:start position:0% +there we have two quadratics we have a + + + align:start position:0% +there we have two quadratics we have a +fourth degree polinomial down there + + align:start position:0% +fourth degree polinomial down there + + + align:start position:0% +fourth degree polinomial down there +partial fractions will work partial + + align:start position:0% +partial fractions will work partial + + + align:start position:0% +partial fractions will work partial +fractions will can simplify this to uh + + align:start position:0% +fractions will can simplify this to uh + + + align:start position:0% +fractions will can simplify this to uh +any for any pols but the algebra gets + + align:start position:0% +any for any pols but the algebra gets + + + align:start position:0% +any for any pols but the algebra gets +quickly worse when you get up to degree + + align:start position:0% +quickly worse when you get up to degree + + + align:start position:0% +quickly worse when you get up to degree +four but actually this this can be it it + + align:start position:0% +four but actually this this can be it it + + + align:start position:0% +four but actually this this can be it it +could be done and I that's I don't plan + + align:start position:0% +could be done and I that's I don't plan + + + align:start position:0% +could be done and I that's I don't plan +to do it to me this would eventually + + align:start position:0% +to do it to me this would eventually + + + align:start position:0% +to do it to me this would eventually +give the solution to this + + align:start position:0% + + + + align:start position:0% + +example but we have other ways to get + + align:start position:0% +example but we have other ways to get + + + align:start position:0% +example but we have other ways to get +that solution and I believe for me at + + align:start position:0% +that solution and I believe for me at + + + align:start position:0% +that solution and I believe for me at +least the other ways are simpler I know + + align:start position:0% +least the other ways are simpler I know + + + align:start position:0% +least the other ways are simpler I know +that the solution is a combination of + + align:start position:0% +that the solution is a combination of + + + align:start position:0% +that the solution is a combination of +cos Omega T and sin Omega + + align:start position:0% +cos Omega T and sin Omega + + + align:start position:0% +cos Omega T and sin Omega +T and this is the particular solution + + align:start position:0% +T and this is the particular solution + + + align:start position:0% +T and this is the particular solution +I'm talking about and I can figure out + + align:start position:0% +I'm talking about and I can figure out + + + align:start position:0% +I'm talking about and I can figure out +what those combinations are because I + + align:start position:0% +what those combinations are because I + + + align:start position:0% +what those combinations are because I +know the right form here I have to deal + + align:start position:0% +know the right form here I have to deal + + + align:start position:0% +know the right form here I have to deal +with partial fractions and degree four + + align:start position:0% +with partial fractions and degree four + + + align:start position:0% +with partial fractions and degree four +down there I'm G to I'm going to chicken + + align:start position:0% +down there I'm G to I'm going to chicken + + + align:start position:0% +down there I'm G to I'm going to chicken +out on that one I I I won't completely + + align:start position:0% +out on that one I I I won't completely + + + align:start position:0% +out on that one I I I won't completely +chicken out I'll say what the pieces + + align:start position:0% +chicken out I'll say what the pieces + + + align:start position:0% +chicken out I'll say what the pieces +pieces look like but I won't figure out + + align:start position:0% +pieces look like but I won't figure out + + + align:start position:0% +pieces look like but I won't figure out +all the numbers okay so this all this + + align:start position:0% +all the numbers okay so this all this + + + align:start position:0% +all the numbers okay so this all this +thing I see as some constant + + align:start position:0% +thing I see as some constant + + + align:start position:0% +thing I see as some constant +over well this factors into s - S1 s - + + align:start position:0% +over well this factors into s - S1 s - + + + align:start position:0% +over well this factors into s - S1 s - +S2 those are the two Roots as we saw uh + + align:start position:0% +S2 those are the two Roots as we saw uh + + + align:start position:0% +S2 those are the two Roots as we saw uh +above so so so I have a linear a linear + + align:start position:0% +above so so so I have a linear a linear + + + align:start position:0% +above so so so I have a linear a linear +and a quadratic and and partial fraction + + align:start position:0% +and a quadratic and and partial fraction + + + align:start position:0% +and a quadratic and and partial fraction +says that that's that I can separate out + + align:start position:0% +says that that's that I can separate out + + + align:start position:0% +says that that's that I can separate out +the first + + align:start position:0% +the first + + + align:start position:0% +the first +linear the second + + align:start position:0% +linear the second + + + align:start position:0% +linear the second +linear and the + + align:start position:0% +linear and the + + + align:start position:0% +linear and the +third + + align:start position:0% +third + + + align:start position:0% +third +quadratic which I could Factor too + + align:start position:0% +quadratic which I could Factor too + + + align:start position:0% +quadratic which I could Factor too +but I could Factor s² + Omega squar into + + align:start position:0% +but I could Factor s² + Omega squar into + + + align:start position:0% +but I could Factor s² + Omega squar into +that times that but it brings in + + align:start position:0% +that times that but it brings in + + + align:start position:0% +that times that but it brings in +imaginary numbers so uh I'll put a Cs + + align:start position:0% +imaginary numbers so uh I'll put a Cs + + + align:start position:0% +imaginary numbers so uh I'll put a Cs +and a d + + align:start position:0% +and a d + + + align:start position:0% +and a d +okay four numbers to be determined or + + align:start position:0% +okay four numbers to be determined or + + + align:start position:0% +okay four numbers to be determined or +rather not to be determined CU I'm going + + align:start position:0% +rather not to be determined CU I'm going + + + align:start position:0% +rather not to be determined CU I'm going +to stop there what I've discovered is + + align:start position:0% +to stop there what I've discovered is + + + align:start position:0% +to stop there what I've discovered is +the this + + align:start position:0% + + + + align:start position:0% + +part would be the null + + align:start position:0% +part would be the null + + + align:start position:0% +part would be the null +solution would be a null solution + + align:start position:0% +solution would be a null solution + + + align:start position:0% +solution would be a null solution +because it's it involves e to the S1 T + + align:start position:0% +because it's it involves e to the S1 T + + + align:start position:0% +because it's it involves e to the S1 T +and e to the s2t this part when I find + + align:start position:0% +and e to the s2t this part when I find + + + align:start position:0% +and e to the s2t this part when I find +the inverse transform will be oh it'll + + align:start position:0% +the inverse transform will be oh it'll + + + align:start position:0% +the inverse transform will be oh it'll +it must be a the combination of cos + + align:start position:0% +it must be a the combination of cos + + + align:start position:0% +it must be a the combination of cos +Omega T and sin Omega T so that's some + + align:start position:0% +Omega T and sin Omega T so that's some + + + align:start position:0% +Omega T and sin Omega T so that's some +combination when I find that it's the + + align:start position:0% +combination when I find that it's the + + + align:start position:0% +combination when I find that it's the +transform of \ No newline at end of file diff --git a/lemfZDGJQaQ.txt b/lemfZDGJQaQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..e8cb77a3396cf88ba803d4e753ba88fddc6ce31d --- /dev/null +++ b/lemfZDGJQaQ.txt @@ -0,0 +1,11915 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so just as kind of a synopsis of some + + align:start position:0% +so just as kind of a synopsis of some + + + align:start position:0% +so just as kind of a synopsis of some +ideas that we're going to get through + + align:start position:0% +ideas that we're going to get through + + + align:start position:0% +ideas that we're going to get through +we're looking at manufacturing which is + + align:start position:0% +we're looking at manufacturing which is + + + align:start position:0% +we're looking at manufacturing which is +a way to profit from innovation it's a + + align:start position:0% +a way to profit from innovation it's a + + + align:start position:0% +a way to profit from innovation it's a +way to scale innovation and we'll do + + align:start position:0% +way to scale innovation and we'll do + + + align:start position:0% +way to scale innovation and we'll do +something in a store overview here today + + align:start position:0% +something in a store overview here today + + + align:start position:0% +something in a store overview here today +so we'll look at the last big + + align:start position:0% +so we'll look at the last big + + + align:start position:0% +so we'll look at the last big +competitive this challenge this went + + align:start position:0% +competitive this challenge this went + + + align:start position:0% +competitive this challenge this went +through the challenge from Germany in + + align:start position:0% +through the challenge from Germany in + + + align:start position:0% +through the challenge from Germany in +Japan + + align:start position:0% +Japan + + + align:start position:0% +Japan +we'll take a typical look at Japan's + + align:start position:0% +we'll take a typical look at Japan's + + + align:start position:0% +we'll take a typical look at Japan's +manufacturing innovations 70s will + + align:start position:0% +manufacturing innovations 70s will + + + align:start position:0% +manufacturing innovations 70s will +review a distributed model of production + + align:start position:0% +review a distributed model of production + + + align:start position:0% +review a distributed model of production +that the US came up with in some ways in + + align:start position:0% +that the US came up with in some ways in + + + align:start position:0% +that the US came up with in some ways in +response we'll look at manufacturing and + + align:start position:0% +response we'll look at manufacturing and + + + align:start position:0% +response we'll look at manufacturing and +innovation organizational shifts within + + align:start position:0% +innovation organizational shifts within + + + align:start position:0% +innovation organizational shifts within +both Korea and Japan and then talk a bit + + align:start position:0% +both Korea and Japan and then talk a bit + + + align:start position:0% +both Korea and Japan and then talk a bit +about how the nature of the competition + + align:start position:0% +about how the nature of the competition + + + align:start position:0% +about how the nature of the competition +has changed as well so that's kind of a + + align:start position:0% +has changed as well so that's kind of a + + + align:start position:0% +has changed as well so that's kind of a +backdrop and then next week will be more + + align:start position:0% +backdrop and then next week will be more + + + align:start position:0% +backdrop and then next week will be more +pointed focus so the first piece will go + + align:start position:0% +pointed focus so the first piece will go + + + align:start position:0% +pointed focus so the first piece will go +through and I'll lay it out and Chris do + + align:start position:0% +through and I'll lay it out and Chris do + + + align:start position:0% +through and I'll lay it out and Chris do +you have you know rushing you got yous + + align:start position:0% +you have you know rushing you got yous + + + align:start position:0% +you have you know rushing you got yous +yeah right okay so this is Ken use can + + align:start position:0% +yeah right okay so this is Ken use can + + + align:start position:0% +yeah right okay so this is Ken use can +use was Joint Economic Committee is a + + align:start position:0% +use was Joint Economic Committee is a + + + align:start position:0% +use was Joint Economic Committee is a +staff director to Congress who's a + + align:start position:0% +staff director to Congress who's a + + + align:start position:0% +staff director to Congress who's a +senior official in his part of commerce + + align:start position:0% +senior official in his part of commerce + + + align:start position:0% +senior official in his part of commerce +and he kind of wrote the history of the + + align:start position:0% +and he kind of wrote the history of the + + + align:start position:0% +and he kind of wrote the history of the +competition over production between the + + align:start position:0% +competition over production between the + + + align:start position:0% +competition over production between the +US and China period of time that he was + + align:start position:0% +US and China period of time that he was + + + align:start position:0% +US and China period of time that he was +very deeply engaged in policy so let's + + align:start position:0% +very deeply engaged in policy so let's + + + align:start position:0% +very deeply engaged in policy so let's +get this backdrop kind of down because I + + align:start position:0% +get this backdrop kind of down because I + + + align:start position:0% +get this backdrop kind of down because I +think it'll help us see a lot about like + + align:start position:0% +think it'll help us see a lot about like + + + align:start position:0% +think it'll help us see a lot about like +what the u.s. is going through now in + + align:start position:0% +what the u.s. is going through now in + + + align:start position:0% +what the u.s. is going through now in +terms of manufacture so in the 1970s the + + align:start position:0% +terms of manufacture so in the 1970s the + + + align:start position:0% +terms of manufacture so in the 1970s the +u.s. faced you know a mess intractable + + align:start position:0% +u.s. faced you know a mess intractable + + + align:start position:0% +u.s. faced you know a mess intractable +of high inflation declining productivity + + align:start position:0% +of high inflation declining productivity + + + align:start position:0% +of high inflation declining productivity +growth a slow therefore a slow growth + + align:start position:0% +growth a slow therefore a slow growth + + + align:start position:0% +growth a slow therefore a slow growth +rate rising economic competition rising + + align:start position:0% +rate rising economic competition rising + + + align:start position:0% +rate rising economic competition rising +national anger frustration with + + align:start position:0% +national anger frustration with + + + align:start position:0% +national anger frustration with +government something like and the u.s. + + align:start position:0% +government something like and the u.s. + + + align:start position:0% +government something like and the u.s. +model have kind of pretty + + align:start position:0% +model have kind of pretty + + + align:start position:0% +model have kind of pretty +unfettered markets of limited government + + align:start position:0% +unfettered markets of limited government + + + align:start position:0% +unfettered markets of limited government +support for industry was a very + + align:start position:0% +support for industry was a very + + + align:start position:0% +support for industry was a very +different innovation model innovation + + align:start position:0% +different innovation model innovation + + + align:start position:0% +different innovation model innovation +system that what Japan and Germany were + + align:start position:0% +system that what Japan and Germany were + + + align:start position:0% +system that what Japan and Germany were +pursuing and then in turn led to the + + align:start position:0% +pursuing and then in turn led to the + + + align:start position:0% +pursuing and then in turn led to the +beginnings of what could be called in + + align:start position:0% +beginnings of what could be called in + + + align:start position:0% +beginnings of what could be called in +the u.s. international competitiveness + + align:start position:0% +the u.s. international competitiveness + + + align:start position:0% +the u.s. international competitiveness +ground so the essential elements of that + + align:start position:0% +ground so the essential elements of that + + + align:start position:0% +ground so the essential elements of that +history the initial response to Japan's + + align:start position:0% +history the initial response to Japan's + + + align:start position:0% +history the initial response to Japan's +develop on a quality of manufacturing + + align:start position:0% +develop on a quality of manufacturing + + + align:start position:0% +develop on a quality of manufacturing +which we'll get into in a minute there + + align:start position:0% +which we'll get into in a minute there + + + align:start position:0% +which we'll get into in a minute there +were different responses from each party + + align:start position:0% +were different responses from each party + + + align:start position:0% +were different responses from each party +and these will be familiar to as well so + + align:start position:0% +and these will be familiar to as well so + + + align:start position:0% +and these will be familiar to as well so +each party was organized remember when + + align:start position:0% +each party was organized remember when + + + align:start position:0% +each party was organized remember when +we discussed classical economics right + + align:start position:0% +we discussed classical economics right + + + align:start position:0% +we discussed classical economics right +and their key factors of bus permits + + align:start position:0% +and their key factors of bus permits + + + align:start position:0% +and their key factors of bus permits +with capitalist opponent labor supply + + align:start position:0% +with capitalist opponent labor supply + + + align:start position:0% +with capitalist opponent labor supply +each of our parties is organized from + + align:start position:0% +each of our parties is organized from + + + align:start position:0% +each of our parties is organized from +entities right so the capital supply + + align:start position:0% +entities right so the capital supply + + + align:start position:0% +entities right so the capital supply +response came from the Republican side + + align:start position:0% +response came from the Republican side + + + align:start position:0% +response came from the Republican side +and Ferguson Jack Kemp Jack Kemp + + align:start position:0% +and Ferguson Jack Kemp Jack Kemp + + + align:start position:0% +and Ferguson Jack Kemp Jack Kemp +of Buffalo and Bill Roth who was + + align:start position:0% +of Buffalo and Bill Roth who was + + + align:start position:0% +of Buffalo and Bill Roth who was +chairman of the Finance Committee of the + + align:start position:0% +chairman of the Finance Committee of the + + + align:start position:0% +chairman of the Finance Committee of the +Senate from Delaware Dame word their + + align:start position:0% +Senate from Delaware Dame word their + + + align:start position:0% +Senate from Delaware Dame word their +argument was let's adjust marginal tax + + align:start position:0% +argument was let's adjust marginal tax + + + align:start position:0% +argument was let's adjust marginal tax +rates that will spur capital + + align:start position:0% +rates that will spur capital + + + align:start position:0% +rates that will spur capital +availability and investment and will + + align:start position:0% +availability and investment and will + + + align:start position:0% +availability and investment and will +recover Democrats were organized around + + align:start position:0% +recover Democrats were organized around + + + align:start position:0% +recover Democrats were organized around +their traditional mantra of labor supply + + align:start position:0% +their traditional mantra of labor supply + + + align:start position:0% +their traditional mantra of labor supply +broadly defined right and they had moved + + align:start position:0% +broadly defined right and they had moved + + + align:start position:0% +broadly defined right and they had moved +towards what was then known as + + align:start position:0% +towards what was then known as + + + align:start position:0% +towards what was then known as +Industrial Policy still known as + + align:start position:0% +Industrial Policy still known as + + + align:start position:0% +Industrial Policy still known as +industrial policy so they were looking + + align:start position:0% +industrial policy so they were looking + + + align:start position:0% +industrial policy so they were looking +to rescuing failing industries and + + align:start position:0% +to rescuing failing industries and + + + align:start position:0% +to rescuing failing industries and +reorganizing them for turnarounds and at + + align:start position:0% +reorganizing them for turnarounds and at + + + align:start position:0% +reorganizing them for turnarounds and at +a later time through the young + + align:start position:0% +a later time through the young + + + align:start position:0% +a later time through the young +Commission another set of ideas begins + + align:start position:0% +Commission another set of ideas begins + + + align:start position:0% +Commission another set of ideas begins +to enter the discussion around quote + + align:start position:0% +to enter the discussion around quote + + + align:start position:0% +to enter the discussion around quote +sunrise in histories the young + + align:start position:0% +sunrise in histories the young + + + align:start position:0% +sunrise in histories the young +Commission tried to cut between these + + align:start position:0% +Commission tried to cut between these + + + align:start position:0% +Commission tried to cut between these +two party perspectives and develop a + + align:start position:0% +two party perspectives and develop a + + + align:start position:0% +two party perspectives and develop a +different approach so John Young was + + align:start position:0% +different approach so John Young was + + + align:start position:0% +different approach so John Young was +head of Hewlett Packard and President + + align:start position:0% +head of Hewlett Packard and President + + + align:start position:0% +head of Hewlett Packard and President +Reagan named him + + align:start position:0% +Reagan named him + + + align:start position:0% +Reagan named him +this commission and their focus was on + + align:start position:0% +this commission and their focus was on + + + align:start position:0% +this commission and their focus was on +national competitiveness and they + + align:start position:0% +national competitiveness and they + + + align:start position:0% +national competitiveness and they +concurred that things like fiscal and + + align:start position:0% +concurred that things like fiscal and + + + align:start position:0% +concurred that things like fiscal and +monetary policy are important but they + + align:start position:0% +monetary policy are important but they + + + align:start position:0% +monetary policy are important but they +were also interested in what the + + align:start position:0% +were also interested in what the + + + align:start position:0% +were also interested in what the +innovation side of the research side + + align:start position:0% +innovation side of the research side + + + align:start position:0% +innovation side of the research side +could do so it was not simply a + + align:start position:0% +could do so it was not simply a + + + align:start position:0% +could do so it was not simply a +governmental role of basic research but + + align:start position:0% +governmental role of basic research but + + + align:start position:0% +governmental role of basic research but +basic technology and they developed a + + align:start position:0% +basic technology and they developed a + + + align:start position:0% +basic technology and they developed a +model that was in this public-private + + align:start position:0% +model that was in this public-private + + + align:start position:0% +model that was in this public-private +partnership that was industry led and + + align:start position:0% +partnership that was industry led and + + + align:start position:0% +partnership that was industry led and +the term partnership nation you know + + align:start position:0% +the term partnership nation you know + + + align:start position:0% +the term partnership nation you know +emerged from some of their work so this + + align:start position:0% +emerged from some of their work so this + + + align:start position:0% +emerged from some of their work so this +was in effect a third way out of the box + + align:start position:0% +was in effect a third way out of the box + + + align:start position:0% +was in effect a third way out of the box +the two parties had their underlying + + align:start position:0% +the two parties had their underlying + + + align:start position:0% +the two parties had their underlying +theories and young walks in with a + + align:start position:0% +theories and young walks in with a + + + align:start position:0% +theories and young walks in with a +different kind of approach so he's out + + align:start position:0% +different kind of approach so he's out + + + align:start position:0% +different kind of approach so he's out +of the Silicon Valley he's used to + + align:start position:0% +of the Silicon Valley he's used to + + + align:start position:0% +of the Silicon Valley he's used to +working with DARPA and the Defense + + align:start position:0% +working with DARPA and the Defense + + + align:start position:0% +working with DARPA and the Defense +Department so he's not afraid of + + align:start position:0% +Department so he's not afraid of + + + align:start position:0% +Department so he's not afraid of +government and its technology support + + align:start position:0% +government and its technology support + + + align:start position:0% +government and its technology support +role and it's it's kind of a this whole + + align:start position:0% +role and it's it's kind of a this whole + + + align:start position:0% +role and it's it's kind of a this whole +effort was called a new growth compact + + align:start position:0% +effort was called a new growth compact + + + align:start position:0% +effort was called a new growth compact +right so it was an attempt to cut + + align:start position:0% +right so it was an attempt to cut + + + align:start position:0% +right so it was an attempt to cut +between the parties and develop a series + + align:start position:0% +between the parties and develop a series + + + align:start position:0% +between the parties and develop a series +of new programmatic elements so some of + + align:start position:0% +of new programmatic elements so some of + + + align:start position:0% +of new programmatic elements so some of +the things that eventually emerge not + + align:start position:0% +the things that eventually emerge not + + + align:start position:0% +the things that eventually emerge not +specifically from their recommendations + + align:start position:0% +specifically from their recommendations + + + align:start position:0% +specifically from their recommendations +necessarily but emerged over time were + + align:start position:0% +necessarily but emerged over time were + + + align:start position:0% +necessarily but emerged over time were +created as cooperative Rd agreements + + align:start position:0% +created as cooperative Rd agreements + + + align:start position:0% +created as cooperative Rd agreements +with industry between governmental + + align:start position:0% +with industry between governmental + + + align:start position:0% +with industry between governmental +laboratories and industry in other words + + align:start position:0% +laboratories and industry in other words + + + align:start position:0% +laboratories and industry in other words +we've got these snappy governmental labs + + align:start position:0% +we've got these snappy governmental labs + + + align:start position:0% +we've got these snappy governmental labs +little emerges from them can we do + + align:start position:0% +little emerges from them can we do + + + align:start position:0% +little emerges from them can we do +cooperative agreements to get + + align:start position:0% 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research that it supported at + + align:start position:0% +of the research that it supported at + + + align:start position:0% +of the research that it supported at +universities now the federal government + + align:start position:0% +universities now the federal government + + + align:start position:0% +universities now the federal government +is not a commercial entity so nothing + + align:start position:0% +is not a commercial entity so nothing + + + align:start position:0% +is not a commercial entity so nothing +happened to it so it was moved to + + align:start position:0% +happened to it so it was moved to + + + align:start position:0% +happened to it so it was moved to +shelves right the IP was not really + + align:start position:0% +shelves right the IP was not really + + + align:start position:0% +shelves right the IP was not really +utilized so the buying dole came up with + + align:start position:0% +utilized so the buying dole came up with + + + align:start position:0% +utilized so the buying dole came up with +the idea of giving the universities that + + align:start position:0% +the idea of giving the universities that + + + align:start position:0% +the idea of giving the universities that +it sponsored the research activities + + align:start position:0% +it sponsored the research activities + + + align:start position:0% +it sponsored the research activities +supported the research activities + + align:start position:0% +supported the research activities + + + align:start position:0% +supported the research activities +with federal funds let's give them + + align:start position:0% +with federal funds let's give them + + + align:start position:0% +with federal funds let's give them +ownership they in turn typically share + + align:start position:0% +ownership they in turn typically share + + + align:start position:0% +ownership they in turn typically share +it with their researchers and give them + + align:start position:0% +it with their researchers and give them + + + align:start position:0% +it with their researchers and give them +a vested stake in developing the + + align:start position:0% +a vested stake in developing the + + + align:start position:0% +a vested stake in developing the +technologies that the research is + + align:start position:0% +technologies that the research is + + + align:start position:0% +technologies that the research is +leading to so this plays a really + + align:start position:0% +leading to so this plays a really + + + align:start position:0% +leading to so this plays a really +critical role in starting to put + + align:start position:0% +critical role in starting to put + + + align:start position:0% +critical role in starting to put +universities on the playing field as + + align:start position:0% +universities on the playing field as + + + align:start position:0% +universities on the playing field as +innovation actors it gives them a stake + + align:start position:0% +innovation actors it gives them a stake + + + align:start position:0% +innovation actors it gives them a stake +the outcomes of their research the + + align:start position:0% +the outcomes of their research the + + + align:start position:0% +the outcomes of their research the +advanced technology program and the + + align:start position:0% +advanced technology program and the + + + align:start position:0% +advanced technology program and the +manufacturing extension program come out + + align:start position:0% +manufacturing extension program come out + + + align:start position:0% +manufacturing extension program come out +of the Commerce Department of the temptu + + align:start position:0% +of the Commerce Department of the temptu + + + align:start position:0% +of the Commerce Department of the temptu +introduced of new technologies and an + + align:start position:0% +introduced of new technologies and an + + + align:start position:0% +introduced of new technologies and an +attempt to and the MEP program to bring + + align:start position:0% +attempt to and the MEP program to bring + + + align:start position:0% +attempt to and the MEP program to bring +the advances Japan had been pushing on + + align:start position:0% +the advances Japan had been pushing on + + + align:start position:0% +the advances Japan had been pushing on +quality production into small US + + align:start position:0% +quality production into small US + + + align:start position:0% +quality production into small US +manufacturers there were education + + align:start position:0% +manufacturers there were education + + + align:start position:0% +manufacturers there were education +proposals the attitude was essentially + + align:start position:0% +proposals the attitude was essentially + + + align:start position:0% +proposals the attitude was essentially +pro trade liberals don't ignore the + + align:start position:0% +pro trade liberals don't ignore the + + + align:start position:0% +pro trade liberals don't ignore the +world let's be successful at trade and + + align:start position:0% +world let's be successful at trade and + + + align:start position:0% +world let's be successful at trade and +the innovative a trade that attitude + + align:start position:0% +the innovative a trade that attitude + + + align:start position:0% +the innovative a trade that attitude +gets adopted by the Clinton + + align:start position:0% +gets adopted by the Clinton + + + align:start position:0% +gets adopted by the Clinton +administration and leaves and things + + align:start position:0% +administration and leaves and things + + + align:start position:0% +administration and leaves and things +like NAFTA the China WTO so that's kind + + align:start position:0% +like NAFTA the China WTO so that's kind + + + align:start position:0% +like NAFTA the China WTO so that's kind +of what was coming out of the young + + align:start position:0% +of what was coming out of the young + + + align:start position:0% +of what was coming out of the young +Commission in terms of new ideas but + + align:start position:0% +Commission in terms of new ideas but + + + align:start position:0% +Commission in terms of new ideas but +let's go back to the challenge that they + + align:start position:0% +let's go back to the challenge that they + + + align:start position:0% +let's go back to the challenge that they +were facing what was this what was this + + align:start position:0% +were facing what was this what was this + + + align:start position:0% +were facing what was this what was this +new model around production pitch on + + align:start position:0% +new model around production pitch on + + + align:start position:0% +new model around production pitch on +that Japan was launching and I would + + align:start position:0% +that Japan was launching and I would + + + align:start position:0% +that Japan was launching and I would +argue that was big enough so that it in + + align:start position:0% +argue that was big enough so 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position:0% +towards its own competitiveness as a + + + align:start position:0% +towards its own competitiveness as a +leading world economic power and before + + align:start position:0% +leading world economic power and before + + + align:start position:0% +leading world economic power and before +the 1970s the US had come up with a way + + align:start position:0% +the 1970s the US had come up with a way + + + align:start position:0% +the 1970s the US had come up with a way +of dealing with quality it's called a + + align:start position:0% +of dealing with quality it's called a + + + align:start position:0% +of dealing with quality it's called a +quality price trade-off so in our mass + + align:start position:0% +quality price trade-off so in our mass + + + align:start position:0% +quality price trade-off so in our mass +production system from the US + + align:start position:0% +production system from the US + + + align:start position:0% +production system from the US +essentially came up with most of the + + align:start position:0% +essentially came up with most of the + + + align:start position:0% +essentially came up with most of the +elements + + align:start position:0% +elements + + + align:start position:0% +elements +mass production starting around the + + align:start position:0% +mass production starting around the + + + align:start position:0% +mass production starting around the +1840s at movies you know from other + + align:start position:0% +1840s at movies you know from other + + + align:start position:0% +1840s at movies you know from other +years the u.s. become most dominant mass + + align:start position:0% +years the u.s. become most dominant mass + + + align:start position:0% +years the u.s. become most dominant mass +we had really invented mass production + + align:start position:0% +we had really invented mass production + + + align:start position:0% +we had really invented mass production +and huge scale and we were selling + + align:start position:0% +and huge scale and we were selling + + + align:start position:0% +and huge scale and we were selling +manufactured goods into a convent sized + + align:start position:0% +manufactured goods into a convent sized + + + align:start position:0% +manufactured goods into a convent sized +economy for his confidence to exist and + + align:start position:0% +economy for his confidence to exist and + + + align:start position:0% +economy for his confidence to exist and +part of the mass production idea was + + align:start position:0% +part of the mass production idea was + + + align:start position:0% +part of the mass production idea was +never stopped the production always keep + + align:start position:0% +never stopped the production always keep + + + align:start position:0% +never stopped the production always keep +it moving always keep produced and how + + align:start position:0% +it moving always keep produced and how + + + align:start position:0% +it moving always keep produced and how +do you do with the quality well whose + + align:start position:0% +do you do with the quality well whose + + + align:start position:0% +do you do with the quality well whose +statistical analysis of the products you + + align:start position:0% +statistical analysis of the products you + + + align:start position:0% +statistical analysis of the products you +were producing you would decide that + + align:start position:0% +were producing you would decide that + + + align:start position:0% +were producing you would decide that +some percent some fixed percentage we're + + align:start position:0% +some percent some fixed percentage we're + + + align:start position:0% +some percent some fixed percentage we're +not meeting those quality standards and + + align:start position:0% +not meeting those quality standards and + + + align:start position:0% +not meeting those quality standards and +so at the end of the system after you + + align:start position:0% +so at the end of the system after you + + + align:start position:0% +so at the end of the system after you +would produce the goods you would have + + align:start position:0% +would produce the goods you would have + + + align:start position:0% +would produce the goods you would have +an inspection group throw out whatever + + align:start position:0% +an inspection group throw out whatever + + + align:start position:0% +an inspection group throw out whatever +it was one point eight percent two point + + align:start position:0% +it was one point eight percent two point + + + align:start position:0% +it was one point eight percent two point +four percent whatever the statistical + + align:start position:0% +four percent whatever the statistical + + + align:start position:0% +four percent whatever the statistical +number told you after the production + + align:start position:0% +number told you after the production + + + align:start position:0% +number told you after the production +system had been developed quality is + + align:start position:0% +system had been developed quality is + + + align:start position:0% +system had been developed quality is +really how good as the product the + + align:start position:0% +really how good as the product the + + + align:start position:0% +really how good as the product the +quality control is what's the unit of + + align:start position:0% +quality control is what's the unit of + + + align:start position:0% +quality control is what's the unit of +are the units of equal quality right + + align:start position:0% +are the units of equal quality right + + + align:start position:0% +are the units of equal quality right +across all that you're producing Japan + + align:start position:0% +across all that you're producing Japan + + + align:start position:0% +across all that you're producing Japan +came up with a completely different + + align:start position:0% +came up with a completely different + + + align:start position:0% +came up with a completely different +system and a much better system and it + + align:start position:0% +system and a much better system and it + + + align:start position:0% +system and a much better system and it +was called here the Toyota model but it + + align:start position:0% +was called here the Toyota model but it + + + align:start position:0% +was called here the Toyota model but it +was pervasive in Japanese procedures the + + align:start position:0% +was pervasive in Japanese procedures the + + + align:start position:0% +was pervasive in Japanese procedures the +idea here was build quality into each + + align:start position:0% +idea here was build quality into each + + + align:start position:0% +idea here was build quality into each +product not at the end of the system + + align:start position:0% +product not at the end of the system + + + align:start position:0% +product not at the end of the system +throw a bunch of stuff away ensured that + + align:start position:0% +throw a bunch of stuff away ensured that + + + align:start position:0% +throw a bunch of stuff away ensured that +the entire system is working to ensure + + align:start position:0% +the entire system is working to ensure + + + align:start position:0% +the entire system is working to ensure +the quality and anyone any worker can + + align:start position:0% +the quality and anyone any worker can + + + align:start position:0% +the quality and anyone any worker can +stop the production line if they see a + + align:start position:0% +stop the production line if they see a + + + align:start position:0% +stop the production line if they see a +quality problem so catch it at the + + align:start position:0% +quality problem so catch it at the + + + align:start position:0% +quality problem so catch it at the +beginning and build quality and your + + align:start position:0% +beginning and build quality and your + + + align:start position:0% +beginning and build quality and your +entire production process the idea came + + align:start position:0% +entire production process the idea came + + + align:start position:0% +entire production process the idea came +actually from an American and Edward + + align:start position:0% +actually from an American and Edward + + + align:start position:0% +actually from an American and Edward +Deming and he was unable to persuade US + + align:start position:0% +Deming and he was unable to persuade US + + + align:start position:0% +Deming and he was unable to persuade US +manufacturers to adopt as well so he + + align:start position:0% +manufacturers to adopt as well so he + + + align:start position:0% +manufacturers to adopt as well so he +takes it to Japan and you know me since + + align:start position:0% +takes it to Japan and you know me since + + + align:start position:0% +takes it to Japan and you know me since +Japan's + + align:start position:0% +Japan's + + + align:start position:0% +Japan's +rich culture here around craftsmanship + + align:start position:0% +rich culture here around craftsmanship + + + align:start position:0% +rich culture here around craftsmanship +why it fits wonderfully but + + align:start position:0% +why it fits wonderfully but + + + align:start position:0% +why it fits wonderfully but +all right so this is you know Japanese + + align:start position:0% +all right so this is you know Japanese + + + align:start position:0% +all right so this is you know Japanese +samurai culture of course respects the + + align:start position:0% +samurai culture of course respects the + + + align:start position:0% +samurai culture of course respects the +samurai but Accords almost equivalent + + align:start position:0% +samurai but Accords almost equivalent + + + align:start position:0% +samurai but Accords almost equivalent +respect to the sword maker right who is + + align:start position:0% +respect to the sword maker right who is + + + align:start position:0% +respect to the sword maker right who is +almost equally as famous so there's a + + align:start position:0% +almost equally as famous so there's a + + + align:start position:0% +almost equally as famous so there's a +huge focus on high quality and + + align:start position:0% +huge focus on high quality and + + + align:start position:0% +huge focus on high quality and +craftsmanship in Japanese culture so + + align:start position:0% +craftsmanship in Japanese culture so + + + align:start position:0% +craftsmanship in Japanese culture so +what Deming is saying this with the kind + + align:start position:0% +what Deming is saying this with the kind + + + align:start position:0% +what Deming is saying this with the kind +of culture of Japan there are other + + align:start position:0% +of culture of Japan there are other + + + align:start position:0% +of culture of Japan there are other +pieces that you can comes up with + + align:start position:0% +pieces that you can comes up with + + + align:start position:0% +pieces that you can comes up with +just-in-time inventory in other words a + + align:start position:0% +just-in-time inventory in other words a + + + align:start position:0% +just-in-time inventory in other words a +major burden that manufacturers face is + + align:start position:0% +major burden that manufacturers face is + + + align:start position:0% +major burden that manufacturers face is +that they have to store up a lot of + + align:start position:0% +that they have to store up a lot of + + + align:start position:0% +that they have to store up a lot of +inventory to have enough Goods available + + align:start position:0% +inventory to have enough Goods available + + + align:start position:0% +inventory to have enough Goods available +for the market list but when you hit an + + align:start position:0% +for the market list but when you hit an + + + align:start position:0% +for the market list but when you hit an +economic downturn then you stuck with + + align:start position:0% +economic downturn then you stuck with + + + align:start position:0% +economic downturn then you stuck with +this massive inventory that you can't + + align:start position:0% +this massive inventory that you can't + + + align:start position:0% +this massive inventory that you can't +get rid of right and it becomes a huge + + align:start position:0% +get rid of right and it becomes a huge + + + align:start position:0% +get rid of right and it becomes a huge +cost burden on your system Japan's idea + + align:start position:0% +cost burden on your system Japan's idea + + + align:start position:0% +cost burden on your system Japan's idea +was produced for what the MEK market is + + align:start position:0% +was produced for what the MEK market is + + + align:start position:0% +was produced for what the MEK market is +actually absorbing in other words + + align:start position:0% +actually absorbing in other words + + + align:start position:0% +actually absorbing in other words +produced just in time to get it to + + align:start position:0% +produced just in time to get it to + + + align:start position:0% +produced just in time to get it to +market so that calls for a whole new + + align:start position:0% +market so that calls for a whole new + + + align:start position:0% +market so that calls for a whole new +level of efficiency and communications + + align:start position:0% +level of efficiency and communications + + + align:start position:0% +level of efficiency and communications +reallyit embedded kind of ways to let + + align:start position:0% +reallyit embedded kind of ways to let + + + align:start position:0% +reallyit embedded kind of ways to let +the whole production system it was and + + align:start position:0% +the whole production system it was and + + + align:start position:0% +the whole production system it was and +it significantly reduced the exposure of + + align:start position:0% +it significantly reduced the exposure of + + + align:start position:0% +it significantly reduced the exposure of +significant manufacturers to economic + + align:start position:0% +significant manufacturers to economic + + + align:start position:0% +significant manufacturers to economic +downturns Japan integrated its its + + align:start position:0% +downturns Japan integrated its its + + + align:start position:0% +downturns Japan integrated its its +dealers and its suppliers into his + + align:start position:0% +dealers and its suppliers into his + + + align:start position:0% +dealers and its suppliers into his +system so in the u.s. major + + align:start position:0% +system so in the u.s. major + + + align:start position:0% +system so in the u.s. major +manufacturers would keep their suppliers + + align:start position:0% +manufacturers would keep their suppliers + + + align:start position:0% +manufacturers would keep their suppliers +at arm's length and have them bid and + + align:start position:0% +at arm's length and have them bid and + + + align:start position:0% +at arm's length and have them bid and +there was no particular relationship + + align:start position:0% +there was no particular relationship + + + align:start position:0% +there was no particular relationship +they were just looking for the lowest + + align:start position:0% +they were just looking for the lowest + + + align:start position:0% +they were just looking for the lowest +price like Japan the supplies were + + align:start position:0% +price like Japan the supplies were + + + align:start position:0% +price like Japan the supplies were +actually integrated into that system and + + align:start position:0% +actually integrated into that system and + + + align:start position:0% +actually integrated into that system and +in turn the dealers who were just you + + align:start position:0% +in turn the dealers who were just you + + + align:start position:0% +in turn the dealers who were just you +know selling these goods were also + + align:start position:0% +know selling these goods were also + + + align:start position:0% +know selling these goods were also +integrated so that you had much closer + + align:start position:0% +integrated so that you had much closer + + + align:start position:0% +integrated so that you had much closer +touch with what customers actually + + align:start position:0% +touch with what customers actually + + + align:start position:0% +touch with what customers actually +needed it wanted as well as what the + + align:start position:0% +needed it wanted as well as what the + + + align:start position:0% +needed it wanted as well as what the +quality of the suppliers + + align:start position:0% +quality of the suppliers + + + align:start position:0% +quality of the suppliers +but they were producing it's gonna be + + align:start position:0% +but they were producing it's gonna be + + + align:start position:0% +but they were producing it's gonna be +Japan had a culture of respecting the + + align:start position:0% +Japan had a culture of respecting the + + + align:start position:0% +Japan had a culture of respecting the +production moment so they would move + + align:start position:0% +production moment so they would move + + + align:start position:0% +production moment so they would move +their engineers on to the factory floor + + align:start position:0% +their engineers on to the factory floor + + + align:start position:0% +their engineers on to the factory floor +cuz the first set of assignments so if + + align:start position:0% +cuz the first set of assignments so if + + + align:start position:0% +cuz the first set of assignments so if +you look at in contrast the u.s. didn't + + align:start position:0% +you look at in contrast the u.s. didn't + + + align:start position:0% +you look at in contrast the u.s. didn't +do that right so the engineering + + align:start position:0% +do that right so the engineering + + + align:start position:0% +do that right so the engineering +profession was won in the 19th century + + align:start position:0% +profession was won in the 19th century + + + align:start position:0% +profession was won in the 19th century +the u.s. that was trying to take a hold + + align:start position:0% +the u.s. that was trying to take a hold + + + align:start position:0% +the u.s. that was trying to take a hold +with those other established professions + + align:start position:0% +with those other established professions + + + align:start position:0% +with those other established professions +doctors lawyers ministers so when you + + align:start position:0% +doctors lawyers ministers so when you + + + align:start position:0% +doctors lawyers ministers so when you +look at these early photographs of MIT + + align:start position:0% +look at these early photographs of MIT + + + align:start position:0% +look at these early photographs of MIT +and you look at photographs of like an + + align:start position:0% +and you look at photographs of like an + + + align:start position:0% +and you look at photographs of like an +entry perhaps there's wonderful + + align:start position:0% +entry perhaps there's wonderful + + + align:start position:0% +entry perhaps there's wonderful +photographs of the steam lab you can't + + align:start position:0% +photographs of the steam lab you can't + + + align:start position:0% +photographs of the steam lab you can't +imagine you know coal dust all over the + + align:start position:0% +imagine you know coal dust all over the + + + align:start position:0% +imagine you know coal dust all over the +place these characters are wearing these + + align:start position:0% +place these characters are wearing these + + + align:start position:0% +place these characters are wearing these +starched white shirts with you know + + align:start position:0% +starched white shirts with you know + + + align:start position:0% +starched white shirts with you know +those fancy weird bowties they wore at + + align:start position:0% +those fancy weird bowties they wore at + + + align:start position:0% +those fancy weird bowties they wore at +the end of the 19th century right they + + align:start position:0% +the end of the 19th century right they + + + align:start position:0% +the end of the 19th century right they +look so lean and proper they're trying + + align:start position:0% +look so lean and proper they're trying + + + align:start position:0% +look so lean and proper they're trying +to be like ministers and doctors right + + align:start position:0% +to be like ministers and doctors right + + + align:start position:0% +to be like ministers and doctors right +they're trying to elevate their + + align:start position:0% +they're trying to elevate their + + + align:start position:0% +they're trying to elevate their +profession and separate themselves in a + + align:start position:0% +profession and separate themselves in a + + + align:start position:0% +profession and separate themselves in a +way from the word floor right so the + + align:start position:0% +way from the word floor right so the + + + align:start position:0% +way from the word floor right so the +engineers want to be in a glass top + + align:start position:0% +engineers want to be in a glass top + + + align:start position:0% +engineers want to be in a glass top +buried up above the above the factory + + align:start position:0% +buried up above the above the factory + + + align:start position:0% +buried up above the above the factory +floor the US I don't want to be done + + align:start position:0% +floor the US I don't want to be done + + + align:start position:0% +floor the US I don't want to be done +with you haven't forbid the workforce so + + align:start position:0% +with you haven't forbid the workforce so + + + align:start position:0% +with you haven't forbid the workforce so +it's it's an attempt by an engineering + + align:start position:0% +it's it's an attempt by an engineering + + + align:start position:0% +it's it's an attempt by an engineering +culture to establish its identity kind + + align:start position:0% +culture to establish its identity kind + + + align:start position:0% +culture to establish its identity kind +of a stamp might happen but Japan hit on + + align:start position:0% +of a stamp might happen but Japan hit on + + + align:start position:0% +of a stamp might happen but Japan hit on +a much better much right integrate the + + align:start position:0% +a much better much right integrate the + + + align:start position:0% +a much better much right integrate the +engineers in the work force and they've + + align:start position:0% +engineers in the work force and they've + + + align:start position:0% +engineers in the work force and they've +got one right much better so we have to + + align:start position:0% +got one right much better so we have to + + + align:start position:0% +got one right much better so we have to +learn to get our engineers into the mix + + align:start position:0% +learn to get our engineers into the mix + + + align:start position:0% +learn to get our engineers into the mix +in the manufacturing sector Japan came + + align:start position:0% +in the manufacturing sector Japan came + + + align:start position:0% +in the manufacturing sector Japan came +up with this quality manufacturing model + + align:start position:0% +up with this quality manufacturing model + + + align:start position:0% +up with this quality manufacturing model +we sometimes we call it here at lean + + align:start position:0% +we sometimes we call it here at lean + + + align:start position:0% +we sometimes we call it here at lean +manufacturing had led to an effort by + + align:start position:0% +manufacturing had led to an effort by + + + align:start position:0% +manufacturing had led to an effort by +the u.s. to us if they copy which Japan + + align:start position:0% +the u.s. to us if they copy which Japan + + + align:start position:0% +the u.s. to us if they copy which Japan +had come up with we had to take apart + + align:start position:0% +had come up with we had to take apart + + + align:start position:0% +had come up with we had to take apart +the Toyota model a lot of that work is + + align:start position:0% +the Toyota model a lot of that work is + + + align:start position:0% +the Toyota model a lot of that work is +being done at IT right so Dan roots and + + align:start position:0% +being done at IT right so Dan roots and + + + align:start position:0% +being done at IT right so Dan roots and +several others in MIT you are writing up + + align:start position:0% +several others in MIT you are writing up + + + align:start position:0% +several others in MIT you are writing up +the Toyota model and explaining into the + + align:start position:0% +the Toyota model and explaining into the + + + align:start position:0% +the Toyota model and explaining into the +rest of the country was really important + + align:start position:0% +rest of the country was really important + + + align:start position:0% +rest of the country was really important +stage standard industry approaches like + + align:start position:0% +stage standard industry approaches like + + + align:start position:0% +stage standard industry approaches like +Six Sigma that came out of GE + + align:start position:0% +Six Sigma that came out of GE + + + align:start position:0% +Six Sigma that came out of GE +have essentially attempted to + + align:start position:0% +have essentially attempted to + + + align:start position:0% +have essentially attempted to +incorporate Japan's quality ideas and + + align:start position:0% +incorporate Japan's quality ideas and + + + align:start position:0% +incorporate Japan's quality ideas and +make them pervasive in US production for + + align:start position:0% +make them pervasive in US production for + + + align:start position:0% +make them pervasive in US production for +major manufacturers om survivors so + + align:start position:0% +major manufacturers om survivors so + + + align:start position:0% +major manufacturers om survivors so +that's a few other things there's + + align:start position:0% +that's a few other things there's + + + align:start position:0% +that's a few other things there's +there's a something called the product + + align:start position:0% +there's a something called the product + + + align:start position:0% +there's a something called the product +cycle and time is a competitive factor + + align:start position:0% +cycle and time is a competitive factor + + + align:start position:0% +cycle and time is a competitive factor +in this so eliminating time delays and + + align:start position:0% +in this so eliminating time delays and + + + align:start position:0% +in this so eliminating time delays and +then something actually the u.s. really + + align:start position:0% +then something actually the u.s. really + + + align:start position:0% +then something actually the u.s. really +contributed to was concurrent + + align:start position:0% +contributed to was concurrent + + + align:start position:0% +contributed to was concurrent +engineering design so you engineers + + align:start position:0% +engineering design so you engineers + + + align:start position:0% +engineering design so you engineers +never know much I know what I'm talking + + align:start position:0% +never know much I know what I'm talking + + + align:start position:0% +never know much I know what I'm talking +about + + align:start position:0% +about + + + align:start position:0% +about +but in other words if we were doesn't if + + align:start position:0% +but in other words if we were doesn't if + + + align:start position:0% +but in other words if we were doesn't if +if if you and I constituted Christman + + align:start position:0% +if if you and I constituted Christman + + + align:start position:0% +if if you and I constituted Christman +motors the way in which we were + + align:start position:0% +motors the way in which we were + + + align:start position:0% +motors the way in which we were +organized by summers in the old days was + + align:start position:0% +organized by summers in the old days was + + + align:start position:0% +organized by summers in the old days was +it would have a bunch of Engineers and + + align:start position:0% +it would have a bunch of Engineers and + + + align:start position:0% +it would have a bunch of Engineers and +they would do to the design and then + + align:start position:0% +they would do to the design and then + + + align:start position:0% +they would do to the design and then +they would finish the design and then + + align:start position:0% +they would finish the design and then + + + align:start position:0% +they would finish the design and then +they would take it to the production + + align:start position:0% +they would take it to the production + + + align:start position:0% +they would take it to the production +people and the production people will + + align:start position:0% +people and the production people will + + + align:start position:0% +people and the production people will +say well that's all very long good but + + align:start position:0% +say well that's all very long good but + + + align:start position:0% +say well that's all very long good but +we can't make that so can you do it + + align:start position:0% +we can't make that so can you do it + + + align:start position:0% +we can't make that so can you do it +right and then it would be redone and + + align:start position:0% +right and then it would be redone and + + + align:start position:0% +right and then it would be redone and +then they would take it will be people + + align:start position:0% +then they would take it will be people + + + align:start position:0% +then they would take it will be people +again and then take it to the marketing + + align:start position:0% +again and then take it to the marketing + + + align:start position:0% +again and then take it to the marketing +people and the market people would say + + align:start position:0% +people and the market people would say + + + align:start position:0% +people and the market people would say +well that's all very well I'm good what + + align:start position:0% +well that's all very well I'm good what + + + align:start position:0% +well that's all very well I'm good what +you engineering people have done it what + + align:start position:0% +you engineering people have done it what + + + align:start position:0% +you engineering people have done it what +your factory for people have done but we + + align:start position:0% +your factory for people have done but we + + + align:start position:0% +your factory for people have done but we +can't sell this thing so completely redo + + align:start position:0% +can't sell this thing so completely redo + + + align:start position:0% +can't sell this thing so completely redo +it though it was it was a stage by stage + + align:start position:0% +it though it was it was a stage by stage + + + align:start position:0% +it though it was it was a stage by stage +process with every stage having a veto + + align:start position:0% +process with every stage having a veto + + + align:start position:0% +process with every stage having a veto +so that the development process for + + align:start position:0% +so that the development process for + + + align:start position:0% +so that the development process for +design was painful and lengthy and often + + align:start position:0% +design was painful and lengthy and often + + + align:start position:0% +design was painful and lengthy and often +adversarial concurrent design is to put + + align:start position:0% +adversarial concurrent design is to put + + + align:start position:0% +adversarial concurrent design is to put +all those teams together at the outset + + align:start position:0% +all those teams together at the outset + + + align:start position:0% +all those teams together at the outset +contributing to the design dramatic time + + align:start position:0% +contributing to the design dramatic time + + + align:start position:0% +contributing to the design dramatic time +savings dramatic efficiencies so these + + align:start position:0% +savings dramatic efficiencies so these + + + align:start position:0% +savings dramatic efficiencies so these +are all kinds of ideas that came out of + + align:start position:0% +are all kinds of ideas that came out of + + + align:start position:0% +are all kinds of ideas that came out of +this time period another idea that Japan + + align:start position:0% +this time period another idea that Japan + + + align:start position:0% +this time period another idea that Japan +had we weren't organized in this way + + align:start position:0% +had we weren't organized in this way + + + align:start position:0% +had we weren't organized in this way +Japan had a whole different way of + + align:start position:0% +Japan had a whole different way of + + + align:start position:0% +Japan had a whole different way of +approaching and what we could call the + + align:start position:0% +approaching and what we could call the + + + align:start position:0% +approaching and what we could call the +labor trade of the labor trade off so + + align:start position:0% +labor trade of the labor trade off so + + + align:start position:0% +labor trade of the labor trade off so +Japan had a system essentially + + align:start position:0% +Japan had a system essentially + + + align:start position:0% +Japan had a system essentially +guaranteed lifetime employment + + align:start position:0% +guaranteed lifetime employment + + + align:start position:0% +guaranteed lifetime employment +so if you're a worker in Japan you were + + align:start position:0% +so if you're a worker in Japan you were + + + align:start position:0% +so if you're a worker in Japan you were +pretty well assured at this in this era + + align:start position:0% +pretty well assured at this in this era + + + align:start position:0% +pretty well assured at this in this era +it's changed a bit now in this era of a + + align:start position:0% +it's changed a bit now in this era of a + + + align:start position:0% +it's changed a bit now in this era of a +lifetime job and in return for the + + align:start position:0% +lifetime job and in return for the + + + align:start position:0% +lifetime job and in return for the +assurance of a lifetime job management + + align:start position:0% +assurance of a lifetime job management + + + align:start position:0% +assurance of a lifetime job management +we control the workflows in other words + + align:start position:0% +we control the workflows in other words + + + align:start position:0% +we control the workflows in other words +what's actually happening on the factory + + align:start position:0% +what's actually happening on the factory + + + align:start position:0% +what's actually happening on the factory +floor right how that work process where + + align:start position:0% +floor right how that work process where + + + align:start position:0% +floor right how that work process where +the rule systems is that was the trade + + align:start position:0% +the rule systems is that was the trade + + + align:start position:0% +the rule systems is that was the trade +off the u.s. had a completely different + + align:start position:0% +off the u.s. had a completely different + + + align:start position:0% +off the u.s. had a completely different +trade off we treated labor not as a + + align:start position:0% +trade off we treated labor not as a + + + align:start position:0% +trade off we treated labor not as a +fixed cost like Japan - we treated it as + + align:start position:0% +fixed cost like Japan - we treated it as + + + align:start position:0% +fixed cost like Japan - we treated it as +a variable cost and the trade the + + align:start position:0% +a variable cost and the trade the + + + align:start position:0% +a variable cost and the trade the +union's insisted on this is there a + + align:start position:0% +union's insisted on this is there a + + + align:start position:0% +union's insisted on this is there a +pretty heavy unionization in that + + align:start position:0% +pretty heavy unionization in that + + + align:start position:0% +pretty heavy unionization in that +factually + + align:start position:0% + + + + align:start position:0% + +unions weren't able to affect who gets + + align:start position:0% +unions weren't able to affect who gets + + + align:start position:0% +unions weren't able to affect who gets +hired and fired in the employment side + + align:start position:0% +hired and fired in the employment side + + + align:start position:0% +hired and fired in the employment side +of the equation but they would control + + align:start position:0% +of the equation but they would control + + + align:start position:0% +of the equation but they would control +the were closed right and they designed + + align:start position:0% +the were closed right and they designed + + + align:start position:0% +the were closed right and they designed +those to be as protected as possible + + align:start position:0% +those to be as protected as possible + + + align:start position:0% +those to be as protected as possible +about their workforces right not + + align:start position:0% +about their workforces right not + + + align:start position:0% +about their workforces right not +necessarily the most efficient assistant + + align:start position:0% +necessarily the most efficient assistant + + + align:start position:0% +necessarily the most efficient assistant +so Japan actually had a better model now + + align:start position:0% +so Japan actually had a better model now + + + align:start position:0% +so Japan actually had a better model now +we continue to treat our workforce as a + + align:start position:0% +we continue to treat our workforce as a + + + align:start position:0% +we continue to treat our workforce as a +variable cost right so whenever there's + + align:start position:0% +variable cost right so whenever there's + + + align:start position:0% +variable cost right so whenever there's +an economic downturn the US companies + + align:start position:0% +an economic downturn the US companies + + + align:start position:0% +an economic downturn the US companies +dump their workforces as a quick + + align:start position:0% +dump their workforces as a quick + + + align:start position:0% +dump their workforces as a quick +response like that's fundamental + + align:start position:0% +response like that's fundamental + + + align:start position:0% +response like that's fundamental +management Theory really give us other + + align:start position:0% +management Theory really give us other + + + align:start position:0% +management Theory really give us other +countries done this we do it + + align:start position:0% +countries done this we do it + + + align:start position:0% +countries done this we do it +Japan is heavy it more flexible in this + + align:start position:0% +Japan is heavy it more flexible in this + + + align:start position:0% +Japan is heavy it more flexible in this +model as it spawned a more global + + align:start position:0% +model as it spawned a more global + + + align:start position:0% +model as it spawned a more global +competition but it had a completely + + align:start position:0% +competition but it had a completely + + + align:start position:0% +competition but it had a completely +different way of organizing this + + align:start position:0% +different way of organizing this + + + align:start position:0% +different way of organizing this +workforce labor became much more + + align:start position:0% +workforce labor became much more + + + align:start position:0% +workforce labor became much more +collaborative rather than adversarial + + align:start position:0% +collaborative rather than adversarial + + + align:start position:0% +collaborative rather than adversarial +and ready to leap on new efficiencies in + + align:start position:0% +and ready to leap on new efficiencies in + + + align:start position:0% +and ready to leap on new efficiencies in +the production process rather than fight + + align:start position:0% +the production process rather than fight + + + align:start position:0% +the production process rather than fight +them every inch of the way so again this + + align:start position:0% +them every inch of the way so again this + + + align:start position:0% +them every inch of the way so again this +was a contributing factor to the kind of + + align:start position:0% +was a contributing factor to the kind of + + + align:start position:0% +was a contributing factor to the kind of +new model that Japan was creating + + align:start position:0% +new model that Japan was creating + + + align:start position:0% +new model that Japan was creating +there's another element here of + + align:start position:0% +there's another element here of + + + align:start position:0% +there's another element here of +industrial pulse so Japan is recovering + + align:start position:0% +industrial pulse so Japan is recovering + + + align:start position:0% +industrial pulse so Japan is recovering +from what war - it develops an + + align:start position:0% +from what war - it develops an + + + align:start position:0% +from what war - it develops an +innovation system that is very focused + + align:start position:0% +innovation system that is very focused + + + align:start position:0% +innovation system that is very focused +on production + + align:start position:0% +on production + + + align:start position:0% +on production +that's what it's got to stand up and + + align:start position:0% +that's what it's got to stand up and + + + align:start position:0% +that's what it's got to stand up and +that's what this quality model comes + + align:start position:0% +that's what this quality model comes + + + align:start position:0% +that's what this quality model comes +from all these other pieces and Japan + + align:start position:0% +from all these other pieces and Japan + + + align:start position:0% +from all these other pieces and Japan +it's very resource poor so starting in + + align:start position:0% +it's very resource poor so starting in + + + align:start position:0% +it's very resource poor so starting in +the 1880s Japan understood that it had + + align:start position:0% +the 1880s Japan understood that it had + + + align:start position:0% +the 1880s Japan understood that it had +to have an export orientation and had to + + align:start position:0% +to have an export orientation and had to + + + align:start position:0% +to have an export orientation and had to +export to live because it had to get the + + align:start position:0% +export to live because it had to get the + + + align:start position:0% +export to live because it had to get the +resources in order to for this right and + + align:start position:0% +resources in order to for this right and + + + align:start position:0% +resources in order to for this right and +by those backs that would need an export + + align:start position:0% +by those backs that would need an export + + + align:start position:0% +by those backs that would need an export +surplus in one of its core institutions + + align:start position:0% +surplus in one of its core institutions + + + align:start position:0% +surplus in one of its core institutions +was called meeting Ministry of + + align:start position:0% +was called meeting Ministry of + + + align:start position:0% +was called meeting Ministry of +International Trade and Industry now + + align:start position:0% +International Trade and Industry now + + + align:start position:0% +International Trade and Industry now +called Medi and that the nickname for + + align:start position:0% +called Medi and that the nickname for + + + align:start position:0% +called Medi and that the nickname for +this was Japan Inc but a very integrated + + align:start position:0% +this was Japan Inc but a very integrated + + + align:start position:0% +this was Japan Inc but a very integrated +system of governmental leadership tied + + align:start position:0% +system of governmental leadership tied + + + align:start position:0% +system of governmental leadership tied +to major industries in the major + + align:start position:0% +to major industries in the major + + + align:start position:0% +to major industries in the major +industries or organized as they were the + + align:start position:0% +industries or organized as they were the + + + align:start position:0% +industries or organized as they were the +u.s. we have any trusted loss of us we + + align:start position:0% +u.s. we have any trusted loss of us we + + + align:start position:0% +u.s. we have any trusted loss of us we +do not really impose them in the + + align:start position:0% +do not really impose them in the + + + align:start position:0% +do not really impose them in the +post-war period and allow Japan to keep + + align:start position:0% +post-war period and allow Japan to keep + + + align:start position:0% +post-war period and allow Japan to keep +its caresses so that's a system of major + + align:start position:0% +its caresses so that's a system of major + + + align:start position:0% +its caresses so that's a system of major +firms typically engaged in production + + align:start position:0% +firms typically engaged in production + + + align:start position:0% +firms typically engaged in production +activities financing global trading and + + align:start position:0% +activities financing global trading and + + + align:start position:0% +activities financing global trading and +then networks of suppliers that are tied + + align:start position:0% +then networks of suppliers that are tied + + + align:start position:0% +then networks of suppliers that are tied +to those so these are groups of related + + align:start position:0% +to those so these are groups of related + + + align:start position:0% +to those so these are groups of related +firms that are all we truly own to tight + + align:start position:0% +firms that are all we truly own to tight + + + align:start position:0% +firms that are all we truly own to tight +each other right they would violate US + + align:start position:0% +each other right they would violate US + + + align:start position:0% +each other right they would violate US +antitrust laws a lot like they would but + + align:start position:0% +antitrust laws a lot like they would but + + + align:start position:0% +antitrust laws a lot like they would but +that's the way Japan organized its core + + align:start position:0% +that's the way Japan organized its core + + + align:start position:0% +that's the way Japan organized its core +industries so now not all Japanese firms + + align:start position:0% +industries so now not all Japanese firms + + + align:start position:0% +industries so now not all Japanese firms +are a part of these Koretz right so + + align:start position:0% +are a part of these Koretz right so + + + align:start position:0% +are a part of these Koretz right so +company like Sony was actually outside + + align:start position:0% +company like Sony was actually outside + + + align:start position:0% +company like Sony was actually outside +of this right but most of its industry + + align:start position:0% +of this right but most of its industry + + + align:start position:0% +of this right but most of its industry +was organized in this very simplest kind + + align:start position:0% +was organized in this very simplest kind + + + align:start position:0% +was organized in this very simplest kind +of way and you could see how their + + align:start position:0% +of way and you could see how their + + + align:start position:0% +of way and you could see how their +distance with a major governmental + + align:start position:0% +distance with a major governmental + + + align:start position:0% +distance with a major governmental +entity like meeting could be readily + + align:start position:0% +entity like meeting could be readily + + + align:start position:0% +entity like meeting could be readily +tied to unify government decision-making + + align:start position:0% +tied to unify government decision-making + + + align:start position:0% +tied to unify government decision-making +and industry precision so when the US + + align:start position:0% +and industry precision so when the US + + + align:start position:0% +and industry precision so when the US +was competing against Japan and this + + align:start position:0% +was competing against Japan and this + + + align:start position:0% +was competing against Japan and this +white centralized quite efficient model + + align:start position:0% +white centralized quite efficient model + + + align:start position:0% +white centralized quite efficient model +you guys have a lot of trouble coping + + align:start position:0% +you guys have a lot of trouble coping + + + align:start position:0% +you guys have a lot of trouble coping +and + + align:start position:0% +and + + + align:start position:0% +and +you've seen them we talked about + + align:start position:0% +you've seen them we talked about + + + align:start position:0% +you've seen them we talked about +Jorgensen you saw some of the of the + + align:start position:0% +Jorgensen you saw some of the of the + + + align:start position:0% +Jorgensen you saw some of the of the +productivity and GE kickers so historic + + align:start position:0% +productivity and GE kickers so historic + + + align:start position:0% +productivity and GE kickers so historic +us productivity rate generally around 3% + + align:start position:0% +us productivity rate generally around 3% + + + align:start position:0% +us productivity rate generally around 3% +around 2% and historic u.s. GDP growth + + align:start position:0% +around 2% and historic u.s. GDP growth + + + align:start position:0% +around 2% and historic u.s. GDP growth +is generally around 3 right between 73 + + align:start position:0% +is generally around 3 right between 73 + + + align:start position:0% +is generally around 3 right between 73 +and 91 those plummet so we fall to + + align:start position:0% +and 91 those plummet so we fall to + + + align:start position:0% +and 91 those plummet so we fall to +fertility rates at around 1% and GDP + + align:start position:0% +fertility rates at around 1% and GDP + + + align:start position:0% +fertility rates at around 1% and GDP +growth about 2% it was a pretty grim + + align:start position:0% +growth about 2% it was a pretty grim + + + align:start position:0% +growth about 2% it was a pretty grim +tiny instance we were up against a + + align:start position:0% +tiny instance we were up against a + + + align:start position:0% +tiny instance we were up against a +powerful an industrial competitor and + + align:start position:0% +powerful an industrial competitor and + + + align:start position:0% +powerful an industrial competitor and +Japan was able to take economic sectors + + align:start position:0% +Japan was able to take economic sectors + + + align:start position:0% +Japan was able to take economic sectors +that the u.s. thought would always have + + align:start position:0% +that the u.s. thought would always have + + + align:start position:0% +that the u.s. thought would always have +light consumer electronics like a large + + align:start position:0% +light consumer electronics like a large + + + align:start position:0% +light consumer electronics like a large +part of the auto sector because it had a + + align:start position:0% +part of the auto sector because it had a + + + align:start position:0% +part of the auto sector because it had a +better innovation model so that's you + + align:start position:0% +better innovation model so that's you + + + align:start position:0% +better innovation model so that's you +know in in a very brief period of time + + align:start position:0% +know in in a very brief period of time + + + align:start position:0% +know in in a very brief period of time +that's kind of what happened in the 70s + + align:start position:0% +that's kind of what happened in the 70s + + + align:start position:0% +that's kind of what happened in the 70s +and 80s the US response as I suggested + + align:start position:0% +and 80s the US response as I suggested + + + align:start position:0% +and 80s the US response as I suggested +earlier was that we would attempt to + + align:start position:0% +earlier was that we would attempt to + + + align:start position:0% +earlier was that we would attempt to +copy Japan on quality and we called it + + align:start position:0% +copy Japan on quality and we called it + + + align:start position:0% +copy Japan on quality and we called it +lean manufacturing but we would attempt + + align:start position:0% +lean manufacturing but we would attempt + + + align:start position:0% +lean manufacturing but we would attempt +to replicate as much as we could at that + + align:start position:0% +to replicate as much as we could at that + + + align:start position:0% +to replicate as much as we could at that +Toyota model and by and large our + + align:start position:0% +Toyota model and by and large our + + + align:start position:0% +Toyota model and by and large our +industries pretty well done that but we + + align:start position:0% +industries pretty well done that but we + + + align:start position:0% +industries pretty well done that but we +also kept focus on our very strong + + align:start position:0% +also kept focus on our very strong + + + align:start position:0% +also kept focus on our very strong +innovation system so we launched in the + + align:start position:0% +innovation system so we launched in the + + + align:start position:0% +innovation system so we launched in the +1990s the IT in addition which Japan + + align:start position:0% +1990s the IT in addition which Japan + + + align:start position:0% +1990s the IT in addition which Japan +misses and if you get your economy to a + + align:start position:0% +misses and if you get your economy to a + + + align:start position:0% +misses and if you get your economy to a +leadership right to the edge of the + + align:start position:0% +leadership right to the edge of the + + + align:start position:0% +leadership right to the edge of the +technological frontier and you organize + + align:start position:0% +technological frontier and you organize + + + align:start position:0% +technological frontier and you organize +your economy around leading innovation + + align:start position:0% +your economy around leading innovation + + + align:start position:0% +your economy around leading innovation +waste which Japan had just organized + + align:start position:0% +waste which Japan had just organized + + + align:start position:0% +waste which Japan had just organized +this economy about doing brand-new + + align:start position:0% +this economy about doing brand-new + + + align:start position:0% +this economy about doing brand-new +production system and then you miss away + + align:start position:0% +production system and then you miss away + + + align:start position:0% +production system and then you miss away +it can be pretty unpleasant + + align:start position:0% +it can be pretty unpleasant + + + align:start position:0% +it can be pretty unpleasant +right so it was unpleasant the us when + + align:start position:0% +right so it was unpleasant the us when + + + align:start position:0% +right so it was unpleasant the us when +we missed away from cities and then + + align:start position:0% +we missed away from cities and then + + + align:start position:0% +we missed away from cities and then +things got tough for Japan oh that's not + + align:start position:0% +things got tough for Japan oh that's not + + + align:start position:0% +things got tough for Japan oh that's not +the only + + align:start position:0% +the only + + + align:start position:0% +the only +it's going on this macro economic + + align:start position:0% +it's going on this macro economic + + + align:start position:0% +it's going on this macro economic +factors this demographic factors is a + + align:start position:0% +factors this demographic factors is a + + + align:start position:0% +factors this demographic factors is a +series of things there are currents on + + align:start position:0% +series of things there are currents on + + + align:start position:0% +series of things there are currents on +containers but one part of the story is + + align:start position:0% +containers but one part of the story is + + + align:start position:0% +containers but one part of the story is +around miss miss condition so that was + + align:start position:0% +around miss miss condition so that was + + + align:start position:0% +around miss miss condition so that was +the kind of response that the u.s. came + + align:start position:0% +the kind of response that the u.s. came + + + align:start position:0% +the kind of response that the u.s. came +up with it used its innovation system to + + align:start position:0% +up with it used its innovation system to + + + align:start position:0% +up with it used its innovation system to +develop effectively radical innovations + + align:start position:0% +develop effectively radical innovations + + + align:start position:0% +develop effectively radical innovations +in the IP space and create whole new + + align:start position:0% +in the IP space and create whole new + + + align:start position:0% +in the IP space and create whole new +industries so we pursue radical + + align:start position:0% +industries so we pursue radical + + + align:start position:0% +industries so we pursue radical +innovation in a way not consciously but + + align:start position:0% +innovation in a way not consciously but + + + align:start position:0% +innovation in a way not consciously but +in a way that was effectively our + + align:start position:0% +in a way that was effectively our + + + align:start position:0% +in a way that was effectively our +response when we stop there and go + + align:start position:0% +response when we stop there and go + + + align:start position:0% +response when we stop there and go +through the sheets discussion can't use + + align:start position:0% +through the sheets discussion can't use + + + align:start position:0% +through the sheets discussion can't use +yeah so in Kent Q's I think he really + + align:start position:0% +yeah so in Kent Q's I think he really + + + align:start position:0% +yeah so in Kent Q's I think he really +talks about sort of this 18th Street and + + align:start position:0% +talks about sort of this 18th Street and + + + align:start position:0% +talks about sort of this 18th Street and +Japan that really isolates this sort of + + align:start position:0% +Japan that really isolates this sort of + + + align:start position:0% +Japan that really isolates this sort of +US response so how is the u.s. going to + + align:start position:0% +US response so how is the u.s. going to + + + align:start position:0% +US response so how is the u.s. going to +respond to kind of larger problems with + + align:start position:0% +respond to kind of larger problems with + + + align:start position:0% +respond to kind of larger problems with +our manufacturing system and really + + align:start position:0% +our manufacturing system and really + + + align:start position:0% +our manufacturing system and really +competing on that global scale now that + + align:start position:0% +competing on that global scale now that + + + align:start position:0% +competing on that global scale now that +Japan's sort of captured a lot of things + + align:start position:0% +Japan's sort of captured a lot of things + + + align:start position:0% +Japan's sort of captured a lot of things +about quality manufacturing and that + + align:start position:0% +about quality manufacturing and that + + + align:start position:0% +about quality manufacturing and that +sort of innovation way I think one of + + align:start position:0% +sort of innovation way I think one of + + + align:start position:0% +sort of innovation way I think one of +the really important things I think II + + align:start position:0% +the really important things I think II + + + align:start position:0% +the really important things I think II +talks about is sort of this bureaucratic + + align:start position:0% +talks about is sort of this bureaucratic + + + align:start position:0% +talks about is sort of this bureaucratic +climate so there's a lot going on sort + + align:start position:0% +climate so there's a lot going on sort + + + align:start position:0% +climate so there's a lot going on sort +of the trading it on the international + + align:start position:0% +of the trading it on the international + + + align:start position:0% +of the trading it on the international +scale but bringing it back home to the + + align:start position:0% +scale but bringing it back home to the + + + align:start position:0% +scale but bringing it back home to the +US like you have to get a lot of people + + align:start position:0% +US like you have to get a lot of people + + + align:start position:0% +US like you have to get a lot of people +on board in order for you to sort of + + align:start position:0% +on board in order for you to sort of + + + align:start position:0% +on board in order for you to sort of +move forward and this goes away unless + + align:start position:0% +move forward and this goes away unless + + + align:start position:0% +move forward and this goes away unless +you're like writing an innovation way + + align:start position:0% +you're like writing an innovation way + + + align:start position:0% +you're like writing an innovation way +and so we're set up in a radically + + align:start position:0% +and so we're set up in a radically + + + align:start position:0% +and so we're set up in a radically +different way than Japan and we have to + + align:start position:0% +different way than Japan and we have to + + + align:start position:0% +different way than Japan and we have to +kind of figure out what to do and so + + align:start position:0% +kind of figure out what to do and so + + + align:start position:0% +kind of figure out what to do and so +talking about Ronald Reagan's response I + + align:start position:0% +talking about Ronald Reagan's response I + + + align:start position:0% +talking about Ronald Reagan's response I +think was pretty cool and important that + + align:start position:0% +think was pretty cool and important that + + + align:start position:0% +think was pretty cool and important that +he Ronald Regan sort of exercises his + + align:start position:0% +he Ronald Regan sort of exercises his + + + align:start position:0% +he Ronald Regan sort of exercises his +discretion with this Commission on + + align:start position:0% +discretion with this Commission on + + + align:start position:0% +discretion with this Commission on +industrial competitiveness with John + + align:start position:0% +industrial competitiveness with John + + + align:start position:0% +industrial competitiveness with John +Young so I was just wondering if any of + + align:start position:0% +Young so I was just wondering if any of + + + align:start position:0% +Young so I was just wondering if any of +you guys have any feelings on sort of + + align:start position:0% +you guys have any feelings on sort of + + + align:start position:0% +you guys have any feelings on sort of +the presidential power to have not only + + align:start position:0% +the presidential power to have not only + + + align:start position:0% +the presidential power to have not only +kind of highlight issues but sort of + + align:start position:0% +kind of highlight issues but sort of + + + align:start position:0% +kind of highlight issues but sort of +take the lead and take action separate + + align:start position:0% +take the lead and take action separate + + + align:start position:0% +take the lead and take action separate +from all the bureaucratic dealers + + align:start position:0% + + + + align:start position:0% + +yeah I saw you Richard oh I want your + + align:start position:0% +yeah I saw you Richard oh I want your + + + align:start position:0% +yeah I saw you Richard oh I want your +attention to them if you couldn't I mean + + align:start position:0% +attention to them if you couldn't I mean + + + align:start position:0% +attention to them if you couldn't I mean +I thought when I read it that direct was + + align:start position:0% +I thought when I read it that direct was + + + align:start position:0% +I thought when I read it that direct was +actually quite slow to act on imagery + + align:start position:0% +actually quite slow to act on imagery + + + align:start position:0% +actually quite slow to act on imagery +congressman kind of pushes the efforts + + align:start position:0% +congressman kind of pushes the efforts + + + align:start position:0% +congressman kind of pushes the efforts +and later on yeah we're making motions + + align:start position:0% +and later on yeah we're making motions + + + align:start position:0% +and later on yeah we're making motions +without actually making actions you know + + align:start position:0% +without actually making actions you know + + + align:start position:0% +without actually making actions you know +it's just to sort of look like Reagan is + + align:start position:0% +it's just to sort of look like Reagan is + + + align:start position:0% +it's just to sort of look like Reagan is +taking action on this thing and yeah I + + align:start position:0% +taking action on this thing and yeah I + + + align:start position:0% +taking action on this thing and yeah I +agree I thought he ended up dragging his + + align:start position:0% +agree I thought he ended up dragging his + + + align:start position:0% +agree I thought he ended up dragging his +feet and other people had this sort of + + align:start position:0% +feet and other people had this sort of + + + align:start position:0% +feet and other people had this sort of +push for anything to be enacted with the + + align:start position:0% +push for anything to be enacted with the + + + align:start position:0% +push for anything to be enacted with the +young Commission so I think one of the + + align:start position:0% +young Commission so I think one of the + + + align:start position:0% +young Commission so I think one of the +big pieces in this young Commission is + + align:start position:0% +big pieces in this young Commission is + + + align:start position:0% +big pieces in this young Commission is +how they decide to choose members and + + align:start position:0% +how they decide to choose members and + + + align:start position:0% +how they decide to choose members and +they take kind of warfighting factors in + + align:start position:0% +they take kind of warfighting factors in + + + align:start position:0% +they take kind of warfighting factors in +industry and they start with John Young + + align:start position:0% +industry and they start with John Young + + + align:start position:0% +industry and they start with John Young +but I thought it was interesting how + + align:start position:0% +but I thought it was interesting how + + + align:start position:0% +but I thought it was interesting how +like he didn't get to sort of paint the + + align:start position:0% +like he didn't get to sort of paint the + + + align:start position:0% +like he didn't get to sort of paint the +metal I can't pick the members that he'd + + align:start position:0% +metal I can't pick the members that he'd + + + align:start position:0% +metal I can't pick the members that he'd +like to be in his own Commission I + + align:start position:0% +like to be in his own Commission I + + + align:start position:0% +like to be in his own Commission I +thought like that might be a little bit + + align:start position:0% +thought like that might be a little bit + + + align:start position:0% +thought like that might be a little bit +short-sighted considering he's gonna + + align:start position:0% +short-sighted considering he's gonna + + + align:start position:0% +short-sighted considering he's gonna +have to like work with all these people + + align:start position:0% +have to like work with all these people + + + align:start position:0% +have to like work with all these people +um and it might be a way of sort of to + + align:start position:0% +um and it might be a way of sort of to + + + align:start position:0% +um and it might be a way of sort of to +drag your feet but I thought the sort of + + align:start position:0% +drag your feet but I thought the sort of + + + align:start position:0% +drag your feet but I thought the sort of +what came out of the Commission which is + + align:start position:0% +what came out of the Commission which is + + + align:start position:0% +what came out of the Commission which is +this new report which highlight is like + + align:start position:0% +this new report which highlight is like + + + align:start position:0% +this new report which highlight is like +a lot of these sort of transformative + + align:start position:0% +a lot of these sort of transformative + + + align:start position:0% +a lot of these sort of transformative +things sort of would have never happened + + align:start position:0% +things sort of would have never happened + + + align:start position:0% +things sort of would have never happened +if he didn't sort of crap from all these + + align:start position:0% +if he didn't sort of crap from all these + + + align:start position:0% +if he didn't sort of crap from all these +places in industry and manufacturers but + + align:start position:0% +places in industry and manufacturers but + + + align:start position:0% +places in industry and manufacturers but +is there any sort of merit to sort of + + align:start position:0% +is there any sort of merit to sort of + + + align:start position:0% +is there any sort of merit to sort of +bringing these people and having them + + align:start position:0% +bringing these people and having them + + + align:start position:0% +bringing these people and having them +work on this commission and then publish + + align:start position:0% +work on this commission and then publish + + + align:start position:0% +work on this commission and then publish +your support even though we don't sort + + align:start position:0% +your support even though we don't sort + + + align:start position:0% +your support even though we don't sort +of act on it but you see like all of + + align:start position:0% +of act on it but you see like all of + + + align:start position:0% +of act on it but you see like all of +these things that II highlighted and + + align:start position:0% +these things that II highlighted and + + + align:start position:0% +these things that II highlighted and +sort of like new growth compact maybe + + align:start position:0% +sort of like new growth compact maybe + + + align:start position:0% +sort of like new growth compact maybe +like ten years down the line like might + + align:start position:0% +like ten years down the line like might + + + align:start position:0% +like ten years down the line like might +really be important and sort of this + + align:start position:0% +really be important and sort of this + + + align:start position:0% +really be important and sort of this +lays the groundwork for you know five or + + align:start position:0% +lays the groundwork for you know five or + + + align:start position:0% +lays the groundwork for you know five or +ten years in the future when you're + + align:start position:0% +ten years in the future when you're + + + align:start position:0% +ten years in the future when you're +ready to sort of act on those things so + + align:start position:0% +ready to sort of act on those things so + + + align:start position:0% +ready to sort of act on those things so +I can smile should be is there merit so + + align:start position:0% +I can smile should be is there merit so + + + align:start position:0% +I can smile should be is there merit so +sort of even if it's + + align:start position:0% +sort of even if it's + + + align:start position:0% +sort of even if it's +kind of haphazard attempt at addressing + + align:start position:0% +kind of haphazard attempt at addressing + + + align:start position:0% +kind of haphazard attempt at addressing +the issues is it that's still important + + align:start position:0% +the issues is it that's still important + + + align:start position:0% +the issues is it that's still important +metric maybe not now five or 20 years + + align:start position:0% +metric maybe not now five or 20 years + + + align:start position:0% +metric maybe not now five or 20 years +ago + + align:start position:0% +ago + + + align:start position:0% +ago +yeah I think so and with the young + + align:start position:0% +yeah I think so and with the young + + + align:start position:0% +yeah I think so and with the young +Commission I think that out of that + + align:start position:0% +Commission I think that out of that + + + align:start position:0% +Commission I think that out of that +Commission young decided to form what's + + align:start position:0% +Commission young decided to form what's + + + align:start position:0% +Commission young decided to form what's +the name and linking them in but that it + + align:start position:0% +the name and linking them in but that it + + + align:start position:0% +the name and linking them in but that it +still exists today I looked it up their + + align:start position:0% +still exists today I looked it up their + + + align:start position:0% +still exists today I looked it up their +couches yes exactly + + align:start position:0% +couches yes exactly + + + align:start position:0% +couches yes exactly +so yes there are lasting lasting + + align:start position:0% +so yes there are lasting lasting + + + align:start position:0% +so yes there are lasting lasting +knowledge and wisdom from a commission + + align:start position:0% +knowledge and wisdom from a commission + + + align:start position:0% +knowledge and wisdom from a commission +like this so yeah definitely it's better + + align:start position:0% +like this so yeah definitely it's better + + + align:start position:0% +like this so yeah definitely it's better +than it started nothing it's better than + + align:start position:0% +than it started nothing it's better than + + + align:start position:0% +than it started nothing it's better than +sticking your head in the ground I think + + align:start position:0% +sticking your head in the ground I think + + + align:start position:0% +sticking your head in the ground I think +some of the stuff they put forward is + + align:start position:0% +some of the stuff they put forward is + + + align:start position:0% +some of the stuff they put forward is +definitely extremely useful it's there + + align:start position:0% +definitely extremely useful it's there + + + align:start position:0% +definitely extremely useful it's there +it's published and it's accessible + + align:start position:0% + + + + align:start position:0% + +better late than never things because it + + align:start position:0% +better late than never things because it + + + align:start position:0% +better late than never things because it +only seems I don't know this is a chance + + align:start position:0% +only seems I don't know this is a chance + + + align:start position:0% +only seems I don't know this is a chance +the US Attorney punches down or the only + + align:start position:0% +the US Attorney punches down or the only + + + align:start position:0% +the US Attorney punches down or the only +see was that they put in all this effort + + align:start position:0% +see was that they put in all this effort + + + align:start position:0% +see was that they put in all this effort +for one specific issue when something's + + align:start position:0% +for one specific issue when something's + + + align:start position:0% +for one specific issue when something's +going wrong right why not prevent things + + align:start position:0% +going wrong right why not prevent things + + + align:start position:0% +going wrong right why not prevent things +from going wrong in the first place + + align:start position:0% + + + + align:start position:0% + +hesitant to change their ways + + align:start position:0% +hesitant to change their ways + + + align:start position:0% +hesitant to change their ways +surrounding the views on specific + + align:start position:0% +surrounding the views on specific + + + align:start position:0% +surrounding the views on specific +policies around innovation so they said + + align:start position:0% +policies around innovation so they said + + + align:start position:0% +policies around innovation so they said +better late than never but I in my + + align:start position:0% +better late than never but I in my + + + align:start position:0% +better late than never but I in my +opinion be better you know why not why + + align:start position:0% +opinion be better you know why not why + + + align:start position:0% +opinion be better you know why not why +did the do this decades before I think + + align:start position:0% +did the do this decades before I think + + + align:start position:0% +did the do this decades before I think +the question is in relation to this + + align:start position:0% +the question is in relation to this + + + align:start position:0% +the question is in relation to this +reading is cues largely characterized as + + align:start position:0% +reading is cues largely characterized as + + + align:start position:0% +reading is cues largely characterized as +domestic policymaking as reactionary I + + align:start position:0% +domestic policymaking as reactionary I + + + align:start position:0% +domestic policymaking as reactionary I +agree + + align:start position:0% +agree + + + align:start position:0% +agree +what hope exists for utilizing a the + + align:start position:0% +what hope exists for utilizing a the + + + align:start position:0% +what hope exists for utilizing a the +courts under in the living Constitution + + align:start position:0% +courts under in the living Constitution + + + align:start position:0% +courts under in the living Constitution +was framed work to really address these + + align:start position:0% +was framed work to really address these + + + align:start position:0% +was framed work to really address these +questions and or meaningfully + + align:start position:0% +questions and or meaningfully + + + align:start position:0% +questions and or meaningfully +integrating the kinds of knowledge and + + align:start position:0% +integrating the kinds of knowledge and + + + align:start position:0% +integrating the kinds of knowledge and +consensus that is created in these + + align:start position:0% +consensus that is created in these + + + align:start position:0% +consensus that is created in these +Commission's and I don't know that + + align:start position:0% +Commission's and I don't know that + + + align:start position:0% +Commission's and I don't know that +there's yet a model for effective + + align:start position:0% +there's yet a model for effective + + + align:start position:0% +there's yet a model for effective +consensus building outside of the + + align:start position:0% +consensus building outside of the + + + align:start position:0% +consensus building outside of the +institutions and translating that to + + align:start position:0% +institutions and translating that to + + + align:start position:0% +institutions and translating that to +policy action with collaboration in the + + align:start position:0% +policy action with collaboration in the + + + align:start position:0% +policy action with collaboration in the +legislative branch + + align:start position:0% +legislative branch + + + align:start position:0% +legislative branch +branch and that's I think where your + + align:start position:0% +branch and that's I think where your + + + align:start position:0% +branch and that's I think where your +point sort of comes into action that + + align:start position:0% +point sort of comes into action that + + + align:start position:0% +point sort of comes into action that +there is an opportunity for pride of + + align:start position:0% +there is an opportunity for pride of + + + align:start position:0% +there is an opportunity for pride of +policymaking but it has to be integrated + + align:start position:0% +policymaking but it has to be integrated + + + align:start position:0% +policymaking but it has to be integrated +with discussions around the branch s it + + align:start position:0% +with discussions around the branch s it + + + align:start position:0% +with discussions around the branch s it +can't just be isolated in one branch + + align:start position:0% +can't just be isolated in one branch + + + align:start position:0% +can't just be isolated in one branch +because then as was pointed out there's + + align:start position:0% +because then as was pointed out there's + + + align:start position:0% +because then as was pointed out there's +going to be competition amongst to do + + align:start position:0% + + + + align:start position:0% + +yeah so that brings maybe my follow up + + align:start position:0% +yeah so that brings maybe my follow up + + + align:start position:0% +yeah so that brings maybe my follow up +question so I think the president in + + align:start position:0% +question so I think the president in + + + align:start position:0% +question so I think the president in +this way like really was able to just + + align:start position:0% +this way like really was able to just + + + align:start position:0% +this way like really was able to just +kind of use his power to this exercise + + align:start position:0% +kind of use his power to this exercise + + + align:start position:0% +kind of use his power to this exercise +call over this studying Commission is + + align:start position:0% +call over this studying Commission is + + + align:start position:0% +call over this studying Commission is +there a way for sort of legislators to + + align:start position:0% +there a way for sort of legislators to + + + align:start position:0% +there a way for sort of legislators to +kind of do the same thing let's say I'm + + align:start position:0% +kind of do the same thing let's say I'm + + + align:start position:0% +kind of do the same thing let's say I'm +committee on energy + + align:start position:0% +committee on energy + + + align:start position:0% +committee on energy +can I call for a study or the committee + + align:start position:0% +can I call for a study or the committee + + + align:start position:0% +can I call for a study or the committee +or the section projects deals with + + align:start position:0% +or the section projects deals with + + + align:start position:0% +or the section projects deals with +manufacturing I'm kind of sort of call + + align:start position:0% +manufacturing I'm kind of sort of call + + + align:start position:0% +manufacturing I'm kind of sort of call +for a study in the same way and then + + align:start position:0% +for a study in the same way and then + + + align:start position:0% +for a study in the same way and then +maybe work with the executive branch I + + align:start position:0% +maybe work with the executive branch I + + + align:start position:0% +maybe work with the executive branch I +do the same thing + + align:start position:0% +do the same thing + + + align:start position:0% +do the same thing +I mean just to comment you know from my + + align:start position:0% +I mean just to comment you know from my + + + align:start position:0% +I mean just to comment you know from my +dog running sprite so within the Senate + + align:start position:0% +dog running sprite so within the Senate + + + align:start position:0% +dog running sprite so within the Senate +for about 15 years + + align:start position:0% +for about 15 years + + + align:start position:0% +for about 15 years +yes that you know the Committees of + + align:start position:0% +yes that you know the Committees of + + + align:start position:0% +yes that you know the Committees of +Congress can function on one basis to + + align:start position:0% +Congress can function on one basis to + + + align:start position:0% +Congress can function on one basis to +try and identify Kevin exactly the + + align:start position:0% +try and identify Kevin exactly the + + + align:start position:0% +try and identify Kevin exactly the +problem you are raising which is be a + + align:start position:0% +problem you are raising which is be a + + + align:start position:0% +problem you are raising which is be a +little for cited some committees are + + align:start position:0% +little for cited some committees are + + + align:start position:0% +little for cited some committees are +actually much better at this than others + + align:start position:0% +actually much better at this than others + + + align:start position:0% +actually much better at this than others +historically and but there's there's no + + align:start position:0% +historically and but there's there's no + + + align:start position:0% +historically and but there's there's no +guarantees and frankly government tends + + align:start position:0% +guarantees and frankly government tends + + + align:start position:0% +guarantees and frankly government tends +to respond to crisis and this is not a + + align:start position:0% +to respond to crisis and this is not a + + + align:start position:0% +to respond to crisis and this is not a +crisis it's hard to get it mobilized + + align:start position:0% +crisis it's hard to get it mobilized + + + align:start position:0% +crisis it's hard to get it mobilized +organizing and moving to be foresighted + + align:start position:0% +organizing and moving to be foresighted + + + align:start position:0% +organizing and moving to be foresighted +that's honestly all dead right there's + + align:start position:0% +that's honestly all dead right there's + + + align:start position:0% +that's honestly all dead right there's +advantages you know having limits on + + align:start position:0% +advantages you know having limits on + + + align:start position:0% +advantages you know having limits on +governmental intervention here and if + + align:start position:0% +governmental intervention here and if + + + align:start position:0% +governmental intervention here and if +the system is working fairly well you + + align:start position:0% +the system is working fairly well you + + + align:start position:0% +the system is working fairly well you +probably build wonder mental attention + + align:start position:0% +probably build wonder mental attention + + + align:start position:0% +probably build wonder mental attention +to something it's only when you hit a + + align:start position:0% +to something it's only when you hit a + + + align:start position:0% +to something it's only when you hit a +crisis that generally wanted + + align:start position:0% +crisis that generally wanted + + + align:start position:0% +crisis that generally wanted +fall into place you know I understand + + align:start position:0% +fall into place you know I understand + + + align:start position:0% +fall into place you know I understand +the you know your points about wouldn't + + align:start position:0% +the you know your points about wouldn't + + + align:start position:0% +the you know your points about wouldn't +it be better we were watching all this + + align:start position:0% +it be better we were watching all this + + + align:start position:0% +it be better we were watching all this +live all the time there is that reality + + align:start position:0% +live all the time there is that reality + + + align:start position:0% +live all the time there is that reality +you've got a hope that somebody is + + align:start position:0% +you've got a hope that somebody is + + + align:start position:0% +you've got a hope that somebody is +somewhere in the society this is + + align:start position:0% +somewhere in the society this is + + + align:start position:0% +somewhere in the society this is +undertaking ever view but it's not + + align:start position:0% +undertaking ever view but it's not + + + align:start position:0% +undertaking ever view but it's not +something that was terribly good at and + + align:start position:0% +something that was terribly good at and + + + align:start position:0% +something that was terribly good at and +it typically responds to a crisis in a + + align:start position:0% +it typically responds to a crisis in a + + + align:start position:0% +it typically responds to a crisis in a +short-term kind of way so we came up + + align:start position:0% +short-term kind of way so we came up + + + align:start position:0% +short-term kind of way so we came up +with these various mechanisms none could + + align:start position:0% +with these various mechanisms none could + + + align:start position:0% +with these various mechanisms none could +really be called a competitiveness + + align:start position:0% +really be called a competitiveness + + + align:start position:0% +really be called a competitiveness +strategy we came up with a bunch of + + align:start position:0% +strategy we came up with a bunch of + + + align:start position:0% +strategy we came up with a bunch of +pieces right one piece that's not on + + align:start position:0% +pieces right one piece that's not on + + + align:start position:0% +pieces right one piece that's not on +here with SEMATECH which is an attempt + + align:start position:0% +here with SEMATECH which is an attempt + + + align:start position:0% +here with SEMATECH which is an attempt +to deal with Japan's effort to really + + align:start position:0% +to deal with Japan's effort to really + + + align:start position:0% +to deal with Japan's effort to really +capture the semiconductor sector which + + align:start position:0% +capture the semiconductor sector which + + + align:start position:0% +capture the semiconductor sector which +was who was again produced very high + + align:start position:0% +was who was again produced very high + + + align:start position:0% +was who was again produced very high +quality production capabilities and in + + align:start position:0% +quality production capabilities and in + + + align:start position:0% +quality production capabilities and in +semiconductor chips Billy Dee brands and + + align:start position:0% +semiconductor chips Billy Dee brands and + + + align:start position:0% +semiconductor chips Billy Dee brands and +you know the US was producing a lot of + + align:start position:0% +you know the US was producing a lot of + + + align:start position:0% +you know the US was producing a lot of +chips but they were not as high-quality + + align:start position:0% +chips but they were not as high-quality + + + align:start position:0% +chips but they were not as high-quality +and the manufacturing processes might as + + align:start position:0% +and the manufacturing processes might as + + + align:start position:0% +and the manufacturing processes might as +efficient as Japan was so Canon and + + align:start position:0% +efficient as Japan was so Canon and + + + align:start position:0% +efficient as Japan was so Canon and +Nikon were posed to be able to capture a + + align:start position:0% +Nikon were posed to be able to capture a + + + align:start position:0% +Nikon were posed to be able to capture a +very large part of that sector the + + align:start position:0% +very large part of that sector the + + + align:start position:0% +very large part of that sector the +solution the u.s. came up with and again + + align:start position:0% +solution the u.s. came up with and again + + + align:start position:0% +solution the u.s. came up with and again +this is DoD Department of Defense which + + align:start position:0% +this is DoD Department of Defense which + + + align:start position:0% +this is DoD Department of Defense which +semuc ductus is a pretty critical + + align:start position:0% +semuc ductus is a pretty critical + + + align:start position:0% +semuc ductus is a pretty critical +national security technology because it + + align:start position:0% +national security technology because it + + + align:start position:0% +national security technology because it +was embedded in all kinds of critical + + align:start position:0% +was embedded in all kinds of critical + + + align:start position:0% +was embedded in all kinds of critical +Defense DoD agreed cost share with a big + + align:start position:0% +Defense DoD agreed cost share with a big + + + align:start position:0% +Defense DoD agreed cost share with a big +industry organization consisting of both + + align:start position:0% +industry organization consisting of both + + + align:start position:0% +industry organization consisting of both +the central fabricators but also the + + align:start position:0% +the central fabricators but also the + + + align:start position:0% +the central fabricators but also the +supplier system the equipment and parts + + align:start position:0% +supplier system the equipment and parts + + + align:start position:0% +supplier system the equipment and parts +supplier system was the semiconductor + + align:start position:0% +supplier system was the semiconductor + + + align:start position:0% +supplier system was the semiconductor +industry + + align:start position:0% +industry + + + align:start position:0% +industry +dad community came together eventually + + align:start position:0% +dad community came together eventually + + + align:start position:0% +dad community came together eventually +settled on a series of steps to build + + align:start position:0% +settled on a series of steps to build + + + align:start position:0% +settled on a series of steps to build +quality into the u.s. semiconductor + + align:start position:0% +quality into the u.s. semiconductor + + + align:start position:0% +quality into the u.s. semiconductor +manufacturing process cost shared with + + align:start position:0% +manufacturing process cost shared with + + + align:start position:0% +manufacturing process cost shared with +DARPA and you know really turned around + + align:start position:0% +DARPA and you know really turned around + + + align:start position:0% +DARPA and you know really turned around +a sector now there are other + + align:start position:0% +a sector now there are other + + + align:start position:0% +a sector now there are other +developments going on here to us they've + + align:start position:0% +developments going on here to us they've + + + align:start position:0% +developments going on here to us they've +taken a leadership of their integrated + + align:start position:0% +taken a leadership of their integrated + + + align:start position:0% +taken a leadership of their integrated +circuits and microprocessor is kind of + + align:start position:0% +circuits and microprocessor is kind of + + + align:start position:0% +circuits and microprocessor is kind of +the next stage of technology so that + + align:start position:0% +the next stage of technology so that + + + align:start position:0% +the next stage of technology so that +certainly helped but nonetheless the + + align:start position:0% +certainly helped but nonetheless the + + + align:start position:0% +certainly helped but nonetheless the +effort to drive + + align:start position:0% +effort to drive + + + align:start position:0% +effort to drive +quality in the city about reproduction + + align:start position:0% +quality in the city about reproduction + + + align:start position:0% +quality in the city about reproduction +was a very concrete example industry and + + align:start position:0% +was a very concrete example industry and + + + align:start position:0% +was a very concrete example industry and +governmental collaboration that actually + + align:start position:0% +governmental collaboration that actually + + + align:start position:0% +governmental collaboration that actually +worked + + align:start position:0% +worked + + + align:start position:0% +worked +so these other pieces here are a little + + align:start position:0% +so these other pieces here are a little + + + align:start position:0% +so these other pieces here are a little +more hands a lot greater bayh-dole act + + align:start position:0% +more hands a lot greater bayh-dole act + + + align:start position:0% +more hands a lot greater bayh-dole act +the advanced technology program they're + + align:start position:0% +the advanced technology program they're + + + align:start position:0% +the advanced technology program they're +not as direct SEMATECH those are fairly + + align:start position:0% +not as direct SEMATECH those are fairly + + + align:start position:0% +not as direct SEMATECH those are fairly +direct therefore than them - they're + + align:start position:0% +direct therefore than them - they're + + + align:start position:0% +direct therefore than them - they're +kind of accepted with national security + + align:start position:0% +kind of accepted with national security + + + align:start position:0% +kind of accepted with national security +ramifications so in some ways that's the + + align:start position:0% +ramifications so in some ways that's the + + + align:start position:0% +ramifications so in some ways that's the +most seminal model that came out of this + + align:start position:0% +most seminal model that came out of this + + + align:start position:0% +most seminal model that came out of this +time period but again the minute that + + align:start position:0% +time period but again the minute that + + + align:start position:0% +time period but again the minute that +the IT revolution starts to take off + + align:start position:0% +the IT revolution starts to take off + + + align:start position:0% +the IT revolution starts to take off +everything any other nineties then us + + align:start position:0% +everything any other nineties then us + + + align:start position:0% +everything any other nineties then us +drops is concerned right and we go on to + + align:start position:0% +drops is concerned right and we go on to + + + align:start position:0% +drops is concerned right and we go on to +having a great time for a decade with + + align:start position:0% +having a great time for a decade with + + + align:start position:0% +having a great time for a decade with +the ideal evolution which is we + + align:start position:0% +the ideal evolution which is we + + + align:start position:0% +the ideal evolution which is we +discussed this remarkable period of + + align:start position:0% +discussed this remarkable period of + + + align:start position:0% +discussed this remarkable period of +growth in an economic influence how + + align:start position:0% +growth in an economic influence how + + + align:start position:0% +growth in an economic influence how +about another one for use yeah I think + + align:start position:0% +about another one for use yeah I think + + + align:start position:0% +about another one for use yeah I think +the we kind of Center our discussion a + + align:start position:0% +the we kind of Center our discussion a + + + align:start position:0% +the we kind of Center our discussion a +little bit on the US response to what's + + align:start position:0% +little bit on the US response to what's + + + align:start position:0% +little bit on the US response to what's +going on in Japan but I thought it might + + align:start position:0% +going on in Japan but I thought it might + + + align:start position:0% +going on in Japan but I thought it might +be interesting to at least touch on how + + align:start position:0% +be interesting to at least touch on how + + + align:start position:0% +be interesting to at least touch on how +different paradigms u.s. Japanese + + align:start position:0% +different paradigms u.s. Japanese + + + align:start position:0% +different paradigms u.s. Japanese +culture so they in Japan we talked about + + align:start position:0% +culture so they in Japan we talked about + + + align:start position:0% +culture so they in Japan we talked about +kind of like these workers have treating + + align:start position:0% +kind of like these workers have treating + + + align:start position:0% +kind of like these workers have treating +Labor's of mixed costs and so you're + + align:start position:0% +Labor's of mixed costs and so you're + + + align:start position:0% +Labor's of mixed costs and so you're +sort of employed for life these + + align:start position:0% +sort of employed for life these + + + align:start position:0% +sort of employed for life these +paradigms play out in Japan and they do + + align:start position:0% +paradigms play out in Japan and they do + + + align:start position:0% +paradigms play out in Japan and they do +send a characteristic to their culture + + align:start position:0% +send a characteristic to their culture + + + align:start position:0% +send a characteristic to their culture +but I think looking at international + + align:start position:0% +but I think looking at international + + + align:start position:0% +but I think looking at international +trade is this sort of the first time + + align:start position:0% +trade is this sort of the first time + + + align:start position:0% +trade is this sort of the first time +that you had to deal with a paradise + + align:start position:0% +that you had to deal with a paradise + + + align:start position:0% +that you had to deal with a paradise +like a difference in paradigm affecting + + align:start position:0% +like a difference in paradigm affecting + + + align:start position:0% +like a difference in paradigm affecting +you know international trade and + + align:start position:0% +you know international trade and + + + align:start position:0% +you know international trade and +basically just like the fundamentals Lee + + align:start position:0% +basically just like the fundamentals Lee + + + align:start position:0% +basically just like the fundamentals Lee +goes free + + align:start position:0% +goes free + + + align:start position:0% +goes free +large and widespread way because I guess + + align:start position:0% +large and widespread way because I guess + + + align:start position:0% +large and widespread way because I guess +lusatian will bring new countries into + + align:start position:0% +lusatian will bring new countries into + + + align:start position:0% +lusatian will bring new countries into +actors at the in different ways that you + + align:start position:0% +actors at the in different ways that you + + + align:start position:0% +actors at the in different ways that you +have there's sort of no competition + + align:start position:0% +have there's sort of no competition + + + align:start position:0% +have there's sort of no competition +until Japan so it's entirely how to do + + align:start position:0% +until Japan so it's entirely how to do + + + align:start position:0% +until Japan so it's entirely how to do +things but I'd like to at least touch on + + align:start position:0% +things but I'd like to at least touch on + + + align:start position:0% +things but I'd like to at least touch on +how does kind of setting up your or + + align:start position:0% +how does kind of setting up your or + + + align:start position:0% +how does kind of setting up your or +calming your paradigms in this way does + + align:start position:0% +calming your paradigms in this way does + + + align:start position:0% +calming your paradigms in this way does +that provide up + + align:start position:0% +that provide up + + + align:start position:0% +that provide up +jv4 sort of new innovation lives in that + + align:start position:0% +jv4 sort of new innovation lives in that + + + align:start position:0% +jv4 sort of new innovation lives in that +like if I set up you know post-war Japan + + align:start position:0% +like if I set up you know post-war Japan + + + align:start position:0% +like if I set up you know post-war Japan +and a slightly different way to do I get + + align:start position:0% +and a slightly different way to do I get + + + align:start position:0% +and a slightly different way to do I get +excited at that time I was wondering + + align:start position:0% +excited at that time I was wondering + + + align:start position:0% +excited at that time I was wondering +this might help answer that does Japan + + align:start position:0% +this might help answer that does Japan + + + align:start position:0% +this might help answer that does Japan +have the equivalent of the US labor + + align:start position:0% +have the equivalent of the US labor + + + align:start position:0% +have the equivalent of the US labor +union yeah this uses organized very + + align:start position:0% +union yeah this uses organized very + + + align:start position:0% +union yeah this uses organized very +differently far less adversarial again + + align:start position:0% +differently far less adversarial again + + + align:start position:0% +differently far less adversarial again +if you have a lifetime guarantee at work + + align:start position:0% +if you have a lifetime guarantee at work + + + align:start position:0% +if you have a lifetime guarantee at work +what's very quiet about I do I do you + + align:start position:0% +what's very quiet about I do I do you + + + align:start position:0% +what's very quiet about I do I do you +want to have fights + + align:start position:0% +want to have fights + + + align:start position:0% +want to have fights +I made it instead very much more + + align:start position:0% +I made it instead very much more + + + align:start position:0% +I made it instead very much more +collaborative institutions that tent or + + align:start position:0% +collaborative institutions that tent or + + + align:start position:0% +collaborative institutions that tent or +is moving towards great efficiency to + + align:start position:0% +is moving towards great efficiency to + + + align:start position:0% +is moving towards great efficiency to +promote their you know their kind of + + align:start position:0% +promote their you know their kind of + + + align:start position:0% +promote their you know their kind of +their economist performance there's much + + align:start position:0% +their economist performance there's much + + + align:start position:0% +their economist performance there's much +greater incentive for collaboration you + + align:start position:0% +greater incentive for collaboration you + + + align:start position:0% +greater incentive for collaboration you +know in the system that they set up + + align:start position:0% +know in the system that they set up + + + align:start position:0% +know in the system that they set up +now again you know some of that is faded + + align:start position:0% +now again you know some of that is faded + + + align:start position:0% +now again you know some of that is faded +as Japan is entered a much more + + align:start position:0% +as Japan is entered a much more + + + align:start position:0% +as Japan is entered a much more +globalized competitive world a little + + align:start position:0% +globalized competitive world a little + + + align:start position:0% +globalized competitive world a little +competition then it faced as a as its + + align:start position:0% +competition then it faced as a as its + + + align:start position:0% +competition then it faced as a as its +system is emerging but it there the + + align:start position:0% +system is emerging but it there the + + + align:start position:0% +system is emerging but it there the +trade off you know getting cooperation + + align:start position:0% +trade off you know getting cooperation + + + align:start position:0% +trade off you know getting cooperation +from labor or not work rules and return + + align:start position:0% +from labor or not work rules and return + + + align:start position:0% +from labor or not work rules and return +for lifetime employment has tended to + + align:start position:0% +for lifetime employment has tended to + + + align:start position:0% +for lifetime employment has tended to +work well for Japan and in fact the US + + align:start position:0% +work well for Japan and in fact the US + + + align:start position:0% +work well for Japan and in fact the US +auto industry was actually moving in + + align:start position:0% +auto industry was actually moving in + + + align:start position:0% +auto industry was actually moving in +that direction you know for a time + + align:start position:0% +that direction you know for a time + + + align:start position:0% +that direction you know for a time +period before again high competition but + + align:start position:0% +period before again high competition but + + + align:start position:0% +period before again high competition but +it's just that that labor trade-off is + + align:start position:0% +it's just that that labor trade-off is + + + align:start position:0% +it's just that that labor trade-off is +just a completely different arrangement + + align:start position:0% + + + + align:start position:0% + +look we can look at I don't want to + + align:start position:0% +look we can look at I don't want to + + + align:start position:0% +look we can look at I don't want to +underestimate these big macro factors + + align:start position:0% +underestimate these big macro factors + + + align:start position:0% +underestimate these big macro factors +that are playing right so at the end of + + align:start position:0% +that are playing right so at the end of + + + align:start position:0% +that are playing right so at the end of +the war to Europe the US and the and the + + align:start position:0% +the war to Europe the US and the and the + + + align:start position:0% +the war to Europe the US and the and the +developed world non-confidence will + + align:start position:0% +developed world non-confidence will + + + align:start position:0% +developed world non-confidence will +essentially came to a set of + + align:start position:0% +essentially came to a set of + + + align:start position:0% +essentially came to a set of +arrangements around free trade concept + + align:start position:0% +arrangements around free trade concept + + + align:start position:0% +arrangements around free trade concept +and you know open economies + + align:start position:0% + + + + align:start position:0% + +you know lowering tariffs and trade + + align:start position:0% +you know lowering tariffs and trade + + + align:start position:0% +you know lowering tariffs and trade +barriers and so forth that was a + + align:start position:0% +barriers and so forth that was a + + + align:start position:0% +barriers and so forth that was a +consensus system of the time when Japan + + align:start position:0% +consensus system of the time when Japan + + + align:start position:0% +consensus system of the time when Japan +organized its economy and really began + + align:start position:0% +organized its economy and really began + + + align:start position:0% +organized its economy and really began +to move on entry is a global economic + + align:start position:0% +to move on entry is a global economic + + + align:start position:0% +to move on entry is a global economic +power it organized running different set + + align:start position:0% +power it organized running different set + + + align:start position:0% +power it organized running different set +of concepts it was not organized + + align:start position:0% +of concepts it was not organized + + + align:start position:0% +of concepts it was not organized +directly free trading system was + + align:start position:0% +directly free trading system was + + + align:start position:0% +directly free trading system was +organized around a pretty perfect list + + align:start position:0% +organized around a pretty perfect list + + + align:start position:0% +organized around a pretty perfect list +of which again as part of Japan's + + align:start position:0% +of which again as part of Japan's + + + align:start position:0% +of which again as part of Japan's +history it has to trade to survive it + + align:start position:0% +history it has to trade to survive it + + + align:start position:0% +history it has to trade to survive it +has to export to survive right so they + + align:start position:0% +has to export to survive right so they + + + align:start position:0% +has to export to survive right so they +developed a very focused export in the + + align:start position:0% +developed a very focused export in the + + + align:start position:0% +developed a very focused export in the +system they undervalued their currency + + align:start position:0% +system they undervalued their currency + + + align:start position:0% +system they undervalued their currency +so that their manufacturers would always + + align:start position:0% +so that their manufacturers would always + + + align:start position:0% +so that their manufacturers would always +have a price advantage over the US + + align:start position:0% +have a price advantage over the US + + + align:start position:0% +have a price advantage over the US +manufacturers right u.s. put up with + + align:start position:0% +manufacturers right u.s. put up with + + + align:start position:0% +manufacturers right u.s. put up with +that for essentially world national + + align:start position:0% +that for essentially world national + + + align:start position:0% +that for essentially world national +security kind of reasons with an ally + + align:start position:0% +security kind of reasons with an ally + + + align:start position:0% +security kind of reasons with an ally +and you know we assumed we were kings of + + align:start position:0% +and you know we assumed we were kings of + + + align:start position:0% +and you know we assumed we were kings of +manufacturing who could interfere with + + align:start position:0% +manufacturing who could interfere with + + + align:start position:0% +manufacturing who could interfere with +us you know Japan had a much more + + align:start position:0% +us you know Japan had a much more + + + align:start position:0% +us you know Japan had a much more +interventionist attitude by its + + align:start position:0% +interventionist attitude by its + + + align:start position:0% +interventionist attitude by its +government and dissapoint occur and + + align:start position:0% +government and dissapoint occur and + + + align:start position:0% +government and dissapoint occur and +assisting particular arms that was not + + align:start position:0% +assisting particular arms that was not + + + align:start position:0% +assisting particular arms that was not +like the u.s. system it made it very + + align:start position:0% +like the u.s. system it made it very + + + align:start position:0% +like the u.s. system it made it very +hard for imports particularly of you + + align:start position:0% +hard for imports particularly of you + + + align:start position:0% +hard for imports particularly of you +know complex technologies to enter + + align:start position:0% +know complex technologies to enter + + + align:start position:0% +know complex technologies to enter +Japanese markets so it was played by a + + align:start position:0% +Japanese markets so it was played by a + + + align:start position:0% +Japanese markets so it was played by a +different set of more mercantilism kinds + + align:start position:0% +different set of more mercantilism kinds + + + align:start position:0% +different set of more mercantilism kinds +of rules and frankly that model became a + + align:start position:0% +of rules and frankly that model became a + + + align:start position:0% +of rules and frankly that model became a +model for other Asian economies so that + + align:start position:0% +model for other Asian economies so that + + + align:start position:0% +model for other Asian economies so that +was a model that worked for Taiwan and + + align:start position:0% +was a model that worked for Taiwan and + + + align:start position:0% +was a model that worked for Taiwan and +for Korea and now China and it's not + + align:start position:0% +for Korea and now China and it's not + + + align:start position:0% +for Korea and now China and it's not +based on that open trading regime + + align:start position:0% +based on that open trading regime + + + align:start position:0% +based on that open trading regime +consensus policy that the u.s. try to + + align:start position:0% +consensus policy that the u.s. try to + + + align:start position:0% +consensus policy that the u.s. try to +build they didn't forward to so we're up + + align:start position:0% +build they didn't forward to so we're up + + + align:start position:0% +build they didn't forward to so we're up +against different economic models here + + align:start position:0% +against different economic models here + + + align:start position:0% +against different economic models here +part of the story is the USS mately + + align:start position:0% +part of the story is the USS mately + + + align:start position:0% +part of the story is the USS mately +figured out what the right strategy is + + align:start position:0% + + + + align:start position:0% + +but Rasheeda I think I interrupted your + + align:start position:0% +but Rasheeda I think I interrupted your + + + align:start position:0% +but Rasheeda I think I interrupted your +ability to get answers to your question + + align:start position:0% +ability to get answers to your question + + + align:start position:0% +ability to get answers to your question +Dave yeah definitely want to talk about + + align:start position:0% +Dave yeah definitely want to talk about + + + align:start position:0% +Dave yeah definitely want to talk about +things + + align:start position:0% +things + + + align:start position:0% +things +Japanese paradigms kind of being a + + align:start position:0% +Japanese paradigms kind of being a + + + align:start position:0% +Japanese paradigms kind of being a +little bit more pervasive in like the + + align:start position:0% +little bit more pervasive in like the + + + align:start position:0% +little bit more pervasive in like the +way that they set up just like the way + + align:start position:0% +way that they set up just like the way + + + align:start position:0% +way that they set up just like the way +they set up their economic structures + + align:start position:0% +they set up their economic structures + + + align:start position:0% +they set up their economic structures +and is there an opportunity for you know + + align:start position:0% +and is there an opportunity for you know + + + align:start position:0% +and is there an opportunity for you know +different countries to sort of adopt + + align:start position:0% +different countries to sort of adopt + + + align:start position:0% +different countries to sort of adopt +different paradigms in this way instead + + align:start position:0% +different paradigms in this way instead + + + align:start position:0% +different paradigms in this way instead +I think it almost goes back to that + + align:start position:0% +I think it almost goes back to that + + + align:start position:0% +I think it almost goes back to that +discussion we had about our innovation + + align:start position:0% +discussion we had about our innovation + + + align:start position:0% +discussion we had about our innovation +system making the best national anything + + align:start position:0% +system making the best national anything + + + align:start position:0% +system making the best national anything +they are wild about paradigm work well + + align:start position:0% +they are wild about paradigm work well + + + align:start position:0% +they are wild about paradigm work well +for Asian countries I think it would + + align:start position:0% +for Asian countries I think it would + + + align:start position:0% +for Asian countries I think it would +definitely be a lot of resistance in in + + align:start position:0% +definitely be a lot of resistance in in + + + align:start position:0% +definitely be a lot of resistance in in +the u.s. each I that have a set of a and + + align:start position:0% +the u.s. each I that have a set of a and + + + align:start position:0% +the u.s. each I that have a set of a and +I think a paradigm here people have + + align:start position:0% +I think a paradigm here people have + + + align:start position:0% +I think a paradigm here people have +these strong beliefs about free trade + + align:start position:0% +these strong beliefs about free trade + + + align:start position:0% +these strong beliefs about free trade +and they say about the right all of + + align:start position:0% +and they say about the right all of + + + align:start position:0% +and they say about the right all of +those those are now right at the center + + align:start position:0% +those those are now right at the center + + + align:start position:0% +those those are now right at the center +of a major political debate really for + + align:start position:0% +of a major political debate really for + + + align:start position:0% +of a major political debate really for +the first time since well there was a + + align:start position:0% +the first time since well there was a + + + align:start position:0% +the first time since well there was a +debate over these issues in the 1970s + + align:start position:0% +debate over these issues in the 1970s + + + align:start position:0% +debate over these issues in the 1970s +and 80s a big debate you know as Japan + + align:start position:0% +and 80s a big debate you know as Japan + + + align:start position:0% +and 80s a big debate you know as Japan +came to the forefront to major economic + + align:start position:0% +came to the forefront to major economic + + + align:start position:0% +came to the forefront to major economic +cycles and we're back to that debate now + + align:start position:0% +cycles and we're back to that debate now + + + align:start position:0% +cycles and we're back to that debate now +we're having it right now and it's so + + align:start position:0% +we're having it right now and it's so + + + align:start position:0% +we're having it right now and it's so +all of this is actually pretty + + align:start position:0% +all of this is actually pretty + + + align:start position:0% +all of this is actually pretty +interesting context to people watching I + + align:start position:0% +interesting context to people watching I + + + align:start position:0% +interesting context to people watching I +think they're currently we'll have to + + align:start position:0% +think they're currently we'll have to + + + align:start position:0% +think they're currently we'll have to +see what the new administration proposes + + align:start position:0% +see what the new administration proposes + + + align:start position:0% +see what the new administration proposes +but they appear to be moving and much + + align:start position:0% +but they appear to be moving and much + + + align:start position:0% +but they appear to be moving and much +more than a department for this kind of + + align:start position:0% +more than a department for this kind of + + + align:start position:0% +more than a department for this kind of +direction and prior regimes so in order + + align:start position:0% +direction and prior regimes so in order + + + align:start position:0% +direction and prior regimes so in order +to figure out whether or not not only if + + align:start position:0% +to figure out whether or not not only if + + + align:start position:0% +to figure out whether or not not only if +like other countries can combat try to + + align:start position:0% +like other countries can combat try to + + + align:start position:0% +like other countries can combat try to +convert their economies to this but was + + align:start position:0% +convert their economies to this but was + + + align:start position:0% +convert their economies to this but was +rather whether they should we have to + + align:start position:0% +rather whether they should we have to + + + align:start position:0% +rather whether they should we have to +figure out what was the so one of the + + align:start position:0% +figure out what was the so one of the + + + align:start position:0% +figure out what was the so one of the +main blocks between any economy and come + + align:start position:0% +main blocks between any economy and come + + + align:start position:0% +main blocks between any economy and come +and Japan's economy is these kinds of + + align:start position:0% +and Japan's economy is these kinds of + + + align:start position:0% +and Japan's economy is these kinds of +what was the term you had for those + + align:start position:0% +what was the term you had for those + + + align:start position:0% +what was the term you had for those +things like for like railroad monopolies + + align:start position:0% +things like for like railroad monopolies + + + align:start position:0% +things like for like railroad monopolies +and oil monopoly + + align:start position:0% +and oil monopoly + + + align:start position:0% +and oil monopoly +oh yeah Holloman sectors what Industrial + + align:start position:0% +oh yeah Holloman sectors what Industrial + + + align:start position:0% +oh yeah Holloman sectors what Industrial +Policy the it's the regulation that keep + + align:start position:0% +Policy the it's the regulation that keep + + + align:start position:0% +Policy the it's the regulation that keep +it from thank you sorry yeah we're on + + align:start position:0% +it from thank you sorry yeah we're on + + + align:start position:0% +it from thank you sorry yeah we're on +the same wavelength okay so those + + align:start position:0% +the same wavelength okay so those + + + align:start position:0% +the same wavelength okay so those +antitrust laws we have to figure out + + align:start position:0% +antitrust laws we have to figure out + + + align:start position:0% +antitrust laws we have to figure out +what is it specifically within Japan + + align:start position:0% +what is it specifically within Japan + + + align:start position:0% +what is it specifically within Japan +that is that would conflict with those + + align:start position:0% +that is that would conflict with those + + + align:start position:0% +that is that would conflict with those +laws and well is that really the best + + align:start position:0% +laws and well is that really the best + + + align:start position:0% +laws and well is that really the best +system for the individual worker so like + + align:start position:0% +system for the individual worker so like + + + align:start position:0% +system for the individual worker so like +from the impression that I've gotten + + align:start position:0% +from the impression that I've gotten + + + align:start position:0% +from the impression that I've gotten +Japan is so the government is so closely + + align:start position:0% +Japan is so the government is so closely + + + align:start position:0% +Japan is so the government is so closely +linked with the industrial sector it + + align:start position:0% +linked with the industrial sector it + + + align:start position:0% +linked with the industrial sector it +would be I feel like it would be and I + + align:start position:0% +would be I feel like it would be and I + + + align:start position:0% +would be I feel like it would be and I +I'm not sure how how that transition + + align:start position:0% +I'm not sure how how that transition + + + align:start position:0% +I'm not sure how how that transition +could occur it's kind of like because + + align:start position:0% +could occur it's kind of like because + + + align:start position:0% +could occur it's kind of like because +they just come out World War two they + + align:start position:0% +they just come out World War two they + + + align:start position:0% +they just come out World War two they +had the opportunity to restructure from + + align:start position:0% +had the opportunity to restructure from + + + align:start position:0% +had the opportunity to restructure from +the ground up so I'm not sure if you + + align:start position:0% +the ground up so I'm not sure if you + + + align:start position:0% +the ground up so I'm not sure if you +could take a an economy that's already + + align:start position:0% +could take a an economy that's already + + + align:start position:0% +could take a an economy that's already +based even if it's a better system and + + align:start position:0% +based even if it's a better system and + + + align:start position:0% +based even if it's a better system and +I'm not sure you can just revamp it at + + align:start position:0% +I'm not sure you can just revamp it at + + + align:start position:0% +I'm not sure you can just revamp it at +least in any reasonable amount of time I + + align:start position:0% +least in any reasonable amount of time I + + + align:start position:0% +least in any reasonable amount of time I +do agree that and that there's also + + align:start position:0% +do agree that and that there's also + + + align:start position:0% +do agree that and that there's also +historical and cultural factors to + + align:start position:0% +historical and cultural factors to + + + align:start position:0% +historical and cultural factors to +consider like a lot about how America + + align:start position:0% +consider like a lot about how America + + + align:start position:0% +consider like a lot about how America +use itself is like you're pulling + + align:start position:0% +use itself is like you're pulling + + + align:start position:0% +use itself is like you're pulling +yourself up by your bootstraps and like + + align:start position:0% +yourself up by your bootstraps and like + + + align:start position:0% +yourself up by your bootstraps and like +competitively like getting ahead less so + + align:start position:0% +competitively like getting ahead less so + + + align:start position:0% +competitively like getting ahead less so +then this kind of more collaborative + + align:start position:0% +then this kind of more collaborative + + + align:start position:0% +then this kind of more collaborative +like industrial conglomerate that it's + + align:start position:0% +like industrial conglomerate that it's + + + align:start position:0% +like industrial conglomerate that it's +making sure everyone's okay so I think + + align:start position:0% +making sure everyone's okay so I think + + + align:start position:0% +making sure everyone's okay so I think +it could encounter resistance and + + align:start position:0% +it could encounter resistance and + + + align:start position:0% +it could encounter resistance and +cultures like ours where that's not as + + align:start position:0% +cultures like ours where that's not as + + + align:start position:0% +cultures like ours where that's not as +respected yeah I think also there's the + + align:start position:0% +respected yeah I think also there's the + + + align:start position:0% +respected yeah I think also there's the +issue of scalability because Japan is so + + align:start position:0% +issue of scalability because Japan is so + + + align:start position:0% +issue of scalability because Japan is so +much of a smaller country than the u.s. + + align:start position:0% +much of a smaller country than the u.s. + + + align:start position:0% +much of a smaller country than the u.s. +their structure might not translate well + + align:start position:0% +their structure might not translate well + + + align:start position:0% +their structure might not translate well +on a broader scale to ours especially + + align:start position:0% +on a broader scale to ours especially + + + align:start position:0% +on a broader scale to ours especially +with the cultural difference cuz I know + + align:start position:0% +with the cultural difference cuz I know + + + align:start position:0% +with the cultural difference cuz I know +I'm like educationally it's very much + + align:start position:0% +I'm like educationally it's very much + + + align:start position:0% +I'm like educationally it's very much +pretty structured like if you do these + + align:start position:0% +pretty structured like if you do these + + + align:start position:0% +pretty structured like if you do these +things and you go to these schools you + + align:start position:0% +things and you go to these schools you + + + align:start position:0% +things and you go to these schools you +tend to go like get slotted in so to + + align:start position:0% +tend to go like get slotted in so to + + + align:start position:0% +tend to go like get slotted in so to +speak into certain industries of certain + + align:start position:0% +speak into certain industries of certain + + + align:start position:0% +speak into certain industries of certain +roles and that's kind of an approach + + align:start position:0% +roles and that's kind of an approach + + + align:start position:0% +roles and that's kind of an approach +that we've tried to avoid + + align:start position:0% +that we've tried to avoid + + + align:start position:0% +that we've tried to avoid +towards here in the US come promote oh + + align:start position:0% +towards here in the US come promote oh + + + align:start position:0% +towards here in the US come promote oh +you can go into whatever kill you want + + align:start position:0% +you can go into whatever kill you want + + + align:start position:0% +you can go into whatever kill you want +you don't necessarily have to you know + + align:start position:0% +you don't necessarily have to you know + + + align:start position:0% +you don't necessarily have to you know +go on a certain path so I think there's + + align:start position:0% +go on a certain path so I think there's + + + align:start position:0% +go on a certain path so I think there's +definitely differences fundamentally in + + align:start position:0% +definitely differences fundamentally in + + + align:start position:0% +definitely differences fundamentally in +ideology that prevent kind of the same + + align:start position:0% +ideology that prevent kind of the same + + + align:start position:0% +ideology that prevent kind of the same +model being imposed upon both countries + + align:start position:0% +model being imposed upon both countries + + + align:start position:0% +model being imposed upon both countries +we're growing at least the scalability + + align:start position:0% +we're growing at least the scalability + + + align:start position:0% +we're growing at least the scalability +thing you could possibly counter that by + + align:start position:0% +thing you could possibly counter that by + + + align:start position:0% +thing you could possibly counter that by +saying well we have a lot of a lot of + + align:start position:0% +saying well we have a lot of a lot of + + + align:start position:0% +saying well we have a lot of a lot of +states so you theoretically could just + + align:start position:0% +states so you theoretically could just + + + align:start position:0% +states so you theoretically could just +have like a couple of states just try + + align:start position:0% +have like a couple of states just try + + + align:start position:0% +have like a couple of states just try +the similar system it'd be easier to + + align:start position:0% +the similar system it'd be easier to + + + align:start position:0% +the similar system it'd be easier to +revamp them because it's a much smaller + + align:start position:0% +revamp them because it's a much smaller + + + align:start position:0% +revamp them because it's a much smaller +area it's fewer people so I mean of + + align:start position:0% +area it's fewer people so I mean of + + + align:start position:0% +area it's fewer people so I mean of +course there's just still plenty of like + + align:start position:0% +course there's just still plenty of like + + + align:start position:0% +course there's just still plenty of like +reasons why you can't or why you + + align:start position:0% +reasons why you can't or why you + + + align:start position:0% +reasons why you can't or why you +shouldn't but it definitely would make + + align:start position:0% +shouldn't but it definitely would make + + + align:start position:0% +shouldn't but it definitely would make +it a lot easier to do at least look at I + + align:start position:0% +it a lot easier to do at least look at I + + + align:start position:0% +it a lot easier to do at least look at I +think one of the riders from the first + + align:start position:0% +think one of the riders from the first + + + align:start position:0% +think one of the riders from the first +class actually has a whole he's written + + align:start position:0% +class actually has a whole he's written + + + align:start position:0% +class actually has a whole he's written +a lot about like these sanctuary cities + + align:start position:0% +a lot about like these sanctuary cities + + + align:start position:0% +a lot about like these sanctuary cities +I think the sarong Karen but it talks + + align:start position:0% +I think the sarong Karen but it talks + + + align:start position:0% +I think the sarong Karen but it talks +about cities where they have special + + align:start position:0% +about cities where they have special + + + align:start position:0% +about cities where they have special +rules for certain industries and that's + + align:start position:0% +rules for certain industries and that's + + + align:start position:0% +rules for certain industries and that's +also especially important because + + align:start position:0% +also especially important because + + + align:start position:0% +also especially important because +especially in the last election there's + + align:start position:0% +especially in the last election there's + + + align:start position:0% +especially in the last election there's +only certain cities that are really + + align:start position:0% +only certain cities that are really + + + align:start position:0% +only certain cities that are really +doing well on because of Technology + + align:start position:0% +doing well on because of Technology + + + align:start position:0% +doing well on because of Technology +since example Cisco New York what he was + + align:start position:0% +since example Cisco New York what he was + + + align:start position:0% +since example Cisco New York what he was +really pushing is like okay well we're + + align:start position:0% +really pushing is like okay well we're + + + align:start position:0% +really pushing is like okay well we're +gonna get jobs in this sector + + align:start position:0% +gonna get jobs in this sector + + + align:start position:0% +gonna get jobs in this sector +Detroit we're getting good jobs in this + + align:start position:0% +Detroit we're getting good jobs in this + + + align:start position:0% +Detroit we're getting good jobs in this +terrain Houston to come back and that + + align:start position:0% +terrain Houston to come back and that + + + align:start position:0% +terrain Houston to come back and that +was kind of what he was arguing so I'm + + align:start position:0% +was kind of what he was arguing so I'm + + + align:start position:0% +was kind of what he was arguing so I'm +gonna cut this all off so we can make + + align:start position:0% +gonna cut this all off so we can make + + + align:start position:0% +gonna cut this all off so we can make +progress for the reasons but I mean this + + align:start position:0% +progress for the reasons but I mean this + + + align:start position:0% +progress for the reasons but I mean this +is a good background for us to lead into + + align:start position:0% +is a good background for us to lead into + + + align:start position:0% +is a good background for us to lead into +you won't raising these cultural stories + + align:start position:0% +you won't raising these cultural stories + + + align:start position:0% +you won't raising these cultural stories +would be great background when we get + + align:start position:0% +would be great background when we get + + + align:start position:0% +would be great background when we get +our discussion of Korea and also how + + align:start position:0% +our discussion of Korea and also how + + + align:start position:0% +our discussion of Korea and also how +Japan had to try and reorganize its + + align:start position:0% +Japan had to try and reorganize its + + + align:start position:0% +Japan had to try and reorganize its +innovation system so hang on to a lot of + + align:start position:0% +innovation system so hang on to a lot of + + + align:start position:0% +innovation system so hang on to a lot of +these ideas let me jump to the next + + align:start position:0% +these ideas let me jump to the next + + + align:start position:0% +these ideas let me jump to the next +reader which i think is very briefly you + + align:start position:0% +reader which i think is very briefly you + + + align:start position:0% +reader which i think is very briefly you +know we're now back it's post 1990s + + align:start position:0% +know we're now back it's post 1990s + + + align:start position:0% +know we're now back it's post 1990s +right we're now back in our time with + + align:start position:0% +right we're now back in our time with + + + align:start position:0% +right we're now back in our time with +that as a backdrop I put this reading in + + align:start position:0% +that as a backdrop I put this reading in + + + align:start position:0% +that as a backdrop I put this reading in +here by Barry Lynn + + align:start position:0% + + + + align:start position:0% + +and a book that he wrote called end of + + align:start position:0% +and a book that he wrote called end of + + + align:start position:0% +and a book that he wrote called end of +the line it's it's not a a lot of + + align:start position:0% +the line it's it's not a a lot of + + + align:start position:0% +the line it's it's not a a lot of +agreement with person interesting + + align:start position:0% +agreement with person interesting + + + align:start position:0% +agreement with person interesting +there's an interesting historical + + align:start position:0% +there's an interesting historical + + + align:start position:0% +there's an interesting historical +perspective here that I especially want + + align:start position:0% +perspective here that I especially want + + + align:start position:0% +perspective here that I especially want +you to get a handle particularly hundred + + align:start position:0% +you to get a handle particularly hundred + + + align:start position:0% +you to get a handle particularly hundred +comments about his dream culture so + + align:start position:0% +comments about his dream culture so + + + align:start position:0% +comments about his dream culture so +earring lien argues that is essentially + + align:start position:0% +earring lien argues that is essentially + + + align:start position:0% +earring lien argues that is essentially +three periods us kind of manufacturing + + align:start position:0% +three periods us kind of manufacturing + + + align:start position:0% +three periods us kind of manufacturing +industry there is a period between + + align:start position:0% +industry there is a period between + + + align:start position:0% +industry there is a period between +Alexander Hamilton Finn you know we call + + align:start position:0% +Alexander Hamilton Finn you know we call + + + align:start position:0% +Alexander Hamilton Finn you know we call +it 1945 unit over to right and I mean + + align:start position:0% +it 1945 unit over to right and I mean + + + align:start position:0% +it 1945 unit over to right and I mean +Hamilton is absolutely critical figure + + align:start position:0% +Hamilton is absolutely critical figure + + + align:start position:0% +Hamilton is absolutely critical figure +in US economic history because he had a + + align:start position:0% +in US economic history because he had a + + + align:start position:0% +in US economic history because he had a +remarkably big picture of what a bigger + + align:start position:0% +remarkably big picture of what a bigger + + + align:start position:0% +remarkably big picture of what a bigger +picture than anybody so and his + + align:start position:0% +picture than anybody so and his + + + align:start position:0% +picture than anybody so and his +fundamental understanding was that in + + align:start position:0% +fundamental understanding was that in + + + align:start position:0% +fundamental understanding was that in +this era a small new power faced with + + align:start position:0% +this era a small new power faced with + + + align:start position:0% +this era a small new power faced with +much larger contending European nations + + align:start position:0% +much larger contending European nations + + + align:start position:0% +much larger contending European nations +that the only way that he was keeps its + + align:start position:0% +that the only way that he was keeps its + + + align:start position:0% +that the only way that he was keeps its +independence is by dueling a strong + + align:start position:0% +independence is by dueling a strong + + + align:start position:0% +independence is by dueling a strong +independent commercial right so Thomas + + align:start position:0% +independent commercial right so Thomas + + + align:start position:0% +independent commercial right so Thomas +Jefferson at the same time is devoted to + + align:start position:0% +Jefferson at the same time is devoted to + + + align:start position:0% +Jefferson at the same time is devoted to +an agricultural economy and a concept + + align:start position:0% +an agricultural economy and a concept + + + align:start position:0% +an agricultural economy and a concept +that young farmer and that's how + + align:start position:0% +that young farmer and that's how + + + align:start position:0% +that young farmer and that's how +democracy is going to take place + + align:start position:0% +democracy is going to take place + + + align:start position:0% +democracy is going to take place +Hamilton is working in a completely + + align:start position:0% +Hamilton is working in a completely + + + align:start position:0% +Hamilton is working in a completely +different direction let's stand up a + + align:start position:0% +different direction let's stand up a + + + align:start position:0% +different direction let's stand up a +major national banking system let's + + align:start position:0% +major national banking system let's + + + align:start position:0% +major national banking system let's +stand up a major commercial nominee and + + align:start position:0% +stand up a major commercial nominee and + + + align:start position:0% +stand up a major commercial nominee and +he himself is strongly dedicated to + + align:start position:0% +he himself is strongly dedicated to + + + align:start position:0% +he himself is strongly dedicated to +early us manufacturing so he's investing + + align:start position:0% +early us manufacturing so he's investing + + + align:start position:0% +early us manufacturing so he's investing +in an early manufacturing plant across + + align:start position:0% +in an early manufacturing plant across + + + align:start position:0% +in an early manufacturing plant across +the river Nazi in New Jersey so + + align:start position:0% +the river Nazi in New Jersey so + + + align:start position:0% +the river Nazi in New Jersey so +Hamilton's concept was that we need + + align:start position:0% +Hamilton's concept was that we need + + + align:start position:0% +Hamilton's concept was that we need +rational national self-dependence in + + align:start position:0% +rational national self-dependence in + + + align:start position:0% +rational national self-dependence in +that lecture and tariffs affine because + + align:start position:0% +that lecture and tariffs affine because + + + align:start position:0% +that lecture and tariffs affine because +that will ensure the growth of US + + align:start position:0% +that will ensure the growth of US + + + align:start position:0% +that will ensure the growth of US +manufacturing and production capability + + align:start position:0% +manufacturing and production capability + + + align:start position:0% +manufacturing and production capability +in a US economy and he creates a lot of + + align:start position:0% +in a US economy and he creates a lot of + + + align:start position:0% +in a US economy and he creates a lot of +the fundamental institutions that + + align:start position:0% +the fundamental institutions that + + + align:start position:0% +the fundamental institutions that +frankly we still rely on and maintaining + + align:start position:0% +frankly we still rely on and maintaining + + + align:start position:0% +frankly we still rely on and maintaining +that burden then there's the post-war to + + align:start position:0% +that burden then there's the post-war to + + + align:start position:0% +that burden then there's the post-war to +emergence of the Cold War and Lynn + + align:start position:0% +emergence of the Cold War and Lynn + + + align:start position:0% +emergence of the Cold War and Lynn +argues that the US government we use is + + align:start position:0% +argues that the US government we use is + + + align:start position:0% +argues that the US government we use is +Hamiltonian notions of national self + + align:start position:0% +Hamiltonian notions of national self + + + align:start position:0% +Hamiltonian notions of national self +dependence in manufacturers to build a + + align:start position:0% +dependence in manufacturers to build a + + + align:start position:0% +dependence in manufacturers to build a +larger concept by confronted with an + + align:start position:0% +larger concept by confronted with an + + + align:start position:0% +larger concept by confronted with an +international confrontation with a + + align:start position:0% +international confrontation with a + + + align:start position:0% +international confrontation with a +different economic system the u.s. + + align:start position:0% +different economic system the u.s. + + + align:start position:0% +different economic system the u.s. +builds a it works towards building a + + align:start position:0% +builds a it works towards building a + + + align:start position:0% +builds a it works towards building a +world economy that integrates the US + + align:start position:0% +world economy that integrates the US + + + align:start position:0% +world economy that integrates the US +Europe and Japan and particularly and + + align:start position:0% +Europe and Japan and particularly and + + + align:start position:0% +Europe and Japan and particularly and +other nations in a system of mutual + + align:start position:0% +other nations in a system of mutual + + + align:start position:0% +other nations in a system of mutual +dependence right so this is not a cell + + align:start position:0% +dependence right so this is not a cell + + + align:start position:0% +dependence right so this is not a cell +dependent manufacturing system this + + align:start position:0% +dependent manufacturing system this + + + align:start position:0% +dependent manufacturing system this +starts to move us in the direction of a + + align:start position:0% +starts to move us in the direction of a + + + align:start position:0% +starts to move us in the direction of a +multi continent production system that's + + align:start position:0% +multi continent production system that's + + + align:start position:0% +multi continent production system that's +gonna be shared by the participants and + + align:start position:0% +gonna be shared by the participants and + + + align:start position:0% +gonna be shared by the participants and +then men argues that the third stage + + align:start position:0% +then men argues that the third stage + + + align:start position:0% +then men argues that the third stage +really occurs in the 1990s as President + + align:start position:0% +really occurs in the 1990s as President + + + align:start position:0% +really occurs in the 1990s as President +Clinton whose to move China into the + + align:start position:0% +Clinton whose to move China into the + + + align:start position:0% +Clinton whose to move China into the +world economic system and the notion + + align:start position:0% +world economic system and the notion + + + align:start position:0% +world economic system and the notion +there is a it's a similar notion to what + + align:start position:0% +there is a it's a similar notion to what + + + align:start position:0% +there is a it's a similar notion to what +occurs in Europe and the post-war period + + align:start position:0% +occurs in Europe and the post-war period + + + align:start position:0% +occurs in Europe and the post-war period +that if they integrate their economies + + align:start position:0% +that if they integrate their economies + + + align:start position:0% +that if they integrate their economies +and they all know each other + + align:start position:0% +and they all know each other + + + align:start position:0% +and they all know each other +they're never gonna fight more to again + + align:start position:0% +they're never gonna fight more to again + + + align:start position:0% +they're never gonna fight more to again +right the long he said for that concept + + align:start position:0% +right the long he said for that concept + + + align:start position:0% +right the long he said for that concept +that an economically interdependent + + align:start position:0% + + + + align:start position:0% + +integrated world is going to + + align:start position:0% +integrated world is going to + + + align:start position:0% +integrated world is going to +significantly reduce national security + + align:start position:0% +significantly reduce national security + + + align:start position:0% +significantly reduce national security +threats over time that's essentially + + align:start position:0% +threats over time that's essentially + + + align:start position:0% +threats over time that's essentially +area argues Clinton's driving + + align:start position:0% +area argues Clinton's driving + + + align:start position:0% +area argues Clinton's driving +conceptual framework that this + + align:start position:0% +conceptual framework that this + + + align:start position:0% +conceptual framework that this +interdependent economic system tied by + + align:start position:0% +interdependent economic system tied by + + + align:start position:0% +interdependent economic system tied by +joint manufacturing and a common set of + + align:start position:0% +joint manufacturing and a common set of + + + align:start position:0% +joint manufacturing and a common set of +economic organizations will enable world + + align:start position:0% +economic organizations will enable world + + + align:start position:0% +economic organizations will enable world +peace right that's the notion so the WTO + + align:start position:0% +peace right that's the notion so the WTO + + + align:start position:0% +peace right that's the notion so the WTO +over a minute and China's entry into the + + align:start position:0% +over a minute and China's entry into the + + + align:start position:0% +over a minute and China's entry into the +WTO is the critical enabling step here + + align:start position:0% +WTO is the critical enabling step here + + + align:start position:0% +WTO is the critical enabling step here +and the West production system is in + + align:start position:0% +and the West production system is in + + + align:start position:0% +and the West production system is in +need to a significant extent merged into + + align:start position:0% +need to a significant extent merged into + + + align:start position:0% +need to a significant extent merged into +China with China's production output + + align:start position:0% +China with China's production output + + + align:start position:0% +China with China's production output +going world + + align:start position:0% +going world + + + align:start position:0% +going world +now there's a whole defense set of + + align:start position:0% +now there's a whole defense set of + + + align:start position:0% +now there's a whole defense set of +perspectives here right there are + + align:start position:0% +perspectives here right there are + + + align:start position:0% +perspectives here right there are +integrationists which clinton would be + + align:start position:0% +integrationists which clinton would be + + + align:start position:0% +integrationists which clinton would be +one according to land essentially + + align:start position:0% +one according to land essentially + + + align:start position:0% +one according to land essentially +extending a western manufacturing + + align:start position:0% +extending a western manufacturing + + + align:start position:0% +extending a western manufacturing +production system into china will bind + + align:start position:0% +production system into china will bind + + + align:start position:0% +production system into china will bind +china to a global economic system + + align:start position:0% +china to a global economic system + + + align:start position:0% +china to a global economic system +substantially reducing national security + + align:start position:0% +substantially reducing national security + + + align:start position:0% +substantially reducing national security +post and then there's a whole different + + align:start position:0% +post and then there's a whole different + + + align:start position:0% +post and then there's a whole different +school of realist as is profound + + align:start position:0% +school of realist as is profound + + + align:start position:0% +school of realist as is profound +differences in these nations and their + + align:start position:0% +differences in these nations and their + + + align:start position:0% +differences in these nations and their +geopolitical systems geopolitical goals + + align:start position:0% +geopolitical systems geopolitical goals + + + align:start position:0% +geopolitical systems geopolitical goals +and their political systems that are + + align:start position:0% +and their political systems that are + + + align:start position:0% +and their political systems that are +going to endure and the only question is + + align:start position:0% +going to endure and the only question is + + + align:start position:0% +going to endure and the only question is +which nation needs the advantage from + + align:start position:0% +which nation needs the advantage from + + + align:start position:0% +which nation needs the advantage from +the economic interdependence but the + + align:start position:0% +the economic interdependence but the + + + align:start position:0% +the economic interdependence but the +next thing that lynn argues is that this + + align:start position:0% +next thing that lynn argues is that this + + + align:start position:0% +next thing that lynn argues is that this +globalism has created its own economic + + align:start position:0% +globalism has created its own economic + + + align:start position:0% +globalism has created its own economic +determinism right that a new global + + align:start position:0% +determinism right that a new global + + + align:start position:0% +determinism right that a new global +economic system is in fact right here + + align:start position:0% +economic system is in fact right here + + + align:start position:0% +economic system is in fact right here +but nobody's really in charge right that + + align:start position:0% +but nobody's really in charge right that + + + align:start position:0% +but nobody's really in charge right that +nobody knows separate countries or even + + align:start position:0% +nobody knows separate countries or even + + + align:start position:0% +nobody knows separate countries or even +groups of countries can emit can manage + + align:start position:0% +groups of countries can emit can manage + + + align:start position:0% +groups of countries can emit can manage +that it's larger than the ability of + + align:start position:0% +that it's larger than the ability of + + + align:start position:0% +that it's larger than the ability of +these countries to manage so Lin writes + + align:start position:0% +these countries to manage so Lin writes + + + align:start position:0% +these countries to manage so Lin writes +this before the 2008 financial meltdown + + align:start position:0% +this before the 2008 financial meltdown + + + align:start position:0% +this before the 2008 financial meltdown +which is truly a world fun + + align:start position:0% +which is truly a world fun + + + align:start position:0% +which is truly a world fun +driven by values this country but + + align:start position:0% +driven by values this country but + + + align:start position:0% +driven by values this country but +pervasive worldwide and then there is + + align:start position:0% +pervasive worldwide and then there is + + + align:start position:0% +pervasive worldwide and then there is +these frantic moments as countries try + + align:start position:0% +these frantic moments as countries try + + + align:start position:0% +these frantic moments as countries try +to figure out how to manage this global + + align:start position:0% +to figure out how to manage this global + + + align:start position:0% +to figure out how to manage this global +finance + + align:start position:0% +finance + + + align:start position:0% +finance +crisis and realize how lacking the tools + + align:start position:0% +crisis and realize how lacking the tools + + + align:start position:0% +crisis and realize how lacking the tools +they are to cope with so kind of a final + + align:start position:0% +they are to cope with so kind of a final + + + align:start position:0% +they are to cope with so kind of a final +point that when makes is that we've now + + align:start position:0% +point that when makes is that we've now + + + align:start position:0% +point that when makes is that we've now +created the system it's larger than the + + align:start position:0% +created the system it's larger than the + + + align:start position:0% +created the system it's larger than the +countries themselves right it's largely + + align:start position:0% +countries themselves right it's largely + + + align:start position:0% +countries themselves right it's largely +frankly deterministic and somebody too + + align:start position:0% +frankly deterministic and somebody too + + + align:start position:0% +frankly deterministic and somebody too +dependent on them and the ability to + + align:start position:0% +dependent on them and the ability to + + + align:start position:0% +dependent on them and the ability to +intervene because much more problematic + + align:start position:0% +intervene because much more problematic + + + align:start position:0% +intervene because much more problematic +right so I thought it was just an + + align:start position:0% +right so I thought it was just an + + + align:start position:0% +right so I thought it was just an +interesting perspective kind of throw + + align:start position:0% +interesting perspective kind of throw + + + align:start position:0% +interesting perspective kind of throw +into the mix here as we begin to think + + align:start position:0% +into the mix here as we begin to think + + + align:start position:0% +into the mix here as we begin to think +about some of these historical questions + + align:start position:0% +about some of these historical questions + + + align:start position:0% +about some of these historical questions +and try to think about the kind of + + align:start position:0% +and try to think about the kind of + + + align:start position:0% +and try to think about the kind of +global economy + + align:start position:0% +global economy + + + align:start position:0% +global economy +so who's got that one yeah yeah we can + + align:start position:0% +so who's got that one yeah yeah we can + + + align:start position:0% +so who's got that one yeah yeah we can +I'm so I thought we just comment on kind + + align:start position:0% +I'm so I thought we just comment on kind + + + align:start position:0% +I'm so I thought we just comment on kind +of the interconnectedness and globalism + + align:start position:0% +of the interconnectedness and globalism + + + align:start position:0% +of the interconnectedness and globalism +might be very specific to this time I + + align:start position:0% +might be very specific to this time I + + + align:start position:0% +might be very specific to this time I +think and so he's like probably just + + align:start position:0% +think and so he's like probably just + + + align:start position:0% +think and so he's like probably just +come from the 90s sort of definitely + + align:start position:0% +come from the 90s sort of definitely + + + align:start position:0% +come from the 90s sort of definitely +push towards laissez faire business + + align:start position:0% +push towards laissez faire business + + + align:start position:0% +push towards laissez faire business +practices on the international scale + + align:start position:0% +practices on the international scale + + + align:start position:0% +practices on the international scale +which is something that like yes + + align:start position:0% +which is something that like yes + + + align:start position:0% +which is something that like yes +Americans were like pretty used to this + + align:start position:0% +Americans were like pretty used to this + + + align:start position:0% +Americans were like pretty used to this +whole idea of the government was very + + align:start position:0% +whole idea of the government was very + + + align:start position:0% +whole idea of the government was very +separate formosus ideals and business + + align:start position:0% +separate formosus ideals and business + + + align:start position:0% +separate formosus ideals and business +practices but also the promotion that + + align:start position:0% +practices but also the promotion that + + + align:start position:0% +practices but also the promotion that +now like it's not just the US that has + + align:start position:0% +now like it's not just the US that has + + + align:start position:0% +now like it's not just the US that has +operating system but now we have to deal + + align:start position:0% +operating system but now we have to deal + + + align:start position:0% +operating system but now we have to deal +with sort of other countries promote + + align:start position:0% +with sort of other countries promote + + + align:start position:0% +with sort of other countries promote +this and so I thought it was pretty + + align:start position:0% +this and so I thought it was pretty + + + align:start position:0% +this and so I thought it was pretty +important that we kind of date him in + + align:start position:0% +important that we kind of date him in + + + align:start position:0% +important that we kind of date him in +2000 where it's we're kind of riding a + + align:start position:0% +2000 where it's we're kind of riding a + + + align:start position:0% +2000 where it's we're kind of riding a +high of a lot of these international + + align:start position:0% +high of a lot of these international + + + align:start position:0% +high of a lot of these international +interdependence but we do see the + + align:start position:0% +interdependence but we do see the + + + align:start position:0% +interdependence but we do see the +trouble it's definitely in like 2008 so + + align:start position:0% +trouble it's definitely in like 2008 so + + + align:start position:0% +trouble it's definitely in like 2008 so +is there sort of room for us not only as + + align:start position:0% +is there sort of room for us not only as + + + align:start position:0% +is there sort of room for us not only as +we develop in sort of this + + align:start position:0% +we develop in sort of this + + + align:start position:0% +we develop in sort of this +interconnected global world is there + + align:start position:0% +interconnected global world is there + + + align:start position:0% +interconnected global world is there +room for regulation and sort of + + align:start position:0% +room for regulation and sort of + + + align:start position:0% +room for regulation and sort of +governments will do intergovernmental + + align:start position:0% +governments will do intergovernmental + + + align:start position:0% +governments will do intergovernmental +business practices that have to be put + + align:start position:0% +business practices that have to be put + + + align:start position:0% +business practices that have to be put +in place to sort of keep us in check + + align:start position:0% + + + + align:start position:0% + +okay data add on to that and also add a + + align:start position:0% +okay data add on to that and also add a + + + align:start position:0% +okay data add on to that and also add a +fourth perspective um so any growth was + + align:start position:0% +fourth perspective um so any growth was + + + align:start position:0% +fourth perspective um so any growth was +one of the three founders of Intel and + + align:start position:0% +one of the three founders of Intel and + + + align:start position:0% +one of the three founders of Intel and +they + + align:start position:0% +they + + + align:start position:0% +they +their big focus and their main working + + align:start position:0% +their big focus and their main working + + + align:start position:0% +their big focus and their main working +ability as a company was manufacturing + + align:start position:0% +ability as a company was manufacturing + + + align:start position:0% +ability as a company was manufacturing +especially very like detailed complex + + align:start position:0% +especially very like detailed complex + + + align:start position:0% +especially very like detailed complex +manufacturing and so he actually wrote a + + align:start position:0% +manufacturing and so he actually wrote a + + + align:start position:0% +manufacturing and so he actually wrote a +love letter in 2010 and then he he best + + align:start position:0% +love letter in 2010 and then he he best + + + align:start position:0% +love letter in 2010 and then he he best +wait we succeed we wrote one about why + + align:start position:0% +wait we succeed we wrote one about why + + + align:start position:0% +wait we succeed we wrote one about why +we need more manufacturing in the US and + + align:start position:0% +we need more manufacturing in the US and + + + align:start position:0% +we need more manufacturing in the US and +how its White's dangerous when we don't + + align:start position:0% +how its White's dangerous when we don't + + + align:start position:0% +how its White's dangerous when we don't +have it and he goes on to say mr. groom + + align:start position:0% +have it and he goes on to say mr. groom + + + align:start position:0% +have it and he goes on to say mr. groom +contrasted the startup phase of a + + align:start position:0% +contrasted the startup phase of a + + + align:start position:0% +contrasted the startup phase of a +business when uses for new technologies + + align:start position:0% +business when uses for new technologies + + + align:start position:0% +business when uses for new technologies +are identified with the scale-up phase + + align:start position:0% +are identified with the scale-up phase + + + align:start position:0% +are identified with the scale-up phase +when technology goes from prototype to + + align:start position:0% +when technology goes from prototype to + + + align:start position:0% +when technology goes from prototype to +mass production both are important but + + align:start position:0% +mass production both are important but + + + align:start position:0% +mass production both are important but +only scale-up is an engine for job + + align:start position:0% +only scale-up is an engine for job + + + align:start position:0% +only scale-up is an engine for job +growth and scale up and jaren no longer + + align:start position:0% +growth and scale up and jaren no longer + + + align:start position:0% +growth and scale up and jaren no longer +occurs in the United States without + + align:start position:0% +occurs in the United States without + + + align:start position:0% +occurs in the United States without +scaling he wrote we don't just lose jobs + + align:start position:0% +scaling he wrote we don't just lose jobs + + + align:start position:0% +scaling he wrote we don't just lose jobs +lose our hold on new technologies and + + align:start position:0% +lose our hold on new technologies and + + + align:start position:0% +lose our hold on new technologies and +ultimately damage our capacity to + + align:start position:0% +ultimately damage our capacity to + + + align:start position:0% +ultimately damage our capacity to +innovate he then goes on to talk a + + align:start position:0% +innovate he then goes on to talk a + + + align:start position:0% +innovate he then goes on to talk a +little bit about les despaired open + + align:start position:0% +little bit about les despaired open + + + align:start position:0% +little bit about les despaired open +markets but then he argues that even + + align:start position:0% +markets but then he argues that even + + + align:start position:0% +markets but then he argues that even +though a lot is fair and those + + align:start position:0% +though a lot is fair and those + + + align:start position:0% +though a lot is fair and those +principles are good there is room for + + align:start position:0% +principles are good there is room for + + + align:start position:0% +principles are good there is room for +improvement he talks about job centric + + align:start position:0% +improvement he talks about job centric + + + align:start position:0% +improvement he talks about job centric +economies and politics where in a job + + align:start position:0% +economies and politics where in a job + + + align:start position:0% +economies and politics where in a job +centered system job creation would be + + align:start position:0% +centered system job creation would be + + + align:start position:0% +centered system job creation would be +the nation's number-one objective or the + + align:start position:0% +the nation's number-one objective or the + + + align:start position:0% +the nation's number-one objective or the +government setting priorities and + + align:start position:0% +government setting priorities and + + + align:start position:0% +government setting priorities and +arraigning the force is necessary to + + align:start position:0% +arraigning the force is necessary to + + + align:start position:0% +arraigning the force is necessary to +achieve the goal and with it is + + align:start position:0% +achieve the goal and with it is + + + align:start position:0% +achieve the goal and with it is +operating not only in their immediate + + align:start position:0% +operating not only in their immediate + + + align:start position:0% +operating not only in their immediate +profit interest but also the interest of + + align:start position:0% +profit interest but also the interest of + + + align:start position:0% +profit interest but also the interest of +employees employees yet to be hired + + align:start position:0% +employees employees yet to be hired + + + align:start position:0% +employees employees yet to be hired +which is beneficial to the country he + + align:start position:0% +which is beneficial to the country he + + + align:start position:0% +which is beneficial to the country he +ends with saying something that we're + + align:start position:0% +ends with saying something that we're + + + align:start position:0% +ends with saying something that we're +seeing right now which is wealth + + align:start position:0% +seeing right now which is wealth + + + align:start position:0% +seeing right now which is wealth +inequality that if if we do have a place + + align:start position:0% +inequality that if if we do have a place + + + align:start position:0% +inequality that if if we do have a place +where we just pretty much outsource + + align:start position:0% +where we just pretty much outsource + + + align:start position:0% +where we just pretty much outsource +everything we're gonna have a country + + align:start position:0% +everything we're gonna have a country + + + align:start position:0% +everything we're gonna have a country +that has very high profitability but low + + align:start position:0% +that has very high profitability but low + + + align:start position:0% +that has very high profitability but low +prosperity which is what we're seeing + + align:start position:0% +prosperity which is what we're seeing + + + align:start position:0% +prosperity which is what we're seeing +right now especially very impactful in + + align:start position:0% +right now especially very impactful in + + + align:start position:0% +right now especially very impactful in +the last like three years and spending + + align:start position:0% +the last like three years and spending + + + align:start position:0% +the last like three years and spending +is afterlife mm well mm everyone started + + align:start position:0% +is afterlife mm well mm everyone started + + + align:start position:0% +is afterlife mm well mm everyone started +outsource all their manufacturing + + align:start position:0% +outsource all their manufacturing + + + align:start position:0% +outsource all their manufacturing +because it's cheaper in China Asia but + + align:start position:0% +because it's cheaper in China Asia but + + + align:start position:0% +because it's cheaper in China Asia but +that's really hurt jobs hurt us a + + align:start position:0% +that's really hurt jobs hurt us a + + + align:start position:0% +that's really hurt jobs hurt us a +statement sorry thanks Marty + + align:start position:0% +statement sorry thanks Marty + + + align:start position:0% +statement sorry thanks Marty +who wrote that Andy Grove so when + + align:start position:0% +who wrote that Andy Grove so when + + + align:start position:0% +who wrote that Andy Grove so when +they're one of the three founders of + + align:start position:0% +they're one of the three founders of + + + align:start position:0% +they're one of the three founders of +Intel any little so very important + + align:start position:0% +Intel any little so very important + + + align:start position:0% +Intel any little so very important +because Andy Grove also has one of my + + align:start position:0% +because Andy Grove also has one of my + + + align:start position:0% +because Andy Grove also has one of my +favorite remarks only the paranoid + + align:start position:0% +favorite remarks only the paranoid + + + align:start position:0% +favorite remarks only the paranoid +survive a lot of great books but the + + align:start position:0% +survive a lot of great books but the + + + align:start position:0% +survive a lot of great books but the +differences in the reason I had him is + + align:start position:0% +differences in the reason I had him is + + + align:start position:0% +differences in the reason I had him is +because this perspective is more of a + + align:start position:0% +because this perspective is more of a + + + align:start position:0% +because this perspective is more of a +business person who's seen kind of the + + align:start position:0% +business person who's seen kind of the + + + align:start position:0% +business person who's seen kind of the +impact versus three sources added were + + align:start position:0% +impact versus three sources added were + + + align:start position:0% +impact versus three sources added were +mostly like politicians and so that + + align:start position:0% +mostly like politicians and so that + + + align:start position:0% +mostly like politicians and so that +would be interesting + + align:start position:0% +would be interesting + + + align:start position:0% +would be interesting +thanks Martine and look a lot of the + + align:start position:0% +thanks Martine and look a lot of the + + + align:start position:0% +thanks Martine and look a lot of the +issues phrase are going to be prime + + align:start position:0% +issues phrase are going to be prime + + + align:start position:0% +issues phrase are going to be prime +topics and next week's class students + + align:start position:0% +topics and next week's class students + + + align:start position:0% +topics and next week's class students +just hang on to a lot of that we can + + align:start position:0% +just hang on to a lot of that we can + + + align:start position:0% +just hang on to a lot of that we can +discuss it here to us but the acceptable + + align:start position:0% +discuss it here to us but the acceptable + + + align:start position:0% +discuss it here to us but the acceptable +way to do a straw poll who agreed + + align:start position:0% +way to do a straw poll who agreed + + + align:start position:0% +way to do a straw poll who agreed +overall the moon's argument versus who + + align:start position:0% +overall the moon's argument versus who + + + align:start position:0% +overall the moon's argument versus who +didn't with Barry Lynn yeah sure + + align:start position:0% +didn't with Barry Lynn yeah sure + + + align:start position:0% +didn't with Barry Lynn yeah sure +whoo-hoo generally you thought that was + + align:start position:0% +whoo-hoo generally you thought that was + + + align:start position:0% +whoo-hoo generally you thought that was +part of this long ago so I think I have + + align:start position:0% +part of this long ago so I think I have + + + align:start position:0% +part of this long ago so I think I have +you the piece I was missing and moved + + align:start position:0% +you the piece I was missing and moved + + + align:start position:0% +you the piece I was missing and moved +chair announces know about his argument + + align:start position:0% +chair announces know about his argument + + + align:start position:0% +chair announces know about his argument +on Clinton is that he didn't think that + + align:start position:0% +on Clinton is that he didn't think that + + + align:start position:0% +on Clinton is that he didn't think that +was a good idea he didn't appreciate the + + align:start position:0% +was a good idea he didn't appreciate the + + + align:start position:0% +was a good idea he didn't appreciate the +integrative approach because he felt + + align:start position:0% +integrative approach because he felt + + + align:start position:0% +integrative approach because he felt +that the invisible hand that we all + + align:start position:0% +that the invisible hand that we all + + + align:start position:0% +that the invisible hand that we all +presumed to exist that would effectively + + align:start position:0% +presumed to exist that would effectively + + + align:start position:0% +presumed to exist that would effectively +regulate market and ensure that everyone + + align:start position:0% +regulate market and ensure that everyone + + + align:start position:0% +regulate market and ensure that everyone +was acting in that room and not only + + align:start position:0% +was acting in that room and not only + + + align:start position:0% +was acting in that room and not only +their own self-interest but also in the + + align:start position:0% +their own self-interest but also in the + + + align:start position:0% +their own self-interest but also in the +self-interest of the system being + + align:start position:0% +self-interest of the system being + + + align:start position:0% +self-interest of the system being +sustainable was dangerous because it + + align:start position:0% +sustainable was dangerous because it + + + align:start position:0% +sustainable was dangerous because it +could collapse and it did so overall I + + align:start position:0% +could collapse and it did so overall I + + + align:start position:0% +could collapse and it did so overall I +agree with that component and I guess + + align:start position:0% +agree with that component and I guess + + + align:start position:0% +agree with that component and I guess +that's what I'm curious about other + + align:start position:0% +that's what I'm curious about other + + + align:start position:0% +that's what I'm curious about other +people's perspectives on do we think + + align:start position:0% +people's perspectives on do we think + + + align:start position:0% +people's perspectives on do we think +that his consumption of how + + align:start position:0% +that his consumption of how + + + align:start position:0% +that his consumption of how +laissez-faire is implemented is + + align:start position:0% +laissez-faire is implemented is + + + align:start position:0% +laissez-faire is implemented is +generally I mean that's look that's a + + align:start position:0% +generally I mean that's look that's a + + + align:start position:0% +generally I mean that's look that's a +good summary of the point that brings us + + align:start position:0% +good summary of the point that brings us + + + align:start position:0% +good summary of the point that brings us +to thank you great some caveats do you + + align:start position:0% +to thank you great some caveats do you + + + align:start position:0% +to thank you great some caveats do you +think laissez-faire economies are + + align:start position:0% +think laissez-faire economies are + + + align:start position:0% +think laissez-faire economies are +dangerous in the way that when has + + align:start position:0% +dangerous in the way that when has + + + align:start position:0% +dangerous in the way that when has +articulated them yes do who does not who + + align:start position:0% +articulated them yes do who does not who + + + align:start position:0% +articulated them yes do who does not who +thinks laissez-faire is good heard of + + align:start position:0% +thinks laissez-faire is good heard of + + + align:start position:0% +thinks laissez-faire is good heard of +the Great Depression so I think my + + align:start position:0% +the Great Depression so I think my + + + align:start position:0% +the Great Depression so I think my +caveats were definitely like you have + + align:start position:0% +caveats were definitely like you have + + + align:start position:0% +caveats were definitely like you have +this opportunity and laissez-faire sort + + align:start position:0% +this opportunity and laissez-faire sort + + + align:start position:0% +this opportunity and laissez-faire sort +of like spread + + align:start position:0% +of like spread + + + align:start position:0% +of like spread +this idea of not only comparative + + align:start position:0% +this idea of not only comparative + + + align:start position:0% +this idea of not only comparative +advantage but you also spread hopefully + + align:start position:0% +advantage but you also spread hopefully + + + align:start position:0% +advantage but you also spread hopefully +if this works possibly sort of likely + + align:start position:0% +if this works possibly sort of likely + + + align:start position:0% +if this works possibly sort of likely +good things if you hit me to our teens + + align:start position:0% +good things if you hit me to our teens + + + align:start position:0% +good things if you hit me to our teens +point and bring in job creation is kind + + align:start position:0% +point and bring in job creation is kind + + + align:start position:0% +point and bring in job creation is kind +of one of the central pieces to sort of + + align:start position:0% +of one of the central pieces to sort of + + + align:start position:0% +of one of the central pieces to sort of +keeping the social tide of sort of + + align:start position:0% +keeping the social tide of sort of + + + align:start position:0% +keeping the social tide of sort of +everybody rising I think you get an + + align:start position:0% +everybody rising I think you get an + + + align:start position:0% +everybody rising I think you get an +opportunity to sort of like spread the + + align:start position:0% +opportunity to sort of like spread the + + + align:start position:0% +opportunity to sort of like spread the +job creation sort of spread all these + + align:start position:0% +job creation sort of spread all these + + + align:start position:0% +job creation sort of spread all these +things with logic there and looking like + + align:start position:0% +things with logic there and looking like + + + align:start position:0% +things with logic there and looking like +Clinton dibs towards sort of not so much + + align:start position:0% +Clinton dibs towards sort of not so much + + + align:start position:0% +Clinton dibs towards sort of not so much +outsourcing but sort of like looking + + align:start position:0% +outsourcing but sort of like looking + + + align:start position:0% +outsourcing but sort of like looking +bigger than just kind of creating jobs + + align:start position:0% +bigger than just kind of creating jobs + + + align:start position:0% +bigger than just kind of creating jobs +in the United States just sort of rights + + align:start position:0% +in the United States just sort of rights + + + align:start position:0% +in the United States just sort of rights +our wealth but like if you look at if + + align:start position:0% +our wealth but like if you look at if + + + align:start position:0% +our wealth but like if you look at if +you can create jobs now all over the + + align:start position:0% +you can create jobs now all over the + + + align:start position:0% +you can create jobs now all over the +globe and integrate them in this + + align:start position:0% +globe and integrate them in this + + + align:start position:0% +globe and integrate them in this +interconnected system you have the + + align:start position:0% +interconnected system you have the + + + align:start position:0% +interconnected system you have the +opportunity to sort of rice tide + + align:start position:0% +opportunity to sort of rice tide + + + align:start position:0% +opportunity to sort of rice tide +globally in LA so I just think the main + + align:start position:0% +globally in LA so I just think the main + + + align:start position:0% +globally in LA so I just think the main +point I got from wins rating is that + + align:start position:0% +point I got from wins rating is that + + + align:start position:0% +point I got from wins rating is that +single scene systems with single point + + align:start position:0% +single scene systems with single point + + + align:start position:0% +single scene systems with single point +failures are dangerous and I feel like + + align:start position:0% +failures are dangerous and I feel like + + + align:start position:0% +failures are dangerous and I feel like +that would be true on any scale he's + + align:start position:0% +that would be true on any scale he's + + + align:start position:0% +that would be true on any scale he's +just talking about like now we're on + + align:start position:0% +just talking about like now we're on + + + align:start position:0% +just talking about like now we're on +such a bigger scale that it's gonna + + align:start position:0% +such a bigger scale that it's gonna + + + align:start position:0% +such a bigger scale that it's gonna +affect everyone's but I think that at + + align:start position:0% +affect everyone's but I think that at + + + align:start position:0% +affect everyone's but I think that at +the national scale that would still be + + align:start position:0% +the national scale that would still be + + + align:start position:0% +the national scale that would still be +dangerous like any system that had a + + align:start position:0% +dangerous like any system that had a + + + align:start position:0% +dangerous like any system that had a +single point failures concern but I + + align:start position:0% +single point failures concern but I + + + align:start position:0% +single point failures concern but I +don't necessarily agree with the fact + + align:start position:0% +don't necessarily agree with the fact + + + align:start position:0% +don't necessarily agree with the fact +that he thinks that can't be corrected + + align:start position:0% +that he thinks that can't be corrected + + + align:start position:0% +that he thinks that can't be corrected +while still having a like somewhat + + align:start position:0% +while still having a like somewhat + + + align:start position:0% +while still having a like somewhat +laissez-faire system I do think it would + + align:start position:0% +laissez-faire system I do think it would + + + align:start position:0% +laissez-faire system I do think it would +require some regulations but like even + + align:start position:0% +require some regulations but like even + + + align:start position:0% +require some regulations but like even +if it was just having a few plans that + + align:start position:0% +if it was just having a few plans that + + + align:start position:0% +if it was just having a few plans that +makes a conductors outside Taiwan like + + align:start position:0% +makes a conductors outside Taiwan like + + + align:start position:0% +makes a conductors outside Taiwan like +that I feel like that could be not a + + align:start position:0% +that I feel like that could be not a + + + align:start position:0% +that I feel like that could be not a +huge imposition on lessees there and + + align:start position:0% +huge imposition on lessees there and + + + align:start position:0% +huge imposition on lessees there and +reduce that's like a problem actually I + + align:start position:0% +reduce that's like a problem actually I + + + align:start position:0% +reduce that's like a problem actually I +was reading that I was thinking would it + + align:start position:0% +was reading that I was thinking would it + + + align:start position:0% +was reading that I was thinking would it +really be saver than to have every + + align:start position:0% +really be saver than to have every + + + align:start position:0% +really be saver than to have every +factory making every component of the + + align:start position:0% +factory making every component of the + + + align:start position:0% +factory making every component of the +phone all India it's like wouldn't that + + align:start position:0% +phone all India it's like wouldn't that + + + align:start position:0% +phone all India it's like wouldn't that +just geographically cause you to be less + + align:start position:0% +just geographically cause you to be less + + + align:start position:0% +just geographically cause you to be less +libraries yeah I think that's + + align:start position:0% +libraries yeah I think that's + + + align:start position:0% +libraries yeah I think that's +interesting because he uses language to + + align:start position:0% +interesting because he uses language to + + + align:start position:0% +interesting because he uses language to +make it seem like this is what a + + align:start position:0% +make it seem like this is what a + + + align:start position:0% +make it seem like this is what a +globally distributed architecture looks + + align:start position:0% +globally distributed architecture looks + + + align:start position:0% +globally distributed architecture looks +like but I agree I think you have all of + + align:start position:0% +like but I agree I think you have all of + + + align:start position:0% +like but I agree I think you have all of +your manufacturing or something + + align:start position:0% +your manufacturing or something + + + align:start position:0% +your manufacturing or something +constituted in one geographical area + + align:start position:0% +constituted in one geographical area + + + align:start position:0% +constituted in one geographical area +it's like it's not globalization it's + + align:start position:0% +it's like it's not globalization it's + + + align:start position:0% +it's like it's not globalization it's +not really + + align:start position:0% +not really + + + align:start position:0% +not really +very complex integrated system it just + + align:start position:0% +very complex integrated system it just + + + align:start position:0% +very complex integrated system it just +happen to speak farm in your country + + align:start position:0% +happen to speak farm in your country + + + align:start position:0% +happen to speak farm in your country +make it see what the wins argument is + + align:start position:0% +make it see what the wins argument is + + + align:start position:0% +make it see what the wins argument is +America first yeah I mean Linda's let + + align:start position:0% +America first yeah I mean Linda's let + + + align:start position:0% +America first yeah I mean Linda's let +his painting you know a dark side here + + align:start position:0% +his painting you know a dark side here + + + align:start position:0% +his painting you know a dark side here +and he's painting a portrayal of opening + + align:start position:0% +and he's painting a portrayal of opening + + + align:start position:0% +and he's painting a portrayal of opening +up this system and then the system + + align:start position:0% +up this system and then the system + + + align:start position:0% +up this system and then the system +itself begins to take control but this + + align:start position:0% +itself begins to take control but this + + + align:start position:0% +itself begins to take control but this +globalized financial system itself + + align:start position:0% +globalized financial system itself + + + align:start position:0% +globalized financial system itself +begins to take control and minimize the + + align:start position:0% +begins to take control and minimize the + + + align:start position:0% +begins to take control and minimize the +ability of any of the players to impact + + align:start position:0% +ability of any of the players to impact + + + align:start position:0% +ability of any of the players to impact +their effect so it's a fundamental + + align:start position:0% +their effect so it's a fundamental + + + align:start position:0% +their effect so it's a fundamental +statement about the fragility and lack + + align:start position:0% +statement about the fragility and lack + + + align:start position:0% +statement about the fragility and lack +of resilience and your you know your + + align:start position:0% +of resilience and your you know your + + + align:start position:0% +of resilience and your you know your +single point of failure point is + + align:start position:0% +single point of failure point is + + + align:start position:0% +single point of failure point is +well-taken + + align:start position:0% + + + + align:start position:0% + +it's it's a dark picture here and what + + align:start position:0% +it's it's a dark picture here and what + + + align:start position:0% +it's it's a dark picture here and what +makes it intriguing the only reason why + + align:start position:0% +makes it intriguing the only reason why + + + align:start position:0% +makes it intriguing the only reason why +I still keep it in here is it sure + + align:start position:0% +I still keep it in here is it sure + + + align:start position:0% +I still keep it in here is it sure +enough you know that's exactly what we + + align:start position:0% +enough you know that's exactly what we + + + align:start position:0% +enough you know that's exactly what we +ended up with in 2008 and boy that was + + align:start position:0% +ended up with in 2008 and boy that was + + + align:start position:0% +ended up with in 2008 and boy that was +so close massive depression it's so it's + + align:start position:0% +so close massive depression it's so it's + + + align:start position:0% +so close massive depression it's so it's +a I put it in as kind of a useful + + align:start position:0% +a I put it in as kind of a useful + + + align:start position:0% +a I put it in as kind of a useful +warning lessons but also a lesson about + + align:start position:0% +warning lessons but also a lesson about + + + align:start position:0% +warning lessons but also a lesson about +how we moved in the international + + align:start position:0% +how we moved in the international + + + align:start position:0% +how we moved in the international +organization of our economy from a + + align:start position:0% +organization of our economy from a + + + align:start position:0% +organization of our economy from a +nation center to an allies Center to + + align:start position:0% +nation center to an allies Center to + + + align:start position:0% +nation center to an allies Center to +which really globalized kind of + + align:start position:0% +which really globalized kind of + + + align:start position:0% +which really globalized kind of +orientation here what is the what are + + align:start position:0% +orientation here what is the what are + + + align:start position:0% +orientation here what is the what are +the implications we need to keep + + align:start position:0% +the implications we need to keep + + + align:start position:0% +the implications we need to keep +thinking about going back to the to that + + align:start position:0% +thinking about going back to the to that + + + align:start position:0% +thinking about going back to the to that +whole the 2008 collapse you were saying + + align:start position:0% +whole the 2008 collapse you were saying + + + align:start position:0% +whole the 2008 collapse you were saying +that it's that it's very difficult to + + align:start position:0% +that it's that it's very difficult to + + + align:start position:0% +that it's that it's very difficult to +regulate some sort of planet as some + + align:start position:0% +regulate some sort of planet as some + + + align:start position:0% +regulate some sort of planet as some +sort of financial system that reaches + + align:start position:0% +sort of financial system that reaches + + + align:start position:0% +sort of financial system that reaches +across borders but at least with the + + align:start position:0% +across borders but at least with the + + + align:start position:0% +across borders but at least with the +2008 crisis a lot of the a lot of the + + align:start position:0% +2008 crisis a lot of the a lot of the + + + align:start position:0% +2008 crisis a lot of the a lot of the +collapse stem directly from the US which + + align:start position:0% +collapse stem directly from the US which + + + align:start position:0% +collapse stem directly from the US which +means that at least with the collapse of + + align:start position:0% +means that at least with the collapse of + + + align:start position:0% +means that at least with the collapse of +that form u.s. regulations clearly would + + align:start position:0% +that form u.s. regulations clearly would + + + align:start position:0% +that form u.s. regulations clearly would +have helped significantly in good friend + + align:start position:0% +have helped significantly in good friend + + + align:start position:0% +have helped significantly in good friend +of crisis altogether so my my feeling is + + align:start position:0% +of crisis altogether so my my feeling is + + + align:start position:0% +of crisis altogether so my my feeling is +at least if we're going to use that as + + align:start position:0% +at least if we're going to use that as + + + align:start position:0% +at least if we're going to use that as +the example then it just is I don't know + + align:start position:0% +the example then it just is I don't know + + + align:start position:0% +the example then it just is I don't know +I don't know how true it is then + + align:start position:0% +I don't know how true it is then + + + align:start position:0% +I don't know how true it is then +that that we can't actually regulate + + align:start position:0% +that that we can't actually regulate + + + align:start position:0% +that that we can't actually regulate +this system does cubes like all these + + align:start position:0% +this system does cubes like all these + + + align:start position:0% +this system does cubes like all these +countries that are all ignoring natural + + align:start position:0% +countries that are all ignoring natural + + + align:start position:0% +countries that are all ignoring natural +disasters like happen in Taiwan if all + + align:start position:0% +disasters like happen in Taiwan if all + + + align:start position:0% +disasters like happen in Taiwan if all +these separate countries are regulating + + align:start position:0% +these separate countries are regulating + + + align:start position:0% +these separate countries are regulating +their industries properly in order to + + align:start position:0% +their industries properly in order to + + + align:start position:0% +their industries properly in order to +make sure that no bank is quote unquote + + align:start position:0% +make sure that no bank is quote unquote + + + align:start position:0% +make sure that no bank is quote unquote +too big to fail then I don't see how + + align:start position:0% +too big to fail then I don't see how + + + align:start position:0% +too big to fail then I don't see how +these system could collapse all the + + align:start position:0% +these system could collapse all the + + + align:start position:0% +these system could collapse all the +individual components and doing what + + align:start position:0% +individual components and doing what + + + align:start position:0% +individual components and doing what +they should be so let me let me put this + + align:start position:0% +they should be so let me let me put this + + + align:start position:0% +they should be so let me let me put this +in a different way I think this is + + align:start position:0% +in a different way I think this is + + + align:start position:0% +in a different way I think this is +significant target an innovation way I + + align:start position:0% +significant target an innovation way I + + + align:start position:0% +significant target an innovation way I +think this is significant argue that the + + align:start position:0% +think this is significant argue that the + + + align:start position:0% +think this is significant argue that the +explosion of the financial services + + align:start position:0% +explosion of the financial services + + + align:start position:0% +explosion of the financial services +sector the incredibly rapid growth of + + align:start position:0% +sector the incredibly rapid growth of + + + align:start position:0% +sector the incredibly rapid growth of +the financial services sector in the + + align:start position:0% +the financial services sector in the + + + align:start position:0% +the financial services sector in the +1990s and 2000 that's an innovation + + align:start position:0% +1990s and 2000 that's an innovation + + + align:start position:0% +1990s and 2000 that's an innovation +there's certainly were technological + + align:start position:0% +there's certainly were technological + + + align:start position:0% +there's certainly were technological +innovations that were at the heart of + + align:start position:0% +innovations that were at the heart of + + + align:start position:0% +innovations that were at the heart of +this the IT revolution was clearly a + + align:start position:0% +this the IT revolution was clearly a + + + align:start position:0% +this the IT revolution was clearly a +great organizing factor the ability of + + align:start position:0% +great organizing factor the ability of + + + align:start position:0% +great organizing factor the ability of +bring mathematics to bear to work on the + + align:start position:0% +bring mathematics to bear to work on the + + + align:start position:0% +bring mathematics to bear to work on the +problem of big data and initial kinds of + + align:start position:0% +problem of big data and initial kinds of + + + align:start position:0% +problem of big data and initial kinds of +analytics to bring algorithms to bear on + + align:start position:0% +analytics to bring algorithms to bear on + + + align:start position:0% +analytics to bring algorithms to bear on +market reading these are all significant + + align:start position:0% +market reading these are all significant + + + align:start position:0% +market reading these are all significant +technology advances that were enabler of + + align:start position:0% +technology advances that were enabler of + + + align:start position:0% +technology advances that were enabler of +creating a truly globalized system and + + align:start position:0% +creating a truly globalized system and + + + align:start position:0% +creating a truly globalized system and +we move and a relatively short period + + align:start position:0% +we move and a relatively short period + + + align:start position:0% +we move and a relatively short period +from national systems financial services + + align:start position:0% +from national systems financial services + + + align:start position:0% +from national systems financial services +and financial services organizations a + + align:start position:0% +and financial services organizations a + + + align:start position:0% +and financial services organizations a +much larger global system so when the US + + align:start position:0% +much larger global system so when the US + + + align:start position:0% +much larger global system so when the US +economy went down it hit the rest of the + + align:start position:0% +economy went down it hit the rest of the + + + align:start position:0% +economy went down it hit the rest of the +world economy US financial system it hit + + align:start position:0% +world economy US financial system it hit + + + align:start position:0% +world economy US financial system it hit +the rest of the world economy and wave + + align:start position:0% +the rest of the world economy and wave + + + align:start position:0% +the rest of the world economy and wave +after wave after wave the end jeopardize + + align:start position:0% +after wave after wave the end jeopardize + + + align:start position:0% +after wave after wave the end jeopardize +a whole nest of other financial + + align:start position:0% +a whole nest of other financial + + + align:start position:0% +a whole nest of other financial +institutions that were caught up in this + + align:start position:0% +institutions that were caught up in this + + + align:start position:0% +institutions that were caught up in this +very integrated kind of system so that's + + align:start position:0% +very integrated kind of system so that's + + + align:start position:0% +very integrated kind of system so that's +more what I'm driving at next and you + + align:start position:0% +more what I'm driving at next and you + + + align:start position:0% +more what I'm driving at next and you +know look as we discuss in innovation + + align:start position:0% +know look as we discuss in innovation + + + align:start position:0% +know look as we discuss in innovation +ways there's always a bubble in contract + + align:start position:0% +ways there's always a bubble in contract + + + align:start position:0% +ways there's always a bubble in contract +and the problem with having a bubble + + align:start position:0% +and the problem with having a bubble + + + align:start position:0% +and the problem with having a bubble +into your financial services sector is + + align:start position:0% +into your financial services sector is + + + align:start position:0% +into your financial services sector is +that it brings down area it's one thing + + align:start position:0% +that it brings down area it's one thing + + + align:start position:0% +that it brings down area it's one thing +to have a bubble with calm + + align:start position:0% +to have a bubble with calm + + + align:start position:0% +to have a bubble with calm +yeah loosen that guns but you know if + + align:start position:0% +yeah loosen that guns but you know if + + + align:start position:0% +yeah loosen that guns but you know if +you lose the world financial system you + + align:start position:0% +you lose the world financial system you + + + align:start position:0% +you lose the world financial system you +know because of a technological bubble + + align:start position:0% +know because of a technological bubble + + + align:start position:0% +know because of a technological bubble +it's pretty powerful Andrew Lowe is a + + align:start position:0% +it's pretty powerful Andrew Lowe is a + + + align:start position:0% +it's pretty powerful Andrew Lowe is a +wonderful professor of finance here at + + align:start position:0% +wonderful professor of finance here at + + + align:start position:0% +wonderful professor of finance here at +MIT as a has it as a remarkable chart + + align:start position:0% +MIT as a has it as a remarkable chart + + + align:start position:0% +MIT as a has it as a remarkable chart +right the chart is it's the history of + + align:start position:0% +right the chart is it's the history of + + + align:start position:0% +right the chart is it's the history of +the value of home prices adjusted for + + align:start position:0% +the value of home prices adjusted for + + + align:start position:0% +the value of home prices adjusted for +inflation in the United States and it's + + align:start position:0% +inflation in the United States and it's + + + align:start position:0% +inflation in the United States and it's +a hockey okay so it's affliction + + align:start position:0% +a hockey okay so it's affliction + + + align:start position:0% +a hockey okay so it's affliction +adjusted its flight and the numbers + + align:start position:0% +adjusted its flight and the numbers + + + align:start position:0% +adjusted its flight and the numbers +start getting put together in about the + + align:start position:0% +start getting put together in about the + + + align:start position:0% +start getting put together in about the +1880s and she won't like me in case you + + align:start position:0% +1880s and she won't like me in case you + + + align:start position:0% +1880s and she won't like me in case you +know there's the Great Depression right + + align:start position:0% +know there's the Great Depression right + + + align:start position:0% +know there's the Great Depression right +cutlery sessions but it's pretty stable + + align:start position:0% +cutlery sessions but it's pretty stable + + + align:start position:0% +cutlery sessions but it's pretty stable +then about 1990 it just skyrockets right + + align:start position:0% +then about 1990 it just skyrockets right + + + align:start position:0% +then about 1990 it just skyrockets right +it just skyrockets and you wonder what + + align:start position:0% +it just skyrockets and you wonder what + + + align:start position:0% +it just skyrockets and you wonder what +were we thinking I mean this is clearly + + align:start position:0% +were we thinking I mean this is clearly + + + align:start position:0% +were we thinking I mean this is clearly +gonna be a bubble you know why was it + + align:start position:0% +gonna be a bubble you know why was it + + + align:start position:0% +gonna be a bubble you know why was it +the financial services sector decided + + align:start position:0% +the financial services sector decided + + + align:start position:0% +the financial services sector decided +that the ultimate fundamental unit of + + align:start position:0% +that the ultimate fundamental unit of + + + align:start position:0% +that the ultimate fundamental unit of +value in the world financial order is + + align:start position:0% +value in the world financial order is + + + align:start position:0% +value in the world financial order is +going to be the American Hall mortgage + + align:start position:0% +going to be the American Hall mortgage + + + align:start position:0% +going to be the American Hall mortgage +why did we do this I don't mean thinking + + align:start position:0% +why did we do this I don't mean thinking + + + align:start position:0% +why did we do this I don't mean thinking +but in a way that's exactly what we do + + align:start position:0% +but in a way that's exactly what we do + + + align:start position:0% +but in a way that's exactly what we do +now Andrew goes on to make an argument + + align:start position:0% +now Andrew goes on to make an argument + + + align:start position:0% +now Andrew goes on to make an argument +we developed all these very interesting + + align:start position:0% +we developed all these very interesting + + + align:start position:0% +we developed all these very interesting +new financial tools in the course of + + align:start position:0% +new financial tools in the course of + + + align:start position:0% +new financial tools in the course of +that innovation wave he wouldn't miss a + + align:start position:0% +that innovation wave he wouldn't miss a + + + align:start position:0% +that innovation wave he wouldn't miss a +call it an innovation wave but I would + + align:start position:0% +call it an innovation wave but I would + + + align:start position:0% +call it an innovation wave but I would +let's figure out if we can settle on + + align:start position:0% +let's figure out if we can settle on + + + align:start position:0% +let's figure out if we can settle on +some better units of value right than + + align:start position:0% +some better units of value right than + + + align:start position:0% +some better units of value right than +the American Home Mortgage right is + + align:start position:0% +the American Home Mortgage right is + + + align:start position:0% +the American Home Mortgage right is +there a way to drive investment which we + + align:start position:0% +there a way to drive investment which we + + + align:start position:0% +there a way to drive investment which we +can now mobilize a global scale onto + + align:start position:0% +can now mobilize a global scale onto + + + align:start position:0% +can now mobilize a global scale onto +much better units of value so the + + align:start position:0% +much better units of value so the + + + align:start position:0% +much better units of value so the +project he's been involved in has been + + align:start position:0% +project he's been involved in has been + + + align:start position:0% +project he's been involved in has been +can we drive it on innovation based + + align:start position:0% +can we drive it on innovation based + + + align:start position:0% +can we drive it on innovation based +research can we create emotions of + + align:start position:0% +research can we create emotions of + + + align:start position:0% +research can we create emotions of +really major capital not just a 60 + + align:start position:0% +really major capital not just a 60 + + + align:start position:0% +really major capital not just a 60 +billion a year and a 19 trillion dollar + + align:start position:0% +billion a year and a 19 trillion dollar + + + align:start position:0% +billion a year and a 19 trillion dollar +economy a venture capital but real + + align:start position:0% +economy a venture capital but real + + + align:start position:0% +economy a venture capital but real +numbers right and move them move those + + align:start position:0% +numbers right and move them move those + + + align:start position:0% +numbers right and move them move those +larger numbers one of the innovations so + + align:start position:0% +larger numbers one of the innovations so + + + align:start position:0% +larger numbers one of the innovations so +he's working on health research in + + align:start position:0% +he's working on health research in + + + align:start position:0% +he's working on health research in +particular but it's you know it's an + + align:start position:0% +particular but it's you know it's an + + + align:start position:0% +particular but it's you know it's an +interesting concept and in a way it + + align:start position:0% +interesting concept and in a way it + + + align:start position:0% +interesting concept and in a way it +comes out of trying to wrestle with some + + align:start position:0% +comes out of trying to wrestle with some + + + align:start position:0% +comes out of trying to wrestle with some +of the points that very limited + + align:start position:0% +of the points that very limited + + + align:start position:0% +of the points that very limited +Rachid a closing thought + + align:start position:0% +Rachid a closing thought + + + align:start position:0% +Rachid a closing thought +yeah um so I think Marilyn probably + + align:start position:0% +yeah um so I think Marilyn probably + + + align:start position:0% +yeah um so I think Marilyn probably +takes maybe a different position than in + + align:start position:0% +takes maybe a different position than in + + + align:start position:0% +takes maybe a different position than in +the time that he was talking about her - + + align:start position:0% +the time that he was talking about her - + + + align:start position:0% +the time that he was talking about her - +I think if we had said this in an + + align:start position:0% +I think if we had said this in an + + + align:start position:0% +I think if we had said this in an +interesting discussion when I was + + align:start position:0% +interesting discussion when I was + + + align:start position:0% +interesting discussion when I was +actually just wondering if we kept + + align:start position:0% +actually just wondering if we kept + + + align:start position:0% +actually just wondering if we kept +talking about this like a little bit + + align:start position:0% +talking about this like a little bit + + + align:start position:0% +talking about this like a little bit +more the critical reception and you know + + align:start position:0% +more the critical reception and you know + + + align:start position:0% +more the critical reception and you know +every mm somebody publishes it seemed + + align:start position:0% +every mm somebody publishes it seemed + + + align:start position:0% +every mm somebody publishes it seemed +like the first guy to say like maybe + + align:start position:0% +like the first guy to say like maybe + + + align:start position:0% +like the first guy to say like maybe +laissez-faire wasn't a good idea guys + + align:start position:0% +laissez-faire wasn't a good idea guys + + + align:start position:0% +laissez-faire wasn't a good idea guys +and then you know we see the outer + + align:start position:0% +and then you know we see the outer + + + align:start position:0% +and then you know we see the outer +effect afterward but critically like I + + align:start position:0% +effect afterward but critically like I + + + align:start position:0% +effect afterward but critically like I +think reading this I was pretty kind of + + align:start position:0% +think reading this I was pretty kind of + + + align:start position:0% +think reading this I was pretty kind of +taken aback by a lot of things he's + + align:start position:0% +taken aback by a lot of things he's + + + align:start position:0% +taken aback by a lot of things he's +saying like is this sort of maybe not + + align:start position:0% +saying like is this sort of maybe not + + + align:start position:0% +saying like is this sort of maybe not +politically bit like socially acceptable + + align:start position:0% +politically bit like socially acceptable + + + align:start position:0% +politically bit like socially acceptable +thought in the u.s. in you know maybe + + align:start position:0% +thought in the u.s. in you know maybe + + + align:start position:0% +thought in the u.s. in you know maybe +2005 yeah it's a it's a moment of + + align:start position:0% +2005 yeah it's a it's a moment of + + + align:start position:0% +2005 yeah it's a it's a moment of +dissonance in our reading list right + + align:start position:0% +dissonance in our reading list right + + + align:start position:0% +dissonance in our reading list right +it's a little contrary so just like + + align:start position:0% +it's a little contrary so just like + + + align:start position:0% +it's a little contrary so just like +Charles Schultz its contrarian last week + + align:start position:0% +Charles Schultz its contrarian last week + + + align:start position:0% +Charles Schultz its contrarian last week +you know very LED is contrary in this + + align:start position:0% +you know very LED is contrary in this + + + align:start position:0% +you know very LED is contrary in this +school so good summer thank you \ No newline at end of file diff --git a/lkeX42KQjac.txt b/lkeX42KQjac.txt new file mode 100644 index 0000000000000000000000000000000000000000..2d61c9c818e0a008b2d36eb45fd628a3be1d5787 --- /dev/null +++ b/lkeX42KQjac.txt @@ -0,0 +1,347 @@ +align:start position:0% + +so now what we'd like to do is try to + + align:start position:0% +so now what we'd like to do is try to + + + align:start position:0% +so now what we'd like to do is try to +understand how to apply the law of + + align:start position:0% +understand how to apply the law of + + + align:start position:0% +understand how to apply the law of +addition of velocities so we can express + + align:start position:0% +addition of velocities so we can express + + + align:start position:0% +addition of velocities so we can express +the velocity to the point on the rim in + + align:start position:0% +the velocity to the point on the rim in + + + align:start position:0% +the velocity to the point on the rim in +the reference frame fixed to the ground + + align:start position:0% +the reference frame fixed to the ground + + + align:start position:0% +the reference frame fixed to the ground +now the important thing to realize is V + + align:start position:0% +now the important thing to realize is V + + + align:start position:0% +now the important thing to realize is V +is the velocity of the center of mass of + + align:start position:0% +is the velocity of the center of mass of + + + align:start position:0% +is the velocity of the center of mass of +the wheel with respect to the ground and + + align:start position:0% +the wheel with respect to the ground and + + + align:start position:0% +the wheel with respect to the ground and +every single point on the wheel has that + + align:start position:0% +every single point on the wheel has that + + + align:start position:0% +every single point on the wheel has that +same velocity V so let's draw a picture + + align:start position:0% +same velocity V so let's draw a picture + + + align:start position:0% +same velocity V so let's draw a picture +of our wheel here we're in the ground + + align:start position:0% +of our wheel here we're in the ground + + + align:start position:0% +of our wheel here we're in the ground +reference frame and let's first draw + + align:start position:0% + + + + align:start position:0% + +four points on the wheel and draw this + + align:start position:0% +four points on the wheel and draw this + + + align:start position:0% +four points on the wheel and draw this +velocity V every single one of these + + align:start position:0% +velocity V every single one of these + + + align:start position:0% +velocity V every single one of these +points has the same velocity V be V and + + align:start position:0% +points has the same velocity V be V and + + + align:start position:0% +points has the same velocity V be V and +V now let's add to that the velocity of + + align:start position:0% +V now let's add to that the velocity of + + + align:start position:0% +V now let's add to that the velocity of +a point of the rim as seen in the + + align:start position:0% +a point of the rim as seen in the + + + align:start position:0% +a point of the rim as seen in the +reference frame moving with the center + + align:start position:0% +reference frame moving with the center + + + align:start position:0% +reference frame moving with the center +of mass we just saw that every single + + align:start position:0% +of mass we just saw that every single + + + align:start position:0% +of mass we just saw that every single +point on the wheel is undergoing + + align:start position:0% +point on the wheel is undergoing + + + align:start position:0% +point on the wheel is undergoing +circular motion in that reference frame + + align:start position:0% +circular motion in that reference frame + + + align:start position:0% +circular motion in that reference frame +so now let's draw those velocities I'll + + align:start position:0% +so now let's draw those velocities I'll + + + align:start position:0% +so now let's draw those velocities I'll +just draw it right below BC MP down here + + align:start position:0% +just draw it right below BC MP down here + + + align:start position:0% +just draw it right below BC MP down here +BC MP notice here it's in the opposite + + align:start position:0% +BC MP notice here it's in the opposite + + + align:start position:0% +BC MP notice here it's in the opposite +direction BC MP and up here it's + + align:start position:0% +direction BC MP and up here it's + + + align:start position:0% +direction BC MP and up here it's +pointing up so when we add these two + + align:start position:0% +pointing up so when we add these two + + + align:start position:0% +pointing up so when we add these two +vectors together what we get is a longer + + align:start position:0% +vectors together what we get is a longer + + + align:start position:0% +vectors together what we get is a longer +vector in this direction it would be the + + align:start position:0% +vector in this direction it would be the + + + align:start position:0% +vector in this direction it would be the +sum of these two pieces so we point like + + align:start position:0% +sum of these two pieces so we point like + + + align:start position:0% +sum of these two pieces so we point like +that + + align:start position:0% +that + + + align:start position:0% +that +that's DP over here it's the vector + + align:start position:0% +that's DP over here it's the vector + + + align:start position:0% +that's DP over here it's the vector +decomposition so it's in that direction + + align:start position:0% +decomposition so it's in that direction + + + align:start position:0% +decomposition so it's in that direction +here it's a shorter vector VP and over + + align:start position:0% +here it's a shorter vector VP and over + + + align:start position:0% +here it's a shorter vector VP and over +here it's the vector sum VP so now what + + align:start position:0% +here it's the vector sum VP so now what + + + align:start position:0% +here it's the vector sum VP so now what +we've been able to do is describe the + + align:start position:0% +we've been able to do is describe the + + + align:start position:0% +we've been able to do is describe the +velocity of the point P as a combination + + align:start position:0% +velocity of the point P as a combination + + + align:start position:0% +velocity of the point P as a combination +the vector addition of how the center of + + align:start position:0% +the vector addition of how the center of + + + align:start position:0% +the vector addition of how the center of +mass of the wheel is moving and the + + align:start position:0% +mass of the wheel is moving and the + + + align:start position:0% +mass of the wheel is moving and the +circular motion as seen in a reference + + align:start position:0% +circular motion as seen in a reference + + + align:start position:0% +circular motion as seen in a reference +frame moving with the center of mass now + + align:start position:0% +frame moving with the center of mass now + + + align:start position:0% +frame moving with the center of mass now +what we want to explore is + + align:start position:0% +what we want to explore is + + + align:start position:0% +what we want to explore is +special conditions which will refer to + + align:start position:0% +special conditions which will refer to + + + align:start position:0% +special conditions which will refer to +as rolling without slipping slipping or + + align:start position:0% +as rolling without slipping slipping or + + + align:start position:0% +as rolling without slipping slipping or +sliding \ No newline at end of file diff --git a/lpR4my-qfQA.txt b/lpR4my-qfQA.txt new file mode 100644 index 0000000000000000000000000000000000000000..2c956d16ec97dd70be8d911b98c608c912ef8218 --- /dev/null +++ b/lpR4my-qfQA.txt @@ -0,0 +1,12208 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +we started talking about the + + align:start position:0% +we started talking about the + + + align:start position:0% +we started talking about the +quantize + + align:start position:0% +quantize + + + align:start position:0% +quantize +the Maxwell Series in the Lorenz cage + + align:start position:0% +the Maxwell Series in the Lorenz cage + + + align:start position:0% +the Maxwell Series in the Lorenz cage +so in the Lauren's cage + + align:start position:0% +so in the Lauren's cage + + + align:start position:0% +so in the Lauren's cage +we can see the + + align:start position:0% +we can see the + + + align:start position:0% +we can see the +the following action + + align:start position:0% + + + + align:start position:0% + +so so we showed earlier + + align:start position:0% +so so we showed earlier + + + align:start position:0% +so so we showed earlier +that the range gauge can be insured just + + align:start position:0% +that the range gauge can be insured just + + + align:start position:0% +that the range gauge can be insured just +following the equation motion + + align:start position:0% +following the equation motion + + + align:start position:0% +following the equation motion +so you just get from here the equation + + align:start position:0% +so you just get from here the equation + + + align:start position:0% +so you just get from here the equation +motion + + align:start position:0% +motion + + + align:start position:0% +motion +and the uh then the equation motion + + align:start position:0% +and the uh then the equation motion + + + align:start position:0% +and the uh then the equation motion +yeah so equation motion + + align:start position:0% +yeah so equation motion + + + align:start position:0% +yeah so equation motion +will lead to partial Square partial mu a + + align:start position:0% +will lead to partial Square partial mu a + + + align:start position:0% +will lead to partial Square partial mu a +mu to zero + + align:start position:0% +mu to zero + + + align:start position:0% +mu to zero +so this is almost ensure a partial mu + + align:start position:0% +so this is almost ensure a partial mu + + + align:start position:0% +so this is almost ensure a partial mu +and mu equal to zero we just have to + + align:start position:0% +and mu equal to zero we just have to + + + align:start position:0% +and mu equal to zero we just have to +make sure your boundary conditions + + align:start position:0% +make sure your boundary conditions + + + align:start position:0% +make sure your boundary conditions +such as the partial mu and mu equal to + + align:start position:0% +such as the partial mu and mu equal to + + + align:start position:0% +such as the partial mu and mu equal to +zero okay + + align:start position:0% + + + + align:start position:0% + +so and in particular the action is + + align:start position:0% +so and in particular the action is + + + align:start position:0% +so and in particular the action is +particularly simple for PSI equal to one + + align:start position:0% +particularly simple for PSI equal to one + + + align:start position:0% +particularly simple for PSI equal to one +and in which case + + align:start position:0% +and in which case + + + align:start position:0% +and in which case +we just have + + align:start position:0% +we just have + + + align:start position:0% +we just have +I can just have reporting form + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so as if you just have four decoupled + + align:start position:0% +so as if you just have four decoupled + + + align:start position:0% +so as if you just have four decoupled +massive scalar + + align:start position:0% +massive scalar + + + align:start position:0% +massive scalar +okay as if you just have four a massive + + align:start position:0% +okay as if you just have four a massive + + + align:start position:0% +okay as if you just have four a massive +scalar okay and the equation motion + + align:start position:0% +scalar okay and the equation motion + + + align:start position:0% +scalar okay and the equation motion +exactly is all very simple + + align:start position:0% +exactly is all very simple + + + align:start position:0% +exactly is all very simple +and + + align:start position:0% +and + + + align:start position:0% +and +um so um so you can just proceeds copy + + align:start position:0% +um so um so you can just proceeds copy + + + align:start position:0% +um so um so you can just proceeds copy +I will be that before for the um + + align:start position:0% +I will be that before for the um + + + align:start position:0% +I will be that before for the um +for massive scalar okay and just treat + + align:start position:0% +for massive scalar okay and just treat + + + align:start position:0% +for massive scalar okay and just treat +each a mu as a massive scalar and then + + align:start position:0% +each a mu as a massive scalar and then + + + align:start position:0% +each a mu as a massive scalar and then +then you can just do it for example the + + align:start position:0% +then you can just do it for example the + + + align:start position:0% +then you can just do it for example the +canonical + + align:start position:0% +canonical + + + align:start position:0% +canonical +so the canonical momentum + + align:start position:0% +so the canonical momentum + + + align:start position:0% +so the canonical momentum +conjugate to a mu + + align:start position:0% +conjugate to a mu + + + align:start position:0% +conjugate to a mu +would be just a mu Dot + + align:start position:0% +would be just a mu Dot + + + align:start position:0% +would be just a mu Dot +okay just a DOT + + align:start position:0% +okay just a DOT + + + align:start position:0% +okay just a DOT +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and uh um yeah so so the canonical + + align:start position:0% +and uh um yeah so so the canonical + + + align:start position:0% +and uh um yeah so so the canonical +connotation condition + + align:start position:0% +connotation condition + + + align:start position:0% +connotation condition +then it's given by + + align:start position:0% + + + + align:start position:0% + +and then we can also just + + align:start position:0% +and then we can also just + + + align:start position:0% +and then we can also just +straightforwardly write down + + align:start position:0% + + + + align:start position:0% + +a mule + + align:start position:0% + + + + align:start position:0% + +the expansion for the the operator + + align:start position:0% +the expansion for the the operator + + + align:start position:0% +the expansion for the the operator +expansion for for a mu + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so um + + align:start position:0% +so um + + + align:start position:0% +so um +so we have four of them + + align:start position:0% +so we have four of them + + + align:start position:0% +so we have four of them +so again we will + + align:start position:0% +so again we will + + + align:start position:0% +so again we will +instead writing them as four Mastery + + align:start position:0% +instead writing them as four Mastery + + + align:start position:0% +instead writing them as four Mastery +scalar we will as we did before for the + + align:start position:0% +scalar we will as we did before for the + + + align:start position:0% +scalar we will as we did before for the +mark for the coolant gauge case we + + align:start position:0% +mark for the coolant gauge case we + + + align:start position:0% +mark for the coolant gauge case we +introduced a polarization Vector okay so + + align:start position:0% +introduced a polarization Vector okay so + + + align:start position:0% +introduced a polarization Vector okay so +we will introduce the prediction Vector + + align:start position:0% +we will introduce the prediction Vector + + + align:start position:0% +we will introduce the prediction Vector +so there are four possible since there + + align:start position:0% +so there are four possible since there + + + align:start position:0% +so there are four possible since there +are four components so there are four + + align:start position:0% +are four components so there are four + + + align:start position:0% +are four components so there are four +possible correlations + + align:start position:0% + + + + align:start position:0% + +times + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we just get that + + align:start position:0% +so we just get that + + + align:start position:0% +so we just get that +so + + align:start position:0% +so + + + align:start position:0% +so +so this Epsilon mu + + align:start position:0% +so this Epsilon mu + + + align:start position:0% +so this Epsilon mu +Alpha + + align:start position:0% +Alpha + + + align:start position:0% +Alpha +for Alpha equal to zero one two three so + + align:start position:0% +for Alpha equal to zero one two three so + + + align:start position:0% +for Alpha equal to zero one two three so +these are four polarization vectors okay + + align:start position:0% + + + + align:start position:0% + +so simplistic + + align:start position:0% +so simplistic + + + align:start position:0% +so simplistic +you can choose you can just choose say + + align:start position:0% +you can choose you can just choose say + + + align:start position:0% +you can choose you can just choose say +one zero zero zero zero one zero zero + + align:start position:0% +one zero zero zero zero one zero zero + + + align:start position:0% +one zero zero zero zero one zero zero +Etc and in that case and then then this + + align:start position:0% +Etc and in that case and then then this + + + align:start position:0% +Etc and in that case and then then this +just like for the coupled scalar okay + + align:start position:0% +just like for the coupled scalar okay + + + align:start position:0% +just like for the coupled scalar okay +but but but this way introduce a + + align:start position:0% +but but but this way introduce a + + + align:start position:0% +but but but this way introduce a +position Vector allows me to write them + + align:start position:0% +position Vector allows me to write them + + + align:start position:0% +position Vector allows me to write them +in a more General way + + align:start position:0% + + + + align:start position:0% + +so we normally pick + + align:start position:0% + + + + align:start position:0% + +Poland + + align:start position:0% +Poland + + + align:start position:0% +Poland +the the nearest validation Vector just + + align:start position:0% +the the nearest validation Vector just + + + align:start position:0% +the the nearest validation Vector just +to be along the time Direction + + align:start position:0% + + + + align:start position:0% + +okay so just along the time Direction + + align:start position:0% +okay so just along the time Direction + + + align:start position:0% +okay so just along the time Direction +and then then we also introduce + + align:start position:0% +and then then we also introduce + + + align:start position:0% +and then then we also introduce +a lot of + + align:start position:0% +a lot of + + + align:start position:0% +a lot of +so so the number three we introduced to + + align:start position:0% +so so the number three we introduced to + + + align:start position:0% +so so the number three we introduced to +be proportional + + align:start position:0% +be proportional + + + align:start position:0% +be proportional +to the direction of the momentum + + align:start position:0% + + + + align:start position:0% + +okay so this is proportional to the + + align:start position:0% +okay so this is proportional to the + + + align:start position:0% +okay so this is proportional to the +parallel to the momentum + + align:start position:0% +parallel to the momentum + + + align:start position:0% +parallel to the momentum +to the spatial momentum so the K mu + + align:start position:0% +to the spatial momentum so the K mu + + + align:start position:0% +to the spatial momentum so the K mu +here would be + + align:start position:0% +here would be + + + align:start position:0% +here would be +because this is Mercedes + + align:start position:0% +because this is Mercedes + + + align:start position:0% +because this is Mercedes +so we just have this okay so so the + + align:start position:0% +so we just have this okay so so the + + + align:start position:0% +so we just have this okay so so the +zeros component is just equal to the + + align:start position:0% +zeros component is just equal to the + + + align:start position:0% +zeros component is just equal to the +magnitude of K + + align:start position:0% +magnitude of K + + + align:start position:0% +magnitude of K +and then then + + align:start position:0% +and then then + + + align:start position:0% +and then then +um + + align:start position:0% +um + + + align:start position:0% +um +then we take the uh Epsilon one two + + align:start position:0% +then we take the uh Epsilon one two + + + align:start position:0% +then we take the uh Epsilon one two +Epsilon mu then one Q + + align:start position:0% +Epsilon mu then one Q + + + align:start position:0% +Epsilon mu then one Q +to be say orthogonal + + align:start position:0% +to be say orthogonal + + + align:start position:0% +to be say orthogonal +to the momentum okay + + align:start position:0% + + + + align:start position:0% + +so these are called the transverse + + align:start position:0% + + + + align:start position:0% + +authorizations + + align:start position:0% + + + + align:start position:0% + +so we take them also to be + + align:start position:0% +so we take them also to be + + + align:start position:0% +so we take them also to be +keep your orthogonal to to to those + + align:start position:0% +keep your orthogonal to to to those + + + align:start position:0% +keep your orthogonal to to to those +component means there's no no the time + + align:start position:0% +component means there's no no the time + + + align:start position:0% +component means there's no no the time +the time component for when Q will be + + align:start position:0% +the time component for when Q will be + + + align:start position:0% +the time component for when Q will be +zero two okay and then also should be uh + + align:start position:0% +zero two okay and then also should be uh + + + align:start position:0% +zero two okay and then also should be uh +proportional uh should also be uh also + + align:start position:0% +proportional uh should also be uh also + + + align:start position:0% +proportional uh should also be uh also +going to the moment + + align:start position:0% +going to the moment + + + align:start position:0% +going to the moment +and uh so um + + align:start position:0% +and uh so um + + + align:start position:0% +and uh so um +yeah so we um + + align:start position:0% +yeah so we um + + + align:start position:0% +yeah so we um +take + + align:start position:0% +take + + + align:start position:0% +take +also them to be orthogonal to each other + + align:start position:0% + + + + align:start position:0% + +material So Gone to each other + + align:start position:0% +material So Gone to each other + + + align:start position:0% +material So Gone to each other +this is also + + align:start position:0% + + + + align:start position:0% + +this is like the normal + + align:start position:0% +this is like the normal + + + align:start position:0% +this is like the normal +condition + + align:start position:0% + + + + align:start position:0% + +okay to take these spaces to be also + + align:start position:0% +okay to take these spaces to be also + + + align:start position:0% +okay to take these spaces to be also +normal and then this is also complete + + align:start position:0% +normal and then this is also complete + + + align:start position:0% +normal and then this is also complete +means that if I + + align:start position:0% +means that if I + + + align:start position:0% +means that if I +sum over different Alpha and beta + + align:start position:0% + + + + align:start position:0% + +and actually I get it back to Italy mu + + align:start position:0% +and actually I get it back to Italy mu + + + align:start position:0% +and actually I get it back to Italy mu +okay + + align:start position:0% + + + + align:start position:0% + +so this is called complete list + + align:start position:0% +so this is called complete list + + + align:start position:0% +so this is called complete list +so they form a complete basis okay + + align:start position:0% +so they form a complete basis okay + + + align:start position:0% +so they form a complete basis okay +any Lorenz Vector can be expanded in + + align:start position:0% +any Lorenz Vector can be expanded in + + + align:start position:0% +any Lorenz Vector can be expanded in +terms of them + + align:start position:0% +terms of them + + + align:start position:0% +terms of them +okay + + align:start position:0% + + + + align:start position:0% + +so so if we take say k to be the Z + + align:start position:0% +so so if we take say k to be the Z + + + align:start position:0% +so so if we take say k to be the Z +Direction + + align:start position:0% + + + + align:start position:0% + +then the simplest choice would be say + + align:start position:0% +then the simplest choice would be say + + + align:start position:0% +then the simplest choice would be say +just to + + align:start position:0% + + + + align:start position:0% + +so we just have that + + align:start position:0% + + + + align:start position:0% + +okay so this is simplist but you can + + align:start position:0% +okay so this is simplist but you can + + + align:start position:0% +okay so this is simplist but you can +consider more General + + align:start position:0% +consider more General + + + align:start position:0% +consider more General +authorization okay + + align:start position:0% + + + + align:start position:0% + +and so now if you plug in this + + align:start position:0% + + + + align:start position:0% + +expansion as we do for the scalar and + + align:start position:0% +expansion as we do for the scalar and + + + align:start position:0% +expansion as we do for the scalar and +then you plug it back to that + + align:start position:0% +then you plug it back to that + + + align:start position:0% +then you plug it back to that +commutation relation + + align:start position:0% +commutation relation + + + align:start position:0% +commutation relation +and then you will get a commutation + + align:start position:0% +and then you will get a commutation + + + align:start position:0% +and then you will get a commutation +relation with a so this is + + align:start position:0% +relation with a so this is + + + align:start position:0% +relation with a so this is +straightforward + + align:start position:0% +straightforward + + + align:start position:0% +straightforward +so if we call this equation star + + align:start position:0% +so if we call this equation star + + + align:start position:0% +so if we call this equation star +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +star + + align:start position:0% +star + + + align:start position:0% +star +this equation star + + align:start position:0% + + + + align:start position:0% + +so plug + + align:start position:0% + + + + align:start position:0% + +star + + align:start position:0% + + + + align:start position:0% + +and then we get the + + align:start position:0% + + + + align:start position:0% + +AK + + align:start position:0% +AK + + + align:start position:0% +AK +Alpha + + align:start position:0% +Alpha + + + align:start position:0% +Alpha +AK Prime + + align:start position:0% +AK Prime + + + align:start position:0% +AK Prime +beta + + align:start position:0% + + + + align:start position:0% + +dagger + + align:start position:0% +dagger + + + align:start position:0% +dagger +should be equal to + + align:start position:0% +should be equal to + + + align:start position:0% +should be equal to +ether Alpha Beta + + align:start position:0% +ether Alpha Beta + + + align:start position:0% +ether Alpha Beta +2 by Cube + + align:start position:0% + + + + align:start position:0% + +Prime okay and the rest + + align:start position:0% +Prime okay and the rest + + + align:start position:0% +Prime okay and the rest +the rest computers are all zero + + align:start position:0% +the rest computers are all zero + + + align:start position:0% +the rest computers are all zero +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and and then you can Define the vacuum + + align:start position:0% + + + + align:start position:0% + +Define the iso violated by + + align:start position:0% +Define the iso violated by + + + align:start position:0% +Define the iso violated by +all the + + align:start position:0% +all the + + + align:start position:0% +all the +Papas + + align:start position:0% +Papas + + + align:start position:0% +Papas +okay for any Alpha and the k + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so and I will + + align:start position:0% +so and I will + + + align:start position:0% +so and I will +introduce the human space + + align:start position:0% +introduce the human space + + + align:start position:0% +introduce the human space +I call it h Peak + + align:start position:0% +I call it h Peak + + + align:start position:0% +I call it h Peak +to be the + + align:start position:0% +to be the + + + align:start position:0% +to be the +PSI + + align:start position:0% +PSI + + + align:start position:0% +PSI +the connection of + + align:start position:0% +the connection of + + + align:start position:0% +the connection of +the connection of the site built by + + align:start position:0% +the connection of the site built by + + + align:start position:0% +the connection of the site built by +acting + + align:start position:0% + + + + align:start position:0% + +AK + + align:start position:0% +AK + + + align:start position:0% +AK +Alpha dagger + + align:start position:0% +Alpha dagger + + + align:start position:0% +Alpha dagger +on zero okay + + align:start position:0% +on zero okay + + + align:start position:0% +on zero okay +so so so you can just + + align:start position:0% +so so so you can just + + + align:start position:0% +so so so you can just +add arbitrary number of them + + align:start position:0% +add arbitrary number of them + + + align:start position:0% +add arbitrary number of them +on zero then you get your help space so + + align:start position:0% +on zero then you get your help space so + + + align:start position:0% +on zero then you get your help space so +we'll call this hillbrow space to be my + + align:start position:0% +we'll call this hillbrow space to be my + + + align:start position:0% +we'll call this hillbrow space to be my +big cube of space and you will see uh + + align:start position:0% +big cube of space and you will see uh + + + align:start position:0% +big cube of space and you will see uh +the reason + + align:start position:0% +the reason + + + align:start position:0% +the reason +we do that okay so later we will see why + + align:start position:0% +we do that okay so later we will see why + + + align:start position:0% +we do that okay so later we will see why +we call this HP + + align:start position:0% +we call this HP + + + align:start position:0% +we call this HP +so this seemingly all fine + + align:start position:0% +so this seemingly all fine + + + align:start position:0% +so this seemingly all fine +but of course their problems this cannot + + align:start position:0% +but of course their problems this cannot + + + align:start position:0% +but of course their problems this cannot +be right + + align:start position:0% +be right + + + align:start position:0% +be right +because the Maxwell Theory we said only + + align:start position:0% +because the Maxwell Theory we said only + + + align:start position:0% +because the Maxwell Theory we said only +have two transverse degrees freedom but + + align:start position:0% +have two transverse degrees freedom but + + + align:start position:0% +have two transverse degrees freedom but +here we have four okay we have four + + align:start position:0% +here we have four okay we have four + + + align:start position:0% +here we have four okay we have four +methods with a degree stream we must + + align:start position:0% +methods with a degree stream we must + + + align:start position:0% +methods with a degree stream we must +have too many okay + + align:start position:0% +have too many okay + + + align:start position:0% +have too many okay +and indeed + + align:start position:0% +and indeed + + + align:start position:0% +and indeed +you see there here are problems + + align:start position:0% +you see there here are problems + + + align:start position:0% +you see there here are problems +so one problem is the following + + align:start position:0% +so one problem is the following + + + align:start position:0% +so one problem is the following +okay + + align:start position:0% + + + + align:start position:0% + +so one problem is falling + + align:start position:0% + + + + align:start position:0% + +so there are problems + + align:start position:0% + + + + align:start position:0% + +so one problem yeah so the deal so the + + align:start position:0% +so one problem yeah so the deal so the + + + align:start position:0% +so one problem yeah so the deal so the +problem is that we have uh we have four + + align:start position:0% +problem is that we have uh we have four + + + align:start position:0% +problem is that we have uh we have four +masses + + align:start position:0% +masses + + + align:start position:0% +masses +degree freedom + + align:start position:0% + + + + align:start position:0% + +too too many okay + + align:start position:0% + + + + align:start position:0% + +okay so we should we know that we only + + align:start position:0% +okay so we should we know that we only + + + align:start position:0% +okay so we should we know that we only +should it should only have two + + align:start position:0% +should it should only have two + + + align:start position:0% +should it should only have two +and the second you see that this is a + + align:start position:0% +and the second you see that this is a + + + align:start position:0% +and the second you see that this is a +have a is problematic + + align:start position:0% + + + + align:start position:0% + +he said you notice so here we have ETA + + align:start position:0% +he said you notice so here we have ETA + + + align:start position:0% +he said you notice so here we have ETA +Alpha Beta e to Mu mu so this is all + + align:start position:0% +Alpha Beta e to Mu mu so this is all + + + align:start position:0% +Alpha Beta e to Mu mu so this is all +just from Lorenz covariance okay + + align:start position:0% +just from Lorenz covariance okay + + + align:start position:0% +just from Lorenz covariance okay +so but this is Alpha Beta + + align:start position:0% +so but this is Alpha Beta + + + align:start position:0% +so but this is Alpha Beta +is problematic because + + align:start position:0% +is problematic because + + + align:start position:0% +is problematic because +if you look at the commutator + + align:start position:0% + + + + align:start position:0% + +for ak0 okay so the zeros are are + + align:start position:0% +for ak0 okay so the zeros are are + + + align:start position:0% +for ak0 okay so the zeros are are +operation + + align:start position:0% + + + + align:start position:0% + +then you have + + align:start position:0% +then you have + + + align:start position:0% +then you have +ak0 + + align:start position:0% + + + + align:start position:0% + +AK Prime + + align:start position:0% +AK Prime + + + align:start position:0% +AK Prime +zero dagger + + align:start position:0% +zero dagger + + + align:start position:0% +zero dagger +you go to minus + + align:start position:0% +you go to minus + + + align:start position:0% +you go to minus +two Pi Cube + + align:start position:0% +two Pi Cube + + + align:start position:0% +two Pi Cube +say Delta K minus K Prime + + align:start position:0% + + + + align:start position:0% + +okay you have a minus sign + + align:start position:0% +okay you have a minus sign + + + align:start position:0% +okay you have a minus sign +okay + + align:start position:0% + + + + align:start position:0% + +so this is problematic because if we + + align:start position:0% +so this is problematic because if we + + + align:start position:0% +so this is problematic because if we +say create particles + + align:start position:0% +say create particles + + + align:start position:0% +say create particles +say if we create the particles + + align:start position:0% +say if we create the particles + + + align:start position:0% +say if we create the particles +by + + align:start position:0% + + + + align:start position:0% + +say um + + align:start position:0% +say um + + + align:start position:0% +say um +by acting + + align:start position:0% +by acting + + + align:start position:0% +by acting +Say by acting on a k + + align:start position:0% +Say by acting on a k + + + align:start position:0% +Say by acting on a k +Alpha dagger on the Zero + + align:start position:0% + + + + align:start position:0% + +and then you find because of this minus + + align:start position:0% +and then you find because of this minus + + + align:start position:0% +and then you find because of this minus +sign + + align:start position:0% + + + + align:start position:0% + +so yeah so this create particle + + align:start position:0% + + + + align:start position:0% + +for addition + + align:start position:0% + + + + align:start position:0% + +Alpha + + align:start position:0% +Alpha + + + align:start position:0% +Alpha +mu okay + + align:start position:0% +mu okay + + + align:start position:0% +mu okay +so now because of this minus sign you + + align:start position:0% +so now because of this minus sign you + + + align:start position:0% +so now because of this minus sign you +see that the if we look at the overlap + + align:start position:0% +see that the if we look at the overlap + + + align:start position:0% +see that the if we look at the overlap +between uh the particle with the zeros + + align:start position:0% +between uh the particle with the zeros + + + align:start position:0% +between uh the particle with the zeros +polarization + + align:start position:0% +polarization + + + align:start position:0% +polarization +okay so if we look at k + + align:start position:0% +okay so if we look at k + + + align:start position:0% +okay so if we look at k + + align:start position:0% + + + align:start position:0% +with some K Prime + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then because of this minus sign + + align:start position:0% +and then because of this minus sign + + + align:start position:0% +and then because of this minus sign +we have minus + + align:start position:0% +we have minus + + + align:start position:0% +we have minus +okay so this will be proportional to + + align:start position:0% +okay so this will be proportional to + + + align:start position:0% +okay so this will be proportional to +minus 2 pi Cube + + align:start position:0% +minus 2 pi Cube + + + align:start position:0% +minus 2 pi Cube +in the Q + + align:start position:0% +in the Q + + + align:start position:0% +in the Q +A minus + + align:start position:0% + + + + align:start position:0% + +so this is smaller than you + + align:start position:0% +so this is smaller than you + + + align:start position:0% +so this is smaller than you +okay so you see actually + + align:start position:0% +okay so you see actually + + + align:start position:0% +okay so you see actually +the in the product + + align:start position:0% +the in the product + + + align:start position:0% +the in the product +okay so that means that this state + + align:start position:0% +okay so that means that this state + + + align:start position:0% +okay so that means that this state +actually has negative law + + align:start position:0% + + + + align:start position:0% + +okay that means this stays a relative + + align:start position:0% +okay that means this stays a relative + + + align:start position:0% +okay that means this stays a relative +law + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +but this is actually + + align:start position:0% +but this is actually + + + align:start position:0% +but this is actually +a good sign so this is another way to + + align:start position:0% +a good sign so this is another way to + + + align:start position:0% +a good sign so this is another way to +see that this is we have too many good + + align:start position:0% +see that this is we have too many good + + + align:start position:0% +see that this is we have too many good +freedom + + align:start position:0% +freedom + + + align:start position:0% +freedom +okay so that means not all the good + + align:start position:0% +okay so that means not all the good + + + align:start position:0% +okay so that means not all the good +Freedom here can be physical + + align:start position:0% +Freedom here can be physical + + + align:start position:0% +Freedom here can be physical +okay so here I just tell you there are + + align:start position:0% +okay so here I just tell you there are + + + align:start position:0% +okay so here I just tell you there are +some legal filament here must be + + align:start position:0% +some legal filament here must be + + + align:start position:0% +some legal filament here must be +unphysical because they have laxative + + align:start position:0% +unphysical because they have laxative + + + align:start position:0% +unphysical because they have laxative +law + + align:start position:0% +law + + + align:start position:0% +law +okay the states they create a uh have + + align:start position:0% +okay the states they create a uh have + + + align:start position:0% +okay the states they create a uh have +active Norm so so they cannot really + + align:start position:0% +active Norm so so they cannot really + + + align:start position:0% +active Norm so so they cannot really +correspond into gender in physical + + align:start position:0% +correspond into gender in physical + + + align:start position:0% +correspond into gender in physical +States + + align:start position:0% +States + + + align:start position:0% +States +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +but those problems should not worry us + + align:start position:0% +but those problems should not worry us + + + align:start position:0% +but those problems should not worry us +because so far what we have done + + align:start position:0% +because so far what we have done + + + align:start position:0% +because so far what we have done +is to quantize this series + + align:start position:0% + + + + align:start position:0% + +okay so far we have done is to contact + + align:start position:0% +okay so far we have done is to contact + + + align:start position:0% +okay so far we have done is to contact +this Theory but this series is not the + + align:start position:0% +this Theory but this series is not the + + + align:start position:0% +this Theory but this series is not the +Maxwell series + + align:start position:0% +Maxwell series + + + align:start position:0% +Maxwell series +okay to get the Maxwell Theory we have + + align:start position:0% +okay to get the Maxwell Theory we have + + + align:start position:0% +okay to get the Maxwell Theory we have +to do two more steps + + align:start position:0% +to do two more steps + + + align:start position:0% +to do two more steps +one more step one step is to + + align:start position:0% +one more step one step is to + + + align:start position:0% +one more step one step is to +impose conditions so that make sure this + + align:start position:0% +impose conditions so that make sure this + + + align:start position:0% +impose conditions so that make sure this +particular mu equal to zero because we + + align:start position:0% +particular mu equal to zero because we + + + align:start position:0% +particular mu equal to zero because we +haven't fixed the gauge okay the second + + align:start position:0% +haven't fixed the gauge okay the second + + + align:start position:0% +haven't fixed the gauge okay the second +condition is we mentioned before + + align:start position:0% +condition is we mentioned before + + + align:start position:0% +condition is we mentioned before +so there are two more things we need to + + align:start position:0% +so there are two more things we need to + + + align:start position:0% +so there are two more things we need to +do + + align:start position:0% + + + + align:start position:0% + +to do + + align:start position:0% +to do + + + align:start position:0% +to do +so first + + align:start position:0% +so first + + + align:start position:0% +so first +you said we need to ensure + + align:start position:0% +you said we need to ensure + + + align:start position:0% +you said we need to ensure +the gauge + + align:start position:0% + + + + align:start position:0% + +mu a mu equal to zero + + align:start position:0% +mu a mu equal to zero + + + align:start position:0% +mu a mu equal to zero +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the the second thing is we mentioned + + align:start position:0% +the the second thing is we mentioned + + + align:start position:0% +the the second thing is we mentioned +before + + align:start position:0% +before + + + align:start position:0% +before +you said after fix fixed in the Lorenz + + align:start position:0% +you said after fix fixed in the Lorenz + + + align:start position:0% +you said after fix fixed in the Lorenz +cage + + align:start position:0% +cage + + + align:start position:0% +cage +they're still ready to engage the good + + align:start position:0% +they're still ready to engage the good + + + align:start position:0% +they're still ready to engage the good +Freedom left + + align:start position:0% +Freedom left + + + align:start position:0% +Freedom left +and we have to fix the + + align:start position:0% +and we have to fix the + + + align:start position:0% +and we have to fix the +the residue + + align:start position:0% + + + + align:start position:0% + +gauge freedom in the Lawrence cage + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% + + + + align:start position:0% + +so when we do do this then you will get + + align:start position:0% +so when we do do this then you will get + + + align:start position:0% +so when we do do this then you will get +a physical healable space + + align:start position:0% +a physical healable space + + + align:start position:0% +a physical healable space +okay and you will get a physical + + align:start position:0% +okay and you will get a physical + + + align:start position:0% +okay and you will get a physical +healable space and this physical + + align:start position:0% +healable space and this physical + + + align:start position:0% +healable space and this physical +healable space you we will see you will + + align:start position:0% +healable space you we will see you will + + + align:start position:0% +healable space you we will see you will +see that will only contain indeed two + + align:start position:0% +see that will only contain indeed two + + + align:start position:0% +see that will only contain indeed two +transverse methodistic with field + + align:start position:0% +transverse methodistic with field + + + align:start position:0% +transverse methodistic with field +okay and the two are the good Freedom + + align:start position:0% +okay and the two are the good Freedom + + + align:start position:0% +okay and the two are the good Freedom +here are are got rid of + + align:start position:0% +here are are got rid of + + + align:start position:0% +here are are got rid of +okay I got the read-off + + align:start position:0% +okay I got the read-off + + + align:start position:0% +okay I got the read-off +so so + + align:start position:0% +so so + + + align:start position:0% +so so +um + + align:start position:0% +um + + + align:start position:0% +um +past + + align:start position:0% +past + + + align:start position:0% +past +I describe those procedure in detail in + + align:start position:0% +I describe those procedure in detail in + + + align:start position:0% +I describe those procedure in detail in +class + + align:start position:0% +class + + + align:start position:0% +class +but actually that didn't have very good + + align:start position:0% +but actually that didn't have very good + + + align:start position:0% +but actually that didn't have very good +effect okay + + align:start position:0% +effect okay + + + align:start position:0% +effect okay +so so later I put it in your preset uh + + align:start position:0% +so so later I put it in your preset uh + + + align:start position:0% +so so later I put it in your preset uh +actually I think it worked better so + + align:start position:0% +actually I think it worked better so + + + align:start position:0% +actually I think it worked better so +force you to go through it and to think + + align:start position:0% +force you to go through it and to think + + + align:start position:0% +force you to go through it and to think +through it how do you how to do these + + align:start position:0% +through it how do you how to do these + + + align:start position:0% +through it how do you how to do these +two steps okay a big because those steps + + align:start position:0% +two steps okay a big because those steps + + + align:start position:0% +two steps okay a big because those steps +there they're a lot difficult uh uh uh + + align:start position:0% +there they're a lot difficult uh uh uh + + + align:start position:0% +there they're a lot difficult uh uh uh +technically but you need to think + + align:start position:0% +technically but you need to think + + + align:start position:0% +technically but you need to think +carefully okay and this thing + + align:start position:0% +carefully okay and this thing + + + align:start position:0% +carefully okay and this thing +so let me just make some comment on this + + align:start position:0% +so let me just make some comment on this + + + align:start position:0% +so let me just make some comment on this +step + + align:start position:0% + + + + align:start position:0% + +so recall in the in the coolant gauge + + align:start position:0% + + + + align:start position:0% + +so in the coolant gauge + + align:start position:0% + + + + align:start position:0% + +so recall + + align:start position:0% + + + + align:start position:0% + +in Colon gauge + + align:start position:0% + + + + align:start position:0% + +we impose this condition + + align:start position:0% + + + + align:start position:0% + +we essentially solve this condition we + + align:start position:0% +we essentially solve this condition we + + + align:start position:0% +we essentially solve this condition we +impose this condition so classically we + + align:start position:0% +impose this condition so classically we + + + align:start position:0% +impose this condition so classically we +impose this condition essentially as + + align:start position:0% +impose this condition essentially as + + + align:start position:0% +impose this condition essentially as +part of equation motion + + align:start position:0% +part of equation motion + + + align:start position:0% +part of equation motion +and we solve the the a which satisfy + + align:start position:0% +and we solve the the a which satisfy + + + align:start position:0% +and we solve the the a which satisfy +this condition which is governed into to + + align:start position:0% +this condition which is governed into to + + + align:start position:0% +this condition which is governed into to +transverse a okay + + align:start position:0% +transverse a okay + + + align:start position:0% +transverse a okay +and then Quantum mechanically + + align:start position:0% +and then Quantum mechanically + + + align:start position:0% +and then Quantum mechanically +because we impose it as a a classical + + align:start position:0% +because we impose it as a a classical + + + align:start position:0% +because we impose it as a a classical +equation we impose it as part of + + align:start position:0% +equation we impose it as part of + + + align:start position:0% +equation we impose it as part of +equation motion a classically so Quantum + + align:start position:0% +equation motion a classically so Quantum + + + align:start position:0% +equation motion a classically so Quantum +mechanically this become an operating + + align:start position:0% +mechanically this become an operating + + + align:start position:0% +mechanically this become an operating +equation which we impose on operators + + align:start position:0% +equation which we impose on operators + + + align:start position:0% +equation which we impose on operators +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but in this case + + align:start position:0% +but in this case + + + align:start position:0% +but in this case +we can no longer impose + + align:start position:0% +we can no longer impose + + + align:start position:0% +we can no longer impose +but in Lawrence cage so so this leads to + + align:start position:0% +but in Lawrence cage so so this leads to + + + align:start position:0% +but in Lawrence cage so so this leads to +the operating equation + + align:start position:0% + + + + align:start position:0% + +but in the Lorenz gauge + + align:start position:0% + + + + align:start position:0% + +we cannot impose + + align:start position:0% + + + + align:start position:0% + +mu a mu as the operator equation + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +because + + align:start position:0% + + + + align:start position:0% + +equation motion already the almost imply + + align:start position:0% +equation motion already the almost imply + + + align:start position:0% +equation motion already the almost imply +this is equal to zero we just have to + + align:start position:0% +this is equal to zero we just have to + + + align:start position:0% +this is equal to zero we just have to +impose some boundary condition to ensure + + align:start position:0% +impose some boundary condition to ensure + + + align:start position:0% +impose some boundary condition to ensure +that indeed this this equation only have + + align:start position:0% +that indeed this this equation only have + + + align:start position:0% +that indeed this this equation only have +Solutions corresponding to particular mu + + align:start position:0% +Solutions corresponding to particular mu + + + align:start position:0% +Solutions corresponding to particular mu +to zero okay so if you impose this + + align:start position:0% +to zero okay so if you impose this + + + align:start position:0% +to zero okay so if you impose this +secretly as the uh uh uh + + align:start position:0% + + + + align:start position:0% + +yeah so so so you only need to impose + + align:start position:0% +yeah so so so you only need to impose + + + align:start position:0% +yeah so so so you only need to impose +the respondary condition + + align:start position:0% +the respondary condition + + + align:start position:0% +the respondary condition +so Quantum mechanically okay so that + + align:start position:0% +so Quantum mechanically okay so that + + + align:start position:0% +so Quantum mechanically okay so that +implies we cannot impose this as operate + + align:start position:0% +implies we cannot impose this as operate + + + align:start position:0% +implies we cannot impose this as operate +equation indeed you are showing your P + + align:start position:0% +equation indeed you are showing your P + + + align:start position:0% +equation indeed you are showing your P +set and it will be inconsistent if you + + align:start position:0% +set and it will be inconsistent if you + + + align:start position:0% +set and it will be inconsistent if you +impose this as operating equation + + align:start position:0% +impose this as operating equation + + + align:start position:0% +impose this as operating equation +so so what does it mean + + align:start position:0% +so so what does it mean + + + align:start position:0% +so so what does it mean +at the quantum level corresponding to + + align:start position:0% +at the quantum level corresponding to + + + align:start position:0% +at the quantum level corresponding to +classically you impose the boundary + + align:start position:0% +classically you impose the boundary + + + align:start position:0% +classically you impose the boundary +condition + + align:start position:0% +condition + + + align:start position:0% +condition +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so classically impulse boundary + + align:start position:0% +so so classically impulse boundary + + + align:start position:0% +so so classically impulse boundary +condition limit possible configurations + + align:start position:0% +condition limit possible configurations + + + align:start position:0% +condition limit possible configurations +you can have + + align:start position:0% +you can have + + + align:start position:0% +you can have +okay name it possible configurations you + + align:start position:0% +okay name it possible configurations you + + + align:start position:0% +okay name it possible configurations you +can have at the quantum mechanical level + + align:start position:0% +can have at the quantum mechanical level + + + align:start position:0% +can have at the quantum mechanical level +corresponding to restriction on the + + align:start position:0% +corresponding to restriction on the + + + align:start position:0% +corresponding to restriction on the +states + + align:start position:0% +states + + + align:start position:0% +states +so so on the quantum level it turns out + + align:start position:0% +so so on the quantum level it turns out + + + align:start position:0% +so so on the quantum level it turns out +the right thing to do is to impose this + + align:start position:0% +the right thing to do is to impose this + + + align:start position:0% +the right thing to do is to impose this +kind of condition + + align:start position:0% +kind of condition + + + align:start position:0% +kind of condition +understate + + align:start position:0% +understate + + + align:start position:0% +understate +require your state + + align:start position:0% +require your state + + + align:start position:0% +require your state +to be annihilated by something like this + + align:start position:0% +to be annihilated by something like this + + + align:start position:0% +to be annihilated by something like this +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but actually the story is more subtle + + align:start position:0% +but actually the story is more subtle + + + align:start position:0% +but actually the story is more subtle +than that + + align:start position:0% +than that + + + align:start position:0% +than that +you can just require the state + + align:start position:0% +you can just require the state + + + align:start position:0% +you can just require the state +allocated by this thing actually does + + align:start position:0% +allocated by this thing actually does + + + align:start position:0% +allocated by this thing actually does +not work and so you have to do a little + + align:start position:0% +not work and so you have to do a little + + + align:start position:0% +not work and so you have to do a little +bit more subtle okay so the fund will be + + align:start position:0% +bit more subtle okay so the fund will be + + + align:start position:0% +bit more subtle okay so the fund will be +in your PSAT okay you will go through + + align:start position:0% +in your PSAT okay you will go through + + + align:start position:0% +in your PSAT okay you will go through +that okay you'll go through it + + align:start position:0% +that okay you'll go through it + + + align:start position:0% +that okay you'll go through it +so do you have any questions + + align:start position:0% + + + + align:start position:0% + +yes why is it too much + + align:start position:0% +yes why is it too much + + + align:start position:0% +yes why is it too much +I guess make sense + + align:start position:0% + + + + align:start position:0% + +yeah so classically does not matter + + align:start position:0% +yeah so classically does not matter + + + align:start position:0% +yeah so classically does not matter +as a classical it doesn't matter you + + align:start position:0% +as a classical it doesn't matter you + + + align:start position:0% +as a classical it doesn't matter you +just uh but mechanically uh uh you will + + align:start position:0% +just uh but mechanically uh uh you will + + + align:start position:0% +just uh but mechanically uh uh you will +show your pizza if you impose this as a + + align:start position:0% +show your pizza if you impose this as a + + + align:start position:0% +show your pizza if you impose this as a +operating equation then that's + + align:start position:0% +operating equation then that's + + + align:start position:0% +operating equation then that's +incompatible uh results canonical + + align:start position:0% +incompatible uh results canonical + + + align:start position:0% +incompatible uh results canonical +quantitation condition + + align:start position:0% + + + + align:start position:0% + +yeah here I just motivate that + + align:start position:0% +yeah here I just motivate that + + + align:start position:0% +yeah here I just motivate that +classically in order to ensure this you + + align:start position:0% +classically in order to ensure this you + + + align:start position:0% +classically in order to ensure this you +only need to impose the boundary + + align:start position:0% +only need to impose the boundary + + + align:start position:0% +only need to impose the boundary +condition not as the equation motion + + align:start position:0% +condition not as the equation motion + + + align:start position:0% +condition not as the equation motion +yeah so so mechanically we just yeah + + align:start position:0% + + + + align:start position:0% + +other questions yes + + align:start position:0% + + + + align:start position:0% + +uh yeah you will see you will see or or + + align:start position:0% +uh yeah you will see you will see or or + + + align:start position:0% +uh yeah you will see you will see or or +you will see what's happening yeah so it + + align:start position:0% +you will see what's happening yeah so it + + + align:start position:0% +you will see what's happening yeah so it +turns out yeah yeah let me just say one + + align:start position:0% +turns out yeah yeah let me just say one + + + align:start position:0% +turns out yeah yeah let me just say one +more say some words + + align:start position:0% +more say some words + + + align:start position:0% +more say some words +so it turns out when you do this step + + align:start position:0% +so it turns out when you do this step + + + align:start position:0% +so it turns out when you do this step +and then you will eliminate + + align:start position:0% +and then you will eliminate + + + align:start position:0% +and then you will eliminate +so the step one + + align:start position:0% + + + + align:start position:0% + +will eliminate + + align:start position:0% + + + + align:start position:0% + +the active alarm state + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so you find once you impose properly + + align:start position:0% +so so you find once you impose properly + + + align:start position:0% +so so you find once you impose properly +this kind of condition on the stage + + align:start position:0% +this kind of condition on the stage + + + align:start position:0% +this kind of condition on the stage +and you actually eliminate the active + + align:start position:0% +and you actually eliminate the active + + + align:start position:0% +and you actually eliminate the active +loan state + + align:start position:0% +loan state + + + align:start position:0% +loan state +but then you find after you eliminate + + align:start position:0% +but then you find after you eliminate + + + align:start position:0% +but then you find after you eliminate +the active long States + + align:start position:0% +the active long States + + + align:start position:0% +the active long States +in this healable space + + align:start position:0% + + + + align:start position:0% + +in this silver space + + align:start position:0% +in this silver space + + + align:start position:0% +in this silver space +there's still states of zero long + + align:start position:0% +there's still states of zero long + + + align:start position:0% +there's still states of zero long +okay there's still states of zero law + + align:start position:0% +okay there's still states of zero law + + + align:start position:0% +okay there's still states of zero law +and then then when you fix the second + + align:start position:0% +and then then when you fix the second + + + align:start position:0% +and then then when you fix the second +and then you eliminated the the alarm + + align:start position:0% +and then you eliminated the the alarm + + + align:start position:0% +and then you eliminated the the alarm +state + + align:start position:0% + + + + align:start position:0% + +and then you get the + + align:start position:0% +and then you get the + + + align:start position:0% +and then you get the +then you get your physical human space + + align:start position:0% +then you get your physical human space + + + align:start position:0% +then you get your physical human space +because remember in the coolant gauge + + align:start position:0% +because remember in the coolant gauge + + + align:start position:0% +because remember in the coolant gauge +everything just + + align:start position:0% +everything just + + + align:start position:0% +everything just +just a harmonic oscillator uh additional + + align:start position:0% +just a harmonic oscillator uh additional + + + align:start position:0% +just a harmonic oscillator uh additional +de alarm States okay you fix the gauge + + align:start position:0% +de alarm States okay you fix the gauge + + + align:start position:0% +de alarm States okay you fix the gauge +completely but here because you didn't + + align:start position:0% +completely but here because you didn't + + + align:start position:0% +completely but here because you didn't +fix the gauge completely and even after + + align:start position:0% +fix the gauge completely and even after + + + align:start position:0% +fix the gauge completely and even after +you enumerate those negative long State + + align:start position:0% +you enumerate those negative long State + + + align:start position:0% +you enumerate those negative long State +you have zero long States and then they + + align:start position:0% +you have zero long States and then they + + + align:start position:0% +you have zero long States and then they +corresponding to gauge free remain + + align:start position:0% +corresponding to gauge free remain + + + align:start position:0% +corresponding to gauge free remain +engaged freedom and once you get rid of + + align:start position:0% +engaged freedom and once you get rid of + + + align:start position:0% +engaged freedom and once you get rid of +them and then you have your + + align:start position:0% +them and then you have your + + + align:start position:0% +them and then you have your +um yeah + + align:start position:0% + + + + align:start position:0% + +good any questions on this yes + + align:start position:0% + + + + align:start position:0% + +good good good good that's a very good + + align:start position:0% +good good good good that's a very good + + + align:start position:0% +good good good good that's a very good +question which I'm waiting for you to uh + + align:start position:0% +question which I'm waiting for you to uh + + + align:start position:0% +question which I'm waiting for you to uh +to ask uh so so the key thing so you say + + align:start position:0% +to ask uh so so the key thing so you say + + + align:start position:0% +to ask uh so so the key thing so you say +we can certainly can see the four + + align:start position:0% +we can certainly can see the four + + + align:start position:0% +we can certainly can see the four +massive scalar field if I consider + + align:start position:0% +massive scalar field if I consider + + + align:start position:0% +massive scalar field if I consider +format scale field there should not be + + align:start position:0% +format scale field there should not be + + + align:start position:0% +format scale field there should not be +problem okay uh uh why this should be + + align:start position:0% +problem okay uh uh why this should be + + + align:start position:0% +problem okay uh uh why this should be +active long set or zero long state but + + align:start position:0% +active long set or zero long state but + + + align:start position:0% +active long set or zero long state but +the key + + align:start position:0% +the key + + + align:start position:0% +the key +is that here + + align:start position:0% +is that here + + + align:start position:0% +is that here +the state a contract disable allu are + + align:start position:0% +the state a contract disable allu are + + + align:start position:0% +the state a contract disable allu are +contracted using the lorenzie metric + + align:start position:0% +contracted using the lorenzie metric + + + align:start position:0% +contracted using the lorenzie metric +and so if you look at this lagrangian + + align:start position:0% +and so if you look at this lagrangian + + + align:start position:0% +and so if you look at this lagrangian +the zeros components + + align:start position:0% +the zeros components + + + align:start position:0% +the zeros components +actually have the opposite sign + + align:start position:0% +actually have the opposite sign + + + align:start position:0% +actually have the opposite sign +to the standards massive scalar field + + align:start position:0% +to the standards massive scalar field + + + align:start position:0% +to the standards massive scalar field +okay and because of that so this is not + + align:start position:0% +okay and because of that so this is not + + + align:start position:0% +okay and because of that so this is not +your ordinary message scale of field + + align:start position:0% +your ordinary message scale of field + + + align:start position:0% +your ordinary message scale of field +they actually have opposite side in your + + align:start position:0% +they actually have opposite side in your + + + align:start position:0% +they actually have opposite side in your +lagrangea + + align:start position:0% +lagrangea + + + align:start position:0% +lagrangea +but you say oh can we just change the + + align:start position:0% +but you say oh can we just change the + + + align:start position:0% +but you say oh can we just change the +sign for that component you cannot + + align:start position:0% +sign for that component you cannot + + + align:start position:0% +sign for that component you cannot +because we have Lawrence image + + align:start position:0% + + + + align:start position:0% + +so the line symmetry forces you somehow + + align:start position:0% +so the line symmetry forces you somehow + + + align:start position:0% +so the line symmetry forces you somehow +when you reduce the Maxwell Theory to + + align:start position:0% +when you reduce the Maxwell Theory to + + + align:start position:0% +when you reduce the Maxwell Theory to +this four massive scalar and one of them + + align:start position:0% +this four massive scalar and one of them + + + align:start position:0% +this four massive scalar and one of them +have the wrong side so that's why so + + align:start position:0% +have the wrong side so that's why so + + + align:start position:0% +have the wrong side so that's why so +that the wrong side is related by you + + align:start position:0% +that the wrong side is related by you + + + align:start position:0% +that the wrong side is related by you +have the wrong side here + + align:start position:0% +have the wrong side here + + + align:start position:0% +have the wrong side here +okay and why yes the same kind of the + + align:start position:0% +okay and why yes the same kind of the + + + align:start position:0% +okay and why yes the same kind of the +Lorenz covariance tell you here is + + align:start position:0% +Lorenz covariance tell you here is + + + align:start position:0% +Lorenz covariance tell you here is +either alphabet rather than Delta + + align:start position:0% +either alphabet rather than Delta + + + align:start position:0% +either alphabet rather than Delta +alphabet + + align:start position:0% +alphabet + + + align:start position:0% +alphabet +on the Delta alphabet + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% +good + + + align:start position:0% +good +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so this concludes our discussion over + + align:start position:0% +so so this concludes our discussion over + + + align:start position:0% +so so this concludes our discussion over +the canonical conversation for the + + align:start position:0% +the canonical conversation for the + + + align:start position:0% +the canonical conversation for the +Maxwell Theory + + align:start position:0% +Maxwell Theory + + + align:start position:0% +Maxwell Theory +so so here I will quickly describe how + + align:start position:0% +so so here I will quickly describe how + + + align:start position:0% +so so here I will quickly describe how +to do it for the past integral + + align:start position:0% +to do it for the past integral + + + align:start position:0% +to do it for the past integral +and uh so so I will just do it very + + align:start position:0% +and uh so so I will just do it very + + + align:start position:0% +and uh so so I will just do it very +quickly + + align:start position:0% +quickly + + + align:start position:0% +quickly +and uh because the many of the elements + + align:start position:0% +and uh because the many of the elements + + + align:start position:0% +and uh because the many of the elements +of mini before + + align:start position:0% +of mini before + + + align:start position:0% +of mini before +and so I will just point out since which + + align:start position:0% +and so I will just point out since which + + + align:start position:0% +and so I will just point out since which +are + + align:start position:0% +are + + + align:start position:0% +are +new in the uh for the uh for the Maxwell + + align:start position:0% +new in the uh for the uh for the Maxwell + + + align:start position:0% +new in the uh for the uh for the Maxwell +case okay + + align:start position:0% + + + + align:start position:0% + +so we already familiar how to do the + + align:start position:0% +so we already familiar how to do the + + + align:start position:0% +so we already familiar how to do the +past integral + + align:start position:0% +past integral + + + align:start position:0% +past integral +so Maxwell series of free Theory + + align:start position:0% +so Maxwell series of free Theory + + + align:start position:0% +so Maxwell series of free Theory +so in principle will know how to do it + + align:start position:0% +so in principle will know how to do it + + + align:start position:0% +so in principle will know how to do it +so let's just + + align:start position:0% +so let's just + + + align:start position:0% +so let's just +yeah so here let's go back without + + align:start position:0% +yeah so here let's go back without + + + align:start position:0% +yeah so here let's go back without +fixing the gauge first okay so so this + + align:start position:0% +fixing the gauge first okay so so this + + + align:start position:0% +fixing the gauge first okay so so this +is not completely uh uh uh starting from + + align:start position:0% +is not completely uh uh uh starting from + + + align:start position:0% +is not completely uh uh uh starting from +the original just starting from the S + + align:start position:0% +the original just starting from the S + + + align:start position:0% +the original just starting from the S +Maxwell + + align:start position:0% +Maxwell + + + align:start position:0% +Maxwell +equal to minus one quarter + + align:start position:0% + + + + align:start position:0% + +and we mu F me mu okay + + align:start position:0% +and we mu F me mu okay + + + align:start position:0% +and we mu F me mu okay +so let's just go back to this series + + align:start position:0% + + + + align:start position:0% + +um let's go back to this series + + align:start position:0% + + + + align:start position:0% + +and then let's just try to do uh uh uh + + align:start position:0% +and then let's just try to do uh uh uh + + + align:start position:0% +and then let's just try to do uh uh uh +try to see how the marks will uh how the + + align:start position:0% +try to see how the marks will uh how the + + + align:start position:0% +try to see how the marks will uh how the +passing works + + align:start position:0% +passing works + + + align:start position:0% +passing works +so so remember so this is a free series + + align:start position:0% +so so remember so this is a free series + + + align:start position:0% +so so remember so this is a free series +so we can just write down the generating + + align:start position:0% +so we can just write down the generating + + + align:start position:0% +so we can just write down the generating +functional for this Theory + + align:start position:0% +functional for this Theory + + + align:start position:0% +functional for this Theory +and then we can in principle calculate + + align:start position:0% +and then we can in principle calculate + + + align:start position:0% +and then we can in principle calculate +all possible correlation functions here + + align:start position:0% +all possible correlation functions here + + + align:start position:0% +all possible correlation functions here +okay freezer is supposed to be very + + align:start position:0% +okay freezer is supposed to be very + + + align:start position:0% +okay freezer is supposed to be very +simple + + align:start position:0% +simple + + + align:start position:0% +simple +so so we just write down the generating + + align:start position:0% +so so we just write down the generating + + + align:start position:0% +so so we just write down the generating +functional which being integrated over + + align:start position:0% +functional which being integrated over + + + align:start position:0% +functional which being integrated over +all of a mu + + align:start position:0% +all of a mu + + + align:start position:0% +all of a mu +and then we have i s so this Maxwell + + align:start position:0% +and then we have i s so this Maxwell + + + align:start position:0% +and then we have i s so this Maxwell +Theory and then plus then we add the + + align:start position:0% +Theory and then plus then we add the + + + align:start position:0% +Theory and then plus then we add the +source + + align:start position:0% + + + + align:start position:0% + +yeah let me just um + + align:start position:0% +yeah let me just um + + + align:start position:0% +yeah let me just um +so this Jamie will have nothing to do + + align:start position:0% +so this Jamie will have nothing to do + + + align:start position:0% +so this Jamie will have nothing to do +with next magnetic current this is just + + align:start position:0% +with next magnetic current this is just + + + align:start position:0% +with next magnetic current this is just +JMU with the generating function used to + + align:start position:0% +JMU with the generating function used to + + + align:start position:0% +JMU with the generating function used to +taking derivatives okay + + align:start position:0% +taking derivatives okay + + + align:start position:0% +taking derivatives okay +so so so this is just a external source + + align:start position:0% + + + + align:start position:0% + +so so now this is a Gauss integral so in + + align:start position:0% +so so now this is a Gauss integral so in + + + align:start position:0% +so so now this is a Gauss integral so in +principle we can just do the + + align:start position:0% +principle we can just do the + + + align:start position:0% +principle we can just do the +to it okay this is because this is + + align:start position:0% +to it okay this is because this is + + + align:start position:0% +to it okay this is because this is +quadratic and now we are familiar how to + + align:start position:0% +quadratic and now we are familiar how to + + + align:start position:0% +quadratic and now we are familiar how to +do the quadratic integral uh we can just + + align:start position:0% +do the quadratic integral uh we can just + + + align:start position:0% +do the quadratic integral uh we can just +do it okay and to do it is that we write + + align:start position:0% +do it okay and to do it is that we write + + + align:start position:0% +do it okay and to do it is that we write +it always write it in the form + + align:start position:0% +it always write it in the form + + + align:start position:0% +it always write it in the form +uh um + + align:start position:0% + + + + align:start position:0% + +like this + + align:start position:0% + + + + align:start position:0% + +we write it in The Matrix form + + align:start position:0% + + + + align:start position:0% + +okay we write it as a matrix form + + align:start position:0% +okay we write it as a matrix form + + + align:start position:0% +okay we write it as a matrix form +and this Amy this came in milk it just + + align:start position:0% +and this Amy this came in milk it just + + + align:start position:0% +and this Amy this came in milk it just +can be read from here by integration by + + align:start position:0% +can be read from here by integration by + + + align:start position:0% +can be read from here by integration by +part Etc so let me just write down the + + align:start position:0% +part Etc so let me just write down the + + + align:start position:0% +part Etc so let me just write down the +answer + + align:start position:0% +answer + + + align:start position:0% +answer +so this came in mu + + align:start position:0% +so this came in mu + + + align:start position:0% +so this came in mu +just equal to + + align:start position:0% + + + + align:start position:0% + +so let me call this zero + + align:start position:0% +so let me call this zero + + + align:start position:0% +so let me call this zero +because this zero can be mu + + align:start position:0% +because this zero can be mu + + + align:start position:0% +because this zero can be mu +so this just given by partial Square + + align:start position:0% +so this just given by partial Square + + + align:start position:0% +so this just given by partial Square +need to be new + + align:start position:0% +need to be new + + + align:start position:0% +need to be new +minus partial mu partial U + + align:start position:0% + + + + align:start position:0% + +and the data function okay + + align:start position:0% + + + + align:start position:0% + +this partial will only act on X okay + + align:start position:0% +this partial will only act on X okay + + + align:start position:0% +this partial will only act on X okay +only X + + align:start position:0% +only X + + + align:start position:0% +only X +X so so like every we can just so so now + + align:start position:0% +X so so like every we can just so so now + + + align:start position:0% +X so so like every we can just so so now +this is just it's a ghost integral so + + align:start position:0% +this is just it's a ghost integral so + + + align:start position:0% +this is just it's a ghost integral so +you can use principle just directly + + align:start position:0% +you can use principle just directly + + + align:start position:0% +you can use principle just directly +write down the answer + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +actually let me keep this here + + align:start position:0% + + + + align:start position:0% + +so we pretty sure we can just directly + + align:start position:0% +so we pretty sure we can just directly + + + align:start position:0% +so we pretty sure we can just directly +write down the answer just this DJ + + align:start position:0% + + + + align:start position:0% + +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +some number some infinite number which + + align:start position:0% +some number some infinite number which + + + align:start position:0% +some number some infinite number which +will be level care + + align:start position:0% +will be level care + + + align:start position:0% +will be level care +and the exponential + + align:start position:0% + + + + align:start position:0% + +ID for X before y + + align:start position:0% + + + + align:start position:0% + +then J mu + + align:start position:0% + + + + align:start position:0% + +X + + align:start position:0% +X + + + align:start position:0% +X +then the k + + align:start position:0% +then the k + + + align:start position:0% +then the k +zero + + align:start position:0% +zero + + + align:start position:0% +zero +mu mu + + align:start position:0% +mu mu + + + align:start position:0% +mu mu +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um + + align:start position:0% +um + + + align:start position:0% +um +minus one + + align:start position:0% +minus one + + + align:start position:0% +minus one +yeah so let me just write it like this + + align:start position:0% +yeah so let me just write it like this + + + align:start position:0% +yeah so let me just write it like this +okay + + align:start position:0% +okay + + + align:start position:0% +okay +zero minus one + + align:start position:0% +zero minus one + + + align:start position:0% +zero minus one +we knew + + align:start position:0% + + + + align:start position:0% + +x minus y + + align:start position:0% +x minus y + + + align:start position:0% +x minus y +J Nu y + + align:start position:0% +J Nu y + + + align:start position:0% +J Nu y +okay + + align:start position:0% + + + + align:start position:0% + +so so this is just almost exactly the + + align:start position:0% +so so this is just almost exactly the + + + align:start position:0% +so so this is just almost exactly the +same as we do before + + align:start position:0% + + + + align:start position:0% + +so this is like the kernel for your + + align:start position:0% +so this is like the kernel for your + + + align:start position:0% +so this is like the kernel for your +gaussian integral + + align:start position:0% +gaussian integral + + + align:start position:0% +gaussian integral +and you just take the inverse of it + + align:start position:0% +and you just take the inverse of it + + + align:start position:0% +and you just take the inverse of it +and then you contract it with the source + + align:start position:0% +and then you contract it with the source + + + align:start position:0% +and then you contract it with the source +okay so so so so you just now uh the + + align:start position:0% +okay so so so so you just now uh the + + + align:start position:0% +okay so so so so you just now uh the +only difference from the scalar case or + + align:start position:0% +only difference from the scalar case or + + + align:start position:0% +only difference from the scalar case or +the or the spinner case just now we uh + + align:start position:0% +the or the spinner case just now we uh + + + align:start position:0% +the or the spinner case just now we uh +now the in the other than the functional + + align:start position:0% +now the in the other than the functional + + + align:start position:0% +now the in the other than the functional +space of X and Y uh now you also have a + + align:start position:0% +space of X and Y uh now you also have a + + + align:start position:0% +space of X and Y uh now you also have a +matrix in terms of low range index okay + + align:start position:0% +matrix in terms of low range index okay + + + align:start position:0% +matrix in terms of low range index okay +uh mu Nu okay everything is the same as + + align:start position:0% +uh mu Nu okay everything is the same as + + + align:start position:0% +uh mu Nu okay everything is the same as +before + + align:start position:0% + + + + align:start position:0% + +so so looks like then we already solved + + align:start position:0% +so so looks like then we already solved + + + align:start position:0% +so so looks like then we already solved +this series okay + + align:start position:0% +this series okay + + + align:start position:0% +this series okay +but you should feel uneasy + + align:start position:0% +but you should feel uneasy + + + align:start position:0% +but you should feel uneasy +you should feel easy because when we + + align:start position:0% +you should feel easy because when we + + + align:start position:0% +you should feel easy because when we +contact the using the canonical method + + align:start position:0% +contact the using the canonical method + + + align:start position:0% +contact the using the canonical method +we do have to go through some trouble + + align:start position:0% +we do have to go through some trouble + + + align:start position:0% +we do have to go through some trouble +okay so how come somehow pass integral + + align:start position:0% +okay so how come somehow pass integral + + + align:start position:0% +okay so how come somehow pass integral +just do it immediately okay somehow the + + align:start position:0% +just do it immediately okay somehow the + + + align:start position:0% +just do it immediately okay somehow the +trouble has to be conserved no matter + + align:start position:0% +trouble has to be conserved no matter + + + align:start position:0% +trouble has to be conserved no matter +what method you use okay and along with + + align:start position:0% +what method you use okay and along with + + + align:start position:0% +what method you use okay and along with +the method you use indeed + + align:start position:0% +the method you use indeed + + + align:start position:0% +the method you use indeed +indeed so can someone guess what would + + align:start position:0% +indeed so can someone guess what would + + + align:start position:0% +indeed so can someone guess what would +be the potential trouble here yes + + align:start position:0% + + + + align:start position:0% + +yeah right + + align:start position:0% +yeah right + + + align:start position:0% +yeah right +yeah so then like your song you + + align:start position:0% +yeah so then like your song you + + + align:start position:0% +yeah so then like your song you +something like you're integrating over + + align:start position:0% +something like you're integrating over + + + align:start position:0% +something like you're integrating over +too many yeah + + align:start position:0% +too many yeah + + + align:start position:0% +too many yeah +indeed that's the correct statement + + align:start position:0% +indeed that's the correct statement + + + align:start position:0% +indeed that's the correct statement +but but if I just do it + + align:start position:0% +but but if I just do it + + + align:start position:0% +but but if I just do it +straightforwardly somehow uh then what's + + align:start position:0% +straightforwardly somehow uh then what's + + + align:start position:0% +straightforwardly somehow uh then what's +wrong with that + + align:start position:0% + + + + align:start position:0% + +so yeah what you said is a conceptually + + align:start position:0% +so yeah what you said is a conceptually + + + align:start position:0% +so yeah what you said is a conceptually +conceptually you should suspect there's + + align:start position:0% +conceptually you should suspect there's + + + align:start position:0% +conceptually you should suspect there's +something wrong here + + align:start position:0% +something wrong here + + + align:start position:0% +something wrong here +uh so whenever you conceptually suspect + + align:start position:0% +uh so whenever you conceptually suspect + + + align:start position:0% +uh so whenever you conceptually suspect +there's something wrong here then you + + align:start position:0% +there's something wrong here then you + + + align:start position:0% +there's something wrong here then you +should technically looking for some + + align:start position:0% +should technically looking for some + + + align:start position:0% +should technically looking for some +mathematical problem + + align:start position:0% +mathematical problem + + + align:start position:0% +mathematical problem +because the conceptual mistake will + + align:start position:0% +because the conceptual mistake will + + + align:start position:0% +because the conceptual mistake will +always reflect in some mathematical + + align:start position:0% +always reflect in some mathematical + + + align:start position:0% +always reflect in some mathematical +difficulty yeah yes + + align:start position:0% + + + + align:start position:0% + +yeah yeah you're right it just you you + + align:start position:0% +yeah yeah you're right it just you you + + + align:start position:0% +yeah yeah you're right it just you you +integrate more sins or you integrate + + align:start position:0% +integrate more sins or you integrate + + + align:start position:0% +integrate more sins or you integrate +more sins then you just get more + + align:start position:0% +more sins then you just get more + + + align:start position:0% +more sins then you just get more +infinite constant but if you don't care + + align:start position:0% +infinite constant but if you don't care + + + align:start position:0% +infinite constant but if you don't care +okay + + align:start position:0% +okay + + + align:start position:0% +okay +maybe like a sign will be off because + + align:start position:0% +maybe like a sign will be off because + + + align:start position:0% +maybe like a sign will be off because +the sign was off earlier right so like + + align:start position:0% +the sign was off earlier right so like + + + align:start position:0% +the sign was off earlier right so like +when you like you like like the + + align:start position:0% +when you like you like like the + + + align:start position:0% +when you like you like like the +eigenvales of the terminal or whatever + + align:start position:0% +eigenvales of the terminal or whatever + + + align:start position:0% +eigenvales of the terminal or whatever +maybe it messes that up yeah yeah but + + align:start position:0% +maybe it messes that up yeah yeah but + + + align:start position:0% +maybe it messes that up yeah yeah but +but we have eyes it doesn't matter the + + align:start position:0% +but we have eyes it doesn't matter the + + + align:start position:0% +but we have eyes it doesn't matter the +side + + align:start position:0% +side + + + align:start position:0% +side +yes + + align:start position:0% + + + + align:start position:0% + +yeah exactly so the key + + align:start position:0% +yeah exactly so the key + + + align:start position:0% +yeah exactly so the key +he said the K is actually not invisible + + align:start position:0% +he said the K is actually not invisible + + + align:start position:0% +he said the K is actually not invisible +and that K minus one + + align:start position:0% +and that K minus one + + + align:start position:0% +and that K minus one +so k + + align:start position:0% + + + + align:start position:0% + +zero actually not invertible + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the reason + + align:start position:0% + + + + align:start position:0% + +so the reason is simple + + align:start position:0% +so the reason is simple + + + align:start position:0% +so the reason is simple +is that because the cage freedom in the + + align:start position:0% +is that because the cage freedom in the + + + align:start position:0% +is that because the cage freedom in the +original Theory + + align:start position:0% + + + + align:start position:0% + +because they're getting freedom in the + + align:start position:0% +because they're getting freedom in the + + + align:start position:0% +because they're getting freedom in the +original Theory + + align:start position:0% +original Theory + + + align:start position:0% +original Theory +package Freedom we mean that when you + + align:start position:0% +package Freedom we mean that when you + + + align:start position:0% +package Freedom we mean that when you +make a transformation by some arbitrary + + align:start position:0% +make a transformation by some arbitrary + + + align:start position:0% +make a transformation by some arbitrary +function + + align:start position:0% +function + + + align:start position:0% +function +you know your action does not change + + align:start position:0% +you know your action does not change + + + align:start position:0% +you know your action does not change +then that means that your this kernel + + align:start position:0% +then that means that your this kernel + + + align:start position:0% +then that means that your this kernel +must be invariant + + align:start position:0% +must be invariant + + + align:start position:0% +must be invariant +under some some + + align:start position:0% +under some some + + + align:start position:0% +under some some +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +it's a more renowned some transformation + + align:start position:0% +it's a more renowned some transformation + + + align:start position:0% +it's a more renowned some transformation +means that this must have zero + + align:start position:0% +means that this must have zero + + + align:start position:0% +means that this must have zero +eigenvector + + align:start position:0% +eigenvector + + + align:start position:0% +eigenvector +okay when it has zero angle Vector then + + align:start position:0% +okay when it has zero angle Vector then + + + align:start position:0% +okay when it has zero angle Vector then +then there must not be invertible okay + + align:start position:0% +then there must not be invertible okay + + + align:start position:0% +then there must not be invertible okay +so so now let's just see the explicitly + + align:start position:0% +so so now let's just see the explicitly + + + align:start position:0% +so so now let's just see the explicitly +you see the explicitly it's easier to + + align:start position:0% +you see the explicitly it's easier to + + + align:start position:0% +you see the explicitly it's easier to +see this momentum space okay + + align:start position:0% +see this momentum space okay + + + align:start position:0% +see this momentum space okay +so so if we see the momentum space + + align:start position:0% + + + + align:start position:0% + +so in momentum space we can just + + align:start position:0% +so in momentum space we can just + + + align:start position:0% +so in momentum space we can just +directly write down the k0 or mu mu + + align:start position:0% +directly write down the k0 or mu mu + + + align:start position:0% +directly write down the k0 or mu mu +it's just equal to K Square + + align:start position:0% + + + + align:start position:0% + +just K mu K Nu + + align:start position:0% +just K mu K Nu + + + align:start position:0% +just K mu K Nu +minus K square is Mu + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so now it's obvious this has a zero + + align:start position:0% +so now it's obvious this has a zero + + + align:start position:0% +so now it's obvious this has a zero +eigenvector + + align:start position:0% +eigenvector + + + align:start position:0% +eigenvector +because this is precisely + + align:start position:0% +because this is precisely + + + align:start position:0% +because this is precisely +the minus K Square the transverse + + align:start position:0% +the minus K Square the transverse + + + align:start position:0% +the minus K Square the transverse +projector + + align:start position:0% + + + + align:start position:0% + +so Community is the projector into the + + align:start position:0% +so Community is the projector into the + + + align:start position:0% +so Community is the projector into the +direction perpendicular to K mu so so so + + align:start position:0% +direction perpendicular to K mu so so so + + + align:start position:0% +direction perpendicular to K mu so so so +this satisfies the property + + align:start position:0% +this satisfies the property + + + align:start position:0% +this satisfies the property +that PT will mu is equal to e to Mu mu + + align:start position:0% +that PT will mu is equal to e to Mu mu + + + align:start position:0% +that PT will mu is equal to e to Mu mu +minus K mu okay Nu + + align:start position:0% +minus K mu okay Nu + + + align:start position:0% +minus K mu okay Nu +divided by K Square + + align:start position:0% +divided by K Square + + + align:start position:0% +divided by K Square +and satisfy the probability P mu mu t + + align:start position:0% +and satisfy the probability P mu mu t + + + align:start position:0% +and satisfy the probability P mu mu t +K Nu is always equal to 0. + + align:start position:0% +K Nu is always equal to 0. + + + align:start position:0% +K Nu is always equal to 0. +okay + + align:start position:0% + + + + align:start position:0% + +so you can easily see because if you + + align:start position:0% +so you can easily see because if you + + + align:start position:0% +so you can easily see because if you +contract with K mu and K mu conject will + + align:start position:0% +contract with K mu and K mu conject will + + + align:start position:0% +contract with K mu and K mu conject will +give you K square and cancel with K + + align:start position:0% +give you K square and cancel with K + + + align:start position:0% +give you K square and cancel with K +squared here and you have K mu and then + + align:start position:0% +squared here and you have K mu and then + + + align:start position:0% +squared here and you have K mu and then +K mu contract with this one just get + + align:start position:0% +K mu contract with this one just get + + + align:start position:0% +K mu contract with this one just get +compute so they get cancel okay so so + + align:start position:0% +compute so they get cancel okay so so + + + align:start position:0% +compute so they get cancel okay so so +this is the projected to the transverse + + align:start position:0% +this is the projected to the transverse + + + align:start position:0% +this is the projected to the transverse +space of course I have zero eigen value + + align:start position:0% +space of course I have zero eigen value + + + align:start position:0% +space of course I have zero eigen value +okay zero eigenvectors so + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so then we see that this is not + + align:start position:0% +so then we see that this is not + + + align:start position:0% +so then we see that this is not +invertible in momentum space and then + + align:start position:0% +invertible in momentum space and then + + + align:start position:0% +invertible in momentum space and then +will not be invertible in coordinate + + align:start position:0% +will not be invertible in coordinate + + + align:start position:0% +will not be invertible in coordinate +space okay we're not doing vertical in + + align:start position:0% +space okay we're not doing vertical in + + + align:start position:0% +space okay we're not doing vertical in +corner space + + align:start position:0% +corner space + + + align:start position:0% +corner space +and now in coordinate space + + align:start position:0% + + + + align:start position:0% + +now we can see this this understanding + + align:start position:0% +now we can see this this understanding + + + align:start position:0% +now we can see this this understanding +then now we can immediately see in + + align:start position:0% +then now we can immediately see in + + + align:start position:0% +then now we can immediately see in +coordinate space + + align:start position:0% +coordinate space + + + align:start position:0% +coordinate space +the eigenvector of zero eigenvalue + + align:start position:0% +the eigenvector of zero eigenvalue + + + align:start position:0% +the eigenvector of zero eigenvalue +precisely corresponding to a gauge + + align:start position:0% +precisely corresponding to a gauge + + + align:start position:0% +precisely corresponding to a gauge +transformation okay it's because + + align:start position:0% + + + + align:start position:0% + +it's because in coordinate space + + align:start position:0% +it's because in coordinate space + + + align:start position:0% +it's because in coordinate space +okay new + + align:start position:0% + + + + align:start position:0% + +can you translate when you translate to + + align:start position:0% +can you translate when you translate to + + + align:start position:0% +can you translate when you translate to +coordinate space means partial mu + + align:start position:0% +coordinate space means partial mu + + + align:start position:0% +coordinate space means partial mu +okay so K mu + + align:start position:0% + + + + align:start position:0% + +to coordinate means partial mu okay so + + align:start position:0% +to coordinate means partial mu okay so + + + align:start position:0% +to coordinate means partial mu okay so +that means + + align:start position:0% +that means + + + align:start position:0% +that means +that for any function + + align:start position:0% + + + + align:start position:0% + +mu Lambda + + align:start position:0% +mu Lambda + + + align:start position:0% +mu Lambda +okay this k0 mu Nu + + align:start position:0% + + + + align:start position:0% + +actually new Lambda must be zero + + align:start position:0% +actually new Lambda must be zero + + + align:start position:0% +actually new Lambda must be zero +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and you can check explicitly + + align:start position:0% +and you can check explicitly + + + align:start position:0% +and you can check explicitly +so if you contract with partial mu here + + align:start position:0% +so if you contract with partial mu here + + + align:start position:0% +so if you contract with partial mu here +and then you have a partial Square + + align:start position:0% +and then you have a partial Square + + + align:start position:0% +and then you have a partial Square +and you have partial mu and then and + + align:start position:0% +and you have partial mu and then and + + + align:start position:0% +and you have partial mu and then and +then interim will give you passion view + + align:start position:0% +then interim will give you passion view + + + align:start position:0% +then interim will give you passion view +okay again the cancer and of course this + + align:start position:0% +okay again the cancer and of course this + + + align:start position:0% +okay again the cancer and of course this +is just precisely the case + + align:start position:0% +is just precisely the case + + + align:start position:0% +is just precisely the case +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +and this is precise indication to + + align:start position:0% +and this is precise indication to + + + align:start position:0% +and this is precise indication to +measure + + align:start position:0% + + + + align:start position:0% + +okay so the gay transformation precisely + + align:start position:0% +okay so the gay transformation precisely + + + align:start position:0% +okay so the gay transformation precisely +is the zero eigenvector + + align:start position:0% +is the zero eigenvector + + + align:start position:0% +is the zero eigenvector +of this kernel okay uh is the uh the + + align:start position:0% +of this kernel okay uh is the uh the + + + align:start position:0% +of this kernel okay uh is the uh the +eigenvector of zero eigenvalue of this + + align:start position:0% +eigenvector of zero eigenvalue of this + + + align:start position:0% +eigenvector of zero eigenvalue of this +candle so that's why this is not + + align:start position:0% +candle so that's why this is not + + + align:start position:0% +candle so that's why this is not +inverted + + align:start position:0% +inverted + + + align:start position:0% +inverted +okay + + align:start position:0% + + + + align:start position:0% + +so yeah so so + + align:start position:0% +so yeah so so + + + align:start position:0% +so yeah so so +um + + align:start position:0% + + + + align:start position:0% + +so so the way to fix is simple + + align:start position:0% +so so the way to fix is simple + + + align:start position:0% +so so the way to fix is simple +because I remember this picture + + align:start position:0% + + + + align:start position:0% + +so this is the space of the full + + align:start position:0% +so this is the space of the full + + + align:start position:0% +so this is the space of the full +configurations of a mu + + align:start position:0% +configurations of a mu + + + align:start position:0% +configurations of a mu +and an AMU alone those trajectories are + + align:start position:0% +and an AMU alone those trajectories are + + + align:start position:0% +and an AMU alone those trajectories are +equivalent + + align:start position:0% +equivalent + + + align:start position:0% +equivalent +and about uh uh to quantize it we need + + align:start position:0% +and about uh uh to quantize it we need + + + align:start position:0% +and about uh uh to quantize it we need +to just uh the physical configuration we + + align:start position:0% +to just uh the physical configuration we + + + align:start position:0% +to just uh the physical configuration we +corresponding to a section of it + + align:start position:0% +corresponding to a section of it + + + align:start position:0% +corresponding to a section of it +so what this said is that k0 + + align:start position:0% +so what this said is that k0 + + + align:start position:0% +so what this said is that k0 +is not immersible in this full space + + align:start position:0% +is not immersible in this full space + + + align:start position:0% +is not immersible in this full space +because you have this zero eigenvectors + + align:start position:0% +because you have this zero eigenvectors + + + align:start position:0% +because you have this zero eigenvectors +along this direction + + align:start position:0% +along this direction + + + align:start position:0% +along this direction +this direction but if we restrict + + align:start position:0% +this direction but if we restrict + + + align:start position:0% +this direction but if we restrict +to cross action + + align:start position:0% +to cross action + + + align:start position:0% +to cross action +and then this zero I come back the long + + align:start position:0% +and then this zero I come back the long + + + align:start position:0% +and then this zero I come back the long +exist okay and then you will be + + align:start position:0% +exist okay and then you will be + + + align:start position:0% +exist okay and then you will be +invertible okay so once we fix the gauge + + align:start position:0% +invertible okay so once we fix the gauge + + + align:start position:0% +invertible okay so once we fix the gauge +and then we then we expect then then the + + align:start position:0% +and then we then we expect then then the + + + align:start position:0% +and then we then we expect then then the +K mu after we fixed skate should be + + align:start position:0% +K mu after we fixed skate should be + + + align:start position:0% +K mu after we fixed skate should be +invertible okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so now let's fix the cage + + align:start position:0% + + + + align:start position:0% + +okay so so it's okay zero we will + + align:start position:0% +okay so so it's okay zero we will + + + align:start position:0% +okay so so it's okay zero we will +restrict it + + align:start position:0% + + + + align:start position:0% + +to a section + + align:start position:0% + + + + align:start position:0% + +to be should be inverted + + align:start position:0% + + + + align:start position:0% + +okay so so we read so we need to + + align:start position:0% +okay so so we read so we need to + + + align:start position:0% +okay so so we read so we need to +fix the gauge + + align:start position:0% + + + + align:start position:0% + +so we will do this for the Lorenz cage + + align:start position:0% +so we will do this for the Lorenz cage + + + align:start position:0% +so we will do this for the Lorenz cage +you can do similar things for the for + + align:start position:0% +you can do similar things for the for + + + align:start position:0% +you can do similar things for the for +the uh for the coolant gauge the Rhythm + + align:start position:0% +the uh for the coolant gauge the Rhythm + + + align:start position:0% +the uh for the coolant gauge the Rhythm +we do to run skate is just the landscape + + align:start position:0% +we do to run skate is just the landscape + + + align:start position:0% +we do to run skate is just the landscape +uh later when we introduce interactions + + align:start position:0% +uh later when we introduce interactions + + + align:start position:0% +uh later when we introduce interactions +we always work with Lawrence Gage okay + + align:start position:0% +we always work with Lawrence Gage okay + + + align:start position:0% +we always work with Lawrence Gage okay +and when we discuss QD we will always + + align:start position:0% +and when we discuss QD we will always + + + align:start position:0% +and when we discuss QD we will always +work with the range gauge so here I will + + align:start position:0% +work with the range gauge so here I will + + + align:start position:0% +work with the range gauge so here I will +elaborate in the Lorenz cage yes + + align:start position:0% + + + + align:start position:0% + +oh yeah + + align:start position:0% +oh yeah + + + align:start position:0% +oh yeah +so so this zero eigenvector so this is a + + align:start position:0% +so so this zero eigenvector so this is a + + + align:start position:0% +so so this zero eigenvector so this is a +zero eigenvector of the k0 right + + align:start position:0% +zero eigenvector of the k0 right + + + align:start position:0% +zero eigenvector of the k0 right +so and the partial mu a partial Lambda + + align:start position:0% +so and the partial mu a partial Lambda + + + align:start position:0% +so and the partial mu a partial Lambda +just parameterized this direction + + align:start position:0% +just parameterized this direction + + + align:start position:0% +just parameterized this direction +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but if you restrict to a section of it + + align:start position:0% +but if you restrict to a section of it + + + align:start position:0% +but if you restrict to a section of it +and then you are not allowed to worry + + align:start position:0% +and then you are not allowed to worry + + + align:start position:0% +and then you are not allowed to worry +along away from it + + align:start position:0% +along away from it + + + align:start position:0% +along away from it +and then this direction just go so you + + align:start position:0% +and then this direction just go so you + + + align:start position:0% +and then this direction just go so you +don't no longer have that zero + + align:start position:0% +don't no longer have that zero + + + align:start position:0% +don't no longer have that zero +eigenvector anymore yeah yes + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +yeah yeah good good yeah so so + + align:start position:0% +yeah yeah good good yeah so so + + + align:start position:0% +yeah yeah good good yeah so so +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +indeed you have to integrate yeah you + + align:start position:0% +indeed you have to integrate yeah you + + + align:start position:0% +indeed you have to integrate yeah you +have to integrate over y yeah + + align:start position:0% +have to integrate over y yeah + + + align:start position:0% +have to integrate over y yeah +thank you yeah yes yeah yeah if I write + + align:start position:0% +thank you yeah yes yeah yeah if I write + + + align:start position:0% +thank you yeah yes yeah yeah if I write +this precisely so you have to integrate + + align:start position:0% +this precisely so you have to integrate + + + align:start position:0% +this precisely so you have to integrate +over this + + align:start position:0% +over this + + + align:start position:0% +over this +why + + align:start position:0% +why + + + align:start position:0% +why +yeah that's right + + align:start position:0% +yeah that's right + + + align:start position:0% +yeah that's right +yeah so this is the powerful way to + + align:start position:0% +yeah so this is the powerful way to + + + align:start position:0% +yeah so this is the powerful way to +write yeah + + align:start position:0% +write yeah + + + align:start position:0% +write yeah +good + + align:start position:0% + + + + align:start position:0% + +yeah yeah because other symmetries + + align:start position:0% +yeah yeah because other symmetries + + + align:start position:0% +yeah yeah because other symmetries +so because because you have local + + align:start position:0% +so because because you have local + + + align:start position:0% +so because because you have local +symmetries so the local symmetry tells + + align:start position:0% +symmetries so the local symmetry tells + + + align:start position:0% +symmetries so the local symmetry tells +you there's really some degree Freedom + + align:start position:0% +you there's really some degree Freedom + + + align:start position:0% +you there's really some degree Freedom +redundant + + align:start position:0% +redundant + + + align:start position:0% +redundant +so this is really corresponding to + + align:start position:0% +so this is really corresponding to + + + align:start position:0% +so this is really corresponding to +so this Lambda X + + align:start position:0% +so this Lambda X + + + align:start position:0% +so this Lambda X +so this all possible choice of Lambda is + + align:start position:0% +so this all possible choice of Lambda is + + + align:start position:0% +so this all possible choice of Lambda is +really corresponding to some finite + + align:start position:0% +really corresponding to some finite + + + align:start position:0% +really corresponding to some finite +trajectory uh uh in your configuration + + align:start position:0% +trajectory uh uh in your configuration + + + align:start position:0% +trajectory uh uh in your configuration +space + + align:start position:0% +space + + + align:start position:0% +space +so if you have Global symmetry Global + + align:start position:0% +so if you have Global symmetry Global + + + align:start position:0% +so if you have Global symmetry Global +symmetry is independent of coordinates + + align:start position:0% +symmetry is independent of coordinates + + + align:start position:0% +symmetry is independent of coordinates +so from this point of view a global + + align:start position:0% +so from this point of view a global + + + align:start position:0% +so from this point of view a global +symmetry just related to the + + align:start position:0% +symmetry just related to the + + + align:start position:0% +symmetry just related to the +configuration at this point to the + + align:start position:0% +configuration at this point to the + + + align:start position:0% +configuration at this point to the +configuration at that point and at that + + align:start position:0% +configuration at that point and at that + + + align:start position:0% +configuration at that point and at that +point okay a global possibility because + + align:start position:0% +point okay a global possibility because + + + align:start position:0% +point okay a global possibility because +it's independent of the space time + + align:start position:0% +it's independent of the space time + + + align:start position:0% +it's independent of the space time +that transformation don't + + align:start position:0% +that transformation don't + + + align:start position:0% +that transformation don't +don't change your number of liquid + + align:start position:0% +don't change your number of liquid + + + align:start position:0% +don't change your number of liquid +freedom yeah they don't corresponding to + + align:start position:0% +freedom yeah they don't corresponding to + + + align:start position:0% +freedom yeah they don't corresponding to +actually a trajectory in your in your + + align:start position:0% +actually a trajectory in your in your + + + align:start position:0% +actually a trajectory in your in your +configuration space + + align:start position:0% + + + + align:start position:0% + +good other questions + + align:start position:0% + + + + align:start position:0% + +okay very good + + align:start position:0% +okay very good + + + align:start position:0% +okay very good +so now we will fix the gauge + + align:start position:0% +so now we will fix the gauge + + + align:start position:0% +so now we will fix the gauge +so in the past integral to fix the gauge + + align:start position:0% +so in the past integral to fix the gauge + + + align:start position:0% +so in the past integral to fix the gauge +would be a in principle is + + align:start position:0% +would be a in principle is + + + align:start position:0% +would be a in principle is +straightforward + + align:start position:0% +straightforward + + + align:start position:0% +straightforward +okay so so we will consider rinse gauge + + align:start position:0% + + + + align:start position:0% + +okay you can do the similar thing with + + align:start position:0% +okay you can do the similar thing with + + + align:start position:0% +okay you can do the similar thing with +the uh with the coolant gauge okay it's + + align:start position:0% +the uh with the coolant gauge okay it's + + + align:start position:0% +the uh with the coolant gauge okay it's +just low range cage normally we work + + align:start position:0% +just low range cage normally we work + + + align:start position:0% +just low range cage normally we work +with + + align:start position:0% +with + + + align:start position:0% +with +so so how do we fix the cage + + align:start position:0% +so so how do we fix the cage + + + align:start position:0% +so so how do we fix the cage +so in the passing ago we do it easily + + align:start position:0% +so in the passing ago we do it easily + + + align:start position:0% +so in the passing ago we do it easily +so we have this + + align:start position:0% +so we have this + + + align:start position:0% +so we have this +in the growth we have + + align:start position:0% +in the growth we have + + + align:start position:0% +in the growth we have +then we insert the Delta function + + align:start position:0% + + + + align:start position:0% + +corresponding to the larynx cage + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so so this is should be considered as + + align:start position:0% +so so so this is should be considered as + + + align:start position:0% +so so so this is should be considered as +a + + align:start position:0% +a + + + align:start position:0% +a +data function + + align:start position:0% +data function + + + align:start position:0% +data function +so you so this is a data function at one + + align:start position:0% +so you so this is a data function at one + + + align:start position:0% +so you so this is a data function at one +point and then you take the product of + + align:start position:0% +point and then you take the product of + + + align:start position:0% +point and then you take the product of +all points okay so this is the data + + align:start position:0% +all points okay so this is the data + + + align:start position:0% +all points okay so this is the data +function the functional space and then + + align:start position:0% +function the functional space and then + + + align:start position:0% +function the functional space and then +we will have them as + + align:start position:0% +we will have them as + + + align:start position:0% +we will have them as +this S Maxwell + + align:start position:0% +this S Maxwell + + + align:start position:0% +this S Maxwell +and then you can have AJ + + align:start position:0% +and then you can have AJ + + + align:start position:0% +and then you can have AJ +okay you can consider the generation + + align:start position:0% +okay you can consider the generation + + + align:start position:0% +okay you can consider the generation +function + + align:start position:0% +function + + + align:start position:0% +function +so this will restrict + + align:start position:0% + + + + align:start position:0% + +okay this will restrict + + align:start position:0% +okay this will restrict + + + align:start position:0% +okay this will restrict +you on this uh on some cross action + + align:start position:0% +you on this uh on some cross action + + + align:start position:0% +you on this uh on some cross action +okay + + align:start position:0% + + + + align:start position:0% + +on some course section + + align:start position:0% +on some course section + + + align:start position:0% +on some course section +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% + + + + align:start position:0% + +so yeah so maybe make a remark here + + align:start position:0% + + + + align:start position:0% + +so here we actually have to be a little + + align:start position:0% +so here we actually have to be a little + + + align:start position:0% +so here we actually have to be a little +bit more careful + + align:start position:0% + + + + align:start position:0% + +so so what we actually really want to do + + align:start position:0% +so so what we actually really want to do + + + align:start position:0% +so so what we actually really want to do +okay what we really want to do + + align:start position:0% +okay what we really want to do + + + align:start position:0% +okay what we really want to do +is we just want to insert here + + align:start position:0% + + + + align:start position:0% + +we just want to insert here Delta a mu + + align:start position:0% +we just want to insert here Delta a mu + + + align:start position:0% +we just want to insert here Delta a mu +equal to a mu + + align:start position:0% +equal to a mu + + + align:start position:0% +equal to a mu +gets fixed okay + + align:start position:0% + + + + align:start position:0% + +we just uh or what we want what we + + align:start position:0% +we just uh or what we want what we + + + align:start position:0% +we just uh or what we want what we +really want to do is we want just to + + align:start position:0% +really want to do is we want just to + + + align:start position:0% +really want to do is we want just to +restrict a mu to some a some cross + + align:start position:0% +restrict a mu to some a some cross + + + align:start position:0% +restrict a mu to some a some cross +section okay + + align:start position:0% +section okay + + + align:start position:0% +section okay +but here for example here for the red + + align:start position:0% +but here for example here for the red + + + align:start position:0% +but here for example here for the red +skate we can normally not solve this + + align:start position:0% +skate we can normally not solve this + + + align:start position:0% +skate we can normally not solve this +condition okay so that's why uh we do + + align:start position:0% +condition okay so that's why uh we do + + + align:start position:0% +condition okay so that's why uh we do +here because we don't know how to write + + align:start position:0% +here because we don't know how to write + + + align:start position:0% +here because we don't know how to write +this emu fixed explicitly okay + + align:start position:0% +this emu fixed explicitly okay + + + align:start position:0% +this emu fixed explicitly okay +but but going from here to here actually + + align:start position:0% +but but going from here to here actually + + + align:start position:0% +but but going from here to here actually +there's a long trip with Jacobin + + align:start position:0% +there's a long trip with Jacobin + + + align:start position:0% +there's a long trip with Jacobin +because this is a a long trivial yeah in + + align:start position:0% +because this is a a long trivial yeah in + + + align:start position:0% +because this is a a long trivial yeah in +the functional space and then this is a + + align:start position:0% +the functional space and then this is a + + + align:start position:0% +the functional space and then this is a +longitude of function on the on a meal + + align:start position:0% +longitude of function on the on a meal + + + align:start position:0% +longitude of function on the on a meal +okay so so so in principle okay so uh + + align:start position:0% +okay so so so in principle okay so uh + + + align:start position:0% +okay so so so in principle okay so uh +this uh the related yeah in principle + + align:start position:0% +this uh the related yeah in principle + + + align:start position:0% +this uh the related yeah in principle +there's a Jacobi + + align:start position:0% + + + + align:start position:0% + +so yeah so let me just write this + + align:start position:0% +so yeah so let me just write this + + + align:start position:0% +so yeah so let me just write this +explicit + + align:start position:0% + + + + align:start position:0% + +a view + + align:start position:0% +a view + + + align:start position:0% +a view +acts are related + + align:start position:0% +acts are related + + + align:start position:0% +acts are related +by some Jacobin + + align:start position:0% + + + + align:start position:0% + +then DOTA a mu + + align:start position:0% +then DOTA a mu + + + align:start position:0% +then DOTA a mu +minus Theta mu fixed or a minus a mean + + align:start position:0% +minus Theta mu fixed or a minus a mean + + + align:start position:0% +minus Theta mu fixed or a minus a mean +fixed + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +but now this + + align:start position:0% +but now this + + + align:start position:0% +but now this +but notice that this can this function + + align:start position:0% +but notice that this can this function + + + align:start position:0% +but notice that this can this function +is a linear function of a + + align:start position:0% +is a linear function of a + + + align:start position:0% +is a linear function of a +so remember when you do the Jacobi you + + align:start position:0% +so remember when you do the Jacobi you + + + align:start position:0% +so remember when you do the Jacobi you +have to take the derivative + + align:start position:0% +have to take the derivative + + + align:start position:0% +have to take the derivative +yeah yeah I just remember this one + + align:start position:0% +yeah yeah I just remember this one + + + align:start position:0% +yeah yeah I just remember this one +remember this formula + + align:start position:0% +remember this formula + + + align:start position:0% +remember this formula +Delta f + + align:start position:0% +Delta f + + + align:start position:0% +Delta f +X + + align:start position:0% +X + + + align:start position:0% +X +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +1 over F Prime X + + align:start position:0% +1 over F Prime X + + + align:start position:0% +1 over F Prime X +Delta x minus X zero so x0 is a solution + + align:start position:0% +Delta x minus X zero so x0 is a solution + + + align:start position:0% +Delta x minus X zero so x0 is a solution +for f x equal to zero okay and so you + + align:start position:0% +for f x equal to zero okay and so you + + + align:start position:0% +for f x equal to zero okay and so you +have to uh + + align:start position:0% +have to uh + + + align:start position:0% +have to uh +uh uh so you have to yeah so this is the + + align:start position:0% +uh uh so you have to yeah so this is the + + + align:start position:0% +uh uh so you have to yeah so this is the +Jacobin + + align:start position:0% +Jacobin + + + align:start position:0% +Jacobin +when you convert the data function + + align:start position:0% +when you convert the data function + + + align:start position:0% +when you convert the data function +so uh yeah if you have a multiple + + align:start position:0% +so uh yeah if you have a multiple + + + align:start position:0% +so uh yeah if you have a multiple +variables then it would be a this will + + align:start position:0% +variables then it would be a this will + + + align:start position:0% +variables then it would be a this will +be the Jacobi + + align:start position:0% +be the Jacobi + + + align:start position:0% +be the Jacobi +and so so this course when you take the + + align:start position:0% +and so so this course when you take the + + + align:start position:0% +and so so this course when you take the +derivative on this function + + align:start position:0% +derivative on this function + + + align:start position:0% +derivative on this function +but this is a linear + + align:start position:0% +but this is a linear + + + align:start position:0% +but this is a linear +this thing is linear in a mu + + align:start position:0% +this thing is linear in a mu + + + align:start position:0% +this thing is linear in a mu +okay when you take the derivative you + + align:start position:0% +okay when you take the derivative you + + + align:start position:0% +okay when you take the derivative you +will get something which is independent + + align:start position:0% +will get something which is independent + + + align:start position:0% +will get something which is independent +of a bill + + align:start position:0% +of a bill + + + align:start position:0% +of a bill +so this Jacobian will just involve in + + align:start position:0% +so this Jacobian will just involve in + + + align:start position:0% +so this Jacobian will just involve in +some + + align:start position:0% +some + + + align:start position:0% +some +yeah we'll be independent about a view + + align:start position:0% +yeah we'll be independent about a view + + + align:start position:0% +yeah we'll be independent about a view +but in the function space + + align:start position:0% +but in the function space + + + align:start position:0% +but in the function space +something independently mu with just + + align:start position:0% +something independently mu with just + + + align:start position:0% +something independently mu with just +some constant okay so so this just gives + + align:start position:0% +some constant okay so so this just gives + + + align:start position:0% +some constant okay so so this just gives +you some infinite constants + + align:start position:0% + + + + align:start position:0% + +and so we always throw in these numbers + + align:start position:0% +and so we always throw in these numbers + + + align:start position:0% +and so we always throw in these numbers +uh infinite number way so so we don't + + align:start position:0% +uh infinite number way so so we don't + + + align:start position:0% +uh infinite number way so so we don't +care about it okay and so we uh we can + + align:start position:0% +care about it okay and so we uh we can + + + align:start position:0% +care about it okay and so we uh we can +just write down this okay + + align:start position:0% +just write down this okay + + + align:start position:0% +just write down this okay +so this is just a mark + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +so now + + align:start position:0% +so now + + + align:start position:0% +so now +we have to evaluate this guy + + align:start position:0% + + + + align:start position:0% + +in this guy + + align:start position:0% +in this guy + + + align:start position:0% +in this guy +even though this guy is still a lot easy + + align:start position:0% +even though this guy is still a lot easy + + + align:start position:0% +even though this guy is still a lot easy +to solve and for the same it's not easy + + align:start position:0% +to solve and for the same it's not easy + + + align:start position:0% +to solve and for the same it's not easy +to do just for the same reason you don't + + align:start position:0% +to do just for the same reason you don't + + + align:start position:0% +to do just for the same reason you don't +know how to solve this IMU fixed okay we + + align:start position:0% +know how to solve this IMU fixed okay we + + + align:start position:0% +know how to solve this IMU fixed okay we +don't know how to solve this condition + + align:start position:0% +don't know how to solve this condition + + + align:start position:0% +don't know how to solve this condition +explicitly + + align:start position:0% +explicitly + + + align:start position:0% +explicitly +so now I'm going to use some trick okay + + align:start position:0% +so now I'm going to use some trick okay + + + align:start position:0% +so now I'm going to use some trick okay +uh I will use + + align:start position:0% + + + + align:start position:0% + +two tricks okay I will use two tricks to + + align:start position:0% +two tricks okay I will use two tricks to + + + align:start position:0% +two tricks okay I will use two tricks to +convert this into something manageable + + align:start position:0% +convert this into something manageable + + + align:start position:0% +convert this into something manageable +okay uh to convert into this magnitude + + align:start position:0% +okay uh to convert into this magnitude + + + align:start position:0% +okay uh to convert into this magnitude +and so so this trick + + align:start position:0% +and so so this trick + + + align:start position:0% +and so so this trick +applying to to the to the Maxwell is + + align:start position:0% +applying to to the to the Maxwell is + + + align:start position:0% +applying to to the to the Maxwell is +like + + align:start position:0% +like + + + align:start position:0% +like +killing a little bit with a big Cannon + + align:start position:0% +killing a little bit with a big Cannon + + + align:start position:0% +killing a little bit with a big Cannon +and so so uh yeah it works here + + align:start position:0% +and so so uh yeah it works here + + + align:start position:0% +and so so uh yeah it works here +but it's real genuine use is actually in + + align:start position:0% +but it's real genuine use is actually in + + + align:start position:0% +but it's real genuine use is actually in +the language I've been engaged Theory so + + align:start position:0% +the language I've been engaged Theory so + + + align:start position:0% +the language I've been engaged Theory so +when you quantize the yamil theory and + + align:start position:0% +when you quantize the yamil theory and + + + align:start position:0% +when you quantize the yamil theory and +that's become essential uh because it + + align:start position:0% +that's become essential uh because it + + + align:start position:0% +that's become essential uh because it +will be very complicated contact using + + align:start position:0% +will be very complicated contact using + + + align:start position:0% +will be very complicated contact using +other methods + + align:start position:0% + + + + align:start position:0% + +let me just tell you these two tricks + + align:start position:0% +let me just tell you these two tricks + + + align:start position:0% +let me just tell you these two tricks +how to treat this here okay + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +Russian + + align:start position:0% +Russian + + + align:start position:0% +Russian +also a former Soviets for this Popoff + + align:start position:0% +also a former Soviets for this Popoff + + + align:start position:0% +also a former Soviets for this Popoff +and in the 60s + + align:start position:0% +and in the 60s + + + align:start position:0% +and in the 60s +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +so yeah so actually there was a story + + align:start position:0% +so yeah so actually there was a story + + + align:start position:0% +so yeah so actually there was a story +behind it + + align:start position:0% +behind it + + + align:start position:0% +behind it +uh so when they when they invented this + + align:start position:0% +uh so when they when they invented this + + + align:start position:0% +uh so when they when they invented this +method they actually want to quantize uh + + align:start position:0% +method they actually want to quantize uh + + + align:start position:0% +method they actually want to quantize uh +not this Maxwell Series this number + + align:start position:0% +not this Maxwell Series this number + + + align:start position:0% +not this Maxwell Series this number +being a young Mill Theory which nature + + align:start position:0% +being a young Mill Theory which nature + + + align:start position:0% +being a young Mill Theory which nature +will become the standard model okay it + + align:start position:0% +will become the standard model okay it + + + align:start position:0% +will become the standard model okay it +becomes standard model particle physics + + align:start position:0% +becomes standard model particle physics + + + align:start position:0% +becomes standard model particle physics +electric qcd + + align:start position:0% +electric qcd + + + align:start position:0% +electric qcd +Etc but when they walked on yamir Siri + + align:start position:0% +Etc but when they walked on yamir Siri + + + align:start position:0% +Etc but when they walked on yamir Siri +yamir Siri was some small corner of + + align:start position:0% +yamir Siri was some small corner of + + + align:start position:0% +yamir Siri was some small corner of +mathematical physics nobody cared okay + + align:start position:0% +mathematical physics nobody cared okay + + + align:start position:0% +mathematical physics nobody cared okay +so when they invented this method nobody + + align:start position:0% +so when they invented this method nobody + + + align:start position:0% +so when they invented this method nobody +really paid attention + + align:start position:0% +really paid attention + + + align:start position:0% +really paid attention +and nobody everybody paid attention but + + align:start position:0% +and nobody everybody paid attention but + + + align:start position:0% +and nobody everybody paid attention but +then in 1971 + + align:start position:0% +then in 1971 + + + align:start position:0% +then in 1971 +who was a 21 year old like a graduate + + align:start position:0% +who was a 21 year old like a graduate + + + align:start position:0% +who was a 21 year old like a graduate +student + + align:start position:0% +student + + + align:start position:0% +student +and then he used that which quantized uh + + align:start position:0% +and then he used that which quantized uh + + + align:start position:0% +and then he used that which quantized uh +the the the now I've been engaged Theory + + align:start position:0% +the the the now I've been engaged Theory + + + align:start position:0% +the the the now I've been engaged Theory +couple to Hicks okay so before that + + align:start position:0% +couple to Hicks okay so before that + + + align:start position:0% +couple to Hicks okay so before that +people thought that theory was + + align:start position:0% +people thought that theory was + + + align:start position:0% +people thought that theory was +inconsistent but then he used this past + + align:start position:0% +inconsistent but then he used this past + + + align:start position:0% +inconsistent but then he used this past +integral to quantize that theory okay + + align:start position:0% +integral to quantize that theory okay + + + align:start position:0% +integral to quantize that theory okay +and so that was a chunk with you know to + + align:start position:0% +and so that was a chunk with you know to + + + align:start position:0% +and so that was a chunk with you know to +Hope because the Lobel prize a number of + + align:start position:0% +Hope because the Lobel prize a number of + + + align:start position:0% +Hope because the Lobel prize a number of +years ago and then when two groups + + align:start position:0% +years ago and then when two groups + + + align:start position:0% +years ago and then when two groups +people come out using this method + + align:start position:0% +people come out using this method + + + align:start position:0% +people come out using this method +nobody could understand it in U.S + + align:start position:0% +nobody could understand it in U.S + + + align:start position:0% +nobody could understand it in U.S +okay + + align:start position:0% +okay + + + align:start position:0% +okay +people like + + align:start position:0% +people like + + + align:start position:0% +people like +people like Weinberg who who wrote the + + align:start position:0% +people like Weinberg who who wrote the + + + align:start position:0% +people like Weinberg who who wrote the +election week series + + align:start position:0% +election week series + + + align:start position:0% +election week series +to hope to quantize it and he couldn't + + align:start position:0% +to hope to quantize it and he couldn't + + + align:start position:0% +to hope to quantize it and he couldn't +understand it + + align:start position:0% +understand it + + + align:start position:0% +understand it +and there's only one person + + align:start position:0% +and there's only one person + + + align:start position:0% +and there's only one person +one person who could understand it in + + align:start position:0% +one person who could understand it in + + + align:start position:0% +one person who could understand it in +the U.S it's a he was a assistant + + align:start position:0% +the U.S it's a he was a assistant + + + align:start position:0% +the U.S it's a he was a assistant +professor at Stony Brook yeah so because + + align:start position:0% +professor at Stony Brook yeah so because + + + align:start position:0% +professor at Stony Brook yeah so because +he so he started his assistant professor + + align:start position:0% +he so he started his assistant professor + + + align:start position:0% +he so he started his assistant professor +going to Stony Brook and in Stony Brook + + align:start position:0% +going to Stony Brook and in Stony Brook + + + align:start position:0% +going to Stony Brook and in Stony Brook +there was a big shot uh the Nobel Prize + + align:start position:0% +there was a big shot uh the Nobel Prize + + + align:start position:0% +there was a big shot uh the Nobel Prize +win the CN young who invented this young + + align:start position:0% +win the CN young who invented this young + + + align:start position:0% +win the CN young who invented this young +Mill City so he was asking yeah oh what + + align:start position:0% +Mill City so he was asking yeah oh what + + + align:start position:0% +Mill City so he was asking yeah oh what +should I do for my research ask for + + align:start position:0% +should I do for my research ask for + + + align:start position:0% +should I do for my research ask for +Nobel Prize even though for for advice + + align:start position:0% +Nobel Prize even though for for advice + + + align:start position:0% +Nobel Prize even though for for advice +and young said maybe you can look at + + align:start position:0% +and young said maybe you can look at + + + align:start position:0% +and young said maybe you can look at +this for deep purple stuff + + align:start position:0% +this for deep purple stuff + + + align:start position:0% +this for deep purple stuff +later only himself could understand the + + align:start position:0% +later only himself could understand the + + + align:start position:0% +later only himself could understand the +host paper and then he immediately of + + align:start position:0% +host paper and then he immediately of + + + align:start position:0% +host paper and then he immediately of +course he also did some other uh good + + align:start position:0% +course he also did some other uh good + + + align:start position:0% +course he also did some other uh good +stuff but but immediately he became the + + align:start position:0% +stuff but but immediately he became the + + + align:start position:0% +stuff but but immediately he became the +only person + + align:start position:0% +only person + + + align:start position:0% +only person +everybody went to okay and because he + + align:start position:0% +everybody went to okay and because he + + + align:start position:0% +everybody went to okay and because he +really understood the story he yeah + + align:start position:0% +really understood the story he yeah + + + align:start position:0% +really understood the story he yeah +anyway yeah so so you're actually a very + + align:start position:0% +anyway yeah so so you're actually a very + + + align:start position:0% +anyway yeah so so you're actually a very +interesting story behind this + + align:start position:0% +interesting story behind this + + + align:start position:0% +interesting story behind this +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so um so first we have to actually + + align:start position:0% +so um so first we have to actually + + + align:start position:0% +so um so first we have to actually +modify this Northern sketch condition a + + align:start position:0% +modify this Northern sketch condition a + + + align:start position:0% +modify this Northern sketch condition a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +so rather than + + align:start position:0% +so rather than + + + align:start position:0% +so rather than +writing as part of new a mu + + align:start position:0% +writing as part of new a mu + + + align:start position:0% +writing as part of new a mu +let's try to impose the gauge + + align:start position:0% + + + + align:start position:0% + +a mu + + align:start position:0% +a mu + + + align:start position:0% +a mu +equal to some arbitrary function DX + + align:start position:0% +equal to some arbitrary function DX + + + align:start position:0% +equal to some arbitrary function DX +okay + + align:start position:0% + + + + align:start position:0% + +because partial mu a mu will give some + + align:start position:0% +because partial mu a mu will give some + + + align:start position:0% +because partial mu a mu will give some +trajectory + + align:start position:0% +trajectory + + + align:start position:0% +trajectory +here + + align:start position:0% +here + + + align:start position:0% +here +but if I choose some arbitrary function + + align:start position:0% +but if I choose some arbitrary function + + + align:start position:0% +but if I choose some arbitrary function +BX + + align:start position:0% +BX + + + align:start position:0% +BX +we'll just give you some other + + align:start position:0% +we'll just give you some other + + + align:start position:0% +we'll just give you some other +trajectory okay it's still some + + align:start position:0% +trajectory okay it's still some + + + align:start position:0% +trajectory okay it's still some +trajectory so so what BX you choose + + align:start position:0% +trajectory so so what BX you choose + + + align:start position:0% +trajectory so so what BX you choose +doesn't matter okay so so so you can + + align:start position:0% +doesn't matter okay so so so you can + + + align:start position:0% +doesn't matter okay so so so you can +just + + align:start position:0% +just + + + align:start position:0% +just +replace + + align:start position:0% +replace + + + align:start position:0% +replace +we start a function partial mu a mu here + + align:start position:0% +we start a function partial mu a mu here + + + align:start position:0% +we start a function partial mu a mu here +by + + align:start position:0% +by + + + align:start position:0% +by +Delta partial mu + + align:start position:0% +Delta partial mu + + + align:start position:0% +Delta partial mu +a mu e x okay so this is the first + + align:start position:0% +a mu e x okay so this is the first + + + align:start position:0% +a mu e x okay so this is the first +non-trivial step okay + + align:start position:0% +non-trivial step okay + + + align:start position:0% +non-trivial step okay +and uh yeah so this will give you some + + align:start position:0% +and uh yeah so this will give you some + + + align:start position:0% +and uh yeah so this will give you some +other trigger actually + + align:start position:0% +other trigger actually + + + align:start position:0% +other trigger actually +so now since the BX does not matter + + align:start position:0% +so now since the BX does not matter + + + align:start position:0% +so now since the BX does not matter +okay since the BX does not matter we can + + align:start position:0% +okay since the BX does not matter we can + + + align:start position:0% +okay since the BX does not matter we can +actually integrate over BX + + align:start position:0% +actually integrate over BX + + + align:start position:0% +actually integrate over BX +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then the next step + + align:start position:0% +and then the next step + + + align:start position:0% +and then the next step +okay is to + + align:start position:0% +okay is to + + + align:start position:0% +okay is to +so first you paste that + + align:start position:0% + + + + align:start position:0% + +so this is the first step and then the + + align:start position:0% +so this is the first step and then the + + + align:start position:0% +so this is the first step and then the +next step is that you replace the + + align:start position:0% +next step is that you replace the + + + align:start position:0% +next step is that you replace the +by you integrate over BX + + align:start position:0% + + + + align:start position:0% + +with a measure + + align:start position:0% + + + + align:start position:0% + +is square X + + align:start position:0% +is square X + + + align:start position:0% +is square X +and then + + align:start position:0% +and then + + + align:start position:0% +and then +original Z okay + + align:start position:0% + + + + align:start position:0% + +so your original DJ + + align:start position:0% + + + + align:start position:0% + +which now depend on B + + align:start position:0% +which now depend on B + + + align:start position:0% +which now depend on B +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +this condition + + align:start position:0% +this condition + + + align:start position:0% +this condition +and now I just + + align:start position:0% +and now I just + + + align:start position:0% +and now I just +since it did since this speed does not + + align:start position:0% +since it did since this speed does not + + + align:start position:0% +since it did since this speed does not +matter + + align:start position:0% +matter + + + align:start position:0% +matter +so I can just integrate over B with some + + align:start position:0% +so I can just integrate over B with some + + + align:start position:0% +so I can just integrate over B with some +arbitrary measure you want + + align:start position:0% +arbitrary measure you want + + + align:start position:0% +arbitrary measure you want +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the only thing this tasks just keep your + + align:start position:0% +the only thing this tasks just keep your + + + align:start position:0% +the only thing this tasks just keep your +infinite constant + + align:start position:0% +infinite constant + + + align:start position:0% +infinite constant +again we don't care infinite constant + + align:start position:0% +again we don't care infinite constant + + + align:start position:0% +again we don't care infinite constant +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so so this gives you some infinite + + align:start position:0% +okay so so this gives you some infinite + + + align:start position:0% +okay so so this gives you some infinite +constant + + align:start position:0% + + + + align:start position:0% + +since this thing is supposed to not to + + align:start position:0% +since this thing is supposed to not to + + + align:start position:0% +since this thing is supposed to not to +be depend on B okay + + align:start position:0% + + + + align:start position:0% + +but this actually is very useful + + align:start position:0% + + + + align:start position:0% + +because the reason we do this is because + + align:start position:0% +because the reason we do this is because + + + align:start position:0% +because the reason we do this is because +now when we do this + + align:start position:0% +now when we do this + + + align:start position:0% +now when we do this +the passing number become the following + + align:start position:0% +the passing number become the following + + + align:start position:0% +the passing number become the following +become DB + + align:start position:0% +become DB + + + align:start position:0% +become DB +the a mu + + align:start position:0% +the a mu + + + align:start position:0% +the a mu +now we have Delta a partial mu + + align:start position:0% +now we have Delta a partial mu + + + align:start position:0% +now we have Delta a partial mu +a mu minus BX + + align:start position:0% + + + + align:start position:0% + +and then we have experiential + + align:start position:0% +and then we have experiential + + + align:start position:0% +and then we have experiential +is + + align:start position:0% +is + + + align:start position:0% +is +the malice this x i one half b squared + + align:start position:0% + + + + align:start position:0% + +and then I have this + + align:start position:0% +and then I have this + + + align:start position:0% +and then I have this +i j dot a + + align:start position:0% + + + + align:start position:0% + +okay so now you see the benefits + + align:start position:0% +okay so now you see the benefits + + + align:start position:0% +okay so now you see the benefits +because now I have integration over B + + align:start position:0% +because now I have integration over B + + + align:start position:0% +because now I have integration over B +but the B appears very simply + + align:start position:0% +but the B appears very simply + + + align:start position:0% +but the B appears very simply +in the Delta function + + align:start position:0% +in the Delta function + + + align:start position:0% +in the Delta function +so now I can evaluate the Delta function + + align:start position:0% +so now I can evaluate the Delta function + + + align:start position:0% +so now I can evaluate the Delta function +by using the integral of P + + align:start position:0% +by using the integral of P + + + align:start position:0% +by using the integral of P +okay by using the integral of B + + align:start position:0% +okay by using the integral of B + + + align:start position:0% +okay by using the integral of B +so now I will get so now I can just do + + align:start position:0% +so now I will get so now I can just do + + + align:start position:0% +so now I will get so now I can just do +the straightforward to do the B integral + + align:start position:0% + + + + align:start position:0% + +so now I get a new action + + align:start position:0% + + + + align:start position:0% + +PSI + + align:start position:0% +PSI + + + align:start position:0% +PSI +plus I J dot a + + align:start position:0% +plus I J dot a + + + align:start position:0% +plus I J dot a +and now this + + align:start position:0% +and now this + + + align:start position:0% +and now this +I ask PSI + + align:start position:0% +I ask PSI + + + align:start position:0% +I ask PSI +so this exercise is just + + align:start position:0% +so this exercise is just + + + align:start position:0% +so this exercise is just +given by your original Maxwell + + align:start position:0% +given by your original Maxwell + + + align:start position:0% +given by your original Maxwell +the minus + + align:start position:0% +the minus + + + align:start position:0% +the minus +PSI over 2 + + align:start position:0% + + + + align:start position:0% + +partial mu a mu squared + + align:start position:0% +partial mu a mu squared + + + align:start position:0% +partial mu a mu squared +foreign + + align:start position:0% + + + + align:start position:0% + +so that's the reason we put B squared + + align:start position:0% +so that's the reason we put B squared + + + align:start position:0% +so that's the reason we put B squared +here + + align:start position:0% +here + + + align:start position:0% +here +he said when we evaluate the B integral + + align:start position:0% +he said when we evaluate the B integral + + + align:start position:0% +he said when we evaluate the B integral +and then we get something quadratic + + align:start position:0% +and then we get something quadratic + + + align:start position:0% +and then we get something quadratic +okay and now we we have that and now you + + align:start position:0% +okay and now we we have that and now you + + + align:start position:0% +okay and now we we have that and now you +see this action + + align:start position:0% +see this action + + + align:start position:0% +see this action +is precisely this action + + align:start position:0% +is precisely this action + + + align:start position:0% +is precisely this action +we have there okay + + align:start position:0% + + + + align:start position:0% + +okay it's precisely that actually given + + align:start position:0% +okay it's precisely that actually given + + + align:start position:0% +okay it's precisely that actually given +there so we also derive it using pass + + align:start position:0% +there so we also derive it using pass + + + align:start position:0% +there so we also derive it using pass +integral okay + + align:start position:0% + + + + align:start position:0% + +using this trick okay + + align:start position:0% + + + + align:start position:0% + +so so now we just have this + + align:start position:0% + + + + align:start position:0% + +now I just have this + + align:start position:0% +now I just have this + + + align:start position:0% +now I just have this +and now + + align:start position:0% +and now + + + align:start position:0% +and now +we can a straightforward to the + + align:start position:0% +we can a straightforward to the + + + align:start position:0% +we can a straightforward to the +calculate now we can straightforward the + + align:start position:0% +calculate now we can straightforward the + + + align:start position:0% +calculate now we can straightforward the +calculator discussing integral + + align:start position:0% + + + + align:start position:0% + +yeah now we can just straightforward we + + align:start position:0% +yeah now we can just straightforward we + + + align:start position:0% +yeah now we can just straightforward we +calculate this integral + + align:start position:0% + + + + align:start position:0% + +thank you + + align:start position:0% + + + + align:start position:0% + +so by the way the reason I say + + align:start position:0% +so by the way the reason I say + + + align:start position:0% +so by the way the reason I say +the um the story here + + align:start position:0% +the um the story here + + + align:start position:0% +the um the story here +is a trivial uh it's a little bit the + + align:start position:0% +is a trivial uh it's a little bit the + + + align:start position:0% +is a trivial uh it's a little bit the +kidding bird with uh it's because for + + align:start position:0% +kidding bird with uh it's because for + + + align:start position:0% +kidding bird with uh it's because for +the Maxwell case this Jacobi is actually + + align:start position:0% +the Maxwell case this Jacobi is actually + + + align:start position:0% +the Maxwell case this Jacobi is actually +trivial okay it's a constant but if you + + align:start position:0% +trivial okay it's a constant but if you + + + align:start position:0% +trivial okay it's a constant but if you +do it for longer being engaged series + + align:start position:0% +do it for longer being engaged series + + + align:start position:0% +do it for longer being engaged series +say for the electric weak theory of a + + align:start position:0% +say for the electric weak theory of a + + + align:start position:0% +say for the electric weak theory of a +qcd and this is Jacoby is highly long + + align:start position:0% +qcd and this is Jacoby is highly long + + + align:start position:0% +qcd and this is Jacoby is highly long +trivial and the and the part of this + + align:start position:0% +trivial and the and the part of this + + + align:start position:0% +trivial and the and the part of this +trick it's also hard to treat this + + align:start position:0% +trick it's also hard to treat this + + + align:start position:0% +trick it's also hard to treat this +Jacobian which we don't have to do here + + align:start position:0% +Jacobian which we don't have to do here + + + align:start position:0% +Jacobian which we don't have to do here +okay so here we have a much simpler + + align:start position:0% +okay so here we have a much simpler + + + align:start position:0% +okay so here we have a much simpler +story + + align:start position:0% +story + + + align:start position:0% +story +so so now we can just look at this + + align:start position:0% +so so now we can just look at this + + + align:start position:0% +so so now we can just look at this +part integral which now become immutable + + align:start position:0% +part integral which now become immutable + + + align:start position:0% +part integral which now become immutable +because we already know from here + + align:start position:0% +because we already know from here + + + align:start position:0% +because we already know from here +this is inverted by this Focus one given + + align:start position:0% +this is inverted by this Focus one given + + + align:start position:0% +this is inverted by this Focus one given +by this this is immutable okay so so you + + align:start position:0% +by this this is immutable okay so so you + + + align:start position:0% +by this this is immutable okay so so you +actually now + + align:start position:0% +actually now + + + align:start position:0% +actually now +now invert so so now we can write this s + + align:start position:0% +now invert so so now we can write this s + + + align:start position:0% +now invert so so now we can write this s +PSI + + align:start position:0% +PSI + + + align:start position:0% +PSI +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +one half + + align:start position:0% +one half + + + align:start position:0% +one half +d4x + + align:start position:0% +d4x + + + align:start position:0% +d4x +mu + + align:start position:0% +mu + + + align:start position:0% +mu +X + + align:start position:0% +X + + + align:start position:0% +X +K mu + + align:start position:0% +K mu + + + align:start position:0% +K mu +okay mu nux I + + align:start position:0% +okay mu nux I + + + align:start position:0% +okay mu nux I +x minus y + + align:start position:0% +x minus y + + + align:start position:0% +x minus y +a new y + + align:start position:0% + + + + align:start position:0% + +and this can be new + + align:start position:0% + + + + align:start position:0% + +so uh yeah okay maybe we just whatever + + align:start position:0% +so uh yeah okay maybe we just whatever + + + align:start position:0% +so uh yeah okay maybe we just whatever +you get + + align:start position:0% +you get + + + align:start position:0% +you get +from that scene okay just whatever you + + align:start position:0% +from that scene okay just whatever you + + + align:start position:0% +from that scene okay just whatever you +get from that scene + + align:start position:0% + + + + align:start position:0% + +is invertible + + align:start position:0% +is invertible + + + align:start position:0% +is invertible +and then you find the uh uh this thing + + align:start position:0% +and then you find the uh uh this thing + + + align:start position:0% +and then you find the uh uh this thing +just becomes some constant + + align:start position:0% + + + + align:start position:0% + +the exponential + + align:start position:0% + + + + align:start position:0% + +before x equal y + + align:start position:0% + + + + align:start position:0% + +J mu X + + align:start position:0% +J mu X + + + align:start position:0% +J mu X +then K PSI minus one + + align:start position:0% +then K PSI minus one + + + align:start position:0% +then K PSI minus one +we knew + + align:start position:0% +we knew + + + align:start position:0% +we knew +x minus one + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and again this inverse give you the Fine + + align:start position:0% +and again this inverse give you the Fine + + + align:start position:0% +and again this inverse give you the Fine +Line function + + align:start position:0% +Line function + + + align:start position:0% +Line function +okay again this gives you the fundament + + align:start position:0% +okay again this gives you the fundament + + + align:start position:0% +okay again this gives you the fundament +function + + align:start position:0% +function + + + align:start position:0% +function +so so the cake PSI + + align:start position:0% +so so the cake PSI + + + align:start position:0% +so so the cake PSI +minus y mu mu + + align:start position:0% +minus y mu mu + + + align:start position:0% +minus y mu mu +okay on mu Nu + + align:start position:0% + + + + align:start position:0% + +so so you can just uh you can yes I will + + align:start position:0% +so so you can just uh you can yes I will + + + align:start position:0% +so so you can just uh you can yes I will +not go into detail here the story is + + align:start position:0% +not go into detail here the story is + + + align:start position:0% +not go into detail here the story is +straightforward so this should + + align:start position:0% +straightforward so this should + + + align:start position:0% +straightforward so this should +corresponding to the filament function + + align:start position:0% + + + + align:start position:0% + +for the two + + align:start position:0% +for the two + + + align:start position:0% +for the two +uh uh a gauge Fields okay + + align:start position:0% + + + + align:start position:0% + +okay this should corresponding to the + + align:start position:0% +okay this should corresponding to the + + + align:start position:0% +okay this should corresponding to the +final function of these two gauge field + + align:start position:0% +final function of these two gauge field + + + align:start position:0% +final function of these two gauge field +so so now let me just write down the + + align:start position:0% +so so now let me just write down the + + + align:start position:0% +so so now let me just write down the +answer + + align:start position:0% +answer + + + align:start position:0% +answer +uh so I urge you to check it yourself + + align:start position:0% +uh so I urge you to check it yourself + + + align:start position:0% +uh so I urge you to check it yourself +explicitly okay + + align:start position:0% +explicitly okay + + + align:start position:0% +explicitly okay +uh so so you can usually write down what + + align:start position:0% +uh so so you can usually write down what + + + align:start position:0% +uh so so you can usually write down what +is kmu here + + align:start position:0% +is kmu here + + + align:start position:0% +is kmu here +okay and then uh + + align:start position:0% +okay and then uh + + + align:start position:0% +okay and then uh +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um + + align:start position:0% +um + + + align:start position:0% +um +uh I didn't write down what is kmu here + + align:start position:0% +uh I didn't write down what is kmu here + + + align:start position:0% +uh I didn't write down what is kmu here +and then you can uh + + align:start position:0% +and then you can uh + + + align:start position:0% +and then you can uh +write down what's the K minus one + + align:start position:0% +write down what's the K minus one + + + align:start position:0% +write down what's the K minus one +so so let me just write down the answer + + align:start position:0% +so so let me just write down the answer + + + align:start position:0% +so so let me just write down the answer +which we actually will use it + + align:start position:0% +which we actually will use it + + + align:start position:0% +which we actually will use it +data for the family diagram calculation + + align:start position:0% +data for the family diagram calculation + + + align:start position:0% +data for the family diagram calculation +okay so you can show + + align:start position:0% +okay so you can show + + + align:start position:0% +okay so you can show +a list given by + + align:start position:0% +a list given by + + + align:start position:0% +a list given by +in momentum space minus I + + align:start position:0% +in momentum space minus I + + + align:start position:0% +in momentum space minus I +K squared minus I abstract remember now + + align:start position:0% +K squared minus I abstract remember now + + + align:start position:0% +K squared minus I abstract remember now +here is Mercedes + + align:start position:0% +here is Mercedes + + + align:start position:0% +here is Mercedes +and you have it mu + + align:start position:0% +and you have it mu + + + align:start position:0% +and you have it mu +minus plus PSI minus 1 + + align:start position:0% +minus plus PSI minus 1 + + + align:start position:0% +minus plus PSI minus 1 +K mu + + align:start position:0% + + + + align:start position:0% + +P new divided by K Square + + align:start position:0% +P new divided by K Square + + + align:start position:0% +P new divided by K Square +okay + + align:start position:0% + + + + align:start position:0% + +so you can work out the inverse given by + + align:start position:0% +so you can work out the inverse given by + + + align:start position:0% +so you can work out the inverse given by +this + + align:start position:0% +this + + + align:start position:0% +this +and so this can also be written as + + align:start position:0% +and so this can also be written as + + + align:start position:0% +and so this can also be written as +in terms of the + + align:start position:0% +in terms of the + + + align:start position:0% +in terms of the +minus I + + align:start position:0% +minus I + + + align:start position:0% +minus I +K square plus I Epsilon + + align:start position:0% + + + + align:start position:0% + +you have + + align:start position:0% +you have + + + align:start position:0% +you have +you can write in terms this transverse + + align:start position:0% +you can write in terms this transverse + + + align:start position:0% +you can write in terms this transverse +projector mu t + + align:start position:0% + + + + align:start position:0% + +then Plus + + align:start position:0% + + + + align:start position:0% + +PSI P mu mu l + + align:start position:0% +PSI P mu mu l + + + align:start position:0% +PSI P mu mu l +so p mean l is the um + + align:start position:0% +so p mean l is the um + + + align:start position:0% +so p mean l is the um +longitudinal projector + + align:start position:0% +longitudinal projector + + + align:start position:0% +longitudinal projector +You just defined it by K mu + + align:start position:0% +You just defined it by K mu + + + align:start position:0% +You just defined it by K mu +okay Nu divided by K squared okay + + align:start position:0% +okay Nu divided by K squared okay + + + align:start position:0% +okay Nu divided by K squared okay +35 by by K squared + + align:start position:0% + + + + align:start position:0% + +so so this is a answer very simple okay + + align:start position:0% +so so this is a answer very simple okay + + + align:start position:0% +so so this is a answer very simple okay +so now the interesting scene + + align:start position:0% +so now the interesting scene + + + align:start position:0% +so now the interesting scene +okay the the two interesting thing here + + align:start position:0% + + + + align:start position:0% + +um yeah so let me just make some remarks + + align:start position:0% + + + + align:start position:0% + +so first + + align:start position:0% + + + + align:start position:0% + +if you look at cosine equal to 1 + + align:start position:0% + + + + align:start position:0% + +then this term vanishes + + align:start position:0% +then this term vanishes + + + align:start position:0% +then this term vanishes +and then you just have etamine mu + + align:start position:0% +and then you just have etamine mu + + + align:start position:0% +and then you just have etamine mu +divided by K Square minus Epsilon + + align:start position:0% +divided by K Square minus Epsilon + + + align:start position:0% +divided by K Square minus Epsilon +okay so that's exactly what you expect + + align:start position:0% +okay so that's exactly what you expect + + + align:start position:0% +okay so that's exactly what you expect +from here + + align:start position:0% +from here + + + align:start position:0% +from here +so here you just have essentially there + + align:start position:0% +so here you just have essentially there + + + align:start position:0% +so here you just have essentially there +but the message + + align:start position:0% +but the message + + + align:start position:0% +but the message +you just have the messages uh uh uh one + + align:start position:0% +you just have the messages uh uh uh one + + + align:start position:0% +you just have the messages uh uh uh one +over K Square uh publication is + + align:start position:0% +over K Square uh publication is + + + align:start position:0% +over K Square uh publication is +propagated for the mass list particle + + align:start position:0% +propagated for the mass list particle + + + align:start position:0% +propagated for the mass list particle +and then you have vitamin milk + + align:start position:0% +and then you have vitamin milk + + + align:start position:0% +and then you have vitamin milk +okay from the low rent uh signature okay + + align:start position:0% +okay from the low rent uh signature okay + + + align:start position:0% +okay from the low rent uh signature okay +uh uh so so for either you could rewind + + align:start position:0% +uh uh so so for either you could rewind + + + align:start position:0% +uh uh so so for either you could rewind +indeed recover that + + align:start position:0% + + + + align:start position:0% + +so a lot of the companies Having side + + align:start position:0% +so a lot of the companies Having side + + + align:start position:0% +so a lot of the companies Having side +equal to zero + + align:start position:0% + + + + align:start position:0% + +so this is just proportional to the + + align:start position:0% +so this is just proportional to the + + + align:start position:0% +so this is just proportional to the +transverse projector + + align:start position:0% +transverse projector + + + align:start position:0% +transverse projector +okay + + align:start position:0% +okay + + + align:start position:0% +okay +to each other projector but remember + + align:start position:0% +to each other projector but remember + + + align:start position:0% +to each other projector but remember +the original Maxwell action + + align:start position:0% +the original Maxwell action + + + align:start position:0% +the original Maxwell action +we use psychic to zero actually that's + + align:start position:0% +we use psychic to zero actually that's + + + align:start position:0% +we use psychic to zero actually that's +not invertible + + align:start position:0% +not invertible + + + align:start position:0% +not invertible +okay so so so here we're actually doing + + align:start position:0% +okay so so so here we're actually doing + + + align:start position:0% +okay so so so here we're actually doing +a different order we we first take a + + align:start position:0% +a different order we we first take a + + + align:start position:0% +a different order we we first take a +laundry oxide we invert it and then you + + align:start position:0% +laundry oxide we invert it and then you + + + align:start position:0% +laundry oxide we invert it and then you +can say it actually PSI equal to zero + + align:start position:0% +can say it actually PSI equal to zero + + + align:start position:0% +can say it actually PSI equal to zero +okay that still works okay and then the + + align:start position:0% +okay that still works okay and then the + + + align:start position:0% +okay that still works okay and then the +deal still works okay + + align:start position:0% +deal still works okay + + + align:start position:0% +deal still works okay +because we already fixed the gauge okay + + align:start position:0% +because we already fixed the gauge okay + + + align:start position:0% +because we already fixed the gauge okay +already fixed okay + + align:start position:0% +already fixed okay + + + align:start position:0% +already fixed okay +so so this is second remark + + align:start position:0% + + + + align:start position:0% + +and then yeah and then the and then the + + align:start position:0% +and then yeah and then the and then the + + + align:start position:0% +and then yeah and then the and then the +weak theorem + + align:start position:0% + + + + align:start position:0% + +for AMU just immediately follows + + align:start position:0% +for AMU just immediately follows + + + align:start position:0% +for AMU just immediately follows +from here just as what uh as in the case + + align:start position:0% +from here just as what uh as in the case + + + align:start position:0% +from here just as what uh as in the case +for the uh for the scalars and fermions + + align:start position:0% +for the uh for the scalars and fermions + + + align:start position:0% +for the uh for the scalars and fermions +uh uh yeah immediately follows + + align:start position:0% + + + + align:start position:0% + +okay you just contract we all get the + + align:start position:0% +okay you just contract we all get the + + + align:start position:0% +okay you just contract we all get the +disappointment + + align:start position:0% +disappointment + + + align:start position:0% +disappointment +functions between them + + align:start position:0% +functions between them + + + align:start position:0% +functions between them +yes + + align:start position:0% + + + + align:start position:0% + +oh no it's not difficult + + align:start position:0% +oh no it's not difficult + + + align:start position:0% +oh no it's not difficult +um so so so when um + + align:start position:0% +um so so so when um + + + align:start position:0% +um so so so when um +or one simple scene + + align:start position:0% +or one simple scene + + + align:start position:0% +or one simple scene +there's one point I'm going to make a + + align:start position:0% +there's one point I'm going to make a + + + align:start position:0% +there's one point I'm going to make a +little bit later + + align:start position:0% +little bit later + + + align:start position:0% +little bit later +uh um yeah in a few minutes later and + + align:start position:0% +uh um yeah in a few minutes later and + + + align:start position:0% +uh um yeah in a few minutes later and +actually uh + + align:start position:0% +actually uh + + + align:start position:0% +actually uh +for uh yeah yeah let me make some + + align:start position:0% +for uh yeah yeah let me make some + + + align:start position:0% +for uh yeah yeah let me make some +comment a little bit later yeah + + align:start position:0% +comment a little bit later yeah + + + align:start position:0% +comment a little bit later yeah +yeah they're completely equivalent yeah + + align:start position:0% + + + + align:start position:0% + +right right yeah + + align:start position:0% +right right yeah + + + align:start position:0% +right right yeah +so for what we for what we want to do it + + align:start position:0% +so for what we for what we want to do it + + + align:start position:0% +so for what we for what we want to do it +it's actually a little bit simpler okay + + align:start position:0% +it's actually a little bit simpler okay + + + align:start position:0% +it's actually a little bit simpler okay +for reasons I'm going to mention yeah + + align:start position:0% +for reasons I'm going to mention yeah + + + align:start position:0% +for reasons I'm going to mention yeah +other questions + + align:start position:0% +other questions + + + align:start position:0% +other questions +yes + + align:start position:0% + + + + align:start position:0% + +yeah it's a big big a big big because + + align:start position:0% +yeah it's a big big a big big because + + + align:start position:0% +yeah it's a big big a big big because +the projector is just a very simple way + + align:start position:0% +the projector is just a very simple way + + + align:start position:0% +the projector is just a very simple way +to + + align:start position:0% +to + + + align:start position:0% +to +so this + + align:start position:0% + + + + align:start position:0% + +so this is just + + align:start position:0% +so this is just + + + align:start position:0% +so this is just +so by definition this is symmetric + + align:start position:0% +so by definition this is symmetric + + + align:start position:0% +so by definition this is symmetric +immuno + + align:start position:0% +immuno + + + align:start position:0% +immuno +okay this would be a definition uh it's + + align:start position:0% +okay this would be a definition uh it's + + + align:start position:0% +okay this would be a definition uh it's +symmetric and you do because on the time + + align:start position:0% +symmetric and you do because on the time + + + align:start position:0% +symmetric and you do because on the time +ordering you can just exchange them + + align:start position:0% +ordering you can just exchange them + + + align:start position:0% +ordering you can just exchange them +then that means + + align:start position:0% +then that means + + + align:start position:0% +then that means +that in terms of Lawrence indices you + + align:start position:0% +that in terms of Lawrence indices you + + + align:start position:0% +that in terms of Lawrence indices you +must be able to expand it in some + + align:start position:0% +must be able to expand it in some + + + align:start position:0% +must be able to expand it in some +symmetric tensors + + align:start position:0% +symmetric tensors + + + align:start position:0% +symmetric tensors +built from kmu + + align:start position:0% +built from kmu + + + align:start position:0% +built from kmu +okay because kmu is only Vector here + + align:start position:0% +okay because kmu is only Vector here + + + align:start position:0% +okay because kmu is only Vector here +so so that means you have to build this + + align:start position:0% +so so that means you have to build this + + + align:start position:0% +so so that means you have to build this +metric tensor from just inter mil and K + + align:start position:0% +metric tensor from just inter mil and K + + + align:start position:0% +metric tensor from just inter mil and K +mu and the under the transverse and the + + align:start position:0% +mu and the under the transverse and the + + + align:start position:0% +mu and the under the transverse and the +and the uh non-depressional projectors + + align:start position:0% +and the uh non-depressional projectors + + + align:start position:0% +and the uh non-depressional projectors +are just the tensors you can build from + + align:start position:0% +are just the tensors you can build from + + + align:start position:0% +are just the tensors you can build from +the kmu + + align:start position:0% +the kmu + + + align:start position:0% +the kmu +yes + + align:start position:0% + + + + align:start position:0% + +no no that's not the radio gauge film + + align:start position:0% +no no that's not the radio gauge film + + + align:start position:0% +no no that's not the radio gauge film +just you can show that the physics is + + align:start position:0% +just you can show that the physics is + + + align:start position:0% +just you can show that the physics is +very independent book see yeah you don't + + align:start position:0% +very independent book see yeah you don't + + + align:start position:0% +very independent book see yeah you don't +you can take a seat with any value + + align:start position:0% + + + + align:start position:0% + +okay good other questions + + align:start position:0% +okay good other questions + + + align:start position:0% +okay good other questions +yes + + align:start position:0% + + + + align:start position:0% + +good good good + + align:start position:0% +good good good + + + align:start position:0% +good good good +so yeah so that's the comment I'm going + + align:start position:0% +so yeah so that's the comment I'm going + + + align:start position:0% +so yeah so that's the comment I'm going +to make later yeah yeah that's common + + align:start position:0% +to make later yeah yeah that's common + + + align:start position:0% +to make later yeah yeah that's common +that's a good question uh obviously I'm + + align:start position:0% +that's a good question uh obviously I'm + + + align:start position:0% +that's a good question uh obviously I'm +going to make later + + align:start position:0% +going to make later + + + align:start position:0% +going to make later +um yeah yeah let me just uh uh make this + + align:start position:0% +um yeah yeah let me just uh uh make this + + + align:start position:0% +um yeah yeah let me just uh uh make this +comment and then we'll be clear + + align:start position:0% +comment and then we'll be clear + + + align:start position:0% +comment and then we'll be clear +I need to make one comment first + + align:start position:0% + + + + align:start position:0% + +so now + + align:start position:0% +so now + + + align:start position:0% +so now +for for what is physical processes which + + align:start position:0% +for for what is physical processes which + + + align:start position:0% +for for what is physical processes which +we will consider later + + align:start position:0% + + + + align:start position:0% + +we are interested + + align:start position:0% +we are interested + + + align:start position:0% +we are interested +in the following scene + + align:start position:0% +in the following scene + + + align:start position:0% +in the following scene +so now we can just generalize + + align:start position:0% +so now we can just generalize + + + align:start position:0% +so now we can just generalize +immediately + + align:start position:0% + + + + align:start position:0% + +so now consider now we can just consider + + align:start position:0% + + + + align:start position:0% + +or in fact in theory + + align:start position:0% + + + + align:start position:0% + +of a mu + + align:start position:0% +of a mu + + + align:start position:0% +of a mu +PSI and Phi + + align:start position:0% +PSI and Phi + + + align:start position:0% +PSI and Phi +okay so so mu will be the Maxwell This + + align:start position:0% +okay so so mu will be the Maxwell This + + + align:start position:0% +okay so so mu will be the Maxwell This +will be some direct field there will be + + align:start position:0% +will be some direct field there will be + + + align:start position:0% +will be some direct field there will be +some scada field or even multiples of + + align:start position:0% +some scada field or even multiples of + + + align:start position:0% +some scada field or even multiples of +them + + align:start position:0% +them + + + align:start position:0% +them +so for for any such Theory + + align:start position:0% +so for for any such Theory + + + align:start position:0% +so for for any such Theory +we know how to compute + + align:start position:0% +we know how to compute + + + align:start position:0% +we know how to compute +the vacuum correlation function + + align:start position:0% + + + + align:start position:0% + +then then just what we did before just + + align:start position:0% +then then just what we did before just + + + align:start position:0% +then then just what we did before just +immediately follow + + align:start position:0% +immediately follow + + + align:start position:0% +immediately follow +just Define + + align:start position:0% +just Define + + + align:start position:0% +just Define +then X + + align:start position:0% +then X + + + align:start position:0% +then X +exponential is + + align:start position:0% + + + + align:start position:0% + +by + + align:start position:0% +by + + + align:start position:0% +by +and then + + align:start position:0% +and then + + + align:start position:0% +and then +Define exponential as + + align:start position:0% +Define exponential as + + + align:start position:0% +Define exponential as +okay so so again I always use Omega to + + align:start position:0% +okay so so again I always use Omega to + + + align:start position:0% +okay so so again I always use Omega to +denote the vacuum of the uh intact in + + align:start position:0% +denote the vacuum of the uh intact in + + + align:start position:0% +denote the vacuum of the uh intact in +theory and then again you can rewrite + + align:start position:0% +theory and then again you can rewrite + + + align:start position:0% +theory and then again you can rewrite +this as a serial free Theory + + align:start position:0% +this as a serial free Theory + + + align:start position:0% +this as a serial free Theory +is now this become in the free series + + align:start position:0% +is now this become in the free series + + + align:start position:0% +is now this become in the free series +zero + + align:start position:0% +zero + + + align:start position:0% +zero +TX + + align:start position:0% +TX + + + align:start position:0% +TX +the experience your eye interacting part + + align:start position:0% +the experience your eye interacting part + + + align:start position:0% +the experience your eye interacting part +zero + + align:start position:0% +zero + + + align:start position:0% +zero +and the zero + + align:start position:0% +and the zero + + + align:start position:0% +and the zero +explain to i t + + align:start position:0% +explain to i t + + + align:start position:0% +explain to i t +s i + + align:start position:0% +s i + + + align:start position:0% +s i +zero okay so so now again for any intact + + align:start position:0% +zero okay so so now again for any intact + + + align:start position:0% +zero okay so so now again for any intact +in theory we can just use the same + + align:start position:0% +in theory we can just use the same + + + align:start position:0% +in theory we can just use the same +procedure and then we can just do five + + align:start position:0% +procedure and then we can just do five + + + align:start position:0% +procedure and then we can just do five +and diagrams + + align:start position:0% +and diagrams + + + align:start position:0% +and diagrams +okay you can just do family diagrams + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and then then the + + align:start position:0% +and then then the + + + align:start position:0% +and then then the +in the family rule + + align:start position:0% +in the family rule + + + align:start position:0% +in the family rule +yeah we can just do fireman + + align:start position:0% + + + + align:start position:0% + +diagrams + + align:start position:0% + + + + align:start position:0% + +and the family Rules just follow + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so now + + align:start position:0% +so now + + + align:start position:0% +so now +yes you already asked + + align:start position:0% +yes you already asked + + + align:start position:0% +yes you already asked +this sounds a little bit too simple + + align:start position:0% +this sounds a little bit too simple + + + align:start position:0% +this sounds a little bit too simple +because we just look at this action + + align:start position:0% + + + + align:start position:0% + +we just look at this action + + align:start position:0% +we just look at this action + + + align:start position:0% +we just look at this action +but we haven't done what we promised you + + align:start position:0% +but we haven't done what we promised you + + + align:start position:0% +but we haven't done what we promised you +would do in your PSAT + + align:start position:0% +would do in your PSAT + + + align:start position:0% +would do in your PSAT +because by doing this we say you haven't + + align:start position:0% +because by doing this we say you haven't + + + align:start position:0% +because by doing this we say you haven't +you really have not + + align:start position:0% +you really have not + + + align:start position:0% +you really have not +completely fix the uh impose the passion + + align:start position:0% +completely fix the uh impose the passion + + + align:start position:0% +completely fix the uh impose the passion +view a meal yet okay + + align:start position:0% +view a meal yet okay + + + align:start position:0% +view a meal yet okay +so so remember we said that when you + + align:start position:0% +so so remember we said that when you + + + align:start position:0% +so so remember we said that when you +have this + + align:start position:0% +have this + + + align:start position:0% +have this +that will lead to + + align:start position:0% +that will lead to + + + align:start position:0% +that will lead to +this kind of equation + + align:start position:0% + + + + align:start position:0% + +you still have to impose the boundary + + align:start position:0% +you still have to impose the boundary + + + align:start position:0% +you still have to impose the boundary +conditions to impose the partial mu and + + align:start position:0% +conditions to impose the partial mu and + + + align:start position:0% +conditions to impose the partial mu and +mu to zero but now it seems like we are + + align:start position:0% +mu to zero but now it seems like we are + + + align:start position:0% +mu to zero but now it seems like we are +not doing anything like that okay we're + + align:start position:0% +not doing anything like that okay we're + + + align:start position:0% +not doing anything like that okay we're +not doing anything like that and also + + align:start position:0% +not doing anything like that and also + + + align:start position:0% +not doing anything like that and also +seems like we are not fixing the bread + + align:start position:0% +seems like we are not fixing the bread + + + align:start position:0% +seems like we are not fixing the bread +that you engage Freedom okay uh why + + align:start position:0% +that you engage Freedom okay uh why + + + align:start position:0% +that you engage Freedom okay uh why +don't we do it + + align:start position:0% +don't we do it + + + align:start position:0% +don't we do it +so we don't have to do it + + align:start position:0% +so we don't have to do it + + + align:start position:0% +so we don't have to do it +because + + align:start position:0% +because + + + align:start position:0% +because +here we are only interested in + + align:start position:0% +here we are only interested in + + + align:start position:0% +here we are only interested in +calculating the vacuum accumulation + + align:start position:0% +calculating the vacuum accumulation + + + align:start position:0% +calculating the vacuum accumulation +functions + + align:start position:0% +functions + + + align:start position:0% +functions +and the vacuum is automatically a + + align:start position:0% +and the vacuum is automatically a + + + align:start position:0% +and the vacuum is automatically a +physical state + + align:start position:0% +physical state + + + align:start position:0% +physical state +okay as you will see your PSAT the + + align:start position:0% +okay as you will see your PSAT the + + + align:start position:0% +okay as you will see your PSAT the +vacuum is automatic physical state and + + align:start position:0% +vacuum is automatic physical state and + + + align:start position:0% +vacuum is automatic physical state and +so uh see it's already in your it's + + align:start position:0% +so uh see it's already in your it's + + + align:start position:0% +so uh see it's already in your it's +already a physical state so so in the + + align:start position:0% +already a physical state so so in the + + + align:start position:0% +already a physical state so so in the +vacuum and all those on physical the + + align:start position:0% +vacuum and all those on physical the + + + align:start position:0% +vacuum and all those on physical the +good three and just automatically will + + align:start position:0% +good three and just automatically will + + + align:start position:0% +good three and just automatically will +decouple okay you don't have to worry + + align:start position:0% +decouple okay you don't have to worry + + + align:start position:0% +decouple okay you don't have to worry +about that + + align:start position:0% +about that + + + align:start position:0% +about that +and uh and so that's why but if you are + + align:start position:0% +and uh and so that's why but if you are + + + align:start position:0% +and uh and so that's why but if you are +interested in the excited States and + + align:start position:0% +interested in the excited States and + + + align:start position:0% +interested in the excited States and +then you have to go through the exactly + + align:start position:0% +then you have to go through the exactly + + + align:start position:0% +then you have to go through the exactly +the same kind of procedure to get rid of + + align:start position:0% +the same kind of procedure to get rid of + + + align:start position:0% +the same kind of procedure to get rid of +uh to do a more complicated thing as you + + align:start position:0% +uh to do a more complicated thing as you + + + align:start position:0% +uh to do a more complicated thing as you +would do in your PSAT okay and uh but + + align:start position:0% +would do in your PSAT okay and uh but + + + align:start position:0% +would do in your PSAT okay and uh but +here since we are Computing just a + + align:start position:0% +here since we are Computing just a + + + align:start position:0% +here since we are Computing just a +special class of physical quantities and + + align:start position:0% +special class of physical quantities and + + + align:start position:0% +special class of physical quantities and +then and then just by doing this it's + + align:start position:0% +then and then just by doing this it's + + + align:start position:0% +then and then just by doing this it's +already enough okay I don't have to + + align:start position:0% +already enough okay I don't have to + + + align:start position:0% +already enough okay I don't have to +worry about other sort of stuff okay you + + align:start position:0% +worry about other sort of stuff okay you + + + align:start position:0% +worry about other sort of stuff okay you +don't have to worry about other sort of + + align:start position:0% +don't have to worry about other sort of + + + align:start position:0% +don't have to worry about other sort of +stuff + + align:start position:0% +stuff + + + align:start position:0% +stuff +okay so so I think we are um + + align:start position:0% +okay so so I think we are um + + + align:start position:0% +okay so so I think we are um +we are done for the uh quantizing the + + align:start position:0% +we are done for the uh quantizing the + + + align:start position:0% +we are done for the uh quantizing the +Maxwell series + + align:start position:0% +Maxwell series + + + align:start position:0% +Maxwell series +so now we have all our element yes + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +oh you do the same thing you do the same + + align:start position:0% +oh you do the same thing you do the same + + + align:start position:0% +oh you do the same thing you do the same +thing right just expand them + + align:start position:0% +thing right just expand them + + + align:start position:0% +thing right just expand them +just expand the SI whatever is in si you + + align:start position:0% +just expand the SI whatever is in si you + + + align:start position:0% +just expand the SI whatever is in si you +just treat them together + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +yeah yeah yeah so so yeah so uh indeed + + align:start position:0% +yeah yeah yeah so so yeah so uh indeed + + + align:start position:0% +yeah yeah yeah so so yeah so uh indeed +so uh normally we assume all the + + align:start position:0% +so uh normally we assume all the + + + align:start position:0% +so uh normally we assume all the +coupling SI are of the same order + + align:start position:0% +coupling SI are of the same order + + + align:start position:0% +coupling SI are of the same order +and then you just expand the SI and then + + align:start position:0% +and then you just expand the SI and then + + + align:start position:0% +and then you just expand the SI and then +yeah but but indeed you can see the + + align:start position:0% +yeah but but indeed you can see the + + + align:start position:0% +yeah but but indeed you can see the +special situation uh you may want to + + align:start position:0% +special situation uh you may want to + + + align:start position:0% +special situation uh you may want to +expand some components not expand some + + align:start position:0% +expand some components not expand some + + + align:start position:0% +expand some components not expand some +other couplings and then that depends on + + align:start position:0% +other couplings and then that depends on + + + align:start position:0% +other couplings and then that depends on +specific situation + + align:start position:0% + + + + align:start position:0% + +other questions + + align:start position:0% + + + + align:start position:0% + +okay good good so so let's conclude our + + align:start position:0% +okay good good so so let's conclude our + + + align:start position:0% +okay good good so so let's conclude our +discussion of quantizing of Maxwell + + align:start position:0% +discussion of quantizing of Maxwell + + + align:start position:0% +discussion of quantizing of Maxwell +Theory + + align:start position:0% +Theory + + + align:start position:0% +Theory +and so so so now + + align:start position:0% +and so so so now + + + align:start position:0% +and so so so now +uh uh uh so we have quantized the photon + + align:start position:0% +uh uh uh so we have quantized the photon + + + align:start position:0% +uh uh uh so we have quantized the photon +okay we have quantize the maximum Theory + + align:start position:0% +okay we have quantize the maximum Theory + + + align:start position:0% +okay we have quantize the maximum Theory +using the coolant gauge then we see the + + align:start position:0% +using the coolant gauge then we see the + + + align:start position:0% +using the coolant gauge then we see the +two photons the good Freedom okay and + + align:start position:0% +two photons the good Freedom okay and + + + align:start position:0% +two photons the good Freedom okay and +then we also did canonical condition for + + align:start position:0% +then we also did canonical condition for + + + align:start position:0% +then we also did canonical condition for +the landscape which you will finish in + + align:start position:0% +the landscape which you will finish in + + + align:start position:0% +the landscape which you will finish in +your PSAT and then we also discussed how + + align:start position:0% +your PSAT and then we also discussed how + + + align:start position:0% +your PSAT and then we also discussed how +to treat the impact integral so that + + align:start position:0% +to treat the impact integral so that + + + align:start position:0% +to treat the impact integral so that +you can calculate these kind of + + align:start position:0% +you can calculate these kind of + + + align:start position:0% +you can calculate these kind of +questions + + align:start position:0% +questions + + + align:start position:0% +questions +okay so that we can treat this kind of + + align:start position:0% +okay so that we can treat this kind of + + + align:start position:0% +okay so that we can treat this kind of +questions + + align:start position:0% +questions + + + align:start position:0% +questions +and uh the knowledge let's go now we + + align:start position:0% +and uh the knowledge let's go now we + + + align:start position:0% +and uh the knowledge let's go now we +have all the technicality all the tools + + align:start position:0% +have all the technicality all the tools + + + align:start position:0% +have all the technicality all the tools +we need now we can tackle QED okay so + + align:start position:0% +we need now we can tackle QED okay so + + + align:start position:0% +we need now we can tackle QED okay so +now finally we can tackle community + + align:start position:0% +now finally we can tackle community + + + align:start position:0% +now finally we can tackle community +so this is the theory of photon + + align:start position:0% +so this is the theory of photon + + + align:start position:0% +so this is the theory of photon +an electron + + align:start position:0% +an electron + + + align:start position:0% +an electron +okay this is the serial Photon electron + + align:start position:0% +okay this is the serial Photon electron + + + align:start position:0% +okay this is the serial Photon electron +and uh uh so we can consider the + + align:start position:0% +and uh uh so we can consider the + + + align:start position:0% +and uh uh so we can consider the +physical process in this series which + + align:start position:0% +physical process in this series which + + + align:start position:0% +physical process in this series which +AMU and PSI are now interacting with + + align:start position:0% +AMU and PSI are now interacting with + + + align:start position:0% +AMU and PSI are now interacting with +each other + + align:start position:0% +each other + + + align:start position:0% +each other +okay immune law interacting with each + + align:start position:0% +okay immune law interacting with each + + + align:start position:0% +okay immune law interacting with each +other and uh so yeah so we will start + + align:start position:0% +other and uh so yeah so we will start + + + align:start position:0% +other and uh so yeah so we will start +doing it uh I think we are out yeah we + + align:start position:0% +doing it uh I think we are out yeah we + + + align:start position:0% +doing it uh I think we are out yeah we +only have two minutes left so so maybe + + align:start position:0% +only have two minutes left so so maybe + + + align:start position:0% +only have two minutes left so so maybe +we will finish a little bit early today + + align:start position:0% +we will finish a little bit early today + + + align:start position:0% +we will finish a little bit early today +okay yeah yeah so that's all for today + + align:start position:0% +okay yeah yeah so that's all for today + + + align:start position:0% +okay yeah yeah so that's all for today +yeah \ No newline at end of file diff --git a/m4salGLUIBg.txt b/m4salGLUIBg.txt new file mode 100644 index 0000000000000000000000000000000000000000..6f3b459c8be911df6568203fbedcb3698979b51c --- /dev/null +++ b/m4salGLUIBg.txt @@ -0,0 +1,12315 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +so again let us first recall + + align:start position:0% + + + + align:start position:0% + +say if we want to calculate + + align:start position:0% +say if we want to calculate + + + align:start position:0% +say if we want to calculate +the endpoint function + + align:start position:0% + + + + align:start position:0% + +in the interacting Theory + + align:start position:0% + + + + align:start position:0% + +and this is given by this foreign ratio + + align:start position:0% +and this is given by this foreign ratio + + + align:start position:0% +and this is given by this foreign ratio +in the free series + + align:start position:0% + + + + align:start position:0% + +look at this t + + align:start position:0% +look at this t + + + align:start position:0% +look at this t +then you look at this again take this + + align:start position:0% +then you look at this again take this + + + align:start position:0% +then you look at this again take this +product to be X + + align:start position:0% +product to be X + + + align:start position:0% +product to be X +take the TX + + align:start position:0% +take the TX + + + align:start position:0% +take the TX +experience isi + + align:start position:0% + + + + align:start position:0% + +free Siri + + align:start position:0% +free Siri + + + align:start position:0% +free Siri +and then divide it + + align:start position:0% +and then divide it + + + align:start position:0% +and then divide it +just by + + align:start position:0% +just by + + + align:start position:0% +just by +time order + + align:start position:0% +time order + + + align:start position:0% +time order +isi in the free series + + align:start position:0% +isi in the free series + + + align:start position:0% +isi in the free series +okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so so what then what we do is we just + + align:start position:0% +so so what then what we do is we just + + + align:start position:0% +so so what then what we do is we just +expand these two exponential in power + + align:start position:0% +expand these two exponential in power + + + align:start position:0% +expand these two exponential in power +series + + align:start position:0% +series + + + align:start position:0% +series +okay we expand this expansion in power + + align:start position:0% +okay we expand this expansion in power + + + align:start position:0% +okay we expand this expansion in power +series + + align:start position:0% +series + + + align:start position:0% +series +and uh so when you expand in power + + align:start position:0% +and uh so when you expand in power + + + align:start position:0% +and uh so when you expand in power +series + + align:start position:0% +series + + + align:start position:0% +series +then then for example the ends or the + + align:start position:0% +then then for example the ends or the + + + align:start position:0% +then then for example the ends or the +term + + align:start position:0% + + + + align:start position:0% + +in the upstairs + + align:start position:0% + + + + align:start position:0% + +say upstairs + + align:start position:0% + + + + align:start position:0% + +then have the following structure + + align:start position:0% +then have the following structure + + + align:start position:0% +then have the following structure +you have I + + align:start position:0% +you have I + + + align:start position:0% +you have I +to the power n and factorial + + align:start position:0% +to the power n and factorial + + + align:start position:0% +to the power n and factorial +then you have + + align:start position:0% +then you have + + + align:start position:0% +then you have +p + + align:start position:0% + + + + align:start position:0% + +X then s i to the power + + align:start position:0% +X then s i to the power + + + align:start position:0% +X then s i to the power +to NSI okay + + align:start position:0% + + + + align:start position:0% + +and the ends order for the + + align:start position:0% +and the ends order for the + + + align:start position:0% +and the ends order for the +downstairs + + align:start position:0% +downstairs + + + align:start position:0% +downstairs +you can also expand the the downstairs + + align:start position:0% + + + + align:start position:0% + +say in the downstairs + + align:start position:0% +say in the downstairs + + + align:start position:0% +say in the downstairs +similarly + + align:start position:0% + + + + align:start position:0% + +then you have + + align:start position:0% +then you have + + + align:start position:0% +then you have +almost identical structure + + align:start position:0% +almost identical structure + + + align:start position:0% +almost identical structure +except you don't have this x okay so you + + align:start position:0% +except you don't have this x okay so you + + + align:start position:0% +except you don't have this x okay so you +have t then you just have n + + align:start position:0% +have t then you just have n + + + align:start position:0% +have t then you just have n +as ice okay + + align:start position:0% +as ice okay + + + align:start position:0% +as ice okay +so this end of them + + align:start position:0% + + + + align:start position:0% + +so they're in opening okay + + align:start position:0% + + + + align:start position:0% + +and the last time so we described + + align:start position:0% +and the last time so we described + + + align:start position:0% +and the last time so we described +how to compute + + align:start position:0% +how to compute + + + align:start position:0% +how to compute +say a typical terms in here okay so let + + align:start position:0% +say a typical terms in here okay so let + + + align:start position:0% +say a typical terms in here okay so let +me call this equation star + + align:start position:0% +me call this equation star + + + align:start position:0% +me call this equation star +equation star star + + align:start position:0% +equation star star + + + align:start position:0% +equation star star +so last time we described + + align:start position:0% +so last time we described + + + align:start position:0% +so last time we described +so the star + + align:start position:0% +so the star + + + align:start position:0% +so the star +and the star star + + align:start position:0% +and the star star + + + align:start position:0% +and the star star +can be computed + + align:start position:0% + + + + align:start position:0% + +using big theorem + + align:start position:0% + + + + align:start position:0% + +okay but in practice + + align:start position:0% + + + + align:start position:0% + +in practice what we do is that we first + + align:start position:0% +in practice what we do is that we first + + + align:start position:0% +in practice what we do is that we first +do + + align:start position:0% +do + + + align:start position:0% +do +permanent diagrams + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% +and then + + + align:start position:0% +and then +we convert the farming diagrams into say + + align:start position:0% +we convert the farming diagrams into say + + + align:start position:0% +we convert the farming diagrams into say +analytic Expressions okay + + align:start position:0% + + + + align:start position:0% + +so normally we go through this procedure + + align:start position:0% +so normally we go through this procedure + + + align:start position:0% +so normally we go through this procedure +okay rather than directly to the weak + + align:start position:0% +okay rather than directly to the weak + + + align:start position:0% +okay rather than directly to the weak +contraction rather than directly + + align:start position:0% +contraction rather than directly + + + align:start position:0% +contraction rather than directly +to the big contraction okay so we + + align:start position:0% +to the big contraction okay so we + + + align:start position:0% +to the big contraction okay so we +mentioned the + + align:start position:0% +mentioned the + + + align:start position:0% +mentioned the +um + + align:start position:0% + + + + align:start position:0% + +and the second line of course is just + + align:start position:0% +and the second line of course is just + + + align:start position:0% +and the second line of course is just +can be considered as a special case of + + align:start position:0% +can be considered as a special case of + + + align:start position:0% +can be considered as a special case of +the first line which you just uh with + + align:start position:0% +the first line which you just uh with + + + align:start position:0% +the first line which you just uh with +this x to be identity okay + + align:start position:0% +this x to be identity okay + + + align:start position:0% +this x to be identity okay +identity + + align:start position:0% +identity + + + align:start position:0% +identity +so so + + align:start position:0% +so so + + + align:start position:0% +so so +um + + align:start position:0% +um + + + align:start position:0% +um +so any diagram + + align:start position:0% + + + + align:start position:0% + +contributing + + align:start position:0% + + + + align:start position:0% + +to Star + + align:start position:0% + + + + align:start position:0% + +okay because the + + align:start position:0% +okay because the + + + align:start position:0% +okay because the +yeah sorry I should actually so here and + + align:start position:0% +yeah sorry I should actually so here and + + + align:start position:0% +yeah sorry I should actually so here and +let me call it m it's so that they don't + + align:start position:0% +let me call it m it's so that they don't + + + align:start position:0% +let me call it m it's so that they don't +uh sorry + + align:start position:0% +uh sorry + + + align:start position:0% +uh sorry +let's show the code M so that they don't + + align:start position:0% +let's show the code M so that they don't + + + align:start position:0% +let's show the code M so that they don't +yeah because we already have M and here + + align:start position:0% +yeah because we already have M and here + + + align:start position:0% +yeah because we already have M and here +okay + + align:start position:0% + + + + align:start position:0% + +so M's order okay + + align:start position:0% + + + + align:start position:0% + +so any diagram contributing to say the + + align:start position:0% +so any diagram contributing to say the + + + align:start position:0% +so any diagram contributing to say the +star + + align:start position:0% +star + + + align:start position:0% +star +as any external X + + align:start position:0% + + + + align:start position:0% + +okay as an external X + + align:start position:0% +okay as an external X + + + align:start position:0% +okay as an external X +so that come from just from this x okay + + align:start position:0% +so that come from just from this x okay + + + align:start position:0% +so that come from just from this x okay +from this five five x one and the 5x n + + align:start position:0% +from this five five x one and the 5x n + + + align:start position:0% +from this five five x one and the 5x n +okay + + align:start position:0% + + + + align:start position:0% + +and then uh um + + align:start position:0% +and then uh um + + + align:start position:0% +and then uh um +also with m + + align:start position:0% + + + + align:start position:0% + +vertices + + align:start position:0% +vertices + + + align:start position:0% +vertices +okay because each vertices + + align:start position:0% +okay because each vertices + + + align:start position:0% +okay because each vertices +come from a power of s i okay + + align:start position:0% +come from a power of s i okay + + + align:start position:0% +come from a power of s i okay +a compound of s i + + align:start position:0% + + + + align:start position:0% + +but for for star star + + align:start position:0% + + + + align:start position:0% + +so diagrams + + align:start position:0% + + + + align:start position:0% + +contributing + + align:start position:0% + + + + align:start position:0% + +to star star + + align:start position:0% + + + + align:start position:0% + +have low external lags okay because + + align:start position:0% +have low external lags okay because + + + align:start position:0% +have low external lags okay because +there's no uh or there's no low X here + + align:start position:0% +there's no uh or there's no low X here + + + align:start position:0% +there's no uh or there's no low X here +there's no Phi here okay there's no x no + + align:start position:0% +there's no Phi here okay there's no x no + + + align:start position:0% +there's no Phi here okay there's no x no +legs + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so that's why they're all called + + align:start position:0% +so so that's why they're all called + + + align:start position:0% +so so that's why they're all called +vacuum diagrams + + align:start position:0% + + + + align:start position:0% + +okay and they're called the vacuum + + align:start position:0% +okay and they're called the vacuum + + + align:start position:0% +okay and they're called the vacuum +diagrams okay + + align:start position:0% +diagrams okay + + + align:start position:0% +diagrams okay +so so the downstairs can be understood + + align:start position:0% +so so the downstairs can be understood + + + align:start position:0% +so so the downstairs can be understood +as in the case which you just + + align:start position:0% +as in the case which you just + + + align:start position:0% +as in the case which you just +essentially take when you take x equal + + align:start position:0% +essentially take when you take x equal + + + align:start position:0% +essentially take when you take x equal +to one + + align:start position:0% +to one + + + align:start position:0% +to one +so essentially we are calculating the uh + + align:start position:0% +so essentially we are calculating the uh + + + align:start position:0% +so essentially we are calculating the uh +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um + + align:start position:0% +um + + + align:start position:0% +um +uh uh yeah some kind of unnormalized + + align:start position:0% +uh uh yeah some kind of unnormalized + + + align:start position:0% +uh uh yeah some kind of unnormalized +transition yeah just the overlap between + + align:start position:0% +transition yeah just the overlap between + + + align:start position:0% +transition yeah just the overlap between +the vacuum itself okay between the + + align:start position:0% +the vacuum itself okay between the + + + align:start position:0% +the vacuum itself okay between the +vacuum itself from balance Infinity to + + align:start position:0% +vacuum itself from balance Infinity to + + + align:start position:0% +vacuum itself from balance Infinity to +plus infinity okay for Mass infinity + + align:start position:0% +plus infinity okay for Mass infinity + + + align:start position:0% +plus infinity okay for Mass infinity +plus infinity + + align:start position:0% +plus infinity + + + align:start position:0% +plus infinity +so um + + align:start position:0% +so um + + + align:start position:0% +so um +so in PSAT 6 + + align:start position:0% +so in PSAT 6 + + + align:start position:0% +so in PSAT 6 +okay in P size 6 + + align:start position:0% + + + + align:start position:0% + +yeah just in the P side we just uh + + align:start position:0% +yeah just in the P side we just uh + + + align:start position:0% +yeah just in the P side we just uh +posted last night + + align:start position:0% +posted last night + + + align:start position:0% +posted last night +you can show that this actually this + + align:start position:0% +you can show that this actually this + + + align:start position:0% +you can show that this actually this +quantity + + align:start position:0% + + + + align:start position:0% + +which come from summing or over all + + align:start position:0% +which come from summing or over all + + + align:start position:0% +which come from summing or over all +possible vacuum diagrams okay at the + + align:start position:0% +possible vacuum diagrams okay at the + + + align:start position:0% +possible vacuum diagrams okay at the +diagrams without external X okay + + align:start position:0% +diagrams without external X okay + + + align:start position:0% +diagrams without external X okay +you know have low sorry I should say + + align:start position:0% +you know have low sorry I should say + + + align:start position:0% +you know have low sorry I should say +hello it's no neck + + align:start position:0% +hello it's no neck + + + align:start position:0% +hello it's no neck +this node is very important + + align:start position:0% +this node is very important + + + align:start position:0% +this node is very important +yeah it has no x no X + + align:start position:0% +yeah it has no x no X + + + align:start position:0% +yeah it has no x no X +and so they're called vacuum diagrams + + align:start position:0% +and so they're called vacuum diagrams + + + align:start position:0% +and so they're called vacuum diagrams +so + + align:start position:0% +so + + + align:start position:0% +so +um so in piece at six you will show + + align:start position:0% +um so in piece at six you will show + + + align:start position:0% +um so in piece at six you will show +yourself okay so it's a pretty simple + + align:start position:0% +yourself okay so it's a pretty simple + + + align:start position:0% +yourself okay so it's a pretty simple +calculation + + align:start position:0% +calculation + + + align:start position:0% +calculation +about this instructive one + + align:start position:0% +about this instructive one + + + align:start position:0% +about this instructive one +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um + + align:start position:0% +um + + + align:start position:0% +um +you can show that this quantity + + align:start position:0% + + + + align:start position:0% + +can be used + + align:start position:0% + + + + align:start position:0% + +to calculate + + align:start position:0% + + + + align:start position:0% + +the vacuum energy + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the vacuum manage + + align:start position:0% +the vacuum manage + + + align:start position:0% +the vacuum manage +of the interacting series of course this + + align:start position:0% +of the interacting series of course this + + + align:start position:0% +of the interacting series of course this +is Divergent + + align:start position:0% +is Divergent + + + align:start position:0% +is Divergent +but uh just as the vacuum energy we can + + align:start position:0% +but uh just as the vacuum energy we can + + + align:start position:0% +but uh just as the vacuum energy we can +be calculated before in free Theory okay + + align:start position:0% +be calculated before in free Theory okay + + + align:start position:0% +be calculated before in free Theory okay +so so this one can be used to calculate + + align:start position:0% +so so this one can be used to calculate + + + align:start position:0% +so so this one can be used to calculate +the vacuum energy + + align:start position:0% +the vacuum energy + + + align:start position:0% +the vacuum energy +of the interacting Theory + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so of course this quantity will uh you + + align:start position:0% +so of course this quantity will uh you + + + align:start position:0% +so of course this quantity will uh you +will see it's Divergent but at least + + align:start position:0% +will see it's Divergent but at least + + + align:start position:0% +will see it's Divergent but at least +this is a formal way to calculate it and + + align:start position:0% +this is a formal way to calculate it and + + + align:start position:0% +this is a formal way to calculate it and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um yeah and how to remove the + + align:start position:0% +um yeah and how to remove the + + + align:start position:0% +um yeah and how to remove the +divergences ETC uh is + + align:start position:0% +divergences ETC uh is + + + align:start position:0% +divergences ETC uh is +something we will not discuss okay in + + align:start position:0% +something we will not discuss okay in + + + align:start position:0% +something we will not discuss okay in +this class will be next class that will + + align:start position:0% +this class will be next class that will + + + align:start position:0% +this class will be next class that will +be in qft2 + + align:start position:0% +be in qft2 + + + align:start position:0% +be in qft2 +so any questions on this + + align:start position:0% + + + + align:start position:0% + +okay great + + align:start position:0% +okay great + + + align:start position:0% +okay great +so let me say a few more words + + align:start position:0% + + + + align:start position:0% + +so so when we compute + + align:start position:0% +so so when we compute + + + align:start position:0% +so so when we compute +to + + align:start position:0% + + + + align:start position:0% + +so there we say they can be computed + + align:start position:0% +so there we say they can be computed + + + align:start position:0% +so there we say they can be computed +using the firmware diagram so let me be + + align:start position:0% +using the firmware diagram so let me be + + + align:start position:0% +using the firmware diagram so let me be +a little bit more uh more explicit + + align:start position:0% +a little bit more uh more explicit + + + align:start position:0% +a little bit more uh more explicit +so the computation + + align:start position:0% +so the computation + + + align:start position:0% +so the computation +of star + + align:start position:0% +of star + + + align:start position:0% +of star +or star star + + align:start position:0% +or star star + + + align:start position:0% +or star star +involved with the essentially involve + + align:start position:0% +involved with the essentially involve + + + align:start position:0% +involved with the essentially involve +two steps + + align:start position:0% + + + + align:start position:0% + +so I just elaborate that remark in the + + align:start position:0% +so I just elaborate that remark in the + + + align:start position:0% +so I just elaborate that remark in the +bracket + + align:start position:0% +bracket + + + align:start position:0% +bracket +is that we first draw + + align:start position:0% + + + + align:start position:0% + +or possible + + align:start position:0% +or possible + + + align:start position:0% +or possible +or in equivalent + + align:start position:0% + + + + align:start position:0% + +filament diagrams okay + + align:start position:0% + + + + align:start position:0% + +so in this case + + align:start position:0% +so in this case + + + align:start position:0% +so in this case +so in this case so at each + + align:start position:0% +so in this case so at each + + + align:start position:0% +so in this case so at each +order of each amps order + + align:start position:0% +order of each amps order + + + align:start position:0% +order of each amps order +you have endpoint and external point + + align:start position:0% +you have endpoint and external point + + + align:start position:0% +you have endpoint and external point +and then you have M vertices + + align:start position:0% +and then you have M vertices + + + align:start position:0% +and then you have M vertices +yeah so so there you have say four star + + align:start position:0% +yeah so so there you have say four star + + + align:start position:0% +yeah so so there you have say four star +you just have say any external point + + align:start position:0% +you just have say any external point + + + align:start position:0% +you just have say any external point +say X1 X2 + + align:start position:0% +say X1 X2 + + + align:start position:0% +say X1 X2 +said in coordinate space you have any + + align:start position:0% +said in coordinate space you have any + + + align:start position:0% +said in coordinate space you have any +external point and then you have M + + align:start position:0% +external point and then you have M + + + align:start position:0% +external point and then you have M +vertices + + align:start position:0% +vertices + + + align:start position:0% +vertices +and that each vertices you have a + + align:start position:0% +and that each vertices you have a + + + align:start position:0% +and that each vertices you have a +um say say let's call it y1 Y2 + + align:start position:0% + + + + align:start position:0% + +ym and each vertices you have four legs + + align:start position:0% +ym and each vertices you have four legs + + + align:start position:0% +ym and each vertices you have four legs +coming out okay and at each external + + align:start position:0% +coming out okay and at each external + + + align:start position:0% +coming out okay and at each external +uh over that a a point you have + + align:start position:0% +uh over that a a point you have + + + align:start position:0% +uh over that a a point you have +when vertex come out a one line come out + + align:start position:0% +when vertex come out a one line come out + + + align:start position:0% +when vertex come out a one line come out +okay and then you just need to find all + + align:start position:0% +okay and then you just need to find all + + + align:start position:0% +okay and then you just need to find all +possible ways to contract to connect + + align:start position:0% +possible ways to contract to connect + + + align:start position:0% +possible ways to contract to connect +them + + align:start position:0% +them + + + align:start position:0% +them +so so that we mean by joining all in + + align:start position:0% +so so that we mean by joining all in + + + align:start position:0% +so so that we mean by joining all in +equivalent diagrams okay you just uh uh + + align:start position:0% +equivalent diagrams okay you just uh uh + + + align:start position:0% +equivalent diagrams okay you just uh uh +this just you just show it okay become + + align:start position:0% +this just you just show it okay become + + + align:start position:0% +this just you just show it okay become +mechanical + + align:start position:0% +mechanical + + + align:start position:0% +mechanical +uh become a mechanical yes + + align:start position:0% + + + + align:start position:0% + +yeah oh we are talking about the here + + align:start position:0% +yeah oh we are talking about the here + + + align:start position:0% +yeah oh we are talking about the here +we're talking about the yeah more + + align:start position:0% +we're talking about the yeah more + + + align:start position:0% +we're talking about the yeah more +specifically here we're talking about + + align:start position:0% +specifically here we're talking about + + + align:start position:0% +specifically here we're talking about +the s i + + align:start position:0% + + + + align:start position:0% + +yeah so this is for the uh + + align:start position:0% +yeah so this is for the uh + + + align:start position:0% +yeah so this is for the uh +s i + + align:start position:0% +s i + + + align:start position:0% +s i +equal to minus Lambda 4 factorial + + align:start position:0% + + + + align:start position:0% + +we consider this particular series okay + + align:start position:0% +we consider this particular series okay + + + align:start position:0% +we consider this particular series okay +we consider yeah yeah I'm going to make + + align:start position:0% +we consider yeah yeah I'm going to make + + + align:start position:0% +we consider yeah yeah I'm going to make +remarks on on other a more General + + align:start position:0% +remarks on on other a more General + + + align:start position:0% +remarks on on other a more General +series uh but yeah yeah here is more + + align:start position:0% +series uh but yeah yeah here is more + + + align:start position:0% +series uh but yeah yeah here is more +specific yeah + + align:start position:0% +specific yeah + + + align:start position:0% +specific yeah +other questions + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so this is for staff + + align:start position:0% +so so this is for staff + + + align:start position:0% +so so this is for staff +so for star star + + align:start position:0% +so for star star + + + align:start position:0% +so for star star +then you just don't have the X you just + + align:start position:0% +then you just don't have the X you just + + + align:start position:0% +then you just don't have the X you just +have y's we have just have m y and each + + align:start position:0% +have y's we have just have m y and each + + + align:start position:0% +have y's we have just have m y and each +y I have four legs you just connect all + + align:start position:0% +y I have four legs you just connect all + + + align:start position:0% +y I have four legs you just connect all +of them together okay you connect all of + + align:start position:0% +of them together okay you connect all of + + + align:start position:0% +of them together okay you connect all of +them together so so so in the in the + + align:start position:0% +them together so so so in the in the + + + align:start position:0% +them together so so so in the in the +star star in the vacuum diagrams + + align:start position:0% +star star in the vacuum diagrams + + + align:start position:0% +star star in the vacuum diagrams +so we'll be always closed okay because + + align:start position:0% +so we'll be always closed okay because + + + align:start position:0% +so we'll be always closed okay because +it's not no external neck just because + + align:start position:0% +it's not no external neck just because + + + align:start position:0% +it's not no external neck just because +all the legs will be contracted and so + + align:start position:0% +all the legs will be contracted and so + + + align:start position:0% +all the legs will be contracted and so +will be a close diagram okay and so + + align:start position:0% +will be a close diagram okay and so + + + align:start position:0% +will be a close diagram okay and so +sometimes also called the vacuum bubble + + align:start position:0% +sometimes also called the vacuum bubble + + + align:start position:0% +sometimes also called the vacuum bubble +okay sometimes we call vacuum diagrams + + align:start position:0% +okay sometimes we call vacuum diagrams + + + align:start position:0% +okay sometimes we call vacuum diagrams +or vacuum bubbles + + align:start position:0% + + + + align:start position:0% + +so so here just know just it's just a + + align:start position:0% +so so here just know just it's just a + + + align:start position:0% +so so here just know just it's just a +it's always a close diagrams + + align:start position:0% + + + + align:start position:0% + +okay stag words + + align:start position:0% + + + + align:start position:0% + +and so the uh this is the and the second + + align:start position:0% +and so the uh this is the and the second + + + align:start position:0% +and so the uh this is the and the second +step + + align:start position:0% +step + + + align:start position:0% +step +you said now once you choose each to all + + align:start position:0% +you said now once you choose each to all + + + align:start position:0% +you said now once you choose each to all +the equivalent diagrams then you can + + align:start position:0% +the equivalent diagrams then you can + + + align:start position:0% +the equivalent diagrams then you can +just convert + + align:start position:0% + + + + align:start position:0% + +each diagram + + align:start position:0% + + + + align:start position:0% + +to + + align:start position:0% +to + + + align:start position:0% +to +an algebraic expression + + align:start position:0% + + + + align:start position:0% + +using find my rules + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then you still sum all of them + + align:start position:0% +and then you still sum all of them + + + align:start position:0% +and then you still sum all of them +together okay using sum all of them + + align:start position:0% +together okay using sum all of them + + + align:start position:0% +together okay using sum all of them +together + + align:start position:0% +together + + + align:start position:0% +together +and then we talk about the family Rules + + align:start position:0% +and then we talk about the family Rules + + + align:start position:0% +and then we talk about the family Rules +last time there's a coordinate space + + align:start position:0% +last time there's a coordinate space + + + align:start position:0% +last time there's a coordinate space +rules there's a momentum space rules you + + align:start position:0% +rules there's a momentum space rules you + + + align:start position:0% +rules there's a momentum space rules you +can do it in coordinate space you can do + + align:start position:0% +can do it in coordinate space you can do + + + align:start position:0% +can do it in coordinate space you can do +it in momentum space so I will not + + align:start position:0% +it in momentum space so I will not + + + align:start position:0% +it in momentum space so I will not +repeat them here to save time + + align:start position:0% +repeat them here to save time + + + align:start position:0% +repeat them here to save time +and so + + align:start position:0% +and so + + + align:start position:0% +and so +once we finish the second step then we + + align:start position:0% +once we finish the second step then we + + + align:start position:0% +once we finish the second step then we +just have a bunch of analytic + + align:start position:0% +just have a bunch of analytic + + + align:start position:0% +just have a bunch of analytic +expressions and then you just need to do + + align:start position:0% +expressions and then you just need to do + + + align:start position:0% +expressions and then you just need to do +the integrals okay so a bunch of + + align:start position:0% +the integrals okay so a bunch of + + + align:start position:0% +the integrals okay so a bunch of +integrals and you just need to do the + + align:start position:0% +integrals and you just need to do the + + + align:start position:0% +integrals and you just need to do the +integrals okay + + align:start position:0% + + + + align:start position:0% + +any questions + + align:start position:0% +any questions + + + align:start position:0% +any questions +good + + align:start position:0% +good + + + align:start position:0% +good +so so some further remarks on one + + align:start position:0% + + + + align:start position:0% + +so further remarks + + align:start position:0% + + + + align:start position:0% + +on this first step + + align:start position:0% +on this first step + + + align:start position:0% +on this first step +so + + align:start position:0% +so + + + align:start position:0% +so +so here + + align:start position:0% +so here + + + align:start position:0% +so here +I consider a very special case okay + + align:start position:0% +I consider a very special case okay + + + align:start position:0% +I consider a very special case okay +I can see the very special case goes + + align:start position:0% +I can see the very special case goes + + + align:start position:0% +I can see the very special case goes +right into this s i to be uh uh just + + align:start position:0% +right into this s i to be uh uh just + + + align:start position:0% +right into this s i to be uh uh just +consists of a single term five four okay + + align:start position:0% +consists of a single term five four okay + + + align:start position:0% +consists of a single term five four okay +so so in principle + + align:start position:0% + + + + align:start position:0% + +of course + + align:start position:0% + + + + align:start position:0% + +s i can contain + + align:start position:0% + + + + align:start position:0% + +multiple terms + + align:start position:0% + + + + align:start position:0% + +okay can contain multiple terms + + align:start position:0% +okay can contain multiple terms + + + align:start position:0% +okay can contain multiple terms +so um + + align:start position:0% +so um + + + align:start position:0% +so um +then yeah if + + align:start position:0% +then yeah if + + + align:start position:0% +then yeah if +so if you contain multiple terms + + align:start position:0% +so if you contain multiple terms + + + align:start position:0% +so if you contain multiple terms +then you will have diff multiple + + align:start position:0% + + + + align:start position:0% + +types of vertices + + align:start position:0% + + + + align:start position:0% + +but the rule is similar you just + + align:start position:0% +but the rule is similar you just + + + align:start position:0% +but the rule is similar you just +you just say if you have + + align:start position:0% +you just say if you have + + + align:start position:0% +you just say if you have +a if you have the uh + + align:start position:0% +a if you have the uh + + + align:start position:0% +a if you have the uh +say suppose s i contains two two two + + align:start position:0% +say suppose s i contains two two two + + + align:start position:0% +say suppose s i contains two two two +terms and then you just multiply them + + align:start position:0% +terms and then you just multiply them + + + align:start position:0% +terms and then you just multiply them +okay and under each and then you get + + align:start position:0% +okay and under each and then you get + + + align:start position:0% +okay and under each and then you get +many terms here + + align:start position:0% +many terms here + + + align:start position:0% +many terms here +and yeah just goes one into different + + align:start position:0% +and yeah just goes one into different + + + align:start position:0% +and yeah just goes one into different +combinations of vertices okay + + align:start position:0% +combinations of vertices okay + + + align:start position:0% +combinations of vertices okay +uh for different type of vertices + + align:start position:0% +uh for different type of vertices + + + align:start position:0% +uh for different type of vertices +and but the Duro is exactly the same + + align:start position:0% +and but the Duro is exactly the same + + + align:start position:0% +and but the Duro is exactly the same +okay just now your diagrams are more + + align:start position:0% +okay just now your diagrams are more + + + align:start position:0% +okay just now your diagrams are more +complicated okay your diagrams will + + align:start position:0% +complicated okay your diagrams will + + + align:start position:0% +complicated okay your diagrams will +complicated + + align:start position:0% +complicated + + + align:start position:0% +complicated +but but essentially it's on uh otherwise + + align:start position:0% +but but essentially it's on uh otherwise + + + align:start position:0% +but but essentially it's on uh otherwise +it's identical + + align:start position:0% + + + + align:start position:0% + +so another thing to mention + + align:start position:0% + + + + align:start position:0% + +is that in principle we can also have + + align:start position:0% +is that in principle we can also have + + + align:start position:0% +is that in principle we can also have +multiple Fields so here we can see that + + align:start position:0% +multiple Fields so here we can see that + + + align:start position:0% +multiple Fields so here we can see that +only a single scalar field Phi + + align:start position:0% +only a single scalar field Phi + + + align:start position:0% +only a single scalar field Phi +but you can also in principle consider + + align:start position:0% +but you can also in principle consider + + + align:start position:0% +but you can also in principle consider +more than one field okay so if there are + + align:start position:0% +more than one field okay so if there are + + + align:start position:0% +more than one field okay so if there are +multiple fields + + align:start position:0% + + + + align:start position:0% + +the story is again very much parallel + + align:start position:0% +the story is again very much parallel + + + align:start position:0% +the story is again very much parallel +and the only difference is that each + + align:start position:0% +and the only difference is that each + + + align:start position:0% +and the only difference is that each +field + + align:start position:0% +field + + + align:start position:0% +field +each + + align:start position:0% +each + + + align:start position:0% +each +propagator + + align:start position:0% + + + + align:start position:0% + +is represented by different nine + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +say other than that uh + + align:start position:0% +say other than that uh + + + align:start position:0% +say other than that uh +um yeah we + + align:start position:0% +um yeah we + + + align:start position:0% +um yeah we +again these two steps again apply okay I + + align:start position:0% +again these two steps again apply okay I + + + align:start position:0% +again these two steps again apply okay I +just allow you actually have not two + + align:start position:0% +just allow you actually have not two + + + align:start position:0% +just allow you actually have not two +different type of lines + + align:start position:0% +different type of lines + + + align:start position:0% +different type of lines +so for example + + align:start position:0% +so for example + + + align:start position:0% +so for example +um + + align:start position:0% +um + + + align:start position:0% +um +so support for example if you consider a + + align:start position:0% +so support for example if you consider a + + + align:start position:0% +so support for example if you consider a +theory with two scalar Fields five one + + align:start position:0% +theory with two scalar Fields five one + + + align:start position:0% +theory with two scalar Fields five one +five two + + align:start position:0% +five two + + + align:start position:0% +five two +okay with s i + + align:start position:0% +okay with s i + + + align:start position:0% +okay with s i +say for example this S I say + + align:start position:0% +say for example this S I say + + + align:start position:0% +say for example this S I say +proportional to + + align:start position:0% +proportional to + + + align:start position:0% +proportional to +Pi one square + + align:start position:0% +Pi one square + + + align:start position:0% +Pi one square +by 2 squared + + align:start position:0% +by 2 squared + + + align:start position:0% +by 2 squared +okay and then in this case then you will + + align:start position:0% +okay and then in this case then you will + + + align:start position:0% +okay and then in this case then you will +have a propagator for Phi one + + align:start position:0% +have a propagator for Phi one + + + align:start position:0% +have a propagator for Phi one +then you also have a propagator 452 so + + align:start position:0% +then you also have a propagator 452 so + + + align:start position:0% +then you also have a propagator 452 so +if now I can use attached 9 + + align:start position:0% +if now I can use attached 9 + + + align:start position:0% +if now I can use attached 9 +and then then the attacking vertex then + + align:start position:0% +and then then the attacking vertex then + + + align:start position:0% +and then then the attacking vertex then +we'll have the following structure you + + align:start position:0% +we'll have the following structure you + + + align:start position:0% +we'll have the following structure you +have two + + align:start position:0% + + + + align:start position:0% + +and then and then you have yeah two uh + + align:start position:0% +and then and then you have yeah two uh + + + align:start position:0% +and then and then you have yeah two uh +sorry and the 2-9 uh uh now that's your + + align:start position:0% +sorry and the 2-9 uh uh now that's your + + + align:start position:0% +sorry and the 2-9 uh uh now that's your +vertex okay + + align:start position:0% +vertex okay + + + align:start position:0% +vertex okay +and uh um + + align:start position:0% + + + + align:start position:0% + +yeah so so yeah again uh uh you you just + + align:start position:0% +yeah so so yeah again uh uh you you just + + + align:start position:0% +yeah so so yeah again uh uh you you just +contract all possible lines according to + + align:start position:0% +contract all possible lines according to + + + align:start position:0% +contract all possible lines according to +to your family Rules okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so so also one remarks I want to make + + align:start position:0% +so so also one remarks I want to make + + + align:start position:0% +so so also one remarks I want to make +to emphasize + + align:start position:0% +to emphasize + + + align:start position:0% +to emphasize +inside the momentum space + + align:start position:0% +inside the momentum space + + + align:start position:0% +inside the momentum space +um + + align:start position:0% +um + + + align:start position:0% +um +yeah so um yeah just also just to + + align:start position:0% +yeah so um yeah just also just to + + + align:start position:0% +yeah so um yeah just also just to +another point to stress so in momentum + + align:start position:0% +another point to stress so in momentum + + + align:start position:0% +another point to stress so in momentum +space + + align:start position:0% +space + + + align:start position:0% +space +so this is obtained + + align:start position:0% +so this is obtained + + + align:start position:0% +so this is obtained +by Fourier transform so this is obtained + + align:start position:0% +by Fourier transform so this is obtained + + + align:start position:0% +by Fourier transform so this is obtained +by Fourier transform cnx1 + + align:start position:0% +by Fourier transform cnx1 + + + align:start position:0% +by Fourier transform cnx1 +xn okay and the times yeah times the + + align:start position:0% +xn okay and the times yeah times the + + + align:start position:0% +xn okay and the times yeah times the +data function + + align:start position:0% + + + + align:start position:0% + +so this + + align:start position:0% +so this + + + align:start position:0% +so this +times this give you the free transform + + align:start position:0% +times this give you the free transform + + + align:start position:0% +times this give you the free transform +of that + + align:start position:0% +of that + + + align:start position:0% +of that +so when you do the Fourier transform + + align:start position:0% +so when you do the Fourier transform + + + align:start position:0% +so when you do the Fourier transform +of course so py and p n they just come + + align:start position:0% +of course so py and p n they just come + + + align:start position:0% +of course so py and p n they just come +from doing fully transform X + + align:start position:0% +from doing fully transform X + + + align:start position:0% +from doing fully transform X +corresponding to momentum for X1 and x n + + align:start position:0% +corresponding to momentum for X1 and x n + + + align:start position:0% +corresponding to momentum for X1 and x n +so here the P1 + + align:start position:0% +so here the P1 + + + align:start position:0% +so here the P1 +and PM just arbitrary okay + + align:start position:0% + + + + align:start position:0% + +they don't they don't have to be uh + + align:start position:0% +they don't they don't have to be uh + + + align:start position:0% +they don't they don't have to be uh +satisfied in the unsure condition + + align:start position:0% +satisfied in the unsure condition + + + align:start position:0% +satisfied in the unsure condition +they're just arbitrary momentum and the + + align:start position:0% +they're just arbitrary momentum and the + + + align:start position:0% +they're just arbitrary momentum and the +only constraint is that this is not + + align:start position:0% +only constraint is that this is not + + + align:start position:0% +only constraint is that this is not +Vanishing only when there can uh only + + align:start position:0% +Vanishing only when there can uh only + + + align:start position:0% +Vanishing only when there can uh only +when the sum of them are equal to zero + + align:start position:0% +when the sum of them are equal to zero + + + align:start position:0% +when the sum of them are equal to zero +otherwise they can be arbitrary okay + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% +good + + + align:start position:0% +good +so so in practice + + align:start position:0% +so so in practice + + + align:start position:0% +so so in practice +now you now you have a way to calculate + + align:start position:0% +now you now you have a way to calculate + + + align:start position:0% +now you now you have a way to calculate +the diagram for both upstairs and + + align:start position:0% +the diagram for both upstairs and + + + align:start position:0% +the diagram for both upstairs and +downstairs + + align:start position:0% +downstairs + + + align:start position:0% +downstairs +and now we we just do the expansion okay + + align:start position:0% +and now we we just do the expansion okay + + + align:start position:0% +and now we we just do the expansion okay +we just do the expansion let me just + + align:start position:0% +we just do the expansion let me just + + + align:start position:0% +we just do the expansion let me just +again now let me summarize the example + + align:start position:0% +again now let me summarize the example + + + align:start position:0% +again now let me summarize the example +we did last time + + align:start position:0% +we did last time + + + align:start position:0% +we did last time +uh are not just only using diagrams okay + + align:start position:0% +uh are not just only using diagrams okay + + + align:start position:0% +uh are not just only using diagrams okay +so for example if we can see the two + + align:start position:0% +so for example if we can see the two + + + align:start position:0% +so for example if we can see the two +point function + + align:start position:0% + + + + align:start position:0% + +okay let's consider two point function + + align:start position:0% +okay let's consider two point function + + + align:start position:0% +okay let's consider two point function +so so now the upstairs + + align:start position:0% + + + + align:start position:0% + +so we have the upstand downstairs so the + + align:start position:0% +so we have the upstand downstairs so the + + + align:start position:0% +so we have the upstand downstairs so the +upstairs the same the lowest order you + + align:start position:0% +upstairs the same the lowest order you + + + align:start position:0% +upstairs the same the lowest order you +just have a single line + + align:start position:0% +just have a single line + + + align:start position:0% +just have a single line +okay it just have a single line X Y into + + align:start position:0% +okay it just have a single line X Y into + + + align:start position:0% +okay it just have a single line X Y into +X2 + + align:start position:0% +X2 + + + align:start position:0% +X2 +so to to save effort that we also uh uh + + align:start position:0% +so to to save effort that we also uh uh + + + align:start position:0% +so to to save effort that we also uh uh +not enable X1 X2 from now on okay and + + align:start position:0% +not enable X1 X2 from now on okay and + + + align:start position:0% +not enable X1 X2 from now on okay and +then the next + + align:start position:0% + + + + align:start position:0% + +the next order is to bring down one + + align:start position:0% +the next order is to bring down one + + + align:start position:0% +the next order is to bring down one +power of this s i + + align:start position:0% +power of this s i + + + align:start position:0% +power of this s i +so you bring down one power of this four + + align:start position:0% +so you bring down one power of this four + + + align:start position:0% +so you bring down one power of this four +indices + + align:start position:0% +indices + + + align:start position:0% +indices +so now there are two possibilities + + align:start position:0% +so now there are two possibilities + + + align:start position:0% +so now there are two possibilities +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so one possibility is that you still + + align:start position:0% +so one possibility is that you still + + + align:start position:0% +so one possibility is that you still +have this + + align:start position:0% +have this + + + align:start position:0% +have this +but then times + + align:start position:0% +but then times + + + align:start position:0% +but then times +this vertex contracts itself + + align:start position:0% +this vertex contracts itself + + + align:start position:0% +this vertex contracts itself +okay contract itself + + align:start position:0% +okay contract itself + + + align:start position:0% +okay contract itself +and then + + align:start position:0% +and then + + + align:start position:0% +and then +well other possibility + + align:start position:0% +well other possibility + + + align:start position:0% +well other possibility +you said you have something like this + + align:start position:0% +you said you have something like this + + + align:start position:0% +you said you have something like this +okay and the uh you can check with the + + align:start position:0% +okay and the uh you can check with the + + + align:start position:0% +okay and the uh you can check with the +vertex so this is then plus Lambda + + align:start position:0% +vertex so this is then plus Lambda + + + align:start position:0% +vertex so this is then plus Lambda +Square + + align:start position:0% +Square + + + align:start position:0% +Square +okay so this is the uh uh all the all + + align:start position:0% +okay so this is the uh uh all the all + + + align:start position:0% +okay so this is the uh uh all the all +the order to the uh um yeah to the + + align:start position:0% +the order to the uh um yeah to the + + + align:start position:0% +the order to the uh um yeah to the +lambdas to Lambda order okay + + align:start position:0% +lambdas to Lambda order okay + + + align:start position:0% +lambdas to Lambda order okay +and downstairs + + align:start position:0% +and downstairs + + + align:start position:0% +and downstairs +you have one + + align:start position:0% +you have one + + + align:start position:0% +you have one +and then you just essentially have the + + align:start position:0% +and then you just essentially have the + + + align:start position:0% +and then you just essentially have the +uh I have a single + + align:start position:0% +uh I have a single + + + align:start position:0% +uh I have a single +s i + + align:start position:0% +s i + + + align:start position:0% +s i +a single SI is the only contraction + + align:start position:0% +a single SI is the only contraction + + + align:start position:0% +a single SI is the only contraction +is just given by this + + align:start position:0% + + + + align:start position:0% + +okay and then plus all the Lambda Square + + align:start position:0% +okay and then plus all the Lambda Square + + + align:start position:0% +okay and then plus all the Lambda Square +okay plus all the Lambda Square okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +so now we can just + + align:start position:0% +so now we can just + + + align:start position:0% +so now we can just +so now each vertex carry so you should + + align:start position:0% +so now each vertex carry so you should + + + align:start position:0% +so now each vertex carry so you should +remember each vertex carry a parameter + + align:start position:0% +remember each vertex carry a parameter + + + align:start position:0% +remember each vertex carry a parameter +Lambda a factor of Lambda which is + + align:start position:0% +Lambda a factor of Lambda which is + + + align:start position:0% +Lambda a factor of Lambda which is +considered to be small + + align:start position:0% +considered to be small + + + align:start position:0% +considered to be small +so so downstairs you have one plus all + + align:start position:0% +so so downstairs you have one plus all + + + align:start position:0% +so so downstairs you have one plus all +the Lambda and we can in the downstairs + + align:start position:0% +the Lambda and we can in the downstairs + + + align:start position:0% +the Lambda and we can in the downstairs +then we have one plus + + align:start position:0% +then we have one plus + + + align:start position:0% +then we have one plus +this power series of Lambda and then we + + align:start position:0% +this power series of Lambda and then we + + + align:start position:0% +this power series of Lambda and then we +can do the Taylor expansion again to + + align:start position:0% +can do the Taylor expansion again to + + + align:start position:0% +can do the Taylor expansion again to +bring them to the upstairs okay so so + + align:start position:0% +bring them to the upstairs okay so so + + + align:start position:0% +bring them to the upstairs okay so so +remember we did before so so now if you + + align:start position:0% +remember we did before so so now if you + + + align:start position:0% +remember we did before so so now if you +do that + + align:start position:0% +do that + + + align:start position:0% +do that +then at the leading order to Lambda then + + align:start position:0% +then at the leading order to Lambda then + + + align:start position:0% +then at the leading order to Lambda then +we still just have X1 X2 + + align:start position:0% +we still just have X1 X2 + + + align:start position:0% +we still just have X1 X2 +because this divided by that just x y x + + align:start position:0% +because this divided by that just x y x + + + align:start position:0% +because this divided by that just x y x +2 and then you have this term + + align:start position:0% + + + + align:start position:0% + +but now we can bring this term to the + + align:start position:0% +but now we can bring this term to the + + + align:start position:0% +but now we can bring this term to the +upstairs and then then this side change + + align:start position:0% +upstairs and then then this side change + + + align:start position:0% +upstairs and then then this side change +it to minus sign + + align:start position:0% +it to minus sign + + + align:start position:0% +it to minus sign +okay so this term can multiply that and + + align:start position:0% +okay so this term can multiply that and + + + align:start position:0% +okay so this term can multiply that and +then you get the term like that + + align:start position:0% + + + + align:start position:0% + +okay coming from bring this term + + align:start position:0% +okay coming from bring this term + + + align:start position:0% +okay coming from bring this term +to upstairs and then you have this term + + align:start position:0% +to upstairs and then you have this term + + + align:start position:0% +to upstairs and then you have this term +okay + + align:start position:0% + + + + align:start position:0% + +and the rest + + align:start position:0% +and the rest + + + align:start position:0% +and the rest +they're all of Lambda squared so you can + + align:start position:0% +they're all of Lambda squared so you can + + + align:start position:0% +they're all of Lambda squared so you can +also have this change to minus sign + + align:start position:0% +also have this change to minus sign + + + align:start position:0% +also have this change to minus sign +multiply that but that will be all the + + align:start position:0% +multiply that but that will be all the + + + align:start position:0% +multiply that but that will be all the +Lambda squared okay and since here we + + align:start position:0% +Lambda squared okay and since here we + + + align:start position:0% +Lambda squared okay and since here we +already neglected since in Lambda square + + align:start position:0% +already neglected since in Lambda square + + + align:start position:0% +already neglected since in Lambda square +and here the next is time the square and + + align:start position:0% +and here the next is time the square and + + + align:start position:0% +and here the next is time the square and +so uh so uh so we don't worry about it + + align:start position:0% +so uh so uh so we don't worry about it + + + align:start position:0% +so uh so uh so we don't worry about it +okay and if you this multiply this also + + align:start position:0% +okay and if you this multiply this also + + + align:start position:0% +okay and if you this multiply this also +give you Lambda squared okay so so up to + + align:start position:0% +give you Lambda squared okay so so up to + + + align:start position:0% +give you Lambda squared okay so so up to +all the Lambda and that you have and + + align:start position:0% +all the Lambda and that you have and + + + align:start position:0% +all the Lambda and that you have and +then + + align:start position:0% +then + + + align:start position:0% +then +as we discussed before these two cancel + + align:start position:0% +as we discussed before these two cancel + + + align:start position:0% +as we discussed before these two cancel +okay so in the end + + align:start position:0% +okay so in the end + + + align:start position:0% +okay so in the end +you just have two diagrams just one and + + align:start position:0% +you just have two diagrams just one and + + + align:start position:0% +you just have two diagrams just one and +then this one okay + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah for here it doesn't matter in this + + align:start position:0% +yeah for here it doesn't matter in this + + + align:start position:0% +yeah for here it doesn't matter in this +case it doesn't matter or how you draw + + align:start position:0% +case it doesn't matter or how you draw + + + align:start position:0% +case it doesn't matter or how you draw +them you mean if I exchange them yeah + + align:start position:0% +them you mean if I exchange them yeah + + + align:start position:0% +them you mean if I exchange them yeah +yeah it doesn't matter yeah + + align:start position:0% + + + + align:start position:0% + +yeah and normally you can add the view + + align:start position:0% +yeah and normally you can add the view + + + align:start position:0% +yeah and normally you can add the view +up and up and down and left and right + + align:start position:0% +up and up and down and left and right + + + align:start position:0% +up and up and down and left and right +here does not mean anything + + align:start position:0% + + + + align:start position:0% + +yeah the order uh is not important + + align:start position:0% +yeah the order uh is not important + + + align:start position:0% +yeah the order uh is not important +um but actually in in in in crafty 2 you + + align:start position:0% +um but actually in in in in crafty 2 you + + + align:start position:0% +um but actually in in in in crafty 2 you +you see you will encounter situations + + align:start position:0% +you see you will encounter situations + + + align:start position:0% +you see you will encounter situations +which these are matrices + + align:start position:0% +which these are matrices + + + align:start position:0% +which these are matrices +and then all the become important but + + align:start position:0% +and then all the become important but + + + align:start position:0% +and then all the become important but +here they just feel because they commute + + align:start position:0% +here they just feel because they commute + + + align:start position:0% +here they just feel because they commute +so no matter how you order them doesn't + + align:start position:0% +so no matter how you order them doesn't + + + align:start position:0% +so no matter how you order them doesn't +matter yeah they're just ordinary Fields + + align:start position:0% +matter yeah they're just ordinary Fields + + + align:start position:0% +matter yeah they're just ordinary Fields +yeah + + align:start position:0% + + + + align:start position:0% + +okay so so this order we just have these + + align:start position:0% +okay so so this order we just have these + + + align:start position:0% +okay so so this order we just have these +two diagrams okay so this is much + + align:start position:0% +two diagrams okay so this is much + + + align:start position:0% +two diagrams okay so this is much +simpler than we did at the first time + + align:start position:0% +simpler than we did at the first time + + + align:start position:0% +simpler than we did at the first time +okay a much simpler than we did than the + + align:start position:0% +okay a much simpler than we did than the + + + align:start position:0% +okay a much simpler than we did than the +first time and the cancellation is much + + align:start position:0% +first time and the cancellation is much + + + align:start position:0% +first time and the cancellation is much +easier + + align:start position:0% +easier + + + align:start position:0% +easier +so let me just show you the cancellation + + align:start position:0% +so let me just show you the cancellation + + + align:start position:0% +so let me just show you the cancellation +in a slightly different way almost + + align:start position:0% +in a slightly different way almost + + + align:start position:0% +in a slightly different way almost +identical but I write slightly + + align:start position:0% +identical but I write slightly + + + align:start position:0% +identical but I write slightly +differently so I can also alternatively + + align:start position:0% +differently so I can also alternatively + + + align:start position:0% +differently so I can also alternatively +I can also write as this + + align:start position:0% + + + + align:start position:0% + +I can also write G2 + + align:start position:0% +I can also write G2 + + + align:start position:0% +I can also write G2 +so we + + align:start position:0% +so we + + + align:start position:0% +so we +look at this two terms + + align:start position:0% +look at this two terms + + + align:start position:0% +look at this two terms +we can just take a fact a common factor + + align:start position:0% +we can just take a fact a common factor + + + align:start position:0% +we can just take a fact a common factor +out so the upstairs the first two term I + + align:start position:0% +out so the upstairs the first two term I + + + align:start position:0% +out so the upstairs the first two term I +can also write it + + align:start position:0% +can also write it + + + align:start position:0% +can also write it +as this times 1 plus + + align:start position:0% +as this times 1 plus + + + align:start position:0% +as this times 1 plus +this scene and then Plus + + align:start position:0% +this scene and then Plus + + + align:start position:0% +this scene and then Plus +this + + align:start position:0% +this + + + align:start position:0% +this +okay and downstairs I just have + + align:start position:0% +okay and downstairs I just have + + + align:start position:0% +okay and downstairs I just have +and then plus Lambda Square + + align:start position:0% + + + + align:start position:0% + +and downstairs I just have one + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now you can just look at these two + + align:start position:0% +so now you can just look at these two + + + align:start position:0% +so now you can just look at these two +you can directly see actually these two + + align:start position:0% +you can directly see actually these two + + + align:start position:0% +you can directly see actually these two +can be canceled + + align:start position:0% +can be canceled + + + align:start position:0% +can be canceled +okay it will cancel you don't have to + + align:start position:0% +okay it will cancel you don't have to + + + align:start position:0% +okay it will cancel you don't have to +worry about this one because when this + + align:start position:0% + + + + align:start position:0% + +when this multiply that you get higher + + align:start position:0% +when this multiply that you get higher + + + align:start position:0% +when this multiply that you get higher +orders okay and so so now you just + + align:start position:0% +orders okay and so so now you just + + + align:start position:0% +orders okay and so so now you just +directly also get from here + + align:start position:0% + + + + align:start position:0% + +okay from here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so the reason + + align:start position:0% + + + + align:start position:0% + +the reason I've been doing this in these + + align:start position:0% +the reason I've been doing this in these + + + align:start position:0% +the reason I've been doing this in these +two different ways + + align:start position:0% +two different ways + + + align:start position:0% +two different ways +is that this cancellation is actually + + align:start position:0% +is that this cancellation is actually + + + align:start position:0% +is that this cancellation is actually +not the accident okay so so such + + align:start position:0% +not the accident okay so so such + + + align:start position:0% +not the accident okay so so such +isolation + + align:start position:0% +isolation + + + align:start position:0% +isolation +so this is not an accident + + align:start position:0% + + + + align:start position:0% + +this is not accident + + align:start position:0% +this is not accident + + + align:start position:0% +this is not accident +this actually happens to all orders + + align:start position:0% +this actually happens to all orders + + + align:start position:0% +this actually happens to all orders +okay this happens to all orders + + align:start position:0% +okay this happens to all orders + + + align:start position:0% +okay this happens to all orders +so you can actually show + + align:start position:0% +so you can actually show + + + align:start position:0% +so you can actually show +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% + + + + align:start position:0% + +okay so if I call + + align:start position:0% +okay so if I call + + + align:start position:0% +okay so if I call +the the upstairs + + align:start position:0% + + + + align:start position:0% + +um yeah so now it's called upstairs + + align:start position:0% +um yeah so now it's called upstairs + + + align:start position:0% +um yeah so now it's called upstairs +to be u n and this to be u0 okay + + align:start position:0% + + + + align:start position:0% + +so un is just the upstairs okay and you + + align:start position:0% +so un is just the upstairs okay and you + + + align:start position:0% +so un is just the upstairs okay and you +zero is the downstairs okay so so the UN + + align:start position:0% + + + + align:start position:0% + +by definition corresponding to sum + + align:start position:0% +by definition corresponding to sum + + + align:start position:0% +by definition corresponding to sum +over all diagrams all five and diagrams + + align:start position:0% + + + + align:start position:0% + +with any external lag + + align:start position:0% + + + + align:start position:0% + +and and the u0 by definition is sum of + + align:start position:0% +and and the u0 by definition is sum of + + + align:start position:0% +and and the u0 by definition is sum of +all five and diagrams + + align:start position:0% +all five and diagrams + + + align:start position:0% +all five and diagrams +with zero external X + + align:start position:0% + + + + align:start position:0% + +okay we see Zero external X + + align:start position:0% + + + + align:start position:0% + +so when you + + align:start position:0% + + + + align:start position:0% + +so then you can show okay you can show + + align:start position:0% +so then you can show okay you can show + + + align:start position:0% +so then you can show okay you can show +in general + + align:start position:0% +in general + + + align:start position:0% +in general +which is the GN + + align:start position:0% +which is the GN + + + align:start position:0% +which is the GN +is just equal to as we wrote there just + + align:start position:0% +is just equal to as we wrote there just + + + align:start position:0% +is just equal to as we wrote there just +u n equal to u0 + + align:start position:0% +u n equal to u0 + + + align:start position:0% +u n equal to u0 +okay you can show that this + + align:start position:0% + + + + align:start position:0% + +this defined to be U and you could use + + align:start position:0% +this defined to be U and you could use + + + align:start position:0% +this defined to be U and you could use +zero is just given by + + align:start position:0% + + + + align:start position:0% + +you find the order you can show to all + + align:start position:0% +you find the order you can show to all + + + align:start position:0% +you find the order you can show to all +orders this downstairs can always always + + align:start position:0% +orders this downstairs can always always + + + align:start position:0% +orders this downstairs can always always +cancel + + align:start position:0% +cancel + + + align:start position:0% +cancel +okay always cancel + + align:start position:0% +okay always cancel + + + align:start position:0% +okay always cancel +so so the statement is that this is + + align:start position:0% +so so the statement is that this is + + + align:start position:0% +so so the statement is that this is +equal to sum + + align:start position:0% + + + + align:start position:0% + +over the ratio or diagrams + + align:start position:0% + + + + align:start position:0% + +of an external ax + + align:start position:0% + + + + align:start position:0% + +an external X + + align:start position:0% +an external X + + + align:start position:0% +an external X +but + + align:start position:0% + + + + align:start position:0% + +without + + align:start position:0% +without + + + align:start position:0% +without +any + + align:start position:0% + + + + align:start position:0% + +vacuum bubbles + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% + + + + align:start position:0% + +okay so so now let me just explain what + + align:start position:0% +okay so so now let me just explain what + + + align:start position:0% +okay so so now let me just explain what +this means that without any vacuum + + align:start position:0% +this means that without any vacuum + + + align:start position:0% +this means that without any vacuum +bubbles okay + + align:start position:0% +bubbles okay + + + align:start position:0% +bubbles okay +so so this diagram + + align:start position:0% + + + + align:start position:0% + +so this diagram is a diagram which + + align:start position:0% +so this diagram is a diagram which + + + align:start position:0% +so this diagram is a diagram which +contains just a straight propagator + + align:start position:0% +contains just a straight propagator + + + align:start position:0% +contains just a straight propagator +times a bubble + + align:start position:0% +times a bubble + + + align:start position:0% +times a bubble +okay so so this diagram contains the + + align:start position:0% +okay so so this diagram contains the + + + align:start position:0% +okay so so this diagram contains the +vacuum bubble okay a container vacuum + + align:start position:0% +vacuum bubble okay a container vacuum + + + align:start position:0% +vacuum bubble okay a container vacuum +diagram + + align:start position:0% +diagram + + + align:start position:0% +diagram +and this diagram does not this diagram + + align:start position:0% +and this diagram does not this diagram + + + align:start position:0% +and this diagram does not this diagram +is connected itself okay + + align:start position:0% +is connected itself okay + + + align:start position:0% +is connected itself okay +so + + align:start position:0% +so + + + align:start position:0% +so +yeah similarly if when you go to next + + align:start position:0% +yeah similarly if when you go to next + + + align:start position:0% +yeah similarly if when you go to next +order as we discussed last time + + align:start position:0% +order as we discussed last time + + + align:start position:0% +order as we discussed last time +that this diagram + + align:start position:0% +that this diagram + + + align:start position:0% +that this diagram +so go to next order times + + align:start position:0% + + + + align:start position:0% + +so this is also a diagram with vacuum + + align:start position:0% +so this is also a diagram with vacuum + + + align:start position:0% +so this is also a diagram with vacuum +bubble because you have this part + + align:start position:0% +bubble because you have this part + + + align:start position:0% +bubble because you have this part +which does not have any external lag + + align:start position:0% +which does not have any external lag + + + align:start position:0% +which does not have any external lag +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so this will not arise okay so so + + align:start position:0% +so so this will not arise okay so so + + + align:start position:0% +so so this will not arise okay so so +when you do the uh when you calculate + + align:start position:0% +when you do the uh when you calculate + + + align:start position:0% +when you do the uh when you calculate +the ratio and then this kind of diagram + + align:start position:0% +the ratio and then this kind of diagram + + + align:start position:0% +the ratio and then this kind of diagram +we automatically don't include them + + align:start position:0% +we automatically don't include them + + + align:start position:0% +we automatically don't include them +okay just don't know I just don't need + + align:start position:0% +okay just don't know I just don't need + + + align:start position:0% +okay just don't know I just don't need +to worry about + + align:start position:0% +to worry about + + + align:start position:0% +to worry about +so so now when you do the uh to the + + align:start position:0% +so so now when you do the uh to the + + + align:start position:0% +so so now when you do the uh to the +ratio you can just forget about those + + align:start position:0% +ratio you can just forget about those + + + align:start position:0% +ratio you can just forget about those +diagrams and directly write down those + + align:start position:0% +diagrams and directly write down those + + + align:start position:0% +diagrams and directly write down those +diagrams without vacuum bubbles okay so + + align:start position:0% +diagrams without vacuum bubbles okay so + + + align:start position:0% +diagrams without vacuum bubbles okay so +that's just a greatly a simplify uh uh + + align:start position:0% +that's just a greatly a simplify uh uh + + + align:start position:0% +that's just a greatly a simplify uh uh +in your life okay + + align:start position:0% +in your life okay + + + align:start position:0% +in your life okay +and the yeah one second so this + + align:start position:0% +and the yeah one second so this + + + align:start position:0% +and the yeah one second so this +statement + + align:start position:0% + + + + align:start position:0% + +is simply + + align:start position:0% +is simply + + + align:start position:0% +is simply +urgent + + align:start position:0% +urgent + + + align:start position:0% +urgent +so if you think a little bit okay and + + align:start position:0% +so if you think a little bit okay and + + + align:start position:0% +so if you think a little bit okay and +then you will see that this cancellation + + align:start position:0% +then you will see that this cancellation + + + align:start position:0% +then you will see that this cancellation +is generic + + align:start position:0% +is generic + + + align:start position:0% +is generic +actually we'll walk to all orders + + align:start position:0% +actually we'll walk to all orders + + + align:start position:0% +actually we'll walk to all orders +and uh and this thinking process is + + align:start position:0% +and uh and this thinking process is + + + align:start position:0% +and uh and this thinking process is +actually quite instructive + + align:start position:0% +actually quite instructive + + + align:start position:0% +actually quite instructive +and so this is left as a homework okay + + align:start position:0% +and so this is left as a homework okay + + + align:start position:0% +and so this is left as a homework okay +you can read the part in passing which + + align:start position:0% +you can read the part in passing which + + + align:start position:0% +you can read the part in passing which +try to explain this uh this cancellation + + align:start position:0% +try to explain this uh this cancellation + + + align:start position:0% +try to explain this uh this cancellation +but that discussion is actually not + + align:start position:0% +but that discussion is actually not + + + align:start position:0% +but that discussion is actually not +great + + align:start position:0% +great + + + align:start position:0% +great +it's not great that discussion but you + + align:start position:0% +it's not great that discussion but you + + + align:start position:0% +it's not great that discussion but you +can still read it and get the main idea + + align:start position:0% +can still read it and get the main idea + + + align:start position:0% +can still read it and get the main idea +and so so in homework and so they ask + + align:start position:0% +and so so in homework and so they ask + + + align:start position:0% +and so so in homework and so they ask +you to show this yourself okay ask you + + align:start position:0% +you to show this yourself okay ask you + + + align:start position:0% +you to show this yourself okay ask you +to show this yourself + + align:start position:0% +to show this yourself + + + align:start position:0% +to show this yourself +it's not difficult once you get the idea + + align:start position:0% +it's not difficult once you get the idea + + + align:start position:0% +it's not difficult once you get the idea +it's actually pretty simple to see okay + + align:start position:0% +it's actually pretty simple to see okay + + + align:start position:0% +it's actually pretty simple to see okay +and uh we'll be Illuminating okay + + align:start position:0% +and uh we'll be Illuminating okay + + + align:start position:0% +and uh we'll be Illuminating okay +yes + + align:start position:0% + + + + align:start position:0% + +no no you pull the whole thing together + + align:start position:0% +no no you pull the whole thing together + + + align:start position:0% +no no you pull the whole thing together +you uh improve the hosting or okay just + + align:start position:0% +you uh improve the hosting or okay just + + + align:start position:0% +you uh improve the hosting or okay just +those terms don't don't matter at the + + align:start position:0% +those terms don't don't matter at the + + + align:start position:0% +those terms don't don't matter at the +disorder + + align:start position:0% + + + + align:start position:0% + +yeah they just whatever here when you + + align:start position:0% +yeah they just whatever here when you + + + align:start position:0% +yeah they just whatever here when you +put + + align:start position:0% +put + + + align:start position:0% +put +when you cancel them you cancel the + + align:start position:0% +when you cancel them you cancel the + + + align:start position:0% +when you cancel them you cancel the +whole thing just this term don't matter + + align:start position:0% +whole thing just this term don't matter + + + align:start position:0% +whole thing just this term don't matter +if you care only of all the Lambda + + align:start position:0% +if you care only of all the Lambda + + + align:start position:0% +if you care only of all the Lambda +Square term and then and then you can + + align:start position:0% +Square term and then and then you can + + + align:start position:0% +Square term and then and then you can +just directly cancel these two + + align:start position:0% +just directly cancel these two + + + align:start position:0% +just directly cancel these two +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah you can easily convince yourself or + + align:start position:0% +yeah you can easily convince yourself or + + + align:start position:0% +yeah you can easily convince yourself or +or a right uh you don't have to do a + + align:start position:0% +or a right uh you don't have to do a + + + align:start position:0% +or a right uh you don't have to do a +diagram just write something a one plus + + align:start position:0% +diagram just write something a one plus + + + align:start position:0% +diagram just write something a one plus +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +plus some other Lambda and the one plus + + align:start position:0% +plus some other Lambda and the one plus + + + align:start position:0% +plus some other Lambda and the one plus +yeah anyway you can just convince + + align:start position:0% +yeah anyway you can just convince + + + align:start position:0% +yeah anyway you can just convince +yourself that this always happens + + align:start position:0% +yourself that this always happens + + + align:start position:0% +yourself that this always happens +yes + + align:start position:0% + + + + align:start position:0% + +um yeah yeah there is a physical + + align:start position:0% +um yeah yeah there is a physical + + + align:start position:0% +um yeah yeah there is a physical +interpretation essentially just say when + + align:start position:0% +interpretation essentially just say when + + + align:start position:0% +interpretation essentially just say when +you look at yeah so + + align:start position:0% +you look at yeah so + + + align:start position:0% +you look at yeah so +so this kind of thing is essentially the + + align:start position:0% +so this kind of thing is essentially the + + + align:start position:0% +so this kind of thing is essentially the +uh come from the normalization of your + + align:start position:0% +uh come from the normalization of your + + + align:start position:0% +uh come from the normalization of your +state + + align:start position:0% +state + + + align:start position:0% +state +uh just this thing is just pure vacuum + + align:start position:0% +uh just this thing is just pure vacuum + + + align:start position:0% +uh just this thing is just pure vacuum +process + + align:start position:0% +process + + + align:start position:0% +process +and just come from normalization with + + align:start position:0% +and just come from normalization with + + + align:start position:0% +and just come from normalization with +the states and we normalize your state + + align:start position:0% +the states and we normalize your state + + + align:start position:0% +the states and we normalize your state +they just should not contribute to your + + align:start position:0% +they just should not contribute to your + + + align:start position:0% +they just should not contribute to your +yeah at your correlation functions + + align:start position:0% +yeah at your correlation functions + + + align:start position:0% +yeah at your correlation functions +just roughly snack that + + align:start position:0% + + + + align:start position:0% + +other questions + + align:start position:0% + + + + align:start position:0% + +okay great + + align:start position:0% +okay great + + + align:start position:0% +okay great +so so now let's just uh put this in + + align:start position:0% +so so now let's just uh put this in + + + align:start position:0% +so so now let's just uh put this in +practice + + align:start position:0% +practice + + + align:start position:0% +practice +okay this food is this in practice let + + align:start position:0% +okay this food is this in practice let + + + align:start position:0% +okay this food is this in practice let +me just write down + + align:start position:0% +me just write down + + + align:start position:0% +me just write down +the um + + align:start position:0% + + + + align:start position:0% + +the most General + + align:start position:0% +the most General + + + align:start position:0% +the most General +all the diagrams + + align:start position:0% +all the diagrams + + + align:start position:0% +all the diagrams +for G2 + + align:start position:0% + + + + align:start position:0% + +Lambda Square Order + + align:start position:0% +Lambda Square Order + + + align:start position:0% +Lambda Square Order +okay so now let's look at G2 to run the + + align:start position:0% +okay so now let's look at G2 to run the + + + align:start position:0% +okay so now let's look at G2 to run the +Square Order + + align:start position:0% +Square Order + + + align:start position:0% +Square Order +so we have already find the Lambda order + + align:start position:0% +so we have already find the Lambda order + + + align:start position:0% +so we have already find the Lambda order +so say Lambda Square Order will be + + align:start position:0% +so say Lambda Square Order will be + + + align:start position:0% +so say Lambda Square Order will be +already draw a bunch of diagrams last + + align:start position:0% +already draw a bunch of diagrams last + + + align:start position:0% +already draw a bunch of diagrams last +time okay + + align:start position:0% +time okay + + + align:start position:0% +time okay +so you only need to keep those + + align:start position:0% +so you only need to keep those + + + align:start position:0% +so you only need to keep those +which don't include these vacuum bubbles + + align:start position:0% +which don't include these vacuum bubbles + + + align:start position:0% +which don't include these vacuum bubbles +so so that just yeah let me just write + + align:start position:0% +so so that just yeah let me just write + + + align:start position:0% +so so that just yeah let me just write +them down + + align:start position:0% +them down + + + align:start position:0% +them down +so including this + + align:start position:0% +so including this + + + align:start position:0% +so including this +including that + + align:start position:0% + + + + align:start position:0% + +and also including which the one I + + align:start position:0% +and also including which the one I + + + align:start position:0% +and also including which the one I +forgot last time + + align:start position:0% +forgot last time + + + align:start position:0% +forgot last time +this one + + align:start position:0% +this one + + + align:start position:0% +this one +okay that's it okay and uh if I remember + + align:start position:0% +okay that's it okay and uh if I remember + + + align:start position:0% +okay that's it okay and uh if I remember +last time we showed many more diagrams + + align:start position:0% +last time we showed many more diagrams + + + align:start position:0% +last time we showed many more diagrams +but you don't need to worry about the + + align:start position:0% +but you don't need to worry about the + + + align:start position:0% +but you don't need to worry about the +others + + align:start position:0% +others + + + align:start position:0% +others +such as diagrams like this okay + + align:start position:0% + + + + align:start position:0% + +okay good so let's do another example + + align:start position:0% + + + + align:start position:0% + +for the four point function + + align:start position:0% + + + + align:start position:0% + +so now it's + + align:start position:0% +so now it's + + + align:start position:0% +so now it's +become + + align:start position:0% +become + + + align:start position:0% +become +much easier because you have much fewer + + align:start position:0% +much easier because you have much fewer + + + align:start position:0% +much easier because you have much fewer +diagrams to to consider okay you have + + align:start position:0% +diagrams to to consider okay you have + + + align:start position:0% +diagrams to to consider okay you have +much fewer diagram consider + + align:start position:0% +much fewer diagram consider + + + align:start position:0% +much fewer diagram consider +so so I took the four point function + + align:start position:0% +so so I took the four point function + + + align:start position:0% +so so I took the four point function +level + + align:start position:0% +level + + + align:start position:0% +level +then you have then you have the uh the + + align:start position:0% +then you have then you have the uh the + + + align:start position:0% +then you have then you have the uh the +you first have your three series terms + + align:start position:0% +you first have your three series terms + + + align:start position:0% +you first have your three series terms +okay so the three series terms you just + + align:start position:0% +okay so the three series terms you just + + + align:start position:0% +okay so the three series terms you just +have like that + + align:start position:0% + + + + align:start position:0% + +it just contracted itself now we have + + align:start position:0% +it just contracted itself now we have + + + align:start position:0% +it just contracted itself now we have +four external points + + align:start position:0% + + + + align:start position:0% + +okay so so this is come from the free + + align:start position:0% +okay so so this is come from the free + + + align:start position:0% +okay so so this is come from the free +series contribution at the zeros order + + align:start position:0% +series contribution at the zeros order + + + align:start position:0% +series contribution at the zeros order +and then at the first order + + align:start position:0% +and then at the first order + + + align:start position:0% +and then at the first order +and all the Lambda you just have this + + align:start position:0% +and all the Lambda you just have this + + + align:start position:0% +and all the Lambda you just have this +so that all the four different files + + align:start position:0% +so that all the four different files + + + align:start position:0% +so that all the four different files +from the vertex are contracted which + + align:start position:0% +from the vertex are contracted which + + + align:start position:0% +from the vertex are contracted which +each of the external files okay so this + + align:start position:0% +each of the external files okay so this + + + align:start position:0% +each of the external files okay so this +is the the first order + + align:start position:0% +is the the first order + + + align:start position:0% +is the the first order +and then you can also have + + align:start position:0% + + + + align:start position:0% + +uh uh uh the diagram like this + + align:start position:0% +uh uh uh the diagram like this + + + align:start position:0% +uh uh uh the diagram like this +okay + + align:start position:0% + + + + align:start position:0% + +and you can also have uh + + align:start position:0% +and you can also have uh + + + align:start position:0% +and you can also have uh +um yeah I will not show all the diagrams + + align:start position:0% +um yeah I will not show all the diagrams + + + align:start position:0% +um yeah I will not show all the diagrams +okay + + align:start position:0% +okay + + + align:start position:0% +okay +I will just show and you can draw more + + align:start position:0% +I will just show and you can draw more + + + align:start position:0% +I will just show and you can draw more +diagrams like this but these are not + + align:start position:0% +diagrams like this but these are not + + + align:start position:0% +diagrams like this but these are not +vacuum bubbles + + align:start position:0% +vacuum bubbles + + + align:start position:0% +vacuum bubbles +and you can also have diagrams like this + + align:start position:0% + + + + align:start position:0% + +the reason I chose them because we are + + align:start position:0% +the reason I chose them because we are + + + align:start position:0% +the reason I chose them because we are +going to do some of them in your PSAT + + align:start position:0% + + + + align:start position:0% + +yeah there's another diagram like that + + align:start position:0% +yeah there's another diagram like that + + + align:start position:0% +yeah there's another diagram like that +Etc okay so so + + align:start position:0% +Etc okay so so + + + align:start position:0% +Etc okay so so +yeah let me just show one two more + + align:start position:0% +yeah let me just show one two more + + + align:start position:0% +yeah let me just show one two more +uh there's still some more diagram you + + align:start position:0% +uh there's still some more diagram you + + + align:start position:0% +uh there's still some more diagram you +can draw + + align:start position:0% + + + + align:start position:0% + +to Lambda Square Order okay + + align:start position:0% + + + + align:start position:0% + +but again you just uh it's mechanical + + align:start position:0% +but again you just uh it's mechanical + + + align:start position:0% +but again you just uh it's mechanical +okay with the DB patients + + align:start position:0% +okay with the DB patients + + + align:start position:0% +okay with the DB patients +there's no no mystery here okay + + align:start position:0% +there's no no mystery here okay + + + align:start position:0% +there's no no mystery here okay +so now let me make some remarks here + + align:start position:0% + + + + align:start position:0% + +and let me make some remarks here + + align:start position:0% + + + + align:start position:0% + +first + + align:start position:0% +first + + + align:start position:0% +first +so the diagram you can see separating + + align:start position:0% +so the diagram you can see separating + + + align:start position:0% +so the diagram you can see separating +the two types + + align:start position:0% +the two types + + + align:start position:0% +the two types +so the full GN separate into two types + + align:start position:0% +so the full GN separate into two types + + + align:start position:0% +so the full GN separate into two types +one type is called connective diagrams + + align:start position:0% + + + + align:start position:0% + +so connect the diagram just by + + align:start position:0% +so connect the diagram just by + + + align:start position:0% +so connect the diagram just by +yeah just essentially + + align:start position:0% +yeah just essentially + + + align:start position:0% +yeah just essentially +by by its name + + align:start position:0% +by by its name + + + align:start position:0% +by by its name +this corresponding to diagrams with all + + align:start position:0% +this corresponding to diagrams with all + + + align:start position:0% +this corresponding to diagrams with all +the external lags they are connected + + align:start position:0% +the external lags they are connected + + + align:start position:0% +the external lags they are connected +within a single diagram okay and so this + + align:start position:0% +within a single diagram okay and so this + + + align:start position:0% +within a single diagram okay and so this +is a connected diagram + + align:start position:0% +is a connected diagram + + + align:start position:0% +is a connected diagram +oh no no this is a connected diagram + + align:start position:0% +oh no no this is a connected diagram + + + align:start position:0% +oh no no this is a connected diagram +but this is not + + align:start position:0% +but this is not + + + align:start position:0% +but this is not +okay and this is connected diagram + + align:start position:0% +okay and this is connected diagram + + + align:start position:0% +okay and this is connected diagram +disconnected diagram disconnected + + align:start position:0% +disconnected diagram disconnected + + + align:start position:0% +disconnected diagram disconnected +diagram this is not okay + + align:start position:0% +diagram this is not okay + + + align:start position:0% +diagram this is not okay +this is also connected diagram okay + + align:start position:0% + + + + align:start position:0% + +and you can also have disconnected + + align:start position:0% +and you can also have disconnected + + + align:start position:0% +and you can also have disconnected +diagrams + + align:start position:0% + + + + align:start position:0% + +so these connective diagrams + + align:start position:0% +so these connective diagrams + + + align:start position:0% +so these connective diagrams +corresponding to diagrams as here + + align:start position:0% +corresponding to diagrams as here + + + align:start position:0% +corresponding to diagrams as here +so so so not + + align:start position:0% +so so so not + + + align:start position:0% +so so so not +so you you external X separated into sub + + align:start position:0% +so you you external X separated into sub + + + align:start position:0% +so you you external X separated into sub +diagrams okay they belong to product of + + align:start position:0% +diagrams okay they belong to product of + + + align:start position:0% +diagrams okay they belong to product of +sub diagrams + + align:start position:0% + + + + align:start position:0% + +and the later we will + + align:start position:0% +and the later we will + + + align:start position:0% +and the later we will +later you will see that actually later + + align:start position:0% +later you will see that actually later + + + align:start position:0% +later you will see that actually later +we argue this is actually not + + align:start position:0% +we argue this is actually not + + + align:start position:0% +we argue this is actually not +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +okay only connected diagrams are + + align:start position:0% +okay only connected diagrams are + + + align:start position:0% +okay only connected diagrams are +interesting but in a few minutes okay so + + align:start position:0% +interesting but in a few minutes okay so + + + align:start position:0% +interesting but in a few minutes okay so +so for the moment let's just still + + align:start position:0% +so for the moment let's just still + + + align:start position:0% +so for the moment let's just still +Define them + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +and then yeah so so + + align:start position:0% +and then yeah so so + + + align:start position:0% +and then yeah so so +so um + + align:start position:0% +so um + + + align:start position:0% +so um +yeah and the and the emphasize again the + + align:start position:0% +yeah and the and the emphasize again the + + + align:start position:0% +yeah and the and the emphasize again the +external + + align:start position:0% + + + + align:start position:0% + +pi + + align:start position:0% +pi + + + align:start position:0% +pi +General okay + + align:start position:0% +General okay + + + align:start position:0% +General okay +so so each + + align:start position:0% +so so each + + + align:start position:0% +so so each +external line + + align:start position:0% +external line + + + align:start position:0% +external line +which you can assign a momentum pi + + align:start position:0% +which you can assign a momentum pi + + + align:start position:0% +which you can assign a momentum pi +okay because from the Fourier transform + + align:start position:0% +okay because from the Fourier transform + + + align:start position:0% +okay because from the Fourier transform +and from the Fourier transform so for + + align:start position:0% +and from the Fourier transform so for + + + align:start position:0% +and from the Fourier transform so for +example here + + align:start position:0% +example here + + + align:start position:0% +example here +you know P1 + + align:start position:0% +you know P1 + + + align:start position:0% +you know P1 +P2 + + align:start position:0% +P2 + + + align:start position:0% +P2 +P3 + + align:start position:0% +P3 + + + align:start position:0% +P3 +P4 in momentum space each one you can + + align:start position:0% +P4 in momentum space each one you can + + + align:start position:0% +P4 in momentum space each one you can +assign a momentum another momentum + + align:start position:0% +assign a momentum another momentum + + + align:start position:0% +assign a momentum another momentum +General okay can be in principle can be + + align:start position:0% +General okay can be in principle can be + + + align:start position:0% +General okay can be in principle can be +anything okay + + align:start position:0% + + + + align:start position:0% + +good any questions on this + + align:start position:0% +good any questions on this + + + align:start position:0% +good any questions on this +yes + + align:start position:0% + + + + align:start position:0% + +no there's no trick to make sure you + + align:start position:0% +no there's no trick to make sure you + + + align:start position:0% +no there's no trick to make sure you +counted all them the only trick is + + align:start position:0% +counted all them the only trick is + + + align:start position:0% +counted all them the only trick is +patience + + align:start position:0% +patience + + + align:start position:0% +patience +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah it just eliminates + + align:start position:0% +yeah it just eliminates + + + align:start position:0% +yeah it just eliminates +yeah I just tried to illuminate all + + align:start position:0% +yeah I just tried to illuminate all + + + align:start position:0% +yeah I just tried to illuminate all +possibilities yeah + + align:start position:0% +possibilities yeah + + + align:start position:0% +possibilities yeah +yeah it's a finite number of them you + + align:start position:0% +yeah it's a finite number of them you + + + align:start position:0% +yeah it's a finite number of them you +can always do it yes + + align:start position:0% + + + + align:start position:0% + +sorry + + align:start position:0% + + + + align:start position:0% + +no there's no I think there's no general + + align:start position:0% +no there's no I think there's no general + + + align:start position:0% +no there's no I think there's no general +formula tell you each over the how many + + align:start position:0% +formula tell you each over the how many + + + align:start position:0% +formula tell you each over the how many +diagrams you should have there's no such + + align:start position:0% +diagrams you should have there's no such + + + align:start position:0% +diagrams you should have there's no such +kind of magic formula + + align:start position:0% + + + + align:start position:0% + +yeah there's only there's only one + + align:start position:0% +yeah there's only there's only one + + + align:start position:0% +yeah there's only there's only one +formula there's only one yeah it's not + + align:start position:0% +formula there's only one yeah it's not + + + align:start position:0% +formula there's only one yeah it's not +the formula just only one chain which + + align:start position:0% +the formula just only one chain which + + + align:start position:0% +the formula just only one chain which +you can show + + align:start position:0% +you can show + + + align:start position:0% +you can show +that when you go to ends order + + align:start position:0% +that when you go to ends order + + + align:start position:0% +that when you go to ends order +okay when you go to ends when you go to + + align:start position:0% +okay when you go to ends when you go to + + + align:start position:0% +okay when you go to ends when you go to +amps order + + align:start position:0% +amps order + + + align:start position:0% +amps order +guess there are how many roughly how + + align:start position:0% +guess there are how many roughly how + + + align:start position:0% +guess there are how many roughly how +many diagrams at AMS order + + align:start position:0% +many diagrams at AMS order + + + align:start position:0% +many diagrams at AMS order +yes + + align:start position:0% +yes + + + align:start position:0% +yes +that's right n factorial so it's quite a + + align:start position:0% +that's right n factorial so it's quite a + + + align:start position:0% +that's right n factorial so it's quite a +lot of them okay so once you go to say + + align:start position:0% +lot of them okay so once you go to say + + + align:start position:0% +lot of them okay so once you go to say +fourth or fifth order and become a lot + + align:start position:0% +fourth or fifth order and become a lot + + + align:start position:0% +fourth or fifth order and become a lot +and uh so uh yeah yeah uh + + align:start position:0% +and uh so uh yeah yeah uh + + + align:start position:0% +and uh so uh yeah yeah uh +you can be assured we will not ask you + + align:start position:0% +you can be assured we will not ask you + + + align:start position:0% +you can be assured we will not ask you +to eliminate to force order in your key + + align:start position:0% +to eliminate to force order in your key + + + align:start position:0% +to eliminate to force order in your key +set + + align:start position:0% +set + + + align:start position:0% +set +yeah and uh um yeah so + + align:start position:0% +yeah and uh um yeah so + + + align:start position:0% +yeah and uh um yeah so +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um + + align:start position:0% +um + + + align:start position:0% +um +yeah actually these girls of the family + + align:start position:0% +yeah actually these girls of the family + + + align:start position:0% +yeah actually these girls of the family +the growth of the number of family + + align:start position:0% +the growth of the number of family + + + align:start position:0% +the growth of the number of family +diagram uh implies something deep + + align:start position:0% +diagram uh implies something deep + + + align:start position:0% +diagram uh implies something deep +actually it implies yeah it may just it + + align:start position:0% +actually it implies yeah it may just it + + + align:start position:0% +actually it implies yeah it may just it +it's a side remark it implies that this + + align:start position:0% +it's a side remark it implies that this + + + align:start position:0% +it's a side remark it implies that this +perturbation theory in namda + + align:start position:0% +perturbation theory in namda + + + align:start position:0% +perturbation theory in namda +is actually not convergent + + align:start position:0% +is actually not convergent + + + align:start position:0% +is actually not convergent +because because the number of diagrams + + align:start position:0% +because because the number of diagrams + + + align:start position:0% +because because the number of diagrams +grow too fast and so at the ends if at + + align:start position:0% +grow too fast and so at the ends if at + + + align:start position:0% +grow too fast and so at the ends if at +amps order become n factorial then that + + align:start position:0% +amps order become n factorial then that + + + align:start position:0% +amps order become n factorial then that +means the the amps or the contribution + + align:start position:0% +means the the amps or the contribution + + + align:start position:0% +means the the amps or the contribution +goes also grow as n factorial and the + + align:start position:0% +goes also grow as n factorial and the + + + align:start position:0% +goes also grow as n factorial and the +math means this power series is actually + + align:start position:0% +math means this power series is actually + + + align:start position:0% +math means this power series is actually +not convergent it's only a symptomatic + + align:start position:0% +not convergent it's only a symptomatic + + + align:start position:0% +not convergent it's only a symptomatic +series and but still for for many + + align:start position:0% +series and but still for for many + + + align:start position:0% +series and but still for for many +physical purpose it's enough okay + + align:start position:0% + + + + align:start position:0% + +good any other questions + + align:start position:0% +good any other questions + + + align:start position:0% +good any other questions +because this concludes our discussion + + align:start position:0% +because this concludes our discussion + + + align:start position:0% +because this concludes our discussion +of calculating such kind of famine or + + align:start position:0% +of calculating such kind of famine or + + + align:start position:0% +of calculating such kind of famine or +correlation functions uh using yeah for + + align:start position:0% +correlation functions uh using yeah for + + + align:start position:0% +correlation functions uh using yeah for +interacting Theory + + align:start position:0% +interacting Theory + + + align:start position:0% +interacting Theory +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yes + + align:start position:0% + + + + align:start position:0% + +yeah it's a symptomatic Series yeah + + align:start position:0% +yeah it's a symptomatic Series yeah + + + align:start position:0% +yeah it's a symptomatic Series yeah +what + + align:start position:0% + + + + align:start position:0% + +yeah yeah synthetic series is the kind + + align:start position:0% +yeah yeah synthetic series is the kind + + + align:start position:0% +yeah yeah synthetic series is the kind +of series which you you since will go + + align:start position:0% +of series which you you since will go + + + align:start position:0% +of series which you you since will go +since we are uh yeah just the higher all + + align:start position:0% +since we are uh yeah just the higher all + + + align:start position:0% +since we are uh yeah just the higher all +the terms will be small or will be + + align:start position:0% +the terms will be small or will be + + + align:start position:0% +the terms will be small or will be +smaller and smaller uh for for a while + + align:start position:0% +smaller and smaller uh for for a while + + + align:start position:0% +smaller and smaller uh for for a while +and then girl then girl again and so if + + align:start position:0% +and then girl then girl again and so if + + + align:start position:0% +and then girl then girl again and so if +you don't calculate too high order + + align:start position:0% +you don't calculate too high order + + + align:start position:0% +you don't calculate too high order +actually they become very they're + + align:start position:0% +actually they become very they're + + + align:start position:0% +actually they become very they're +actually quite reliable you can you can + + align:start position:0% +actually quite reliable you can you can + + + align:start position:0% +actually quite reliable you can you can +bound the arrows yeah + + align:start position:0% +bound the arrows yeah + + + align:start position:0% +bound the arrows yeah +yeah so this is the heuristic way to say + + align:start position:0% +yeah so this is the heuristic way to say + + + align:start position:0% +yeah so this is the heuristic way to say +it yeah + + align:start position:0% + + + + align:start position:0% + +yeah it's just when you look at the + + align:start position:0% +yeah it's just when you look at the + + + align:start position:0% +yeah it's just when you look at the +first few order terms it still can be + + align:start position:0% +first few order terms it still can be + + + align:start position:0% +first few order terms it still can be +reliably or or it's a reliable + + align:start position:0% +reliably or or it's a reliable + + + align:start position:0% +reliably or or it's a reliable +approximation to your true answer + + align:start position:0% + + + + align:start position:0% + +I have some series + + align:start position:0% + + + + align:start position:0% + +no no depend on your specific Theory + + align:start position:0% +no no depend on your specific Theory + + + align:start position:0% +no no depend on your specific Theory +right so so maybe your series that is + + align:start position:0% +right so so maybe your series that is + + + align:start position:0% +right so so maybe your series that is +just the uh or maybe that's just your + + align:start position:0% +just the uh or maybe that's just your + + + align:start position:0% +just the uh or maybe that's just your +theory + + align:start position:0% + + + + align:start position:0% + +oh yeah yeah in physical problem you you + + align:start position:0% +oh yeah yeah in physical problem you you + + + align:start position:0% +oh yeah yeah in physical problem you you +yeah so + + align:start position:0% +yeah so + + + align:start position:0% +yeah so +yeah in one second uh we will tell you + + align:start position:0% +yeah in one second uh we will tell you + + + align:start position:0% +yeah in one second uh we will tell you +how you come from here to calculate the + + align:start position:0% +how you come from here to calculate the + + + align:start position:0% +how you come from here to calculate the +scattering amplitude and when you find + + align:start position:0% +scattering amplitude and when you find + + + align:start position:0% +scattering amplitude and when you find +the scattering amplitude then you can + + align:start position:0% +the scattering amplitude then you can + + + align:start position:0% +the scattering amplitude then you can +measure the experiment then you try to + + align:start position:0% +measure the experiment then you try to + + + align:start position:0% +measure the experiment then you try to +deduce back the action + + align:start position:0% + + + + align:start position:0% + +yeah that's right that's right + + align:start position:0% + + + + align:start position:0% + +oh it can happen as a a as a toy model + + align:start position:0% +oh it can happen as a a as a toy model + + + align:start position:0% +oh it can happen as a a as a toy model +you can always write whatever Theory you + + align:start position:0% +you can always write whatever Theory you + + + align:start position:0% +you can always write whatever Theory you +want but but in nature somehow the the + + align:start position:0% +want but but in nature somehow the the + + + align:start position:0% +want but but in nature somehow the the +series we discovered so far is all + + align:start position:0% +series we discovered so far is all + + + align:start position:0% +series we discovered so far is all +polynomial + + align:start position:0% + + + + align:start position:0% + +okay good + + align:start position:0% +okay good + + + align:start position:0% +okay good +so now + + align:start position:0% +so now + + + align:start position:0% +so now +so earlier we mentioned that this SL LSD + + align:start position:0% +so earlier we mentioned that this SL LSD + + + align:start position:0% +so earlier we mentioned that this SL LSD +serum which tells you that the + + align:start position:0% +serum which tells you that the + + + align:start position:0% +serum which tells you that the +scattering amplitude + + align:start position:0% +scattering amplitude + + + align:start position:0% +scattering amplitude +are are + + align:start position:0% +are are + + + align:start position:0% +are are +can be obtained from this time ordered + + align:start position:0% +can be obtained from this time ordered + + + align:start position:0% +can be obtained from this time ordered +correlation functions okay so so now + + align:start position:0% +correlation functions okay so so now + + + align:start position:0% +correlation functions okay so so now +let's go go back to this LSD story again + + align:start position:0% +let's go go back to this LSD story again + + + align:start position:0% +let's go go back to this LSD story again +tell you actually how to obtain + + align:start position:0% +tell you actually how to obtain + + + align:start position:0% +tell you actually how to obtain +scattering amplitude from uh our + + align:start position:0% +scattering amplitude from uh our + + + align:start position:0% +scattering amplitude from uh our +correlation functions okay and from + + align:start position:0% +correlation functions okay and from + + + align:start position:0% +correlation functions okay and from +correlation functions + + align:start position:0% + + + + align:start position:0% + +so so the basic idea is the following + + align:start position:0% +so so the basic idea is the following + + + align:start position:0% +so so the basic idea is the following +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the basic idea is following is that + + align:start position:0% +so the basic idea is following is that + + + align:start position:0% +so the basic idea is following is that +you take + + align:start position:0% +you take + + + align:start position:0% +you take +your endpoint function + + align:start position:0% + + + + align:start position:0% + +okay with any external momentum P1 to p + + align:start position:0% +okay with any external momentum P1 to p + + + align:start position:0% +okay with any external momentum P1 to p +n + + align:start position:0% +n + + + align:start position:0% +n +okay and then take all so I say + + align:start position:0% +okay and then take all so I say + + + align:start position:0% +okay and then take all so I say +emphasized here each Pi is General okay + + align:start position:0% +emphasized here each Pi is General okay + + + align:start position:0% +emphasized here each Pi is General okay +but now suppose + + align:start position:0% +but now suppose + + + align:start position:0% +but now suppose +you take + + align:start position:0% +you take + + + align:start position:0% +you take +all momentum + + align:start position:0% +all momentum + + + align:start position:0% +all momentum +OPI + + align:start position:0% +OPI + + + align:start position:0% +OPI +okay to be on shell + + align:start position:0% + + + + align:start position:0% + +so now you can see the them to satisfy + + align:start position:0% +so now you can see the them to satisfy + + + align:start position:0% +so now you can see the them to satisfy +Pi Square equal to minus M Square + + align:start position:0% +Pi Square equal to minus M Square + + + align:start position:0% +Pi Square equal to minus M Square +hmm + + align:start position:0% +hmm + + + align:start position:0% +hmm +okay + + align:start position:0% + + + + align:start position:0% + +so um yeah so in order to get the + + align:start position:0% +so um yeah so in order to get the + + + align:start position:0% +so um yeah so in order to get the +amplitude you need to do this step you + + align:start position:0% +amplitude you need to do this step you + + + align:start position:0% +amplitude you need to do this step you +take all the external momentum yeah this + + align:start position:0% +take all the external momentum yeah this + + + align:start position:0% +take all the external momentum yeah this +is very reasonable to expect + + align:start position:0% +is very reasonable to expect + + + align:start position:0% +is very reasonable to expect +because when we're scattering particles + + align:start position:0% +because when we're scattering particles + + + align:start position:0% +because when we're scattering particles +uh uh uh remember we say the initial + + align:start position:0% +uh uh uh remember we say the initial + + + align:start position:0% +uh uh uh remember we say the initial +particle can be considered as a free + + align:start position:0% +particle can be considered as a free + + + align:start position:0% +particle can be considered as a free +particle fellow particle can also be + + align:start position:0% +particle fellow particle can also be + + + align:start position:0% +particle fellow particle can also be +considered as three particle if they are + + align:start position:0% +considered as three particle if they are + + + align:start position:0% +considered as three particle if they are +free particles then then their momentum + + align:start position:0% +free particles then then their momentum + + + align:start position:0% +free particles then then their momentum +satisfied this on shell condition + + align:start position:0% +satisfied this on shell condition + + + align:start position:0% +satisfied this on shell condition +okay so so in order to relate this to a + + align:start position:0% +okay so so in order to relate this to a + + + align:start position:0% +okay so so in order to relate this to a +schedule amplitude and then we need to + + align:start position:0% +schedule amplitude and then we need to + + + align:start position:0% +schedule amplitude and then we need to +take a standard momentum to be on shell + + align:start position:0% +take a standard momentum to be on shell + + + align:start position:0% +take a standard momentum to be on shell +okay + + align:start position:0% + + + + align:start position:0% + +but now if you look at this you say + + align:start position:0% +but now if you look at this you say + + + align:start position:0% +but now if you look at this you say +there are two possible choice for this + + align:start position:0% +there are two possible choice for this + + + align:start position:0% +there are two possible choice for this +equation + + align:start position:0% + + + + align:start position:0% + +because this equation has two solutions + + align:start position:0% + + + + align:start position:0% + +okay so so for each p i + + align:start position:0% +okay so so for each p i + + + align:start position:0% +okay so so for each p i +so p i zero + + align:start position:0% +so p i zero + + + align:start position:0% +so p i zero +can either be + + align:start position:0% +can either be + + + align:start position:0% +can either be +plus minus + + align:start position:0% +plus minus + + + align:start position:0% +plus minus +Omega pi + + align:start position:0% +Omega pi + + + align:start position:0% +Omega pi +so so we are using the same notation we + + align:start position:0% +so so we are using the same notation we + + + align:start position:0% +so so we are using the same notation we +used before okay so so this Pi Vector is + + align:start position:0% +used before okay so so this Pi Vector is + + + align:start position:0% +used before okay so so this Pi Vector is +the spatial part and then we have omega + + align:start position:0% +the spatial part and then we have omega + + + align:start position:0% +the spatial part and then we have omega +Pi okay so this Omega Pi is just the + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so you have two uh possible solutions + + align:start position:0% +so you have two uh possible solutions + + + align:start position:0% +so you have two uh possible solutions +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +so now the rule is the following okay + + align:start position:0% +so now the rule is the following okay + + + align:start position:0% +so now the rule is the following okay +now is the rule is following + + align:start position:0% +now is the rule is following + + + align:start position:0% +now is the rule is following +take + + align:start position:0% + + + + align:start position:0% + +say let's take + + align:start position:0% +say let's take + + + align:start position:0% +say let's take +P1 + + align:start position:0% +P1 + + + align:start position:0% +P1 +say take take M of them okay + + align:start position:0% +say take take M of them okay + + + align:start position:0% +say take take M of them okay +we take their uh uh + + align:start position:0% +we take their uh uh + + + align:start position:0% +we take their uh uh +we take the negative root + + align:start position:0% + + + + align:start position:0% + +supposed to be + + align:start position:0% + + + + align:start position:0% + +so Alpha would be one over + + align:start position:0% +so Alpha would be one over + + + align:start position:0% +so Alpha would be one over +to m + + align:start position:0% +to m + + + align:start position:0% +to m +and then then for the rest say PM Plus + + align:start position:0% +and then then for the rest say PM Plus + + + align:start position:0% +and then then for the rest say PM Plus +One + + align:start position:0% + + + + align:start position:0% + +so let's consider the following + + align:start position:0% +so let's consider the following + + + align:start position:0% +so let's consider the following +situation okay and then you take the + + align:start position:0% +situation okay and then you take the + + + align:start position:0% +situation okay and then you take the +positive root + + align:start position:0% + + + + align:start position:0% + +okay so so let's consider the following + + align:start position:0% +okay so so let's consider the following + + + align:start position:0% +okay so so let's consider the following +situation + + align:start position:0% + + + + align:start position:0% + +okay so let's imagine + + align:start position:0% + + + + align:start position:0% + +we take such a endpoint + + align:start position:0% +we take such a endpoint + + + align:start position:0% +we take such a endpoint +function in momentum space + + align:start position:0% +function in momentum space + + + align:start position:0% +function in momentum space +and then we take + + align:start position:0% +and then we take + + + align:start position:0% +and then we take +all the momentum on shell but for for + + align:start position:0% +all the momentum on shell but for for + + + align:start position:0% +all the momentum on shell but for for +some of them + + align:start position:0% +some of them + + + align:start position:0% +some of them +we take them to be take the negative + + align:start position:0% +we take them to be take the negative + + + align:start position:0% +we take them to be take the negative +root and some of them we take it to be + + align:start position:0% +root and some of them we take it to be + + + align:start position:0% +root and some of them we take it to be +the positive root + + align:start position:0% +the positive root + + + align:start position:0% +the positive root +and then there's a theorem okay so this + + align:start position:0% +and then there's a theorem okay so this + + + align:start position:0% +and then there's a theorem okay so this +is called LSD serum which is three + + align:start position:0% +is called LSD serum which is three + + + align:start position:0% +is called LSD serum which is three +percent + + align:start position:0% + + + + align:start position:0% + +moment + + align:start position:0% + + + + align:start position:0% + +so this serum sets under this limit + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +under this limit + + align:start position:0% +under this limit + + + align:start position:0% +under this limit +under this unsure limit + + align:start position:0% + + + + align:start position:0% + +so you will see why we we emphasize we + + align:start position:0% +so you will see why we we emphasize we + + + align:start position:0% +so you will see why we we emphasize we +called it on share limit + + align:start position:0% +called it on share limit + + + align:start position:0% +called it on share limit +so you so imagine you don't actually put + + align:start position:0% +so you so imagine you don't actually put + + + align:start position:0% +so you so imagine you don't actually put +them + + align:start position:0% + + + + align:start position:0% + +to be exactly a momentum you take the + + align:start position:0% +to be exactly a momentum you take the + + + align:start position:0% +to be exactly a momentum you take the +momentum to approach that okay + + align:start position:0% +momentum to approach that okay + + + align:start position:0% +momentum to approach that okay +we approach that we just emphasize + + align:start position:0% + + + + align:start position:0% + +so in this limit + + align:start position:0% + + + + align:start position:0% + +then you find that your momentum space + + align:start position:0% +then you find that your momentum space + + + align:start position:0% +then you find that your momentum space +correlation function + + align:start position:0% + + + + align:start position:0% + +can you find your momentum space + + align:start position:0% +can you find your momentum space + + + align:start position:0% +can you find your momentum space +correlation function approach to the + + align:start position:0% +correlation function approach to the + + + align:start position:0% +correlation function approach to the +following + + align:start position:0% +following + + + align:start position:0% +following +quantity + + align:start position:0% + + + + align:start position:0% + +in this limit + + align:start position:0% +in this limit + + + align:start position:0% +in this limit +yeah so um + + align:start position:0% + + + + align:start position:0% + +so first + + align:start position:0% +so first + + + align:start position:0% +so first +we write down the expression + + align:start position:0% +we write down the expression + + + align:start position:0% +we write down the expression +and then we will explain what this means + + align:start position:0% + + + + align:start position:0% + +and let me just do it downstairs sorry + + align:start position:0% +and let me just do it downstairs sorry + + + align:start position:0% +and let me just do it downstairs sorry +times + + align:start position:0% + + + + align:start position:0% + +do it downstairs + + align:start position:0% +do it downstairs + + + align:start position:0% +do it downstairs +times + + align:start position:0% + + + + align:start position:0% + +plus infinity + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so the statement is the following + + align:start position:0% +so the statement is the following + + + align:start position:0% +so the statement is the following +and here Z do some constant + + align:start position:0% + + + + align:start position:0% + +so so we don't need to worry about it + + align:start position:0% +so so we don't need to worry about it + + + align:start position:0% +so so we don't need to worry about it +so this is just some constant + + align:start position:0% +so this is just some constant + + + align:start position:0% +so this is just some constant +and and so this is square root Z divided + + align:start position:0% +and and so this is square root Z divided + + + align:start position:0% +and and so this is square root Z divided +by this factor for each external + + align:start position:0% +by this factor for each external + + + align:start position:0% +by this factor for each external +momentum + + align:start position:0% +momentum + + + align:start position:0% +momentum +and this is just the skeleton into the + + align:start position:0% +and this is just the skeleton into the + + + align:start position:0% +and this is just the skeleton into the +this is the scattering amplitude + + align:start position:0% + + + + align:start position:0% + +for M initial particles oh sorry I + + align:start position:0% +for M initial particles oh sorry I + + + align:start position:0% +for M initial particles oh sorry I +forgot the minus sign should be minus P1 + + align:start position:0% +forgot the minus sign should be minus P1 + + + align:start position:0% +forgot the minus sign should be minus P1 +minus P2 to minus PN okay + + align:start position:0% +minus P2 to minus PN okay + + + align:start position:0% +minus P2 to minus PN okay +so this is the scattering amplitude + + align:start position:0% +so this is the scattering amplitude + + + align:start position:0% +so this is the scattering amplitude +for particles with initial + + align:start position:0% +for particles with initial + + + align:start position:0% +for particles with initial +momentum minus P1 to minus PM into + + align:start position:0% +momentum minus P1 to minus PM into + + + align:start position:0% +momentum minus P1 to minus PM into +particles + + align:start position:0% +particles + + + align:start position:0% +particles +with final momentum M plus 1 p m plus 1 + + align:start position:0% +with final momentum M plus 1 p m plus 1 + + + align:start position:0% +with final momentum M plus 1 p m plus 1 +to p n okay + + align:start position:0% +to p n okay + + + align:start position:0% +to p n okay +so essentially whether you choose the + + align:start position:0% +so essentially whether you choose the + + + align:start position:0% +so essentially whether you choose the +negative root or the positive root + + align:start position:0% +negative root or the positive root + + + align:start position:0% +negative root or the positive root +decides whether this you are in the + + align:start position:0% +decides whether this you are in the + + + align:start position:0% +decides whether this you are in the +initial States or in the in the final + + align:start position:0% +initial States or in the in the final + + + align:start position:0% +initial States or in the in the final +state + + align:start position:0% +state + + + align:start position:0% +state +okay whether you're in the final state + + align:start position:0% +okay whether you're in the final state + + + align:start position:0% +okay whether you're in the final state +in the scattering amplitude + + align:start position:0% +in the scattering amplitude + + + align:start position:0% +in the scattering amplitude +okay + + align:start position:0% + + + + align:start position:0% + +so so let me just write here + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so let me just copy this again + + align:start position:0% +so let me just copy this again + + + align:start position:0% +so let me just copy this again +uh so so this + + align:start position:0% +uh so so this + + + align:start position:0% +uh so so this +skeleton amplitude yeah so this is the + + align:start position:0% +skeleton amplitude yeah so this is the + + + align:start position:0% +skeleton amplitude yeah so this is the +yeah let me just write here + + align:start position:0% +yeah let me just write here + + + align:start position:0% +yeah let me just write here +so this p n + + align:start position:0% +so this p n + + + align:start position:0% +so this p n +p m Plus 1. + + align:start position:0% + + + + align:start position:0% + +p n + + align:start position:0% +p n + + + align:start position:0% +p n +plus infinity + + align:start position:0% + + + + align:start position:0% + +minus P1 + + align:start position:0% +minus P1 + + + align:start position:0% +minus P1 +minus PM minus infinity so this is the + + align:start position:0% +minus PM minus infinity so this is the + + + align:start position:0% +minus PM minus infinity so this is the +scattering amplitude + + align:start position:0% +scattering amplitude + + + align:start position:0% +scattering amplitude +from so this is the scattering amplitude + + align:start position:0% + + + + align:start position:0% + +this is amplitude + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% +for + + + align:start position:0% +for +the particle with momentum P1 + + align:start position:0% + + + + align:start position:0% + +pm + + align:start position:0% +pm + + + align:start position:0% +pm +and the minus and t equal to minus + + align:start position:0% +and the minus and t equal to minus + + + align:start position:0% +and the minus and t equal to minus +infinity + + align:start position:0% +infinity + + + align:start position:0% +infinity +transition into + + align:start position:0% + + + + align:start position:0% + +to the product to end to to the rest + + align:start position:0% +to the product to end to to the rest + + + align:start position:0% +to the product to end to to the rest +particles + + align:start position:0% +particles + + + align:start position:0% +particles +at this momentum at t plus infinity + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% + + + + align:start position:0% + +so to save the uh + + align:start position:0% +so to save the uh + + + align:start position:0% +so to save the uh +to save the notation + + align:start position:0% +to save the notation + + + align:start position:0% +to save the notation +so so again this will + + align:start position:0% +so so again this will + + + align:start position:0% +so so again this will +so remember previously we defined + + align:start position:0% + + + + align:start position:0% + +so if you remember before + + align:start position:0% +so if you remember before + + + align:start position:0% +so if you remember before +we defined this object + + align:start position:0% +we defined this object + + + align:start position:0% +we defined this object +this object should also preserve the + + align:start position:0% +this object should also preserve the + + + align:start position:0% +this object should also preserve the +because of its time translation symmetry + + align:start position:0% +because of its time translation symmetry + + + align:start position:0% +because of its time translation symmetry +uh this object will also preserves the + + align:start position:0% +uh this object will also preserves the + + + align:start position:0% +uh this object will also preserves the +energy and momentum + + align:start position:0% +energy and momentum + + + align:start position:0% +energy and momentum +so this object is also proportional + + align:start position:0% +so this object is also proportional + + + align:start position:0% +so this object is also proportional +to + + align:start position:0% +to + + + align:start position:0% +to +so you can extract out the data function + + align:start position:0% + + + + align:start position:0% + +and then times a quantity which we call + + align:start position:0% +and then times a quantity which we call + + + align:start position:0% +and then times a quantity which we call +describing amplitude before say Alpha to + + align:start position:0% +describing amplitude before say Alpha to + + + align:start position:0% +describing amplitude before say Alpha to +Beta okay so Alpha denotes the initial + + align:start position:0% +Beta okay so Alpha denotes the initial + + + align:start position:0% +Beta okay so Alpha denotes the initial +state + + align:start position:0% +state + + + align:start position:0% +state +so this is the initial State Alpha + + align:start position:0% +so this is the initial State Alpha + + + align:start position:0% +so this is the initial State Alpha +and this is a final State beta okay + + align:start position:0% +and this is a final State beta okay + + + align:start position:0% +and this is a final State beta okay +okay + + align:start position:0% + + + + align:start position:0% + +so now if you plug this into plug this + + align:start position:0% +so now if you plug this into plug this + + + align:start position:0% +so now if you plug this into plug this +expression into here + + align:start position:0% +expression into here + + + align:start position:0% +expression into here +and then you will find then the data + + align:start position:0% +and then you will find then the data + + + align:start position:0% +and then you will find then the data +function will just cancel on both sides + + align:start position:0% +function will just cancel on both sides + + + align:start position:0% +function will just cancel on both sides +okay on both sides and then you find + + align:start position:0% +okay on both sides and then you find + + + align:start position:0% +okay on both sides and then you find +this GN + + align:start position:0% + + + + align:start position:0% + +P1 PN is just equal to + + align:start position:0% +P1 PN is just equal to + + + align:start position:0% +P1 PN is just equal to +approach this product of the data + + align:start position:0% +approach this product of the data + + + align:start position:0% +approach this product of the data +functions + + align:start position:0% +functions + + + align:start position:0% +functions +or approach this uh + + align:start position:0% +or approach this uh + + + align:start position:0% +or approach this uh +this Factor + + align:start position:0% +this Factor + + + align:start position:0% +this Factor +and then m alpha 2 Beta + + align:start position:0% +and then m alpha 2 Beta + + + align:start position:0% +and then m alpha 2 Beta +okay + + align:start position:0% + + + + align:start position:0% + +so this is a statement of the slsd + + align:start position:0% +so this is a statement of the slsd + + + align:start position:0% +so this is a statement of the slsd +serum + + align:start position:0% +serum + + + align:start position:0% +serum +you see essentially tell you + + align:start position:0% +you see essentially tell you + + + align:start position:0% +you see essentially tell you +that the uh + + align:start position:0% + + + + align:start position:0% + +tell you that the such a trans such a + + align:start position:0% +tell you that the such a trans such a + + + align:start position:0% +tell you that the such a trans such a +scatter amplitude + + align:start position:0% +scatter amplitude + + + align:start position:0% +scatter amplitude +just can be obtained from this + + align:start position:0% +just can be obtained from this + + + align:start position:0% +just can be obtained from this +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and yeah you multiply those scenes and + + align:start position:0% +and yeah you multiply those scenes and + + + align:start position:0% +and yeah you multiply those scenes and +then just equal to that + + align:start position:0% +then just equal to that + + + align:start position:0% +then just equal to that +so now you observe + + align:start position:0% +so now you observe + + + align:start position:0% +so now you observe +these are precisely + + align:start position:0% +these are precisely + + + align:start position:0% +these are precisely +after this factor of Z these are + + align:start position:0% +after this factor of Z these are + + + align:start position:0% +after this factor of Z these are +precisely just propagators for the + + align:start position:0% +precisely just propagators for the + + + align:start position:0% +precisely just propagators for the +external lags + + align:start position:0% +external lags + + + align:start position:0% +external lags +okay so so now you conclude + + align:start position:0% +okay so so now you conclude + + + align:start position:0% +okay so so now you conclude +okay so so in other words + + align:start position:0% + + + + align:start position:0% + +so so that means that the m alpha beta + + align:start position:0% +so so that means that the m alpha beta + + + align:start position:0% +so so that means that the m alpha beta +then corresponding to you just take the + + align:start position:0% +then corresponding to you just take the + + + align:start position:0% +then corresponding to you just take the +G + + align:start position:0% +G + + + align:start position:0% +G +then you get rid of all these all the + + align:start position:0% +then you get rid of all these all the + + + align:start position:0% +then you get rid of all these all the +external propagators + + align:start position:0% +external propagators + + + align:start position:0% +external propagators +okay because they just corresponding to + + align:start position:0% +okay because they just corresponding to + + + align:start position:0% +okay because they just corresponding to +the external propagators for each + + align:start position:0% +the external propagators for each + + + align:start position:0% +the external propagators for each +external next okay just get rid of the + + align:start position:0% +external next okay just get rid of the + + + align:start position:0% +external next okay just get rid of the +external lags okay + + align:start position:0% +external lags okay + + + align:start position:0% +external lags okay +here I'm just telling you the theorem + + align:start position:0% +here I'm just telling you the theorem + + + align:start position:0% +here I'm just telling you the theorem +and we are going to uh or we will use it + + align:start position:0% +and we are going to uh or we will use it + + + align:start position:0% +and we are going to uh or we will use it +but of course the derivation is a little + + align:start position:0% +but of course the derivation is a little + + + align:start position:0% +but of course the derivation is a little +bit complicated okay + + align:start position:0% + + + + align:start position:0% + +so uh yeah so let me just since this is + + align:start position:0% +so uh yeah so let me just since this is + + + align:start position:0% +so uh yeah so let me just since this is +a little bit + + align:start position:0% +a little bit + + + align:start position:0% +a little bit +so let me just write it in words okay + + align:start position:0% + + + + align:start position:0% + +in words + + align:start position:0% +in words + + + align:start position:0% +in words +to obtain + + align:start position:0% + + + + align:start position:0% + +the scattering to amplitude M to Alpha + + align:start position:0% +the scattering to amplitude M to Alpha + + + align:start position:0% +the scattering to amplitude M to Alpha +Beta + + align:start position:0% + + + + align:start position:0% + +is I first you calculate + + align:start position:0% + + + + align:start position:0% + +so so suppose we have Empire yeah just + + align:start position:0% +so so suppose we have Empire yeah just + + + align:start position:0% +so so suppose we have Empire yeah just +uh you suppose the total number we need + + align:start position:0% +uh you suppose the total number we need + + + align:start position:0% +uh you suppose the total number we need +your particle and final particle are n + + align:start position:0% +your particle and final particle are n + + + align:start position:0% +your particle and final particle are n +and then you just First Take GN first + + align:start position:0% +and then you just First Take GN first + + + align:start position:0% +and then you just First Take GN first +calculate + + align:start position:0% +calculate + + + align:start position:0% +calculate +yeah just take + + align:start position:0% +yeah just take + + + align:start position:0% +yeah just take +GN for for n particles + + align:start position:0% +GN for for n particles + + + align:start position:0% +GN for for n particles +okay so suppose and then + + align:start position:0% + + + + align:start position:0% + +take + + align:start position:0% +take + + + align:start position:0% +take +p i + + align:start position:0% +p i + + + align:start position:0% +p i +on shell + + align:start position:0% + + + + align:start position:0% + +and the initial momentum + + align:start position:0% + + + + align:start position:0% + +take the negative root + + align:start position:0% + + + + align:start position:0% + +root + + align:start position:0% +root + + + align:start position:0% +root +and the in the final momentum + + align:start position:0% +and the in the final momentum + + + align:start position:0% +and the in the final momentum +you take a positive root okay + + align:start position:0% + + + + align:start position:0% + +of that equation + + align:start position:0% +of that equation + + + align:start position:0% +of that equation +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then + + align:start position:0% +and then + + + align:start position:0% +and then +the last step + + align:start position:0% +the last step + + + align:start position:0% +the last step +you just truncate + + align:start position:0% + + + + align:start position:0% + +all the external propagators + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then you truncated all the external + + align:start position:0% +and then you truncated all the external + + + align:start position:0% +and then you truncated all the external +legs + + align:start position:0% +legs + + + align:start position:0% +legs +so so so so so that just comes from you + + align:start position:0% +so so so so so that just comes from you + + + align:start position:0% +so so so so so that just comes from you +need to + + align:start position:0% +need to + + + align:start position:0% +need to +to obtain M while you need to divide + + align:start position:0% +to obtain M while you need to divide + + + align:start position:0% +to obtain M while you need to divide +this side by this Factor then up to the + + align:start position:0% +this side by this Factor then up to the + + + align:start position:0% +this side by this Factor then up to the +fact of Z okay this Factor Z will only + + align:start position:0% +fact of Z okay this Factor Z will only + + + align:start position:0% +fact of Z okay this Factor Z will only +give you a constant which lets uh which + + align:start position:0% +give you a constant which lets uh which + + + align:start position:0% +give you a constant which lets uh which +uh let's not worry about it for now okay + + align:start position:0% +uh let's not worry about it for now okay + + + align:start position:0% +uh let's not worry about it for now okay +yes + + align:start position:0% + + + + align:start position:0% + +this is putting ad hoc + + align:start position:0% + + + + align:start position:0% + +oh yeah yeah that I will explain uh that + + align:start position:0% +oh yeah yeah that I will explain uh that + + + align:start position:0% +oh yeah yeah that I will explain uh that +will explain uh uh yeah yeah + + align:start position:0% +will explain uh uh yeah yeah + + + align:start position:0% +will explain uh uh yeah yeah +first let me just state the rule + + align:start position:0% +first let me just state the rule + + + align:start position:0% +first let me just state the rule +first you understand the rootlets then + + align:start position:0% +first you understand the rootlets then + + + align:start position:0% +first you understand the rootlets then +I'll try to make you more comfortable + + align:start position:0% +I'll try to make you more comfortable + + + align:start position:0% +I'll try to make you more comfortable +okay now this is the rule yes + + align:start position:0% +okay now this is the rule yes + + + align:start position:0% +okay now this is the rule yes +okay yeah yeah here is just the rule + + align:start position:0% +okay yeah yeah here is just the rule + + + align:start position:0% +okay yeah yeah here is just the rule +okay here I'm just explaining uh here is + + align:start position:0% +okay here I'm just explaining uh here is + + + align:start position:0% +okay here I'm just explaining uh here is +the rule uh uh uh this this is a + + align:start position:0% +the rule uh uh uh this this is a + + + align:start position:0% +the rule uh uh uh this this is a +statement you can prove mathematically + + align:start position:0% +statement you can prove mathematically + + + align:start position:0% +statement you can prove mathematically +so this is a mathematical statement you + + align:start position:0% +so this is a mathematical statement you + + + align:start position:0% +so this is a mathematical statement you +can prove + + align:start position:0% +can prove + + + align:start position:0% +can prove +okay and then following from this + + align:start position:0% +okay and then following from this + + + align:start position:0% +okay and then following from this +statement + + align:start position:0% +statement + + + align:start position:0% +statement +and then here is the rule of to obtain + + align:start position:0% +and then here is the rule of to obtain + + + align:start position:0% +and then here is the rule of to obtain +the MFR beta from the G okay + + align:start position:0% + + + + align:start position:0% + +and the ah yeah + + align:start position:0% +and the ah yeah + + + align:start position:0% +and the ah yeah +so so so yeah if I want to write it in + + align:start position:0% +so so so yeah if I want to write it in + + + align:start position:0% +so so so yeah if I want to write it in +one sentence + + align:start position:0% + + + + align:start position:0% + +so so scattering amplitude + + align:start position:0% + + + + align:start position:0% + +just equal to sum Over All + + align:start position:0% + + + + align:start position:0% + +truncated + + align:start position:0% + + + + align:start position:0% + +diagrams + + align:start position:0% + + + + align:start position:0% + +with + + align:start position:0% +with + + + align:start position:0% +with +external momentum Marshall + + align:start position:0% + + + + align:start position:0% + +okay so if I summarize into one sentence + + align:start position:0% +okay so if I summarize into one sentence + + + align:start position:0% +okay so if I summarize into one sentence +it's just this + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +I would say the only thing unintuitive + + align:start position:0% +I would say the only thing unintuitive + + + align:start position:0% +I would say the only thing unintuitive +here + + align:start position:0% +here + + + align:start position:0% +here +the only thing on intuitive here is + + align:start position:0% +the only thing on intuitive here is + + + align:start position:0% +the only thing on intuitive here is +design choice + + align:start position:0% +design choice + + + align:start position:0% +design choice +okay so this sign Choice everything else + + align:start position:0% +okay so this sign Choice everything else + + + align:start position:0% +okay so this sign Choice everything else +I think is intuitive + + align:start position:0% +I think is intuitive + + + align:start position:0% +I think is intuitive +uh everything else in the intuitive view + + align:start position:0% +uh everything else in the intuitive view + + + align:start position:0% +uh everything else in the intuitive view +you take the screen function which + + align:start position:0% +you take the screen function which + + + align:start position:0% +you take the screen function which +contains essentially an external X and + + align:start position:0% +contains essentially an external X and + + + align:start position:0% +contains essentially an external X and +now you just imagine this any internal + + align:start position:0% +now you just imagine this any internal + + + align:start position:0% +now you just imagine this any internal +ax corresponding to initial and fellow + + align:start position:0% +ax corresponding to initial and fellow + + + align:start position:0% +ax corresponding to initial and fellow +particles + + align:start position:0% +particles + + + align:start position:0% +particles +and then it's very reasonable we make + + align:start position:0% +and then it's very reasonable we make + + + align:start position:0% +and then it's very reasonable we make +them on shell okay a big big because + + align:start position:0% +them on shell okay a big big because + + + align:start position:0% +them on shell okay a big big because +they are physical particles + + align:start position:0% +they are physical particles + + + align:start position:0% +they are physical particles +and then the only thing which may be + + align:start position:0% +and then the only thing which may be + + + align:start position:0% +and then the only thing which may be +unintuitive is that Y for the initial + + align:start position:0% +unintuitive is that Y for the initial + + + align:start position:0% +unintuitive is that Y for the initial +moment we need to take the elective + + align:start position:0% +moment we need to take the elective + + + align:start position:0% +moment we need to take the elective +Roots but for the final moment we need + + align:start position:0% +Roots but for the final moment we need + + + align:start position:0% +Roots but for the final moment we need +to take a positive root + + align:start position:0% +to take a positive root + + + align:start position:0% +to take a positive root +and then and then the final thing here + + align:start position:0% +and then and then the final thing here + + + align:start position:0% +and then and then the final thing here +is just uh + + align:start position:0% +is just uh + + + align:start position:0% +is just uh +if you imagine when you scatter + + align:start position:0% +if you imagine when you scatter + + + align:start position:0% +if you imagine when you scatter +particles + + align:start position:0% +particles + + + align:start position:0% +particles +and and how they propagate to to the + + align:start position:0% +and and how they propagate to to the + + + align:start position:0% +and and how they propagate to to the +scattering does not matter + + align:start position:0% +scattering does not matter + + + align:start position:0% +scattering does not matter +okay so so the propagator just + + align:start position:0% +okay so so the propagator just + + + align:start position:0% +okay so so the propagator just +essentially tell you this particle how + + align:start position:0% +essentially tell you this particle how + + + align:start position:0% +essentially tell you this particle how +they how they propagate to the uh to the + + align:start position:0% +they how they propagate to the uh to the + + + align:start position:0% +they how they propagate to the uh to the +scattering Point okay and uh uh uh so + + align:start position:0% +scattering Point okay and uh uh uh so + + + align:start position:0% +scattering Point okay and uh uh uh so +this should not matter for the + + align:start position:0% +this should not matter for the + + + align:start position:0% +this should not matter for the +scattering process for skating process + + align:start position:0% +scattering process for skating process + + + align:start position:0% +scattering process for skating process +and essentially yeah so so so so so we + + align:start position:0% +and essentially yeah so so so so so we + + + align:start position:0% +and essentially yeah so so so so so we +will explain this at the end okay and + + align:start position:0% +will explain this at the end okay and + + + align:start position:0% +will explain this at the end okay and +but before we do that let's just look at + + align:start position:0% +but before we do that let's just look at + + + align:start position:0% +but before we do that let's just look at +uh uh one one example okay do you have + + align:start position:0% +uh uh one one example okay do you have + + + align:start position:0% +uh uh one one example okay do you have +any questions + + align:start position:0% +any questions + + + align:start position:0% +any questions +yes + + align:start position:0% + + + + align:start position:0% + +yeah yeah yeah yeah you just not include + + align:start position:0% +yeah yeah yeah yeah you just not include + + + align:start position:0% +yeah yeah yeah yeah you just not include +just yeah you will see explicitly just + + align:start position:0% +just yeah you will see explicitly just + + + align:start position:0% +just yeah you will see explicitly just +we just don't include the oh the all the + + align:start position:0% +we just don't include the oh the all the + + + align:start position:0% +we just don't include the oh the all the +external propagator + + align:start position:0% +external propagator + + + align:start position:0% +external propagator +okay yeah let me give you an example + + align:start position:0% +okay yeah let me give you an example + + + align:start position:0% +okay yeah let me give you an example +we'll be clear + + align:start position:0% +we'll be clear + + + align:start position:0% +we'll be clear +so so let me just give you examples so + + align:start position:0% +so so let me just give you examples so + + + align:start position:0% +so so let me just give you examples so +let's consider + + align:start position:0% +let's consider + + + align:start position:0% +let's consider +chief + + align:start position:0% +chief + + + align:start position:0% +chief +four particles scattering okay let's + + align:start position:0% +four particles scattering okay let's + + + align:start position:0% +four particles scattering okay let's +consider + + align:start position:0% + + + + align:start position:0% + +say imagine you have + + align:start position:0% +say imagine you have + + + align:start position:0% +say imagine you have +some + + align:start position:0% +some + + + align:start position:0% +some +yeah so so far in the convention here is + + align:start position:0% +yeah so so far in the convention here is + + + align:start position:0% +yeah so so far in the convention here is +the minus P1 P2 okay so you have minus + + align:start position:0% +the minus P1 P2 okay so you have minus + + + align:start position:0% +the minus P1 P2 okay so you have minus +P1 + + align:start position:0% + + + + align:start position:0% + +and the minus P2 + + align:start position:0% + + + + align:start position:0% + +and then you have P3 + + align:start position:0% +and then you have P3 + + + align:start position:0% +and then you have P3 +before okay + + align:start position:0% +before okay + + + align:start position:0% +before okay +so let's suppose we want to calculate a + + align:start position:0% +so let's suppose we want to calculate a + + + align:start position:0% +so let's suppose we want to calculate a +such kind of calcium amplitude two + + align:start position:0% +such kind of calcium amplitude two + + + align:start position:0% +such kind of calcium amplitude two +initial particles + + align:start position:0% +initial particles + + + align:start position:0% +initial particles +of this momentum minus P1 and minus P2 + + align:start position:0% +of this momentum minus P1 and minus P2 + + + align:start position:0% +of this momentum minus P1 and minus P2 +you see when you take these two with the + + align:start position:0% +you see when you take these two with the + + + align:start position:0% +you see when you take these two with the +active Roots then the minus P will + + align:start position:0% +active Roots then the minus P will + + + align:start position:0% +active Roots then the minus P will +actually have positive energy okay so + + align:start position:0% +actually have positive energy okay so + + + align:start position:0% +actually have positive energy okay so +the minus P will actually have a + + align:start position:0% +the minus P will actually have a + + + align:start position:0% +the minus P will actually have a +positive energy so all of them have + + align:start position:0% +positive energy so all of them have + + + align:start position:0% +positive energy so all of them have +positive energy okay + + align:start position:0% +positive energy okay + + + align:start position:0% +positive energy okay +all of them has positive energy + + align:start position:0% +all of them has positive energy + + + align:start position:0% +all of them has positive energy +okay so so if you want to calculate in + + align:start position:0% +okay so so if you want to calculate in + + + align:start position:0% +okay so so if you want to calculate in +this case + + align:start position:0% +this case + + + align:start position:0% +this case +and then you just take the G4 + + align:start position:0% + + + + align:start position:0% + +P1 P4 + + align:start position:0% +P1 P4 + + + align:start position:0% +P1 P4 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then you just take P1 + + align:start position:0% +and then you just take P1 + + + align:start position:0% +and then you just take P1 +and the P2 + + align:start position:0% +and the P2 + + + align:start position:0% +and the P2 +to take to be negative root + + align:start position:0% + + + + align:start position:0% + +yeah just to save the time say to take + + align:start position:0% +yeah just to save the time say to take + + + align:start position:0% +yeah just to save the time say to take +to the active Roots okay and then P3 + + align:start position:0% +to the active Roots okay and then P3 + + + align:start position:0% +to the active Roots okay and then P3 +P4 + + align:start position:0% +P4 + + + align:start position:0% +P4 +to be the positive Roots okay + + align:start position:0% +to be the positive Roots okay + + + align:start position:0% +to be the positive Roots okay +with a positive root and then you don't + + align:start position:0% +with a positive root and then you don't + + + align:start position:0% +with a positive root and then you don't +and there's a the name you put the C + + align:start position:0% +and there's a the name you put the C + + + align:start position:0% +and there's a the name you put the C +here then you truncate and they put the + + align:start position:0% +here then you truncate and they put the + + + align:start position:0% +here then you truncate and they put the +heat T here then you truncate your + + align:start position:0% +heat T here then you truncate your + + + align:start position:0% +heat T here then you truncate your +external or a propagate okay then you + + align:start position:0% +external or a propagate okay then you + + + align:start position:0% +external or a propagate okay then you +truncate your external propagate so so + + align:start position:0% +truncate your external propagate so so + + + align:start position:0% +truncate your external propagate so so +what this means + + align:start position:0% +what this means + + + align:start position:0% +what this means +so let's look at the leading all the + + align:start position:0% +so let's look at the leading all the + + + align:start position:0% +so let's look at the leading all the +contribution to this + + align:start position:0% + + + + align:start position:0% + +so the leading all the contribution to + + align:start position:0% +so the leading all the contribution to + + + align:start position:0% +so the leading all the contribution to +that we already have the diagram there + + align:start position:0% + + + + align:start position:0% + +so the leading order + + align:start position:0% +so the leading order + + + align:start position:0% +so the leading order +so that in the free Theory those process + + align:start position:0% +so that in the free Theory those process + + + align:start position:0% +so that in the free Theory those process +don't contribute okay because those + + align:start position:0% +don't contribute okay because those + + + align:start position:0% +don't contribute okay because those +things there's no interaction here + + align:start position:0% +things there's no interaction here + + + align:start position:0% +things there's no interaction here +particle just propagates okay so so the + + align:start position:0% +particle just propagates okay so so the + + + align:start position:0% +particle just propagates okay so so the +lowest diagram is this one + + align:start position:0% +lowest diagram is this one + + + align:start position:0% +lowest diagram is this one +okay the lowest diagram is this one so + + align:start position:0% +okay the lowest diagram is this one so + + + align:start position:0% +okay the lowest diagram is this one so +so we just can see the that diagram so + + align:start position:0% +so we just can see the that diagram so + + + align:start position:0% +so we just can see the that diagram so +that's just leading order just given by + + align:start position:0% +that's just leading order just given by + + + align:start position:0% +that's just leading order just given by +that diagram + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and then you have minus P1 + + align:start position:0% + + + + align:start position:0% + +minus P2 + + align:start position:0% +minus P2 + + + align:start position:0% +minus P2 +and the minus than P3 and P4 + + align:start position:0% +and the minus than P3 and P4 + + + align:start position:0% +and the minus than P3 and P4 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now according to + + align:start position:0% +so now according to + + + align:start position:0% +so now according to +I will find my rule + + align:start position:0% +I will find my rule + + + align:start position:0% +I will find my rule +this vertex just give you a fact of + + align:start position:0% +this vertex just give you a fact of + + + align:start position:0% +this vertex just give you a fact of +minus diameter + + align:start position:0% + + + + align:start position:0% + +so if we want to calculate this green + + align:start position:0% +so if we want to calculate this green + + + align:start position:0% +so if we want to calculate this green +function + + align:start position:0% +function + + + align:start position:0% +function +then we need to include all these four + + align:start position:0% +then we need to include all these four + + + align:start position:0% +then we need to include all these four +propagators + + align:start position:0% +propagators + + + align:start position:0% +propagators +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but here it tells us to truncate all the + + align:start position:0% +but here it tells us to truncate all the + + + align:start position:0% +but here it tells us to truncate all the +but all the propagators here are + + align:start position:0% +but all the propagators here are + + + align:start position:0% +but all the propagators here are +external + + align:start position:0% +external + + + align:start position:0% +external +so we don't include them + + align:start position:0% +so we don't include them + + + align:start position:0% +so we don't include them +so the answer here is simple just minus + + align:start position:0% +so the answer here is simple just minus + + + align:start position:0% +so the answer here is simple just minus +the Lambda + + align:start position:0% +the Lambda + + + align:start position:0% +the Lambda +okay and so so this so the leading order + + align:start position:0% +okay and so so this so the leading order + + + align:start position:0% +okay and so so this so the leading order +contribution to this four particle + + align:start position:0% +contribution to this four particle + + + align:start position:0% +contribution to this four particle +scattering just minus the Lambda + + align:start position:0% +scattering just minus the Lambda + + + align:start position:0% +scattering just minus the Lambda +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then you have all the Lambda + + align:start position:0% +and then you have all the Lambda + + + align:start position:0% +and then you have all the Lambda +contributions + + align:start position:0% +contributions + + + align:start position:0% +contributions +then the square contributions + + align:start position:0% +then the square contributions + + + align:start position:0% +then the square contributions +yes + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +yeah yeah I'm going to mention that good + + align:start position:0% +yeah yeah I'm going to mention that good + + + align:start position:0% +yeah yeah I'm going to mention that good +good I'm going to uh that's a good + + align:start position:0% +good I'm going to uh that's a good + + + align:start position:0% +good I'm going to uh that's a good +question yeah I'm going to mention that + + align:start position:0% +question yeah I'm going to mention that + + + align:start position:0% +question yeah I'm going to mention that +yeah so again that one does not + + align:start position:0% +yeah so again that one does not + + + align:start position:0% +yeah so again that one does not +correspond into the scattering I think + + align:start position:0% +correspond into the scattering I think + + + align:start position:0% +correspond into the scattering I think +it just corresponding to one particle + + align:start position:0% +it just corresponding to one particle + + + align:start position:0% +it just corresponding to one particle +propagated yeah + + align:start position:0% +propagated yeah + + + align:start position:0% +propagated yeah +because there's no no interaction + + align:start position:0% +because there's no no interaction + + + align:start position:0% +because there's no no interaction +between the particles + + align:start position:0% +between the particles + + + align:start position:0% +between the particles +the factorize + + align:start position:0% + + + + align:start position:0% + +so so this one involves uh two particles + + align:start position:0% +so so this one involves uh two particles + + + align:start position:0% +so so this one involves uh two particles +then uh there's an attacking you go to + + align:start position:0% +then uh there's an attacking you go to + + + align:start position:0% +then uh there's an attacking you go to +two other particles here you just one + + align:start position:0% +two other particles here you just one + + + align:start position:0% +two other particles here you just one +particle straight to go to the other + + align:start position:0% +particle straight to go to the other + + + align:start position:0% +particle straight to go to the other +particle so this particle by definition + + align:start position:0% +particle so this particle by definition + + + align:start position:0% +particle so this particle by definition +will be the same this one this had to be + + align:start position:0% +will be the same this one this had to be + + + align:start position:0% +will be the same this one this had to be +the same so there's no scattering + + align:start position:0% +the same so there's no scattering + + + align:start position:0% +the same so there's no scattering +yeah but but I will mention this point + + align:start position:0% +yeah but but I will mention this point + + + align:start position:0% +yeah but but I will mention this point +separately or a little bit later + + align:start position:0% +separately or a little bit later + + + align:start position:0% +separately or a little bit later +so so a lot of the possibility + + align:start position:0% + + + + align:start position:0% + +so if we want to consider the decay + + align:start position:0% + + + + align:start position:0% + +of a particle + + align:start position:0% + + + + align:start position:0% + +into three other particles + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the decay of a particle into three + + align:start position:0% +so the decay of a particle into three + + + align:start position:0% +so the decay of a particle into three +other particles + + align:start position:0% +other particles + + + align:start position:0% +other particles +so in this case then then again we take + + align:start position:0% +so in this case then then again we take + + + align:start position:0% +so in this case then then again we take +G4 + + align:start position:0% + + + + align:start position:0% + +so now we take minus P1 and then P2 P3 + + align:start position:0% +so now we take minus P1 and then P2 P3 + + + align:start position:0% +so now we take minus P1 and then P2 P3 +P4 + + align:start position:0% +P4 + + + align:start position:0% +P4 +and now we take P1 P4 now we take P1 + + align:start position:0% +and now we take P1 P4 now we take P1 + + + align:start position:0% +and now we take P1 P4 now we take P1 +goes to minus root + + align:start position:0% + + + + align:start position:0% + +P 1 0 is the minus Omega and then P3 + + align:start position:0% +P 1 0 is the minus Omega and then P3 + + + align:start position:0% +P 1 0 is the minus Omega and then P3 +2 3 4 take it to be the positive root + + align:start position:0% +2 3 4 take it to be the positive root + + + align:start position:0% +2 3 4 take it to be the positive root +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then that corresponding to this + + align:start position:0% +and then that corresponding to this + + + align:start position:0% +and then that corresponding to this +process okay and again the leading term + + align:start position:0% +process okay and again the leading term + + + align:start position:0% +process okay and again the leading term +the long travel term just this + + align:start position:0% + + + + align:start position:0% + +term is this so so now this is minus P1 + + align:start position:0% +term is this so so now this is minus P1 + + + align:start position:0% +term is this so so now this is minus P1 +so now this is P2 + + align:start position:0% +so now this is P2 + + + align:start position:0% +so now this is P2 +P3 + + align:start position:0% +P3 + + + align:start position:0% +P3 +P4 + + align:start position:0% +P4 + + + align:start position:0% +P4 +again the leading order this just minus + + align:start position:0% +again the leading order this just minus + + + align:start position:0% +again the leading order this just minus +and Lambda okay a big because you don't + + align:start position:0% +and Lambda okay a big because you don't + + + align:start position:0% +and Lambda okay a big because you don't +need to include external lags + + align:start position:0% +need to include external lags + + + align:start position:0% +need to include external lags +okay and and then yeah so this goes on + + align:start position:0% +okay and and then yeah so this goes on + + + align:start position:0% +okay and and then yeah so this goes on +to a single particle decaying to three + + align:start position:0% +to a single particle decaying to three + + + align:start position:0% +to a single particle decaying to three +other particles + + align:start position:0% +other particles + + + align:start position:0% +other particles +okay + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +or anything for + + align:start position:0% + + + + align:start position:0% + +no no yeah yeah yeah + + align:start position:0% + + + + align:start position:0% + +synonymy make some remarks + + align:start position:0% + + + + align:start position:0% + +why + + align:start position:0% +why + + + align:start position:0% +why +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% + + + + align:start position:0% + +oh yeah I erased this but yeah fine + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% + + + + align:start position:0% + +so the remarks + + align:start position:0% + + + + align:start position:0% + +so first + + align:start position:0% +so first + + + align:start position:0% +so first +we + + align:start position:0% +we + + + align:start position:0% +we +when we say yeah you already asked when + + align:start position:0% +when we say yeah you already asked when + + + align:start position:0% +when we say yeah you already asked when +we calculate this to the leading order + + align:start position:0% +we calculate this to the leading order + + + align:start position:0% +we calculate this to the leading order +we only included the connected diagrams + + align:start position:0% +we only included the connected diagrams + + + align:start position:0% +we only included the connected diagrams +okay + + align:start position:0% + + + + align:start position:0% + +so so these can actually diagrams in + + align:start position:0% +so so these can actually diagrams in + + + align:start position:0% +so so these can actually diagrams in +general + + align:start position:0% + + + + align:start position:0% + +factorize this means that the + + align:start position:0% +factorize this means that the + + + align:start position:0% +factorize this means that the +when you have disconnected diagram + + align:start position:0% +when you have disconnected diagram + + + align:start position:0% +when you have disconnected diagram +means that your your process factorize + + align:start position:0% +means that your your process factorize + + + align:start position:0% +means that your your process factorize +this + + align:start position:0% + + + + align:start position:0% + +into + + align:start position:0% +into + + + align:start position:0% +into +soft scattering process + + align:start position:0% + + + + align:start position:0% + +of law orders + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so yeah so um + + align:start position:0% +so so yeah so um + + + align:start position:0% +so so yeah so um +as we were doing here + + align:start position:0% +as we were doing here + + + align:start position:0% +as we were doing here +so there's one other diagram which goes + + align:start position:0% +so there's one other diagram which goes + + + align:start position:0% +so there's one other diagram which goes +one into + + align:start position:0% +one into + + + align:start position:0% +one into +just this one + + align:start position:0% + + + + align:start position:0% + +okay just corresponding to this you have + + align:start position:0% +okay just corresponding to this you have + + + align:start position:0% +okay just corresponding to this you have +P1 minus P1 say minus P2 + + align:start position:0% +P1 minus P1 say minus P2 + + + align:start position:0% +P1 minus P1 say minus P2 +P3 + + align:start position:0% +P3 + + + align:start position:0% +P3 +P4 okay + + align:start position:0% +P4 okay + + + align:start position:0% +P4 okay +so you can also have a a diagram like + + align:start position:0% +so you can also have a a diagram like + + + align:start position:0% +so you can also have a a diagram like +this + + align:start position:0% +this + + + align:start position:0% +this +but in this case just goes 1 into P1 + + align:start position:0% +but in this case just goes 1 into P1 + + + align:start position:0% +but in this case just goes 1 into P1 +separate they go to P3 and P2 separates + + align:start position:0% +separate they go to P3 and P2 separates + + + align:start position:0% +separate they go to P3 and P2 separates +go to P4 okay so so that's nothing + + align:start position:0% +go to P4 okay so so that's nothing + + + align:start position:0% +go to P4 okay so so that's nothing +really happens + + align:start position:0% +really happens + + + align:start position:0% +really happens +so so in general + + align:start position:0% +so so in general + + + align:start position:0% +so so in general +if you have an empirical scattering + + align:start position:0% +if you have an empirical scattering + + + align:start position:0% +if you have an empirical scattering +you have a particle scattering + + align:start position:0% +you have a particle scattering + + + align:start position:0% +you have a particle scattering +so with some number of + + align:start position:0% +so with some number of + + + align:start position:0% +so with some number of +initial particles and some uh uh uh some + + align:start position:0% +initial particles and some uh uh uh some + + + align:start position:0% +initial particles and some uh uh uh some +number of parallel particles when you + + align:start position:0% +number of parallel particles when you + + + align:start position:0% +number of parallel particles when you +have a + + align:start position:0% +have a + + + align:start position:0% +have a +when you have a disconnected diagram + + align:start position:0% +when you have a disconnected diagram + + + align:start position:0% +when you have a disconnected diagram +means that you have + + align:start position:0% +means that you have + + + align:start position:0% +means that you have +means you have a situation like this you + + align:start position:0% +means you have a situation like this you + + + align:start position:0% +means you have a situation like this you +have one diagram + + align:start position:0% +have one diagram + + + align:start position:0% +have one diagram +with some some subset of particles go to + + align:start position:0% +with some some subset of particles go to + + + align:start position:0% +with some some subset of particles go to +some subset of particles and with a lot + + align:start position:0% +some subset of particles and with a lot + + + align:start position:0% +some subset of particles and with a lot +of diagrams some side of the particles + + align:start position:0% +of diagrams some side of the particles + + + align:start position:0% +of diagrams some side of the particles +go some size of particles okay so this + + align:start position:0% +go some size of particles okay so this + + + align:start position:0% +go some size of particles okay so this +involves cat so this is a three to three + + align:start position:0% +involves cat so this is a three to three + + + align:start position:0% +involves cat so this is a three to three +scattering and then essentially this + + align:start position:0% +scattering and then essentially this + + + align:start position:0% +scattering and then essentially this +factorized into two to two scattering + + align:start position:0% +factorized into two to two scattering + + + align:start position:0% +factorized into two to two scattering +and then one particle just go to another + + align:start position:0% +and then one particle just go to another + + + align:start position:0% +and then one particle just go to another +particle okay and so this can already be + + align:start position:0% +particle okay and so this can already be + + + align:start position:0% +particle okay and so this can already be +understood in terms of low order process + + align:start position:0% +understood in terms of low order process + + + align:start position:0% +understood in terms of low order process +okay so so normally uh uh we don't yeah + + align:start position:0% +okay so so normally uh uh we don't yeah + + + align:start position:0% +okay so so normally uh uh we don't yeah +so so we don't include them uh uh uh + + align:start position:0% +so so we don't include them uh uh uh + + + align:start position:0% +so so we don't include them uh uh uh +yeah so so essentially they already + + align:start position:0% +yeah so so essentially they already + + + align:start position:0% +yeah so so essentially they already +understood okay they already understood + + align:start position:0% +understood okay they already understood + + + align:start position:0% +understood okay they already understood +so when we uh Define the scatter + + align:start position:0% +so when we uh Define the scatter + + + align:start position:0% +so when we uh Define the scatter +amplitude we don't include them okay + + align:start position:0% + + + + align:start position:0% + +okay so we are only interested + + align:start position:0% + + + + align:start position:0% + +in process + + align:start position:0% + + + + align:start position:0% + +involving + + align:start position:0% + + + + align:start position:0% + +all participate in particles + + align:start position:0% + + + + align:start position:0% + +so we are actually running out of time + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +so let me + + align:start position:0% +so let me + + + align:start position:0% +so let me +so this is first remark + + align:start position:0% + + + + align:start position:0% + +so second remark + + align:start position:0% + + + + align:start position:0% + +is that since we truncate all the + + align:start position:0% +is that since we truncate all the + + + align:start position:0% +is that since we truncate all the +external lags + + align:start position:0% +external lags + + + align:start position:0% +external lags +okay we translate all the external + + align:start position:0% +okay we translate all the external + + + align:start position:0% +okay we translate all the external +propagators + + align:start position:0% +propagators + + + align:start position:0% +propagators +so this kind of diagram + + align:start position:0% + + + + align:start position:0% + +you have a loop + + align:start position:0% +you have a loop + + + align:start position:0% +you have a loop +and one of the external propagators so + + align:start position:0% +and one of the external propagators so + + + align:start position:0% +and one of the external propagators so +this diagram don't contribute okay do + + align:start position:0% +this diagram don't contribute okay do + + + align:start position:0% +this diagram don't contribute okay do +not contribute + + align:start position:0% + + + + align:start position:0% + +because this wine + + align:start position:0% +because this wine + + + align:start position:0% +because this wine +after you have truncated the external + + align:start position:0% +after you have truncated the external + + + align:start position:0% +after you have truncated the external +legs it's no different from this one + + align:start position:0% +legs it's no different from this one + + + align:start position:0% +legs it's no different from this one +okay it's no different from that one and + + align:start position:0% +okay it's no different from that one and + + + align:start position:0% +okay it's no different from that one and +so so you don't have to count these ones + + align:start position:0% +so so you don't have to count these ones + + + align:start position:0% +so so you don't have to count these ones +uh separately okay so this one just + + align:start position:0% +uh separately okay so this one just + + + align:start position:0% +uh separately okay so this one just +corresponding to + + align:start position:0% +corresponding to + + + align:start position:0% +corresponding to +say uh when the particle propagate to + + align:start position:0% +say uh when the particle propagate to + + + align:start position:0% +say uh when the particle propagate to +Infinity somehow there's some other + + align:start position:0% +Infinity somehow there's some other + + + align:start position:0% +Infinity somehow there's some other +process to happen to this particular + + align:start position:0% +process to happen to this particular + + + align:start position:0% +process to happen to this particular +particle so we can create the external + + align:start position:0% +particle so we can create the external + + + align:start position:0% +particle so we can create the external +next as they don't include them + + align:start position:0% +next as they don't include them + + + align:start position:0% +next as they don't include them +okay I don't include them + + align:start position:0% +okay I don't include them + + + align:start position:0% +okay I don't include them +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so that means + + align:start position:0% +so so that means + + + align:start position:0% +so so that means +so with these two + + align:start position:0% +so with these two + + + align:start position:0% +so with these two +so means that the scattering amplitude + + align:start position:0% + + + + align:start position:0% + +okay so so can forget + + align:start position:0% + + + + align:start position:0% + +so essentially you can forget anything + + align:start position:0% + + + + align:start position:0% + +happening to the external ax okay + + align:start position:0% + + + + align:start position:0% + +you can have complicated things happen + + align:start position:0% +you can have complicated things happen + + + align:start position:0% +you can have complicated things happen +to external legs but they don't matter + + align:start position:0% +to external legs but they don't matter + + + align:start position:0% +to external legs but they don't matter +okay they don't matter + + align:start position:0% +okay they don't matter + + + align:start position:0% +okay they don't matter +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so to summarize + + align:start position:0% + + + + align:start position:0% + +the skeleton amplitude + + align:start position:0% + + + + align:start position:0% + +when you compute the square amplitude + + align:start position:0% +when you compute the square amplitude + + + align:start position:0% +when you compute the square amplitude +you just sum over + + align:start position:0% + + + + align:start position:0% + +following this definition you sum over + + align:start position:0% +following this definition you sum over + + + align:start position:0% +following this definition you sum over +all truncated + + align:start position:0% +all truncated + + + align:start position:0% +all truncated +means you truncate all the external lags + + align:start position:0% + + + + align:start position:0% + +connect it + + align:start position:0% + + + + align:start position:0% + +because we want all particles to + + align:start position:0% +because we want all particles to + + + align:start position:0% +because we want all particles to +participate + + align:start position:0% +participate + + + align:start position:0% +participate +and then the external particle on shell + + align:start position:0% + + + + align:start position:0% + +okay so so this is a simplification + + align:start position:0% +okay so so this is a simplification + + + align:start position:0% +okay so so this is a simplification +compared to calculate the general + + align:start position:0% +compared to calculate the general + + + align:start position:0% +compared to calculate the general +correlation functions + + align:start position:0% +correlation functions + + + align:start position:0% +correlation functions +so uh so I have two other remarks to + + align:start position:0% +so uh so I have two other remarks to + + + align:start position:0% +so uh so I have two other remarks to +make but we don't have time so one + + align:start position:0% +make but we don't have time so one + + + align:start position:0% +make but we don't have time so one +remark + + align:start position:0% +remark + + + align:start position:0% +remark +contains the choice of this sign + + align:start position:0% +contains the choice of this sign + + + align:start position:0% +contains the choice of this sign +why initial momentum corresponding to + + align:start position:0% +why initial momentum corresponding to + + + align:start position:0% +why initial momentum corresponding to +active root and and why this + + align:start position:0% +active root and and why this + + + align:start position:0% +active root and and why this +corresponding to positive root and a lot + + align:start position:0% +corresponding to positive root and a lot + + + align:start position:0% +corresponding to positive root and a lot +of remark related to this factor of Z + + align:start position:0% +of remark related to this factor of Z + + + align:start position:0% +of remark related to this factor of Z +when I raising this factor of Z and so + + align:start position:0% +when I raising this factor of Z and so + + + align:start position:0% +when I raising this factor of Z and so +uh we will talk about them at the + + align:start position:0% +uh we will talk about them at the + + + align:start position:0% +uh we will talk about them at the +beginning of next lecture + + align:start position:0% +beginning of next lecture + + + align:start position:0% +beginning of next lecture +and then after that then we are done + + align:start position:0% +and then after that then we are done + + + align:start position:0% +and then after that then we are done +okay then we are done with the general + + align:start position:0% +okay then we are done with the general + + + align:start position:0% +okay then we are done with the general +formulation of interacting Theory and + + align:start position:0% +formulation of interacting Theory and + + + align:start position:0% +formulation of interacting Theory and +now we will be equipped + + align:start position:0% +now we will be equipped + + + align:start position:0% +now we will be equipped +with the power + + align:start position:0% +with the power + + + align:start position:0% +with the power +essentially you can calculate any + + align:start position:0% +essentially you can calculate any + + + align:start position:0% +essentially you can calculate any +interacting Theory any amplitude a union + + align:start position:0% +interacting Theory any amplitude a union + + + align:start position:0% +interacting Theory any amplitude a union +perturbation Theory and uh and then but + + align:start position:0% +perturbation Theory and uh and then but + + + align:start position:0% +perturbation Theory and uh and then but +but in order to calculate anything + + align:start position:0% +but in order to calculate anything + + + align:start position:0% +but in order to calculate anything +useful we still have to first learn how + + align:start position:0% +useful we still have to first learn how + + + align:start position:0% +useful we still have to first learn how +to treat the fermions how to treat the + + align:start position:0% +to treat the fermions how to treat the + + + align:start position:0% +to treat the fermions how to treat the +photons + + align:start position:0% +photons + + + align:start position:0% +photons +and and that's what we'll do next so we + + align:start position:0% +and and that's what we'll do next so we + + + align:start position:0% +and and that's what we'll do next so we +will start in lecture a lesson actually + + align:start position:0% +will start in lecture a lesson actually + + + align:start position:0% +will start in lecture a lesson actually +will talk about how to how how to deal + + align:start position:0% +will talk about how to how how to deal + + + align:start position:0% +will talk about how to how how to deal +with fermions how to introduce ferments + + align:start position:0% +with fermions how to introduce ferments + + + align:start position:0% +with fermions how to introduce ferments +and after that we talk about how to + + align:start position:0% +and after that we talk about how to + + + align:start position:0% +and after that we talk about how to +introduce photons and then we can talk + + align:start position:0% +introduce photons and then we can talk + + + align:start position:0% +introduce photons and then we can talk +about QED how photons interact with + + align:start position:0% +about QED how photons interact with + + + align:start position:0% +about QED how photons interact with +selection succession + + align:start position:0% +selection succession + + + align:start position:0% +selection succession +okay good \ No newline at end of file diff --git a/mEI7ACWmx_8.txt b/mEI7ACWmx_8.txt new file mode 100644 index 0000000000000000000000000000000000000000..3f6da4654392b15e69bad85680be0c15c1229557 --- /dev/null +++ b/mEI7ACWmx_8.txt @@ -0,0 +1,2763 @@ +align:start position:0% + +welcome back to recitation in this video + + align:start position:0% +welcome back to recitation in this video + + + align:start position:0% +welcome back to recitation in this video +I'd like to see I'd like us to see how + + align:start position:0% +I'd like to see I'd like us to see how + + + align:start position:0% +I'd like to see I'd like us to see how +geometric methods can help us understand + + align:start position:0% +geometric methods can help us understand + + + align:start position:0% +geometric methods can help us understand +the flux of a vector field across a + + align:start position:0% +the flux of a vector field across a + + + align:start position:0% +the flux of a vector field across a +curve so in particular what we're going + + align:start position:0% +curve so in particular what we're going + + + align:start position:0% +curve so in particular what we're going +to do is try and use geometric methods + + align:start position:0% +to do is try and use geometric methods + + + align:start position:0% +to do is try and use geometric methods +to compute the flux of four different + + align:start position:0% +to compute the flux of four different + + + align:start position:0% +to compute the flux of four different +Vector Fields F across curve C so I've + + align:start position:0% +Vector Fields F across curve C so I've + + + align:start position:0% +Vector Fields F across curve C so I've +labeled them for later purposes I've + + align:start position:0% +labeled them for later purposes I've + + + align:start position:0% +labeled them for later purposes I've +labeled them fub1 F2 F3 and F four and + + align:start position:0% +labeled them fub1 F2 F3 and F four and + + + align:start position:0% +labeled them fub1 F2 F3 and F four and +they are as follows F sub one is the + + align:start position:0% +they are as follows F sub one is the + + + align:start position:0% +they are as follows F sub one is the +vector field that is a scalar function + + align:start position:0% +vector field that is a scalar function + + + align:start position:0% +vector field that is a scalar function +of only the radius times the vector X + + align:start position:0% +of only the radius times the vector X + + + align:start position:0% +of only the radius times the vector X +comma Y and the curve I'm interested in + + align:start position:0% +comma Y and the curve I'm interested in + + + align:start position:0% +comma Y and the curve I'm interested in +this part is the unit circle the second + + align:start position:0% +this part is the unit circle the second + + + align:start position:0% +this part is the unit circle the second +part the second one part B is the vector + + align:start position:0% +part the second one part B is the vector + + + align:start position:0% +part the second one part B is the vector +field that is g of R again where G is a + + align:start position:0% +field that is g of R again where G is a + + + align:start position:0% +field that is g of R again where G is a +scalar function and R is the radius so + + align:start position:0% +scalar function and R is the radius so + + + align:start position:0% +scalar function and R is the radius so +it depends only on the radius times the + + align:start position:0% +it depends only on the radius times the + + + align:start position:0% +it depends only on the radius times the +vector minus YX and again the C will be + + align:start position:0% +vector minus YX and again the C will be + + + align:start position:0% +vector minus YX and again the C will be +the unit circle the third and fourth + + align:start position:0% +the unit circle the third and fourth + + + align:start position:0% +the unit circle the third and fourth +ones will use a a different C but they + + align:start position:0% +ones will use a a different C but they + + + align:start position:0% +ones will use a a different C but they +will be the same there I'll point that + + align:start position:0% +will be the same there I'll point that + + + align:start position:0% +will be the same there I'll point that +out so the third one the vector field is + + align:start position:0% +out so the third one the vector field is + + + align:start position:0% +out so the third one the vector field is +3 times the vector 1 one and C in this + + align:start position:0% +3 times the vector 1 one and C in this + + + align:start position:0% +3 times the vector 1 one and C in this +case will be the segment connecting 0 0 + + align:start position:0% +case will be the segment connecting 0 0 + + + align:start position:0% +case will be the segment connecting 0 0 +to 1 one so it's a a piece of the line + + align:start position:0% +to 1 one so it's a a piece of the line + + + align:start position:0% +to 1 one so it's a a piece of the line +yal X and then in part d f will be 3 * + + align:start position:0% +yal X and then in part d f will be 3 * + + + align:start position:0% +yal X and then in part d f will be 3 * +the vector minus 1 one and C is again + + align:start position:0% +the vector minus 1 one and C is again + + + align:start position:0% +the vector minus 1 one and C is again +the segment from 0 0 to 1 one so again + + align:start position:0% +the segment from 0 0 to 1 one so again + + + align:start position:0% +the segment from 0 0 to 1 one so again +what I'd like you to do is rather than + + align:start position:0% +what I'd like you to do is rather than + + + align:start position:0% +what I'd like you to do is rather than +trying to parameterize the curve and do + + align:start position:0% +trying to parameterize the curve and do + + + align:start position:0% +trying to parameterize the curve and do +the entire calculation I'd like to see + + align:start position:0% +the entire calculation I'd like to see + + + align:start position:0% +the entire calculation I'd like to see +you try and understand the relationship + + align:start position:0% +you try and understand the relationship + + + align:start position:0% +you try and understand the relationship +between each of these Vector Fields F + + align:start position:0% +between each of these Vector Fields F + + + align:start position:0% +between each of these Vector Fields F +and the normal to the to the curve that + + align:start position:0% +and the normal to the to the curve that + + + align:start position:0% +and the normal to the to the curve that +they're on and see if you can figure out + + align:start position:0% +they're on and see if you can figure out + + + align:start position:0% +they're on and see if you can figure out +the flux based on that relationship so + + align:start position:0% +the flux based on that relationship so + + + align:start position:0% +the flux based on that relationship so +why don't you pause the video give that + + align:start position:0% +why don't you pause the video give that + + + align:start position:0% +why don't you pause the video give that +a shot and then when you're ready to see + + align:start position:0% +a shot and then when you're ready to see + + + align:start position:0% +a shot and then when you're ready to see +how I did it you can bring the video + + align:start position:0% +how I did it you can bring the video + + + align:start position:0% +how I did it you can bring the video +back up + + align:start position:0% + + + + align:start position:0% + +okay welcome back so I again I'm going + + align:start position:0% +okay welcome back so I again I'm going + + + align:start position:0% +okay welcome back so I again I'm going +to try and use my geometric intuition to + + align:start position:0% +to try and use my geometric intuition to + + + align:start position:0% +to try and use my geometric intuition to +understand what the flux is for each of + + align:start position:0% +understand what the flux is for each of + + + align:start position:0% +understand what the flux is for each of +these four Vector Fields along these + + align:start position:0% +these four Vector Fields along these + + + align:start position:0% +these four Vector Fields along these +four curves so what I'd like to do is is + + align:start position:0% +four curves so what I'd like to do is is + + + align:start position:0% +four curves so what I'd like to do is is +if I'm going to try and understand + + align:start position:0% +if I'm going to try and understand + + + align:start position:0% +if I'm going to try and understand +geometrically what's happening it's + + align:start position:0% +geometrically what's happening it's + + + align:start position:0% +geometrically what's happening it's +always good to draw a picture so I'm + + align:start position:0% +always good to draw a picture so I'm + + + align:start position:0% +always good to draw a picture so I'm +going to draw a picture that I'll use + + align:start position:0% +going to draw a picture that I'll use + + + align:start position:0% +going to draw a picture that I'll use +for a and b and then I'll draw another + + align:start position:0% +for a and b and then I'll draw another + + + align:start position:0% +for a and b and then I'll draw another +picture later that I'll use for C and D + + align:start position:0% +picture later that I'll use for C and D + + + align:start position:0% +picture later that I'll use for C and D +so notice again a my curve is a unit + + align:start position:0% +so notice again a my curve is a unit + + + align:start position:0% +so notice again a my curve is a unit +circle and I have somewhat explicit + + align:start position:0% +circle and I have somewhat explicit + + + align:start position:0% +circle and I have somewhat explicit +understanding of what the vector fields + + align:start position:0% +understanding of what the vector fields + + + align:start position:0% +understanding of what the vector fields +are so I'm going to draw the unit circle + + align:start position:0% +are so I'm going to draw the unit circle + + + align:start position:0% +are so I'm going to draw the unit circle +and see if I can figure out where F1 and + + align:start position:0% +and see if I can figure out where F1 and + + + align:start position:0% +and see if I can figure out where F1 and +F2 are so let + + align:start position:0% + + + + align:start position:0% + +me it's not a perfect unit circle but it + + align:start position:0% +me it's not a perfect unit circle but it + + + align:start position:0% +me it's not a perfect unit circle but it +looks sort of like the unit circle so + + align:start position:0% +looks sort of like the unit circle so + + + align:start position:0% +looks sort of like the unit circle so +this is going to be my unit circle and + + align:start position:0% +this is going to be my unit circle and + + + align:start position:0% +this is going to be my unit circle and +what I want to point out first is I was + + align:start position:0% +what I want to point out first is I was + + + align:start position:0% +what I want to point out first is I was +not trying to trick you but just to help + + align:start position:0% +not trying to trick you but just to help + + + align:start position:0% +not trying to trick you but just to help +you notice that in a and b they both + + align:start position:0% +you notice that in a and b they both + + + align:start position:0% +you notice that in a and b they both +depended on this radial function but the + + align:start position:0% +depended on this radial function but the + + + align:start position:0% +depended on this radial function but the +radi Rus on the unit circle is fixed at + + align:start position:0% +radi Rus on the unit circle is fixed at + + + align:start position:0% +radi Rus on the unit circle is fixed at +one so both of these Vector Fields it + + align:start position:0% +one so both of these Vector Fields it + + + align:start position:0% +one so both of these Vector Fields it +will simply be G of 1 so that will be a + + align:start position:0% +will simply be G of 1 so that will be a + + + align:start position:0% +will simply be G of 1 so that will be a +constant value so all that's giving me + + align:start position:0% +constant value so all that's giving me + + + align:start position:0% +constant value so all that's giving me +is some scalar multiple of whatever the + + align:start position:0% +is some scalar multiple of whatever the + + + align:start position:0% +is some scalar multiple of whatever the +length of this one is so it's this + + align:start position:0% +length of this one is so it's this + + + align:start position:0% +length of this one is so it's this +direction times this scal or G of one + + align:start position:0% +direction times this scal or G of one + + + align:start position:0% +direction times this scal or G of one +one other thing I want to point out is + + align:start position:0% +one other thing I want to point out is + + + align:start position:0% +one other thing I want to point out is +that both of these vectors F1 and F2 if + + align:start position:0% +that both of these vectors F1 and F2 if + + + align:start position:0% +that both of these vectors F1 and F2 if +I look if I ignore the G part and I look + + align:start position:0% +I look if I ignore the G part and I look + + + align:start position:0% +I look if I ignore the G part and I look +at just the X comma Y and the minus y + + align:start position:0% +at just the X comma Y and the minus y + + + align:start position:0% +at just the X comma Y and the minus y +comma X is these Parts have unit length + + align:start position:0% +comma X is these Parts have unit length + + + align:start position:0% +comma X is these Parts have unit length +and you should be able to see that right + + align:start position:0% +and you should be able to see that right + + + align:start position:0% +and you should be able to see that right +away because X and Y are on the unit + + align:start position:0% +away because X and Y are on the unit + + + align:start position:0% +away because X and Y are on the unit +circle and so the the length of the + + align:start position:0% +circle and so the the length of the + + + align:start position:0% +circle and so the the length of the +vector that's that's tail is at the + + align:start position:0% +vector that's that's tail is at the + + + align:start position:0% +vector that's that's tail is at the +origin and head is on the edge of the + + align:start position:0% +origin and head is on the edge of the + + + align:start position:0% +origin and head is on the edge of the +unit circle has length one and then you + + align:start position:0% +unit circle has length one and then you + + + align:start position:0% +unit circle has length one and then you +can easily see that this vector and this + + align:start position:0% +can easily see that this vector and this + + + align:start position:0% +can easily see that this vector and this +Vector have the same length because + + align:start position:0% +Vector have the same length because + + + align:start position:0% +Vector have the same length because +their individual components are the same + + align:start position:0% +their individual components are the same + + + align:start position:0% +their individual components are the same +absolute value so we should see we + + align:start position:0% +absolute value so we should see we + + + align:start position:0% +absolute value so we should see we +already understand a few things about F1 + + align:start position:0% +already understand a few things about F1 + + + align:start position:0% +already understand a few things about F1 +and F2 right away that all the length is + + align:start position:0% +and F2 right away that all the length is + + + align:start position:0% +and F2 right away that all the length is +coming from this G and G is fixed all + + align:start position:0% +coming from this G and G is fixed all + + + align:start position:0% +coming from this G and G is fixed all +the way around the unit circle at G of 1 + + align:start position:0% +the way around the unit circle at G of 1 + + + align:start position:0% +the way around the unit circle at G of 1 +now let's figure out uh what the flux is + + align:start position:0% +now let's figure out uh what the flux is + + + align:start position:0% +now let's figure out uh what the flux is +for these two things so if you notice + + align:start position:0% +for these two things so if you notice + + + align:start position:0% +for these two things so if you notice +first okay F sub one it's the vector XY + + align:start position:0% +first okay F sub one it's the vector XY + + + align:start position:0% +first okay F sub one it's the vector XY +times the scalar G of 1 so if I come + + align:start position:0% +times the scalar G of 1 so if I come + + + align:start position:0% +times the scalar G of 1 so if I come +over here I want to point out I'll do + + align:start position:0% +over here I want to point out I'll do + + + align:start position:0% +over here I want to point out I'll do +this part in white first that if I'm at + + align:start position:0% +this part in white first that if I'm at + + + align:start position:0% +this part in white first that if I'm at +this point this is this is the point XY + + align:start position:0% +this point this is this is the point XY + + + align:start position:0% +this point this is this is the point XY +so the vector there is actually going to + + align:start position:0% +so the vector there is actually going to + + + align:start position:0% +so the vector there is actually going to +be equal to the the vector XY is equal + + align:start position:0% +be equal to the the vector XY is equal + + + align:start position:0% +be equal to the the vector XY is equal +to this Vector so if I think about + + align:start position:0% +to this Vector so if I think about + + + align:start position:0% +to this Vector so if I think about +putting that that at this point I'm + + align:start position:0% +putting that that at this point I'm + + + align:start position:0% +putting that that at this point I'm +going to draw it here I get something + + align:start position:0% +going to draw it here I get something + + + align:start position:0% +going to draw it here I get something +that looks like this so this is f sub + + align:start position:0% +that looks like this so this is f sub + + + align:start position:0% +that looks like this so this is f sub +one probably I'm going to have to make + + align:start position:0% +one probably I'm going to have to make + + + align:start position:0% +one probably I'm going to have to make +one comment about that but notice this + + align:start position:0% +one comment about that but notice this + + + align:start position:0% +one comment about that but notice this +should look like it's All in One + + align:start position:0% +should look like it's All in One + + + align:start position:0% +should look like it's All in One +Direction so this is XY the vector XY if + + align:start position:0% +Direction so this is XY the vector XY if + + + align:start position:0% +Direction so this is XY the vector XY if +I slide it so its tail is here it's + + align:start position:0% +I slide it so its tail is here it's + + + align:start position:0% +I slide it so its tail is here it's +again in the same direction and now I've + + align:start position:0% +again in the same direction and now I've + + + align:start position:0% +again in the same direction and now I've +just scaled it by G of one now this is + + align:start position:0% +just scaled it by G of one now this is + + + align:start position:0% +just scaled it by G of one now this is +assuming obviously that g of one is + + align:start position:0% +assuming obviously that g of one is + + + align:start position:0% +assuming obviously that g of one is +positive so we're going to assume that + + align:start position:0% +positive so we're going to assume that + + + align:start position:0% +positive so we're going to assume that +throughout this problem I'll mention + + align:start position:0% +throughout this problem I'll mention + + + align:start position:0% +throughout this problem I'll mention +what happens when G is negative at the + + align:start position:0% +what happens when G is negative at the + + + align:start position:0% +what happens when G is negative at the +end so if this is my Vector F sub one + + align:start position:0% +end so if this is my Vector F sub one + + + align:start position:0% +end so if this is my Vector F sub one +let's think about what is the normal to + + align:start position:0% +let's think about what is the normal to + + + align:start position:0% +let's think about what is the normal to +this curve the normal to this curve + + align:start position:0% +this curve the normal to this curve + + + align:start position:0% +this curve the normal to this curve +actually at each point on the circle + + align:start position:0% +actually at each point on the circle + + + align:start position:0% +actually at each point on the circle +points in exactly the same direction as + + align:start position:0% +points in exactly the same direction as + + + align:start position:0% +points in exactly the same direction as +F sub one because if I'm parameterizing + + align:start position:0% +F sub one because if I'm parameterizing + + + align:start position:0% +F sub one because if I'm parameterizing +in this direction the normal I'll draw + + align:start position:0% +in this direction the normal I'll draw + + + align:start position:0% +in this direction the normal I'll draw +one down here so we can see what it + + align:start position:0% +one down here so we can see what it + + + align:start position:0% +one down here so we can see what it +looks like the normal actually let me + + align:start position:0% +looks like the normal actually let me + + + align:start position:0% +looks like the normal actually let me +come from there the normal is going to + + align:start position:0% +come from there the normal is going to + + + align:start position:0% +come from there the normal is going to +look something like this okay so it + + align:start position:0% +look something like this okay so it + + + align:start position:0% +look something like this okay so it +would be connecting from the origin to + + align:start position:0% +would be connecting from the origin to + + + align:start position:0% +would be connecting from the origin to +that point on the circle and keep going + + align:start position:0% +that point on the circle and keep going + + + align:start position:0% +that point on the circle and keep going +out in that direction that's the normal + + align:start position:0% +out in that direction that's the normal + + + align:start position:0% +out in that direction that's the normal +Direction so F sub one if G is a + + align:start position:0% +Direction so F sub one if G is a + + + align:start position:0% +Direction so F sub one if G is a +positive function points in exactly the + + align:start position:0% +positive function points in exactly the + + + align:start position:0% +positive function points in exactly the +same direction is the normal if G is a + + align:start position:0% +same direction is the normal if G is a + + + align:start position:0% +same direction is the normal if G is a +negative function it points in exactly + + align:start position:0% +negative function it points in exactly + + + align:start position:0% +negative function it points in exactly +the opposite direction so F1 would be + + align:start position:0% +the opposite direction so F1 would be + + + align:start position:0% +the opposite direction so F1 would be +flipped exactly around if G was a + + align:start position:0% +flipped exactly around if G was a + + + align:start position:0% +flipped exactly around if G was a +negative function so if I want to + + align:start position:0% +negative function so if I want to + + + align:start position:0% +negative function so if I want to +compute the flux for part A actually + + align:start position:0% +compute the flux for part A actually + + + align:start position:0% +compute the flux for part A actually +I'll do it down here if I want to + + align:start position:0% +I'll do it down here if I want to + + + align:start position:0% +I'll do it down here if I want to +compute the flux remember I'm taking the + + align:start position:0% +compute the flux remember I'm taking the + + + align:start position:0% +compute the flux remember I'm taking the +integral along the curve of f dotted + + align:start position:0% +integral along the curve of f dotted + + + align:start position:0% +integral along the curve of f dotted +with n DS well F dotted with n is Con + + align:start position:0% +with n DS well F dotted with n is Con + + + align:start position:0% +with n DS well F dotted with n is Con +and that's the main point that's going + + align:start position:0% +and that's the main point that's going + + + align:start position:0% +and that's the main point that's going +to make this easier F dotted with n at + + align:start position:0% +to make this easier F dotted with n at + + + align:start position:0% +to make this easier F dotted with n at +each point F I guess I should say sorry + + align:start position:0% +each point F I guess I should say sorry + + + align:start position:0% +each point F I guess I should say sorry +F1 F1 dotted with n is always equal to + + align:start position:0% +F1 F1 dotted with n is always equal to + + + align:start position:0% +F1 F1 dotted with n is always equal to +the length of f 1 * the length of n time + + align:start position:0% +the length of f 1 * the length of n time + + + align:start position:0% +the length of f 1 * the length of n time +cosine of the angle between them and + + align:start position:0% +cosine of the angle between them and + + + align:start position:0% +cosine of the angle between them and +that winds up being with a very quick + + align:start position:0% +that winds up being with a very quick + + + align:start position:0% +that winds up being with a very quick +calculation you can see that that winds + + align:start position:0% +calculation you can see that that winds + + + align:start position:0% +calculation you can see that that winds +up being G of one so this the only + + align:start position:0% +up being G of one so this the only + + + align:start position:0% +up being G of one so this the only +reason I don't have to worry about + + align:start position:0% +reason I don't have to worry about + + + align:start position:0% +reason I don't have to worry about +absolute value is if G is positive I'm + + align:start position:0% +absolute value is if G is positive I'm + + + align:start position:0% +absolute value is if G is positive I'm +pointing in the same direction if G is + + align:start position:0% +pointing in the same direction if G is + + + align:start position:0% +pointing in the same direction if G is +negative I'm pointing in opposite + + align:start position:0% +negative I'm pointing in opposite + + + align:start position:0% +negative I'm pointing in opposite +direction and so the Theta cosine Theta + + align:start position:0% +direction and so the Theta cosine Theta + + + align:start position:0% +direction and so the Theta cosine Theta +is minus one instead of plus one so + + align:start position:0% +is minus one instead of plus one so + + + align:start position:0% +is minus one instead of plus one so +that's you might want to check that for + + align:start position:0% +that's you might want to check that for + + + align:start position:0% +that's you might want to check that for +yourself but this is just G of one so + + align:start position:0% +yourself but this is just G of one so + + + align:start position:0% +yourself but this is just G of one so +that's a constant so this is actually + + align:start position:0% +that's a constant so this is actually + + + align:start position:0% +that's a constant so this is actually +equal to G of 1 * the integral over C DS + + align:start position:0% +equal to G of 1 * the integral over C DS + + + align:start position:0% +equal to G of 1 * the integral over C DS +now what is this if I integrate this I + + align:start position:0% +now what is this if I integrate this I + + + align:start position:0% +now what is this if I integrate this I +should pick up exactly the length of the + + align:start position:0% +should pick up exactly the length of the + + + align:start position:0% +should pick up exactly the length of the +curve okay because this is the + + align:start position:0% +curve okay because this is the + + + align:start position:0% +curve okay because this is the +derivative of Arc Length so when I + + align:start position:0% +derivative of Arc Length so when I + + + align:start position:0% +derivative of Arc Length so when I +integrate this I get Arc Length but it's + + align:start position:0% +integrate this I get Arc Length but it's + + + align:start position:0% +integrate this I get Arc Length but it's +a unit circle so the arc length is just + + align:start position:0% +a unit circle so the arc length is just + + + align:start position:0% +a unit circle so the arc length is just +the circumference of the unit circle so + + align:start position:0% +the circumference of the unit circle so + + + align:start position:0% +the circumference of the unit circle so +that's 2 pi * G1 + + align:start position:0% +that's 2 pi * G1 + + + align:start position:0% +that's 2 pi * G1 +G of one + + align:start position:0% +G of one + + + align:start position:0% +G of one +sorry okay that's all you get that's it + + align:start position:0% +sorry okay that's all you get that's it + + + align:start position:0% +sorry okay that's all you get that's it +so we didn't actually have to + + align:start position:0% +so we didn't actually have to + + + align:start position:0% +so we didn't actually have to +parameterize anything we just had to + + align:start position:0% +parameterize anything we just had to + + + align:start position:0% +parameterize anything we just had to +understand F1 relating to the normal so + + align:start position:0% +understand F1 relating to the normal so + + + align:start position:0% +understand F1 relating to the normal so +I didn't draw the normal here but if I + + align:start position:0% +I didn't draw the normal here but if I + + + align:start position:0% +I didn't draw the normal here but if I +take this normal and I spin around to + + align:start position:0% +take this normal and I spin around to + + + align:start position:0% +take this normal and I spin around to +here the normal is in the same direction + + align:start position:0% +here the normal is in the same direction + + + align:start position:0% +here the normal is in the same direction +as F sub one so now let's look at F + + align:start position:0% +as F sub one so now let's look at F + + + align:start position:0% +as F sub one so now let's look at F +sub2 and let's do this first by pointing + + align:start position:0% +sub2 and let's do this first by pointing + + + align:start position:0% +sub2 and let's do this first by pointing +something out about the relationship + + align:start position:0% +something out about the relationship + + + align:start position:0% +something out about the relationship +between F sub2 and F + + align:start position:0% +between F sub2 and F + + + align:start position:0% +between F sub2 and F +sub1 notice that if I take F sub one and + + align:start position:0% +sub1 notice that if I take F sub one and + + + align:start position:0% +sub1 notice that if I take F sub one and +I dot it with f sub2 i get zero right + + align:start position:0% +I dot it with f sub2 i get zero right + + + align:start position:0% +I dot it with f sub2 i get zero right +because ignoring even the scalar part I + + align:start position:0% +because ignoring even the scalar part I + + + align:start position:0% +because ignoring even the scalar part I +get x * - + + align:start position:0% +get x * - + + + align:start position:0% +get x * - +y plus y * X which gives me zero and the + + align:start position:0% +y plus y * X which gives me zero and the + + + align:start position:0% +y plus y * X which gives me zero and the +scalars come along for the right I still + + align:start position:0% +scalars come along for the right I still + + + align:start position:0% +scalars come along for the right I still +get zero so F sub1 and F sub2 are + + align:start position:0% +get zero so F sub1 and F sub2 are + + + align:start position:0% +get zero so F sub1 and F sub2 are +orthogonal and in fact if I come over + + align:start position:0% +orthogonal and in fact if I come over + + + align:start position:0% +orthogonal and in fact if I come over +and draw the picture you can do this for + + align:start position:0% +and draw the picture you can do this for + + + align:start position:0% +and draw the picture you can do this for +yourself but if I come over and draw the + + align:start position:0% +yourself but if I come over and draw the + + + align:start position:0% +yourself but if I come over and draw the +picture f sub2 is going to be F sub one + + align:start position:0% +picture f sub2 is going to be F sub one + + + align:start position:0% +picture f sub2 is going to be F sub one +rotated by + + align:start position:0% + + + + align:start position:0% + +90° something like this this is my f + + align:start position:0% +90° something like this this is my f + + + align:start position:0% +90° something like this this is my f +sub2 again if F sub one if if G of one + + align:start position:0% +sub2 again if F sub one if if G of one + + + align:start position:0% +sub2 again if F sub one if if G of one +was negative f sub one would be this + + align:start position:0% +was negative f sub one would be this + + + align:start position:0% +was negative f sub one would be this +direction and F sub2 would then be + + align:start position:0% +direction and F sub2 would then be + + + align:start position:0% +direction and F sub2 would then be +around here but ultimately it's not + + align:start position:0% +around here but ultimately it's not + + + align:start position:0% +around here but ultimately it's not +going to matter in this case whether G + + align:start position:0% +going to matter in this case whether G + + + align:start position:0% +going to matter in this case whether G +is positive or negative because notice + + align:start position:0% +is positive or negative because notice + + + align:start position:0% +is positive or negative because notice +what happens if I want to integrate F + + align:start position:0% +what happens if I want to integrate F + + + align:start position:0% +what happens if I want to integrate F +sub 2 dotted with the normal notice the + + align:start position:0% +sub 2 dotted with the normal notice the + + + align:start position:0% +sub 2 dotted with the normal notice the +normal is in the same direction as F sub + + align:start position:0% +normal is in the same direction as F sub + + + align:start position:0% +normal is in the same direction as F sub +one so F sub2 dotted with the normal is + + align:start position:0% +one so F sub2 dotted with the normal is + + + align:start position:0% +one so F sub2 dotted with the normal is +zero so if I'm going to integrate the + + align:start position:0% +zero so if I'm going to integrate the + + + align:start position:0% +zero so if I'm going to integrate the +function zero All Along The Curve I + + align:start position:0% +function zero All Along The Curve I + + + align:start position:0% +function zero All Along The Curve I +shouldn't be surprised that my answer to + + align:start position:0% +shouldn't be surprised that my answer to + + + align:start position:0% +shouldn't be surprised that my answer to +Part B is + + align:start position:0% +Part B is + + + align:start position:0% +Part B is +zero so there was even less work in Part + + align:start position:0% +zero so there was even less work in Part + + + align:start position:0% +zero so there was even less work in Part +B because I immediately had that F sub + + align:start position:0% +B because I immediately had that F sub + + + align:start position:0% +B because I immediately had that F sub +two is really in the direction of the + + align:start position:0% +two is really in the direction of the + + + align:start position:0% +two is really in the direction of the +tangent to the curve and so I have + + align:start position:0% +tangent to the curve and so I have + + + align:start position:0% +tangent to the curve and so I have +something in the direction of the + + align:start position:0% +something in the direction of the + + + align:start position:0% +something in the direction of the +tangent dotted with with the something + + align:start position:0% +tangent dotted with with the something + + + align:start position:0% +tangent dotted with with the something +in the direction of the normal in fact + + align:start position:0% +in the direction of the normal in fact + + + align:start position:0% +in the direction of the normal in fact +the normal so I get zero all right so + + align:start position:0% +the normal so I get zero all right so + + + align:start position:0% +the normal so I get zero all right so +now I'm going to draw a picture for c + + align:start position:0% +now I'm going to draw a picture for c + + + align:start position:0% +now I'm going to draw a picture for c +and d and then we're going to use that + + align:start position:0% + + + + align:start position:0% + +one and I got to make sure I come on + + align:start position:0% +one and I got to make sure I come on + + + align:start position:0% +one and I got to make sure I come on +this side sorry about that so here's 0 + + align:start position:0% + + + + align:start position:0% + +0 and here's 1 + + align:start position:0% +0 and here's 1 + + + align:start position:0% +0 and here's 1 +one oh actually you know what I'm going + + align:start position:0% +one oh actually you know what I'm going + + + align:start position:0% +one oh actually you know what I'm going +to make it a little longer I might need + + align:start position:0% +to make it a little longer I might need + + + align:start position:0% +to make it a little longer I might need +more room so one one I'll make a little + + align:start position:0% +more room so one one I'll make a little + + + align:start position:0% +more room so one one I'll make a little +further up there's one one okay 0 0 and + + align:start position:0% +further up there's one one okay 0 0 and + + + align:start position:0% +further up there's one one okay 0 0 and +one one and that's my curve there's one + + align:start position:0% +one one and that's my curve there's one + + + align:start position:0% +one one and that's my curve there's one +one okay now if I parameterize it in + + align:start position:0% +one okay now if I parameterize it in + + + align:start position:0% +one okay now if I parameterize it in +this direction then I can draw my normal + + align:start position:0% +this direction then I can draw my normal + + + align:start position:0% +this direction then I can draw my normal +my normal because it's a because it's a + + align:start position:0% +my normal because it's a because it's a + + + align:start position:0% +my normal because it's a because it's a +line segment my normal is constant in + + align:start position:0% +line segment my normal is constant in + + + align:start position:0% +line segment my normal is constant in +its length and Direction so at any given + + align:start position:0% +its length and Direction so at any given + + + align:start position:0% +its length and Direction so at any given +point it's exactly equal to this this + + align:start position:0% +point it's exactly equal to this this + + + align:start position:0% +point it's exactly equal to this this +function up to the right scaling or this + + align:start position:0% +function up to the right scaling or this + + + align:start position:0% +function up to the right scaling or this +sorry this Vector up to the right + + align:start position:0% +sorry this Vector up to the right + + + align:start position:0% +sorry this Vector up to the right +scaling and it should be something like + + align:start position:0% +scaling and it should be something like + + + align:start position:0% +scaling and it should be something like +uh 1 minus + + align:start position:0% +uh 1 minus + + + align:start position:0% +uh 1 minus +one / < tk2 that's my normal if you want + + align:start position:0% +one / < tk2 that's my normal if you want + + + align:start position:0% +one / < tk2 that's my normal if you want +it precisely that's what it is you don't + + align:start position:0% +it precisely that's what it is you don't + + + align:start position:0% +it precisely that's what it is you don't +actually need it to solve this problem + + align:start position:0% +actually need it to solve this problem + + + align:start position:0% +actually need it to solve this problem +though but that's what it is if you want + + align:start position:0% +though but that's what it is if you want + + + align:start position:0% +though but that's what it is if you want +it precisely now let's look at what f is + + align:start position:0% +it precisely now let's look at what f is + + + align:start position:0% +it precisely now let's look at what f is +F3 is and then we'll look at what F4 + + align:start position:0% +F3 is and then we'll look at what F4 + + + align:start position:0% +F3 is and then we'll look at what F4 +actually is so let's look at f + + align:start position:0% +actually is so let's look at f + + + align:start position:0% +actually is so let's look at f +sub3 f sub3 was the vector 3 * one one + + align:start position:0% +sub3 f sub3 was the vector 3 * one one + + + align:start position:0% +sub3 f sub3 was the vector 3 * one one +so if we come back to our picture at any + + align:start position:0% +so if we come back to our picture at any + + + align:start position:0% +so if we come back to our picture at any +point on this curve if I go in the one + + align:start position:0% +point on this curve if I go in the one + + + align:start position:0% +point on this curve if I go in the one +One Direction I stay parallel to this + + align:start position:0% +One Direction I stay parallel to this + + + align:start position:0% +One Direction I stay parallel to this +curve which means that F sub3 I don't + + align:start position:0% +curve which means that F sub3 I don't + + + align:start position:0% +curve which means that F sub3 I don't +want to draw the whole thing because it' + + align:start position:0% +want to draw the whole thing because it' + + + align:start position:0% +want to draw the whole thing because it' +take up the entire curve it's longer + + align:start position:0% +take up the entire curve it's longer + + + align:start position:0% +take up the entire curve it's longer +than the than the curve itself but F + + align:start position:0% +than the than the curve itself but F + + + align:start position:0% +than the than the curve itself but F +sub3 at any given point points in this + + align:start position:0% +sub3 at any given point points in this + + + align:start position:0% +sub3 at any given point points in this +direction so this is this is f + + align:start position:0% +direction so this is this is f + + + align:start position:0% +direction so this is this is f +sub3 but not as long as it actually is + + align:start position:0% +sub3 but not as long as it actually is + + + align:start position:0% +sub3 but not as long as it actually is +but only the direction is going to + + align:start position:0% +but only the direction is going to + + + align:start position:0% +but only the direction is going to +matter in this case so f sub3 is + + align:start position:0% +matter in this case so f sub3 is + + + align:start position:0% +matter in this case so f sub3 is +pointing in this direction so if I want + + align:start position:0% +pointing in this direction so if I want + + + align:start position:0% +pointing in this direction so if I want +to compute the flux I dot it with the + + align:start position:0% +to compute the flux I dot it with the + + + align:start position:0% +to compute the flux I dot it with the +normal but look at what happens the + + align:start position:0% +normal but look at what happens the + + + align:start position:0% +normal but look at what happens the +normal is orthogonal to F sub3 at every + + align:start position:0% +normal is orthogonal to F sub3 at every + + + align:start position:0% +normal is orthogonal to F sub3 at every +point and so F sub3 dotted with the + + align:start position:0% +point and so F sub3 dotted with the + + + align:start position:0% +point and so F sub3 dotted with the +normal is zero and so again for exactly + + align:start position:0% +normal is zero and so again for exactly + + + align:start position:0% +normal is zero and so again for exactly +the same reason as Part B part C the + + align:start position:0% +the same reason as Part B part C the + + + align:start position:0% +the same reason as Part B part C the +flux is zero + + align:start position:0% +flux is zero + + + align:start position:0% +flux is zero +so again it's exactly the same that the + + align:start position:0% +so again it's exactly the same that the + + + align:start position:0% +so again it's exactly the same that the +vector field I was looking at and I + + align:start position:0% +vector field I was looking at and I + + + align:start position:0% +vector field I was looking at and I +wanted to compute the flux for is + + align:start position:0% +wanted to compute the flux for is + + + align:start position:0% +wanted to compute the flux for is +actually tangent to the curve at every + + align:start position:0% +actually tangent to the curve at every + + + align:start position:0% +actually tangent to the curve at every +point and so when I dot it to the normal + + align:start position:0% +point and so when I dot it to the normal + + + align:start position:0% +point and so when I dot it to the normal +of the curve the normal to the curve at + + align:start position:0% +of the curve the normal to the curve at + + + align:start position:0% +of the curve the normal to the curve at +every point I get zero and so Computing + + align:start position:0% +every point I get zero and so Computing + + + align:start position:0% +every point I get zero and so Computing +the flux is zero so now I have one more + + align:start position:0% +the flux is zero so now I have one more + + + align:start position:0% +the flux is zero so now I have one more +to do and that one is Part D and in this + + align:start position:0% +to do and that one is Part D and in this + + + align:start position:0% +to do and that one is Part D and in this +case f sub4 let me just remind you is 3 + + align:start position:0% +case f sub4 let me just remind you is 3 + + + align:start position:0% +case f sub4 let me just remind you is 3 +* the vector minus1 + + align:start position:0% +* the vector minus1 + + + align:start position:0% +* the vector minus1 +one and so if we go back to our picture + + align:start position:0% +one and so if we go back to our picture + + + align:start position:0% +one and so if we go back to our picture +here F sub4 if I compare it to the + + align:start position:0% +here F sub4 if I compare it to the + + + align:start position:0% +here F sub4 if I compare it to the +normal in fact what I get is it's very + + align:start position:0% +normal in fact what I get is it's very + + + align:start position:0% +normal in fact what I get is it's very +long this is probably not quite long + + align:start position:0% +long this is probably not quite long + + + align:start position:0% +long this is probably not quite long +enough but that should be that should be + + align:start position:0% +enough but that should be that should be + + + align:start position:0% +enough but that should be that should be +sort of the that's at least the + + align:start position:0% +sort of the that's at least the + + + align:start position:0% +sort of the that's at least the +direction of F sub4 and so f sub4 is + + align:start position:0% +direction of F sub4 and so f sub4 is + + + align:start position:0% +direction of F sub4 and so f sub4 is +exactly the opposite direction to the + + align:start position:0% +exactly the opposite direction to the + + + align:start position:0% +exactly the opposite direction to the +normal so if I want to compute the flux + + align:start position:0% +normal so if I want to compute the flux + + + align:start position:0% +normal so if I want to compute the flux +of f sub4 along this + + align:start position:0% +of f sub4 along this + + + align:start position:0% +of f sub4 along this +curve all I have to understand is f sub4 + + align:start position:0% +curve all I have to understand is f sub4 + + + align:start position:0% +curve all I have to understand is f sub4 +dotted with the normal and the length of + + align:start position:0% +dotted with the normal and the length of + + + align:start position:0% +dotted with the normal and the length of +the curve exactly this is exactly the + + align:start position:0% +the curve exactly this is exactly the + + + align:start position:0% +the curve exactly this is exactly the +same type of solution as part A so let's + + align:start position:0% +same type of solution as part A so let's + + + align:start position:0% +same type of solution as part A so let's +notice this first F sub4 the length is 3 + + align:start position:0% +notice this first F sub4 the length is 3 + + + align:start position:0% +notice this first F sub4 the length is 3 +< tk2 you can compute that pretty + + align:start position:0% +< tk2 you can compute that pretty + + + align:start position:0% +< tk2 you can compute that pretty +quickly the length of n is just one it's + + align:start position:0% +quickly the length of n is just one it's + + + align:start position:0% +quickly the length of n is just one it's +a normal that's why this stuff didn't + + align:start position:0% +a normal that's why this stuff didn't + + + align:start position:0% +a normal that's why this stuff didn't +really matter what exactly it was it's + + align:start position:0% +really matter what exactly it was it's + + + align:start position:0% +really matter what exactly it was it's +good to know what what direction it + + align:start position:0% +good to know what what direction it + + + align:start position:0% +good to know what what direction it +points in so F sub4 dotted with n is + + align:start position:0% +points in so F sub4 dotted with n is + + + align:start position:0% +points in so F sub4 dotted with n is +exactly 3 < tk2 times cosine of the + + align:start position:0% +exactly 3 < tk2 times cosine of the + + + align:start position:0% +exactly 3 < tk2 times cosine of the +angle between n and F sub4 the angle is + + align:start position:0% +angle between n and F sub4 the angle is + + + align:start position:0% +angle between n and F sub4 the angle is +pi you notice they're they differ by + + align:start position:0% +pi you notice they're they differ by + + + align:start position:0% +pi you notice they're they differ by +180° right right so the it's cosine Pi + + align:start position:0% +180° right right so the it's cosine Pi + + + align:start position:0% +180° right right so the it's cosine Pi +which is minus one so what I do in in + + align:start position:0% +which is minus one so what I do in in + + + align:start position:0% +which is minus one so what I do in in +part D is I'm integrating along the + + align:start position:0% +part D is I'm integrating along the + + + align:start position:0% +part D is I'm integrating along the +curve the constant -3 < tk2 DS this is + + align:start position:0% +curve the constant -3 < tk2 DS this is + + + align:start position:0% +curve the constant -3 < tk2 DS this is +exactly F dotted with the normal F sub4 + + align:start position:0% +exactly F dotted with the normal F sub4 + + + align:start position:0% +exactly F dotted with the normal F sub4 +DOA with the normal and so as before + + align:start position:0% +DOA with the normal and so as before + + + align:start position:0% +DOA with the normal and so as before +this is going to equal to -3 < tk2 times + + align:start position:0% +this is going to equal to -3 < tk2 times + + + align:start position:0% +this is going to equal to -3 < tk2 times +the Arc Length because the integral DS + + align:start position:0% +the Arc Length because the integral DS + + + align:start position:0% +the Arc Length because the integral DS +the integral over the curve DS is going + + align:start position:0% +the integral over the curve DS is going + + + align:start position:0% +the integral over the curve DS is going +to be the arc length and the arc length + + align:start position:0% +to be the arc length and the arc length + + + align:start position:0% +to be the arc length and the arc length +is very easy to see you've got a you've + + align:start position:0% +is very easy to see you've got a you've + + + align:start position:0% +is very easy to see you've got a you've +got gone over one and up one right so + + align:start position:0% +got gone over one and up one right so + + + align:start position:0% +got gone over one and up one right so +Pythagorean theorem understanding right + + align:start position:0% +Pythagorean theorem understanding right + + + align:start position:0% +Pythagorean theorem understanding right +triangles however you want to do it the + + align:start position:0% +triangles however you want to do it the + + + align:start position:0% +triangles however you want to do it the +length of this curve is < tk2 so this + + align:start position:0% +length of this curve is < tk2 so this + + + align:start position:0% +length of this curve is < tk2 so this +works out to be -3 < tk2 < tk2 which is + + align:start position:0% +works out to be -3 < tk2 < tk2 which is + + + align:start position:0% +works out to be -3 < tk2 < tk2 which is +just + + align:start position:0% +just + + + align:start position:0% +just +-6 so let me just remind you there were + + align:start position:0% +-6 so let me just remind you there were + + + align:start position:0% +-6 so let me just remind you there were +four problems here there's sort of two + + align:start position:0% +four problems here there's sort of two + + + align:start position:0% +four problems here there's sort of two +sets of problems where in each in each + + align:start position:0% +sets of problems where in each in each + + + align:start position:0% +sets of problems where in each in each +case you have one similar to the other + + align:start position:0% +case you have one similar to the other + + + align:start position:0% +case you have one similar to the other +so let me let me point point this out + + align:start position:0% +so let me let me point point this out + + + align:start position:0% +so let me let me point point this out +one more time and just sort of step back + + align:start position:0% +one more time and just sort of step back + + + align:start position:0% +one more time and just sort of step back +we had a circle and then the next part + + align:start position:0% +we had a circle and then the next part + + + align:start position:0% +we had a circle and then the next part +we had a line segment but in the circle + + align:start position:0% +we had a line segment but in the circle + + + align:start position:0% +we had a line segment but in the circle +one of the problems the vector was in + + align:start position:0% +one of the problems the vector was in + + + align:start position:0% +one of the problems the vector was in +the direction of the normal and you + + align:start position:0% +the direction of the normal and you + + + align:start position:0% +the direction of the normal and you +wanted to compute the flux for that and + + align:start position:0% +wanted to compute the flux for that and + + + align:start position:0% +wanted to compute the flux for that and +the other the vector was tangent to the + + align:start position:0% +the other the vector was tangent to the + + + align:start position:0% +the other the vector was tangent to the +curve and so it was orthogonal to the + + align:start position:0% +curve and so it was orthogonal to the + + + align:start position:0% +curve and so it was orthogonal to the +normal and you wanted to compute the + + align:start position:0% +normal and you wanted to compute the + + + align:start position:0% +normal and you wanted to compute the +flux for that obviously when you're + + align:start position:0% +flux for that obviously when you're + + + align:start position:0% +flux for that obviously when you're +tangent to the curve and then orthogonal + + align:start position:0% +tangent to the curve and then orthogonal + + + align:start position:0% +tangent to the curve and then orthogonal +to the normal you get zero and that was + + align:start position:0% +to the normal you get zero and that was + + + align:start position:0% +to the normal you get zero and that was +the case for B and for C when you're + + align:start position:0% +the case for B and for C when you're + + + align:start position:0% +the case for B and for C when you're +normal to the Curve and of constant + + align:start position:0% +normal to the Curve and of constant + + + align:start position:0% +normal to the Curve and of constant +length which was the case actually for + + align:start position:0% +length which was the case actually for + + + align:start position:0% +length which was the case actually for +both A and D then all you have to do is + + align:start position:0% +both A and D then all you have to do is + + + align:start position:0% +both A and D then all you have to do is +find the find F dotted with the normal + + align:start position:0% +find the find F dotted with the normal + + + align:start position:0% +find the find F dotted with the normal +and then find the arc length and + + align:start position:0% +and then find the arc length and + + + align:start position:0% +and then find the arc length and +multiply them together so that was the + + align:start position:0% +multiply them together so that was the + + + align:start position:0% +multiply them together so that was the +real strategy we had to use for a and + + align:start position:0% +real strategy we had to use for a and + + + align:start position:0% +real strategy we had to use for a and +for D so hopefully this helps you see + + align:start position:0% +for D so hopefully this helps you see + + + align:start position:0% +for D so hopefully this helps you see +sort of how the the geometric quantities + + align:start position:0% +sort of how the the geometric quantities + + + align:start position:0% +sort of how the the geometric quantities +are interacting to understand the flux + + align:start position:0% +are interacting to understand the flux + + + align:start position:0% +are interacting to understand the flux +of a vector field across a curve and + + align:start position:0% +of a vector field across a curve and + + + align:start position:0% +of a vector field across a curve and +that's where I'll stop \ No newline at end of file diff --git a/mJAf9OYfLV8.txt b/mJAf9OYfLV8.txt new file mode 100644 index 0000000000000000000000000000000000000000..94856b027376787fc02378edc951486f9219ce3a --- /dev/null +++ b/mJAf9OYfLV8.txt @@ -0,0 +1,2001 @@ +The following content is +provided by MIT OpenCourseWare + +under a Creative Commons +license. + +Additional information about +our license and MIT + +OpenCourseWare in general is +available at ocw.mit.edu. + +Let's pick up from where we +were on Friday. + +We had discovered the nucleus. +Now we were faced with the + +problem, as all the scientific +community was in 1911, + +in trying to understand the +structure of the atom. + +Where was the nucleus in the +atom? + +Where was the electron? +How were they bound? + +How did they hang together? +And we talked about the fact + +that the electron in the +nucleus, the force of + +interaction is the Coulomb +force. + +And we started talking about +how, at that time, + +the only equation of motion +that was going to allow us to + +figure out how the electron and +nucleus moved under influence of + +this Coulomb force was Newton's +equations of motion, + +in particular the Second Law, +F equals ma. + +And so, in order to apply that +equation of motion, + +we needed a model for the atom. +And what was the simplest and + +most obvious thing to do was to +suggest the planetary model. + +After all, that is how the +astronomical bodies moved around + +the sun. +And so the model that is set up + +is one where this electron has a +uniform circular motion around + +the nucleus with a well-defined +radius, which we called r star. + +We said that given this, + +the acceleration was a +constant. + +It was given by v squared over. + +The linear velocity over r. +We plugged that into F equals, + +put in the Coulomb force, + +and from that we were able to +calculate the kinetic energy of + +that electron going around the +nucleus. + +Well, the reason I want to +calculate the kinetic energy + +from this model is because I +want to ultimately calculate the + +total energy. +And why I want to calculate the + +total energy is going to be +obvious in just a few minutes. + +My goal is to get the total +energy. + +Actually, I am using my notes +from Friday because I didn't + +finish them. +You may need to get them out. + +This will probably often be the +case, is that I won't quite + +finish the notes from the other +lecture. + +I will start out the next +lecture where I left off, + +so you should bring your +previous day's notes to class + +if, in fact, you use them during +class. + +I want the kinetic energy plus +the potential energy because I + +want both of them to add them up +to get the total energy. + +I know the kinetic energy. +Now, we need the potential + +energy. +What is the potential energy? + +Well, the potential energy is +the integral over the operating + +force over the appropriate +limits. + +In this case, +if our force of interaction is + +the Coulomb force, +which I will just represent as + +F of r, +I am going to integrate this + +from r star out, +and this is going to be minus + +the integral of the force. +Now, some of you may have seen + +this before. +This is a general case, + +the potential energy of +anything is minus the integral + +of the operating force over the +appropriate coordinates. + +If you have seen it before, +that is fine, + +you are happy. +If you have not seen this + +before, you are panicked. +Don't panic. + +I do not hold you responsible +for this. + +You will see it in 8.01 later +on this semester. + +When you see it later on, +you can come back here and say, + +okay, now I know what is going +on. + +But I just need it right now to +make a point about the total + +energy of the system. +And that is what is going to + +lead me to the conundrum. +I need the potential energy. + +It is the integral of the +force. + +Let me plug in, +here, my force that is + +operating, e squared 4 pi +epsilon nought r squared. + +I do that integral and put in + +the appropriate limits. +It is minus e squared over 4 pi + +epsilon nought r star. + +Now I have kinetic energy plus +potential energy. + +Let me add them up. +The kinetic is one-half e + +squared 4 pi epsilon nought r +star. + +Potential, minus e squared over + +4 pi epsilon nought r star. + +The result is minus one-half e +squared 4 pi epsilon nought r + +star. + +That is the total energy here + +of this particular system. +Well, why I wanted this total + +energy is to show you that this +total energy is negative. + +What that negative means to us +is that the system is bound. + +The electron and the nucleus +are stuck together. + +And I can show you that maybe a +little more clearly if I draw an + +energy level diagram. +Let me plot here the total + +energy. +And I am plotting it as a + +function of r, +the distance between the + +electron and the nucleus. +Well, what you can see is that + +for very large r, +the energy here is going to be + +zero. +Way out here, + +for very large r, +where we have the electron and + +the nucleus separated infinitely +apart, the energy is zero. + +And, of course, +as you bring them closer + +together, the energy goes down. +And when you are exactly, + +and we calculated this, +at r star here, + +well, then the total energy is +minus one-half e squared over 4 + +pi epsilon nought times r star. + +If you brought the electron and + +the nucleus into this value here +of r star, + +the energy would change like +that. + +But the big point is this +energy is negative, + +or it is lower than the +electron and the nucleus + +separated. +That means that the electron + +and nucleus are stuck together. +You are going to have to put + +this much energy into the system +in order to pull them apart. + +That is the big point here, +is that this model so far looks + +like everything is hunky-dory. +Everything is working. + +The electron stuck to the +nucleus. + +It is not going anywhere. +It looks terrific. + +But here comes the conundrum. +The conundrum is that classical + +electromagnetism, +which was pretty well + +understood by this time, +1911, 1912. + +Maxwell's equations, +that was down pat. + +But what classical +electromagnetism says is that + +when you have a charge, +and this electron is a charge, + +that is accelerating, +that charge has to be emitting + +radiation. +It has to be giving off energy. + +After all, that is actually how +an antenna works. + +In an antenna, +what you are doing is taking + +charge and sloshing it, +accelerating it. + +When it accelerates, +it emits radiation. + +That is how you broadcast. +That is true, + +it was known in 1911. +Synchrotron radiation works the + +same way. +When you have a synchrotron, + +the way you get synchrotron +radiation is essentially by + +accelerating charge. +That is a given and is + +actually, again, +something you will talk about + +in much more detail in 8.02. +But the point here is if this + +charge is being accelerated, +and it is, then it must be + +giving off radiation. +It must be giving off energy. + +Well, if it is giving off +energy, we look at our energy + +expression here. +That must mean that the energy + +in the system is going down +because it is losing the energy. + +It is giving it off to +radiation. + +If E is going down, +it is getting more negative + +here. +The only way for E to get more + +negative is for this r star +right here to be changing. + +Is for r star to be getting +smaller and smaller and smaller. + +Well, we could set up another +set of equations using what we + +know from classical +electromagnetism and from what + +we have already done here. +What we would find is that this + +value here of r star would go to +zero in t equal 10^-10 seconds + +if r was originally on the order +of an angstrom to begin with. + +Here is the problem. +Classical equations of motion + +coupled with classical +electromagnetism, + +they are making a prediction +that my atom is not going to + +live more than 10^-10 seconds. +Because in 10^-10 seconds, + +that electron is on top of the +nucleus. + +We no longer have an atom that +was already known to have a + +volume associated with a +diameter that is about an + +angstrom. +The classical way of thinking + +is making a prediction that is +not consistent with the + +observations at that time. +And even now, + +it is predicted that the atom +essentially kind of annihilates, + +collapses in 10^-10 seconds. +And that is the problem that + +the scientific community had in +1911. + +That is the problem we have +right now. + +And they had it for 10, +12 years. + +Now you can say what is wrong +here? + +Well, it is possible, +and they were thinking about + +this, too. +It is possible that maybe this + +force is wrong, +this Coulomb force. + +That is a possibility. +Or, of course, + +maybe it is the equations of +motion that are wrong. + +That is possible. +Or, maybe it is classical + +electromagnetism that is wrong. +Well, of course what it is + +going to turn out to be is the +equations of motion, + +F equals ma. +Bottom line is that you cannot + +use classical mechanics to +explain the motion of this + +microscopic particle, +the atom, in the constrained + +environment of an atom. +That is the bottom line. + +We need different mechanics. +We cannot use classical + +mechanics to describe how that +electron hangs on that nucleus, + +how they are bound. +And so that was the problem. + +This signaled something was +really amiss in the scientific + +community in the world at that +time. + +That is our problem now, +too. + +What is the next step? +Well, historically the clues + +about why the electron did not +actually collapse into the + +nucleus, like classical physics +predicted, came from a + +completely different area of +discussion. + +It came from the discussion of +the wave-particle duality of + +light and matter. +It was long believed that + +matter, with its particle-like +behavior, was distinct from + +light, which was this +transmission of energy through + +space. +But, in the last 1800s and + +early 1900s, there were a few +experiments that appeared on the + +horizon that began to suggest +that maybe this boundary between + +matter with its particle-like +behavior and radiation with its + +wave-like behavior was not as +rigid as thought. + +And, in fact, +what we are going to see is + +that radiation has both +wave-like properties and + +particle-like properties. +It depends on the particular + +experiment that you do which one +of those behaviors you see. + +And, consequently, +matter behaves both as a + +particle and a wave. +Again, it depends on exactly + +what experiment you do, +which one of those properties + +you observe. +What we are going to do right + +now is put aside the discussion +of the structure of the atom. + +We are going to put it aside +until next Monday. + +We have to do that because we +need some more information in + +order to take a big leap to get +us out of this constraint of + +classical mechanics. +And those clues, + +as I said, came from this +discussion of the wave-particle + +duality of light and matter. +And that is what we are going + +to be talking about for the next +three lectures. + +Then we are going to come back +and tie in those results to the + +structure of the atom. +Of course, where that is going + +to lead us is a new equation of +motion called quantum mechanics. + +That is where we are going. +Let's start off by talking + +about radiation or light. +We are going to talk about its + +wave-like properties, +then Wednesday we are going to + +talk about the particle-like +properties of light, + +and Friday we are going to talk +about the wave-like properties + +of matter. +That is where we are going. + +Let's talk about waves here. +You all know that waves are + +some periodic variation of a +quantity. + +A water wave, +for example, + +is a periodic variation of the +level of water. + +At some points in space, +the water level is high. + +At other points, +the water level is low. + +Sound wave. +Well, a sound wave is the + +periodic variation of the +density of air. + +At some points in space, +the air is very dense. + +At other points in space, +the air is not dense. + +Well, light or radiation is a +period variation of an electric + +field, as I depict here on this +slide. + +Electric field versus position. +There is a periodic variation + +of the electric field. +Now, exactly what is an + +electric field? +Some of you know this, + +some of you don't, +but an electric field is + +literally the space through +which the Coulomb force + +operates. +For example, + +if we have a negatively charged +plate and a positively charged + +plate here. +The space through which the + +Coulomb force is operating here, +and the Coulomb force is + +operating because we have two +plates here that are oppositely + +charged. +The electric field is the space + +through which the Coulomb force +operates. + +If we put a positive charge in +that space, you know what is + +going to happen. +In this coordinated system, + +the positive charge is going to +float up. + +Because the negatively charged +plate is up above. + +If we reversed the potential +difference and put a positively + +charged particle in this +electric field, + +in this space, +it is going to move down + +because now the negatively +charged plate is lower. + +This electric field here has +not only magnitude -- + +You can imagine here the +magnitude is given by the + +difference in the potentials of +these plates. + +The larger the difference, +the larger the magnitude. + +But it also has direction. +In one case, + +it is pointed this way. +In the other case, + +it is pointed that way. +And that is reflected here on + +this plot of the electric field +here. + +What you see is that right +here, the magnitude of the + +electric field is small. +As you move along in x, + +that magnitude increases, +goes to a maximum, + +then turns around and at some +point literally is zero. + +And then the electric field +changes direction and its + +magnitude increases in the +opposite direction. + +Increases, increases, +gets to a point, + +then turns around and becomes +zero again. + +If you have a charge in a +radiation field and you put it + +right here -- +Well, it would be pulled in one + +direction. +If you put it over here, + +it would be pulled in the other +direction. + +We have a magnitude and we have +a direction. + +Now, not only is light a +periodic variation of the + +electric field in space, +it is also a periodic variation + +of the electric field in time. +That is, this is a picture of + +that field, that one instant in +time. + +We will call it t equals 0. + +However, that electric field +moves. + +It propagates. +And the distance, + +or the time it takes for the +electric field here to move over + +one wavelength, +I have shown this as a star. + +The time it takes for this +maximum to go from here to here, + +one wavelength, +is defined as one period. + +And a period is given by one +over nu, + +where nu is the frequency of +the radiation. + +It is the number of cycles per +second. + +In other words, +if you were sitting here at x + +equals 0, +you were tied at x equals 0, + +and you were just watching this +electric field come by. + +You would see a maximum in that +electric field, + +one maximum every second if the +frequency is one Hertz. + +In other words, +the frequency is the number of + +maxima you would see pass by you +per second. + +Well, we have a unit to +characterize frequency. + +I call it cycles per second. +It is cycles per second, + +but the formal unit is Hertz. +Hertz is inverse seconds. + +We leave out the number of +cycles. + +The number of cycles is implied +in the unit of Hertz. + +To give another example, +here, suppose we had some + +radiation and the frequency of +that radiation was one Hertz. + +Suppose we had an electron, +an electron is charged, + +and we put here at x equals 0 +and we tie it at x equals 0. + +What is going to happen to this +electron? + +Well, what is going to happen +is that this electron is going + +to be pulled down and then it is +going to be pushed back up once + +every second because the +frequency, here, + +is one Hertz. +It is charged, + +and we are tying it at x equals +0. + +It is going to go like this. +It is going to oscillate once + +every second if this frequency +is one hertz. + +Here it goes. +An electron is pulled down and + +then pushed back up once every +second. + +Now, we, of course, +can write an equation to + +describe this oscillation of the +electric field in both space and + +time. +x is the position variable, + +t, the time variable, +and I have written it down + +here. +I will explain this more in + +just a moment, +but what I also want to point + +out is that an oscillating +electric field always, + +always, always has +perpendicular to it an + +oscillating magnetic field. +That is well described by + +Maxwell's equations. +Again, you are going to see + +that in 8.02. +And the magnetic field here has + +the same essentially function +form and characteristics as this + +electric field. +And, because it does, + +I am just going to talk about +the electric field. + +Here is the expression for the +magnetic field. + +I just call it H. +But, again, it is a function of + +position and time. +Here is an illustration, + +just the variation of the +electric field. + +Light, radiation is actually a +variation in space and time of + +both the electric and a magnetic +field. + +That is why it is +electromagnetic radiation. + +Now, let me show you on the +8.02 website. + +Let me get that rolling. +There it is. + +Now we have to start it. +All right. + +One of these is the electric +field. + +The other one is the magnetic +field. + +This is a simulation that 8.02 +has made for you. + +You can go and look at it on +the 8.02 website, + +but you can see it propagating +here in time, + +and you can see its variation +in space of this electromagnetic + +field. +Let's look at this functional + +form just a little more +carefully, just to make sure + +everybody is on the same page. +I think many of you have seen + +this before. +What we are going to do, + +because we have two variables, +is we are going to hold one + +variable constant and plot it as +a function of the other + +variable, just to explain the +parameters that go into this + +functional form. +At time t equals 0, + +if in this equation here I +stick in t equals 0, + +I have a form that looks like +this. + +It is just the cosine function +in x. + +And you can see that the +amplitude goes from positive A + +to minus A. +And so what you see is that + +this A in front of the cosine, +the physical meaning of it is + +just the maximum amplitude. +If you were given a functional + +form with a number in front of a +cosine, well, + +you could read off the +amplitude immediately. + +The other parameter that +characterizes this wave is the + +wavelength. +It is the distance between two + +successive maxima or two +successive minima. + +And you can also see here that +the field is going to be at its + +maximum amplitude whenever this +x is an integral multiple of the + +wavelength, lambda, +2 lambda, 3 lambda, + +or minus lambda, +minus 2 lambda or zero. + +If you were given a waveform +and there was a number in front + +of the x, you can almost, +by inspection, + +tell what the wavelength is. +That number would be equal to 2 + +pi over lambda. +Now what we are going to do is + +hold x constant and set it equal +to zero, and then plot this + +functional form as a function of +time. + +Again, we have the cosine +function, oscillates from plus A + +to minus A. +Now the time between two + +successive maxima or minima is +what we spoke earlier of as the + +period. +It is the time for one cycle. + +In other words, +is it one over the frequency. + +And you get the maxima then +whenever the time is an integral + +multiple of the period, +whenever time is 1 over nu, + +2 over nu, 3 over nu, +or minus 1 over nu, + +minus 2 over nu, +or zero. + +These are the +characteristics of the + +functional form, +amplitudes, wavelengths, + +frequencies. +Now, I told you that the period + +was given by 1 over nu. + +Let's just do a quick proof +that the period is actually 1 + +over nu, one over frequency. +How are we going to do that? + +Well, what I said was the +definition for a period was the + +time it takes the wave to move +one wavelength. + +If this is the wave at t equals +0, this then coming up here + +should be the wave at one period +later. + +And so, if we moved over +exactly one cycle, + +what this means is that at one +period later the functional form + +ought to look exactly like it +did at t equals 0. + +If I take my general expression +for the waveform and plug in t + +equals 1 over nu, +I get this. + +What you can see at first +glance is that it doesn't really + +look like this, +or at least not just yet, + +but we are going to make it +look like this and we are going + +to do so legally. +What are we going do? + +This just repeats that +equation. + +You can already see we have +some cancellation here. + +These two nu's go away, +so I just have cosine ((2 pi x) + +over lambda minus 2 pi). + +In order to simplify this, +I am going to need a + +trigonometric identity, +which you may or may not + +remember, cosine (alpha minus +beta) is the cosine alpha times + +cosine beta plus the sine of the +alpha sine beta. + +I am going to let 2(pi)x be +alpha, and beta will be 2pi. + +I am going to plug that in. +Here, we can see some nice + +simplification. +This cosine 2pi, + +of course, is one. +The sign of + +2pi is zero, this term goes +away, and what I have left is A + +cosine 2 pi x over lambda at t +equals 1 over nu. + +And, indeed, + +that is the same functional +field as the field at t equals + +0. +That is our proof that the + +period is equal to 1 over nu. + +Now, this wave also propagates +in space. + +It moves. +It goes from here to here. + +And another important +characteristic of + +electromagnetic reaction is the +speed with which it propagates. + +Let's just quickly calculate +what that speed is. + +We have enough information to +do that. + +Speed is always distance +traveled divided by time + +elapsed. +And we said that at t equals 0, + +this is what our waveform +looked like. + +We also said that one period +later, this is what our waveform + +looked like. +We know at one period that the + +waveform moved over one +wavelength. + +The speed is the distance +traveled, which is a wavelength, + +divided by the time elapsed, +which is 1 over nu, + +the period. +Therefore, the speed is lambda + +times nu. +That is the speed with which + +this wave propagates. +And, of course, + +you already know that all +electromagnetic radiation has a + +constant speed of about 3x10^8 +meters per second, + +or we call it c. +And what that is, + +is the product of the +wavelength times the frequency. + +The electromagnetic spectrum, +of course, is infinitely wide. + +And here is the electromagnetic +spectrum. + +We won't do this in any kind of +detail, but I just want you to + +note here that on the long +wavelength end, + +we have what we call radio +waves. + +And on the short wavelength, +then, we have our gamma rays + +and cosmic rays. +And, in the case of the gamma + +and the cosmic rays, +because the wavelength is + +small, lambda is small, +that means those waves have a + +high frequency. +In the case of the radio waves, + +because those wavelengths are +long, that means those waves + +have a lower frequency because +the frequency times the + +wavelength is a constant. +It is this c. + +It is 3x10^8 meters per second. +And, of course, + +right in here, +a very small region, + +narrow region of the +electromagnetic spectrum, + +are the light waves that are +sensitive to our eye. + +What you do need to know is +that the red wavelengths are + +longer and the blue wavelengths +are shorter. + +Again, the important thing is +lambda times nu is always, + +for every kind of radiation, +equal to a constant. + +And that constant is c. Now, + +the other thing that you just +need to know is the relative + +ordering here in wavelengths. +You do need to know that + +microwaves are longer +wavelengths than gamma rays. + +All MIT students should know +that. + +And one other thing I might +say, because we are going to + +talk about this a little later +in the course. + +See these microwaves? +Well, molecules will absorb + +microwaves, take it in. +That kind of radiation is going + +to set the molecule rotating. +Molecules will absorb infrared + +radiation, and that kind of +radiation is going to set the + +molecules vibrating. +Molecules will absorb visible + +and ultraviolet radiation. +What that is going to do is + +promote an electron to an +excited state. + +Then sometimes those electrons, +in the excited state, + +want to relax back down to the +ground state. + +When they do so they give off +radiation. + +That is the origin of +fluorescence and sometimes + +phosphorescence. +Then sometimes molecules will + +also fluoresce if they absorb +X-rays, but with X-rays, + +if a molecule absorbs them, +it also kicks out an electron. + +And we will be looking at that +in a few days to identify the + +energy levels in atoms and +molecules. + +This, I think, +you are familiar with. + +So far I have just told you +what electromagnetic radiation + +is, how we characterize it: +speed, frequency, + +wavelength, maximum amplitude. +But what I have not shown you, + +yet, is any evidence that +indeed light has wave-like + +characteristics. +And to do that we are going to + +do the experiment that +essentially was done to + +demonstrate the wave-like +behavior of light, + +and that is Young's two-slit +experiment. + +This is the late 1800s. +What was done was to take a + +source of monochromatic +radiation. + +We are going to use 6,330 +angstroms, 633 nanometers. + +It is a helium neon laser. +And it is going to impinge on + +just a thin metal plate. +It does not have to be metal. + +It can be anything. +But what we did was poke two + +holes in it, made two slits. +And naively you might think, + +if you looked at a screen out +here, that this screen will + +light up in spots that are +directly opposite those slights. + +Because, after all, +light travels in straight + +lines. +And so if the slits here are + +0.005 meters apart, +you might think that the two + +bright spots on the slit will be +about 0.02 inches apart. + +Well, of course, +that isn't the case. + +What you really see is an array +of bright spots. + +And Christine has up there in +the projection booth a helium + +neon laser that is shinning +behind two slits. + +You've got really beautifully +now, Christine. + +That is great. +And what you see is that there + +is a whole array of spots. +There aren't just two spots. + +There is a bunch of spots here, +bright spot, + +dark spot, bright spot, +dark spot. + +You've also got another pattern +superimposed on that. + +It almost looks like you would +see the single slit diffraction, + +too, on top of the double slit, +but we won't get into that. + +But this is not just two spots. +Let's see if we can try to + +understand how this pattern +arises, what this pattern comes + +from. +Well, waves have the property + +of superposition. +Superposition means that if I + +take a wave and have it in +space, but now I take a second + +wave and put it in the same +place in space but make it such + +that the maxima of both waves +are in the identical place in + +space, what I have is a +situation where the two waves + +add that property of addition of +waves -- + +When they are in the same place +in space, that property is + +called superposition. +That is the property of waves. + +And in this particular case, +we are going to have what we + +call constructive interference. +They are going to add up such + +that the amplitude here of the +resulting wave is going to be + +twice the amplitude of each of +the individual waves. + +This is constructive +interference. + +On the other hand, +I can have two waves in the + +same place in space, +but they can be positioned so + +that the maximum of one wave is +at the same point in space as + +the minimum of the other. +And because we have these + +positive and negative +amplitudes, well, + +then these are going to cancel +when they add up and we are + +going to have the null result. +We are going to have no + +intensity. +That is called destructive + +interference. +Well, in order to understand + +how this property of +interference gives rise to these + +array of bright spots in the two +slit experiment, + +let me actually use water waves +as an example to try to + +understand why we get this array +of spots, or this row of bright + +spots and dark spots. +Here is the beach. + +Here is the water. +This is the top view. + +Here is the water. +Here is the sand. + +Here is where I wanted to be +all weekend. + +And the waves are rolling in to +the shore. + +There are the wave fronts. +And then suppose I get + +ambitious and, +for whatever perverse reason, + +I decide to build a barrier to +prevent these waves from coming + +onto the beach. +Except I poke two holes in the + +barrier, two little holes. +Well, you know what is going to + +happen. +When the wave approaches that + +barrier, well, +through that little hole a + +little bit of the wave is going +to sneak through. + +And because that little hole is +really pretty little, + +what is going to happen is that +the wave front is going to + +spread out isotropically. +And so that wave front is going + +to look like a semicircle +centered on that little hole. + +And, of course, +this wave front is going to + +keep propagating. +And it propagates out. + +And then soon enough, +a wavelength later, + +another wave sneaks through and +I have two semi-circles. + +And the distance between those +two semi-circles is lambda. + +That is the wavelength. +That is the wave crest. + +That is the maximum of the +wave. + +Keep going. +That propagates out. + +Keep going. +That propagates out. + +Well, at the same time that the +waves are sneaking out through + +that little hole, +waves are sneaking out through + +this little hole. +And I will color them green. + +That wave propagates out and +keeps propagating. + +The other one sneaks through +and keeps propagating. + +And now let me clean up the +drawing a little bit. + +And I am going to call this +slit one. + +The green waves are the waves +that have come through slit one. + +The blue waves are the ones +that have come through slit two. + +And the distance between any +two successive maxima here, + +or any two semi-circles is, +of course, lambda. + +And lambda is the same for slit +one and slit two. + +Now, I want you to look at this +spot that I just circled right + +here. +Right here what do you see? + +Interference. +Absolutely. + +You have two maxima at the same +place in space. + +You are going to have +constructive interference right + +there. +What about this spot? + +Constructive interference. +What about this spot? + +Right. +Everywhere along that line you + +are going to have constructive +interference. + +Now, let me just tell you one +other thing. + +We have every constructive +interference all along this + +line. +Now look right at this point + +here. +What you see is you have the + +superposition of the blue wave +that has come from slit two, + +and this blue wave has traveled +out from slit two a distance + +four lambda. +One, two, three, + +four lambda. +That is the radius. + +It has traveled out a distance +four lambda. + +It is constructively +interfering with a wave coming + +from slit one that has traveled +out a distance three lambda. + +One, two, three. +The difference in the distance + +traveled by those two waves that +are constructively interfering + +is one lambda. +Let's keep going in order to + +understand this diagram. +Let's look at this spot. + +Right here, what do you have? +Constructive interference. + +Right here you have +constructive interference. + +If you kept going you would +see, everywhere along this line, + +constructive interference. +Now let's look at the + +difference in the distance +traveled by the waves that are + +constructively interfering along +that line. + +Well, you see the green wave +here? + +The wave that is constructively +interfering is one that has + +traveled out a distance two +lambda. + +That is, r sub one is equal to +two lambda. + +It is interfering +with this wave front + +that has traveled out a distance +four lambda. + +The difference in the distance +traveled by those two waves is + +two lambda. +4 lambda minus 2 lambda equals + +2 lambda. +I think on your notes, + +it is actually this case that I +have written it down. + +Here is another point of +constructive interference. + +Here is another point of +constructive interference. + +Everywhere along this line, +we have constructive + +interference. +And, if you analyze this, + +the difference in the distance +traveled would be zero. + +What you would expect, +if you were to image this, + +you'd expect right here very +bright spot, very bright spot, + +very bright spot. +This is going to be symmetric + +around the center, +so there will be a bright spot + +out here, a bright spot out +there. + +Let's look at this actually in +real life in a water tank. + +There we go, +up here on the side boards. + +Here are the waves coming this +way onto some barrier, + +and here are the holes. +Here is one hole. + +Here is the other hole. +And then these bright + +semi-circles are the wave +fronts. + +And what I want you to notice, +and you have to kind of look + +out here, right there you see a +whole bunch of very bright + +spots. +Well, if this were light and we + +had a screen then right here we +would see the screen light up. + +And then right here you see +kind of nothing. + +That nothing is destructive +interference. + +That would be a dark spot if, +in fact, this were light and we + +were looking at a screen. +Then here is another very + +bright spot. +Here is another very bright + +spot. +This is on a website from the + +University of Colorado, +which, if you are not familiar + +with, is actually kind of a very +neat website. + +It has some very elementary +topics in it, + +but it also has some topics +that even you would be + +interested in. +And that is actually the name + +of the website. +And so what is going on here, + +in the case of the light, +is just what we have explained. + +We've got this line of +constructive interference that + +is going to result on the screen +as a very bright spot. + +And then another line with +another bright spot and another + +line with a very bright spot. +And this is symmetric around + +the zero. +Right at this point we have + +constructive interference. +In between we have destructive + +interference. +Constructive, + +destructive, +constructive. + +And that is the origin of the +many different bright spots. + +And now there is a condition +that has to obtain in order for + +there to be maximum constructive +interference, + +and that is this condition. +The difference in the distance + +traveled of the two waves that +are interfering to give us that + +maximum constructive +interference has to be an + +integral multiple of the +wavelength. + +I will explain this a little +bit more starting on Wednesday. + +Okay. +See you then. \ No newline at end of file diff --git a/mKYlNJhK_2o.txt b/mKYlNJhK_2o.txt new file mode 100644 index 0000000000000000000000000000000000000000..5bd9bcc12d7d51057e85ff5b7321513b7fe0ff79 --- /dev/null +++ b/mKYlNJhK_2o.txt @@ -0,0 +1,2379 @@ +align:start position:0% + +okay um so this is about the world's + + align:start position:0% +okay um so this is about the world's + + + align:start position:0% +okay um so this is about the world's +fastest way to solve differential + + align:start position:0% +fastest way to solve differential + + + align:start position:0% +fastest way to solve differential +equations and uh you'll like that method + + align:start position:0% +equations and uh you'll like that method + + + align:start position:0% +equations and uh you'll like that method +first we have to see what equations will + + align:start position:0% +first we have to see what equations will + + + align:start position:0% +first we have to see what equations will +we be able to solve well + + align:start position:0% +we be able to solve well + + + align:start position:0% +we be able to solve well +linear constant coefficients I made all + + align:start position:0% +linear constant coefficients I made all + + + align:start position:0% +linear constant coefficients I made all +the coefficients one but no problem to + + align:start position:0% +the coefficients one but no problem to + + + align:start position:0% +the coefficients one but no problem to +change those to ABC so the nice left + + align:start position:0% +change those to ABC so the nice left + + + align:start position:0% +change those to ABC so the nice left +hand side and on the right hand side we + + align:start position:0% +hand side and on the right hand side we + + + align:start position:0% +hand side and on the right hand side we +also need something nice we want a nice + + align:start position:0% +also need something nice we want a nice + + + align:start position:0% +also need something nice we want a nice +function and I'll tell you which are the + + align:start position:0% +function and I'll tell you which are the + + + align:start position:0% +function and I'll tell you which are the +nice + + align:start position:0% +nice + + + align:start position:0% +nice +functions so I I can say right away that + + align:start position:0% +functions so I I can say right away that + + + align:start position:0% +functions so I I can say right away that +e to the E exponentials are nice + + align:start position:0% +e to the E exponentials are nice + + + align:start position:0% +e to the E exponentials are nice +functions of course they're always at + + align:start position:0% +functions of course they're always at + + + align:start position:0% +functions of course they're always at +the center of this course so for example + + align:start position:0% +the center of this course so for example + + + align:start position:0% +the center of this course so for example +equal e to the + + align:start position:0% +equal e to the + + + align:start position:0% +equal e to the +St that would be a nice + + align:start position:0% +St that would be a nice + + + align:start position:0% +St that would be a nice +function okay and the the py is we're + + align:start position:0% +function okay and the the py is we're + + + align:start position:0% +function okay and the the py is we're +looking for a particular solution we + + align:start position:0% +looking for a particular solution we + + + align:start position:0% +looking for a particular solution we +know cuz we know how to find null + + align:start position:0% +know cuz we know how to find null + + + align:start position:0% +know cuz we know how to find null +Solutions we're looking for particular + + align:start position:0% +Solutions we're looking for particular + + + align:start position:0% +Solutions we're looking for particular +solution for this equation one function + + align:start position:0% +solution for this equation one function + + + align:start position:0% +solution for this equation one function +some function that solves this equation + + align:start position:0% +some function that solves this equation + + + align:start position:0% +some function that solves this equation +with right hand side e to the + + align:start position:0% +with right hand side e to the + + + align:start position:0% +with right hand side e to the +St and uh the point is we know what to + + align:start position:0% +St and uh the point is we know what to + + + align:start position:0% +St and uh the point is we know what to +look + + align:start position:0% +look + + + align:start position:0% +look +for we just have some coefficient to + + align:start position:0% +for we just have some coefficient to + + + align:start position:0% +for we just have some coefficient to +find and we'll find that by substituting + + align:start position:0% +find and we'll find that by substituting + + + align:start position:0% +find and we'll find that by substituting +in the equation now do you remember what + + align:start position:0% +in the equation now do you remember what + + + align:start position:0% +in the equation now do you remember what +we look for when the right hand side is + + align:start position:0% +we look for when the right hand side is + + + align:start position:0% +we look for when the right hand side is +e to the St then look + + align:start position:0% + + + + align:start position:0% + +for y + + align:start position:0% +for y + + + align:start position:0% +for y +equal some constant time e to St right + + align:start position:0% +equal some constant time e to St right + + + align:start position:0% +equal some constant time e to St right +when F of T maybe I'll put the equal + + align:start position:0% +when F of T maybe I'll put the equal + + + align:start position:0% +when F of T maybe I'll put the equal +sign down there if F of T is e to the St + + align:start position:0% +sign down there if F of T is e to the St + + + align:start position:0% +sign down there if F of T is e to the St +then I just look for a multiple of it + + align:start position:0% +then I just look for a multiple of it + + + align:start position:0% +then I just look for a multiple of it +that's the S that's one coefficient to + + align:start position:0% +that's the S that's one coefficient to + + + align:start position:0% +that's the S that's one coefficient to +be determined by substitute this into + + align:start position:0% +be determined by substitute this into + + + align:start position:0% +be determined by substitute this into +the equation do you remember the results + + align:start position:0% +the equation do you remember the results + + + align:start position:0% +the equation do you remember the results +so this is the our best example when I + + align:start position:0% +so this is the our best example when I + + + align:start position:0% +so this is the our best example when I +put this in the equation I'll get the + + align:start position:0% +put this in the equation I'll get the + + + align:start position:0% +put this in the equation I'll get the +derivative brings an S second derivative + + align:start position:0% +derivative brings an S second derivative + + + align:start position:0% +derivative brings an S second derivative +brings another s so I get s² and an S + + align:start position:0% +brings another s so I get s² and an S + + + align:start position:0% +brings another s so I get s² and an S +and A 1 * y e to the St is equal to e to + + align:start position:0% +and A 1 * y e to the St is equal to e to + + + align:start position:0% +and A 1 * y e to the St is equal to e to +the + + align:start position:0% +the + + + align:start position:0% +the +St we've done that before here it here + + align:start position:0% +St we've done that before here it here + + + align:start position:0% +St we've done that before here it here +we see it as a case with undetermined + + align:start position:0% +we see it as a case with undetermined + + + align:start position:0% +we see it as a case with undetermined +coefficient y but by plugging it in I've + + align:start position:0% +coefficient y but by plugging it in I've + + + align:start position:0% +coefficient y but by plugging it in I've +discovered that Y is one over + + align:start position:0% +discovered that Y is one over + + + align:start position:0% +discovered that Y is one over +that so what that's a nice function then + + align:start position:0% +that so what that's a nice function then + + + align:start position:0% +that so what that's a nice function then +e to the St is a nice function what are + + align:start position:0% +e to the St is a nice function what are + + + align:start position:0% +e to the St is a nice function what are +the other nice + + align:start position:0% +the other nice + + + align:start position:0% +the other nice +functions so I'm now let me move to the + + align:start position:0% +functions so I'm now let me move to the + + + align:start position:0% +functions so I'm now let me move to the +other board next board and and ask what + + align:start position:0% +other board next board and and ask what + + + align:start position:0% +other board next board and and ask what +other right hand sides could we solve so + + align:start position:0% +other right hand sides could we solve so + + + align:start position:0% +other right hand sides could we solve so +I'll + + align:start position:0% +I'll + + + align:start position:0% +I'll +I'll keep this left hand side equal to + + align:start position:0% +I'll keep this left hand side equal to + + + align:start position:0% +I'll keep this left hand side equal to +so e to the St was + + align:start position:0% + + + + align:start position:0% + +one what + + align:start position:0% +one what + + + align:start position:0% +one what +about t what about + + align:start position:0% +about t what about + + + align:start position:0% +about t what about +t a + + align:start position:0% +t a + + + align:start position:0% +t a +polom well that only has one + + align:start position:0% +polom well that only has one + + + align:start position:0% +polom well that only has one +term but so what would be a particular + + align:start position:0% +term but so what would be a particular + + + align:start position:0% +term but so what would be a particular +solution to that equation try so I I + + align:start position:0% +solution to that equation try so I I + + + align:start position:0% +solution to that equation try so I I +really have to say what is the + + align:start position:0% +really have to say what is the + + + align:start position:0% +really have to say what is the +try y particular + + align:start position:0% +try y particular + + + align:start position:0% +try y particular +equals now if with if I see a t + + align:start position:0% +equals now if with if I see a t + + + align:start position:0% +equals now if with if I see a t +there then I'm looking going to look for + + align:start position:0% +there then I'm looking going to look for + + + align:start position:0% +there then I'm looking going to look for +a a t in the in y so so and I'll also + + align:start position:0% +a a t in the in y so so and I'll also + + + align:start position:0% +a a t in the in y so so and I'll also +look for a constant so a + BT would be + + align:start position:0% +look for a constant so a + BT would be + + + align:start position:0% +look for a constant so a + BT would be +the correct form to look for let me just + + align:start position:0% +the correct form to look for let me just + + + align:start position:0% +the correct form to look for let me just +show you how that works so this now has + + align:start position:0% +show you how that works so this now has + + + align:start position:0% +show you how that works so this now has +two undetermined coefficients and we + + align:start position:0% +two undetermined coefficients and we + + + align:start position:0% +two undetermined coefficients and we +determine them by putting that into the + + align:start position:0% +determine them by putting that into the + + + align:start position:0% +determine them by putting that into the +equation + + align:start position:0% +equation + + + align:start position:0% +equation +and making it right so put try YP is a + + align:start position:0% +and making it right so put try YP is a + + + align:start position:0% +and making it right so put try YP is a +plus BT in this equation okay the second + + align:start position:0% +plus BT in this equation okay the second + + + align:start position:0% +plus BT in this equation okay the second +derivative of a plus BT is zero the + + align:start position:0% +derivative of a plus BT is zero the + + + align:start position:0% +derivative of a plus BT is zero the +first derivative of that is B so I get a + + align:start position:0% +first derivative of that is B so I get a + + + align:start position:0% +first derivative of that is B so I get a +B from that and Y itself is a + BT and + + align:start position:0% +B from that and Y itself is a + BT and + + + align:start position:0% +B from that and Y itself is a + BT and +that's supposed to give + + align:start position:0% +that's supposed to give + + + align:start position:0% +that's supposed to give +T you see I plugged it in I got to this + + align:start position:0% +T you see I plugged it in I got to this + + + align:start position:0% +T you see I plugged it in I got to this +equation now I can determine A and + + align:start position:0% +equation now I can determine A and + + + align:start position:0% +equation now I can determine A and +B because this by matching T so that B + + align:start position:0% +B because this by matching T so that B + + + align:start position:0% +B because this by matching T so that B +has to be one we get b equal to 1 so + + align:start position:0% +has to be one we get b equal to 1 so + + + align:start position:0% +has to be one we get b equal to 1 so +that t equals T but if B is one I need a + + align:start position:0% +that t equals T but if B is one I need a + + + align:start position:0% +that t equals T but if B is one I need a +to be minus one to cancel that so A is + + align:start position:0% +to be minus one to cancel that so A is + + + align:start position:0% +to be minus one to cancel that so A is +minus1 and my answer + + align:start position:0% +minus1 and my answer + + + align:start position:0% +minus1 and my answer +is -1 + 1 t T minus + + align:start position:0% +is -1 + 1 t T minus + + + align:start position:0% +is -1 + 1 t T minus +one and if I put that into the equation + + align:start position:0% +one and if I put that into the equation + + + align:start position:0% +one and if I put that into the equation +it'll be correct so I have found a + + align:start position:0% +it'll be correct so I have found a + + + align:start position:0% +it'll be correct so I have found a +particular solution and that's my goal + + align:start position:0% +particular solution and that's my goal + + + align:start position:0% +particular solution and that's my goal +because I know how to find null + + align:start position:0% +because I know how to find null + + + align:start position:0% +because I know how to find null +Solutions and then together that's the + + align:start position:0% +Solutions and then together that's the + + + align:start position:0% +Solutions and then together that's the +complete solution + + align:start position:0% +complete solution + + + align:start position:0% +complete solution +so we've learned what to try with pols + + align:start position:0% +so we've learned what to try with pols + + + align:start position:0% +so we've learned what to try with pols +with a power of T we want to include + + align:start position:0% +with a power of T we want to include + + + align:start position:0% +with a power of T we want to include +that power and all lower Powers all the + + align:start position:0% +that power and all lower Powers all the + + + align:start position:0% +that power and all lower Powers all the +way down through the constants + + align:start position:0% +way down through the constants + + + align:start position:0% +way down through the constants +okay uh with exponentials we just have + + align:start position:0% +okay uh with exponentials we just have + + + align:start position:0% +okay uh with exponentials we just have +to include the exponential what next how + + align:start position:0% +to include the exponential what next how + + + align:start position:0% +to include the exponential what next how +about Sin t or cosine T say s t all + + align:start position:0% +about Sin t or cosine T say s t all + + + align:start position:0% +about Sin t or cosine T say s t all +right so that that case works now we + + align:start position:0% +right so that that case works now we + + + align:start position:0% +right so that that case works now we +want to try y Prime + y Prime + y = say + + align:start position:0% +want to try y Prime + y Prime + y = say + + + align:start position:0% +want to try y Prime + y Prime + y = say +sin + + align:start position:0% +sin + + + align:start position:0% +sin +T okay what form do we assume for + + align:start position:0% +T okay what form do we assume for + + + align:start position:0% +T okay what form do we assume for +that well I can can tell you quickly we + + align:start position:0% +that well I can can tell you quickly we + + + align:start position:0% +that well I can can tell you quickly we +have to assume we assume a sin t in it + + align:start position:0% +have to assume we assume a sin t in it + + + align:start position:0% +have to assume we assume a sin t in it +and we also need to assume a cosine T + + align:start position:0% +and we also need to assume a cosine T + + + align:start position:0% +and we also need to assume a cosine T +the rule is that what the the things we + + align:start position:0% +the rule is that what the the things we + + + align:start position:0% +the rule is that what the the things we +try so I'll + + align:start position:0% +try so I'll + + + align:start position:0% +try so I'll +try y y particular is what we're always + + align:start position:0% +try y y particular is what we're always + + + align:start position:0% +try y y particular is what we're always +finding uh some + + align:start position:0% +finding uh some + + + align:start position:0% +finding uh some +C1 cos T and some C2 s of + + align:start position:0% +C1 cos T and some C2 s of + + + align:start position:0% +C1 cos T and some C2 s of +T that that will do it in fact it's if I + + align:start position:0% +T that that will do it in fact it's if I + + + align:start position:0% +T that that will do it in fact it's if I +plug that in I match the match the two + + align:start position:0% +plug that in I match the match the two + + + align:start position:0% +plug that in I match the match the two +sides I determine C1 and C2 I'm + + align:start position:0% +sides I determine C1 and C2 I'm + + + align:start position:0% +sides I determine C1 and C2 I'm +golden let me just comment on that + + align:start position:0% +golden let me just comment on that + + + align:start position:0% +golden let me just comment on that +rather than doing out every step uh + + align:start position:0% +rather than doing out every step uh + + + align:start position:0% +rather than doing out every step uh +again the steps are just substitute that + + align:start position:0% +again the steps are just substitute that + + + align:start position:0% +again the steps are just substitute that +in and make the equation correct by + + align:start position:0% +in and make the equation correct by + + + align:start position:0% +in and make the equation correct by +choosing a good C1 and C2 I I'll just + + align:start position:0% +choosing a good C1 and C2 I I'll just + + + align:start position:0% +choosing a good C1 and C2 I I'll just +notice that you remember + + align:start position:0% + + + + align:start position:0% + +from oil's great formula that the cosine + + align:start position:0% +from oil's great formula that the cosine + + + align:start position:0% +from oil's great formula that the cosine +is a combination of e to the it and e to + + align:start position:0% +is a combination of e to the it and e to + + + align:start position:0% +is a combination of e to the it and e to +the minus it so in a way we're really + + align:start position:0% +the minus it so in a way we're really + + + align:start position:0% +the minus it so in a way we're really +using the original example we're using + + align:start position:0% +using the original example we're using + + + align:start position:0% +using the original example we're using +this example e to the + + align:start position:0% +this example e to the + + + align:start position:0% +this example e to the +St with two s's e to the it t and e to + + align:start position:0% +St with two s's e to the it t and e to + + + align:start position:0% +St with two s's e to the it t and e to +the minus it so we have two two + + align:start position:0% +the minus it so we have two two + + + align:start position:0% +the minus it so we have two two +exponentials + + align:start position:0% +exponentials + + + align:start position:0% +exponentials +in a in a cosine so I'm not surprised + + align:start position:0% +in a in a cosine so I'm not surprised + + + align:start position:0% +in a in a cosine so I'm not surprised +that there are two constants to find + + align:start position:0% +that there are two constants to find + + + align:start position:0% +that there are two constants to find +yeah and now finally I have to say what + + align:start position:0% +yeah and now finally I have to say what + + + align:start position:0% +yeah and now finally I have to say what +do we is is this the end of nice + + align:start position:0% +do we is is this the end of nice + + + align:start position:0% +do we is is this the end of nice +functions so nice functions include + + align:start position:0% +functions so nice functions include + + + align:start position:0% +functions so nice functions include +exponentials pols these are really + + align:start position:0% +exponentials pols these are really + + + align:start position:0% +exponentials pols these are really +exponentials complex exponentials and no + + align:start position:0% +exponentials complex exponentials and no + + + align:start position:0% +exponentials complex exponentials and no +there's + + align:start position:0% +there's + + + align:start position:0% +there's +one more possibility that we can deal + + align:start position:0% +one more possibility that we can deal + + + align:start position:0% +one more possibility that we can deal +with with in this simple way and that + + align:start position:0% +with with in this simple way and that + + + align:start position:0% +with with in this simple way and that +possibility is a product of so now I'm + + align:start position:0% +possibility is a product of so now I'm + + + align:start position:0% +possibility is a product of so now I'm +going to I'll show you what to do if it + + align:start position:0% +going to I'll show you what to do if it + + + align:start position:0% +going to I'll show you what to do if it +was T * sin + + align:start position:0% +was T * sin + + + align:start position:0% +was T * sin +T suppose we have the right hand side + + align:start position:0% +T suppose we have the right hand side + + + align:start position:0% +T suppose we have the right hand side +the F of T the forcing term is T * sin T + + align:start position:0% +the F of T the forcing term is T * sin T + + + align:start position:0% +the F of T the forcing term is T * sin T +what is the form to assume that that's + + align:start position:0% +what is the form to assume that that's + + + align:start position:0% +what is the form to assume that that's +really all you have to know is what form + + align:start position:0% +really all you have to know is what form + + + align:start position:0% +really all you have to know is what form +to assume okay now that t so it it's so + + align:start position:0% +to assume okay now that t so it it's so + + + align:start position:0% +to assume okay now that t so it it's so +we have here a product a polinomial + + align:start position:0% +we have here a product a polinomial + + + align:start position:0% +we have here a product a polinomial +times a s or cosine or exponential I + + align:start position:0% +times a s or cosine or exponential I + + + align:start position:0% +times a s or cosine or exponential I +could have done t e to the St there so + + align:start position:0% +could have done t e to the St there so + + + align:start position:0% +could have done t e to the St there so +let me but what do I have to do when the + + align:start position:0% +let me but what do I have to do when the + + + align:start position:0% +let me but what do I have to do when the +T shows up there then I have to try + + align:start position:0% +T shows up there then I have to try + + + align:start position:0% +T shows up there then I have to try +something + + align:start position:0% +something + + + align:start position:0% +something +more with a t in + + align:start position:0% +more with a t in + + + align:start position:0% +more with a t in +there so now I have a product of + + align:start position:0% +there so now I have a product of + + + align:start position:0% +there so now I have a product of +polinomial times + + align:start position:0% +polinomial times + + + align:start position:0% +polinomial times +s cosine or exponential so what I try is + + align:start position:0% +s cosine or exponential so what I try is + + + align:start position:0% +s cosine or exponential so what I try is +a t + or rather a plus + + align:start position:0% +a t + or rather a plus + + + align:start position:0% +a t + or rather a plus +BT I try a product times + + align:start position:0% + + + + align:start position:0% + +C + + align:start position:0% +C + + + align:start position:0% +C +T + + align:start position:0% +T + + + align:start position:0% +T +and C + + + align:start position:0% +and C + + + + align:start position:0% +and C + +DT time sin + + align:start position:0% +DT time sin + + + align:start position:0% +DT time sin +T that that's about as bad a case as + + align:start position:0% +T that that's about as bad a case as + + + align:start position:0% +T that that's about as bad a case as +we're going to see but it's still quite + + align:start position:0% +we're going to see but it's still quite + + + align:start position:0% +we're going to see but it's still quite +Pleasant so what do what do I see there + + align:start position:0% +Pleasant so what do what do I see there + + + align:start position:0% +Pleasant so what do what do I see there +because of the T here I needed to + + align:start position:0% +because of the T here I needed to + + + align:start position:0% +because of the T here I needed to +assume polinomial up to that same degree + + align:start position:0% +assume polinomial up to that same degree + + + align:start position:0% +assume polinomial up to that same degree +one so a plus BT had to do that just + + align:start position:0% +one so a plus BT had to do that just + + + align:start position:0% +one so a plus BT had to do that just +just the way I did up there when there + + align:start position:0% +just the way I did up there when there + + + align:start position:0% +just the way I did up there when there +was a t but now it multiplies sin T so I + + align:start position:0% +was a t but now it multiplies sin T so I + + + align:start position:0% +was a t but now it multiplies sin T so I +have to allow s t and also cosine t + + align:start position:0% + + + + align:start position:0% + +the the pattern is really we've we've + + align:start position:0% +the the pattern is really we've we've + + + align:start position:0% +the the pattern is really we've we've +sort of completed the list of nice + + align:start position:0% +sort of completed the list of nice + + + align:start position:0% +sort of completed the list of nice +functions + + align:start position:0% +functions + + + align:start position:0% +functions +exponentials + + align:start position:0% +exponentials + + + align:start position:0% +exponentials +pols and polinomial times exponential + + align:start position:0% +pols and polinomial times exponential + + + align:start position:0% +pols and polinomial times exponential +that that's really what a nice function + + align:start position:0% +that that's really what a nice function + + + align:start position:0% +that that's really what a nice function +is a polinomial times an exponential or + + align:start position:0% +is a polinomial times an exponential or + + + align:start position:0% +is a polinomial times an exponential or +we could have a sum of those guys we + + align:start position:0% +we could have a sum of those guys we + + + align:start position:0% +we could have a sum of those guys we +could have two or three polinomial times + + align:start position:0% +could have two or three polinomial times + + + align:start position:0% +could have two or three polinomial times +exponential like there and another + + align:start position:0% +exponential like there and another + + + align:start position:0% +exponential like there and another +one and and that's still enough nice + + align:start position:0% +one and and that's still enough nice + + + align:start position:0% +one and and that's still enough nice +function and what's the real key to nice + + align:start position:0% +function and what's the real key to nice + + + align:start position:0% +function and what's the real key to nice +functions the key point was is why why + + align:start position:0% +functions the key point was is why why + + + align:start position:0% +functions the key point was is why why +is this s such a good bunch of functions + + align:start position:0% +is this s such a good bunch of functions + + + align:start position:0% +is this s such a good bunch of functions +because if I take its derivative I get a + + align:start position:0% +because if I take its derivative I get a + + + align:start position:0% +because if I take its derivative I get a +function of the same form if I take the + + align:start position:0% +function of the same form if I take the + + + align:start position:0% +function of the same form if I take the +derivative of that right hand side and I + + align:start position:0% +derivative of that right hand side and I + + + align:start position:0% +derivative of that right hand side and I +use the product rule you see I'll get + + align:start position:0% +use the product rule you see I'll get + + + align:start position:0% +use the product rule you see I'll get +this times the derivative of that so + + align:start position:0% +this times the derivative of that so + + + align:start position:0% +this times the derivative of that so +I'll have something looking with a sign + + align:start position:0% +I'll have something looking with a sign + + + align:start position:0% +I'll have something looking with a sign +in there and like get uh this times the + + align:start position:0% +in there and like get uh this times the + + + align:start position:0% +in there and like get uh this times the +derivative of that which is just a b so + + align:start position:0% +derivative of that which is just a b so + + + align:start position:0% +derivative of that which is just a b so +again it fits the same form polinomial + + align:start position:0% +again it fits the same form polinomial + + + align:start position:0% +again it fits the same form polinomial +time cosine polinomial Time s so here I + + align:start position:0% +time cosine polinomial Time s so here I + + + align:start position:0% +time cosine polinomial Time s so here I +have a case where I have actually Four + + align:start position:0% +have a case where I have actually Four + + + align:start position:0% +have a case where I have actually Four +coefficients but they'll all fall out + + align:start position:0% +coefficients but they'll all fall out + + + align:start position:0% +coefficients but they'll all fall out +when you plug that into the + + align:start position:0% +when you plug that into the + + + align:start position:0% +when you plug that into the +equation you just match terms and you're + + align:start position:0% +equation you just match terms and you're + + + align:start position:0% +equation you just match terms and you're +you're golden so it really is a + + align:start position:0% +you're golden so it really is a + + + align:start position:0% +you're golden so it really is a +straightforward method straight + + align:start position:0% +straightforward method straight + + + align:start position:0% +straightforward method straight +forward + + align:start position:0% +forward + + + align:start position:0% +forward +and so the the key about nice functions + + align:start position:0% +and so the the key about nice functions + + + align:start position:0% +and so the the key about nice functions +is and they're nice for llast transforms + + align:start position:0% +is and they're nice for llast transforms + + + align:start position:0% +is and they're nice for llast transforms +they're nice at every step it's the same + + align:start position:0% +they're nice at every step it's the same + + + align:start position:0% +they're nice at every step it's the same +good functions that we keep uh + + align:start position:0% +good functions that we keep uh + + + align:start position:0% +good functions that we keep uh +discovering as our best examples the key + + align:start position:0% +discovering as our best examples the key + + + align:start position:0% +discovering as our best examples the key +about nice functions is that the that's + + align:start position:0% +about nice functions is that the that's + + + align:start position:0% +about nice functions is that the that's +a that's a form of a nice function + + align:start position:0% +a that's a form of a nice function + + + align:start position:0% +a that's a form of a nice function +because its derivative has the same form + + align:start position:0% +because its derivative has the same form + + + align:start position:0% +because its derivative has the same form +the derivative of that function fits + + align:start position:0% +the derivative of that function fits + + + align:start position:0% +the derivative of that function fits +that pattern again and then the second + + align:start position:0% +that pattern again and then the second + + + align:start position:0% +that pattern again and then the second +derivative fits all the derivatives fit + + align:start position:0% +derivative fits all the derivatives fit + + + align:start position:0% +derivative fits all the derivatives fit +so when we put them in the equation + + align:start position:0% +so when we put them in the equation + + + align:start position:0% +so when we put them in the equation +everything + + align:start position:0% +everything + + + align:start position:0% +everything +fits and always in the last minute of a + + align:start position:0% +fits and always in the last minute of a + + + align:start position:0% +fits and always in the last minute of a +lecture there's a special case there's a + + align:start position:0% +lecture there's a special case there's a + + + align:start position:0% +lecture there's a special case there's a +special case and let's remember what + + align:start position:0% +special case and let's remember what + + + align:start position:0% +special case and let's remember what +that is so special case when we have to + + align:start position:0% +that is so special case when we have to + + + align:start position:0% +that is so special case when we have to +change change the form and why would we + + align:start position:0% +change change the form and why would we + + + align:start position:0% +change change the form and why would we +have to do that let me do y primeus y + + align:start position:0% +have to do that let me do y primeus y + + + align:start position:0% +have to do that let me do y primeus y +say is e to the + + align:start position:0% +say is e to the + + + align:start position:0% +say is e to the +T what is special about + + align:start position:0% +T what is special about + + + align:start position:0% +T what is special about +that what's special is that this right + + align:start position:0% +that what's special is that this right + + + align:start position:0% +that what's special is that this right +hand side this F function solves the + + align:start position:0% +hand side this F function solves the + + + align:start position:0% +hand side this F function solves the +equation if I tried if I tried to assume + + align:start position:0% +equation if I tried if I tried to assume + + + align:start position:0% +equation if I tried if I tried to assume +if I if I try e to the T it will fail + + align:start position:0% +if I if I try e to the T it will fail + + + align:start position:0% +if I if I try e to the T it will fail +try + + align:start position:0% +try + + + align:start position:0% +try +i y = some y e to the + + align:start position:0% +i y = some y e to the + + + align:start position:0% +i y = some y e to the +T do you see how that's going to fail if + + align:start position:0% +T do you see how that's going to fail if + + + align:start position:0% +T do you see how that's going to fail if +I put that into the + + align:start position:0% +I put that into the + + + align:start position:0% +I put that into the +equation the second derivative will + + align:start position:0% +equation the second derivative will + + + align:start position:0% +equation the second derivative will +cancel the Y and I have zero on the left + + align:start position:0% +cancel the Y and I have zero on the left + + + align:start position:0% +cancel the Y and I have zero on the left +side failure because that's that's the + + align:start position:0% +side failure because that's that's the + + + align:start position:0% +side failure because that's that's the +case called resonance this is a case of + + align:start position:0% +case called resonance this is a case of + + + align:start position:0% +case called resonance this is a case of +resonance when the form of the right + + align:start position:0% +resonance when the form of the right + + + align:start position:0% +resonance when the form of the right +hand side is a null solution at the same + + align:start position:0% +hand side is a null solution at the same + + + align:start position:0% +hand side is a null solution at the same +time we can't have it can't be a + + align:start position:0% +time we can't have it can't be a + + + align:start position:0% +time we can't have it can't be a +particular + + align:start position:0% +particular + + + align:start position:0% +particular +solution it won't work because it's also + + align:start position:0% +solution it won't work because it's also + + + align:start position:0% +solution it won't work because it's also +a null solution and do you remember how + + align:start position:0% +a null solution and do you remember how + + + align:start position:0% +a null solution and do you remember how +to escape resonance how to deal with + + align:start position:0% +to escape resonance how to deal with + + + align:start position:0% +to escape resonance how to deal with +resonance what happens with resonance + + align:start position:0% +resonance what happens with resonance + + + align:start position:0% +resonance what happens with resonance +the solution is a little more + + align:start position:0% +the solution is a little more + + + align:start position:0% +the solution is a little more +complicated but it fits everything here + + align:start position:0% +complicated but it fits everything here + + + align:start position:0% +complicated but it fits everything here +we have to assume to allow a t we have + + align:start position:0% +we have to assume to allow a t we have + + + align:start position:0% +we have to assume to allow a t we have +to allow a t so instead of this multiple + + align:start position:0% +to allow a t so instead of this multiple + + + align:start position:0% +to allow a t so instead of this multiple +of the and and and in this thing we have + + align:start position:0% +of the and and and in this thing we have + + + align:start position:0% +of the and and and in this thing we have +to allow so I'm going to + + align:start position:0% + + + + align:start position:0% + +assume I have to have I I need a t in + + align:start position:0% +assume I have to have I I need a t in + + + align:start position:0% +assume I have to have I I need a t in +there oh no I actually I don't know I + + align:start position:0% +there oh no I actually I don't know I + + + align:start position:0% +there oh no I actually I don't know I +just need uh a t that would do it that + + align:start position:0% +just need uh a t that would do it that + + + align:start position:0% +just need uh a t that would do it that +would do it when when there's + + align:start position:0% +would do it when when there's + + + align:start position:0% +would do it when when there's +resonance take your take the form you + + align:start position:0% +resonance take your take the form you + + + align:start position:0% +resonance take your take the form you +would normally + + align:start position:0% +would normally + + + align:start position:0% +would normally +assume but and and multiply by that + + align:start position:0% +assume but and and multiply by that + + + align:start position:0% +assume but and and multiply by that +extra Factor t + + align:start position:0% +extra Factor t + + + align:start position:0% +extra Factor t +then when I substitute that into the + + align:start position:0% +then when I substitute that into the + + + align:start position:0% +then when I substitute that into the +differential equation I'll find y quite + + align:start position:0% +differential equation I'll find y quite + + + align:start position:0% +differential equation I'll find y quite +safely I'll find why entirely safely + + align:start position:0% +safely I'll find why entirely safely + + + align:start position:0% +safely I'll find why entirely safely +shall I do that so that's the resonant + + align:start position:0% +shall I do that so that's the resonant + + + align:start position:0% +shall I do that so that's the resonant +case the sort of special situation when + + align:start position:0% +case the sort of special situation when + + + align:start position:0% +case the sort of special situation when +when e to the T solved + + align:start position:0% +when e to the T solved + + + align:start position:0% +when e to the T solved +this so we need something new and the + + align:start position:0% +this so we need something new and the + + + align:start position:0% +this so we need something new and the +way we get the right new thing is to + + align:start position:0% +way we get the right new thing is to + + + align:start position:0% +way we get the right new thing is to +have a t in there so when I plug that in + + align:start position:0% +have a t in there so when I plug that in + + + align:start position:0% +have a t in there so when I plug that in +I take the second derivative of that + + align:start position:0% +I take the second derivative of that + + + align:start position:0% +I take the second derivative of that +that subtract off that itself match e to + + align:start position:0% +that subtract off that itself match e to + + + align:start position:0% +that subtract off that itself match e to +the T and that will tell me the number + + align:start position:0% +the T and that will tell me the number + + + align:start position:0% +the T and that will tell me the number +y perhaps it's one2 or one I I won't do + + align:start position:0% +y perhaps it's one2 or one I I won't do + + + align:start position:0% +y perhaps it's one2 or one I I won't do +it uh maybe I leave that as an + + align:start position:0% +it uh maybe I leave that as an + + + align:start position:0% +it uh maybe I leave that as an +exercise put that into the equation and + + align:start position:0% +exercise put that into the equation and + + + align:start position:0% +exercise put that into the equation and +determine the number capital Y okay let + + align:start position:0% +determine the number capital Y okay let + + + align:start position:0% +determine the number capital Y okay let +me pull it together so we have certain + + align:start position:0% +me pull it together so we have certain + + + align:start position:0% +me pull it together so we have certain +nice functions which we're going to see + + align:start position:0% +nice functions which we're going to see + + + align:start position:0% +nice functions which we're going to see +again because nice every method is works + + align:start position:0% +again because nice every method is works + + + align:start position:0% +again because nice every method is works +well for these functions and these + + align:start position:0% +well for these functions and these + + + align:start position:0% +well for these functions and these +functions are + + align:start position:0% +functions are + + + align:start position:0% +functions are +exponentials pols or polinomial times + + align:start position:0% +exponentials pols or polinomial times + + + align:start position:0% +exponentials pols or polinomial times +exponentials and within exponentials I + + align:start position:0% +exponentials and within exponentials I + + + align:start position:0% +exponentials and within exponentials I +include s and cosine and for those + + align:start position:0% +include s and cosine and for those + + + align:start position:0% +include s and cosine and for those +functions we know the + + align:start position:0% +functions we know the + + + align:start position:0% +functions we know the +form we plug it into the equation we + + align:start position:0% +form we plug it into the equation we + + + align:start position:0% +form we plug it into the equation we +make it match choose the we choose these + + align:start position:0% +make it match choose the we choose these + + + align:start position:0% +make it match choose the we choose these +undetermined coefficients we determine + + align:start position:0% +undetermined coefficients we determine + + + align:start position:0% +undetermined coefficients we determine +them so that they solve the equation and + + align:start position:0% +them so that they solve the equation and + + + align:start position:0% +them so that they solve the equation and +then we've got a particular solution so + + align:start position:0% +then we've got a particular solution so + + + align:start position:0% +then we've got a particular solution so +that's this is + + align:start position:0% +that's this is + + + align:start position:0% +that's this is +the best + + align:start position:0% +the best + + + align:start position:0% +the best +equations uh to solve to find particular + + align:start position:0% +equations uh to solve to find particular + + + align:start position:0% +equations uh to solve to find particular +Solutions just by knowing the right form + + align:start position:0% +Solutions just by knowing the right form + + + align:start position:0% +Solutions just by knowing the right form +and finding the constants that that come + + align:start position:0% +and finding the constants that that come + + + align:start position:0% +and finding the constants that that come +out of the particular of the particular + + align:start position:0% +out of the particular of the particular + + + align:start position:0% +out of the particular of the particular +equation okay all good thanks \ No newline at end of file diff --git a/mVqLF6FU1-o.txt b/mVqLF6FU1-o.txt new file mode 100644 index 0000000000000000000000000000000000000000..be476e09e5c3f0095e6fe9fdd5e50109dbfb67d8 --- /dev/null +++ b/mVqLF6FU1-o.txt @@ -0,0 +1,13475 @@ +align:start position:0% + +good evening and welcome to exploring + + align:start position:0% +good evening and welcome to exploring + + + align:start position:0% +good evening and welcome to exploring +black holes today we're delighted to + + align:start position:0% +black holes today we're delighted to + + + align:start position:0% +black holes today we're delighted to +have Dr Jeffrey mlenuk of the Harvard + + align:start position:0% +have Dr Jeffrey mlenuk of the Harvard + + + align:start position:0% +have Dr Jeffrey mlenuk of the Harvard +Smithsonian Center for astrophysics to + + align:start position:0% +Smithsonian Center for astrophysics to + + + align:start position:0% +Smithsonian Center for astrophysics to +speak to us on x-ray binaries and the + + align:start position:0% +speak to us on x-ray binaries and the + + + align:start position:0% +speak to us on x-ray binaries and the +search for black holes Dr mcclint talk + + align:start position:0% +search for black holes Dr mcclint talk + + + align:start position:0% +search for black holes Dr mcclint talk +was an MIT graduate student and got his + + align:start position:0% +was an MIT graduate student and got his + + + align:start position:0% +was an MIT graduate student and got his +PhD a little while ago but since that + + align:start position:0% +PhD a little while ago but since that + + + align:start position:0% +PhD a little while ago but since that +time has made a terrific name in the + + align:start position:0% +time has made a terrific name in the + + + align:start position:0% +time has made a terrific name in the +observational search for black holes and + + align:start position:0% +observational search for black holes and + + + align:start position:0% +observational search for black holes and +in fact he did some of the ping work + + align:start position:0% +in fact he did some of the ping work + + + align:start position:0% +in fact he did some of the ping work +that he's going to report on + + align:start position:0% +that he's going to report on + + + align:start position:0% +that he's going to report on +today is the mic + + align:start position:0% +today is the mic + + + align:start position:0% +today is the mic +okay okay just want to make sure that + + align:start position:0% +okay okay just want to make sure that + + + align:start position:0% +okay okay just want to make sure that +we're audible here to the audience uh so + + align:start position:0% +we're audible here to the audience uh so + + + align:start position:0% +we're audible here to the audience uh so +we're delighted that uh Jeff could come + + align:start position:0% +we're delighted that uh Jeff could come + + + align:start position:0% +we're delighted that uh Jeff could come +down from the CFA and he'll be using the + + align:start position:0% +down from the CFA and he'll be using the + + + align:start position:0% +down from the CFA and he'll be using the +transparencies this evening and telling + + align:start position:0% +transparencies this evening and telling + + + align:start position:0% +transparencies this evening and telling +us about the search for black holes in + + align:start position:0% +us about the search for black holes in + + + align:start position:0% +us about the search for black holes in +x-ray binaries welcome + + align:start position:0% +x-ray binaries welcome + + + align:start position:0% +x-ray binaries welcome +Jeff thanks + + align:start position:0% + + + + align:start position:0% + +in this uh short time I can only give + + align:start position:0% +in this uh short time I can only give + + + align:start position:0% +in this uh short time I can only give +you a rough idea of the kinds of things + + align:start position:0% +you a rough idea of the kinds of things + + + align:start position:0% +you a rough idea of the kinds of things +that we do and uh if you want to get the + + align:start position:0% +that we do and uh if you want to get the + + + align:start position:0% +that we do and uh if you want to get the +whole story uh I suggest that you get + + align:start position:0% +whole story uh I suggest that you get + + + align:start position:0% +whole story uh I suggest that you get +this book compact Stellar x-ray sources + + align:start position:0% +this book compact Stellar x-ray sources + + + align:start position:0% +this book compact Stellar x-ray sources +which won't be out till 2004 but the + + align:start position:0% +which won't be out till 2004 but the + + + align:start position:0% +which won't be out till 2004 but the +Articles will be listed in astral pH + + align:start position:0% +Articles will be listed in astral pH + + + align:start position:0% +Articles will be listed in astral pH +this year sometime as they get done mine + + align:start position:0% +this year sometime as they get done mine + + + align:start position:0% +this year sometime as they get done mine +is not yet done but uh these are three + + align:start position:0% +is not yet done but uh these are three + + + align:start position:0% +is not yet done but uh these are three +of the 12 articles in the volume and + + align:start position:0% +of the 12 articles in the volume and + + + align:start position:0% +of the 12 articles in the volume and +they all deal with the kind of material + + align:start position:0% +they all deal with the kind of material + + + align:start position:0% +they all deal with the kind of material +that I'll be talking about today but in + + align:start position:0% +that I'll be talking about today but in + + + align:start position:0% +that I'll be talking about today but in +great detail with all the references and + + align:start position:0% +great detail with all the references and + + + align:start position:0% +great detail with all the references and +all the information so I can only hint + + align:start position:0% +all the information so I can only hint + + + align:start position:0% +all the information so I can only hint +at the the kinds of things we're doing + + align:start position:0% +at the the kinds of things we're doing + + + align:start position:0% +at the the kinds of things we're doing +in the short time that that I have + + align:start position:0% + + + + align:start position:0% + +today we're talking here about Stellar + + align:start position:0% +today we're talking here about Stellar + + + align:start position:0% +today we're talking here about Stellar +Mass black holes which have been formed + + align:start position:0% +Mass black holes which have been formed + + + align:start position:0% +Mass black holes which have been formed +from the collapse of massive stars and + + align:start position:0% +from the collapse of massive stars and + + + align:start position:0% +from the collapse of massive stars and +uh there beli to be about 10 e8th to 10 + + align:start position:0% +uh there beli to be about 10 e8th to 10 + + + align:start position:0% +uh there beli to be about 10 e8th to 10 +the 9th of these in the Galaxy out of 10 + + align:start position:0% +the 9th of these in the Galaxy out of 10 + + + align:start position:0% +the 9th of these in the Galaxy out of 10 +the 11 Stars so you can see that there's + + align:start position:0% +the 11 Stars so you can see that there's + + + align:start position:0% +the 11 Stars so you can see that there's +a very large number of these objects and + + align:start position:0% +a very large number of these objects and + + + align:start position:0% +a very large number of these objects and +uh we only know about a very small + + align:start position:0% +uh we only know about a very small + + + align:start position:0% +uh we only know about a very small +number which I'll come to here in a + + align:start position:0% +number which I'll come to here in a + + + align:start position:0% +number which I'll come to here in a +moment uh we believe that about a + + align:start position:0% +moment uh we believe that about a + + + align:start position:0% +moment uh we believe that about a +thousand of these are in Mass exchange + + align:start position:0% +thousand of these are in Mass exchange + + + align:start position:0% +thousand of these are in Mass exchange +binaries meaning that the black hole is + + align:start position:0% +binaries meaning that the black hole is + + + align:start position:0% +binaries meaning that the black hole is +close enough to an ordinary star that + + align:start position:0% +close enough to an ordinary star that + + + align:start position:0% +close enough to an ordinary star that +the ordinary star can deposit matter + + align:start position:0% +the ordinary star can deposit matter + + + align:start position:0% +the ordinary star can deposit matter +over onto the black hole and when that + + align:start position:0% +over onto the black hole and when that + + + align:start position:0% +over onto the black hole and when that +happens we see x-rays we see uh very + + align:start position:0% +happens we see x-rays we see uh very + + + align:start position:0% +happens we see x-rays we see uh very +energetic light from the material + + align:start position:0% +energetic light from the material + + + align:start position:0% +energetic light from the material +falling into the deep gravitational + + align:start position:0% +falling into the deep gravitational + + + align:start position:0% +falling into the deep gravitational +potential well of the black hole and uh + + align:start position:0% +potential well of the black hole and uh + + + align:start position:0% +potential well of the black hole and uh +of these thousand that are believed to + + align:start position:0% +of these thousand that are believed to + + + align:start position:0% +of these thousand that are believed to +be in these close Mass exchange binaries + + align:start position:0% +be in these close Mass exchange binaries + + + align:start position:0% +be in these close Mass exchange binaries +most of them are dormant so we haven't + + align:start position:0% +most of them are dormant so we haven't + + + align:start position:0% +most of them are dormant so we haven't +seen them go off yet and the time + + align:start position:0% +seen them go off yet and the time + + + align:start position:0% +seen them go off yet and the time +between when they go off it's maybe 100 + + align:start position:0% +between when they go off it's maybe 100 + + + align:start position:0% +between when they go off it's maybe 100 +years 200 years no one knows quite what + + align:start position:0% +years 200 years no one knows quite what + + + align:start position:0% +years 200 years no one knows quite what +the duty cycle is and they're only on + + align:start position:0% +the duty cycle is and they're only on + + + align:start position:0% +the duty cycle is and they're only on +for a year or so they're transient + + align:start position:0% +for a year or so they're transient + + + align:start position:0% +for a year or so they're transient +systems and the number that we've + + align:start position:0% +systems and the number that we've + + + align:start position:0% +systems and the number that we've +measured the masses in which is really + + align:start position:0% +measured the masses in which is really + + + align:start position:0% +measured the masses in which is really +the most important uh set of subset of + + align:start position:0% +the most important uh set of subset of + + + align:start position:0% +the most important uh set of subset of +these objects are 18 objects and uh I'll + + align:start position:0% +these objects are 18 objects and uh I'll + + + align:start position:0% +these objects are 18 objects and uh I'll +come back to this a little later now + + align:start position:0% +come back to this a little later now + + + align:start position:0% +come back to this a little later now +there's there's these black holes have a + + align:start position:0% +there's there's these black holes have a + + + align:start position:0% +there's there's these black holes have a +lot of significance to astronomy uh you + + align:start position:0% +lot of significance to astronomy uh you + + + align:start position:0% +lot of significance to astronomy uh you +know they're they're obviously an + + align:start position:0% +know they're they're obviously an + + + align:start position:0% +know they're they're obviously an +endpoint of Stellar Evolution um they're + + align:start position:0% +endpoint of Stellar Evolution um they're + + + align:start position:0% +endpoint of Stellar Evolution um they're +very important to people who compute + + align:start position:0% +very important to people who compute + + + align:start position:0% +very important to people who compute +Supernova explosions because it's very + + align:start position:0% +Supernova explosions because it's very + + + align:start position:0% +Supernova explosions because it's very +hard to do that and you'd like to know + + align:start position:0% +hard to do that and you'd like to know + + + align:start position:0% +hard to do that and you'd like to know +what the mass of the remnants are the + + align:start position:0% +what the mass of the remnants are the + + + align:start position:0% +what the mass of the remnants are the +black holes that are formed so we + + align:start position:0% +black holes that are formed so we + + + align:start position:0% +black holes that are formed so we +measure the masses of these that gives a + + align:start position:0% +measure the masses of these that gives a + + + align:start position:0% +measure the masses of these that gives a +constraint on those kinds of models and + + align:start position:0% +constraint on those kinds of models and + + + align:start position:0% +constraint on those kinds of models and +the stars that form these black holes + + align:start position:0% +the stars that form these black holes + + + align:start position:0% +the stars that form these black holes +also spew a lot of enriched material + + align:start position:0% +also spew a lot of enriched material + + + align:start position:0% +also spew a lot of enriched material +into the um interstellar medium so it's + + align:start position:0% +into the um interstellar medium so it's + + + align:start position:0% +into the um interstellar medium so it's +very important to what's called + + align:start position:0% +very important to what's called + + + align:start position:0% +very important to what's called +cosmochemistry as well I could go into + + align:start position:0% +cosmochemistry as well I could go into + + + align:start position:0% +cosmochemistry as well I could go into +all of those things too but I'm going to + + align:start position:0% +all of those things too but I'm going to + + + align:start position:0% +all of those things too but I'm going to +skip all of that because I know this is + + align:start position:0% +skip all of that because I know this is + + + align:start position:0% +skip all of that because I know this is +a course in general relativity so I'll + + align:start position:0% +a course in general relativity so I'll + + + align:start position:0% +a course in general relativity so I'll +cut right to this significance of black + + align:start position:0% +cut right to this significance of black + + + align:start position:0% +cut right to this significance of black +holes to physics because the + + align:start position:0% +holes to physics because the + + + align:start position:0% +holes to physics because the +significance of these black holes to + + align:start position:0% +significance of these black holes to + + + align:start position:0% +significance of these black holes to +physics is that we may be able to make a + + align:start position:0% +physics is that we may be able to make a + + + align:start position:0% +physics is that we may be able to make a +test of general relativity in the strong + + align:start position:0% +test of general relativity in the strong + + + align:start position:0% +test of general relativity in the strong +field gravitational limit and that's the + + align:start position:0% +field gravitational limit and that's the + + + align:start position:0% +field gravitational limit and that's the +importance of these black holes at least + + align:start position:0% +importance of these black holes at least + + + align:start position:0% +importance of these black holes at least +for this evening's discussion + + align:start position:0% +for this evening's discussion + + + align:start position:0% +for this evening's discussion +now there's two kinds of black holes uh + + align:start position:0% +now there's two kinds of black holes uh + + + align:start position:0% +now there's two kinds of black holes uh +well there's more than two of course + + align:start position:0% +well there's more than two of course + + + align:start position:0% +well there's more than two of course +there's a gradiation between them but + + align:start position:0% +there's a gradiation between them but + + + align:start position:0% +there's a gradiation between them but +the Schwarz seal black hole is an + + align:start position:0% +the Schwarz seal black hole is an + + + align:start position:0% +the Schwarz seal black hole is an +idealization it's a black hole it isn't + + align:start position:0% +idealization it's a black hole it isn't + + + align:start position:0% +idealization it's a black hole it isn't +rotating at all and I'm sure you've had + + align:start position:0% +rotating at all and I'm sure you've had + + + align:start position:0% +rotating at all and I'm sure you've had +this in your course and this parameter a + + align:start position:0% +this in your course and this parameter a + + + align:start position:0% +this in your course and this parameter a +star indicates how much rotation there + + align:start position:0% +star indicates how much rotation there + + + align:start position:0% +star indicates how much rotation there +is and it goes from zero to one for an + + align:start position:0% +is and it goes from zero to one for an + + + align:start position:0% +is and it goes from zero to one for an +extreme Cur black hole it's one but all + + align:start position:0% +extreme Cur black hole it's one but all + + + align:start position:0% +extreme Cur black hole it's one but all +any black hole might be anywhere in + + align:start position:0% +any black hole might be anywhere in + + + align:start position:0% +any black hole might be anywhere in +between zero and one in terms of this + + align:start position:0% +between zero and one in terms of this + + + align:start position:0% +between zero and one in terms of this +parameter it's just a dimensionless + + align:start position:0% +parameter it's just a dimensionless + + + align:start position:0% +parameter it's just a dimensionless +measure of the angular momentum of the + + align:start position:0% +measure of the angular momentum of the + + + align:start position:0% +measure of the angular momentum of the +black hole and + + align:start position:0% +black hole and + + + align:start position:0% +black hole and +if you take a short Shield black hole + + align:start position:0% +if you take a short Shield black hole + + + align:start position:0% +if you take a short Shield black hole +well I've just said let's make it 10 + + align:start position:0% +well I've just said let's make it 10 + + + align:start position:0% +well I've just said let's make it 10 +solar masses you'll see that's a very + + align:start position:0% +solar masses you'll see that's a very + + + align:start position:0% +solar masses you'll see that's a very +typical mass for the masses that we + + align:start position:0% +typical mass for the masses that we + + + align:start position:0% +typical mass for the masses that we +measure for these black holes then the + + align:start position:0% +measure for these black holes then the + + + align:start position:0% +measure for these black holes then the +radius of that black hole is just 30 km + + align:start position:0% +radius of that black hole is just 30 km + + + align:start position:0% +radius of that black hole is just 30 km +and it scales directly with a mass so so + + align:start position:0% +and it scales directly with a mass so so + + + align:start position:0% +and it scales directly with a mass so so +it just gives you a feeling for the size + + align:start position:0% +it just gives you a feeling for the size + + + align:start position:0% +it just gives you a feeling for the size +uh there is a last stable orbit as you + + align:start position:0% +uh there is a last stable orbit as you + + + align:start position:0% +uh there is a last stable orbit as you +get into the strong gravitational field + + align:start position:0% +get into the strong gravitational field + + + align:start position:0% +get into the strong gravitational field +I don't know whether you've covered of + + align:start position:0% +I don't know whether you've covered of + + + align:start position:0% +I don't know whether you've covered of +this in the course but it's out of three + + align:start position:0% +this in the course but it's out of three + + + align:start position:0% +this in the course but it's out of three +schw Shield radi and inside there there + + align:start position:0% +schw Shield radi and inside there there + + + align:start position:0% +schw Shield radi and inside there there +are no stable orbits the material + + align:start position:0% +are no stable orbits the material + + + align:start position:0% +are no stable orbits the material +tumbles in quickly so that's really + + align:start position:0% +tumbles in quickly so that's really + + + align:start position:0% +tumbles in quickly so that's really +where we see an accretion disc of + + align:start position:0% +where we see an accretion disc of + + + align:start position:0% +where we see an accretion disc of +material which I'll come to in a moment + + align:start position:0% +material which I'll come to in a moment + + + align:start position:0% +material which I'll come to in a moment +as as it being terminated on the inside + + align:start position:0% +as as it being terminated on the inside + + + align:start position:0% +as as it being terminated on the inside +at three short Shield radi for an + + align:start position:0% +at three short Shield radi for an + + + align:start position:0% +at three short Shield radi for an +extreme curve black hole the numbers are + + align:start position:0% +extreme curve black hole the numbers are + + + align:start position:0% +extreme curve black hole the numbers are +uh shown here again I say 10 solar + + align:start position:0% +uh shown here again I say 10 solar + + + align:start position:0% +uh shown here again I say 10 solar +masses just for illustration and the + + align:start position:0% +masses just for illustration and the + + + align:start position:0% +masses just for illustration and the +radius of the Event Horizon in this case + + align:start position:0% +radius of the Event Horizon in this case + + + align:start position:0% +radius of the Event Horizon in this case +is 15 kmers half of what it is here and + + align:start position:0% +is 15 kmers half of what it is here and + + + align:start position:0% +is 15 kmers half of what it is here and +obviously then you can uh well then even + + align:start position:0% +obviously then you can uh well then even + + + align:start position:0% +obviously then you can uh well then even +even more important the last stable + + align:start position:0% +even more important the last stable + + + align:start position:0% +even more important the last stable +orbit prograde orbit for the Black Hole + + align:start position:0% +orbit prograde orbit for the Black Hole + + + align:start position:0% +orbit prograde orbit for the Black Hole +uh material orbiting in the same sense + + align:start position:0% +uh material orbiting in the same sense + + + align:start position:0% +uh material orbiting in the same sense +as the hole is rotating is also 15 km so + + align:start position:0% +as the hole is rotating is also 15 km so + + + align:start position:0% +as the hole is rotating is also 15 km so +this is a very uh the point is you can + + align:start position:0% +this is a very uh the point is you can + + + align:start position:0% +this is a very uh the point is you can +get a disc going right on down into the + + align:start position:0% +get a disc going right on down into the + + + align:start position:0% +get a disc going right on down into the +very deep gravitational potential well + + align:start position:0% +very deep gravitational potential well + + + align:start position:0% +very deep gravitational potential well +much more so than you can in the case of + + align:start position:0% +much more so than you can in the case of + + + align:start position:0% +much more so than you can in the case of +the Schwarz Shield black hole so you can + + align:start position:0% +the Schwarz Shield black hole so you can + + + align:start position:0% +the Schwarz Shield black hole so you can +expect you know much greater uh energy + + align:start position:0% +expect you know much greater uh energy + + + align:start position:0% +expect you know much greater uh energy +releases here and the energy release + + align:start position:0% +releases here and the energy release + + + align:start position:0% +releases here and the energy release +Here can be 6% of MC squ when you drop + + align:start position:0% +Here can be 6% of MC squ when you drop + + + align:start position:0% +Here can be 6% of MC squ when you drop +material in you can get six % of the + + align:start position:0% +material in you can get six % of the + + + align:start position:0% +material in you can get six % of the +energy out here you can get up to + + align:start position:0% +energy out here you can get up to + + + align:start position:0% +energy out here you can get up to +42% + + align:start position:0% +42% + + + align:start position:0% +42% +theoretically a very important number + + align:start position:0% +theoretically a very important number + + + align:start position:0% +theoretically a very important number +for the kind of thing we'll come back to + + align:start position:0% +for the kind of thing we'll come back to + + + align:start position:0% +for the kind of thing we'll come back to +in a moment is that the maximum + + align:start position:0% +in a moment is that the maximum + + + align:start position:0% +in a moment is that the maximum +frequency in this last stable orbit here + + align:start position:0% +frequency in this last stable orbit here + + + align:start position:0% +frequency in this last stable orbit here +is 220 Herz for a 10 solar mass black + + align:start position:0% +is 220 Herz for a 10 solar mass black + + + align:start position:0% +is 220 Herz for a 10 solar mass black +hole and this scales inversely as the + + align:start position:0% +hole and this scales inversely as the + + + align:start position:0% +hole and this scales inversely as the +mass so the more massive the black hole + + align:start position:0% +mass so the more massive the black hole + + + align:start position:0% +mass so the more massive the black hole +the larger it is the slower will be the + + align:start position:0% +the larger it is the slower will be the + + + align:start position:0% +the larger it is the slower will be the +orbit so this is for a 10 solar mass + + align:start position:0% +orbit so this is for a 10 solar mass + + + align:start position:0% +orbit so this is for a 10 solar mass +black hole and for an extreme Cur hole + + align:start position:0% +black hole and for an extreme Cur hole + + + align:start position:0% +black hole and for an extreme Cur hole +you see you can get the much higher + + align:start position:0% +you see you can get the much higher + + + align:start position:0% +you see you can get the much higher +frequency so that's something we can + + align:start position:0% +frequency so that's something we can + + + align:start position:0% +frequency so that's something we can +measure we can hope to measure and I'll + + align:start position:0% +measure we can hope to measure and I'll + + + align:start position:0% +measure we can hope to measure and I'll +show you that we have some evidence of + + align:start position:0% +show you that we have some evidence of + + + align:start position:0% +show you that we have some evidence of +measuring it which is very + + align:start position:0% + + + + align:start position:0% + +important now I just want to remind you + + align:start position:0% +important now I just want to remind you + + + align:start position:0% +important now I just want to remind you +so this won't be completely abstract + + align:start position:0% +so this won't be completely abstract + + + align:start position:0% +so this won't be completely abstract +that these black holes just come from o + + align:start position:0% +that these black holes just come from o + + + align:start position:0% +that these black holes just come from o +stars and this + + align:start position:0% +stars and this + + + align:start position:0% +stars and this +is they come from massive stars like 40 + + align:start position:0% +is they come from massive stars like 40 + + + align:start position:0% +is they come from massive stars like 40 +solar masses 30 40 50 solar masses and + + align:start position:0% +solar masses 30 40 50 solar masses and + + + align:start position:0% +solar masses 30 40 50 solar masses and +such Stars only last a couple a couple + + align:start position:0% +such Stars only last a couple a couple + + + align:start position:0% +such Stars only last a couple a couple +million years this is a cluster of them + + align:start position:0% +million years this is a cluster of them + + + align:start position:0% +million years this is a cluster of them +here a few hundred oars in 30 dadus + + align:start position:0% +here a few hundred oars in 30 dadus + + + align:start position:0% +here a few hundred oars in 30 dadus +which is in the large mag cloud and + + align:start position:0% +which is in the large mag cloud and + + + align:start position:0% +which is in the large mag cloud and +those Stars don't last any longer than + + align:start position:0% +those Stars don't last any longer than + + + align:start position:0% +those Stars don't last any longer than +you know humans have been on the earth I + + align:start position:0% +you know humans have been on the earth I + + + align:start position:0% +you know humans have been on the earth I +mean a couple million years which is + + align:start position:0% +mean a couple million years which is + + + align:start position:0% +mean a couple million years which is +really nothing in astronomy and of + + align:start position:0% +really nothing in astronomy and of + + + align:start position:0% +really nothing in astronomy and of +course when they've burnt their fuel out + + align:start position:0% +course when they've burnt their fuel out + + + align:start position:0% +course when they've burnt their fuel out +they collapse and they may shed a lot of + + align:start position:0% +they collapse and they may shed a lot of + + + align:start position:0% +they collapse and they may shed a lot of +material as wind before they collapse + + align:start position:0% +material as wind before they collapse + + + align:start position:0% +material as wind before they collapse +and they may also produce a violent + + align:start position:0% +and they may also produce a violent + + + align:start position:0% +and they may also produce a violent +explosion that blows a lot of material + + align:start position:0% +explosion that blows a lot of material + + + align:start position:0% +explosion that blows a lot of material +out into the interstellar medium but + + align:start position:0% +out into the interstellar medium but + + + align:start position:0% +out into the interstellar medium but +this core goes on down and nothing can + + align:start position:0% +this core goes on down and nothing can + + + align:start position:0% +this core goes on down and nothing can +stop it and you get complete + + align:start position:0% +stop it and you get complete + + + align:start position:0% +stop it and you get complete +gravitational collapse of matter into a + + align:start position:0% +gravitational collapse of matter into a + + + align:start position:0% +gravitational collapse of matter into a +singularity and it's cloaked of course + + align:start position:0% +singularity and it's cloaked of course + + + align:start position:0% +singularity and it's cloaked of course +in this event horizon so that's where + + align:start position:0% +in this event horizon so that's where + + + align:start position:0% +in this event horizon so that's where +they come from that's where the 100 + + align:start position:0% +they come from that's where the 100 + + + align:start position:0% +they come from that's where the 100 +million to a billion come from and there + + align:start position:0% +million to a billion come from and there + + + align:start position:0% +million to a billion come from and there +aren't very many oars in the Galaxy just + + align:start position:0% +aren't very many oars in the Galaxy just + + + align:start position:0% +aren't very many oars in the Galaxy just +because they don't live very long right + + align:start position:0% +because they don't live very long right + + + align:start position:0% +because they don't live very long right +and uh so they're always being cycled + + align:start position:0% +and uh so they're always being cycled + + + align:start position:0% +and uh so they're always being cycled +born and then dying into black + + align:start position:0% +born and then dying into black + + + align:start position:0% +born and then dying into black +holes now there's there's some + + align:start position:0% +holes now there's there's some + + + align:start position:0% +holes now there's there's some +abstraction to all of this so I brought + + align:start position:0% +abstraction to all of this so I brought + + + align:start position:0% +abstraction to all of this so I brought +one slide that cuts maybe through some + + align:start position:0% +one slide that cuts maybe through some + + + align:start position:0% +one slide that cuts maybe through some +abstraction at least it's one way of + + align:start position:0% +abstraction at least it's one way of + + + align:start position:0% +abstraction at least it's one way of +saying what does it mean you know to go + + align:start position:0% +saying what does it mean you know to go + + + align:start position:0% +saying what does it mean you know to go +to complete gravitational collapse of + + align:start position:0% +to complete gravitational collapse of + + + align:start position:0% +to complete gravitational collapse of +matter I mean I don't think anyone + + align:start position:0% +matter I mean I don't think anyone + + + align:start position:0% +matter I mean I don't think anyone +really has a good feeling for that I + + align:start position:0% +really has a good feeling for that I + + + align:start position:0% +really has a good feeling for that I +mean everything in this room you know + + align:start position:0% +mean everything in this room you know + + + align:start position:0% +mean everything in this room you know +everything uh the oceans the the whole + + align:start position:0% +everything uh the oceans the the whole + + + align:start position:0% +everything uh the oceans the the whole +crust of the Earth the whole earth the + + align:start position:0% +crust of the Earth the whole earth the + + + align:start position:0% +crust of the Earth the whole earth the +whole solar system the whole Sun + + align:start position:0% +whole solar system the whole Sun + + + align:start position:0% +whole solar system the whole Sun +everything going to a point we don't + + align:start position:0% +everything going to a point we don't + + + align:start position:0% +everything going to a point we don't +have too much feeling for that I don't + + align:start position:0% +have too much feeling for that I don't + + + align:start position:0% +have too much feeling for that I don't +think I mean it's it's rather abstract + + align:start position:0% +think I mean it's it's rather abstract + + + align:start position:0% +think I mean it's it's rather abstract +so I have this one illustration that I + + align:start position:0% +so I have this one illustration that I + + + align:start position:0% +so I have this one illustration that I +put in a popular level article one time + + align:start position:0% +put in a popular level article one time + + + align:start position:0% +put in a popular level article one time +which shows uh pressure on this axis for + + align:start position:0% +which shows uh pressure on this axis for + + + align:start position:0% +which shows uh pressure on this axis for +various object objects and it starts at + + align:start position:0% +various object objects and it starts at + + + align:start position:0% +various object objects and it starts at +sea level and this is atmospheres here + + align:start position:0% +sea level and this is atmospheres here + + + align:start position:0% +sea level and this is atmospheres here +so one atmosphere is sea level right + + align:start position:0% +so one atmosphere is sea level right + + + align:start position:0% +so one atmosphere is sea level right +here and then when you're down 200 miles + + align:start position:0% +here and then when you're down 200 miles + + + align:start position:0% +here and then when you're down 200 miles +into the Earth you get pressure of about + + align:start position:0% +into the Earth you get pressure of about + + + align:start position:0% +into the Earth you get pressure of about +a about where diamonds form you get + + align:start position:0% +a about where diamonds form you get + + + align:start position:0% +a about where diamonds form you get +about a million uh atmospheres so forth + + align:start position:0% +about a million uh atmospheres so forth + + + align:start position:0% +about a million uh atmospheres so forth +in the center of the sun you get about + + align:start position:0% +in the center of the sun you get about + + + align:start position:0% +in the center of the sun you get about +10 to the 10th atmospheres center of a + + align:start position:0% +10 to the 10th atmospheres center of a + + + align:start position:0% +10 to the 10th atmospheres center of a +white dwarf center of a neutron star you + + align:start position:0% +white dwarf center of a neutron star you + + + align:start position:0% +white dwarf center of a neutron star you +get 10 to the 28th atmospheres well I + + align:start position:0% +get 10 to the 28th atmospheres well I + + + align:start position:0% +get 10 to the 28th atmospheres well I +don't know how many of you work with + + align:start position:0% +don't know how many of you work with + + + align:start position:0% +don't know how many of you work with +atmospheres but mean a few atmospheres + + align:start position:0% +atmospheres but mean a few atmospheres + + + align:start position:0% +atmospheres but mean a few atmospheres +is all it takes to scare you if you have + + align:start position:0% +is all it takes to scare you if you have + + + align:start position:0% +is all it takes to scare you if you have +something a pressure vessel or something + + align:start position:0% +something a pressure vessel or something + + + align:start position:0% +something a pressure vessel or something +and it's it's had a few atmospheres and + + align:start position:0% +and it's it's had a few atmospheres and + + + align:start position:0% +and it's it's had a few atmospheres and +a window might break and it can be kind + + align:start position:0% +a window might break and it can be kind + + + align:start position:0% +a window might break and it can be kind +of violent or if you've ever pumped + + align:start position:0% +of violent or if you've ever pumped + + + align:start position:0% +of violent or if you've ever pumped +water up 5,000 feet up a hill or + + align:start position:0% +water up 5,000 feet up a hill or + + + align:start position:0% +water up 5,000 feet up a hill or +something and you just have to deal with + + align:start position:0% +something and you just have to deal with + + + align:start position:0% +something and you just have to deal with +you know the seals and the pumps and so + + align:start position:0% +you know the seals and the pumps and so + + + align:start position:0% +you know the seals and the pumps and so +forth you get a feeling or if you've + + align:start position:0% +forth you get a feeling or if you've + + + align:start position:0% +forth you get a feeling or if you've +ever seen material that's been crushed + + align:start position:0% +ever seen material that's been crushed + + + align:start position:0% +ever seen material that's been crushed +in a deep submersible in in the ocean or + + align:start position:0% +in a deep submersible in in the ocean or + + + align:start position:0% +in a deep submersible in in the ocean or +something at 30,000 ft you get some idea + + align:start position:0% +something at 30,000 ft you get some idea + + + align:start position:0% +something at 30,000 ft you get some idea +for pressure at 10 to the 28th + + align:start position:0% +for pressure at 10 to the 28th + + + align:start position:0% +for pressure at 10 to the 28th +atmospheres uh it's an incredible + + align:start position:0% +atmospheres uh it's an incredible + + + align:start position:0% +atmospheres uh it's an incredible +pressure but that's the pressure that's + + align:start position:0% +pressure but that's the pressure that's + + + align:start position:0% +pressure but that's the pressure that's +pushing on the center of a neutron star + + align:start position:0% +pushing on the center of a neutron star + + + align:start position:0% +pushing on the center of a neutron star +and the problem of course is that that + + align:start position:0% +and the problem of course is that that + + + align:start position:0% +and the problem of course is that that +pressure is so great that it's at the + + align:start position:0% +pressure is so great that it's at the + + + align:start position:0% +pressure is so great that it's at the +point where it's ready to destroy the + + align:start position:0% +point where it's ready to destroy the + + + align:start position:0% +point where it's ready to destroy the +matter and a neutron star is very close + + align:start position:0% +matter and a neutron star is very close + + + align:start position:0% +matter and a neutron star is very close +to going under and into a black hole and + + align:start position:0% +to going under and into a black hole and + + + align:start position:0% +to going under and into a black hole and +in fact there is some limiting mass of a + + align:start position:0% +in fact there is some limiting mass of a + + + align:start position:0% +in fact there is some limiting mass of a +neutron star not well known not really + + align:start position:0% +neutron star not well known not really + + + align:start position:0% +neutron star not well known not really +known but around three solar masses + + align:start position:0% +known but around three solar masses + + + align:start position:0% +known but around three solar masses +perhaps two solar masses where if you + + align:start position:0% +perhaps two solar masses where if you + + + align:start position:0% +perhaps two solar masses where if you +just put a little bit more on it it will + + align:start position:0% +just put a little bit more on it it will + + + align:start position:0% +just put a little bit more on it it will +go because the gravity is so powerful + + align:start position:0% +go because the gravity is so powerful + + + align:start position:0% +go because the gravity is so powerful +and at this point the um pressure force + + align:start position:0% +and at this point the um pressure force + + + align:start position:0% +and at this point the um pressure force +is actually ATT 10 of row C squ so it's + + align:start position:0% +is actually ATT 10 of row C squ so it's + + + align:start position:0% +is actually ATT 10 of row C squ so it's +a tenth of the matter energy density of + + align:start position:0% +a tenth of the matter energy density of + + + align:start position:0% +a tenth of the matter energy density of +the material so it's already very very + + align:start position:0% +the material so it's already very very + + + align:start position:0% +the material so it's already very very +uh significant source of gravitation + + align:start position:0% +uh significant source of gravitation + + + align:start position:0% +uh significant source of gravitation +which is so ironic because it's the + + align:start position:0% +which is so ironic because it's the + + + align:start position:0% +which is so ironic because it's the +thing you count on for holding the star + + align:start position:0% +thing you count on for holding the star + + + align:start position:0% +thing you count on for holding the star +out the pressure Force but now it's + + align:start position:0% +out the pressure Force but now it's + + + align:start position:0% +out the pressure Force but now it's +gravitating at about a tenth of what the + + align:start position:0% +gravitating at about a tenth of what the + + + align:start position:0% +gravitating at about a tenth of what the +mass is in the star itself just because + + align:start position:0% +mass is in the star itself just because + + + align:start position:0% +mass is in the star itself just because +that's it's energy that's holding off + + align:start position:0% +that's it's energy that's holding off + + + align:start position:0% +that's it's energy that's holding off +this this collapse and um so all of a + + align:start position:0% +this this collapse and um so all of a + + + align:start position:0% +this this collapse and um so all of a +sudden the pressure is uh turning + + align:start position:0% +sudden the pressure is uh turning + + + align:start position:0% +sudden the pressure is uh turning +traitorous by making this because it's + + align:start position:0% +traitorous by making this because it's + + + align:start position:0% +traitorous by making this because it's +got energy it's got mass and it's + + align:start position:0% +got energy it's got mass and it's + + + align:start position:0% +got energy it's got mass and it's +causing so you say okay well let's just + + align:start position:0% +causing so you say okay well let's just + + + align:start position:0% +causing so you say okay well let's just +crank up the pressure a little more but + + align:start position:0% +crank up the pressure a little more but + + + align:start position:0% +crank up the pressure a little more but +if you crank up the pressure to stop the + + align:start position:0% +if you crank up the pressure to stop the + + + align:start position:0% +if you crank up the pressure to stop the +collapse of course you're just producing + + align:start position:0% +collapse of course you're just producing + + + align:start position:0% +collapse of course you're just producing +more gravitating matter by E equals mc^2 + + align:start position:0% +more gravitating matter by E equals mc^2 + + + align:start position:0% +more gravitating matter by E equals mc^2 +the energy and the pressure field so + + align:start position:0% +the energy and the pressure field so + + + align:start position:0% +the energy and the pressure field so +it's and you see this if you look in the + + align:start position:0% +it's and you see this if you look in the + + + align:start position:0% +it's and you see this if you look in the +Oppenheimer vov equation maybe you've + + align:start position:0% +Oppenheimer vov equation maybe you've + + + align:start position:0% +Oppenheimer vov equation maybe you've +had that the equation for hydrostatic + + align:start position:0% +had that the equation for hydrostatic + + + align:start position:0% +had that the equation for hydrostatic +equilibrium in general relativity so + + align:start position:0% +equilibrium in general relativity so + + + align:start position:0% +equilibrium in general relativity so +it's uh it's it's really really very uh + + align:start position:0% +it's uh it's it's really really very uh + + + align:start position:0% +it's uh it's it's really really very uh +very difficult and I obviously I don't + + align:start position:0% +very difficult and I obviously I don't + + + align:start position:0% +very difficult and I obviously I don't +put the black hole on here because we + + align:start position:0% +put the black hole on here because we + + + align:start position:0% +put the black hole on here because we +don't speak of the pressure it's + + align:start position:0% +don't speak of the pressure it's + + + align:start position:0% +don't speak of the pressure it's +unspeakable it's off the graph + + align:start position:0% +unspeakable it's off the graph + + + align:start position:0% +unspeakable it's off the graph +totally now I'll start talking about the + + align:start position:0% +totally now I'll start talking about the + + + align:start position:0% +totally now I'll start talking about the +black hole binaries which are the + + align:start position:0% +black hole binaries which are the + + + align:start position:0% +black hole binaries which are the +objects that I work on and this is a + + align:start position:0% +objects that I work on and this is a + + + align:start position:0% +objects that I work on and this is a +schematic drawing sort of an anatomy of + + align:start position:0% +schematic drawing sort of an anatomy of + + + align:start position:0% +schematic drawing sort of an anatomy of +one of + + align:start position:0% +one of + + + align:start position:0% +one of +these + + align:start position:0% +these + + + align:start position:0% +these +and this is a sort of a typical one I'll + + align:start position:0% +and this is a sort of a typical one I'll + + + align:start position:0% +and this is a sort of a typical one I'll +show you schematic that shows 14 of + + align:start position:0% +show you schematic that shows 14 of + + + align:start position:0% +show you schematic that shows 14 of +these objects but this is just one of + + align:start position:0% +these objects but this is just one of + + + align:start position:0% +these objects but this is just one of +them and what you have here is a star + + align:start position:0% +them and what you have here is a star + + + align:start position:0% +them and what you have here is a star +that's tily distorted an ordinary star + + align:start position:0% +that's tily distorted an ordinary star + + + align:start position:0% +that's tily distorted an ordinary star +like the sun tightly distorted by the + + align:start position:0% +like the sun tightly distorted by the + + + align:start position:0% +like the sun tightly distorted by the +gravity of the black hole which is here + + align:start position:0% +gravity of the black hole which is here + + + align:start position:0% +gravity of the black hole which is here +in the center of this disc which is an + + align:start position:0% +in the center of this disc which is an + + + align:start position:0% +in the center of this disc which is an +accretion disc so what one imagines is + + align:start position:0% +accretion disc so what one imagines is + + + align:start position:0% +accretion disc so what one imagines is +material flows through from this inner + + align:start position:0% +material flows through from this inner + + + align:start position:0% +material flows through from this inner +lran point here and flows on to the + + align:start position:0% +lran point here and flows on to the + + + align:start position:0% +lran point here and flows on to the +secretion disc and goes into orbits and + + align:start position:0% +secretion disc and goes into orbits and + + + align:start position:0% +secretion disc and goes into orbits and +finally winds its way down into the + + align:start position:0% +finally winds its way down into the + + + align:start position:0% +finally winds its way down into the +center of the black hole so this is for + + align:start position:0% +center of the black hole so this is for + + + align:start position:0% +center of the black hole so this is for +a system with a period of about one day + + align:start position:0% +a system with a period of about one day + + + align:start position:0% +a system with a period of about one day +and again about a 10 solar mass black + + align:start position:0% +and again about a 10 solar mass black + + + align:start position:0% +and again about a 10 solar mass black +hole and uh interestingly the black hole + + align:start position:0% +hole and uh interestingly the black hole + + + align:start position:0% +hole and uh interestingly the black hole +down in the center here I've expanded it + + align:start position:0% +down in the center here I've expanded it + + + align:start position:0% +down in the center here I've expanded it +and shown it here is only about 30 km + + align:start position:0% +and shown it here is only about 30 km + + + align:start position:0% +and shown it here is only about 30 km +across and the ratio of this size the + + align:start position:0% +across and the ratio of this size the + + + align:start position:0% +across and the ratio of this size the +black hole size to the size of this + + align:start position:0% +black hole size to the size of this + + + align:start position:0% +black hole size to the size of this +orbit here is about the ratio of uh of a + + align:start position:0% +orbit here is about the ratio of uh of a + + + align:start position:0% +orbit here is about the ratio of uh of a +uh uh a an an atom to its nucleus you + + align:start position:0% +uh uh a an an atom to its nucleus you + + + align:start position:0% +uh uh a an an atom to its nucleus you +know it's the same 10 the 5th more or + + align:start position:0% +know it's the same 10 the 5th more or + + + align:start position:0% +know it's the same 10 the 5th more or +less that you're familiar with not that + + align:start position:0% +less that you're familiar with not that + + + align:start position:0% +less that you're familiar with not that +that has any connection to this but I + + align:start position:0% +that has any connection to this but I + + + align:start position:0% +that has any connection to this but I +mean it's just the scale is very large + + align:start position:0% +mean it's just the scale is very large + + + align:start position:0% +mean it's just the scale is very large +is what I'm saying that little object in + + align:start position:0% +is what I'm saying that little object in + + + align:start position:0% +is what I'm saying that little object in +the center with t solar masses and of + + align:start position:0% +the center with t solar masses and of + + + align:start position:0% +the center with t solar masses and of +course the object is actually much + + align:start position:0% +course the object is actually much + + + align:start position:0% +course the object is actually much +smaller than this event horizon it's + + align:start position:0% +smaller than this event horizon it's + + + align:start position:0% +smaller than this event horizon it's +something down inside here we don't know + + align:start position:0% +something down inside here we don't know + + + align:start position:0% +something down inside here we don't know +very much about but uh this is the kind + + align:start position:0% +very much about but uh this is the kind + + + align:start position:0% +very much about but uh this is the kind +of object we're we're we're dealing + + align:start position:0% +of object we're we're we're dealing + + + align:start position:0% +of object we're we're we're dealing +with now we've we've measured the masses + + align:start position:0% +with now we've we've measured the masses + + + align:start position:0% +with now we've we've measured the masses +of 18 actually and these are 14 of these + + align:start position:0% +of 18 actually and these are 14 of these + + + align:start position:0% +of 18 actually and these are 14 of these +systems here that I've drawn in on a + + align:start position:0% +systems here that I've drawn in on a + + + align:start position:0% +systems here that I've drawn in on a +picture here actually my colleague Jerry + + align:start position:0% +picture here actually my colleague Jerry + + + align:start position:0% +picture here actually my colleague Jerry +Rose drew them and uh you can see + + align:start position:0% + + + + align:start position:0% + +that that they range from tiny little + + align:start position:0% +that that they range from tiny little + + + align:start position:0% +that that they range from tiny little +systems like this one here these are + + align:start position:0% +systems like this one here these are + + + align:start position:0% +systems like this one here these are +just the same kind of sketches sketch I + + align:start position:0% +just the same kind of sketches sketch I + + + align:start position:0% +just the same kind of sketches sketch I +just showed you with a star and a black + + align:start position:0% +just showed you with a star and a black + + + align:start position:0% +just showed you with a star and a black +hole and this disc of material around + + align:start position:0% +hole and this disc of material around + + + align:start position:0% +hole and this disc of material around +the black hole and this one here for + + align:start position:0% +the black hole and this one here for + + + align:start position:0% +the black hole and this one here for +example has a 4H hour orbital period + + align:start position:0% +example has a 4H hour orbital period + + + align:start position:0% +example has a 4H hour orbital period +this one up here and they're all drawn + + align:start position:0% +this one up here and they're all drawn + + + align:start position:0% +this one up here and they're all drawn +to relative scale here this you know all + + align:start position:0% +to relative scale here this you know all + + + align:start position:0% +to relative scale here this you know all +drawn to schematic relative scale so + + align:start position:0% +drawn to schematic relative scale so + + + align:start position:0% +drawn to schematic relative scale so +this has a 35 day period this is the + + align:start position:0% +this has a 35 day period this is the + + + align:start position:0% +this has a 35 day period this is the +Giant and this is 4our period so this is + + align:start position:0% +Giant and this is 4our period so this is + + + align:start position:0% +Giant and this is 4our period so this is +tiny little system and then you can see + + align:start position:0% +tiny little system and then you can see + + + align:start position:0% +tiny little system and then you can see +they vary in different uh different uh + + align:start position:0% +they vary in different uh different uh + + + align:start position:0% +they vary in different uh different uh +periods here different or the orbital + + align:start position:0% +periods here different or the orbital + + + align:start position:0% +periods here different or the orbital +period pretty much sets the size of the + + align:start position:0% +period pretty much sets the size of the + + + align:start position:0% +period pretty much sets the size of the +system and you can see we we've actually + + align:start position:0% +system and you can see we we've actually + + + align:start position:0% +system and you can see we we've actually +measured the inclination of the orbit + + align:start position:0% +measured the inclination of the orbit + + + align:start position:0% +measured the inclination of the orbit +too so you can see for example this + + align:start position:0% +too so you can see for example this + + + align:start position:0% +too so you can see for example this +system is almost face on as a sketch + + align:start position:0% +system is almost face on as a sketch + + + align:start position:0% +system is almost face on as a sketch +would indicate you're looking right down + + align:start position:0% +would indicate you're looking right down + + + align:start position:0% +would indicate you're looking right down +on the plane of the disc almost in that + + align:start position:0% +on the plane of the disc almost in that + + + align:start position:0% +on the plane of the disc almost in that +system whereas some of them are more + + align:start position:0% +system whereas some of them are more + + + align:start position:0% +system whereas some of them are more +Edge on as you can see here for example + + align:start position:0% +Edge on as you can see here for example + + + align:start position:0% +Edge on as you can see here for example +nearly Ed we don't yet have an eclipsing + + align:start position:0% +nearly Ed we don't yet have an eclipsing + + + align:start position:0% +nearly Ed we don't yet have an eclipsing +system which of course we'd love to have + + align:start position:0% +system which of course we'd love to have + + + align:start position:0% +system which of course we'd love to have +because then you might be able to see + + align:start position:0% +because then you might be able to see + + + align:start position:0% +because then you might be able to see +the star swing in front of the black uh + + align:start position:0% +the star swing in front of the black uh + + + align:start position:0% +the star swing in front of the black uh +of the X-ray emitting region around the + + align:start position:0% +of the X-ray emitting region around the + + + align:start position:0% +of the X-ray emitting region around the +black hole and map out the X-ray + + align:start position:0% +black hole and map out the X-ray + + + align:start position:0% +black hole and map out the X-ray +emitting region around the black hole + + align:start position:0% +emitting region around the black hole + + + align:start position:0% +emitting region around the black hole +with this disc of the star going in + + align:start position:0% +with this disc of the star going in + + + align:start position:0% +with this disc of the star going in +front of it so we're extremely uh + + align:start position:0% +front of it so we're extremely uh + + + align:start position:0% +front of it so we're extremely uh +excited about the possibility of finding + + align:start position:0% +excited about the possibility of finding + + + align:start position:0% +excited about the possibility of finding +such an object uh and I I don't want to + + align:start position:0% +such an object uh and I I don't want to + + + align:start position:0% +such an object uh and I I don't want to +go into that anymore because we are we + + align:start position:0% +go into that anymore because we are we + + + align:start position:0% +go into that anymore because we are we +have some plans in that direction um now + + align:start position:0% +have some plans in that direction um now + + + align:start position:0% +have some plans in that direction um now +just to this is a painting of these + + align:start position:0% +just to this is a painting of these + + + align:start position:0% +just to this is a painting of these +kinds of of things and there's two + + align:start position:0% +kinds of of things and there's two + + + align:start position:0% +kinds of of things and there's two +states of these systems and I'll come to + + align:start position:0% +states of these systems and I'll come to + + + align:start position:0% +states of these systems and I'll come to +that in a moment they get either + + align:start position:0% +that in a moment they get either + + + align:start position:0% +that in a moment they get either +extremely luminous when they go off for + + align:start position:0% +extremely luminous when they go off for + + + align:start position:0% +extremely luminous when they go off for +a year or so and then they get extremely + + align:start position:0% +a year or so and then they get extremely + + + align:start position:0% +a year or so and then they get extremely +faint and when they're faint they remain + + align:start position:0% +faint and when they're faint they remain + + + align:start position:0% +faint and when they're faint they remain +faint for perhaps a 100 years I mean + + align:start position:0% +faint for perhaps a 100 years I mean + + + align:start position:0% +faint for perhaps a 100 years I mean +this one in particular is sketched for a + + align:start position:0% +this one in particular is sketched for a + + + align:start position:0% +this one in particular is sketched for a +particular system I worked on with Ron + + align:start position:0% +particular system I worked on with Ron + + + align:start position:0% +particular system I worked on with Ron +Remillard here at MIT it's called 80620 + + align:start position:0% +Remillard here at MIT it's called 80620 + + + align:start position:0% +Remillard here at MIT it's called 80620 +minus 00 they're all by their coordinate + + align:start position:0% +minus 00 they're all by their coordinate + + + align:start position:0% +minus 00 they're all by their coordinate +names so they're not very pretty names + + align:start position:0% +names so they're not very pretty names + + + align:start position:0% +names so they're not very pretty names +and uh this is a little K5 star a little + + align:start position:0% +and uh this is a little K5 star a little + + + align:start position:0% +and uh this is a little K5 star a little +smaller than the Sun and you can see the + + align:start position:0% +smaller than the Sun and you can see the + + + align:start position:0% +smaller than the Sun and you can see the +material dribbling over into the + + align:start position:0% +material dribbling over into the + + + align:start position:0% +material dribbling over into the +accretion disc and the black hole is + + align:start position:0% +accretion disc and the black hole is + + + align:start position:0% +accretion disc and the black hole is +down here in the center um + + align:start position:0% +down here in the center um + + + align:start position:0% +down here in the center um +and this is just to give you an idea + + align:start position:0% +and this is just to give you an idea + + + align:start position:0% +and this is just to give you an idea +what what it might kind of look like in + + align:start position:0% +what what it might kind of look like in + + + align:start position:0% +what what it might kind of look like in +its quiessence state but when it becomes + + align:start position:0% +its quiessence state but when it becomes + + + align:start position:0% +its quiessence state but when it becomes +extremely luminous what happens is not + + align:start position:0% +extremely luminous what happens is not + + + align:start position:0% +extremely luminous what happens is not +that a lot of material comes over from + + align:start position:0% +that a lot of material comes over from + + + align:start position:0% +that a lot of material comes over from +this star onto here but that all the + + align:start position:0% +this star onto here but that all the + + + align:start position:0% +this star onto here but that all the +material stored in this disc suddenly + + align:start position:0% +material stored in this disc suddenly + + + align:start position:0% +material stored in this disc suddenly +breaks loose like a dam it goes the disc + + align:start position:0% +breaks loose like a dam it goes the disc + + + align:start position:0% +breaks loose like a dam it goes the disc +goes unstable it suddenly gets hot and + + align:start position:0% +goes unstable it suddenly gets hot and + + + align:start position:0% +goes unstable it suddenly gets hot and +and the material gets viscous and the + + align:start position:0% +and the material gets viscous and the + + + align:start position:0% +and the material gets viscous and the +material can then fall down onto the you + + align:start position:0% +material can then fall down onto the you + + + align:start position:0% +material can then fall down onto the you +know quickly wind on down the black hole + + align:start position:0% +know quickly wind on down the black hole + + + align:start position:0% +know quickly wind on down the black hole +at a very high mass secretion rate onto + + align:start position:0% +at a very high mass secretion rate onto + + + align:start position:0% +at a very high mass secretion rate onto +the black hole but it isn't because this + + align:start position:0% +the black hole but it isn't because this + + + align:start position:0% +the black hole but it isn't because this +star suddenly erupts it's because this + + align:start position:0% +star suddenly erupts it's because this + + + align:start position:0% +star suddenly erupts it's because this +disc which has been damned up for a 100 + + align:start position:0% +disc which has been damned up for a 100 + + + align:start position:0% +disc which has been damned up for a 100 +years suddenly goes into an unstable + + align:start position:0% +years suddenly goes into an unstable + + + align:start position:0% +years suddenly goes into an unstable +State and uh I don't have a picture of + + align:start position:0% +State and uh I don't have a picture of + + + align:start position:0% +State and uh I don't have a picture of +what they might look like in a violent + + align:start position:0% +what they might look like in a violent + + + align:start position:0% +what they might look like in a violent +Outburst but you get the idea now for + + align:start position:0% +Outburst but you get the idea now for + + + align:start position:0% +Outburst but you get the idea now for +the same system that that was drawn for + + align:start position:0% +the same system that that was drawn for + + + align:start position:0% +the same system that that was drawn for +a620 I've show here what happened in + + align:start position:0% +a620 I've show here what happened in + + + align:start position:0% +a620 I've show here what happened in +1975 which was measured by the um MIT uh + + align:start position:0% +1975 which was measured by the um MIT uh + + + align:start position:0% +1975 which was measured by the um MIT uh +SAS 3 satellite and uh and other + + align:start position:0% +SAS 3 satellite and uh and other + + + align:start position:0% +SAS 3 satellite and uh and other +satellites too and the the system got up + + align:start position:0% +satellites too and the the system got up + + + align:start position:0% +satellites too and the the system got up +to 10 to the 38 ergs per second and + + align:start position:0% +to 10 to the 38 ergs per second and + + + align:start position:0% +to 10 to the 38 ergs per second and +that's I don't know 10,000 solar + + align:start position:0% +that's I don't know 10,000 solar + + + align:start position:0% +that's I don't know 10,000 solar +luminosities or so but all in pure + + align:start position:0% +luminosities or so but all in pure + + + align:start position:0% +luminosities or so but all in pure +X-rays and um and then it decayed over a + + align:start position:0% +X-rays and um and then it decayed over a + + + align:start position:0% +X-rays and um and then it decayed over a +period of about several 100 days which + + align:start position:0% +period of about several 100 days which + + + align:start position:0% +period of about several 100 days which +is about a year like I said and it goes + + align:start position:0% +is about a year like I said and it goes + + + align:start position:0% +is about a year like I said and it goes +from 10 to the 38 ORS per second down to + + align:start position:0% +from 10 to the 38 ORS per second down to + + + align:start position:0% +from 10 to the 38 ORS per second down to +the 10 the 30th so this is the quiet + + align:start position:0% +the 10 the 30th so this is the quiet + + + align:start position:0% +the 10 the 30th so this is the quiet +phase that that last painting was for + + align:start position:0% +phase that that last painting was for + + + align:start position:0% +phase that that last painting was for +and this is the Outburst phase up here + + align:start position:0% +and this is the Outburst phase up here + + + align:start position:0% +and this is the Outburst phase up here +and we discover all of these objects in + + align:start position:0% +and we discover all of these objects in + + + align:start position:0% +and we discover all of these objects in +Outburst we don't discover them in the + + align:start position:0% +Outburst we don't discover them in the + + + align:start position:0% +Outburst we don't discover them in the +Qui we have never discovered one in the + + align:start position:0% +Qui we have never discovered one in the + + + align:start position:0% +Qui we have never discovered one in the +Qui and phase we discover them when + + align:start position:0% +Qui and phase we discover them when + + + align:start position:0% +Qui and phase we discover them when +they're brilliant and easy to find and + + align:start position:0% +they're brilliant and easy to find and + + + align:start position:0% +they're brilliant and easy to find and +then we follow up on them later when + + align:start position:0% +then we follow up on them later when + + + align:start position:0% +then we follow up on them later when +they quiet down and when they quiet down + + align:start position:0% +they quiet down and when they quiet down + + + align:start position:0% +they quiet down and when they quiet down +we can measure these masses that I talk + + align:start position:0% +we can measure these masses that I talk + + + align:start position:0% +we can measure these masses that I talk +to you about the optical object the also + + align:start position:0% +to you about the optical object the also + + + align:start position:0% +to you about the optical object the also +gets bright it gets bright only by a + + align:start position:0% +gets bright it gets bright only by a + + + align:start position:0% +gets bright it gets bright only by a +factor of about a thousand or so so the + + align:start position:0% +factor of about a thousand or so so the + + + align:start position:0% +factor of about a thousand or so so the +optical object gets bright and that + + align:start position:0% +optical object gets bright and that + + + align:start position:0% +optical object gets bright and that +brightness is mostly the x-rays slamming + + align:start position:0% +brightness is mostly the x-rays slamming + + + align:start position:0% +brightness is mostly the x-rays slamming +into that accretion disc heating the + + align:start position:0% +into that accretion disc heating the + + + align:start position:0% +into that accretion disc heating the +accretion disc and producing a very + + align:start position:0% +accretion disc and producing a very + + + align:start position:0% +accretion disc and producing a very +brilliant you know 35,000 Dee uh source + + align:start position:0% +brilliant you know 35,000 Dee uh source + + + align:start position:0% +brilliant you know 35,000 Dee uh source +and uh that's that's that's what you see + + align:start position:0% +and uh that's that's that's what you see + + + align:start position:0% +and uh that's that's that's what you see +is the accretion disc and then when you + + align:start position:0% +is the accretion disc and then when you + + + align:start position:0% +is the accretion disc and then when you +come down like this and you get back + + align:start position:0% +come down like this and you get back + + + align:start position:0% +come down like this and you get back +into the quiescent phase here you see + + align:start position:0% +into the quiescent phase here you see + + + align:start position:0% +into the quiescent phase here you see +about half the light from the accretion + + align:start position:0% +about half the light from the accretion + + + align:start position:0% +about half the light from the accretion +disc and about half the light from the + + align:start position:0% +disc and about half the light from the + + + align:start position:0% +disc and about half the light from the +ordinary + + align:start position:0% +ordinary + + + align:start position:0% +ordinary +star and this is the very nice thing + + align:start position:0% +star and this is the very nice thing + + + align:start position:0% +star and this is the very nice thing +about these systems they get so quiet + + align:start position:0% +about these systems they get so quiet + + + align:start position:0% +about these systems they get so quiet +see I mean 10 to the 30th ergs per + + align:start position:0% +see I mean 10 to the 30th ergs per + + + align:start position:0% +see I mean 10 to the 30th ergs per +second in x-rays is so so little that it + + align:start position:0% +second in x-rays is so so little that it + + + align:start position:0% +second in x-rays is so so little that it +doesn't affect the star very much so you + + align:start position:0% +doesn't affect the star very much so you + + + align:start position:0% +doesn't affect the star very much so you +get a very clean star to measure and you + + align:start position:0% +get a very clean star to measure and you + + + align:start position:0% +get a very clean star to measure and you +can measure the radial velocities of + + align:start position:0% +can measure the radial velocities of + + + align:start position:0% +can measure the radial velocities of +that star very accurately and then you + + align:start position:0% +that star very accurately and then you + + + align:start position:0% +that star very accurately and then you +can measure the mass of the black hole + + align:start position:0% +can measure the mass of the black hole + + + align:start position:0% +can measure the mass of the black hole +and that's one of the major things that + + align:start position:0% +and that's one of the major things that + + + align:start position:0% +and that's one of the major things that +we've done with these + + align:start position:0% + + + + align:start position:0% + +objects now this is a very uh Elementary + + align:start position:0% +objects now this is a very uh Elementary + + + align:start position:0% +objects now this is a very uh Elementary +idea but um I just want to make it maybe + + align:start position:0% +idea but um I just want to make it maybe + + + align:start position:0% +idea but um I just want to make it maybe +less abstract of course Newton did + + align:start position:0% +less abstract of course Newton did + + + align:start position:0% +less abstract of course Newton did +Gravity in 1687 you still couldn't + + align:start position:0% +Gravity in 1687 you still couldn't + + + align:start position:0% +Gravity in 1687 you still couldn't +measure masses until Cavendish in the + + align:start position:0% +measure masses until Cavendish in the + + + align:start position:0% +measure masses until Cavendish in the +laboratory measured G and together you + + align:start position:0% +laboratory measured G and together you + + + align:start position:0% +laboratory measured G and together you +can put the formula in this form or some + + align:start position:0% +can put the formula in this form or some + + + align:start position:0% +can put the formula in this form or some +other forms if you would like and in + + align:start position:0% +other forms if you would like and in + + + align:start position:0% +other forms if you would like and in +this form you can then go ahead and + + align:start position:0% +this form you can then go ahead and + + + align:start position:0% +this form you can then go ahead and +measure the mass of the Sun for example + + align:start position:0% +measure the mass of the Sun for example + + + align:start position:0% +measure the mass of the Sun for example +by looking at the uh orbit of the Earth + + align:start position:0% +by looking at the uh orbit of the Earth + + + align:start position:0% +by looking at the uh orbit of the Earth +around the Sun by sticking in the + + align:start position:0% +around the Sun by sticking in the + + + align:start position:0% +around the Sun by sticking in the +velocity of the Earth the orbital period + + align:start position:0% +velocity of the Earth the orbital period + + + align:start position:0% +velocity of the Earth the orbital period +it's one year right 2 pi G and you can + + align:start position:0% +it's one year right 2 pi G and you can + + + align:start position:0% +it's one year right 2 pi G and you can +then get the mass of the Sun two times + + align:start position:0% +then get the mass of the Sun two times + + + align:start position:0% +then get the mass of the Sun two times +or you can get the mass of the Earth in + + align:start position:0% +or you can get the mass of the Earth in + + + align:start position:0% +or you can get the mass of the Earth in +the same way or you can get the mass of + + align:start position:0% +the same way or you can get the mass of + + + align:start position:0% +the same way or you can get the mass of +jup uh Jupiter from eo's moon and so you + + align:start position:0% +jup uh Jupiter from eo's moon and so you + + + align:start position:0% +jup uh Jupiter from eo's moon and so you +get solar mass three micro solar masses + + align:start position:0% +get solar mass three micro solar masses + + + align:start position:0% +get solar mass three micro solar masses +a mil solar mass um and we we've known + + align:start position:0% +a mil solar mass um and we we've known + + + align:start position:0% +a mil solar mass um and we we've known +this now for a long time and so it's + + align:start position:0% +this now for a long time and so it's + + + align:start position:0% +this now for a long time and so it's +this is one thing we really it doesn't + + align:start position:0% +this is one thing we really it doesn't + + + align:start position:0% +this is one thing we really it doesn't +matter that you studying black holes + + align:start position:0% +matter that you studying black holes + + + align:start position:0% +matter that you studying black holes +this is this is simple Dynamics so this + + align:start position:0% +this is this is simple Dynamics so this + + + align:start position:0% +this is this is simple Dynamics so this +works and you don't have any doubt about + + align:start position:0% +works and you don't have any doubt about + + + align:start position:0% +works and you don't have any doubt about +it and that's what's what's so good + + align:start position:0% +it and that's what's what's so good + + + align:start position:0% +it and that's what's what's so good +about it uh of course there are little + + align:start position:0% +about it uh of course there are little + + + align:start position:0% +about it uh of course there are little +complications and they'll come in in a + + align:start position:0% +complications and they'll come in in a + + + align:start position:0% +complications and they'll come in in a +moment because we don't know the mass of + + align:start position:0% +moment because we don't know the mass of + + + align:start position:0% +moment because we don't know the mass of +the uh I mean I If This Were a point + + align:start position:0% +the uh I mean I If This Were a point + + + align:start position:0% +the uh I mean I If This Were a point +particle like a little light satellite + + align:start position:0% +particle like a little light satellite + + + align:start position:0% +particle like a little light satellite +going around the earth that would be one + + align:start position:0% +going around the earth that would be one + + + align:start position:0% +going around the earth that would be one +thing but the moon of course has some + + align:start position:0% +thing but the moon of course has some + + + align:start position:0% +thing but the moon of course has some +Mass so you have to take that into + + align:start position:0% +Mass so you have to take that into + + + align:start position:0% +Mass so you have to take that into +account you have to really determine the + + align:start position:0% +account you have to really determine the + + + align:start position:0% +account you have to really determine the +mass of the Moon independently if you + + align:start position:0% +mass of the Moon independently if you + + + align:start position:0% +mass of the Moon independently if you +really want the mass of the Earth + + align:start position:0% +really want the mass of the Earth + + + align:start position:0% +really want the mass of the Earth +accurately by measuring it in this + + align:start position:0% +accurately by measuring it in this + + + align:start position:0% +accurately by measuring it in this +fashion so it's just a detail now for + + align:start position:0% +fashion so it's just a detail now for + + + align:start position:0% +fashion so it's just a detail now for +these + + align:start position:0% +these + + + align:start position:0% +these +objects this is uh some of the very + + align:start position:0% +objects this is uh some of the very + + + align:start position:0% +objects this is uh some of the very +better the best data that we have for + + align:start position:0% +better the best data that we have for + + + align:start position:0% +better the best data that we have for +these + + align:start position:0% + + + + align:start position:0% + +objects this is a what's called a radial + + align:start position:0% +objects this is a what's called a radial + + + align:start position:0% +objects this is a what's called a radial +velocity curve for one particular system + + align:start position:0% +velocity curve for one particular system + + + align:start position:0% +velocity curve for one particular system +v404 Sig with a period of 6 and 1/2 + + align:start position:0% + + + + align:start position:0% + +days and there's there all you do is you + + align:start position:0% +days and there's there all you do is you + + + align:start position:0% +days and there's there all you do is you +look at this star with a telescope and + + align:start position:0% +look at this star with a telescope and + + + align:start position:0% +look at this star with a telescope and +you're measuring the spectrum of the + + align:start position:0% +you're measuring the spectrum of the + + + align:start position:0% +you're measuring the spectrum of the +optical star and you see that of course + + align:start position:0% +optical star and you see that of course + + + align:start position:0% +optical star and you see that of course +for a while it's moving away from you + + align:start position:0% +for a while it's moving away from you + + + align:start position:0% +for a while it's moving away from you +and the light is uh red shifted and then + + align:start position:0% +and the light is uh red shifted and then + + + align:start position:0% +and the light is uh red shifted and then +it's moving transverse to your line of + + align:start position:0% +it's moving transverse to your line of + + + align:start position:0% +it's moving transverse to your line of +sight and it's not sh and then it's + + align:start position:0% +sight and it's not sh and then it's + + + align:start position:0% +sight and it's not sh and then it's +coming toward you it's blue shifted and + + align:start position:0% +coming toward you it's blue shifted and + + + align:start position:0% +coming toward you it's blue shifted and +so basically that's what this curve is + + align:start position:0% +so basically that's what this curve is + + + align:start position:0% +so basically that's what this curve is +here and uh you do this by we have to + + align:start position:0% +here and uh you do this by we have to + + + align:start position:0% +here and uh you do this by we have to +cross-correlate the radial Vel we cross + + align:start position:0% +cross-correlate the radial Vel we cross + + + align:start position:0% +cross-correlate the radial Vel we cross +correlate the optical spectrum of the + + align:start position:0% +correlate the optical spectrum of the + + + align:start position:0% +correlate the optical spectrum of the +star that's orbiting the black hole + + align:start position:0% +star that's orbiting the black hole + + + align:start position:0% +star that's orbiting the black hole +against the spectrum of a field star + + align:start position:0% +against the spectrum of a field star + + + align:start position:0% +against the spectrum of a field star +which is stationary or moving at a + + align:start position:0% +which is stationary or moving at a + + + align:start position:0% +which is stationary or moving at a +constant velocity and then we get this + + align:start position:0% +constant velocity and then we get this + + + align:start position:0% +constant velocity and then we get this +curve that's all it is it's very simple + + align:start position:0% +curve that's all it is it's very simple + + + align:start position:0% +curve that's all it is it's very simple +and the two numbers you get from this + + align:start position:0% +and the two numbers you get from this + + + align:start position:0% +and the two numbers you get from this +curve immediately are the uh orbital + + align:start position:0% +curve immediately are the uh orbital + + + align:start position:0% +curve immediately are the uh orbital +period because that's just the time from + + align:start position:0% +period because that's just the time from + + + align:start position:0% +period because that's just the time from +Max to Max and you get this + + align:start position:0% +Max to Max and you get this + + + align:start position:0% +Max to Max and you get this +semi-amplitude of the Velocity curve and + + align:start position:0% +semi-amplitude of the Velocity curve and + + + align:start position:0% +semi-amplitude of the Velocity curve and +those two numbers are all you need to + + align:start position:0% +those two numbers are all you need to + + + align:start position:0% +those two numbers are all you need to +get the absolute minimum mass of the + + align:start position:0% +get the absolute minimum mass of the + + + align:start position:0% +get the absolute minimum mass of the +compact star that you're dealing with + + align:start position:0% +compact star that you're dealing with + + + align:start position:0% +compact star that you're dealing with +what you're measuring then is you + + align:start position:0% +what you're measuring then is you + + + align:start position:0% +what you're measuring then is you +measure What's called the mass function + + align:start position:0% +measure What's called the mass function + + + align:start position:0% +measure What's called the mass function +this is the mass + + align:start position:0% +this is the mass + + + align:start position:0% +this is the mass +function and by measuring the period and + + align:start position:0% +function and by measuring the period and + + + align:start position:0% +function and by measuring the period and +the semi-amplitude and you have + + align:start position:0% +the semi-amplitude and you have + + + align:start position:0% +the semi-amplitude and you have +constants here you can calculate a + + align:start position:0% +constants here you can calculate a + + + align:start position:0% +constants here you can calculate a +number and in the right units you can + + align:start position:0% +number and in the right units you can + + + align:start position:0% +number and in the right units you can +have it in solar masses for this system + + align:start position:0% +have it in solar masses for this system + + + align:start position:0% +have it in solar masses for this system +it comes out to be + + align:start position:0% +it comes out to be + + + align:start position:0% +it comes out to be +6.1 solar masses with this + + align:start position:0% +6.1 solar masses with this + + + align:start position:0% +6.1 solar masses with this +uncertainty over on this side of the + + align:start position:0% +uncertainty over on this side of the + + + align:start position:0% +uncertainty over on this side of the +equation you have the math this M1 is + + align:start position:0% +equation you have the math this M1 is + + + align:start position:0% +equation you have the math this M1 is +the mass of the black hole M2 is the + + align:start position:0% +the mass of the black hole M2 is the + + + align:start position:0% +the mass of the black hole M2 is the +mass of the optical star so it comes in + + align:start position:0% +mass of the optical star so it comes in + + + align:start position:0% +mass of the optical star so it comes in +here and if you really want to get M1 + + align:start position:0% +here and if you really want to get M1 + + + align:start position:0% +here and if you really want to get M1 +the mass of the black hole which we do + + align:start position:0% +the mass of the black hole which we do + + + align:start position:0% +the mass of the black hole which we do +then you have to get M2 the mass of the + + align:start position:0% +then you have to get M2 the mass of the + + + align:start position:0% +then you have to get M2 the mass of the +other star but more important than that + + align:start position:0% +other star but more important than that + + + align:start position:0% +other star but more important than that +you need the I mean all you're measuring + + align:start position:0% +you need the I mean all you're measuring + + + align:start position:0% +you need the I mean all you're measuring +is the velocity and the line of sight + + align:start position:0% +is the velocity and the line of sight + + + align:start position:0% +is the velocity and the line of sight +and this orbit could be tilted to you + + align:start position:0% +and this orbit could be tilted to you + + + align:start position:0% +and this orbit could be tilted to you +like this or like this so you need that + + align:start position:0% +like this or like this so you need that + + + align:start position:0% +like this or like this so you need that +tilt you need that angle of inclination + + align:start position:0% +tilt you need that angle of inclination + + + align:start position:0% +tilt you need that angle of inclination +of the orbit that's the I that's in this + + align:start position:0% +of the orbit that's the I that's in this + + + align:start position:0% +of the orbit that's the I that's in this +equation so to get the mass you really + + align:start position:0% +equation so to get the mass you really + + + align:start position:0% +equation so to get the mass you really +need both both of them but without + + align:start position:0% +need both both of them but without + + + align:start position:0% +need both both of them but without +getting those just by measuring this you + + align:start position:0% +getting those just by measuring this you + + + align:start position:0% +getting those just by measuring this you +can say that the minimum mass of that + + align:start position:0% +can say that the minimum mass of that + + + align:start position:0% +can say that the minimum mass of that +compact star in this system it can't be + + align:start position:0% +compact star in this system it can't be + + + align:start position:0% +compact star in this system it can't be +less than this value right here the + + align:start position:0% +less than this value right here the + + + align:start position:0% +less than this value right here the +value of the mass function it can't be + + align:start position:0% +value of the mass function it can't be + + + align:start position:0% +value of the mass function it can't be +less than six solar masses and uh mean I + + align:start position:0% +less than six solar masses and uh mean I + + + align:start position:0% +less than six solar masses and uh mean I +I could show that but isn't isn't too + + align:start position:0% +I could show that but isn't isn't too + + + align:start position:0% +I could show that but isn't isn't too +important to do it I don't think the + + align:start position:0% +important to do it I don't think the + + + align:start position:0% +important to do it I don't think the +main thing here is uh how massive can a + + align:start position:0% +main thing here is uh how massive can a + + + align:start position:0% +main thing here is uh how massive can a +neutron star be and there you go to + + align:start position:0% +neutron star be and there you go to + + + align:start position:0% +neutron star be and there you go to +general relativity and general + + align:start position:0% +general relativity and general + + + align:start position:0% +general relativity and general +relativity says and there's proofs of + + align:start position:0% +relativity says and there's proofs of + + + align:start position:0% +relativity says and there's proofs of +this that three solar masses is as + + align:start position:0% +this that three solar masses is as + + + align:start position:0% +this that three solar masses is as +massive as you can go in general + + align:start position:0% +massive as you can go in general + + + align:start position:0% +massive as you can go in general +relativity unless you make some + + align:start position:0% +relativity unless you make some + + + align:start position:0% +relativity unless you make some +extraordinary uh you you I mean there's + + align:start position:0% +extraordinary uh you you I mean there's + + + align:start position:0% +extraordinary uh you you I mean there's +there's some there's some there's + + align:start position:0% +there's some there's some there's + + + align:start position:0% +there's some there's some there's +there's slight conditions on that um for + + align:start position:0% +there's slight conditions on that um for + + + align:start position:0% +there's slight conditions on that um for +example if you want to set a limit of + + align:start position:0% +example if you want to set a limit of + + + align:start position:0% +example if you want to set a limit of +three solar masses on the limit on the + + align:start position:0% +three solar masses on the limit on the + + + align:start position:0% +three solar masses on the limit on the +mass of a neutron star then you have to + + align:start position:0% +mass of a neutron star then you have to + + + align:start position:0% +mass of a neutron star then you have to +say that you know the equation of State + + align:start position:0% +say that you know the equation of State + + + align:start position:0% +say that you know the equation of State +up to some density in the cruster in the + + align:start position:0% +up to some density in the cruster in the + + + align:start position:0% +up to some density in the cruster in the +outer part of the of the star and um and + + align:start position:0% +outer part of the of the star and um and + + + align:start position:0% +outer part of the of the star and um and +uh uh and you also have to make the + + align:start position:0% +uh uh and you also have to make the + + + align:start position:0% +uh uh and you also have to make the +assumption that dpd row which is a + + align:start position:0% +assumption that dpd row which is a + + + align:start position:0% +assumption that dpd row which is a +velocity of usually velocity of light uh + + align:start position:0% +velocity of usually velocity of light uh + + + align:start position:0% +velocity of usually velocity of light uh +the velocity of sound rather in material + + align:start position:0% +the velocity of sound rather in material + + + align:start position:0% +the velocity of sound rather in material +the PD row um is U uh you have to assume + + align:start position:0% +the PD row um is U uh you have to assume + + + align:start position:0% +the PD row um is U uh you have to assume +that that's less than uh c^ s and most + + align:start position:0% +that that's less than uh c^ s and most + + + align:start position:0% +that that's less than uh c^ s and most +people accept the you know knowing the + + align:start position:0% +people accept the you know knowing the + + + align:start position:0% +people accept the you know knowing the +equation of State up to some fiducial + + align:start position:0% +equation of State up to some fiducial + + + align:start position:0% +equation of State up to some fiducial +density like maybe one two times nuclear + + align:start position:0% +density like maybe one two times nuclear + + + align:start position:0% +density like maybe one two times nuclear +density or saturated nuclear density + + align:start position:0% +density or saturated nuclear density + + + align:start position:0% +density or saturated nuclear density +like an uranium nucleus and they assume + + align:start position:0% +like an uranium nucleus and they assume + + + align:start position:0% +like an uranium nucleus and they assume +that + + align:start position:0% +that + + + align:start position:0% +that +that dpd row is less than C squ and so + + align:start position:0% +that dpd row is less than C squ and so + + + align:start position:0% +that dpd row is less than C squ and so +most people say three solar masses is a + + align:start position:0% +most people say three solar masses is a + + + align:start position:0% +most people say three solar masses is a +really hard limit on the mass of a + + align:start position:0% +really hard limit on the mass of a + + + align:start position:0% +really hard limit on the mass of a +neutron star but even if you drop those + + align:start position:0% +neutron star but even if you drop those + + + align:start position:0% +neutron star but even if you drop those +assumptions it only goes up to like six + + align:start position:0% +assumptions it only goes up to like six + + + align:start position:0% +assumptions it only goes up to like six +solar masses or so so uh it's you do + + align:start position:0% +solar masses or so so uh it's you do + + + align:start position:0% +solar masses or so so uh it's you do +need general relativity to make the + + align:start position:0% +need general relativity to make the + + + align:start position:0% +need general relativity to make the +claim that these things are black holes + + align:start position:0% +claim that these things are black holes + + + align:start position:0% +claim that these things are black holes +and + + align:start position:0% + + + + align:start position:0% + +um so that's what the the data looks + + align:start position:0% +um so that's what the the data looks + + + align:start position:0% +um so that's what the the data looks +like for the mass now you can measure + + align:start position:0% +like for the mass now you can measure + + + align:start position:0% +like for the mass now you can measure +the mass function of of all of those + + align:start position:0% +the mass function of of all of those + + + align:start position:0% +the mass function of of all of those +that I had in that earlier picture and + + align:start position:0% +that I had in that earlier picture and + + + align:start position:0% +that I had in that earlier picture and +when you do that you + + align:start position:0% + + + + align:start position:0% + +get + + align:start position:0% +get + + + align:start position:0% +get +um the mass function being a lower limit + + align:start position:0% +um the mass function being a lower limit + + + align:start position:0% +um the mass function being a lower limit +on the mass of the black hole you get + + align:start position:0% +on the mass of the black hole you get + + + align:start position:0% +on the mass of the black hole you get +some of them in particular this is the + + align:start position:0% +some of them in particular this is the + + + align:start position:0% +some of them in particular this is the +one we just looked at at six solar + + align:start position:0% +one we just looked at at six solar + + + align:start position:0% +one we just looked at at six solar +masses right here uh you're saying that + + align:start position:0% +masses right here uh you're saying that + + + align:start position:0% +masses right here uh you're saying that +the mass of the compact object is + + align:start position:0% +the mass of the compact object is + + + align:start position:0% +the mass of the compact object is +greater than six solar masses and this + + align:start position:0% +greater than six solar masses and this + + + align:start position:0% +greater than six solar masses and this +one likewise and so forth this group + + align:start position:0% +one likewise and so forth this group + + + align:start position:0% +one likewise and so forth this group +here uh you know they're Diamond hard + + align:start position:0% +here uh you know they're Diamond hard + + + align:start position:0% +here uh you know they're Diamond hard +black holes I mean they're not even in + + align:start position:0% +black holes I mean they're not even in + + + align:start position:0% +black holes I mean they're not even in +question I mean you know there's no way + + align:start position:0% +question I mean you know there's no way + + + align:start position:0% +question I mean you know there's no way +that couldn't be black holes and this is + + align:start position:0% +that couldn't be black holes and this is + + + align:start position:0% +that couldn't be black holes and this is +not yet taking into account that these + + align:start position:0% +not yet taking into account that these + + + align:start position:0% +not yet taking into account that these +are minimum uh POS possibilities the + + align:start position:0% +are minimum uh POS possibilities the + + + align:start position:0% +are minimum uh POS possibilities the +masses will only be greater than this + + align:start position:0% +masses will only be greater than this + + + align:start position:0% +masses will only be greater than this +once you determine the inclination and + + align:start position:0% +once you determine the inclination and + + + align:start position:0% +once you determine the inclination and +once you determine the mass of the + + align:start position:0% +once you determine the mass of the + + + align:start position:0% +once you determine the mass of the +secondary so these these this group here + + align:start position:0% +secondary so these these this group here + + + align:start position:0% +secondary so these these this group here +are certain uh black holes and these are + + align:start position:0% +are certain uh black holes and these are + + + align:start position:0% +are certain uh black holes and these are +extremely uh good good black holes as + + align:start position:0% +extremely uh good good black holes as + + + align:start position:0% +extremely uh good good black holes as +well these require extra supporting + + align:start position:0% +well these require extra supporting + + + align:start position:0% +well these require extra supporting +information like you really do need the + + align:start position:0% +information like you really do need the + + + align:start position:0% +information like you really do need the +inclination of the orbit to make the + + align:start position:0% +inclination of the orbit to make the + + + align:start position:0% +inclination of the orbit to make the +case that these are black holes so then + + align:start position:0% +case that these are black holes so then + + + align:start position:0% +case that these are black holes so then +you go on and you measure the mass of + + align:start position:0% +you go on and you measure the mass of + + + align:start position:0% +you go on and you measure the mass of +the black holes and those measurements + + align:start position:0% +the black holes and those measurements + + + align:start position:0% +the black holes and those measurements +are not so easy because the measurement + + align:start position:0% +are not so easy because the measurement + + + align:start position:0% +are not so easy because the measurement +of the radial velocities is very + + align:start position:0% +of the radial velocities is very + + + align:start position:0% +of the radial velocities is very +straightforward there's no systematics + + align:start position:0% +straightforward there's no systematics + + + align:start position:0% +straightforward there's no systematics +it's extremely simple but to measure the + + align:start position:0% +it's extremely simple but to measure the + + + align:start position:0% +it's extremely simple but to measure the +inclination and to measure the mass of + + align:start position:0% +inclination and to measure the mass of + + + align:start position:0% +inclination and to measure the mass of +the secondary is is is is a is a bit + + align:start position:0% +the secondary is is is is a is a bit + + + align:start position:0% +the secondary is is is is a is a bit +more of an art which means it's a little + + align:start position:0% +more of an art which means it's a little + + + align:start position:0% +more of an art which means it's a little +less certain nevertheless you can do it + + align:start position:0% +less certain nevertheless you can do it + + + align:start position:0% +less certain nevertheless you can do it +and there are techniques which I won't + + align:start position:0% +and there are techniques which I won't + + + align:start position:0% +and there are techniques which I won't +describe now but when you do it you get + + align:start position:0% +describe now but when you do it you get + + + align:start position:0% +describe now but when you do it you get +the masses of the black holes as shown + + align:start position:0% +the masses of the black holes as shown + + + align:start position:0% +the masses of the black holes as shown +here these black dots are the minimum + + align:start position:0% +here these black dots are the minimum + + + align:start position:0% +here these black dots are the minimum +are the minimum limits that I mentioned + + align:start position:0% +are the minimum limits that I mentioned + + + align:start position:0% +are the minimum limits that I mentioned +before + + align:start position:0% + + + + align:start position:0% + +and these open circles with the arrow + + align:start position:0% +and these open circles with the arrow + + + align:start position:0% +and these open circles with the arrow +bars are the actual masses inferred by + + align:start position:0% +bars are the actual masses inferred by + + + align:start position:0% +bars are the actual masses inferred by +measuring the inclination and mass of + + align:start position:0% +measuring the inclination and mass of + + + align:start position:0% +measuring the inclination and mass of +the secondary star and you'll see that + + align:start position:0% +the secondary star and you'll see that + + + align:start position:0% +the secondary star and you'll see that +the masses are generally right around + + align:start position:0% +the masses are generally right around + + + align:start position:0% +the masses are generally right around +nine or 10 solar masses and uh you'll + + align:start position:0% +nine or 10 solar masses and uh you'll + + + align:start position:0% +nine or 10 solar masses and uh you'll +also see that there are a few that are + + align:start position:0% +also see that there are a few that are + + + align:start position:0% +also see that there are a few that are +well measured I think we have the + + align:start position:0% +well measured I think we have the + + + align:start position:0% +well measured I think we have the +capacity now of course it depends how + + align:start position:0% +capacity now of course it depends how + + + align:start position:0% +capacity now of course it depends how +well behaved a given system is to + + align:start position:0% +well behaved a given system is to + + + align:start position:0% +well behaved a given system is to +improve a lot of them to this level + + align:start position:0% +improve a lot of them to this level + + + align:start position:0% +improve a lot of them to this level +which would be of course a major Advance + + align:start position:0% +which would be of course a major Advance + + + align:start position:0% +which would be of course a major Advance +because uh you can use these masses for + + align:start position:0% +because uh you can use these masses for + + + align:start position:0% +because uh you can use these masses for +quite a few things I already mentioned + + align:start position:0% +quite a few things I already mentioned + + + align:start position:0% +quite a few things I already mentioned +one thing namely the Supernova + + align:start position:0% +one thing namely the Supernova + + + align:start position:0% +one thing namely the Supernova +explosions and you try to uh uh + + align:start position:0% +explosions and you try to uh uh + + + align:start position:0% +explosions and you try to uh uh +determine the masses of the remnants + + align:start position:0% +determine the masses of the remnants + + + align:start position:0% +determine the masses of the remnants +that are left you can put better + + align:start position:0% +that are left you can put better + + + align:start position:0% +that are left you can put better +constraints and you get a better better + + align:start position:0% +constraints and you get a better better + + + align:start position:0% +constraints and you get a better better +Mass distribution in this so this is + + align:start position:0% +Mass distribution in this so this is + + + align:start position:0% +Mass distribution in this so this is +what's been done in terms of measuring + + align:start position:0% +what's been done in terms of measuring + + + align:start position:0% +what's been done in terms of measuring +the masses of these + + align:start position:0% + + + + align:start position:0% + +objects now of course you want to do + + align:start position:0% +objects now of course you want to do + + + align:start position:0% +objects now of course you want to do +something better than just measure mass + + align:start position:0% +something better than just measure mass + + + align:start position:0% +something better than just measure mass +because measuring mass is still not yet + + align:start position:0% +because measuring mass is still not yet + + + align:start position:0% +because measuring mass is still not yet +satisfying in terms of General Rel ity + + align:start position:0% +satisfying in terms of General Rel ity + + + align:start position:0% +satisfying in terms of General Rel ity +in terms of strong field gravity you + + align:start position:0% +in terms of strong field gravity you + + + align:start position:0% +in terms of strong field gravity you +want to measure something now very close + + align:start position:0% +want to measure something now very close + + + align:start position:0% +want to measure something now very close +in to the black hole that's that's what + + align:start position:0% +in to the black hole that's that's what + + + align:start position:0% +in to the black hole that's that's what +you really would like to do some Physics + + align:start position:0% +you really would like to do some Physics + + + align:start position:0% +you really would like to do some Physics +there that you understand uh and there + + align:start position:0% +there that you understand uh and there + + + align:start position:0% +there that you understand uh and there +are a few possibilities and + + align:start position:0% +are a few possibilities and + + + align:start position:0% +are a few possibilities and +I'll and I'll mention just a couple of + + align:start position:0% +I'll and I'll mention just a couple of + + + align:start position:0% +I'll and I'll mention just a couple of +them uh one of them that people talk + + align:start position:0% +them uh one of them that people talk + + + align:start position:0% +them uh one of them that people talk +about is um measuring um and and there + + align:start position:0% +about is um measuring um and and there + + + align:start position:0% +about is um measuring um and and there +have been some measurements of such of + + align:start position:0% +have been some measurements of such of + + + align:start position:0% +have been some measurements of such of +lines like this the accretion disc the + + align:start position:0% +lines like this the accretion disc the + + + align:start position:0% +lines like this the accretion disc the +very inner accretion disc which is + + align:start position:0% +very inner accretion disc which is + + + align:start position:0% +very inner accretion disc which is +truncated at the last stable orbit as we + + align:start position:0% +truncated at the last stable orbit as we + + + align:start position:0% +truncated at the last stable orbit as we +said um has very strong gravity or can + + align:start position:0% +said um has very strong gravity or can + + + align:start position:0% +said um has very strong gravity or can +have very strong gravity and that strong + + align:start position:0% +have very strong gravity and that strong + + + align:start position:0% +have very strong gravity and that strong +gravity can have an effect on a spectral + + align:start position:0% +gravity can have an effect on a spectral + + + align:start position:0% +gravity can have an effect on a spectral +line that's being emitted by the dis and + + align:start position:0% +line that's being emitted by the dis and + + + align:start position:0% +line that's being emitted by the dis and +uh this is a schematic indication of how + + align:start position:0% +uh this is a schematic indication of how + + + align:start position:0% +uh this is a schematic indication of how +that would go there's emitters that are + + align:start position:0% +that would go there's emitters that are + + + align:start position:0% +that would go there's emitters that are +here for examp iron is the line to look + + align:start position:0% +here for examp iron is the line to look + + + align:start position:0% +here for examp iron is the line to look +at because it's the iron iron line is + + align:start position:0% +at because it's the iron iron line is + + + align:start position:0% +at because it's the iron iron line is +the one that remains at six you know at + + align:start position:0% +the one that remains at six you know at + + + align:start position:0% +the one that remains at six you know at +uh uh at the energies and temperatures + + align:start position:0% +uh uh at the energies and temperatures + + + align:start position:0% +uh uh at the energies and temperatures +of the inner disc and everything and + + align:start position:0% +of the inner disc and everything and + + + align:start position:0% +of the inner disc and everything and +iron is also also a very abundant + + align:start position:0% +iron is also also a very abundant + + + align:start position:0% +iron is also also a very abundant +species and uh so it's it's the one that + + align:start position:0% +species and uh so it's it's the one that + + + align:start position:0% +species and uh so it's it's the one that +that one works on and the iron line you + + align:start position:0% +that one works on and the iron line you + + + align:start position:0% +that one works on and the iron line you +see Iron emitters in this disc and + + align:start position:0% +see Iron emitters in this disc and + + + align:start position:0% +see Iron emitters in this disc and +they're coming toward you so you know + + align:start position:0% +they're coming toward you so you know + + + align:start position:0% +they're coming toward you so you know +that will blue shift uh the emission + + align:start position:0% +that will blue shift uh the emission + + + align:start position:0% +that will blue shift uh the emission +that's coming from that region will be + + align:start position:0% +that's coming from that region will be + + + align:start position:0% +that's coming from that region will be +blue shifted and this region will be red + + align:start position:0% +blue shifted and this region will be red + + + align:start position:0% +blue shifted and this region will be red +shifted um there's a gravitational red + + align:start position:0% +shifted um there's a gravitational red + + + align:start position:0% +shifted um there's a gravitational red +shift that you have to take into account + + align:start position:0% +shift that you have to take into account + + + align:start position:0% +shift that you have to take into account +that's indicated here this is a + + align:start position:0% +that's indicated here this is a + + + align:start position:0% +that's indicated here this is a +schematic this is a schematic idea of + + align:start position:0% +schematic this is a schematic idea of + + + align:start position:0% +schematic this is a schematic idea of +what an iron line would look like if the + + align:start position:0% +what an iron line would look like if the + + + align:start position:0% +what an iron line would look like if the +iron atoms were it rest it would just be + + align:start position:0% +iron atoms were it rest it would just be + + + align:start position:0% +iron atoms were it rest it would just be +a sharp line right up right up well be + + align:start position:0% +a sharp line right up right up well be + + + align:start position:0% +a sharp line right up right up well be +more like up here and U and then all of + + align:start position:0% +more like up here and U and then all of + + + align:start position:0% +more like up here and U and then all of +these effects namely the Doppler the + + align:start position:0% +these effects namely the Doppler the + + + align:start position:0% +these effects namely the Doppler the +longitudinal Doppler effect in the dis + + align:start position:0% +longitudinal Doppler effect in the dis + + + align:start position:0% +longitudinal Doppler effect in the dis +which affects obviously the uh place at + + align:start position:0% +which affects obviously the uh place at + + + align:start position:0% +which affects obviously the uh place at +which a particular mission is registered + + align:start position:0% +which a particular mission is registered + + + align:start position:0% +which a particular mission is registered +by you and uh and also the gravitational + + align:start position:0% +by you and uh and also the gravitational + + + align:start position:0% +by you and uh and also the gravitational +red shift just by the strong gravity + + align:start position:0% +red shift just by the strong gravity + + + align:start position:0% +red shift just by the strong gravity +pulling uh and that moves everything + + align:start position:0% +pulling uh and that moves everything + + + align:start position:0% +pulling uh and that moves everything +toward the red part of the spectrum + + align:start position:0% +toward the red part of the spectrum + + + align:start position:0% +toward the red part of the spectrum +and then um there's also the transverse + + align:start position:0% +and then um there's also the transverse + + + align:start position:0% +and then um there's also the transverse +Doppler shift just in this like second + + align:start position:0% +Doppler shift just in this like second + + + align:start position:0% +Doppler shift just in this like second +order Doppler shift which we don't + + align:start position:0% +order Doppler shift which we don't + + + align:start position:0% +order Doppler shift which we don't +usually talk about but is certainly + + align:start position:0% +usually talk about but is certainly + + + align:start position:0% +usually talk about but is certainly +important here so those three things the + + align:start position:0% +important here so those three things the + + + align:start position:0% +important here so those three things the +longitudinal transverse and + + align:start position:0% +longitudinal transverse and + + + align:start position:0% +longitudinal transverse and +gravitational red shift shape this line + + align:start position:0% +gravitational red shift shape this line + + + align:start position:0% +gravitational red shift shape this line +into a shape like this these are + + align:start position:0% +into a shape like this these are + + + align:start position:0% +into a shape like this these are +simulations by a theorist by his name of + + align:start position:0% +simulations by a theorist by his name of + + + align:start position:0% +simulations by a theorist by his name of +Chris Chris Reynolds and I I really like + + align:start position:0% +Chris Chris Reynolds and I I really like + + + align:start position:0% +Chris Chris Reynolds and I I really like +this energy scale 3 five + + align:start position:0% + + + + align:start position:0% + +69 I mean it's a I I would never do that + + align:start position:0% +69 I mean it's a I I would never do that + + + align:start position:0% +69 I mean it's a I I would never do that +but + + align:start position:0% +but + + + align:start position:0% +but +uh but in any case U there I I could + + align:start position:0% +uh but in any case U there I I could + + + align:start position:0% +uh but in any case U there I I could +have brought a real profile but there + + align:start position:0% +have brought a real profile but there + + + align:start position:0% +have brought a real profile but there +are profiles not as good as this this is + + align:start position:0% +are profiles not as good as this this is + + + align:start position:0% +are profiles not as good as this this is +what we hope to see from the new conx + + align:start position:0% +what we hope to see from the new conx + + + align:start position:0% +what we hope to see from the new conx +Observatory that's being uh studied + + align:start position:0% +Observatory that's being uh studied + + + align:start position:0% +Observatory that's being uh studied +right now and and to be built soon + + align:start position:0% +right now and and to be built soon + + + align:start position:0% +right now and and to be built soon +hopefully um and this shows that you can + + align:start position:0% +hopefully um and this shows that you can + + + align:start position:0% +hopefully um and this shows that you can +tell the difference between a short + + align:start position:0% +tell the difference between a short + + + align:start position:0% +tell the difference between a short +Shield black hole and a curve black hole + + align:start position:0% +Shield black hole and a curve black hole + + + align:start position:0% +Shield black hole and a curve black hole +the curve black hole you have the + + align:start position:0% +the curve black hole you have the + + + align:start position:0% +the curve black hole you have the +stronger gravitational red shift out + + align:start position:0% +stronger gravitational red shift out + + + align:start position:0% +stronger gravitational red shift out +here uh because you get down deeper into + + align:start position:0% +here uh because you get down deeper into + + + align:start position:0% +here uh because you get down deeper into +the gra ational potential well and the + + align:start position:0% +the gra ational potential well and the + + + align:start position:0% +the gra ational potential well and the +schw shield black hole U gives you a + + align:start position:0% +schw shield black hole U gives you a + + + align:start position:0% +schw shield black hole U gives you a +bigger Spike there and um so you can + + align:start position:0% +bigger Spike there and um so you can + + + align:start position:0% +bigger Spike there and um so you can +tell the metric you can get the rotation + + align:start position:0% +tell the metric you can get the rotation + + + align:start position:0% +tell the metric you can get the rotation +of the black hole from this and uh in + + align:start position:0% +of the black hole from this and uh in + + + align:start position:0% +of the black hole from this and uh in +principle uh there the the thing about + + align:start position:0% +principle uh there the the thing about + + + align:start position:0% +principle uh there the the thing about +this is you are making an assumption + + align:start position:0% +this is you are making an assumption + + + align:start position:0% +this is you are making an assumption +because you have to + + align:start position:0% +because you have to + + + align:start position:0% +because you have to +know you know I just said the that the + + align:start position:0% +know you know I just said the that the + + + align:start position:0% +know you know I just said the that the +iron atoms are emitting from this disc + + align:start position:0% +iron atoms are emitting from this disc + + + align:start position:0% +iron atoms are emitting from this disc +but why are these iron atoms emitting + + align:start position:0% +but why are these iron atoms emitting + + + align:start position:0% +but why are these iron atoms emitting +from this cold disc the reason they're + + align:start position:0% +from this cold disc the reason they're + + + align:start position:0% +from this cold disc the reason they're +emitting from this disc which really + + align:start position:0% +emitting from this disc which really + + + align:start position:0% +emitting from this disc which really +isn't that hot is because there is a + + align:start position:0% +isn't that hot is because there is a + + + align:start position:0% +isn't that hot is because there is a +Corona of hotter x-rays which I haven't + + align:start position:0% +Corona of hotter x-rays which I haven't + + + align:start position:0% +Corona of hotter x-rays which I haven't +talked about that are shining down onto + + align:start position:0% +talked about that are shining down onto + + + align:start position:0% +talked about that are shining down onto +the disk and fluorescing the x-rays up + + align:start position:0% +the disk and fluorescing the x-rays up + + + align:start position:0% +the disk and fluorescing the x-rays up +out of the disc that's the model so if + + align:start position:0% +out of the disc that's the model so if + + + align:start position:0% +out of the disc that's the model so if +you're going to make such a model and + + align:start position:0% +you're going to make such a model and + + + align:start position:0% +you're going to make such a model and +try to solve for things you have to have + + align:start position:0% +try to solve for things you have to have + + + align:start position:0% +try to solve for things you have to have +an idea of what that flu that uh hard + + align:start position:0% +an idea of what that flu that uh hard + + + align:start position:0% +an idea of what that flu that uh hard +hard radiation is that radiation from + + align:start position:0% +hard radiation is that radiation from + + + align:start position:0% +hard radiation is that radiation from +the Corona That's fluorescing you have + + align:start position:0% +the Corona That's fluorescing you have + + + align:start position:0% +the Corona That's fluorescing you have +to have a model for that and that seems + + align:start position:0% +to have a model for that and that seems + + + align:start position:0% +to have a model for that and that seems +to be changeable that seems to be but + + align:start position:0% +to be changeable that seems to be but + + + align:start position:0% +to be changeable that seems to be but +it's it's it's it's the kind of thing + + align:start position:0% +it's it's it's it's the kind of thing + + + align:start position:0% +it's it's it's it's the kind of thing +that if you had enough data you you + + align:start position:0% +that if you had enough data you you + + + align:start position:0% +that if you had enough data you you +really feel you could put it together + + align:start position:0% +really feel you could put it together + + + align:start position:0% +really feel you could put it together +you could make some sense out of it you + + align:start position:0% +you could make some sense out of it you + + + align:start position:0% +you could make some sense out of it you +could get a consistent model of what + + align:start position:0% +could get a consistent model of what + + + align:start position:0% +could get a consistent model of what +that x-ray emitting uh hot x-ray + + align:start position:0% +that x-ray emitting uh hot x-ray + + + align:start position:0% +that x-ray emitting uh hot x-ray +emitting gas is above and below the disc + + align:start position:0% +emitting gas is above and below the disc + + + align:start position:0% +emitting gas is above and below the disc +um and also uh determine the uh the + + align:start position:0% +um and also uh determine the uh the + + + align:start position:0% +um and also uh determine the uh the +metric now another so that's that's + + align:start position:0% +metric now another so that's that's + + + align:start position:0% +metric now another so that's that's +spectroscopy okay now another technique + + align:start position:0% +spectroscopy okay now another technique + + + align:start position:0% +spectroscopy okay now another technique +that's extremely important is uh timing + + align:start position:0% +that's extremely important is uh timing + + + align:start position:0% +that's extremely important is uh timing +data and this is from the timing + + align:start position:0% +data and this is from the timing + + + align:start position:0% +data and this is from the timing +Explorer at MIT here they've had a lot + + align:start position:0% +Explorer at MIT here they've had a lot + + + align:start position:0% +Explorer at MIT here they've had a lot +of um uh uh participation in the U The + + align:start position:0% +of um uh uh participation in the U The + + + align:start position:0% +of um uh uh participation in the U The +Rossi x-ray timing Explorer which was + + align:start position:0% +Rossi x-ray timing Explorer which was + + + align:start position:0% +Rossi x-ray timing Explorer which was +launched in January 1996 and this + + align:start position:0% +launched in January 1996 and this + + + align:start position:0% +launched in January 1996 and this +satellite its purpose was to is it's + + align:start position:0% +satellite its purpose was to is it's + + + align:start position:0% +satellite its purpose was to is it's +still there is to measure the time of + + align:start position:0% +still there is to measure the time of + + + align:start position:0% +still there is to measure the time of +the x-rays as they come in and you know + + align:start position:0% +the x-rays as they come in and you know + + + align:start position:0% +the x-rays as they come in and you know +for sources that aren't too bright it + + align:start position:0% +for sources that aren't too bright it + + + align:start position:0% +for sources that aren't too bright it +can actually measure every x-ray to a + + align:start position:0% +can actually measure every x-ray to a + + + align:start position:0% +can actually measure every x-ray to a +microsc you know the time that it came + + align:start position:0% +microsc you know the time that it came + + + align:start position:0% +microsc you know the time that it came +in and you'd say well so what well I + + align:start position:0% +in and you'd say well so what well I + + + align:start position:0% +in and you'd say well so what well I +mean you know maybe it's just kind of a + + align:start position:0% +mean you know maybe it's just kind of a + + + align:start position:0% +mean you know maybe it's just kind of a +vanilla and nothing's happening and all + + align:start position:0% +vanilla and nothing's happening and all + + + align:start position:0% +vanilla and nothing's happening and all +that but here I'll just show you one + + align:start position:0% +that but here I'll just show you one + + + align:start position:0% +that but here I'll just show you one +source this is happens to be a pretty + + align:start position:0% +source this is happens to be a pretty + + + align:start position:0% +source this is happens to be a pretty +good source um and on the top is a power + + align:start position:0% +good source um and on the top is a power + + + align:start position:0% +good source um and on the top is a power +Spectrum uh and this is like a forer + + align:start position:0% +Spectrum uh and this is like a forer + + + align:start position:0% +Spectrum uh and this is like a forer +transform squared more or less and uh + + align:start position:0% +transform squared more or less and uh + + + align:start position:0% +transform squared more or less and uh +when you take such a for transform of + + align:start position:0% +when you take such a for transform of + + + align:start position:0% +when you take such a for transform of +this system this is for a 3,000 second + + align:start position:0% +this system this is for a 3,000 second + + + align:start position:0% +this system this is for a 3,000 second +observation of this particular black + + align:start position:0% +observation of this particular black + + + align:start position:0% +observation of this particular black +hole x-ray Nova what you see is a big + + align:start position:0% +hole x-ray Nova what you see is a big + + + align:start position:0% +hole x-ray Nova what you see is a big +thumping uh frequency here but it's not + + align:start position:0% +thumping uh frequency here but it's not + + + align:start position:0% +thumping uh frequency here but it's not +monochromatic you see it's not like a + + align:start position:0% +monochromatic you see it's not like a + + + align:start position:0% +monochromatic you see it's not like a +pulsar or something it's in one + + align:start position:0% +pulsar or something it's in one + + + align:start position:0% +pulsar or something it's in one +frequency bin it's in a wide range of + + align:start position:0% +frequency bin it's in a wide range of + + + align:start position:0% +frequency bin it's in a wide range of +frequency bins so it's a quasi periodic + + align:start position:0% +frequency bins so it's a quasi periodic + + + align:start position:0% +frequency bins so it's a quasi periodic +oscillation it isn't constant in Phase + + align:start position:0% +oscillation it isn't constant in Phase + + + align:start position:0% +oscillation it isn't constant in Phase +it appears it seems to wander in Phase + + align:start position:0% +it appears it seems to wander in Phase + + + align:start position:0% +it appears it seems to wander in Phase +nevertheless it gives you quite a big + + align:start position:0% +nevertheless it gives you quite a big + + + align:start position:0% +nevertheless it gives you quite a big +spike and you can see here also some + + align:start position:0% +spike and you can see here also some + + + align:start position:0% +spike and you can see here also some +satellite harmonics that appear here + + align:start position:0% +satellite harmonics that appear here + + + align:start position:0% +satellite harmonics that appear here +too that and you have we had something + + align:start position:0% +too that and you have we had something + + + align:start position:0% +too that and you have we had something +like uh 340 observations of this source + + align:start position:0% +like uh 340 observations of this source + + + align:start position:0% +like uh 340 observations of this source +with the rxt that are like this and uh + + align:start position:0% +with the rxt that are like this and uh + + + align:start position:0% +with the rxt that are like this and uh +something like 200 of them showed power + + align:start position:0% +something like 200 of them showed power + + + align:start position:0% +something like 200 of them showed power +like this so it isn't just that you get + + align:start position:0% +like this so it isn't just that you get + + + align:start position:0% +like this so it isn't just that you get +it once you get it a lot of times and + + align:start position:0% +it once you get it a lot of times and + + + align:start position:0% +it once you get it a lot of times and +you see a lot of regularities and I'll + + align:start position:0% +you see a lot of regularities and I'll + + + align:start position:0% +you see a lot of regularities and I'll +come to that in a moment uh what but + + align:start position:0% +come to that in a moment uh what but + + + align:start position:0% +come to that in a moment uh what but +just to give you a feeling it doesn't + + align:start position:0% +just to give you a feeling it doesn't + + + align:start position:0% +just to give you a feeling it doesn't +look like much because it's a log scale + + align:start position:0% +look like much because it's a log scale + + + align:start position:0% +look like much because it's a log scale +you have to keep an eye on the log scale + + align:start position:0% +you have to keep an eye on the log scale + + + align:start position:0% +you have to keep an eye on the log scale +here so if you just plot it as a Time + + align:start position:0% +here so if you just plot it as a Time + + + align:start position:0% +here so if you just plot it as a Time +series this is zero counts here per 16 + + align:start position:0% +series this is zero counts here per 16 + + + align:start position:0% +series this is zero counts here per 16 +millisecs and it goes up to like 100 + + align:start position:0% +millisecs and it goes up to like 100 + + + align:start position:0% +millisecs and it goes up to like 100 +counts per 16 milliseconds it's a + + align:start position:0% +counts per 16 milliseconds it's a + + + align:start position:0% +counts per 16 milliseconds it's a +10-second record so here you + + align:start position:0% +10-second record so here you + + + align:start position:0% +10-second record so here you +see the time series that makes this qpo + + align:start position:0% +see the time series that makes this qpo + + + align:start position:0% +see the time series that makes this qpo +pattern so it's huge now the source is + + align:start position:0% +pattern so it's huge now the source is + + + align:start position:0% +pattern so it's huge now the source is +radiating at like 10 the 39 URS per + + align:start position:0% +radiating at like 10 the 39 URS per + + + align:start position:0% +radiating at like 10 the 39 URS per +second in X-rays and uh something like + + align:start position:0% +second in X-rays and uh something like + + + align:start position:0% +second in X-rays and uh something like +25% of the photons that are being + + align:start position:0% +25% of the photons that are being + + + align:start position:0% +25% of the photons that are being +emitted a quarter of that 10 39 hergs + + align:start position:0% +emitted a quarter of that 10 39 hergs + + + align:start position:0% +emitted a quarter of that 10 39 hergs +per second are thumping away like this + + align:start position:0% +per second are thumping away like this + + + align:start position:0% +per second are thumping away like this +so this isn't an incidental detail on + + align:start position:0% +so this isn't an incidental detail on + + + align:start position:0% +so this isn't an incidental detail on +the accretion for flow or on the + + align:start position:0% +the accretion for flow or on the + + + align:start position:0% +the accretion for flow or on the +phenomena it's really extremely + + align:start position:0% +phenomena it's really extremely + + + align:start position:0% +phenomena it's really extremely +important and the frequency of this is + + align:start position:0% +important and the frequency of this is + + + align:start position:0% +important and the frequency of this is +these are what we call low frequency + + align:start position:0% +these are what we call low frequency + + + align:start position:0% +these are what we call low frequency +qpos meaning they're below 30 Herz or so + + align:start position:0% +qpos meaning they're below 30 Herz or so + + + align:start position:0% +qpos meaning they're below 30 Herz or so +and this one happened to be 2.7 Hertz + + align:start position:0% +and this one happened to be 2.7 Hertz + + + align:start position:0% +and this one happened to be 2.7 Hertz +but it it varies different it moves + + align:start position:0% +but it it varies different it moves + + + align:start position:0% +but it it varies different it moves +smoothly it correlates with the spectral + + align:start position:0% +smoothly it correlates with the spectral + + + align:start position:0% +smoothly it correlates with the spectral +parameters there's a lot of information + + align:start position:0% +parameters there's a lot of information + + + align:start position:0% +parameters there's a lot of information +you can get from this but we're not as + + align:start position:0% +you can get from this but we're not as + + + align:start position:0% +you can get from this but we're not as +interested in this as we are in the one + + align:start position:0% +interested in this as we are in the one + + + align:start position:0% +interested in this as we are in the one +I'm going to show you + + align:start position:0% +I'm going to show you + + + align:start position:0% +I'm going to show you +now because we this is a low frequency + + align:start position:0% +now because we this is a low frequency + + + align:start position:0% +now because we this is a low frequency +and it probably comes from pretty far + + align:start position:0% +and it probably comes from pretty far + + + align:start position:0% +and it probably comes from pretty far +out it doesn't have to come you know + + align:start position:0% +out it doesn't have to come you know + + + align:start position:0% +out it doesn't have to come you know +from close in it doesn't have the + + align:start position:0% +from close in it doesn't have the + + + align:start position:0% +from close in it doesn't have the +dynamical time of that 200 HZ or that + + align:start position:0% +dynamical time of that 200 HZ or that + + + align:start position:0% +dynamical time of that 200 HZ or that +1500 htz I was talking about at the + + align:start position:0% +1500 htz I was talking about at the + + + align:start position:0% +1500 htz I was talking about at the +beginning which is a time of of the disc + + align:start position:0% +beginning which is a time of of the disc + + + align:start position:0% +beginning which is a time of of the disc +to go around no it's much further out + + align:start position:0% +to go around no it's much further out + + + align:start position:0% +to go around no it's much further out +and neutron stars can produce this to + + align:start position:0% +and neutron stars can produce this to + + + align:start position:0% +and neutron stars can produce this to +some extent too so this is something + + align:start position:0% +some extent too so this is something + + + align:start position:0% +some extent too so this is something +that no one understands really in terms + + align:start position:0% +that no one understands really in terms + + + align:start position:0% +that no one understands really in terms +of model or anything and uh we would all + + align:start position:0% +of model or anything and uh we would all + + + align:start position:0% +of model or anything and uh we would all +love to understand it how what what is + + align:start position:0% +love to understand it how what what is + + + align:start position:0% +love to understand it how what what is +driving this and how it how it works and + + align:start position:0% +driving this and how it how it works and + + + align:start position:0% +driving this and how it how it works and +so forth but I will turn now to a more + + align:start position:0% +so forth but I will turn now to a more + + + align:start position:0% +so forth but I will turn now to a more +important aspect of these quasi periodic + + align:start position:0% +important aspect of these quasi periodic + + + align:start position:0% +important aspect of these quasi periodic +oscillations and this is the high + + align:start position:0% +oscillations and this is the high + + + align:start position:0% +oscillations and this is the high +frequency + + align:start position:0% +frequency + + + align:start position:0% +frequency +qpos and this is for another system uh + + align:start position:0% +qpos and this is for another system uh + + + align:start position:0% +qpos and this is for another system uh +1655 minus 40 and um what you see again + + align:start position:0% +1655 minus 40 and um what you see again + + + align:start position:0% +1655 minus 40 and um what you see again +is a power spectrum and we can't even + + align:start position:0% +is a power spectrum and we can't even + + + align:start position:0% +is a power spectrum and we can't even +make the time series here because this + + align:start position:0% +make the time series here because this + + + align:start position:0% +make the time series here because this +is 450 Hertz what does it say yeah it's + + align:start position:0% +is 450 Hertz what does it say yeah it's + + + align:start position:0% +is 450 Hertz what does it say yeah it's +here it's 450 htz right 450z Herz you + + align:start position:0% +here it's 450 htz right 450z Herz you + + + align:start position:0% +here it's 450 htz right 450z Herz you +can see it here on the axis too okay so + + align:start position:0% +can see it here on the axis too okay so + + + align:start position:0% +can see it here on the axis too okay so +this is this is quite serious now 450 HZ + + align:start position:0% +this is this is quite serious now 450 HZ + + + align:start position:0% +this is this is quite serious now 450 HZ +um this is a very high frequency so + + align:start position:0% +um this is a very high frequency so + + + align:start position:0% +um this is a very high frequency so +where would this be coming from and + + align:start position:0% +where would this be coming from and + + + align:start position:0% +where would this be coming from and +uh we believe that the clock that's + + align:start position:0% +uh we believe that the clock that's + + + align:start position:0% +uh we believe that the clock that's +producing this is really the disc + + align:start position:0% +producing this is really the disc + + + align:start position:0% +producing this is really the disc +rotation and already you learn something + + align:start position:0% +rotation and already you learn something + + + align:start position:0% +rotation and already you learn something +from 450 Hertz and what you learn from + + align:start position:0% +from 450 Hertz and what you learn from + + + align:start position:0% +from 450 Hertz and what you learn from +450 Hertz is that if you take the mass + + align:start position:0% +450 Hertz is that if you take the mass + + + align:start position:0% +450 Hertz is that if you take the mass +of this black hole this was the one I + + align:start position:0% +of this black hole this was the one I + + + align:start position:0% +of this black hole this was the one I +pointed out the way was the best + + align:start position:0% +pointed out the way was the best + + + align:start position:0% +pointed out the way was the best +measured one it's 6 and A2 solar masses + + align:start position:0% +measured one it's 6 and A2 solar masses + + + align:start position:0% +measured one it's 6 and A2 solar masses +we know it extremely well 6 and A2 plus + + align:start position:0% +we know it extremely well 6 and A2 plus + + + align:start position:0% +we know it extremely well 6 and A2 plus +orus 2/10 and uh so there's its + + align:start position:0% +orus 2/10 and uh so there's its + + + align:start position:0% +orus 2/10 and uh so there's its +mass and uh if you say 6 and a half + + align:start position:0% +mass and uh if you say 6 and a half + + + align:start position:0% +mass and uh if you say 6 and a half +solar masses what's the frequency of a + + align:start position:0% +solar masses what's the frequency of a + + + align:start position:0% +solar masses what's the frequency of a +schwar shield black + + align:start position:0% +schwar shield black + + + align:start position:0% +schwar shield black +hole at the last stable orbit well I + + align:start position:0% +hole at the last stable orbit well I + + + align:start position:0% +hole at the last stable orbit well I +just wrote it down here it's 340 Hertz + + align:start position:0% +just wrote it down here it's 340 Hertz + + + align:start position:0% +just wrote it down here it's 340 Hertz +you have to scale it from the number + + align:start position:0% +you have to scale it from the number + + + align:start position:0% +you have to scale it from the number +that I had in the earlier 220 HZ you go + + align:start position:0% +that I had in the earlier 220 HZ you go + + + align:start position:0% +that I had in the earlier 220 HZ you go +so 340 HZ is the fastest that this + + align:start position:0% +so 340 HZ is the fastest that this + + + align:start position:0% +so 340 HZ is the fastest that this +Schwarz Shield black hole could do we + + align:start position:0% +Schwarz Shield black hole could do we + + + align:start position:0% +Schwarz Shield black hole could do we +know its mass you see so we we know its + + align:start position:0% +know its mass you see so we we know its + + + align:start position:0% +know its mass you see so we we know its +mass so we know what the frequency of + + align:start position:0% +mass so we know what the frequency of + + + align:start position:0% +mass so we know what the frequency of +the last stable orbit is for a sh Shield + + align:start position:0% +the last stable orbit is for a sh Shield + + + align:start position:0% +the last stable orbit is for a sh Shield +hole and this thing is doing 450 htz so + + align:start position:0% +hole and this thing is doing 450 htz so + + + align:start position:0% +hole and this thing is doing 450 htz so +how is it doing 450 htz which is faster + + align:start position:0% +how is it doing 450 htz which is faster + + + align:start position:0% +how is it doing 450 htz which is faster +than the last stable + + align:start position:0% +than the last stable + + + align:start position:0% +than the last stable +orbit so anyone want to say what + + align:start position:0% +orbit so anyone want to say what + + + align:start position:0% +orbit so anyone want to say what +that it's ker ker so this is a really + + align:start position:0% +that it's ker ker so this is a really + + + align:start position:0% +that it's ker ker so this is a really +good case of a rotating black hole and + + align:start position:0% +good case of a rotating black hole and + + + align:start position:0% +good case of a rotating black hole and +uh so this is getting there you know I + + align:start position:0% +uh so this is getting there you know I + + + align:start position:0% +uh so this is getting there you know I +mean this is the kind of thing that + + align:start position:0% +mean this is the kind of thing that + + + align:start position:0% +mean this is the kind of thing that +makes you now the other thing that's + + align:start position:0% +makes you now the other thing that's + + + align:start position:0% +makes you now the other thing that's +very interesting is this system uh + + align:start position:0% +very interesting is this system uh + + + align:start position:0% +very interesting is this system uh +produces 450 and 300 so it produces an + + align:start position:0% +produces 450 and 300 so it produces an + + + align:start position:0% +produces 450 and 300 so it produces an +harmonic uh connection there you see you + + align:start position:0% +harmonic uh connection there you see you + + + align:start position:0% +harmonic uh connection there you see you +see those two frequencies fairly often + + align:start position:0% +see those two frequencies fairly often + + + align:start position:0% +see those two frequencies fairly often +and another system produces uh that kind + + align:start position:0% +and another system produces uh that kind + + + align:start position:0% +and another system produces uh that kind +of ratio + + align:start position:0% + + + + align:start position:0% + +also now what you would like to do again + + align:start position:0% +also now what you would like to do again + + + align:start position:0% +also now what you would like to do again +of course and why would you like to do + + align:start position:0% +of course and why would you like to do + + + align:start position:0% +of course and why would you like to do +it you'd like to get the black hole Spin + + align:start position:0% +it you'd like to get the black hole Spin + + + align:start position:0% +it you'd like to get the black hole Spin +and why do you want the black hole spin + + align:start position:0% +and why do you want the black hole spin + + + align:start position:0% +and why do you want the black hole spin +because you've already got its mass so + + align:start position:0% +because you've already got its mass so + + + align:start position:0% +because you've already got its mass so +if you had it spin that's it that's you + + align:start position:0% +if you had it spin that's it that's you + + + align:start position:0% +if you had it spin that's it that's you +know the no hair theorem I mean you've + + align:start position:0% +know the no hair theorem I mean you've + + + align:start position:0% +know the no hair theorem I mean you've +got it all so uh you really want it spin + + align:start position:0% +got it all so uh you really want it spin + + + align:start position:0% +got it all so uh you really want it spin +and uh I was already hinting maybe with + + align:start position:0% +and uh I was already hinting maybe with + + + align:start position:0% +and uh I was already hinting maybe with +the spectroscopy we might be able to do + + align:start position:0% +the spectroscopy we might be able to do + + + align:start position:0% +the spectroscopy we might be able to do +it on the iron line if we understood + + align:start position:0% +it on the iron line if we understood + + + align:start position:0% +it on the iron line if we understood +things well enough and these qpos + + align:start position:0% +things well enough and these qpos + + + align:start position:0% +things well enough and these qpos +another possible Avenue for getting the + + align:start position:0% +another possible Avenue for getting the + + + align:start position:0% +another possible Avenue for getting the +spin and here we have a system that gee + + align:start position:0% +spin and here we have a system that gee + + + align:start position:0% +spin and here we have a system that gee +we're we're pretty sure it has to be + + align:start position:0% +we're we're pretty sure it has to be + + + align:start position:0% +we're we're pretty sure it has to be +spinning because the frequency is just + + align:start position:0% +spinning because the frequency is just + + + align:start position:0% +spinning because the frequency is just +too high for schw shield hole + + align:start position:0% +too high for schw shield hole + + + align:start position:0% +too high for schw shield hole +um so in this case + + align:start position:0% +um so in this case + + + align:start position:0% +um so in this case +um it's got 300 and 450 Hertz so it has + + align:start position:0% +um it's got 300 and 450 Hertz so it has + + + align:start position:0% +um it's got 300 and 450 Hertz so it has +this 2:3 harmonic ratio that I mentioned + + align:start position:0% +this 2:3 harmonic ratio that I mentioned + + + align:start position:0% +this 2:3 harmonic ratio that I mentioned +before and here's another one that has a + + align:start position:0% +before and here's another one that has a + + + align:start position:0% +before and here's another one that has a +2 to3 harmonic + + align:start position:0% +2 to3 harmonic + + + align:start position:0% +2 to3 harmonic +ratio uh another system that I mentioned + + align:start position:0% +ratio uh another system that I mentioned + + + align:start position:0% +ratio uh another system that I mentioned +it another time actually and now there + + align:start position:0% +it another time actually and now there + + + align:start position:0% +it another time actually and now there +are something like three models that + + align:start position:0% +are something like three models that + + + align:start position:0% +are something like three models that +people have developed to say uh can we + + align:start position:0% +people have developed to say uh can we + + + align:start position:0% +people have developed to say uh can we +take uh these highfrequency qpos and + + align:start position:0% +take uh these highfrequency qpos and + + + align:start position:0% +take uh these highfrequency qpos and +deduce the spin and uh I don't want to + + align:start position:0% +deduce the spin and uh I don't want to + + + align:start position:0% +deduce the spin and uh I don't want to +go through those three models that would + + align:start position:0% +go through those three models that would + + + align:start position:0% +go through those three models that would +just take a little too long but one one + + align:start position:0% +just take a little too long but one one + + + align:start position:0% +just take a little too long but one one +simple model for example um and each one + + align:start position:0% +simple model for example um and each one + + + align:start position:0% +simple model for example um and each one +of them has their problems but uh one + + align:start position:0% +of them has their problems but uh one + + + align:start position:0% +of them has their problems but uh one +simple model is to say that and and + + align:start position:0% +simple model is to say that and and + + + align:start position:0% +simple model is to say that and and +maybe you know this I don't know uh but + + align:start position:0% +maybe you know this I don't know uh but + + + align:start position:0% +maybe you know this I don't know uh but +if you take like in the Kepler problem + + align:start position:0% +if you take like in the Kepler problem + + + align:start position:0% +if you take like in the Kepler problem +like in the solar system and you take a + + align:start position:0% +like in the solar system and you take a + + + align:start position:0% +like in the solar system and you take a +plan or uh and you and you have it going + + align:start position:0% +plan or uh and you and you have it going + + + align:start position:0% +plan or uh and you and you have it going +around at the Kepler frequency just the + + align:start position:0% +around at the Kepler frequency just the + + + align:start position:0% +around at the Kepler frequency just the +orbital period of the system and then + + align:start position:0% +orbital period of the system and then + + + align:start position:0% +orbital period of the system and then +you perturb it radially for example so + + align:start position:0% +you perturb it radially for example so + + + align:start position:0% +you perturb it radially for example so +that it isn't going around A Perfect + + align:start position:0% +that it isn't going around A Perfect + + + align:start position:0% +that it isn't going around A Perfect +Circle but it's it's it wants to go has + + align:start position:0% +Circle but it's it's it wants to go has + + + align:start position:0% +Circle but it's it's it wants to go has +has also got an oscillation in the + + align:start position:0% +has also got an oscillation in the + + + align:start position:0% +has also got an oscillation in the +radial direction or an oscillation out + + align:start position:0% +radial direction or an oscillation out + + + align:start position:0% +radial direction or an oscillation out +of the plane out of the ecliptic plane + + align:start position:0% +of the plane out of the ecliptic plane + + + align:start position:0% +of the plane out of the ecliptic plane +make it oscillate and you could go push + + align:start position:0% +make it oscillate and you could go push + + + align:start position:0% +make it oscillate and you could go push +on a planet really hard and get it to do + + align:start position:0% +on a planet really hard and get it to do + + + align:start position:0% +on a planet really hard and get it to do +that or you know set up another problem + + align:start position:0% +that or you know set up another problem + + + align:start position:0% +that or you know set up another problem +if you can't do that one and uh and then + + align:start position:0% +if you can't do that one and uh and then + + + align:start position:0% +if you can't do that one and uh and then +it it's those frequencies in the radial + + align:start position:0% +it it's those frequencies in the radial + + + align:start position:0% +it it's those frequencies in the radial +Direction and the Z direction are + + align:start position:0% +Direction and the Z direction are + + + align:start position:0% +Direction and the Z direction are +degenerate with the Kepler frequency and + + align:start position:0% +degenerate with the Kepler frequency and + + + align:start position:0% +degenerate with the Kepler frequency and +that's a property of the uh of the um of + + align:start position:0% +that's a property of the uh of the um of + + + align:start position:0% +that's a property of the uh of the um of +that uh simple uh uh classical problem + + align:start position:0% +that uh simple uh uh classical problem + + + align:start position:0% +that uh simple uh uh classical problem +but in general relativity those + + align:start position:0% +but in general relativity those + + + align:start position:0% +but in general relativity those +frequencies are not degenerate and uh so + + align:start position:0% +frequencies are not degenerate and uh so + + + align:start position:0% +frequencies are not degenerate and uh so +one could say well maybe there's some + + align:start position:0% +one could say well maybe there's some + + + align:start position:0% +one could say well maybe there's some +resonances going on between these + + align:start position:0% +resonances going on between these + + + align:start position:0% +resonances going on between these +different frequencies and that's what's + + align:start position:0% +different frequencies and that's what's + + + align:start position:0% +different frequencies and that's what's +driving these highfrequency + + align:start position:0% +driving these highfrequency + + + align:start position:0% +driving these highfrequency +qpos and uh these these people have + + align:start position:0% +qpos and uh these these people have + + + align:start position:0% +qpos and uh these these people have +pushed that particular model and I don't + + align:start position:0% +pushed that particular model and I don't + + + align:start position:0% +pushed that particular model and I don't +I don't want to get into the details of + + align:start position:0% +I don't want to get into the details of + + + align:start position:0% +I don't want to get into the details of +it it but U the idea would be that you + + align:start position:0% +it it but U the idea would be that you + + + align:start position:0% +it it but U the idea would be that you +know here's here's be the radial + + align:start position:0% +know here's here's be the radial + + + align:start position:0% +know here's here's be the radial +frequency the Z dependent frequency the + + align:start position:0% +frequency the Z dependent frequency the + + + align:start position:0% +frequency the Z dependent frequency the +Kepler frequency and all of these things + + align:start position:0% +Kepler frequency and all of these things + + + align:start position:0% +Kepler frequency and all of these things +depend on the mass of the black hole and + + align:start position:0% +depend on the mass of the black hole and + + + align:start position:0% +depend on the mass of the black hole and +on the spin and uh so you know if you + + align:start position:0% +on the spin and uh so you know if you + + + align:start position:0% +on the spin and uh so you know if you +could make good enough measurements you + + align:start position:0% +could make good enough measurements you + + + align:start position:0% +could make good enough measurements you +might be able to determine the the the + + align:start position:0% +might be able to determine the the the + + + align:start position:0% +might be able to determine the the the +spin of the black hole and what's so + + align:start position:0% +spin of the black hole and what's so + + + align:start position:0% +spin of the black hole and what's so +nice is we actually measure the mass + + align:start position:0% +nice is we actually measure the mass + + + align:start position:0% +nice is we actually measure the mass +dynamically and this is a way we really + + align:start position:0% +dynamically and this is a way we really + + + align:start position:0% +dynamically and this is a way we really +understand it so we're not forced to try + + align:start position:0% +understand it so we're not forced to try + + + align:start position:0% +understand it so we're not forced to try +to fit two parameters here when we don't + + align:start position:0% +to fit two parameters here when we don't + + + align:start position:0% +to fit two parameters here when we don't +really understand one you know we we can + + align:start position:0% +really understand one you know we we can + + + align:start position:0% +really understand one you know we we can +go only for the second one because we've + + align:start position:0% +go only for the second one because we've + + + align:start position:0% +go only for the second one because we've +already got the first one and we have + + align:start position:0% +already got the first one and we have + + + align:start position:0% +already got the first one and we have +the capacity to even you know measure + + align:start position:0% +the capacity to even you know measure + + + align:start position:0% +the capacity to even you know measure +those much better um but all of the + + align:start position:0% +those much better um but all of the + + + align:start position:0% +those much better um but all of the +three models depend on strong field + + align:start position:0% +three models depend on strong field + + + align:start position:0% +three models depend on strong field +general relativity for producing these + + align:start position:0% +general relativity for producing these + + + align:start position:0% +general relativity for producing these +high frequency qpos and uh uh needs to + + align:start position:0% +high frequency qpos and uh uh needs to + + + align:start position:0% +high frequency qpos and uh uh needs to +be sorted out and here's my attitude my + + align:start position:0% +be sorted out and here's my attitude my + + + align:start position:0% +be sorted out and here's my attitude my +attitude is that only in the last you + + align:start position:0% +attitude is that only in the last you + + + align:start position:0% +attitude is that only in the last you +can see 2001 2002 we've got these + + align:start position:0% +can see 2001 2002 we've got these + + + align:start position:0% +can see 2001 2002 we've got these +resonances here or whatever you want to + + align:start position:0% +resonances here or whatever you want to + + + align:start position:0% +resonances here or whatever you want to +call them these harmonic relationships + + align:start position:0% +call them these harmonic relationships + + + align:start position:0% +call them these harmonic relationships +um and we've got Rossy x-ray timing + + align:start position:0% +um and we've got Rossy x-ray timing + + + align:start position:0% +um and we've got Rossy x-ray timing +Explorer which has an area of about + + align:start position:0% +Explorer which has an area of about + + + align:start position:0% +Explorer which has an area of about +square meter of detector area and what + + align:start position:0% +square meter of detector area and what + + + align:start position:0% +square meter of detector area and what +we need now is 10 square meters of + + align:start position:0% +we need now is 10 square meters of + + + align:start position:0% +we need now is 10 square meters of +detector area and not you know 50 kilo + + align:start position:0% +detector area and not you know 50 kilo + + + align:start position:0% +detector area and not you know 50 kilo +kilobits per second of telemetry but we + + align:start position:0% +kilobits per second of telemetry but we + + + align:start position:0% +kilobits per second of telemetry but we +need you know a megabit per second of + + align:start position:0% +need you know a megabit per second of + + + align:start position:0% +need you know a megabit per second of +telemetry in other words we need a + + align:start position:0% +telemetry in other words we need a + + + align:start position:0% +telemetry in other words we need a +bigger Mission we're right you know just + + align:start position:0% +bigger Mission we're right you know just + + + align:start position:0% +bigger Mission we're right you know just +hanging on by our fingernails to measure + + align:start position:0% +hanging on by our fingernails to measure + + + align:start position:0% +hanging on by our fingernails to measure +these things but these things would + + align:start position:0% +these things but these things would + + + align:start position:0% +these things but these things would +become like you know right fruit if you + + align:start position:0% +become like you know right fruit if you + + + align:start position:0% +become like you know right fruit if you +had the right you know system big enough + + align:start position:0% +had the right you know system big enough + + + align:start position:0% +had the right you know system big enough +telescope to really collect + + align:start position:0% +telescope to really collect + + + align:start position:0% +telescope to really collect +so uh one one thing you can do that was + + align:start position:0% +so uh one one thing you can do that was + + + align:start position:0% +so uh one one thing you can do that was +kind of interesting and I I just did + + align:start position:0% +kind of interesting and I I just did + + + align:start position:0% +kind of interesting and I I just did +this as a slight + + align:start position:0% + + + + align:start position:0% + +quantitative this is a sort of a + + align:start position:0% +quantitative this is a sort of a + + + align:start position:0% +quantitative this is a sort of a +continuation of what I was just showing + + align:start position:0% +continuation of what I was just showing + + + align:start position:0% +continuation of what I was just showing +you again here's these two systems 1655 + + align:start position:0% +you again here's these two systems 1655 + + + align:start position:0% +you again here's these two systems 1655 +and + + align:start position:0% +and + + + align:start position:0% +and +1550 and here's their frequencies the + + align:start position:0% +1550 and here's their frequencies the + + + align:start position:0% +1550 and here's their frequencies the +ratios of their + + align:start position:0% +ratios of their + + + align:start position:0% +ratios of their +frequencies and that ratio comes out to + + align:start position:0% +frequencies and that ratio comes out to + + + align:start position:0% +frequencies and that ratio comes out to +be that + + align:start position:0% +be that + + + align:start position:0% +be that +number and this is Ron rard who works at + + align:start position:0% +number and this is Ron rard who works at + + + align:start position:0% +number and this is Ron rard who works at +CSR if any of you hav to know him um and + + align:start position:0% +CSR if any of you hav to know him um and + + + align:start position:0% +CSR if any of you hav to know him um and +uh if you take the ratios of the masses + + align:start position:0% +uh if you take the ratios of the masses + + + align:start position:0% +uh if you take the ratios of the masses +that have been measured for these black + + align:start position:0% +that have been measured for these black + + + align:start position:0% +that have been measured for these black +holes you get the same number it has a + + align:start position:0% +holes you get the same number it has a + + + align:start position:0% +holes you get the same number it has a +rather large uncertainty unfortunately + + align:start position:0% +rather large uncertainty unfortunately + + + align:start position:0% +rather large uncertainty unfortunately +because of this one black hole which is + + align:start position:0% +because of this one black hole which is + + + align:start position:0% +because of this one black hole which is +not so well + + align:start position:0% +not so well + + + align:start position:0% +not so well +measured but uh it's actually the + + align:start position:0% +measured but uh it's actually the + + + align:start position:0% +measured but uh it's actually the +reciprocal the point is the frequency we + + align:start position:0% +reciprocal the point is the frequency we + + + align:start position:0% +reciprocal the point is the frequency we +expect the frequency to scale as one + + align:start position:0% +expect the frequency to scale as one + + + align:start position:0% +expect the frequency to scale as one +over the mass you know the more massive + + align:start position:0% +over the mass you know the more massive + + + align:start position:0% +over the mass you know the more massive +a black hole is the larger it is the + + align:start position:0% +a black hole is the larger it is the + + + align:start position:0% +a black hole is the larger it is the +longer it takes to make an orbit the + + align:start position:0% +longer it takes to make an orbit the + + + align:start position:0% +longer it takes to make an orbit the +lower the dynamical time L lower the + + align:start position:0% +lower the dynamical time L lower the + + + align:start position:0% +lower the dynamical time L lower the +frequency rather I mean so uh you you + + align:start position:0% +frequency rather I mean so uh you you + + + align:start position:0% +frequency rather I mean so uh you you +get some agreement here on this that + + align:start position:0% +get some agreement here on this that + + + align:start position:0% +get some agreement here on this that +these two black holes are are scaling + + align:start position:0% +these two black holes are are scaling + + + align:start position:0% +these two black holes are are scaling +approximately correctly but again we + + align:start position:0% +approximately correctly but again we + + + align:start position:0% +approximately correctly but again we +need a lot more and a lot better + + align:start position:0% +need a lot more and a lot better + + + align:start position:0% +need a lot more and a lot better +data I mean when you consider that all + + align:start position:0% +data I mean when you consider that all + + + align:start position:0% +data I mean when you consider that all +of this just came from rxte which was + + align:start position:0% +of this just came from rxte which was + + + align:start position:0% +of this just came from rxte which was +launched in January of 96 uh it's you + + align:start position:0% +launched in January of 96 uh it's you + + + align:start position:0% +launched in January of 96 uh it's you +know it's very impressive I think + + align:start position:0% +know it's very impressive I think + + + align:start position:0% +know it's very impressive I think +there's + + align:start position:0% +there's + + + align:start position:0% +there's +a with a lot of other missions coming + + align:start position:0% +a with a lot of other missions coming + + + align:start position:0% +a with a lot of other missions coming +along I think we've got a lot of uh + + align:start position:0% +along I think we've got a lot of uh + + + align:start position:0% +along I think we've got a lot of uh +things to look forward to and now U I + + align:start position:0% +things to look forward to and now U I + + + align:start position:0% +things to look forward to and now U I +wanted to mention this micro quazar idea + + align:start position:0% +wanted to mention this micro quazar idea + + + align:start position:0% +wanted to mention this micro quazar idea +which is really just saying that these + + align:start position:0% +which is really just saying that these + + + align:start position:0% +which is really just saying that these +objects look like these objects look + + align:start position:0% +objects look like these objects look + + + align:start position:0% +objects look like these objects look +like + + align:start position:0% +like + + + align:start position:0% +like +um quazar so this is the red this is the + + align:start position:0% +um quazar so this is the red this is the + + + align:start position:0% +um quazar so this is the red this is the +ordinary star over here and this is the + + align:start position:0% +ordinary star over here and this is the + + + align:start position:0% +ordinary star over here and this is the +accretion disc around here and this is a + + align:start position:0% +accretion disc around here and this is a + + + align:start position:0% +accretion disc around here and this is a +sketch that uh Felix Mirabel drew the + + align:start position:0% +sketch that uh Felix Mirabel drew the + + + align:start position:0% +sketch that uh Felix Mirabel drew the +black holes down here in the center and + + align:start position:0% +black holes down here in the center and + + + align:start position:0% +black holes down here in the center and +then you see these Jets coming out well + + align:start position:0% +then you see these Jets coming out well + + + align:start position:0% +then you see these Jets coming out well +there's been a lot of radio Jets + + align:start position:0% +there's been a lot of radio Jets + + + align:start position:0% +there's been a lot of radio Jets +observed now perhaps 10 systems have had + + align:start position:0% +observed now perhaps 10 systems have had + + + align:start position:0% +observed now perhaps 10 systems have had +radio Jets coming out relativistic radio + + align:start position:0% +radio Jets coming out relativistic radio + + + align:start position:0% +radio Jets coming out relativistic radio +Jets and as opposed to the AG type the + + align:start position:0% +Jets and as opposed to the AG type the + + + align:start position:0% +Jets and as opposed to the AG type the +ones that are from external galaxies + + align:start position:0% +ones that are from external galaxies + + + align:start position:0% +ones that are from external galaxies +which are kind of like Frozen on the sky + + align:start position:0% +which are kind of like Frozen on the sky + + + align:start position:0% +which are kind of like Frozen on the sky +these things move across the sky and + + align:start position:0% +these things move across the sky and + + + align:start position:0% +these things move across the sky and +I'll show you in the next picture here U + + align:start position:0% +I'll show you in the next picture here U + + + align:start position:0% +I'll show you in the next picture here U +and uh they're typically a few light + + align:start position:0% +and uh they're typically a few light + + + align:start position:0% +and uh they're typically a few light +years long as indicated here um and one + + align:start position:0% +years long as indicated here um and one + + + align:start position:0% +years long as indicated here um and one +imagines that probably they're driven + + align:start position:0% +imagines that probably they're driven + + + align:start position:0% +imagines that probably they're driven +when maybe the mass secretion rate onto + + align:start position:0% +when maybe the mass secretion rate onto + + + align:start position:0% +when maybe the mass secretion rate onto +the black hole is just a little too high + + align:start position:0% +the black hole is just a little too high + + + align:start position:0% +the black hole is just a little too high +and the matter coming in and in the + + align:start position:0% +and the matter coming in and in the + + + align:start position:0% +and the matter coming in and in the +black hole and people think well the + + align:start position:0% +black hole and people think well the + + + align:start position:0% +black hole and people think well the +black hole is probably spinning for + + align:start position:0% +black hole is probably spinning for + + + align:start position:0% +black hole is probably spinning for +these systems and there's some evidence + + align:start position:0% +these systems and there's some evidence + + + align:start position:0% +these systems and there's some evidence +in a couple of cases that they are like + + align:start position:0% +in a couple of cases that they are like + + + align:start position:0% +in a couple of cases that they are like +this one that I just showed you the 1655 + + align:start position:0% +this one that I just showed you the 1655 + + + align:start position:0% +this one that I just showed you the 1655 +from the qpo data and the materials + + align:start position:0% +from the qpo data and the materials + + + align:start position:0% +from the qpo data and the materials +coming in and excess material just get + + align:start position:0% +coming in and excess material just get + + + align:start position:0% +coming in and excess material just get +squirted out the axis the spin axis of + + align:start position:0% +squirted out the axis the spin axis of + + + align:start position:0% +squirted out the axis the spin axis of +the black hole and that's sort of a hand + + align:start position:0% +the black hole and that's sort of a hand + + + align:start position:0% +the black hole and that's sort of a hand +waving picture of how it might go to + + align:start position:0% +waving picture of how it might go to + + + align:start position:0% +waving picture of how it might go to +produce these Jets but these Jets exist + + align:start position:0% +produce these Jets but these Jets exist + + + align:start position:0% +produce these Jets but these Jets exist +you know you can wave your hands or not + + align:start position:0% +you know you can wave your hands or not + + + align:start position:0% +you know you can wave your hands or not +w wave your hands it doesn't matter they + + align:start position:0% +w wave your hands it doesn't matter they + + + align:start position:0% +w wave your hands it doesn't matter they +exist whether you know no matter what um + + align:start position:0% +exist whether you know no matter what um + + + align:start position:0% +exist whether you know no matter what um +and that's and and very recently I + + align:start position:0% +and that's and and very recently I + + + align:start position:0% +and that's and and very recently I +should mention while this is here uh the + + align:start position:0% +should mention while this is here uh the + + + align:start position:0% +should mention while this is here uh the +discovery of X-ray Jets from these black + + align:start position:0% +discovery of X-ray Jets from these black + + + align:start position:0% +discovery of X-ray Jets from these black +holes and uh the one system has an x-ray + + align:start position:0% +holes and uh the one system has an x-ray + + + align:start position:0% +holes and uh the one system has an x-ray +jet here and one on the other side and + + align:start position:0% +jet here and one on the other side and + + + align:start position:0% +jet here and one on the other side and +the Jets are decelerating and they're + + align:start position:0% +the Jets are decelerating and they're + + + align:start position:0% +the Jets are decelerating and they're +quite a way out and these x-ray jets are + + align:start position:0% +quite a way out and these x-ray jets are + + + align:start position:0% +quite a way out and these x-ray jets are +not understood I mean this is about a + + align:start position:0% +not understood I mean this is about a + + + align:start position:0% +not understood I mean this is about a +year perhaps no not that old six months + + align:start position:0% +year perhaps no not that old six months + + + align:start position:0% +year perhaps no not that old six months +old something like that um so x-ray jets + + align:start position:0% +old something like that um so x-ray jets + + + align:start position:0% +old something like that um so x-ray jets +are are are yet another thing coming + + align:start position:0% +are are are yet another thing coming + + + align:start position:0% +are are are yet another thing coming +from these systems um but the radio Jets + + align:start position:0% +from these systems um but the radio Jets + + + align:start position:0% +from these systems um but the radio Jets +as I say have been seen in 10 systems or + + align:start position:0% +as I say have been seen in 10 systems or + + + align:start position:0% +as I say have been seen in 10 systems or +so and just to give you a feeling for + + align:start position:0% +so and just to give you a feeling for + + + align:start position:0% +so and just to give you a feeling for +the radio jets in uh this is the large + + align:start position:0% +the radio jets in uh this is the large + + + align:start position:0% +the radio jets in uh this is the large +system that had 35-day period was the + + align:start position:0% +system that had 35-day period was the + + + align:start position:0% +system that had 35-day period was the +top of the original figure I showed grs1 + + align:start position:0% +top of the original figure I showed grs1 + + + align:start position:0% +top of the original figure I showed grs1 +1915 plus + + align:start position:0% +1915 plus + + + align:start position:0% +1915 plus +105 and this jet is coming out uh the + + align:start position:0% +105 and this jet is coming out uh the + + + align:start position:0% +105 and this jet is coming out uh the +velocity of the jet the beta is 0.92 as + + align:start position:0% +velocity of the jet the beta is 0.92 as + + + align:start position:0% +velocity of the jet the beta is 0.92 as +you see here and this is what the jet + + align:start position:0% +you see here and this is what the jet + + + align:start position:0% +you see here and this is what the jet +looked like in the at at end of March + + align:start position:0% +looked like in the at at end of March + + + align:start position:0% +looked like in the at at end of March +and this is what it looked like the end + + align:start position:0% +and this is what it looked like the end + + + align:start position:0% +and this is what it looked like the end +of April so what you're seeing is + + align:start position:0% +of April so what you're seeing is + + + align:start position:0% +of April so what you're seeing is +there's a a core source here I guess + + align:start position:0% +there's a a core source here I guess + + + align:start position:0% +there's a a core source here I guess +it's marked by the X it's stationary + + align:start position:0% +it's marked by the X it's stationary + + + align:start position:0% +it's marked by the X it's stationary +right which is really where the binary + + align:start position:0% +right which is really where the binary + + + align:start position:0% +right which is really where the binary +is and then you're seeing these radio + + align:start position:0% +is and then you're seeing these radio + + + align:start position:0% +is and then you're seeing these radio +blobs coming out and you can see that + + align:start position:0% +blobs coming out and you can see that + + + align:start position:0% +blobs coming out and you can see that +they're + + align:start position:0% +they're + + + align:start position:0% +they're +separating and unlike the ones in in the + + align:start position:0% +separating and unlike the ones in in the + + + align:start position:0% +separating and unlike the ones in in the +extragalactic case in just a month the + + align:start position:0% +extragalactic case in just a month the + + + align:start position:0% +extragalactic case in just a month the +two blobs are an arcc apart so that's + + align:start position:0% +two blobs are an arcc apart so that's + + + align:start position:0% +two blobs are an arcc apart so that's +rather High proper motion when you + + align:start position:0% +rather High proper motion when you + + + align:start position:0% +rather High proper motion when you +consider the systems that are living + + align:start position:0% +consider the systems that are living + + + align:start position:0% +consider the systems that are living +kill a Parx so uh so this is perhaps the + + align:start position:0% +kill a Parx so uh so this is perhaps the + + + align:start position:0% +kill a Parx so uh so this is perhaps the +best performer of the black ho Jet + + align:start position:0% +best performer of the black ho Jet + + + align:start position:0% +best performer of the black ho Jet +Systems + + align:start position:0% +Systems + + + align:start position:0% +Systems +1915 and uh so the the the jet the Jets + + align:start position:0% +1915 and uh so the the the jet the Jets + + + align:start position:0% +1915 and uh so the the the jet the Jets +I would say aren't giving you + + align:start position:0% +I would say aren't giving you + + + align:start position:0% +I would say aren't giving you +fundamental + + align:start position:0% +fundamental + + + align:start position:0% +fundamental +information maybe they will sometime but + + align:start position:0% +information maybe they will sometime but + + + align:start position:0% +information maybe they will sometime but +uh they aren't going to they we don't + + align:start position:0% +uh they aren't going to they we don't + + + align:start position:0% +uh they aren't going to they we don't +know how to use them say to measure the + + align:start position:0% +know how to use them say to measure the + + + align:start position:0% +know how to use them say to measure the +spin that's more like the spectroscopy + + align:start position:0% +spin that's more like the spectroscopy + + + align:start position:0% +spin that's more like the spectroscopy +and the iron line and the qpos but this + + align:start position:0% +and the iron line and the qpos but this + + + align:start position:0% +and the iron line and the qpos but this +is not but this is obviously very + + align:start position:0% +is not but this is obviously very + + + align:start position:0% +is not but this is obviously very +interesting for understanding + + align:start position:0% +interesting for understanding + + + align:start position:0% +interesting for understanding +extragalactic Jets and uh being able to + + align:start position:0% +extragalactic Jets and uh being able to + + + align:start position:0% +extragalactic Jets and uh being able to +uh study jets in a in a much more + + align:start position:0% +uh study jets in a in a much more + + + align:start position:0% +uh study jets in a in a much more +Dynamic + + align:start position:0% + + + + align:start position:0% + +way now in the in the quiescent + + align:start position:0% +way now in the in the quiescent + + + align:start position:0% +way now in the in the quiescent +state when these systems are quiescent + + align:start position:0% +state when these systems are quiescent + + + align:start position:0% +state when these systems are quiescent +now this is just a matter of fact and + + align:start position:0% +now this is just a matter of fact and + + + align:start position:0% +now this is just a matter of fact and +then we can talk about the + + align:start position:0% +then we can talk about the + + + align:start position:0% +then we can talk about the +interpretation but in this quiet State + + align:start position:0% +interpretation but in this quiet State + + + align:start position:0% +interpretation but in this quiet State +you can measure the emission from these + + align:start position:0% +you can measure the emission from these + + + align:start position:0% +you can measure the emission from these +black holes but as I told you at the + + align:start position:0% +black holes but as I told you at the + + + align:start position:0% +black holes but as I told you at the +beginning in that one diagram instead of + + align:start position:0% +beginning in that one diagram instead of + + + align:start position:0% +beginning in that one diagram instead of +being 10 38 or 10 39 ergs per second + + align:start position:0% +being 10 38 or 10 39 ergs per second + + + align:start position:0% +being 10 38 or 10 39 ergs per second +you're now down at 10 to the 30th hers + + align:start position:0% +you're now down at 10 to the 30th hers + + + align:start position:0% +you're now down at 10 to the 30th hers +per second so you can only measure them + + align:start position:0% +per second so you can only measure them + + + align:start position:0% +per second so you can only measure them +effectively with these brand new + + align:start position:0% +effectively with these brand new + + + align:start position:0% +effectively with these brand new +beautiful x-ray telescopes like Chandra + + align:start position:0% +beautiful x-ray telescopes like Chandra + + + align:start position:0% +beautiful x-ray telescopes like Chandra +and xmm if you're familiar with them and + + align:start position:0% +and xmm if you're familiar with them and + + + align:start position:0% +and xmm if you're familiar with them and +uh so you have to go to very sensitive + + align:start position:0% +uh so you have to go to very sensitive + + + align:start position:0% +uh so you have to go to very sensitive +focusing Optics to make these + + align:start position:0% +focusing Optics to make these + + + align:start position:0% +focusing Optics to make these +measurements and when you do it you find + + align:start position:0% +measurements and when you do it you find + + + align:start position:0% +measurements and when you do it you find +that these black holes are extremely + + align:start position:0% +that these black holes are extremely + + + align:start position:0% +that these black holes are extremely +faint just a matter of fact you know and + + align:start position:0% +faint just a matter of fact you know and + + + align:start position:0% +faint just a matter of fact you know and +here's here's their + + align:start position:0% +here's here's their + + + align:start position:0% +here's here's their +Luminosity scale to the Edington + + align:start position:0% +Luminosity scale to the Edington + + + align:start position:0% +Luminosity scale to the Edington +luminosity and we have reasons for that + + align:start position:0% +luminosity and we have reasons for that + + + align:start position:0% +luminosity and we have reasons for that +but it's the Luminosity scale to the + + align:start position:0% +but it's the Luminosity scale to the + + + align:start position:0% +but it's the Luminosity scale to the +Edington Luminosity so for the black + + align:start position:0% +Edington Luminosity so for the black + + + align:start position:0% +Edington Luminosity so for the black +holes that number is tends to be very + + align:start position:0% +holes that number is tends to be very + + + align:start position:0% +holes that number is tends to be very +very low now these over here are not + + align:start position:0% +very low now these over here are not + + + align:start position:0% +very low now these over here are not +really we don't have any neutron stars + + align:start position:0% +really we don't have any neutron stars + + + align:start position:0% +really we don't have any neutron stars +to compare them to and these are not + + align:start position:0% +to compare them to and these are not + + + align:start position:0% +to compare them to and these are not +really too comparable uh this is a long + + align:start position:0% +really too comparable uh this is a long + + + align:start position:0% +really too comparable uh this is a long +story but basically these are the long + + align:start position:0% +story but basically these are the long + + + align:start position:0% +story but basically these are the long +orbital period systems and in these + + align:start position:0% +orbital period systems and in these + + + align:start position:0% +orbital period systems and in these +systems the mass secretion rate is much + + align:start position:0% +systems the mass secretion rate is much + + + align:start position:0% +systems the mass secretion rate is much +higher and it's just they're not + + align:start position:0% +higher and it's just they're not + + + align:start position:0% +higher and it's just they're not +comparable to the short period ones but + + align:start position:0% +comparable to the short period ones but + + + align:start position:0% +comparable to the short period ones but +if you restrict yourself to the area + + align:start position:0% +if you restrict yourself to the area + + + align:start position:0% +if you restrict yourself to the area +that's not cross-hatched here and you + + align:start position:0% +that's not cross-hatched here and you + + + align:start position:0% +that's not cross-hatched here and you +compare the luminosities of the black + + align:start position:0% +compare the luminosities of the black + + + align:start position:0% +compare the luminosities of the black +holes well first of all they're + + align:start position:0% +holes well first of all they're + + + align:start position:0% +holes well first of all they're +radiating at 10 the minus 8 of Edington + + align:start position:0% +radiating at 10 the minus 8 of Edington + + + align:start position:0% +radiating at 10 the minus 8 of Edington +and by that I mean Edington would be uh + + align:start position:0% +and by that I mean Edington would be uh + + + align:start position:0% +and by that I mean Edington would be uh +well Edington is 1.3 * 10 38 ergs per + + align:start position:0% +well Edington is 1.3 * 10 38 ergs per + + + align:start position:0% +well Edington is 1.3 * 10 38 ergs per +second for a solar mass for a 10 solar + + align:start position:0% +second for a solar mass for a 10 solar + + + align:start position:0% +second for a solar mass for a 10 solar +mass black hole be like 10 39 ergs per + + align:start position:0% +mass black hole be like 10 39 ergs per + + + align:start position:0% +mass black hole be like 10 39 ergs per +second and that's the maximum Luminosity + + align:start position:0% +second and that's the maximum Luminosity + + + align:start position:0% +second and that's the maximum Luminosity +that you can get in a spherical radiator + + align:start position:0% +that you can get in a spherical radiator + + + align:start position:0% +that you can get in a spherical radiator +because at that point the uh scattering + + align:start position:0% +because at that point the uh scattering + + + align:start position:0% +because at that point the uh scattering +opacity is it's the scattering the + + align:start position:0% +opacity is it's the scattering the + + + align:start position:0% +opacity is it's the scattering the +photons coming out stop the matter + + align:start position:0% +photons coming out stop the matter + + + align:start position:0% +photons coming out stop the matter +coming in the gravity is just canceled + + align:start position:0% +coming in the gravity is just canceled + + + align:start position:0% +coming in the gravity is just canceled +by the uh by the photon pressure going + + align:start position:0% +by the uh by the photon pressure going + + + align:start position:0% +by the uh by the photon pressure going +out if you like in the matter so uh the + + align:start position:0% +out if you like in the matter so uh the + + + align:start position:0% +out if you like in the matter so uh the +Edington Luminosity for a TENS Mass + + align:start position:0% +Edington Luminosity for a TENS Mass + + + align:start position:0% +Edington Luminosity for a TENS Mass +objects 10 39 and these things are + + align:start position:0% +objects 10 39 and these things are + + + align:start position:0% +objects 10 39 and these things are +radiating at right 10 31 or so + + align:start position:0% +radiating at right 10 31 or so + + + align:start position:0% +radiating at right 10 31 or so +these are upper limits here they're less + + align:start position:0% +these are upper limits here they're less + + + align:start position:0% +these are upper limits here they're less +than that so the black holes are down + + align:start position:0% +than that so the black holes are down + + + align:start position:0% +than that so the black holes are down +here and these are systems that are + + align:start position:0% +here and these are systems that are + + + align:start position:0% +here and these are systems that are +essentially identical but they have + + align:start position:0% +essentially identical but they have + + + align:start position:0% +essentially identical but they have +neutron + + align:start position:0% +neutron + + + align:start position:0% +neutron +stars they have neutron stars instead of + + align:start position:0% +stars they have neutron stars instead of + + + align:start position:0% +stars they have neutron stars instead of +black holes and how do we know that + + align:start position:0% +black holes and how do we know that + + + align:start position:0% +black holes and how do we know that +because they produce these bursts that + + align:start position:0% +because they produce these bursts that + + + align:start position:0% +because they produce these bursts that +come from the surface of the neutron + + align:start position:0% +come from the surface of the neutron + + + align:start position:0% +come from the surface of the neutron +star or they produce regular pulsations + + align:start position:0% +star or they produce regular pulsations + + + align:start position:0% +star or they produce regular pulsations +they produce things that black holes + + align:start position:0% +they produce things that black holes + + + align:start position:0% +they produce things that black holes +can't produce for example a burst a type + + align:start position:0% +can't produce for example a burst a type + + + align:start position:0% +can't produce for example a burst a type +one burst is where material accretes + + align:start position:0% +one burst is where material accretes + + + align:start position:0% +one burst is where material accretes +onto the surface of a neutron stle it's + + align:start position:0% +onto the surface of a neutron stle it's + + + align:start position:0% +onto the surface of a neutron stle it's +about a meter thick or so and then the + + align:start position:0% +about a meter thick or so and then the + + + align:start position:0% +about a meter thick or so and then the +bottom of that layer gets so hot that + + align:start position:0% +bottom of that layer gets so hot that + + + align:start position:0% +bottom of that layer gets so hot that +the thing suddenly flashes and burns and + + align:start position:0% +the thing suddenly flashes and burns and + + + align:start position:0% +the thing suddenly flashes and burns and +then the whole star in a few seconds you + + align:start position:0% +then the whole star in a few seconds you + + + align:start position:0% +then the whole star in a few seconds you +know lights up and gets very very + + align:start position:0% +know lights up and gets very very + + + align:start position:0% +know lights up and gets very very +luminous and such bursts don't happen on + + align:start position:0% +luminous and such bursts don't happen on + + + align:start position:0% +luminous and such bursts don't happen on +any any of the black hole sources we're + + align:start position:0% +any any of the black hole sources we're + + + align:start position:0% +any any of the black hole sources we're +talking about but they do happen on a + + align:start position:0% +talking about but they do happen on a + + + align:start position:0% +talking about but they do happen on a +lot of the neutron star sources so we + + align:start position:0% +lot of the neutron star sources so we + + + align:start position:0% +lot of the neutron star sources so we +know we know these these objects are + + align:start position:0% +know we know these these objects are + + + align:start position:0% +know we know these these objects are +neutron stars the one are open circles + + align:start position:0% +neutron stars the one are open circles + + + align:start position:0% +neutron stars the one are open circles +here and they're about a 100 times more + + align:start position:0% +here and they're about a 100 times more + + + align:start position:0% +here and they're about a 100 times more +luminous so why are the neutrons and I + + align:start position:0% +luminous so why are the neutrons and I + + + align:start position:0% +luminous so why are the neutrons and I +should say the the orbital period is the + + align:start position:0% +should say the the orbital period is the + + + align:start position:0% +should say the the orbital period is the +same there's every reason to believe + + align:start position:0% +same there's every reason to believe + + + align:start position:0% +same there's every reason to believe +that the systems are the same and the + + align:start position:0% +that the systems are the same and the + + + align:start position:0% +that the systems are the same and the +mass secretion rates are correct and so + + align:start position:0% +mass secretion rates are correct and so + + + align:start position:0% +mass secretion rates are correct and so +forth so I mean they're they're they're + + align:start position:0% +forth so I mean they're they're they're + + + align:start position:0% +forth so I mean they're they're they're +they're really a good comparison sample + + align:start position:0% +they're really a good comparison sample + + + align:start position:0% +they're really a good comparison sample +to the black holes and they're hundred + + align:start position:0% +to the black holes and they're hundred + + + align:start position:0% +to the black holes and they're hundred +times more + + align:start position:0% +times more + + + align:start position:0% +times more +luminous so this depends on a mode of + + align:start position:0% +luminous so this depends on a mode of + + + align:start position:0% +luminous so this depends on a mode of +accretion that I haven't mentioned I + + align:start position:0% +accretion that I haven't mentioned I + + + align:start position:0% +accretion that I haven't mentioned I +mean I haven't really discussed in + + align:start position:0% +mean I haven't really discussed in + + + align:start position:0% +mean I haven't really discussed in +detail the accretion onto the black hole + + align:start position:0% +detail the accretion onto the black hole + + + align:start position:0% +detail the accretion onto the black hole +me I don't know how much of this you've + + align:start position:0% +me I don't know how much of this you've + + + align:start position:0% +me I don't know how much of this you've +covered but you know in the case of the + + align:start position:0% +covered but you know in the case of the + + + align:start position:0% +covered but you know in the case of the +accretion disc one has the material + + align:start position:0% +accretion disc one has the material + + + align:start position:0% +accretion disc one has the material +coming in spiraling in and there's uh + + align:start position:0% +coming in spiraling in and there's uh + + + align:start position:0% +coming in spiraling in and there's uh +friction between the gas atoms that's + + align:start position:0% +friction between the gas atoms that's + + + align:start position:0% +friction between the gas atoms that's +the agency that produces the uh releases + + align:start position:0% +the agency that produces the uh releases + + + align:start position:0% +the agency that produces the uh releases +the gravitational energy because you're + + align:start position:0% +the gravitational energy because you're + + + align:start position:0% +the gravitational energy because you're +getting essentially GM over R you're + + align:start position:0% +getting essentially GM over R you're + + + align:start position:0% +getting essentially GM over R you're +just getting the gravitational energy as + + align:start position:0% +just getting the gravitational energy as + + + align:start position:0% +just getting the gravitational energy as +material goes into to that last stable + + align:start position:0% +material goes into to that last stable + + + align:start position:0% +material goes into to that last stable +orbit and it's heating the material by + + align:start position:0% +orbit and it's heating the material by + + + align:start position:0% +orbit and it's heating the material by +the friction between the gas atoms and + + align:start position:0% +the friction between the gas atoms and + + + align:start position:0% +the friction between the gas atoms and +so you're getting this hot disc and as + + align:start position:0% +so you're getting this hot disc and as + + + align:start position:0% +so you're getting this hot disc and as +soon as the heat is generated somewhere + + align:start position:0% +soon as the heat is generated somewhere + + + align:start position:0% +soon as the heat is generated somewhere +in the disc it radiates immediately + + align:start position:0% +in the disc it radiates immediately + + + align:start position:0% +in the disc it radiates immediately +locally it just radiates from that's how + + align:start position:0% +locally it just radiates from that's how + + + align:start position:0% +locally it just radiates from that's how +a disc works it's a very efficient + + align:start position:0% +a disc works it's a very efficient + + + align:start position:0% +a disc works it's a very efficient +radiator and it radiates very + + align:start position:0% +radiator and it radiates very + + + align:start position:0% +radiator and it radiates very +however when you get the very low + + align:start position:0% +however when you get the very low + + + align:start position:0% +however when you get the very low +accretion rates when you get the very + + align:start position:0% +accretion rates when you get the very + + + align:start position:0% +accretion rates when you get the very +low accretion rates like in this + + align:start position:0% +low accretion rates like in this + + + align:start position:0% +low accretion rates like in this +quiessence state like these systems are + + align:start position:0% +quiessence state like these systems are + + + align:start position:0% +quiessence state like these systems are +in you can show I can't do it right now + + align:start position:0% +in you can show I can't do it right now + + + align:start position:0% +in you can show I can't do it right now +but you can show that you cannot have + + align:start position:0% +but you can show that you cannot have + + + align:start position:0% +but you can show that you cannot have +this disc go all the way into the last + + align:start position:0% +this disc go all the way into the last + + + align:start position:0% +this disc go all the way into the last +stable orbit it gets stopped quite a way + + align:start position:0% +stable orbit it gets stopped quite a way + + + align:start position:0% +stable orbit it gets stopped quite a way +out at a th 10 1,000 to 10,000 short + + align:start position:0% +out at a th 10 1,000 to 10,000 short + + + align:start position:0% +out at a th 10 1,000 to 10,000 short +Shield radi it gets stopped out there + + align:start position:0% +Shield radi it gets stopped out there + + + align:start position:0% +Shield radi it gets stopped out there +and then you say well there's still + + align:start position:0% +and then you say well there's still + + + align:start position:0% +and then you say well there's still +material going in because we see an + + align:start position:0% +material going in because we see an + + + align:start position:0% +material going in because we see an +x-ray source so how is it getting in + + align:start position:0% +x-ray source so how is it getting in + + + align:start position:0% +x-ray source so how is it getting in +there and then there's a whole new flow + + align:start position:0% +there and then there's a whole new flow + + + align:start position:0% +there and then there's a whole new flow +pattern called the advection dominated + + align:start position:0% +pattern called the advection dominated + + + align:start position:0% +pattern called the advection dominated +decretion flow model which just means + + align:start position:0% +decretion flow model which just means + + + align:start position:0% +decretion flow model which just means +that the material is going in and it's + + align:start position:0% +that the material is going in and it's + + + align:start position:0% +that the material is going in and it's +advecting in so it as as by advection + + align:start position:0% +advecting in so it as as by advection + + + align:start position:0% +advecting in so it as as by advection +you mean that the material is Flowing + + align:start position:0% +you mean that the material is Flowing + + + align:start position:0% +you mean that the material is Flowing +but not radiating efficiently so it's + + align:start position:0% +but not radiating efficiently so it's + + + align:start position:0% +but not radiating efficiently so it's +flowing into the center uh toward the + + align:start position:0% +flowing into the center uh toward the + + + align:start position:0% +flowing into the center uh toward the +black hole but it's not radiating but + + align:start position:0% +black hole but it's not radiating but + + + align:start position:0% +black hole but it's not radiating but +it's heating up all the time because + + align:start position:0% +it's heating up all the time because + + + align:start position:0% +it's heating up all the time because +there's still friction between the gas + + align:start position:0% +there's still friction between the gas + + + align:start position:0% +there's still friction between the gas +atoms so the material gets very hot and + + align:start position:0% +atoms so the material gets very hot and + + + align:start position:0% +atoms so the material gets very hot and +if in an idealized case + + align:start position:0% +if in an idealized case + + + align:start position:0% +if in an idealized case +uh that there would be no radiation at + + align:start position:0% +uh that there would be no radiation at + + + align:start position:0% +uh that there would be no radiation at +all and uh the electrons uh the ions get + + align:start position:0% +all and uh the electrons uh the ions get + + + align:start position:0% +all and uh the electrons uh the ions get +all the energy more or less because + + align:start position:0% +all the energy more or less because + + + align:start position:0% +all the energy more or less because +they're more massive and they can't get + + align:start position:0% +they're more massive and they can't get + + + align:start position:0% +they're more massive and they can't get +their energy off out to the electrons in + + align:start position:0% +their energy off out to the electrons in + + + align:start position:0% +their energy off out to the electrons in +the time that they have before they go + + align:start position:0% +the time that they have before they go + + + align:start position:0% +the time that they have before they go +down the hole so what happens is a + + align:start position:0% +down the hole so what happens is a + + + align:start position:0% +down the hole so what happens is a +tremendous amount of heat energy is + + align:start position:0% +tremendous amount of heat energy is + + + align:start position:0% +tremendous amount of heat energy is +generated in this gas as it's rushing + + align:start position:0% +generated in this gas as it's rushing + + + align:start position:0% +generated in this gas as it's rushing +toward the center and the flow is no + + align:start position:0% +toward the center and the flow is no + + + align:start position:0% +toward the center and the flow is no +longer in a in a disc either it's more + + align:start position:0% +longer in a in a disc either it's more + + + align:start position:0% +longer in a in a disc either it's more +almost quasi sperical in this picture + + align:start position:0% +almost quasi sperical in this picture + + + align:start position:0% +almost quasi sperical in this picture +and the material is racing in toward the + + align:start position:0% +and the material is racing in toward the + + + align:start position:0% +and the material is racing in toward the +center the temperature could reach the + + align:start position:0% +center the temperature could reach the + + + align:start position:0% +center the temperature could reach the +verial temperature near the black hole + + align:start position:0% +verial temperature near the black hole + + + align:start position:0% +verial temperature near the black hole +which would be GM over R which would be + + align:start position:0% +which would be GM over R which would be + + + align:start position:0% +which would be GM over R which would be +which would be 10 the 12th degrees a + + align:start position:0% +which would be 10 the 12th degrees a + + + align:start position:0% +which would be 10 the 12th degrees a +trillion degrees we don't know that that + + align:start position:0% +trillion degrees we don't know that that + + + align:start position:0% +trillion degrees we don't know that that +happens but I mean that's certainly a + + align:start position:0% +happens but I mean that's certainly a + + + align:start position:0% +happens but I mean that's certainly a +possibility in any case that would be + + align:start position:0% +possibility in any case that would be + + + align:start position:0% +possibility in any case that would be +about the hottest material you know the + + align:start position:0% +about the hottest material you know the + + + align:start position:0% +about the hottest material you know the +side of the big bang and uh that that + + align:start position:0% +side of the big bang and uh that that + + + align:start position:0% +side of the big bang and uh that that +material um anyway the point is the gas + + align:start position:0% +material um anyway the point is the gas + + + align:start position:0% +material um anyway the point is the gas +doesn't have time to radiate it finds + + align:start position:0% +doesn't have time to radiate it finds + + + align:start position:0% +doesn't have time to radiate it finds +itself heading toward the black hole + + align:start position:0% +itself heading toward the black hole + + + align:start position:0% +itself heading toward the black hole +it's got all this thermal energy in it + + align:start position:0% +it's got all this thermal energy in it + + + align:start position:0% +it's got all this thermal energy in it +which is + + align:start position:0% +which is + + + align:start position:0% +which is +the M the 6% of MC s or whatever that is + + align:start position:0% +the M the 6% of MC s or whatever that is + + + align:start position:0% +the M the 6% of MC s or whatever that is +achieved and it suddenly goes through + + align:start position:0% +achieved and it suddenly goes through + + + align:start position:0% +achieved and it suddenly goes through +the Event Horizon and that's it it goes + + align:start position:0% +the Event Horizon and that's it it goes + + + align:start position:0% +the Event Horizon and that's it it goes +into the mass of the black hole it no + + align:start position:0% +into the mass of the black hole it no + + + align:start position:0% +into the mass of the black hole it no +longer can radiate out into space so + + align:start position:0% +longer can radiate out into space so + + + align:start position:0% +longer can radiate out into space so +that energy is lost compare that to the + + align:start position:0% +that energy is lost compare that to the + + + align:start position:0% +that energy is lost compare that to the +case of if that advected energy in that + + align:start position:0% +case of if that advected energy in that + + + align:start position:0% +case of if that advected energy in that +hot gas is heading toward a a solid + + align:start position:0% +hot gas is heading toward a a solid + + + align:start position:0% +hot gas is heading toward a a solid +neutron star it's going to pile into the + + align:start position:0% +neutron star it's going to pile into the + + + align:start position:0% +neutron star it's going to pile into the +surface of that neutron star heat the + + align:start position:0% +surface of that neutron star heat the + + + align:start position:0% +surface of that neutron star heat the +surface of the neutron star and that + + align:start position:0% +surface of the neutron star and that + + + align:start position:0% +surface of the neutron star and that +neutron star is going to radiate and + + align:start position:0% +neutron star is going to radiate and + + + align:start position:0% +neutron star is going to radiate and +produce uh a lot you + + align:start position:0% +produce uh a lot you + + + align:start position:0% +produce uh a lot you +know well 100 times more Luminosity I + + align:start position:0% +know well 100 times more Luminosity I + + + align:start position:0% +know well 100 times more Luminosity I +guess you know in fact we expected the + + align:start position:0% +guess you know in fact we expected the + + + align:start position:0% +guess you know in fact we expected the +neutron stars to be brighter than they + + align:start position:0% +neutron stars to be brighter than they + + + align:start position:0% +neutron stars to be brighter than they +are and so there's some there's some un + + align:start position:0% +are and so there's some there's some un + + + align:start position:0% +are and so there's some there's some un +there's some uncertainties in all of + + align:start position:0% +there's some uncertainties in all of + + + align:start position:0% +there's some uncertainties in all of +these things because and for those who + + align:start position:0% +these things because and for those who + + + align:start position:0% +these things because and for those who +haven't done astrophysics you know + + align:start position:0% +haven't done astrophysics you know + + + align:start position:0% +haven't done astrophysics you know +astrophysics is one of those frustrating + + align:start position:0% +astrophysics is one of those frustrating + + + align:start position:0% +astrophysics is one of those frustrating +things where you know if you're in the + + align:start position:0% +things where you know if you're in the + + + align:start position:0% +things where you know if you're in the +laboratory you can go and put a wrench + + align:start position:0% +laboratory you can go and put a wrench + + + align:start position:0% +laboratory you can go and put a wrench +on it and you can you know measure and + + align:start position:0% +on it and you can you know measure and + + + align:start position:0% +on it and you can you know measure and +you can line things a little better and + + align:start position:0% +you can line things a little better and + + + align:start position:0% +you can line things a little better and +so we basically have to take whatever we + + align:start position:0% +so we basically have to take whatever we + + + align:start position:0% +so we basically have to take whatever we +get and uh and we don't always get + + align:start position:0% +get and uh and we don't always get + + + align:start position:0% +get and uh and we don't always get +exactly what we want you know and so uh + + align:start position:0% +exactly what we want you know and so uh + + + align:start position:0% +exactly what we want you know and so uh +we we can reach certain conclusions and + + align:start position:0% +we we can reach certain conclusions and + + + align:start position:0% +we we can reach certain conclusions and +then we keep looking and we find + + align:start position:0% +then we keep looking and we find + + + align:start position:0% +then we keep looking and we find +something a better system and so forth + + align:start position:0% +something a better system and so forth + + + align:start position:0% +something a better system and so forth +but it's it's certainly different than + + align:start position:0% +but it's it's certainly different than + + + align:start position:0% +but it's it's certainly different than +physics you know certainly different + + align:start position:0% +physics you know certainly different + + + align:start position:0% +physics you know certainly different +than physics so I think I think things + + align:start position:0% +than physics so I think I think things + + + align:start position:0% +than physics so I think I think things +are very bright for this uh for this + + align:start position:0% +are very bright for this uh for this + + + align:start position:0% +are very bright for this uh for this +field I think there's a lot of uh um uh + + align:start position:0% +field I think there's a lot of uh um uh + + + align:start position:0% +field I think there's a lot of uh um uh +possibilities here and and some that I + + align:start position:0% +possibilities here and and some that I + + + align:start position:0% +possibilities here and and some that I +haven't mentioned uh where we have a + + align:start position:0% +haven't mentioned uh where we have a + + + align:start position:0% +haven't mentioned uh where we have a +chance to get at uh strong field gravity + + align:start position:0% +chance to get at uh strong field gravity + + + align:start position:0% +chance to get at uh strong field gravity +oh I should say I should I should I + + align:start position:0% +oh I should say I should I should I + + + align:start position:0% +oh I should say I should I should I +should wind up that other discussion by + + align:start position:0% +should wind up that other discussion by + + + align:start position:0% +should wind up that other discussion by +saying okay so the neutron stars are are + + align:start position:0% +saying okay so the neutron stars are are + + + align:start position:0% +saying okay so the neutron stars are are +more luminous for the reason I said the + + align:start position:0% +more luminous for the reason I said the + + + align:start position:0% +more luminous for the reason I said the +black holes are less luminous because + + align:start position:0% +black holes are less luminous because + + + align:start position:0% +black holes are less luminous because +they have this event horizon that is + + align:start position:0% +they have this event horizon that is + + + align:start position:0% +they have this event horizon that is +evidence for the event horizon that's + + align:start position:0% +evidence for the event horizon that's + + + align:start position:0% +evidence for the event horizon that's +the point that is evidence for the event + + align:start position:0% +the point that is evidence for the event + + + align:start position:0% +the point that is evidence for the event +horizon because it's only the Event + + align:start position:0% +horizon because it's only the Event + + + align:start position:0% +horizon because it's only the Event +Horizon that allows you to hide that + + align:start position:0% +Horizon that allows you to hide that + + + align:start position:0% +Horizon that allows you to hide that +thermal energy so it's a strong piece of + + align:start position:0% +thermal energy so it's a strong piece of + + + align:start position:0% +thermal energy so it's a strong piece of +evidence for the event horizon and + + align:start position:0% +evidence for the event horizon and + + + align:start position:0% +evidence for the event horizon and +that's what rsh nian and Mike Garcia and + + align:start position:0% +that's what rsh nian and Mike Garcia and + + + align:start position:0% +that's what rsh nian and Mike Garcia and +I have been saying for some time uh and + + align:start position:0% +I have been saying for some time uh and + + + align:start position:0% +I have been saying for some time uh and +we have our + + align:start position:0% +we have our + + + align:start position:0% +we have our +detractors but uh that's uh that's + + align:start position:0% +detractors but uh that's uh that's + + + align:start position:0% +detractors but uh that's uh that's +that's um you know you what what are the + + align:start position:0% +that's um you know you what what are the + + + align:start position:0% +that's um you know you what what are the +things you can hope to do about a black + + align:start position:0% +things you can hope to do about a black + + + align:start position:0% +things you can hope to do about a black +hole with spin the mass you know you + + align:start position:0% +hole with spin the mass you know you + + + align:start position:0% +hole with spin the mass you know you +really The Event Horizon is defining + + align:start position:0% +really The Event Horizon is defining + + + align:start position:0% +really The Event Horizon is defining +property you would like to find as much + + align:start position:0% +property you would like to find as much + + + align:start position:0% +property you would like to find as much +as as much as you can you'd like to find + + align:start position:0% +as as much as you can you'd like to find + + + align:start position:0% +as as much as you can you'd like to find +some evidence for that event horizon and + + align:start position:0% +some evidence for that event horizon and + + + align:start position:0% +some evidence for that event horizon and +its effects and and and this is is one + + align:start position:0% +its effects and and and this is is one + + + align:start position:0% +its effects and and and this is is one +way of doing it but I I think that um uh + + align:start position:0% +way of doing it but I I think that um uh + + + align:start position:0% +way of doing it but I I think that um uh +with conx which is a very big thing + + align:start position:0% +with conx which is a very big thing + + + align:start position:0% +with conx which is a very big thing +that'll be able to do that that spectral + + align:start position:0% +that'll be able to do that that spectral + + + align:start position:0% +that'll be able to do that that spectral +line work that I was talking about so + + align:start position:0% +line work that I was talking about so + + + align:start position:0% +line work that I was talking about so +much better than anything else if we can + + align:start position:0% +much better than anything else if we can + + + align:start position:0% +much better than anything else if we can +get another Rossy x-ray timing Explorer + + align:start position:0% +get another Rossy x-ray timing Explorer + + + align:start position:0% +get another Rossy x-ray timing Explorer +it'll measure the timing of these things + + align:start position:0% +it'll measure the timing of these things + + + align:start position:0% +it'll measure the timing of these things +that has like 10 times the area like + + align:start position:0% +that has like 10 times the area like + + + align:start position:0% +that has like 10 times the area like +these three tables together here or + + align:start position:0% +these three tables together here or + + + align:start position:0% +these three tables together here or +something like this and uh and if we can + + align:start position:0% +something like this and uh and if we can + + + align:start position:0% +something like this and uh and if we can +uh uh and and the optical telescopes are + + align:start position:0% +uh uh and and the optical telescopes are + + + align:start position:0% +uh uh and and the optical telescopes are +amazing what you can do today to measure + + align:start position:0% +amazing what you can do today to measure + + + align:start position:0% +amazing what you can do today to measure +the masses of these things and I know + + align:start position:0% +the masses of these things and I know + + + align:start position:0% +the masses of these things and I know +that can be done so much better and we + + align:start position:0% +that can be done so much better and we + + + align:start position:0% +that can be done so much better and we +can go to fainter limits there too just + + align:start position:0% +can go to fainter limits there too just + + + align:start position:0% +can go to fainter limits there too just +to give you an + + align:start position:0% +to give you an + + + align:start position:0% +to give you an +idea the first mass measurement was made + + align:start position:0% +idea the first mass measurement was made + + + align:start position:0% +idea the first mass measurement was made +1971 that was signis X1 and then there + + align:start position:0% +1971 that was signis X1 and then there + + + align:start position:0% +1971 that was signis X1 and then there +was 1 in 83 and there was 1 in + + align:start position:0% +was 1 in 83 and there was 1 in + + + align:start position:0% +was 1 in 83 and there was 1 in +86 and uh something so there's 18 Mass + + align:start position:0% +86 and uh something so there's 18 Mass + + + align:start position:0% +86 and uh something so there's 18 Mass +measurements now and 11 of them have + + align:start position:0% +measurements now and 11 of them have + + + align:start position:0% +measurements now and 11 of them have +been made in the last uh 11 of them have + + align:start position:0% +been made in the last uh 11 of them have + + + align:start position:0% +been made in the last uh 11 of them have +been made in the last yeah the last 10 + + align:start position:0% +been made in the last yeah the last 10 + + + align:start position:0% +been made in the last yeah the last 10 +years okay so 11 of the 18 have been + + align:start position:0% +years okay so 11 of the 18 have been + + + align:start position:0% +years okay so 11 of the 18 have been +made in the last 10 years and the reason + + align:start position:0% +made in the last 10 years and the reason + + + align:start position:0% +made in the last 10 years and the reason +for that is not that more x-ray Novi are + + align:start position:0% +for that is not that more x-ray Novi are + + + align:start position:0% +for that is not that more x-ray Novi are +popping off you know that they keep + + align:start position:0% +popping off you know that they keep + + + align:start position:0% +popping off you know that they keep +popping off at just the same more or + + align:start position:0% +popping off at just the same more or + + + align:start position:0% +popping off at just the same more or +less level but that the optical + + align:start position:0% +less level but that the optical + + + align:start position:0% +less level but that the optical +telescopes are so much more powerful the + + align:start position:0% +telescopes are so much more powerful the + + + align:start position:0% +telescopes are so much more powerful the +new 10 m telescopes not only are they + + align:start position:0% +new 10 m telescopes not only are they + + + align:start position:0% +new 10 m telescopes not only are they +bigger in collecting area than the four + + align:start position:0% +bigger in collecting area than the four + + + align:start position:0% +bigger in collecting area than the four +meters that we always had before but the + + align:start position:0% +meters that we always had before but the + + + align:start position:0% +meters that we always had before but the +quality of the images are just so much + + align:start position:0% +quality of the images are just so much + + + align:start position:0% +quality of the images are just so much +better I mean you're talking uh 310 of + + align:start position:0% +better I mean you're talking uh 310 of + + + align:start position:0% +better I mean you're talking uh 310 of +an arcc image some of the time you never + + align:start position:0% +an arcc image some of the time you never + + + align:start position:0% +an arcc image some of the time you never +could talk better than one arcc in the + + align:start position:0% +could talk better than one arcc in the + + + align:start position:0% +could talk better than one arcc in the +old days that makes it tremendous + + align:start position:0% +old days that makes it tremendous + + + align:start position:0% +old days that makes it tremendous +difference when you're studying Galactic + + align:start position:0% +difference when you're studying Galactic + + + align:start position:0% +difference when you're studying Galactic +sources in crowded field and uh the CCD + + align:start position:0% +sources in crowded field and uh the CCD + + + align:start position:0% +sources in crowded field and uh the CCD +detectors which sort of got started at + + align:start position:0% +detectors which sort of got started at + + + align:start position:0% +detectors which sort of got started at +some level in 1985 or so they've made a + + align:start position:0% +some level in 1985 or so they've made a + + + align:start position:0% +some level in 1985 or so they've made a +tremendous Revol because they you know + + align:start position:0% +tremendous Revol because they you know + + + align:start position:0% +tremendous Revol because they you know +unit efficiency and the you know they're + + align:start position:0% +unit efficiency and the you know they're + + + align:start position:0% +unit efficiency and the you know they're +really you get a nice image you're not + + align:start position:0% +really you get a nice image you're not + + + align:start position:0% +really you get a nice image you're not +measuring one stinking photo multiplier + + align:start position:0% +measuring one stinking photo multiplier + + + align:start position:0% +measuring one stinking photo multiplier +you know one little point or something + + align:start position:0% +you know one little point or something + + + align:start position:0% +you know one little point or something +but you've got you can then measure you + + align:start position:0% +but you've got you can then measure you + + + align:start position:0% +but you've got you can then measure you +can fit the profile and you know really + + align:start position:0% +can fit the profile and you know really + + + align:start position:0% +can fit the profile and you know really +do good photometry and so so you know I + + align:start position:0% +do good photometry and so so you know I + + + align:start position:0% +do good photometry and so so you know I +I'm I well there's I I just think this + + align:start position:0% +I'm I well there's I I just think this + + + align:start position:0% +I'm I well there's I I just think this +is a a very exciting field for anyone + + align:start position:0% +is a a very exciting field for anyone + + + align:start position:0% +is a a very exciting field for anyone +who uh is maybe thinking of uh you know + + align:start position:0% +who uh is maybe thinking of uh you know + + + align:start position:0% +who uh is maybe thinking of uh you know +researching + + align:start position:0% +researching + + + align:start position:0% +researching +astronomy I'll stop there I know you + + align:start position:0% +astronomy I'll stop there I know you + + + align:start position:0% +astronomy I'll stop there I know you +want to ask questions + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% + + + + align:start position:0% + +convey yeah The Field's really going + + align:start position:0% +convey yeah The Field's really going + + + align:start position:0% +convey yeah The Field's really going +ahead yeah we just the + + align:start position:0% +ahead yeah we just the + + + align:start position:0% +ahead yeah we just the +instrumentation I hear that anyone + + align:start position:0% +instrumentation I hear that anyone + + + align:start position:0% +instrumentation I hear that anyone +listening + + align:start position:0% + + + + align:start position:0% + +with well it's the only way to do + + align:start position:0% + + + + align:start position:0% + +it uh students have any + + align:start position:0% +it uh students have any + + + align:start position:0% +it uh students have any +questions Talking + + align:start position:0% + + + + align:start position:0% + +l t the 450 Herz signal yes I mean how + + align:start position:0% +l t the 450 Herz signal yes I mean how + + + align:start position:0% +l t the 450 Herz signal yes I mean how +do you know that's actually coming from + + align:start position:0% +do you know that's actually coming from + + + align:start position:0% +do you know that's actually coming from +the rotation of the creation + + align:start position:0% +the rotation of the creation + + + align:start position:0% +the rotation of the creation +I mean you mention you didn't what the + + align:start position:0% +I mean you mention you didn't what the + + + align:start position:0% +I mean you mention you didn't what the +mechanism is would you repeat the oh + + align:start position:0% +mechanism is would you repeat the oh + + + align:start position:0% +mechanism is would you repeat the oh +yeah uh the question is the 450 HZ + + align:start position:0% +yeah uh the question is the 450 HZ + + + align:start position:0% +yeah uh the question is the 450 HZ +signal uh whether that how do we know or + + align:start position:0% +signal uh whether that how do we know or + + + align:start position:0% +signal uh whether that how do we know or +why do we think that that's coming from + + align:start position:0% +why do we think that that's coming from + + + align:start position:0% +why do we think that that's coming from +the accretion disc + + align:start position:0% +the accretion disc + + + align:start position:0% +the accretion disc +um it's it's just that you know no one + + align:start position:0% +um it's it's just that you know no one + + + align:start position:0% +um it's it's just that you know no one +really knows how to take and get say 3% + + align:start position:0% +really knows how to take and get say 3% + + + align:start position:0% +really knows how to take and get say 3% +of the photons to produce a 450 HZ + + align:start position:0% +of the photons to produce a 450 HZ + + + align:start position:0% +of the photons to produce a 450 HZ +signal uh + + align:start position:0% +signal uh + + + align:start position:0% +signal uh +in any other way it seems like the + + align:start position:0% +in any other way it seems like the + + + align:start position:0% +in any other way it seems like the +timing belt is the accretion disc and uh + + align:start position:0% +timing belt is the accretion disc and uh + + + align:start position:0% +timing belt is the accretion disc and uh +most people go with that but uh it + + align:start position:0% +most people go with that but uh it + + + align:start position:0% +most people go with that but uh it +doesn't mean that other things aren't + + align:start position:0% +doesn't mean that other things aren't + + + align:start position:0% +doesn't mean that other things aren't +involved in addition to the accretion + + align:start position:0% +involved in addition to the accretion + + + align:start position:0% +involved in addition to the accretion +disc including this kind of like a Chona + + align:start position:0% +disc including this kind of like a Chona + + + align:start position:0% +disc including this kind of like a Chona +I was talking about the hot material + + align:start position:0% +I was talking about the hot material + + + align:start position:0% +I was talking about the hot material +around and so forth interacting with the + + align:start position:0% +around and so forth interacting with the + + + align:start position:0% +around and so forth interacting with the +accretion disc and there's a lot of um + + align:start position:0% +accretion disc and there's a lot of um + + + align:start position:0% +accretion disc and there's a lot of um +sort of gooey details I could go into + + align:start position:0% +sort of gooey details I could go into + + + align:start position:0% +sort of gooey details I could go into +about the relations between uh the uh + + align:start position:0% +about the relations between uh the uh + + + align:start position:0% +about the relations between uh the uh +that other component this hot accre this + + align:start position:0% +that other component this hot accre this + + + align:start position:0% +that other component this hot accre this +hot uh uh Corona that's around the + + align:start position:0% +hot uh uh Corona that's around the + + + align:start position:0% +hot uh uh Corona that's around the +accretion disc and the accretion disc + + align:start position:0% +accretion disc and the accretion disc + + + align:start position:0% +accretion disc and the accretion disc +itself but um it's + + align:start position:0% +itself but um it's + + + align:start position:0% +itself but um it's +it's I mean and and people could be + + align:start position:0% +it's I mean and and people could be + + + align:start position:0% +it's I mean and and people could be +wrong but the three models that are out + + align:start position:0% +wrong but the three models that are out + + + align:start position:0% +wrong but the three models that are out +there right now you know all invoke the + + align:start position:0% +there right now you know all invoke the + + + align:start position:0% +there right now you know all invoke the +accretion disc doing something either + + align:start position:0% +accretion disc doing something either + + + align:start position:0% +accretion disc doing something either +like this thing I was just mentioning + + align:start position:0% +like this thing I was just mentioning + + + align:start position:0% +like this thing I was just mentioning +here with the non the radial motion or + + align:start position:0% +here with the non the radial motion or + + + align:start position:0% +here with the non the radial motion or +so another one is oscillations in the + + align:start position:0% +so another one is oscillations in the + + + align:start position:0% +so another one is oscillations in the +inner dis that are kind of Trapped and + + align:start position:0% +inner dis that are kind of Trapped and + + + align:start position:0% +inner dis that are kind of Trapped and +they do an igen value problem and so + + align:start position:0% +they do an igen value problem and so + + + align:start position:0% +they do an igen value problem and so +forth but it's all strongfield gr and + + align:start position:0% +forth but it's all strongfield gr and + + + align:start position:0% +forth but it's all strongfield gr and +it's all radi again it's in the disc and + + align:start position:0% +it's all radi again it's in the disc and + + + align:start position:0% +it's all radi again it's in the disc and +um and then uh the third one is uh is + + align:start position:0% +um and then uh the third one is uh is + + + align:start position:0% +um and then uh the third one is uh is +like lens Turing procession kinds of + + align:start position:0% +like lens Turing procession kinds of + + + align:start position:0% +like lens Turing procession kinds of +things so this is almost geodesic kinds + + align:start position:0% +things so this is almost geodesic kinds + + + align:start position:0% +things so this is almost geodesic kinds +of things so people criticize that + + align:start position:0% +of things so people criticize that + + + align:start position:0% +of things so people criticize that +because how could you have really Free + + align:start position:0% +because how could you have really Free + + + align:start position:0% +because how could you have really Free +Motion in in such a circumstance uh but + + align:start position:0% +Motion in in such a circumstance uh but + + + align:start position:0% +Motion in in such a circumstance uh but +all of them invoke the dis but we could + + align:start position:0% +all of them invoke the dis but we could + + + align:start position:0% +all of them invoke the dis but we could +be + + align:start position:0% +be + + + align:start position:0% +be +wrong we could be wrong yeah I I just + + align:start position:0% +wrong we could be wrong yeah I I just + + + align:start position:0% +wrong we could be wrong yeah I I just +add we don't resolve any of these discs + + align:start position:0% +add we don't resolve any of these discs + + + align:start position:0% +add we don't resolve any of these discs +no one has ever seen an incre disc + + align:start position:0% +no one has ever seen an incre disc + + + align:start position:0% +no one has ever seen an incre disc +around a black hole because the angles + + align:start position:0% +around a black hole because the angles + + + align:start position:0% +around a black hole because the angles +they subtend in the sky are just too + + align:start position:0% +they subtend in the sky are just too + + + align:start position:0% +they subtend in the sky are just too +small we're simply measuring the total + + align:start position:0% +small we're simply measuring the total + + + align:start position:0% +small we're simply measuring the total +light or x-ray output from these things + + align:start position:0% +light or x-ray output from these things + + + align:start position:0% +light or x-ray output from these things +and then making + + align:start position:0% +and then making + + + align:start position:0% +and then making +models nonetheless there's really no way + + align:start position:0% +models nonetheless there's really no way + + + align:start position:0% +models nonetheless there's really no way +that we can conceive of the radiation + + align:start position:0% +that we can conceive of the radiation + + + align:start position:0% +that we can conceive of the radiation +coming from around these black holes + + align:start position:0% +coming from around these black holes + + + align:start position:0% +coming from around these black holes +except through the secretion disc + + align:start position:0% +except through the secretion disc + + + align:start position:0% +except through the secretion disc +mechanism um so that really is the + + align:start position:0% +mechanism um so that really is the + + + align:start position:0% +mechanism um so that really is the +starting point for for any theoretical + + align:start position:0% +starting point for for any theoretical + + + align:start position:0% +starting point for for any theoretical +model of of the oscillations or any + + align:start position:0% +model of of the oscillations or any + + + align:start position:0% +model of of the oscillations or any +other property yeah yeah IR + + align:start position:0% +other property yeah yeah IR + + + align:start position:0% +other property yeah yeah IR +one uh relative to the mass of the + + align:start position:0% +one uh relative to the mass of the + + + align:start position:0% +one uh relative to the mass of the +binary star and the black hole do we + + align:start position:0% +binary star and the black hole do we + + + align:start position:0% +binary star and the black hole do we +have any idea how much mass might be in + + align:start position:0% +have any idea how much mass might be in + + + align:start position:0% +have any idea how much mass might be in +the actual accretion disc let me just + + align:start position:0% +the actual accretion disc let me just + + + align:start position:0% +the actual accretion disc let me just +repeat that question how much mass is in + + align:start position:0% +repeat that question how much mass is in + + + align:start position:0% +repeat that question how much mass is in +the accretion disc compared with the + + align:start position:0% +the accretion disc compared with the + + + align:start position:0% +the accretion disc compared with the +primary and secondary Stars right well + + align:start position:0% +primary and secondary Stars right well + + + align:start position:0% +primary and secondary Stars right well +it's it's not very much uh it'd probably + + align:start position:0% +it's it's not very much uh it'd probably + + + align:start position:0% +it's it's not very much uh it'd probably +be like 10 Theus 9 solar masses or so so + + align:start position:0% +be like 10 Theus 9 solar masses or so so + + + align:start position:0% +be like 10 Theus 9 solar masses or so so +it's really a minuscal amount compared + + align:start position:0% +it's really a minuscal amount compared + + + align:start position:0% +it's really a minuscal amount compared +to the other two components the ordinary + + align:start position:0% +to the other two components the ordinary + + + align:start position:0% +to the other two components the ordinary +star and the black hole um people have + + align:start position:0% +star and the black hole um people have + + + align:start position:0% +star and the black hole um people have +uh had models in the past but they've + + align:start position:0% +uh had models in the past but they've + + + align:start position:0% +uh had models in the past but they've +sort of been laughed away uh about uh + + align:start position:0% +sort of been laughed away uh about uh + + + align:start position:0% +sort of been laughed away uh about uh +very massive discs and systems and so + + align:start position:0% +very massive discs and systems and so + + + align:start position:0% +very massive discs and systems and so +forth and in fact that was one antiblack + + align:start position:0% +forth and in fact that was one antiblack + + + align:start position:0% +forth and in fact that was one antiblack +hole argument for example this was 15 + + align:start position:0% +hole argument for example this was 15 + + + align:start position:0% +hole argument for example this was 15 +years ago but uh a person published a + + align:start position:0% +years ago but uh a person published a + + + align:start position:0% +years ago but uh a person published a +couple of Articles saying that this + + align:start position:0% +couple of Articles saying that this + + + align:start position:0% +couple of Articles saying that this +object a620 which is one of these early + + align:start position:0% +object a620 which is one of these early + + + align:start position:0% +object a620 which is one of these early +black holes that were found that the + + align:start position:0% +black holes that were found that the + + + align:start position:0% +black holes that were found that the +disc around it was like five solar + + align:start position:0% +disc around it was like five solar + + + align:start position:0% +disc around it was like five solar +masses and that it only had a neutron + + align:start position:0% +masses and that it only had a neutron + + + align:start position:0% +masses and that it only had a neutron +star in the center there was a solar + + align:start position:0% +star in the center there was a solar + + + align:start position:0% +star in the center there was a solar +mass or so and then you know then + + align:start position:0% +mass or so and then you know then + + + align:start position:0% +mass or so and then you know then +there's an ordinary K star over here was + + align:start position:0% +there's an ordinary K star over here was + + + align:start position:0% +there's an ordinary K star over here was +a half a solar mass or something so you + + align:start position:0% +a half a solar mass or something so you + + + align:start position:0% +a half a solar mass or something so you +have a five solar mass disc around a uh + + align:start position:0% +have a five solar mass disc around a uh + + + align:start position:0% +have a five solar mass disc around a uh +say one solar mass neutron star but then + + align:start position:0% +say one solar mass neutron star but then + + + align:start position:0% +say one solar mass neutron star but then +you ask yourself well is that disc + + align:start position:0% +you ask yourself well is that disc + + + align:start position:0% +you ask yourself well is that disc +stable you know I mean that's a pretty + + align:start position:0% +stable you know I mean that's a pretty + + + align:start position:0% +stable you know I mean that's a pretty +massive disc and uh and uh most people + + align:start position:0% +massive disc and uh and uh most people + + + align:start position:0% +massive disc and uh and uh most people +were able to say that that isn't stable + + align:start position:0% +were able to say that that isn't stable + + + align:start position:0% +were able to say that that isn't stable +and it would be a a big problem but you + + align:start position:0% +and it would be a a big problem but you + + + align:start position:0% +and it would be a a big problem but you +have some idea of the mass the masses in + + align:start position:0% +have some idea of the mass the masses in + + + align:start position:0% +have some idea of the mass the masses in +these discs from various arguments about + + align:start position:0% +these discs from various arguments about + + + align:start position:0% +these discs from various arguments about +how much radiation's coming from them + + align:start position:0% +how much radiation's coming from them + + + align:start position:0% +how much radiation's coming from them +and uh it's see I'm trying to think of + + align:start position:0% +and uh it's see I'm trying to think of + + + align:start position:0% +and uh it's see I'm trying to think of +the best argument to get the mass of a + + align:start position:0% +the best argument to get the mass of a + + + align:start position:0% +the best argument to get the mass of a +disc + + align:start position:0% + + + + align:start position:0% + +um I I I can't think of a really great + + align:start position:0% +um I I I can't think of a really great + + + align:start position:0% +um I I I can't think of a really great +argument right now I mean if they got + + align:start position:0% +argument right now I mean if they got + + + align:start position:0% +argument right now I mean if they got +too massive then they you'd probably + + align:start position:0% +too massive then they you'd probably + + + align:start position:0% +too massive then they you'd probably +start to get into procession effects and + + align:start position:0% +start to get into procession effects and + + + align:start position:0% +start to get into procession effects and +things and it would be some complicated + + align:start position:0% +things and it would be some complicated + + + align:start position:0% +things and it would be some complicated +Dynamics but 10us 8 10-9 solar masses I + + align:start position:0% +Dynamics but 10us 8 10-9 solar masses I + + + align:start position:0% +Dynamics but 10us 8 10-9 solar masses I +think that's more or less what they are + + align:start position:0% +think that's more or less what they are + + + align:start position:0% +think that's more or less what they are +and if you look right straight through + + align:start position:0% +and if you look right straight through + + + align:start position:0% +and if you look right straight through +the dis plane you might see something + + align:start position:0% +the dis plane you might see something + + + align:start position:0% +the dis plane you might see something +like 100 gr per square centimeter maybe + + align:start position:0% +like 100 gr per square centimeter maybe + + + align:start position:0% +like 100 gr per square centimeter maybe +up to th000 gr per square centimeter at + + align:start position:0% +up to th000 gr per square centimeter at + + + align:start position:0% +up to th000 gr per square centimeter at +most or something like that it's not + + align:start position:0% +most or something like that it's not + + + align:start position:0% +most or something like that it's not +going to be a lot those discs are have + + align:start position:0% +going to be a lot those discs are have + + + align:start position:0% +going to be a lot those discs are have +even less mass than the um solar system + + align:start position:0% +even less mass than the um solar system + + + align:start position:0% +even less mass than the um solar system +disc compared with the sun because + + align:start position:0% +disc compared with the sun because + + + align:start position:0% +disc compared with the sun because +remember Jupiter contains 0.1% of the + + align:start position:0% +remember Jupiter contains 0.1% of the + + + align:start position:0% +remember Jupiter contains 0.1% of the +mass of the Sun here these discs have + + align:start position:0% +mass of the Sun here these discs have + + + align:start position:0% +mass of the Sun here these discs have +even a smaller fraction so whatever + + align:start position:0% +even a smaller fraction so whatever + + + align:start position:0% +even a smaller fraction so whatever +planets existed around these Stars + + align:start position:0% +planets existed around these Stars + + + align:start position:0% +planets existed around these Stars +before they became supern noi they're + + align:start position:0% +before they became supern noi they're + + + align:start position:0% +before they became supern noi they're +gone yeah I think + + align:start position:0% +gone yeah I think + + + align:start position:0% +gone yeah I think +so um I understood you to say that the + + align:start position:0% +so um I understood you to say that the + + + align:start position:0% +so um I understood you to say that the +discs that the discs emit x-rays because + + align:start position:0% +discs that the discs emit x-rays because + + + align:start position:0% +discs that the discs emit x-rays because +they're being illuminated by x-rays now + + align:start position:0% +they're being illuminated by x-rays now + + + align:start position:0% +they're being illuminated by x-rays now +I understand how the discs get hot by + + align:start position:0% +I understand how the discs get hot by + + + align:start position:0% +I understand how the discs get hot by +friction as the material goes in but how + + align:start position:0% +friction as the material goes in but how + + + align:start position:0% +friction as the material goes in but how +does what is Illuminating them and where + + align:start position:0% +does what is Illuminating them and where + + + align:start position:0% +does what is Illuminating them and where +does that illumination Source get its + + align:start position:0% +does that illumination Source get its + + + align:start position:0% +does that illumination Source get its +energy right um I I think I was perhaps + + align:start position:0% +energy right um I I think I was perhaps + + + align:start position:0% +energy right um I I think I was perhaps +confuse things slightly there I mean + + align:start position:0% +confuse things slightly there I mean + + + align:start position:0% +confuse things slightly there I mean +there's there's five states that black + + align:start position:0% +there's there's five states that black + + + align:start position:0% +there's there's five states that black +holes go into they're not like + + align:start position:0% +holes go into they're not like + + + align:start position:0% +holes go into they're not like +thermodynamic States or states of a + + align:start position:0% +thermodynamic States or states of a + + + align:start position:0% +thermodynamic States or states of a +Quantum system or something but they + + align:start position:0% +Quantum system or something but they + + + align:start position:0% +Quantum system or something but they +really are rather distinct states of + + align:start position:0% +really are rather distinct states of + + + align:start position:0% +really are rather distinct states of +emission and so I sort of blurred some + + align:start position:0% +emission and so I sort of blurred some + + + align:start position:0% +emission and so I sort of blurred some +of that together but uh the disc itself + + align:start position:0% +of that together but uh the disc itself + + + align:start position:0% +of that together but uh the disc itself +is a significant radiator but it's not a + + align:start position:0% +is a significant radiator but it's not a + + + align:start position:0% +is a significant radiator but it's not a +very hard radiation that comes from the + + align:start position:0% +very hard radiation that comes from the + + + align:start position:0% +very hard radiation that comes from the +disc it's a thermal component that's + + align:start position:0% +disc it's a thermal component that's + + + align:start position:0% +disc it's a thermal component that's +more or less like a like a 1kv black + + align:start position:0% +more or less like a like a 1kv black + + + align:start position:0% +more or less like a like a 1kv black +body and it's really modeled usually as + + align:start position:0% +body and it's really modeled usually as + + + align:start position:0% +body and it's really modeled usually as +a succession of black bodies of + + align:start position:0% +a succession of black bodies of + + + align:start position:0% +a succession of black bodies of +increasing temperatures as you go in + + align:start position:0% +increasing temperatures as you go in + + + align:start position:0% +increasing temperatures as you go in +radially toward the last stable orbit + + align:start position:0% +radially toward the last stable orbit + + + align:start position:0% +radially toward the last stable orbit +and so you have a multi we call they + + align:start position:0% +and so you have a multi we call they + + + align:start position:0% +and so you have a multi we call they +call it a multi- temperature black body + + align:start position:0% +call it a multi- temperature black body + + + align:start position:0% +call it a multi- temperature black body +or something like that but it's more or + + align:start position:0% +or something like that but it's more or + + + align:start position:0% +or something like that but it's more or +less one k but what you see in these + + align:start position:0% +less one k but what you see in these + + + align:start position:0% +less one k but what you see in these +systems and I didn't bring Spectra but + + align:start position:0% +systems and I didn't bring Spectra but + + + align:start position:0% +systems and I didn't bring Spectra but +in these systems you see radiation it + + align:start position:0% +in these systems you see radiation it + + + align:start position:0% +in these systems you see radiation it +goes out to several hundred K in What's + + align:start position:0% +goes out to several hundred K in What's + + + align:start position:0% +goes out to several hundred K in What's +called the very high state of these + + align:start position:0% +called the very high state of these + + + align:start position:0% +called the very high state of these +systems and that cannot be coming from + + align:start position:0% +systems and that cannot be coming from + + + align:start position:0% +systems and that cannot be coming from +the accretion disc that radiation that's + + align:start position:0% +the accretion disc that radiation that's + + + align:start position:0% +the accretion disc that radiation that's +way out there at very high energies must + + align:start position:0% +way out there at very high energies must + + + align:start position:0% +way out there at very high energies must +be coming from some other structure and + + align:start position:0% +be coming from some other structure and + + + align:start position:0% +be coming from some other structure and +it's generally called a Corona but + + align:start position:0% +it's generally called a Corona but + + + align:start position:0% +it's generally called a Corona but +beyond that there are like you know 30 + + align:start position:0% +beyond that there are like you know 30 + + + align:start position:0% +beyond that there are like you know 30 +models of the Corona and it's not a very + + align:start position:0% +models of the Corona and it's not a very + + + align:start position:0% +models of the Corona and it's not a very +satisfying picture that we have of the + + align:start position:0% +satisfying picture that we have of the + + + align:start position:0% +satisfying picture that we have of the +Corona and the corona must be involved + + align:start position:0% +Corona and the corona must be involved + + + align:start position:0% +Corona and the corona must be involved +in things like these very large low + + align:start position:0% +in things like these very large low + + + align:start position:0% +in things like these very large low +frequency oscillations that I was + + align:start position:0% +frequency oscillations that I was + + + align:start position:0% +frequency oscillations that I was +showing earlier it they must be you + + align:start position:0% +showing earlier it they must be you + + + align:start position:0% +showing earlier it they must be you +know again because because you look at + + align:start position:0% +know again because because you look at + + + align:start position:0% +know again because because you look at +the Spectrum and you see there's a lot + + align:start position:0% +the Spectrum and you see there's a lot + + + align:start position:0% +the Spectrum and you see there's a lot +of hard radiation out at these uh at + + align:start position:0% +of hard radiation out at these uh at + + + align:start position:0% +of hard radiation out at these uh at +these frequencies and so forth but it's + + align:start position:0% +these frequencies and so forth but it's + + + align:start position:0% +these frequencies and so forth but it's +not it's not clear uh you know it's it's + + align:start position:0% +not it's not clear uh you know it's it's + + + align:start position:0% +not it's not clear uh you know it's it's +not quite clear what this Corona is but + + align:start position:0% +not quite clear what this Corona is but + + + align:start position:0% +not quite clear what this Corona is but +it's material that I mean if if I wanted + + align:start position:0% +it's material that I mean if if I wanted + + + align:start position:0% +it's material that I mean if if I wanted +to wave my hands here's what I would say + + align:start position:0% +to wave my hands here's what I would say + + + align:start position:0% +to wave my hands here's what I would say +what it is you've got this disc it's + + align:start position:0% +what it is you've got this disc it's + + + align:start position:0% +what it is you've got this disc it's +going to have magnetic fields in it the + + align:start position:0% +going to have magnetic fields in it the + + + align:start position:0% +going to have magnetic fields in it the +magnetic fields are going to erupt and + + align:start position:0% +magnetic fields are going to erupt and + + + align:start position:0% +magnetic fields are going to erupt and +so forth just by Dynamo effects more or + + align:start position:0% +so forth just by Dynamo effects more or + + + align:start position:0% +so forth just by Dynamo effects more or +less like the sun and that material is + + align:start position:0% +less like the sun and that material is + + + align:start position:0% +less like the sun and that material is +going to erupt up and it's going to be + + align:start position:0% +going to erupt up and it's going to be + + + align:start position:0% +going to erupt up and it's going to be +rather hot just like the stuff that + + align:start position:0% +rather hot just like the stuff that + + + align:start position:0% +rather hot just like the stuff that +produces prominences and so forth in the + + align:start position:0% +produces prominences and so forth in the + + + align:start position:0% +produces prominences and so forth in the +sun and it feeds into this Mater this + + align:start position:0% +sun and it feeds into this Mater this + + + align:start position:0% +sun and it feeds into this Mater this +bigger structure around the disc which + + align:start position:0% +bigger structure around the disc which + + + align:start position:0% +bigger structure around the disc which +is the Corona and people talk in that + + align:start position:0% +is the Corona and people talk in that + + + align:start position:0% +is the Corona and people talk in that +way about the Corona and they talk in + + align:start position:0% +way about the Corona and they talk in + + + align:start position:0% +way about the Corona and they talk in +other ways about the Corona and but the + + align:start position:0% +other ways about the Corona and but the + + + align:start position:0% +other ways about the Corona and but the +understanding of the corona is very poor + + align:start position:0% +understanding of the corona is very poor + + + align:start position:0% +understanding of the corona is very poor +the understanding of the dis is + + align:start position:0% +the understanding of the dis is + + + align:start position:0% +the understanding of the dis is +relatively + + align:start position:0% + + + + align:start position:0% + +good and yeah I'm sorry but the the + + align:start position:0% +good and yeah I'm sorry but the the + + + align:start position:0% +good and yeah I'm sorry but the the +other point on that is that this Corona + + align:start position:0% +other point on that is that this Corona + + + align:start position:0% +other point on that is that this Corona +is this thing that's + + align:start position:0% +is this thing that's + + + align:start position:0% +is this thing that's +Illuminating the disc and fluorescing + + align:start position:0% +Illuminating the disc and fluorescing + + + align:start position:0% +Illuminating the disc and fluorescing +the iron line because the iron line is + + align:start position:0% +the iron line because the iron line is + + + align:start position:0% +the iron line because the iron line is +at like six kilovolts and so it has to + + align:start position:0% +at like six kilovolts and so it has to + + + align:start position:0% +at like six kilovolts and so it has to +be radiation above 6 kilovolts that's + + align:start position:0% +be radiation above 6 kilovolts that's + + + align:start position:0% +be radiation above 6 kilovolts that's +hitting the disc so it's pretty hard + + align:start position:0% +hitting the disc so it's pretty hard + + + align:start position:0% +hitting the disc so it's pretty hard +radiation that's coming from this Corona + + align:start position:0% +radiation that's coming from this Corona + + + align:start position:0% +radiation that's coming from this Corona +That's Illuminating this disc and + + align:start position:0% +That's Illuminating this disc and + + + align:start position:0% +That's Illuminating this disc and +producing this Florest iron line that + + align:start position:0% +producing this Florest iron line that + + + align:start position:0% +producing this Florest iron line that +we're seeing in this very broad very + + align:start position:0% +we're seeing in this very broad very + + + align:start position:0% +we're seeing in this very broad very +broad iron + + align:start position:0% +broad iron + + + align:start position:0% +broad iron +line that that iron line comes when you + + align:start position:0% +line that that iron line comes when you + + + align:start position:0% +line that that iron line comes when you +excite one of the inner shell electrons + + align:start position:0% +excite one of the inner shell electrons + + + align:start position:0% +excite one of the inner shell electrons +iron has 20 26 electrons a lot of them + + align:start position:0% +iron has 20 26 electrons a lot of them + + + align:start position:0% +iron has 20 26 electrons a lot of them +are removed because the gas is quite hot + + align:start position:0% +are removed because the gas is quite hot + + + align:start position:0% +are removed because the gas is quite hot +but if you strike iron with sufficiently + + align:start position:0% +but if you strike iron with sufficiently + + + align:start position:0% +but if you strike iron with sufficiently +high uh energy radiation you can kick + + align:start position:0% +high uh energy radiation you can kick + + + align:start position:0% +high uh energy radiation you can kick +one of the inner shell innermost + + align:start position:0% +one of the inner shell innermost + + + align:start position:0% +one of the inner shell innermost +electrons to a higher energy level and + + align:start position:0% +electrons to a higher energy level and + + + align:start position:0% +electrons to a higher energy level and +then it will Cascade back down just like + + align:start position:0% +then it will Cascade back down just like + + + align:start position:0% +then it will Cascade back down just like +in a hydrogen atom producing uh in the + + align:start position:0% +in a hydrogen atom producing uh in the + + + align:start position:0% +in a hydrogen atom producing uh in the +case of iron x-rays right and and and + + align:start position:0% +case of iron x-rays right and and and + + + align:start position:0% +case of iron x-rays right and and and +this was the iron K line so this is the + + align:start position:0% +this was the iron K line so this is the + + + align:start position:0% +this was the iron K line so this is the +inner shell the electrons in the inner + + align:start position:0% +inner shell the electrons in the inner + + + align:start position:0% +inner shell the electrons in the inner +shell right and the disc just isn't hot + + align:start position:0% +shell right and the disc just isn't hot + + + align:start position:0% +shell right and the disc just isn't hot +enough to heat the iron and excite its + + align:start position:0% +enough to heat the iron and excite its + + + align:start position:0% +enough to heat the iron and excite its +inner shell by itself right if the disc + + align:start position:0% +inner shell by itself right if the disc + + + align:start position:0% +inner shell by itself right if the disc +were that hot we would see black body + + align:start position:0% +were that hot we would see black body + + + align:start position:0% +were that hot we would see black body +radiation coming at 6 or 10 K EV and we + + align:start position:0% +radiation coming at 6 or 10 K EV and we + + + align:start position:0% +radiation coming at 6 or 10 K EV and we +don't right the black body radiation is + + align:start position:0% +don't right the black body radiation is + + + align:start position:0% +don't right the black body radiation is +more like 1 K uh temperature which is + + align:start position:0% +more like 1 K uh temperature which is + + + align:start position:0% +more like 1 K uh temperature which is +not enough to excite its own Iron line + + align:start position:0% +not enough to excite its own Iron line + + + align:start position:0% +not enough to excite its own Iron line +so but then that was the question how + + align:start position:0% +so but then that was the question how + + + align:start position:0% +so but then that was the question how +well do you understand this Illuminating + + align:start position:0% +well do you understand this Illuminating + + + align:start position:0% +well do you understand this Illuminating +Source that's fluorescent the iron and + + align:start position:0% +Source that's fluorescent the iron and + + + align:start position:0% +Source that's fluorescent the iron and +the answer is you don't understand it + + align:start position:0% +the answer is you don't understand it + + + align:start position:0% +the answer is you don't understand it +very well which is really unsatisfying + + align:start position:0% +very well which is really unsatisfying + + + align:start position:0% +very well which is really unsatisfying +for well we don't understand everything + + align:start position:0% +for well we don't understand everything + + + align:start position:0% +for well we don't understand everything +about these systems but on the other + + align:start position:0% +about these systems but on the other + + + align:start position:0% +about these systems but on the other +hand hand it's a great opportunity for + + align:start position:0% +hand hand it's a great opportunity for + + + align:start position:0% +hand hand it's a great opportunity for +learning oh yeah and let me just put in + + align:start position:0% +learning oh yeah and let me just put in + + + align:start position:0% +learning oh yeah and let me just put in +a plug here for any of the students and + + align:start position:0% +a plug here for any of the students and + + + align:start position:0% +a plug here for any of the students and +and those who might be watching a lot of + + align:start position:0% +and those who might be watching a lot of + + + align:start position:0% +and those who might be watching a lot of +the research in this field the + + align:start position:0% +the research in this field the + + + align:start position:0% +the research in this field the +observational research is being done at + + align:start position:0% +observational research is being done at + + + align:start position:0% +observational research is being done at +MIT and also at Harvard using especially + + align:start position:0% +MIT and also at Harvard using especially + + + align:start position:0% +MIT and also at Harvard using especially +this Rossy x-ray timing Explorer + + align:start position:0% +this Rossy x-ray timing Explorer + + + align:start position:0% +this Rossy x-ray timing Explorer +satellite uh Braun remar's Group in the + + align:start position:0% +satellite uh Braun remar's Group in the + + + align:start position:0% +satellite uh Braun remar's Group in the +center for space research together with + + align:start position:0% +center for space research together with + + + align:start position:0% +center for space research together with +Jeff and others are are leaders in this + + align:start position:0% +Jeff and others are are leaders in this + + + align:start position:0% +Jeff and others are are leaders in this +and there are europ positions available + + align:start position:0% +and there are europ positions available + + + align:start position:0% +and there are europ positions available +senior thesis and and so on so if you'd + + align:start position:0% +senior thesis and and so on so if you'd + + + align:start position:0% +senior thesis and and so on so if you'd +like to measure the spin and mass of a + + align:start position:0% +like to measure the spin and mass of a + + + align:start position:0% +like to measure the spin and mass of a +black hole here's a great + + align:start position:0% +black hole here's a great + + + align:start position:0% +black hole here's a great +opportunity let's thank Jeff again for a + + align:start position:0% +opportunity let's thank Jeff again for a + + + align:start position:0% +opportunity let's thank Jeff again for a +great + + align:start position:0% + + + + align:start position:0% + +talk that's really impressive \ No newline at end of file diff --git a/mhQebe1Y4d0.txt b/mhQebe1Y4d0.txt new file mode 100644 index 0000000000000000000000000000000000000000..e591c6ef798ae7070bf47161d9c5db08ac28a652 --- /dev/null +++ b/mhQebe1Y4d0.txt @@ -0,0 +1,13379 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +today we're going to talk about wallets + + align:start position:0% +today we're going to talk about wallets + + + align:start position:0% +today we're going to talk about wallets +and SPV and if you don't know what SPV + + align:start position:0% +and SPV and if you don't know what SPV + + + align:start position:0% +and SPV and if you don't know what SPV +stands for that will be defined as well + + align:start position:0% +stands for that will be defined as well + + + align:start position:0% +stands for that will be defined as well +so don't worry first you get your + + align:start position:0% +so don't worry first you get your + + + align:start position:0% +so don't worry first you get your +software that's something of a problem + + align:start position:0% +software that's something of a problem + + + align:start position:0% +software that's something of a problem +but like how do you know you got the + + align:start position:0% +but like how do you know you got the + + + align:start position:0% +but like how do you know you got the +right Bitcoin software there can be + + align:start position:0% +right Bitcoin software there can be + + + align:start position:0% +right Bitcoin software there can be +issues there but anyway there are + + align:start position:0% +issues there but anyway there are + + + align:start position:0% +issues there but anyway there are +multiple implementations that should be + + align:start position:0% +multiple implementations that should be + + + align:start position:0% +multiple implementations that should be +consensus compatible I often use btcd + + align:start position:0% +consensus compatible I often use btcd + + + align:start position:0% +consensus compatible I often use btcd +which is a version written in go but + + align:start position:0% +which is a version written in go but + + + align:start position:0% +which is a version written in go but +sort of the the main implementation is + + align:start position:0% +sort of the the main implementation is + + + align:start position:0% +sort of the the main implementation is +written in C++ so you get the software + + align:start position:0% +written in C++ so you get the software + + + align:start position:0% +written in C++ so you get the software +and then you somehow connect to peers in + + align:start position:0% +and then you somehow connect to peers in + + + align:start position:0% +and then you somehow connect to peers in +the network there's there's all these + + align:start position:0% +the network there's there's all these + + + align:start position:0% +the network there's there's all these +sort of asterixis which means it's not + + align:start position:0% +sort of asterixis which means it's not + + + align:start position:0% +sort of asterixis which means it's not +completely decentralized you have to + + align:start position:0% +completely decentralized you have to + + + align:start position:0% +completely decentralized you have to +find where to get it you have to find + + align:start position:0% +find where to get it you have to find + + + align:start position:0% +find where to get it you have to find +who to connect you once you do that you + + align:start position:0% +who to connect you once you do that you + + + align:start position:0% +who to connect you once you do that you +get all the headers which are 80 bytes + + align:start position:0% +get all the headers which are 80 bytes + + + align:start position:0% +get all the headers which are 80 bytes +each you verify all the work and then + + align:start position:0% +each you verify all the work and then + + + align:start position:0% +each you verify all the work and then +you start getting the blocks looking + + align:start position:0% +you start getting the blocks looking + + + align:start position:0% +you start getting the blocks looking +through the transactions you replay the + + align:start position:0% +through the transactions you replay the + + + align:start position:0% +through the transactions you replay the +history of the last nine years of the + + align:start position:0% +history of the last nine years of the + + + align:start position:0% +history of the last nine years of the +coin and then you arrive at a UT Exocet + + align:start position:0% +coin and then you arrive at a UT Exocet + + + align:start position:0% +coin and then you arrive at a UT Exocet +an unspent unspent transaction output + + align:start position:0% +an unspent unspent transaction output + + + align:start position:0% +an unspent unspent transaction output +set and it should be the same as + + align:start position:0% +set and it should be the same as + + + align:start position:0% +set and it should be the same as +everyone else got right everyone else's + + align:start position:0% +everyone else got right everyone else's + + + align:start position:0% +everyone else got right everyone else's +have the same headers the same work the + + align:start position:0% +have the same headers the same work the + + + align:start position:0% +have the same headers the same work the +same transactions they'll get the same + + align:start position:0% +same transactions they'll get the same + + + align:start position:0% +same transactions they'll get the same +set of who's you know which which coins + + align:start position:0% +set of who's you know which which coins + + + align:start position:0% +set of who's you know which which coins +are encumbered by which keys as you do + + align:start position:0% +are encumbered by which keys as you do + + + align:start position:0% +are encumbered by which keys as you do +and the idea is it would be very + + align:start position:0% +and the idea is it would be very + + + align:start position:0% +and the idea is it would be very +expensive to you know have different UT + + align:start position:0% +expensive to you know have different UT + + + align:start position:0% +expensive to you know have different UT +EXO sets because you'd have to do all + + align:start position:0% +EXO sets because you'd have to do all + + + align:start position:0% +EXO sets because you'd have to do all +that work okay so that's the full band + + align:start position:0% +that work okay so that's the full band + + + align:start position:0% +that work okay so that's the full band +that's you know how a node works but + + align:start position:0% +that's you know how a node works but + + + align:start position:0% +that's you know how a node works but +what about dealing with actually money + + align:start position:0% +what about dealing with actually money + + + align:start position:0% +what about dealing with actually money +so far we've just looked at okay here's + + align:start position:0% +so far we've just looked at okay here's + + + align:start position:0% +so far we've just looked at okay here's +how to get your node running here's how + + align:start position:0% +how to get your node running here's how + + + align:start position:0% +how to get your node running here's how +to observe the network and come to the + + align:start position:0% +to observe the network and come to the + + + align:start position:0% +to observe the network and come to the +same conclusions everyone else but you + + align:start position:0% +same conclusions everyone else but you + + + align:start position:0% +same conclusions everyone else but you +probably want to actually do something + + align:start position:0% +probably want to actually do something + + + align:start position:0% +probably want to actually do something +with this right you want to pay people + + align:start position:0% +with this right you want to pay people + + + align:start position:0% +with this right you want to pay people +or get paid those are sort of the two + + align:start position:0% +or get paid those are sort of the two + + + align:start position:0% +or get paid those are sort of the two +fundamental functions that this tries to + + align:start position:0% +fundamental functions that this tries to + + + align:start position:0% +fundamental functions that this tries to +address so the software that manages + + align:start position:0% +address so the software that manages + + + align:start position:0% +address so the software that manages +this feature is called a wallet and it's + + align:start position:0% +this feature is called a wallet and it's + + + align:start position:0% +this feature is called a wallet and it's +not necessarily the same software as + + align:start position:0% +not necessarily the same software as + + + align:start position:0% +not necessarily the same software as +what's connecting to the network + + align:start position:0% +what's connecting to the network + + + align:start position:0% +what's connecting to the network +downloading and verifying in the case of + + align:start position:0% +downloading and verifying in the case of + + + align:start position:0% +downloading and verifying in the case of +Bitcoin core it is although many of the + + align:start position:0% +Bitcoin core it is although many of the + + + align:start position:0% +Bitcoin core it is although many of the +programmers of Bitcoin core wish that it + + align:start position:0% +programmers of Bitcoin core wish that it + + + align:start position:0% +programmers of Bitcoin core wish that it +weren't and there's sort of a long-term + + align:start position:0% +weren't and there's sort of a long-term + + + align:start position:0% +weren't and there's sort of a long-term +goal of it'd be really great if we could + + align:start position:0% +goal of it'd be really great if we could + + + align:start position:0% +goal of it'd be really great if we could +sort of pull these two things apart into + + align:start position:0% +sort of pull these two things apart into + + + align:start position:0% +sort of pull these two things apart into +maybe separate binaries separate + + align:start position:0% +maybe separate binaries separate + + + align:start position:0% +maybe separate binaries separate +programs something but they're really + + align:start position:0% +programs something but they're really + + + align:start position:0% +programs something but they're really +intertwined and it's kind of ugly + + align:start position:0% +intertwined and it's kind of ugly + + + align:start position:0% +intertwined and it's kind of ugly +but there are other things that that are + + align:start position:0% +but there are other things that that are + + + align:start position:0% +but there are other things that that are +separate ok so + + align:start position:0% +separate ok so + + + align:start position:0% +separate ok so +wallet software functionality seems + + align:start position:0% +wallet software functionality seems + + + align:start position:0% +wallet software functionality seems +simple right you send and receive money + + align:start position:0% +simple right you send and receive money + + + align:start position:0% +simple right you send and receive money +simple of course you need to resend + + align:start position:0% +simple of course you need to resend + + + align:start position:0% +simple of course you need to resend +money before you can send it so let's + + align:start position:0% +money before you can send it so let's + + + align:start position:0% +money before you can send it so let's +start with that okay so we talked about + + align:start position:0% +start with that okay so we talked about + + + align:start position:0% +start with that okay so we talked about +receive of we did not talk about receive + + align:start position:0% +receive of we did not talk about receive + + + align:start position:0% +receive of we did not talk about receive +addresses we did talk about the script + + align:start position:0% +addresses we did talk about the script + + + align:start position:0% +addresses we did talk about the script +and how it's a generally used paid to + + align:start position:0% +and how it's a generally used paid to + + + align:start position:0% +and how it's a generally used paid to +punky hash where you have you know you + + align:start position:0% +punky hash where you have you know you + + + align:start position:0% +punky hash where you have you know you +you put the hash of your pub key in your + + align:start position:0% +you put the hash of your pub key in your + + + align:start position:0% +you put the hash of your pub key in your +output script and then in your redeem + + align:start position:0% +output script and then in your redeem + + + align:start position:0% +output script and then in your redeem +script and your input + + align:start position:0% +script and your input + + + align:start position:0% +script and your input +you put the pub key itself which is then + + align:start position:0% +you put the pub key itself which is then + + + align:start position:0% +you put the pub key itself which is then +checked against the hash and then the + + align:start position:0% +checked against the hash and then the + + + align:start position:0% +checked against the hash and then the +signature is verified most likely you've + + align:start position:0% +signature is verified most likely you've + + + align:start position:0% +signature is verified most likely you've +if you've looked at Bitcoin at all + + align:start position:0% +if you've looked at Bitcoin at all + + + align:start position:0% +if you've looked at Bitcoin at all +you've seen these types of addresses + + align:start position:0% +you've seen these types of addresses + + + align:start position:0% +you've seen these types of addresses +they usually start with one there a + + align:start position:0% +they usually start with one there a + + + align:start position:0% +they usually start with one there a +bunch of characters long weird mix of + + align:start position:0% +bunch of characters long weird mix of + + + align:start position:0% +bunch of characters long weird mix of +lowercase uppercase Letten umbers and + + align:start position:0% +lowercase uppercase Letten umbers and + + + align:start position:0% +lowercase uppercase Letten umbers and +letters there's a standard for + + align:start position:0% +letters there's a standard for + + + align:start position:0% +letters there's a standard for +converting a 20-byte pub key hash into + + align:start position:0% +converting a 20-byte pub key hash into + + + align:start position:0% +converting a 20-byte pub key hash into +this address + + align:start position:0% +this address + + + align:start position:0% +this address +so the idea since almost everything is + + align:start position:0% +so the idea since almost everything is + + + align:start position:0% +so the idea since almost everything is +using the same pub key hash script you + + align:start position:0% +using the same pub key hash script you + + + align:start position:0% +using the same pub key hash script you +can forget about the op codes like op do + + align:start position:0% +can forget about the op codes like op do + + + align:start position:0% +can forget about the op codes like op do +op hash 160 off equal verify because + + align:start position:0% +op hash 160 off equal verify because + + + align:start position:0% +op hash 160 off equal verify because +they're they're always the same and so + + align:start position:0% +they're they're always the same and so + + + align:start position:0% +they're they're always the same and so +it's the standard like okay we're just + + align:start position:0% +it's the standard like okay we're just + + + align:start position:0% +it's the standard like okay we're just +taking that 20 byte hash and now let's + + align:start position:0% +taking that 20 byte hash and now let's + + + align:start position:0% +taking that 20 byte hash and now let's +convert it to something hopefully + + align:start position:0% +convert it to something hopefully + + + align:start position:0% +convert it to something hopefully +somewhat human readable and writeable so + + align:start position:0% +somewhat human readable and writeable so + + + align:start position:0% +somewhat human readable and writeable so +that people can write it down say it + + align:start position:0% +that people can write it down say it + + + align:start position:0% +that people can write it down say it +over the phone + + align:start position:0% +over the phone + + + align:start position:0% +over the phone +this is the one Satoshi made it's got 58 + + align:start position:0% +this is the one Satoshi made it's got 58 + + + align:start position:0% +this is the one Satoshi made it's got 58 +characters and then the last well the + + align:start position:0% +characters and then the last well the + + + align:start position:0% +characters and then the last well the +last four bytes which ends up being like + + align:start position:0% +last four bytes which ends up being like + + + align:start position:0% +last four bytes which ends up being like +five or six of the letters is sort of a + + align:start position:0% +five or six of the letters is sort of a + + + align:start position:0% +five or six of the letters is sort of a +checksum where you take the hash of the + + align:start position:0% +checksum where you take the hash of the + + + align:start position:0% +checksum where you take the hash of the +first however many letters and then + + align:start position:0% +first however many letters and then + + + align:start position:0% +first however many letters and then +that's supposed to be like equal to the + + align:start position:0% +that's supposed to be like equal to the + + + align:start position:0% +that's supposed to be like equal to the +next one so hopefully if you type + + align:start position:0% +next one so hopefully if you type + + + align:start position:0% +next one so hopefully if you type +something wrong it doesn't change the + + align:start position:0% +something wrong it doesn't change the + + + align:start position:0% +something wrong it doesn't change the +hash and then you send it to the wrong + + align:start position:0% +hash and then you send it to the wrong + + + align:start position:0% +hash and then you send it to the wrong +place and then no one has a matching key + + align:start position:0% +place and then no one has a matching key + + + align:start position:0% +place and then no one has a matching key +for that there's a newer standard for + + align:start position:0% +for that there's a newer standard for + + + align:start position:0% +for that there's a newer standard for +this where all the lowers all the + + align:start position:0% +this where all the lowers all the + + + align:start position:0% +this where all the lowers all the +letters are lowercase that's introduced + + align:start position:0% +letters are lowercase that's introduced + + + align:start position:0% +letters are lowercase that's introduced +actually today in Bitcoin core version + + align:start position:0% +actually today in Bitcoin core version + + + align:start position:0% +actually today in Bitcoin core version +0.16 came out and so there's a new + + align:start position:0% +0.16 came out and so there's a new + + + align:start position:0% +0.16 came out and so there's a new +standard called BEC 32 they they did + + align:start position:0% +standard called BEC 32 they they did + + + align:start position:0% +standard called BEC 32 they they did +some research and they found it was + + align:start position:0% +some research and they found it was + + + align:start position:0% +some research and they found it was +actually much faster to transmit over + + align:start position:0% +actually much faster to transmit over + + + align:start position:0% +actually much faster to transmit over +the phone via voice because you didn't + + align:start position:0% +the phone via voice because you didn't + + + align:start position:0% +the phone via voice because you didn't +have to say whether things were + + align:start position:0% +have to say whether things were + + + align:start position:0% +have to say whether things were +uppercase or lowercase which ended up + + align:start position:0% +uppercase or lowercase which ended up + + + align:start position:0% +uppercase or lowercase which ended up +being very annoying for people one + + align:start position:0% +being very annoying for people one + + + align:start position:0% +being very annoying for people one +bigger a little f1 to biggie for it's + + align:start position:0% +bigger a little f1 to biggie for it's + + + align:start position:0% +bigger a little f1 to biggie for it's +annoying anyway but the idea is this is + + align:start position:0% +annoying anyway but the idea is this is + + + align:start position:0% +annoying anyway but the idea is this is +just this + + align:start position:0% +just this + + + align:start position:0% +just this +just an encoding of the 20-byte funky + + align:start position:0% +just an encoding of the 20-byte funky + + + align:start position:0% +just an encoding of the 20-byte funky +hash so when you type this into a + + align:start position:0% +hash so when you type this into a + + + align:start position:0% +hash so when you type this into a +program it reads this converts it into a + + align:start position:0% +program it reads this converts it into a + + + align:start position:0% +program it reads this converts it into a +20-byte hash builds the output script + + align:start position:0% +20-byte hash builds the output script + + + align:start position:0% +20-byte hash builds the output script +okay so y'all outputs are all the same + + align:start position:0% +okay so y'all outputs are all the same + + + align:start position:0% +okay so y'all outputs are all the same +um so this is sort of like a UI thing it + + align:start position:0% +um so this is sort of like a UI thing it + + + align:start position:0% +um so this is sort of like a UI thing it +the addresses don't really exist at the + + align:start position:0% +the addresses don't really exist at the + + + align:start position:0% +the addresses don't really exist at the +look at the protocol level ok any + + align:start position:0% +look at the protocol level ok any + + + align:start position:0% +look at the protocol level ok any +questions about addresses clearly ok + + align:start position:0% +questions about addresses clearly ok + + + align:start position:0% +questions about addresses clearly ok +we're not gonna put there you know UI + + align:start position:0% +we're not gonna put there you know UI + + + align:start position:0% +we're not gonna put there you know UI +and like usability is super important + + align:start position:0% +and like usability is super important + + + align:start position:0% +and like usability is super important +but not to the focus yet I've ordered ok + + align:start position:0% +but not to the focus yet I've ordered ok + + + align:start position:0% +but not to the focus yet I've ordered ok +the idea in a lot of cases is you want + + align:start position:0% +the idea in a lot of cases is you want + + + align:start position:0% +the idea in a lot of cases is you want +to receive money and know that you + + align:start position:0% +to receive money and know that you + + + align:start position:0% +to receive money and know that you +received it or somehow interact with + + align:start position:0% +received it or somehow interact with + + + align:start position:0% +received it or somehow interact with +people over computers and you couldn't + + align:start position:0% +people over computers and you couldn't + + + align:start position:0% +people over computers and you couldn't +put a bunch of addresses on a server but + + align:start position:0% +put a bunch of addresses on a server but + + + align:start position:0% +put a bunch of addresses on a server but +keep your private keys offline because + + align:start position:0% +keep your private keys offline because + + + align:start position:0% +keep your private keys offline because +if you keep both your public key and + + align:start position:0% +if you keep both your public key and + + + align:start position:0% +if you keep both your public key and +your private key on the same computer + + align:start position:0% +your private key on the same computer + + + align:start position:0% +your private key on the same computer +that's kind of a attractive target for + + align:start position:0% +that's kind of a attractive target for + + + align:start position:0% +that's kind of a attractive target for +someone to break into your system + + align:start position:0% +someone to break into your system + + + align:start position:0% +someone to break into your system +because they say oh like you know this + + align:start position:0% +because they say oh like you know this + + + align:start position:0% +because they say oh like you know this +guy's running Bitcoin and he's accepting + + align:start position:0% +guy's running Bitcoin and he's accepting + + + align:start position:0% +guy's running Bitcoin and he's accepting +payments there might be a bunch of money + + align:start position:0% +payments there might be a bunch of money + + + align:start position:0% +payments there might be a bunch of money +in this computer if I can get into it I + + align:start position:0% +in this computer if I can get into it I + + + align:start position:0% +in this computer if I can get into it I +can take all the money so one issue that + + align:start position:0% +can take all the money so one issue that + + + align:start position:0% +can take all the money so one issue that +people ran up against pretty early is + + align:start position:0% +people ran up against pretty early is + + + align:start position:0% +people ran up against pretty early is +well let's say I generate 10 10 keys you + + align:start position:0% +well let's say I generate 10 10 keys you + + + align:start position:0% +well let's say I generate 10 10 keys you +know 10 private keys 10 public keys 10 + + align:start position:0% +know 10 private keys 10 public keys 10 + + + align:start position:0% +know 10 private keys 10 public keys 10 +addresses put them on the server and + + align:start position:0% +addresses put them on the server and + + + align:start position:0% +addresses put them on the server and +then I run out and I can reuse addresses + + align:start position:0% +then I run out and I can reuse addresses + + + align:start position:0% +then I run out and I can reuse addresses +but that can hurt privacy because people + + align:start position:0% +but that can hurt privacy because people + + + align:start position:0% +but that can hurt privacy because people +can then see that the same you know the + + align:start position:0% +can then see that the same you know the + + + align:start position:0% +can then see that the same you know the +same people are using these keys so is + + align:start position:0% +same people are using these keys so is + + + align:start position:0% +same people are using these keys so is +there any clever way we can generate pub + + align:start position:0% +there any clever way we can generate pub + + + align:start position:0% +there any clever way we can generate pub +keys without the private key is there + + align:start position:0% +keys without the private key is there + + + align:start position:0% +keys without the private key is there +any given all the fun key stuff we've + + align:start position:0% +any given all the fun key stuff we've + + + align:start position:0% +any given all the fun key stuff we've +talked about could anyone think of any + + align:start position:0% +talked about could anyone think of any + + + align:start position:0% +talked about could anyone think of any +clever ways to do that ok well pretty + + align:start position:0% +clever ways to do that ok well pretty + + + align:start position:0% +clever ways to do that ok well pretty +straightforward this is this is called + + align:start position:0% +straightforward this is this is called + + + align:start position:0% +straightforward this is this is called +BIP 32 Bitcoin improvement protocol 32 a + + align:start position:0% +BIP 32 Bitcoin improvement protocol 32 a + + + align:start position:0% +BIP 32 Bitcoin improvement protocol 32 a +proposal 32 it's actually this is a + + align:start position:0% +proposal 32 it's actually this is a + + + align:start position:0% +proposal 32 it's actually this is a +super simplified version but this is the + + align:start position:0% +super simplified version but this is the + + + align:start position:0% +super simplified version but this is the +basic idea of what they do they do it + + align:start position:0% +basic idea of what they do they do it + + + align:start position:0% +basic idea of what they do they do it +much more involved and complicated but + + align:start position:0% +much more involved and complicated but + + + align:start position:0% +much more involved and complicated but +basically you've got your public key P + + align:start position:0% +basically you've got your public key P + + + align:start position:0% +basically you've got your public key P +big P and some kind of randomized data + + align:start position:0% +big P and some kind of randomized data + + + align:start position:0% +big P and some kind of randomized data +randomizer data are and you know oops + + align:start position:0% +randomizer data are and you know oops + + + align:start position:0% +randomizer data are and you know oops +sorry your private key is just little P + + align:start position:0% + + + + align:start position:0% + +so the idea is you want to send to an + + align:start position:0% +so the idea is you want to send to an + + + align:start position:0% +so the idea is you want to send to an +address you want to generate a new + + align:start position:0% +address you want to generate a new + + + align:start position:0% +address you want to generate a new +address well it's just your + + align:start position:0% +address well it's just your + + + align:start position:0% +address well it's just your +plus the hash of our concatenated 1 + + align:start position:0% +plus the hash of our concatenated 1 + + + align:start position:0% +plus the hash of our concatenated 1 +times G and if you wanted to make this 2 + + align:start position:0% +times G and if you wanted to make this 2 + + + align:start position:0% +times G and if you wanted to make this 2 +3 you can make this any number you want + + align:start position:0% +3 you can make this any number you want + + + align:start position:0% +3 you can make this any number you want +and then your private key is just gonna + + align:start position:0% +and then your private key is just gonna + + + align:start position:0% +and then your private key is just gonna +be your that same public key plus the + + align:start position:0% +be your that same public key plus the + + + align:start position:0% +be your that same public key plus the +hash of our right so you give someone + + align:start position:0% +hash of our right so you give someone + + + align:start position:0% +hash of our right so you give someone +some extra data which they can throw + + align:start position:0% +some extra data which they can throw + + + align:start position:0% +some extra data which they can throw +into a hash function + + align:start position:0% +into a hash function + + + align:start position:0% +into a hash function +use this sort of as a every you know an + + align:start position:0% +use this sort of as a every you know an + + + align:start position:0% +use this sort of as a every you know an +own private key and you add it to your + + align:start position:0% +own private key and you add it to your + + + align:start position:0% +own private key and you add it to your +private key so no one you know no one + + align:start position:0% +private key so no one you know no one + + + align:start position:0% +private key so no one you know no one +just knowing this data can spend from it + + align:start position:0% +just knowing this data can spend from it + + + align:start position:0% +just knowing this data can spend from it +that's really nice because then the + + align:start position:0% +that's really nice because then the + + + align:start position:0% +that's really nice because then the +server can generate arbitrary numbers + + align:start position:0% +server can generate arbitrary numbers + + + align:start position:0% +server can generate arbitrary numbers +this makes sense ok oh yes so in the + + align:start position:0% +this makes sense ok oh yes so in the + + + align:start position:0% +this makes sense ok oh yes so in the +last one's big a is a public key it's a + + align:start position:0% +last one's big a is a public key it's a + + + align:start position:0% +last one's big a is a public key it's a +point on the curve little a is a private + + align:start position:0% +point on the curve little a is a private + + + align:start position:0% +point on the curve little a is a private +key I that should not have a G right so + + align:start position:0% +key I that should not have a G right so + + + align:start position:0% +key I that should not have a G right so +G is the generator for the group G is + + align:start position:0% +G is the generator for the group G is + + + align:start position:0% +G is the generator for the group G is +sort of how you convert from a private + + align:start position:0% +sort of how you convert from a private + + + align:start position:0% +sort of how you convert from a private +key to a public key he just multiplied + + align:start position:0% +key to a public key he just multiplied + + + align:start position:0% +key to a public key he just multiplied +by G which is just an arbitrary point + + align:start position:0% +by G which is just an arbitrary point + + + align:start position:0% +by G which is just an arbitrary point +yes so in this case there's sort of two + + align:start position:0% +yes so in this case there's sort of two + + + align:start position:0% +yes so in this case there's sort of two +private keys there's your your standard + + align:start position:0% +private keys there's your your standard + + + align:start position:0% +private keys there's your your standard +private key that you actually just + + align:start position:0% +private key that you actually just + + + align:start position:0% +private key that you actually just +randomly created this number P multiply + + align:start position:0% +randomly created this number P multiply + + + align:start position:0% +randomly created this number P multiply +it by G to get big P but your private + + align:start position:0% +it by G to get big P but your private + + + align:start position:0% +it by G to get big P but your private +key for any particular address does + + align:start position:0% +key for any particular address does + + + align:start position:0% +key for any particular address does +change right you're adding the hash of + + align:start position:0% +change right you're adding the hash of + + + align:start position:0% +change right you're adding the hash of +our comma 1 or R comma 2 R comma three R + + align:start position:0% +our comma 1 or R comma 2 R comma three R + + + align:start position:0% +our comma 1 or R comma 2 R comma three R +should be like 32 bytes or something you + + align:start position:0% +should be like 32 bytes or something you + + + align:start position:0% +should be like 32 bytes or something you +know you don't want anyone you sort of + + align:start position:0% +know you don't want anyone you sort of + + + align:start position:0% +know you don't want anyone you sort of +don't what you can do is you can have + + align:start position:0% +don't what you can do is you can have + + + align:start position:0% +don't what you can do is you can have +the server you you you have your server + + align:start position:0% +the server you you you have your server + + + align:start position:0% +the server you you you have your server +and you say hey I'm gonna accept + + align:start position:0% +and you say hey I'm gonna accept + + + align:start position:0% +and you say hey I'm gonna accept +payments for cookies or shoes or + + align:start position:0% +payments for cookies or shoes or + + + align:start position:0% +payments for cookies or shoes or +whatever I'm selling and then you give + + align:start position:0% +whatever I'm selling and then you give + + + align:start position:0% +whatever I'm selling and then you give +the pit the server your public key P and + + align:start position:0% +the pit the server your public key P and + + + align:start position:0% +the pit the server your public key P and +this randomizer R and you just say the + + align:start position:0% +this randomizer R and you just say the + + + align:start position:0% +this randomizer R and you just say the +server go wild make whatever number you + + align:start position:0% +server go wild make whatever number you + + + align:start position:0% +server go wild make whatever number you +want here it has to be this number + + align:start position:0% +want here it has to be this number + + + align:start position:0% +want here it has to be this number +should be fairly small let's say less + + align:start position:0% +should be fairly small let's say less + + + align:start position:0% +should be fairly small let's say less +than a billion and then when you want to + + align:start position:0% +than a billion and then when you want to + + + align:start position:0% +than a billion and then when you want to +find how much you've gotten paid well + + align:start position:0% +find how much you've gotten paid well + + + align:start position:0% +find how much you've gotten paid well +you can generate a billion private keys + + align:start position:0% +you can generate a billion private keys + + + align:start position:0% +you can generate a billion private keys +here some reasonable numbers of the + + align:start position:0% +here some reasonable numbers of the + + + align:start position:0% +here some reasonable numbers of the +computer can actually do it and you can + + align:start position:0% +computer can actually do it and you can + + + align:start position:0% +computer can actually do it and you can +generate you know you can just increment + + align:start position:0% +generate you know you can just increment + + + align:start position:0% +generate you know you can just increment +this generate a ton of address + + align:start position:0% +this generate a ton of address + + + align:start position:0% +this generate a ton of address +and look for them on the blockchain yes + + align:start position:0% +and look for them on the blockchain yes + + + align:start position:0% +and look for them on the blockchain yes +oh that makes sense at all bit 32 is + + align:start position:0% +oh that makes sense at all bit 32 is + + + align:start position:0% +oh that makes sense at all bit 32 is +actually quite a bit more involved and + + align:start position:0% +actually quite a bit more involved and + + + align:start position:0% +actually quite a bit more involved and +complicated this is the basic idea but + + align:start position:0% +complicated this is the basic idea but + + + align:start position:0% +complicated this is the basic idea but +they make sort of trees of it and you + + align:start position:0% +they make sort of trees of it and you + + + align:start position:0% +they make sort of trees of it and you +can say oh well like you know make + + align:start position:0% +can say oh well like you know make + + + align:start position:0% +can say oh well like you know make +instead of just one level we can make + + align:start position:0% +instead of just one level we can make + + + align:start position:0% +instead of just one level we can make +like a whole tree of these things and + + align:start position:0% +like a whole tree of these things and + + + align:start position:0% +like a whole tree of these things and +like have different accounts and like + + align:start position:0% +like have different accounts and like + + + align:start position:0% +like have different accounts and like +make a really full-featured system in + + align:start position:0% +make a really full-featured system in + + + align:start position:0% +make a really full-featured system in +case people want to use this kind of + + align:start position:0% +case people want to use this kind of + + + align:start position:0% +case people want to use this kind of +thing yeah so you can put public key and + + align:start position:0% +thing yeah so you can put public key and + + + align:start position:0% +thing yeah so you can put public key and +this random data on the server the + + align:start position:0% +this random data on the server the + + + align:start position:0% +this random data on the server the +server can make addresses as needed + + align:start position:0% +server can make addresses as needed + + + align:start position:0% +server can make addresses as needed +really quickly and what's nice is + + align:start position:0% +really quickly and what's nice is + + + align:start position:0% +really quickly and what's nice is +observers can't link these addresses + + align:start position:0% +observers can't link these addresses + + + align:start position:0% +observers can't link these addresses +right if you're just looking at the + + align:start position:0% +right if you're just looking at the + + + align:start position:0% +right if you're just looking at the +blockchain you won't see the difference + + align:start position:0% +blockchain you won't see the difference + + + align:start position:0% +blockchain you won't see the difference +between like a sub 1 + a sub 2 if this + + align:start position:0% +between like a sub 1 + a sub 2 if this + + + align:start position:0% +between like a sub 1 + a sub 2 if this +number and 1 or 2 because it's going + + align:start position:0% +number and 1 or 2 because it's going + + + align:start position:0% +number and 1 or 2 because it's going +through this hash function you ever see + + align:start position:0% +through this hash function you ever see + + + align:start position:0% +through this hash function you ever see +that to an observer it looks like all + + align:start position:0% +that to an observer it looks like all + + + align:start position:0% +that to an observer it looks like all +completely different addresses and if + + align:start position:0% +completely different addresses and if + + + align:start position:0% +completely different addresses and if +someone hacks into the server and finds + + align:start position:0% +someone hacks into the server and finds + + + align:start position:0% +someone hacks into the server and finds +this P point and this our randomizer + + align:start position:0% +this P point and this our randomizer + + + align:start position:0% +this P point and this our randomizer +well that will allow them to link + + align:start position:0% +well that will allow them to link + + + align:start position:0% +well that will allow them to link +everything now they can see oh we can we + + align:start position:0% +everything now they can see oh we can we + + + align:start position:0% +everything now they can see oh we can we +can also generate all these addresses we + + align:start position:0% +can also generate all these addresses we + + + align:start position:0% +can also generate all these addresses we +can see that it's all the same person + + align:start position:0% +can see that it's all the same person + + + align:start position:0% +can see that it's all the same person +but that doesn't let them steal any of + + align:start position:0% +but that doesn't let them steal any of + + + align:start position:0% +but that doesn't let them steal any of +the funds so compromising the server + + align:start position:0% +the funds so compromising the server + + + align:start position:0% +the funds so compromising the server +with this well you lose the privacy but + + align:start position:0% +with this well you lose the privacy but + + + align:start position:0% +with this well you lose the privacy but +you don't lose your money so that's a + + align:start position:0% +you don't lose your money so that's a + + + align:start position:0% +you don't lose your money so that's a +pretty good trade-off ok other questions + + align:start position:0% +pretty good trade-off ok other questions + + + align:start position:0% +pretty good trade-off ok other questions +about cool so that's one of the features + + align:start position:0% +about cool so that's one of the features + + + align:start position:0% +about cool so that's one of the features +for like wallets got to do this ok so + + align:start position:0% +for like wallets got to do this ok so + + + align:start position:0% +for like wallets got to do this ok so +the basic procedure you're gonna request + + align:start position:0% +the basic procedure you're gonna request + + + align:start position:0% +the basic procedure you're gonna request +a payment and you're gonna say hey if + + align:start position:0% +a payment and you're gonna say hey if + + + align:start position:0% +a payment and you're gonna say hey if +you want this jacket send one coin to + + align:start position:0% +you want this jacket send one coin to + + + align:start position:0% +you want this jacket send one coin to +address f8f one to e and it's sort of + + align:start position:0% +address f8f one to e and it's sort of + + + align:start position:0% +address f8f one to e and it's sort of +important to note that Bitcoin doesn't + + align:start position:0% +important to note that Bitcoin doesn't + + + align:start position:0% +important to note that Bitcoin doesn't +solve the problem of people paying money + + align:start position:0% +solve the problem of people paying money + + + align:start position:0% +solve the problem of people paying money +and not getting what they paid for + + align:start position:0% +and not getting what they paid for + + + align:start position:0% +and not getting what they paid for +right that's out of the scope of this + + align:start position:0% +right that's out of the scope of this + + + align:start position:0% +right that's out of the scope of this +although there's a lot of people like + + align:start position:0% +although there's a lot of people like + + + align:start position:0% +although there's a lot of people like +you know it should but you know it + + align:start position:0% +you know it should but you know it + + + align:start position:0% +you know it should but you know it +doesn't do fraud protection it's like + + align:start position:0% +doesn't do fraud protection it's like + + + align:start position:0% +doesn't do fraud protection it's like +hey I gave you the coin you didn't give + + align:start position:0% +hey I gave you the coin you didn't give + + + align:start position:0% +hey I gave you the coin you didn't give +me the jacket + + align:start position:0% +me the jacket + + + align:start position:0% +me the jacket +well Bitcoin worked fine Bitcoin made + + align:start position:0% +well Bitcoin worked fine Bitcoin made + + + align:start position:0% +well Bitcoin worked fine Bitcoin made +the coin move that's that's bitcoins job + + align:start position:0% +the coin move that's that's bitcoins job + + + align:start position:0% +the coin move that's that's bitcoins job +the fact that FedEx never delivered your + + align:start position:0% +the fact that FedEx never delivered your + + + align:start position:0% +the fact that FedEx never delivered your +jacket well that's sort of FedEx or the + + align:start position:0% +jacket well that's sort of FedEx or the + + + align:start position:0% +jacket well that's sort of FedEx or the +retailer or all sorts of things like + + align:start position:0% +retailer or all sorts of things like + + + align:start position:0% +retailer or all sorts of things like +that so that's you know I don't want to + + align:start position:0% +that so that's you know I don't want to + + + align:start position:0% +that so that's you know I don't want to +say it's not a problem it certainly is + + align:start position:0% +say it's not a problem it certainly is + + + align:start position:0% +say it's not a problem it certainly is +but it is sort of seen as out of scope + + align:start position:0% +but it is sort of seen as out of scope + + + align:start position:0% +but it is sort of seen as out of scope +it's like you know this is a money + + align:start position:0% +it's like you know this is a money + + + align:start position:0% +it's like you know this is a money +system is his money the dollar you know + + align:start position:0% +system is his money the dollar you know + + + align:start position:0% +system is his money the dollar you know +your dollar bills don't insure + + align:start position:0% +your dollar bills don't insure + + + align:start position:0% +your dollar bills don't insure +that you're getting what you paid for + + align:start position:0% +that you're getting what you paid for + + + align:start position:0% +that you're getting what you paid for +that said there's all sorts of things + + align:start position:0% +that said there's all sorts of things + + + align:start position:0% +that said there's all sorts of things +that do this kind of thing and do try to + + align:start position:0% +that do this kind of thing and do try to + + + align:start position:0% +that do this kind of thing and do try to +ensure delivery versus payment atomic + + align:start position:0% +ensure delivery versus payment atomic + + + align:start position:0% +ensure delivery versus payment atomic +sauce HDL sees that we'll talk about + + align:start position:0% +sauce HDL sees that we'll talk about + + + align:start position:0% +sauce HDL sees that we'll talk about +later zero knowledge can improve like + + align:start position:0% +later zero knowledge can improve like + + + align:start position:0% +later zero knowledge can improve like +all these different things do sort of + + align:start position:0% +all these different things do sort of + + + align:start position:0% +all these different things do sort of +work on top of Bitcoin to try to help + + align:start position:0% +work on top of Bitcoin to try to help + + + align:start position:0% +work on top of Bitcoin to try to help +these kinds of things in practice though + + align:start position:0% +these kinds of things in practice though + + + align:start position:0% +these kinds of things in practice though +if you're actually buying like a + + align:start position:0% +if you're actually buying like a + + + align:start position:0% +if you're actually buying like a +physical jacket that someone's going to + + align:start position:0% +physical jacket that someone's going to + + + align:start position:0% +physical jacket that someone's going to +deliver to you there's not really a good + + align:start position:0% +deliver to you there's not really a good + + + align:start position:0% +deliver to you there's not really a good +cryptographic proof of jacket delivery + + align:start position:0% +cryptographic proof of jacket delivery + + + align:start position:0% +cryptographic proof of jacket delivery +so it's some reputation is involved + + align:start position:0% +so it's some reputation is involved + + + align:start position:0% +so it's some reputation is involved +right then from the merchants + + align:start position:0% +right then from the merchants + + + align:start position:0% +right then from the merchants +perspective so I sell jackets I want to + + align:start position:0% +perspective so I sell jackets I want to + + + align:start position:0% +perspective so I sell jackets I want to +know if someone paid me right I have + + align:start position:0% +know if someone paid me right I have + + + align:start position:0% +know if someone paid me right I have +something on the website put in your + + align:start position:0% +something on the website put in your + + + align:start position:0% +something on the website put in your +address ok now pay this address so you + + align:start position:0% +address ok now pay this address so you + + + align:start position:0% +address ok now pay this address so you +add all your pub key hashes to a big + + align:start position:0% +add all your pub key hashes to a big + + + align:start position:0% +add all your pub key hashes to a big +list in your software you say ok here's + + align:start position:0% +list in your software you say ok here's + + + align:start position:0% +list in your software you say ok here's +all the addresses I've created they're + + align:start position:0% +all the addresses I've created they're + + + align:start position:0% +all the addresses I've created they're +all you know these 20-byte pub key + + align:start position:0% +all you know these 20-byte pub key + + + align:start position:0% +all you know these 20-byte pub key +hashes I put them in a map or some kind + + align:start position:0% +hashes I put them in a map or some kind + + + align:start position:0% +hashes I put them in a map or some kind +of array or some database whatever and + + align:start position:0% +of array or some database whatever and + + + align:start position:0% +of array or some database whatever and +then from then on every transaction I + + align:start position:0% +then from then on every transaction I + + + align:start position:0% +then from then on every transaction I +see on the network I also look at the + + align:start position:0% +see on the network I also look at the + + + align:start position:0% +see on the network I also look at the +output scripts so before when I was + + align:start position:0% +output scripts so before when I was + + + align:start position:0% +output scripts so before when I was +verifying the blockchain I actually + + align:start position:0% +verifying the blockchain I actually + + + align:start position:0% +verifying the blockchain I actually +never had to look at the output scripts + + align:start position:0% +never had to look at the output scripts + + + align:start position:0% +never had to look at the output scripts +until they got spent right so when I was + + align:start position:0% +until they got spent right so when I was + + + align:start position:0% +until they got spent right so when I was +downloading transactions I would look at + + align:start position:0% +downloading transactions I would look at + + + align:start position:0% +downloading transactions I would look at +their signatures and look at old you + + align:start position:0% +their signatures and look at old you + + + align:start position:0% +their signatures and look at old you +know the old UT exo's in the UT Exocet + + align:start position:0% +know the old UT exo's in the UT Exocet + + + align:start position:0% +know the old UT exo's in the UT Exocet +and match him up and verify but where + + align:start position:0% +and match him up and verify but where + + + align:start position:0% +and match him up and verify but where +the money got sent in these new + + align:start position:0% +the money got sent in these new + + + align:start position:0% +the money got sent in these new +transactions I didn't really care right + + align:start position:0% +transactions I didn't really care right + + + align:start position:0% +transactions I didn't really care right +it could have been sending it to zero it + + align:start position:0% +it could have been sending it to zero it + + + align:start position:0% +it could have been sending it to zero it +could have been sending it to some weird + + align:start position:0% +could have been sending it to some weird + + + align:start position:0% +could have been sending it to some weird +address that probably was wrong I there + + align:start position:0% +address that probably was wrong I there + + + align:start position:0% +address that probably was wrong I there +was no there and I believe to this day + + align:start position:0% +was no there and I believe to this day + + + align:start position:0% +was no there and I believe to this day +there's still no output validation that + + align:start position:0% +there's still no output validation that + + + align:start position:0% +there's still no output validation that +happens in Bitcoin as a consensus rule + + align:start position:0% +happens in Bitcoin as a consensus rule + + + align:start position:0% +happens in Bitcoin as a consensus rule +because it's not important right where + + align:start position:0% +because it's not important right where + + + align:start position:0% +because it's not important right where +are you sending the money well wherever + + align:start position:0% +are you sending the money well wherever + + + align:start position:0% +are you sending the money well wherever +you want and are you able to spend it + + align:start position:0% +you want and are you able to spend it + + + align:start position:0% +you want and are you able to spend it +we'll deal with that later right if you + + align:start position:0% +we'll deal with that later right if you + + + align:start position:0% +we'll deal with that later right if you +want to destroy your money fine I'm not + + align:start position:0% +want to destroy your money fine I'm not + + + align:start position:0% +want to destroy your money fine I'm not +gonna look at the output there's no + + align:start position:0% +gonna look at the output there's no + + + align:start position:0% +gonna look at the output there's no +invalid output right there can be an + + align:start position:0% +invalid output right there can be an + + + align:start position:0% +invalid output right there can be an +invalid input which there can be an + + align:start position:0% +invalid input which there can be an + + + align:start position:0% +invalid input which there can be an +output which you can never actually use + + align:start position:0% +output which you can never actually use + + + align:start position:0% +output which you can never actually use +but you're free to send to it so that's + + align:start position:0% +but you're free to send to it so that's + + + align:start position:0% +but you're free to send to it so that's +sort of one of the you know rules in + + align:start position:0% +sort of one of the you know rules in + + + align:start position:0% +sort of one of the you know rules in +Bitcoin however in this new in you know + + align:start position:0% +Bitcoin however in this new in you know + + + align:start position:0% +Bitcoin however in this new in you know +when we're actually looking at our own + + align:start position:0% +when we're actually looking at our own + + + align:start position:0% +when we're actually looking at our own +money + + align:start position:0% +money + + + align:start position:0% +money +the wallet we do look at the output + + align:start position:0% +the wallet we do look at the output + + + align:start position:0% +the wallet we do look at the output +scripts mainly to say hey is this ours + + align:start position:0% +scripts mainly to say hey is this ours + + + align:start position:0% +scripts mainly to say hey is this ours +are we getting paid with this + + align:start position:0% +are we getting paid with this + + + align:start position:0% +are we getting paid with this +transaction so you look at every output + + align:start position:0% +transaction so you look at every output + + + align:start position:0% +transaction so you look at every output +script and if you see one that matches + + align:start position:0% +script and if you see one that matches + + + align:start position:0% +script and if you see one that matches +hey we got paid right so you see a + + align:start position:0% +hey we got paid right so you see a + + + align:start position:0% +hey we got paid right so you see a +transaction one of the outputs hey look + + align:start position:0% +transaction one of the outputs hey look + + + align:start position:0% +transaction one of the outputs hey look +that 20 bytes that's that's me cool + + align:start position:0% +that 20 bytes that's that's me cool + + + align:start position:0% +that 20 bytes that's that's me cool +that's one of the addresses that I have + + align:start position:0% +that's one of the addresses that I have + + + align:start position:0% +that's one of the addresses that I have +let me keep track of this this is now + + align:start position:0% +let me keep track of this this is now + + + align:start position:0% +let me keep track of this this is now +money that's in my wallet um so you keep + + align:start position:0% +money that's in my wallet um so you keep + + + align:start position:0% +money that's in my wallet um so you keep +track of the received payments you save + + align:start position:0% +track of the received payments you save + + + align:start position:0% +track of the received payments you save +them to disk in a similar way to your + + align:start position:0% +them to disk in a similar way to your + + + align:start position:0% +them to disk in a similar way to your +addresses you use some kind of database + + align:start position:0% +addresses you use some kind of database + + + align:start position:0% +addresses you use some kind of database +or map or something something efficient + + align:start position:0% +or map or something something efficient + + + align:start position:0% +or map or something something efficient +and then you don't need to save too much + + align:start position:0% +and then you don't need to save too much + + + align:start position:0% +and then you don't need to save too much +information right you need to save the + + align:start position:0% +information right you need to save the + + + align:start position:0% +information right you need to save the +out point right the TX ID of the + + align:start position:0% +out point right the TX ID of the + + + align:start position:0% +out point right the TX ID of the +transaction the index you probably want + + align:start position:0% +transaction the index you probably want + + + align:start position:0% +transaction the index you probably want +to save how much you're my own and which + + align:start position:0% +to save how much you're my own and which + + + align:start position:0% +to save how much you're my own and which +key it was so the actual 20 byte pub key + + align:start position:0% +key it was so the actual 20 byte pub key + + + align:start position:0% +key it was so the actual 20 byte pub key +hash you could look through all your + + align:start position:0% +hash you could look through all your + + + align:start position:0% +hash you could look through all your +keys but it might be nice oh that's my + + align:start position:0% +keys but it might be nice oh that's my + + + align:start position:0% +keys but it might be nice oh that's my +17th key that I've saved in my database + + align:start position:0% +17th key that I've saved in my database + + + align:start position:0% +17th key that I've saved in my database +or something you may also want to save + + align:start position:0% +or something you may also want to save + + + align:start position:0% +or something you may also want to save +the height information when it got + + align:start position:0% +the height information when it got + + + align:start position:0% +the height information when it got +confirmed so we're not gonna talk too + + align:start position:0% +confirmed so we're not gonna talk too + + + align:start position:0% +confirmed so we're not gonna talk too +much about unconfirmed versus confirmed + + align:start position:0% +much about unconfirmed versus confirmed + + + align:start position:0% +much about unconfirmed versus confirmed +today but this can be an issue if you + + align:start position:0% +today but this can be an issue if you + + + align:start position:0% +today but this can be an issue if you +see a transaction on the network that's + + align:start position:0% +see a transaction on the network that's + + + align:start position:0% +see a transaction on the network that's +not yet in a block and it pays you okay + + align:start position:0% +not yet in a block and it pays you okay + + + align:start position:0% +not yet in a block and it pays you okay +I got money but it's not confirmed yet + + align:start position:0% +I got money but it's not confirmed yet + + + align:start position:0% +I got money but it's not confirmed yet +so have I really gotten money I am able + + align:start position:0% +so have I really gotten money I am able + + + align:start position:0% +so have I really gotten money I am able +to use that output to spend somewhere + + align:start position:0% +to use that output to spend somewhere + + + align:start position:0% +to use that output to spend somewhere +else but now I've got to sort of chained + + align:start position:0% +else but now I've got to sort of chained + + + align:start position:0% +else but now I've got to sort of chained +transactions neither of which is + + align:start position:0% +transactions neither of which is + + + align:start position:0% +transactions neither of which is +confirmed and now the second one can + + align:start position:0% +confirmed and now the second one can + + + align:start position:0% +confirmed and now the second one can +only be confirmed if the first one is so + + align:start position:0% +only be confirmed if the first one is so + + + align:start position:0% +only be confirmed if the first one is so +that can get ugly kind of quick for + + align:start position:0% +that can get ugly kind of quick for + + + align:start position:0% +that can get ugly kind of quick for +simplicity sake let's just say that you + + align:start position:0% +simplicity sake let's just say that you + + + align:start position:0% +simplicity sake let's just say that you +wait until it's in a block before your + + align:start position:0% +wait until it's in a block before your + + + align:start position:0% +wait until it's in a block before your +wallet recognizes it most wallets do not + + align:start position:0% +wallet recognizes it most wallets do not + + + align:start position:0% +wallet recognizes it most wallets do not +do that but most ones maybe should there + + align:start position:0% +do that but most ones maybe should there + + + align:start position:0% +do that but most ones maybe should there +can be a lot of weird attacks where you + + align:start position:0% +can be a lot of weird attacks where you + + + align:start position:0% +can be a lot of weird attacks where you +say like oh I got money and then since + + align:start position:0% +say like oh I got money and then since + + + align:start position:0% +say like oh I got money and then since +it never really was confirmed at all + + align:start position:0% +it never really was confirmed at all + + + align:start position:0% +it never really was confirmed at all +it's pretty easy for someone to double + + align:start position:0% +it's pretty easy for someone to double + + + align:start position:0% +it's pretty easy for someone to double +spent right the whole point of the + + align:start position:0% +spent right the whole point of the + + + align:start position:0% +spent right the whole point of the +Bitcoin system was you can't double + + align:start position:0% +Bitcoin system was you can't double + + + align:start position:0% +Bitcoin system was you can't double +spend because it's got all this proof of + + align:start position:0% +spend because it's got all this proof of + + + align:start position:0% +spend because it's got all this proof of +work on top of it it's in a block but if + + align:start position:0% +work on top of it it's in a block but if + + + align:start position:0% +work on top of it it's in a block but if +we show in the UI hey you got a payment + + align:start position:0% +we show in the UI hey you got a payment + + + align:start position:0% +we show in the UI hey you got a payment +that has not yet become you know gone + + align:start position:0% +that has not yet become you know gone + + + align:start position:0% +that has not yet become you know gone +into a block well there's no assurance + + align:start position:0% +into a block well there's no assurance + + + align:start position:0% +into a block well there's no assurance +that it won't be double spent yet + + align:start position:0% +that it won't be double spent yet + + + align:start position:0% +that it won't be double spent yet +because it's not in the blockchain + + align:start position:0% +because it's not in the blockchain + + + align:start position:0% +because it's not in the blockchain +but most wallets will show that and + + align:start position:0% +but most wallets will show that and + + + align:start position:0% +but most wallets will show that and +usually they'll make it in like red or + + align:start position:0% +usually they'll make it in like red or + + + align:start position:0% +usually they'll make it in like red or +put a little exclamation point or + + align:start position:0% +put a little exclamation point or + + + align:start position:0% +put a little exclamation point or +something to try to indicate like hey + + align:start position:0% +something to try to indicate like hey + + + align:start position:0% +something to try to indicate like hey +this is unconfirmed but that doesn't + + align:start position:0% +this is unconfirmed but that doesn't + + + align:start position:0% +this is unconfirmed but that doesn't +always get across to people so maybe + + align:start position:0% +always get across to people so maybe + + + align:start position:0% +always get across to people so maybe +safer to just not show it at all until + + align:start position:0% +safer to just not show it at all until + + + align:start position:0% +safer to just not show it at all until +it's in a block okay so yeah you you + + align:start position:0% +it's in a block okay so yeah you you + + + align:start position:0% +it's in a block okay so yeah you you +sort of amass all these UT exos right + + align:start position:0% +sort of amass all these UT exos right + + + align:start position:0% +sort of amass all these UT exos right +you're running you're you're running + + align:start position:0% +you're running you're you're running + + + align:start position:0% +you're running you're you're running +your node you've got all these addresses + + align:start position:0% +your node you've got all these addresses + + + align:start position:0% +your node you've got all these addresses +you've given out to people and then + + align:start position:0% +you've given out to people and then + + + align:start position:0% +you've given out to people and then +every transaction that comes in you look + + align:start position:0% +every transaction that comes in you look + + + align:start position:0% +every transaction that comes in you look +hey do any of these pay me and sometimes + + align:start position:0% +hey do any of these pay me and sometimes + + + align:start position:0% +hey do any of these pay me and sometimes +you'll find one that does which is great + + align:start position:0% +you'll find one that does which is great + + + align:start position:0% +you'll find one that does which is great +and then you save that to your disk and + + align:start position:0% +and then you save that to your disk and + + + align:start position:0% +and then you save that to your disk and +great now next I want to spend them okay + + align:start position:0% +great now next I want to spend them okay + + + align:start position:0% +great now next I want to spend them okay +any any questions about the sort of + + align:start position:0% +any any questions about the sort of + + + align:start position:0% +any any questions about the sort of +getting money procedure yes the height + + align:start position:0% +getting money procedure yes the height + + + align:start position:0% +getting money procedure yes the height +is what block its in so like height zero + + align:start position:0% +is what block its in so like height zero + + + align:start position:0% +is what block its in so like height zero +is the first block you know zeros block + + align:start position:0% +is the first block you know zeros block + + + align:start position:0% +is the first block you know zeros block +and we're now at height five hundred + + align:start position:0% +and we're now at height five hundred + + + align:start position:0% +and we're now at height five hundred +thousand yeah usually in diagrams who + + align:start position:0% +thousand yeah usually in diagrams who + + + align:start position:0% +thousand yeah usually in diagrams who +goes this way but I guess it could go up + + align:start position:0% +goes this way but I guess it could go up + + + align:start position:0% +goes this way but I guess it could go up +and numbers I don't know yeah so next + + align:start position:0% +and numbers I don't know yeah so next + + + align:start position:0% +and numbers I don't know yeah so next +you need to spend them the spending is + + align:start position:0% +you need to spend them the spending is + + + align:start position:0% +you need to spend them the spending is +makes sense right it's not too crazy + + align:start position:0% +makes sense right it's not too crazy + + + align:start position:0% +makes sense right it's not too crazy +let's say you want to send six coins to + + align:start position:0% +let's say you want to send six coins to + + + align:start position:0% +let's say you want to send six coins to +someone so what you do is you look + + align:start position:0% +someone so what you do is you look + + + align:start position:0% +someone so what you do is you look +through your set of UT X OS that are + + align:start position:0% +through your set of UT X OS that are + + + align:start position:0% +through your set of UT X OS that are +your UT X OS and you try to find thumb + + align:start position:0% +your UT X OS and you try to find thumb + + + align:start position:0% +your UT X OS and you try to find thumb +such that the total you know the total + + align:start position:0% +such that the total you know the total + + + align:start position:0% +such that the total you know the total +number of coins is over six and then you + + align:start position:0% +number of coins is over six and then you + + + align:start position:0% +number of coins is over six and then you +use them as inputs and then you add your + + align:start position:0% +use them as inputs and then you add your + + + align:start position:0% +use them as inputs and then you add your +outputs so for example I've got two UT x + + align:start position:0% +outputs so for example I've got two UT x + + + align:start position:0% +outputs so for example I've got two UT x +those these are you know much more + + align:start position:0% +those these are you know much more + + + align:start position:0% +those these are you know much more +numbers but this one has five coins in + + align:start position:0% +numbers but this one has five coins in + + + align:start position:0% +numbers but this one has five coins in +it and this one has three coins so I + + align:start position:0% +it and this one has three coins so I + + + align:start position:0% +it and this one has three coins so I +received at two different times once I + + align:start position:0% +received at two different times once I + + + align:start position:0% +received at two different times once I +got five coins for a fancy jacket once I + + align:start position:0% +got five coins for a fancy jacket once I + + + align:start position:0% +got five coins for a fancy jacket once I +got three coins for a less fancy jacket + + align:start position:0% +got three coins for a less fancy jacket + + + align:start position:0% +got three coins for a less fancy jacket +and now I want to buy something and I + + align:start position:0% +and now I want to buy something and I + + + align:start position:0% +and now I want to buy something and I +want to send it to Bob and I want to + + align:start position:0% +want to send it to Bob and I want to + + + align:start position:0% +want to send it to Bob and I want to +send six coins well I've got eight coins + + align:start position:0% +send six coins well I've got eight coins + + + align:start position:0% +send six coins well I've got eight coins +and my inputs so I'll send them said + + align:start position:0% +and my inputs so I'll send them said + + + align:start position:0% +and my inputs so I'll send them said +coin six coins there's two coins left + + align:start position:0% +coin six coins there's two coins left + + + align:start position:0% +coin six coins there's two coins left +over if I don't have this it just goes + + align:start position:0% +over if I don't have this it just goes + + + align:start position:0% +over if I don't have this it just goes +to the miners so I create my a new + + align:start position:0% +to the miners so I create my a new + + + align:start position:0% +to the miners so I create my a new +output which is my change output and + + align:start position:0% +output which is my change output and + + + align:start position:0% +output which is my change output and +then I send the remainder two coins here + + align:start position:0% +then I send the remainder two coins here + + + align:start position:0% +then I send the remainder two coins here +now if it's actually these round nice + + align:start position:0% +now if it's actually these round nice + + + align:start position:0% +now if it's actually these round nice +round numbers the fee would be zero and + + align:start position:0% +round numbers the fee would be zero and + + + align:start position:0% +round numbers the fee would be zero and +it would probably not get confirmed on + + align:start position:0% +it would probably not get confirmed on + + + align:start position:0% +it would probably not get confirmed on +the Bitcoin network you do have to have + + align:start position:0% +the Bitcoin network you do have to have + + + align:start position:0% +the Bitcoin network you do have to have +a small fee right now + + align:start position:0% +a small fee right now + + + align:start position:0% +a small fee right now +it's really small though it's like a + + align:start position:0% +it's really small though it's like a + + + align:start position:0% +it's really small though it's like a +couple cents now it was pretty high a + + align:start position:0% +couple cents now it was pretty high a + + + align:start position:0% +couple cents now it was pretty high a +few months ago but with this this will + + align:start position:0% +few months ago but with this this will + + + align:start position:0% +few months ago but with this this will +work this is the basic idea so you look + + align:start position:0% +work this is the basic idea so you look + + + align:start position:0% +work this is the basic idea so you look +through your UT exo's find some okay + + align:start position:0% +through your UT exo's find some okay + + + align:start position:0% +through your UT exo's find some okay +output 6 output to something then you + + align:start position:0% +output 6 output to something then you + + + align:start position:0% +output 6 output to something then you +know once you've built this sign it all + + align:start position:0% +know once you've built this sign it all + + + align:start position:0% +know once you've built this sign it all +broadcast in the network make sense yep + + align:start position:0% + + + + align:start position:0% + +yep yep + + align:start position:0% +yep yep + + + align:start position:0% +yep yep +you make generally what you'll do is + + align:start position:0% +you make generally what you'll do is + + + align:start position:0% +you make generally what you'll do is +you'll make a new private key calculate + + align:start position:0% +you'll make a new private key calculate + + + align:start position:0% +you'll make a new private key calculate +the public key hash it make this address + + align:start position:0% +the public key hash it make this address + + + align:start position:0% +the public key hash it make this address +and then add it in here all + + align:start position:0% +and then add it in here all + + + align:start position:0% +and then add it in here all +automatically you can and some software + + align:start position:0% +automatically you can and some software + + + align:start position:0% +automatically you can and some software +does just only use one key in one + + align:start position:0% +does just only use one key in one + + + align:start position:0% +does just only use one key in one +address and so it'll be pretty clear + + align:start position:0% +address and so it'll be pretty clear + + + align:start position:0% +address and so it'll be pretty clear +because like the keys for this signature + + align:start position:0% +because like the keys for this signature + + + align:start position:0% +because like the keys for this signature +will be the same as this key that it's + + align:start position:0% +will be the same as this key that it's + + + align:start position:0% +will be the same as this key that it's +sending to and so then it's really clear + + align:start position:0% +sending to and so then it's really clear + + + align:start position:0% +sending to and so then it's really clear +even without doing that it's usually + + align:start position:0% +even without doing that it's usually + + + align:start position:0% +even without doing that it's usually +pretty clear and people can sort of + + align:start position:0% +pretty clear and people can sort of + + + align:start position:0% +pretty clear and people can sort of +guess like well either she you know + + align:start position:0% +guess like well either she you know + + + align:start position:0% +guess like well either she you know +either alice is sending six coins back + + align:start position:0% +either alice is sending six coins back + + + align:start position:0% +either alice is sending six coins back +to herself and two coins to Bob or she's + + align:start position:0% +to herself and two coins to Bob or she's + + + align:start position:0% +to herself and two coins to Bob or she's +sending six guns to Bob and two back to + + align:start position:0% +sending six guns to Bob and two back to + + + align:start position:0% +sending six guns to Bob and two back to +herself right or maybe six coins to one + + align:start position:0% +herself right or maybe six coins to one + + + align:start position:0% +herself right or maybe six coins to one +person two coins to someone else + + align:start position:0% +person two coins to someone else + + + align:start position:0% +person two coins to someone else +entirely that's pretty unlikely usually + + align:start position:0% +entirely that's pretty unlikely usually + + + align:start position:0% +entirely that's pretty unlikely usually +metrics will try to like analyze the + + align:start position:0% +metrics will try to like analyze the + + + align:start position:0% +metrics will try to like analyze the +transaction graph and say like oh the + + align:start position:0% +transaction graph and say like oh the + + + align:start position:0% +transaction graph and say like oh the +smaller outputs are usually the payments + + align:start position:0% +smaller outputs are usually the payments + + + align:start position:0% +smaller outputs are usually the payments +and the larger ones are the change but + + align:start position:0% +and the larger ones are the change but + + + align:start position:0% +and the larger ones are the change but +but you don't know so if the if the + + align:start position:0% +but you don't know so if the if the + + + align:start position:0% +but you don't know so if the if the +addresses are all different yes + + align:start position:0% + + + + align:start position:0% + +the fee is the difference between the + + align:start position:0% +the fee is the difference between the + + + align:start position:0% +the fee is the difference between the +inputs amounts and the output amounts so + + align:start position:0% +inputs amounts and the output amounts so + + + align:start position:0% +inputs amounts and the output amounts so +in this case the fee is zero because I + + align:start position:0% +in this case the fee is zero because I + + + align:start position:0% +in this case the fee is zero because I +got five three you know eight and then + + align:start position:0% +got five three you know eight and then + + + align:start position:0% +got five three you know eight and then +eight here so really what you do in real + + align:start position:0% +eight here so really what you do in real + + + align:start position:0% +eight here so really what you do in real +life is you'd make this like one point + + align:start position:0% +life is you'd make this like one point + + + align:start position:0% +life is you'd make this like one point +nine nine nine and then the fee would be + + align:start position:0% +nine nine nine and then the fee would be + + + align:start position:0% +nine nine nine and then the fee would be +that point all one or whatever that the + + align:start position:0% +that point all one or whatever that the + + + align:start position:0% +that point all one or whatever that the +miner gets in the coin based transaction + + align:start position:0% +miner gets in the coin based transaction + + + align:start position:0% +miner gets in the coin based transaction +that's another way to try to identify + + align:start position:0% +that's another way to try to identify + + + align:start position:0% +that's another way to try to identify +change outputs if you actually had five + + align:start position:0% +change outputs if you actually had five + + + align:start position:0% +change outputs if you actually had five +three six and one point nine nine nine + + align:start position:0% +three six and one point nine nine nine + + + align:start position:0% +three six and one point nine nine nine +I bet the one point nine nine nine is + + align:start position:0% +I bet the one point nine nine nine is + + + align:start position:0% +I bet the one point nine nine nine is +going back to yourself right nice even + + align:start position:0% +going back to yourself right nice even + + + align:start position:0% +going back to yourself right nice even +round numbers are seem like real + + align:start position:0% +round numbers are seem like real + + + align:start position:0% +round numbers are seem like real +payments and then these and if you've + + align:start position:0% +payments and then these and if you've + + + align:start position:0% +payments and then these and if you've +got one sort of bunch of nines at the + + align:start position:0% +got one sort of bunch of nines at the + + + align:start position:0% +got one sort of bunch of nines at the +end all that was probably just reduced + + align:start position:0% +end all that was probably just reduced + + + align:start position:0% +end all that was probably just reduced +it a little to make this with the fee + + align:start position:0% +it a little to make this with the fee + + + align:start position:0% +it a little to make this with the fee +but these are all sort of guesses if + + align:start position:0% +but these are all sort of guesses if + + + align:start position:0% +but these are all sort of guesses if +you're if you're a third party observer + + align:start position:0% +you're if you're a third party observer + + + align:start position:0% +you're if you're a third party observer +looking at a transaction you don't know + + align:start position:0% +looking at a transaction you don't know + + + align:start position:0% +looking at a transaction you don't know +this could be two different people or + + align:start position:0% +this could be two different people or + + + align:start position:0% +this could be two different people or +this could be an exchange and you know + + align:start position:0% +this could be an exchange and you know + + + align:start position:0% +this could be an exchange and you know +like it's hard to tell but you get some + + align:start position:0% +like it's hard to tell but you get some + + + align:start position:0% +like it's hard to tell but you get some +pretty good guesses there are multiple + + align:start position:0% +pretty good guesses there are multiple + + + align:start position:0% +pretty good guesses there are multiple +thresholds so there's the real a + + align:start position:0% +thresholds so there's the real a + + + align:start position:0% +thresholds so there's the real a +threshold which right now I believe in + + align:start position:0% +threshold which right now I believe in + + + align:start position:0% +threshold which right now I believe in +Bitcoin is one Satoshi per byte so I + + align:start position:0% +Bitcoin is one Satoshi per byte so I + + + align:start position:0% +Bitcoin is one Satoshi per byte so I +think we said Satoshi's are the smallest + + align:start position:0% +think we said Satoshi's are the smallest + + + align:start position:0% +think we said Satoshi's are the smallest +unit possible a Bitcoin so one coin is + + align:start position:0% +unit possible a Bitcoin so one coin is + + + align:start position:0% +unit possible a Bitcoin so one coin is +actually a hundred million Satoshi's and + + align:start position:0% +actually a hundred million Satoshi's and + + + align:start position:0% +actually a hundred million Satoshi's and +there's no decimal places so that's + + align:start position:0% +there's no decimal places so that's + + + align:start position:0% +there's no decimal places so that's +there's the you I think so right now the + + align:start position:0% +there's the you I think so right now the + + + align:start position:0% +there's the you I think so right now the +the minimum relay fee by default is one + + align:start position:0% +the minimum relay fee by default is one + + + align:start position:0% +the minimum relay fee by default is one +Satoshi per byte so for a 250 byte + + align:start position:0% +Satoshi per byte so for a 250 byte + + + align:start position:0% +Satoshi per byte so for a 250 byte +transaction you need 250 Satoshi's which + + align:start position:0% +transaction you need 250 Satoshi's which + + + align:start position:0% +transaction you need 250 Satoshi's which +is some fraction of a cent maybe more + + align:start position:0% +is some fraction of a cent maybe more + + + align:start position:0% +is some fraction of a cent maybe more +than a cent now I'm not sure and then + + align:start position:0% +than a cent now I'm not sure and then + + + align:start position:0% +than a cent now I'm not sure and then +the idea is if you see that a + + align:start position:0% +the idea is if you see that a + + + align:start position:0% +the idea is if you see that a +transaction below that you won't even + + align:start position:0% +transaction below that you won't even + + + align:start position:0% +transaction below that you won't even +relay it to anyone else you'll be like + + align:start position:0% +relay it to anyone else you'll be like + + + align:start position:0% +relay it to anyone else you'll be like +this is so cheap that I'm not gonna + + align:start position:0% +this is so cheap that I'm not gonna + + + align:start position:0% +this is so cheap that I'm not gonna +bother sending it to everyone else I'm + + align:start position:0% +bother sending it to everyone else I'm + + + align:start position:0% +bother sending it to everyone else I'm +just gonna ignore it but above that one + + align:start position:0% +just gonna ignore it but above that one + + + align:start position:0% +just gonna ignore it but above that one +Satoshi threshold you will you know + + align:start position:0% +Satoshi threshold you will you know + + + align:start position:0% +Satoshi threshold you will you know +accept it verify the signatures and then + + align:start position:0% +accept it verify the signatures and then + + + align:start position:0% +accept it verify the signatures and then +you know pass it on to everyone else + + align:start position:0% +you know pass it on to everyone else + + + align:start position:0% +you know pass it on to everyone else +you're connected to but that doesn't + + align:start position:0% +you're connected to but that doesn't + + + align:start position:0% +you're connected to but that doesn't +necessarily mean it will get into a + + align:start position:0% +necessarily mean it will get into a + + + align:start position:0% +necessarily mean it will get into a +block anytime soon + + align:start position:0% +block anytime soon + + + align:start position:0% +block anytime soon +it's actually been really interesting + + align:start position:0% +it's actually been really interesting + + + align:start position:0% +it's actually been really interesting +the last I'd say six months where the + + align:start position:0% +the last I'd say six months where the + + + align:start position:0% +the last I'd say six months where the +fees + + align:start position:0% +fees + + + align:start position:0% +fees +went up enormous ly and you see sort of + + align:start position:0% +went up enormous ly and you see sort of + + + align:start position:0% +went up enormous ly and you see sort of +this like you know really crazy price in + + align:start position:0% +this like you know really crazy price in + + + align:start position:0% +this like you know really crazy price in +elasticity where people who were paying + + align:start position:0% +elasticity where people who were paying + + + align:start position:0% +elasticity where people who were paying +one cent then started paying $0.10 $1 + + align:start position:0% +one cent then started paying $0.10 $1 + + + align:start position:0% +one cent then started paying $0.10 $1 +$10 $20 and like and like you I guess + + align:start position:0% +$10 $20 and like and like you I guess + + + align:start position:0% +$10 $20 and like and like you I guess +the in it what's also sort of optimist + + align:start position:0% +the in it what's also sort of optimist + + + align:start position:0% +the in it what's also sort of optimist +it made me feel good it's like well + + align:start position:0% +it made me feel good it's like well + + + align:start position:0% +it made me feel good it's like well +clearly there they were getting 20 bucks + + align:start position:0% +clearly there they were getting 20 bucks + + + align:start position:0% +clearly there they were getting 20 bucks +worth of utility out of this because + + align:start position:0% +worth of utility out of this because + + + align:start position:0% +worth of utility out of this because +they're now perfectly willing to pay 20 + + align:start position:0% +they're now perfectly willing to pay 20 + + + align:start position:0% +they're now perfectly willing to pay 20 +bucks and they were paying one cent a + + align:start position:0% +bucks and they were paying one cent a + + + align:start position:0% +bucks and they were paying one cent a +few weeks ago that's kind of weird and + + align:start position:0% +few weeks ago that's kind of weird and + + + align:start position:0% +few weeks ago that's kind of weird and +then it's now gone back down to like 1 + + align:start position:0% +then it's now gone back down to like 1 + + + align:start position:0% +then it's now gone back down to like 1 +cent but it's if there's it's very + + align:start position:0% +cent but it's if there's it's very + + + align:start position:0% +cent but it's if there's it's very +inelastic in that you know there's a + + align:start position:0% +inelastic in that you know there's a + + + align:start position:0% +inelastic in that you know there's a +fixed size for how many transactions you + + align:start position:0% +fixed size for how many transactions you + + + align:start position:0% +fixed size for how many transactions you +can have per minute or per hour and when + + align:start position:0% +can have per minute or per hour and when + + + align:start position:0% +can have per minute or per hour and when +people really want to get in there they + + align:start position:0% +people really want to get in there they + + + align:start position:0% +people really want to get in there they +have to just bid everyone else out so + + align:start position:0% +have to just bid everyone else out so + + + align:start position:0% +have to just bid everyone else out so +we'll talk about the fee mark it's in a + + align:start position:0% +we'll talk about the fee mark it's in a + + + align:start position:0% +we'll talk about the fee mark it's in a +few weeks and replace by fee and that's + + align:start position:0% +few weeks and replace by fee and that's + + + align:start position:0% +few weeks and replace by fee and that's +sort of a new evolving thing but it's + + align:start position:0% +sort of a new evolving thing but it's + + + align:start position:0% +sort of a new evolving thing but it's +been really interesting to see in the + + align:start position:0% +been really interesting to see in the + + + align:start position:0% +been really interesting to see in the +last few months how it's changed tenth + + align:start position:0% +last few months how it's changed tenth + + + align:start position:0% +last few months how it's changed tenth +of a cent a hundredth of a cent so ok so + + align:start position:0% +of a cent a hundredth of a cent so ok so + + + align:start position:0% +of a cent a hundredth of a cent so ok so +the minimum really thing would be more + + align:start position:0% +the minimum really thing would be more + + + align:start position:0% +the minimum really thing would be more +like two and a half cents so that's you + + align:start position:0% +like two and a half cents so that's you + + + align:start position:0% +like two and a half cents so that's you +know it's not zero that's still a fee + + align:start position:0% +know it's not zero that's still a fee + + + align:start position:0% +know it's not zero that's still a fee +right and you got enough of those and + + align:start position:0% +right and you got enough of those and + + + align:start position:0% +right and you got enough of those and +you start making money but it's also + + align:start position:0% +you start making money but it's also + + + align:start position:0% +you start making money but it's also +interesting recently it used to be that + + align:start position:0% +interesting recently it used to be that + + + align:start position:0% +interesting recently it used to be that +the the initial new coins coming up to + + align:start position:0% +the the initial new coins coming up to + + + align:start position:0% +the the initial new coins coming up to +miners was just overwhelmingly the + + align:start position:0% +miners was just overwhelmingly the + + + align:start position:0% +miners was just overwhelmingly the +majority of what they earned and people + + align:start position:0% +majority of what they earned and people + + + align:start position:0% +majority of what they earned and people +would sort of ignore fees as a miner but + + align:start position:0% +would sort of ignore fees as a miner but + + + align:start position:0% +would sort of ignore fees as a miner but +then in like December January I believe + + align:start position:0% +then in like December January I believe + + + align:start position:0% +then in like December January I believe +miners made more money in fees than in + + align:start position:0% +miners made more money in fees than in + + + align:start position:0% +miners made more money in fees than in +new coins being generated I'm not sure + + align:start position:0% +new coins being generated I'm not sure + + + align:start position:0% +new coins being generated I'm not sure +if that averages out like there were + + align:start position:0% +if that averages out like there were + + + align:start position:0% +if that averages out like there were +definitely weeks where that was the case + + align:start position:0% +definitely weeks where that was the case + + + align:start position:0% +definitely weeks where that was the case +or at least days I'm not sure if it's + + align:start position:0% +or at least days I'm not sure if it's + + + align:start position:0% +or at least days I'm not sure if it's +average of the whole month but but it if + + align:start position:0% +average of the whole month but but it if + + + align:start position:0% +average of the whole month but but it if +you total aside sorry but this guy site + + align:start position:0% +you total aside sorry but this guy site + + + align:start position:0% +you total aside sorry but this guy site +is like a cool way to look at the fees + + align:start position:0% +is like a cool way to look at the fees + + + align:start position:0% +is like a cool way to look at the fees +so you can see like here's he sort of + + align:start position:0% +so you can see like here's he sort of + + + align:start position:0% +so you can see like here's he sort of +organizes transactions by fee rate it's + + align:start position:0% +organizes transactions by fee rate it's + + + align:start position:0% +organizes transactions by fee rate it's +to low res to really get everything but + + align:start position:0% +to low res to really get everything but + + + align:start position:0% +to low res to really get everything but +it's if you just search for Joe ho Joh + + align:start position:0% +it's if you just search for Joe ho Joh + + + align:start position:0% +it's if you just search for Joe ho Joh +EEO he's he works on Bitcoin stuff and + + align:start position:0% +EEO he's he works on Bitcoin stuff and + + + align:start position:0% +EEO he's he works on Bitcoin stuff and +he made this cool site which is open + + align:start position:0% +he made this cool site which is open + + + align:start position:0% +he made this cool site which is open +and you could ream and run it on your + + align:start position:0% +and you could ream and run it on your + + + align:start position:0% +and you could ream and run it on your +own note if you wanted to and generate + + align:start position:0% +own note if you wanted to and generate + + + align:start position:0% +own note if you wanted to and generate +the same cool JavaScript color readings + + align:start position:0% +the same cool JavaScript color readings + + + align:start position:0% +the same cool JavaScript color readings +and you can see the the fee mark and + + align:start position:0% +and you can see the the fee mark and + + + align:start position:0% +and you can see the the fee mark and +they're like from an I'm not into I'm + + align:start position:0% +they're like from an I'm not into I'm + + + align:start position:0% +they're like from an I'm not into I'm +not like a economist but it is really + + align:start position:0% +not like a economist but it is really + + + align:start position:0% +not like a economist but it is really +interesting seeing like there's there's + + align:start position:0% +interesting seeing like there's there's + + + align:start position:0% +interesting seeing like there's there's +clearly market failures occurring here + + align:start position:0% +clearly market failures occurring here + + + align:start position:0% +clearly market failures occurring here +in that so you can pay so the green you + + align:start position:0% +in that so you can pay so the green you + + + align:start position:0% +in that so you can pay so the green you +can pay ten satoshis per bite and you'll + + align:start position:0% +can pay ten satoshis per bite and you'll + + + align:start position:0% +can pay ten satoshis per bite and you'll +get confirmed in ten minutes or you can + + align:start position:0% +get confirmed in ten minutes or you can + + + align:start position:0% +get confirmed in ten minutes or you can +pay a thousand Satoshi's per bite and + + align:start position:0% +pay a thousand Satoshi's per bite and + + + align:start position:0% +pay a thousand Satoshi's per bite and +you will also get confirmed in ten + + align:start position:0% +you will also get confirmed in ten + + + align:start position:0% +you will also get confirmed in ten +minutes + + align:start position:0% +minutes + + + align:start position:0% +minutes +and most people are paying ten someone's + + align:start position:0% +and most people are paying ten someone's + + + align:start position:0% +and most people are paying ten someone's +paying a thousand you know it's got the + + align:start position:0% +paying a thousand you know it's got the + + + align:start position:0% +paying a thousand you know it's got the +whole spectrum you've got multiple + + align:start position:0% +whole spectrum you've got multiple + + + align:start position:0% +whole spectrum you've got multiple +orders of magnitude of people paying for + + align:start position:0% +orders of magnitude of people paying for + + + align:start position:0% +orders of magnitude of people paying for +the exact same thing and they can all + + align:start position:0% +the exact same thing and they can all + + + align:start position:0% +the exact same thing and they can all +see that each other it's it's just a + + align:start position:0% +see that each other it's it's just a + + + align:start position:0% +see that each other it's it's just a +weird sort of seems broken and and part + + align:start position:0% +weird sort of seems broken and and part + + + align:start position:0% +weird sort of seems broken and and part +of it is just the costs to write the + + align:start position:0% +of it is just the costs to write the + + + align:start position:0% +of it is just the costs to write the +software if you're like you know an + + align:start position:0% +software if you're like you know an + + + align:start position:0% +software if you're like you know an +exchange and you're like everyone's + + align:start position:0% +exchange and you're like everyone's + + + align:start position:0% +exchange and you're like everyone's +sending you support requests and let's + + align:start position:0% +sending you support requests and let's + + + align:start position:0% +sending you support requests and let's +have it okay I don't know just just pay + + align:start position:0% +have it okay I don't know just just pay + + + align:start position:0% +have it okay I don't know just just pay +a 500-seat oshi per bite fee and then it + + align:start position:0% +a 500-seat oshi per bite fee and then it + + + align:start position:0% +a 500-seat oshi per bite fee and then it +seems to work and yeah we're losing a + + align:start position:0% +seems to work and yeah we're losing a + + + align:start position:0% +seems to work and yeah we're losing a +couple thousand bucks a day but let's + + align:start position:0% +couple thousand bucks a day but let's + + + align:start position:0% +couple thousand bucks a day but let's +just not deal with that and I think + + align:start position:0% +just not deal with that and I think + + + align:start position:0% +just not deal with that and I think +that's part of it is that you know + + align:start position:0% +that's part of it is that you know + + + align:start position:0% +that's part of it is that you know +there's a lot of software out there that + + align:start position:0% +there's a lot of software out there that + + + align:start position:0% +there's a lot of software out there that +just has a fixed fee rate or even a + + align:start position:0% +just has a fixed fee rate or even a + + + align:start position:0% +just has a fixed fee rate or even a +fixed fee regardless of how big the + + align:start position:0% +fixed fee regardless of how big the + + + align:start position:0% +fixed fee regardless of how big the +transaction is or you know it's there's + + align:start position:0% +transaction is or you know it's there's + + + align:start position:0% +transaction is or you know it's there's +a lot of software that years ago + + align:start position:0% +a lot of software that years ago + + + align:start position:0% +a lot of software that years ago +wouldn't have to deal with this issue + + align:start position:0% +wouldn't have to deal with this issue + + + align:start position:0% +wouldn't have to deal with this issue +because there wasn't really competition + + align:start position:0% +because there wasn't really competition + + + align:start position:0% +because there wasn't really competition +to get into a block and now they do so + + align:start position:0% +to get into a block and now they do so + + + align:start position:0% +to get into a block and now they do so +it's kind of cool what to look at and + + align:start position:0% +it's kind of cool what to look at and + + + align:start position:0% +it's kind of cool what to look at and +see the history of it but I'll get into + + align:start position:0% +see the history of it but I'll get into + + + align:start position:0% +see the history of it but I'll get into +like the into the depth of fees and + + align:start position:0% +like the into the depth of fees and + + + align:start position:0% +like the into the depth of fees and +stuff and I think two weeks or something + + align:start position:0% +stuff and I think two weeks or something + + + align:start position:0% +stuff and I think two weeks or something +okay any questions about last yeah yeah + + align:start position:0% + + + + align:start position:0% + +well it's in some Dutch or something + + align:start position:0% +well it's in some Dutch or something + + + align:start position:0% +well it's in some Dutch or something +just search jo-jo h OE jo ho + + align:start position:0% +just search jo-jo h OE jo ho + + + align:start position:0% +just search jo-jo h OE jo ho +he's the get like it's the first thing + + align:start position:0% +he's the get like it's the first thing + + + align:start position:0% +he's the get like it's the first thing +on google right yeah jo h OE is his like + + align:start position:0% +on google right yeah jo h OE is his like + + + align:start position:0% +on google right yeah jo h OE is his like +dutch nickname or something i don't he's + + align:start position:0% +dutch nickname or something i don't he's + + + align:start position:0% +dutch nickname or something i don't he's +a cool guy he actually um I think I + + align:start position:0% +a cool guy he actually um I think I + + + align:start position:0% +a cool guy he actually um I think I +talked did I talk there was some + + align:start position:0% +talked did I talk there was some + + + align:start position:0% +talked did I talk there was some +randomness problems at some sites + + align:start position:0% +randomness problems at some sites + + + align:start position:0% +randomness problems at some sites +he stole a bunch of bitcoins and gave + + align:start position:0% +he stole a bunch of bitcoins and gave + + + align:start position:0% +he stole a bunch of bitcoins and gave +them back to their owners like he found + + align:start position:0% +them back to their owners like he found + + + align:start position:0% +them back to their owners like he found +some there was like K reuse like none + + align:start position:0% +some there was like K reuse like none + + + align:start position:0% +some there was like K reuse like none +sory use vulnerability and some wallets + + align:start position:0% +sory use vulnerability and some wallets + + + align:start position:0% +sory use vulnerability and some wallets +and so he's like hey look there's like a + + align:start position:0% +and so he's like hey look there's like a + + + align:start position:0% +and so he's like hey look there's like a +hundred bitcoins that I can just take + + align:start position:0% +hundred bitcoins that I can just take + + + align:start position:0% +hundred bitcoins that I can just take +because I can calculate the private key + + align:start position:0% +because I can calculate the private key + + + align:start position:0% +because I can calculate the private key +and he took him and he was like I think + + align:start position:0% +and he took him and he was like I think + + + align:start position:0% +and he took him and he was like I think +I know who these are and like can you + + align:start position:0% +I know who these are and like can you + + + align:start position:0% +I know who these are and like can you +prove it and then I'll give him back you + + align:start position:0% +prove it and then I'll give him back you + + + align:start position:0% +prove it and then I'll give him back you +know so he sort of grabs you know + + align:start position:0% +know so he sort of grabs you know + + + align:start position:0% +know so he sort of grabs you know +finding a wallet with like thousands of + + align:start position:0% +finding a wallet with like thousands of + + + align:start position:0% +finding a wallet with like thousands of +dollars you know coming out of it on the + + align:start position:0% +dollars you know coming out of it on the + + + align:start position:0% +dollars you know coming out of it on the +street and he sort of grabbed them all + + align:start position:0% +street and he sort of grabbed them all + + + align:start position:0% +street and he sort of grabbed them all +and like tried to get him back to people + + align:start position:0% +and like tried to get him back to people + + + align:start position:0% +and like tried to get him back to people +so I don't know that I've never met him + + align:start position:0% +so I don't know that I've never met him + + + align:start position:0% +so I don't know that I've never met him +but seems like a nice guy anyway that's + + align:start position:0% +but seems like a nice guy anyway that's + + + align:start position:0% +but seems like a nice guy anyway that's +how Bitcoin works there's Lee you don't + + align:start position:0% +how Bitcoin works there's Lee you don't + + + align:start position:0% +how Bitcoin works there's Lee you don't +meet anyone but you see these people oh + + align:start position:0% +meet anyone but you see these people oh + + + align:start position:0% +meet anyone but you see these people oh +he's a nice guy he's a jerk so I'm sure + + align:start position:0% +he's a nice guy he's a jerk so I'm sure + + + align:start position:0% +he's a nice guy he's a jerk so I'm sure +if yeah I've the weekend was kind of + + align:start position:0% +if yeah I've the weekend was kind of + + + align:start position:0% +if yeah I've the weekend was kind of +interesting over Twitter but anyways + + align:start position:0% +interesting over Twitter but anyways + + + align:start position:0% +interesting over Twitter but anyways +yeah okay so you build these + + align:start position:0% +yeah okay so you build these + + + align:start position:0% +yeah okay so you build these +transactions there are issues here + + align:start position:0% +transactions there are issues here + + + align:start position:0% +transactions there are issues here +two inputs to outputs that's gonna be + + align:start position:0% +two inputs to outputs that's gonna be + + + align:start position:0% +two inputs to outputs that's gonna be +kind of big you're gonna have two + + align:start position:0% +kind of big you're gonna have two + + + align:start position:0% +kind of big you're gonna have two +different signatures it's gonna be a + + align:start position:0% +different signatures it's gonna be a + + + align:start position:0% +different signatures it's gonna be a +little bit higher fee what would work + + align:start position:0% +little bit higher fee what would work + + + align:start position:0% +little bit higher fee what would work +better than this it's kind of a silly + + align:start position:0% +better than this it's kind of a silly + + + align:start position:0% +better than this it's kind of a silly +question + + align:start position:0% +question + + + align:start position:0% +question +what would work better than having two + + align:start position:0% +what would work better than having two + + + align:start position:0% +what would work better than having two +inputs and two outputs to make this + + align:start position:0% +inputs and two outputs to make this + + + align:start position:0% +inputs and two outputs to make this +transaction to pay someone six coins + + align:start position:0% + + + + align:start position:0% + +sure yeah that's you could send so + + align:start position:0% +sure yeah that's you could send so + + + align:start position:0% +sure yeah that's you could send so +that's actually two slides from now the + + align:start position:0% +that's actually two slides from now the + + + align:start position:0% +that's actually two slides from now the +next slide was just well what if you had + + align:start position:0% +next slide was just well what if you had + + + align:start position:0% +next slide was just well what if you had +a UTX over that was acting exactly the + + align:start position:0% +a UTX over that was acting exactly the + + + align:start position:0% +a UTX over that was acting exactly the +right size then it's easy you just send + + align:start position:0% +right size then it's easy you just send + + + align:start position:0% +right size then it's easy you just send +them the six clips if you have the exact + + align:start position:0% +them the six clips if you have the exact + + + align:start position:0% +them the six clips if you have the exact +right size you TXO and your wallet great + + align:start position:0% +right size you TXO and your wallet great + + + align:start position:0% +right size you TXO and your wallet great +you just send it over it's it's like if + + align:start position:0% +you just send it over it's it's like if + + + align:start position:0% +you just send it over it's it's like if +you go to a shop and they're like okay + + align:start position:0% +you go to a shop and they're like okay + + + align:start position:0% +you go to a shop and they're like okay +that's ten dollars for lunch you're like + + align:start position:0% +that's ten dollars for lunch you're like + + + align:start position:0% +that's ten dollars for lunch you're like +great I have a ten dollar bill here it + + align:start position:0% +great I have a ten dollar bill here it + + + align:start position:0% +great I have a ten dollar bill here it +is we don't to deal with like pennies + + align:start position:0% +is we don't to deal with like pennies + + + align:start position:0% +is we don't to deal with like pennies +and quarters and stuff it's annoying so + + align:start position:0% +and quarters and stuff it's annoying so + + + align:start position:0% +and quarters and stuff it's annoying so +sometimes this happens it's great + + align:start position:0% +sometimes this happens it's great + + + align:start position:0% +sometimes this happens it's great +generally well right generally you will + + align:start position:0% +generally well right generally you will + + + align:start position:0% +generally well right generally you will +have change in multiple inputs and + + align:start position:0% +have change in multiple inputs and + + + align:start position:0% +have change in multiple inputs and +outputs and it's kind of annoying so + + align:start position:0% +outputs and it's kind of annoying so + + + align:start position:0% +outputs and it's kind of annoying so +coin selection is a tricky problem for + + align:start position:0% +coin selection is a tricky problem for + + + align:start position:0% +coin selection is a tricky problem for +CSE you know terms it's np-hard actually + + align:start position:0% +CSE you know terms it's np-hard actually + + + align:start position:0% +CSE you know terms it's np-hard actually +but there's heuristics that work okay if + + align:start position:0% +but there's heuristics that work okay if + + + align:start position:0% +but there's heuristics that work okay if +you have a ton of you TX OS and you have + + align:start position:0% +you have a ton of you TX OS and you have + + + align:start position:0% +you have a ton of you TX OS and you have +to send these payments you can't + + align:start position:0% +to send these payments you can't + + + align:start position:0% +to send these payments you can't +actually in reasonable amount of time + + align:start position:0% +actually in reasonable amount of time + + + align:start position:0% +actually in reasonable amount of time +calculate the optimal way to do it but + + align:start position:0% +calculate the optimal way to do it but + + + align:start position:0% +calculate the optimal way to do it but +you know there's some there's some + + align:start position:0% +you know there's some there's some + + + align:start position:0% +you know there's some there's some +heuristics that work okay and the + + align:start position:0% +heuristics that work okay and the + + + align:start position:0% +heuristics that work okay and the +question is what are we optimizing for + + align:start position:0% +question is what are we optimizing for + + + align:start position:0% +question is what are we optimizing for +so generally you want to optimize the + + align:start position:0% +so generally you want to optimize the + + + align:start position:0% +so generally you want to optimize the +minimize the number of inputs used right + + align:start position:0% +minimize the number of inputs used right + + + align:start position:0% +minimize the number of inputs used right +so the fewer in the inputs are much + + align:start position:0% +so the fewer in the inputs are much + + + align:start position:0% +so the fewer in the inputs are much +bigger they're gonna be like a hundred + + align:start position:0% +bigger they're gonna be like a hundred + + + align:start position:0% +bigger they're gonna be like a hundred +something bytes and the outputs are + + align:start position:0% +something bytes and the outputs are + + + align:start position:0% +something bytes and the outputs are +pretty small they're like 20 30 bytes so + + align:start position:0% +pretty small they're like 20 30 bytes so + + + align:start position:0% +pretty small they're like 20 30 bytes so +they're real if you want to minimize + + align:start position:0% +they're real if you want to minimize + + + align:start position:0% +they're real if you want to minimize +size of your transaction minimize the + + align:start position:0% +size of your transaction minimize the + + + align:start position:0% +size of your transaction minimize the +number of inputs which is easy right you + + align:start position:0% +number of inputs which is easy right you + + + align:start position:0% +number of inputs which is easy right you +just pick your biggest you TXO and spend + + align:start position:0% +just pick your biggest you TXO and spend + + + align:start position:0% +just pick your biggest you TXO and spend +that one yes yeah it's basically as you + + align:start position:0% +that one yes yeah it's basically as you + + + align:start position:0% +that one yes yeah it's basically as you +what because it's multi iteration so if + + align:start position:0% +what because it's multi iteration so if + + + align:start position:0% +what because it's multi iteration so if +you're just trying to optimize your + + align:start position:0% +you're just trying to optimize your + + + align:start position:0% +you're just trying to optimize your +transaction right now you just use your + + align:start position:0% +transaction right now you just use your + + + align:start position:0% +transaction right now you just use your +biggest EXO so for example if you want + + align:start position:0% +biggest EXO so for example if you want + + + align:start position:0% +biggest EXO so for example if you want +like it's sort of in the analogy of + + align:start position:0% +like it's sort of in the analogy of + + + align:start position:0% +like it's sort of in the analogy of +you're at a checkout counter and there's + + align:start position:0% +you're at a checkout counter and there's + + + align:start position:0% +you're at a checkout counter and there's +gonna be you someone says okay that's + + align:start position:0% +gonna be you someone says okay that's + + + align:start position:0% +gonna be you someone says okay that's +you know $12.93 if you want to minimize + + align:start position:0% +you know $12.93 if you want to minimize + + + align:start position:0% +you know $12.93 if you want to minimize +the number of bills you're handing to + + align:start position:0% +the number of bills you're handing to + + + align:start position:0% +the number of bills you're handing to +the cashier you just take the hundred + + align:start position:0% +the cashier you just take the hundred + + + align:start position:0% +the cashier you just take the hundred +out of your wallet right that'll always + + align:start position:0% +out of your wallet right that'll always + + + align:start position:0% +out of your wallet right that'll always +work and you know and you just say I + + align:start position:0% +work and you know and you just say I + + + align:start position:0% +work and you know and you just say I +take the my biggest bill hand it to you + + align:start position:0% +take the my biggest bill hand it to you + + + align:start position:0% +take the my biggest bill hand it to you +okay I'm minimizing the amount of bills + + align:start position:0% +okay I'm minimizing the amount of bills + + + align:start position:0% +okay I'm minimizing the amount of bills +I'm handing you and this one transaction + + align:start position:0% +I'm handing you and this one transaction + + + align:start position:0% +I'm handing you and this one transaction +however that could result in a whole + + align:start position:0% +however that could result in a whole + + + align:start position:0% +however that could result in a whole +bunch of bills coming back right a bunch + + align:start position:0% +bunch of bills coming back right a bunch + + + align:start position:0% +bunch of bills coming back right a bunch +of weird change and then also long term + + align:start position:0% +of weird change and then also long term + + + align:start position:0% +of weird change and then also long term +that doesn't + + align:start position:0% +that doesn't + + + align:start position:0% +that doesn't +if your strategies always just just hand + + align:start position:0% +if your strategies always just just hand + + + align:start position:0% +if your strategies always just just hand +over the hundred or you know go through + + align:start position:0% +over the hundred or you know go through + + + align:start position:0% +over the hundred or you know go through +your wallet just hand over the biggest + + align:start position:0% +your wallet just hand over the biggest + + + align:start position:0% +your wallet just hand over the biggest +bill you have every time no matter what + + align:start position:0% +bill you have every time no matter what + + + align:start position:0% +bill you have every time no matter what +they ask + + align:start position:0% +they ask + + + align:start position:0% +they ask +that's super suboptimal because if they + + align:start position:0% +that's super suboptimal because if they + + + align:start position:0% +that's super suboptimal because if they +say 1293 and you have a twenty and a + + align:start position:0% +say 1293 and you have a twenty and a + + + align:start position:0% +say 1293 and you have a twenty and a +hundred and you hand over the hundred + + align:start position:0% +hundred and you hand over the hundred + + + align:start position:0% +hundred and you hand over the hundred +like why did you do that you know so and + + align:start position:0% +like why did you do that you know so and + + + align:start position:0% +like why did you do that you know so and +then you're gonna have like four 20s so + + align:start position:0% +then you're gonna have like four 20s so + + + align:start position:0% +then you're gonna have like four 20s so +it's very similar to that except now + + align:start position:0% +it's very similar to that except now + + + align:start position:0% +it's very similar to that except now +that it's similar to problems like that + + align:start position:0% +that it's similar to problems like that + + + align:start position:0% +that it's similar to problems like that +except the change and bills have + + align:start position:0% +except the change and bills have + + + align:start position:0% +except the change and bills have +arbitrary denominations there there + + align:start position:0% +arbitrary denominations there there + + + align:start position:0% +arbitrary denominations there there +isn't a fix you know you have hundreds + + align:start position:0% +isn't a fix you know you have hundreds + + + align:start position:0% +isn't a fix you know you have hundreds +twenty hundreds 50s 20s tens fives now + + align:start position:0% +twenty hundreds 50s 20s tens fives now + + + align:start position:0% +twenty hundreds 50s 20s tens fives now +it can be any number so yeah so if + + align:start position:0% +it can be any number so yeah so if + + + align:start position:0% +it can be any number so yeah so if +you're just looking at one time just + + align:start position:0% +you're just looking at one time just + + + align:start position:0% +you're just looking at one time just +pick your big issue at exo you'll have + + align:start position:0% +pick your big issue at exo you'll have + + + align:start position:0% +pick your big issue at exo you'll have +the smallest rands action but you want + + align:start position:0% +the smallest rands action but you want + + + align:start position:0% +the smallest rands action but you want +to minimize next time + + align:start position:0% +to minimize next time + + + align:start position:0% +to minimize next time +so you ideally can eliminate the change + + align:start position:0% +so you ideally can eliminate the change + + + align:start position:0% +so you ideally can eliminate the change +output and just get you know perfect + + align:start position:0% +output and just get you know perfect + + + align:start position:0% +output and just get you know perfect +target it's it's actually really + + align:start position:0% +target it's it's actually really + + + align:start position:0% +target it's it's actually really +complicated there's really cool research + + align:start position:0% +complicated there's really cool research + + + align:start position:0% +complicated there's really cool research +on how do we select coins for like long + + align:start position:0% +on how do we select coins for like long + + + align:start position:0% +on how do we select coins for like long +term yeah yep that can work that's not + + align:start position:0% +term yeah yep that can work that's not + + + align:start position:0% +term yeah yep that can work that's not +optic that's a good heuristic right + + align:start position:0% +optic that's a good heuristic right + + + align:start position:0% +optic that's a good heuristic right +that's a good like pretty easy to code + + align:start position:0% +that's a good like pretty easy to code + + + align:start position:0% +that's a good like pretty easy to code +you know sort your etx those go here use + + align:start position:0% +you know sort your etx those go here use + + + align:start position:0% +you know sort your etx those go here use +that one it's not super it's not really + + align:start position:0% +that one it's not super it's not really + + + align:start position:0% +that one it's not super it's not really +optimal because then it's a lot better + + align:start position:0% +optimal because then it's a lot better + + + align:start position:0% +optimal because then it's a lot better +than picking biggest what do I have in + + align:start position:0% +than picking biggest what do I have in + + + align:start position:0% +than picking biggest what do I have in +my wallet so I've actually written an + + align:start position:0% +my wallet so I've actually written an + + + align:start position:0% +my wallet so I've actually written an +SPB wallet and like all this stuff just + + align:start position:0% +SPB wallet and like all this stuff just + + + align:start position:0% +SPB wallet and like all this stuff just +from scratch and it's kind of + + align:start position:0% +from scratch and it's kind of + + + align:start position:0% +from scratch and it's kind of +interesting you learn a lot about how it + + align:start position:0% +interesting you learn a lot about how it + + + align:start position:0% +interesting you learn a lot about how it +works + + align:start position:0% +works + + + align:start position:0% +works +I hate our 'get two inputs instead of + + align:start position:0% +I hate our 'get two inputs instead of + + + align:start position:0% +I hate our 'get two inputs instead of +one because then eventually if you do + + align:start position:0% +one because then eventually if you do + + + align:start position:0% +one because then eventually if you do +that what will happen is you're always + + align:start position:0% +that what will happen is you're always + + + align:start position:0% +that what will happen is you're always +you're gonna be using one input which is + + align:start position:0% +you're gonna be using one input which is + + + align:start position:0% +you're gonna be using one input which is +great and then you're gonna run out of + + align:start position:0% +great and then you're gonna run out of + + + align:start position:0% +great and then you're gonna run out of +you're gonna have run out of big inputs + + align:start position:0% +you're gonna have run out of big inputs + + + align:start position:0% +you're gonna have run out of big inputs +and then you're gonna always have to + + align:start position:0% +and then you're gonna always have to + + + align:start position:0% +and then you're gonna always have to +like use two or three and you can get + + align:start position:0% +like use two or three and you can get + + + align:start position:0% +like use two or three and you can get +kind of a lot of dust dust it's dust is + + align:start position:0% +kind of a lot of dust dust it's dust is + + + align:start position:0% +kind of a lot of dust dust it's dust is +like the sort of colloquial term for + + align:start position:0% +like the sort of colloquial term for + + + align:start position:0% +like the sort of colloquial term for +really small UT exos we're like you've + + align:start position:0% +really small UT exos we're like you've + + + align:start position:0% +really small UT exos we're like you've +got a bunch of pennies and stuff so + + align:start position:0% +got a bunch of pennies and stuff so + + + align:start position:0% +got a bunch of pennies and stuff so +that's one issue + + align:start position:0% +that's one issue + + + align:start position:0% +that's one issue +another issue is privacy concerns so + + align:start position:0% +another issue is privacy concerns so + + + align:start position:0% +another issue is privacy concerns so +when you use to UT exo's or have two + + align:start position:0% +when you use to UT exo's or have two + + + align:start position:0% +when you use to UT exo's or have two +inputs in the same transaction that's + + align:start position:0% +inputs in the same transaction that's + + + align:start position:0% +inputs in the same transaction that's +linking those transactions linking those + + align:start position:0% +linking those transactions linking those + + + align:start position:0% +linking those transactions linking those +two UT exo's it's not definitive right + + align:start position:0% +two UT exo's it's not definitive right + + + align:start position:0% +two UT exo's it's not definitive right +you can + + align:start position:0% +you can + + + align:start position:0% +you can +interactively create transactions with + + align:start position:0% +interactively create transactions with + + + align:start position:0% +interactively create transactions with +other people in practice that doesn't + + align:start position:0% +other people in practice that doesn't + + + align:start position:0% +other people in practice that doesn't +happen right you could say hey I want to + + align:start position:0% +happen right you could say hey I want to + + + align:start position:0% +happen right you could say hey I want to +pay Alice five coins and you want to pay + + align:start position:0% +pay Alice five coins and you want to pay + + + align:start position:0% +pay Alice five coins and you want to pay +a bob six coins and let's put our my two + + align:start position:0% +a bob six coins and let's put our my two + + + align:start position:0% +a bob six coins and let's put our my two +year to EXO's and your two York to EXO's + + align:start position:0% +year to EXO's and your two York to EXO's + + + align:start position:0% +year to EXO's and your two York to EXO's +and we'll pay these two people and we'll + + align:start position:0% +and we'll pay these two people and we'll + + + align:start position:0% +and we'll pay these two people and we'll +put our own change outputs and we'll + + align:start position:0% +put our own change outputs and we'll + + + align:start position:0% +put our own change outputs and we'll +sort of mix this transaction together + + align:start position:0% +sort of mix this transaction together + + + align:start position:0% +sort of mix this transaction together +and we'll all sign it and you can do + + align:start position:0% +and we'll all sign it and you can do + + + align:start position:0% +and we'll all sign it and you can do +that securely that sense you know you + + align:start position:0% +that securely that sense you know you + + + align:start position:0% +that securely that sense you know you +only sign when it all looks right to you + + align:start position:0% +only sign when it all looks right to you + + + align:start position:0% +only sign when it all looks right to you +and everyone only signs when it's done + + align:start position:0% +and everyone only signs when it's done + + + align:start position:0% +and everyone only signs when it's done +but the coordination problem is pretty + + align:start position:0% +but the coordination problem is pretty + + + align:start position:0% +but the coordination problem is pretty +severe right you have to find other + + align:start position:0% +severe right you have to find other + + + align:start position:0% +severe right you have to find other +people who want to pay you know make + + align:start position:0% +people who want to pay you know make + + + align:start position:0% +people who want to pay you know make +transactions at the same time that you + + align:start position:0% +transactions at the same time that you + + + align:start position:0% +transactions at the same time that you +do it's annoying so in practice since + + align:start position:0% +do it's annoying so in practice since + + + align:start position:0% +do it's annoying so in practice since +you're just using your wallet if you see + + align:start position:0% +you're just using your wallet if you see + + + align:start position:0% +you're just using your wallet if you see +a transaction with multiple inputs you + + align:start position:0% +a transaction with multiple inputs you + + + align:start position:0% +a transaction with multiple inputs you +can you can surmise okay those are the + + align:start position:0% +can you can surmise okay those are the + + + align:start position:0% +can you can surmise okay those are the +same person or the same company and if + + align:start position:0% +same person or the same company and if + + + align:start position:0% +same person or the same company and if +you want privacy if you want to maximum + + align:start position:0% +you want privacy if you want to maximum + + + align:start position:0% +you want privacy if you want to maximum +anonymity what kind of coin selection or + + align:start position:0% +anonymity what kind of coin selection or + + + align:start position:0% +anonymity what kind of coin selection or +payment strategy would you use and yeah + + align:start position:0% +payment strategy would you use and yeah + + + align:start position:0% +payment strategy would you use and yeah +if someone says hey pay me six coins + + align:start position:0% +if someone says hey pay me six coins + + + align:start position:0% +if someone says hey pay me six coins +okay well I have these three inputs and + + align:start position:0% +okay well I have these three inputs and + + + align:start position:0% +okay well I have these three inputs and +I'm paying you two coins here and one + + align:start position:0% +I'm paying you two coins here and one + + + align:start position:0% +I'm paying you two coins here and one +coin here and three coins here and I + + align:start position:0% +coin here and three coins here and I + + + align:start position:0% +coin here and three coins here and I +paid you six coins but in three + + align:start position:0% +paid you six coins but in three + + + align:start position:0% +paid you six coins but in three +completely separate transactions that no + + align:start position:0% +completely separate transactions that no + + + align:start position:0% +completely separate transactions that no +one does either because it's annoying + + align:start position:0% +one does either because it's annoying + + + align:start position:0% +one does either because it's annoying +you could it would it would be the most + + align:start position:0% +you could it would it would be the most + + + align:start position:0% +you could it would it would be the most +anonymous but even then like well what + + align:start position:0% +anonymous but even then like well what + + + align:start position:0% +anonymous but even then like well what +if they all happened at the same time + + align:start position:0% +if they all happened at the same time + + + align:start position:0% +if they all happened at the same time +and you see they all get in the same + + align:start position:0% +and you see they all get in the same + + + align:start position:0% +and you see they all get in the same +block and you're like okay well they're + + align:start position:0% +block and you're like okay well they're + + + align:start position:0% +block and you're like okay well they're +not linked nearly as closely but I am + + align:start position:0% +not linked nearly as closely but I am + + + align:start position:0% +not linked nearly as closely but I am +seeing that these three transactions + + align:start position:0% +seeing that these three transactions + + + align:start position:0% +seeing that these three transactions +happen temporarily similar time so + + align:start position:0% +happen temporarily similar time so + + + align:start position:0% +happen temporarily similar time so +there's all sorts of things to try to + + align:start position:0% +there's all sorts of things to try to + + + align:start position:0% +there's all sorts of things to try to +optimize for okay any other questions + + align:start position:0% +optimize for okay any other questions + + + align:start position:0% +optimize for okay any other questions +about okay media like short term yes + + align:start position:0% +about okay media like short term yes + + + align:start position:0% +about okay media like short term yes +like if you start out with a bunch of + + align:start position:0% +like if you start out with a bunch of + + + align:start position:0% +like if you start out with a bunch of +coins then start using it yes but it + + align:start position:0% +coins then start using it yes but it + + + align:start position:0% +coins then start using it yes but it +does reach equilibrium right in that + + align:start position:0% +does reach equilibrium right in that + + + align:start position:0% +does reach equilibrium right in that +let's say you've got all these little + + align:start position:0% +let's say you've got all these little + + + align:start position:0% +let's say you've got all these little +tiny outputs of like you've got all + + align:start position:0% +tiny outputs of like you've got all + + + align:start position:0% +tiny outputs of like you've got all +these $1 bills + + align:start position:0% +these $1 bills + + + align:start position:0% +these $1 bills +but then you need to buy something that + + align:start position:0% +but then you need to buy something that + + + align:start position:0% +but then you need to buy something that +is 20 bucks you have 20 inputs and one + + align:start position:0% +is 20 bucks you have 20 inputs and one + + + align:start position:0% +is 20 bucks you have 20 inputs and one +output and whoever you're sending to now + + align:start position:0% +output and whoever you're sending to now + + + align:start position:0% +output and whoever you're sending to now +gets that one big output and so so like + + align:start position:0% +gets that one big output and so so like + + + align:start position:0% +gets that one big output and so so like +yeah if it sort of vanished compared to + + align:start position:0% +yeah if it sort of vanished compared to + + + align:start position:0% +yeah if it sort of vanished compared to +if you graph that over time yeah + + align:start position:0% +if you graph that over time yeah + + + align:start position:0% +if you graph that over time yeah +initially everyone was getting all their + + align:start position:0% +initially everyone was getting all their + + + align:start position:0% +initially everyone was getting all their +outputs were 50 coins each right cuz + + align:start position:0% +outputs were 50 coins each right cuz + + + align:start position:0% +outputs were 50 coins each right cuz +that's how you mind them and then now + + align:start position:0% +that's how you mind them and then now + + + align:start position:0% +that's how you mind them and then now +they're getting you know smaller but but + + align:start position:0% +they're getting you know smaller but but + + + align:start position:0% +they're getting you know smaller but but +there is sort of an equilibrium once + + align:start position:0% +there is sort of an equilibrium once + + + align:start position:0% +there is sort of an equilibrium once +after you've used it for a while any + + align:start position:0% +after you've used it for a while any + + + align:start position:0% +after you've used it for a while any +other questions about sort of coin + + align:start position:0% +other questions about sort of coin + + + align:start position:0% +other questions about sort of coin +selection you TXO selection yes yeah + + align:start position:0% +selection you TXO selection yes yeah + + + align:start position:0% +selection you TXO selection yes yeah +yeah so that's that's costly I that's + + align:start position:0% +yeah so that's that's costly I that's + + + align:start position:0% +yeah so that's that's costly I that's +another reason probably people don't do + + align:start position:0% +another reason probably people don't do + + + align:start position:0% +another reason probably people don't do +this there's I think the biggest reason + + align:start position:0% +this there's I think the biggest reason + + + align:start position:0% +this there's I think the biggest reason +is it's just annoying the code and it's + + align:start position:0% +is it's just annoying the code and it's + + + align:start position:0% +is it's just annoying the code and it's +like and and you can have failures where + + align:start position:0% +like and and you can have failures where + + + align:start position:0% +like and and you can have failures where +like here give me six coins okay I'll + + align:start position:0% +like here give me six coins okay I'll + + + align:start position:0% +like here give me six coins okay I'll +give you three two and one oh the three + + align:start position:0% +give you three two and one oh the three + + + align:start position:0% +give you three two and one oh the three +didn't work but the two and one did well + + align:start position:0% +didn't work but the two and one did well + + + align:start position:0% +didn't work but the two and one did well +now what do we like you paid me half of + + align:start position:0% +now what do we like you paid me half of + + + align:start position:0% +now what do we like you paid me half of +it like it's nice to have sort of + + align:start position:0% +it like it's nice to have sort of + + + align:start position:0% +it like it's nice to have sort of +all-or-nothing + + align:start position:0% +all-or-nothing + + + align:start position:0% +all-or-nothing +payments so and also we have to send + + align:start position:0% +payments so and also we have to send + + + align:start position:0% +payments so and also we have to send +different addresses you know there's all + + align:start position:0% +different addresses you know there's all + + + align:start position:0% +different addresses you know there's all +sorts of things also it will be higher + + align:start position:0% +sorts of things also it will be higher + + + align:start position:0% +sorts of things also it will be higher +fees in practice it's actually not much + + align:start position:0% +fees in practice it's actually not much + + + align:start position:0% +fees in practice it's actually not much +higher you don't gain if you if you did + + align:start position:0% +higher you don't gain if you if you did + + + align:start position:0% +higher you don't gain if you if you did +let's say having three one input one + + align:start position:0% +let's say having three one input one + + + align:start position:0% +let's say having three one input one +output transactions versus one three + + align:start position:0% +output transactions versus one three + + + align:start position:0% +output transactions versus one three +input three output transaction you don't + + align:start position:0% +input three output transaction you don't + + + align:start position:0% +input three output transaction you don't +say too much space most of the space is + + align:start position:0% +say too much space most of the space is + + + align:start position:0% +say too much space most of the space is +taken by the inputs and the overhead for + + align:start position:0% +taken by the inputs and the overhead for + + + align:start position:0% +taken by the inputs and the overhead for +a transaction is only 10 or 20 bytes or + + align:start position:0% +a transaction is only 10 or 20 bytes or + + + align:start position:0% +a transaction is only 10 or 20 bytes or +something so it's not a huge difference + + align:start position:0% +something so it's not a huge difference + + + align:start position:0% +something so it's not a huge difference +the main difference is that you are + + align:start position:0% +the main difference is that you are + + + align:start position:0% +the main difference is that you are +never coalescing into larger output + + align:start position:0% +never coalescing into larger output + + + align:start position:0% +never coalescing into larger output +sizes so you're gonna always have to + + align:start position:0% +sizes so you're gonna always have to + + + align:start position:0% +sizes so you're gonna always have to +sign it so you can have more inputs + + align:start position:0% +sign it so you can have more inputs + + + align:start position:0% +sign it so you can have more inputs +overall but yeah this is a really it's a + + align:start position:0% +overall but yeah this is a really it's a + + + align:start position:0% +overall but yeah this is a really it's a +kind of cool problem there's like a lot + + align:start position:0% +kind of cool problem there's like a lot + + + align:start position:0% +kind of cool problem there's like a lot +of computer science II stuff but a lot + + align:start position:0% +of computer science II stuff but a lot + + + align:start position:0% +of computer science II stuff but a lot +of sort of heuristics and like how + + align:start position:0% +of sort of heuristics and like how + + + align:start position:0% +of sort of heuristics and like how +people use it and also the fact that + + align:start position:0% +people use it and also the fact that + + + align:start position:0% +people use it and also the fact that +fees are variable over time means you + + align:start position:0% +fees are variable over time means you + + + align:start position:0% +fees are variable over time means you +might want different strategies when + + align:start position:0% +might want different strategies when + + + align:start position:0% +might want different strategies when +fees are low versus one fees are high so + + align:start position:0% +fees are low versus one fees are high so + + + align:start position:0% +fees are low versus one fees are high so +right when fees are low now I should + + align:start position:0% +right when fees are low now I should + + + align:start position:0% +right when fees are low now I should +make or maybe I just make a transaction + + align:start position:0% +make or maybe I just make a transaction + + + align:start position:0% +make or maybe I just make a transaction +to myself + + align:start position:0% +to myself + + + align:start position:0% +to myself +where I condensed all my little + + align:start position:0% +where I condensed all my little + + + align:start position:0% +where I condensed all my little +two-dollar outputs into one big thousand + + align:start position:0% +two-dollar outputs into one big thousand + + + align:start position:0% +two-dollar outputs into one big thousand +dollar output so that when later on if + + align:start position:0% +dollar output so that when later on if + + + align:start position:0% +dollar output so that when later on if +fees are higher I want to spend my money + + align:start position:0% +fees are higher I want to spend my money + + + align:start position:0% +fees are higher I want to spend my money +I can do so more efficiently and and + + align:start position:0% +I can do so more efficiently and and + + + align:start position:0% +I can do so more efficiently and and +there is evidence of this with like + + align:start position:0% +there is evidence of this with like + + + align:start position:0% +there is evidence of this with like +exchange ins and stuff where a lot of + + align:start position:0% +exchange ins and stuff where a lot of + + + align:start position:0% +exchange ins and stuff where a lot of +times fees will be lower on the weekends + + align:start position:0% +times fees will be lower on the weekends + + + align:start position:0% +times fees will be lower on the weekends +because people aren't buying and + + align:start position:0% +because people aren't buying and + + + align:start position:0% +because people aren't buying and +spending Bitcoin as much I guess and so + + align:start position:0% +spending Bitcoin as much I guess and so + + + align:start position:0% +spending Bitcoin as much I guess and so +certain companies would say okay over + + align:start position:0% +certain companies would say okay over + + + align:start position:0% +certain companies would say okay over +the weekends we're going to sort of + + align:start position:0% +the weekends we're going to sort of + + + align:start position:0% +the weekends we're going to sort of +condense all our UT exos and like + + align:start position:0% +condense all our UT exos and like + + + align:start position:0% +condense all our UT exos and like +combine them and then we can make + + align:start position:0% +combine them and then we can make + + + align:start position:0% +combine them and then we can make +smaller transactions during the week so + + align:start position:0% +smaller transactions during the week so + + + align:start position:0% +smaller transactions during the week so +there's all sorts of cool strategies + + align:start position:0% +there's all sorts of cool strategies + + + align:start position:0% +there's all sorts of cool strategies +here so it's an interesting topic I + + align:start position:0% +here so it's an interesting topic I + + + align:start position:0% +here so it's an interesting topic I +haven't like gone super in-depth but the + + align:start position:0% +haven't like gone super in-depth but the + + + align:start position:0% +haven't like gone super in-depth but the +guys that chain code work on it I don't + + align:start position:0% +guys that chain code work on it I don't + + + align:start position:0% +guys that chain code work on it I don't +know there's like a lot of discussion + + align:start position:0% +know there's like a lot of discussion + + + align:start position:0% +know there's like a lot of discussion +about it so it's kind of cool ok oh and + + align:start position:0% +about it so it's kind of cool ok oh and + + + align:start position:0% +about it so it's kind of cool ok oh and +a little bit behind ok next we'll talk + + align:start position:0% +a little bit behind ok next we'll talk + + + align:start position:0% +a little bit behind ok next we'll talk +about losing money and that's another + + align:start position:0% +about losing money and that's another + + + align:start position:0% +about losing money and that's another +really important part of detecting the + + align:start position:0% +really important part of detecting the + + + align:start position:0% +really important part of detecting the +blockchain it's it's hard to do but you + + align:start position:0% +blockchain it's it's hard to do but you + + + align:start position:0% +blockchain it's it's hard to do but you +you have to detect when you've lost + + align:start position:0% +you have to detect when you've lost + + + align:start position:0% +you have to detect when you've lost +money and it's tricky because just + + align:start position:0% +money and it's tricky because just + + + align:start position:0% +money and it's tricky because just +because you sign the transaction doesn't + + align:start position:0% +because you sign the transaction doesn't + + + align:start position:0% +because you sign the transaction doesn't +really mean your money's gone + + align:start position:0% +really mean your money's gone + + + align:start position:0% +really mean your money's gone +you can't just unilaterally say ok well + + align:start position:0% +you can't just unilaterally say ok well + + + align:start position:0% +you can't just unilaterally say ok well +I'm making this I signed it they're my + + align:start position:0% +I'm making this I signed it they're my + + + align:start position:0% +I'm making this I signed it they're my +money's gone from my wallet well not + + align:start position:0% +money's gone from my wallet well not + + + align:start position:0% +money's gone from my wallet well not +necessarily + + align:start position:0% +necessarily + + + align:start position:0% +necessarily +maybe this never gets confirmed right so + + align:start position:0% +maybe this never gets confirmed right so + + + align:start position:0% +maybe this never gets confirmed right so +maybe you still have that money so you + + align:start position:0% +maybe you still have that money so you + + + align:start position:0% +maybe you still have that money so you +broadcast it but you sort of have to + + align:start position:0% +broadcast it but you sort of have to + + + align:start position:0% +broadcast it but you sort of have to +wait until it gets into a block and you + + align:start position:0% +wait until it gets into a block and you + + + align:start position:0% +wait until it gets into a block and you +also need to listen for your own UTX + + align:start position:0% +also need to listen for your own UTX + + + align:start position:0% +also need to listen for your own UTX +owes even if you haven't made a + + align:start position:0% +owes even if you haven't made a + + + align:start position:0% +owes even if you haven't made a +transaction and see if they've gotten + + align:start position:0% +transaction and see if they've gotten + + + align:start position:0% +transaction and see if they've gotten +spent and why would that be like can + + align:start position:0% +spent and why would that be like can + + + align:start position:0% +spent and why would that be like can +anyone think of reason why I haven't + + align:start position:0% +anyone think of reason why I haven't + + + align:start position:0% +anyone think of reason why I haven't +signed anything as far as my program is + + align:start position:0% +signed anything as far as my program is + + + align:start position:0% +signed anything as far as my program is +concerned but I might lose money anyway + + align:start position:0% +concerned but I might lose money anyway + + + align:start position:0% +concerned but I might lose money anyway +why would that be yeah sure you get + + align:start position:0% +why would that be yeah sure you get + + + align:start position:0% +why would that be yeah sure you get +hacked that's the bad reason a good + + align:start position:0% +hacked that's the bad reason a good + + + align:start position:0% +hacked that's the bad reason a good +reason is well maybe you have the same + + align:start position:0% +reason is well maybe you have the same + + + align:start position:0% +reason is well maybe you have the same +wallet on multiple computers right + + align:start position:0% +wallet on multiple computers right + + + align:start position:0% +wallet on multiple computers right +you've got the same keys and say so this + + align:start position:0% +you've got the same keys and say so this + + + align:start position:0% +you've got the same keys and say so this +is getting hacked is sort of a malicious + + align:start position:0% +is getting hacked is sort of a malicious + + + align:start position:0% +is getting hacked is sort of a malicious +version instance of this problem where + + align:start position:0% +version instance of this problem where + + + align:start position:0% +version instance of this problem where +you know I thought the wallet was only + + align:start position:0% +you know I thought the wallet was only + + + align:start position:0% +you know I thought the wallet was only +on my computer but actually someone else + + align:start position:0% +on my computer but actually someone else + + + align:start position:0% +on my computer but actually someone else +has a copy but even even non maliciously + + align:start position:0% +has a copy but even even non maliciously + + + align:start position:0% +has a copy but even even non maliciously +I've got a copy on my phone I got a copy + + align:start position:0% +I've got a copy on my phone I got a copy + + + align:start position:0% +I've got a copy on my phone I got a copy +on my computer it's the same address as + + align:start position:0% +on my computer it's the same address as + + + align:start position:0% +on my computer it's the same address as +the same keys the same UTX O's + + align:start position:0% +the same keys the same UTX O's + + + align:start position:0% +the same keys the same UTX O's +that's totally doable and then when I + + align:start position:0% +that's totally doable and then when I + + + align:start position:0% +that's totally doable and then when I +you know spend money with my phone and + + align:start position:0% +you know spend money with my phone and + + + align:start position:0% +you know spend money with my phone and +get to my desktop my desktop needs to + + align:start position:0% +get to my desktop my desktop needs to + + + align:start position:0% +get to my desktop my desktop needs to +sort of download and see Oh money got + + align:start position:0% +sort of download and see Oh money got + + + align:start position:0% +sort of download and see Oh money got +you know you lost money and it's like oh + + align:start position:0% +you know you lost money and it's like oh + + + align:start position:0% +you know you lost money and it's like oh +yeah yeah I remember spending that so + + align:start position:0% +yeah yeah I remember spending that so + + + align:start position:0% +yeah yeah I remember spending that so +you can have that you know over multiple + + align:start position:0% +you can have that you know over multiple + + + align:start position:0% +you can have that you know over multiple +computers so if you're designing wallet + + align:start position:0% +computers so if you're designing wallet + + + align:start position:0% +computers so if you're designing wallet +software you do definitely need to make + + align:start position:0% +software you do definitely need to make + + + align:start position:0% +software you do definitely need to make +sure that even if it's sort of + + align:start position:0% +sure that even if it's sort of + + + align:start position:0% +sure that even if it's sort of +unexpected from the wallet itself and it + + align:start position:0% +unexpected from the wallet itself and it + + + align:start position:0% +unexpected from the wallet itself and it +doesn't seem like I generated a + + align:start position:0% +doesn't seem like I generated a + + + align:start position:0% +doesn't seem like I generated a +transaction you can still can still be a + + align:start position:0% +transaction you can still can still be a + + + align:start position:0% +transaction you can still can still be a +transaction taking your money way + + align:start position:0% +transaction taking your money way + + + align:start position:0% +transaction taking your money way +wallets without Bitcoin and that's sort + + align:start position:0% +wallets without Bitcoin and that's sort + + + align:start position:0% +wallets without Bitcoin and that's sort +of a cheeky fray okay I don't mean they + + align:start position:0% +of a cheeky fray okay I don't mean they + + + align:start position:0% +of a cheeky fray okay I don't mean they +don't have any bitcoins in their wallets + + align:start position:0% +don't have any bitcoins in their wallets + + + align:start position:0% +don't have any bitcoins in their wallets +I sort of mean they're not running + + align:start position:0% +I sort of mean they're not running + + + align:start position:0% +I sort of mean they're not running +Bitcoin in the same sense that we've + + align:start position:0% +Bitcoin in the same sense that we've + + + align:start position:0% +Bitcoin in the same sense that we've +talked of so we talked about running + + align:start position:0% +talked of so we talked about running + + + align:start position:0% +talked of so we talked about running +Bitcoin right where you download the + + align:start position:0% +Bitcoin right where you download the + + + align:start position:0% +Bitcoin right where you download the +software you get the headers you verify + + align:start position:0% +software you get the headers you verify + + + align:start position:0% +software you get the headers you verify +all the signatures you build the UT + + align:start position:0% +all the signatures you build the UT + + + align:start position:0% +all the signatures you build the UT +Exocet can you use Bitcoin without doing + + align:start position:0% +Exocet can you use Bitcoin without doing + + + align:start position:0% +Exocet can you use Bitcoin without doing +this what do you guys think what's a + + align:start position:0% +this what do you guys think what's a + + + align:start position:0% +this what do you guys think what's a +simple way to possibly use Bitcoin + + align:start position:0% +simple way to possibly use Bitcoin + + + align:start position:0% +simple way to possibly use Bitcoin +without having to do all these things so + + align:start position:0% +without having to do all these things so + + + align:start position:0% +without having to do all these things so +like a really really simple way if you + + align:start position:0% +like a really really simple way if you + + + align:start position:0% +like a really really simple way if you +don't want to do work what's the + + align:start position:0% +don't want to do work what's the + + + align:start position:0% +don't want to do work what's the +simplest way to not have to do work + + align:start position:0% +simplest way to not have to do work + + + align:start position:0% +simplest way to not have to do work +someone else to do it so for example my + + align:start position:0% +someone else to do it so for example my + + + align:start position:0% +someone else to do it so for example my +dad has Bitcoin but he just gives it + + align:start position:0% +dad has Bitcoin but he just gives it + + + align:start position:0% +dad has Bitcoin but he just gives it +these like you you deal with it so I've + + align:start position:0% +these like you you deal with it so I've + + + align:start position:0% +these like you you deal with it so I've +got a couple of bitcoins that's my dad's + + align:start position:0% +got a couple of bitcoins that's my dad's + + + align:start position:0% +got a couple of bitcoins that's my dad's +I have to make sure like no this is not + + align:start position:0% +I have to make sure like no this is not + + + align:start position:0% +I have to make sure like no this is not +my money + + align:start position:0% +my money + + + align:start position:0% +my money +yeah get someone else to do it right so + + align:start position:0% +yeah get someone else to do it right so + + + align:start position:0% +yeah get someone else to do it right so +that's sort of a we're gonna talk about + + align:start position:0% +that's sort of a we're gonna talk about + + + align:start position:0% +that's sort of a we're gonna talk about +the different ways to get someone else + + align:start position:0% +the different ways to get someone else + + + align:start position:0% +the different ways to get someone else +to do this and what we called before + + align:start position:0% +to do this and what we called before + + + align:start position:0% +to do this and what we called before +bit running Bitcoin many now call a full + + align:start position:0% +bit running Bitcoin many now call a full + + + align:start position:0% +bit running Bitcoin many now call a full +node and there's also the idea of like a + + align:start position:0% +node and there's also the idea of like a + + + align:start position:0% +node and there's also the idea of like a +light node or SPV node which we'll talk + + align:start position:0% +light node or SPV node which we'll talk + + + align:start position:0% +light node or SPV node which we'll talk +about some people don't really like this + + align:start position:0% +about some people don't really like this + + + align:start position:0% +about some people don't really like this +distinction and it's like well wait full + + align:start position:0% +distinction and it's like well wait full + + + align:start position:0% +distinction and it's like well wait full +node is running Bitcoin these other + + align:start position:0% +node is running Bitcoin these other + + + align:start position:0% +node is running Bitcoin these other +things are sort of you know we shouldn't + + align:start position:0% +things are sort of you know we shouldn't + + + align:start position:0% +things are sort of you know we shouldn't +have to call it a full node we should + + align:start position:0% +have to call it a full node we should + + + align:start position:0% +have to call it a full node we should +just call this a Bitcoin node and these + + align:start position:0% +just call this a Bitcoin node and these + + + align:start position:0% +just call this a Bitcoin node and these +other things are like not quite there + + align:start position:0% +other things are like not quite there + + + align:start position:0% +other things are like not quite there +but there's a lot a little preface + + align:start position:0% +but there's a lot a little preface + + + align:start position:0% +but there's a lot a little preface +there's a lot of argument about terms in + + align:start position:0% +there's a lot of argument about terms in + + + align:start position:0% +there's a lot of argument about terms in +this space so there are some people who + + align:start position:0% +this space so there are some people who + + + align:start position:0% +this space so there are some people who +say svv doesn't exist and other people + + align:start position:0% +say svv doesn't exist and other people + + + align:start position:0% +say svv doesn't exist and other people +this is an SV v8 it's so people argue + + align:start position:0% +this is an SV v8 it's so people argue + + + align:start position:0% +this is an SV v8 it's so people argue +about the words it's + + align:start position:0% +about the words it's + + + align:start position:0% +about the words it's +not like we have really nice definitive + + align:start position:0% +not like we have really nice definitive + + + align:start position:0% +not like we have really nice definitive +terms I'm generally trying to use the + + align:start position:0% +terms I'm generally trying to use the + + + align:start position:0% +terms I'm generally trying to use the +most widely used terms but there's + + align:start position:0% +most widely used terms but there's + + + align:start position:0% +most widely used terms but there's +probably people who'll take issue with + + align:start position:0% +probably people who'll take issue with + + + align:start position:0% +probably people who'll take issue with +it so sorry + + align:start position:0% +it so sorry + + + align:start position:0% +it so sorry +so svv is is sort of a step down below + + align:start position:0% +so svv is is sort of a step down below + + + align:start position:0% +so svv is is sort of a step down below +running a full note in terms of security + + align:start position:0% +running a full note in terms of security + + + align:start position:0% +running a full note in terms of security +it's called simplified payment + + align:start position:0% +it's called simplified payment + + + align:start position:0% +it's called simplified payment +verification it's written up in the + + align:start position:0% +verification it's written up in the + + + align:start position:0% +verification it's written up in the +white paper on how to do it and you can + + align:start position:0% +white paper on how to do it and you can + + + align:start position:0% +white paper on how to do it and you can +verify all the work without doing too + + align:start position:0% +verify all the work without doing too + + + align:start position:0% +verify all the work without doing too +much you know + + align:start position:0% +much you know + + + align:start position:0% +much you know +signature verification or having too + + align:start position:0% +signature verification or having too + + + align:start position:0% +signature verification or having too +much data so the basic idea is you're + + align:start position:0% +much data so the basic idea is you're + + + align:start position:0% +much data so the basic idea is you're +optimizing for not having to download as + + align:start position:0% +optimizing for not having to download as + + + align:start position:0% +optimizing for not having to download as +much and not having to store as much at + + align:start position:0% +much and not having to store as much at + + + align:start position:0% +much and not having to store as much at +the cost of some security and I'll talk + + align:start position:0% +the cost of some security and I'll talk + + + align:start position:0% +the cost of some security and I'll talk +about those those costs okay so before + + align:start position:0% +about those those costs okay so before + + + align:start position:0% +about those those costs okay so before +we had the sort of list of what you do + + align:start position:0% +we had the sort of list of what you do + + + align:start position:0% +we had the sort of list of what you do +for a full note the SPV method is a bit + + align:start position:0% +for a full note the SPV method is a bit + + + align:start position:0% +for a full note the SPV method is a bit +different right you still do the same + + align:start position:0% +different right you still do the same + + + align:start position:0% +different right you still do the same +part in the beginning right you'd + + align:start position:0% +part in the beginning right you'd + + + align:start position:0% +part in the beginning right you'd +connect you get your headers you verify + + align:start position:0% +connect you get your headers you verify + + + align:start position:0% +connect you get your headers you verify +all the work okay cool + + align:start position:0% +all the work okay cool + + + align:start position:0% +all the work okay cool +the next step you tell another node that + + align:start position:0% +the next step you tell another node that + + + align:start position:0% +the next step you tell another node that +you're connected to all of your + + align:start position:0% +you're connected to all of your + + + align:start position:0% +you're connected to all of your +addresses all the all of the key public + + align:start position:0% +addresses all the all of the key public + + + align:start position:0% +addresses all the all of the key public +keys that you've ever generated you tell + + align:start position:0% +keys that you've ever generated you tell + + + align:start position:0% +keys that you've ever generated you tell +it to them then you for each header you + + align:start position:0% +it to them then you for each header you + + + align:start position:0% +it to them then you for each header you +go through instead of downloading the + + align:start position:0% +go through instead of downloading the + + + align:start position:0% +go through instead of downloading the +whole block and getting all the + + align:start position:0% +whole block and getting all the + + + align:start position:0% +whole block and getting all the +transactions and verifying them you ask + + align:start position:0% +transactions and verifying them you ask + + + align:start position:0% +transactions and verifying them you ask +the other node hey did I get any money + + align:start position:0% +the other node hey did I get any money + + + align:start position:0% +the other node hey did I get any money +or did I lose any money in this block + + align:start position:0% +or did I lose any money in this block + + + align:start position:0% +or did I lose any money in this block +because I told you all my addresses oh + + align:start position:0% +because I told you all my addresses oh + + + align:start position:0% +because I told you all my addresses oh +sorry you also told them all your UT + + align:start position:0% +sorry you also told them all your UT + + + align:start position:0% +sorry you also told them all your UT +exos you also tell them here's all my + + align:start position:0% +exos you also tell them here's all my + + + align:start position:0% +exos you also tell them here's all my +here's all the money I have here's all + + align:start position:0% +here's all the money I have here's all + + + align:start position:0% +here's all the money I have here's all +the addresses I could possibly receive + + align:start position:0% +the addresses I could possibly receive + + + align:start position:0% +the addresses I could possibly receive +money on did I get or lose any money in + + align:start position:0% +money on did I get or lose any money in + + + align:start position:0% +money on did I get or lose any money in +this block and then they will return to + + align:start position:0% +this block and then they will return to + + + align:start position:0% +this block and then they will return to +you a merkel proof of the transactions + + align:start position:0% +you a merkel proof of the transactions + + + align:start position:0% +you a merkel proof of the transactions +where they think yeah you got some money + + align:start position:0% +where they think yeah you got some money + + + align:start position:0% +where they think yeah you got some money +here yeah you lost some money here and + + align:start position:0% +here yeah you lost some money here and + + + align:start position:0% +here yeah you lost some money here and +you can verify those yes there there is + + align:start position:0% +you can verify those yes there there is + + + align:start position:0% +you can verify those yes there there is +none you're not paying them they don't + + align:start position:0% +none you're not paying them they don't + + + align:start position:0% +none you're not paying them they don't +know who you are there's sort of a meta + + align:start position:0% +know who you are there's sort of a meta + + + align:start position:0% +know who you are there's sort of a meta +incentive in that like you know I run a + + align:start position:0% +incentive in that like you know I run a + + + align:start position:0% +incentive in that like you know I run a +node that will provide these merkel + + align:start position:0% +node that will provide these merkel + + + align:start position:0% +node that will provide these merkel +proofs because it's like well it helps + + align:start position:0% +proofs because it's like well it helps + + + align:start position:0% +proofs because it's like well it helps +bitcoin and maybe if I have some Bitcoin + + align:start position:0% +bitcoin and maybe if I have some Bitcoin + + + align:start position:0% +bitcoin and maybe if I have some Bitcoin +and I'm helping other people use it my + + align:start position:0% +and I'm helping other people use it my + + + align:start position:0% +and I'm helping other people use it my +Bitcoin will be worth more but that's a + + align:start position:0% +Bitcoin will be worth more but that's a + + + align:start position:0% +Bitcoin will be worth more but that's a +pretty yeah a few sort of thing and it + + align:start position:0% +pretty yeah a few sort of thing and it + + + align:start position:0% +pretty yeah a few sort of thing and it +can be a problematic because because + + align:start position:0% +can be a problematic because because + + + align:start position:0% +can be a problematic because because +some of these things I didn't + + align:start position:0% +some of these things I didn't + + + align:start position:0% +some of these things I didn't +mention that in these slides but the + + align:start position:0% +mention that in these slides but the + + + align:start position:0% +mention that in these slides but the +server-side can get a little bit costly + + align:start position:0% +server-side can get a little bit costly + + + align:start position:0% +server-side can get a little bit costly +in terms of CPU because you're + + align:start position:0% +in terms of CPU because you're + + + align:start position:0% +in terms of CPU because you're +potentially as a server you're the + + align:start position:0% +potentially as a server you're the + + + align:start position:0% +potentially as a server you're the +client requests hey here's this block + + align:start position:0% +client requests hey here's this block + + + align:start position:0% +client requests hey here's this block +can you sort of filter it for me find + + align:start position:0% +can you sort of filter it for me find + + + align:start position:0% +can you sort of filter it for me find +things that I'm looking for see now you + + align:start position:0% +things that I'm looking for see now you + + + align:start position:0% +things that I'm looking for see now you +have to load that block in the memory + + align:start position:0% +have to load that block in the memory + + + align:start position:0% +have to load that block in the memory +look through it it's not too CPU + + align:start position:0% +look through it it's not too CPU + + + align:start position:0% +look through it it's not too CPU +intensive but it can be you know when + + align:start position:0% +intensive but it can be you know when + + + align:start position:0% +intensive but it can be you know when +you have a bunch of them like a 20 or 30 + + align:start position:0% +you have a bunch of them like a 20 or 30 + + + align:start position:0% +you have a bunch of them like a 20 or 30 +of them connecting to you I've gotten + + align:start position:0% +of them connecting to you I've gotten + + + align:start position:0% +of them connecting to you I've gotten +you know 30% 40% CPU for doing this kind + + align:start position:0% +you know 30% 40% CPU for doing this kind + + + align:start position:0% +you know 30% 40% CPU for doing this kind +of thing to serve other users just at + + align:start position:0% +of thing to serve other users just at + + + align:start position:0% +of thing to serve other users just at +like a most almost all phone wallet well + + align:start position:0% +like a most almost all phone wallet well + + + align:start position:0% +like a most almost all phone wallet well +many phone wallets and many desktop + + align:start position:0% +many phone wallets and many desktop + + + align:start position:0% +many phone wallets and many desktop +wallets are using this model and so + + align:start position:0% +wallets are using this model and so + + + align:start position:0% +wallets are using this model and so +you'll see let me go so for example if I + + align:start position:0% +you'll see let me go so for example if I + + + align:start position:0% +you'll see let me go so for example if I +here's a full node the this building + + align:start position:0% +here's a full node the this building + + + align:start position:0% +here's a full node the this building +I actually rebooted it recently so + + align:start position:0% +I actually rebooted it recently so + + + align:start position:0% +I actually rebooted it recently so +there's not very many connections + + align:start position:0% +there's not very many connections + + + align:start position:0% +there's not very many connections +incoming but most in practice ok these + + align:start position:0% +incoming but most in practice ok these + + + align:start position:0% +incoming but most in practice ok these +two are Li are like actual full nodes I + + align:start position:0% +two are Li are like actual full nodes I + + + align:start position:0% +two are Li are like actual full nodes I +bet this is a fake node this is a fake + + align:start position:0% +bet this is a fake node this is a fake + + + align:start position:0% +bet this is a fake node this is a fake +node this is they're all fake + + align:start position:0% +node this is they're all fake + + + align:start position:0% +node this is they're all fake +yeah well sorry these are all know that + + align:start position:0% +yeah well sorry these are all know that + + + align:start position:0% +yeah well sorry these are all know that +one maybe not well you can look but like + + align:start position:0% +one maybe not well you can look but like + + + align:start position:0% +one maybe not well you can look but like +a lot of nodes will say they're nodes + + align:start position:0% +a lot of nodes will say they're nodes + + + align:start position:0% +a lot of nodes will say they're nodes +and they're not and they're just trying + + align:start position:0% +and they're not and they're just trying + + + align:start position:0% +and they're not and they're just trying +to track where transactions are coming + + align:start position:0% +to track where transactions are coming + + + align:start position:0% +to track where transactions are coming +from and like keep tabs on you and stuff + + align:start position:0% +from and like keep tabs on you and stuff + + + align:start position:0% +from and like keep tabs on you and stuff +and these are SPV notes these bit core + + align:start position:0% +and these are SPV notes these bit core + + + align:start position:0% +and these are SPV notes these bit core +because they never act they don't really + + align:start position:0% +because they never act they don't really + + + align:start position:0% +because they never act they don't really +ask for I don't know what they're doing + + align:start position:0% +ask for I don't know what they're doing + + + align:start position:0% +ask for I don't know what they're doing +they're not asking for anything so you + + align:start position:0% +they're not asking for anything so you + + + align:start position:0% +they're not asking for anything so you +can look through all the messages I + + align:start position:0% +can look through all the messages I + + + align:start position:0% +can look through all the messages I +think Ethan will talk about this a bit + + align:start position:0% +think Ethan will talk about this a bit + + + align:start position:0% +think Ethan will talk about this a bit +more Wednesday but there are a lot of + + align:start position:0% +more Wednesday but there are a lot of + + + align:start position:0% +more Wednesday but there are a lot of +SPV nodes there's a lot of stuff out in + + align:start position:0% +SPV nodes there's a lot of stuff out in + + + align:start position:0% +SPV nodes there's a lot of stuff out in +the network you have no idea what it's + + align:start position:0% +the network you have no idea what it's + + + align:start position:0% +the network you have no idea what it's +doing it's it's but it's pretty clearly + + align:start position:0% +doing it's it's but it's pretty clearly + + + align:start position:0% +doing it's it's but it's pretty clearly +not running a Bitcoin node so yeah so + + align:start position:0% +not running a Bitcoin node so yeah so + + + align:start position:0% +not running a Bitcoin node so yeah so +I'll go through these steps a little bit + + align:start position:0% +I'll go through these steps a little bit + + + align:start position:0% +I'll go through these steps a little bit +and oh yeah so the merkel verification + + align:start position:0% +and oh yeah so the merkel verification + + + align:start position:0% +and oh yeah so the merkel verification +we talked about last week I think we're + + align:start position:0% +we talked about last week I think we're + + + align:start position:0% +we talked about last week I think we're +if there's a block and there's thousands + + align:start position:0% +if there's a block and there's thousands + + + align:start position:0% +if there's a block and there's thousands +of transactions in it and this server + + align:start position:0% +of transactions in it and this server + + + align:start position:0% +of transactions in it and this server +wants to prove that one of these + + align:start position:0% +wants to prove that one of these + + + align:start position:0% +wants to prove that one of these +transactions is yours and is in there + + align:start position:0% +transactions is yours and is in there + + + align:start position:0% +transactions is yours and is in there +say okay here's my transaction they just + + align:start position:0% +say okay here's my transaction they just + + + align:start position:0% +say okay here's my transaction they just +need to provide you this transaction ID + + align:start position:0% +need to provide you this transaction ID + + + align:start position:0% +need to provide you this transaction ID +this hash and then you're able to see + + align:start position:0% +this hash and then you're able to see + + + align:start position:0% +this hash and then you're able to see +okay yeah it was in the header right so + + align:start position:0% +okay yeah it was in the header right so + + + align:start position:0% +okay yeah it was in the header right so +my transaction + + align:start position:0% +my transaction + + + align:start position:0% +my transaction +you're not just making it up I didn't + + align:start position:0% +you're not just making it up I didn't + + + align:start position:0% +you're not just making it up I didn't +talk about the good part well the good + + align:start position:0% +talk about the good part well the good + + + align:start position:0% +talk about the good part well the good +part is you don't really need to + + align:start position:0% +part is you don't really need to + + + align:start position:0% +part is you don't really need to +maintain aut Exocet and it's pretty + + align:start position:0% +maintain aut Exocet and it's pretty + + + align:start position:0% +maintain aut Exocet and it's pretty +small so it saves space saves time what + + align:start position:0% +small so it saves space saves time what + + + align:start position:0% +small so it saves space saves time what +are the problems there's a lot and I + + align:start position:0% +are the problems there's a lot and I + + + align:start position:0% +are the problems there's a lot and I +definitely admit I before writing my own + + align:start position:0% +definitely admit I before writing my own + + + align:start position:0% +definitely admit I before writing my own +SPV wallet code I didn't think there + + align:start position:0% +SPV wallet code I didn't think there + + + align:start position:0% +SPV wallet code I didn't think there +were a lot of problems with it I thought + + align:start position:0% +were a lot of problems with it I thought + + + align:start position:0% +were a lot of problems with it I thought +it was like oh this is a CV this is cool + + align:start position:0% +it was like oh this is a CV this is cool + + + align:start position:0% +it was like oh this is a CV this is cool +this is how wallets work but when + + align:start position:0% +this is how wallets work but when + + + align:start position:0% +this is how wallets work but when +writing the code myself I'm like wait + + align:start position:0% +writing the code myself I'm like wait + + + align:start position:0% +writing the code myself I'm like wait +this is horrible what do we do okay so + + align:start position:0% +this is horrible what do we do okay so + + + align:start position:0% +this is horrible what do we do okay so +the first thing you do is you connect + + align:start position:0% +the first thing you do is you connect + + + align:start position:0% +the first thing you do is you connect +you get the headers you verify them this + + align:start position:0% +you get the headers you verify them this + + + align:start position:0% +you get the headers you verify them this +is exactly the same procedure as what a + + align:start position:0% +is exactly the same procedure as what a + + + align:start position:0% +is exactly the same procedure as what a +full node does so there's no difference + + align:start position:0% +full node does so there's no difference + + + align:start position:0% +full node does so there's no difference +it works right no difference there the + + align:start position:0% +it works right no difference there the + + + align:start position:0% +it works right no difference there the +next step you tell a node all of your + + align:start position:0% +next step you tell a node all of your + + + align:start position:0% +next step you tell a node all of your +addresses Wow there goes all your + + align:start position:0% +addresses Wow there goes all your + + + align:start position:0% +addresses Wow there goes all your +privacy right because you're just + + align:start position:0% +privacy right because you're just + + + align:start position:0% +privacy right because you're just +connecting to a computer you have no + + align:start position:0% +connecting to a computer you have no + + + align:start position:0% +connecting to a computer you have no +idea who they are who's running it and + + align:start position:0% +idea who they are who's running it and + + + align:start position:0% +idea who they are who's running it and +you're telling them hey here's all of my + + align:start position:0% +you're telling them hey here's all of my + + + align:start position:0% +you're telling them hey here's all of my +addresses and also here's how much money + + align:start position:0% +addresses and also here's how much money + + + align:start position:0% +addresses and also here's how much money +I have + + align:start position:0% +I have + + + align:start position:0% +I have +right here's all my UT X OS you can lie + + align:start position:0% +right here's all my UT X OS you can lie + + + align:start position:0% +right here's all my UT X OS you can lie +you can add things that are not so you + + align:start position:0% +you can add things that are not so you + + + align:start position:0% +you can add things that are not so you +can also add some addresses that aren't + + align:start position:0% +can also add some addresses that aren't + + + align:start position:0% +can also add some addresses that aren't +yours or add some UT X OS that aren't + + align:start position:0% +yours or add some UT X OS that aren't + + + align:start position:0% +yours or add some UT X OS that aren't +yours and you'll get some some + + align:start position:0% +yours and you'll get some some + + + align:start position:0% +yours and you'll get some some +transactions back that you can then + + align:start position:0% +transactions back that you can then + + + align:start position:0% +transactions back that you can then +filter out on your own right so you can + + align:start position:0% +filter out on your own right so you can + + + align:start position:0% +filter out on your own right so you can +you can raise the rate of false + + align:start position:0% +you can raise the rate of false + + + align:start position:0% +you can raise the rate of false +positives for that server and so there's + + align:start position:0% +positives for that server and so there's + + + align:start position:0% +positives for that server and so there's +these these bloom filters that are in + + align:start position:0% +these these bloom filters that are in + + + align:start position:0% +these these bloom filters that are in +the Bitcoin code core code that they + + align:start position:0% +the Bitcoin code core code that they + + + align:start position:0% +the Bitcoin code core code that they +said like the idea was well you can sort + + align:start position:0% +said like the idea was well you can sort + + + align:start position:0% +said like the idea was well you can sort +of dial your own false positive rate + + align:start position:0% +of dial your own false positive rate + + + align:start position:0% +of dial your own false positive rate +right I'm not gonna go into our bloom + + align:start position:0% +right I'm not gonna go into our bloom + + + align:start position:0% +right I'm not gonna go into our bloom +filters work if you've used those in + + align:start position:0% +filters work if you've used those in + + + align:start position:0% +filters work if you've used those in +other classes cool but it basically sort + + align:start position:0% +other classes cool but it basically sort + + + align:start position:0% +other classes cool but it basically sort +of gives some data which allows people + + align:start position:0% +of gives some data which allows people + + + align:start position:0% +of gives some data which allows people +to match things but they don't in + + align:start position:0% +to match things but they don't in + + + align:start position:0% +to match things but they don't in +practice have good privacy you can + + align:start position:0% +practice have good privacy you can + + + align:start position:0% +practice have good privacy you can +create a bloom filter where they've you + + align:start position:0% +create a bloom filter where they've you + + + align:start position:0% +create a bloom filter where they've you +know got 10% false positive rate and so + + align:start position:0% +know got 10% false positive rate and so + + + align:start position:0% +know got 10% false positive rate and so +when the server says oh looks like their + + align:start position:0% +when the server says oh looks like their + + + align:start position:0% +when the server says oh looks like their +transaction maybe it's not because 10% + + align:start position:0% +transaction maybe it's not because 10% + + + align:start position:0% +transaction maybe it's not because 10% +of the time it's just a false positive + + align:start position:0% +of the time it's just a false positive + + + align:start position:0% +of the time it's just a false positive +however when you have really high false + + align:start position:0% +however when you have really high false + + + align:start position:0% +however when you have really high false +positives you lose all the efficiency + + align:start position:0% +positives you lose all the efficiency + + + align:start position:0% +positives you lose all the efficiency +savings of SPV and it's sort of Cascades + + align:start position:0% +savings of SPV and it's sort of Cascades + + + align:start position:0% +savings of SPV and it's sort of Cascades +where you've got these false positives + + align:start position:0% +where you've got these false positives + + + align:start position:0% +where you've got these false positives +and the server thinks oh you got money + + align:start position:0% +and the server thinks oh you got money + + + align:start position:0% +and the server thinks oh you got money +but it's a false positive and they add + + align:start position:0% +but it's a false positive and they add + + + align:start position:0% +but it's a false positive and they add +that you got + + align:start position:0% +that you got + + + align:start position:0% +that you got +money into the bloom filter itself and + + align:start position:0% +money into the bloom filter itself and + + + align:start position:0% +money into the bloom filter itself and +the bloom filter can like really quickly + + align:start position:0% +the bloom filter can like really quickly + + + align:start position:0% +the bloom filter can like really quickly +become saturated then you start giving + + align:start position:0% +become saturated then you start giving + + + align:start position:0% +become saturated then you start giving +you everything so in practice and + + align:start position:0% +you everything so in practice and + + + align:start position:0% +you everything so in practice and +there's some papers about how the people + + align:start position:0% +there's some papers about how the people + + + align:start position:0% +there's some papers about how the people +who put the bloom filters into Bitcoin + + align:start position:0% +who put the bloom filters into Bitcoin + + + align:start position:0% +who put the bloom filters into Bitcoin +like oh this is good for privacy it's + + align:start position:0% +like oh this is good for privacy it's + + + align:start position:0% +like oh this is good for privacy it's +fine and in practice it really is not + + align:start position:0% +fine and in practice it really is not + + + align:start position:0% +fine and in practice it really is not +good for privacy so you end it you end + + align:start position:0% +good for privacy so you end it you end + + + align:start position:0% +good for privacy so you end it you end +up basically telling a note all your + + align:start position:0% +up basically telling a note all your + + + align:start position:0% +up basically telling a note all your +addresses and there's there's research + + align:start position:0% +addresses and there's there's research + + + align:start position:0% +addresses and there's there's research +on how to do this in a better way and + + align:start position:0% +on how to do this in a better way and + + + align:start position:0% +on how to do this in a better way and +it's one of those kind of things where + + align:start position:0% +it's one of those kind of things where + + + align:start position:0% +it's one of those kind of things where +some random anonymous person with a I + + align:start position:0% +some random anonymous person with a I + + + align:start position:0% +some random anonymous person with a I +think like inappropriate swear word + + align:start position:0% +think like inappropriate swear word + + + align:start position:0% +think like inappropriate swear word +email address posted to the mailing list + + align:start position:0% +email address posted to the mailing list + + + align:start position:0% +email address posted to the mailing list +and say hey why don't you guys do it + + align:start position:0% +and say hey why don't you guys do it + + + align:start position:0% +and say hey why don't you guys do it +this way and it was like oh yeah we + + align:start position:0% +this way and it was like oh yeah we + + + align:start position:0% +this way and it was like oh yeah we +should have done it that way + + align:start position:0% +should have done it that way + + + align:start position:0% +should have done it that way +oops the basic idea is instead of + + align:start position:0% +oops the basic idea is instead of + + + align:start position:0% +oops the basic idea is instead of +creating a bloom filter as a client + + align:start position:0% +creating a bloom filter as a client + + + align:start position:0% +creating a bloom filter as a client +sending it to a server basically instead + + align:start position:0% +sending it to a server basically instead + + + align:start position:0% +sending it to a server basically instead +of telling the note all your addresses + + align:start position:0% +of telling the note all your addresses + + + align:start position:0% +of telling the note all your addresses +and asking what the nodes will do the + + align:start position:0% +and asking what the nodes will do the + + + align:start position:0% +and asking what the nodes will do the +full nodes will create a bloom filter + + align:start position:0% +full nodes will create a bloom filter + + + align:start position:0% +full nodes will create a bloom filter +based on the entire block and then the + + align:start position:0% +based on the entire block and then the + + + align:start position:0% +based on the entire block and then the +client can retrieve that match that + + align:start position:0% +client can retrieve that match that + + + align:start position:0% +client can retrieve that match that +against their addresses and see hey then + + align:start position:0% +against their addresses and see hey then + + + align:start position:0% +against their addresses and see hey then +this block have anything of interest to + + align:start position:0% +this block have anything of interest to + + + align:start position:0% +this block have anything of interest to +me and if so request it much better + + align:start position:0% +me and if so request it much better + + + align:start position:0% +me and if so request it much better +privacy at a pretty small cost in + + align:start position:0% +privacy at a pretty small cost in + + + align:start position:0% +privacy at a pretty small cost in +overhead and so just no one thought of + + align:start position:0% +overhead and so just no one thought of + + + align:start position:0% +overhead and so just no one thought of +it there's a lot of things in Bitcoin + + align:start position:0% +it there's a lot of things in Bitcoin + + + align:start position:0% +it there's a lot of things in Bitcoin +weird like no one thought of it and we + + align:start position:0% +weird like no one thought of it and we + + + align:start position:0% +weird like no one thought of it and we +did something Dahman then something + + align:start position:0% +did something Dahman then something + + + align:start position:0% +did something Dahman then something +better came out and now we're working on + + align:start position:0% +better came out and now we're working on + + + align:start position:0% +better came out and now we're working on +that okay so the tell-tell the node all + + align:start position:0% +that okay so the tell-tell the node all + + + align:start position:0% +that okay so the tell-tell the node all +your addresses that's a problem for each + + align:start position:0% +your addresses that's a problem for each + + + align:start position:0% +your addresses that's a problem for each +header ask if you gained or lost you TX + + align:start position:0% +header ask if you gained or lost you TX + + + align:start position:0% +header ask if you gained or lost you TX +owes so can you think of any problems + + align:start position:0% +owes so can you think of any problems + + + align:start position:0% +owes so can you think of any problems +here not yeah yeah yep easy to lie you + + align:start position:0% +here not yeah yeah yep easy to lie you + + + align:start position:0% +here not yeah yeah yep easy to lie you +just don't tell them you know if you're + + align:start position:0% +just don't tell them you know if you're + + + align:start position:0% +just don't tell them you know if you're +a server you just omit things and you + + align:start position:0% +a server you just omit things and you + + + align:start position:0% +a server you just omit things and you +can maybe mitigate that by connecting to + + align:start position:0% +can maybe mitigate that by connecting to + + + align:start position:0% +can maybe mitigate that by connecting to +a bunch of different nodes but then you + + align:start position:0% +a bunch of different nodes but then you + + + align:start position:0% +a bunch of different nodes but then you +lose even more privacy because you've + + align:start position:0% +lose even more privacy because you've + + + align:start position:0% +lose even more privacy because you've +now shared all your addresses and money + + align:start position:0% +now shared all your addresses and money + + + align:start position:0% +now shared all your addresses and money +with multiple anonymous notes but yeah + + align:start position:0% +with multiple anonymous notes but yeah + + + align:start position:0% +with multiple anonymous notes but yeah +it's really easy to lie by omission you + + align:start position:0% +it's really easy to lie by omission you + + + align:start position:0% +it's really easy to lie by omission you +know if someone says hey here's all I'm + + align:start position:0% +know if someone says hey here's all I'm + + + align:start position:0% +know if someone says hey here's all I'm +at my addresses okay did I get any money + + align:start position:0% +at my addresses okay did I get any money + + + align:start position:0% +at my addresses okay did I get any money +yep yep and then you see one where they + + align:start position:0% +yep yep and then you see one where they + + + align:start position:0% +yep yep and then you see one where they +got a bunch of money and just don't tell + + align:start position:0% +got a bunch of money and just don't tell + + + align:start position:0% +got a bunch of money and just don't tell +them and they don't know this can be + + align:start position:0% +them and they don't know this can be + + + align:start position:0% +them and they don't know this can be +annoying in regular wallets in the + + align:start position:0% +annoying in regular wallets in the + + + align:start position:0% +annoying in regular wallets in the +Lightning Network stuff that I work on + + align:start position:0% +Lightning Network stuff that I work on + + + align:start position:0% +Lightning Network stuff that I work on +I'll talk about hopefully later this can + + align:start position:0% +I'll talk about hopefully later this can + + + align:start position:0% +I'll talk about hopefully later this can +actually be very damaging you could lose + + align:start position:0% +actually be very damaging you could lose + + + align:start position:0% +actually be very damaging you could lose +money because of this but in general in + + align:start position:0% +money because of this but in general in + + + align:start position:0% +money because of this but in general in +Bitcoin you won't lose money because + + align:start position:0% +Bitcoin you won't lose money because + + + align:start position:0% +Bitcoin you won't lose money because +you're not aware of a transaction so + + align:start position:0% +you're not aware of a transaction so + + + align:start position:0% +you're not aware of a transaction so +this is this is also a problem right + + align:start position:0% +this is this is also a problem right + + + align:start position:0% +this is this is also a problem right +easy to live on mission + + align:start position:0% +easy to live on mission + + + align:start position:0% +easy to live on mission +the merkel proofs help but they prove + + align:start position:0% +the merkel proofs help but they prove + + + align:start position:0% +the merkel proofs help but they prove +inclusion not exclusion there's no way + + align:start position:0% +inclusion not exclusion there's no way + + + align:start position:0% +inclusion not exclusion there's no way +to construct a proof that you know I'm + + align:start position:0% +to construct a proof that you know I'm + + + align:start position:0% +to construct a proof that you know I'm +gonna I'm gonna give you a proof that + + align:start position:0% +gonna I'm gonna give you a proof that + + + align:start position:0% +gonna I'm gonna give you a proof that +I'm not emitting anything although with + + align:start position:0% +I'm not emitting anything although with + + + align:start position:0% +I'm not emitting anything although with +the idea of the block based filters + + align:start position:0% +the idea of the block based filters + + + align:start position:0% +the idea of the block based filters +sending there's there are ways to + + align:start position:0% +sending there's there are ways to + + + align:start position:0% +sending there's there are ways to +construct that so it's even better in + + align:start position:0% +construct that so it's even better in + + + align:start position:0% +construct that so it's even better in +that sense okay so these are some of the + + align:start position:0% +that sense okay so these are some of the + + + align:start position:0% +that sense okay so these are some of the +disadvantages of SBV can anyone think of + + align:start position:0% +disadvantages of SBV can anyone think of + + + align:start position:0% +disadvantages of SBV can anyone think of +any other problems with it or yeah yeah + + align:start position:0% +any other problems with it or yeah yeah + + + align:start position:0% +any other problems with it or yeah yeah +okay so yeah you don't know since you're + + align:start position:0% +okay so yeah you don't know since you're + + + align:start position:0% +okay so yeah you don't know since you're +not downloading the blocks you don't + + align:start position:0% +not downloading the blocks you don't + + + align:start position:0% +not downloading the blocks you don't +really know how much fees other people + + align:start position:0% +really know how much fees other people + + + align:start position:0% +really know how much fees other people +are paying you're not verifying so even + + align:start position:0% +are paying you're not verifying so even + + + align:start position:0% +are paying you're not verifying so even +when you get transactions you cannot + + align:start position:0% +when you get transactions you cannot + + + align:start position:0% +when you get transactions you cannot +verify any signatures because you don't + + align:start position:0% +verify any signatures because you don't + + + align:start position:0% +verify any signatures because you don't +have UT Exocet so you just see that it + + align:start position:0% +have UT Exocet so you just see that it + + + align:start position:0% +have UT Exocet so you just see that it +came from somewhere but you don't know + + align:start position:0% +came from somewhere but you don't know + + + align:start position:0% +came from somewhere but you don't know +if the thing it's spending even exists + + align:start position:0% +if the thing it's spending even exists + + + align:start position:0% +if the thing it's spending even exists +or has a key or anything so you can't + + align:start position:0% +or has a key or anything so you can't + + + align:start position:0% +or has a key or anything so you can't +verify the signature you don't know how + + align:start position:0% +verify the signature you don't know how + + + align:start position:0% +verify the signature you don't know how +much money was coming in so even if you + + align:start position:0% +much money was coming in so even if you + + + align:start position:0% +much money was coming in so even if you +look at the transactions you can't tell + + align:start position:0% +look at the transactions you can't tell + + + align:start position:0% +look at the transactions you can't tell +what fees they're paying you sort of can + + align:start position:0% +what fees they're paying you sort of can + + + align:start position:0% +what fees they're paying you sort of can +if you download an entire block there's + + align:start position:0% +if you download an entire block there's + + + align:start position:0% +if you download an entire block there's +there's ways around it but it's like + + align:start position:0% +there's ways around it but it's like + + + align:start position:0% +there's ways around it but it's like +really ugly so it's it can be very + + align:start position:0% +really ugly so it's it can be very + + + align:start position:0% +really ugly so it's it can be very +difficult to estimate fees so in + + align:start position:0% +difficult to estimate fees so in + + + align:start position:0% +difficult to estimate fees so in +practice you probably ask the same + + align:start position:0% +practice you probably ask the same + + + align:start position:0% +practice you probably ask the same +server that you've told all your + + align:start position:0% +server that you've told all your + + + align:start position:0% +server that you've told all your +addresses and all your UT X those two + + align:start position:0% +addresses and all your UT X those two + + + align:start position:0% +addresses and all your UT X those two +hey what fee should I use then they tell + + align:start position:0% +hey what fee should I use then they tell + + + align:start position:0% +hey what fee should I use then they tell +you that and the idea is well if I asked + + align:start position:0% +you that and the idea is well if I asked + + + align:start position:0% +you that and the idea is well if I asked +five people hopefully most of them will + + align:start position:0% +five people hopefully most of them will + + + align:start position:0% +five people hopefully most of them will +be around the same so there's a bunch of + + align:start position:0% +be around the same so there's a bunch of + + + align:start position:0% +be around the same so there's a bunch of +problems with SBT + + align:start position:0% +problems with SBT + + + align:start position:0% +problems with SBT +okay so it's TV sounds pretty bad right + + align:start position:0% +okay so it's TV sounds pretty bad right + + + align:start position:0% +okay so it's TV sounds pretty bad right +and I think I'll stick my phone note but + + align:start position:0% +and I think I'll stick my phone note but + + + align:start position:0% +and I think I'll stick my phone note but +uh is there anything worse than SPV + + align:start position:0% +uh is there anything worse than SPV + + + align:start position:0% +uh is there anything worse than SPV +asking for a friend + + align:start position:0% +asking for a friend + + + align:start position:0% +asking for a friend +can I can I can I go worse so does + + align:start position:0% +can I can I can I go worse so does + + + align:start position:0% +can I can I can I go worse so does +anyone know something we can do that's + + align:start position:0% +anyone know something we can do that's + + + align:start position:0% +anyone know something we can do that's +that's worse security worse privacy than + + align:start position:0% +that's worse security worse privacy than + + + align:start position:0% +that's worse security worse privacy than +SPV it's also very much yeah + + align:start position:0% +SPV it's also very much yeah + + + align:start position:0% +SPV it's also very much yeah +okay that's that's even worse but yeah + + align:start position:0% +okay that's that's even worse but yeah + + + align:start position:0% +okay that's that's even worse but yeah +there's there's a step in between so you + + align:start position:0% +there's there's a step in between so you + + + align:start position:0% +there's there's a step in between so you +can take out some of these steps where + + align:start position:0% +can take out some of these steps where + + + align:start position:0% +can take out some of these steps where +you just used to have an API and you ask + + align:start position:0% +you just used to have an API and you ask + + + align:start position:0% +you just used to have an API and you ask +people you have a website you know + + align:start position:0% +people you have a website you know + + + align:start position:0% +people you have a website you know +blockchain not info or mycelium wallet + + align:start position:0% +blockchain not info or mycelium wallet + + + align:start position:0% +blockchain not info or mycelium wallet +or bunch of all a bit pays a copay + + align:start position:0% +or bunch of all a bit pays a copay + + + align:start position:0% +or bunch of all a bit pays a copay +things like that work you don't verify + + align:start position:0% +things like that work you don't verify + + + align:start position:0% +things like that work you don't verify +any headers you don't look at any merkel + + align:start position:0% +any headers you don't look at any merkel + + + align:start position:0% +any headers you don't look at any merkel +proofs you just skip right to the tell + + align:start position:0% +proofs you just skip right to the tell + + + align:start position:0% +proofs you just skip right to the tell +the remote node all your addresses and + + align:start position:0% +the remote node all your addresses and + + + align:start position:0% +the remote node all your addresses and +you TX OS and ask how much money you've + + align:start position:0% +you TX OS and ask how much money you've + + + align:start position:0% +you TX OS and ask how much money you've +gained or lost right so you sort of + + align:start position:0% +gained or lost right so you sort of + + + align:start position:0% +gained or lost right so you sort of +outsource the entire process you don't + + align:start position:0% +outsource the entire process you don't + + + align:start position:0% +outsource the entire process you don't +store really anything on your computer + + align:start position:0% +store really anything on your computer + + + align:start position:0% +store really anything on your computer +and you say well I've got but you do + + align:start position:0% +and you say well I've got but you do + + + align:start position:0% +and you say well I've got but you do +have your private keys right you say I + + align:start position:0% +have your private keys right you say I + + + align:start position:0% +have your private keys right you say I +made some private keys I made some + + align:start position:0% +made some private keys I made some + + + align:start position:0% +made some private keys I made some +addresses and then I tell this website + + align:start position:0% +addresses and then I tell this website + + + align:start position:0% +addresses and then I tell this website +hey here's all my addresses how much + + align:start position:0% +hey here's all my addresses how much + + + align:start position:0% +hey here's all my addresses how much +money do I have in the server's fronds + + align:start position:0% +money do I have in the server's fronds + + + align:start position:0% +money do I have in the server's fronds +yeah you've got UT exo's cool so then + + align:start position:0% +yeah you've got UT exo's cool so then + + + align:start position:0% +yeah you've got UT exo's cool so then +you can build the transaction sign them + + align:start position:0% +you can build the transaction sign them + + + align:start position:0% +you can build the transaction sign them +and send them on the server so what are + + align:start position:0% +and send them on the server so what are + + + align:start position:0% +and send them on the server so what are +some advantages and disadvantages of + + align:start position:0% +some advantages and disadvantages of + + + align:start position:0% +some advantages and disadvantages of +this there's probably some obvious + + align:start position:0% +this there's probably some obvious + + + align:start position:0% +this there's probably some obvious +disadvantages right and then you would + + align:start position:0% +disadvantages right and then you would + + + align:start position:0% +disadvantages right and then you would +think of an attack this does not help + + align:start position:0% +think of an attack this does not help + + + align:start position:0% +think of an attack this does not help +you against the server can just say hey + + align:start position:0% +you against the server can just say hey + + + align:start position:0% +you against the server can just say hey +you got the thousand bitcoins you're + + align:start position:0% +you got the thousand bitcoins you're + + + align:start position:0% +you got the thousand bitcoins you're +like awesome but it's just completely + + align:start position:0% +like awesome but it's just completely + + + align:start position:0% +like awesome but it's just completely +made-up right you you you don't verify + + align:start position:0% +made-up right you you you don't verify + + + align:start position:0% +made-up right you you you don't verify +as the client you don't verify anything + + align:start position:0% +as the client you don't verify anything + + + align:start position:0% +as the client you don't verify anything +about these transactions so that's a + + align:start position:0% +about these transactions so that's a + + + align:start position:0% +about these transactions so that's a +pretty big problem and and the thing is + + align:start position:0% +pretty big problem and and the thing is + + + align:start position:0% +pretty big problem and and the thing is +in practice like one of the issues is + + align:start position:0% +in practice like one of the issues is + + + align:start position:0% +in practice like one of the issues is +that people are generally not as aware + + align:start position:0% +that people are generally not as aware + + + align:start position:0% +that people are generally not as aware +of these types of attacks because mostly + + align:start position:0% +of these types of attacks because mostly + + + align:start position:0% +of these types of attacks because mostly +people worry about spending their money + + align:start position:0% +people worry about spending their money + + + align:start position:0% +people worry about spending their money +and they don't really you know merchants + + align:start position:0% +and they don't really you know merchants + + + align:start position:0% +and they don't really you know merchants +worry about charge backs and worry about + + align:start position:0% +worry about charge backs and worry about + + + align:start position:0% +worry about charge backs and worry about +receiving and verifying that they've + + align:start position:0% +receiving and verifying that they've + + + align:start position:0% +receiving and verifying that they've +received funds all the time but most + + align:start position:0% +received funds all the time but most + + + align:start position:0% +received funds all the time but most +people's experience is you know they get + + align:start position:0% +people's experience is you know they get + + + align:start position:0% +people's experience is you know they get +paid once a month or twice a month with + + align:start position:0% +paid once a month or twice a month with + + + align:start position:0% +paid once a month or twice a month with +a paycheck and the money shows up in + + align:start position:0% +a paycheck and the money shows up in + + + align:start position:0% +a paycheck and the money shows up in +their bank or whatever and they never + + align:start position:0% +their bank or whatever and they never + + + align:start position:0% +their bank or whatever and they never +really worry about that and they worry + + align:start position:0% +really worry about that and they worry + + + align:start position:0% +really worry about that and they worry +about spending their money and getting + + align:start position:0% +about spending their money and getting + + + align:start position:0% +about spending their money and getting +defrauded or things like that so it's + + align:start position:0% +defrauded or things like that so it's + + + align:start position:0% +defrauded or things like that so it's +not something a lot of people think + + align:start position:0% +not something a lot of people think + + + align:start position:0% +not something a lot of people think +about all the time is + + align:start position:0% +about all the time is + + + align:start position:0% +about all the time is +did I actually get paid so there you + + align:start position:0% +did I actually get paid so there you + + + align:start position:0% +did I actually get paid so there you +know there's easy fraud that you can do + + align:start position:0% +know there's easy fraud that you can do + + + align:start position:0% +know there's easy fraud that you can do +with this kind of attack vector where + + align:start position:0% +with this kind of attack vector where + + + align:start position:0% +with this kind of attack vector where +you know you sell a car on Craigslist + + align:start position:0% +you know you sell a car on Craigslist + + + align:start position:0% +you know you sell a car on Craigslist +and someone comes and says yeah I paid + + align:start position:0% +and someone comes and says yeah I paid + + + align:start position:0% +and someone comes and says yeah I paid +you the bitcoins but they've actually + + align:start position:0% +you the bitcoins but they've actually + + + align:start position:0% +you the bitcoins but they've actually +compromised the server and you haven't + + align:start position:0% +compromised the server and you haven't + + + align:start position:0% +compromised the server and you haven't +gotten paid at all but you think you + + align:start position:0% +gotten paid at all but you think you + + + align:start position:0% +gotten paid at all but you think you +have you give over the goods so yeah + + align:start position:0% +have you give over the goods so yeah + + + align:start position:0% +have you give over the goods so yeah +potential problems they can say you got + + align:start position:0% +potential problems they can say you got + + + align:start position:0% +potential problems they can say you got +paid when you didn't they can say you + + align:start position:0% +paid when you didn't they can say you + + + align:start position:0% +paid when you didn't they can say you +lost money when you didn't and if it's + + align:start position:0% +lost money when you didn't and if it's + + + align:start position:0% +lost money when you didn't and if it's +in a browser that's even more fun + + align:start position:0% +in a browser that's even more fun + + + align:start position:0% +in a browser that's even more fun +because they can change the code without + + align:start position:0% +because they can change the code without + + + align:start position:0% +because they can change the code without +you know the javascript is not pinned to + + align:start position:0% +you know the javascript is not pinned to + + + align:start position:0% +you know the javascript is not pinned to +anything so if someone compromises that + + align:start position:0% +anything so if someone compromises that + + + align:start position:0% +anything so if someone compromises that +server they can change the code and + + align:start position:0% +server they can change the code and + + + align:start position:0% +server they can change the code and +potentially get your private keys so so + + align:start position:0% +potentially get your private keys so so + + + align:start position:0% +potentially get your private keys so so +you have really very little security the + + align:start position:0% +you have really very little security the + + + align:start position:0% +you have really very little security the +blockchain is not really providing + + align:start position:0% +blockchain is not really providing + + + align:start position:0% +blockchain is not really providing +anything in this case however this is + + align:start position:0% +anything in this case however this is + + + align:start position:0% +anything in this case however this is +one of them this is much more popular + + align:start position:0% +one of them this is much more popular + + + align:start position:0% +one of them this is much more popular +than running a full or svv node because + + align:start position:0% +than running a full or svv node because + + + align:start position:0% +than running a full or svv node because +you know blockchain and info you just + + align:start position:0% +you know blockchain and info you just + + + align:start position:0% +you know blockchain and info you just +sign in there's a lot of wallets on the + + align:start position:0% +sign in there's a lot of wallets on the + + + align:start position:0% +sign in there's a lot of wallets on the +phones that work this way as well and + + align:start position:0% +phones that work this way as well and + + + align:start position:0% +phones that work this way as well and +you do at least have your private keys + + align:start position:0% +you do at least have your private keys + + + align:start position:0% +you do at least have your private keys +right hopefully so you've got that right + + align:start position:0% +right hopefully so you've got that right + + + align:start position:0% +right hopefully so you've got that right +you're you're not giving custody in any + + align:start position:0% +you're you're not giving custody in any + + + align:start position:0% +you're you're not giving custody in any +sense to them but they learn a lot of + + align:start position:0% +sense to them but they learn a lot of + + + align:start position:0% +sense to them but they learn a lot of +information okay so not even SPV can we + + align:start position:0% +information okay so not even SPV can we + + + align:start position:0% +information okay so not even SPV can we +do worse and wait you someone yeah + + align:start position:0% +do worse and wait you someone yeah + + + align:start position:0% +do worse and wait you someone yeah +coinbase + + align:start position:0% +coinbase + + + align:start position:0% +coinbase +well so the coin base company who is an + + align:start position:0% +well so the coin base company who is an + + + align:start position:0% +well so the coin base company who is an +example of can we do worse yes you can + + align:start position:0% +example of can we do worse yes you can + + + align:start position:0% +example of can we do worse yes you can +someone else's coins is worse the case + + align:start position:0% +someone else's coins is worse the case + + + align:start position:0% +someone else's coins is worse the case +where my dad you know said hey can you + + align:start position:0% +where my dad you know said hey can you + + + align:start position:0% +where my dad you know said hey can you +hold on to these coins for me it's worse + + align:start position:0% +hold on to these coins for me it's worse + + + align:start position:0% +hold on to these coins for me it's worse +right he doesn't run a node he doesn't + + align:start position:0% +right he doesn't run a node he doesn't + + + align:start position:0% +right he doesn't run a node he doesn't +have his private keys he doesn't really + + align:start position:0% +have his private keys he doesn't really + + + align:start position:0% +have his private keys he doesn't really +understand Bitcoin that well he wants to + + align:start position:0% +understand Bitcoin that well he wants to + + + align:start position:0% +understand Bitcoin that well he wants to +but he's busy and he's like hey you know + + align:start position:0% +but he's busy and he's like hey you know + + + align:start position:0% +but he's busy and he's like hey you know +this stuff you deal with it I you know + + align:start position:0% +this stuff you deal with it I you know + + + align:start position:0% +this stuff you deal with it I you know +way more about this than I do + + align:start position:0% +way more about this than I do + + + align:start position:0% +way more about this than I do +I trust you since you know were dad and + + align:start position:0% +I trust you since you know were dad and + + + align:start position:0% +I trust you since you know were dad and +son and stuff so like not a huge trust + + align:start position:0% +son and stuff so like not a huge trust + + + align:start position:0% +son and stuff so like not a huge trust +problem there so I do it for but you + + align:start position:0% +problem there so I do it for but you + + + align:start position:0% +problem there so I do it for but you +know banks right you don't even have so + + align:start position:0% +know banks right you don't even have so + + + align:start position:0% +know banks right you don't even have so +the idea of a site or an exchange or + + align:start position:0% +the idea of a site or an exchange or + + + align:start position:0% +the idea of a site or an exchange or +think something like this where you + + align:start position:0% +think something like this where you + + + align:start position:0% +think something like this where you +don't even have your private keys + + align:start position:0% +don't even have your private keys + + + align:start position:0% +don't even have your private keys +you just have a website where they run a + + align:start position:0% +you just have a website where they run a + + + align:start position:0% +you just have a website where they run a +node arrow and a wallet and they owe you + + align:start position:0% +node arrow and a wallet and they owe you + + + align:start position:0% +node arrow and a wallet and they owe you +the money it tends to end badly and it + + align:start position:0% +the money it tends to end badly and it + + + align:start position:0% +the money it tends to end badly and it +you know even if it doesn't end badly it + + align:start position:0% +you know even if it doesn't end badly it + + + align:start position:0% +you know even if it doesn't end badly it +misses the point right the whole idea of + + align:start position:0% +misses the point right the whole idea of + + + align:start position:0% +misses the point right the whole idea of +Bitcoin was like hey you can sort of + + align:start position:0% +Bitcoin was like hey you can sort of + + + align:start position:0% +Bitcoin was like hey you can sort of +have your own + + align:start position:0% +have your own + + + align:start position:0% +have your own +money it's kind of cool it's running on + + align:start position:0% +money it's kind of cool it's running on + + + align:start position:0% +money it's kind of cool it's running on +your computer it feels like it's missing + + align:start position:0% +your computer it feels like it's missing + + + align:start position:0% +your computer it feels like it's missing +the point to just hand it over to some + + align:start position:0% +the point to just hand it over to some + + + align:start position:0% +the point to just hand it over to some +bank it's not even a bank right most of + + align:start position:0% +bank it's not even a bank right most of + + + align:start position:0% +bank it's not even a bank right most of +these sites a big reason why it tends to + + align:start position:0% +these sites a big reason why it tends to + + + align:start position:0% +these sites a big reason why it tends to +end badly is there aren't the same + + align:start position:0% +end badly is there aren't the same + + + align:start position:0% +end badly is there aren't the same +protections that banks you know the + + align:start position:0% +protections that banks you know the + + + align:start position:0% +protections that banks you know the +banks have to do a lot of work and + + align:start position:0% +banks have to do a lot of work and + + + align:start position:0% +banks have to do a lot of work and +there's FDIC there's all sorts of rules + + align:start position:0% +there's FDIC there's all sorts of rules + + + align:start position:0% +there's FDIC there's all sorts of rules +and and they also build these big + + align:start position:0% +and and they also build these big + + + align:start position:0% +and and they also build these big +structures it's really heavy stone + + align:start position:0% +structures it's really heavy stone + + + align:start position:0% +structures it's really heavy stone +pillars so you're like yeah they can't + + align:start position:0% +pillars so you're like yeah they can't + + + align:start position:0% +pillars so you're like yeah they can't +run off because this banks not gonna + + align:start position:0% +run off because this banks not gonna + + + align:start position:0% +run off because this banks not gonna +move its me other rocks in the banks in + + align:start position:0% +move its me other rocks in the banks in + + + align:start position:0% +move its me other rocks in the banks in +Bitcoin do not have big stone pillars IP + + align:start position:0% +Bitcoin do not have big stone pillars IP + + + align:start position:0% +Bitcoin do not have big stone pillars IP +addresses are really easy to change and + + align:start position:0% +addresses are really easy to change and + + + align:start position:0% +addresses are really easy to change and +just move the computers around another + + align:start position:0% +just move the computers around another + + + align:start position:0% +just move the computers around another +thing they're running a node right these + + align:start position:0% +thing they're running a node right these + + + align:start position:0% +thing they're running a node right these +these Bitcoin banks that hold all your + + align:start position:0% +these Bitcoin banks that hold all your + + + align:start position:0% +these Bitcoin banks that hold all your +funds sometimes they don't + + align:start position:0% +funds sometimes they don't + + + align:start position:0% +funds sometimes they don't +so these banks themselves might run sqv + + align:start position:0% +so these banks themselves might run sqv + + + align:start position:0% +so these banks themselves might run sqv +nodes or API things I don't want to like + + align:start position:0% +nodes or API things I don't want to like + + + align:start position:0% +nodes or API things I don't want to like +name any names but like there's pretty + + align:start position:0% +name any names but like there's pretty + + + align:start position:0% +name any names but like there's pretty +good evidence that like you know big + + align:start position:0% +good evidence that like you know big + + + align:start position:0% +good evidence that like you know big +exchanges might even just connect to an + + align:start position:0% +exchanges might even just connect to an + + + align:start position:0% +exchanges might even just connect to an +API and not even run their own node + + align:start position:0% +API and not even run their own node + + + align:start position:0% +API and not even run their own node +another there's a lot of things like + + align:start position:0% +another there's a lot of things like + + + align:start position:0% +another there's a lot of things like +this where when something bad doesn't + + align:start position:0% +this where when something bad doesn't + + + align:start position:0% +this where when something bad doesn't +happen people just keep pushing it where + + align:start position:0% +happen people just keep pushing it where + + + align:start position:0% +happen people just keep pushing it where +miners themselves don't verify the + + align:start position:0% +miners themselves don't verify the + + + align:start position:0% +miners themselves don't verify the +blocks because they think well you must + + align:start position:0% +blocks because they think well you must + + + align:start position:0% +blocks because they think well you must +have created a valid block and I'm not + + align:start position:0% +have created a valid block and I'm not + + + align:start position:0% +have created a valid block and I'm not +gonna verify it and everything works so + + align:start position:0% +gonna verify it and everything works so + + + align:start position:0% +gonna verify it and everything works so +the other thing is while well it sounds + + align:start position:0% +the other thing is while well it sounds + + + align:start position:0% +the other thing is while well it sounds +really bad + + align:start position:0% +really bad + + + align:start position:0% +really bad +in practice there haven't been really + + align:start position:0% +in practice there haven't been really + + + align:start position:0% +in practice there haven't been really +many SPV attacks or API attacks right we + + align:start position:0% +many SPV attacks or API attacks right we + + + align:start position:0% +many SPV attacks or API attacks right we +know of this but in practice it's it's + + align:start position:0% +know of this but in practice it's it's + + + align:start position:0% +know of this but in practice it's it's +hard to do right you're if you want to + + align:start position:0% +hard to do right you're if you want to + + + align:start position:0% +hard to do right you're if you want to +defraud someone with say the you know by + + align:start position:0% +defraud someone with say the you know by + + + align:start position:0% +defraud someone with say the you know by +compromising watching on info you have + + align:start position:0% +compromising watching on info you have + + + align:start position:0% +compromising watching on info you have +to compromise blockchain on info you + + align:start position:0% +to compromise blockchain on info you + + + align:start position:0% +to compromise blockchain on info you +don't have to do all the proof of work + + align:start position:0% +don't have to do all the proof of work + + + align:start position:0% +don't have to do all the proof of work +because they're not validating it but + + align:start position:0% +because they're not validating it but + + + align:start position:0% +because they're not validating it but +it's still hard to do and you know it + + align:start position:0% +it's still hard to do and you know it + + + align:start position:0% +it's still hard to do and you know it +requires a coordinated active attacker + + align:start position:0% +requires a coordinated active attacker + + + align:start position:0% +requires a coordinated active attacker +with quite a bit of resources and so + + align:start position:0% +with quite a bit of resources and so + + + align:start position:0% +with quite a bit of resources and so +when it doesn't happen people say well + + align:start position:0% +when it doesn't happen people say well + + + align:start position:0% +when it doesn't happen people say well +sPB's just as good right we don't have + + align:start position:0% +sPB's just as good right we don't have + + + align:start position:0% +sPB's just as good right we don't have +any evidence of people being defrauded + + align:start position:0% +any evidence of people being defrauded + + + align:start position:0% +any evidence of people being defrauded +so it's just as good but that is kind of + + align:start position:0% +so it's just as good but that is kind of + + + align:start position:0% +so it's just as good but that is kind of +dangerous because when everyone starts + + align:start position:0% +dangerous because when everyone starts + + + align:start position:0% +dangerous because when everyone starts +doing it you start to lose these + + align:start position:0% +doing it you start to lose these + + + align:start position:0% +doing it you start to lose these +protections any questions about the + + align:start position:0% +protections any questions about the + + + align:start position:0% +protections any questions about the +someone else's coins model + + align:start position:0% +someone else's coins model + + + align:start position:0% +someone else's coins model +there's all sorts of legal issues + + align:start position:0% +there's all sorts of legal issues + + + align:start position:0% +there's all sorts of legal issues +there's a very long list of ways it ends + + align:start position:0% +there's a very long list of ways it ends + + + align:start position:0% +there's a very long list of ways it ends +badly I don't know what what is the + + align:start position:0% +badly I don't know what what is the + + + align:start position:0% +badly I don't know what what is the +half-life of a custodial exchange in + + align:start position:0% +half-life of a custodial exchange in + + + align:start position:0% +half-life of a custodial exchange in +Bitcoin it's like a year or two and they + + align:start position:0% +Bitcoin it's like a year or two and they + + + align:start position:0% +Bitcoin it's like a year or two and they +they drop off okay so why do people do + + align:start position:0% +they drop off okay so why do people do + + + align:start position:0% +they drop off okay so why do people do +this + + align:start position:0% +this + + + align:start position:0% +this +and here's sort of a table of trade-offs + + align:start position:0% +and here's sort of a table of trade-offs + + + align:start position:0% +and here's sort of a table of trade-offs +with these things it's mainly + + align:start position:0% +with these things it's mainly + + + align:start position:0% +with these things it's mainly +convenience and so that's you know it's + + align:start position:0% +convenience and so that's you know it's + + + align:start position:0% +convenience and so that's you know it's +a real reason to do it so if you're + + align:start position:0% +a real reason to do it so if you're + + + align:start position:0% +a real reason to do it so if you're +running a full node you're gonna have to + + align:start position:0% +running a full node you're gonna have to + + + align:start position:0% +running a full node you're gonna have to +download at least 170 gigabytes that's a + + align:start position:0% +download at least 170 gigabytes that's a + + + align:start position:0% +download at least 170 gigabytes that's a +lot right it's gonna take a while + + align:start position:0% +lot right it's gonna take a while + + + align:start position:0% +lot right it's gonna take a while +storage you're gonna have to store at + + align:start position:0% +storage you're gonna have to store at + + + align:start position:0% +storage you're gonna have to store at +least 4 gigabytes like long term and it + + align:start position:0% +least 4 gigabytes like long term and it + + + align:start position:0% +least 4 gigabytes like long term and it +that's going up but not going up too + + align:start position:0% +that's going up but not going up too + + + align:start position:0% +that's going up but not going up too +much it's actually gone down the last + + align:start position:0% +much it's actually gone down the last + + + align:start position:0% +much it's actually gone down the last +few weeks that's sort of the UT exocet + + align:start position:0% +few weeks that's sort of the UT exocet + + + align:start position:0% +few weeks that's sort of the UT exocet +right you have to keep track of you + + align:start position:0% +right you have to keep track of you + + + align:start position:0% +right you have to keep track of you +don't have to keep track of this hundred + + align:start position:0% +don't have to keep track of this hundred + + + align:start position:0% +don't have to keep track of this hundred +70 gigabytes it by default does but you + + align:start position:0% +70 gigabytes it by default does but you + + + align:start position:0% +70 gigabytes it by default does but you +can turn on pruning but that's also + + align:start position:0% +can turn on pruning but that's also + + + align:start position:0% +can turn on pruning but that's also +super user unfriendly you have to edit a + + align:start position:0% +super user unfriendly you have to edit a + + + align:start position:0% +super user unfriendly you have to edit a +Bitcoin comm file and type pruning + + align:start position:0% +Bitcoin comm file and type pruning + + + align:start position:0% +Bitcoin comm file and type pruning +equals 500 or something and then save it + + align:start position:0% +equals 500 or something and then save it + + + align:start position:0% +equals 500 or something and then save it +and then it'll prune down to four gigs + + align:start position:0% +and then it'll prune down to four gigs + + + align:start position:0% +and then it'll prune down to four gigs +there's no at least that I'm aware of + + align:start position:0% +there's no at least that I'm aware of + + + align:start position:0% +there's no at least that I'm aware of +there's no GUI nice menu thing where you + + align:start position:0% +there's no GUI nice menu thing where you + + + align:start position:0% +there's no GUI nice menu thing where you +can say hey I want to enable pruning I + + align:start position:0% +can say hey I want to enable pruning I + + + align:start position:0% +can say hey I want to enable pruning I +don't have to store this speed on a + + align:start position:0% +don't have to store this speed on a + + + align:start position:0% +don't have to store this speed on a +really nice computer it will take at + + align:start position:0% +really nice computer it will take at + + + align:start position:0% +really nice computer it will take at +least six hours to download all this and + + align:start position:0% +least six hours to download all this and + + + align:start position:0% +least six hours to download all this and +verify it it's pretty impressive because + + align:start position:0% +verify it it's pretty impressive because + + + align:start position:0% +verify it it's pretty impressive because +it used to be more but that's still six + + align:start position:0% +it used to be more but that's still six + + + align:start position:0% +it used to be more but that's still six +hours people don't want to deal with + + align:start position:0% +hours people don't want to deal with + + + align:start position:0% +hours people don't want to deal with +that privacy okay certainly we can do + + align:start position:0% +that privacy okay certainly we can do + + + align:start position:0% +that privacy okay certainly we can do +better there's a lot of research on how + + align:start position:0% +better there's a lot of research on how + + + align:start position:0% +better there's a lot of research on how +to make privacy and Bitcoin better but + + align:start position:0% +to make privacy and Bitcoin better but + + + align:start position:0% +to make privacy and Bitcoin better but +this is what we got you know it's okay + + align:start position:0% +this is what we got you know it's okay + + + align:start position:0% +this is what we got you know it's okay +security okay we you know this is as + + align:start position:0% +security okay we you know this is as + + + align:start position:0% +security okay we you know this is as +good as we've got okay so then you go + + align:start position:0% +good as we've got okay so then you go + + + align:start position:0% +good as we've got okay so then you go +down to SBB network you only have to + + align:start position:0% +down to SBB network you only have to + + + align:start position:0% +down to SBB network you only have to +download about 50 Meg's all those + + align:start position:0% +download about 50 Meg's all those + + + align:start position:0% +download about 50 Meg's all those +headers if you've got a wallet with lots + + align:start position:0% +headers if you've got a wallet with lots + + + align:start position:0% +headers if you've got a wallet with lots +of transactions you're gonna download + + align:start position:0% +of transactions you're gonna download + + + align:start position:0% +of transactions you're gonna download +100 200 300 Meg's is you're gonna have + + align:start position:0% +100 200 300 Meg's is you're gonna have + + + align:start position:0% +100 200 300 Meg's is you're gonna have +to download all the transactions that + + align:start position:0% +to download all the transactions that + + + align:start position:0% +to download all the transactions that +you you know that pay you or you're + + align:start position:0% +you you know that pay you or you're + + + align:start position:0% +you you know that pay you or you're +paying out to speed I said seconds I + + align:start position:0% +paying out to speed I said seconds I + + + align:start position:0% +paying out to speed I said seconds I +think I want to change it to minutes I + + align:start position:0% +think I want to change it to minutes I + + + align:start position:0% +think I want to change it to minutes I +don't know it's not it's not that fast + + align:start position:0% +don't know it's not it's not that fast + + + align:start position:0% +don't know it's not it's not that fast +it's it's a lot faster + + align:start position:0% +it's it's a lot faster + + + align:start position:0% +it's it's a lot faster +I think seconds is an exaggeration well + + align:start position:0% +I think seconds is an exaggeration well + + + align:start position:0% +I think seconds is an exaggeration well +it's like 60 second + + align:start position:0% +it's like 60 second + + + align:start position:0% +it's like 60 second +it's pretty fast right you download all + + align:start position:0% +it's pretty fast right you download all + + + align:start position:0% +it's pretty fast right you download all +the headers that takes the same amount + + align:start position:0% +the headers that takes the same amount + + + align:start position:0% +the headers that takes the same amount +of time but that can be a minute or two + + align:start position:0% +of time but that can be a minute or two + + + align:start position:0% +of time but that can be a minute or two +and then you're sinking the blocks it's + + align:start position:0% +and then you're sinking the blocks it's + + + align:start position:0% +and then you're sinking the blocks it's +really quick they're small privacy is + + align:start position:0% +really quick they're small privacy is + + + align:start position:0% +really quick they're small privacy is +poor right you you lose a lot of your + + align:start position:0% +poor right you you lose a lot of your + + + align:start position:0% +poor right you you lose a lot of your +privacy in SPV because you're basically + + align:start position:0% +privacy in SPV because you're basically + + + align:start position:0% +privacy in SPV because you're basically +telling random computers on the Internet + + align:start position:0% +telling random computers on the Internet + + + align:start position:0% +telling random computers on the Internet +hey here's all my money and here's all + + align:start position:0% +hey here's all my money and here's all + + + align:start position:0% +hey here's all my money and here's all +my addresses there's it's not you're not + + align:start position:0% +my addresses there's it's not you're not + + + align:start position:0% +my addresses there's it's not you're not +completely losing everything but but + + align:start position:0% +completely losing everything but but + + + align:start position:0% +completely losing everything but but +it's pretty easy for actors to + + align:start position:0% +it's pretty easy for actors to + + + align:start position:0% +it's pretty easy for actors to +reconstruct your wallet from that + + align:start position:0% +reconstruct your wallet from that + + + align:start position:0% +reconstruct your wallet from that +security medium I don't know it's there + + align:start position:0% +security medium I don't know it's there + + + align:start position:0% +security medium I don't know it's there +haven't been any real attacks on this + + align:start position:0% +haven't been any real attacks on this + + + align:start position:0% +haven't been any real attacks on this +but you're not verifying the rules of + + align:start position:0% +but you're not verifying the rules of + + + align:start position:0% +but you're not verifying the rules of +Bitcoin right if everyone's running SPV + + align:start position:0% +Bitcoin right if everyone's running SPV + + + align:start position:0% +Bitcoin right if everyone's running SPV +then a minor can say hey I just + + align:start position:0% +then a minor can say hey I just + + + align:start position:0% +then a minor can say hey I just +generated a thousand coins out of + + align:start position:0% +generated a thousand coins out of + + + align:start position:0% +generated a thousand coins out of +nowhere and no one's looking for that + + align:start position:0% +nowhere and no one's looking for that + + + align:start position:0% +nowhere and no one's looking for that +transaction it only pays me and no one's + + align:start position:0% +transaction it only pays me and no one's + + + align:start position:0% +transaction it only pays me and no one's +gonna see that and reject the block + + align:start position:0% +gonna see that and reject the block + + + align:start position:0% +gonna see that and reject the block +right so so if everyone runs SPV you're + + align:start position:0% +right so so if everyone runs SPV you're + + + align:start position:0% +right so so if everyone runs SPV you're +sort of not checking up on the miners + + align:start position:0% +sort of not checking up on the miners + + + align:start position:0% +sort of not checking up on the miners +which is a very real threat like miners + + align:start position:0% +which is a very real threat like miners + + + align:start position:0% +which is a very real threat like miners +do crazy stuff and you gotta watch out + + align:start position:0% +do crazy stuff and you gotta watch out + + + align:start position:0% +do crazy stuff and you gotta watch out +for that yeah so security question API + + align:start position:0% +for that yeah so security question API + + + align:start position:0% +for that yeah so security question API +query where you just ask a website hey + + align:start position:0% +query where you just ask a website hey + + + align:start position:0% +query where you just ask a website hey +here's all my addresses how much money + + align:start position:0% +here's all my addresses how much money + + + align:start position:0% +here's all my addresses how much money +do I have network traffic I don't know + + align:start position:0% +do I have network traffic I don't know + + + align:start position:0% +do I have network traffic I don't know +less than a megabyte you have to load + + align:start position:0% +less than a megabyte you have to load + + + align:start position:0% +less than a megabyte you have to load +the websites and stuff but it's pretty + + align:start position:0% +the websites and stuff but it's pretty + + + align:start position:0% +the websites and stuff but it's pretty +light storage you basically don't have + + align:start position:0% +light storage you basically don't have + + + align:start position:0% +light storage you basically don't have +to store anything I mean you have to + + align:start position:0% +to store anything I mean you have to + + + align:start position:0% +to store anything I mean you have to +store your private keys but those can be + + align:start position:0% +store your private keys but those can be + + + align:start position:0% +store your private keys but those can be +sort of password based and derived on + + align:start position:0% +sort of password based and derived on + + + align:start position:0% +sort of password based and derived on +the fly speed like a second right it's + + align:start position:0% +the fly speed like a second right it's + + + align:start position:0% +the fly speed like a second right it's +real quick you're you're making an HTTP + + align:start position:0% +real quick you're you're making an HTTP + + + align:start position:0% +real quick you're you're making an HTTP +query you're getting a response you're + + align:start position:0% +query you're getting a response you're + + + align:start position:0% +query you're getting a response you're +parsing it it's real quick + + align:start position:0% +parsing it it's real quick + + + align:start position:0% +parsing it it's real quick +privacy is poor it's worse than svv but + + align:start position:0% +privacy is poor it's worse than svv but + + + align:start position:0% +privacy is poor it's worse than svv but +because it's like now it's really easy + + align:start position:0% +because it's like now it's really easy + + + align:start position:0% +because it's like now it's really easy +because they just you just hand them + + align:start position:0% +because they just you just hand them + + + align:start position:0% +because they just you just hand them +over over all your addresses in the + + align:start position:0% +over over all your addresses in the + + + align:start position:0% +over over all your addresses in the +clear and security is also quite poor + + align:start position:0% +clear and security is also quite poor + + + align:start position:0% +clear and security is also quite poor +right in that they can say hey you got + + align:start position:0% +right in that they can say hey you got + + + align:start position:0% +right in that they can say hey you got +money or you lost money and you just + + align:start position:0% +money or you lost money and you just + + + align:start position:0% +money or you lost money and you just +accept what they say hold my key + + align:start position:0% +accept what they say hold my key + + + align:start position:0% +accept what they say hold my key +this is network traffic I don't know you + + align:start position:0% +this is network traffic I don't know you + + + align:start position:0% +this is network traffic I don't know you +have to go to a website I guess there's + + align:start position:0% +have to go to a website I guess there's + + + align:start position:0% +have to go to a website I guess there's +no storage there's no speed there's no + + align:start position:0% +no storage there's no speed there's no + + + align:start position:0% +no storage there's no speed there's no +privacy there's no security you're just + + align:start position:0% +privacy there's no security you're just + + + align:start position:0% +privacy there's no security you're just +handing the entire thing off to someone + + align:start position:0% +handing the entire thing off to someone + + + align:start position:0% +handing the entire thing off to someone +else so what + + align:start position:0% +else so what + + + align:start position:0% +else so what +what would you guys guess are the most + + align:start position:0% +what would you guys guess are the most + + + align:start position:0% +what would you guys guess are the most +liked popularity of the different models + + align:start position:0% +liked popularity of the different models + + + align:start position:0% +liked popularity of the different models +most popular least popular yeah this is + + align:start position:0% +most popular least popular yeah this is + + + align:start position:0% +most popular least popular yeah this is +definitely the most popular second most + + align:start position:0% +definitely the most popular second most + + + align:start position:0% +definitely the most popular second most +third mouth force mode yeah so it + + align:start position:0% +third mouth force mode yeah so it + + + align:start position:0% +third mouth force mode yeah so it +everyone does this people do this people + + align:start position:0% +everyone does this people do this people + + + align:start position:0% +everyone does this people do this people +do this a couple thousand people do this + + align:start position:0% +do this a couple thousand people do this + + + align:start position:0% +do this a couple thousand people do this +it's a problem and this is something + + align:start position:0% +it's a problem and this is something + + + align:start position:0% +it's a problem and this is something +like that is one of the ongoing problems + + align:start position:0% +like that is one of the ongoing problems + + + align:start position:0% +like that is one of the ongoing problems +not just in Bitcoin aetherium if your + + align:start position:0% +not just in Bitcoin aetherium if your + + + align:start position:0% +not just in Bitcoin aetherium if your +name would be a little different but + + align:start position:0% +name would be a little different but + + + align:start position:0% +name would be a little different but +still it's gonna be a lot of this sort + + align:start position:0% +still it's gonna be a lot of this sort + + + align:start position:0% +still it's gonna be a lot of this sort +of weird different SPV there's there's + + align:start position:0% +of weird different SPV there's there's + + + align:start position:0% +of weird different SPV there's there's +like other s models there's sort of one + + align:start position:0% +like other s models there's sort of one + + + align:start position:0% +like other s models there's sort of one +in the middle for aetherium that's also + + align:start position:0% +in the middle for aetherium that's also + + + align:start position:0% +in the middle for aetherium that's also +quite popular oh it's like STV with UT + + align:start position:0% +quite popular oh it's like STV with UT + + + align:start position:0% +quite popular oh it's like STV with UT +EXO commitments well I guess it would be + + align:start position:0% +EXO commitments well I guess it would be + + + align:start position:0% +EXO commitments well I guess it would be +more here anyway I'm not gonna go but + + align:start position:0% +more here anyway I'm not gonna go but + + + align:start position:0% +more here anyway I'm not gonna go but +yeah so it's it's a problem and like + + align:start position:0% +yeah so it's it's a problem and like + + + align:start position:0% +yeah so it's it's a problem and like +there's different ways to attack it like + + align:start position:0% +there's different ways to attack it like + + + align:start position:0% +there's different ways to attack it like +one of the issues is with a lot of + + align:start position:0% +one of the issues is with a lot of + + + align:start position:0% +one of the issues is with a lot of +people who program Bitcoin itself really + + align:start position:0% +people who program Bitcoin itself really + + + align:start position:0% +people who program Bitcoin itself really +only focus on this and they say look + + align:start position:0% +only focus on this and they say look + + + align:start position:0% +only focus on this and they say look +we're not this is not our problem right + + align:start position:0% +we're not this is not our problem right + + + align:start position:0% +we're not this is not our problem right +like we don't we can't solve this we're + + align:start position:0% +like we don't we can't solve this we're + + + align:start position:0% +like we don't we can't solve this we're +gonna try to make this the way we're + + align:start position:0% +gonna try to make this the way we're + + + align:start position:0% +gonna try to make this the way we're +gonna try to solve this is to let's try + + align:start position:0% +gonna try to solve this is to let's try + + + align:start position:0% +gonna try to solve this is to let's try +to get the speed down right if it takes + + align:start position:0% +to get the speed down right if it takes + + + align:start position:0% +to get the speed down right if it takes +days people are gonna move this way if + + align:start position:0% +days people are gonna move this way if + + + align:start position:0% +days people are gonna move this way if +it takes hours maybe a lot of people say + + align:start position:0% +it takes hours maybe a lot of people say + + + align:start position:0% +it takes hours maybe a lot of people say +hey I was using SPV but yeah it's not + + align:start position:0% +hey I was using SPV but yeah it's not + + + align:start position:0% +hey I was using SPV but yeah it's not +too bad running this I'm gonna run this + + align:start position:0% +too bad running this I'm gonna run this + + + align:start position:0% +too bad running this I'm gonna run this +and get the more security let's try to + + align:start position:0% +and get the more security let's try to + + + align:start position:0% +and get the more security let's try to +keep this number down let's try to keep + + align:start position:0% +keep this number down let's try to keep + + + align:start position:0% +keep this number down let's try to keep +you know speed down let's try to improve + + align:start position:0% +you know speed down let's try to improve + + + align:start position:0% +you know speed down let's try to improve +privacy and security of the full node + + align:start position:0% +privacy and security of the full node + + + align:start position:0% +privacy and security of the full node +that is generally what most of the + + align:start position:0% +that is generally what most of the + + + align:start position:0% +that is generally what most of the +Bitcoin core developers focus on which + + align:start position:0% +Bitcoin core developers focus on which + + + align:start position:0% +Bitcoin core developers focus on which +you know I don't argue it but it does + + align:start position:0% +you know I don't argue it but it does + + + align:start position:0% +you know I don't argue it but it does +lead to some neglect of like the SPV + + align:start position:0% +lead to some neglect of like the SPV + + + align:start position:0% +lead to some neglect of like the SPV +where there's not you know that it's + + align:start position:0% +where there's not you know that it's + + + align:start position:0% +where there's not you know that it's +been over a year year and a half almost + + align:start position:0% +been over a year year and a half almost + + + align:start position:0% +been over a year year and a half almost +two years where we know how to make SPV + + align:start position:0% +two years where we know how to make SPV + + + align:start position:0% +two years where we know how to make SPV +better and more secure but there's not a + + align:start position:0% +better and more secure but there's not a + + + align:start position:0% +better and more secure but there's not a +lot of enthusiasm and people working on + + align:start position:0% +lot of enthusiasm and people working on + + + align:start position:0% +lot of enthusiasm and people working on +it + + align:start position:0% +it + + + align:start position:0% +it +and people argue about the security of + + align:start position:0% +and people argue about the security of + + + align:start position:0% +and people argue about the security of +these things this there's not much you + + align:start position:0% +these things this there's not much you + + + align:start position:0% +these things this there's not much you +can do I mean there is kind of + + align:start position:0% +can do I mean there is kind of + + + align:start position:0% +can do I mean there is kind of +cryptography research like hey how can I + + align:start position:0% +cryptography research like hey how can I + + + align:start position:0% +cryptography research like hey how can I +you know is there some cool way I can + + align:start position:0% +you know is there some cool way I can + + + align:start position:0% +you know is there some cool way I can +send you all my addresses so that you + + align:start position:0% +send you all my addresses so that you + + + align:start position:0% +send you all my addresses so that you +can figure out how much money I have + + align:start position:0% +can figure out how much money I have + + + align:start position:0% +can figure out how much money I have +without you learning all my addresses + + align:start position:0% +without you learning all my addresses + + + align:start position:0% +without you learning all my addresses +some kind of that's called private + + align:start position:0% +some kind of that's called private + + + align:start position:0% +some kind of that's called private +nation retrieval and there's all sorts + + align:start position:0% +nation retrieval and there's all sorts + + + align:start position:0% +nation retrieval and there's all sorts +of papers on that in practice there + + align:start position:0% +of papers on that in practice there + + + align:start position:0% +of papers on that in practice there +aren't any that used that and this well + + align:start position:0% +aren't any that used that and this well + + + align:start position:0% +aren't any that used that and this well +yeah multi-sig like have that's more + + align:start position:0% +yeah multi-sig like have that's more + + + align:start position:0% +yeah multi-sig like have that's more +like regulation right can we have sort + + align:start position:0% +like regulation right can we have sort + + + align:start position:0% +like regulation right can we have sort +of restrictions and rules on these + + align:start position:0% +of restrictions and rules on these + + + align:start position:0% +of restrictions and rules on these +essentially banks to try to make it + + align:start position:0% +essentially banks to try to make it + + + align:start position:0% +essentially banks to try to make it +safer + + align:start position:0% +safer + + + align:start position:0% +safer +maybe but yeah this is these are sort of + + align:start position:0% +maybe but yeah this is these are sort of + + + align:start position:0% +maybe but yeah this is these are sort of +the two where you know software + + align:start position:0% +the two where you know software + + + align:start position:0% +the two where you know software +development can definitely help you know + + align:start position:0% +development can definitely help you know + + + align:start position:0% +development can definitely help you know +make this a lot easier to use and so you + + align:start position:0% +make this a lot easier to use and so you + + + align:start position:0% +make this a lot easier to use and so you +know we can encourage people to use it + + align:start position:0% +know we can encourage people to use it + + + align:start position:0% +know we can encourage people to use it +but most people since Security's hard + + align:start position:0% +but most people since Security's hard + + + align:start position:0% +but most people since Security's hard +because most people if you don't see a + + align:start position:0% +because most people if you don't see a + + + align:start position:0% +because most people if you don't see a +problem this is a lot easier and a lot + + align:start position:0% +problem this is a lot easier and a lot + + + align:start position:0% +problem this is a lot easier and a lot +of people think well I'm not good at + + align:start position:0% +of people think well I'm not good at + + + align:start position:0% +of people think well I'm not good at +computers so they are and it's safer if + + align:start position:0% +computers so they are and it's safer if + + + align:start position:0% +computers so they are and it's safer if +I give all my money to someone else in + + align:start position:0% +I give all my money to someone else in + + + align:start position:0% +I give all my money to someone else in +in some cases it could be true but that + + align:start position:0% +in some cases it could be true but that + + + align:start position:0% +in some cases it could be true but that +has sort of systemic effects where now + + align:start position:0% +has sort of systemic effects where now + + + align:start position:0% +has sort of systemic effects where now +you've got these you know there's like + + align:start position:0% +you've got these you know there's like + + + align:start position:0% +you've got these you know there's like +five computers in the world and if + + align:start position:0% +five computers in the world and if + + + align:start position:0% +five computers in the world and if +you're able to compromise those like + + align:start position:0% +you're able to compromise those like + + + align:start position:0% +you're able to compromise those like +they have just billions of dollars worth + + align:start position:0% +they have just billions of dollars worth + + + align:start position:0% +they have just billions of dollars worth +of bitcoins on them and so that's why + + align:start position:0% +of bitcoins on them and so that's why + + + align:start position:0% +of bitcoins on them and so that's why +you know for for blackhat attacker + + align:start position:0% +you know for for blackhat attacker + + + align:start position:0% +you know for for blackhat attacker +hacker kind of people it's like the best + + align:start position:0% +hacker kind of people it's like the best + + + align:start position:0% +hacker kind of people it's like the best +thing to do it's like so I was like + + align:start position:0% +thing to do it's like so I was like + + + align:start position:0% +thing to do it's like so I was like +there's a computer somewhere and it's + + align:start position:0% +there's a computer somewhere and it's + + + align:start position:0% +there's a computer somewhere and it's +got a billion dollars of like + + align:start position:0% +got a billion dollars of like + + + align:start position:0% +got a billion dollars of like +untraceable money that I can just steal + + align:start position:0% +untraceable money that I can just steal + + + align:start position:0% +untraceable money that I can just steal +like it's what could be yeah I could get + + align:start position:0% +like it's what could be yeah I could get + + + align:start position:0% +like it's what could be yeah I could get +everyone's passwords that's cool or like + + align:start position:0% +everyone's passwords that's cool or like + + + align:start position:0% +everyone's passwords that's cool or like +yeah I could like read people's emails + + align:start position:0% +yeah I could like read people's emails + + + align:start position:0% +yeah I could like read people's emails +whatever or I can just steal a billion + + align:start position:0% +whatever or I can just steal a billion + + + align:start position:0% +whatever or I can just steal a billion +dollars like so what do you think + + align:start position:0% +dollars like so what do you think + + + align:start position:0% +dollars like so what do you think +they're gonna do so yeah so this leads + + align:start position:0% +they're gonna do so yeah so this leads + + + align:start position:0% +they're gonna do so yeah so this leads +to you know huge concentrations of coins + + align:start position:0% +to you know huge concentrations of coins + + + align:start position:0% +to you know huge concentrations of coins +on in a very small number of nodes and + + align:start position:0% +on in a very small number of nodes and + + + align:start position:0% +on in a very small number of nodes and +people try to attack it so this is sort + + align:start position:0% +people try to attack it so this is sort + + + align:start position:0% +people try to attack it so this is sort +of the landscape were in now it's + + align:start position:0% +of the landscape were in now it's + + + align:start position:0% +of the landscape were in now it's +certainly not ideal there's a lot of + + align:start position:0% +certainly not ideal there's a lot of + + + align:start position:0% +certainly not ideal there's a lot of +technology that's pretty good that's not + + align:start position:0% +technology that's pretty good that's not + + + align:start position:0% +technology that's pretty good that's not +being used there's a lot of technologies + + align:start position:0% +being used there's a lot of technologies + + + align:start position:0% +being used there's a lot of technologies +scrummy that's being used a lot and you + + align:start position:0% +scrummy that's being used a lot and you + + + align:start position:0% +scrummy that's being used a lot and you +know how to make this stronger and + + align:start position:0% +know how to make this stronger and + + + align:start position:0% +know how to make this stronger and +faster how to make this faster things + + align:start position:0% +faster how to make this faster things + + + align:start position:0% +faster how to make this faster things +like that are really interesting + + align:start position:0% +like that are really interesting + + + align:start position:0% +like that are really interesting +research areas working on ok and yeah + + align:start position:0% +research areas working on ok and yeah + + + align:start position:0% +research areas working on ok and yeah +almost done wallets are fun big + + align:start position:0% +almost done wallets are fun big + + + align:start position:0% +almost done wallets are fun big +usability issues try if you want to try + + align:start position:0% +usability issues try if you want to try + + + align:start position:0% +usability issues try if you want to try +test net wallets you can try downloading + + align:start position:0% +test net wallets you can try downloading + + + align:start position:0% +test net wallets you can try downloading +them playing around with them they often + + align:start position:0% +them playing around with them they often + + + align:start position:0% +them playing around with them they often +leave quite a bit to be desired the one + + align:start position:0% +leave quite a bit to be desired the one + + + align:start position:0% +leave quite a bit to be desired the one +work on lit leaves enormous amounts to + + align:start position:0% +work on lit leaves enormous amounts to + + + align:start position:0% +work on lit leaves enormous amounts to +be decided there's like it's all in text + + align:start position:0% +be decided there's like it's all in text + + + align:start position:0% +be decided there's like it's all in text +and Ethan should be here Wednesday and + + align:start position:0% +and Ethan should be here Wednesday and + + + align:start position:0% +and Ethan should be here Wednesday and +good luck with the problem set \ No newline at end of file diff --git a/n9eMl6uLZeU.txt b/n9eMl6uLZeU.txt new file mode 100644 index 0000000000000000000000000000000000000000..d7f4967d0c6b4541b75952e9342e50a9ad65e89c --- /dev/null +++ b/n9eMl6uLZeU.txt @@ -0,0 +1,1019 @@ +align:start position:0% + +have you ever wondered how diverse flow + + align:start position:0% +have you ever wondered how diverse flow + + + align:start position:0% +have you ever wondered how diverse flow +how fluids travel inside pipes watch + + align:start position:0% +how fluids travel inside pipes watch + + + align:start position:0% +how fluids travel inside pipes watch +this video and you will learn how if you + + align:start position:0% +this video and you will learn how if you + + + align:start position:0% +this video and you will learn how if you +apply Newton's second law to fluid + + align:start position:0% +apply Newton's second law to fluid + + + align:start position:0% +apply Newton's second law to fluid +motion and at the same time consider the + + align:start position:0% +motion and at the same time consider the + + + align:start position:0% +motion and at the same time consider the +viscosity of the fluid you will get the + + align:start position:0% +viscosity of the fluid you will get the + + + align:start position:0% +viscosity of the fluid you will get the +equations you need to describe fluid + + align:start position:0% +equations you need to describe fluid + + + align:start position:0% +equations you need to describe fluid +flow the equations that you get this way + + align:start position:0% +flow the equations that you get this way + + + align:start position:0% +flow the equations that you get this way +are called the navier-stokes equations + + align:start position:0% +are called the navier-stokes equations + + + align:start position:0% +are called the navier-stokes equations +this is the general form of the + + align:start position:0% +this is the general form of the + + + align:start position:0% +this is the general form of the +navier-stokes equations solving this + + align:start position:0% +navier-stokes equations solving this + + + align:start position:0% +navier-stokes equations solving this +equation in this form is not easy + + align:start position:0% +equation in this form is not easy + + + align:start position:0% +equation in this form is not easy +interestingly mathematicians have not + + align:start position:0% +interestingly mathematicians have not + + + align:start position:0% +interestingly mathematicians have not +yet proven that the solutions exist to + + align:start position:0% +yet proven that the solutions exist to + + + align:start position:0% +yet proven that the solutions exist to +the navier-stokes equations in three + + align:start position:0% +the navier-stokes equations in three + + + align:start position:0% +the navier-stokes equations in three +dimensions to make our life easy let's + + align:start position:0% +dimensions to make our life easy let's + + + align:start position:0% +dimensions to make our life easy let's +consider motion of a fluid in one + + align:start position:0% +consider motion of a fluid in one + + + align:start position:0% +consider motion of a fluid in one +dimension the navier-stokes equations + + align:start position:0% +dimension the navier-stokes equations + + + align:start position:0% +dimension the navier-stokes equations +then become this as you can see have + + align:start position:0% +then become this as you can see have + + + align:start position:0% +then become this as you can see have +broken down the previous problem in two + + align:start position:0% +broken down the previous problem in two + + + align:start position:0% +broken down the previous problem in two +dimensions into just one dimension the X + + align:start position:0% +dimensions into just one dimension the X + + + align:start position:0% +dimensions into just one dimension the X +dimension the main body force that is f + + align:start position:0% +dimension the main body force that is f + + + align:start position:0% +dimension the main body force that is f +X acting on a fluid will be the force + + align:start position:0% +X acting on a fluid will be the force + + + align:start position:0% +X acting on a fluid will be the force +due to gravity if the fluid is flowing + + align:start position:0% +due to gravity if the fluid is flowing + + + align:start position:0% +due to gravity if the fluid is flowing +at an angle theta to the horizontal then + + align:start position:0% +at an angle theta to the horizontal then + + + align:start position:0% +at an angle theta to the horizontal then +the component of gravity in the + + align:start position:0% +the component of gravity in the + + + align:start position:0% +the component of gravity in the +direction of fluid motion is going to be + + align:start position:0% +direction of fluid motion is going to be + + + align:start position:0% +direction of fluid motion is going to be +G sine theta we now have an equation + + align:start position:0% +G sine theta we now have an equation + + + align:start position:0% +G sine theta we now have an equation +that looks much easier than the general + + align:start position:0% +that looks much easier than the general + + + align:start position:0% +that looks much easier than the general +Pole as you can see this is just a + + align:start position:0% +Pole as you can see this is just a + + + align:start position:0% +Pole as you can see this is just a +restatement of Newton's second law with + + align:start position:0% +restatement of Newton's second law with + + + align:start position:0% +restatement of Newton's second law with +a viscosity term included on the left + + align:start position:0% +a viscosity term included on the left + + + align:start position:0% +a viscosity term included on the left +side of this equation you get the net + + align:start position:0% +side of this equation you get the net + + + align:start position:0% +side of this equation you get the net +force acting on a unit volume of the + + align:start position:0% +force acting on a unit volume of the + + + align:start position:0% +force acting on a unit volume of the +fluid the three terms on the right side + + align:start position:0% +fluid the three terms on the right side + + + align:start position:0% +fluid the three terms on the right side +of the equation which are governed by + + align:start position:0% +of the equation which are governed by + + + align:start position:0% +of the equation which are governed by +the viscosity the pressure gradient and + + align:start position:0% +the viscosity the pressure gradient and + + + align:start position:0% +the viscosity the pressure gradient and +the force due to gravity together give + + align:start position:0% +the force due to gravity together give + + + align:start position:0% +the force due to gravity together give +the net force acting on a unit volume as + + align:start position:0% +the net force acting on a unit volume as + + + align:start position:0% +the net force acting on a unit volume as +you can see from this term here this is + + align:start position:0% +you can see from this term here this is + + + align:start position:0% +you can see from this term here this is +a second-order differential equation to + + align:start position:0% +a second-order differential equation to + + + align:start position:0% +a second-order differential equation to +solve this we will have to impose two + + align:start position:0% +solve this we will have to impose two + + + align:start position:0% +solve this we will have to impose two +boundary conditions for the river + + align:start position:0% +boundary conditions for the river + + + align:start position:0% +boundary conditions for the river +problem we will consider the velocity at + + align:start position:0% +problem we will consider the velocity at + + + align:start position:0% +problem we will consider the velocity at +the bottom of the river to be zero this + + align:start position:0% +the bottom of the river to be zero this + + + align:start position:0% +the bottom of the river to be zero this +is true because the riverbed imposes + + align:start position:0% +is true because the riverbed imposes + + + align:start position:0% +is true because the riverbed imposes +resistance to the fluid layer just above + + align:start position:0% +resistance to the fluid layer just above + + + align:start position:0% +resistance to the fluid layer just above +it preventing its motion the velocity of + + align:start position:0% +it preventing its motion the velocity of + + + align:start position:0% +it preventing its motion the velocity of +the river reaches a maximum + + align:start position:0% +the river reaches a maximum + + + align:start position:0% +the river reaches a maximum +was the top of the river so we get the + + align:start position:0% +was the top of the river so we get the + + + align:start position:0% +was the top of the river so we get the +condition that D be x over D y equals + + align:start position:0% +condition that D be x over D y equals + + + align:start position:0% +condition that D be x over D y equals +zero at the top for the pipe problem + + align:start position:0% +zero at the top for the pipe problem + + + align:start position:0% +zero at the top for the pipe problem +using the same argument the velocity at + + align:start position:0% +using the same argument the velocity at + + + align:start position:0% +using the same argument the velocity at +the rim of the pipe is zero and at the + + align:start position:0% +the rim of the pipe is zero and at the + + + align:start position:0% +the rim of the pipe is zero and at the +center of the pipe B be x over D R + + align:start position:0% +center of the pipe B be x over D R + + + align:start position:0% +center of the pipe B be x over D R +equals zero where R in this case is the + + align:start position:0% +equals zero where R in this case is the + + + align:start position:0% +equals zero where R in this case is the +distance from the centre of the pipe to + + align:start position:0% +distance from the centre of the pipe to + + + align:start position:0% +distance from the centre of the pipe to +the point we are looking at now that we + + align:start position:0% +the point we are looking at now that we + + + align:start position:0% +the point we are looking at now that we +have our differential equation in one + + align:start position:0% +have our differential equation in one + + + align:start position:0% +have our differential equation in one +dimension and the two boundary + + align:start position:0% +dimension and the two boundary + + + align:start position:0% +dimension and the two boundary +conditions needed to solve it there is + + align:start position:0% +conditions needed to solve it there is + + + align:start position:0% +conditions needed to solve it there is +nothing left to do but the solvent we + + align:start position:0% +nothing left to do but the solvent we + + + align:start position:0% +nothing left to do but the solvent we +can do this using Mathematica I was able + + align:start position:0% +can do this using Mathematica I was able + + + align:start position:0% +can do this using Mathematica I was able +to solve this equation using Mathematica + + align:start position:0% +to solve this equation using Mathematica + + + align:start position:0% +to solve this equation using Mathematica +in the pipe the velocity at a distance R + + align:start position:0% +in the pipe the velocity at a distance R + + + align:start position:0% +in the pipe the velocity at a distance R +from the center is given by this formula + + align:start position:0% +from the center is given by this formula + + + align:start position:0% +from the center is given by this formula +and in the river the velocity at a + + align:start position:0% +and in the river the velocity at a + + + align:start position:0% +and in the river the velocity at a +height Y from the riverbed is given by + + align:start position:0% +height Y from the riverbed is given by + + + align:start position:0% +height Y from the riverbed is given by +this formula if you want to know the + + align:start position:0% +this formula if you want to know the + + + align:start position:0% +this formula if you want to know the +average velocity and set the pipe inside + + align:start position:0% +average velocity and set the pipe inside + + + align:start position:0% +average velocity and set the pipe inside +the river all you have to do is add up + + align:start position:0% +the river all you have to do is add up + + + align:start position:0% +the river all you have to do is add up +each individual velocity at all possible + + align:start position:0% +each individual velocity at all possible + + + align:start position:0% +each individual velocity at all possible +radii or Heights you can think of and + + align:start position:0% +radii or Heights you can think of and + + + align:start position:0% +radii or Heights you can think of and +then divide that sum by the area that + + align:start position:0% +then divide that sum by the area that + + + align:start position:0% +then divide that sum by the area that +you added it over it's just integrating + + align:start position:0% +you added it over it's just integrating + + + align:start position:0% +you added it over it's just integrating +and dividing Mathematica gave me this + + align:start position:0% +and dividing Mathematica gave me this + + + align:start position:0% +and dividing Mathematica gave me this +result you can see that the average + + align:start position:0% +result you can see that the average + + + align:start position:0% +result you can see that the average +velocity of the fluid in a pipe and in a + + align:start position:0% +velocity of the fluid in a pipe and in a + + + align:start position:0% +velocity of the fluid in a pipe and in a +river increases if you increase the + + align:start position:0% +river increases if you increase the + + + align:start position:0% +river increases if you increase the +density of the fluid if you increase the + + align:start position:0% +density of the fluid if you increase the + + + align:start position:0% +density of the fluid if you increase the +inclination of the pipe or the slope of + + align:start position:0% +inclination of the pipe or the slope of + + + align:start position:0% +inclination of the pipe or the slope of +the river to the horizontal also if you + + align:start position:0% +the river to the horizontal also if you + + + align:start position:0% +the river to the horizontal also if you +increase the negative pressure gradient + + align:start position:0% +increase the negative pressure gradient + + + align:start position:0% +increase the negative pressure gradient +the velocity increases the lower + + align:start position:0% +the velocity increases the lower + + + align:start position:0% +the velocity increases the lower +viscosity of the fluid also increases + + align:start position:0% +viscosity of the fluid also increases + + + align:start position:0% +viscosity of the fluid also increases +the average velocity this is all that + + align:start position:0% +the average velocity this is all that + + + align:start position:0% +the average velocity this is all that +you do but wouldn't it be cool if we + + align:start position:0% +you do but wouldn't it be cool if we + + + align:start position:0% +you do but wouldn't it be cool if we +could actually model how the velocity + + align:start position:0% +could actually model how the velocity + + + align:start position:0% +could actually model how the velocity +profile looks like inside a pipe and + + align:start position:0% +profile looks like inside a pipe and + + + align:start position:0% +profile looks like inside a pipe and +inside a river I'll do this using + + align:start position:0% +inside a river I'll do this using + + + align:start position:0% +inside a river I'll do this using +Mathematica I will start with the river + + align:start position:0% +Mathematica I will start with the river + + + align:start position:0% +Mathematica I will start with the river +problem first I will create a grid of + + align:start position:0% +problem first I will create a grid of + + + align:start position:0% +problem first I will create a grid of +coordinates and for each coordinate on + + align:start position:0% +coordinates and for each coordinate on + + + align:start position:0% +coordinates and for each coordinate on +the screen I will assign a vector this + + align:start position:0% +the screen I will assign a vector this + + + align:start position:0% +the screen I will assign a vector this +vector will correspond to the velocity + + align:start position:0% +vector will correspond to the velocity + + + align:start position:0% +vector will correspond to the velocity +at that point we know how this velocity + + align:start position:0% +at that point we know how this velocity + + + align:start position:0% +at that point we know how this velocity +looks like because we solve the + + align:start position:0% +looks like because we solve the + + + align:start position:0% +looks like because we solve the +differential equation for velocity once + + align:start position:0% +differential equation for velocity once + + + align:start position:0% +differential equation for velocity once +we have vectors for each of these points + + align:start position:0% +we have vectors for each of these points + + + align:start position:0% +we have vectors for each of these points +you + + align:start position:0% +you + + + align:start position:0% +you +a picture that looks like this as you + + align:start position:0% +a picture that looks like this as you + + + align:start position:0% +a picture that looks like this as you +can see at the bottom of the river where + + align:start position:0% +can see at the bottom of the river where + + + align:start position:0% +can see at the bottom of the river where +y equals zero you have zero velocity as + + align:start position:0% +y equals zero you have zero velocity as + + + align:start position:0% +y equals zero you have zero velocity as +you increase Y the velocity increases + + align:start position:0% +you increase Y the velocity increases + + + align:start position:0% +you increase Y the velocity increases +let's look at just one slice of the + + align:start position:0% +let's look at just one slice of the + + + align:start position:0% +let's look at just one slice of the +previous image let's see what happens + + align:start position:0% +previous image let's see what happens + + + align:start position:0% +previous image let's see what happens +when you change parameters when you + + align:start position:0% +when you change parameters when you + + + align:start position:0% +when you change parameters when you +change milk the average velocity + + align:start position:0% +change milk the average velocity + + + align:start position:0% +change milk the average velocity +decreases think of these dark blue dots + + align:start position:0% +decreases think of these dark blue dots + + + align:start position:0% +decreases think of these dark blue dots +as fixed these are the front frame with + + align:start position:0% +as fixed these are the front frame with + + + align:start position:0% +as fixed these are the front frame with +high mu you have lower velocities you + + align:start position:0% +high mu you have lower velocities you + + + align:start position:0% +high mu you have lower velocities you +can do the same for other parameters i + + align:start position:0% + + + + align:start position:0% + +used a similar method to model the + + align:start position:0% +used a similar method to model the + + + align:start position:0% +used a similar method to model the +velocity profile inside a pipe i first + + align:start position:0% +velocity profile inside a pipe i first + + + align:start position:0% +velocity profile inside a pipe i first +created a circular grid and then i + + align:start position:0% +created a circular grid and then i + + + align:start position:0% +created a circular grid and then i +assigned each point on the grid a vector + + align:start position:0% +assigned each point on the grid a vector + + + align:start position:0% +assigned each point on the grid a vector +as you can see on the rim of the pipe + + align:start position:0% +as you can see on the rim of the pipe + + + align:start position:0% +as you can see on the rim of the pipe +you have zero velocity and towards the + + align:start position:0% +you have zero velocity and towards the + + + align:start position:0% +you have zero velocity and towards the +center this dark blue line here you have + + align:start position:0% +center this dark blue line here you have + + + align:start position:0% +center this dark blue line here you have +the highest velocity + + align:start position:0% +the highest velocity + + + align:start position:0% +the highest velocity +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +I hope you now understand how fluids + + align:start position:0% +I hope you now understand how fluids + + + align:start position:0% +I hope you now understand how fluids +flow in pipes and rivers and that you + + align:start position:0% +flow in pipes and rivers and that you + + + align:start position:0% +flow in pipes and rivers and that you +will be able to apply the navier-stokes + + align:start position:0% +will be able to apply the navier-stokes + + + align:start position:0% +will be able to apply the navier-stokes +equations to solve similar problems + + align:start position:0% +equations to solve similar problems + + + align:start position:0% +equations to solve similar problems +thank you for watching + + align:start position:0% +thank you for watching + + + align:start position:0% +thank you for watching +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +you \ No newline at end of file diff --git a/nQukfQgIIqw.txt b/nQukfQgIIqw.txt new file mode 100644 index 0000000000000000000000000000000000000000..393c956135bd19bb86a67e404409305aa850f4ba --- /dev/null +++ b/nQukfQgIIqw.txt @@ -0,0 +1,315 @@ +align:start position:0% + +in this lecture we complete our + + align:start position:0% +in this lecture we complete our + + + align:start position:0% +in this lecture we complete our +discussion of multiple continuous random + + align:start position:0% +discussion of multiple continuous random + + + align:start position:0% +discussion of multiple continuous random +variables in the first half we talked + + align:start position:0% +variables in the first half we talked + + + align:start position:0% +variables in the first half we talked +about the conditional distribution of + + align:start position:0% +about the conditional distribution of + + + align:start position:0% +about the conditional distribution of +one random variable given the value of + + align:start position:0% +one random variable given the value of + + + align:start position:0% +one random variable given the value of +another we will see that the mechanics + + align:start position:0% +another we will see that the mechanics + + + align:start position:0% +another we will see that the mechanics +are essentially the same as in the + + align:start position:0% +are essentially the same as in the + + + align:start position:0% +are essentially the same as in the +discrete case here we will actually face + + align:start position:0% +discrete case here we will actually face + + + align:start position:0% +discrete case here we will actually face +some subtle issues because we will be + + align:start position:0% +some subtle issues because we will be + + + align:start position:0% +some subtle issues because we will be +conditioning on an event that has zero + + align:start position:0% +conditioning on an event that has zero + + + align:start position:0% +conditioning on an event that has zero +probability nevertheless all formulas + + align:start position:0% +probability nevertheless all formulas + + + align:start position:0% +probability nevertheless all formulas +will still have the form that one should + + align:start position:0% +will still have the form that one should + + + align:start position:0% +will still have the form that one should +expect and in particular we will see + + align:start position:0% +expect and in particular we will see + + + align:start position:0% +expect and in particular we will see +natural versions of the total + + align:start position:0% +natural versions of the total + + + align:start position:0% +natural versions of the total +probability and total expectation + + align:start position:0% +probability and total expectation + + + align:start position:0% +probability and total expectation +theorem we will also define independence + + align:start position:0% +theorem we will also define independence + + + align:start position:0% +theorem we will also define independence +of continuous random variables a concept + + align:start position:0% +of continuous random variables a concept + + + align:start position:0% +of continuous random variables a concept +that has the same intuitive content as + + align:start position:0% +that has the same intuitive content as + + + align:start position:0% +that has the same intuitive content as +in the discrete case that is when we + + align:start position:0% +in the discrete case that is when we + + + align:start position:0% +in the discrete case that is when we +have independent random variables the + + align:start position:0% +have independent random variables the + + + align:start position:0% +have independent random variables the +values of some of them do not cause any + + align:start position:0% +values of some of them do not cause any + + + align:start position:0% +values of some of them do not cause any +revision of our beliefs about the + + align:start position:0% +revision of our beliefs about the + + + align:start position:0% +revision of our beliefs about the +remaining ones then in the second half + + align:start position:0% +remaining ones then in the second half + + + align:start position:0% +remaining ones then in the second half +of the lecture we will focus on the + + align:start position:0% +of the lecture we will focus on the + + + align:start position:0% +of the lecture we will focus on the +Bayes rule this will be the + + align:start position:0% +Bayes rule this will be the + + + align:start position:0% +Bayes rule this will be the +methodological foundation for when later + + align:start position:0% +methodological foundation for when later + + + align:start position:0% +methodological foundation for when later +in this course we dive into the subject + + align:start position:0% +in this course we dive into the subject + + + align:start position:0% +in this course we dive into the subject +of inference the Bayes rule allows us to + + align:start position:0% +of inference the Bayes rule allows us to + + + align:start position:0% +of inference the Bayes rule allows us to +revise our beliefs about a random + + align:start position:0% +revise our beliefs about a random + + + align:start position:0% +revise our beliefs about a random +variable that is replace an original + + align:start position:0% +variable that is replace an original + + + align:start position:0% +variable that is replace an original +probability distribution by a + + align:start position:0% +probability distribution by a + + + align:start position:0% +probability distribution by a +conditional one after we observe the + + align:start position:0% +conditional one after we observe the + + + align:start position:0% +conditional one after we observe the +value of some other random variable + + align:start position:0% +value of some other random variable + + + align:start position:0% +value of some other random variable +depending on whether the random + + align:start position:0% +depending on whether the random + + + align:start position:0% +depending on whether the random +variables involved are discrete or + + align:start position:0% +variables involved are discrete or + + + align:start position:0% +variables involved are discrete or +continuous we will get four different + + align:start position:0% +continuous we will get four different + + + align:start position:0% +continuous we will get four different +versions of the Bayes rule they all have + + align:start position:0% +versions of the Bayes rule they all have + + + align:start position:0% +versions of the Bayes rule they all have +the same form with small differences and + + align:start position:0% +the same form with small differences and + + + align:start position:0% +the same form with small differences and +we will see how to apply them through + + align:start position:0% +we will see how to apply them through + + + align:start position:0% +we will see how to apply them through +some examples \ No newline at end of file diff --git a/nW4vp_upvmE.txt b/nW4vp_upvmE.txt new file mode 100644 index 0000000000000000000000000000000000000000..5beff41b74dd8ec645586a78005cba46d0ea307f --- /dev/null +++ b/nW4vp_upvmE.txt @@ -0,0 +1,12667 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay so so last time we talk + + align:start position:0% +ocw.mit.edu okay so so last time we talk + + + align:start position:0% +ocw.mit.edu okay so so last time we talk +about this uh IR UV + + align:start position:0% +about this uh IR UV + + + align:start position:0% +about this uh IR UV +connection between the B and the + + align:start position:0% +connection between the B and the + + + align:start position:0% +connection between the B and the +boundary + + align:start position:0% +boundary + + + align:start position:0% +boundary +so the key thing is that let me write + + align:start position:0% +so the key thing is that let me write + + + align:start position:0% +so the key thing is that let me write +down the matric here the ads matric in + + align:start position:0% +down the matric here the ads matric in + + + align:start position:0% +down the matric here the ads matric in +this P + + align:start position:0% + + + + align:start position:0% + +coordinates so so this is the the + + align:start position:0% +coordinates so so this is the the + + + align:start position:0% +coordinates so so this is the the +boundary is at Z equal to + + align:start position:0% +boundary is at Z equal to + + + align:start position:0% +boundary is at Z equal to +zero and when you increase Z you go to + + align:start position:0% +zero and when you increase Z you go to + + + align:start position:0% +zero and when you increase Z you go to +interial and then then for each constant + + align:start position:0% +interial and then then for each constant + + + align:start position:0% +interial and then then for each constant +Z you have a minkovski space time + + align:start position:0% +Z you have a minkovski space time + + + align:start position:0% +Z you have a minkovski space time +you have minkovski D so this is ADS D + + + align:start position:0% +you have minkovski D so this is ADS D + + + + align:start position:0% +you have minkovski D so this is ADS D + +one so so each SL is a d dimensional + + align:start position:0% +one so so each SL is a d dimensional + + + align:start position:0% +one so so each SL is a d dimensional +minkovski + + align:start position:0% +minkovski + + + align:start position:0% +minkovski +space and due to this red shift + + align:start position:0% +space and due to this red shift + + + align:start position:0% +space and due to this red shift +Factor the the more you go to the + + align:start position:0% +Factor the the more you go to the + + + align:start position:0% +Factor the the more you go to the +interior of the space time then + + align:start position:0% +interior of the space time then + + + align:start position:0% +interior of the space time then +corresponding to the lower energy + + align:start position:0% +corresponding to the lower energy + + + align:start position:0% +corresponding to the lower energy +process when viewed from the field + + align:start position:0% +process when viewed from the field + + + align:start position:0% +process when viewed from the field +the when view from field the so so here + + align:start position:0% +the when view from field the so so here + + + align:start position:0% +the when view from field the so so here +is + + align:start position:0% +is + + + align:start position:0% +is +the same process happening here compared + + align:start position:0% +the same process happening here compared + + + align:start position:0% +the same process happening here compared +to happening here and here corresponding + + align:start position:0% +to happening here and here corresponding + + + align:start position:0% +to happening here and here corresponding +to the IR process and Le the boundary + + align:start position:0% +to the IR process and Le the boundary + + + align:start position:0% +to the IR process and Le the boundary +corresponding to the UV process okay so + + align:start position:0% +corresponding to the UV process okay so + + + align:start position:0% +corresponding to the UV process okay so +so this is a key + + align:start position:0% +so this is a key + + + align:start position:0% +so this is a key +relation + + align:start position:0% +relation + + + align:start position:0% +relation +between um the bar and the boundary + + align:start position:0% +between um the bar and the boundary + + + align:start position:0% +between um the bar and the boundary +series and also this give you a + + align:start position:0% +series and also this give you a + + + align:start position:0% +series and also this give you a +intuitive understanding where does this + + align:start position:0% +intuitive understanding where does this + + + align:start position:0% +intuitive understanding where does this +actual Dimension come from from the + + align:start position:0% +actual Dimension come from from the + + + align:start position:0% +actual Dimension come from from the +field three point view then from the F + + align:start position:0% +field three point view then from the F + + + align:start position:0% +field three point view then from the F +Theory perspective this actual Dimension + + align:start position:0% +Theory perspective this actual Dimension + + + align:start position:0% +Theory perspective this actual Dimension +can be considered as a + + align:start position:0% +can be considered as a + + + align:start position:0% +can be considered as a +geometrization of the energy scale okay + + align:start position:0% +geometrization of the energy scale okay + + + align:start position:0% +geometrization of the energy scale okay +and we know that the phys exchange with + + align:start position:0% +and we know that the phys exchange with + + + align:start position:0% +and we know that the phys exchange with +the energy scale from the FI point of + + align:start position:0% +the energy scale from the FI point of + + + align:start position:0% +the energy scale from the FI point of +view is called the imization group flow + + align:start position:0% +view is called the imization group flow + + + align:start position:0% +view is called the imization group flow +say how physics evolves when you change + + align:start position:0% +say how physics evolves when you change + + + align:start position:0% +say how physics evolves when you change +the energy or land scale in the field + + align:start position:0% +the energy or land scale in the field + + + align:start position:0% +the energy or land scale in the field +series is called mization grow flow so + + align:start position:0% +series is called mization grow flow so + + + align:start position:0% +series is called mization grow flow so +so you can also view that the evolution + + align:start position:0% +so you can also view that the evolution + + + align:start position:0% +so you can also view that the evolution +in the the gravity SES say from the from + + align:start position:0% +in the the gravity SES say from the from + + + align:start position:0% +in the the gravity SES say from the from +the boundary to the interior and this + + align:start position:0% +the boundary to the interior and this + + + align:start position:0% +the boundary to the interior and this +flow in the Z Direction maybe considered + + align:start position:0% +flow in the Z Direction maybe considered + + + align:start position:0% +flow in the Z Direction maybe considered +can be considered as a GE again to + + align:start position:0% +can be considered as a GE again to + + + align:start position:0% +can be considered as a GE again to +geometrize the relation gr flow of the + + align:start position:0% +geometrize the relation gr flow of the + + + align:start position:0% +geometrize the relation gr flow of the +field Theory + + align:start position:0% +field Theory + + + align:start position:0% +field Theory +okay so any questions regarding + + align:start position:0% + + + + align:start position:0% + +this good so now let's let's talk about + + align:start position:0% +this good so now let's let's talk about + + + align:start position:0% +this good so now let's let's talk about +some further aspect of The + + align:start position:0% +some further aspect of The + + + align:start position:0% +some further aspect of The +Duality + + align:start position:0% +Duality + + + align:start position:0% +Duality +so so The Duality is that once you + + align:start position:0% +so so The Duality is that once you + + + align:start position:0% +so so The Duality is that once you +realize this + + align:start position:0% + + + + align:start position:0% + +saturation since the two sides are + + align:start position:0% +saturation since the two sides are + + + align:start position:0% +saturation since the two sides are +completely different + + align:start position:0% +completely different + + + align:start position:0% +completely different +object so so the game is that you really + + align:start position:0% +object so so the game is that you really + + + align:start position:0% +object so so the game is that you really +have to do lots of Gess work so you + + align:start position:0% +have to do lots of Gess work so you + + + align:start position:0% +have to do lots of Gess work so you +guess how should this quantity yeah + + align:start position:0% +guess how should this quantity yeah + + + align:start position:0% +guess how should this quantity yeah +essentially you have two Sid you want to + + align:start position:0% +essentially you have two Sid you want to + + + align:start position:0% +essentially you have two Sid you want to +relate things on two sides and uh you + + align:start position:0% +relate things on two sides and uh you + + + align:start position:0% +relate things on two sides and uh you +have to do do guess work so how how does + + align:start position:0% +have to do do guess work so how how does + + + align:start position:0% +have to do do guess work so how how does +this quantity translate into that + + align:start position:0% +this quantity translate into that + + + align:start position:0% +this quantity translate into that +quantity Etc and then check the + + align:start position:0% +quantity Etc and then check the + + + align:start position:0% +quantity Etc and then check the +consistency okay yeah just like you + + align:start position:0% +consistency okay yeah just like you + + + align:start position:0% +consistency okay yeah just like you +don't know two languages and uh and then + + align:start position:0% +don't know two languages and uh and then + + + align:start position:0% +don't know two languages and uh and then +you have to guess between the two + + align:start position:0% +you have to guess between the two + + + align:start position:0% +you have to guess between the two +languages and then build out the + + align:start position:0% +languages and then build out the + + + align:start position:0% +languages and then build out the +dictionary and we will be doing the same + + align:start position:0% +dictionary and we will be doing the same + + + align:start position:0% +dictionary and we will be doing the same +so we will be doing the + + align:start position:0% +so we will be doing the + + + align:start position:0% +so we will be doing the +same + + align:start position:0% + + + + align:start position:0% + +good so now let's do the um + + align:start position:0% + + + + align:start position:0% + +so this is more like a + + align:start position:0% +so this is more like a + + + align:start position:0% +so this is more like a +review of what we already + + align:start position:0% + + + + align:start position:0% + +said so we have so let me be more + + align:start position:0% +said so we have so let me be more + + + align:start position:0% +said so we have so let me be more +explicit we have in for y + + align:start position:0% + + + + align:start position:0% + +Ser we have in m and then here you have + + align:start position:0% +Ser we have in m and then here you have + + + align:start position:0% +Ser we have in m and then here you have +type to B + + align:start position:0% + + + + align:start position:0% + +in a S5 * + + align:start position:0% +in a S5 * + + + align:start position:0% +in a S5 * +S5 so let me just write down a S5 just + + align:start position:0% +S5 so let me just write down a S5 just + + + align:start position:0% +S5 so let me just write down a S5 just +for Simplicity yeah say S5 + + align:start position:0% +for Simplicity yeah say S5 + + + align:start position:0% +for Simplicity yeah say S5 +okay so here on this + + align:start position:0% +okay so here on this + + + align:start position:0% +okay so here on this +side there's a conformal + + align:start position:0% + + + + align:start position:0% + +symmetry which we explained before + + align:start position:0% +symmetry which we explained before + + + align:start position:0% +symmetry which we explained before +because this is a four dimensional + + align:start position:0% +because this is a four dimensional + + + align:start position:0% +because this is a four dimensional +Theory so the conform of IM + + align:start position:0% +Theory so the conform of IM + + + align:start position:0% +Theory so the conform of IM +of a d dimensional series s o d comma + + align:start position:0% + + + + align:start position:0% + +2 and on this side there's a a precise + + align:start position:0% +2 and on this side there's a a precise + + + align:start position:0% +2 and on this side there's a a precise +the same + + align:start position:0% +the same + + + align:start position:0% +the same +group which is + + align:start position:0% + + + + align:start position:0% + +isometry of + + align:start position:0% + + + + align:start position:0% + +ads5 which is precisely also s so4 comma + + align:start position:0% +ads5 which is precisely also s so4 comma + + + align:start position:0% +ads5 which is precisely also s so4 comma +2 okay which we reviewed + + align:start position:0% +2 okay which we reviewed + + + align:start position:0% +2 okay which we reviewed +before and you can write down the + + align:start position:0% +before and you can write down the + + + align:start position:0% +before and you can write down the +transformation on both sides in your P + + align:start position:0% +transformation on both sides in your P + + + align:start position:0% +transformation on both sides in your P +set you have + + align:start position:0% +set you have + + + align:start position:0% +set you have +checked some of them uh that they + + align:start position:0% +checked some of them uh that they + + + align:start position:0% +checked some of them uh that they +actually one to one correspond to each + + align:start position:0% +actually one to one correspond to each + + + align:start position:0% +actually one to one correspond to each +other for example this special conformal + + align:start position:0% +other for example this special conformal + + + align:start position:0% +other for example this special conformal +transformation and uh the others like + + align:start position:0% +transformation and uh the others like + + + align:start position:0% +transformation and uh the others like +translation or rotation Etc it's a it's + + align:start position:0% +translation or rotation Etc it's a it's + + + align:start position:0% +translation or rotation Etc it's a it's +it's more is + + align:start position:0% +it's more is + + + align:start position:0% +it's more is +clear so but in the right hand side we + + align:start position:0% +clear so but in the right hand side we + + + align:start position:0% +clear so but in the right hand side we +still have some like s o so5 + + align:start position:0% +still have some like s o so5 + + + align:start position:0% +still have some like s o so5 +S5 I will talk about that okay yeah um + + align:start position:0% +S5 I will talk about that okay yeah um + + + align:start position:0% +S5 I will talk about that okay yeah um +and then so this is more like A + + align:start position:0% +and then so this is more like A + + + align:start position:0% +and then so this is more like A +Spacetime symmetry so this is more like + + align:start position:0% +Spacetime symmetry so this is more like + + + align:start position:0% +Spacetime symmetry so this is more like +um so this is a space time symmetry + + align:start position:0% +um so this is a space time symmetry + + + align:start position:0% +um so this is a space time symmetry +related to the from fil point of view + + align:start position:0% +related to the from fil point of view + + + align:start position:0% +related to the from fil point of view +this is the SpaceTime + + align:start position:0% +this is the SpaceTime + + + align:start position:0% +this is the SpaceTime +symmetry so in for there's also Global + + align:start position:0% + + + + align:start position:0% + +symmetry we discussed before this is + + align:start position:0% +symmetry we discussed before this is + + + align:start position:0% +symmetry we discussed before this is +also Global Symmetry and uh and but this + + align:start position:0% +also Global Symmetry and uh and but this + + + align:start position:0% +also Global Symmetry and uh and but this +is a global symmetry associated with the + + align:start position:0% +is a global symmetry associated with the + + + align:start position:0% +is a global symmetry associated with the +SpaceTime and there also a global + + align:start position:0% +SpaceTime and there also a global + + + align:start position:0% +SpaceTime and there also a global +internal symmetry + + align:start position:0% +internal symmetry + + + align:start position:0% +internal symmetry +uh uh s so6 internal symmetry uh in anle + + align:start position:0% +uh uh s so6 internal symmetry uh in anle + + + align:start position:0% +uh uh s so6 internal symmetry uh in anle +y we discussed last time the six scal + + align:start position:0% +y we discussed last time the six scal + + + align:start position:0% +y we discussed last time the six scal +Fields you can rotate them each other + + align:start position:0% +Fields you can rotate them each other + + + align:start position:0% +Fields you can rotate them each other +and this is can be considered as coming + + align:start position:0% +and this is can be considered as coming + + + align:start position:0% +and this is can be considered as coming +from the D3 brain uh you can rotate the + + align:start position:0% +from the D3 brain uh you can rotate the + + + align:start position:0% +from the D3 brain uh you can rotate the +say six transverse directions or the + + align:start position:0% +say six transverse directions or the + + + align:start position:0% +say six transverse directions or the +Symmetry in rotate in rotate in rotating + + align:start position:0% +Symmetry in rotate in rotate in rotating + + + align:start position:0% +Symmetry in rotate in rotate in rotating +the six + + align:start position:0% +the six + + + align:start position:0% +the six +transverse directions and and on this + + align:start position:0% +transverse directions and and on this + + + align:start position:0% +transverse directions and and on this +side there's exactly the same symmetry + + align:start position:0% +side there's exactly the same symmetry + + + align:start position:0% +side there's exactly the same symmetry +so now this is isometry of uh uh uh um + + align:start position:0% +so now this is isometry of uh uh uh um + + + align:start position:0% +so now this is isometry of uh uh uh um +S5 okay so the so of S5 precisely give + + align:start position:0% +S5 okay so the so of S5 precisely give + + + align:start position:0% +S5 okay so the so of S5 precisely give +you s + + align:start position:0% +you s + + + align:start position:0% +you s +so6 so you + + align:start position:0% +so6 so you + + + align:start position:0% +so6 so you +have exactly the same s + + align:start position:0% +have exactly the same s + + + align:start position:0% +have exactly the same s +so6 + + align:start position:0% + + + + align:start position:0% + +okay and uh we will not be explicit you + + align:start position:0% +okay and uh we will not be explicit you + + + align:start position:0% +okay and uh we will not be explicit you +can also actually map the super symmetry + + align:start position:0% +can also actually map the super symmetry + + + align:start position:0% +can also actually map the super symmetry +between + + align:start position:0% + + + + align:start position:0% + +them you can also map the super symmetry + + align:start position:0% +them you can also map the super symmetry + + + align:start position:0% +them you can also map the super symmetry +between them + + align:start position:0% +between them + + + align:start position:0% +between them +so I includ four super symmetry so + + align:start position:0% +so I includ four super symmetry so + + + align:start position:0% +so I includ four super symmetry so +there's a + + align:start position:0% +there's a + + + align:start position:0% +there's a +four uh four super symmetry which just + + align:start position:0% +four uh four super symmetry which just + + + align:start position:0% +four uh four super symmetry which just +come from inqu four and uh and because + + align:start position:0% +come from inqu four and uh and because + + + align:start position:0% +come from inqu four and uh and because +you have conform symmetry then the + + align:start position:0% +you have conform symmetry then the + + + align:start position:0% +you have conform symmetry then the +conform symmetry does not actually + + align:start position:0% +conform symmetry does not actually + + + align:start position:0% +conform symmetry does not actually +commute with this four super symmetry + + align:start position:0% +commute with this four super symmetry + + + align:start position:0% +commute with this four super symmetry +then generate the L four super + + align:start position:0% +then generate the L four super + + + align:start position:0% +then generate the L four super +Symmetry and anyway so so essentially + + align:start position:0% +Symmetry and anyway so so essentially + + + align:start position:0% +Symmetry and anyway so so essentially +you have eight uh supercharge of the + + align:start position:0% +you have eight uh supercharge of the + + + align:start position:0% +you have eight uh supercharge of the +wild + + align:start position:0% +wild + + + align:start position:0% +wild +spinder and uh yes so this all together + + align:start position:0% +spinder and uh yes so this all together + + + align:start position:0% +spinder and uh yes so this all together +is 32 say real supercharges sometimes + + align:start position:0% + + + + align:start position:0% + +we okay so when we say an four so this + + align:start position:0% +we okay so when we say an four so this + + + align:start position:0% +we okay so when we say an four so this +is an four in terms of four dimensional + + align:start position:0% +is an four in terms of four dimensional + + + align:start position:0% +is an four in terms of four dimensional +wild spinder so your super symmetry have + + align:start position:0% +wild spinder so your super symmetry have + + + align:start position:0% +wild spinder so your super symmetry have +uh uh four four wild spinder as the uh + + align:start position:0% +uh uh four four wild spinder as the uh + + + align:start position:0% +uh uh four four wild spinder as the uh +as the + + align:start position:0% +as the + + + align:start position:0% +as the +supercharge but the conform imim + + align:start position:0% +supercharge but the conform imim + + + align:start position:0% +supercharge but the conform imim +generate a lot of four so all together + + align:start position:0% +generate a lot of four so all together + + + align:start position:0% +generate a lot of four so all together +you have eight wild spinner four + + align:start position:0% +you have eight wild spinner four + + + align:start position:0% +you have eight wild spinner four +dimensional wild spinner as the + + align:start position:0% +dimensional wild spinner as the + + + align:start position:0% +dimensional wild spinner as the +supercharge and you know that for each + + align:start position:0% +supercharge and you know that for each + + + align:start position:0% +supercharge and you know that for each +wild spinner in four dimension there how + + align:start position:0% +wild spinner in four dimension there how + + + align:start position:0% +wild spinner in four dimension there how +many + + align:start position:0% + + + + align:start position:0% + +components how many components are there + + align:start position:0% +components how many components are there + + + align:start position:0% +components how many components are there +for wild spinner in four dimension four + + align:start position:0% +for wild spinner in four dimension four + + + align:start position:0% +for wild spinner in four dimension four +four because the two component but each + + align:start position:0% +four because the two component but each + + + align:start position:0% +four because the two component but each +component is complex and so there four + + align:start position:0% +component is complex and so there four + + + align:start position:0% +component is complex and so there four +real components so all together you have + + align:start position:0% +real components so all together you have + + + align:start position:0% +real components so all together you have +32 real charges okay and uh similarly + + align:start position:0% +32 real charges okay and uh similarly + + + align:start position:0% +32 real charges okay and uh similarly +you find I will not do this side you + + align:start position:0% +you find I will not do this side you + + + align:start position:0% +you find I will not do this side you +find the same + + align:start position:0% + + + + align:start position:0% + +amount same amount of super + + align:start position:0% + + + + align:start position:0% + +symmetry but in this case for example + + align:start position:0% +symmetry but in this case for example + + + align:start position:0% +symmetry but in this case for example +the L + + align:start position:0% +the L + + + align:start position:0% +the L +limit uh uh let's just talk about the L + + align:start position:0% +limit uh uh let's just talk about the L + + + align:start position:0% +limit uh uh let's just talk about the L +limit of this the so the L limit as we + + align:start position:0% +limit of this the so the L limit as we + + + align:start position:0% +limit of this the so the L limit as we +said before just type to be super + + align:start position:0% +said before just type to be super + + + align:start position:0% +said before just type to be super +gravity so intive spe gravity then you + + align:start position:0% +gravity so intive spe gravity then you + + + align:start position:0% +gravity so intive spe gravity then you +find you actually have exact exact the + + align:start position:0% +find you actually have exact exact the + + + align:start position:0% +find you actually have exact exact the +same amount of super symmetry in this uh + + align:start position:0% +same amount of super symmetry in this uh + + + align:start position:0% +same amount of super symmetry in this uh +in this + + align:start position:0% +in this + + + align:start position:0% +in this +geometry in this geometry and uh but the + + align:start position:0% +geometry in this geometry and uh but the + + + align:start position:0% +geometry in this geometry and uh but the +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +thing is that the by definition super + + align:start position:0% +thing is that the by definition super + + + align:start position:0% +thing is that the by definition super +gravity uh the super symmetry on the + + align:start position:0% +gravity uh the super symmetry on the + + + align:start position:0% +gravity uh the super symmetry on the +gravity side is actually local so so you + + align:start position:0% +gravity side is actually local so so you + + + align:start position:0% +gravity side is actually local so so you +actually have same amount of local super + + align:start position:0% +actually have same amount of local super + + + align:start position:0% +actually have same amount of local super +symmetries okay + + align:start position:0% + + + + align:start position:0% + +so if you look at this correspondence + + align:start position:0% +so if you look at this correspondence + + + align:start position:0% +so if you look at this correspondence +between each + + align:start position:0% + + + + align:start position:0% + +other then you see actually see a + + align:start position:0% +other then you see actually see a + + + align:start position:0% +other then you see actually see a +pattern okay so so now let me make some + + align:start position:0% +pattern okay so so now let me make some + + + align:start position:0% +pattern okay so so now let me make some +remarks + + align:start position:0% + + + + align:start position:0% + +okay so if you look at this structure uh + + align:start position:0% +okay so if you look at this structure uh + + + align:start position:0% +okay so if you look at this structure uh +this math you see a + + align:start position:0% + + + + align:start position:0% + +pattern on this side all these + + align:start position:0% +pattern on this side all these + + + align:start position:0% +pattern on this side all these +symmetries are Global + + align:start position:0% + + + + align:start position:0% + +symmetries but on this side all these + + align:start position:0% +symmetries but on this side all these + + + align:start position:0% +symmetries but on this side all these +symmetries are local + + align:start position:0% +symmetries are local + + + align:start position:0% +symmetries are local +symmetries so so this I just said that + + align:start position:0% +symmetries so so this I just said that + + + align:start position:0% +symmetries so so this I just said that +the uh in super gravity the super + + align:start position:0% +the uh in super gravity the super + + + align:start position:0% +the uh in super gravity the super +symmetry is nocal um and uh uh + + align:start position:0% +symmetry is nocal um and uh uh + + + align:start position:0% +symmetry is nocal um and uh uh +uh the SpaceTime + + align:start position:0% +uh the SpaceTime + + + align:start position:0% +uh the SpaceTime +isometry is just subset of a a space + + align:start position:0% +isometry is just subset of a a space + + + align:start position:0% +isometry is just subset of a a space +time qu + + align:start position:0% +time qu + + + align:start position:0% +time qu +transformation and SpaceTime coordinate + + align:start position:0% +transformation and SpaceTime coordinate + + + align:start position:0% +transformation and SpaceTime coordinate +transformation uh uh um are local + + align:start position:0% +transformation uh uh um are local + + + align:start position:0% +transformation uh uh um are local +symmetries okay uh uh so the + + align:start position:0% + + + + align:start position:0% + +isometry is a + + align:start position:0% + + + + align:start position:0% + +subgroup + + align:start position:0% + + + + align:start position:0% + +ofm So Def morphism mean just means the + + align:start position:0% +ofm So Def morphism mean just means the + + + align:start position:0% +ofm So Def morphism mean just means the +coordinate + + align:start position:0% +coordinate + + + align:start position:0% +coordinate +Transformations and + + align:start position:0% +Transformations and + + + align:start position:0% +Transformations and +and these are local + + align:start position:0% + + + + align:start position:0% + +symmetries okay local + + align:start position:0% +symmetries okay local + + + align:start position:0% +symmetries okay local +symmetries so so we + + align:start position:0% +symmetries so so we + + + align:start position:0% +symmetries so so we +find now we actually have + + align:start position:0% +find now we actually have + + + align:start position:0% +find now we actually have +a now we find the mapping is that the + + align:start position:0% +a now we find the mapping is that the + + + align:start position:0% +a now we find the mapping is that the +glob on the field series side the global + + align:start position:0% + + + + align:start position:0% + +symmetries is m on the gravity side into + + align:start position:0% +symmetries is m on the gravity side into + + + align:start position:0% +symmetries is m on the gravity side into +the local + + align:start position:0% +the local + + + align:start position:0% +the local +symmetries + + align:start position:0% + + + + align:start position:0% + +okay so for each Global symmetry in the + + align:start position:0% +okay so for each Global symmetry in the + + + align:start position:0% +okay so for each Global symmetry in the +filer side there's a corresponding local + + align:start position:0% +filer side there's a corresponding local + + + align:start position:0% +filer side there's a corresponding local +symmetry on the gravity side okay there + + align:start position:0% +symmetry on the gravity side okay there + + + align:start position:0% +symmetry on the gravity side okay there +a corresponding local symetry on the gra + + align:start position:0% + + + + align:start position:0% + +side but you may immediately ask a + + align:start position:0% +side but you may immediately ask a + + + align:start position:0% +side but you may immediately ask a +question on the gravity side if you talk + + align:start position:0% +question on the gravity side if you talk + + + align:start position:0% +question on the gravity side if you talk +about def morphism then then this is a + + align:start position:0% +about def morphism then then this is a + + + align:start position:0% +about def morphism then then this is a +huge group certainly much much larger + + align:start position:0% +huge group certainly much much larger + + + align:start position:0% +huge group certainly much much larger +than than what we are talking about the + + align:start position:0% +than than what we are talking about the + + + align:start position:0% +than than what we are talking about the +isometry here so why we are only talking + + align:start position:0% +isometry here so why we are only talking + + + align:start position:0% +isometry here so why we are only talking +about isometry rather than talking about + + align:start position:0% +about isometry rather than talking about + + + align:start position:0% +about isometry rather than talking about +the um yeah why why we don't talk about + + align:start position:0% +the um yeah why why we don't talk about + + + align:start position:0% +the um yeah why why we don't talk about +other part of the def only talk about + + align:start position:0% +other part of the def only talk about + + + align:start position:0% +other part of the def only talk about +isometry + + align:start position:0% +isometry + + + align:start position:0% +isometry +so so what's special about + + align:start position:0% + + + + align:start position:0% + +isometry so the second + + align:start position:0% +isometry so the second + + + align:start position:0% +isometry so the second +remark why isometry + + align:start position:0% + + + + align:start position:0% + +why only isometry why only isometry yeah + + align:start position:0% +why only isometry why only isometry yeah + + + align:start position:0% +why only isometry why only isometry yeah +why only look at isometry but but let me + + align:start position:0% +why only look at isometry but but let me + + + align:start position:0% +why only look at isometry but but let me +just save time not to + + align:start position:0% +just save time not to + + + align:start position:0% +just save time not to +read + + align:start position:0% +read + + + align:start position:0% +read +okay + + align:start position:0% + + + + align:start position:0% + +so the isometry is important for the + + align:start position:0% +so the isometry is important for the + + + align:start position:0% +so the isometry is important for the +following + + align:start position:0% +following + + + align:start position:0% +following +reason because even though this is a + + align:start position:0% +reason because even though this is a + + + align:start position:0% +reason because even though this is a +subgroup but this is a so I I mentioned + + align:start position:0% +subgroup but this is a so I I mentioned + + + align:start position:0% +subgroup but this is a so I I mentioned +last time when we talk about the quantum + + align:start position:0% +last time when we talk about the quantum + + + align:start position:0% +last time when we talk about the quantum +gravity when we talk about string Ser an + + align:start position:0% +gravity when we talk about string Ser an + + + align:start position:0% +gravity when we talk about string Ser an +times + + align:start position:0% +times + + + align:start position:0% +times +S5 in terms of ads5 * S5 you should keep + + align:start position:0% +S5 in terms of ads5 * S5 you should keep + + + align:start position:0% +S5 in terms of ads5 * S5 you should keep +in mind that this ads5 * S5 refers to + + align:start position:0% +in mind that this ads5 * S5 refers to + + + align:start position:0% +in mind that this ads5 * S5 refers to +the asymptotic + + align:start position:0% +the asymptotic + + + align:start position:0% +the asymptotic +geometry because as a quantum theory the + + align:start position:0% +geometry because as a quantum theory the + + + align:start position:0% +geometry because as a quantum theory the +theory can fluctuate in the middle + + align:start position:0% +theory can fluctuate in the middle + + + align:start position:0% +theory can fluctuate in the middle +okay and the isometry can be considered + + align:start position:0% +okay and the isometry can be considered + + + align:start position:0% +okay and the isometry can be considered +as a subgroup + + align:start position:0% + + + + align:start position:0% + +but the level L even though even though + + align:start position:0% +but the level L even though even though + + + align:start position:0% +but the level L even though even though +the space time fluctuates but the but S5 + + align:start position:0% +the space time fluctuates but the but S5 + + + align:start position:0% +the space time fluctuates but the but S5 +* S5 specify the symic geometry of the + + align:start position:0% +* S5 specify the symic geometry of the + + + align:start position:0% +* S5 specify the symic geometry of the +space time + + align:start position:0% +space time + + + align:start position:0% +space time +okay specify the ometry of space time + + align:start position:0% +okay specify the ometry of space time + + + align:start position:0% +okay specify the ometry of space time +and the isometry is precisely the sub + + align:start position:0% + + + + align:start position:0% + +Group + + align:start position:0% +Group + + + align:start position:0% +Group +which + + align:start position:0% + + + + align:start position:0% + +leaves the symic + + align:start position:0% + + + + align:start position:0% + +form of the metric + + align:start position:0% + + + + align:start position:0% + +invariant + + align:start position:0% +invariant + + + align:start position:0% +invariant +okay so these are not ordinary def + + align:start position:0% +okay so these are not ordinary def + + + align:start position:0% +okay so these are not ordinary def +morphisms so the ordinary def + + align:start position:0% +morphisms so the ordinary def + + + align:start position:0% +morphisms so the ordinary def +morphisms the ordinary gauge + + align:start position:0% +morphisms the ordinary gauge + + + align:start position:0% +morphisms the ordinary gauge +Transformations let me just say say it + + align:start position:0% +Transformations let me just say say it + + + align:start position:0% +Transformations let me just say say it +more generally by gauge transformation + + align:start position:0% +more generally by gauge transformation + + + align:start position:0% +more generally by gauge transformation +also means the def morphism + + align:start position:0% +also means the def morphism + + + align:start position:0% +also means the def morphism +or just general gaug + + align:start position:0% +or just general gaug + + + align:start position:0% +or just general gaug +Transformations so when we talk about + + align:start position:0% +Transformations so when we talk about + + + align:start position:0% +Transformations so when we talk about +the gaug + + align:start position:0% +the gaug + + + align:start position:0% +the gaug +Transformations say for example in Q or + + align:start position:0% +Transformations say for example in Q or + + + align:start position:0% +Transformations say for example in Q or +in qcd ETC we always assume we + + align:start position:0% +in qcd ETC we always assume we + + + align:start position:0% +in qcd ETC we always assume we +always so the class of a gauge + + align:start position:0% +always so the class of a gauge + + + align:start position:0% +always so the class of a gauge +transformation we consider we always + + align:start position:0% +transformation we consider we always + + + align:start position:0% +transformation we consider we always +take them to be for all sufficiently + + align:start position:0% +take them to be for all sufficiently + + + align:start position:0% +take them to be for all sufficiently +fast at Infinity + + align:start position:0% + + + + align:start position:0% + +at Infinity + + align:start position:0% + + + + align:start position:0% + +okay so we always when we talk about G + + align:start position:0% +okay so we always when we talk about G + + + align:start position:0% +okay so we always when we talk about G +Transformations so when we talk about + + align:start position:0% +Transformations so when we talk about + + + align:start position:0% +Transformations so when we talk about +typical def + + align:start position:0% +typical def + + + align:start position:0% +typical def +morphisms uh these are kind of + + align:start position:0% +morphisms uh these are kind of + + + align:start position:0% +morphisms uh these are kind of +Transformations where we assume it goes + + align:start position:0% +Transformations where we assume it goes + + + align:start position:0% +Transformations where we assume it goes +to one say uh at Infinity + + align:start position:0% + + + + align:start position:0% + +and and this + + align:start position:0% +and and this + + + align:start position:0% +and and this +isometries which Lees the SYM totic of + + align:start position:0% +isometries which Lees the SYM totic of + + + align:start position:0% +isometries which Lees the SYM totic of +the metric + + align:start position:0% +the metric + + + align:start position:0% +the metric +invariant so these are essentially the + + align:start position:0% +invariant so these are essentially the + + + align:start position:0% +invariant so these are essentially the +large gate + + align:start position:0% + + + + align:start position:0% + +Transformations because they + + align:start position:0% + + + + align:start position:0% + +don't okay and uh and so so called large + + align:start position:0% +don't okay and uh and so so called large + + + align:start position:0% +don't okay and uh and so so called large +transformation that is that they don't + + align:start position:0% +transformation that is that they don't + + + align:start position:0% +transformation that is that they don't +go to the identity at + + align:start position:0% +go to the identity at + + + align:start position:0% +go to the identity at +Infinity okay and of course this is + + align:start position:0% +Infinity okay and of course this is + + + align:start position:0% +Infinity okay and of course this is +precisely the the those not transform + + align:start position:0% +precisely the the those not transform + + + align:start position:0% +precisely the the those not transform +not Transformations which leaves + + align:start position:0% +not Transformations which leaves + + + align:start position:0% +not Transformations which leaves +thetic + + align:start position:0% +thetic + + + align:start position:0% +thetic +envirment so so in the + + align:start position:0% +envirment so so in the + + + align:start position:0% +envirment so so in the +sense in the sense this n + + align:start position:0% +sense in the sense this n + + + align:start position:0% +sense in the sense this n +Transformations can be + + align:start position:0% + + + + align:start position:0% + +considered as the + + align:start position:0% + + + + align:start position:0% + +global part of the def morphism okay + + align:start position:0% + + + + align:start position:0% + +okay so any questions on + + align:start position:0% + + + + align:start position:0% + +this yes what does it mean that those + + align:start position:0% +this yes what does it mean that those + + + align:start position:0% +this yes what does it mean that those +isometries are local I mean when you do + + align:start position:0% +isometries are local I mean when you do + + + align:start position:0% +isometries are local I mean when you do +isometry + + align:start position:0% +isometry + + + align:start position:0% +isometry +coordination H what do you mean when you + + align:start position:0% +coordination H what do you mean when you + + + align:start position:0% +coordination H what do you mean when you +say that isometry yeah uh yeah these are + + align:start position:0% +say that isometry yeah uh yeah these are + + + align:start position:0% +say that isometry yeah uh yeah these are +just coordinate transformation + + align:start position:0% +just coordinate transformation + + + align:start position:0% +just coordinate transformation +coordinate coordinate transformation + + align:start position:0% +coordinate coordinate transformation + + + align:start position:0% +coordinate coordinate transformation +always defined Point by point right yeah + + align:start position:0% +always defined Point by point right yeah + + + align:start position:0% +always defined Point by point right yeah +yeah just these are specific coordinate + + align:start position:0% +yeah just these are specific coordinate + + + align:start position:0% +yeah just these are specific coordinate +Transformations and what happen to G + + align:start position:0% +Transformations and what happen to G + + + align:start position:0% +Transformations and what happen to G +Symmetry and + + align:start position:0% +Symmetry and + + + align:start position:0% +Symmetry and +for sorry transation in + + align:start position:0% +for sorry transation in + + + align:start position:0% +for sorry transation in +the no the the gaug transformation in + + align:start position:0% +the no the the gaug transformation in + + + align:start position:0% +the no the the gaug transformation in +the Y part you don't you don't see + + align:start position:0% +the Y part you don't you don't see + + + align:start position:0% +the Y part you don't you don't see +it gug Freedom just redundant Freedom + + align:start position:0% +it gug Freedom just redundant Freedom + + + align:start position:0% +it gug Freedom just redundant Freedom +level + + align:start position:0% +level + + + align:start position:0% +level +seats on the other side so this this ex + + align:start position:0% +seats on the other side so this this ex + + + align:start position:0% +seats on the other side so this this ex +all symmetries + + align:start position:0% +all symmetries + + + align:start position:0% +all symmetries +of Y part yeah yeah + + align:start position:0% +of Y part yeah yeah + + + align:start position:0% +of Y part yeah yeah +yeah exhaust all Global symmetries in + + align:start position:0% +yeah exhaust all Global symmetries in + + + align:start position:0% +yeah exhaust all Global symmetries in +the yam the + + align:start position:0% +the yam the + + + align:start position:0% +the yam the +part uh uh all the global series on the + + align:start position:0% +part uh uh all the global series on the + + + align:start position:0% +part uh uh all the global series on the +Y site and not noal immes we are didn't + + align:start position:0% +Y site and not noal immes we are didn't + + + align:start position:0% +Y site and not noal immes we are didn't +discuss but there there there's a unage + + align:start position:0% +discuss but there there there's a unage + + + align:start position:0% +discuss but there there there's a unage +group there and uh but they don't have + + align:start position:0% +group there and uh but they don't have + + + align:start position:0% +group there and uh but they don't have +correspondence in the in the gravity + + align:start position:0% +correspondence in the in the gravity + + + align:start position:0% +correspondence in the in the gravity +site and we know the reason we don't + + align:start position:0% +site and we know the reason we don't + + + align:start position:0% +site and we know the reason we don't +consider the the gug SYM because the + + align:start position:0% +consider the the gug SYM because the + + + align:start position:0% +consider the the gug SYM because the +corresponding to redundancies and they + + align:start position:0% +corresponding to redundancies and they + + + align:start position:0% +corresponding to redundancies and they +don't have to be present on the other + + align:start position:0% +don't have to be present on the other + + + align:start position:0% +don't have to be present on the other +side they only need to the physical + + align:start position:0% +side they only need to the physical + + + align:start position:0% +side they only need to the physical +degrees freedom to be identical and this + + align:start position:0% +degrees freedom to be identical and this + + + align:start position:0% +degrees freedom to be identical and this +also is the + + align:start position:0% +also is the + + + align:start position:0% +also is the +reason I make this remark + + align:start position:0% +reason I make this remark + + + align:start position:0% +reason I make this remark +here even though all this global simes + + align:start position:0% +here even though all this global simes + + + align:start position:0% +here even though all this global simes +they find the corresponding local + + align:start position:0% +they find the corresponding local + + + align:start position:0% +they find the corresponding local +symmetries on the gravity + + align:start position:0% +symmetries on the gravity + + + align:start position:0% +symmetries on the gravity +side but precisely due to this + + align:start position:0% +side but precisely due to this + + + align:start position:0% +side but precisely due to this +remark precisely due to this + + align:start position:0% +remark precisely due to this + + + align:start position:0% +remark precisely due to this +remark those things which really map to + + align:start position:0% +remark those things which really map to + + + align:start position:0% +remark those things which really map to +the global symmetries in the yam in the + + align:start position:0% +the global symmetries in the yam in the + + + align:start position:0% +the global symmetries in the yam in the +in the Fielder can be considered as a + + align:start position:0% +in the Fielder can be considered as a + + + align:start position:0% +in the Fielder can be considered as a +global part of the local symmetries on + + align:start position:0% +global part of the local symmetries on + + + align:start position:0% +global part of the local symmetries on +the gravity side so even on the gravity + + align:start position:0% +the gravity side so even on the gravity + + + align:start position:0% +the gravity side so even on the gravity +side in some sense you should think of + + align:start position:0% +side in some sense you should think of + + + align:start position:0% +side in some sense you should think of +them as Global symmetries and and the uh + + align:start position:0% +them as Global symmetries and and the uh + + + align:start position:0% +them as Global symmetries and and the uh +their uh their their not gate + + align:start position:0% +their uh their their not gate + + + align:start position:0% +their uh their their not gate +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +okay yeah because of the because the + + align:start position:0% +okay yeah because of the because the + + + align:start position:0% +okay yeah because of the because the +ordinary gug transformation just + + align:start position:0% +ordinary gug transformation just + + + align:start position:0% +ordinary gug transformation just +corresponding to redundancies of + + align:start position:0% +corresponding to redundancies of + + + align:start position:0% +corresponding to redundancies of +redundancy of deges freedom and they + + align:start position:0% +redundancy of deges freedom and they + + + align:start position:0% +redundancy of deges freedom and they +that should not be reflected on the + + align:start position:0% +that should not be reflected on the + + + align:start position:0% +that should not be reflected on the +other side what do youan by large guge + + align:start position:0% +other side what do youan by large guge + + + align:start position:0% +other side what do youan by large guge +transformation the large gug + + align:start position:0% +transformation the large gug + + + align:start position:0% +transformation the large gug +transformation means the gug transation + + align:start position:0% +transformation means the gug transation + + + align:start position:0% +transformation means the gug transation +which don't vanish at + + align:start position:0% +which don't vanish at + + + align:start position:0% +which don't vanish at +Infinity yeah so the ordinary gug + + align:start position:0% +Infinity yeah so the ordinary gug + + + align:start position:0% +Infinity yeah so the ordinary gug +transformation yeah just like in Q when + + align:start position:0% +transformation yeah just like in Q when + + + align:start position:0% +transformation yeah just like in Q when +we talk about the in in in Quantum + + align:start position:0% +we talk about the in in in Quantum + + + align:start position:0% +we talk about the in in in Quantum +electr dnamic when we talk about gug + + align:start position:0% +electr dnamic when we talk about gug + + + align:start position:0% +electr dnamic when we talk about gug +transformation we talk about gug + + align:start position:0% +transformation we talk about gug + + + align:start position:0% +transformation we talk about gug +transformation the gug transformation we + + align:start position:0% +transformation the gug transformation we + + + align:start position:0% +transformation the gug transformation we +consider all the gate trans which go to + + align:start position:0% +consider all the gate trans which go to + + + align:start position:0% +consider all the gate trans which go to +zero at + + align:start position:0% +zero at + + + align:start position:0% +zero at +infinity and if you consider those gug + + align:start position:0% +infinity and if you consider those gug + + + align:start position:0% +infinity and if you consider those gug +trans which don't go to zero at infinity + + align:start position:0% +trans which don't go to zero at infinity + + + align:start position:0% +trans which don't go to zero at infinity +and that's what we call logic + + align:start position:0% +and that's what we call logic + + + align:start position:0% +and that's what we call logic +Transformations and those logic + + align:start position:0% +Transformations and those logic + + + align:start position:0% +Transformations and those logic +Transformations essentially is like the + + align:start position:0% +Transformations essentially is like the + + + align:start position:0% +Transformations essentially is like the +global part of the U1 a gauge symm in + + align:start position:0% +global part of the U1 a gauge symm in + + + align:start position:0% +global part of the U1 a gauge symm in +some sense can be considered as + + align:start position:0% +some sense can be considered as + + + align:start position:0% +some sense can be considered as +yeah but that is the gauge symmetry in + + align:start position:0% +yeah but that is the gauge symmetry in + + + align:start position:0% +yeah but that is the gauge symmetry in +the uh gravity yeah that's right yeah so + + align:start position:0% +the uh gravity yeah that's right yeah so + + + align:start position:0% +the uh gravity yeah that's right yeah so +this is the part + + align:start position:0% +this is the part + + + align:start position:0% +this is the part +of the gug IM in the gravity side but + + align:start position:0% +of the gug IM in the gravity side but + + + align:start position:0% +of the gug IM in the gravity side but +this the part but the part corresponding + + align:start position:0% +this the part but the part corresponding + + + align:start position:0% +this the part but the part corresponding +to the boundary is the part associated + + align:start position:0% +to the boundary is the part associated + + + align:start position:0% +to the boundary is the part associated +with the + + align:start position:0% + + + + align:start position:0% + +infinity here in isometry of ads5 we + + align:start position:0% +infinity here in isometry of ads5 we + + + align:start position:0% +infinity here in isometry of ads5 we +shown like in P set it's point to point + + align:start position:0% +shown like in P set it's point to point + + + align:start position:0% +shown like in P set it's point to point +local symmetry it's like just the space + + align:start position:0% +local symmetry it's like just the space + + + align:start position:0% +local symmetry it's like just the space +time point but uh how about this conform + + align:start position:0% +time point but uh how about this conform + + + align:start position:0% +time point but uh how about this conform +in this + + align:start position:0% +in this + + + align:start position:0% +in this +uh yam Theory what is this symmetry of + + align:start position:0% +uh yam Theory what is this symmetry of + + + align:start position:0% +uh yam Theory what is this symmetry of +the + + align:start position:0% +the + + + align:start position:0% +the +object sorry what kind of object does + + align:start position:0% +object sorry what kind of object does + + + align:start position:0% +object sorry what kind of object does +this symmetry correspond to because it + + align:start position:0% +this symmetry correspond to because it + + + align:start position:0% +this symmetry correspond to because it +seems is the conform + + align:start position:0% + + + + align:start position:0% + +symmetry conformal symmetry of the + + align:start position:0% +symmetry conformal symmetry of the + + + align:start position:0% +symmetry conformal symmetry of the +component of the field of no no no no + + align:start position:0% +component of the field of no no no no + + + align:start position:0% +component of the field of no no no no +it's a conformal symmetry of the movy + + align:start position:0% +it's a conformal symmetry of the movy + + + align:start position:0% +it's a conformal symmetry of the movy +space so on this side you have aom of + + align:start position:0% +space so on this side you have aom of + + + align:start position:0% +space so on this side you have aom of +ads on the other side you have conform + + align:start position:0% +ads on the other side you have conform + + + align:start position:0% +ads on the other side you have conform +image of the movi space so you're asking + + align:start position:0% +image of the movi space so you're asking + + + align:start position:0% +image of the movi space so you're asking +what the corresponding to on the FI + + align:start position:0% +what the corresponding to on the FI + + + align:start position:0% +what the corresponding to on the FI +three side right yeah so that's a map to + + align:start position:0% +three side right yeah so that's a map to + + + align:start position:0% +three side right yeah so that's a map to +the con symmetry of the of the minkovski + + align:start position:0% +the con symmetry of the of the minkovski + + + align:start position:0% +the con symmetry of the of the minkovski +space + + align:start position:0% + + + + align:start position:0% + +yeah so so the isometry is actually a + + align:start position:0% +yeah so so the isometry is actually a + + + align:start position:0% +yeah so so the isometry is actually a +large is is large gauge Transformations + + align:start position:0% + + + + align:start position:0% + +right so the story actually is more + + align:start position:0% +right so the story actually is more + + + align:start position:0% +right so the story actually is more +General + + align:start position:0% +General + + + align:start position:0% +General +[Applause] + + align:start position:0% + + + + align:start position:0% + +so the story is actually works more + + align:start position:0% +so the story is actually works more + + + align:start position:0% +so the story is actually works more +General so this is the statement for the + + align:start position:0% +General so this is the statement for the + + + align:start position:0% +General so this is the statement for the +in super Ser so the story is more + + align:start position:0% + + + + align:start position:0% + +General so in the case which you have + + align:start position:0% +General so in the case which you have + + + align:start position:0% +General so in the case which you have +say more + + align:start position:0% +say more + + + align:start position:0% +say more +General say duality between a saf T in D + + align:start position:0% +General say duality between a saf T in D + + + align:start position:0% +General say duality between a saf T in D +dimension in movi + + align:start position:0% + + + + align:start position:0% + +D with the uh ads + + align:start position:0% +D with the uh ads + + + align:start position:0% +D with the uh ads +gravity ads D+ one dimensional + + align:start position:0% + + + + align:start position:0% + +gravity in any such + + align:start position:0% +gravity in any such + + + align:start position:0% +gravity in any such +Duality then you always have the + + align:start position:0% +Duality then you always have the + + + align:start position:0% +Duality then you always have the +conformal + + align:start position:0% + + + + align:start position:0% + +symmetry which is s so D comma 2 on this + + align:start position:0% +symmetry which is s so D comma 2 on this + + + align:start position:0% +symmetry which is s so D comma 2 on this +here map to a DS + + align:start position:0% + + + + align:start position:0% + +isometry this comma two and any say + + align:start position:0% +isometry this comma two and any say + + + align:start position:0% +isometry this comma two and any say +internal gauge symmetry say if you have + + align:start position:0% +internal gauge symmetry say if you have + + + align:start position:0% +internal gauge symmetry say if you have +some U1 Global symmetry + + align:start position:0% + + + + align:start position:0% + +here then this will be + + align:start position:0% +here then this will be + + + align:start position:0% +here then this will be +mapped + + align:start position:0% +mapped + + + align:start position:0% +mapped +into a you gaug symmetry + + align:start position:0% + + + + align:start position:0% + +again in the sense that this U1 Global + + align:start position:0% +again in the sense that this U1 Global + + + align:start position:0% +again in the sense that this U1 Global +symmetry can be considered as the global + + align:start position:0% +symmetry can be considered as the global + + + align:start position:0% +symmetry can be considered as the global +part of this U1 gauge symmetry the part + + align:start position:0% +part of this U1 gauge symmetry the part + + + align:start position:0% +part of this U1 gauge symmetry the part +which does not vanish at + + align:start position:0% +which does not vanish at + + + align:start position:0% +which does not vanish at +infinity and uh and it's always the case + + align:start position:0% +infinity and uh and it's always the case + + + align:start position:0% +infinity and uh and it's always the case +that Global super symmetry + + align:start position:0% +that Global super symmetry + + + align:start position:0% +that Global super symmetry +here will corresponding to the local + + align:start position:0% +here will corresponding to the local + + + align:start position:0% +here will corresponding to the local +super + + align:start position:0% + + + + align:start position:0% + +symmetry here and exactly also in the + + align:start position:0% +symmetry here and exactly also in the + + + align:start position:0% +symmetry here and exactly also in the +EXA the sense that even for the the + + align:start position:0% +EXA the sense that even for the the + + + align:start position:0% +EXA the sense that even for the the +local local super symmetric + + align:start position:0% +local local super symmetric + + + align:start position:0% +local local super symmetric +transformation in the gravity site + + align:start position:0% +transformation in the gravity site + + + align:start position:0% +transformation in the gravity site +there's also a part which does not Bish + + align:start position:0% +there's also a part which does not Bish + + + align:start position:0% +there's also a part which does not Bish +at infinity and that's the path + + align:start position:0% +at infinity and that's the path + + + align:start position:0% +at infinity and that's the path +corresponding to the global super + + align:start position:0% +corresponding to the global super + + + align:start position:0% +corresponding to the global super +symmetry on the field series SES + + align:start position:0% +symmetry on the field series SES + + + align:start position:0% +symmetry on the field series SES +okay yes + + align:start position:0% + + + + align:start position:0% + +what sorry in the low energy limit on + + align:start position:0% +what sorry in the low energy limit on + + + align:start position:0% +what sorry in the low energy limit on +the ads yeah what are the in the super + + align:start position:0% +the ads yeah what are the in the super + + + align:start position:0% +the ads yeah what are the in the super +oh + + align:start position:0% +oh + + + align:start position:0% +oh +the it's the same + + align:start position:0% +the it's the same + + + align:start position:0% +the it's the same +thing what do you mean what about fans + + align:start position:0% +thing what do you mean what about fans + + + align:start position:0% +thing what do you mean what about fans +there will be some + + align:start position:0% + + + + align:start position:0% + +Fons so there is more than gravitons on + + align:start position:0% +Fons so there is more than gravitons on + + + align:start position:0% +Fons so there is more than gravitons on +ads side in low low energy yeah there + + align:start position:0% +ads side in low low energy yeah there + + + align:start position:0% +ads side in low low energy yeah there +there gravitons and there also some fans + + align:start position:0% +there gravitons and there also some fans + + + align:start position:0% +there gravitons and there also some fans +there's something called gravitino there + + align:start position:0% +there's something called gravitino there + + + align:start position:0% +there's something called gravitino there +are some other fans ex yeah is it they + + align:start position:0% +are some other fans ex yeah is it they + + + align:start position:0% +are some other fans ex yeah is it they +who carry the you want G no no no here + + align:start position:0% +who carry the you want G no no no here + + + align:start position:0% +who carry the you want G no no no here +is more General here is more General I'm + + align:start position:0% +is more General here is more General I'm + + + align:start position:0% +is more General here is more General I'm +just saying yeah in this case in this + + align:start position:0% +just saying yeah in this case in this + + + align:start position:0% +just saying yeah in this case in this +case indeed those + + align:start position:0% +case indeed those + + + align:start position:0% +case indeed those +um so this assom of S5 once you reduce + + align:start position:0% +um so this assom of S5 once you reduce + + + align:start position:0% +um so this assom of S5 once you reduce +to ads5 and so that just become again + + align:start position:0% +to ads5 and so that just become again + + + align:start position:0% +to ads5 and so that just become again +become a gauge symmetry H6 gauge + + align:start position:0% +become a gauge symmetry H6 gauge + + + align:start position:0% +become a gauge symmetry H6 gauge +Symmetry and and some for me indeed are + + align:start position:0% +Symmetry and and some for me indeed are + + + align:start position:0% +Symmetry and and some for me indeed are +charged on + + align:start position:0% +charged on + + + align:start position:0% +charged on +this gaug symmetry yeah and uh here just + + align:start position:0% +this gaug symmetry yeah and uh here just + + + align:start position:0% +this gaug symmetry yeah and uh here just +more General so whatever since uh just + + align:start position:0% +more General so whatever since uh just + + + align:start position:0% +more General so whatever since uh just +if you anytime if you have some Global + + align:start position:0% +if you anytime if you have some Global + + + align:start position:0% +if you anytime if you have some Global +symmetry here you be map to some Glo + + align:start position:0% +symmetry here you be map to some Glo + + + align:start position:0% +symmetry here you be map to some Glo +gauge image here okay and uh and we will + + align:start position:0% +gauge image here okay and uh and we will + + + align:start position:0% +gauge image here okay and uh and we will +say this a little bit more uh uh uh a + + align:start position:0% +say this a little bit more uh uh uh a + + + align:start position:0% +say this a little bit more uh uh uh a +little bit later do you have any other + + align:start position:0% +little bit later do you have any other + + + align:start position:0% +little bit later do you have any other +questions okay so now let's move + + align:start position:0% +questions okay so now let's move + + + align:start position:0% +questions okay so now let's move +to the matching of parameters again this + + align:start position:0% +to the matching of parameters again this + + + align:start position:0% +to the matching of parameters again this +is more like + + align:start position:0% + + + + align:start position:0% + +um review what we discussed + + align:start position:0% + + + + align:start position:0% + +before and so again let's first + + align:start position:0% +before and so again let's first + + + align:start position:0% +before and so again let's first +so so so in the and then this is Type 2 + + align:start position:0% +so so so in the and then this is Type 2 + + + align:start position:0% +so so so in the and then this is Type 2 +B on ads5 * + + align:start position:0% +B on ads5 * + + + align:start position:0% +B on ads5 * +S5 okay so previously we said from the + + align:start position:0% +S5 okay so previously we said from the + + + align:start position:0% +S5 okay so previously we said from the +relation of the D brain so the G Square + + align:start position:0% +relation of the D brain so the G Square + + + align:start position:0% +relation of the D brain so the G Square +here is related to the 4 Pi GS here + + align:start position:0% +here is related to the 4 Pi GS here + + + align:start position:0% +here is related to the 4 Pi GS here +string + + align:start position:0% +string + + + align:start position:0% +string +cing and also from the this Rebrand + + align:start position:0% +cing and also from the this Rebrand + + + align:start position:0% +cing and also from the this Rebrand +solution we find that the G Square + + align:start position:0% +solution we find that the G Square + + + align:start position:0% +solution we find that the G Square +we find for example here the curvature + + align:start position:0% +we find for example here the curvature + + + align:start position:0% +we find for example here the curvature +so here the curvature radius R have the + + align:start position:0% +so here the curvature radius R have the + + + align:start position:0% +so here the curvature radius R have the +following form 4 Pi + + align:start position:0% +following form 4 Pi + + + align:start position:0% +following form 4 Pi +GSN Alpha Prime Square so the N is the + + align:start position:0% +GSN Alpha Prime Square so the N is the + + + align:start position:0% +GSN Alpha Prime Square so the N is the +the same n on this side okay so the N is + + align:start position:0% +the same n on this side okay so the N is + + + align:start position:0% +the same n on this side okay so the N is +the gauge group N yeah I should say the + + align:start position:0% +the gauge group N yeah I should say the + + + align:start position:0% +the gauge group N yeah I should say the +the flux n yeah uh uh anyway uh uh yeah + + align:start position:0% +the flux n yeah uh uh anyway uh uh yeah + + + align:start position:0% +the flux n yeah uh uh anyway uh uh yeah +let me add so so n so the flux so the N + + align:start position:0% +let me add so so n so the flux so the N + + + align:start position:0% +let me add so so n so the flux so the N +is the number of de brains on this side + + align:start position:0% +is the number of de brains on this side + + + align:start position:0% +is the number of de brains on this side +we translate into the flux and so so the + + align:start position:0% +we translate into the flux and so so the + + + align:start position:0% +we translate into the flux and so so the +flux n and then trans here is + + align:start position:0% +flux n and then trans here is + + + align:start position:0% +flux n and then trans here is +coresponding to you have S + + align:start position:0% + + + + align:start position:0% + +okay and so so this R this curvature + + align:start position:0% +okay and so so this R this curvature + + + align:start position:0% +okay and so so this R this curvature +radius related to the alpha Prime square + + align:start position:0% +radius related to the alpha Prime square + + + align:start position:0% +radius related to the alpha Prime square +and the GS in this way and so so on the + + align:start position:0% +and the GS in this way and so so on the + + + align:start position:0% +and the GS in this way and so so on the +on this + + align:start position:0% +on this + + + align:start position:0% +on this +side so so the dimension is parameter is + + align:start position:0% +side so so the dimension is parameter is + + + align:start position:0% +side so so the dimension is parameter is +given by R squ divid by Alpha Prime + + align:start position:0% +given by R squ divid by Alpha Prime + + + align:start position:0% +given by R squ divid by Alpha Prime +so so if you look at this relation so if + + align:start position:0% +so so if you look at this relation so if + + + align:start position:0% +so so if you look at this relation so if +you look at Alpha Prime 4 to the alpha + + align:start position:0% +you look at Alpha Prime 4 to the alpha + + + align:start position:0% +you look at Alpha Prime 4 to the alpha +Prime Square then you find this is just + + align:start position:0% +Prime Square then you find this is just + + + align:start position:0% +Prime Square then you find this is just +related + + align:start position:0% +related + + + align:start position:0% +related +up okay from this relation 4 Pi GS is + + align:start position:0% +up okay from this relation 4 Pi GS is + + + align:start position:0% +up okay from this relation 4 Pi GS is +equal just G square and the N is n okay + + align:start position:0% +equal just G square and the N is n okay + + + align:start position:0% +equal just G square and the N is n okay +so this is the relation between the + + align:start position:0% +so this is the relation between the + + + align:start position:0% +so this is the relation between the +parameter + + align:start position:0% + + + + align:start position:0% + +any questions regarding + + align:start position:0% + + + + align:start position:0% + +this okay and uh so on the gravity side + + align:start position:0% +this okay and uh so on the gravity side + + + align:start position:0% +this okay and uh so on the gravity side +we said this this is are the two + + align:start position:0% +we said this this is are the two + + + align:start position:0% +we said this this is are the two +parameters okay and of course you also + + align:start position:0% +parameters okay and of course you also + + + align:start position:0% +parameters okay and of course you also +have this + + align:start position:0% +have this + + + align:start position:0% +have this +n but these are the two basic + + align:start position:0% +n but these are the two basic + + + align:start position:0% +n but these are the two basic +parameters and we can also instead of + + align:start position:0% +parameters and we can also instead of + + + align:start position:0% +parameters and we can also instead of +using + + align:start position:0% +using + + + align:start position:0% +using +GS as we said before you can also use + + align:start position:0% +GS as we said before you can also use + + + align:start position:0% +GS as we said before you can also use +the Newton + + align:start position:0% +the Newton + + + align:start position:0% +the Newton +constant so the 10 dimensional Newton + + align:start position:0% +constant so the 10 dimensional Newton + + + align:start position:0% +constant so the 10 dimensional Newton +constant + + align:start position:0% +constant + + + align:start position:0% +constant +is dimension n Dimension eight8 then the + + align:start position:0% +is dimension n Dimension eight8 then the + + + align:start position:0% +is dimension n Dimension eight8 then the +dimension is then the dimension is + + align:start position:0% +dimension is then the dimension is + + + align:start position:0% +dimension is then the dimension is +parameter will be GN divided by R2 Power + + align:start position:0% + + + + align:start position:0% + +8 and the GN is related to + + align:start position:0% +8 and the GN is related to + + + align:start position:0% +8 and the GN is related to +the GS and AL Prime by this + + align:start position:0% + + + + align:start position:0% + +formula okay so now now you can just use + + align:start position:0% +formula okay so now now you can just use + + + align:start position:0% +formula okay so now now you can just use +the relation between the GS exactly + + align:start position:0% +the relation between the GS exactly + + + align:start position:0% +the relation between the GS exactly +translate this into your M coupling can + + align:start position:0% +translate this into your M coupling can + + + align:start position:0% +translate this into your M coupling can +M yeah just can use this relation and + + align:start position:0% +M yeah just can use this relation and + + + align:start position:0% +M yeah just can use this relation and +then use that to translate this into the + + align:start position:0% +then use that to translate this into the + + + align:start position:0% +then use that to translate this into the +parameter in the yam site then you find + + align:start position:0% +parameter in the yam site then you find + + + align:start position:0% +parameter in the yam site then you find +once you plug all those relation in how + + align:start position:0% +once you plug all those relation in how + + + align:start position:0% +once you plug all those relation in how +the GS and Alpha Prime ex related in + + align:start position:0% +the GS and Alpha Prime ex related in + + + align:start position:0% +the GS and Alpha Prime ex related in +then you find here actually GS have + + align:start position:0% +then you find here actually GS have + + + align:start position:0% +then you find here actually GS have +disappeared in this relation what you + + align:start position:0% +disappeared in this relation what you + + + align:start position:0% +disappeared in this relation what you +find is that the Newton constant + + align:start position:0% +find is that the Newton constant + + + align:start position:0% +find is that the Newton constant +essentially just related to one/ n + + align:start position:0% +essentially just related to one/ n + + + align:start position:0% +essentially just related to one/ n +Square okay after some up to some + + align:start position:0% +Square okay after some up to some + + + align:start position:0% +Square okay after some up to some +parameter just Rel to one/ n Square + + align:start position:0% +parameter just Rel to one/ n Square + + + align:start position:0% +parameter just Rel to one/ n Square +so if you expand in G Newton just like + + align:start position:0% +so if you expand in G Newton just like + + + align:start position:0% +so if you expand in G Newton just like +expanding one/ n + + align:start position:0% + + + + align:start position:0% + +s so as we said before we often do + + align:start position:0% +s so as we said before we often do + + + align:start position:0% +s so as we said before we often do +dimensional + + align:start position:0% + + + + align:start position:0% + +reduction Dimension reduction + + align:start position:0% + + + + align:start position:0% + +S5 then we get the five dimensional + + align:start position:0% +S5 then we get the five dimensional + + + align:start position:0% +S5 then we get the five dimensional +Newton + + align:start position:0% +Newton + + + align:start position:0% +Newton +constant so five dimensional Newton + + align:start position:0% +constant so five dimensional Newton + + + align:start position:0% +constant so five dimensional Newton +constant is equal to the 10 dimensional + + align:start position:0% +constant is equal to the 10 dimensional + + + align:start position:0% +constant is equal to the 10 dimensional +Newton constant and the difference is + + align:start position:0% +Newton constant and the difference is + + + align:start position:0% +Newton constant and the difference is +the volume of + + align:start position:0% + + + + align:start position:0% + +S5 volume of S5 okay this from this uh + + align:start position:0% +S5 volume of S5 okay this from this uh + + + align:start position:0% +S5 volume of S5 okay this from this uh +uh uh we wrote this down before and V + + align:start position:0% + + + + align:start position:0% + +S5 is equal to Pi Cube R to the^ 5th + + align:start position:0% +S5 is equal to Pi Cube R to the^ 5th + + + align:start position:0% +S5 is equal to Pi Cube R to the^ 5th +and then from here you can just work + + align:start position:0% +and then from here you can just work + + + align:start position:0% +and then from here you can just work +out so G5 have Dimension + + align:start position:0% +out so G5 have Dimension + + + align:start position:0% +out so G5 have Dimension +three then G5 divided R + + align:start position:0% +three then G5 divided R + + + align:start position:0% +three then G5 divided R +Cube again only related to n given by + + align:start position:0% +Cube again only related to n given by + + + align:start position:0% +Cube again only related to n given by +pi/ 2 + + align:start position:0% + + + + align:start position:0% + +n² + + align:start position:0% + + + + align:start position:0% + +okay so these relations are often useful + + align:start position:0% +okay so these relations are often useful + + + align:start position:0% +okay so these relations are often useful +in the future + + align:start position:0% + + + + align:start position:0% + +so now let's look at what is + + align:start position:0% +so now let's look at what is + + + align:start position:0% +so now let's look at what is +limits of this + + align:start position:0% +limits of this + + + align:start position:0% +limits of this +relation what is the limit of this + + align:start position:0% +relation what is the limit of this + + + align:start position:0% +relation what is the limit of this +relation so let's first look at the + + align:start position:0% +relation so let's first look at the + + + align:start position:0% +relation so let's first look at the +classical gravity limit on the gravity + + align:start position:0% +classical gravity limit on the gravity + + + align:start position:0% +classical gravity limit on the gravity +side + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +we as we discussed at the beginning of + + align:start position:0% +we as we discussed at the beginning of + + + align:start position:0% +we as we discussed at the beginning of +this uh uh + + align:start position:0% +this uh uh + + + align:start position:0% +this uh uh +class by classic we + + align:start position:0% +class by classic we + + + align:start position:0% +class by classic we +always use H bar equal to one so our H + + align:start position:0% +always use H bar equal to one so our H + + + align:start position:0% +always use H bar equal to one so our H +bar is always equal to one + + align:start position:0% + + + + align:start position:0% + +okay but quantum + + align:start position:0% +okay but quantum + + + align:start position:0% +okay but quantum +gravity is captured by this parameter H + + align:start position:0% +gravity is captured by this parameter H + + + align:start position:0% +gravity is captured by this parameter H +bar * GN okay even the H bar equal to + + align:start position:0% +bar * GN okay even the H bar equal to + + + align:start position:0% +bar * GN okay even the H bar equal to +one in the limit when GN goes to zero + + align:start position:0% +one in the limit when GN goes to zero + + + align:start position:0% +one in the limit when GN goes to zero +then you then you are in the regime + + align:start position:0% +then you then you are in the regime + + + align:start position:0% +then you then you are in the regime +which you can ignore the quantum gravity + + align:start position:0% +which you can ignore the quantum gravity + + + align:start position:0% +which you can ignore the quantum gravity +effect so that's what we mean by the uh + + align:start position:0% +effect so that's what we mean by the uh + + + align:start position:0% +effect so that's what we mean by the uh +by the classical gravity limit okay is + + align:start position:0% +by the classical gravity limit okay is + + + align:start position:0% +by the classical gravity limit okay is +that this should go to zero and then + + align:start position:0% +that this should go to zero and then + + + align:start position:0% +that this should go to zero and then +Alpha Prime should go to zero okay so + + align:start position:0% +Alpha Prime should go to zero okay so + + + align:start position:0% +Alpha Prime should go to zero okay so +this is means the stringy effect is not + + align:start position:0% +this is means the stringy effect is not + + + align:start position:0% +this is means the stringy effect is not +important and this is all in the unit of + + align:start position:0% +important and this is all in the unit of + + + align:start position:0% +important and this is all in the unit of +the r + + align:start position:0% + + + + align:start position:0% + +okay uh and here when I write those + + align:start position:0% +okay uh and here when I write those + + + align:start position:0% +okay uh and here when I write those +relations I have all set H bar equal to + + align:start position:0% +relations I have all set H bar equal to + + + align:start position:0% +relations I have all set H bar equal to +one + + align:start position:0% +one + + + align:start position:0% +one +okay so when I say the classical gravity + + align:start position:0% +okay so when I say the classical gravity + + + align:start position:0% +okay so when I say the classical gravity +limit which is disced which H byal to + + align:start position:0% +limit which is disced which H byal to + + + align:start position:0% +limit which is disced which H byal to +one but the but the effect of the Newton + + align:start position:0% +one but the but the effect of the Newton + + + align:start position:0% +one but the but the effect of the Newton +constant goes zero and the reason I'm + + align:start position:0% +constant goes zero and the reason I'm + + + align:start position:0% +constant goes zero and the reason I'm +emphasized + + align:start position:0% +emphasized + + + align:start position:0% +emphasized +it is that if you have some matter + + align:start position:0% +it is that if you have some matter + + + align:start position:0% +it is that if you have some matter +field in the in this geometry then this + + align:start position:0% +field in the in this geometry then this + + + align:start position:0% +field in the in this geometry then this +matter field should be treated as full + + align:start position:0% +matter field should be treated as full + + + align:start position:0% +matter field should be treated as full +Quantum okay they just we just don't + + align:start position:0% +Quantum okay they just we just don't + + + align:start position:0% +Quantum okay they just we just don't +treat the gravity as Quantum but those + + align:start position:0% +treat the gravity as Quantum but those + + + align:start position:0% +treat the gravity as Quantum but those +matter field should be treated as + + align:start position:0% +matter field should be treated as + + + align:start position:0% +matter field should be treated as +Quantum so the classical gravity limit + + align:start position:0% +Quantum so the classical gravity limit + + + align:start position:0% +Quantum so the classical gravity limit +is the same as + + align:start position:0% +is the same as + + + align:start position:0% +is the same as +qft Quantum field the in curve space + + align:start position:0% + + + + align:start position:0% + +time okay so gravity does not fluctuate + + align:start position:0% +time okay so gravity does not fluctuate + + + align:start position:0% +time okay so gravity does not fluctuate +so you have rigid curve space time but + + align:start position:0% +so you have rigid curve space time but + + + align:start position:0% +so you have rigid curve space time but +your math field can fluctuate H bar + + align:start position:0% +your math field can fluctuate H bar + + + align:start position:0% +your math field can fluctuate H bar +equal to one and uh so essentially we + + align:start position:0% +equal to one and uh so essentially we + + + align:start position:0% +equal to one and uh so essentially we +are dealing dealing with Quantum filter + + align:start position:0% +are dealing dealing with Quantum filter + + + align:start position:0% +are dealing dealing with Quantum filter +in curve space time okay so uh um in the + + align:start position:0% +in curve space time okay so uh um in the + + + align:start position:0% +in curve space time okay so uh um in the +in the type + + align:start position:0% +in the type + + + align:start position:0% +in the type +2B super gravity there are many many + + align:start position:0% +2B super gravity there are many many + + + align:start position:0% +2B super gravity there are many many +such kind of matter fields and they they + + align:start position:0% +such kind of matter fields and they they + + + align:start position:0% +such kind of matter fields and they they +all should be + + align:start position:0% +all should be + + + align:start position:0% +all should be +treat Quantum + + align:start position:0% + + + + align:start position:0% + +mechanically yeah it just you should + + align:start position:0% +mechanically yeah it just you should + + + align:start position:0% +mechanically yeah it just you should +consider this + + align:start position:0% +consider this + + + align:start position:0% +consider this +more so let's consider what this + + align:start position:0% +more so let's consider what this + + + align:start position:0% +more so let's consider what this +means so so GN small + + align:start position:0% +means so so GN small + + + align:start position:0% +means so so GN small +as Dimension this + + align:start position:0% +as Dimension this + + + align:start position:0% +as Dimension this +parameter this translate into field + + align:start position:0% +parameter this translate into field + + + align:start position:0% +parameter this translate into field +three + + align:start position:0% + + + + align:start position:0% + +side if we use this relation so that + + align:start position:0% +side if we use this relation so that + + + align:start position:0% +side if we use this relation so that +means n Go to Infinity so this is n + + align:start position:0% +means n Go to Infinity so this is n + + + align:start position:0% +means n Go to Infinity so this is n +limit of the yam Theory okay this is n + + align:start position:0% +limit of the yam Theory okay this is n + + + align:start position:0% +limit of the yam Theory okay this is n +limit of the Y Ser which + + align:start position:0% +limit of the Y Ser which + + + align:start position:0% +limit of the Y Ser which +we and then Alpha Prime goes to + + align:start position:0% + + + + align:start position:0% + +zero okay from the relation between the + + align:start position:0% +zero okay from the relation between the + + + align:start position:0% +zero okay from the relation between the +alpha Prime + + align:start position:0% +alpha Prime + + + align:start position:0% +alpha Prime +and here when our Prime goes zero so + + align:start position:0% +and here when our Prime goes zero so + + + align:start position:0% +and here when our Prime goes zero so +this is in the downstairs then that + + align:start position:0% +this is in the downstairs then that + + + align:start position:0% +this is in the downstairs then that +means this should go to Infinity so this + + align:start position:0% +means this should go to Infinity so this + + + align:start position:0% +means this should go to Infinity so this +means so this is what the to C we + + align:start position:0% +means so this is what the to C we + + + align:start position:0% +means so this is what the to C we +defined before Okay g Square n so this + + align:start position:0% +defined before Okay g Square n so this + + + align:start position:0% +defined before Okay g Square n so this +means the to goes to + + align:start position:0% + + + + align:start position:0% + +Infinity so now we see a remarkable + + align:start position:0% +Infinity so now we see a remarkable + + + align:start position:0% +Infinity so now we see a remarkable +relation so now we a remarkable + + align:start position:0% +relation so now we a remarkable + + + align:start position:0% +relation so now we a remarkable +relation is that so this is essentially + + align:start position:0% +relation is that so this is essentially + + + align:start position:0% +relation is that so this is essentially +what so this is what we + + align:start position:0% +what so this is what we + + + align:start position:0% +what so this is what we +expect if you still remember what we did + + align:start position:0% +expect if you still remember what we did + + + align:start position:0% +expect if you still remember what we did +before in the nigeran gauge theory in + + align:start position:0% +before in the nigeran gauge theory in + + + align:start position:0% +before in the nigeran gauge theory in +the Lage the in the L limit the + + align:start position:0% +the Lage the in the L limit the + + + align:start position:0% +the Lage the in the L limit the +fluctuations become very small Etc so + + align:start position:0% +fluctuations become very small Etc so + + + align:start position:0% +fluctuations become very small Etc so +this is consistent uh that on the + + align:start position:0% +this is consistent uh that on the + + + align:start position:0% +this is consistent uh that on the +gravity side the fluctuation in the + + align:start position:0% +gravity side the fluctuation in the + + + align:start position:0% +gravity side the fluctuation in the +geometry is very + + align:start position:0% +geometry is very + + + align:start position:0% +geometry is very +small and now we see that this the uh uh + + align:start position:0% +small and now we see that this the uh uh + + + align:start position:0% +small and now we see that this the uh uh +uh the + + align:start position:0% +uh the + + + align:start position:0% +uh the +CL the decoupling of the stringy effect + + align:start position:0% +CL the decoupling of the stringy effect + + + align:start position:0% +CL the decoupling of the stringy effect +requests on the fil series side with + + align:start position:0% +requests on the fil series side with + + + align:start position:0% +requests on the fil series side with +strong + + align:start position:0% +strong + + + align:start position:0% +strong +cing okay this is also something roughly + + align:start position:0% +cing okay this is also something roughly + + + align:start position:0% +cing okay this is also something roughly +we said + + align:start position:0% +we said + + + align:start position:0% +we said +before remember when we talk about log + + align:start position:0% +before remember when we talk about log + + + align:start position:0% +before remember when we talk about log +engage Theory when we talk about log + + align:start position:0% +engage Theory when we talk about log + + + align:start position:0% +engage Theory when we talk about log +engage + + align:start position:0% +engage + + + align:start position:0% +engage +theory in log engage Theory you have + + align:start position:0% +theory in log engage Theory you have + + + align:start position:0% +theory in log engage Theory you have +Planet diagram non Planet diagram + + align:start position:0% +Planet diagram non Planet diagram + + + align:start position:0% +Planet diagram non Planet diagram +Etc and and it at each level say at the + + align:start position:0% +Etc and and it at each level say at the + + + align:start position:0% +Etc and and it at each level say at the +planet diagram you lead to sum of + + align:start position:0% +planet diagram you lead to sum of + + + align:start position:0% +planet diagram you lead to sum of +infinite number of f diagram which are + + align:start position:0% +infinite number of f diagram which are + + + align:start position:0% +infinite number of f diagram which are +all of Planet + + align:start position:0% +all of Planet + + + align:start position:0% +all of Planet +topology and if you look at this those + + align:start position:0% +topology and if you look at this those + + + align:start position:0% +topology and if you look at this those +fan diagrams of course you don't see A + + align:start position:0% +fan diagrams of course you don't see A + + + align:start position:0% +fan diagrams of course you don't see A +Spacetime + + align:start position:0% + + + + align:start position:0% + +interpretation and because they are just + + align:start position:0% +interpretation and because they are just + + + align:start position:0% +interpretation and because they are just +fan diagrams you don't see a continuous + + align:start position:0% +fan diagrams you don't see a continuous + + + align:start position:0% +fan diagrams you don't see a continuous +surface and I already looted before that + + align:start position:0% +surface and I already looted before that + + + align:start position:0% +surface and I already looted before that +a continuous surface can + + align:start position:0% +a continuous surface can + + + align:start position:0% +a continuous surface can +emerge if that diagram become + + align:start position:0% +emerge if that diagram become + + + align:start position:0% +emerge if that diagram become +sufficiently + + align:start position:0% + + + + align:start position:0% + +complicated and the way make that + + align:start position:0% +complicated and the way make that + + + align:start position:0% +complicated and the way make that +diagram sufficiently complicated is to + + align:start position:0% +diagram sufficiently complicated is to + + + align:start position:0% +diagram sufficiently complicated is to +make this to be at strong coupling then + + align:start position:0% +make this to be at strong coupling then + + + align:start position:0% +make this to be at strong coupling then +the strong coupling then the the diagram + + align:start position:0% +the strong coupling then the the diagram + + + align:start position:0% +the strong coupling then the the diagram +is many many vertices will dominate and + + align:start position:0% +is many many vertices will dominate and + + + align:start position:0% +is many many vertices will dominate and +then the most dominate diagrams are + + align:start position:0% +then the most dominate diagrams are + + + align:start position:0% +then the most dominate diagrams are +those diagram is not those vertices and + + align:start position:0% +those diagram is not those vertices and + + + align:start position:0% +those diagram is not those vertices and +then essentially uh you go to continum + + align:start position:0% +then essentially uh you go to continum + + + align:start position:0% +then essentially uh you go to continum +limits and so this + + align:start position:0% +limits and so this + + + align:start position:0% +limits and so this +relation Express realize that kind of + + align:start position:0% +relation Express realize that kind of + + + align:start position:0% +relation Express realize that kind of +intuition okay yeah if you don't + + align:start position:0% +intuition okay yeah if you don't + + + align:start position:0% +intuition okay yeah if you don't +remember go back to your to your loads + + align:start position:0% +remember go back to your to your loads + + + align:start position:0% +remember go back to your to your loads +regarding the L andage Theory uh um + + align:start position:0% +regarding the L andage Theory uh um + + + align:start position:0% +regarding the L andage Theory uh um +yeah so this relation is also remarkable + + align:start position:0% +yeah so this relation is also remarkable + + + align:start position:0% +yeah so this relation is also remarkable +for the following + + align:start position:0% +for the following + + + align:start position:0% +for the following +reason because this limit on the gravity + + align:start position:0% +reason because this limit on the gravity + + + align:start position:0% +reason because this limit on the gravity +side is simple we can just deal + + align:start position:0% +side is simple we can just deal + + + align:start position:0% +side is simple we can just deal +with Quantum F in the curve space time + + align:start position:0% +with Quantum F in the curve space time + + + align:start position:0% +with Quantum F in the curve space time +which we know how to + + align:start position:0% +which we know how to + + + align:start position:0% +which we know how to +do but on this side it's highly long + + align:start position:0% +do but on this side it's highly long + + + align:start position:0% +do but on this side it's highly long +trivial because this is a infinite + + align:start position:0% +trivial because this is a infinite + + + align:start position:0% +trivial because this is a infinite +component limit so this is tell you that + + align:start position:0% +component limit so this is tell you that + + + align:start position:0% +component limit so this is tell you that +the strong comping limit + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +described by classical + + align:start position:0% + + + + align:start position:0% + +gravity + + align:start position:0% + + + + align:start position:0% + +okay so that means that we can actually + + align:start position:0% +okay so that means that we can actually + + + align:start position:0% +okay so that means that we can actually +use classical + + align:start position:0% +use classical + + + align:start position:0% +use classical +gravity to in principle s + + align:start position:0% +gravity to in principle s + + + align:start position:0% +gravity to in principle s +problems which are sh + + align:start position:0% + + + + align:start position:0% + +coupl so there also of course there are + + align:start position:0% +coupl so there also of course there are + + + align:start position:0% +coupl so there also of course there are +Corrections Beyond this there + + align:start position:0% +Corrections Beyond this there + + + align:start position:0% +Corrections Beyond this there +Corrections Beyond this so so quantum + + align:start position:0% +Corrections Beyond this so so quantum + + + align:start position:0% +Corrections Beyond this so so quantum +gravity + + align:start position:0% + + + + align:start position:0% + +Corrections on the gravity on this side + + align:start position:0% +Corrections on the gravity on this side + + + align:start position:0% +Corrections on the gravity on this side +you can say this is a a classic gravity + + align:start position:0% +you can say this is a a classic gravity + + + align:start position:0% +you can say this is a a classic gravity +limit if you take those parameter to go + + align:start position:0% +limit if you take those parameter to go + + + align:start position:0% +limit if you take those parameter to go +to zero but suppose those parameters are + + align:start position:0% +to zero but suppose those parameters are + + + align:start position:0% +to zero but suppose those parameters are +not zero just small then you can just + + align:start position:0% +not zero just small then you can just + + + align:start position:0% +not zero just small then you can just +expand in those parameters for example + + align:start position:0% +expand in those parameters for example + + + align:start position:0% +expand in those parameters for example +you can expand in GN divide by by R8 and + + align:start position:0% +you can expand in GN divide by by R8 and + + + align:start position:0% +you can expand in GN divide by by R8 and +that expansion essentially give you a + + align:start position:0% +that expansion essentially give you a + + + align:start position:0% +that expansion essentially give you a +quantum gravity Corrections pertivity + + align:start position:0% +quantum gravity Corrections pertivity + + + align:start position:0% +quantum gravity Corrections pertivity +and now this is from this + + align:start position:0% +and now this is from this + + + align:start position:0% +and now this is from this +relation and the expansion of GN then is + + align:start position:0% +relation and the expansion of GN then is + + + align:start position:0% +relation and the expansion of GN then is +translated so this is + + align:start position:0% + + + + align:start position:0% + +expansion in + + align:start position:0% +expansion in + + + align:start position:0% +expansion in +Newton so from that relation we see this + + align:start position:0% +Newton so from that relation we see this + + + align:start position:0% +Newton so from that relation we see this +is + + align:start position:0% +is + + + align:start position:0% +is +become the expansion one of square in + + align:start position:0% +become the expansion one of square in + + + align:start position:0% +become the expansion one of square in +the field series + + align:start position:0% + + + + align:start position:0% + +site okay yeah just uh yeah just uh + + align:start position:0% + + + + align:start position:0% + +expansion n + + align:start position:0% +expansion n + + + align:start position:0% +expansion n +squ okay + + align:start position:0% + + + + align:start position:0% + +so on this side you can also take take + + align:start position:0% +so on this side you can also take take + + + align:start position:0% +so on this side you can also take take +into account that the alpha Prime uh is + + align:start position:0% +into account that the alpha Prime uh is + + + align:start position:0% +into account that the alpha Prime uh is +non zero then the alpha Prime + + align:start position:0% +non zero then the alpha Prime + + + align:start position:0% +non zero then the alpha Prime +Corrections then the expansion in Alpha + + align:start position:0% + + + + align:start position:0% + +Prime so from this relation translate in + + align:start position:0% +Prime so from this relation translate in + + + align:start position:0% +Prime so from this relation translate in +the expansion in one over square root + + align:start position:0% +the expansion in one over square root + + + align:start position:0% +the expansion in one over square root +Lambda okay Square + + align:start position:0% +Lambda okay Square + + + align:start position:0% +Lambda okay Square +Lambda so so in + + align:start position:0% +Lambda so so in + + + align:start position:0% +Lambda so so in +principle the corrections in this uh + + align:start position:0% +principle the corrections in this uh + + + align:start position:0% +principle the corrections in this uh +Beyond this + + align:start position:0% +Beyond this + + + align:start position:0% +Beyond this +limit can again be studied on the + + align:start position:0% +limit can again be studied on the + + + align:start position:0% +limit can again be studied on the +gravity side and then and then the one / + + align:start position:0% +gravity side and then and then the one / + + + align:start position:0% +gravity side and then and then the one / +square root Lambda Corrections and + + align:start position:0% +square root Lambda Corrections and + + + align:start position:0% +square root Lambda Corrections and +corresponding to the stringy Corrections + + align:start position:0% +corresponding to the stringy Corrections + + + align:start position:0% +corresponding to the stringy Corrections +and the one over n Square Corrections + + align:start position:0% +and the one over n Square Corrections + + + align:start position:0% +and the one over n Square Corrections +corresponding to the quantum gravity + + align:start position:0% +corresponding to the quantum gravity + + + align:start position:0% +corresponding to the quantum gravity +Corrections + + align:start position:0% + + + + align:start position:0% + +okay and so this is a classical limit + + align:start position:0% +okay and so this is a classical limit + + + align:start position:0% +okay and so this is a classical limit +you can also consider a classical string + + align:start position:0% +you can also consider a classical string + + + align:start position:0% +you can also consider a classical string +limit + + align:start position:0% +limit + + + align:start position:0% +limit +we can before we discussed before in the + + align:start position:0% +we can before we discussed before in the + + + align:start position:0% +we can before we discussed before in the +classical string limit then still you + + align:start position:0% +classical string limit then still you + + + align:start position:0% +classical string limit then still you +can see the angle to + + align:start position:0% +can see the angle to + + + align:start position:0% +can see the angle to +Infinity which corresponding to + + align:start position:0% +Infinity which corresponding to + + + align:start position:0% +Infinity which corresponding to +GN R8 goes to + + align:start position:0% +GN R8 goes to + + + align:start position:0% +GN R8 goes to +zero but here the the alpha Prime can be + + align:start position:0% + + + + align:start position:0% + +arbitary and and here is the to cing can + + align:start position:0% +arbitary and and here is the to cing can + + + align:start position:0% +arbitary and and here is the to cing can +be + + align:start position:0% +be + + + align:start position:0% +be +arbitary so it can fin it yes let me + + align:start position:0% +arbitary so it can fin it yes let me + + + align:start position:0% +arbitary so it can fin it yes let me +just say Alpha Prime fin + + align:start position:0% +just say Alpha Prime fin + + + align:start position:0% +just say Alpha Prime fin +it no longer zero and then this just + + align:start position:0% +it no longer zero and then this just + + + align:start position:0% +it no longer zero and then this just +corresponding to Lambda finite which no + + align:start position:0% +corresponding to Lambda finite which no + + + align:start position:0% +corresponding to Lambda finite which no +longer + + align:start position:0% +longer + + + align:start position:0% +longer +infinite okay so this is just a standard + + align:start position:0% +infinite okay so this is just a standard + + + align:start position:0% +infinite okay so this is just a standard +to H the + + align:start position:0% +to H the + + + align:start position:0% +to H the +limit so this is just standard to limit + + align:start position:0% +limit so this is just standard to limit + + + align:start position:0% +limit so this is just standard to limit +which will take angle to Infinity but + + align:start position:0% +which will take angle to Infinity but + + + align:start position:0% +which will take angle to Infinity but +keep Lambda to be finite okay standard + + align:start position:0% +keep Lambda to be finite okay standard + + + align:start position:0% +keep Lambda to be finite okay standard +to Pro the limit which we talk about + + align:start position:0% +to Pro the limit which we talk about + + + align:start position:0% +to Pro the limit which we talk about +before in the lar engage Theory + + align:start position:0% +before in the lar engage Theory + + + align:start position:0% +before in the lar engage Theory +and then again the corrections in GN + + align:start position:0% +and then again the corrections in GN + + + align:start position:0% +and then again the corrections in GN +will be Corrections in one n + + align:start position:0% + + + + align:start position:0% + +Square so any questions yes doesn't + + align:start position:0% +Square so any questions yes doesn't + + + align:start position:0% +Square so any questions yes doesn't +small Alp R squ means a large GS no no + + align:start position:0% +small Alp R squ means a large GS no no + + + align:start position:0% +small Alp R squ means a large GS no no +that have nothing to do with + + align:start position:0% +that have nothing to do with + + + align:start position:0% +that have nothing to do with +GS uh this is independ these are two + + align:start position:0% +GS uh this is independ these are two + + + align:start position:0% +GS uh this is independ these are two +independent parameters + + align:start position:0% +independent parameters + + + align:start position:0% +independent parameters +these are two independent parameters + + align:start position:0% +these are two independent parameters + + + align:start position:0% +these are two independent parameters +yeah expression parentheses + + align:start position:0% +yeah expression parentheses + + + align:start position:0% +yeah expression parentheses +so okay okay yeah this is the um + + align:start position:0% + + + + align:start position:0% + +yeah sorry so + + align:start position:0% +yeah sorry so + + + align:start position:0% +yeah sorry so +in + + align:start position:0% +in + + + align:start position:0% +in +that LDA + + align:start position:0% + + + + align:start position:0% + +is sorry I mean lamb is fin G + + align:start position:0% +is sorry I mean lamb is fin G + + + align:start position:0% +is sorry I mean lamb is fin G +is no no that's what we discussed before + + align:start position:0% +is no no that's what we discussed before + + + align:start position:0% +is no no that's what we discussed before +in the uh in the + + align:start position:0% +in the uh in the + + + align:start position:0% +in the uh in the +um uh in the lar Engage The the + + align:start position:0% +um uh in the lar Engage The the + + + align:start position:0% +um uh in the lar Engage The the +effective coupling is Lambda Lambda is + + align:start position:0% +effective coupling is Lambda Lambda is + + + align:start position:0% +effective coupling is Lambda Lambda is +your effective coupling in the in the uh + + align:start position:0% +your effective coupling in the in the uh + + + align:start position:0% +your effective coupling in the in the uh +um in the lar + + align:start position:0% + + + + align:start position:0% + +limit yeah yeah so the so the Lambda is + + align:start position:0% +limit yeah yeah so the so the Lambda is + + + align:start position:0% +limit yeah yeah so the so the Lambda is +your coupling yeah so the + + align:start position:0% +your coupling yeah so the + + + align:start position:0% +your coupling yeah so the +gml gml indeed in that in the to limit + + align:start position:0% +gml gml indeed in that in the to limit + + + align:start position:0% +gml gml indeed in that in the to limit +the gml will go to zero when n goes + + align:start position:0% +the gml will go to zero when n goes + + + align:start position:0% +the gml will go to zero when n goes +Infinity but um but G is not the right + + align:start position:0% +Infinity but um but G is not the right + + + align:start position:0% +Infinity but um but G is not the right +parameter to look at + + align:start position:0% + + + + align:start position:0% + +things any other + + align:start position:0% + + + + align:start position:0% + +questions okay good so now we can move + + align:start position:0% +questions okay good so now we can move + + + align:start position:0% +questions okay good so now we can move +on further + + align:start position:0% + + + + align:start position:0% + +we can talk about the matching of the + + align:start position:0% + + + + align:start position:0% + +spectrum on two + + align:start position:0% + + + + align:start position:0% + +sides + + align:start position:0% +sides + + + align:start position:0% +sides +okay so from now on I will uh just + + align:start position:0% +okay so from now on I will uh just + + + align:start position:0% +okay so from now on I will uh just +restrict the essentially the semil + + align:start position:0% +restrict the essentially the semil + + + align:start position:0% +restrict the essentially the semil +classical here I should call semil + + align:start position:0% +classical here I should call semil + + + align:start position:0% +classical here I should call semil +classical gravity + + align:start position:0% + + + + align:start position:0% + +limit because we still treat the matter + + align:start position:0% +limit because we still treat the matter + + + align:start position:0% +limit because we still treat the matter +Fields essentially as Quantum so we call + + align:start position:0% +Fields essentially as Quantum so we call + + + align:start position:0% +Fields essentially as Quantum so we call +it semiclassical gravity + + align:start position:0% +it semiclassical gravity + + + align:start position:0% +it semiclassical gravity +limit so from from now on so we will + + align:start position:0% +limit so from from now on so we will + + + align:start position:0% +limit so from from now on so we will +mostly just consider the semic classical + + align:start position:0% +mostly just consider the semic classical + + + align:start position:0% +mostly just consider the semic classical +gravity regime in the gravity side + + align:start position:0% +gravity regime in the gravity side + + + align:start position:0% +gravity regime in the gravity side +because essentially we know nothing + + align:start position:0% +because essentially we know nothing + + + align:start position:0% +because essentially we know nothing +about we know very little about the + + align:start position:0% +about we know very little about the + + + align:start position:0% +about we know very little about the +string + + align:start position:0% + + + + align:start position:0% + +in uh in this + + align:start position:0% + + + + align:start position:0% + +geometry and also I will often use the + + align:start position:0% +geometry and also I will often use the + + + align:start position:0% +geometry and also I will often use the +phrase which apply to the general + + align:start position:0% +phrase which apply to the general + + + align:start position:0% +phrase which apply to the general +correspondence and not necessarily just + + align:start position:0% +correspondence and not necessarily just + + + align:start position:0% +correspondence and not necessarily just +in for super M and the type 2B stren the + + align:start position:0% +in for super M and the type 2B stren the + + + align:start position:0% +in for super M and the type 2B stren the +and + + align:start position:0% +and + + + align:start position:0% +and +uh I just use the language assuming this + + align:start position:0% +uh I just use the language assuming this + + + align:start position:0% +uh I just use the language assuming this +General correspondence between some + + align:start position:0% +General correspondence between some + + + align:start position:0% +General correspondence between some +conformal field Theory and some ads + + align:start position:0% +conformal field Theory and some ads + + + align:start position:0% +conformal field Theory and some ads +gravity Theory okay + + align:start position:0% + + + + align:start position:0% + +so so now + + align:start position:0% +so so now + + + align:start position:0% +so so now +let so if the two series have to be the + + align:start position:0% +let so if the two series have to be the + + + align:start position:0% +let so if the two series have to be the +same two side have to be the same then + + align:start position:0% +same two side have to be the same then + + + align:start position:0% +same two side have to be the same then +you should be able to map their Spectrum + + align:start position:0% +you should be able to map their Spectrum + + + align:start position:0% +you should be able to map their Spectrum +okay so you should be able to map their + + align:start position:0% +okay so you should be able to map their + + + align:start position:0% +okay so you should be able to map their +h space for + + align:start position:0% + + + + align:start position:0% + +example so uh so again just not use the + + align:start position:0% +example so uh so again just not use the + + + align:start position:0% +example so uh so again just not use the +general uh language of the boundary and + + align:start position:0% +general uh language of the boundary and + + + align:start position:0% +general uh language of the boundary and +the + + align:start position:0% +the + + + align:start position:0% +the +bo the boundary of box Theory + + align:start position:0% +bo the boundary of box Theory + + + align:start position:0% +bo the boundary of box Theory +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% + + + + align:start position:0% + +further so the boundary series is a + + align:start position:0% +further so the boundary series is a + + + align:start position:0% +further so the boundary series is a +conformal + + align:start position:0% +conformal + + + align:start position:0% +conformal +the with this + + align:start position:0% +the with this + + + align:start position:0% +the with this +symmetry + + align:start position:0% +symmetry + + + align:start position:0% +symmetry +okay so so for the moment I don't have a + + align:start position:0% +okay so so for the moment I don't have a + + + align:start position:0% +okay so so for the moment I don't have a +we see symmetry so that means that your + + align:start position:0% +we see symmetry so that means that your + + + align:start position:0% +we see symmetry so that means that your +her + + align:start position:0% + + + + align:start position:0% + +space should be organized as + + align:start position:0% + + + + align:start position:0% + +representations of the conformal + + align:start position:0% +representations of the conformal + + + align:start position:0% +representations of the conformal +group say of this a so D + + align:start position:0% +group say of this a so D + + + align:start position:0% +group say of this a so D +D2 okay + + align:start position:0% +D2 okay + + + align:start position:0% +D2 okay +and similarly here because here the The + + align:start position:0% +and similarly here because here the The + + + align:start position:0% +and similarly here because here the The +Sod comma 2 is the isometric group and + + align:start position:0% +Sod comma 2 is the isometric group and + + + align:start position:0% +Sod comma 2 is the isometric group and +which Le infinity warant and again you + + align:start position:0% +which Le infinity warant and again you + + + align:start position:0% +which Le infinity warant and again you +can you should be able to organize your + + align:start position:0% +can you should be able to organize your + + + align:start position:0% +can you should be able to organize your +her space using the representations of + + align:start position:0% +her space using the representations of + + + align:start position:0% +her space using the representations of +the S Comm and and those representation + + align:start position:0% +the S Comm and and those representation + + + align:start position:0% +the S Comm and and those representation +of course should be should be the same + + align:start position:0% +of course should be should be the same + + + align:start position:0% +of course should be should be the same +okay so say say if there's one + + align:start position:0% +okay so say say if there's one + + + align:start position:0% +okay so say say if there's one +representation here then there must be a + + align:start position:0% +representation here then there must be a + + + align:start position:0% +representation here then there must be a +rid representation here and if there's + + align:start position:0% +rid representation here and if there's + + + align:start position:0% +rid representation here and if there's +two representation two such two some + + align:start position:0% +two representation two such two some + + + align:start position:0% +two representation two such two some +representation here there will be two + + align:start position:0% +representation here there will be two + + + align:start position:0% +representation here there will be two +identical representation here okay the + + align:start position:0% +identical representation here okay the + + + align:start position:0% +identical representation here okay the +representation they must + + align:start position:0% +representation they must + + + align:start position:0% +representation they must +match and on the gra on the on the + + align:start position:0% +match and on the gra on the on the + + + align:start position:0% +match and on the gra on the on the +boundary + + align:start position:0% + + + + align:start position:0% + +side The Operators they should also + + align:start position:0% +side The Operators they should also + + + align:start position:0% +side The Operators they should also +local operators they also should also + + align:start position:0% +local operators they also should also + + + align:start position:0% +local operators they also should also +transform the under rations of the + + align:start position:0% +transform the under rations of the + + + align:start position:0% +transform the under rations of the +conformance between and uh and again + + align:start position:0% + + + + align:start position:0% + +then they can form a local operators + + align:start position:0% + + + + align:start position:0% + +can also be + + align:start position:0% +can also be + + + align:start position:0% +can also be +mapped to say the field on the gravity + + align:start position:0% +mapped to say the field on the gravity + + + align:start position:0% +mapped to say the field on the gravity +so so in the gravity + + align:start position:0% +so so in the gravity + + + align:start position:0% +so so in the gravity +site and the and the field which also + + align:start position:0% +site and the and the field which also + + + align:start position:0% +site and the and the field which also +transform under the uh field should also + + align:start position:0% +transform under the uh field should also + + + align:start position:0% +transform under the uh field should also +transform under this isometry this s so + + align:start position:0% +transform under this isometry this s so + + + align:start position:0% +transform under this isometry this s so +comma 2 isometry then that should means + + align:start position:0% +comma 2 isometry then that should means + + + align:start position:0% +comma 2 isometry then that should means +that should be a one to1 correspondence + + align:start position:0% +that should be a one to1 correspondence + + + align:start position:0% +that should be a one to1 correspondence +between the local operators here and the + + align:start position:0% +between the local operators here and the + + + align:start position:0% +between the local operators here and the +bo field in the in the gravity side okay + + align:start position:0% +bo field in the in the gravity side okay + + + align:start position:0% +bo field in the in the gravity side okay +uh uh there should be one one to one + + align:start position:0% +uh uh there should be one one to one + + + align:start position:0% +uh uh there should be one one to one +correspondence on that side for + + align:start position:0% +correspondence on that side for + + + align:start position:0% +correspondence on that side for +example in the boundary if there's some + + align:start position:0% +example in the boundary if there's some + + + align:start position:0% +example in the boundary if there's some +Scala + + align:start position:0% + + + + align:start position:0% + +operator there must be a corresponding + + align:start position:0% +operator there must be a corresponding + + + align:start position:0% +operator there must be a corresponding +uh uh scal of field on the gravity + + align:start position:0% + + + + align:start position:0% + +side okay similarly if there's some + + align:start position:0% +side okay similarly if there's some + + + align:start position:0% +side okay similarly if there's some +Vector operator in the in the boundary + + align:start position:0% +Vector operator in the in the boundary + + + align:start position:0% +Vector operator in the in the boundary +the there must be a corresponding the + + align:start position:0% +the there must be a corresponding the + + + align:start position:0% +the there must be a corresponding the +Back Field back back field on the in the + + align:start position:0% +Back Field back back field on the in the + + + align:start position:0% +Back Field back back field on the in the +in the gravity side and similarly if you + + align:start position:0% +in the gravity side and similarly if you + + + align:start position:0% +in the gravity side and similarly if you +have some symmetric tensor then this + + align:start position:0% +have some symmetric tensor then this + + + align:start position:0% +have some symmetric tensor then this +must also be related to some symmetric + + align:start position:0% +must also be related to some symmetric + + + align:start position:0% +must also be related to some symmetric +tensor okay so so now I will open use + + align:start position:0% +tensor okay so so now I will open use + + + align:start position:0% +tensor okay so so now I will open use +the rotation that I use mu mu refers to + + align:start position:0% +the rotation that I use mu mu refers to + + + align:start position:0% +the rotation that I use mu mu refers to +the boundary indices and the capital m + + align:start position:0% +the boundary indices and the capital m + + + align:start position:0% +the boundary indices and the capital m +capital m capital N refers to the back + + align:start position:0% +capital m capital N refers to the back + + + align:start position:0% +capital m capital N refers to the back +indices because they run different + + align:start position:0% +indices because they run different + + + align:start position:0% +indices because they run different +dimensions so so so then the they're not + + align:start position:0% +dimensions so so so then the they're not + + + align:start position:0% +dimensions so so so then the they're not +quite the + + align:start position:0% +quite the + + + align:start position:0% +quite the +same + + align:start position:0% +same + + + align:start position:0% +same +okay yeah one second uh yeah let me just + + align:start position:0% +okay yeah one second uh yeah let me just + + + align:start position:0% +okay yeah one second uh yeah let me just +finish so so here I'm just talking about + + align:start position:0% +finish so so here I'm just talking about + + + align:start position:0% +finish so so here I'm just talking about +the conformer symmetries and if you are + + align:start position:0% +the conformer symmetries and if you are + + + align:start position:0% +the conformer symmetries and if you are +if the Ser have some other symmetries + + align:start position:0% +if the Ser have some other symmetries + + + align:start position:0% +if the Ser have some other symmetries +say some some uh Global symmetries or + + align:start position:0% +say some some uh Global symmetries or + + + align:start position:0% +say some some uh Global symmetries or +super symmetries then again + + align:start position:0% +super symmetries then again + + + align:start position:0% +super symmetries then again +the all those fields and the state they + + align:start position:0% +the all those fields and the state they + + + align:start position:0% +the all those fields and the state they +should transform on the representations + + align:start position:0% +should transform on the representations + + + align:start position:0% +should transform on the representations +of those symmetries and again they + + align:start position:0% +of those symmetries and again they + + + align:start position:0% +of those symmetries and again they +should all match together okay they + + align:start position:0% +should all match together okay they + + + align:start position:0% +should all match together okay they +should all match together uh um yes so + + align:start position:0% +should all match together uh um yes so + + + align:start position:0% +should all match together uh um yes so +uh will we prove that the the uh how is + + align:start position:0% +uh will we prove that the the uh how is + + + align:start position:0% +uh will we prove that the the uh how is +it the uh Su Jam theor is really lived + + align:start position:0% +it the uh Su Jam theor is really lived + + + align:start position:0% +it the uh Su Jam theor is really lived +on the boundary of the ads no we did not + + align:start position:0% +on the boundary of the ads no we did not + + + align:start position:0% +on the boundary of the ads no we did not +prove that no this is just a postulate + + align:start position:0% +prove that no this is just a postulate + + + align:start position:0% +prove that no this is just a postulate +okay yeah yeah this is just a + + align:start position:0% +okay yeah yeah this is just a + + + align:start position:0% +okay yeah yeah this is just a +postulate uh + + align:start position:0% +postulate uh + + + align:start position:0% +postulate uh +first yeah let me just repeat again + + align:start position:0% + + + + align:start position:0% + +yam Siri lives on minkovski + + align:start position:0% +yam Siri lives on minkovski + + + align:start position:0% +yam Siri lives on minkovski +space and it's just a observation that + + align:start position:0% +space and it's just a observation that + + + align:start position:0% +space and it's just a observation that +minkovski space is the boundary of ads + + align:start position:0% +minkovski space is the boundary of ads + + + align:start position:0% +minkovski space is the boundary of ads +and then you say we can imagine that + + align:start position:0% +and then you say we can imagine that + + + align:start position:0% +and then you say we can imagine that +this is the + + align:start position:0% +this is the + + + align:start position:0% +this is the +boundary uh yeah yeah this relation is + + align:start position:0% +boundary uh yeah yeah this relation is + + + align:start position:0% +boundary uh yeah yeah this relation is +related to the BK and the boundary okay + + align:start position:0% +related to the BK and the boundary okay + + + align:start position:0% +related to the BK and the boundary okay +and this is a postulate based on that + + align:start position:0% +and this is a postulate based on that + + + align:start position:0% +and this is a postulate based on that +fact + + align:start position:0% + + + + align:start position:0% + +yeah yes um one of the I one of the + + align:start position:0% +yeah yes um one of the I one of the + + + align:start position:0% +yeah yes um one of the I one of the +motivations for um for thinking about + + align:start position:0% +motivations for um for thinking about + + + align:start position:0% +motivations for um for thinking about +the holographic Duality was to try to + + align:start position:0% +the holographic Duality was to try to + + + align:start position:0% +the holographic Duality was to try to +escape um wiberg WIS and theor okay and + + align:start position:0% +escape um wiberg WIS and theor okay and + + + align:start position:0% +escape um wiberg WIS and theor okay and +all of a sudden it strikes me like so so + + align:start position:0% +all of a sudden it strikes me like so so + + + align:start position:0% +all of a sudden it strikes me like so so +we're trying to get on the boundary + + align:start position:0% +we're trying to get on the boundary + + + align:start position:0% +we're trying to get on the boundary +um uh spin to mass this particles but + + align:start position:0% +um uh spin to mass this particles but + + + align:start position:0% +um uh spin to mass this particles but +then this then they will also exist in + + align:start position:0% +then this then they will also exist in + + + align:start position:0% +then this then they will also exist in +the bul sorry + + align:start position:0% +the bul sorry + + + align:start position:0% +the bul sorry +so no in the field series said there's + + align:start position:0% +so no in the field series said there's + + + align:start position:0% +so no in the field series said there's +no Mass between two particles + + align:start position:0% + + + + align:start position:0% + +the map to some field in the gravity + + align:start position:0% +the map to some field in the gravity + + + align:start position:0% +the map to some field in the gravity +side in the five Dimensions so this is + + align:start position:0% +side in the five Dimensions so this is + + + align:start position:0% +side in the five Dimensions so this is +four some four dimensional operator then + + align:start position:0% +four some four dimensional operator then + + + align:start position:0% +four some four dimensional operator then +uh then this map to some five + + align:start position:0% +uh then this map to some five + + + align:start position:0% +uh then this map to some five +dimensional + + align:start position:0% + + + + align:start position:0% + +Fields I need to think about my question + + align:start position:0% +Fields I need to think about my question + + + align:start position:0% +Fields I need to think about my question +okay good yes so one so if it's if it's + + align:start position:0% +okay good yes so one so if it's if it's + + + align:start position:0% +okay good yes so one so if it's if it's +a postulate that okay so I mean it's not + + align:start position:0% +a postulate that okay so I mean it's not + + + align:start position:0% +a postulate that okay so I mean it's not +required that the theory live on the + + align:start position:0% +required that the theory live on the + + + align:start position:0% +required that the theory live on the +boundary + + align:start position:0% +boundary + + + align:start position:0% +boundary +so it seems that that's just sort of a + + align:start position:0% +so it seems that that's just sort of a + + + align:start position:0% +so it seems that that's just sort of a +convenient way of thinking about it but + + align:start position:0% +convenient way of thinking about it but + + + align:start position:0% +convenient way of thinking about it but +if but what implications would it have + + align:start position:0% +if but what implications would it have + + + align:start position:0% +if but what implications would it have +if it live down the boundary would it + + align:start position:0% +if it live down the boundary would it + + + align:start position:0% +if it live down the boundary would it +change anything oh yeah that's what I + + align:start position:0% +change anything oh yeah that's what I + + + align:start position:0% +change anything oh yeah that's what I +said before so so this + + align:start position:0% +said before so so this + + + align:start position:0% +said before so so this +discussion does not depend on that right + + align:start position:0% +discussion does not depend on that right + + + align:start position:0% +discussion does not depend on that right +right this discussion does not depend on + + align:start position:0% +right this discussion does not depend on + + + align:start position:0% +right this discussion does not depend on +that uh you can say I don't need to + + align:start position:0% +that uh you can say I don't need to + + + align:start position:0% +that uh you can say I don't need to +worry about that whether this is on + + align:start position:0% +worry about that whether this is on + + + align:start position:0% +worry about that whether this is on +Boundary of B Etc these are just some + + align:start position:0% +Boundary of B Etc these are just some + + + align:start position:0% +Boundary of B Etc these are just some +different series I want them to be the + + align:start position:0% +different series I want them to be the + + + align:start position:0% +different series I want them to be the +same right okay but as I said last time + + align:start position:0% +same right okay but as I said last time + + + align:start position:0% +same right okay but as I said last time +if you believe this spk and the boundary + + align:start position:0% +if you believe this spk and the boundary + + + align:start position:0% +if you believe this spk and the boundary +relation then this is powerful because + + align:start position:0% +relation then this is powerful because + + + align:start position:0% +relation then this is powerful because +then you can immediately deduce that the + + align:start position:0% +then you can immediately deduce that the + + + align:start position:0% +then you can immediately deduce that the +yam Ser on the on + + align:start position:0% +yam Ser on the on + + + align:start position:0% +yam Ser on the on +S3 on S3 times time then is related to + + align:start position:0% +S3 on S3 times time then is related to + + + align:start position:0% +S3 on S3 times time then is related to +the gravity Series in the global + + align:start position:0% +the gravity Series in the global + + + align:start position:0% +the gravity Series in the global +ads and uh and that's is a non trial a + + align:start position:0% +ads and uh and that's is a non trial a + + + align:start position:0% +ads and uh and that's is a non trial a +prediction from thinking the boundary + + align:start position:0% +prediction from thinking the boundary + + + align:start position:0% +prediction from thinking the boundary +and bar relation I see yeah now you can + + align:start position:0% +and bar relation I see yeah now you can + + + align:start position:0% +and bar relation I see yeah now you can +generalize it got + + align:start position:0% +generalize it got + + + align:start position:0% +generalize it got +yeah yeah because if I just look at this + + align:start position:0% +yeah yeah because if I just look at this + + + align:start position:0% +yeah yeah because if I just look at this +relation I have no reason to to suspect + + align:start position:0% +relation I have no reason to to suspect + + + align:start position:0% +relation I have no reason to to suspect +why uh uh yeah you can argue from the + + align:start position:0% +why uh uh yeah you can argue from the + + + align:start position:0% +why uh uh yeah you can argue from the +simy point of view also uh but but that + + align:start position:0% +simy point of view also uh but but that + + + align:start position:0% +simy point of view also uh but but that +language is more + + align:start position:0% + + + + align:start position:0% + +direct yeah um in + + align:start position:0% +direct yeah um in + + + align:start position:0% +direct yeah um in +principle after establishing the + + align:start position:0% +principle after establishing the + + + align:start position:0% +principle after establishing the +relation between the yam in minkovski + + align:start position:0% +relation between the yam in minkovski + + + align:start position:0% +relation between the yam in minkovski +space time and the uh and the dis + + align:start position:0% +space time and the uh and the dis + + + align:start position:0% +space time and the uh and the dis +gravity in the P + + align:start position:0% +gravity in the P + + + align:start position:0% +gravity in the P +patch I may also uh uh just based on the + + align:start position:0% +patch I may also uh uh just based on the + + + align:start position:0% +patch I may also uh uh just based on the +group Theory aspect this say that + + align:start position:0% +group Theory aspect this say that + + + align:start position:0% +group Theory aspect this say that +should that should generalize to the am + + align:start position:0% +should that should generalize to the am + + + align:start position:0% +should that should generalize to the am +on S sphere and the global Adas you may + + align:start position:0% +on S sphere and the global Adas you may + + + align:start position:0% +on S sphere and the global Adas you may +also be able to do it that way but + + align:start position:0% +also be able to do it that way but + + + align:start position:0% +also be able to do it that way but +thinking from the holographic point of + + align:start position:0% +thinking from the holographic point of + + + align:start position:0% +thinking from the holographic point of +view give you a direct way to uh to + + align:start position:0% +view give you a direct way to uh to + + + align:start position:0% +view give you a direct way to uh to +argue that now give you alternative way + + align:start position:0% +argue that now give you alternative way + + + align:start position:0% +argue that now give you alternative way +to argue that + + align:start position:0% +to argue that + + + align:start position:0% +to argue that +yeah yes yeah also in your P set you + + align:start position:0% +yeah yes yeah also in your P set you + + + align:start position:0% +yeah yes yeah also in your P set you +have checked this holographic bound and + + align:start position:0% +have checked this holographic bound and + + + align:start position:0% +have checked this holographic bound and +uh and so that's a confirmation of this + + align:start position:0% +uh and so that's a confirmation of this + + + align:start position:0% +uh and so that's a confirmation of this +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yes so what does the M field on the + + align:start position:0% +yes so what does the M field on the + + + align:start position:0% +yes so what does the M field on the +right map to if it's same representation + + align:start position:0% +right map to if it's same representation + + + align:start position:0% +right map to if it's same representation +of sorry say it again so in the the + + align:start position:0% +of sorry say it again so in the the + + + align:start position:0% +of sorry say it again so in the the +representation line so if you have the + + align:start position:0% +representation line so if you have the + + + align:start position:0% +representation line so if you have the +mass SP to field on the right what is it + + align:start position:0% +mass SP to field on the right what is it + + + align:start position:0% +mass SP to field on the right what is it +mapped on the left uh yeah we were going + + align:start position:0% +mapped on the left uh yeah we were going + + + align:start position:0% +mapped on the left uh yeah we were going +to talk about it we are going to talk + + align:start position:0% +to talk about it we are going to talk + + + align:start position:0% +to talk about it we are going to talk +about it oh + + align:start position:0% + + + + align:start position:0% + +yeah okay so um + + align:start position:0% +yeah okay so um + + + align:start position:0% +yeah okay so um +yeah so if other symmetries then + + align:start position:0% +yeah so if other symmetries then + + + align:start position:0% +yeah so if other symmetries then +everything should match okay so now as a + + align:start position:0% +everything should match okay so now as a + + + align:start position:0% +everything should match okay so now as a +immediate + + align:start position:0% +immediate + + + align:start position:0% +immediate +check you can now just open your old + + align:start position:0% +check you can now just open your old + + + align:start position:0% +check you can now just open your old +papers and uh and if you load them and + + align:start position:0% +papers and uh and if you load them and + + + align:start position:0% +papers and uh and if you load them and +because in 8s people have worked out the + + align:start position:0% +because in 8s people have worked out the + + + align:start position:0% +because in 8s people have worked out the +super gravity Spectrum precisely on this + + align:start position:0% +super gravity Spectrum precisely on this + + + align:start position:0% +super gravity Spectrum precisely on this +space + + align:start position:0% +space + + + align:start position:0% +space +okay so even though this was this + + align:start position:0% +okay so even though this was this + + + align:start position:0% +okay so even though this was this +relation was discovered in the uh + + align:start position:0% +relation was discovered in the uh + + + align:start position:0% +relation was discovered in the uh +1997 and but actually in the ' 80s + + align:start position:0% +1997 and but actually in the ' 80s + + + align:start position:0% +1997 and but actually in the ' 80s +people worked a lot uh uh uh to consider + + align:start position:0% +people worked a lot uh uh uh to consider + + + align:start position:0% +people worked a lot uh uh uh to consider +this type to be super gravity on this + + align:start position:0% +this type to be super gravity on this + + + align:start position:0% +this type to be super gravity on this +space uh because this is a maximally + + align:start position:0% +space uh because this is a maximally + + + align:start position:0% +space uh because this is a maximally +super symmetric space Etc anyway so + + align:start position:0% +super symmetric space Etc anyway so + + + align:start position:0% +super symmetric space Etc anyway so +people have + + align:start position:0% +people have + + + align:start position:0% +people have +already spent lots of trouble actually + + align:start position:0% +already spent lots of trouble actually + + + align:start position:0% +already spent lots of trouble actually +work out those + + align:start position:0% +work out those + + + align:start position:0% +work out those +spectrum and I can just open their table + + align:start position:0% +spectrum and I can just open their table + + + align:start position:0% +spectrum and I can just open their table +open their paper then there's a big + + align:start position:0% +open their paper then there's a big + + + align:start position:0% +open their paper then there's a big +table about the different fields and + + align:start position:0% +table about the different fields and + + + align:start position:0% +table about the different fields and +their representations ET and then you + + align:start position:0% +their representations ET and then you + + + align:start position:0% +their representations ET and then you +can map them then you can immediately + + align:start position:0% +can map them then you can immediately + + + align:start position:0% +can map them then you can immediately +see they actually map to certain + + align:start position:0% +see they actually map to certain + + + align:start position:0% +see they actually map to certain +representations uh to certain operators + + align:start position:0% +representations uh to certain operators + + + align:start position:0% +representations uh to certain operators +yeah certain reputation of operators on + + align:start position:0% +yeah certain reputation of operators on + + + align:start position:0% +yeah certain reputation of operators on +the in in force of ulary then you can + + align:start position:0% +the in in force of ulary then you can + + + align:start position:0% +the in in force of ulary then you can +immediately check them okay and you can + + align:start position:0% +immediately check them okay and you can + + + align:start position:0% +immediately check them okay and you can +immediately check just based on the + + align:start position:0% +immediately check just based on the + + + align:start position:0% +immediately check just based on the +group + + align:start position:0% +group + + + align:start position:0% +group +Theory just based on group Theory check + + align:start position:0% +Theory just based on group Theory check + + + align:start position:0% +Theory just based on group Theory check +them but so I W so I won't go to those + + align:start position:0% +them but so I W so I won't go to those + + + align:start position:0% +them but so I W so I won't go to those +details but let me just mention the most + + align:start position:0% +details but let me just mention the most + + + align:start position:0% +details but let me just mention the most +important uh such kind of a mapping for + + align:start position:0% +important uh such kind of a mapping for + + + align:start position:0% +important uh such kind of a mapping for +the uh for the uh + + align:start position:0% +the uh for the uh + + + align:start position:0% +the uh for the uh +um uh for these two series and uh and + + align:start position:0% +um uh for these two series and uh and + + + align:start position:0% +um uh for these two series and uh and +actually does have consequences for + + align:start position:0% + + + + align:start position:0% + +um for for the general + + align:start position:0% + + + + align:start position:0% + +story so the most + + align:start position:0% + + + + align:start position:0% + +important so the most important uh + + align:start position:0% +important so the most important uh + + + align:start position:0% +important so the most important uh +mapping so as we said on the stren + + align:start position:0% +mapping so as we said on the stren + + + align:start position:0% +mapping so as we said on the stren +series side you always have this + + align:start position:0% +series side you always have this + + + align:start position:0% +series side you always have this +dong say this this is some scalar + + align:start position:0% +dong say this this is some scalar + + + align:start position:0% +dong say this this is some scalar +field and this will this the will appear + + align:start position:0% +field and this will this the will appear + + + align:start position:0% +field and this will this the will appear +in the scalar field in ads 5 say for + + align:start position:0% +in the scalar field in ads 5 say for + + + align:start position:0% +in the scalar field in ads 5 say for +example and now this the field is mapped + + align:start position:0% +example and now this the field is mapped + + + align:start position:0% +example and now this the field is mapped +to the L of the in + + align:start position:0% + + + + align:start position:0% + +force okay so the L of the be so the L + + align:start position:0% +force okay so the L of the be so the L + + + align:start position:0% +force okay so the L of the be so the L +is is a Lin of the in 3 say Trace M + + align:start position:0% +is is a Lin of the in 3 say Trace M + + + align:start position:0% +is is a Lin of the in 3 say Trace M +Trace F square plus five square ex so + + align:start position:0% +Trace F square plus five square ex so + + + align:start position:0% +Trace F square plus five square ex so +that's local operator and the T that + + align:start position:0% +that's local operator and the T that + + + align:start position:0% +that's local operator and the T that +operator is mapped to this + + align:start position:0% + + + + align:start position:0% + +Theon and on in for side we have this6 + + align:start position:0% +Theon and on in for side we have this6 + + + align:start position:0% +Theon and on in for side we have this6 +gaate symmetry did I just erase them + + align:start position:0% +gaate symmetry did I just erase them + + + align:start position:0% +gaate symmetry did I just erase them +yeah just have we have this s Sox SK + + align:start position:0% +yeah just have we have this s Sox SK + + + align:start position:0% +yeah just have we have this s Sox SK +symmetry then we have the current + + align:start position:0% +symmetry then we have the current + + + align:start position:0% +symmetry then we have the current +conserved + + align:start position:0% +conserved + + + align:start position:0% +conserved +current S6 conserved + + align:start position:0% +current S6 conserved + + + align:start position:0% +current S6 conserved +current and this on the gravity side + + align:start position:0% +current and this on the gravity side + + + align:start position:0% +current and this on the gravity side +it's just mapped + + align:start position:0% +it's just mapped + + + align:start position:0% +it's just mapped +to6 gauge + + align:start position:0% +to6 gauge + + + align:start position:0% +to6 gauge +field said6 + + align:start position:0% +field said6 + + + align:start position:0% +field said6 +G no in the in four this is a global + + align:start position:0% +G no in the in four this is a global + + + align:start position:0% +G no in the in four this is a global +symmetry but on this side so this + + align:start position:0% +symmetry but on this side so this + + + align:start position:0% +symmetry but on this side so this +appears as a isometry on + + align:start position:0% +appears as a isometry on + + + align:start position:0% +appears as a isometry on +S5 but when you dimensionally reduce on + + align:start position:0% +S5 but when you dimensionally reduce on + + + align:start position:0% +S5 but when you dimensionally reduce on +S5 then in a S5 then there will be a p + + align:start position:0% +S5 then in a S5 then there will be a p + + + align:start position:0% +S5 then in a S5 then there will be a p +gauge field which corresponding to to + + align:start position:0% +gauge field which corresponding to to + + + align:start position:0% +gauge field which corresponding to to +each s generators of S5 and uh and that + + align:start position:0% +each s generators of S5 and uh and that + + + align:start position:0% +each s generators of S5 and uh and that +the naturally then mapped to the this + + align:start position:0% +the naturally then mapped to the this + + + align:start position:0% +the naturally then mapped to the this +conserved current on the field series + + align:start position:0% +conserved current on the field series + + + align:start position:0% +conserved current on the field series +side + + align:start position:0% +side + + + align:start position:0% +side +okay and then then another Universal + + align:start position:0% +okay and then then another Universal + + + align:start position:0% +okay and then then another Universal +operator on the F side is a stress + + align:start position:0% +operator on the F side is a stress + + + align:start position:0% +operator on the F side is a stress +tensor so no matter what Ser you + + align:start position:0% +tensor so no matter what Ser you + + + align:start position:0% +tensor so no matter what Ser you +consider you have stress + + align:start position:0% + + + + align:start position:0% + +tensor and this is mapped + + align:start position:0% +tensor and this is mapped + + + align:start position:0% +tensor and this is mapped +to turn out to the matric + + align:start position:0% + + + + align:start position:0% + +pations it's the Matrix perations say + + align:start position:0% +pations it's the Matrix perations say + + + align:start position:0% +pations it's the Matrix perations say +deviation from the ads matric + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +again so at the representation level + + align:start position:0% +again so at the representation level + + + align:start position:0% +again so at the representation level +this is very lateral yes so this is a + + align:start position:0% +this is very lateral yes so this is a + + + align:start position:0% +this is very lateral yes so this is a +symmetric tensor this ismetric + + align:start position:0% +symmetric tensor this ismetric + + + align:start position:0% +symmetric tensor this ismetric +tensor and uh um but physically this is + + align:start position:0% +tensor and uh um but physically this is + + + align:start position:0% +tensor and uh um but physically this is +also latal uh physically also lat I we + + align:start position:0% +also latal uh physically also lat I we + + + align:start position:0% +also latal uh physically also lat I we +elaborated this a little bit uh further + + align:start position:0% +elaborated this a little bit uh further + + + align:start position:0% +elaborated this a little bit uh further +um from a different spe a a a + + align:start position:0% +um from a different spe a a a + + + align:start position:0% +um from a different spe a a a +perspective + + align:start position:0% +perspective + + + align:start position:0% +perspective +um yeah in a few + + align:start position:0% +um yeah in a few + + + align:start position:0% +um yeah in a few +minutes + + align:start position:0% + + + + align:start position:0% + +okay so do you have any questions + + align:start position:0% +okay so do you have any questions + + + align:start position:0% +okay so do you have any questions +regarding + + align:start position:0% + + + + align:start position:0% + +this so now given this mapping any + + align:start position:0% +this so now given this mapping any + + + align:start position:0% +this so now given this mapping any +operator is dual to a Back Field then + + align:start position:0% +operator is dual to a Back Field then + + + align:start position:0% +operator is dual to a Back Field then +you can ask some immediate questions + + align:start position:0% +you can ask some immediate questions + + + align:start position:0% +you can ask some immediate questions +okay you can ask some immediate question + + align:start position:0% +okay you can ask some immediate question + + + align:start position:0% +okay you can ask some immediate question +for example the quantum uh uh the uh the + + align:start position:0% +for example the quantum uh uh the uh the + + + align:start position:0% +for example the quantum uh uh the uh the +quantum numbers of these operators will + + align:start position:0% +quantum numbers of these operators will + + + align:start position:0% +quantum numbers of these operators will +map to the quantum numbers of the back + + align:start position:0% +map to the quantum numbers of the back + + + align:start position:0% +map to the quantum numbers of the back +field and and that's something I said + + align:start position:0% +field and and that's something I said + + + align:start position:0% +field and and that's something I said +you can check them the their symmetries + + align:start position:0% +you can check them the their symmetries + + + align:start position:0% +you can check them the their symmetries +uh for example not only the reputations + + align:start position:0% +uh for example not only the reputations + + + align:start position:0% +uh for example not only the reputations +on the a of under this conformance IM + + align:start position:0% +on the a of under this conformance IM + + + align:start position:0% +on the a of under this conformance IM +should map and L pations and also the + + align:start position:0% +should map and L pations and also the + + + align:start position:0% +should map and L pations and also the +the uh um the representation on the that + + align:start position:0% +the uh um the representation on the that + + + align:start position:0% +the uh um the representation on the that +S6 we also match ex okay + + align:start position:0% + + + + align:start position:0% + +and uh so for local operator on the + + align:start position:0% +and uh so for local operator on the + + + align:start position:0% +and uh so for local operator on the +field series + + align:start position:0% +field series + + + align:start position:0% +field series +side yeah so so once we have this + + align:start position:0% +side yeah so so once we have this + + + align:start position:0% +side yeah so so once we have this +mapping we can immediately ask questions + + align:start position:0% +mapping we can immediately ask questions + + + align:start position:0% +mapping we can immediately ask questions +related to uh uh uh to uh uh + + align:start position:0% +related to uh uh uh to uh uh + + + align:start position:0% +related to uh uh uh to uh uh +uh related to operators on this side and + + align:start position:0% +uh related to operators on this side and + + + align:start position:0% +uh related to operators on this side and +try to ask what's the counterpart on the + + align:start position:0% +try to ask what's the counterpart on the + + + align:start position:0% +try to ask what's the counterpart on the +other side and ask the field ask the + + align:start position:0% +other side and ask the field ask the + + + align:start position:0% +other side and ask the field ask the +story about the field on the gravity + + align:start position:0% +story about the field on the gravity + + + align:start position:0% +story about the field on the gravity +side and ask what's happened on this + + align:start position:0% +side and ask what's happened on this + + + align:start position:0% +side and ask what's happened on this +side okay we can we can then start + + align:start position:0% +side okay we can we can then start + + + align:start position:0% +side okay we can we can then start +developing the + + align:start position:0% +developing the + + + align:start position:0% +developing the +relations so + + align:start position:0% +relations so + + + align:start position:0% +relations so +so now let's start discussing them so + + align:start position:0% +so now let's start discussing them so + + + align:start position:0% +so now let's start discussing them so +the first thing you can do so immediate + + align:start position:0% +the first thing you can do so immediate + + + align:start position:0% +the first thing you can do so immediate +question you can + + align:start position:0% +question you can + + + align:start position:0% +question you can +ask is that given + + align:start position:0% + + + + align:start position:0% + +operator say operate + + align:start position:0% + + + + align:start position:0% + +all on the in the field + + align:start position:0% + + + + align:start position:0% + +Theory + + align:start position:0% +Theory + + + align:start position:0% +Theory +okay so there are some natural questions + + align:start position:0% +okay so there are some natural questions + + + align:start position:0% +okay so there are some natural questions +one can raise about this operator for + + align:start position:0% +one can raise about this operator for + + + align:start position:0% +one can raise about this operator for +example what is correlation functions + + align:start position:0% +example what is correlation functions + + + align:start position:0% +example what is correlation functions +Etc and that we will discuss a little + + align:start position:0% +Etc and that we will discuss a little + + + align:start position:0% +Etc and that we will discuss a little +bit later but now let + + align:start position:0% +bit later but now let + + + align:start position:0% +bit later but now let +me discuss a lot of natural question and + + align:start position:0% +me discuss a lot of natural question and + + + align:start position:0% +me discuss a lot of natural question and +and the Lal thing to + + align:start position:0% + + + + align:start position:0% + +do is to + + align:start position:0% + + + + align:start position:0% + +deform your original Theory + + align:start position:0% + + + + align:start position:0% + +by + + align:start position:0% + + + + align:start position:0% + +adding this operator to the + + align:start position:0% + + + + align:start position:0% + +Lin so this is + + align:start position:0% +Lin so this is + + + align:start position:0% +Lin so this is +some + + align:start position:0% +some + + + align:start position:0% +some +okay so I have operator I can put the + + align:start position:0% +okay so I have operator I can put the + + + align:start position:0% +okay so I have operator I can put the +source I can put the coefficient and + + align:start position:0% +source I can put the coefficient and + + + align:start position:0% +source I can put the coefficient and +this coefficients say may depend or not + + align:start position:0% +this coefficients say may depend or not + + + align:start position:0% +this coefficients say may depend or not +depend on the spatial SpaceTime + + align:start position:0% +depend on the spatial SpaceTime + + + align:start position:0% +depend on the spatial SpaceTime +coordinate and I can always add add such + + align:start position:0% +coordinate and I can always add add such + + + align:start position:0% +coordinate and I can always add add such +a term to Lin and then this deform my + + align:start position:0% +a term to Lin and then this deform my + + + align:start position:0% +a term to Lin and then this deform my +Ser away from the original the so this + + align:start position:0% +Ser away from the original the so this + + + align:start position:0% +Ser away from the original the so this +is a natural thing to do and this 5 Z is + + align:start position:0% +is a natural thing to do and this 5 Z is + + + align:start position:0% +is a natural thing to do and this 5 Z is +often called the + + align:start position:0% + + + + align:start position:0% + +source so this 5 Z is called The + + align:start position:0% + + + + align:start position:0% + +Source + + align:start position:0% +Source + + + align:start position:0% +Source +okay so immediate question you can ask + + align:start position:0% +okay so immediate question you can ask + + + align:start position:0% +okay so immediate question you can ask +askk and when 5 Z is equal to + + align:start position:0% +askk and when 5 Z is equal to + + + align:start position:0% +askk and when 5 Z is equal to +constant when it's 5 Z equal to + + align:start position:0% +constant when it's 5 Z equal to + + + align:start position:0% +constant when it's 5 Z equal to +constant then this corresponding to a + + align:start position:0% +constant then this corresponding to a + + + align:start position:0% +constant then this corresponding to a +change in the + + align:start position:0% + + + + align:start position:0% + +coupling for for for this + + align:start position:0% +coupling for for for this + + + align:start position:0% +coupling for for for this +operator okay say if you L say if your l + + align:start position:0% +operator okay say if you L say if your l + + + align:start position:0% +operator okay say if you L say if your l +previously already included this + + align:start position:0% +previously already included this + + + align:start position:0% +previously already included this +operator and then if you add such a term + + align:start position:0% +operator and then if you add such a term + + + align:start position:0% +operator and then if you add such a term +say with 5 Z equal to constant then you + + align:start position:0% +say with 5 Z equal to constant then you + + + align:start position:0% +say with 5 Z equal to constant then you +are just changing the coing uh for that + + align:start position:0% +are just changing the coing uh for that + + + align:start position:0% +are just changing the coing uh for that +operator and if this operator is not + + align:start position:0% +operator and if this operator is not + + + align:start position:0% +operator and if this operator is not +there then then you just uh add a new + + align:start position:0% +there then then you just uh add a new + + + align:start position:0% +there then then you just uh add a new +cing okay but in general you can make it + + align:start position:0% +cing okay but in general you can make it + + + align:start position:0% +cing okay but in general you can make it +space time dependent and uh uh um yeah + + align:start position:0% +space time dependent and uh uh um yeah + + + align:start position:0% +space time dependent and uh uh um yeah +okay why is cing since there is no other + + align:start position:0% +okay why is cing since there is no other + + + align:start position:0% +okay why is cing since there is no other +operators coupling with our if we say 5 + + align:start position:0% +operators coupling with our if we say 5 + + + align:start position:0% +operators coupling with our if we say 5 +Z is a constant sorry if 5 Z is a + + align:start position:0% +Z is a constant sorry if 5 Z is a + + + align:start position:0% +Z is a constant sorry if 5 Z is a +constant no O is a operator it's a local + + align:start position:0% +constant no O is a operator it's a local + + + align:start position:0% +constant no O is a operator it's a local +operator yes but yeah but there is no + + align:start position:0% +operator yes but yeah but there is no + + + align:start position:0% +operator yes but yeah but there is no +other operators this operator are + + align:start position:0% +other operators this operator are + + + align:start position:0% +other operators this operator are +coupling with no no no + + align:start position:0% +coupling with no no no + + + align:start position:0% +coupling with no no no +no what is the meaning of operator the + + align:start position:0% +no what is the meaning of operator the + + + align:start position:0% +no what is the meaning of operator the +meaning of operator is that O is + + align:start position:0% +meaning of operator is that O is + + + align:start position:0% +meaning of operator is that O is +a is a it's a sum of the product of + + align:start position:0% +a is a it's a sum of the product of + + + align:start position:0% +a is a it's a sum of the product of +fields oh okay and and so uh so this + + align:start position:0% +fields oh okay and and so uh so this + + + align:start position:0% +fields oh okay and and so uh so this +already say this all might be 5 Cube or + + align:start position:0% +already say this all might be 5 Cube or + + + align:start position:0% +already say this all might be 5 Cube or +maybe be 54 Etc okay + + align:start position:0% +maybe be 54 Etc okay + + + align:start position:0% +maybe be 54 Etc okay +okay okay yeah so example so so example + + align:start position:0% +okay okay yeah so example so so example + + + align:start position:0% +okay okay yeah so example so so example +is O say in the scaler field the uh if + + align:start position:0% +is O say in the scaler field the uh if + + + align:start position:0% +is O say in the scaler field the uh if +the field Theory uh have a scaler yeah + + align:start position:0% +the field Theory uh have a scaler yeah + + + align:start position:0% +the field Theory uh have a scaler yeah +if a scal field have a have a a gauge + + align:start position:0% +if a scal field have a have a a gauge + + + align:start position:0% +if a scal field have a have a a gauge +field then I can say write all as Trace + + align:start position:0% +field then I can say write all as Trace + + + align:start position:0% +field then I can say write all as Trace +F square and then then this + + align:start position:0% +F square and then then this + + + align:start position:0% +F square and then then this +corresponding to change the cooning for + + align:start position:0% +corresponding to change the cooning for + + + align:start position:0% +corresponding to change the cooning for +for Trace F Square okay + + align:start position:0% + + + + align:start position:0% + +so so immediate question is what does + + align:start position:0% +so so immediate question is what does + + + align:start position:0% +so so immediate question is what does +this operation so so in the fil three + + align:start position:0% +this operation so so in the fil three + + + align:start position:0% +this operation so so in the fil three +point of view you can always do this + + align:start position:0% +point of view you can always do this + + + align:start position:0% +point of view you can always do this +operation okay so the immediate question + + align:start position:0% +operation okay so the immediate question + + + align:start position:0% +operation okay so the immediate question +what does this corresponding to in the + + align:start position:0% +what does this corresponding to in the + + + align:start position:0% +what does this corresponding to in the +bo + + align:start position:0% +bo + + + align:start position:0% +bo +okay what does + + align:start position:0% +okay what does + + + align:start position:0% +okay what does +this + + align:start position:0% + + + + align:start position:0% + +operation corespond to + + align:start position:0% + + + + align:start position:0% + +in the + + align:start position:0% + + + + align:start position:0% + +B + + align:start position:0% + + + + align:start position:0% + +okay so now I try to answer this + + align:start position:0% +okay so now I try to answer this + + + align:start position:0% +okay so now I try to answer this +question as I said before in doing in + + align:start position:0% +question as I said before in doing in + + + align:start position:0% +question as I said before in doing in +establishing such + + align:start position:0% +establishing such + + + align:start position:0% +establishing such +dictionary you often have to do lots of + + align:start position:0% +dictionary you often have to do lots of + + + align:start position:0% +dictionary you often have to do lots of +gas work and then you check and the gas + + align:start position:0% +gas work and then you check and the gas + + + align:start position:0% +gas work and then you check and the gas +work is based on some very small Clues + + align:start position:0% +work is based on some very small Clues + + + align:start position:0% +work is based on some very small Clues +so so people who are able to make good + + align:start position:0% +so so people who are able to make good + + + align:start position:0% +so so people who are able to make good +guesses is that they able to grasp uh + + align:start position:0% +guesses is that they able to grasp uh + + + align:start position:0% +guesses is that they able to grasp uh +important Clues sometimes from very + + align:start position:0% +important Clues sometimes from very + + + align:start position:0% +important Clues sometimes from very +simple fact okay from very simple fact + + align:start position:0% +simple fact okay from very simple fact + + + align:start position:0% +simple fact okay from very simple fact +and so that is what good physicists do + + align:start position:0% +and so that is what good physicists do + + + align:start position:0% +and so that is what good physicists do +is that they can see non-ordinary Sin + + align:start position:0% +is that they can see non-ordinary Sin + + + align:start position:0% +is that they can see non-ordinary Sin +from the ordinary + + align:start position:0% +from the ordinary + + + align:start position:0% +from the ordinary +sin so um so here I will try to + + align:start position:0% + + + + align:start position:0% + +deduce the answer to this + + align:start position:0% +deduce the answer to this + + + align:start position:0% +deduce the answer to this +question by starting from this + + align:start position:0% + + + + align:start position:0% + +relation + + align:start position:0% +relation + + + align:start position:0% +relation +okay so uh so let me start with that + + align:start position:0% + + + + align:start position:0% + +relation so related to the GS okay so + + align:start position:0% +relation so related to the GS okay so + + + align:start position:0% +relation so related to the GS okay so +let's forget about P for + + align:start position:0% +let's forget about P for + + + align:start position:0% +let's forget about P for +pi and now we talked about before GS + + align:start position:0% +pi and now we talked about before GS + + + align:start position:0% +pi and now we talked about before GS +string coupling can be considered as the + + align:start position:0% +string coupling can be considered as the + + + align:start position:0% +string coupling can be considered as the +expectation value of the Daton field let + + align:start position:0% +expectation value of the Daton field let + + + align:start position:0% +expectation value of the Daton field let +me actually call it capital + + align:start position:0% + + + + align:start position:0% + +F so so we mentioned before when we talk + + align:start position:0% +F so so we mentioned before when we talk + + + align:start position:0% +F so so we mentioned before when we talk +about string theory that this string + + align:start position:0% +about string theory that this string + + + align:start position:0% +about string theory that this string +cing can be considered as expectation + + align:start position:0% +cing can be considered as expectation + + + align:start position:0% +cing can be considered as expectation +value of the um Daton + + align:start position:0% + + + + align:start position:0% + +field and what of course in general + + align:start position:0% +field and what of course in general + + + align:start position:0% +field and what of course in general +again the DAT time can be fluctuate Etc + + align:start position:0% +again the DAT time can be fluctuate Etc + + + align:start position:0% +again the DAT time can be fluctuate Etc +so what normally we mean say normally in + + align:start position:0% +so what normally we mean say normally in + + + align:start position:0% +so what normally we mean say normally in +flat space when we say the D has + + align:start position:0% +flat space when we say the D has + + + align:start position:0% +flat space when we say the D has +expectation value what we normally say + + align:start position:0% +expectation value what we normally say + + + align:start position:0% +expectation value what we normally say +is that the value of the D time at the + + align:start position:0% +is that the value of the D time at the + + + align:start position:0% +is that the value of the D time at the +infinity okay because the the boundary + + align:start position:0% +infinity okay because the the boundary + + + align:start position:0% +infinity okay because the the boundary +value at Infinity that's how + + align:start position:0% +value at Infinity that's how + + + align:start position:0% +value at Infinity that's how +you fix the + + align:start position:0% +you fix the + + + align:start position:0% +you fix the +um + + align:start position:0% +um + + + align:start position:0% +um +yeah and and similarly for space time + + align:start position:0% +yeah and and similarly for space time + + + align:start position:0% +yeah and and similarly for space time +like ads with a + + align:start position:0% + + + + align:start position:0% + +boundary and the expectation + + align:start position:0% +boundary and the expectation + + + align:start position:0% +boundary and the expectation +value of this the can be can be + + align:start position:0% +value of this the can be can be + + + align:start position:0% +value of this the can be can be +identified with the value of the D at + + align:start position:0% +identified with the value of the D at + + + align:start position:0% +identified with the value of the D at +the boundary of + + align:start position:0% +the boundary of + + + align:start position:0% +the boundary of +ads okay so here write partial ads means + + align:start position:0% +ads okay so here write partial ads means + + + align:start position:0% +ads okay so here write partial ads means +the boundary of ads + + align:start position:0% +the boundary of ads + + + align:start position:0% +the boundary of ads +okay so so this is the value of + + align:start position:0% +okay so so this is the value of + + + align:start position:0% +okay so so this is the value of +ads value of five at the + + align:start position:0% + + + + align:start position:0% + +boundary okay the expectation value + + align:start position:0% +boundary okay the expectation value + + + align:start position:0% +boundary okay the expectation value +essentially can be associated with the + + align:start position:0% +essentially can be associated with the + + + align:start position:0% +essentially can be associated with the +bound foundary value of the field + + align:start position:0% +bound foundary value of the field + + + align:start position:0% +bound foundary value of the field +okay you mean if it is a constant if the + + align:start position:0% +okay you mean if it is a constant if the + + + align:start position:0% +okay you mean if it is a constant if the +explation value of the f is constant or + + align:start position:0% +explation value of the f is constant or + + + align:start position:0% +explation value of the f is constant or +if function y equal to the boundary no + + align:start position:0% +if function y equal to the boundary no + + + align:start position:0% +if function y equal to the boundary no +no no think about the following thing + + align:start position:0% +no no think about the following thing + + + align:start position:0% +no no think about the following thing +yes I said uh fire in principle can + + align:start position:0% +yes I said uh fire in principle can + + + align:start position:0% +yes I said uh fire in principle can +fluctuate and its expectation may also + + align:start position:0% +fluctuate and its expectation may also + + + align:start position:0% +fluctuate and its expectation may also +be able to fluctuate in the space time + + align:start position:0% +be able to fluctuate in the space time + + + align:start position:0% +be able to fluctuate in the space time +but the only sensible way to talk about + + align:start position:0% +but the only sensible way to talk about + + + align:start position:0% +but the only sensible way to talk about +expectation value uh is to talk about + + align:start position:0% +expectation value uh is to talk about + + + align:start position:0% +expectation value uh is to talk about +its value at the boundary because we + + align:start position:0% +its value at the boundary because we + + + align:start position:0% +its value at the boundary because we +assume the boundary condition don't + + align:start position:0% +assume the boundary condition don't + + + align:start position:0% +assume the boundary condition don't +fluctuates yeah uh it's the same thing + + align:start position:0% +fluctuates yeah uh it's the same thing + + + align:start position:0% +fluctuates yeah uh it's the same thing +for flat space and we always specify the + + align:start position:0% +for flat space and we always specify the + + + align:start position:0% +for flat space and we always specify the +boundary condition at the spatial + + align:start position:0% +boundary condition at the spatial + + + align:start position:0% +boundary condition at the spatial +Infinity for example and in the in the + + align:start position:0% +Infinity for example and in the in the + + + align:start position:0% +Infinity for example and in the in the +ads which is also space time with a + + align:start position:0% +ads which is also space time with a + + + align:start position:0% +ads which is also space time with a +boundary then then we can associate this + + align:start position:0% +boundary then then we can associate this + + + align:start position:0% +boundary then then we can associate this +uh uh the constant parts of the the + + align:start position:0% +uh uh the constant parts of the the + + + align:start position:0% +uh uh the constant parts of the the +expectation value as the value at the + + align:start position:0% +expectation value as the value at the + + + align:start position:0% +expectation value as the value at the +boundary okay + + align:start position:0% + + + + align:start position:0% + +now now you have to use a little bit + + align:start position:0% +now now you have to use a little bit + + + align:start position:0% +now now you have to use a little bit +stretch of + + align:start position:0% + + + + align:start position:0% + +imagination of the following fact you + + align:start position:0% +imagination of the following fact you + + + align:start position:0% +imagination of the following fact you +don't need to so now we have now with + + align:start position:0% +don't need to so now we have now with + + + align:start position:0% +don't need to so now we have now with +this relation we have exact the + + align:start position:0% +this relation we have exact the + + + align:start position:0% +this relation we have exact the +connection between the yam Ser + + align:start position:0% +connection between the yam Ser + + + align:start position:0% +connection between the yam Ser +comping with the value of five at the + + align:start position:0% +comping with the value of five at the + + + align:start position:0% +comping with the value of five at the +boundary of ads okay + + align:start position:0% +boundary of ads okay + + + align:start position:0% +boundary of ads okay +the boundary value of + + align:start position:0% +the boundary value of + + + align:start position:0% +the boundary value of +ads + + align:start position:0% +ads + + + align:start position:0% +ads +okay and now remember this + + align:start position:0% +okay and now remember this + + + align:start position:0% +okay and now remember this +yam cing say up + + align:start position:0% +yam cing say up + + + align:start position:0% +yam cing say up +to yes I will not be careful about one + + align:start position:0% +to yes I will not be careful about one + + + align:start position:0% +to yes I will not be careful about one +over y square or just this is related + + align:start position:0% +over y square or just this is related + + + align:start position:0% +over y square or just this is related +this is the + + align:start position:0% + + + + align:start position:0% + +cing or + + align:start position:0% + + + + align:start position:0% + +source for the lrin of in for super ser + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +now we can deduce + + align:start position:0% +now we can deduce + + + align:start position:0% +now we can deduce +here two + + align:start position:0% +here two + + + align:start position:0% +here two +things in + + align:start position:0% +things in + + + align:start position:0% +things in +particular if we deform + + align:start position:0% + + + + align:start position:0% + +deform the Lin say say change this cing + + align:start position:0% +deform the Lin say say change this cing + + + align:start position:0% +deform the Lin say say change this cing +okay deform the + + align:start position:0% +okay deform the + + + align:start position:0% +okay deform the +boundary by changing the by changing the + + align:start position:0% +boundary by changing the by changing the + + + align:start position:0% +boundary by changing the by changing the +coupling which corresponding you add + + align:start position:0% +coupling which corresponding you add + + + align:start position:0% +coupling which corresponding you add +some data G say say the L + + align:start position:0% +some data G say say the L + + + align:start position:0% +some data G say say the L +of + + align:start position:0% +of + + + align:start position:0% +of +okay def the boundary by changing the + + align:start position:0% +okay def the boundary by changing the + + + align:start position:0% +okay def the boundary by changing the +cing and this corresponding + + align:start position:0% +cing and this corresponding + + + align:start position:0% +cing and this corresponding +to you essentially change the value + + align:start position:0% +to you essentially change the value + + + align:start position:0% +to you essentially change the value +change the boundary value + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% + + + + align:start position:0% + +D okay because these are + + align:start position:0% + + + + align:start position:0% + +related so + + align:start position:0% +related so + + + align:start position:0% +related so +now this example give us the answer to + + align:start position:0% +now this example give us the answer to + + + align:start position:0% +now this example give us the answer to +this + + align:start position:0% + + + + align:start position:0% + +question + + align:start position:0% +question + + + align:start position:0% +question +this + + align:start position:0% + + + + align:start position:0% + +this example of + + align:start position:0% +this example of + + + align:start position:0% +this example of +give us this + + align:start position:0% + + + + align:start position:0% + +question from here we can deduce + + align:start position:0% +question from here we can deduce + + + align:start position:0% +question from here we can deduce +first that the + + align:start position:0% +first that the + + + align:start position:0% +first that the +dat say must + + align:start position:0% +dat say must + + + align:start position:0% +dat say must +be the the operator corresponding to the + + align:start position:0% +be the the operator corresponding to the + + + align:start position:0% +be the the operator corresponding to the +D must be + + align:start position:0% + + + + align:start position:0% + +the as you can already deduce from some + + align:start position:0% +the as you can already deduce from some + + + align:start position:0% +the as you can already deduce from some +other methods say using uh group Theory + + align:start position:0% +other methods say using uh group Theory + + + align:start position:0% +other methods say using uh group Theory +Etc + + align:start position:0% + + + + align:start position:0% + +and the + + align:start position:0% +and the + + + align:start position:0% +and the +second is + + align:start position:0% +second is + + + align:start position:0% +second is +that is at 5 z + + align:start position:0% +that is at 5 z + + + align:start position:0% +that is at 5 z +o in the boundary Theory adding a 0 in + + align:start position:0% +o in the boundary Theory adding a 0 in + + + align:start position:0% +o in the boundary Theory adding a 0 in +the boundary + + align:start position:0% + + + + align:start position:0% + +Theory must be + + align:start position:0% +Theory must be + + + align:start position:0% +Theory must be +related so now I'm generalizing this + + align:start position:0% +related so now I'm generalizing this + + + align:start position:0% +related so now I'm generalizing this +story that the Back Field five so now + + align:start position:0% +story that the Back Field five so now + + + align:start position:0% +story that the Back Field five so now +I'm no longer not necessarily using the + + align:start position:0% +I'm no longer not necessarily using the + + + align:start position:0% +I'm no longer not necessarily using the +Daton the Back Field five I dual + + align:start position:0% +Daton the Back Field five I dual + + + align:start position:0% +Daton the Back Field five I dual +to + + align:start position:0% +to + + + align:start position:0% +to +O has a boundary + + align:start position:0% + + + + align:start position:0% + +value 5 + + align:start position:0% +value 5 + + + align:start position:0% +value 5 +Z + + align:start position:0% + + + + align:start position:0% + +okay any questions about this + + align:start position:0% + + + + align:start position:0% + +yes the choice of operator o should be + + align:start position:0% +yes the choice of operator o should be + + + align:start position:0% +yes the choice of operator o should be +consistent to those symmetries right + + align:start position:0% +consistent to those symmetries right + + + align:start position:0% +consistent to those symmetries right +you're not pre choosing o no o can be + + align:start position:0% +you're not pre choosing o no o can be + + + align:start position:0% +you're not pre choosing o no o can be +anything consistent with original + + align:start position:0% +anything consistent with original + + + align:start position:0% +anything consistent with original +symmetries of the no it doesn't have to + + align:start position:0% +symmetries of the no it doesn't have to + + + align:start position:0% +symmetries of the no it doesn't have to +you can deform the theory without be + + align:start position:0% +you can deform the theory without be + + + align:start position:0% +you can deform the theory without be +cons yeah you can break the Symmetry + + align:start position:0% +cons yeah you can break the Symmetry + + + align:start position:0% +cons yeah you can break the Symmetry +that deformation can break the Symmetry + + align:start position:0% +that deformation can break the Symmetry + + + align:start position:0% +that deformation can break the Symmetry +and if you want to preserve the symmetry + + align:start position:0% +and if you want to preserve the symmetry + + + align:start position:0% +and if you want to preserve the symmetry +of the original groundin then then you + + align:start position:0% +of the original groundin then then you + + + align:start position:0% +of the original groundin then then you +can choose a certain low but in + + align:start position:0% +can choose a certain low but in + + + align:start position:0% +can choose a certain low but in +principle you can add any o you can + + align:start position:0% +principle you can add any o you can + + + align:start position:0% +principle you can add any o you can +break the Symmetry if you + + align:start position:0% +break the Symmetry if you + + + align:start position:0% +break the Symmetry if you +want you have to always break some + + align:start position:0% +want you have to always break some + + + align:start position:0% +want you have to always break some +symmetry on the ads part yeah yeah + + align:start position:0% +symmetry on the ads part yeah yeah + + + align:start position:0% +symmetry on the ads part yeah yeah +yeah impose this kind of boundary + + align:start position:0% +yeah impose this kind of boundary + + + align:start position:0% +yeah impose this kind of boundary +conditions then you may break ads image + + align:start position:0% +conditions then you may break ads image + + + align:start position:0% +conditions then you may break ads image +too okay so now we have answered this + + align:start position:0% +too okay so now we have answered this + + + align:start position:0% +too okay so now we have answered this +question and then of + + align:start position:0% +question and then of + + + align:start position:0% +question and then of +course yeah this just provide answer + + align:start position:0% +course yeah this just provide answer + + + align:start position:0% +course yeah this just provide answer +then you will check it and we will check + + align:start position:0% +then you will check it and we will check + + + align:start position:0% +then you will check it and we will check +it later using other methods uh now I'm + + align:start position:0% +it later using other methods uh now I'm + + + align:start position:0% +it later using other methods uh now I'm +saying because I already know it's true + + align:start position:0% +saying because I already know it's true + + + align:start position:0% +saying because I already know it's true +but but in real life what we do + + align:start position:0% +but but in real life what we do + + + align:start position:0% +but but in real life what we do +from this example you will say ah this + + align:start position:0% +from this example you will say ah this + + + align:start position:0% +from this example you will say ah this +must be the case then you start trying + + align:start position:0% +must be the case then you start trying + + + align:start position:0% +must be the case then you start trying +to find examples to check it okay it + + align:start position:0% +to find examples to check it okay it + + + align:start position:0% +to find examples to check it okay it +start to find other ways to check it and + + align:start position:0% +start to find other ways to check it and + + + align:start position:0% +start to find other ways to check it and +we we will describe it later so uh uh in + + align:start position:0% +we we will describe it later so uh uh in + + + align:start position:0% +we we will describe it later so uh uh in +the end what we will describe is a self + + align:start position:0% +the end what we will describe is a self + + + align:start position:0% +the end what we will describe is a self +consistent story I will not contradict + + align:start position:0% +consistent story I will not contradict + + + align:start position:0% +consistent story I will not contradict +myself in my later + + align:start position:0% +myself in my later + + + align:start position:0% +myself in my later +discussion so if we assume + + align:start position:0% + + + + align:start position:0% + +this if we assume this + + align:start position:0% + + + + align:start position:0% + +I can also use this to + + align:start position:0% + + + + align:start position:0% + +argue I can also make use this + + align:start position:0% +argue I can also make use this + + + align:start position:0% +argue I can also make use this +identification okay use this + + align:start position:0% + + + + align:start position:0% + +identification to argue these two so let + + align:start position:0% +identification to argue these two so let + + + align:start position:0% +identification to argue these two so let +me call this star + + align:start position:0% +me call this star + + + align:start position:0% +me call this star +and star + + align:start position:0% +and star + + + align:start position:0% +and star +star can use this identification to ask + + align:start position:0% +star can use this identification to ask + + + align:start position:0% +star can use this identification to ask +to + + align:start position:0% +to + + + align:start position:0% +to +make + + align:start position:0% + + + + align:start position:0% + +star and star star + + align:start position:0% + + + + align:start position:0% + +natural for any for any + + align:start position:0% +natural for any for any + + + align:start position:0% +natural for any for any +Duality not only say Ang for super and + + align:start position:0% +Duality not only say Ang for super and + + + align:start position:0% +Duality not only say Ang for super and +and the + + align:start position:0% +and the + + + align:start position:0% +and the +and this type to be + + align:start position:0% + + + + align:start position:0% + +gravity is that any conserved current in + + align:start position:0% +gravity is that any conserved current in + + + align:start position:0% +gravity is that any conserved current in +the foundary C must be dual to some + + align:start position:0% +the foundary C must be dual to some + + + align:start position:0% +the foundary C must be dual to some +gauge field in the gravity s and the + + align:start position:0% +gauge field in the gravity s and the + + + align:start position:0% +gauge field in the gravity s and the +stress tensor should always be dual to + + align:start position:0% +stress tensor should always be dual to + + + align:start position:0% +stress tensor should always be dual to +the metric okay so so now I'm trying now + + align:start position:0% +the metric okay so so now I'm trying now + + + align:start position:0% +the metric okay so so now I'm trying now +I'm going to use this + + align:start position:0% +I'm going to use this + + + align:start position:0% +I'm going to use this +argument to make that a little bit more + + align:start position:0% +argument to make that a little bit more + + + align:start position:0% +argument to make that a little bit more +latal + + align:start position:0% +latal + + + align:start position:0% +latal +okay so + + align:start position:0% + + + + align:start position:0% + +first so so let's first consider this + + align:start position:0% +first so so let's first consider this + + + align:start position:0% +first so so let's first consider this +so suppose I have a corrent suppose I + + align:start position:0% +so suppose I have a corrent suppose I + + + align:start position:0% +so suppose I have a corrent suppose I +have a conserved current J + + align:start position:0% + + + + align:start position:0% + +J I have a j mu say for for Simplicity + + align:start position:0% +J I have a j mu say for for Simplicity + + + align:start position:0% +J I have a j mu say for for Simplicity +letbe just take it to be + + align:start position:0% +letbe just take it to be + + + align:start position:0% +letbe just take it to be +U1 then I can deform the boundary Theory + + align:start position:0% +U1 then I can deform the boundary Theory + + + align:start position:0% +U1 then I can deform the boundary Theory +by by adding a source for this J + + align:start position:0% +by by adding a source for this J + + + align:start position:0% +by by adding a source for this J +mu so by adding the boundary ling a term + + align:start position:0% +mu so by adding the boundary ling a term + + + align:start position:0% +mu so by adding the boundary ling a term +like this and am is a + + align:start position:0% +like this and am is a + + + align:start position:0% +like this and am is a +source okay + + align:start position:0% +source okay + + + align:start position:0% +source okay +it me is a + + align:start position:0% +it me is a + + + align:start position:0% +it me is a +source and then according to this + + align:start position:0% +source and then according to this + + + align:start position:0% +source and then according to this +identification then a mu must + + align:start position:0% +identification then a mu must + + + align:start position:0% +identification then a mu must +be a + + align:start position:0% +be a + + + align:start position:0% +be a +mu we should be able to identify + + align:start position:0% +mu we should be able to identify + + + align:start position:0% +mu we should be able to identify +it as the boundary value of some back + + align:start position:0% +it as the boundary value of some back + + + align:start position:0% +it as the boundary value of some back +field a mu evaluated at Z equal to + + align:start position:0% +field a mu evaluated at Z equal to + + + align:start position:0% +field a mu evaluated at Z equal to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay so this is a b Vector field + + align:start position:0% + + + + align:start position:0% + +so yeah yeah back back field so if this + + align:start position:0% +so yeah yeah back back field so if this + + + align:start position:0% +so yeah yeah back back field so if this +is true there must exist a v field du to + + align:start position:0% +is true there must exist a v field du to + + + align:start position:0% +is true there must exist a v field du to +to this Vector field and this must + + align:start position:0% +to this Vector field and this must + + + align:start position:0% +to this Vector field and this must +corresponding to the boundary value of + + align:start position:0% +corresponding to the boundary value of + + + align:start position:0% +corresponding to the boundary value of +that but now we can argue why this + + align:start position:0% +that but now we can argue why this + + + align:start position:0% +that but now we can argue why this +should be a gauge field okay so now I + + align:start position:0% +should be a gauge field okay so now I + + + align:start position:0% +should be a gauge field okay so now I +want to argue this is a gauge field and + + align:start position:0% +want to argue this is a gauge field and + + + align:start position:0% +want to argue this is a gauge field and +you see this is very easy + + align:start position:0% +you see this is very easy + + + align:start position:0% +you see this is very easy +because since J mu is + + align:start position:0% +because since J mu is + + + align:start position:0% +because since J mu is +conserved and then this cing so let me + + align:start position:0% +conserved and then this cing so let me + + + align:start position:0% +conserved and then this cing so let me +call this star star star + + align:start position:0% +call this star star star + + + align:start position:0% +call this star star star +St so let me call it + + align:start position:0% +St so let me call it + + + align:start position:0% +St so let me call it +um star star + + align:start position:0% +um star star + + + align:start position:0% +um star star +star so since this is conserved and this + + align:start position:0% +star so since this is conserved and this + + + align:start position:0% +star so since this is conserved and this +star star + + align:start position:0% + + + + align:start position:0% + +star is + + align:start position:0% + + + + align:start position:0% + +invariant under the following + + align:start position:0% +invariant under the following + + + align:start position:0% +invariant under the following +transformation a mu goes to a mu plus + + align:start position:0% +transformation a mu goes to a mu plus + + + align:start position:0% +transformation a mu goes to a mu plus +partial mu Lambda X for any Lambda X + + align:start position:0% + + + + align:start position:0% + +okay so that means that the boundary so + + align:start position:0% +okay so that means that the boundary so + + + align:start position:0% +okay so that means that the boundary so +that means the a + + align:start position:0% +that means the a + + + align:start position:0% +that means the a +mu this a is the boundary value of a so + + align:start position:0% +mu this a is the boundary value of a so + + + align:start position:0% +mu this a is the boundary value of a so +that means this capital A oh that means + + align:start position:0% +that means this capital A oh that means + + + align:start position:0% +that means this capital A oh that means +the Dynamics of the + + align:start position:0% + + + + align:start position:0% + +Dynamics of this a mu should also be in + + align:start position:0% +Dynamics of this a mu should also be in + + + align:start position:0% +Dynamics of this a mu should also be in +wariant + + align:start position:0% + + + + align:start position:0% + +okay if I change the boundary value of a + + align:start position:0% +okay if I change the boundary value of a + + + align:start position:0% +okay if I change the boundary value of a +by this transformation dynamics of a mu + + align:start position:0% +by this transformation dynamics of a mu + + + align:start position:0% +by this transformation dynamics of a mu +should also not change let me call a m + + align:start position:0% +should also not change let me call a m + + + align:start position:0% +should also not change let me call a m +so the b in general have a different uh + + align:start position:0% +so the b in general have a different uh + + + align:start position:0% +so the b in general have a different uh +uh uh will be different but this is like + + align:start position:0% +uh uh will be different but this is like + + + align:start position:0% +uh uh will be different but this is like +a gauge + + align:start position:0% +a gauge + + + align:start position:0% +a gauge +transformation so this is like gaug + + align:start position:0% +transformation so this is like gaug + + + align:start position:0% +transformation so this is like gaug +transformation so so we deduce that + + align:start position:0% +transformation so so we deduce that + + + align:start position:0% +transformation so so we deduce that +somehow this must be some subset of the + + align:start position:0% +somehow this must be some subset of the + + + align:start position:0% +somehow this must be some subset of the +b g trans information + + align:start position:0% +b g trans information + + + align:start position:0% +b g trans information +okay so uh uh so uh so + + align:start position:0% +okay so uh uh so uh so + + + align:start position:0% +okay so uh uh so uh so +this + + align:start position:0% +this + + + align:start position:0% +this +yeah now call it star to the power + + align:start position:0% +yeah now call it star to the power + + + align:start position:0% +yeah now call it star to the power +four then then star to the power + + align:start position:0% +four then then star to the power + + + align:start position:0% +four then then star to the power +four must + + align:start position:0% + + + + align:start position:0% + +be also must be a + + align:start position:0% + + + + align:start position:0% + +subset of + + align:start position:0% +subset of + + + align:start position:0% +subset of +some back gate transformation + + align:start position:0% + + + + align:start position:0% + +okay so so this does not prove it but + + align:start position:0% +okay so so this does not prove it but + + + align:start position:0% +okay so so this does not prove it but +make it more latal this argument make it + + align:start position:0% +make it more latal this argument make it + + + align:start position:0% +make it more latal this argument make it +more latal the fact that the boundary uh + + align:start position:0% +more latal the fact that the boundary uh + + + align:start position:0% +more latal the fact that the boundary uh +the boundary value of a have such kind + + align:start position:0% +the boundary value of a have such kind + + + align:start position:0% +the boundary value of a have such kind +of gauge + + align:start position:0% +of gauge + + + align:start position:0% +of gauge +Im so so there must be in some sense + + align:start position:0% +Im so so there must be in some sense + + + align:start position:0% +Im so so there must be in some sense +this must generalize some gauge image in + + align:start position:0% +this must generalize some gauge image in + + + align:start position:0% +this must generalize some gauge image in +the in the in the full gravity site so + + align:start position:0% +the in the in the full gravity site so + + + align:start position:0% +the in the in the full gravity site so +similarly you can do this for for the + + align:start position:0% +similarly you can do this for for the + + + align:start position:0% +similarly you can do this for for the +for the matric for the for the stress + + align:start position:0% + + + + align:start position:0% + +tensor similarly you can do this for the + + align:start position:0% +tensor similarly you can do this for the + + + align:start position:0% +tensor similarly you can do this for the +stress + + align:start position:0% + + + + align:start position:0% + +tensor so for the stress + + align:start position:0% +tensor so for the stress + + + align:start position:0% +tensor so for the stress +tensor so for the uh star + + align:start position:0% +tensor so for the uh star + + + align:start position:0% +tensor so for the uh star +star we can add again we can add + + align:start position:0% + + + + align:start position:0% + +H mu mu x t mu + + align:start position:0% +H mu mu x t mu + + + align:start position:0% +H mu mu x t mu +mu to the boundary Lin and this is the + + align:start position:0% +mu to the boundary Lin and this is the + + + align:start position:0% +mu to the boundary Lin and this is the +source to the stress + + align:start position:0% +source to the stress + + + align:start position:0% +source to the stress +tensor okay to the stress + + align:start position:0% +tensor okay to the stress + + + align:start position:0% +tensor okay to the stress +tensor and now from your knowledge of + + align:start position:0% +tensor and now from your knowledge of + + + align:start position:0% +tensor and now from your knowledge of +quantum field + + align:start position:0% +quantum field + + + align:start position:0% +quantum field +Theory when I add + + align:start position:0% +Theory when I add + + + align:start position:0% +Theory when I add +something when I add such a term to the + + align:start position:0% +something when I add such a term to the + + + align:start position:0% +something when I add such a term to the +field + + align:start position:0% +field + + + align:start position:0% +field +theory is the same so this is equival + + align:start position:0% +theory is the same so this is equival + + + align:start position:0% +theory is the same so this is equival +ENT to I + + align:start position:0% + + + + align:start position:0% + +deform the boundary + + align:start position:0% +deform the boundary + + + align:start position:0% +deform the boundary +Matrix boundary SpaceTime + + align:start position:0% + + + + align:start position:0% + +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +from just it mu + + align:start position:0% +from just it mu + + + align:start position:0% +from just it mu +mu to e mu mu plus h mu + + align:start position:0% +mu to e mu mu plus h mu + + + align:start position:0% +mu to e mu mu plus h mu +mu okay so let me call this quantity G + + align:start position:0% +mu okay so let me call this quantity G + + + align:start position:0% +mu okay so let me call this quantity G +mu mu B + + align:start position:0% + + + + align:start position:0% + +okay so so adding such a term source for + + align:start position:0% +okay so so adding such a term source for + + + align:start position:0% +okay so so adding such a term source for +the stress tensor is like you deform + + align:start position:0% +the stress tensor is like you deform + + + align:start position:0% +the stress tensor is like you deform +your SpaceTime geometry a little bit by + + align:start position:0% +your SpaceTime geometry a little bit by + + + align:start position:0% +your SpaceTime geometry a little bit by +this Source okay at least for for when H + + align:start position:0% +this Source okay at least for for when H + + + align:start position:0% +this Source okay at least for for when H +is very small yeah when we consider the + + align:start position:0% +is very small yeah when we consider the + + + align:start position:0% +is very small yeah when we consider the +information we always consider the + + align:start position:0% +information we always consider the + + + align:start position:0% +information we always consider the +source is small + + align:start position:0% + + + + align:start position:0% + +okay but + + align:start position:0% +okay but + + + align:start position:0% +okay but +now we can + + align:start position:0% +now we can + + + align:start position:0% +now we can +argue this thing must corresponding to + + align:start position:0% +argue this thing must corresponding to + + + align:start position:0% +argue this thing must corresponding to +the boundary value + + align:start position:0% +the boundary value + + + align:start position:0% +the boundary value +of the + + align:start position:0% +of the + + + align:start position:0% +of the +Matrix in the in the gravity site okay + + align:start position:0% +Matrix in the in the gravity site okay + + + align:start position:0% +Matrix in the in the gravity site okay +for the following reason so if you look + + align:start position:0% +for the following reason so if you look + + + align:start position:0% +for the following reason so if you look +at this + + align:start position:0% +at this + + + align:start position:0% +at this +expression so if you look at even the + + align:start position:0% +expression so if you look at even the + + + align:start position:0% +expression so if you look at even the +pure ads Matrix before you do any + + align:start position:0% +pure ads Matrix before you do any + + + align:start position:0% +pure ads Matrix before you do any +deformation so this is just dual to the + + align:start position:0% +deformation so this is just dual to the + + + align:start position:0% +deformation so this is just dual to the +say for just do to the an original + + align:start position:0% +say for just do to the an original + + + align:start position:0% +say for just do to the an original +Theory so so from the ads Matrix so the + + align:start position:0% +Theory so so from the ads Matrix so the + + + align:start position:0% +Theory so so from the ads Matrix so the +original ads matric + + align:start position:0% + + + + align:start position:0% + +the G mu component Okay g + + align:start position:0% +the G mu component Okay g + + + align:start position:0% +the G mu component Okay g +mu so let me write this uh a matric in + + align:start position:0% +mu so let me write this uh a matric in + + + align:start position:0% +mu so let me write this uh a matric in +the + + align:start position:0% +the + + + align:start position:0% +the +form say r sare z Square separate Z + + align:start position:0% +form say r sare z Square separate Z + + + align:start position:0% +form say r sare z Square separate Z +square and with the + + align:start position:0% + + + + align:start position:0% + +rest okay so this is the essentially the + + align:start position:0% +rest okay so this is the essentially the + + + align:start position:0% +rest okay so this is the essentially the +component of the b matric along the + + align:start position:0% +component of the b matric along the + + + align:start position:0% +component of the b matric along the +boundary + + align:start position:0% +boundary + + + align:start position:0% +boundary +Direction the boundary value + + align:start position:0% + + + + align:start position:0% + +the boundary value of this uh uh uh um + + align:start position:0% +the boundary value of this uh uh uh um + + + align:start position:0% +the boundary value of this uh uh uh um +the boundary value of this matri + + align:start position:0% +the boundary value of this matri + + + align:start position:0% +the boundary value of this matri +component EV valate zal to Zer is equal + + align:start position:0% +component EV valate zal to Zer is equal + + + align:start position:0% +component EV valate zal to Zer is equal +to r s/ z sare + + align:start position:0% +to r s/ z sare + + + align:start position:0% +to r s/ z sare +mu okay so so that just come from the + + align:start position:0% +mu okay so so that just come from the + + + align:start position:0% +mu okay so so that just come from the +ABS matric okay I'm just this G mu mu + + align:start position:0% +ABS matric okay I'm just this G mu mu + + + align:start position:0% +ABS matric okay I'm just this G mu mu +and when you go to the boundary just G + + align:start position:0% +and when you go to the boundary just G + + + align:start position:0% +and when you go to the boundary just G +by this okay and this is it me we + + align:start position:0% +by this okay and this is it me we + + + align:start position:0% +by this okay and this is it me we +recognize just as the boundary matric + + align:start position:0% +recognize just as the boundary matric + + + align:start position:0% +recognize just as the boundary matric +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +expect so this coron to + + align:start position:0% + + + + align:start position:0% + +deform so this coson to deform since + + align:start position:0% +deform so this coson to deform since + + + align:start position:0% +deform so this coson to deform since +adding this teron to deform the boundary + + align:start position:0% +adding this teron to deform the boundary + + + align:start position:0% +adding this teron to deform the boundary +magic so we expect when we add this term + + align:start position:0% +magic so we expect when we add this term + + + align:start position:0% +magic so we expect when we add this term +so this correspondent to + + align:start position:0% + + + + align:start position:0% + +deform the G mu + + align:start position:0% +deform the G mu + + + align:start position:0% +deform the G mu +mu now to the zero + + align:start position:0% +mu now to the zero + + + align:start position:0% +mu now to the zero +become so we expect this become equal to + + align:start position:0% +become so we expect this become equal to + + + align:start position:0% +become so we expect this become equal to +G mu mu + + align:start position:0% +G mu mu + + + align:start position:0% +G mu mu +B + + align:start position:0% +B + + + align:start position:0% +B +Okay g mu mu B okay so this tells you so + + align:start position:0% +Okay g mu mu B okay so this tells you so + + + align:start position:0% +Okay g mu mu B okay so this tells you so +this tells you that the stress + + align:start position:0% +this tells you that the stress + + + align:start position:0% +this tells you that the stress +tensor must be + + align:start position:0% +tensor must be + + + align:start position:0% +tensor must be +dual to the metric perations in the + + align:start position:0% +dual to the metric perations in the + + + align:start position:0% +dual to the metric perations in the +gravity site + + align:start position:0% +gravity site + + + align:start position:0% +gravity site +okay the stress must be corresponding to + + align:start position:0% +okay the stress must be corresponding to + + + align:start position:0% +okay the stress must be corresponding to +the magri peration of gravity side + + align:start position:0% +the magri peration of gravity side + + + align:start position:0% +the magri peration of gravity side +because it's corresponding to perur the + + align:start position:0% +because it's corresponding to perur the + + + align:start position:0% +because it's corresponding to perur the +the boundary conditions of the B + + align:start position:0% +the boundary conditions of the B + + + align:start position:0% +the boundary conditions of the B +matric corresponding to the with the + + align:start position:0% +matric corresponding to the with the + + + align:start position:0% +matric corresponding to the with the +boundary condition for the matric so + + align:start position:0% +boundary condition for the matric so + + + align:start position:0% +boundary condition for the matric so +this is a very general + + align:start position:0% +this is a very general + + + align:start position:0% +this is a very general +statement this is a very general + + align:start position:0% +statement this is a very general + + + align:start position:0% +statement this is a very general +statement valid for any + + align:start position:0% +statement valid for any + + + align:start position:0% +statement valid for any +correspondence uh between the gravity + + align:start position:0% +correspondence uh between the gravity + + + align:start position:0% +correspondence uh between the gravity +and and the field + + align:start position:0% +and and the field + + + align:start position:0% +and and the field +Theory and that also tells you that if + + align:start position:0% +Theory and that also tells you that if + + + align:start position:0% +Theory and that also tells you that if +you have a theory which du to a higher + + align:start position:0% +you have a theory which du to a higher + + + align:start position:0% +you have a theory which du to a higher +dimensional Theory and then that theory + + align:start position:0% +dimensional Theory and then that theory + + + align:start position:0% +dimensional Theory and then that theory +if the field Theory have a stretch + + align:start position:0% +if the field Theory have a stretch + + + align:start position:0% +if the field Theory have a stretch +tensor then this gravity Theory must + + align:start position:0% +tensor then this gravity Theory must + + + align:start position:0% +tensor then this gravity Theory must +have + + align:start position:0% +have + + + align:start position:0% +have +gravity this box Theory must have + + align:start position:0% +gravity this box Theory must have + + + align:start position:0% +gravity this box Theory must have +gravity uh uh because this box Theory + + align:start position:0% +gravity uh uh because this box Theory + + + align:start position:0% +gravity uh uh because this box Theory +must have a dynamical matric okay must + + align:start position:0% +must have a dynamical matric okay must + + + align:start position:0% +must have a dynamical matric okay must +have to have a dynamical matric and if + + align:start position:0% +have to have a dynamical matric and if + + + align:start position:0% +have to have a dynamical matric and if +you have a dynamical metric then you + + align:start position:0% +you have a dynamical metric then you + + + align:start position:0% +you have a dynamical metric then you +have gravity so so you can say if any + + align:start position:0% +have gravity so so you can say if any + + + align:start position:0% +have gravity so so you can say if any +field the is Du dual to a to a Ser of + + align:start position:0% +field the is Du dual to a to a Ser of + + + align:start position:0% +field the is Du dual to a to a Ser of +one Higher Dimension that Ser of one + + align:start position:0% +one Higher Dimension that Ser of one + + + align:start position:0% +one Higher Dimension that Ser of one +Higher Dimension must involve gravity + + align:start position:0% +Higher Dimension must involve gravity + + + align:start position:0% +Higher Dimension must involve gravity +okay must involve quantum gravity + + align:start position:0% +okay must involve quantum gravity + + + align:start position:0% +okay must involve quantum gravity +okay yeah let's stop here \ No newline at end of file diff --git a/nXzur-2hbkI.txt b/nXzur-2hbkI.txt new file mode 100644 index 0000000000000000000000000000000000000000..0e51383c34fe2eaee4e745d5508290264b8c1f63 --- /dev/null +++ b/nXzur-2hbkI.txt @@ -0,0 +1,1131 @@ +align:start position:0% + +welcome back to 8701 + + align:start position:0% +welcome back to 8701 + + + align:start position:0% +welcome back to 8701 +we have seen in the previous video how + + align:start position:0% +we have seen in the previous video how + + + align:start position:0% +we have seen in the previous video how +neutrinos can acquire mars + + align:start position:0% +neutrinos can acquire mars + + + align:start position:0% +neutrinos can acquire mars +when they have mask their weak + + align:start position:0% +when they have mask their weak + + + align:start position:0% +when they have mask their weak +eigenstate is not equal to their + + align:start position:0% +eigenstate is not equal to their + + + align:start position:0% +eigenstate is not equal to their +massaging state + + align:start position:0% +massaging state + + + align:start position:0% +massaging state +so we observe the same mixing as we have + + align:start position:0% +so we observe the same mixing as we have + + + align:start position:0% +so we observe the same mixing as we have +seen in the quark sector + + align:start position:0% +seen in the quark sector + + + align:start position:0% +seen in the quark sector +so let's review this a little bit so + + align:start position:0% +so let's review this a little bit so + + + align:start position:0% +so let's review this a little bit so +you know just starting from two neutrino + + align:start position:0% +you know just starting from two neutrino + + + align:start position:0% +you know just starting from two neutrino +generations + + align:start position:0% +generations + + + align:start position:0% +generations +we can write the flavoring states we are + + align:start position:0% +we can write the flavoring states we are + + + align:start position:0% +we can write the flavoring states we are +a mixing of mass eigenstates if we do + + align:start position:0% +a mixing of mass eigenstates if we do + + + align:start position:0% +a mixing of mass eigenstates if we do +this + + align:start position:0% +this + + + align:start position:0% +this +with a simple matrix we find that there + + align:start position:0% +with a simple matrix we find that there + + + align:start position:0% +with a simple matrix we find that there +is one angle + + align:start position:0% +is one angle + + + align:start position:0% +is one angle +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +used for the rotation of the mass + + align:start position:0% +used for the rotation of the mass + + + align:start position:0% +used for the rotation of the mass +eigenstate into the flavoring states + + align:start position:0% +eigenstate into the flavoring states + + + align:start position:0% +eigenstate into the flavoring states +all right so we can at some time d0 + + align:start position:0% +all right so we can at some time d0 + + + align:start position:0% +all right so we can at some time d0 +write our neutrino or mule neutrino as a + + align:start position:0% +write our neutrino or mule neutrino as a + + + align:start position:0% +write our neutrino or mule neutrino as a +combination of the one + + align:start position:0% +combination of the one + + + align:start position:0% +combination of the one +and two massaging states if we then have + + align:start position:0% +and two massaging states if we then have + + + align:start position:0% +and two massaging states if we then have +this neutrino + + align:start position:0% +this neutrino + + + align:start position:0% +this neutrino +evolve with time we see that + + align:start position:0% +evolve with time we see that + + + align:start position:0% +evolve with time we see that +the relative contribution of the one and + + align:start position:0% +the relative contribution of the one and + + + align:start position:0% +the relative contribution of the one and +two mass eggs that actually changes + + align:start position:0% +two mass eggs that actually changes + + + align:start position:0% +two mass eggs that actually changes +so if we do that so we see we find some + + align:start position:0% +so if we do that so we see we find some + + + align:start position:0% +so if we do that so we see we find some +time evolution + + align:start position:0% +time evolution + + + align:start position:0% +time evolution +if we then ask ourselves what is the + + align:start position:0% +if we then ask ourselves what is the + + + align:start position:0% +if we then ask ourselves what is the +probability + + align:start position:0% +probability + + + align:start position:0% +probability +um that you know we start from a + + align:start position:0% +um that you know we start from a + + + align:start position:0% +um that you know we start from a +neural neutrino that we actually find in + + align:start position:0% +neural neutrino that we actually find in + + + align:start position:0% +neural neutrino that we actually find in +an interaction + + align:start position:0% +an interaction + + + align:start position:0% +an interaction +electron neutrino through this mixing of + + align:start position:0% +electron neutrino through this mixing of + + + align:start position:0% +electron neutrino through this mixing of +mass eigenstates + + align:start position:0% +mass eigenstates + + + align:start position:0% +mass eigenstates +we can calculate this probability + + align:start position:0% +we can calculate this probability + + + align:start position:0% +we can calculate this probability +just by squaring the amplitudes um if we + + align:start position:0% +just by squaring the amplitudes um if we + + + align:start position:0% +just by squaring the amplitudes um if we +do this we just + + align:start position:0% +do this we just + + + align:start position:0% +do this we just +use this part here and we find that + + align:start position:0% +use this part here and we find that + + + align:start position:0% +use this part here and we find that +there's a cosine + + align:start position:0% +there's a cosine + + + align:start position:0% +there's a cosine +e2 minus e1 term + + align:start position:0% +e2 minus e1 term + + + align:start position:0% +e2 minus e1 term +all right good so let's analyze this a + + align:start position:0% +all right good so let's analyze this a + + + align:start position:0% +all right good so let's analyze this a +little bit further + + align:start position:0% +little bit further + + + align:start position:0% +little bit further +we know that the masses need to be small + + align:start position:0% +we know that the masses need to be small + + + align:start position:0% +we know that the masses need to be small +so one thing we can also do here + + align:start position:0% +so one thing we can also do here + + + align:start position:0% +so one thing we can also do here +is do a taylor expansion of our energy + + align:start position:0% +is do a taylor expansion of our energy + + + align:start position:0% +is do a taylor expansion of our energy +and then just rewrite the term if we + + align:start position:0% +and then just rewrite the term if we + + + align:start position:0% +and then just rewrite the term if we +then + + align:start position:0% +then + + + align:start position:0% +then +analyze this some more we find that + + align:start position:0% +analyze this some more we find that + + + align:start position:0% +analyze this some more we find that +the oscillation probability simply + + align:start position:0% +the oscillation probability simply + + + align:start position:0% +the oscillation probability simply +depends + + align:start position:0% +depends + + + align:start position:0% +depends +on the mass difference squared + + align:start position:0% +on the mass difference squared + + + align:start position:0% +on the mass difference squared +the length of distance the neutrino had + + align:start position:0% +the length of distance the neutrino had + + + align:start position:0% +the length of distance the neutrino had +time from t 0 + + align:start position:0% +time from t 0 + + + align:start position:0% +time from t 0 +to oscillate and the energy of the + + align:start position:0% +to oscillate and the energy of the + + + align:start position:0% +to oscillate and the energy of the +neutrino + + align:start position:0% +neutrino + + + align:start position:0% +neutrino +so this is fantastic because now by + + align:start position:0% +so this is fantastic because now by + + + align:start position:0% +so this is fantastic because now by +studying the not + + align:start position:0% +studying the not + + + align:start position:0% +studying the not +the the probability for a neutrino to + + align:start position:0% +the the probability for a neutrino to + + + align:start position:0% +the the probability for a neutrino to +change its flavor + + align:start position:0% +change its flavor + + + align:start position:0% +change its flavor +we can infer the mass differences of two + + align:start position:0% +we can infer the mass differences of two + + + align:start position:0% +we can infer the mass differences of two +states + + align:start position:0% +states + + + align:start position:0% +states +this is fantastic i should add here that + + align:start position:0% +this is fantastic i should add here that + + + align:start position:0% +this is fantastic i should add here that +in this case + + align:start position:0% +in this case + + + align:start position:0% +in this case +in this formula the length is given + + align:start position:0% +in this formula the length is given + + + align:start position:0% +in this formula the length is given +in meters the energy + + align:start position:0% +in meters the energy + + + align:start position:0% +in meters the energy +is given oops unit of the energy mav + + align:start position:0% +is given oops unit of the energy mav + + + align:start position:0% +is given oops unit of the energy mav +and the mass difference is in ev + + align:start position:0% +and the mass difference is in ev + + + align:start position:0% +and the mass difference is in ev +otherwise equation doesn't make sense + + align:start position:0% +otherwise equation doesn't make sense + + + align:start position:0% +otherwise equation doesn't make sense +good + + align:start position:0% +good + + + align:start position:0% +good +so again we have um seen if we start + + align:start position:0% +so again we have um seen if we start + + + align:start position:0% +so again we have um seen if we start +from + + align:start position:0% +from + + + align:start position:0% +from +a two neutrino kind of model two + + align:start position:0% +a two neutrino kind of model two + + + align:start position:0% +a two neutrino kind of model two +neutrino flavor model + + align:start position:0% +neutrino flavor model + + + align:start position:0% +neutrino flavor model +that the experimental parameters of of + + align:start position:0% +that the experimental parameters of of + + + align:start position:0% +that the experimental parameters of of +interest here are the lengths + + align:start position:0% +interest here are the lengths + + + align:start position:0% +interest here are the lengths +of distance from the neutrino source to + + align:start position:0% +of distance from the neutrino source to + + + align:start position:0% +of distance from the neutrino source to +the detector + + align:start position:0% +the detector + + + align:start position:0% +the detector +from the place where we generate a + + align:start position:0% +from the place where we generate a + + + align:start position:0% +from the place where we generate a +specific neutrino of a specific flavor + + align:start position:0% +specific neutrino of a specific flavor + + + align:start position:0% +specific neutrino of a specific flavor +to + + align:start position:0% +to + + + align:start position:0% +to +where we actually observe the flavor of + + align:start position:0% +where we actually observe the flavor of + + + align:start position:0% +where we actually observe the flavor of +the neutrino + + align:start position:0% +the neutrino + + + align:start position:0% +the neutrino +and the energy of the neutrino and then + + align:start position:0% +and the energy of the neutrino and then + + + align:start position:0% +and the energy of the neutrino and then +you know the appearance of disappearance + + align:start position:0% +you know the appearance of disappearance + + + align:start position:0% +you know the appearance of disappearance +of an immune neutrino for example if we + + align:start position:0% +of an immune neutrino for example if we + + + align:start position:0% +of an immune neutrino for example if we +start from a beam + + align:start position:0% +start from a beam + + + align:start position:0% +start from a beam +of neural neutrinos is a function of the + + align:start position:0% +of neural neutrinos is a function of the + + + align:start position:0% +of neural neutrinos is a function of the +of the length of the source and this is + + align:start position:0% +of the length of the source and this is + + + align:start position:0% +of the length of the source and this is +shown here + + align:start position:0% +shown here + + + align:start position:0% +shown here +for neutrinos of a specific energy + + align:start position:0% +for neutrinos of a specific energy + + + align:start position:0% +for neutrinos of a specific energy +so you can observe or can try to measure + + align:start position:0% +so you can observe or can try to measure + + + align:start position:0% +so you can observe or can try to measure +the disappearance of neural neutrinos + + align:start position:0% +the disappearance of neural neutrinos + + + align:start position:0% +the disappearance of neural neutrinos +or you can try to find the appearance + + align:start position:0% +or you can try to find the appearance + + + align:start position:0% +or you can try to find the appearance +of electron neutrinos in the specific + + align:start position:0% +of electron neutrinos in the specific + + + align:start position:0% +of electron neutrinos in the specific +two neutrino model + + align:start position:0% +two neutrino model + + + align:start position:0% +two neutrino model +all right so all we find later is that + + align:start position:0% +all right so all we find later is that + + + align:start position:0% +all right so all we find later is that +we want to + + align:start position:0% +we want to + + + align:start position:0% +we want to +look for disappearance and appearance + + align:start position:0% +look for disappearance and appearance + + + align:start position:0% +look for disappearance and appearance +from of neutrinos of specific flavors in + + align:start position:0% +from of neutrinos of specific flavors in + + + align:start position:0% +from of neutrinos of specific flavors in +order to probe + + align:start position:0% +order to probe + + + align:start position:0% +order to probe +mass differences + + align:start position:0% + + + + align:start position:0% + +instead of doing this for two + + align:start position:0% +instead of doing this for two + + + align:start position:0% +instead of doing this for two +generations we already know how to do + + align:start position:0% +generations we already know how to do + + + align:start position:0% +generations we already know how to do +this in three generations we + + align:start position:0% +this in three generations we + + + align:start position:0% +this in three generations we +find that the unitarian matrix has three + + align:start position:0% +find that the unitarian matrix has three + + + align:start position:0% +find that the unitarian matrix has three +angles three rotates rotations + + align:start position:0% +angles three rotates rotations + + + align:start position:0% +angles three rotates rotations +and one complex phase and this looks + + align:start position:0% +and one complex phase and this looks + + + align:start position:0% +and one complex phase and this looks +very much the same here as in the clock + + align:start position:0% +very much the same here as in the clock + + + align:start position:0% +very much the same here as in the clock +sector + + align:start position:0% +sector + + + align:start position:0% +sector +the big difference is that the values of + + align:start position:0% +the big difference is that the values of + + + align:start position:0% +the big difference is that the values of +those parameters + + align:start position:0% +those parameters + + + align:start position:0% +those parameters +are quite different for the quarks we + + align:start position:0% +are quite different for the quarks we + + + align:start position:0% +are quite different for the quarks we +have seen it's dominated by the diagonal + + align:start position:0% +have seen it's dominated by the diagonal + + + align:start position:0% +have seen it's dominated by the diagonal +and then we have seen for example in the + + align:start position:0% +and then we have seen for example in the + + + align:start position:0% +and then we have seen for example in the +wolfenstein parametrization + + align:start position:0% +wolfenstein parametrization + + + align:start position:0% +wolfenstein parametrization +that we can you know do an expansion of + + align:start position:0% +that we can you know do an expansion of + + + align:start position:0% +that we can you know do an expansion of +of the matrix and see + + align:start position:0% +of the matrix and see + + + align:start position:0% +of the matrix and see +terms which of all of this lambda which + + align:start position:0% +terms which of all of this lambda which + + + align:start position:0% +terms which of all of this lambda which +was 0.22 and lambda square and numbers + + align:start position:0% +was 0.22 and lambda square and numbers + + + align:start position:0% +was 0.22 and lambda square and numbers +cubed here in the lepton sector the + + align:start position:0% +cubed here in the lepton sector the + + + align:start position:0% +cubed here in the lepton sector the +situation seems to be quite different + + align:start position:0% +situation seems to be quite different + + + align:start position:0% +situation seems to be quite different +we have a later lecture where we look at + + align:start position:0% +we have a later lecture where we look at + + + align:start position:0% +we have a later lecture where we look at +the actual parameters + + align:start position:0% +the actual parameters + + + align:start position:0% +the actual parameters +and the numerical values but what you + + align:start position:0% +and the numerical values but what you + + + align:start position:0% +and the numerical values but what you +see here is that + + align:start position:0% +see here is that + + + align:start position:0% +see here is that +you know there's more like a democracy + + align:start position:0% +you know there's more like a democracy + + + align:start position:0% +you know there's more like a democracy +between the + + align:start position:0% +between the + + + align:start position:0% +between the +values question is do we have + + align:start position:0% +values question is do we have + + + align:start position:0% +values question is do we have +sensitivity to the complex phase + + align:start position:0% +sensitivity to the complex phase + + + align:start position:0% +sensitivity to the complex phase +we can only have that sensitivity if the + + align:start position:0% +we can only have that sensitivity if the + + + align:start position:0% +we can only have that sensitivity if the +value of this matrix element is non-zero + + align:start position:0% +value of this matrix element is non-zero + + + align:start position:0% +value of this matrix element is non-zero +and this has been observed already so + + align:start position:0% +and this has been observed already so + + + align:start position:0% +and this has been observed already so +that's good news in order to allow + + align:start position:0% +that's good news in order to allow + + + align:start position:0% +that's good news in order to allow +further neutrino studies so in + + align:start position:0% +further neutrino studies so in + + + align:start position:0% +further neutrino studies so in +in general you can write the oscillation + + align:start position:0% +in general you can write the oscillation + + + align:start position:0% +in general you can write the oscillation +from one flavor to another flavor state + + align:start position:0% +from one flavor to another flavor state + + + align:start position:0% +from one flavor to another flavor state +using this rotational matrix as we have + + align:start position:0% +using this rotational matrix as we have + + + align:start position:0% +using this rotational matrix as we have +seen + + align:start position:0% +seen + + + align:start position:0% +seen +and with that measure you know the + + align:start position:0% +and with that measure you know the + + + align:start position:0% +and with that measure you know the +individual components of the matrix \ No newline at end of file diff --git a/oLbTUpxhE24.txt b/oLbTUpxhE24.txt new file mode 100644 index 0000000000000000000000000000000000000000..6874154689209d4ff71c68702d97705f059b9f41 --- /dev/null +++ b/oLbTUpxhE24.txt @@ -0,0 +1,7699 @@ +align:start position:0% + +The following content is provided by MIT + + align:start position:0% +The following content is provided by MIT + + + align:start position:0% +The following content is provided by MIT +Open Courseware under a Creative Common + + align:start position:0% +Open Courseware under a Creative Common + + + align:start position:0% +Open Courseware under a Creative Common +License. Additional information about + + align:start position:0% +License. Additional information about + + + align:start position:0% +License. Additional information about +our license and MIT Open Courseware in + + align:start position:0% +our license and MIT Open Courseware in + + + align:start position:0% +our license and MIT Open Courseware in +general is available at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Let's get going + + align:start position:0% +Let's get going + + + align:start position:0% +Let's get going +here. Uh remember where we were? We were + + align:start position:0% +here. Uh remember where we were? We were + + + align:start position:0% +here. Uh remember where we were? We were +uh trying to figure out the structure of + + align:start position:0% +uh trying to figure out the structure of + + + align:start position:0% +uh trying to figure out the structure of +the atom at the beginning of the course. + + align:start position:0% +the atom at the beginning of the course. + + + align:start position:0% +the atom at the beginning of the course. +We saw classical physics, classical + + align:start position:0% +We saw classical physics, classical + + + align:start position:0% +We saw classical physics, classical +mechanics failed to uh describe how that + + align:start position:0% +mechanics failed to uh describe how that + + + align:start position:0% +mechanics failed to uh describe how that +electron and the nucleus hung + + align:start position:0% +electron and the nucleus hung + + + align:start position:0% +electron and the nucleus hung +together. So then we started talking + + align:start position:0% +together. So then we started talking + + + align:start position:0% +together. So then we started talking +about this wave particle duality of + + align:start position:0% +about this wave particle duality of + + + align:start position:0% +about this wave particle duality of +light and matter. We saw that radiation + + align:start position:0% +light and matter. We saw that radiation + + + align:start position:0% +light and matter. We saw that radiation +and matter both can exhibit both + + align:start position:0% +and matter both can exhibit both + + + align:start position:0% +and matter both can exhibit both +wavelike properties and particle-like + + align:start position:0% +wavelike properties and particle-like + + + align:start position:0% +wavelike properties and particle-like +properties. And it was really important + + align:start position:0% +properties. And it was really important + + + align:start position:0% +properties. And it was really important +this observation of Davidson and Gurmer + + align:start position:0% +this observation of Davidson and Gurmer + + + align:start position:0% +this observation of Davidson and Gurmer +and Thompson, George Thompson, this + + align:start position:0% +and Thompson, George Thompson, this + + + align:start position:0% +and Thompson, George Thompson, this +observation that electrons exhibited + + align:start position:0% +observation that electrons exhibited + + + align:start position:0% +observation that electrons exhibited +interference phenomena. That is when you + + align:start position:0% +interference phenomena. That is when you + + + align:start position:0% +interference phenomena. That is when you +took electrons and you scattered them + + align:start position:0% +took electrons and you scattered them + + + align:start position:0% +took electrons and you scattered them +from a nickel single crystal, the + + align:start position:0% +from a nickel single crystal, the + + + align:start position:0% +from a nickel single crystal, the +electrons scattered back as if they were + + align:start position:0% +electrons scattered back as if they were + + + align:start position:0% +electrons scattered back as if they were +behaving as waves. There were defraction + + align:start position:0% +behaving as waves. There were defraction + + + align:start position:0% +behaving as waves. There were defraction +phenomena, interference phenomena, + + align:start position:0% +phenomena, interference phenomena, + + + align:start position:0% +phenomena, interference phenomena, +light, bright, bright, dark, bright + + align:start position:0% +light, bright, bright, dark, bright + + + align:start position:0% +light, bright, bright, dark, bright +patterns of electrons. + + align:start position:0% +patterns of electrons. + + + align:start position:0% +patterns of electrons. +Okay. And um + + align:start position:0% +Okay. And um + + + align:start position:0% +Okay. And um +that and actually that Davidson and + + align:start position:0% +that and actually that Davidson and + + + align:start position:0% +that and actually that Davidson and +Gurmer paper is on our website. You can + + align:start position:0% +Gurmer paper is on our website. You can + + + align:start position:0% +Gurmer paper is on our website. You can +welcome to take a look at that. But it + + align:start position:0% +welcome to take a look at that. But it + + + align:start position:0% +welcome to take a look at that. But it +was just that observation coupled with + + align:start position:0% +was just that observation coupled with + + + align:start position:0% +was just that observation coupled with +uh De Brogley's insight into + + align:start position:0% +uh De Brogley's insight into + + + align:start position:0% +uh De Brogley's insight into +Schroinger's relativistic equations of + + align:start position:0% +Schroinger's relativistic equations of + + + align:start position:0% +Schroinger's relativistic equations of +motion + + align:start position:0% +motion + + + align:start position:0% +motion +That led Schroinger to say, well, you + + align:start position:0% +That led Schroinger to say, well, you + + + align:start position:0% +That led Schroinger to say, well, you +know, maybe what I need to do is I need + + align:start position:0% +know, maybe what I need to do is I need + + + align:start position:0% +know, maybe what I need to do is I need +to treat the electron in a hydrogen + + align:start position:0% +to treat the electron in a hydrogen + + + align:start position:0% +to treat the electron in a hydrogen +atom. I need to treat the wavelike + + align:start position:0% +atom. I need to treat the wavelike + + + align:start position:0% +atom. I need to treat the wavelike +properties of that electron in a + + align:start position:0% +properties of that electron in a + + + align:start position:0% +properties of that electron in a +hydrogen atom. Maybe that's the key in + + align:start position:0% +hydrogen atom. Maybe that's the key in + + + align:start position:0% +hydrogen atom. Maybe that's the key in +particular. Maybe that's the key + + align:start position:0% + + + + align:start position:0% + +because maybe that's the key because the + + align:start position:0% +because maybe that's the key because the + + + align:start position:0% +because maybe that's the key because the +electron has a debrogly wavelength + + align:start position:0% +electron has a debrogly wavelength + + + align:start position:0% +electron has a debrogly wavelength +that's on the order the size of its + + align:start position:0% +that's on the order the size of its + + + align:start position:0% +that's on the order the size of its +environment. Maybe in those cases I need + + align:start position:0% +environment. Maybe in those cases I need + + + align:start position:0% +environment. Maybe in those cases I need +to treat the particle as a wave and not + + align:start position:0% +to treat the particle as a wave and not + + + align:start position:0% +to treat the particle as a wave and not +as a particle with classical mechanics. + + align:start position:0% +as a particle with classical mechanics. + + + align:start position:0% +as a particle with classical mechanics. +Right? So he wrote down this wave + + align:start position:0% +Right? So he wrote down this wave + + + align:start position:0% +Right? So he wrote down this wave +equation, an equation of motion for + + align:start position:0% +equation, an equation of motion for + + + align:start position:0% +equation, an equation of motion for +waves. This h si equal e si where we + + align:start position:0% +waves. This h si equal e si where we + + + align:start position:0% +waves. This h si equal e si where we +said last time we're going to represent + + align:start position:0% +said last time we're going to represent + + + align:start position:0% +said last time we're going to represent +the electron our particle by this s this + + align:start position:0% +the electron our particle by this s this + + + align:start position:0% +the electron our particle by this s this +wave. We're going to call it a wave + + align:start position:0% +wave. We're going to call it a wave + + + align:start position:0% +wave. We're going to call it a wave +function because uh we're going to put a + + align:start position:0% +function because uh we're going to put a + + + align:start position:0% +function because uh we're going to put a +functional form to it very soon. + + align:start position:0% +functional form to it very soon. + + + align:start position:0% +functional form to it very soon. +And we there was some kind of operator + + align:start position:0% +And we there was some kind of operator + + + align:start position:0% +And we there was some kind of operator +here called the Hamiltonian operator + + align:start position:0% +here called the Hamiltonian operator + + + align:start position:0% +here called the Hamiltonian operator +that operated on this wave + + align:start position:0% +that operated on this wave + + + align:start position:0% +that operated on this wave +function. And when it did, you got back + + align:start position:0% +function. And when it did, you got back + + + align:start position:0% +function. And when it did, you got back +the same wave function times a constant + + align:start position:0% +the same wave function times a constant + + + align:start position:0% +the same wave function times a constant +E. And this constant, as we're going to + + align:start position:0% +E. And this constant, as we're going to + + + align:start position:0% +E. And this constant, as we're going to +see, is going to be the binding energy + + align:start position:0% +see, is going to be the binding energy + + + align:start position:0% +see, is going to be the binding energy +of the electron to the to the + + align:start position:0% +of the electron to the to the + + + align:start position:0% +of the electron to the to the +nucleus. All right. But then we took a + + align:start position:0% +nucleus. All right. But then we took a + + + align:start position:0% +nucleus. All right. But then we took a +little detour and I said, well, let's uh + + align:start position:0% +little detour and I said, well, let's uh + + + align:start position:0% +little detour and I said, well, let's uh +see if we can derive in a sense the + + align:start position:0% +see if we can derive in a sense the + + + align:start position:0% +see if we can derive in a sense the +Schroinger equation. And that's what we + + align:start position:0% +Schroinger equation. And that's what we + + + align:start position:0% +Schroinger equation. And that's what we +started to do. And I'm doing this and + + align:start position:0% +started to do. And I'm doing this and + + + align:start position:0% +started to do. And I'm doing this and +I'm really doing this for fun. You're + + align:start position:0% +I'm really doing this for fun. You're + + + align:start position:0% +I'm really doing this for fun. You're +not responsible for it, but I'm doing it + + align:start position:0% +not responsible for it, but I'm doing it + + + align:start position:0% +not responsible for it, but I'm doing it +because I want you to see just how easy + + align:start position:0% +because I want you to see just how easy + + + align:start position:0% +because I want you to see just how easy +this is. + + align:start position:0% +this is. + + + align:start position:0% +this is. +Okay. Okay. + + align:start position:0% +Okay. Okay. + + + align:start position:0% +Okay. Okay. +So to illustrate this, I'm just going to + + align:start position:0% +So to illustrate this, I'm just going to + + + align:start position:0% +So to illustrate this, I'm just going to +take a one-dimensional problem, right? + + align:start position:0% +take a one-dimensional problem, right? + + + align:start position:0% +take a one-dimensional problem, right? +I'm going to let my electron be + + align:start position:0% +I'm going to let my electron be + + + align:start position:0% +I'm going to let my electron be +represented by this wave. One dimension + + align:start position:0% +represented by this wave. One dimension + + + align:start position:0% +represented by this wave. One dimension +s of x 2 a cosine 2 pix over lambda. And + + align:start position:0% +s of x 2 a cosine 2 pix over lambda. And + + + align:start position:0% +s of x 2 a cosine 2 pix over lambda. And +then I said suppose I want an equation + + align:start position:0% +then I said suppose I want an equation + + + align:start position:0% +then I said suppose I want an equation +of motion. I want to know how that s + + align:start position:0% +of motion. I want to know how that s + + + align:start position:0% +of motion. I want to know how that s +changes with x. Well, you already know + + align:start position:0% +changes with x. Well, you already know + + + align:start position:0% +changes with x. Well, you already know +that if I take the derivative of S with + + align:start position:0% +that if I take the derivative of S with + + + align:start position:0% +that if I take the derivative of S with +X, that's going to tell me how S changes + + align:start position:0% +X, that's going to tell me how S changes + + + align:start position:0% +X, that's going to tell me how S changes +with X. And we did that last time. And + + align:start position:0% +with X. And we did that last time. And + + + align:start position:0% +with X. And we did that last time. And +then I said, well, then I want to know + + align:start position:0% +then I said, well, then I want to know + + + align:start position:0% +then I said, well, then I want to know +the rate of change of S with X. So, I'm + + align:start position:0% +the rate of change of S with X. So, I'm + + + align:start position:0% +the rate of change of S with X. So, I'm +going to take the + + align:start position:0% +going to take the + + + align:start position:0% +going to take the +derivative again. So, I have the second + + align:start position:0% +derivative again. So, I have the second + + + align:start position:0% +derivative again. So, I have the second +derivative of S of X. And that's what we + + align:start position:0% +derivative of S of X. And that's what we + + + align:start position:0% +derivative of S of X. And that's what we +got last time. + + align:start position:0% +got last time. + + + align:start position:0% +got last time. +And then I noticed that in the second + + align:start position:0% +And then I noticed that in the second + + + align:start position:0% +And then I noticed that in the second +derivative, and you noticed too, + + align:start position:0% +derivative, and you noticed too, + + + align:start position:0% +derivative, and you noticed too, +somebody said this was recursive, that + + align:start position:0% +somebody said this was recursive, that + + + align:start position:0% +somebody said this was recursive, that +we have our original wave function back + + align:start position:0% +we have our original wave function back + + + align:start position:0% +we have our original wave function back +in this expression. So I can rewrite + + align:start position:0% +in this expression. So I can rewrite + + + align:start position:0% +in this expression. So I can rewrite +that whole second derivative here just + + align:start position:0% +that whole second derivative here just + + + align:start position:0% +that whole second derivative here just +as min - + + align:start position:0% +as min - + + + align:start position:0% +as min - +2<unk>i^2 over lambda s of x. All right. + + align:start position:0% +2<unk>i^2 over lambda s of x. All right. + + + align:start position:0% +2<unk>i^2 over lambda s of x. All right. +So so far this is just any old wave + + align:start position:0% +So so far this is just any old wave + + + align:start position:0% +So so far this is just any old wave +equation, right? Nothing special about + + align:start position:0% +equation, right? Nothing special about + + + align:start position:0% +equation, right? Nothing special about +this. This anybody could and had written + + align:start position:0% +this. This anybody could and had written + + + align:start position:0% +this. This anybody could and had written +down + + align:start position:0% +down + + + align:start position:0% +down +before. But what's special is that + + align:start position:0% +before. But what's special is that + + + align:start position:0% +before. But what's special is that +Schroinger realized + + align:start position:0% +Schroinger realized + + + align:start position:0% +Schroinger realized +here that if this is going to be a wave + + align:start position:0% +here that if this is going to be a wave + + + align:start position:0% +here that if this is going to be a wave +equation for a + + align:start position:0% +equation for a + + + align:start position:0% +equation for a +particle, then maybe this lambda here, + + align:start position:0% +particle, then maybe this lambda here, + + + align:start position:0% +particle, then maybe this lambda here, +maybe I ought to put in for lambda what + + align:start position:0% +maybe I ought to put in for lambda what + + + align:start position:0% +maybe I ought to put in for lambda what +D Brogley told me, and that is H over P. + + align:start position:0% +D Brogley told me, and that is H over P. + + + align:start position:0% +D Brogley told me, and that is H over P. +Maybe this lambda here is the wavelength + + align:start position:0% +Maybe this lambda here is the wavelength + + + align:start position:0% +Maybe this lambda here is the wavelength +of a matter wave. So let me write this + + align:start position:0% +of a matter wave. So let me write this + + + align:start position:0% +of a matter wave. So let me write this +expression in terms of the momentum of + + align:start position:0% +expression in terms of the momentum of + + + align:start position:0% +expression in terms of the momentum of +the particle where the momentum has this + + align:start position:0% +the particle where the momentum has this + + + align:start position:0% +the particle where the momentum has this +mass m in it. And so when he did this + + align:start position:0% +mass m in it. And so when he did this + + + align:start position:0% +mass m in it. And so when he did this +this became minus p^2 over h bar 2. We + + align:start position:0% +this became minus p^2 over h bar 2. We + + + align:start position:0% +this became minus p^2 over h bar 2. We +said h bar is h over 2 pi time s of x. + + align:start position:0% +said h bar is h over 2 pi time s of x. + + + align:start position:0% +said h bar is h over 2 pi time s of x. +All right. Hey, this is getting good + + align:start position:0% +All right. Hey, this is getting good + + + align:start position:0% +All right. Hey, this is getting good +because now we got a s of x over here. + + align:start position:0% +because now we got a s of x over here. + + + align:start position:0% +because now we got a s of x over here. +All right. But then what he + + align:start position:0% +All right. But then what he + + + align:start position:0% +All right. But then what he +did is he said, well, I want to write + + align:start position:0% +did is he said, well, I want to write + + + align:start position:0% +did is he said, well, I want to write +this + + align:start position:0% +this + + + align:start position:0% +this +momentum. I want to write it in terms of + + align:start position:0% +momentum. I want to write it in terms of + + + align:start position:0% +momentum. I want to write it in terms of +the total + + align:start position:0% +the total + + + align:start position:0% +the total +energy. Total + + align:start position:0% +energy. Total + + + align:start position:0% +energy. Total +energy is always kinetic plus + + align:start position:0% +energy is always kinetic plus + + + align:start position:0% +energy is always kinetic plus +potential. The kinetic energy we said + + align:start position:0% +potential. The kinetic energy we said + + + align:start position:0% +potential. The kinetic energy we said +the other day can be written in terms of + + align:start position:0% +the other day can be written in terms of + + + align:start position:0% +the other day can be written in terms of +the momentum. The kinetic energy is P^2 + + align:start position:0% +the momentum. The kinetic energy is P^2 + + + align:start position:0% +the momentum. The kinetic energy is P^2 +over + + align:start position:0% +over + + + align:start position:0% +over +2M and plus the potential energy and I'm + + align:start position:0% +2M and plus the potential energy and I'm + + + align:start position:0% +2M and plus the potential energy and I'm +going to make this as a function of X + + align:start position:0% +going to make this as a function of X + + + align:start position:0% +going to make this as a function of X +the potential energy. All right. So now + + align:start position:0% +the potential energy. All right. So now + + + align:start position:0% +the potential energy. All right. So now +I'm just going to solve this for + + align:start position:0% +I'm just going to solve this for + + + align:start position:0% +I'm just going to solve this for +P^2. Right? So P^2 is equal to + + align:start position:0% +P^2. Right? So P^2 is equal to + + + align:start position:0% +P^2. Right? So P^2 is equal to +2M times the total energy minus this + + align:start position:0% +2M times the total energy minus this + + + align:start position:0% +2M times the total energy minus this +potential + + align:start position:0% +potential + + + align:start position:0% +potential +energy. And I'm going to plug this into + + align:start position:0% +energy. And I'm going to plug this into + + + align:start position:0% +energy. And I'm going to plug this into +here right in there. All + + align:start position:0% +here right in there. All + + + align:start position:0% +here right in there. All +right. And when I do that, I'm going to + + align:start position:0% +right. And when I do that, I'm going to + + + align:start position:0% +right. And when I do that, I'm going to +get the second derivative of s of x with + + align:start position:0% +get the second derivative of s of x with + + + align:start position:0% +get the second derivative of s of x with +respect to x= - 2m over h bar 2* e minus + + align:start position:0% +respect to x= - 2m over h bar 2* e minus + + + align:start position:0% +respect to x= - 2m over h bar 2* e minus +minus u of + + align:start position:0% +minus u of + + + align:start position:0% +minus u of +x time s of x. All right, just simple + + align:start position:0% +x time s of x. All right, just simple + + + align:start position:0% +x time s of x. All right, just simple +substitution for p ^2 there. Nothing + + align:start position:0% +substitution for p ^2 there. Nothing + + + align:start position:0% +substitution for p ^2 there. Nothing +else. And now I'm going to do some + + align:start position:0% +else. And now I'm going to do some + + + align:start position:0% +else. And now I'm going to do some +rearranging. And the rearranging is I'm + + align:start position:0% +rearranging. And the rearranging is I'm + + + align:start position:0% +rearranging. And the rearranging is I'm +going to on the right hand + + align:start position:0% +going to on the right hand + + + align:start position:0% +going to on the right hand +side have only e * s of x. e * s of x. + + align:start position:0% +side have only e * s of x. e * s of x. + + + align:start position:0% +side have only e * s of x. e * s of x. +Hey, that looks like the right hand side + + align:start position:0% +Hey, that looks like the right hand side + + + align:start position:0% +Hey, that looks like the right hand side +of the Schroinger equation as I wrote it + + align:start position:0% +of the Schroinger equation as I wrote it + + + align:start position:0% +of the Schroinger equation as I wrote it +down, right? So that's good. So when I + + align:start position:0% +down, right? So that's good. So when I + + + align:start position:0% +down, right? So that's good. So when I +rearrange this I get minus h^ 2 / 2n + + align:start position:0% +rearrange this I get minus h^ 2 / 2n + + + align:start position:0% +rearrange this I get minus h^ 2 / 2n +time the second derivative of s of x + + align:start position:0% +time the second derivative of s of x + + + align:start position:0% +time the second derivative of s of x +with respect to + + align:start position:0% +with respect to + + + align:start position:0% +with respect to +x plus u of x * s of + + align:start position:0% +x plus u of x * s of + + + align:start position:0% +x plus u of x * s of +x= e * s of x + + align:start position:0% +x= e * s of x + + + align:start position:0% +x= e * s of x +right and now I'm going to pull out a s + + align:start position:0% +right and now I'm going to pull out a s + + + align:start position:0% +right and now I'm going to pull out a s +of x here so that's - h bar 2 over 2m + + align:start position:0% +of x here so that's - h bar 2 over 2m + + + align:start position:0% +of x here so that's - h bar 2 over 2m +second derivative with respect to x + u + + align:start position:0% +second derivative with respect to x + u + + + align:start position:0% +second derivative with respect to x + u +of x the + + align:start position:0% +of x the + + + align:start position:0% +of x the +quantity time s of x = e * s of x and + + align:start position:0% +quantity time s of x = e * s of x and + + + align:start position:0% +quantity time s of x = e * s of x and +guess what we got it right we got it + + align:start position:0% +guess what we got it right we got it + + + align:start position:0% +guess what we got it right we got it +because all of this right all of this is + + align:start position:0% +because all of this right all of this is + + + align:start position:0% +because all of this right all of this is +what we define as the + + align:start position:0% +what we define as the + + + align:start position:0% +what we define as the +Hamiltonian all of this is h + + align:start position:0% +Hamiltonian all of this is h + + + align:start position:0% +Hamiltonian all of this is h +hat H operating on S of X gives us E * S + + align:start position:0% +hat H operating on S of X gives us E * S + + + align:start position:0% +hat H operating on S of X gives us E * S +of X. All right. This Hamiltonian as you + + align:start position:0% +of X. All right. This Hamiltonian as you + + + align:start position:0% +of X. All right. This Hamiltonian as you +will um learn later on this is a kinetic + + align:start position:0% +will um learn later on this is a kinetic + + + align:start position:0% +will um learn later on this is a kinetic +energy + + align:start position:0% +energy + + + align:start position:0% +energy +operator. This is the potential energy + + align:start position:0% +operator. This is the potential energy + + + align:start position:0% +operator. This is the potential energy +operator operating on S. That's the + + align:start position:0% +operator operating on S. That's the + + + align:start position:0% +operator operating on S. That's the +Schroinger equation, right? It's hardly + + align:start position:0% +Schroinger equation, right? It's hardly + + + align:start position:0% +Schroinger equation, right? It's hardly +a derivation. It's taking derivatives. + + align:start position:0% +a derivation. It's taking derivatives. + + + align:start position:0% +a derivation. It's taking derivatives. +It's a wave equation. The insight came + + align:start position:0% +It's a wave equation. The insight came + + + align:start position:0% +It's a wave equation. The insight came +right here. The insight is this + + align:start position:0% +right here. The insight is this + + + align:start position:0% +right here. The insight is this +substitution of the debrogaly wavelength + + align:start position:0% +substitution of the debrogaly wavelength + + + align:start position:0% +substitution of the debrogaly wavelength +in an ordinary wave + + align:start position:0% +in an ordinary wave + + + align:start position:0% +in an ordinary wave +equation. Um it's in an ordinary wave + + align:start position:0% +equation. Um it's in an ordinary wave + + + align:start position:0% +equation. Um it's in an ordinary wave +equation. Right? This is the insight is + + align:start position:0% +equation. Right? This is the insight is + + + align:start position:0% +equation. Right? This is the insight is +getting that momentum in there with the + + align:start position:0% +getting that momentum in there with the + + + align:start position:0% +getting that momentum in there with the +mass making this then an equation for a + + align:start position:0% +mass making this then an equation for a + + + align:start position:0% +mass making this then an equation for a +matter wave. All right? That's it. Okay. + + align:start position:0% +matter wave. All right? That's it. Okay. + + + align:start position:0% +matter wave. All right? That's it. Okay. +So you just quote unquote drive the + + align:start position:0% +So you just quote unquote drive the + + + align:start position:0% +So you just quote unquote drive the +Schroinger equation. Yay. All right. + + align:start position:0% +Schroinger equation. Yay. All right. + + + align:start position:0% +Schroinger equation. Yay. All right. +So + + align:start position:0% +So + + + align:start position:0% +So +easy. All + + align:start position:0% +easy. All + + + align:start position:0% +easy. All +right. + + align:start position:0% + + + + align:start position:0% + +Now so bottom line here is that the + + align:start position:0% +Now so bottom line here is that the + + + align:start position:0% +Now so bottom line here is that the +Schroinger equation is to quantum + + align:start position:0% +Schroinger equation is to quantum + + + align:start position:0% +Schroinger equation is to quantum +mechanics like uh Newton's equations are + + align:start position:0% +mechanics like uh Newton's equations are + + + align:start position:0% +mechanics like uh Newton's equations are +to classical mechanics. When the + + align:start position:0% +to classical mechanics. When the + + + align:start position:0% +to classical mechanics. When the +wavelength of a particle is on the order + + align:start position:0% +wavelength of a particle is on the order + + + align:start position:0% +wavelength of a particle is on the order +of the size of its environment, the + + align:start position:0% +of the size of its environment, the + + + align:start position:0% +of the size of its environment, the +equation of motion that you have to use + + align:start position:0% +equation of motion that you have to use + + + align:start position:0% +equation of motion that you have to use +to describe that particle moving within + + align:start position:0% +to describe that particle moving within + + + align:start position:0% +to describe that particle moving within +some potential field uh u of x or you + + align:start position:0% +some potential field uh u of x or you + + + align:start position:0% +some potential field uh u of x or you +you have to use this equation of motion + + align:start position:0% +you have to use this equation of motion + + + align:start position:0% +you have to use this equation of motion +and not Newton's equations. Newton's + + align:start position:0% +and not Newton's equations. Newton's + + + align:start position:0% +and not Newton's equations. Newton's +equations don't work to describe the + + align:start position:0% +equations don't work to describe the + + + align:start position:0% +equations don't work to describe the +motion of any particle whose wavelength + + align:start position:0% +motion of any particle whose wavelength + + + align:start position:0% +motion of any particle whose wavelength +is on the order of the size of the + + align:start position:0% +is on the order of the size of the + + + align:start position:0% +is on the order of the size of the +environment. All right? It just doesn't + + align:start position:0% +environment. All right? It just doesn't + + + align:start position:0% +environment. All right? It just doesn't +work. Now, just as an + + align:start position:0% +work. Now, just as an + + + align:start position:0% +work. Now, just as an +aside, classical mechanics really is + + align:start position:0% +aside, classical mechanics really is + + + align:start position:0% +aside, classical mechanics really is +embedded in quantum mechanics. + + align:start position:0% +embedded in quantum mechanics. + + + align:start position:0% +embedded in quantum mechanics. +That is if you took a + + align:start position:0% +That is if you took a + + + align:start position:0% +That is if you took a +problem that and solved it quantum + + align:start position:0% +problem that and solved it quantum + + + align:start position:0% +problem that and solved it quantum +mechanically and you solved the + + align:start position:0% +mechanically and you solved the + + + align:start position:0% +mechanically and you solved the +problem and you solved the problem a + + align:start position:0% +problem and you solved the problem a + + + align:start position:0% +problem and you solved the problem a +problem for which the wavelength of a + + align:start position:0% +problem for which the wavelength of a + + + align:start position:0% +problem for which the wavelength of a +particle was much much greater than the + + align:start position:0% +particle was much much greater than the + + + align:start position:0% +particle was much much greater than the +size of the environment which is the + + align:start position:0% +size of the environment which is the + + + align:start position:0% +size of the environment which is the +classical limit. Quantum mechanics would + + align:start position:0% +classical limit. Quantum mechanics would + + + align:start position:0% +classical limit. Quantum mechanics would +give you the right answer. Right? + + align:start position:0% +give you the right answer. Right? + + + align:start position:0% +give you the right answer. Right? +In other words, say say you say you took + + align:start position:0% +In other words, say say you say you took + + + align:start position:0% +In other words, say say you say you took +some problem where the wavelength of the + + align:start position:0% +some problem where the wavelength of the + + + align:start position:0% +some problem where the wavelength of the +particle is larger than the size of the + + align:start position:0% +particle is larger than the size of the + + + align:start position:0% +particle is larger than the size of the +environment. That's a problem where you + + align:start position:0% +environment. That's a problem where you + + + align:start position:0% +environment. That's a problem where you +would normally use classical mechanics. + + align:start position:0% +would normally use classical mechanics. + + + align:start position:0% +would normally use classical mechanics. +But if you use quantum + + align:start position:0% +But if you use quantum + + + align:start position:0% +But if you use quantum +mechanics, you would get the right + + align:start position:0% +mechanics, you would get the right + + + align:start position:0% +mechanics, you would get the right +answer if you could solve the problem. + + align:start position:0% +answer if you could solve the problem. + + + align:start position:0% +answer if you could solve the problem. +Equations are very difficult, but in + + align:start position:0% +Equations are very difficult, but in + + + align:start position:0% +Equations are very difficult, but in +principle, you would get the right + + align:start position:0% +principle, you would get the right + + + align:start position:0% +principle, you would get the right +answer. + + align:start position:0% +answer. + + + align:start position:0% +answer. +However, if you took a quantum + + align:start position:0% +However, if you took a quantum + + + align:start position:0% +However, if you took a quantum +mechanical problem, that is a problem + + align:start position:0% +mechanical problem, that is a problem + + + align:start position:0% +mechanical problem, that is a problem +where the wavelength is of the particle + + align:start position:0% +where the wavelength is of the particle + + + align:start position:0% +where the wavelength is of the particle +is on the order of the size of the + + align:start position:0% +is on the order of the size of the + + + align:start position:0% +is on the order of the size of the +environment and you use classical + + align:start position:0% +environment and you use classical + + + align:start position:0% +environment and you use classical +mechanics, well, you won't get the right + + align:start position:0% +mechanics, well, you won't get the right + + + align:start position:0% +mechanics, well, you won't get the right +answer, right? Because classical + + align:start position:0% +answer, right? Because classical + + + align:start position:0% +answer, right? Because classical +mechanics is in a sense a subset. It's + + align:start position:0% +mechanics is in a sense a subset. It's + + + align:start position:0% +mechanics is in a sense a subset. It's +contained within uh quantum mechanics. + + align:start position:0% +contained within uh quantum mechanics. + + + align:start position:0% +contained within uh quantum mechanics. +All right? It's a limit of quantum + + align:start position:0% +All right? It's a limit of quantum + + + align:start position:0% +All right? It's a limit of quantum +mechanics. All right? So we have to + + align:start position:0% +mechanics. All right? So we have to + + + align:start position:0% +mechanics. All right? So we have to +learn a new kind of mechanics here. Uh + + align:start position:0% +learn a new kind of mechanics here. Uh + + + align:start position:0% +learn a new kind of mechanics here. Uh +this mechanics for the motion of + + align:start position:0% +this mechanics for the motion of + + + align:start position:0% +this mechanics for the motion of +waves. + + align:start position:0% +waves. + + + align:start position:0% +waves. +Okay. So now for a hydrogen atom um we + + align:start position:0% +Okay. So now for a hydrogen atom um we + + + align:start position:0% +Okay. So now for a hydrogen atom um we +have to think of the wave function in + + align:start position:0% +have to think of the wave function in + + + align:start position:0% +have to think of the wave function in +three dimensions instead of just one + + align:start position:0% +three dimensions instead of just one + + + align:start position:0% +three dimensions instead of just one +dimension here. And so we're going to + + align:start position:0% +dimension here. And so we're going to + + + align:start position:0% +dimension here. And so we're going to +have to + + align:start position:0% +have to + + + align:start position:0% +have to +describe the particle in terms of three + + align:start position:0% +describe the particle in terms of three + + + align:start position:0% +describe the particle in terms of three +position + + align:start position:0% +position + + + align:start position:0% +position +coordinates. Usually you use cartisian + + align:start position:0% +coordinates. Usually you use cartisian + + + align:start position:0% +coordinates. Usually you use cartisian +coordinates x, y, and z. But this + + align:start position:0% +coordinates x, y, and z. But this + + + align:start position:0% +coordinates x, y, and z. But this +problem is soluble exactly if we use + + align:start position:0% +problem is soluble exactly if we use + + + align:start position:0% +problem is soluble exactly if we use +spherical coordinates. So how many of + + align:start position:0% +spherical coordinates. So how many of + + + align:start position:0% +spherical coordinates. So how many of +you have had spherical coordinates + + align:start position:0% +you have had spherical coordinates + + + align:start position:0% +you have had spherical coordinates +before and know what we're talking + + align:start position:0% +before and know what we're talking + + + align:start position:0% +before and know what we're talking +about? Okay. Not everybody, right? Okay. + + align:start position:0% +about? Okay. Not everybody, right? Okay. + + + align:start position:0% +about? Okay. Not everybody, right? Okay. +All right. So if I gave you an X, Y, and + + align:start position:0% +All right. So if I gave you an X, Y, and + + + align:start position:0% +All right. So if I gave you an X, Y, and +Z for this electron in this atom where + + align:start position:0% +Z for this electron in this atom where + + + align:start position:0% +Z for this electron in this atom where +the nucleus was pinned at the origin, if + + align:start position:0% +the nucleus was pinned at the origin, if + + + align:start position:0% +the nucleus was pinned at the origin, if +I gave you an X, Y, and Z coordinate, + + align:start position:0% +I gave you an X, Y, and Z coordinate, + + + align:start position:0% +I gave you an X, Y, and Z coordinate, +you'd know where that electron was. But + + align:start position:0% +you'd know where that electron was. But + + + align:start position:0% +you'd know where that electron was. But +alternatively, I could tell you the + + align:start position:0% +alternatively, I could tell you the + + + align:start position:0% +alternatively, I could tell you the +position of this electron using + + align:start position:0% +position of this electron using + + + align:start position:0% +position of this electron using +spherical coordinates. That is, I could + + align:start position:0% +spherical coordinates. That is, I could + + + align:start position:0% +spherical coordinates. That is, I could +tell you what the distance is of the + + align:start position:0% +tell you what the distance is of the + + + align:start position:0% +tell you what the distance is of the +electron from the nucleus. I'm going to + + align:start position:0% +electron from the nucleus. I'm going to + + + align:start position:0% +electron from the nucleus. I'm going to +call that r. That will be one of the + + align:start position:0% +call that r. That will be one of the + + + align:start position:0% +call that r. That will be one of the +variables. + + align:start position:0% +variables. + + + align:start position:0% +variables. +I could then also tell you this angle + + align:start position:0% +I could then also tell you this angle + + + align:start position:0% +I could then also tell you this angle +theta. Theta is the angle that r makes + + align:start position:0% +theta. Theta is the angle that r makes + + + align:start position:0% +theta. Theta is the angle that r makes +from the z-axis. That's the second + + align:start position:0% +from the z-axis. That's the second + + + align:start position:0% +from the z-axis. That's the second +coordinate. And then finally the third + + align:start position:0% +coordinate. And then finally the third + + + align:start position:0% +coordinate. And then finally the third +coordinate is phi. Phi is the angle made + + align:start position:0% +coordinate is phi. Phi is the angle made + + + align:start position:0% +coordinate is phi. Phi is the angle made +by the following. If I take the electron + + align:start position:0% +by the following. If I take the electron + + + align:start position:0% +by the following. If I take the electron +and I drop a perpendicular to the xy + + align:start position:0% +and I drop a perpendicular to the xy + + + align:start position:0% +and I drop a perpendicular to the xy +plane, right? And then I draw a line + + align:start position:0% +plane, right? And then I draw a line + + + align:start position:0% +plane, right? And then I draw a line +here. + + align:start position:0% +here. + + + align:start position:0% +here. +Well, the angle between that line and + + align:start position:0% +Well, the angle between that line and + + + align:start position:0% +Well, the angle between that line and +the x axis, that's the angle phi. So + + align:start position:0% +the x axis, that's the angle phi. So + + + align:start position:0% +the x axis, that's the angle phi. So +instead of giving you x, y, and z, I'm + + align:start position:0% +instead of giving you x, y, and z, I'm + + + align:start position:0% +instead of giving you x, y, and z, I'm +just going to give you r, theta, and phi + + align:start position:0% +just going to give you r, theta, and phi + + + align:start position:0% +just going to give you r, theta, and phi +in spherical coordinates. All + + align:start position:0% +in spherical coordinates. All + + + align:start position:0% +in spherical coordinates. All +right. And now this wave function is + + align:start position:0% +right. And now this wave function is + + + align:start position:0% +right. And now this wave function is +also a function of time. And I'll talk + + align:start position:0% +also a function of time. And I'll talk + + + align:start position:0% +also a function of time. And I'll talk +about that a little bit probably uh next + + align:start position:0% +about that a little bit probably uh next + + + align:start position:0% +about that a little bit probably uh next +time. All right. So uh that's the wave + + align:start position:0% +time. All right. So uh that's the wave + + + align:start position:0% +time. All right. So uh that's the wave +function that is in some way + + align:start position:0% +function that is in some way + + + align:start position:0% +function that is in some way +going to represent our electron. I + + align:start position:0% +going to represent our electron. I + + + align:start position:0% +going to represent our electron. I +haven't told you exactly yet how Sai + + align:start position:0% +haven't told you exactly yet how Sai + + + align:start position:0% +haven't told you exactly yet how Sai +represents the electron and I won't tell + + align:start position:0% +represents the electron and I won't tell + + + align:start position:0% +represents the electron and I won't tell +you that for another few days question. + + align:start position:0% +you that for another few days question. + + + align:start position:0% +you that for another few days question. +Yeah. Um, + + align:start position:0% +Yeah. Um, + + + align:start position:0% +Yeah. Um, +yeah. + + align:start position:0% + + + + align:start position:0% + +Uhhuh. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um, no, it will just uh uh I actually + + align:start position:0% +Um, no, it will just uh uh I actually + + + align:start position:0% +Um, no, it will just uh uh I actually +thought this is the way the book set it + + align:start position:0% +thought this is the way the book set it + + + align:start position:0% +thought this is the way the book set it +up, but I may have it backwards. + + align:start position:0% + + + + align:start position:0% + +Right. Right. I think this is the way + + align:start position:0% +Right. Right. I think this is the way + + + align:start position:0% +Right. Right. I think this is the way +our book does it. sets it up. So, + + align:start position:0% +our book does it. sets it up. So, + + + align:start position:0% +our book does it. sets it up. So, +uh it let's see it it won't make a + + align:start position:0% +uh it let's see it it won't make a + + + align:start position:0% +uh it let's see it it won't make a +difference in any of the problems we + + align:start position:0% +difference in any of the problems we + + + align:start position:0% +difference in any of the problems we +solve here, but in general, if you're + + align:start position:0% +solve here, but in general, if you're + + + align:start position:0% +solve here, but in general, if you're +given a problem to solve, you're going + + align:start position:0% +given a problem to solve, you're going + + + align:start position:0% +given a problem to solve, you're going +to have to look and see how they define + + align:start position:0% +to have to look and see how they define + + + align:start position:0% +to have to look and see how they define +their coordinate system. Okay. Okay. + + align:start position:0% +their coordinate system. Okay. Okay. + + + align:start position:0% +their coordinate system. Okay. Okay. +Actually, somebody else asked me that + + align:start position:0% +Actually, somebody else asked me that + + + align:start position:0% +Actually, somebody else asked me that +the other day. Right. + + align:start position:0% +the other day. Right. + + + align:start position:0% +the other day. Right. +Right. + + align:start position:0% +Right. + + + align:start position:0% +Right. +Okay. All right. + + align:start position:0% + + + + align:start position:0% + +So now what we've got to do is we + + align:start position:0% +So now what we've got to do is we + + + align:start position:0% +So now what we've got to do is we +actually have to set up the Hamiltonian + + align:start position:0% +actually have to set up the Hamiltonian + + + align:start position:0% +actually have to set up the Hamiltonian +for the hydrogen atom. Um that is we + + align:start position:0% +for the hydrogen atom. Um that is we + + + align:start position:0% +for the hydrogen atom. Um that is we +have to set up the Hamiltonian + + align:start position:0% +have to set up the Hamiltonian + + + align:start position:0% +have to set up the Hamiltonian +specifically for the hydrogen atom. And + + align:start position:0% +specifically for the hydrogen atom. And + + + align:start position:0% +specifically for the hydrogen atom. And +we've got to set it up in terms of + + align:start position:0% +we've got to set it up in terms of + + + align:start position:0% +we've got to set it up in terms of +spherical coordinates r theta and phi. + + align:start position:0% +spherical coordinates r theta and phi. + + + align:start position:0% +spherical coordinates r theta and phi. +And um when we do that, and we're not + + align:start position:0% +And um when we do that, and we're not + + + align:start position:0% +And um when we do that, and we're not +actually going to do that, but when we + + align:start position:0% +actually going to do that, but when we + + + align:start position:0% +actually going to do that, but when we +do that, that's what the Hamiltonian + + align:start position:0% +do that, that's what the Hamiltonian + + + align:start position:0% +do that, that's what the Hamiltonian +looks like. Okay. + + align:start position:0% +looks like. Okay. + + + align:start position:0% +looks like. Okay. +Yeah. And actually, um you know, this is + + align:start position:0% +Yeah. And actually, um you know, this is + + + align:start position:0% +Yeah. And actually, um you know, this is +in three dimensions. And so if I were + + align:start position:0% +in three dimensions. And so if I were + + + align:start position:0% +in three dimensions. And so if I were +doing it in the XYZ, what I would have + + align:start position:0% +doing it in the XYZ, what I would have + + + align:start position:0% +doing it in the XYZ, what I would have +here is a second derivative with respect + + align:start position:0% +here is a second derivative with respect + + + align:start position:0% +here is a second derivative with respect +to y plus a second derivative with + + align:start position:0% +to y plus a second derivative with + + + align:start position:0% +to y plus a second derivative with +respect to z. All right, that's what it + + align:start position:0% +respect to z. All right, that's what it + + + align:start position:0% +respect to z. All right, that's what it +would look like in three dimensions in + + align:start position:0% +would look like in three dimensions in + + + align:start position:0% +would look like in three dimensions in +cartisian coordinates. But when I + + align:start position:0% +cartisian coordinates. But when I + + + align:start position:0% +cartisian coordinates. But when I +transform from cartisian coordinates to + + align:start position:0% +transform from cartisian coordinates to + + + align:start position:0% +transform from cartisian coordinates to +spherical coordinates and that's an + + align:start position:0% +spherical coordinates and that's an + + + align:start position:0% +spherical coordinates and that's an +exercise which takes five pages and + + align:start position:0% +exercise which takes five pages and + + + align:start position:0% +exercise which takes five pages and +everybody should have that experience + + align:start position:0% +everybody should have that experience + + + align:start position:0% +everybody should have that experience +once in their life but maybe now is not + + align:start position:0% +once in their life but maybe now is not + + + align:start position:0% +once in their life but maybe now is not +the right time for that experience. You + + align:start position:0% +the right time for that experience. You + + + align:start position:0% +the right time for that experience. You +do get this. Okay. And essentially what + + align:start position:0% +do get this. Okay. And essentially what + + + align:start position:0% +do get this. Okay. And essentially what +this is the Hamiltonian is a sum of + + align:start position:0% +this is the Hamiltonian is a sum of + + + align:start position:0% +this is the Hamiltonian is a sum of +second derivatives with respect to each + + align:start position:0% +second derivatives with respect to each + + + align:start position:0% +second derivatives with respect to each +one of the coordinates because + + align:start position:0% +one of the coordinates because + + + align:start position:0% +one of the coordinates because +essentially this term hey that's a + + align:start position:0% +essentially this term hey that's a + + + align:start position:0% +essentially this term hey that's a +second derivative with respect to r. + + align:start position:0% +second derivative with respect to r. + + + align:start position:0% +second derivative with respect to r. +This term is a second derivative with + + align:start position:0% +This term is a second derivative with + + + align:start position:0% +This term is a second derivative with +respect to theta. This term's a second + + align:start position:0% +respect to theta. This term's a second + + + align:start position:0% +respect to theta. This term's a second +derivative with respect to phi. All + + align:start position:0% +derivative with respect to phi. All + + + align:start position:0% +derivative with respect to phi. All +right. So that's the specific + + align:start position:0% +right. So that's the specific + + + align:start position:0% +right. So that's the specific +Hamiltonian. These are all kinetic + + align:start position:0% +Hamiltonian. These are all kinetic + + + align:start position:0% +Hamiltonian. These are all kinetic +energy operators as you will learn later + + align:start position:0% +energy operators as you will learn later + + + align:start position:0% +energy operators as you will learn later +on. + + align:start position:0% +on. + + + align:start position:0% +on. +And then there's this term here, U of R. + + align:start position:0% +And then there's this term here, U of R. + + + align:start position:0% +And then there's this term here, U of R. +Hey, this U of R, what is + + align:start position:0% +Hey, this U of R, what is + + + align:start position:0% +Hey, this U of R, what is +that? What is U of R? Potential energy, + + align:start position:0% +that? What is U of R? Potential energy, + + + align:start position:0% +that? What is U of R? Potential energy, +right? It's the kum potential energy of + + align:start position:0% +right? It's the kum potential energy of + + + align:start position:0% +right? It's the kum potential energy of +interaction. It is + + align:start position:0% +interaction. It is + + + align:start position:0% +interaction. It is +isotropic, meaning it's the same at all + + align:start position:0% +isotropic, meaning it's the same at all + + + align:start position:0% +isotropic, meaning it's the same at all +angles. The only thing it depends on is + + align:start position:0% +angles. The only thing it depends on is + + + align:start position:0% +angles. The only thing it depends on is +the distance of the electron from the + + align:start position:0% +the distance of the electron from the + + + align:start position:0% +the distance of the electron from the +nucleus. It only depends on r. It + + align:start position:0% +nucleus. It only depends on r. It + + + align:start position:0% +nucleus. It only depends on r. It +doesn't depend on theta and phi. + + align:start position:0% +doesn't depend on theta and phi. + + + align:start position:0% +doesn't depend on theta and phi. +All right. So that is the Schroinger + + align:start position:0% +All right. So that is the Schroinger + + + align:start position:0% +All right. So that is the Schroinger +equation for the hydrogen + + align:start position:0% +equation for the hydrogen + + + align:start position:0% +equation for the hydrogen +atom. All right. It's a differential + + align:start position:0% +atom. All right. It's a differential + + + align:start position:0% +atom. All right. It's a differential +equation. Second order ordinary + + align:start position:0% +equation. Second order ordinary + + + align:start position:0% +equation. Second order ordinary +differential equation. In 1803 you're + + align:start position:0% +differential equation. In 1803 you're + + + align:start position:0% +differential equation. In 1803 you're +going to learn how to solve that in 561 + + align:start position:0% +going to learn how to solve that in 561 + + + align:start position:0% +going to learn how to solve that in 561 +or 804 I think it is in physics in + + align:start position:0% +or 804 I think it is in physics in + + + align:start position:0% +or 804 I think it is in physics in +quantum mechanics. You're going to solve + + align:start position:0% +quantum mechanics. You're going to solve + + + align:start position:0% +quantum mechanics. You're going to solve +that. You can do that. It's not it's not + + align:start position:0% +that. You can do that. It's not it's not + + + align:start position:0% +that. You can do that. It's not it's not +hard. Okay. But what do I mean when I + + align:start position:0% +hard. Okay. But what do I mean when I + + + align:start position:0% +hard. Okay. But what do I mean when I +say + + align:start position:0% +say + + + align:start position:0% +say +solve? What I mean + + align:start position:0% +solve? What I mean + + + align:start position:0% +solve? What I mean +is that we're going to calculate these E + + align:start position:0% +is that we're going to calculate these E + + + align:start position:0% +is that we're going to calculate these E +these binding energies this constant in + + align:start position:0% +these binding energies this constant in + + + align:start position:0% +these binding energies this constant in +front of the side. That's called an igen + + align:start position:0% +front of the side. That's called an igen + + + align:start position:0% +front of the side. That's called an igen +value for those of you who uh might know + + align:start position:0% +value for those of you who uh might know + + + align:start position:0% +value for those of you who uh might know +something already about these kinds of + + align:start position:0% +something already about these kinds of + + + align:start position:0% +something already about these kinds of +differential equations. This E here, + + align:start position:0% +differential equations. This E here, + + + align:start position:0% +differential equations. This E here, +it's the binding energy of the electron + + align:start position:0% +it's the binding energy of the electron + + + align:start position:0% +it's the binding energy of the electron +to the nucleus. We're going to look at + + align:start position:0% +to the nucleus. We're going to look at + + + align:start position:0% +to the nucleus. We're going to look at +those results in just a moment. + + align:start position:0% +those results in just a moment. + + + align:start position:0% +those results in just a moment. +And the other quantity we're going to + + align:start position:0% +And the other quantity we're going to + + + align:start position:0% +And the other quantity we're going to +solve for here is + + align:start position:0% +solve for here is + + + align:start position:0% +solve for here is +S. What we're going to want to find is + + align:start position:0% +S. What we're going to want to find is + + + align:start position:0% +S. What we're going to want to find is +the actual functional form for the wave + + align:start position:0% +the actual functional form for the wave + + + align:start position:0% +the actual functional form for the wave +functions that we can get out of solving + + align:start position:0% +functions that we can get out of solving + + + align:start position:0% +functions that we can get out of solving +this differential equation. Right? The + + align:start position:0% +this differential equation. Right? The + + + align:start position:0% +this differential equation. Right? The +actual functional form for S. The + + align:start position:0% +actual functional form for S. The + + + align:start position:0% +actual functional form for S. The +functional form is going to be more + + align:start position:0% +functional form is going to be more + + + align:start position:0% +functional form is going to be more +complicated than what I wrote here. + + align:start position:0% +complicated than what I wrote here. + + + align:start position:0% +complicated than what I wrote here. +Right. Okay. But we can we can get that + + align:start position:0% +Right. Okay. But we can we can get that + + + align:start position:0% +Right. Okay. But we can we can get that +and we'll look at that in a few days + + align:start position:0% +and we'll look at that in a few days + + + align:start position:0% +and we'll look at that in a few days +from now. And those wave functions, hey, + + align:start position:0% +from now. And those wave functions, hey, + + + align:start position:0% +from now. And those wave functions, hey, +you know what those wave functions are? + + align:start position:0% +you know what those wave functions are? + + + align:start position:0% +you know what those wave functions are? +Those wave functions are what you uh + + align:start position:0% +Those wave functions are what you uh + + + align:start position:0% +Those wave functions are what you uh +studied in high school as orbitals. You + + align:start position:0% +studied in high school as orbitals. You + + + align:start position:0% +studied in high school as orbitals. You +talked about an S orbital, P orbital, D + + align:start position:0% +talked about an S orbital, P orbital, D + + + align:start position:0% +talked about an S orbital, P orbital, D +orbital. Hey, orbitals are wave + + align:start position:0% +orbital. Hey, orbitals are wave + + + align:start position:0% +orbital. Hey, orbitals are wave +functions. That's where they come from. + + align:start position:0% +functions. That's where they come from. + + + align:start position:0% +functions. That's where they come from. +Orbitals from solving the Schroinger + + align:start position:0% +Orbitals from solving the Schroinger + + + align:start position:0% +Orbitals from solving the Schroinger +equation. Now, specifically, orbitals + + align:start position:0% +equation. Now, specifically, orbitals + + + align:start position:0% +equation. Now, specifically, orbitals +are the spatial part of a wave function. + + align:start position:0% +are the spatial part of a wave function. + + + align:start position:0% +are the spatial part of a wave function. +There's also a spin part to the wave + + align:start position:0% +There's also a spin part to the wave + + + align:start position:0% +There's also a spin part to the wave +function, but for all intents of + + align:start position:0% +function, but for all intents of + + + align:start position:0% +function, but for all intents of +purposes, we're going to use the term + + align:start position:0% +purposes, we're going to use the term + + + align:start position:0% +purposes, we're going to use the term +orbital and wave function + + align:start position:0% +orbital and wave function + + + align:start position:0% +orbital and wave function +interchangeably because they're the same + + align:start position:0% +interchangeably because they're the same + + + align:start position:0% +interchangeably because they're the same +thing. Okay, question. How is binding + + align:start position:0% +thing. Okay, question. How is binding + + + align:start position:0% +thing. Okay, question. How is binding +energy different from like a work + + align:start position:0% +energy different from like a work + + + align:start position:0% +energy different from like a work +function? Okay, we're going to get to + + align:start position:0% +function? Okay, we're going to get to + + + align:start position:0% +function? Okay, we're going to get to +that in just a moment. Okay, then I'll + + align:start position:0% +that in just a moment. Okay, then I'll + + + align:start position:0% +that in just a moment. Okay, then I'll +come if I don't if you think I don't + + align:start position:0% +come if I don't if you think I don't + + + align:start position:0% +come if I don't if you think I don't +answer it, then uh we'll go back to + + align:start position:0% +answer it, then uh we'll go back to + + + align:start position:0% +answer it, then uh we'll go back to +that. + + align:start position:0% +that. + + + align:start position:0% +that. +Okay. Okay. So we're going to solve + + align:start position:0% +Okay. Okay. So we're going to solve + + + align:start position:0% +Okay. Okay. So we're going to solve +this. We're going to and this equation + + align:start position:0% +this. We're going to and this equation + + + align:start position:0% +this. We're going to and this equation +is going to predict binding energies and + + align:start position:0% +is going to predict binding energies and + + + align:start position:0% +is going to predict binding energies and +it's going to predict these uh wave + + align:start position:0% +it's going to predict these uh wave + + + align:start position:0% +it's going to predict these uh wave +functions in agreement with our + + align:start position:0% +functions in agreement with our + + + align:start position:0% +functions in agreement with our +observations and it's going to predict + + align:start position:0% +observations and it's going to predict + + + align:start position:0% +observations and it's going to predict +that the hydrogen atom is stable. + + align:start position:0% +that the hydrogen atom is stable. + + + align:start position:0% +that the hydrogen atom is stable. +Remember when we tried to predict the + + align:start position:0% +Remember when we tried to predict the + + + align:start position:0% +Remember when we tried to predict the +hydrogen atom using classical ideas, we + + align:start position:0% +hydrogen atom using classical ideas, we + + + align:start position:0% +hydrogen atom using classical ideas, we +found it lived a whole whopping 10us 10 + + align:start position:0% +found it lived a whole whopping 10us 10 + + + align:start position:0% +found it lived a whole whopping 10us 10 +seconds. Not so when we treat the + + align:start position:0% +seconds. Not so when we treat the + + + align:start position:0% +seconds. Not so when we treat the +hydrogen atom with the quantum + + align:start position:0% +hydrogen atom with the quantum + + + align:start position:0% +hydrogen atom with the quantum +mechanical equations of motion. Right? + + align:start position:0% +mechanical equations of motion. Right? + + + align:start position:0% +mechanical equations of motion. Right? +Okay. So let's write down the results + + align:start position:0% +Okay. So let's write down the results + + + align:start position:0% +Okay. So let's write down the results +for solving the Schroinger equation. And + + align:start position:0% +for solving the Schroinger equation. And + + + align:start position:0% +for solving the Schroinger equation. And +the part I'm going to concentrate on + + align:start position:0% +the part I'm going to concentrate on + + + align:start position:0% +the part I'm going to concentrate on +today are these binding energies. And on + + align:start position:0% +today are these binding energies. And on + + + align:start position:0% +today are these binding energies. And on +Friday we'll talk about the wave + + align:start position:0% +Friday we'll talk about the wave + + + align:start position:0% +Friday we'll talk about the wave +function solving the Schroinger equation + + align:start position:0% +function solving the Schroinger equation + + + align:start position:0% +function solving the Schroinger equation +for those uh wave functions. + + align:start position:0% +for those uh wave functions. + + + align:start position:0% +for those uh wave functions. +Okay, let me put this up. + + align:start position:0% + + + + align:start position:0% + +So, what does the binding energy look + + align:start position:0% +So, what does the binding energy look + + + align:start position:0% +So, what does the binding energy look +like? Well, the binding energies here + + align:start position:0% +like? Well, the binding energies here + + + align:start position:0% +like? Well, the binding energies here +coming out of the Schroinger + + align:start position:0% +coming out of the Schroinger + + + align:start position:0% +coming out of the Schroinger +equation look like this. + + align:start position:0% +equation look like this. + + + align:start position:0% +equation look like this. +-1 / + + align:start position:0% +-1 / + + + align:start position:0% +-1 / +n^2* m e 4th over 8 epsilon^ 2 * h^ + + align:start position:0% +n^2* m e 4th over 8 epsilon^ 2 * h^ + + + align:start position:0% +n^2* m e 4th over 8 epsilon^ 2 * h^ +2 m is the mass of the electron. E is + + align:start position:0% +2 m is the mass of the electron. E is + + + align:start position:0% +2 m is the mass of the electron. E is +the charge on the + + align:start position:0% +the charge on the + + + align:start position:0% +the charge on the +electron. Epsilon kn is this permitivity + + align:start position:0% +electron. Epsilon kn is this permitivity + + + align:start position:0% +electron. Epsilon kn is this permitivity +of vacuum we talked about before. This + + align:start position:0% +of vacuum we talked about before. This + + + align:start position:0% +of vacuum we talked about before. This +is a conversion between SESU units and + + align:start position:0% +is a conversion between SESU units and + + + align:start position:0% +is a conversion between SESU units and +SI units. H planks constant blanks + + align:start position:0% +SI units. H planks constant blanks + + + align:start position:0% +SI units. H planks constant blanks +constant is ubiquitous. It's everywhere, + + align:start position:0% +constant is ubiquitous. It's everywhere, + + + align:start position:0% +constant is ubiquitous. It's everywhere, +right? What we typically do is we lump + + align:start position:0% +right? What we typically do is we lump + + + align:start position:0% +right? What we typically do is we lump +these constants + + align:start position:0% +these constants + + + align:start position:0% +these constants +together and we call those constants a + + align:start position:0% +together and we call those constants a + + + align:start position:0% +together and we call those constants a +new constant. We call it the RBER + + align:start position:0% +new constant. We call it the RBER + + + align:start position:0% +new constant. We call it the RBER +constant R subH. Right? And so our + + align:start position:0% +constant R subH. Right? And so our + + + align:start position:0% +constant R subH. Right? And so our +expression is equal to minus 1 / r subh + + align:start position:0% +expression is equal to minus 1 / r subh + + + align:start position:0% +expression is equal to minus 1 / r subh +/ + + align:start position:0% +/ + + + align:start position:0% +/ +n^2. The value of r subh here the value + + align:start position:0% +n^2. The value of r subh here the value + + + align:start position:0% +n^2. The value of r subh here the value +of r subh is equal to 2.17987 + + align:start position:0% + + + + align:start position:0% + +* 10 -8 jewels. Right? That's a number + + align:start position:0% +* 10 -8 jewels. Right? That's a number + + + align:start position:0% +* 10 -8 jewels. Right? That's a number +that you're going to use a lot in the + + align:start position:0% +that you're going to use a lot in the + + + align:start position:0% +that you're going to use a lot in the +next few + + align:start position:0% +next few + + + align:start position:0% +next few +days. All right? + + align:start position:0% +days. All right? + + + align:start position:0% +days. All right? +But what you also see here is an n. + + align:start position:0% +But what you also see here is an n. + + + align:start position:0% +But what you also see here is an n. +What's n? Well, n is what we call the + + align:start position:0% +What's n? Well, n is what we call the + + + align:start position:0% +What's n? Well, n is what we call the +principal quantum + + align:start position:0% + + + + align:start position:0% + +number. And its allowed values are + + align:start position:0% +number. And its allowed values are + + + align:start position:0% +number. And its allowed values are +integers where the integers start with + + align:start position:0% +integers where the integers start with + + + align:start position:0% +integers where the integers start with +one 2 3 all the way up to n is equal to + + align:start position:0% +one 2 3 all the way up to n is equal to + + + align:start position:0% +one 2 3 all the way up to n is equal to +infinity. + + align:start position:0% +infinity. + + + align:start position:0% +infinity. +Okay. Well, let's uh try to understand + + align:start position:0% +Okay. Well, let's uh try to understand + + + align:start position:0% +Okay. Well, let's uh try to understand +this a little bit more by looking at an + + align:start position:0% +this a little bit more by looking at an + + + align:start position:0% +this a little bit more by looking at an +energy level diagram + + align:start position:0% +energy level diagram + + + align:start position:0% +energy level diagram +again. + + align:start position:0% +again. + + + align:start position:0% +again. +And okay, we need to turn. Okay, good. + + align:start position:0% +And okay, we need to turn. Okay, good. + + + align:start position:0% +And okay, we need to turn. Okay, good. +All right. So, I'm just plotting here + + align:start position:0% +All right. So, I'm just plotting here + + + align:start position:0% +All right. So, I'm just plotting here +energy. Here's the zero of + + align:start position:0% +energy. Here's the zero of + + + align:start position:0% +energy. Here's the zero of +energy, right? Here's the expression for + + align:start position:0% +energy, right? Here's the expression for + + + align:start position:0% +energy, right? Here's the expression for +the energy levels that uh come out of + + align:start position:0% +the energy levels that uh come out of + + + align:start position:0% +the energy levels that uh come out of +the Schroinger equation. So when n is + + align:start position:0% +the Schroinger equation. So when n is + + + align:start position:0% +the Schroinger equation. So when n is +equal to one, that's the lowest allowed + + align:start position:0% +equal to one, that's the lowest allowed + + + align:start position:0% +equal to one, that's the lowest allowed +value for n. Binding energy is + + align:start position:0% +value for n. Binding energy is + + + align:start position:0% +value for n. Binding energy is +essentially the rberg constant equal to + + align:start position:0% +essentially the rberg constant equal to + + + align:start position:0% +essentially the rberg constant equal to +minus the rberg constant. Right? + + align:start position:0% +minus the rberg constant. Right? + + + align:start position:0% +minus the rberg constant. Right? +But our equation says the binding energy + + align:start position:0% +But our equation says the binding energy + + + align:start position:0% +But our equation says the binding energy +of the electron can also be this value + + align:start position:0% +of the electron can also be this value + + + align:start position:0% +of the electron can also be this value +because when n is equal to two well the + + align:start position:0% +because when n is equal to two well the + + + align:start position:0% +because when n is equal to two well the +binding energy now is only a quarter of + + align:start position:0% +binding energy now is only a quarter of + + + align:start position:0% +binding energy now is only a quarter of +the redberg constant. It's higher in + + align:start position:0% +the redberg constant. It's higher in + + + align:start position:0% +the redberg constant. It's higher in +energy when n is equal to three. Well + + align:start position:0% +energy when n is equal to three. Well + + + align:start position:0% +energy when n is equal to three. Well +the binding energy of that electron to + + align:start position:0% +the binding energy of that electron to + + + align:start position:0% +the binding energy of that electron to +the nucleus is a ninth of the rberg + + align:start position:0% +the nucleus is a ninth of the rberg + + + align:start position:0% +the nucleus is a ninth of the rberg +constant. When it's equal to four, it's + + align:start position:0% +constant. When it's equal to four, it's + + + align:start position:0% +constant. When it's equal to four, it's +a 16th. When it's equal to five, it's a + + align:start position:0% +a 16th. When it's equal to five, it's a + + + align:start position:0% +a 16th. When it's equal to five, it's a +25th. When it's equal to six, it's a 36. + + align:start position:0% +25th. When it's equal to six, it's a 36. + + + align:start position:0% +25th. When it's equal to six, it's a 36. +So on so on, so on until it gets n= to + + align:start position:0% +So on so on, so on until it gets n= to + + + align:start position:0% +So on so on, so on until it gets n= to +infinity. When n is equal to infinity, + + align:start position:0% +infinity. When n is equal to infinity, + + + align:start position:0% +infinity. When n is equal to infinity, +then the binding energy is zero. When n + + align:start position:0% +then the binding energy is zero. When n + + + align:start position:0% +then the binding energy is zero. When n +is equal to infinity, the electron and + + align:start position:0% +is equal to infinity, the electron and + + + align:start position:0% +is equal to infinity, the electron and +the nucleus are no longer bound. They're + + align:start position:0% +the nucleus are no longer bound. They're + + + align:start position:0% +the nucleus are no longer bound. They're +separated from each other. They're not + + align:start position:0% +separated from each other. They're not + + + align:start position:0% +separated from each other. They're not +they don't hang together when n is equal + + align:start position:0% +they don't hang together when n is equal + + + align:start position:0% +they don't hang together when n is equal +to + + align:start position:0% +to + + + align:start position:0% +to +infinity. + + align:start position:0% +infinity. + + + align:start position:0% +infinity. +Now this is rather peculiar. This is + + align:start position:0% +Now this is rather peculiar. This is + + + align:start position:0% +Now this is rather peculiar. This is +saying that the binding energy of the + + align:start position:0% +saying that the binding energy of the + + + align:start position:0% +saying that the binding energy of the +electron to the nucleus can have + + align:start position:0% +electron to the nucleus can have + + + align:start position:0% +electron to the nucleus can have +essentially an infinite number of values + + align:start position:0% +essentially an infinite number of values + + + align:start position:0% +essentially an infinite number of values +except it's a discrete number of + + align:start position:0% +except it's a discrete number of + + + align:start position:0% +except it's a discrete number of +infinite number of values. Right? in the + + align:start position:0% +infinite number of values. Right? in the + + + align:start position:0% +infinite number of values. Right? in the +sense that the binding energy can be + + align:start position:0% +sense that the binding energy can be + + + align:start position:0% +sense that the binding energy can be +this or this or this but it can't be + + align:start position:0% +this or this or this but it can't be + + + align:start position:0% +this or this or this but it can't be +something in between here or here or + + align:start position:0% +something in between here or here or + + + align:start position:0% +something in between here or here or +here. Right? This is the quantum nature + + align:start position:0% +here. Right? This is the quantum nature + + + align:start position:0% +here. Right? This is the quantum nature +of the hydrogen atom. There are allowed + + align:start position:0% +of the hydrogen atom. There are allowed + + + align:start position:0% +of the hydrogen atom. There are allowed +energy + + align:start position:0% +energy + + + align:start position:0% +energy +levels. Where did this quantization come + + align:start position:0% +levels. Where did this quantization come + + + align:start position:0% +levels. Where did this quantization come +from? It came from solving the + + align:start position:0% +from? It came from solving the + + + align:start position:0% +from? It came from solving the +Schroinger equation. All right. When you + + align:start position:0% +Schroinger equation. All right. When you + + + align:start position:0% +Schroinger equation. All right. When you +solve a differential equation, as you + + align:start position:0% +solve a differential equation, as you + + + align:start position:0% +solve a differential equation, as you +will + + align:start position:0% +will + + + align:start position:0% +will +learn, and that differential equation + + align:start position:0% +learn, and that differential equation + + + align:start position:0% +learn, and that differential equation +applies to some physical problem, in + + align:start position:0% +applies to some physical problem, in + + + align:start position:0% +applies to some physical problem, in +order to make that differential equation + + align:start position:0% +order to make that differential equation + + + align:start position:0% +order to make that differential equation +specific to your physical problem, you + + align:start position:0% +specific to your physical problem, you + + + align:start position:0% +specific to your physical problem, you +often have to apply something called + + align:start position:0% +often have to apply something called + + + align:start position:0% +often have to apply something called +boundary conditions to the + + align:start position:0% +boundary conditions to the + + + align:start position:0% +boundary conditions to the +problem. When you do that, that's when + + align:start position:0% +problem. When you do that, that's when + + + align:start position:0% +problem. When you do that, that's when +this quantization comes out. it drops + + align:start position:0% +this quantization comes out. it drops + + + align:start position:0% +this quantization comes out. it drops +out of solving the differential + + align:start position:0% +out of solving the differential + + + align:start position:0% +out of solving the differential +equation. What are boundary conditions? + + align:start position:0% +equation. What are boundary conditions? + + + align:start position:0% +equation. What are boundary conditions? +Well, remember I told you + + align:start position:0% +Well, remember I told you + + + align:start position:0% +Well, remember I told you +um in the spherical coordinate system r + + align:start position:0% +um in the spherical coordinate system r + + + align:start position:0% +um in the spherical coordinate system r +theta phi. Well, phi, you know, sweeps + + align:start position:0% +theta phi. Well, phi, you know, sweeps + + + align:start position:0% +theta phi. Well, phi, you know, sweeps +from 0 to 360 degrees. + + align:start position:0% +from 0 to 360 degrees. + + + align:start position:0% +from 0 to 360 degrees. +Well, if you just went 90 degrees + + align:start position:0% +Well, if you just went 90 degrees + + + align:start position:0% +Well, if you just went 90 degrees +further, so if you went to 450 degrees, + + align:start position:0% +further, so if you went to 450 degrees, + + + align:start position:0% +further, so if you went to 450 degrees, +well, you really have the same situation + + align:start position:0% +well, you really have the same situation + + + align:start position:0% +well, you really have the same situation +as you have when phi was equal to 90 + + align:start position:0% +as you have when phi was equal to 90 + + + align:start position:0% +as you have when phi was equal to 90 +degrees, right? All right. So, what you + + align:start position:0% +degrees, right? All right. So, what you + + + align:start position:0% +degrees, right? All right. So, what you +have to do in a differential equation, + + align:start position:0% +have to do in a differential equation, + + + align:start position:0% +have to do in a differential equation, +which usually has a series as a + + align:start position:0% +which usually has a series as a + + + align:start position:0% +which usually has a series as a +solution, is that you have to cut it + + align:start position:0% +solution, is that you have to cut it + + + align:start position:0% +solution, is that you have to cut it +off. You have to apply boundary + + align:start position:0% +off. You have to apply boundary + + + align:start position:0% +off. You have to apply boundary +conditions. you have to cut it off at + + align:start position:0% +conditions. you have to cut it off at + + + align:start position:0% +conditions. you have to cut it off at +360 degrees because otherwise you just + + align:start position:0% +360 degrees because otherwise you just + + + align:start position:0% +360 degrees because otherwise you just +you have the same problem that you had + + align:start position:0% +you have the same problem that you had + + + align:start position:0% +you have the same problem that you had +before. This is a cyclical boundary + + align:start position:0% +before. This is a cyclical boundary + + + align:start position:0% +before. This is a cyclical boundary +condition and it's that cutting it off + + align:start position:0% +condition and it's that cutting it off + + + align:start position:0% +condition and it's that cutting it off +to make the equation be really pertinent + + align:start position:0% +to make the equation be really pertinent + + + align:start position:0% +to make the equation be really pertinent +or or uh uh apply to your physical + + align:start position:0% +or or uh uh apply to your physical + + + align:start position:0% +or or uh uh apply to your physical +problem. That's what leads to these + + align:start position:0% +problem. That's what leads to these + + + align:start position:0% +problem. That's what leads to these +boundary conditions mathematically. All + + align:start position:0% +boundary conditions mathematically. All + + + align:start position:0% +boundary conditions mathematically. All +right, that's where it comes from. + + align:start position:0% +right, that's where it comes from. + + + align:start position:0% +right, that's where it comes from. +That's where all the quantization comes + + align:start position:0% +That's where all the quantization comes + + + align:start position:0% +That's where all the quantization comes +from. All + + align:start position:0% +from. All + + + align:start position:0% +from. All +right. So now let's talk a little bit + + align:start position:0% +right. So now let's talk a little bit + + + align:start position:0% +right. So now let's talk a little bit +about the significance here of these + + align:start position:0% +about the significance here of these + + + align:start position:0% +about the significance here of these +binding energies because somebody + + align:start position:0% +binding energies because somebody + + + align:start position:0% +binding energies because somebody +actually asked me about it already. + + align:start position:0% +actually asked me about it already. + + + align:start position:0% +actually asked me about it already. +When the electron is bound to the + + align:start position:0% +When the electron is bound to the + + + align:start position:0% +When the electron is bound to the +nucleus with this much + + align:start position:0% +nucleus with this much + + + align:start position:0% +nucleus with this much +energy, we say that that electron is in + + align:start position:0% +energy, we say that that electron is in + + + align:start position:0% +energy, we say that that electron is in +the n equal1 state or equivalently we + + align:start position:0% +the n equal1 state or equivalently we + + + align:start position:0% +the n equal1 state or equivalently we +say that hydrogen atom is in the n + + align:start position:0% +say that hydrogen atom is in the n + + + align:start position:0% +say that hydrogen atom is in the n +equal1 state. We use both kinds of + + align:start position:0% +equal1 state. We use both kinds of + + + align:start position:0% +equal1 state. We use both kinds of +expressions + + align:start position:0% +expressions + + + align:start position:0% +expressions +equivalently. When the hydrogen atom or + + align:start position:0% +equivalently. When the hydrogen atom or + + + align:start position:0% +equivalently. When the hydrogen atom or +the electron is in the n equal1 state, + + align:start position:0% +the electron is in the n equal1 state, + + + align:start position:0% +the electron is in the n equal1 state, +we call that the ground state. The + + align:start position:0% +we call that the ground state. The + + + align:start position:0% +we call that the ground state. The +ground state is the lowest energy state. + + align:start position:0% +ground state is the lowest energy state. + + + align:start position:0% +ground state is the lowest energy state. +The electron is most strongly bound + + align:start position:0% +The electron is most strongly bound + + + align:start position:0% +The electron is most strongly bound +there. The binding energy is most + + align:start position:0% +there. The binding energy is most + + + align:start position:0% +there. The binding energy is most +negative. And the physical significance + + align:start position:0% +negative. And the physical significance + + + align:start position:0% +negative. And the physical significance +of that binding energy is that it is + + align:start position:0% +of that binding energy is that it is + + + align:start position:0% +of that binding energy is that it is +minus the ionization energy, right? + + align:start position:0% +minus the ionization energy, right? + + + align:start position:0% +minus the ionization energy, right? +Or alternatively, the ionization energy + + align:start position:0% +Or alternatively, the ionization energy + + + align:start position:0% +Or alternatively, the ionization energy +is minus the binding energy. It's going + + align:start position:0% +is minus the binding energy. It's going + + + align:start position:0% +is minus the binding energy. It's going +to require this much energy from here to + + align:start position:0% +to require this much energy from here to + + + align:start position:0% +to require this much energy from here to +here to rip the electron off of the + + align:start position:0% +here to rip the electron off of the + + + align:start position:0% +here to rip the electron off of the +nucleus. + + align:start position:0% +nucleus. + + + align:start position:0% +nucleus. +Right? So the ionization energy here is + + align:start position:0% +Right? So the ionization energy here is + + + align:start position:0% +Right? So the ionization energy here is +the binding energy here is minus the + + align:start position:0% +the binding energy here is minus the + + + align:start position:0% +the binding energy here is minus the +ionization energy. That's the physical + + align:start position:0% +ionization energy. That's the physical + + + align:start position:0% +ionization energy. That's the physical +significance of it. All right. Now I + + align:start position:0% +significance of it. All right. Now I + + + align:start position:0% +significance of it. All right. Now I +think did you ask me about the work + + align:start position:0% +think did you ask me about the work + + + align:start position:0% +think did you ask me about the work +function? How's it work? Okay. The work + + align:start position:0% +function? How's it work? Okay. The work + + + align:start position:0% +function? How's it work? Okay. The work +function is the ionization energy when + + align:start position:0% +function is the ionization energy when + + + align:start position:0% +function is the ionization energy when +we talk about a solid. All right, that's + + align:start position:0% +we talk about a solid. All right, that's + + + align:start position:0% +we talk about a solid. All right, that's +just a terminology that's historical. So + + align:start position:0% +just a terminology that's historical. So + + + align:start position:0% +just a terminology that's historical. So +when we talk about ripping an electron + + align:start position:0% +when we talk about ripping an electron + + + align:start position:0% +when we talk about ripping an electron +off of a solid, we call it the work + + align:start position:0% +off of a solid, we call it the work + + + align:start position:0% +off of a solid, we call it the work +function. When we talk about ripping it + + align:start position:0% +function. When we talk about ripping it + + + align:start position:0% +function. When we talk about ripping it +off of an atom or a molecule, we call it + + align:start position:0% +off of an atom or a molecule, we call it + + + align:start position:0% +off of an atom or a molecule, we call it +the ionization energy. Right? And the + + align:start position:0% +the ionization energy. Right? And the + + + align:start position:0% +the ionization energy. Right? And the +other important thing to note here is + + align:start position:0% +other important thing to note here is + + + align:start position:0% +other important thing to note here is +that when we talk about an ionization + + align:start position:0% +that when we talk about an ionization + + + align:start position:0% +that when we talk about an ionization +energy, we are usually talking about the + + align:start position:0% +energy, we are usually talking about the + + + align:start position:0% +energy, we are usually talking about the +energy required to pull the electron off + + align:start position:0% +energy required to pull the electron off + + + align:start position:0% +energy required to pull the electron off +when the molecule or the atom is in the + + align:start position:0% +when the molecule or the atom is in the + + + align:start position:0% +when the molecule or the atom is in the +lowest energy state, the ground state. + + align:start position:0% +lowest energy state, the ground state. + + + align:start position:0% +lowest energy state, the ground state. +All right, that's also important. + + align:start position:0% +All right, that's also important. + + + align:start position:0% +All right, that's also important. +Okay, but our equations tell us we also + + align:start position:0% +Okay, but our equations tell us we also + + + align:start position:0% +Okay, but our equations tell us we also +can have a hydrogen atom in the N equal + + align:start position:0% +can have a hydrogen atom in the N equal + + + align:start position:0% +can have a hydrogen atom in the N equal +2 state, right? If the hydrogen atom is + + align:start position:0% +2 state, right? If the hydrogen atom is + + + align:start position:0% +2 state, right? If the hydrogen atom is +in the N equal 2 state, it's in an + + align:start position:0% +in the N equal 2 state, it's in an + + + align:start position:0% +in the N equal 2 state, it's in an +excited state and actually it's the + + align:start position:0% +excited state and actually it's the + + + align:start position:0% +excited state and actually it's the +first excited state. The electron is + + align:start position:0% +first excited state. The electron is + + + align:start position:0% +first excited state. The electron is +bound less strongly, right? it's bound + + align:start position:0% +bound less strongly, right? it's bound + + + align:start position:0% +bound less strongly, right? it's bound +less strongly and consequently the + + align:start position:0% +less strongly and consequently the + + + align:start position:0% +less strongly and consequently the +ionization energy from an excited state + + align:start position:0% +ionization energy from an excited state + + + align:start position:0% +ionization energy from an excited state +hydrogen atom that ionization energy is + + align:start position:0% +hydrogen atom that ionization energy is + + + align:start position:0% +hydrogen atom that ionization energy is +less because the electron isn't bound so + + align:start position:0% +less because the electron isn't bound so + + + align:start position:0% +less because the electron isn't bound so +strongly. + + align:start position:0% +strongly. + + + align:start position:0% +strongly. +And of course we could have a hydrogen + + align:start position:0% +And of course we could have a hydrogen + + + align:start position:0% +And of course we could have a hydrogen +atom in n= 3 and n equal 4 and n equal 5 + + align:start position:0% +atom in n= 3 and n equal 4 and n equal 5 + + + align:start position:0% +atom in n= 3 and n equal 4 and n equal 5 +any of these allowed energy levels. Not + + align:start position:0% +any of these allowed energy levels. Not + + + align:start position:0% +any of these allowed energy levels. Not +all at the same time but um in any any + + align:start position:0% +all at the same time but um in any any + + + align:start position:0% +all at the same time but um in any any +given time if you had a lot of hydrogen + + align:start position:0% +given time if you had a lot of hydrogen + + + align:start position:0% +given time if you had a lot of hydrogen +atoms you could have hydrogen atoms in + + align:start position:0% +atoms you could have hydrogen atoms in + + + align:start position:0% +atoms you could have hydrogen atoms in +all of these different + + align:start position:0% +all of these different + + + align:start position:0% +all of these different +states. Okay. Now the other point that I + + align:start position:0% +states. Okay. Now the other point that I + + + align:start position:0% +states. Okay. Now the other point that I +want to make is that um this Schroinger + + align:start position:0% +want to make is that um this Schroinger + + + align:start position:0% +want to make is that um this Schroinger +result here for the energy levels + + align:start position:0% +result here for the energy levels + + + align:start position:0% +result here for the energy levels +predicts the energy levels of all one + + align:start position:0% +predicts the energy levels of all one + + + align:start position:0% +predicts the energy levels of all one +electron + + align:start position:0% +electron + + + align:start position:0% +electron +atoms. What's a one electron atom? Well, + + align:start position:0% +atoms. What's a one electron atom? Well, + + + align:start position:0% +atoms. What's a one electron atom? Well, +helium plus that's a one electron atom + + align:start position:0% +helium plus that's a one electron atom + + + align:start position:0% +helium plus that's a one electron atom +or a one electron ion, right? Helium + + align:start position:0% +or a one electron ion, right? Helium + + + align:start position:0% +or a one electron ion, right? Helium +plus. Helium usually has two electrons, + + align:start position:0% +plus. Helium usually has two electrons, + + + align:start position:0% +plus. Helium usually has two electrons, +but if we pull one off, it's only got + + align:start position:0% +but if we pull one off, it's only got + + + align:start position:0% +but if we pull one off, it's only got +one left, so it's one electron atom. + + align:start position:0% +one left, so it's one electron atom. + + + align:start position:0% +one left, so it's one electron atom. +Lithium double plus is a one electron + + align:start position:0% +Lithium double plus is a one electron + + + align:start position:0% +Lithium double plus is a one electron +atom because we pulled two of its three + + align:start position:0% +atom because we pulled two of its three + + + align:start position:0% +atom because we pulled two of its three +electrons off. Hey, one electrons left. + + align:start position:0% +electrons off. Hey, one electrons left. + + + align:start position:0% +electrons off. Hey, one electrons left. +That's a one electron atom. Or an + + align:start position:0% +That's a one electron atom. Or an + + + align:start position:0% +That's a one electron atom. Or an +ion. Uranium plus 91. Hey, that's a one + + align:start position:0% +ion. Uranium plus 91. Hey, that's a one + + + align:start position:0% +ion. Uranium plus 91. Hey, that's a one +electron atom, right? We pulled 90 uh + + align:start position:0% +electron atom, right? We pulled 90 uh + + + align:start position:0% +electron atom, right? We pulled 90 uh +two 91 electrons off. We got one left. + + align:start position:0% +two 91 electrons off. We got one left. + + + align:start position:0% +two 91 electrons off. We got one left. +Hey, that's one electron atom. The + + align:start position:0% +Hey, that's one electron atom. The + + + align:start position:0% +Hey, that's one electron atom. The +Schroinger equation will predict what + + align:start position:0% +Schroinger equation will predict what + + + align:start position:0% +Schroinger equation will predict what +those energy levels are as long as you + + align:start position:0% +those energy levels are as long as you + + + align:start position:0% +those energy levels are as long as you +remember the Z squared up here, right? + + align:start position:0% +remember the Z squared up here, right? + + + align:start position:0% +remember the Z squared up here, right? +For Z for hydrogen, Z is one. And so it + + align:start position:0% +For Z for hydrogen, Z is one. And so it + + + align:start position:0% +For Z for hydrogen, Z is one. And so it +doesn't appear. But Z is not one for all + + align:start position:0% +doesn't appear. But Z is not one for all + + + align:start position:0% +doesn't appear. But Z is not one for all +of these other one electron atoms. Where + + align:start position:0% +of these other one electron atoms. Where + + + align:start position:0% +of these other one electron atoms. Where +does the Z come from? Comes from the + + align:start position:0% +does the Z come from? Comes from the + + + align:start position:0% +does the Z come from? Comes from the +culum interaction. That potential energy + + align:start position:0% +culum interaction. That potential energy + + + align:start position:0% +culum interaction. That potential energy +of interaction is the charge on the + + align:start position:0% +of interaction is the charge on the + + + align:start position:0% +of interaction is the charge on the +electron times the charge on the nucleus + + align:start position:0% +electron times the charge on the nucleus + + + align:start position:0% +electron times the charge on the nucleus +which is Z * E. That's where the Z + + align:start position:0% +which is Z * E. That's where the Z + + + align:start position:0% +which is Z * E. That's where the Z +squared comes from. So you have to + + align:start position:0% +squared comes from. So you have to + + + align:start position:0% +squared comes from. So you have to +remember + + align:start position:0% +remember + + + align:start position:0% +remember +that. All right. So now how do we know + + align:start position:0% +that. All right. So now how do we know + + + align:start position:0% +that. All right. So now how do we know +that um the Schroinger's predictions for + + align:start position:0% +that um the Schroinger's predictions for + + + align:start position:0% +that um the Schroinger's predictions for +these energy levels are correct are + + align:start position:0% +these energy levels are correct are + + + align:start position:0% +these energy levels are correct are +accurate? Well, we got to do an + + align:start position:0% +accurate? Well, we got to do an + + + align:start position:0% +accurate? Well, we got to do an +experiment. So, the experiment we're + + align:start position:0% +experiment. So, the experiment we're + + + align:start position:0% +experiment. So, the experiment we're +going to do is we're going to take a + + align:start position:0% +going to do is we're going to take a + + + align:start position:0% +going to do is we're going to take a +bulb here, pump it out, and then we're + + align:start position:0% +bulb here, pump it out, and then we're + + + align:start position:0% +bulb here, pump it out, and then we're +going to fill it up with hydrogen, + + align:start position:0% +going to fill it up with hydrogen, + + + align:start position:0% +going to fill it up with hydrogen, +molecular + + align:start position:0% +molecular + + + align:start position:0% +molecular +hydrogen. And then in this bulb, there's + + align:start position:0% +hydrogen. And then in this bulb, there's + + + align:start position:0% +hydrogen. And then in this bulb, there's +a negative and a positive + + align:start position:0% +a negative and a positive + + + align:start position:0% +a negative and a positive +electrode. What we're going to do is + + align:start position:0% +electrode. What we're going to do is + + + align:start position:0% +electrode. What we're going to do is +we're going to crank up the potential + + align:start position:0% +we're going to crank up the potential + + + align:start position:0% +we're going to crank up the potential +energy difference between those + + align:start position:0% +energy difference between those + + + align:start position:0% +energy difference between those +two so high until finally that gas is + + align:start position:0% +two so high until finally that gas is + + + align:start position:0% +two so high until finally that gas is +going to ignite just like that. All + + align:start position:0% +going to ignite just like that. All + + + align:start position:0% +going to ignite just like that. All +right? + + align:start position:0% +right? + + + align:start position:0% +right? +And we're going to look at the light + + align:start position:0% +And we're going to look at the light + + + align:start position:0% +And we're going to look at the light +coming + + align:start position:0% +coming + + + align:start position:0% +coming +out. And what we're going to do is we're + + align:start position:0% +out. And what we're going to do is we're + + + align:start position:0% +out. And what we're going to do is we're +going to disperse that + + align:start position:0% +going to disperse that + + + align:start position:0% +going to disperse that +light. We're going to um send it through + + align:start position:0% +light. We're going to um send it through + + + align:start position:0% +light. We're going to um send it through +a defraction grading essentially. And + + align:start position:0% +a defraction grading essentially. And + + + align:start position:0% +a defraction grading essentially. And +that's like an array array of slits. And + + align:start position:0% +that's like an array array of slits. And + + + align:start position:0% +that's like an array array of slits. And +what you're going to see are points of + + align:start position:0% +what you're going to see are points of + + + align:start position:0% +what you're going to see are points of +constructive and destructive + + align:start position:0% +constructive and destructive + + + align:start position:0% +constructive and destructive +interference. But in the constructive + + align:start position:0% +interference. But in the constructive + + + align:start position:0% +interference. But in the constructive +interference, you're going to see the + + align:start position:0% +interference, you're going to see the + + + align:start position:0% +interference, you're going to see the +colors separated. So there's going to be + + align:start position:0% +colors separated. So there's going to be + + + align:start position:0% +colors separated. So there's going to be +purple, blue, green, etc. And the reason + + align:start position:0% +purple, blue, green, etc. And the reason + + + align:start position:0% +purple, blue, green, etc. And the reason +is that the different uh radiation, the + + align:start position:0% +is that the different uh radiation, the + + + align:start position:0% +is that the different uh radiation, the +different colors have different + + align:start position:0% +different colors have different + + + align:start position:0% +different colors have different +wavelengths. They have different + + align:start position:0% +wavelengths. They have different + + + align:start position:0% +wavelengths. They have different +wavelengths. Then they have slightly + + align:start position:0% +wavelengths. Then they have slightly + + + align:start position:0% +wavelengths. Then they have slightly +different points in space at which + + align:start position:0% +different points in space at which + + + align:start position:0% +different points in space at which +constructive interference occurs. And so + + align:start position:0% +constructive interference occurs. And so + + + align:start position:0% +constructive interference occurs. And so +the light is dispersed right in space. + + align:start position:0% +the light is dispersed right in space. + + + align:start position:0% +the light is dispersed right in space. +So, we're going to analyze what are the + + align:start position:0% +So, we're going to analyze what are the + + + align:start position:0% +So, we're going to analyze what are the +wavelengths of the light that are being + + align:start position:0% +wavelengths of the light that are being + + + align:start position:0% +wavelengths of the light that are being +emitted from these hydrogen atoms. See, + + align:start position:0% +emitted from these hydrogen atoms. See, + + + align:start position:0% +emitted from these hydrogen atoms. See, +the discharge pulls apart the H2 and + + align:start position:0% +the discharge pulls apart the H2 and + + + align:start position:0% +the discharge pulls apart the H2 and +makes hydrogen atoms. All right? So, we + + align:start position:0% +makes hydrogen atoms. All right? So, we + + + align:start position:0% +makes hydrogen atoms. All right? So, we +got to do this by um taking a defraction + + align:start position:0% +got to do this by um taking a defraction + + + align:start position:0% +got to do this by um taking a defraction +grading and the TAS are going to give + + align:start position:0% +grading and the TAS are going to give + + + align:start position:0% +grading and the TAS are going to give +you a pair of defraction grading + + align:start position:0% +you a pair of defraction grading + + + align:start position:0% +you a pair of defraction grading +glasses. You're supposed to come and uh + + align:start position:0% +glasses. You're supposed to come and uh + + + align:start position:0% +glasses. You're supposed to come and uh +look at the uh discharge here. you can + + align:start position:0% +look at the uh discharge here. you can + + + align:start position:0% +look at the uh discharge here. you can +see it. I'll turn it a little bit for + + align:start position:0% +see it. I'll turn it a little bit for + + + align:start position:0% +see it. I'll turn it a little bit for +those of you uh on the sides + + align:start position:0% +those of you uh on the sides + + + align:start position:0% +those of you uh on the sides +here and we'll see what we see. + + align:start position:0% + + + + align:start position:0% + +Okay, sorry. + + align:start position:0% + + + + align:start position:0% + +And if you can't see the lamp, you're + + align:start position:0% +And if you can't see the lamp, you're + + + align:start position:0% +And if you can't see the lamp, you're +welcome to uh get up and move around and + + align:start position:0% +welcome to uh get up and move around and + + + align:start position:0% +welcome to uh get up and move around and +so that you can see it. + + align:start position:0% + + + + align:start position:0% + +Thank + + align:start position:0% +Thank + + + align:start position:0% +Thank +you. How can you do this light too? This + + align:start position:0% +you. How can you do this light too? This + + + align:start position:0% +you. How can you do this light too? This +one over here, sir. + + align:start position:0% +one over here, sir. + + + align:start position:0% +one over here, sir. +Can you move this one away? + + align:start position:0% +Can you move this one away? + + + align:start position:0% +Can you move this one away? +All right. + + align:start position:0% + + + + align:start position:0% + +Okay. And if you look up at the lights + + align:start position:0% +Okay. And if you look up at the lights + + + align:start position:0% +Okay. And if you look up at the lights +in the room, you can see the whole + + align:start position:0% +in the room, you can see the whole + + + align:start position:0% +in the room, you can see the whole +spectrum, right? Because that's white + + align:start position:0% +spectrum, right? Because that's white + + + align:start position:0% +spectrum, right? Because that's white +light. + + align:start position:0% + + + + align:start position:0% + +All + + align:start position:0% +All + + + align:start position:0% +All +right. So, + + align:start position:0% + + + + align:start position:0% + +um, I'm going to turn the lamp over here + + align:start position:0% +um, I'm going to turn the lamp over here + + + align:start position:0% +um, I'm going to turn the lamp over here +so that you can see this a little + + align:start position:0% +so that you can see this a little + + + align:start position:0% +so that you can see this a little +better. All right. + + align:start position:0% +better. All right. + + + align:start position:0% +better. All right. +The spectrum that you should see is + + align:start position:0% +The spectrum that you should see is + + + align:start position:0% +The spectrum that you should see is +what's shown on the board. + + align:start position:0% +what's shown on the board. + + + align:start position:0% +what's shown on the board. +Uh if you look to the uh + + align:start position:0% + + + + align:start position:0% + +if you look to the right of the lamp + + align:start position:0% +if you look to the right of the lamp + + + align:start position:0% +if you look to the right of the lamp +here, you could you should see a purple + + align:start position:0% +here, you could you should see a purple + + + align:start position:0% +here, you could you should see a purple +line. The purple line is actually very + + align:start position:0% +line. The purple line is actually very + + + align:start position:0% +line. The purple line is actually very +light. So only if you're up close are + + align:start position:0% +light. So only if you're up close are + + + align:start position:0% +light. So only if you're up close are +you going to see the purple + + align:start position:0% +you going to see the purple + + + align:start position:0% +you going to see the purple +line. You can see the blue line very + + align:start position:0% +line. You can see the blue line very + + + align:start position:0% +line. You can see the blue line very +well. That's very + + align:start position:0% +well. That's very + + + align:start position:0% +well. That's very +intense. Uh the green line is also very + + align:start position:0% +intense. Uh the green line is also very + + + align:start position:0% +intense. Uh the green line is also very +diffuse. So again, only if you're up + + align:start position:0% +diffuse. So again, only if you're up + + + align:start position:0% +diffuse. So again, only if you're up +close are you going to be able to see + + align:start position:0% +close are you going to be able to see + + + align:start position:0% +close are you going to be able to see +the green + + align:start position:0% +the green + + + align:start position:0% +the green +line. And then the red line's very + + align:start position:0% +line. And then the red line's very + + + align:start position:0% +line. And then the red line's very +bright. And now I'm going to move this + + align:start position:0% +bright. And now I'm going to move this + + + align:start position:0% +bright. And now I'm going to move this +over here so you have the opportunity to + + align:start position:0% +over here so you have the opportunity to + + + align:start position:0% +over here so you have the opportunity to +uh to see it. And again, you're welcome + + align:start position:0% +uh to see it. And again, you're welcome + + + align:start position:0% +uh to see it. And again, you're welcome +to get out of your seats and uh move + + align:start position:0% +to get out of your seats and uh move + + + align:start position:0% +to get out of your seats and uh move +around so that you can in fact see + + align:start position:0% +around so that you can in fact see + + + align:start position:0% +around so that you can in fact see +it. Okay. All + + align:start position:0% + + + + align:start position:0% + +right. So what you should be seeing and + + align:start position:0% +right. So what you should be seeing and + + + align:start position:0% +right. So what you should be seeing and +now if you look + + align:start position:0% +now if you look + + + align:start position:0% +now if you look +Oh wow. + + align:start position:0% + + + + align:start position:0% + +Hey, interference works, huh? + + align:start position:0% + + + + align:start position:0% + +Useful pointer. + + align:start position:0% + + + + align:start position:0% + +No. Right. Right. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So, uh, what you should see, uh, + + align:start position:0% +So, uh, what you should see, uh, + + + align:start position:0% +So, uh, what you should see, uh, +depending on which one of the the + + align:start position:0% +depending on which one of the the + + + align:start position:0% +depending on which one of the the +constructive interference patterns + + align:start position:0% +constructive interference patterns + + + align:start position:0% +constructive interference patterns +you're looking at, um, there should be + + align:start position:0% +you're looking at, um, there should be + + + align:start position:0% +you're looking at, um, there should be +the purple line, right? There should be + + align:start position:0% +the purple line, right? There should be + + + align:start position:0% +the purple line, right? There should be +a blue line, very intense. Purple's + + align:start position:0% +a blue line, very intense. Purple's + + + align:start position:0% +a blue line, very intense. Purple's +weak, green is rather weak, and the red + + align:start position:0% +weak, green is rather weak, and the red + + + align:start position:0% +weak, green is rather weak, and the red +is very + + align:start position:0% +is very + + + align:start position:0% +is very +intense. All right? So, uh, what's + + align:start position:0% +intense. All right? So, uh, what's + + + align:start position:0% +intense. All right? So, uh, what's +happening here? Well, what's happening + + align:start position:0% +happening here? Well, what's happening + + + align:start position:0% +happening here? Well, what's happening +is that in this + + align:start position:0% +is that in this + + + align:start position:0% +is that in this +discharge, there's enough energy in that + + align:start position:0% +discharge, there's enough energy in that + + + align:start position:0% +discharge, there's enough energy in that +discharge to put some of the hydrogen + + align:start position:0% +discharge to put some of the hydrogen + + + align:start position:0% +discharge to put some of the hydrogen +atoms in um a high energy state. And + + align:start position:0% +atoms in um a high energy state. And + + + align:start position:0% +atoms in um a high energy state. And +we'll call that state E subi, the energy + + align:start position:0% +we'll call that state E subi, the energy + + + align:start position:0% +we'll call that state E subi, the energy +of the initial + + align:start position:0% +of the initial + + + align:start position:0% +of the initial +state. And actually, that's an unstable + + align:start position:0% +state. And actually, that's an unstable + + + align:start position:0% +state. And actually, that's an unstable +situation. There's a that hydrogen atom + + align:start position:0% +situation. There's a that hydrogen atom + + + align:start position:0% +situation. There's a that hydrogen atom +wants to relax. It wants to be in the + + align:start position:0% +wants to relax. It wants to be in the + + + align:start position:0% +wants to relax. It wants to be in the +lower energy + + align:start position:0% +lower energy + + + align:start position:0% +lower energy +state and um what happens is that it + + align:start position:0% +state and um what happens is that it + + + align:start position:0% +state and um what happens is that it +does relax, right? It relaxes, right? + + align:start position:0% +does relax, right? It relaxes, right? + + + align:start position:0% +does relax, right? It relaxes, right? +The electron falls into the lower energy + + align:start position:0% +The electron falls into the lower energy + + + align:start position:0% +The electron falls into the lower energy +state, but because it's lower energy, it + + align:start position:0% +state, but because it's lower energy, it + + + align:start position:0% +state, but because it's lower energy, it +has to give up a + + align:start position:0% +has to give up a + + + align:start position:0% +has to give up a +photon. And + + align:start position:0% +photon. And + + + align:start position:0% +photon. And +so the photon that is + + align:start position:0% +so the photon that is + + + align:start position:0% +so the photon that is +emitted, the energy of that photon has + + align:start position:0% +emitted, the energy of that photon has + + + align:start position:0% +emitted, the energy of that photon has +to be exactly the difference in energy + + align:start position:0% +to be exactly the difference in energy + + + align:start position:0% +to be exactly the difference in energy +between the energy of the initial state + + align:start position:0% +between the energy of the initial state + + + align:start position:0% +between the energy of the initial state +and the final state. Right? That's the + + align:start position:0% +and the final state. Right? That's the + + + align:start position:0% +and the final state. Right? That's the +quantum nature of the hydrogen atom. The + + align:start position:0% +quantum nature of the hydrogen atom. The + + + align:start position:0% +quantum nature of the hydrogen atom. The +photon that comes out has to have that + + align:start position:0% +photon that comes out has to have that + + + align:start position:0% +photon that comes out has to have that +energy difference exactly. + + align:start position:0% +energy difference exactly. + + + align:start position:0% +energy difference exactly. +And therefore the frequency here of the + + align:start position:0% +And therefore the frequency here of the + + + align:start position:0% +And therefore the frequency here of the +radiation coming out is going to + + align:start position:0% +radiation coming out is going to + + + align:start position:0% +radiation coming out is going to +correspond to that exact energy + + align:start position:0% +correspond to that exact energy + + + align:start position:0% +correspond to that exact energy +difference. All right? And for the + + align:start position:0% +difference. All right? And for the + + + align:start position:0% +difference. All right? And for the +different + + align:start position:0% +different + + + align:start position:0% +different +energies for the different transitions + + align:start position:0% +energies for the different transitions + + + align:start position:0% +energies for the different transitions +you're going to have very specific + + align:start position:0% +you're going to have very specific + + + align:start position:0% +you're going to have very specific +values of the frequency of the radiation + + align:start position:0% +values of the frequency of the radiation + + + align:start position:0% +values of the frequency of the radiation +or the wavelength of the radiation. So + + align:start position:0% +or the wavelength of the radiation. So + + + align:start position:0% +or the wavelength of the radiation. So +for example, some of those hydrogen + + align:start position:0% +for example, some of those hydrogen + + + align:start position:0% +for example, some of those hydrogen +atoms in this + + align:start position:0% +atoms in this + + + align:start position:0% +atoms in this +discharge, they've been excited to this + + align:start position:0% +discharge, they've been excited to this + + + align:start position:0% +discharge, they've been excited to this +excited state, which we'll call + + align:start position:0% +excited state, which we'll call + + + align:start position:0% +excited state, which we'll call +B. The energy difference between B and + + align:start position:0% +B. The energy difference between B and + + + align:start position:0% +B. The energy difference between B and +this ground state here is + + align:start position:0% +this ground state here is + + + align:start position:0% +this ground state here is +small. Therefore, we're going to have + + align:start position:0% +small. Therefore, we're going to have + + + align:start position:0% +small. Therefore, we're going to have +some radiation that is low frequency + + align:start position:0% +some radiation that is low frequency + + + align:start position:0% +some radiation that is low frequency +because delta E, the difference in the + + align:start position:0% +because delta E, the difference in the + + + align:start position:0% +because delta E, the difference in the +energy between the two states is small. + + align:start position:0% +energy between the two states is small. + + + align:start position:0% +energy between the two states is small. +And then there are going to be some + + align:start position:0% +And then there are going to be some + + + align:start position:0% +And then there are going to be some +hydrogen atoms that are going to be + + align:start position:0% +hydrogen atoms that are going to be + + + align:start position:0% +hydrogen atoms that are going to be +excited to this state, the A state. And + + align:start position:0% +excited to this state, the A state. And + + + align:start position:0% +excited to this state, the A state. And +relatively speaking, that energy + + align:start position:0% +relatively speaking, that energy + + + align:start position:0% +relatively speaking, that energy +difference is large. So there are going + + align:start position:0% +difference is large. So there are going + + + align:start position:0% +difference is large. So there are going +to be some hydrogen atoms that are going + + align:start position:0% +to be some hydrogen atoms that are going + + + align:start position:0% +to be some hydrogen atoms that are going +to be relaxing to this ground state. And + + align:start position:0% +to be relaxing to this ground state. And + + + align:start position:0% +to be relaxing to this ground state. And +when they do, since that energy + + align:start position:0% +when they do, since that energy + + + align:start position:0% +when they do, since that energy +difference is large, the frequency of + + align:start position:0% +difference is large, the frequency of + + + align:start position:0% +difference is large, the frequency of +the radiation coming off, it's going to + + align:start position:0% +the radiation coming off, it's going to + + + align:start position:0% +the radiation coming off, it's going to +be high. + + align:start position:0% +be high. + + + align:start position:0% +be high. +or correspondingly the frequency of the + + align:start position:0% +or correspondingly the frequency of the + + + align:start position:0% +or correspondingly the frequency of the +radiation the wavelength of the + + align:start position:0% +radiation the wavelength of the + + + align:start position:0% +radiation the wavelength of the +radiation coming off is going to be low + + align:start position:0% +radiation coming off is going to be low + + + align:start position:0% +radiation coming off is going to be low +because the wavelength is in inversely + + align:start position:0% +because the wavelength is in inversely + + + align:start position:0% +because the wavelength is in inversely +proportional to the + + align:start position:0% +proportional to the + + + align:start position:0% +proportional to the +frequency and likewise for this + + align:start position:0% +frequency and likewise for this + + + align:start position:0% +frequency and likewise for this +transition we're going to have some long + + align:start position:0% +transition we're going to have some long + + + align:start position:0% +transition we're going to have some long +wavelength radiation + + align:start position:0% +wavelength radiation + + + align:start position:0% +wavelength radiation +emitted. All right. Well, let's see if + + align:start position:0% +emitted. All right. Well, let's see if + + + align:start position:0% +emitted. All right. Well, let's see if +we can understand specifically the + + align:start position:0% +we can understand specifically the + + + align:start position:0% +we can understand specifically the +spectrum here in the visible range for + + align:start position:0% +spectrum here in the visible range for + + + align:start position:0% +spectrum here in the visible range for +the hydrogen atom. + + align:start position:0% +the hydrogen atom. + + + align:start position:0% +the hydrogen atom. +So what I've done is to uh draw an + + align:start position:0% +So what I've done is to uh draw an + + + align:start position:0% +So what I've done is to uh draw an +energy level diagram again. Here's the + + align:start position:0% +energy level diagram again. Here's the + + + align:start position:0% +energy level diagram again. Here's the +energy of n= 1, n= 2, n= 3, etc. Here's + + align:start position:0% +energy of n= 1, n= 2, n= 3, etc. Here's + + + align:start position:0% +energy of n= 1, n= 2, n= 3, etc. Here's +the n= infinity up + + align:start position:0% + + + + align:start position:0% + +here. All right. So, it turns out that + + align:start position:0% +here. All right. So, it turns out that + + + align:start position:0% +here. All right. So, it turns out that +this purple line, that's a transition + + align:start position:0% +this purple line, that's a transition + + + align:start position:0% +this purple line, that's a transition +from a hydrogen atom in the n= 6 state + + align:start position:0% +from a hydrogen atom in the n= 6 state + + + align:start position:0% +from a hydrogen atom in the n= 6 state +to the n equal2 + + align:start position:0% +to the n equal2 + + + align:start position:0% +to the n equal2 +state. That blue line is a transition + + align:start position:0% +state. That blue line is a transition + + + align:start position:0% +state. That blue line is a transition +from n= 5 to + + align:start position:0% +from n= 5 to + + + align:start position:0% +from n= 5 to +n=2. The green line is a transition from + + align:start position:0% +n=2. The green line is a transition from + + + align:start position:0% +n=2. The green line is a transition from +n=4 to n= 2 and the red line from n= 3 + + align:start position:0% +n=4 to n= 2 and the red line from n= 3 + + + align:start position:0% +n=4 to n= 2 and the red line from n= 3 +to n= 2. Notice that since this energy + + align:start position:0% +to n= 2. Notice that since this energy + + + align:start position:0% +to n= 2. Notice that since this energy +difference here, oops, since this energy + + align:start position:0% +difference here, oops, since this energy + + + align:start position:0% +difference here, oops, since this energy +difference is small, right, this line + + align:start position:0% +difference is small, right, this line + + + align:start position:0% +difference is small, right, this line +has a long wavelength. Since this energy + + align:start position:0% +has a long wavelength. Since this energy + + + align:start position:0% +has a long wavelength. Since this energy +difference is larger, this line has a + + align:start position:0% +difference is larger, this line has a + + + align:start position:0% +difference is larger, this line has a +shorter + + align:start position:0% +shorter + + + align:start position:0% +shorter +wavelength. So all of these transitions + + align:start position:0% +wavelength. So all of these transitions + + + align:start position:0% +wavelength. So all of these transitions +that you're seeing in the visible range, + + align:start position:0% +that you're seeing in the visible range, + + + align:start position:0% +that you're seeing in the visible range, +all of these transitions have the final + + align:start position:0% +all of these transitions have the final + + + align:start position:0% +all of these transitions have the final +state of n is equal to 2. + + align:start position:0% +state of n is equal to 2. + + + align:start position:0% +state of n is equal to 2. +Now, how do we know that the Schroinger + + align:start position:0% +Now, how do we know that the Schroinger + + + align:start position:0% +Now, how do we know that the Schroinger +equation is making predictions that are + + align:start position:0% +equation is making predictions that are + + + align:start position:0% +equation is making predictions that are +consistent with the frequencies or the + + align:start position:0% +consistent with the frequencies or the + + + align:start position:0% +consistent with the frequencies or the +wavelengths of the radiation that we + + align:start position:0% +wavelengths of the radiation that we + + + align:start position:0% +wavelengths of the radiation that we +observe here? Well, we got to do a plug + + align:start position:0% +observe here? Well, we got to do a plug + + + align:start position:0% +observe here? Well, we got to do a plug +here. This is the frequency that we + + align:start position:0% +here. This is the frequency that we + + + align:start position:0% +here. This is the frequency that we +would expect. It's the energy difference + + align:start position:0% +would expect. It's the energy difference + + + align:start position:0% +would expect. It's the energy difference +between two states over H. Here's the + + align:start position:0% +between two states over H. Here's the + + + align:start position:0% +between two states over H. Here's the +initial energy. Here's the final energy. + + align:start position:0% +initial energy. Here's the final energy. + + + align:start position:0% +initial energy. Here's the final energy. +We said that the Schroinger equation + + align:start position:0% +We said that the Schroinger equation + + + align:start position:0% +We said that the Schroinger equation +tells us that the energies of the state + + align:start position:0% +tells us that the energies of the state + + + align:start position:0% +tells us that the energies of the state +are minus R subh / N. So for the initial + + align:start position:0% +are minus R subh / N. So for the initial + + + align:start position:0% +are minus R subh / N. So for the initial +energy level, it's minus R subh / N subi + + align:start position:0% +energy level, it's minus R subh / N subi + + + align:start position:0% +energy level, it's minus R subh / N subi +squared. We plug that in. For the final + + align:start position:0% +squared. We plug that in. For the final + + + align:start position:0% +squared. We plug that in. For the final +energy level, well, it's minus R subh + + align:start position:0% +energy level, well, it's minus R subh + + + align:start position:0% +energy level, well, it's minus R subh +over N subf, the final quantum number + + align:start position:0% +over N subf, the final quantum number + + + align:start position:0% +over N subf, the final quantum number +squared. We plug that in. We rearrange + + align:start position:0% +squared. We plug that in. We rearrange + + + align:start position:0% +squared. We plug that in. We rearrange +some + + align:start position:0% +some + + + align:start position:0% +some +things. And then this is the prediction + + align:start position:0% +things. And then this is the prediction + + + align:start position:0% +things. And then this is the prediction +for the frequency. I said that this + + align:start position:0% +for the frequency. I said that this + + + align:start position:0% +for the frequency. I said that this +level right here is the n equal 2 level. + + align:start position:0% +level right here is the n equal 2 level. + + + align:start position:0% +level right here is the n equal 2 level. +So we'll plug in the two for the final + + align:start position:0% +So we'll plug in the two for the final + + + align:start position:0% +So we'll plug in the two for the final +quantum state. And so this is then the + + align:start position:0% +quantum state. And so this is then the + + + align:start position:0% +quantum state. And so this is then the +prediction for the frequencies of the + + align:start position:0% +prediction for the frequencies of the + + + align:start position:0% +prediction for the frequencies of the +radiation to the n=2 level. And so you + + align:start position:0% +radiation to the n=2 level. And so you + + + align:start position:0% +radiation to the n=2 level. And so you +just plug in n= 6, n= 5, n= 4, n= 3. And + + align:start position:0% +just plug in n= 6, n= 5, n= 4, n= 3. And + + + align:start position:0% +just plug in n= 6, n= 5, n= 4, n= 3. And +you know what? The frequencies that are + + align:start position:0% +you know what? The frequencies that are + + + align:start position:0% +you know what? The frequencies that are +predicted match what we observe to one + + align:start position:0% +predicted match what we observe to one + + + align:start position:0% +predicted match what we observe to one +part in 10 to the eth. There really is + + align:start position:0% +part in 10 to the eth. There really is + + + align:start position:0% +part in 10 to the eth. There really is +precise agreement between the results of + + align:start position:0% +precise agreement between the results of + + + align:start position:0% +precise agreement between the results of +the Schroinger equation and what we + + align:start position:0% +the Schroinger equation and what we + + + align:start position:0% +the Schroinger equation and what we +actually observe in nature. Therefore, + + align:start position:0% +actually observe in nature. Therefore, + + + align:start position:0% +actually observe in nature. Therefore, +we think it's correct. Right? And there + + align:start position:0% +we think it's correct. Right? And there + + + align:start position:0% +we think it's correct. Right? And there +are no experiments that cast any doubt + + align:start position:0% +are no experiments that cast any doubt + + + align:start position:0% +are no experiments that cast any doubt +so far on the Schroinger equation. All + + align:start position:0% +so far on the Schroinger equation. All + + + align:start position:0% +so far on the Schroinger equation. All +right? + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now, the set of transitions that we just + + align:start position:0% +Now, the set of transitions that we just + + + align:start position:0% +Now, the set of transitions that we just +looked at are these transitions plotted. + + align:start position:0% +looked at are these transitions plotted. + + + align:start position:0% +looked at are these transitions plotted. +Here's another energy level diagram for + + align:start position:0% +Here's another energy level diagram for + + + align:start position:0% +Here's another energy level diagram for +the hydrogen atom. Here's the n equal1 + + align:start position:0% +the hydrogen atom. Here's the n equal1 + + + align:start position:0% +the hydrogen atom. Here's the n equal1 +state. N= 2, n= 3, n= 4. Right? And we + + align:start position:0% +state. N= 2, n= 3, n= 4. Right? And we + + + align:start position:0% +state. N= 2, n= 3, n= 4. Right? And we +looked at all of the transitions that + + align:start position:0% +looked at all of the transitions that + + + align:start position:0% +looked at all of the transitions that +end up in the n equal2 state. this set + + align:start position:0% +end up in the n equal2 state. this set + + + align:start position:0% +end up in the n equal2 state. this set +of transitions it's called the Balmer + + align:start position:0% +of transitions it's called the Balmer + + + align:start position:0% +of transitions it's called the Balmer +series now the n equal2 state is not the + + align:start position:0% +series now the n equal2 state is not the + + + align:start position:0% +series now the n equal2 state is not the +ground state right there is a transition + + align:start position:0% +ground state right there is a transition + + + align:start position:0% +ground state right there is a transition +from n= 6 to n=1 the ground state it's + + align:start position:0% +from n= 6 to n=1 the ground state it's + + + align:start position:0% +from n= 6 to n=1 the ground state it's +this one right here but you see that's a + + align:start position:0% +this one right here but you see that's a + + + align:start position:0% +this one right here but you see that's a +very high energy transition actually + + align:start position:0% +very high energy transition actually + + + align:start position:0% +very high energy transition actually +this transition from n= 6 to n equal1 is + + align:start position:0% +this transition from n= 6 to n equal1 is + + + align:start position:0% +this transition from n= 6 to n equal1 is +in the ultraviolet range of the + + align:start position:0% +in the ultraviolet range of the + + + align:start position:0% +in the ultraviolet range of the +electromagnetic spectrum and so you + + align:start position:0% +electromagnetic spectrum and so you + + + align:start position:0% +electromagnetic spectrum and so you +can't see it with what the experiment + + align:start position:0% +can't see it with what the experiment + + + align:start position:0% +can't see it with what the experiment +experiment that we did, but it's there. + + align:start position:0% +experiment that we did, but it's there. + + + align:start position:0% +experiment that we did, but it's there. +And then of course the um hydrogen atoms + + align:start position:0% +And then of course the um hydrogen atoms + + + align:start position:0% +And then of course the um hydrogen atoms +that relax to n equal 2, well they + + align:start position:0% +that relax to n equal 2, well they + + + align:start position:0% +that relax to n equal 2, well they +actually eventually relax to n equal1. + + align:start position:0% +actually eventually relax to n equal1. + + + align:start position:0% +actually eventually relax to n equal1. +And there is a transition there. It's + + align:start position:0% +And there is a transition there. It's + + + align:start position:0% +And there is a transition there. It's +over here. N=2 to n equal 1. But again, + + align:start position:0% +over here. N=2 to n equal 1. But again, + + + align:start position:0% +over here. N=2 to n equal 1. But again, +that's a high energy transition. It's + + align:start position:0% +that's a high energy transition. It's + + + align:start position:0% +that's a high energy transition. It's +also in the ultraviolet range of the + + align:start position:0% +also in the ultraviolet range of the + + + align:start position:0% +also in the ultraviolet range of the +electromagnetic + + align:start position:0% +electromagnetic + + + align:start position:0% +electromagnetic +spectrum. And so all of these + + align:start position:0% +spectrum. And so all of these + + + align:start position:0% +spectrum. And so all of these +transitions that end up in n equal1 are + + align:start position:0% +transitions that end up in n equal1 are + + + align:start position:0% +transitions that end up in n equal1 are +in the UV range. They're called the + + align:start position:0% +in the UV range. They're called the + + + align:start position:0% +in the UV range. They're called the +Lyman series. All the transitions that + + align:start position:0% +Lyman series. All the transitions that + + + align:start position:0% +Lyman series. All the transitions that +end up in N equal 2 are in the visible. + + align:start position:0% +end up in N equal 2 are in the visible. + + + align:start position:0% +end up in N equal 2 are in the visible. +They're called the Balmer. N equal 3, + + align:start position:0% +They're called the Balmer. N equal 3, + + + align:start position:0% +They're called the Balmer. N equal 3, +the passion in the infrared. Bracket is + + align:start position:0% +the passion in the infrared. Bracket is + + + align:start position:0% +the passion in the infrared. Bracket is +in the infrared. Fund is in the + + align:start position:0% +in the infrared. Fund is in the + + + align:start position:0% +in the infrared. Fund is in the +infrared. Okay? And so we can't see + + align:start position:0% +infrared. Okay? And so we can't see + + + align:start position:0% +infrared. Okay? And so we can't see +these easily. Now, these are named for + + align:start position:0% +these easily. Now, these are named for + + + align:start position:0% +these easily. Now, these are named for +the different discoverers. The reason + + align:start position:0% +the different discoverers. The reason + + + align:start position:0% +the different discoverers. The reason +there's so many different discoverers is + + align:start position:0% +there's so many different discoverers is + + + align:start position:0% +there's so many different discoverers is +because these are all different + + align:start position:0% +because these are all different + + + align:start position:0% +because these are all different +frequency ranges. + + align:start position:0% +frequency ranges. + + + align:start position:0% +frequency ranges. +Different frequencies of radiation + + align:start position:0% +Different frequencies of radiation + + + align:start position:0% +Different frequencies of radiation +require different kinds of detectors. + + align:start position:0% +require different kinds of detectors. + + + align:start position:0% +require different kinds of detectors. +And so depending on exactly what kind of + + align:start position:0% +And so depending on exactly what kind of + + + align:start position:0% +And so depending on exactly what kind of +detector the experimentalist had, that + + align:start position:0% +detector the experimentalist had, that + + + align:start position:0% +detector the experimentalist had, that +will dictate then which one of these uh + + align:start position:0% +will dictate then which one of these uh + + + align:start position:0% +will dictate then which one of these uh +sets of transitions he was able to + + align:start position:0% +sets of transitions he was able to + + + align:start position:0% +sets of transitions he was able to +discover. All right. But not only does + + align:start position:0% +discover. All right. But not only does + + + align:start position:0% +discover. All right. But not only does +this work for + + align:start position:0% +this work for + + + align:start position:0% +this work for +emission, but this also works for + + align:start position:0% +emission, but this also works for + + + align:start position:0% +emission, but this also works for +absorption. And that is we can have a + + align:start position:0% +absorption. And that is we can have a + + + align:start position:0% +absorption. And that is we can have a +hydrogen atom in the ground state, a low + + align:start position:0% +hydrogen atom in the ground state, a low + + + align:start position:0% +hydrogen atom in the ground state, a low +energy state. And if there's a photon + + align:start position:0% +energy state. And if there's a photon + + + align:start position:0% +energy state. And if there's a photon +around that ex is exactly the energy + + align:start position:0% +around that ex is exactly the energy + + + align:start position:0% +around that ex is exactly the energy +difference between these two states, + + align:start position:0% +difference between these two states, + + + align:start position:0% +difference between these two states, +well, that photon can be absorbed. If + + align:start position:0% +well, that photon can be absorbed. If + + + align:start position:0% +well, that photon can be absorbed. If +that photon is a little bit higher in + + align:start position:0% +that photon is a little bit higher in + + + align:start position:0% +that photon is a little bit higher in +energy, it won't be absorbed. If it's a + + align:start position:0% +energy, it won't be absorbed. If it's a + + + align:start position:0% +energy, it won't be absorbed. If it's a +little lower, it won't be absorbed. It + + align:start position:0% +little lower, it won't be absorbed. It + + + align:start position:0% +little lower, it won't be absorbed. It +has to be exactly the difference in the + + align:start position:0% +has to be exactly the difference in the + + + align:start position:0% +has to be exactly the difference in the +energies between these two states. + + align:start position:0% +energies between these two states. + + + align:start position:0% +energies between these two states. +Again, that's the quantum nature of the + + align:start position:0% +Again, that's the quantum nature of the + + + align:start position:0% +Again, that's the quantum nature of the +hydrogen + + align:start position:0% +hydrogen + + + align:start position:0% +hydrogen +atom. And now, if you're calculating the + + align:start position:0% +atom. And now, if you're calculating the + + + align:start position:0% +atom. And now, if you're calculating the +frequency for + + align:start position:0% +frequency for + + + align:start position:0% +frequency for +absorption, well, what I've done here is + + align:start position:0% +absorption, well, what I've done here is + + + align:start position:0% +absorption, well, what I've done here is +I've turned I've reversed n subi and m + + align:start position:0% +I've turned I've reversed n subi and m + + + align:start position:0% +I've turned I've reversed n subi and m +subf. So, this is 1 over n + + align:start position:0% +subf. So, this is 1 over n + + + align:start position:0% +subf. So, this is 1 over n +subi^2 instead of 1 over n subf^2, which + + align:start position:0% +subi^2 instead of 1 over n subf^2, which + + + align:start position:0% +subi^2 instead of 1 over n subf^2, which +was which was the case in emission. And + + align:start position:0% +was which was the case in emission. And + + + align:start position:0% +was which was the case in emission. And +I've reversed this so that you get a + + align:start position:0% +I've reversed this so that you get a + + + align:start position:0% +I've reversed this so that you get a +positive value for the frequency of the + + align:start position:0% +positive value for the frequency of the + + + align:start position:0% +positive value for the frequency of the +radiation absorbed. Right? So we'll have + + align:start position:0% +radiation absorbed. Right? So we'll have + + + align:start position:0% +radiation absorbed. Right? So we'll have +two different equations for absorption + + align:start position:0% +two different equations for absorption + + + align:start position:0% +two different equations for absorption +and for uh + + align:start position:0% +and for uh + + + align:start position:0% +and for uh +emission. Okay? So those are the + + align:start position:0% +emission. Okay? So those are the + + + align:start position:0% +emission. Okay? So those are the +Schroinger equation results. Uh I forgot + + align:start position:0% +Schroinger equation results. Uh I forgot + + + align:start position:0% +Schroinger equation results. Uh I forgot +to announce uh there's a forum this + + align:start position:0% +to announce uh there's a forum this + + + align:start position:0% +to announce uh there's a forum this +evening from 5 to 6. Uh should have + + align:start position:0% +evening from 5 to 6. Uh should have + + + align:start position:0% +evening from 5 to 6. Uh should have +signed up in recitation. If you didn't + + align:start position:0% +signed up in recitation. If you didn't + + + align:start position:0% +signed up in recitation. If you didn't +and still want to come, send us an email + + align:start position:0% +and still want to come, send us an email + + + align:start position:0% +and still want to come, send us an email +and come. And uh we need the defraction + + align:start position:0% +and come. And uh we need the defraction + + + align:start position:0% +and come. And uh we need the defraction +glasses back as you're uh + + align:start position:0% +glasses back as you're uh + + + align:start position:0% +glasses back as you're uh +exiting. Okay, see you Friday. \ No newline at end of file diff --git a/oTnXMW4mx-c.txt b/oTnXMW4mx-c.txt new file mode 100644 index 0000000000000000000000000000000000000000..31e2e435bd0bd7126adb807287d57b781b12cd13 --- /dev/null +++ b/oTnXMW4mx-c.txt @@ -0,0 +1,715 @@ +align:start position:0% + +let's go ahead and start our the first + + align:start position:0% +let's go ahead and start our the first + + + align:start position:0% +let's go ahead and start our the first +thing you'll see in the our console is + + align:start position:0% +thing you'll see in the our console is + + + align:start position:0% +thing you'll see in the our console is +the version of our you are using and + + align:start position:0% +the version of our you are using and + + + align:start position:0% +the version of our you are using and +other basic information related to + + align:start position:0% +other basic information related to + + + align:start position:0% +other basic information related to +licensing citations and demos to clear + + align:start position:0% +licensing citations and demos to clear + + + align:start position:0% +licensing citations and demos to clear +the console you can simply go to edit + + align:start position:0% +the console you can simply go to edit + + + align:start position:0% +the console you can simply go to edit +and select clear console we'll start by + + align:start position:0% +and select clear console we'll start by + + + align:start position:0% +and select clear console we'll start by +reading in our data set usda dot csv + + align:start position:0% +reading in our data set usda dot csv + + + align:start position:0% +reading in our data set usda dot csv +which contains all foods in the usda + + align:start position:0% +which contains all foods in the usda + + + align:start position:0% +which contains all foods in the usda +database in 100 gram amounts you should + + align:start position:0% +database in 100 gram amounts you should + + + align:start position:0% +database in 100 gram amounts you should +have already downloaded the data set to + + align:start position:0% +have already downloaded the data set to + + + align:start position:0% +have already downloaded the data set to +your computer to be able to read the + + align:start position:0% +your computer to be able to read the + + + align:start position:0% +your computer to be able to read the +data set in our we first need to + + align:start position:0% +data set in our we first need to + + + align:start position:0% +data set in our we first need to +navigate to the directory in our + + align:start position:0% +navigate to the directory in our + + + align:start position:0% +navigate to the directory in our +computer where the data file usda dot + + align:start position:0% +computer where the data file usda dot + + + align:start position:0% +computer where the data file usda dot +csv is saved to do so if you are on a + + align:start position:0% +csv is saved to do so if you are on a + + + align:start position:0% +csv is saved to do so if you are on a +mac go to the miscellaneous menu and + + align:start position:0% +mac go to the miscellaneous menu and + + + align:start position:0% +mac go to the miscellaneous menu and +select change working directory if you + + align:start position:0% +select change working directory if you + + + align:start position:0% +select change working directory if you +are on a pc go to the file menu select + + align:start position:0% +are on a pc go to the file menu select + + + align:start position:0% +are on a pc go to the file menu select +change directory and then navigate to + + align:start position:0% +change directory and then navigate to + + + align:start position:0% +change directory and then navigate to +the folder where you saved the csv file + + align:start position:0% +the folder where you saved the csv file + + + align:start position:0% +the folder where you saved the csv file +then press ok nothing has happened in + + align:start position:0% +then press ok nothing has happened in + + + align:start position:0% +then press ok nothing has happened in +our until now except changing the + + align:start position:0% +our until now except changing the + + + align:start position:0% +our until now except changing the +working directory to double check that + + align:start position:0% +working directory to double check that + + + align:start position:0% +working directory to double check that +we are in the right working directory we + + align:start position:0% +we are in the right working directory we + + + align:start position:0% +we are in the right working directory we +can type get WD which stands for get + + align:start position:0% +can type get WD which stands for get + + + align:start position:0% +can type get WD which stands for get +working directory and then our gives us + + align:start position:0% +working directory and then our gives us + + + align:start position:0% +working directory and then our gives us +the path to the folder we just selected + + align:start position:0% +the path to the folder we just selected + + + align:start position:0% +the path to the folder we just selected +now we should be ready to read in our + + align:start position:0% +now we should be ready to read in our + + + align:start position:0% +now we should be ready to read in our +data set we will use the function read + + align:start position:0% +data set we will use the function read + + + align:start position:0% +data set we will use the function read +dot csv since the data set was given to + + align:start position:0% +dot csv since the data set was given to + + + align:start position:0% +dot csv since the data set was given to +us in a csv format and let's save the + + align:start position:0% +us in a csv format and let's save the + + + align:start position:0% +us in a csv format and let's save the +output to a data frame and call it usda + + align:start position:0% +output to a data frame and call it usda + + + align:start position:0% +output to a data frame and call it usda +and this is equal to read CSV and this + + align:start position:0% +and this is equal to read CSV and this + + + align:start position:0% +and this is equal to read CSV and this +takes as an input the name of the CSV + + align:start position:0% +takes as an input the name of the CSV + + + align:start position:0% +takes as an input the name of the CSV +file which is USDA dot CSV and don't + + align:start position:0% +file which is USDA dot CSV and don't + + + align:start position:0% +file which is USDA dot CSV and don't +forget the quotation marks around the + + align:start position:0% +forget the quotation marks around the + + + align:start position:0% +forget the quotation marks around the +name of the CSV file pressing enter are + + align:start position:0% +name of the CSV file pressing enter are + + + align:start position:0% +name of the CSV file pressing enter are +now read the information from the data + + align:start position:0% +now read the information from the data + + + align:start position:0% +now read the information from the data +set and saved it to the data frame USDA + + align:start position:0% +set and saved it to the data frame USDA + + + align:start position:0% +set and saved it to the data frame USDA +now it's time to learn about our data we + + align:start position:0% +now it's time to learn about our data we + + + align:start position:0% +now it's time to learn about our data we +can use the structure function or STR + + align:start position:0% +can use the structure function or STR + + + align:start position:0% +can use the structure function or STR +and R and give it the input USDA this + + align:start position:0% +and R and give it the input USDA this + + + align:start position:0% +and R and give it the input USDA this +gives us the following information we + + align:start position:0% +gives us the following information we + + + align:start position:0% +gives us the following information we +have seven thousand fifty eight + + align:start position:0% +have seven thousand fifty eight + + + align:start position:0% +have seven thousand fifty eight +observations or Foods in our data set + + align:start position:0% +observations or Foods in our data set + + + align:start position:0% +observations or Foods in our data set +along with sixteen different variables + + align:start position:0% +along with sixteen different variables + + + align:start position:0% +along with sixteen different variables +first variable gives a unique + + align:start position:0% +first variable gives a unique + + + align:start position:0% +first variable gives a unique +identification number for each of the + + align:start position:0% +identification number for each of the + + + align:start position:0% +identification number for each of the +food starting with the number 1001 the + + align:start position:0% +food starting with the number 1001 the + + + align:start position:0% +food starting with the number 1001 the +second variable gives a text description + + align:start position:0% +second variable gives a text description + + + align:start position:0% +second variable gives a text description +of each of the foods the third variable + + align:start position:0% +of each of the foods the third variable + + + align:start position:0% +of each of the foods the third variable +is the amount of calories and 100 grams + + align:start position:0% +is the amount of calories and 100 grams + + + align:start position:0% +is the amount of calories and 100 grams +of these foods and it's given to us in + + align:start position:0% +of these foods and it's given to us in + + + align:start position:0% +of these foods and it's given to us in +kilocalories then we also have + + align:start position:0% +kilocalories then we also have + + + align:start position:0% +kilocalories then we also have +information about the protein total fat + + align:start position:0% +information about the protein total fat + + + align:start position:0% +information about the protein total fat +carbohydrate saturated fat and sugar + + align:start position:0% +carbohydrate saturated fat and sugar + + + align:start position:0% +carbohydrate saturated fat and sugar +levels in grams as well as the sodium + + align:start position:0% +levels in grams as well as the sodium + + + align:start position:0% +levels in grams as well as the sodium +cholesterol calcium iron potassium and + + align:start position:0% +cholesterol calcium iron potassium and + + + align:start position:0% +cholesterol calcium iron potassium and +vitamin C levels in milligrams and + + align:start position:0% +vitamin C levels in milligrams and + + + align:start position:0% +vitamin C levels in milligrams and +finally the amount of vitamin E and + + align:start position:0% +finally the amount of vitamin E and + + + align:start position:0% +finally the amount of vitamin E and +vitamin D in what is known as + + align:start position:0% +vitamin D in what is known as + + + align:start position:0% +vitamin D in what is known as +international units and this is a + + align:start position:0% +international units and this is a + + + align:start position:0% +international units and this is a +standard measurement for drugs and + + align:start position:0% +standard measurement for drugs and + + + align:start position:0% +standard measurement for drugs and +vitamins now to obtain high-level + + align:start position:0% +vitamins now to obtain high-level + + + align:start position:0% +vitamins now to obtain high-level +statistical information about our + + align:start position:0% +statistical information about our + + + align:start position:0% +statistical information about our +dataset we can use the summary function + + align:start position:0% +dataset we can use the summary function + + + align:start position:0% +dataset we can use the summary function +and give it as an input the USDA data + + align:start position:0% +and give it as an input the USDA data + + + align:start position:0% +and give it as an input the USDA data +frame the summary function gives us + + align:start position:0% +frame the summary function gives us + + + align:start position:0% +frame the summary function gives us +information such as the minimum the + + align:start position:0% +information such as the minimum the + + + align:start position:0% +information such as the minimum the +maximum and the mean values across all + + align:start position:0% +maximum and the mean values across all + + + align:start position:0% +maximum and the mean values across all +seven thousand and fifty-eight foods for + + align:start position:0% +seven thousand and fifty-eight foods for + + + align:start position:0% +seven thousand and fifty-eight foods for +each of the 16 different variables for + + align:start position:0% +each of the 16 different variables for + + + align:start position:0% +each of the 16 different variables for +instance the maximum amount of + + align:start position:0% +instance the maximum amount of + + + align:start position:0% +instance the maximum amount of +cholesterol is three thousand one + + align:start position:0% +cholesterol is three thousand one + + + align:start position:0% +cholesterol is three thousand one +hundred milligrams whereas the mean is + + align:start position:0% +hundred milligrams whereas the mean is + + + align:start position:0% +hundred milligrams whereas the mean is +only forty one point 55 milligrams we + + align:start position:0% +only forty one point 55 milligrams we + + + align:start position:0% +only forty one point 55 milligrams we +also have information about the number + + align:start position:0% +also have information about the number + + + align:start position:0% +also have information about the number +of non-available + + align:start position:0% +of non-available + + + align:start position:0% +of non-available +entries for instance we have 1910 foods + + align:start position:0% +entries for instance we have 1910 foods + + + align:start position:0% +entries for instance we have 1910 foods +that are missing entries for their sugar + + align:start position:0% +that are missing entries for their sugar + + + align:start position:0% +that are missing entries for their sugar +levels now scrolling through this + + align:start position:0% +levels now scrolling through this + + + align:start position:0% +levels now scrolling through this +information a startling observation is + + align:start position:0% +information a startling observation is + + + align:start position:0% +information a startling observation is +the maximum level of sodium which is + + align:start position:0% +the maximum level of sodium which is + + + align:start position:0% +the maximum level of sodium which is +thirty-eight thousand seven hundred and + + align:start position:0% +thirty-eight thousand seven hundred and + + + align:start position:0% +thirty-eight thousand seven hundred and +fifty eight milligrams this number is + + align:start position:0% +fifty eight milligrams this number is + + + align:start position:0% +fifty eight milligrams this number is +huge given that the daily recommended + + align:start position:0% +huge given that the daily recommended + + + align:start position:0% +huge given that the daily recommended +maximum is only two thousand three + + align:start position:0% +maximum is only two thousand three + + + align:start position:0% +maximum is only two thousand three +hundred milligrams let's investigate + + align:start position:0% +hundred milligrams let's investigate + + + align:start position:0% +hundred milligrams let's investigate +this variable further in our next video \ No newline at end of file diff --git a/oyPesljk2Ak.txt b/oyPesljk2Ak.txt new file mode 100644 index 0000000000000000000000000000000000000000..06300cf26182e3beea52871cace92ba3ea34a6c6 --- /dev/null +++ b/oyPesljk2Ak.txt @@ -0,0 +1,9091 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common license. Your support + + align:start position:0% +a Creative Common license. Your support + + + align:start position:0% +a Creative Common license. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Okay, let's get started. Settle down. + + align:start position:0% +Okay, let's get started. Settle down. + + + align:start position:0% +Okay, let's get started. Settle down. +Settle down. The weekend has not quite + + align:start position:0% +Settle down. The weekend has not quite + + + align:start position:0% +Settle down. The weekend has not quite +started. + + align:start position:0% + + + + align:start position:0% + +Um let's look at what happened on + + align:start position:0% +Um let's look at what happened on + + + align:start position:0% +Um let's look at what happened on +Wednesday. Uh there's the scores. Class + + align:start position:0% +Wednesday. Uh there's the scores. Class + + + align:start position:0% +Wednesday. Uh there's the scores. Class +average about + + align:start position:0% +average about + + + align:start position:0% +average about +67. Uh standard deviation about 17. So + + align:start position:0% +67. Uh standard deviation about 17. So + + + align:start position:0% +67. Uh standard deviation about 17. So +that that means it's bell curve sitting + + align:start position:0% +that that means it's bell curve sitting + + + align:start position:0% +that that means it's bell curve sitting +right on the 50. Right on the 50. A lot + + align:start position:0% +right on the 50. Right on the 50. A lot + + + align:start position:0% +right on the 50. Right on the 50. A lot +of people improved. There were a lot of + + align:start position:0% +of people improved. There were a lot of + + + align:start position:0% +of people improved. There were a lot of +rags to rich's stories. Um, but there + + align:start position:0% +rags to rich's stories. Um, but there + + + align:start position:0% +rags to rich's stories. Um, but there +are still fair number of people down + + align:start position:0% +are still fair number of people down + + + align:start position:0% +are still fair number of people down +here. And so my uh my suggestion to you + + align:start position:0% +here. And so my uh my suggestion to you + + + align:start position:0% +here. And so my uh my suggestion to you +is that if you're if you're down here + + align:start position:0% +is that if you're if you're down here + + + align:start position:0% +is that if you're if you're down here +and you want + + align:start position:0% +and you want + + + align:start position:0% +and you want +to still too much talking people, you + + align:start position:0% +to still too much talking people, you + + + align:start position:0% +to still too much talking people, you +want to start your weekend soon, I'll + + align:start position:0% +want to start your weekend soon, I'll + + + align:start position:0% +want to start your weekend soon, I'll +help you by inviting you to leave. You + + align:start position:0% +help you by inviting you to leave. You + + + align:start position:0% +help you by inviting you to leave. You +don't have to stay here if you don't + + align:start position:0% +don't have to stay here if you don't + + + align:start position:0% +don't have to stay here if you don't +want to. But if you do choose to stay, + + align:start position:0% +want to. But if you do choose to stay, + + + align:start position:0% +want to. But if you do choose to stay, +please sit in + + align:start position:0% +please sit in + + + align:start position:0% +please sit in +silence. This is 3091. + + align:start position:0% + + + + align:start position:0% + +So, um, if you're down here, get in and + + align:start position:0% +So, um, if you're down here, get in and + + + align:start position:0% +So, um, if you're down here, get in and +see us. Please talk to your recitation + + align:start position:0% +see us. Please talk to your recitation + + + align:start position:0% +see us. Please talk to your recitation +instructor. Uh, come on in and see me. + + align:start position:0% +instructor. Uh, come on in and see me. + + + align:start position:0% +instructor. Uh, come on in and see me. +We'll talk about strategies for + + align:start position:0% +We'll talk about strategies for + + + align:start position:0% +We'll talk about strategies for +studying, strategies for success. I want + + align:start position:0% +studying, strategies for success. I want + + + align:start position:0% +studying, strategies for success. I want +you to pass this class, but just doing + + align:start position:0% +you to pass this class, but just doing + + + align:start position:0% +you to pass this class, but just doing +the same thing over. You know, this is, + + align:start position:0% +the same thing over. You know, this is, + + + align:start position:0% +the same thing over. You know, this is, +I think, Einstein's definition of + + align:start position:0% +I think, Einstein's definition of + + + align:start position:0% +I think, Einstein's definition of +insanity is doing the same thing over + + align:start position:0% +insanity is doing the same thing over + + + align:start position:0% +insanity is doing the same thing over +and over again expecting a different + + align:start position:0% +and over again expecting a different + + + align:start position:0% +and over again expecting a different +outcome. + + align:start position:0% +outcome. + + + align:start position:0% +outcome. +So if what you're doing up to now isn't + + align:start position:0% +So if what you're doing up to now isn't + + + align:start position:0% +So if what you're doing up to now isn't +working, let's try something else and we + + align:start position:0% +working, let's try something else and we + + + align:start position:0% +working, let's try something else and we +can help + + align:start position:0% +can help + + + align:start position:0% +can help +you. + + align:start position:0% +you. + + + align:start position:0% +you. +Um so the model solutions are up and if + + align:start position:0% +Um so the model solutions are up and if + + + align:start position:0% +Um so the model solutions are up and if +there are changes that need to be made, + + align:start position:0% +there are changes that need to be made, + + + align:start position:0% +there are changes that need to be made, +please get in uh to see me. Uh why don't + + align:start position:0% +please get in uh to see me. Uh why don't + + + align:start position:0% +please get in uh to see me. Uh why don't +why don't we agree not to do it until + + align:start position:0% +why don't we agree not to do it until + + + align:start position:0% +why don't we agree not to do it until +Monday? I'd like you to first talk to + + align:start position:0% +Monday? I'd like you to first talk to + + + align:start position:0% +Monday? I'd like you to first talk to +your recitation instructor and make sure + + align:start position:0% +your recitation instructor and make sure + + + align:start position:0% +your recitation instructor and make sure +that there's something worth uh + + align:start position:0% +that there's something worth uh + + + align:start position:0% +that there's something worth uh +exploring. And + + align:start position:0% +exploring. And + + + align:start position:0% +exploring. And +um the final exam is on the 15th of + + align:start position:0% +um the final exam is on the 15th of + + + align:start position:0% +um the final exam is on the 15th of +December. The final exam is going to + + align:start position:0% +December. The final exam is going to + + + align:start position:0% +December. The final exam is going to +essentially represent the uh equivalent + + align:start position:0% +essentially represent the uh equivalent + + + align:start position:0% +essentially represent the uh equivalent +of of a double monthly test. You'll have + + align:start position:0% +of of a double monthly test. You'll have + + + align:start position:0% +of of a double monthly test. You'll have +three hours, but I give about double the + + align:start position:0% +three hours, but I give about double the + + + align:start position:0% +three hours, but I give about double the +amount of work. So it should give you + + align:start position:0% +amount of work. So it should give you + + + align:start position:0% +amount of work. So it should give you +enough time to finish. But the final + + align:start position:0% +enough time to finish. But the final + + + align:start position:0% +enough time to finish. But the final +exam will consist of a mix of what's + + align:start position:0% +exam will consist of a mix of what's + + + align:start position:0% +exam will consist of a mix of what's +covered since test three. So it's like a + + align:start position:0% +covered since test three. So it's like a + + + align:start position:0% +covered since test three. So it's like a +test four monthly. Okay? and also some + + align:start position:0% +test four monthly. Okay? and also some + + + align:start position:0% +test four monthly. Okay? and also some +material going all the way back to the + + align:start position:0% +material going all the way back to the + + + align:start position:0% +material going all the way back to the +beginning of the semester. So, it's both + + align:start position:0% +beginning of the semester. So, it's both + + + align:start position:0% +beginning of the semester. So, it's both +cumulative and focused. So, it has + + align:start position:0% +cumulative and focused. So, it has + + + align:start position:0% +cumulative and focused. So, it has +breadth and depth. And it's really good + + align:start position:0% +breadth and depth. And it's really good + + + align:start position:0% +breadth and depth. And it's really good +to pass the final. It's really good to + + align:start position:0% +to pass the final. It's really good to + + + align:start position:0% +to pass the final. It's really good to +pass the final. You know, if you're + + align:start position:0% +pass the final. You know, if you're + + + align:start position:0% +pass the final. You know, if you're +going to if if if people pass the final, + + align:start position:0% +going to if if if people pass the final, + + + align:start position:0% +going to if if if people pass the final, +it tilts things in favor of passing the + + align:start position:0% +it tilts things in favor of passing the + + + align:start position:0% +it tilts things in favor of passing the +class. If you crash and burn on the + + align:start position:0% +class. If you crash and burn on the + + + align:start position:0% +class. If you crash and burn on the +final, it raises a lot of questions as + + align:start position:0% +final, it raises a lot of questions as + + + align:start position:0% +final, it raises a lot of questions as +to whether you've been working all along + + align:start position:0% +to whether you've been working all along + + + align:start position:0% +to whether you've been working all along +or you gave up around uh Veterans Day + + align:start position:0% +or you gave up around uh Veterans Day + + + align:start position:0% +or you gave up around uh Veterans Day +and so on. So, uh I urge you to keep at + + align:start position:0% +and so on. So, uh I urge you to keep at + + + align:start position:0% +and so on. So, uh I urge you to keep at +it and you know, + + align:start position:0% +it and you know, + + + align:start position:0% +it and you know, +don't leave everything to the last + + align:start position:0% +don't leave everything to the last + + + align:start position:0% +don't leave everything to the last +minute. If you take a look at your final + + align:start position:0% +minute. If you take a look at your final + + + align:start position:0% +minute. If you take a look at your final +exam schedule, this is the third day of + + align:start position:0% +exam schedule, this is the third day of + + + align:start position:0% +exam schedule, this is the third day of +the final exam period. Some of you may + + align:start position:0% +the final exam period. Some of you may + + + align:start position:0% +the final exam period. Some of you may +have exams Monday and Tuesday. If you + + align:start position:0% +have exams Monday and Tuesday. If you + + + align:start position:0% +have exams Monday and Tuesday. If you +think you're going to cram it all in on + + align:start position:0% +think you're going to cram it all in on + + + align:start position:0% +think you're going to cram it all in on +a Tuesday night, it's not going to work. + + align:start position:0% +a Tuesday night, it's not going to work. + + + align:start position:0% +a Tuesday night, it's not going to work. +you're going to be very tired by the + + align:start position:0% +you're going to be very tired by the + + + align:start position:0% +you're going to be very tired by the +middle of that week. So, you need to + + align:start position:0% +middle of that week. So, you need to + + + align:start position:0% +middle of that week. So, you need to +have a plan. You have to work + + align:start position:0% +have a plan. You have to work + + + align:start position:0% +have a plan. You have to work +incrementally so that things sink in. + + align:start position:0% +incrementally so that things sink in. + + + align:start position:0% +incrementally so that things sink in. +You can't just do high-speed fixed + + align:start position:0% +You can't just do high-speed fixed + + + align:start position:0% +You can't just do high-speed fixed +second law and expect it's all just + + align:start position:0% +second law and expect it's all just + + + align:start position:0% +second law and expect it's all just +going to go zooming in. It won't. It'll + + align:start position:0% +going to go zooming in. It won't. It'll + + + align:start position:0% +going to go zooming in. It won't. It'll +look like first law. It'll go in this + + align:start position:0% +look like first law. It'll go in this + + + align:start position:0% +look like first law. It'll go in this +side, out the other + + align:start position:0% +side, out the other + + + align:start position:0% +side, out the other +side. + + align:start position:0% +side. + + + align:start position:0% +side. +So, keep keep at it. All right. Well, + + align:start position:0% +So, keep keep at it. All right. Well, + + + align:start position:0% +So, keep keep at it. All right. Well, +let's get on with the the lesson. Uh + + align:start position:0% +let's get on with the the lesson. Uh + + + align:start position:0% +let's get on with the the lesson. Uh +today is going to be a chance to apply + + align:start position:0% +today is going to be a chance to apply + + + align:start position:0% +today is going to be a chance to apply +the or organic chemistry that we learned + + align:start position:0% +the or organic chemistry that we learned + + + align:start position:0% +the or organic chemistry that we learned +on Monday. I said we learned enough + + align:start position:0% +on Monday. I said we learned enough + + + align:start position:0% +on Monday. I said we learned enough +organic chemistry to set the stage for + + align:start position:0% +organic chemistry to set the stage for + + + align:start position:0% +organic chemistry to set the stage for +polymers. So today we're going to talk + + align:start position:0% +polymers. So today we're going to talk + + + align:start position:0% +polymers. So today we're going to talk +about polymers. Monday we'll come back + + align:start position:0% +about polymers. Monday we'll come back + + + align:start position:0% +about polymers. Monday we'll come back +and finish up polymers and then that'll + + align:start position:0% +and finish up polymers and then that'll + + + align:start position:0% +and finish up polymers and then that'll +lead us into biochemistry. So this is + + align:start position:0% +lead us into biochemistry. So this is + + + align:start position:0% +lead us into biochemistry. So this is +all part of applied organic chemistry to + + align:start position:0% +all part of applied organic chemistry to + + + align:start position:0% +all part of applied organic chemistry to +date. What are the types of solids that + + align:start position:0% +date. What are the types of solids that + + + align:start position:0% +date. What are the types of solids that +we've seen in 3091? We saw solids that + + align:start position:0% +we've seen in 3091? We saw solids that + + + align:start position:0% +we've seen in 3091? We saw solids that +are consisting of single atoms stacked. + + align:start position:0% +are consisting of single atoms stacked. + + + align:start position:0% +are consisting of single atoms stacked. +Then we saw compounds stacked. We last + + align:start position:0% +Then we saw compounds stacked. We last + + + align:start position:0% +Then we saw compounds stacked. We last +day we started looking at chains and + + align:start position:0% +day we started looking at chains and + + + align:start position:0% +day we started looking at chains and +we've even seen networks, some of them + + align:start position:0% +we've even seen networks, some of them + + + align:start position:0% +we've even seen networks, some of them +amorphous, some of them crystallin. + + align:start position:0% +amorphous, some of them crystallin. + + + align:start position:0% +amorphous, some of them crystallin. +Today what we're going to look at is a + + align:start position:0% +Today what we're going to look at is a + + + align:start position:0% +Today what we're going to look at is a +new form of solid where the building + + align:start position:0% +new form of solid where the building + + + align:start position:0% +new form of solid where the building +block is a long chain long in quotation + + align:start position:0% +block is a long chain long in quotation + + + align:start position:0% +block is a long chain long in quotation +marks. And this is a polymer. Polymers + + align:start position:0% +marks. And this is a polymer. Polymers + + + align:start position:0% +marks. And this is a polymer. Polymers +are pervasive in our society. We see + + align:start position:0% +are pervasive in our society. We see + + + align:start position:0% +are pervasive in our society. We see +them in everything from your your CDs, + + align:start position:0% +them in everything from your your CDs, + + + align:start position:0% +them in everything from your your CDs, +the CD cases. You see them in trash + + align:start position:0% +the CD cases. You see them in trash + + + align:start position:0% +the CD cases. You see them in trash +bags. You see them in clothing. + + align:start position:0% +bags. You see them in clothing. + + + align:start position:0% +bags. You see them in clothing. +microfiber. Some of these new fibers + + align:start position:0% +microfiber. Some of these new fibers + + + align:start position:0% +microfiber. Some of these new fibers +have uh incredible mix of properties in + + align:start position:0% +have uh incredible mix of properties in + + + align:start position:0% +have uh incredible mix of properties in +terms of uh comfort and uh security. Um + + align:start position:0% +terms of uh comfort and uh security. Um + + + align:start position:0% +terms of uh comfort and uh security. Um +auto parts all over the map. And when it + + align:start position:0% +auto parts all over the map. And when it + + + align:start position:0% +auto parts all over the map. And when it +comes to uh soft matter, we as human + + align:start position:0% +comes to uh soft matter, we as human + + + align:start position:0% +comes to uh soft matter, we as human +beings, we are solid state devices. + + align:start position:0% +beings, we are solid state devices. + + + align:start position:0% +beings, we are solid state devices. +Mother nature is a polymer chemist. + + align:start position:0% +Mother nature is a polymer chemist. + + + align:start position:0% +Mother nature is a polymer chemist. +Mother nature is a polymer chemist. It's + + align:start position:0% +Mother nature is a polymer chemist. It's + + + align:start position:0% +Mother nature is a polymer chemist. It's +all macromolecular chemistry. So we want + + align:start position:0% +all macromolecular chemistry. So we want + + + align:start position:0% +all macromolecular chemistry. So we want +to introduce polymers today. Let's have + + align:start position:0% +to introduce polymers today. Let's have + + + align:start position:0% +to introduce polymers today. Let's have +an operating definition. A polymer is a + + align:start position:0% +an operating definition. A polymer is a + + + align:start position:0% +an operating definition. A polymer is a +longchain molecule with a repeating + + align:start position:0% +longchain molecule with a repeating + + + align:start position:0% +longchain molecule with a repeating +chemical structure with a repeating + + align:start position:0% +chemical structure with a repeating + + + align:start position:0% +chemical structure with a repeating +chemical structure. And let me give you + + align:start position:0% +chemical structure. And let me give you + + + align:start position:0% +chemical structure. And let me give you +an example. I'll give you one that uh + + align:start position:0% +an example. I'll give you one that uh + + + align:start position:0% +an example. I'll give you one that uh +builds on something we saw the other + + align:start position:0% +builds on something we saw the other + + + align:start position:0% +builds on something we saw the other +day. We've seen um uh ethylene. We've + + align:start position:0% +day. We've seen um uh ethylene. We've + + + align:start position:0% +day. We've seen um uh ethylene. We've +seen + + align:start position:0% + + + + align:start position:0% + +ethylene or ethne. This is C2 H4. And it + + align:start position:0% +ethylene or ethne. This is C2 H4. And it + + + align:start position:0% +ethylene or ethne. This is C2 H4. And it +has the chemical structure + + align:start position:0% + + + + align:start position:0% + +Okay, what we can do what we can do is + + align:start position:0% +Okay, what we can do what we can do is + + + align:start position:0% +Okay, what we can do what we can do is +turn this into a longchain molecule with + + align:start position:0% +turn this into a longchain molecule with + + + align:start position:0% +turn this into a longchain molecule with +a repeating chemical structure in the + + align:start position:0% +a repeating chemical structure in the + + + align:start position:0% +a repeating chemical structure in the +following manner. We can react it with + + align:start position:0% +following manner. We can react it with + + + align:start position:0% +following manner. We can react it with +something that will catalyze the + + align:start position:0% +something that will catalyze the + + + align:start position:0% +something that will catalyze the +destruction of this double bond. And + + align:start position:0% +destruction of this double bond. And + + + align:start position:0% +destruction of this double bond. And +once this double bond is broken, we can + + align:start position:0% +once this double bond is broken, we can + + + align:start position:0% +once this double bond is broken, we can +flip it over to the other side of the + + align:start position:0% +flip it over to the other side of the + + + align:start position:0% +flip it over to the other side of the +carbon, giving us the opportunity to + + align:start position:0% +carbon, giving us the opportunity to + + + align:start position:0% +carbon, giving us the opportunity to +continue to link. So this is done with a + + align:start position:0% +continue to link. So this is done with a + + + align:start position:0% +continue to link. So this is done with a +radical. So we can denote the radical R. + + align:start position:0% +radical. So we can denote the radical R. + + + align:start position:0% +radical. So we can denote the radical R. +And I'm going to put this remember the + + align:start position:0% +And I'm going to put this remember the + + + align:start position:0% +And I'm going to put this remember the +unpaired electron. So this is a radical + + align:start position:0% +unpaired electron. So this is a radical + + + align:start position:0% +unpaired electron. So this is a radical +with its unpaired electron which we term + + align:start position:0% +with its unpaired electron which we term + + + align:start position:0% +with its unpaired electron which we term +an initiator. And so this initiator when + + align:start position:0% +an initiator. And so this initiator when + + + align:start position:0% +an initiator. And so this initiator when +it meets something with a double bond + + align:start position:0% +it meets something with a double bond + + + align:start position:0% +it meets something with a double bond +reacts. The double bond is something + + align:start position:0% +reacts. The double bond is something + + + align:start position:0% +reacts. The double bond is something +that could be turned into two single + + align:start position:0% +that could be turned into two single + + + align:start position:0% +that could be turned into two single +bonds. So let's go to maximize bonds. So + + align:start position:0% +bonds. So let's go to maximize bonds. So + + + align:start position:0% +bonds. So let's go to maximize bonds. So +this one has no bond broken. This one + + align:start position:0% +this one has no bond broken. This one + + + align:start position:0% +this one has no bond broken. This one +has a double bond. We could react the + + align:start position:0% +has a double bond. We could react the + + + align:start position:0% +has a double bond. We could react the +two + + align:start position:0% +two + + + align:start position:0% +two +and result in the + + align:start position:0% +and result in the + + + align:start position:0% +and result in the +following build this so that we + + align:start position:0% + + + + align:start position:0% + +have and now this goes over to + + align:start position:0% +have and now this goes over to + + + align:start position:0% +have and now this goes over to +here. So now the initiator has attacked + + align:start position:0% +here. So now the initiator has attacked + + + align:start position:0% +here. So now the initiator has attacked +this double bond built the bridge and + + align:start position:0% +this double bond built the bridge and + + + align:start position:0% +this double bond built the bridge and +now the radical is at the end here. Well + + align:start position:0% +now the radical is at the end here. Well + + + align:start position:0% +now the radical is at the end here. Well +ethylene is a gas. If this is sitting in + + align:start position:0% +ethylene is a gas. If this is sitting in + + + align:start position:0% +ethylene is a gas. If this is sitting in +a reactor gas molecules are colliding + + align:start position:0% +a reactor gas molecules are colliding + + + align:start position:0% +a reactor gas molecules are colliding +with this. So now we can attack another + + align:start position:0% +with this. So now we can attack another + + + align:start position:0% +with this. So now we can attack another +ethylene and so on. You get the picture. + + align:start position:0% +ethylene and so on. You get the picture. + + + align:start position:0% +ethylene and so on. You get the picture. +Eventually, this thing + + align:start position:0% +Eventually, this thing + + + align:start position:0% +Eventually, this thing +is thousands and thousands of of atoms + + align:start position:0% +is thousands and thousands of of atoms + + + align:start position:0% +is thousands and thousands of of atoms +long. Let's do one more just + + align:start position:0% + + + + align:start position:0% + +for now. We'll have the the bond here. + + align:start position:0% +for now. We'll have the the bond here. + + + align:start position:0% +for now. We'll have the the bond here. +One, two, three, four. Like so. And so + + align:start position:0% +One, two, three, four. Like so. And so + + + align:start position:0% +One, two, three, four. Like so. And so +now you see a repeat unit. Here's a + + align:start position:0% +now you see a repeat unit. Here's a + + + align:start position:0% +now you see a repeat unit. Here's a +repeat unit. And this repeat unit can go + + align:start position:0% +repeat unit. And this repeat unit can go + + + align:start position:0% +repeat unit. And this repeat unit can go +n times where n is very very large. N + + align:start position:0% +n times where n is very very large. N + + + align:start position:0% +n times where n is very very large. N +can be on the order of oh 10,000 or so + + align:start position:0% +can be on the order of oh 10,000 or so + + + align:start position:0% +can be on the order of oh 10,000 or so +giving us molecules that have atomic + + align:start position:0% +giving us molecules that have atomic + + + align:start position:0% +giving us molecules that have atomic +masses of oh a + + align:start position:0% +masses of oh a + + + align:start position:0% +masses of oh a +million grams per + + align:start position:0% +million grams per + + + align:start position:0% +million grams per +mole. These are huge. These are + + align:start position:0% + + + + align:start position:0% + +huge. So we call this n I'm using n now + + align:start position:0% +huge. So we call this n I'm using n now + + + align:start position:0% +huge. So we call this n I'm using n now +in a new way. N is called the + + align:start position:0% +in a new way. N is called the + + + align:start position:0% +in a new way. N is called the +polymerization index. + + align:start position:0% +polymerization index. + + + align:start position:0% +polymerization index. +N is the polymerization + + align:start position:0% +N is the polymerization + + + align:start position:0% +N is the polymerization +index and it represents the number of + + align:start position:0% +index and it represents the number of + + + align:start position:0% +index and it represents the number of +repeats of the myrr unit. The myrr is + + align:start position:0% +repeats of the myrr unit. The myrr is + + + align:start position:0% +repeats of the myrr unit. The myrr is +the repeat unit. And what's the length + + align:start position:0% +the repeat unit. And what's the length + + + align:start position:0% +the repeat unit. And what's the length +of this thing? Let's let's get a sense + + align:start position:0% +of this thing? Let's let's get a sense + + + align:start position:0% +of this thing? Let's let's get a sense +of this. Uh suppose we had something + + align:start position:0% +of this. Uh suppose we had something + + + align:start position:0% +of this. Uh suppose we had something +that was so say 10,000 units long. So + + align:start position:0% +that was so say 10,000 units long. So + + + align:start position:0% +that was so say 10,000 units long. So +let's say n is 10,000. So that might + + align:start position:0% +let's say n is 10,000. So that might + + + align:start position:0% +let's say n is 10,000. So that might +give me oh something on the order of + + align:start position:0% +give me oh something on the order of + + + align:start position:0% +give me oh something on the order of +about a million grams per mole. Let me + + align:start position:0% +about a million grams per mole. Let me + + + align:start position:0% +about a million grams per mole. Let me +do the let me do the calculation a + + align:start position:0% +do the let me do the calculation a + + + align:start position:0% +do the let me do the calculation a +different way. Let me say suppose I had + + align:start position:0% +different way. Let me say suppose I had + + + align:start position:0% +different way. Let me say suppose I had +something that had a an atomic mass of + + align:start position:0% +something that had a an atomic mass of + + + align:start position:0% +something that had a an atomic mass of +100,000. We'll choose + + align:start position:0% +100,000. We'll choose + + + align:start position:0% +100,000. We'll choose +a 100,000 g per mole. This is the atomic + + align:start position:0% +a 100,000 g per mole. This is the atomic + + + align:start position:0% +a 100,000 g per mole. This is the atomic +mass of the polymer. And uh divide that + + align:start position:0% +mass of the polymer. And uh divide that + + + align:start position:0% +mass of the polymer. And uh divide that +by the atomic mass of uh of ethylene. + + align:start position:0% +by the atomic mass of uh of ethylene. + + + align:start position:0% +by the atomic mass of uh of ethylene. +Ethylene is 28 g per mole. So this is + + align:start position:0% +Ethylene is 28 g per mole. So this is + + + align:start position:0% +Ethylene is 28 g per mole. So this is +the mass of + + align:start position:0% +the mass of + + + align:start position:0% +the mass of +C2H4. And this is the mass of of the + + align:start position:0% +C2H4. And this is the mass of of the + + + align:start position:0% +C2H4. And this is the mass of of the +polyethylene one molecule. So that would + + align:start position:0% +polyethylene one molecule. So that would + + + align:start position:0% +polyethylene one molecule. So that would +give us then a polymerization index of + + align:start position:0% +give us then a polymerization index of + + + align:start position:0% +give us then a polymerization index of +3571 about 3600. + + align:start position:0% +3571 about 3600. + + + align:start position:0% +3571 about 3600. +And if we estimate a carbonarbon bond + + align:start position:0% +And if we estimate a carbonarbon bond + + + align:start position:0% +And if we estimate a carbonarbon bond +distance about one and a half angstroms + + align:start position:0% +distance about one and a half angstroms + + + align:start position:0% +distance about one and a half angstroms +for carbon carbon bond distance that + + align:start position:0% +for carbon carbon bond distance that + + + align:start position:0% +for carbon carbon bond distance that +gives us something that's on the order + + align:start position:0% +gives us something that's on the order + + + align:start position:0% +gives us something that's on the order +of about a half a micron a half a micron + + align:start position:0% +of about a half a micron a half a micron + + + align:start position:0% +of about a half a micron a half a micron +in length for + + align:start position:0% +in length for + + + align:start position:0% +in length for +one one + + align:start position:0% +one one + + + align:start position:0% +one one +molecule. And to give you a sense of + + align:start position:0% +molecule. And to give you a sense of + + + align:start position:0% +molecule. And to give you a sense of +what that really means I want to show + + align:start position:0% +what that really means I want to show + + + align:start position:0% +what that really means I want to show +you a demo here. What I've got is a a + + align:start position:0% +you a demo here. What I've got is a a + + + align:start position:0% +you a demo here. What I've got is a a +pull chain that you use in um oh + + align:start position:0% +pull chain that you use in um oh + + + align:start position:0% +pull chain that you use in um oh +downstairs in grandma's house to uh turn + + align:start position:0% +downstairs in grandma's house to uh turn + + + align:start position:0% +downstairs in grandma's house to uh turn +on the lights. So this is a whole bunch + + align:start position:0% +on the lights. So this is a whole bunch + + + align:start position:0% +on the lights. So this is a whole bunch +of these + + align:start position:0% +of these + + + align:start position:0% +of these +brass balls that are held together by + + align:start position:0% +brass balls that are held together by + + + align:start position:0% +brass balls that are held together by +metal. And so let's have each of these + + align:start position:0% +metal. And so let's have each of these + + + align:start position:0% +metal. And so let's have each of these +represent carbon. And this one is about + + align:start position:0% +represent carbon. And this one is about + + + align:start position:0% +represent carbon. And this one is about +3,000 units long. It's about 40 feet. 40 + + align:start position:0% +3,000 units long. It's about 40 feet. 40 + + + align:start position:0% +3,000 units long. It's about 40 feet. 40 +feet. So there's about 3,000 of these uh + + align:start position:0% +feet. So there's about 3,000 of these uh + + + align:start position:0% +feet. So there's about 3,000 of these uh +units here. So let's get a sense of + + align:start position:0% +units here. So let's get a sense of + + + align:start position:0% +units here. So let's get a sense of +how how big this is. So what I'll do is + + align:start position:0% + + + + align:start position:0% + +I'll + + align:start position:0% +I'll + + + align:start position:0% +I'll +molecule. This is one + + align:start position:0% +molecule. This is one + + + align:start position:0% +molecule. This is one +molecule. Okay. + + align:start position:0% + + + + align:start position:0% + +So imagine what happens when this in the + + align:start position:0% +So imagine what happens when this in the + + + align:start position:0% +So imagine what happens when this in the +melt state it's flowing. What happens + + align:start position:0% +melt state it's flowing. What happens + + + align:start position:0% +melt state it's flowing. What happens +when the melt decreases in temperature + + align:start position:0% +when the melt decreases in temperature + + + align:start position:0% +when the melt decreases in temperature +and this attempts to solidify. What are + + align:start position:0% +and this attempts to solidify. What are + + + align:start position:0% +and this attempts to solidify. What are +the chances that this is going to come + + align:start position:0% +the chances that this is going to come + + + align:start position:0% +the chances that this is going to come +out in one of the 14 brev lises? It's + + align:start position:0% +out in one of the 14 brev lises? It's + + + align:start position:0% +out in one of the 14 brev lises? It's +vanishingly small, isn't it? This is one + + align:start position:0% +vanishingly small, isn't it? This is one + + + align:start position:0% +vanishingly small, isn't it? This is one +molecule. I feel like I just came back + + align:start position:0% +molecule. I feel like I just came back + + + align:start position:0% +molecule. I feel like I just came back +from New + + align:start position:0% +from New + + + align:start position:0% +from New +Orleans. I didn't even have to lift my + + align:start position:0% +Orleans. I didn't even have to lift my + + + align:start position:0% +Orleans. I didn't even have to lift my +shirt. I look at all this stuff I got. + + align:start position:0% +shirt. I look at all this stuff I got. + + + align:start position:0% +shirt. I look at all this stuff I got. +This is terrific. All right, so that's + + align:start position:0% +This is terrific. All right, so that's + + + align:start position:0% +This is terrific. All right, so that's +one molecule. And uh if we imagine if we + + align:start position:0% +one molecule. And uh if we imagine if we + + + align:start position:0% +one molecule. And uh if we imagine if we +imagine what happens um let's say that + + align:start position:0% +imagine what happens um let's say that + + + align:start position:0% +imagine what happens um let's say that +it's pretty clear that that + + align:start position:0% +it's pretty clear that that + + + align:start position:0% +it's pretty clear that that +solid let's call this macroolelecule + + align:start position:0% +solid let's call this macroolelecule + + + align:start position:0% +solid let's call this macroolelecule +solid + + align:start position:0% + + + + align:start position:0% + +macroolecules favor + + align:start position:0% + + + + align:start position:0% + +u favor being + + align:start position:0% + + + + align:start position:0% + +amorphous favor the amorphous state. is + + align:start position:0% +amorphous favor the amorphous state. is + + + align:start position:0% +amorphous favor the amorphous state. is +the notion of pure crystallization is is + + align:start position:0% +the notion of pure crystallization is is + + + align:start position:0% +the notion of pure crystallization is is +not and we can imagine for example all + + align:start position:0% +not and we can imagine for example all + + + align:start position:0% +not and we can imagine for example all +of the rules that we learn for the + + align:start position:0% +of the rules that we learn for the + + + align:start position:0% +of the rules that we learn for the +inorganic glasses the silicates apply to + + align:start position:0% +inorganic glasses the silicates apply to + + + align:start position:0% +inorganic glasses the silicates apply to +organic glasses so let's look at say + + align:start position:0% +organic glasses so let's look at say + + + align:start position:0% +organic glasses so let's look at say +volume versus temperature for something + + align:start position:0% +volume versus temperature for something + + + align:start position:0% +volume versus temperature for something +like polyethylene so I'm just going to + + align:start position:0% +like polyethylene so I'm just going to + + + align:start position:0% +like polyethylene so I'm just going to +call this PE + + align:start position:0% +call this PE + + + align:start position:0% +call this PE +polyethylene for short so we can imagine + + align:start position:0% +polyethylene for short so we can imagine + + + align:start position:0% +polyethylene for short so we can imagine +we're up here in the melt state we cool + + align:start position:0% +we're up here in the melt state we cool + + + align:start position:0% +we're up here in the melt state we cool +down we go through a normal melting + + align:start position:0% +down we go through a normal melting + + + align:start position:0% +down we go through a normal melting +point And then we reach a + + align:start position:0% +point And then we reach a + + + align:start position:0% +point And then we reach a +solidification at some glass transition + + align:start position:0% +solidification at some glass transition + + + align:start position:0% +solidification at some glass transition +temperature. But let's say this is at a + + align:start position:0% +temperature. But let's say this is at a + + + align:start position:0% +temperature. But let's say this is at a +slow cooling rate. So this is Tg slow. + + align:start position:0% +slow cooling rate. So this is Tg slow. + + + align:start position:0% +slow cooling rate. So this is Tg slow. +And maybe another occasion we cool at a + + align:start position:0% +And maybe another occasion we cool at a + + + align:start position:0% +And maybe another occasion we cool at a +fast rate. And so we will have a + + align:start position:0% +fast rate. And so we will have a + + + align:start position:0% +fast rate. And so we will have a +different glass transition temperature + + align:start position:0% +different glass transition temperature + + + align:start position:0% +different glass transition temperature +and it will be higher. It will be + + align:start position:0% +and it will be higher. It will be + + + align:start position:0% +and it will be higher. It will be +higher. And let's say this over here at + + align:start position:0% +higher. And let's say this over here at + + + align:start position:0% +higher. And let's say this over here at +uh is room temperature. + + align:start position:0% +uh is room temperature. + + + align:start position:0% +uh is room temperature. +This is room temperature. So what do I + + align:start position:0% +This is room temperature. So what do I + + + align:start position:0% +This is room temperature. So what do I +find? I have two different volumes. + + align:start position:0% +find? I have two different volumes. + + + align:start position:0% +find? I have two different volumes. +You've seen this before. So if I have + + align:start position:0% +You've seen this before. So if I have + + + align:start position:0% +You've seen this before. So if I have +constant uh constant + + align:start position:0% +constant uh constant + + + align:start position:0% +constant uh constant +mass constant for constant mass equal + + align:start position:0% +mass constant for constant mass equal + + + align:start position:0% +mass constant for constant mass equal +masses, the one with the higher volume + + align:start position:0% +masses, the one with the higher volume + + + align:start position:0% +masses, the one with the higher volume +has a lower density. Right? So this one + + align:start position:0% +has a lower density. Right? So this one + + + align:start position:0% +has a lower density. Right? So this one +this should be low density. This is + + align:start position:0% +this should be low density. This is + + + align:start position:0% +this should be low density. This is +let's let me just put the fast cooling + + align:start position:0% +let's let me just put the fast cooling + + + align:start position:0% +let's let me just put the fast cooling +rate. Fast cool. This is slow cool. + + align:start position:0% +rate. Fast cool. This is slow cool. + + + align:start position:0% +rate. Fast cool. This is slow cool. +So this will be low density polyethylene + + align:start position:0% +So this will be low density polyethylene + + + align:start position:0% +So this will be low density polyethylene +formed here and this will be high + + align:start position:0% +formed here and this will be high + + + align:start position:0% +formed here and this will be high +density polyethylene simply by the + + align:start position:0% +density polyethylene simply by the + + + align:start position:0% +density polyethylene simply by the +different rates of uh cooling constant + + align:start position:0% +different rates of uh cooling constant + + + align:start position:0% +different rates of uh cooling constant +mass means then that you have density is + + align:start position:0% +mass means then that you have density is + + + align:start position:0% +mass means then that you have density is +mass over volume. So the one with the + + align:start position:0% +mass over volume. So the one with the + + + align:start position:0% +mass over volume. So the one with the +higher volume gives us the lower mass. + + align:start position:0% +higher volume gives us the lower mass. + + + align:start position:0% +higher volume gives us the lower mass. +So we can see how by different + + align:start position:0% +So we can see how by different + + + align:start position:0% +So we can see how by different +processing we have the ability to change + + align:start position:0% +processing we have the ability to change + + + align:start position:0% +processing we have the ability to change +between uh high density and low density + + align:start position:0% +between uh high density and low density + + + align:start position:0% +between uh high density and low density +polyethylene as a function of the + + align:start position:0% +polyethylene as a function of the + + + align:start position:0% +polyethylene as a function of the +cooling rate. + + align:start position:0% +cooling rate. + + + align:start position:0% +cooling rate. +Now other things can happen. If we go at + + align:start position:0% +Now other things can happen. If we go at + + + align:start position:0% +Now other things can happen. If we go at +a at a low rate of cooling, we can get + + align:start position:0% +a at a low rate of cooling, we can get + + + align:start position:0% +a at a low rate of cooling, we can get +even down here at very very uh low + + align:start position:0% +even down here at very very uh low + + + align:start position:0% +even down here at very very uh low +cooling rates. We might even get some + + align:start position:0% +cooling rates. We might even get some + + + align:start position:0% +cooling rates. We might even get some +degree of crystallization. And Tom, + + align:start position:0% +degree of crystallization. And Tom, + + + align:start position:0% +degree of crystallization. And Tom, +could we switch over to the document + + align:start position:0% +could we switch over to the document + + + align:start position:0% +could we switch over to the document +camera feed, please? So, let's see what + + align:start position:0% +camera feed, please? So, let's see what + + + align:start position:0% +camera feed, please? So, let's see what +happens when this thing attempts to + + align:start position:0% +happens when this thing attempts to + + + align:start position:0% +happens when this thing attempts to +crystallize. So, here we are. So what + + align:start position:0% +crystallize. So, here we are. So what + + + align:start position:0% +crystallize. So, here we are. So what +can happen is if we cool at a slow + + align:start position:0% +can happen is if we cool at a slow + + + align:start position:0% +can happen is if we cool at a slow +enough rate, this can't form a single + + align:start position:0% +enough rate, this can't form a single + + + align:start position:0% +enough rate, this can't form a single +crystal, but what it can do is fold back + + align:start position:0% +crystal, but what it can do is fold back + + + align:start position:0% +crystal, but what it can do is fold back +on itself and thereby put these atoms + + align:start position:0% +on itself and thereby put these atoms + + + align:start position:0% +on itself and thereby put these atoms +into a regular uh + + align:start position:0% + + + + align:start position:0% + +arrangement. So this is now forming a + + align:start position:0% +arrangement. So this is now forming a + + + align:start position:0% +arrangement. So this is now forming a +zone of crystallinity. A zone of + + align:start position:0% +zone of crystallinity. A zone of + + + align:start position:0% +zone of crystallinity. A zone of +crystallinity. And why is it doing this? + + align:start position:0% +crystallinity. And why is it doing this? + + + align:start position:0% +crystallinity. And why is it doing this? +It's doing this to maximize Vanderval's + + align:start position:0% +It's doing this to maximize Vanderval's + + + align:start position:0% +It's doing this to maximize Vanderval's +bonding here. The tighter it packs, the + + align:start position:0% +bonding here. The tighter it packs, the + + + align:start position:0% +bonding here. The tighter it packs, the +the greater the uh intensity of bond + + align:start position:0% +the greater the uh intensity of bond + + + align:start position:0% +the greater the uh intensity of bond +formation. So we see this happening in + + align:start position:0% +formation. So we see this happening in + + + align:start position:0% +formation. So we see this happening in +the formation of such zones of of + + align:start position:0% +the formation of such zones of of + + + align:start position:0% +the formation of such zones of of +crystallinity. And when this happens, we + + align:start position:0% +crystallinity. And when this happens, we + + + align:start position:0% +crystallinity. And when this happens, we +have a change in properties. We have a + + align:start position:0% +have a change in properties. We have a + + + align:start position:0% +have a change in properties. We have a +change in properties. Let's consider low + + align:start position:0% +change in properties. Let's consider low + + + align:start position:0% +change in properties. Let's consider low +density polyethylene. Well, we know that + + align:start position:0% +density polyethylene. Well, we know that + + + align:start position:0% +density polyethylene. Well, we know that +this thing is going to be mechanically + + align:start position:0% +this thing is going to be mechanically + + + align:start position:0% +this thing is going to be mechanically +flexible. It's going to be + + align:start position:0% +flexible. It's going to be + + + align:start position:0% +flexible. It's going to be +flexible because all we have what are + + align:start position:0% +flexible because all we have what are + + + align:start position:0% +flexible because all we have what are +the only bonds operative here? They're + + align:start position:0% +the only bonds operative here? They're + + + align:start position:0% +the only bonds operative here? They're +just weak Vanderval's + + align:start position:0% +just weak Vanderval's + + + align:start position:0% +just weak Vanderval's +bonds, mechanically flexible. It's high + + align:start position:0% +bonds, mechanically flexible. It's high + + + align:start position:0% +bonds, mechanically flexible. It's high +band gap material and it's amorphous. + + align:start position:0% +band gap material and it's amorphous. + + + align:start position:0% +band gap material and it's amorphous. +There are no grains. There's no grain + + align:start position:0% +There are no grains. There's no grain + + + align:start position:0% +There are no grains. There's no grain +boundaries. So, it is transparent + + align:start position:0% +boundaries. So, it is transparent + + + align:start position:0% +boundaries. So, it is transparent +because of the high band gap and it's + + align:start position:0% +because of the high band gap and it's + + + align:start position:0% +because of the high band gap and it's +clear. We can see through it because + + align:start position:0% +clear. We can see through it because + + + align:start position:0% +clear. We can see through it because +there are no internal surfaces. So, + + align:start position:0% +there are no internal surfaces. So, + + + align:start position:0% +there are no internal surfaces. So, +that's low density polyethylene. + + align:start position:0% +that's low density polyethylene. + + + align:start position:0% +that's low density polyethylene. +highdensity polyethylene. Well, it has + + align:start position:0% +highdensity polyethylene. Well, it has + + + align:start position:0% +highdensity polyethylene. Well, it has +some zones of + + align:start position:0% +some zones of + + + align:start position:0% +some zones of +this. So, the highdensity polyethylene + + align:start position:0% +this. So, the highdensity polyethylene + + + align:start position:0% +this. So, the highdensity polyethylene +has these has these near crystallin + + align:start position:0% + + + + align:start position:0% + +zones near crystallin zones and then + + align:start position:0% +zones near crystallin zones and then + + + align:start position:0% +zones near crystallin zones and then +it's broadly + + align:start position:0% +it's broadly + + + align:start position:0% +it's broadly +amorphous. The difference here is small. + + align:start position:0% +amorphous. The difference here is small. + + + align:start position:0% +amorphous. The difference here is small. +This density here is about 0.92 g per + + align:start position:0% +This density here is about 0.92 g per + + + align:start position:0% +This density here is about 0.92 g per +cime cubed and this is + + align:start position:0% +cime cubed and this is + + + align:start position:0% +cime cubed and this is +about.96 g per cime cubed. So there's a + + align:start position:0% +about.96 g per cime cubed. So there's a + + + align:start position:0% +about.96 g per cime cubed. So there's a +little bit of tighter packing here. But + + align:start position:0% +little bit of tighter packing here. But + + + align:start position:0% +little bit of tighter packing here. But +what happens when we get into these + + align:start position:0% +what happens when we get into these + + + align:start position:0% +what happens when we get into these +zones, these zones of of regularity + + align:start position:0% +zones, these zones of of regularity + + + align:start position:0% +zones, these zones of of regularity +because there's a higher atom density, + + align:start position:0% +because there's a higher atom density, + + + align:start position:0% +because there's a higher atom density, +this turns out to have a higher + + align:start position:0% +this turns out to have a higher + + + align:start position:0% +this turns out to have a higher +reactivity with light. And therefore, + + align:start position:0% +reactivity with light. And therefore, + + + align:start position:0% +reactivity with light. And therefore, +I'm using N here not to mean index of + + align:start position:0% +I'm using N here not to mean index of + + + align:start position:0% +I'm using N here not to mean index of +polymerization. This is index of + + align:start position:0% +polymerization. This is index of + + + align:start position:0% +polymerization. This is index of +refraction. The index of refraction in + + align:start position:0% +refraction. The index of refraction in + + + align:start position:0% +refraction. The index of refraction in +the near crystallin zones is not equal + + align:start position:0% +the near crystallin zones is not equal + + + align:start position:0% +the near crystallin zones is not equal +to the index of refraction in the + + align:start position:0% +to the index of refraction in the + + + align:start position:0% +to the index of refraction in the +amorphous + + align:start position:0% + + + + align:start position:0% + +zones. So now we have zones that are + + align:start position:0% +zones. So now we have zones that are + + + align:start position:0% +zones. So now we have zones that are +near crystallin in zones that are + + align:start position:0% +near crystallin in zones that are + + + align:start position:0% +near crystallin in zones that are +amorphous and so we have the effect of + + align:start position:0% +amorphous and so we have the effect of + + + align:start position:0% +amorphous and so we have the effect of +internal interface and as a result the + + align:start position:0% +internal interface and as a result the + + + align:start position:0% +internal interface and as a result the +highdensity polyethylene is + + align:start position:0% +highdensity polyethylene is + + + align:start position:0% +highdensity polyethylene is +opaque. It's + + align:start position:0% + + + + align:start position:0% + +opaque. These zones here add + + align:start position:0% +opaque. These zones here add + + + align:start position:0% +opaque. These zones here add +rigidity. Add rigidity. There's there's + + align:start position:0% +rigidity. Add rigidity. There's there's + + + align:start position:0% +rigidity. Add rigidity. There's there's +a stiffness here. So, this one is + + align:start position:0% + + + + align:start position:0% + +rigid. So, what do we have? We have + + align:start position:0% +rigid. So, what do we have? We have + + + align:start position:0% +rigid. So, what do we have? We have +lowdensity polyethylene. This is what + + align:start position:0% +lowdensity polyethylene. This is what + + + align:start position:0% +lowdensity polyethylene. This is what +you see in use in food + + align:start position:0% +you see in use in food + + + align:start position:0% +you see in use in food +wrap. Food wrap. Whereas this is what + + align:start position:0% +wrap. Food wrap. Whereas this is what + + + align:start position:0% +wrap. Food wrap. Whereas this is what +you see in uh in the milk jugs. + + align:start position:0% +you see in uh in the milk jugs. + + + align:start position:0% +you see in uh in the milk jugs. +the trans the uh the milk jugs that are + + align:start position:0% +the trans the uh the milk jugs that are + + + align:start position:0% +the trans the uh the milk jugs that are +somewhat hardened and do not admit + + align:start position:0% +somewhat hardened and do not admit + + + align:start position:0% +somewhat hardened and do not admit +light. Both the same material, but + + align:start position:0% +light. Both the same material, but + + + align:start position:0% +light. Both the same material, but +what's happened is just a slight change + + align:start position:0% +what's happened is just a slight change + + + align:start position:0% +what's happened is just a slight change +in + + align:start position:0% +in + + + align:start position:0% +in +the in the uh strength of the material + + align:start position:0% +the in the uh strength of the material + + + align:start position:0% +the in the uh strength of the material +through a change in processing, change + + align:start position:0% +through a change in processing, change + + + align:start position:0% +through a change in processing, change +in cooling rate. So let's look at how we + + align:start position:0% +in cooling rate. So let's look at how we + + + align:start position:0% +in cooling rate. So let's look at how we +can take this idea of tailoring + + align:start position:0% +can take this idea of tailoring + + + align:start position:0% +can take this idea of tailoring +properties and and extend it more + + align:start position:0% +properties and and extend it more + + + align:start position:0% +properties and and extend it more +broadly and maybe put it on a firmer + + align:start position:0% +broadly and maybe put it on a firmer + + + align:start position:0% +broadly and maybe put it on a firmer +footing. + + align:start position:0% +footing. + + + align:start position:0% +footing. +So let's look + + align:start position:0% + + + + align:start position:0% + +at the + + align:start position:0% +at the + + + align:start position:0% +at the +various items in our toolbox. So we want + + align:start position:0% +various items in our toolbox. So we want + + + align:start position:0% +various items in our toolbox. So we want +to tailor the properties. First thing we + + align:start position:0% +to tailor the properties. First thing we + + + align:start position:0% +to tailor the properties. First thing we +can do is control + + align:start position:0% +can do is control + + + align:start position:0% +can do is control +composition. Control of + + align:start position:0% +composition. Control of + + + align:start position:0% +composition. Control of +composition. That's + + align:start position:0% +composition. That's + + + align:start position:0% +composition. That's +purity. So we can start with pure + + align:start position:0% +purity. So we can start with pure + + + align:start position:0% +purity. So we can start with pure +polymers and polymers that are made of + + align:start position:0% +polymers and polymers that are made of + + + align:start position:0% +polymers and polymers that are made of +combinations of different polymers. So + + align:start position:0% +combinations of different polymers. So + + + align:start position:0% +combinations of different polymers. So +let's start with the pure. The pure + + align:start position:0% +let's start with the pure. The pure + + + align:start position:0% +let's start with the pure. The pure +polymer they have their own because it + + align:start position:0% +polymer they have their own because it + + + align:start position:0% +polymer they have their own because it +comes from a different heritage they + + align:start position:0% +comes from a different heritage they + + + align:start position:0% +comes from a different heritage they +have their own terminology. So pure + + align:start position:0% +have their own terminology. So pure + + + align:start position:0% +have their own terminology. So pure +polymers or polymers consisting of a + + align:start position:0% +polymers or polymers consisting of a + + + align:start position:0% +polymers or polymers consisting of a +single myrr are called + + align:start position:0% + + + + align:start position:0% + +homopolymers called + + align:start position:0% +homopolymers called + + + align:start position:0% +homopolymers called +homopolymers consist of a single myrr + + align:start position:0% +homopolymers consist of a single myrr + + + align:start position:0% +homopolymers consist of a single myrr +one myrr type. One myrr type and it's + + align:start position:0% +one myrr type. One myrr type and it's + + + align:start position:0% +one myrr type. One myrr type and it's +repeated. So for example + + align:start position:0% +repeated. So for example + + + align:start position:0% +repeated. So for example +polyethylene polyethylene ethylene is + + align:start position:0% +polyethylene polyethylene ethylene is + + + align:start position:0% +polyethylene polyethylene ethylene is +the repeat unit and that's all you see + + align:start position:0% +the repeat unit and that's all you see + + + align:start position:0% +the repeat unit and that's all you see +it's polyethylene from end to end. Um + + align:start position:0% +it's polyethylene from end to end. Um + + + align:start position:0% +it's polyethylene from end to end. Um +then if we want to mix different MRS we + + align:start position:0% +then if we want to mix different MRS we + + + align:start position:0% +then if we want to mix different MRS we +get what is to a a polymer what we would + + align:start position:0% +get what is to a a polymer what we would + + + align:start position:0% +get what is to a a polymer what we would +call an alloy in a metal system and this + + align:start position:0% +call an alloy in a metal system and this + + + align:start position:0% +call an alloy in a metal system and this +is called a + + align:start position:0% +is called a + + + align:start position:0% +is called a +co-olymer. a + + align:start position:0% +co-olymer. a + + + align:start position:0% +co-olymer. a +co-olymer, it has more than one type, + + align:start position:0% +co-olymer, it has more than one type, + + + align:start position:0% +co-olymer, it has more than one type, +greater than + + align:start position:0% +greater than + + + align:start position:0% +greater than +one myrr + + align:start position:0% +one myrr + + + align:start position:0% +one myrr +type, greater than one myrr + + align:start position:0% +type, greater than one myrr + + + align:start position:0% +type, greater than one myrr +type. And so, for example, we could make + + align:start position:0% +type. And so, for example, we could make + + + align:start position:0% +type. And so, for example, we could make +a a co-olymer of say + + align:start position:0% +a a co-olymer of say + + + align:start position:0% +a a co-olymer of say +polyethylene with say polyvinyl + + align:start position:0% +polyethylene with say polyvinyl + + + align:start position:0% +polyethylene with say polyvinyl +chloride. Polyethylene and polyvinyl + + align:start position:0% +chloride. Polyethylene and polyvinyl + + + align:start position:0% +chloride. Polyethylene and polyvinyl +chloride. in this notation, this + + align:start position:0% +chloride. in this notation, this + + + align:start position:0% +chloride. in this notation, this +lowercase C with the hyphens on either + + align:start position:0% +lowercase C with the hyphens on either + + + align:start position:0% +lowercase C with the hyphens on either +side indicate that we're talking about a + + align:start position:0% +side indicate that we're talking about a + + + align:start position:0% +side indicate that we're talking about a +co-olymer of these two units. So, you + + align:start position:0% +co-olymer of these two units. So, you + + + align:start position:0% +co-olymer of these two units. So, you +know what you know what the parent unit + + align:start position:0% +know what you know what the parent unit + + + align:start position:0% +know what you know what the parent unit +is of ethylene. I've shown you that. And + + align:start position:0% +is of ethylene. I've shown you that. And + + + align:start position:0% +is of ethylene. I've shown you that. And +we saw last day if we + + align:start position:0% +we saw last day if we + + + align:start position:0% +we saw last day if we +took ethylene, dropped the hydrogen, + + align:start position:0% +took ethylene, dropped the hydrogen, + + + align:start position:0% +took ethylene, dropped the hydrogen, +this became the vinyl radical. And then + + align:start position:0% +this became the vinyl radical. And then + + + align:start position:0% +this became the vinyl radical. And then +if we put a chlorine here, this is vinyl + + align:start position:0% +if we put a chlorine here, this is vinyl + + + align:start position:0% +if we put a chlorine here, this is vinyl +chloride. It's got a double bond here. + + align:start position:0% +chloride. It's got a double bond here. + + + align:start position:0% +chloride. It's got a double bond here. +We can use the same uh polymerization + + align:start position:0% +We can use the same uh polymerization + + + align:start position:0% +We can use the same uh polymerization +technique propagate this by converting + + align:start position:0% +technique propagate this by converting + + + align:start position:0% +technique propagate this by converting +it to a single bond and now instead of + + align:start position:0% +it to a single bond and now instead of + + + align:start position:0% +it to a single bond and now instead of +vinyl chloride we will have the polymer + + align:start position:0% +vinyl chloride we will have the polymer + + + align:start position:0% +vinyl chloride we will have the polymer +polyvinyl chloride and if we had both + + align:start position:0% +polyvinyl chloride and if we had both + + + align:start position:0% +polyvinyl chloride and if we had both +vinyl chloride in the reactor and + + align:start position:0% +vinyl chloride in the reactor and + + + align:start position:0% +vinyl chloride in the reactor and +ethylene in the reactor we would be + + align:start position:0% +ethylene in the reactor we would be + + + align:start position:0% +ethylene in the reactor we would be +grabbing molecules of both types and + + align:start position:0% +grabbing molecules of both types and + + + align:start position:0% +grabbing molecules of both types and +attaching them. So as you move down the + + align:start position:0% +attaching them. So as you move down the + + + align:start position:0% +attaching them. So as you move down the +chain you might have uh ethylene unit, + + align:start position:0% +chain you might have uh ethylene unit, + + + align:start position:0% +chain you might have uh ethylene unit, +vinyl chloride unit, ethylene unit and + + align:start position:0% +vinyl chloride unit, ethylene unit and + + + align:start position:0% +vinyl chloride unit, ethylene unit and +so on. And Tom if we could go to the uh + + align:start position:0% +so on. And Tom if we could go to the uh + + + align:start position:0% +so on. And Tom if we could go to the uh +computer feed I can show some examples + + align:start position:0% +computer feed I can show some examples + + + align:start position:0% +computer feed I can show some examples +of different ways in which we can uh put + + align:start position:0% +of different ways in which we can uh put + + + align:start position:0% +of different ways in which we can uh put +these on the chain. So the first one + + align:start position:0% +these on the chain. So the first one + + + align:start position:0% +these on the chain. So the first one +this is taken right from your reading. + + align:start position:0% +this is taken right from your reading. + + + align:start position:0% +this is taken right from your reading. +The first one is called the random + + align:start position:0% +The first one is called the random + + + align:start position:0% +The first one is called the random +co-olymer where A and B represent + + align:start position:0% +co-olymer where A and B represent + + + align:start position:0% +co-olymer where A and B represent +different myr units. So A could be + + align:start position:0% +different myr units. So A could be + + + align:start position:0% +different myr units. So A could be +ethylene and B could be vinyl chloride. + + align:start position:0% +ethylene and B could be vinyl chloride. + + + align:start position:0% +ethylene and B could be vinyl chloride. +And here they're just random. You get + + align:start position:0% +And here they're just random. You get + + + align:start position:0% +And here they're just random. You get +some unit of of uh vinyl chloride then + + align:start position:0% +some unit of of uh vinyl chloride then + + + align:start position:0% +some unit of of uh vinyl chloride then +several units and so on. So that's and + + align:start position:0% +several units and so on. So that's and + + + align:start position:0% +several units and so on. So that's and +some people want this for a particular + + align:start position:0% +some people want this for a particular + + + align:start position:0% +some people want this for a particular +mechanical properties. So let's uh + + align:start position:0% +mechanical properties. So let's uh + + + align:start position:0% +mechanical properties. So let's uh +document these different types. So if we + + align:start position:0% +document these different types. So if we + + + align:start position:0% +document these different types. So if we +have a random + + align:start position:0% +have a random + + + align:start position:0% +have a random +arrangement if we have random + + align:start position:0% +arrangement if we have random + + + align:start position:0% +arrangement if we have random +arrangement of the of the myrr + + align:start position:0% + + + + align:start position:0% + +groups random + + align:start position:0% +groups random + + + align:start position:0% +groups random +arrangement of the myrr + + align:start position:0% +arrangement of the myrr + + + align:start position:0% +arrangement of the myrr +types random arrangement of myrr types + + align:start position:0% +types random arrangement of myrr types + + + align:start position:0% +types random arrangement of myrr types +we have what is called the random + + align:start position:0% +we have what is called the random + + + align:start position:0% +we have what is called the random +c-olymer so let's just use the same + + align:start position:0% +c-olymer so let's just use the same + + + align:start position:0% +c-olymer so let's just use the same +example this could be polyethylene + + align:start position:0% +example this could be polyethylene + + + align:start position:0% +example this could be polyethylene +lowercase rvc so that tells you it's a + + align:start position:0% +lowercase rvc so that tells you it's a + + + align:start position:0% +lowercase rvc so that tells you it's a +it's a random c-olymer the next one + + align:start position:0% +it's a random c-olymer the next one + + + align:start position:0% +it's a random c-olymer the next one +shows + + align:start position:0% +shows + + + align:start position:0% +shows +they're calling a regular co-olymer + + align:start position:0% +they're calling a regular co-olymer + + + align:start position:0% +they're calling a regular co-olymer +where you have + + align:start position:0% +where you have + + + align:start position:0% +where you have +alternating alternating so it's strict + + align:start position:0% +alternating alternating so it's strict + + + align:start position:0% +alternating alternating so it's strict +it's strict alternating arrangement of + + align:start position:0% +it's strict alternating arrangement of + + + align:start position:0% +it's strict alternating arrangement of +merr type so it moves from one to the + + align:start position:0% +merr type so it moves from one to the + + + align:start position:0% +merr type so it moves from one to the +other in alternating sequence and this + + align:start position:0% +other in alternating sequence and this + + + align:start position:0% +other in alternating sequence and this +is known + + align:start position:0% +is known + + + align:start position:0% +is known +as the uh + + align:start position:0% +as the uh + + + align:start position:0% +as the uh +alternating co-olymer to distinguish it + + align:start position:0% +alternating co-olymer to distinguish it + + + align:start position:0% +alternating co-olymer to distinguish it +you can't call it regular because r is + + align:start position:0% +you can't call it regular because r is + + + align:start position:0% +you can't call it regular because r is +already taken for the random co-olymer + + align:start position:0% +already taken for the random co-olymer + + + align:start position:0% +already taken for the random co-olymer +uh The third one is shown up here where + + align:start position:0% +uh The third one is shown up here where + + + align:start position:0% +uh The third one is shown up here where +we take and we we cluster the different + + align:start position:0% +we take and we we cluster the different + + + align:start position:0% +we take and we we cluster the different +mer types. So instead of having + + align:start position:0% +mer types. So instead of having + + + align:start position:0% +mer types. So instead of having +alternating one to the other, we take a + + align:start position:0% +alternating one to the other, we take a + + + align:start position:0% +alternating one to the other, we take a +run of one type of myrr and then a run + + align:start position:0% +run of one type of myrr and then a run + + + align:start position:0% +run of one type of myrr and then a run +of another type of myrr. So we cluster + + align:start position:0% +of another type of myrr. So we cluster + + + align:start position:0% +of another type of myrr. So we cluster +this + + align:start position:0% +this + + + align:start position:0% +this +is clustered arrangement of myrr types + + align:start position:0% +is clustered arrangement of myrr types + + + align:start position:0% +is clustered arrangement of myrr types +into what we call these clusters are + + align:start position:0% +into what we call these clusters are + + + align:start position:0% +into what we call these clusters are +called blocks. blocks of the same type + + align:start position:0% +called blocks. blocks of the same type + + + align:start position:0% +called blocks. blocks of the same type +of myrr and such a material is called a + + align:start position:0% +of myrr and such a material is called a + + + align:start position:0% +of myrr and such a material is called a +block c-olymer. A block copolymer and + + align:start position:0% +block c-olymer. A block copolymer and + + + align:start position:0% +block c-olymer. A block copolymer and +that's showing up here where you see uh + + align:start position:0% +that's showing up here where you see uh + + + align:start position:0% +that's showing up here where you see uh +there's what four units of A and then + + align:start position:0% +there's what four units of A and then + + + align:start position:0% +there's what four units of A and then +there's four units of B and then two + + align:start position:0% +there's four units of B and then two + + + align:start position:0% +there's four units of B and then two +units of A, four units of B. This is a + + align:start position:0% +units of A, four units of B. This is a + + + align:start position:0% +units of A, four units of B. This is a +little bit unrealistic. Typically + + align:start position:0% +little bit unrealistic. Typically + + + align:start position:0% +little bit unrealistic. Typically +commercial block copolymers are usually + + align:start position:0% +commercial block copolymers are usually + + + align:start position:0% +commercial block copolymers are usually +die blocks or trib blocks. They'll + + align:start position:0% +die blocks or trib blocks. They'll + + + align:start position:0% +die blocks or trib blocks. They'll +usually have if it were a die block of + + align:start position:0% +usually have if it were a die block of + + + align:start position:0% +usually have if it were a die block of +polyethylene, it would be one run of + + align:start position:0% +polyethylene, it would be one run of + + + align:start position:0% +polyethylene, it would be one run of +polyethylene and one run of polyvinyl + + align:start position:0% +polyethylene and one run of polyvinyl + + + align:start position:0% +polyethylene and one run of polyvinyl +chloride and that's it. You don't you + + align:start position:0% +chloride and that's it. You don't you + + + align:start position:0% +chloride and that's it. You don't you +don't do this sort of thing, but the + + align:start position:0% +don't do this sort of thing, but the + + + align:start position:0% +don't do this sort of thing, but the +artist got carried away and somebody + + align:start position:0% +artist got carried away and somebody + + + align:start position:0% +artist got carried away and somebody +didn't proofread. So So there it is. And + + align:start position:0% +didn't proofread. So So there it is. And + + + align:start position:0% +didn't proofread. So So there it is. And +the last thing you can do is the one on + + align:start position:0% +the last thing you can do is the one on + + + align:start position:0% +the last thing you can do is the one on +the bottom which is called the graft. + + align:start position:0% +the bottom which is called the graft. + + + align:start position:0% +the bottom which is called the graft. +The graft is sort of a a type. It's a + + align:start position:0% +The graft is sort of a a type. It's a + + + align:start position:0% +The graft is sort of a a type. It's a +type of a block copolymer where what you + + align:start position:0% +type of a block copolymer where what you + + + align:start position:0% +type of a block copolymer where what you +have is you have graft + + align:start position:0% +have is you have graft + + + align:start position:0% +have is you have graft +of one merr + + align:start position:0% +of one merr + + + align:start position:0% +of one merr +type in the form of a side + + align:start position:0% + + + + align:start position:0% + +chain onto uh another mer type of + + align:start position:0% +chain onto uh another mer type of + + + align:start position:0% +chain onto uh another mer type of +backbone another mer type for the + + align:start position:0% +backbone another mer type for the + + + align:start position:0% +backbone another mer type for the +backbone. So you cluster them, but you + + align:start position:0% +backbone. So you cluster them, but you + + + align:start position:0% +backbone. So you cluster them, but you +cluster them very deliberately in this + + align:start position:0% +cluster them very deliberately in this + + + align:start position:0% +cluster them very deliberately in this +manner. And that's shown in the in the + + align:start position:0% +manner. And that's shown in the in the + + + align:start position:0% +manner. And that's shown in the in the +bottom one. So the backbone is all A's + + align:start position:0% +bottom one. So the backbone is all A's + + + align:start position:0% +bottom one. So the backbone is all A's +and the side chain is all B's. And + + align:start position:0% +and the side chain is all B's. And + + + align:start position:0% +and the side chain is all B's. And +here's one. Some of you are going to be + + align:start position:0% +here's one. Some of you are going to be + + + align:start position:0% +here's one. Some of you are going to be +doing some traveling. So I've I've put + + align:start position:0% +doing some traveling. So I've I've put + + + align:start position:0% +doing some traveling. So I've I've put +up a very common one. This is uh ABS uh + + align:start position:0% +up a very common one. This is uh ABS uh + + + align:start position:0% +up a very common one. This is uh ABS uh +acryin nitrial butadine styrene. So + + align:start position:0% +acryin nitrial butadine styrene. So + + + align:start position:0% +acryin nitrial butadine styrene. So +you've seen butadine. We saw that last + + align:start position:0% +you've seen butadine. We saw that last + + + align:start position:0% +you've seen butadine. We saw that last +day. Styrene. What what what this is the + + align:start position:0% +day. Styrene. What what what this is the + + + align:start position:0% +day. Styrene. What what what this is the +the backbone is all uh butadine and then + + align:start position:0% +the backbone is all uh butadine and then + + + align:start position:0% +the backbone is all uh butadine and then +the side chains are alternately um + + align:start position:0% +the side chains are alternately um + + + align:start position:0% +the side chains are alternately um +acryin nitral and styrene and this is + + align:start position:0% +acryin nitral and styrene and this is + + + align:start position:0% +acryin nitral and styrene and this is +what's used for hard-sided luggage and + + align:start position:0% +what's used for hard-sided luggage and + + + align:start position:0% +what's used for hard-sided luggage and +also this all these old telephones are + + align:start position:0% +also this all these old telephones are + + + align:start position:0% +also this all these old telephones are +made of this uh graft copolymer and by + + align:start position:0% +made of this uh graft copolymer and by + + + align:start position:0% +made of this uh graft copolymer and by +playing with the the nature of these + + align:start position:0% +playing with the the nature of these + + + align:start position:0% +playing with the the nature of these +side chains we can obviously make this + + align:start position:0% +side chains we can obviously make this + + + align:start position:0% +side chains we can obviously make this +so that it's somewhat flexible or we can + + align:start position:0% +so that it's somewhat flexible or we can + + + align:start position:0% +so that it's somewhat flexible or we can +make it so that it's rather rigid. So + + align:start position:0% +make it so that it's rather rigid. So + + + align:start position:0% +make it so that it's rather rigid. So +again examples of of architecture at the + + align:start position:0% +again examples of of architecture at the + + + align:start position:0% +again examples of of architecture at the +at the local level uh dictating uh + + align:start position:0% + + + + align:start position:0% + +properties. So we have these uh examples + + align:start position:0% +properties. So we have these uh examples + + + align:start position:0% +properties. So we have these uh examples +of how we can tailor the properties. The + + align:start position:0% +of how we can tailor the properties. The + + + align:start position:0% +of how we can tailor the properties. The +second thing is the configurations of + + align:start position:0% +second thing is the configurations of + + + align:start position:0% +second thing is the configurations of +the side groups. + + align:start position:0% +the side groups. + + + align:start position:0% +the side groups. +side group + + align:start position:0% + + + + align:start position:0% + +configuration. These are all options + + align:start position:0% +configuration. These are all options + + + align:start position:0% +configuration. These are all options +that we have and we exercise them in the + + align:start position:0% +that we have and we exercise them in the + + + align:start position:0% +that we have and we exercise them in the +synthesis by playing with the synthesis + + align:start position:0% +synthesis by playing with the synthesis + + + align:start position:0% +synthesis by playing with the synthesis +conditions and also the catalysts that + + align:start position:0% +conditions and also the catalysts that + + + align:start position:0% +conditions and also the catalysts that +are present and that's shown here. + + align:start position:0% +are present and that's shown here. + + + align:start position:0% +are present and that's shown here. +There's basically three ways you can put + + align:start position:0% +There's basically three ways you can put + + + align:start position:0% +There's basically three ways you can put +the side groups on. So the the upper one + + align:start position:0% +the side groups on. So the the upper one + + + align:start position:0% +the side groups on. So the the upper one +the upper one shows the the methyl group + + align:start position:0% +the upper one shows the the methyl group + + + align:start position:0% +the upper one shows the the methyl group +uh randomly going. Sometimes it's above, + + align:start position:0% +uh randomly going. Sometimes it's above, + + + align:start position:0% +uh randomly going. Sometimes it's above, +sometimes it's below and there seems to + + align:start position:0% +sometimes it's below and there seems to + + + align:start position:0% +sometimes it's below and there seems to +be no pattern. This whole uh notion of + + align:start position:0% +be no pattern. This whole uh notion of + + + align:start position:0% +be no pattern. This whole uh notion of +side group configuration is referred to + + align:start position:0% +side group configuration is referred to + + + align:start position:0% +side group configuration is referred to +as + + align:start position:0% +as + + + align:start position:0% +as +tacticity. Tacticity it means the + + align:start position:0% +tacticity. Tacticity it means the + + + align:start position:0% +tacticity. Tacticity it means the +placement of the side groups. So you I + + align:start position:0% +placement of the side groups. So you I + + + align:start position:0% +placement of the side groups. So you I +mean there's only three choices here. + + align:start position:0% +mean there's only three choices here. + + + align:start position:0% +mean there's only three choices here. +Either you put them all on the same side + + align:start position:0% +Either you put them all on the same side + + + align:start position:0% +Either you put them all on the same side +of the chain that's the bottom one + + align:start position:0% +of the chain that's the bottom one + + + align:start position:0% +of the chain that's the bottom one +isotactic or you put them on alternate. + + align:start position:0% +isotactic or you put them on alternate. + + + align:start position:0% +isotactic or you put them on alternate. +Once it's on one side of the chain then + + align:start position:0% +Once it's on one side of the chain then + + + align:start position:0% +Once it's on one side of the chain then +it's on the other side of the chain. So + + align:start position:0% +it's on the other side of the chain. So + + + align:start position:0% +it's on the other side of the chain. So +you alternate back and forth with + + align:start position:0% +you alternate back and forth with + + + align:start position:0% +you alternate back and forth with +regularity. That's synotactic. And then + + align:start position:0% +regularity. That's synotactic. And then + + + align:start position:0% +regularity. That's synotactic. And then +the third case is come what may there's + + align:start position:0% +the third case is come what may there's + + + align:start position:0% +the third case is come what may there's +no no uh seeming uh plan and that's the + + align:start position:0% +no no uh seeming uh plan and that's the + + + align:start position:0% +no no uh seeming uh plan and that's the +A tactic. So those are the those are the + + align:start position:0% +A tactic. So those are the those are the + + + align:start position:0% +A tactic. So those are the those are the +three types that you need to + + align:start position:0% +three types that you need to + + + align:start position:0% +three types that you need to +be aware of. + + align:start position:0% +be aware of. + + + align:start position:0% +be aware of. +Isotactic, + + align:start position:0% + + + + align:start position:0% + +synotactic and + + align:start position:0% +synotactic and + + + align:start position:0% +synotactic and +atactic. We can figure those out. ISO + + align:start position:0% +atactic. We can figure those out. ISO + + + align:start position:0% +atactic. We can figure those out. ISO +obviously means they're all on the same + + align:start position:0% +obviously means they're all on the same + + + align:start position:0% +obviously means they're all on the same +side of the + + align:start position:0% +side of the + + + align:start position:0% +side of the +chain. A tactic is as amoral apolitical. + + align:start position:0% +chain. A tactic is as amoral apolitical. + + + align:start position:0% +chain. A tactic is as amoral apolitical. +So this is random and then by + + align:start position:0% +So this is random and then by + + + align:start position:0% +So this is random and then by +elimination this must be + + align:start position:0% + + + + align:start position:0% + +alternating alternating and I think I've + + align:start position:0% +alternating alternating and I think I've + + + align:start position:0% +alternating alternating and I think I've +I think on the next one I did a little + + align:start position:0% +I think on the next one I did a little + + + align:start position:0% +I think on the next one I did a little +doodling for you. Yeah. So here just to + + align:start position:0% +doodling for you. Yeah. So here just to + + + align:start position:0% +doodling for you. Yeah. So here just to +bring home what's going on the first one + + align:start position:0% +bring home what's going on the first one + + + align:start position:0% +bring home what's going on the first one +the top is atactic polyropylene. So you + + align:start position:0% +the top is atactic polyropylene. So you + + + align:start position:0% +the top is atactic polyropylene. So you +see uh there's the there's propyline and + + align:start position:0% +see uh there's the there's propyline and + + + align:start position:0% +see uh there's the there's propyline and +what what's happened is this double bond + + align:start position:0% +what what's happened is this double bond + + + align:start position:0% +what what's happened is this double bond +has been broken and now it can propagate + + align:start position:0% +has been broken and now it can propagate + + + align:start position:0% +has been broken and now it can propagate +and this methyl group in some cases is + + align:start position:0% +and this methyl group in some cases is + + + align:start position:0% +and this methyl group in some cases is +above in some cases below the chain. + + align:start position:0% +above in some cases below the chain. + + + align:start position:0% +above in some cases below the chain. +Here's uh polystyrene. This is vinyl + + align:start position:0% +Here's uh polystyrene. This is vinyl + + + align:start position:0% +Here's uh polystyrene. This is vinyl +benzene or phenyl u ethne or styrene and + + align:start position:0% +benzene or phenyl u ethne or styrene and + + + align:start position:0% +benzene or phenyl u ethne or styrene and +this double bond is broken and you got + + align:start position:0% +this double bond is broken and you got + + + align:start position:0% +this double bond is broken and you got +these phenal groups hanging off the side + + align:start position:0% +these phenal groups hanging off the side + + + align:start position:0% +these phenal groups hanging off the side +and this is just vinyl chloride which we + + align:start position:0% +and this is just vinyl chloride which we + + + align:start position:0% +and this is just vinyl chloride which we +saw over here. So again seeing how the + + align:start position:0% +saw over here. So again seeing how the + + + align:start position:0% +saw over here. So again seeing how the +the synthesis okay and then the last + + align:start position:0% +the synthesis okay and then the last + + + align:start position:0% +the synthesis okay and then the last +thing we can look at is is the backbone + + align:start position:0% +thing we can look at is is the backbone + + + align:start position:0% +thing we can look at is is the backbone +is backbone + + align:start position:0% +is backbone + + + align:start position:0% +is backbone +architecture or chain + + align:start position:0% +architecture or chain + + + align:start position:0% +architecture or chain +architecture chain here referring to the + + align:start position:0% +architecture chain here referring to the + + + align:start position:0% +architecture chain here referring to the +main + + align:start position:0% + + + + align:start position:0% + +chain chain + + align:start position:0% +chain chain + + + align:start position:0% +chain chain +architecture and this uh falls under the + + align:start position:0% +architecture and this uh falls under the + + + align:start position:0% +architecture and this uh falls under the +the general term of conformality. + + align:start position:0% +the general term of conformality. + + + align:start position:0% +the general term of conformality. +conformality and we're going to revisit + + align:start position:0% +conformality and we're going to revisit + + + align:start position:0% +conformality and we're going to revisit +this when we talk about uh proteins. + + align:start position:0% +this when we talk about uh proteins. + + + align:start position:0% +this when we talk about uh proteins. +It's very important in biological + + align:start position:0% +It's very important in biological + + + align:start position:0% +It's very important in biological +systems and it it it's a direct result + + align:start position:0% +systems and it it it's a direct result + + + align:start position:0% +systems and it it it's a direct result +of this which I showed you last day that + + align:start position:0% +of this which I showed you last day that + + + align:start position:0% +of this which I showed you last day that +the this bond is free to rotate and if + + align:start position:0% +the this bond is free to rotate and if + + + align:start position:0% +the this bond is free to rotate and if +it rotates in certain uh ways so that + + align:start position:0% +it rotates in certain uh ways so that + + + align:start position:0% +it rotates in certain uh ways so that +all of the uh side groups line up + + align:start position:0% +all of the uh side groups line up + + + align:start position:0% +all of the uh side groups line up +perfectly you end up with this so-called + + align:start position:0% +perfectly you end up with this so-called + + + align:start position:0% +perfectly you end up with this so-called +eclipsed version. So if you look at the + + align:start position:0% +eclipsed version. So if you look at the + + + align:start position:0% +eclipsed version. So if you look at the +chain on the very end, you'd see one dot + + align:start position:0% +chain on the very end, you'd see one dot + + + align:start position:0% +chain on the very end, you'd see one dot +that represents the backbone or actually + + align:start position:0% +that represents the backbone or actually + + + align:start position:0% +that represents the backbone or actually +it's zigzagging. So you'd see the the + + align:start position:0% +it's zigzagging. So you'd see the the + + + align:start position:0% +it's zigzagging. So you'd see the the +the edge of the zigzag and then all of + + align:start position:0% +the edge of the zigzag and then all of + + + align:start position:0% +the edge of the zigzag and then all of +the pendant groups would be lined up in + + align:start position:0% +the pendant groups would be lined up in + + + align:start position:0% +the pendant groups would be lined up in +front of one another and you'd see + + align:start position:0% +front of one another and you'd see + + + align:start position:0% +front of one another and you'd see +nothing except the very first one. + + align:start position:0% +nothing except the very first one. + + + align:start position:0% +nothing except the very first one. +That's the eclipsed and that's the most + + align:start position:0% +That's the eclipsed and that's the most + + + align:start position:0% +That's the eclipsed and that's the most +regular straight line. And this is + + align:start position:0% +regular straight line. And this is + + + align:start position:0% +regular straight line. And this is +staggered where it uh it rotates where + + align:start position:0% +staggered where it uh it rotates where + + + align:start position:0% +staggered where it uh it rotates where +it wishes. And I showed you this one + + align:start position:0% +it wishes. And I showed you this one + + + align:start position:0% +it wishes. And I showed you this one +where this is this is hardly something + + align:start position:0% +where this is this is hardly something + + + align:start position:0% +where this is this is hardly something +with a polymerization index of 3600. But + + align:start position:0% +with a polymerization index of 3600. But + + + align:start position:0% +with a polymerization index of 3600. But +it starts giving you the sense of some + + align:start position:0% +it starts giving you the sense of some + + + align:start position:0% +it starts giving you the sense of some +are more nearly straight and some are + + align:start position:0% +are more nearly straight and some are + + + align:start position:0% +are more nearly straight and some are +very uh heavily coiled. Both of these + + align:start position:0% +very uh heavily coiled. Both of these + + + align:start position:0% +very uh heavily coiled. Both of these +are still called straight chains. Both + + align:start position:0% +are still called straight chains. Both + + + align:start position:0% +are still called straight chains. Both +of these are still called straight + + align:start position:0% +of these are still called straight + + + align:start position:0% +of these are still called straight +chains but there are some things that we + + align:start position:0% +chains but there are some things that we + + + align:start position:0% +chains but there are some things that we +can look at. So first we have the linear + + align:start position:0% +can look at. So first we have the linear + + + align:start position:0% +can look at. So first we have the linear +one. the + + align:start position:0% + + + + align:start position:0% + +linear the linear chain molecule. + + align:start position:0% +linear the linear chain molecule. + + + align:start position:0% +linear the linear chain molecule. +And so that's one. All right. And + + align:start position:0% +And so that's one. All right. And + + + align:start position:0% +And so that's one. All right. And +furthermore, if you look here, there's + + align:start position:0% +furthermore, if you look here, there's + + + align:start position:0% +furthermore, if you look here, there's +some fine structure. You may even see + + align:start position:0% +some fine structure. You may even see + + + align:start position:0% +some fine structure. You may even see +that at some point along here, there's + + align:start position:0% +that at some point along here, there's + + + align:start position:0% +that at some point along here, there's +even uh some attempt at uh + + align:start position:0% +even uh some attempt at uh + + + align:start position:0% +even uh some attempt at uh +crystallization. But even so, the the + + align:start position:0% +crystallization. But even so, the the + + + align:start position:0% +crystallization. But even so, the the +system moves in one direction from one + + align:start position:0% +system moves in one direction from one + + + align:start position:0% +system moves in one direction from one +end to another. The alternative is + + align:start position:0% +end to another. The alternative is + + + align:start position:0% +end to another. The alternative is +branched + + align:start position:0% +branched + + + align:start position:0% +branched +chain. Branched + + align:start position:0% +chain. Branched + + + align:start position:0% +chain. Branched +chain. It's a different type of + + align:start position:0% +chain. It's a different type of + + + align:start position:0% +chain. It's a different type of +architecture. And in that case, you + + align:start position:0% +architecture. And in that case, you + + + align:start position:0% +architecture. And in that case, you +actually have something + + align:start position:0% +actually have something + + + align:start position:0% +actually have something +that so this is not graph. This is + + align:start position:0% +that so this is not graph. This is + + + align:start position:0% +that so this is not graph. This is +actually the the main uh component of + + align:start position:0% +actually the the main uh component of + + + align:start position:0% +actually the the main uh component of +the backbone continuing to grow but + + align:start position:0% +the backbone continuing to grow but + + + align:start position:0% +the backbone continuing to grow but +growing in a plurality of paths. So you + + align:start position:0% +growing in a plurality of paths. So you + + + align:start position:0% +growing in a plurality of paths. So you +can imagine that one of these is going + + align:start position:0% +can imagine that one of these is going + + + align:start position:0% +can imagine that one of these is going +to pack much better than the other. One + + align:start position:0% +to pack much better than the other. One + + + align:start position:0% +to pack much better than the other. One +is going to have a greater chance of + + align:start position:0% +is going to have a greater chance of + + + align:start position:0% +is going to have a greater chance of +forming such zones of crystallinity and + + align:start position:0% +forming such zones of crystallinity and + + + align:start position:0% +forming such zones of crystallinity and +clearly it's going to be the linear + + align:start position:0% +clearly it's going to be the linear + + + align:start position:0% +clearly it's going to be the linear +chain. These branches stick out and they + + align:start position:0% +chain. These branches stick out and they + + + align:start position:0% +chain. These branches stick out and they +prevent tight packing. They prevent + + align:start position:0% +prevent tight packing. They prevent + + + align:start position:0% +prevent tight packing. They prevent +tight packing. So the branch chain is + + align:start position:0% +tight packing. So the branch chain is + + + align:start position:0% +tight packing. So the branch chain is +harder to crystallize. + + align:start position:0% +harder to crystallize. + + + align:start position:0% +harder to crystallize. +harder to crystallize and when it forms + + align:start position:0% +harder to crystallize and when it forms + + + align:start position:0% +harder to crystallize and when it forms +its amorphous structures it has more + + align:start position:0% +its amorphous structures it has more + + + align:start position:0% +its amorphous structures it has more +free + + align:start position:0% + + + + align:start position:0% + +volume more free volume and also you can + + align:start position:0% +volume more free volume and also you can + + + align:start position:0% +volume more free volume and also you can +think about the glass transition + + align:start position:0% +think about the glass transition + + + align:start position:0% +think about the glass transition +temperature Tg how is that going to work + + align:start position:0% +temperature Tg how is that going to work + + + align:start position:0% +temperature Tg how is that going to work +so on so by looking at the the branching + + align:start position:0% +so on so by looking at the the branching + + + align:start position:0% +so on so by looking at the the branching +you end up with such structures there's + + align:start position:0% +you end up with such structures there's + + + align:start position:0% +you end up with such structures there's +one other one and that's shown + + align:start position:0% +one other one and that's shown + + + align:start position:0% +one other one and that's shown +here and that's to + + align:start position:0% +here and that's to + + + align:start position:0% +here and that's to +take several chains whether they're + + align:start position:0% +take several chains whether they're + + + align:start position:0% +take several chains whether they're +linear or branched. I'm just going to + + align:start position:0% +linear or branched. I'm just going to + + + align:start position:0% +linear or branched. I'm just going to +draw several straight chains here. And + + align:start position:0% +draw several straight chains here. And + + + align:start position:0% +draw several straight chains here. And +it's possible to link + + align:start position:0% +it's possible to link + + + align:start position:0% +it's possible to link +chains by joining them with some + + align:start position:0% +chains by joining them with some + + + align:start position:0% +chains by joining them with some +covealent + + align:start position:0% +covealent + + + align:start position:0% +covealent +bridges. Covealent bridges. This is a + + align:start position:0% +bridges. Covealent bridges. This is a + + + align:start position:0% +bridges. Covealent bridges. This is a +covealent bridge. This is a covealent + + align:start position:0% +covealent bridge. This is a covealent + + + align:start position:0% +covealent bridge. This is a covealent +bridge. And it actually links one chain + + align:start position:0% +bridge. And it actually links one chain + + + align:start position:0% +bridge. And it actually links one chain +to another. + + align:start position:0% +to another. + + + align:start position:0% +to another. +And imagine the mechanical properties of + + align:start position:0% +And imagine the mechanical properties of + + + align:start position:0% +And imagine the mechanical properties of +this material. The otherwise there would + + align:start position:0% +this material. The otherwise there would + + + align:start position:0% +this material. The otherwise there would +be weak Vanderval's bonds and if we + + align:start position:0% +be weak Vanderval's bonds and if we + + + align:start position:0% +be weak Vanderval's bonds and if we +apply a sheer stress we can cause the + + align:start position:0% +apply a sheer stress we can cause the + + + align:start position:0% +apply a sheer stress we can cause the +material to plastically deform. But + + align:start position:0% +material to plastically deform. But + + + align:start position:0% +material to plastically deform. But +these are strong covealent bonds. So + + align:start position:0% +these are strong covealent bonds. So + + + align:start position:0% +these are strong covealent bonds. So +what will happen is I can move this + + align:start position:0% +what will happen is I can move this + + + align:start position:0% +what will happen is I can move this +material shear it up to a point but then + + align:start position:0% +material shear it up to a point but then + + + align:start position:0% +material shear it up to a point but then +I encounter the resistance of these + + align:start position:0% +I encounter the resistance of these + + + align:start position:0% +I encounter the resistance of these +bonds and as soon as I let go of the + + align:start position:0% +bonds and as soon as I let go of the + + + align:start position:0% +bonds and as soon as I let go of the +applied force it springs back. So by + + align:start position:0% +applied force it springs back. So by + + + align:start position:0% +applied force it springs back. So by +cross-linking by cross-linking this is a + + align:start position:0% +cross-linking by cross-linking this is a + + + align:start position:0% +cross-linking by cross-linking this is a +cross- linked architecture. By + + align:start position:0% +cross- linked architecture. By + + + align:start position:0% +cross- linked architecture. By +cross-linking + + align:start position:0% +cross-linking + + + align:start position:0% +cross-linking +I impart some uh uh elasticity and this + + align:start position:0% +I impart some uh uh elasticity and this + + + align:start position:0% +I impart some uh uh elasticity and this +is the in fact the structure of a rubber + + align:start position:0% +is the in fact the structure of a rubber + + + align:start position:0% +is the in fact the structure of a rubber +and we call such polymers + + align:start position:0% +and we call such polymers + + + align:start position:0% +and we call such polymers +elastors elastors because they will they + + align:start position:0% +elastors elastors because they will they + + + align:start position:0% +elastors elastors because they will they +will spring back to shape and uh what + + align:start position:0% +will spring back to shape and uh what + + + align:start position:0% +will spring back to shape and uh what +would have to happen here in order to + + align:start position:0% +would have to happen here in order to + + + align:start position:0% +would have to happen here in order to +allow for the cross links we have to be + + align:start position:0% +allow for the cross links we have to be + + + align:start position:0% +allow for the cross links we have to be +able to form covealent bonds if we're + + align:start position:0% +able to form covealent bonds if we're + + + align:start position:0% +able to form covealent bonds if we're +going to form covealent bonds we have to + + align:start position:0% +going to form covealent bonds we have to + + + align:start position:0% +going to form covealent bonds we have to +break some bonds that are present in the + + align:start position:0% +break some bonds that are present in the + + + align:start position:0% +break some bonds that are present in the +backbone. So if I've got a if I've got + + align:start position:0% +backbone. So if I've got a if I've got + + + align:start position:0% +backbone. So if I've got a if I've got +bonds such as this in the backbone and + + align:start position:0% +bonds such as this in the backbone and + + + align:start position:0% +bonds such as this in the backbone and +then I come up with this R group that + + align:start position:0% +then I come up with this R group that + + + align:start position:0% +then I come up with this R group that +wants to somehow attach, it's pretty + + align:start position:0% +wants to somehow attach, it's pretty + + + align:start position:0% +wants to somehow attach, it's pretty +clear that if I break one of these bonds + + align:start position:0% +clear that if I break one of these bonds + + + align:start position:0% +clear that if I break one of these bonds +in order to make the attachment, I cut + + align:start position:0% +in order to make the attachment, I cut + + + align:start position:0% +in order to make the attachment, I cut +the chain. So by it's axiomatic then if + + align:start position:0% +the chain. So by it's axiomatic then if + + + align:start position:0% +the chain. So by it's axiomatic then if +I'm going to form cross lengths I need + + align:start position:0% +I'm going to form cross lengths I need + + + align:start position:0% +I'm going to form cross lengths I need +to find a position along the backbone + + align:start position:0% +to find a position along the backbone + + + align:start position:0% +to find a position along the backbone +that has a double bond thereby I can + + align:start position:0% +that has a double bond thereby I can + + + align:start position:0% +that has a double bond thereby I can +break the double bond convert it to a + + align:start position:0% +break the double bond convert it to a + + + align:start position:0% +break the double bond convert it to a +single bond link up with the + + align:start position:0% +single bond link up with the + + + align:start position:0% +single bond link up with the +cross-linking bridge and keep the + + align:start position:0% +cross-linking bridge and keep the + + + align:start position:0% +cross-linking bridge and keep the +integrity of the backbone while forming + + align:start position:0% +integrity of the backbone while forming + + + align:start position:0% +integrity of the backbone while forming +a new bond to an adjacent uh chain. So + + align:start position:0% +a new bond to an adjacent uh chain. So + + + align:start position:0% +a new bond to an adjacent uh chain. So +this is the this is the condition for + + align:start position:0% +this is the this is the condition for + + + align:start position:0% +this is the this is the condition for +which we form elastimemers and uh this + + align:start position:0% +which we form elastimemers and uh this + + + align:start position:0% +which we form elastimemers and uh this +is the basis for rubber. This is the + + align:start position:0% +is the basis for rubber. This is the + + + align:start position:0% +is the basis for rubber. This is the +basis for rubber and I think this next + + align:start position:0% +basis for rubber and I think this next + + + align:start position:0% +basis for rubber and I think this next +cartoon shows that uh here's a here's + + align:start position:0% +cartoon shows that uh here's a here's + + + align:start position:0% +cartoon shows that uh here's a here's +polyisoprne and you can see there's a + + align:start position:0% +polyisoprne and you can see there's a + + + align:start position:0% +polyisoprne and you can see there's a +double bond in the backbone and by + + align:start position:0% +double bond in the backbone and by + + + align:start position:0% +double bond in the backbone and by +presenting sulfur sulfur is capable as + + align:start position:0% +presenting sulfur sulfur is capable as + + + align:start position:0% +presenting sulfur sulfur is capable as +is oxygen of forming bridges. We saw in + + align:start position:0% +is oxygen of forming bridges. We saw in + + + align:start position:0% +is oxygen of forming bridges. We saw in +the silicates in the borates how the + + align:start position:0% +the silicates in the borates how the + + + align:start position:0% +the silicates in the borates how the +oxygen forms covealent bonds on either + + align:start position:0% +oxygen forms covealent bonds on either + + + align:start position:0% +oxygen forms covealent bonds on either +side thereby linking silicate units. + + align:start position:0% +side thereby linking silicate units. + + + align:start position:0% +side thereby linking silicate units. +Well sulfur is below oxygen if we + + align:start position:0% +Well sulfur is below oxygen if we + + + align:start position:0% +Well sulfur is below oxygen if we +believe men of it should have similar + + align:start position:0% +believe men of it should have similar + + + align:start position:0% +believe men of it should have similar +properties and so sulfur is forming + + align:start position:0% +properties and so sulfur is forming + + + align:start position:0% +properties and so sulfur is forming +bridging structures breaking these + + align:start position:0% +bridging structures breaking these + + + align:start position:0% +bridging structures breaking these +double bonds and now linking the one + + align:start position:0% +double bonds and now linking the one + + + align:start position:0% +double bonds and now linking the one +orange backbone with the adjacent orange + + align:start position:0% +orange backbone with the adjacent orange + + + align:start position:0% +orange backbone with the adjacent orange +backbone. So sulfur enables + + align:start position:0% +backbone. So sulfur enables + + + align:start position:0% +backbone. So sulfur enables +cross-linking and this in fact was + + align:start position:0% +cross-linking and this in fact was + + + align:start position:0% +cross-linking and this in fact was +discovered here in Boston. It was uh + + align:start position:0% +discovered here in Boston. It was uh + + + align:start position:0% +discovered here in Boston. It was uh +Nathaniel um Hawthorne who was working + + align:start position:0% +Nathaniel um Hawthorne who was working + + + align:start position:0% +Nathaniel um Hawthorne who was working +in Roxbury and was trying to stabilize + + align:start position:0% +in Roxbury and was trying to stabilize + + + align:start position:0% +in Roxbury and was trying to stabilize +rubber. Natural rubber is very sticky. + + align:start position:0% +rubber. Natural rubber is very sticky. + + + align:start position:0% +rubber. Natural rubber is very sticky. +And so he found that by adding sulfur he + + align:start position:0% +And so he found that by adding sulfur he + + + align:start position:0% +And so he found that by adding sulfur he +could cause the the rubber to lose its + + align:start position:0% +could cause the the rubber to lose its + + + align:start position:0% +could cause the the rubber to lose its +stickiness and thereby uh develop a + + align:start position:0% +stickiness and thereby uh develop a + + + align:start position:0% +stickiness and thereby uh develop a +synthetic rubber that had superior + + align:start position:0% +synthetic rubber that had superior + + + align:start position:0% +synthetic rubber that had superior +properties. And then it was Charles + + align:start position:0% +properties. And then it was Charles + + + align:start position:0% +properties. And then it was Charles +Goodyear who came to Boston, saw this, + + align:start position:0% +Goodyear who came to Boston, saw this, + + + align:start position:0% +Goodyear who came to Boston, saw this, +took the invention, licensed it, and it + + align:start position:0% +took the invention, licensed it, and it + + + align:start position:0% +took the invention, licensed it, and it +was Goodyear who accidentally spilled + + align:start position:0% +was Goodyear who accidentally spilled + + + align:start position:0% +was Goodyear who accidentally spilled +some of um this cross- linked rubber + + align:start position:0% +some of um this cross- linked rubber + + + align:start position:0% +some of um this cross- linked rubber +onto a hot stove. And the uh the thermal + + align:start position:0% +onto a hot stove. And the uh the thermal + + + align:start position:0% +onto a hot stove. And the uh the thermal +treatment gave a far superior rubber + + align:start position:0% +treatment gave a far superior rubber + + + align:start position:0% +treatment gave a far superior rubber +which gave birth to vulcanization. And + + align:start position:0% +which gave birth to vulcanization. And + + + align:start position:0% +which gave birth to vulcanization. And +then from there, it's all history of uh + + align:start position:0% +then from there, it's all history of uh + + + align:start position:0% +then from there, it's all history of uh +automobile tires and and whatnot. So + + align:start position:0% +automobile tires and and whatnot. So + + + align:start position:0% +automobile tires and and whatnot. So +this is advantageous from a property + + align:start position:0% +this is advantageous from a property + + + align:start position:0% +this is advantageous from a property +standpoint, but it's very + + align:start position:0% +standpoint, but it's very + + + align:start position:0% +standpoint, but it's very +disadvantageous from the standpoint of + + align:start position:0% +disadvantageous from the standpoint of + + + align:start position:0% +disadvantageous from the standpoint of +recycling. How could one possibly + + align:start position:0% +recycling. How could one possibly + + + align:start position:0% +recycling. How could one possibly +recycle this material? Let's compare + + align:start position:0% +recycle this material? Let's compare + + + align:start position:0% +recycle this material? Let's compare +these two. Let's compare the case of + + align:start position:0% +these two. Let's compare the case of + + + align:start position:0% +these two. Let's compare the case of +polyethylene. So polyethylene consists + + align:start position:0% +polyethylene. So polyethylene consists + + + align:start position:0% +polyethylene. So polyethylene consists +of many chains and they will + + align:start position:0% +of many chains and they will + + + align:start position:0% +of many chains and they will +interpenetrate and entangle. What are + + align:start position:0% +interpenetrate and entangle. What are + + + align:start position:0% +interpenetrate and entangle. What are +the bonds between these chains? The + + align:start position:0% +the bonds between these chains? The + + + align:start position:0% +the bonds between these chains? The +bonds between these chains are + + align:start position:0% +bonds between these chains are + + + align:start position:0% +bonds between these chains are +Vanderval's. This is a Vanderval solid. + + align:start position:0% +Vanderval's. This is a Vanderval solid. + + + align:start position:0% +Vanderval's. This is a Vanderval solid. +These are Vanderval's bonds. And we know + + align:start position:0% +These are Vanderval's bonds. And we know + + + align:start position:0% +These are Vanderval's bonds. And we know +Vanderval's bonds are operative at low + + align:start position:0% +Vanderval's bonds are operative at low + + + align:start position:0% +Vanderval's bonds are operative at low +temperatures but not operative at high + + align:start position:0% +temperatures but not operative at high + + + align:start position:0% +temperatures but not operative at high +temperatures. So if we take polyethylene + + align:start position:0% +temperatures. So if we take polyethylene + + + align:start position:0% +temperatures. So if we take polyethylene +and heat it, these bonds will weaken and + + align:start position:0% +and heat it, these bonds will weaken and + + + align:start position:0% +and heat it, these bonds will weaken and +this will turn liquid. And we can + + align:start position:0% +this will turn liquid. And we can + + + align:start position:0% +this will turn liquid. And we can +reprocess this. So + + align:start position:0% +reprocess this. So + + + align:start position:0% +reprocess this. So +by going to high temperature we can + + align:start position:0% +by going to high temperature we can + + + align:start position:0% +by going to high temperature we can +reprocess because we're only breaking + + align:start position:0% +reprocess because we're only breaking + + + align:start position:0% +reprocess because we're only breaking +these weak Vanderval's bonds. Now if we + + align:start position:0% +these weak Vanderval's bonds. Now if we + + + align:start position:0% +these weak Vanderval's bonds. Now if we +take this cross- + + align:start position:0% + + + + align:start position:0% + +linked cross-l + + align:start position:0% +linked cross-l + + + align:start position:0% +linked cross-l +polyisoprene cross-link + + align:start position:0% +polyisoprene cross-link + + + align:start position:0% +polyisoprene cross-link +polyisoprene I'll show it in this + + align:start position:0% +polyisoprene I'll show it in this + + + align:start position:0% +polyisoprene I'll show it in this +manner. How are we going to reprocess + + align:start position:0% +manner. How are we going to reprocess + + + align:start position:0% +manner. How are we going to reprocess +this? If we if we begin to heat this, + + align:start position:0% +this? If we if we begin to heat this, + + + align:start position:0% +this? If we if we begin to heat this, +we're going to have to go to an + + align:start position:0% +we're going to have to go to an + + + align:start position:0% +we're going to have to go to an +extremely high temperature because we + + align:start position:0% +extremely high temperature because we + + + align:start position:0% +extremely high temperature because we +have to break covealent bonds. Well, if + + align:start position:0% +have to break covealent bonds. Well, if + + + align:start position:0% +have to break covealent bonds. Well, if +we go to a temperature high enough to + + align:start position:0% +we go to a temperature high enough to + + + align:start position:0% +we go to a temperature high enough to +break these bonds, we go to a + + align:start position:0% +break these bonds, we go to a + + + align:start position:0% +break these bonds, we go to a +temperature high enough to break the + + align:start position:0% +temperature high enough to break the + + + align:start position:0% +temperature high enough to break the +backbone, we go to thermal destruction + + align:start position:0% +backbone, we go to thermal destruction + + + align:start position:0% +backbone, we go to thermal destruction +of the entire material. So such + + align:start position:0% +of the entire material. So such + + + align:start position:0% +of the entire material. So such +materials cannot be reprocessed by + + align:start position:0% +materials cannot be reprocessed by + + + align:start position:0% +materials cannot be reprocessed by +heating. So these are called + + align:start position:0% +heating. So these are called + + + align:start position:0% +heating. So these are called +thermoset. + + align:start position:0% +thermoset. + + + align:start position:0% +thermoset. +Thermoset thermoset and thermoset are + + align:start position:0% +Thermoset thermoset and thermoset are + + + align:start position:0% +Thermoset thermoset and thermoset are +very difficult to process. + + align:start position:0% +very difficult to process. + + + align:start position:0% +very difficult to process. +difficult to + + align:start position:0% +difficult to + + + align:start position:0% +difficult to +recycle. You might say, well, you don't + + align:start position:0% +recycle. You might say, well, you don't + + + align:start position:0% +recycle. You might say, well, you don't +have to just do it by uh by thermally + + align:start position:0% +have to just do it by uh by thermally + + + align:start position:0% +have to just do it by uh by thermally +reprocessing. Why don't you use some + + align:start position:0% +reprocessing. Why don't you use some + + + align:start position:0% +reprocessing. Why don't you use some +kind of a chemistry? Go in there with + + align:start position:0% +kind of a chemistry? Go in there with + + + align:start position:0% +kind of a chemistry? Go in there with +chemistry that will attack these bonds. + + align:start position:0% +chemistry that will attack these bonds. + + + align:start position:0% +chemistry that will attack these bonds. +These are strong covealent bonds. What + + align:start position:0% +These are strong covealent bonds. What + + + align:start position:0% +These are strong covealent bonds. What +kind of a solvent is going to be strong + + align:start position:0% +kind of a solvent is going to be strong + + + align:start position:0% +kind of a solvent is going to be strong +enough to snip those bonds? It's going + + align:start position:0% +enough to snip those bonds? It's going + + + align:start position:0% +enough to snip those bonds? It's going +to be a very aggressive solvent. And uh + + align:start position:0% +to be a very aggressive solvent. And uh + + + align:start position:0% +to be a very aggressive solvent. And uh +you know what are the health effects of + + align:start position:0% +you know what are the health effects of + + + align:start position:0% +you know what are the health effects of +the use of that solvent? you want to bet + + align:start position:0% +the use of that solvent? you want to bet + + + align:start position:0% +the use of that solvent? you want to bet +the company on the use of that and find + + align:start position:0% +the company on the use of that and find + + + align:start position:0% +the company on the use of that and find +out later that uh you've got class + + align:start position:0% +out later that uh you've got class + + + align:start position:0% +out later that uh you've got class +action lawsuits using such chemicals. So + + align:start position:0% +action lawsuits using such chemicals. So + + + align:start position:0% +action lawsuits using such chemicals. So +this is the issue when you you drive + + align:start position:0% +this is the issue when you you drive + + + align:start position:0% +this is the issue when you you drive +down the highway and you see these + + align:start position:0% +down the highway and you see these + + + align:start position:0% +down the highway and you see these +mounds these mountains of spent + + align:start position:0% +mounds these mountains of spent + + + align:start position:0% +mounds these mountains of spent +automobile tires how to recycle them. + + align:start position:0% +automobile tires how to recycle them. + + + align:start position:0% +automobile tires how to recycle them. +This is the issue. All right. Whereas + + align:start position:0% +This is the issue. All right. Whereas + + + align:start position:0% +This is the issue. All right. Whereas +over here you heat this up and you can + + align:start position:0% +over here you heat this up and you can + + + align:start position:0% +over here you heat this up and you can +redo it. So such materials are called + + align:start position:0% +redo it. So such materials are called + + + align:start position:0% +redo it. So such materials are called +thermoplastic. + + align:start position:0% +thermoplastic. + + + align:start position:0% +thermoplastic. +Thermoplastic. they can be reprocessed + + align:start position:0% +Thermoplastic. they can be reprocessed + + + align:start position:0% +Thermoplastic. they can be reprocessed +or rendered plastic by uh temperature + + align:start position:0% +or rendered plastic by uh temperature + + + align:start position:0% +or rendered plastic by uh temperature +rise. So they're environmentally much + + align:start position:0% +rise. So they're environmentally much + + + align:start position:0% +rise. So they're environmentally much +much easier to + + align:start position:0% +much easier to + + + align:start position:0% +much easier to +process. A few more things here with the + + align:start position:0% +process. A few more things here with the + + + align:start position:0% +process. A few more things here with the +polyethylene. Uh this shows what I was + + align:start position:0% +polyethylene. Uh this shows what I was + + + align:start position:0% +polyethylene. Uh this shows what I was +just doing on the uh on the projector, + + align:start position:0% +just doing on the uh on the projector, + + + align:start position:0% +just doing on the uh on the projector, +the uh the document camera rather. This + + align:start position:0% +the uh the document camera rather. This + + + align:start position:0% +the uh the document camera rather. This +is the partially crystallized + + align:start position:0% +is the partially crystallized + + + align:start position:0% +is the partially crystallized +polyethylene and this is what it looks + + align:start position:0% +polyethylene and this is what it looks + + + align:start position:0% +polyethylene and this is what it looks +like in these zones. you don't have all + + align:start position:0% +like in these zones. you don't have all + + + align:start position:0% +like in these zones. you don't have all +of the uh chains lining up, but if you + + align:start position:0% +of the uh chains lining up, but if you + + + align:start position:0% +of the uh chains lining up, but if you +look at the atoms on end, you will see + + align:start position:0% +look at the atoms on end, you will see + + + align:start position:0% +look at the atoms on end, you will see +there's the C2H4 unit and the C2H4 units + + align:start position:0% +there's the C2H4 unit and the C2H4 units + + + align:start position:0% +there's the C2H4 unit and the C2H4 units +are lined up. Okay? And sure enough, + + align:start position:0% +are lined up. Okay? And sure enough, + + + align:start position:0% +are lined up. Okay? And sure enough, +what is the basis uh unit here? It looks + + align:start position:0% +what is the basis uh unit here? It looks + + + align:start position:0% +what is the basis uh unit here? It looks +orthoromic as you would expect. The + + align:start position:0% +orthoromic as you would expect. The + + + align:start position:0% +orthoromic as you would expect. The +molecule that has the aspect ratio of + + align:start position:0% +molecule that has the aspect ratio of + + + align:start position:0% +molecule that has the aspect ratio of +2:1, you expect is going to come out in + + align:start position:0% +2:1, you expect is going to come out in + + + align:start position:0% +2:1, you expect is going to come out in +one of the uh brev lises that also has + + align:start position:0% +one of the uh brev lises that also has + + + align:start position:0% +one of the uh brev lises that also has +uh some anisotropy associated with it. + + align:start position:0% +uh some anisotropy associated with it. + + + align:start position:0% +uh some anisotropy associated with it. +And here's some X-ray defraction data. + + align:start position:0% +And here's some X-ray defraction data. + + + align:start position:0% +And here's some X-ray defraction data. +This is the defraction of a fully + + align:start position:0% +This is the defraction of a fully + + + align:start position:0% +This is the defraction of a fully +crystallin polymer. So if we took a + + align:start position:0% +crystallin polymer. So if we took a + + + align:start position:0% +crystallin polymer. So if we took a +short length polyethylene and cooled it + + align:start position:0% +short length polyethylene and cooled it + + + align:start position:0% +short length polyethylene and cooled it +very slowly or took it out of a solvent, + + align:start position:0% +very slowly or took it out of a solvent, + + + align:start position:0% +very slowly or took it out of a solvent, +we would end up with something that's + + align:start position:0% +we would end up with something that's + + + align:start position:0% +we would end up with something that's +totally crystallin and we see we have + + align:start position:0% +totally crystallin and we see we have + + + align:start position:0% +totally crystallin and we see we have +discrete peaks. Here it's the same + + align:start position:0% +discrete peaks. Here it's the same + + + align:start position:0% +discrete peaks. Here it's the same +material amorphous. And this uh if it's + + align:start position:0% +material amorphous. And this uh if it's + + + align:start position:0% +material amorphous. And this uh if it's +a little bit painful to look at this + + align:start position:0% +a little bit painful to look at this + + + align:start position:0% +a little bit painful to look at this +because it's reminiscent of a question + + align:start position:0% +because it's reminiscent of a question + + + align:start position:0% +because it's reminiscent of a question +on the recent test. This is what the uh + + align:start position:0% +on the recent test. This is what the uh + + + align:start position:0% +on the recent test. This is what the uh +this is what the data show. + + align:start position:0% +this is what the data show. + + + align:start position:0% +this is what the data show. +So by looking at this uh mixed spectrum + + align:start position:0% +So by looking at this uh mixed spectrum + + + align:start position:0% +So by looking at this uh mixed spectrum +you can get a measure of the extent of + + align:start position:0% +you can get a measure of the extent of + + + align:start position:0% +you can get a measure of the extent of +crystallization by looking at the + + align:start position:0% +crystallization by looking at the + + + align:start position:0% +crystallization by looking at the +relative intensity of the peaks versus + + align:start position:0% +relative intensity of the peaks versus + + + align:start position:0% +relative intensity of the peaks versus +this broad single peak which is + + align:start position:0% +this broad single peak which is + + + align:start position:0% +this broad single peak which is +associated with the first nearest + + align:start position:0% +associated with the first nearest + + + align:start position:0% +associated with the first nearest +neighbors because in ethylene we know + + align:start position:0% +neighbors because in ethylene we know + + + align:start position:0% +neighbors because in ethylene we know +that carbon has hydrogens as its nearest + + align:start position:0% +that carbon has hydrogens as its nearest + + + align:start position:0% +that carbon has hydrogens as its nearest +neighbors and and so on. So this works + + align:start position:0% +neighbors and and so on. So this works + + + align:start position:0% +neighbors and and so on. So this works +just as well as the the free volume as a + + align:start position:0% +just as well as the the free volume as a + + + align:start position:0% +just as well as the the free volume as a +measure of the degree of uh + + align:start position:0% +measure of the degree of uh + + + align:start position:0% +measure of the degree of uh +crystallization. So we see this and the + + align:start position:0% +crystallization. So we see this and the + + + align:start position:0% +crystallization. So we see this and the +last thing I want to touch upon is uh + + align:start position:0% +last thing I want to touch upon is uh + + + align:start position:0% +last thing I want to touch upon is uh +the uh polymer synthesis just to put + + align:start position:0% +the uh polymer synthesis just to put + + + align:start position:0% +the uh polymer synthesis just to put +that into uh uh + + align:start position:0% +that into uh uh + + + align:start position:0% +that into uh uh +formal setting. I've already shown you + + align:start position:0% +formal setting. I've already shown you + + + align:start position:0% +formal setting. I've already shown you +addition + + align:start position:0% +addition + + + align:start position:0% +addition +polymerization. Addition polymerization + + align:start position:0% + + + + align:start position:0% + +And addition polymerization involves the + + align:start position:0% +And addition polymerization involves the + + + align:start position:0% +And addition polymerization involves the +use of a radical or + + align:start position:0% +use of a radical or + + + align:start position:0% +use of a radical or +catalyst radical or catalyst + + align:start position:0% + + + + align:start position:0% + +assisted and it characterized by three + + align:start position:0% +assisted and it characterized by three + + + align:start position:0% +assisted and it characterized by three +stages where I showed you the initiation + + align:start position:0% +stages where I showed you the initiation + + + align:start position:0% +stages where I showed you the initiation +in which we generate the the radical + + align:start position:0% +in which we generate the the radical + + + align:start position:0% +in which we generate the the radical +then there's the growth of the of the uh + + align:start position:0% +then there's the growth of the of the uh + + + align:start position:0% +then there's the growth of the of the uh +polymer until we get to the length of + + align:start position:0% +polymer until we get to the length of + + + align:start position:0% +polymer until we get to the length of +chain that we want and then finally the + + align:start position:0% +chain that we want and then finally the + + + align:start position:0% +chain that we want and then finally the +extinguishing of the reaction called + + align:start position:0% +extinguishing of the reaction called + + + align:start position:0% +extinguishing of the reaction called +termination. So what's really going on + + align:start position:0% +termination. So what's really going on + + + align:start position:0% +termination. So what's really going on +here is in the initiation stage we + + align:start position:0% +here is in the initiation stage we + + + align:start position:0% +here is in the initiation stage we +create the + + align:start position:0% +create the + + + align:start position:0% +create the +radical here the growth is simply uh + + align:start position:0% +radical here the growth is simply uh + + + align:start position:0% +radical here the growth is simply uh +this is the + + align:start position:0% + + + + align:start position:0% + +polymerization polymerize or if you like + + align:start position:0% +polymerization polymerize or if you like + + + align:start position:0% +polymerization polymerize or if you like +attachment and then over here is quench + + align:start position:0% +attachment and then over here is quench + + + align:start position:0% +attachment and then over here is quench +the + + align:start position:0% +the + + + align:start position:0% +the +radical to quench the + + align:start position:0% + + + + align:start position:0% + +radical and those are the stages that + + align:start position:0% +radical and those are the stages that + + + align:start position:0% +radical and those are the stages that +are involved. So, all we're really + + align:start position:0% +are involved. So, all we're really + + + align:start position:0% +are involved. So, all we're really +looking at here is monomer + + align:start position:0% + + + + align:start position:0% + +attachment. Monomer + + align:start position:0% + + + + align:start position:0% + +attachment. And in this case, the + + align:start position:0% +attachment. And in this case, the + + + align:start position:0% +attachment. And in this case, the +composition of the polymer is equal to + + align:start position:0% +composition of the polymer is equal to + + + align:start position:0% +composition of the polymer is equal to +the composition of the myrr unit. + + align:start position:0% +the composition of the myrr unit. + + + align:start position:0% +the composition of the myrr unit. +composition of + + align:start position:0% + + + + align:start position:0% + +polymer is simply end is identical to + + align:start position:0% +polymer is simply end is identical to + + + align:start position:0% +polymer is simply end is identical to +the composition of the the mer + + align:start position:0% +the composition of the the mer + + + align:start position:0% +the composition of the the mer +unit. We simply use the radical to + + align:start position:0% +unit. We simply use the radical to + + + align:start position:0% +unit. We simply use the radical to +catalyze and that's the only effect. But + + align:start position:0% +catalyze and that's the only effect. But + + + align:start position:0% +catalyze and that's the only effect. But +there's one other way to + + align:start position:0% +there's one other way to + + + align:start position:0% +there's one other way to +form and this is called condensation + + align:start position:0% +form and this is called condensation + + + align:start position:0% +form and this is called condensation +polymerization. + + align:start position:0% + + + + align:start position:0% + +condensation + + align:start position:0% + + + + align:start position:0% + +polymerization and it works a little bit + + align:start position:0% +polymerization and it works a little bit + + + align:start position:0% +polymerization and it works a little bit +differently and it involves more than + + align:start position:0% +differently and it involves more than + + + align:start position:0% +differently and it involves more than +one mer type. So I'm going to show this + + align:start position:0% +one mer type. So I'm going to show this + + + align:start position:0% +one mer type. So I'm going to show this +as uh myrrh type number one which has + + align:start position:0% +as uh myrrh type number one which has + + + align:start position:0% +as uh myrrh type number one which has +associated with it a terminal hydrogen + + align:start position:0% +associated with it a terminal hydrogen + + + align:start position:0% +associated with it a terminal hydrogen +and myrrh number two that has associated + + align:start position:0% +and myrrh number two that has associated + + + align:start position:0% +and myrrh number two that has associated +with it a terminal hydroxil and + + align:start position:0% +with it a terminal hydroxil and + + + align:start position:0% +with it a terminal hydroxil and +condensation polymerization works + + align:start position:0% +condensation polymerization works + + + align:start position:0% +condensation polymerization works +to attach the hydroxil to the terminal + + align:start position:0% +to attach the hydroxil to the terminal + + + align:start position:0% +to attach the hydroxil to the terminal +hydrogen to form a covealent bond + + align:start position:0% +hydrogen to form a covealent bond + + + align:start position:0% +hydrogen to form a covealent bond +between the residual R1 and R2 and + + align:start position:0% +between the residual R1 and R2 and + + + align:start position:0% +between the residual R1 and R2 and +expels water vapor. These are reactions + + align:start position:0% +expels water vapor. These are reactions + + + align:start position:0% +expels water vapor. These are reactions +are conducted at temperatures above 100° + + align:start position:0% +are conducted at temperatures above 100° + + + align:start position:0% +are conducted at temperatures above 100° +C. So this is expelled and ultimately + + align:start position:0% +C. So this is expelled and ultimately + + + align:start position:0% +C. So this is expelled and ultimately +is captured as a condensate. So, oddly + + align:start position:0% +is captured as a condensate. So, oddly + + + align:start position:0% +is captured as a condensate. So, oddly +enough, condensation polymerization, + + align:start position:0% +enough, condensation polymerization, + + + align:start position:0% +enough, condensation polymerization, +which involves the the the step-wise + + align:start position:0% +which involves the the the step-wise + + + align:start position:0% +which involves the the the step-wise +building of the polymer by reaction + + align:start position:0% +building of the polymer by reaction + + + align:start position:0% +building of the polymer by reaction +between two different myrt types and + + align:start position:0% +between two different myrt types and + + + align:start position:0% +between two different myrt types and +expulsion of uh water vapor other uh + + align:start position:0% +expulsion of uh water vapor other uh + + + align:start position:0% +expulsion of uh water vapor other uh +condensate is named not for what it is + + align:start position:0% +condensate is named not for what it is + + + align:start position:0% +condensate is named not for what it is +but for the byproduct that is not part + + align:start position:0% +but for the byproduct that is not part + + + align:start position:0% +but for the byproduct that is not part +of it. So, this is the prototypical + + align:start position:0% +of it. So, this is the prototypical + + + align:start position:0% +of it. So, this is the prototypical +reaction and clearly here you keep + + align:start position:0% +reaction and clearly here you keep + + + align:start position:0% +reaction and clearly here you keep +losing water. So in this case the + + align:start position:0% +losing water. So in this case the + + + align:start position:0% +losing water. So in this case the +composition differs the + + align:start position:0% +composition differs the + + + align:start position:0% +composition differs the +composition and the final mass of the of + + align:start position:0% +composition and the final mass of the of + + + align:start position:0% +composition and the final mass of the of +polymer is not equal to the + + align:start position:0% +polymer is not equal to the + + + align:start position:0% +polymer is not equal to the +composition of the merg groups. + + align:start position:0% + + + + align:start position:0% + +and the mass is is less + + align:start position:0% +and the mass is is less + + + align:start position:0% +and the mass is is less +than less than the sum of the masses of + + align:start position:0% +than less than the sum of the masses of + + + align:start position:0% +than less than the sum of the masses of +all of the mer groups because we keep + + align:start position:0% +all of the mer groups because we keep + + + align:start position:0% +all of the mer groups because we keep +losing water. So I think here we've got + + align:start position:0% +losing water. So I think here we've got + + + align:start position:0% +losing water. So I think here we've got +some examples of the various materials. + + align:start position:0% +some examples of the various materials. + + + align:start position:0% +some examples of the various materials. +So these this again is taken from your + + align:start position:0% +So these this again is taken from your + + + align:start position:0% +So these this again is taken from your +reading. Here's a a a suite of uh + + align:start position:0% +reading. Here's a a a suite of uh + + + align:start position:0% +reading. Here's a a a suite of uh +addition polymers. Many of these you you + + align:start position:0% +addition polymers. Many of these you you + + + align:start position:0% +addition polymers. Many of these you you +encounter in uh everyday life. I've been + + align:start position:0% +encounter in uh everyday life. I've been + + + align:start position:0% +encounter in uh everyday life. I've been +talking about polyethylene. If we + + align:start position:0% +talking about polyethylene. If we + + + align:start position:0% +talking about polyethylene. If we +replace the hydrogens's with florines, + + align:start position:0% +replace the hydrogens's with florines, + + + align:start position:0% +replace the hydrogens's with florines, +we get PTFE, which you know by the trade + + align:start position:0% +we get PTFE, which you know by the trade + + + align:start position:0% +we get PTFE, which you know by the trade +name Teflon, polyropylene, + + align:start position:0% +name Teflon, polyropylene, + + + align:start position:0% +name Teflon, polyropylene, +uh polystyrene, which you've seen in + + align:start position:0% +uh polystyrene, which you've seen in + + + align:start position:0% +uh polystyrene, which you've seen in +these clamshells and and uh uh not so + + align:start position:0% +these clamshells and and uh uh not so + + + align:start position:0% +these clamshells and and uh uh not so +much today in in coffee cups for their + + align:start position:0% +much today in in coffee cups for their + + + align:start position:0% +much today in in coffee cups for their +insulating capability. Polyacry nitral + + align:start position:0% +insulating capability. Polyacry nitral + + + align:start position:0% +insulating capability. Polyacry nitral +is a fabric oralon. PVC is that white uh + + align:start position:0% +is a fabric oralon. PVC is that white uh + + + align:start position:0% +is a fabric oralon. PVC is that white uh +uh tubing that you see used in plumbing + + align:start position:0% +uh tubing that you see used in plumbing + + + align:start position:0% +uh tubing that you see used in plumbing +facilities. + + align:start position:0% +facilities. + + + align:start position:0% +facilities. +polymethylmethacrylate. Many of you are + + align:start position:0% +polymethylmethacrylate. Many of you are + + + align:start position:0% +polymethylmethacrylate. Many of you are +wearing uh eyeglasses that are made of + + align:start position:0% +wearing uh eyeglasses that are made of + + + align:start position:0% +wearing uh eyeglasses that are made of +this material. This is uh plexiglass or + + align:start position:0% +this material. This is uh plexiglass or + + + align:start position:0% +this material. This is uh plexiglass or +uh lucite and so on. So, and then down + + align:start position:0% +uh lucite and so on. So, and then down + + + align:start position:0% +uh lucite and so on. So, and then down +here even some of the some of the uh + + align:start position:0% +here even some of the some of the uh + + + align:start position:0% +here even some of the some of the uh +rubbers. Uh on the other hand here are + + align:start position:0% +rubbers. Uh on the other hand here are + + + align:start position:0% +rubbers. Uh on the other hand here are +the condensation polymers and the + + align:start position:0% +the condensation polymers and the + + + align:start position:0% +the condensation polymers and the +notably are the nylons. The nylons are + + align:start position:0% +notably are the nylons. The nylons are + + + align:start position:0% +notably are the nylons. The nylons are +made by condensation polymerization and + + align:start position:0% +made by condensation polymerization and + + + align:start position:0% +made by condensation polymerization and +I've put a little bit of fine structure + + align:start position:0% +I've put a little bit of fine structure + + + align:start position:0% +I've put a little bit of fine structure +on here. You can look at this at the + + align:start position:0% +on here. You can look at this at the + + + align:start position:0% +on here. You can look at this at the +website that the the bond that will link + + align:start position:0% +website that the the bond that will link + + + align:start position:0% +website that the the bond that will link +the R1 to R2 is called the amid bond. + + align:start position:0% +the R1 to R2 is called the amid bond. + + + align:start position:0% +the R1 to R2 is called the amid bond. +This is the amid + + align:start position:0% + + + + align:start position:0% + +bond. And so the nylons are known + + align:start position:0% +bond. And so the nylons are known + + + align:start position:0% +bond. And so the nylons are known +generically as polyamids. And uh + + align:start position:0% +generically as polyamids. And uh + + + align:start position:0% +generically as polyamids. And uh +furthermore there's one end that has the + + align:start position:0% +furthermore there's one end that has the + + + align:start position:0% +furthermore there's one end that has the +pardon me the caroxyic acid end and then + + align:start position:0% +pardon me the caroxyic acid end and then + + + align:start position:0% +pardon me the caroxyic acid end and then +the other end which has uh the amino + + align:start position:0% +the other end which has uh the amino + + + align:start position:0% +the other end which has uh the amino +end. And as you go down you see kevlars + + align:start position:0% +end. And as you go down you see kevlars + + + align:start position:0% +end. And as you go down you see kevlars +here which you know is used as a + + align:start position:0% +here which you know is used as a + + + align:start position:0% +here which you know is used as a +substitute for steel belting and tires + + align:start position:0% +substitute for steel belting and tires + + + align:start position:0% +substitute for steel belting and tires +also used as the fiber and bulletproof + + align:start position:0% +also used as the fiber and bulletproof + + + align:start position:0% +also used as the fiber and bulletproof +vests. Um some fabrics here dacron and + + align:start position:0% +vests. Um some fabrics here dacron and + + + align:start position:0% +vests. Um some fabrics here dacron and +myar various polyesters. the + + align:start position:0% +myar various polyesters. the + + + align:start position:0% +myar various polyesters. the +polycarbonates. This rigid uh phenyl + + align:start position:0% +polycarbonates. This rigid uh phenyl + + + align:start position:0% +polycarbonates. This rigid uh phenyl +group here is what gives the + + align:start position:0% +group here is what gives the + + + align:start position:0% +group here is what gives the +polycarbonates their high strength. This + + align:start position:0% +polycarbonates their high strength. This + + + align:start position:0% +polycarbonates their high strength. This +is Lexan which is used in uh jet engine + + align:start position:0% +is Lexan which is used in uh jet engine + + + align:start position:0% +is Lexan which is used in uh jet engine +windshields and it's also used in um + + align:start position:0% +windshields and it's also used in um + + + align:start position:0% +windshields and it's also used in um +sports goggles to give you the uh + + align:start position:0% +sports goggles to give you the uh + + + align:start position:0% +sports goggles to give you the uh +resistance against impact and so on. So + + align:start position:0% +resistance against impact and so on. So + + + align:start position:0% +resistance against impact and so on. So +these are made by this uh process and + + align:start position:0% +these are made by this uh process and + + + align:start position:0% +these are made by this uh process and +we're going to see this process again we + + align:start position:0% +we're going to see this process again we + + + align:start position:0% +we're going to see this process again we +talk about protein synthesis because uh + + align:start position:0% +talk about protein synthesis because uh + + + align:start position:0% +talk about protein synthesis because uh +mother nature works by condensation + + align:start position:0% +mother nature works by condensation + + + align:start position:0% +mother nature works by condensation +polymerization. So uh there are many + + align:start position:0% +polymerization. So uh there are many + + + align:start position:0% +polymerization. So uh there are many +similarities between the nylons and the + + align:start position:0% +similarities between the nylons and the + + + align:start position:0% +similarities between the nylons and the +uh and the proteins that + + align:start position:0% +uh and the proteins that + + + align:start position:0% +uh and the proteins that +uh make up our bodies. Okay. So what I'd + + align:start position:0% +uh make up our bodies. Okay. So what I'd + + + align:start position:0% +uh make up our bodies. Okay. So what I'd +like to do in the last five minutes is + + align:start position:0% +like to do in the last five minutes is + + + align:start position:0% +like to do in the last five minutes is +talk about an example of the use of + + align:start position:0% +talk about an example of the use of + + + align:start position:0% +talk about an example of the use of +block copolymers in uh uh energy and uh + + align:start position:0% +block copolymers in uh uh energy and uh + + + align:start position:0% +block copolymers in uh uh energy and uh +some research that's been going on here + + align:start position:0% +some research that's been going on here + + + align:start position:0% +some research that's been going on here +at MIT for about oh 10 years now looking + + align:start position:0% +at MIT for about oh 10 years now looking + + + align:start position:0% +at MIT for about oh 10 years now looking +at new materials to make superior + + align:start position:0% +at new materials to make superior + + + align:start position:0% +at new materials to make superior +batteries batteries for the wireless + + align:start position:0% +batteries batteries for the wireless + + + align:start position:0% +batteries batteries for the wireless +age. And uh this is these are the kinds + + align:start position:0% +age. And uh this is these are the kinds + + + align:start position:0% +age. And uh this is these are the kinds +of uh batteries that exist today in + + align:start position:0% +of uh batteries that exist today in + + + align:start position:0% +of uh batteries that exist today in +terms of uh the amount of energy they + + align:start position:0% +terms of uh the amount of energy they + + + align:start position:0% +terms of uh the amount of energy they +store per charge. And you see lead acid + + align:start position:0% +store per charge. And you see lead acid + + + align:start position:0% +store per charge. And you see lead acid +which is abundant and cheap is actually + + align:start position:0% +which is abundant and cheap is actually + + + align:start position:0% +which is abundant and cheap is actually +quite uh low in terms of how much energy + + align:start position:0% +quite uh low in terms of how much energy + + + align:start position:0% +quite uh low in terms of how much energy +it's it stores. And what's in your cell + + align:start position:0% +it's it stores. And what's in your cell + + + align:start position:0% +it's it stores. And what's in your cell +phone and your laptop is the lithium ion + + align:start position:0% +phone and your laptop is the lithium ion + + + align:start position:0% +phone and your laptop is the lithium ion +battery which is 150 watt hours per + + align:start position:0% +battery which is 150 watt hours per + + + align:start position:0% +battery which is 150 watt hours per +kilogram by this metric. And in fact it + + align:start position:0% +kilogram by this metric. And in fact it + + + align:start position:0% +kilogram by this metric. And in fact it +was the advent of the nickel metal + + align:start position:0% +was the advent of the nickel metal + + + align:start position:0% +was the advent of the nickel metal +hydride battery that enabled the laptop + + align:start position:0% +hydride battery that enabled the laptop + + + align:start position:0% +hydride battery that enabled the laptop +computer. All of the components were in + + align:start position:0% +computer. All of the components were in + + + align:start position:0% +computer. All of the components were in +place in the 1980s, but sodium sulfur is + + align:start position:0% +place in the 1980s, but sodium sulfur is + + + align:start position:0% +place in the 1980s, but sodium sulfur is +a molten salt battery. It operates at + + align:start position:0% +a molten salt battery. It operates at + + + align:start position:0% +a molten salt battery. It operates at +300 degrees C. So that was not very + + align:start position:0% +300 degrees C. So that was not very + + + align:start position:0% +300 degrees C. So that was not very +popular for laptop use. So the only + + align:start position:0% +popular for laptop use. So the only + + + align:start position:0% +popular for laptop use. So the only +thing that was available was down here + + align:start position:0% +thing that was available was down here + + + align:start position:0% +thing that was available was down here +in Niads. And people were not going to + + align:start position:0% +in Niads. And people were not going to + + + align:start position:0% +in Niads. And people were not going to +release laptops that had a runtime of + + align:start position:0% +release laptops that had a runtime of + + + align:start position:0% +release laptops that had a runtime of +about 1 hour. But with the advent of + + align:start position:0% +about 1 hour. But with the advent of + + + align:start position:0% +about 1 hour. But with the advent of +nickel metal hydride, it all of a sudden + + align:start position:0% +nickel metal hydride, it all of a sudden + + + align:start position:0% +nickel metal hydride, it all of a sudden +became sensible to to put out such + + align:start position:0% +became sensible to to put out such + + + align:start position:0% +became sensible to to put out such +devices. And now we've gone to lithium + + align:start position:0% +devices. And now we've gone to lithium + + + align:start position:0% +devices. And now we've gone to lithium +ion. And ironically, as the capacity of + + align:start position:0% +ion. And ironically, as the capacity of + + + align:start position:0% +ion. And ironically, as the capacity of +the battery has risen, the appliances + + align:start position:0% +the battery has risen, the appliances + + + align:start position:0% +the battery has risen, the appliances +that go on the laptop have risen and so + + align:start position:0% +that go on the laptop have risen and so + + + align:start position:0% +that go on the laptop have risen and so +the runtime doesn't change because each + + align:start position:0% +the runtime doesn't change because each + + + align:start position:0% +the runtime doesn't change because each +next generation has a more intense uh + + align:start position:0% +next generation has a more intense uh + + + align:start position:0% +next generation has a more intense uh +power hog of a CPU, you want a DVD, you + + align:start position:0% +power hog of a CPU, you want a DVD, you + + + align:start position:0% +power hog of a CPU, you want a DVD, you +want fancy screen and so on. And all of + + align:start position:0% +want fancy screen and so on. And all of + + + align:start position:0% +want fancy screen and so on. And all of +that is consuming energy. But if you + + align:start position:0% +that is consuming energy. But if you + + + align:start position:0% +that is consuming energy. But if you +knew how to power it down and and run it + + align:start position:0% +knew how to power it down and and run it + + + align:start position:0% +knew how to power it down and and run it +minimally, you'd find that you could get + + align:start position:0% +minimally, you'd find that you could get + + + align:start position:0% +minimally, you'd find that you could get +run times of uh uh six, seven hours. So + + align:start position:0% +run times of uh uh six, seven hours. So + + + align:start position:0% +run times of uh uh six, seven hours. So +the the approach that we used here was + + align:start position:0% +the the approach that we used here was + + + align:start position:0% +the the approach that we used here was +to use black c-olymers and we used black + + align:start position:0% +to use black c-olymers and we used black + + + align:start position:0% +to use black c-olymers and we used black +copolymers such that we wanted to get a + + align:start position:0% +copolymers such that we wanted to get a + + + align:start position:0% +copolymers such that we wanted to get a +solid. You see people think of batteries + + align:start position:0% +solid. You see people think of batteries + + + align:start position:0% +solid. You see people think of batteries +as these cylindrical devices that uh are + + align:start position:0% +as these cylindrical devices that uh are + + + align:start position:0% +as these cylindrical devices that uh are +very heavy but we had a different image. + + align:start position:0% +very heavy but we had a different image. + + + align:start position:0% +very heavy but we had a different image. +We thought that this should be the + + align:start position:0% +We thought that this should be the + + + align:start position:0% +We thought that this should be the +battery. Battery should remind us of + + align:start position:0% +battery. Battery should remind us of + + + align:start position:0% +battery. Battery should remind us of +something like + + align:start position:0% +something like + + + align:start position:0% +something like +this. This is called dreaming. This is a + + align:start position:0% +this. This is called dreaming. This is a + + + align:start position:0% +this. This is called dreaming. This is a +potato chip bag. You think it's just + + align:start position:0% +potato chip bag. You think it's just + + + align:start position:0% +potato chip bag. You think it's just +nothing but a lowly potato chip bag. + + align:start position:0% +nothing but a lowly potato chip bag. + + + align:start position:0% +nothing but a lowly potato chip bag. +Open it up sometime. What do you find? + + align:start position:0% +Open it up sometime. What do you find? + + + align:start position:0% +Open it up sometime. What do you find? +You see, it's a multi-layer laminate of + + align:start position:0% +You see, it's a multi-layer laminate of + + + align:start position:0% +You see, it's a multi-layer laminate of +polymer and metal because a potato chip + + align:start position:0% +polymer and metal because a potato chip + + + align:start position:0% +polymer and metal because a potato chip +is precious. You know, you have to + + align:start position:0% +is precious. You know, you have to + + + align:start position:0% +is precious. You know, you have to +protect it against spoilage. So, it can + + align:start position:0% +protect it against spoilage. So, it can + + + align:start position:0% +protect it against spoilage. So, it can +spoil by becoming soggy from humidity or + + align:start position:0% +spoil by becoming soggy from humidity or + + + align:start position:0% +spoil by becoming soggy from humidity or +it can become rancid from oxidation. So, + + align:start position:0% +it can become rancid from oxidation. So, + + + align:start position:0% +it can become rancid from oxidation. So, +you need the polymer to protect it from + + align:start position:0% +you need the polymer to protect it from + + + align:start position:0% +you need the polymer to protect it from +one and the metal to protect it from the + + align:start position:0% +one and the metal to protect it from the + + + align:start position:0% +one and the metal to protect it from the +other. But this tells me that you can + + align:start position:0% +other. But this tells me that you can + + + align:start position:0% +other. But this tells me that you can +make a multi-layer thin film laminate + + align:start position:0% +make a multi-layer thin film laminate + + + align:start position:0% +make a multi-layer thin film laminate +very cheaply. Now, if this polymer could + + align:start position:0% +very cheaply. Now, if this polymer could + + + align:start position:0% +very cheaply. Now, if this polymer could +be made into a lithium ion conductor, we + + align:start position:0% +be made into a lithium ion conductor, we + + + align:start position:0% +be made into a lithium ion conductor, we +would have a solid state battery. + + align:start position:0% +would have a solid state battery. + + + align:start position:0% +would have a solid state battery. +Instead of aluminum, we put lithium. + + align:start position:0% +Instead of aluminum, we put lithium. + + + align:start position:0% +Instead of aluminum, we put lithium. +Instead of this polymer, we put + + align:start position:0% +Instead of this polymer, we put + + + align:start position:0% +Instead of this polymer, we put +something that could conduct lithium + + align:start position:0% +something that could conduct lithium + + + align:start position:0% +something that could conduct lithium +ions. And then we put the cathode on + + align:start position:0% +ions. And then we put the cathode on + + + align:start position:0% +ions. And then we put the cathode on +here. And now we have something that is + + align:start position:0% +here. And now we have something that is + + + align:start position:0% +here. And now we have something that is +solid state. It's very light. And it has + + align:start position:0% +solid state. It's very light. And it has + + + align:start position:0% +solid state. It's very light. And it has +a property that no other battery has. + + align:start position:0% +a property that no other battery has. + + + align:start position:0% +a property that no other battery has. +You can reshape + + align:start position:0% +You can reshape + + + align:start position:0% +You can reshape +it. Okay? You can wear it. You can put + + align:start position:0% +it. Okay? You can wear it. You can put + + + align:start position:0% +it. Okay? You can wear it. You can put +it in the body of a car. You can have + + align:start position:0% +it in the body of a car. You can have + + + align:start position:0% +it in the body of a car. You can have +it. You change the watch band to change + + align:start position:0% +it. You change the watch band to change + + + align:start position:0% +it. You change the watch band to change +the battery. See, you can think + + align:start position:0% +the battery. See, you can think + + + align:start position:0% +the battery. See, you can think +conceptually, you can do different + + align:start position:0% +conceptually, you can do different + + + align:start position:0% +conceptually, you can do different +things. So, that's how it began. And + + align:start position:0% +things. So, that's how it began. And + + + align:start position:0% +things. So, that's how it began. And +with my colleague uh professor Anne + + align:start position:0% +with my colleague uh professor Anne + + + align:start position:0% +with my colleague uh professor Anne +Maize who started a program to look at a + + align:start position:0% +Maize who started a program to look at a + + + align:start position:0% +Maize who started a program to look at a +class of materials block copolymers that + + align:start position:0% +class of materials block copolymers that + + + align:start position:0% +class of materials block copolymers that +were chosen in such a way to give + + align:start position:0% +were chosen in such a way to give + + + align:start position:0% +were chosen in such a way to give +lithium ion conduction at room + + align:start position:0% +lithium ion conduction at room + + + align:start position:0% +lithium ion conduction at room +temperature. Solids are very poor ionic + + align:start position:0% +temperature. Solids are very poor ionic + + + align:start position:0% +temperature. Solids are very poor ionic +conductors. Most solids that you know + + align:start position:0% +conductors. Most solids that you know + + + align:start position:0% +conductors. Most solids that you know +that conduct ions only operate at high + + align:start position:0% +that conduct ions only operate at high + + + align:start position:0% +that conduct ions only operate at high +temperatures. The oxygen sensor in your + + align:start position:0% +temperatures. The oxygen sensor in your + + + align:start position:0% +temperatures. The oxygen sensor in your +car doesn't work for about the first 15 + + align:start position:0% +car doesn't work for about the first 15 + + + align:start position:0% +car doesn't work for about the first 15 +minutes. When the car is cold, the + + align:start position:0% +minutes. When the car is cold, the + + + align:start position:0% +minutes. When the car is cold, the +oxygen sensor is getting garbage for a + + align:start position:0% +oxygen sensor is getting garbage for a + + + align:start position:0% +oxygen sensor is getting garbage for a +signal. It has to heat up. But we don't + + align:start position:0% +signal. It has to heat up. But we don't + + + align:start position:0% +signal. It has to heat up. But we don't +want a battery that runs at 300° C. At + + align:start position:0% +want a battery that runs at 300° C. At + + + align:start position:0% +want a battery that runs at 300° C. At +least I don't. + + align:start position:0% +least I don't. + + + align:start position:0% +least I don't. +I'm So there's selection rules here that + + align:start position:0% +I'm So there's selection rules here that + + + align:start position:0% +I'm So there's selection rules here that +went into play. And ultimately we built + + align:start position:0% +went into play. And ultimately we built + + + align:start position:0% +went into play. And ultimately we built +something that looks like this that has + + align:start position:0% +something that looks like this that has + + + align:start position:0% +something that looks like this that has +a methacrylate backbone and different + + align:start position:0% +a methacrylate backbone and different + + + align:start position:0% +a methacrylate backbone and different +side groups that could salvate lithium + + align:start position:0% +side groups that could salvate lithium + + + align:start position:0% +side groups that could salvate lithium +ions. And we made materials and + + align:start position:0% +ions. And we made materials and + + + align:start position:0% +ions. And we made materials and +ultimately uh made first generation + + align:start position:0% +ultimately uh made first generation + + + align:start position:0% +ultimately uh made first generation +batteries that are thin film + + align:start position:0% +batteries that are thin film + + + align:start position:0% +batteries that are thin film +mechanically flexible and the choice of + + align:start position:0% +mechanically flexible and the choice of + + + align:start position:0% +mechanically flexible and the choice of +electrode materials provided it's + + align:start position:0% +electrode materials provided it's + + + align:start position:0% +electrode materials provided it's +lithium based chemistry and so on allow + + align:start position:0% +lithium based chemistry and so on allow + + + align:start position:0% +lithium based chemistry and so on allow +us to go forward. And it was by using + + align:start position:0% +us to go forward. And it was by using + + + align:start position:0% +us to go forward. And it was by using +the principles shown here on these + + align:start position:0% +the principles shown here on these + + + align:start position:0% +the principles shown here on these +boards that we were able to engineer a + + align:start position:0% +boards that we were able to engineer a + + + align:start position:0% +boards that we were able to engineer a +polymer that could have the mechanical + + align:start position:0% +polymer that could have the mechanical + + + align:start position:0% +polymer that could have the mechanical +properties of something like saran wrap + + align:start position:0% +properties of something like saran wrap + + + align:start position:0% +properties of something like saran wrap +but have the electrical properties of + + align:start position:0% +but have the electrical properties of + + + align:start position:0% +but have the electrical properties of +sulfuric acid in your lead acid battery. + + align:start position:0% +sulfuric acid in your lead acid battery. + + + align:start position:0% +sulfuric acid in your lead acid battery. +That was the that was the paradox. How + + align:start position:0% +That was the that was the paradox. How + + + align:start position:0% +That was the that was the paradox. How +to engineer those seemingly + + align:start position:0% +to engineer those seemingly + + + align:start position:0% +to engineer those seemingly +irreconcilable properties right there. + + align:start position:0% +irreconcilable properties right there. + + + align:start position:0% +irreconcilable properties right there. +Control of local structure. And so, you + + align:start position:0% +Control of local structure. And so, you + + + align:start position:0% +Control of local structure. And so, you +know, I've got all this stuff up here, + + align:start position:0% +know, I've got all this stuff up here, + + + align:start position:0% +know, I've got all this stuff up here, +which we don't have time to go through, + + align:start position:0% +which we don't have time to go through, + + + align:start position:0% +which we don't have time to go through, +but let me show you where you can go + + align:start position:0% +but let me show you where you can go + + + align:start position:0% +but let me show you where you can go +when you get something that's really + + align:start position:0% +when you get something that's really + + + align:start position:0% +when you get something that's really +nice. Look at this. This is really This + + align:start position:0% +nice. Look at this. This is really This + + + align:start position:0% +nice. Look at this. This is really This +is flexible solar cell. This is silicon + + align:start position:0% +is flexible solar cell. This is silicon + + + align:start position:0% +is flexible solar cell. This is silicon +on a polymer substrate. So, it's + + align:start position:0% +on a polymer substrate. So, it's + + + align:start position:0% +on a polymer substrate. So, it's +collecting photons and converting them + + align:start position:0% +collecting photons and converting them + + + align:start position:0% +collecting photons and converting them +into electrons. And then you take + + align:start position:0% +into electrons. And then you take + + + align:start position:0% +into electrons. And then you take +something like this and you put it on + + align:start position:0% +something like this and you put it on + + + align:start position:0% +something like this and you put it on +the back of a flexible solar + + align:start position:0% +the back of a flexible solar + + + align:start position:0% +the back of a flexible solar +cell. And then you put on the front of + + align:start position:0% +cell. And then you put on the front of + + + align:start position:0% +cell. And then you put on the front of +this, you put the LEDs. So, you put this + + align:start position:0% +this, you put the LEDs. So, you put this + + + align:start position:0% +this, you put the LEDs. So, you put this +up in the roof, you collect the photons, + + align:start position:0% +up in the roof, you collect the photons, + + + align:start position:0% +up in the roof, you collect the photons, +and then afterwards the you get the + + align:start position:0% +and then afterwards the you get the + + + align:start position:0% +and then afterwards the you get the +photons back. Now, that's change. That's + + align:start position:0% +photons back. Now, that's change. That's + + + align:start position:0% +photons back. Now, that's change. That's +change. Learn your chemistry. Have a + + align:start position:0% +change. Learn your chemistry. Have a + + + align:start position:0% +change. Learn your chemistry. Have a +nice weekend. \ No newline at end of file diff --git a/pAP1HKzueqc.txt b/pAP1HKzueqc.txt new file mode 100644 index 0000000000000000000000000000000000000000..f7c8f55466153ae9b8d79783322d70555b04962b --- /dev/null +++ b/pAP1HKzueqc.txt @@ -0,0 +1,12424 @@ +align:start position:0% + +as usual let's find out where we + + align:start position:0% +as usual let's find out where we + + + align:start position:0% +as usual let's find out where we +are we did + + align:start position:0% +are we did + + + align:start position:0% +are we did +the first two sections of general + + align:start position:0% +the first two sections of general + + + align:start position:0% +the first two sections of general +equilibrium on welfare and existence and + + align:start position:0% +equilibrium on welfare and existence and + + + align:start position:0% +equilibrium on welfare and existence and +now we're going to do gorman aggregation + + align:start position:0% +now we're going to do gorman aggregation + + + align:start position:0% +now we're going to do gorman aggregation +today and then finish this segment with + + align:start position:0% +today and then finish this segment with + + + align:start position:0% +today and then finish this segment with +identification + + align:start position:0% +identification + + + align:start position:0% +identification +we have two lectures to finish out the + + align:start position:0% +we have two lectures to finish out the + + + align:start position:0% +we have two lectures to finish out the +class so that's + + align:start position:0% +class so that's + + + align:start position:0% +class so that's +where we are in terms of the reading + + align:start position:0% +where we are in terms of the reading + + + align:start position:0% +where we are in terms of the reading +list for today + + align:start position:0% +list for today + + + align:start position:0% +list for today +there's only + + align:start position:0% +there's only + + + align:start position:0% +there's only +one thing there + + align:start position:0% +one thing there + + + align:start position:0% +one thing there +and it's the place from where i drew a + + align:start position:0% +and it's the place from where i drew a + + + align:start position:0% +and it's the place from where i drew a +lot of the material for the welfare + + align:start position:0% +lot of the material for the welfare + + + align:start position:0% +lot of the material for the welfare +theorem for the gorman aggregation my + + align:start position:0% +theorem for the gorman aggregation my + + + align:start position:0% +theorem for the gorman aggregation my +colleague jerome it is starred and but + + align:start position:0% +colleague jerome it is starred and but + + + align:start position:0% +colleague jerome it is starred and but +it is also pretty extensively covered + + align:start position:0% +it is also pretty extensively covered + + + align:start position:0% +it is also pretty extensively covered +today + + align:start position:0% +today + + + align:start position:0% +today +as well + + align:start position:0% +as well + + + align:start position:0% +as well +and we have the study guide so + + align:start position:0% +and we have the study guide so + + + align:start position:0% +and we have the study guide so +last time we did + + align:start position:0% +last time we did + + + align:start position:0% +last time we did +concepts of existence and in various + + align:start position:0% +concepts of existence and in various + + + align:start position:0% +concepts of existence and in various +distinct ways + + align:start position:0% +distinct ways + + + align:start position:0% +distinct ways +there weren't too many review questions + + align:start position:0% +there weren't too many review questions + + + align:start position:0% +there weren't too many review questions +here i didn't ask the first set of them + + align:start position:0% +here i didn't ask the first set of them + + + align:start position:0% +here i didn't ask the first set of them +but + + align:start position:0% +but + + + align:start position:0% +but +we get down to nikishi + + align:start position:0% +we get down to nikishi + + + align:start position:0% +we get down to nikishi +so how does negishi use the first and + + align:start position:0% +so how does negishi use the first and + + + align:start position:0% +so how does negishi use the first and +second welfare theorems to generate a + + align:start position:0% +second welfare theorems to generate a + + + align:start position:0% +second welfare theorems to generate a +mapping in lambda + + align:start position:0% +mapping in lambda + + + align:start position:0% +mapping in lambda +weights + + align:start position:0% +weights + + + align:start position:0% +weights +the fixed point of which is a + + align:start position:0% +the fixed point of which is a + + + align:start position:0% +the fixed point of which is a +competitive equilibrium and since i was + + align:start position:0% +competitive equilibrium and since i was + + + align:start position:0% +competitive equilibrium and since i was +calling on everyone last time let's let + + align:start position:0% +calling on everyone last time let's let + + + align:start position:0% +calling on everyone last time let's let +me just take volunteers + + align:start position:0% + + + + align:start position:0% + +hopefully there are volunteers + + align:start position:0% + + + + align:start position:0% + +i was + + align:start position:0% +i was + + + align:start position:0% +i was +going you go ahead + + align:start position:0% +going you go ahead + + + align:start position:0% +going you go ahead +oh + + align:start position:0% +oh + + + align:start position:0% +oh +um i was about to say that i was a + + align:start position:0% +um i was about to say that i was a + + + align:start position:0% +um i was about to say that i was a +little unclear on the proof overall but + + align:start position:0% +little unclear on the proof overall but + + + align:start position:0% +little unclear on the proof overall but +i remember that + + align:start position:0% +i remember that + + + align:start position:0% +i remember that +um we use the fact that like for any + + align:start position:0% +um we use the fact that like for any + + + align:start position:0% +um we use the fact that like for any +lambda + + align:start position:0% +lambda + + + align:start position:0% +lambda +um the corresponding pareto optimal + + align:start position:0% +um the corresponding pareto optimal + + + align:start position:0% +um the corresponding pareto optimal +allocation + + align:start position:0% +allocation + + + align:start position:0% +allocation +would be in equilibrium with uh + + align:start position:0% +would be in equilibrium with uh + + + align:start position:0% +would be in equilibrium with uh +transfers uh like by the second welfare + + align:start position:0% +transfers uh like by the second welfare + + + align:start position:0% +transfers uh like by the second welfare +theorem and we like to use that to prove + + align:start position:0% +theorem and we like to use that to prove + + + align:start position:0% +theorem and we like to use that to prove +negishi's theorem + + align:start position:0% +negishi's theorem + + + align:start position:0% +negishi's theorem +yeah that's right we used to have the + + align:start position:0% +yeah that's right we used to have the + + + align:start position:0% +yeah that's right we used to have the +second one heavily the first one is that + + align:start position:0% +second one heavily the first one is that + + + align:start position:0% +second one heavily the first one is that +any competitive equilibrium is pareto + + align:start position:0% +any competitive equilibrium is pareto + + + align:start position:0% +any competitive equilibrium is pareto +optimal + + align:start position:0% +optimal + + + align:start position:0% +optimal +and hence corresponds to some lambda + + align:start position:0% +and hence corresponds to some lambda + + + align:start position:0% +and hence corresponds to some lambda +weights + + align:start position:0% +weights + + + align:start position:0% +weights +in the pareto problem so the + + align:start position:0% +in the pareto problem so the + + + align:start position:0% +in the pareto problem so the +negishi's + + align:start position:0% +negishi's + + + align:start position:0% +negishi's +mapping + + align:start position:0% +mapping + + + align:start position:0% +mapping +is to find + + align:start position:0% +is to find + + + align:start position:0% +is to find +a way to find + + align:start position:0% +a way to find + + + align:start position:0% +a way to find +particular special lambdas + + align:start position:0% +particular special lambdas + + + align:start position:0% +particular special lambdas +of the competitive equilibrium with + + align:start position:0% +of the competitive equilibrium with + + + align:start position:0% +of the competitive equilibrium with +private ownership + + align:start position:0% +private ownership + + + align:start position:0% +private ownership +that is a fixed point of his mapping + + align:start position:0% + + + + align:start position:0% + +i realized after class in part talking + + align:start position:0% +i realized after class in part talking + + + align:start position:0% +i realized after class in part talking +with one of you who + + align:start position:0% + + + + align:start position:0% + +came to office hours that um + + align:start position:0% + + + + align:start position:0% + +i i never i think i neglected to say the + + align:start position:0% +i i never i think i neglected to say the + + + align:start position:0% +i i never i think i neglected to say the +the obvious + + align:start position:0% +the obvious + + + align:start position:0% +the obvious +what i did say is to find the lambda + + align:start position:0% +what i did say is to find the lambda + + + align:start position:0% +what i did say is to find the lambda +such that + + align:start position:0% +such that + + + align:start position:0% +such that +the valuation of expenditures under the + + align:start position:0% +the valuation of expenditures under the + + + align:start position:0% +the valuation of expenditures under the +pareto optimum uses using the second + + align:start position:0% +pareto optimum uses using the second + + + align:start position:0% +pareto optimum uses using the second +welfare theorem is equal to + + align:start position:0% +welfare theorem is equal to + + + align:start position:0% +welfare theorem is equal to +the valuation of the endowment plus + + align:start position:0% +the valuation of the endowment plus + + + align:start position:0% +the valuation of the endowment plus +shares on profits + + align:start position:0% +shares on profits + + + align:start position:0% +shares on profits +that corresponds to the competitive + + align:start position:0% +that corresponds to the competitive + + + align:start position:0% +that corresponds to the competitive +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +um + + align:start position:0% +um + + + align:start position:0% +um +but what i + + align:start position:0% +but what i + + + align:start position:0% +but what i +i think i neglected to say was + + align:start position:0% +i think i neglected to say was + + + align:start position:0% +i think i neglected to say was +maybe i did say it bears repeating + + align:start position:0% +maybe i did say it bears repeating + + + align:start position:0% +maybe i did say it bears repeating +that if you initially guess a lambda + + align:start position:0% +that if you initially guess a lambda + + + align:start position:0% +that if you initially guess a lambda +which is high + + align:start position:0% +which is high + + + align:start position:0% +which is high +than the value for a particular + + align:start position:0% +than the value for a particular + + + align:start position:0% +than the value for a particular +household then the valuation of that + + align:start position:0% +household then the valuation of that + + + align:start position:0% +household then the valuation of that +household's expenditures will be + + align:start position:0% +household's expenditures will be + + + align:start position:0% +household's expenditures will be +large relative to + + align:start position:0% +large relative to + + + align:start position:0% +large relative to +the valuation + + align:start position:0% +the valuation + + + align:start position:0% +the valuation +of + + align:start position:0% +of + + + align:start position:0% +of +the wealth and the private ownership + + align:start position:0% +the wealth and the private ownership + + + align:start position:0% +the wealth and the private ownership +economy + + align:start position:0% +economy + + + align:start position:0% +economy +so you know sort of intuitively then you + + align:start position:0% +so you know sort of intuitively then you + + + align:start position:0% +so you know sort of intuitively then you +lower that lambda weight + + align:start position:0% +lower that lambda weight + + + align:start position:0% +lower that lambda weight +that links up to something we learned + + align:start position:0% +that links up to something we learned + + + align:start position:0% +that links up to something we learned +when we did this the second welfare + + align:start position:0% +when we did this the second welfare + + + align:start position:0% +when we did this the second welfare +theorem which is + + align:start position:0% +theorem which is + + + align:start position:0% +theorem which is +those lambdas are inversely proportional + + align:start position:0% +those lambdas are inversely proportional + + + align:start position:0% +those lambdas are inversely proportional +to the marginal utility of wealth + + align:start position:0% +to the marginal utility of wealth + + + align:start position:0% +to the marginal utility of wealth +so + + align:start position:0% +so + + + align:start position:0% +so +you know if the land is too high the guy + + align:start position:0% +you know if the land is too high the guy + + + align:start position:0% +you know if the land is too high the guy +has too much + + align:start position:0% +has too much + + + align:start position:0% +has too much +the evaluation of expenditures is too + + align:start position:0% +the evaluation of expenditures is too + + + align:start position:0% +the evaluation of expenditures is too +high + + align:start position:0% +high + + + align:start position:0% +high +so the margin utility of wealth with + + align:start position:0% +so the margin utility of wealth with + + + align:start position:0% +so the margin utility of wealth with +concave utility is low + + align:start position:0% +concave utility is low + + + align:start position:0% +concave utility is low +so you want to move in the direction of + + align:start position:0% +so you want to move in the direction of + + + align:start position:0% +so you want to move in the direction of +increasing + + align:start position:0% +increasing + + + align:start position:0% +increasing +the margin utility + + align:start position:0% +the margin utility + + + align:start position:0% +the margin utility +of wealth which effectively removes + + align:start position:0% +of wealth which effectively removes + + + align:start position:0% +of wealth which effectively removes +wealth by lowering lambda + + align:start position:0% + + + + align:start position:0% + +so anyway + + align:start position:0% +so anyway + + + align:start position:0% +so anyway +thank you + + align:start position:0% + + + + align:start position:0% + +uh next question define a mixed strategy + + align:start position:0% +uh next question define a mixed strategy + + + align:start position:0% +uh next question define a mixed strategy +nash equilibrium + + align:start position:0% +nash equilibrium + + + align:start position:0% +nash equilibrium +i think i i can do this one + + align:start position:0% +i think i i can do this one + + + align:start position:0% +i think i i can do this one +um so like a mixed strategy nash + + align:start position:0% +um so like a mixed strategy nash + + + align:start position:0% +um so like a mixed strategy nash +equilibrium is it's it's it's a type of + + align:start position:0% +equilibrium is it's it's it's a type of + + + align:start position:0% +equilibrium is it's it's it's a type of +nash equilibrium where at least some of + + align:start position:0% +nash equilibrium where at least some of + + + align:start position:0% +nash equilibrium where at least some of +the players are + + align:start position:0% +the players are + + + align:start position:0% +the players are +um are choosing some choose some of the + + align:start position:0% +um are choosing some choose some of the + + + align:start position:0% +um are choosing some choose some of the +options at random so like there's some + + align:start position:0% +options at random so like there's some + + + align:start position:0% +options at random so like there's some +weighted probabilities + + align:start position:0% +weighted probabilities + + + align:start position:0% +weighted probabilities +where um you can have some chance of + + align:start position:0% +where um you can have some chance of + + + align:start position:0% +where um you can have some chance of +doing option a sometimes you're doing + + align:start position:0% +doing option a sometimes you're doing + + + align:start position:0% +doing option a sometimes you're doing +option b and so on and the + + align:start position:0% +option b and so on and the + + + align:start position:0% +option b and so on and the +in order for this to work that the + + align:start position:0% +in order for this to work that the + + + align:start position:0% +in order for this to work that the +the player who's doing mixed stuff has + + align:start position:0% +the player who's doing mixed stuff has + + + align:start position:0% +the player who's doing mixed stuff has +to be indifferent from all the things + + align:start position:0% +to be indifferent from all the things + + + align:start position:0% +to be indifferent from all the things +with non-zero between all the different + + align:start position:0% +with non-zero between all the different + + + align:start position:0% +with non-zero between all the different +options with nonzero probabilities and + + align:start position:0% +options with nonzero probabilities and + + + align:start position:0% +options with nonzero probabilities and +it also has to be in such in such a way + + align:start position:0% +it also has to be in such in such a way + + + align:start position:0% +it also has to be in such in such a way +that like again no one has any incentive + + align:start position:0% +that like again no one has any incentive + + + align:start position:0% +that like again no one has any incentive +to deviate from the strategy + + align:start position:0% +to deviate from the strategy + + + align:start position:0% +to deviate from the strategy +right the last thing especially is key + + align:start position:0% +right the last thing especially is key + + + align:start position:0% +right the last thing especially is key +so + + align:start position:0% +so + + + align:start position:0% +so +the the mixed strategy nash equilibrium + + align:start position:0% +the the mixed strategy nash equilibrium + + + align:start position:0% +the the mixed strategy nash equilibrium +is taking each player takes as given + + align:start position:0% +is taking each player takes as given + + + align:start position:0% +is taking each player takes as given +a configuration of mixed strategies of + + align:start position:0% +a configuration of mixed strategies of + + + align:start position:0% +a configuration of mixed strategies of +the others + + align:start position:0% +the others + + + align:start position:0% +the others +sort of a star strategy so to speak and + + align:start position:0% +sort of a star strategy so to speak and + + + align:start position:0% +sort of a star strategy so to speak and +then feels free to + + align:start position:0% +then feels free to + + + align:start position:0% +then feels free to +choose the best one for his or herself + + align:start position:0% +choose the best one for his or herself + + + align:start position:0% +choose the best one for his or herself +but that will end up being exactly the + + align:start position:0% +but that will end up being exactly the + + + align:start position:0% +but that will end up being exactly the +star strategy to begin with + + align:start position:0% +star strategy to begin with + + + align:start position:0% +star strategy to begin with +so it's like + + align:start position:0% +so it's like + + + align:start position:0% +so it's like +self-fulfilling + + align:start position:0% +self-fulfilling + + + align:start position:0% +self-fulfilling +in the space of strategies thank you + + align:start position:0% +in the space of strategies thank you + + + align:start position:0% +in the space of strategies thank you +that was a good answer + + align:start position:0% +that was a good answer + + + align:start position:0% +that was a good answer +and then the last one + + align:start position:0% +and then the last one + + + align:start position:0% +and then the last one +how do we give an incentive for traders + + align:start position:0% +how do we give an incentive for traders + + + align:start position:0% +how do we give an incentive for traders +to live up to their promises and achieve + + align:start position:0% +to live up to their promises and achieve + + + align:start position:0% +to live up to their promises and achieve +a raising equilibrium + + align:start position:0% +a raising equilibrium + + + align:start position:0% +a raising equilibrium +so i did this in the context of + + align:start position:0% +so i did this in the context of + + + align:start position:0% +so i did this in the context of +the market for trades in u.s treasuries + + align:start position:0% +the market for trades in u.s treasuries + + + align:start position:0% +the market for trades in u.s treasuries +in new york + + align:start position:0% +in new york + + + align:start position:0% +in new york +which is a trade agreed to buy treasury + + align:start position:0% +which is a trade agreed to buy treasury + + + align:start position:0% +which is a trade agreed to buy treasury +for liquidity + + align:start position:0% +for liquidity + + + align:start position:0% +for liquidity +i mentioned that in fact there were + + align:start position:0% +i mentioned that in fact there were + + + align:start position:0% +i mentioned that in fact there were +trade fails + + align:start position:0% +trade fails + + + align:start position:0% +trade fails +where they don't live up to their + + align:start position:0% +where they don't live up to their + + + align:start position:0% +where they don't live up to their +agreement because + + align:start position:0% +agreement because + + + align:start position:0% +agreement because +the party selling the treasury doesn't + + align:start position:0% +the party selling the treasury doesn't + + + align:start position:0% +the party selling the treasury doesn't +own it + + align:start position:0% +own it + + + align:start position:0% +own it +can't transfer it at the time + + align:start position:0% +can't transfer it at the time + + + align:start position:0% +can't transfer it at the time +when settlement is due or the person who + + align:start position:0% +when settlement is due or the person who + + + align:start position:0% +when settlement is due or the person who +promised to pay liquidity doesn't have + + align:start position:0% +promised to pay liquidity doesn't have + + + align:start position:0% +promised to pay liquidity doesn't have +sufficient liquidity and then i mapped + + align:start position:0% +sufficient liquidity and then i mapped + + + align:start position:0% +sufficient liquidity and then i mapped +that into + + align:start position:0% +that into + + + align:start position:0% +that into +the volrazian equilibrium framework + + align:start position:0% + + + + align:start position:0% + +so let me ask it again how do we give an + + align:start position:0% +so let me ask it again how do we give an + + + align:start position:0% +so let me ask it again how do we give an +incentive for trade trade + + align:start position:0% +incentive for trade trade + + + align:start position:0% +incentive for trade trade +for traders i guess it should be + + align:start position:0% +for traders i guess it should be + + + align:start position:0% +for traders i guess it should be +to live up to their promise and + + align:start position:0% +to live up to their promise and + + + align:start position:0% +to live up to their promise and +achievable raising equilibrium + + align:start position:0% + + + + align:start position:0% + +anybody remember + + align:start position:0% + + + + align:start position:0% + +i remember there was a penalty for + + align:start position:0% +i remember there was a penalty for + + + align:start position:0% +i remember there was a penalty for +liquidity right if the credit was + + align:start position:0% +liquidity right if the credit was + + + align:start position:0% +liquidity right if the credit was +negative then + + align:start position:0% +negative then + + + align:start position:0% +negative then +um it will have uh this utility and so + + align:start position:0% +um it will have uh this utility and so + + + align:start position:0% +um it will have uh this utility and so +you're in + + align:start position:0% +you're in + + + align:start position:0% +you're in +so in the end in order to achieve the + + align:start position:0% +so in the end in order to achieve the + + + align:start position:0% +so in the end in order to achieve the +variation allocation we need to + + align:start position:0% +variation allocation we need to + + + align:start position:0% +variation allocation we need to +um a lot of all the + + align:start position:0% +um a lot of all the + + + align:start position:0% +um a lot of all the +that was uh + + align:start position:0% +that was uh + + + align:start position:0% +that was uh +there was a bait we need to let it open + + align:start position:0% +there was a bait we need to let it open + + + align:start position:0% +there was a bait we need to let it open +equal to zero so that there was no + + align:start position:0% +equal to zero so that there was no + + + align:start position:0% +equal to zero so that there was no +exercise uh demand no + + align:start position:0% +exercise uh demand no + + + align:start position:0% +exercise uh demand no +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +i mean + + align:start position:0% +i mean + + + align:start position:0% +i mean +yeah yeah that's good + + align:start position:0% + + + + align:start position:0% + +we should we want to promise that the + + align:start position:0% +we should we want to promise that the + + + align:start position:0% +we should we want to promise that the +the endowment is + + align:start position:0% +the endowment is + + + align:start position:0% +the endowment is +the endowment is equal to the + + align:start position:0% +the endowment is equal to the + + + align:start position:0% +the endowment is equal to the +the allocation station of the allocation + + align:start position:0% +the allocation station of the allocation + + + align:start position:0% +the allocation station of the allocation +right that's good so the the problem is + + align:start position:0% +right that's good so the the problem is + + + align:start position:0% +right that's good so the the problem is +um they're submitting bids and we're + + align:start position:0% +um they're submitting bids and we're + + + align:start position:0% +um they're submitting bids and we're +looking for a nash equilibrium + + align:start position:0% +looking for a nash equilibrium + + + align:start position:0% +looking for a nash equilibrium +um + + align:start position:0% +um + + + align:start position:0% +um +the bids consist of + + align:start position:0% +the bids consist of + + + align:start position:0% +the bids consist of +orders to buy and also orders to sell + + align:start position:0% +orders to buy and also orders to sell + + + align:start position:0% +orders to buy and also orders to sell +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +we're shooting for the valrazian + + align:start position:0% +we're shooting for the valrazian + + + align:start position:0% +we're shooting for the valrazian +equilibrium in particular the budget + + align:start position:0% +equilibrium in particular the budget + + + align:start position:0% +equilibrium in particular the budget +constraints so we want for each trader + + align:start position:0% +constraints so we want for each trader + + + align:start position:0% +constraints so we want for each trader +that the valuation + + align:start position:0% +that the valuation + + + align:start position:0% +that the valuation +of what they're buying is at least + + align:start position:0% +of what they're buying is at least + + + align:start position:0% +of what they're buying is at least +matched by the valuation of what they're + + align:start position:0% +matched by the valuation of what they're + + + align:start position:0% +matched by the valuation of what they're +selling in other words + + align:start position:0% +selling in other words + + + align:start position:0% +selling in other words +they have sufficient liquidity + + align:start position:0% +they have sufficient liquidity + + + align:start position:0% +they have sufficient liquidity +and if we didn't put in a penalty + + align:start position:0% +and if we didn't put in a penalty + + + align:start position:0% +and if we didn't put in a penalty +everybody would overspend + + align:start position:0% +everybody would overspend + + + align:start position:0% +everybody would overspend +because + + align:start position:0% +because + + + align:start position:0% +because +why not + + align:start position:0% +why not + + + align:start position:0% +why not +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so yeah so then the penalty that you + + align:start position:0% +so yeah so then the penalty that you + + + align:start position:0% +so yeah so then the penalty that you +mentioned so beta is + + align:start position:0% +mentioned so beta is + + + align:start position:0% +mentioned so beta is +negative when beta is negative that + + align:start position:0% +negative when beta is negative that + + + align:start position:0% +negative when beta is negative that +means they're spending more than their + + align:start position:0% +means they're spending more than their + + + align:start position:0% +means they're spending more than their +they have in revenue that's a bad thing + + align:start position:0% +they have in revenue that's a bad thing + + + align:start position:0% +they have in revenue that's a bad thing +so we effectively make the penalty beta + + align:start position:0% +so we effectively make the penalty beta + + + align:start position:0% +so we effectively make the penalty beta +or sorry + + align:start position:0% +or sorry + + + align:start position:0% +or sorry +i can't remember the notation i think it + + align:start position:0% +i can't remember the notation i think it + + + align:start position:0% +i can't remember the notation i think it +was lambda times beta sufficiently high + + align:start position:0% +was lambda times beta sufficiently high + + + align:start position:0% +was lambda times beta sufficiently high +so that + + align:start position:0% + + + + align:start position:0% + +so then they do the right trade-off they + + align:start position:0% +so then they do the right trade-off they + + + align:start position:0% +so then they do the right trade-off they +look at how much they would get in + + align:start position:0% +look at how much they would get in + + + align:start position:0% +look at how much they would get in +utility from buying this stuff + + align:start position:0% +utility from buying this stuff + + + align:start position:0% +utility from buying this stuff +directly + + align:start position:0% +directly + + + align:start position:0% +directly +and weigh that against the disutility of + + align:start position:0% +and weigh that against the disutility of + + + align:start position:0% +and weigh that against the disutility of +the penalty + + align:start position:0% +the penalty + + + align:start position:0% +the penalty +the the + + align:start position:0% +the the + + + align:start position:0% +the the +magnitude of the penalty had to do with + + align:start position:0% +magnitude of the penalty had to do with + + + align:start position:0% +magnitude of the penalty had to do with +the marginal utility of income + + align:start position:0% +the marginal utility of income + + + align:start position:0% +the marginal utility of income +that lagrange multiplier we keep + + align:start position:0% +that lagrange multiplier we keep + + + align:start position:0% +that lagrange multiplier we keep +focusing on + + align:start position:0% +focusing on + + + align:start position:0% +focusing on +in the competitive equilibrium in the + + align:start position:0% +in the competitive equilibrium in the + + + align:start position:0% +in the competitive equilibrium in the +budget constraint + + align:start position:0% +budget constraint + + + align:start position:0% +budget constraint +so the marginal utility of income + + align:start position:0% +so the marginal utility of income + + + align:start position:0% +so the marginal utility of income +represents + + align:start position:0% +represents + + + align:start position:0% +represents +the incremental gain from having epsilon + + align:start position:0% +the incremental gain from having epsilon + + + align:start position:0% +the incremental gain from having epsilon +more liquidity + + align:start position:0% +more liquidity + + + align:start position:0% +more liquidity +and they're tempted to spend more than + + align:start position:0% +and they're tempted to spend more than + + + align:start position:0% +and they're tempted to spend more than +they have + + align:start position:0% +they have + + + align:start position:0% +they have +to go in that epsilon direction + + align:start position:0% +to go in that epsilon direction + + + align:start position:0% +to go in that epsilon direction +but the penalty + + align:start position:0% +but the penalty + + + align:start position:0% +but the penalty +is large enough + + align:start position:0% +is large enough + + + align:start position:0% +is large enough +so as to dominate that gain and they + + align:start position:0% +so as to dominate that gain and they + + + align:start position:0% +so as to dominate that gain and they +don't deviate + + align:start position:0% + + + + align:start position:0% + +well i i + + align:start position:0% +well i i + + + align:start position:0% +well i i +in ear marking this question i recognize + + align:start position:0% +in ear marking this question i recognize + + + align:start position:0% +in ear marking this question i recognize +that we rushed a bit at the end in fact + + align:start position:0% +that we rushed a bit at the end in fact + + + align:start position:0% +that we rushed a bit at the end in fact +i went over + + align:start position:0% +i went over + + + align:start position:0% +i went over +the class time by a couple of minutes so + + align:start position:0% +the class time by a couple of minutes so + + + align:start position:0% +the class time by a couple of minutes so +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +hopefully that was a useful review + + align:start position:0% +hopefully that was a useful review + + + align:start position:0% +hopefully that was a useful review +any other questions from last time + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so now i want to get to aggregation this + + align:start position:0% +so now i want to get to aggregation this + + + align:start position:0% +so now i want to get to aggregation this +is kind of an exciting lecture + + align:start position:0% +is kind of an exciting lecture + + + align:start position:0% +is kind of an exciting lecture +in the sense that + + align:start position:0% +in the sense that + + + align:start position:0% +in the sense that +it goes back and + + align:start position:0% +it goes back and + + + align:start position:0% +it goes back and +reviews some of the things we've been + + align:start position:0% +reviews some of the things we've been + + + align:start position:0% +reviews some of the things we've been +doing before certainly + + align:start position:0% +doing before certainly + + + align:start position:0% +doing before certainly +the basics of consumer theory + + align:start position:0% +the basics of consumer theory + + + align:start position:0% +the basics of consumer theory +with utility maximization + + align:start position:0% +with utility maximization + + + align:start position:0% +with utility maximization +some things about lagrangians and + + align:start position:0% +some things about lagrangians and + + + align:start position:0% +some things about lagrangians and +envelope theorems + + align:start position:0% +envelope theorems + + + align:start position:0% +envelope theorems +it also goes back to the first + + align:start position:0% +it also goes back to the first + + + align:start position:0% +it also goes back to the first +application we have had of consumers + + align:start position:0% +application we have had of consumers + + + align:start position:0% +application we have had of consumers +maximizing utility subject to budgets + + align:start position:0% +maximizing utility subject to budgets + + + align:start position:0% +maximizing utility subject to budgets +and what happens when income changes and + + align:start position:0% +and what happens when income changes and + + + align:start position:0% +and what happens when income changes and +so on so + + align:start position:0% +so on so + + + align:start position:0% +so on so +we already talked about angles curves + + align:start position:0% +we already talked about angles curves + + + align:start position:0% +we already talked about angles curves +and given goods and so on and + + align:start position:0% +and given goods and so on and + + + align:start position:0% +and given goods and so on and +so you have the micro background already + + align:start position:0% +so you have the micro background already + + + align:start position:0% +so you have the micro background already +so you can judge the plausibility of the + + align:start position:0% +so you can judge the plausibility of the + + + align:start position:0% +so you can judge the plausibility of the +assumptions we're about to make in order + + align:start position:0% +assumptions we're about to make in order + + + align:start position:0% +assumptions we're about to make in order +to allow the aggregation and the + + align:start position:0% +to allow the aggregation and the + + + align:start position:0% +to allow the aggregation and the +aggregation was used when we did like + + align:start position:0% +aggregation was used when we did like + + + align:start position:0% +aggregation was used when we did like +free trade + + align:start position:0% +free trade + + + align:start position:0% +free trade +we would talk about a representative + + align:start position:0% +we would talk about a representative + + + align:start position:0% +we would talk about a representative +consumer not just robinson crusoe one + + align:start position:0% +consumer not just robinson crusoe one + + + align:start position:0% +consumer not just robinson crusoe one +man on the island but someone + + align:start position:0% +man on the island but someone + + + align:start position:0% +man on the island but someone +representing the entire u.s population + + align:start position:0% +representing the entire u.s population + + + align:start position:0% +representing the entire u.s population +so that is a big leap of faith today + + align:start position:0% +so that is a big leap of faith today + + + align:start position:0% +so that is a big leap of faith today +we'll spell out what it takes to do that + + align:start position:0% +we'll spell out what it takes to do that + + + align:start position:0% +we'll spell out what it takes to do that +so this is going to be gorman + + align:start position:0% +so this is going to be gorman + + + align:start position:0% +so this is going to be gorman +aggregation and we're going to do it in + + align:start position:0% +aggregation and we're going to do it in + + + align:start position:0% +aggregation and we're going to do it in +the positive sense of predicting what + + align:start position:0% +the positive sense of predicting what + + + align:start position:0% +the positive sense of predicting what +will happen and in the normative sense + + align:start position:0% +will happen and in the normative sense + + + align:start position:0% +will happen and in the normative sense +of making statements about consumer + + align:start position:0% +of making statements about consumer + + + align:start position:0% +of making statements about consumer +welfare and then we're going to have + + align:start position:0% +welfare and then we're going to have + + + align:start position:0% +welfare and then we're going to have +indirect utility functions gorman polar + + align:start position:0% +indirect utility functions gorman polar + + + align:start position:0% +indirect utility functions gorman polar +forms and the rest i already mentioned + + align:start position:0% +forms and the rest i already mentioned + + + align:start position:0% +forms and the rest i already mentioned +so + + align:start position:0% +so + + + align:start position:0% +so +some micro but mostly macro economists + + align:start position:0% +some micro but mostly macro economists + + + align:start position:0% +some micro but mostly macro economists +assume the representative consumer or + + align:start position:0% +assume the representative consumer or + + + align:start position:0% +assume the representative consumer or +representative agents it kind of comes + + align:start position:0% +representative agents it kind of comes + + + align:start position:0% +representative agents it kind of comes +naturally because they're worried + + align:start position:0% +naturally because they're worried + + + align:start position:0% +naturally because they're worried +worrying about aggregates not + + align:start position:0% +worrying about aggregates not + + + align:start position:0% +worrying about aggregates not +distributional aspects + + align:start position:0% +distributional aspects + + + align:start position:0% +distributional aspects +so + + align:start position:0% +so + + + align:start position:0% +so +that gives them and us a tractable way + + align:start position:0% +that gives them and us a tractable way + + + align:start position:0% +that gives them and us a tractable way +of understanding market demand and + + align:start position:0% +of understanding market demand and + + + align:start position:0% +of understanding market demand and +supply for that matter and allows pretty + + align:start position:0% +supply for that matter and allows pretty + + + align:start position:0% +supply for that matter and allows pretty +easy welfare analysis because there's + + align:start position:0% +easy welfare analysis because there's + + + align:start position:0% +easy welfare analysis because there's +only one person so those are all the + + align:start position:0% +only one person so those are all the + + + align:start position:0% +only one person so those are all the +advantages but we'll see how realistic + + align:start position:0% +advantages but we'll see how realistic + + + align:start position:0% +advantages but we'll see how realistic +it is okay so here's the utility + + align:start position:0% +it is okay so here's the utility + + + align:start position:0% +it is okay so here's the utility +maximization problem + + align:start position:0% +maximization problem + + + align:start position:0% +maximization problem +maximizing + + align:start position:0% +maximizing + + + align:start position:0% +maximizing +we'll suppress the labels here for + + align:start position:0% +we'll suppress the labels here for + + + align:start position:0% +we'll suppress the labels here for +households i and h and so on so this + + align:start position:0% +households i and h and so on so this + + + align:start position:0% +households i and h and so on so this +household has a utility function + + align:start position:0% +household has a utility function + + + align:start position:0% +household has a utility function +represented by u of x where x is in the + + align:start position:0% +represented by u of x where x is in the + + + align:start position:0% +represented by u of x where x is in the +consumption set + + align:start position:0% +consumption set + + + align:start position:0% +consumption set +and the valuation of expenditures at + + align:start position:0% +and the valuation of expenditures at + + + align:start position:0% +and the valuation of expenditures at +prices p cannot exceed wealth w + + align:start position:0% +prices p cannot exceed wealth w + + + align:start position:0% +prices p cannot exceed wealth w +so we call the solution to this problem + + align:start position:0% +so we call the solution to this problem + + + align:start position:0% +so we call the solution to this problem +after maxing it out the achieved + + align:start position:0% +after maxing it out the achieved + + + align:start position:0% +after maxing it out the achieved +maximized utility + + align:start position:0% +maximized utility + + + align:start position:0% +maximized utility +is called the value and this function v + + align:start position:0% +is called the value and this function v + + + align:start position:0% +is called the value and this function v +is called the indirect utility function + + align:start position:0% +is called the indirect utility function + + + align:start position:0% +is called the indirect utility function +v for value so + + align:start position:0% +v for value so + + + align:start position:0% +v for value so +it takes as given the parameters that + + align:start position:0% +it takes as given the parameters that + + + align:start position:0% +it takes as given the parameters that +the household takes is given namely the + + align:start position:0% +the household takes is given namely the + + + align:start position:0% +the household takes is given namely the +price vector p and wealth w + + align:start position:0% +price vector p and wealth w + + + align:start position:0% +price vector p and wealth w +so it is the maximal attainable utility + + align:start position:0% +so it is the maximal attainable utility + + + align:start position:0% +so it is the maximal attainable utility +in the budget set as a function of those + + align:start position:0% +in the budget set as a function of those + + + align:start position:0% +in the budget set as a function of those +parameters + + align:start position:0% +parameters + + + align:start position:0% +parameters +and the bottom line here you can just + + align:start position:0% +and the bottom line here you can just + + + align:start position:0% +and the bottom line here you can just +see + + align:start position:0% +see + + + align:start position:0% +see +if x of p and w is the maximizer we just + + align:start position:0% +if x of p and w is the maximizer we just + + + align:start position:0% +if x of p and w is the maximizer we just +stick it back into the utility function + + align:start position:0% +stick it back into the utility function + + + align:start position:0% +stick it back into the utility function +and that would be the optimized value + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so there are very + + align:start position:0% +so there are very + + + align:start position:0% +so there are very +useful properties of this indirect + + align:start position:0% +useful properties of this indirect + + + align:start position:0% +useful properties of this indirect +utility function + + align:start position:0% +utility function + + + align:start position:0% +utility function +and they are reviewed on this slide + + align:start position:0% +and they are reviewed on this slide + + + align:start position:0% +and they are reviewed on this slide +let's assume the consumption set is a + + align:start position:0% +let's assume the consumption set is a + + + align:start position:0% +let's assume the consumption set is a +subset of + + align:start position:0% +subset of + + + align:start position:0% +subset of +finite dimensional l dimensional + + align:start position:0% +finite dimensional l dimensional + + + align:start position:0% +finite dimensional l dimensional +euclidean space utility functions are + + align:start position:0% +euclidean space utility functions are + + + align:start position:0% +euclidean space utility functions are +continuous representing a preference + + align:start position:0% +continuous representing a preference + + + align:start position:0% +continuous representing a preference +relation that is rational and continuous + + align:start position:0% +relation that is rational and continuous + + + align:start position:0% +relation that is rational and continuous +the the indirect utility just defined + + align:start position:0% +the the indirect utility just defined + + + align:start position:0% +the the indirect utility just defined +first of all this v + + align:start position:0% +first of all this v + + + align:start position:0% +first of all this v +as a function of p and w is homogeneous + + align:start position:0% +as a function of p and w is homogeneous + + + align:start position:0% +as a function of p and w is homogeneous +of degree zero and p and w + + align:start position:0% +of degree zero and p and w + + + align:start position:0% +of degree zero and p and w +because as you already know if you for + + align:start position:0% +because as you already know if you for + + + align:start position:0% +because as you already know if you for +example double prices and wealth it + + align:start position:0% +example double prices and wealth it + + + align:start position:0% +example double prices and wealth it +doesn't change the picture of consumer + + align:start position:0% +doesn't change the picture of consumer + + + align:start position:0% +doesn't change the picture of consumer +maximization + + align:start position:0% +maximization + + + align:start position:0% +maximization +and you get the same solution it's like + + align:start position:0% +and you get the same solution it's like + + + align:start position:0% +and you get the same solution it's like +there's no money illusion here if price + + align:start position:0% +there's no money illusion here if price + + + align:start position:0% +there's no money illusion here if price +is double but wealth + + align:start position:0% +is double but wealth + + + align:start position:0% +is double but wealth +also doubles + + align:start position:0% +also doubles + + + align:start position:0% +also doubles +you're just as well off as you were + + align:start position:0% +you're just as well off as you were + + + align:start position:0% +you're just as well off as you were +before and not worse off + + align:start position:0% +before and not worse off + + + align:start position:0% +before and not worse off +this indirect utility function + + align:start position:0% +this indirect utility function + + + align:start position:0% +this indirect utility function +has intuitive derivatives with respect + + align:start position:0% +has intuitive derivatives with respect + + + align:start position:0% +has intuitive derivatives with respect +to p and w + + align:start position:0% +to p and w + + + align:start position:0% +to p and w +increasing p makes you worse off or at + + align:start position:0% +increasing p makes you worse off or at + + + align:start position:0% +increasing p makes you worse off or at +least not better off + + align:start position:0% +least not better off + + + align:start position:0% +least not better off +increasing w makes you better off + + align:start position:0% +increasing w makes you better off + + + align:start position:0% +increasing w makes you better off +w is wealth prices are what you have to + + align:start position:0% +w is wealth prices are what you have to + + + align:start position:0% +w is wealth prices are what you have to +pay + + align:start position:0% +pay + + + align:start position:0% +pay +in fact that indirect utility will be + + align:start position:0% +in fact that indirect utility will be + + + align:start position:0% +in fact that indirect utility will be +strictly increasing in w when we have + + align:start position:0% +strictly increasing in w when we have + + + align:start position:0% +strictly increasing in w when we have +local non-satiation which is what we're + + align:start position:0% +local non-satiation which is what we're + + + align:start position:0% +local non-satiation which is what we're +always going to be assuming here the + + align:start position:0% +always going to be assuming here the + + + align:start position:0% +always going to be assuming here the +indirect utility function is quasi + + align:start position:0% +indirect utility function is quasi + + + align:start position:0% +indirect utility function is quasi +convex + + align:start position:0% +convex + + + align:start position:0% +convex +not concave + + align:start position:0% +not concave + + + align:start position:0% +not concave +convex n p and w + + align:start position:0% +convex n p and w + + + align:start position:0% +convex n p and w +so again when we did consumer theory we + + align:start position:0% +so again when we did consumer theory we + + + align:start position:0% +so again when we did consumer theory we +had concave utility upper contour sets + + align:start position:0% +had concave utility upper contour sets + + + align:start position:0% +had concave utility upper contour sets +were quasi convex but the utility + + align:start position:0% +were quasi convex but the utility + + + align:start position:0% +were quasi convex but the utility +function was concave this maximized + + align:start position:0% +function was concave this maximized + + + align:start position:0% +function was concave this maximized +utility over the budget is convex or at + + align:start position:0% +utility over the budget is convex or at + + + align:start position:0% +utility over the budget is convex or at +least quasi convex continuous which is + + align:start position:0% +least quasi convex continuous which is + + + align:start position:0% +least quasi convex continuous which is +easy + + align:start position:0% +easy + + + align:start position:0% +easy +to assume + + align:start position:0% +to assume + + + align:start position:0% +to assume +and differentiable and when + + align:start position:0% +and differentiable and when + + + align:start position:0% +and differentiable and when +the indirect utility function is + + align:start position:0% +the indirect utility function is + + + align:start position:0% +the indirect utility function is +differentiable we can use it to recover + + align:start position:0% +differentiable we can use it to recover + + + align:start position:0% +differentiable we can use it to recover +demand + + align:start position:0% +demand + + + align:start position:0% +demand +and the proof is pretty easy but here it + + align:start position:0% +and the proof is pretty easy but here it + + + align:start position:0% +and the proof is pretty easy but here it +looks kind of amazing i suppose which is + + align:start position:0% +looks kind of amazing i suppose which is + + + align:start position:0% +looks kind of amazing i suppose which is +if we want the maximized quantity of + + align:start position:0% +if we want the maximized quantity of + + + align:start position:0% +if we want the maximized quantity of +good l + + align:start position:0% +good l + + + align:start position:0% +good l +for this consumer + + align:start position:0% +for this consumer + + + align:start position:0% +for this consumer +facing price factor p and w and wealth w + + align:start position:0% +facing price factor p and w and wealth w + + + align:start position:0% +facing price factor p and w and wealth w +the answer will be take the derivative + + align:start position:0% +the answer will be take the derivative + + + align:start position:0% +the answer will be take the derivative +of the indirect utility function with + + align:start position:0% +of the indirect utility function with + + + align:start position:0% +of the indirect utility function with +respect to the the elf price + + align:start position:0% +respect to the the elf price + + + align:start position:0% +respect to the the elf price +and divide by the derivative of the + + align:start position:0% +and divide by the derivative of the + + + align:start position:0% +and divide by the derivative of the +indirect utility function with respect + + align:start position:0% +indirect utility function with respect + + + align:start position:0% +indirect utility function with respect +to wealth and stick a negative sign in + + align:start position:0% +to wealth and stick a negative sign in + + + align:start position:0% +to wealth and stick a negative sign in +front of all of that + + align:start position:0% +front of all of that + + + align:start position:0% +front of all of that +so + + align:start position:0% +so + + + align:start position:0% +so +so here's a little proof of it + + align:start position:0% +so here's a little proof of it + + + align:start position:0% +so here's a little proof of it +we have the lagrangian which represents + + align:start position:0% +we have the lagrangian which represents + + + align:start position:0% +we have the lagrangian which represents +utility maximization problem + + align:start position:0% +utility maximization problem + + + align:start position:0% +utility maximization problem +with + + align:start position:0% +with + + + align:start position:0% +with +l0 being the shadow price of the budget + + align:start position:0% +l0 being the shadow price of the budget + + + align:start position:0% +l0 being the shadow price of the budget +and the l + + align:start position:0% +and the l + + + align:start position:0% +and the l +lamps are lambda sub zero and lambda sub + + align:start position:0% +lamps are lambda sub zero and lambda sub + + + align:start position:0% +lamps are lambda sub zero and lambda sub +l being + + align:start position:0% +l being + + + align:start position:0% +l being +potential shadow prices on + + align:start position:0% +potential shadow prices on + + + align:start position:0% +potential shadow prices on +non-negativity constraints + + align:start position:0% +non-negativity constraints + + + align:start position:0% +non-negativity constraints +so we're going to use the envelope + + align:start position:0% +so we're going to use the envelope + + + align:start position:0% +so we're going to use the envelope +theorem which to remind you + + align:start position:0% +theorem which to remind you + + + align:start position:0% +theorem which to remind you +states that you can take a derivative + + align:start position:0% +states that you can take a derivative + + + align:start position:0% +states that you can take a derivative +with respect to the parameters of the + + align:start position:0% +with respect to the parameters of the + + + align:start position:0% +with respect to the parameters of the +optimization problem in this case p and + + align:start position:0% +optimization problem in this case p and + + + align:start position:0% +optimization problem in this case p and +w + + align:start position:0% +w + + + align:start position:0% +w +and if you take the derivatives at the + + align:start position:0% +and if you take the derivatives at the + + + align:start position:0% +and if you take the derivatives at the +optimizing solution + + align:start position:0% +optimizing solution + + + align:start position:0% +optimizing solution +you get sort of the the increment in + + align:start position:0% +you get sort of the the increment in + + + align:start position:0% +you get sort of the the increment in +utility associated with changing those + + align:start position:0% +utility associated with changing those + + + align:start position:0% +utility associated with changing those +parameters + + align:start position:0% +parameters + + + align:start position:0% +parameters +so the increment in utility from solving + + align:start position:0% +so the increment in utility from solving + + + align:start position:0% +so the increment in utility from solving +the max problem at those parameters is + + align:start position:0% +the max problem at those parameters is + + + align:start position:0% +the max problem at those parameters is +also the derivative of the lagrangian + + align:start position:0% +also the derivative of the lagrangian + + + align:start position:0% +also the derivative of the lagrangian +with with respect to those parameters so + + align:start position:0% +with with respect to those parameters so + + + align:start position:0% +with with respect to those parameters so +there's like two steps there how to + + align:start position:0% +there's like two steps there how to + + + align:start position:0% +there's like two steps there how to +represent the maximum value namely as + + align:start position:0% +represent the maximum value namely as + + + align:start position:0% +represent the maximum value namely as +the solution to the lagrangian and also + + align:start position:0% +the solution to the lagrangian and also + + + align:start position:0% +the solution to the lagrangian and also +the envelope theorem that tells you + + align:start position:0% +the envelope theorem that tells you + + + align:start position:0% +the envelope theorem that tells you +reminds you that the derivative of the + + align:start position:0% +reminds you that the derivative of the + + + align:start position:0% +reminds you that the derivative of the +optimized solution with respect to the + + align:start position:0% +optimized solution with respect to the + + + align:start position:0% +optimized solution with respect to the +parameter is like differentiating at the + + align:start position:0% +parameter is like differentiating at the + + + align:start position:0% +parameter is like differentiating at the +maximizing quantities okay so too many + + align:start position:0% +maximizing quantities okay so too many + + + align:start position:0% +maximizing quantities okay so too many +words so the first derivative here and + + align:start position:0% +words so the first derivative here and + + + align:start position:0% +words so the first derivative here and +equation three the derivative of the + + align:start position:0% +equation three the derivative of the + + + align:start position:0% +equation three the derivative of the +value function with respect to a + + align:start position:0% +value function with respect to a + + + align:start position:0% +value function with respect to a +particular price p l is the derivative + + align:start position:0% +particular price p l is the derivative + + + align:start position:0% +particular price p l is the derivative +of the lagrangian with respect to at + + align:start position:0% +of the lagrangian with respect to at + + + align:start position:0% +of the lagrangian with respect to at +price pl evaluated at the maximum namely + + align:start position:0% +price pl evaluated at the maximum namely + + + align:start position:0% +price pl evaluated at the maximum namely +x of p and w + + align:start position:0% +x of p and w + + + align:start position:0% +x of p and w +is the demand and going back upstairs + + align:start position:0% +is the demand and going back upstairs + + + align:start position:0% +is the demand and going back upstairs +here derivative of the lounge with + + align:start position:0% +here derivative of the lounge with + + + align:start position:0% +here derivative of the lounge with +respect to pl where does it appear only + + align:start position:0% +respect to pl where does it appear only + + + align:start position:0% +respect to pl where does it appear only +appears here in the budget so you get a + + align:start position:0% +appears here in the budget so you get a + + + align:start position:0% +appears here in the budget so you get a +lambda zero and p is linear in x so you + + align:start position:0% +lambda zero and p is linear in x so you + + + align:start position:0% +lambda zero and p is linear in x so you +get the x of l back and that's this + + align:start position:0% +get the x of l back and that's this + + + align:start position:0% +get the x of l back and that's this +object + + align:start position:0% +object + + + align:start position:0% +object +likewise the derivative with the + + align:start position:0% +likewise the derivative with the + + + align:start position:0% +likewise the derivative with the +indirect utility with respect to w the + + align:start position:0% +indirect utility with respect to w the + + + align:start position:0% +indirect utility with respect to w the +lagrangian expected w wealth evaluated + + align:start position:0% +lagrangian expected w wealth evaluated + + + align:start position:0% +lagrangian expected w wealth evaluated +at the maximizing solution there's only + + align:start position:0% +at the maximizing solution there's only + + + align:start position:0% +at the maximizing solution there's only +one place that w appears it's up here so + + align:start position:0% +one place that w appears it's up here so + + + align:start position:0% +one place that w appears it's up here so +you just get lambda zero + + align:start position:0% +you just get lambda zero + + + align:start position:0% +you just get lambda zero +so lambda zero is now + + align:start position:0% +so lambda zero is now + + + align:start position:0% +so lambda zero is now +in four and in three substitute the + + align:start position:0% +in four and in three substitute the + + + align:start position:0% +in four and in three substitute the +expression in four into three and you + + align:start position:0% +expression in four into three and you + + + align:start position:0% +expression in four into three and you +get dv dpl equal to + + align:start position:0% +get dv dpl equal to + + + align:start position:0% +get dv dpl equal to +well it's all written out here + + align:start position:0% +well it's all written out here + + + align:start position:0% +well it's all written out here +just basically taking the lamb to zero + + align:start position:0% +just basically taking the lamb to zero + + + align:start position:0% +just basically taking the lamb to zero +looking at the left hand side sticking + + align:start position:0% +looking at the left hand side sticking + + + align:start position:0% +looking at the left hand side sticking +it in here and then repeating the x of l + + align:start position:0% +it in here and then repeating the x of l + + + align:start position:0% +it in here and then repeating the x of l +so now solve this equation for x sub l + + align:start position:0% +so now solve this equation for x sub l + + + align:start position:0% +so now solve this equation for x sub l +and you get what we wanted namely the + + align:start position:0% +and you get what we wanted namely the + + + align:start position:0% +and you get what we wanted namely the +ratio of the derivative with respect to + + align:start position:0% +ratio of the derivative with respect to + + + align:start position:0% +ratio of the derivative with respect to +p divided by with respect to w with the + + align:start position:0% +p divided by with respect to w with the + + + align:start position:0% +p divided by with respect to w with the +minus sign in front of it so we get what + + align:start position:0% +minus sign in front of it so we get what + + + align:start position:0% +minus sign in front of it so we get what +we wanted + + align:start position:0% +we wanted + + + align:start position:0% +we wanted +questions + + align:start position:0% + + + + align:start position:0% + +all right so that's an interesting + + align:start position:0% +all right so that's an interesting + + + align:start position:0% +all right so that's an interesting +problem of the indirect utilities now + + align:start position:0% +problem of the indirect utilities now + + + align:start position:0% +problem of the indirect utilities now +we're ready to define a + + align:start position:0% +we're ready to define a + + + align:start position:0% +we're ready to define a +particular version of the indirect + + align:start position:0% +particular version of the indirect + + + align:start position:0% +particular version of the indirect +utility function called gorman polar + + align:start position:0% +utility function called gorman polar + + + align:start position:0% +utility function called gorman polar +form or gorman form + + align:start position:0% +form or gorman form + + + align:start position:0% +form or gorman form +this doesn't always happen but it can + + align:start position:0% +this doesn't always happen but it can + + + align:start position:0% +this doesn't always happen but it can +happen + + align:start position:0% +happen + + + align:start position:0% +happen +for particular utility functions the + + align:start position:0% +for particular utility functions the + + + align:start position:0% +for particular utility functions the +indirect utility function in p and w has + + align:start position:0% +indirect utility function in p and w has + + + align:start position:0% +indirect utility function in p and w has +an intercept and a slope and the + + align:start position:0% +an intercept and a slope and the + + + align:start position:0% +an intercept and a slope and the +intercept is a function of vector p + + align:start position:0% +intercept is a function of vector p + + + align:start position:0% +intercept is a function of vector p +the slope b with respect to w is a + + align:start position:0% +the slope b with respect to w is a + + + align:start position:0% +the slope b with respect to w is a +function of vector p and it's linear in + + align:start position:0% +function of vector p and it's linear in + + + align:start position:0% +function of vector p and it's linear in +w and i'll show you example right now + + align:start position:0% +w and i'll show you example right now + + + align:start position:0% +w and i'll show you example right now +because this seems a bit mysterious so + + align:start position:0% +because this seems a bit mysterious so + + + align:start position:0% +because this seems a bit mysterious so +let's go back to our favorite utility + + align:start position:0% +let's go back to our favorite utility + + + align:start position:0% +let's go back to our favorite utility +function this sort of cobb douglas with + + align:start position:0% +function this sort of cobb douglas with + + + align:start position:0% +function this sort of cobb douglas with +two goods x1 and x2 raised to the power + + align:start position:0% +two goods x1 and x2 raised to the power + + + align:start position:0% +two goods x1 and x2 raised to the power +alpha and one minus alpha you may + + align:start position:0% +alpha and one minus alpha you may + + + align:start position:0% +alpha and one minus alpha you may +remember that these alphas and 1 minus + + align:start position:0% +remember that these alphas and 1 minus + + + align:start position:0% +remember that these alphas and 1 minus +alpha represent the expenditure share in + + align:start position:0% +alpha represent the expenditure share in + + + align:start position:0% +alpha represent the expenditure share in +the optimized solution so p1 times x1 is + + align:start position:0% +the optimized solution so p1 times x1 is + + + align:start position:0% +the optimized solution so p1 times x1 is +alpha times w so this household spends + + align:start position:0% +alpha times w so this household spends + + + align:start position:0% +alpha times w so this household spends +alpha fraction of its wealth w on good + + align:start position:0% +alpha fraction of its wealth w on good + + + align:start position:0% +alpha fraction of its wealth w on good +one and spends one minus alpha times w + + align:start position:0% +one and spends one minus alpha times w + + + align:start position:0% +one and spends one minus alpha times w +on good two i'm just shifting these + + align:start position:0% +on good two i'm just shifting these + + + align:start position:0% +on good two i'm just shifting these +prices over here to the left-hand side + + align:start position:0% +prices over here to the left-hand side + + + align:start position:0% +prices over here to the left-hand side +so it's not just quantity it's quantity + + align:start position:0% +so it's not just quantity it's quantity + + + align:start position:0% +so it's not just quantity it's quantity +times price or value so with these cobb + + align:start position:0% +times price or value so with these cobb + + + align:start position:0% +times price or value so with these cobb +douglas it's constant expenditure shares + + align:start position:0% +douglas it's constant expenditure shares + + + align:start position:0% +douglas it's constant expenditure shares +more on that momentarily + + align:start position:0% +more on that momentarily + + + align:start position:0% +more on that momentarily +and now the definition of indirect + + align:start position:0% +and now the definition of indirect + + + align:start position:0% +and now the definition of indirect +utility says just substitute in the + + align:start position:0% +utility says just substitute in the + + + align:start position:0% +utility says just substitute in the +maximized value so we take you know you + + align:start position:0% +maximized value so we take you know you + + + align:start position:0% +maximized value so we take you know you +x1 but use this expression for x1 to the + + align:start position:0% +x1 but use this expression for x1 to the + + + align:start position:0% +x1 but use this expression for x1 to the +alpha x2 this expression for x2 to the 1 + + align:start position:0% +alpha x2 this expression for x2 to the 1 + + + align:start position:0% +alpha x2 this expression for x2 to the 1 +minus alpha that's this business and + + align:start position:0% +minus alpha that's this business and + + + align:start position:0% +minus alpha that's this business and +when you solve it out you get a of p + + align:start position:0% +when you solve it out you get a of p + + + align:start position:0% +when you solve it out you get a of p +you know looking for it to be + + align:start position:0% +you know looking for it to be + + + align:start position:0% +you know looking for it to be +be in this form + + align:start position:0% +be in this form + + + align:start position:0% +be in this form +a ifp is zero and b of p is this + + align:start position:0% +a ifp is zero and b of p is this + + + align:start position:0% +a ifp is zero and b of p is this +coefficient which has alpha and one + + align:start position:0% +coefficient which has alpha and one + + + align:start position:0% +coefficient which has alpha and one +minus alpha p1 and p2 to the to these + + align:start position:0% +minus alpha p1 and p2 to the to these + + + align:start position:0% +minus alpha p1 and p2 to the to these +powers alpha and one minus alpha that's + + align:start position:0% +powers alpha and one minus alpha that's + + + align:start position:0% +powers alpha and one minus alpha that's +b of p it depends on p and on nothing + + align:start position:0% +b of p it depends on p and on nothing + + + align:start position:0% +b of p it depends on p and on nothing +else + + align:start position:0% +else + + + align:start position:0% +else +and it is indeed linear in w the + + align:start position:0% +and it is indeed linear in w the + + + align:start position:0% +and it is indeed linear in w the +linearity in w just has comes from the + + align:start position:0% +linearity in w just has comes from the + + + align:start position:0% +linearity in w just has comes from the +property that alpha plus one minus alpha + + align:start position:0% +property that alpha plus one minus alpha + + + align:start position:0% +property that alpha plus one minus alpha +is one + + align:start position:0% +is one + + + align:start position:0% +is one +w the alpha times w to the one minus + + align:start position:0% +w the alpha times w to the one minus + + + align:start position:0% +w the alpha times w to the one minus +alpha just add up the power coefficients + + align:start position:0% +alpha just add up the power coefficients + + + align:start position:0% +alpha just add up the power coefficients +so this is all so far for a single + + align:start position:0% +so this is all so far for a single + + + align:start position:0% +so this is all so far for a single +household hence neglecting to put in + + align:start position:0% +household hence neglecting to put in + + + align:start position:0% +household hence neglecting to put in +notation h or i or whatever label the + + align:start position:0% +notation h or i or whatever label the + + + align:start position:0% +notation h or i or whatever label the +household is however if this cobb + + align:start position:0% +household is however if this cobb + + + align:start position:0% +household is however if this cobb +douglas function were the same over all + + align:start position:0% +douglas function were the same over all + + + align:start position:0% +douglas function were the same over all +the households then we have a + + align:start position:0% +the households then we have a + + + align:start position:0% +the households then we have a +gorman polar form + + align:start position:0% +gorman polar form + + + align:start position:0% +gorman polar form +where all the households have the same + + align:start position:0% +where all the households have the same + + + align:start position:0% +where all the households have the same +intercept a of p and the same slope term + + align:start position:0% +intercept a of p and the same slope term + + + align:start position:0% +intercept a of p and the same slope term +b of p likewise if it were to be the + + align:start position:0% +b of p likewise if it were to be the + + + align:start position:0% +b of p likewise if it were to be the +case that the alpha coefficient varies + + align:start position:0% +case that the alpha coefficient varies + + + align:start position:0% +case that the alpha coefficient varies +across over the households then this b + + align:start position:0% +across over the households then this b + + + align:start position:0% +across over the households then this b +of p is not going to be common all the + + align:start position:0% +of p is not going to be common all the + + + align:start position:0% +of p is not going to be common all the +over all the households it's going to + + align:start position:0% +over all the households it's going to + + + align:start position:0% +over all the households it's going to +depend on + + align:start position:0% +depend on + + + align:start position:0% +depend on +on particular preferences so maybe + + align:start position:0% +on particular preferences so maybe + + + align:start position:0% +on particular preferences so maybe +that's illustrative just how tenuous + + align:start position:0% +that's illustrative just how tenuous + + + align:start position:0% +that's illustrative just how tenuous +already the assumption is going to be + + align:start position:0% +already the assumption is going to be + + + align:start position:0% +already the assumption is going to be +but it is going to be very powerful if + + align:start position:0% +but it is going to be very powerful if + + + align:start position:0% +but it is going to be very powerful if +it's true okay so let's go at it and + + align:start position:0% +it's true okay so let's go at it and + + + align:start position:0% +it's true okay so let's go at it and +talk about aggregate demand so we have + + align:start position:0% +talk about aggregate demand so we have + + + align:start position:0% +talk about aggregate demand so we have +an economy with i households i agents + + align:start position:0% +an economy with i households i agents + + + align:start position:0% +an economy with i households i agents +their wealths are w1 through wi + + align:start position:0% +their wealths are w1 through wi + + + align:start position:0% +their wealths are w1 through wi +a wealth profile let's define w bar to + + align:start position:0% +a wealth profile let's define w bar to + + + align:start position:0% +a wealth profile let's define w bar to +be the aggregate total wealth just by + + align:start position:0% +be the aggregate total wealth just by + + + align:start position:0% +be the aggregate total wealth just by +summing up all the individual wells + + align:start position:0% +summing up all the individual wells + + + align:start position:0% +summing up all the individual wells +and retain this notation that x i of p + + align:start position:0% +and retain this notation that x i of p + + + align:start position:0% +and retain this notation that x i of p +and w i is the demand function for agent + + align:start position:0% +and w i is the demand function for agent + + + align:start position:0% +and w i is the demand function for agent +i + + align:start position:0% +i + + + align:start position:0% +i +the aggregate demand + + align:start position:0% +the aggregate demand + + + align:start position:0% +the aggregate demand +x bar + + align:start position:0% +x bar + + + align:start position:0% +x bar +by definition will be the sum of the + + align:start position:0% +by definition will be the sum of the + + + align:start position:0% +by definition will be the sum of the +individual demands + + align:start position:0% +individual demands + + + align:start position:0% +individual demands +and we write that notationally as + + align:start position:0% +and we write that notationally as + + + align:start position:0% +and we write that notationally as +x bar of the vector the parameters of + + align:start position:0% +x bar of the vector the parameters of + + + align:start position:0% +x bar of the vector the parameters of +the problem + + align:start position:0% +the problem + + + align:start position:0% +the problem +namely the common price vector and + + align:start position:0% +namely the common price vector and + + + align:start position:0% +namely the common price vector and +individual wealth so that's a definition + + align:start position:0% +individual wealth so that's a definition + + + align:start position:0% +individual wealth so that's a definition +of aggregate demand + + align:start position:0% +of aggregate demand + + + align:start position:0% +of aggregate demand +nothing + + align:start position:0% +nothing + + + align:start position:0% +nothing +so far other than the definition + + align:start position:0% +so far other than the definition + + + align:start position:0% +so far other than the definition +but the first question about aggregation + + align:start position:0% +but the first question about aggregation + + + align:start position:0% +but the first question about aggregation +is can we find + + align:start position:0% +is can we find + + + align:start position:0% +is can we find +an aggregate demand function that is + + align:start position:0% +an aggregate demand function that is + + + align:start position:0% +an aggregate demand function that is +special in that it only depends on total + + align:start position:0% +special in that it only depends on total + + + align:start position:0% +special in that it only depends on total +wealth in the population + + align:start position:0% +wealth in the population + + + align:start position:0% +wealth in the population +not how the wealth is distributed in the + + align:start position:0% +not how the wealth is distributed in the + + + align:start position:0% +not how the wealth is distributed in the +population so + + align:start position:0% +population so + + + align:start position:0% +population so +the idea here is this x bar of l which + + align:start position:0% +the idea here is this x bar of l which + + + align:start position:0% +the idea here is this x bar of l which +again was just defined but + + align:start position:0% +again was just defined but + + + align:start position:0% +again was just defined but +now + + align:start position:0% +now + + + align:start position:0% +now +for the elf good + + align:start position:0% +for the elf good + + + align:start position:0% +for the elf good +x bar of l at p and w + + align:start position:0% +x bar of l at p and w + + + align:start position:0% +x bar of l at p and w +is the aggregate demand + + align:start position:0% +is the aggregate demand + + + align:start position:0% +is the aggregate demand +we're looking for this function + + align:start position:0% +we're looking for this function + + + align:start position:0% +we're looking for this function +capital x now of l + + align:start position:0% +capital x now of l + + + align:start position:0% +capital x now of l +capital i guess for big aggregate which + + align:start position:0% +capital i guess for big aggregate which + + + align:start position:0% +capital i guess for big aggregate which +is a function of p of course but now w + + align:start position:0% +is a function of p of course but now w + + + align:start position:0% +is a function of p of course but now w +bar so here's the content of it or + + align:start position:0% +bar so here's the content of it or + + + align:start position:0% +bar so here's the content of it or +looking at it this way vector p s but + + align:start position:0% +looking at it this way vector p s but + + + align:start position:0% +looking at it this way vector p s but +the wealth component in the aggregate + + align:start position:0% +the wealth component in the aggregate + + + align:start position:0% +the wealth component in the aggregate +demand + + align:start position:0% +demand + + + align:start position:0% +demand +depends on the sum of individual wealth + + align:start position:0% +depends on the sum of individual wealth + + + align:start position:0% +depends on the sum of individual wealth +only it doesn't depend on the + + align:start position:0% +only it doesn't depend on the + + + align:start position:0% +only it doesn't depend on the +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +on this slide you know wealth enter each + + align:start position:0% +on this slide you know wealth enter each + + + align:start position:0% +on this slide you know wealth enter each +agent's demand function and there's no + + align:start position:0% +agent's demand function and there's no + + + align:start position:0% +agent's demand function and there's no +reason why it should be representable to + + align:start position:0% +reason why it should be representable to + + + align:start position:0% +reason why it should be representable to +depend only on + + align:start position:0% +depend only on + + + align:start position:0% +depend only on +the aggregate but we're going to look + + align:start position:0% +the aggregate but we're going to look + + + align:start position:0% +the aggregate but we're going to look +for specifications of utility where + + align:start position:0% +for specifications of utility where + + + align:start position:0% +for specifications of utility where +that's true + + align:start position:0% +that's true + + + align:start position:0% +that's true +and we haven't even asked whether that + + align:start position:0% +and we haven't even asked whether that + + + align:start position:0% +and we haven't even asked whether that +aggregate demand function that capital x + + align:start position:0% +aggregate demand function that capital x + + + align:start position:0% +aggregate demand function that capital x +comes from some underlying utility + + align:start position:0% +comes from some underlying utility + + + align:start position:0% +comes from some underlying utility +function as a solution we're just + + align:start position:0% +function as a solution we're just + + + align:start position:0% +function as a solution we're just +looking for whether it depends only on + + align:start position:0% +looking for whether it depends only on + + + align:start position:0% +looking for whether it depends only on +aggregate wealth or rather might depend + + align:start position:0% +aggregate wealth or rather might depend + + + align:start position:0% +aggregate wealth or rather might depend +on the distribution + + align:start position:0% +on the distribution + + + align:start position:0% +on the distribution +but this is a necessary condition for + + align:start position:0% +but this is a necessary condition for + + + align:start position:0% +but this is a necessary condition for +there to be a representative household + + align:start position:0% +there to be a representative household + + + align:start position:0% +there to be a representative household +that's maximizing some pseudo utility + + align:start position:0% +that's maximizing some pseudo utility + + + align:start position:0% +that's maximizing some pseudo utility +function that's going to represent + + align:start position:0% +function that's going to represent + + + align:start position:0% +function that's going to represent +aggregate demand so we're kind of doing + + align:start position:0% +aggregate demand so we're kind of doing + + + align:start position:0% +aggregate demand so we're kind of doing +one thing at a time so what is a + + align:start position:0% +one thing at a time so what is a + + + align:start position:0% +one thing at a time so what is a +necessary condition for us to be able to + + align:start position:0% +necessary condition for us to be able to + + + align:start position:0% +necessary condition for us to be able to +aggregate up like that + + align:start position:0% +aggregate up like that + + + align:start position:0% +aggregate up like that +and it is that the marginal impact of + + align:start position:0% +and it is that the marginal impact of + + + align:start position:0% +and it is that the marginal impact of +wealth changes on demands say for the + + align:start position:0% +wealth changes on demands say for the + + + align:start position:0% +wealth changes on demands say for the +health good is the same over all the + + align:start position:0% +health good is the same over all the + + + align:start position:0% +health good is the same over all the +households + + align:start position:0% +households + + + align:start position:0% +households +and that that is also true for all the + + align:start position:0% +and that that is also true for all the + + + align:start position:0% +and that that is also true for all the +goods so whatever good l you pick + + align:start position:0% +goods so whatever good l you pick + + + align:start position:0% +goods so whatever good l you pick +whatever pairwise households i and j you + + align:start position:0% +whatever pairwise households i and j you + + + align:start position:0% +whatever pairwise households i and j you +pick + + align:start position:0% +pick + + + align:start position:0% +pick +they need each to have the same income + + align:start position:0% +they need each to have the same income + + + align:start position:0% +they need each to have the same income +effect of how demand changes with wealth + + align:start position:0% +effect of how demand changes with wealth + + + align:start position:0% +effect of how demand changes with wealth +and here's the picture + + align:start position:0% +and here's the picture + + + align:start position:0% +and here's the picture +which you've kind of seen before + + align:start position:0% +which you've kind of seen before + + + align:start position:0% +which you've kind of seen before +these are linear wealth expansion paths + + align:start position:0% +these are linear wealth expansion paths + + + align:start position:0% +these are linear wealth expansion paths +we're holding prices fixed of the two + + align:start position:0% +we're holding prices fixed of the two + + + align:start position:0% +we're holding prices fixed of the two +goods in this case + + align:start position:0% +goods in this case + + + align:start position:0% +goods in this case +and for consumer + + align:start position:0% +and for consumer + + + align:start position:0% +and for consumer +one of these consumers + + align:start position:0% +one of these consumers + + + align:start position:0% +one of these consumers +were + + align:start position:0% +were + + + align:start position:0% +were +tracing out the optimized solution as we + + align:start position:0% +tracing out the optimized solution as we + + + align:start position:0% +tracing out the optimized solution as we +change wealth + + align:start position:0% +change wealth + + + align:start position:0% +change wealth +optimizing in the sense that the + + align:start position:0% +optimizing in the sense that the + + + align:start position:0% +optimizing in the sense that the +household has achieved maximal utility + + align:start position:0% +household has achieved maximal utility + + + align:start position:0% +household has achieved maximal utility +for any given wealth characterized by a + + align:start position:0% +for any given wealth characterized by a + + + align:start position:0% +for any given wealth characterized by a +tangency between the indifference curve + + align:start position:0% +tangency between the indifference curve + + + align:start position:0% +tangency between the indifference curve +and the budget line + + align:start position:0% +and the budget line + + + align:start position:0% +and the budget line +the other households up here + + align:start position:0% +the other households up here + + + align:start position:0% +the other households up here +also has a linear expansion path now + + align:start position:0% +also has a linear expansion path now + + + align:start position:0% +also has a linear expansion path now +it's true that this household + + align:start position:0% +it's true that this household + + + align:start position:0% +it's true that this household +i it is has higher levels of demand + + align:start position:0% +i it is has higher levels of demand + + + align:start position:0% +i it is has higher levels of demand +for good two relative to good one + + align:start position:0% +for good two relative to good one + + + align:start position:0% +for good two relative to good one +then is the case for household j + + align:start position:0% +then is the case for household j + + + align:start position:0% +then is the case for household j +so they're not identical + + align:start position:0% +so they're not identical + + + align:start position:0% +so they're not identical +but when you think about what happens + + align:start position:0% +but when you think about what happens + + + align:start position:0% +but when you think about what happens +when when you redistribute wealth with + + align:start position:0% +when when you redistribute wealth with + + + align:start position:0% +when when you redistribute wealth with +these parallel linear expansion paths + + align:start position:0% +these parallel linear expansion paths + + + align:start position:0% +these parallel linear expansion paths +the derivatives are the same we could + + align:start position:0% +the derivatives are the same we could + + + align:start position:0% +the derivatives are the same we could +for example take some wealth away from + + align:start position:0% +for example take some wealth away from + + + align:start position:0% +for example take some wealth away from +household i + + align:start position:0% +household i + + + align:start position:0% +household i +we would move + + align:start position:0% +we would move + + + align:start position:0% +we would move +southwest + + align:start position:0% +southwest + + + align:start position:0% +southwest +we'd have the change in x1 x2 and the + + align:start position:0% +we'd have the change in x1 x2 and the + + + align:start position:0% +we'd have the change in x1 x2 and the +change in x one little + + align:start position:0% +change in x one little + + + align:start position:0% +change in x one little +triangle over there + + align:start position:0% +triangle over there + + + align:start position:0% +triangle over there +and + + align:start position:0% +and + + + align:start position:0% +and +give that wealth to household j who + + align:start position:0% +give that wealth to household j who + + + align:start position:0% +give that wealth to household j who +would be moving + + align:start position:0% +would be moving + + + align:start position:0% +would be moving +north east but again because these lines + + align:start position:0% +north east but again because these lines + + + align:start position:0% +north east but again because these lines +are parallel we're going to have exactly + + align:start position:0% +are parallel we're going to have exactly + + + align:start position:0% +are parallel we're going to have exactly +the same changes in good x + + align:start position:0% +the same changes in good x + + + align:start position:0% +the same changes in good x +so the levels can be different but the + + align:start position:0% +so the levels can be different but the + + + align:start position:0% +so the levels can be different but the +derivatives are the same and that + + align:start position:0% +derivatives are the same and that + + + align:start position:0% +derivatives are the same and that +picture represents this + + align:start position:0% +picture represents this + + + align:start position:0% +picture represents this +condition 10 + + align:start position:0% +condition 10 + + + align:start position:0% +condition 10 +that the income effects of the claim + + align:start position:0% +that the income effects of the claim + + + align:start position:0% +that the income effects of the claim +over all the households + + align:start position:0% +over all the households + + + align:start position:0% +over all the households +and that's a + + align:start position:0% +and that's a + + + align:start position:0% +and that's a +necessary condition for + + align:start position:0% +necessary condition for + + + align:start position:0% +necessary condition for +for only aggregate wealth to matter + + align:start position:0% +for only aggregate wealth to matter + + + align:start position:0% +for only aggregate wealth to matter +individual demands are moving as you + + align:start position:0% +individual demands are moving as you + + + align:start position:0% +individual demands are moving as you +redistribute the wealth + + align:start position:0% +redistribute the wealth + + + align:start position:0% +redistribute the wealth +but what one guy gives up is what the + + align:start position:0% +but what one guy gives up is what the + + + align:start position:0% +but what one guy gives up is what the +other guy gains so the total demand + + align:start position:0% +other guy gains so the total demand + + + align:start position:0% +other guy gains so the total demand +isn't moving + + align:start position:0% +isn't moving + + + align:start position:0% +isn't moving +who gets what is moving but not the + + align:start position:0% +who gets what is moving but not the + + + align:start position:0% +who gets what is moving but not the +total demand + + align:start position:0% +total demand + + + align:start position:0% +total demand +as we redistribute the wealth + + align:start position:0% +as we redistribute the wealth + + + align:start position:0% +as we redistribute the wealth +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the next step is to find the utility + + align:start position:0% +the next step is to find the utility + + + align:start position:0% +the next step is to find the utility +function that's going to + + align:start position:0% +function that's going to + + + align:start position:0% +function that's going to +give that aggregate demand + + align:start position:0% +give that aggregate demand + + + align:start position:0% +give that aggregate demand +we're going to call this sky the + + align:start position:0% +we're going to call this sky the + + + align:start position:0% +we're going to call this sky the +positive representative household + + align:start position:0% +positive representative household + + + align:start position:0% +positive representative household +so let's have the consumption set the + + align:start position:0% +so let's have the consumption set the + + + align:start position:0% +so let's have the consumption set the +subset of this l dimension euclidean + + align:start position:0% +subset of this l dimension euclidean + + + align:start position:0% +subset of this l dimension euclidean +space + + align:start position:0% +space + + + align:start position:0% +space +the individual demands + + align:start position:0% +the individual demands + + + align:start position:0% +the individual demands +x i of vector p and w i for households i + + align:start position:0% +x i of vector p and w i for households i + + + align:start position:0% +x i of vector p and w i for households i +over all of them to be the individual + + align:start position:0% +over all of them to be the individual + + + align:start position:0% +over all of them to be the individual +demands we're looking for a preference + + align:start position:0% +demands we're looking for a preference + + + align:start position:0% +demands we're looking for a preference +ordering + + align:start position:0% +ordering + + + align:start position:0% +ordering +with a star on it on the + + align:start position:0% +with a star on it on the + + + align:start position:0% +with a star on it on the +aggregate consumption set + + align:start position:0% +aggregate consumption set + + + align:start position:0% +aggregate consumption set +and a particular utility function u star + + align:start position:0% +and a particular utility function u star + + + align:start position:0% +and a particular utility function u star +that represents this preference ordering + + align:start position:0% +that represents this preference ordering + + + align:start position:0% +that represents this preference ordering +and that object consumption set and the + + align:start position:0% +and that object consumption set and the + + + align:start position:0% +and that object consumption set and the +preference ordering in particular is + + align:start position:0% +preference ordering in particular is + + + align:start position:0% +preference ordering in particular is +said to represent or correspond with a + + align:start position:0% +said to represent or correspond with a + + + align:start position:0% +said to represent or correspond with a +positive representative household if and + + align:start position:0% +positive representative household if and + + + align:start position:0% +positive representative household if and +only if the aggregate demand that + + align:start position:0% +only if the aggregate demand that + + + align:start position:0% +only if the aggregate demand that +capital x of p and w bar + + align:start position:0% +capital x of p and w bar + + + align:start position:0% +capital x of p and w bar +comes from the utility maximization + + align:start position:0% +comes from the utility maximization + + + align:start position:0% +comes from the utility maximization +problem where the utility function + + align:start position:0% +problem where the utility function + + + align:start position:0% +problem where the utility function +is of the form u star + + align:start position:0% +is of the form u star + + + align:start position:0% +is of the form u star +so again we're used to utility + + align:start position:0% +so again we're used to utility + + + align:start position:0% +so again we're used to utility +maximization you start as some utility + + align:start position:0% +maximization you start as some utility + + + align:start position:0% +maximization you start as some utility +function + + align:start position:0% +function + + + align:start position:0% +function +we maximize it oh + + align:start position:0% +we maximize it oh + + + align:start position:0% +we maximize it oh +subject to the budget what is the budget + + align:start position:0% +subject to the budget what is the budget + + + align:start position:0% +subject to the budget what is the budget +it's like giving this quote person this + + align:start position:0% +it's like giving this quote person this + + + align:start position:0% +it's like giving this quote person this +representative household the entire + + align:start position:0% +representative household the entire + + + align:start position:0% +representative household the entire +wealth of the economy w bar and this x + + align:start position:0% +wealth of the economy w bar and this x + + + align:start position:0% +wealth of the economy w bar and this x +thing in case you've forgotten this + + align:start position:0% +thing in case you've forgotten this + + + align:start position:0% +thing in case you've forgotten this +capital x of p and w bar was the object + + align:start position:0% +capital x of p and w bar was the object + + + align:start position:0% +capital x of p and w bar was the object +way back here that we were looking for + + align:start position:0% +way back here that we were looking for + + + align:start position:0% +way back here that we were looking for +the aggregate demand as a function only + + align:start position:0% +the aggregate demand as a function only + + + align:start position:0% +the aggregate demand as a function only +of the sum of the wealths or aggregate + + align:start position:0% +of the sum of the wealths or aggregate + + + align:start position:0% +of the sum of the wealths or aggregate +wealth + + align:start position:0% +wealth + + + align:start position:0% +wealth +okay so under what conditions can we + + align:start position:0% +okay so under what conditions can we + + + align:start position:0% +okay so under what conditions can we +find this amazing u star + + align:start position:0% +find this amazing u star + + + align:start position:0% +find this amazing u star +yep + + align:start position:0% +yep + + + align:start position:0% +yep +gorman polar form + + align:start position:0% +gorman polar form + + + align:start position:0% +gorman polar form +so a necessary and sufficient condition + + align:start position:0% +so a necessary and sufficient condition + + + align:start position:0% +so a necessary and sufficient condition +to get that equation 10 to be true + + align:start position:0% +to get that equation 10 to be true + + + align:start position:0% +to get that equation 10 to be true +is that everybody's preferences can be + + align:start position:0% +is that everybody's preferences can be + + + align:start position:0% +is that everybody's preferences can be +represented by 16. + + align:start position:0% +represented by 16. + + + align:start position:0% +represented by 16. +namely + + align:start position:0% +namely + + + align:start position:0% +namely +now with the i's to be explicit the + + align:start position:0% +now with the i's to be explicit the + + + align:start position:0% +now with the i's to be explicit the +indirect utility function for household + + align:start position:0% +indirect utility function for household + + + align:start position:0% +indirect utility function for household +or agent i + + align:start position:0% +or agent i + + + align:start position:0% +or agent i +has this intercept and slope + + align:start position:0% +has this intercept and slope + + + align:start position:0% +has this intercept and slope +the + + align:start position:0% +the + + + align:start position:0% +the +intercept term can actually depend on i + + align:start position:0% +intercept term can actually depend on i + + + align:start position:0% +intercept term can actually depend on i +we do allow that degree of heterogeneity + + align:start position:0% +we do allow that degree of heterogeneity + + + align:start position:0% +we do allow that degree of heterogeneity +but the slope with respect to w + + align:start position:0% +but the slope with respect to w + + + align:start position:0% +but the slope with respect to w +and w i for household i does not depend + + align:start position:0% +and w i for household i does not depend + + + align:start position:0% +and w i for household i does not depend +on i + + align:start position:0% +on i + + + align:start position:0% +on i +common slog terms + + align:start position:0% +common slog terms + + + align:start position:0% +common slog terms +so again to write it out the way the + + align:start position:0% +so again to write it out the way the + + + align:start position:0% +so again to write it out the way the +indirect utility functions for i and j + + align:start position:0% +indirect utility functions for i and j + + + align:start position:0% +indirect utility functions for i and j +respond to wealth is the same namely its + + align:start position:0% +respond to wealth is the same namely its + + + align:start position:0% +respond to wealth is the same namely its +bp + + align:start position:0% +bp + + + align:start position:0% +bp +which is not quite the picture we were + + align:start position:0% +which is not quite the picture we were + + + align:start position:0% +which is not quite the picture we were +looking at but it's getting close as you + + align:start position:0% +looking at but it's getting close as you + + + align:start position:0% +looking at but it's getting close as you +can imagine + + align:start position:0% +can imagine + + + align:start position:0% +can imagine +so if this is + + align:start position:0% +so if this is + + + align:start position:0% +so if this is +if 16 is true over all households i + + align:start position:0% +if 16 is true over all households i + + + align:start position:0% +if 16 is true over all households i +then we can find our amazing u star + + align:start position:0% +then we can find our amazing u star + + + align:start position:0% +then we can find our amazing u star +or in particular the indirect utility + + align:start position:0% +or in particular the indirect utility + + + align:start position:0% +or in particular the indirect utility +function corresponding + + align:start position:0% +function corresponding + + + align:start position:0% +function corresponding +to u star and it's going to look a lot + + align:start position:0% +to u star and it's going to look a lot + + + align:start position:0% +to u star and it's going to look a lot +like the individual indirect utility + + align:start position:0% +like the individual indirect utility + + + align:start position:0% +like the individual indirect utility +functions in the sense that it's written + + align:start position:0% +functions in the sense that it's written + + + align:start position:0% +functions in the sense that it's written +down as a times b of w + + align:start position:0% +down as a times b of w + + + align:start position:0% +down as a times b of w +the a + + align:start position:0% +the a + + + align:start position:0% +the a +star + + align:start position:0% +star + + + align:start position:0% +star +for the representative consumer is the + + align:start position:0% +for the representative consumer is the + + + align:start position:0% +for the representative consumer is the +sum of the ai of ps over i + + align:start position:0% +sum of the ai of ps over i + + + align:start position:0% +sum of the ai of ps over i +so we just add them up and the b star + + align:start position:0% +so we just add them up and the b star + + + align:start position:0% +so we just add them up and the b star +is the common b of p + + align:start position:0% +is the common b of p + + + align:start position:0% +is the common b of p +over all the households eye + + align:start position:0% +over all the households eye + + + align:start position:0% +over all the households eye +so then this guy + + align:start position:0% +so then this guy + + + align:start position:0% +so then this guy +represented by the indirect utility + + align:start position:0% +represented by the indirect utility + + + align:start position:0% +represented by the indirect utility +function is the positive representative + + align:start position:0% +function is the positive representative + + + align:start position:0% +function is the positive representative +household + + align:start position:0% +household + + + align:start position:0% +household +so it's an if and only a thing + + align:start position:0% +so it's an if and only a thing + + + align:start position:0% +so it's an if and only a thing +but let's just go one way + + align:start position:0% +but let's just go one way + + + align:start position:0% +but let's just go one way +and if and only if means if they have + + align:start position:0% +and if and only if means if they have + + + align:start position:0% +and if and only if means if they have +these polar forms then it's gorman + + align:start position:0% +these polar forms then it's gorman + + + align:start position:0% +these polar forms then it's gorman +aggregable we have a representative + + align:start position:0% +aggregable we have a representative + + + align:start position:0% +aggregable we have a representative +consumer and also if we have a + + align:start position:0% +consumer and also if we have a + + + align:start position:0% +consumer and also if we have a +representative consumer + + align:start position:0% +representative consumer + + + align:start position:0% +representative consumer +then the underlying households have to + + align:start position:0% +then the underlying households have to + + + align:start position:0% +then the underlying households have to +have utility represented by + + align:start position:0% +have utility represented by + + + align:start position:0% +have utility represented by +by 16. + + align:start position:0% +by 16. + + + align:start position:0% +by 16. +so let's just go one way suppose that + + align:start position:0% +so let's just go one way suppose that + + + align:start position:0% +so let's just go one way suppose that +preferences are + + align:start position:0% +preferences are + + + align:start position:0% +preferences are +have indirect utility functions that + + align:start position:0% +have indirect utility functions that + + + align:start position:0% +have indirect utility functions that +satisfy 16 will go from the micro to the + + align:start position:0% +satisfy 16 will go from the micro to the + + + align:start position:0% +satisfy 16 will go from the micro to the +macro so to speak + + align:start position:0% +macro so to speak + + + align:start position:0% +macro so to speak +now we use roy's identity you're + + align:start position:0% +now we use roy's identity you're + + + align:start position:0% +now we use roy's identity you're +probably wondering why + + align:start position:0% +probably wondering why + + + align:start position:0% +probably wondering why +why we ever had that so + + align:start position:0% +why we ever had that so + + + align:start position:0% +why we ever had that so +demand of household i for good l at + + align:start position:0% +demand of household i for good l at + + + align:start position:0% +demand of household i for good l at +price vector p and wealth w i is just + + align:start position:0% +price vector p and wealth w i is just + + + align:start position:0% +price vector p and wealth w i is just +this ratio + + align:start position:0% +this ratio + + + align:start position:0% +this ratio +of derivatives with the minus sign out + + align:start position:0% +of derivatives with the minus sign out + + + align:start position:0% +of derivatives with the minus sign out +front and now we use the particular + + align:start position:0% +front and now we use the particular + + + align:start position:0% +front and now we use the particular +forms namely the derivative of the + + align:start position:0% +forms namely the derivative of the + + + align:start position:0% +forms namely the derivative of the +indirect utility function with respect + + align:start position:0% +indirect utility function with respect + + + align:start position:0% +indirect utility function with respect +to w i is namely just b of p + + align:start position:0% +to w i is namely just b of p + + + align:start position:0% +to w i is namely just b of p +because that's that coefficient there + + align:start position:0% +because that's that coefficient there + + + align:start position:0% +because that's that coefficient there +and the derivative of the indirect + + align:start position:0% +and the derivative of the indirect + + + align:start position:0% +and the derivative of the indirect +utility function with respect to p + + align:start position:0% +utility function with respect to p + + + align:start position:0% +utility function with respect to p +is what well go back here it's the + + align:start position:0% +is what well go back here it's the + + + align:start position:0% +is what well go back here it's the +integrativity function for household i + + align:start position:0% +integrativity function for household i + + + align:start position:0% +integrativity function for household i +take derivatives with respect to the + + align:start position:0% +take derivatives with respect to the + + + align:start position:0% +take derivatives with respect to the +intercept and the slope term with + + align:start position:0% +intercept and the slope term with + + + align:start position:0% +intercept and the slope term with +respect to p + + align:start position:0% +respect to p + + + align:start position:0% +respect to p +so that's what's written out here the + + align:start position:0% +so that's what's written out here the + + + align:start position:0% +so that's what's written out here the +derivative of the intercept and slope + + align:start position:0% +derivative of the intercept and slope + + + align:start position:0% +derivative of the intercept and slope +terms with respect to p and of course + + align:start position:0% +terms with respect to p and of course + + + align:start position:0% +terms with respect to p and of course +that w is hanging on there as a + + align:start position:0% +that w is hanging on there as a + + + align:start position:0% +that w is hanging on there as a +coefficient so this must be true + + align:start position:0% +coefficient so this must be true + + + align:start position:0% +coefficient so this must be true +now having derived the demands of + + align:start position:0% +now having derived the demands of + + + align:start position:0% +now having derived the demands of +household i we can take the derivative + + align:start position:0% +household i we can take the derivative + + + align:start position:0% +household i we can take the derivative +with respect to wealth and it's just + + align:start position:0% +with respect to wealth and it's just + + + align:start position:0% +with respect to wealth and it's just +going to appear here so we get this + + align:start position:0% +going to appear here so we get this + + + align:start position:0% +going to appear here so we get this +times this as the + + align:start position:0% +times this as the + + + align:start position:0% +times this as the +way demand is changing well one thing + + align:start position:0% +way demand is changing well one thing + + + align:start position:0% +way demand is changing well one thing +you can see on the right hand side here + + align:start position:0% +you can see on the right hand side here + + + align:start position:0% +you can see on the right hand side here +there's no i so the + + align:start position:0% +there's no i so the + + + align:start position:0% +there's no i so the +change in demands with respect to wealth + + align:start position:0% +change in demands with respect to wealth + + + align:start position:0% +change in demands with respect to wealth +are the same across all the households + + align:start position:0% +are the same across all the households + + + align:start position:0% +are the same across all the households +and equal to this common term on the + + align:start position:0% +and equal to this common term on the + + + align:start position:0% +and equal to this common term on the +right hand side + + align:start position:0% +right hand side + + + align:start position:0% +right hand side +so this gives us that with the indirect + + align:start position:0% +so this gives us that with the indirect + + + align:start position:0% +so this gives us that with the indirect +utility function we have these constant + + align:start position:0% +utility function we have these constant + + + align:start position:0% +utility function we have these constant +income effects over all the households + + align:start position:0% +income effects over all the households + + + align:start position:0% +income effects over all the households +now the second thing we want to show + + align:start position:0% +now the second thing we want to show + + + align:start position:0% +now the second thing we want to show +is not just that but that we can find + + align:start position:0% +is not just that but that we can find + + + align:start position:0% +is not just that but that we can find +this amazing representative consumer + + align:start position:0% +this amazing representative consumer + + + align:start position:0% +this amazing representative consumer +so + + align:start position:0% +so + + + align:start position:0% +so +so we want when we maximize whatever + + align:start position:0% +so we want when we maximize whatever + + + align:start position:0% +so we want when we maximize whatever +this v star is with respect to + + align:start position:0% +this v star is with respect to + + + align:start position:0% +this v star is with respect to +when we get this maximized solution for + + align:start position:0% +when we get this maximized solution for + + + align:start position:0% +when we get this maximized solution for +this star representative consumer + + align:start position:0% +this star representative consumer + + + align:start position:0% +this star representative consumer +at aggregate wealth w it should + + align:start position:0% +at aggregate wealth w it should + + + align:start position:0% +at aggregate wealth w it should +represent the sum of the individual + + align:start position:0% +represent the sum of the individual + + + align:start position:0% +represent the sum of the individual +demands + + align:start position:0% +demands + + + align:start position:0% +demands +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +you have this expression already + + align:start position:0% +you have this expression already + + + align:start position:0% +you have this expression already +for + + align:start position:0% +for + + + align:start position:0% +for +let me remind you + + align:start position:0% +let me remind you + + + align:start position:0% +let me remind you +the v star the candidate is 17. so we're + + align:start position:0% +the v star the candidate is 17. so we're + + + align:start position:0% +the v star the candidate is 17. so we're +we're going to prove that it works + + align:start position:0% +we're going to prove that it works + + + align:start position:0% +we're going to prove that it works +take v star indirect utility to be this + + align:start position:0% +take v star indirect utility to be this + + + align:start position:0% +take v star indirect utility to be this +a star b star w bar + + align:start position:0% +a star b star w bar + + + align:start position:0% +a star b star w bar +term + + align:start position:0% +term + + + align:start position:0% +term +then + + align:start position:0% +then + + + align:start position:0% +then +by roy's identity that's just another + + align:start position:0% +by roy's identity that's just another + + + align:start position:0% +by roy's identity that's just another +indirect utility function + + align:start position:0% +indirect utility function + + + align:start position:0% +indirect utility function +so the demand that comes from it at the + + align:start position:0% +so the demand that comes from it at the + + + align:start position:0% +so the demand that comes from it at the +aggregate wealth w bar and price vector + + align:start position:0% +aggregate wealth w bar and price vector + + + align:start position:0% +aggregate wealth w bar and price vector +p would just be + + align:start position:0% +p would just be + + + align:start position:0% +p would just be +the + + align:start position:0% +the + + + align:start position:0% +the +ratio of these marginal + + align:start position:0% +ratio of these marginal + + + align:start position:0% +ratio of these marginal +effects + + align:start position:0% +effects + + + align:start position:0% +effects +within a negative sign out in front of + + align:start position:0% +within a negative sign out in front of + + + align:start position:0% +within a negative sign out in front of +it + + align:start position:0% +it + + + align:start position:0% +it +and of course we know the form of the + + align:start position:0% +and of course we know the form of the + + + align:start position:0% +and of course we know the form of the +star + + align:start position:0% +star + + + align:start position:0% +star +so at an aggregated level it's very much + + align:start position:0% +so at an aggregated level it's very much + + + align:start position:0% +so at an aggregated level it's very much +like before one over bp because that's + + align:start position:0% +like before one over bp because that's + + + align:start position:0% +like before one over bp because that's +that's just the in the wealth + + align:start position:0% +that's just the in the wealth + + + align:start position:0% +that's just the in the wealth +coefficient + + align:start position:0% +coefficient + + + align:start position:0% +coefficient +and p enters into the intercept and + + align:start position:0% +and p enters into the intercept and + + + align:start position:0% +and p enters into the intercept and +slope term in this aggregated equation + + align:start position:0% +slope term in this aggregated equation + + + align:start position:0% +slope term in this aggregated equation +aggregate indirect utility 17 + + align:start position:0% +aggregate indirect utility 17 + + + align:start position:0% +aggregate indirect utility 17 +so we get + + align:start position:0% +so we get + + + align:start position:0% +so we get +we get this remember that the the a star + + align:start position:0% +we get this remember that the the a star + + + align:start position:0% +we get this remember that the the a star +is the sum of the ais by construction + + align:start position:0% +is the sum of the ais by construction + + + align:start position:0% +is the sum of the ais by construction +so now that is all written out very + + align:start position:0% +so now that is all written out very + + + align:start position:0% +so now that is all written out very +explicitly + + align:start position:0% +explicitly + + + align:start position:0% +explicitly +nothing going on with wealth + + align:start position:0% +nothing going on with wealth + + + align:start position:0% +nothing going on with wealth +but now we get to just + + align:start position:0% +but now we get to just + + + align:start position:0% +but now we get to just +take this summation + + align:start position:0% +take this summation + + + align:start position:0% +take this summation +and pull it outside + + align:start position:0% +and pull it outside + + + align:start position:0% +and pull it outside +so we have the demand that we want is + + align:start position:0% +so we have the demand that we want is + + + align:start position:0% +so we have the demand that we want is +the summation over i + + align:start position:0% +the summation over i + + + align:start position:0% +the summation over i +of + + align:start position:0% +of + + + align:start position:0% +of +what's left over after pulling out the + + align:start position:0% +what's left over after pulling out the + + + align:start position:0% +what's left over after pulling out the +summation we have the individual terms + + align:start position:0% +summation we have the individual terms + + + align:start position:0% +summation we have the individual terms +but of course that is nothing other than + + align:start position:0% +but of course that is nothing other than + + + align:start position:0% +but of course that is nothing other than +again + + align:start position:0% +again + + + align:start position:0% +again +from roy's identity the + + align:start position:0% +from roy's identity the + + + align:start position:0% +from roy's identity the +underlying demands + + align:start position:0% +underlying demands + + + align:start position:0% +underlying demands +which when we sum them up is aggregate + + align:start position:0% +which when we sum them up is aggregate + + + align:start position:0% +which when we sum them up is aggregate +demand + + align:start position:0% +demand + + + align:start position:0% +demand +okay so we've used this + + align:start position:0% +okay so we've used this + + + align:start position:0% +okay so we've used this +particular utility function 17 + + align:start position:0% +particular utility function 17 + + + align:start position:0% +particular utility function 17 +to derive the aggregate demand + + align:start position:0% +to derive the aggregate demand + + + align:start position:0% +to derive the aggregate demand +which is now proved to be the sum of the + + align:start position:0% +which is now proved to be the sum of the + + + align:start position:0% +which is now proved to be the sum of the +individual demands and by this + + align:start position:0% +individual demands and by this + + + align:start position:0% +individual demands and by this +construction depends only on + + align:start position:0% +construction depends only on + + + align:start position:0% +construction depends only on +on aggregate wealth the w bar is missing + + align:start position:0% +on aggregate wealth the w bar is missing + + + align:start position:0% +on aggregate wealth the w bar is missing +there + + align:start position:0% +there + + + align:start position:0% +there +questions + + align:start position:0% + + + + align:start position:0% + +all right so + + align:start position:0% +all right so + + + align:start position:0% +all right so +let me give you an example + + align:start position:0% +let me give you an example + + + align:start position:0% +let me give you an example +of the underlying utility functions and + + align:start position:0% +of the underlying utility functions and + + + align:start position:0% +of the underlying utility functions and +consumption sets + + align:start position:0% +consumption sets + + + align:start position:0% +consumption sets +suppose + + align:start position:0% +suppose + + + align:start position:0% +suppose +being explicit about the heterogeneity + + align:start position:0% +being explicit about the heterogeneity + + + align:start position:0% +being explicit about the heterogeneity +each household i + + align:start position:0% +each household i + + + align:start position:0% +each household i +consumption set is a subset of this l + + align:start position:0% +consumption set is a subset of this l + + + align:start position:0% +consumption set is a subset of this l +dimensional space namely their like + + align:start position:0% +dimensional space namely their like + + + align:start position:0% +dimensional space namely their like +subsistence or minimal bundles + + align:start position:0% +subsistence or minimal bundles + + + align:start position:0% +subsistence or minimal bundles +so the amount of good l + + align:start position:0% +so the amount of good l + + + align:start position:0% +so the amount of good l +cannot be lower than some x lower bar + + align:start position:0% +cannot be lower than some x lower bar + + + align:start position:0% +cannot be lower than some x lower bar +l for household i + + align:start position:0% +l for household i + + + align:start position:0% +l for household i +this is the heterogeneity it can depend + + align:start position:0% +this is the heterogeneity it can depend + + + align:start position:0% +this is the heterogeneity it can depend +on household i + + align:start position:0% +on household i + + + align:start position:0% +on household i +and let's have utility + + align:start position:0% +and let's have utility + + + align:start position:0% +and let's have utility +of household i over + + align:start position:0% +of household i over + + + align:start position:0% +of household i over +over vector x just be the difference + + align:start position:0% +over vector x just be the difference + + + align:start position:0% +over vector x just be the difference +to a power + + align:start position:0% +to a power + + + align:start position:0% +to a power +between xl and those minimal subsistence + + align:start position:0% +between xl and those minimal subsistence + + + align:start position:0% +between xl and those minimal subsistence +bundles + + align:start position:0% +bundles + + + align:start position:0% +bundles +so the heterogeneity is in the + + align:start position:0% +so the heterogeneity is in the + + + align:start position:0% +so the heterogeneity is in the +subsistence bundles which can vary over + + align:start position:0% +subsistence bundles which can vary over + + + align:start position:0% +subsistence bundles which can vary over +households but the sigmas are the same + + align:start position:0% +households but the sigmas are the same + + + align:start position:0% +households but the sigmas are the same +it's not sigma i it's sigma common + + align:start position:0% +it's not sigma i it's sigma common + + + align:start position:0% +it's not sigma i it's sigma common +across all the households + + align:start position:0% +across all the households + + + align:start position:0% +across all the households +so if we had an economy represented by + + align:start position:0% +so if we had an economy represented by + + + align:start position:0% +so if we had an economy represented by +these consumption sets and these + + align:start position:0% +these consumption sets and these + + + align:start position:0% +these consumption sets and these +preferences + + align:start position:0% +preferences + + + align:start position:0% +preferences +we could + + align:start position:0% +we could + + + align:start position:0% +we could +look at their indirect utility + + align:start position:0% +look at their indirect utility + + + align:start position:0% +look at their indirect utility +if you do the math you get this ugly + + align:start position:0% +if you do the math you get this ugly + + + align:start position:0% +if you do the math you get this ugly +thing but it does have the right form a + + align:start position:0% +thing but it does have the right form a + + + align:start position:0% +thing but it does have the right form a +i of p plus bp times w i or household i + + align:start position:0% +i of p plus bp times w i or household i + + + align:start position:0% +i of p plus bp times w i or household i +and then you add it up namely add up + + align:start position:0% +and then you add it up namely add up + + + align:start position:0% +and then you add it up namely add up +this guy + + align:start position:0% +this guy + + + align:start position:0% +this guy +over households i + + align:start position:0% +over households i + + + align:start position:0% +over households i +and you get the expression at the bottom + + align:start position:0% +and you get the expression at the bottom + + + align:start position:0% +and you get the expression at the bottom +of the of the slide + + align:start position:0% +of the of the slide + + + align:start position:0% +of the of the slide +and in particular the heterogeneity and + + align:start position:0% +and in particular the heterogeneity and + + + align:start position:0% +and in particular the heterogeneity and +the subsistence bundles is right here + + align:start position:0% +the subsistence bundles is right here + + + align:start position:0% +the subsistence bundles is right here +so + + align:start position:0% +so + + + align:start position:0% +so +they're all different they have + + align:start position:0% +they're all different they have + + + align:start position:0% +they're all different they have +different minimums + + align:start position:0% +different minimums + + + align:start position:0% +different minimums +but miraculously we're able to add up + + align:start position:0% +but miraculously we're able to add up + + + align:start position:0% +but miraculously we're able to add up +those minimums and call it kind of a + + align:start position:0% +those minimums and call it kind of a + + + align:start position:0% +those minimums and call it kind of a +pseudo subsistence bundle for an + + align:start position:0% +pseudo subsistence bundle for an + + + align:start position:0% +pseudo subsistence bundle for an +aggregated representative household who + + align:start position:0% +aggregated representative household who + + + align:start position:0% +aggregated representative household who +would have the indirect utility + + align:start position:0% +would have the indirect utility + + + align:start position:0% +would have the indirect utility +that's written out here at the bottom of + + align:start position:0% +that's written out here at the bottom of + + + align:start position:0% +that's written out here at the bottom of +the slide + + align:start position:0% +the slide + + + align:start position:0% +the slide +i don't have too many more examples in + + align:start position:0% +i don't have too many more examples in + + + align:start position:0% +i don't have too many more examples in +front of me today but i mean i do wanted + + align:start position:0% +front of me today but i mean i do wanted + + + align:start position:0% +front of me today but i mean i do wanted +to give i did want to give you one + + align:start position:0% +to give i did want to give you one + + + align:start position:0% +to give i did want to give you one +example because this indirect utility + + align:start position:0% +example because this indirect utility + + + align:start position:0% +example because this indirect utility +space is a bit different and a bit + + align:start position:0% +space is a bit different and a bit + + + align:start position:0% +space is a bit different and a bit +abstract so here we actually start with + + align:start position:0% +abstract so here we actually start with + + + align:start position:0% +abstract so here we actually start with +underlying utility functions + + align:start position:0% +underlying utility functions + + + align:start position:0% +underlying utility functions +all right + + align:start position:0% +all right + + + align:start position:0% +all right +well i said all that in words + + align:start position:0% +well i said all that in words + + + align:start position:0% +well i said all that in words +so now let's go to the normative + + align:start position:0% +so now let's go to the normative + + + align:start position:0% +so now let's go to the normative +representative household + + align:start position:0% +representative household + + + align:start position:0% +representative household +i should say it's the same guy it's the + + align:start position:0% +i should say it's the same guy it's the + + + align:start position:0% +i should say it's the same guy it's the +same person + + align:start position:0% +same person + + + align:start position:0% +same person +it just has two characteristics + + align:start position:0% +it just has two characteristics + + + align:start position:0% +it just has two characteristics +it can be used for positive economics in + + align:start position:0% +it can be used for positive economics in + + + align:start position:0% +it can be used for positive economics in +the sense that it's predictive of what + + align:start position:0% +the sense that it's predictive of what + + + align:start position:0% +the sense that it's predictive of what +the + + align:start position:0% +the + + + align:start position:0% +the +entire economy is doing and it can also + + align:start position:0% +entire economy is doing and it can also + + + align:start position:0% +entire economy is doing and it can also +be used to make welfare statements + + align:start position:0% +be used to make welfare statements + + + align:start position:0% +be used to make welfare statements +by + + align:start position:0% +by + + + align:start position:0% +by +a rank ordering over the utility + + align:start position:0% +a rank ordering over the utility + + + align:start position:0% +a rank ordering over the utility +function + + align:start position:0% +function + + + align:start position:0% +function +but there's not like one representative + + align:start position:0% +but there's not like one representative + + + align:start position:0% +but there's not like one representative +normative household and one + + align:start position:0% +normative household and one + + + align:start position:0% +normative household and one +representative positive household + + align:start position:0% +representative positive household + + + align:start position:0% +representative positive household +it's a given representative household + + align:start position:0% +it's a given representative household + + + align:start position:0% +it's a given representative household +with both positive and normative + + align:start position:0% +with both positive and normative + + + align:start position:0% +with both positive and normative +characteristics and we are about to go + + align:start position:0% +characteristics and we are about to go + + + align:start position:0% +characteristics and we are about to go +through the normative part + + align:start position:0% +through the normative part + + + align:start position:0% +through the normative part +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so let's have the individual demand + + align:start position:0% +so let's have the individual demand + + + align:start position:0% +so let's have the individual demand +functions this is the the first little + + align:start position:0% +functions this is the the first little + + + align:start position:0% +functions this is the the first little +paragraph here is the positive part that + + align:start position:0% +paragraph here is the positive part that + + + align:start position:0% +paragraph here is the positive part that +these demands can be derived as if + + align:start position:0% +these demands can be derived as if + + + align:start position:0% +these demands can be derived as if +through an aggregated demand function + + align:start position:0% +through an aggregated demand function + + + align:start position:0% +through an aggregated demand function +given the total wealth of the economy + + align:start position:0% +given the total wealth of the economy + + + align:start position:0% +given the total wealth of the economy +now we want to ask the normative + + align:start position:0% +now we want to ask the normative + + + align:start position:0% +now we want to ask the normative +question + + align:start position:0% +question + + + align:start position:0% +question +given a set of in-dual demand functions + + align:start position:0% +given a set of in-dual demand functions + + + align:start position:0% +given a set of in-dual demand functions +can we find this fictitious household i + + align:start position:0% +can we find this fictitious household i + + + align:start position:0% +can we find this fictitious household i +star such that pareto optimal + + align:start position:0% +star such that pareto optimal + + + align:start position:0% +star such that pareto optimal +allocations in the in the economy can be + + align:start position:0% +allocations in the in the economy can be + + + align:start position:0% +allocations in the in the economy can be +thought of as coming from this + + align:start position:0% +thought of as coming from this + + + align:start position:0% +thought of as coming from this +representative household maximizing + + align:start position:0% +representative household maximizing + + + align:start position:0% +representative household maximizing +utility i keep emphasizing fictitious + + align:start position:0% +utility i keep emphasizing fictitious + + + align:start position:0% +utility i keep emphasizing fictitious +amazing because i don't want you to + + align:start position:0% +amazing because i don't want you to + + + align:start position:0% +amazing because i don't want you to +think that this is a real person it's a + + align:start position:0% +think that this is a real person it's a + + + align:start position:0% +think that this is a real person it's a +construct + + align:start position:0% +construct + + + align:start position:0% +construct +so let's take our underlying economy + + align:start position:0% +so let's take our underlying economy + + + align:start position:0% +so let's take our underlying economy +which we've been reading this line + + align:start position:0% +which we've been reading this line + + + align:start position:0% +which we've been reading this line +for the last two or three lectures + + align:start position:0% +for the last two or three lectures + + + align:start position:0% +for the last two or three lectures +underlying economy is script e + + align:start position:0% +underlying economy is script e + + + align:start position:0% +underlying economy is script e +characterized by + + align:start position:0% +characterized by + + + align:start position:0% +characterized by +consumption sets utility functions over + + align:start position:0% +consumption sets utility functions over + + + align:start position:0% +consumption sets utility functions over +all the households production + + align:start position:0% +all the households production + + + align:start position:0% +all the households production +possibility sets over all the firms some + + align:start position:0% +possibility sets over all the firms some + + + align:start position:0% +possibility sets over all the firms some +aggregate endowment w bar + + align:start position:0% +aggregate endowment w bar + + + align:start position:0% +aggregate endowment w bar +now finally we define a normative + + align:start position:0% +now finally we define a normative + + + align:start position:0% +now finally we define a normative +representative household + + align:start position:0% +representative household + + + align:start position:0% +representative household +with two characteristics + + align:start position:0% +with two characteristics + + + align:start position:0% +with two characteristics +if + + align:start position:0% +if + + + align:start position:0% +if +we started with an allocation x and y + + align:start position:0% +we started with an allocation x and y + + + align:start position:0% +we started with an allocation x and y +and we found an alternative allocation x + + align:start position:0% +and we found an alternative allocation x + + + align:start position:0% +and we found an alternative allocation x +prime y prime which pareto dominates + + align:start position:0% +prime y prime which pareto dominates + + + align:start position:0% +prime y prime which pareto dominates +x y + + align:start position:0% +x y + + + align:start position:0% +x y +meaning + + align:start position:0% +meaning + + + align:start position:0% +meaning +at least is good for some and strictly + + align:start position:0% +at least is good for some and strictly + + + align:start position:0% +at least is good for some and strictly +better for others + + align:start position:0% +better for others + + + align:start position:0% +better for others +then + + align:start position:0% +then + + + align:start position:0% +then +under u star + + align:start position:0% +under u star + + + align:start position:0% +under u star +evaluated that the sum of the prime + + align:start position:0% +evaluated that the sum of the prime + + + align:start position:0% +evaluated that the sum of the prime +bundle + + align:start position:0% +bundle + + + align:start position:0% +bundle +is greater than + + align:start position:0% +is greater than + + + align:start position:0% +is greater than +u star evaluated at the original bundle + + align:start position:0% +u star evaluated at the original bundle + + + align:start position:0% +u star evaluated at the original bundle +in other words it's kind of intuitive + + align:start position:0% +in other words it's kind of intuitive + + + align:start position:0% +in other words it's kind of intuitive +but it's not always true + + align:start position:0% +but it's not always true + + + align:start position:0% +but it's not always true +here for the definition of pareto + + align:start position:0% +here for the definition of pareto + + + align:start position:0% +here for the definition of pareto +dominance we're looking at individual + + align:start position:0% +dominance we're looking at individual + + + align:start position:0% +dominance we're looking at individual +allocations over all the households + + align:start position:0% +allocations over all the households + + + align:start position:0% +allocations over all the households +and trying to find something that's at + + align:start position:0% +and trying to find something that's at + + + align:start position:0% +and trying to find something that's at +least as good for some and strictly + + align:start position:0% +least as good for some and strictly + + + align:start position:0% +least as good for some and strictly +better for the others if we can find + + align:start position:0% +better for the others if we can find + + + align:start position:0% +better for the others if we can find +this amazing u star + + align:start position:0% +this amazing u star + + + align:start position:0% +this amazing u star +then all we need to do is evaluate the + + align:start position:0% +then all we need to do is evaluate the + + + align:start position:0% +then all we need to do is evaluate the +aggregates namely the aggregate under x + + align:start position:0% +aggregates namely the aggregate under x + + + align:start position:0% +aggregates namely the aggregate under x +prime and aggregate under x and what we + + align:start position:0% +prime and aggregate under x and what we + + + align:start position:0% +prime and aggregate under x and what we +need and apart from condition two the + + align:start position:0% +need and apart from condition two the + + + align:start position:0% +need and apart from condition two the +only thing we need is that u-star + + align:start position:0% +only thing we need is that u-star + + + align:start position:0% +only thing we need is that u-star +assigns a higher value in other words + + align:start position:0% +assigns a higher value in other words + + + align:start position:0% +assigns a higher value in other words +it's easy to to look for pareto + + align:start position:0% +it's easy to to look for pareto + + + align:start position:0% +it's easy to to look for pareto +improvements just by looking at the + + align:start position:0% +improvements just by looking at the + + + align:start position:0% +improvements just by looking at the +value under this pseudo-utility function + + align:start position:0% +value under this pseudo-utility function + + + align:start position:0% +value under this pseudo-utility function +evaluated at the aggregates + + align:start position:0% +evaluated at the aggregates + + + align:start position:0% +evaluated at the aggregates +so the second thing is similar but not + + align:start position:0% +so the second thing is similar but not + + + align:start position:0% +so the second thing is similar but not +quite instead of starting with the + + align:start position:0% +quite instead of starting with the + + + align:start position:0% +quite instead of starting with the +underlying micro distributions suppose + + align:start position:0% +underlying micro distributions suppose + + + align:start position:0% +underlying micro distributions suppose +that we had a feasible allocation x and + + align:start position:0% +that we had a feasible allocation x and + + + align:start position:0% +that we had a feasible allocation x and +y as before + + align:start position:0% +y as before + + + align:start position:0% +y as before +and an alternative feasible allocation x + + align:start position:0% +and an alternative feasible allocation x + + + align:start position:0% +and an alternative feasible allocation x +prime y prime and we're given that under + + align:start position:0% +prime y prime and we're given that under + + + align:start position:0% +prime y prime and we're given that under +u star + + align:start position:0% +u star + + + align:start position:0% +u star +the utility is higher at the aggregates + + align:start position:0% +the utility is higher at the aggregates + + + align:start position:0% +the utility is higher at the aggregates +then we want to claim that there is an + + align:start position:0% +then we want to claim that there is an + + + align:start position:0% +then we want to claim that there is an +alternative feasible allocation which + + align:start position:0% +alternative feasible allocation which + + + align:start position:0% +alternative feasible allocation which +pareto dominates in other words is this + + align:start position:0% +pareto dominates in other words is this + + + align:start position:0% +pareto dominates in other words is this +x i allocation pareto optimal or not not + + align:start position:0% +x i allocation pareto optimal or not not + + + align:start position:0% +x i allocation pareto optimal or not not +if we can find another allocation x + + align:start position:0% +if we can find another allocation x + + + align:start position:0% +if we can find another allocation x +prime which dominates the dominates in + + align:start position:0% +prime which dominates the dominates in + + + align:start position:0% +prime which dominates the dominates in +sense of u star and u star is just + + align:start position:0% +sense of u star and u star is just + + + align:start position:0% +sense of u star and u star is just +evaluating these things at the summed up + + align:start position:0% +evaluating these things at the summed up + + + align:start position:0% +evaluating these things at the summed up +aggregates and actually there's a + + align:start position:0% +aggregates and actually there's a + + + align:start position:0% +aggregates and actually there's a +subtlety here which is important you + + align:start position:0% +subtlety here which is important you + + + align:start position:0% +subtlety here which is important you +can't just stop + + align:start position:0% +can't just stop + + + align:start position:0% +can't just stop +you may have to redistribute well here's + + align:start position:0% +you may have to redistribute well here's + + + align:start position:0% +you may have to redistribute well here's +what i mean by that + + align:start position:0% +what i mean by that + + + align:start position:0% +what i mean by that +if this is true there exists an + + align:start position:0% +if this is true there exists an + + + align:start position:0% +if this is true there exists an +alternative feasible allocation + + align:start position:0% +alternative feasible allocation + + + align:start position:0% +alternative feasible allocation +tilde x tilde y tilde such that the + + align:start position:0% +tilde x tilde y tilde such that the + + + align:start position:0% +tilde x tilde y tilde such that the +summation over x tilde of the demands + + align:start position:0% +summation over x tilde of the demands + + + align:start position:0% +summation over x tilde of the demands +and so on allocations is exactly the + + align:start position:0% +and so on allocations is exactly the + + + align:start position:0% +and so on allocations is exactly the +same aggregate as under the prime + + align:start position:0% +same aggregate as under the prime + + + align:start position:0% +same aggregate as under the prime +and the y's aren't changing so this kind + + align:start position:0% +and the y's aren't changing so this kind + + + align:start position:0% +and the y's aren't changing so this kind +of subtle step here it doesn't mean + + align:start position:0% +of subtle step here it doesn't mean + + + align:start position:0% +of subtle step here it doesn't mean +necessarily + + align:start position:0% +necessarily + + + align:start position:0% +necessarily +that you can stop with x prime and y + + align:start position:0% +that you can stop with x prime and y + + + align:start position:0% +that you can stop with x prime and y +prime + + align:start position:0% +prime + + + align:start position:0% +prime +and claim victory + + align:start position:0% +and claim victory + + + align:start position:0% +and claim victory +because if you stop there it's not + + align:start position:0% +because if you stop there it's not + + + align:start position:0% +because if you stop there it's not +necessarily true that everyone's better + + align:start position:0% +necessarily true that everyone's better + + + align:start position:0% +necessarily true that everyone's better +off or no worse off + + align:start position:0% +off or no worse off + + + align:start position:0% +off or no worse off +some people may be damaged in fact maybe + + align:start position:0% +some people may be damaged in fact maybe + + + align:start position:0% +some people may be damaged in fact maybe +this is the time to talk about free + + align:start position:0% +this is the time to talk about free + + + align:start position:0% +this is the time to talk about free +trade when we were looking at that + + align:start position:0% +trade when we were looking at that + + + align:start position:0% +trade when we were looking at that +lecture we represented a country by some + + align:start position:0% +lecture we represented a country by some + + + align:start position:0% +lecture we represented a country by some +indifference curve as if from some + + align:start position:0% +indifference curve as if from some + + + align:start position:0% +indifference curve as if from some +u-star representative household for the + + align:start position:0% +u-star representative household for the + + + align:start position:0% +u-star representative household for the +whole country + + align:start position:0% +whole country + + + align:start position:0% +whole country +to look at the direction of trade so we + + align:start position:0% +to look at the direction of trade so we + + + align:start position:0% +to look at the direction of trade so we +were getting the country's aggregate + + align:start position:0% +were getting the country's aggregate + + + align:start position:0% +were getting the country's aggregate +demand in a positive sense + + align:start position:0% +demand in a positive sense + + + align:start position:0% +demand in a positive sense +by looking at that representative agent + + align:start position:0% +by looking at that representative agent + + + align:start position:0% +by looking at that representative agent +indifference curve and it might have + + align:start position:0% +indifference curve and it might have + + + align:start position:0% +indifference curve and it might have +appeared that the whole country could be + + align:start position:0% +appeared that the whole country could be + + + align:start position:0% +appeared that the whole country could be +made better off by free trade on the + + align:start position:0% +made better off by free trade on the + + + align:start position:0% +made better off by free trade on the +other hand you saw in detail in two + + align:start position:0% +other hand you saw in detail in two + + + align:start position:0% +other hand you saw in detail in two +different lectures uh three really + + align:start position:0% +different lectures uh three really + + + align:start position:0% +different lectures uh three really +that + + align:start position:0% +that + + + align:start position:0% +that +not everyone is made off by free under + + align:start position:0% +not everyone is made off by free under + + + align:start position:0% +not everyone is made off by free under +free trade + + align:start position:0% +free trade + + + align:start position:0% +free trade +remember the households that are + + align:start position:0% +remember the households that are + + + align:start position:0% +remember the households that are +relatively well endowed with a factor + + align:start position:0% +relatively well endowed with a factor + + + align:start position:0% +relatively well endowed with a factor +that's abundant + + align:start position:0% +that's abundant + + + align:start position:0% +that's abundant +are helped by exports the other guys are + + align:start position:0% +are helped by exports the other guys are + + + align:start position:0% +are helped by exports the other guys are +hurt etc + + align:start position:0% +hurt etc + + + align:start position:0% +hurt etc +so how can we claim that free trade + + align:start position:0% +so how can we claim that free trade + + + align:start position:0% +so how can we claim that free trade +makes everyone better off we have to + + align:start position:0% +makes everyone better off we have to + + + align:start position:0% +makes everyone better off we have to +redistribute + + align:start position:0% +redistribute + + + align:start position:0% +redistribute +which is not always done hence people + + align:start position:0% +which is not always done hence people + + + align:start position:0% +which is not always done hence people +complain about free trade and they want + + align:start position:0% +complain about free trade and they want + + + align:start position:0% +complain about free trade and they want +tariffs + + align:start position:0% +tariffs + + + align:start position:0% +tariffs +anyway i'm belaboring the fact that this + + align:start position:0% +anyway i'm belaboring the fact that this + + + align:start position:0% +anyway i'm belaboring the fact that this +lecture is consistent with the other + + align:start position:0% +lecture is consistent with the other + + + align:start position:0% +lecture is consistent with the other +ones except now we're finally in a + + align:start position:0% +ones except now we're finally in a + + + align:start position:0% +ones except now we're finally in a +position to be able to talk explicitly + + align:start position:0% +position to be able to talk explicitly + + + align:start position:0% +position to be able to talk explicitly +about redistribution as a necessary part + + align:start position:0% +about redistribution as a necessary part + + + align:start position:0% +about redistribution as a necessary part +of making everyone better off okay + + align:start position:0% +of making everyone better off okay + + + align:start position:0% +of making everyone better off okay +in other words to sum up even when we + + align:start position:0% +in other words to sum up even when we + + + align:start position:0% +in other words to sum up even when we +have preferences aggregating it is not + + align:start position:0% +have preferences aggregating it is not + + + align:start position:0% +have preferences aggregating it is not +necessarily the case + + align:start position:0% +necessarily the case + + + align:start position:0% +necessarily the case +that everyone is made better off under + + align:start position:0% +that everyone is made better off under + + + align:start position:0% +that everyone is made better off under +some alternative allocation xi prime you + + align:start position:0% +some alternative allocation xi prime you + + + align:start position:0% +some alternative allocation xi prime you +have to redistribute the underlying + + align:start position:0% +have to redistribute the underlying + + + align:start position:0% +have to redistribute the underlying +bundles + + align:start position:0% +bundles + + + align:start position:0% +bundles +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so let's do the same definition but do + + align:start position:0% +so let's do the same definition but do + + + align:start position:0% +so let's do the same definition but do +it in the space of indirect utility + + align:start position:0% +it in the space of indirect utility + + + align:start position:0% +it in the space of indirect utility +instead of direct utility + + align:start position:0% +instead of direct utility + + + align:start position:0% +instead of direct utility +suppose we're given a vector of wealth + + align:start position:0% +suppose we're given a vector of wealth + + + align:start position:0% +suppose we're given a vector of wealth +as in the distribution of income and + + align:start position:0% +as in the distribution of income and + + + align:start position:0% +as in the distribution of income and +some aggregate wealth that corresponds + + align:start position:0% +some aggregate wealth that corresponds + + + align:start position:0% +some aggregate wealth that corresponds +with that + + align:start position:0% +with that + + + align:start position:0% +with that +p is a + + align:start position:0% +p is a + + + align:start position:0% +p is a +price vector define the indirect utility + + align:start position:0% +price vector define the indirect utility + + + align:start position:0% +price vector define the indirect utility +functions again as we have been doing + + align:start position:0% +functions again as we have been doing + + + align:start position:0% +functions again as we have been doing +we now we want to find this miraculous + + align:start position:0% +we now we want to find this miraculous + + + align:start position:0% +we now we want to find this miraculous +star person + + align:start position:0% +star person + + + align:start position:0% +star person +this normative + + align:start position:0% +this normative + + + align:start position:0% +this normative +representative household + + align:start position:0% +representative household + + + align:start position:0% +representative household +i star + + align:start position:0% +i star + + + align:start position:0% +i star +that has an indirect utility function v + + align:start position:0% +that has an indirect utility function v + + + align:start position:0% +that has an indirect utility function v +star + + align:start position:0% +star + + + align:start position:0% +star +evaluated at the price vector p n the + + align:start position:0% +evaluated at the price vector p n the + + + align:start position:0% +evaluated at the price vector p n the +aggregate wealth w bar + + align:start position:0% +aggregate wealth w bar + + + align:start position:0% +aggregate wealth w bar +and there are two conditions + + align:start position:0% +and there are two conditions + + + align:start position:0% +and there are two conditions +one and two that correspond with the one + + align:start position:0% +one and two that correspond with the one + + + align:start position:0% +one and two that correspond with the one +in the allocation space x i on the + + align:start position:0% +in the allocation space x i on the + + + align:start position:0% +in the allocation space x i on the +previous slide namely + + align:start position:0% +previous slide namely + + + align:start position:0% +previous slide namely +if you have two configurations you start + + align:start position:0% +if you have two configurations you start + + + align:start position:0% +if you have two configurations you start +with a pnw + + align:start position:0% +with a pnw + + + align:start position:0% +with a pnw +wealth you're looking at an alternative + + align:start position:0% +wealth you're looking at an alternative + + + align:start position:0% +wealth you're looking at an alternative +p prime w prime price factor in wealth + + align:start position:0% +p prime w prime price factor in wealth + + + align:start position:0% +p prime w prime price factor in wealth +such that looking at the actual real + + align:start position:0% +such that looking at the actual real + + + align:start position:0% +such that looking at the actual real +indirect utilities of all the households + + align:start position:0% +indirect utilities of all the households + + + align:start position:0% +indirect utilities of all the households +some people are no worse off and other + + align:start position:0% +some people are no worse off and other + + + align:start position:0% +some people are no worse off and other +people are strictly better off under the + + align:start position:0% +people are strictly better off under the + + + align:start position:0% +people are strictly better off under the +prime allocation so that's the statement + + align:start position:0% +prime allocation so that's the statement + + + align:start position:0% +prime allocation so that's the statement +of pareto dominance in the space of + + align:start position:0% +of pareto dominance in the space of + + + align:start position:0% +of pareto dominance in the space of +indirect utility functions and what we + + align:start position:0% +indirect utility functions and what we + + + align:start position:0% +indirect utility functions and what we +want is a way to do it more easily + + align:start position:0% +want is a way to do it more easily + + + align:start position:0% +want is a way to do it more easily +through v star the indirect utility of + + align:start position:0% +through v star the indirect utility of + + + align:start position:0% +through v star the indirect utility of +the normative representative household + + align:start position:0% +the normative representative household + + + align:start position:0% +the normative representative household +which is just evaluating the alternative + + align:start position:0% +which is just evaluating the alternative + + + align:start position:0% +which is just evaluating the alternative +scenario p prime and w prime but it's w + + align:start position:0% +scenario p prime and w prime but it's w + + + align:start position:0% +scenario p prime and w prime but it's w +prime added up over all the households + + align:start position:0% +prime added up over all the households + + + align:start position:0% +prime added up over all the households +so we're just using aggregate wealth + + align:start position:0% +so we're just using aggregate wealth + + + align:start position:0% +so we're just using aggregate wealth +here on the left-hand side and also + + align:start position:0% +here on the left-hand side and also + + + align:start position:0% +here on the left-hand side and also +aggregate wealth on the right-hand side + + align:start position:0% +aggregate wealth on the right-hand side + + + align:start position:0% +aggregate wealth on the right-hand side +when we're thinking about trying to + + align:start position:0% +when we're thinking about trying to + + + align:start position:0% +when we're thinking about trying to +quote-unquote pareto dominate so just + + align:start position:0% +quote-unquote pareto dominate so just + + + align:start position:0% +quote-unquote pareto dominate so just +like before it's very intuitive but + + align:start position:0% +like before it's very intuitive but + + + align:start position:0% +like before it's very intuitive but +amazing when it's true that the way to + + align:start position:0% +amazing when it's true that the way to + + + align:start position:0% +amazing when it's true that the way to +look for pareto dominating allocations + + align:start position:0% +look for pareto dominating allocations + + + align:start position:0% +look for pareto dominating allocations +is just to evaluate the uh aggregated + + align:start position:0% +is just to evaluate the uh aggregated + + + align:start position:0% +is just to evaluate the uh aggregated +allocations and see whether you get a + + align:start position:0% +allocations and see whether you get a + + + align:start position:0% +allocations and see whether you get a +higher value under v star + + align:start position:0% +higher value under v star + + + align:start position:0% +higher value under v star +likewise going the other way start with + + align:start position:0% +likewise going the other way start with + + + align:start position:0% +likewise going the other way start with +the aggregate wealth + + align:start position:0% +the aggregate wealth + + + align:start position:0% +the aggregate wealth +and price vector p look at an + + align:start position:0% +and price vector p look at an + + + align:start position:0% +and price vector p look at an +alternative scenario p prime and w bar + + align:start position:0% +alternative scenario p prime and w bar + + + align:start position:0% +alternative scenario p prime and w bar +prime + + align:start position:0% +prime + + + align:start position:0% +prime +such that the utility under v star is + + align:start position:0% +such that the utility under v star is + + + align:start position:0% +such that the utility under v star is +higher in the alternative allocation if + + align:start position:0% +higher in the alternative allocation if + + + align:start position:0% +higher in the alternative allocation if +that's true then there exists an + + align:start position:0% +that's true then there exists an + + + align:start position:0% +that's true then there exists an +alternative income distribution w prime + + align:start position:0% +alternative income distribution w prime + + + align:start position:0% +alternative income distribution w prime +which adds up to the aggregate wealth in + + align:start position:0% +which adds up to the aggregate wealth in + + + align:start position:0% +which adds up to the aggregate wealth in +the alternative the dominating + + align:start position:0% +the alternative the dominating + + + align:start position:0% +the alternative the dominating +allocation with a prime on it now again + + align:start position:0% +allocation with a prime on it now again + + + align:start position:0% +allocation with a prime on it now again +let's pause here + + align:start position:0% +let's pause here + + + align:start position:0% +let's pause here +this alternative income means an income + + align:start position:0% +this alternative income means an income + + + align:start position:0% +this alternative income means an income +distribution that works under the prime + + align:start position:0% +distribution that works under the prime + + + align:start position:0% +distribution that works under the prime +scenario + + align:start position:0% +scenario + + + align:start position:0% +scenario +relative to the initial income + + align:start position:0% +relative to the initial income + + + align:start position:0% +relative to the initial income +distribution in the baseline without the + + align:start position:0% +distribution in the baseline without the + + + align:start position:0% +distribution in the baseline without the +prime so we have to have the freedom to + + align:start position:0% +prime so we have to have the freedom to + + + align:start position:0% +prime so we have to have the freedom to +distribute wealth + + align:start position:0% +distribute wealth + + + align:start position:0% +distribute wealth +not necessarily according to private + + align:start position:0% +not necessarily according to private + + + align:start position:0% +not necessarily according to private +ownership when we change the prices and + + align:start position:0% +ownership when we change the prices and + + + align:start position:0% +ownership when we change the prices and +so on but potentially with transfers of + + align:start position:0% +so on but potentially with transfers of + + + align:start position:0% +so on but potentially with transfers of +wealth across the agents + + align:start position:0% +wealth across the agents + + + align:start position:0% +wealth across the agents +giving to some taking away from others + + align:start position:0% +giving to some taking away from others + + + align:start position:0% +giving to some taking away from others +as in the second welfare theorem + + align:start position:0% +as in the second welfare theorem + + + align:start position:0% +as in the second welfare theorem +where we've seen this kind of + + align:start position:0% +where we've seen this kind of + + + align:start position:0% +where we've seen this kind of +redistribution before so we we find this + + align:start position:0% +redistribution before so we we find this + + + align:start position:0% +redistribution before so we we find this +alternative you know such that we're + + align:start position:0% +alternative you know such that we're + + + align:start position:0% +alternative you know such that we're +getting pareto dominance in the + + align:start position:0% +getting pareto dominance in the + + + align:start position:0% +getting pareto dominance in the +underlying indirect utility functions + + align:start position:0% +underlying indirect utility functions + + + align:start position:0% +underlying indirect utility functions +not worse for anyone and strictly better + + align:start position:0% +not worse for anyone and strictly better + + + align:start position:0% +not worse for anyone and strictly better +for some + + align:start position:0% +for some + + + align:start position:0% +for some +so how do we find this representative + + align:start position:0% +so how do we find this representative + + + align:start position:0% +so how do we find this representative +household or the representative + + align:start position:0% +household or the representative + + + align:start position:0% +household or the representative +household with this normative property + + align:start position:0% +household with this normative property + + + align:start position:0% +household with this normative property +same guy gorman polar form + + align:start position:0% +same guy gorman polar form + + + align:start position:0% +same guy gorman polar form +although this is getting stated as a + + align:start position:0% +although this is getting stated as a + + + align:start position:0% +although this is getting stated as a +proposition + + align:start position:0% +proposition + + + align:start position:0% +proposition +if we have this gorman polar form with + + align:start position:0% +if we have this gorman polar form with + + + align:start position:0% +if we have this gorman polar form with +this particular way that heterogeneity + + align:start position:0% +this particular way that heterogeneity + + + align:start position:0% +this particular way that heterogeneity +is entering into the indirect utility + + align:start position:0% +is entering into the indirect utility + + + align:start position:0% +is entering into the indirect utility +functions then when we look at the + + align:start position:0% +functions then when we look at the + + + align:start position:0% +functions then when we look at the +indirect utility function under the + + align:start position:0% +indirect utility function under the + + + align:start position:0% +indirect utility function under the +aggregate being in particular the sum of + + align:start position:0% +aggregate being in particular the sum of + + + align:start position:0% +aggregate being in particular the sum of +the a i plus b times w + + align:start position:0% +the a i plus b times w + + + align:start position:0% +the a i plus b times w +that is the normative household we + + align:start position:0% +that is the normative household we + + + align:start position:0% +that is the normative household we +already proved the positive part earlier + + align:start position:0% +already proved the positive part earlier + + + align:start position:0% +already proved the positive part earlier +now it's normative i put positive and + + align:start position:0% +now it's normative i put positive and + + + align:start position:0% +now it's normative i put positive and +normative both on the slide to make the + + align:start position:0% +normative both on the slide to make the + + + align:start position:0% +normative both on the slide to make the +point that as i've said we're not + + align:start position:0% +point that as i've said we're not + + + align:start position:0% +point that as i've said we're not +looking for a normative household that + + align:start position:0% +looking for a normative household that + + + align:start position:0% +looking for a normative household that +different from the positive household + + align:start position:0% +different from the positive household + + + align:start position:0% +different from the positive household +we're looking for this representative + + align:start position:0% +we're looking for this representative + + + align:start position:0% +we're looking for this representative +household with both attributes + + align:start position:0% +household with both attributes + + + align:start position:0% +household with both attributes +we proved the positive thing earlier now + + align:start position:0% +we proved the positive thing earlier now + + + align:start position:0% +we proved the positive thing earlier now +we need to prove the normative part + + align:start position:0% +we need to prove the normative part + + + align:start position:0% +we need to prove the normative part +so + + align:start position:0% +so + + + align:start position:0% +so +suppose we have those gorman polar form + + align:start position:0% +suppose we have those gorman polar form + + + align:start position:0% +suppose we have those gorman polar form +and particular figure out which + + align:start position:0% +and particular figure out which + + + align:start position:0% +and particular figure out which +direction we're going + + align:start position:0% +direction we're going + + + align:start position:0% +direction we're going +from the un condition one + + align:start position:0% +from the un condition one + + + align:start position:0% +from the un condition one +this guy here condition one + + align:start position:0% +this guy here condition one + + + align:start position:0% +this guy here condition one +so we have a rank ordering under the + + align:start position:0% +so we have a rank ordering under the + + + align:start position:0% +so we have a rank ordering under the +actual indirect utility functions being + + align:start position:0% +actual indirect utility functions being + + + align:start position:0% +actual indirect utility functions being +explicit about household eye so + + align:start position:0% +explicit about household eye so + + + align:start position:0% +explicit about household eye so +under the vi's strict not worse + + align:start position:0% +under the vi's strict not worse + + + align:start position:0% +under the vi's strict not worse +for some + + align:start position:0% +for some + + + align:start position:0% +for some +and strictly better for others so we're + + align:start position:0% +and strictly better for others so we're + + + align:start position:0% +and strictly better for others so we're +given that + + align:start position:0% +given that + + + align:start position:0% +given that +now we want to prove + + align:start position:0% +now we want to prove + + + align:start position:0% +now we want to prove +that when we evaluate under v star using + + align:start position:0% +that when we evaluate under v star using + + + align:start position:0% +that when we evaluate under v star using +the aggregates we get strict dominance + + align:start position:0% +the aggregates we get strict dominance + + + align:start position:0% +the aggregates we get strict dominance +so let's look at it v star under the + + align:start position:0% +so let's look at it v star under the + + + align:start position:0% +so let's look at it v star under the +aggregate + + align:start position:0% +aggregate + + + align:start position:0% +aggregate +alternative prime allocation + + align:start position:0% +alternative prime allocation + + + align:start position:0% +alternative prime allocation +is and this is just now writing things + + align:start position:0% +is and this is just now writing things + + + align:start position:0% +is and this is just now writing things +out this this is the definition + + align:start position:0% +out this this is the definition + + + align:start position:0% +out this this is the definition +of the indirect utility function star + + align:start position:0% +of the indirect utility function star + + + align:start position:0% +of the indirect utility function star +the one that's going to work + + align:start position:0% +the one that's going to work + + + align:start position:0% +the one that's going to work +and then on the you know as we keep + + align:start position:0% +and then on the you know as we keep + + + align:start position:0% +and then on the you know as we keep +going across these equations we + + align:start position:0% +going across these equations we + + + align:start position:0% +going across these equations we +recognize again + + align:start position:0% +recognize again + + + align:start position:0% +recognize again +that taking the submission over i out in + + align:start position:0% +that taking the submission over i out in + + + align:start position:0% +that taking the submission over i out in +front of all of it that we're just + + align:start position:0% +front of all of it that we're just + + + align:start position:0% +front of all of it that we're just +adding up the indirect utility functions + + align:start position:0% +adding up the indirect utility functions + + + align:start position:0% +adding up the indirect utility functions +but again we're given not worse for some + + align:start position:0% +but again we're given not worse for some + + + align:start position:0% +but again we're given not worse for some +and strictly better for others so when + + align:start position:0% +and strictly better for others so when + + + align:start position:0% +and strictly better for others so when +we add up the indirect utility functions + + align:start position:0% +we add up the indirect utility functions + + + align:start position:0% +we add up the indirect utility functions +under the prime allocation and compare + + align:start position:0% +under the prime allocation and compare + + + align:start position:0% +under the prime allocation and compare +it to the original allocation it must be + + align:start position:0% +it to the original allocation it must be + + + align:start position:0% +it to the original allocation it must be +strict dominance and then if you re + + align:start position:0% +strict dominance and then if you re + + + align:start position:0% +strict dominance and then if you re +reverse the ordering of these v i's + + align:start position:0% +reverse the ordering of these v i's + + + align:start position:0% +reverse the ordering of these v i's +collecting terms and going back toward + + align:start position:0% +collecting terms and going back toward + + + align:start position:0% +collecting terms and going back toward +the left hand side not under prime but + + align:start position:0% +the left hand side not under prime but + + + align:start position:0% +the left hand side not under prime but +under the baseline you would get this + + align:start position:0% +under the baseline you would get this + + + align:start position:0% +under the baseline you would get this +star indirect utility for the + + align:start position:0% +star indirect utility for the + + + align:start position:0% +star indirect utility for the +representative household so in the + + align:start position:0% +representative household so in the + + + align:start position:0% +representative household so in the +bottom line is the v star under prime + + align:start position:0% +bottom line is the v star under prime + + + align:start position:0% +bottom line is the v star under prime +strictly greater than v star under the + + align:start position:0% +strictly greater than v star under the + + + align:start position:0% +strictly greater than v star under the +baseline + + align:start position:0% +baseline + + + align:start position:0% +baseline +and we proved + + align:start position:0% +and we proved + + + align:start position:0% +and we proved +1. the second thing we want to prove is + + align:start position:0% +1. the second thing we want to prove is + + + align:start position:0% +1. the second thing we want to prove is +this that we have an initial allocation + + align:start position:0% +this that we have an initial allocation + + + align:start position:0% +this that we have an initial allocation +and we're looking at a prime allocation + + align:start position:0% +and we're looking at a prime allocation + + + align:start position:0% +and we're looking at a prime allocation +that gives higher indirect utility for + + align:start position:0% +that gives higher indirect utility for + + + align:start position:0% +that gives higher indirect utility for +the aggregated household + + align:start position:0% +the aggregated household + + + align:start position:0% +the aggregated household +and then we want to find a way to assign + + align:start position:0% +and then we want to find a way to assign + + + align:start position:0% +and then we want to find a way to assign +wealth that makes everyone + + align:start position:0% +wealth that makes everyone + + + align:start position:0% +wealth that makes everyone +better off essentially + + align:start position:0% +better off essentially + + + align:start position:0% +better off essentially +so again from 2 + + align:start position:0% +so again from 2 + + + align:start position:0% +so again from 2 +we have this as a given + + align:start position:0% +we have this as a given + + + align:start position:0% +we have this as a given +that v star returns a higher value under + + align:start position:0% +that v star returns a higher value under + + + align:start position:0% +that v star returns a higher value under +the prime relative to the baseline + + align:start position:0% +the prime relative to the baseline + + + align:start position:0% +the prime relative to the baseline +we want to construct an alternative + + align:start position:0% +we want to construct an alternative + + + align:start position:0% +we want to construct an alternative +income distribution seems like it might + + align:start position:0% +income distribution seems like it might + + + align:start position:0% +income distribution seems like it might +be hard to do + + align:start position:0% +be hard to do + + + align:start position:0% +be hard to do +that makes everyone + + align:start position:0% +that makes everyone + + + align:start position:0% +that makes everyone +in fact i'm going to show you strictly + + align:start position:0% +in fact i'm going to show you strictly + + + align:start position:0% +in fact i'm going to show you strictly +better off + + align:start position:0% +better off + + + align:start position:0% +better off +actually strict dominance for everyone + + align:start position:0% +actually strict dominance for everyone + + + align:start position:0% +actually strict dominance for everyone +and + + align:start position:0% +and + + + align:start position:0% +and +it's actually very constructive and + + align:start position:0% +it's actually very constructive and + + + align:start position:0% +it's actually very constructive and +intuitive + + align:start position:0% +intuitive + + + align:start position:0% +intuitive +we're already given here that we have + + align:start position:0% +we're already given here that we have + + + align:start position:0% +we're already given here that we have +this equation 30 + + align:start position:0% +this equation 30 + + + align:start position:0% +this equation 30 +at the aggregates + + align:start position:0% +at the aggregates + + + align:start position:0% +at the aggregates +the left hand side being greater than + + align:start position:0% +the left hand side being greater than + + + align:start position:0% +the left hand side being greater than +the right hand side so take the + + align:start position:0% +the right hand side so take the + + + align:start position:0% +the right hand side so take the +difference + + align:start position:0% +difference + + + align:start position:0% +difference +and call it c it's a positive constant + + align:start position:0% +and call it c it's a positive constant + + + align:start position:0% +and call it c it's a positive constant +now the rest of this thing is just + + align:start position:0% +now the rest of this thing is just + + + align:start position:0% +now the rest of this thing is just +writing out what b star is under prime + + align:start position:0% +writing out what b star is under prime + + + align:start position:0% +writing out what b star is under prime +and v star is under the baseline + + align:start position:0% +and v star is under the baseline + + + align:start position:0% +and v star is under the baseline +and then collecting terms + + align:start position:0% +and then collecting terms + + + align:start position:0% +and then collecting terms +the only reason to do this part + + align:start position:0% +the only reason to do this part + + + align:start position:0% +the only reason to do this part +using the definition of v star is to go + + align:start position:0% +using the definition of v star is to go + + + align:start position:0% +using the definition of v star is to go +searching for the wealth levels that we + + align:start position:0% +searching for the wealth levels that we + + + align:start position:0% +searching for the wealth levels that we +want + + align:start position:0% +want + + + align:start position:0% +want +namely + + align:start position:0% +namely + + + align:start position:0% +namely +let's give each household + + align:start position:0% +let's give each household + + + align:start position:0% +let's give each household +their proportion of c their i households + + align:start position:0% +their proportion of c their i households + + + align:start position:0% +their proportion of c their i households +in the economy + + align:start position:0% +in the economy + + + align:start position:0% +in the economy +give each one c over i + + align:start position:0% +give each one c over i + + + align:start position:0% +give each one c over i +so we start with the baseline + + align:start position:0% +so we start with the baseline + + + align:start position:0% +so we start with the baseline +in terms of the indirect utility + + align:start position:0% +in terms of the indirect utility + + + align:start position:0% +in terms of the indirect utility +function we add onto the baseline this + + align:start position:0% +function we add onto the baseline this + + + align:start position:0% +function we add onto the baseline this +positive constant + + align:start position:0% +positive constant + + + align:start position:0% +positive constant +and + + align:start position:0% +and + + + align:start position:0% +and +we want that to be + + align:start position:0% +we want that to be + + + align:start position:0% +we want that to be +the indirect utility for household i + + align:start position:0% +the indirect utility for household i + + + align:start position:0% +the indirect utility for household i +under the alternative + + align:start position:0% +under the alternative + + + align:start position:0% +under the alternative +so now we can just solve this equation + + align:start position:0% +so now we can just solve this equation + + + align:start position:0% +so now we can just solve this equation +for wi it's almost mechanical + + align:start position:0% +for wi it's almost mechanical + + + align:start position:0% +for wi it's almost mechanical +these are though the required new + + align:start position:0% +these are though the required new + + + align:start position:0% +these are though the required new +distributions of wealth that will work + + align:start position:0% +distributions of wealth that will work + + + align:start position:0% +distributions of wealth that will work +why does it work well working backwards + + align:start position:0% +why does it work well working backwards + + + align:start position:0% +why does it work well working backwards +if you give them this then we have this + + align:start position:0% +if you give them this then we have this + + + align:start position:0% +if you give them this then we have this +equation + + align:start position:0% +equation + + + align:start position:0% +equation +and you can also see + + align:start position:0% +and you can also see + + + align:start position:0% +and you can also see +because we've just added a constant to + + align:start position:0% +because we've just added a constant to + + + align:start position:0% +because we've just added a constant to +the indirect utility function that each + + align:start position:0% +the indirect utility function that each + + + align:start position:0% +the indirect utility function that each +household i under the alternative + + align:start position:0% +household i under the alternative + + + align:start position:0% +household i under the alternative +is having more utility than under the + + align:start position:0% +is having more utility than under the + + + align:start position:0% +is having more utility than under the +baseline that's this v i of p prime w + + align:start position:0% +baseline that's this v i of p prime w + + + align:start position:0% +baseline that's this v i of p prime w +prime + + align:start position:0% +prime + + + align:start position:0% +prime +e i of p and w i + + align:start position:0% +e i of p and w i + + + align:start position:0% +e i of p and w i +plus this + + align:start position:0% +plus this + + + align:start position:0% +plus this +proportional constant + + align:start position:0% +proportional constant + + + align:start position:0% +proportional constant +so it's almost trivial + + align:start position:0% +so it's almost trivial + + + align:start position:0% +so it's almost trivial +now we've gone the other way we proved + + align:start position:0% +now we've gone the other way we proved + + + align:start position:0% +now we've gone the other way we proved +to + + align:start position:0% +to + + + align:start position:0% +to +this thing + + align:start position:0% +this thing + + + align:start position:0% +this thing +so we've + + align:start position:0% +so we've + + + align:start position:0% +so we've +succeeded if they have these gorman + + align:start position:0% +succeeded if they have these gorman + + + align:start position:0% +succeeded if they have these gorman +polar forms + + align:start position:0% +polar forms + + + align:start position:0% +polar forms +in constructing a pseudo + + align:start position:0% +in constructing a pseudo + + + align:start position:0% +in constructing a pseudo +utility function over the indirect + + align:start position:0% +utility function over the indirect + + + align:start position:0% +utility function over the indirect +utility function over the aggregates + + align:start position:0% +utility function over the aggregates + + + align:start position:0% +utility function over the aggregates +questions + + align:start position:0% +questions + + + align:start position:0% +questions +okay so now let's go back + + align:start position:0% +okay so now let's go back + + + align:start position:0% +okay so now let's go back +to the pareto problem in particular + + align:start position:0% +to the pareto problem in particular + + + align:start position:0% +to the pareto problem in particular +we did a version of this slide when we + + align:start position:0% +we did a version of this slide when we + + + align:start position:0% +we did a version of this slide when we +did the second welfare theorem we have + + align:start position:0% +did the second welfare theorem we have + + + align:start position:0% +did the second welfare theorem we have +this underlying economy with + + align:start position:0% +this underlying economy with + + + align:start position:0% +this underlying economy with +consumptions preferences production + + align:start position:0% +consumptions preferences production + + + align:start position:0% +consumptions preferences production +functions aggregate endowments + + align:start position:0% +functions aggregate endowments + + + align:start position:0% +functions aggregate endowments +satisfying + + align:start position:0% +satisfying + + + align:start position:0% +satisfying +non-negative orthot + + align:start position:0% +non-negative orthot + + + align:start position:0% +non-negative orthot +differentiable convex + + align:start position:0% +differentiable convex + + + align:start position:0% +differentiable convex +production sets or concave + + align:start position:0% +production sets or concave + + + align:start position:0% +production sets or concave +transformations + + align:start position:0% +transformations + + + align:start position:0% +transformations +non-negative aggregate resources + + align:start position:0% +non-negative aggregate resources + + + align:start position:0% +non-negative aggregate resources +consumption sets having interior points + + align:start position:0% +consumption sets having interior points + + + align:start position:0% +consumption sets having interior points +utility functions being strictly concave + + align:start position:0% +utility functions being strictly concave + + + align:start position:0% +utility functions being strictly concave +and also an interior point with respect + + align:start position:0% +and also an interior point with respect + + + align:start position:0% +and also an interior point with respect +to aggregate resources + + align:start position:0% +to aggregate resources + + + align:start position:0% +to aggregate resources +i'm rushing a bit but only because + + align:start position:0% +i'm rushing a bit but only because + + + align:start position:0% +i'm rushing a bit but only because +you've seen this slide before + + align:start position:0% +you've seen this slide before + + + align:start position:0% +you've seen this slide before +if all of that is true + + align:start position:0% +if all of that is true + + + align:start position:0% +if all of that is true +then we can solve this pareto problem to + + align:start position:0% +then we can solve this pareto problem to + + + align:start position:0% +then we can solve this pareto problem to +get pareto optimal allocations + + align:start position:0% +get pareto optimal allocations + + + align:start position:0% +get pareto optimal allocations +right + + align:start position:0% +right + + + align:start position:0% +right +this is just maximizing lambda wave sums + + align:start position:0% +this is just maximizing lambda wave sums + + + align:start position:0% +this is just maximizing lambda wave sums +of utilities + + align:start position:0% +of utilities + + + align:start position:0% +of utilities +subject to consumption being feasible + + align:start position:0% +subject to consumption being feasible + + + align:start position:0% +subject to consumption being feasible +production being feasible + + align:start position:0% +production being feasible + + + align:start position:0% +production being feasible +and the resource constraints being + + align:start position:0% +and the resource constraints being + + + align:start position:0% +and the resource constraints being +satisfied demand equals supply + + align:start position:0% +satisfied demand equals supply + + + align:start position:0% +satisfied demand equals supply +i should say allocations are feasible + + align:start position:0% +i should say allocations are feasible + + + align:start position:0% +i should say allocations are feasible +given endowments in the production set + + align:start position:0% +given endowments in the production set + + + align:start position:0% +given endowments in the production set +problem + + align:start position:0% +problem + + + align:start position:0% +problem +what are the lambdas + + align:start position:0% +what are the lambdas + + + align:start position:0% +what are the lambdas +we move the lambdas around we get + + align:start position:0% +we move the lambdas around we get + + + align:start position:0% +we move the lambdas around we get +different pareto optimum that's what we + + align:start position:0% +different pareto optimum that's what we + + + align:start position:0% +different pareto optimum that's what we +did with the second welfare theorem + + align:start position:0% +did with the second welfare theorem + + + align:start position:0% +did with the second welfare theorem +and we've used this with risk sharing in + + align:start position:0% +and we've used this with risk sharing in + + + align:start position:0% +and we've used this with risk sharing in +many + + align:start position:0% +many + + + align:start position:0% +many +applications previously + + align:start position:0% +applications previously + + + align:start position:0% +applications previously +but we had to keep track of the lambdas + + align:start position:0% +but we had to keep track of the lambdas + + + align:start position:0% +but we had to keep track of the lambdas +here's what happens with the + + align:start position:0% +here's what happens with the + + + align:start position:0% +here's what happens with the +representative consumer + + align:start position:0% +representative consumer + + + align:start position:0% +representative consumer +no more lambdas + + align:start position:0% +no more lambdas + + + align:start position:0% +no more lambdas +now we just maximize utility well this x + + align:start position:0% +now we just maximize utility well this x + + + align:start position:0% +now we just maximize utility well this x +is now aggregate consumption + + align:start position:0% +is now aggregate consumption + + + align:start position:0% +is now aggregate consumption +production sets are the same as before + + align:start position:0% +production sets are the same as before + + + align:start position:0% +production sets are the same as before +resource constraints the same + + align:start position:0% +resource constraints the same + + + align:start position:0% +resource constraints the same +in the aggregate + + align:start position:0% +in the aggregate + + + align:start position:0% +in the aggregate +i mean x is aggregate aggregated x is + + align:start position:0% +i mean x is aggregate aggregated x is + + + align:start position:0% +i mean x is aggregate aggregated x is +entering into this pseudo-utility + + align:start position:0% +entering into this pseudo-utility + + + align:start position:0% +entering into this pseudo-utility +function u star and we want to find the + + align:start position:0% +function u star and we want to find the + + + align:start position:0% +function u star and we want to find the +highest u + + align:start position:0% +highest u + + + align:start position:0% +highest u +now remember why because we already + + align:start position:0% +now remember why because we already + + + align:start position:0% +now remember why because we already +proved + + align:start position:0% +proved + + + align:start position:0% +proved +this right + + align:start position:0% +this right + + + align:start position:0% +this right +when it's enough to look at you star in + + align:start position:0% +when it's enough to look at you star in + + + align:start position:0% +when it's enough to look at you star in +the aggregates in the sense of + + align:start position:0% +the aggregates in the sense of + + + align:start position:0% +the aggregates in the sense of +satisfying + + align:start position:0% +satisfying + + + align:start position:0% +satisfying +both these conditions + + align:start position:0% +both these conditions + + + align:start position:0% +both these conditions +and that's what we're doing here we're + + align:start position:0% +and that's what we're doing here we're + + + align:start position:0% +and that's what we're doing here we're +just + + align:start position:0% +just + + + align:start position:0% +just +looking in the space of aggregates under + + align:start position:0% +looking in the space of aggregates under + + + align:start position:0% +looking in the space of aggregates under +this pseudo-utility function u star + + align:start position:0% +this pseudo-utility function u star + + + align:start position:0% +this pseudo-utility function u star +if we're not maximizing it then when we + + align:start position:0% +if we're not maximizing it then when we + + + align:start position:0% +if we're not maximizing it then when we +move in a direction that improves it + + align:start position:0% +move in a direction that improves it + + + align:start position:0% +move in a direction that improves it +we're actually improving the welfare of + + align:start position:0% +we're actually improving the welfare of + + + align:start position:0% +we're actually improving the welfare of +all the individual households well in a + + align:start position:0% +all the individual households well in a + + + align:start position:0% +all the individual households well in a +sense pareto dominate + + align:start position:0% +sense pareto dominate + + + align:start position:0% +sense pareto dominate +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +simple to write but extremely powerful + + align:start position:0% +simple to write but extremely powerful + + + align:start position:0% +simple to write but extremely powerful +and this so this is contemporary macro + + align:start position:0% +and this so this is contemporary macro + + + align:start position:0% +and this so this is contemporary macro +right this is what is usually assumed + + align:start position:0% +right this is what is usually assumed + + + align:start position:0% +right this is what is usually assumed +in macroeconomics or aggregative + + align:start position:0% +in macroeconomics or aggregative + + + align:start position:0% +in macroeconomics or aggregative +economics + + align:start position:0% +economics + + + align:start position:0% +economics +no reference to redistributions or + + align:start position:0% +no reference to redistributions or + + + align:start position:0% +no reference to redistributions or +wealth underlying wealths or whatever so + + align:start position:0% +wealth underlying wealths or whatever so + + + align:start position:0% +wealth underlying wealths or whatever so +mesmerized by the individual household + + align:start position:0% +mesmerized by the individual household + + + align:start position:0% +mesmerized by the individual household +that we forget to spell out the + + align:start position:0% +that we forget to spell out the + + + align:start position:0% +that we forget to spell out the +underpinnings and in particular the + + align:start position:0% +underpinnings and in particular the + + + align:start position:0% +underpinnings and in particular the +assumptions that are needed are they + + align:start position:0% +assumptions that are needed are they + + + align:start position:0% +assumptions that are needed are they +satisfied no + + align:start position:0% +satisfied no + + + align:start position:0% +satisfied no +typically not + + align:start position:0% +typically not + + + align:start position:0% +typically not +that previous lecture on microdata we + + align:start position:0% +that previous lecture on microdata we + + + align:start position:0% +that previous lecture on microdata we +saw that + + align:start position:0% +saw that + + + align:start position:0% +saw that +income expansion paths are a special + + align:start position:0% +income expansion paths are a special + + + align:start position:0% +income expansion paths are a special +case in particular + + align:start position:0% +case in particular + + + align:start position:0% +case in particular +there are + + align:start position:0% +there are + + + align:start position:0% +there are +non-linear expansion paths as we change + + align:start position:0% +non-linear expansion paths as we change + + + align:start position:0% +non-linear expansion paths as we change +income expenditure shares go up for some + + align:start position:0% +income expenditure shares go up for some + + + align:start position:0% +income expenditure shares go up for some +goods we call them luxury goods + + align:start position:0% +goods we call them luxury goods + + + align:start position:0% +goods we call them luxury goods +expenditure shares go down for other + + align:start position:0% +expenditure shares go down for other + + + align:start position:0% +expenditure shares go down for other +goods we call them necessities + + align:start position:0% +goods we call them necessities + + + align:start position:0% +goods we call them necessities +and so on so that's what's in the data + + align:start position:0% +and so on so that's what's in the data + + + align:start position:0% +and so on so that's what's in the data +angle found this very early on + + align:start position:0% +angle found this very early on + + + align:start position:0% +angle found this very early on +and we presented other applications + + align:start position:0% +and we presented other applications + + + align:start position:0% +and we presented other applications +giffin goods being an extreme version + + align:start position:0% +giffin goods being an extreme version + + + align:start position:0% +giffin goods being an extreme version +of the case when the income effects + + align:start position:0% +of the case when the income effects + + + align:start position:0% +of the case when the income effects +through necessities are so strong that + + align:start position:0% +through necessities are so strong that + + + align:start position:0% +through necessities are so strong that +they dominate the price effects well + + align:start position:0% +they dominate the price effects well + + + align:start position:0% +they dominate the price effects well +maybe one can hope that as an + + align:start position:0% +maybe one can hope that as an + + + align:start position:0% +maybe one can hope that as an +approximation even though we would not + + align:start position:0% +approximation even though we would not + + + align:start position:0% +approximation even though we would not +literally satisfy the assumptions that + + align:start position:0% +literally satisfy the assumptions that + + + align:start position:0% +literally satisfy the assumptions that +those income effects come close to + + align:start position:0% +those income effects come close to + + + align:start position:0% +those income effects come close to +canceling out that's kind of the best + + align:start position:0% +canceling out that's kind of the best + + + align:start position:0% +canceling out that's kind of the best +case + + align:start position:0% +case + + + align:start position:0% +case +macro with micro underpinnings is a + + align:start position:0% +macro with micro underpinnings is a + + + align:start position:0% +macro with micro underpinnings is a +reference to the trade lecture i've + + align:start position:0% +reference to the trade lecture i've + + + align:start position:0% +reference to the trade lecture i've +already given you my spiel on that this + + align:start position:0% +already given you my spiel on that this + + + align:start position:0% +already given you my spiel on that this +afternoon + + align:start position:0% +afternoon + + + align:start position:0% +afternoon +about the gains to trade and the fact + + align:start position:0% +about the gains to trade and the fact + + + align:start position:0% +about the gains to trade and the fact +that we have losers although the theorem + + align:start position:0% +that we have losers although the theorem + + + align:start position:0% +that we have losers although the theorem +is telling us that if we have + + align:start position:0% +is telling us that if we have + + + align:start position:0% +is telling us that if we have +representative consumer then we're safe + + align:start position:0% +representative consumer then we're safe + + + align:start position:0% +representative consumer then we're safe +in looking at the max both the positive + + align:start position:0% +in looking at the max both the positive + + + align:start position:0% +in looking at the max both the positive +and the normative but it will require + + align:start position:0% +and the normative but it will require + + + align:start position:0% +and the normative but it will require +redistribution of a particular kind + + align:start position:0% +redistribution of a particular kind + + + align:start position:0% +redistribution of a particular kind +and finally + + align:start position:0% +and finally + + + align:start position:0% +and finally +the economic impact of coba 19 + + align:start position:0% +the economic impact of coba 19 + + + align:start position:0% +the economic impact of coba 19 +i put that in there to remind you of + + align:start position:0% +i put that in there to remind you of + + + align:start position:0% +i put that in there to remind you of +things that we found in that lecture + + align:start position:0% +things that we found in that lecture + + + align:start position:0% +things that we found in that lecture +when i was reviewing what the impact has + + align:start position:0% +when i was reviewing what the impact has + + + align:start position:0% +when i was reviewing what the impact has +been and we had relatively poor + + align:start position:0% +been and we had relatively poor + + + align:start position:0% +been and we had relatively poor +households who were + + align:start position:0% +households who were + + + align:start position:0% +households who were +unemployed cutting back on expenditure + + align:start position:0% +unemployed cutting back on expenditure + + + align:start position:0% +unemployed cutting back on expenditure +or potentially increasing expenditure + + align:start position:0% +or potentially increasing expenditure + + + align:start position:0% +or potentially increasing expenditure +only if they got the government money + + align:start position:0% +only if they got the government money + + + align:start position:0% +only if they got the government money +and also looked at higher income + + align:start position:0% +and also looked at higher income + + + align:start position:0% +and also looked at higher income +households + + align:start position:0% +households + + + align:start position:0% +households +through jp morgan's data set and um + + align:start position:0% +through jp morgan's data set and um + + + align:start position:0% +through jp morgan's data set and um +those guys had different expenditure + + align:start position:0% +those guys had different expenditure + + + align:start position:0% +those guys had different expenditure +patterns + + align:start position:0% +patterns + + + align:start position:0% +patterns +so it does not seem as though these + + align:start position:0% +so it does not seem as though these + + + align:start position:0% +so it does not seem as though these +effects are cancelling out when we + + align:start position:0% +effects are cancelling out when we + + + align:start position:0% +effects are cancelling out when we +actually look at the underlying micro + + align:start position:0% +actually look at the underlying micro + + + align:start position:0% +actually look at the underlying micro +data + + align:start position:0% +data + + + align:start position:0% +data +i mean to cancel out we wouldn't see + + align:start position:0% +i mean to cancel out we wouldn't see + + + align:start position:0% +i mean to cancel out we wouldn't see +anything happening + + align:start position:0% +anything happening + + + align:start position:0% +anything happening +well i should be careful here there is + + align:start position:0% +well i should be careful here there is + + + align:start position:0% +well i should be careful here there is +an aggregate adverse shock obviously + + align:start position:0% +an aggregate adverse shock obviously + + + align:start position:0% +an aggregate adverse shock obviously +we're all suffering from it at least + + align:start position:0% +we're all suffering from it at least + + + align:start position:0% +we're all suffering from it at least +indirectly + + align:start position:0% +indirectly + + + align:start position:0% +indirectly +so so the aggregates are down but then + + align:start position:0% +so so the aggregates are down but then + + + align:start position:0% +so so the aggregates are down but then +the question is do other + + align:start position:0% +the question is do other + + + align:start position:0% +the question is do other +changes balance out at the aggregate and + + align:start position:0% +changes balance out at the aggregate and + + + align:start position:0% +changes balance out at the aggregate and +the data i presented to you suggests + + align:start position:0% +the data i presented to you suggests + + + align:start position:0% +the data i presented to you suggests +that's not true + + align:start position:0% +that's not true + + + align:start position:0% +that's not true +so questions + + align:start position:0% + + + + align:start position:0% + +can i ask a question about this slide 22 + + align:start position:0% +can i ask a question about this slide 22 + + + align:start position:0% +can i ask a question about this slide 22 + + align:start position:0% + + + align:start position:0% +yeah + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +here um + + align:start position:0% +here um + + + align:start position:0% +here um +i'm a little bit confusing that + + align:start position:0% +i'm a little bit confusing that + + + align:start position:0% +i'm a little bit confusing that +do we still assume that the sum of x + + align:start position:0% +do we still assume that the sum of x + + + align:start position:0% +do we still assume that the sum of x +prime world equal to the sum of x here + + align:start position:0% +prime world equal to the sum of x here + + + align:start position:0% +prime world equal to the sum of x here +because in the slides 21 we say that the + + align:start position:0% +because in the slides 21 we say that the + + + align:start position:0% +because in the slides 21 we say that the +descent of the + + align:start position:0% +descent of the + + + align:start position:0% +descent of the +allocation should be the same as + + align:start position:0% +allocation should be the same as + + + align:start position:0% +allocation should be the same as +original + + align:start position:0% +original + + + align:start position:0% +original +and decimal of production uh the + + align:start position:0% +and decimal of production uh the + + + align:start position:0% +and decimal of production uh the +production is the equal to + + align:start position:0% +production is the equal to + + + align:start position:0% +production is the equal to +the original so + + align:start position:0% +the original so + + + align:start position:0% +the original so +when you go + + align:start position:0% +when you go + + + align:start position:0% +when you go +from 21 to 22 do we still assume this + + align:start position:0% +from 21 to 22 do we still assume this + + + align:start position:0% +from 21 to 22 do we still assume this +it's only implicit in the sense that + + align:start position:0% +it's only implicit in the sense that + + + align:start position:0% +it's only implicit in the sense that +that we're looking at individual wells + + align:start position:0% +that we're looking at individual wells + + + align:start position:0% +that we're looking at individual wells +and aggregating it up + + align:start position:0% + + + + align:start position:0% + +so i agree it's probably not obvious but + + align:start position:0% +so i agree it's probably not obvious but + + + align:start position:0% +so i agree it's probably not obvious but +it + + align:start position:0% +it + + + align:start position:0% +it +they're just two representations one in + + align:start position:0% +they're just two representations one in + + + align:start position:0% +they're just two representations one in +this space of indirect utility functions + + align:start position:0% +this space of indirect utility functions + + + align:start position:0% +this space of indirect utility functions +with the parameters p and w and the + + align:start position:0% +with the parameters p and w and the + + + align:start position:0% +with the parameters p and w and the +other in the actual underlying + + align:start position:0% +other in the actual underlying + + + align:start position:0% +other in the actual underlying +allocations + + align:start position:0% + + + + align:start position:0% + +another another way to put that is if we + + align:start position:0% +another another way to put that is if we + + + align:start position:0% +another another way to put that is if we +where is it if we went with can't find + + align:start position:0% +where is it if we went with can't find + + + align:start position:0% +where is it if we went with can't find +it + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +take as an example this utility function + + align:start position:0% + + + + align:start position:0% + +and the associated indirect utilities + + align:start position:0% + + + + align:start position:0% + +these guys + + align:start position:0% +these guys + + + align:start position:0% +these guys +you could go back and forth you could do + + align:start position:0% +you could go back and forth you could do + + + align:start position:0% +you could go back and forth you could do +it one way or do it the other way you're + + align:start position:0% +it one way or do it the other way you're + + + align:start position:0% +it one way or do it the other way you're +gonna get the same answer + + align:start position:0% +gonna get the same answer + + + align:start position:0% +gonna get the same answer +oh + + align:start position:0% +oh + + + align:start position:0% +oh +i get it okay + + align:start position:0% +i get it okay + + + align:start position:0% +i get it okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's gorman aggregation + + align:start position:0% +so that's gorman aggregation + + + align:start position:0% +so that's gorman aggregation +uh with a lot of the pieces coming + + align:start position:0% +uh with a lot of the pieces coming + + + align:start position:0% +uh with a lot of the pieces coming +together next time + + align:start position:0% +together next time + + + align:start position:0% +together next time +we're going to go back in the other + + align:start position:0% +we're going to go back in the other + + + align:start position:0% +we're going to go back in the other +direction we're going to ask + + align:start position:0% +direction we're going to ask + + + align:start position:0% +direction we're going to ask +if we don't do anything special like + + align:start position:0% +if we don't do anything special like + + + align:start position:0% +if we don't do anything special like +this parametrically + + align:start position:0% +this parametrically + + + align:start position:0% +this parametrically +does economic theory put any + + align:start position:0% +does economic theory put any + + + align:start position:0% +does economic theory put any +restrictions on data at all + + align:start position:0% +restrictions on data at all + + + align:start position:0% +restrictions on data at all +and the answer is going to be yes + + align:start position:0% +and the answer is going to be yes + + + align:start position:0% +and the answer is going to be yes +so we'll talk about uh + + align:start position:0% +so we'll talk about uh + + + align:start position:0% +so we'll talk about uh +theory + + align:start position:0% +theory + + + align:start position:0% +theory +that can be rejected + + align:start position:0% +that can be rejected + + + align:start position:0% +that can be rejected +in the data + + align:start position:0% +in the data + + + align:start position:0% +in the data +which is a good thing otherwise there's + + align:start position:0% +which is a good thing otherwise there's + + + align:start position:0% +which is a good thing otherwise there's +no content + + align:start position:0% +no content + + + align:start position:0% +no content +so that's all for today + + align:start position:0% +so that's all for today + + + align:start position:0% +so that's all for today +thank you for coming + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/pCyWp8R4zsA.txt b/pCyWp8R4zsA.txt new file mode 100644 index 0000000000000000000000000000000000000000..e7c2909c193e1d0cb31bcadae214d13760277dc8 --- /dev/null +++ b/pCyWp8R4zsA.txt @@ -0,0 +1,10347 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so yeah I'm going to spend the rest of + + align:start position:0% +so yeah I'm going to spend the rest of + + + align:start position:0% +so yeah I'm going to spend the rest of +the tutorial talking about Amazon + + align:start position:0% +the tutorial talking about Amazon + + + align:start position:0% +the tutorial talking about Amazon +Mechanical Turk although some of this + + align:start position:0% +Mechanical Turk although some of this + + + align:start position:0% +Mechanical Turk although some of this +stuff just applies to in general sort of + + align:start position:0% +stuff just applies to in general sort of + + + align:start position:0% +stuff just applies to in general sort of +making large-scale experiments on people + + align:start position:0% +making large-scale experiments on people + + + align:start position:0% +making large-scale experiments on people +and crowds and things like that there + + align:start position:0% +and crowds and things like that there + + + align:start position:0% +and crowds and things like that there +are other alternatives I think they're + + align:start position:0% +are other alternatives I think they're + + + align:start position:0% +are other alternatives I think they're +Google has some in-house things there's + + align:start position:0% +Google has some in-house things there's + + + align:start position:0% +Google has some in-house things there's +like crowd flower crowd clicker or + + align:start position:0% +like crowd flower crowd clicker or + + + align:start position:0% +like crowd flower crowd clicker or +things like that but most of the + + align:start position:0% +things like that but most of the + + + align:start position:0% +things like that but most of the +psychologists I know that are doing + + align:start position:0% +psychologists I know that are doing + + + align:start position:0% +psychologists I know that are doing +stuff online and large large scale + + align:start position:0% +stuff online and large large scale + + + align:start position:0% +stuff online and large large scale +things use Amazon Mechanical Turk so + + align:start position:0% +things use Amazon Mechanical Turk so + + + align:start position:0% +things use Amazon Mechanical Turk so +I'll be talking about that this is a + + align:start position:0% +I'll be talking about that this is a + + + align:start position:0% +I'll be talking about that this is a +crowdsourcing platform which is designed + + align:start position:0% +crowdsourcing platform which is designed + + + align:start position:0% +crowdsourcing platform which is designed +to do all sorts of small tasks not + + align:start position:0% +to do all sorts of small tasks not + + + align:start position:0% +to do all sorts of small tasks not +necessarily psychophysics it was + + align:start position:0% +necessarily psychophysics it was + + + align:start position:0% +necessarily psychophysics it was +invented in around or built in around + + align:start position:0% +invented in around or built in around + + + align:start position:0% +invented in around or built in around +2005 and the the signature tagline for + + align:start position:0% +2005 and the the signature tagline for + + + align:start position:0% +2005 and the the signature tagline for +it is artificial artificial intelligence + + align:start position:0% +it is artificial artificial intelligence + + + align:start position:0% +it is artificial artificial intelligence +so these are all sorts of tasks that you + + align:start position:0% +so these are all sorts of tasks that you + + + align:start position:0% +so these are all sorts of tasks that you +wish computers could do you don't want + + align:start position:0% +wish computers could do you don't want + + + align:start position:0% +wish computers could do you don't want +to put people through it but computers + + align:start position:0% +to put people through it but computers + + + align:start position:0% +to put people through it but computers +can't do it yet so let's have people do + + align:start position:0% +can't do it yet so let's have people do + + + align:start position:0% +can't do it yet so let's have people do +it for now + + align:start position:0% +it for now + + + align:start position:0% +it for now +Amazon's sort of invented it for + + align:start position:0% +Amazon's sort of invented it for + + + align:start position:0% +Amazon's sort of invented it for +in-house purposes to get rid of + + align:start position:0% +in-house purposes to get rid of + + + align:start position:0% +in-house purposes to get rid of +duplicate pages they really wanted you + + align:start position:0% +duplicate pages they really wanted you + + + align:start position:0% +duplicate pages they really wanted you +know an algorithm to do that for + + align:start position:0% +know an algorithm to do that for + + + align:start position:0% +know an algorithm to do that for +duplicate postings but there really + + align:start position:0% +duplicate postings but there really + + + align:start position:0% +duplicate postings but there really +wasn't one so they just paid some people + + align:start position:0% +wasn't one so they just paid some people + + + align:start position:0% +wasn't one so they just paid some people +very little money to do a lot of these + + align:start position:0% +very little money to do a lot of these + + + align:start position:0% +very little money to do a lot of these +pages and then they figured wait a + + align:start position:0% +pages and then they figured wait a + + + align:start position:0% +pages and then they figured wait a +minute a lot of companies probably want + + align:start position:0% +minute a lot of companies probably want + + + align:start position:0% +minute a lot of companies probably want +this sort of service so they offered it + + align:start position:0% +this sort of service so they offered it + + + align:start position:0% +this sort of service so they offered it +for the general public do people know + + align:start position:0% +for the general public do people know + + + align:start position:0% +for the general public do people know +what the original Turk was the original + + align:start position:0% +what the original Turk was the original + + + align:start position:0% +what the original Turk was the original +Mechanical Turk who doesn't know raise + + align:start position:0% +Mechanical Turk who doesn't know raise + + + align:start position:0% +Mechanical Turk who doesn't know raise +your hands okay so Mechanical Turk the + + align:start position:0% +your hands okay so Mechanical Turk the + + + align:start position:0% +your hands okay so Mechanical Turk the +name comes from this 18th century + + align:start position:0% +name comes from this 18th century + + + align:start position:0% +name comes from this 18th century +mechanical contraption called the Turk + + align:start position:0% +mechanical contraption called the Turk + + + align:start position:0% +mechanical contraption called the Turk +which was a chess playing device that + + align:start position:0% +which was a chess playing device that + + + align:start position:0% +which was a chess playing device that +supposedly ran on clockwork and could + + align:start position:0% +supposedly ran on clockwork and could + + + align:start position:0% +supposedly ran on clockwork and could +beat some of the finest minds in Europe + + align:start position:0% +beat some of the finest minds in Europe + + + align:start position:0% +beat some of the finest minds in Europe +I think it's some point to played like + + align:start position:0% +I think it's some point to played like + + + align:start position:0% +I think it's some point to played like +the Austrian Duchess or whatever it was + + align:start position:0% +the Austrian Duchess or whatever it was + + + align:start position:0% +the Austrian Duchess or whatever it was +the Empress and Napoleon and things like + + align:start position:0% +the Empress and Napoleon and things like + + + align:start position:0% +the Empress and Napoleon and things like +that and it floored people how could + + align:start position:0% +that and it floored people how could + + + align:start position:0% +that and it floored people how could +this work and you know the inventor said + + align:start position:0% +this work and you know the inventor said + + + align:start position:0% +this work and you know the inventor said +well I've invented a thinking device and + + align:start position:0% +well I've invented a thinking device and + + + align:start position:0% +well I've invented a thinking device and +the clockwork just solves it and a lot + + align:start position:0% +the clockwork just solves it and a lot + + + align:start position:0% +the clockwork just solves it and a lot +of people of course figured that it must + + align:start position:0% +of people of course figured that it must + + + align:start position:0% +of people of course figured that it must +be a hoax but they couldn't be sure + + align:start position:0% +be a hoax but they couldn't be sure + + + align:start position:0% +be a hoax but they couldn't be sure +exactly how it + + align:start position:0% +exactly how it + + + align:start position:0% +exactly how it +and it was of course a hoax all these + + align:start position:0% +and it was of course a hoax all these + + + align:start position:0% +and it was of course a hoax all these +gears and boxes and clockwork is just + + align:start position:0% +gears and boxes and clockwork is just + + + align:start position:0% +gears and boxes and clockwork is just +designed to distract you from the fact + + align:start position:0% +designed to distract you from the fact + + + align:start position:0% +designed to distract you from the fact +that you could fit a person inside I + + align:start position:0% +that you could fit a person inside I + + + align:start position:0% +that you could fit a person inside I +mean people have thought of that + + align:start position:0% +mean people have thought of that + + + align:start position:0% +mean people have thought of that +obviously but it was cleverly designed + + align:start position:0% +obviously but it was cleverly designed + + + align:start position:0% +obviously but it was cleverly designed +so that you couldn't quite find it and + + align:start position:0% +so that you couldn't quite find it and + + + align:start position:0% +so that you couldn't quite find it and +nobody knows for sure because the + + align:start position:0% +nobody knows for sure because the + + + align:start position:0% +nobody knows for sure because the +original torque was destroyed before + + align:start position:0% +original torque was destroyed before + + + align:start position:0% +original torque was destroyed before +people put forward the exact hypothesis + + align:start position:0% +people put forward the exact hypothesis + + + align:start position:0% +people put forward the exact hypothesis +but the consensus now is that it must + + align:start position:0% +but the consensus now is that it must + + + align:start position:0% +but the consensus now is that it must +have been just some person inside making + + align:start position:0% +have been just some person inside making + + + align:start position:0% +have been just some person inside making +the moves at some point people have + + align:start position:0% +the moves at some point people have + + + align:start position:0% +the moves at some point people have +suggested that must have been a + + align:start position:0% +suggested that must have been a + + + align:start position:0% +suggested that must have been a +well-trained child or a small person or + + align:start position:0% +well-trained child or a small person or + + + align:start position:0% +well-trained child or a small person or +something like that because the + + align:start position:0% +something like that because the + + + align:start position:0% +something like that because the +compartment must be really small they + + align:start position:0% +compartment must be really small they + + + align:start position:0% +compartment must be really small they +that's not the thinking right now is + + align:start position:0% +that's not the thinking right now is + + + align:start position:0% +that's not the thinking right now is +just some more magic but not magic in + + align:start position:0% +just some more magic but not magic in + + + align:start position:0% +just some more magic but not magic in +the you know Harry Potter sense magic in + + align:start position:0% +the you know Harry Potter sense magic in + + + align:start position:0% +the you know Harry Potter sense magic in +the stage magical sense okay so what + + align:start position:0% +the stage magical sense okay so what + + + align:start position:0% +the stage magical sense okay so what +sorts of tasks do people run on Amazon + + align:start position:0% +sorts of tasks do people run on Amazon + + + align:start position:0% +sorts of tasks do people run on Amazon +Mechanical Turk + + align:start position:0% +Mechanical Turk + + + align:start position:0% +Mechanical Turk +well actually the majority is not + + align:start position:0% +well actually the majority is not + + + align:start position:0% +well actually the majority is not +psychophysics or psychologists there are + + align:start position:0% +psychophysics or psychologists there are + + + align:start position:0% +psychophysics or psychologists there are +a lot of companies using Amazon + + align:start position:0% +a lot of companies using Amazon + + + align:start position:0% +a lot of companies using Amazon +Mechanical Turk to do things like hey + + align:start position:0% +Mechanical Turk to do things like hey + + + align:start position:0% +Mechanical Turk to do things like hey +garner positive reviews for us go to + + align:start position:0% +garner positive reviews for us go to + + + align:start position:0% +garner positive reviews for us go to +this website and write something nice + + align:start position:0% +this website and write something nice + + + align:start position:0% +this website and write something nice +about our product or you know translate + + align:start position:0% +about our product or you know translate + + + align:start position:0% +about our product or you know translate +some text for me instead of hiring some + + align:start position:0% +some text for me instead of hiring some + + + align:start position:0% +some text for me instead of hiring some +professional to do it most people who + + align:start position:0% +professional to do it most people who + + + align:start position:0% +professional to do it most people who +you know there's a lot of people on + + align:start position:0% +you know there's a lot of people on + + + align:start position:0% +you know there's a lot of people on +Amazon Mechanical Turk that could + + align:start position:0% +Amazon Mechanical Turk that could + + + align:start position:0% +Amazon Mechanical Turk that could +probably translate something for you + + align:start position:0% +probably translate something for you + + + align:start position:0% +probably translate something for you +from English to Spanish and back English + + align:start position:0% +from English to Spanish and back English + + + align:start position:0% +from English to Spanish and back English +to Chinese and back things like that and + + align:start position:0% +to Chinese and back things like that and + + + align:start position:0% +to Chinese and back things like that and +they can do it for much less money then + + align:start position:0% +they can do it for much less money then + + + align:start position:0% +they can do it for much less money then +you we need to pay a professional + + align:start position:0% +you we need to pay a professional + + + align:start position:0% +you we need to pay a professional +translator + + align:start position:0% +translator + + + align:start position:0% +translator +another thing that's maybe more up your + + align:start position:0% +another thing that's maybe more up your + + + align:start position:0% +another thing that's maybe more up your +alley is you know you've heard a lot + + align:start position:0% +alley is you know you've heard a lot + + + align:start position:0% +alley is you know you've heard a lot +about supervised training and things + + align:start position:0% +about supervised training and things + + + align:start position:0% +about supervised training and things +like that and big datasets that are used + + align:start position:0% +like that and big datasets that are used + + + align:start position:0% +like that and big datasets that are used +to train things like convolutional + + align:start position:0% +to train things like convolutional + + + align:start position:0% +to train things like convolutional +neural networks the supervised part + + align:start position:0% +neural networks the supervised part + + + align:start position:0% +neural networks the supervised part +usually comes from somewhere somebody + + align:start position:0% +usually comes from somewhere somebody + + + align:start position:0% +usually comes from somewhere somebody +has to tag those images somebody has to + + align:start position:0% +has to tag those images somebody has to + + + align:start position:0% +has to tag those images somebody has to +go over a million images and say dog not + + align:start position:0% +go over a million images and say dog not + + + align:start position:0% +go over a million images and say dog not +dog dog not dog not dog two dogs one dog + + align:start position:0% +dog dog not dog not dog two dogs one dog + + + align:start position:0% +dog dog not dog not dog two dogs one dog +you want somebody to go ahead and do + + align:start position:0% +you want somebody to go ahead and do + + + align:start position:0% +you want somebody to go ahead and do +that and you don't have artificial + + align:start position:0% +that and you don't have artificial + + + align:start position:0% +that and you don't have artificial +intelligence to do it for you + + align:start position:0% +intelligence to do it for you + + + align:start position:0% +intelligence to do it for you +yet I mean cnn's are getting better but + + align:start position:0% +yet I mean cnn's are getting better but + + + align:start position:0% +yet I mean cnn's are getting better but +someone had to take it for them and + + align:start position:0% +someone had to take it for them and + + + align:start position:0% +someone had to take it for them and +that's the sort of thing that you would + + align:start position:0% +that's the sort of thing that you would + + + align:start position:0% +that's the sort of thing that you would +use Amazon Mechanical Turk for look at + + align:start position:0% +use Amazon Mechanical Turk for look at + + + align:start position:0% +use Amazon Mechanical Turk for look at +this image tell me is there a social + + align:start position:0% +this image tell me is there a social + + + align:start position:0% +this image tell me is there a social +interaction or isn't there now do that + + align:start position:0% +interaction or isn't there now do that + + + align:start position:0% +interaction or isn't there now do that +for the next hundred images let's get a + + align:start position:0% +for the next hundred images let's get a + + + align:start position:0% +for the next hundred images let's get a +thousand people to do that all right you + + align:start position:0% +thousand people to do that all right you + + + align:start position:0% +thousand people to do that all right you +get the sense of like why you would want + + align:start position:0% +get the sense of like why you would want + + + align:start position:0% +get the sense of like why you would want +to crowdsource this kind of problem but + + align:start position:0% +to crowdsource this kind of problem but + + + align:start position:0% +to crowdsource this kind of problem but +there's also you know just psychology + + align:start position:0% +there's also you know just psychology + + + align:start position:0% +there's also you know just psychology +psychophysics the sort of thing that you + + align:start position:0% +psychophysics the sort of thing that you + + + align:start position:0% +psychophysics the sort of thing that you +would bring people into the lab to do + + align:start position:0% +would bring people into the lab to do + + + align:start position:0% +would bring people into the lab to do +but you don't want to do for various + + align:start position:0% +but you don't want to do for various + + + align:start position:0% +but you don't want to do for various +reasons so the idea is you could collect + + align:start position:0% +reasons so the idea is you could collect + + + align:start position:0% +reasons so the idea is you could collect +a lot of people respond to the stuff on + + align:start position:0% +a lot of people respond to the stuff on + + + align:start position:0% +a lot of people respond to the stuff on +the screen right + + align:start position:0% +the screen right + + + align:start position:0% +the screen right +the sort of thing that you would bring + + align:start position:0% +the sort of thing that you would bring + + + align:start position:0% +the sort of thing that you would bring +them into the lab and measure something + + align:start position:0% +them into the lab and measure something + + + align:start position:0% +them into the lab and measure something +that they're doing to a screen you could + + align:start position:0% +that they're doing to a screen you could + + + align:start position:0% +that they're doing to a screen you could +just have them doing that to the screen + + align:start position:0% +just have them doing that to the screen + + + align:start position:0% +just have them doing that to the screen +at home or wherever the hell it is that + + align:start position:0% +at home or wherever the hell it is that + + + align:start position:0% +at home or wherever the hell it is that +they're doing this thing so let's see + + align:start position:0% +they're doing this thing so let's see + + + align:start position:0% +they're doing this thing so let's see +you could do things like perception you + + align:start position:0% +you could do things like perception you + + + align:start position:0% +you could do things like perception you +know just look at this is it a dog yes + + align:start position:0% +know just look at this is it a dog yes + + + align:start position:0% +know just look at this is it a dog yes +or no or rather things like the Stroop + + align:start position:0% +or no or rather things like the Stroop + + + align:start position:0% +or no or rather things like the Stroop +task right if nobody had invented the + + align:start position:0% +task right if nobody had invented the + + + align:start position:0% +task right if nobody had invented the +Stroop task you could do that on Amazon + + align:start position:0% +Stroop task you could do that on Amazon + + + align:start position:0% +Stroop task you could do that on Amazon +Mechanical Turk and get famous I was + + align:start position:0% +Mechanical Turk and get famous I was + + + align:start position:0% +Mechanical Turk and get famous I was +going to say rich and famous but just + + align:start position:0% +going to say rich and famous but just + + + align:start position:0% +going to say rich and famous but just +famous you could do various attention + + align:start position:0% +famous you could do various attention + + + align:start position:0% +famous you could do various attention +tasks you can do things like learning + + align:start position:0% +tasks you can do things like learning + + + align:start position:0% +tasks you can do things like learning +and categorization and bias learning + + align:start position:0% +and categorization and bias learning + + + align:start position:0% +and categorization and bias learning +things like um you know here's a to foe + + align:start position:0% +things like um you know here's a to foe + + + align:start position:0% +things like um you know here's a to foe +here's a tooth but here's the tufa is + + align:start position:0% +here's a tooth but here's the tufa is + + + align:start position:0% +here's a tooth but here's the tufa is +this a to foe right I mean it's very + + align:start position:0% +this a to foe right I mean it's very + + + align:start position:0% +this a to foe right I mean it's very +easy to do that on a screen you could do + + align:start position:0% +easy to do that on a screen you could do + + + align:start position:0% +easy to do that on a screen you could do +that on Amazon Mechanical Turk you could + + align:start position:0% +that on Amazon Mechanical Turk you could + + + align:start position:0% +that on Amazon Mechanical Turk you could +do things like implicit bias a lot of + + align:start position:0% +do things like implicit bias a lot of + + + align:start position:0% +do things like implicit bias a lot of +social psychologists are interested in + + align:start position:0% +social psychologists are interested in + + + align:start position:0% +social psychologists are interested in +that sort of thing let's see what else + + align:start position:0% +that sort of thing let's see what else + + + align:start position:0% +that sort of thing let's see what else +you could do things like morality the + + align:start position:0% +you could do things like morality the + + + align:start position:0% +you could do things like morality the +trollee problem you can do things like + + align:start position:0% +trollee problem you can do things like + + + align:start position:0% +trollee problem you can do things like +decision making any cano makes and + + align:start position:0% +decision making any cano makes and + + + align:start position:0% +decision making any cano makes and +prisoner dilemmas and making predictions + + align:start position:0% +prisoner dilemmas and making predictions + + + align:start position:0% +prisoner dilemmas and making predictions +and tell us which one of these two + + align:start position:0% +and tell us which one of these two + + + align:start position:0% +and tell us which one of these two +movies based on the trailers do you + + align:start position:0% +movies based on the trailers do you + + + align:start position:0% +movies based on the trailers do you +think will win the Best Actor Award or + + align:start position:0% +think will win the Best Actor Award or + + + align:start position:0% +think will win the Best Actor Award or +things like that okay how would you + + align:start position:0% +things like that okay how would you + + + align:start position:0% +things like that okay how would you +actually run something on Amazon + + align:start position:0% +actually run something on Amazon + + + align:start position:0% +actually run something on Amazon +Mechanical Turk the first thing you + + align:start position:0% +Mechanical Turk the first thing you + + + align:start position:0% +Mechanical Turk the first thing you +would do is register as a requester you + + align:start position:0% +would do is register as a requester you + + + align:start position:0% +would do is register as a requester you +would go to requester or adult Amazon + + align:start position:0% +would go to requester or adult Amazon + + + align:start position:0% +would go to requester or adult Amazon +dog I'll send you the slides you can + + align:start position:0% +dog I'll send you the slides you can + + + align:start position:0% +dog I'll send you the slides you can +just click on that link and it will take + + align:start position:0% +just click on that link and it will take + + + align:start position:0% +just click on that link and it will take +you to the page to register as a + + align:start position:0% +you to the page to register as a + + + align:start position:0% +you to the page to register as a +requester you would then you do one of + + align:start position:0% +requester you would then you do one of + + + align:start position:0% +requester you would then you do one of +two things + + align:start position:0% +two things + + + align:start position:0% +two things +you could either do the vanilla version + + align:start position:0% +you could either do the vanilla version + + + align:start position:0% +you could either do the vanilla version +which is to just use the Amazon template + + align:start position:0% +which is to just use the Amazon template + + + align:start position:0% +which is to just use the Amazon template +Amazon has made it very simple for you + + align:start position:0% +Amazon has made it very simple for you + + + align:start position:0% +Amazon has made it very simple for you +as a requester to bring up a new + + align:start position:0% +as a requester to bring up a new + + + align:start position:0% +as a requester to bring up a new +experiment and just say I want to ask a + + align:start position:0% +experiment and just say I want to ask a + + + align:start position:0% +experiment and just say I want to ask a +simple set of questions now go and + + align:start position:0% +simple set of questions now go and + + + align:start position:0% +simple set of questions now go and +there's some parameters that you need to + + align:start position:0% +there's some parameters that you need to + + + align:start position:0% +there's some parameters that you need to +set and I'll show you those in a second + + align:start position:0% +set and I'll show you those in a second + + + align:start position:0% +set and I'll show you those in a second +what they do and if you're only + + align:start position:0% +what they do and if you're only + + + align:start position:0% +what they do and if you're only +interested in very simple things like + + align:start position:0% +interested in very simple things like + + + align:start position:0% +interested in very simple things like +fill out this box or click on one of + + align:start position:0% +fill out this box or click on one of + + + align:start position:0% +fill out this box or click on one of +these two images or something like that + + align:start position:0% +these two images or something like that + + + align:start position:0% +these two images or something like that +that's perfect then it's fine and Amazon + + align:start position:0% +that's perfect then it's fine and Amazon + + + align:start position:0% +that's perfect then it's fine and Amazon +takes care of a lot of things for you + + align:start position:0% +takes care of a lot of things for you + + + align:start position:0% +takes care of a lot of things for you +like saving the data you don't have to + + align:start position:0% +like saving the data you don't have to + + + align:start position:0% +like saving the data you don't have to +you know mess around with like SQL + + align:start position:0% +you know mess around with like SQL + + + align:start position:0% +you know mess around with like SQL +databases and things like that on your + + align:start position:0% +databases and things like that on your + + + align:start position:0% +databases and things like that on your +own the other thing that you could do is + + align:start position:0% +own the other thing that you could do is + + + align:start position:0% +own the other thing that you could do is +to point people to an external website + + align:start position:0% +to point people to an external website + + + align:start position:0% +to point people to an external website +then you would have to host it somehow + + align:start position:0% +then you would have to host it somehow + + + align:start position:0% +then you would have to host it somehow +right the advantage there is that you + + align:start position:0% +right the advantage there is that you + + + align:start position:0% +right the advantage there is that you +then you could do any sort of fanciness + + align:start position:0% +then you could do any sort of fanciness + + + align:start position:0% +then you could do any sort of fanciness +that you want you could show them custom + + align:start position:0% +that you want you could show them custom + + + align:start position:0% +that you want you could show them custom +animations have them play a game record + + align:start position:0% +animations have them play a game record + + + align:start position:0% +animations have them play a game record +how they're playing that game send them + + align:start position:0% +how they're playing that game send them + + + align:start position:0% +how they're playing that game send them +new things based on the how they're + + align:start position:0% +new things based on the how they're + + + align:start position:0% +new things based on the how they're +playing at that game or you can do + + align:start position:0% +playing at that game or you can do + + + align:start position:0% +playing at that game or you can do +things like you know you wait until you + + align:start position:0% +things like you know you wait until you + + + align:start position:0% +things like you know you wait until you +record two people you recruit to two + + align:start position:0% +record two people you recruit to two + + + align:start position:0% +record two people you recruit to two +people if you just recruit one person is + + align:start position:0% +people if you just recruit one person is + + + align:start position:0% +people if you just recruit one person is +just as waiting waiting waiting + + align:start position:0% +just as waiting waiting waiting + + + align:start position:0% +just as waiting waiting waiting +now you + + align:start position:0% +now you + + + align:start position:0% +now you +wait for the next person I have to + + align:start position:0% +wait for the next person I have to + + + align:start position:0% +wait for the next person I have to +pitted against one another in some sort + + align:start position:0% +pitted against one another in some sort + + + align:start position:0% +pitted against one another in some sort +of game right this has become more + + align:start position:0% +of game right this has become more + + + align:start position:0% +of game right this has become more +popular in economics that's not the sort + + align:start position:0% +popular in economics that's not the sort + + + align:start position:0% +popular in economics that's not the sort +of thing you could do with the Amazon + + align:start position:0% +of thing you could do with the Amazon + + + align:start position:0% +of thing you could do with the Amazon +template but if you're good at coding or + + align:start position:0% +template but if you're good at coding or + + + align:start position:0% +template but if you're good at coding or +you can hire someone that's reasonably + + align:start position:0% +you can hire someone that's reasonably + + + align:start position:0% +you can hire someone that's reasonably +coding you can do that by pointing them + + align:start position:0% +coding you can do that by pointing them + + + align:start position:0% +coding you can do that by pointing them +to an external website and we can show + + align:start position:0% +to an external website and we can show + + + align:start position:0% +to an external website and we can show +some examples of that then once you you + + align:start position:0% +some examples of that then once you you + + + align:start position:0% +some examples of that then once you you +know you decide you were you I'd + + align:start position:0% +know you decide you were you I'd + + + align:start position:0% +know you decide you were you I'd +reserves the requester you decide which + + align:start position:0% +reserves the requester you decide which + + + align:start position:0% +reserves the requester you decide which +one of these things you want you build + + align:start position:0% +one of these things you want you build + + + align:start position:0% +one of these things you want you build +your website either you build the + + align:start position:0% +your website either you build the + + + align:start position:0% +your website either you build the +external website or you just use the + + align:start position:0% +external website or you just use the + + + align:start position:0% +external website or you just use the +Amazon template and then you test it on + + align:start position:0% +Amazon template and then you test it on + + + align:start position:0% +Amazon template and then you test it on +the sandbox don't run your experiments + + align:start position:0% +the sandbox don't run your experiments + + + align:start position:0% +the sandbox don't run your experiments +live immediately and I'll be giving sort + + align:start position:0% +live immediately and I'll be giving sort + + + align:start position:0% +live immediately and I'll be giving sort +of tips throughout the thing this might + + align:start position:0% +of tips throughout the thing this might + + + align:start position:0% +of tips throughout the thing this might +be redundant for some of you but not + + align:start position:0% +be redundant for some of you but not + + + align:start position:0% +be redundant for some of you but not +redundant for others so there's a + + align:start position:0% +redundant for others so there's a + + + align:start position:0% +redundant for others so there's a +sandbox where you can just run it and + + align:start position:0% +sandbox where you can just run it and + + + align:start position:0% +sandbox where you can just run it and +get sort of false responses that don't + + align:start position:0% +get sort of false responses that don't + + + align:start position:0% +get sort of false responses that don't +count exactly where people can sort of + + align:start position:0% +count exactly where people can sort of + + + align:start position:0% +count exactly where people can sort of +fill it in you might want to use that + + align:start position:0% +fill it in you might want to use that + + + align:start position:0% +fill it in you might want to use that +before you go alive with a thousand + + align:start position:0% +before you go alive with a thousand + + + align:start position:0% +before you go alive with a thousand +people and say oh god I miss coded that + + align:start position:0% +people and say oh god I miss coded that + + + align:start position:0% +people and say oh god I miss coded that +variable and nothing is working so test + + align:start position:0% +variable and nothing is working so test + + + align:start position:0% +variable and nothing is working so test +it ahead of time and then once you're + + align:start position:0% +it ahead of time and then once you're + + + align:start position:0% +it ahead of time and then once you're +finally finally done you would submit it + + align:start position:0% +finally finally done you would submit it + + + align:start position:0% +finally finally done you would submit it +you would just click you know submit + + align:start position:0% +you would just click you know submit + + + align:start position:0% +you would just click you know submit +this thing you would pay the money to + + align:start position:0% +this thing you would pay the money to + + + align:start position:0% +this thing you would pay the money to +Amazon and you also want to announce it + + align:start position:0% +Amazon and you also want to announce it + + + align:start position:0% +Amazon and you also want to announce it +on several Mechanical Turk forums which + + align:start position:0% +on several Mechanical Turk forums which + + + align:start position:0% +on several Mechanical Turk forums which +I'll get to in the end these are very + + align:start position:0% +I'll get to in the end these are very + + + align:start position:0% +I'll get to in the end these are very +hopeful people they're very nice to you + + align:start position:0% +hopeful people they're very nice to you + + + align:start position:0% +hopeful people they're very nice to you +if you're nice to them and it gets you a + + align:start position:0% +if you're nice to them and it gets you a + + + align:start position:0% +if you're nice to them and it gets you a +lot more results very fast okay let's + + align:start position:0% +lot more results very fast okay let's + + + align:start position:0% +lot more results very fast okay let's +see why don't I show you an example you + + align:start position:0% +see why don't I show you an example you + + + align:start position:0% +see why don't I show you an example you +guys I don't know let me show you an + + align:start position:0% +guys I don't know let me show you an + + + align:start position:0% +guys I don't know let me show you an +example of what a request our page looks + + align:start position:0% +example of what a request our page looks + + + align:start position:0% +example of what a request our page looks +like just to get a sense of it for those + + align:start position:0% +like just to get a sense of it for those + + + align:start position:0% +like just to get a sense of it for those +of you have not seen the sort of thing + + align:start position:0% +of you have not seen the sort of thing + + + align:start position:0% +of you have not seen the sort of thing +before you can see our experiment is + + align:start position:0% +before you can see our experiment is + + + align:start position:0% +before you can see our experiment is +almost finished I asked for a hundred + + align:start position:0% +almost finished I asked for a hundred + + + align:start position:0% +almost finished I asked for a hundred +people on that okay so let's go to + + align:start position:0% +people on that okay so let's go to + + + align:start position:0% +people on that okay so let's go to +something like create right so this is + + align:start position:0% +something like create right so this is + + + align:start position:0% +something like create right so this is +that what the requestor page looks like + + align:start position:0% +that what the requestor page looks like + + + align:start position:0% +that what the requestor page looks like +here's all sorts of projects that I run + + align:start position:0% +here's all sorts of projects that I run + + + align:start position:0% +here's all sorts of projects that I run +on Amazon Mechanical Turk and you would + + align:start position:0% +on Amazon Mechanical Turk and you would + + + align:start position:0% +on Amazon Mechanical Turk and you would +do something like new or you would copy + + align:start position:0% +do something like new or you would copy + + + align:start position:0% +do something like new or you would copy +something from something old that you + + align:start position:0% +something from something old that you + + + align:start position:0% +something from something old that you +already did let's just edit that and + + align:start position:0% +already did let's just edit that and + + + align:start position:0% +already did let's just edit that and +show you some examples of what you can + + align:start position:0% +show you some examples of what you can + + + align:start position:0% +show you some examples of what you can +do you give a name you know a title for + + align:start position:0% +do you give a name you know a title for + + + align:start position:0% +do you give a name you know a title for +your own internal title like a I + + align:start position:0% +your own internal title like a I + + + align:start position:0% +your own internal title like a I +estimate you then give a title that + + align:start position:0% +estimate you then give a title that + + + align:start position:0% +estimate you then give a title that +Amazon Mechanical Turk or see something + + align:start position:0% +Amazon Mechanical Turk or see something + + + align:start position:0% +Amazon Mechanical Turk or see something +like artificial intelligence estimate + + align:start position:0% +like artificial intelligence estimate + + + align:start position:0% +like artificial intelligence estimate +short psychology study there you + + align:start position:0% +short psychology study there you + + + align:start position:0% +short psychology study there you +probably want to give a Thainess timet + + align:start position:0% +probably want to give a Thainess timet + + + align:start position:0% +probably want to give a Thainess timet +Turkish would prefer it if you give them + + align:start position:0% +Turkish would prefer it if you give them + + + align:start position:0% +Turkish would prefer it if you give them +a time estimate okay they care about + + align:start position:0% +a time estimate okay they care about + + + align:start position:0% +a time estimate okay they care about +their time they care about their money + + align:start position:0% +their time they care about their money + + + align:start position:0% +their time they care about their money +they do like doing psychology they don't + + align:start position:0% +they do like doing psychology they don't + + + align:start position:0% +they do like doing psychology they don't +like filling in endless bubbles you know + + align:start position:0% +like filling in endless bubbles you know + + + align:start position:0% +like filling in endless bubbles you know +the standard psychology things + + align:start position:0% +the standard psychology things + + + align:start position:0% +the standard psychology things +you rate a hundred things of like I feel + + align:start position:0% +you rate a hundred things of like I feel + + + align:start position:0% +you rate a hundred things of like I feel +this way or that way don't do that but + + align:start position:0% +this way or that way don't do that but + + + align:start position:0% +this way or that way don't do that but +the sort of fun psychology they're + + align:start position:0% +the sort of fun psychology they're + + + align:start position:0% +the sort of fun psychology they're +actually on board with it's much more + + align:start position:0% +actually on board with it's much more + + + align:start position:0% +actually on board with it's much more +fun than writing show reviews you might + + align:start position:0% +fun than writing show reviews you might + + + align:start position:0% +fun than writing show reviews you might +want to give it a nice title that will + + align:start position:0% +want to give it a nice title that will + + + align:start position:0% +want to give it a nice title that will +entice them an honest description like + + align:start position:0% +entice them an honest description like + + + align:start position:0% +entice them an honest description like +you know you'll answer a few simple + + align:start position:0% +you know you'll answer a few simple + + + align:start position:0% +you know you'll answer a few simple +questions or you'll watch a movie and + + align:start position:0% +questions or you'll watch a movie and + + + align:start position:0% +questions or you'll watch a movie and +then answer to questions or things like + + align:start position:0% +then answer to questions or things like + + + align:start position:0% +then answer to questions or things like +that key words like easy fun something + + align:start position:0% +that key words like easy fun something + + + align:start position:0% +that key words like easy fun something +descriptive about the test like AI short + + align:start position:0% +descriptive about the test like AI short + + + align:start position:0% +descriptive about the test like AI short +again this is sort of luring and it's + + align:start position:0% +again this is sort of luring and it's + + + align:start position:0% +again this is sort of luring and it's +good to do that if you're honest about + + align:start position:0% +good to do that if you're honest about + + + align:start position:0% +good to do that if you're honest about +it okay don't do some people do things + + align:start position:0% +it okay don't do some people do things + + + align:start position:0% +it okay don't do some people do things +like easy fun a hundred pages of filling + + align:start position:0% +like easy fun a hundred pages of filling + + + align:start position:0% +like easy fun a hundred pages of filling +in bubbles and things like that don't do + + align:start position:0% +in bubbles and things like that don't do + + + align:start position:0% +in bubbles and things like that don't do +that they publish it in the forums like + + align:start position:0% +that they publish it in the forums like + + + align:start position:0% +that they publish it in the forums like +this is a lie + + align:start position:0% +this is a lie + + + align:start position:0% +this is a lie +don't do that this is where you say how + + align:start position:0% +don't do that this is where you say how + + + align:start position:0% +don't do that this is where you say how +much you want to pay per assignment and + + align:start position:0% +much you want to pay per assignment and + + + align:start position:0% +much you want to pay per assignment and +we'll get to how much you should pay + + align:start position:0% +we'll get to how much you should pay + + + align:start position:0% +we'll get to how much you should pay +pear assignment you'll notice it's very + + align:start position:0% +pear assignment you'll notice it's very + + + align:start position:0% +pear assignment you'll notice it's very +little you're paying these people very + + align:start position:0% +little you're paying these people very + + + align:start position:0% +little you're paying these people very +little how much assignments you want per + + align:start position:0% +little how much assignments you want per + + + align:start position:0% +little how much assignments you want per +hit hit is just the name for your task + + align:start position:0% +hit hit is just the name for your task + + + align:start position:0% +hit hit is just the name for your task +how much time you are a loading them + + align:start position:0% +how much time you are a loading them + + + align:start position:0% +how much time you are a loading them +pear assignment so that some someone has + + align:start position:0% +pear assignment so that some someone has + + + align:start position:0% +pear assignment so that some someone has +accepted your head now how long do they + + align:start position:0% +accepted your head now how long do they + + + align:start position:0% +accepted your head now how long do they +have to carry it out you might think oh + + align:start position:0% +have to carry it out you might think oh + + + align:start position:0% +have to carry it out you might think oh +my tusks only takes two to three minutes + + align:start position:0% +my tusks only takes two to three minutes + + + align:start position:0% +my tusks only takes two to three minutes +so only give people two to three minutes + + align:start position:0% +so only give people two to three minutes + + + align:start position:0% +so only give people two to three minutes +I don't want them like you know taking + + align:start position:0% +I don't want them like you know taking + + + align:start position:0% +I don't want them like you know taking +the head and then going and drinking + + align:start position:0% +the head and then going and drinking + + + align:start position:0% +the head and then going and drinking +some coffee and then coming back to it + + align:start position:0% +some coffee and then coming back to it + + + align:start position:0% +some coffee and then coming back to it +or something like that + + align:start position:0% +or something like that + + + align:start position:0% +or something like that +consider still giving them a whole bunch + + align:start position:0% +consider still giving them a whole bunch + + + align:start position:0% +consider still giving them a whole bunch +of time because a lot of the time you'll + + align:start position:0% +of time because a lot of the time you'll + + + align:start position:0% +of time because a lot of the time you'll +find that people if they see that + + align:start position:0% +find that people if they see that + + + align:start position:0% +find that people if they see that +there's only a five-minute mark on edge + + align:start position:0% +there's only a five-minute mark on edge + + + align:start position:0% +there's only a five-minute mark on edge +and if they don't complete it in five + + align:start position:0% +and if they don't complete it in five + + + align:start position:0% +and if they don't complete it in five +minutes they're sort of concern like + + align:start position:0% +minutes they're sort of concern like + + + align:start position:0% +minutes they're sort of concern like +what is this thing and if I won't get + + align:start position:0% +what is this thing and if I won't get + + + align:start position:0% +what is this thing and if I won't get +done through it in five minutes you know + + align:start position:0% +done through it in five minutes you know + + + align:start position:0% +done through it in five minutes you know +get disqualified or something like that + + align:start position:0% +get disqualified or something like that + + + align:start position:0% +get disqualified or something like that +give them some time even more than the + + align:start position:0% +give them some time even more than the + + + align:start position:0% +give them some time even more than the +ample time to finish this thing you can + + align:start position:0% +ample time to finish this thing you can + + + align:start position:0% +ample time to finish this thing you can +yourself keep around some timer within + + align:start position:0% +yourself keep around some timer within + + + align:start position:0% +yourself keep around some timer within +the external website or something like + + align:start position:0% +the external website or something like + + + align:start position:0% +the external website or something like +that are they actually proactively + + align:start position:0% +that are they actually proactively + + + align:start position:0% +that are they actually proactively +participating right now how long will + + align:start position:0% +participating right now how long will + + + align:start position:0% +participating right now how long will +this hit stay up for and although + + align:start position:0% +this hit stay up for and although + + + align:start position:0% +this hit stay up for and although +approve and things like that I'll talk a + + align:start position:0% +approve and things like that I'll talk a + + + align:start position:0% +approve and things like that I'll talk a +little bit about rewards and incentives + + align:start position:0% +little bit about rewards and incentives + + + align:start position:0% +little bit about rewards and incentives +and things like that obviously they care + + align:start position:0% +and things like that obviously they care + + + align:start position:0% +and things like that obviously they care +a lot about things like money they care + + align:start position:0% +a lot about things like money they care + + + align:start position:0% +a lot about things like money they care +a lot about things like how much you're + + align:start position:0% +a lot about things like how much you're + + + align:start position:0% +a lot about things like how much you're +going to pay them they care about doing + + align:start position:0% +going to pay them they care about doing + + + align:start position:0% +going to pay them they care about doing +it quickly so that they can move on and + + align:start position:0% +it quickly so that they can move on and + + + align:start position:0% +it quickly so that they can move on and +get more money they care about it being + + align:start position:0% +get more money they care about it being + + + align:start position:0% +get more money they care about it being +somewhat fun but that's not such a big + + align:start position:0% +somewhat fun but that's not such a big + + + align:start position:0% +somewhat fun but that's not such a big +deal for them and they care about + + align:start position:0% +deal for them and they care about + + + align:start position:0% +deal for them and they care about +getting it approved quickly okay so you + + align:start position:0% +getting it approved quickly okay so you + + + align:start position:0% +getting it approved quickly okay so you +as a requester you will get reviewed on + + align:start position:0% +as a requester you will get reviewed on + + + align:start position:0% +as a requester you will get reviewed on +various forums and things like that if + + align:start position:0% +various forums and things like that if + + + align:start position:0% +various forums and things like that if +you get bad reviews people don't want to + + align:start position:0% +you get bad reviews people don't want to + + + align:start position:0% +you get bad reviews people don't want to +do your things one of the things that + + align:start position:0% +do your things one of the things that + + + align:start position:0% +do your things one of the things that +people care a lot about is something + + align:start position:0% +people care a lot about is something + + + align:start position:0% +people care a lot about is something +like getting approved quickly and + + align:start position:0% +like getting approved quickly and + + + align:start position:0% +like getting approved quickly and +quickly can be in a day or two so + + align:start position:0% +quickly can be in a day or two so + + + align:start position:0% +quickly can be in a day or two so +knowing that they don't want to have to + + align:start position:0% +knowing that they don't want to have to + + + align:start position:0% +knowing that they don't want to have to +wait two weeks + + align:start position:0% +wait two weeks + + + align:start position:0% +wait two weeks +that 50 Cent's that you were supposed to + + align:start position:0% +that 50 Cent's that you were supposed to + + + align:start position:0% +that 50 Cent's that you were supposed to +give them okay okay you can do that if + + align:start position:0% +give them okay okay you can do that if + + + align:start position:0% +give them okay okay you can do that if +you want to you have the power as the + + align:start position:0% +you want to you have the power as the + + + align:start position:0% +you want to you have the power as the +requester but if you want to incentivize + + align:start position:0% +requester but if you want to incentivize + + + align:start position:0% +requester but if you want to incentivize +people try to make sure that you approve + + align:start position:0% +people try to make sure that you approve + + + align:start position:0% +people try to make sure that you approve +them quickly and let them know that + + align:start position:0% +them quickly and let them know that + + + align:start position:0% +them quickly and let them know that +you're going to approve them quickly + + align:start position:0% +you're going to approve them quickly + + + align:start position:0% +you're going to approve them quickly +okay so that was just a very general so + + align:start position:0% +okay so that was just a very general so + + + align:start position:0% +okay so that was just a very general so +who are the sort of people that are on + + align:start position:0% +who are the sort of people that are on + + + align:start position:0% +who are the sort of people that are on +Amazon Mechanical Turk have people read + + align:start position:0% +Amazon Mechanical Turk have people read + + + align:start position:0% +Amazon Mechanical Turk have people read +these sort of papers and things like + + align:start position:0% +these sort of papers and things like + + + align:start position:0% +these sort of papers and things like +that do you know more or less some of + + align:start position:0% +that do you know more or less some of + + + align:start position:0% +that do you know more or less some of +you do some of you don't + + align:start position:0% +you do some of you don't + + + align:start position:0% +you do some of you don't +okay the use in India make about 80 + + align:start position:0% +okay the use in India make about 80 + + + align:start position:0% +okay the use in India make about 80 +percent by the way this is influx like a + + align:start position:0% +percent by the way this is influx like a + + + align:start position:0% +percent by the way this is influx like a +study came out two years ago about the + + align:start position:0% +study came out two years ago about the + + + align:start position:0% +study came out two years ago about the +sort of thing it's changed since then + + align:start position:0% +sort of thing it's changed since then + + + align:start position:0% +sort of thing it's changed since then +but the study two years ago the US and + + align:start position:0% +but the study two years ago the US and + + + align:start position:0% +but the study two years ago the US and +India make up about 80 percent for the + + align:start position:0% +India make up about 80 percent for the + + + align:start position:0% +India make up about 80 percent for the +u.s. taking up 50 something percent + + align:start position:0% +u.s. taking up 50 something percent + + + align:start position:0% +u.s. taking up 50 something percent +India taking up the rest there's + + align:start position:0% +India taking up the rest there's + + + align:start position:0% +India taking up the rest there's +slightly more females than males on + + align:start position:0% +slightly more females than males on + + + align:start position:0% +slightly more females than males on +Amazon Mechanical Turk and at least the + + align:start position:0% +Amazon Mechanical Turk and at least the + + + align:start position:0% +Amazon Mechanical Turk and at least the +u.s. population is biased towards young + + align:start position:0% +u.s. population is biased towards young + + + align:start position:0% +u.s. population is biased towards young +and educated people educated meaning a + + align:start position:0% +and educated people educated meaning a + + + align:start position:0% +and educated people educated meaning a +bachelor's degree it's certainly more + + align:start position:0% +bachelor's degree it's certainly more + + + align:start position:0% +bachelor's degree it's certainly more +representative of the general population + + align:start position:0% +representative of the general population + + + align:start position:0% +representative of the general population +than just hiring you know college + + align:start position:0% +than just hiring you know college + + + align:start position:0% +than just hiring you know college +students doing their their bachelor's + + align:start position:0% +students doing their their bachelor's + + + align:start position:0% +students doing their their bachelor's +degree but it is still skewed keep that + + align:start position:0% +degree but it is still skewed keep that + + + align:start position:0% +degree but it is still skewed keep that +in mind it's skewed towards basically + + align:start position:0% +in mind it's skewed towards basically + + + align:start position:0% +in mind it's skewed towards basically +the sort of population you would expect + + align:start position:0% +the sort of population you would expect + + + align:start position:0% +the sort of population you would expect +to find on the Internet in the United + + align:start position:0% +to find on the Internet in the United + + + align:start position:0% +to find on the Internet in the United +States + + align:start position:0% +States + + + align:start position:0% +States +okay so somewhat younger people somewhat + + align:start position:0% +okay so somewhat younger people somewhat + + + align:start position:0% +okay so somewhat younger people somewhat +more educated in general you might want + + align:start position:0% +more educated in general you might want + + + align:start position:0% +more educated in general you might want +to look at something like Mason and + + align:start position:0% +to look at something like Mason and + + + align:start position:0% +to look at something like Mason and +Siddharth we're looking at these sort of + + align:start position:0% +Siddharth we're looking at these sort of + + + align:start position:0% +Siddharth we're looking at these sort of +things I can send you the links later I + + align:start position:0% +things I can send you the links later I + + + align:start position:0% +things I can send you the links later I +was talking a little bit about payments + + align:start position:0% +was talking a little bit about payments + + + align:start position:0% +was talking a little bit about payments +that there's been a whole lot of studies + + align:start position:0% +that there's been a whole lot of studies + + + align:start position:0% +that there's been a whole lot of studies +looking at you know querying the Amazon + + align:start position:0% +looking at you know querying the Amazon + + + align:start position:0% +looking at you know querying the Amazon +Mechanical Turk pool who are you what's + + align:start position:0% +Mechanical Turk pool who are you what's + + + align:start position:0% +Mechanical Turk pool who are you what's +your education why are you doing this + + align:start position:0% +your education why are you doing this + + + align:start position:0% +your education why are you doing this +and then they asked why are you doing + + align:start position:0% +and then they asked why are you doing + + + align:start position:0% +and then they asked why are you doing +this in various ways are you doing it + + align:start position:0% +this in various ways are you doing it + + + align:start position:0% +this in various ways are you doing it +for fun are you doing it to kill time + + align:start position:0% +for fun are you doing it to kill time + + + align:start position:0% +for fun are you doing it to kill time +are you doing this a supplementary thing + + align:start position:0% +are you doing this a supplementary thing + + + align:start position:0% +are you doing this a supplementary thing +they're in it for money it's very + + align:start position:0% +they're in it for money it's very + + + align:start position:0% +they're in it for money it's very +obvious that they're in it for money + + align:start position:0% +obvious that they're in it for money + + + align:start position:0% +obvious that they're in it for money +that's okay and keep that in mind when + + align:start position:0% +that's okay and keep that in mind when + + + align:start position:0% +that's okay and keep that in mind when +you give when you post hits you have a + + align:start position:0% +you give when you post hits you have a + + + align:start position:0% +you give when you post hits you have a +lot of power as a requester you have a + + align:start position:0% +lot of power as a requester you have a + + + align:start position:0% +lot of power as a requester you have a +ton of power you have a ton of power to + + align:start position:0% +ton of power you have a ton of power to + + + align:start position:0% +ton of power you have a ton of power to +dictate the terms of what you're going + + align:start position:0% +dictate the terms of what you're going + + + align:start position:0% +dictate the terms of what you're going +to pay them you have a ton of power to + + align:start position:0% +to pay them you have a ton of power to + + + align:start position:0% +to pay them you have a ton of power to +reject their work once they basically do + + align:start position:0% +reject their work once they basically do + + + align:start position:0% +reject their work once they basically do +the hit for you you can then go back and + + align:start position:0% +the hit for you you can then go back and + + + align:start position:0% +the hit for you you can then go back and +say you failed this Quach question or + + align:start position:0% +say you failed this Quach question or + + + align:start position:0% +say you failed this Quach question or +you didn't quite get what we wanted or + + align:start position:0% +you didn't quite get what we wanted or + + + align:start position:0% +you didn't quite get what we wanted or +you actually did the study two months + + align:start position:0% +you actually did the study two months + + + align:start position:0% +you actually did the study two months +ago but I didn't implement checks for + + align:start position:0% +ago but I didn't implement checks for + + + align:start position:0% +ago but I didn't implement checks for +that I just asked you did you take the + + align:start position:0% +that I just asked you did you take the + + + align:start position:0% +that I just asked you did you take the +study before and they didn't remember + + align:start position:0% +study before and they didn't remember + + + align:start position:0% +study before and they didn't remember +something like that and then you reject + + align:start position:0% +something like that and then you reject + + + align:start position:0% +something like that and then you reject +their work and if you reject it too many + + align:start position:0% +their work and if you reject it too many + + + align:start position:0% +their work and if you reject it too many +times and they get bad first of all if + + align:start position:0% +times and they get bad first of all if + + + align:start position:0% +times and they get bad first of all if +you're rejected they don't get paid if + + align:start position:0% +you're rejected they don't get paid if + + + align:start position:0% +you're rejected they don't get paid if +you reject it too many times they get + + align:start position:0% +you reject it too many times they get + + + align:start position:0% +you reject it too many times they get +these are people that are doing it + + align:start position:0% +these are people that are doing it + + + align:start position:0% +these are people that are doing it +either as supplementary or as their main + + align:start position:0% +either as supplementary or as their main + + + align:start position:0% +either as supplementary or as their main +income I I don't know this it may seem + + align:start position:0% +income I I don't know this it may seem + + + align:start position:0% +income I I don't know this it may seem +obvious to some of you if this doesn't + + align:start position:0% +obvious to some of you if this doesn't + + + align:start position:0% +obvious to some of you if this doesn't +seem obvious to at least one of you the + + align:start position:0% +seem obvious to at least one of you the + + + align:start position:0% +seem obvious to at least one of you the +no I'll count it as as worth while to + + align:start position:0% +no I'll count it as as worth while to + + + align:start position:0% +no I'll count it as as worth while to +stress this you don't care about the 20 + + align:start position:0% +stress this you don't care about the 20 + + + align:start position:0% +stress this you don't care about the 20 +cents okay these people do care about + + align:start position:0% +cents okay these people do care about + + + align:start position:0% +cents okay these people do care about +the 20 cents and again it's not because + + align:start position:0% +the 20 cents and again it's not because + + + align:start position:0% +the 20 cents and again it's not because +they're necessarily from poor economical + + align:start position:0% +they're necessarily from poor economical + + + align:start position:0% +they're necessarily from poor economical +backgrounds but they're in it for the + + align:start position:0% +backgrounds but they're in it for the + + + align:start position:0% +backgrounds but they're in it for the +money and that's what they're doing this + + align:start position:0% +money and that's what they're doing this + + + align:start position:0% +money and that's what they're doing this +for try to give them fair pay and we'll + + align:start position:0% +for try to give them fair pay and we'll + + + align:start position:0% +for try to give them fair pay and we'll +stress that again and tell you what I + + align:start position:0% +stress that again and tell you what I + + + align:start position:0% +stress that again and tell you what I +mean by fair pay try not to reject them + + align:start position:0% +mean by fair pay try not to reject them + + + align:start position:0% +mean by fair pay try not to reject them +okay except in extreme situations even + + align:start position:0% +okay except in extreme situations even + + + align:start position:0% +okay except in extreme situations even +if they failed even if they didn't do + + align:start position:0% +if they failed even if they didn't do + + + align:start position:0% +if they failed even if they didn't do +your catch question even if you think + + align:start position:0% +your catch question even if you think + + + align:start position:0% +your catch question even if you think +that they just zoom through this or + + align:start position:0% +that they just zoom through this or + + + align:start position:0% +that they just zoom through this or +something like that that's usually on + + align:start position:0% +something like that that's usually on + + + align:start position:0% +something like that that's usually on +you to catch that okay as a psychology + + align:start position:0% +you to catch that okay as a psychology + + + align:start position:0% +you to catch that okay as a psychology +researcher you're not the company you're + + align:start position:0% +researcher you're not the company you're + + + align:start position:0% +researcher you're not the company you're +a psychology researcher try not to + + align:start position:0% +a psychology researcher try not to + + + align:start position:0% +a psychology researcher try not to +reject people make sure you have some + + align:start position:0% +reject people make sure you have some + + + align:start position:0% +reject people make sure you have some +way set up ahead of time and I'll get to + + align:start position:0% +way set up ahead of time and I'll get to + + + align:start position:0% +way set up ahead of time and I'll get to +that to know who to reject but don't + + align:start position:0% +that to know who to reject but don't + + + align:start position:0% +that to know who to reject but don't +actually reject people accept in really + + align:start position:0% +actually reject people accept in really + + + align:start position:0% +actually reject people accept in really +extreme situations okay + + align:start position:0% +extreme situations okay + + + align:start position:0% +extreme situations okay +something about payments is that Amazon + + align:start position:0% +something about payments is that Amazon + + + align:start position:0% +something about payments is that Amazon +takes up about ten they actually raised + + align:start position:0% +takes up about ten they actually raised + + + align:start position:0% +takes up about ten they actually raised +this to twenty to forty percent of the + + align:start position:0% +this to twenty to forty percent of the + + + align:start position:0% +this to twenty to forty percent of the +payments and this is what I was going to + + align:start position:0% +payments and this is what I was going to + + + align:start position:0% +payments and this is what I was going to +say there have been some attempts within + + align:start position:0% +say there have been some attempts within + + + align:start position:0% +say there have been some attempts within +sort of the psychologist has been doing + + align:start position:0% +sort of the psychologist has been doing + + + align:start position:0% +sort of the psychologist has been doing +Amazon Mechanical Turk studies and this + + align:start position:0% +Amazon Mechanical Turk studies and this + + + align:start position:0% +Amazon Mechanical Turk studies and this +has also been fueled by the community of + + align:start position:0% +has also been fueled by the community of + + + align:start position:0% +has also been fueled by the community of +Amazon Mechanical Turk or Turkish to + + align:start position:0% +Amazon Mechanical Turk or Turkish to + + + align:start position:0% +Amazon Mechanical Turk or Turkish to +establish some sort of guidelines for + + align:start position:0% +establish some sort of guidelines for + + + align:start position:0% +establish some sort of guidelines for +minimum pays so you know if people come + + align:start position:0% +minimum pays so you know if people come + + + align:start position:0% +minimum pays so you know if people come +into the lab there are some guidelines + + align:start position:0% +into the lab there are some guidelines + + + align:start position:0% +into the lab there are some guidelines +on what you're supposed to pay them + + align:start position:0% +on what you're supposed to pay them + + + align:start position:0% +on what you're supposed to pay them +there are no exact guidelines there's no + + align:start position:0% +there are no exact guidelines there's no + + + align:start position:0% +there are no exact guidelines there's no +enforcing guidelines at least not maybe + + align:start position:0% +enforcing guidelines at least not maybe + + + align:start position:0% +enforcing guidelines at least not maybe +there are within particular universities + + align:start position:0% +there are within particular universities + + + align:start position:0% +there are within particular universities +but there's no cross university one + + align:start position:0% +but there's no cross university one + + + align:start position:0% +but there's no cross university one +guideline to tell you you have to pay + + align:start position:0% +guideline to tell you you have to pay + + + align:start position:0% +guideline to tell you you have to pay +people this much and that might be + + align:start position:0% +people this much and that might be + + + align:start position:0% +people this much and that might be +tempting to say oh I'll just pay people + + align:start position:0% +tempting to say oh I'll just pay people + + + align:start position:0% +tempting to say oh I'll just pay people +you know the minimum I can get away with + + align:start position:0% +you know the minimum I can get away with + + + align:start position:0% +you know the minimum I can get away with +right I mean if I can pay people five + + align:start position:0% +right I mean if I can pay people five + + + align:start position:0% +right I mean if I can pay people five +cents to do a ten minute ask I'll do + + align:start position:0% +cents to do a ten minute ask I'll do + + + align:start position:0% +cents to do a ten minute ask I'll do +that fine I can get the twenty subjects + + align:start position:0% +that fine I can get the twenty subjects + + + align:start position:0% +that fine I can get the twenty subjects +I need it's a free market right well + + align:start position:0% +I need it's a free market right well + + + align:start position:0% +I need it's a free market right well +we're not trying to live here in some + + align:start position:0% +we're not trying to live here in some + + + align:start position:0% +we're not trying to live here in some +sort of I don't know capitalist fantasy + + align:start position:0% +sort of I don't know capitalist fantasy + + + align:start position:0% +sort of I don't know capitalist fantasy +of some sort I'm not going to get into + + align:start position:0% +of some sort I'm not going to get into + + + align:start position:0% +of some sort I'm not going to get into +economics too much because I think you + + align:start position:0% +economics too much because I think you + + + align:start position:0% +economics too much because I think you +guys know that better than I do you + + align:start position:0% +guys know that better than I do you + + + align:start position:0% +guys know that better than I do you +don't need my my lecturing in that sense + + align:start position:0% +don't need my my lecturing in that sense + + + align:start position:0% +don't need my my lecturing in that sense +but a lot of people have looked into the + + align:start position:0% +but a lot of people have looked into the + + + align:start position:0% +but a lot of people have looked into the +ethic of this recommend that you try to + + align:start position:0% +ethic of this recommend that you try to + + + align:start position:0% +ethic of this recommend that you try to +estimate ahead of time through a pilot + + align:start position:0% +estimate ahead of time through a pilot + + + align:start position:0% +estimate ahead of time through a pilot +how long is this test going to take + + align:start position:0% +how long is this test going to take + + + align:start position:0% +how long is this test going to take +based on that pay them such that it + + align:start position:0% +based on that pay them such that it + + + align:start position:0% +based on that pay them such that it +matches + + align:start position:0% +matches + + + align:start position:0% +matches +the mortgage okay minimal wage being + + align:start position:0% +the mortgage okay minimal wage being + + + align:start position:0% +the mortgage okay minimal wage being +somewhat flux like you know I figure if + + align:start position:0% +somewhat flux like you know I figure if + + + align:start position:0% +somewhat flux like you know I figure if +it's like ten dollars an hour or + + align:start position:0% +it's like ten dollars an hour or + + + align:start position:0% +it's like ten dollars an hour or +something like that maybe it's probably + + align:start position:0% +something like that maybe it's probably + + + align:start position:0% +something like that maybe it's probably +less than that but something like that + + align:start position:0% +less than that but something like that + + + align:start position:0% +less than that but something like that +okay so there's no I'm not going to tell + + align:start position:0% +okay so there's no I'm not going to tell + + + align:start position:0% +okay so there's no I'm not going to tell +you exactly how much you should pay them + + align:start position:0% +you exactly how much you should pay them + + + align:start position:0% +you exactly how much you should pay them +but try to figure out more or less + + align:start position:0% +but try to figure out more or less + + + align:start position:0% +but try to figure out more or less +minimum wage more or less how long your + + align:start position:0% +minimum wage more or less how long your + + + align:start position:0% +minimum wage more or less how long your +task takes and pay them according to + + align:start position:0% +task takes and pay them according to + + + align:start position:0% +task takes and pay them according to +that okay + + align:start position:0% +that okay + + + align:start position:0% +that okay +some general advantages in Mechanical + + align:start position:0% +some general advantages in Mechanical + + + align:start position:0% +some general advantages in Mechanical +Turk incase you guys have not been + + align:start position:0% +Turk incase you guys have not been + + + align:start position:0% +Turk incase you guys have not been +persuaded yet let me say you can run + + align:start position:0% +persuaded yet let me say you can run + + + align:start position:0% +persuaded yet let me say you can run +large-scale experiments I started + + align:start position:0% +large-scale experiments I started + + + align:start position:0% +large-scale experiments I started +running this experiment on a hundred + + align:start position:0% +running this experiment on a hundred + + + align:start position:0% +running this experiment on a hundred +people that would have taken me a long + + align:start position:0% +people that would have taken me a long + + + align:start position:0% +people that would have taken me a long +time it's a silly experiment dozen Toria + + align:start position:0% +time it's a silly experiment dozen Toria + + + align:start position:0% +time it's a silly experiment dozen Toria +pointed out it's not even exactly an + + align:start position:0% +pointed out it's not even exactly an + + + align:start position:0% +pointed out it's not even exactly an +experiment but I wanted to you know + + align:start position:0% +experiment but I wanted to you know + + + align:start position:0% +experiment but I wanted to you know +check how people's responses compared to + + align:start position:0% +check how people's responses compared to + + + align:start position:0% +check how people's responses compared to +people in CBMM first of all I wouldn't + + align:start position:0% +people in CBMM first of all I wouldn't + + + align:start position:0% +people in CBMM first of all I wouldn't +do that in the lab so there's that but + + align:start position:0% +do that in the lab so there's that but + + + align:start position:0% +do that in the lab so there's that but +even if I were to do it in lab getting a + + align:start position:0% +even if I were to do it in lab getting a + + + align:start position:0% +even if I were to do it in lab getting a +hundred participants would take a long + + align:start position:0% +hundred participants would take a long + + + align:start position:0% +hundred participants would take a long +long time okay and then for more you're + + align:start position:0% +long time okay and then for more you're + + + align:start position:0% +long time okay and then for more you're +more serious experiments getting a + + align:start position:0% +more serious experiments getting a + + + align:start position:0% +more serious experiments getting a +hundred dissidents would take a long + + align:start position:0% +hundred dissidents would take a long + + + align:start position:0% +hundred dissidents would take a long +long time each one has to come in and + + align:start position:0% +long time each one has to come in and + + + align:start position:0% +long time each one has to come in and +you have to talk to them and you have to + + align:start position:0% +you have to talk to them and you have to + + + align:start position:0% +you have to talk to them and you have to +explain to them exactly what's going on + + align:start position:0% +explain to them exactly what's going on + + + align:start position:0% +explain to them exactly what's going on +and you usually can't run them in + + align:start position:0% +and you usually can't run them in + + + align:start position:0% +and you usually can't run them in +parallel or at least you can run only + + align:start position:0% +parallel or at least you can run only + + + align:start position:0% +parallel or at least you can run only +one or two in parallel here we ran a + + align:start position:0% +one or two in parallel here we ran a + + + align:start position:0% +one or two in parallel here we ran a +hundred subjects in an hour + + align:start position:0% +hundred subjects in an hour + + + align:start position:0% +hundred subjects in an hour +okay and that's that's still amazing + + align:start position:0% +okay and that's that's still amazing + + + align:start position:0% +okay and that's that's still amazing +right that's still flooring me and we + + align:start position:0% +right that's still flooring me and we + + + align:start position:0% +right that's still flooring me and we +can do it so we can do it very quickly a + + align:start position:0% +can do it so we can do it very quickly a + + + align:start position:0% +can do it so we can do it very quickly a +lot of people very quickly and what you + + align:start position:0% +lot of people very quickly and what you + + + align:start position:0% +lot of people very quickly and what you +can do with large new experiments is + + align:start position:0% +can do with large new experiments is + + + align:start position:0% +can do with large new experiments is +usually test some very fine-grained + + align:start position:0% +usually test some very fine-grained + + + align:start position:0% +usually test some very fine-grained +things of your mobile right if your + + align:start position:0% +things of your mobile right if your + + + align:start position:0% +things of your mobile right if your +mobile has some things like well I need + + align:start position:0% +mobile has some things like well I need + + + align:start position:0% +mobile has some things like well I need +to show people all of these different + + align:start position:0% +to show people all of these different + + + align:start position:0% +to show people all of these different +things and make all these different + + align:start position:0% +things and make all these different + + + align:start position:0% +things and make all these different +predictions and I just need 300 people + + align:start position:0% +predictions and I just need 300 people + + + align:start position:0% +predictions and I just need 300 people +to do that or for example what my dad + + align:start position:0% +to do that or for example what my dad + + + align:start position:0% +to do that or for example what my dad +was presenting yesterday these minimal + + align:start position:0% +was presenting yesterday these minimal + + + align:start position:0% +was presenting yesterday these minimal +images right did he mention how many + + align:start position:0% +images right did he mention how many + + + align:start position:0% +images right did he mention how many +people they have to recruit on Amazon + + align:start position:0% +people they have to recruit on Amazon + + + align:start position:0% +people they have to recruit on Amazon +Mechanical Turk to do those minimal + + align:start position:0% +Mechanical Turk to do those minimal + + + align:start position:0% +Mechanical Turk to do those minimal +images yes it's it's like it's thousands + + align:start position:0% +images yes it's it's like it's thousands + + + align:start position:0% +images yes it's it's like it's thousands +right I think is over ten thousand at + + align:start position:0% +right I think is over ten thousand at + + + align:start position:0% +right I think is over ten thousand at +this point or something like that and + + align:start position:0% +this point or something like that and + + + align:start position:0% +this point or something like that and +the reason is because once you've seen + + align:start position:0% +the reason is because once you've seen + + + align:start position:0% +the reason is because once you've seen +that thing once you've seen any normal + + align:start position:0% +that thing once you've seen any normal + + + align:start position:0% +that thing once you've seen any normal +image you already know what it is you're + + align:start position:0% +image you already know what it is you're + + + align:start position:0% +image you already know what it is you're +biased you see you know it's a horse + + align:start position:0% +biased you see you know it's a horse + + + align:start position:0% +biased you see you know it's a horse +even though a naive participant wouldn't + + align:start position:0% +even though a naive participant wouldn't + + + align:start position:0% +even though a naive participant wouldn't +know it's a horse so you want to make + + align:start position:0% +know it's a horse so you want to make + + + align:start position:0% +know it's a horse so you want to make +sure that you know you want ten thousand + + align:start position:0% +sure that you know you want ten thousand + + + align:start position:0% +sure that you know you want ten thousand +participants for this thing you're not + + align:start position:0% +participants for this thing you're not + + + align:start position:0% +participants for this thing you're not +going to get ten thousand participants + + align:start position:0% +going to get ten thousand participants + + + align:start position:0% +going to get ten thousand participants +in the lab no way so another thing is + + align:start position:0% +in the lab no way so another thing is + + + align:start position:0% +in the lab no way so another thing is +that as I said even if you're paying + + align:start position:0% +that as I said even if you're paying + + + align:start position:0% +that as I said even if you're paying +people minimum wage and things like that + + align:start position:0% +people minimum wage and things like that + + + align:start position:0% +people minimum wage and things like that +it's still pretty cheap to get 100 + + align:start position:0% +it's still pretty cheap to get 100 + + + align:start position:0% +it's still pretty cheap to get 100 +subjects it's cheap ish the issues + + align:start position:0% +subjects it's cheap ish the issues + + + align:start position:0% +subjects it's cheap ish the issues +because you should pay people some + + align:start position:0% +because you should pay people some + + + align:start position:0% +because you should pay people some +minimum wage it's replicable ish what I + + align:start position:0% +minimum wage it's replicable ish what I + + + align:start position:0% +minimum wage it's replicable ish what I +mean here by replicable is + + align:start position:0% +mean here by replicable is + + + align:start position:0% +mean here by replicable is +not what you might think which I'll get + + align:start position:0% +not what you might think which I'll get + + + align:start position:0% +not what you might think which I'll get +you in another slide it's just if you + + align:start position:0% +you in another slide it's just if you + + + align:start position:0% +you in another slide it's just if you +want to hand it off to another person + + align:start position:0% +want to hand it off to another person + + + align:start position:0% +want to hand it off to another person +someone says I don't quite understand + + align:start position:0% +someone says I don't quite understand + + + align:start position:0% +someone says I don't quite understand +your protocol or I don't quite believe + + align:start position:0% +your protocol or I don't quite believe + + + align:start position:0% +your protocol or I don't quite believe +it or I want to tweak it in some way + + align:start position:0% +it or I want to tweak it in some way + + + align:start position:0% +it or I want to tweak it in some way +it's much harder usually with lab + + align:start position:0% +it's much harder usually with lab + + + align:start position:0% +it's much harder usually with lab +protocols and things like that we + + align:start position:0% +protocols and things like that we + + + align:start position:0% +protocols and things like that we +certainly know that in baby experiments + + align:start position:0% +certainly know that in baby experiments + + + align:start position:0% +certainly know that in baby experiments +wouldn't it be nice if we could just + + align:start position:0% +wouldn't it be nice if we could just + + + align:start position:0% +wouldn't it be nice if we could just +port you know I won't say who because it + + align:start position:0% +port you know I won't say who because it + + + align:start position:0% +port you know I won't say who because it +doesn't really matter but some + + align:start position:0% +doesn't really matter but some + + + align:start position:0% +doesn't really matter but some +experiments of people they describe + + align:start position:0% +experiments of people they describe + + + align:start position:0% +experiments of people they describe +their methods in the paper it's not + + align:start position:0% +their methods in the paper it's not + + + align:start position:0% +their methods in the paper it's not +really that great wouldn't be great if + + align:start position:0% +really that great wouldn't be great if + + + align:start position:0% +really that great wouldn't be great if +we could just copy-paste their + + align:start position:0% +we could just copy-paste their + + + align:start position:0% +we could just copy-paste their +experiment and run it with some tweaking + + align:start position:0% +experiment and run it with some tweaking + + + align:start position:0% +experiment and run it with some tweaking +with this sort of thing you can I mean + + align:start position:0% +with this sort of thing you can I mean + + + align:start position:0% +with this sort of thing you can I mean +you need to be somewhat on good terms + + align:start position:0% +you need to be somewhat on good terms + + + align:start position:0% +you need to be somewhat on good terms +with the person you're asking for but + + align:start position:0% +with the person you're asking for but + + + align:start position:0% +with the person you're asking for but +they can just tell you oh yeah sure + + align:start position:0% +they can just tell you oh yeah sure + + + align:start position:0% +they can just tell you oh yeah sure +here's the code for my website right + + align:start position:0% +here's the code for my website right + + + align:start position:0% +here's the code for my website right +just run it again run it with your with + + align:start position:0% +just run it again run it with your with + + + align:start position:0% +just run it again run it with your with +your tweaks and things like that there's + + align:start position:0% +your tweaks and things like that there's + + + align:start position:0% +your tweaks and things like that there's +an ish there and I'll get to it in a + + align:start position:0% +an ish there and I'll get to it in a + + + align:start position:0% +an ish there and I'll get to it in a +second the participant pool as I said + + align:start position:0% +second the participant pool as I said + + + align:start position:0% +second the participant pool as I said +it's more diverse so I was I was harping + + align:start position:0% +it's more diverse so I was I was harping + + + align:start position:0% +it's more diverse so I was I was harping +before about this point that the pool + + align:start position:0% +before about this point that the pool + + + align:start position:0% +before about this point that the pool +doesn't quite represent the u.s. in + + align:start position:0% +doesn't quite represent the u.s. in + + + align:start position:0% +doesn't quite represent the u.s. in +general it's more like the US population + + align:start position:0% +general it's more like the US population + + + align:start position:0% +general it's more like the US population +on the internet that's still a lot more + + align:start position:0% +on the internet that's still a lot more + + + align:start position:0% +on the internet that's still a lot more +diverse than recruiting college students + + align:start position:0% +diverse than recruiting college students + + + align:start position:0% +diverse than recruiting college students +okay it's a lot more diverse let's see I + + align:start position:0% +okay it's a lot more diverse let's see I + + + align:start position:0% +okay it's a lot more diverse let's see I +have here in response to gender + + align:start position:0% +have here in response to gender + + + align:start position:0% +have here in response to gender +socioeconomic status geographic region + + align:start position:0% +socioeconomic status geographic region + + + align:start position:0% +socioeconomic status geographic region +and age on all these things that people + + align:start position:0% +and age on all these things that people + + + align:start position:0% +and age on all these things that people +have tested Amazon Mechanical Turk this + + align:start position:0% +have tested Amazon Mechanical Turk this + + + align:start position:0% +have tested Amazon Mechanical Turk this +sample is a lot more diverse as a lot + + align:start position:0% +sample is a lot more diverse as a lot + + + align:start position:0% +sample is a lot more diverse as a lot +more representative of the general + + align:start position:0% +more representative of the general + + + align:start position:0% +more representative of the general +population is a lot less weird right + + align:start position:0% +population is a lot less weird right + + + align:start position:0% +population is a lot less weird right +weird being like Western educated + + align:start position:0% +weird being like Western educated + + + align:start position:0% +weird being like Western educated +industrialized rich democracies which is + + align:start position:0% +industrialized rich democracies which is + + + align:start position:0% +industrialized rich democracies which is +usually the pool that's been studied in + + align:start position:0% +usually the pool that's been studied in + + + align:start position:0% +usually the pool that's been studied in +psychology these pools are a lot more + + align:start position:0% +psychology these pools are a lot more + + + align:start position:0% +psychology these pools are a lot more +diverse they're not diverse enough for + + align:start position:0% +diverse they're not diverse enough for + + + align:start position:0% +diverse they're not diverse enough for +certain things in social psychology and + + align:start position:0% +certain things in social psychology and + + + align:start position:0% +certain things in social psychology and +that's this paper by Weinberg where he + + align:start position:0% +that's this paper by Weinberg where he + + + align:start position:0% +that's this paper by Weinberg where he +says you know sometimes social + + align:start position:0% +says you know sometimes social + + + align:start position:0% +says you know sometimes social +psychologists really really really want + + align:start position:0% +psychologists really really really want + + + align:start position:0% +psychologists really really really want +to control for making sure that age is + + align:start position:0% +to control for making sure that age is + + + align:start position:0% +to control for making sure that age is +not a factor or something like that or + + align:start position:0% +not a factor or something like that or + + + align:start position:0% +not a factor or something like that or +they really want to get it what the + + align:start position:0% +they really want to get it what the + + + align:start position:0% +they really want to get it what the +population is where age they think plays + + align:start position:0% +population is where age they think plays + + + align:start position:0% +population is where age they think plays +a factor or something like that so you + + align:start position:0% +a factor or something like that so you + + + align:start position:0% +a factor or something like that so you +need a population where they call it + + align:start position:0% +need a population where they call it + + + align:start position:0% +need a population where they call it +sort of like knowledge experts you build + + align:start position:0% +sort of like knowledge experts you build + + + align:start position:0% +sort of like knowledge experts you build +some pool you build some pool that you + + align:start position:0% +some pool you build some pool that you + + + align:start position:0% +some pool you build some pool that you +say okay the reason this pool exists is + + align:start position:0% +say okay the reason this pool exists is + + + align:start position:0% +say okay the reason this pool exists is +because it's represented the population + + align:start position:0% +because it's represented the population + + + align:start position:0% +because it's represented the population +and now we're going to go to this pool + + align:start position:0% +and now we're going to go to this pool + + + align:start position:0% +and now we're going to go to this pool +and just try them again and again and + + align:start position:0% +and just try them again and again and + + + align:start position:0% +and just try them again and again and +again on many different experiments it's + + align:start position:0% +again on many different experiments it's + + + align:start position:0% +again on many different experiments it's +sort like you're you know some not + + align:start position:0% +sort like you're you know some not + + + align:start position:0% +sort like you're you know some not +exactly private but share between some + + align:start position:0% +exactly private but share between some + + + align:start position:0% +exactly private but share between some +universities pool of social psychology + + align:start position:0% +universities pool of social psychology + + + align:start position:0% +universities pool of social psychology +participants they've tested that and + + align:start position:0% +participants they've tested that and + + + align:start position:0% +participants they've tested that and +they've shown that Mechanical Turk ORS + + align:start position:0% +they've shown that Mechanical Turk ORS + + + align:start position:0% +they've shown that Mechanical Turk ORS +are better than those pools in terms of + + align:start position:0% +are better than those pools in terms of + + + align:start position:0% +are better than those pools in terms of +things like attention + + align:start position:0% +things like attention + + + align:start position:0% +things like attention +filling out the correct responses and + + align:start position:0% +filling out the correct responses and + + + align:start position:0% +filling out the correct responses and +things like that so yeah Mechanical Turk + + align:start position:0% +things like that so yeah Mechanical Turk + + + align:start position:0% +things like that so yeah Mechanical Turk +but there are some things like implicit + + align:start position:0% +but there are some things like implicit + + + align:start position:0% +but there are some things like implicit +biases on things that such like all just + + align:start position:0% +biases on things that such like all just + + + align:start position:0% +biases on things that such like all just +care about where you don't know if the + + align:start position:0% +care about where you don't know if the + + + align:start position:0% +care about where you don't know if the +effect is something like age or + + align:start position:0% +effect is something like age or + + + align:start position:0% +effect is something like age or +something like that I don't know if this + + align:start position:0% +something like that I don't know if this + + + align:start position:0% +something like that I don't know if this +matters to a lot of you but it's it's + + align:start position:0% +matters to a lot of you but it's it's + + + align:start position:0% +matters to a lot of you but it's it's +important to keep in mind + + align:start position:0% +important to keep in mind + + + align:start position:0% +important to keep in mind +for those of you here's this point about + + align:start position:0% +for those of you here's this point about + + + align:start position:0% +for those of you here's this point about +will it replicate you know some people + + align:start position:0% +will it replicate you know some people + + + align:start position:0% +will it replicate you know some people +who are being introduced on is on + + align:start position:0% +who are being introduced on is on + + + align:start position:0% +who are being introduced on is on +Mechanical Turk or thinking about it + + align:start position:0% +Mechanical Turk or thinking about it + + + align:start position:0% +Mechanical Turk or thinking about it +usually say yeah that's fine but how do + + align:start position:0% +usually say yeah that's fine but how do + + + align:start position:0% +usually say yeah that's fine but how do +I know that people are actually doing + + align:start position:0% +I know that people are actually doing + + + align:start position:0% +I know that people are actually doing +what will happen in the lab right I + + align:start position:0% +what will happen in the lab right I + + + align:start position:0% +what will happen in the lab right I +might just do it on Mechanical Turk but + + align:start position:0% +might just do it on Mechanical Turk but + + + align:start position:0% +might just do it on Mechanical Turk but +then if I do it in the lab it won't + + align:start position:0% +then if I do it in the lab it won't + + + align:start position:0% +then if I do it in the lab it won't +replicate or things like that so people + + align:start position:0% +replicate or things like that so people + + + align:start position:0% +replicate or things like that so people +have tried a bunch of the psychophysics + + align:start position:0% +have tried a bunch of the psychophysics + + + align:start position:0% +have tried a bunch of the psychophysics +that Leila was talking about before and + + align:start position:0% +that Leila was talking about before and + + + align:start position:0% +that Leila was talking about before and +more they try it's troop switching + + align:start position:0% +more they try it's troop switching + + + align:start position:0% +more they try it's troop switching +flanker Simon Posner cueing attentional + + align:start position:0% +flanker Simon Posner cueing attentional + + + align:start position:0% +flanker Simon Posner cueing attentional +blink subliminal priming and category + + align:start position:0% +blink subliminal priming and category + + + align:start position:0% +blink subliminal priming and category +learning and they've done a whole lot + + align:start position:0% +learning and they've done a whole lot + + + align:start position:0% +learning and they've done a whole lot +more this is just from one study by + + align:start position:0% +more this is just from one study by + + + align:start position:0% +more this is just from one study by +Crump at all where one of the atoll is + + align:start position:0% +Crump at all where one of the atoll is + + + align:start position:0% +Crump at all where one of the atoll is +Todd Lucas who we'll get to in a second + + align:start position:0% +Todd Lucas who we'll get to in a second + + + align:start position:0% +Todd Lucas who we'll get to in a second +and what they find was basically + + align:start position:0% +and what they find was basically + + + align:start position:0% +and what they find was basically +replication on all of these classic + + align:start position:0% +replication on all of these classic + + + align:start position:0% +replication on all of these classic +psychology stuff the sort of effects you + + align:start position:0% +psychology stuff the sort of effects you + + + align:start position:0% +psychology stuff the sort of effects you +would expect the sort of effect sizes + + align:start position:0% +would expect the sort of effect sizes + + + align:start position:0% +would expect the sort of effect sizes +you would expect the only thing that was + + align:start position:0% +you would expect the only thing that was + + + align:start position:0% +you would expect the only thing that was +a bit different was in Category learning + + align:start position:0% +a bit different was in Category learning + + + align:start position:0% +a bit different was in Category learning +where you show people something like + + align:start position:0% +where you show people something like + + + align:start position:0% +where you show people something like +this is a twofer this is a twofer this + + align:start position:0% +this is a twofer this is a twofer this + + + align:start position:0% +this is a twofer this is a twofer this +is a twofer is this a twofer where there + + align:start position:0% +is a twofer is this a twofer where there + + + align:start position:0% +is a twofer is this a twofer where there +are different types of learning type one + + align:start position:0% +are different types of learning type one + + + align:start position:0% +are different types of learning type one +being easier type two being a little + + align:start position:0% +being easier type two being a little + + + align:start position:0% +being easier type two being a little +harder type three being much harder with + + align:start position:0% +harder type three being much harder with + + + align:start position:0% +harder type three being much harder with +the classic finding was something like a + + align:start position:0% +the classic finding was something like a + + + align:start position:0% +the classic finding was something like a +graded thing and for Amazon Mechanical + + align:start position:0% +graded thing and for Amazon Mechanical + + + align:start position:0% +graded thing and for Amazon Mechanical +Turk it was more it was just really hard + + align:start position:0% +Turk it was more it was just really hard + + + align:start position:0% +Turk it was more it was just really hard +for them beyond type one now is that a + + align:start position:0% +for them beyond type one now is that a + + + align:start position:0% +for them beyond type one now is that a +failure replication or is that because + + align:start position:0% +failure replication or is that because + + + align:start position:0% +failure replication or is that because +the original study was done on college + + align:start position:0% +the original study was done on college + + + align:start position:0% +the original study was done on college +students who are young and educated and + + align:start position:0% +students who are young and educated and + + + align:start position:0% +students who are young and educated and +this is actually more representative the + + align:start position:0% +this is actually more representative the + + + align:start position:0% +this is actually more representative the +population but this is harder to learn + + align:start position:0% +population but this is harder to learn + + + align:start position:0% +population but this is harder to learn +I'm not quite sure but the takeaway here + + align:start position:0% +I'm not quite sure but the takeaway here + + + align:start position:0% +I'm not quite sure but the takeaway here +is that yeah it seems like in general it + + align:start position:0% +is that yeah it seems like in general it + + + align:start position:0% +is that yeah it seems like in general it +will replicate at least certainly for + + align:start position:0% +will replicate at least certainly for + + + align:start position:0% +will replicate at least certainly for +simple perceptual stuff concerns of + + align:start position:0% +simple perceptual stuff concerns of + + + align:start position:0% +simple perceptual stuff concerns of +running things on Amazon Mechanical Turk + + align:start position:0% +running things on Amazon Mechanical Turk + + + align:start position:0% +running things on Amazon Mechanical Turk +and I can send you a whole bunch of + + align:start position:0% +and I can send you a whole bunch of + + + align:start position:0% +and I can send you a whole bunch of +recent papers that are very nice about + + align:start position:0% +recent papers that are very nice about + + + align:start position:0% +recent papers that are very nice about +it one of them was specifically there's + + align:start position:0% +it one of them was specifically there's + + + align:start position:0% +it one of them was specifically there's +been a bunch of like New York Times + + align:start position:0% +been a bunch of like New York Times + + + align:start position:0% +been a bunch of like New York Times +papers on Amazon Mechanical Turk in + + align:start position:0% +papers on Amazon Mechanical Turk in + + + align:start position:0% +papers on Amazon Mechanical Turk in +general there's been a very recent one a + + align:start position:0% +general there's been a very recent one a + + + align:start position:0% +general there's been a very recent one a +few months ago on using it for + + align:start position:0% +few months ago on using it for + + + align:start position:0% +few months ago on using it for +psychophysics experiments in particular + + align:start position:0% +psychophysics experiments in particular + + + align:start position:0% +psychophysics experiments in particular +it's called the Internet's hidden + + align:start position:0% +it's called the Internet's hidden + + + align:start position:0% +it's called the Internet's hidden +science Factory it's a very nice paper + + align:start position:0% +science Factory it's a very nice paper + + + align:start position:0% +science Factory it's a very nice paper +to check out and they make all these + + align:start position:0% +to check out and they make all these + + + align:start position:0% +to check out and they make all these +points about like the sort of things + + align:start position:0% +points about like the sort of things + + + align:start position:0% +points about like the sort of things +that you you know you probably thought + + align:start position:0% +that you you know you probably thought + + + align:start position:0% +that you you know you probably thought +about as a researcher but it bears + + align:start position:0% +about as a researcher but it bears + + + align:start position:0% +about as a researcher but it bears +thinking about again + + align:start position:0% +thinking about again + + + align:start position:0% +thinking about again +which is people don't necessarily pay + + align:start position:0% +which is people don't necessarily pay + + + align:start position:0% +which is people don't necessarily pay +that much attention to your task you'd + + align:start position:0% +that much attention to your task you'd + + + align:start position:0% +that much attention to your task you'd +have no control they're not in the lab + + align:start position:0% +have no control they're not in the lab + + + align:start position:0% +have no control they're not in the lab +they give some quote there which is you + + align:start position:0% +they give some quote there which is you + + + align:start position:0% +they give some quote there which is you +know + + align:start position:0% +know + + + align:start position:0% +know +Nancy's employees don't know oh sorry + + align:start position:0% +Nancy's employees don't know oh sorry + + + align:start position:0% +Nancy's employees don't know oh sorry +yeah I think it's not same to me + + align:start position:0% +yeah I think it's not same to me + + + align:start position:0% +yeah I think it's not same to me +Nancy's employers don't know that Nancy + + align:start position:0% +Nancy's employers don't know that Nancy + + + align:start position:0% +Nancy's employers don't know that Nancy +works while negotiating her toddlers + + align:start position:0% +works while negotiating her toddlers + + + align:start position:0% +works while negotiating her toddlers +milk bottles and giving him hugs they + + align:start position:0% +milk bottles and giving him hugs they + + + align:start position:0% +milk bottles and giving him hugs they +don't know that she's seen studies + + align:start position:0% +don't know that she's seen studies + + + align:start position:0% +don't know that she's seen studies +similar to theirs maybe hundreds + + align:start position:0% +similar to theirs maybe hundreds + + + align:start position:0% +similar to theirs maybe hundreds +possibly thousands of times okay so that + + align:start position:0% +possibly thousands of times okay so that + + + align:start position:0% +possibly thousands of times okay so that +brings us actually to another thing + + align:start position:0% +brings us actually to another thing + + + align:start position:0% +brings us actually to another thing +which is repeated exposure okay this is + + align:start position:0% +which is repeated exposure okay this is + + + align:start position:0% +which is repeated exposure okay this is +a big concern by the way what sorry I'm + + align:start position:0% +a big concern by the way what sorry I'm + + + align:start position:0% +a big concern by the way what sorry I'm +I'm going sort of back and forth here + + align:start position:0% +I'm going sort of back and forth here + + + align:start position:0% +I'm going sort of back and forth here +because before I leave attention I want + + align:start position:0% +because before I leave attention I want + + + align:start position:0% +because before I leave attention I want +to mention just one thing which is + + align:start position:0% +to mention just one thing which is + + + align:start position:0% +to mention just one thing which is +attention is a problem you want to put + + align:start position:0% +attention is a problem you want to put + + + align:start position:0% +attention is a problem you want to put +in attention cues and I'll talk about + + align:start position:0% +in attention cues and I'll talk about + + + align:start position:0% +in attention cues and I'll talk about +how to do that in a second but we've had + + align:start position:0% +how to do that in a second but we've had + + + align:start position:0% +how to do that in a second but we've had +this a lot with people in the lab I'm + + align:start position:0% +this a lot with people in the lab I'm + + + align:start position:0% +this a lot with people in the lab I'm +sure that some of you experienced this + + align:start position:0% +sure that some of you experienced this + + + align:start position:0% +sure that some of you experienced this +as well you put them in a room because + + align:start position:0% +as well you put them in a room because + + + align:start position:0% +as well you put them in a room because +they need to have privacy while they're + + align:start position:0% +they need to have privacy while they're + + + align:start position:0% +they need to have privacy while they're +doing the task you're going to check on + + align:start position:0% +doing the task you're going to check on + + + align:start position:0% +doing the task you're going to check on +them and they're on their phone okay + + align:start position:0% +them and they're on their phone okay + + + align:start position:0% +them and they're on their phone okay +this this happens a lot so attention is + + align:start position:0% +this this happens a lot so attention is + + + align:start position:0% +this this happens a lot so attention is +something that you want to check in the + + align:start position:0% +something that you want to check in the + + + align:start position:0% +something that you want to check in the +lab as well a lot of these concerns are + + align:start position:0% +lab as well a lot of these concerns are + + + align:start position:0% +lab as well a lot of these concerns are +not just about Mechanical Turk but it's + + align:start position:0% +not just about Mechanical Turk but it's + + + align:start position:0% +not just about Mechanical Turk but it's +certainly easier for people on + + align:start position:0% +certainly easier for people on + + + align:start position:0% +certainly easier for people on +Mechanical Turk to not quite pay + + align:start position:0% +Mechanical Turk to not quite pay + + + align:start position:0% +Mechanical Turk to not quite pay +attention + + align:start position:0% +attention + + + align:start position:0% +attention +repeated exposure is a huge problem and + + align:start position:0% +repeated exposure is a huge problem and + + + align:start position:0% +repeated exposure is a huge problem and +it it's a problem for two for two + + align:start position:0% +it it's a problem for two for two + + + align:start position:0% +it it's a problem for two for two +different reasons one is that a destroys + + align:start position:0% +different reasons one is that a destroys + + + align:start position:0% +different reasons one is that a destroys +intuition okay + + align:start position:0% +intuition okay + + + align:start position:0% +intuition okay +I was asking about the trolley problem + + align:start position:0% +I was asking about the trolley problem + + + align:start position:0% +I was asking about the trolley problem +and you all went oh the trolley problem + + align:start position:0% +and you all went oh the trolley problem + + + align:start position:0% +and you all went oh the trolley problem +people on Turk are doing that even more + + align:start position:0% +people on Turk are doing that even more + + + align:start position:0% +people on Turk are doing that even more +than you are okay they see the trolley + + align:start position:0% +than you are okay they see the trolley + + + align:start position:0% +than you are okay they see the trolley +problem they've seen it I guarantee you + + align:start position:0% +problem they've seen it I guarantee you + + + align:start position:0% +problem they've seen it I guarantee you +it's it's very difficult to find the + + align:start position:0% +it's it's very difficult to find the + + + align:start position:0% +it's it's very difficult to find the +Turk or that has not seen the trolley + + align:start position:0% +Turk or that has not seen the trolley + + + align:start position:0% +Turk or that has not seen the trolley +problem they've seen it they've seen it + + align:start position:0% +problem they've seen it they've seen it + + + align:start position:0% +problem they've seen it they've seen it +a thousand times they've seen all the + + align:start position:0% +a thousand times they've seen all the + + + align:start position:0% +a thousand times they've seen all the +variations and they complain about it + + align:start position:0% +variations and they complain about it + + + align:start position:0% +variations and they complain about it +and they're satiated and they're sick of + + align:start position:0% +and they're satiated and they're sick of + + + align:start position:0% +and they're satiated and they're sick of +it they will say things like if I see + + align:start position:0% +it they will say things like if I see + + + align:start position:0% +it they will say things like if I see +one more trolley problem just killed + + align:start position:0% +one more trolley problem just killed + + + align:start position:0% +one more trolley problem just killed +them all is their way to kill the five + + align:start position:0% +them all is their way to kill the five + + + align:start position:0% +them all is their way to kill the five +and the other person on the other side + + align:start position:0% +and the other person on the other side + + + align:start position:0% +and the other person on the other side +of the track I don't care anymore + + align:start position:0% +of the track I don't care anymore + + + align:start position:0% +of the track I don't care anymore +okay they're completely satiated it's + + align:start position:0% +okay they're completely satiated it's + + + align:start position:0% +okay they're completely satiated it's +kind of like saying hammer Hammer hammer + + align:start position:0% +kind of like saying hammer Hammer hammer + + + align:start position:0% +kind of like saying hammer Hammer hammer +Hammer it loses all meaning at some + + align:start position:0% +Hammer it loses all meaning at some + + + align:start position:0% +Hammer it loses all meaning at some +point right there you don't have the gut + + align:start position:0% +point right there you don't have the gut + + + align:start position:0% +point right there you don't have the gut +intuitive response and even if they're + + align:start position:0% +intuitive response and even if they're + + + align:start position:0% +intuitive response and even if they're +doing their best ok even if they're not + + align:start position:0% +doing their best ok even if they're not + + + align:start position:0% +doing their best ok even if they're not +trying to fool you even though they're + + align:start position:0% +trying to fool you even though they're + + + align:start position:0% +trying to fool you even though they're +honestly trying to answer they just + + align:start position:0% +honestly trying to answer they just + + + align:start position:0% +honestly trying to answer they just +can't they don't have the gut intuitive + + align:start position:0% +can't they don't have the gut intuitive + + + align:start position:0% +can't they don't have the gut intuitive +response anymore to this stuff that + + align:start position:0% +response anymore to this stuff that + + + align:start position:0% +response anymore to this stuff that +you're asking them ok some ways to get + + align:start position:0% +you're asking them ok some ways to get + + + align:start position:0% +you're asking them ok some ways to get +around that is to try even simple + + align:start position:0% +around that is to try even simple + + + align:start position:0% +around that is to try even simple +changes right just don't call it the + + align:start position:0% +changes right just don't call it the + + + align:start position:0% +changes right just don't call it the +trolley problem anymore set up something + + align:start position:0% +trolley problem anymore set up something + + + align:start position:0% +trolley problem anymore set up something +else which is not 5 versus 1 which is 10 + + align:start position:0% +else which is not 5 versus 1 which is 10 + + + align:start position:0% +else which is not 5 versus 1 which is 10 +versus 2 and it involves pineapples and + + align:start position:0% +versus 2 and it involves pineapples and + + + align:start position:0% +versus 2 and it involves pineapples and +people on Mars + + align:start position:0% +people on Mars + + + align:start position:0% +people on Mars +something you know these small changes + + align:start position:0% +something you know these small changes + + + align:start position:0% +something you know these small changes +can not a reward so that's one thing + + align:start position:0% +can not a reward so that's one thing + + + align:start position:0% +can not a reward so that's one thing +about repeated exposure that it destroys + + align:start position:0% +about repeated exposure that it destroys + + + align:start position:0% +about repeated exposure that it destroys +intuition and related to that there's + + align:start position:0% +intuition and related to that there's + + + align:start position:0% +intuition and related to that there's +something called super Turker as these + + align:start position:0% +something called super Turker as these + + + align:start position:0% +something called super Turker as these +are people that you know 1% of turquoise + + align:start position:0% +are people that you know 1% of turquoise + + + align:start position:0% +are people that you know 1% of turquoise +is responsible for about 10 to 15 + + align:start position:0% +is responsible for about 10 to 15 + + + align:start position:0% +is responsible for about 10 to 15 +percent of all studies so when I say + + align:start position:0% +percent of all studies so when I say + + + align:start position:0% +percent of all studies so when I say +people have seen it a lot that's part of + + align:start position:0% +people have seen it a lot that's part of + + + align:start position:0% +people have seen it a lot that's part of +the reason there's a lot of people doing + + align:start position:0% +the reason there's a lot of people doing + + + align:start position:0% +the reason there's a lot of people doing +there's the same small group of people + + align:start position:0% +there's the same small group of people + + + align:start position:0% +there's the same small group of people +is probably responsible for a lot of + + align:start position:0% +is probably responsible for a lot of + + + align:start position:0% +is probably responsible for a lot of +these studies the other reason that + + align:start position:0% +these studies the other reason that + + + align:start position:0% +these studies the other reason that +repeated exposure ruin things for us is + + align:start position:0% +repeated exposure ruin things for us is + + + align:start position:0% +repeated exposure ruin things for us is +because of you know it just ruins basic + + align:start position:0% +because of you know it just ruins basic + + + align:start position:0% +because of you know it just ruins basic +correlations so let me let me give you + + align:start position:0% +correlations so let me let me give you + + + align:start position:0% +correlations so let me let me give you +an example who here has heard of the + + align:start position:0% +an example who here has heard of the + + + align:start position:0% +an example who here has heard of the +ball and bat question who here has not + + align:start position:0% +ball and bat question who here has not + + + align:start position:0% +ball and bat question who here has not +heard of the ball and bad question okay + + align:start position:0% +heard of the ball and bad question okay + + + align:start position:0% +heard of the ball and bad question okay +let me let me pose it to you those of + + align:start position:0% +let me let me pose it to you those of + + + align:start position:0% +let me let me pose it to you those of +you suddenly say oh yeah I know this + + align:start position:0% +you suddenly say oh yeah I know this + + + align:start position:0% +you suddenly say oh yeah I know this +okay I'm interested in people who have + + align:start position:0% +okay I'm interested in people who have + + + align:start position:0% +okay I'm interested in people who have +not heard this before so it's a simple + + align:start position:0% +not heard this before so it's a simple + + + align:start position:0% +not heard this before so it's a simple +question a ball and a bat together cost + + align:start position:0% +question a ball and a bat together cost + + + align:start position:0% +question a ball and a bat together cost +a dollar and ten cents okay + + align:start position:0% +a dollar and ten cents okay + + + align:start position:0% +a dollar and ten cents okay +the bat costs a dollar more than the + + align:start position:0% +the bat costs a dollar more than the + + + align:start position:0% +the bat costs a dollar more than the +ball how much does the ball cost I'll + + align:start position:0% +ball how much does the ball cost I'll + + + align:start position:0% +ball how much does the ball cost I'll +explain that again a bat in a bowl cost + + align:start position:0% +explain that again a bat in a bowl cost + + + align:start position:0% +explain that again a bat in a bowl cost +a dollar and ten cents together the bat + + align:start position:0% +a dollar and ten cents together the bat + + + align:start position:0% +a dollar and ten cents together the bat +costs a dollar more than the ball okay + + align:start position:0% +costs a dollar more than the ball okay + + + align:start position:0% +costs a dollar more than the ball okay +how much does the ball cost any one shut + + align:start position:0% +how much does the ball cost any one shut + + + align:start position:0% +how much does the ball cost any one shut +it out hmm yeah five cents who would + + align:start position:0% +it out hmm yeah five cents who would + + + align:start position:0% +it out hmm yeah five cents who would +have said ten cents don't be shy thank + + align:start position:0% +have said ten cents don't be shy thank + + + align:start position:0% +have said ten cents don't be shy thank +you thank you for bringing brave enough + + align:start position:0% +you thank you for bringing brave enough + + + align:start position:0% +you thank you for bringing brave enough +a lot of people say ten cents okay they + + align:start position:0% +a lot of people say ten cents okay they + + + align:start position:0% +a lot of people say ten cents okay they +say immediately the ball costs 10 cents + + align:start position:0% +say immediately the ball costs 10 cents + + + align:start position:0% +say immediately the ball costs 10 cents +the bat costs a dollar wait but it costs + + align:start position:0% +the bat costs a dollar wait but it costs + + + align:start position:0% +the bat costs a dollar wait but it costs +a dollar no no it costs a dollar more so + + align:start position:0% +a dollar no no it costs a dollar more so + + + align:start position:0% +a dollar no no it costs a dollar more so +it's a dollar does everyone get white by + + align:start position:0% +it's a dollar does everyone get white by + + + align:start position:0% +it's a dollar does everyone get white by +10 cents is not the answer it should be + + align:start position:0% +10 cents is not the answer it should be + + + align:start position:0% +10 cents is not the answer it should be +five cents okay good + + align:start position:0% +five cents okay good + + + align:start position:0% +five cents okay good +this was sort of a classic question + + align:start position:0% +this was sort of a classic question + + + align:start position:0% +this was sort of a classic question +along with two other questions called + + align:start position:0% +along with two other questions called + + + align:start position:0% +along with two other questions called +the lilypad question and the widget + + align:start position:0% +the lilypad question and the widget + + + align:start position:0% +the lilypad question and the widget +question the widget question is + + align:start position:0% +question the widget question is + + + align:start position:0% +question the widget question is +something like five widget machines make + + align:start position:0% +something like five widget machines make + + + align:start position:0% +something like five widget machines make +five widgets in five minutes how long + + align:start position:0% +five widgets in five minutes how long + + + align:start position:0% +five widgets in five minutes how long +does it take a hundred widget machines + + align:start position:0% +does it take a hundred widget machines + + + align:start position:0% +does it take a hundred widget machines +to take to make a hundred widgets five + + align:start position:0% +to take to make a hundred widgets five + + + align:start position:0% +to take to make a hundred widgets five +minutes these are the three questions + + align:start position:0% +minutes these are the three questions + + + align:start position:0% +minutes these are the three questions +were found out to correlate a lot better + + align:start position:0% +were found out to correlate a lot better + + + align:start position:0% +were found out to correlate a lot better +with things like IQ tests or even better + + align:start position:0% +with things like IQ tests or even better + + + align:start position:0% +with things like IQ tests or even better +sorry than IQ on a lot of different + + align:start position:0% +sorry than IQ on a lot of different + + + align:start position:0% +sorry than IQ on a lot of different +things they've been found + + align:start position:0% +things they've been found + + + align:start position:0% +things they've been found +you know many smart people from MIT and + + align:start position:0% +you know many smart people from MIT and + + + align:start position:0% +you know many smart people from MIT and +Harvard + + align:start position:0% +Harvard + + + align:start position:0% +Harvard +included failed this question and the + + align:start position:0% +included failed this question and the + + + align:start position:0% +included failed this question and the +point was you know people have made a + + align:start position:0% +point was you know people have made a + + + align:start position:0% +point was you know people have made a +big deal about it like this is even + + align:start position:0% +big deal about it like this is even + + + align:start position:0% +big deal about it like this is even +better than IQ tests on all sorts of + + align:start position:0% +better than IQ tests on all sorts of + + + align:start position:0% +better than IQ tests on all sorts of +measures and it's so simple we don't + + align:start position:0% +measures and it's so simple we don't + + + align:start position:0% +measures and it's so simple we don't +have to run a hundred IQ test questions + + align:start position:0% +have to run a hundred IQ test questions + + + align:start position:0% +have to run a hundred IQ test questions +let's just ask the ball in that question + + align:start position:0% +let's just ask the ball in that question + + + align:start position:0% +let's just ask the ball in that question +and then see what that correlates with + + align:start position:0% +and then see what that correlates with + + + align:start position:0% +and then see what that correlates with +and it also relates to you know kana + + align:start position:0% +and it also relates to you know kana + + + align:start position:0% +and it also relates to you know kana +makes a big deal about it it's system + + align:start position:0% +makes a big deal about it it's system + + + align:start position:0% +makes a big deal about it it's system +one versus system to system one really + + align:start position:0% +one versus system to system one really + + + align:start position:0% +one versus system to system one really +wants to answer that it costs ten cents + + align:start position:0% +wants to answer that it costs ten cents + + + align:start position:0% +wants to answer that it costs ten cents +and you could solve it of course you + + align:start position:0% +and you could solve it of course you + + + align:start position:0% +and you could solve it of course you +could all solve it it's not hard for you + + align:start position:0% +could all solve it it's not hard for you + + + align:start position:0% +could all solve it it's not hard for you +if you wrote down the simple equation + + align:start position:0% +if you wrote down the simple equation + + + align:start position:0% +if you wrote down the simple equation +it's trivial right you wrote it down as + + align:start position:0% +it's trivial right you wrote it down as + + + align:start position:0% +it's trivial right you wrote it down as +like X and X costs this and you could + + align:start position:0% +like X and X costs this and you could + + + align:start position:0% +like X and X costs this and you could +all solve this you could also this in + + align:start position:0% +all solve this you could also this in + + + align:start position:0% +all solve this you could also this in +middle school but you don't like system + + align:start position:0% +middle school but you don't like system + + + align:start position:0% +middle school but you don't like system +two or you know some of you do but + + align:start position:0% +two or you know some of you do but + + + align:start position:0% +two or you know some of you do but +usually the first time you hear it you + + align:start position:0% +usually the first time you hear it you + + + align:start position:0% +usually the first time you hear it you +don't and you don't even if you even + + align:start position:0% +don't and you don't even if you even + + + align:start position:0% +don't and you don't even if you even +people are warned like this is a bit of + + align:start position:0% +people are warned like this is a bit of + + + align:start position:0% +people are warned like this is a bit of +a trick question you know think about it + + align:start position:0% +a trick question you know think about it + + + align:start position:0% +a trick question you know think about it +they don't usually and people have used + + align:start position:0% +they don't usually and people have used + + + align:start position:0% +they don't usually and people have used +this as like ways to test system Wan + + align:start position:0% +this as like ways to test system Wan + + + align:start position:0% +this as like ways to test system Wan +versus do people know what I mean when I + + align:start position:0% +versus do people know what I mean when I + + + align:start position:0% +versus do people know what I mean when I +say system one versus system two common + + align:start position:0% +say system one versus system two common + + + align:start position:0% +say system one versus system two common +who doesn't raise your hand okay so very + + align:start position:0% +who doesn't raise your hand okay so very + + + align:start position:0% +who doesn't raise your hand okay so very +very quickly because it's not that + + align:start position:0% +very quickly because it's not that + + + align:start position:0% +very quickly because it's not that +relevant to Mechanical Turk but very + + align:start position:0% +relevant to Mechanical Turk but very + + + align:start position:0% +relevant to Mechanical Turk but very +very quickly + + align:start position:0% +very quickly + + + align:start position:0% +very quickly +you should read Thinking Fast and Slow + + align:start position:0% +you should read Thinking Fast and Slow + + + align:start position:0% +you should read Thinking Fast and Slow +by cohn mom the point is that the mind + + align:start position:0% +by cohn mom the point is that the mind + + + align:start position:0% +by cohn mom the point is that the mind +can generally be categorized into two + + align:start position:0% +can generally be categorized into two + + + align:start position:0% +can generally be categorized into two +systems even Kahneman doesn't quite + + align:start position:0% +systems even Kahneman doesn't quite + + + align:start position:0% +systems even Kahneman doesn't quite +believe that but it's sort of this thing + + align:start position:0% +believe that but it's sort of this thing + + + align:start position:0% +believe that but it's sort of this thing +that's easy to talk about system one is + + align:start position:0% +that's easy to talk about system one is + + + align:start position:0% +that's easy to talk about system one is +the fast heuristic system that gives you + + align:start position:0% +the fast heuristic system that gives you + + + align:start position:0% +the fast heuristic system that gives you +the cached response assistant who is the + + align:start position:0% +the cached response assistant who is the + + + align:start position:0% +the cached response assistant who is the +slow laborious can't do many things at + + align:start position:0% +slow laborious can't do many things at + + + align:start position:0% +slow laborious can't do many things at +one time system that's the sort of thing + + align:start position:0% +one time system that's the sort of thing + + + align:start position:0% +one time system that's the sort of thing +that you would use to solve algebra + + align:start position:0% +that you would use to solve algebra + + + align:start position:0% +that you would use to solve algebra +problems that's the reason you need to + + align:start position:0% +problems that's the reason you need to + + + align:start position:0% +problems that's the reason you need to +slow down when you're thinking about + + align:start position:0% +slow down when you're thinking about + + + align:start position:0% +slow down when you're thinking about +something very hard system one is the + + align:start position:0% +something very hard system one is the + + + align:start position:0% +something very hard system one is the +sort of thing that gives you biases and + + align:start position:0% +sort of thing that gives you biases and + + + align:start position:0% +sort of thing that gives you biases and +heuristics and things like that this was + + align:start position:0% +heuristics and things like that this was + + + align:start position:0% +heuristics and things like that this was +given as an example of the baton ball + + align:start position:0% +given as an example of the baton ball + + + align:start position:0% +given as an example of the baton ball +was like one of the prime examples of + + align:start position:0% +was like one of the prime examples of + + + align:start position:0% +was like one of the prime examples of +system one wants to do the assistant he + + align:start position:0% +system one wants to do the assistant he + + + align:start position:0% +system one wants to do the assistant he +wants to do that system two is lazy it + + align:start position:0% +wants to do that system two is lazy it + + + align:start position:0% +wants to do that system two is lazy it +doesn't actually get engaged unless it + + align:start position:0% +doesn't actually get engaged unless it + + + align:start position:0% +doesn't actually get engaged unless it +really really has to why am i bringing + + align:start position:0% +really really has to why am i bringing + + + align:start position:0% +really really has to why am i bringing +this up the reason I bring this up is + + align:start position:0% +this up the reason I bring this up is + + + align:start position:0% +this up the reason I bring this up is +because people thought it was a great + + align:start position:0% +because people thought it was a great + + + align:start position:0% +because people thought it was a great +idea to put it on Amazon Mechanical Turk + + align:start position:0% +idea to put it on Amazon Mechanical Turk + + + align:start position:0% +idea to put it on Amazon Mechanical Turk +and ask people a lot of questions to see + + align:start position:0% +and ask people a lot of questions to see + + + align:start position:0% +and ask people a lot of questions to see +what it correlates with everybody knows + + align:start position:0% +what it correlates with everybody knows + + + align:start position:0% +what it correlates with everybody knows +about the ball and bat problem on Amazon + + align:start position:0% +about the ball and bat problem on Amazon + + + align:start position:0% +about the ball and bat problem on Amazon +Mechanical Turk everybody okay don't + + align:start position:0% +Mechanical Turk everybody okay don't + + + align:start position:0% +Mechanical Turk everybody okay don't +think that you're being unique don't + + align:start position:0% +think that you're being unique don't + + + align:start position:0% +think that you're being unique don't +think don't ask them the widget problem + + align:start position:0% +think don't ask them the widget problem + + + align:start position:0% +think don't ask them the widget problem +but asking the the lilypad problem they + + align:start position:0% +but asking the the lilypad problem they + + + align:start position:0% +but asking the the lilypad problem they +all know about it and here it's no + + align:start position:0% +all know about it and here it's no + + + align:start position:0% +all know about it and here it's no +problem for intuitive you know being + + align:start position:0% +problem for intuitive you know being + + + align:start position:0% +problem for intuitive you know being +satiated and things like that even if + + align:start position:0% +satiated and things like that even if + + + align:start position:0% +satiated and things like that even if +they want to right I said before like + + align:start position:0% +they want to right I said before like + + + align:start position:0% +they want to right I said before like +they want to tell you what the thing is + + align:start position:0% +they want to tell you what the thing is + + + align:start position:0% +they want to tell you what the thing is +they just don't have the gutter sponsz + + align:start position:0% +they just don't have the gutter sponsz + + + align:start position:0% +they just don't have the gutter sponsz +anymore + + align:start position:0% +anymore + + + align:start position:0% +anymore +here they just know it right the reason + + align:start position:0% +here they just know it right the reason + + + align:start position:0% +here they just know it right the reason +most of you answered or those of you who + + align:start position:0% +most of you answered or those of you who + + + align:start position:0% +most of you answered or those of you who +knew about it said ha ha 5 cents I know + + align:start position:0% +knew about it said ha ha 5 cents I know + + + align:start position:0% +knew about it said ha ha 5 cents I know +that one I've sold it before people on + + align:start position:0% +that one I've sold it before people on + + + align:start position:0% +that one I've sold it before people on +Mechanical Turk know that too and that + + align:start position:0% +Mechanical Turk know that too and that + + + align:start position:0% +Mechanical Turk know that too and that +sort of destroyed any sort of measure it + + align:start position:0% +sort of destroyed any sort of measure it + + + align:start position:0% +sort of destroyed any sort of measure it +had for whatever the heck it was trying + + align:start position:0% +had for whatever the heck it was trying + + + align:start position:0% +had for whatever the heck it was trying +to measure okay in general there's sort + + align:start position:0% +to measure okay in general there's sort + + + align:start position:0% +to measure okay in general there's sort +of this growing sense that since 2010 + + align:start position:0% +of this growing sense that since 2010 + + + align:start position:0% +of this growing sense that since 2010 +were people world people have been + + align:start position:0% +were people world people have been + + + align:start position:0% +were people world people have been +trying to make Amazon Mechanical Turk + + align:start position:0% +trying to make Amazon Mechanical Turk + + + align:start position:0% +trying to make Amazon Mechanical Turk +more popular for a few years it feels + + align:start position:0% +more popular for a few years it feels + + + align:start position:0% +more popular for a few years it feels +almost like an over exploited resource a + + align:start position:0% +almost like an over exploited resource a + + + align:start position:0% +almost like an over exploited resource a +little bit right like you have this + + align:start position:0% +little bit right like you have this + + + align:start position:0% +little bit right like you have this +tribe which doesn't know about numbers + + align:start position:0% +tribe which doesn't know about numbers + + + align:start position:0% +tribe which doesn't know about numbers +let's all go and study them and ask them + + align:start position:0% +let's all go and study them and ask them + + + align:start position:0% +let's all go and study them and ask them +a billion questions and the reason they + + align:start position:0% +a billion questions and the reason they + + + align:start position:0% +a billion questions and the reason they +don't know about a number is because + + align:start position:0% +don't know about a number is because + + + align:start position:0% +don't know about a number is because +they don't know English and by the time + + align:start position:0% +they don't know English and by the time + + + align:start position:0% +they don't know English and by the time +we were done with them they will know + + align:start position:0% +we were done with them they will know + + + align:start position:0% +we were done with them they will know +English and the one thing they'll know + + align:start position:0% +English and the one thing they'll know + + + align:start position:0% +English and the one thing they'll know +in English is how to count to ten + + align:start position:0% +in English is how to count to ten + + + align:start position:0% +in English is how to count to ten +because we've asked them all these + + align:start position:0% +because we've asked them all these + + + align:start position:0% +because we've asked them all these +questions and one Mechanical Turk feels + + align:start position:0% +questions and one Mechanical Turk feels + + + align:start position:0% +questions and one Mechanical Turk feels +a little bit like this overexploited of + + align:start position:0% +a little bit like this overexploited of + + + align:start position:0% +a little bit like this overexploited of +resources at sometimes these are been + + align:start position:0% +resources at sometimes these are been + + + align:start position:0% +resources at sometimes these are been +more concerns for you as a requester + + align:start position:0% +more concerns for you as a requester + + + align:start position:0% +more concerns for you as a requester +working on Amazon Mechanical Turk things + + align:start position:0% +working on Amazon Mechanical Turk things + + + align:start position:0% +working on Amazon Mechanical Turk things +to sort of keep in mind and watch out + + align:start position:0% +to sort of keep in mind and watch out + + + align:start position:0% +to sort of keep in mind and watch out +for here are some concerns for people on + + align:start position:0% +for here are some concerns for people on + + + align:start position:0% +for here are some concerns for people on +Mechanical Turk that you can try to + + align:start position:0% +Mechanical Turk that you can try to + + + align:start position:0% +Mechanical Turk that you can try to +alleviate and these are sort of things + + align:start position:0% +alleviate and these are sort of things + + + align:start position:0% +alleviate and these are sort of things +about you know I've already mentioned + + align:start position:0% +about you know I've already mentioned + + + align:start position:0% +about you know I've already mentioned +sort of two of them about low pay and + + align:start position:0% +sort of two of them about low pay and + + + align:start position:0% +sort of two of them about low pay and +rejecting people for no good reason and + + align:start position:0% +rejecting people for no good reason and + + + align:start position:0% +rejecting people for no good reason and +things like that one more thing I want + + align:start position:0% +things like that one more thing I want + + + align:start position:0% +things like that one more thing I want +to point out is this this thing about no + + align:start position:0% +to point out is this this thing about no + + + align:start position:0% +to point out is this this thing about no +debriefing when people come into the lab + + align:start position:0% +debriefing when people come into the lab + + + align:start position:0% +debriefing when people come into the lab +you can tell them why they were in this + + align:start position:0% +you can tell them why they were in this + + + align:start position:0% +you can tell them why they were in this +study right that's a basic part of the + + align:start position:0% +study right that's a basic part of the + + + align:start position:0% +study right that's a basic part of the +protocol of psychology when people on + + align:start position:0% +protocol of psychology when people on + + + align:start position:0% +protocol of psychology when people on +Amazon Mechanical Turk it's a good thing + + align:start position:0% +Amazon Mechanical Turk it's a good thing + + + align:start position:0% +Amazon Mechanical Turk it's a good thing +to put at the end the experiment why + + align:start position:0% +to put at the end the experiment why + + + align:start position:0% +to put at the end the experiment why +were you in this experiment if you have + + align:start position:0% +were you in this experiment if you have + + + align:start position:0% +were you in this experiment if you have +such a thing and you're running an + + align:start position:0% +such a thing and you're running an + + + align:start position:0% +such a thing and you're running an +experiment people might drop out in the + + align:start position:0% +experiment people might drop out in the + + + align:start position:0% +experiment people might drop out in the +middle might decide it's not for me + + align:start position:0% +middle might decide it's not for me + + + align:start position:0% +middle might decide it's not for me +actually I'm done and they never + + align:start position:0% +actually I'm done and they never + + + align:start position:0% +actually I'm done and they never +actually figure out what the point of + + align:start position:0% +actually figure out what the point of + + + align:start position:0% +actually figure out what the point of +the experiment was you might say well + + align:start position:0% +the experiment was you might say well + + + align:start position:0% +the experiment was you might say well +who cares but you might say well who + + align:start position:0% +who cares but you might say well who + + + align:start position:0% +who cares but you might say well who +cares two debriefing people in the lab + + align:start position:0% +cares two debriefing people in the lab + + + align:start position:0% +cares two debriefing people in the lab +if there's a reason for debriefing + + align:start position:0% +if there's a reason for debriefing + + + align:start position:0% +if there's a reason for debriefing +people in the lab there's probably a + + align:start position:0% +people in the lab there's probably a + + + align:start position:0% +people in the lab there's probably a +good reason for debriefing people on + + align:start position:0% +good reason for debriefing people on + + + align:start position:0% +good reason for debriefing people on +Mechanical Turk if they drop out before + + align:start position:0% +Mechanical Turk if they drop out before + + + align:start position:0% +Mechanical Turk if they drop out before +the debrief that's kind of a problem I + + align:start position:0% +the debrief that's kind of a problem I + + + align:start position:0% +the debrief that's kind of a problem I +don't have a good solution for it it's + + align:start position:0% +don't have a good solution for it it's + + + align:start position:0% +don't have a good solution for it it's +something to keep in mind there's also + + align:start position:0% +something to keep in mind there's also + + + align:start position:0% +something to keep in mind there's also +the problem that you should keep in mind + + align:start position:0% +the problem that you should keep in mind + + + align:start position:0% +the problem that you should keep in mind +and report probably if it's a problem + + align:start position:0% +and report probably if it's a problem + + + align:start position:0% +and report probably if it's a problem +the amount of people who've dropped out + + align:start position:0% +the amount of people who've dropped out + + + align:start position:0% +the amount of people who've dropped out +in the middle because otherwise they can + + align:start position:0% +in the middle because otherwise they can + + + align:start position:0% +in the middle because otherwise they can +lead to all sorts of all sorts of small + + align:start position:0% +lead to all sorts of all sorts of small + + + align:start position:0% +lead to all sorts of all sorts of small +effects like if your task is really hard + + align:start position:0% +effects like if your task is really hard + + + align:start position:0% +effects like if your task is really hard +and a lot of people drop out you have + + align:start position:0% +and a lot of people drop out you have + + + align:start position:0% +and a lot of people drop out you have +like a 90% drop out and then you say ah + + align:start position:0% +like a 90% drop out and then you say ah + + + align:start position:0% +like a 90% drop out and then you say ah +people are brilliant at my task because + + align:start position:0% +people are brilliant at my task because + + + align:start position:0% +people are brilliant at my task because +the 10% who actually stuck through with + + align:start position:0% +the 10% who actually stuck through with + + + align:start position:0% +the 10% who actually stuck through with +it are the sort of crazy people are + + align:start position:0% +it are the sort of crazy people are + + + align:start position:0% +it are the sort of crazy people are +willing to do it that's actually really + + align:start position:0% +willing to do it that's actually really + + + align:start position:0% +willing to do it that's actually really +really skewed okay so keep in mind + + align:start position:0% +really skewed okay so keep in mind + + + align:start position:0% +really skewed okay so keep in mind +how should be low it should be like a + + align:start position:0% +how should be low it should be like a + + + align:start position:0% +how should be low it should be like a +few percent or something like that the + + align:start position:0% +few percent or something like that the + + + align:start position:0% +few percent or something like that the +flip fly by the way that no debriefing + + align:start position:0% +flip fly by the way that no debriefing + + + align:start position:0% +flip fly by the way that no debriefing +problem is a coercion coercion problem + + align:start position:0% +problem is a coercion coercion problem + + + align:start position:0% +problem is a coercion coercion problem +so when you bring people into the lab + + align:start position:0% +so when you bring people into the lab + + + align:start position:0% +so when you bring people into the lab +and you say you know dude this study you + + align:start position:0% +and you say you know dude this study you + + + align:start position:0% +and you say you know dude this study you +can stop at any time no problem at all + + align:start position:0% +can stop at any time no problem at all + + + align:start position:0% +can stop at any time no problem at all +let me shut this door and wait over here + + align:start position:0% +let me shut this door and wait over here + + + align:start position:0% +let me shut this door and wait over here +right there's sort of a slight feeling + + align:start position:0% +right there's sort of a slight feeling + + + align:start position:0% +right there's sort of a slight feeling +of coercion and even if the study is not + + align:start position:0% +of coercion and even if the study is not + + + align:start position:0% +of coercion and even if the study is not +something they really are enjoying doing + + align:start position:0% +something they really are enjoying doing + + + align:start position:0% +something they really are enjoying doing +they'll still do it because they feel + + align:start position:0% +they'll still do it because they feel + + + align:start position:0% +they'll still do it because they feel +pressured to that problem doesn't exist + + align:start position:0% +pressured to that problem doesn't exist + + + align:start position:0% +pressured to that problem doesn't exist +at least on Amazon Mechanical Turk I + + align:start position:0% +at least on Amazon Mechanical Turk I + + + align:start position:0% +at least on Amazon Mechanical Turk I +mean they're in it for the pay and + + align:start position:0% +mean they're in it for the pay and + + + align:start position:0% +mean they're in it for the pay and +there's some cost and all that but if + + align:start position:0% +there's some cost and all that but if + + + align:start position:0% +there's some cost and all that but if +they really don't want to do it if it + + align:start position:0% +they really don't want to do it if it + + + align:start position:0% +they really don't want to do it if it +offends them in some way they'll stop so + + align:start position:0% +offends them in some way they'll stop so + + + align:start position:0% +offends them in some way they'll stop so +that's actually a bonus some general + + align:start position:0% +that's actually a bonus some general + + + align:start position:0% +that's actually a bonus some general +tips let's see I think I'll have two + + align:start position:0% +tips let's see I think I'll have two + + + align:start position:0% +tips let's see I think I'll have two +more slides in the more reputable some + + align:start position:0% +more slides in the more reputable some + + + align:start position:0% +more slides in the more reputable some +general tips in general when you're + + align:start position:0% +general tips in general when you're + + + align:start position:0% +general tips in general when you're +thinking about your task the lower level + + align:start position:0% +thinking about your task the lower level + + + align:start position:0% +thinking about your task the lower level +it is the closer level it is to think + + align:start position:0% +it is the closer level it is to think + + + align:start position:0% +it is the closer level it is to think +about like with Stroop task okay let's + + align:start position:0% +about like with Stroop task okay let's + + + align:start position:0% +about like with Stroop task okay let's +put the strip tasks in one case and the + + align:start position:0% +put the strip tasks in one case and the + + + align:start position:0% +put the strip tasks in one case and the +question I actually asked you in another + + align:start position:0% +question I actually asked you in another + + + align:start position:0% +question I actually asked you in another +case ok the Stroop task is low level + + align:start position:0% +case ok the Stroop task is low level + + + align:start position:0% +case ok the Stroop task is low level +hard to beat even if you've seen it a + + align:start position:0% +hard to beat even if you've seen it a + + + align:start position:0% +hard to beat even if you've seen it a +million times you will still find that + + align:start position:0% +million times you will still find that + + + align:start position:0% +million times you will still find that +effect okay if your task is like that + + align:start position:0% +effect okay if your task is like that + + + align:start position:0% +effect okay if your task is like that +you should expect to replicate it if + + align:start position:0% +you should expect to replicate it if + + + align:start position:0% +you should expect to replicate it if +it's much more higher level the sort of + + align:start position:0% +it's much more higher level the sort of + + + align:start position:0% +it's much more higher level the sort of +thing that relies on then not having + + align:start position:0% +thing that relies on then not having + + + align:start position:0% +thing that relies on then not having +seen that before it's hard to replicate + + align:start position:0% +seen that before it's hard to replicate + + + align:start position:0% +seen that before it's hard to replicate +you want to make sure the people who see + + align:start position:0% +you want to make sure the people who see + + + align:start position:0% +you want to make sure the people who see +it have not seen it before if it's high + + align:start position:0% +it have not seen it before if it's high + + + align:start position:0% +it have not seen it before if it's high +level and relies on some sort of + + align:start position:0% +level and relies on some sort of + + + align:start position:0% +level and relies on some sort of +zeitgeist like what people think about + + align:start position:0% +zeitgeist like what people think about + + + align:start position:0% +zeitgeist like what people think about +AI right now in two years we'll find a + + align:start position:0% +AI right now in two years we'll find a + + + align:start position:0% +AI right now in two years we'll find a +different result okay I don't expect the + + align:start position:0% +different result okay I don't expect the + + + align:start position:0% +different result okay I don't expect the +thing that I put online today to + + align:start position:0% +thing that I put online today to + + + align:start position:0% +thing that I put online today to +replicate in some sense in two years + + align:start position:0% +replicate in some sense in two years + + + align:start position:0% +replicate in some sense in two years +half participants give comments at the + + align:start position:0% +half participants give comments at the + + + align:start position:0% +half participants give comments at the +end of your survey once they're done + + align:start position:0% +end of your survey once they're done + + + align:start position:0% +end of your survey once they're done +before the debriefing collect some + + align:start position:0% +before the debriefing collect some + + + align:start position:0% +before the debriefing collect some +demographics and leave them something + + align:start position:0% +demographics and leave them something + + + align:start position:0% +demographics and leave them something +optional you just say what did you think + + align:start position:0% +optional you just say what did you think + + + align:start position:0% +optional you just say what did you think +of this study do you have any comments + + align:start position:0% +of this study do you have any comments + + + align:start position:0% +of this study do you have any comments +or anything like that most of the time + + align:start position:0% +or anything like that most of the time + + + align:start position:0% +or anything like that most of the time +you won't get any comments after that + + align:start position:0% +you won't get any comments after that + + + align:start position:0% +you won't get any comments after that +the most likely thing is they'll say fun + + align:start position:0% +the most likely thing is they'll say fun + + + align:start position:0% +the most likely thing is they'll say fun +study thanks if you've done it correctly + + align:start position:0% +study thanks if you've done it correctly + + + align:start position:0% +study thanks if you've done it correctly +interesting stuff like that + + align:start position:0% +interesting stuff like that + + + align:start position:0% +interesting stuff like that +some studies we've done have been crazy + + align:start position:0% +some studies we've done have been crazy + + + align:start position:0% +some studies we've done have been crazy +and they're very you know they really + + align:start position:0% +and they're very you know they really + + + align:start position:0% +and they're very you know they really +like it and it's nice to get good + + align:start position:0% +like it and it's nice to get good + + + align:start position:0% +like it and it's nice to get good +feedback or they'll tell you something + + align:start position:0% +feedback or they'll tell you something + + + align:start position:0% +feedback or they'll tell you something +like that was really interesting could + + align:start position:0% +like that was really interesting could + + + align:start position:0% +like that was really interesting could +you tell me a bit more here's my email + + align:start position:0% +you tell me a bit more here's my email + + + align:start position:0% +you tell me a bit more here's my email +address or this button didn't work for + + align:start position:0% +address or this button didn't work for + + + align:start position:0% +address or this button didn't work for +me or I was actually a bit bothered by + + align:start position:0% +me or I was actually a bit bothered by + + + align:start position:0% +me or I was actually a bit bothered by +the fact that you said that you would + + align:start position:0% +the fact that you said that you would + + + align:start position:0% +the fact that you said that you would +kill the robot and things like that you + + align:start position:0% +kill the robot and things like that you + + + align:start position:0% +kill the robot and things like that you +know you were you ask them things like + + align:start position:0% +know you were you ask them things like + + + align:start position:0% +know you were you ask them things like +give them comments like why right you + + align:start position:0% +give them comments like why right you + + + align:start position:0% +give them comments like why right you +don't put that necessarily in your + + align:start position:0% +don't put that necessarily in your + + + align:start position:0% +don't put that necessarily in your +experiment but you tell them like you + + align:start position:0% +experiment but you tell them like you + + + align:start position:0% +experiment but you tell them like you +know do this do that make a decision why + + align:start position:0% +know do this do that make a decision why + + + align:start position:0% +know do this do that make a decision why +like the trolley problem + + align:start position:0% +like the trolley problem + + + align:start position:0% +like the trolley problem +okay it's the sort of thing that's not + + align:start position:0% +okay it's the sort of thing that's not + + + align:start position:0% +okay it's the sort of thing that's not +likely to be published immediately but + + align:start position:0% +likely to be published immediately but + + + align:start position:0% +likely to be published immediately but +it's definitely the sort of thing + + align:start position:0% +it's definitely the sort of thing + + + align:start position:0% +it's definitely the sort of thing +that'll help you think of where to take + + align:start position:0% +that'll help you think of where to take + + + align:start position:0% +that'll help you think of where to take +your experiment next it's very very + + align:start position:0% +your experiment next it's very very + + + align:start position:0% +your experiment next it's very very +important to communicate and that's what + + align:start position:0% +important to communicate and that's what + + + align:start position:0% +important to communicate and that's what +I mean by that is give them an email at + + align:start position:0% +I mean by that is give them an email at + + + align:start position:0% +I mean by that is give them an email at +the beginning to reach you in some way + + align:start position:0% +the beginning to reach you in some way + + + align:start position:0% +the beginning to reach you in some way +say like you know the in the consent + + align:start position:0% +say like you know the in the consent + + + align:start position:0% +say like you know the in the consent +statement you're doing this experiment + + align:start position:0% +statement you're doing this experiment + + + align:start position:0% +statement you're doing this experiment +you're doing it for X here's a way to + + align:start position:0% +you're doing it for X here's a way to + + + align:start position:0% +you're doing it for X here's a way to +reach X if you want to okay and what you + + align:start position:0% +reach X if you want to okay and what you + + + align:start position:0% +reach X if you want to okay and what you +could set up a bonus a bogus email in + + align:start position:0% +could set up a bonus a bogus email in + + + align:start position:0% +could set up a bonus a bogus email in +the sense of like Tomer at Mechanical + + align:start position:0% +the sense of like Tomer at Mechanical + + + align:start position:0% +the sense of like Tomer at Mechanical +Turk I personally give them my email at + + align:start position:0% +Turk I personally give them my email at + + + align:start position:0% +Turk I personally give them my email at +MIT yeah I do and make sure that you + + align:start position:0% +MIT yeah I do and make sure that you + + + align:start position:0% +MIT yeah I do and make sure that you +respond to their concerns and they will + + align:start position:0% +respond to their concerns and they will + + + align:start position:0% +respond to their concerns and they will +they will write to you especially + + align:start position:0% +they will write to you especially + + + align:start position:0% +they will write to you especially +something goes technically wrong they'll + + align:start position:0% +something goes technically wrong they'll + + + align:start position:0% +something goes technically wrong they'll +say like oh you know the screen did load + + align:start position:0% +say like oh you know the screen did load + + + align:start position:0% +say like oh you know the screen did load +for me I forgot to paste in the code + + align:start position:0% +for me I forgot to paste in the code + + + align:start position:0% +for me I forgot to paste in the code +that you wanted things like that or this + + align:start position:0% +that you wanted things like that or this + + + align:start position:0% +that you wanted things like that or this +doesn't work quite well write back to + + align:start position:0% +doesn't work quite well write back to + + + align:start position:0% +doesn't work quite well write back to +them explain what happened if they want + + align:start position:0% +them explain what happened if they want + + + align:start position:0% +them explain what happened if they want +to know what the studies about you + + align:start position:0% +to know what the studies about you + + + align:start position:0% +to know what the studies about you +should explain to them what the studies + + align:start position:0% +should explain to them what the studies + + + align:start position:0% +should explain to them what the studies +about you should do that for two reasons + + align:start position:0% +about you should do that for two reasons + + + align:start position:0% +about you should do that for two reasons +it feels silly to like mention this I'm + + align:start position:0% +it feels silly to like mention this I'm + + + align:start position:0% +it feels silly to like mention this I'm +sure you're all you know you've figured + + align:start position:0% +sure you're all you know you've figured + + + align:start position:0% +sure you're all you know you've figured +it out by yourselves but I'll mention it + + align:start position:0% +it out by yourselves but I'll mention it + + + align:start position:0% +it out by yourselves but I'll mention it +anyway just on the off-chance there's + + align:start position:0% +anyway just on the off-chance there's + + + align:start position:0% +anyway just on the off-chance there's +one person says oh yeah that's a good + + align:start position:0% +one person says oh yeah that's a good + + + align:start position:0% +one person says oh yeah that's a good +reason for two reasons one is that + + align:start position:0% +reason for two reasons one is that + + + align:start position:0% +reason for two reasons one is that +they'll like you a lot more okay these + + align:start position:0% +they'll like you a lot more okay these + + + align:start position:0% +they'll like you a lot more okay these +people they go to their own forums + + align:start position:0% +people they go to their own forums + + + align:start position:0% +people they go to their own forums +there's a lot of Mechanical Turk forums + + align:start position:0% +there's a lot of Mechanical Turk forums + + + align:start position:0% +there's a lot of Mechanical Turk forums +or there's hundreds of them and they + + align:start position:0% +or there's hundreds of them and they + + + align:start position:0% +or there's hundreds of them and they +tell each other what things they should + + align:start position:0% +tell each other what things they should + + + align:start position:0% +tell each other what things they should +do they do a good job of policing each + + align:start position:0% +do they do a good job of policing each + + + align:start position:0% +do they do a good job of policing each +other they're like they never they try + + align:start position:0% +other they're like they never they try + + + align:start position:0% +other they're like they never they try +never to post answers to things or like + + align:start position:0% +never to post answers to things or like + + + align:start position:0% +never to post answers to things or like +oh you can do this by answering this + + align:start position:0% +oh you can do this by answering this + + + align:start position:0% +oh you can do this by answering this +question no it's like they don't + + align:start position:0% +question no it's like they don't + + + align:start position:0% +question no it's like they don't +tolerate that because they know that we + + align:start position:0% +tolerate that because they know that we + + + align:start position:0% +tolerate that because they know that we +don't tolerate that you want them to + + align:start position:0% +don't tolerate that you want them to + + + align:start position:0% +don't tolerate that you want them to +like you in that sense you want to get + + align:start position:0% +like you in that sense you want to get + + + align:start position:0% +like you in that sense you want to get +good reviews on these things and one way + + align:start position:0% +good reviews on these things and one way + + + align:start position:0% +good reviews on these things and one way +to get to garner good favors to + + align:start position:0% +to get to garner good favors to + + + align:start position:0% +to get to garner good favors to +communicate the other reason is because + + align:start position:0% +communicate the other reason is because + + + align:start position:0% +communicate the other reason is because +it's just a good idea these are people + + align:start position:0% +it's just a good idea these are people + + + align:start position:0% +it's just a good idea these are people +in the public right you wouldn't think + + align:start position:0% +in the public right you wouldn't think + + + align:start position:0% +in the public right you wouldn't think +about not answering a question of + + align:start position:0% +about not answering a question of + + + align:start position:0% +about not answering a question of +someone who came into the lab and asked + + align:start position:0% +someone who came into the lab and asked + + + align:start position:0% +someone who came into the lab and asked +you something right keep in mind there's + + align:start position:0% +you something right keep in mind there's + + + align:start position:0% +you something right keep in mind there's +a real people behind the screen make + + align:start position:0% +a real people behind the screen make + + + align:start position:0% +a real people behind the screen make +sure that you would treat them as real + + align:start position:0% +sure that you would treat them as real + + + align:start position:0% +sure that you would treat them as real +people I don't mean I sound like I'm + + align:start position:0% +people I don't mean I sound like I'm + + + align:start position:0% +people I don't mean I sound like I'm +berating you or something like that you + + align:start position:0% +berating you or something like that you + + + align:start position:0% +berating you or something like that you +guys have not been communicating and + + align:start position:0% +guys have not been communicating and + + + align:start position:0% +guys have not been communicating and +it's awful no that's not the point I'm + + align:start position:0% +it's awful no that's not the point I'm + + + align:start position:0% +it's awful no that's not the point I'm +sure you all mean to do that I'm just + + align:start position:0% +sure you all mean to do that I'm just + + + align:start position:0% +sure you all mean to do that I'm just +trying to emphasize it like I said + + align:start position:0% +trying to emphasize it like I said + + + align:start position:0% +trying to emphasize it like I said +before don't reject unless it's an + + align:start position:0% +before don't reject unless it's an + + + align:start position:0% +before don't reject unless it's an +extreme situation also decide ahead of + + align:start position:0% +extreme situation also decide ahead of + + + align:start position:0% +extreme situation also decide ahead of +time how you're going to reject okay you + + align:start position:0% +time how you're going to reject okay you + + + align:start position:0% +time how you're going to reject okay you +decide ahead of time on a catch question + + align:start position:0% +decide ahead of time on a catch question + + + align:start position:0% +decide ahead of time on a catch question +something I'll get to in a second and + + align:start position:0% +something I'll get to in a second and + + + align:start position:0% +something I'll get to in a second and +say I'm going to reject people if they + + align:start position:0% +say I'm going to reject people if they + + + align:start position:0% +say I'm going to reject people if they +do this and stick to it because + + align:start position:0% +do this and stick to it because + + + align:start position:0% +do this and stick to it because +otherwise if you don't do that then when + + align:start position:0% +otherwise if you don't do that then when + + + align:start position:0% +otherwise if you don't do that then when +it comes time to actually try and write + + align:start position:0% +it comes time to actually try and write + + + align:start position:0% +it comes time to actually try and write +a paper you'll say well + + align:start position:0% +a paper you'll say well + + + align:start position:0% +a paper you'll say well +I think I'll try throwing out all the + + align:start position:0% +I think I'll try throwing out all the + + + align:start position:0% +I think I'll try throwing out all the +people that did it in under 20 seconds + + align:start position:0% +people that did it in under 20 seconds + + + align:start position:0% +people that did it in under 20 seconds +the other thing that we're paying + + align:start position:0% +the other thing that we're paying + + + align:start position:0% +the other thing that we're paying +attention that much maybe 30 seconds + + align:start position:0% +attention that much maybe 30 seconds + + + align:start position:0% +attention that much maybe 30 seconds +yeah this toss we only take 40 select + + align:start position:0% +yeah this toss we only take 40 select + + + align:start position:0% +yeah this toss we only take 40 select +you got the point right like decide + + align:start position:0% +you got the point right like decide + + + align:start position:0% +you got the point right like decide +ahead of time on the rejection criteria + + align:start position:0% +ahead of time on the rejection criteria + + + align:start position:0% +ahead of time on the rejection criteria +have good catch questions this is good + + align:start position:0% +have good catch questions this is good + + + align:start position:0% +have good catch questions this is good +both for you know knowing who to reject + + align:start position:0% +both for you know knowing who to reject + + + align:start position:0% +both for you know knowing who to reject +and making sure that they're paying + + align:start position:0% +and making sure that they're paying + + + align:start position:0% +and making sure that they're paying +attention + + align:start position:0% +attention + + + align:start position:0% +attention +catch questions are the sort of thing + + align:start position:0% +catch questions are the sort of thing + + + align:start position:0% +catch questions are the sort of thing +that you would put in the middle of your + + align:start position:0% +that you would put in the middle of your + + + align:start position:0% +that you would put in the middle of your +survey at the end of your survey that + + align:start position:0% +survey at the end of your survey that + + + align:start position:0% +survey at the end of your survey that +started the survey just to make sure + + align:start position:0% +started the survey just to make sure + + + align:start position:0% +started the survey just to make sure +that they are paying attention ideally + + align:start position:0% +that they are paying attention ideally + + + align:start position:0% +that they are paying attention ideally +would be also that they have actually + + align:start position:0% +would be also that they have actually + + + align:start position:0% +would be also that they have actually +read the instructions and know what + + align:start position:0% +read the instructions and know what + + + align:start position:0% +read the instructions and know what +they're supposed to be doing okay so + + align:start position:0% +they're supposed to be doing okay so + + + align:start position:0% +they're supposed to be doing okay so +sometimes even if they're paying + + align:start position:0% +sometimes even if they're paying + + + align:start position:0% +sometimes even if they're paying +attention they didn't get the + + align:start position:0% +attention they didn't get the + + + align:start position:0% +attention they didn't get the +instructions or something like that + + align:start position:0% +instructions or something like that + + + align:start position:0% +instructions or something like that +there's a bunch of different ways of + + align:start position:0% +there's a bunch of different ways of + + + align:start position:0% +there's a bunch of different ways of +doing this one way of doing it you know + + align:start position:0% +doing this one way of doing it you know + + + align:start position:0% +doing this one way of doing it you know +that I'm sure you guys can come up with + + align:start position:0% +that I'm sure you guys can come up with + + + align:start position:0% +that I'm sure you guys can come up with +your own ways I'm just giving you some + + align:start position:0% +your own ways I'm just giving you some + + + align:start position:0% +your own ways I'm just giving you some +examples of this stuff the people I know + + align:start position:0% +examples of this stuff the people I know + + + align:start position:0% +examples of this stuff the people I know +have done Toby for example that you've + + align:start position:0% +have done Toby for example that you've + + + align:start position:0% +have done Toby for example that you've +seen doing some counterfactual stuff + + align:start position:0% +seen doing some counterfactual stuff + + + align:start position:0% +seen doing some counterfactual stuff +maybe he just gives people a screen with + + align:start position:0% +maybe he just gives people a screen with + + + align:start position:0% +maybe he just gives people a screen with +the instructions and asked him some + + align:start position:0% +the instructions and asked him some + + + align:start position:0% +the instructions and asked him some +questions and until they get the + + align:start position:0% +questions and until they get the + + + align:start position:0% +questions and until they get the +question right they don't move on to the + + align:start position:0% +question right they don't move on to the + + + align:start position:0% +question right they don't move on to the +next screen okay so he doesn't reject + + align:start position:0% +next screen okay so he doesn't reject + + + align:start position:0% +next screen okay so he doesn't reject +him later + + align:start position:0% +him later + + + align:start position:0% +him later +he just says in order to pass to the + + align:start position:0% +he just says in order to pass to the + + + align:start position:0% +he just says in order to pass to the +next screen you have to answer this + + align:start position:0% +next screen you have to answer this + + + align:start position:0% +next screen you have to answer this +question correctly and he has some way + + align:start position:0% +question correctly and he has some way + + + align:start position:0% +question correctly and he has some way +of like checking that and that's been + + align:start position:0% +of like checking that and that's been + + + align:start position:0% +of like checking that and that's been +really good like once he implemented + + align:start position:0% +really good like once he implemented + + + align:start position:0% +really good like once he implemented +that the data is much much better and + + align:start position:0% +that the data is much much better and + + + align:start position:0% +that the data is much much better and +cleaner here's the sort of catch + + align:start position:0% +cleaner here's the sort of catch + + + align:start position:0% +cleaner here's the sort of catch +questions you don't necessarily want to + + align:start position:0% +questions you don't necessarily want to + + + align:start position:0% +questions you don't necessarily want to +do it's they're very popular you don't + + align:start position:0% +do it's they're very popular you don't + + + align:start position:0% +do it's they're very popular you don't +necessarily want to do them they're + + align:start position:0% +necessarily want to do them they're + + + align:start position:0% +necessarily want to do them they're +things like have you ever had a fatal + + align:start position:0% +things like have you ever had a fatal + + + align:start position:0% +things like have you ever had a fatal +heart attack and the answer is of course + + align:start position:0% +heart attack and the answer is of course + + + align:start position:0% +heart attack and the answer is of course +no right have you ever eaten a sandwich + + align:start position:0% +no right have you ever eaten a sandwich + + + align:start position:0% +no right have you ever eaten a sandwich +on Mars it's a sort of thing that like + + align:start position:0% +on Mars it's a sort of thing that like + + + align:start position:0% +on Mars it's a sort of thing that like +you're trying to catch people that are + + align:start position:0% +you're trying to catch people that are + + + align:start position:0% +you're trying to catch people that are +going through it very quickly and I'm + + align:start position:0% +going through it very quickly and I'm + + + align:start position:0% +going through it very quickly and I'm +just marking things randomly one of the + + align:start position:0% +just marking things randomly one of the + + + align:start position:0% +just marking things randomly one of the +reasons you don't want to do that is + + align:start position:0% +reasons you don't want to do that is + + + align:start position:0% +reasons you don't want to do that is +because even if they're answering + + align:start position:0% +because even if they're answering + + + align:start position:0% +because even if they're answering +randomly yes or no you'll still miss 50% + + align:start position:0% +randomly yes or no you'll still miss 50% + + + align:start position:0% +randomly yes or no you'll still miss 50% +we just got it right by you know by + + align:start position:0% +we just got it right by you know by + + + align:start position:0% +we just got it right by you know by +error the other reason is that the + + align:start position:0% +error the other reason is that the + + + align:start position:0% +error the other reason is that the +standard stuff I mean I'm sure you guys + + align:start position:0% +standard stuff I mean I'm sure you guys + + + align:start position:0% +standard stuff I mean I'm sure you guys +could come up with something but there's + + align:start position:0% +could come up with something but there's + + + align:start position:0% +could come up with something but there's +a lot of standard stuff like the two + + align:start position:0% +a lot of standard stuff like the two + + + align:start position:0% +a lot of standard stuff like the two +examples I just gave you the Martian the + + align:start position:0% +examples I just gave you the Martian the + + + align:start position:0% +examples I just gave you the Martian the +fatal heart attack this is stuff that + + align:start position:0% +fatal heart attack this is stuff that + + + align:start position:0% +fatal heart attack this is stuff that +gets used over and over and over again + + align:start position:0% +gets used over and over and over again + + + align:start position:0% +gets used over and over and over again +and they sort of just know it + + align:start position:0% +and they sort of just know it + + + align:start position:0% +and they sort of just know it +okay one of them said like any time I + + align:start position:0% +okay one of them said like any time I + + + align:start position:0% +okay one of them said like any time I +see that the person I told you before + + align:start position:0% +see that the person I told you before + + + align:start position:0% +see that the person I told you before +was like juggling kids and trying to + + align:start position:0% +was like juggling kids and trying to + + + align:start position:0% +was like juggling kids and trying to +answer at the same time oh yeah whenever + + align:start position:0% +answer at the same time oh yeah whenever + + + align:start position:0% +answer at the same time oh yeah whenever +I see the word vacuum I know it's time + + align:start position:0% +I see the word vacuum I know it's time + + + align:start position:0% +I see the word vacuum I know it's time +for an attention check because it's + + align:start position:0% +for an attention check because it's + + + align:start position:0% +for an attention check because it's +going to be like have you ever eaten a + + align:start position:0% +going to be like have you ever eaten a + + + align:start position:0% +going to be like have you ever eaten a +sandwich in a vacuum or like something + + align:start position:0% +sandwich in a vacuum or like something + + + align:start position:0% +sandwich in a vacuum or like something +like that but whenever see documents + + align:start position:0% +like that but whenever see documents + + + align:start position:0% +like that but whenever see documents +like it's obviously an attention check + + align:start position:0% +like it's obviously an attention check + + + align:start position:0% +like it's obviously an attention check +you don't want to do that ideally you + + align:start position:0% +you don't want to do that ideally you + + + align:start position:0% +you don't want to do that ideally you +want to have something that relates to + + align:start position:0% +want to have something that relates to + + + align:start position:0% +want to have something that relates to +the task okay so in one our one of our + + align:start position:0% +the task okay so in one our one of our + + + align:start position:0% +the task okay so in one our one of our +examples we were doing some sort of + + align:start position:0% +examples we were doing some sort of + + + align:start position:0% +examples we were doing some sort of +Turing task and we just wanted to say + + align:start position:0% +Turing task and we just wanted to say + + + align:start position:0% +Turing task and we just wanted to say +like here + + align:start position:0% +like here + + + align:start position:0% +like here +complete the following sentence you were + + align:start position:0% +complete the following sentence you were + + + align:start position:0% +complete the following sentence you were +playing the game against a and then it's + + align:start position:0% +playing the game against a and then it's + + + align:start position:0% +playing the game against a and then it's +an open text box + + align:start position:0% +an open text box + + + align:start position:0% +an open text box +okay some of these people have like + + align:start position:0% +okay some of these people have like + + + align:start position:0% +okay some of these people have like +automatic robots that fill it in so + + align:start position:0% +automatic robots that fill it in so + + + align:start position:0% +automatic robots that fill it in so +though you do something like thanks or + + align:start position:0% +though you do something like thanks or + + + align:start position:0% +though you do something like thanks or +yes or something like that then just + + align:start position:0% +yes or something like that then just + + + align:start position:0% +yes or something like that then just +hope that yes will match right but here + + align:start position:0% +hope that yes will match right but here + + + align:start position:0% +hope that yes will match right but here +the correct answer was robot you were + + align:start position:0% +the correct answer was robot you were + + + align:start position:0% +the correct answer was robot you were +playing the game against a robot or + + align:start position:0% +playing the game against a robot or + + + align:start position:0% +playing the game against a robot or +against a human or something like that + + align:start position:0% +against a human or something like that + + + align:start position:0% +against a human or something like that +do people get that example I can okay + + align:start position:0% +do people get that example I can okay + + + align:start position:0% +do people get that example I can okay +so ideally the good catch question is an + + align:start position:0% +so ideally the good catch question is an + + + align:start position:0% +so ideally the good catch question is an +open field something that's not just you + + align:start position:0% +open field something that's not just you + + + align:start position:0% +open field something that's not just you +can click and get right by mistake and + + align:start position:0% +can click and get right by mistake and + + + align:start position:0% +can click and get right by mistake and +relate something to the instructions + + align:start position:0% +relate something to the instructions + + + align:start position:0% +relate something to the instructions +that you were giving this is not a tip + + align:start position:0% +that you were giving this is not a tip + + + align:start position:0% +that you were giving this is not a tip +this is something you should do again + + align:start position:0% +this is something you should do again + + + align:start position:0% +this is something you should do again +it's it's trivial you'll have to do it + + align:start position:0% +it's it's trivial you'll have to do it + + + align:start position:0% +it's it's trivial you'll have to do it +if you're thinking of running it in your + + align:start position:0% +if you're thinking of running it in your + + + align:start position:0% +if you're thinking of running it in your +own university and your university is + + align:start position:0% +own university and your university is + + + align:start position:0% +own university and your university is +never done Mechanical Turk before get + + align:start position:0% +never done Mechanical Turk before get + + + align:start position:0% +never done Mechanical Turk before get +IRB approval specifically from + + align:start position:0% +IRB approval specifically from + + + align:start position:0% +IRB approval specifically from +Mechanical Turk so just make sure you + + align:start position:0% +Mechanical Turk so just make sure you + + + align:start position:0% +Mechanical Turk so just make sure you +get IRB approval make sure you get + + align:start position:0% +get IRB approval make sure you get + + + align:start position:0% +get IRB approval make sure you get +informed consent at the beginning of + + align:start position:0% +informed consent at the beginning of + + + align:start position:0% +informed consent at the beginning of +your study say you like we're going to + + align:start position:0% +your study say you like we're going to + + + align:start position:0% +your study say you like we're going to +be doing this if it's okay click on this + + align:start position:0% +be doing this if it's okay click on this + + + align:start position:0% +be doing this if it's okay click on this +button that says I agree + + align:start position:0% +button that says I agree + + + align:start position:0% +button that says I agree +usually the IRB will force you to do + + align:start position:0% +usually the IRB will force you to do + + + align:start position:0% +usually the IRB will force you to do +that anyway and as I said I think okay I + + align:start position:0% +that anyway and as I said I think okay I + + + align:start position:0% +that anyway and as I said I think okay I +just keep going back to that okay + + align:start position:0% +just keep going back to that okay + + + align:start position:0% +just keep going back to that okay +there's various helpful tools for + + align:start position:0% +there's various helpful tools for + + + align:start position:0% +there's various helpful tools for +running things for running experiments + + align:start position:0% +running things for running experiments + + + align:start position:0% +running things for running experiments +if any of you are interested in this + + align:start position:0% +if any of you are interested in this + + + align:start position:0% +if any of you are interested in this +reading more about it much more in-depth + + align:start position:0% +reading more about it much more in-depth + + + align:start position:0% +reading more about it much more in-depth +how to actually run an experiment things + + align:start position:0% +how to actually run an experiment things + + + align:start position:0% +how to actually run an experiment things +like that come talk to me afterwards or + + align:start position:0% +like that come talk to me afterwards or + + + align:start position:0% +like that come talk to me afterwards or +look at Todd Lucas's website the other + + align:start position:0% +look at Todd Lucas's website the other + + + align:start position:0% +look at Todd Lucas's website the other +websites that you should take out these + + align:start position:0% +websites that you should take out these + + + align:start position:0% +websites that you should take out these +are the forms you should probably know + + align:start position:0% +are the forms you should probably know + + + align:start position:0% +are the forms you should probably know +about your carnation and tour grind and + + align:start position:0% +about your carnation and tour grind and + + + align:start position:0% +about your carnation and tour grind and +Terk optic on these are useful both to + + align:start position:0% +Terk optic on these are useful both to + + + align:start position:0% +Terk optic on these are useful both to +get a sense of how your task is doing + + align:start position:0% +get a sense of how your task is doing + + + align:start position:0% +get a sense of how your task is doing +are people sort of you know responding + + align:start position:0% +are people sort of you know responding + + + align:start position:0% +are people sort of you know responding +to it saying something about it it's + + align:start position:0% +to it saying something about it it's + + + align:start position:0% +to it saying something about it it's +also a good place to publicize your + + align:start position:0% +also a good place to publicize your + + + align:start position:0% +also a good place to publicize your +study if I need 300 participants within + + align:start position:0% +study if I need 300 participants within + + + align:start position:0% +study if I need 300 participants within +two hours I can put it on Turek and hope + + align:start position:0% +two hours I can put it on Turek and hope + + + align:start position:0% +two hours I can put it on Turek and hope +the pay is enough or I can put a limit + + align:start position:0% +the pay is enough or I can put a limit + + + align:start position:0% +the pay is enough or I can put a limit +or grind people there have liked our + + align:start position:0% +or grind people there have liked our + + + align:start position:0% +or grind people there have liked our +tasks before and they'll give you a + + align:start position:0% +tasks before and they'll give you a + + + align:start position:0% +tasks before and they'll give you a +thumbs up and you'll get 200 people + + align:start position:0% +thumbs up and you'll get 200 people + + + align:start position:0% +thumbs up and you'll get 200 people +within an hour just because they know + + align:start position:0% +within an hour just because they know + + + align:start position:0% +within an hour just because they know +about you and they know that you're an + + align:start position:0% +about you and they know that you're an + + + align:start position:0% +about you and they know that you're an +okay person and you communicate okay so + + align:start position:0% +okay person and you communicate okay so + + + align:start position:0% +okay person and you communicate okay so +it's a good part it's a good practice to + + align:start position:0% +it's a good part it's a good practice to + + + align:start position:0% +it's a good part it's a good practice to +get my user name on one of these things + + align:start position:0% +get my user name on one of these things + + + align:start position:0% +get my user name on one of these things +or both of them when you run an actual + + align:start position:0% +or both of them when you run an actual + + + align:start position:0% +or both of them when you run an actual +wide scale experiment explain what + + align:start position:0% +wide scale experiment explain what + + + align:start position:0% +wide scale experiment explain what +you're doing put it on there be willing + + align:start position:0% +you're doing put it on there be willing + + + align:start position:0% +you're doing put it on there be willing +to answer questions + + align:start position:0% +to answer questions + + + align:start position:0% +to answer questions +Terk opticon is the usual thing that + + align:start position:0% +Terk opticon is the usual thing that + + + align:start position:0% +Terk opticon is the usual thing that +will then be used to this is what one of + + align:start position:0% +will then be used to this is what one of + + + align:start position:0% +will then be used to this is what one of +these forums looks like by the way + + align:start position:0% +these forums looks like by the way + + + align:start position:0% +these forums looks like by the way +they're like you know oh it's terrible + + align:start position:0% +they're like you know oh it's terrible + + + align:start position:0% +they're like you know oh it's terrible +it's Tuesday what should + + align:start position:0% +it's Tuesday what should + + + align:start position:0% +it's Tuesday what should +do today here's how much I've done today + + align:start position:0% +do today here's how much I've done today + + + align:start position:0% +do today here's how much I've done today +somebody says I didn't see this posted + + align:start position:0% +somebody says I didn't see this posted + + + align:start position:0% +somebody says I didn't see this posted +anywhere very interested very + + align:start position:0% +anywhere very interested very + + + align:start position:0% +anywhere very interested very +interesting to those of you who want to + + align:start position:0% +interesting to those of you who want to + + + align:start position:0% +interesting to those of you who want to +do 3d printing and there's like the + + align:start position:0% +do 3d printing and there's like the + + + align:start position:0% +do 3d printing and there's like the +title of the experiment and the + + align:start position:0% +title of the experiment and the + + + align:start position:0% +title of the experiment and the +description of it and people can just + + align:start position:0% +description of it and people can just + + + align:start position:0% +description of it and people can just +click directly from there to the + + align:start position:0% +click directly from there to the + + + align:start position:0% +click directly from there to the +experiment usually the experiment that + + align:start position:0% +experiment usually the experiment that + + + align:start position:0% +experiment usually the experiment that +they post on the forums looks something + + align:start position:0% +they post on the forums looks something + + + align:start position:0% +they post on the forums looks something +like this + + align:start position:0% +like this + + + align:start position:0% +like this +they're getting these numbers off of + + align:start position:0% +they're getting these numbers off of + + + align:start position:0% +they're getting these numbers off of +that last website but I just mentioned + + align:start position:0% +that last website but I just mentioned + + + align:start position:0% +that last website but I just mentioned +Turk optical so usually when people want + + align:start position:0% +Turk optical so usually when people want + + + align:start position:0% +Turk optical so usually when people want +to rate you on Mechanical Turk they're + + align:start position:0% +to rate you on Mechanical Turk they're + + + align:start position:0% +to rate you on Mechanical Turk they're +not going to complain to Amazon because + + align:start position:0% +not going to complain to Amazon because + + + align:start position:0% +not going to complain to Amazon because +Amazon's not going to do anything about + + align:start position:0% +Amazon's not going to do anything about + + + align:start position:0% +Amazon's not going to do anything about +it like I said before requesters have a + + align:start position:0% +it like I said before requesters have a + + + align:start position:0% +it like I said before requesters have a +lot of power and Amazon doesn't bother + + align:start position:0% +lot of power and Amazon doesn't bother + + + align:start position:0% +lot of power and Amazon doesn't bother +to arbitrate usually so one of the ways + + align:start position:0% +to arbitrate usually so one of the ways + + + align:start position:0% +to arbitrate usually so one of the ways +that they do have of either rewarding or + + align:start position:0% +that they do have of either rewarding or + + + align:start position:0% +that they do have of either rewarding or +punishing you is to go to Turk optical + + align:start position:0% +punishing you is to go to Turk optical + + + align:start position:0% +punishing you is to go to Turk optical +and give you a rating for communication + + align:start position:0% +and give you a rating for communication + + + align:start position:0% +and give you a rating for communication +generosity fairness and promptness and + + align:start position:0% +generosity fairness and promptness and + + + align:start position:0% +generosity fairness and promptness and +those numbers will then be used on most + + align:start position:0% +those numbers will then be used on most + + + align:start position:0% +those numbers will then be used on most +of the forums when you publish your + + align:start position:0% +of the forums when you publish your + + + align:start position:0% +of the forums when you publish your +tests people can see like these guys + + align:start position:0% +tests people can see like these guys + + + align:start position:0% +tests people can see like these guys +have actually cheated people before or + + align:start position:0% +have actually cheated people before or + + + align:start position:0% +have actually cheated people before or +something like that so you can go once + + align:start position:0% +something like that so you can go once + + + align:start position:0% +something like that so you can go once +you've registered go to Turk optical and + + align:start position:0% +you've registered go to Turk optical and + + + align:start position:0% +you've registered go to Turk optical and +you can check out your own ratings and + + align:start position:0% +you can check out your own ratings and + + + align:start position:0% +you can check out your own ratings and +things like that so yeah in summary + + align:start position:0% +things like that so yeah in summary + + + align:start position:0% +things like that so yeah in summary +Mechanical Turk is a wonderful resource + + align:start position:0% +Mechanical Turk is a wonderful resource + + + align:start position:0% +Mechanical Turk is a wonderful resource +I hope I haven't scared you away from it + + align:start position:0% +I hope I haven't scared you away from it + + + align:start position:0% +I hope I haven't scared you away from it +those of you who are thinking about + + align:start position:0% +those of you who are thinking about + + + align:start position:0% +those of you who are thinking about +doing it it just it amplifies everything + + align:start position:0% +doing it it just it amplifies everything + + + align:start position:0% +doing it it just it amplifies everything +okay you can do a lot more a lot faster + + align:start position:0% +okay you can do a lot more a lot faster + + + align:start position:0% +okay you can do a lot more a lot faster +but it doesn't get rid of concerns it + + align:start position:0% +but it doesn't get rid of concerns it + + + align:start position:0% +but it doesn't get rid of concerns it +amplifies those concerns so things like + + align:start position:0% +amplifies those concerns so things like + + + align:start position:0% +amplifies those concerns so things like +ethical concerns and payment concerns + + align:start position:0% +ethical concerns and payment concerns + + + align:start position:0% +ethical concerns and payment concerns +and things like that the sort of same + + align:start position:0% +and things like that the sort of same + + + align:start position:0% +and things like that the sort of same +sort of concerns that you would have in + + align:start position:0% +sort of concerns that you would have in + + + align:start position:0% +sort of concerns that you would have in +the lab those are included there another + + align:start position:0% +the lab those are included there another + + + align:start position:0% +the lab those are included there another +magnifier magnified a hundredfold + + align:start position:0% +magnifier magnified a hundredfold + + + align:start position:0% +magnifier magnified a hundredfold +because you're recruiting a lot more + + align:start position:0% +because you're recruiting a lot more + + + align:start position:0% +because you're recruiting a lot more +people + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/pHOPafutFSo.txt b/pHOPafutFSo.txt new file mode 100644 index 0000000000000000000000000000000000000000..64f624c32059618160adda0c7b7a1f834ff96e63 --- /dev/null +++ b/pHOPafutFSo.txt @@ -0,0 +1,9067 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right we're going to get + + align:start position:0% +ocw.mit.edu all right we're going to get + + + align:start position:0% +ocw.mit.edu all right we're going to get +started here + + align:start position:0% +started here + + + align:start position:0% +started here +everyone and uh I know we have a lot + + align:start position:0% +everyone and uh I know we have a lot + + + align:start position:0% +everyone and uh I know we have a lot +going on here at the lab today and I'm + + align:start position:0% +going on here at the lab today and I'm + + + align:start position:0% +going on here at the lab today and I'm +very pleased that those of you decided + + align:start position:0% +very pleased that those of you decided + + + align:start position:0% +very pleased that those of you decided +to choose us today over all the other + + align:start position:0% +to choose us today over all the other + + + align:start position:0% +to choose us today over all the other +things that are going on so that's + + align:start position:0% +things that are going on so that's + + + align:start position:0% +things that are going on so that's +that's great I'm very + + align:start position:0% +that's great I'm very + + + align:start position:0% +that's great I'm very +pleased um I wanted to say I've uh I + + align:start position:0% +pleased um I wanted to say I've uh I + + + align:start position:0% +pleased um I wanted to say I've uh I +think I provided feedback to everyone + + align:start position:0% +think I provided feedback to everyone + + + align:start position:0% +think I provided feedback to everyone +who submitted their earlier first + + align:start position:0% +who submitted their earlier first + + + align:start position:0% +who submitted their earlier first +homework um over the over the weekend + + align:start position:0% +homework um over the over the weekend + + + align:start position:0% +homework um over the over the weekend +and I was very impressed and pleased by + + align:start position:0% +and I was very impressed and pleased by + + + align:start position:0% +and I was very impressed and pleased by +those of you who did the homework I + + align:start position:0% +those of you who did the homework I + + + align:start position:0% +those of you who did the homework I +think you really embraced the spirit of + + align:start position:0% +think you really embraced the spirit of + + + align:start position:0% +think you really embraced the spirit of +the homework very well I know the + + align:start position:0% +the homework very well I know the + + + align:start position:0% +the homework very well I know the +homework that just happened is is one + + align:start position:0% +homework that just happened is is one + + + align:start position:0% +homework that just happened is is one +that kind of really Builds on that for + + align:start position:0% +that kind of really Builds on that for + + + align:start position:0% +that kind of really Builds on that for +those of you who didn't do the first one + + align:start position:0% +those of you who didn't do the first one + + + align:start position:0% +those of you who didn't do the first one +then you're kind of let out of left out + + align:start position:0% +then you're kind of let out of left out + + + align:start position:0% +then you're kind of let out of left out +of cold and but I would like to uh give + + align:start position:0% +of cold and but I would like to uh give + + + align:start position:0% +of cold and but I would like to uh give +my congratulations for those who took on + + align:start position:0% +my congratulations for those who took on + + + align:start position:0% +my congratulations for those who took on +that second homework which was uh + + align:start position:0% +that second homework which was uh + + + align:start position:0% +that second homework which was uh +significantly uh definitely required a a + + align:start position:0% +significantly uh definitely required a a + + + align:start position:0% +significantly uh definitely required a a +fair amount of contemplation to sort of + + align:start position:0% +fair amount of contemplation to sort of + + + align:start position:0% +fair amount of contemplation to sort of +attempt that homework so I want to thank + + align:start position:0% +attempt that homework so I want to thank + + + align:start position:0% +attempt that homework so I want to thank +those of you who did + + align:start position:0% +those of you who did + + + align:start position:0% +those of you who did +that so uh we're going to get started + + align:start position:0% +that so uh we're going to get started + + + align:start position:0% +that so uh we're going to get started +here and so we're going to bring up the + + align:start position:0% +here and so we're going to bring up the + + + align:start position:0% +here and so we're going to bring up the +uh slide slides here so we're going to + + align:start position:0% +uh slide slides here so we're going to + + + align:start position:0% +uh slide slides here so we're going to +be getting a little bit more uh we're + + align:start position:0% +be getting a little bit more uh we're + + + align:start position:0% +be getting a little bit more uh we're +kind of entering the the second of the + + align:start position:0% +kind of entering the the second of the + + + align:start position:0% +kind of entering the the second of the +three sections we these first three + + align:start position:0% +three sections we these first three + + + align:start position:0% +three sections we these first three +courses here that really was the first + + align:start position:0% +courses here that really was the first + + + align:start position:0% +courses here that really was the first +part did a lot with motivation and a lot + + align:start position:0% +part did a lot with motivation and a lot + + + align:start position:0% +part did a lot with motivation and a lot +with Theory and now we're going to do + + align:start position:0% +with Theory and now we're going to do + + + align:start position:0% +with Theory and now we're going to do +stuff that's a little bit more you know + + align:start position:0% +stuff that's a little bit more you know + + + align:start position:0% +stuff that's a little bit more you know +we'll be continuing that that that Trend + + align:start position:0% +we'll be continuing that that that Trend + + + align:start position:0% +we'll be continuing that that that Trend +we'll still always have plenty of + + align:start position:0% +we'll still always have plenty of + + + align:start position:0% +we'll still always have plenty of +motivation and a little bit of theory + + align:start position:0% +motivation and a little bit of theory + + + align:start position:0% +motivation and a little bit of theory +but getting more and more towards things + + align:start position:0% +but getting more and more towards things + + + align:start position:0% +but getting more and more towards things +that feel like the things you might + + align:start position:0% +that feel like the things you might + + + align:start position:0% +that feel like the things you might +really do and so we're kind of entering + + align:start position:0% +really do and so we're kind of entering + + + align:start position:0% +really do and so we're kind of entering +into that next phase of the course here + + align:start position:0% +into that next phase of the course here + + + align:start position:0% +into that next phase of the course here +so let's get started here so this is the + + align:start position:0% +so let's get started here so this is the + + + align:start position:0% +so let's get started here so this is the +lecture + + align:start position:0% + + + + align:start position:0% + +03 we'll have some example here from + + align:start position:0% +03 we'll have some example here from + + + align:start position:0% +03 we'll have some example here from +some real data and talking about that um + + align:start position:0% +some real data and talking about that um + + + align:start position:0% +some real data and talking about that um +here's the outline of the course uh + + align:start position:0% +here's the outline of the course uh + + + align:start position:0% +here's the outline of the course uh +actually just before we that sort of + + align:start position:0% +actually just before we that sort of + + + align:start position:0% +actually just before we that sort of +somewhat mandatory for those of you who + + align:start position:0% +somewhat mandatory for those of you who + + + align:start position:0% +somewhat mandatory for those of you who +are just joining us or watching on the + + align:start position:0% +are just joining us or watching on the + + + align:start position:0% +are just joining us or watching on the +web and have jumped ahead to this + + align:start position:0% +web and have jumped ahead to this + + + align:start position:0% +web and have jumped ahead to this +lecture the title of the class is signal + + align:start position:0% +lecture the title of the class is signal + + + align:start position:0% +lecture the title of the class is signal +processing on databases to words that we + + align:start position:0% +processing on databases to words that we + + + align:start position:0% +processing on databases to words that we +don't normally see together or to + + align:start position:0% +don't normally see together or to + + + align:start position:0% +don't normally see together or to +phrases signal processing which is + + align:start position:0% +phrases signal processing which is + + + align:start position:0% +phrases signal processing which is +really alluding to uh detection Theory + + align:start position:0% +really alluding to uh detection Theory + + + align:start position:0% +really alluding to uh detection Theory +formal detection Theory and it's linear + + align:start position:0% +formal detection Theory and it's linear + + + align:start position:0% +formal detection Theory and it's linear +algebraic foundations and databases + + align:start position:0% +algebraic foundations and databases + + + align:start position:0% +algebraic foundations and databases +which is really alluding to to dealing + + align:start position:0% +which is really alluding to to dealing + + + align:start position:0% +which is really alluding to to dealing +with strings and unstructured data and + + align:start position:0% +with strings and unstructured data and + + + align:start position:0% +with strings and unstructured data and +graphs and so we're in this course + + align:start position:0% +graphs and so we're in this course + + + align:start position:0% +graphs and so we're in this course +talking about a technology d4m which + + align:start position:0% +talking about a technology d4m which + + + align:start position:0% +talking about a technology d4m which +allows us to to pull these two views + + align:start position:0% +allows us to to pull these two views + + + align:start position:0% +allows us to to pull these two views +together and so again we're now uh the + + align:start position:0% +together and so again we're now uh the + + + align:start position:0% +together and so again we're now uh the +lecture + + align:start position:0% +lecture + + + align:start position:0% +lecture +03 and uh we will continue on this + + align:start position:0% +03 and uh we will continue on this + + + align:start position:0% +03 and uh we will continue on this +journey that we have + + align:start position:0% +journey that we have + + + align:start position:0% +journey that we have +started here's the outline + + align:start position:0% +started here's the outline + + + align:start position:0% +started here's the outline +um a little bit of of History I'm going + + align:start position:0% +um a little bit of of History I'm going + + + align:start position:0% +um a little bit of of History I'm going +to talk about kind of how the web became + + align:start position:0% +to talk about kind of how the web became + + + align:start position:0% +to talk about kind of how the web became +the thing it is today which I think + + align:start position:0% +the thing it is today which I think + + + align:start position:0% +the thing it is today which I think +talks a lot about why we invented the + + align:start position:0% +talks a lot about why we invented the + + + align:start position:0% +talks a lot about why we invented the +deform technology so it's going to talk + + align:start position:0% +deform technology so it's going to talk + + + align:start position:0% +deform technology so it's going to talk +about the specific Gap + + align:start position:0% +about the specific Gap + + + align:start position:0% +about the specific Gap +that it that it that it fills and talk a + + align:start position:0% +that it that it that it fills and talk a + + + align:start position:0% +that it that it that it fills and talk a +little bit about the deform technology + + align:start position:0% +little bit about the deform technology + + + align:start position:0% +little bit about the deform technology +um some of the results that we've had + + align:start position:0% +um some of the results that we've had + + + align:start position:0% +um some of the results that we've had +and then hopefully today uh the demo is + + align:start position:0% +and then hopefully today uh the demo is + + + align:start position:0% +and then hopefully today uh the demo is +a lot more substantive and so we'll + + align:start position:0% +a lot more substantive and so we'll + + + align:start position:0% +a lot more substantive and so we'll +spend more time on that uh than we uh + + align:start position:0% +spend more time on that uh than we uh + + + align:start position:0% +spend more time on that uh than we uh +did last time where last time was more + + align:start position:0% +did last time where last time was more + + + align:start position:0% +did last time where last time was more +Theory and the demo was really fairly + + align:start position:0% +Theory and the demo was really fairly + + + align:start position:0% +Theory and the demo was really fairly +small + + align:start position:0% + + + + align:start position:0% + +so for those of you who don't remember + + align:start position:0% +so for those of you who don't remember + + + align:start position:0% +so for those of you who don't remember +back in the ancient primordial days of + + align:start position:0% +back in the ancient primordial days of + + + align:start position:0% +back in the ancient primordial days of +the web back in the early + + align:start position:0% +the web back in the early + + + align:start position:0% +the web back in the early +90s um you know uh uh this is what it + + align:start position:0% +90s um you know uh uh this is what it + + + align:start position:0% +90s um you know uh uh this is what it +looked + + align:start position:0% +looked + + + align:start position:0% +looked +like so uh uh if I talk about the + + align:start position:0% +like so uh uh if I talk about the + + + align:start position:0% +like so uh uh if I talk about the +hardware side of the web it was quite + + align:start position:0% +hardware side of the web it was quite + + + align:start position:0% +hardware side of the web it was quite +simple + + align:start position:0% +simple + + + align:start position:0% +simple +so there we go the hardware side of the + + align:start position:0% +so there we go the hardware side of the + + + align:start position:0% +so there we go the hardware side of the +web was uh all + + align:start position:0% +web was uh all + + + align:start position:0% +web was uh all +sunbox we all had our sun workstations + + align:start position:0% +sunbox we all had our sun workstations + + + align:start position:0% +sunbox we all had our sun workstations +and they were clients and they were + + align:start position:0% +and they were clients and they were + + + align:start position:0% +and they were clients and they were +servers and they were + + align:start position:0% +servers and they were + + + align:start position:0% +servers and they were +databases and and the databases that we + + align:start position:0% +databases and and the databases that we + + + align:start position:0% +databases and and the databases that we +had at the time were were SQL databases + + align:start position:0% +had at the time were were SQL databases + + + align:start position:0% +had at the time were were SQL databases +uh Oracle was sort of really kind of + + align:start position:0% +uh Oracle was sort of really kind of + + + align:start position:0% +uh Oracle was sort of really kind of +just beginning to get going then sbase + + align:start position:0% +just beginning to get going then sbase + + + align:start position:0% +just beginning to get going then sbase +was sort of a dominant player at that + + align:start position:0% +was sort of a dominant player at that + + + align:start position:0% +was sort of a dominant player at that +stage + + align:start position:0% +stage + + + align:start position:0% +stage +um this is sort of the an example of the + + align:start position:0% +um this is sort of the an example of the + + + align:start position:0% +um this is sort of the an example of the +very first modern web page or website + + align:start position:0% +very first modern web page or website + + + align:start position:0% +very first modern web page or website +that was built it was built + + align:start position:0% +that was built it was built + + + align:start position:0% +that was built it was built +by I'm sure there were other people who + + align:start position:0% +by I'm sure there were other people who + + + align:start position:0% +by I'm sure there were other people who +were doing very similar things at the + + align:start position:0% +were doing very similar things at the + + + align:start position:0% +were doing very similar things at the +same time so it's among the first it's + + align:start position:0% +same time so it's among the first it's + + + align:start position:0% +same time so it's among the first it's +it's difficult to not going to be like + + align:start position:0% +it's difficult to not going to be like + + + align:start position:0% +it's difficult to not going to be like +alore and say I invented the Internet uh + + align:start position:0% +alore and say I invented the Internet uh + + + align:start position:0% +alore and say I invented the Internet uh +but a friend of mine Don bodri and I + + align:start position:0% +but a friend of mine Don bodri and I + + + align:start position:0% +but a friend of mine Don bodri and I +were working for a company called visual + + align:start position:0% +were working for a company called visual + + + align:start position:0% +were working for a company called visual +intelligence corporation which is now + + align:start position:0% +intelligence corporation which is now + + + align:start position:0% +intelligence corporation which is now +part of GE and um we had a data set in + + align:start position:0% +part of GE and um we had a data set in + + + align:start position:0% +part of GE and um we had a data set in +an SQL database and we wanted to make it + + align:start position:0% +an SQL database and we wanted to make it + + + align:start position:0% +an SQL database and we wanted to make it +available and there were a lot of thick + + align:start position:0% +available and there were a lot of thick + + + align:start position:0% +available and there were a lot of thick +client tools that came with our sbase + + align:start position:0% +client tools that came with our sbase + + + align:start position:0% +client tools that came with our sbase +package for doing that but we found them + + align:start position:0% +package for doing that but we found them + + + align:start position:0% +package for doing that but we found them +a little bit clunky and so a friend of + + align:start position:0% +a little bit clunky and so a friend of + + + align:start position:0% +a little bit clunky and so a friend of +mine uh don he downloaded this uh this + + align:start position:0% +mine uh don he downloaded this uh this + + + align:start position:0% +mine uh don he downloaded this uh this +he he he said hey I found this new + + align:start position:0% +he he he said hey I found this new + + + align:start position:0% +he he he said hey I found this new +software I found a Beta release of this + + align:start position:0% +software I found a Beta release of this + + + align:start position:0% +software I found a Beta release of this +software called NCSA + + align:start position:0% +software called NCSA + + + align:start position:0% +software called NCSA +Mosaic and so for those of you don't + + align:start position:0% +Mosaic and so for those of you don't + + + align:start position:0% +Mosaic and so for those of you don't +know ncso Mosaic was the first browser + + align:start position:0% +know ncso Mosaic was the first browser + + + align:start position:0% +know ncso Mosaic was the first browser +and it was invented at the national + + align:start position:0% +and it was invented at the national + + + align:start position:0% +and it was invented at the national +Center for super Computing + + align:start position:0% +Center for super Computing + + + align:start position:0% +Center for super Computing +applications and um and and they + + align:start position:0% +applications and um and and they + + + align:start position:0% +applications and um and and they +released it and um and it was awesome it + + align:start position:0% +released it and um and it was awesome it + + + align:start position:0% +released it and um and it was awesome it +changed everything + + align:start position:0% +changed everything + + + align:start position:0% +changed everything +just so you know prior to that and not + + align:start position:0% +just so you know prior to that and not + + + align:start position:0% +just so you know prior to that and not +to disrespect anybody who who's + + align:start position:0% +to disrespect anybody who who's + + + align:start position:0% +to disrespect anybody who who's +inventing anything but HTTP and + + align:start position:0% +inventing anything but HTTP and + + + align:start position:0% +inventing anything but HTTP and +HTML were + + align:start position:0% +HTML were + + + align:start position:0% +HTML were +dying they had actually come out in + + align:start position:0% +dying they had actually come out in + + + align:start position:0% +dying they had actually come out in +1989 and everyone like this is silly + + align:start position:0% +1989 and everyone like this is silly + + + align:start position:0% +1989 and everyone like this is silly +what's this why do I have to type this + + align:start position:0% +what's this why do I have to type this + + + align:start position:0% +what's this why do I have to type this +HTTP and then there's this HTML and it's + + align:start position:0% +HTTP and then there's this HTML and it's + + + align:start position:0% +HTTP and then there's this HTML and it's +just very clunky and stuff like that and + + align:start position:0% +just very clunky and stuff like that and + + + align:start position:0% +just very clunky and stuff like that and +it was getting its clocked pretty well + + align:start position:0% +it was getting its clocked pretty well + + + align:start position:0% +it was getting its clocked pretty well +cleaned by another technology called + + align:start position:0% +cleaned by another technology called + + + align:start position:0% +cleaned by another technology called +gopher which existed at which was + + align:start position:0% +gopher which existed at which was + + + align:start position:0% +gopher which existed at which was +developed the University of Minnesota + + align:start position:0% +developed the University of Minnesota + + + align:start position:0% +developed the University of Minnesota +which was a much easier interface the + + align:start position:0% +which was a much easier interface the + + + align:start position:0% +which was a much easier interface the +server was a lot better the the it was a + + align:start position:0% +server was a lot better the the it was a + + + align:start position:0% +server was a lot better the the it was a +lot easier to do links than in + + align:start position:0% +lot easier to do links than in + + + align:start position:0% +lot easier to do links than in +HTML and it was just a menu driven text + + align:start position:0% +HTML and it was just a menu driven text + + + align:start position:0% +HTML and it was just a menu driven text +based way to do + + align:start position:0% +based way to do + + + align:start position:0% +based way to do +that well + + align:start position:0% +that well + + + align:start position:0% +that well +Mosaic + + align:start position:0% +Mosaic + + + align:start position:0% +Mosaic +created a gooey front end to HTML and + + align:start position:0% +created a gooey front end to HTML and + + + align:start position:0% +created a gooey front end to HTML and +allowed you to have pictures + + align:start position:0% +allowed you to have pictures + + + align:start position:0% +allowed you to have pictures +and that changed everything that just + + align:start position:0% +and that changed everything that just + + + align:start position:0% +and that changed everything that just +absolutely that was that was and it just + + align:start position:0% +absolutely that was that was and it just + + + align:start position:0% +absolutely that was that was and it just +sort of caught on like wildfire but it + + align:start position:0% +sort of caught on like wildfire but it + + + align:start position:0% +sort of caught on like wildfire but it +was just a beta at that point in time + + align:start position:0% +was just a beta at that point in time + + + align:start position:0% +was just a beta at that point in time +and I don't think it could really do + + align:start position:0% +and I don't think it could really do + + + align:start position:0% +and I don't think it could really do +pictures but it was still it rendered + + align:start position:0% +pictures but it was still it rendered + + + align:start position:0% +pictures but it was still it rendered +fonts nicely and gopher did not gopher + + align:start position:0% +fonts nicely and gopher did not gopher + + + align:start position:0% +fonts nicely and gopher did not gopher +was like just plain text so you could + + align:start position:0% +was like just plain text so you could + + + align:start position:0% +was like just plain text so you could +have like underline and Bold and The + + align:start position:0% +have like underline and Bold and The + + + align:start position:0% +have like underline and Bold and The +Links were very clear you could click at + + align:start position:0% +Links were very clear you could click at + + + align:start position:0% +Links were very clear you could click at +them you could even have indents and + + align:start position:0% +them you could even have indents and + + + align:start position:0% +them you could even have indents and +bullets you could imagine organizing + + align:start position:0% +bullets you could imagine organizing + + + align:start position:0% +bullets you could imagine organizing +with with something that would be look + + align:start position:0% +with with something that would be look + + + align:start position:0% +with with something that would be look +like a web page + + align:start position:0% +like a web page + + + align:start position:0% +like a web page +today um and so uh so we had that and + + align:start position:0% +today um and so uh so we had that and + + + align:start position:0% +today um and so uh so we had that and +they're like oh well we'll talk to our + + align:start position:0% +they're like oh well we'll talk to our + + + align:start position:0% +they're like oh well we'll talk to our +database using that we'll use you know + + align:start position:0% +database using that we'll use you know + + + align:start position:0% +database using that we'll use you know +HTT put to post a a request uh the + + align:start position:0% +HTT put to post a a request uh the + + + align:start position:0% +HTT put to post a a request uh the +server uh mosa the Mosaic server was so + + align:start position:0% +server uh mosa the Mosaic server was so + + + align:start position:0% +server uh mosa the Mosaic server was so +bad we actually just used the Gopher + + align:start position:0% +bad we actually just used the Gopher + + + align:start position:0% +bad we actually just used the Gopher +server to talk to the Mosaic browser and + + align:start position:0% +server to talk to the Mosaic browser and + + + align:start position:0% +server to talk to the Mosaic browser and +so we would do puts and then we used a + + align:start position:0% +so we would do puts and then we used a + + + align:start position:0% +so we would do puts and then we used a +language called Pearl which many of you + + align:start position:0% +language called Pearl which many of you + + + align:start position:0% +language called Pearl which many of you +know because it actually had a direct + + align:start position:0% +know because it actually had a direct + + + align:start position:0% +know because it actually had a direct +binding to to to sbase and so we would + + align:start position:0% +binding to to to sbase and so we would + + + align:start position:0% +binding to to to sbase and so we would +take that format it and um and uh and + + align:start position:0% +take that format it and um and uh and + + + align:start position:0% +take that format it and um and uh and +create SQL query and then it would send + + align:start position:0% +create SQL query and then it would send + + + align:start position:0% +create SQL query and then it would send +us back strings which we would then + + align:start position:0% +us back strings which we would then + + + align:start position:0% +us back strings which we would then +format as HTML and approach to the + + align:start position:0% +format as HTML and approach to the + + + align:start position:0% +format as HTML and approach to the +browser and it was great you know it was + + align:start position:0% +browser and it was great you know it was + + + align:start position:0% +browser and it was great you know it was +like very very very nice and it was sort + + align:start position:0% +like very very very nice and it was sort + + + align:start position:0% +like very very very nice and it was sort +of kind of the first modern you know web + + align:start position:0% +of kind of the first modern you know web + + + align:start position:0% +of kind of the first modern you know web +page that we did in in 1992 and + + align:start position:0% +page that we did in in 1992 and + + + align:start position:0% +page that we did in in 1992 and +essentially a good fraction of the + + align:start position:0% +essentially a good fraction of the + + + align:start position:0% +essentially a good fraction of the +internet kind of looks like this + + align:start position:0% +internet kind of looks like this + + + align:start position:0% +internet kind of looks like this +today um our conclusion at that time was + + align:start position:0% +today um our conclusion at that time was + + + align:start position:0% +today um our conclusion at that time was +that this browser was a really lousy + + align:start position:0% +that this browser was a really lousy + + + align:start position:0% +that this browser was a really lousy +gooey and that HTTP was really trying to + + align:start position:0% +gooey and that HTTP was really trying to + + + align:start position:0% +gooey and that HTTP was really trying to +be a file system but it was a really lad + + align:start position:0% +be a file system but it was a really lad + + + align:start position:0% +be a file system but it was a really lad +bad file system and Pearl was really bad + + align:start position:0% +bad file system and Pearl was really bad + + + align:start position:0% +bad file system and Pearl was really bad +for analysis and SQL really wasn't you + + align:start position:0% +for analysis and SQL really wasn't you + + + align:start position:0% +for analysis and SQL really wasn't you +know it's good for credit card + + align:start position:0% +know it's good for credit card + + + align:start position:0% +know it's good for credit card +transaction but it wasn't really good + + align:start position:0% +transaction but it wasn't really good + + + align:start position:0% +transaction but it wasn't really good +for data data analys so our our + + align:start position:0% +for data data analys so our our + + + align:start position:0% +for data data analys so our our +conclusion was this is an awful lot of + + align:start position:0% +conclusion was this is an awful lot of + + + align:start position:0% +conclusion was this is an awful lot of +work just to kind of view some documents + + align:start position:0% +work just to kind of view some documents + + + align:start position:0% +work just to kind of view some documents +and it won't catch on our conclusion was + + align:start position:0% +and it won't catch on our conclusion was + + + align:start position:0% +and it won't catch on our conclusion was +it won't catch on so with that + + align:start position:0% +it won't catch on so with that + + + align:start position:0% +it won't catch on so with that +conclusion so that sort of under maybe + + align:start position:0% +conclusion so that sort of under maybe + + + align:start position:0% +conclusion so that sort of under maybe +I'm underscoring my judgment for the + + align:start position:0% +I'm underscoring my judgment for the + + + align:start position:0% +I'm underscoring my judgment for the +entire course that you know I decided + + align:start position:0% +entire course that you know I decided + + + align:start position:0% +entire course that you know I decided +this that we decided this was a bad idea + + align:start position:0% +this that we decided this was a bad idea + + + align:start position:0% +this that we decided this was a bad idea +so after that we had sort of what we + + align:start position:0% +so after that we had sort of what we + + + align:start position:0% +so after that we had sort of what we +call the Cambrian explosion of the + + align:start position:0% +call the Cambrian explosion of the + + + align:start position:0% +call the Cambrian explosion of the +internet which is uh we have an + + align:start position:0% +internet which is uh we have an + + + align:start position:0% +internet which is uh we have an +explosion you know on the hardware side + + align:start position:0% +explosion you know on the hardware side + + + align:start position:0% +explosion you know on the hardware side +we had you know big giant data centers + + align:start position:0% +we had you know big giant data centers + + + align:start position:0% +we had you know big giant data centers +merging servers and databases which is + + align:start position:0% +merging servers and databases which is + + + align:start position:0% +merging servers and databases which is +great and we had all these new types of + + align:start position:0% +great and we had all these new types of + + + align:start position:0% +great and we had all these new types of +Hardware Technologies here laptops and + + align:start position:0% +Hardware Technologies here laptops and + + + align:start position:0% +Hardware Technologies here laptops and +tablets and iPhones and all that kind of + + align:start position:0% +tablets and iPhones and all that kind of + + + align:start position:0% +tablets and iPhones and all that kind of +stuff so the hardware technology went + + align:start position:0% +stuff so the hardware technology went + + + align:start position:0% +stuff so the hardware technology went +forward and Leaps and Bounds and then + + align:start position:0% +forward and Leaps and Bounds and then + + + align:start position:0% +forward and Leaps and Bounds and then +and then and then the web the browsers + + align:start position:0% +and then and then the web the browsers + + + align:start position:0% +and then and then the web the browsers +really took off you know all of them you + + align:start position:0% +really took off you know all of them you + + + align:start position:0% +really took off you know all of them you +have all these different browsers you + + align:start position:0% +have all these different browsers you + + + align:start position:0% +have all these different browsers you +can still the I have the Mosaic sort of + + align:start position:0% +can still the I have the Mosaic sort of + + + align:start position:0% +can still the I have the Mosaic sort of +logo back there still a little bit + + align:start position:0% +logo back there still a little bit + + + align:start position:0% +logo back there still a little bit +because they're still showing for those + + align:start position:0% +because they're still showing for those + + + align:start position:0% +because they're still showing for those +of you who don't + + align:start position:0% +of you who don't + + + align:start position:0% +of you who don't +know um the author of Mosaic at NCSA was + + align:start position:0% +know um the author of Mosaic at NCSA was + + + align:start position:0% +know um the author of Mosaic at NCSA was +a guy by the name of Mark andrees he + + align:start position:0% +a guy by the name of Mark andrees he + + + align:start position:0% +a guy by the name of Mark andrees he +left NCSA and formed a company called + + align:start position:0% +left NCSA and formed a company called + + + align:start position:0% +left NCSA and formed a company called +Netscape which actually at a moment in + + align:start position:0% +Netscape which actually at a moment in + + + align:start position:0% +Netscape which actually at a moment in +time was the dominance they were the + + align:start position:0% +time was the dominance they were the + + + align:start position:0% +time was the dominance they were the +internet you know they were like um they + + align:start position:0% +internet you know they were like um they + + + align:start position:0% +internet you know they were like um they +got crushed you know um although I think + + align:start position:0% +got crushed you know um although I think + + + align:start position:0% +got crushed you know um although I think +Mark andreon made a fair amount of money + + align:start position:0% +Mark andreon made a fair amount of money + + + align:start position:0% +Mark andreon made a fair amount of money +and um and uh and they but they did open + + align:start position:0% +and um and uh and they but they did open + + + align:start position:0% +and um and uh and they but they did open +source all their soft Ware and so they + + align:start position:0% +source all their soft Ware and so they + + + align:start position:0% +source all their soft Ware and so they +basically rewrote Mosaic from the ground + + align:start position:0% +basically rewrote Mosaic from the ground + + + align:start position:0% +basically rewrote Mosaic from the ground +up and that became um uh Mozilla and + + align:start position:0% +up and that became um uh Mozilla and + + + align:start position:0% +up and that became um uh Mozilla and +Firefox and all that so that's still + + align:start position:0% +Firefox and all that so that's still + + + align:start position:0% +Firefox and all that so that's still +still around + + align:start position:0% +still around + + + align:start position:0% +still around +today um Safari may have borrowed from + + align:start position:0% +today um Safari may have borrowed from + + + align:start position:0% +today um Safari may have borrowed from +this I I don't really know um when net + + align:start position:0% +this I I don't really know um when net + + + align:start position:0% +this I I don't really know um when net +skate was dominating the internet um + + align:start position:0% +skate was dominating the internet um + + + align:start position:0% +skate was dominating the internet um +Microsoft needed to they're like this we + + align:start position:0% +Microsoft needed to they're like this we + + + align:start position:0% +Microsoft needed to they're like this we +you know first they thought the internet + + align:start position:0% +you know first they thought the internet + + + align:start position:0% +you know first they thought the internet +was going to be a fad and then they're + + align:start position:0% +was going to be a fad and then they're + + + align:start position:0% +was going to be a fad and then they're +like all right this is serious we need a + + align:start position:0% +like all right this is serious we need a + + + align:start position:0% +like all right this is serious we need a +browser + + align:start position:0% +browser + + + align:start position:0% +browser +and so they then um and Mosaic had + + align:start position:0% +and so they then um and Mosaic had + + + align:start position:0% +and so they then um and Mosaic had +actually been spun out of illino the + + align:start position:0% +actually been spun out of illino the + + + align:start position:0% +actually been spun out of illino the +University of Illinois into a company + + align:start position:0% +University of Illinois into a company + + + align:start position:0% +University of Illinois into a company +called spy glass which may actually + + align:start position:0% +called spy glass which may actually + + + align:start position:0% +called spy glass which may actually +still exist today and then um Microsoft + + align:start position:0% +still exist today and then um Microsoft + + + align:start position:0% +still exist today and then um Microsoft +bought the browser which was the + + align:start position:0% +bought the browser which was the + + + align:start position:0% +bought the browser which was the +original NCSA Mosaic code and that + + align:start position:0% +original NCSA Mosaic code and that + + + align:start position:0% +original NCSA Mosaic code and that +became Internet Explorer so it's still + + align:start position:0% +became Internet Explorer so it's still + + + align:start position:0% +became Internet Explorer so it's still +around today uh this is Chrome and as + + align:start position:0% +around today uh this is Chrome and as + + + align:start position:0% +around today uh this is Chrome and as +far as I know Chrome is a complete + + align:start position:0% +far as I know Chrome is a complete + + + align:start position:0% +far as I know Chrome is a complete +rewrite from the ground up so you know + + align:start position:0% +rewrite from the ground up so you know + + + align:start position:0% +rewrite from the ground up so you know +that's and probably some of the other + + align:start position:0% +that's and probably some of the other + + + align:start position:0% +that's and probably some of the other +like op Opera and other other browsers + + align:start position:0% +like op Opera and other other browsers + + + align:start position:0% +like op Opera and other other browsers +around today are complete but they still + + align:start position:0% +around today are complete but they still + + + align:start position:0% +around today are complete but they still +use it it's a browser to uses HTML still + + align:start position:0% +use it it's a browser to uses HTML still + + + align:start position:0% +use it it's a browser to uses HTML still +uses the basic put get syntax uh our SQL + + align:start position:0% +uses the basic put get syntax uh our SQL + + + align:start position:0% +uses the basic put get syntax uh our SQL +we're still using it today we have a + + align:start position:0% +we're still using it today we have a + + + align:start position:0% +we're still using it today we have a +whole explosion of Technologies Oracle + + align:start position:0% +whole explosion of Technologies Oracle + + + align:start position:0% +whole explosion of Technologies Oracle +being very dominant but you know MySQL + + align:start position:0% +being very dominant but you know MySQL + + + align:start position:0% +being very dominant but you know MySQL +SQL Server other types of things sbas + + align:start position:0% +SQL Server other types of things sbas + + + align:start position:0% +SQL Server other types of things sbas +still around very very very common and + + align:start position:0% +still around very very very common and + + + align:start position:0% +still around very very very common and +we have a uh we still have a uh you know + + align:start position:0% +we have a uh we still have a uh you know + + + align:start position:0% +we have a uh we still have a uh you know +uh we have the two major servers out + + align:start position:0% +uh we have the two major servers out + + + align:start position:0% +uh we have the two major servers out +there Apache and windows so aache was + + align:start position:0% +there Apache and windows so aache was + + + align:start position:0% +there Apache and windows so aache was +the Mosaic server and just so you know + + align:start position:0% +the Mosaic server and just so you know + + + align:start position:0% +the Mosaic server and just so you know +Apache was it's a Pache server meaning + + align:start position:0% +Apache was it's a Pache server meaning + + + align:start position:0% +Apache was it's a Pache server meaning +it was very buggy so it was the Apache + + align:start position:0% +it was very buggy so it was the Apache + + + align:start position:0% +it was very buggy so it was the Apache +server and that became Apache so that + + align:start position:0% +server and that became Apache so that + + + align:start position:0% +server and that became Apache so that +was the Mosaic server became Apache + + align:start position:0% +was the Mosaic server became Apache + + + align:start position:0% +was the Mosaic server became Apache +because it was aache server and so uh so + + align:start position:0% +because it was aache server and so uh so + + + align:start position:0% +because it was aache server and so uh so +and I bet they borrowed code from gopher + + align:start position:0% +and I bet they borrowed code from gopher + + + align:start position:0% +and I bet they borrowed code from gopher +so that's why the Gopher I think is + + align:start position:0% +so that's why the Gopher I think is + + + align:start position:0% +so that's why the Gopher I think is +still showing there a little bit um + + align:start position:0% +still showing there a little bit um + + + align:start position:0% +still showing there a little bit um +we've had a proliferation of languages + + align:start position:0% +we've had a proliferation of languages + + + align:start position:0% +we've had a proliferation of languages +that are very similar so people in terms + + align:start position:0% +that are very similar so people in terms + + + align:start position:0% +that are very similar so people in terms +of gluing these two together together + + align:start position:0% +of gluing these two together together + + + align:start position:0% +of gluing these two together together +Java Etc all that type of stuff but but + + align:start position:0% +Java Etc all that type of stuff but but + + + align:start position:0% +Java Etc all that type of stuff but but +the important thing to recognize is that + + align:start position:0% +the important thing to recognize is that + + + align:start position:0% +the important thing to recognize is that +this whole architecture was not put + + align:start position:0% +this whole architecture was not put + + + align:start position:0% +this whole architecture was not put +together because somehow we felt the web + + align:start position:0% +together because somehow we felt the web + + + align:start position:0% +together because somehow we felt the web +browser was the optimal tool or SQL was + + align:start position:0% +browser was the optimal tool or SQL was + + + align:start position:0% +browser was the optimal tool or SQL was +the optimal tool or these languages were + + align:start position:0% +the optimal tool or these languages were + + + align:start position:0% +the optimal tool or these languages were +the optimal tool they were just things + + align:start position:0% +the optimal tool they were just things + + + align:start position:0% +the optimal tool they were just things +that were laying down that could be + + align:start position:0% +that were laying down that could be + + + align:start position:0% +that were laying down that could be +repurposed for this job and so that's + + align:start position:0% +repurposed for this job and so that's + + + align:start position:0% +repurposed for this job and so that's +why they're not necessarily the optimal + + align:start position:0% +why they're not necessarily the optimal + + + align:start position:0% +why they're not necessarily the optimal +thing so but nevertheless our conclusion + + align:start position:0% +thing so but nevertheless our conclusion + + + align:start position:0% +thing so but nevertheless our conclusion +has to be slightly r that it would not + + align:start position:0% +has to be slightly r that it would not + + + align:start position:0% +has to be slightly r that it would not +catch on because obviously it did catch + + align:start position:0% +catch on because obviously it did catch + + + align:start position:0% +catch on because obviously it did catch +on the the desire to share information + + align:start position:0% +on the the desire to share information + + + align:start position:0% +on the the desire to share information +was so great that it overcome overcame + + align:start position:0% +was so great that it overcome overcame + + + align:start position:0% +was so great that it overcome overcame +the the high barrier entry you know just + + align:start position:0% +the the high barrier entry you know just + + + align:start position:0% +the the high barrier entry you know just +to you know set up a a web page or + + align:start position:0% +to you know set up a a web page or + + + align:start position:0% +to you know set up a a web page or +something like that now things have + + align:start position:0% +something like that now things have + + + align:start position:0% +something like that now things have +changed significantly we're not the + + align:start position:0% +changed significantly we're not the + + + align:start position:0% +changed significantly we're not the +first people to observe that this sort + + align:start position:0% +first people to observe that this sort + + + align:start position:0% +first people to observe that this sort +of original architecture is somewhat + + align:start position:0% +of original architecture is somewhat + + + align:start position:0% +of original architecture is somewhat +broken for this type of model and so + + align:start position:0% +broken for this type of model and so + + + align:start position:0% +broken for this type of model and so +today the web looks a lot more like + + align:start position:0% +today the web looks a lot more like + + + align:start position:0% +today the web looks a lot more like +this we still have our awesome client + + align:start position:0% +this we still have our awesome client + + + align:start position:0% +this we still have our awesome client +Hardware which is is great um we have + + align:start position:0% +Hardware which is is great um we have + + + align:start position:0% +Hardware which is is great um we have +servers and databases that have now + + align:start position:0% +servers and databases that have now + + + align:start position:0% +servers and databases that have now +moved in inside of out out of the data + + align:start position:0% +moved in inside of out out of the data + + + align:start position:0% +moved in inside of out out of the data +center into shipping containers and + + align:start position:0% +center into shipping containers and + + + align:start position:0% +center into shipping containers and +other types of things which is great um + + align:start position:0% +other types of things which is great um + + + align:start position:0% +other types of things which is great um +increasingly our interfaces will look a + + align:start position:0% +increasingly our interfaces will look a + + + align:start position:0% +increasingly our interfaces will look a +lot more like video games I would uh + + align:start position:0% +lot more like video games I would uh + + + align:start position:0% +lot more like video games I would uh +tell you that a typical app on the iPad + + align:start position:0% +tell you that a typical app on the iPad + + + align:start position:0% +tell you that a typical app on the iPad +feels a lot more like a video game than + + align:start position:0% +feels a lot more like a video game than + + + align:start position:0% +feels a lot more like a video game than +a browser which is great so we've really + + align:start position:0% +a browser which is great so we've really + + + align:start position:0% +a browser which is great so we've really +kind of moving beyond the browser is a + + align:start position:0% +kind of moving beyond the browser is a + + + align:start position:0% +kind of moving beyond the browser is a +dominant way for getting our information + + align:start position:0% +dominant way for getting our information + + + align:start position:0% +dominant way for getting our information +and companies like Google and others + + align:start position:0% +and companies like Google and others + + + align:start position:0% +and companies like Google and others +recognize that if you're just presenting + + align:start position:0% +recognize that if you're just presenting + + + align:start position:0% +recognize that if you're just presenting +data to people and you're not doing say + + align:start position:0% +data to people and you're not doing say + + + align:start position:0% +data to people and you're not doing say +credit card transactions then then a lot + + align:start position:0% +credit card transactions then then a lot + + + align:start position:0% +credit card transactions then then a lot +of the features of SQL and those types + + align:start position:0% +of the features of SQL and those types + + + align:start position:0% +of the features of SQL and those types +of databases are are maybe more than you + + align:start position:0% +of databases are are maybe more than you + + + align:start position:0% +of databases are are maybe more than you +need and you can actually make these + + align:start position:0% +need and you can actually make these + + + align:start position:0% +need and you can actually make these +sort of very scalable databases more + + align:start position:0% +sort of very scalable databases more + + + align:start position:0% +sort of very scalable databases more +simply that are called triple stores and + + align:start position:0% +simply that are called triple stores and + + + align:start position:0% +simply that are called triple stores and +so Google big table being the original + + align:start position:0% +so Google big table being the original + + + align:start position:0% +so Google big table being the original +sort of sort of one um react is another + + align:start position:0% +sort of sort of one um react is another + + + align:start position:0% +sort of sort of one um react is another +Cassandra is another hbas another + + align:start position:0% +Cassandra is another hbas another + + + align:start position:0% +Cassandra is another hbas another +accumulo which is the one we use in this + + align:start position:0% +accumulo which is the one we use in this + + + align:start position:0% +accumulo which is the one we use in this +class there's another so so this whole + + align:start position:0% +class there's another so so this whole + + + align:start position:0% +class there's another so so this whole +new technology space has really driven + + align:start position:0% +new technology space has really driven + + + align:start position:0% +new technology space has really driven +you know uh uh that and has made that a + + align:start position:0% +you know uh uh that and has made that a + + + align:start position:0% +you know uh uh that and has made that a +lot more scalable when people in but + + align:start position:0% +lot more scalable when people in but + + + align:start position:0% +lot more scalable when people in but +unfortunately in the middle here we're + + align:start position:0% +unfortunately in the middle here we're + + + align:start position:0% +unfortunately in the middle here we're +still very much left with much of the + + align:start position:0% +still very much left with much of the + + + align:start position:0% +still very much left with much of the +same technology you know and this is + + align:start position:0% +same technology you know and this is + + + align:start position:0% +same technology you know and this is +kind of the last piece this sort of glue + + align:start position:0% +kind of the last piece this sort of glue + + + align:start position:0% +kind of the last piece this sort of glue +uh that uh and so our conclusion is now + + align:start position:0% +uh that uh and so our conclusion is now + + + align:start position:0% +uh that uh and so our conclusion is now +that you know it's a lot of work to view + + align:start position:0% +that you know it's a lot of work to view + + + align:start position:0% +that you know it's a lot of work to view +a lot of data but it's a pretty great + + align:start position:0% +a lot of data but it's a pretty great + + + align:start position:0% +a lot of data but it's a pretty great +View and we can really view a lot of + + align:start position:0% +View and we can really view a lot of + + + align:start position:0% +View and we can really view a lot of +data but we still have this middle + + align:start position:0% +data but we still have this middle + + + align:start position:0% +data but we still have this middle +problem there's this Gap and so we're + + align:start position:0% +problem there's this Gap and so we're + + + align:start position:0% +problem there's this Gap and so we're +trying to address that Gap and so we + + align:start position:0% +trying to address that Gap and so we + + + align:start position:0% +trying to address that Gap and so we +address that Gap with d4m so d4m is + + align:start position:0% +address that Gap with d4m so d4m is + + + align:start position:0% +address that Gap with d4m so d4m is +formally designed from the ground up to + + align:start position:0% +formally designed from the ground up to + + + align:start position:0% +formally designed from the ground up to +be something that is really designed to + + align:start position:0% +be something that is really designed to + + + align:start position:0% +be something that is really designed to +work on triples the kind of data we + + align:start position:0% +work on triples the kind of data we + + + align:start position:0% +work on triples the kind of data we +store in these modern databases and do + + align:start position:0% +store in these modern databases and do + + + align:start position:0% +store in these modern databases and do +the kind of analysis in less code than + + align:start position:0% +the kind of analysis in less code than + + + align:start position:0% +the kind of analysis in less code than +you than than you would + + align:start position:0% + + + + align:start position:0% + +otherwise so d4m which stands for + + align:start position:0% +otherwise so d4m which stands for + + + align:start position:0% +otherwise so d4m which stands for +dynamic distributed dimensional data + + align:start position:0% +dynamic distributed dimensional data + + + align:start position:0% +dynamic distributed dimensional data +model which is sometimes you know quotes + + align:start position:0% +model which is sometimes you know quotes + + + align:start position:0% +model which is sometimes you know quotes +databases for matlb because it happens + + align:start position:0% +databases for matlb because it happens + + + align:start position:0% +databases for matlb because it happens +to be written in mat lab um it connects + + align:start position:0% +to be written in mat lab um it connects + + + align:start position:0% +to be written in mat lab um it connects +the triple stores which can view their + + align:start position:0% +the triple stores which can view their + + + align:start position:0% +the triple stores which can view their +data as very large sparse matrices of + + align:start position:0% +data as very large sparse matrices of + + + align:start position:0% +data as very large sparse matrices of +triples with these uh the mathematical + + align:start position:0% +triples with these uh the mathematical + + + align:start position:0% +triples with these uh the mathematical +concepts of associative arrays that we + + align:start position:0% +concepts of associative arrays that we + + + align:start position:0% +concepts of associative arrays that we +talked about last class that's + + align:start position:0% +talked about last class that's + + + align:start position:0% +talked about last class that's +essentially what dform does for + + align:start position:0% +essentially what dform does for + + + align:start position:0% +essentially what dform does for +you so that's kind of one sort of + + align:start position:0% +you so that's kind of one sort of + + + align:start position:0% +you so that's kind of one sort of +holistic view of the technology space + + align:start position:0% +holistic view of the technology space + + + align:start position:0% +holistic view of the technology space +that we're dealing with + + align:start position:0% +that we're dealing with + + + align:start position:0% +that we're dealing with +here another way to view at it which is + + align:start position:0% +here another way to view at it which is + + + align:start position:0% +here another way to view at it which is +uh I'm going to talk a little bit about + + align:start position:0% +uh I'm going to talk a little bit about + + + align:start position:0% +uh I'm going to talk a little bit about +kind of how the technologies that we + + align:start position:0% +kind of how the technologies that we + + + align:start position:0% +kind of how the technologies that we +have brought this to you so I'm going to + + align:start position:0% +have brought this to you so I'm going to + + + align:start position:0% +have brought this to you so I'm going to +tell you a little bit about L grid and + + align:start position:0% +tell you a little bit about L grid and + + + align:start position:0% +tell you a little bit about L grid and +what we do there because you're going to + + align:start position:0% +what we do there because you're going to + + + align:start position:0% +what we do there because you're going to +be using you're using your L grid + + align:start position:0% +be using you're using your L grid + + + align:start position:0% +be using you're using your L grid +accounts uh for this and so I want to + + align:start position:0% +accounts uh for this and so I want to + + + align:start position:0% +accounts uh for this and so I want to +tell you a little bit about + + align:start position:0% +tell you a little bit about + + + align:start position:0% +tell you a little bit about +that so uh L grid is the + + align:start position:0% +that so uh L grid is the + + + align:start position:0% +that so uh L grid is the +core supercomputer at Lincoln laboratory + + align:start position:0% +core supercomputer at Lincoln laboratory + + + align:start position:0% +core supercomputer at Lincoln laboratory +and we're here to help uh you know with + + align:start position:0% +and we're here to help uh you know with + + + align:start position:0% +and we're here to help uh you know with +with all your Computing needs uh + + align:start position:0% +with all your Computing needs uh + + + align:start position:0% +with all your Computing needs uh +likewise we're here to help with your DM + + align:start position:0% +likewise we're here to help with your DM + + + align:start position:0% +likewise we're here to help with your DM +needs uh if you have a project and you + + align:start position:0% +needs uh if you have a project and you + + + align:start position:0% +needs uh if you have a project and you +think it would be useful to use d4m in + + align:start position:0% +think it would be useful to use d4m in + + + align:start position:0% +think it would be useful to use d4m in +that project please contact us we don't + + align:start position:0% +that project please contact us we don't + + + align:start position:0% +that project please contact us we don't +have to just take this class and think + + align:start position:0% +have to just take this class and think + + + align:start position:0% +have to just take this class and think +that you're on your own I mean we are a + + align:start position:0% +that you're on your own I mean we are a + + + align:start position:0% +that you're on your own I mean we are a +service we will help + + align:start position:0% +service we will help + + + align:start position:0% +service we will help +you do the schemas get the code going + + align:start position:0% +you do the schemas get the code going + + + align:start position:0% +you do the schemas get the code going +get it you know get it sort of adapted + + align:start position:0% +get it you know get it sort of adapted + + + align:start position:0% +get it you know get it sort of adapted +to your problem that's that's that's + + align:start position:0% +to your problem that's that's that's + + + align:start position:0% +to your problem that's that's that's +what we do um L grid we have about we + + align:start position:0% +what we do um L grid we have about we + + + align:start position:0% +what we do um L grid we have about we +have actually well over this but you + + align:start position:0% +have actually well over this but you + + + align:start position:0% +have actually well over this but you +know just so I don't have to keep + + align:start position:0% +know just so I don't have to keep + + + align:start position:0% +know just so I don't have to keep +changing the slide we always say it's + + align:start position:0% +changing the slide we always say it's + + + align:start position:0% +changing the slide we always say it's +about 500 users about 2,000 processors + + align:start position:0% +about 500 users about 2,000 processors + + + align:start position:0% +about 500 users about 2,000 processors +it's more than that um to our knowledge + + align:start position:0% +it's more than that um to our knowledge + + + align:start position:0% +it's more than that um to our knowledge +it's really the world's only desktop + + align:start position:0% +it's really the world's only desktop + + + align:start position:0% +it's really the world's only desktop +interactive supercomputer it's + + align:start position:0% +interactive supercomputer it's + + + align:start position:0% +interactive supercomputer it's +dramatically easier to use any other + + align:start position:0% +dramatically easier to use any other + + + align:start position:0% +dramatically easier to use any other +supercomputer and as a result as an + + align:start position:0% +supercomputer and as a result as an + + + align:start position:0% +supercomputer and as a result as an +organization we have the highest + + align:start position:0% +organization we have the highest + + + align:start position:0% +organization we have the highest +fraction of Staff using supercomputing + + align:start position:0% +fraction of Staff using supercomputing + + + align:start position:0% +fraction of Staff using supercomputing +on a regular basis of any organization + + align:start position:0% +on a regular basis of any organization + + + align:start position:0% +on a regular basis of any organization +just because it's so easy and it's also + + align:start position:0% +just because it's so easy and it's also + + + align:start position:0% +just because it's so easy and it's also +kind of been the foundation the vision + + align:start position:0% +kind of been the foundation the vision + + + align:start position:0% +kind of been the foundation the vision +for supercomputing in the enti entire + + align:start position:0% +for supercomputing in the enti entire + + + align:start position:0% +for supercomputing in the enti entire +state of Massachusetts a all of our our + + align:start position:0% +state of Massachusetts a all of our our + + + align:start position:0% +state of Massachusetts a all of our our +ideas have been adopted by other organ + + align:start position:0% +ideas have been adopted by other organ + + + align:start position:0% +ideas have been adopted by other organ +you know universities in the state and + + align:start position:0% +you know universities in the state and + + + align:start position:0% +you know universities in the state and +and moving + + align:start position:0% +and moving + + + align:start position:0% +and moving +forward not really the techn ology that + + align:start position:0% +forward not really the techn ology that + + + align:start position:0% +forward not really the techn ology that +we're talking about + + align:start position:0% +we're talking about + + + align:start position:0% +we're talking about +today but something that is really kind + + align:start position:0% +today but something that is really kind + + + align:start position:0% +today but something that is really kind +of the bread and butter of L grid is our + + align:start position:0% +of the bread and butter of L grid is our + + + align:start position:0% +of the bread and butter of L grid is our +parallel metlab technology which uh is + + align:start position:0% +parallel metlab technology which uh is + + + align:start position:0% +parallel metlab technology which uh is +now going to be start celebrating its + + align:start position:0% +now going to be start celebrating its + + + align:start position:0% +now going to be start celebrating its +10th anniversary this year um and uh and + + align:start position:0% +10th anniversary this year um and uh and + + + align:start position:0% +10th anniversary this year um and uh and +it's really a way to allow people to do + + align:start position:0% +it's really a way to allow people to do + + + align:start position:0% +it's really a way to allow people to do +parallel programming relatively easily + + align:start position:0% +parallel programming relatively easily + + + align:start position:0% +parallel programming relatively easily +uh + + align:start position:0% +uh + + + align:start position:0% +uh +d4m interacts seamlessly with this + + align:start position:0% +d4m interacts seamlessly with this + + + align:start position:0% +d4m interacts seamlessly with this +technology and so you will also be doing + + align:start position:0% +technology and so you will also be doing + + + align:start position:0% +technology and so you will also be doing +parallel database codes by the end of + + align:start position:0% +parallel database codes by the end of + + + align:start position:0% +parallel database codes by the end of +this as well uh with with this + + align:start position:0% +this as well uh with with this + + + align:start position:0% +this as well uh with with this +technology so we have this thing called + + align:start position:0% +technology so we have this thing called + + + align:start position:0% +technology so we have this thing called +parallel mat laab uh if you're an L grid + + align:start position:0% +parallel mat laab uh if you're an L grid + + + align:start position:0% +parallel mat laab uh if you're an L grid +user you you you are entitled to or you + + align:start position:0% +user you you you are entitled to or you + + + align:start position:0% +user you you you are entitled to or you +almost always get the book on Parallel + + align:start position:0% +almost always get the book on Parallel + + + align:start position:0% +almost always get the book on Parallel +mat lab and allows you to take things + + align:start position:0% +mat lab and allows you to take things + + + align:start position:0% +mat lab and allows you to take things +like matrices and chop them up very + + align:start position:0% +like matrices and chop them up very + + + align:start position:0% +like matrices and chop them up very +easily uh to do uh complicated + + align:start position:0% +easily uh to do uh complicated + + + align:start position:0% +easily uh to do uh complicated +calculations and almost every single uh + + align:start position:0% +calculations and almost every single uh + + + align:start position:0% +calculations and almost every single uh +parallel program that you would want to + + align:start position:0% +parallel program that you would want to + + + align:start position:0% +parallel program that you would want to +write can be written with just the + + align:start position:0% +write can be written with just the + + + align:start position:0% +write can be written with just the +addition of a handful of additional + + align:start position:0% +addition of a handful of additional + + + align:start position:0% +addition of a handful of additional +functions and so um and we get to use + + align:start position:0% +functions and so um and we get to use + + + align:start position:0% +functions and so um and we get to use +what is called the distributed arrays + + align:start position:0% +what is called the distributed arrays + + + align:start position:0% +what is called the distributed arrays +parallel program model which is + + align:start position:0% +parallel program model which is + + + align:start position:0% +parallel program model which is +generally recognized as by far the best + + align:start position:0% +generally recognized as by far the best + + + align:start position:0% +generally recognized as by far the best +of all the parallel programming models + + align:start position:0% +of all the parallel programming models + + + align:start position:0% +of all the parallel programming models +if you are comfortable with + + align:start position:0% +if you are comfortable with + + + align:start position:0% +if you are comfortable with +multi-dimensional + + align:start position:0% +multi-dimensional + + + align:start position:0% +multi-dimensional +arrays everyone in MIT is so this is + + align:start position:0% +arrays everyone in MIT is so this is + + + align:start position:0% +arrays everyone in MIT is so this is +easy however this is not generally true + + align:start position:0% +easy however this is not generally true + + + align:start position:0% +easy however this is not generally true +thinking in matrices is not a universal + + align:start position:0% +thinking in matrices is not a universal + + + align:start position:0% +thinking in matrices is not a universal +skill or Universal training and so it is + + align:start position:0% +skill or Universal training and so it is + + + align:start position:0% +skill or Universal training and so it is +a bit of a sometimes we do say this is + + align:start position:0% +a bit of a sometimes we do say this is + + + align:start position:0% +a bit of a sometimes we do say this is +software for the 1% so you know it it it + + align:start position:0% +software for the 1% so you know it it it + + + align:start position:0% +software for the 1% so you know it it it +it uh it is it is not for everyone but + + align:start position:0% +it uh it is it is not for everyone but + + + align:start position:0% +it uh it is it is not for everyone but +if you can if you do have this knowledge + + align:start position:0% +if you can if you do have this knowledge + + + align:start position:0% +if you can if you do have this knowledge +and background allows you to do things + + align:start position:0% +and background allows you to do things + + + align:start position:0% +and background allows you to do things +very very naturally and as you know + + align:start position:0% +very very naturally and as you know + + + align:start position:0% +very very naturally and as you know +we've talked about all of our associate + + align:start position:0% +we've talked about all of our associate + + + align:start position:0% +we've talked about all of our associate +arrays as using looking at data in + + align:start position:0% +arrays as using looking at data in + + + align:start position:0% +arrays as using looking at data in +matrices and so these two technologies + + align:start position:0% +matrices and so these two technologies + + + align:start position:0% +matrices and so these two technologies +come together very + + align:start position:0% +come together very + + + align:start position:0% +come together very +nicely and we are really the only place + + align:start position:0% +nicely and we are really the only place + + + align:start position:0% +nicely and we are really the only place +in the world where you can routinely use + + align:start position:0% +in the world where you can routinely use + + + align:start position:0% +in the world where you can routinely use +this model this is the dominant model + + align:start position:0% +this model this is the dominant model + + + align:start position:0% +this model this is the dominant model +that people use when they do parallel + + align:start position:0% +that people use when they do parallel + + + align:start position:0% +that people use when they do parallel +programming which is generally and and + + align:start position:0% +programming which is generally and and + + + align:start position:0% +programming which is generally and and +you might say well why do I say it's the + + align:start position:0% +you might say well why do I say it's the + + + align:start position:0% +you might say well why do I say it's the +best well we run cont contests there's a + + align:start position:0% +best well we run cont contests there's a + + + align:start position:0% +best well we run cont contests there's a +contest every year where we bake off the + + align:start position:0% +contest every year where we bake off the + + + align:start position:0% +contest every year where we bake off the +best parallel programming models and + + align:start position:0% +best parallel programming models and + + + align:start position:0% +best parallel programming models and +distributed rays and highle environments + + align:start position:0% +distributed rays and highle environments + + + align:start position:0% +distributed rays and highle environments +wins every year and uh and so it's it's + + align:start position:0% +wins every year and uh and so it's it's + + + align:start position:0% +wins every year and uh and so it's it's +kind of the best model if you if you can + + align:start position:0% +kind of the best model if you if you can + + + align:start position:0% +kind of the best model if you if you can +understand + + align:start position:0% +understand + + + align:start position:0% +understand +it it wouldn't be a class on Computing + + align:start position:0% +it it wouldn't be a class on Computing + + + align:start position:0% +it it wouldn't be a class on Computing +in 2012 unless we talked about the cloud + + align:start position:0% +in 2012 unless we talked about the cloud + + + align:start position:0% +in 2012 unless we talked about the cloud +so we definitely need to talk about the + + align:start position:0% +so we definitely need to talk about the + + + align:start position:0% +so we definitely need to talk about the +cloud and to make it simple for people + + align:start position:0% +cloud and to make it simple for people + + + align:start position:0% +cloud and to make it simple for people +we're going to divide the cloud into + + align:start position:0% +we're going to divide the cloud into + + + align:start position:0% +we're going to divide the cloud into +sort of two halves you can sub divide + + align:start position:0% +sort of two halves you can sub divide + + + align:start position:0% +sort of two halves you can sub divide +the cloud into many many different + + align:start position:0% +the cloud into many many different + + + align:start position:0% +the cloud into many many different +components um there's what we call + + align:start position:0% +components um there's what we call + + + align:start position:0% +components um there's what we call +utility cloud computing which is what + + align:start position:0% +utility cloud computing which is what + + + align:start position:0% +utility cloud computing which is what +most people use the cloud for so + + align:start position:0% +most people use the cloud for so + + + align:start position:0% +most people use the cloud for so +Gmail what are Enterprise Services + + align:start position:0% +Gmail what are Enterprise Services + + + align:start position:0% +Gmail what are Enterprise Services +calendars online all that kind of stuff + + align:start position:0% +calendars online all that kind of stuff + + + align:start position:0% +calendars online all that kind of stuff +basic data sharing photo sharing and + + align:start position:0% +basic data sharing photo sharing and + + + align:start position:0% +basic data sharing photo sharing and +stuff like that that's what we call + + align:start position:0% +stuff like that that's what we call + + + align:start position:0% +stuff like that that's what we call +utility Cloud commuting Computing people + + align:start position:0% +utility Cloud commuting Computing people + + + align:start position:0% +utility Cloud commuting Computing people +who do you know you can do human + + align:start position:0% +who do you know you can do human + + + align:start position:0% +who do you know you can do human +resources on on the cloud you can do + + align:start position:0% +resources on on the cloud you can do + + + align:start position:0% +resources on on the cloud you can do +accounting on the cloud all this type + + align:start position:0% +accounting on the cloud all this type + + + align:start position:0% +accounting on the cloud all this type +stuff that's on the cloud and it's a + + align:start position:0% +stuff that's on the cloud and it's a + + + align:start position:0% +stuff that's on the cloud and it's a +very very ex successful uh business what + + align:start position:0% +very very ex successful uh business what + + + align:start position:0% +very very ex successful uh business what +we mostly focus is what is called Data + + align:start position:0% +we mostly focus is what is called Data + + + align:start position:0% +we mostly focus is what is called Data +intensive cloud computing you know it's + + align:start position:0% +intensive cloud computing you know it's + + + align:start position:0% +intensive cloud computing you know it's +based on Hadoop and other types of + + align:start position:0% +based on Hadoop and other types of + + + align:start position:0% +based on Hadoop and other types of +Technologies um but but even still a lot + + align:start position:0% +Technologies um but but even still a lot + + + align:start position:0% +Technologies um but but even still a lot +of that is technologies that are used by + + align:start position:0% +of that is technologies that are used by + + + align:start position:0% +of that is technologies that are used by +large scale Cloud companies but they + + align:start position:0% +large scale Cloud companies but they + + + align:start position:0% +large scale Cloud companies but they +don't really share with you + + align:start position:0% +don't really share with you + + + align:start position:0% +don't really share with you +Google although it's often called Hadoop + + align:start position:0% +Google although it's often called Hadoop + + + align:start position:0% +Google although it's often called Hadoop +Google doesn't actually use Hadoop + + align:start position:0% +Google doesn't actually use Hadoop + + + align:start position:0% +Google doesn't actually use Hadoop +Hadoop is based on a small part of the + + align:start position:0% +Hadoop is based on a small part of the + + + align:start position:0% +Hadoop is based on a small part of the +Google infrastructure Google's + + align:start position:0% +Google infrastructure Google's + + + align:start position:0% +Google infrastructure Google's +infrastructure is vastly larger than + + align:start position:0% +infrastructure is vastly larger than + + + align:start position:0% +infrastructure is vastly larger than +that and they don't just let anybody log + + align:start position:0% +that and they don't just let anybody log + + + align:start position:0% +that and they don't just let anybody log +into it and say oh go ahead and mine all + + align:start position:0% +into it and say oh go ahead and mine all + + + align:start position:0% +into it and say oh go ahead and mine all +the Google data they they provide they + + align:start position:0% +the Google data they they provide they + + + align:start position:0% +the Google data they they provide they +expose it through Services allow you to + + align:start position:0% +expose it through Services allow you to + + + align:start position:0% +expose it through Services allow you to +do some of that but the core technology + + align:start position:0% +do some of that but the core technology + + + align:start position:0% +do some of that but the core technology +that they do they don't Expose and all + + align:start position:0% +that they do they don't Expose and all + + + align:start position:0% +that they do they don't Expose and all +large companies they don't expose that + + align:start position:0% +large companies they don't expose that + + + align:start position:0% +large companies they don't expose that +to you they give you selected services + + align:start position:0% +to you they give you selected services + + + align:start position:0% +to you they give you selected services +and such um but this is really what + + align:start position:0% +and such um but this is really what + + + align:start position:0% +and such um but this is really what +we're focused on is this data + + align:start position:0% +we're focused on is this data + + + align:start position:0% +we're focused on is this data +intensive if I wanted to further uh + + align:start position:0% +intensive if I wanted to further uh + + + align:start position:0% +intensive if I wanted to further uh +subdivide the cloud into into um you + + align:start position:0% +subdivide the cloud into into um you + + + align:start position:0% +subdivide the cloud into into um you +know from a from a an implementer + + align:start position:0% +know from a from a an implementer + + + align:start position:0% +know from a from a an implementer +perspective if + + align:start position:0% +perspective if + + + align:start position:0% +perspective if +you own a lot of computing Hardware I + + align:start position:0% +you own a lot of computing Hardware I + + + align:start position:0% +you own a lot of computing Hardware I +mean hundreds of kilowatts or megawatts + + align:start position:0% +mean hundreds of kilowatts or megawatts + + + align:start position:0% +mean hundreds of kilowatts or megawatts +of computing Hardware you're most likely + + align:start position:0% +of computing Hardware you're most likely + + + align:start position:0% +of computing Hardware you're most likely +doing one of these four + + align:start position:0% +doing one of these four + + + align:start position:0% +doing one of these four +things you could be doing + + align:start position:0% +things you could be doing + + + align:start position:0% +things you could be doing +uh you could be doing traditional super + + align:start position:0% +uh you could be doing traditional super + + + align:start position:0% +uh you could be doing traditional super +Computing which we all know and love + + align:start position:0% +Computing which we all know and love + + + align:start position:0% +Computing which we all know and love +which is sort of closest to what we do + + align:start position:0% +which is sort of closest to what we do + + + align:start position:0% +which is sort of closest to what we do +in L grid you could do traditional + + align:start position:0% +in L grid you could do traditional + + + align:start position:0% +in L grid you could do traditional +database management system so every + + align:start position:0% +database management system so every + + + align:start position:0% +database management system so every +single time you use a credit card make a + + align:start position:0% +single time you use a credit card make a + + + align:start position:0% +single time you use a credit card make a +purchase you're probably connecting to a + + align:start position:0% +purchase you're probably connecting to a + + + align:start position:0% +purchase you're probably connecting to a +traditional database management system + + align:start position:0% +traditional database management system + + + align:start position:0% +traditional database management system +you could be doing Enterprise Computing + + align:start position:0% +you could be doing Enterprise Computing + + + align:start position:0% +you could be doing Enterprise Computing +which mostly this day this day and age + + align:start position:0% +which mostly this day this day and age + + + align:start position:0% +which mostly this day this day and age +is run out of VMware so this is the + + align:start position:0% +is run out of VMware so this is the + + + align:start position:0% +is run out of VMware so this is the +VMware logo and so uh so you could be + + align:start position:0% +VMware logo and so uh so you could be + + + align:start position:0% +VMware logo and so uh so you could be +doing that so that's you know all the + + align:start position:0% +doing that so that's you know all the + + + align:start position:0% +doing that so that's you know all the +things I earlier mentioned or this new + + align:start position:0% +things I earlier mentioned or this new + + + align:start position:0% +things I earlier mentioned or this new +kit on the Block big data which is all + + align:start position:0% +kit on the Block big data which is all + + + align:start position:0% +kit on the Block big data which is all +the buzz today uh using Java and map + + align:start position:0% +the buzz today uh using Java and map + + + align:start position:0% +the buzz today uh using Java and map +produce and and other types of things + + align:start position:0% +produce and and other types of things + + + align:start position:0% +produce and and other types of things +the important thing to recognize is + + align:start position:0% +the important thing to recognize is + + + align:start position:0% +the important thing to recognize is +these four areas each of these are + + align:start position:0% +these four areas each of these are + + + align:start position:0% +these four areas each of these are +multi- tens of billions of dollars + + align:start position:0% +multi- tens of billions of dollars + + + align:start position:0% +multi- tens of billions of dollars +industry the the the the the the IT + + align:start position:0% +industry the the the the the the IT + + + align:start position:0% +industry the the the the the the IT +world has gotten large enough that we + + align:start position:0% +world has gotten large enough that we + + + align:start position:0% +world has gotten large enough that we +now see specialization down to the + + align:start position:0% +now see specialization down to the + + + align:start position:0% +now see specialization down to the +hardware level the hardware the + + align:start position:0% +hardware level the hardware the + + + align:start position:0% +hardware level the hardware the +processors that these folks use is + + align:start position:0% +processors that these folks use is + + + align:start position:0% +processors that these folks use is +different likewise for these folks and + + align:start position:0% +different likewise for these folks and + + + align:start position:0% +different likewise for these folks and +these folks you see specialization of + + align:start position:0% +these folks you see specialization of + + + align:start position:0% +these folks you see specialization of +chips now to these different types of + + align:start position:0% +chips now to these different types of + + + align:start position:0% +chips now to these different types of +things so each of these is at the center + + align:start position:0% +things so each of these is at the center + + + align:start position:0% +things so each of these is at the center +of a multi-billion dollar eco ecosystem + + align:start position:0% +of a multi-billion dollar eco ecosystem + + + align:start position:0% +of a multi-billion dollar eco ecosystem +and they each have pros and cons and + + align:start position:0% +and they each have pros and cons and + + + align:start position:0% +and they each have pros and cons and +sometimes you can do your mission wholly + + align:start position:0% +sometimes you can do your mission wholly + + + align:start position:0% +sometimes you can do your mission wholly +in one but sometimes you have to cross + + align:start position:0% +in one but sometimes you have to cross + + + align:start position:0% +in one but sometimes you have to cross +and when you do cross it can be quite a + + align:start position:0% +and when you do cross it can be quite a + + + align:start position:0% +and when you do cross it can be quite a +challenge because these worlds are not + + align:start position:0% +challenge because these worlds are not + + + align:start position:0% +challenge because these worlds are not +necessarily uh compatible and I would + + align:start position:0% +necessarily uh compatible and I would + + + align:start position:0% +necessarily uh compatible and I would +say just to help people understand Hado + + align:start position:0% +say just to help people understand Hado + + + align:start position:0% +say just to help people understand Hado +one one one must recognize that it's + + align:start position:0% +one one one must recognize that it's + + + align:start position:0% +one one one must recognize that it's +that it's very much Java is the first + + align:start position:0% +that it's very much Java is the first + + + align:start position:0% +that it's very much Java is the first +class citizen in the Hadoop world it is + + align:start position:0% +class citizen in the Hadoop world it is + + + align:start position:0% +class citizen in the Hadoop world it is +a a world the entire infrastructure is + + align:start position:0% +a a world the entire infrastructure is + + + align:start position:0% +a a world the entire infrastructure is +written in Java it's designed so that + + align:start position:0% +written in Java it's designed so that + + + align:start position:0% +written in Java it's designed so that +only if you only Java you can actually + + align:start position:0% +only if you only Java you can actually + + + align:start position:0% +only if you only Java you can actually +administer and manage a cluster which is + + align:start position:0% +administer and manage a cluster which is + + + align:start position:0% +administer and manage a cluster which is +why it's become so popular there are so + + align:start position:0% +why it's become so popular there are so + + + align:start position:0% +why it's become so popular there are so +many Java programmers and now they just + + align:start position:0% +many Java programmers and now they just + + + align:start position:0% +many Java programmers and now they just +know Java and they download hop and they + + align:start position:0% +know Java and they download hop and they + + + align:start position:0% +know Java and they download hop and they +have rudimentary access to some computer + + align:start position:0% +have rudimentary access to some computer + + + align:start position:0% +have rudimentary access to some computer +systems they can sort of Cobble together + + align:start position:0% +systems they can sort of Cobble together + + + align:start position:0% +systems they can sort of Cobble together +a cluster I should say the same thing + + align:start position:0% +a cluster I should say the same thing + + + align:start position:0% +a cluster I should say the same thing +occurred in the sea and Fortran + + align:start position:0% +occurred in the sea and Fortran + + + align:start position:0% +occurred in the sea and Fortran +community in the mid 90s there was a + + align:start position:0% +community in the mid 90s there was a + + + align:start position:0% +community in the mid 90s there was a +technology called MPI in fact this is + + align:start position:0% +technology called MPI in fact this is + + + align:start position:0% +technology called MPI in fact this is +the MPI logo today which allowed you if + + align:start position:0% +the MPI logo today which allowed you if + + + align:start position:0% +the MPI logo today which allowed you if +you knew C and Fortran had rudimentary + + align:start position:0% +you knew C and Fortran had rudimentary + + + align:start position:0% +you knew C and Fortran had rudimentary +access on a on a on a network of a set + + align:start position:0% +access on a on a on a network of a set + + + align:start position:0% +access on a on a on a network of a set +of workstations you could create a + + align:start position:0% +of workstations you could create a + + + align:start position:0% +of workstations you could create a +cluster with MPI and that really sort of + + align:start position:0% +cluster with MPI and that really sort of + + + align:start position:0% +cluster with MPI and that really sort of +began the whole sort of parallel cluster + + align:start position:0% +began the whole sort of parallel cluster + + + align:start position:0% +began the whole sort of parallel cluster +Computing Revolution this does the same + + align:start position:0% +Computing Revolution this does the same + + + align:start position:0% +Computing Revolution this does the same +thing in Java and so for Java + + align:start position:0% +thing in Java and so for Java + + + align:start position:0% +thing in Java and so for Java +programmers that's you know it's been a + + align:start position:0% +programmers that's you know it's been a + + + align:start position:0% +programmers that's you know it's been a +huge success uh in that + + align:start position:0% +huge success uh in that + + + align:start position:0% +huge success uh in that +regard just so you know how where we sit + + align:start position:0% +regard just so you know how where we sit + + + align:start position:0% +regard just so you know how where we sit +in with that so we have L grid here + + align:start position:0% +in with that so we have L grid here + + + align:start position:0% +in with that so we have L grid here +which has really made traditional + + align:start position:0% +which has really made traditional + + + align:start position:0% +which has really made traditional +supercomputing uh feel interactive and + + align:start position:0% +supercomputing uh feel interactive and + + + align:start position:0% +supercomputing uh feel interactive and +on demand and elastic so that's one of + + align:start position:0% +on demand and elastic so that's one of + + + align:start position:0% +on demand and elastic so that's one of +the things that we do that's El grid + + align:start position:0% +the things that we do that's El grid + + + align:start position:0% +the things that we do that's El grid +very very unique you launch your job it + + align:start position:0% +very very unique you launch your job it + + + align:start position:0% +very very unique you launch your job it +runs immediately that is different than + + align:start position:0% +runs immediately that is different than + + + align:start position:0% +runs immediately that is different than +the way every other supercomputing + + align:start position:0% +the way every other supercomputing + + + align:start position:0% +the way every other supercomputing +Center in the country is run most superu + + align:start position:0% +Center in the country is run most superu + + + align:start position:0% +Center in the country is run most superu +centers are run by you write your + + align:start position:0% +centers are run by you write your + + + align:start position:0% +centers are run by you write your +program and you launch it and you wait + + align:start position:0% +program and you launch it and you wait + + + align:start position:0% +program and you launch it and you wait +until the queue says that it that it + + align:start position:0% +until the queue says that it that it + + + align:start position:0% +until the queue says that it that it +that it run and in fact some centers + + align:start position:0% +that it run and in fact some centers + + + align:start position:0% +that it run and in fact some centers +will even use as a metric of success how + + align:start position:0% +will even use as a metric of success how + + + align:start position:0% +will even use as a metric of success how +long their waight is it's kind of like a + + align:start position:0% +long their waight is it's kind of like a + + + align:start position:0% +long their waight is it's kind of like a +restaurant right you know how how many + + align:start position:0% +restaurant right you know how how many + + + align:start position:0% +restaurant right you know how how many +years do you have to wait to get a good + + align:start position:0% +years do you have to wait to get a good + + + align:start position:0% +years do you have to wait to get a good +reservation or a good doctor right and I + + align:start position:0% +reservation or a good doctor right and I + + + align:start position:0% +reservation or a good doctor right and I +remember someone saying oh our system is + + align:start position:0% +remember someone saying oh our system is + + + align:start position:0% +remember someone saying oh our system is +so so successful that our weight is a + + align:start position:0% +so so successful that our weight is a + + + align:start position:0% +so so successful that our weight is a +week you hit go submit and you will have + + align:start position:0% +week you hit go submit and you will have + + + align:start position:0% +week you hit go submit and you will have +to await a week to run your job so we + + align:start position:0% +to await a week to run your job so we + + + align:start position:0% +to await a week to run your job so we +don't really feel that's not really + + align:start position:0% +don't really feel that's not really + + + align:start position:0% +don't really feel that's not really +consistent with the way we do business + + align:start position:0% +consistent with the way we do business + + + align:start position:0% +consistent with the way we do business +around here you're under very tight + + align:start position:0% +around here you're under very tight + + + align:start position:0% +around here you're under very tight +deadlines so we created a very different + + align:start position:0% +deadlines so we created a very different + + + align:start position:0% +deadlines so we created a very different +type of system uh 10 years ago which + + align:start position:0% +type of system uh 10 years ago which + + + align:start position:0% +type of system uh 10 years ago which +sort of feels more like what you people + + align:start position:0% +sort of feels more like what you people + + + align:start position:0% +sort of feels more like what you people +are trying to do in the cloud and theup + + align:start position:0% +are trying to do in the cloud and theup + + + align:start position:0% +are trying to do in the cloud and theup +Community there's been a lot of work to + + align:start position:0% +Community there's been a lot of work to + + + align:start position:0% +Community there's been a lot of work to +try and make databases what these + + align:start position:0% +try and make databases what these + + + align:start position:0% +try and make databases what these +Technologies give you is is sort of + + align:start position:0% +Technologies give you is is sort of + + + align:start position:0% +Technologies give you is is sort of +efficient search and so there are a + + align:start position:0% +efficient search and so there are a + + + align:start position:0% +efficient search and so there are a +number of databases that been developed + + align:start position:0% +number of databases that been developed + + + align:start position:0% +number of databases that been developed +that sit on top of Hadoop hbas being one + + align:start position:0% +that sit on top of Hadoop hbas being one + + + align:start position:0% +that sit on top of Hadoop hbas being one +and acumulo being another you know which + + align:start position:0% +and acumulo being another you know which + + + align:start position:0% +and acumulo being another you know which +to my knowledge is the highest + + align:start position:0% +to my knowledge is the highest + + + align:start position:0% +to my knowledge is the highest +performance open source triple store in + + align:start position:0% +performance open source triple store in + + + align:start position:0% +performance open source triple store in +the world and probably will remain that + + align:start position:0% +the world and probably will remain that + + + align:start position:0% +the world and probably will remain that +way for a very long time and so we will + + align:start position:0% +way for a very long time and so we will + + + align:start position:0% +way for a very long time and so we will +be using the accumulo + + align:start position:0% +be using the accumulo + + + align:start position:0% +be using the accumulo +database and then we've created bindings + + align:start position:0% +database and then we've created bindings + + + align:start position:0% +database and then we've created bindings +to that so we have our d4m technology + + align:start position:0% +to that so we have our d4m technology + + + align:start position:0% +to that so we have our d4m technology +which allows you to bind uh to databases + + align:start position:0% +which allows you to bind uh to databases + + + align:start position:0% +which allows you to bind uh to databases +and we also something called el grid map + + align:start position:0% +and we also something called el grid map + + + align:start position:0% +and we also something called el grid map +produce a map produces sort of the core + + align:start position:0% +produce a map produces sort of the core + + + align:start position:0% +produce a map produces sort of the core +programming model within um within the + + align:start position:0% +programming model within um within the + + + align:start position:0% +programming model within um within the +Hadoop Community it's it's such a + + align:start position:0% +Hadoop Community it's it's such a + + + align:start position:0% +Hadoop Community it's it's such a +trivial model it almost doesn't even + + align:start position:0% +trivial model it almost doesn't even + + + align:start position:0% +trivial model it almost doesn't even +deserve a name it's basically like write + + align:start position:0% +deserve a name it's basically like write + + + align:start position:0% +deserve a name it's basically like write +a program given a list of files each + + align:start position:0% +a program given a list of files each + + + align:start position:0% +a program given a list of files each +program runs on each file independently + + align:start position:0% +program runs on each file independently + + + align:start position:0% +program runs on each file independently +I mean it's a very very simple model + + align:start position:0% +I mean it's a very very simple model + + + align:start position:0% +I mean it's a very very simple model +it's been around since the beginning of + + align:start position:0% +it's been around since the beginning of + + + align:start position:0% +it's been around since the beginning of +of computing but you know it's become + + align:start position:0% +of computing but you know it's become + + + align:start position:0% +of computing but you know it's become +the name has become popularized uh here + + align:start position:0% +the name has become popularized uh here + + + align:start position:0% +the name has become popularized uh here +and um and we now have a way to do map + + align:start position:0% +and um and we now have a way to do map + + + align:start position:0% +and um and we now have a way to do map +produced right in L Grid it's very easy + + align:start position:0% +produced right in L Grid it's very easy + + + align:start position:0% +produced right in L Grid it's very easy +and people enjoy it and if you're uh you + + align:start position:0% +and people enjoy it and if you're uh you + + + align:start position:0% +and people enjoy it and if you're uh you +can of course do the same thing with + + align:start position:0% +can of course do the same thing with + + + align:start position:0% +can of course do the same thing with +other other Technologies in L grid but + + align:start position:0% +other other Technologies in L grid but + + + align:start position:0% +other other Technologies in L grid but +for those people particularly if you're + + align:start position:0% +for those people particularly if you're + + + align:start position:0% +for those people particularly if you're +writing Java or not mat lab we don't + + align:start position:0% +writing Java or not mat lab we don't + + + align:start position:0% +writing Java or not mat lab we don't +recommend people use this for mat lab + + align:start position:0% +recommend people use this for mat lab + + + align:start position:0% +recommend people use this for mat lab +because we have better Technologies for + + align:start position:0% +because we have better Technologies for + + + align:start position:0% +because we have better Technologies for +doing that but if you're using You Know + + align:start position:0% +doing that but if you're using You Know + + + align:start position:0% +doing that but if you're using You Know +M uh you know python or or Java or other + + align:start position:0% +M uh you know python or or Java or other + + + align:start position:0% +M uh you know python or or Java or other +programs then map produc is there for + + align:start position:0% +programs then map produc is there for + + + align:start position:0% +programs then map produc is there for +you as we move towards combining so our + + align:start position:0% +you as we move towards combining so our + + + align:start position:0% +you as we move towards combining so our +big Vision here is to combine big big + + align:start position:0% +big Vision here is to combine big big + + + align:start position:0% +big Vision here is to combine big big +comput and big data and so we have a + + align:start position:0% +comput and big data and so we have a + + + align:start position:0% +comput and big data and so we have a +whole stack here as we deal with new + + align:start position:0% +whole stack here as we deal with new + + + align:start position:0% +whole stack here as we deal with new +applications text cyber bio other types + + align:start position:0% +applications text cyber bio other types + + + align:start position:0% +applications text cyber bio other types +of things the new apis that people + + align:start position:0% +of things the new apis that people + + + align:start position:0% +of things the new apis that people +writing the new types of distributed + + align:start position:0% +writing the new types of distributed + + + align:start position:0% +writing the new types of distributed +databases so it's really affecting + + align:start position:0% +databases so it's really affecting + + + align:start position:0% +databases so it's really affecting +everything just an example of the Hadoop + + align:start position:0% +everything just an example of the Hadoop + + + align:start position:0% +everything just an example of the Hadoop +architecture just so you you you know + + align:start position:0% +architecture just so you you you know + + + align:start position:0% +architecture just so you you you know +you've had this course you should at + + align:start position:0% +you've had this course you should at + + + align:start position:0% +you've had this course you should at +least have a few minutes so that if + + align:start position:0% +least have a few minutes so that if + + + align:start position:0% +least have a few minutes so that if +someone ask what does Hadoop if you know + + align:start position:0% +someone ask what does Hadoop if you know + + + align:start position:0% +someone ask what does Hadoop if you know +what it know what it does this is the + + align:start position:0% +what it know what it does this is the + + + align:start position:0% +what it know what it does this is the +basic architecture so you have a Hadoop + + align:start position:0% +basic architecture so you have a Hadoop + + + align:start position:0% +basic architecture so you have a Hadoop +map uce job you submit it and it goes to + + align:start position:0% +map uce job you submit it and it goes to + + + align:start position:0% +map uce job you submit it and it goes to +a job tracker the job tracker then + + align:start position:0% +a job tracker the job tracker then + + + align:start position:0% +a job tracker the job tracker then +breaks that up into subtasks each of + + align:start position:0% +breaks that up into subtasks each of + + + align:start position:0% +breaks that up into subtasks each of +which has its own tracker those tasks + + align:start position:0% +which has its own tracker those tasks + + + align:start position:0% +which has its own tracker those tasks +then get sent to the data nodes in the + + align:start position:0% +then get sent to the data nodes in the + + + align:start position:0% +then get sent to the data nodes in the +architecture and and uh and and it gets + + align:start position:0% +architecture and and uh and and it gets + + + align:start position:0% +architecture and and uh and and it gets +those data nodes and name node keeps + + align:start position:0% +those data nodes and name node keeps + + + align:start position:0% +those data nodes and name node keeps +track of the actual names of of the + + align:start position:0% +track of the actual names of of the + + + align:start position:0% +track of the actual names of of the +things it's a very simple Hadoop cluster + + align:start position:0% +things it's a very simple Hadoop cluster + + + align:start position:0% +things it's a very simple Hadoop cluster +this is the different types of of of of + + align:start position:0% +this is the different types of of of of + + + align:start position:0% +this is the different types of of of of +nodes that are in in and and processes + + align:start position:0% +nodes that are in in and and processes + + + align:start position:0% +nodes that are in in and and processes +in in the architecture + + align:start position:0% +in in the architecture + + + align:start position:0% +in in the architecture +hadoop's strengths and weaknesses well + + align:start position:0% +hadoop's strengths and weaknesses well + + + align:start position:0% +hadoop's strengths and weaknesses well +it's it does allow you to distribute + + align:start position:0% +it's it does allow you to distribute + + + align:start position:0% +it's it does allow you to distribute +processing a large data uh it's it's + + align:start position:0% +processing a large data uh it's it's + + + align:start position:0% +processing a large data uh it's it's +sort + + align:start position:0% +sort + + + align:start position:0% +sort +of best use case is if you wanted to + + align:start position:0% +of best use case is if you wanted to + + + align:start position:0% +of best use case is if you wanted to +let's say you had an enormous number of + + align:start position:0% +let's say you had an enormous number of + + + align:start position:0% +let's say you had an enormous number of +log files and you decided you only + + align:start position:0% +log files and you decided you only + + + align:start position:0% +log files and you decided you only +wanted to search them once for + + align:start position:0% +wanted to search them once for + + + align:start position:0% +wanted to search them once for +one string that's the perfect use case + + align:start position:0% +one string that's the perfect use case + + + align:start position:0% +one string that's the perfect use case +for Hado if you decide though that you + + align:start position:0% +for Hado if you decide though that you + + + align:start position:0% +for Hado if you decide though that you +would like to actually do more than one + + align:start position:0% +would like to actually do more than one + + + align:start position:0% +would like to actually do more than one +search you know then uh it's not it + + align:start position:0% +search you know then uh it's not it + + + align:start position:0% +search you know then uh it's not it +doesn't necessarily always make sense uh + + align:start position:0% +doesn't necessarily always make sense uh + + + align:start position:0% +doesn't necessarily always make sense uh +so it's basically designed to run grep + + align:start position:0% +so it's basically designed to run grep + + + align:start position:0% +so it's basically designed to run grep +on an enormous number of files and I kid + + align:start position:0% +on an enormous number of files and I kid + + + align:start position:0% +on an enormous number of files and I kid +you not there are companies today that + + align:start position:0% +you not there are companies today that + + + align:start position:0% +you not there are companies today that +actually do this like at production + + align:start position:0% +actually do this like at production + + + align:start position:0% +actually do this like at production +scale all their analytics are done by + + align:start position:0% +scale all their analytics are done by + + + align:start position:0% +scale all their analytics are done by +just grepping enormous numbers of log + + align:start position:0% +just grepping enormous numbers of log + + + align:start position:0% +just grepping enormous numbers of log +files needless to say that the entire + + align:start position:0% +files needless to say that the entire + + + align:start position:0% +files needless to say that the entire +database Community you know cringes and + + align:start position:0% +database Community you know cringes and + + + align:start position:0% +database Community you know cringes and +rolls over in their graves if they're + + align:start position:0% +rolls over in their graves if they're + + + align:start position:0% +rolls over in their graves if they're +not alive uh that this because we have + + align:start position:0% +not alive uh that this because we have + + + align:start position:0% +not alive uh that this because we have +solved this problem with by by creating + + align:start position:0% +solved this problem with by by creating + + + align:start position:0% +solved this problem with by by creating +in by indexing our data and that allows + + align:start position:0% +in by indexing our data and that allows + + + align:start position:0% +in by indexing our data and that allows +you to do fast search and people that's + + align:start position:0% +you to do fast search and people that's + + + align:start position:0% +you to do fast search and people that's +why people have invented databases like + + align:start position:0% +why people have invented databases like + + + align:start position:0% +why people have invented databases like +hbase and accumula which should sit on + + align:start position:0% +hbase and accumula which should sit on + + + align:start position:0% +hbase and accumula which should sit on +top of a d because they recognize that + + align:start position:0% +top of a d because they recognize that + + + align:start position:0% +top of a d because they recognize that +you know really if you're going to + + align:start position:0% +you know really if you're going to + + + align:start position:0% +you know really if you're going to +search more than once you should index + + align:start position:0% +search more than once you should index + + + align:start position:0% +search more than once you should index +your + + align:start position:0% +your + + + align:start position:0% +your +data again um it it is very scalable it + + align:start position:0% +data again um it it is very scalable it + + + align:start position:0% +data again um it it is very scalable it +is fundamentally designed to have + + align:start position:0% +is fundamentally designed to have + + + align:start position:0% +is fundamentally designed to have +extremely unreliable Hardware in it so + + align:start position:0% +extremely unreliable Hardware in it so + + + align:start position:0% +extremely unreliable Hardware in it so +it is quite resilient it does this + + align:start position:0% +it is quite resilient it does this + + + align:start position:0% +it is quite resilient it does this +resiliency at a cost it relies on a + + align:start position:0% +resiliency at a cost it relies on a + + + align:start position:0% +resiliency at a cost it relies on a +significant amount of + + align:start position:0% +significant amount of + + + align:start position:0% +significant amount of +replication typically the standard + + align:start position:0% +replication typically the standard + + + align:start position:0% +replication typically the standard +replication in a Hadoop cluster is a + + align:start position:0% +replication in a Hadoop cluster is a + + + align:start position:0% +replication in a Hadoop cluster is a +factor of + + align:start position:0% +factor of + + + align:start position:0% +factor of +three if you're in the high performance + + align:start position:0% +three if you're in the high performance + + + align:start position:0% +three if you're in the high performance +storage business this also makes you + + align:start position:0% +storage business this also makes you + + + align:start position:0% +storage business this also makes you +cringe because this makes you you're + + align:start position:0% +cringe because this makes you you're + + + align:start position:0% +cringe because this makes you you're +paying 3x for your storage we have + + align:start position:0% +paying 3x for your storage we have + + + align:start position:0% +paying 3x for your storage we have +techniques like raid which allow us to + + align:start position:0% +techniques like raid which allow us to + + + align:start position:0% +techniques like raid which allow us to +to to do that but again the expertise + + align:start position:0% +to to do that but again the expertise + + + align:start position:0% +to to do that but again the expertise +required to set up a cluster and do 3x + + align:start position:0% +required to set up a cluster and do 3x + + + align:start position:0% +required to set up a cluster and do 3x +uh replication is relatively low and so + + align:start position:0% +uh replication is relatively low and so + + + align:start position:0% +uh replication is relatively low and so +that makes it very appealing to many + + align:start position:0% +that makes it very appealing to many + + + align:start position:0% +that makes it very appealing to many +many many folks and so it's very useful + + align:start position:0% +many many folks and so it's very useful + + + align:start position:0% +many many folks and so it's very useful +for that um some of the difficulties um + + align:start position:0% +for that um some of the difficulties um + + + align:start position:0% +for that um some of the difficulties um +the scheduler in Hadoop is very + + align:start position:0% +the scheduler in Hadoop is very + + + align:start position:0% +the scheduler in Hadoop is very +immature um it is schedulers are very + + align:start position:0% +immature um it is schedulers are very + + + align:start position:0% +immature um it is schedulers are very +well defin there's about two or three + + align:start position:0% +well defin there's about two or three + + + align:start position:0% +well defin there's about two or three +standard schedulers in the + + align:start position:0% +standard schedulers in the + + + align:start position:0% +standard schedulers in the +supercomputing community they're each + + align:start position:0% +supercomputing community they're each + + + align:start position:0% +supercomputing community they're each +about 20 years old they all have the + + align:start position:0% +about 20 years old they all have the + + + align:start position:0% +about 20 years old they all have the +same 200 features and you need about 200 + + align:start position:0% +same 200 features and you need about 200 + + + align:start position:0% +same 200 features and you need about 200 +features to really do a proper scheduler + + align:start position:0% +features to really do a proper scheduler + + + align:start position:0% +features to really do a proper scheduler +had dup is about four or 5 years old and + + align:start position:0% +had dup is about four or 5 years old and + + + align:start position:0% +had dup is about four or 5 years old and +it's got about that many features and so + + align:start position:0% +it's got about that many features and so + + + align:start position:0% +it's got about that many features and so +uh you do often have to deal with + + align:start position:0% +uh you do often have to deal with + + + align:start position:0% +uh you do often have to deal with +collisions it's easy for one user to hog + + align:start position:0% +collisions it's easy for one user to hog + + + align:start position:0% +collisions it's easy for one user to hog +and monopolize the entire cluster uh + + align:start position:0% +and monopolize the entire cluster uh + + + align:start position:0% +and monopolize the entire cluster uh +you're often dealing with various + + align:start position:0% +you're often dealing with various + + + align:start position:0% +you're often dealing with various +overheads from the scheduler itself so + + align:start position:0% +overheads from the scheduler itself so + + + align:start position:0% +overheads from the scheduler itself so +that and this is well known to the hudo + + align:start position:0% +that and this is well known to the hudo + + + align:start position:0% +that and this is well known to the hudo +community they're working on it actively + + align:start position:0% +community they're working on it actively + + + align:start position:0% +community they're working on it actively +um and and we will see how that uh you + + align:start position:0% +um and and we will see how that uh you + + + align:start position:0% +um and and we will see how that uh you +know it's not an easy multi-user + + align:start position:0% +know it's not an easy multi-user + + + align:start position:0% +know it's not an easy multi-user +environment and as I've said before it + + align:start position:0% +environment and as I've said before it + + + align:start position:0% +environment and as I've said before it +fundamentally relies on the fact that + + align:start position:0% +fundamentally relies on the fact that + + + align:start position:0% +fundamentally relies on the fact that +the JV m is on every node because when + + align:start position:0% +the JV m is on every node because when + + + align:start position:0% +the JV m is on every node because when +you're sending a program to every node + + align:start position:0% +you're sending a program to every node + + + align:start position:0% +you're sending a program to every node +The Interpreter for that must exist on + + align:start position:0% +The Interpreter for that must exist on + + + align:start position:0% +The Interpreter for that must exist on +every node and by definition the only + + align:start position:0% +every node and by definition the only + + + align:start position:0% +every node and by definition the only +language that you're guaranteed to have + + align:start position:0% +language that you're guaranteed to have + + + align:start position:0% +language that you're guaranteed to have +every node in a Hadoop cluster is Java + + align:start position:0% +every node in a Hadoop cluster is Java + + + align:start position:0% +every node in a Hadoop cluster is Java +any other language any other tool has to + + align:start position:0% +any other language any other tool has to + + + align:start position:0% +any other language any other tool has to +be installed and become a part of the + + align:start position:0% +be installed and become a part of the + + + align:start position:0% +be installed and become a part of the +the image for the entire system so that + + align:start position:0% +the image for the entire system so that + + + align:start position:0% +the image for the entire system so that +it can be run on on every note so that + + align:start position:0% +it can be run on on every note so that + + + align:start position:0% +it can be run on on every note so that +is that is something that one has to be + + align:start position:0% +is that is something that one has to be + + + align:start position:0% +is that is something that one has to be +aware of and we've certainly seen this + + align:start position:0% +aware of and we've certainly seen this + + + align:start position:0% +aware of and we've certainly seen this +like oh I wrote These great programs in + + align:start position:0% +like oh I wrote These great programs in + + + align:start position:0% +like oh I wrote These great programs in +another language and it's like well can + + align:start position:0% +another language and it's like well can + + + align:start position:0% +another language and it's like well can +I just run them it's like no that that + + align:start position:0% +I just run them it's like no that that + + + align:start position:0% +I just run them it's like no that that +that doesn't exist you know even + + align:start position:0% +that doesn't exist you know even + + + align:start position:0% +that doesn't exist you know even +Distributing a a fat binary can be be + + align:start position:0% +Distributing a a fat binary can be be + + + align:start position:0% +Distributing a a fat binary can be be +difficult because it has to be + + align:start position:0% +difficult because it has to be + + + align:start position:0% +difficult because it has to be +distributed through the Hadoop + + align:start position:0% +distributed through the Hadoop + + + align:start position:0% +distributed through the Hadoop +distributed file system all data is + + align:start position:0% +distributed file system all data is + + + align:start position:0% +distributed file system all data is +distributed there and that is not you + + align:start position:0% +distributed there and that is not you + + + align:start position:0% +distributed there and that is not you +have to essentially write a wrapper + + align:start position:0% +have to essentially write a wrapper + + + align:start position:0% +have to essentially write a wrapper +program that then recognizes where to + + align:start position:0% +program that then recognizes where to + + + align:start position:0% +program that then recognizes where to +get your binary and then then execs that + + align:start position:0% +get your binary and then then execs that + + + align:start position:0% +get your binary and then then execs that +thing and it can be + + align:start position:0% +thing and it can be + + + align:start position:0% +thing and it can be +tricky the basic L grid map produce + + align:start position:0% +tricky the basic L grid map produce + + + align:start position:0% +tricky the basic L grid map produce +architecture simplifies this + + align:start position:0% +architecture simplifies this + + + align:start position:0% +architecture simplifies this +significantly although this maybe + + align:start position:0% +significantly although this maybe + + + align:start position:0% +significantly although this maybe +doesn't look like it + + align:start position:0% +doesn't look like it + + + align:start position:0% +doesn't look like it +um it basically you know essentially you + + align:start position:0% +um it basically you know essentially you + + + align:start position:0% +um it basically you know essentially you +call elog good map map produce it + + align:start position:0% +call elog good map map produce it + + + align:start position:0% +call elog good map map produce it +launches a bunch of what are called + + align:start position:0% +launches a bunch of what are called + + + align:start position:0% +launches a bunch of what are called +mapper tasks it runs them on your + + align:start position:0% +mapper tasks it runs them on your + + + align:start position:0% +mapper tasks it runs them on your +different input files when they have + + align:start position:0% +different input files when they have + + + align:start position:0% +different input files when they have +done they've created output files and + + align:start position:0% +done they've created output files and + + + align:start position:0% +done they've created output files and +then runs another program if you + + align:start position:0% +then runs another program if you + + + align:start position:0% +then runs another program if you +specified that then combines the output + + align:start position:0% +specified that then combines the output + + + align:start position:0% +specified that then combines the output +so that's the basic model of map produce + + align:start position:0% +so that's the basic model of map produce + + + align:start position:0% +so that's the basic model of map produce +which is you have a what's called a map + + align:start position:0% +which is you have a what's called a map + + + align:start position:0% +which is you have a what's called a map +program and a reduced program and the + + align:start position:0% +program and a reduced program and the + + + align:start position:0% +program and a reduced program and the +map program is given a list of files it + + align:start position:0% +map program is given a list of files it + + + align:start position:0% +map program is given a list of files it +runs those programs one at a time each + + align:start position:0% +runs those programs one at a time each + + + align:start position:0% +runs those programs one at a time each +one of them generates an output and a + + align:start position:0% +one of them generates an output and a + + + align:start position:0% +one of them generates an output and a +reduced program pulls them all together + + align:start position:0% +reduced program pulls them all together + + + align:start position:0% +reduced program pulls them all together +all right so that's our little tutorial + + align:start position:0% +all right so that's our little tutorial + + + align:start position:0% +all right so that's our little tutorial +on Hadoop and because I felt an + + align:start position:0% +on Hadoop and because I felt an + + + align:start position:0% +on Hadoop and because I felt an +obligation to to explain that to you uh + + align:start position:0% +obligation to to explain that to you uh + + + align:start position:0% +obligation to to explain that to you uh +we couldn't be a big data course without + + align:start position:0% +we couldn't be a big data course without + + + align:start position:0% +we couldn't be a big data course without +without having going that but it's very + + align:start position:0% +without having going that but it's very + + + align:start position:0% +without having going that but it's very +simple and it very popular I expect it + + align:start position:0% +simple and it very popular I expect it + + + align:start position:0% +simple and it very popular I expect it +to be M maintain its popularity for a + + align:start position:0% +to be M maintain its popularity for a + + + align:start position:0% +to be M maintain its popularity for a +very long time you know I think it will + + align:start position:0% +very long time you know I think it will + + + align:start position:0% +very long time you know I think it will +evolve and get better but for the vast + + align:start position:0% +evolve and get better but for the vast + + + align:start position:0% +evolve and get better but for the vast +majority of people on planet Earth this + + align:start position:0% +majority of people on planet Earth this + + + align:start position:0% +majority of people on planet Earth this +is really the most accessible form of + + align:start position:0% +is really the most accessible form of + + + align:start position:0% +is really the most accessible form of +parallel Computing technology that they + + align:start position:0% +parallel Computing technology that they + + + align:start position:0% +parallel Computing technology that they +have available so we should all be aware + + align:start position:0% +have available so we should all be aware + + + align:start position:0% +have available so we should all be aware +of Hadoop and its existence and what it + + align:start position:0% +of Hadoop and its existence and what it + + + align:start position:0% +of Hadoop and its existence and what it +can do because uh many of our customers + + align:start position:0% +can do because uh many of our customers + + + align:start position:0% +can do because uh many of our customers +use Hadoop and we we need to work with + + align:start position:0% +use Hadoop and we we need to work with + + + align:start position:0% +use Hadoop and we we need to work with +them all right so getting back now to + + align:start position:0% +them all right so getting back now to + + + align:start position:0% +them all right so getting back now to +d4m I think I've mentioned a lot of this + + align:start position:0% +d4m I think I've mentioned a lot of this + + + align:start position:0% +d4m I think I've mentioned a lot of this +before the core concept of d4m is + + align:start position:0% +before the core concept of d4m is + + + align:start position:0% +before the core concept of d4m is +multi-dimensional associative arrays + + align:start position:0% +multi-dimensional associative arrays + + + align:start position:0% +multi-dimensional associative arrays +again d4m is designed to sort of + + align:start position:0% +again d4m is designed to sort of + + + align:start position:0% +again d4m is designed to sort of +overcomes for those of us who have more + + align:start position:0% +overcomes for those of us who have more + + + align:start position:0% +overcomes for those of us who have more +mathematical uh expertise we can take we + + align:start position:0% +mathematical uh expertise we can take we + + + align:start position:0% +mathematical uh expertise we can take we +can do uh much more sophisticated things + + align:start position:0% +can do uh much more sophisticated things + + + align:start position:0% +can do uh much more sophisticated things +than you might be able to do in in + + align:start position:0% +than you might be able to do in in + + + align:start position:0% +than you might be able to do in in +Hadoop again it allows you to uh uh look + + align:start position:0% +Hadoop again it allows you to uh uh look + + + align:start position:0% +Hadoop again it allows you to uh uh look +at your data in four ways at once you + + align:start position:0% +at your data in four ways at once you + + + align:start position:0% +at your data in four ways at once you +can view it as 2D matrices and and + + align:start position:0% +can view it as 2D matrices and and + + + align:start position:0% +can view it as 2D matrices and and +reference rows and columns with with + + align:start position:0% +reference rows and columns with with + + + align:start position:0% +reference rows and columns with with +with strings and have values that are + + align:start position:0% +with strings and have values that are + + + align:start position:0% +with strings and have values that are +strings it's one to one with a triple + + align:start position:0% +strings it's one to one with a triple + + + align:start position:0% +strings it's one to one with a triple +store so you can easily connect to + + align:start position:0% +store so you can easily connect to + + + align:start position:0% +store so you can easily connect to +databases again uh it it it looks like + + align:start position:0% +databases again uh it it it looks like + + + align:start position:0% +databases again uh it it it looks like +matrices so you can do linear algebra + + align:start position:0% +matrices so you can do linear algebra + + + align:start position:0% +matrices so you can do linear algebra +and also uh between The Duality between + + align:start position:0% +and also uh between The Duality between + + + align:start position:0% +and also uh between The Duality between +adjacency matrices and graphs you can + + align:start position:0% +adjacency matrices and graphs you can + + + align:start position:0% +adjacency matrices and graphs you can +also think about your data as + + align:start position:0% +also think about your data as + + + align:start position:0% +also think about your data as +graphs this is composable as I've said + + align:start position:0% +graphs this is composable as I've said + + + align:start position:0% +graphs this is composable as I've said +before uh almost all of our operations + + align:start position:0% +before uh almost all of our operations + + + align:start position:0% +before uh almost all of our operations +that are perform an associative array + + align:start position:0% +that are perform an associative array + + + align:start position:0% +that are perform an associative array +return another associative array and so + + align:start position:0% +return another associative array and so + + + align:start position:0% +return another associative array and so +we have uh we can do things like add + + align:start position:0% +we have uh we can do things like add + + + align:start position:0% +we have uh we can do things like add +them subtract them and them order them + + align:start position:0% +them subtract them and them order them + + + align:start position:0% +them subtract them and them order them +multiply them and we can do very + + align:start position:0% +multiply them and we can do very + + + align:start position:0% +multiply them and we can do very +complicated queries very easily and + + align:start position:0% +complicated queries very easily and + + + align:start position:0% +complicated queries very easily and +these can work in associate arrays and + + align:start position:0% +these can work in associate arrays and + + + align:start position:0% +these can work in associate arrays and +if we're bound to table they can also + + align:start position:0% +if we're bound to table they can also + + + align:start position:0% +if we're bound to table they can also +also do + + align:start position:0% +also do + + + align:start position:0% +also do +that speaking of tables I've already + + align:start position:0% +that speaking of tables I've already + + + align:start position:0% +that speaking of tables I've already +talked about our schema in this class + + align:start position:0% +talked about our schema in this class + + + align:start position:0% +talked about our schema in this class +that we always use so if your standard + + align:start position:0% +that we always use so if your standard + + + align:start position:0% +that we always use so if your standard +data might look like this say this is a + + align:start position:0% +data might look like this say this is a + + + align:start position:0% +data might look like this say this is a +cyber record of a source IP domain and + + align:start position:0% +cyber record of a source IP domain and + + + align:start position:0% +cyber record of a source IP domain and +destination IP this is sort of the + + align:start position:0% +destination IP this is sort of the + + + align:start position:0% +destination IP this is sort of the +standard tabular view we explode it by + + align:start position:0% +standard tabular view we explode it by + + + align:start position:0% +standard tabular view we explode it by +taking the source uh pending the value + + align:start position:0% +taking the source uh pending the value + + + align:start position:0% +taking the source uh pending the value +to it which creates this a very large + + align:start position:0% +to it which creates this a very large + + + align:start position:0% +to it which creates this a very large +sparse table here which will naturally + + align:start position:0% +sparse table here which will naturally + + + align:start position:0% +sparse table here which will naturally +go into our triple store of course by + + align:start position:0% +go into our triple store of course by + + + align:start position:0% +go into our triple store of course by +itself it doesn't really gain as + + align:start position:0% +itself it doesn't really gain as + + + align:start position:0% +itself it doesn't really gain as +anything because most tables have a + + align:start position:0% +anything because most tables have a + + + align:start position:0% +anything because most tables have a +either a row based or column based the + + align:start position:0% +either a row based or column based the + + + align:start position:0% +either a row based or column based the +the databases that we are working with + + align:start position:0% +the databases that we are working with + + + align:start position:0% +the databases that we are working with +are row based which allow you to do fast + + align:start position:0% +are row based which allow you to do fast + + + align:start position:0% +are row based which allow you to do fast +lookup of a row key however once we've + + align:start position:0% +lookup of a row key however once we've + + + align:start position:0% +lookup of a row key however once we've +exploded the schema if we also store the + + align:start position:0% +exploded the schema if we also store the + + + align:start position:0% +exploded the schema if we also store the +transpose we now can index everything + + align:start position:0% +transpose we now can index everything + + + align:start position:0% +transpose we now can index everything +here quickly and effectively effectively + + align:start position:0% +here quickly and effectively effectively + + + align:start position:0% +here quickly and effectively effectively +to the user it looks like we have + + align:start position:0% +to the user it looks like we have + + + align:start position:0% +to the user it looks like we have +indexed every single string in the + + align:start position:0% +indexed every single string in the + + + align:start position:0% +indexed every single string in the +database with one schema which is very + + align:start position:0% +database with one schema which is very + + + align:start position:0% +database with one schema which is very +nice very powerful stepping stone for uh + + align:start position:0% +nice very powerful stepping stone for uh + + + align:start position:0% +nice very powerful stepping stone for uh +for uh for for getting + + align:start position:0% +for uh for for getting + + + align:start position:0% +for uh for for getting +results all right now I'm going to talk + + align:start position:0% +results all right now I'm going to talk + + + align:start position:0% +results all right now I'm going to talk +a little bit about what we have done + + align:start position:0% +a little bit about what we have done + + + align:start position:0% +a little bit about what we have done +here so I'm just going to go over some + + align:start position:0% +here so I'm just going to go over some + + + align:start position:0% +here so I'm just going to go over some +basic analytics and show you a little + + align:start position:0% +basic analytics and show you a little + + + align:start position:0% +basic analytics and show you a little +bit more code so for example here's our + + align:start position:0% +bit more code so for example here's our + + + align:start position:0% +bit more code so for example here's our +table and uh you know with these various + + align:start position:0% +table and uh you know with these various + + + align:start position:0% +table and uh you know with these various +so this could be viewed as the sparse + + align:start position:0% +so this could be viewed as the sparse + + + align:start position:0% +so this could be viewed as the sparse +Matrix we have various Source IPS here + + align:start position:0% +Matrix we have various Source IPS here + + + align:start position:0% +Matrix we have various Source IPS here +and I want to just compute some very + + align:start position:0% +and I want to just compute some very + + + align:start position:0% +and I want to just compute some very +elementary statistics on this + + align:start position:0% +elementary statistics on this + + + align:start position:0% +elementary statistics on this +data I should say + + align:start position:0% +data I should say + + + align:start position:0% +data I should say +Computing things like sums and averages + + align:start position:0% +Computing things like sums and averages + + + align:start position:0% +Computing things like sums and averages +may sound like not very sophisticated + + align:start position:0% +may sound like not very sophisticated + + + align:start position:0% +may sound like not very sophisticated +statistic um it's still extraordinarily + + align:start position:0% +statistic um it's still extraordinarily + + + align:start position:0% +statistic um it's still extraordinarily +powerful and we are amazed uh how + + align:start position:0% +powerful and we are amazed uh how + + + align:start position:0% +powerful and we are amazed uh how +valuable it is because it usually shows + + align:start position:0% +valuable it is because it usually shows + + + align:start position:0% +valuable it is because it usually shows +you right + + align:start position:0% +you right + + + align:start position:0% +you right +away the bad data in your data and you + + align:start position:0% +away the bad data in your data and you + + + align:start position:0% +away the bad data in your data and you +will always have bad data but for many + + align:start position:0% +will always have bad data but for many + + + align:start position:0% +will always have bad data but for many +of the and this is probably the first + + align:start position:0% +of the and this is probably the first + + + align:start position:0% +of the and this is probably the first +bit of value ad we Prov provide to + + align:start position:0% +bit of value ad we Prov provide to + + + align:start position:0% +bit of value ad we Prov provide to +almost any customer that we work with on + + align:start position:0% +almost any customer that we work with on + + + align:start position:0% +almost any customer that we work with on +d4m is it's the first time anybody's + + align:start position:0% +d4m is it's the first time anybody's + + + align:start position:0% +d4m is it's the first time anybody's +actually sort of looked at their data + + align:start position:0% +actually sort of looked at their data + + + align:start position:0% +actually sort of looked at their data +and totality and being able to do these + + align:start position:0% +and totality and being able to do these + + + align:start position:0% +and totality and being able to do these +types of things and so the usually the + + align:start position:0% +types of things and so the usually the + + + align:start position:0% +types of things and so the usually the +first thing we do is like all right + + align:start position:0% +first thing we do is like all right + + + align:start position:0% +first thing we do is like all right +we've loaded their data in schema we've + + align:start position:0% +we've loaded their data in schema we've + + + align:start position:0% +we've loaded their data in schema we've +done some basic sum and we'll say do you + + align:start position:0% +done some basic sum and we'll say do you + + + align:start position:0% +done some basic sum and we'll say do you +know that you have the following stuck + + align:start position:0% +know that you have the following stuck + + + align:start position:0% +know that you have the following stuck +on + + align:start position:0% +on + + + align:start position:0% +on +switches you know 8% of your data all + + align:start position:0% +switches you know 8% of your data all + + + align:start position:0% +switches you know 8% of your data all +has this value in this column which + + align:start position:0% +has this value in this column which + + + align:start position:0% +has this value in this column which +absolutely can't be right you know and + + align:start position:0% +absolutely can't be right you know and + + + align:start position:0% +absolutely can't be right you know and +8% could be a low enough number that you + + align:start position:0% +8% could be a low enough number that you + + + align:start position:0% +8% could be a low enough number that you +might not just encounter it through + + align:start position:0% +might not just encounter it through + + + align:start position:0% +might not just encounter it through +routine traversal but it will stand out + + align:start position:0% +routine traversal but it will stand out + + + align:start position:0% +routine traversal but it will stand out +in just the most rudimentary histogram + + align:start position:0% +in just the most rudimentary histogram + + + align:start position:0% +in just the most rudimentary histogram +you know extremely and so that's usually + + align:start position:0% +you know extremely and so that's usually + + + align:start position:0% +you know extremely and so that's usually +incredibly valuable P of abys like oh my + + align:start position:0% +incredibly valuable P of abys like oh my + + + align:start position:0% +incredibly valuable P of abys like oh my +goodness they'll usually like there's + + align:start position:0% +goodness they'll usually like there's + + + align:start position:0% +goodness they'll usually like there's +something broken in our system or you'll + + align:start position:0% +something broken in our system or you'll + + + align:start position:0% +something broken in our system or you'll +be like you know you have this column + + align:start position:0% +be like you know you have this column + + + align:start position:0% +be like you know you have this column +but it's almost never filled in and it + + align:start position:0% +but it's almost never filled in and it + + + align:start position:0% +but it's almost never filled in and it +sure looks like it should be filled in + + align:start position:0% +sure looks like it should be filled in + + + align:start position:0% +sure looks like it should be filled in +so these switches are stuck off and so + + align:start position:0% +so these switches are stuck off and so + + + align:start position:0% +so these switches are stuck off and so +that's often a you know I encourage when + + align:start position:0% +that's often a you know I encourage when + + + align:start position:0% +that's often a you know I encourage when +you do first thing to just kind of do + + align:start position:0% +you do first thing to just kind of do + + + align:start position:0% +you do first thing to just kind of do +the basic statistics on the data and see + + align:start position:0% +the basic statistics on the data and see + + + align:start position:0% +the basic statistics on the data and see +where things are are working and where + + align:start position:0% +where things are are working and where + + + align:start position:0% +where things are are working and where +things are broken and usually you can + + align:start position:0% +things are broken and usually you can + + + align:start position:0% +things are broken and usually you can +then um either fix them and most of the + + align:start position:0% +then um either fix them and most of the + + + align:start position:0% +then um either fix them and most of the +time when we tell a customers like we're + + align:start position:0% +time when we tell a customers like we're + + + align:start position:0% +time when we tell a customers like we're +just letting you know these are these + + align:start position:0% +just letting you know these are these + + + align:start position:0% +just letting you know these are these +are issues in your data we can work + + align:start position:0% +are issues in your data we can work + + + align:start position:0% +are issues in your data we can work +around them we can sort of ignore them + + align:start position:0% +around them we can sort of ignore them + + + align:start position:0% +around them we can sort of ignore them +and still proceed or you can fix them + + align:start position:0% +and still proceed or you can fix them + + + align:start position:0% +and still proceed or you can fix them +yourselves and almost always like no we + + align:start position:0% +yourselves and almost always like no we + + + align:start position:0% +yourselves and almost always like no we +want to fix that ourselves that's + + align:start position:0% +want to fix that ourselves that's + + + align:start position:0% +want to fix that ourselves that's +something that's fundamentally broken + + align:start position:0% +something that's fundamentally broken + + + align:start position:0% +something that's fundamentally broken +our our system we want to make sure that + + align:start position:0% +our our system we want to make sure that + + + align:start position:0% +our our system we want to make sure that +that data is correct because usually + + align:start position:0% +that data is correct because usually + + + align:start position:0% +that data is correct because usually +that data is flowing into all other + + align:start position:0% +that data is flowing into all other + + + align:start position:0% +that data is flowing into all other +places too and being acted on and so so + + align:start position:0% +places too and being acted on and so so + + + align:start position:0% +places too and being acted on and so so +that's one thing we we going to so we're + + align:start position:0% +that's one thing we we going to so we're + + + align:start position:0% +that's one thing we we going to so we're +just do some basic statistics here we're + + align:start position:0% +just do some basic statistics here we're + + + align:start position:0% +just do some basic statistics here we're +going to compute how many times uh each + + align:start position:0% +going to compute how many times uh each + + + align:start position:0% +going to compute how many times uh each +column type appears we're going to + + align:start position:0% +column type appears we're going to + + + align:start position:0% +column type appears we're going to +compute how many times each type appears + + align:start position:0% +compute how many times each type appears + + + align:start position:0% +compute how many times each type appears +um we'll compute some covariance + + align:start position:0% +um we'll compute some covariance + + + align:start position:0% +um we'll compute some covariance +matrices just some very very simple + + align:start position:0% +matrices just some very very simple + + + align:start position:0% +matrices just some very very simple +types of things here + + align:start position:0% + + + + align:start position:0% + +all right so we move on here so this is + + align:start position:0% +all right so we move on here so this is + + + align:start position:0% +all right so we move on here so this is +the basic uh + + align:start position:0% +the basic uh + + + align:start position:0% +the basic uh +implementation so we're going to give it + + align:start position:0% +implementation so we're going to give it + + + align:start position:0% +implementation so we're going to give it +a row a set of rows that we're looking + + align:start position:0% +a row a set of rows that we're looking + + + align:start position:0% +a row a set of rows that we're looking +at here this could be very + + align:start position:0% +at here this could be very + + + align:start position:0% +at here this could be very +large we have a table binding T so we + + align:start position:0% +large we have a table binding T so we + + + align:start position:0% +large we have a table binding T so we +say please go and get + + align:start position:0% +say please go and get + + + align:start position:0% +say please go and get +me all the uh all those rows so we get + + align:start position:0% +me all the uh all those rows so we get + + + align:start position:0% +me all the uh all those rows so we get +the whole swath of rows and that will + + align:start position:0% +the whole swath of rows and that will + + + align:start position:0% +the whole swath of rows and that will +return that as an associ of array and + + align:start position:0% +return that as an associ of array and + + + align:start position:0% +return that as an associ of array and +then normally I shorten this as double + + align:start position:0% +then normally I shorten this as double + + + align:start position:0% +then normally I shorten this as double +Loy but we since the uh the table always + + align:start position:0% +Loy but we since the uh the table always + + + align:start position:0% +Loy but we since the uh the table always +contains strings and return strings + + align:start position:0% +contains strings and return strings + + + align:start position:0% +contains strings and return strings +values the first thing we need is kind + + align:start position:0% +values the first thing we need is kind + + + align:start position:0% +values the first thing we need is kind +of get rid of those because we're going + + align:start position:0% +of get rid of those because we're going + + + align:start position:0% +of get rid of those because we're going +to do math so we turn them into logicals + + align:start position:0% +to do math so we turn them into logicals + + + align:start position:0% +to do math so we turn them into logicals +and then we turn them back into double + + align:start position:0% +and then we turn them back into double + + + align:start position:0% +and then we turn them back into double +so we can do + + align:start position:0% +so we can do + + + align:start position:0% +so we can do +math + + align:start position:0% +math + + + align:start position:0% +math +um you can actually pass regular + + align:start position:0% +um you can actually pass regular + + + align:start position:0% +um you can actually pass regular +Expressions you can also do the starts + + align:start position:0% +Expressions you can also do the starts + + + align:start position:0% +Expressions you can also do the starts +with command we want to get the the + + align:start position:0% +with command we want to get the the + + + align:start position:0% +with command we want to get the the +source IP just we're just interested in + + align:start position:0% +source IP just we're just interested in + + + align:start position:0% +source IP just we're just interested in +Source IP domain and the first thing we + + align:start position:0% +Source IP domain and the first thing we + + + align:start position:0% +Source IP domain and the first thing we +going do is find some popular columns so + + align:start position:0% +going do is find some popular columns so + + + align:start position:0% +going do is find some popular columns so +we just type some + + align:start position:0% +we just type some + + + align:start position:0% +we just type some +and that shows us popular columns we + + align:start position:0% +and that shows us popular columns we + + + align:start position:0% +and that shows us popular columns we +want to find popular pairs there coari + + align:start position:0% +want to find popular pairs there coari + + + align:start position:0% +want to find popular pairs there coari +Matrix calculation there or Square in + + align:start position:0% +Matrix calculation there or Square in + + + align:start position:0% +Matrix calculation there or Square in +and find domains with many destination + + align:start position:0% +and find domains with many destination + + + align:start position:0% +and find domains with many destination +IPS an example in this data set is this + + align:start position:0% +IPS an example in this data set is this + + + align:start position:0% +IPS an example in this data set is this +was the most popular in the data set + + align:start position:0% +was the most popular in the data set + + + align:start position:0% +was the most popular in the data set +that we had these are the most popular + + align:start position:0% +that we had these are the most popular + + + align:start position:0% +that we had these are the most popular +things that uh that appeared here and + + align:start position:0% +things that uh that appeared here and + + + align:start position:0% +things that uh that appeared here and +you can see this is all fairly + + align:start position:0% +you can see this is all fairly + + + align:start position:0% +you can see this is all fairly +reasonable stuff + + align:start position:0% +reasonable stuff + + + align:start position:0% +reasonable stuff +Lan um a lot of New England Patriots + + align:start position:0% +Lan um a lot of New England Patriots + + + align:start position:0% +Lan um a lot of New England Patriots +fans in this data set all of ads Staples + + align:start position:0% +fans in this data set all of ads Staples + + + align:start position:0% +fans in this data set all of ads Staples +these are the types of things it shows + + align:start position:0% +these are the types of things it shows + + + align:start position:0% +these are the types of things it shows +you right + + align:start position:0% + + + + align:start position:0% + +away here's the covariance Matrix of + + align:start position:0% +away here's the covariance Matrix of + + + align:start position:0% +away here's the covariance Matrix of +this data so as you can see it's it's + + align:start position:0% +this data so as you can see it's it's + + + align:start position:0% +this data so as you can see it's it's +symmetric so obviously there's a + + align:start position:0% +symmetric so obviously there's a + + + align:start position:0% +symmetric so obviously there's a +diagonal and you have uh it has the + + align:start position:0% +diagonal and you have uh it has the + + + align:start position:0% +diagonal and you have uh it has the +bipartite structure there's there's no + + align:start position:0% +bipartite structure there's there's no + + + align:start position:0% +bipartite structure there's there's no +destination to destination IP links + + align:start position:0% +destination to destination IP links + + + align:start position:0% +destination to destination IP links +there's no and you know we have Source + + align:start position:0% +there's no and you know we have Source + + + align:start position:0% +there's no and you know we have Source +IP to destination a domain all that type + + align:start position:0% +IP to destination a domain all that type + + + align:start position:0% +IP to destination a domain all that type +of stuff exactly the covariance Matrix + + align:start position:0% +of stuff exactly the covariance Matrix + + + align:start position:0% +of stuff exactly the covariance Matrix +is often extremely helpful thing to look + + align:start position:0% +is often extremely helpful thing to look + + + align:start position:0% +is often extremely helpful thing to look +at because it'll be the first time it + + align:start position:0% +at because it'll be the first time it + + + align:start position:0% +at because it'll be the first time it +shows you the full interrelated + + align:start position:0% +shows you the full interrelated + + + align:start position:0% +shows you the full interrelated +structure of your data and you can + + align:start position:0% +structure of your data and you can + + + align:start position:0% +structure of your data and you can +quickly identify dense rows dense + + align:start position:0% +quickly identify dense rows dense + + + align:start position:0% +quickly identify dense rows dense +columns blocks chunks sub things where + + align:start position:0% +columns blocks chunks sub things where + + + align:start position:0% +columns blocks chunks sub things where +you want to look at chunks that aren't + + align:start position:0% +you want to look at chunks that aren't + + + align:start position:0% +you want to look at chunks that aren't +going to be interesting because they're + + align:start position:0% +going to be interesting because they're + + + align:start position:0% +going to be interesting because they're +very very dense or very very sparse + + align:start position:0% +very very dense or very very sparse + + + align:start position:0% +very very dense or very very sparse +again a very very just sort of survey + + align:start position:0% +again a very very just sort of survey + + + align:start position:0% +again a very very just sort of survey +type of tool + + align:start position:0% + + + + align:start position:0% + +a little shout out here to our + + align:start position:0% +a little shout out here to our + + + align:start position:0% +a little shout out here to our +colleagues in in the other group Who + + align:start position:0% +colleagues in in the other group Who + + + align:start position:0% +colleagues in in the other group Who +develops structured knowledge space + + align:start position:0% +develops structured knowledge space + + + align:start position:0% +develops structured knowledge space +structured knowledge space is a very + + align:start position:0% +structured knowledge space is a very + + + align:start position:0% +structured knowledge space is a very +powerful analytic data set um I kind of + + align:start position:0% +powerful analytic data set um I kind of + + + align:start position:0% +powerful analytic data set um I kind of +tell people it's like the Google search + + align:start position:0% +tell people it's like the Google search + + + align:start position:0% +tell people it's like the Google search +where be when you type a search key it + + align:start position:0% +where be when you type a search key it + + + align:start position:0% +where be when you type a search key it +starts uh guessing what your next answer + + align:start position:0% +starts uh guessing what your next answer + + + align:start position:0% +starts uh guessing what your next answer +is but Google does that based on a sort + + align:start position:0% +is but Google does that based on a sort + + + align:start position:0% +is but Google does that based on a sort +of a long sort of analysis of all the + + align:start position:0% +of a long sort of analysis of all the + + + align:start position:0% +of a long sort of analysis of all the +different types of searches people have + + align:start position:0% +different types of searches people have + + + align:start position:0% +different types of searches people have +done and it can make a good guess SKS + + align:start position:0% +done and it can make a good guess SKS + + + align:start position:0% +done and it can make a good guess SKS +does that much more deeply in that if it + + align:start position:0% +does that much more deeply in that if it + + + align:start position:0% +does that much more deeply in that if it +it maintains a database on a collection + + align:start position:0% +it maintains a database on a collection + + + align:start position:0% +it maintains a database on a collection +of documents and in this case if you + + align:start position:0% +of documents and in this case if you + + + align:start position:0% +of documents and in this case if you +type + + align:start position:0% +type + + + align:start position:0% +type +Afghanistan okay it will then show you + + align:start position:0% +Afghanistan okay it will then show you + + + align:start position:0% +Afghanistan okay it will then show you +will then actually go and count the + + align:start position:0% +will then actually go and count the + + + align:start position:0% +will then actually go and count the +occurrences of different types of + + align:start position:0% +occurrences of different types of + + + align:start position:0% +occurrences of different types of +entities in those documents and then + + align:start position:0% +entities in those documents and then + + + align:start position:0% +entities in those documents and then +show you what the possible next keyw + + align:start position:0% +show you what the possible next keyw + + + align:start position:0% +show you what the possible next keyw +choices can be so in the actual data + + align:start position:0% +choices can be so in the actual data + + + align:start position:0% +choices can be so in the actual data +itself not based on a set of cached uh + + align:start position:0% +itself not based on a set of cached uh + + + align:start position:0% +itself not based on a set of cached uh +queries and other types of things I'm + + align:start position:0% +queries and other types of things I'm + + + align:start position:0% +queries and other types of things I'm +not to say I don't really know what + + align:start position:0% +not to say I don't really know what + + + align:start position:0% +not to say I don't really know what +Google actually does I'm just guessing + + align:start position:0% +Google actually does I'm just guessing + + + align:start position:0% +Google actually does I'm just guessing +I'm sure they do use some data for + + align:start position:0% +I'm sure they do use some data for + + + align:start position:0% +I'm sure they do use some data for +guiding their search but this is a + + align:start position:0% +guiding their search but this is a + + + align:start position:0% +guiding their search but this is a +fairly sophisticated analytic and uh one + + align:start position:0% +fairly sophisticated analytic and uh one + + + align:start position:0% +fairly sophisticated analytic and uh one +of the big sort of wins for we knew we + + align:start position:0% +of the big sort of wins for we knew we + + + align:start position:0% +of the big sort of wins for we knew we +were on the right track with dform is + + align:start position:0% +were on the right track with dform is + + + align:start position:0% +were on the right track with dform is +that this is been implemented in + + align:start position:0% +that this is been implemented in + + + align:start position:0% +that this is been implemented in +hundreds or thousands of lines of java + + align:start position:0% +hundreds or thousands of lines of java + + + align:start position:0% +hundreds or thousands of lines of java +SQL and we're going to show you how we + + align:start position:0% +SQL and we're going to show you how we + + + align:start position:0% +SQL and we're going to show you how we +implemented in one line in + + align:start position:0% +implemented in one line in + + + align:start position:0% +implemented in one line in +d4m so let's uh let's go over that + + align:start position:0% +d4m so let's uh let's go over that + + + align:start position:0% +d4m so let's uh let's go over that +algorithm so here's an example of of + + align:start position:0% +algorithm so here's an example of of + + + align:start position:0% +algorithm so here's an example of of +what my data might look like I have a + + align:start position:0% +what my data might look like I have a + + + align:start position:0% +what my data might look like I have a +bunch of documents here I have a bunch + + align:start position:0% +bunch of documents here I have a bunch + + + align:start position:0% +bunch of documents here I have a bunch +of entities where an entity appears + + align:start position:0% +of entities where an entity appears + + + align:start position:0% +of entities where an entity appears +going to document I have a DOT I'm going + + align:start position:0% +going to document I have a DOT I'm going + + + align:start position:0% +going to document I have a DOT I'm going +to have my associative array over here + + align:start position:0% +to have my associative array over here + + + align:start position:0% +to have my associative array over here +which is a you know matching from the + + align:start position:0% +which is a you know matching from the + + + align:start position:0% +which is a you know matching from the +strings to the reals and my two facets + + align:start position:0% +strings to the reals and my two facets + + + align:start position:0% +strings to the reals and my two facets +are facets are just going to be two + + align:start position:0% +are facets are just going to be two + + + align:start position:0% +are facets are just going to be two +columns names here so I'm going to pick + + align:start position:0% +columns names here so I'm going to pick + + + align:start position:0% +columns names here so I'm going to pick +a facet y1 and Y2 so I'm going to pick + + align:start position:0% +a facet y1 and Y2 so I'm going to pick + + + align:start position:0% +a facet y1 and Y2 so I'm going to pick +these two columns all right and then so + + align:start position:0% +these two columns all right and then so + + + align:start position:0% +these two columns all right and then so +basically that's what this does this + + align:start position:0% +basically that's what this does this + + + align:start position:0% +basically that's what this does this +says get me y1 and get me + + align:start position:0% +says get me y1 and get me + + + align:start position:0% +says get me y1 and get me +Y2 I'm using this bar here to say I'm + + align:start position:0% +Y2 I'm using this bar here to say I'm + + + align:start position:0% +Y2 I'm using this bar here to say I'm +going to knock away the the facet name + + align:start position:0% +going to knock away the the facet name + + + align:start position:0% +going to knock away the the facet name +afterwards so I can and them together so + + align:start position:0% +afterwards so I can and them together so + + + align:start position:0% +afterwards so I can and them together so +that gets me all the documents that + + align:start position:0% +that gets me all the documents that + + + align:start position:0% +that gets me all the documents that +basically contain both U and Carl and + + align:start position:0% +basically contain both U and Carl and + + + align:start position:0% +basically contain both U and Carl and +then I can go and compute the counts + + align:start position:0% +then I can go and compute the counts + + + align:start position:0% +then I can go and compute the counts +that you saw on the previous page there + + align:start position:0% +that you saw on the previous page there + + + align:start position:0% +that you saw on the previous page there +uh just by doing this Matrix multiply so + + align:start position:0% +uh just by doing this Matrix multiply so + + + align:start position:0% +uh just by doing this Matrix multiply so +I and them I transpose them and I Matrix + + align:start position:0% +I and them I transpose them and I Matrix + + + align:start position:0% +I and them I transpose them and I Matrix +multiply to get them together and then + + align:start position:0% +multiply to get them together and then + + + align:start position:0% +multiply to get them together and then +there we + + align:start position:0% + + + + align:start position:0% + +go all right so now I'm going to get + + align:start position:0% +go all right so now I'm going to get + + + align:start position:0% +go all right so now I'm going to get +into the demo and I think we have plenty + + align:start position:0% +into the demo and I think we have plenty + + + align:start position:0% +into the demo and I think we have plenty +of time for that um I'll sort of set it + + align:start position:0% +of time for that um I'll sort of set it + + + align:start position:0% +of time for that um I'll sort of set it +up and then we'll take a short break + + align:start position:0% +up and then we'll take a short break + + + align:start position:0% +up and then we'll take a short break +people can have cookies and um and then + + align:start position:0% +people can have cookies and um and then + + + align:start position:0% +people can have cookies and um and then +we will and then we'll get into the demo + + align:start position:0% +we will and then we'll get into the demo + + + align:start position:0% +we will and then we'll get into the demo +which really begins to show you kind of + + align:start position:0% +which really begins to show you kind of + + + align:start position:0% +which really begins to show you kind of +a way to use use d4m on real data so the + + align:start position:0% +a way to use use d4m on real data so the + + + align:start position:0% +a way to use use d4m on real data so the +data set we're going to work with here + + align:start position:0% +data set we're going to work with here + + + align:start position:0% +data set we're going to work with here +is the reuter's Corpus so this was a + + align:start position:0% +is the reuter's Corpus so this was a + + + align:start position:0% +is the reuter's Corpus so this was a +corpus of data uh released uh in 2000 to + + align:start position:0% +corpus of data uh released uh in 2000 to + + + align:start position:0% +corpus of data uh released uh in 2000 to +help spur research in this community + + align:start position:0% +help spur research in this community + + + align:start position:0% +help spur research in this community +we're very greater grateful for Reuters + + align:start position:0% +we're very greater grateful for Reuters + + + align:start position:0% +we're very greater grateful for Reuters +to do this they they gave the data to + + align:start position:0% +to do this they they gave the data to + + + align:start position:0% +to do this they they gave the data to +nist to actually uh stewards the data + + align:start position:0% +nist to actually uh stewards the data + + + align:start position:0% +nist to actually uh stewards the data +set um it's a set of Reuters news + + align:start position:0% +set um it's a set of Reuters news + + + align:start position:0% +set um it's a set of Reuters news +reports over this particular time frame + + align:start position:0% +reports over this particular time frame + + + align:start position:0% +reports over this particular time frame +the late uh the mid + + align:start position:0% +the late uh the mid + + + align:start position:0% +the late uh the mid +90s and it's like 800,000 total and what + + align:start position:0% +90s and it's like 800,000 total and what + + + align:start position:0% +90s and it's like 800,000 total and what +we have done we're not actually working + + align:start position:0% +we have done we're not actually working + + + align:start position:0% +we have done we're not actually working +with the straight Reuters data we've run + + align:start position:0% +with the straight Reuters data we've run + + + align:start position:0% +with the straight Reuters data we've run +it through various parsers that have + + align:start position:0% +it through various parsers that have + + + align:start position:0% +it through various parsers that have +extracted just the entities so the the + + align:start position:0% +extracted just the entities so the the + + + align:start position:0% +extracted just the entities so the the +people the places and the organization + + align:start position:0% +people the places and the organization + + + align:start position:0% +people the places and the organization +so it's sort of a a summary you know + + align:start position:0% +so it's sort of a a summary you know + + + align:start position:0% +so it's sort of a a summary you know +very T summarization of of the data if + + align:start position:0% +very T summarization of of the data if + + + align:start position:0% +very T summarization of of the data if +that it's really sort of a derived + + align:start position:0% +that it's really sort of a derived + + + align:start position:0% +that it's really sort of a derived +product um the data is power law so if + + align:start position:0% +product um the data is power law so if + + + align:start position:0% +product um the data is power law so if +we look at the documents per entity you + + align:start position:0% +we look at the documents per entity you + + + align:start position:0% +we look at the documents per entity you +see here that you know certain people + + align:start position:0% +see here that you know certain people + + + align:start position:0% +see here that you know certain people +places and organizations you know appear + + align:start position:0% +places and organizations you know appear + + + align:start position:0% +places and organizations you know appear +a few of them appear lots of places and + + align:start position:0% +a few of them appear lots of places and + + + align:start position:0% +a few of them appear lots of places and +most of them are appear in just a few + + align:start position:0% +most of them are appear in just a few + + + align:start position:0% +most of them are appear in just a few +documents and uh you see the same thing + + align:start position:0% +documents and uh you see the same thing + + + align:start position:0% +documents and uh you see the same thing +when you look at the entities per + + align:start position:0% +when you look at the entities per + + + align:start position:0% +when you look at the entities per +document so there's essentially you + + align:start position:0% +document so there's essentially you + + + align:start position:0% +document so there's essentially you +could view this as Computing the in + + align:start position:0% +could view this as Computing the in + + + align:start position:0% +could view this as Computing the in +degrees and the out degrees of this + + align:start position:0% +degrees and the out degrees of this + + + align:start position:0% +degrees and the out degrees of this +bipartite graph and it has the classic + + align:start position:0% +bipartite graph and it has the classic + + + align:start position:0% +bipartite graph and it has the classic +power law shape that we expect to see in + + align:start position:0% +power law shape that we expect to see in + + + align:start position:0% +power law shape that we expect to see in +our data so with that we're going to do + + align:start position:0% +our data so with that we're going to do + + + align:start position:0% +our data so with that we're going to do +to the demo and just to summarize so + + align:start position:0% +to the demo and just to summarize so + + + align:start position:0% +to the demo and just to summarize so +just you know recall you know we we you + + align:start position:0% +just you know recall you know we we you + + + align:start position:0% +just you know recall you know we we you +know the evolution of the web is really + + align:start position:0% +know the evolution of the web is really + + + align:start position:0% +know the evolution of the web is really +created a new class of Technologies we + + align:start position:0% +created a new class of Technologies we + + + align:start position:0% +created a new class of Technologies we +really see the the web moving towards + + align:start position:0% +really see the the web moving towards + + + align:start position:0% +really see the the web moving towards +you know game style interfaces triple + + align:start position:0% +you know game style interfaces triple + + + align:start position:0% +you know game style interfaces triple +store databases and Technologies like + + align:start position:0% +store databases and Technologies like + + + align:start position:0% +store databases and Technologies like +d4m for doing analysis very new + + align:start position:0% +d4m for doing analysis very new + + + align:start position:0% +d4m for doing analysis very new +technology and just so the we for the + + align:start position:0% +technology and just so the we for the + + + align:start position:0% +technology and just so the we for the +record um there is no assignment this + + align:start position:0% +record um there is no assignment this + + + align:start position:0% +record um there is no assignment this +week so for those of you are still doing + + align:start position:0% +week so for those of you are still doing + + + align:start position:0% +week so for those of you are still doing +thiss yay um the uh the example actually + + align:start position:0% +thiss yay um the uh the example actually + + + align:start position:0% +thiss yay um the uh the example actually +we won't do both of these today we'll + + align:start position:0% +we won't do both of these today we'll + + + align:start position:0% +we won't do both of these today we'll +just do one of them oh and I keep making + + align:start position:0% +just do one of them oh and I keep making + + + align:start position:0% +just do one of them oh and I keep making +this mistake I'll fix it I'll fix it + + align:start position:0% +this mistake I'll fix it I'll fix it + + + align:start position:0% +this mistake I'll fix it I'll fix it +later but that's it's it's a it's in the + + align:start position:0% +later but that's it's it's a it's in the + + + align:start position:0% +later but that's it's it's a it's in the +examples directory uh We've now moved on + + align:start position:0% +examples directory uh We've now moved on + + + align:start position:0% +examples directory uh We've now moved on +to the second subfolder apps entity + + align:start position:0% +to the second subfolder apps entity + + + align:start position:0% +to the second subfolder apps entity +analysis and uh and you guys are + + align:start position:0% +analysis and uh and you guys are + + + align:start position:0% +analysis and uh and you guys are +encouraged to run those examples which + + align:start position:0% +encouraged to run those examples which + + + align:start position:0% +encouraged to run those examples which +we will now do shortly so we will take a + + align:start position:0% +we will now do shortly so we will take a + + + align:start position:0% +we will now do shortly so we will take a +short 5 minute break and then um + + align:start position:0% +short 5 minute break and then um + + + align:start position:0% +short 5 minute break and then um +continue on with the uh the demo \ No newline at end of file diff --git a/pOKy3RZbSws.txt b/pOKy3RZbSws.txt new file mode 100644 index 0000000000000000000000000000000000000000..09adf8796ba2eb811f7922115781f939ff7f1931 --- /dev/null +++ b/pOKy3RZbSws.txt @@ -0,0 +1,14256 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mmit.edu. All right. Today we + + align:start position:0% +ocw.mmit.edu. All right. Today we + + + align:start position:0% +ocw.mmit.edu. All right. Today we +continue our theme of integer data + + align:start position:0% +continue our theme of integer data + + + align:start position:0% +continue our theme of integer data +structures and today we're going to look + + align:start position:0% +structures and today we're going to look + + + align:start position:0% +structures and today we're going to look +at priority cues instead of the + + align:start position:0% +at priority cues instead of the + + + align:start position:0% +at priority cues instead of the +predecessor problem. So something a + + align:start position:0% +predecessor problem. So something a + + + align:start position:0% +predecessor problem. So something a +little different. Insert, delete, and + + align:start position:0% +little different. Insert, delete, and + + + align:start position:0% +little different. Insert, delete, and +find min. Uh it turns out priority cues + + align:start position:0% +find min. Uh it turns out priority cues + + + align:start position:0% +find min. Uh it turns out priority cues +are equivalent to sorting in the sense + + align:start position:0% + + + + align:start position:0% + +that if you have uh let's see if you + + align:start position:0% +that if you have uh let's see if you + + + align:start position:0% +that if you have uh let's see if you +have a an f of n normally say f of n but + + align:start position:0% +have a an f of n normally say f of n but + + + align:start position:0% +have a an f of n normally say f of n but +here we're going to depend on both n and + + align:start position:0% +here we're going to depend on both n and + + + align:start position:0% +here we're going to depend on both n and +the word + + align:start position:0% +the word + + + align:start position:0% +the word +size priority + + align:start position:0% + + + + align:start position:0% + +q. Well, then of course you get a + + align:start position:0% +q. Well, then of course you get a + + + align:start position:0% +q. Well, then of course you get a +sorting algorithm. Just insert + + align:start position:0% +sorting algorithm. Just insert + + + align:start position:0% +sorting algorithm. Just insert +everything into the priority queue and + + align:start position:0% +everything into the priority queue and + + + align:start position:0% +everything into the priority queue and +then find min, delete, find min, delete + + align:start position:0% +then find min, delete, find min, delete + + + align:start position:0% +then find min, delete, find min, delete +and so + + align:start position:0% + + + + align:start position:0% + +on. So that's the trivial direction of + + align:start position:0% +on. So that's the trivial direction of + + + align:start position:0% +on. So that's the trivial direction of +the + + align:start position:0% +the + + + align:start position:0% +the +equivalence. But it turns out both of + + align:start position:0% +equivalence. But it turns out both of + + + align:start position:0% +equivalence. But it turns out both of +these are true. If you have a sorting + + align:start position:0% +these are true. If you have a sorting + + + align:start position:0% +these are true. If you have a sorting +algorithm with n* f uh time then you can + + align:start position:0% +algorithm with n* f uh time then you can + + + align:start position:0% +algorithm with n* f uh time then you can +convert it into a priority q that in the + + align:start position:0% +convert it into a priority q that in the + + + align:start position:0% +convert it into a priority q that in the +worst case every operation takes only f + + align:start position:0% +worst case every operation takes only f + + + align:start position:0% +worst case every operation takes only f +of n comma w. + + align:start position:0% +of n comma w. + + + align:start position:0% +of n comma w. +So that's the + + align:start position:0% +So that's the + + + align:start position:0% +So that's the +uh that's the equivalence as a result of + + align:start position:0% +uh that's the equivalence as a result of + + + align:start position:0% +uh that's the equivalence as a result of +thor from a few years ago + + align:start position:0% +thor from a few years ago + + + align:start position:0% +thor from a few years ago +2007 kind of a a cool breakthrough. + + align:start position:0% +2007 kind of a a cool breakthrough. + + + align:start position:0% +2007 kind of a a cool breakthrough. +There were earlier versions that weren't + + align:start position:0% +There were earlier versions that weren't + + + align:start position:0% +There were earlier versions that weren't +quite as efficient, but this gives you + + align:start position:0% +quite as efficient, but this gives you + + + align:start position:0% +quite as efficient, but this gives you +perfect efficiency turning as any + + align:start position:0% +perfect efficiency turning as any + + + align:start position:0% +perfect efficiency turning as any +sorting algorithm to priority Q. Rough + + align:start position:0% +sorting algorithm to priority Q. Rough + + + align:start position:0% +sorting algorithm to priority Q. Rough +sketch of the data structure is you have + + align:start position:0% +sketch of the data structure is you have + + + align:start position:0% +sketch of the data structure is you have +a bunch of sorting algorithms which you + + align:start position:0% +a bunch of sorting algorithms which you + + + align:start position:0% +a bunch of sorting algorithms which you +run now and then to get on little parts + + align:start position:0% +run now and then to get on little parts + + + align:start position:0% +run now and then to get on little parts +of the input in order to build an + + align:start position:0% +of the input in order to build an + + + align:start position:0% +of the input in order to build an +overall priority queue, but it's very + + align:start position:0% +overall priority queue, but it's very + + + align:start position:0% +overall priority queue, but it's very +complicated. Um there was an entire + + align:start position:0% +complicated. Um there was an entire + + + align:start position:0% +complicated. Um there was an entire +class project on assimilating it and + + align:start position:0% +class project on assimilating it and + + + align:start position:0% +class project on assimilating it and +understanding it. Um it's a bit beyond + + align:start position:0% +understanding it. Um it's a bit beyond + + + align:start position:0% +understanding it. Um it's a bit beyond +what we can cover in the class. Uh so + + align:start position:0% +what we can cover in the class. Uh so + + + align:start position:0% +what we can cover in the class. Uh so +I'm going to take this as given and tell + + align:start position:0% +I'm going to take this as given and tell + + + align:start position:0% +I'm going to take this as given and tell +you instead about sorting algorithms + + align:start position:0% +you instead about sorting algorithms + + + align:start position:0% +you instead about sorting algorithms +because there's a major open problem + + align:start position:0% +because there's a major open problem + + + align:start position:0% +because there's a major open problem +here which is can you sort n integers n + + align:start position:0% +here which is can you sort n integers n + + + align:start position:0% +here which is can you sort n integers n +w bit integers in a word ram's word size + + align:start position:0% +w bit integers in a word ram's word size + + + align:start position:0% +w bit integers in a word ram's word size +w in linear time we still don't know uh + + align:start position:0% +w in linear time we still don't know uh + + + align:start position:0% +w in linear time we still don't know uh +but we have a bunch of results in + + align:start position:0% +but we have a bunch of results in + + + align:start position:0% +but we have a bunch of results in +particular we're going to talk about a + + align:start position:0% +particular we're going to talk about a + + + align:start position:0% +particular we're going to talk about a +couple uh interesting cases where we can + + align:start position:0% +couple uh interesting cases where we can + + + align:start position:0% +couple uh interesting cases where we can +get linear time sorting uh if you've + + align:start position:0% +get linear time sorting uh if you've + + + align:start position:0% +get linear time sorting uh if you've +seen radic sort you know another + + align:start position:0% +seen radic sort you know another + + + align:start position:0% +seen radic sort you know another +interesting case where linear time + + align:start position:0% +interesting case where linear time + + + align:start position:0% +interesting case where linear time +sorting is possible + + align:start position:0% +sorting is possible + + + align:start position:0% +sorting is possible +Uh let's see it's interesting open + + align:start position:0% +Uh let's see it's interesting open + + + align:start position:0% +Uh let's see it's interesting open +problem + + align:start position:0% +problem + + + align:start position:0% +problem +here. Can you get constant time decrease + + align:start position:0% +here. Can you get constant time decrease + + + align:start position:0% +here. Can you get constant time decrease +key and ideally also insertion? Uh but + + align:start position:0% +key and ideally also insertion? Uh but + + + align:start position:0% +key and ideally also insertion? Uh but +decrease key would be handy because this + + align:start position:0% +decrease key would be handy because this + + + align:start position:0% +decrease key would be handy because this +would then this would be useful for + + align:start position:0% +would then this would be useful for + + + align:start position:0% +would then this would be useful for +uh uh for do in this reduction if you + + align:start position:0% +uh uh for do in this reduction if you + + + align:start position:0% +uh uh for do in this reduction if you +have a sorting algorithm like to get a + + align:start position:0% +have a sorting algorithm like to get a + + + align:start position:0% +have a sorting algorithm like to get a +priority Q with constant time decrease + + align:start position:0% +priority Q with constant time decrease + + + align:start position:0% +priority Q with constant time decrease +key that would have applications to + + align:start position:0% +key that would have applications to + + + align:start position:0% +key that would have applications to +Dystra's algorithm. Of course, if you + + align:start position:0% +Dystra's algorithm. Of course, if you + + + align:start position:0% +Dystra's algorithm. Of course, if you +can sort in linear time, then everything + + align:start position:0% +can sort in linear time, then everything + + + align:start position:0% +can sort in linear time, then everything +can be done in constant time. So, this + + align:start position:0% +can be done in constant time. So, this + + + align:start position:0% +can be done in constant time. So, this +is not the most interesting open + + align:start position:0% +is not the most interesting open + + + align:start position:0% +is not the most interesting open +problem, but it would be a step in that + + align:start position:0% +problem, but it would be a step in that + + + align:start position:0% +problem, but it would be a step in that +direction. Uh, cool. So, let me tell + + align:start position:0% +direction. Uh, cool. So, let me tell + + + align:start position:0% +direction. Uh, cool. So, let me tell +you some bounds about sorting. + + align:start position:0% + + + + align:start position:0% + +So we have n w + + align:start position:0% +So we have n w + + + align:start position:0% +So we have n w +bit integers and you take any of these + + align:start position:0% +bit integers and you take any of these + + + align:start position:0% +bit integers and you take any of these +bounds divide by n you get the priority + + align:start position:0% +bounds divide by n you get the priority + + + align:start position:0% +bounds divide by n you get the priority +qbound the best best that we + + align:start position:0% +qbound the best best that we + + + align:start position:0% +qbound the best best that we +know. So of course there's comparison + + align:start position:0% +know. So of course there's comparison + + + align:start position:0% +know. So of course there's comparison +sorting which takes n login. Okay so + + align:start position:0% +sorting which takes n login. Okay so + + + align:start position:0% +sorting which takes n login. Okay so +that's an upper bound trying to beat + + align:start position:0% +that's an upper bound trying to beat + + + align:start position:0% +that's an upper bound trying to beat +that try to get rid of the log. Uh + + align:start position:0% +that try to get rid of the log. Uh + + + align:start position:0% +that try to get rid of the log. Uh +there's counting sort from undergraduate + + align:start position:0% +there's counting sort from undergraduate + + + align:start position:0% +there's counting sort from undergraduate +algorithms that takes n plus u time + + align:start position:0% +algorithms that takes n plus u time + + + align:start position:0% +algorithms that takes n plus u time +because you need a t build a table of + + align:start position:0% +because you need a t build a table of + + + align:start position:0% +because you need a t build a table of +size u you've got to zero out all the + + align:start position:0% +size u you've got to zero out all the + + + align:start position:0% +size u you've got to zero out all the +initial counts. So that requires order u + + align:start position:0% +initial counts. So that requires order u + + + align:start position:0% +initial counts. So that requires order u +time. Uh this is + + align:start position:0% +time. Uh this is + + + align:start position:0% +time. Uh this is +interesting really + + align:start position:0% +interesting really + + + align:start position:0% +interesting really +when the word size equals log n. So + + align:start position:0% +when the word size equals log n. So + + + align:start position:0% +when the word size equals log n. So +that's a case of potential interest + + align:start position:0% +that's a case of potential interest + + + align:start position:0% +that's a case of potential interest +because then you know 2 to the w is just + + align:start position:0% +because then you know 2 to the w is just + + + align:start position:0% +because then you know 2 to the w is just +n. So this is linear time. uh but it's + + align:start position:0% +n. So this is linear time. uh but it's + + + align:start position:0% +n. So this is linear time. uh but it's +even if w is two times log n or 1.1* + + align:start position:0% +even if w is two times log n or 1.1* + + + align:start position:0% +even if w is two times log n or 1.1* +login then this is uh bigger than n log + + align:start position:0% +login then this is uh bigger than n log + + + align:start position:0% +login then this is uh bigger than n log +n so not very good but we have radic + + align:start position:0% + + + + align:start position:0% + +sort which is a bit better and this is n + + align:start position:0% +sort which is a bit better and this is n + + + align:start position:0% +sort which is a bit better and this is n +* + + align:start position:0% +* + + + align:start position:0% +* +w / + + align:start position:0% +w / + + + align:start position:0% +w / +login if you do it right um you have + + align:start position:0% +login if you do it right um you have + + + align:start position:0% +login if you do it right um you have +some word size w you're using counting + + align:start position:0% +some word size w you're using counting + + + align:start position:0% +some word size w you're using counting +sort for each digit in the radics + + align:start position:0% +sort for each digit in the radics + + + align:start position:0% +sort for each digit in the radics +Uh so you can afford that the word size + + align:start position:0% +Uh so you can afford that the word size + + + align:start position:0% +Uh so you can afford that the word size +of doing counting sort to be exactly + + align:start position:0% +of doing counting sort to be exactly + + + align:start position:0% +of doing counting sort to be exactly +login which means you have your overall + + align:start position:0% +login which means you have your overall + + + align:start position:0% +login which means you have your overall +word you're dividing into chunks of size + + align:start position:0% +word you're dividing into chunks of size + + + align:start position:0% +word you're dividing into chunks of size +log n each of them you can do in linear + + align:start position:0% +log n each of them you can do in linear + + + align:start position:0% +log n each of them you can do in linear +time so the number of chunks you have to + + align:start position:0% +time so the number of chunks you have to + + + align:start position:0% +time so the number of chunks you have to +do is w divided by login and this is + + align:start position:0% +do is w divided by login and this is + + + align:start position:0% +do is w divided by login and this is +linear if w equals order + + align:start position:0% + + + + align:start position:0% + +login right but only then so it spies + + align:start position:0% +login right but only then so it spies + + + align:start position:0% +login right but only then so it spies +you a little it + + align:start position:0% +you a little it + + + align:start position:0% +you a little it +uh but still not great. Okay, there's + + align:start position:0% +uh but still not great. Okay, there's + + + align:start position:0% +uh but still not great. Okay, there's +some other sorting algorithms we've + + align:start position:0% +some other sorting algorithms we've + + + align:start position:0% +some other sorting algorithms we've +implicitly seen because we've seen Venom + + align:start position:0% +implicitly seen because we've seen Venom + + + align:start position:0% +implicitly seen because we've seen Venom +DOS. I mean any predecessor data + + align:start position:0% +DOS. I mean any predecessor data + + + align:start position:0% +DOS. I mean any predecessor data +structure gives you a priority Q data + + align:start position:0% +structure gives you a priority Q data + + + align:start position:0% +structure gives you a priority Q data +structure. Priority Q's uh didn't say or + + align:start position:0% +structure. Priority Q's uh didn't say or + + + align:start position:0% +structure. Priority Q's uh didn't say or +didn't write it but I mentioned insert + + align:start position:0% +didn't write it but I mentioned insert + + + align:start position:0% +didn't write it but I mentioned insert +delete find + + align:start position:0% +delete find + + + align:start position:0% +delete find +min is a weaker operation than + + align:start position:0% +min is a weaker operation than + + + align:start position:0% +min is a weaker operation than +predecessor or successor. + + align:start position:0% +predecessor or successor. + + + align:start position:0% +predecessor or successor. +So we can take Venom Dau's + + align:start position:0% + + + + align:start position:0% + +uh predecessor data structure and + + align:start position:0% +uh predecessor data structure and + + + align:start position:0% +uh predecessor data structure and +convert it into a sorting algorithm and + + align:start position:0% +convert it into a sorting algorithm and + + + align:start position:0% +convert it into a sorting algorithm and +we get order n * log + + align:start position:0% +we get order n * log + + + align:start position:0% +we get order n * log +w. Now this is a little bit tricky to + + align:start position:0% +w. Now this is a little bit tricky to + + + align:start position:0% +w. Now this is a little bit tricky to +compare. Of course log w sounds better + + align:start position:0% +compare. Of course log w sounds better + + + align:start position:0% +compare. Of course log w sounds better +than w but there's this divided by log n + + align:start position:0% +than w but there's this divided by log n + + + align:start position:0% +than w but there's this divided by log n +which makes it a little hard to compare. + + align:start position:0% +which makes it a little hard to compare. + + + align:start position:0% +which makes it a little hard to compare. +Um it turns + + align:start position:0% +Um it turns + + + align:start position:0% +Um it turns +out there's a another version or you can + + align:start position:0% +out there's a another version or you can + + + align:start position:0% +out there's a another version or you can +take this sorting + + align:start position:0% +take this sorting + + + align:start position:0% +take this sorting +algorithm and achieve a bound of n log w + + align:start position:0% +algorithm and achieve a bound of n log w + + + align:start position:0% +algorithm and achieve a bound of n log w +over log + + align:start position:0% + + + + align:start position:0% + +n. Okay, so this is a slight improvement + + align:start position:0% +n. Okay, so this is a slight improvement + + + align:start position:0% +n. Okay, so this is a slight improvement +in here. It's similar to your problem + + align:start position:0% +in here. It's similar to your problem + + + align:start position:0% +in here. It's similar to your problem +set this week. Um this specific problem + + align:start position:0% +set this week. Um this specific problem + + + align:start position:0% +set this week. Um this specific problem +was a problem set in 2005 of this class. + + align:start position:0% +was a problem set in 2005 of this class. + + + align:start position:0% +was a problem set in 2005 of this class. +Uh so you can check out check it out if + + align:start position:0% +Uh so you can check out check it out if + + + align:start position:0% +Uh so you can check out check it out if +you want to see how to do this slight + + align:start position:0% +you want to see how to do this slight + + + align:start position:0% +you want to see how to do this slight +improvement. But now this is clearly + + align:start position:0% +improvement. But now this is clearly + + + align:start position:0% +improvement. But now this is clearly +better than this because here we have W + + align:start position:0% +better than this because here we have W + + + align:start position:0% +better than this because here we have W +over login. Here I've got a login front. + + align:start position:0% +over login. Here I've got a login front. + + + align:start position:0% +over login. Here I've got a login front. +So this is a win over radic sort. So + + align:start position:0% +So this is a win over radic sort. So + + + align:start position:0% +So this is a win over radic sort. So +venonos here's another way in which it's + + align:start position:0% +venonos here's another way in which it's + + + align:start position:0% +venonos here's another way in which it's +interesting. It gives us a strict + + align:start position:0% +interesting. It gives us a strict + + + align:start position:0% +interesting. It gives us a strict +improvement over radic sort. And in + + align:start position:0% +improvement over radic sort. And in + + + align:start position:0% +improvement over radic sort. And in +particular + + align:start position:0% +particular + + + align:start position:0% +particular +uh do I care? Well, actually both of + + align:start position:0% +uh do I care? Well, actually both of + + + align:start position:0% +uh do I care? Well, actually both of +these are order n log log n if w is not + + align:start position:0% +these are order n log log n if w is not + + + align:start position:0% +these are order n log log n if w is not +too + + align:start position:0% + + + + align:start position:0% + +big poly log + + align:start position:0% + + + + align:start position:0% + +n. Uh so this doesn't actually matter + + align:start position:0% +n. Uh so this doesn't actually matter + + + align:start position:0% +n. Uh so this doesn't actually matter +but it's it's clearly better than this + + align:start position:0% +but it's it's clearly better than this + + + align:start position:0% +but it's it's clearly better than this +one. Again if W is order log N you get + + align:start position:0% +one. Again if W is order log N you get + + + align:start position:0% +one. Again if W is order log N you get +this to be linear but in particular it + + align:start position:0% +this to be linear but in particular it + + + align:start position:0% +this to be linear but in particular it +says overall you get n log log n up to w + + align:start position:0% +says overall you get n log log n up to w + + + align:start position:0% +says overall you get n log log n up to w +being polylo. Okay why do we + + align:start position:0% +being polylo. Okay why do we + + + align:start position:0% +being polylo. Okay why do we +care? Uh because there's this other nice + + align:start position:0% +care? Uh because there's this other nice + + + align:start position:0% +care? Uh because there's this other nice +algorithm signature sort which covers + + align:start position:0% +algorithm signature sort which covers + + + align:start position:0% +algorithm signature sort which covers +all large word sizes and this is an + + align:start position:0% +all large word sizes and this is an + + + align:start position:0% +all large word sizes and this is an +algorithm we will cover today. + + align:start position:0% + + + + align:start position:0% + +It only works when w is large. And large + + align:start position:0% +It only works when w is large. And large + + + align:start position:0% +It only works when w is large. And large +means log to the 2 + epsilon n. This is + + align:start position:0% +means log to the 2 + epsilon n. This is + + + align:start position:0% +means log to the 2 + epsilon n. This is +no matter what epsilon is. In reality, + + align:start position:0% +no matter what epsilon is. In reality, + + + align:start position:0% +no matter what epsilon is. In reality, +it's probably log 2 n * log n^ 2. But uh + + align:start position:0% +it's probably log 2 n * log n^ 2. But uh + + + align:start position:0% +it's probably log 2 n * log n^ 2. But uh +be a little sloppy and just say a little + + align:start position:0% +be a little sloppy and just say a little + + + align:start position:0% +be a little sloppy and just say a little +bit bigger than log + + align:start position:0% +bit bigger than log + + + align:start position:0% +bit bigger than log +squ. And then it runs in linear time. + + align:start position:0% +squ. And then it runs in linear time. + + + align:start position:0% +squ. And then it runs in linear time. +Okay. So if you were if you were + + align:start position:0% +Okay. So if you were if you were + + + align:start position:0% +Okay. So if you were if you were +graphing this in your mind, you've got + + align:start position:0% +graphing this in your mind, you've got + + + align:start position:0% +graphing this in your mind, you've got +you know time and there's a nice bound + + align:start position:0% +you know time and there's a nice bound + + + align:start position:0% +you know time and there's a nice bound +here which is order n and we have other + + align:start position:0% +here which is order n and we have other + + + align:start position:0% +here which is order n and we have other +you know everything's above n log n + + align:start position:0% +you know everything's above n log n + + + align:start position:0% +you know everything's above n log n +maybe here we have this is hard to draw + + align:start position:0% +maybe here we have this is hard to draw + + + align:start position:0% +maybe here we have this is hard to draw +n log log n okay I'm I'm imag this is + + align:start position:0% +n log log n okay I'm I'm imag this is + + + align:start position:0% +n log log n okay I'm I'm imag this is +asmtoic space which doesn't really exist + + align:start position:0% +asmtoic space which doesn't really exist + + + align:start position:0% +asmtoic space which doesn't really exist +but you know what I mean uh and then + + align:start position:0% +but you know what I mean uh and then + + + align:start position:0% +but you know what I mean uh and then +this is the word + + align:start position:0% +this is the word + + + align:start position:0% +this is the word +size versus log n this is hard This is a + + align:start position:0% +size versus log n this is hard This is a + + + align:start position:0% +size versus log n this is hard This is a +really weird picture. Never drawn this + + align:start position:0% +really weird picture. Never drawn this + + + align:start position:0% +really weird picture. Never drawn this +before. Uh so you know we initially you + + align:start position:0% +before. Uh so you know we initially you + + + align:start position:0% +before. Uh so you know we initially you +know radic sort okay log n we could do + + align:start position:0% +know radic sort okay log n we could do + + + align:start position:0% +know radic sort okay log n we could do +the we could get linear time. Okay. Uh + + align:start position:0% +the we could get linear time. Okay. Uh + + + align:start position:0% +the we could get linear time. Okay. Uh +or order login. Great. Uh what this is + + align:start position:0% +or order login. Great. Uh what this is + + + align:start position:0% +or order login. Great. Uh what this is +saying is once you get out to log to the + + align:start position:0% +saying is once you get out to log to the + + + align:start position:0% +saying is once you get out to log to the +2 plus epsilon + + align:start position:0% +2 plus epsilon + + + align:start position:0% +2 plus epsilon +n you can also do linear and from here + + align:start position:0% +n you can also do linear and from here + + + align:start position:0% +n you can also do linear and from here +over we have linear time and here over + + align:start position:0% +over we have linear time and here over + + + align:start position:0% +over we have linear time and here over +we have linear time. So the question is + + align:start position:0% +we have linear time. So the question is + + + align:start position:0% +we have linear time. So the question is +what about this middle range between log + + align:start position:0% +what about this middle range between log + + + align:start position:0% +what about this middle range between log +n and log 2 plus epsilon. Uh well one + + align:start position:0% +n and log 2 plus epsilon. Uh well one + + + align:start position:0% +n and log 2 plus epsilon. Uh well one +thing we could do is use ben and noa + + align:start position:0% +thing we could do is use ben and noa + + + align:start position:0% +thing we could do is use ben and noa +sort get an n log n bound and so that's + + align:start position:0% +sort get an n log n bound and so that's + + + align:start position:0% +sort get an n log n bound and so that's +one way to fill in this range in the + + align:start position:0% +one way to fill in this range in the + + + align:start position:0% +one way to fill in this range in the +middle and that means overall you can + + align:start position:0% +middle and that means overall you can + + + align:start position:0% +middle and that means overall you can +always sort n integers in n log log n + + align:start position:0% +always sort n integers in n log log n + + + align:start position:0% +always sort n integers in n log log n +time if if w's big you use signature + + align:start position:0% +time if if w's big you use signature + + + align:start position:0% +time if if w's big you use signature +sort if w's small use venom to both + + align:start position:0% +sort if w's small use venom to both + + + align:start position:0% +sort if w's small use venom to both +sort. So this + + align:start position:0% +sort. So this + + + align:start position:0% +sort. So this +implies n log log + + align:start position:0% +implies n log log + + + align:start position:0% +implies n log log +n for all w. So that's something uh it's + + align:start position:0% +n for all w. So that's something uh it's + + + align:start position:0% +n for all w. So that's something uh it's +not the best + + align:start position:0% +not the best + + + align:start position:0% +not the best +known. Uh let's see first result in this + + align:start position:0% +known. Uh let's see first result in this + + + align:start position:0% +known. Uh let's see first result in this +direction by han in + + align:start position:0% +direction by han in + + + align:start position:0% +direction by han in +2001 and it achieved this bound uh + + align:start position:0% + + + + align:start position:0% + +deterministic and in the AC0 RAM. So + + align:start position:0% +deterministic and in the AC0 RAM. So + + + align:start position:0% +deterministic and in the AC0 RAM. So +without using multiplication + + align:start position:0% +without using multiplication + + + align:start position:0% +without using multiplication +uh which I guess venom devos doesn't + + align:start position:0% +uh which I guess venom devos doesn't + + + align:start position:0% +uh which I guess venom devos doesn't +either unless I'm missing something. So + + align:start position:0% +either unless I'm missing something. So + + + align:start position:0% +either unless I'm missing something. So +uh but it got rid of the randomization + + align:start position:0% +uh but it got rid of the randomization + + + align:start position:0% +uh but it got rid of the randomization +which is necessary to get linear space + + align:start position:0% +which is necessary to get linear space + + + align:start position:0% +which is necessary to get linear space +in venom deos. Uh and the current best + + align:start position:0% +in venom deos. Uh and the current best + + + align:start position:0% +in venom deos. Uh and the current best +result on + + align:start position:0% +result on + + + align:start position:0% +result on +sorting. It's by Han and Thorup in 2002 + + align:start position:0% +sorting. It's by Han and Thorup in 2002 + + + align:start position:0% +sorting. It's by Han and Thorup in 2002 +so a while ago. They achieved + + align:start position:0% +so a while ago. They achieved + + + align:start position:0% +so a while ago. They achieved +n square<unk> log w over log n which is + + align:start position:0% +n square<unk> log w over log n which is + + + align:start position:0% +n square<unk> log w over log n which is +similar + + align:start position:0% +similar + + + align:start position:0% +similar +to this bound just has an extra square + + align:start position:0% +to this bound just has an extra square + + + align:start position:0% +to this bound just has an extra square +root + + align:start position:0% +root + + + align:start position:0% +root +here. So it's a little bit better than + + align:start position:0% +here. So it's a little bit better than + + + align:start position:0% +here. So it's a little bit better than +phenom debose sword. It uses some clever + + align:start position:0% +phenom debose sword. It uses some clever + + + align:start position:0% +phenom debose sword. It uses some clever +tricks. It is + + align:start position:0% + + + + align:start position:0% + +randomized. So still the best + + align:start position:0% +randomized. So still the best + + + align:start position:0% +randomized. So still the best +deterministic bound is n log log n. uh + + align:start position:0% +deterministic bound is n log log n. uh + + + align:start position:0% +deterministic bound is n log log n. uh +and let's see we can plug that in for + + align:start position:0% +and let's see we can plug that in for + + + align:start position:0% +and let's see we can plug that in for +this range here and it will imply that + + align:start position:0% +this range here and it will imply that + + + align:start position:0% +this range here and it will imply that +you get n square + + align:start position:0% +you get n square + + + align:start position:0% +you get n square +root log log n + + align:start position:0% +root log log n + + + align:start position:0% +root log log n +uh for all w because in particular if w + + align:start position:0% +uh for all w because in particular if w + + + align:start position:0% +uh for all w because in particular if w +is order uh is if it's pol if w is poly + + align:start position:0% +is order uh is if it's pol if w is poly + + + align:start position:0% +is order uh is if it's pol if w is poly +log n then this is just log log n uh so + + align:start position:0% +log n then this is just log log n uh so + + + align:start position:0% +log n then this is just log log n uh so +you get this bound + + align:start position:0% +you get this bound + + + align:start position:0% +you get this bound +uh of course for all w because large w + + align:start position:0% +uh of course for all w because large w + + + align:start position:0% +uh of course for all w because large w +are already covered. So uh this sorting + + align:start position:0% +are already covered. So uh this sorting + + + align:start position:0% +are already covered. So uh this sorting +algorithm is a little bit messy and + + align:start position:0% +algorithm is a little bit messy and + + + align:start position:0% +algorithm is a little bit messy and +possibly not the right answer. I would + + align:start position:0% +possibly not the right answer. I would + + + align:start position:0% +possibly not the right answer. I would +conjecture you can sort n integers in + + align:start position:0% +conjecture you can sort n integers in + + + align:start position:0% +conjecture you can sort n integers in +linear time for all w but that is big + + align:start position:0% +linear time for all w but that is big + + + align:start position:0% +linear time for all w but that is big +open + + align:start position:0% + + + + align:start position:0% + +problem. This is the current + + align:start position:0% +problem. This is the current + + + align:start position:0% +problem. This is the current +state-of-the-art. Uh so um this this + + align:start position:0% +state-of-the-art. Uh so um this this + + + align:start position:0% +state-of-the-art. Uh so um this this +open question is really about for small + + align:start position:0% +open question is really about for small + + + align:start position:0% +open question is really about for small +w when w is poly log n or actually when + + align:start position:0% +w when w is poly log n or actually when + + + align:start position:0% +w when w is poly log n or actually when +it's between log and poly log. Uh so to + + align:start position:0% +it's between log and poly log. Uh so to + + + align:start position:0% +it's between log and poly log. Uh so to +give you a piece of the complete picture + + align:start position:0% +give you a piece of the complete picture + + + align:start position:0% +give you a piece of the complete picture +I want to uh tell you about signature + + align:start position:0% +I want to uh tell you about signature + + + align:start position:0% +I want to uh tell you about signature +sort because I think you have to use + + align:start position:0% +sort because I think you have to use + + + align:start position:0% +sort because I think you have to use +different techniques when w is small + + align:start position:0% +different techniques when w is small + + + align:start position:0% +different techniques when w is small +versus large. We know that from fusion + + align:start position:0% +versus large. We know that from fusion + + + align:start position:0% +versus large. We know that from fusion +trees and venoas. Uh so I'll tell you + + align:start position:0% +trees and venoas. Uh so I'll tell you + + + align:start position:0% +trees and venoas. Uh so I'll tell you +about the slightly large case when w is + + align:start position:0% +about the slightly large case when w is + + + align:start position:0% +about the slightly large case when w is +at least log to 2 plus epsilon. how to + + align:start position:0% +at least log to 2 plus epsilon. how to + + + align:start position:0% +at least log to 2 plus epsilon. how to +get linear time. And this is fun. Uses + + align:start position:0% +get linear time. And this is fun. Uses + + + align:start position:0% +get linear time. And this is fun. Uses +bit tricks. It uses a lot of cool ideas. + + align:start position:0% +bit tricks. It uses a lot of cool ideas. + + + align:start position:0% +bit tricks. It uses a lot of cool ideas. +Uses hashing, lots of things. Um, it + + align:start position:0% +Uses hashing, lots of things. Um, it + + + align:start position:0% +Uses hashing, lots of things. Um, it +also uses uh another sorting algorithm + + align:start position:0% +also uses uh another sorting algorithm + + + align:start position:0% +also uses uh another sorting algorithm +called packed sort. This is not doesn't + + align:start position:0% +called packed sort. This is not doesn't + + + align:start position:0% +called packed sort. This is not doesn't +fit in the regular table because it's + + align:start position:0% +fit in the regular table because it's + + + align:start position:0% +fit in the regular table because it's +for a situation when more than one input + + align:start position:0% +for a situation when more than one input + + + align:start position:0% +for a situation when more than one input +number fits in a word. So, we're going + + align:start position:0% +number fits in a word. So, we're going + + + align:start position:0% +number fits in a word. So, we're going +to let B denote the number of bits in + + align:start position:0% +to let B denote the number of bits in + + + align:start position:0% +to let B denote the number of bits in +the inputs. So, we have Bit integers. + + align:start position:0% +the inputs. So, we have Bit integers. + + + align:start position:0% +the inputs. So, we have Bit integers. +Then when w is at least b times login + + align:start position:0% +Then when w is at least b times login + + + align:start position:0% +Then when w is at least b times login +log login lo login. So you can fit login + + align:start position:0% +log login lo login. So you can fit login + + + align:start position:0% +log login lo login. So you can fit login +lo login integers in a single word then + + align:start position:0% +lo login integers in a single word then + + + align:start position:0% +lo login integers in a single word then +you can sort them in linear time. So + + align:start position:0% +you can sort them in linear time. So + + + align:start position:0% +you can sort them in linear time. So +it's like your machine is just a little + + align:start position:0% +it's like your machine is just a little + + + align:start position:0% +it's like your machine is just a little +bit bigger than what you'd need to + + align:start position:0% +bit bigger than what you'd need to + + + align:start position:0% +bit bigger than what you'd need to +represent the integers. Then the all + + align:start position:0% +represent the integers. Then the all + + + align:start position:0% +represent the integers. Then the all +sorting can be done in linear time. And + + align:start position:0% +sorting can be done in linear time. And + + + align:start position:0% +sorting can be done in linear time. And +as you might imagine this two this log + + align:start position:0% +as you might imagine this two this log + + + align:start position:0% +as you might imagine this two this log +to the two plus epsilon buys you a + + align:start position:0% +to the two plus epsilon buys you a + + + align:start position:0% +to the two plus epsilon buys you a +little bit of room with some tricks + + align:start position:0% +little bit of room with some tricks + + + align:start position:0% +little bit of room with some tricks +namely sorting namely + + align:start position:0% +namely sorting namely + + + align:start position:0% +namely sorting namely +hashing. All right, but that's where + + align:start position:0% +hashing. All right, but that's where + + + align:start position:0% +hashing. All right, but that's where +we're + + align:start position:0% +we're + + + align:start position:0% +we're +going. And we'll use another yet another + + align:start position:0% +going. And we'll use another yet another + + + align:start position:0% +going. And we'll use another yet another +sorting algorithm, Bonic Sort, which you + + align:start position:0% +sorting algorithm, Bonic Sort, which you + + + align:start position:0% +sorting algorithm, Bonic Sort, which you +may have seen. It's a sorting network. + + align:start position:0% +may have seen. It's a sorting network. + + + align:start position:0% +may have seen. It's a sorting network. +It's in uh it's in CLRS up to second + + align:start position:0% +It's in uh it's in CLRS up to second + + + align:start position:0% +It's in uh it's in CLRS up to second +edition, but it got removed from third + + align:start position:0% +edition, but it got removed from third + + + align:start position:0% +edition, but it got removed from third +edition. I guess they thought people + + align:start position:0% +edition. I guess they thought people + + + align:start position:0% +edition. I guess they thought people +didn't use sorting networks, but we use + + align:start position:0% +didn't use sorting networks, but we use + + + align:start position:0% +didn't use sorting networks, but we use +sorting networks here + + align:start position:0% +sorting networks here + + + align:start position:0% +sorting networks here +uh because it gives us parallel sorting + + align:start position:0% +uh because it gives us parallel sorting + + + align:start position:0% +uh because it gives us parallel sorting +and the word RAM is all about using the + + align:start position:0% +and the word RAM is all about using the + + + align:start position:0% +and the word RAM is all about using the +parallelism in your word. + + align:start position:0% + + + + align:start position:0% + +So we'll get to those. I'm going to + + align:start position:0% +So we'll get to those. I'm going to + + + align:start position:0% +So we'll get to those. I'm going to +start at the top + + align:start position:0% +start at the top + + + align:start position:0% +start at the top +level which is signature sort and we're + + align:start position:0% +level which is signature sort and we're + + + align:start position:0% +level which is signature sort and we're +going to leave things to be done and + + align:start position:0% +going to leave things to be done and + + + align:start position:0% +going to leave things to be done and +then pack sorting will be one of them + + align:start position:0% +then pack sorting will be one of them + + + align:start position:0% +then pack sorting will be one of them +and bonic sorting will be used in pack + + align:start position:0% +and bonic sorting will be used in pack + + + align:start position:0% +and bonic sorting will be used in pack +sorting. So it's it's a chain like + + align:start position:0% + + + + align:start position:0% + +this. Cool. So I'm going to + + align:start position:0% +this. Cool. So I'm going to + + + align:start position:0% +this. Cool. So I'm going to +assume my signature sort that w is at + + align:start position:0% +assume my signature sort that w is at + + + align:start position:0% +assume my signature sort that w is at +least log to the 2 + epsilon n times log + + align:start position:0% +least log to the 2 + epsilon n times log + + + align:start position:0% +least log to the 2 + epsilon n times log +log n. Okay, this is really just a + + align:start position:0% +log n. Okay, this is really just a + + + align:start position:0% +log n. Okay, this is really just a +change in what epsilon means. You make + + align:start position:0% +change in what epsilon means. You make + + + align:start position:0% +change in what epsilon means. You make +it a little bit if you're given some + + align:start position:0% +it a little bit if you're given some + + + align:start position:0% +it a little bit if you're given some +particular epsilon, make it a little + + align:start position:0% +particular epsilon, make it a little + + + align:start position:0% +particular epsilon, make it a little +smaller than you can afford to add that + + align:start position:0% +smaller than you can afford to add that + + + align:start position:0% +smaller than you can afford to add that +log n factor. This is just for + + align:start position:0% +log n factor. This is just for + + + align:start position:0% +log n factor. This is just for +convenience. + + align:start position:0% +convenience. + + + align:start position:0% +convenience. +Uh, now + + align:start position:0% +Uh, now + + + align:start position:0% +Uh, now +here's the + + align:start position:0% +here's the + + + align:start position:0% +here's the +idea. This is a pretty cool idea, I have + + align:start position:0% +idea. This is a pretty cool idea, I have + + + align:start position:0% +idea. This is a pretty cool idea, I have +to say. It's by Anderson and others in + + align:start position:0% + + + + align:start position:0% + +1998. Okay. Okay, a word size is big + + align:start position:0% +1998. Okay. Okay, a word size is big + + + align:start position:0% +1998. Okay. Okay, a word size is big +which is both good and bad. It means the + + align:start position:0% +which is both good and bad. It means the + + + align:start position:0% +which is both good and bad. It means the +numbers we have to sort are big. They + + align:start position:0% +numbers we have to sort are big. They + + + align:start position:0% +numbers we have to sort are big. They +have a lot of bits in them, way more + + align:start position:0% +have a lot of bits in them, way more + + + align:start position:0% +have a lot of bits in them, way more +than login bits. Uh but also we have + + align:start position:0% +than login bits. Uh but also we have + + + align:start position:0% +than login bits. Uh but also we have +this powerful machine that can handle uh + + align:start position:0% +this powerful machine that can handle uh + + + align:start position:0% +this powerful machine that can handle uh +words of of very large size and do + + align:start position:0% +words of of very large size and do + + + align:start position:0% +words of of very large size and do +things in constant time on them. So what + + align:start position:0% +things in constant time on them. So what + + + align:start position:0% +things in constant time on them. So what +I'm going to do, I need to I'd like to + + align:start position:0% +I'm going to do, I need to I'd like to + + + align:start position:0% +I'm going to do, I need to I'd like to +make some some slop. I want my words to + + align:start position:0% +make some some slop. I want my words to + + + align:start position:0% +make some some slop. I want my words to +be bigger than my items. So first few + + align:start position:0% +be bigger than my items. So first few + + + align:start position:0% +be bigger than my items. So first few +steps are about doing that. The first + + align:start position:0% +steps are about doing that. The first + + + align:start position:0% +steps are about doing that. The first +idea is well you've got this giant + + align:start position:0% +idea is well you've got this giant + + + align:start position:0% +idea is well you've got this giant +word log to 2 plus epsilon. So let's + + align:start position:0% +word log to 2 plus epsilon. So let's + + + align:start position:0% +word log to 2 plus epsilon. So let's +split it into chunks and the number of + + align:start position:0% +split it into chunks and the number of + + + align:start position:0% +split it into chunks and the number of +chunks is log to the + + align:start position:0% +chunks is log to the + + + align:start position:0% +chunks is log to the +epsilon. So that means each chunk is uh + + align:start position:0% +epsilon. So that means each chunk is uh + + + align:start position:0% +epsilon. So that means each chunk is uh +well it could be even bigger. So it's at + + align:start position:0% +well it could be even bigger. So it's at + + + align:start position:0% +well it could be even bigger. So it's at +least log 2 n but could be bigger than + + align:start position:0% +least log 2 n but could be bigger than + + + align:start position:0% +least log 2 n but could be bigger than +that because w is at least log to 2 plus + + align:start position:0% +that because w is at least log to 2 plus + + + align:start position:0% +that because w is at least log to 2 plus +epsilon. So we don't know these things + + align:start position:0% +epsilon. So we don't know these things + + + align:start position:0% +epsilon. So we don't know these things +are of size w / log to the epsilon n at + + align:start position:0% +are of size w / log to the epsilon n at + + + align:start position:0% +are of size w / log to the epsilon n at +least log + + align:start position:0% +least log + + + align:start position:0% +least log +squ. Okay, here's the crazy idea. Uh we + + align:start position:0% +squ. Okay, here's the crazy idea. Uh we + + + align:start position:0% +squ. Okay, here's the crazy idea. Uh we +have the so we're thinking of our our + + align:start position:0% +have the so we're thinking of our our + + + align:start position:0% +have the so we're thinking of our our +number being divided into these chunks. + + align:start position:0% +number being divided into these chunks. + + + align:start position:0% +number being divided into these chunks. +you know it's being represented in some + + align:start position:0% +you know it's being represented in some + + + align:start position:0% +you know it's being represented in some +base 2 the w / log to the epsilon n a + + align:start position:0% +base 2 the w / log to the epsilon n a + + + align:start position:0% +base 2 the w / log to the epsilon n a +bit of a + + align:start position:0% +bit of a + + + align:start position:0% +bit of a +mouthful but think about these digits + + align:start position:0% +mouthful but think about these digits + + + align:start position:0% +mouthful but think about these digits +right uh I claim if you look at a digit + + align:start position:0% +right uh I claim if you look at a digit + + + align:start position:0% +right uh I claim if you look at a digit +most values don't + + align:start position:0% +most values don't + + + align:start position:0% +most values don't +appear okay because how many values are + + align:start position:0% +appear okay because how many values are + + + align:start position:0% +appear okay because how many values are +there for a digit well it's at least 2 + + align:start position:0% +there for a digit well it's at least 2 + + + align:start position:0% +there for a digit well it's at least 2 +log 2 n that's a big number that's way + + align:start position:0% +log 2 n that's a big number that's way + + + align:start position:0% +log 2 n that's a big number that's way +bigger than polomial and n but how many + + align:start position:0% +bigger than polomial and n but how many + + + align:start position:0% +bigger than polomial and n but how many +different digits are + + align:start position:0% +different digits are + + + align:start position:0% +different digits are +uh well there's n numbers each of them + + align:start position:0% +uh well there's n numbers each of them + + + align:start position:0% +uh well there's n numbers each of them +has log to the epsilonn n uh digits in + + align:start position:0% +has log to the epsilonn n uh digits in + + + align:start position:0% +has log to the epsilonn n uh digits in +it appearing and so there's you know + + align:start position:0% +it appearing and so there's you know + + + align:start position:0% +it appearing and so there's you know +roughly a linear number of digit values + + align:start position:0% +roughly a linear number of digit values + + + align:start position:0% +roughly a linear number of digit values +total but the number of possible digit + + align:start position:0% +total but the number of possible digit + + + align:start position:0% +total but the number of possible digit +values is 2 to the log log squared n + + align:start position:0% +values is 2 to the log log squared n + + + align:start position:0% +values is 2 to the log log squared n +which is huge super + + align:start position:0% +which is huge super + + + align:start position:0% +which is huge super +polomial so most digit values don't + + align:start position:0% +polomial so most digit values don't + + + align:start position:0% +polomial so most digit values don't +appear in our numbers so what we're + + align:start position:0% +appear in our numbers so what we're + + + align:start position:0% +appear in our numbers so what we're +going to do is hash the digit values + + align:start position:0% +going to do is hash the digit values + + + align:start position:0% +going to do is hash the digit values +to reduce their space because they're + + align:start position:0% +to reduce their space because they're + + + align:start position:0% +to reduce their space because they're +currently living in a universe of 2 log + + align:start position:0% +currently living in a universe of 2 log + + + align:start position:0% +currently living in a universe of 2 log +n but there's only n * log epsilon n of + + align:start position:0% +n but there's only n * log epsilon n of + + + align:start position:0% +n but there's only n * log epsilon n of +them. So we should be able to reduce to + + align:start position:0% +them. So we should be able to reduce to + + + align:start position:0% +them. So we should be able to reduce to +a much smaller universe + + align:start position:0% +a much smaller universe + + + align:start position:0% +a much smaller universe +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and uh using hashing maybe uh + + align:start position:0% +and uh using hashing maybe uh + + + align:start position:0% +and uh using hashing maybe uh +yeah perfect hashing even I mean we + + align:start position:0% +yeah perfect hashing even I mean we + + + align:start position:0% +yeah perfect hashing even I mean we +don't have to be too intelligent here + + align:start position:0% +don't have to be too intelligent here + + + align:start position:0% +don't have to be too intelligent here +tell you what we + + align:start position:0% + + + + align:start position:0% + +get what I'd like is to reduce to a + + align:start position:0% +get what I'd like is to reduce to a + + + align:start position:0% +get what I'd like is to reduce to a +polomial universe + + align:start position:0% +polomial universe + + + align:start position:0% +polomial universe +And another way to say + + align:start position:0% + + + + align:start position:0% + +that is that the hash values are order + + align:start position:0% +that is that the hash values are order + + + align:start position:0% +that is that the hash values are order +login bits. So this lets us go to n to + + align:start position:0% +login bits. So this lets us go to n to + + + align:start position:0% +login bits. So this lets us go to n to +the 10 or whatever which is plenty of + + align:start position:0% +the 10 or whatever which is plenty of + + + align:start position:0% +the 10 or whatever which is plenty of +room right we take any universal hash + + align:start position:0% +room right we take any universal hash + + + align:start position:0% +room right we take any universal hash +function then with uh you know as soon + + align:start position:0% +function then with uh you know as soon + + + align:start position:0% +function then with uh you know as soon +as you get to roughly n squared size I + + align:start position:0% +as you get to roughly n squared size I + + + align:start position:0% +as you get to roughly n squared size I +mean the square of the number of things + + align:start position:0% +mean the square of the number of things + + + align:start position:0% +mean the square of the number of things +by a birthday paradox constant + + align:start position:0% +by a birthday paradox constant + + + align:start position:0% +by a birthday paradox constant +probability none of them will hit each + + align:start position:0% +probability none of them will hit each + + + align:start position:0% +probability none of them will hit each +other. That was the second level of + + align:start position:0% +other. That was the second level of + + + align:start position:0% +other. That was the second level of +perfect hashing. We don't need two + + align:start position:0% +perfect hashing. We don't need two + + + align:start position:0% +perfect hashing. We don't need two +levels here. Just say okay uh use order + + align:start position:0% +levels here. Just say okay uh use order + + + align:start position:0% +levels here. Just say okay uh use order +login bits. You can set this to 100 + + align:start position:0% +login bits. You can set this to 100 + + + align:start position:0% +login bits. You can set this to 100 +whatever. Uh then with high probability + + align:start position:0% +whatever. Uh then with high probability + + + align:start position:0% +whatever. Uh then with high probability +you will not get collisions. So none of + + align:start position:0% +you will not get collisions. So none of + + + align:start position:0% +you will not get collisions. So none of +the chunks will hit each other. So I'm + + align:start position:0% +the chunks will hit each other. So I'm + + + align:start position:0% +the chunks will hit each other. So I'm +emitting a step here which is how to + + align:start position:0% +emitting a step here which is how to + + + align:start position:0% +emitting a step here which is how to +okay I'm emitting a couple things here. + + align:start position:0% +okay I'm emitting a couple things here. + + + align:start position:0% +okay I'm emitting a couple things here. +Um one of them is I want to do this in + + align:start position:0% +Um one of them is I want to do this in + + + align:start position:0% +Um one of them is I want to do this in +linear time. Everything has to be in + + align:start position:0% +linear time. Everything has to be in + + + align:start position:0% +linear time. Everything has to be in +linear time. So one fun part is I have + + align:start position:0% +linear time. So one fun part is I have + + + align:start position:0% +linear time. So one fun part is I have +to compute the hash value of all of + + align:start position:0% +to compute the hash value of all of + + + align:start position:0% +to compute the hash value of all of +these digits in a single word in + + align:start position:0% +these digits in a single word in + + + align:start position:0% +these digits in a single word in +constant + + align:start position:0% +constant + + + align:start position:0% +constant +time. Okay, so brief aside, how would I + + align:start position:0% +time. Okay, so brief aside, how would I + + + align:start position:0% +time. Okay, so brief aside, how would I +compute uh a universal hash function on + + align:start position:0% +compute uh a universal hash function on + + + align:start position:0% +compute uh a universal hash function on +all of these digits individually in + + align:start position:0% +all of these digits individually in + + + align:start position:0% +all of these digits individually in +constant time? Well, + + align:start position:0% + + + + align:start position:0% + +uh my personal favorite universal + + align:start position:0% +uh my personal favorite universal + + + align:start position:0% +uh my personal favorite universal +hashing scheme is the multiplication + + align:start position:0% +hashing scheme is the multiplication + + + align:start position:0% +hashing scheme is the multiplication +method. you just need to multiply by a + + align:start position:0% +method. you just need to multiply by a + + + align:start position:0% +method. you just need to multiply by a +single value m and then take it modulo + + align:start position:0% +single value m and then take it modulo + + + align:start position:0% +single value m and then take it modulo +something. Uh so if I do multiplication + + align:start position:0% + + + + align:start position:0% + +uh I mean if you think of there being + + align:start position:0% +uh I mean if you think of there being + + + align:start position:0% +uh I mean if you think of there being +something here, something here, + + align:start position:0% +something here, something here, + + + align:start position:0% +something here, something here, +something here, something here, + + align:start position:0% +something here, something here, + + + align:start position:0% +something here, something here, +something here, m does multiply + + align:start position:0% +something here, m does multiply + + + align:start position:0% +something here, m does multiply +uh each of these individually. + + align:start position:0% + + + + align:start position:0% + +Wow, that's a rough sketch. I want to + + align:start position:0% +Wow, that's a rough sketch. I want to + + + align:start position:0% +Wow, that's a rough sketch. I want to +hash each of these guys, multiply them + + align:start position:0% +hash each of these guys, multiply them + + + align:start position:0% +hash each of these guys, multiply them +by the multiplication method. Uh, this + + align:start position:0% +by the multiplication method. Uh, this + + + align:start position:0% +by the multiplication method. Uh, this +would work fine except you get + + align:start position:0% +would work fine except you get + + + align:start position:0% +would work fine except you get +overflows, which is a bit messy. So, in + + align:start position:0% +overflows, which is a bit messy. So, in + + + align:start position:0% +overflows, which is a bit messy. So, in +fact, I'm going to have to do it for the + + align:start position:0% +fact, I'm going to have to do it for the + + + align:start position:0% +fact, I'm going to have to do it for the +odd guys first, multiply them out, mask + + align:start position:0% +odd guys first, multiply them out, mask + + + align:start position:0% +odd guys first, multiply them out, mask +out the bits I care about, then do it + + align:start position:0% +out the bits I care about, then do it + + + align:start position:0% +out the bits I care about, then do it +for the even guys separately. Uh, so + + align:start position:0% +for the even guys separately. Uh, so + + + align:start position:0% +for the even guys separately. Uh, so +it's a bit messy, but handwavy proof, + + align:start position:0% +it's a bit messy, but handwavy proof, + + + align:start position:0% +it's a bit messy, but handwavy proof, +you can compute the hash function of + + align:start position:0% +you can compute the hash function of + + + align:start position:0% +you can compute the hash function of +each of these guys individually, but in + + align:start position:0% +each of these guys individually, but in + + + align:start position:0% +each of these guys individually, but in +constant time. + + align:start position:0% +constant time. + + + align:start position:0% +constant time. +So that lets me do this. You have to + + align:start position:0% +So that lets me do this. You have to + + + align:start position:0% +So that lets me do this. You have to +then check for collisions which is kind + + align:start position:0% +then check for collisions which is kind + + + align:start position:0% +then check for collisions which is kind +of annoying. Let's not worry about that. + + align:start position:0% +of annoying. Let's not worry about that. + + + align:start position:0% +of annoying. Let's not worry about that. +Set this really high. Very high + + align:start position:0% +Set this really high. Very high + + + align:start position:0% +Set this really high. Very high +probability. There will be no + + align:start position:0% +probability. There will be no + + + align:start position:0% +probability. There will be no +collisions. + + align:start position:0% +collisions. + + + align:start position:0% +collisions. +Cool. So at this point we have mucked up + + align:start position:0% +Cool. So at this point we have mucked up + + + align:start position:0% +Cool. So at this point we have mucked up +all the digits. The annoying thing about + + align:start position:0% +all the digits. The annoying thing about + + + align:start position:0% +all the digits. The annoying thing about +this hashing is we do not preserve + + align:start position:0% + + + + align:start position:0% + +order. It's a little weird for a sorting + + align:start position:0% +order. It's a little weird for a sorting + + + align:start position:0% +order. It's a little weird for a sorting +algorithm to not preserve order. The + + align:start position:0% +algorithm to not preserve order. The + + + align:start position:0% +algorithm to not preserve order. The +whole point is to put things in order, + + align:start position:0% +whole point is to put things in order, + + + align:start position:0% +whole point is to put things in order, +but it's going to be useful nonetheless. + + align:start position:0% +but it's going to be useful nonetheless. + + + align:start position:0% +but it's going to be useful nonetheless. +Right? So each digit has been mangled. + + align:start position:0% +Right? So each digit has been mangled. + + + align:start position:0% +Right? So each digit has been mangled. +Each digit is out of order, but of + + align:start position:0% +Each digit is out of order, but of + + + align:start position:0% +Each digit is out of order, but of +course the I mean the sequence of digits + + align:start position:0% +course the I mean the sequence of digits + + + align:start position:0% +course the I mean the sequence of digits +has been preserved. Some + + align:start position:0% +has been preserved. Some + + + align:start position:0% +has been preserved. Some +sense all right. So what? Well, at this + + align:start position:0% +sense all right. So what? Well, at this + + + align:start position:0% +sense all right. So what? Well, at this +point we can use pack sorting to sort + + align:start position:0% +point we can use pack sorting to sort + + + align:start position:0% +point we can use pack sorting to sort +what what + + align:start position:0% + + + + align:start position:0% + +remains. In general, pack sorting can + + align:start position:0% +remains. In general, pack sorting can + + + align:start position:0% +remains. In general, pack sorting can +sort n bid + + align:start position:0% +sort n bid + + + align:start position:0% +sort n bid +integers provided b is small. So w is at + + align:start position:0% +integers provided b is small. So w is at + + + align:start position:0% +integers provided b is small. So w is at +least b log n log login lo login. That's + + align:start position:0% +least b log n log login lo login. That's + + + align:start position:0% +least b log n log login lo login. That's +the that's the theorem of pack sorting. + + align:start position:0% +the that's the theorem of pack sorting. + + + align:start position:0% +the that's the theorem of pack sorting. +We're going to delay the coverage of + + align:start position:0% +We're going to delay the coverage of + + + align:start position:0% +We're going to delay the coverage of +this uh result till later. And I claim + + align:start position:0% +this uh result till later. And I claim + + + align:start position:0% +this uh result till later. And I claim +that that applies here because let's see + + align:start position:0% +that that applies here because let's see + + + align:start position:0% +that that applies here because let's see +um each + + align:start position:0% + + + + align:start position:0% + +chunk each chunk is now order log n bits + + align:start position:0% +chunk each chunk is now order log n bits + + + align:start position:0% +chunk each chunk is now order log n bits +and there's log to the epsilon n bits. + + align:start position:0% +and there's log to the epsilon n bits. + + + align:start position:0% +and there's log to the epsilon n bits. +So b is theta log to the 1 + epsilon + + align:start position:0% +So b is theta log to the 1 + epsilon + + + align:start position:0% +So b is theta log to the 1 + epsilon +n and + + align:start position:0% +n and + + + align:start position:0% +n and +w it's at least uh log 2 + + + align:start position:0% +w it's at least uh log 2 + + + + align:start position:0% +w it's at least uh log 2 + +epsilon time log + + align:start position:0% +epsilon time log + + + align:start position:0% +epsilon time log +n. Okay, so the ratio between these is + + align:start position:0% +n. Okay, so the ratio between these is + + + align:start position:0% +n. Okay, so the ratio between these is +as needed. It's at least log n * log + + align:start position:0% + + + + align:start position:0% + +n. Okay, so that's why this is good. + + align:start position:0% +n. Okay, so that's why this is good. + + + align:start position:0% +n. Okay, so that's why this is good. +There were these things were huge + + align:start position:0% +There were these things were huge + + + align:start position:0% +There were these things were huge +before. We've compressed them a lot. + + align:start position:0% +before. We've compressed them a lot. + + + align:start position:0% +before. We've compressed them a lot. +They were at least log square. Now + + align:start position:0% +They were at least log square. Now + + + align:start position:0% +They were at least log square. Now +they're only log. Uh and so now we can + + align:start position:0% +they're only log. Uh and so now we can + + + align:start position:0% +they're only log. Uh and so now we can +apply pack sorting. You can fit all + + align:start position:0% +apply pack sorting. You can fit all + + + align:start position:0% +apply pack sorting. You can fit all +these guys into you can fit log* log + + align:start position:0% +these guys into you can fit log* log + + + align:start position:0% +these guys into you can fit log* log +items into one word and that's going to + + align:start position:0% +items into one word and that's going to + + + align:start position:0% +items into one word and that's going to +make sorting easy somehow. That's to be + + align:start position:0% +make sorting easy somehow. That's to be + + + align:start position:0% +make sorting easy somehow. That's to be +done. But now the question is what would + + align:start position:0% +done. But now the question is what would + + + align:start position:0% +done. But now the question is what would +you do if this suppose we had pack + + align:start position:0% +you do if this suppose we had pack + + + align:start position:0% +you do if this suppose we had pack +sorting. How does this help you? Because + + align:start position:0% +sorting. How does this help you? Because + + + align:start position:0% +sorting. How does this help you? Because +this does not sort the original + + align:start position:0% +this does not sort the original + + + align:start position:0% +this does not sort the original +integers. It sorts these integers that + + align:start position:0% +integers. It sorts these integers that + + + align:start position:0% +integers. It sorts these integers that +have all of their digits permuted in + + align:start position:0% +have all of their digits permuted in + + + align:start position:0% +have all of their digits permuted in +some random way. We have no idea how the + + align:start position:0% +some random way. We have no idea how the + + + align:start position:0% +some random way. We have no idea how the +hash function reorders things. So, we're + + align:start position:0% +hash function reorders things. So, we're + + + align:start position:0% +hash function reorders things. So, we're +not done with signature sort. It's + + align:start position:0% +not done with signature sort. It's + + + align:start position:0% +not done with signature sort. It's +called signature sort, of course, + + align:start position:0% +called signature sort, of course, + + + align:start position:0% +called signature sort, of course, +because of the hashing. You're taking + + align:start position:0% +because of the hashing. You're taking + + + align:start position:0% +because of the hashing. You're taking +signatures of each of these digits. + + align:start position:0% +signatures of each of these digits. + + + align:start position:0% +signatures of each of these digits. +Another word for + + align:start position:0% +Another word for + + + align:start position:0% +Another word for +hashes. All right. Next + + align:start position:0% +hashes. All right. Next + + + align:start position:0% +hashes. All right. Next +step is + + align:start position:0% +step is + + + align:start position:0% +step is +to build a compressed try. + + align:start position:0% + + + + align:start position:0% + +This is a term we haven't used + + align:start position:0% + + + + align:start position:0% + +yet. So, I'm going to call these things + + align:start position:0% +yet. So, I'm going to call these things + + + align:start position:0% +yet. So, I'm going to call these things +that we sorted + + align:start position:0% +that we sorted + + + align:start position:0% +that we sorted +signatures. And uh how many people know + + align:start position:0% +signatures. And uh how many people know + + + align:start position:0% +signatures. And uh how many people know +what a compressed try + + align:start position:0% +what a compressed try + + + align:start position:0% +what a compressed try +is? Okay. No one. Wow. Just a few. So, + + align:start position:0% +is? Okay. No one. Wow. Just a few. So, + + + align:start position:0% +is? Okay. No one. Wow. Just a few. So, +you haven't seen suffix trees yet. We're + + align:start position:0% +you haven't seen suffix trees yet. We're + + + align:start position:0% +you haven't seen suffix trees yet. We're +going to cover uh where compressed tries + + align:start position:0% +going to cover uh where compressed tries + + + align:start position:0% +going to cover uh where compressed tries +come from in a couple of lectures, but + + align:start position:0% +come from in a couple of lectures, but + + + align:start position:0% +come from in a couple of lectures, but +we get to see them a little early + + align:start position:0% +we get to see them a little early + + + align:start position:0% +we get to see them a little early +because they're cool uh and needed for + + align:start position:0% +because they're cool uh and needed for + + + align:start position:0% +because they're cool uh and needed for +this uh algorithm. So, first notion is + + align:start position:0% +this uh algorithm. So, first notion is + + + align:start position:0% +this uh algorithm. So, first notion is +the notion of a try. The word try comes + + align:start position:0% +the notion of a try. The word try comes + + + align:start position:0% +the notion of a try. The word try comes +re from retrieval + + align:start position:0% +re from retrieval + + + align:start position:0% +re from retrieval +uh from old days when information + + align:start position:0% +uh from old days when information + + + align:start position:0% +uh from old days when information +retrieval was what's now called I don't + + align:start position:0% +retrieval was what's now called I don't + + + align:start position:0% +retrieval was what's now called I don't +know web searching or whatever. Uh so + + align:start position:0% +know web searching or whatever. Uh so + + + align:start position:0% +know web searching or whatever. Uh so +it's but now it's pronounced try. uh + + align:start position:0% +it's but now it's pronounced try. uh + + + align:start position:0% +it's but now it's pronounced try. uh +it's just another word for tree but + + align:start position:0% +it's just another word for tree but + + + align:start position:0% +it's just another word for tree but +where the children of a tree uh come + + align:start position:0% +where the children of a tree uh come + + + align:start position:0% +where the children of a tree uh come +from a fixed universe. + + align:start position:0% +from a fixed universe. + + + align:start position:0% +from a fixed universe. +So this is some we've been working with + + align:start position:0% +So this is some we've been working with + + + align:start position:0% +So this is some we've been working with +tree with tries all the time in pretty + + align:start position:0% +tree with tries all the time in pretty + + + align:start position:0% +tree with tries all the time in pretty +much every lecture for the last n + + align:start position:0% +much every lecture for the last n + + + align:start position:0% +much every lecture for the last n +lectures last w lectures I don't know a + + align:start position:0% +lectures last w lectures I don't know a + + + align:start position:0% +lectures last w lectures I don't know a +lot of them we said oh okay well let's + + align:start position:0% +lot of them we said oh okay well let's + + + align:start position:0% +lot of them we said oh okay well let's +just consider the space of all possible + + align:start position:0% +just consider the space of all possible + + + align:start position:0% +just consider the space of all possible +keys you know I've drawn this picture a + + align:start position:0% +keys you know I've drawn this picture a + + + align:start position:0% +keys you know I've drawn this picture a +zillion times even when we weren't doing + + align:start position:0% +zillion times even when we weren't doing + + + align:start position:0% +zillion times even when we weren't doing +phenom dus which actually stores all of + + align:start position:0% +phenom dus which actually stores all of + + + align:start position:0% +phenom dus which actually stores all of +these things uh when we're thinking + + align:start position:0% +these things uh when we're thinking + + + align:start position:0% +these things uh when we're thinking +about fusion trees like oh yeah so we're + + align:start position:0% +about fusion trees like oh yeah so we're + + + align:start position:0% +about fusion trees like oh yeah so we're +storing this value and we're storing + + align:start position:0% +storing this value and we're storing + + + align:start position:0% +storing this value and we're storing +this value and maybe this value and we + + align:start position:0% +this value and maybe this value and we + + + align:start position:0% +this value and maybe this value and we +understand you know this corresponds to + + align:start position:0% +understand you know this corresponds to + + + align:start position:0% +understand you know this corresponds to +a zero bit these are 0 and one bits this + + align:start position:0% +a zero bit these are 0 and one bits this + + + align:start position:0% +a zero bit these are 0 and one bits this +is a one zero one whatever so we + + align:start position:0% +is a one zero one whatever so we + + + align:start position:0% +is a one zero one whatever so we +understand how to convert a bit string + + align:start position:0% +understand how to convert a bit string + + + align:start position:0% +understand how to convert a bit string +into this picture this is what we call a + + align:start position:0% +into this picture this is what we call a + + + align:start position:0% +into this picture this is what we call a +binary try I want to do the same thing + + align:start position:0% +binary try I want to do the same thing + + + align:start position:0% +binary try I want to do the same thing +over here except it's not a binary try + + align:start position:0% +over here except it's not a binary try + + + align:start position:0% +over here except it's not a binary try +now each digit is giant so we're going + + align:start position:0% +now each digit is giant so we're going + + + align:start position:0% +now each digit is giant so we're going +to have some huge branching factor so + + align:start position:0% +to have some huge branching factor so + + + align:start position:0% +to have some huge branching factor so +it's going to be more like a b tree the + + align:start position:0% +it's going to be more like a b tree the + + + align:start position:0% +it's going to be more like a b tree the +first node has a whole bunch of children + + align:start position:0% +first node has a whole bunch of children + + + align:start position:0% +first node has a whole bunch of children +I'm not going to even like I mean it's + + align:start position:0% +I'm not going to even like I mean it's + + + align:start position:0% +I'm not going to even like I mean it's +two to the w / uh log to the epsilon n + + align:start position:0% +two to the w / uh log to the epsilon n + + + align:start position:0% +two to the w / uh log to the epsilon n +that's the branching + + align:start position:0% +that's the branching + + + align:start position:0% +that's the branching +factor okay it's big that's the number + + align:start position:0% +factor okay it's big that's the number + + + align:start position:0% +factor okay it's big that's the number +of possible values in the first + + align:start position:0% +of possible values in the first + + + align:start position:0% +of possible values in the first +digit okay uh so you know then maybe + + align:start position:0% +digit okay uh so you know then maybe + + + align:start position:0% +digit okay uh so you know then maybe +this child has some node there and maybe + + align:start position:0% +this child has some node there and maybe + + + align:start position:0% +this child has some node there and maybe +you know this + + align:start position:0% + + + + align:start position:0% + +one actually sorry I didn't want to draw + + align:start position:0% +one actually sorry I didn't want to draw + + + align:start position:0% +one actually sorry I didn't want to draw +that + + align:start position:0% +that + + + align:start position:0% +that +way I have a specific try in mind or + + align:start position:0% +way I have a specific try in mind or + + + align:start position:0% +way I have a specific try in mind or +part of + + align:start position:0% + + + + align:start position:0% + +it. Okay, I mean try is going to look + + align:start position:0% +it. Okay, I mean try is going to look + + + align:start position:0% +it. Okay, I mean try is going to look +something like this. It's just the it's + + align:start position:0% +something like this. It's just the it's + + + align:start position:0% +something like this. It's just the it's +harder to draw but it's the uh larger + + align:start position:0% +harder to draw but it's the uh larger + + + align:start position:0% +harder to draw but it's the uh larger +than binary equivalent of this picture. + + align:start position:0% +than binary equivalent of this picture. + + + align:start position:0% +than binary equivalent of this picture. +This would be a try. + + align:start position:0% +This would be a try. + + + align:start position:0% +This would be a try. +So let's think about uh a particular + + align:start position:0% +So let's think about uh a particular + + + align:start position:0% +So let's think about uh a particular +situation which is uh suppose we just + + align:start position:0% +situation which is uh suppose we just + + + align:start position:0% +situation which is uh suppose we just +have two items in this structure. Okay + + align:start position:0% +have two items in this structure. Okay + + + align:start position:0% +have two items in this structure. Okay +then it's easier to draw. So let's + + align:start position:0% +then it's easier to draw. So let's + + + align:start position:0% +then it's easier to draw. So let's +suppose there's some item over here + + align:start position:0% +suppose there's some item over here + + + align:start position:0% +suppose there's some item over here +x1. There's some item over here x2. Now + + align:start position:0% +x1. There's some item over here x2. Now + + + align:start position:0% +x1. There's some item over here x2. Now +generic picture is they have they share + + align:start position:0% +generic picture is they have they share + + + align:start position:0% +generic picture is they have they share +some common prefix. This is the common + + align:start position:0% + + + + align:start position:0% + +prefix. It's just to understand some + + align:start position:0% +prefix. It's just to understand some + + + align:start position:0% +prefix. It's just to understand some +particular picture here. then they + + align:start position:0% +particular picture here. then they + + + align:start position:0% +particular picture here. then they +diverge, you know, then they have their + + align:start position:0% +diverge, you know, then they have their + + + align:start position:0% +diverge, you know, then they have their +own digit values. In some sense, this is + + align:start position:0% +own digit values. In some sense, this is + + + align:start position:0% +own digit values. In some sense, this is +the digit value we care about because it + + align:start position:0% +the digit value we care about because it + + + align:start position:0% +the digit value we care about because it +distinguishes them. Uh so there's this + + align:start position:0% +distinguishes them. Uh so there's this + + + align:start position:0% +distinguishes them. Uh so there's this +idea of a compressed + + align:start position:0% + + + + align:start position:0% + +try which cleans up this picture a + + align:start position:0% +try which cleans up this picture a + + + align:start position:0% +try which cleans up this picture a +little + + align:start position:0% + + + + align:start position:0% + +bit. The idea with a compressed try is + + align:start position:0% +bit. The idea with a compressed try is + + + align:start position:0% +bit. The idea with a compressed try is +very simple. You draw this try. So I + + align:start position:0% +very simple. You draw this try. So I + + + align:start position:0% +very simple. You draw this try. So I +mean here, imagine I'm erasing all the + + align:start position:0% +mean here, imagine I'm erasing all the + + + align:start position:0% +mean here, imagine I'm erasing all the +things that do not appear. Okay, maybe + + align:start position:0% +things that do not appear. Okay, maybe + + + align:start position:0% +things that do not appear. Okay, maybe +all this is gone. So I'm just keeping + + align:start position:0% +all this is gone. So I'm just keeping + + + align:start position:0% +all this is gone. So I'm just keeping +this part of the structure. Let's do it + + align:start position:0% +this part of the structure. Let's do it + + + align:start position:0% +this part of the structure. Let's do it +for the binary case first. The idea in a + + align:start position:0% +for the binary case first. The idea in a + + + align:start position:0% +for the binary case first. The idea in a +compressed try is very simple. Uh I'm + + align:start position:0% +compressed try is very simple. Uh I'm + + + align:start position:0% +compressed try is very simple. Uh I'm +going to contract + + align:start position:0% + + + + align:start position:0% + +uh every non-branching + + align:start position:0% +uh every non-branching + + + align:start position:0% +uh every non-branching +node into its + + align:start position:0% + + + + align:start position:0% + +parent. So what that means? So here I'm + + align:start position:0% +parent. So what that means? So here I'm + + + align:start position:0% +parent. So what that means? So here I'm +storing three values uh 0 0 1 1 uh 0 1 0 + + align:start position:0% +storing three values uh 0 0 1 1 uh 0 1 0 + + + align:start position:0% +storing three values uh 0 0 1 1 uh 0 1 0 +0 and 0 1 1 + + align:start position:0% +0 and 0 1 1 + + + align:start position:0% +0 and 0 1 1 +uh so some nodes are non-branching + + align:start position:0% +uh so some nodes are non-branching + + + align:start position:0% +uh so some nodes are non-branching +that's this node this node and this node + + align:start position:0% +that's this node this node and this node + + + align:start position:0% +that's this node this node and this node +and the point is well why store those + + align:start position:0% +and the point is well why store those + + + align:start position:0% +and the point is well why store those +nodes I mean there was nothing being + + align:start position:0% +nodes I mean there was nothing being + + + align:start position:0% +nodes I mean there was nothing being +distinguished at that node so contract + + align:start position:0% +distinguished at that node so contract + + + align:start position:0% +distinguished at that node so contract +it so the new picture if I redrew this + + align:start position:0% +it so the new picture if I redrew this + + + align:start position:0% +it so the new picture if I redrew this +would be + + align:start position:0% +would be + + + align:start position:0% +would be +0 01 + + align:start position:0% +0 01 + + + align:start position:0% +0 01 +uh oh sorry Also this is non- branching. + + align:start position:0% +uh oh sorry Also this is non- branching. + + + align:start position:0% +uh oh sorry Also this is non- branching. +Okay. So in fact I'm going to contract + + align:start position:0% +Okay. So in fact I'm going to contract + + + align:start position:0% +Okay. So in fact I'm going to contract +this into its parent or this into its + + align:start position:0% +this into its parent or this into its + + + align:start position:0% +this into its parent or this into its +parent this into its parent. So this + + align:start position:0% +parent this into its parent. So this + + + align:start position:0% +parent this into its parent. So this +whole path this non-branching path will + + align:start position:0% +whole path this non-branching path will + + + align:start position:0% +whole path this non-branching path will +be left with a single edge which I will + + align:start position:0% +be left with a single edge which I will + + + align:start position:0% +be left with a single edge which I will +label + + align:start position:0% +label + + + align:start position:0% +label +011. But it's a single edge in the + + align:start position:0% +011. But it's a single edge in the + + + align:start position:0% +011. But it's a single edge in the +structure. Over here we have an edge one + + align:start position:0% +structure. Over here we have an edge one + + + align:start position:0% +structure. Over here we have an edge one +and now we have 0 0 here and one one + + align:start position:0% +and now we have 0 0 here and one one + + + align:start position:0% +and now we have 0 0 here and one one +here. Okay is the compressed try + + align:start position:0% +here. Okay is the compressed try + + + align:start position:0% +here. Okay is the compressed try +representation of these three values. + + align:start position:0% +representation of these three values. + + + align:start position:0% +representation of these three values. +The nice thing about this structure is + + align:start position:0% +The nice thing about this structure is + + + align:start position:0% +The nice thing about this structure is +every node is branching except the + + align:start position:0% +every node is branching except the + + + align:start position:0% +every node is branching except the +leaves which means the number of nodes + + align:start position:0% +leaves which means the number of nodes + + + align:start position:0% +leaves which means the number of nodes +here is linear in the number of leaves. + + align:start position:0% +here is linear in the number of leaves. + + + align:start position:0% +here is linear in the number of leaves. +It's like twice the number of leaves + + align:start position:0% +It's like twice the number of leaves + + + align:start position:0% +It's like twice the number of leaves +minus one roughly. I guess the root + + align:start position:0% +minus one roughly. I guess the root + + + align:start position:0% +minus one roughly. I guess the root +might not be branching but it has no + + align:start position:0% +might not be branching but it has no + + + align:start position:0% +might not be branching but it has no +parent to contract into whatever one + + align:start position:0% +parent to contract into whatever one + + + align:start position:0% +parent to contract into whatever one +more nodes two end nodes. That's the + + align:start position:0% +more nodes two end nodes. That's the + + + align:start position:0% +more nodes two end nodes. That's the +binary case. Now over here what we do is + + align:start position:0% +binary case. Now over here what we do is + + + align:start position:0% +binary case. Now over here what we do is +the corresponding contracted try picture + + align:start position:0% +the corresponding contracted try picture + + + align:start position:0% +the corresponding contracted try picture +of this thing will be let's see it's the + + align:start position:0% +of this thing will be let's see it's the + + + align:start position:0% +of this thing will be let's see it's the +second edge I'm going to put just a + + align:start position:0% +second edge I'm going to put just a + + + align:start position:0% +second edge I'm going to put just a +label of two on this edge to say well + + align:start position:0% +label of two on this edge to say well + + + align:start position:0% +label of two on this edge to say well +I'm skipping this node this guy is + + align:start position:0% +I'm skipping this node this guy is + + + align:start position:0% +I'm skipping this node this guy is +non-branching so I want to get rid of it + + align:start position:0% +non-branching so I want to get rid of it + + + align:start position:0% +non-branching so I want to get rid of it +and contract it into the parent so now + + align:start position:0% +and contract it into the parent so now + + + align:start position:0% +and contract it into the parent so now +this corresponds to two edges here there + + align:start position:0% +this corresponds to two edges here there + + + align:start position:0% +this corresponds to two edges here there +are two digits which I could write the + + align:start position:0% +are two digits which I could write the + + + align:start position:0% +are two digits which I could write the +digits if I knew what they were but + + align:start position:0% +digits if I knew what they were but + + + align:start position:0% +digits if I knew what they were but +particularly I want to keep track of the + + align:start position:0% +particularly I want to keep track of the + + + align:start position:0% +particularly I want to keep track of the +fact that they're exactly two of + + align:start position:0% +fact that they're exactly two of + + + align:start position:0% +fact that they're exactly two of +them and then there's a branching node. + + align:start position:0% +them and then there's a branching node. + + + align:start position:0% +them and then there's a branching node. +That one stays uh but then uh actually + + align:start position:0% +That one stays uh but then uh actually + + + align:start position:0% +That one stays uh but then uh actually +we'll go straight to the leaves here. + + align:start position:0% +we'll go straight to the leaves here. + + + align:start position:0% +we'll go straight to the leaves here. +This will be uh x1 and + + align:start position:0% +This will be uh x1 and + + + align:start position:0% +This will be uh x1 and +x2 and this will have a lot of + + align:start position:0% +x2 and this will have a lot of + + + align:start position:0% +x2 and this will have a lot of +digits. Okay, so some large number + + align:start position:0% +digits. Okay, so some large number + + + align:start position:0% +digits. Okay, so some large number +written here. So that's the idea with a + + align:start position:0% +written here. So that's the idea with a + + + align:start position:0% +written here. So that's the idea with a +compressed try. Now the nice thing about + + align:start position:0% +compressed try. Now the nice thing about + + + align:start position:0% +compressed try. Now the nice thing about +a compressed try is they have linear + + align:start position:0% +a compressed try is they have linear + + + align:start position:0% +a compressed try is they have linear +size. + + align:start position:0% + + + + align:start position:0% + +number of edges and vertices is linear + + align:start position:0% +number of edges and vertices is linear + + + align:start position:0% +number of edges and vertices is linear +in the number of leaves which is the + + align:start position:0% +in the number of leaves which is the + + + align:start position:0% +in the number of leaves which is the +number of values we have here. Uh + + align:start position:0% +number of values we have here. Uh + + + align:start position:0% +number of values we have here. Uh +another nice thing about compressed + + align:start position:0% +another nice thing about compressed + + + align:start position:0% +another nice thing about compressed +tries is they preserve order. So if you + + align:start position:0% +tries is they preserve order. So if you + + + align:start position:0% +tries is they preserve order. So if you +look at the order of the leaves down + + align:start position:0% +look at the order of the leaves down + + + align:start position:0% +look at the order of the leaves down +here, uh it's the same as the order of + + align:start position:0% +here, uh it's the same as the order of + + + align:start position:0% +here, uh it's the same as the order of +the leaves over here, right? We're not + + align:start position:0% +the leaves over here, right? We're not + + + align:start position:0% +the leaves over here, right? We're not +really changing order. We're just making + + align:start position:0% +really changing order. We're just making + + + align:start position:0% +really changing order. We're just making +things a little shorter to write down. + + align:start position:0% +things a little shorter to write down. + + + align:start position:0% +things a little shorter to write down. +Uh same thing over here. I mean x1 + + align:start position:0% +Uh same thing over here. I mean x1 + + + align:start position:0% +Uh same thing over here. I mean x1 +appears to the left of x2. + + align:start position:0% + + + + align:start position:0% + +So say the order of the leaves is + + align:start position:0% +So say the order of the leaves is + + + align:start position:0% +So say the order of the leaves is +preserved. Uh the other cool thing about + + align:start position:0% +preserved. Uh the other cool thing about + + + align:start position:0% +preserved. Uh the other cool thing about +compressed tries is you can compute them + + align:start position:0% +compressed tries is you can compute them + + + align:start position:0% +compressed tries is you can compute them +in linear time. But let me tell you why + + align:start position:0% +in linear time. But let me tell you why + + + align:start position:0% +in linear time. But let me tell you why +we're drawing this picture, right? We + + align:start position:0% +we're drawing this picture, right? We + + + align:start position:0% +we're drawing this picture, right? We +messed up all these chunks, all these + + align:start position:0% +messed up all these chunks, all these + + + align:start position:0% +messed up all these chunks, all these +digits. What does that correspond to in + + align:start position:0% +digits. What does that correspond to in + + + align:start position:0% +digits. What does that correspond to in +this picture? We've permuted all of the + + align:start position:0% +this picture? We've permuted all of the + + + align:start position:0% +this picture? We've permuted all of the +children in this node. We've permuted + + align:start position:0% +children in this node. We've permuted + + + align:start position:0% +children in this node. We've permuted +all the children in this node. Permuted + + align:start position:0% +all the children in this node. Permuted + + + align:start position:0% +all the children in this node. Permuted +all the children in this node. But + + align:start position:0% +all the children in this node. But + + + align:start position:0% +all the children in this node. But +otherwise, the structure of the tree is + + align:start position:0% +otherwise, the structure of the tree is + + + align:start position:0% +otherwise, the structure of the tree is +correct. What we wanted to do was + + align:start position:0% +correct. What we wanted to do was + + + align:start position:0% +correct. What we wanted to do was +compute if we could compute the + + align:start position:0% +compute if we could compute the + + + align:start position:0% +compute if we could compute the +compressed try representation of the + + align:start position:0% +compressed try representation of the + + + align:start position:0% +compressed try representation of the +original + + align:start position:0% +original + + + align:start position:0% +original +values just having broken the integers + + align:start position:0% +values just having broken the integers + + + align:start position:0% +values just having broken the integers +into these pieces. Then if we had that + + align:start position:0% +into these pieces. Then if we had that + + + align:start position:0% +into these pieces. Then if we had that +try, we could just do an in order + + align:start position:0% +try, we could just do an in order + + + align:start position:0% +try, we could just do an in order +traversal, find the order of the leaves, + + align:start position:0% +traversal, find the order of the leaves, + + + align:start position:0% +traversal, find the order of the leaves, +then we'd have the sorted order of the + + align:start position:0% +then we'd have the sorted order of the + + + align:start position:0% +then we'd have the sorted order of the +integers. Instead, what we've computed + + align:start position:0% +integers. Instead, what we've computed + + + align:start position:0% +integers. Instead, what we've computed +is not the correct, we didn't compute + + align:start position:0% +is not the correct, we didn't compute + + + align:start position:0% +is not the correct, we didn't compute +the correct compressed try, but we + + align:start position:0% +the correct compressed try, but we + + + align:start position:0% +the correct compressed try, but we +computed a different compressed try + + align:start position:0% +computed a different compressed try + + + align:start position:0% +computed a different compressed try +where every node has its not has its + + align:start position:0% +where every node has its not has its + + + align:start position:0% +where every node has its not has its +children permuted. So all we need to do + + align:start position:0% +children permuted. So all we need to do + + + align:start position:0% +children permuted. So all we need to do +is put the children within each node in + + align:start position:0% +is put the children within each node in + + + align:start position:0% +is put the children within each node in +the correct order. Then we would have + + align:start position:0% +the correct order. Then we would have + + + align:start position:0% +the correct order. Then we would have +the correct compressed try. Okay, that's + + align:start position:0% +the correct compressed try. Okay, that's + + + align:start position:0% +the correct compressed try. Okay, that's +why we're doing this. Uh but first how + + align:start position:0% +why we're doing this. Uh but first how + + + align:start position:0% +why we're doing this. Uh but first how +do we compute a compressed try in linear + + align:start position:0% + + + + align:start position:0% + +time? Uh this is a simple amortization + + align:start position:0% + + + + align:start position:0% + +argument. Okay, remember what we're + + align:start position:0% +argument. Okay, remember what we're + + + align:start position:0% +argument. Okay, remember what we're +given. + + align:start position:0% + + + + align:start position:0% + +At this point, we are given the leaves + + align:start position:0% +At this point, we are given the leaves + + + align:start position:0% +At this point, we are given the leaves +in sorted order, right? We've just + + align:start position:0% +in sorted order, right? We've just + + + align:start position:0% +in sorted order, right? We've just +sorted our things. So, all I'm trying to + + align:start position:0% +sorted our things. So, all I'm trying to + + + align:start position:0% +sorted our things. So, all I'm trying to +do is compute the try of the stuff above + + align:start position:0% +do is compute the try of the stuff above + + + align:start position:0% +do is compute the try of the stuff above +the things. Okay? We're given the leaves + + align:start position:0% +the things. Okay? We're given the leaves + + + align:start position:0% +the things. Okay? We're given the leaves +of the try in in the correct order. I + + align:start position:0% +of the try in in the correct order. I + + + align:start position:0% +of the try in in the correct order. I +just need to build the compressed try. + + align:start position:0% +just need to build the compressed try. + + + align:start position:0% +just need to build the compressed try. +The reason I'm building the compressed + + align:start position:0% +The reason I'm building the compressed + + + align:start position:0% +The reason I'm building the compressed +try is so I can do it in linear time. + + align:start position:0% +try is so I can do it in linear time. + + + align:start position:0% +try is so I can do it in linear time. +Constructing the the uncompressed try + + align:start position:0% +Constructing the the uncompressed try + + + align:start position:0% +Constructing the the uncompressed try +would take too + + align:start position:0% +would take too + + + align:start position:0% +would take too +long. Okay. So, how do we do this? + + align:start position:0% + + + + align:start position:0% + +Um, so we have our items XN in + + align:start position:0% + + + + align:start position:0% + +order. I want to just insert + + align:start position:0% +order. I want to just insert + + + align:start position:0% +order. I want to just insert +it into the compressed try. So I start + + align:start position:0% +it into the compressed try. So I start + + + align:start position:0% +it into the compressed try. So I start +with an empty compressed try. Uh, first + + align:start position:0% +with an empty compressed try. Uh, first + + + align:start position:0% +with an empty compressed try. Uh, first +thing I do is add X1. So it's just a + + align:start position:0% +thing I do is add X1. So it's just a + + + align:start position:0% +thing I do is add X1. So it's just a +single leaf. Then I add x2 to the try, + + align:start position:0% +single leaf. Then I add x2 to the try, + + + align:start position:0% +single leaf. Then I add x2 to the try, +x3 to the try. In general, I'll have + + align:start position:0% +x3 to the try. In general, I'll have + + + align:start position:0% +x3 to the try. In general, I'll have +computed draw a picture uh how to draw a + + align:start position:0% +computed draw a picture uh how to draw a + + + align:start position:0% +computed draw a picture uh how to draw a +partial try something like this. I've + + align:start position:0% +partial try something like this. I've + + + align:start position:0% +partial try something like this. I've +computed the left part of the try + + align:start position:0% +computed the left part of the try + + + align:start position:0% +computed the left part of the try +already. All the these x i have been + + align:start position:0% +already. All the these x i have been + + + align:start position:0% +already. All the these x i have been +done. And now I need to compute I need + + align:start position:0% +done. And now I need to compute I need + + + align:start position:0% +done. And now I need to compute I need +to add on the ne say x i over here + + align:start position:0% +to add on the ne say x i over here + + + align:start position:0% +to add on the ne say x i over here +somewhere. So think of how that would + + align:start position:0% +somewhere. So think of how that would + + + align:start position:0% +somewhere. So think of how that would +look in the try. Uh it has to come off + + align:start position:0% +look in the try. Uh it has to come off + + + align:start position:0% +look in the try. Uh it has to come off +of the right side. uh I guess what would + + align:start position:0% +of the right side. uh I guess what would + + + align:start position:0% +of the right side. uh I guess what would +you call this the right spine of the + + align:start position:0% +you call this the right spine of the + + + align:start position:0% +you call this the right spine of the +tree some rightmost node over here we + + align:start position:0% +tree some rightmost node over here we + + + align:start position:0% +tree some rightmost node over here we +want x i to be a new to the right child + + align:start position:0% +want x i to be a new to the right child + + + align:start position:0% +want x i to be a new to the right child +so maybe uh so one possible picture + + align:start position:0% +so maybe uh so one possible picture + + + align:start position:0% +so maybe uh so one possible picture +is there's some node which had some + + align:start position:0% +is there's some node which had some + + + align:start position:0% +is there's some node which had some +other children maybe this one had x i + + align:start position:0% +other children maybe this one had x i + + + align:start position:0% +other children maybe this one had x i +minus one and maybe x i belongs over + + align:start position:0% +minus one and maybe x i belongs over + + + align:start position:0% +minus one and maybe x i belongs over +here maybe this leads to x i in the + + align:start position:0% +here maybe this leads to x i in the + + + align:start position:0% +here maybe this leads to x i in the +uncompressed try this could be potential + + align:start position:0% +uncompressed try this could be potential + + + align:start position:0% +uncompressed try this could be potential +picture uh in the compressed try this + + align:start position:0% +picture uh in the compressed try this + + + align:start position:0% +picture uh in the compressed try this +node either exists or got contracted. If + + align:start position:0% +node either exists or got contracted. If + + + align:start position:0% +node either exists or got contracted. If +it exists maybe there was a previous + + align:start position:0% +it exists maybe there was a previous + + + align:start position:0% +it exists maybe there was a previous +like x i minus 2 belongs over here. So + + align:start position:0% +like x i minus 2 belongs over here. So + + + align:start position:0% +like x i minus 2 belongs over here. So +we already had this node because it + + align:start position:0% +we already had this node because it + + + align:start position:0% +we already had this node because it +distinguished these two xjs. Uh to add + + align:start position:0% +distinguished these two xjs. Uh to add + + + align:start position:0% +distinguished these two xjs. Uh to add +the x i is really easy. I just add a + + align:start position:0% +the x i is really easy. I just add a + + + align:start position:0% +the x i is really easy. I just add a +node here which and then which points to + + align:start position:0% +node here which and then which points to + + + align:start position:0% +node here which and then which points to +a leaf of x i. So that could be one + + align:start position:0% +a leaf of x i. So that could be one + + + align:start position:0% +a leaf of x i. So that could be one +situation. Uh the the other situation is + + align:start position:0% +situation. Uh the the other situation is + + + align:start position:0% +situation. Uh the the other situation is +only slightly more complicated. + + align:start position:0% + + + + align:start position:0% + +So the other possibility is this node + + align:start position:0% +So the other possibility is this node + + + align:start position:0% +So the other possibility is this node +didn't exist in the compressed try which + + align:start position:0% +didn't exist in the compressed try which + + + align:start position:0% +didn't exist in the compressed try which +means we jumped over it in the + + align:start position:0% +means we jumped over it in the + + + align:start position:0% +means we jumped over it in the +compressed + + align:start position:0% +compressed + + + align:start position:0% +compressed +try. You know some number bigger than + + align:start position:0% +try. You know some number bigger than + + + align:start position:0% +try. You know some number bigger than +one here. Maybe you skipped three nodes. + + align:start position:0% +one here. Maybe you skipped three nodes. + + + align:start position:0% +one here. Maybe you skipped three nodes. +Who knows? Um so now this node matters. + + align:start position:0% +Who knows? Um so now this node matters. + + + align:start position:0% +Who knows? Um so now this node matters. +It didn't matter before. Before it was + + align:start position:0% +It didn't matter before. Before it was + + + align:start position:0% +It didn't matter before. Before it was +non- branching, but now we add XI. It's + + align:start position:0% +non- branching, but now we add XI. It's + + + align:start position:0% +non- branching, but now we add XI. It's +branching. All we do is update, add this + + align:start position:0% +branching. All we do is update, add this + + + align:start position:0% +branching. All we do is update, add this +new guy, add the new pointer to XI. + + align:start position:0% +new guy, add the new pointer to XI. + + + align:start position:0% +new guy, add the new pointer to XI. +Okay, so constant + + align:start position:0% +Okay, so constant + + + align:start position:0% +Okay, so constant +work. Great. Constant work per XI + + align:start position:0% +work. Great. Constant work per XI + + + align:start position:0% +work. Great. Constant work per XI +inserted linear time + + align:start position:0% +inserted linear time + + + align:start position:0% +inserted linear time +overall. Not really. Uh, I've cheated a + + align:start position:0% +overall. Not really. Uh, I've cheated a + + + align:start position:0% +overall. Not really. Uh, I've cheated a +little bit here, which is how do we know + + align:start position:0% +little bit here, which is how do we know + + + align:start position:0% +little bit here, which is how do we know +where to do this operation? So the + + align:start position:0% +where to do this operation? So the + + + align:start position:0% +where to do this operation? So the +changes we make is constant. That's + + align:start position:0% +changes we make is constant. That's + + + align:start position:0% +changes we make is constant. That's +fine. But how did I find that this was + + align:start position:0% +fine. But how did I find that this was + + + align:start position:0% +fine. But how did I find that this was +the edge where I need to put XI in? You + + align:start position:0% +the edge where I need to put XI in? You + + + align:start position:0% +the edge where I need to put XI in? You +can't do it in constant time, but we can + + align:start position:0% +can't do it in constant time, but we can + + + align:start position:0% +can't do it in constant time, but we can +do it in constant amortized time. So + + align:start position:0% +do it in constant amortized time. So + + + align:start position:0% +do it in constant amortized time. So +what we're going to do + + align:start position:0% +what we're going to do + + + align:start position:0% +what we're going to do +is start at the rightmost. Oh, that is + + align:start position:0% +is start at the rightmost. Oh, that is + + + align:start position:0% +is start at the rightmost. Oh, that is +not very + + align:start position:0% +not very + + + align:start position:0% +not very +red. It's not a red + + align:start position:0% +red. It's not a red + + + align:start position:0% +red. It's not a red +chalk. Okay, some red chalk. Uh we start + + align:start position:0% +chalk. Okay, some red chalk. Uh we start + + + align:start position:0% +chalk. Okay, some red chalk. Uh we start +at this leaf, the rightmost leaf, which + + align:start position:0% +at this leaf, the rightmost leaf, which + + + align:start position:0% +at this leaf, the rightmost leaf, which +you go going rightmost as possible. + + align:start position:0% +you go going rightmost as possible. + + + align:start position:0% +you go going rightmost as possible. +We're going to walk up the tree until we + + align:start position:0% +We're going to walk up the tree until we + + + align:start position:0% +We're going to walk up the tree until we +find the right point. I'm going to spend + + align:start position:0% +find the right point. I'm going to spend + + + align:start position:0% +find the right point. I'm going to spend +linear time in this + + align:start position:0% +linear time in this + + + align:start position:0% +linear time in this +pathwalk. Okay, how could this possibly + + align:start position:0% +pathwalk. Okay, how could this possibly + + + align:start position:0% +pathwalk. Okay, how could this possibly +be? Okay, I think you believe that I can + + align:start position:0% +be? Okay, I think you believe that I can + + + align:start position:0% +be? Okay, I think you believe that I can +do it in linear time, right? Each each + + align:start position:0% +do it in linear time, right? Each each + + + align:start position:0% +do it in linear time, right? Each each +point I see do what is my common prefix + + align:start position:0% +point I see do what is my common prefix + + + align:start position:0% +point I see do what is my common prefix +with actually an easy way is right up + + align:start position:0% +with actually an easy way is right up + + + align:start position:0% +with actually an easy way is right up +front. This this thing right here is x i + + align:start position:0% +front. This this thing right here is x i + + + align:start position:0% +front. This this thing right here is x i +minus one. These are in these are single + + align:start position:0% +minus one. These are in these are single + + + align:start position:0% +minus one. These are in these are single +integers. So I can just uh compute their + + align:start position:0% +integers. So I can just uh compute their + + + align:start position:0% +integers. So I can just uh compute their +exor find the most significant one bit + + align:start position:0% +exor find the most significant one bit + + + align:start position:0% +exor find the most significant one bit +which we did with fusion tree lecture. + + align:start position:0% +which we did with fusion tree lecture. + + + align:start position:0% +which we did with fusion tree lecture. +Uh and boom I know where they differ in + + align:start position:0% +Uh and boom I know where they differ in + + + align:start position:0% +Uh and boom I know where they differ in +bit position. Uh by some rounding I can + + align:start position:0% +bit position. Uh by some rounding I can + + + align:start position:0% +bit position. Uh by some rounding I can +figure out which chunk they differ in + + align:start position:0% +figure out which chunk they differ in + + + align:start position:0% +figure out which chunk they differ in +just by you know dividing taking the + + align:start position:0% +just by you know dividing taking the + + + align:start position:0% +just by you know dividing taking the +ceiling. + + align:start position:0% +ceiling. + + + align:start position:0% +ceiling. +uh so I know the correct depth and then + + align:start position:0% +uh so I know the correct depth and then + + + align:start position:0% +uh so I know the correct depth and then +these numbers tell me how much uh how + + align:start position:0% +these numbers tell me how much uh how + + + align:start position:0% +these numbers tell me how much uh how +much depth I'm losing as I walk up at + + align:start position:0% +much depth I'm losing as I walk up at + + + align:start position:0% +much depth I'm losing as I walk up at +some point I'll discover oops I just + + align:start position:0% +some point I'll discover oops I just + + + align:start position:0% +some point I'll discover oops I just +jumped over the depth I care about where + + align:start position:0% +jumped over the depth I care about where + + + align:start position:0% +jumped over the depth I care about where +they differ and so at that point I know + + align:start position:0% +they differ and so at that point I know + + + align:start position:0% +they differ and so at that point I know +to do the operation so if this is if + + align:start position:0% +to do the operation so if this is if + + + align:start position:0% +to do the operation so if this is if +there are k edges here on the compressed + + align:start position:0% +there are k edges here on the compressed + + + align:start position:0% +there are k edges here on the compressed +try I can do this in order k time k plus + + align:start position:0% +try I can do this in order k time k plus + + + align:start position:0% +try I can do this in order k time k plus +one let's + + align:start position:0% +one let's + + + align:start position:0% +one let's +say why is that okay because + + align:start position:0% +say why is that okay because + + + align:start position:0% +say why is that okay because +uh my potential function amortization is + + align:start position:0% +uh my potential function amortization is + + + align:start position:0% +uh my potential function amortization is +going to be the length of the right + + align:start position:0% +going to be the length of the right + + + align:start position:0% +going to be the length of the right +uh let's call it the rightmost + + align:start position:0% + + + + align:start position:0% + +path. Okay. And before my rightmost path + + align:start position:0% +path. Okay. And before my rightmost path + + + align:start position:0% +path. Okay. And before my rightmost path +was this thing. Afterwards my rightmost + + align:start position:0% +was this thing. Afterwards my rightmost + + + align:start position:0% +was this thing. Afterwards my rightmost +path is going to be this thing. So it + + align:start position:0% +path is going to be this thing. So it + + + align:start position:0% +path is going to be this thing. So it +got roughly k shorter. K minus one + + align:start position:0% +got roughly k shorter. K minus one + + + align:start position:0% +got roughly k shorter. K minus one +shorter. Okay. Okay, so I charge this k + + align:start position:0% +shorter. Okay. Okay, so I charge this k + + + align:start position:0% +shorter. Okay. Okay, so I charge this k ++ one cost to a uh potential decrease of + + align:start position:0% ++ one cost to a uh potential decrease of + + + align:start position:0% ++ one cost to a uh potential decrease of +k minus one and so the advertised cost + + align:start position:0% +k minus one and so the advertised cost + + + align:start position:0% +k minus one and so the advertised cost +is only constant. Okay, easy + + align:start position:0% +is only constant. Okay, easy + + + align:start position:0% +is only constant. Okay, easy +amortization. Another way to see this is + + align:start position:0% +amortization. Another way to see this is + + + align:start position:0% +amortization. Another way to see this is +overall we're basically doing an inorder + + align:start position:0% +overall we're basically doing an inorder + + + align:start position:0% +overall we're basically doing an inorder +traversal of the tree. So whenever we + + align:start position:0% +traversal of the tree. So whenever we + + + align:start position:0% +traversal of the tree. So whenever we +walk up we'll never visit these nodes + + align:start position:0% +walk up we'll never visit these nodes + + + align:start position:0% +walk up we'll never visit these nodes +again and then we go down a different + + align:start position:0% +again and then we go down a different + + + align:start position:0% +again and then we go down a different +place. Okay, yeah this guy we're going + + align:start position:0% +place. Okay, yeah this guy we're going + + + align:start position:0% +place. Okay, yeah this guy we're going +to walk up again because in order in + + align:start position:0% +to walk up again because in order in + + + align:start position:0% +to walk up again because in order in +order traversal we would have gone left + + align:start position:0% +order traversal we would have gone left + + + align:start position:0% +order traversal we would have gone left +and then come back to it and then gone + + align:start position:0% +and then come back to it and then gone + + + align:start position:0% +and then come back to it and then gone +down. So overall we're doing an in order + + align:start position:0% +down. So overall we're doing an in order + + + align:start position:0% +down. So overall we're doing an in order +traversal of the compressed try. So it's + + align:start position:0% +traversal of the compressed try. So it's + + + align:start position:0% +traversal of the compressed try. So it's +order it's linear time + + align:start position:0% + + + + align:start position:0% + +total. + + align:start position:0% + + + + align:start position:0% + +Okay. Still not done though. What we + + align:start position:0% +Okay. Still not done though. What we + + + align:start position:0% +Okay. Still not done though. What we +have so far, what have we done? We've + + align:start position:0% +have so far, what have we done? We've + + + align:start position:0% +have so far, what have we done? We've +taken our numbers. We split them into + + align:start position:0% +taken our numbers. We split them into + + + align:start position:0% +taken our numbers. We split them into +digits. We randomly permuted the digits + + align:start position:0% +digits. We randomly permuted the digits + + + align:start position:0% +digits. We randomly permuted the digits +by a hash function that magically let us + + align:start position:0% +by a hash function that magically let us + + + align:start position:0% +by a hash function that magically let us +sort them in linear time. Now we've + + align:start position:0% +sort them in linear time. Now we've + + + align:start position:0% +sort them in linear time. Now we've +built a compressed try of that + + align:start position:0% +built a compressed try of that + + + align:start position:0% +built a compressed try of that +representation. The last thing to do is + + align:start position:0% +representation. The last thing to do is + + + align:start position:0% +representation. The last thing to do is +to fix the order of the children from + + align:start position:0% +to fix the order of the children from + + + align:start position:0% +to fix the order of the children from +each node. The tree is correct except + + align:start position:0% +each node. The tree is correct except + + + align:start position:0% +each node. The tree is correct except +for the order of the children in each + + align:start position:0% +for the order of the children in each + + + align:start position:0% +for the order of the children in each +node. So we've kind of sorted a little + + align:start position:0% +node. So we've kind of sorted a little + + + align:start position:0% +node. So we've kind of sorted a little +bit but haven't fully + + align:start position:0% +bit but haven't fully + + + align:start position:0% +bit but haven't fully +sorted. + + align:start position:0% +sorted. + + + align:start position:0% +sorted. +So that's the last step + + align:start position:0% +So that's the last step + + + align:start position:0% +So that's the last step +and we're going to do that with + + align:start position:0% +and we're going to do that with + + + align:start position:0% +and we're going to do that with +recursion. + + align:start position:0% + + + + align:start position:0% + +We're only going to recurse a constant + + align:start position:0% +We're only going to recurse a constant + + + align:start position:0% +We're only going to recurse a constant +number of + + align:start position:0% +number of + + + align:start position:0% +number of +times recursively sort + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay. Uh, I'm going to walk through this + + align:start position:0% +Okay. Uh, I'm going to walk through this + + + align:start position:0% +Okay. Uh, I'm going to walk through this +compressed try that we've + + align:start position:0% +compressed try that we've + + + align:start position:0% +compressed try that we've +built. And I guess it looks more like + + align:start position:0% +built. And I guess it looks more like + + + align:start position:0% +built. And I guess it looks more like +this. And for each edge, I'm going to + + align:start position:0% +this. And for each edge, I'm going to + + + align:start position:0% +this. And for each edge, I'm going to +write down this key. First thing I'm + + align:start position:0% +write down this key. First thing I'm + + + align:start position:0% +write down this key. First thing I'm +going to write down is the ID of the + + align:start position:0% +going to write down is the ID of the + + + align:start position:0% +going to write down is the ID of the +node. Let's say uh the ID is the in + + align:start position:0% +node. Let's say uh the ID is the in + + + align:start position:0% +node. Let's say uh the ID is the in +order traversal index of the + + align:start position:0% +order traversal index of the + + + align:start position:0% +order traversal index of the +node. Okay. So boom. As we traverse the + + align:start position:0% +node. Okay. So boom. As we traverse the + + + align:start position:0% +node. Okay. So boom. As we traverse the +tree, we can just increment this + + align:start position:0% +tree, we can just increment this + + + align:start position:0% +tree, we can just increment this +counter. Uh then we also want the uh + + align:start position:0% +counter. Uh then we also want the uh + + + align:start position:0% +counter. Uh then we also want the uh +what I'm going to put in here is the + + align:start position:0% +what I'm going to put in here is the + + + align:start position:0% +what I'm going to put in here is the +actual chunk + + align:start position:0% +actual chunk + + + align:start position:0% +actual chunk +value that uh that's at the top of the + + align:start position:0% +value that uh that's at the top of the + + + align:start position:0% +value that uh that's at the top of the +node. So some something like this or I + + align:start position:0% +node. So some something like this or I + + + align:start position:0% +node. So some something like this or I +guess this one. This one consists of two + + align:start position:0% +guess this one. This one consists of two + + + align:start position:0% +guess this one. This one consists of two +chunk values. So let's call them + + align:start position:0% +chunk values. So let's call them + + + align:start position:0% +chunk values. So let's call them +C1. Two chunk values. C1 and C2. There's + + align:start position:0% +C1. Two chunk values. C1 and C2. There's + + + align:start position:0% +C1. Two chunk values. C1 and C2. There's +the first chunk value and the second + + align:start position:0% +the first chunk value and the second + + + align:start position:0% +the first chunk value and the second +chunk value. First digit and the second + + align:start position:0% +chunk value. First digit and the second + + + align:start position:0% +chunk value. First digit and the second +digit. Just write down the first + + align:start position:0% + + + + align:start position:0% + +one. That's really the only one we care + + align:start position:0% +one. That's really the only one we care + + + align:start position:0% +one. That's really the only one we care +about. The second one wasn't branching. + + align:start position:0% +about. The second one wasn't branching. + + + align:start position:0% +about. The second one wasn't branching. +So it's no big + + align:start position:0% +So it's no big + + + align:start position:0% +So it's no big +deal. Okay. So there's some chunk value. + + align:start position:0% +deal. Okay. So there's some chunk value. + + + align:start position:0% +deal. Okay. So there's some chunk value. +Now I don't want to write down the + + align:start position:0% +Now I don't want to write down the + + + align:start position:0% +Now I don't want to write down the +signature chunk value. I don't want to + + align:start position:0% +signature chunk value. I don't want to + + + align:start position:0% +signature chunk value. I don't want to +write down the hash value. I want the + + align:start position:0% +write down the hash value. I want the + + + align:start position:0% +write down the hash value. I want the +actual chunk original chunk not the hash + + align:start position:0% +actual chunk original chunk not the hash + + + align:start position:0% +actual chunk original chunk not the hash +that's why I write actual over here and + + align:start position:0% +that's why I write actual over here and + + + align:start position:0% +that's why I write actual over here and +then also I'm going to write down the + + align:start position:0% +then also I'm going to write down the + + + align:start position:0% +then also I'm going to write down the +index of the edge so this is the second + + align:start position:0% +index of the edge so this is the second + + + align:start position:0% +index of the edge so this is the second +edge for + + align:start position:0% +edge for + + + align:start position:0% +edge for +example okay now this is in some sense + + align:start position:0% +example okay now this is in some sense + + + align:start position:0% +example okay now this is in some sense +the wrong index and what I want to + + align:start position:0% +the wrong index and what I want to + + + align:start position:0% +the wrong index and what I want to +compute is where it's supposed to be the + + align:start position:0% +compute is where it's supposed to be the + + + align:start position:0% +compute is where it's supposed to be the +edges have been permuted so if I sort + + align:start position:0% +edges have been permuted so if I sort + + + align:start position:0% +edges have been permuted so if I sort +this thing I claim that I'll find the + + align:start position:0% +this thing I claim that I'll find the + + + align:start position:0% +this thing I claim that I'll find the +all the desired + + align:start position:0% + + + + align:start position:0% + +permutations okay Why? Because uh if I + + align:start position:0% +permutations okay Why? Because uh if I + + + align:start position:0% +permutations okay Why? Because uh if I +sort by this uh three valued uh this + + align:start position:0% +sort by this uh three valued uh this + + + align:start position:0% +sort by this uh three valued uh this +triple, first thing I sort by is by node + + align:start position:0% +triple, first thing I sort by is by node + + + align:start position:0% +triple, first thing I sort by is by node +ID. Then I'm sorting by actual chunk + + align:start position:0% +ID. Then I'm sorting by actual chunk + + + align:start position:0% +ID. Then I'm sorting by actual chunk +value, then uh edge index. I don't care + + align:start position:0% +value, then uh edge index. I don't care + + + align:start position:0% +value, then uh edge index. I don't care +that I'm sorting by it. That's just + + align:start position:0% +that I'm sorting by it. That's just + + + align:start position:0% +that I'm sorting by it. That's just +coming along for the ride. So what this + + align:start position:0% +coming along for the ride. So what this + + + align:start position:0% +coming along for the ride. So what this +tells me is for each node, + + align:start position:0% +tells me is for each node, + + + align:start position:0% +tells me is for each node, +uh it gives me the sorted value of the + + align:start position:0% +uh it gives me the sorted value of the + + + align:start position:0% +uh it gives me the sorted value of the +actual chunks, not the hash chunks, and + + align:start position:0% +actual chunks, not the hash chunks, and + + + align:start position:0% +actual chunks, not the hash chunks, and +then it tells me the order they used to + + align:start position:0% +then it tells me the order they used to + + + align:start position:0% +then it tells me the order they used to +be in. + + align:start position:0% +be in. + + + align:start position:0% +be in. +So uh this is a way to to figure out the + + align:start position:0% +So uh this is a way to to figure out the + + + align:start position:0% +So uh this is a way to to figure out the +correct per you want to figure out the + + align:start position:0% +correct per you want to figure out the + + + align:start position:0% +correct per you want to figure out the +sorted permutation of these things. This + + align:start position:0% +sorted permutation of these things. This + + + align:start position:0% +sorted permutation of these things. This +gives you the old index and so once + + align:start position:0% +gives you the old index and so once + + + align:start position:0% +gives you the old index and so once +you've sorted them you know the new + + align:start position:0% +you've sorted them you know the new + + + align:start position:0% +you've sorted them you know the new +correct order is in order by chunk and + + align:start position:0% +correct order is in order by chunk and + + + align:start position:0% +correct order is in order by chunk and +so this gives you I guess the inverse of + + align:start position:0% +so this gives you I guess the inverse of + + + align:start position:0% +so this gives you I guess the inverse of +the permutation over here of where each + + align:start position:0% +the permutation over here of where each + + + align:start position:0% +the permutation over here of where each +edge should be. So once I've done this, + + align:start position:0% +edge should be. So once I've done this, + + + align:start position:0% +edge should be. So once I've done this, +the last step is uh you for each node + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +permute the + + align:start position:0% +permute the + + + align:start position:0% +permute the +edges as given by this inverse + + align:start position:0% +edges as given by this inverse + + + align:start position:0% +edges as given by this inverse +permutation. + + align:start position:0% +permutation. + + + align:start position:0% +permutation. +Question explain again that like you're + + align:start position:0% +Question explain again that like you're + + + align:start position:0% +Question explain again that like you're +basically sorting three times. No, I'm + + align:start position:0% +basically sorting three times. No, I'm + + + align:start position:0% +basically sorting three times. No, I'm +sorting I'm sorting these single key + + align:start position:0% +sorting I'm sorting these single key + + + align:start position:0% +sorting I'm sorting these single key +values. the key value, the most + + align:start position:0% +values. the key value, the most + + + align:start position:0% +values. the key value, the most +significant part of the key is this. The + + align:start position:0% +significant part of the key is this. The + + + align:start position:0% +significant part of the key is this. The +next most significant part of the key is + + align:start position:0% +next most significant part of the key is + + + align:start position:0% +next most significant part of the key is +this. And the least significant part of + + align:start position:0% +this. And the least significant part of + + + align:start position:0% +this. And the least significant part of +the key is this. So imagine + + align:start position:0% +the key is this. So imagine + + + align:start position:0% +the key is this. So imagine +concatenating these things together into + + align:start position:0% +concatenating these things together into + + + align:start position:0% +concatenating these things together into +a single key value. Yeah, good question. + + align:start position:0% +a single key value. Yeah, good question. + + + align:start position:0% +a single key value. Yeah, good question. +Well, I'll talk about in a moment how + + align:start position:0% +Well, I'll talk about in a moment how + + + align:start position:0% +Well, I'll talk about in a moment how +big this key is. But if I sort by the + + align:start position:0% +big this key is. But if I sort by the + + + align:start position:0% +big this key is. But if I sort by the +concatenation of those keys, then what + + align:start position:0% +concatenation of those keys, then what + + + align:start position:0% +concatenation of those keys, then what +happens is I'm sorting by this and then + + align:start position:0% +happens is I'm sorting by this and then + + + align:start position:0% +happens is I'm sorting by this and then +sorting by this. But really, I'm doing + + align:start position:0% +sorting by this. But really, I'm doing + + + align:start position:0% +sorting by this. But really, I'm doing +one sort operation. This is one + + align:start position:0% +one sort operation. This is one + + + align:start position:0% +one sort operation. This is one +recursion. Other + + align:start position:0% +recursion. Other + + + align:start position:0% +recursion. Other +questions? Okay. + + align:start position:0% +questions? Okay. + + + align:start position:0% +questions? Okay. +Do you see why this gives us what we + + align:start position:0% +Do you see why this gives us what we + + + align:start position:0% +Do you see why this gives us what we +need? Right? For every node, we want to + + align:start position:0% +need? Right? For every node, we want to + + + align:start position:0% +need? Right? For every node, we want to +sort all those chunks. And so this + + align:start position:0% +sort all those chunks. And so this + + + align:start position:0% +sort all those chunks. And so this +thing, this information is just so we + + align:start position:0% +thing, this information is just so we + + + align:start position:0% +thing, this information is just so we +can keep track of the permutation when + + align:start position:0% +can keep track of the permutation when + + + align:start position:0% +can keep track of the permutation when +we're just sorting by value and not + + align:start position:0% +we're just sorting by value and not + + + align:start position:0% +we're just sorting by value and not +keeping the permutation. This lets us + + align:start position:0% +keeping the permutation. This lets us + + + align:start position:0% +keeping the permutation. This lets us +keep track of it. But our our real goal + + align:start position:0% +keep track of it. But our our real goal + + + align:start position:0% +keep track of it. But our our real goal +is to sort all the chunk values. And we + + align:start position:0% +is to sort all the chunk values. And we + + + align:start position:0% +is to sort all the chunk values. And we +add in the node ID so that uh we just + + align:start position:0% +add in the node ID so that uh we just + + + align:start position:0% +add in the node ID so that uh we just +learn for every node what we're supposed + + align:start position:0% +learn for every node what we're supposed + + + align:start position:0% +learn for every node what we're supposed +to do instead of globally what we need + + align:start position:0% +to do instead of globally what we need + + + align:start position:0% +to do instead of globally what we need +to do. Maybe you don't have to do this, + + align:start position:0% +to do. Maybe you don't have to do this, + + + align:start position:0% +to do. Maybe you don't have to do this, +but it's easier to keep the node ID in + + align:start position:0% +but it's easier to keep the node ID in + + + align:start position:0% +but it's easier to keep the node ID in +there. Okay. How many bits are in this + + align:start position:0% +there. Okay. How many bits are in this + + + align:start position:0% +there. Okay. How many bits are in this +key? So our whole point was to make + + align:start position:0% +key? So our whole point was to make + + + align:start position:0% +key? So our whole point was to make +chunks small so that the keys were + + align:start position:0% +chunks small so that the keys were + + + align:start position:0% +chunks small so that the keys were +small, but I claim this will be a little + + align:start position:0% +small, but I claim this will be a little + + + align:start position:0% +small, but I claim this will be a little +bit smaller than what we started with. + + align:start position:0% +bit smaller than what we started with. + + + align:start position:0% +bit smaller than what we started with. +So the node ID, well, there's only + + align:start position:0% +So the node ID, well, there's only + + + align:start position:0% +So the node ID, well, there's only +nodes. So this is log n + + align:start position:0% +nodes. So this is log n + + + align:start position:0% +nodes. So this is log n +bits. Chunk + + align:start position:0% +bits. Chunk + + + align:start position:0% +bits. Chunk +value is I guess W / log to the + + align:start position:0% +value is I guess W / log to the + + + align:start position:0% +value is I guess W / log to the +epsilonn bits, right? Because there are + + align:start position:0% +epsilonn bits, right? Because there are + + + align:start position:0% +epsilonn bits, right? Because there are +log to the epsilon n chunks. + + align:start position:0% +log to the epsilon n chunks. + + + align:start position:0% +log to the epsilon n chunks. +So it's w divided by log epsilon bits. + + align:start position:0% +So it's w divided by log epsilon bits. + + + align:start position:0% +So it's w divided by log epsilon bits. +The edge index + + align:start position:0% +The edge index + + + align:start position:0% +The edge index +uh how many different things were there? + + align:start position:0% +uh how many different things were there? + + + align:start position:0% +uh how many different things were there? +H + + align:start position:0% +H + + + align:start position:0% +H +whatever is it also w divided by log + + align:start position:0% +whatever is it also w divided by log + + + align:start position:0% +whatever is it also w divided by log +epsilon I guess. + + align:start position:0% +epsilon I guess. + + + align:start position:0% +epsilon I guess. +So depends how you count. + + align:start position:0% + + + + align:start position:0% + +Um let me think for a second how these + + align:start position:0% +Um let me think for a second how these + + + align:start position:0% +Um let me think for a second how these +ed indices should be stored. + + align:start position:0% + + + + align:start position:0% + +I think I'd like to store the edge + + align:start position:0% +I think I'd like to store the edge + + + align:start position:0% +I think I'd like to store the edge +indicy. I don't want to store the absent + + align:start position:0% +indicy. I don't want to store the absent + + + align:start position:0% +indicy. I don't want to store the absent +down pointers. Okay. Um the way that I + + align:start position:0% +down pointers. Okay. Um the way that I + + + align:start position:0% +down pointers. Okay. Um the way that I +built this tree, this compressed try, I + + align:start position:0% +built this tree, this compressed try, I + + + align:start position:0% +built this tree, this compressed try, I +was always adding things to the right. + + align:start position:0% +was always adding things to the right. + + + align:start position:0% +was always adding things to the right. +So it's like, okay, um storing here, + + align:start position:0% +So it's like, okay, um storing here, + + + align:start position:0% +So it's like, okay, um storing here, +here's the first child, here's the next + + align:start position:0% +here's the first child, here's the next + + + align:start position:0% +here's the first child, here's the next +child, here's the next child, here's the + + align:start position:0% +child, here's the next child, here's the + + + align:start position:0% +child, here's the next child, here's the +next child. I just keep appending on. + + align:start position:0% +next child. I just keep appending on. + + + align:start position:0% +next child. I just keep appending on. +It's like an array that you can grow to + + align:start position:0% +It's like an array that you can grow to + + + align:start position:0% +It's like an array that you can grow to +the right, which you should know how to + + align:start position:0% +the right, which you should know how to + + + align:start position:0% +the right, which you should know how to +do in constant time. Even a linked list + + align:start position:0% +do in constant time. Even a linked list + + + align:start position:0% +do in constant time. Even a linked list +is probably fine. Uh I don't want to + + align:start position:0% +is probably fine. Uh I don't want to + + + align:start position:0% +is probably fine. Uh I don't want to +store if there are a bunch of values + + align:start position:0% +store if there are a bunch of values + + + align:start position:0% +store if there are a bunch of values +here that are just null pointers. I + + align:start position:0% +here that are just null pointers. I + + + align:start position:0% +here that are just null pointers. I +don't want to store those items in the + + align:start position:0% +don't want to store those items in the + + + align:start position:0% +don't want to store those items in the +array. Okay. So in fact the maximum + + align:start position:0% +array. Okay. So in fact the maximum + + + align:start position:0% +array. Okay. So in fact the maximum +number of children of a node is n. I + + align:start position:0% +number of children of a node is n. I + + + align:start position:0% +number of children of a node is n. I +mean at the worst case you have + + align:start position:0% +mean at the worst case you have + + + align:start position:0% +mean at the worst case you have +branching everywhere. So this is only + + align:start position:0% +branching everywhere. So this is only + + + align:start position:0% +branching everywhere. So this is only +log n + + align:start position:0% + + + + align:start position:0% + +bits to store the index in that array. + + align:start position:0% +bits to store the index in that array. + + + align:start position:0% +bits to store the index in that array. +So, it's an extra level of compression + + align:start position:0% +So, it's an extra level of compression + + + align:start position:0% +So, it's an extra level of compression +because I didn't mention + + align:start position:0% +because I didn't mention + + + align:start position:0% +because I didn't mention +uh don't + + align:start position:0% +uh don't + + + align:start position:0% +uh don't +store null pointers, just skip + + align:start position:0% +store null pointers, just skip + + + align:start position:0% +store null pointers, just skip +them. That's easy to do because always + + align:start position:0% +them. That's easy to do because always + + + align:start position:0% +them. That's easy to do because always +just appending. And in the end, what do + + align:start position:0% +just appending. And in the end, what do + + + align:start position:0% +just appending. And in the end, what do +I need to do here? + + align:start position:0% +I need to do here? + + + align:start position:0% +I need to do here? +Uh step seven is in order + + align:start position:0% + + + + align:start position:0% + +traversal of the compressed + + align:start position:0% + + + + align:start position:0% + +try and I output all the leaves I + + align:start position:0% +try and I output all the leaves I + + + align:start position:0% +try and I output all the leaves I +get in + + align:start position:0% +get in + + + align:start position:0% +get in +order. And the point is we computed the + + align:start position:0% +order. And the point is we computed the + + + align:start position:0% +order. And the point is we computed the +compressed try which has the rough + + align:start position:0% +compressed try which has the rough + + + align:start position:0% +compressed try which has the rough +correct topological structure. Then we + + align:start position:0% +correct topological structure. Then we + + + align:start position:0% +correct topological structure. Then we +fixed the order within each node. Now we + + align:start position:0% +fixed the order within each node. Now we + + + align:start position:0% +fixed the order within each node. Now we +have the correctly sorted compressed try + + align:start position:0% +have the correctly sorted compressed try + + + align:start position:0% +have the correctly sorted compressed try +and so you just do an in order traversal + + align:start position:0% +and so you just do an in order traversal + + + align:start position:0% +and so you just do an in order traversal +output the leads you get in order boom + + align:start position:0% +output the leads you get in order boom + + + align:start position:0% +output the leads you get in order boom +we've sorted all the items. Okay little + + align:start position:0% +we've sorted all the items. Okay little + + + align:start position:0% +we've sorted all the items. Okay little +crazy. + + align:start position:0% +crazy. + + + align:start position:0% +crazy. +Uh so if all we need to do in the end is + + align:start position:0% +Uh so if all we need to do in the end is + + + align:start position:0% +Uh so if all we need to do in the end is +in order traversal then it's fine. We + + align:start position:0% +in order traversal then it's fine. We + + + align:start position:0% +in order traversal then it's fine. We +don't need to store the null pointers. + + align:start position:0% +don't need to store the null pointers. + + + align:start position:0% +don't need to store the null pointers. +So we don't need to be able to search in + + align:start position:0% +So we don't need to be able to search in + + + align:start position:0% +So we don't need to be able to search in +this try. So this is + + align:start position:0% + + + + align:start position:0% + +enough clear. Okay. The remaining + + align:start position:0% +enough clear. Okay. The remaining + + + align:start position:0% +enough clear. Okay. The remaining +question is why how how expensive is + + align:start position:0% +question is why how how expensive is + + + align:start position:0% +question is why how how expensive is +this recursion? So I computed the number + + align:start position:0% +this recursion? So I computed the number + + + align:start position:0% +this recursion? So I computed the number +of bits is basically w / log to the + + align:start position:0% +of bits is basically w / log to the + + + align:start position:0% +of bits is basically w / log to the +epsilon n plus order log n the order log + + align:start position:0% +epsilon n plus order log n the order log + + + align:start position:0% +epsilon n plus order log n the order log +n won't hurt us. Now we started with + + align:start position:0% +n won't hurt us. Now we started with + + + align:start position:0% +n won't hurt us. Now we started with +integers of size w total size here was w + + align:start position:0% +integers of size w total size here was w + + + align:start position:0% +integers of size w total size here was w +now we have integers that their size is + + align:start position:0% +now we have integers that their size is + + + align:start position:0% +now we have integers that their size is +w divided by log epsilon n. So we've + + align:start position:0% +w divided by log epsilon n. So we've + + + align:start position:0% +w divided by log epsilon n. So we've +made + + align:start position:0% + + + + align:start position:0% + +progress. Cool. + + align:start position:0% +progress. Cool. + + + align:start position:0% +progress. Cool. +How much + + align:start position:0% + + + + align:start position:0% + +progress over here + + align:start position:0% + + + + align:start position:0% + +maybe + + align:start position:0% + + + + align:start position:0% + +so after let's say 1 over epsilon + 1 + + align:start position:0% + + + + align:start position:0% + +recursions we will have reached + + align:start position:0% + + + + align:start position:0% + +uh E will have + + align:start position:0% + + + + align:start position:0% + +decreased excuse me to order log N I + + align:start position:0% +decreased excuse me to order log N I + + + align:start position:0% +decreased excuse me to order log N I +guess like 1 / epsilon log N + + align:start position:0% +guess like 1 / epsilon log N + + + align:start position:0% +guess like 1 / epsilon log N +plus W over log to the 1 + + + align:start position:0% +plus W over log to the 1 + + + + align:start position:0% +plus W over log to the 1 + +epsilon N + + align:start position:0% + + + + align:start position:0% + +Okay. Right. If we take W and every time + + align:start position:0% +Okay. Right. If we take W and every time + + + align:start position:0% +Okay. Right. If we take W and every time +we divide by log to the epsilon n then + + align:start position:0% +we divide by log to the epsilon n then + + + align:start position:0% +we divide by log to the epsilon n then +after 1 / epsilon times we have divided + + align:start position:0% +after 1 / epsilon times we have divided + + + align:start position:0% +after 1 / epsilon times we have divided +by log n. Get rid of the epsilon. Do it + + align:start position:0% +by log n. Get rid of the epsilon. Do it + + + align:start position:0% +by log n. Get rid of the epsilon. Do it +one more time. We get w / log to the 1 + + + align:start position:0% +one more time. We get w / log to the 1 + + + + align:start position:0% +one more time. We get w / log to the 1 + +epsilon n. Okay. And at this point we're + + align:start position:0% +epsilon n. Okay. And at this point we're + + + align:start position:0% +epsilon n. Okay. And at this point we're +in good + + align:start position:0% +in good + + + align:start position:0% +in good +shape. Okay. + + align:start position:0% +shape. Okay. + + + align:start position:0% +shape. Okay. +How if we get the size of our integers + + align:start position:0% +How if we get the size of our integers + + + align:start position:0% +How if we get the size of our integers +to be only w / log to the 1 plus epsilon + + align:start position:0% +to be only w / log to the 1 plus epsilon + + + align:start position:0% +to be only w / log to the 1 plus epsilon +n then we can use pack sorting because + + align:start position:0% +n then we can use pack sorting because + + + align:start position:0% +n then we can use pack sorting because +pack sorting conveniently it's a black + + align:start position:0% +pack sorting conveniently it's a black + + + align:start position:0% +pack sorting conveniently it's a black +box at the moment says well as long as w + + align:start position:0% +box at the moment says well as long as w + + + align:start position:0% +box at the moment says well as long as w +/ b is a little bigger than log n so + + align:start position:0% +/ b is a little bigger than log n so + + + align:start position:0% +/ b is a little bigger than log n so +here we've made it quite a bit bigger + + align:start position:0% +here we've made it quite a bit bigger + + + align:start position:0% +here we've made it quite a bit bigger +than log n I mean log to the 1 plus + + align:start position:0% +than log n I mean log to the 1 plus + + + align:start position:0% +than log n I mean log to the 1 plus +epsilon n bigger then we can use pack + + align:start position:0% +epsilon n bigger then we can use pack + + + align:start position:0% +epsilon n bigger then we can use pack +sorting so + + align:start position:0% +sorting so + + + align:start position:0% +sorting so +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +uh reach base + + align:start position:0% + + + + align:start position:0% + +case and then use packed + + align:start position:0% + + + + align:start position:0% + +sorting. Okay, the only thing is there's + + align:start position:0% +sorting. Okay, the only thing is there's + + + align:start position:0% +sorting. Okay, the only thing is there's +this log n. Now epsilon is a constant + + align:start position:0% +this log n. Now epsilon is a constant + + + align:start position:0% +this log n. Now epsilon is a constant +here. So one over epsilon is constant. + + align:start position:0% +here. So one over epsilon is constant. + + + align:start position:0% +here. So one over epsilon is constant. +So this is just order log n. Order log n + + align:start position:0% +So this is just order log n. Order log n + + + align:start position:0% +So this is just order log n. Order log n +doesn't hurt you. I mean if this + + align:start position:0% +doesn't hurt you. I mean if this + + + align:start position:0% +doesn't hurt you. I mean if this +happened to dominate this then you're + + align:start position:0% +happened to dominate this then you're + + + align:start position:0% +happened to dominate this then you're +saying your values are order log n bits + + align:start position:0% +saying your values are order log n bits + + + align:start position:0% +saying your values are order log n bits +long and so you use radic sort okay so + + align:start position:0% +long and so you use radic sort okay so + + + align:start position:0% +long and so you use radic sort okay so +that's not going to dominate in fact you + + align:start position:0% +that's not going to dominate in fact you + + + align:start position:0% +that's not going to dominate in fact you +can prove in this case it's not going to + + align:start position:0% +can prove in this case it's not going to + + + align:start position:0% +can prove in this case it's not going to +dominate w is at least log to the 2 plus + + align:start position:0% +dominate w is at least log to the 2 plus + + + align:start position:0% +dominate w is at least log to the 2 plus +epsilon so you take w / log to 1 plus + + align:start position:0% +epsilon so you take w / log to 1 plus + + + align:start position:0% +epsilon so you take w / log to 1 plus +epsilon that's still at least log n okay + + align:start position:0% +epsilon that's still at least log n okay + + + align:start position:0% +epsilon that's still at least log n okay +so this will always + + align:start position:0% + + + + align:start position:0% + +dominate okay so we did all this work + + align:start position:0% +dominate okay so we did all this work + + + align:start position:0% +dominate okay so we did all this work +and all we did was reduce our word size + + align:start position:0% +and all we did was reduce our word size + + + align:start position:0% +and all we did was reduce our word size +by a log to the epsilon factor. But + + align:start position:0% +by a log to the epsilon factor. But + + + align:start position:0% +by a log to the epsilon factor. But +that's enough because after we do that 1 + + align:start position:0% +that's enough because after we do that 1 + + + align:start position:0% +that's enough because after we do that 1 +over epsilon + one times we're small + + align:start position:0% +over epsilon + one times we're small + + + align:start position:0% +over epsilon + one times we're small +enough the words are small enough or the + + align:start position:0% +enough the words are small enough or the + + + align:start position:0% +enough the words are small enough or the +items we're sorting are small enough + + align:start position:0% +items we're sorting are small enough + + + align:start position:0% +items we're sorting are small enough +that we can use pack sorting and boom + + align:start position:0% +that we can use pack sorting and boom + + + align:start position:0% +that we can use pack sorting and boom +we're done. Okay, that is the beauty of + + align:start position:0% +we're done. Okay, that is the beauty of + + + align:start position:0% +we're done. Okay, that is the beauty of +signature sort. Any questions about + + align:start position:0% +signature sort. Any questions about + + + align:start position:0% +signature sort. Any questions about +that? Definitely not easy. + + align:start position:0% +that? Definitely not easy. + + + align:start position:0% +that? Definitely not easy. +uh but it works. The crazy idea is well + + align:start position:0% +uh but it works. The crazy idea is well + + + align:start position:0% +uh but it works. The crazy idea is well +decompose into these digits. I mean we + + align:start position:0% +decompose into these digits. I mean we + + + align:start position:0% +decompose into these digits. I mean we +decompose into logs epsilon digits + + align:start position:0% +decompose into logs epsilon digits + + + align:start position:0% +decompose into logs epsilon digits +because that would be enough. If we + + align:start position:0% +because that would be enough. If we + + + align:start position:0% +because that would be enough. If we +could get things down to a single digit + + align:start position:0% +could get things down to a single digit + + + align:start position:0% +could get things down to a single digit +life would be + + align:start position:0% +life would be + + + align:start position:0% +life would be +easy which I guess is kind of like venom + + align:start position:0% +easy which I guess is kind of like venom + + + align:start position:0% +easy which I guess is kind of like venom +to boas right I mean uh or it's it's + + align:start position:0% +to boas right I mean uh or it's it's + + + align:start position:0% +to boas right I mean uh or it's it's +like our lower bounds from last time. I + + align:start position:0% +like our lower bounds from last time. I + + + align:start position:0% +like our lower bounds from last time. I +don't know only one if we could make it + + align:start position:0% +don't know only one if we could make it + + + align:start position:0% +don't know only one if we could make it +so only one digit mattered then we could + + align:start position:0% +so only one digit mattered then we could + + + align:start position:0% +so only one digit mattered then we could +afford to do it because each digit is + + align:start position:0% +afford to do it because each digit is + + + align:start position:0% +afford to do it because each digit is +quite a bit smaller. I mean it's smaller + + align:start position:0% +quite a bit smaller. I mean it's smaller + + + align:start position:0% +quite a bit smaller. I mean it's smaller +by a factor of log to the epsilon + + align:start position:0% +by a factor of log to the epsilon + + + align:start position:0% +by a factor of log to the epsilon +n. Uh so we did that splitting and then + + align:start position:0% +n. Uh so we did that splitting and then + + + align:start position:0% +n. Uh so we did that splitting and then +there was this observation that well + + align:start position:0% +there was this observation that well + + + align:start position:0% +there was this observation that well +most digit values aren't used. So if we + + align:start position:0% +most digit values aren't used. So if we + + + align:start position:0% +most digit values aren't used. So if we +hash then things got a lot smaller then + + align:start position:0% +hash then things got a lot smaller then + + + align:start position:0% +hash then things got a lot smaller then +we can afford to pack sort except that + + align:start position:0% +we can afford to pack sort except that + + + align:start position:0% +we can afford to pack sort except that +hash didn't preserve the order. How + + align:start position:0% +hash didn't preserve the order. How + + + align:start position:0% +hash didn't preserve the order. How +didn't it preserve the order? Well when + + align:start position:0% +didn't it preserve the order? Well when + + + align:start position:0% +didn't it preserve the order? Well when +you look at the compressed try you see + + align:start position:0% +you look at the compressed try you see + + + align:start position:0% +you look at the compressed try you see +how it got messed up. Each node got + + align:start position:0% +how it got messed up. Each node got + + + align:start position:0% +how it got messed up. Each node got +messed up individually but overall the + + align:start position:0% +messed up individually but overall the + + + align:start position:0% +messed up individually but overall the +structure of the try was correct. So we + + align:start position:0% +structure of the try was correct. So we + + + align:start position:0% +structure of the try was correct. So we +did all this work to get the structure + + align:start position:0% +did all this work to get the structure + + + align:start position:0% +did all this work to get the structure +of the try. Then we had to fix the node + + align:start position:0% +of the try. Then we had to fix the node + + + align:start position:0% +of the try. Then we had to fix the node +order. But that's really just sorting a + + align:start position:0% +order. But that's really just sorting a + + + align:start position:0% +order. But that's really just sorting a +single digit. And yeah, we have to do it + + align:start position:0% +single digit. And yeah, we have to do it + + + align:start position:0% +single digit. And yeah, we have to do it +for all nodes. But you add them up. It's + + align:start position:0% +for all nodes. But you add them up. It's + + + align:start position:0% +for all nodes. But you add them up. It's +still only n items that we need to sort. + + align:start position:0% +still only n items that we need to sort. + + + align:start position:0% +still only n items that we need to sort. +So I I wrote that B went down. Um N + + align:start position:0% +So I I wrote that B went down. Um N + + + align:start position:0% +So I I wrote that B went down. Um N +stays the same. The number of things we + + align:start position:0% +stays the same. The number of things we + + + align:start position:0% +stays the same. The number of things we +have to sort stays the same, which is + + align:start position:0% +have to sort stays the same, which is + + + align:start position:0% +have to sort stays the same, which is +which is fine. Not trying to reduce N. + + align:start position:0% +which is fine. Not trying to reduce N. + + + align:start position:0% +which is fine. Not trying to reduce N. +Just trying to reduce the size of our + + align:start position:0% +Just trying to reduce the size of our + + + align:start position:0% +Just trying to reduce the size of our +items to be a little bit smaller than W. + + align:start position:0% +items to be a little bit smaller than W. + + + align:start position:0% +items to be a little bit smaller than W. +So then we can use pack sorting. Okay. + + align:start position:0% +So then we can use pack sorting. Okay. + + + align:start position:0% +So then we can use pack sorting. Okay. +Okay, I think I've gone over this + + align:start position:0% +Okay, I think I've gone over this + + + align:start position:0% +Okay, I think I've gone over this +algorithm enough times. The next step is + + align:start position:0% +algorithm enough times. The next step is + + + align:start position:0% +algorithm enough times. The next step is +pack + + align:start position:0% +pack + + + align:start position:0% +pack +sorting. Now that if we have val uh + + align:start position:0% +sorting. Now that if we have val uh + + + align:start position:0% +sorting. Now that if we have val uh +integers that are much smaller than our + + align:start position:0% +integers that are much smaller than our + + + align:start position:0% +integers that are much smaller than our +word, how do we sort in linear time? And + + align:start position:0% +word, how do we sort in linear time? And + + + align:start position:0% +word, how do we sort in linear time? And +this is going to be essentially a fancy + + align:start position:0% +this is going to be essentially a fancy + + + align:start position:0% +this is going to be essentially a fancy +merge sort. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +It's done in the same paper. + + align:start position:0% + + + + align:start position:0% + +uh before we said + + align:start position:0% +uh before we said + + + align:start position:0% +uh before we said +omega I'm going to essentially make + + align:start position:0% +omega I'm going to essentially make + + + align:start position:0% +omega I'm going to essentially make +omega a little bit bigger than two. So I + + align:start position:0% +omega a little bit bigger than two. So I + + + align:start position:0% +omega a little bit bigger than two. So I +want to assume the w is at least twice b + + align:start position:0% +want to assume the w is at least twice b + + + align:start position:0% +want to assume the w is at least twice b ++ one log n log n. That's just to make + + align:start position:0% ++ one log n log n. That's just to make + + + align:start position:0% ++ one log n log n. That's just to make +this convenient. But of course it + + align:start position:0% +this convenient. But of course it + + + align:start position:0% +this convenient. But of course it +doesn't really matter what the constants + + align:start position:0% +doesn't really matter what the constants + + + align:start position:0% +doesn't really matter what the constants +are. This will make everything fit in + + align:start position:0% +are. This will make everything fit in + + + align:start position:0% +are. This will make everything fit in +one word though instead of a constant + + align:start position:0% +one word though instead of a constant + + + align:start position:0% +one word though instead of a constant +number of words. Okay, step zero of this + + align:start position:0% + + + + align:start position:0% + +algorithm is the packing + + align:start position:0% + + + + align:start position:0% + +part. We can fit more than one element + + align:start position:0% +part. We can fit more than one element + + + align:start position:0% +part. We can fit more than one element +into each word. So, put them in + + align:start position:0% +into each word. So, put them in + + + align:start position:0% +into each word. So, put them in +Okay, now we have linear time overall. + + align:start position:0% +Okay, now we have linear time overall. + + + align:start position:0% +Okay, now we have linear time overall. +This is easy to do. Just uh you have + + align:start position:0% +This is easy to do. Just uh you have + + + align:start position:0% +This is easy to do. Just uh you have +some word + + align:start position:0% +some word + + + align:start position:0% +some word +already. Take those items, shift them + + align:start position:0% +already. Take those items, shift them + + + align:start position:0% +already. Take those items, shift them +left or in the next item. Shift them + + align:start position:0% +left or in the next item. Shift them + + + align:start position:0% +left or in the next item. Shift them +left or in the next item. Shift them + + align:start position:0% +left or in the next item. Shift them + + + align:start position:0% +left or in the next item. Shift them +left or in the next item. Okay, linear + + align:start position:0% +left or in the next item. Okay, linear + + + align:start position:0% +left or in the next item. Okay, linear +time. So in the end, what it's going to + + align:start position:0% +time. So in the end, what it's going to + + + align:start position:0% +time. So in the end, what it's going to +look like, oh, I also want to leave a + + align:start position:0% +look like, oh, I also want to leave a + + + align:start position:0% +look like, oh, I also want to leave a +zero bit in between each of them. So + + align:start position:0% +zero bit in between each of them. So + + + align:start position:0% +zero bit in between each of them. So +we're going to have B. This is going to + + align:start position:0% +we're going to have B. This is going to + + + align:start position:0% +we're going to have B. This is going to +be x1 + + align:start position:0% +be x1 + + + align:start position:0% +be x1 +here + + align:start position:0% + + + + align:start position:0% + +x2 + + align:start position:0% +x2 + + + align:start position:0% +x2 +xn. Each of these is b bits long. And + + align:start position:0% +xn. Each of these is b bits long. And + + + align:start position:0% +xn. Each of these is b bits long. And +then we have one more + + align:start position:0% +then we have one more + + + align:start position:0% +then we have one more +bit. Uh and in fact the way we set + + align:start position:0% +bit. Uh and in fact the way we set + + + align:start position:0% +bit. Uh and in fact the way we set +things up this is only half the word. So + + align:start position:0% +things up this is only half the word. So + + + align:start position:0% +things up this is only half the word. So +there's another half over here which is + + align:start position:0% +there's another half over here which is + + + align:start position:0% +there's another half over here which is +going to be all zero for now. + + align:start position:0% +going to be all zero for now. + + + align:start position:0% +going to be all zero for now. +So we have one word contains or sorry + + align:start position:0% +So we have one word contains or sorry + + + align:start position:0% +So we have one word contains or sorry +this is not n items. This is going to be + + align:start position:0% +this is not n items. This is going to be + + + align:start position:0% +this is not n items. This is going to be +login log login lo + + align:start position:0% +login log login lo + + + align:start position:0% +login log login lo +login. Can't fit them all in one word. + + align:start position:0% +login. Can't fit them all in one word. + + + align:start position:0% +login. Can't fit them all in one word. +That would make life really easy. But + + align:start position:0% +That would make life really easy. But + + + align:start position:0% +That would make life really easy. But +you can fit login items in the first + + align:start position:0% +you can fit login items in the first + + + align:start position:0% +you can fit login items in the first +word. Then the next word is the next + + align:start position:0% +word. Then the next word is the next + + + align:start position:0% +word. Then the next word is the next +login loan items and so on. Okay. Linear + + align:start position:0% +login loan items and so on. Okay. Linear + + + align:start position:0% +login loan items and so on. Okay. Linear +time to do + + align:start position:0% +time to do + + + align:start position:0% +time to do +that. + + align:start position:0% +that. + + + align:start position:0% +that. +Uh next + + align:start position:0% +Uh next + + + align:start position:0% +Uh next +step. This is an algorithm. It's not + + align:start position:0% +step. This is an algorithm. It's not + + + align:start position:0% +step. This is an algorithm. It's not +really a step. I should say these are + + align:start position:0% +really a step. I should say these are + + + align:start position:0% +really a step. I should say these are +things that we're going to we're able to + + align:start position:0% +things that we're going to we're able to + + + align:start position:0% +things that we're going to we're able to +do and we're going to combine them in + + align:start position:0% +do and we're going to combine them in + + + align:start position:0% +do and we're going to combine them in +different + + align:start position:0% +different + + + align:start position:0% +different +ways. So the next thing to observe this + + align:start position:0% +ways. So the next thing to observe this + + + align:start position:0% +ways. So the next thing to observe this +is a sort of bottom up perspective. So + + align:start position:0% +is a sort of bottom up perspective. So + + + align:start position:0% +is a sort of bottom up perspective. So +first thing we can do is pack things + + align:start position:0% +first thing we can do is pack things + + + align:start position:0% +first thing we can do is pack things +into a word. Next thing we can do is + + align:start position:0% +into a word. Next thing we can do is + + + align:start position:0% +into a word. Next thing we can do is +merge two sorted words. Let's say they + + align:start position:0% +merge two sorted words. Let's say they + + + align:start position:0% +merge two sorted words. Let's say they +each have K items and K is at most + + align:start position:0% +each have K items and K is at most + + + align:start position:0% +each have K items and K is at most +login. + + align:start position:0% + + + + align:start position:0% + +and I want to merge them into one sorted + + align:start position:0% + + + + align:start position:0% + +word with two K + + align:start position:0% + + + + align:start position:0% + +elements. So I have two of these things + + align:start position:0% +elements. So I have two of these things + + + align:start position:0% +elements. So I have two of these things +and I'll merge them in sorted + + align:start position:0% +and I'll merge them in sorted + + + align:start position:0% +and I'll merge them in sorted +order. Okay, these when I did this + + align:start position:0% +order. Okay, these when I did this + + + align:start position:0% +order. Okay, these when I did this +packing nothing sorted but don't worry + + align:start position:0% +packing nothing sorted but don't worry + + + align:start position:0% +packing nothing sorted but don't worry +about that at the moment. Just if I had + + align:start position:0% +about that at the moment. Just if I had + + + align:start position:0% +about that at the moment. Just if I had +two of these words and suppose they were + + align:start position:0% +two of these words and suppose they were + + + align:start position:0% +two of these words and suppose they were +already + + align:start position:0% +already + + + align:start position:0% +already +sorted, then I want to merge them and + + align:start position:0% +sorted, then I want to merge them and + + + align:start position:0% +sorted, then I want to merge them and +make keep make them still + + align:start position:0% +make keep make them still + + + align:start position:0% +make keep make them still +sorted. Okay, X I want X1 to be less + + align:start position:0% +sorted. Okay, X I want X1 to be less + + + align:start position:0% +sorted. Okay, X I want X1 to be less +than X2 and so + + align:start position:0% +than X2 and so + + + align:start position:0% +than X2 and so +on. How much + + align:start position:0% +on. How much + + + align:start position:0% +on. How much +time? It'd be cool if you could do this + + align:start position:0% +time? It'd be cool if you could do this + + + align:start position:0% +time? It'd be cool if you could do this +in constant time on a trans dichomous + + align:start position:0% +in constant time on a trans dichomous + + + align:start position:0% +in constant time on a trans dichomous +RAM. You could do anything on a constant + + align:start position:0% +RAM. You could do anything on a constant + + + align:start position:0% +RAM. You could do anything on a constant +number of words in constant time. We're + + align:start position:0% +number of words in constant time. We're + + + align:start position:0% +number of words in constant time. We're +not going to achieve constant time, but + + align:start position:0% +not going to achieve constant time, but + + + align:start position:0% +not going to achieve constant time, but +we don't need to. We're going to do + + align:start position:0% +we don't need to. We're going to do + + + align:start position:0% +we don't need to. We're going to do +order log k + + align:start position:0% + + + + align:start position:0% + +time. This is the hardest step of pack + + align:start position:0% +time. This is the hardest step of pack + + + align:start position:0% +time. This is the hardest step of pack +sorting and I'm not going to tell you + + align:start position:0% +sorting and I'm not going to tell you + + + align:start position:0% +sorting and I'm not going to tell you +how to do it until later. I will tell + + align:start position:0% +how to do it until later. I will tell + + + align:start position:0% +how to do it until later. I will tell +you, don't worry. Uh but this is going + + align:start position:0% +you, don't worry. Uh but this is going + + + align:start position:0% +you, don't worry. Uh but this is going +to require bonic + + align:start position:0% +to require bonic + + + align:start position:0% +to require bonic +sorting. So I have to delay it a little + + align:start position:0% +sorting. So I have to delay it a little + + + align:start position:0% +sorting. So I have to delay it a little +bit. Suppose you had that for now. Let + + align:start position:0% +bit. Suppose you had that for now. Let + + + align:start position:0% +bit. Suppose you had that for now. Let +me tell you how the rest is easy. + + align:start position:0% + + + + align:start position:0% + +So many black boxes, but they're all + + align:start position:0% +So many black boxes, but they're all + + + align:start position:0% +So many black boxes, but they're all +filled in in this + + align:start position:0% + + + + align:start position:0% + +lecture. + + align:start position:0% + + + + align:start position:0% + +Okay. Next thing you might ask is, well, + + align:start position:0% +Okay. Next thing you might ask is, well, + + + align:start position:0% +Okay. Next thing you might ask is, well, +how do I get a sorted word? I see how to + + align:start position:0% +how do I get a sorted word? I see how to + + + align:start position:0% +how do I get a sorted word? I see how to +get a single word that has login log + + align:start position:0% +get a single word that has login log + + + align:start position:0% +get a single word that has login log +login items. But how would I sort those + + align:start position:0% +login items. But how would I sort those + + + align:start position:0% +login items. But how would I sort those +items? Use merge sort. Here's a merger. + + align:start position:0% +items? Use merge sort. Here's a merger. + + + align:start position:0% +items? Use merge sort. Here's a merger. +You have a way to merge two sorted + + align:start position:0% +You have a way to merge two sorted + + + align:start position:0% +You have a way to merge two sorted +lists. So use merge sort. that will give + + align:start position:0% +lists. So use merge sort. that will give + + + align:start position:0% +lists. So use merge sort. that will give +you a way to sort the whole thing. So + + align:start position:0% +you a way to sort the whole thing. So + + + align:start position:0% +you a way to sort the whole thing. So +I'm going to merge sort k equals log n + + align:start position:0% +I'm going to merge sort k equals log n + + + align:start position:0% +I'm going to merge sort k equals log n +log log n + + align:start position:0% + + + + align:start position:0% + +items into one sorted + + align:start position:0% + + + + align:start position:0% + +word. So I start out with a word that's + + align:start position:0% +word. So I start out with a word that's + + + align:start position:0% +word. So I start out with a word that's +unsorted. I do merge sort and I sort + + align:start position:0% +unsorted. I do merge sort and I sort + + + align:start position:0% +unsorted. I do merge sort and I sort +them. Okay. So this is not the whole + + align:start position:0% +them. Okay. So this is not the whole + + + align:start position:0% +them. Okay. So this is not the whole +sorting problem, but it's sorting the + + align:start position:0% +sorting problem, but it's sorting the + + + align:start position:0% +sorting problem, but it's sorting the +it's the oneword sorting problem. So how + + align:start position:0% +it's the oneword sorting problem. So how + + + align:start position:0% +it's the oneword sorting problem. So how +long does this take? Well, it's the + + align:start position:0% +long does this take? Well, it's the + + + align:start position:0% +long does this take? Well, it's the +usual merge sort + + align:start position:0% +usual merge sort + + + align:start position:0% +usual merge sort +recurrence, but then it's plus how long + + align:start position:0% +recurrence, but then it's plus how long + + + align:start position:0% +recurrence, but then it's plus how long +it takes me to split the word. Well, + + align:start position:0% +it takes me to split the word. Well, + + + align:start position:0% +it takes me to split the word. Well, +splitting a word is easy. You just mask + + align:start position:0% +splitting a word is easy. You just mask + + + align:start position:0% +splitting a word is easy. You just mask +out the low end or the high end and then + + align:start position:0% +out the low end or the high end and then + + + align:start position:0% +out the low end or the high end and then +maybe shift over. So in constant time, I + + align:start position:0% +maybe shift over. So in constant time, I + + + align:start position:0% +maybe shift over. So in constant time, I +can get the left half and the right half + + align:start position:0% +can get the left half and the right half + + + align:start position:0% +can get the left half and the right half +of the array, which is the word. Then + + align:start position:0% +of the array, which is the word. Then + + + align:start position:0% +of the array, which is the word. Then +the hard part is merging them. and + + align:start position:0% +the hard part is merging them. and + + + align:start position:0% +the hard part is merging them. and +merging them is + + align:start position:0% +merging them is + + + align:start position:0% +merging them is +one and that takes log + + align:start position:0% +one and that takes log + + + align:start position:0% +one and that takes log +k. So this is step + + align:start position:0% +k. So this is step + + + align:start position:0% +k. So this is step +one. That's our merger. And so what does + + align:start position:0% +one. That's our merger. And so what does + + + align:start position:0% +one. That's our merger. And so what does +this solve to? Well, uh probably easiest + + align:start position:0% +this solve to? Well, uh probably easiest + + + align:start position:0% +this solve to? Well, uh probably easiest +to draw the recursion tree. So at the + + align:start position:0% +to draw the recursion tree. So at the + + + align:start position:0% +to draw the recursion tree. So at the +root we pay log k. Then we have 2 * + + align:start position:0% +root we pay log k. Then we have 2 * + + + align:start position:0% +root we pay log k. Then we have 2 * +log I guess k over + + align:start position:0% +log I guess k over + + + align:start position:0% +log I guess k over +two log k over + + align:start position:0% +two log k over + + + align:start position:0% +two log k over +two. Okay. So at this level we're paying + + align:start position:0% +two. Okay. So at this level we're paying + + + align:start position:0% +two. Okay. So at this level we're paying +log k this pay at this level we're + + align:start position:0% +log k this pay at this level we're + + + align:start position:0% +log k this pay at this level we're +paying uh two log k minus one I + + align:start position:0% +paying uh two log k minus one I + + + align:start position:0% +paying uh two log k minus one I +guess okay uh I'm just going to call + + align:start position:0% +guess okay uh I'm just going to call + + + align:start position:0% +guess okay uh I'm just going to call +this maybe well yeah I do need to do + + align:start position:0% +this maybe well yeah I do need to do + + + align:start position:0% +this maybe well yeah I do need to do +that at the bottom I mean everything's + + align:start position:0% +that at the bottom I mean everything's + + + align:start position:0% +that at the bottom I mean everything's +constant size so you pay constant how + + align:start position:0% +constant size so you pay constant how + + + align:start position:0% +constant size so you pay constant how +many leaves are there at the bottom + + align:start position:0% +many leaves are there at the bottom + + + align:start position:0% +many leaves are there at the bottom +level + + align:start position:0% +level + + + align:start position:0% +level +uh k of + + align:start position:0% +uh k of + + + align:start position:0% +uh k of +them okay so at the root we're paying + + align:start position:0% +them okay so at the root we're paying + + + align:start position:0% +them okay so at the root we're paying +log k at the leaves we're paying k this + + align:start position:0% +log k at the leaves we're paying k this + + + align:start position:0% +log k at the leaves we're paying k this +is roughly geometric. There's this minus + + align:start position:0% +is roughly geometric. There's this minus + + + align:start position:0% +is roughly geometric. There's this minus +one, but it's geometric enough that when + + align:start position:0% +one, but it's geometric enough that when + + + align:start position:0% +one, but it's geometric enough that when +you add up all these levels, it's + + align:start position:0% +you add up all these levels, it's + + + align:start position:0% +you add up all these levels, it's +dominated by K. And so this ends up + + align:start position:0% +dominated by K. And so this ends up + + + align:start position:0% +dominated by K. And so this ends up +being order K + + align:start position:0% +being order K + + + align:start position:0% +being order K +time. Okay, the the minus one here turns + + align:start position:0% +time. Okay, the the minus one here turns + + + align:start position:0% +time. Okay, the the minus one here turns +out not to matter + + align:start position:0% +out not to matter + + + align:start position:0% +out not to matter +much. Cool. So this is linear time + + align:start position:0% +much. Cool. So this is linear time + + + align:start position:0% +much. Cool. So this is linear time +sorting on login log login items. + + align:start position:0% +sorting on login log login items. + + + align:start position:0% +sorting on login log login items. +Everything that fits in a word. Cool. + + align:start position:0% +Everything that fits in a word. Cool. + + + align:start position:0% +Everything that fits in a word. Cool. +But we're not done yet. We need another + + align:start position:0% +But we're not done yet. We need another + + + align:start position:0% +But we're not done yet. We need another +level. + + align:start position:0% +level. + + + align:start position:0% +level. +The rest is pretty + + align:start position:0% +The rest is pretty + + + align:start position:0% +The rest is pretty +easy. It's just uh scaling up. + + align:start position:0% + + + + align:start position:0% + +Okay. Uh, let's see. At this point, + + align:start position:0% +Okay. Uh, let's see. At this point, + + + align:start position:0% +Okay. Uh, let's see. At this point, +we're going to assume that all of our + + align:start position:0% +we're going to assume that all of our + + + align:start position:0% +we're going to assume that all of our +words are completely full. So, this + + align:start position:0% +words are completely full. So, this + + + align:start position:0% +words are completely full. So, this +merging and stuff was in order to fill + + align:start position:0% +merging and stuff was in order to fill + + + align:start position:0% +merging and stuff was in order to fill +up words and to make those words sorted. + + align:start position:0% +up words and to make those words sorted. + + + align:start position:0% +up words and to make those words sorted. +But once we've done that for each + + align:start position:0% +But once we've done that for each + + + align:start position:0% +But once we've done that for each +cluster of log n log n items now we can + + align:start position:0% +cluster of log n log n items now we can + + + align:start position:0% +cluster of log n log n items now we can +assume each word is sorted and + + align:start position:0% +assume each word is sorted and + + + align:start position:0% +assume each word is sorted and +completely full has exactly k elements + + align:start position:0% +completely full has exactly k elements + + + align:start position:0% +completely full has exactly k elements +in it. So each of these rs sorted words + + align:start position:0% +in it. So each of these rs sorted words + + + align:start position:0% +in it. So each of these rs sorted words +uh + + align:start position:0% +uh + + + align:start position:0% +uh +has k + + align:start position:0% +has k + + + align:start position:0% +has k +elements. Okay so now the issue is + + align:start position:0% +elements. Okay so now the issue is + + + align:start position:0% +elements. Okay so now the issue is +things don't fit in a word and so now + + align:start position:0% +things don't fit in a word and so now + + + align:start position:0% +things don't fit in a word and so now +suppose they fit in our sorted words. So + + align:start position:0% +suppose they fit in our sorted words. So + + + align:start position:0% +suppose they fit in our sorted words. So +suppose we've already made a sorted list + + align:start position:0% +suppose we've already made a sorted list + + + align:start position:0% +suppose we've already made a sorted list +of R item or sorry of R time K items + + align:start position:0% +of R item or sorry of R time K items + + + align:start position:0% +of R item or sorry of R time K items +which fit in R words words each with K + + align:start position:0% +which fit in R words words each with K + + + align:start position:0% +which fit in R words words each with K +items in it. Then I want to take two of + + align:start position:0% +items in it. Then I want to take two of + + + align:start position:0% +items in it. Then I want to take two of +these lists and merge them together and + + align:start position:0% +these lists and merge them together and + + + align:start position:0% +these lists and merge them together and +get one sorted list of sorted words. So + + align:start position:0% +get one sorted list of sorted words. So + + + align:start position:0% +get one sorted list of sorted words. So +it's it's uh two RK items that are + + align:start position:0% +it's it's uh two RK items that are + + + align:start position:0% +it's it's uh two RK items that are +distributed into two R words each of + + align:start position:0% +distributed into two R words each of + + + align:start position:0% +distributed into two R words each of +size + + align:start position:0% +size + + + align:start position:0% +size +K. How do I do that merge in linear + + align:start position:0% +K. How do I do that merge in linear + + + align:start position:0% +K. How do I do that merge in linear +time? And I only need to do it in R log + + align:start position:0% +time? And I only need to do it in R log + + + align:start position:0% +time? And I only need to do it in R log +K + + align:start position:0% +K + + + align:start position:0% +K +time + + align:start position:0% +time + + + align:start position:0% +time +only. Yeah. Question. I'm assuming K is + + align:start position:0% +only. Yeah. Question. I'm assuming K is + + + align:start position:0% +only. Yeah. Question. I'm assuming K is +a number word is the number of elements + + align:start position:0% +a number word is the number of elements + + + align:start position:0% +a number word is the number of elements +per word. Now K. Yeah. K is this from + + align:start position:0% +per word. Now K. Yeah. K is this from + + + align:start position:0% +per word. Now K. Yeah. K is this from +now on. And they're exactly K elements + + align:start position:0% +now on. And they're exactly K elements + + + align:start position:0% +now on. And they're exactly K elements +per word which I mean we've we've + + align:start position:0% +per word which I mean we've we've + + + align:start position:0% +per word which I mean we've we've +already filled up the words. So at this + + align:start position:0% +already filled up the words. So at this + + + align:start position:0% +already filled up the words. So at this +point we can assume that. Okay. But it's + + align:start position:0% +point we can assume that. Okay. But it's + + + align:start position:0% +point we can assume that. Okay. But it's +exactly equal not less than or equal. + + align:start position:0% +exactly equal not less than or equal. + + + align:start position:0% +exactly equal not less than or equal. +Right. Yeah. Over here it's less than or + + align:start position:0% +Right. Yeah. Over here it's less than or + + + align:start position:0% +Right. Yeah. Over here it's less than or +equal to. I know it's a little + + align:start position:0% +equal to. I know it's a little + + + align:start position:0% +equal to. I know it's a little +confusing. I use K for a different call + + align:start position:0% +confusing. I use K for a different call + + + align:start position:0% +confusing. I use K for a different call +this K + + align:start position:0% +this K + + + align:start position:0% +this K +prime. Okay. And at this point we filled + + align:start position:0% +prime. Okay. And at this point we filled + + + align:start position:0% +prime. Okay. And at this point we filled +up to this value of K and now everything + + align:start position:0% +up to this value of K and now everything + + + align:start position:0% +up to this value of K and now everything +has exactly login log login log N items. + + align:start position:0% +has exactly login log login log N items. + + + align:start position:0% +has exactly login log login log N items. +Thanks. Okay. Uh let's see. I mean + + align:start position:0% +Thanks. Okay. Uh let's see. I mean + + + align:start position:0% +Thanks. Okay. Uh let's see. I mean +regular sorting regular merging + + align:start position:0% +regular sorting regular merging + + + align:start position:0% +regular sorting regular merging +algorithm would take R* K time because + + align:start position:0% +algorithm would take R* K time because + + + align:start position:0% +algorithm would take R* K time because +there are R* K items. But we have this + + align:start position:0% +there are R* K items. But we have this + + + align:start position:0% +there are R* K items. But we have this +merger over here which will merge two + + align:start position:0% +merger over here which will merge two + + + align:start position:0% +merger over here which will merge two +words in log K time. So that's why it's + + align:start position:0% +words in log K time. So that's why it's + + + align:start position:0% +words in log K time. So that's why it's +going to be r log + + align:start position:0% +going to be r log + + + align:start position:0% +going to be r log +k. What's the picture? Well, let me draw + + align:start position:0% + + + + align:start position:0% + +it. Uh, we have a list of + + align:start position:0% +it. Uh, we have a list of + + + align:start position:0% +it. Uh, we have a list of +words. A list of words. + + align:start position:0% +words. A list of words. + + + align:start position:0% +words. A list of words. +How do we merge? Well, we take the first + + align:start position:0% +How do we merge? Well, we take the first + + + align:start position:0% +How do we merge? Well, we take the first +two words, merge them. When we merge + + align:start position:0% +two words, merge them. When we merge + + + align:start position:0% +two words, merge them. When we merge +them, and we know how to do this in log + + align:start position:0% +them, and we know how to do this in log + + + align:start position:0% +them, and we know how to do this in log +k time by step one. When we merge them, + + align:start position:0% +k time by step one. When we merge them, + + + align:start position:0% +k time by step one. When we merge them, +we get two words. They just are now + + align:start position:0% +we get two words. They just are now + + + align:start position:0% +we get two words. They just are now +sorted. Okay, so we've got these two + + align:start position:0% +sorted. Okay, so we've got these two + + + align:start position:0% +sorted. Okay, so we've got these two +guys sorted and then there's the rest. + + align:start position:0% +guys sorted and then there's the rest. + + + align:start position:0% +guys sorted and then there's the rest. +Uh, I'd like to say output these and + + align:start position:0% +Uh, I'd like to say output these and + + + align:start position:0% +Uh, I'd like to say output these and +repeat, but that wouldn't be quite + + align:start position:0% +repeat, but that wouldn't be quite + + + align:start position:0% +repeat, but that wouldn't be quite +correct because uh, well, these guys I + + align:start position:0% +correct because uh, well, these guys I + + + align:start position:0% +correct because uh, well, these guys I +can + + align:start position:0% +can + + + align:start position:0% +can +output because I've got, you know, K + + align:start position:0% +output because I've got, you know, K + + + align:start position:0% +output because I've got, you know, K +items here, K items here. These are the + + align:start position:0% +items here, K items here. These are the + + + align:start position:0% +items here, K items here. These are the +K smallest among all of them. Those must + + align:start position:0% +K smallest among all of them. Those must + + + align:start position:0% +K smallest among all of them. Those must +be the overall smallest K items because + + align:start position:0% +be the overall smallest K items because + + + align:start position:0% +be the overall smallest K items because +I compared K with K. These higher K + + align:start position:0% +I compared K with K. These higher K + + + align:start position:0% +I compared K with K. These higher K +items, I don't know. They could, you + + align:start position:0% +items, I don't know. They could, you + + + align:start position:0% +items, I don't know. They could, you +know, they might be good or bad. So, I + + align:start position:0% +know, they might be good or bad. So, I + + + align:start position:0% +know, they might be good or bad. So, I +have to put this high part back into one + + align:start position:0% +have to put this high part back into one + + + align:start position:0% +have to put this high part back into one +of these lists. You have to think a + + align:start position:0% +of these lists. You have to think a + + + align:start position:0% +of these lists. You have to think a +little bit about which list to put it + + align:start position:0% +little bit about which list to put it + + + align:start position:0% +little bit about which list to put it +into. It turns out if you look at the + + align:start position:0% +into. It turns out if you look at the + + + align:start position:0% +into. It turns out if you look at the +max item say where did this come from + + align:start position:0% +max item say where did this come from + + + align:start position:0% +max item say where did this come from +list one or list two you put it into + + align:start position:0% +list one or list two you put it into + + + align:start position:0% +list one or list two you put it into +that list. Let's say this came from list + + align:start position:0% +that list. Let's say this came from list + + + align:start position:0% +that list. Let's say this came from list +two and you put it back into list two + + align:start position:0% +two and you put it back into list two + + + align:start position:0% +two and you put it back into list two +and then repeat. Okay. So in log k time + + align:start position:0% +and then repeat. Okay. So in log k time + + + align:start position:0% +and then repeat. Okay. So in log k time +here we have output k items and so we + + align:start position:0% +here we have output k items and so we + + + align:start position:0% +here we have output k items and so we +end up with an r log k running time + + align:start position:0% +end up with an r log k running time + + + align:start position:0% +end up with an r log k running time +overall. Okay. Okay, so it's like + + align:start position:0% +overall. Okay. Okay, so it's like + + + align:start position:0% +overall. Okay. Okay, so it's like +regular merge the regular merge + + align:start position:0% +regular merge the regular merge + + + align:start position:0% +regular merge the regular merge +algorithm except we use step one to + + align:start position:0% +algorithm except we use step one to + + + align:start position:0% +algorithm except we use step one to +merge words and then there's a little + + align:start position:0% +merge words and then there's a little + + + align:start position:0% +merge words and then there's a little +bit of work but this was like old + + align:start position:0% +bit of work but this was like old + + + align:start position:0% +bit of work but this was like old +merging algorithm right you take the min + + align:start position:0% +merging algorithm right you take the min + + + align:start position:0% +merging algorithm right you take the min +and you put the max back in okay except + + align:start position:0% +and you put the max back in okay except + + + align:start position:0% +and you put the max back in okay except +now the max is a whole + + align:start position:0% +now the max is a whole + + + align:start position:0% +now the max is a whole +word okay that's how we merge now why do + + align:start position:0% +word okay that's how we merge now why do + + + align:start position:0% +word okay that's how we merge now why do +we do a merger because next thing we do + + align:start position:0% +we do a merger because next thing we do + + + align:start position:0% +we do a merger because next thing we do +is merge sort + + align:start position:0% + + + + align:start position:0% + +And this is the overall algorithm. It's + + align:start position:0% +And this is the overall algorithm. It's + + + align:start position:0% +And this is the overall algorithm. It's +one merge sort. We're going to use this + + align:start position:0% +one merge sort. We're going to use this + + + align:start position:0% +one merge sort. We're going to use this +as the merger and we're going to use + + align:start position:0% +as the merger and we're going to use + + + align:start position:0% +as the merger and we're going to use +this as the base case. So it's actually + + align:start position:0% +this as the base case. So it's actually + + + align:start position:0% +this as the base case. So it's actually +two recursive levels of merge sort. + + align:start position:0% +two recursive levels of merge sort. + + + align:start position:0% +two recursive levels of merge sort. +Merur is recursive in within step four + + align:start position:0% +Merur is recursive in within step four + + + align:start position:0% +Merur is recursive in within step four +for a while until we get down to the + + align:start position:0% +for a while until we get down to the + + + align:start position:0% +for a while until we get down to the +level of a single word. Then we use this + + align:start position:0% +level of a single word. Then we use this + + + align:start position:0% +level of a single word. Then we use this +thing to deal with things in a single + + align:start position:0% +thing to deal with things in a single + + + align:start position:0% +thing to deal with things in a single +word. + + align:start position:0% +word. + + + align:start position:0% +word. +Okay. So we end up with t of n is 2 * t + + align:start position:0% +Okay. So we end up with t of n is 2 * t + + + align:start position:0% +Okay. So we end up with t of n is 2 * t +of n / + + align:start position:0% +of n / + + + align:start position:0% +of n / + + align:start position:0% + + + align:start position:0% +plus n / k log k. + + align:start position:0% +plus n / k log k. + + + align:start position:0% +plus n / k log k. +And a base case of t of k is order + + align:start position:0% + + + + align:start position:0% + +k. Okay. + + align:start position:0% +k. Okay. + + + align:start position:0% +k. Okay. +Uh why is it all this? Okay. This + + align:start position:0% +Uh why is it all this? Okay. This + + + align:start position:0% +Uh why is it all this? Okay. This +thing is r. + + align:start position:0% +thing is r. + + + align:start position:0% +thing is r. +Okay. Uh so we have r log k to do a + + align:start position:0% +Okay. Uh so we have r log k to do a + + + align:start position:0% +Okay. Uh so we have r log k to do a +merge. R here is n over k. Why is n over + + align:start position:0% +merge. R here is n over k. Why is n over + + + align:start position:0% +merge. R here is n over k. Why is n over +k? + + align:start position:0% +k? + + + align:start position:0% +k? +uh because uh n is the total number of + + align:start position:0% +uh because uh n is the total number of + + + align:start position:0% +uh because uh n is the total number of +items. We had r * k items. So n= r k. So + + align:start position:0% +items. We had r * k items. So n= r k. So + + + align:start position:0% +items. We had r * k items. So n= r k. So +r equ= n / k. Okay, that's that. So this + + align:start position:0% +r equ= n / k. Okay, that's that. So this + + + align:start position:0% +r equ= n / k. Okay, that's that. So this +is our merge cost. This is the cost of + + align:start position:0% +is our merge cost. This is the cost of + + + align:start position:0% +is our merge cost. This is the cost of +three. This is the cost of two from our + + align:start position:0% +three. This is the cost of two from our + + + align:start position:0% +three. This is the cost of two from our +if if we have only login log items, so k + + align:start position:0% +if if we have only login log items, so k + + + align:start position:0% +if if we have only login log items, so k +items, then we can merge in linear time + + align:start position:0% +items, then we can merge in linear time + + + align:start position:0% +items, then we can merge in linear time +or sorry we can sort in linear time. So + + align:start position:0% +or sorry we can sort in linear time. So + + + align:start position:0% +or sorry we can sort in linear time. So +we just need to solve this recurrence. + + align:start position:0% +we just need to solve this recurrence. + + + align:start position:0% +we just need to solve this recurrence. +Uh + + align:start position:0% +Uh + + + align:start position:0% +Uh +well, how's it gonna work? It's gonna be + + align:start position:0% +well, how's it gonna work? It's gonna be + + + align:start position:0% +well, how's it gonna work? It's gonna be +kind of like merge sort, but not quite. + + align:start position:0% +kind of like merge sort, but not quite. + + + align:start position:0% +kind of like merge sort, but not quite. +So question + + align:start position:0% +So question + + + align:start position:0% +So question +um when you say so you have in step two + + align:start position:0% +um when you say so you have in step two + + + align:start position:0% +um when you say so you have in step two +you're merging two list of sorted words + + align:start position:0% +you're merging two list of sorted words + + + align:start position:0% +you're merging two list of sorted words +into one sorted list of two sort of + + align:start position:0% +into one sorted list of two sort of + + + align:start position:0% +into one sorted list of two sort of +words. Does that imply actually taking + + align:start position:0% +words. Does that imply actually taking + + + align:start position:0% +words. Does that imply actually taking +the elements within the words and + + align:start position:0% +the elements within the words and + + + align:start position:0% +the elements within the words and +reshuffling them across or you may have + + align:start position:0% +reshuffling them across or you may have + + + align:start position:0% +reshuffling them across or you may have +to do that right? + + align:start position:0% + + + + align:start position:0% + +Uh say that again. So you have two + + align:start position:0% +Uh say that again. So you have two + + + align:start position:0% +Uh say that again. So you have two +sorted two sorted list of are sorted + + align:start position:0% +sorted two sorted list of are sorted + + + align:start position:0% +sorted two sorted list of are sorted +words. Yeah. The words are are going to + + align:start position:0% +words. Yeah. The words are are going to + + + align:start position:0% +words. Yeah. The words are are going to +change which elements are in which words + + align:start position:0% +change which elements are in which words + + + align:start position:0% +change which elements are in which words +are changing. But that's thanks to step + + align:start position:0% +are changing. But that's thanks to step + + + align:start position:0% +are changing. But that's thanks to step +one. Uh for example, I mean step one can + + align:start position:0% +one. Uh for example, I mean step one can + + + align:start position:0% +one. Uh for example, I mean step one can +merge any two sorted words and make one + + align:start position:0% +merge any two sorted words and make one + + + align:start position:0% +merge any two sorted words and make one +sorted word or + + align:start position:0% +sorted word or + + + align:start position:0% +sorted word or +actually yeah one sorted word. In our + + align:start position:0% +actually yeah one sorted word. In our + + + align:start position:0% +actually yeah one sorted word. In our +case, we're going to actually need we're + + align:start position:0% +case, we're going to actually need we're + + + align:start position:0% +case, we're going to actually need we're +going to get two sorted words. That was + + align:start position:0% +going to get two sorted words. That was + + + align:start position:0% +going to get two sorted words. That was +the picture over here. I merge the two + + align:start position:0% +the picture over here. I merge the two + + + align:start position:0% +the picture over here. I merge the two +guys. I could represent it as one word + + align:start position:0% +guys. I could represent it as one word + + + align:start position:0% +guys. I could represent it as one word +that's kind of double full and then I + + align:start position:0% +that's kind of double full and then I + + + align:start position:0% +that's kind of double full and then I +can split that into two words. Uh so we + + align:start position:0% +can split that into two words. Uh so we + + + align:start position:0% +can split that into two words. Uh so we +again need the split operation but split + + align:start position:0% +again need the split operation but split + + + align:start position:0% +again need the split operation but split +is just uh you mask this these guys out + + align:start position:0% +is just uh you mask this these guys out + + + align:start position:0% +is just uh you mask this these guys out +and you get the high part. This is all + + align:start position:0% +and you get the high part. This is all + + + align:start position:0% +and you get the high part. This is all +zero. Then you shift it over to the left + + align:start position:0% +zero. Then you shift it over to the left + + + align:start position:0% +zero. Then you shift it over to the left +and you get now you've got the high word + + align:start position:0% +and you get now you've got the high word + + + align:start position:0% +and you get now you've got the high word +over as a single word. Yep. So they are + + align:start position:0% +over as a single word. Yep. So they are + + + align:start position:0% +over as a single word. Yep. So they are +shuffling within those two words uh or + + align:start position:0% +shuffling within those two words uh or + + + align:start position:0% +shuffling within those two words uh or +within one word essentially. + + align:start position:0% +within one word essentially. + + + align:start position:0% +within one word essentially. +via this procedure which we haven't + + align:start position:0% +via this procedure which we haven't + + + align:start position:0% +via this procedure which we haven't +covered. So everything's going to mix + + align:start position:0% +covered. So everything's going to mix + + + align:start position:0% +covered. So everything's going to mix +around but then there's the low items + + align:start position:0% +around but then there's the low items + + + align:start position:0% +around but then there's the low items +and the high items and so all the items + + align:start position:0% +and the high items and so all the items + + + align:start position:0% +and the high items and so all the items +in here are less than all the items in + + align:start position:0% +in here are less than all the items in + + + align:start position:0% +in here are less than all the items in +here. Other questions? Cool. Uh so I + + align:start position:0% +here. Other questions? Cool. Uh so I + + + align:start position:0% +here. Other questions? Cool. Uh so I +need to solve this recurrence. So let's + + align:start position:0% +need to solve this recurrence. So let's + + + align:start position:0% +need to solve this recurrence. So let's +draw another recursion tree. It's easy + + align:start position:0% +draw another recursion tree. It's easy + + + align:start position:0% +draw another recursion tree. It's easy +way solve recurrences. Root is n over k + + align:start position:0% +way solve recurrences. Root is n over k + + + align:start position:0% +way solve recurrences. Root is n over k +log k. Uh, next level down. See, n got + + align:start position:0% +log k. Uh, next level down. See, n got + + + align:start position:0% +log k. Uh, next level down. See, n got +divided by two. So, it's going to be + + align:start position:0% +divided by two. So, it's going to be + + + align:start position:0% +divided by two. So, it's going to be +half n over k log + + align:start position:0% +half n over k log + + + align:start position:0% +half n over k log +k half n over k log + + align:start position:0% +k half n over k log + + + align:start position:0% +k half n over k log +k. The end gets divided by two. So, if I + + align:start position:0% +k. The end gets divided by two. So, if I + + + align:start position:0% +k. The end gets divided by two. So, if I +add up everything on this level, I get n + + align:start position:0% +add up everything on this level, I get n + + + align:start position:0% +add up everything on this level, I get n +over k log k. And in general, as I go + + align:start position:0% +over k log k. And in general, as I go + + + align:start position:0% +over k log k. And in general, as I go +down, all levels are going to sum to the + + align:start position:0% +down, all levels are going to sum to the + + + align:start position:0% +down, all levels are going to sum to the +same value, n over k log k. So up here + + align:start position:0% +same value, n over k log k. So up here + + + align:start position:0% +same value, n over k log k. So up here +we're going to have a cost of n over k + + align:start position:0% +we're going to have a cost of n over k + + + align:start position:0% +we're going to have a cost of n over k +log + + align:start position:0% +log + + + align:start position:0% +log +k times the number of levels. Now this + + align:start position:0% +k times the number of levels. Now this + + + align:start position:0% +k times the number of levels. Now this +is where it's a little tricky. This is + + align:start position:0% +is where it's a little tricky. This is + + + align:start position:0% +is where it's a little tricky. This is +not log n levels like regular merge + + align:start position:0% +not log n levels like regular merge + + + align:start position:0% +not log n levels like regular merge +sort. We stop at level + + align:start position:0% +sort. We stop at level + + + align:start position:0% +sort. We stop at level +k. So it's going to be + + align:start position:0% +k. So it's going to be + + + align:start position:0% +k. So it's going to be +log of n over + + align:start position:0% + + + + align:start position:0% + +k. That's the number of levels we get + + align:start position:0% +k. That's the number of levels we get + + + align:start position:0% +k. That's the number of levels we get +to. Now at the leaf level finally we + + align:start position:0% +to. Now at the leaf level finally we + + + align:start position:0% +to. Now at the leaf level finally we +have things of size order K and we only + + align:start position:0% +have things of size order K and we only + + + align:start position:0% +have things of size order K and we only +pay order + + align:start position:0% +pay order + + + align:start position:0% +pay order +K. Great. Uh and then how many leaves + + align:start position:0% +K. Great. Uh and then how many leaves + + + align:start position:0% +K. Great. Uh and then how many leaves +are there? Uh there's n over k + + align:start position:0% + + + + align:start position:0% + +leaves. Okay. So that's an order n cost. + + align:start position:0% +leaves. Okay. So that's an order n cost. + + + align:start position:0% +leaves. Okay. So that's an order n cost. +This is order + + align:start position:0% +This is order + + + align:start position:0% +This is order +k order + + align:start position:0% +k order + + + align:start position:0% +k order +n. What's this + + align:start position:0% +n. What's this + + + align:start position:0% +n. What's this +thing? Well, what's k? k was log n log + + align:start position:0% +thing? Well, what's k? k was log n log + + + align:start position:0% +thing? Well, what's k? k was log n log +log n. So this is n / log n log n. This + + align:start position:0% +log n. So this is n / log n log n. This + + + align:start position:0% +log n. So this is n / log n log n. This +therefore is approximately log log n. So + + align:start position:0% +therefore is approximately log log n. So + + + align:start position:0% +therefore is approximately log log n. So +that log n cancels with this one. This + + align:start position:0% +that log n cancels with this one. This + + + align:start position:0% +that log n cancels with this one. This +is approximately log n. So that cancels + + align:start position:0% +is approximately log n. So that cancels + + + align:start position:0% +is approximately log n. So that cancels +with this one. So this is order n. + + align:start position:0% +with this one. So this is order n. + + + align:start position:0% +with this one. So this is order n. +That's why we chose these values. So + + align:start position:0% +That's why we chose these values. So + + + align:start position:0% +That's why we chose these values. So +this n overk was not actually that + + align:start position:0% +this n overk was not actually that + + + align:start position:0% +this n overk was not actually that +significant. We could have called that + + align:start position:0% +significant. We could have called that + + + align:start position:0% +significant. We could have called that +n. What is important is that this + + align:start position:0% +n. What is important is that this + + + align:start position:0% +n. What is important is that this +recursion doesn't work when you get down + + align:start position:0% +recursion doesn't work when you get down + + + align:start position:0% +recursion doesn't work when you get down +to a single word. Can't do the same + + align:start position:0% +to a single word. Can't do the same + + + align:start position:0% +to a single word. Can't do the same +strategy. You need to use a different + + align:start position:0% +strategy. You need to use a different + + + align:start position:0% +strategy. You need to use a different +merger + + align:start position:0% +merger + + + align:start position:0% +merger +uh for single words because here we have + + align:start position:0% +uh for single words because here we have + + + align:start position:0% +uh for single words because here we have +to do bit tricks. For this merge + + align:start position:0% +to do bit tricks. For this merge + + + align:start position:0% +to do bit tricks. For this merge +strategy we didn't have to do bit tricks + + align:start position:0% +strategy we didn't have to do bit tricks + + + align:start position:0% +strategy we didn't have to do bit tricks +because everything was bigger than a + + align:start position:0% +because everything was bigger than a + + + align:start position:0% +because everything was bigger than a +word. Okay. So that's the reason the + + align:start position:0% +word. Okay. So that's the reason the + + + align:start position:0% +word. Okay. So that's the reason the +reason why we have these two levels is + + align:start position:0% +reason why we have these two levels is + + + align:start position:0% +reason why we have these two levels is +not to make the time fast. It's just uh + + align:start position:0% +not to make the time fast. It's just uh + + + align:start position:0% +not to make the time fast. It's just uh +to make the algorithm work. I mean to + + align:start position:0% +to make the algorithm work. I mean to + + + align:start position:0% +to make the algorithm work. I mean to +define the algorithm there's within a + + align:start position:0% +define the algorithm there's within a + + + align:start position:0% +define the algorithm there's within a +word merging and over many words + + align:start position:0% +word merging and over many words + + + align:start position:0% +word merging and over many words +merging. The hard part is this one + + align:start position:0% +merging. The hard part is this one + + + align:start position:0% +merging. The hard part is this one +within a word merging. So that's our + + align:start position:0% +within a word merging. So that's our + + + align:start position:0% +within a word merging. So that's our +next goal. But if we could do + + align:start position:0% +next goal. But if we could do + + + align:start position:0% +next goal. But if we could do +that we get linear time sorting for pack + + align:start position:0% +that we get linear time sorting for pack + + + align:start position:0% +that we get linear time sorting for pack +sorting when you can fit login things in + + align:start position:0% +sorting when you can fit login things in + + + align:start position:0% +sorting when you can fit login things in +a word. Any questions about packed + + align:start position:0% + + + + align:start position:0% + +sorting? Good. So, last thing is how do + + align:start position:0% +sorting? Good. So, last thing is how do + + + align:start position:0% +sorting? Good. So, last thing is how do +we merge two + + align:start position:0% +we merge two + + + align:start position:0% +we merge two +words, two sorted words into one sorted + + align:start position:0% +words, two sorted words into one sorted + + + align:start position:0% +words, two sorted words into one sorted +word? And this is where we're going to + + align:start position:0% +word? And this is where we're going to + + + align:start position:0% +word? And this is where we're going to +use bonic sorting. See, it says right + + align:start position:0% +use bonic sorting. See, it says right + + + align:start position:0% +use bonic sorting. See, it says right +here, bonic sort for merging sorted + + align:start position:0% +here, bonic sort for merging sorted + + + align:start position:0% +here, bonic sort for merging sorted +words. Here we know what to + + align:start position:0% +words. Here we know what to + + + align:start position:0% +words. Here we know what to +do. Much easier in hindsight. + + align:start position:0% + + + + align:start position:0% + +So I'm going to take a little diversion + + align:start position:0% +So I'm going to take a little diversion + + + align:start position:0% +So I'm going to take a little diversion +and tell you about bonic + + align:start position:0% +and tell you about bonic + + + align:start position:0% +and tell you about bonic +sorting briefly + + align:start position:0% + + + + align:start position:0% + +uh because it's in CLRS. I don't want to + + align:start position:0% +uh because it's in CLRS. I don't want to + + + align:start position:0% +uh because it's in CLRS. I don't want to +spend too much time on it but uh it is + + align:start position:0% +spend too much time on it but uh it is + + + align:start position:0% +spend too much time on it but uh it is +something we need. So you need to know + + align:start position:0% +something we need. So you need to know + + + align:start position:0% +something we need. So you need to know +how it + + align:start position:0% + + + + align:start position:0% + +works. So first thing is the idea of a + + align:start position:0% +works. So first thing is the idea of a + + + align:start position:0% +works. So first thing is the idea of a +botonic sequence. This is going to + + align:start position:0% +botonic sequence. This is going to + + + align:start position:0% +botonic sequence. This is going to +be a cyclic + + align:start position:0% + + + + align:start position:0% + +shift of a unimodal sequence. So a + + align:start position:0% +shift of a unimodal sequence. So a + + + align:start position:0% +shift of a unimodal sequence. So a +non-deasreasing plus a non + + align:start position:0% +non-deasreasing plus a non + + + align:start position:0% +non-deasreasing plus a non +increasing + + align:start position:0% + + + + align:start position:0% + +sequence. So I want non-deasing and then + + align:start position:0% +sequence. So I want non-deasing and then + + + align:start position:0% +sequence. So I want non-deasing and then +non-increasing. So this is a botonic + + align:start position:0% +non-increasing. So this is a botonic + + + align:start position:0% +non-increasing. So this is a botonic +sequence. I think you know what this + + align:start position:0% +sequence. I think you know what this + + + align:start position:0% +sequence. I think you know what this +means. Um or it could be a cyclic shift + + align:start position:0% +means. Um or it could be a cyclic shift + + + align:start position:0% +means. Um or it could be a cyclic shift +thereof. So I could, for example, take + + align:start position:0% +thereof. So I could, for example, take + + + align:start position:0% +thereof. So I could, for example, take +this part here and shift it over to this + + align:start position:0% +this part here and shift it over to this + + + align:start position:0% +this part here and shift it over to this +side. So then I'd end up with this, + + align:start position:0% +side. So then I'd end up with this, + + + align:start position:0% +side. So then I'd end up with this, +this, and this. This is also bonic. Or I + + align:start position:0% +this, and this. This is also bonic. Or I + + + align:start position:0% +this, and this. This is also bonic. Or I +could shift this whole thing and put it + + align:start position:0% +could shift this whole thing and put it + + + align:start position:0% +could shift this whole thing and put it +over there. And so I end up with that. + + align:start position:0% +over there. And so I end up with that. + + + align:start position:0% +over there. And so I end up with that. +That's also bonic. So it basically has + + align:start position:0% +That's also bonic. So it basically has + + + align:start position:0% +That's also bonic. So it basically has +one min, one max, one min if you're + + align:start position:0% +one min, one max, one min if you're + + + align:start position:0% +one min, one max, one min if you're +reading it cyclically. One local max, + + align:start position:0% +reading it cyclically. One local max, + + + align:start position:0% +reading it cyclically. One local max, +one local min, except it's + + align:start position:0% +one local min, except it's + + + align:start position:0% +one local min, except it's +non-deasreasing. So a little mess here, + + align:start position:0% +non-deasreasing. So a little mess here, + + + align:start position:0% +non-deasreasing. So a little mess here, +but same thing. + + align:start position:0% +but same thing. + + + align:start position:0% +but same thing. +Okay. Uh let's + + align:start position:0% +Okay. Uh let's + + + align:start position:0% +Okay. Uh let's +go be over here. + + align:start position:0% + + + + align:start position:0% + +So if you have a bonic sequence, there's + + align:start position:0% +So if you have a bonic sequence, there's + + + align:start position:0% +So if you have a bonic sequence, there's +something called a bonic sorting + + align:start position:0% +something called a bonic sorting + + + align:start position:0% +something called a bonic sorting +network which you can think of as a + + align:start position:0% +network which you can think of as a + + + align:start position:0% +network which you can think of as a +parallel sorting algorithm to sort such + + align:start position:0% +parallel sorting algorithm to sort such + + + align:start position:0% +parallel sorting algorithm to sort such +a thing. So it's almost sorted but not + + align:start position:0% +a thing. So it's almost sorted but not + + + align:start position:0% +a thing. So it's almost sorted but not +quite. And there's this way of sorting + + align:start position:0% +quite. And there's this way of sorting + + + align:start position:0% +quite. And there's this way of sorting +them. So I'm going to write down I'm + + align:start position:0% +them. So I'm going to write down I'm + + + align:start position:0% +them. So I'm going to write down I'm +going to draw a picture to make it + + align:start position:0% +going to draw a picture to make it + + + align:start position:0% +going to draw a picture to make it +easier for + + align:start position:0% +easier for + + + align:start position:0% +easier for +me a little harder. It's a little more + + align:start position:0% +me a little harder. It's a little more + + + align:start position:0% +me a little harder. It's a little more +annoying to write down the general + + align:start position:0% +annoying to write down the general + + + align:start position:0% +annoying to write down the general +algorithm. But so what I want to do + + align:start position:0% +algorithm. But so what I want to do + + + align:start position:0% +algorithm. But so what I want to do +suppose the number of elements is a + + align:start position:0% +suppose the number of elements is a + + + align:start position:0% +suppose the number of elements is a +power of two. Here's what I'm going to + + align:start position:0% +power of two. Here's what I'm going to + + + align:start position:0% +power of two. Here's what I'm going to +do. First I compare the the first and + + align:start position:0% +do. First I compare the the first and + + + align:start position:0% +do. First I compare the the first and +the midway element and then the next one + + align:start position:0% +the midway element and then the next one + + + align:start position:0% +the midway element and then the next one +with the next one and then the next one + + align:start position:0% +with the next one and then the next one + + + align:start position:0% +with the next one and then the next one +with the next one. The next one with the + + align:start position:0% +with the next one. The next one with the + + + align:start position:0% +with the next one. The next one with the +next one. For each of these comparisons + + align:start position:0% +next one. For each of these comparisons + + + align:start position:0% +next one. For each of these comparisons +I put those items in the correct order. + + align:start position:0% +I put those items in the correct order. + + + align:start position:0% +I put those items in the correct order. +So if I do that three versus six, three + + align:start position:0% +So if I do that three versus six, three + + + align:start position:0% +So if I do that three versus six, three +is less than six. So three stays here. + + align:start position:0% +is less than six. So three stays here. + + + align:start position:0% +is less than six. So three stays here. +Six stays there. Five is bigger than + + align:start position:0% +Six stays there. Five is bigger than + + + align:start position:0% +Six stays there. Five is bigger than +four though. So four comes over here. + + align:start position:0% +four though. So four comes over here. + + + align:start position:0% +four though. So four comes over here. +Five goes over here. Next is seven + + align:start position:0% +Five goes over here. Next is seven + + + align:start position:0% +Five goes over here. Next is seven +versus two. So two comes over here, + + align:start position:0% +versus two. So two comes over here, + + + align:start position:0% +versus two. So two comes over here, +seven comes over here. Nine versus zero. + + align:start position:0% +seven comes over here. Nine versus zero. + + + align:start position:0% +seven comes over here. Nine versus zero. +So zero's over here, nine's over there. + + align:start position:0% +So zero's over here, nine's over there. + + + align:start position:0% +So zero's over here, nine's over there. +Okay, that's an easy set of things, set + + align:start position:0% +Okay, that's an easy set of things, set + + + align:start position:0% +Okay, that's an easy set of things, set +of comparisons to do. The nice thing is + + align:start position:0% +of comparisons to do. The nice thing is + + + align:start position:0% +of comparisons to do. The nice thing is +you can do all those in + + align:start position:0% +you can do all those in + + + align:start position:0% +you can do all those in +parallel. Okay. Uh just to check here, + + align:start position:0% +parallel. Okay. Uh just to check here, + + + align:start position:0% +parallel. Okay. Uh just to check here, +this was a monotone increasing + + align:start position:0% +this was a monotone increasing + + + align:start position:0% +this was a monotone increasing +subsequence and then a monotone + + align:start position:0% +subsequence and then a monotone + + + align:start position:0% +subsequence and then a monotone +decreasing. Okay. Now we have increasing + + align:start position:0% +decreasing. Okay. Now we have increasing + + + align:start position:0% +decreasing. Okay. Now we have increasing +then decreasing and then we have uh + + align:start position:0% +then decreasing and then we have uh + + + align:start position:0% +then decreasing and then we have uh +decreasing then increasing. + + align:start position:0% +decreasing then increasing. + + + align:start position:0% +decreasing then increasing. +uh but if you look at the left half or + + align:start position:0% +uh but if you look at the left half or + + + align:start position:0% +uh but if you look at the left half or +the right half they are still bonic and + + align:start position:0% +the right half they are still bonic and + + + align:start position:0% +the right half they are still bonic and +that's an invariant bonic will be + + align:start position:0% +that's an invariant bonic will be + + + align:start position:0% +that's an invariant bonic will be +preserved here also notice all the + + align:start position:0% +preserved here also notice all the + + + align:start position:0% +preserved here also notice all the +elements in the left are smaller than + + align:start position:0% +elements in the left are smaller than + + + align:start position:0% +elements in the left are smaller than +all the elements in the right that's not + + align:start position:0% +all the elements in the right that's not + + + align:start position:0% +all the elements in the right that's not +true for an arbitrary sequence but it + + align:start position:0% +true for an arbitrary sequence but it + + + align:start position:0% +true for an arbitrary sequence but it +will be true for a bonic sequence + + align:start position:0% +will be true for a bonic sequence + + + align:start position:0% +will be true for a bonic sequence +essentially the the the max is somewhere + + align:start position:0% +essentially the the the max is somewhere + + + align:start position:0% +essentially the the the max is somewhere +here and so it's going to be spanned by + + align:start position:0% +here and so it's going to be spanned by + + + align:start position:0% +here and so it's going to be spanned by +uh some of these intervals that max and + + align:start position:0% +uh some of these intervals that max and + + + align:start position:0% +uh some of these intervals that max and +by spanning those intervals and in + + align:start position:0% +by spanning those intervals and in + + + align:start position:0% +by spanning those intervals and in +particular comparing that guy with + + align:start position:0% +particular comparing that guy with + + + align:start position:0% +particular comparing that guy with +somebody on the + + align:start position:0% +somebody on the + + + align:start position:0% +somebody on the +the max will get over to the right and + + align:start position:0% +the max will get over to the right and + + + align:start position:0% +the max will get over to the right and +uh then the rest of the increasing and + + align:start position:0% +uh then the rest of the increasing and + + + align:start position:0% +uh then the rest of the increasing and +decreasing subsequences will follow. + + align:start position:0% +decreasing subsequences will follow. + + + align:start position:0% +decreasing subsequences will follow. +It's a very hand wavy argument. You can + + align:start position:0% +It's a very hand wavy argument. You can + + + align:start position:0% +It's a very hand wavy argument. You can +see clrs for a way to prove that. Okay, + + align:start position:0% +see clrs for a way to prove that. Okay, + + + align:start position:0% +see clrs for a way to prove that. Okay, +just take it for granted. Now, now we + + align:start position:0% +just take it for granted. Now, now we + + + align:start position:0% +just take it for granted. Now, now we +recurse on the two sides. So I compare + + align:start position:0% +recurse on the two sides. So I compare + + + align:start position:0% +recurse on the two sides. So I compare +three with two, four with zero. I + + align:start position:0% +three with two, four with zero. I + + + align:start position:0% +three with two, four with zero. I +compare six with seven and five with + + align:start position:0% +compare six with seven and five with + + + align:start position:0% +compare six with seven and five with +nine. So what do I get? Uh two is less + + align:start position:0% +nine. So what do I get? Uh two is less + + + align:start position:0% +nine. So what do I get? Uh two is less +than three, 0 is less than four. Then I + + align:start position:0% +than three, 0 is less than four. Then I + + + align:start position:0% +than three, 0 is less than four. Then I +compare six seven less than seven. Five + + align:start position:0% +compare six seven less than seven. Five + + + align:start position:0% +compare six seven less than seven. Five +is less than + + align:start position:0% +is less than + + + align:start position:0% +is less than +nine. Uh so now I've got four chunks. + + align:start position:0% +nine. Uh so now I've got four chunks. + + + align:start position:0% +nine. Uh so now I've got four chunks. +This one, this one, this one, this one. + + align:start position:0% +This one, this one, this one, this one. + + + align:start position:0% +This one, this one, this one, this one. +I recurse on each of them. So 0 is less + + align:start position:0% +I recurse on each of them. So 0 is less + + + align:start position:0% +I recurse on each of them. So 0 is less +than two, three is less than four, five + + align:start position:0% +than two, three is less than four, five + + + align:start position:0% +than two, three is less than four, five +is less than six, seven is less than + + align:start position:0% +is less than six, seven is less than + + + align:start position:0% +is less than six, seven is less than +nine. And now I have all my items in + + align:start position:0% +nine. And now I have all my items in + + + align:start position:0% +nine. And now I have all my items in +sorted order magically. Okay. Okay, but + + align:start position:0% +sorted order magically. Okay. Okay, but + + + align:start position:0% +sorted order magically. Okay. Okay, but +if you believe that invariant that the + + align:start position:0% +if you believe that invariant that the + + + align:start position:0% +if you believe that invariant that the +the smallest n over2 items get to the + + align:start position:0% +the smallest n over2 items get to the + + + align:start position:0% +the smallest n over2 items get to the +left and the larger n over2 items get to + + align:start position:0% +left and the larger n over2 items get to + + + align:start position:0% +left and the larger n over2 items get to +the right. Uh then by induction this + + align:start position:0% +the right. Uh then by induction this + + + align:start position:0% +the right. Uh then by induction this +will sort them. It's kind of like quick + + align:start position:0% +will sort them. It's kind of like quick + + + align:start position:0% +will sort them. It's kind of like quick +sort in that + + align:start position:0% +sort in that + + + align:start position:0% +sort in that +sense. Okay, the cool thing is I can do + + align:start position:0% +sense. Okay, the cool thing is I can do + + + align:start position:0% +sense. Okay, the cool thing is I can do +all these in parallel, all these in + + align:start position:0% +all these in parallel, all these in + + + align:start position:0% +all these in parallel, all these in +parallel, all these in parallel. So the + + align:start position:0% +parallel, all these in parallel. So the + + + align:start position:0% +parallel, all these in parallel. So the +total time is log k if I'm a sorting if + + align:start position:0% +total time is log k if I'm a sorting if + + + align:start position:0% +total time is log k if I'm a sorting if +I'm a parallel sorting algorithm or + + align:start position:0% +I'm a parallel sorting algorithm or + + + align:start position:0% +I'm a parallel sorting algorithm or +sorting network. And log k is exactly + + align:start position:0% +sorting network. And log k is exactly + + + align:start position:0% +sorting network. And log k is exactly +what I can afford. So the last thing to + + align:start position:0% +what I can afford. So the last thing to + + + align:start position:0% +what I can afford. So the last thing to +do is to implement an operation like + + align:start position:0% +do is to implement an operation like + + + align:start position:0% +do is to implement an operation like +this or like this. This is kind of the + + align:start position:0% +this or like this. This is kind of the + + + align:start position:0% +this or like this. This is kind of the +generic picture + + align:start position:0% +generic picture + + + align:start position:0% +generic picture +here in constant time on a word + + align:start position:0% + + + + align:start position:0% + +RAM. Uh one other thing is I don't want + + align:start position:0% +RAM. Uh one other thing is I don't want + + + align:start position:0% +RAM. Uh one other thing is I don't want +to sort a bonic sequence. That wasn't my + + align:start position:0% +to sort a bonic sequence. That wasn't my + + + align:start position:0% +to sort a bonic sequence. That wasn't my +goal. My goal was to merge two sorted + + align:start position:0% +goal. My goal was to merge two sorted + + + align:start position:0% +goal. My goal was to merge two sorted +sequences. Okay, so I have two sorted + + align:start position:0% +sequences. Okay, so I have two sorted + + + align:start position:0% +sequences. Okay, so I have two sorted +sequences. I want to merge them. How do + + align:start position:0% +sequences. I want to merge them. How do + + + align:start position:0% +sequences. I want to merge them. How do +I make that + + align:start position:0% +I make that + + + align:start position:0% +I make that +bonic? I just flip. Okay, like that. I + + align:start position:0% +bonic? I just flip. Okay, like that. I + + + align:start position:0% +bonic? I just flip. Okay, like that. I +take this sequence and I reverse it. If + + align:start position:0% +take this sequence and I reverse it. If + + + align:start position:0% +take this sequence and I reverse it. If +I take a sorted sequence and reverse it, + + align:start position:0% +I take a sorted sequence and reverse it, + + + align:start position:0% +I take a sorted sequence and reverse it, +then it looks like this. And so then the + + align:start position:0% +then it looks like this. And so then the + + + align:start position:0% +then it looks like this. And so then the +result is botonic. Then I can use bonic + + align:start position:0% +result is botonic. Then I can use bonic + + + align:start position:0% +result is botonic. Then I can use bonic +sorting to sort it. So this is the merge + + align:start position:0% +sorting to sort it. So this is the merge + + + align:start position:0% +sorting to sort it. So this is the merge +problem and I've just reduced it to + + align:start position:0% +problem and I've just reduced it to + + + align:start position:0% +problem and I've just reduced it to +bonic + + align:start position:0% +bonic + + + align:start position:0% +bonic +sorting. Cool. + + align:start position:0% +sorting. Cool. + + + align:start position:0% +sorting. Cool. +except how do I reverse a + + align:start position:0% +except how do I reverse a + + + align:start position:0% +except how do I reverse a +sequence in log k time on a word ram. Uh + + align:start position:0% +sequence in log k time on a word ram. Uh + + + align:start position:0% +sequence in log k time on a word ram. Uh +cute + + align:start position:0% + + + + align:start position:0% + +trick. If I have a word and you know it + + align:start position:0% +trick. If I have a word and you know it + + + align:start position:0% +trick. If I have a word and you know it +has many items in it, that's our + + align:start position:0% +has many items in it, that's our + + + align:start position:0% +has many items in it, that's our +picture. That's our setup here. And I + + align:start position:0% +picture. That's our setup here. And I + + + align:start position:0% +picture. That's our setup here. And I +want to reverse it overall. What I'll do + + align:start position:0% +want to reverse it overall. What I'll do + + + align:start position:0% +want to reverse it overall. What I'll do +is cut it in half. Take all these guys, + + align:start position:0% +is cut it in half. Take all these guys, + + + align:start position:0% +is cut it in half. Take all these guys, +put them over here. Take all these guys, + + align:start position:0% +put them over here. Take all these guys, + + + align:start position:0% +put them over here. Take all these guys, +put them over here. So, I've got the + + align:start position:0% +put them over here. So, I've got the + + + align:start position:0% +put them over here. So, I've got the +right side, sorry, it's only + + align:start position:0% +right side, sorry, it's only + + + align:start position:0% +right side, sorry, it's only +four cells over here. I've got the left + + align:start position:0% +four cells over here. I've got the left + + + align:start position:0% +four cells over here. I've got the left +side over here. Then I recursively sort + + align:start position:0% +side over here. Then I recursively sort + + + align:start position:0% +side over here. Then I recursively sort +uh sorry, recursively reverse this + + align:start position:0% +uh sorry, recursively reverse this + + + align:start position:0% +uh sorry, recursively reverse this +sequence and recursively reverse this + + align:start position:0% +sequence and recursively reverse this + + + align:start position:0% +sequence and recursively reverse this +sequence. And then I have the reverse + + align:start position:0% +sequence. And then I have the reverse + + + align:start position:0% +sequence. And then I have the reverse +sequence. Right? This is a standard or + + align:start position:0% +sequence. Right? This is a standard or + + + align:start position:0% +sequence. Right? This is a standard or +you know one way to reverse items is to + + align:start position:0% +you know one way to reverse items is to + + + align:start position:0% +you know one way to reverse items is to +do the big part and then recursively + + align:start position:0% +do the big part and then recursively + + + align:start position:0% +do the big part and then recursively +reverse. then I will get I mean this is + + align:start position:0% +reverse. then I will get I mean this is + + + align:start position:0% +reverse. then I will get I mean this is +like uh you know AB reverse is equal to + + align:start position:0% +like uh you know AB reverse is equal to + + + align:start position:0% +like uh you know AB reverse is equal to +B reverse A reverse just a fun fact so + + align:start position:0% +B reverse A reverse just a fun fact so + + + align:start position:0% +B reverse A reverse just a fun fact so +we're implementing that uh now how do I + + align:start position:0% +we're implementing that uh now how do I + + + align:start position:0% +we're implementing that uh now how do I +do this well this is the thing I've been + + align:start position:0% +do this well this is the thing I've been + + + align:start position:0% +do this well this is the thing I've been +talking about uh over here you want to + + align:start position:0% +talking about uh over here you want to + + + align:start position:0% +talking about uh over here you want to +take the high part you just mask that + + align:start position:0% +take the high part you just mask that + + + align:start position:0% +take the high part you just mask that +part out shift it to the right you want + + align:start position:0% +part out shift it to the right you want + + + align:start position:0% +part out shift it to the right you want +to take the low part just mask that part + + align:start position:0% +to take the low part just mask that part + + + align:start position:0% +to take the low part just mask that part +out and so I can take each of these + + align:start position:0% +out and so I can take each of these + + + align:start position:0% +out and so I can take each of these +parts individually shift this one to the + + align:start position:0% +parts individually shift this one to the + + + align:start position:0% +parts individually shift this one to the +left shift this one to the right or them + + align:start position:0% +left shift this one to the right or them + + + align:start position:0% +left shift this one to the right or them +together and I've reversed So this takes + + align:start position:0% +together and I've reversed So this takes + + + align:start position:0% +together and I've reversed So this takes +constant time. This is recursion. But + + align:start position:0% +constant time. This is recursion. But + + + align:start position:0% +constant time. This is recursion. But +the total number of steps will be order + + align:start position:0% +the total number of steps will be order + + + align:start position:0% +the total number of steps will be order +log k which is exactly what I can + + align:start position:0% +log k which is exactly what I can + + + align:start position:0% +log k which is exactly what I can +afford. Okay. So that's how I do the + + align:start position:0% +afford. Okay. So that's how I do the + + + align:start position:0% +afford. Okay. So that's how I do the +reverse reverse part. So if I want to + + align:start position:0% +reverse reverse part. So if I want to + + + align:start position:0% +reverse reverse part. So if I want to +merge now I have a bonic sequence. Last + + align:start position:0% +merge now I have a bonic sequence. Last + + + align:start position:0% +merge now I have a bonic sequence. Last +thing to do is how do I do this bonic + + align:start position:0% + + + + align:start position:0% + +comparison in constant time. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +do + + align:start position:0% +do + + + align:start position:0% +do +this. So that's next + + align:start position:0% + + + + align:start position:0% + +page. Here's a quick + + align:start position:0% + + + + align:start position:0% + +sketch. Going to try to draw the generic + + align:start position:0% +sketch. Going to try to draw the generic + + + align:start position:0% +sketch. Going to try to draw the generic +picture. So the generic picture is I + + align:start position:0% +picture. So the generic picture is I + + + align:start position:0% +picture. So the generic picture is I +have this this thing which I call A and + + align:start position:0% +have this this thing which I call A and + + + align:start position:0% +have this this thing which I call A and +this thing which I call B. And we + + align:start position:0% +this thing which I call B. And we + + + align:start position:0% +this thing which I call B. And we +basically want to compare corresponding + + align:start position:0% +basically want to compare corresponding + + + align:start position:0% +basically want to compare corresponding +items in A and B. Though, in fact, + + align:start position:0% +items in A and B. Though, in fact, + + + align:start position:0% +items in A and B. Though, in fact, +there's another A over here and another + + align:start position:0% +there's another A over here and another + + + align:start position:0% +there's another A over here and another +B over here. In general, there are many + + align:start position:0% +B over here. In general, there are many + + + align:start position:0% +B over here. In general, there are many +A's, many B's, but they appear in this + + align:start position:0% +A's, many B's, but they appear in this + + + align:start position:0% +A's, many B's, but they appear in this +nice periodic pattern. And so, I'm just + + align:start position:0% +nice periodic pattern. And so, I'm just + + + align:start position:0% +nice periodic pattern. And so, I'm just +just going to look at one AB pair, but + + align:start position:0% +just going to look at one AB pair, but + + + align:start position:0% +just going to look at one AB pair, but +it's going to simultaneously work for + + align:start position:0% +it's going to simultaneously work for + + + align:start position:0% +it's going to simultaneously work for +all of them with the same operations. + + align:start position:0% +all of them with the same operations. + + + align:start position:0% +all of them with the same operations. +So, that's the dot dot dot here. There's + + align:start position:0% +So, that's the dot dot dot here. There's + + + align:start position:0% +So, that's the dot dot dot here. There's +another A and then another B and another + + align:start position:0% +another A and then another B and another + + + align:start position:0% +another A and then another B and another +A and another B. So, what do I do? First + + align:start position:0% +A and another B. So, what do I do? First + + + align:start position:0% +A and another B. So, what do I do? First +thing I do is make one a a one a a one + + align:start position:0% +thing I do is make one a a one a a one + + + align:start position:0% +thing I do is make one a a one a a one +aa. In other words, I add in these one + + align:start position:0% +aa. In other words, I add in these one + + + align:start position:0% +aa. In other words, I add in these one +bits. Remember, we had zeros + + align:start position:0% +bits. Remember, we had zeros + + + align:start position:0% +bits. Remember, we had zeros +there hanging out. That was when we're + + align:start position:0% +there hanging out. That was when we're + + + align:start position:0% +there hanging out. That was when we're +going to use them. So, I set them all to + + align:start position:0% +going to use them. So, I set them all to + + + align:start position:0% +going to use them. So, I set them all to +ones in the A list. I take the B list. I + + align:start position:0% +ones in the A list. I take the B list. I + + + align:start position:0% +ones in the A list. I take the B list. I +just shift it over and leave them as + + align:start position:0% + + + + align:start position:0% + +zeros. Okay, time for bit tricks. All + + align:start position:0% +zeros. Okay, time for bit tricks. All + + + align:start position:0% +zeros. Okay, time for bit tricks. All +right. Then I take this number, I + + align:start position:0% +right. Then I take this number, I + + + align:start position:0% +right. Then I take this number, I +subtract it from this number. What do I + + align:start position:0% +subtract it from this number. What do I + + + align:start position:0% +subtract it from this number. What do I +get? I get zeros or ones uh for the + + align:start position:0% +get? I get zeros or ones uh for the + + + align:start position:0% +get? I get zeros or ones uh for the +whether this bit got borrowed, which + + align:start position:0% +whether this bit got borrowed, which + + + align:start position:0% +whether this bit got borrowed, which +tells me whether little a is bigger than + + align:start position:0% +tells me whether little a is bigger than + + + align:start position:0% +tells me whether little a is bigger than +little b. Then I get some junk. Then I + + align:start position:0% +little b. Then I get some junk. Then I + + + align:start position:0% +little b. Then I get some junk. Then I +get 01 junk. So on 01 junk. Sure. So + + align:start position:0% +get 01 junk. So on 01 junk. Sure. So + + + align:start position:0% +get 01 junk. So on 01 junk. Sure. So +zero corresponds to a being smaller than + + align:start position:0% +zero corresponds to a being smaller than + + + align:start position:0% +zero corresponds to a being smaller than +b and one corresponds to the reverse. + + align:start position:0% +b and one corresponds to the reverse. + + + align:start position:0% +b and one corresponds to the reverse. +Okay. Whatever. Uh then I do my usual + + align:start position:0% +Okay. Whatever. Uh then I do my usual + + + align:start position:0% +Okay. Whatever. Uh then I do my usual +masking just the 01 bits. Then there's + + align:start position:0% +masking just the 01 bits. Then there's + + + align:start position:0% +masking just the 01 bits. Then there's +some + + align:start position:0% + + + + align:start position:0% + +zeros. Okay, here's a new trick which we + + align:start position:0% +zeros. Okay, here's a new trick which we + + + align:start position:0% +zeros. Okay, here's a new trick which we +haven't seen yet. I'm going to shift + + align:start position:0% +haven't seen yet. I'm going to shift + + + align:start position:0% +haven't seen yet. I'm going to shift +this to the right by two or in general + + align:start position:0% +this to the right by two or in general + + + align:start position:0% +this to the right by two or in general +by the size of those items. So now I + + align:start position:0% +by the size of those items. So now I + + + align:start position:0% +by the size of those items. So now I +have 01 here, 01 here, and 01 here. Each + + align:start position:0% +have 01 here, 01 here, and 01 here. Each + + + align:start position:0% +have 01 here, 01 here, and 01 here. Each +of these bits might be different. So I + + align:start position:0% +of these bits might be different. So I + + + align:start position:0% +of these bits might be different. So I +take this, shift it to the right. Now I + + align:start position:0% +take this, shift it to the right. Now I + + + align:start position:0% +take this, shift it to the right. Now I +subtract. what this gives + + align:start position:0% +subtract. what this gives + + + align:start position:0% +subtract. what this gives +me. So I'm taking one 0 0 minus one. + + align:start position:0% +me. So I'm taking one 0 0 minus one. + + + align:start position:0% +me. So I'm taking one 0 0 minus one. +What I get is 0 one one one. Okay, in + + align:start position:0% +What I get is 0 one one one. Okay, in + + + align:start position:0% +What I get is 0 one one one. Okay, in +this case there's just two bits except + + align:start position:0% +this case there's just two bits except + + + align:start position:0% +this case there's just two bits except +it's not one one. It's either uh + + align:start position:0% +it's not one one. It's either uh + + + align:start position:0% +it's not one one. It's either uh +0. Get it right. Either 0 0 or one one. + + align:start position:0% +0. Get it right. Either 0 0 or one one. + + + align:start position:0% +0. Get it right. Either 0 0 or one one. +And then we have here zero and then 0 0 + + align:start position:0% +And then we have here zero and then 0 0 + + + align:start position:0% +And then we have here zero and then 0 0 +or one + + align:start position:0% +or one + + + align:start position:0% +or one +one. Okay. And so on. So now these are + + align:start position:0% +one. Okay. And so on. So now these are + + + align:start position:0% +one. Okay. And so on. So now these are +masks. + + align:start position:0% +masks. + + + align:start position:0% +masks. +The zeros correspond to when the A's + + align:start position:0% +The zeros correspond to when the A's + + + align:start position:0% +The zeros correspond to when the A's +were smaller. The ones correspond to + + align:start position:0% +were smaller. The ones correspond to + + + align:start position:0% +were smaller. The ones correspond to +when the B's are smaller. So if I take + + align:start position:0% +when the B's are smaller. So if I take + + + align:start position:0% +when the B's are smaller. So if I take +this anded with this, I get the large + + align:start position:0% +this anded with this, I get the large + + + align:start position:0% +this anded with this, I get the large +B's. If I take this anded with this, I + + align:start position:0% +B's. If I take this anded with this, I + + + align:start position:0% +B's. If I take this anded with this, I +get the small A's or one of some of + + align:start position:0% +get the small A's or one of some of + + + align:start position:0% +get the small A's or one of some of +those + + align:start position:0% +those + + + align:start position:0% +those +combinations. Okay. The point is I take + + align:start position:0% +combinations. Okay. The point is I take + + + align:start position:0% +combinations. Okay. The point is I take +Yeah, I think here I get + + align:start position:0% +Yeah, I think here I get + + + align:start position:0% +Yeah, I think here I get +the small A's. + + align:start position:0% + + + + align:start position:0% + +And then if I take this thing and negate + + align:start position:0% +And then if I take this thing and negate + + + align:start position:0% +And then if I take this thing and negate +it and then + + align:start position:0% +it and then + + + align:start position:0% +it and then +mask and mask it with this, I get the + + align:start position:0% +mask and mask it with this, I get the + + + align:start position:0% +mask and mask it with this, I get the +small + + align:start position:0% + + + + align:start position:0% + +B's. And then I take this thing. I ran + + align:start position:0% +B's. And then I take this thing. I ran + + + align:start position:0% +B's. And then I take this thing. I ran +out of room. So we've got small + + align:start position:0% +out of room. So we've got small + + + align:start position:0% +out of room. So we've got small +A's, small B's. + + align:start position:0% + + + + align:start position:0% + +I take this thing, I shift it over. So I + + align:start position:0% +I take this thing, I shift it over. So I + + + align:start position:0% +I take this thing, I shift it over. So I +have small B's + + align:start position:0% + + + + align:start position:0% + +here. And then I or these together, I + + align:start position:0% +here. And then I or these together, I + + + align:start position:0% +here. And then I or these together, I +get all the + + align:start position:0% +get all the + + + align:start position:0% +get all the +smalls. Okay, these are designed to + + align:start position:0% +smalls. Okay, these are designed to + + + align:start position:0% +smalls. Okay, these are designed to +never conflict because I took the + + align:start position:0% +never conflict because I took the + + + align:start position:0% +never conflict because I took the +inversion here. So I get the smaller of + + align:start position:0% +inversion here. So I get the smaller of + + + align:start position:0% +inversion here. So I get the smaller of +the A's, smaller of the B's. So now I've + + align:start position:0% +the A's, smaller of the B's. So now I've + + + align:start position:0% +the A's, smaller of the B's. So now I've +I put the sorted thing, the smaller + + align:start position:0% +I put the sorted thing, the smaller + + + align:start position:0% +I put the sorted thing, the smaller +things in the right order. I do the + + align:start position:0% +things in the right order. I do the + + + align:start position:0% +things in the right order. I do the +exactly the same procedure negated. and + + align:start position:0% +exactly the same procedure negated. and + + + align:start position:0% +exactly the same procedure negated. and +I get the + + align:start position:0% + + + + align:start position:0% + +largest. Okay. Then I or these together + + align:start position:0% +largest. Okay. Then I or these together + + + align:start position:0% +largest. Okay. Then I or these together +and I get + + align:start position:0% + + + + align:start position:0% + +sorted. Well, not sorted. I get whatever + + align:start position:0% +sorted. Well, not sorted. I get whatever + + + align:start position:0% +sorted. Well, not sorted. I get whatever +bonic sort would have done, right? It's + + align:start position:0% +bonic sort would have done, right? It's + + + align:start position:0% +bonic sort would have done, right? It's +doing these pair-wise comparisons by + + align:start position:0% +doing these pair-wise comparisons by + + + align:start position:0% +doing these pair-wise comparisons by +doing this shift and it's putting things + + align:start position:0% +doing this shift and it's putting things + + + align:start position:0% +doing this shift and it's putting things +in the right order. Taking the small + + align:start position:0% +in the right order. Taking the small + + + align:start position:0% +in the right order. Taking the small +ones always end up on the left. The + + align:start position:0% +ones always end up on the left. The + + + align:start position:0% +ones always end up on the left. The +large ones always end up on the right. + + align:start position:0% +large ones always end up on the right. + + + align:start position:0% +large ones always end up on the right. +That's the definition of the operation + + align:start position:0% +That's the definition of the operation + + + align:start position:0% +That's the definition of the operation +we want to do or + + align:start position:0% +we want to do or + + + align:start position:0% +we want to do or +botonic operated. And because we're just + + align:start position:0% +botonic operated. And because we're just + + + align:start position:0% +botonic operated. And because we're just +doing shifts and subtractions and all + + align:start position:0% +doing shifts and subtractions and all + + + align:start position:0% +doing shifts and subtractions and all +these things, it works. Even though + + align:start position:0% +these things, it works. Even though + + + align:start position:0% +these things, it works. Even though +there's not just one AB pair, but + + align:start position:0% +there's not just one AB pair, but + + + align:start position:0% +there's not just one AB pair, but +there's a whole bunch of AB pairs, they + + align:start position:0% +there's a whole bunch of AB pairs, they + + + align:start position:0% +there's a whole bunch of AB pairs, they +will all be shifted and computed and + + align:start position:0% +will all be shifted and computed and + + + align:start position:0% +will all be shifted and computed and +sorted together. And so a little hard to + + align:start position:0% +sorted together. And so a little hard to + + + align:start position:0% +sorted together. And so a little hard to +visualize, but this will do one bonic + + align:start position:0% +visualize, but this will do one bonic + + + align:start position:0% +visualize, but this will do one bonic +operation and a constant number of word + + align:start position:0% +operation and a constant number of word + + + align:start position:0% +operation and a constant number of word +RAM operations. And so you pop out all + + align:start position:0% +RAM operations. And so you pop out all + + + align:start position:0% +RAM operations. And so you pop out all +these stacks. This gives us a merger + + align:start position:0% +these stacks. This gives us a merger + + + align:start position:0% +these stacks. This gives us a merger +that gives us pack sorting. And with + + align:start position:0% +that gives us pack sorting. And with + + + align:start position:0% +that gives us pack sorting. And with +pack sorting, we get uh signature + + align:start position:0% +pack sorting, we get uh signature + + + align:start position:0% +pack sorting, we get uh signature +sorting. Easy, right? + + align:start position:0% +sorting. Easy, right? + + + align:start position:0% +sorting. Easy, right? +All right, that's probably one of the + + align:start position:0% +All right, that's probably one of the + + + align:start position:0% +All right, that's probably one of the +most complicated algorithms we'll see in + + align:start position:0% +most complicated algorithms we'll see in + + + align:start position:0% +most complicated algorithms we'll see in +this class. But from that, you get a + + align:start position:0% +this class. But from that, you get a + + + align:start position:0% +this class. But from that, you get a +priority Q that runs in constant time + + align:start position:0% +priority Q that runs in constant time + + + align:start position:0% +priority Q that runs in constant time +provided W is a little bigger than log + + align:start position:0% +provided W is a little bigger than log + + + align:start position:0% +provided W is a little bigger than log +square M. Boom. \ No newline at end of file diff --git a/q4mwO2qS2z4.txt b/q4mwO2qS2z4.txt new file mode 100644 index 0000000000000000000000000000000000000000..b833fe908c521c0e7c0cbdd65faa786b5a46b436 --- /dev/null +++ b/q4mwO2qS2z4.txt @@ -0,0 +1,13144 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mmit.edu. Uh so today we're going to + + align:start position:0% +ocw.mmit.edu. Uh so today we're going to + + + align:start position:0% +ocw.mmit.edu. Uh so today we're going to +talk about the probability that a random + + align:start position:0% +talk about the probability that a random + + + align:start position:0% +talk about the probability that a random +variable deviates by a certain amount + + align:start position:0% +variable deviates by a certain amount + + + align:start position:0% +variable deviates by a certain amount +from its expectation. Now we've seen + + align:start position:0% +from its expectation. Now we've seen + + + align:start position:0% +from its expectation. Now we've seen +examples where a random variable is very + + align:start position:0% +examples where a random variable is very + + + align:start position:0% +examples where a random variable is very +unlikely to deviate much from its + + align:start position:0% +unlikely to deviate much from its + + + align:start position:0% +unlikely to deviate much from its +expectation. For example, if you flip a + + align:start position:0% +expectation. For example, if you flip a + + + align:start position:0% +expectation. For example, if you flip a +100 mutually independent fair coins, + + align:start position:0% +100 mutually independent fair coins, + + + align:start position:0% +100 mutually independent fair coins, +you're very likely to wind up with close + + align:start position:0% +you're very likely to wind up with close + + + align:start position:0% +you're very likely to wind up with close +to 50 heads, very unlikely to wind up + + align:start position:0% +to 50 heads, very unlikely to wind up + + + align:start position:0% +to 50 heads, very unlikely to wind up +with 25 or fewer heads, for example. + + align:start position:0% +with 25 or fewer heads, for example. + + + align:start position:0% +with 25 or fewer heads, for example. +We've also seen examples of + + align:start position:0% +We've also seen examples of + + + align:start position:0% +We've also seen examples of +distributions where you are very likely + + align:start position:0% +distributions where you are very likely + + + align:start position:0% +distributions where you are very likely +to be far from your expectation. For + + align:start position:0% +to be far from your expectation. For + + + align:start position:0% +to be far from your expectation. For +example, that problem where we had the + + align:start position:0% +example, that problem where we had the + + + align:start position:0% +example, that problem where we had the +communications channel and we were + + align:start position:0% +communications channel and we were + + + align:start position:0% +communications channel and we were +measuring the latency of a packet + + align:start position:0% +measuring the latency of a packet + + + align:start position:0% +measuring the latency of a packet +crossing the channel. There most of the + + align:start position:0% +crossing the channel. There most of the + + + align:start position:0% +crossing the channel. There most of the +time your latency would be 10 + + align:start position:0% +time your latency would be 10 + + + align:start position:0% +time your latency would be 10 +milliseconds but the expected latency + + align:start position:0% +milliseconds but the expected latency + + + align:start position:0% +milliseconds but the expected latency +was infinite. So you're very likely to + + align:start position:0% +was infinite. So you're very likely to + + + align:start position:0% +was infinite. So you're very likely to +deviate a lot from your expectation in + + align:start position:0% +deviate a lot from your expectation in + + + align:start position:0% +deviate a lot from your expectation in +that case. Last time we looked at the + + align:start position:0% +that case. Last time we looked at the + + + align:start position:0% +that case. Last time we looked at the +variance and we saw how that gave us + + align:start position:0% +variance and we saw how that gave us + + + align:start position:0% +variance and we saw how that gave us +some feel for the likelihood of being + + align:start position:0% +some feel for the likelihood of being + + + align:start position:0% +some feel for the likelihood of being +far from the expectation. High variance + + align:start position:0% +far from the expectation. High variance + + + align:start position:0% +far from the expectation. High variance +meaning you're more likely to deviate + + align:start position:0% +meaning you're more likely to deviate + + + align:start position:0% +meaning you're more likely to deviate +from the expectation. Today we're going + + align:start position:0% +from the expectation. Today we're going + + + align:start position:0% +from the expectation. Today we're going +to develop specific tools for bounding + + align:start position:0% +to develop specific tools for bounding + + + align:start position:0% +to develop specific tools for bounding +or limiting the probability you deviate + + align:start position:0% +or limiting the probability you deviate + + + align:start position:0% +or limiting the probability you deviate +by a specified amount from the + + align:start position:0% +by a specified amount from the + + + align:start position:0% +by a specified amount from the +expectation. And the first tool is known + + align:start position:0% +expectation. And the first tool is known + + + align:start position:0% +expectation. And the first tool is known +as Marov's theorem. Marov's theorem says + + align:start position:0% +as Marov's theorem. Marov's theorem says + + + align:start position:0% +as Marov's theorem. Marov's theorem says +that if the random variable is always + + align:start position:0% +that if the random variable is always + + + align:start position:0% +that if the random variable is always +non- + + align:start position:0% +non- + + + align:start position:0% +non- +negative then it is unlikely to greatly + + align:start position:0% +negative then it is unlikely to greatly + + + align:start position:0% +negative then it is unlikely to greatly +exceed its expectation in + + align:start position:0% + + + + align:start position:0% + +particular if + + align:start position:0% +particular if + + + align:start position:0% +particular if +r is a non- negative + + align:start position:0% + + + + align:start position:0% + +random + + align:start position:0% + + + + align:start position:0% + +variable. Then for all X bigger than + + align:start position:0% + + + + align:start position:0% + +zero, the probability that R is at least + + align:start position:0% +zero, the probability that R is at least + + + align:start position:0% +zero, the probability that R is at least +X is at most the expected value of R, + + align:start position:0% +X is at most the expected value of R, + + + align:start position:0% +X is at most the expected value of R, +the mean, divided by + + align:start position:0% +the mean, divided by + + + align:start position:0% +the mean, divided by +X. All right? All right. So in other + + align:start position:0% +X. All right? All right. So in other + + + align:start position:0% +X. All right? All right. So in other +words, if R is never never + + align:start position:0% +words, if R is never never + + + align:start position:0% +words, if R is never never +negative and for example, say the + + align:start position:0% +negative and for example, say the + + + align:start position:0% +negative and for example, say the +expected value is + + align:start position:0% +expected value is + + + align:start position:0% +expected value is +small, then the probability R is large + + align:start position:0% +small, then the probability R is large + + + align:start position:0% +small, then the probability R is large +will be a small number because I have a + + align:start position:0% +will be a small number because I have a + + + align:start position:0% +will be a small number because I have a +small number over a big number. All + + align:start position:0% +small number over a big number. All + + + align:start position:0% +small number over a big number. All +right? So it says that you are unlikely + + align:start position:0% +right? So it says that you are unlikely + + + align:start position:0% +right? So it says that you are unlikely +to greatly exceed the expected value. So + + align:start position:0% +to greatly exceed the expected value. So + + + align:start position:0% +to greatly exceed the expected value. So +let's prove + + align:start position:0% + + + + align:start position:0% + +that. Now from the theorem of total + + align:start position:0% +that. Now from the theorem of total + + + align:start position:0% +that. Now from the theorem of total +expectation that you did in recitation + + align:start position:0% +expectation that you did in recitation + + + align:start position:0% +expectation that you did in recitation +last week, we can compute the expected + + align:start position:0% +last week, we can compute the expected + + + align:start position:0% +last week, we can compute the expected +value of R by looking at two + + align:start position:0% + + + + align:start position:0% + +cases. the case when r is at least + + align:start position:0% + + + + align:start position:0% + +x and the case when r is less than + + align:start position:0% + + + + align:start position:0% + +x right that's from the theorem of total + + align:start position:0% +x right that's from the theorem of total + + + align:start position:0% +x right that's from the theorem of total +expectation I look at two cases r is + + align:start position:0% +expectation I look at two cases r is + + + align:start position:0% +expectation I look at two cases r is +bigger than x take the expect expected + + align:start position:0% +bigger than x take the expect expected + + + align:start position:0% +bigger than x take the expect expected +value there times the probability of + + align:start position:0% +value there times the probability of + + + align:start position:0% +value there times the probability of +this case happening plus the case when r + + align:start position:0% +this case happening plus the case when r + + + align:start position:0% +this case happening plus the case when r +is less than + + align:start position:0% +is less than + + + align:start position:0% +is less than +x. Okay. + + align:start position:0% +x. Okay. + + + align:start position:0% +x. Okay. +Now since r is non- negative this is at + + align:start position:0% +Now since r is non- negative this is at + + + align:start position:0% +Now since r is non- negative this is at +least + + align:start position:0% +least + + + align:start position:0% +least +zero. r can't ever be negative. So the + + align:start position:0% +zero. r can't ever be negative. So the + + + align:start position:0% +zero. r can't ever be negative. So the +expectation can't be negative. A + + align:start position:0% +expectation can't be negative. A + + + align:start position:0% +expectation can't be negative. A +probability can't be negative. So this + + align:start position:0% +probability can't be negative. So this + + + align:start position:0% +probability can't be negative. So this +this is at least zero. + + align:start position:0% +this is at least zero. + + + align:start position:0% +this is at least zero. +And this is trivially at least + + align:start position:0% +And this is trivially at least + + + align:start position:0% +And this is trivially at least +x because I'm taking the expected value + + align:start position:0% +x because I'm taking the expected value + + + align:start position:0% +x because I'm taking the expected value +of r in the case when r is at least x. + + align:start position:0% +of r in the case when r is at least x. + + + align:start position:0% +of r in the case when r is at least x. +So all r is always at least x. So it's + + align:start position:0% +So all r is always at least x. So it's + + + align:start position:0% +So all r is always at least x. So it's +in this case. So it's expected value is + + align:start position:0% +in this case. So it's expected value is + + + align:start position:0% +in this case. So it's expected value is +at least + + align:start position:0% +at least + + + align:start position:0% +at least +x. Okay. So that means that the expected + + align:start position:0% +x. Okay. So that means that the expected + + + align:start position:0% +x. Okay. So that means that the expected +value of r is at least x times the + + align:start position:0% +value of r is at least x times the + + + align:start position:0% +value of r is at least x times the +probability r is greater than x. r is + + align:start position:0% +probability r is greater than x. r is + + + align:start position:0% +probability r is greater than x. r is +greater than equal to x. + + align:start position:0% +greater than equal to x. + + + align:start position:0% +greater than equal to x. +And now I can get the theorem by just + + align:start position:0% +And now I can get the theorem by just + + + align:start position:0% +And now I can get the theorem by just +dividing by + + align:start position:0% + + + + align:start position:0% + +x. I'm less than or equal to the + + align:start position:0% +x. I'm less than or equal to the + + + align:start position:0% +x. I'm less than or equal to the +expected value of + + align:start position:0% +expected value of + + + align:start position:0% +expected value of +r / + + align:start position:0% +r / + + + align:start position:0% +r / +x. Right? So it's a very easy theorem to + + align:start position:0% +x. Right? So it's a very easy theorem to + + + align:start position:0% +x. Right? So it's a very easy theorem to +prove, but it's going to have amazing + + align:start position:0% +prove, but it's going to have amazing + + + align:start position:0% +prove, but it's going to have amazing +consequences that we're going to build + + align:start position:0% +consequences that we're going to build + + + align:start position:0% +consequences that we're going to build +up through a series of of results today. + + align:start position:0% +up through a series of of results today. + + + align:start position:0% +up through a series of of results today. +Any questions about Marov's theorem and + + align:start position:0% +Any questions about Marov's theorem and + + + align:start position:0% +Any questions about Marov's theorem and +the + + align:start position:0% + + + + align:start position:0% + +proof? All right. There's a simple + + align:start position:0% +proof? All right. There's a simple + + + align:start position:0% +proof? All right. There's a simple +correlary which is + + align:start position:0% + + + + align:start position:0% + +useful again. If R is a non- + + align:start position:0% +useful again. If R is a non- + + + align:start position:0% +useful again. If R is a non- +negative random + + align:start position:0% +negative random + + + align:start position:0% +negative random +variable, then for all C bigger than + + align:start position:0% +variable, then for all C bigger than + + + align:start position:0% +variable, then for all C bigger than +zero, the probability that R is at least + + align:start position:0% +zero, the probability that R is at least + + + align:start position:0% +zero, the probability that R is at least +C times its expected + + align:start position:0% +C times its expected + + + align:start position:0% +C times its expected +value is at most one and + + align:start position:0% +value is at most one and + + + align:start position:0% +value is at most one and +C. So the probability you're twice your + + align:start position:0% +C. So the probability you're twice your + + + align:start position:0% +C. So the probability you're twice your +expected value is at most a half. + + align:start position:0% +expected value is at most a half. + + + align:start position:0% +expected value is at most a half. +The proof is very + + align:start position:0% +The proof is very + + + align:start position:0% +The proof is very +easy. We just set x to be equal to c + + align:start position:0% +easy. We just set x to be equal to c + + + align:start position:0% +easy. We just set x to be equal to c +times the expected value of + + align:start position:0% +times the expected value of + + + align:start position:0% +times the expected value of +r in the + + align:start position:0% + + + + align:start position:0% + +theorem. So I just plug in + + align:start position:0% +theorem. So I just plug in + + + align:start position:0% +theorem. So I just plug in +x is c times the expected value of + + align:start position:0% +x is c times the expected value of + + + align:start position:0% +x is c times the expected value of +r. All right? And I get expected value + + align:start position:0% +r. All right? And I get expected value + + + align:start position:0% +r. All right? And I get expected value +of r over c times the expected value of + + align:start position:0% +of r over c times the expected value of + + + align:start position:0% +of r over c times the expected value of +r, which is 1 over c. So you just plug + + align:start position:0% +r, which is 1 over c. So you just plug + + + align:start position:0% +r, which is 1 over c. So you just plug +in that value in Marov's theorem and it + + align:start position:0% +in that value in Marov's theorem and it + + + align:start position:0% +in that value in Marov's theorem and it +comes + + align:start position:0% +comes + + + align:start position:0% +comes +out. All right, let's do some examples. + + align:start position:0% + + + + align:start position:0% + +Let's let R be the + + align:start position:0% + + + + align:start position:0% + +weight of a random person uniformly + + align:start position:0% + + + + align:start position:0% + +selected and + + align:start position:0% +selected and + + + align:start position:0% +selected and +suppose I don't know what the + + align:start position:0% +suppose I don't know what the + + + align:start position:0% +suppose I don't know what the +distribution of weights is in the + + align:start position:0% +distribution of weights is in the + + + align:start position:0% +distribution of weights is in the +country but suppose that the expected + + align:start position:0% +country but suppose that the expected + + + align:start position:0% +country but suppose that the expected +value of R which is the average weight + + align:start position:0% +value of R which is the average weight + + + align:start position:0% +value of R which is the average weight +is 100 + + align:start position:0% +is 100 + + + align:start position:0% +is 100 +pounds all right so that a by average + + align:start position:0% +pounds all right so that a by average + + + align:start position:0% +pounds all right so that a by average +overall people their weight is 100 + + align:start position:0% +overall people their weight is 100 + + + align:start position:0% +overall people their weight is 100 +pounds and suppose I want to know the + + align:start position:0% +pounds and suppose I want to know the + + + align:start position:0% +pounds and suppose I want to know the +probability that the random person + + align:start position:0% +probability that the random person + + + align:start position:0% +probability that the random person +weighs at least 200 + + align:start position:0% + + + + align:start position:0% + +lb. What can I say about that + + align:start position:0% + + + + align:start position:0% + +probability? Do I know it + + align:start position:0% + + + + align:start position:0% + +exactly? I don't think so because I + + align:start position:0% +exactly? I don't think so because I + + + align:start position:0% +exactly? I don't think so because I +don't know what the distribution of + + align:start position:0% +don't know what the distribution of + + + align:start position:0% +don't know what the distribution of +weights is. But I can still get an upper + + align:start position:0% +weights is. But I can still get an upper + + + align:start position:0% +weights is. But I can still get an upper +bound on this + + align:start position:0% +bound on this + + + align:start position:0% +bound on this +probability. What bound can I get on the + + align:start position:0% +probability. What bound can I get on the + + + align:start position:0% +probability. What bound can I get on the +probability that a random person has a + + align:start position:0% +probability that a random person has a + + + align:start position:0% +probability that a random person has a +weight of 200 given the facts here? + + align:start position:0% +weight of 200 given the facts here? + + + align:start position:0% +weight of 200 given the facts here? +Yeah. + + align:start position:0% + + + + align:start position:0% + +Yes. Okay. Well, it's it's 100 over 200, + + align:start position:0% +Yes. Okay. Well, it's it's 100 over 200, + + + align:start position:0% +Yes. Okay. Well, it's it's 100 over 200, +right? It's at most the expected value + + align:start position:0% +right? It's at most the expected value + + + align:start position:0% +right? It's at most the expected value +which is 100 over the x which is 200 and + + align:start position:0% +which is 100 over the x which is 200 and + + + align:start position:0% +which is 100 over the x which is 200 and +that's equal to a half. + + align:start position:0% +that's equal to a half. + + + align:start position:0% +that's equal to a half. +So the probability the random person + + align:start position:0% +So the probability the random person + + + align:start position:0% +So the probability the random person +weighs 200 lb or more is at most a half. + + align:start position:0% +weighs 200 lb or more is at most a half. + + + align:start position:0% +weighs 200 lb or more is at most a half. +Or I could plug it in here. The expected + + align:start position:0% +Or I could plug it in here. The expected + + + align:start position:0% +Or I could plug it in here. The expected +value is + + align:start position:0% +value is + + + align:start position:0% +value is +100. 200 is twice that. So C would be + + align:start position:0% +100. 200 is twice that. So C would be + + + align:start position:0% +100. 200 is twice that. So C would be +two here. So the probability of being + + align:start position:0% +two here. So the probability of being + + + align:start position:0% +two here. So the probability of being +twice the expectation is at most a half. + + align:start position:0% +twice the expectation is at most a half. + + + align:start position:0% +twice the expectation is at most a half. +Now of course I'm using the fact that + + align:start position:0% +Now of course I'm using the fact that + + + align:start position:0% +Now of course I'm using the fact that +weight is never negative. That's + + align:start position:0% +weight is never negative. That's + + + align:start position:0% +weight is never negative. That's +obviously true but is is implicitly + + align:start position:0% +obviously true but is is implicitly + + + align:start position:0% +obviously true but is is implicitly +being used here. + + align:start position:0% + + + + align:start position:0% + +So, what fraction of the population + + align:start position:0% +So, what fraction of the population + + + align:start position:0% +So, what fraction of the population +now can weigh at least 200 lb? Slightly + + align:start position:0% +now can weigh at least 200 lb? Slightly + + + align:start position:0% +now can weigh at least 200 lb? Slightly +different question. Before I ask you, I + + align:start position:0% +different question. Before I ask you, I + + + align:start position:0% +different question. Before I ask you, I +take a random + + align:start position:0% +take a random + + + align:start position:0% +take a random +person, what's the probability they + + align:start position:0% +person, what's the probability they + + + align:start position:0% +person, what's the probability they +weigh at least 200 lb? Now, I'm + + align:start position:0% +weigh at least 200 lb? Now, I'm + + + align:start position:0% +weigh at least 200 lb? Now, I'm +asking what fraction of the population + + align:start position:0% +asking what fraction of the population + + + align:start position:0% +asking what fraction of the population +can weigh at least 200 + + align:start position:0% + + + + align:start position:0% + +lb if the average is 100. + + align:start position:0% + + + + align:start position:0% + +What is it? + + align:start position:0% +What is it? + + + align:start position:0% +What is it? +Yeah. At most one half. At most a half. + + align:start position:0% +Yeah. At most one half. At most a half. + + + align:start position:0% +Yeah. At most one half. At most a half. +In fact, it's the same + + align:start position:0% +In fact, it's the same + + + align:start position:0% +In fact, it's the same +answer. And you know + + align:start position:0% +answer. And you know + + + align:start position:0% +answer. And you know +why can why can't everybody weigh 200 + + align:start position:0% +why can why can't everybody weigh 200 + + + align:start position:0% +why can why can't everybody weigh 200 +lb? So it would be all the population + + align:start position:0% +lb? So it would be all the population + + + align:start position:0% +lb? So it would be all the population +weighs 200 pounds at least. + + align:start position:0% +weighs 200 pounds at least. + + + align:start position:0% +weighs 200 pounds at least. +Probability be one and that can't + + align:start position:0% +Probability be one and that can't + + + align:start position:0% +Probability be one and that can't +happen. And in fact, you know, + + align:start position:0% +happen. And in fact, you know, + + + align:start position:0% +happen. And in fact, you know, +intuitively, if everybody weighs at + + align:start position:0% +intuitively, if everybody weighs at + + + align:start position:0% +intuitively, if everybody weighs at +least 200 pounds, the average is going + + align:start position:0% +least 200 pounds, the average is going + + + align:start position:0% +least 200 pounds, the average is going +to be at least 200 pounds. And we said + + align:start position:0% +to be at least 200 pounds. And we said + + + align:start position:0% +to be at least 200 pounds. And we said +the average was + + align:start position:0% +the average was + + + align:start position:0% +the average was +100. Okay? And this is illustrating this + + align:start position:0% +100. Okay? And this is illustrating this + + + align:start position:0% +100. Okay? And this is illustrating this +interesting thing that probability + + align:start position:0% +interesting thing that probability + + + align:start position:0% +interesting thing that probability +implies things about averages and + + align:start position:0% +implies things about averages and + + + align:start position:0% +implies things about averages and +fractions because it's really the same + + align:start position:0% +fractions because it's really the same + + + align:start position:0% +fractions because it's really the same +thing in disguise. The connection is if + + align:start position:0% +thing in disguise. The connection is if + + + align:start position:0% +thing in disguise. The connection is if +I've got a bunch of people say in the + + align:start position:0% +I've got a bunch of people say in the + + + align:start position:0% +I've got a bunch of people say in the +country, I can convert a fraction that + + align:start position:0% +country, I can convert a fraction that + + + align:start position:0% +country, I can convert a fraction that +have some property into a probability by + + align:start position:0% +have some property into a probability by + + + align:start position:0% +have some property into a probability by +just selecting the random person. Yeah. + + align:start position:0% + + + + align:start position:0% + +Um the no the variance could be very big + + align:start position:0% +Um the no the variance could be very big + + + align:start position:0% +Um the no the variance could be very big +because I might have a person that + + align:start position:0% +because I might have a person that + + + align:start position:0% +because I might have a person that +weighs a million pounds say. So you have + + align:start position:0% +weighs a million pounds say. So you have + + + align:start position:0% +weighs a million pounds say. So you have +to wor get into that but it it gets a + + align:start position:0% +to wor get into that but it it gets a + + + align:start position:0% +to wor get into that but it it gets a +little bit more complicated. Yeah. I + + align:start position:0% +little bit more complicated. Yeah. I + + + align:start position:0% +little bit more complicated. Yeah. I +guess this is assuming a normal + + align:start position:0% +guess this is assuming a normal + + + align:start position:0% +guess this is assuming a normal +distribution. No, there's nothing being + + align:start position:0% +distribution. No, there's nothing being + + + align:start position:0% +distribution. No, there's nothing being +assumed about the + + align:start position:0% +assumed about the + + + align:start position:0% +assumed about the +distribution. Nothing at + + align:start position:0% +distribution. Nothing at + + + align:start position:0% +distribution. Nothing at +all. Okay. So that's the beauty of + + align:start position:0% +all. Okay. So that's the beauty of + + + align:start position:0% +all. Okay. So that's the beauty of +Marov's theorem is all I assumed one + + align:start position:0% +Marov's theorem is all I assumed one + + + align:start position:0% +Marov's theorem is all I assumed one +thing. I assumed that there's no + + align:start position:0% +thing. I assumed that there's no + + + align:start position:0% +thing. I assumed that there's no +negative values. That's it. + + align:start position:0% + + + + align:start position:0% + +That's correct. they can distribute it + + align:start position:0% +That's correct. they can distribute it + + + align:start position:0% +That's correct. they can distribute it +any way with positive values. But we + + align:start position:0% +any way with positive values. But we + + + align:start position:0% +any way with positive values. But we +have a fact here we've used that the + + align:start position:0% +have a fact here we've used that the + + + align:start position:0% +have a fact here we've used that the +average was 100. So that does limit your + + align:start position:0% +average was 100. So that does limit your + + + align:start position:0% +average was 100. So that does limit your +distribution. In other words, you + + align:start position:0% +distribution. In other words, you + + + align:start position:0% +distribution. In other words, you +couldn't have a distribution where + + align:start position:0% +couldn't have a distribution where + + + align:start position:0% +couldn't have a distribution where +everybody weighs 200 pounds because then + + align:start position:0% +everybody weighs 200 pounds because then + + + align:start position:0% +everybody weighs 200 pounds because then +the average would be 200, not + + align:start position:0% +the average would be 200, not + + + align:start position:0% +the average would be 200, not +100, right? But anything else where the + + align:start position:0% +100, right? But anything else where the + + + align:start position:0% +100, right? But anything else where the +they're all positive and they average + + align:start position:0% +they're all positive and they average + + + align:start position:0% +they're all positive and they average +100, you know that at most half can be + + align:start position:0% +100, you know that at most half can be + + + align:start position:0% +100, you know that at most half can be +200 because if you pick a random one, + + align:start position:0% +200 because if you pick a random one, + + + align:start position:0% +200 because if you pick a random one, +the probability of getting one that's + + align:start position:0% +the probability of getting one that's + + + align:start position:0% +the probability of getting one that's +200 is at most a half, which follows + + align:start position:0% +200 is at most a half, which follows + + + align:start position:0% +200 is at most a half, which follows +from Marov's theorem. And that's partly + + align:start position:0% +from Marov's theorem. And that's partly + + + align:start position:0% +from Marov's theorem. And that's partly +why it's so powerful. You didn't know + + align:start position:0% +why it's so powerful. You didn't know + + + align:start position:0% +why it's so powerful. You didn't know +anything about the distribution really + + align:start position:0% +anything about the distribution really + + + align:start position:0% +anything about the distribution really +except that it's expectation and that it + + align:start position:0% +except that it's expectation and that it + + + align:start position:0% +except that it's expectation and that it +was non- negative. + + align:start position:0% +was non- negative. + + + align:start position:0% +was non- negative. +Any other + + align:start position:0% +Any other + + + align:start position:0% +Any other +questions about this? Here's some more + + align:start position:0% +questions about this? Here's some more + + + align:start position:0% +questions about this? Here's some more +examples. All right, here here's another + + align:start position:0% +examples. All right, here here's another + + + align:start position:0% +examples. All right, here here's another +example. Is it possible on the final + + align:start position:0% +example. Is it possible on the final + + + align:start position:0% +example. Is it possible on the final +exam for everybody in the class to do + + align:start position:0% +exam for everybody in the class to do + + + align:start position:0% +exam for everybody in the class to do +better than the mean + + align:start position:0% +better than the mean + + + align:start position:0% +better than the mean +score? No, of course not. Because if + + align:start position:0% +score? No, of course not. Because if + + + align:start position:0% +score? No, of course not. Because if +they did, the mean would be higher + + align:start position:0% +they did, the mean would be higher + + + align:start position:0% +they did, the mean would be higher +because the mean is the average. Okay. + + align:start position:0% +because the mean is the average. Okay. + + + align:start position:0% +because the mean is the average. Okay. +Um, let's do another example. Remember + + align:start position:0% +Um, let's do another example. Remember + + + align:start position:0% +Um, let's do another example. Remember +the uh Chinese appetizer problem? You're + + align:start position:0% +the uh Chinese appetizer problem? You're + + + align:start position:0% +the uh Chinese appetizer problem? You're +at the restaurant, big circular table. + + align:start position:0% +at the restaurant, big circular table. + + + align:start position:0% +at the restaurant, big circular table. +There's n people at the table. Everybody + + align:start position:0% +There's n people at the table. Everybody + + + align:start position:0% +There's n people at the table. Everybody +has one appetizer in front of them and + + align:start position:0% +has one appetizer in front of them and + + + align:start position:0% +has one appetizer in front of them and +then the joker spins the thing in the + + align:start position:0% +then the joker spins the thing in the + + + align:start position:0% +then the joker spins the thing in the +middle of the table. So, it goes around + + align:start position:0% +middle of the table. So, it goes around + + + align:start position:0% +middle of the table. So, it goes around +and around and it stops in a random + + align:start position:0% +and around and it stops in a random + + + align:start position:0% +and around and it stops in a random +uniform position. And we wanted to know + + align:start position:0% +uniform position. And we wanted to know + + + align:start position:0% +uniform position. And we wanted to know +what's the expected number of people to + + align:start position:0% +what's the expected number of people to + + + align:start position:0% +what's the expected number of people to +get the right appetizer back. What was + + align:start position:0% +get the right appetizer back. What was + + + align:start position:0% +get the right appetizer back. What was +the answer? Anybody + + align:start position:0% +the answer? Anybody + + + align:start position:0% +the answer? Anybody +remember? One. So, you expect one person + + align:start position:0% +remember? One. So, you expect one person + + + align:start position:0% +remember? One. So, you expect one person +to get the right appetizer back. + + align:start position:0% +to get the right appetizer back. + + + align:start position:0% +to get the right appetizer back. +Well, say I want to know the probability + + align:start position:0% +Well, say I want to know the probability + + + align:start position:0% +Well, say I want to know the probability +that all n people got the right + + align:start position:0% +that all n people got the right + + + align:start position:0% +that all n people got the right +appetizer back. What does Markov tell + + align:start position:0% +appetizer back. What does Markov tell + + + align:start position:0% +appetizer back. What does Markov tell +you about the probability that all n + + align:start position:0% +you about the probability that all n + + + align:start position:0% +you about the probability that all n +people get the right appetizer + + align:start position:0% +people get the right appetizer + + + align:start position:0% +people get the right appetizer +back? One overn. The expected value is + + align:start position:0% +back? One overn. The expected value is + + + align:start position:0% +back? One overn. The expected value is +one. And now you're asking the + + align:start position:0% +one. And now you're asking the + + + align:start position:0% +one. And now you're asking the +probability that you get at least X is + + align:start position:0% +probability that you get at least X is + + + align:start position:0% +probability that you get at least X is +at least N. R is at least N. So X is N. + + align:start position:0% +at least N. R is at least N. So X is N. + + + align:start position:0% +at least N. R is at least N. So X is N. +So it's one and N. And what was the + + align:start position:0% +So it's one and N. And what was the + + + align:start position:0% +So it's one and N. And what was the +probability or what is the actual + + align:start position:0% +probability or what is the actual + + + align:start position:0% +probability or what is the actual +probability in this case? should know + + align:start position:0% +probability in this case? should know + + + align:start position:0% +probability in this case? should know +the distribution that everybody gets the + + align:start position:0% +the distribution that everybody gets the + + + align:start position:0% +the distribution that everybody gets the +right appetizer back all in one and n. + + align:start position:0% +right appetizer back all in one and n. + + + align:start position:0% +right appetizer back all in one and n. +So in the case of the Chinese appetizer + + align:start position:0% +So in the case of the Chinese appetizer + + + align:start position:0% +So in the case of the Chinese appetizer +problem, marov's bound is actually the + + align:start position:0% +problem, marov's bound is actually the + + + align:start position:0% +problem, marov's bound is actually the +right answer right on target which gives + + align:start position:0% +right answer right on target which gives + + + align:start position:0% +right answer right on target which gives +you an you know an example where you + + align:start position:0% +you an you know an example where you + + + align:start position:0% +you an you know an example where you +can't improve it by itself is if you + + align:start position:0% +can't improve it by itself is if you + + + align:start position:0% +can't improve it by itself is if you +just know the expected value there's no + + align:start position:0% +just know the expected value there's no + + + align:start position:0% +just know the expected value there's no +stronger theorem that way because + + align:start position:0% +stronger theorem that way because + + + align:start position:0% +stronger theorem that way because +Chinese appetizer is an example where + + align:start position:0% +Chinese appetizer is an example where + + + align:start position:0% +Chinese appetizer is an example where +the bound you get one overn of n people + + align:start position:0% +the bound you get one overn of n people + + + align:start position:0% +the bound you get one overn of n people +getting the right appetizer is in fact + + align:start position:0% +getting the right appetizer is in fact + + + align:start position:0% +getting the right appetizer is in fact +the true probability. + + align:start position:0% + + + + align:start position:0% + +Okay, what about the hat check problem? + + align:start position:0% +Okay, what about the hat check problem? + + + align:start position:0% +Okay, what about the hat check problem? +Remember that? So there's n men put the + + align:start position:0% +Remember that? So there's n men put the + + + align:start position:0% +Remember that? So there's n men put the +hats in the coat closet. They get + + align:start position:0% +hats in the coat closet. They get + + + align:start position:0% +hats in the coat closet. They get +uniformly randomly scrambled. So it's a + + align:start position:0% +uniformly randomly scrambled. So it's a + + + align:start position:0% +uniformly randomly scrambled. So it's a +random permutation applied to the hats. + + align:start position:0% +random permutation applied to the hats. + + + align:start position:0% +random permutation applied to the hats. +Now each man gets a hat + + align:start position:0% +Now each man gets a hat + + + align:start position:0% +Now each man gets a hat +back. What's the expected number of men + + align:start position:0% +back. What's the expected number of men + + + align:start position:0% +back. What's the expected number of men +to get the right hat + + align:start position:0% + + + + align:start position:0% + +back? One. Same as the other one. Uh + + align:start position:0% +back? One. Same as the other one. Uh + + + align:start position:0% +back? One. Same as the other one. Uh +because you got n men each with a one + + align:start position:0% +because you got n men each with a one + + + align:start position:0% +because you got n men each with a one +and n chance. So it's one. Marov says + + align:start position:0% +and n chance. So it's one. Marov says + + + align:start position:0% +and n chance. So it's one. Marov says +the probability that n men get the right + + align:start position:0% +the probability that n men get the right + + + align:start position:0% +the probability that n men get the right +hat back is at most one and n same as + + align:start position:0% +hat back is at most one and n same as + + + align:start position:0% +hat back is at most one and n same as +before. What's the actual probability + + align:start position:0% +before. What's the actual probability + + + align:start position:0% +before. What's the actual probability +that all n men get the right hat back? + + align:start position:0% +that all n men get the right hat back? + + + align:start position:0% +that all n men get the right hat back? +Yeah, one and n + + align:start position:0% +Yeah, one and n + + + align:start position:0% +Yeah, one and n +factorial. So in this case, markoff is + + align:start position:0% +factorial. So in this case, markoff is + + + align:start position:0% +factorial. So in this case, markoff is +way off the mark. It says one and n but + + align:start position:0% +way off the mark. It says one and n but + + + align:start position:0% +way off the mark. It says one and n but +in fact the real bound is much + + align:start position:0% +in fact the real bound is much + + + align:start position:0% +in fact the real bound is much +smaller. All right. So markoff is not + + align:start position:0% +smaller. All right. So markoff is not + + + align:start position:0% +smaller. All right. So markoff is not +always is not always tight. It's always + + align:start position:0% +always is not always tight. It's always + + + align:start position:0% +always is not always tight. It's always +an upper bound, but it sometimes is not + + align:start position:0% +an upper bound, but it sometimes is not + + + align:start position:0% +an upper bound, but it sometimes is not +the right answer. And to get the right + + align:start position:0% +the right answer. And to get the right + + + align:start position:0% +the right answer. And to get the right +answer, often you need to know more + + align:start position:0% +answer, often you need to know more + + + align:start position:0% +answer, often you need to know more +about the + + align:start position:0% + + + + align:start position:0% + +distribution. + + align:start position:0% +distribution. + + + align:start position:0% +distribution. +Okay, what if R can be + + align:start position:0% +Okay, what if R can be + + + align:start position:0% +Okay, what if R can be +negative? Is it possible that Marov's + + align:start position:0% +negative? Is it possible that Marov's + + + align:start position:0% +negative? Is it possible that Marov's +theorem holds + + align:start position:0% + + + + align:start position:0% + +there? Because I use that I use the + + align:start position:0% +there? Because I use that I use the + + + align:start position:0% +there? Because I use that I use the +assumption in the theorem. Anybody give + + align:start position:0% +assumption in the theorem. Anybody give + + + align:start position:0% +assumption in the theorem. Anybody give +me an example where it doesn't work if R + + align:start position:0% +me an example where it doesn't work if R + + + align:start position:0% +me an example where it doesn't work if R +can be negative? + + align:start position:0% + + + + align:start position:0% + +Yeah, good. So for example, say + + align:start position:0% +Yeah, good. So for example, say + + + align:start position:0% +Yeah, good. So for example, say +probability R equals + + align:start position:0% +probability R equals + + + align:start position:0% +probability R equals +a,000 is a half and the probability R + + align:start position:0% +a,000 is a half and the probability R + + + align:start position:0% +a,000 is a half and the probability R +equals minus a,000 is a half. Then the + + align:start position:0% +equals minus a,000 is a half. Then the + + + align:start position:0% +equals minus a,000 is a half. Then the +expected value of R is + + align:start position:0% +expected value of R is + + + align:start position:0% +expected value of R is +zero. And say we ask the probability + + align:start position:0% +zero. And say we ask the probability + + + align:start position:0% +zero. And say we ask the probability +that R is at least a thousand. + + align:start position:0% +that R is at least a thousand. + + + align:start position:0% +that R is at least a thousand. +Well, that's going to be a half, but + + align:start position:0% +Well, that's going to be a half, but + + + align:start position:0% +Well, that's going to be a half, but +that does not equal the expected value + + align:start position:0% +that does not equal the expected value + + + align:start position:0% +that does not equal the expected value +of r over a th00and, which would be + + align:start position:0% +of r over a th00and, which would be + + + align:start position:0% +of r over a th00and, which would be +zero. So, Marov's theorem really does + + align:start position:0% +zero. So, Marov's theorem really does + + + align:start position:0% +zero. So, Marov's theorem really does +need that r be non- negative. In fact, + + align:start position:0% +need that r be non- negative. In fact, + + + align:start position:0% +need that r be non- negative. In fact, +let's see if we saw where we used it in + + align:start position:0% +let's see if we saw where we used it in + + + align:start position:0% +let's see if we saw where we used it in +the + + align:start position:0% +the + + + align:start position:0% +the +proof. Anybody see where we use that + + align:start position:0% +proof. Anybody see where we use that + + + align:start position:0% +proof. Anybody see where we use that +fact in the proof that R can't be + + align:start position:0% +fact in the proof that R can't be + + + align:start position:0% +fact in the proof that R can't be +negative? What is it? + + align:start position:0% +negative? What is it? + + + align:start position:0% +negative? What is it? +Um well no because x is + + align:start position:0% +Um well no because x is + + + align:start position:0% +Um well no because x is +positive said x is + + align:start position:0% +positive said x is + + + align:start position:0% +positive said x is +positive so it's not used there but + + align:start position:0% +positive so it's not used there but + + + align:start position:0% +positive so it's not used there but +that's a good one to look at. Yeah + + align:start position:0% + + + + align:start position:0% + +is greater than or equal to zero. Yeah + + align:start position:0% +is greater than or equal to zero. Yeah + + + align:start position:0% +is greater than or equal to zero. Yeah +if r can be + + align:start position:0% +if r can be + + + align:start position:0% +if r can be +negative then this is not necessarily a + + align:start position:0% +negative then this is not necessarily a + + + align:start position:0% +negative then this is not necessarily a +positive number. It could be a negative + + align:start position:0% +positive number. It could be a negative + + + align:start position:0% +positive number. It could be a negative +number and then this inequality doesn't + + align:start position:0% +number and then this inequality doesn't + + + align:start position:0% +number and then this inequality doesn't +hold. + + align:start position:0% +hold. + + + align:start position:0% +hold. +Okay. Okay. + + align:start position:0% + + + + align:start position:0% + +Good. All right. Now, it turns out there + + align:start position:0% +Good. All right. Now, it turns out there + + + align:start position:0% +Good. All right. Now, it turns out there +is a variation of Marov's theorem you + + align:start position:0% +is a variation of Marov's theorem you + + + align:start position:0% +is a variation of Marov's theorem you +can use when R is negative. Yeah. + + align:start position:0% + + + + align:start position:0% + +Just to shift everything up. Yeah. Yeah. + + align:start position:0% +Just to shift everything up. Yeah. Yeah. + + + align:start position:0% +Just to shift everything up. Yeah. Yeah. +That's great. If R doesn't has a limit + + align:start position:0% +That's great. If R doesn't has a limit + + + align:start position:0% +That's great. If R doesn't has a limit +on how negative it can be then you make + + align:start position:0% +on how negative it can be then you make + + + align:start position:0% +on how negative it can be then you make +a R prime which just adds that limit to + + align:start position:0% +a R prime which just adds that limit to + + + align:start position:0% +a R prime which just adds that limit to +R makes it positive or non- negative and + + align:start position:0% +R makes it positive or non- negative and + + + align:start position:0% +R makes it positive or non- negative and +now use Marov's theorem there and that + + align:start position:0% +now use Marov's theorem there and that + + + align:start position:0% +now use Marov's theorem there and that +is now an analogous form of Marov's + + align:start position:0% +is now an analogous form of Marov's + + + align:start position:0% +is now an analogous form of Marov's +theorem when R can be negative but + + align:start position:0% +theorem when R can be negative but + + + align:start position:0% +theorem when R can be negative but +there's a lower limit to it and I won't + + align:start position:0% +there's a lower limit to it and I won't + + + align:start position:0% +there's a lower limit to it and I won't +state and prove that here that's in the + + align:start position:0% +state and prove that here that's in the + + + align:start position:0% +state and prove that here that's in the +text and something you want to be + + align:start position:0% +text and something you want to be + + + align:start position:0% +text and something you want to be +familiar with. + + align:start position:0% +familiar with. + + + align:start position:0% +familiar with. +uh what I do want to do in class is + + align:start position:0% +uh what I do want to do in class is + + + align:start position:0% +uh what I do want to do in class is +another case + + align:start position:0% +another case + + + align:start position:0% +another case +where you can use marov's theorem to + + align:start position:0% +where you can use marov's theorem to + + + align:start position:0% +where you can use marov's theorem to +analyze the probability or upperbound + + align:start position:0% +analyze the probability or upperbound + + + align:start position:0% +analyze the probability or upperbound +the probability that r is very small + + align:start position:0% +the probability that r is very small + + + align:start position:0% +the probability that r is very small +less than its expectation and it's the + + align:start position:0% +less than its expectation and it's the + + + align:start position:0% +less than its expectation and it's the +same idea as you just + + align:start position:0% +same idea as you just + + + align:start position:0% +same idea as you just +suggested okay so let's state + + align:start position:0% + + + + align:start position:0% + +that if r is upperbounded has a hard + + align:start position:0% +that if r is upperbounded has a hard + + + align:start position:0% +that if r is upperbounded has a hard +limit on the upper bound by + + align:start position:0% + + + + align:start position:0% + +Q for some U in the real + + align:start position:0% + + + + align:start position:0% + +numbers. Then for all X less than + + align:start position:0% + + + + align:start position:0% + +U, the probability that R + + align:start position:0% +U, the probability that R + + + align:start position:0% +U, the probability that R +is less than equal to + + align:start position:0% +is less than equal to + + + align:start position:0% +is less than equal to +X is at most U minus the expected value + + align:start position:0% +X is at most U minus the expected value + + + align:start position:0% +X is at most U minus the expected value +of + + align:start position:0% +of + + + align:start position:0% +of +R over U - X. + + align:start position:0% +R over U - X. + + + align:start position:0% +R over U - X. +So in this case, we're getting a + + align:start position:0% +So in this case, we're getting a + + + align:start position:0% +So in this case, we're getting a +probability + + align:start position:0% +probability + + + align:start position:0% +probability +that R is less than something instead of + + align:start position:0% +that R is less than something instead of + + + align:start position:0% +that R is less than something instead of +R is bigger than + + align:start position:0% +R is bigger than + + + align:start position:0% +R is bigger than +something. All right? And we're going to + + align:start position:0% +something. All right? And we're going to + + + align:start position:0% +something. All right? And we're going to +do + + align:start position:0% + + + + align:start position:0% + +it using a simple trick that we'll be + + align:start position:0% +it using a simple trick that we'll be + + + align:start position:0% +it using a simple trick that we'll be +sort of using all day really. + + align:start position:0% +sort of using all day really. + + + align:start position:0% +sort of using all day really. +The probability that r is less than + + align:start position:0% +The probability that r is less than + + + align:start position:0% +The probability that r is less than +x. This event r is less than x is the + + align:start position:0% +x. This event r is less than x is the + + + align:start position:0% +x. This event r is less than x is the +same as the event + + align:start position:0% +same as the event + + + align:start position:0% +same as the event +u minus + + align:start position:0% +u minus + + + align:start position:0% +u minus +r is least u - + + align:start position:0% +r is least u - + + + align:start position:0% +r is least u - +x. All right. So what have I done? I sub + + align:start position:0% +x. All right. So what have I done? I sub + + + align:start position:0% +x. All right. So what have I done? I sub +put r over negative r over here. + + align:start position:0% +put r over negative r over here. + + + align:start position:0% +put r over negative r over here. +Subtract x from each side. Add u to each + + align:start position:0% +Subtract x from each side. Add u to each + + + align:start position:0% +Subtract x from each side. Add u to each +side. All right. I got to put a less + + align:start position:0% +side. All right. I got to put a less + + + align:start position:0% +side. All right. I got to put a less +than equal to here. + + align:start position:0% +than equal to here. + + + align:start position:0% +than equal to here. +All right. So, r is less than equal to x + + align:start position:0% +All right. So, r is less than equal to x + + + align:start position:0% +All right. So, r is less than equal to x +if and only if u minus r is at least u - + + align:start position:0% +if and only if u minus r is at least u - + + + align:start position:0% +if and only if u minus r is at least u - +x, you know, simple math + + align:start position:0% +x, you know, simple math + + + align:start position:0% +x, you know, simple math +there. And now I'm going to apply marov + + align:start position:0% +there. And now I'm going to apply marov + + + align:start position:0% +there. And now I'm going to apply marov +to + + align:start position:0% +to + + + align:start position:0% +to +this. I'm going to apply marov to this + + align:start position:0% +this. I'm going to apply marov to this + + + align:start position:0% +this. I'm going to apply marov to this +random + + align:start position:0% +random + + + align:start position:0% +random +variable. Right? And this will be the + + align:start position:0% +variable. Right? And this will be the + + + align:start position:0% +variable. Right? And this will be the +value I would have had for x up in + + align:start position:0% +value I would have had for x up in + + + align:start position:0% +value I would have had for x up in +marov's + + align:start position:0% +marov's + + + align:start position:0% +marov's +theorem. Why is it okay to apply marov + + align:start position:0% +theorem. Why is it okay to apply marov + + + align:start position:0% +theorem. Why is it okay to apply marov +to u minus r? + + align:start position:0% +to u minus r? + + + align:start position:0% +to u minus r? +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Okay. You can just define a new random + + align:start position:0% +Okay. You can just define a new random + + + align:start position:0% +Okay. You can just define a new random +variable to be U minus R. Yeah. So I got + + align:start position:0% +variable to be U minus R. Yeah. So I got + + + align:start position:0% +variable to be U minus R. Yeah. So I got +a new random variable. But what do I + + align:start position:0% +a new random variable. But what do I + + + align:start position:0% +a new random variable. But what do I +need to know about that new random + + align:start position:0% +need to know about that new random + + + align:start position:0% +need to know about that new random +variable to apply marov? U is always + + align:start position:0% +variable to apply marov? U is always + + + align:start position:0% +variable to apply marov? U is always +greater than r. U is always greater than + + align:start position:0% +greater than r. U is always greater than + + + align:start position:0% +greater than r. U is always greater than +r. So u or at least as big as r. So u + + align:start position:0% +r. So u or at least as big as r. So u + + + align:start position:0% +r. So u or at least as big as r. So u +minus r is always non- negative. So I + + align:start position:0% +minus r is always non- negative. So I + + + align:start position:0% +minus r is always non- negative. So I +can apply marov now. All right. Right. + + align:start position:0% +can apply marov now. All right. Right. + + + align:start position:0% +can apply marov now. All right. Right. +And when I apply + + align:start position:0% + + + + align:start position:0% + +marov I'll get this is at most well let + + align:start position:0% +marov I'll get this is at most well let + + + align:start position:0% +marov I'll get this is at most well let +me maybe I'll go over + + align:start position:0% + + + + align:start position:0% + +here probability + + align:start position:0% +here probability + + + align:start position:0% +here probability +that not r here this is + + align:start position:0% +that not r here this is + + + align:start position:0% +that not r here this is +probability probability that u minus + + align:start position:0% +probability probability that u minus + + + align:start position:0% +probability probability that u minus +r is at least u - x is at most the + + align:start position:0% +r is at least u - x is at most the + + + align:start position:0% +r is at least u - x is at most the +expected value of that random variable. + + align:start position:0% + + + + align:start position:0% + +over this + + align:start position:0% + + + + align:start position:0% + +value. All right. And well, now I just + + align:start position:0% +value. All right. And well, now I just + + + align:start position:0% +value. All right. And well, now I just +use the linearity of expectation. I got + + align:start position:0% +use the linearity of expectation. I got + + + align:start position:0% +use the linearity of expectation. I got +a scaler here. So this is u minus + + align:start position:0% +a scaler here. So this is u minus + + + align:start position:0% +a scaler here. So this is u minus +expected value of r over u minus + + align:start position:0% + + + + align:start position:0% + +x. All right. So I've used marov theorem + + align:start position:0% +x. All right. So I've used marov theorem + + + align:start position:0% +x. All right. So I've used marov theorem +to get a a different version of + + align:start position:0% + + + + align:start position:0% + +it. All right. Let's do an + + align:start position:0% +it. All right. Let's do an + + + align:start position:0% +it. All right. Let's do an +example. Say I'm looking at test + + align:start position:0% +example. Say I'm looking at test + + + align:start position:0% +example. Say I'm looking at test +scores and I'll let R be the score of a + + align:start position:0% +scores and I'll let R be the score of a + + + align:start position:0% +scores and I'll let R be the score of a +random + + align:start position:0% +random + + + align:start position:0% +random +student uniformly + + align:start position:0% + + + + align:start position:0% + +selected and say that the max + + align:start position:0% +selected and say that the max + + + align:start position:0% +selected and say that the max +score is 100. + + align:start position:0% +score is 100. + + + align:start position:0% +score is 100. +So that's + + align:start position:0% +So that's + + + align:start position:0% +So that's +u all scores are at most 100. And say + + align:start position:0% +u all scores are at most 100. And say + + + align:start position:0% +u all scores are at most 100. And say +that I tell you the class + + align:start position:0% +that I tell you the class + + + align:start position:0% +that I tell you the class +average or the expected value of + + align:start position:0% + + + + align:start position:0% + +R is + + align:start position:0% + + + + align:start position:0% + +75. And now I want to know what's the + + align:start position:0% +75. And now I want to know what's the + + + align:start position:0% +75. And now I want to know what's the +probability that a random student scores + + align:start position:0% +probability that a random student scores + + + align:start position:0% +probability that a random student scores +50 or + + align:start position:0% + + + + align:start position:0% + +below. Okay, can we figure that out? I + + align:start position:0% +below. Okay, can we figure that out? I + + + align:start position:0% +below. Okay, can we figure that out? I +don't know anything about the + + align:start position:0% +don't know anything about the + + + align:start position:0% +don't know anything about the +distribution, just that the max score is + + align:start position:0% +distribution, just that the max score is + + + align:start position:0% +distribution, just that the max score is +100 and the average score is 75. What's + + align:start position:0% +100 and the average score is 75. What's + + + align:start position:0% +100 and the average score is 75. What's +the + + align:start position:0% +the + + + align:start position:0% +the +probability that a random student scores + + align:start position:0% +probability that a random student scores + + + align:start position:0% +probability that a random student scores +50 or less? I want to upper bound + + align:start position:0% +50 or less? I want to upper bound + + + align:start position:0% +50 or less? I want to upper bound +that. Okay. So, we just plug it into the + + align:start position:0% +that. Okay. So, we just plug it into the + + + align:start position:0% +that. Okay. So, we just plug it into the +formula. U is + + align:start position:0% +formula. U is + + + align:start position:0% +formula. U is +100. The expected value is + + align:start position:0% +100. The expected value is + + + align:start position:0% +100. The expected value is +75. U is + + align:start position:0% +75. U is + + + align:start position:0% +75. U is +100 and X is + + align:start position:0% +100 and X is + + + align:start position:0% +100 and X is +50. And that's 25 over + + align:start position:0% +50. And that's 25 over + + + align:start position:0% +50. And that's 25 over +50 is a half. + + align:start position:0% +50 is a half. + + + align:start position:0% +50 is a half. +So at most half the class can score 50 + + align:start position:0% +So at most half the class can score 50 + + + align:start position:0% +So at most half the class can score 50 +or + + align:start position:0% +or + + + align:start position:0% +or +below and stated as a probability + + align:start position:0% +below and stated as a probability + + + align:start position:0% +below and stated as a probability +question or deterministic fact. If I + + align:start position:0% +question or deterministic fact. If I + + + align:start position:0% +question or deterministic fact. If I +know the average is 75 and the max is + + align:start position:0% +know the average is 75 and the max is + + + align:start position:0% +know the average is 75 and the max is +100. Of course another way of thinking + + align:start position:0% +100. Of course another way of thinking + + + align:start position:0% +100. Of course another way of thinking +about that is if more than half the + + align:start position:0% +about that is if more than half the + + + align:start position:0% +about that is if more than half the +class scored 50 or below your average + + align:start position:0% +class scored 50 or below your average + + + align:start position:0% +class scored 50 or below your average +would have had to be + + align:start position:0% +would have had to be + + + align:start position:0% +would have had to be +lower. Even if everybody else was right + + align:start position:0% +lower. Even if everybody else was right + + + align:start position:0% +lower. Even if everybody else was right +at 100, it wouldn't average out to + + align:start position:0% + + + + align:start position:0% + +75. All right. Any + + align:start position:0% +75. All right. Any + + + align:start position:0% +75. All right. Any +questions about + + align:start position:0% +questions about + + + align:start position:0% +questions about +that? + + align:start position:0% + + + + align:start position:0% + +Okay. Okay. So, sometimes Markov is dead + + align:start position:0% +Okay. Okay. So, sometimes Markov is dead + + + align:start position:0% +Okay. Okay. So, sometimes Markov is dead +on right gives the right answer. For + + align:start position:0% +on right gives the right answer. For + + + align:start position:0% +on right gives the right answer. For +example, half the class could have + + align:start position:0% +example, half the class could have + + + align:start position:0% +example, half the class could have +scored 50 and half could have gotten 100 + + align:start position:0% +scored 50 and half could have gotten 100 + + + align:start position:0% +scored 50 and half could have gotten 100 +to make it be 75. And sometimes it's way + + align:start position:0% +to make it be 75. And sometimes it's way + + + align:start position:0% +to make it be 75. And sometimes it's way +off like in the hatch check problem. + + align:start position:0% +off like in the hatch check problem. + + + align:start position:0% +off like in the hatch check problem. +Now if you know more about the + + align:start position:0% +Now if you know more about the + + + align:start position:0% +Now if you know more about the +distribution then you can get better + + align:start position:0% +distribution then you can get better + + + align:start position:0% +distribution then you can get better +bounds in the cases when you're you're + + align:start position:0% +bounds in the cases when you're you're + + + align:start position:0% +bounds in the cases when you're you're +far off. For example, if you know the + + align:start position:0% +far off. For example, if you know the + + + align:start position:0% +far off. For example, if you know the +variance in addition to the expectation + + align:start position:0% +variance in addition to the expectation + + + align:start position:0% +variance in addition to the expectation +or aside from the expectation, then you + + align:start position:0% +or aside from the expectation, then you + + + align:start position:0% +or aside from the expectation, then you +can get better bounds on the probability + + align:start position:0% +can get better bounds on the probability + + + align:start position:0% +can get better bounds on the probability +that the random variable is large. And + + align:start position:0% +that the random variable is large. And + + + align:start position:0% +that the random variable is large. And +in this case, the result is known as + + align:start position:0% +in this case, the result is known as + + + align:start position:0% +in this case, the result is known as +chbbyev + + align:start position:0% +chbbyev + + + align:start position:0% +chbbyev +theorem. Do that over + + align:start position:0% +theorem. Do that over + + + align:start position:0% +theorem. Do that over +here. And it's the analog of Marov's + + align:start position:0% +here. And it's the analog of Marov's + + + align:start position:0% +here. And it's the analog of Marov's +theorem based on + + align:start position:0% + + + + align:start position:0% + +variance says for all X bigger than + + align:start position:0% +variance says for all X bigger than + + + align:start position:0% +variance says for all X bigger than +zero and any random variable R could + + align:start position:0% +zero and any random variable R could + + + align:start position:0% +zero and any random variable R could +even be + + align:start position:0% +even be + + + align:start position:0% +even be +negative. The + + align:start position:0% +negative. The + + + align:start position:0% +negative. The +probability that R deviates from its + + align:start position:0% +probability that R deviates from its + + + align:start position:0% +probability that R deviates from its +expected value in either + + align:start position:0% +expected value in either + + + align:start position:0% +expected value in either +direction by at least + + align:start position:0% +direction by at least + + + align:start position:0% +direction by at least +X is at most the variance of + + align:start position:0% +X is at most the variance of + + + align:start position:0% +X is at most the variance of +R divided by + + align:start position:0% +R divided by + + + align:start position:0% +R divided by +X^2. All right? So this is like + + align:start position:0% +X^2. All right? So this is like + + + align:start position:0% +X^2. All right? So this is like +Markoff's theorem except that we're now + + align:start position:0% +Markoff's theorem except that we're now + + + align:start position:0% +Markoff's theorem except that we're now +bounding the deviation in either + + align:start position:0% +bounding the deviation in either + + + align:start position:0% +bounding the deviation in either +direction. Instead of expected value, + + align:start position:0% +direction. Instead of expected value, + + + align:start position:0% +direction. Instead of expected value, +you have variance. Instead of X, you got + + align:start position:0% +you have variance. Instead of X, you got + + + align:start position:0% +you have variance. Instead of X, you got +X squ. But the same idea, right? In + + align:start position:0% +X squ. But the same idea, right? In + + + align:start position:0% +X squ. But the same idea, right? In +fact, the proof uses Marov's + + align:start position:0% + + + + align:start position:0% + +theorem. All right. Well, the + + align:start position:0% +theorem. All right. Well, the + + + align:start position:0% +theorem. All right. Well, the +probability that R deviates from its + + align:start position:0% +probability that R deviates from its + + + align:start position:0% +probability that R deviates from its +expected value by at least X. + + align:start position:0% +expected value by at least X. + + + align:start position:0% +expected value by at least X. +This is the same event or happens if and + + align:start position:0% +This is the same event or happens if and + + + align:start position:0% +This is the same event or happens if and +only if r minus expected value squared + + align:start position:0% +only if r minus expected value squared + + + align:start position:0% +only if r minus expected value squared +is at least x^2. I'm just going to + + align:start position:0% +is at least x^2. I'm just going to + + + align:start position:0% +is at least x^2. I'm just going to +square both sides + + align:start position:0% + + + + align:start position:0% + +here. Okay. I square both sides and + + align:start position:0% +here. Okay. I square both sides and + + + align:start position:0% +here. Okay. I square both sides and +since this is positive and this is + + align:start position:0% +since this is positive and this is + + + align:start position:0% +since this is positive and this is +positive I can square both sides and + + align:start position:0% +positive I can square both sides and + + + align:start position:0% +positive I can square both sides and +maintain the + + align:start position:0% +maintain the + + + align:start position:0% +maintain the +inequality. All + + align:start position:0% +inequality. All + + + align:start position:0% +inequality. All +right. Now, I'm going to apply Marov's + + align:start position:0% +right. Now, I'm going to apply Marov's + + + align:start position:0% +right. Now, I'm going to apply Marov's +theorem to that random + + align:start position:0% +theorem to that random + + + align:start position:0% +theorem to that random +variable. It's a random variable. It's r + + align:start position:0% +variable. It's a random variable. It's r + + + align:start position:0% +variable. It's a random variable. It's r +minus expected value squared. So, it's a + + align:start position:0% +minus expected value squared. So, it's a + + + align:start position:0% +minus expected value squared. So, it's a +random variable. And what's nice about + + align:start position:0% +random variable. And what's nice about + + + align:start position:0% +random variable. And what's nice about +this random variable that lets me apply + + align:start position:0% + + + + align:start position:0% + +marov's + + align:start position:0% +marov's + + + align:start position:0% +marov's +a non- negative. So, I can apply marov's + + align:start position:0% +a non- negative. So, I can apply marov's + + + align:start position:0% +a non- negative. So, I can apply marov's +theorem. + + align:start position:0% +theorem. + + + align:start position:0% +theorem. +And by Marov's theorem, this probability + + align:start position:0% +And by Marov's theorem, this probability + + + align:start position:0% +And by Marov's theorem, this probability +is at most the expected value of + + align:start position:0% + + + + align:start position:0% + +that divided by + + align:start position:0% +that divided by + + + align:start position:0% +that divided by +this. That's what Marov's theorem says. + + align:start position:0% +this. That's what Marov's theorem says. + + + align:start position:0% +this. That's what Marov's theorem says. +As long as this is always non- + + align:start position:0% +As long as this is always non- + + + align:start position:0% +As long as this is always non- +negative. All right. What's a simpler + + align:start position:0% +negative. All right. What's a simpler + + + align:start position:0% +negative. All right. What's a simpler +expression for this? + + align:start position:0% +expression for this? + + + align:start position:0% +expression for this? +the expected value of a the square of + + align:start position:0% +the expected value of a the square of + + + align:start position:0% +the expected value of a the square of +the deviation of a random + + align:start position:0% +the deviation of a random + + + align:start position:0% +the deviation of a random +variable. That's the variance. That's + + align:start position:0% +variable. That's the variance. That's + + + align:start position:0% +variable. That's the variance. That's +the definition of + + align:start position:0% +the definition of + + + align:start position:0% +the definition of +variance. Okay, so that is just the + + align:start position:0% +variance. Okay, so that is just the + + + align:start position:0% +variance. Okay, so that is just the +variance of R over X2 and we're + + align:start position:0% +variance of R over X2 and we're + + + align:start position:0% +variance of R over X2 and we're +done. All right, so Chvy Chev's theorem + + align:start position:0% +done. All right, so Chvy Chev's theorem + + + align:start position:0% +done. All right, so Chvy Chev's theorem +is really just another version of + + align:start position:0% +is really just another version of + + + align:start position:0% +is really just another version of +Marov's + + align:start position:0% +Marov's + + + align:start position:0% +Marov's +theorem, but now it's based on the + + align:start position:0% +theorem, but now it's based on the + + + align:start position:0% +theorem, but now it's based on the +variance. + + align:start position:0% + + + + align:start position:0% + +Okay, any any + + align:start position:0% + + + + align:start position:0% + +questions? Okay, so there's a nice + + align:start position:0% +questions? Okay, so there's a nice + + + align:start position:0% +questions? Okay, so there's a nice +correlary for + + align:start position:0% +correlary for + + + align:start position:0% +correlary for +this just as with Marov's + + align:start position:0% +this just as with Marov's + + + align:start position:0% +this just as with Marov's +theorem says the probability that the + + align:start position:0% +theorem says the probability that the + + + align:start position:0% +theorem says the probability that the +absolute value the + + align:start position:0% + + + + align:start position:0% + +deviation is at least C times the + + align:start position:0% +deviation is at least C times the + + + align:start position:0% +deviation is at least C times the +standard deviation of + + align:start position:0% +standard deviation of + + + align:start position:0% +standard deviation of +R. All right. So, I'm I'm looking at the + + align:start position:0% +R. All right. So, I'm I'm looking at the + + + align:start position:0% +R. All right. So, I'm I'm looking at the +probability that R differs from its + + align:start position:0% +probability that R differs from its + + + align:start position:0% +probability that R differs from its +expectation by at least some scaler C + + align:start position:0% +expectation by at least some scaler C + + + align:start position:0% +expectation by at least some scaler C +times the standard + + align:start position:0% +times the standard + + + align:start position:0% +times the standard +deviation. Well, what's + + align:start position:0% +deviation. Well, what's + + + align:start position:0% +deviation. Well, what's +that? Well, that's the + + align:start position:0% +that? Well, that's the + + + align:start position:0% +that? Well, that's the +variance of + + align:start position:0% +variance of + + + align:start position:0% +variance of +R over the square of this + + align:start position:0% +R over the square of this + + + align:start position:0% +R over the square of this +thing. + + align:start position:0% +thing. + + + align:start position:0% +thing. +C^2 times the standard deviation + + align:start position:0% +C^2 times the standard deviation + + + align:start position:0% +C^2 times the standard deviation +squared. + + align:start position:0% +squared. + + + align:start position:0% +squared. +What's the square of the standard + + align:start position:0% +What's the square of the standard + + + align:start position:0% +What's the square of the standard +deviation? That's the + + align:start position:0% +deviation? That's the + + + align:start position:0% +deviation? That's the +variance. They cancel. So it's just 1 + + align:start position:0% +variance. They cancel. So it's just 1 + + + align:start position:0% +variance. They cancel. So it's just 1 +over + + align:start position:0% + + + + align:start position:0% + +c^2. Okay. So the ch the probability of + + align:start position:0% +c^2. Okay. So the ch the probability of + + + align:start position:0% +c^2. Okay. So the ch the probability of +more than two times off expect twice the + + align:start position:0% +more than two times off expect twice the + + + align:start position:0% +more than two times off expect twice the +standard deviation off the expectations + + align:start position:0% +standard deviation off the expectations + + + align:start position:0% +standard deviation off the expectations +at most one one quarter for + + align:start position:0% + + + + align:start position:0% + +example. All right, let's do some + + align:start position:0% +example. All right, let's do some + + + align:start position:0% +example. All right, let's do some +examples of that. + + align:start position:0% + + + + align:start position:0% + +Maybe we'll + + align:start position:0% +Maybe we'll + + + align:start position:0% +Maybe we'll +leave Marov up + + align:start position:0% + + + + align:start position:0% + +there. Okay, say we're looking at + + align:start position:0% + + + + align:start position:0% + +IQ's. And in this case, we're going to + + align:start position:0% +IQ's. And in this case, we're going to + + + align:start position:0% +IQ's. And in this case, we're going to +let R be the + + align:start position:0% +let R be the + + + align:start position:0% +let R be the +IQ of a random + + align:start position:0% +IQ of a random + + + align:start position:0% +IQ of a random +person. All + + align:start position:0% + + + + align:start position:0% + +right. Now, we're going to + + align:start position:0% +right. Now, we're going to + + + align:start position:0% +right. Now, we're going to +assume, and this actually is the + + align:start position:0% + + + + align:start position:0% + +case, that R is always at least + + align:start position:0% +case, that R is always at least + + + align:start position:0% +case, that R is always at least +zero despite the fact that probably most + + align:start position:0% +zero despite the fact that probably most + + + align:start position:0% +zero despite the fact that probably most +of you have somebody you know who you + + align:start position:0% +of you have somebody you know who you + + + align:start position:0% +of you have somebody you know who you +think has a negative IQ. Uh they can't + + align:start position:0% +think has a negative IQ. Uh they can't + + + align:start position:0% +think has a negative IQ. Uh they can't +be negative. They have to be non zero. + + align:start position:0% +be negative. They have to be non zero. + + + align:start position:0% +be negative. They have to be non zero. +In fact, um, IQ's are adjusted so the + + align:start position:0% +In fact, um, IQ's are adjusted so the + + + align:start position:0% +In fact, um, IQ's are adjusted so the +expected IQ is supposed to be 100, + + align:start position:0% +expected IQ is supposed to be 100, + + + align:start position:0% +expected IQ is supposed to be 100, +although it may may actually averages + + align:start position:0% +although it may may actually averages + + + align:start position:0% +although it may may actually averages +maybe in the 90s and it's set up so that + + align:start position:0% +maybe in the 90s and it's set up so that + + + align:start position:0% +maybe in the 90s and it's set up so that +the standard deviation of IQ is supposed + + align:start position:0% +the standard deviation of IQ is supposed + + + align:start position:0% +the standard deviation of IQ is supposed +to be + + align:start position:0% +to be + + + align:start position:0% +to be +15. So, we're just going to assume those + + align:start position:0% +15. So, we're just going to assume those + + + align:start position:0% +15. So, we're just going to assume those +are facts on IQ and they're that's what + + align:start position:0% +are facts on IQ and they're that's what + + + align:start position:0% +are facts on IQ and they're that's what +it's meant to be. + + align:start position:0% +it's meant to be. + + + align:start position:0% +it's meant to be. +And now we want to + + align:start position:0% +And now we want to + + + align:start position:0% +And now we want to +know what's the probability a random + + align:start position:0% +know what's the probability a random + + + align:start position:0% +know what's the probability a random +person has an IQ of at least + + align:start position:0% +person has an IQ of at least + + + align:start position:0% +person has an IQ of at least +250. Now Marilyn from ask Marilyn has a + + align:start position:0% +250. Now Marilyn from ask Marilyn has a + + + align:start position:0% +250. Now Marilyn from ask Marilyn has a +IQ pretty close to 250 and she thinks + + align:start position:0% +IQ pretty close to 250 and she thinks + + + align:start position:0% +IQ pretty close to 250 and she thinks +that's pretty special pretty + + align:start position:0% +that's pretty special pretty + + + align:start position:0% +that's pretty special pretty +rare. So what can we say about that? In + + align:start position:0% +rare. So what can we say about that? In + + + align:start position:0% +rare. So what can we say about that? In +particular say we used + + align:start position:0% +particular say we used + + + align:start position:0% +particular say we used +Marov. What could you say about the + + align:start position:0% +Marov. What could you say about the + + + align:start position:0% +Marov. What could you say about the +probability of having an IQ of at least + + align:start position:0% + + + + align:start position:0% + +250? What does Marov tell + + align:start position:0% + + + + align:start position:0% + +us? What What is + + align:start position:0% +us? What What is + + + align:start position:0% +us? What What is +it? Not quite 25, but you're on the + + align:start position:0% +it? Not quite 25, but you're on the + + + align:start position:0% +it? Not quite 25, but you're on the +right track. + + align:start position:0% + + + + align:start position:0% + +It's uh not quite 2/3. It's the expected + + align:start position:0% +It's uh not quite 2/3. It's the expected + + + align:start position:0% +It's uh not quite 2/3. It's the expected +value which is + + align:start position:0% +value which is + + + align:start position:0% +value which is + + align:start position:0% + + + align:start position:0% +over the x value which is + + align:start position:0% +over the x value which is + + + align:start position:0% +over the x value which is +250. So it's one in one and + + align:start position:0% +250. So it's one in one and + + + align:start position:0% +250. So it's one in one and +2.5 or + + align:start position:0% +2.5 or + + + align:start position:0% +2.5 or +04. So the probability is at most + + align:start position:0% +04. So the probability is at most + + + align:start position:0% +04. So the probability is at most +point4. So 40% chance it could happen + + align:start position:0% +point4. So 40% chance it could happen + + + align:start position:0% +point4. So 40% chance it could happen +potentially but no no bigger than that. + + align:start position:0% +potentially but no no bigger than that. + + + align:start position:0% +potentially but no no bigger than that. +What about + + align:start position:0% +What about + + + align:start position:0% +What about +chbbyev? What is see if you can figure + + align:start position:0% +chbbyev? What is see if you can figure + + + align:start position:0% +chbbyev? What is see if you can figure +out what chbbyev says about the + + align:start position:0% +out what chbbyev says about the + + + align:start position:0% +out what chbbyev says about the +probability of having an IQ of at least + + align:start position:0% + + + + align:start position:0% + +250. It's a little tricky. You got to + + align:start position:0% +250. It's a little tricky. You got to + + + align:start position:0% +250. It's a little tricky. You got to +sort of plug it into the equation there + + align:start position:0% +sort of plug it into the equation there + + + align:start position:0% +sort of plug it into the equation there +and get it to fit in the right form. + + align:start position:0% + + + + align:start position:0% + +Chevy says + + align:start position:0% +Chevy says + + + align:start position:0% +Chevy says +that let's get it in the right form. + + align:start position:0% +that let's get it in the right form. + + + align:start position:0% +that let's get it in the right form. +I've got probability R is at least 250. + + align:start position:0% +I've got probability R is at least 250. + + + align:start position:0% +I've got probability R is at least 250. +I got to get it into that form up + + align:start position:0% +I got to get it into that form up + + + align:start position:0% +I got to get it into that form up +there. So that's the probability + + align:start position:0% +there. So that's the probability + + + align:start position:0% +there. So that's the probability +that well first r minus 100 is at least + + align:start position:0% +that well first r minus 100 is at least + + + align:start position:0% +that well first r minus 100 is at least +150. All right. So I've got r minus the + + align:start position:0% +150. All right. So I've got r minus the + + + align:start position:0% +150. All right. So I've got r minus the +expected value. I'm sort of getting it + + align:start position:0% +expected value. I'm sort of getting it + + + align:start position:0% +expected value. I'm sort of getting it +ready to apply chbbyev here. + + align:start position:0% +ready to apply chbbyev here. + + + align:start position:0% +ready to apply chbbyev here. +Uh and then 150. How many standard + + align:start position:0% +Uh and then 150. How many standard + + + align:start position:0% +Uh and then 150. How many standard +deviations is + + align:start position:0% +deviations is + + + align:start position:0% +deviations is +150? 10. All right. So this is is the + + align:start position:0% +150? 10. All right. So this is is the + + + align:start position:0% +150? 10. All right. So this is is the +probability that R minus expected value + + align:start position:0% +probability that R minus expected value + + + align:start position:0% +probability that R minus expected value +of R is at least 10 standard + + align:start position:0% +of R is at least 10 standard + + + align:start position:0% +of R is at least 10 standard +deviations. That's what I'm asking. And + + align:start position:0% +deviations. That's what I'm asking. And + + + align:start position:0% +deviations. That's what I'm asking. And +I'm not quite there. I'm going to use + + align:start position:0% +I'm not quite there. I'm going to use + + + align:start position:0% +I'm not quite there. I'm going to use +the correlary there, but I got to get + + align:start position:0% +the correlary there, but I got to get + + + align:start position:0% +the correlary there, but I got to get +that absolute value thing in. + + align:start position:0% +that absolute value thing in. + + + align:start position:0% +that absolute value thing in. +But it's + + align:start position:0% +But it's + + + align:start position:0% +But it's +upperbounded by the probability of the + + align:start position:0% +upperbounded by the probability of the + + + align:start position:0% +upperbounded by the probability of the +absolute value of R minus expected + + align:start position:0% +absolute value of R minus expected + + + align:start position:0% +absolute value of R minus expected +value bigger than equal to 10 standard + + align:start position:0% +value bigger than equal to 10 standard + + + align:start position:0% +value bigger than equal to 10 standard +deviations because this allows for two + + align:start position:0% +deviations because this allows for two + + + align:start position:0% +deviations because this allows for two +cases. R is 10 standard deviations high + + align:start position:0% +cases. R is 10 standard deviations high + + + align:start position:0% +cases. R is 10 standard deviations high +and R is 10 standard deviations low or + + align:start position:0% +and R is 10 standard deviations low or + + + align:start position:0% +and R is 10 standard deviations low or +more. So this is upper bounded by that. + + align:start position:0% +more. So this is upper bounded by that. + + + align:start position:0% +more. So this is upper bounded by that. +And now I can plug in chvbychev in the + + align:start position:0% +And now I can plug in chvbychev in the + + + align:start position:0% +And now I can plug in chvbychev in the +corlary form. And what's the answer when + + align:start position:0% +corlary form. And what's the answer when + + + align:start position:0% +corlary form. And what's the answer when +I do + + align:start position:0% + + + + align:start position:0% + +that? One in 100. Probability of being + + align:start position:0% +that? One in 100. Probability of being + + + align:start position:0% +that? One in 100. Probability of being +off by 10 standard deviations or more is + + align:start position:0% +off by 10 standard deviations or more is + + + align:start position:0% +off by 10 standard deviations or more is +at most one in 100. One in 10 + + align:start position:0% +at most one in 100. One in 10 + + + align:start position:0% +at most one in 100. One in 10 +squared. So it's a lot better bound. + + align:start position:0% +squared. So it's a lot better bound. + + + align:start position:0% +squared. So it's a lot better bound. +It's 1% instead of + + align:start position:0% +It's 1% instead of + + + align:start position:0% +It's 1% instead of +40%. All right. And so knowing the + + align:start position:0% +40%. All right. And so knowing the + + + align:start position:0% +40%. All right. And so knowing the +variance or the standard + + align:start position:0% +variance or the standard + + + align:start position:0% +variance or the standard +deviation gives you a lot more + + align:start position:0% +deviation gives you a lot more + + + align:start position:0% +deviation gives you a lot more +information and generally gives you much + + align:start position:0% +information and generally gives you much + + + align:start position:0% +information and generally gives you much +better bounds on the probability of + + align:start position:0% +better bounds on the probability of + + + align:start position:0% +better bounds on the probability of +deviating from the mean. And the reason + + align:start position:0% +deviating from the mean. And the reason + + + align:start position:0% +deviating from the mean. And the reason +it gives you better bounds is because + + align:start position:0% +it gives you better bounds is because + + + align:start position:0% +it gives you better bounds is because +the variance is squaring deviations. So + + align:start position:0% +the variance is squaring deviations. So + + + align:start position:0% +the variance is squaring deviations. So +they count a lot + + align:start position:0% + + + + align:start position:0% + +more. All right. + + align:start position:0% +more. All right. + + + align:start position:0% +more. All right. +Now let's look at this step a little bit + + align:start position:0% +Now let's look at this step a little bit + + + align:start position:0% +Now let's look at this step a little bit +more. + + align:start position:0% + + + + align:start position:0% + +All right, + + align:start position:0% +All right, + + + align:start position:0% +All right, +let's say here's a line and here's the + + align:start position:0% +let's say here's a line and here's the + + + align:start position:0% +let's say here's a line and here's the +expected value of + + align:start position:0% +expected value of + + + align:start position:0% +expected value of +R and say here's 10 standard + + align:start position:0% +R and say here's 10 standard + + + align:start position:0% +R and say here's 10 standard +deviations high here. So this will be + + align:start position:0% +deviations high here. So this will be + + + align:start position:0% +deviations high here. So this will be +more than 10 standard + + align:start position:0% +more than 10 standard + + + align:start position:0% +more than 10 standard +deviations and this will be 10 standard + + align:start position:0% +deviations and this will be 10 standard + + + align:start position:0% +deviations and this will be 10 standard +deviations on the low side. So here I'm + + align:start position:0% +deviations on the low side. So here I'm + + + align:start position:0% +deviations on the low side. So here I'm +low. + + align:start position:0% +low. + + + align:start position:0% +low. +Now this line here with the absolute + + align:start position:0% +Now this line here with the absolute + + + align:start position:0% +Now this line here with the absolute +value is figuring out the probability of + + align:start position:0% +value is figuring out the probability of + + + align:start position:0% +value is figuring out the probability of +being low or high. This is probability + + align:start position:0% +being low or high. This is probability + + + align:start position:0% +being low or high. This is probability +that the absolute value of r minus its + + align:start position:0% +that the absolute value of r minus its + + + align:start position:0% +that the absolute value of r minus its +expected + + align:start position:0% +expected + + + align:start position:0% +expected +value is at least 10 standard + + align:start position:0% + + + + align:start position:0% + +deviations. What we really wanted to + + align:start position:0% +deviations. What we really wanted to + + + align:start position:0% +deviations. What we really wanted to +know or bound was just the high side. + + align:start position:0% + + + + align:start position:0% + +Now is it true that then since the + + align:start position:0% +Now is it true that then since the + + + align:start position:0% +Now is it true that then since the +probability of high or low is one in 100 + + align:start position:0% +probability of high or low is one in 100 + + + align:start position:0% +probability of high or low is one in 100 +is it true that the probability being + + align:start position:0% +is it true that the probability being + + + align:start position:0% +is it true that the probability being +high is at most one in 200 + + align:start position:0% + + + + align:start position:0% + +half. Is that true? + + align:start position:0% +half. Is that true? + + + align:start position:0% +half. Is that true? +Yeah. + + align:start position:0% + + + + align:start position:0% + +Yeah. It is not necessarily true that + + align:start position:0% +Yeah. It is not necessarily true that + + + align:start position:0% +Yeah. It is not necessarily true that +the high and the low are equal and + + align:start position:0% +the high and the low are equal and + + + align:start position:0% +the high and the low are equal and +therefore the high is half the total. + + align:start position:0% +therefore the high is half the total. + + + align:start position:0% +therefore the high is half the total. +Might be true but not necessarily true. + + align:start position:0% +Might be true but not necessarily true. + + + align:start position:0% +Might be true but not necessarily true. +And it's a mistake that often gets made + + align:start position:0% +And it's a mistake that often gets made + + + align:start position:0% +And it's a mistake that often gets made +where you'll + + align:start position:0% +where you'll + + + align:start position:0% +where you'll +take this fact as being less than 100 to + + align:start position:0% +take this fact as being less than 100 to + + + align:start position:0% +take this fact as being less than 100 to +conclude that's less than one and 200. + + align:start position:0% +conclude that's less than one and 200. + + + align:start position:0% +conclude that's less than one and 200. +And that you can't do unless the + + align:start position:0% +And that you can't do unless the + + + align:start position:0% +And that you can't do unless the +distribution is symmetric, you know, + + align:start position:0% +distribution is symmetric, you know, + + + align:start position:0% +distribution is symmetric, you know, +around the expected value. Then you + + align:start position:0% +around the expected value. Then you + + + align:start position:0% +around the expected value. Then you +could do it if it's a symmetric + + align:start position:0% +could do it if it's a symmetric + + + align:start position:0% +could do it if it's a symmetric +distribution around the expected value. + + align:start position:0% +distribution around the expected value. + + + align:start position:0% +distribution around the expected value. +But usually it's + + align:start position:0% +But usually it's + + + align:start position:0% +But usually it's +not. + + align:start position:0% +not. + + + align:start position:0% +not. +Um, now there is something better you + + align:start position:0% +Um, now there is something better you + + + align:start position:0% +Um, now there is something better you +can + + align:start position:0% +can + + + align:start position:0% +can +say. So let me tell you what it is, but + + align:start position:0% +say. So let me tell you what it is, but + + + align:start position:0% +say. So let me tell you what it is, but +we won't prove it. I think we might + + align:start position:0% +we won't prove it. I think we might + + + align:start position:0% +we won't prove it. I think we might +prove it in the text. I'm not + + align:start position:0% +prove it in the text. I'm not + + + align:start position:0% +prove it in the text. I'm not +sure. If you just want the high side or + + align:start position:0% +sure. If you just want the high side or + + + align:start position:0% +sure. If you just want the high side or +just want the low side, you can do + + align:start position:0% +just want the low side, you can do + + + align:start position:0% +just want the low side, you can do +slightly + + align:start position:0% +slightly + + + align:start position:0% +slightly +better than one and C ^2. + + align:start position:0% + + + + align:start position:0% + +All right, that's the following + + align:start position:0% + + + + align:start position:0% + +theorem. For any random variable + + align:start position:0% +theorem. For any random variable + + + align:start position:0% +theorem. For any random variable +R, the probability that + + align:start position:0% +R, the probability that + + + align:start position:0% +R, the probability that +R is on the high + + align:start position:0% +R is on the high + + + align:start position:0% +R is on the high +side by C standard + + align:start position:0% +side by C standard + + + align:start position:0% +side by C standard +deviations is at most 1 over C^2 + 1. + + align:start position:0% +deviations is at most 1 over C^2 + 1. + + + align:start position:0% +deviations is at most 1 over C^2 + 1. +So it's not 1 over 2 c^2. It's 1 over + + align:start position:0% +So it's not 1 over 2 c^2. It's 1 over + + + align:start position:0% +So it's not 1 over 2 c^2. It's 1 over +c^2 + 1. And the same thing for the + + align:start position:0% +c^2 + 1. And the same thing for the + + + align:start position:0% +c^2 + 1. And the same thing for the +probability of being on the low + + align:start position:0% + + + + align:start position:0% + +side. Let's see. I want + + align:start position:0% +side. Let's see. I want + + + align:start position:0% +side. Let's see. I want +to I written this + + align:start position:0% +to I written this + + + align:start position:0% +to I written this +right. I want to get this + + align:start position:0% +right. I want to get this + + + align:start position:0% +right. I want to get this +is as is less than or equal to + + align:start position:0% +is as is less than or equal to + + + align:start position:0% +is as is less than or equal to +negative c times standard deviation. So + + align:start position:0% +negative c times standard deviation. So + + + align:start position:0% +negative c times standard deviation. So +here I'm high by C or more standard + + align:start position:0% +here I'm high by C or more standard + + + align:start position:0% +here I'm high by C or more standard +deviations. Here I'm low. So R is less + + align:start position:0% +deviations. Here I'm low. So R is less + + + align:start position:0% +deviations. Here I'm low. So R is less +than the expected value by at least + + align:start position:0% +than the expected value by at least + + + align:start position:0% +than the expected value by at least +standard dev C standard deviations. And + + align:start position:0% +standard dev C standard deviations. And + + + align:start position:0% +standard dev C standard deviations. And +that is also 1 over C ^2 + + + align:start position:0% +that is also 1 over C ^2 + + + + align:start position:0% +that is also 1 over C ^2 + +1. And it is possible to find + + align:start position:0% +1. And it is possible to find + + + align:start position:0% +1. And it is possible to find +distributions that hit these targets. + + align:start position:0% +distributions that hit these targets. + + + align:start position:0% +distributions that hit these targets. +Not both at the same time, but one one + + align:start position:0% +Not both at the same time, but one one + + + align:start position:0% +Not both at the same time, but one one +or the other hit those targets. So + + align:start position:0% +or the other hit those targets. So + + + align:start position:0% +or the other hit those targets. So +that's the best you can say in + + align:start position:0% +that's the best you can say in + + + align:start position:0% +that's the best you can say in +general. All right. So using this bound, + + align:start position:0% +general. All right. So using this bound, + + + align:start position:0% +general. All right. So using this bound, +what's the probability that a random + + align:start position:0% +what's the probability that a random + + + align:start position:0% +what's the probability that a random +person has an IQ of at least + + align:start position:0% +person has an IQ of at least + + + align:start position:0% +person has an IQ of at least +250? A little better than one in + + align:start position:0% + + + + align:start position:0% + +100. Yeah, one over 101. So in fact, the + + align:start position:0% +100. Yeah, one over 101. So in fact, the + + + align:start position:0% +100. Yeah, one over 101. So in fact, the +best we can say without knowing any more + + align:start position:0% +best we can say without knowing any more + + + align:start position:0% +best we can say without knowing any more +information about + + align:start position:0% +information about + + + align:start position:0% +information about +IQ's is that it's most at most one over + + align:start position:0% +IQ's is that it's most at most one over + + + align:start position:0% +IQ's is that it's most at most one over +101. Slightly + + align:start position:0% + + + + align:start position:0% + +better. Now in fact with IQ's they know + + align:start position:0% +better. Now in fact with IQ's they know + + + align:start position:0% +better. Now in fact with IQ's they know +more about the distribution and the + + align:start position:0% +more about the distribution and the + + + align:start position:0% +more about the distribution and the +probability is a lot less because you + + align:start position:0% +probability is a lot less because you + + + align:start position:0% +probability is a lot less because you +know more about the distribution than + + align:start position:0% +know more about the distribution than + + + align:start position:0% +know more about the distribution than +we've assumed here. In fact I don't + + align:start position:0% +we've assumed here. In fact I don't + + + align:start position:0% +we've assumed here. In fact I don't +think anybody has an IQ over 250 as far + + align:start position:0% +think anybody has an IQ over 250 as far + + + align:start position:0% +think anybody has an IQ over 250 as far +as I + + align:start position:0% +as I + + + align:start position:0% +as I +know. Any uh + + align:start position:0% +know. Any uh + + + align:start position:0% +know. Any uh +questions about + + align:start position:0% +questions about + + + align:start position:0% +questions about +this? Okay. All right. Say we we give + + align:start position:0% +this? Okay. All right. Say we we give + + + align:start position:0% +this? Okay. All right. Say we we give +the exam. + + align:start position:0% +the exam. + + + align:start position:0% +the exam. +What fraction of the + + align:start position:0% +What fraction of the + + + align:start position:0% +What fraction of the +class can score more than two standard + + align:start position:0% +class can score more than two standard + + + align:start position:0% +class can score more than two standard +deviations get two standard deviations + + align:start position:0% +deviations get two standard deviations + + + align:start position:0% +deviations get two standard deviations +or more away from the average above or + + align:start position:0% + + + + align:start position:0% + +below? Could half the class be two + + align:start position:0% +below? Could half the class be two + + + align:start position:0% +below? Could half the class be two +standard deviations off the + + align:start position:0% +standard deviations off the + + + align:start position:0% +standard deviations off the +mean? No. What's the biggest fraction + + align:start position:0% +mean? No. What's the biggest fraction + + + align:start position:0% +mean? No. What's the biggest fraction +that that could + + align:start position:0% + + + + align:start position:0% + +happen? What do I do? + + align:start position:0% +happen? What do I do? + + + align:start position:0% +happen? What do I do? +What fraction of the class can be more + + align:start position:0% +What fraction of the class can be more + + + align:start position:0% +What fraction of the class can be more +than two two standard deviations or more + + align:start position:0% +than two two standard deviations or more + + + align:start position:0% +than two two standard deviations or more +from the + + align:start position:0% + + + + align:start position:0% + +mean? What is it? One quarter because C + + align:start position:0% +mean? What is it? One quarter because C + + + align:start position:0% +mean? What is it? One quarter because C +is two. You don't even know what the + + align:start position:0% +is two. You don't even know what the + + + align:start position:0% +is two. You don't even know what the +mean is. You don't know what the + + align:start position:0% +mean is. You don't know what the + + + align:start position:0% +mean is. You don't know what the +standard deviation is. You don't need + + align:start position:0% +standard deviation is. You don't need + + + align:start position:0% +standard deviation is. You don't need +to. I just ask there's you're two + + align:start position:0% +to. I just ask there's you're two + + + align:start position:0% +to. I just ask there's you're two +standard deviations off or more. At most + + align:start position:0% +standard deviations off or more. At most + + + align:start position:0% +standard deviations off or more. At most +a + + align:start position:0% +a + + + align:start position:0% +a +quarter. How many could be two standard + + align:start position:0% +quarter. How many could be two standard + + + align:start position:0% +quarter. How many could be two standard +deviations high or better at + + align:start position:0% +deviations high or better at + + + align:start position:0% +deviations high or better at +most? A fifth. One over four plus one. + + align:start position:0% +most? A fifth. One over four plus one. + + + align:start position:0% +most? A fifth. One over four plus one. +Good. + + align:start position:0% +Good. + + + align:start position:0% +Good. +Okay. This holds true no matter what the + + align:start position:0% +Okay. This holds true no matter what the + + + align:start position:0% +Okay. This holds true no matter what the +distribution of test scores is. Yeah. + + align:start position:0% +distribution of test scores is. Yeah. + + + align:start position:0% +distribution of test scores is. Yeah. +Which one? This one. Uh that's more + + align:start position:0% +Which one? This one. Uh that's more + + + align:start position:0% +Which one? This one. Uh that's more +complicated. All right. That that'll + + align:start position:0% +complicated. All right. That that'll + + + align:start position:0% +complicated. All right. That that'll +take several boards to do to prove that. + + align:start position:0% +take several boards to do to prove that. + + + align:start position:0% +take several boards to do to prove that. +And I forget if we put it in the text or + + align:start position:0% +And I forget if we put it in the text or + + + align:start position:0% +And I forget if we put it in the text or +not. uh might be in the text to prove + + align:start position:0% + + + + align:start position:0% + +that any other + + align:start position:0% + + + + align:start position:0% + +questions. + + align:start position:0% +questions. + + + align:start position:0% +questions. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Uh so Marov and Chvy Chv are sometimes + + align:start position:0% +Uh so Marov and Chvy Chv are sometimes + + + align:start position:0% +Uh so Marov and Chvy Chv are sometimes +close, sometimes not. + + align:start position:0% +close, sometimes not. + + + align:start position:0% +close, sometimes not. +Um now for the rest of today, we're + + align:start position:0% +Um now for the rest of today, we're + + + align:start position:0% +Um now for the rest of today, we're +going to talk about a much more powerful + + align:start position:0% +going to talk about a much more powerful + + + align:start position:0% +going to talk about a much more powerful +technique. U but it only works in a + + align:start position:0% +technique. U but it only works in a + + + align:start position:0% +technique. U but it only works in a +special case. Now, the good news is a + + align:start position:0% +special case. Now, the good news is a + + + align:start position:0% +special case. Now, the good news is a +special case happens all the time in + + align:start position:0% +special case happens all the time in + + + align:start position:0% +special case happens all the time in +practice and it's the case when you're + + align:start position:0% +practice and it's the case when you're + + + align:start position:0% +practice and it's the case when you're +analyzing a random variable that itself + + align:start position:0% +analyzing a random variable that itself + + + align:start position:0% +analyzing a random variable that itself +is the sum of a bunch of other random + + align:start position:0% +is the sum of a bunch of other random + + + align:start position:0% +is the sum of a bunch of other random +variables. And we've seen already + + align:start position:0% +variables. And we've seen already + + + align:start position:0% +variables. And we've seen already +examples like that. And the other random + + align:start position:0% +examples like that. And the other random + + + align:start position:0% +examples like that. And the other random +variables have to be mutually + + align:start position:0% +variables have to be mutually + + + align:start position:0% +variables have to be mutually +independent. And in this case, you get a + + align:start position:0% +independent. And in this case, you get a + + + align:start position:0% +independent. And in this case, you get a +a bound that's called a churnoff bound. + + align:start position:0% +a bound that's called a churnoff bound. + + + align:start position:0% +a bound that's called a churnoff bound. +And this is the same churnoff who + + align:start position:0% +And this is the same churnoff who + + + align:start position:0% +And this is the same churnoff who +figured out how to beat the lottery. + + align:start position:0% +figured out how to beat the lottery. + + + align:start position:0% +figured out how to beat the lottery. +And uh you know it's + + align:start position:0% +And uh you know it's + + + align:start position:0% +And uh you know it's +interesting long after we started + + align:start position:0% +interesting long after we started + + + align:start position:0% +interesting long after we started +teaching this originally this stuff was + + align:start position:0% +teaching this originally this stuff was + + + align:start position:0% +teaching this originally this stuff was +only taught for turnoff bounds only + + align:start position:0% +only taught for turnoff bounds only + + + align:start position:0% +only taught for turnoff bounds only +taught for graduate students and now we + + align:start position:0% +taught for graduate students and now we + + + align:start position:0% +taught for graduate students and now we +we teach it here because it's so + + align:start position:0% +we teach it here because it's so + + + align:start position:0% +we teach it here because it's so +important and it really is accessible. + + align:start position:0% +important and it really is accessible. + + + align:start position:0% +important and it really is accessible. +Uh it'll be the probably the most + + align:start position:0% +Uh it'll be the probably the most + + + align:start position:0% +Uh it'll be the probably the most +complicated proof we've done to + + align:start position:0% +complicated proof we've done to + + + align:start position:0% +complicated proof we've done to +establish a turnoff bound. But Chernoff + + align:start position:0% +establish a turnoff bound. But Chernoff + + + align:start position:0% +establish a turnoff bound. But Chernoff +himself when he discovered this thought + + align:start position:0% +himself when he discovered this thought + + + align:start position:0% +himself when he discovered this thought +it was no big deal. In fact, he couldn't + + align:start position:0% +it was no big deal. In fact, he couldn't + + + align:start position:0% +it was no big deal. In fact, he couldn't +figure out why everybody in computer + + align:start position:0% +figure out why everybody in computer + + + align:start position:0% +figure out why everybody in computer +science was always writing papers with + + align:start position:0% +science was always writing papers with + + + align:start position:0% +science was always writing papers with +churnoff bounds in them, you know, and + + align:start position:0% +churnoff bounds in them, you know, and + + + align:start position:0% +churnoff bounds in them, you know, and +that's because he didn't put any + + align:start position:0% +that's because he didn't put any + + + align:start position:0% +that's because he didn't put any +emphasis on the bounds in his work, but + + align:start position:0% +emphasis on the bounds in his work, but + + + align:start position:0% +emphasis on the bounds in his work, but +computer scientists who came later found + + align:start position:0% +computer scientists who came later found + + + align:start position:0% +computer scientists who came later found +all sorts of important applications and + + align:start position:0% +all sorts of important applications and + + + align:start position:0% +all sorts of important applications and +we'll see some of those uh today. So, + + align:start position:0% +we'll see some of those uh today. So, + + + align:start position:0% +we'll see some of those uh today. So, +let me tell you what the bound + + align:start position:0% +let me tell you what the bound + + + align:start position:0% +let me tell you what the bound +is. And the nice thing is it it really + + align:start position:0% +is. And the nice thing is it it really + + + align:start position:0% +is. And the nice thing is it it really +is Marov's theorem again in disguise, + + align:start position:0% +is Marov's theorem again in disguise, + + + align:start position:0% +is Marov's theorem again in disguise, +just a little more complicated. + + align:start position:0% + + + + align:start position:0% + +theorem. Let's call it a turnoff bound. + + align:start position:0% + + + + align:start position:0% + +Let t1, + + align:start position:0% +Let t1, + + + align:start position:0% +Let t1, +t2 up to + + align:start position:0% +t2 up to + + + align:start position:0% +t2 up to +tn be + + align:start position:0% +tn be + + + align:start position:0% +tn be +any mutually + + align:start position:0% + + + + align:start position:0% + +independent. That's really + + align:start position:0% +independent. That's really + + + align:start position:0% +independent. That's really +important random + + align:start position:0% +important random + + + align:start position:0% +important random +variables such + + align:start position:0% + + + + align:start position:0% + +that each of them takes values only + + align:start position:0% +that each of them takes values only + + + align:start position:0% +that each of them takes values only +between zero and one. + + align:start position:0% +between zero and one. + + + align:start position:0% +between zero and one. +And if they don't normal, just normalize + + align:start position:0% +And if they don't normal, just normalize + + + align:start position:0% +And if they don't normal, just normalize +them. So they do. All right. So we're + + align:start position:0% +them. So they do. All right. So we're + + + align:start position:0% +them. So they do. All right. So we're +going to take a bunch of random + + align:start position:0% +going to take a bunch of random + + + align:start position:0% +going to take a bunch of random +variables that are mutually independent + + align:start position:0% +variables that are mutually independent + + + align:start position:0% +variables that are mutually independent +and they are all between zero and + + align:start position:0% + + + + align:start position:0% + +one. Then we're going to look at the + + align:start position:0% + + + + align:start position:0% + +sum of those random + + align:start position:0% + + + + align:start position:0% + +variables. Call that t. + + align:start position:0% + + + + align:start position:0% + +Then for any + + align:start position:0% +Then for any + + + align:start position:0% +Then for any +C at least + + align:start position:0% +C at least + + + align:start position:0% +C at least +one the probability that the sum random + + align:start position:0% +one the probability that the sum random + + + align:start position:0% +one the probability that the sum random +variable is at least C times its + + align:start position:0% +variable is at least C times its + + + align:start position:0% +variable is at least C times its +expected + + align:start position:0% +expected + + + align:start position:0% +expected +value so it's going to be the high side + + align:start position:0% +value so it's going to be the high side + + + align:start position:0% +value so it's going to be the high side +here is at most e to the minus Z and + + align:start position:0% +here is at most e to the minus Z and + + + align:start position:0% +here is at most e to the minus Z and +I'll tell you what that is in a minute + + align:start position:0% +I'll tell you what that is in a minute + + + align:start position:0% +I'll tell you what that is in a minute +times the expected value of + + align:start position:0% +times the expected value of + + + align:start position:0% +times the expected value of +t where + + align:start position:0% + + + + align:start position:0% + +Z + + align:start position:0% +Z + + + align:start position:0% +Z +is C natural log of + + align:start position:0% +is C natural log of + + + align:start position:0% +is C natural log of +C + 1 minus C. And it turns out if C is + + align:start position:0% +C + 1 minus C. And it turns out if C is + + + align:start position:0% +C + 1 minus C. And it turns out if C is +bigger than one, this is + + align:start position:0% + + + + align:start position:0% + +positive. All right, so that's a lot. + + align:start position:0% +positive. All right, so that's a lot. + + + align:start position:0% +positive. All right, so that's a lot. +You know, one of the longest theorems we + + align:start position:0% +You know, one of the longest theorems we + + + align:start position:0% +You know, one of the longest theorems we +wrote down here. Um but what it says is + + align:start position:0% +wrote down here. Um but what it says is + + + align:start position:0% +wrote down here. Um but what it says is +the probability we're + + align:start position:0% +the probability we're + + + align:start position:0% +the probability we're +high is exponentially + + align:start position:0% +high is exponentially + + + align:start position:0% +high is exponentially +small. As the expected value is big, the + + align:start position:0% +small. As the expected value is big, the + + + align:start position:0% +small. As the expected value is big, the +chance of being high gets really really + + align:start position:0% +chance of being high gets really really + + + align:start position:0% +chance of being high gets really really +tiny. Okay. Now I'm going to prove it in + + align:start position:0% +tiny. Okay. Now I'm going to prove it in + + + align:start position:0% +tiny. Okay. Now I'm going to prove it in +a minute, but let's let's just plug in + + align:start position:0% +a minute, but let's let's just plug in + + + align:start position:0% +a minute, but let's let's just plug in +some examples to see what's going on + + align:start position:0% +some examples to see what's going on + + + align:start position:0% +some examples to see what's going on +here. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +So for + + align:start position:0% + + + + align:start position:0% + +example + + align:start position:0% +example + + + align:start position:0% +example +suppose the expected value of + + align:start position:0% +suppose the expected value of + + + align:start position:0% +suppose the expected value of +t is + + align:start position:0% +t is + + + align:start position:0% +t is +100 and + + align:start position:0% +100 and + + + align:start position:0% +100 and +suppose c is + + align:start position:0% +suppose c is + + + align:start position:0% +suppose c is +two. So we expect to have a hundred come + + align:start position:0% +two. So we expect to have a hundred come + + + align:start position:0% +two. So we expect to have a hundred come +out of the sum. The probability we get + + align:start position:0% +out of the sum. The probability we get + + + align:start position:0% +out of the sum. The probability we get +at least + + align:start position:0% +at least + + + align:start position:0% +at least +200. Well, let's figure out what that + + align:start position:0% +200. Well, let's figure out what that + + + align:start position:0% +200. Well, let's figure out what that +is. C being two, we can evaluate Z. + + align:start position:0% +is. C being two, we can evaluate Z. + + + align:start position:0% +is. C being two, we can evaluate Z. +Now it's 2 natural log of 2 + 1 - 2. And + + align:start position:0% +Now it's 2 natural log of 2 + 1 - 2. And + + + align:start position:0% +Now it's 2 natural log of 2 + 1 - 2. And +that's close to but a little larger than + + align:start position:0% +that's close to but a little larger than + + + align:start position:0% +that's close to but a little larger than +38. + + align:start position:0% +38. + + + align:start position:0% +38. +So we can plug Z in the exponent up + + align:start position:0% +So we can plug Z in the exponent up + + + align:start position:0% +So we can plug Z in the exponent up +there and find that probability that T + + align:start position:0% +there and find that probability that T + + + align:start position:0% +there and find that probability that T +is at least twice its expected value + + align:start position:0% +is at least twice its expected value + + + align:start position:0% +is at least twice its expected value +namely at least + + align:start position:0% +namely at least + + + align:start position:0% +namely at least +200 is at most eus 38 * + + align:start position:0% +200 is at most eus 38 * + + + align:start position:0% +200 is at most eus 38 * +100 which is e to the minus + + align:start position:0% +100 which is e to the minus + + + align:start position:0% +100 which is e to the minus +38 which is just really + + align:start position:0% +38 which is just really + + + align:start position:0% +38 which is just really +small. All right. So that's just way + + align:start position:0% +small. All right. So that's just way + + + align:start position:0% +small. All right. So that's just way +better than any result you get with + + align:start position:0% +better than any result you get with + + + align:start position:0% +better than any result you get with +Marov or + + align:start position:0% +Marov or + + + align:start position:0% +Marov or +Chvby. Okay. So if you have a bunch of + + align:start position:0% +Chvby. Okay. So if you have a bunch of + + + align:start position:0% +Chvby. Okay. So if you have a bunch of +random variables between zero and one + + align:start position:0% +random variables between zero and one + + + align:start position:0% +random variables between zero and one +and they're mutually independent, you + + align:start position:0% +and they're mutually independent, you + + + align:start position:0% +and they're mutually independent, you +add them up. If you expect a 100 as the + + align:start position:0% +add them up. If you expect a 100 as the + + + align:start position:0% +add them up. If you expect a 100 as the +answer, the chance of getting 200 or + + align:start position:0% +answer, the chance of getting 200 or + + + align:start position:0% +answer, the chance of getting 200 or +more, forget about it. Not going to + + align:start position:0% +more, forget about it. Not going to + + + align:start position:0% +more, forget about it. Not going to +happen. Um now, of course, churnoff + + align:start position:0% +happen. Um now, of course, churnoff + + + align:start position:0% +happen. Um now, of course, churnoff +doesn't apply to all distributions. It + + align:start position:0% +doesn't apply to all distributions. It + + + align:start position:0% +doesn't apply to all distributions. It +has to be this type. This is a pretty + + align:start position:0% +has to be this type. This is a pretty + + + align:start position:0% +has to be this type. This is a pretty +broad class. In fact, it contains the + + align:start position:0% +broad class. In fact, it contains the + + + align:start position:0% +broad class. In fact, it contains the +class of all Berni + + align:start position:0% +class of all Berni + + + align:start position:0% +class of all Berni +distributions. Sorry, binomial + + align:start position:0% +distributions. Sorry, binomial + + + align:start position:0% +distributions. Sorry, binomial +distributions because remember a + + align:start position:0% +distributions because remember a + + + align:start position:0% +distributions because remember a +binomial + + align:start position:0% +binomial + + + align:start position:0% +binomial +distribution. Well, what's remember + + align:start position:0% +distribution. Well, what's remember + + + align:start position:0% +distribution. Well, what's remember +binomial distributions? That's where T + + align:start position:0% +binomial distributions? That's where T + + + align:start position:0% +binomial distributions? That's where T +is the sum of TI's. In binomial, you + + align:start position:0% +is the sum of TI's. In binomial, you + + + align:start position:0% +is the sum of TI's. In binomial, you +have TJ is zero or one. Can't be in + + align:start position:0% +have TJ is zero or one. Can't be in + + + align:start position:0% +have TJ is zero or one. Can't be in +between. And with binomial, all TJs have + + align:start position:0% +between. And with binomial, all TJs have + + + align:start position:0% +between. And with binomial, all TJs have +the same distribution. With turnoff, + + align:start position:0% +the same distribution. With turnoff, + + + align:start position:0% +the same distribution. With turnoff, +they can all be different. + + align:start position:0% +they can all be different. + + + align:start position:0% +they can all be different. +So turnoff is much broader than + + align:start position:0% +So turnoff is much broader than + + + align:start position:0% +So turnoff is much broader than +binomial. The individual guys here can + + align:start position:0% +binomial. The individual guys here can + + + align:start position:0% +binomial. The individual guys here can +have different distributions and attain + + align:start position:0% +have different distributions and attain + + + align:start position:0% +have different distributions and attain +values anywhere between zero and one as + + align:start position:0% +values anywhere between zero and one as + + + align:start position:0% +values anywhere between zero and one as +opposed to just one or the + + align:start position:0% + + + + align:start position:0% + +other. Any questions + + align:start position:0% +other. Any questions + + + align:start position:0% +other. Any questions +about this this theorem and what it says + + align:start position:0% +about this this theorem and what it says + + + align:start position:0% +about this this theorem and what it says +and the terms + + align:start position:0% +and the terms + + + align:start position:0% +and the terms +there. You know, one nice thing about it + + align:start position:0% +there. You know, one nice thing about it + + + align:start position:0% +there. You know, one nice thing about it +is the number of random variables + + align:start position:0% +is the number of random variables + + + align:start position:0% +is the number of random variables +doesn't even show up in the answer here. + + align:start position:0% +doesn't even show up in the answer here. + + + align:start position:0% +doesn't even show up in the answer here. +N doesn't even + + align:start position:0% +N doesn't even + + + align:start position:0% +N doesn't even +appear. Yeah. + + align:start position:0% +appear. Yeah. + + + align:start position:0% +appear. Yeah. +Does not apply to what? + + align:start position:0% +Does not apply to what? + + + align:start position:0% +Does not apply to what? +Uh yeah, when C equals 1, what happens + + align:start position:0% +Uh yeah, when C equals 1, what happens + + + align:start position:0% +Uh yeah, when C equals 1, what happens +is Z is zero? Because I have log of one + + align:start position:0% +is Z is zero? Because I have log of one + + + align:start position:0% +is Z is zero? Because I have log of one +is zero and 1 minus one is zero. And if + + align:start position:0% +is zero and 1 minus one is zero. And if + + + align:start position:0% +is zero and 1 minus one is zero. And if +Z is zero, it says your probability is + + align:start position:0% +Z is zero, it says your probability is + + + align:start position:0% +Z is zero, it says your probability is +upperbounded by one. Well, not too + + align:start position:0% +upperbounded by one. Well, not too + + + align:start position:0% +upperbounded by one. Well, not too +interesting because any probability is + + align:start position:0% +interesting because any probability is + + + align:start position:0% +interesting because any probability is +upperbounded by one. So it doesn't give + + align:start position:0% +upperbounded by one. So it doesn't give + + + align:start position:0% +upperbounded by one. So it doesn't give +you any information when C is zero. None + + align:start position:0% +you any information when C is zero. None + + + align:start position:0% +you any information when C is zero. None +at all. But as soon as C starts being + + align:start position:0% +at all. But as soon as C starts being + + + align:start position:0% +at all. But as soon as C starts being +sorry, C is one. Soon as C starts being + + align:start position:0% +sorry, C is one. Soon as C starts being + + + align:start position:0% +sorry, C is one. Soon as C starts being +bigger than one, which is sort of a case + + align:start position:0% +bigger than one, which is sort of a case + + + align:start position:0% +bigger than one, which is sort of a case +you're interested in, you're bigger than + + align:start position:0% +you're interested in, you're bigger than + + + align:start position:0% +you're interested in, you're bigger than +your expectation, then it gives very + + align:start position:0% +your expectation, then it gives very + + + align:start position:0% +your expectation, then it gives very +powerful results. Yeah. + + align:start position:0% + + + + align:start position:0% + +Uh yeah, you can it's true for n equals + + align:start position:0% +Uh yeah, you can it's true for n equals + + + align:start position:0% +Uh yeah, you can it's true for n equals +one as well. + + align:start position:0% +one as well. + + + align:start position:0% +one as well. +Now it doesn't give you a lot of + + align:start position:0% +Now it doesn't give you a lot of + + + align:start position:0% +Now it doesn't give you a lot of +information because what is the probab + + align:start position:0% +information because what is the probab + + + align:start position:0% +information because what is the probab +if c is bigger than one and n was one? + + align:start position:0% +if c is bigger than one and n was one? + + + align:start position:0% +if c is bigger than one and n was one? +So there's only one variable. What's the + + align:start position:0% +So there's only one variable. What's the + + + align:start position:0% +So there's only one variable. What's the +probability that a random variable + + align:start position:0% +probability that a random variable + + + align:start position:0% +probability that a random variable +exceeds + + align:start position:0% +exceeds + + + align:start position:0% +exceeds +um its expectation? C times it + + align:start position:0% +um its expectation? C times it + + + align:start position:0% +um its expectation? C times it +expectation. + + align:start position:0% + + + + align:start position:0% + +Yeah, let's let's see now. Maybe it does + + align:start position:0% +Yeah, let's let's see now. Maybe it does + + + align:start position:0% +Yeah, let's let's see now. Maybe it does +give you + + align:start position:0% +give you + + + align:start position:0% +give you +information because a random variable + + align:start position:0% +information because a random variable + + + align:start position:0% +information because a random variable +has a distribution on + + align:start position:0% + + + + align:start position:0% + +01. That's it. So, it does give you some + + align:start position:0% +01. That's it. So, it does give you some + + + align:start position:0% +01. That's it. So, it does give you some +information, but I don't think it gives + + align:start position:0% +information, but I don't think it gives + + + align:start position:0% +information, but I don't think it gives +you a lot. I don't have to think about + + align:start position:0% +you a lot. I don't have to think about + + + align:start position:0% +you a lot. I don't have to think about +that. What happens when there's just one + + align:start position:0% +that. What happens when there's just one + + + align:start position:0% +that. What happens when there's just one +guy? Because the same thing is true. + + align:start position:0% +guy? Because the same thing is true. + + + align:start position:0% +guy? Because the same thing is true. +Just now for a single random variable on + + align:start position:0% +Just now for a single random variable on + + + align:start position:0% +Just now for a single random variable on +01 the chance that + + align:start position:0% +01 the chance that + + + align:start position:0% +01 the chance that +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +you're twice the expected value. I have + + align:start position:0% +you're twice the expected value. I have + + + align:start position:0% +you're twice the expected value. I have +to think about that. That's a good + + align:start position:0% +to think about that. That's a good + + + align:start position:0% +to think about that. That's a good +question. Does it do anything + + align:start position:0% +question. Does it do anything + + + align:start position:0% +question. Does it do anything +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +there? + + align:start position:0% +there? + + + align:start position:0% +there? +Okay. All right. So, let's do an + + align:start position:0% +Okay. All right. So, let's do an + + + align:start position:0% +Okay. All right. So, let's do an +example how you might apply this. + + align:start position:0% + + + + align:start position:0% + +Say that you're playing pick + + align:start position:0% +Say that you're playing pick + + + align:start position:0% +Say that you're playing pick +four and there's 10 million people are + + align:start position:0% + + + + align:start position:0% + +playing and say in this version of pick + + align:start position:0% +playing and say in this version of pick + + + align:start position:0% +playing and say in this version of pick +four uh you're picking a four-digit + + align:start position:0% +four uh you're picking a four-digit + + + align:start position:0% +four uh you're picking a four-digit +number four single digits and you win if + + align:start position:0% +number four single digits and you win if + + + align:start position:0% +number four single digits and you win if +you get an exact match. So the + + align:start position:0% +you get an exact match. So the + + + align:start position:0% +you get an exact match. So the +probability of + + align:start position:0% +probability of + + + align:start position:0% +probability of +winning a person winning well they got + + align:start position:0% +winning a person winning well they got + + + align:start position:0% +winning a person winning well they got +to get all four digits right. That's one + + align:start position:0% +to get all four digits right. That's one + + + align:start position:0% +to get all four digits right. That's one +in 10,000 10 the + + align:start position:0% + + + + align:start position:0% + +4th. What's the expected number of + + align:start position:0% + + + + align:start position:0% + +winners if I got 10 million + + align:start position:0% +winners if I got 10 million + + + align:start position:0% +winners if I got 10 million +people? What's the expected number of + + align:start position:0% +people? What's the expected number of + + + align:start position:0% +people? What's the expected number of +winners? + + align:start position:0% + + + + align:start position:0% + +What is it? + + align:start position:0% + + + + align:start position:0% + +Got 10 + + align:start position:0% + + + + align:start position:0% + +million over + + align:start position:0% +million over + + + align:start position:0% +million over +10,000, right? Because what I'm doing + + align:start position:0% +10,000, right? Because what I'm doing + + + align:start position:0% +10,000, right? Because what I'm doing +here is the number of winners t is going + + align:start position:0% +here is the number of winners t is going + + + align:start position:0% +here is the number of winners t is going +to be the sum of 10 million indicator + + align:start position:0% + + + + align:start position:0% + +variables, right? And the probability + + align:start position:0% +variables, right? And the probability + + + align:start position:0% +variables, right? And the probability +that any one of these guys wins is 1 in + + align:start position:0% + + + + align:start position:0% + +10,000. So the expected number of + + align:start position:0% +10,000. So the expected number of + + + align:start position:0% +10,000. So the expected number of +winners is one in 10,000 added 10 + + align:start position:0% +winners is one in 10,000 added 10 + + + align:start position:0% +winners is one in 10,000 added 10 +million + + align:start position:0% +million + + + align:start position:0% +million +times, which is this. + + align:start position:0% + + + + align:start position:0% + +Is that okay? Everybody should be really + + align:start position:0% +Is that okay? Everybody should be really + + + align:start position:0% +Is that okay? Everybody should be really +familiar with how to whip these things + + align:start position:0% +familiar with how to whip these things + + + align:start position:0% +familiar with how to whip these things +out. This for sure will have probably at + + align:start position:0% +out. This for sure will have probably at + + + align:start position:0% +out. This for sure will have probably at +least a couple questions where you're + + align:start position:0% +least a couple questions where you're + + + align:start position:0% +least a couple questions where you're +going to need to be able to do that kind + + align:start position:0% +going to need to be able to do that kind + + + align:start position:0% +going to need to be able to do that kind +of stuff on the + + align:start position:0% +of stuff on the + + + align:start position:0% +of stuff on the +final. + + align:start position:0% +final. + + + align:start position:0% +final. +Okay. All right. Say I want to know the + + align:start position:0% +Okay. All right. Say I want to know the + + + align:start position:0% +Okay. All right. Say I want to know the +probability of getting at least 2,000 + + align:start position:0% +probability of getting at least 2,000 + + + align:start position:0% +probability of getting at least 2,000 +winners. + + align:start position:0% + + + + align:start position:0% + +And I want to upper bound + + align:start position:0% +And I want to upper bound + + + align:start position:0% +And I want to upper bound +that just with the information I've + + align:start position:0% +that just with the information I've + + + align:start position:0% +that just with the information I've +given + + align:start position:0% + + + + align:start position:0% + +you. + + align:start position:0% +you. + + + align:start position:0% +you. +Well, any thoughts about an upper + + align:start position:0% +Well, any thoughts about an upper + + + align:start position:0% +Well, any thoughts about an upper +bound? What's + + align:start position:0% +bound? What's + + + align:start position:0% +bound? What's +that? Yeah, that's a good good upper + + align:start position:0% +that? Yeah, that's a good good upper + + + align:start position:0% +that? Yeah, that's a good good upper +bound. Um, what did you have to assume + + align:start position:0% +bound. Um, what did you have to assume + + + align:start position:0% +bound. Um, what did you have to assume +to get + + align:start position:0% + + + + align:start position:0% + +there? E to the minus 380 is a great + + align:start position:0% +there? E to the minus 380 is a great + + + align:start position:0% +there? E to the minus 380 is a great +bound because you're going to plug in + + align:start position:0% +bound because you're going to plug in + + + align:start position:0% +bound because you're going to plug in +expected value is a,000 and you're + + align:start position:0% +expected value is a,000 and you're + + + align:start position:0% +expected value is a,000 and you're +asking we're asking for more than twice + + align:start position:0% +asking we're asking for more than twice + + + align:start position:0% +asking we're asking for more than twice +the expected value. So it's eus 38 *,000 + + align:start position:0% +the expected value. So it's eus 38 *,000 + + + align:start position:0% +the expected value. So it's eus 38 *,000 +and that for sure + + align:start position:0% + + + + align:start position:0% + +is so you computed this and that equals + + align:start position:0% +is so you computed this and that equals + + + align:start position:0% +is so you computed this and that equals +e to the minus + + align:start position:0% +e to the minus + + + align:start position:0% +e to the minus +380. So that's really small but what did + + align:start position:0% +380. So that's really small but what did + + + align:start position:0% +380. So that's really small but what did +you have to assume to apply + + align:start position:0% +you have to assume to apply + + + align:start position:0% +you have to assume to apply +churnoff? Mutual independence. A mutual + + align:start position:0% +churnoff? Mutual independence. A mutual + + + align:start position:0% +churnoff? Mutual independence. A mutual +independence of + + align:start position:0% + + + + align:start position:0% + +what? The numbers people + + align:start position:0% +what? The numbers people + + + align:start position:0% +what? The numbers people +picked. And we already know if people + + align:start position:0% +picked. And we already know if people + + + align:start position:0% +picked. And we already know if people +are picking + + align:start position:0% +are picking + + + align:start position:0% +are picking +numbers, they don't tend to be mutually + + align:start position:0% +numbers, they don't tend to be mutually + + + align:start position:0% +numbers, they don't tend to be mutually +independent. They tend to gang + + align:start position:0% +independent. They tend to gang + + + align:start position:0% +independent. They tend to gang +up. So, but if you had a computer + + align:start position:0% +up. So, but if you had a computer + + + align:start position:0% +up. So, but if you had a computer +picking the numbers randomly and + + align:start position:0% +picking the numbers randomly and + + + align:start position:0% +picking the numbers randomly and +mutually independently, then you would + + align:start position:0% +mutually independently, then you would + + + align:start position:0% +mutually independently, then you would +be e to the minus + + align:start position:0% +be e to the minus + + + align:start position:0% +be e to the minus +380 by + + align:start position:0% +380 by + + + align:start position:0% +380 by +turnoff. + + align:start position:0% +turnoff. + + + align:start position:0% +turnoff. +If mutually + + align:start position:0% +If mutually + + + align:start position:0% +If mutually +independent + + align:start position:0% + + + + align:start position:0% + +picks, everybody see why we did that? + + align:start position:0% +picks, everybody see why we did that? + + + align:start position:0% +picks, everybody see why we did that? +because it's the probability of twice + + align:start position:0% +because it's the probability of twice + + + align:start position:0% +because it's the probability of twice +your + + align:start position:0% +your + + + align:start position:0% +your +expectation. The total number of winners + + align:start position:0% +expectation. The total number of winners + + + align:start position:0% +expectation. The total number of winners +is the sum of 10 million indicator + + align:start position:0% +is the sum of 10 million indicator + + + align:start position:0% +is the sum of 10 million indicator +variables. And indicator variables are + + align:start position:0% +variables. And indicator variables are + + + align:start position:0% +variables. And indicator variables are +zero or one. So they fit that definition + + align:start position:0% +zero or one. So they fit that definition + + + align:start position:0% +zero or one. So they fit that definition +up + + align:start position:0% +up + + + align:start position:0% +up +there. All right? And so that would be + + align:start position:0% +there. All right? And so that would be + + + align:start position:0% +there. All right? And so that would be +we already figured out Z is at least + + align:start position:0% +we already figured out Z is at least + + + align:start position:0% +we already figured out Z is at least +38 and you're multiplying by the + + align:start position:0% +38 and you're multiplying by the + + + align:start position:0% +38 and you're multiplying by the +expected values of th00and that's EUS + + align:start position:0% +expected values of th00and that's EUS + + + align:start position:0% +expected values of th00and that's EUS +380. + + align:start position:0% +380. + + + align:start position:0% +380. +So very very unlikely. What if they + + align:start position:0% +So very very unlikely. What if they + + + align:start position:0% +So very very unlikely. What if they +weren't mutually independent? Can you + + align:start position:0% +weren't mutually independent? Can you + + + align:start position:0% +weren't mutually independent? Can you +say anything about + + align:start position:0% +say anything about + + + align:start position:0% +say anything about +this? Anything at all better than one, + + align:start position:0% +this? Anything at all better than one, + + + align:start position:0% +this? Anything at all better than one, +which we know for any probability? Yeah. + + align:start position:0% +which we know for any probability? Yeah. + + + align:start position:0% +which we know for any probability? Yeah. +It's possible that everyone chose the + + align:start position:0% +It's possible that everyone chose the + + + align:start position:0% +It's possible that everyone chose the +same numbers. + + align:start position:0% + + + + align:start position:0% + +Yes, everyone could have chosen the same + + align:start position:0% +Yes, everyone could have chosen the same + + + align:start position:0% +Yes, everyone could have chosen the same +number, but that number only comes up if + + align:start position:0% +number, but that number only comes up if + + + align:start position:0% +number, but that number only comes up if +with a one in 10,000 + + align:start position:0% + + + + align:start position:0% + +chance. So is you can say something can + + align:start position:0% +chance. So is you can say something can + + + align:start position:0% +chance. So is you can say something can +use Marov. Use Marov. What does Marov + + align:start position:0% +use Marov. Use Marov. What does Marov + + + align:start position:0% +use Marov. Use Marov. What does Marov +give + + align:start position:0% + + + + align:start position:0% + +you? What does Marov give you? + + align:start position:0% + + + + align:start position:0% + +12. Yeah, because you've got the + + align:start position:0% +12. Yeah, because you've got the + + + align:start position:0% +12. Yeah, because you've got the +expected + + align:start position:0% +expected + + + align:start position:0% +expected +value is + + align:start position:0% +value is + + + align:start position:0% +value is +1,00 divided by the bound threshold is + + align:start position:0% +1,00 divided by the bound threshold is + + + align:start position:0% +1,00 divided by the bound threshold is +2,00 is 1/2 by markoff and that holds + + align:start position:0% +2,00 is 1/2 by markoff and that holds + + + align:start position:0% +2,00 is 1/2 by markoff and that holds +true without any independence + + align:start position:0% + + + + align:start position:0% + +assumption. Now there's an enormous + + align:start position:0% +assumption. Now there's an enormous + + + align:start position:0% +assumption. Now there's an enormous +difference between a half and e to theus + + align:start position:0% +difference between a half and e to theus + + + align:start position:0% +difference between a half and e to theus +380. + + align:start position:0% +380. + + + align:start position:0% +380. +independence really makes a huge + + align:start position:0% +independence really makes a huge + + + align:start position:0% +independence really makes a huge +difference in the bounds you can + + align:start position:0% + + + + align:start position:0% + +compute. Okay. Um now there's another + + align:start position:0% +compute. Okay. Um now there's another + + + align:start position:0% +compute. Okay. Um now there's another +way we could have gone about this. What + + align:start position:0% +way we could have gone about this. What + + + align:start position:0% +way we could have gone about this. What +kind of distribution does t + + align:start position:0% +kind of distribution does t + + + align:start position:0% +kind of distribution does t +have in this + + align:start position:0% + + + + align:start position:0% + +case? + + align:start position:0% +case? + + + align:start position:0% +case? +Binomial because it's the sum of + + align:start position:0% +Binomial because it's the sum of + + + align:start position:0% +Binomial because it's the sum of +indicator random variables 01's. Each of + + align:start position:0% +indicator random variables 01's. Each of + + + align:start position:0% +indicator random variables 01's. Each of +these is 01 and they're all the same + + align:start position:0% +these is 01 and they're all the same + + + align:start position:0% +these is 01 and they're all the same +distribution. There's a one in 10,000 + + align:start position:0% +distribution. There's a one in 10,000 + + + align:start position:0% +distribution. There's a one in 10,000 +chance of winning for each one of them. + + align:start position:0% +chance of winning for each one of them. + + + align:start position:0% +chance of winning for each one of them. +So, it's a binomial. So, we could have + + align:start position:0% +So, it's a binomial. So, we could have + + + align:start position:0% +So, it's a binomial. So, we could have +gone back and used the formulas we had + + align:start position:0% +gone back and used the formulas we had + + + align:start position:0% +gone back and used the formulas we had +for the binomial distribution, plugged + + align:start position:0% +for the binomial distribution, plugged + + + align:start position:0% +for the binomial distribution, plugged +it all + + align:start position:0% +it all + + + align:start position:0% +it all +in, and we'd have gotten something + + align:start position:0% +in, and we'd have gotten something + + + align:start position:0% +in, and we'd have gotten something +pretty similar here, but churnoff was so + + align:start position:0% +pretty similar here, but churnoff was so + + + align:start position:0% +pretty similar here, but churnoff was so +much easier. Remember that pain we would + + align:start position:0% +much easier. Remember that pain we would + + + align:start position:0% +much easier. Remember that pain we would +go through with the binomial + + align:start position:0% +go through with the binomial + + + align:start position:0% +go through with the binomial +distribution the approximation + + align:start position:0% +distribution the approximation + + + align:start position:0% +distribution the approximation +Sterling's formula n shoes whatever you + + align:start position:0% +Sterling's formula n shoes whatever you + + + align:start position:0% +Sterling's formula n shoes whatever you +know the factorials and stuff that's a + + align:start position:0% +know the factorials and stuff that's a + + + align:start position:0% +know the factorials and stuff that's a +nightmare this was easy e to theus 380 + + align:start position:0% +nightmare this was easy e to theus 380 + + + align:start position:0% +nightmare this was easy e to theus 380 +was very easy to compute and really I + + align:start position:0% +was very easy to compute and really I + + + align:start position:0% +was very easy to compute and really I +mean at that point it doesn't matter if + + align:start position:0% +mean at that point it doesn't matter if + + + align:start position:0% +mean at that point it doesn't matter if +it's minus 381 or - 382 or whatever + + align:start position:0% +it's minus 381 or - 382 or whatever + + + align:start position:0% +it's minus 381 or - 382 or whatever +because it's really small so often even + + align:start position:0% +because it's really small so often even + + + align:start position:0% +because it's really small so often even +when you have a binomial distribution + + align:start position:0% +when you have a binomial distribution + + + align:start position:0% +when you have a binomial distribution +well churnoff will apply and that's a + + align:start position:0% +well churnoff will apply and that's a + + + align:start position:0% +well churnoff will apply and that's a +great way to go because it gives you + + align:start position:0% +great way to go because it gives you + + + align:start position:0% +great way to go because it gives you +should bounce + + align:start position:0% +should bounce + + + align:start position:0% +should bounce +generally. All right, let's figure out + + align:start position:0% +generally. All right, let's figure out + + + align:start position:0% +generally. All right, let's figure out +the probability + + align:start position:0% +the probability + + + align:start position:0% +the probability +of at least,00 winners instead of a + + align:start position:0% +of at least,00 winners instead of a + + + align:start position:0% +of at least,00 winners instead of a +thousand. So, let's look at the + + align:start position:0% +thousand. So, let's look at the + + + align:start position:0% +thousand. So, let's look at the +probability of at least 100 extra + + align:start position:0% +probability of at least 100 extra + + + align:start position:0% +probability of at least 100 extra +winners over what we expect out of 10 + + align:start position:0% +winners over what we expect out of 10 + + + align:start position:0% +winners over what we expect out of 10 +million. We got 10 million people. You + + align:start position:0% +million. We got 10 million people. You + + + align:start position:0% +million. We got 10 million people. You +expect a thousand. We're going to + + align:start position:0% +expect a thousand. We're going to + + + align:start position:0% +expect a thousand. We're going to +analyze a probability + + align:start position:0% +analyze a probability + + + align:start position:0% +analyze a probability +of,00. What's C in this case? We're + + align:start position:0% +of,00. What's C in this case? We're + + + align:start position:0% +of,00. What's C in this case? We're +going to use + + align:start position:0% +going to use + + + align:start position:0% +going to use +turnoff + + align:start position:0% +turnoff + + + align:start position:0% +turnoff +1.1. So this is 1.1 * + + align:start position:0% +1.1. So this is 1.1 * + + + align:start position:0% +1.1. So this is 1.1 * +a,000. And that means that + + align:start position:0% +a,000. And that means that + + + align:start position:0% +a,000. And that means that +Z is 1.1 * the natural log of 1.1 + 1 - + + align:start position:0% +Z is 1.1 * the natural log of 1.1 + 1 - + + + align:start position:0% +Z is 1.1 * the natural log of 1.1 + 1 - +1.1. And that is close to but at + + align:start position:0% +1.1. And that is close to but at + + + align:start position:0% +1.1. And that is close to but at +least 048. + + align:start position:0% + + + + align:start position:0% + +So this probability is at most by + + align:start position:0% +So this probability is at most by + + + align:start position:0% +So this probability is at most by +turnoff e to the + + align:start position:0% + + + + align:start position:0% + +minus.0048 + + align:start position:0% +minus.0048 + + + align:start position:0% +minus.0048 +times the expected number of winners is + + align:start position:0% +times the expected number of winners is + + + align:start position:0% +times the expected number of winners is +a + + align:start position:0% +a + + + align:start position:0% +a +thousand. So that + + align:start position:0% +thousand. So that + + + align:start position:0% +thousand. So that +is e to the + + align:start position:0% +is e to the + + + align:start position:0% +is e to the +minus4.8 which is less than 1% one in a + + align:start position:0% + + + + align:start position:0% + +100. So that's pretty powerful. says you + + align:start position:0% +100. So that's pretty powerful. says you + + + align:start position:0% +100. So that's pretty powerful. says you +got 10 million people who could win. The + + align:start position:0% +got 10 million people who could win. The + + + align:start position:0% +got 10 million people who could win. The +chance of even having a hundred more + + align:start position:0% +chance of even having a hundred more + + + align:start position:0% +chance of even having a hundred more +than the thousand you + + align:start position:0% +than the thousand you + + + align:start position:0% +than the thousand you +expect 1% chance at + + align:start position:0% +expect 1% chance at + + + align:start position:0% +expect 1% chance at +most. Very very powerful. It says you + + align:start position:0% +most. Very very powerful. It says you + + + align:start position:0% +most. Very very powerful. It says you +really expect to get really close to the + + align:start position:0% +really expect to get really close to the + + + align:start position:0% +really expect to get really close to the +mean in this + + align:start position:0% +mean in this + + + align:start position:0% +mean in this +situation. Okay, a lot better. I mean + + align:start position:0% +situation. Okay, a lot better. I mean + + + align:start position:0% +situation. Okay, a lot better. I mean +marov here gives you what a th00and over + + align:start position:0% +marov here gives you what a th00and over + + + align:start position:0% +marov here gives you what a th00and over +1100 says your probability could be 90% + + align:start position:0% +1100 says your probability could be 90% + + + align:start position:0% +1100 says your probability could be 90% +or something not very useful chbby chev + + align:start position:0% +or something not very useful chbby chev + + + align:start position:0% +or something not very useful chbby chev +won't give you much here either so if + + align:start position:0% +won't give you much here either so if + + + align:start position:0% +won't give you much here either so if +you can ever if you're in a situation to + + align:start position:0% +you can ever if you're in a situation to + + + align:start position:0% +you can ever if you're in a situation to +apply churnoff always go there gives you + + align:start position:0% +apply churnoff always go there gives you + + + align:start position:0% +apply churnoff always go there gives you +the best bounce any + + align:start position:0% +the best bounce any + + + align:start position:0% +the best bounce any +questions and this of course is why + + align:start position:0% +questions and this of course is why + + + align:start position:0% +questions and this of course is why +computer scientists use it all the time + + align:start position:0% +computer scientists use it all the time + + + align:start position:0% +computer scientists use it all the time +um okay let me actually before I two + + align:start position:0% +um okay let me actually before I two + + + align:start position:0% +um okay let me actually before I two +more examples. Let me prove the theorem + + align:start position:0% +more examples. Let me prove the theorem + + + align:start position:0% +more examples. Let me prove the theorem +in a special case to give you a feel for + + align:start position:0% +in a special case to give you a feel for + + + align:start position:0% +in a special case to give you a feel for +what's involved. The full proof is in + + align:start position:0% +what's involved. The full proof is in + + + align:start position:0% +what's involved. The full proof is in +the + + align:start position:0% +the + + + align:start position:0% +the +text. I'm going to prove it in the + + align:start position:0% +text. I'm going to prove it in the + + + align:start position:0% +text. I'm going to prove it in the +special case where the TJ are01. So + + align:start position:0% +special case where the TJ are01. So + + + align:start position:0% +special case where the TJ are01. So +they're indicator random variables, but + + align:start position:0% +they're indicator random variables, but + + + align:start position:0% +they're indicator random variables, but +they don't have to have the same + + align:start position:0% +they don't have to have the same + + + align:start position:0% +they don't have to have the same +distribution. So it's still more general + + align:start position:0% +distribution. So it's still more general + + + align:start position:0% +distribution. So it's still more general +than you get with a binomial + + align:start position:0% +than you get with a binomial + + + align:start position:0% +than you get with a binomial +distribution. All right. So we're going + + align:start position:0% +distribution. All right. So we're going + + + align:start position:0% +distribution. All right. So we're going +to do a + + align:start position:0% +to do a + + + align:start position:0% +to do a +proof of + + align:start position:0% + + + + align:start position:0% + +churnoff for the special + + align:start position:0% +churnoff for the special + + + align:start position:0% +churnoff for the special +case where the + + align:start position:0% +case where the + + + align:start position:0% +case where the +TJ are either zero or + + align:start position:0% +TJ are either zero or + + + align:start position:0% +TJ are either zero or +one. So they're indicator + + align:start position:0% + + + + align:start position:0% + +variables. Okay, so the first step is + + align:start position:0% +variables. Okay, so the first step is + + + align:start position:0% +variables. Okay, so the first step is +going to seem pretty mysterious, but + + align:start position:0% +going to seem pretty mysterious, but + + + align:start position:0% +going to seem pretty mysterious, but +we've been doing something like it all + + align:start position:0% +we've been doing something like it all + + + align:start position:0% +we've been doing something like it all +day. + + align:start position:0% + + + + align:start position:0% + +I'm trying to compute the probability T + + align:start position:0% +I'm trying to compute the probability T + + + align:start position:0% +I'm trying to compute the probability T +is bigger than C times its + + align:start position:0% +is bigger than C times its + + + align:start position:0% +is bigger than C times its +expectation. Well, what I'm going to do + + align:start position:0% +expectation. Well, what I'm going to do + + + align:start position:0% +expectation. Well, what I'm going to do +is exponentiate both of these guys and + + align:start position:0% +is exponentiate both of these guys and + + + align:start position:0% +is exponentiate both of these guys and +compute the probability that C to the T + + align:start position:0% +compute the probability that C to the T + + + align:start position:0% +compute the probability that C to the T +is at least C to the C times the + + align:start position:0% +is at least C to the C times the + + + align:start position:0% +is at least C to the C times the +expected value of + + align:start position:0% +expected value of + + + align:start position:0% +expected value of +T. All right. Now, this is not the first + + align:start position:0% +T. All right. Now, this is not the first + + + align:start position:0% +T. All right. Now, this is not the first +thing you'd expect to do probably if you + + align:start position:0% +thing you'd expect to do probably if you + + + align:start position:0% +thing you'd expect to do probably if you +were trying to prove this. So, it's one + + align:start position:0% +were trying to prove this. So, it's one + + + align:start position:0% +were trying to prove this. So, it's one +of those divine insights, right, that + + align:start position:0% +of those divine insights, right, that + + + align:start position:0% +of those divine insights, right, that +you make this step. + + align:start position:0% +you make this step. + + + align:start position:0% +you make this step. +Um, and then I'm going to apply Markoff + + align:start position:0% +Um, and then I'm going to apply Markoff + + + align:start position:0% +Um, and then I'm going to apply Markoff +like we've been doing all day to + + align:start position:0% +like we've been doing all day to + + + align:start position:0% +like we've been doing all day to +this. Now, since T is positive and C is + + align:start position:0% +this. Now, since T is positive and C is + + + align:start position:0% +this. Now, since T is positive and C is +positive, these are equal and this is + + align:start position:0% +positive, these are equal and this is + + + align:start position:0% +positive, these are equal and this is +never non- negative. + + align:start position:0% +never non- negative. + + + align:start position:0% +never non- negative. +So now by + + align:start position:0% +So now by + + + align:start position:0% +So now by +markov this is simply upper bounded by + + align:start position:0% +markov this is simply upper bounded by + + + align:start position:0% +markov this is simply upper bounded by +the expected value of + + align:start position:0% +the expected value of + + + align:start position:0% +the expected value of +that expected value of c to the + + align:start position:0% +that expected value of c to the + + + align:start position:0% +that expected value of c to the +t divided by + + align:start position:0% + + + + align:start position:0% + +this. All right and that's by marov. So + + align:start position:0% +this. All right and that's by marov. So + + + align:start position:0% +this. All right and that's by marov. So +everything we've done today is really + + align:start position:0% +everything we've done today is really + + + align:start position:0% +everything we've done today is really +marov in + + align:start position:0% + + + + align:start position:0% + +disguise. Any questions about so far? I + + align:start position:0% +disguise. Any questions about so far? I + + + align:start position:0% +disguise. Any questions about so far? I +mean this you start looking at this you + + align:start position:0% +mean this you start looking at this you + + + align:start position:0% +mean this you start looking at this you +go oh my god I got the random variable + + align:start position:0% +go oh my god I got the random variable + + + align:start position:0% +go oh my god I got the random variable +in the exponent you know this is looking + + align:start position:0% +in the exponent you know this is looking + + + align:start position:0% +in the exponent you know this is looking +like a nightmare what is the expected + + align:start position:0% +like a nightmare what is the expected + + + align:start position:0% +like a nightmare what is the expected +value of c to the t and this kind of + + align:start position:0% +value of c to the t and this kind of + + + align:start position:0% +value of c to the t and this kind of +stuff but we're going to hack through it + + align:start position:0% +stuff but we're going to hack through it + + + align:start position:0% +stuff but we're going to hack through it +all right because it gives you just + + align:start position:0% +all right because it gives you just + + + align:start position:0% +all right because it gives you just +amazingly powerful result when you're + + align:start position:0% + + + + align:start position:0% + +done all right so we got to evaluate the + + align:start position:0% +done all right so we got to evaluate the + + + align:start position:0% +done all right so we got to evaluate the +expected value of c to the + + align:start position:0% +expected value of c to the + + + align:start position:0% +expected value of c to the +t and we're going to use the fact that t + + align:start position:0% +t and we're going to use the fact that t + + + align:start position:0% +t and we're going to use the fact that t +is the sum of the + + align:start position:0% + + + + align:start position:0% + +TJs. And that means that C to the + + align:start position:0% +TJs. And that means that C to the + + + align:start position:0% +TJs. And that means that C to the +T equals C to the T1 * C to the + + align:start position:0% +T equals C to the T1 * C to the + + + align:start position:0% +T equals C to the T1 * C to the +T2 time C to the TN. Yeah. The weird + + align:start position:0% +T2 time C to the TN. Yeah. The weird + + + align:start position:0% +T2 time C to the TN. Yeah. The weird +thing about this proof is that every + + align:start position:0% +thing about this proof is that every + + + align:start position:0% +thing about this proof is that every +step sort of makes it more complicated + + align:start position:0% +step sort of makes it more complicated + + + align:start position:0% +step sort of makes it more complicated +looking until we get to the end. So, + + align:start position:0% +looking until we get to the end. So, + + + align:start position:0% +looking until we get to the end. So, +it's one of those that's hard to figure + + align:start position:0% +it's one of those that's hard to figure + + + align:start position:0% +it's one of those that's hard to figure +out the first + + align:start position:0% +out the first + + + align:start position:0% +out the first +time. All right, that means the expected + + align:start position:0% +time. All right, that means the expected + + + align:start position:0% +time. All right, that means the expected +value of C to the + + align:start position:0% +value of C to the + + + align:start position:0% +value of C to the +T is the expected value of the product + + align:start position:0% +T is the expected value of the product + + + align:start position:0% +T is the expected value of the product +of these + + align:start position:0% + + + + align:start position:0% + +things. All right. + + align:start position:0% +things. All right. + + + align:start position:0% +things. All right. +Now, going to use the product rule for + + align:start position:0% +Now, going to use the product rule for + + + align:start position:0% +Now, going to use the product rule for +expectation. + + align:start position:0% + + + + align:start position:0% + +Now, why can I use the product rule? + + align:start position:0% +Now, why can I use the product rule? + + + align:start position:0% +Now, why can I use the product rule? +What am I assuming to be able to do + + align:start position:0% + + + + align:start position:0% + +that? That they're mutually independent. + + align:start position:0% +that? That they're mutually independent. + + + align:start position:0% +that? That they're mutually independent. +That the C to the TJs are mutually + + align:start position:0% +That the C to the TJs are mutually + + + align:start position:0% +That the C to the TJs are mutually +independent of each other. And that + + align:start position:0% +independent of each other. And that + + + align:start position:0% +independent of each other. And that +follows because the TJs are mutually + + align:start position:0% +follows because the TJs are mutually + + + align:start position:0% +follows because the TJs are mutually +independent. + + align:start position:0% +independent. + + + align:start position:0% +independent. +So if a bunch of random variables are + + align:start position:0% +So if a bunch of random variables are + + + align:start position:0% +So if a bunch of random variables are +mutually independent then their + + align:start position:0% +mutually independent then their + + + align:start position:0% +mutually independent then their +exponentiations are mutually + + align:start position:0% +exponentiations are mutually + + + align:start position:0% +exponentiations are mutually +independent. All right. So this is + + align:start position:0% +independent. All right. So this is + + + align:start position:0% +independent. All right. So this is +by product rule for + + align:start position:0% +by product rule for + + + align:start position:0% +by product rule for +expectation and mutual + + align:start position:0% + + + + align:start position:0% + +independence. Okay. So now we got to + + align:start position:0% +independence. Okay. So now we got to + + + align:start position:0% +independence. Okay. So now we got to +evaluate the expected + + align:start position:0% +evaluate the expected + + + align:start position:0% +evaluate the expected +value of C to the TJ. + + align:start position:0% + + + + align:start position:0% + +And this is where we're going to make it + + align:start position:0% +And this is where we're going to make it + + + align:start position:0% +And this is where we're going to make it +simpler by assuming that TJ is just a 01 + + align:start position:0% +simpler by assuming that TJ is just a 01 + + + align:start position:0% +simpler by assuming that TJ is just a 01 +random + + align:start position:0% +random + + + align:start position:0% +random +variable. So it's the simplification + + align:start position:0% +variable. So it's the simplification + + + align:start position:0% +variable. So it's the simplification +comes in + + align:start position:0% + + + + align:start position:0% + +here. All right. So the expected value + + align:start position:0% +here. All right. So the expected value + + + align:start position:0% +here. All right. So the expected value +of + + align:start position:0% +of + + + align:start position:0% +of +TJ well there's two cases. TJ is one or + + align:start position:0% +TJ well there's two cases. TJ is one or + + + align:start position:0% +TJ well there's two cases. TJ is one or +it's zero because we made this + + align:start position:0% +it's zero because we made this + + + align:start position:0% +it's zero because we made this +simplification. If it's one, I get C to + + align:start position:0% +simplification. If it's one, I get C to + + + align:start position:0% +simplification. If it's one, I get C to +the one. Oh, expected value of C to the + + align:start position:0% +the one. Oh, expected value of C to the + + + align:start position:0% +the one. Oh, expected value of C to the +TJ. Get that + + align:start position:0% + + + + align:start position:0% + +right. It could be one in which case I + + align:start position:0% +right. It could be one in which case I + + + align:start position:0% +right. It could be one in which case I +get a contribution of C to the + + align:start position:0% +get a contribution of C to the + + + align:start position:0% +get a contribution of C to the +1 times the probability TJ equals 1 plus + + align:start position:0% +1 times the probability TJ equals 1 plus + + + align:start position:0% +1 times the probability TJ equals 1 plus +the case at zero. So I get C to the 0 + + align:start position:0% +the case at zero. So I get C to the 0 + + + align:start position:0% +the case at zero. So I get C to the 0 +times the probability TJ is zero. + + align:start position:0% + + + + align:start position:0% + +Well, C to the one is just + + align:start position:0% + + + + align:start position:0% + +C. C to the 0 is one. And I'm going to + + align:start position:0% +C. C to the 0 is one. And I'm going to + + + align:start position:0% +C. C to the 0 is one. And I'm going to +rewrite the TJ being zero as one minus + + align:start position:0% +rewrite the TJ being zero as one minus + + + align:start position:0% +rewrite the TJ being zero as one minus +the probability TJ is + + align:start position:0% + + + + align:start position:0% + +one. All right, this equals that. And of + + align:start position:0% +one. All right, this equals that. And of + + + align:start position:0% +one. All right, this equals that. And of +course, the one cancels. + + align:start position:0% +course, the one cancels. + + + align:start position:0% +course, the one cancels. +Now I'm going to collect terms here to + + align:start position:0% +Now I'm going to collect terms here to + + + align:start position:0% +Now I'm going to collect terms here to +get 1 + + align:start position:0% +get 1 + + + align:start position:0% +get 1 +minus 1 + c minus one times the + + align:start position:0% +minus 1 + c minus one times the + + + align:start position:0% +minus 1 + c minus one times the +probability tj = + + align:start position:0% + + + + align:start position:0% + +1. All + + align:start position:0% +1. All + + + align:start position:0% +1. All +right. + + align:start position:0% +right. + + + align:start position:0% +right. +Okay. Then I'm going to do one more step + + align:start position:0% +Okay. Then I'm going to do one more step + + + align:start position:0% +Okay. Then I'm going to do one more step +here. This is 1 + c minus one time the + + align:start position:0% +here. This is 1 + c minus one time the + + + align:start position:0% +here. This is 1 + c minus one time the +expected value of + + align:start position:0% +expected value of + + + align:start position:0% +expected value of +tj. Because if I have an indicator + + align:start position:0% +tj. Because if I have an indicator + + + align:start position:0% +tj. Because if I have an indicator +random + + align:start position:0% +random + + + align:start position:0% +random +variable, the expected value is the same + + align:start position:0% +variable, the expected value is the same + + + align:start position:0% +variable, the expected value is the same +as the probability that it's one because + + align:start position:0% +as the probability that it's one because + + + align:start position:0% +as the probability that it's one because +the other case is + + align:start position:0% +the other case is + + + align:start position:0% +the other case is +zero. And now I'm going to use the trick + + align:start position:0% +zero. And now I'm going to use the trick + + + align:start position:0% +zero. And now I'm going to use the trick +from last time. Remember 1 plus x is + + align:start position:0% +from last time. Remember 1 plus x is + + + align:start position:0% +from last time. Remember 1 plus x is +always at most e to the + + align:start position:0% +always at most e to the + + + align:start position:0% +always at most e to the +x from last time. None of these steps is + + align:start position:0% +x from last time. None of these steps is + + + align:start position:0% +x from last time. None of these steps is +obvious why we're doing them, but we're + + align:start position:0% +obvious why we're doing them, but we're + + + align:start position:0% +obvious why we're doing them, but we're +going to do them + + align:start position:0% +going to do them + + + align:start position:0% +going to do them +anyway. So this is at most + + align:start position:0% +anyway. So this is at most + + + align:start position:0% +anyway. So this is at most +E to + + align:start position:0% +E to + + + align:start position:0% +E to +this C minus one expected value of + + align:start position:0% + + + + align:start position:0% + +TJ. Okay, because 1 plus anything is at + + align:start position:0% +TJ. Okay, because 1 plus anything is at + + + align:start position:0% +TJ. Okay, because 1 plus anything is at +most the exponential of that. And I'm + + align:start position:0% +most the exponential of that. And I'm + + + align:start position:0% +most the exponential of that. And I'm +doing this step because I got a product + + align:start position:0% +doing this step because I got a product + + + align:start position:0% +doing this step because I got a product +of these guys and I want to put them in + + align:start position:0% +of these guys and I want to put them in + + + align:start position:0% +of these guys and I want to put them in +the exponent so I can then sum them so + + align:start position:0% +the exponent so I can then sum them so + + + align:start position:0% +the exponent so I can then sum them so +it gets easy. + + align:start position:0% + + + + align:start position:0% + +All + + align:start position:0% + + + + align:start position:0% + +right. Okay. + + align:start position:0% +right. Okay. + + + align:start position:0% +right. Okay. +Um, now we just plug + + align:start position:0% +Um, now we just plug + + + align:start position:0% +Um, now we just plug +this back in + + align:start position:0% +this back in + + + align:start position:0% +this back in +here. All right. So that means that the + + align:start position:0% +here. All right. So that means that the + + + align:start position:0% +here. All right. So that means that the +expected value of C to the + + align:start position:0% + + + + align:start position:0% + +T is at + + align:start position:0% +T is at + + + align:start position:0% +T is at +most the + + align:start position:0% + + + + align:start position:0% + +product of expected value of E to the C + + align:start position:0% +product of expected value of E to the C + + + align:start position:0% +product of expected value of E to the C +TJ is this E to the C minus one expected + + align:start position:0% +TJ is this E to the C minus one expected + + + align:start position:0% +TJ is this E to the C minus one expected +value of + + align:start position:0% +value of + + + align:start position:0% +value of +TJ and now I can convert this to a sum + + align:start position:0% +TJ and now I can convert this to a sum + + + align:start position:0% +TJ and now I can convert this to a sum +in the exponent. + + align:start position:0% + + + + align:start position:0% + +And this is J = 1 to N. And what do I do + + align:start position:0% +And this is J = 1 to N. And what do I do + + + align:start position:0% +And this is J = 1 to N. And what do I do +to simplify + + align:start position:0% + + + + align:start position:0% + +that? Linearity of expectation. + + align:start position:0% + + + + align:start position:0% + +C minus one times the sum j = 1 to n + + align:start position:0% +C minus one times the sum j = 1 to n + + + align:start position:0% +C minus one times the sum j = 1 to n +expected value of + + align:start position:0% + + + + align:start position:0% + +tj let's see did I actually I use + + align:start position:0% +tj let's see did I actually I use + + + align:start position:0% +tj let's see did I actually I use +linearity coming out I already used + + align:start position:0% +linearity coming out I already used + + + align:start position:0% +linearity coming out I already used +linearity wait I screwed up + + align:start position:0% +linearity wait I screwed up + + + align:start position:0% +linearity wait I screwed up +here so here I used the linearity when I + + align:start position:0% +here so here I used the linearity when I + + + align:start position:0% +here so here I used the linearity when I +took the sum up here inside the + + align:start position:0% +took the sum up here inside the + + + align:start position:0% +took the sum up here inside the +expectation I've already used linearity + + align:start position:0% +expectation I've already used linearity + + + align:start position:0% +expectation I've already used linearity +what is the sum of the + + align:start position:0% +what is the sum of the + + + align:start position:0% +what is the sum of the +TJs. T Yeah, that's what I needed to do + + align:start position:0% + + + + align:start position:0% + +here. Okay, we're now almost done. We + + align:start position:0% +here. Okay, we're now almost done. We + + + align:start position:0% +here. Okay, we're now almost done. We +got now an upper bound on the expected + + align:start position:0% +got now an upper bound on the expected + + + align:start position:0% +got now an upper bound on the expected +value of C to the T and it is this. And + + align:start position:0% +value of C to the T and it is this. And + + + align:start position:0% +value of C to the T and it is this. And +we just plug that in back up + + align:start position:0% + + + + align:start position:0% + +here. All right. So now this is at + + align:start position:0% +here. All right. So now this is at + + + align:start position:0% +here. All right. So now this is at +most e cus1 expected value of + + align:start position:0% +most e cus1 expected value of + + + align:start position:0% +most e cus1 expected value of +t over c to the c * the expected value + + align:start position:0% +t over c to the c * the expected value + + + align:start position:0% +t over c to the c * the expected value +of + + align:start position:0% +of + + + align:start position:0% +of +t. And now I just do + + align:start position:0% +t. And now I just do + + + align:start position:0% +t. And now I just do +manipulation. C to something is the same + + align:start position:0% +manipulation. C to something is the same + + + align:start position:0% +manipulation. C to something is the same +as e to the log of c times that + + align:start position:0% +as e to the log of c times that + + + align:start position:0% +as e to the log of c times that +something. So this is e to + + align:start position:0% +something. So this is e to + + + align:start position:0% +something. So this is e to +the minus c ln c expected value of + + align:start position:0% +the minus c ln c expected value of + + + align:start position:0% +the minus c ln c expected value of +t plus + + align:start position:0% + + + + align:start position:0% + +that and then I'm running out of + + align:start position:0% +that and then I'm running out of + + + align:start position:0% +that and then I'm running out of +room that equals I can just pull out the + + align:start position:0% +room that equals I can just pull out the + + + align:start position:0% +room that equals I can just pull out the +expected values of t. I get e to the + + align:start position:0% +expected values of t. I get e to the + + + align:start position:0% +expected values of t. I get e to the +minus c log of c + + align:start position:0% + + + + align:start position:0% + +plus c minus one expected value of + + align:start position:0% +plus c minus one expected value of + + + align:start position:0% +plus c minus one expected value of +t and that's e to the minus z expected + + align:start position:0% +t and that's e to the minus z expected + + + align:start position:0% +t and that's e to the minus z expected +value of + + align:start position:0% + + + + align:start position:0% + +t. All right, so that's a marathon + + align:start position:0% +t. All right, so that's a marathon + + + align:start position:0% +t. All right, so that's a marathon +proof. It's the worst proof I think. Now + + align:start position:0% +proof. It's the worst proof I think. Now + + + align:start position:0% +proof. It's the worst proof I think. Now +maybe minimum spanning trees was worth + + align:start position:0% +maybe minimum spanning trees was worth + + + align:start position:0% +maybe minimum spanning trees was worth +but this is one of the worst proofs + + align:start position:0% +but this is one of the worst proofs + + + align:start position:0% +but this is one of the worst proofs +we've seen this year but I wanted to + + align:start position:0% +we've seen this year but I wanted to + + + align:start position:0% +we've seen this year but I wanted to +show it to you uh because it's one of + + align:start position:0% +show it to you uh because it's one of + + + align:start position:0% +show it to you uh because it's one of +the most important results that we'll + + align:start position:0% +the most important results that we'll + + + align:start position:0% +the most important results that we'll +cover certainly in probability that can + + align:start position:0% +cover certainly in probability that can + + + align:start position:0% +cover certainly in probability that can +be very useful in practice and it gives + + align:start position:0% +be very useful in practice and it gives + + + align:start position:0% +be very useful in practice and it gives +you some feel for hey this wasn't so + + align:start position:0% +you some feel for hey this wasn't so + + + align:start position:0% +you some feel for hey this wasn't so +obvious to do it the first time uh and + + align:start position:0% +obvious to do it the first time uh and + + + align:start position:0% +obvious to do it the first time uh and +also some of the techniques that are + + align:start position:0% +also some of the techniques that are + + + align:start position:0% +also some of the techniques that are +used which is really marov's + + align:start position:0% +used which is really marov's + + + align:start position:0% +used which is really marov's +theorem any + + align:start position:0% +theorem any + + + align:start position:0% +theorem any +questions yeah + + align:start position:0% +questions yeah + + + align:start position:0% +questions yeah +zus + + align:start position:0% + + + + align:start position:0% + +Uh, did I do it wrong? + + align:start position:0% + + + + align:start position:0% + +Oh, I got to change the sign because I + + align:start position:0% +Oh, I got to change the sign because I + + + align:start position:0% +Oh, I got to change the sign because I +pulled a negative out in front. So, it's + + align:start position:0% +pulled a negative out in front. So, it's + + + align:start position:0% +pulled a negative out in front. So, it's +got to be negative C minus one, which + + align:start position:0% +got to be negative C minus one, which + + + align:start position:0% +got to be negative C minus one, which +means C + one. Yep. + + align:start position:0% +means C + one. Yep. + + + align:start position:0% +means C + one. Yep. +Good. Yeah, this was okay. I just made a + + align:start position:0% +Good. Yeah, this was okay. I just made a + + + align:start position:0% +Good. Yeah, this was okay. I just made a +mistake going to there. Any other + + align:start position:0% +mistake going to there. Any other + + + align:start position:0% +mistake going to there. Any other +questions? + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So the common theme here in using + + align:start position:0% +So the common theme here in using + + + align:start position:0% +So the common theme here in using +marov to get chby to get churnoff to get + + align:start position:0% +marov to get chby to get churnoff to get + + + align:start position:0% +marov to get chby to get churnoff to get +the marov extensions is always the same. + + align:start position:0% +the marov extensions is always the same. + + + align:start position:0% +the marov extensions is always the same. +And let me show you what that theme + + align:start position:0% + + + + align:start position:0% + +is because you can use it to get even + + align:start position:0% +is because you can use it to get even + + + align:start position:0% +is because you can use it to get even +other + + align:start position:0% +other + + + align:start position:0% +other +results. when we're trying to figure out + + align:start position:0% +results. when we're trying to figure out + + + align:start position:0% +results. when we're trying to figure out +the probability that t is at least c + + align:start position:0% +the probability that t is at least c + + + align:start position:0% +the probability that t is at least c +times its expected + + align:start position:0% +times its expected + + + align:start position:0% +times its expected +value or actually even in general even + + align:start position:0% +value or actually even in general even + + + align:start position:0% +value or actually even in general even +more generally than that the probability + + align:start position:0% +more generally than that the probability + + + align:start position:0% +more generally than that the probability +that a is bigger than b even more + + align:start position:0% +that a is bigger than b even more + + + align:start position:0% +that a is bigger than b even more +generally well that's the same as the + + align:start position:0% +generally well that's the same as the + + + align:start position:0% +generally well that's the same as the +probability that f of a is bigger than f + + align:start position:0% +probability that f of a is bigger than f + + + align:start position:0% +probability that f of a is bigger than f +of b as long as you don't change + + align:start position:0% +of b as long as you don't change + + + align:start position:0% +of b as long as you don't change +signs okay and then by marov this is at + + align:start position:0% +signs okay and then by marov this is at + + + align:start position:0% +signs okay and then by marov this is at +most the expected value of that as long + + align:start position:0% +most the expected value of that as long + + + align:start position:0% +most the expected value of that as long +as it's non- + + align:start position:0% +as it's non- + + + align:start position:0% +as it's non- +negative over + + align:start position:0% + + + + align:start position:0% + +that. All right. And chbbyev, what + + align:start position:0% +that. All right. And chbbyev, what + + + align:start position:0% +that. All right. And chbbyev, what +function f did we use for chvy in + + align:start position:0% +function f did we use for chvy in + + + align:start position:0% +function f did we use for chvy in +deriving chbbyev + + align:start position:0% +deriving chbbyev + + + align:start position:0% +deriving chbbyev +theorem? What was f doing in chby? I + + align:start position:0% +theorem? What was f doing in chby? I + + + align:start position:0% +theorem? What was f doing in chby? I +just actually I probably just erased + + align:start position:0% + + + + align:start position:0% + +it. What operation were we doing with + + align:start position:0% +it. What operation were we doing with + + + align:start position:0% +it. What operation were we doing with +chubby chav? + + align:start position:0% +chubby chav? + + + align:start position:0% +chubby chav? +Variance. And that meant we were + + align:start position:0% +Variance. And that meant we were + + + align:start position:0% +Variance. And that meant we were +squaring + + align:start position:0% +squaring + + + align:start position:0% +squaring +it. All right. So the technique used to + + align:start position:0% +it. All right. So the technique used to + + + align:start position:0% +it. All right. So the technique used to +prove chubby chev was f was the square + + align:start position:0% +prove chubby chev was f was the square + + + align:start position:0% +prove chubby chev was f was the square +function. For turnoff f is the + + align:start position:0% +function. For turnoff f is the + + + align:start position:0% +function. For turnoff f is the +exponentiation + + align:start position:0% +exponentiation + + + align:start position:0% +exponentiation +function which turns out to be in fact + + align:start position:0% +function which turns out to be in fact + + + align:start position:0% +function which turns out to be in fact +when we did it for churnoff that's the + + align:start position:0% +when we did it for churnoff that's the + + + align:start position:0% +when we did it for churnoff that's the +optimal choice of functions to get good + + align:start position:0% + + + + align:start position:0% + +bounds. All right any + + align:start position:0% +bounds. All right any + + + align:start position:0% +bounds. All right any +questions on that? + + align:start position:0% +questions on that? + + + align:start position:0% +questions on that? +All right, let's do one more example + + align:start position:0% +All right, let's do one more example + + + align:start position:0% +All right, let's do one more example +here with + + align:start position:0% + + + + align:start position:0% + +numbers. And this is a load balancing + + align:start position:0% +numbers. And this is a load balancing + + + align:start position:0% +numbers. And this is a load balancing +application. For example, you might have + + align:start position:0% +application. For example, you might have + + + align:start position:0% +application. For example, you might have +with web servers. Um, say you got to + + align:start position:0% +with web servers. Um, say you got to + + + align:start position:0% +with web servers. Um, say you got to +build a load balancing device and it's + + align:start position:0% +build a load balancing device and it's + + + align:start position:0% +build a load balancing device and it's +got to balance n + + align:start position:0% +got to balance n + + + align:start position:0% +got to balance n +jobs B1, + + align:start position:0% +jobs B1, + + + align:start position:0% +jobs B1, +B2 to + + align:start position:0% +B2 to + + + align:start position:0% +B2 to +BN across a set of M servers. + + align:start position:0% + + + + align:start position:0% + +S1, + + align:start position:0% +S1, + + + align:start position:0% +S1, +S2 to + + align:start position:0% +S2 to + + + align:start position:0% +S2 to +SN. And say you're doing this for a + + align:start position:0% +SN. And say you're doing this for a + + + align:start position:0% +SN. And say you're doing this for a +decent sized website. So maybe N is + + align:start position:0% +decent sized website. So maybe N is + + + align:start position:0% +decent sized website. So maybe N is +100,000. You got 100,000 requests a + + align:start position:0% +100,000. You got 100,000 requests a + + + align:start position:0% +100,000. You got 100,000 requests a +minute. And say you've got 10 + + align:start position:0% +minute. And say you've got 10 + + + align:start position:0% +minute. And say you've got 10 +servers to handle those + + align:start position:0% +servers to handle those + + + align:start position:0% +servers to handle those +requests. And say the requests are the + + align:start position:0% +requests. And say the requests are the + + + align:start position:0% +requests. And say the requests are the +time for the J request + + align:start position:0% +time for the J request + + + align:start position:0% +time for the J request +is say BJ takes the J job a J request + + align:start position:0% +is say BJ takes the J job a J request + + + align:start position:0% +is say BJ takes the J job a J request +takes LJ + + align:start position:0% +takes LJ + + + align:start position:0% +takes LJ +time and the time is the same on any + + align:start position:0% +time and the time is the same on any + + + align:start position:0% +time and the time is the same on any +server. The servers are all equivalent + + align:start position:0% +server. The servers are all equivalent + + + align:start position:0% +server. The servers are all equivalent +and let's assume it's normalized so that + + align:start position:0% +and let's assume it's normalized so that + + + align:start position:0% +and let's assume it's normalized so that +LJ is between zero and one. Maybe each + + align:start position:0% +LJ is between zero and one. Maybe each + + + align:start position:0% +LJ is between zero and one. Maybe each +the worst job takes a second to do. + + align:start position:0% +the worst job takes a second to do. + + + align:start position:0% +the worst job takes a second to do. +Let's + + align:start position:0% +Let's + + + align:start position:0% +Let's +say and say that if you sum up the + + align:start position:0% +say and say that if you sum up the + + + align:start position:0% +say and say that if you sum up the +length of all the jobs you get L total + + align:start position:0% + + + + align:start position:0% + +workload is the sum of all of + + align:start position:0% +workload is the sum of all of + + + align:start position:0% +workload is the sum of all of +them J = 1 to + + align:start position:0% + + + + align:start position:0% + +N. All right. And we're going to assume + + align:start position:0% +N. All right. And we're going to assume + + + align:start position:0% +N. All right. And we're going to assume +that the average job length is a quarter + + align:start position:0% +that the average job length is a quarter + + + align:start position:0% +that the average job length is a quarter +second. So we're going to assume + + align:start position:0% +second. So we're going to assume + + + align:start position:0% +second. So we're going to assume +that the total amount of work is + + align:start position:0% +that the total amount of work is + + + align:start position:0% +that the total amount of work is +25,000 seconds say so the average job + + align:start position:0% +25,000 seconds say so the average job + + + align:start position:0% +25,000 seconds say so the average job +length is a quarter + + align:start position:0% +length is a quarter + + + align:start position:0% +length is a quarter +second and the job is to assign these + + align:start position:0% +second and the job is to assign these + + + align:start position:0% +second and the job is to assign these +tasks to the 10 servers. + + align:start position:0% +tasks to the 10 servers. + + + align:start position:0% +tasks to the 10 servers. +Well, so that hopefully every server is + + align:start position:0% +Well, so that hopefully every server is + + + align:start position:0% +Well, so that hopefully every server is +doing L overM work, which would be + + align:start position:0% +doing L overM work, which would be + + + align:start position:0% +doing L overM work, which would be +25,000 over 10 or 2500 milliseconds of + + align:start position:0% +25,000 over 10 or 2500 milliseconds of + + + align:start position:0% +25,000 over 10 or 2500 milliseconds of +work, something like that. I don't + + align:start position:0% +work, something like that. I don't + + + align:start position:0% +work, something like that. I don't +know, right? Because when you're doing + + align:start position:0% +know, right? Because when you're doing + + + align:start position:0% +know, right? Because when you're doing +load balancing, you want to take your + + align:start position:0% +load balancing, you want to take your + + + align:start position:0% +load balancing, you want to take your +load and spread it evenly equally among + + align:start position:0% +load and spread it evenly equally among + + + align:start position:0% +load and spread it evenly equally among +all the + + align:start position:0% +all the + + + align:start position:0% +all the +servers. Any questions about the + + align:start position:0% +servers. Any questions about the + + + align:start position:0% +servers. Any questions about the +problem? You got bunch of jobs, bunch of + + align:start position:0% +problem? You got bunch of jobs, bunch of + + + align:start position:0% +problem? You got bunch of jobs, bunch of +servers. You want to assign the jobs to + + align:start position:0% +servers. You want to assign the jobs to + + + align:start position:0% +servers. You want to assign the jobs to +the servers to balance the + + align:start position:0% +the servers to balance the + + + align:start position:0% +the servers to balance the +load. + + align:start position:0% +load. + + + align:start position:0% +load. +Well, what is the simplest algorithm you + + align:start position:0% +Well, what is the simplest algorithm you + + + align:start position:0% +Well, what is the simplest algorithm you +can think of to do this? + + align:start position:0% +can think of to do this? + + + align:start position:0% +can think of to do this? +Ah, that's a good algorithm to do this. + + align:start position:0% +Ah, that's a good algorithm to do this. + + + align:start position:0% +Ah, that's a good algorithm to do this. +In practice, the first thing people do + + align:start position:0% +In practice, the first thing people do + + + align:start position:0% +In practice, the first thing people do +is well, take the first L + + align:start position:0% +is well, take the first L + + + align:start position:0% +is well, take the first L +overM take the first N /M jobs, put them + + align:start position:0% +overM take the first N /M jobs, put them + + + align:start position:0% +overM take the first N /M jobs, put them +on server one, the next N /M on server + + align:start position:0% +on server one, the next N /M on server + + + align:start position:0% +on server one, the next N /M on server +two. Or they'll use something called + + align:start position:0% +two. Or they'll use something called + + + align:start position:0% +two. Or they'll use something called +roundroin. First job goes here, second + + align:start position:0% +roundroin. First job goes here, second + + + align:start position:0% +roundroin. First job goes here, second +here, third here, 10th here, back and + + align:start position:0% +here, third here, 10th here, back and + + + align:start position:0% +here, third here, 10th here, back and +start over. And they hope that it'll + + align:start position:0% +start over. And they hope that it'll + + + align:start position:0% +start over. And they hope that it'll +balance the load, but it might well not + + align:start position:0% +balance the load, but it might well not + + + align:start position:0% +balance the load, but it might well not +because maybe every tenth job is a big + + align:start position:0% +because maybe every tenth job is a big + + + align:start position:0% +because maybe every tenth job is a big +one. All right. So, what's much better + + align:start position:0% +one. All right. So, what's much better + + + align:start position:0% +one. All right. So, what's much better +to do in practice is to assign them + + align:start position:0% +to do in practice is to assign them + + + align:start position:0% +to do in practice is to assign them +randomly. So, a job comes in, you don't + + align:start position:0% +randomly. So, a job comes in, you don't + + + align:start position:0% +randomly. So, a job comes in, you don't +even pay attention to how hard it is, + + align:start position:0% +even pay attention to how hard it is, + + + align:start position:0% +even pay attention to how hard it is, +how much time you think it'll take. You + + align:start position:0% +how much time you think it'll take. You + + + align:start position:0% +how much time you think it'll take. You +might not even know before you start the + + align:start position:0% +might not even know before you start the + + + align:start position:0% +might not even know before you start the +job how long it's going to take to + + align:start position:0% +job how long it's going to take to + + + align:start position:0% +job how long it's going to take to +complete. give it to a random server. + + align:start position:0% +complete. give it to a random server. + + + align:start position:0% +complete. give it to a random server. +Don't even look at how much work that + + align:start position:0% +Don't even look at how much work that + + + align:start position:0% +Don't even look at how much work that +server has. Just give it to a random + + align:start position:0% +server has. Just give it to a random + + + align:start position:0% +server has. Just give it to a random +one. And it turns out this does very + + align:start position:0% +one. And it turns out this does very + + + align:start position:0% +one. And it turns out this does very +very well without knowing anything. Just + + align:start position:0% +very well without knowing anything. Just + + + align:start position:0% +very well without knowing anything. Just +that simple approach does great in + + align:start position:0% +that simple approach does great in + + + align:start position:0% +that simple approach does great in +practice. And today state-of-the-art + + align:start position:0% +practice. And today state-of-the-art + + + align:start position:0% +practice. And today state-of-the-art +uh load balancers do + + align:start position:0% + + + + align:start position:0% + +this. In fact, we've been doing + + align:start position:0% +this. In fact, we've been doing + + + align:start position:0% +this. In fact, we've been doing +randomized kinds of things like this at + + align:start position:0% +randomized kinds of things like this at + + + align:start position:0% +randomized kinds of things like this at +Okami now for a decade. And it's just + + align:start position:0% +Okami now for a decade. And it's just + + + align:start position:0% +Okami now for a decade. And it's just +stunning how well it works. And so let's + + align:start position:0% +stunning how well it works. And so let's + + + align:start position:0% +stunning how well it works. And so let's +see why that + + align:start position:0% + + + + align:start position:0% + +is. Of course, we're going to use the + + align:start position:0% +is. Of course, we're going to use the + + + align:start position:0% +is. Of course, we're going to use the +churnoff bound to do it. + + align:start position:0% +churnoff bound to do it. + + + align:start position:0% +churnoff bound to do it. +So let's + + align:start position:0% +So let's + + + align:start position:0% +So let's +let + + align:start position:0% +let + + + align:start position:0% +let +ri be the + + align:start position:0% +ri be the + + + align:start position:0% +ri be the +load + + align:start position:0% +load + + + align:start position:0% +load +on server + + align:start position:0% +on server + + + align:start position:0% +on server +si + + align:start position:0% +si + + + align:start position:0% +si +from job + + align:start position:0% +from job + + + align:start position:0% +from job +bj. + + align:start position:0% +bj. + + + align:start position:0% +bj. +Now if bj is not assigned to si it's + + align:start position:0% +Now if bj is not assigned to si it's + + + align:start position:0% +Now if bj is not assigned to si it's +zero load because it's not even doing + + align:start position:0% +zero load because it's not even doing + + + align:start position:0% +zero load because it's not even doing +the work there. So we know that RI + + align:start position:0% +the work there. So we know that RI + + + align:start position:0% +the work there. So we know that RI +equals the load of BJ if it's + + align:start position:0% +equals the load of BJ if it's + + + align:start position:0% +equals the load of BJ if it's +assigned to + + align:start position:0% + + + + align:start position:0% + +SI and that happens with + + align:start position:0% +SI and that happens with + + + align:start position:0% +SI and that happens with +probability one over + + align:start position:0% +probability one over + + + align:start position:0% +probability one over +M. the job gets picks one of the M + + align:start position:0% +M. the job gets picks one of the M + + + align:start position:0% +M. the job gets picks one of the M +servers at random and otherwise the load + + align:start position:0% +servers at random and otherwise the load + + + align:start position:0% +servers at random and otherwise the load +is + + align:start position:0% +is + + + align:start position:0% +is +zero because it's not assigned to that + + align:start position:0% +zero because it's not assigned to that + + + align:start position:0% +zero because it's not assigned to that +server and that is + + align:start position:0% +server and that is + + + align:start position:0% +server and that is +probability 1 minus 1 / + + align:start position:0% +probability 1 minus 1 / + + + align:start position:0% +probability 1 minus 1 / +m. Now let's look at how much load gets + + align:start position:0% +m. Now let's look at how much load gets + + + align:start position:0% +m. Now let's look at how much load gets +assigned by this random algorithm to + + align:start position:0% +assigned by this random algorithm to + + + align:start position:0% +assigned by this random algorithm to +server + + align:start position:0% +server + + + align:start position:0% +server +I. So we'll let R + + align:start position:0% +I. So we'll let R + + + align:start position:0% +I. So we'll let R +I + + align:start position:0% +I + + + align:start position:0% +I +be the sum of all the + + align:start position:0% +be the sum of all the + + + align:start position:0% +be the sum of all the +load assigned to server + + align:start position:0% + + + + align:start position:0% + +I. All right. So we've got + + align:start position:0% +I. All right. So we've got + + + align:start position:0% +I. All right. So we've got +these indicator or the random variables + + align:start position:0% +these indicator or the random variables + + + align:start position:0% +these indicator or the random variables +not zero one. There's zero and whatever + + align:start position:0% +not zero one. There's zero and whatever + + + align:start position:0% +not zero one. There's zero and whatever +this load happens to be for the Jth job + + align:start position:0% +this load happens to be for the Jth job + + + align:start position:0% +this load happens to be for the Jth job +at most one. + + align:start position:0% +at most one. + + + align:start position:0% +at most one. +and we sum up the value for the + + align:start position:0% +and we sum up the value for the + + + align:start position:0% +and we sum up the value for the +contribution to SI over all the + + align:start position:0% + + + + align:start position:0% + +jobs. So now we compute the expected + + align:start position:0% +jobs. So now we compute the expected + + + align:start position:0% +jobs. So now we compute the expected +value of RA the expected load on the E + + align:start position:0% + + + + align:start position:0% + +server. All right. The expected load on + + align:start position:0% +server. All right. The expected load on + + + align:start position:0% +server. All right. The expected load on +the E + + align:start position:0% +the E + + + align:start position:0% +the E +server is well we use linearity of + + align:start position:0% + + + + align:start position:0% + +expectation. + + align:start position:0% +expectation. + + + align:start position:0% +expectation. +Okay. And the expected value of + + align:start position:0% +Okay. And the expected value of + + + align:start position:0% +Okay. And the expected value of +rij well it's zero or LJ. It's it's LJ + + align:start position:0% +rij well it's zero or LJ. It's it's LJ + + + align:start position:0% +rij well it's zero or LJ. It's it's LJ +with probability 1 over M. This is just + + align:start position:0% +with probability 1 over M. This is just + + + align:start position:0% +with probability 1 over M. This is just +now the + + align:start position:0% +now the + + + align:start position:0% +now the +sum of LJ over + + align:start position:0% +sum of LJ over + + + align:start position:0% +sum of LJ over +M. And the sum of LJ is just + + align:start position:0% + + + + align:start position:0% + +L. So the expected load of the I server + + align:start position:0% +L. So the expected load of the I server + + + align:start position:0% +L. So the expected load of the I server +is the total load divided by the number + + align:start position:0% +is the total load divided by the number + + + align:start position:0% +is the total load divided by the number +of servers which is perfect. It's + + align:start position:0% +of servers which is perfect. It's + + + align:start position:0% +of servers which is perfect. It's +optimal. Can't do better than + + align:start position:0% + + + + align:start position:0% + +that. All right. Right? And it makes + + align:start position:0% +that. All right. Right? And it makes + + + align:start position:0% +that. All right. Right? And it makes +sense. If you assign all the jobs + + align:start position:0% +sense. If you assign all the jobs + + + align:start position:0% +sense. If you assign all the jobs +randomly, every server is expecting to + + align:start position:0% +randomly, every server is expecting to + + + align:start position:0% +randomly, every server is expecting to +get one over m of the total + + align:start position:0% +get one over m of the total + + + align:start position:0% +get one over m of the total +load. Now, we want to know the + + align:start position:0% +load. Now, we want to know the + + + align:start position:0% +load. Now, we want to know the +probability you deviate from that. That + + align:start position:0% +probability you deviate from that. That + + + align:start position:0% +probability you deviate from that. That +you have too much load on the E + + align:start position:0% + + + + align:start position:0% + +server. All + + align:start position:0% + + + + align:start position:0% + +right. The probability that the E server + + align:start position:0% +right. The probability that the E server + + + align:start position:0% +right. The probability that the E server +has C times the optimal + + align:start position:0% + + + + align:start position:0% + +load is at most by turnoff if the jobs + + align:start position:0% +load is at most by turnoff if the jobs + + + align:start position:0% +load is at most by turnoff if the jobs +are independent minus ZL over M minus Z + + align:start position:0% +are independent minus ZL over M minus Z + + + align:start position:0% +are independent minus ZL over M minus Z +times the expected load where Z is C ln + + align:start position:0% +times the expected load where Z is C ln + + + align:start position:0% +times the expected load where Z is C ln +C + 1 minus C. This is churnoff. Now + + align:start position:0% +C + 1 minus C. This is churnoff. Now + + + align:start position:0% +C + 1 minus C. This is churnoff. Now +just straight from the formula turnoff + + align:start position:0% +just straight from the formula turnoff + + + align:start position:0% +just straight from the formula turnoff +as long as these loads are mutually + + align:start position:0% +as long as these loads are mutually + + + align:start position:0% +as long as these loads are mutually +independent. All right. + + align:start position:0% + + + + align:start position:0% + +So so we know that when C gets to be I + + align:start position:0% +So so we know that when C gets to be I + + + align:start position:0% +So so we know that when C gets to be I +don't know you pick you know 10% above + + align:start position:0% +don't know you pick you know 10% above + + + align:start position:0% +don't know you pick you know 10% above +optimal you know C equals + + align:start position:0% +optimal you know C equals + + + align:start position:0% +optimal you know C equals +1.1. Well we know that this is going to + + align:start position:0% +1.1. Well we know that this is going to + + + align:start position:0% +1.1. Well we know that this is going to +be a very small number. L over M is 2500 + + align:start position:0% +be a very small number. L over M is 2500 + + + align:start position:0% +be a very small number. L over M is 2500 +and Z in this case we found was + + align:start position:0% +and Z in this case we found was + + + align:start position:0% +and Z in this case we found was +0.0048. So we get E to the + + align:start position:0% + + + + align:start position:0% + +minus.0048* + + align:start position:0% +minus.0048* + + + align:start position:0% +minus.0048* +2500 and that is really tiny. That's uh + + align:start position:0% +2500 and that is really tiny. That's uh + + + align:start position:0% +2500 and that is really tiny. That's uh +less than one in 160,000. + + align:start position:0% + + + + align:start position:0% + +So turnoff tells us the probability that + + align:start position:0% +So turnoff tells us the probability that + + + align:start position:0% +So turnoff tells us the probability that +any server that a particular server gets + + align:start position:0% +any server that a particular server gets + + + align:start position:0% +any server that a particular server gets +10% load more than you expect is + + align:start position:0% +10% load more than you expect is + + + align:start position:0% +10% load more than you expect is +minuscule. Now we're not quite + + align:start position:0% +minuscule. Now we're not quite + + + align:start position:0% +minuscule. Now we're not quite +done. That tells us the probability the + + align:start position:0% +done. That tells us the probability the + + + align:start position:0% +done. That tells us the probability the +first server gets 10% too much + + align:start position:0% +first server gets 10% too much + + + align:start position:0% +first server gets 10% too much +load or the probability the second + + align:start position:0% +load or the probability the second + + + align:start position:0% +load or the probability the second +server got 10% too much load and so + + align:start position:0% +server got 10% too much load and so + + + align:start position:0% +server got 10% too much load and so +forth. But what we really care about is + + align:start position:0% +forth. But what we really care about is + + + align:start position:0% +forth. But what we really care about is +the worst + + align:start position:0% +the worst + + + align:start position:0% +the worst +server. I mean, if all of them are good + + align:start position:0% +server. I mean, if all of them are good + + + align:start position:0% +server. I mean, if all of them are good +except for one, you're still in trouble + + align:start position:0% +except for one, you're still in trouble + + + align:start position:0% +except for one, you're still in trouble +because the one ruins your day because + + align:start position:0% +because the one ruins your day because + + + align:start position:0% +because the one ruins your day because +it didn't get the work + + align:start position:0% +it didn't get the work + + + align:start position:0% +it didn't get the work +done. So, what do you do to bound the + + align:start position:0% +done. So, what do you do to bound the + + + align:start position:0% +done. So, what do you do to bound the +probability that any of the servers got + + align:start position:0% +probability that any of the servers got + + + align:start position:0% +probability that any of the servers got +too much + + align:start position:0% +too much + + + align:start position:0% +too much +load? Any of the + + align:start position:0% +load? Any of the + + + align:start position:0% +load? Any of the +10. All right. So, I want to know what I + + align:start position:0% +10. All right. So, I want to know what I + + + align:start position:0% +10. All right. So, I want to know what I +really want to know is the probability + + align:start position:0% +really want to know is the probability + + + align:start position:0% +really want to know is the probability +that the worst server of M + + align:start position:0% + + + + align:start position:0% + +takes more than CL over + + align:start position:0% +takes more than CL over + + + align:start position:0% +takes more than CL over +M. Well, that's the probability that the + + align:start position:0% +M. Well, that's the probability that the + + + align:start position:0% +M. Well, that's the probability that the +first one has more than CL over M union + + align:start position:0% +first one has more than CL over M union + + + align:start position:0% +first one has more than CL over M union +the second one has more than CL over M + + align:start position:0% +the second one has more than CL over M + + + align:start position:0% +the second one has more than CL over M +union the M + + align:start position:0% + + + + align:start position:0% + +one. What do I do to get that + + align:start position:0% +one. What do I do to get that + + + align:start position:0% +one. What do I do to get that +probability? + + align:start position:0% +probability? + + + align:start position:0% +probability? +the probability of a union of events + + align:start position:0% +the probability of a union of events + + + align:start position:0% +the probability of a union of events +upper bounded + + align:start position:0% + + + + align:start position:0% + +upper bounded by the sum of the + + align:start position:0% +upper bounded by the sum of the + + + align:start position:0% +upper bounded by the sum of the +individual guys. It's the sum i = 1 to m + + align:start position:0% +individual guys. It's the sum i = 1 to m + + + align:start position:0% +individual guys. It's the sum i = 1 to m +probability r i greater than equal to cl + + align:start position:0% +probability r i greater than equal to cl + + + align:start position:0% +probability r i greater than equal to cl +over m. And so that each of these is at + + align:start position:0% +over m. And so that each of these is at + + + align:start position:0% +over m. And so that each of these is at +most one and 160,000. This is at most m + + align:start position:0% +most one and 160,000. This is at most m + + + align:start position:0% +most one and 160,000. This is at most m +over + + align:start position:0% + + + + align:start position:0% + +160,000 and that is equal to 1 + + align:start position:0% + + + + align:start position:0% + +in6,000. All right. So now we have the + + align:start position:0% +in6,000. All right. So now we have the + + + align:start position:0% +in6,000. All right. So now we have the +answer. The chance that any server got + + align:start position:0% +answer. The chance that any server got + + + align:start position:0% +answer. The chance that any server got +10% load or more is 1 in6,000 at + + align:start position:0% +10% load or more is 1 in6,000 at + + + align:start position:0% +10% load or more is 1 in6,000 at +most. Okay. Which is why randomized load + + align:start position:0% +most. Okay. Which is why randomized load + + + align:start position:0% +most. Okay. Which is why randomized load +balancing is used a lot in practice. Now + + align:start position:0% +balancing is used a lot in practice. Now + + + align:start position:0% +balancing is used a lot in practice. Now +tomorrow you're going to do a real world + + align:start position:0% +tomorrow you're going to do a real world + + + align:start position:0% +tomorrow you're going to do a real world +example + + align:start position:0% +example + + + align:start position:0% +example +where people used this kind of analysis + + align:start position:0% +where people used this kind of analysis + + + align:start position:0% +where people used this kind of analysis +and it led to utter + + align:start position:0% +and it led to utter + + + align:start position:0% +and it led to utter +disaster. And the reason + + align:start position:0% +disaster. And the reason + + + align:start position:0% +disaster. And the reason +was that the components they were + + align:start position:0% +was that the components they were + + + align:start position:0% +was that the components they were +looking at were not independent. And the + + align:start position:0% +looking at were not independent. And the + + + align:start position:0% +looking at were not independent. And the +example has to do with the subprime + + align:start position:0% +example has to do with the subprime + + + align:start position:0% +example has to do with the subprime +mortgage disaster. And I don't have time + + align:start position:0% +mortgage disaster. And I don't have time + + + align:start position:0% +mortgage disaster. And I don't have time +today to go through it all, but you it's + + align:start position:0% +today to go through it all, but you it's + + + align:start position:0% +today to go through it all, but you it's +in the text and you'll see it tomorrow. + + align:start position:0% +in the text and you'll see it tomorrow. + + + align:start position:0% +in the text and you'll see it tomorrow. +But basically what happened is they took + + align:start position:0% +But basically what happened is they took + + + align:start position:0% +But basically what happened is they took +a whole bunch of loans, subprime loans, + + align:start position:0% +a whole bunch of loans, subprime loans, + + + align:start position:0% +a whole bunch of loans, subprime loans, +put them into these things called + + align:start position:0% +put them into these things called + + + align:start position:0% +put them into these things called +bonds, and then did an analysis about + + align:start position:0% +bonds, and then did an analysis about + + + align:start position:0% +bonds, and then did an analysis about +how many failures they'd expect to have. + + align:start position:0% +how many failures they'd expect to have. + + + align:start position:0% +how many failures they'd expect to have. +And they assumed the loans were all + + align:start position:0% +And they assumed the loans were all + + + align:start position:0% +And they assumed the loans were all +mutually independent. And they applied + + align:start position:0% +mutually independent. And they applied + + + align:start position:0% +mutually independent. And they applied +their turnoff bounds, and that concluded + + align:start position:0% +their turnoff bounds, and that concluded + + + align:start position:0% +their turnoff bounds, and that concluded +that the chances of being off from the + + align:start position:0% +that the chances of being off from the + + + align:start position:0% +that the chances of being off from the +expectation were nil, like e to the + + align:start position:0% +expectation were nil, like e to the + + + align:start position:0% +expectation were nil, like e to the +minus + + align:start position:0% +minus + + + align:start position:0% +minus +380. In reality, the loans were highly + + align:start position:0% +380. In reality, the loans were highly + + + align:start position:0% +380. In reality, the loans were highly +dependent. When one failed, a lot tended + + align:start position:0% +dependent. When one failed, a lot tended + + + align:start position:0% +dependent. When one failed, a lot tended +to fail and that led to disaster. And + + align:start position:0% +to fail and that led to disaster. And + + + align:start position:0% +to fail and that led to disaster. And +you'll go through some of the math on + + align:start position:0% +you'll go through some of the math on + + + align:start position:0% +you'll go through some of the math on +that tomorrow. Recitation. \ No newline at end of file diff --git a/qKh4mOlEZpE.txt b/qKh4mOlEZpE.txt new file mode 100644 index 0000000000000000000000000000000000000000..2194140135d8cb10fe8cabb50beb75a11e44c3ae --- /dev/null +++ b/qKh4mOlEZpE.txt @@ -0,0 +1,308 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Hi, I'm Jocelyn, and +today we're going to go + +over Fall 2009 Exam 2, +Problem number 5. + +As always, we're going to read +the problem first. Which + +compound do you expect to have +the higher boiling point: HF + +or ammonia? + +Justify your choice with an +explanation, using narrative + +or cartoons or both that makes +reference to the operative + +chemical bonding. + +So first, we are trying to +figure out which has a greater + +temperature of vaporization, +or boiling point; and we're + +looking at HF and ammonia. + +Now when we're talking about +boiling points, we're talking + +about breaking a certain type of +bond, and that type of bond + +is intermolecular bonds. + +We're not going to be breaking +the actual molecular bonds + +bonding hydrogen to fluorine +or nitrogen, we're breaking + +the bonds in between molecules +of HF or ammonia, and so what + +types of bond do we +have to look at? + +And Professor Sadoway, in class, +went over a couple of + +different types of +intermolecular bonds. + +And I'm going to write +them down in order + +of increasing strengths. + +So the weakest intermolecular +bonds we + +have are Van der Waals. + +The next is induced +dipole-dipole. + +Next we have dipole-dipole, and +finally a special type of + +dipole-dipole is the +hydrogen-bond, which is the + +strongest. So here we're +increasing strength. + +Van der Waals is an induced +dipole-dipole. + +That means that although your +atom or molecule does not have + +a net dipole, the electrons can +shift, and at some point + +will cause a difference in +polarity between different + +sides of the molecule. + +Induced dipole-dipole is +two different molecules + +interacting: one that has no net +dipole and one that does. + +Dipole-dipole: pretty +self-explanatory. + +You have two molecules that +have dipoles, and they are + +interacting. + +And then hydrogen-bond is when +you have hydrogen bonded with + +x, where x is nitrogen, +oxygen, and fluorine. + +We call that a hydrogen-bond, +because these are really, + +really strong dipole-dipole +interactions and cause much + +different behaviors in +molecules, and so we, kind of, + +separate it out at the subset. + +So now that we've reviewed +intermolecular bonds, let's go + +back to the problem. + +So we were asked to figure out +the difference, or which one + +has a higher vapor pressure, or +temperature of boiling, so + +that's a relative thing. + +And as we now know that we need +to look at intermolecular + +bonds, a good place to start is +with the Lewis structure, + +because that will tell us if +we have dipoles or not, and + +then we can see what the +strongest intermolecular bond + +is that we need to break to +boil these molecules. + +So starting with HF, we have +hydrogen bonded to fluorine. + +We know that fluorine has a much +higher electronegativity + +than hydrogen, so we're going +to have a net dipole. + +Well, we have a polarized +bond and a net + +dipole towards fluorine. + +This causes there to be a +partial positive charge on the + +hydrogen and a partial negative + +charge on the fluorine. + +So what is our strongest +intermolecular bond that we + +have for HF? + +Going back to our list of bonds, +we see that we have a + +dipole, so we might first think +about dipole-dipole. + +However, we need to remember +about hydrogen bonds, and here + +in HF, we have hydrogen bonded +to fluorine, and so that would + +be our strongest interaction. + +So let's write that down +to keep track. + +Now for ammonia, we have +nitrogen bonded to three + +hydrogens, and again we +have a difference in + +electronegativity, and so each +of these bonds is polar. + +And because of the asymmetric +geometry, we will have a net + +dipole, and each of these +have a partially -- + +sorry, the hydrogens have a +partially positive charge, + +right, because they are less +electronegative, and the + +nitrogen has a partial +negative charge. + +So, which is our highest or +strongest intermolecular bond + +that we have here. + +Again, we have a net dipole, and +so we have dipole-dipole + +interactions, but because +hydrogen is bonded to one of + +the special three atoms, we +have hydrogen bonding, and + +that is the strongest. So, that +is what we care about. + +So now, we're, kind of, at a +roadblock here; both have + +hydrogen bonding, which is the +strongest intermolecular bond. + +So how do we decide which one +is actually going to be + +stronger than the other, and +therefore, have the higher + +boiling point. + +Well even though they're both +hydrogen bonds, they will have + +difference in strength, and +that's going to depend on the + +partial positive and partial +negative charges, because all + +of these interactions are due +to coulombic attraction. + +In fluorine, we know that +fluorine is the most + +electronegative element and has +a higher electronegativity + +than nitrogen, so just to keep +track of our thought process + +here: this will cause the +partial positive on hydrogen + +to be larger in the HF than in +the ammonia, and so from this + +we can say that the hydrogen +bonding in HF will be stronger + +than the hydrogen bonding in +ammonia, and therefore, the t + +evaporation of HF will be +greater than the t-- + +the boiling point of ammonia. + +So now we're going to +move on to Part B. \ No newline at end of file diff --git a/qiz-ywBpQlo.txt b/qiz-ywBpQlo.txt new file mode 100644 index 0000000000000000000000000000000000000000..02aaf1aa07e1bb6814391eedb8db8248d78174df --- /dev/null +++ b/qiz-ywBpQlo.txt @@ -0,0 +1,12970 @@ +align:start position:0% + +the following content is provided by mit + + align:start position:0% +the following content is provided by mit + + + align:start position:0% +the following content is provided by mit +opencourseware under a creative commons + + align:start position:0% +opencourseware under a creative commons + + + align:start position:0% +opencourseware under a creative commons +license + + align:start position:0% +license + + + align:start position:0% +license +additional information about our license + + align:start position:0% +additional information about our license + + + align:start position:0% +additional information about our license +and mit opencourseware in general is + + align:start position:0% +and mit opencourseware in general is + + + align:start position:0% +and mit opencourseware in general is +available at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +welcome to + + align:start position:0% +welcome to + + + align:start position:0% +welcome to +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +fifth lecture the first of the series on + + align:start position:0% +fifth lecture the first of the series on + + + align:start position:0% +fifth lecture the first of the series on +uh + + align:start position:0% +uh + + + align:start position:0% +uh +on rna and + + align:start position:0% +on rna and + + + align:start position:0% +on rna and +uh expression analysis + + align:start position:0% +uh expression analysis + + + align:start position:0% +uh expression analysis +first a quick review of uh last week and + + align:start position:0% +first a quick review of uh last week and + + + align:start position:0% +first a quick review of uh last week and +it's it has significant connections with + + align:start position:0% +it's it has significant connections with + + + align:start position:0% +it's it has significant connections with +this week + + align:start position:0% +this week + + + align:start position:0% +this week +where we talked to + + align:start position:0% +where we talked to + + + align:start position:0% +where we talked to +the topic of alignments and different + + align:start position:0% +the topic of alignments and different + + + align:start position:0% +the topic of alignments and different +algorithms for obtaining pairwise + + align:start position:0% +algorithms for obtaining pairwise + + + align:start position:0% +algorithms for obtaining pairwise +alignments + + align:start position:0% +alignments + + + align:start position:0% +alignments +in particular dynamic programming this + + align:start position:0% +in particular dynamic programming this + + + align:start position:0% +in particular dynamic programming this +led to even harder problem which is + + align:start position:0% +led to even harder problem which is + + + align:start position:0% +led to even harder problem which is +multi-sequence alignment from which we + + align:start position:0% +multi-sequence alignment from which we + + + align:start position:0% +multi-sequence alignment from which we +will + + align:start position:0% +will + + + align:start position:0% +will +draw pretty heavily at the beginning of + + align:start position:0% +draw pretty heavily at the beginning of + + + align:start position:0% +draw pretty heavily at the beginning of +the discussion today + + align:start position:0% +the discussion today + + + align:start position:0% +the discussion today +and then + + align:start position:0% +and then + + + align:start position:0% +and then +the the issues of getting the + + align:start position:0% +the the issues of getting the + + + align:start position:0% +the the issues of getting the +motifs another topic we will touch upon + + align:start position:0% +motifs another topic we will touch upon + + + align:start position:0% +motifs another topic we will touch upon +several times today how you get once you + + align:start position:0% +several times today how you get once you + + + align:start position:0% +several times today how you get once you +have a multi-sequence alignment how this + + align:start position:0% +have a multi-sequence alignment how this + + + align:start position:0% +have a multi-sequence alignment how this +gives you + + align:start position:0% +gives you + + + align:start position:0% +gives you +either a independent weight matrix where + + align:start position:0% +either a independent weight matrix where + + + align:start position:0% +either a independent weight matrix where +different positions are independent + + align:start position:0% +different positions are independent + + + align:start position:0% +different positions are independent +or in a hidden markov model where there + + align:start position:0% +or in a hidden markov model where there + + + align:start position:0% +or in a hidden markov model where there +is some dependence between + + align:start position:0% +is some dependence between + + + align:start position:0% +is some dependence between +say adjacent nucleotides in a simple + + align:start position:0% +say adjacent nucleotides in a simple + + + align:start position:0% +say adjacent nucleotides in a simple +sequence such as cg + + align:start position:0% + + + + align:start position:0% + +so that + + align:start position:0% +so that + + + align:start position:0% +so that +just carry over these these thoughts + + align:start position:0% +just carry over these these thoughts + + + align:start position:0% +just carry over these these thoughts +about uh + + align:start position:0% +about uh + + + align:start position:0% +about uh +multi-sequence alignment motifs and + + align:start position:0% +multi-sequence alignment motifs and + + + align:start position:0% +multi-sequence alignment motifs and +non-independence of positions in + + align:start position:0% +non-independence of positions in + + + align:start position:0% +non-independence of positions in +sequences + + align:start position:0% +sequences + + + align:start position:0% +sequences +to the next + + align:start position:0% +to the next + + + align:start position:0% +to the next +level higher we will eventually talk + + align:start position:0% +level higher we will eventually talk + + + align:start position:0% +level higher we will eventually talk +about protein three-dimensional + + align:start position:0% +about protein three-dimensional + + + align:start position:0% +about protein three-dimensional +structure but a really + + align:start position:0% +structure but a really + + + align:start position:0% +structure but a really +beautiful intermediate between + + align:start position:0% +beautiful intermediate between + + + align:start position:0% +beautiful intermediate between +proteins + + align:start position:0% +proteins + + + align:start position:0% +proteins +uh the complexity of the protein + + align:start position:0% +uh the complexity of the protein + + + align:start position:0% +uh the complexity of the protein +structure and the simplicity of + + align:start position:0% +structure and the simplicity of + + + align:start position:0% +structure and the simplicity of +double-stranded dna + + align:start position:0% +double-stranded dna + + + align:start position:0% +double-stranded dna +is the is the folding of rnas + + align:start position:0% + + + + align:start position:0% + +because they base some of the same rules + + align:start position:0% +because they base some of the same rules + + + align:start position:0% +because they base some of the same rules +of double-strand dna + + align:start position:0% +of double-strand dna + + + align:start position:0% +of double-strand dna +but they + + align:start position:0% + + + + align:start position:0% + +have the complicated structures of begin + + align:start position:0% +have the complicated structures of begin + + + align:start position:0% +have the complicated structures of begin +to have complicated structures of + + align:start position:0% +to have complicated structures of + + + align:start position:0% +to have complicated structures of +proteins so we'll we'll start with this + + align:start position:0% +proteins so we'll we'll start with this + + + align:start position:0% +proteins so we'll we'll start with this +integration of + + align:start position:0% +integration of + + + align:start position:0% +integration of +multi-sequence alignment motifs with rna + + align:start position:0% +multi-sequence alignment motifs with rna + + + align:start position:0% +multi-sequence alignment motifs with rna +structure + + align:start position:0% +structure + + + align:start position:0% +structure +and then we'll + + align:start position:0% +and then we'll + + + align:start position:0% +and then we'll +switch to a + + align:start position:0% +switch to a + + + align:start position:0% +switch to a +to tell about how these rna structures + + align:start position:0% +to tell about how these rna structures + + + align:start position:0% +to tell about how these rna structures +play their role + + align:start position:0% +play their role + + + align:start position:0% +play their role +by achieving different + + align:start position:0% +by achieving different + + + align:start position:0% +by achieving different +levels + + align:start position:0% +levels + + + align:start position:0% +levels +in the cell in other words we want to be + + align:start position:0% +in the cell in other words we want to be + + + align:start position:0% +in the cell in other words we want to be +start to introduce how we become + + align:start position:0% +start to introduce how we become + + + align:start position:0% +start to introduce how we become +quantitative about them the amounts and + + align:start position:0% +quantitative about them the amounts and + + + align:start position:0% +quantitative about them the amounts and +localization of rnas in the cell + + align:start position:0% +localization of rnas in the cell + + + align:start position:0% +localization of rnas in the cell +some of these some of the measures that + + align:start position:0% +some of these some of the measures that + + + align:start position:0% +some of these some of the measures that +we'll be talking about and the tool the + + align:start position:0% +we'll be talking about and the tool the + + + align:start position:0% +we'll be talking about and the tool the +computational tools will be more + + align:start position:0% +computational tools will be more + + + align:start position:0% +computational tools will be more +appropriate + + align:start position:0% + + + + align:start position:0% + +for individual measures and others will + + align:start position:0% +for individual measures and others will + + + align:start position:0% +for individual measures and others will +be more what we call genomics grade + + align:start position:0% +be more what we call genomics grade + + + align:start position:0% +be more what we call genomics grade +or + + align:start position:0% +or + + + align:start position:0% +or +high throughput and high + + align:start position:0% +high throughput and high + + + align:start position:0% +high throughput and high +accuracy + + align:start position:0% +accuracy + + + align:start position:0% +accuracy +and we have + + align:start position:0% +and we have + + + align:start position:0% +and we have +this + + align:start position:0% +this + + + align:start position:0% +this +since this is a + + align:start position:0% +since this is a + + + align:start position:0% +since this is a +a new + + align:start position:0% +a new + + + align:start position:0% +a new +category of + + align:start position:0% +category of + + + align:start position:0% +category of +biological data + + align:start position:0% +biological data + + + align:start position:0% +biological data +we we have to address random and + + align:start position:0% +we we have to address random and + + + align:start position:0% +we we have to address random and +systematic errors just as we did for + + align:start position:0% +systematic errors just as we did for + + + align:start position:0% +systematic errors just as we did for +genotyping and sequence data this is a + + align:start position:0% +genotyping and sequence data this is a + + + align:start position:0% +genotyping and sequence data this is a +new a new set of them and a new set of + + align:start position:0% +new a new set of them and a new set of + + + align:start position:0% +new a new set of them and a new set of +solutions + + align:start position:0% +solutions + + + align:start position:0% +solutions +about the same themes of random and + + align:start position:0% +about the same themes of random and + + + align:start position:0% +about the same themes of random and +systematic errors and then we'll talk + + align:start position:0% +systematic errors and then we'll talk + + + align:start position:0% +systematic errors and then we'll talk +about + + align:start position:0% +about + + + align:start position:0% +about +uh a particular set of interpretation + + align:start position:0% +uh a particular set of interpretation + + + align:start position:0% +uh a particular set of interpretation +issues that lead to additional + + align:start position:0% +issues that lead to additional + + + align:start position:0% +issues that lead to additional +considerations and and will end on time + + align:start position:0% +considerations and and will end on time + + + align:start position:0% +considerations and and will end on time +series data which will be a + + align:start position:0% +series data which will be a + + + align:start position:0% +series data which will be a +theme that will connect this talk to + + align:start position:0% +theme that will connect this talk to + + + align:start position:0% +theme that will connect this talk to +much later talks on system biology where + + align:start position:0% +much later talks on system biology where + + + align:start position:0% +much later talks on system biology where +the ability to connect + + align:start position:0% +the ability to connect + + + align:start position:0% +the ability to connect +with time series will help + + align:start position:0% +with time series will help + + + align:start position:0% +with time series will help +establish causality + + align:start position:0% +establish causality + + + align:start position:0% +establish causality +and + + align:start position:0% +and + + + align:start position:0% +and +connectivity + + align:start position:0% +connectivity + + + align:start position:0% +connectivity +and we'll do it and we'll tie it to the + + align:start position:0% +and we'll do it and we'll tie it to the + + + align:start position:0% +and we'll do it and we'll tie it to the +subject of rna analysis by looking at + + align:start position:0% +subject of rna analysis by looking at + + + align:start position:0% +subject of rna analysis by looking at +messenger rna to k + + align:start position:0% +messenger rna to k + + + align:start position:0% +messenger rna to k +now slide three + + align:start position:0% +now slide three + + + align:start position:0% +now slide three +is a + + align:start position:0% +is a + + + align:start position:0% +is a +a reminder that we'll we'll use in two + + align:start position:0% +a reminder that we'll we'll use in two + + + align:start position:0% +a reminder that we'll we'll use in two +different contexts tonight + + align:start position:0% +different contexts tonight + + + align:start position:0% +different contexts tonight +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +these are the bell curves that you've + + align:start position:0% +these are the bell curves that you've + + + align:start position:0% +these are the bell curves that you've +seen at least three of them + + align:start position:0% +seen at least three of them + + + align:start position:0% +seen at least three of them +integrated before + + align:start position:0% +integrated before + + + align:start position:0% +integrated before +the the two discrete binomial poisson + + align:start position:0% +the the two discrete binomial poisson + + + align:start position:0% +the the two discrete binomial poisson +and the normal which is + + align:start position:0% +and the normal which is + + + align:start position:0% +and the normal which is +symmetric around the mean of 20 in this + + align:start position:0% +symmetric around the mean of 20 in this + + + align:start position:0% +symmetric around the mean of 20 in this +case + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +we're + + align:start position:0% +we're + + + align:start position:0% +we're +just to connect to the discussion from + + align:start position:0% +just to connect to the discussion from + + + align:start position:0% +just to connect to the discussion from +the last time + + align:start position:0% +the last time + + + align:start position:0% +the last time +where we were + + align:start position:0% +where we were + + + align:start position:0% +where we were +asking what the significance of a + + align:start position:0% +asking what the significance of a + + + align:start position:0% +asking what the significance of a +match of a single sequence to a database + + align:start position:0% +match of a single sequence to a database + + + align:start position:0% +match of a single sequence to a database +might be + + align:start position:0% +might be + + + align:start position:0% +might be +when you're asking for a match of a + + align:start position:0% +when you're asking for a match of a + + + align:start position:0% +when you're asking for a match of a +single sequence to the database you're + + align:start position:0% +single sequence to the database you're + + + align:start position:0% +single sequence to the database you're +typically really asking for the maximum + + align:start position:0% +typically really asking for the maximum + + + align:start position:0% +typically really asking for the maximum +match or the maximum + + align:start position:0% +match or the maximum + + + align:start position:0% +match or the maximum +the the most extreme uh matches and so + + align:start position:0% +the the most extreme uh matches and so + + + align:start position:0% +the the most extreme uh matches and so +when you talk about extremes when you're + + align:start position:0% +when you talk about extremes when you're + + + align:start position:0% +when you talk about extremes when you're +sampling from a distribution + + align:start position:0% +sampling from a distribution + + + align:start position:0% +sampling from a distribution +and you're looking for the most extreme + + align:start position:0% +and you're looking for the most extreme + + + align:start position:0% +and you're looking for the most extreme +value for finite sampling of that + + align:start position:0% +value for finite sampling of that + + + align:start position:0% +value for finite sampling of that +distribution that tends to be not from + + align:start position:0% +distribution that tends to be not from + + + align:start position:0% +distribution that tends to be not from +the normal distribution which would be + + align:start position:0% +the normal distribution which would be + + + align:start position:0% +the normal distribution which would be +random sampling but from which is this + + align:start position:0% + + + + align:start position:0% + +middle magenta curve + + align:start position:0% +middle magenta curve + + + align:start position:0% +middle magenta curve +but instead it would be extreme value + + align:start position:0% +but instead it would be extreme value + + + align:start position:0% +but instead it would be extreme value +distribution which is this blue curve + + align:start position:0% +distribution which is this blue curve + + + align:start position:0% +distribution which is this blue curve +which you can see in this case since + + align:start position:0% +which you can see in this case since + + + align:start position:0% +which you can see in this case since +we're looking for extreme maxima is + + align:start position:0% +we're looking for extreme maxima is + + + align:start position:0% +we're looking for extreme maxima is +shifted slightly to the right + + align:start position:0% +shifted slightly to the right + + + align:start position:0% +shifted slightly to the right +and + + align:start position:0% +and + + + align:start position:0% +and +so you can see + + align:start position:0% +so you can see + + + align:start position:0% +so you can see +that it comes inside of the of the other + + align:start position:0% +that it comes inside of the of the other + + + align:start position:0% +that it comes inside of the of the other +bell curves + + align:start position:0% +bell curves + + + align:start position:0% +bell curves +on the left hand side and goes out side + + align:start position:0% +on the left hand side and goes out side + + + align:start position:0% +on the left hand side and goes out side +on the right hand side if we were + + align:start position:0% +on the right hand side if we were + + + align:start position:0% +on the right hand side if we were +looking for + + align:start position:0% +looking for + + + align:start position:0% +looking for +extreme + + align:start position:0% +extreme + + + align:start position:0% +extreme +low values then it would have been + + align:start position:0% +low values then it would have been + + + align:start position:0% +low values then it would have been +shifted to the left and remember all + + align:start position:0% +shifted to the left and remember all + + + align:start position:0% +shifted to the left and remember all +these continuous functions + + align:start position:0% +these continuous functions + + + align:start position:0% +these continuous functions +uh + + align:start position:0% +uh + + + align:start position:0% +uh +go off to negative infinity and positive + + align:start position:0% +go off to negative infinity and positive + + + align:start position:0% +go off to negative infinity and positive +infinity although extremely low levels + + align:start position:0% +infinity although extremely low levels + + + align:start position:0% +infinity although extremely low levels +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +that and then the + + align:start position:0% +that and then the + + + align:start position:0% +that and then the +that's the extreme value distribution + + align:start position:0% +that's the extreme value distribution + + + align:start position:0% +that's the extreme value distribution +now in order to + + align:start position:0% +now in order to + + + align:start position:0% +now in order to +connect this + + align:start position:0% +connect this + + + align:start position:0% +connect this +nucleotide sequence which we've been + + align:start position:0% +nucleotide sequence which we've been + + + align:start position:0% +nucleotide sequence which we've been +seeing it had has these wonderful watson + + align:start position:0% +seeing it had has these wonderful watson + + + align:start position:0% +seeing it had has these wonderful watson +quick base pairs of where tna and so + + align:start position:0% +quick base pairs of where tna and so + + + align:start position:0% +quick base pairs of where tna and so +forth + + align:start position:0% +forth + + + align:start position:0% +forth +is + + align:start position:0% +is + + + align:start position:0% +is +to this + + align:start position:0% +to this + + + align:start position:0% +to this +more complicated tertiary structure + + align:start position:0% +more complicated tertiary structure + + + align:start position:0% +more complicated tertiary structure +we're going to go through an + + align:start position:0% +we're going to go through an + + + align:start position:0% +we're going to go through an +intermediate of secondary structure + + align:start position:0% +intermediate of secondary structure + + + align:start position:0% +intermediate of secondary structure +where we really look at + + align:start position:0% +where we really look at + + + align:start position:0% +where we really look at +whether what kind of base pairs can form + + align:start position:0% +whether what kind of base pairs can form + + + align:start position:0% +whether what kind of base pairs can form +and i'm going to immediately introduce + + align:start position:0% +and i'm going to immediately introduce + + + align:start position:0% +and i'm going to immediately introduce +some complexities so you don't + + align:start position:0% +some complexities so you don't + + + align:start position:0% +some complexities so you don't +get + + align:start position:0% +get + + + align:start position:0% +get +too complacent right off the bat + + align:start position:0% +too complacent right off the bat + + + align:start position:0% +too complacent right off the bat +somewhere in this + + align:start position:0% +somewhere in this + + + align:start position:0% +somewhere in this +slide of non-watson creek base pairs is + + align:start position:0% +slide of non-watson creek base pairs is + + + align:start position:0% +slide of non-watson creek base pairs is +a watson quick face there + + align:start position:0% + + + + align:start position:0% + +take a moment to find it + + align:start position:0% +take a moment to find it + + + align:start position:0% +take a moment to find it +fine okay so since we haven't introduced + + align:start position:0% +fine okay so since we haven't introduced + + + align:start position:0% +fine okay so since we haven't introduced +base pairs you it's gonna well we've + + align:start position:0% +base pairs you it's gonna well we've + + + align:start position:0% +base pairs you it's gonna well we've +seen it twice now in double stranded dna + + align:start position:0% +seen it twice now in double stranded dna + + + align:start position:0% +seen it twice now in double stranded dna +right in the middle here labeled a is an + + align:start position:0% +right in the middle here labeled a is an + + + align:start position:0% +right in the middle here labeled a is an +au base pair + + align:start position:0% +au base pair + + + align:start position:0% +au base pair +which is watson crick where the black + + align:start position:0% +which is watson crick where the black + + + align:start position:0% +which is watson crick where the black +dot indicates the + + align:start position:0% +dot indicates the + + + align:start position:0% +dot indicates the +the attachment to the ribose + + align:start position:0% +the attachment to the ribose + + + align:start position:0% +the attachment to the ribose +in rna or the deoxyribose and dna and + + align:start position:0% +in rna or the deoxyribose and dna and + + + align:start position:0% +in rna or the deoxyribose and dna and +you'll find three other at base pairs + + align:start position:0% +you'll find three other at base pairs + + + align:start position:0% +you'll find three other at base pairs +one right to the right of it and uh + + align:start position:0% +one right to the right of it and uh + + + align:start position:0% +one right to the right of it and uh +two down below and these these four at + + align:start position:0% +two down below and these these four at + + + align:start position:0% +two down below and these these four at +base pairs are all different from one + + align:start position:0% +base pairs are all different from one + + + align:start position:0% +base pairs are all different from one +another + + align:start position:0% +another + + + align:start position:0% +another +uh in terms of it most easily imagined + + align:start position:0% +uh in terms of it most easily imagined + + + align:start position:0% +uh in terms of it most easily imagined +in terms of the orientation of the uh of + + align:start position:0% +in terms of the orientation of the uh of + + + align:start position:0% +in terms of the orientation of the uh of +the riboses these black dots relative to + + align:start position:0% +the riboses these black dots relative to + + + align:start position:0% +the riboses these black dots relative to +one another + + align:start position:0% +one another + + + align:start position:0% +one another +and each have names but the important + + align:start position:0% +and each have names but the important + + + align:start position:0% +and each have names but the important +thing is that the all of these are are + + align:start position:0% +thing is that the all of these are are + + + align:start position:0% +thing is that the all of these are are +illustrated such that they maintain the + + align:start position:0% +illustrated such that they maintain the + + + align:start position:0% +illustrated such that they maintain the +coplanarity of the bases they typically + + align:start position:0% +coplanarity of the bases they typically + + + align:start position:0% +coplanarity of the bases they typically +maintain one or two or even three + + align:start position:0% +maintain one or two or even three + + + align:start position:0% +maintain one or two or even three +hydrogen bonds and the planarity allows + + align:start position:0% +hydrogen bonds and the planarity allows + + + align:start position:0% +hydrogen bonds and the planarity allows +them to stack on bases base pairs below + + align:start position:0% +them to stack on bases base pairs below + + + align:start position:0% +them to stack on bases base pairs below +and above them + + align:start position:0% +and above them + + + align:start position:0% +and above them +just as you would in in normal double + + align:start position:0% +just as you would in in normal double + + + align:start position:0% +just as you would in in normal double +stranded dna + + align:start position:0% + + + + align:start position:0% + +but sometimes the geometry distorts the + + align:start position:0% +but sometimes the geometry distorts the + + + align:start position:0% +but sometimes the geometry distorts the +double helix enough that you might get a + + align:start position:0% +double helix enough that you might get a + + + align:start position:0% +double helix enough that you might get a +penalty + + align:start position:0% +penalty + + + align:start position:0% +penalty +in the uh + + align:start position:0% +in the uh + + + align:start position:0% +in the uh +in the in the uh free energy in the + + align:start position:0% +in the in the uh free energy in the + + + align:start position:0% +in the in the uh free energy in the +thermodynamic sense or the kinetics in + + align:start position:0% +thermodynamic sense or the kinetics in + + + align:start position:0% +thermodynamic sense or the kinetics in +the in a + + align:start position:0% +the in a + + + align:start position:0% +the in a +sense now here's another so you can find + + align:start position:0% +sense now here's another so you can find + + + align:start position:0% +sense now here's another so you can find +almost you can basically make one of + + align:start position:0% +almost you can basically make one of + + + align:start position:0% +almost you can basically make one of +these base pairs for ev all of the + + align:start position:0% +these base pairs for ev all of the + + + align:start position:0% +these base pairs for ev all of the +possible + + align:start position:0% +possible + + + align:start position:0% +possible +um + + align:start position:0% +um + + + align:start position:0% +um +combinations of + + align:start position:0% +combinations of + + + align:start position:0% +combinations of +a c g + + align:start position:0% +a c g + + + align:start position:0% +a c g +and u + + align:start position:0% +and u + + + align:start position:0% +and u +in rna + + align:start position:0% +in rna + + + align:start position:0% +in rna +so mo and all of them will be coplanar + + align:start position:0% +so mo and all of them will be coplanar + + + align:start position:0% +so mo and all of them will be coplanar +and they'll have + + align:start position:0% +and they'll have + + + align:start position:0% +and they'll have +one or more hydrogen bonds + + align:start position:0% +one or more hydrogen bonds + + + align:start position:0% +one or more hydrogen bonds +probably the most stable and most + + align:start position:0% +probably the most stable and most + + + align:start position:0% +probably the most stable and most +commonly encountered + + align:start position:0% +commonly encountered + + + align:start position:0% +commonly encountered +in + + align:start position:0% +in + + + align:start position:0% +in +otherwise normal rna double helices is + + align:start position:0% +otherwise normal rna double helices is + + + align:start position:0% +otherwise normal rna double helices is +the gu based pair and you can see this + + align:start position:0% +the gu based pair and you can see this + + + align:start position:0% +the gu based pair and you can see this +look this has fairly similar geometry to + + align:start position:0% +look this has fairly similar geometry to + + + align:start position:0% +look this has fairly similar geometry to +the au base pair or for them out of the + + align:start position:0% +the au base pair or for them out of the + + + align:start position:0% +the au base pair or for them out of the +gc base pair + + align:start position:0% +gc base pair + + + align:start position:0% +gc base pair +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +let's see how these non-watson creek + + align:start position:0% +let's see how these non-watson creek + + + align:start position:0% +let's see how these non-watson creek +base pairs appear in in + + align:start position:0% +base pairs appear in in + + + align:start position:0% +base pairs appear in in +this this is this is the transfer rna + + align:start position:0% +this this is this is the transfer rna + + + align:start position:0% +this this is this is the transfer rna +that we saw a couple of slides ago + + align:start position:0% +that we saw a couple of slides ago + + + align:start position:0% +that we saw a couple of slides ago +spinning around in three dimensions and + + align:start position:0% +spinning around in three dimensions and + + + align:start position:0% +spinning around in three dimensions and +the sequence that was behind it uh + + align:start position:0% +the sequence that was behind it uh + + + align:start position:0% +the sequence that was behind it uh +was the the the dna sequence that + + align:start position:0% +was the the the dna sequence that + + + align:start position:0% +was the the the dna sequence that +corresponds to this unmodified rna + + align:start position:0% +corresponds to this unmodified rna + + + align:start position:0% +corresponds to this unmodified rna +sequence on the right hand side + + align:start position:0% +sequence on the right hand side + + + align:start position:0% +sequence on the right hand side +let's + + align:start position:0% +let's + + + align:start position:0% +let's +what we have you can think of this as + + align:start position:0% +what we have you can think of this as + + + align:start position:0% +what we have you can think of this as +four + + align:start position:0% +four + + + align:start position:0% +four +fairly canonical watson crick type + + align:start position:0% +fairly canonical watson crick type + + + align:start position:0% +fairly canonical watson crick type +double helices for + + align:start position:0% +double helices for + + + align:start position:0% +double helices for +rna double helices which are + + align:start position:0% +rna double helices which are + + + align:start position:0% +rna double helices which are +slightly different from the dna double + + align:start position:0% +slightly different from the dna double + + + align:start position:0% +slightly different from the dna double +helixes + + align:start position:0% +helixes + + + align:start position:0% +helixes +but in this + + align:start position:0% +but in this + + + align:start position:0% +but in this +so we have seven + + align:start position:0% +so we have seven + + + align:start position:0% +so we have seven +base pairs six of which are + + align:start position:0% +base pairs six of which are + + + align:start position:0% +base pairs six of which are +watson crick in the the top stem loop + + align:start position:0% +watson crick in the the top stem loop + + + align:start position:0% +watson crick in the the top stem loop +starting at position number one with the + + align:start position:0% +starting at position number one with the + + + align:start position:0% +starting at position number one with the +five prime end and ending at position 72 + + align:start position:0% +five prime end and ending at position 72 + + + align:start position:0% +five prime end and ending at position 72 +so 1 and 72 is a gc base pair + + align:start position:0% +so 1 and 72 is a gc base pair + + + align:start position:0% +so 1 and 72 is a gc base pair +and you can see that the anticodon where + + align:start position:0% +and you can see that the anticodon where + + + align:start position:0% +and you can see that the anticodon where +it meets the messenger rna is at the + + align:start position:0% +it meets the messenger rna is at the + + + align:start position:0% +it meets the messenger rna is at the +bottom + + align:start position:0% +bottom + + + align:start position:0% +bottom +right hand part of the slide and there's + + align:start position:0% +right hand part of the slide and there's + + + align:start position:0% +right hand part of the slide and there's +this if you just look at that loop and + + align:start position:0% +this if you just look at that loop and + + + align:start position:0% +this if you just look at that loop and +you've got a + + align:start position:0% +you've got a + + + align:start position:0% +you've got a +seven base loop and a five base pair + + align:start position:0% +seven base loop and a five base pair + + + align:start position:0% +seven base loop and a five base pair +anti-codon stem + + align:start position:0% +anti-codon stem + + + align:start position:0% +anti-codon stem +and so each of these so that each of + + align:start position:0% +and so each of these so that each of + + + align:start position:0% +and so each of these so that each of +these stems has uh some distinguishing + + align:start position:0% +these stems has uh some distinguishing + + + align:start position:0% +these stems has uh some distinguishing +features a number of base pairs ranges + + align:start position:0% +features a number of base pairs ranges + + + align:start position:0% +features a number of base pairs ranges +from four to seven you've got a g base + + align:start position:0% +from four to seven you've got a g base + + + align:start position:0% +from four to seven you've got a g base +pair in the middle of the top stem + + align:start position:0% +pair in the middle of the top stem + + + align:start position:0% +pair in the middle of the top stem +and you've got little sequence + + align:start position:0% +and you've got little sequence + + + align:start position:0% +and you've got little sequence +boxes which are fairly conserved such as + + align:start position:0% +boxes which are fairly conserved such as + + + align:start position:0% +boxes which are fairly conserved such as +this + + align:start position:0% + + + + align:start position:0% + +t size cg + + align:start position:0% +t size cg + + + align:start position:0% +t size cg +is actually in its original form is a + + align:start position:0% +is actually in its original form is a + + + align:start position:0% +is actually in its original form is a +uucg + + align:start position:0% +uucg + + + align:start position:0% +uucg +and the t in the the sci + + align:start position:0% +and the t in the the sci + + + align:start position:0% +and the t in the the sci +or pseudoeurodean are examples of + + align:start position:0% +or pseudoeurodean are examples of + + + align:start position:0% +or pseudoeurodean are examples of +modified bases which are shown on the + + align:start position:0% +modified bases which are shown on the + + + align:start position:0% +modified bases which are shown on the +left side of the slide you can see + + align:start position:0% +left side of the slide you can see + + + align:start position:0% +left side of the slide you can see +there's quite a number of them + + align:start position:0% +there's quite a number of them + + + align:start position:0% +there's quite a number of them +you can either methyl you can add a + + align:start position:0% +you can either methyl you can add a + + + align:start position:0% +you can either methyl you can add a +methyl group a ch3 group to either the + + align:start position:0% +methyl group a ch3 group to either the + + + align:start position:0% +methyl group a ch3 group to either the +bases such as one methyl group on on g + + align:start position:0% +bases such as one methyl group on on g + + + align:start position:0% +bases such as one methyl group on on g +or you can add them to the riboses such + + align:start position:0% +or you can add them to the riboses such + + + align:start position:0% +or you can add them to the riboses such +as the two prime methyl groups which can + + align:start position:0% +as the two prime methyl groups which can + + + align:start position:0% +as the two prime methyl groups which can +go on any of the + + align:start position:0% +go on any of the + + + align:start position:0% +go on any of the +of the four bases because it's modifying + + align:start position:0% +of the four bases because it's modifying + + + align:start position:0% +of the four bases because it's modifying +the ribose which is generic most of the + + align:start position:0% +the ribose which is generic most of the + + + align:start position:0% +the ribose which is generic most of the +other ones are very specific to a base + + align:start position:0% +other ones are very specific to a base + + + align:start position:0% +other ones are very specific to a base +so for example dihydrouridine is a + + align:start position:0% +so for example dihydrouridine is a + + + align:start position:0% +so for example dihydrouridine is a +modification that can only occur to + + align:start position:0% +modification that can only occur to + + + align:start position:0% +modification that can only occur to +uridines the pseudo-uridine + + align:start position:0% +uridines the pseudo-uridine + + + align:start position:0% +uridines the pseudo-uridine +similar thing + + align:start position:0% + + + + align:start position:0% + +and so on so + + align:start position:0% +and so on so + + + align:start position:0% +and so on so +each each of these requires an enzyme + + align:start position:0% +each each of these requires an enzyme + + + align:start position:0% +each each of these requires an enzyme +and we will highlight one of the enzymes + + align:start position:0% +and we will highlight one of the enzymes + + + align:start position:0% +and we will highlight one of the enzymes +that's involved in putting the methyl + + align:start position:0% +that's involved in putting the methyl + + + align:start position:0% +that's involved in putting the methyl +groups onto + + align:start position:0% +groups onto + + + align:start position:0% +groups onto +onto + + align:start position:0% +onto + + + align:start position:0% +onto +the sugars the o2 prime methyl and just + + align:start position:0% +the sugars the o2 prime methyl and just + + + align:start position:0% +the sugars the o2 prime methyl and just +a few slides but right now what we want + + align:start position:0% +a few slides but right now what we want + + + align:start position:0% +a few slides but right now what we want +to ask is how did we get this folding + + align:start position:0% +to ask is how did we get this folding + + + align:start position:0% +to ask is how did we get this folding +structure now this is not the + + align:start position:0% +structure now this is not the + + + align:start position:0% +structure now this is not the +three-dimensional structure this is the + + align:start position:0% +three-dimensional structure this is the + + + align:start position:0% +three-dimensional structure this is the +intermediate between the primary dna + + align:start position:0% +intermediate between the primary dna + + + align:start position:0% +intermediate between the primary dna +sequence and the fully modified fully + + align:start position:0% +sequence and the fully modified fully + + + align:start position:0% +sequence and the fully modified fully +folded three-dimensional structure that + + align:start position:0% +folded three-dimensional structure that + + + align:start position:0% +folded three-dimensional structure that +we saw spinning around a couple slots + + align:start position:0% +we saw spinning around a couple slots + + + align:start position:0% +we saw spinning around a couple slots +ago + + align:start position:0% +ago + + + align:start position:0% +ago +so the first thing is + + align:start position:0% +so the first thing is + + + align:start position:0% +so the first thing is +the way you can + + align:start position:0% +the way you can + + + align:start position:0% +the way you can +try folding this + + align:start position:0% +try folding this + + + align:start position:0% +try folding this +or you oppose + + align:start position:0% +or you oppose + + + align:start position:0% +or you oppose +each base pair in turn + + align:start position:0% +each base pair in turn + + + align:start position:0% +each base pair in turn +to look for possible matches + + align:start position:0% +to look for possible matches + + + align:start position:0% +to look for possible matches +and then + + align:start position:0% +and then + + + align:start position:0% +and then +what was done historically this is in + + align:start position:0% +what was done historically this is in + + + align:start position:0% +what was done historically this is in +the mid to late 60s was you take each + + align:start position:0% +the mid to late 60s was you take each + + + align:start position:0% +the mid to late 60s was you take each +new transfer rna sequence and ask + + align:start position:0% +new transfer rna sequence and ask + + + align:start position:0% +new transfer rna sequence and ask +whether it fold whether it makes a + + align:start position:0% +whether it fold whether it makes a + + + align:start position:0% +whether it fold whether it makes a +decent fold in this simple planar + + align:start position:0% +decent fold in this simple planar + + + align:start position:0% +decent fold in this simple planar +representation that's related to the + + align:start position:0% +representation that's related to the + + + align:start position:0% +representation that's related to the +previous ones under the assumption the + + align:start position:0% +previous ones under the assumption the + + + align:start position:0% +previous ones under the assumption the +hope that there would be some + + align:start position:0% +hope that there would be some + + + align:start position:0% +hope that there would be some +conservation not only of a sequence of + + align:start position:0% +conservation not only of a sequence of + + + align:start position:0% +conservation not only of a sequence of +some of these motifs like the t-size cg + + align:start position:0% +some of these motifs like the t-size cg + + + align:start position:0% +some of these motifs like the t-size cg +but also the way that it folds up and + + align:start position:0% +but also the way that it folds up and + + + align:start position:0% +but also the way that it folds up and +you might even hypothesize that maybe it + + align:start position:0% +you might even hypothesize that maybe it + + + align:start position:0% +you might even hypothesize that maybe it +doesn't matter what the sequence is in + + align:start position:0% +doesn't matter what the sequence is in + + + align:start position:0% +doesn't matter what the sequence is in +some of these stems what's important is + + align:start position:0% +some of these stems what's important is + + + align:start position:0% +some of these stems what's important is +that it's capable of forming a stem that + + align:start position:0% +that it's capable of forming a stem that + + + align:start position:0% +that it's capable of forming a stem that +it is that position one + + align:start position:0% +it is that position one + + + align:start position:0% +it is that position one +is + + align:start position:0% +is + + + align:start position:0% +is +complementary to position 72. if + + align:start position:0% +complementary to position 72. if + + + align:start position:0% +complementary to position 72. if +position 1 were to change from a g to an + + align:start position:0% +position 1 were to change from a g to an + + + align:start position:0% +position 1 were to change from a g to an +a then position 72 should change from a + + align:start position:0% +a then position 72 should change from a + + + align:start position:0% +a then position 72 should change from a +c to a u + + align:start position:0% +c to a u + + + align:start position:0% +c to a u +okay so how do we formalize this okay + + align:start position:0% +okay so how do we formalize this okay + + + align:start position:0% +okay so how do we formalize this okay +this was um + + align:start position:0% +this was um + + + align:start position:0% +this was um +how do we + + align:start position:0% +how do we + + + align:start position:0% +how do we +formalize the process by which we + + align:start position:0% +formalize the process by which we + + + align:start position:0% +formalize the process by which we +generate this so-called cloverleaf + + align:start position:0% +generate this so-called cloverleaf + + + align:start position:0% +generate this so-called cloverleaf +structure or any similar folding pattern + + align:start position:0% +structure or any similar folding pattern + + + align:start position:0% +structure or any similar folding pattern +for + + align:start position:0% +for + + + align:start position:0% +for +for + + align:start position:0% +for + + + align:start position:0% +for +for small nucleic acids + + align:start position:0% +for small nucleic acids + + + align:start position:0% +for small nucleic acids +and what are the limitations of those of + + align:start position:0% +and what are the limitations of those of + + + align:start position:0% +and what are the limitations of those of +those algorithms and these dotted lines + + align:start position:0% +those algorithms and these dotted lines + + + align:start position:0% +those algorithms and these dotted lines +you see are non are some of the + + align:start position:0% +you see are non are some of the + + + align:start position:0% +you see are non are some of the +non-watson quick base pairs some of them + + align:start position:0% +non-watson quick base pairs some of them + + + align:start position:0% +non-watson quick base pairs some of them +will stack many of them some of them + + align:start position:0% +will stack many of them some of them + + + align:start position:0% +will stack many of them some of them +will actually form + + align:start position:0% +will actually form + + + align:start position:0% +will actually form +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the hydrogen bonds of a watson creek + + align:start position:0% +the hydrogen bonds of a watson creek + + + align:start position:0% +the hydrogen bonds of a watson creek +based pair but they won't have the + + align:start position:0% +based pair but they won't have the + + + align:start position:0% +based pair but they won't have the +otherwise have the rest of the geometry + + align:start position:0% +otherwise have the rest of the geometry + + + align:start position:0% +otherwise have the rest of the geometry +these and you can see that some of these + + align:start position:0% +these and you can see that some of these + + + align:start position:0% +these and you can see that some of these +will provide connections between two + + align:start position:0% +will provide connections between two + + + align:start position:0% +will provide connections between two +loops which are separated by stems and + + align:start position:0% +loops which are separated by stems and + + + align:start position:0% +loops which are separated by stems and +this kind of + + align:start position:0% +this kind of + + + align:start position:0% +this kind of +folding back means that it's not a it's + + align:start position:0% +folding back means that it's not a it's + + + align:start position:0% +folding back means that it's not a it's +not a simple set of + + align:start position:0% +not a simple set of + + + align:start position:0% +not a simple set of +helices + + align:start position:0% +helices + + + align:start position:0% +helices +so the way that we formalize this is we + + align:start position:0% +so the way that we formalize this is we + + + align:start position:0% +so the way that we formalize this is we +say that position number one + + align:start position:0% +say that position number one + + + align:start position:0% +say that position number one +uh + + align:start position:0% +uh + + + align:start position:0% +uh +if it's bound to position number 72 and + + align:start position:0% +if it's bound to position number 72 and + + + align:start position:0% +if it's bound to position number 72 and +the exact sequence + + align:start position:0% + + + + align:start position:0% + +maybe isn't as important as their + + align:start position:0% +maybe isn't as important as their + + + align:start position:0% +maybe isn't as important as their +ability to pair with one another then + + align:start position:0% +ability to pair with one another then + + + align:start position:0% +ability to pair with one another then +you expect if you take a large number of + + align:start position:0% +you expect if you take a large number of + + + align:start position:0% +you expect if you take a large number of +of transfer rnas and do a multi-sequence + + align:start position:0% +of transfer rnas and do a multi-sequence + + + align:start position:0% +of transfer rnas and do a multi-sequence +alignment as we did last time + + align:start position:0% +alignment as we did last time + + + align:start position:0% +alignment as we did last time +then + + align:start position:0% +then + + + align:start position:0% +then +the + + align:start position:0% +the + + + align:start position:0% +the +in that multi-sequence alignment you + + align:start position:0% +in that multi-sequence alignment you + + + align:start position:0% +in that multi-sequence alignment you +expect + + align:start position:0% +expect + + + align:start position:0% +expect +that the the when the g changes the c + + align:start position:0% +that the the when the g changes the c + + + align:start position:0% +that the the when the g changes the c +will change too and that's called + + align:start position:0% +will change too and that's called + + + align:start position:0% +will change too and that's called +covariance and if you look at the + + align:start position:0% +covariance and if you look at the + + + align:start position:0% +covariance and if you look at the +vertical axis the maximum + + align:start position:0% +vertical axis the maximum + + + align:start position:0% +vertical axis the maximum +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +uh that can be achieved is the same kind + + align:start position:0% +uh that can be achieved is the same kind + + + align:start position:0% +uh that can be achieved is the same kind +of maximum that we had in the motifs uh + + align:start position:0% +of maximum that we had in the motifs uh + + + align:start position:0% +of maximum that we had in the motifs uh +last lecture the motifs + + align:start position:0% +last lecture the motifs + + + align:start position:0% +last lecture the motifs +and we've actually had a couple of times + + align:start position:0% +and we've actually had a couple of times + + + align:start position:0% +and we've actually had a couple of times +it can get up to two bits two bits is + + align:start position:0% +it can get up to two bits two bits is + + + align:start position:0% +it can get up to two bits two bits is +the is the full scale for a for a base + + align:start position:0% +the is the full scale for a for a base + + + align:start position:0% +the is the full scale for a for a base +pair + + align:start position:0% +pair + + + align:start position:0% +pair +or base which can have four different + + align:start position:0% +or base which can have four different + + + align:start position:0% +or base which can have four different +values a c g or t + + align:start position:0% +values a c g or t + + + align:start position:0% +values a c g or t +and we're calling this mutual + + align:start position:0% +and we're calling this mutual + + + align:start position:0% +and we're calling this mutual +information it has the same units a full + + align:start position:0% +information it has the same units a full + + + align:start position:0% +information it has the same units a full +scale of zero to two bits + + align:start position:0% +scale of zero to two bits + + + align:start position:0% +scale of zero to two bits +and so we see + + align:start position:0% +and so we see + + + align:start position:0% +and so we see +along the horizontal axis here called a + + align:start position:0% +along the horizontal axis here called a + + + align:start position:0% +along the horizontal axis here called a +position i and j + + align:start position:0% +position i and j + + + align:start position:0% +position i and j +which range from one to 72 which is the + + align:start position:0% +which range from one to 72 which is the + + + align:start position:0% +which range from one to 72 which is the +core part of the transfer rna the last + + align:start position:0% +core part of the transfer rna the last + + + align:start position:0% +core part of the transfer rna the last +four bases are added by a um + + align:start position:0% +four bases are added by a um + + + align:start position:0% +four bases are added by a um +a specialized enzyme + + align:start position:0% +a specialized enzyme + + + align:start position:0% +a specialized enzyme +but position number one and position 72 + + align:start position:0% +but position number one and position 72 + + + align:start position:0% +but position number one and position 72 +covaria is shown by this peak in the + + align:start position:0% +covaria is shown by this peak in the + + + align:start position:0% +covaria is shown by this peak in the +far left hand + + align:start position:0% +far left hand + + + align:start position:0% +far left hand +region and in fact there's seven peaks + + align:start position:0% +region and in fact there's seven peaks + + + align:start position:0% +region and in fact there's seven peaks +in a row there + + align:start position:0% +in a row there + + + align:start position:0% +in a row there +where uh which corresponds to the seven + + align:start position:0% +where uh which corresponds to the seven + + + align:start position:0% +where uh which corresponds to the seven +stacked base pairs they covari + + align:start position:0% +stacked base pairs they covari + + + align:start position:0% +stacked base pairs they covari +similarly in the + + align:start position:0% +similarly in the + + + align:start position:0% +similarly in the +pseudo-uc stem that we talked about a + + align:start position:0% +pseudo-uc stem that we talked about a + + + align:start position:0% +pseudo-uc stem that we talked about a +couple times there that + + align:start position:0% +couple times there that + + + align:start position:0% +couple times there that +those + + align:start position:0% +those + + + align:start position:0% +those +five + + align:start position:0% +five + + + align:start position:0% +five +nucleotides covariate as you would get + + align:start position:0% +nucleotides covariate as you would get + + + align:start position:0% +nucleotides covariate as you would get +in a + + align:start position:0% +in a + + + align:start position:0% +in a +in a + + align:start position:0% + + + + align:start position:0% + +stem the anticodon stem is another five + + align:start position:0% +stem the anticodon stem is another five + + + align:start position:0% +stem the anticodon stem is another five +and the and the d stem so named after + + align:start position:0% +and the and the d stem so named after + + + align:start position:0% +and the and the d stem so named after +the the hydro uridine modifications is + + align:start position:0% +the the hydro uridine modifications is + + + align:start position:0% +the the hydro uridine modifications is +four base pairs and the way that this is + + align:start position:0% +four base pairs and the way that this is + + + align:start position:0% +four base pairs and the way that this is +derived and we're going to work through + + align:start position:0% +derived and we're going to work through + + + align:start position:0% +derived and we're going to work through +this an example in the next slide but + + align:start position:0% +this an example in the next slide but + + + align:start position:0% +this an example in the next slide but +just + + align:start position:0% +just + + + align:start position:0% +just +just as a + + align:start position:0% +just as a + + + align:start position:0% +just as a +a labeling of this axis here the mutual + + align:start position:0% +a labeling of this axis here the mutual + + + align:start position:0% +a labeling of this axis here the mutual +information between the i face and the j + + align:start position:0% +information between the i face and the j + + + align:start position:0% +information between the i face and the j +face that is the c for example between i + + align:start position:0% +face that is the c for example between i + + + align:start position:0% +face that is the c for example between i +equals 1 and j equals 72 + + align:start position:0% +equals 1 and j equals 72 + + + align:start position:0% +equals 1 and j equals 72 +is simply + + align:start position:0% +is simply + + + align:start position:0% +is simply +the sum of the frequency of getting + + align:start position:0% +the sum of the frequency of getting + + + align:start position:0% +the sum of the frequency of getting +that particular i and j + + align:start position:0% +that particular i and j + + + align:start position:0% +that particular i and j +f + + align:start position:0% +f + + + align:start position:0% +f +is the frequency of getting say a g as + + align:start position:0% +is the frequency of getting say a g as + + + align:start position:0% +is the frequency of getting say a g as +position 1 and a c at position 72 + + align:start position:0% +position 1 and a c at position 72 + + + align:start position:0% +position 1 and a c at position 72 +times the the log base two remember when + + align:start position:0% +times the the log base two remember when + + + align:start position:0% +times the the log base two remember when +we're talking about information content + + align:start position:0% +we're talking about information content + + + align:start position:0% +we're talking about information content +of uh nucle or + + align:start position:0% +of uh nucle or + + + align:start position:0% +of uh nucle or +information in general bits in a + + align:start position:0% +information in general bits in a + + + align:start position:0% +information in general bits in a +computer or or nucleotides in a sequence + + align:start position:0% +computer or or nucleotides in a sequence + + + align:start position:0% +computer or or nucleotides in a sequence +we do log base two + + align:start position:0% +we do log base two + + + align:start position:0% +we do log base two +and uh as introduced by shannon and + + align:start position:0% +and uh as introduced by shannon and + + + align:start position:0% +and uh as introduced by shannon and +others so now it's going to be the log + + align:start position:0% +others so now it's going to be the log + + + align:start position:0% +others so now it's going to be the log +of that same frequency so the frequency + + align:start position:0% +of that same frequency so the frequency + + + align:start position:0% +of that same frequency so the frequency +of getting + + align:start position:0% +of getting + + + align:start position:0% +of getting +that particular i and that particular j + + align:start position:0% +that particular i and that particular j + + + align:start position:0% +that particular i and that particular j +type type of base + + align:start position:0% +type type of base + + + align:start position:0% +type type of base +normalized now to the the how how + + align:start position:0% +normalized now to the the how how + + + align:start position:0% +normalized now to the the how how +frequently that those two bases occur + + align:start position:0% +frequently that those two bases occur + + + align:start position:0% +frequently that those two bases occur +throughout the uh + + align:start position:0% + + + + align:start position:0% + +throughout those positions in other + + align:start position:0% +throughout those positions in other + + + align:start position:0% +throughout those positions in other +words you know how often they co-occur + + align:start position:0% +words you know how often they co-occur + + + align:start position:0% +words you know how often they co-occur +at that at those two positions now how + + align:start position:0% +at that at those two positions now how + + + align:start position:0% +at that at those two positions now how +often do they occur independently of one + + align:start position:0% +often do they occur independently of one + + + align:start position:0% +often do they occur independently of one +another and that's what + + align:start position:0% +another and that's what + + + align:start position:0% +another and that's what +the denominator is here so when you take + + align:start position:0% +the denominator is here so when you take + + + align:start position:0% +the denominator is here so when you take +this ratio you put it on a on a uh + + align:start position:0% +this ratio you put it on a on a uh + + + align:start position:0% +this ratio you put it on a on a uh +on a conventional scale and then then + + align:start position:0% +on a conventional scale and then then + + + align:start position:0% +on a conventional scale and then then +you have something that's analogous to + + align:start position:0% +you have something that's analogous to + + + align:start position:0% +you have something that's analogous to +the p log p of information theory and + + align:start position:0% +the p log p of information theory and + + + align:start position:0% +the p log p of information theory and +you sum over + + align:start position:0% +you sum over + + + align:start position:0% +you sum over +all of the + + align:start position:0% +all of the + + + align:start position:0% +all of the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +observed bases at positions i and j + + align:start position:0% + + + + align:start position:0% + +okay and that could that's for a + + align:start position:0% +okay and that could that's for a + + + align:start position:0% +okay and that could that's for a +particular i and j you sum over all the + + align:start position:0% +particular i and j you sum over all the + + + align:start position:0% +particular i and j you sum over all the +x's uh that occur at positions say 1 and + + align:start position:0% +x's uh that occur at positions say 1 and + + + align:start position:0% +x's uh that occur at positions say 1 and + + align:start position:0% + + + align:start position:0% +and then you do that and then you repeat + + align:start position:0% +and then you do that and then you repeat + + + align:start position:0% +and then you do that and then you repeat +that you can get this m sub i j for + + align:start position:0% +that you can get this m sub i j for + + + align:start position:0% +that you can get this m sub i j for +every + + align:start position:0% +every + + + align:start position:0% +every +matrix element going from 1 to 72 in a + + align:start position:0% +matrix element going from 1 to 72 in a + + + align:start position:0% +matrix element going from 1 to 72 in a +in a + + align:start position:0% +in a + + + align:start position:0% +in a +symmetric square matrix + + align:start position:0% +symmetric square matrix + + + align:start position:0% +symmetric square matrix +okay so now let's work through this for + + align:start position:0% +okay so now let's work through this for + + + align:start position:0% +okay so now let's work through this for +two extreme examples the extreme case + + align:start position:0% +two extreme examples the extreme case + + + align:start position:0% +two extreme examples the extreme case +where you have + + align:start position:0% +where you have + + + align:start position:0% +where you have +perfect covariance in this extreme case + + align:start position:0% +perfect covariance in this extreme case + + + align:start position:0% +perfect covariance in this extreme case +where you have no no real association + + align:start position:0% +where you have no no real association + + + align:start position:0% +where you have no no real association +so we're going to illustrate this with a + + align:start position:0% +so we're going to illustrate this with a + + + align:start position:0% +so we're going to illustrate this with a +with a toy + + align:start position:0% +with a toy + + + align:start position:0% +with a toy +multi-sequence alignment here this is + + align:start position:0% +multi-sequence alignment here this is + + + align:start position:0% +multi-sequence alignment here this is +just the same way we did a + + align:start position:0% +just the same way we did a + + + align:start position:0% +just the same way we did a +multi-sequence alignment + + align:start position:0% +multi-sequence alignment + + + align:start position:0% +multi-sequence alignment +in the last class here note there are no + + align:start position:0% +in the last class here note there are no + + + align:start position:0% +in the last class here note there are no +insertions or deletions but you can it's + + align:start position:0% +insertions or deletions but you can it's + + + align:start position:0% +insertions or deletions but you can it's +the same thing you could derive a weight + + align:start position:0% +the same thing you could derive a weight + + + align:start position:0% +the same thing you could derive a weight +matrix for this + + align:start position:0% +matrix for this + + + align:start position:0% +matrix for this +and you would see that the first co the + + align:start position:0% +and you would see that the first co the + + + align:start position:0% +and you would see that the first co the +far left hand column i equals one + + align:start position:0% +far left hand column i equals one + + + align:start position:0% +far left hand column i equals one +is has all four possibilities + + align:start position:0% +is has all four possibilities + + + align:start position:0% +is has all four possibilities +and the uh so does the the rightmost + + align:start position:0% +and the uh so does the the rightmost + + + align:start position:0% +and the uh so does the the rightmost +column + + align:start position:0% +column + + + align:start position:0% +column +of that multi-sequence alignment j + + align:start position:0% +of that multi-sequence alignment j + + + align:start position:0% +of that multi-sequence alignment j +equals six + + align:start position:0% +equals six + + + align:start position:0% +equals six +and so let's calculate these two are + + align:start position:0% +and so let's calculate these two are + + + align:start position:0% +and so let's calculate these two are +these + + align:start position:0% +these + + + align:start position:0% +these +uh + + align:start position:0% +uh + + + align:start position:0% +uh +co-varying in this simple multi-sequence + + align:start position:0% +co-varying in this simple multi-sequence + + + align:start position:0% +co-varying in this simple multi-sequence +alignment of four + + align:start position:0% +alignment of four + + + align:start position:0% +alignment of four +uh six mers + + align:start position:0% +uh six mers + + + align:start position:0% +uh six mers +so we calculate the mutual information + + align:start position:0% +so we calculate the mutual information + + + align:start position:0% +so we calculate the mutual information +for i equals one j equals six + + align:start position:0% +for i equals one j equals six + + + align:start position:0% +for i equals one j equals six +um m sub one six it's going to be equal + + align:start position:0% +um m sub one six it's going to be equal + + + align:start position:0% +um m sub one six it's going to be equal +to sum + + align:start position:0% +to sum + + + align:start position:0% +to sum +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the first term in the sum is for the a u + + align:start position:0% +the first term in the sum is for the a u + + + align:start position:0% +the first term in the sum is for the a u +and then we're going to walk through c g + + align:start position:0% +and then we're going to walk through c g + + + align:start position:0% +and then we're going to walk through c g +g c u a so there'll be four terms in the + + align:start position:0% +g c u a so there'll be four terms in the + + + align:start position:0% +g c u a so there'll be four terms in the +sum + + align:start position:0% +sum + + + align:start position:0% +sum +each of the terms will have + + align:start position:0% +each of the terms will have + + + align:start position:0% +each of the terms will have +coincidentally in this case have the + + align:start position:0% +coincidentally in this case have the + + + align:start position:0% +coincidentally in this case have the +same frequency for that particular + + align:start position:0% +same frequency for that particular + + + align:start position:0% +same frequency for that particular +pairing of aau remember this is not a + + align:start position:0% +pairing of aau remember this is not a + + + align:start position:0% +pairing of aau remember this is not a +base pair this is a co-varying pair of + + align:start position:0% +base pair this is a co-varying pair of + + + align:start position:0% +base pair this is a co-varying pair of +nucleotides it could have been anywhere + + align:start position:0% +nucleotides it could have been anywhere + + + align:start position:0% +nucleotides it could have been anywhere +in the sequence we happen to pick the + + align:start position:0% +in the sequence we happen to pick the + + + align:start position:0% +in the sequence we happen to pick the +first and the last base + + align:start position:0% + + + + align:start position:0% + +so they all have the same frequency that + + align:start position:0% +so they all have the same frequency that + + + align:start position:0% +so they all have the same frequency that +frequency is one quarter so the au + + align:start position:0% +frequency is one quarter so the au + + + align:start position:0% +frequency is one quarter so the au +occurs one quarter of the of the four + + align:start position:0% +occurs one quarter of the of the four + + + align:start position:0% +occurs one quarter of the of the four +sequences of multi-sequence alignment so + + align:start position:0% +sequences of multi-sequence alignment so + + + align:start position:0% +sequences of multi-sequence alignment so +that's one quarter + + align:start position:0% +that's one quarter + + + align:start position:0% +that's one quarter +and then + + align:start position:0% +and then + + + align:start position:0% +and then +that remembers the same frequency inside + + align:start position:0% +that remembers the same frequency inside + + + align:start position:0% +that remembers the same frequency inside +the logarithm but now in the denominator + + align:start position:0% +the logarithm but now in the denominator + + + align:start position:0% +the logarithm but now in the denominator +we're going to normalize it to the + + align:start position:0% +we're going to normalize it to the + + + align:start position:0% +we're going to normalize it to the +frequency that the a occurs in the i + + align:start position:0% +frequency that the a occurs in the i + + + align:start position:0% +frequency that the a occurs in the i +equals one position which is one quarter + + align:start position:0% +equals one position which is one quarter + + + align:start position:0% +equals one position which is one quarter +and the frequency that u occurs in the j + + align:start position:0% +and the frequency that u occurs in the j + + + align:start position:0% +and the frequency that u occurs in the j +equals six position which is one quarter + + align:start position:0% +equals six position which is one quarter + + + align:start position:0% +equals six position which is one quarter +so it's one quarter over one quarter + + align:start position:0% +so it's one quarter over one quarter + + + align:start position:0% +so it's one quarter over one quarter +squared + + align:start position:0% +squared + + + align:start position:0% +squared +or four + + align:start position:0% +or four + + + align:start position:0% +or four +so 0.25 times + + align:start position:0% +so 0.25 times + + + align:start position:0% +so 0.25 times +log log base 2 of 4 is going to be 2 + + align:start position:0% +log log base 2 of 4 is going to be 2 + + + align:start position:0% +log log base 2 of 4 is going to be 2 +and .25 times 2 + + align:start position:0% +and .25 times 2 + + + align:start position:0% +and .25 times 2 +is going to be + + align:start position:0% +is going to be + + + align:start position:0% +is going to be +0.5 + + align:start position:0% + + + + align:start position:0% + +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +that's the first term right that's for + + align:start position:0% +that's the first term right that's for + + + align:start position:0% +that's the first term right that's for +the au uh pairing if you go down through + + align:start position:0% +the au uh pairing if you go down through + + + align:start position:0% +the au uh pairing if you go down through +all four terms they all end up being the + + align:start position:0% +all four terms they all end up being the + + + align:start position:0% +all four terms they all end up being the +same form right the frequency is always + + align:start position:0% +same form right the frequency is always + + + align:start position:0% +same form right the frequency is always +going to be 0.25 for the pair and 0.25 + + align:start position:0% +going to be 0.25 for the pair and 0.25 + + + align:start position:0% +going to be 0.25 for the pair and 0.25 +for each individual basis so you end up + + align:start position:0% +for each individual basis so you end up + + + align:start position:0% +for each individual basis so you end up +with four of those four examples of + + align:start position:0% +with four of those four examples of + + + align:start position:0% +with four of those four examples of +those + + align:start position:0% +those + + + align:start position:0% +those +for each of the + + align:start position:0% +for each of the + + + align:start position:0% +for each of the +four cases and so four times 0.5 is is + + align:start position:0% +four cases and so four times 0.5 is is + + + align:start position:0% +four cases and so four times 0.5 is is +two + + align:start position:0% +two + + + align:start position:0% +two +so that's + + align:start position:0% +so that's + + + align:start position:0% +so that's +consistent hopefully with what you would + + align:start position:0% +consistent hopefully with what you would + + + align:start position:0% +consistent hopefully with what you would +have expected for perfect covariance + + align:start position:0% +have expected for perfect covariance + + + align:start position:0% +have expected for perfect covariance +you're getting the full information + + align:start position:0% +you're getting the full information + + + align:start position:0% +you're getting the full information +content the full range of two bits + + align:start position:0% +content the full range of two bits + + + align:start position:0% +content the full range of two bits +uh and so that's what we achieved so now + + align:start position:0% +uh and so that's what we achieved so now + + + align:start position:0% +uh and so that's what we achieved so now +as a controller it's just further + + align:start position:0% +as a controller it's just further + + + align:start position:0% +as a controller it's just further +gratification that we actually + + align:start position:0% +gratification that we actually + + + align:start position:0% +gratification that we actually +understand this um + + align:start position:0% +understand this um + + + align:start position:0% +understand this um +as we're working through the example of + + align:start position:0% +as we're working through the example of + + + align:start position:0% +as we're working through the example of +comparing i equals one with j equals two + + align:start position:0% +comparing i equals one with j equals two + + + align:start position:0% +comparing i equals one with j equals two +so there's two far columns and here + + align:start position:0% +so there's two far columns and here + + + align:start position:0% +so there's two far columns and here +you're familiar with life one j j equals + + align:start position:0% +you're familiar with life one j j equals + + + align:start position:0% +you're familiar with life one j j equals +two is always c and so it's not + + align:start position:0% +two is always c and so it's not + + + align:start position:0% +two is always c and so it's not +covariating with the first column + + align:start position:0% +covariating with the first column + + + align:start position:0% +covariating with the first column +as + + align:start position:0% +as + + + align:start position:0% +as +as in the previous example so let's just + + align:start position:0% +as in the previous example so let's just + + + align:start position:0% +as in the previous example so let's just +work through it um same way so + + align:start position:0% +work through it um same way so + + + align:start position:0% +work through it um same way so +the first + + align:start position:0% +the first + + + align:start position:0% +the first +term in the series is 0.25 again because + + align:start position:0% +term in the series is 0.25 again because + + + align:start position:0% +term in the series is 0.25 again because +the ac pair not base pair but but but + + align:start position:0% +the ac pair not base pair but but but + + + align:start position:0% +the ac pair not base pair but but but +pair of bases + + align:start position:0% +pair of bases + + + align:start position:0% +pair of bases +is uh + + align:start position:0% +is uh + + + align:start position:0% +is uh +it occurs only once in the four of the + + align:start position:0% +it occurs only once in the four of the + + + align:start position:0% +it occurs only once in the four of the +multi-sequence alignment says 0.25 they + + align:start position:0% +multi-sequence alignment says 0.25 they + + + align:start position:0% +multi-sequence alignment says 0.25 they +have the logarithm base 2 of that same + + align:start position:0% +have the logarithm base 2 of that same + + + align:start position:0% +have the logarithm base 2 of that same +0.25 now + + align:start position:0% +0.25 now + + + align:start position:0% +0.25 now +normalized to the frequency of the a in + + align:start position:0% +normalized to the frequency of the a in + + + align:start position:0% +normalized to the frequency of the a in +that in its column + + align:start position:0% +that in its column + + + align:start position:0% +that in its column +the one column + + align:start position:0% +the one column + + + align:start position:0% +the one column +which is 0.25 and the c in the j equals + + align:start position:0% +which is 0.25 and the c in the j equals + + + align:start position:0% +which is 0.25 and the c in the j equals +2 column which is + + align:start position:0% +2 column which is + + + align:start position:0% +2 column which is +it's always there it's unity so it's 1. + + align:start position:0% +it's always there it's unity so it's 1. + + + align:start position:0% +it's always there it's unity so it's 1. +so now that's the big change here is + + align:start position:0% +so now that's the big change here is + + + align:start position:0% +so now that's the big change here is +instead of having 0.25 in both the + + align:start position:0% +instead of having 0.25 in both the + + + align:start position:0% +instead of having 0.25 in both the +denominator terms it's now 0.25 times 1. + + align:start position:0% +denominator terms it's now 0.25 times 1. + + + align:start position:0% +denominator terms it's now 0.25 times 1. +it's now it's + + align:start position:0% +it's now it's + + + align:start position:0% +it's now it's +0.25 over 0.25 so you have the log base + + align:start position:0% +0.25 over 0.25 so you have the log base + + + align:start position:0% +0.25 over 0.25 so you have the log base +2 of 1 + + align:start position:0% +2 of 1 + + + align:start position:0% +2 of 1 +which will be 0 + + align:start position:0% +which will be 0 + + + align:start position:0% +which will be 0 +and that zeroes out the whole term and + + align:start position:0% +and that zeroes out the whole term and + + + align:start position:0% +and that zeroes out the whole term and +so you have mutual information + + align:start position:0% +so you have mutual information + + + align:start position:0% +so you have mutual information +of 0 + + align:start position:0% +of 0 + + + align:start position:0% +of 0 +as you would expect from this particular + + align:start position:0% +as you would expect from this particular + + + align:start position:0% +as you would expect from this particular +toy example where columns 1 and 2 do not + + align:start position:0% +toy example where columns 1 and 2 do not + + + align:start position:0% +toy example where columns 1 and 2 do not +covaria + + align:start position:0% +covaria + + + align:start position:0% +covaria +so this is that the same formulas in the + + align:start position:0% +so this is that the same formulas in the + + + align:start position:0% +so this is that the same formulas in the +previous slide generalization of the one + + align:start position:0% +previous slide generalization of the one + + + align:start position:0% +previous slide generalization of the one +that we walked through + + align:start position:0% +that we walked through + + + align:start position:0% +that we walked through +term by term + + align:start position:0% +term by term + + + align:start position:0% +term by term +and here's the reference + + align:start position:0% + + + + align:start position:0% + +for that + + align:start position:0% + + + + align:start position:0% + +so now how do we go so that was we've + + align:start position:0% +so now how do we go so that was we've + + + align:start position:0% +so now how do we go so that was we've +taken now + + align:start position:0% +taken now + + + align:start position:0% +taken now +hundreds possibly thousands of transfer + + align:start position:0% +hundreds possibly thousands of transfer + + + align:start position:0% +hundreds possibly thousands of transfer +rnas we've done a multi-sequence + + align:start position:0% +rnas we've done a multi-sequence + + + align:start position:0% +rnas we've done a multi-sequence +alignment we've produced that mutual + + align:start position:0% +alignment we've produced that mutual + + + align:start position:0% +alignment we've produced that mutual +information + + align:start position:0% +information + + + align:start position:0% +information +uh + + align:start position:0% +uh + + + align:start position:0% +uh +pattern that we saw before with a 1 by + + align:start position:0% +pattern that we saw before with a 1 by + + + align:start position:0% +pattern that we saw before with a 1 by + + align:start position:0% + + + align:start position:0% +1 to 72 by 1 to 72 + + align:start position:0% +1 to 72 by 1 to 72 + + + align:start position:0% +1 to 72 by 1 to 72 +comparison where you've got the spikes + + align:start position:0% +comparison where you've got the spikes + + + align:start position:0% +comparison where you've got the spikes +at each of the + + align:start position:0% +at each of the + + + align:start position:0% +at each of the +each of the + + align:start position:0% +each of the + + + align:start position:0% +each of the +double helixes + + align:start position:0% +double helixes + + + align:start position:0% +double helixes +now how do we turn + + align:start position:0% +now how do we turn + + + align:start position:0% +now how do we turn +how do we turn that into more general + + align:start position:0% +how do we turn that into more general + + + align:start position:0% +how do we turn that into more general +practice how do we generate uh + + align:start position:0% + + + + align:start position:0% + +secondary structures which are kind of + + align:start position:0% +secondary structures which are kind of + + + align:start position:0% +secondary structures which are kind of +at this intermediate in between the + + align:start position:0% +at this intermediate in between the + + + align:start position:0% +at this intermediate in between the +primary sequence and the + + align:start position:0% +primary sequence and the + + + align:start position:0% +primary sequence and the +three-dimensional structure + + align:start position:0% +three-dimensional structure + + + align:start position:0% +three-dimensional structure +using a particular class of + + align:start position:0% +using a particular class of + + + align:start position:0% +using a particular class of +experimental + + align:start position:0% +experimental + + + align:start position:0% +experimental +data + + align:start position:0% +data + + + align:start position:0% +data +combined with the sequence data + + align:start position:0% +combined with the sequence data + + + align:start position:0% +combined with the sequence data +this does not necessarily require + + align:start position:0% +this does not necessarily require + + + align:start position:0% +this does not necessarily require +the large + + align:start position:0% +the large + + + align:start position:0% +the large +uh set of + + align:start position:0% +uh set of + + + align:start position:0% +uh set of +line sequences but it will obviously + + align:start position:0% +line sequences but it will obviously + + + align:start position:0% +line sequences but it will obviously +benefits from it you want you could do a + + align:start position:0% +benefits from it you want you could do a + + + align:start position:0% +benefits from it you want you could do a +secondary structure for each element + + align:start position:0% +secondary structure for each element + + + align:start position:0% +secondary structure for each element +in the align sequence + + align:start position:0% +in the align sequence + + + align:start position:0% +in the align sequence +in order to + + align:start position:0% +in order to + + + align:start position:0% +in order to +and use the mutual information if you uh + + align:start position:0% +and use the mutual information if you uh + + + align:start position:0% +and use the mutual information if you uh +have it + + align:start position:0% +have it + + + align:start position:0% +have it +but let's just talk about just the just + + align:start position:0% +but let's just talk about just the just + + + align:start position:0% +but let's just talk about just the just +the simple application of the these + + align:start position:0% +the simple application of the these + + + align:start position:0% +the simple application of the these +thermodynamic parameters to the + + align:start position:0% +thermodynamic parameters to the + + + align:start position:0% +thermodynamic parameters to the +prediction of secondary structure and + + align:start position:0% +prediction of secondary structure and + + + align:start position:0% +prediction of secondary structure and +what are our expectations before we go + + align:start position:0% +what are our expectations before we go + + + align:start position:0% +what are our expectations before we go +through the algorithm how good is it + + align:start position:0% +through the algorithm how good is it + + + align:start position:0% +through the algorithm how good is it +in this + + align:start position:0% + + + + align:start position:0% + +fairly close to state of the art paper + + align:start position:0% +fairly close to state of the art paper + + + align:start position:0% +fairly close to state of the art paper +looking through + + align:start position:0% +looking through + + + align:start position:0% +looking through +over 700 generated structures + + align:start position:0% +over 700 generated structures + + + align:start position:0% +over 700 generated structures +they have + + align:start position:0% + + + + align:start position:0% + +in each set at they can it contains one + + align:start position:0% +in each set at they can it contains one + + + align:start position:0% +in each set at they can it contains one +structure that on average has 86 percent + + align:start position:0% +structure that on average has 86 percent + + + align:start position:0% +structure that on average has 86 percent +of its known base pairs + + align:start position:0% +of its known base pairs + + + align:start position:0% +of its known base pairs +that's not saying that it's necessarily + + align:start position:0% +that's not saying that it's necessarily + + + align:start position:0% +that's not saying that it's necessarily +identified as the top the best + + align:start position:0% +identified as the top the best + + + align:start position:0% +identified as the top the best +structure it's saying that it has one + + align:start position:0% +structure it's saying that it has one + + + align:start position:0% +structure it's saying that it has one +structure by the criterion they're using + + align:start position:0% +structure by the criterion they're using + + + align:start position:0% +structure by the criterion they're using +this is a weak + + align:start position:0% +this is a weak + + + align:start position:0% +this is a weak +self-praise + + align:start position:0% + + + + align:start position:0% + +but let's walk through how that works + + align:start position:0% +but let's walk through how that works + + + align:start position:0% +but let's walk through how that works +when when when someone says that they're + + align:start position:0% +when when when someone says that they're + + + align:start position:0% +when when when someone says that they're +going to + + align:start position:0% +going to + + + align:start position:0% +going to +predict + + align:start position:0% +predict + + + align:start position:0% +predict +a + + align:start position:0% +a + + + align:start position:0% +a +secondary structure or a + + align:start position:0% +secondary structure or a + + + align:start position:0% +secondary structure or a +three-dimensional structure from a + + align:start position:0% +three-dimensional structure from a + + + align:start position:0% +three-dimensional structure from a +primary sequence + + align:start position:0% +primary sequence + + + align:start position:0% +primary sequence +more or less from scratch they really + + align:start position:0% +more or less from scratch they really + + + align:start position:0% +more or less from scratch they really +don't they really typically mean that + + align:start position:0% +don't they really typically mean that + + + align:start position:0% +don't they really typically mean that +there's going to be a variety of + + align:start position:0% +there's going to be a variety of + + + align:start position:0% +there's going to be a variety of +other chemical data that they take into + + align:start position:0% +other chemical data that they take into + + + align:start position:0% +other chemical data that they take into +account + + align:start position:0% +account + + + align:start position:0% +account +but it will be generic data it will not + + align:start position:0% +but it will be generic data it will not + + + align:start position:0% +but it will be generic data it will not +be specific chemical data for this + + align:start position:0% +be specific chemical data for this + + + align:start position:0% +be specific chemical data for this +particular molecule and the generic data + + align:start position:0% +particular molecule and the generic data + + + align:start position:0% +particular molecule and the generic data +in this case + + align:start position:0% +in this case + + + align:start position:0% +in this case +are measurements of + + align:start position:0% + + + + align:start position:0% + +of the the thermodynamics of melting of + + align:start position:0% +of the the thermodynamics of melting of + + + align:start position:0% +of the the thermodynamics of melting of +model + + align:start position:0% +model + + + align:start position:0% +model +oligonucleotides usually large amounts + + align:start position:0% +oligonucleotides usually large amounts + + + align:start position:0% +oligonucleotides usually large amounts +of them monitor spectrophotometrically + + align:start position:0% +of them monitor spectrophotometrically + + + align:start position:0% +of them monitor spectrophotometrically +and from these from the temperatures and + + align:start position:0% +and from these from the temperatures and + + + align:start position:0% +and from these from the temperatures and +of ma of melting basically at + + align:start position:0% +of ma of melting basically at + + + align:start position:0% +of ma of melting basically at +equilibrium where you're getting + + align:start position:0% +equilibrium where you're getting + + + align:start position:0% +equilibrium where you're getting +half + + align:start position:0% +half + + + align:start position:0% +half +melted structures you can determine the + + align:start position:0% +melted structures you can determine the + + + align:start position:0% +melted structures you can determine the +free energies + + align:start position:0% +free energies + + + align:start position:0% +free energies +where the negative free energies are the + + align:start position:0% +where the negative free energies are the + + + align:start position:0% +where the negative free energies are the +desirable ones the ones that are that + + align:start position:0% +desirable ones the ones that are that + + + align:start position:0% +desirable ones the ones that are that +are likely to happen + + align:start position:0% +are likely to happen + + + align:start position:0% +are likely to happen +if you let the system + + align:start position:0% +if you let the system + + + align:start position:0% +if you let the system +go to equilibrium + + align:start position:0% +go to equilibrium + + + align:start position:0% +go to equilibrium +and + + align:start position:0% +and + + + align:start position:0% +and +this is a kind of interesting + + align:start position:0% +this is a kind of interesting + + + align:start position:0% +this is a kind of interesting +application of the free energies for + + align:start position:0% +application of the free energies for + + + align:start position:0% +application of the free energies for +nucleic acids + + align:start position:0% +nucleic acids + + + align:start position:0% +nucleic acids +here + + align:start position:0% +here + + + align:start position:0% +here +the algorithm that one uses it is + + align:start position:0% +the algorithm that one uses it is + + + align:start position:0% +the algorithm that one uses it is +concerned mostly with + + align:start position:0% +concerned mostly with + + + align:start position:0% +concerned mostly with +adjacent base pairs of base pairs so + + align:start position:0% +adjacent base pairs of base pairs so + + + align:start position:0% +adjacent base pairs of base pairs so +it's not a base pair as you might as you + + align:start position:0% +it's not a base pair as you might as you + + + align:start position:0% +it's not a base pair as you might as you +might think that the hydrogen bonds that + + align:start position:0% +might think that the hydrogen bonds that + + + align:start position:0% +might think that the hydrogen bonds that +determine + + align:start position:0% +determine + + + align:start position:0% +determine +uh the watson crick and non-watson creek + + align:start position:0% +uh the watson crick and non-watson creek + + + align:start position:0% +uh the watson crick and non-watson creek +base pairs would dominate instead it's + + align:start position:0% +base pairs would dominate instead it's + + + align:start position:0% +base pairs would dominate instead it's +the stacking interactions to dominate + + align:start position:0% +the stacking interactions to dominate + + + align:start position:0% +the stacking interactions to dominate +and since it's the stacking interactions + + align:start position:0% +and since it's the stacking interactions + + + align:start position:0% +and since it's the stacking interactions +that dominate the hydrogen bonds are + + align:start position:0% +that dominate the hydrogen bonds are + + + align:start position:0% +that dominate the hydrogen bonds are +basically exchanging a water hydrogen + + align:start position:0% +basically exchanging a water hydrogen + + + align:start position:0% +basically exchanging a water hydrogen +bond for a base pair hydrogen bond + + align:start position:0% +bond for a base pair hydrogen bond + + + align:start position:0% +bond for a base pair hydrogen bond +it looks very specific but in terms of + + align:start position:0% +it looks very specific but in terms of + + + align:start position:0% +it looks very specific but in terms of +free energy is fairly weak the free + + align:start position:0% +free energy is fairly weak the free + + + align:start position:0% +free energy is fairly weak the free +energy determine is determined more by + + align:start position:0% +energy determine is determined more by + + + align:start position:0% +energy determine is determined more by +the stacking of pi orbitals as depending + + align:start position:0% +the stacking of pi orbitals as depending + + + align:start position:0% +the stacking of pi orbitals as depending +on the geometry that you get say when + + align:start position:0% +on the geometry that you get say when + + + align:start position:0% +on the geometry that you get say when +you have a gc a cg base pair on top of a + + align:start position:0% +you have a gc a cg base pair on top of a + + + align:start position:0% +you have a gc a cg base pair on top of a +u base pair here at the bottom of this + + align:start position:0% +u base pair here at the bottom of this + + + align:start position:0% +u base pair here at the bottom of this +helix and that that stack + + align:start position:0% +helix and that that stack + + + align:start position:0% +helix and that that stack +gives you a minus 2.1 kilocalories per + + align:start position:0% +gives you a minus 2.1 kilocalories per + + + align:start position:0% +gives you a minus 2.1 kilocalories per +mole all the units on this are + + align:start position:0% +mole all the units on this are + + + align:start position:0% +mole all the units on this are +kilocalories per mole + + align:start position:0% +kilocalories per mole + + + align:start position:0% +kilocalories per mole +and by going along and taking each of + + align:start position:0% +and by going along and taking each of + + + align:start position:0% +and by going along and taking each of +these stacks remember a pair of base + + align:start position:0% +these stacks remember a pair of base + + + align:start position:0% +these stacks remember a pair of base +pairs is what you're measuring you can + + align:start position:0% +pairs is what you're measuring you can + + + align:start position:0% +pairs is what you're measuring you can +get you can get all the + + align:start position:0% +get you can get all the + + + align:start position:0% +get you can get all the +negative free energies for the stacking + + align:start position:0% +negative free energies for the stacking + + + align:start position:0% +negative free energies for the stacking +then you have some penalties some things + + align:start position:0% +then you have some penalties some things + + + align:start position:0% +then you have some penalties some things +that are less favorable would not happen + + align:start position:0% +that are less favorable would not happen + + + align:start position:0% +that are less favorable would not happen +spontaneously if they did not + + align:start position:0% +spontaneously if they did not + + + align:start position:0% +spontaneously if they did not +have these mitigating negative free + + align:start position:0% +have these mitigating negative free + + + align:start position:0% +have these mitigating negative free +energies already accumulated which would + + align:start position:0% +energies already accumulated which would + + + align:start position:0% +energies already accumulated which would +be the loop + + align:start position:0% +be the loop + + + align:start position:0% +be the loop +and the bulbs here this is a this + + align:start position:0% +and the bulbs here this is a this + + + align:start position:0% +and the bulbs here this is a this +the the base pairs on either side of + + align:start position:0% +the the base pairs on either side of + + + align:start position:0% +the the base pairs on either side of +that bulbs will stack up on one another + + align:start position:0% +that bulbs will stack up on one another + + + align:start position:0% +that bulbs will stack up on one another +and that bulbs + + align:start position:0% +and that bulbs + + + align:start position:0% +and that bulbs +will will kind of flip out of the double + + align:start position:0% +will will kind of flip out of the double + + + align:start position:0% +will will kind of flip out of the double +otherwise regular double helix + + align:start position:0% +otherwise regular double helix + + + align:start position:0% +otherwise regular double helix +similarly bases at the end have a slight + + align:start position:0% +similarly bases at the end have a slight + + + align:start position:0% +similarly bases at the end have a slight +penalty + + align:start position:0% +penalty + + + align:start position:0% +penalty +or lo or + + align:start position:0% +or lo or + + + align:start position:0% +or lo or +and so then you can add it all up and + + align:start position:0% +and so then you can add it all up and + + + align:start position:0% +and so then you can add it all up and +you can calculate overall delta g for + + align:start position:0% +you can calculate overall delta g for + + + align:start position:0% +you can calculate overall delta g for +the entire structure and if you do + + align:start position:0% +the entire structure and if you do + + + align:start position:0% +the entire structure and if you do +enough of these things you can get a + + align:start position:0% +enough of these things you can get a + + + align:start position:0% +enough of these things you can get a +feeling for which ones are likely to be + + align:start position:0% +feeling for which ones are likely to be + + + align:start position:0% +feeling for which ones are likely to be +um occurring in in your rnas + + align:start position:0% + + + + align:start position:0% + +now this is this this this should + + align:start position:0% +now this is this this this should + + + align:start position:0% +now this is this this this should +trigger in your mind + + align:start position:0% +trigger in your mind + + + align:start position:0% +trigger in your mind +as the + + align:start position:0% +as the + + + align:start position:0% +as the +third example we've had + + align:start position:0% +third example we've had + + + align:start position:0% +third example we've had +where + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +the conceit of the motif analysis that + + align:start position:0% +the conceit of the motif analysis that + + + align:start position:0% +the conceit of the motif analysis that +you can want do a multi-sequence + + align:start position:0% +you can want do a multi-sequence + + + align:start position:0% +you can want do a multi-sequence +alignment uh + + align:start position:0% +alignment uh + + + align:start position:0% +alignment uh +and each each column animal sequence + + align:start position:0% +and each each column animal sequence + + + align:start position:0% +and each each column animal sequence +alignment is independent this is the + + align:start position:0% +alignment is independent this is the + + + align:start position:0% +alignment is independent this is the +third example where that's not true + + align:start position:0% +third example where that's not true + + + align:start position:0% +third example where that's not true +the + + align:start position:0% +the + + + align:start position:0% +the +we have uh we + + align:start position:0% +we have uh we + + + align:start position:0% +we have uh we +we have here the free energies are + + align:start position:0% +we have here the free energies are + + + align:start position:0% +we have here the free energies are +dependent on pairs of base pairs + + align:start position:0% +dependent on pairs of base pairs + + + align:start position:0% +dependent on pairs of base pairs +the + + align:start position:0% +the + + + align:start position:0% +the +previous examples were + + align:start position:0% +previous examples were + + + align:start position:0% +previous examples were +the very distant connections that you + + align:start position:0% +the very distant connections that you + + + align:start position:0% +the very distant connections that you +can get in folding up a transfer rna in + + align:start position:0% +can get in folding up a transfer rna in + + + align:start position:0% +can get in folding up a transfer rna in +the in the earlier example was the cg + + align:start position:0% +the in the earlier example was the cg + + + align:start position:0% +the in the earlier example was the cg +dinucleotides + + align:start position:0% +dinucleotides + + + align:start position:0% +dinucleotides +the assumption of independence of + + align:start position:0% +the assumption of independence of + + + align:start position:0% +the assumption of independence of +columns in a multi-sequence alignment is + + align:start position:0% +columns in a multi-sequence alignment is + + + align:start position:0% +columns in a multi-sequence alignment is +a very powerful one i don't want to + + align:start position:0% +a very powerful one i don't want to + + + align:start position:0% +a very powerful one i don't want to +undermine it too much but it it doesn't + + align:start position:0% +undermine it too much but it it doesn't + + + align:start position:0% +undermine it too much but it it doesn't +hurt you to have three examples this + + align:start position:0% +hurt you to have three examples this + + + align:start position:0% +hurt you to have three examples this +early on + + align:start position:0% +early on + + + align:start position:0% +early on +in the course + + align:start position:0% +in the course + + + align:start position:0% +in the course +question the independence of columns of + + align:start position:0% +question the independence of columns of + + + align:start position:0% +question the independence of columns of +multi-sequence alignments very important + + align:start position:0% +multi-sequence alignments very important + + + align:start position:0% +multi-sequence alignments very important +thing to question we've got mutual + + align:start position:0% +thing to question we've got mutual + + + align:start position:0% +thing to question we've got mutual +information + + align:start position:0% +information + + + align:start position:0% +information +theory that we had a couple slides ago + + align:start position:0% +theory that we had a couple slides ago + + + align:start position:0% +theory that we had a couple slides ago +was one of the most powerful ways of + + align:start position:0% +was one of the most powerful ways of + + + align:start position:0% +was one of the most powerful ways of +questioning that when you see it + + align:start position:0% +questioning that when you see it + + + align:start position:0% +questioning that when you see it +now + + align:start position:0% +now + + + align:start position:0% +now +that's the way that + + align:start position:0% +that's the way that + + + align:start position:0% +that's the way that +this uh + + align:start position:0% + + + + align:start position:0% + +this particular base pairing that we see + + align:start position:0% +this particular base pairing that we see + + + align:start position:0% +this particular base pairing that we see +here is one example now you could take + + align:start position:0% +here is one example now you could take + + + align:start position:0% +here is one example now you could take +each of these + + align:start position:0% +each of these + + + align:start position:0% +each of these +uh + + align:start position:0% +uh + + + align:start position:0% +uh +this + + align:start position:0% +this + + + align:start position:0% +this +and shift the the + + align:start position:0% +and shift the the + + + align:start position:0% +and shift the the +right hand half of the molecule relative + + align:start position:0% +right hand half of the molecule relative + + + align:start position:0% +right hand half of the molecule relative +left hand by one base pair that would + + align:start position:0% +left hand by one base pair that would + + + align:start position:0% +left hand by one base pair that would +give you a much poorer + + align:start position:0% + + + + align:start position:0% + +set of + + align:start position:0% +set of + + + align:start position:0% +set of +energies and much + + align:start position:0% +energies and much + + + align:start position:0% +energies and much +much + + align:start position:0% +much + + + align:start position:0% +much +you know more bulges and more longer + + align:start position:0% +you know more bulges and more longer + + + align:start position:0% +you know more bulges and more longer +loops and so forth and you'd end up with + + align:start position:0% +loops and so forth and you'd end up with + + + align:start position:0% +loops and so forth and you'd end up with +a poor + + align:start position:0% +a poor + + + align:start position:0% +a poor +delta g + + align:start position:0% +delta g + + + align:start position:0% +delta g +and what you can do is you can rank + + align:start position:0% +and what you can do is you can rank + + + align:start position:0% +and what you can do is you can rank +and do one of these + + align:start position:0% + + + + align:start position:0% + +maximum value + + align:start position:0% +maximum value + + + align:start position:0% +maximum value +searches + + align:start position:0% +searches + + + align:start position:0% +searches +by going through that that's this should + + align:start position:0% +by going through that that's this should + + + align:start position:0% +by going through that that's this should +trigger in your mind this is a another + + align:start position:0% +trigger in your mind this is a another + + + align:start position:0% +trigger in your mind this is a another +way of of thinking about that search you + + align:start position:0% +way of of thinking about that search you + + + align:start position:0% +way of of thinking about that search you +you take the entire uh sequence where + + align:start position:0% +you take the entire uh sequence where + + + align:start position:0% +you take the entire uh sequence where +there's transfer rna or in this case a + + align:start position:0% +there's transfer rna or in this case a + + + align:start position:0% +there's transfer rna or in this case a + + align:start position:0% + + + align:start position:0% +nucleic acid sequence and you draw lines + + align:start position:0% +nucleic acid sequence and you draw lines + + + align:start position:0% +nucleic acid sequence and you draw lines +between every base every basis that that + + align:start position:0% +between every base every basis that that + + + align:start position:0% +between every base every basis that that +uh where you have a favorable free + + align:start position:0% +uh where you have a favorable free + + + align:start position:0% +uh where you have a favorable free +energy and you look for a set of lines + + align:start position:0% +energy and you look for a set of lines + + + align:start position:0% +energy and you look for a set of lines +which do not + + align:start position:0% +which do not + + + align:start position:0% +which do not +overlap one another + + align:start position:0% +overlap one another + + + align:start position:0% +overlap one another +because + + align:start position:0% + + + + align:start position:0% + +because th these would represent + + align:start position:0% +because th these would represent + + + align:start position:0% +because th these would represent +short sequences a local you could think + + align:start position:0% +short sequences a local you could think + + + align:start position:0% +short sequences a local you could think +of this as a local sequence alignment + + align:start position:0% +of this as a local sequence alignment + + + align:start position:0% +of this as a local sequence alignment +between one half of the + + align:start position:0% +between one half of the + + + align:start position:0% +between one half of the +of the + + align:start position:0% +of the + + + align:start position:0% +of the +nucleic acid and the other half + + align:start position:0% +nucleic acid and the other half + + + align:start position:0% +nucleic acid and the other half +now this is not a sequence identity + + align:start position:0% +now this is not a sequence identity + + + align:start position:0% +now this is not a sequence identity +remember this is a sequence + + align:start position:0% +remember this is a sequence + + + align:start position:0% +remember this is a sequence +complementarity that is to say a reverse + + align:start position:0% +complementarity that is to say a reverse + + + align:start position:0% +complementarity that is to say a reverse +complement + + align:start position:0% +complement + + + align:start position:0% +complement +uh where you sub complement means you've + + align:start position:0% +uh where you sub complement means you've + + + align:start position:0% +uh where you sub complement means you've +substituted a's for u's and c's for g's + + align:start position:0% +substituted a's for u's and c's for g's + + + align:start position:0% +substituted a's for u's and c's for g's +so you're looking for + + align:start position:0% +so you're looking for + + + align:start position:0% +so you're looking for +but in other in many other ways this is + + align:start position:0% +but in other in many other ways this is + + + align:start position:0% +but in other in many other ways this is +analogous to the dynamic programming + + align:start position:0% +analogous to the dynamic programming + + + align:start position:0% +analogous to the dynamic programming +where we took two independent sequences + + align:start position:0% +where we took two independent sequences + + + align:start position:0% +where we took two independent sequences +and slid them along one another and + + align:start position:0% +and slid them along one another and + + + align:start position:0% +and slid them along one another and +allowed for insertions and deletions + + align:start position:0% +allowed for insertions and deletions + + + align:start position:0% +allowed for insertions and deletions +in that in that dynamic program before + + align:start position:0% +in that in that dynamic program before + + + align:start position:0% +in that in that dynamic program before +we we've did that formally all possible + + align:start position:0% +we we've did that formally all possible + + + align:start position:0% +we we've did that formally all possible +such slippages by setting them + + align:start position:0% +such slippages by setting them + + + align:start position:0% +such slippages by setting them +as the two + + align:start position:0% +as the two + + + align:start position:0% +as the two +uh axes of a table and then filled in + + align:start position:0% +uh axes of a table and then filled in + + + align:start position:0% +uh axes of a table and then filled in +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +the squares for all the matches here we + + align:start position:0% +the squares for all the matches here we + + + align:start position:0% +the squares for all the matches here we +fill in the squares not for the + + align:start position:0% +fill in the squares not for the + + + align:start position:0% +fill in the squares not for the +matches but for the free energy of + + align:start position:0% +matches but for the free energy of + + + align:start position:0% +matches but for the free energy of +of + + align:start position:0% +of + + + align:start position:0% +of +the stacking for these short + + align:start position:0% +the stacking for these short + + + align:start position:0% +the stacking for these short +subsequences + + align:start position:0% +subsequences + + + align:start position:0% +subsequences +now + + align:start position:0% +now + + + align:start position:0% +now +the reason that they don't cross over + + align:start position:0% +the reason that they don't cross over + + + align:start position:0% +the reason that they don't cross over +and the reason for this little note in + + align:start position:0% +and the reason for this little note in + + + align:start position:0% +and the reason for this little note in +the uh lower left hand corner of slide + + align:start position:0% +the uh lower left hand corner of slide + + + align:start position:0% +the uh lower left hand corner of slide +11 that does not handle pseudoknots + + align:start position:0% +11 that does not handle pseudoknots + + + align:start position:0% +11 that does not handle pseudoknots +pseudonymous will explain in the next + + align:start position:0% +pseudonymous will explain in the next + + + align:start position:0% +pseudonymous will explain in the next +we'll show graphic examples in the next + + align:start position:0% +we'll show graphic examples in the next + + + align:start position:0% +we'll show graphic examples in the next +slide but it basically means that if you + + align:start position:0% +slide but it basically means that if you + + + align:start position:0% +slide but it basically means that if you +allow subsequences to occur really + + align:start position:0% +allow subsequences to occur really + + + align:start position:0% +allow subsequences to occur really +nearly throughout the sequence and + + align:start position:0% +nearly throughout the sequence and + + + align:start position:0% +nearly throughout the sequence and +you'll get uh + + align:start position:0% +you'll get uh + + + align:start position:0% +you'll get uh +you'll get these tangles that uh + + align:start position:0% +you'll get these tangles that uh + + + align:start position:0% +you'll get these tangles that uh +that for a while people + + align:start position:0% +that for a while people + + + align:start position:0% +that for a while people +weren't sure whether they occurred or + + align:start position:0% +weren't sure whether they occurred or + + + align:start position:0% +weren't sure whether they occurred or +not the the the one or two non-watson + + align:start position:0% +not the the the one or two non-watson + + + align:start position:0% +not the the the one or two non-watson +quick base pairs that you might find + + align:start position:0% +quick base pairs that you might find + + + align:start position:0% +quick base pairs that you might find +connecting up trna on these tangles were + + align:start position:0% +connecting up trna on these tangles were + + + align:start position:0% +connecting up trna on these tangles were +not considered long stretches that would + + align:start position:0% +not considered long stretches that would + + + align:start position:0% +not considered long stretches that would +connect loops + + align:start position:0% +connect loops + + + align:start position:0% +connect loops +but since then they've been proven to be + + align:start position:0% +but since then they've been proven to be + + + align:start position:0% +but since then they've been proven to be +of great biological significance + + align:start position:0% +of great biological significance + + + align:start position:0% +of great biological significance +in any case to do this without the + + align:start position:0% +in any case to do this without the + + + align:start position:0% +in any case to do this without the +pseudo nuts without allowing any crosses + + align:start position:0% +pseudo nuts without allowing any crosses + + + align:start position:0% +pseudo nuts without allowing any crosses +it's still a challenging problem it's + + align:start position:0% +it's still a challenging problem it's + + + align:start position:0% +it's still a challenging problem it's +it's basically the + + align:start position:0% +it's basically the + + + align:start position:0% +it's basically the +dynamic programming where where n is the + + align:start position:0% +dynamic programming where where n is the + + + align:start position:0% +dynamic programming where where n is the +length of the of the primary sequence + + align:start position:0% +length of the of the primary sequence + + + align:start position:0% +length of the of the primary sequence +then takes on the order of n squared and + + align:start position:0% +then takes on the order of n squared and + + + align:start position:0% +then takes on the order of n squared and +compute time and space + + align:start position:0% +compute time and space + + + align:start position:0% +compute time and space +in order to + + align:start position:0% +in order to + + + align:start position:0% +in order to +figure out + + align:start position:0% + + + + align:start position:0% + +all the + + align:start position:0% +all the + + + align:start position:0% +all the +all the possible + + align:start position:0% +all the possible + + + align:start position:0% +all the possible +pairings that can occur and then you go + + align:start position:0% +pairings that can occur and then you go + + + align:start position:0% +pairings that can occur and then you go +through and you rank them + + align:start position:0% +through and you rank them + + + align:start position:0% +through and you rank them +which one gives the best free energy and + + align:start position:0% +which one gives the best free energy and + + + align:start position:0% +which one gives the best free energy and +then you do the trace back and you get + + align:start position:0% +then you do the trace back and you get + + + align:start position:0% +then you do the trace back and you get +the top scores + + align:start position:0% +the top scores + + + align:start position:0% +the top scores +for that molecule + + align:start position:0% +for that molecule + + + align:start position:0% +for that molecule +now let's talk about pseudo-knots that + + align:start position:0% +now let's talk about pseudo-knots that + + + align:start position:0% +now let's talk about pseudo-knots that +we excluded that but now we'll re-invite + + align:start position:0% +we excluded that but now we'll re-invite + + + align:start position:0% +we excluded that but now we'll re-invite +it + + align:start position:0% +it + + + align:start position:0% +it +we have uh + + align:start position:0% +we have uh + + + align:start position:0% +we have uh +we had those those little ones you know + + align:start position:0% +we had those those little ones you know + + + align:start position:0% +we had those those little ones you know +a couple of base pairs in transfer rna + + align:start position:0% +a couple of base pairs in transfer rna + + + align:start position:0% +a couple of base pairs in transfer rna +but a much more dramatic one we alluded + + align:start position:0% +but a much more dramatic one we alluded + + + align:start position:0% +but a much more dramatic one we alluded +to + + align:start position:0% +to + + + align:start position:0% +to +in this in the second lecture we talked + + align:start position:0% +in this in the second lecture we talked + + + align:start position:0% +in this in the second lecture we talked +about the genetic code and + + align:start position:0% +about the genetic code and + + + align:start position:0% +about the genetic code and +and in order to introduce you to + + align:start position:0% +and in order to introduce you to + + + align:start position:0% +and in order to introduce you to +exceptions of genetic code i gave an + + align:start position:0% +exceptions of genetic code i gave an + + + align:start position:0% +exceptions of genetic code i gave an +example where the ribosome jumped over + + align:start position:0% +example where the ribosome jumped over + + + align:start position:0% +example where the ribosome jumped over +50 base pairs if presented with the + + align:start position:0% +50 base pairs if presented with the + + + align:start position:0% +50 base pairs if presented with the +right context it didn't follow the the + + align:start position:0% +right context it didn't follow the the + + + align:start position:0% +right context it didn't follow the the +normal code of having a triplet and + + align:start position:0% +normal code of having a triplet and + + + align:start position:0% +normal code of having a triplet and +another triplet right in a row with no + + align:start position:0% +another triplet right in a row with no + + + align:start position:0% +another triplet right in a row with no +punctuation here we had the punctuation + + align:start position:0% +punctuation here we had the punctuation + + + align:start position:0% +punctuation here we had the punctuation +that required + + align:start position:0% +that required + + + align:start position:0% +that required +what may have flipped by at the time a + + align:start position:0% +what may have flipped by at the time a + + + align:start position:0% +what may have flipped by at the time a +pseudo knot this is an example of one + + align:start position:0% +pseudo knot this is an example of one + + + align:start position:0% +pseudo knot this is an example of one +such pseudo knot in a the best that we + + align:start position:0% +such pseudo knot in a the best that we + + + align:start position:0% +such pseudo knot in a the best that we +can do of a two dimensional + + align:start position:0% +can do of a two dimensional + + + align:start position:0% +can do of a two dimensional +schematic and then something slightly + + align:start position:0% +schematic and then something slightly + + + align:start position:0% +schematic and then something slightly +better where if we have a more + + align:start position:0% +better where if we have a more + + + align:start position:0% +better where if we have a more +three-dimensional and another + + align:start position:0% +three-dimensional and another + + + align:start position:0% +three-dimensional and another +three-dimensional view of this and this + + align:start position:0% +three-dimensional view of this and this + + + align:start position:0% +three-dimensional view of this and this +is + + align:start position:0% +is + + + align:start position:0% +is +the rna pseudo knot which is one of them + + align:start position:0% +the rna pseudo knot which is one of them + + + align:start position:0% +the rna pseudo knot which is one of them +which is responsible for frame shifting + + align:start position:0% +which is responsible for frame shifting + + + align:start position:0% +which is responsible for frame shifting +in the + + align:start position:0% +in the + + + align:start position:0% +in the +that breaks this genetic code + + align:start position:0% +that breaks this genetic code + + + align:start position:0% +that breaks this genetic code +and so just follow how this how this + + align:start position:0% +and so just follow how this how this + + + align:start position:0% +and so just follow how this how this +goes you've got basically a normal helix + + align:start position:0% +goes you've got basically a normal helix + + + align:start position:0% +goes you've got basically a normal helix +here at the bottom starting at the five + + align:start position:0% +here at the bottom starting at the five + + + align:start position:0% +here at the bottom starting at the five +prime end with position one to seven + + align:start position:0% +prime end with position one to seven + + + align:start position:0% +prime end with position one to seven +then it would go through a normal + + align:start position:0% +then it would go through a normal + + + align:start position:0% +then it would go through a normal +five base + + align:start position:0% +five base + + + align:start position:0% +five base +sorry six space loop from eight to + + align:start position:0% +sorry six space loop from eight to + + + align:start position:0% +sorry six space loop from eight to +thirteen + + align:start position:0% +thirteen + + + align:start position:0% +thirteen +and then finish the the stem fourteen + + align:start position:0% +and then finish the the stem fourteen + + + align:start position:0% +and then finish the the stem fourteen +through eighteen that would be a normal + + align:start position:0% +through eighteen that would be a normal + + + align:start position:0% +through eighteen that would be a normal +stem loop um where the loop is uh six + + align:start position:0% +stem loop um where the loop is uh six + + + align:start position:0% +stem loop um where the loop is uh six +long eight to thirteen + + align:start position:0% +long eight to thirteen + + + align:start position:0% +long eight to thirteen +but at the end of eighteen you have this + + align:start position:0% +but at the end of eighteen you have this + + + align:start position:0% +but at the end of eighteen you have this +little green loop that that goes back + + align:start position:0% +little green loop that that goes back + + + align:start position:0% +little green loop that that goes back +and now makes a nice + + align:start position:0% +and now makes a nice + + + align:start position:0% +and now makes a nice +perfect four base + + align:start position:0% +perfect four base + + + align:start position:0% +perfect four base +watson creek uh + + align:start position:0% + + + + align:start position:0% + +stem + + align:start position:0% +stem + + + align:start position:0% +stem +now in the middle of what would have + + align:start position:0% +now in the middle of what would have + + + align:start position:0% +now in the middle of what would have +been a loop so this fold back is what we + + align:start position:0% +been a loop so this fold back is what we + + + align:start position:0% +been a loop so this fold back is what we +meant by + + align:start position:0% +meant by + + + align:start position:0% +meant by +a pseudo knot and what would have been + + align:start position:0% +a pseudo knot and what would have been + + + align:start position:0% +a pseudo knot and what would have been +represented by a crossover of those red + + align:start position:0% +represented by a crossover of those red + + + align:start position:0% +represented by a crossover of those red +lines in the previous slide something + + align:start position:0% +lines in the previous slide something + + + align:start position:0% +lines in the previous slide something +that makes it much harder to compute + + align:start position:0% +that makes it much harder to compute + + + align:start position:0% +that makes it much harder to compute +in fact it makes it so much harder + + align:start position:0% +in fact it makes it so much harder + + + align:start position:0% +in fact it makes it so much harder +in the next slide that it goes up from + + align:start position:0% +in the next slide that it goes up from + + + align:start position:0% +in the next slide that it goes up from +an order of n squared which is your + + align:start position:0% +an order of n squared which is your + + + align:start position:0% +an order of n squared which is your +typical + + align:start position:0% +typical + + + align:start position:0% +typical +dynamic programming of in a pairwise + + align:start position:0% +dynamic programming of in a pairwise + + + align:start position:0% +dynamic programming of in a pairwise +alignment + + align:start position:0% +alignment + + + align:start position:0% +alignment +to order in sixth in cpu time and order + + align:start position:0% +to order in sixth in cpu time and order + + + align:start position:0% +to order in sixth in cpu time and order +n to the fourth power in memory space uh + + align:start position:0% +n to the fourth power in memory space uh + + + align:start position:0% +n to the fourth power in memory space uh +that you need to set aside for storing + + align:start position:0% +that you need to set aside for storing + + + align:start position:0% +that you need to set aside for storing +up the table of + + align:start position:0% +up the table of + + + align:start position:0% +up the table of +possible pseudo knots that can occur in + + align:start position:0% +possible pseudo knots that can occur in + + + align:start position:0% +possible pseudo knots that can occur in +the context of the otherwise normal + + align:start position:0% +the context of the otherwise normal + + + align:start position:0% +the context of the otherwise normal +circle with the non-overlapping + + align:start position:0% +circle with the non-overlapping + + + align:start position:0% +circle with the non-overlapping +connections + + align:start position:0% +connections + + + align:start position:0% +connections +this is a relatively recent uh + + align:start position:0% + + + + align:start position:0% + +innovation + + align:start position:0% + + + + align:start position:0% + +where a dynamic it's still a dynamic + + align:start position:0% +where a dynamic it's still a dynamic + + + align:start position:0% +where a dynamic it's still a dynamic +programming algorithm it just has more + + align:start position:0% +programming algorithm it just has more + + + align:start position:0% +programming algorithm it just has more +uh + + align:start position:0% +uh + + + align:start position:0% +uh +more possibilities more comp more higher + + align:start position:0% +more possibilities more comp more higher + + + align:start position:0% +more possibilities more comp more higher +algorithmic complexity + + align:start position:0% +algorithmic complexity + + + align:start position:0% +algorithmic complexity +and a combination of the biological + + align:start position:0% +and a combination of the biological + + + align:start position:0% +and a combination of the biological +discovery that pseudo knots are + + align:start position:0% +discovery that pseudo knots are + + + align:start position:0% +discovery that pseudo knots are +important for frame shifting a variety + + align:start position:0% +important for frame shifting a variety + + + align:start position:0% +important for frame shifting a variety +of other biological phenomena + + align:start position:0% +of other biological phenomena + + + align:start position:0% +of other biological phenomena +and the now three dimensional structure + + align:start position:0% +and the now three dimensional structure + + + align:start position:0% +and the now three dimensional structure +and now an algorithm puts pseudonauts + + align:start position:0% +and now an algorithm puts pseudonauts + + + align:start position:0% +and now an algorithm puts pseudonauts +well within the sort of things that you + + align:start position:0% +well within the sort of things that you + + + align:start position:0% +well within the sort of things that you +should feel comfortable + + align:start position:0% +should feel comfortable + + + align:start position:0% +should feel comfortable +now we're going to go back to hidden + + align:start position:0% +now we're going to go back to hidden + + + align:start position:0% +now we're going to go back to hidden +markov models in a slightly + + align:start position:0% +markov models in a slightly + + + align:start position:0% +markov models in a slightly +more complicated context here then we + + align:start position:0% +more complicated context here then we + + + align:start position:0% +more complicated context here then we +picked the simplest one we could which + + align:start position:0% +picked the simplest one we could which + + + align:start position:0% +picked the simplest one we could which +was a dinucleotide + + align:start position:0% +was a dinucleotide + + + align:start position:0% +was a dinucleotide +um + + align:start position:0% +um + + + align:start position:0% +um +you know simple unfolded straight dna + + align:start position:0% +you know simple unfolded straight dna + + + align:start position:0% +you know simple unfolded straight dna +and the part that was hidden as you + + align:start position:0% +and the part that was hidden as you + + + align:start position:0% +and the part that was hidden as you +recall was whether the + + align:start position:0% +recall was whether the + + + align:start position:0% +recall was whether the +cg dinucleotides or sorry the + + align:start position:0% +cg dinucleotides or sorry the + + + align:start position:0% +cg dinucleotides or sorry the +dinucleotides which could be any of + + align:start position:0% +dinucleotides which could be any of + + + align:start position:0% +dinucleotides which could be any of +those + + align:start position:0% +those + + + align:start position:0% +those +possible by nucleotides including aaa cg + + align:start position:0% +possible by nucleotides including aaa cg + + + align:start position:0% +possible by nucleotides including aaa cg +and so on whether it was present in a cg + + align:start position:0% +and so on whether it was present in a cg + + + align:start position:0% +and so on whether it was present in a cg +island whether it was in a region of of + + align:start position:0% +island whether it was in a region of of + + + align:start position:0% +island whether it was in a region of of +the chromosome which was likely to have + + align:start position:0% +the chromosome which was likely to have + + + align:start position:0% +the chromosome which was likely to have +cgs or whether it was in a cg + + align:start position:0% +cgs or whether it was in a cg + + + align:start position:0% +cgs or whether it was in a cg +ocean which was + + align:start position:0% +ocean which was + + + align:start position:0% +ocean which was +low in ccg by nucleotide content so the + + align:start position:0% +low in ccg by nucleotide content so the + + + align:start position:0% +low in ccg by nucleotide content so the +hidden part was a plus minus whether it + + align:start position:0% +hidden part was a plus minus whether it + + + align:start position:0% +hidden part was a plus minus whether it +was in an island or not + + align:start position:0% +was in an island or not + + + align:start position:0% +was in an island or not +now what we're going to do now is take + + align:start position:0% +now what we're going to do now is take + + + align:start position:0% +now what we're going to do now is take +this and transfer this over to the kinds + + align:start position:0% +this and transfer this over to the kinds + + + align:start position:0% +this and transfer this over to the kinds +of + + align:start position:0% +of + + + align:start position:0% +of +motifs we're finding in rnas like + + align:start position:0% +motifs we're finding in rnas like + + + align:start position:0% +motifs we're finding in rnas like +transfer rna and another class of rna + + align:start position:0% +transfer rna and another class of rna + + + align:start position:0% +transfer rna and another class of rna +and say okay now whether it's the hidden + + align:start position:0% +and say okay now whether it's the hidden + + + align:start position:0% +and say okay now whether it's the hidden +part of the markup the markov model is + + align:start position:0% +part of the markup the markov model is + + + align:start position:0% +part of the markup the markov model is +these transition probabilities the + + align:start position:0% +these transition probabilities the + + + align:start position:0% +these transition probabilities the +hidden part is whether it's in a + + align:start position:0% +hidden part is whether it's in a + + + align:start position:0% +hidden part is whether it's in a +particular secondary structure or not + + align:start position:0% +particular secondary structure or not + + + align:start position:0% +particular secondary structure or not +not whether it's in an island or not but + + align:start position:0% +not whether it's in an island or not but + + + align:start position:0% +not whether it's in an island or not but +a secondary structure okay + + align:start position:0% +a secondary structure okay + + + align:start position:0% +a secondary structure okay +in this particular case we're going to + + align:start position:0% +in this particular case we're going to + + + align:start position:0% +in this particular case we're going to +talk about very interesting biological + + align:start position:0% +talk about very interesting biological + + + align:start position:0% +talk about very interesting biological +illustration + + align:start position:0% + + + + align:start position:0% + +where + + align:start position:0% +where + + + align:start position:0% +where +the + + align:start position:0% + + + + align:start position:0% + +hidden markov models will be + + align:start position:0% +hidden markov models will be + + + align:start position:0% +hidden markov models will be +modeling these boxes these motifs that + + align:start position:0% +modeling these boxes these motifs that + + + align:start position:0% +modeling these boxes these motifs that +are involved in base pairing + + align:start position:0% +are involved in base pairing + + + align:start position:0% +are involved in base pairing +or recognition + + align:start position:0% +or recognition + + + align:start position:0% +or recognition +that forms the secondary structure of + + align:start position:0% +that forms the secondary structure of + + + align:start position:0% +that forms the secondary structure of +that's necessary for guiding a + + align:start position:0% +that's necessary for guiding a + + + align:start position:0% +that's necessary for guiding a +particular enzyme now remember we had + + align:start position:0% +particular enzyme now remember we had + + + align:start position:0% +particular enzyme now remember we had +all these + + align:start position:0% +all these + + + align:start position:0% +all these +modified bases that we used that we saw + + align:start position:0% +modified bases that we used that we saw + + + align:start position:0% +modified bases that we used that we saw +on transfer rna some of those are simple + + align:start position:0% +on transfer rna some of those are simple + + + align:start position:0% +on transfer rna some of those are simple +protein interactions with the transfer + + align:start position:0% +protein interactions with the transfer + + + align:start position:0% +protein interactions with the transfer +rna that adds a methyl group here there + + align:start position:0% +rna that adds a methyl group here there + + + align:start position:0% +rna that adds a methyl group here there +it turns out that all the methyl groups + + align:start position:0% +it turns out that all the methyl groups + + + align:start position:0% +it turns out that all the methyl groups +the o2 prime methyl groups these are on + + align:start position:0% +the o2 prime methyl groups these are on + + + align:start position:0% +the o2 prime methyl groups these are on +the on the sugar + + align:start position:0% +the on the sugar + + + align:start position:0% +the on the sugar +of the uh + + align:start position:0% +of the uh + + + align:start position:0% +of the uh +the ribose + + align:start position:0% +the ribose + + + align:start position:0% +the ribose +in ribosomal rna a few just a small + + align:start position:0% +in ribosomal rna a few just a small + + + align:start position:0% +in ribosomal rna a few just a small +number of a few dozen of the riboses in + + align:start position:0% +number of a few dozen of the riboses in + + + align:start position:0% +number of a few dozen of the riboses in +this + + align:start position:0% +this + + + align:start position:0% +this +multi-kilobase + + align:start position:0% +multi-kilobase + + + align:start position:0% +multi-kilobase +ribosomal rna are methylated o2 position + + align:start position:0% +ribosomal rna are methylated o2 position + + + align:start position:0% +ribosomal rna are methylated o2 position +how does the enzyme know or the enzymes + + align:start position:0% +how does the enzyme know or the enzymes + + + align:start position:0% +how does the enzyme know or the enzymes +know to get exactly those bases the way + + align:start position:0% +know to get exactly those bases the way + + + align:start position:0% +know to get exactly those bases the way +it knows + + align:start position:0% +it knows + + + align:start position:0% +it knows +is it + + align:start position:0% +is it + + + align:start position:0% +is it +it doesn't use pure protein + + align:start position:0% +it doesn't use pure protein + + + align:start position:0% +it doesn't use pure protein +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +brute force + + align:start position:0% +brute force + + + align:start position:0% +brute force +to make a complimentary surface of + + align:start position:0% +to make a complimentary surface of + + + align:start position:0% +to make a complimentary surface of +protein nucleic acid it actually uses + + align:start position:0% +protein nucleic acid it actually uses + + + align:start position:0% +protein nucleic acid it actually uses +this elegance of of + + align:start position:0% +this elegance of of + + + align:start position:0% +this elegance of of +base pairing to make a guide sequence + + align:start position:0% +base pairing to make a guide sequence + + + align:start position:0% +base pairing to make a guide sequence +and so what it's looking for is + + align:start position:0% +and so what it's looking for is + + + align:start position:0% +and so what it's looking for is +the protein + + align:start position:0% +the protein + + + align:start position:0% +the protein +cooperates with a small rna so-called + + align:start position:0% +cooperates with a small rna so-called + + + align:start position:0% +cooperates with a small rna so-called +snow rna or small nucleolar rna to + + align:start position:0% +snow rna or small nucleolar rna to + + + align:start position:0% +snow rna or small nucleolar rna to +to find a place where the snow will + + align:start position:0% +to find a place where the snow will + + + align:start position:0% +to find a place where the snow will +recognize the place that you want to + + align:start position:0% +recognize the place that you want to + + + align:start position:0% +recognize the place that you want to +methylate and the protein methylates + + align:start position:0% +methylate and the protein methylates + + + align:start position:0% +methylate and the protein methylates +that the + + align:start position:0% +that the + + + align:start position:0% +that the +the base in the middle of that guide + + align:start position:0% +the base in the middle of that guide + + + align:start position:0% +the base in the middle of that guide +sequence + + align:start position:0% +sequence + + + align:start position:0% +sequence +so + + align:start position:0% + + + + align:start position:0% + +so then the the + + align:start position:0% +so then the the + + + align:start position:0% +so then the the +the game the by the computational + + align:start position:0% +the game the by the computational + + + align:start position:0% +the game the by the computational +biology game that these authors played + + align:start position:0% +biology game that these authors played + + + align:start position:0% +biology game that these authors played +was how can we find all the small + + align:start position:0% +was how can we find all the small + + + align:start position:0% +was how can we find all the small +rnas the snow rnas present in a genome + + align:start position:0% +rnas the snow rnas present in a genome + + + align:start position:0% +rnas the snow rnas present in a genome +when we know very little + + align:start position:0% +when we know very little + + + align:start position:0% +when we know very little +about that that the + + align:start position:0% +about that that the + + + align:start position:0% +about that that the +genome + + align:start position:0% +genome + + + align:start position:0% +genome +what they knew was they knew the genome + + align:start position:0% +what they knew was they knew the genome + + + align:start position:0% +what they knew was they knew the genome +sequence this is for yeast they had a + + align:start position:0% +sequence this is for yeast they had a + + + align:start position:0% +sequence this is for yeast they had a +few examples of snow rnas in humans + + align:start position:0% +few examples of snow rnas in humans + + + align:start position:0% +few examples of snow rnas in humans +almost none in yeast they had the + + align:start position:0% +almost none in yeast they had the + + + align:start position:0% +almost none in yeast they had the +sequence of the ribosomal rna of course + + align:start position:0% +sequence of the ribosomal rna of course + + + align:start position:0% +sequence of the ribosomal rna of course +and they could they could + + align:start position:0% + + + + align:start position:0% + +they what we they wanted to do then is + + align:start position:0% +they what we they wanted to do then is + + + align:start position:0% +they what we they wanted to do then is +ask + + align:start position:0% +ask + + + align:start position:0% +ask +where where in the genome do we have + + align:start position:0% +where where in the genome do we have + + + align:start position:0% +where where in the genome do we have +little guide sequences flanked by some + + align:start position:0% +little guide sequences flanked by some + + + align:start position:0% +little guide sequences flanked by some +of these other uh motifs and + + align:start position:0% +of these other uh motifs and + + + align:start position:0% +of these other uh motifs and +characteristics like us a base pair uh + + align:start position:0% +characteristics like us a base pair uh + + + align:start position:0% +characteristics like us a base pair uh +48 base pair stem + + align:start position:0% +48 base pair stem + + + align:start position:0% +48 base pair stem +that will match the ribosomal rna so you + + align:start position:0% +that will match the ribosomal rna so you + + + align:start position:0% +that will match the ribosomal rna so you +basically march along the algorithms you + + align:start position:0% +basically march along the algorithms you + + + align:start position:0% +basically march along the algorithms you +march along the ribosomal rna looking + + align:start position:0% +march along the ribosomal rna looking + + + align:start position:0% +march along the ribosomal rna looking +for matches elsewhere in the genome and + + align:start position:0% +for matches elsewhere in the genome and + + + align:start position:0% +for matches elsewhere in the genome and +then ask whether those matches elsewhere + + align:start position:0% +then ask whether those matches elsewhere + + + align:start position:0% +then ask whether those matches elsewhere +in the genome have some of these other + + align:start position:0% +in the genome have some of these other + + + align:start position:0% +in the genome have some of these other +context + + align:start position:0% +context + + + align:start position:0% +context +features + + align:start position:0% +features + + + align:start position:0% +features +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you can see this is going to be a more + + align:start position:0% +you can see this is going to be a more + + + align:start position:0% +you can see this is going to be a more +complicated algorithm than just looking + + align:start position:0% +complicated algorithm than just looking + + + align:start position:0% +complicated algorithm than just looking +for cgs okay + + align:start position:0% +for cgs okay + + + align:start position:0% +for cgs okay +so this is this is how it works + + align:start position:0% +so this is this is how it works + + + align:start position:0% +so this is this is how it works +that stem that we had + + align:start position:0% + + + + align:start position:0% + +is is now item number one the various + + align:start position:0% +is is now item number one the various + + + align:start position:0% +is is now item number one the various +boxes which were basically sequences are + + align:start position:0% +boxes which were basically sequences are + + + align:start position:0% +boxes which were basically sequences are +now turned into ungapped hidden markov + + align:start position:0% +now turned into ungapped hidden markov + + + align:start position:0% +now turned into ungapped hidden markov +models the hidden + + align:start position:0% +models the hidden + + + align:start position:0% +models the hidden +part of his whether it is present or not + + align:start position:0% +part of his whether it is present or not + + + align:start position:0% +part of his whether it is present or not +in this + + align:start position:0% +in this + + + align:start position:0% +in this +in the context that adds up to this + + align:start position:0% +in the context that adds up to this + + + align:start position:0% +in the context that adds up to this +guide sequence + + align:start position:0% +guide sequence + + + align:start position:0% +guide sequence +the guide sequence itself is a hidden + + align:start position:0% +the guide sequence itself is a hidden + + + align:start position:0% +the guide sequence itself is a hidden +markov model which has to be + + align:start position:0% +markov model which has to be + + + align:start position:0% +markov model which has to be +a + + align:start position:0% +a + + + align:start position:0% +a +imperfect probably imperfect duplex with + + align:start position:0% +imperfect probably imperfect duplex with + + + align:start position:0% +imperfect probably imperfect duplex with +the ribosomal rna so that's how that's + + align:start position:0% +the ribosomal rna so that's how that's + + + align:start position:0% +the ribosomal rna so that's how that's +modeled + + align:start position:0% + + + + align:start position:0% + +the most complicated is that terminal + + align:start position:0% +the most complicated is that terminal + + + align:start position:0% +the most complicated is that terminal +stem number one which is a so-called + + align:start position:0% +stem number one which is a so-called + + + align:start position:0% +stem number one which is a so-called +stochastic context-free grammar that's + + align:start position:0% +stochastic context-free grammar that's + + + align:start position:0% +stochastic context-free grammar that's +what the scfg stands for and that just + + align:start position:0% +what the scfg stands for and that just + + + align:start position:0% +what the scfg stands for and that just +means that it is even less constrained + + align:start position:0% +means that it is even less constrained + + + align:start position:0% +means that it is even less constrained +than the hmm the hmm is less constrained + + align:start position:0% +than the hmm the hmm is less constrained + + + align:start position:0% +than the hmm the hmm is less constrained +than a simple motif which is less + + align:start position:0% +than a simple motif which is less + + + align:start position:0% +than a simple motif which is less +constrained than say a consensus + + align:start position:0% +constrained than say a consensus + + + align:start position:0% +constrained than say a consensus +sequence it's it is constrained it has + + align:start position:0% +sequence it's it is constrained it has + + + align:start position:0% +sequence it's it is constrained it has +the grammar if you will are the + + align:start position:0% +the grammar if you will are the + + + align:start position:0% +the grammar if you will are the +particular rules for the base pairing + + align:start position:0% +particular rules for the base pairing + + + align:start position:0% +particular rules for the base pairing +that have to occur over a certain region + + align:start position:0% +that have to occur over a certain region + + + align:start position:0% +that have to occur over a certain region +in a certain part of the putatives no + + align:start position:0% +in a certain part of the putatives no + + + align:start position:0% +in a certain part of the putatives no +rna so anyway you apply each of these + + align:start position:0% +rna so anyway you apply each of these + + + align:start position:0% +rna so anyway you apply each of these +criteria and you have transition + + align:start position:0% +criteria and you have transition + + + align:start position:0% +criteria and you have transition +probabilities which come in from a + + align:start position:0% +probabilities which come in from a + + + align:start position:0% +probabilities which come in from a +learning set such as the human snow rnas + + align:start position:0% +learning set such as the human snow rnas + + + align:start position:0% +learning set such as the human snow rnas +you have a learning set that tells you + + align:start position:0% +you have a learning set that tells you + + + align:start position:0% +you have a learning set that tells you +what these transition probabilities will + + align:start position:0% +what these transition probabilities will + + + align:start position:0% +what these transition probabilities will +be + + align:start position:0% +be + + + align:start position:0% +be +and you and you now apply this to the + + align:start position:0% +and you and you now apply this to the + + + align:start position:0% +and you and you now apply this to the +entire yeast genome and you get a bunch + + align:start position:0% +entire yeast genome and you get a bunch + + + align:start position:0% +entire yeast genome and you get a bunch +of candidates no rna encoding genes now + + align:start position:0% +of candidates no rna encoding genes now + + + align:start position:0% +of candidates no rna encoding genes now +you can't use things like the long open + + align:start position:0% +you can't use things like the long open + + + align:start position:0% +you can't use things like the long open +reading frames that you normally use for + + align:start position:0% +reading frames that you normally use for + + + align:start position:0% +reading frames that you normally use for +finding genes so this is a very valuable + + align:start position:0% +finding genes so this is a very valuable + + + align:start position:0% +finding genes so this is a very valuable +tool + + align:start position:0% +tool + + + align:start position:0% +tool +but now how do you convince yourself + + align:start position:0% +but now how do you convince yourself + + + align:start position:0% +but now how do you convince yourself +that + + align:start position:0% +that + + + align:start position:0% +that +you that you know + + align:start position:0% +you that you know + + + align:start position:0% +you that you know +that this is a gene this actually + + align:start position:0% +that this is a gene this actually + + + align:start position:0% +that this is a gene this actually +encodes a small + + align:start position:0% +encodes a small + + + align:start position:0% +encodes a small +snow rna and that those are responsible + + align:start position:0% +snow rna and that those are responsible + + + align:start position:0% +snow rna and that those are responsible +for guiding the methylation of + + align:start position:0% +for guiding the methylation of + + + align:start position:0% +for guiding the methylation of +particular positions in the ribosomal + + align:start position:0% +particular positions in the ribosomal + + + align:start position:0% +particular positions in the ribosomal +rna + + align:start position:0% +rna + + + align:start position:0% +rna +the way you do that + + align:start position:0% +the way you do that + + + align:start position:0% +the way you do that +is + + align:start position:0% +is + + + align:start position:0% +is +well before we get to how you do that we + + align:start position:0% +well before we get to how you do that we + + + align:start position:0% +well before we get to how you do that we +want to we want to ask how does this + + align:start position:0% +want to we want to ask how does this + + + align:start position:0% +want to we want to ask how does this +algorithm perform relative to other the + + align:start position:0% +algorithm perform relative to other the + + + align:start position:0% +algorithm perform relative to other the +few other algorithms are for finding + + align:start position:0% +few other algorithms are for finding + + + align:start position:0% +few other algorithms are for finding +genes which do not encode proteins + + align:start position:0% +genes which do not encode proteins + + + align:start position:0% +genes which do not encode proteins +and the first + + align:start position:0% +and the first + + + align:start position:0% +and the first +of these actually dates well before 1991 + + align:start position:0% +of these actually dates well before 1991 + + + align:start position:0% +of these actually dates well before 1991 +but there were ways of looking for + + align:start position:0% +but there were ways of looking for + + + align:start position:0% +but there were ways of looking for +transfer rnas in sequence they would use + + align:start position:0% +transfer rnas in sequence they would use + + + align:start position:0% +transfer rnas in sequence they would use +everything we know about transfer rnas + + align:start position:0% +everything we know about transfer rnas + + + align:start position:0% +everything we know about transfer rnas +the little boxes that are conserved as + + align:start position:0% +the little boxes that are conserved as + + + align:start position:0% +the little boxes that are conserved as +sequences the regions that are conserved + + align:start position:0% +sequences the regions that are conserved + + + align:start position:0% +sequences the regions that are conserved +only at not as sequences but as base + + align:start position:0% +only at not as sequences but as base + + + align:start position:0% +only at not as sequences but as base +pairing potential + + align:start position:0% +pairing potential + + + align:start position:0% +pairing potential +uh etc the the loop lengths + + align:start position:0% +uh etc the the loop lengths + + + align:start position:0% +uh etc the the loop lengths +were are constrained all the constraints + + align:start position:0% +were are constrained all the constraints + + + align:start position:0% +were are constrained all the constraints +you can muster + + align:start position:0% +you can muster + + + align:start position:0% +you can muster +back in 91 were applied and it was + + align:start position:0% +back in 91 were applied and it was + + + align:start position:0% +back in 91 were applied and it was +fairly slow it would only do 400 base + + align:start position:0% +fairly slow it would only do 400 base + + + align:start position:0% +fairly slow it would only do 400 base +pairs of + + align:start position:0% +pairs of + + + align:start position:0% +pairs of +genome chunk + + align:start position:0% +genome chunk + + + align:start position:0% +genome chunk +per second + + align:start position:0% +per second + + + align:start position:0% +per second +and when you have genomes on the order + + align:start position:0% +and when you have genomes on the order + + + align:start position:0% +and when you have genomes on the order +of many megabases this is this is slow + + align:start position:0% +of many megabases this is this is slow + + + align:start position:0% +of many megabases this is this is slow +and it it had uh + + align:start position:0% +and it it had uh + + + align:start position:0% +and it it had uh +it missed about five percent of the true + + align:start position:0% +it missed about five percent of the true + + + align:start position:0% +it missed about five percent of the true +positives it had 95 percent and false + + align:start position:0% +positives it had 95 percent and false + + + align:start position:0% +positives it had 95 percent and false +positive sounds impressive only + + align:start position:0% +positive sounds impressive only + + + align:start position:0% +positive sounds impressive only +10 to the minus six but when you think + + align:start position:0% +10 to the minus six but when you think + + + align:start position:0% +10 to the minus six but when you think +of a + + align:start position:0% +of a + + + align:start position:0% +of a +double strand both strands of e coli + + align:start position:0% +double strand both strands of e coli + + + align:start position:0% +double strand both strands of e coli +being about 10 million + + align:start position:0% +being about 10 million + + + align:start position:0% +being about 10 million +bases + + align:start position:0% +bases + + + align:start position:0% +bases +then this is about four false positives + + align:start position:0% +then this is about four false positives + + + align:start position:0% +then this is about four false positives +and bigger genomes of course would be + + align:start position:0% +and bigger genomes of course would be + + + align:start position:0% +and bigger genomes of course would be +even a larger number an absolute scale + + align:start position:0% +even a larger number an absolute scale + + + align:start position:0% +even a larger number an absolute scale +so then uh six years later the the + + align:start position:0% +so then uh six years later the the + + + align:start position:0% +so then uh six years later the the +speed is now 100 times faster you're now + + align:start position:0% +speed is now 100 times faster you're now + + + align:start position:0% +speed is now 100 times faster you're now +only missing point five percent of the + + align:start position:0% +only missing point five percent of the + + + align:start position:0% +only missing point five percent of the +true positives instead of five percent + + align:start position:0% +true positives instead of five percent + + + align:start position:0% +true positives instead of five percent +and the false positives is now + + align:start position:0% +and the false positives is now + + + align:start position:0% +and the false positives is now +vanishingly small so very often you can + + align:start position:0% +vanishingly small so very often you can + + + align:start position:0% +vanishingly small so very often you can +you can just arbitrarily trade off + + align:start position:0% +you can just arbitrarily trade off + + + align:start position:0% +you can just arbitrarily trade off +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the number of true positives you miss + + align:start position:0% +the number of true positives you miss + + + align:start position:0% +the number of true positives you miss +with the number of false positives you + + align:start position:0% +with the number of false positives you + + + align:start position:0% +with the number of false positives you +get and make one you know take one + + align:start position:0% +get and make one you know take one + + + align:start position:0% +get and make one you know take one +advantage of the other but here was the + + align:start position:0% +advantage of the other but here was the + + + align:start position:0% +advantage of the other but here was the +win-win situation they both + + align:start position:0% +win-win situation they both + + + align:start position:0% +win-win situation they both +went in a favorable direction so how do + + align:start position:0% +went in a favorable direction so how do + + + align:start position:0% +went in a favorable direction so how do +the snow rnas compare with that + + align:start position:0% +the snow rnas compare with that + + + align:start position:0% +the snow rnas compare with that +here uh another two years past we have + + align:start position:0% +here uh another two years past we have + + + align:start position:0% +here uh another two years past we have +the snow rnas are just starting out they + + align:start position:0% +the snow rnas are just starting out they + + + align:start position:0% +the snow rnas are just starting out they +have probably a little better than 93 + + align:start position:0% +have probably a little better than 93 + + + align:start position:0% +have probably a little better than 93 +percent true positives this is not as + + align:start position:0% +percent true positives this is not as + + + align:start position:0% +percent true positives this is not as +good as transfer rna it's just maybe + + align:start position:0% + + + + align:start position:0% + +this may improve or it may not uh the + + align:start position:0% +this may improve or it may not uh the + + + align:start position:0% +this may improve or it may not uh the +false positive rate is acceptable + + align:start position:0% +false positive rate is acceptable + + + align:start position:0% +false positive rate is acceptable +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +so then the question becomes how do you + + align:start position:0% +so then the question becomes how do you + + + align:start position:0% +so then the question becomes how do you +track down the after you've tracked down + + align:start position:0% +track down the after you've tracked down + + + align:start position:0% +track down the after you've tracked down +these genes how do you then + + align:start position:0% +these genes how do you then + + + align:start position:0% +these genes how do you then +prove + + align:start position:0% +prove + + + align:start position:0% +prove +that they do what you think they do that + + align:start position:0% +that they do what you think they do that + + + align:start position:0% +that they do what you think they do that +they actually are responsible for + + align:start position:0% +they actually are responsible for + + + align:start position:0% +they actually are responsible for +methylating the riboses or the bases + + align:start position:0% +methylating the riboses or the bases + + + align:start position:0% +methylating the riboses or the bases +in question + + align:start position:0% +in question + + + align:start position:0% +in question +so + + align:start position:0% +so + + + align:start position:0% +so +it turns out that + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +technology we set up in the sequencing + + align:start position:0% +technology we set up in the sequencing + + + align:start position:0% +technology we set up in the sequencing +and genotyping lecture where you extend + + align:start position:0% +and genotyping lecture where you extend + + + align:start position:0% +and genotyping lecture where you extend +uh + + align:start position:0% +uh + + + align:start position:0% +uh +with dna polymerase + + align:start position:0% +with dna polymerase + + + align:start position:0% +with dna polymerase +a primer on a template so the primer + + align:start position:0% +a primer on a template so the primer + + + align:start position:0% +a primer on a template so the primer +binds to the template and you extend by + + align:start position:0% +binds to the template and you extend by + + + align:start position:0% +binds to the template and you extend by +either + + align:start position:0% +either + + + align:start position:0% +either +many base pairs as in the conventional + + align:start position:0% +many base pairs as in the conventional + + + align:start position:0% +many base pairs as in the conventional +ideoxy sequencing or well one or two + + align:start position:0% +ideoxy sequencing or well one or two + + + align:start position:0% +ideoxy sequencing or well one or two +base pairs in some of the more + + align:start position:0% +base pairs in some of the more + + + align:start position:0% +base pairs in some of the more +up and coming + + align:start position:0% +up and coming + + + align:start position:0% +up and coming +genotyping methods + + align:start position:0% +genotyping methods + + + align:start position:0% +genotyping methods +those extension methods those dna + + align:start position:0% +those extension methods those dna + + + align:start position:0% +those extension methods those dna +polymerase based extension methods + + align:start position:0% +polymerase based extension methods + + + align:start position:0% +polymerase based extension methods +will will stall + + align:start position:0% +will will stall + + + align:start position:0% +will will stall +when you run into this particular kind + + align:start position:0% +when you run into this particular kind + + + align:start position:0% +when you run into this particular kind +of modified base where the + + align:start position:0% +of modified base where the + + + align:start position:0% +of modified base where the +or a bulky group is introduced onto the + + align:start position:0% +or a bulky group is introduced onto the + + + align:start position:0% +or a bulky group is introduced onto the +uh two prime position of the ribose on + + align:start position:0% +uh two prime position of the ribose on + + + align:start position:0% +uh two prime position of the ribose on +the template so you're extending the + + align:start position:0% +the template so you're extending the + + + align:start position:0% +the template so you're extending the +primer sitting on the template and it + + align:start position:0% +primer sitting on the template and it + + + align:start position:0% +primer sitting on the template and it +will stall there and it stalls more when + + align:start position:0% +will stall there and it stalls more when + + + align:start position:0% +will stall there and it stalls more when +you decrease the concentration of the + + align:start position:0% +you decrease the concentration of the + + + align:start position:0% +you decrease the concentration of the +deoxynucleotide triphosphates in the + + align:start position:0% +deoxynucleotide triphosphates in the + + + align:start position:0% +deoxynucleotide triphosphates in the +extension reaction so that's what these + + align:start position:0% +extension reaction so that's what these + + + align:start position:0% +extension reaction so that's what these +little wedges mean at the top of each of + + align:start position:0% +little wedges mean at the top of each of + + + align:start position:0% +little wedges mean at the top of each of +these columns they've done an extension + + align:start position:0% +these columns they've done an extension + + + align:start position:0% +these columns they've done an extension +with all four triphosphates present + + align:start position:0% +with all four triphosphates present + + + align:start position:0% +with all four triphosphates present +either in high amounts at the big end of + + align:start position:0% +either in high amounts at the big end of + + + align:start position:0% +either in high amounts at the big end of +the wedge or low amounts in the small + + align:start position:0% +the wedge or low amounts in the small + + + align:start position:0% +the wedge or low amounts in the small +ends of the wedge and to tell where you + + align:start position:0% +ends of the wedge and to tell where you + + + align:start position:0% +ends of the wedge and to tell where you +are in the sequence this is with using + + align:start position:0% +are in the sequence this is with using + + + align:start position:0% +are in the sequence this is with using +reverse transcriptase polymerase on a + + align:start position:0% +reverse transcriptase polymerase on a + + + align:start position:0% +reverse transcriptase polymerase on a +ribosomal rna template to find out where + + align:start position:0% +ribosomal rna template to find out where + + + align:start position:0% +ribosomal rna template to find out where +you are you do this dideoxy which is + + align:start position:0% +you are you do this dideoxy which is + + + align:start position:0% +you are you do this dideoxy which is +basically the conventional dna + + align:start position:0% +basically the conventional dna + + + align:start position:0% +basically the conventional dna +sequencing where you terminate it either + + align:start position:0% +sequencing where you terminate it either + + + align:start position:0% +sequencing where you terminate it either +use gcs or a's in the template + + align:start position:0% + + + + align:start position:0% + +this allows you to get oriented + + align:start position:0% +this allows you to get oriented + + + align:start position:0% +this allows you to get oriented +basically you're sequencing on the far + + align:start position:0% +basically you're sequencing on the far + + + align:start position:0% +basically you're sequencing on the far +left hand set of lanes and these pause + + align:start position:0% +left hand set of lanes and these pause + + + align:start position:0% +left hand set of lanes and these pause +sites + + align:start position:0% +sites + + + align:start position:0% +sites +are present say the wild type is the + + align:start position:0% +are present say the wild type is the + + + align:start position:0% +are present say the wild type is the +first + + align:start position:0% +first + + + align:start position:0% +first +pair of lanes next to the sequence lanes + + align:start position:0% +pair of lanes next to the sequence lanes + + + align:start position:0% +pair of lanes next to the sequence lanes +on the left-hand side of this display + + align:start position:0% +on the left-hand side of this display + + + align:start position:0% +on the left-hand side of this display +and you can see there's a pause at every + + align:start position:0% +and you can see there's a pause at every + + + align:start position:0% +and you can see there's a pause at every +single uh known methylated base you can + + align:start position:0% +single uh known methylated base you can + + + align:start position:0% +single uh known methylated base you can +determine methylated bases by other + + align:start position:0% +determine methylated bases by other + + + align:start position:0% +determine methylated bases by other +methods as well + + align:start position:0% + + + + align:start position:0% + +but so now then the computational + + align:start position:0% +but so now then the computational + + + align:start position:0% +but so now then the computational +biology predicted + + align:start position:0% +biology predicted + + + align:start position:0% +biology predicted +a set of snow genes in fact ultimately + + align:start position:0% +a set of snow genes in fact ultimately + + + align:start position:0% +a set of snow genes in fact ultimately +all of the snow genes in the yeast + + align:start position:0% +all of the snow genes in the yeast + + + align:start position:0% +all of the snow genes in the yeast +genome we think + + align:start position:0% +genome we think + + + align:start position:0% +genome we think +explaining all of the methyl groups at + + align:start position:0% +explaining all of the methyl groups at + + + align:start position:0% +explaining all of the methyl groups at +least + + align:start position:0% +least + + + align:start position:0% +least +and one by one these were knocked out + + align:start position:0% +and one by one these were knocked out + + + align:start position:0% +and one by one these were knocked out +cleanly so there's no gene there anymore + + align:start position:0% +cleanly so there's no gene there anymore + + + align:start position:0% +cleanly so there's no gene there anymore +for the small rna + + align:start position:0% +for the small rna + + + align:start position:0% +for the small rna +and then you ask well how does this + + align:start position:0% +and then you ask well how does this + + + align:start position:0% +and then you ask well how does this +affect the methylation as detected by + + align:start position:0% +affect the methylation as detected by + + + align:start position:0% +affect the methylation as detected by +this extension assay if you look on the + + align:start position:0% +this extension assay if you look on the + + + align:start position:0% +this extension assay if you look on the +far right hand side for deleted + + align:start position:0% +far right hand side for deleted + + + align:start position:0% +far right hand side for deleted +number 40 and you can see that uh + + align:start position:0% +number 40 and you can see that uh + + + align:start position:0% +number 40 and you can see that uh +position number uh 596 + + align:start position:0% +position number uh 596 + + + align:start position:0% +position number uh 596 +near the near the bottom circle in red + + align:start position:0% +near the near the bottom circle in red + + + align:start position:0% +near the near the bottom circle in red +which is present in the wild type and + + align:start position:0% +which is present in the wild type and + + + align:start position:0% +which is present in the wild type and +all the other mutants is absent from + + align:start position:0% +all the other mutants is absent from + + + align:start position:0% +all the other mutants is absent from +that particular mutant number 40. so + + align:start position:0% +that particular mutant number 40. so + + + align:start position:0% +that particular mutant number 40. so +there's no pause there one infers + + align:start position:0% +there's no pause there one infers + + + align:start position:0% +there's no pause there one infers +there's no methylation + + align:start position:0% +there's no methylation + + + align:start position:0% +there's no methylation +and that was the specific site that + + align:start position:0% +and that was the specific site that + + + align:start position:0% +and that was the specific site that +that's no rna guide sequence was + + align:start position:0% +that's no rna guide sequence was + + + align:start position:0% +that's no rna guide sequence was +predicted to bind it's it's it's aligned + + align:start position:0% +predicted to bind it's it's it's aligned + + + align:start position:0% +predicted to bind it's it's it's aligned +with the position in the guide where you + + align:start position:0% +with the position in the guide where you + + + align:start position:0% +with the position in the guide where you +expect it to be a + + align:start position:0% +expect it to be a + + + align:start position:0% +expect it to be a +methylation occurring and this and you + + align:start position:0% +methylation occurring and this and you + + + align:start position:0% +methylation occurring and this and you +can see in each lane there's a different + + align:start position:0% +can see in each lane there's a different + + + align:start position:0% +can see in each lane there's a different +circled red missing uh black pause site + + align:start position:0% +circled red missing uh black pause site + + + align:start position:0% +circled red missing uh black pause site +um + + align:start position:0% +um + + + align:start position:0% +um +and until we get + + align:start position:0% +and until we get + + + align:start position:0% +and until we get +to the one in the middle of + + align:start position:0% +to the one in the middle of + + + align:start position:0% +to the one in the middle of +newton numbers for snow rna number 60 + + align:start position:0% +newton numbers for snow rna number 60 + + + align:start position:0% +newton numbers for snow rna number 60 +and here's actually two missing bands in + + align:start position:0% +and here's actually two missing bands in + + + align:start position:0% +and here's actually two missing bands in +the same lane and how that can occur + + align:start position:0% +the same lane and how that can occur + + + align:start position:0% +the same lane and how that can occur +there's two different ways that a snow + + align:start position:0% +there's two different ways that a snow + + + align:start position:0% +there's two different ways that a snow +rna can + + align:start position:0% +rna can + + + align:start position:0% +rna can +knocking out a single gene a singles rna + + align:start position:0% +knocking out a single gene a singles rna + + + align:start position:0% +knocking out a single gene a singles rna +can have + + align:start position:0% +can have + + + align:start position:0% +can have +effect on two different methyl groups + + align:start position:0% +effect on two different methyl groups + + + align:start position:0% +effect on two different methyl groups +one is if the if the uh + + align:start position:0% + + + + align:start position:0% + +guide sequence can bind to two different + + align:start position:0% +guide sequence can bind to two different + + + align:start position:0% +guide sequence can bind to two different +places in the ribosomal rna and the + + align:start position:0% +places in the ribosomal rna and the + + + align:start position:0% +places in the ribosomal rna and the +other is if there are two guide + + align:start position:0% +other is if there are two guide + + + align:start position:0% +other is if there are two guide +sequences within the same snow rna + + align:start position:0% +sequences within the same snow rna + + + align:start position:0% +sequences within the same snow rna +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +now that we have at least some grounding + + align:start position:0% +now that we have at least some grounding + + + align:start position:0% +now that we have at least some grounding +in + + align:start position:0% +in + + + align:start position:0% +in +in the kind of structures that can occur + + align:start position:0% +in the kind of structures that can occur + + + align:start position:0% +in the kind of structures that can occur +now we're going to ask how we + + align:start position:0% +now we're going to ask how we + + + align:start position:0% +now we're going to ask how we +monitor and measure + + align:start position:0% +monitor and measure + + + align:start position:0% +monitor and measure +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the amounts of these structures + + align:start position:0% +the amounts of these structures + + + align:start position:0% +the amounts of these structures +in uh + + align:start position:0% +in uh + + + align:start position:0% +in uh +in biological systems and we will also + + align:start position:0% +in biological systems and we will also + + + align:start position:0% +in biological systems and we will also +see how these structures impact the + + align:start position:0% +see how these structures impact the + + + align:start position:0% +see how these structures impact the +methods that we use for the quantitation + + align:start position:0% +methods that we use for the quantitation + + + align:start position:0% +methods that we use for the quantitation +of the structures + + align:start position:0% +of the structures + + + align:start position:0% +of the structures +so + + align:start position:0% +so + + + align:start position:0% +so +we have + + align:start position:0% + + + + align:start position:0% + +choices of a molecule that we're going + + align:start position:0% +choices of a molecule that we're going + + + align:start position:0% +choices of a molecule that we're going +to measure uh when we're monitoring the + + align:start position:0% +to measure uh when we're monitoring the + + + align:start position:0% +to measure uh when we're monitoring the +ex the various molecules in the cell why + + align:start position:0% +ex the various molecules in the cell why + + + align:start position:0% +ex the various molecules in the cell why +are we focusing on rna well part of it + + align:start position:0% +are we focusing on rna well part of it + + + align:start position:0% +are we focusing on rna well part of it +is because of this nice + + align:start position:0% +is because of this nice + + + align:start position:0% +is because of this nice +structural continuity between the simple + + align:start position:0% +structural continuity between the simple + + + align:start position:0% +structural continuity between the simple +dna and the very complicated proteins + + align:start position:0% +dna and the very complicated proteins + + + align:start position:0% +dna and the very complicated proteins +but the other is that we want if we want + + align:start position:0% +but the other is that we want if we want + + + align:start position:0% +but the other is that we want if we want +to study different points in the + + align:start position:0% +to study different points in the + + + align:start position:0% +to study different points in the +regulatory + + align:start position:0% +regulatory + + + align:start position:0% +regulatory +and + + align:start position:0% +and + + + align:start position:0% +and +metabolic networks that we'll be talking + + align:start position:0% +metabolic networks that we'll be talking + + + align:start position:0% +metabolic networks that we'll be talking +about at the end of this course having + + align:start position:0% +about at the end of this course having + + + align:start position:0% +about at the end of this course having +to do with + + align:start position:0% +to do with + + + align:start position:0% +to do with +systems biology + + align:start position:0% +systems biology + + + align:start position:0% +systems biology +if we choose + + align:start position:0% +if we choose + + + align:start position:0% +if we choose +we want it + + align:start position:0% +we want it + + + align:start position:0% +we want it +every part of the is subject to some + + align:start position:0% +every part of the is subject to some + + + align:start position:0% +every part of the is subject to some +kind of control transcriptional control + + align:start position:0% +kind of control transcriptional control + + + align:start position:0% +kind of control transcriptional control +is one of the early stages and then + + align:start position:0% +is one of the early stages and then + + + align:start position:0% +is one of the early stages and then +there are many stages subsequent that + + align:start position:0% +there are many stages subsequent that + + + align:start position:0% +there are many stages subsequent that +that lead to the protein and ultimate + + align:start position:0% +that lead to the protein and ultimate + + + align:start position:0% +that lead to the protein and ultimate +phenotypes that result in proliferation + + align:start position:0% +phenotypes that result in proliferation + + + align:start position:0% +phenotypes that result in proliferation +of the species + + align:start position:0% +of the species + + + align:start position:0% +of the species +if you want to look at transcriptional + + align:start position:0% +if you want to look at transcriptional + + + align:start position:0% +if you want to look at transcriptional +control + + align:start position:0% +control + + + align:start position:0% +control +it would not do well to study protein + + align:start position:0% +it would not do well to study protein + + + align:start position:0% +it would not do well to study protein +because + + align:start position:0% +because + + + align:start position:0% +because +the closest thing to transcriptional + + align:start position:0% +the closest thing to transcriptional + + + align:start position:0% +the closest thing to transcriptional +control that you can measure is the rna + + align:start position:0% +control that you can measure is the rna + + + align:start position:0% +control that you can measure is the rna +products you can you can study the + + align:start position:0% +products you can you can study the + + + align:start position:0% +products you can you can study the +transcriptional control itself directly + + align:start position:0% +transcriptional control itself directly + + + align:start position:0% +transcriptional control itself directly +as well by studying the dna protein + + align:start position:0% +as well by studying the dna protein + + + align:start position:0% +as well by studying the dna protein +interactions but if you want to measure + + align:start position:0% +interactions but if you want to measure + + + align:start position:0% +interactions but if you want to measure +a diffusible + + align:start position:0% +a diffusible + + + align:start position:0% +a diffusible +molecule rna is the thing to do and + + align:start position:0% +molecule rna is the thing to do and + + + align:start position:0% +molecule rna is the thing to do and +there are multiple + + align:start position:0% +there are multiple + + + align:start position:0% +there are multiple +different uh methods for getting at + + align:start position:0% +different uh methods for getting at + + + align:start position:0% +different uh methods for getting at +co-regulated set of genes co-regulated + + align:start position:0% +co-regulated set of genes co-regulated + + + align:start position:0% +co-regulated set of genes co-regulated +at the transcriptional level + + align:start position:0% +at the transcriptional level + + + align:start position:0% +at the transcriptional level +it will illustrate a few here + + align:start position:0% +it will illustrate a few here + + + align:start position:0% +it will illustrate a few here +and why why do we need multiple methods + + align:start position:0% +and why why do we need multiple methods + + + align:start position:0% +and why why do we need multiple methods +well we've talked about random and + + align:start position:0% +well we've talked about random and + + + align:start position:0% +well we've talked about random and +systematic errors random errors you can + + align:start position:0% +systematic errors random errors you can + + + align:start position:0% +systematic errors random errors you can +compensate + + align:start position:0% +compensate + + + align:start position:0% +compensate +by + + align:start position:0% +by + + + align:start position:0% +by +repeating the experiment the random + + align:start position:0% +repeating the experiment the random + + + align:start position:0% +repeating the experiment the random +errors will average out ultimately + + align:start position:0% +errors will average out ultimately + + + align:start position:0% +errors will average out ultimately +systematic errors will happen the same + + align:start position:0% +systematic errors will happen the same + + + align:start position:0% +systematic errors will happen the same +way over and over again so you want to + + align:start position:0% +way over and over again so you want to + + + align:start position:0% +way over and over again so you want to +have something out of the box to allow + + align:start position:0% +have something out of the box to allow + + + align:start position:0% +have something out of the box to allow +you to to check it or to model it or to + + align:start position:0% +you to to check it or to model it or to + + + align:start position:0% +you to to check it or to model it or to +to allow you to do + + align:start position:0% +to allow you to do + + + align:start position:0% +to allow you to do +integration as you might want to have in + + align:start position:0% +integration as you might want to have in + + + align:start position:0% +integration as you might want to have in +uh in complicated systems so here just + + align:start position:0% +uh in complicated systems so here just + + + align:start position:0% +uh in complicated systems so here just +to start us thinking about integration + + align:start position:0% +to start us thinking about integration + + + align:start position:0% +to start us thinking about integration +and checking different + + align:start position:0% +and checking different + + + align:start position:0% +and checking different +ways of getting transcriptional + + align:start position:0% +ways of getting transcriptional + + + align:start position:0% +ways of getting transcriptional +co-regulation + + align:start position:0% +co-regulation + + + align:start position:0% +co-regulation +let's let's think about + + align:start position:0% + + + + align:start position:0% + +if you look through all the + + align:start position:0% +if you look through all the + + + align:start position:0% +if you look through all the +proteins that occur you'll find proteins + + align:start position:0% +proteins that occur you'll find proteins + + + align:start position:0% +proteins that occur you'll find proteins +that + + align:start position:0% +that + + + align:start position:0% +that +occur together frequently as a either + + align:start position:0% +occur together frequently as a either + + + align:start position:0% +occur together frequently as a either +as fusions or as separate of proteins or + + align:start position:0% +as fusions or as separate of proteins or + + + align:start position:0% +as fusions or as separate of proteins or +in operons they'll occur as + + align:start position:0% +in operons they'll occur as + + + align:start position:0% +in operons they'll occur as +coating regions that are clustered + + align:start position:0% +coating regions that are clustered + + + align:start position:0% +coating regions that are clustered +together in some species or maybe less + + align:start position:0% +together in some species or maybe less + + + align:start position:0% +together in some species or maybe less +clustered in other species + + align:start position:0% +clustered in other species + + + align:start position:0% +clustered in other species +when we have metabolic pathways where a + + align:start position:0% +when we have metabolic pathways where a + + + align:start position:0% +when we have metabolic pathways where a +small molecule will be shared by + + align:start position:0% +small molecule will be shared by + + + align:start position:0% +small molecule will be shared by +as the product of one will be the + + align:start position:0% +as the product of one will be the + + + align:start position:0% +as the product of one will be the +substrate of another and so on you'll + + align:start position:0% +substrate of another and so on you'll + + + align:start position:0% +substrate of another and so on you'll +have this chain of events + + align:start position:0% +have this chain of events + + + align:start position:0% +have this chain of events +as in the + + align:start position:0% +as in the + + + align:start position:0% +as in the +lower left-hand corner + + align:start position:0% +lower left-hand corner + + + align:start position:0% +lower left-hand corner +and these these + + align:start position:0% +and these these + + + align:start position:0% +and these these +sets of + + align:start position:0% +sets of + + + align:start position:0% +sets of +enzymes that need to be + + align:start position:0% + + + + align:start position:0% + +working together need to be co-expressed + + align:start position:0% +working together need to be co-expressed + + + align:start position:0% +working together need to be co-expressed +they they need to + + align:start position:0% +they they need to + + + align:start position:0% +they they need to +come up together and go down together + + align:start position:0% +come up together and go down together + + + align:start position:0% +come up together and go down together +when they're not needed need to come up + + align:start position:0% +when they're not needed need to come up + + + align:start position:0% +when they're not needed need to come up +when they're suddenly needed and so you + + align:start position:0% +when they're suddenly needed and so you + + + align:start position:0% +when they're suddenly needed and so you +might have an entire pathway or set of + + align:start position:0% +might have an entire pathway or set of + + + align:start position:0% +might have an entire pathway or set of +pathways that are co-expressed and one + + align:start position:0% +pathways that are co-expressed and one + + + align:start position:0% +pathways that are co-expressed and one +way to do that is to cluster them in the + + align:start position:0% +way to do that is to cluster them in the + + + align:start position:0% +way to do that is to cluster them in the +genome + + align:start position:0% +genome + + + align:start position:0% +genome +when they are co-expressed you will + + align:start position:0% +when they are co-expressed you will + + + align:start position:0% +when they are co-expressed you will +sometimes find upstream of them + + align:start position:0% +sometimes find upstream of them + + + align:start position:0% +sometimes find upstream of them +motifs such as such as this again here's + + align:start position:0% +motifs such as such as this again here's + + + align:start position:0% +motifs such as such as this again here's +the two bits + + align:start position:0% +the two bits + + + align:start position:0% +the two bits +for the vertical scale + + align:start position:0% +for the vertical scale + + + align:start position:0% +for the vertical scale +where this this might be + + align:start position:0% +where this this might be + + + align:start position:0% +where this this might be +enriched and so this would be another + + align:start position:0% +enriched and so this would be another + + + align:start position:0% +enriched and so this would be another +indicate so when you find these + + align:start position:0% +indicate so when you find these + + + align:start position:0% +indicate so when you find these +in front of genes you might expect them + + align:start position:0% +in front of genes you might expect them + + + align:start position:0% +in front of genes you might expect them +to be co-regulated + + align:start position:0% +to be co-regulated + + + align:start position:0% +to be co-regulated +when you find a set of proteins that are + + align:start position:0% +when you find a set of proteins that are + + + align:start position:0% +when you find a set of proteins that are +consistently together in different + + align:start position:0% +consistently together in different + + + align:start position:0% +consistently together in different +organisms so-called phylogenetic + + align:start position:0% +organisms so-called phylogenetic + + + align:start position:0% +organisms so-called phylogenetic +profiles you will find + + align:start position:0% +profiles you will find + + + align:start position:0% +profiles you will find +that this + + align:start position:0% +that this + + + align:start position:0% +that this +set of proteins that is involved in a + + align:start position:0% +set of proteins that is involved in a + + + align:start position:0% +set of proteins that is involved in a +common enzymatic pathway metabolic + + align:start position:0% +common enzymatic pathway metabolic + + + align:start position:0% +common enzymatic pathway metabolic +pathway + + align:start position:0% +pathway + + + align:start position:0% +pathway +not only co-regulated and found together + + align:start position:0% +not only co-regulated and found together + + + align:start position:0% +not only co-regulated and found together +but in + + align:start position:0% +but in + + + align:start position:0% +but in +along the chromosome but they're found + + align:start position:0% +along the chromosome but they're found + + + align:start position:0% +along the chromosome but they're found +together when you go through many + + align:start position:0% +together when you go through many + + + align:start position:0% +together when you go through many +different species they will be deleted + + align:start position:0% +different species they will be deleted + + + align:start position:0% +different species they will be deleted +or inserted as a block or or they'll be + + align:start position:0% +or inserted as a block or or they'll be + + + align:start position:0% +or inserted as a block or or they'll be +found scattered around the genome but + + align:start position:0% +found scattered around the genome but + + + align:start position:0% +found scattered around the genome but +but if but you'll find that that when + + align:start position:0% +but if but you'll find that that when + + + align:start position:0% +but if but you'll find that that when +one disappears they all disappear + + align:start position:0% +one disappears they all disappear + + + align:start position:0% +one disappears they all disappear +in general statistically speaking this + + align:start position:0% +in general statistically speaking this + + + align:start position:0% +in general statistically speaking this +this phylogenetic co-occurrence is + + align:start position:0% +this phylogenetic co-occurrence is + + + align:start position:0% +this phylogenetic co-occurrence is +another clue that you might expect to be + + align:start position:0% +another clue that you might expect to be + + + align:start position:0% +another clue that you might expect to be +co-regulated in those genomes in which + + align:start position:0% +co-regulated in those genomes in which + + + align:start position:0% +co-regulated in those genomes in which +there they do co-occur + + align:start position:0% +there they do co-occur + + + align:start position:0% +there they do co-occur +anyway and microarrays will be + + align:start position:0% +anyway and microarrays will be + + + align:start position:0% +anyway and microarrays will be +and variations on that theme will be the + + align:start position:0% +and variations on that theme will be the + + + align:start position:0% +and variations on that theme will be the +main thing we'll talk about but i wanted + + align:start position:0% +main thing we'll talk about but i wanted + + + align:start position:0% +main thing we'll talk about but i wanted +to put it in the context and i'll just + + align:start position:0% +to put it in the context and i'll just + + + align:start position:0% +to put it in the context and i'll just +expand + + align:start position:0% +expand + + + align:start position:0% +expand +on one of these + + align:start position:0% + + + + align:start position:0% + +at the bottom here + + align:start position:0% +at the bottom here + + + align:start position:0% +at the bottom here +the + + align:start position:0% +the + + + align:start position:0% +the +in slide 22. + + align:start position:0% +in slide 22. + + + align:start position:0% +in slide 22. +this is an algorithm for reconstructing + + align:start position:0% +this is an algorithm for reconstructing + + + align:start position:0% +this is an algorithm for reconstructing +likely combinations + + align:start position:0% +likely combinations + + + align:start position:0% +likely combinations +where in some organisms you might have + + align:start position:0% +where in some organisms you might have + + + align:start position:0% +where in some organisms you might have +the entire biosynthetic pathway as + + align:start position:0% +the entire biosynthetic pathway as + + + align:start position:0% +the entire biosynthetic pathway as +as a series of + + align:start position:0% +as a series of + + + align:start position:0% +as a series of +genes which encode one by one all the + + align:start position:0% +genes which encode one by one all the + + + align:start position:0% +genes which encode one by one all the +proteins in this case they're involved + + align:start position:0% +proteins in this case they're involved + + + align:start position:0% +proteins in this case they're involved +in curing biosynthesis + + align:start position:0% +in curing biosynthesis + + + align:start position:0% +in curing biosynthesis +from simpler molecules + + align:start position:0% +from simpler molecules + + + align:start position:0% +from simpler molecules +but in other organisms you might have + + align:start position:0% +but in other organisms you might have + + + align:start position:0% +but in other organisms you might have +them scattered all over the genome but + + align:start position:0% +them scattered all over the genome but + + + align:start position:0% +them scattered all over the genome but +they might be co-regulated their rnas + + align:start position:0% +they might be co-regulated their rnas + + + align:start position:0% +they might be co-regulated their rnas +might go up and down together and so you + + align:start position:0% +might go up and down together and so you + + + align:start position:0% +might go up and down together and so you +so if you look at enough genomes you can + + align:start position:0% +so if you look at enough genomes you can + + + align:start position:0% +so if you look at enough genomes you can +reconstruct + + align:start position:0% +reconstruct + + + align:start position:0% +reconstruct +the likely combination of + + align:start position:0% +the likely combination of + + + align:start position:0% +the likely combination of +of enzymes and here's how it might work + + align:start position:0% +of enzymes and here's how it might work + + + align:start position:0% +of enzymes and here's how it might work +in any one of these for example e coli + + align:start position:0% +in any one of these for example e coli + + + align:start position:0% +in any one of these for example e coli +you might see that they're scattered + + align:start position:0% +you might see that they're scattered + + + align:start position:0% +you might see that they're scattered +about a pair here a pair there + + align:start position:0% +about a pair here a pair there + + + align:start position:0% +about a pair here a pair there +singletons don't help much but if you + + align:start position:0% +singletons don't help much but if you + + + align:start position:0% +singletons don't help much but if you +take all the pairs from a lot of + + align:start position:0% +take all the pairs from a lot of + + + align:start position:0% +take all the pairs from a lot of +different organisms + + align:start position:0% +different organisms + + + align:start position:0% +different organisms +you can you can reconstruct this network + + align:start position:0% +you can you can reconstruct this network + + + align:start position:0% +you can you can reconstruct this network +where you say oh uh + + align:start position:0% +where you say oh uh + + + align:start position:0% +where you say oh uh +this gene we'll call lqic all these are + + align:start position:0% +this gene we'll call lqic all these are + + + align:start position:0% +this gene we'll call lqic all these are +probably involved in the same process if + + align:start position:0% +probably involved in the same process if + + + align:start position:0% +probably involved in the same process if +you get a hint for what any one of them + + align:start position:0% +you get a hint for what any one of them + + + align:start position:0% +you get a hint for what any one of them +does + + align:start position:0% +does + + + align:start position:0% +does +say one of them is involved in purine + + align:start position:0% +say one of them is involved in purine + + + align:start position:0% +say one of them is involved in purine +biosynthesis then you find that they all + + align:start position:0% +biosynthesis then you find that they all + + + align:start position:0% +biosynthesis then you find that they all +are and you guess they might be + + align:start position:0% +are and you guess they might be + + + align:start position:0% +are and you guess they might be +co-regulated + + align:start position:0% +co-regulated + + + align:start position:0% +co-regulated +very tightly + + align:start position:0% +very tightly + + + align:start position:0% +very tightly +so now let's figure out how we actually + + align:start position:0% +so now let's figure out how we actually + + + align:start position:0% +so now let's figure out how we actually +measure that they're co-regulated + + align:start position:0% +measure that they're co-regulated + + + align:start position:0% +measure that they're co-regulated +very tightly + + align:start position:0% +very tightly + + + align:start position:0% +very tightly +and the way we can do that + + align:start position:0% +and the way we can do that + + + align:start position:0% +and the way we can do that +as we do that whatever method we use we + + align:start position:0% +as we do that whatever method we use we + + + align:start position:0% +as we do that whatever method we use we +want to ask are we interested in ratios + + align:start position:0% +want to ask are we interested in ratios + + + align:start position:0% +want to ask are we interested in ratios +relative changes or we're interested in + + align:start position:0% +relative changes or we're interested in + + + align:start position:0% +relative changes or we're interested in +absolute values the various things that + + align:start position:0% +absolute values the various things that + + + align:start position:0% +absolute values the various things that +we + + align:start position:0% +we + + + align:start position:0% +we +can do with absolute amounts that are + + align:start position:0% +can do with absolute amounts that are + + + align:start position:0% +can do with absolute amounts that are +very hard to do with ratios in + + align:start position:0% +very hard to do with ratios in + + + align:start position:0% +very hard to do with ratios in +particular if we want to ask + + align:start position:0% + + + + align:start position:0% + +is a particular protein level high + + align:start position:0% +is a particular protein level high + + + align:start position:0% +is a particular protein level high +because its + + align:start position:0% +because its + + + align:start position:0% +because its +translation is efficient or is it high + + align:start position:0% +translation is efficient or is it high + + + align:start position:0% +translation is efficient or is it high +because its transcription is efficient + + align:start position:0% +because its transcription is efficient + + + align:start position:0% +because its transcription is efficient +if you find that it's full of + + align:start position:0% +if you find that it's full of + + + align:start position:0% +if you find that it's full of +of abundant codons as if it wants to be + + align:start position:0% +of abundant codons as if it wants to be + + + align:start position:0% +of abundant codons as if it wants to be +efficiently translated is it also have a + + align:start position:0% +efficiently translated is it also have a + + + align:start position:0% +efficiently translated is it also have a +high level promoter as if it wants to be + + align:start position:0% +high level promoter as if it wants to be + + + align:start position:0% +high level promoter as if it wants to be +transcriptionally + + align:start position:0% +transcriptionally + + + align:start position:0% +transcriptionally +active these sorts of questions + + align:start position:0% +active these sorts of questions + + + align:start position:0% +active these sorts of questions +um really benefit from having absolute + + align:start position:0% +um really benefit from having absolute + + + align:start position:0% +um really benefit from having absolute +amounts + + align:start position:0% +amounts + + + align:start position:0% +amounts +meaning + + align:start position:0% +meaning + + + align:start position:0% +meaning +you know so many molecules of rna per + + align:start position:0% +you know so many molecules of rna per + + + align:start position:0% +you know so many molecules of rna per +cell so many molecules of protein per + + align:start position:0% +cell so many molecules of protein per + + + align:start position:0% +cell so many molecules of protein per +cell + + align:start position:0% +cell + + + align:start position:0% +cell +when we get to direct causality we want + + align:start position:0% +when we get to direct causality we want + + + align:start position:0% +when we get to direct causality we want +to get at the motifs + + align:start position:0% +to get at the motifs + + + align:start position:0% +to get at the motifs +this would be one of the objectives of + + align:start position:0% +this would be one of the objectives of + + + align:start position:0% +this would be one of the objectives of +doing the rna quantitation to allow us + + align:start position:0% +doing the rna quantitation to allow us + + + align:start position:0% +doing the rna quantitation to allow us +to to cluster rnas that that are + + align:start position:0% +to to cluster rnas that that are + + + align:start position:0% +to to cluster rnas that that are +co-expressed and then to start looking + + align:start position:0% +co-expressed and then to start looking + + + align:start position:0% +co-expressed and then to start looking +for motifs and direct causality + + align:start position:0% +for motifs and direct causality + + + align:start position:0% +for motifs and direct causality +another thing that we might want to do + + align:start position:0% +another thing that we might want to do + + + align:start position:0% +another thing that we might want to do +is to classify we can ask whether + + align:start position:0% +is to classify we can ask whether + + + align:start position:0% +is to classify we can ask whether +small molecules or mutations such as the + + align:start position:0% +small molecules or mutations such as the + + + align:start position:0% +small molecules or mutations such as the +current cancers cause + + align:start position:0% +current cancers cause + + + align:start position:0% +current cancers cause +enough of a signature that you can then + + align:start position:0% +enough of a signature that you can then + + + align:start position:0% +enough of a signature that you can then +use those to say okay this + + align:start position:0% +use those to say okay this + + + align:start position:0% +use those to say okay this +cell state that we see is a recognizable + + align:start position:0% +cell state that we see is a recognizable + + + align:start position:0% +cell state that we see is a recognizable +small molecule effect or stress effect + + align:start position:0% +small molecule effect or stress effect + + + align:start position:0% +small molecule effect or stress effect +or mutational effect cancer + + align:start position:0% +or mutational effect cancer + + + align:start position:0% +or mutational effect cancer +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% + + + + align:start position:0% + +when we uh + + align:start position:0% + + + + align:start position:0% + +we will be talking about microarray and + + align:start position:0% +we will be talking about microarray and + + + align:start position:0% +we will be talking about microarray and +related + + align:start position:0% +related + + + align:start position:0% +related +methods + + align:start position:0% +methods + + + align:start position:0% +methods +but i want you to to + + align:start position:0% +but i want you to to + + + align:start position:0% +but i want you to to +question + + align:start position:0% +question + + + align:start position:0% +question +uh the advantages and disadvantages of + + align:start position:0% +uh the advantages and disadvantages of + + + align:start position:0% +uh the advantages and disadvantages of +these methods and so i'll uh i'll + + align:start position:0% +these methods and so i'll uh i'll + + + align:start position:0% +these methods and so i'll uh i'll +compare it to a number a number but + + align:start position:0% +compare it to a number a number but + + + align:start position:0% +compare it to a number a number but +let's start with the the most dramatic + + align:start position:0% +let's start with the the most dramatic + + + align:start position:0% +let's start with the the most dramatic +comparison which is uh with uh in cpu + + align:start position:0% +comparison which is uh with uh in cpu + + + align:start position:0% +comparison which is uh with uh in cpu +hybridization so an array hybridization + + align:start position:0% +hybridization so an array hybridization + + + align:start position:0% +hybridization so an array hybridization +you'll have + + align:start position:0% +you'll have + + + align:start position:0% +you'll have +tens of thousands of different + + align:start position:0% + + + + align:start position:0% + +gene probes mobilized on a solid surface + + align:start position:0% + + + + align:start position:0% + +and you'll label up + + align:start position:0% +and you'll label up + + + align:start position:0% +and you'll label up +the rna from a a mixture of different + + align:start position:0% +the rna from a a mixture of different + + + align:start position:0% +the rna from a a mixture of different +cells + + align:start position:0% +cells + + + align:start position:0% +cells +different mixture of different rnas + + align:start position:0% +different mixture of different rnas + + + align:start position:0% +different mixture of different rnas +within a cell + + align:start position:0% +within a cell + + + align:start position:0% +within a cell +but you'll be able to ask questions + + align:start position:0% +but you'll be able to ask questions + + + align:start position:0% +but you'll be able to ask questions +about 10 000 genes at a time in an in + + align:start position:0% +about 10 000 genes at a time in an in + + + align:start position:0% +about 10 000 genes at a time in an in +situ experiment that's the other way + + align:start position:0% +situ experiment that's the other way + + + align:start position:0% +situ experiment that's the other way +around you take a cell and it's fairly + + align:start position:0% +around you take a cell and it's fairly + + + align:start position:0% +around you take a cell and it's fairly +natural environment + + align:start position:0% +natural environment + + + align:start position:0% +natural environment +usually fixed but fixed with maintaining + + align:start position:0% +usually fixed but fixed with maintaining + + + align:start position:0% +usually fixed but fixed with maintaining +the spatial uh + + align:start position:0% +the spatial uh + + + align:start position:0% +the spatial uh +aspects + + align:start position:0% +aspects + + + align:start position:0% +aspects +then + + align:start position:0% +then + + + align:start position:0% +then +if you look within the cell with a + + align:start position:0% +if you look within the cell with a + + + align:start position:0% +if you look within the cell with a +single gene at a time or maybe two or + + align:start position:0% +single gene at a time or maybe two or + + + align:start position:0% +single gene at a time or maybe two or +three at a time a very small number not + + align:start position:0% +three at a time a very small number not + + + align:start position:0% +three at a time a very small number not +tens of thousands you can look to see + + align:start position:0% +tens of thousands you can look to see + + + align:start position:0% +tens of thousands you can look to see +whether the rna is is uniformly spread + + align:start position:0% +whether the rna is is uniformly spread + + + align:start position:0% +whether the rna is is uniformly spread +throughout the cell and uniformly spread + + align:start position:0% +throughout the cell and uniformly spread + + + align:start position:0% +throughout the cell and uniformly spread +throughout all the cells in the tissue + + align:start position:0% +throughout all the cells in the tissue + + + align:start position:0% +throughout all the cells in the tissue +or in say you've got a + + align:start position:0% +or in say you've got a + + + align:start position:0% +or in say you've got a +mixed population of yeast cells whatever + + align:start position:0% +mixed population of yeast cells whatever + + + align:start position:0% +mixed population of yeast cells whatever +and you all and you can find cases in + + align:start position:0% +and you all and you can find cases in + + + align:start position:0% +and you all and you can find cases in +the literature where it is not uniformly + + align:start position:0% +the literature where it is not uniformly + + + align:start position:0% +the literature where it is not uniformly +present in all the cells and not even + + align:start position:0% +present in all the cells and not even + + + align:start position:0% +present in all the cells and not even +uniformly within a cell here is one of + + align:start position:0% +uniformly within a cell here is one of + + + align:start position:0% +uniformly within a cell here is one of +the more dramatic cases where + + align:start position:0% +the more dramatic cases where + + + align:start position:0% +the more dramatic cases where +the two x chromosomes in + + align:start position:0% +the two x chromosomes in + + + align:start position:0% +the two x chromosomes in +mammals + + align:start position:0% +mammals + + + align:start position:0% +mammals +behave differently from one another + + align:start position:0% +behave differently from one another + + + align:start position:0% +behave differently from one another +female mammals will have + + align:start position:0% +female mammals will have + + + align:start position:0% +female mammals will have +one rna + + align:start position:0% +one rna + + + align:start position:0% +one rna +one chromosome expressing most of its + + align:start position:0% +one chromosome expressing most of its + + + align:start position:0% +one chromosome expressing most of its +rnas at normal levels + + align:start position:0% +rnas at normal levels + + + align:start position:0% +rnas at normal levels +and the other chromosome expressing + + align:start position:0% +and the other chromosome expressing + + + align:start position:0% +and the other chromosome expressing +almost no rnas it is expressing at least + + align:start position:0% +almost no rnas it is expressing at least + + + align:start position:0% +almost no rnas it is expressing at least +one rna and that rna is lo which is uh + + align:start position:0% +one rna and that rna is lo which is uh + + + align:start position:0% +one rna and that rna is lo which is uh +xist and it's a + + align:start position:0% +xist and it's a + + + align:start position:0% +xist and it's a +uh covering that + + align:start position:0% +uh covering that + + + align:start position:0% +uh covering that +whole chromosome whereas localized over + + align:start position:0% +whole chromosome whereas localized over + + + align:start position:0% +whole chromosome whereas localized over +that chromosome and not the rest of the + + align:start position:0% +that chromosome and not the rest of the + + + align:start position:0% +that chromosome and not the rest of the +cell this is an extreme case of + + align:start position:0% +cell this is an extreme case of + + + align:start position:0% +cell this is an extreme case of +localization + + align:start position:0% +localization + + + align:start position:0% +localization +that you can monitor with microscopic + + align:start position:0% +that you can monitor with microscopic + + + align:start position:0% +that you can monitor with microscopic +methods + + align:start position:0% +methods + + + align:start position:0% +methods +fluorescent microscopic methods + + align:start position:0% +fluorescent microscopic methods + + + align:start position:0% +fluorescent microscopic methods +instead we'll + + align:start position:0% +instead we'll + + + align:start position:0% +instead we'll +keep this in the back of your mind as + + align:start position:0% +keep this in the back of your mind as + + + align:start position:0% +keep this in the back of your mind as +you look through + + align:start position:0% +you look through + + + align:start position:0% +you look through +the sort of microarray and other + + align:start position:0% +the sort of microarray and other + + + align:start position:0% +the sort of microarray and other +experiments where you're pushing + + align:start position:0% +experiments where you're pushing + + + align:start position:0% +experiments where you're pushing +together + + align:start position:0% +together + + + align:start position:0% +together +a variety of cells that might be in + + align:start position:0% +a variety of cells that might be in + + + align:start position:0% +a variety of cells that might be in +different stages of the cell cycle might + + align:start position:0% +different stages of the cell cycle might + + + align:start position:0% +different stages of the cell cycle might +have slightly different environments and + + align:start position:0% +have slightly different environments and + + + align:start position:0% +have slightly different environments and +even within the cell the rna you're + + align:start position:0% +even within the cell the rna you're + + + align:start position:0% +even within the cell the rna you're +losing the information about the rna + + align:start position:0% +losing the information about the rna + + + align:start position:0% +losing the information about the rna +localization + + align:start position:0% + + + + align:start position:0% + +let's + + align:start position:0% +let's + + + align:start position:0% +let's +take a short + + align:start position:0% +take a short + + + align:start position:0% +take a short +break and then come back and + + align:start position:0% +break and then come back and + + + align:start position:0% +break and then come back and +connect on finish up on the nc2 + + align:start position:0% +connect on finish up on the nc2 + + + align:start position:0% +connect on finish up on the nc2 +hybridization and + + align:start position:0% +hybridization and + + + align:start position:0% +hybridization and +connect to other methods for + + align:start position:0% +connect to other methods for + + + align:start position:0% +connect to other methods for +quantitation of rna \ No newline at end of file diff --git a/r3YSpzhq72A.txt b/r3YSpzhq72A.txt new file mode 100644 index 0000000000000000000000000000000000000000..ffa1e4cd58a53fe445b09fded6870376b90b6e3b --- /dev/null +++ b/r3YSpzhq72A.txt @@ -0,0 +1,13883 @@ +align:start position:0% + +okay so a little bit of a review I want + + align:start position:0% +okay so a little bit of a review I want + + + align:start position:0% +okay so a little bit of a review I want +to put the the um what Esther has been + + align:start position:0% +to put the the um what Esther has been + + + align:start position:0% +to put the the um what Esther has been +doing the last few lectures into a + + align:start position:0% +doing the last few lectures into a + + + align:start position:0% +doing the last few lectures into a +little bit broader context and that's + + align:start position:0% +little bit broader context and that's + + + align:start position:0% +little bit broader context and that's +going to be a sort of a nice segue into + + align:start position:0% +going to be a sort of a nice segue into + + + align:start position:0% +going to be a sort of a nice segue into +talking about linear regression so what + + align:start position:0% +talking about linear regression so what + + + align:start position:0% +talking about linear regression so what +did we do for the first sort of half of + + align:start position:0% +did we do for the first sort of half of + + + align:start position:0% +did we do for the first sort of half of +the semester we established a foundation + + align:start position:0% +the semester we established a foundation + + + align:start position:0% +the semester we established a foundation +in probability and we proceeded uh to + + align:start position:0% +in probability and we proceeded uh to + + + align:start position:0% +in probability and we proceeded uh to +talk about how to estimate um unknown + + align:start position:0% +talk about how to estimate um unknown + + + align:start position:0% +talk about how to estimate um unknown +parameters okay um most if not all of + + align:start position:0% +parameters okay um most if not all of + + + align:start position:0% +parameters okay um most if not all of +that discussion was focused on + + align:start position:0% +that discussion was focused on + + + align:start position:0% +that discussion was focused on +estimating parameters of a univariant + + align:start position:0% +estimating parameters of a univariant + + + align:start position:0% +estimating parameters of a univariant +distribution okay so we we were talking + + align:start position:0% +distribution okay so we we were talking + + + align:start position:0% +distribution okay so we we were talking +about estimating the mean or estimating + + align:start position:0% +about estimating the mean or estimating + + + align:start position:0% +about estimating the mean or estimating +the variance or something like that that + + align:start position:0% +the variance or something like that that + + + align:start position:0% +the variance or something like that that +some other parameter that characterizes + + align:start position:0% +some other parameter that characterizes + + + align:start position:0% +some other parameter that characterizes +uh you know sort of a um Univar + + align:start position:0% +uh you know sort of a um Univar + + + align:start position:0% +uh you know sort of a um Univar +distribution but so much of what we care + + align:start position:0% +distribution but so much of what we care + + + align:start position:0% +distribution but so much of what we care +about in social science and in lots of + + align:start position:0% +about in social science and in lots of + + + align:start position:0% +about in social science and in lots of +other settings I mean maybe sort of most + + align:start position:0% +other settings I mean maybe sort of most + + + align:start position:0% +other settings I mean maybe sort of most +other settings involves joint + + align:start position:0% +other settings involves joint + + + align:start position:0% +other settings involves joint +distributions though and so we really + + align:start position:0% +distributions though and so we really + + + align:start position:0% +distributions though and so we really +have to be concerned with how to + + align:start position:0% +have to be concerned with how to + + + align:start position:0% +have to be concerned with how to +estimate parameters characterizing + + align:start position:0% +estimate parameters characterizing + + + align:start position:0% +estimate parameters characterizing +either joint distributions or + + align:start position:0% +either joint distributions or + + + align:start position:0% +either joint distributions or +conditional distributions or something + + align:start position:0% +conditional distributions or something + + + align:start position:0% +conditional distributions or something +like that + + align:start position:0% +like that + + + align:start position:0% +like that +okay so Esther's discussion of causality + + align:start position:0% +okay so Esther's discussion of causality + + + align:start position:0% +okay so Esther's discussion of causality +was really the beginning of this and it + + align:start position:0% +was really the beginning of this and it + + + align:start position:0% +was really the beginning of this and it +was also we could think of it as a + + align:start position:0% +was also we could think of it as a + + + align:start position:0% +was also we could think of it as a +special case okay so + + align:start position:0% +special case okay so + + + align:start position:0% +special case okay so +um you can think of much of what she did + + align:start position:0% +um you can think of much of what she did + + + align:start position:0% +um you can think of much of what she did +is considering the joint distribution uh + + align:start position:0% +is considering the joint distribution uh + + + align:start position:0% +is considering the joint distribution uh +of two variables where one was simply a + + align:start position:0% +of two variables where one was simply a + + + align:start position:0% +of two variables where one was simply a +coin flip um so if you you flip the coin + + align:start position:0% +coin flip um so if you you flip the coin + + + align:start position:0% +coin flip um so if you you flip the coin +and it comes up heads that's a treatment + + align:start position:0% +and it comes up heads that's a treatment + + + align:start position:0% +and it comes up heads that's a treatment +that uh observation has a treatment and + + align:start position:0% +that uh observation has a treatment and + + + align:start position:0% +that uh observation has a treatment and +if it comes up tails that observation is + + align:start position:0% +if it comes up tails that observation is + + + align:start position:0% +if it comes up tails that observation is +assigned to control okay and then the + + align:start position:0% +assigned to control okay and then the + + + align:start position:0% +assigned to control okay and then the +other random variable that was defined + + align:start position:0% +other random variable that was defined + + + align:start position:0% +other random variable that was defined +on this uh sample uh was the outcome of + + align:start position:0% +on this uh sample uh was the outcome of + + + align:start position:0% +on this uh sample uh was the outcome of +Interest say infant mortality or website + + align:start position:0% +Interest say infant mortality or website + + + align:start position:0% +Interest say infant mortality or website +Effectiveness or something like that + + align:start position:0% +Effectiveness or something like that + + + align:start position:0% +Effectiveness or something like that +okay so we didn't always uh talk about + + align:start position:0% +okay so we didn't always uh talk about + + + align:start position:0% +okay so we didn't always uh talk about +oh and I should say in fact we were + + align:start position:0% +oh and I should say in fact we were + + + align:start position:0% +oh and I should say in fact we were +mostly concerned with the conditional + + align:start position:0% +mostly concerned with the conditional + + + align:start position:0% +mostly concerned with the conditional +distribution of the outcome variable + + align:start position:0% +distribution of the outcome variable + + + align:start position:0% +distribution of the outcome variable +conditional on this coin flip okay so we + + align:start position:0% +conditional on this coin flip okay so we + + + align:start position:0% +conditional on this coin flip okay so we +can and we did think of the treatment + + align:start position:0% +can and we did think of the treatment + + + align:start position:0% +can and we did think of the treatment +and the control group sometimes as being + + align:start position:0% +and the control group sometimes as being + + + align:start position:0% +and the control group sometimes as being +sort of two separate populations and so + + align:start position:0% +sort of two separate populations and so + + + align:start position:0% +sort of two separate populations and so +then we asked the question well how + + align:start position:0% +then we asked the question well how + + + align:start position:0% +then we asked the question well how +could we test whether uh they had a + + align:start position:0% +could we test whether uh they had a + + + align:start position:0% +could we test whether uh they had a +common mean okay but we can also think + + align:start position:0% +common mean okay but we can also think + + + align:start position:0% +common mean okay but we can also think +of them as having one population and a + + align:start position:0% +of them as having one population and a + + + align:start position:0% +of them as having one population and a +joint distribution of two random + + align:start position:0% +joint distribution of two random + + + align:start position:0% +joint distribution of two random +variables on that population okay and + + align:start position:0% +variables on that population okay and + + + align:start position:0% +variables on that population okay and +what we're really what we were really + + align:start position:0% +what we're really what we were really + + + align:start position:0% +what we're really what we were really +doing is estimating conditional means a + + align:start position:0% +doing is estimating conditional means a + + + align:start position:0% +doing is estimating conditional means a +conditional on this coin flip a random + + align:start position:0% +conditional on this coin flip a random + + + align:start position:0% +conditional on this coin flip a random +variable okay so these are these are + + align:start position:0% +variable okay so these are these are + + + align:start position:0% +variable okay so these are these are +sort of two different ways to think + + align:start position:0% +sort of two different ways to think + + + align:start position:0% +sort of two different ways to think +about like random control trials and and + + align:start position:0% +about like random control trials and and + + + align:start position:0% +about like random control trials and and +the the things that Esther was talking + + align:start position:0% +the the things that Esther was talking + + + align:start position:0% +the the things that Esther was talking +about the C uh last couple of lectures + + align:start position:0% +about the C uh last couple of lectures + + + align:start position:0% +about the C uh last couple of lectures +okay and they're they're sort of + + align:start position:0% +okay and they're they're sort of + + + align:start position:0% +okay and they're they're sort of +equivalent uh ways to think about + + align:start position:0% +equivalent uh ways to think about + + + align:start position:0% +equivalent uh ways to think about +them okay now I want to pose a question + + align:start position:0% +them okay now I want to pose a question + + + align:start position:0% +them okay now I want to pose a question +What If instead of a coin flip the + + align:start position:0% +What If instead of a coin flip the + + + align:start position:0% +What If instead of a coin flip the +second random variable is continuous + + align:start position:0% +second random variable is continuous + + + align:start position:0% +second random variable is continuous +instead okay so let's suppose we have a + + align:start position:0% +instead okay so let's suppose we have a + + + align:start position:0% +instead okay so let's suppose we have a +random variable it can take on a whole + + align:start position:0% +random variable it can take on a whole + + + align:start position:0% +random variable it can take on a whole +range of values we can still think of it + + align:start position:0% +range of values we can still think of it + + + align:start position:0% +range of values we can still think of it +as being sort of levels of treatment or + + align:start position:0% +as being sort of levels of treatment or + + + align:start position:0% +as being sort of levels of treatment or +something like that we don't necessarily + + align:start position:0% +something like that we don't necessarily + + + align:start position:0% +something like that we don't necessarily +have to think of it that way but you can + + align:start position:0% +have to think of it that way but you can + + + align:start position:0% +have to think of it that way but you can +think of it that way uh but instead of + + align:start position:0% +think of it that way uh but instead of + + + align:start position:0% +think of it that way uh but instead of +just being a coin flip treatment control + + align:start position:0% +just being a coin flip treatment control + + + align:start position:0% +just being a coin flip treatment control +um it can uh you know take on uh um many + + align:start position:0% +um it can uh you know take on uh um many + + + align:start position:0% +um it can uh you know take on uh um many +different values okay how do we analyze + + align:start position:0% +different values okay how do we analyze + + + align:start position:0% +different values okay how do we analyze +the conditional distribution of our + + align:start position:0% +the conditional distribution of our + + + align:start position:0% +the conditional distribution of our +outcome variable conditional on + + align:start position:0% +outcome variable conditional on + + + align:start position:0% +outcome variable conditional on +something like a continuous random + + align:start position:0% +something like a continuous random + + + align:start position:0% +something like a continuous random +variable and furthermore how do we + + align:start position:0% +variable and furthermore how do we + + + align:start position:0% +variable and furthermore how do we +estimate the parameters of that + + align:start position:0% +estimate the parameters of that + + + align:start position:0% +estimate the parameters of that +conditional distribution and that's what + + align:start position:0% +conditional distribution and that's what + + + align:start position:0% +conditional distribution and that's what +we're going to be talking about + + align:start position:0% +we're going to be talking about + + + align:start position:0% +we're going to be talking about +today okay the Workhorse model mod we + + align:start position:0% +today okay the Workhorse model mod we + + + align:start position:0% +today okay the Workhorse model mod we +use is called the linear model and the + + align:start position:0% +use is called the linear model and the + + + align:start position:0% +use is called the linear model and the +way that we estimate the parameters in a + + align:start position:0% +way that we estimate the parameters in a + + + align:start position:0% +way that we estimate the parameters in a +linear model is linear regression or + + align:start position:0% +linear model is linear regression or + + + align:start position:0% +linear model is linear regression or +that's typically the way that we + + align:start position:0% +that's typically the way that we + + + align:start position:0% +that's typically the way that we +estimate + + align:start position:0% +estimate + + + align:start position:0% +estimate +them so why do we care about joint + + align:start position:0% +them so why do we care about joint + + + align:start position:0% +them so why do we care about joint +distributions and estimating the + + align:start position:0% +distributions and estimating the + + + align:start position:0% +distributions and estimating the +parameters associated with them well + + align:start position:0% +parameters associated with them well + + + align:start position:0% +parameters associated with them well +we've seen a bunch of examples but let + + align:start position:0% +we've seen a bunch of examples but let + + + align:start position:0% +we've seen a bunch of examples but let +me just sort of throw out a couple more + + align:start position:0% +me just sort of throw out a couple more + + + align:start position:0% +me just sort of throw out a couple more +um so the the we might be interested in + + align:start position:0% +um so the the we might be interested in + + + align:start position:0% +um so the the we might be interested in +prediction we might be interested in + + align:start position:0% +prediction we might be interested in + + + align:start position:0% +prediction we might be interested in +determining causality and we might just + + align:start position:0% +determining causality and we might just + + + align:start position:0% +determining causality and we might just +be interested in understanding the world + + align:start position:0% +be interested in understanding the world + + + align:start position:0% +be interested in understanding the world +better so let me give you sort of + + align:start position:0% +better so let me give you sort of + + + align:start position:0% +better so let me give you sort of +examples of each of + + align:start position:0% + + + + align:start position:0% + +these okay so let's + + align:start position:0% +these okay so let's + + + align:start position:0% +these okay so let's +suppose uh I let's let's imagine that + + align:start position:0% +suppose uh I let's let's imagine that + + + align:start position:0% +suppose uh I let's let's imagine that +I'm the type of person who reads XKCD + + align:start position:0% +I'm the type of person who reads XKCD + + + align:start position:0% +I'm the type of person who reads XKCD +comics and I'm also the type of person + + align:start position:0% +comics and I'm also the type of person + + + align:start position:0% +comics and I'm also the type of person +who is likely to click on an ad for a + + align:start position:0% +who is likely to click on an ad for a + + + align:start position:0% +who is likely to click on an ad for a +t-shirt bearing the Russian covered + + align:start position:0% +t-shirt bearing the Russian covered + + + align:start position:0% +t-shirt bearing the Russian covered +design of Moby Dick okay so who might be + + align:start position:0% +design of Moby Dick okay so who might be + + + align:start position:0% +design of Moby Dick okay so who might be +interested in whether that statement is + + align:start position:0% +interested in whether that statement is + + + align:start position:0% +interested in whether that statement is +true Amazon or whoever's selling the + + align:start position:0% +true Amazon or whoever's selling the + + + align:start position:0% +true Amazon or whoever's selling the +t-shirts with the sort of cover of uh + + align:start position:0% +t-shirts with the sort of cover of uh + + + align:start position:0% +t-shirts with the sort of cover of uh +the Russian Moby Dick on them right okay + + align:start position:0% +the Russian Moby Dick on them right okay + + + align:start position:0% +the Russian Moby Dick on them right okay +so anyone basically anyone who wants to + + align:start position:0% +so anyone basically anyone who wants to + + + align:start position:0% +so anyone basically anyone who wants to +sell me that product or anyone who wants + + align:start position:0% +sell me that product or anyone who wants + + + align:start position:0% +sell me that product or anyone who wants +to serve me an ad that might get me to + + align:start position:0% +to serve me an ad that might get me to + + + align:start position:0% +to serve me an ad that might get me to +click on the ad and buy the product + + align:start position:0% +click on the ad and buy the product + + + align:start position:0% +click on the ad and buy the product +cares about whether the the kind of + + align:start position:0% +cares about whether the the kind of + + + align:start position:0% +cares about whether the the kind of +person who reads XK kcd Comics is also + + align:start position:0% +person who reads XK kcd Comics is also + + + align:start position:0% +person who reads XK kcd Comics is also +the kind of person who buys such + + align:start position:0% +the kind of person who buys such + + + align:start position:0% +the kind of person who buys such +t-shirts it turns out I am such a person + + align:start position:0% +t-shirts it turns out I am such a person + + + align:start position:0% +t-shirts it turns out I am such a person +I do both of those things and I thought + + align:start position:0% +I do both of those things and I thought + + + align:start position:0% +I do both of those things and I thought +I'll just show you my favorite XKCD + + align:start position:0% +I'll just show you my favorite XKCD + + + align:start position:0% +I'll just show you my favorite XKCD +comic um and let you read it for a + + align:start position:0% +comic um and let you read it for a + + + align:start position:0% +comic um and let you read it for a +second and I did just order this t-shirt + + align:start position:0% +second and I did just order this t-shirt + + + align:start position:0% +second and I did just order this t-shirt +um from out of print U which I think is + + align:start position:0% +um from out of print U which I think is + + + align:start position:0% +um from out of print U which I think is +a pretty nice looking + + align:start position:0% + + + + align:start position:0% + +t-shirt that's for all you course six + + align:start position:0% +t-shirt that's for all you course six + + + align:start position:0% +t-shirt that's for all you course six +Majors I guess + + align:start position:0% + + + + align:start position:0% + +okay can I go + + align:start position:0% +okay can I go + + + align:start position:0% +okay can I go +ahead okay so so anyhow this this is + + align:start position:0% +ahead okay so so anyhow this this is + + + align:start position:0% +ahead okay so so anyhow this this is +there's nothing about causality in this + + align:start position:0% +there's nothing about causality in this + + + align:start position:0% +there's nothing about causality in this +example right I mean it's not I didn't + + align:start position:0% +example right I mean it's not I didn't + + + align:start position:0% +example right I mean it's not I didn't +read the xkcd comic and think oh now I + + align:start position:0% +read the xkcd comic and think oh now I + + + align:start position:0% +read the xkcd comic and think oh now I +have to go buy this sort of t-shirt it's + + align:start position:0% +have to go buy this sort of t-shirt it's + + + align:start position:0% +have to go buy this sort of t-shirt it's +just that I'm the kind of person who + + align:start position:0% +just that I'm the kind of person who + + + align:start position:0% +just that I'm the kind of person who +might do both of those things so someone + + align:start position:0% +might do both of those things so someone + + + align:start position:0% +might do both of those things so someone +wanting to sell me that t-shirt would + + align:start position:0% +wanting to sell me that t-shirt would + + + align:start position:0% +wanting to sell me that t-shirt would +like to know that so they can serve me + + align:start position:0% +like to know that so they can serve me + + + align:start position:0% +like to know that so they can serve me +the ad when I'm reading XKCD + + align:start position:0% +the ad when I'm reading XKCD + + + align:start position:0% +the ad when I'm reading XKCD +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +we might want to determine causality + + align:start position:0% +we might want to determine causality + + + align:start position:0% +we might want to determine causality +Esther talked about a number of examples + + align:start position:0% +Esther talked about a number of examples + + + align:start position:0% +Esther talked about a number of examples +um in this vein so let's suppose I I + + align:start position:0% +um in this vein so let's suppose I I + + + align:start position:0% +um in this vein so let's suppose I I +want to know the the answer to the + + align:start position:0% +want to know the the answer to the + + + align:start position:0% +want to know the the answer to the +following question if I give my dog a + + align:start position:0% +following question if I give my dog a + + + align:start position:0% +following question if I give my dog a +treat every time he does not bark at + + align:start position:0% +treat every time he does not bark at + + + align:start position:0% +treat every time he does not bark at +another dog walking by our house will he + + align:start position:0% +another dog walking by our house will he + + + align:start position:0% +another dog walking by our house will he +stop barking at other + + align:start position:0% +stop barking at other + + + align:start position:0% +stop barking at other +dogs so that's the kind of you know sort + + align:start position:0% +dogs so that's the kind of you know sort + + + align:start position:0% +dogs so that's the kind of you know sort +of a causal question I might want to + + align:start position:0% +of a causal question I might want to + + + align:start position:0% +of a causal question I might want to +answer to right the answer by the way is + + align:start position:0% +answer to right the answer by the way is + + + align:start position:0% +answer to right the answer by the way is +no + + align:start position:0% +no + + + align:start position:0% +no +um and the only reason I brought up this + + align:start position:0% +um and the only reason I brought up this + + + align:start position:0% +um and the only reason I brought up this +example is so I would have an excuse to + + align:start position:0% +example is so I would have an excuse to + + + align:start position:0% +example is so I would have an excuse to +show you my sweet little + + align:start position:0% +show you my sweet little + + + align:start position:0% +show you my sweet little +dog okay but I have not carried out such + + align:start position:0% +dog okay but I have not carried out such + + + align:start position:0% +dog okay but I have not carried out such +a + + align:start position:0% +a + + + align:start position:0% +a +statistical um such a statistical + + align:start position:0% +statistical um such a statistical + + + align:start position:0% +statistical um such a statistical +analysis I'm pretty sure the answer is + + align:start position:0% +analysis I'm pretty sure the answer is + + + align:start position:0% +analysis I'm pretty sure the answer is +no though okay and then maybe we just + + align:start position:0% +no though okay and then maybe we just + + + align:start position:0% +no though okay and then maybe we just +care about joint distributions um + + align:start position:0% +care about joint distributions um + + + align:start position:0% +care about joint distributions um +because we want to understand the world + + align:start position:0% +because we want to understand the world + + + align:start position:0% +because we want to understand the world +better so if we were behavioral + + align:start position:0% +better so if we were behavioral + + + align:start position:0% +better so if we were behavioral +economists we might be interested in the + + align:start position:0% +economists we might be interested in the + + + align:start position:0% +economists we might be interested in the +following question are people when are + + align:start position:0% +following question are people when are + + + align:start position:0% +following question are people when are +people only influenced by Price quality + + align:start position:0% +people only influenced by Price quality + + + align:start position:0% +people only influenced by Price quality +characteristics and the uh expected + + align:start position:0% +characteristics and the uh expected + + + align:start position:0% +characteristics and the uh expected +weather that they have in the area of + + align:start position:0% +weather that they have in the area of + + + align:start position:0% +weather that they have in the area of +the country where they live um when + + align:start position:0% +the country where they live um when + + + align:start position:0% +the country where they live um when +they're deciding whether to purchase a + + align:start position:0% +they're deciding whether to purchase a + + + align:start position:0% +they're deciding whether to purchase a +convertible or are they also influenced + + align:start position:0% +convertible or are they also influenced + + + align:start position:0% +convertible or are they also influenced +by the weather on that particular day + + align:start position:0% +by the weather on that particular day + + + align:start position:0% +by the weather on that particular day +okay so behavioral economists might be + + align:start position:0% +okay so behavioral economists might be + + + align:start position:0% +okay so behavioral economists might be +interested in a question like this + + align:start position:0% +interested in a question like this + + + align:start position:0% +interested in a question like this +because um they want to understand you + + align:start position:0% +because um they want to understand you + + + align:start position:0% +because um they want to understand you +know sort of what influences sort of + + align:start position:0% +know sort of what influences sort of + + + align:start position:0% +know sort of what influences sort of +economic decisions that agents make do + + align:start position:0% +economic decisions that agents make do + + + align:start position:0% +economic decisions that agents make do +they make sort of rational decisions or + + align:start position:0% +they make sort of rational decisions or + + + align:start position:0% +they make sort of rational decisions or +you know are they deciding to buy a a + + align:start position:0% +you know are they deciding to buy a a + + + align:start position:0% +you know are they deciding to buy a a +convertible because they know what the + + align:start position:0% +convertible because they know what the + + + align:start position:0% +convertible because they know what the +weather is going to be like over the + + align:start position:0% +weather is going to be like over the + + + align:start position:0% +weather is going to be like over the +next five years and that's sort of the + + align:start position:0% +next five years and that's sort of the + + + align:start position:0% +next five years and that's sort of the +the period of time they're going to own + + align:start position:0% +the period of time they're going to own + + + align:start position:0% +the period of time they're going to own +the car or are they likely to make these + + align:start position:0% +the car or are they likely to make these + + + align:start position:0% +the car or are they likely to make these +sort of uh decisions that are hard to + + align:start position:0% +sort of uh decisions that are hard to + + + align:start position:0% +sort of uh decisions that are hard to +justified by any sort of rational + + align:start position:0% +justified by any sort of rational + + + align:start position:0% +justified by any sort of rational +economic model like gosh it's really + + align:start position:0% +economic model like gosh it's really + + + align:start position:0% +economic model like gosh it's really +sunny today maybe I'll buy a convertible + + align:start position:0% +sunny today maybe I'll buy a convertible + + + align:start position:0% +sunny today maybe I'll buy a convertible +that I'm going to now have for the next + + align:start position:0% +that I'm going to now have for the next + + + align:start position:0% +that I'm going to now have for the next +5 years well uh turns + + align:start position:0% +5 years well uh turns + + + align:start position:0% +5 years well uh turns +out that they are and this was a recent + + align:start position:0% +out that they are and this was a recent + + + align:start position:0% +out that they are and this was a recent +paper in the QJ the psy psychological + + align:start position:0% +paper in the QJ the psy psychological + + + align:start position:0% +paper in the QJ the psy psychological +effect of weather and car purchases uh + + align:start position:0% +effect of weather and car purchases uh + + + align:start position:0% +effect of weather and car purchases uh +that uh fairly um uh convincing + + align:start position:0% +that uh fairly um uh convincing + + + align:start position:0% +that uh fairly um uh convincing +convincingly established that people are + + align:start position:0% +convincingly established that people are + + + align:start position:0% +convincingly established that people are +in fact influenced by the weather on the + + align:start position:0% +in fact influenced by the weather on the + + + align:start position:0% +in fact influenced by the weather on the +day that they make a purchase uh when + + align:start position:0% +day that they make a purchase uh when + + + align:start position:0% +day that they make a purchase uh when +it's when the weather's bad snowy uh + + align:start position:0% +it's when the weather's bad snowy uh + + + align:start position:0% +it's when the weather's bad snowy uh +they're more likely to to um make a + + align:start position:0% +they're more likely to to um make a + + + align:start position:0% +they're more likely to to um make a +purchase of an SUV and this is + + align:start position:0% +purchase of an SUV and this is + + + align:start position:0% +purchase of an SUV and this is +controlling for uh you know sort of the + + align:start position:0% +controlling for uh you know sort of the + + + align:start position:0% +controlling for uh you know sort of the +expected weather uh you know sort of + + align:start position:0% +expected weather uh you know sort of + + + align:start position:0% +expected weather uh you know sort of +going forward and likewise if it's sunny + + align:start position:0% +going forward and likewise if it's sunny + + + align:start position:0% +going forward and likewise if it's sunny +they're more likely to buy a convertible + + align:start position:0% +they're more likely to buy a convertible + + + align:start position:0% +they're more likely to buy a convertible +controlling for the expected weather so + + align:start position:0% +controlling for the expected weather so + + + align:start position:0% +controlling for the expected weather so +anyhow I I actually I I went to a talk I + + align:start position:0% +anyhow I I actually I I went to a talk I + + + align:start position:0% +anyhow I I actually I I went to a talk I +saw this paper a few years ago I was + + align:start position:0% +saw this paper a few years ago I was + + + align:start position:0% +saw this paper a few years ago I was +convinced by the results but I also sort + + align:start position:0% +convinced by the results but I also sort + + + align:start position:0% +convinced by the results but I also sort +of chuckled I thought oh that's so + + align:start position:0% +of chuckled I thought oh that's so + + + align:start position:0% +of chuckled I thought oh that's so +ridiculous what how could someone be so + + align:start position:0% +ridiculous what how could someone be so + + + align:start position:0% +ridiculous what how could someone be so +influenced Well turns out that last + + align:start position:0% +influenced Well turns out that last + + + align:start position:0% +influenced Well turns out that last +summer um I decided I was going to buy + + align:start position:0% +summer um I decided I was going to buy + + + align:start position:0% +summer um I decided I was going to buy +this + + align:start position:0% +this + + + align:start position:0% +this +car and the car so I was waiting for the + + align:start position:0% +car and the car so I was waiting for the + + + align:start position:0% +car and the car so I was waiting for the +2016 model to come out and it was a + + align:start position:0% +2016 model to come out and it was a + + + align:start position:0% +2016 model to come out and it was a +really hot model of car I couldn't even + + align:start position:0% +really hot model of car I couldn't even + + + align:start position:0% +really hot model of car I couldn't even +uh test drive it I mean it was like + + align:start position:0% +uh test drive it I mean it was like + + + align:start position:0% +uh test drive it I mean it was like +really hard to sort of and I thought + + align:start position:0% +really hard to sort of and I thought + + + align:start position:0% +really hard to sort of and I thought +okay I thought about the QJ paper and I + + align:start position:0% +okay I thought about the QJ paper and I + + + align:start position:0% +okay I thought about the QJ paper and I +said all I have to do is wait until the + + align:start position:0% +said all I have to do is wait until the + + + align:start position:0% +said all I have to do is wait until the +weather gets bad and then the the you + + align:start position:0% +weather gets bad and then the the you + + + align:start position:0% +weather gets bad and then the the you +know models of this car will sort of + + align:start position:0% +know models of this car will sort of + + + align:start position:0% +know models of this car will sort of +build up on the Dealer's lots and I'll + + align:start position:0% +build up on the Dealer's lots and I'll + + + align:start position:0% +build up on the Dealer's lots and I'll +just Waltz in be able to buy would maybe + + align:start position:0% +just Waltz in be able to buy would maybe + + + align:start position:0% +just Waltz in be able to buy would maybe +I'll even get a deal on it right well + + align:start position:0% +I'll even get a deal on it right well + + + align:start position:0% +I'll even get a deal on it right well +turns out as soon as the weather got bad + + align:start position:0% +turns out as soon as the weather got bad + + + align:start position:0% +turns out as soon as the weather got bad +I kind of lost my interest in buying the + + align:start position:0% +I kind of lost my interest in buying the + + + align:start position:0% +I kind of lost my interest in buying the +convertible and I just ended up buying a + + align:start position:0% +convertible and I just ended up buying a + + + align:start position:0% +convertible and I just ended up buying a +sedan + + align:start position:0% + + + + align:start position:0% + +so okay so in each of these examples we + + align:start position:0% +so okay so in each of these examples we + + + align:start position:0% +so okay so in each of these examples we +had two or more random variables that + + align:start position:0% +had two or more random variables that + + + align:start position:0% +had two or more random variables that +had a joint distribution and we wanted + + align:start position:0% +had a joint distribution and we wanted + + + align:start position:0% +had a joint distribution and we wanted +to know the characteristics of their + + align:start position:0% +to know the characteristics of their + + + align:start position:0% +to know the characteristics of their +joint distribution in order to answer + + align:start position:0% +joint distribution in order to answer + + + align:start position:0% +joint distribution in order to answer +the questions that we were interested + + align:start position:0% +the questions that we were interested + + + align:start position:0% +the questions that we were interested +in + + align:start position:0% +in + + + align:start position:0% +in +okay so how do we do this well I told + + align:start position:0% +okay so how do we do this well I told + + + align:start position:0% +okay so how do we do this well I told +you already the Workhorse model to do + + align:start position:0% +you already the Workhorse model to do + + + align:start position:0% +you already the Workhorse model to do +this is the linear model so let me + + align:start position:0% +this is the linear model so let me + + + align:start position:0% +this is the linear model so let me +introduce the lineate model by variant + + align:start position:0% +introduce the lineate model by variant + + + align:start position:0% +introduce the lineate model by variant +style we'll sort of generalize that + + align:start position:0% +style we'll sort of generalize that + + + align:start position:0% +style we'll sort of generalize that +later um and let me just sort of go + + align:start position:0% +later um and let me just sort of go + + + align:start position:0% +later um and let me just sort of go +through and Define what the things in + + align:start position:0% +through and Define what the things in + + + align:start position:0% +through and Define what the things in +this linear model are okay and then + + align:start position:0% +this linear model are okay and then + + + align:start position:0% +this linear model are okay and then +we'll talk about uh sort of properties + + align:start position:0% +we'll talk about uh sort of properties + + + align:start position:0% +we'll talk about uh sort of properties +of it we'll talk about how to estimate + + align:start position:0% +of it we'll talk about how to estimate + + + align:start position:0% +of it we'll talk about how to estimate +the parameters in it and so forth okay + + align:start position:0% +the parameters in it and so forth okay + + + align:start position:0% +the parameters in it and so forth okay +well the linear model is is a model that + + align:start position:0% +well the linear model is is a model that + + + align:start position:0% +well the linear model is is a model that +sort of establishes a relationship + + align:start position:0% +sort of establishes a relationship + + + align:start position:0% +sort of establishes a relationship +between two random variables on which we + + align:start position:0% +between two random variables on which we + + + align:start position:0% +between two random variables on which we +have repeated observations so these are + + align:start position:0% +have repeated observations so these are + + + align:start position:0% +have repeated observations so these are +uh Y and X so Y is what we call the + + align:start position:0% +uh Y and X so Y is what we call the + + + align:start position:0% +uh Y and X so Y is what we call the +dependent variable okay sometimes you + + align:start position:0% +dependent variable okay sometimes you + + + align:start position:0% +dependent variable okay sometimes you +will re hear that referred to as the + + align:start position:0% +will re hear that referred to as the + + + align:start position:0% +will re hear that referred to as the +explained variable or the + + align:start position:0% +explained variable or the + + + align:start position:0% +explained variable or the +regressand I would say hardly ever do I + + align:start position:0% +regressand I would say hardly ever do I + + + align:start position:0% +regressand I would say hardly ever do I +hear those terms but those are both you + + align:start position:0% +hear those terms but those are both you + + + align:start position:0% +hear those terms but those are both you +know sort of legitimate terms I guess + + align:start position:0% +know sort of legitimate terms I guess + + + align:start position:0% +know sort of legitimate terms I guess +for the dependent variable + + align:start position:0% +for the dependent variable + + + align:start position:0% +for the dependent variable +and then the X variable is typically + + align:start position:0% +and then the X variable is typically + + + align:start position:0% +and then the X variable is typically +called the regressor or explanatory + + align:start position:0% +called the regressor or explanatory + + + align:start position:0% +called the regressor or explanatory +variable or sometimes called the in + + align:start position:0% +variable or sometimes called the in + + + align:start position:0% +variable or sometimes called the in +independent variable so even though like + + align:start position:0% +independent variable so even though like + + + align:start position:0% +independent variable so even though like +regressor and regress and seem to go + + align:start position:0% +regressor and regress and seem to go + + + align:start position:0% +regressor and regress and seem to go +together or independent variable + + align:start position:0% +together or independent variable + + + align:start position:0% +together or independent variable +independent variables seem to go + + align:start position:0% +independent variables seem to go + + + align:start position:0% +independent variables seem to go +together that that's not the way these + + align:start position:0% +together that that's not the way these + + + align:start position:0% +together that that's not the way these +terms are used typically we refer to the + + align:start position:0% +terms are used typically we refer to the + + + align:start position:0% +terms are used typically we refer to the +uh the Y variable as the dependent + + align:start position:0% +uh the Y variable as the dependent + + + align:start position:0% +uh the Y variable as the dependent +variable and typically you'll refer to + + align:start position:0% +variable and typically you'll refer to + + + align:start position:0% +variable and typically you'll refer to +the X variable as either the regress or + + align:start position:0% +the X variable as either the regress or + + + align:start position:0% +the X variable as either the regress or +the explanatory + + align:start position:0% +the explanatory + + + align:start position:0% +the explanatory +variable okay and there there some + + align:start position:0% +variable okay and there there some + + + align:start position:0% +variable okay and there there some +reasons for that but this is just + + align:start position:0% +reasons for that but this is just + + + align:start position:0% +reasons for that but this is just +basically what people do just so you're + + align:start position:0% +basically what people do just so you're + + + align:start position:0% +basically what people do just so you're +uh familiar with the + + align:start position:0% +uh familiar with the + + + align:start position:0% +uh familiar with the +terms and then we have a third random + + align:start position:0% +terms and then we have a third random + + + align:start position:0% +terms and then we have a third random +variable thrown into the mix an + + align:start position:0% +variable thrown into the mix an + + + align:start position:0% +variable thrown into the mix an +unobserved random variable and we call + + align:start position:0% +unobserved random variable and we call + + + align:start position:0% +unobserved random variable and we call +that the + + align:start position:0% +that the + + + align:start position:0% +that the +error + + align:start position:0% + + + + align:start position:0% + +okay we also have two parameters in this + + align:start position:0% +okay we also have two parameters in this + + + align:start position:0% +okay we also have two parameters in this +model or at least two obvious parameters + + align:start position:0% +model or at least two obvious parameters + + + align:start position:0% +model or at least two obvious parameters +we have another one that we'll talk + + align:start position:0% +we have another one that we'll talk + + + align:start position:0% +we have another one that we'll talk +about later uh and these are uh + + align:start position:0% +about later uh and these are uh + + + align:start position:0% +about later uh and these are uh +parameters we want to estimate and we + + align:start position:0% +parameters we want to estimate and we + + + align:start position:0% +parameters we want to estimate and we +call these the regression + + align:start position:0% + + + + align:start position:0% + +coefficients okay so what does this + + align:start position:0% +coefficients okay so what does this + + + align:start position:0% +coefficients okay so what does this +model do it allows us to consider the + + align:start position:0% +model do it allows us to consider the + + + align:start position:0% +model do it allows us to consider the +mean of a random variable y as a + + align:start position:0% +mean of a random variable y as a + + + align:start position:0% +mean of a random variable y as a +function of another random variable X + + align:start position:0% +function of another random variable X + + + align:start position:0% +function of another random variable X +and if we obtain estimates for beta KN + + align:start position:0% +and if we obtain estimates for beta KN + + + align:start position:0% +and if we obtain estimates for beta KN +and beta 1 then we have an estimated + + align:start position:0% +and beta 1 then we have an estimated + + + align:start position:0% +and beta 1 then we have an estimated +conditional mean function for + + align:start position:0% +conditional mean function for + + + align:start position:0% +conditional mean function for +y + + align:start position:0% + + + + align:start position:0% + +so let's add some basic assumptions and + + align:start position:0% +so let's add some basic assumptions and + + + align:start position:0% +so let's add some basic assumptions and +then we will get to something called the + + align:start position:0% +then we will get to something called the + + + align:start position:0% +then we will get to something called the +classical linear regression model when + + align:start position:0% +classical linear regression model when + + + align:start position:0% +classical linear regression model when +we sort of pile on a few more + + align:start position:0% +we sort of pile on a few more + + + align:start position:0% +we sort of pile on a few more +assumptions okay first of all let's + + align:start position:0% +assumptions okay first of all let's + + + align:start position:0% +assumptions okay first of all let's +assume that our two uh random variables + + align:start position:0% +assume that our two uh random variables + + + align:start position:0% +assume that our two uh random variables +on the right side are uncorrelated okay + + align:start position:0% +on the right side are uncorrelated okay + + + align:start position:0% +on the right side are uncorrelated okay +so X subbi and Epsilon subi are uh + + align:start position:0% +so X subbi and Epsilon subi are uh + + + align:start position:0% +so X subbi and Epsilon subi are uh +uncorrelated random + + align:start position:0% +uncorrelated random + + + align:start position:0% +uncorrelated random +variables um let's + + align:start position:0% +variables um let's + + + align:start position:0% +variables um let's +assume uh that this what this uh second + + align:start position:0% +assume uh that this what this uh second + + + align:start position:0% +assume uh that this what this uh second +assumption called identification means + + align:start position:0% +assumption called identification means + + + align:start position:0% +assumption called identification means +is just basically that we have some + + align:start position:0% +is just basically that we have some + + + align:start position:0% +is just basically that we have some +variation in our X variable I'm going to + + align:start position:0% +variation in our X variable I'm going to + + + align:start position:0% +variation in our X variable I'm going to +show you a picture illustrating this in + + align:start position:0% +show you a picture illustrating this in + + + align:start position:0% +show you a picture illustrating this in +a second but basically that just means + + align:start position:0% +a second but basically that just means + + + align:start position:0% +a second but basically that just means +that um the X variable is not the re the + + align:start position:0% +that um the X variable is not the re the + + + align:start position:0% +that um the X variable is not the re the +sort of um repeated observations on the + + align:start position:0% +sort of um repeated observations on the + + + align:start position:0% +sort of um repeated observations on the +X variable are not all on the same uh + + align:start position:0% +X variable are not all on the same uh + + + align:start position:0% +X variable are not all on the same uh +Point okay we're going to assume that uh + + align:start position:0% +Point okay we're going to assume that uh + + + align:start position:0% +Point okay we're going to assume that uh +the expectation of our error is equal to + + align:start position:0% +the expectation of our error is equal to + + + align:start position:0% +the expectation of our error is equal to +zero we assume a + + align:start position:0% +zero we assume a + + + align:start position:0% +zero we assume a +homoskedasticity which means that the + + align:start position:0% +homoskedasticity which means that the + + + align:start position:0% +homoskedasticity which means that the +expectation of our error squared is + + align:start position:0% +expectation of our error squared is + + + align:start position:0% +expectation of our error squared is +equal to Sigma squar for all I and we're + + align:start position:0% +equal to Sigma squar for all I and we're + + + align:start position:0% +equal to Sigma squar for all I and we're +going to also assume uh that we do not + + align:start position:0% +going to also assume uh that we do not + + + align:start position:0% +going to also assume uh that we do not +have serial correlation so in particular + + align:start position:0% +have serial correlation so in particular + + + align:start position:0% +have serial correlation so in particular +the expectation of Epsilon I Epsilon J + + align:start position:0% +the expectation of Epsilon I Epsilon J + + + align:start position:0% +the expectation of Epsilon I Epsilon J +is equal to zero for all I and J okay so + + align:start position:0% +is equal to zero for all I and J okay so + + + align:start position:0% +is equal to zero for all I and J okay so +let me talk about each one of these in + + align:start position:0% +let me talk about each one of these in + + + align:start position:0% +let me talk about each one of these in +turn and uh show you some pictures so + + align:start position:0% +turn and uh show you some pictures so + + + align:start position:0% +turn and uh show you some pictures so +you sort of understand exactly what the + + align:start position:0% +you sort of understand exactly what the + + + align:start position:0% +you sort of understand exactly what the +need of these assumptions + + align:start position:0% +need of these assumptions + + + align:start position:0% +need of these assumptions +is okay oh I should a couple notes we + + align:start position:0% +is okay oh I should a couple notes we + + + align:start position:0% +is okay oh I should a couple notes we +sometimes impose an alternate assumption + + align:start position:0% +sometimes impose an alternate assumption + + + align:start position:0% +sometimes impose an alternate assumption +to one uh for our convenience and that's + + align:start position:0% +to one uh for our convenience and that's + + + align:start position:0% +to one uh for our convenience and that's +sometimes we assume that instead of X + + align:start position:0% +sometimes we assume that instead of X + + + align:start position:0% +sometimes we assume that instead of X +being a random variable XI being a + + align:start position:0% +being a random variable XI being a + + + align:start position:0% +being a random variable XI being a +random variable um we assume that XIs + + align:start position:0% +random variable um we assume that XIs + + + align:start position:0% +random variable um we assume that XIs +are fixed in repeated samples or + + align:start position:0% +are fixed in repeated samples or + + + align:start position:0% +are fixed in repeated samples or +non-stochastic this makes some of the + + align:start position:0% +non-stochastic this makes some of the + + + align:start position:0% +non-stochastic this makes some of the +proofs easier sometimes we do it for + + align:start position:0% +proofs easier sometimes we do it for + + + align:start position:0% +proofs easier sometimes we do it for +convenience it the the results + + align:start position:0% +convenience it the the results + + + align:start position:0% +convenience it the the results +essentially go through through uh + + align:start position:0% +essentially go through through uh + + + align:start position:0% +essentially go through through uh +without that assumption but we'll sort + + align:start position:0% +without that assumption but we'll sort + + + align:start position:0% +without that assumption but we'll sort +of go back and forth between + + align:start position:0% +of go back and forth between + + + align:start position:0% +of go back and forth between +that and then the other note is that + + align:start position:0% +that and then the other note is that + + + align:start position:0% +that and then the other note is that +assumptions I we had the three different + + align:start position:0% +assumptions I we had the three different + + + align:start position:0% +assumptions I we had the three different +assumptions on the error term and all of + + align:start position:0% +assumptions on the error term and all of + + + align:start position:0% +assumptions on the error term and all of +those assumptions could be subsumed + + align:start position:0% +those assumptions could be subsumed + + + align:start position:0% +those assumptions could be subsumed +under one stronger assumption that the + + align:start position:0% +under one stronger assumption that the + + + align:start position:0% +under one stronger assumption that the +epsilons are IID uh normal 0 Sigma squ + + align:start position:0% +epsilons are IID uh normal 0 Sigma squ + + + align:start position:0% +epsilons are IID uh normal 0 Sigma squ +okay so sometimes especially when we + + align:start position:0% +okay so sometimes especially when we + + + align:start position:0% +okay so sometimes especially when we +talk about inference will impose that + + align:start position:0% +talk about inference will impose that + + + align:start position:0% +talk about inference will impose that +assumption uh again that assumption is + + align:start position:0% +assumption uh again that assumption is + + + align:start position:0% +assumption uh again that assumption is +not necessary for almost anything that + + align:start position:0% +not necessary for almost anything that + + + align:start position:0% +not necessary for almost anything that +we do in linear regression but uh + + align:start position:0% +we do in linear regression but uh + + + align:start position:0% +we do in linear regression but uh +sometimes it's sort of convenient it + + align:start position:0% +sometimes it's sort of convenient it + + + align:start position:0% +sometimes it's sort of convenient it +makes the proofs EAS easier and uh sort + + align:start position:0% +makes the proofs EAS easier and uh sort + + + align:start position:0% +makes the proofs EAS easier and uh sort +of more elegant I + + align:start position:0% +of more elegant I + + + align:start position:0% +of more elegant I +guess okay so let's look at uh this + + align:start position:0% +guess okay so let's look at uh this + + + align:start position:0% +guess okay so let's look at uh this +assumption number two called + + align:start position:0% +assumption number two called + + + align:start position:0% +assumption number two called +identification so um I have this kind of + + align:start position:0% +identification so um I have this kind of + + + align:start position:0% +identification so um I have this kind of +uh Strang looking um equation up at the + + align:start position:0% +uh Strang looking um equation up at the + + + align:start position:0% +uh Strang looking um equation up at the +top but all that means is that we're + + align:start position:0% +top but all that means is that we're + + + align:start position:0% +top but all that means is that we're +ruling out a case where all of our OB + + align:start position:0% +ruling out a case where all of our OB + + + align:start position:0% +ruling out a case where all of our OB +observations on X or on a particular + + align:start position:0% +observations on X or on a particular + + + align:start position:0% +observations on X or on a particular +value X notot okay and the reason we + + align:start position:0% +value X notot okay and the reason we + + + align:start position:0% +value X notot okay and the reason we +rule out this case is because this + + align:start position:0% +rule out this case is because this + + + align:start position:0% +rule out this case is because this +doesn't give us any variation in X that + + align:start position:0% +doesn't give us any variation in X that + + + align:start position:0% +doesn't give us any variation in X that +we need to identify the mean of Y as a + + align:start position:0% +we need to identify the mean of Y as a + + + align:start position:0% +we need to identify the mean of Y as a +function of X okay if we're trying to + + align:start position:0% +function of X okay if we're trying to + + + align:start position:0% +function of X okay if we're trying to +fit a a a you know sort of a regression + + align:start position:0% +fit a a a you know sort of a regression + + + align:start position:0% +fit a a a you know sort of a regression +line we just have a bunch of um + + align:start position:0% +line we just have a bunch of um + + + align:start position:0% +line we just have a bunch of um +observations on a particular point and + + align:start position:0% +observations on a particular point and + + + align:start position:0% +observations on a particular point and +we can't do it + + align:start position:0% + + + + align:start position:0% + +okay uh the the third um assumption is + + align:start position:0% +okay uh the the third um assumption is + + + align:start position:0% +okay uh the the third um assumption is +that the error has a zero mean well so + + align:start position:0% +that the error has a zero mean well so + + + align:start position:0% +that the error has a zero mean well so +basically what we rule out so here I've + + align:start position:0% +basically what we rule out so here I've + + + align:start position:0% +basically what we rule out so here I've +drawn a picture of an error having a + + align:start position:0% +drawn a picture of an error having a + + + align:start position:0% +drawn a picture of an error having a +positive mean okay and we just rule this + + align:start position:0% +positive mean okay and we just rule this + + + align:start position:0% +positive mean okay and we just rule this +out because we don't have any + + align:start position:0% +out because we don't have any + + + align:start position:0% +out because we don't have any +information that would help us + + align:start position:0% +information that would help us + + + align:start position:0% +information that would help us +separately you know sort out whether our + + align:start position:0% +separately you know sort out whether our + + + align:start position:0% +separately you know sort out whether our +error just had a a a zero mean and the + + align:start position:0% +error just had a a a zero mean and the + + + align:start position:0% +error just had a a a zero mean and the +uh the regression line was shifted up or + + align:start position:0% +uh the regression line was shifted up or + + + align:start position:0% +uh the regression line was shifted up or +whether the zero whether the error had a + + align:start position:0% +whether the zero whether the error had a + + + align:start position:0% +whether the zero whether the error had a +positive mean and our regression line + + align:start position:0% +positive mean and our regression line + + + align:start position:0% +positive mean and our regression line +was shifted down okay we can't we don't + + align:start position:0% +was shifted down okay we can't we don't + + + align:start position:0% +was shifted down okay we can't we don't +have any information to sort of + + align:start position:0% +have any information to sort of + + + align:start position:0% +have any information to sort of +separately to sort those two + + align:start position:0% +separately to sort those two + + + align:start position:0% +separately to sort those two +possibilities out so we just assume that + + align:start position:0% +possibilities out so we just assume that + + + align:start position:0% +possibilities out so we just assume that +the error has zero variant or uh zero + + align:start position:0% +the error has zero variant or uh zero + + + align:start position:0% +the error has zero variant or uh zero +expectation + + align:start position:0% + + + + align:start position:0% + +okay and I should say uh well another + + align:start position:0% +okay and I should say uh well another + + + align:start position:0% +okay and I should say uh well another +another way to say this is that those + + align:start position:0% +another way to say this is that those + + + align:start position:0% +another way to say this is that those +two the the the expectation of the error + + align:start position:0% +two the the the expectation of the error + + + align:start position:0% +two the the the expectation of the error +and The Intercept of the regression line + + align:start position:0% +and The Intercept of the regression line + + + align:start position:0% +and The Intercept of the regression line +are not separately identified that's + + align:start position:0% +are not separately identified that's + + + align:start position:0% +are not separately identified that's +another sort of piece of + + align:start position:0% +another sort of piece of + + + align:start position:0% +another sort of piece of +terminology that just means we don't + + align:start position:0% +terminology that just means we don't + + + align:start position:0% +terminology that just means we don't +have any way to to you know sort them + + align:start position:0% +have any way to to you know sort them + + + align:start position:0% +have any way to to you know sort them +out with the + + align:start position:0% +out with the + + + align:start position:0% +out with the +data okay our fourth assumption is + + align:start position:0% +data okay our fourth assumption is + + + align:start position:0% +data okay our fourth assumption is +homoskedasticity so what is + + align:start position:0% +homoskedasticity so what is + + + align:start position:0% +homoskedasticity so what is +homoskedasticity it just means that + + align:start position:0% +homoskedasticity it just means that + + + align:start position:0% +homoskedasticity it just means that +we're going to assume that the variance + + align:start position:0% +we're going to assume that the variance + + + align:start position:0% +we're going to assume that the variance +for all of our errors the the variance + + align:start position:0% +for all of our errors the the variance + + + align:start position:0% +for all of our errors the the variance +is is uh equal to Sigma squar okay for + + align:start position:0% +is is uh equal to Sigma squar okay for + + + align:start position:0% +is is uh equal to Sigma squar okay for +all oh that's supposed to be all little + + align:start position:0% +all oh that's supposed to be all little + + + align:start position:0% +all oh that's supposed to be all little +I but my auto correct made it capital I + + align:start position:0% +I but my auto correct made it capital I + + + align:start position:0% +I but my auto correct made it capital I +I think okay um so this is a picture of + + align:start position:0% +I think okay um so this is a picture of + + + align:start position:0% +I think okay um so this is a picture of +what the opposite of homoscedasticity + + align:start position:0% +what the opposite of homoscedasticity + + + align:start position:0% +what the opposite of homoscedasticity +might look like this is called + + align:start position:0% +might look like this is called + + + align:start position:0% +might look like this is called +heteroscedasticity and here I've drawn + + align:start position:0% +heteroscedasticity and here I've drawn + + + align:start position:0% +heteroscedasticity and here I've drawn +it so that it looks like the error + + align:start position:0% +it so that it looks like the error + + + align:start position:0% +it so that it looks like the error +variance for low values of X is much + + align:start position:0% +variance for low values of X is much + + + align:start position:0% +variance for low values of X is much +higher than the airor variance for + + align:start position:0% +higher than the airor variance for + + + align:start position:0% +higher than the airor variance for +higher value + + align:start position:0% +higher value + + + align:start position:0% +higher value +specs okay and so we're we're going to + + align:start position:0% +specs okay and so we're we're going to + + + align:start position:0% +specs okay and so we're we're going to +rule that out for now that's actually + + align:start position:0% +rule that out for now that's actually + + + align:start position:0% +rule that out for now that's actually +not a fatal problem we can deal with it + + align:start position:0% +not a fatal problem we can deal with it + + + align:start position:0% +not a fatal problem we can deal with it +but at least for now we're going to + + align:start position:0% +but at least for now we're going to + + + align:start position:0% +but at least for now we're going to +assume that we have homoscedasticity and + + align:start position:0% +assume that we have homoscedasticity and + + + align:start position:0% +assume that we have homoscedasticity and +not + + align:start position:0% +not + + + align:start position:0% +not +heteroscedasticity so right about now + + align:start position:0% +heteroscedasticity so right about now + + + align:start position:0% +heteroscedasticity so right about now +you're probably thinking what is the + + align:start position:0% +you're probably thinking what is the + + + align:start position:0% +you're probably thinking what is the +emology of homo and heteroscedasticity + + align:start position:0% +emology of homo and heteroscedasticity + + + align:start position:0% +emology of homo and heteroscedasticity +and is she even spelling it right um + + align:start position:0% +and is she even spelling it right um + + + align:start position:0% +and is she even spelling it right um +because in fact my autoc correct kept + + align:start position:0% +because in fact my autoc correct kept + + + align:start position:0% +because in fact my autoc correct kept +trying to replace K with C whenever I + + align:start position:0% +trying to replace K with C whenever I + + + align:start position:0% +trying to replace K with C whenever I +was typing + + align:start position:0% +was typing + + + align:start position:0% +was typing +homoscedasticity turns out out that the + + align:start position:0% +homoscedasticity turns out out that the + + + align:start position:0% +homoscedasticity turns out out that the +auto correct in PowerPoint has not read + + align:start position:0% +auto correct in PowerPoint has not read + + + align:start position:0% +auto correct in PowerPoint has not read +this article in econometrica on the + + align:start position:0% +this article in econometrica on the + + + align:start position:0% +this article in econometrica on the +atmology and the correct spelling of + + align:start position:0% +atmology and the correct spelling of + + + align:start position:0% +atmology and the correct spelling of +homoscedasticity and + + align:start position:0% +homoscedasticity and + + + align:start position:0% +homoscedasticity and +heteroscedasticity so anyhow you can + + align:start position:0% +heteroscedasticity so anyhow you can + + + align:start position:0% +heteroscedasticity so anyhow you can +I've put this up in the website you can + + align:start position:0% +I've put this up in the website you can + + + align:start position:0% +I've put this up in the website you can +peruse this uh at your leisure but uh + + align:start position:0% +peruse this uh at your leisure but uh + + + align:start position:0% +peruse this uh at your leisure but uh +this will answer all your questions + + align:start position:0% +this will answer all your questions + + + align:start position:0% +this will answer all your questions +about the origin of these + + align:start position:0% + + + + align:start position:0% + +words okay and then the fifth um + + align:start position:0% +words okay and then the fifth um + + + align:start position:0% +words okay and then the fifth um +assumption is that we have no serial + + align:start position:0% +assumption is that we have no serial + + + align:start position:0% +assumption is that we have no serial +correlation so that means in other words + + align:start position:0% +correlation so that means in other words + + + align:start position:0% +correlation so that means in other words +that the um the air the sort of errors + + align:start position:0% +that the um the air the sort of errors + + + align:start position:0% +that the um the air the sort of errors +are not correlated uh if they're coming + + align:start position:0% +are not correlated uh if they're coming + + + align:start position:0% +are not correlated uh if they're coming +from different if they're associated + + align:start position:0% +from different if they're associated + + + align:start position:0% +from different if they're associated +with different observations okay so a + + align:start position:0% +with different observations okay so a + + + align:start position:0% +with different observations okay so a +stronger way of saying this is that the + + align:start position:0% +stronger way of saying this is that the + + + align:start position:0% +stronger way of saying this is that the +errors are independent across + + align:start position:0% +errors are independent across + + + align:start position:0% +errors are independent across +observations we don't we don't need to + + align:start position:0% +observations we don't we don't need to + + + align:start position:0% +observations we don't we don't need to +impose that we're just going to say that + + align:start position:0% +impose that we're just going to say that + + + align:start position:0% +impose that we're just going to say that +they're uncorrelated okay um here's a + + align:start position:0% +they're uncorrelated okay um here's a + + + align:start position:0% +they're uncorrelated okay um here's a +picture I drew a picture of positive + + align:start position:0% +picture I drew a picture of positive + + + align:start position:0% +picture I drew a picture of positive +what positive serial correlation might + + align:start position:0% +what positive serial correlation might + + + align:start position:0% +what positive serial correlation might +look look like so here we have um you + + align:start position:0% +look look like so here we have um you + + + align:start position:0% +look look like so here we have um you +know here we have sort of some positive + + align:start position:0% +know here we have sort of some positive + + + align:start position:0% +know here we have sort of some positive +errors over on the left side and then if + + align:start position:0% +errors over on the left side and then if + + + align:start position:0% +errors over on the left side and then if +you have one positive error the uh you + + align:start position:0% +you have one positive error the uh you + + + align:start position:0% +you have one positive error the uh you +know sort of uh uh close by errors are + + align:start position:0% +know sort of uh uh close by errors are + + + align:start position:0% +know sort of uh uh close by errors are +also likely to be positive so you have + + align:start position:0% +also likely to be positive so you have + + + align:start position:0% +also likely to be positive so you have +sort of an area where errors are mostly + + align:start position:0% +sort of an area where errors are mostly + + + align:start position:0% +sort of an area where errors are mostly +positive and then you get sort of a + + align:start position:0% +positive and then you get sort of a + + + align:start position:0% +positive and then you get sort of a +negative error and then you know sort of + + align:start position:0% +negative error and then you know sort of + + + align:start position:0% +negative error and then you know sort of +most of the errors close by are likely + + align:start position:0% +most of the errors close by are likely + + + align:start position:0% +most of the errors close by are likely +to be negative so that's what this is + + align:start position:0% +to be negative so that's what this is + + + align:start position:0% +to be negative so that's what this is +what positive seral correlation might + + align:start position:0% +what positive seral correlation might + + + align:start position:0% +what positive seral correlation might +look like the the errors are kind of + + align:start position:0% +look like the the errors are kind of + + + align:start position:0% +look like the the errors are kind of +clumped spatially like this okay again + + align:start position:0% +clumped spatially like this okay again + + + align:start position:0% +clumped spatially like this okay again +this is not fatal we can deal with this + + align:start position:0% +this is not fatal we can deal with this + + + align:start position:0% +this is not fatal we can deal with this +but we're going to assume for now that + + align:start position:0% +but we're going to assume for now that + + + align:start position:0% +but we're going to assume for now that +we don't have + + align:start position:0% + + + + align:start position:0% + +it okay and then as I said assumptions 3 + + align:start position:0% +it okay and then as I said assumptions 3 + + + align:start position:0% +it okay and then as I said assumptions 3 +through five could be subsumed under a + + align:start position:0% +through five could be subsumed under a + + + align:start position:0% +through five could be subsumed under a +stronger assumption that Epsilon I are + + align:start position:0% +stronger assumption that Epsilon I are + + + align:start position:0% +stronger assumption that Epsilon I are +IID normal 0 Sigma squ okay so we don't + + align:start position:0% +IID normal 0 Sigma squ okay so we don't + + + align:start position:0% +IID normal 0 Sigma squ okay so we don't +typically need this assumption sometimes + + align:start position:0% +typically need this assumption sometimes + + + align:start position:0% +typically need this assumption sometimes +we impose it + + align:start position:0% +we impose it + + + align:start position:0% +we impose it +that just means that you know + + align:start position:0% +that just means that you know + + + align:start position:0% +that just means that you know +conditional yeah basically there the + + align:start position:0% +conditional yeah basically there the + + + align:start position:0% +conditional yeah basically there the +error just has a distri a little normal + + align:start position:0% +error just has a distri a little normal + + + align:start position:0% +error just has a distri a little normal +distribution that looks like + + align:start position:0% + + + + align:start position:0% + +that okay so what are the things that we + + align:start position:0% +that okay so what are the things that we + + + align:start position:0% +that okay so what are the things that we +can say about this model first of all + + align:start position:0% +can say about this model first of all + + + align:start position:0% +can say about this model first of all +what are some some of the properties + + align:start position:0% +what are some some of the properties + + + align:start position:0% +what are some some of the properties +well we can uh we can calculate what the + + align:start position:0% +well we can uh we can calculate what the + + + align:start position:0% +well we can uh we can calculate what the +expectation of Y is and I should say we + + align:start position:0% +expectation of Y is and I should say we + + + align:start position:0% +expectation of Y is and I should say we +can we can think of this so right now + + align:start position:0% +can we can think of this so right now + + + align:start position:0% +can we can think of this so right now +during this calculation I'm making + + align:start position:0% +during this calculation I'm making + + + align:start position:0% +during this calculation I'm making +assumption just for my convenience that + + align:start position:0% +assumption just for my convenience that + + + align:start position:0% +assumption just for my convenience that +the X's are nonstochastic and so I + + align:start position:0% +the X's are nonstochastic and so I + + + align:start position:0% +the X's are nonstochastic and so I +haven't said that the expectation of Y + + align:start position:0% +haven't said that the expectation of Y + + + align:start position:0% +haven't said that the expectation of Y +is conditional on X but we can think of + + align:start position:0% +is conditional on X but we can think of + + + align:start position:0% +is conditional on X but we can think of +this as basically the the conditional + + align:start position:0% +this as basically the the conditional + + + align:start position:0% +this as basically the the conditional +distribution of Y given X and so + + align:start position:0% +distribution of Y given X and so + + + align:start position:0% +distribution of Y given X and so +basically if I'm assuming uh that the + + align:start position:0% +basically if I'm assuming uh that the + + + align:start position:0% +basically if I'm assuming uh that the +X's are non-stochastic it makes my life + + align:start position:0% +X's are non-stochastic it makes my life + + + align:start position:0% +X's are non-stochastic it makes my life +a little bit easier because I take the + + align:start position:0% +a little bit easier because I take the + + + align:start position:0% +a little bit easier because I take the +expectation of beta KN plus beta 1 uh X + + align:start position:0% +expectation of beta KN plus beta 1 uh X + + + align:start position:0% +expectation of beta KN plus beta 1 uh X +subi Plus Epsilon subi and the X's are + + align:start position:0% +subi Plus Epsilon subi and the X's are + + + align:start position:0% +subi Plus Epsilon subi and the X's are +non-stochastic so they just come they're + + align:start position:0% +non-stochastic so they just come they're + + + align:start position:0% +non-stochastic so they just come they're +just a constants they come outside the + + align:start position:0% +just a constants they come outside the + + + align:start position:0% +just a constants they come outside the +expectation and it just sort of makes + + align:start position:0% +expectation and it just sort of makes + + + align:start position:0% +expectation and it just sort of makes +the calculations easy okay and so we get + + align:start position:0% +the calculations easy okay and so we get + + + align:start position:0% +the calculations easy okay and so we get +in particular that the expectation of + + align:start position:0% +in particular that the expectation of + + + align:start position:0% +in particular that the expectation of +yui is equal to Beta KN plus beta 1 + + align:start position:0% +yui is equal to Beta KN plus beta 1 + + + align:start position:0% +yui is equal to Beta KN plus beta 1 +xui okay uh we can do a similar + + align:start position:0% +xui okay uh we can do a similar + + + align:start position:0% +xui okay uh we can do a similar +calculation with variance of Y subi and + + align:start position:0% +calculation with variance of Y subi and + + + align:start position:0% +calculation with variance of Y subi and +we get that that is just equal to uh + + align:start position:0% +we get that that is just equal to uh + + + align:start position:0% +we get that that is just equal to uh +Sigma squar so it's the same variance as + + align:start position:0% +Sigma squar so it's the same variance as + + + align:start position:0% +Sigma squar so it's the same variance as +the + + align:start position:0% +the + + + align:start position:0% +the +error + + align:start position:0% +error + + + align:start position:0% +error +and then we can also do a calcul similar + + align:start position:0% +and then we can also do a calcul similar + + + align:start position:0% +and then we can also do a calcul similar +calculation uh showing that uh for any I + + align:start position:0% +calculation uh showing that uh for any I + + + align:start position:0% +calculation uh showing that uh for any I +and J where I is not equal to J the + + align:start position:0% +and J where I is not equal to J the + + + align:start position:0% +and J where I is not equal to J the +co-variance between y sub I and Y subj + + align:start position:0% +co-variance between y sub I and Y subj + + + align:start position:0% +co-variance between y sub I and Y subj +is equal to zero + + align:start position:0% + + + + align:start position:0% + +okay yeah oh and so I just want to + + align:start position:0% +okay yeah oh and so I just want to + + + align:start position:0% +okay yeah oh and so I just want to +emphasize the bet is then are parameters + + align:start position:0% +emphasize the bet is then are parameters + + + align:start position:0% +emphasize the bet is then are parameters +in the conditional mean + + align:start position:0% + + + + align:start position:0% + +function + + align:start position:0% + + + + align:start position:0% + +Okay so we've got this linear function + + align:start position:0% +Okay so we've got this linear function + + + align:start position:0% +Okay so we've got this linear function +we've got sort of a set of assumptions + + align:start position:0% +we've got sort of a set of assumptions + + + align:start position:0% +we've got sort of a set of assumptions +that we're willing to impose for now so + + align:start position:0% +that we're willing to impose for now so + + + align:start position:0% +that we're willing to impose for now so +our next question is how do we find + + align:start position:0% +our next question is how do we find + + + align:start position:0% +our next question is how do we find +estimates for beta KN and beta 1 well + + align:start position:0% +estimates for beta KN and beta 1 well + + + align:start position:0% +estimates for beta KN and beta 1 well +here's I'm just going to throw up three + + align:start position:0% +here's I'm just going to throw up three + + + align:start position:0% +here's I'm just going to throw up three +different options and I'll very quickly + + align:start position:0% +different options and I'll very quickly + + + align:start position:0% +different options and I'll very quickly +dismiss two of them but just so you know + + align:start position:0% +dismiss two of them but just so you know + + + align:start position:0% +dismiss two of them but just so you know +that there are sort of other things that + + align:start position:0% +that there are sort of other things that + + + align:start position:0% +that there are sort of other things that +you can consider other than least + + align:start position:0% +you can consider other than least + + + align:start position:0% +you can consider other than least +squares estimates um so one thing that + + align:start position:0% +squares estimates um so one thing that + + + align:start position:0% +squares estimates um so one thing that +we do is we could uh we could find the + + align:start position:0% +we do is we could uh we could find the + + + align:start position:0% +we do is we could uh we could find the +least squares estimates in other words + + align:start position:0% +least squares estimates in other words + + + align:start position:0% +least squares estimates in other words +the values of beta not hat and beta one + + align:start position:0% +the values of beta not hat and beta one + + + align:start position:0% +the values of beta not hat and beta one +hat such that this uh expression here is + + align:start position:0% +hat such that this uh expression here is + + + align:start position:0% +hat such that this uh expression here is +minimized okay um and I'll show you + + align:start position:0% +minimized okay um and I'll show you + + + align:start position:0% +minimized okay um and I'll show you +pictures of what these look like in a + + align:start position:0% +pictures of what these look like in a + + + align:start position:0% +pictures of what these look like in a +second we could instead of minimizing + + align:start position:0% +second we could instead of minimizing + + + align:start position:0% +second we could instead of minimizing +the sum of squared errors which is what + + align:start position:0% +the sum of squared errors which is what + + + align:start position:0% +the sum of squared errors which is what +so each one of these uh each one of + + align:start position:0% +so each one of these uh each one of + + + align:start position:0% +so each one of these uh each one of +these in this parenthe in the + + align:start position:0% +these in this parenthe in the + + + align:start position:0% +these in this parenthe in the +parenthesis is um is is a res well if it + + align:start position:0% +parenthesis is um is is a res well if it + + + align:start position:0% +parenthesis is um is is a res well if it +it's an error if beta not and beta 1 are + + align:start position:0% +it's an error if beta not and beta 1 are + + + align:start position:0% +it's an error if beta not and beta 1 are +the true parameters it's a residual if + + align:start position:0% +the true parameters it's a residual if + + + align:start position:0% +the true parameters it's a residual if +they're the estimates but uh what we do + + align:start position:0% +they're the estimates but uh what we do + + + align:start position:0% +they're the estimates but uh what we do +is um you know we call if we plug in the + + align:start position:0% +is um you know we call if we plug in the + + + align:start position:0% +is um you know we call if we plug in the +estimates we call that a residual and + + align:start position:0% +estimates we call that a residual and + + + align:start position:0% +estimates we call that a residual and +then uh if we Square the residuals and + + align:start position:0% +then uh if we Square the residuals and + + + align:start position:0% +then uh if we Square the residuals and +sum them up and find the parameters that + + align:start position:0% +sum them up and find the parameters that + + + align:start position:0% +sum them up and find the parameters that +minimize that sum of squares that's + + align:start position:0% +minimize that sum of squares that's + + + align:start position:0% +minimize that sum of squares that's +called a least squares estimator we + + align:start position:0% +called a least squares estimator we + + + align:start position:0% +called a least squares estimator we +instead of squaring them we could just + + align:start position:0% +instead of squaring them we could just + + + align:start position:0% +instead of squaring them we could just +take their absolute values instead and + + align:start position:0% +take their absolute values instead and + + + align:start position:0% +take their absolute values instead and +come up with something called the least + + align:start position:0% +come up with something called the least + + + align:start position:0% +come up with something called the least +absolute deviations um uh uh estimator + + align:start position:0% +absolute deviations um uh uh estimator + + + align:start position:0% +absolute deviations um uh uh estimator +that's the second uh possibility or + + align:start position:0% +that's the second uh possibility or + + + align:start position:0% +that's the second uh possibility or +third possibility I'll throw out is + + align:start position:0% +third possibility I'll throw out is + + + align:start position:0% +third possibility I'll throw out is +something called the revers Le squares + + align:start position:0% +something called the revers Le squares + + + align:start position:0% +something called the revers Le squares +estimator okay let me just show you + + align:start position:0% +estimator okay let me just show you + + + align:start position:0% +estimator okay let me just show you +pictures of each of these in + + align:start position:0% +pictures of each of these in + + + align:start position:0% +pictures of each of these in +turn so actually the um the least + + align:start position:0% +turn so actually the um the least + + + align:start position:0% +turn so actually the um the least +squares estimator and the least absolute + + align:start position:0% +squares estimator and the least absolute + + + align:start position:0% +squares estimator and the least absolute +deviation estimator have the same + + align:start position:0% +deviation estimator have the same + + + align:start position:0% +deviation estimator have the same +picture because what we're doing is for + + align:start position:0% +picture because what we're doing is for + + + align:start position:0% +picture because what we're doing is for +the least squares estimators we're just + + align:start position:0% +the least squares estimators we're just + + + align:start position:0% +the least squares estimators we're just +taking this uh this quantity here and + + align:start position:0% +taking this uh this quantity here and + + + align:start position:0% +taking this uh this quantity here and +squaring it and for the least absolute + + align:start position:0% +squaring it and for the least absolute + + + align:start position:0% +squaring it and for the least absolute +deviations we're not squaring it we're + + align:start position:0% +deviations we're not squaring it we're + + + align:start position:0% +deviations we're not squaring it we're +just taking the absolute value okay so + + align:start position:0% +just taking the absolute value okay so + + + align:start position:0% +just taking the absolute value okay so +they have the same pictures but what we + + align:start position:0% +they have the same pictures but what we + + + align:start position:0% +they have the same pictures but what we +do is uh for the least squares estimator + + align:start position:0% +do is uh for the least squares estimator + + + align:start position:0% +do is uh for the least squares estimator +we compute all of these + + align:start position:0% +we compute all of these + + + align:start position:0% +we compute all of these +deviations and we choose the line that + + align:start position:0% +deviations and we choose the line that + + + align:start position:0% +deviations and we choose the line that +minimizes those squared deviations + + align:start position:0% +minimizes those squared deviations + + + align:start position:0% +minimizes those squared deviations +yes so I guess at the end how do these + + align:start position:0% +yes so I guess at the end how do these + + + align:start position:0% +yes so I guess at the end how do these +two + + align:start position:0% +two + + + align:start position:0% +two +differ so I'm going to talk just a + + align:start position:0% +differ so I'm going to talk just a + + + align:start position:0% +differ so I'm going to talk just a +little bit I'm going to have a slide + + align:start position:0% +little bit I'm going to have a slide + + + align:start position:0% +little bit I'm going to have a slide +maybe two slides or something about the + + align:start position:0% +maybe two slides or something about the + + + align:start position:0% +maybe two slides or something about the +uh properties of leas squares and why we + + align:start position:0% +uh properties of leas squares and why we + + + align:start position:0% +uh properties of leas squares and why we +almost always use leas squares instead + + align:start position:0% +almost always use leas squares instead + + + align:start position:0% +almost always use leas squares instead +of least absolute deviations um I'm not + + align:start position:0% +of least absolute deviations um I'm not + + + align:start position:0% +of least absolute deviations um I'm not +going to actually say too much about + + align:start position:0% +going to actually say too much about + + + align:start position:0% +going to actually say too much about +them but when we get to that slide if + + align:start position:0% +them but when we get to that slide if + + + align:start position:0% +them but when we get to that slide if +you have any any other questions let me + + align:start position:0% +you have any any other questions let me + + + align:start position:0% +you have any any other questions let me +know okay um so these are the first two + + align:start position:0% +know okay um so these are the first two + + + align:start position:0% +know okay um so these are the first two +possibilities and and then the picture + + align:start position:0% +possibilities and and then the picture + + + align:start position:0% +possibilities and and then the picture +for the third possibility just looks + + align:start position:0% +for the third possibility just looks + + + align:start position:0% +for the third possibility just looks +like this we're minimizing the sum of + + align:start position:0% +like this we're minimizing the sum of + + + align:start position:0% +like this we're minimizing the sum of +squares of those deviations instead in a + + align:start position:0% +squares of those deviations instead in a + + + align:start position:0% +squares of those deviations instead in a +reverse least squares + + align:start position:0% + + + + align:start position:0% + +estimator so why do we always just focus + + align:start position:0% +estimator so why do we always just focus + + + align:start position:0% +estimator so why do we always just focus +on leas squares estimators why do we why + + align:start position:0% +on leas squares estimators why do we why + + + align:start position:0% +on leas squares estimators why do we why +is that sort of what we always do well + + align:start position:0% +is that sort of what we always do well + + + align:start position:0% +is that sort of what we always do well +um under the assumptions of the + + align:start position:0% +um under the assumptions of the + + + align:start position:0% +um under the assumptions of the +classical linear regression model that I + + align:start position:0% +classical linear regression model that I + + + align:start position:0% +classical linear regression model that I +had up a few minutes ago uh OS which + + align:start position:0% +had up a few minutes ago uh OS which + + + align:start position:0% +had up a few minutes ago uh OS which +stands for ordinary lease squares + + align:start position:0% +stands for ordinary lease squares + + + align:start position:0% +stands for ordinary lease squares +provides the minimum variance in other + + align:start position:0% +provides the minimum variance in other + + + align:start position:0% +provides the minimum variance in other +words the most efficient unbiased + + align:start position:0% +words the most efficient unbiased + + + align:start position:0% +words the most efficient unbiased +estimator of beta KN and beta 1 it is + + align:start position:0% +estimator of beta KN and beta 1 it is + + + align:start position:0% +estimator of beta KN and beta 1 it is +also the maximum likelihood estimator + + align:start position:0% +also the maximum likelihood estimator + + + align:start position:0% +also the maximum likelihood estimator +under normality of errors and the + + align:start position:0% +under normality of errors and the + + + align:start position:0% +under normality of errors and the +estimates are consistent and ASM + + align:start position:0% +estimates are consistent and ASM + + + align:start position:0% +estimates are consistent and ASM +totically normal okay and these things + + align:start position:0% +totically normal okay and these things + + + align:start position:0% +totically normal okay and these things +are not true of the other estimators so + + align:start position:0% +are not true of the other estimators so + + + align:start position:0% +are not true of the other estimators so +that's why we typically always use the + + align:start position:0% +that's why we typically always use the + + + align:start position:0% +that's why we typically always use the +least least squares estimators uh are + + align:start position:0% +least least squares estimators uh are + + + align:start position:0% +least least squares estimators uh are +there cases when you might want to use a + + align:start position:0% +there cases when you might want to use a + + + align:start position:0% +there cases when you might want to use a +least absolute deviations estimator + + align:start position:0% +least absolute deviations estimator + + + align:start position:0% +least absolute deviations estimator +maybe I mean maybe if you're + + align:start position:0% +maybe I mean maybe if you're + + + align:start position:0% +maybe I mean maybe if you're +particularly worried about the + + align:start position:0% +particularly worried about the + + + align:start position:0% +particularly worried about the +credibility of your data and you think + + align:start position:0% +credibility of your data and you think + + + align:start position:0% +credibility of your data and you think +you might have some outliers that you + + align:start position:0% +you might have some outliers that you + + + align:start position:0% +you might have some outliers that you +don't want to take out of your data set + + align:start position:0% +don't want to take out of your data set + + + align:start position:0% +don't want to take out of your data set +but you don't want them to have undue + + align:start position:0% +but you don't want them to have undue + + + align:start position:0% +but you don't want them to have undue +influence on your parameter estimates uh + + align:start position:0% +influence on your parameter estimates uh + + + align:start position:0% +influence on your parameter estimates uh +you might be able to justify using a + + align:start position:0% +you might be able to justify using a + + + align:start position:0% +you might be able to justify using a +least absolute deviations estimator but + + align:start position:0% +least absolute deviations estimator but + + + align:start position:0% +least absolute deviations estimator but +uh typically people are going to go for + + align:start position:0% +uh typically people are going to go for + + + align:start position:0% +uh typically people are going to go for +the least squares estimators because its + + align:start position:0% +the least squares estimators because its + + + align:start position:0% +the least squares estimators because its +properties are so good yeah oh sorry + + align:start position:0% +properties are so good yeah oh sorry + + + align:start position:0% +properties are so good yeah oh sorry +yeah go ahead and so is the reason that + + align:start position:0% +yeah go ahead and so is the reason that + + + align:start position:0% +yeah go ahead and so is the reason that +is + + align:start position:0% +is + + + align:start position:0% +is +like even though they're both based on + + align:start position:0% +like even though they're both based on + + + align:start position:0% +like even though they're both based on +the same distance I guess the + + align:start position:0% +the same distance I guess the + + + align:start position:0% +the same distance I guess the +sensitivity + + align:start position:0% +sensitivity + + + align:start position:0% +sensitivity +in the OS is higher because it's just + + align:start position:0% +in the OS is higher because it's just + + + align:start position:0% +in the OS is higher because it's just +squ yeah it it it's more sensitive to + + align:start position:0% +squ yeah it it it's more sensitive to + + + align:start position:0% +squ yeah it it it's more sensitive to +sort of observations that are kind of + + align:start position:0% +sort of observations that are kind of + + + align:start position:0% +sort of observations that are kind of +out in the Tails because it's squared um + + align:start position:0% +out in the Tails because it's squared um + + + align:start position:0% +out in the Tails because it's squared um +but even G you know given that it still + + align:start position:0% +but even G you know given that it still + + + align:start position:0% +but even G you know given that it still +has all of these favorable properties so + + align:start position:0% +has all of these favorable properties so + + + align:start position:0% +has all of these favorable properties so +you have a + + align:start position:0% +you have a + + + align:start position:0% +you have a +question uh I guess not really anymore I + + align:start position:0% +question uh I guess not really anymore I + + + align:start position:0% +question uh I guess not really anymore I +was sort of thinking of the first first + + align:start position:0% +was sort of thinking of the first first + + + align:start position:0% +was sort of thinking of the first first +characteristic is a little bit circular + + align:start position:0% +characteristic is a little bit circular + + + align:start position:0% +characteristic is a little bit circular +because we Define efficiency in terms of + + align:start position:0% +because we Define efficiency in terms of + + + align:start position:0% +because we Define efficiency in terms of +variance so if you had another metric + + align:start position:0% +variance so if you had another metric + + + align:start position:0% +variance so if you had another metric +for efficiency to be but I guess what + + align:start position:0% +for efficiency to be but I guess what + + + align:start position:0% +for efficiency to be but I guess what +you're really saying is that it provides + + align:start position:0% +you're really saying is that it provides + + + align:start position:0% +you're really saying is that it provides +the minimum variance exactly yeah so I + + align:start position:0% +the minimum variance exactly yeah so I + + + align:start position:0% +the minimum variance exactly yeah so I +just put in in parenthesis most + + align:start position:0% +just put in in parenthesis most + + + align:start position:0% +just put in in parenthesis most +efficient to just remind you that that's + + align:start position:0% +efficient to just remind you that that's + + + align:start position:0% +efficient to just remind you that that's +how we that's sort of um how we defined + + align:start position:0% +how we that's sort of um how we defined + + + align:start position:0% +how we that's sort of um how we defined +yeah that's that's the terminology we + + align:start position:0% +yeah that's that's the terminology we + + + align:start position:0% +yeah that's that's the terminology we +used basically but yeah yep these + + align:start position:0% +used basically but yeah yep these + + + align:start position:0% +used basically but yeah yep these +properties less C + + align:start position:0% +properties less C + + + align:start position:0% +properties less C +if homos acity goes out the + + align:start position:0% +if homos acity goes out the + + + align:start position:0% +if homos acity goes out the +so uh good question um I would have to + + align:start position:0% +so uh good question um I would have to + + + align:start position:0% +so uh good question um I would have to +think for just a second so uh basically + + align:start position:0% +think for just a second so uh basically + + + align:start position:0% +think for just a second so uh basically +it that's no longer the most efficient + + align:start position:0% +it that's no longer the most efficient + + + align:start position:0% +it that's no longer the most efficient +it's still unbiased it's no longer the + + align:start position:0% +it's still unbiased it's no longer the + + + align:start position:0% +it's still unbiased it's no longer the +most efficient the um the uh inference + + align:start position:0% +most efficient the um the uh inference + + + align:start position:0% +most efficient the um the uh inference +has to be yeah under under + + align:start position:0% +has to be yeah under under + + + align:start position:0% +has to be yeah under under +heteroscedasticity uh the sort of + + align:start position:0% +heteroscedasticity uh the sort of + + + align:start position:0% +heteroscedasticity uh the sort of +standard inference that we'll see over + + align:start position:0% +standard inference that we'll see over + + + align:start position:0% +standard inference that we'll see over +the next couple of lectures has to be + + align:start position:0% +the next couple of lectures has to be + + + align:start position:0% +the next couple of lectures has to be +modified because then + + align:start position:0% +modified because then + + + align:start position:0% +modified because then +the the standard errors uh if you use + + align:start position:0% +the the standard errors uh if you use + + + align:start position:0% +the the standard errors uh if you use +kind of the standard inference are + + align:start position:0% +kind of the standard inference are + + + align:start position:0% +kind of the standard inference are +biased uh but it's still it's still + + align:start position:0% +biased uh but it's still it's still + + + align:start position:0% +biased uh but it's still it's still +going to have good properties and + + align:start position:0% +going to have good properties and + + + align:start position:0% +going to have good properties and +they're there we have very good ways of + + align:start position:0% +they're there we have very good ways of + + + align:start position:0% +they're there we have very good ways of +sort of fixing of of recapturing the + + align:start position:0% +sort of fixing of of recapturing the + + + align:start position:0% +sort of fixing of of recapturing the +best properties under the case of het + + align:start position:0% +best properties under the case of het + + + align:start position:0% +best properties under the case of het +orisk ad + + align:start position:0% + + + + align:start position:0% + +acticity + + align:start position:0% +acticity + + + align:start position:0% +acticity +okay okay so fine maybe I hope I've + + align:start position:0% +okay okay so fine maybe I hope I've + + + align:start position:0% +okay okay so fine maybe I hope I've +convinced you that uh lease squares + + align:start position:0% +convinced you that uh lease squares + + + align:start position:0% +convinced you that uh lease squares +estimators uh are the way to go and the + + align:start position:0% +estimators uh are the way to go and the + + + align:start position:0% +estimators uh are the way to go and the +way that we're typically going to + + align:start position:0% +way that we're typically going to + + + align:start position:0% +way that we're typically going to +estimate this linear model um so we've + + align:start position:0% +estimate this linear model um so we've + + + align:start position:0% +estimate this linear model um so we've +got you know sort of all of these uh + + align:start position:0% +got you know sort of all of these uh + + + align:start position:0% +got you know sort of all of these uh +like sum of squared um you know sort of + + align:start position:0% +like sum of squared um you know sort of + + + align:start position:0% +like sum of squared um you know sort of +residuals and we're trying to choose the + + align:start position:0% +residuals and we're trying to choose the + + + align:start position:0% +residuals and we're trying to choose the +the line that's sort of U minimizing + + align:start position:0% +the line that's sort of U minimizing + + + align:start position:0% +the line that's sort of U minimizing +those does that mean we have to do a + + align:start position:0% +those does that mean we have to do a + + + align:start position:0% +those does that mean we have to do a +numerical minimization every time we + + align:start position:0% +numerical minimization every time we + + + align:start position:0% +numerical minimization every time we +want to solve for our leas squares + + align:start position:0% +want to solve for our leas squares + + + align:start position:0% +want to solve for our leas squares +estimators no we don't we have these + + align:start position:0% +estimators no we don't we have these + + + align:start position:0% +estimators no we don't we have these +lovely closed form Solutions okay so all + + align:start position:0% +lovely closed form Solutions okay so all + + + align:start position:0% +lovely closed form Solutions okay so all +we have to do is plug into these + + align:start position:0% +we have to do is plug into these + + + align:start position:0% +we have to do is plug into these +formulas and realistically speaking all + + align:start position:0% +formulas and realistically speaking all + + + align:start position:0% +formulas and realistically speaking all +we have to do is type you know like the + + align:start position:0% +we have to do is type you know like the + + + align:start position:0% +we have to do is type you know like the +command into R + + align:start position:0% +command into R + + + align:start position:0% +command into R +so so anyhow it it so there there if you + + align:start position:0% +so so anyhow it it so there there if you + + + align:start position:0% +so so anyhow it it so there there if you +sort of went on to do more advanced + + align:start position:0% +sort of went on to do more advanced + + + align:start position:0% +sort of went on to do more advanced +econometrics you would in fact encounter + + align:start position:0% +econometrics you would in fact encounter + + + align:start position:0% +econometrics you would in fact encounter +estimators where you have to do + + align:start position:0% +estimators where you have to do + + + align:start position:0% +estimators where you have to do +complicated numerical minimizations + + align:start position:0% +complicated numerical minimizations + + + align:start position:0% +complicated numerical minimizations +every time to get parameter estimates OS + + align:start position:0% +every time to get parameter estimates OS + + + align:start position:0% +every time to get parameter estimates OS +is not one of them we have these nice + + align:start position:0% +is not one of them we have these nice + + + align:start position:0% +is not one of them we have these nice +close form Solutions okay how did I get + + align:start position:0% +close form Solutions okay how did I get + + + align:start position:0% +close form Solutions okay how did I get +these pages of tedious calculations that + + align:start position:0% +these pages of tedious calculations that + + + align:start position:0% +these pages of tedious calculations that +are up on the website for your viewing + + align:start position:0% +are up on the website for your viewing + + + align:start position:0% +are up on the website for your viewing +pleasure so it's the I have a couple + + align:start position:0% +pleasure so it's the I have a couple + + + align:start position:0% +pleasure so it's the I have a couple +things to say about this first of all + + align:start position:0% +things to say about this first of all + + + align:start position:0% +things to say about this first of all +where um the the I can't remember what I + + align:start position:0% +where um the the I can't remember what I + + + align:start position:0% +where um the the I can't remember what I +put in under I think I put in under + + align:start position:0% +put in under I think I put in under + + + align:start position:0% +put in under I think I put in under +derivation there's a page of notes under + + align:start position:0% +derivation there's a page of notes under + + + align:start position:0% +derivation there's a page of notes under +um what's it under resources maybe and + + align:start position:0% +um what's it under resources maybe and + + + align:start position:0% +um what's it under resources maybe and +it's called derivation of os estimators + + align:start position:0% +it's called derivation of os estimators + + + align:start position:0% +it's called derivation of os estimators +and so you're uh welcome to look look on + + align:start position:0% +and so you're uh welcome to look look on + + + align:start position:0% +and so you're uh welcome to look look on +those notes and see uh the calculations + + align:start position:0% +those notes and see uh the calculations + + + align:start position:0% +those notes and see uh the calculations +that are whereby I arrived at at the Le + + align:start position:0% +that are whereby I arrived at at the Le + + + align:start position:0% +that are whereby I arrived at at the Le +squares estimators the um the notation + + align:start position:0% +squares estimators the um the notation + + + align:start position:0% +squares estimators the um the notation +is slightly different I believe in those + + align:start position:0% +is slightly different I believe in those + + + align:start position:0% +is slightly different I believe in those +notes instead of having the uh intercept + + align:start position:0% +notes instead of having the uh intercept + + + align:start position:0% +notes instead of having the uh intercept +um denoted by Beta not I think I used an + + align:start position:0% +um denoted by Beta not I think I used an + + + align:start position:0% +um denoted by Beta not I think I used an +alpha instead and then a beta for the + + align:start position:0% +alpha instead and then a beta for the + + + align:start position:0% +alpha instead and then a beta for the +slope uh and I so I changed the the the + + align:start position:0% +slope uh and I so I changed the the the + + + align:start position:0% +slope uh and I so I changed the the the +notation is slightly different but + + align:start position:0% +notation is slightly different but + + + align:start position:0% +notation is slightly different but +anyhow you can look at those if you want + + align:start position:0% +anyhow you can look at those if you want + + + align:start position:0% +anyhow you can look at those if you want +um + + align:start position:0% +um + + + align:start position:0% +um +however I don't want you to get the idea + + align:start position:0% +however I don't want you to get the idea + + + align:start position:0% +however I don't want you to get the idea +that Os estimators are horrible + + align:start position:0% +that Os estimators are horrible + + + align:start position:0% +that Os estimators are horrible +complicated things they're really very + + align:start position:0% +complicated things they're really very + + + align:start position:0% +complicated things they're really very +elegant and they're very intuitive but + + align:start position:0% +elegant and they're very intuitive but + + + align:start position:0% +elegant and they're very intuitive but +the the thing that's holding us back is + + align:start position:0% +the the thing that's holding us back is + + + align:start position:0% +the the thing that's holding us back is +this notation okay so actually next time + + align:start position:0% +this notation okay so actually next time + + + align:start position:0% +this notation okay so actually next time +we will derive the least squares + + align:start position:0% +we will derive the least squares + + + align:start position:0% +we will derive the least squares +estimators using Matrix notation and you + + align:start position:0% +estimators using Matrix notation and you + + + align:start position:0% +estimators using Matrix notation and you +will see how beautiful they are uh I'm + + align:start position:0% +will see how beautiful they are uh I'm + + + align:start position:0% +will see how beautiful they are uh I'm +not going to drag you through the + + align:start position:0% +not going to drag you through the + + + align:start position:0% +not going to drag you through the +derivation using the summation notation + + align:start position:0% +derivation using the summation notation + + + align:start position:0% +derivation using the summation notation +because it's just it's painful yeah um + + align:start position:0% +because it's just it's painful yeah um + + + align:start position:0% +because it's just it's painful yeah um +wouldn't the one over ends + + align:start position:0% +wouldn't the one over ends + + + align:start position:0% +wouldn't the one over ends +cancel + + align:start position:0% +cancel + + + align:start position:0% +cancel +why + + align:start position:0% +why + + + align:start position:0% +why +uh oh uh they would I think it's just + + align:start position:0% +uh oh uh they would I think it's just + + + align:start position:0% +uh oh uh they would I think it's just +because oh yeah I think it's just + + align:start position:0% +because oh yeah I think it's just + + + align:start position:0% +because oh yeah I think it's just +because this the well often time right + + align:start position:0% +because this the well often time right + + + align:start position:0% +because this the well often time right +so that thing on the bottom is is like a + + align:start position:0% +so that thing on the bottom is is like a + + + align:start position:0% +so that thing on the bottom is is like a +a sample variance and so the you might + + align:start position:0% +a sample variance and so the you might + + + align:start position:0% +a sample variance and so the you might +compute that separately and then just + + align:start position:0% + + + + align:start position:0% + +yeah okay and as I just said uh they + + align:start position:0% +yeah okay and as I just said uh they + + + align:start position:0% +yeah okay and as I just said uh they +could be Lovelier still if we weren't + + align:start position:0% +could be Lovelier still if we weren't + + + align:start position:0% +could be Lovelier still if we weren't +too afraid of using Matrix notation + + align:start position:0% +too afraid of using Matrix notation + + + align:start position:0% +too afraid of using Matrix notation +which we're not so we'll do it next time + + align:start position:0% +which we're not so we'll do it next time + + + align:start position:0% +which we're not so we'll do it next time +okay okay a couple of important + + align:start position:0% +okay okay a couple of important + + + align:start position:0% +okay okay a couple of important +definitions so I already told you u u + + align:start position:0% +definitions so I already told you u u + + + align:start position:0% +definitions so I already told you u u +just sort of verbally what a residual is + + align:start position:0% +just sort of verbally what a residual is + + + align:start position:0% +just sort of verbally what a residual is +but here's a picture of residual idual + + align:start position:0% +but here's a picture of residual idual + + + align:start position:0% +but here's a picture of residual idual +and you have the formula here so + + align:start position:0% +and you have the formula here so + + + align:start position:0% +and you have the formula here so +residual is + + align:start position:0% +residual is + + + align:start position:0% +residual is +basically the deviation between uh the + + align:start position:0% +basically the deviation between uh the + + + align:start position:0% +basically the deviation between uh the +an ordered pair of a particular X and Y + + align:start position:0% +an ordered pair of a particular X and Y + + + align:start position:0% +an ordered pair of a particular X and Y +and the fitted regression line okay and + + align:start position:0% +and the fitted regression line okay and + + + align:start position:0% +and the fitted regression line okay and +we denote that as Epsilon uh subi hat + + align:start position:0% +we denote that as Epsilon uh subi hat + + + align:start position:0% +we denote that as Epsilon uh subi hat +typically okay you sometimes we'll see + + align:start position:0% +typically okay you sometimes we'll see + + + align:start position:0% +typically okay you sometimes we'll see +other notation as well uh here I've + + align:start position:0% +other notation as well uh here I've + + + align:start position:0% +other notation as well uh here I've +drawn in the regression line also known + + align:start position:0% +drawn in the regression line also known + + + align:start position:0% +drawn in the regression line also known +as the fitted line so that's just beta + + align:start position:0% +as the fitted line so that's just beta + + + align:start position:0% +as the fitted line so that's just beta +KN plus beta not hat plus beta 1 Hat uh + + align:start position:0% +KN plus beta not hat plus beta 1 Hat uh + + + align:start position:0% +KN plus beta not hat plus beta 1 Hat uh +time + + align:start position:0% +time + + + align:start position:0% +time +x and then uh it's also convenient to + + align:start position:0% +x and then uh it's also convenient to + + + align:start position:0% +x and then uh it's also convenient to +define something called a fitted value + + align:start position:0% +define something called a fitted value + + + align:start position:0% +define something called a fitted value +and that's basically just for any + + align:start position:0% +and that's basically just for any + + + align:start position:0% +and that's basically just for any +particular value of x the value of y on + + align:start position:0% +particular value of x the value of y on + + + align:start position:0% +particular value of x the value of y on +the fitted line associated with that + + align:start position:0% +the fitted line associated with that + + + align:start position:0% +the fitted line associated with that +value of x okay on the estimated + + align:start position:0% +value of x okay on the estimated + + + align:start position:0% +value of x okay on the estimated +regression line so we'll sort of come + + align:start position:0% +regression line so we'll sort of come + + + align:start position:0% +regression line so we'll sort of come +back we'll use this notation the Y subi + + align:start position:0% +back we'll use this notation the Y subi + + + align:start position:0% +back we'll use this notation the Y subi +hat and the Epsilon subi hat notation uh + + align:start position:0% +hat and the Epsilon subi hat notation uh + + + align:start position:0% +hat and the Epsilon subi hat notation uh +and we'll sort of come back to these um + + align:start position:0% +and we'll sort of come back to these um + + + align:start position:0% +and we'll sort of come back to these um +quantities uh in the next couple + + align:start position:0% + + + + align:start position:0% + +lectures okay what do we always ask when + + align:start position:0% +lectures okay what do we always ask when + + + align:start position:0% +lectures okay what do we always ask when +we learn about a new estimator and why + + align:start position:0% +we learn about a new estimator and why + + + align:start position:0% +we learn about a new estimator and why +do we ask + + align:start position:0% +do we ask + + + align:start position:0% +do we ask +it what do we always want to know about + + align:start position:0% +it what do we always want to know about + + + align:start position:0% +it what do we always want to know about +an + + align:start position:0% + + + + align:start position:0% + +estimator well that's a specific case so + + align:start position:0% +estimator well that's a specific case so + + + align:start position:0% +estimator well that's a specific case so +we want know it's distribution right we + + align:start position:0% +we want know it's distribution right we + + + align:start position:0% +we want know it's distribution right we +always want to know its distribution and + + align:start position:0% +always want to know its distribution and + + + align:start position:0% +always want to know its distribution and +not I mean we already I already told you + + align:start position:0% +not I mean we already I already told you + + + align:start position:0% +not I mean we already I already told you +these are unbiased estimators but uh we + + align:start position:0% +these are unbiased estimators but uh we + + + align:start position:0% +these are unbiased estimators but uh we +want to know its distribution and why do + + align:start position:0% +want to know its distribution and why do + + + align:start position:0% +want to know its distribution and why do +we want to know its distribution because + + align:start position:0% +we want to know its distribution because + + + align:start position:0% +we want to know its distribution because +we're not going to be able to perform + + align:start position:0% +we're not going to be able to perform + + + align:start position:0% +we're not going to be able to perform +inference we're not going to be able to + + align:start position:0% +inference we're not going to be able to + + + align:start position:0% +inference we're not going to be able to +to create a um a uh a hypothesis test or + + align:start position:0% +to create a um a uh a hypothesis test or + + + align:start position:0% +to create a um a uh a hypothesis test or +a confidence interval if we don't know + + align:start position:0% +a confidence interval if we don't know + + + align:start position:0% +a confidence interval if we don't know +the distribution or we don't know at + + align:start position:0% +the distribution or we don't know at + + + align:start position:0% +the distribution or we don't know at +least the variance of uh our estimators + + align:start position:0% +least the variance of uh our estimators + + + align:start position:0% +least the variance of uh our estimators +Okay so so let let me just uh Define a + + align:start position:0% +Okay so so let let me just uh Define a + + + align:start position:0% +Okay so so let let me just uh Define a +couple things let's uh let xar just + + align:start position:0% +couple things let's uh let xar just + + + align:start position:0% +couple things let's uh let xar just +equal what it typically is equal just 1/ + + align:start position:0% +equal what it typically is equal just 1/ + + + align:start position:0% +equal what it typically is equal just 1/ +n * the sum of the XI and then let's + + align:start position:0% +n * the sum of the XI and then let's + + + align:start position:0% +n * the sum of the XI and then let's +define this thing called Sigma squ hat + + align:start position:0% +define this thing called Sigma squ hat + + + align:start position:0% +define this thing called Sigma squ hat +subx which is 1 over n times the sum + + align:start position:0% +subx which is 1 over n times the sum + + + align:start position:0% +subx which is 1 over n times the sum +over I of x i - xar s + + align:start position:0% +over I of x i - xar s + + + align:start position:0% +over I of x i - xar s +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and if we uh if we use that notation + + align:start position:0% +and if we uh if we use that notation + + + align:start position:0% +and if we uh if we use that notation +then we can uh figure out what the mean + + align:start position:0% +then we can uh figure out what the mean + + + align:start position:0% +then we can uh figure out what the mean +and the variance and the co-variance of + + align:start position:0% +and the variance and the co-variance of + + + align:start position:0% +and the variance and the co-variance of +uh beta hat beta not hat and beta one + + align:start position:0% +uh beta hat beta not hat and beta one + + + align:start position:0% +uh beta hat beta not hat and beta one +hat are + + align:start position:0% +hat are + + + align:start position:0% +hat are +okay and again how did I get these pages + + align:start position:0% +okay and again how did I get these pages + + + align:start position:0% +okay and again how did I get these pages +of tedious calculations up on the + + align:start position:0% +of tedious calculations up on the + + + align:start position:0% +of tedious calculations up on the +website for your viewing pleasure um but + + align:start position:0% +website for your viewing pleasure um but + + + align:start position:0% +website for your viewing pleasure um but +you can skip them if you want because as + + align:start position:0% +you can skip them if you want because as + + + align:start position:0% +you can skip them if you want because as +I said we'll see a nice a much nicer way + + align:start position:0% +I said we'll see a nice a much nicer way + + + align:start position:0% +I said we'll see a nice a much nicer way +to to come up with these uh with these + + align:start position:0% +to to come up with these uh with these + + + align:start position:0% +to to come up with these uh with these +formulas next + + align:start position:0% +formulas next + + + align:start position:0% +formulas next +time and then how did I get the the mean + + align:start position:0% +time and then how did I get the the mean + + + align:start position:0% +time and then how did I get the the mean +actually I think the calc the sort of + + align:start position:0% +actually I think the calc the sort of + + + align:start position:0% +actually I think the calc the sort of +calculation of the mean of these is also + + align:start position:0% +calculation of the mean of these is also + + + align:start position:0% +calculation of the mean of these is also +up on the website but in fact I didn't I + + align:start position:0% +up on the website but in fact I didn't I + + + align:start position:0% +up on the website but in fact I didn't I +already told you they were unbiased + + align:start position:0% +already told you they were unbiased + + + align:start position:0% +already told you they were unbiased +estimators so we already knew that uh + + align:start position:0% +estimators so we already knew that uh + + + align:start position:0% +estimators so we already knew that uh +the mean of beta hat was equal to Beta + + align:start position:0% +the mean of beta hat was equal to Beta + + + align:start position:0% +the mean of beta hat was equal to Beta +hat not was equal to Beta + + align:start position:0% +hat not was equal to Beta + + + align:start position:0% +hat not was equal to Beta +not same thing with beta one + + align:start position:0% +not same thing with beta one + + + align:start position:0% +not same thing with beta one +okay okay so let's just talk let me take + + align:start position:0% +okay okay so let's just talk let me take + + + align:start position:0% +okay okay so let's just talk let me take +a moment to talk about a little bit of + + align:start position:0% +a moment to talk about a little bit of + + + align:start position:0% +a moment to talk about a little bit of +comparative Statics I think that this + + align:start position:0% +comparative Statics I think that this + + + align:start position:0% +comparative Statics I think that this +discussion will give you a little bit + + align:start position:0% +discussion will give you a little bit + + + align:start position:0% +discussion will give you a little bit +more of a feel for uh the mechanics of a + + align:start position:0% +more of a feel for uh the mechanics of a + + + align:start position:0% +more of a feel for uh the mechanics of a +linear regression and how um you know + + align:start position:0% +linear regression and how um you know + + + align:start position:0% +linear regression and how um you know +sort of how how this thing + + align:start position:0% +sort of how how this thing + + + align:start position:0% +sort of how how this thing +works so of so I list them here and I'll + + align:start position:0% +works so of so I list them here and I'll + + + align:start position:0% +works so of so I list them here and I'll +go through each one separately if we + + align:start position:0% +go through each one separately if we + + + align:start position:0% +go through each one separately if we +have a larger Sigma squared so imagine + + align:start position:0% +have a larger Sigma squared so imagine + + + align:start position:0% +have a larger Sigma squared so imagine +having sort of two different data sets + + align:start position:0% +having sort of two different data sets + + + align:start position:0% +having sort of two different data sets +they're identical except for one of them + + align:start position:0% +they're identical except for one of them + + + align:start position:0% +they're identical except for one of them +has a larger error variance + + align:start position:0% +has a larger error variance + + + align:start position:0% +has a larger error variance +what is how is that going to affect uh + + align:start position:0% +what is how is that going to affect uh + + + align:start position:0% +what is how is that going to affect uh +our estimates well you can just look at + + align:start position:0% +our estimates well you can just look at + + + align:start position:0% +our estimates well you can just look at +the the um the formulas for the variance + + align:start position:0% +the the um the formulas for the variance + + + align:start position:0% +the the um the formulas for the variance +and and the covariance and so forth of + + align:start position:0% +and and the covariance and so forth of + + + align:start position:0% +and and the covariance and so forth of +um of beta of our estimates and you can + + align:start position:0% +um of beta of our estimates and you can + + + align:start position:0% +um of beta of our estimates and you can +see that if we have a larger Sigma + + align:start position:0% +see that if we have a larger Sigma + + + align:start position:0% +see that if we have a larger Sigma +squared that's going to mean that the + + align:start position:0% +squared that's going to mean that the + + + align:start position:0% +squared that's going to mean that the +variance of beta hat is larger okay I'll + + align:start position:0% +variance of beta hat is larger okay I'll + + + align:start position:0% +variance of beta hat is larger okay I'll +show you a picture of that in a second + + align:start position:0% +show you a picture of that in a second + + + align:start position:0% +show you a picture of that in a second +uh if we have a larger uh variance of X + + align:start position:0% +uh if we have a larger uh variance of X + + + align:start position:0% +uh if we have a larger uh variance of X +so in other words our X's are more + + align:start position:0% +so in other words our X's are more + + + align:start position:0% +so in other words our X's are more +spread out that's going to lead to a + + align:start position:0% +spread out that's going to lead to a + + + align:start position:0% +spread out that's going to lead to a +smaller variance in beta hat and a + + align:start position:0% +smaller variance in beta hat and a + + + align:start position:0% +smaller variance in beta hat and a +larger n also means a smaller variance + + align:start position:0% +larger n also means a smaller variance + + + align:start position:0% +larger n also means a smaller variance +of beta + + align:start position:0% +of beta + + + align:start position:0% +of beta +hat and then furthermore um the if uh if + + align:start position:0% +hat and then furthermore um the if uh if + + + align:start position:0% +hat and then furthermore um the if uh if +the um mean of X is positive then we're + + align:start position:0% +the um mean of X is positive then we're + + + align:start position:0% +the um mean of X is positive then we're +going to have a sort of negative + + align:start position:0% +going to have a sort of negative + + + align:start position:0% +going to have a sort of negative +co-variance a negative relation + + align:start position:0% +co-variance a negative relation + + + align:start position:0% +co-variance a negative relation +relationship between beta not hat and + + align:start position:0% +relationship between beta not hat and + + + align:start position:0% +relationship between beta not hat and +beta one hat and I didn't write it down + + align:start position:0% +beta one hat and I didn't write it down + + + align:start position:0% +beta one hat and I didn't write it down +here but if xbar is negative then that + + align:start position:0% +here but if xbar is negative then that + + + align:start position:0% +here but if xbar is negative then that +flips okay so let me show you pictures + + align:start position:0% +flips okay so let me show you pictures + + + align:start position:0% +flips okay so let me show you pictures +of these and that'll make uh the + + align:start position:0% +of these and that'll make uh the + + + align:start position:0% +of these and that'll make uh the +comparative Statics a little little + + align:start position:0% +comparative Statics a little little + + + align:start position:0% +comparative Statics a little little +clear I think oh and I should say oh + + align:start position:0% +clear I think oh and I should say oh + + + align:start position:0% +clear I think oh and I should say oh +just a point of notation um I'm often + + align:start position:0% +just a point of notation um I'm often + + + align:start position:0% +just a point of notation um I'm often +going to just start sliding into sort of + + align:start position:0% +going to just start sliding into sort of + + + align:start position:0% +going to just start sliding into sort of +Matrix and Vector notation and when I + + align:start position:0% +Matrix and Vector notation and when I + + + align:start position:0% +Matrix and Vector notation and when I +say beta hat I'm talking about the + + align:start position:0% +say beta hat I'm talking about the + + + align:start position:0% +say beta hat I'm talking about the +vector um + + align:start position:0% +vector um + + + align:start position:0% +vector um +beta uh not hat and beta one hat + + align:start position:0% + + + + align:start position:0% + +okay okay so what's the first + + align:start position:0% +okay okay so what's the first + + + align:start position:0% +okay okay so what's the first +comparative static um what is what does + + align:start position:0% +comparative static um what is what does + + + align:start position:0% +comparative static um what is what does +that suggest about the mechanics of + + align:start position:0% +that suggest about the mechanics of + + + align:start position:0% +that suggest about the mechanics of +regression so we have two identical data + + align:start position:0% +regression so we have two identical data + + + align:start position:0% +regression so we have two identical data +sets the only difference is that the + + align:start position:0% +sets the only difference is that the + + + align:start position:0% +sets the only difference is that the +error variance is greater than one what + + align:start position:0% +error variance is greater than one what + + + align:start position:0% +error variance is greater than one what +does that mean uh that in this case + + align:start position:0% +does that mean uh that in this case + + + align:start position:0% +does that mean uh that in this case +we're going to be less sure of our + + align:start position:0% +we're going to be less sure of our + + + align:start position:0% +we're going to be less sure of our +estimates the variance of beta hat is + + align:start position:0% +estimates the variance of beta hat is + + + align:start position:0% +estimates the variance of beta hat is +greater okay we're just going to have + + align:start position:0% +greater okay we're just going to have + + + align:start position:0% +greater okay we're just going to have +less confidence in our estimat that + + align:start position:0% +less confidence in our estimat that + + + align:start position:0% +less confidence in our estimat that +makes sense right if we have very small + + align:start position:0% +makes sense right if we have very small + + + align:start position:0% +makes sense right if we have very small +error variances we're going to be able + + align:start position:0% +error variances we're going to be able + + + align:start position:0% +error variances we're going to be able +to estimate that linear relationship + + align:start position:0% +to estimate that linear relationship + + + align:start position:0% +to estimate that linear relationship +very + + align:start position:0% + + + + align:start position:0% + +precisely How about if our we have the + + align:start position:0% +precisely How about if our we have the + + + align:start position:0% +precisely How about if our we have the +two same data sets but in this case the + + align:start position:0% +two same data sets but in this case the + + + align:start position:0% +two same data sets but in this case the +x's on the left are very spread out we + + align:start position:0% +x's on the left are very spread out we + + + align:start position:0% +x's on the left are very spread out we +have a lot of variation in the x's and + + align:start position:0% +have a lot of variation in the x's and + + + align:start position:0% +have a lot of variation in the x's and +in the other case the xes Are all uh + + align:start position:0% +in the other case the xes Are all uh + + + align:start position:0% +in the other case the xes Are all uh +smooshed together into one little + + align:start position:0% +smooshed together into one little + + + align:start position:0% +smooshed together into one little +area well in the case where they're all + + align:start position:0% +area well in the case where they're all + + + align:start position:0% +area well in the case where they're all +smooshed together remember in the limit + + align:start position:0% +smooshed together remember in the limit + + + align:start position:0% +smooshed together remember in the limit +we can't even estimate our linear + + align:start position:0% +we can't even estimate our linear + + + align:start position:0% +we can't even estimate our linear +regression uh coefficients right + + align:start position:0% +regression uh coefficients right + + + align:start position:0% +regression uh coefficients right +remember the picture I showed you at the + + align:start position:0% +remember the picture I showed you at the + + + align:start position:0% +remember the picture I showed you at the +beginning where all of the observations + + align:start position:0% +beginning where all of the observations + + + align:start position:0% +beginning where all of the observations +on X were on a single um point we + + align:start position:0% +on X were on a single um point we + + + align:start position:0% +on X were on a single um point we +couldn't even estimate the linear + + align:start position:0% +couldn't even estimate the linear + + + align:start position:0% +couldn't even estimate the linear +regression coefficients there here we + + align:start position:0% +regression coefficients there here we + + + align:start position:0% +regression coefficients there here we +can estimate them but uh the variance is + + align:start position:0% +can estimate them but uh the variance is + + + align:start position:0% +can estimate them but uh the variance is +going to be pretty big we're going to be + + align:start position:0% +going to be pretty big we're going to be + + + align:start position:0% +going to be pretty big we're going to be +less sure of our estimates in this case + + align:start position:0% +less sure of our estimates in this case + + + align:start position:0% +less sure of our estimates in this case +uh because we don't have a lot of of + + align:start position:0% +uh because we don't have a lot of of + + + align:start position:0% +uh because we don't have a lot of of +variation of x to help help us identify + + align:start position:0% +variation of x to help help us identify + + + align:start position:0% +variation of x to help help us identify +the effect we're interested in + + align:start position:0% + + + + align:start position:0% + +okay a larger N means a smaller variance + + align:start position:0% +okay a larger N means a smaller variance + + + align:start position:0% +okay a larger N means a smaller variance +of beta hat well I don't need to draw a + + align:start position:0% +of beta hat well I don't need to draw a + + + align:start position:0% +of beta hat well I don't need to draw a +picture of this uh we'll just note that + + align:start position:0% +picture of this uh we'll just note that + + + align:start position:0% +picture of this uh we'll just note that +this follows from the fact that beta hat + + align:start position:0% +this follows from the fact that beta hat + + + align:start position:0% +this follows from the fact that beta hat +uh are consistent estimators + + align:start position:0% + + + + align:start position:0% + +okay and then finally there uh is this + + align:start position:0% +okay and then finally there uh is this + + + align:start position:0% +okay and then finally there uh is this +mechanical relationship between the two + + align:start position:0% +mechanical relationship between the two + + + align:start position:0% +mechanical relationship between the two +estimates so if we have for uh the mean + + align:start position:0% +estimates so if we have for uh the mean + + + align:start position:0% +estimates so if we have for uh the mean +of our X's is positive then basically if + + align:start position:0% +of our X's is positive then basically if + + + align:start position:0% +of our X's is positive then basically if +we have if we sort of uh + + align:start position:0% +we have if we sort of uh + + + align:start position:0% +we have if we sort of uh +overestimate the the um intercept of the + + align:start position:0% +overestimate the the um intercept of the + + + align:start position:0% +overestimate the the um intercept of the +line we're going to underestimate the + + align:start position:0% +line we're going to underestimate the + + + align:start position:0% +line we're going to underestimate the +slope or an overestimate of The + + align:start position:0% +slope or an overestimate of The + + + align:start position:0% +slope or an overestimate of The +Intercept is associated with an + + align:start position:0% +Intercept is associated with an + + + align:start position:0% +Intercept is associated with an +underestimate of the slope an + + align:start position:0% +underestimate of the slope an + + + align:start position:0% +underestimate of the slope an +underestimate of the uh intercept is + + align:start position:0% +underestimate of the uh intercept is + + + align:start position:0% +underestimate of the uh intercept is +associated with an overestimate of the + + align:start position:0% +associated with an overestimate of the + + + align:start position:0% +associated with an overestimate of the +slope okay so it's just this mechanical + + align:start position:0% +slope okay so it's just this mechanical + + + align:start position:0% +slope okay so it's just this mechanical +relation ship and then if the if xar is + + align:start position:0% +relation ship and then if the if xar is + + + align:start position:0% +relation ship and then if the if xar is +negative the mechanical relationship + + align:start position:0% +negative the mechanical relationship + + + align:start position:0% +negative the mechanical relationship +shifts okay or + + align:start position:0% +shifts okay or + + + align:start position:0% +shifts okay or +flips + + align:start position:0% +flips + + + align:start position:0% +flips +okay okay so one step further if we use + + align:start position:0% +okay okay so one step further if we use + + + align:start position:0% +okay okay so one step further if we use +the stronger assumption that the errors + + align:start position:0% +the stronger assumption that the errors + + + align:start position:0% +the stronger assumption that the errors +are IID normal uh 0 Sigma squar then we + + align:start position:0% +are IID normal uh 0 Sigma squar then we + + + align:start position:0% +are IID normal uh 0 Sigma squar then we +obtain in addition so we already have + + align:start position:0% +obtain in addition so we already have + + + align:start position:0% +obtain in addition so we already have +the mean and the variance and the + + align:start position:0% +the mean and the variance and the + + + align:start position:0% +the mean and the variance and the +co-variance of these two estimates but + + align:start position:0% +co-variance of these two estimates but + + + align:start position:0% +co-variance of these two estimates but +we also have that they um they have + + align:start position:0% +we also have that they um they have + + + align:start position:0% +we also have that they um they have +normal distributions if the errors have + + align:start position:0% +normal distributions if the errors have + + + align:start position:0% +normal distributions if the errors have +normal distributions okay so if we're + + align:start position:0% +normal distributions okay so if we're + + + align:start position:0% +normal distributions okay so if we're +willing or if we we feel like imposing + + align:start position:0% +willing or if we we feel like imposing + + + align:start position:0% +willing or if we we feel like imposing +that extra Assumption of normality of + + align:start position:0% +that extra Assumption of normality of + + + align:start position:0% +that extra Assumption of normality of +Errors then what we get out of it is + + align:start position:0% +Errors then what we get out of it is + + + align:start position:0% +Errors then what we get out of it is +normality of our estimators + + align:start position:0% + + + + align:start position:0% + +okay okay one loose end um if the note + + align:start position:0% +okay okay one loose end um if the note + + + align:start position:0% +okay okay one loose end um if the note +that the dist distributions of beta not + + align:start position:0% +that the dist distributions of beta not + + + align:start position:0% +that the dist distributions of beta not +hat and beta 1 Hat are functions of + + align:start position:0% +hat and beta 1 Hat are functions of + + + align:start position:0% +hat and beta 1 Hat are functions of +Sigma squ um that is the the error + + align:start position:0% +Sigma squ um that is the the error + + + align:start position:0% +Sigma squ um that is the the error +variance we often don't know the error + + align:start position:0% +variance we often don't know the error + + + align:start position:0% +variance we often don't know the error +variance why would we know the error + + align:start position:0% +variance why would we know the error + + + align:start position:0% +variance why would we know the error +variance uh so we estimate it okay and + + align:start position:0% +variance uh so we estimate it okay and + + + align:start position:0% +variance uh so we estimate it okay and +we're going to use a different estimator + + align:start position:0% +we're going to use a different estimator + + + align:start position:0% +we're going to use a different estimator +than uh than estimators we've seen + + align:start position:0% +than uh than estimators we've seen + + + align:start position:0% +than uh than estimators we've seen +before so we're going to use an + + align:start position:0% +before so we're going to use an + + + align:start position:0% +before so we're going to use an +estimator uh that's equal to 1 over nus + + align:start position:0% +estimator uh that's equal to 1 over nus + + + align:start position:0% +estimator uh that's equal to 1 over nus +2 times the sum of the uh residual + + align:start position:0% +2 times the sum of the uh residual + + + align:start position:0% +2 times the sum of the uh residual +squared + + align:start position:0% +squared + + + align:start position:0% +squared +okay and this estimator turns out is + + align:start position:0% +okay and this estimator turns out is + + + align:start position:0% +okay and this estimator turns out is +unbiased for Sigma squar in the linear + + align:start position:0% +unbiased for Sigma squar in the linear + + + align:start position:0% +unbiased for Sigma squar in the linear +model that's why we use it uh why the + + align:start position:0% +model that's why we use it uh why the + + + align:start position:0% +model that's why we use it uh why the +minus 2 in the denominator well it's + + align:start position:0% +minus 2 in the denominator well it's + + + align:start position:0% +minus 2 in the denominator well it's +because we're estimating two parameters + + align:start position:0% +because we're estimating two parameters + + + align:start position:0% +because we're estimating two parameters +do you remember our unbiased estimator + + align:start position:0% +do you remember our unbiased estimator + + + align:start position:0% +do you remember our unbiased estimator +for the variance when we were just + + align:start position:0% +for the variance when we were just + + + align:start position:0% +for the variance when we were just +estimating the mean was uh had an N + + align:start position:0% +estimating the mean was uh had an N + + + align:start position:0% +estimating the mean was uh had an N +minus one in the the denominator well + + align:start position:0% +minus one in the the denominator well + + + align:start position:0% +minus one in the the denominator well +here we need the n minus two because + + align:start position:0% +here we need the n minus two because + + + align:start position:0% +here we need the n minus two because +we're estimating two parameters a beta + + align:start position:0% +we're estimating two parameters a beta + + + align:start position:0% +we're estimating two parameters a beta +beta not and a beta 1 and it turns out + + align:start position:0% +beta not and a beta 1 and it turns out + + + align:start position:0% +beta not and a beta 1 and it turns out +that that's what we need for Sigma + + align:start position:0% +that that's what we need for Sigma + + + align:start position:0% +that that's what we need for Sigma +Square to be unbiased okay yep you + + align:start position:0% +Square to be unbiased okay yep you + + + align:start position:0% +Square to be unbiased okay yep you +remind us why that is or why so I didn't + + align:start position:0% +remind us why that is or why so I didn't + + + align:start position:0% +remind us why that is or why so I didn't +do the + + align:start position:0% +do the + + + align:start position:0% +do the +proof um and to be honest I don't have I + + align:start position:0% +proof um and to be honest I don't have I + + + align:start position:0% +proof um and to be honest I don't have I +don't feel like I have a a useful + + align:start position:0% +don't feel like I have a a useful + + + align:start position:0% +don't feel like I have a a useful +intuition to tell you I mean I you know + + align:start position:0% +intuition to tell you I mean I you know + + + align:start position:0% +intuition to tell you I mean I you know +I'm happy to give you the proof and the + + align:start position:0% +I'm happy to give you the proof and the + + + align:start position:0% +I'm happy to give you the proof and the +proof of this you know the proof of this + + align:start position:0% +proof of this you know the proof of this + + + align:start position:0% +proof of this you know the proof of this +isn't much more complicated than in the + + align:start position:0% +isn't much more complicated than in the + + + align:start position:0% +isn't much more complicated than in the +sort of univariant case um but yeah it's + + align:start position:0% +sort of univariant case um but yeah it's + + + align:start position:0% +sort of univariant case um but yeah it's +just that's it just turns out that that + + align:start position:0% +just that's it just turns out that that + + + align:start position:0% +just that's it just turns out that that +that's what you need to do to have an + + align:start position:0% +that's what you need to do to have an + + + align:start position:0% +that's what you need to do to have an +unbiased estimator of the variance do + + align:start position:0% +unbiased estimator of the variance do + + + align:start position:0% +unbiased estimator of the variance do +you have a useful intuition I don't know + + align:start position:0% +you have a useful intuition I don't know + + + align:start position:0% +you have a useful intuition I don't know +no + + align:start position:0% + + + + align:start position:0% + +okay if you twist me three + + align:start position:0% +okay if you twist me three + + + align:start position:0% +okay if you twist me three +things yes yes exactly I don't know + + align:start position:0% +things yes yes exactly I don't know + + + align:start position:0% +things yes yes exactly I don't know +why it does + + align:start position:0% + + + + align:start position:0% + +okay so now I want to ask you to think + + align:start position:0% +okay so now I want to ask you to think + + + align:start position:0% +okay so now I want to ask you to think +back + + align:start position:0% +back + + + align:start position:0% +back +to um when we were doing univariant + + align:start position:0% +to um when we were doing univariant + + + align:start position:0% +to um when we were doing univariant +inference and we replaced an unknown + + align:start position:0% +inference and we replaced an unknown + + + align:start position:0% +inference and we replaced an unknown +variance with an estimate of the + + align:start position:0% +variance with an estimate of the + + + align:start position:0% +variance with an estimate of the +variance so we had a sample mean and the + + align:start position:0% +variance so we had a sample mean and the + + + align:start position:0% +variance so we had a sample mean and the +sample mean had a normal + + align:start position:0% +sample mean had a normal + + + align:start position:0% +sample mean had a normal +distribution but we didn't know the + + align:start position:0% +distribution but we didn't know the + + + align:start position:0% +distribution but we didn't know the +variance the sorry the standardized + + align:start position:0% +variance the sorry the standardized + + + align:start position:0% +variance the sorry the standardized +sample the you know standardized sample + + align:start position:0% +sample the you know standardized sample + + + align:start position:0% +sample the you know standardized sample +mean had a standard normal distribution + + align:start position:0% +mean had a standard normal distribution + + + align:start position:0% +mean had a standard normal distribution +but we actually didn't know what the + + align:start position:0% +but we actually didn't know what the + + + align:start position:0% +but we actually didn't know what the +variance was and we replaced an estimate + + align:start position:0% +variance was and we replaced an estimate + + + align:start position:0% +variance was and we replaced an estimate +for the variance what + + align:start position:0% +for the variance what + + + align:start position:0% +for the variance what +happened you guys remember that's what + + align:start position:0% +happened you guys remember that's what + + + align:start position:0% +happened you guys remember that's what +happened T distribution right okay well + + align:start position:0% +happened T distribution right okay well + + + align:start position:0% +happened T distribution right okay well +the same thing's going to happen here um + + align:start position:0% +the same thing's going to happen here um + + + align:start position:0% +the same thing's going to happen here um +we'll we'll talk I won't talk about sort + + align:start position:0% +we'll we'll talk I won't talk about sort + + + align:start position:0% +we'll we'll talk I won't talk about sort +of T tests in the the context of linear + + align:start position:0% +of T tests in the the context of linear + + + align:start position:0% +of T tests in the the context of linear +regression today um I should be able to + + align:start position:0% +regression today um I should be able to + + + align:start position:0% +regression today um I should be able to +get to them next time um but basically + + align:start position:0% +get to them next time um but basically + + + align:start position:0% +get to them next time um but basically +just to give you a little bit of a + + align:start position:0% +just to give you a little bit of a + + + align:start position:0% +just to give you a little bit of a +preview the same thing's going to happen + + align:start position:0% +preview the same thing's going to happen + + + align:start position:0% +preview the same thing's going to happen +here we have under the assumption of + + align:start position:0% +here we have under the assumption of + + + align:start position:0% +here we have under the assumption of +normal errors we have that beta not hat + + align:start position:0% +normal errors we have that beta not hat + + + align:start position:0% +normal errors we have that beta not hat +and beta 1 Hat have normal distributions + + align:start position:0% +and beta 1 Hat have normal distributions + + + align:start position:0% +and beta 1 Hat have normal distributions +but we don't know what their variance is + + align:start position:0% +but we don't know what their variance is + + + align:start position:0% +but we don't know what their variance is +we're going to have to use an estimated + + align:start position:0% +we're going to have to use an estimated + + + align:start position:0% +we're going to have to use an estimated +variance instead typically and so that's + + align:start position:0% +variance instead typically and so that's + + + align:start position:0% +variance instead typically and so that's +where the sort of test in the in the + + align:start position:0% +where the sort of test in the in the + + + align:start position:0% +where the sort of test in the in the +linear regression context comes from + + align:start position:0% +linear regression context comes from + + + align:start position:0% +linear regression context comes from +okay so now we're sort of we have most + + align:start position:0% +okay so now we're sort of we have most + + + align:start position:0% +okay so now we're sort of we have most +of the pieces the model the estimators + + align:start position:0% +of the pieces the model the estimators + + + align:start position:0% +of the pieces the model the estimators +information about the distribution of + + align:start position:0% +information about the distribution of + + + align:start position:0% +information about the distribution of +the estimators we could proceed with + + align:start position:0% +the estimators we could proceed with + + + align:start position:0% +the estimators we could proceed with +inference but I'm going to put that off + + align:start position:0% +inference but I'm going to put that off + + + align:start position:0% +inference but I'm going to put that off +for a little while and um what we're + + align:start position:0% +for a little while and um what we're + + + align:start position:0% +for a little while and um what we're +going to do now is take uh you know a + + align:start position:0% +going to do now is take uh you know a + + + align:start position:0% +going to do now is take uh you know a +quick detour into something called + + align:start position:0% +quick detour into something called + + + align:start position:0% +quick detour into something called +analysis of variance and then I'm also + + align:start position:0% +analysis of variance and then I'm also + + + align:start position:0% +analysis of variance and then I'm also +going to talk about some sort of + + align:start position:0% +going to talk about some sort of + + + align:start position:0% +going to talk about some sort of +practical issues uh in estimating uh + + align:start position:0% +practical issues uh in estimating uh + + + align:start position:0% +practical issues uh in estimating uh +linear regressions before we get to + + align:start position:0% +linear regressions before we get to + + + align:start position:0% +linear regressions before we get to +inference we'll do influence next + + align:start position:0% +inference we'll do influence next + + + align:start position:0% +inference we'll do influence next +time + + align:start position:0% +time + + + align:start position:0% +time +okay so we we want some way uh typically + + align:start position:0% +okay so we we want some way uh typically + + + align:start position:0% +okay so we we want some way uh typically +to indicate how closely associated X and + + align:start position:0% +to indicate how closely associated X and + + + align:start position:0% +to indicate how closely associated X and +Y are or how much of y's variation is + + align:start position:0% +Y are or how much of y's variation is + + + align:start position:0% +Y are or how much of y's variation is +explained by X's variation okay and what + + align:start position:0% +explained by X's variation okay and what + + + align:start position:0% +explained by X's variation okay and what +we do is we perform an analysis of + + align:start position:0% +we do is we perform an analysis of + + + align:start position:0% +we do is we perform an analysis of +variance um that I'll do in just a + + align:start position:0% +variance um that I'll do in just a + + + align:start position:0% +variance um that I'll do in just a +second and that's going to lead us to a + + align:start position:0% +second and that's going to lead us to a + + + align:start position:0% +second and that's going to lead us to a +measure of goodness of fit for our + + align:start position:0% +measure of goodness of fit for our + + + align:start position:0% +measure of goodness of fit for our +linear regression and that's uh you know + + align:start position:0% +linear regression and that's uh you know + + + align:start position:0% +linear regression and that's uh you know +typically sort of a useful gauge of of + + align:start position:0% +typically sort of a useful gauge of of + + + align:start position:0% +typically sort of a useful gauge of of +you know sort of how the regression is + + align:start position:0% +you know sort of how the regression is + + + align:start position:0% +you know sort of how the regression is +doing in some sense okay so let's start + + align:start position:0% +doing in some sense okay so let's start + + + align:start position:0% +doing in some sense okay so let's start +by defining the sum of squared residuals + + align:start position:0% +by defining the sum of squared residuals + + + align:start position:0% +by defining the sum of squared residuals +Okay so we've actually already seen the + + align:start position:0% +Okay so we've actually already seen the + + + align:start position:0% +Okay so we've actually already seen the +sum of squared residuals that's what we + + align:start position:0% +sum of squared residuals that's what we + + + align:start position:0% +sum of squared residuals that's what we +were minimizing choosing you know beta + + align:start position:0% +were minimizing choosing you know beta + + + align:start position:0% +were minimizing choosing you know beta +not hat and beta one hat to minimize + + align:start position:0% +not hat and beta one hat to minimize + + + align:start position:0% +not hat and beta one hat to minimize +okay let's just Define this quantity + + align:start position:0% +okay let's just Define this quantity + + + align:start position:0% +okay let's just Define this quantity +here as the sum of squared + + align:start position:0% + + + + align:start position:0% + +residuals and here's a picture of it so + + align:start position:0% +residuals and here's a picture of it so + + + align:start position:0% +residuals and here's a picture of it so +the picture can't indicate I mean each + + align:start position:0% +the picture can't indicate I mean each + + + align:start position:0% +the picture can't indicate I mean each +one of these so what we do is we we + + align:start position:0% +one of these so what we do is we we + + + align:start position:0% +one of these so what we do is we we +calculate each one of these we Square it + + align:start position:0% +calculate each one of these we Square it + + + align:start position:0% +calculate each one of these we Square it +and we add them together that's the sum + + align:start position:0% +and we add them together that's the sum + + + align:start position:0% +and we add them together that's the sum +of squared + + align:start position:0% + + + + align:start position:0% + +residuals and this is in some sense a + + align:start position:0% +residuals and this is in some sense a + + + align:start position:0% +residuals and this is in some sense a +measure of goodness of fit right um but + + align:start position:0% +measure of goodness of fit right um but + + + align:start position:0% +measure of goodness of fit right um but +it's not a very useful measure of + + align:start position:0% +it's not a very useful measure of + + + align:start position:0% +it's not a very useful measure of +goodness of fit because it's not unit + + align:start position:0% +goodness of fit because it's not unit + + + align:start position:0% +goodness of fit because it's not unit +free okay which is inconvenient so let's + + align:start position:0% +free okay which is inconvenient so let's + + + align:start position:0% +free okay which is inconvenient so let's +say we have a data set and both of the + + align:start position:0% +say we have a data set and both of the + + + align:start position:0% +say we have a data set and both of the +variables are measured measured in um + + align:start position:0% +variables are measured measured in um + + + align:start position:0% +variables are measured measured in um +you know uh pounds British pounds and + + align:start position:0% +you know uh pounds British pounds and + + + align:start position:0% +you know uh pounds British pounds and +then we uh uh translate uh both of the + + align:start position:0% +then we uh uh translate uh both of the + + + align:start position:0% +then we uh uh translate uh both of the +variables to Dollars um then the sum of + + align:start position:0% +variables to Dollars um then the sum of + + + align:start position:0% +variables to Dollars um then the sum of +squared residuals will actually change + + align:start position:0% +squared residuals will actually change + + + align:start position:0% +squared residuals will actually change +and that's not a very convenient feature + + align:start position:0% +and that's not a very convenient feature + + + align:start position:0% +and that's not a very convenient feature +for sort of a measure of fit to have + + align:start position:0% +for sort of a measure of fit to have + + + align:start position:0% +for sort of a measure of fit to have +okay but if we divide the sum of squared + + align:start position:0% +okay but if we divide the sum of squared + + + align:start position:0% +okay but if we divide the sum of squared +residuals by uh some other sum of + + align:start position:0% +residuals by uh some other sum of + + + align:start position:0% +residuals by uh some other sum of +squares the total sum of squares for + + align:start position:0% +squares the total sum of squares for + + + align:start position:0% +squares the total sum of squares for +instance then that gives us a unit free + + align:start position:0% +instance then that gives us a unit free + + + align:start position:0% +instance then that gives us a unit free +measure because the units cancel so + + align:start position:0% +measure because the units cancel so + + + align:start position:0% +measure because the units cancel so +what's the total sum of squares well the + + align:start position:0% +what's the total sum of squares well the + + + align:start position:0% +what's the total sum of squares well the +total sum of squares is we don't even + + align:start position:0% +total sum of squares is we don't even + + + align:start position:0% +total sum of squares is we don't even +fit a regression line we just take the + + align:start position:0% +fit a regression line we just take the + + + align:start position:0% +fit a regression line we just take the +uh the the uh sample mean of Y and just + + align:start position:0% +uh the the uh sample mean of Y and just + + + align:start position:0% +uh the the uh sample mean of Y and just +uh calculate all of the deviations from + + align:start position:0% +uh calculate all of the deviations from + + + align:start position:0% +uh calculate all of the deviations from +the sample mean and square those up so + + align:start position:0% +the sample mean and square those up so + + + align:start position:0% +the sample mean and square those up so +graphically what does that look like so + + align:start position:0% +graphically what does that look like so + + + align:start position:0% +graphically what does that look like so +let's say this line is Y Bar okay so + + align:start position:0% +let's say this line is Y Bar okay so + + + align:start position:0% +let's say this line is Y Bar okay so +what we've done is we've just taken all + + align:start position:0% +what we've done is we've just taken all + + + align:start position:0% +what we've done is we've just taken all +of the the deviations from Yar squared + + align:start position:0% +of the the deviations from Yar squared + + + align:start position:0% +of the the deviations from Yar squared +them and sum them up that's the total + + align:start position:0% +them and sum them up that's the total + + + align:start position:0% +them and sum them up that's the total +sum of squares + + align:start position:0% +sum of squares + + + align:start position:0% +sum of squares +okay so that + + align:start position:0% +okay so that + + + align:start position:0% +okay so that +um so we've got the residual sum of + + align:start position:0% +um so we've got the residual sum of + + + align:start position:0% +um so we've got the residual sum of +squares and we've got the total sum of + + align:start position:0% +squares and we've got the total sum of + + + align:start position:0% +squares and we've got the total sum of +squares and note that that is going to + + align:start position:0% +squares and note that that is going to + + + align:start position:0% +squares and note that that is going to +be a unit-free measure of goodness of + + align:start position:0% +be a unit-free measure of goodness of + + + align:start position:0% +be a unit-free measure of goodness of +fit uh that's always going to be between + + align:start position:0% +fit uh that's always going to be between + + + align:start position:0% +fit uh that's always going to be between +zero and one why is it always between + + align:start position:0% +zero and one why is it always between + + + align:start position:0% +zero and one why is it always between +zero and + + align:start position:0% +zero and + + + align:start position:0% +zero and +one yep both values are always all right + + align:start position:0% +one yep both values are always all right + + + align:start position:0% +one yep both values are always all right +so I guess the question is actually why + + align:start position:0% +so I guess the question is actually why + + + align:start position:0% +so I guess the question is actually why +is uh the SSR always less than S since + + align:start position:0% +is uh the SSR always less than S since + + + align:start position:0% +is uh the SSR always less than S since +they're both positive yeah yeah they're + + align:start position:0% +they're both positive yeah yeah they're + + + align:start position:0% +they're both positive yeah yeah they're +both positive yes so you got half of it + + align:start position:0% +both positive yes so you got half of it + + + align:start position:0% +both positive yes so you got half of it +right okay yep is like the maximum error + + align:start position:0% +right okay yep is like the maximum error + + + align:start position:0% +right okay yep is like the maximum error +you have uh no well no I could I could + + align:start position:0% +you have uh no well no I could I could + + + align:start position:0% +you have uh no well no I could I could +draw I could draw a line that gave + + align:start position:0% +draw I could draw a line that gave + + + align:start position:0% +draw I could draw a line that gave +me um more air but basically the the + + align:start position:0% +me um more air but basically the the + + + align:start position:0% +me um more air but basically the the +you're you're on the right track the SSR + + align:start position:0% +you're you're on the right track the SSR + + + align:start position:0% +you're you're on the right track the SSR +is the least error you can have why is + + align:start position:0% +is the least error you can have why is + + + align:start position:0% +is the least error you can have why is +that that's how we chose the regression + + align:start position:0% +that that's how we chose the regression + + + align:start position:0% +that that's how we chose the regression +line to minimize that quantity okay so + + align:start position:0% +line to minimize that quantity okay so + + + align:start position:0% +line to minimize that quantity okay so +any other line is going to have it's + + align:start position:0% +any other line is going to have it's + + + align:start position:0% +any other line is going to have it's +going to give you higher sum of squared + + align:start position:0% +going to give you higher sum of squared + + + align:start position:0% +going to give you higher sum of squared +errors any anything else you do is going + + align:start position:0% +errors any anything else you do is going + + + align:start position:0% +errors any anything else you do is going +to give a higher sum of squared errors + + align:start position:0% +to give a higher sum of squared errors + + + align:start position:0% +to give a higher sum of squared errors +than the SSR okay and so that's what yes + + align:start position:0% +than the SSR okay and so that's what yes + + + align:start position:0% +than the SSR okay and so that's what yes +so you got half of it they're both non- + + align:start position:0% +so you got half of it they're both non- + + + align:start position:0% +so you got half of it they're both non- +negative by construction and the fact + + align:start position:0% +negative by construction and the fact + + + align:start position:0% +negative by construction and the fact +that the regression line is the least + + align:start position:0% +that the regression line is the least + + + align:start position:0% +that the regression line is the least +squares line ensures that SSR is always + + align:start position:0% +squares line ensures that SSR is always + + + align:start position:0% +squares line ensures that SSR is always +less than or equal to SST + + align:start position:0% + + + + align:start position:0% + +okay okay so that could be our goodness + + align:start position:0% +okay okay so that could be our goodness + + + align:start position:0% +okay okay so that could be our goodness +of fit measure actually I guess we + + align:start position:0% +of fit measure actually I guess we + + + align:start position:0% +of fit measure actually I guess we +wanted a goodness of fit measure um that + + align:start position:0% +wanted a goodness of fit measure um that + + + align:start position:0% +wanted a goodness of fit measure um that +had larger values when the fit was + + align:start position:0% +had larger values when the fit was + + + align:start position:0% +had larger values when the fit was +better or explained more so instead what + + align:start position:0% +better or explained more so instead what + + + align:start position:0% +better or explained more so instead what +we decided is uh we' use we Define our + + align:start position:0% +we decided is uh we' use we Define our + + + align:start position:0% +we decided is uh we' use we Define our +goodness of fit measure r s to be equal + + align:start position:0% +goodness of fit measure r s to be equal + + + align:start position:0% +goodness of fit measure r s to be equal +to 1 minus SSR over SST okay it's a it's + + align:start position:0% +to 1 minus SSR over SST okay it's a it's + + + align:start position:0% +to 1 minus SSR over SST okay it's a it's +an arbitrary decision but that's that's + + align:start position:0% +an arbitrary decision but that's that's + + + align:start position:0% +an arbitrary decision but that's that's +what it is + + align:start position:0% + + + + align:start position:0% + +and it turns out that the total sum of + + align:start position:0% +and it turns out that the total sum of + + + align:start position:0% +and it turns out that the total sum of +squares can be decomposed into two terms + + align:start position:0% +squares can be decomposed into two terms + + + align:start position:0% +squares can be decomposed into two terms +the residual sum of squares and + + align:start position:0% +the residual sum of squares and + + + align:start position:0% +the residual sum of squares and +something called the model sum of + + align:start position:0% +something called the model sum of + + + align:start position:0% +something called the model sum of +squares um and so then R squar it could + + align:start position:0% +squares um and so then R squar it could + + + align:start position:0% +squares um and so then R squar it could +also be written as just the model sum of + + align:start position:0% +also be written as just the model sum of + + + align:start position:0% +also be written as just the model sum of +squares over the total sum of squares + + align:start position:0% +squares over the total sum of squares + + + align:start position:0% +squares over the total sum of squares +okay here's the model sum of squares and + + align:start position:0% +okay here's the model sum of squares and + + + align:start position:0% +okay here's the model sum of squares and +here's a picture of + + align:start position:0% + + + + align:start position:0% + +it okay it's just the fitted value the + + align:start position:0% +it okay it's just the fitted value the + + + align:start position:0% +it okay it's just the fitted value the +sort of difference between the fitted + + align:start position:0% +sort of difference between the fitted + + + align:start position:0% +sort of difference between the fitted +value and the and Y + + align:start position:0% + + + + align:start position:0% + +Bar oh that's just something about the + + align:start position:0% +Bar oh that's just something about the + + + align:start position:0% +Bar oh that's just something about the +decomposition + + align:start position:0% +decomposition + + + align:start position:0% +decomposition +Okay Okay so we've got this thing called + + align:start position:0% +Okay Okay so we've got this thing called + + + align:start position:0% +Okay Okay so we've got this thing called +R squar and in a b variant regression so + + align:start position:0% +R squar and in a b variant regression so + + + align:start position:0% +R squar and in a b variant regression so +in the in the regressions we've seen so + + align:start position:0% +in the in the regressions we've seen so + + + align:start position:0% +in the in the regressions we've seen so +far that just have one explanatory + + align:start position:0% +far that just have one explanatory + + + align:start position:0% +far that just have one explanatory +variable this R 2 is actually equal to + + align:start position:0% +variable this R 2 is actually equal to + + + align:start position:0% +variable this R 2 is actually equal to +the sample correlation coefficient for X + + align:start position:0% +the sample correlation coefficient for X + + + align:start position:0% +the sample correlation coefficient for X +and Y so we've we have in fact seen this + + align:start position:0% +and Y so we've we have in fact seen this + + + align:start position:0% +and Y so we've we have in fact seen this +measure before um why do we feel like we + + align:start position:0% +measure before um why do we feel like we + + + align:start position:0% +measure before um why do we feel like we +have to Define this new goodness of fit + + align:start position:0% +have to Define this new goodness of fit + + + align:start position:0% +have to Define this new goodness of fit +uh measure for linear regression well it + + align:start position:0% +uh measure for linear regression well it + + + align:start position:0% +uh measure for linear regression well it +is in fact a more General formulation + + align:start position:0% +is in fact a more General formulation + + + align:start position:0% +is in fact a more General formulation +and it's defined for linear models with + + align:start position:0% +and it's defined for linear models with + + + align:start position:0% +and it's defined for linear models with +more than one explanatory variable so + + align:start position:0% +more than one explanatory variable so + + + align:start position:0% +more than one explanatory variable so +when we get to multiple regression we + + align:start position:0% +when we get to multiple regression we + + + align:start position:0% +when we get to multiple regression we +can have the same we can Define the r + + align:start position:0% +can have the same we can Define the r + + + align:start position:0% +can have the same we can Define the r +squ exactly the same way as we just + + align:start position:0% +squ exactly the same way as we just + + + align:start position:0% +squ exactly the same way as we just +defined it + + align:start position:0% +defined it + + + align:start position:0% +defined it +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +and in addition to using r squar as a + + align:start position:0% +and in addition to using r squar as a + + + align:start position:0% +and in addition to using r squar as a +basic measure of goodness of fit of our + + align:start position:0% +basic measure of goodness of fit of our + + + align:start position:0% +basic measure of goodness of fit of our +regression we can also use as the basis + + align:start position:0% +regression we can also use as the basis + + + align:start position:0% +regression we can also use as the basis +of a test of the + + align:start position:0% +of a test of the + + + align:start position:0% +of a test of the +hypothesis that uh our slope is equal to + + align:start position:0% +hypothesis that uh our slope is equal to + + + align:start position:0% +hypothesis that uh our slope is equal to +zero okay and when we get to multiple + + align:start position:0% +zero okay and when we get to multiple + + + align:start position:0% +zero okay and when we get to multiple +regression um it it's going to be a test + + align:start position:0% +regression um it it's going to be a test + + + align:start position:0% +regression um it it's going to be a test +of the hypothesis that beta 1 that that + + align:start position:0% +of the hypothesis that beta 1 that that + + + align:start position:0% +of the hypothesis that beta 1 that that +sort of the slopes on all of our + + align:start position:0% +sort of the slopes on all of our + + + align:start position:0% +sort of the slopes on all of our +explanatory variables are equal to zero + + align:start position:0% +explanatory variables are equal to zero + + + align:start position:0% +explanatory variables are equal to zero +okay if we have K explanatory variables + + align:start position:0% +okay if we have K explanatory variables + + + align:start position:0% +okay if we have K explanatory variables +and what is uh so what's you know what + + align:start position:0% +and what is uh so what's you know what + + + align:start position:0% +and what is uh so what's you know what +exactly is this test well we create this + + align:start position:0% +exactly is this test well we create this + + + align:start position:0% +exactly is this test well we create this +test statistic which is just equal to N + + align:start position:0% +test statistic which is just equal to N + + + align:start position:0% +test statistic which is just equal to N +- 2 * r^ 2 over 1 - R 2 and it turns out + + align:start position:0% +- 2 * r^ 2 over 1 - R 2 and it turns out + + + align:start position:0% +- 2 * r^ 2 over 1 - R 2 and it turns out +that this thing under the uh under + + align:start position:0% +that this thing under the uh under + + + align:start position:0% +that this thing under the uh under +assumption that the errors are normally + + align:start position:0% +assumption that the errors are normally + + + align:start position:0% +assumption that the errors are normally +distributed has an F distribution under + + align:start position:0% +distributed has an F distribution under + + + align:start position:0% +distributed has an F distribution under +the null and uh it's it's um going to be + + align:start position:0% +the null and uh it's it's um going to be + + + align:start position:0% +the null and uh it's it's um going to be +large so we're going to reject the null + + align:start position:0% +large so we're going to reject the null + + + align:start position:0% +large so we're going to reject the null +if it's large okay so why does that make + + align:start position:0% +if it's large okay so why does that make + + + align:start position:0% +if it's large okay so why does that make +sense is is anyone willing to take a + + align:start position:0% +sense is is anyone willing to take a + + + align:start position:0% +sense is is anyone willing to take a +stab at sort of explaining the intuition + + align:start position:0% +stab at sort of explaining the intuition + + + align:start position:0% +stab at sort of explaining the intuition +behind this no okay um I'll take a stab + + align:start position:0% +behind this no okay um I'll take a stab + + + align:start position:0% +behind this no okay um I'll take a stab +at it then so basically the idea is if + + align:start position:0% +at it then so basically the idea is if + + + align:start position:0% +at it then so basically the idea is if +our r s is large that means that the + + align:start position:0% +our r s is large that means that the + + + align:start position:0% +our r s is large that means that the +variation in X is explaining a lot of + + align:start position:0% +variation in X is explaining a lot of + + + align:start position:0% +variation in X is explaining a lot of +the variation in y okay we have a a a + + align:start position:0% +the variation in y okay we have a a a + + + align:start position:0% +the variation in y okay we have a a a +High measure for a goodness of fit and + + align:start position:0% +High measure for a goodness of fit and + + + align:start position:0% +High measure for a goodness of fit and +so this thing is going to be large okay + + align:start position:0% +so this thing is going to be large okay + + + align:start position:0% +so this thing is going to be large okay +this quantity is going to be large and + + align:start position:0% +this quantity is going to be large and + + + align:start position:0% +this quantity is going to be large and +so we want to reject the null that the + + align:start position:0% +so we want to reject the null that the + + + align:start position:0% +so we want to reject the null that the +the um coefficient on X this beta 1 is + + align:start position:0% +the um coefficient on X this beta 1 is + + + align:start position:0% +the um coefficient on X this beta 1 is +equal to zero okay if the X does a good + + align:start position:0% +equal to zero okay if the X does a good + + + align:start position:0% +equal to zero okay if the X does a good +job of explaining the variation in X + + align:start position:0% +job of explaining the variation in X + + + align:start position:0% +job of explaining the variation in X +does a good job of explaining the + + align:start position:0% +does a good job of explaining the + + + align:start position:0% +does a good job of explaining the +variation we're seeing in y then beta 1 + + align:start position:0% +variation we're seeing in y then beta 1 + + + align:start position:0% +variation we're seeing in y then beta 1 +isn't equal to zero okay or or + + align:start position:0% +isn't equal to zero okay or or + + + align:start position:0% +isn't equal to zero okay or or +with high pro probability we can reject + + align:start position:0% +with high pro probability we can reject + + + align:start position:0% +with high pro probability we can reject +the hypothesis that beta 1 is equal to + + align:start position:0% +the hypothesis that beta 1 is equal to + + + align:start position:0% +the hypothesis that beta 1 is equal to +zero in that case okay and so that then + + align:start position:0% +zero in that case okay and so that then + + + align:start position:0% +zero in that case okay and so that then +we want to you know when this is large + + align:start position:0% +we want to you know when this is large + + + align:start position:0% +we want to you know when this is large +that's when we want to reject this + + align:start position:0% +that's when we want to reject this + + + align:start position:0% +that's when we want to reject this +hypothesis okay does that make + + align:start position:0% +hypothesis okay does that make + + + align:start position:0% +hypothesis okay does that make +sense somewhat okay we'll see the F + + align:start position:0% +sense somewhat okay we'll see the F + + + align:start position:0% +sense somewhat okay we'll see the F +we'll see the F test again if it doesn't + + align:start position:0% +we'll see the F test again if it doesn't + + + align:start position:0% +we'll see the F test again if it doesn't +here represents uh number of variables + + align:start position:0% +here represents uh number of variables + + + align:start position:0% +here represents uh number of variables +or observations sorry n here represents + + align:start position:0% +or observations sorry n here represents + + + align:start position:0% +or observations sorry n here represents +number of variables number of + + align:start position:0% +number of variables number of + + + align:start position:0% +number of variables number of +observations number of observations + + align:start position:0% +observations number of observations + + + align:start position:0% +observations number of observations +right + + align:start position:0% +right + + + align:start position:0% +right +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay okay so let's talk about a few + + align:start position:0% +okay okay so let's talk about a few + + + align:start position:0% +okay okay so let's talk about a few +practical issues um then we'll introduce + + align:start position:0% +practical issues um then we'll introduce + + + align:start position:0% +practical issues um then we'll introduce +multiple regression although I don't + + align:start position:0% +multiple regression although I don't + + + align:start position:0% +multiple regression although I don't +think we'll get to that this time and + + align:start position:0% +think we'll get to that this time and + + + align:start position:0% +think we'll get to that this time and +then we'll return to inference after + + align:start position:0% +then we'll return to inference after + + + align:start position:0% +then we'll return to inference after +that + + align:start position:0% + + + + align:start position:0% + +okay okay so what does regression output + + align:start position:0% +okay okay so what does regression output + + + align:start position:0% +okay okay so what does regression output +look like and how how do we interpret it + + align:start position:0% +look like and how how do we interpret it + + + align:start position:0% +look like and how how do we interpret it +so uh first let me show you some uh + + align:start position:0% +so uh first let me show you some uh + + + align:start position:0% +so uh first let me show you some uh +regression output from sta so I know + + align:start position:0% +regression output from sta so I know + + + align:start position:0% +regression output from sta so I know +that you guys are using R and I'll show + + align:start position:0% +that you guys are using R and I'll show + + + align:start position:0% +that you guys are using R and I'll show +you some R output in a second um but + + align:start position:0% +you some R output in a second um but + + + align:start position:0% +you some R output in a second um but +most of the uh regression output I have + + align:start position:0% +most of the uh regression output I have + + + align:start position:0% +most of the uh regression output I have +sitting on my computer happens to be in + + align:start position:0% +sitting on my computer happens to be in + + + align:start position:0% +sitting on my computer happens to be in +STA and it's probably good for you to + + align:start position:0% +STA and it's probably good for you to + + + align:start position:0% +STA and it's probably good for you to +see the elements in sort of different uh + + align:start position:0% +see the elements in sort of different uh + + + align:start position:0% +see the elements in sort of different uh +statistical packages and be able to sort + + align:start position:0% +statistical packages and be able to sort + + + align:start position:0% +statistical packages and be able to sort +of uh figure out what all of these + + align:start position:0% +of uh figure out what all of these + + + align:start position:0% +of uh figure out what all of these +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +mean so here on this data output we have + + align:start position:0% +mean so here on this data output we have + + + align:start position:0% +mean so here on this data output we have +have a beta one hat is just uh listed + + align:start position:0% +have a beta one hat is just uh listed + + + align:start position:0% +have a beta one hat is just uh listed +under this column that says coefficient + + align:start position:0% +under this column that says coefficient + + + align:start position:0% +under this column that says coefficient +and then beta not hat is um at the + + align:start position:0% +and then beta not hat is um at the + + + align:start position:0% +and then beta not hat is um at the +bottom sta always puts the the sort of + + align:start position:0% +bottom sta always puts the the sort of + + + align:start position:0% +bottom sta always puts the the sort of +estimated constant U beta not hat at the + + align:start position:0% +estimated constant U beta not hat at the + + + align:start position:0% +estimated constant U beta not hat at the +bottom okay right after the estimated + + align:start position:0% +bottom okay right after the estimated + + + align:start position:0% +bottom okay right after the estimated +coefficients for um you know sort of uh + + align:start position:0% +coefficients for um you know sort of uh + + + align:start position:0% +coefficients for um you know sort of uh +beta one H or you know for beta 1 and + + align:start position:0% +beta one H or you know for beta 1 and + + + align:start position:0% +beta one H or you know for beta 1 and +beta not we have uh the standard errors + + align:start position:0% +beta not we have uh the standard errors + + + align:start position:0% +beta not we have uh the standard errors +listed okay so those are the estimated + + align:start position:0% +listed okay so those are the estimated + + + align:start position:0% +listed okay so those are the estimated +uh standard deviations of the + + align:start position:0% +uh standard deviations of the + + + align:start position:0% +uh standard deviations of the +distributions of those + + align:start position:0% + + + + align:start position:0% + +estimators so I was the one who gave lhd + + align:start position:0% +estimators so I was the one who gave lhd + + + align:start position:0% +estimators so I was the one who gave lhd +3 rev its name and that's uh that's just + + align:start position:0% +3 rev its name and that's uh that's just + + + align:start position:0% +3 rev its name and that's uh that's just +a variable I mean I could tell you + + align:start position:0% +a variable I mean I could tell you + + + align:start position:0% +a variable I mean I could tell you +what's in this regression this is + + align:start position:0% +what's in this regression this is + + + align:start position:0% +what's in this regression this is +basically a regression taken from one of + + align:start position:0% +basically a regression taken from one of + + + align:start position:0% +basically a regression taken from one of +my papers + + align:start position:0% +my papers + + + align:start position:0% +my papers +where we were trying to explain uh the + + align:start position:0% +where we were trying to explain uh the + + + align:start position:0% +where we were trying to explain uh the +the the uh sort of ratio of AD detail + + align:start position:0% +the the uh sort of ratio of AD detail + + + align:start position:0% +the the uh sort of ratio of AD detail +advertising in + + align:start position:0% +advertising in + + + align:start position:0% +advertising in +Pharmaceuticals uh to sales trying to + + align:start position:0% +Pharmaceuticals uh to sales trying to + + + align:start position:0% +Pharmaceuticals uh to sales trying to +explain that ratio uh with um sort of + + align:start position:0% +explain that ratio uh with um sort of + + + align:start position:0% +explain that ratio uh with um sort of +characteristics of the market like + + align:start position:0% +characteristics of the market like + + + align:start position:0% +characteristics of the market like +Revenue okay so that's one of our + + align:start position:0% +Revenue okay so that's one of our + + + align:start position:0% +Revenue okay so that's one of our +measures of Revenue that's so that's + + align:start position:0% +measures of Revenue that's so that's + + + align:start position:0% +measures of Revenue that's so that's +that's a crazy name for a variable um we + + align:start position:0% +that's a crazy name for a variable um we + + + align:start position:0% +that's a crazy name for a variable um we +called it something different in the + + align:start position:0% +called it something different in the + + + align:start position:0% +called it something different in the +paper but you know in our you know in my + + align:start position:0% +paper but you know in our you know in my + + + align:start position:0% +paper but you know in our you know in my +sort of crazy sta code that's what it + + align:start position:0% +sort of crazy sta code that's what it + + + align:start position:0% +sort of crazy sta code that's what it +ended up being uh the unders underscore + + align:start position:0% +ended up being uh the unders underscore + + + align:start position:0% +ended up being uh the unders underscore +cons that's uh a name given by sta so + + align:start position:0% +cons that's uh a name given by sta so + + + align:start position:0% +cons that's uh a name given by sta so +that's basically just saying that's the + + align:start position:0% +that's basically just saying that's the + + + align:start position:0% +that's basically just saying that's the +estimator for the constant or The + + align:start position:0% +estimator for the constant or The + + + align:start position:0% +estimator for the constant or The +Intercept in the regression + + align:start position:0% +Intercept in the regression + + + align:start position:0% +Intercept in the regression +okay um so the standard errors are + + align:start position:0% +okay um so the standard errors are + + + align:start position:0% +okay um so the standard errors are +listed there and then we also have we'll + + align:start position:0% +listed there and then we also have we'll + + + align:start position:0% +listed there and then we also have we'll +get to the I'll point out the T Test in + + align:start position:0% +get to the I'll point out the T Test in + + + align:start position:0% +get to the I'll point out the T Test in +a second um but here are the results for + + align:start position:0% +a second um but here are the results for + + + align:start position:0% +a second um but here are the results for +the f test that I uh mentioned so + + align:start position:0% +the f test that I uh mentioned so + + + align:start position:0% +the f test that I uh mentioned so +typically oh let me just say something + + align:start position:0% +typically oh let me just say something + + + align:start position:0% +typically oh let me just say something +so typically uh statistical packages + + align:start position:0% +so typically uh statistical packages + + + align:start position:0% +so typically uh statistical packages +when they give you the output for + + align:start position:0% +when they give you the output for + + + align:start position:0% +when they give you the output for +regression give you a bunch of stuff for + + align:start position:0% +regression give you a bunch of stuff for + + + align:start position:0% +regression give you a bunch of stuff for +free and one of the things they give you + + align:start position:0% +free and one of the things they give you + + + align:start position:0% +free and one of the things they give you +for free is the standard F test I just + + align:start position:0% +for free is the standard F test I just + + + align:start position:0% +for free is the standard F test I just +mentioned okay so they'll they'll just + + align:start position:0% +mentioned okay so they'll they'll just + + + align:start position:0% +mentioned okay so they'll they'll just +run it for you for free and they'll + + align:start position:0% +run it for you for free and they'll + + + align:start position:0% +run it for you for free and they'll +report the the results and here are the + + align:start position:0% +report the the results and here are the + + + align:start position:0% +report the the results and here are the +results um let me take this question and + + align:start position:0% +results um let me take this question and + + + align:start position:0% +results um let me take this question and +then I'll explain it y so when you're + + align:start position:0% +then I'll explain it y so when you're + + + align:start position:0% +then I'll explain it y so when you're +describing literature General what's the + + align:start position:0% +describing literature General what's the + + + align:start position:0% +describing literature General what's the +convention for how much of this you Shar + + align:start position:0% +convention for how much of this you Shar + + + align:start position:0% +convention for how much of this you Shar +like what if ah I'm so glad you asked + + align:start position:0% +like what if ah I'm so glad you asked + + + align:start position:0% +like what if ah I'm so glad you asked +and I will talk about that next time so + + align:start position:0% +and I will talk about that next time so + + + align:start position:0% +and I will talk about that next time so +uh I will have um I'll have examples of + + align:start position:0% +uh I will have um I'll have examples of + + + align:start position:0% +uh I will have um I'll have examples of +tables that I want your well they're + + align:start position:0% +tables that I want your well they're + + + align:start position:0% +tables that I want your well they're +they're examples of tables from my + + align:start position:0% +they're examples of tables from my + + + align:start position:0% +they're examples of tables from my +papers but they're also examples of + + align:start position:0% +papers but they're also examples of + + + align:start position:0% +papers but they're also examples of +tables that I want your the tables in + + align:start position:0% +tables that I want your the tables in + + + align:start position:0% +tables that I want your the tables in +your empirical project to look like and + + align:start position:0% +your empirical project to look like and + + + align:start position:0% +your empirical project to look like and +and it yeah it will be clear next time + + align:start position:0% +and it yeah it will be clear next time + + + align:start position:0% +and it yeah it will be clear next time +so good question okay so that here are + + align:start position:0% +so good question okay so that here are + + + align:start position:0% +so good question okay so that here are +the results of the the sort of standard + + align:start position:0% +the results of the the sort of standard + + + align:start position:0% +the results of the the sort of standard +F test and what this particular F test + + align:start position:0% +F test and what this particular F test + + + align:start position:0% +F test and what this particular F test +says remember we want to reject for + + align:start position:0% +says remember we want to reject for + + + align:start position:0% +says remember we want to reject for +large values of uh the test statistic we + + align:start position:0% +large values of uh the test statistic we + + + align:start position:0% +large values of uh the test statistic we +want to reject the null that beta 1 is + + align:start position:0% +want to reject the null that beta 1 is + + + align:start position:0% +want to reject the null that beta 1 is +equal to zero if we get large values of + + align:start position:0% +equal to zero if we get large values of + + + align:start position:0% +equal to zero if we get large values of +that F test okay so they perform the F + + align:start position:0% +that F test okay so they perform the F + + + align:start position:0% +that F test okay so they perform the F +test and they also gave us the P value + + align:start position:0% +test and they also gave us the P value + + + align:start position:0% +test and they also gave us the P value +so last time Esther defined what the P + + align:start position:0% +so last time Esther defined what the P + + + align:start position:0% +so last time Esther defined what the P +value is that's basically the + + align:start position:0% +value is that's basically the + + + align:start position:0% +value is that's basically the +probability that I hope I don't screw up + + align:start position:0% +probability that I hope I don't screw up + + + align:start position:0% +probability that I hope I don't screw up +this this uh verbal definitions the + + align:start position:0% +this this uh verbal definitions the + + + align:start position:0% +this this uh verbal definitions the +probability that it's it's the point at + + align:start position:0% +probability that it's it's the point at + + + align:start position:0% +probability that it's it's the point at +which if you were doing a size P test + + align:start position:0% +which if you were doing a size P test + + + align:start position:0% +which if you were doing a size P test +you would reject the null okay so what + + align:start position:0% +you would reject the null okay so what + + + align:start position:0% +you would reject the null okay so what +size test do we usually do we do 5% + + align:start position:0% +size test do we usually do we do 5% + + + align:start position:0% +size test do we usually do we do 5% +tests we do 1% tests things like that + + align:start position:0% +tests we do 1% tests things like that + + + align:start position:0% +tests we do 1% tests things like that +here we have to do a test as large as an + + align:start position:0% +here we have to do a test as large as an + + + align:start position:0% +here we have to do a test as large as an +basically an 18% test in order to reject + + align:start position:0% +basically an 18% test in order to reject + + + align:start position:0% +basically an 18% test in order to reject +the null we're going to do an 18% test + + align:start position:0% +the null we're going to do an 18% test + + + align:start position:0% +the null we're going to do an 18% test +so we don't reject the null here okay so + + align:start position:0% +so we don't reject the null here okay so + + + align:start position:0% +so we don't reject the null here okay so +basically if you looked up you know 1. n + + align:start position:0% +basically if you looked up you know 1. n + + + align:start position:0% +basically if you looked up you know 1. n +which is the value of our F statistic uh + + align:start position:0% +which is the value of our F statistic uh + + + align:start position:0% +which is the value of our F statistic uh +for this particular regression if you + + align:start position:0% +for this particular regression if you + + + align:start position:0% +for this particular regression if you +looked up the critical values in an F + + align:start position:0% +looked up the critical values in an F + + + align:start position:0% +looked up the critical values in an F +table you would you know conclude that + + align:start position:0% +table you would you know conclude that + + + align:start position:0% +table you would you know conclude that +you don't want to reject the null under + + align:start position:0% +you don't want to reject the null under + + + align:start position:0% +you don't want to reject the null under +this case and that's exactly what the uh + + align:start position:0% +this case and that's exactly what the uh + + + align:start position:0% +this case and that's exactly what the uh +the results here tell you they say uh + + align:start position:0% +the results here tell you they say uh + + + align:start position:0% +the results here tell you they say uh +unless you're just you're you're doing + + align:start position:0% +unless you're just you're you're doing + + + align:start position:0% +unless you're just you're you're doing +you know you're choosing a ridiculously + + align:start position:0% +you know you're choosing a ridiculously + + + align:start position:0% +you know you're choosing a ridiculously +high alpha for your test you don't want + + align:start position:0% +high alpha for your test you don't want + + + align:start position:0% +high alpha for your test you don't want +to reject the null + + align:start position:0% + + + + align:start position:0% + +okay how about this one though for this + + align:start position:0% +okay how about this one though for this + + + align:start position:0% +okay how about this one though for this +one we would reject the null um for that + + align:start position:0% +one we would reject the null um for that + + + align:start position:0% +one we would reject the null um for that +beta 1 is equal to zero if we were + + align:start position:0% +beta 1 is equal to zero if we were + + + align:start position:0% +beta 1 is equal to zero if we were +either doing or sorry if we were doing a + + align:start position:0% +either doing or sorry if we were doing a + + + align:start position:0% +either doing or sorry if we were doing a +5% test if we were doing a 1% test we + + align:start position:0% +5% test if we were doing a 1% test we + + + align:start position:0% +5% test if we were doing a 1% test we +would not reject the null so basically + + align:start position:0% +would not reject the null so basically + + + align:start position:0% +would not reject the null so basically +what this F test is telling us is that + + align:start position:0% +what this F test is telling us is that + + + align:start position:0% +what this F test is telling us is that +if we want to do + + align:start position:0% +if we want to do + + + align:start position:0% +if we want to do +uh you know sort of um yeah a three this + + align:start position:0% +uh you know sort of um yeah a three this + + + align:start position:0% +uh you know sort of um yeah a three this +is this is the P value the P value sort + + align:start position:0% +is this is the P value the P value sort + + + align:start position:0% +is this is the P value the P value sort +of tells us the boundary of the size of + + align:start position:0% +of tells us the boundary of the size of + + + align:start position:0% +of tells us the boundary of the size of +the test you know at which we would + + align:start position:0% +the test you know at which we would + + + align:start position:0% +the test you know at which we would +reject + + align:start position:0% +reject + + + align:start position:0% +reject +okay is that + + align:start position:0% + + + + align:start position:0% + +clear and here uh we also get this for + + align:start position:0% +clear and here uh we also get this for + + + align:start position:0% +clear and here uh we also get this for +free every time we run a regression they + + align:start position:0% +free every time we run a regression they + + + align:start position:0% +free every time we run a regression they +perform a t test for um you know + + align:start position:0% +perform a t test for um you know + + + align:start position:0% +perform a t test for um you know +basically the hypothesis that that + + align:start position:0% +basically the hypothesis that that + + + align:start position:0% +basically the hypothesis that that +particular coefficient is equal to zero + + align:start position:0% +particular coefficient is equal to zero + + + align:start position:0% +particular coefficient is equal to zero +okay and we'll talk about you know sort + + align:start position:0% +okay and we'll talk about you know sort + + + align:start position:0% +okay and we'll talk about you know sort +of I'll make uh more precise next time + + align:start position:0% +of I'll make uh more precise next time + + + align:start position:0% +of I'll make uh more precise next time +what exactly what these tests are um but + + align:start position:0% +what exactly what these tests are um but + + + align:start position:0% +what exactly what these tests are um but +this is just a t test for the um you + + align:start position:0% +this is just a t test for the um you + + + align:start position:0% +this is just a t test for the um you +know for the each coefficient being + + align:start position:0% +know for the each coefficient being + + + align:start position:0% +know for the each coefficient being +equal to zero and in this case we do + + align:start position:0% +equal to zero and in this case we do + + + align:start position:0% +equal to zero and in this case we do +not uh we don't reject the null for + + align:start position:0% +not uh we don't reject the null for + + + align:start position:0% +not uh we don't reject the null for +either one I guess down here uh we + + align:start position:0% +either one I guess down here uh we + + + align:start position:0% +either one I guess down here uh we +reject the null for this one + + align:start position:0% +reject the null for this one + + + align:start position:0% +reject the null for this one +at at + + align:start position:0% + + + + align:start position:0% + +5% + + align:start position:0% +5% + + + align:start position:0% +5% +okay okay so here's some R output um + + align:start position:0% +okay okay so here's some R output um + + + align:start position:0% +okay okay so here's some R output um +courtesy of Angela who was up late last + + align:start position:0% +courtesy of Angela who was up late last + + + align:start position:0% +courtesy of Angela who was up late last +night running my running some + + align:start position:0% +night running my running some + + + align:start position:0% +night running my running some +regressions so it looks a little + + align:start position:0% +regressions so it looks a little + + + align:start position:0% +regressions so it looks a little +different it has most of the same + + align:start position:0% +different it has most of the same + + + align:start position:0% +different it has most of the same +elements in it so here they put the in + + align:start position:0% +elements in it so here they put the in + + + align:start position:0% +elements in it so here they put the in +they instead of calling it the constant + + align:start position:0% +they instead of calling it the constant + + + align:start position:0% +they instead of calling it the constant +they call it the intercept and they put + + align:start position:0% +they call it the intercept and they put + + + align:start position:0% +they call it the intercept and they put +it first instead of second this is the + + align:start position:0% +it first instead of second this is the + + + align:start position:0% +it first instead of second this is the +uh the the + + align:start position:0% +uh the the + + + align:start position:0% +uh the the +variable uh name that Angela came up + + align:start position:0% +variable uh name that Angela came up + + + align:start position:0% +variable uh name that Angela came up +with uh so again that's sort of you know + + align:start position:0% +with uh so again that's sort of you know + + + align:start position:0% +with uh so again that's sort of you know +your choice when you're programming you + + align:start position:0% +your choice when you're programming you + + + align:start position:0% +your choice when you're programming you +sort of call your variables what you + + align:start position:0% +sort of call your variables what you + + + align:start position:0% +sort of call your variables what you +want and uh you also get you get the + + align:start position:0% +want and uh you also get you get the + + + align:start position:0% +want and uh you also get you get the +standard errors and you get the T tests + + align:start position:0% +standard errors and you get the T tests + + + align:start position:0% +standard errors and you get the T tests +for free um the F test here instead of + + align:start position:0% +for free um the F test here instead of + + + align:start position:0% +for free um the F test here instead of +being listed in the upper right corner + + align:start position:0% +being listed in the upper right corner + + + align:start position:0% +being listed in the upper right corner +like it is in the statea output it's + + align:start position:0% +like it is in the statea output it's + + + align:start position:0% +like it is in the statea output it's +listed at the bottom uh but it's a same + + align:start position:0% +listed at the bottom uh but it's a same + + + align:start position:0% +listed at the bottom uh but it's a same +information it's basically gives you the + + align:start position:0% +information it's basically gives you the + + + align:start position:0% +information it's basically gives you the +value of the F statistic and then tells + + align:start position:0% +value of the F statistic and then tells + + + align:start position:0% +value of the F statistic and then tells +you the P value um at which or you know + + align:start position:0% +you the P value um at which or you know + + + align:start position:0% +you the P value um at which or you know +sort of the size of the test at which + + align:start position:0% +sort of the size of the test at which + + + align:start position:0% +sort of the size of the test at which +you would reject the null and here this + + align:start position:0% +you would reject the null and here this + + + align:start position:0% +you would reject the null and here this +is a very small P value so any + + align:start position:0% +is a very small P value so any + + + align:start position:0% +is a very small P value so any +traditional test you would reject the + + align:start position:0% +traditional test you would reject the + + + align:start position:0% +traditional test you would reject the +null that beta 1 is equal to zero + + align:start position:0% +null that beta 1 is equal to zero + + + align:start position:0% +null that beta 1 is equal to zero +here + + align:start position:0% +here + + + align:start position:0% +here +okay and then you can even this is um + + align:start position:0% +okay and then you can even this is um + + + align:start position:0% +okay and then you can even this is um +well let me just go back for a second + + align:start position:0% +well let me just go back for a second + + + align:start position:0% +well let me just go back for a second +and note that the r squar of this + + align:start position:0% +and note that the r squar of this + + + align:start position:0% +and note that the r squar of this +regression is uh 0 41 okay and if you're + + align:start position:0% +regression is uh 0 41 okay and if you're + + + align:start position:0% +regression is uh 0 41 okay and if you're +wondering what a0 41r 2 might look like + + align:start position:0% +wondering what a0 41r 2 might look like + + + align:start position:0% +wondering what a0 41r 2 might look like +in a scatter plot so this is a scatter + + align:start position:0% +in a scatter plot so this is a scatter + + + align:start position:0% +in a scatter plot so this is a scatter +plot of the variables and uh the fitted + + align:start position:0% +plot of the variables and uh the fitted + + + align:start position:0% +plot of the variables and uh the fitted +regression line through them + + align:start position:0% + + + + align:start position:0% + +okay and if you're curious about the + + align:start position:0% +okay and if you're curious about the + + + align:start position:0% +okay and if you're curious about the +particular variables this is just these + + align:start position:0% +particular variables this is just these + + + align:start position:0% +particular variables this is just these +are variables from The General Social + + align:start position:0% +are variables from The General Social + + + align:start position:0% +are variables from The General Social +Survey about attitudes on abortion and + + align:start position:0% +Survey about attitudes on abortion and + + + align:start position:0% +Survey about attitudes on abortion and +how they have sort of been uh evolving + + align:start position:0% +how they have sort of been uh evolving + + + align:start position:0% +how they have sort of been uh evolving +over the past couple of decades in the + + align:start position:0% + + + + align:start position:0% + +US okay + + align:start position:0% + + + + align:start position:0% + +questions okay so how do we interpret + + align:start position:0% +questions okay so how do we interpret + + + align:start position:0% +questions okay so how do we interpret +these uh these parameter estimates and + + align:start position:0% +these uh these parameter estimates and + + + align:start position:0% +these uh these parameter estimates and +in particular how do we + + align:start position:0% +in particular how do we + + + align:start position:0% +in particular how do we +interpret uh the estimated coefficient + + align:start position:0% +interpret uh the estimated coefficient + + + align:start position:0% +interpret uh the estimated coefficient +on our X variable this sort of beta one + + align:start position:0% +on our X variable this sort of beta one + + + align:start position:0% +on our X variable this sort of beta one +hat + + align:start position:0% +hat + + + align:start position:0% +hat +well beta one hat is the estimated + + align:start position:0% +well beta one hat is the estimated + + + align:start position:0% +well beta one hat is the estimated +effect of Y of a one unit increase in X + + align:start position:0% +effect of Y of a one unit increase in X + + + align:start position:0% +effect of Y of a one unit increase in X +okay so the precise nuances of the + + align:start position:0% +okay so the precise nuances of the + + + align:start position:0% +okay so the precise nuances of the +interpretation are going to depend a + + align:start position:0% +interpretation are going to depend a + + + align:start position:0% +interpretation are going to depend a +little bit on whether we think that + + align:start position:0% +little bit on whether we think that + + + align:start position:0% +little bit on whether we think that +we've estimated a causal relationship or + + align:start position:0% +we've estimated a causal relationship or + + + align:start position:0% +we've estimated a causal relationship or +whether we think we've estimated + + align:start position:0% +whether we think we've estimated + + + align:start position:0% +whether we think we've estimated +something else okay so the language you + + align:start position:0% +something else okay so the language you + + + align:start position:0% +something else okay so the language you +might use could be a little bit + + align:start position:0% +might use could be a little bit + + + align:start position:0% +might use could be a little bit +different but this is the basic idea + + align:start position:0% +different but this is the basic idea + + + align:start position:0% +different but this is the basic idea +this is how we interpret uh What uh beta + + align:start position:0% +this is how we interpret uh What uh beta + + + align:start position:0% +this is how we interpret uh What uh beta +one hat + + align:start position:0% +one hat + + + align:start position:0% +one hat +means okay so let me show you these are + + align:start position:0% +means okay so let me show you these are + + + align:start position:0% +means okay so let me show you these are +some data um that I downloaded from + + align:start position:0% +some data um that I downloaded from + + + align:start position:0% +some data um that I downloaded from +let's see uh the ESPN website uh this is + + align:start position:0% +let's see uh the ESPN website uh this is + + + align:start position:0% +let's see uh the ESPN website uh this is +I did this several years ago so this is + + align:start position:0% +I did this several years ago so this is + + + align:start position:0% +I did this several years ago so this is +data involving the 2005 Major League + + align:start position:0% +data involving the 2005 Major League + + + align:start position:0% +data involving the 2005 Major League +Baseball season and what I did is I + + align:start position:0% +Baseball season and what I did is I + + + align:start position:0% +Baseball season and what I did is I +downloaded um the number of wins of each + + align:start position:0% +downloaded um the number of wins of each + + + align:start position:0% +downloaded um the number of wins of each +team and the attendance the the complete + + align:start position:0% +team and the attendance the the complete + + + align:start position:0% +team and the attendance the the complete +uh uh season long attendance uh for each + + align:start position:0% +uh uh season long attendance uh for each + + + align:start position:0% +uh uh season long attendance uh for each +team and wanted to see see if there was + + align:start position:0% +team and wanted to see see if there was + + + align:start position:0% +team and wanted to see see if there was +some uh relationship between attendance + + align:start position:0% +some uh relationship between attendance + + + align:start position:0% +some uh relationship between attendance +and number of + + align:start position:0% +and number of + + + align:start position:0% +and number of +wins okay so what did I do I regressed + + align:start position:0% +wins okay so what did I do I regressed + + + align:start position:0% +wins okay so what did I do I regressed +attendance that's my dependent variable + + align:start position:0% +attendance that's my dependent variable + + + align:start position:0% +attendance that's my dependent variable +my y variable on the number of wins that + + align:start position:0% +my y variable on the number of wins that + + + align:start position:0% +my y variable on the number of wins that +each team had and we see here based on + + align:start position:0% +each team had and we see here based on + + + align:start position:0% +each team had and we see here based on +this regression that one additional win + + align:start position:0% +this regression that one additional win + + + align:start position:0% +this regression that one additional win +is associated oh and I should say the + + align:start position:0% +is associated oh and I should say the + + + align:start position:0% +is associated oh and I should say the +attendance was in thousands that was the + + align:start position:0% +attendance was in thousands that was the + + + align:start position:0% +attendance was in thousands that was the +unit I used so one additional win is + + align:start position:0% +unit I used so one additional win is + + + align:start position:0% +unit I used so one additional win is +associated with an additional 31,000 fan + + align:start position:0% +associated with an additional 31,000 fan + + + align:start position:0% +associated with an additional 31,000 fan +in attendance over the course of the + + align:start position:0% +in attendance over the course of the + + + align:start position:0% +in attendance over the course of the +Season okay so we might want to exercise + + align:start position:0% +Season okay so we might want to exercise + + + align:start position:0% +Season okay so we might want to exercise +a little Caution to think that this is a + + align:start position:0% +a little Caution to think that this is a + + + align:start position:0% +a little Caution to think that this is a +causal relationship we'll sort of get to + + align:start position:0% +causal relationship we'll sort of get to + + + align:start position:0% +causal relationship we'll sort of get to +that more later in the semester but at + + align:start position:0% +that more later in the semester but at + + + align:start position:0% +that more later in the semester but at +least uh sort of this regression uh + + align:start position:0% +least uh sort of this regression uh + + + align:start position:0% +least uh sort of this regression uh +suggests that an additional win is + + align:start position:0% +suggests that an additional win is + + + align:start position:0% +suggests that an additional win is +associated with 31,000 fans in + + align:start position:0% +associated with 31,000 fans in + + + align:start position:0% +associated with 31,000 fans in +attendance and an additional 31,000 fans + + align:start position:0% +attendance and an additional 31,000 fans + + + align:start position:0% +attendance and an additional 31,000 fans +in + + align:start position:0% +in + + + align:start position:0% +in +attendance + + align:start position:0% +attendance + + + align:start position:0% +attendance +okay + + align:start position:0% + + + + align:start position:0% + +okay uh another practical issue what if + + align:start position:0% +okay uh another practical issue what if + + + align:start position:0% +okay uh another practical issue what if +x only takes on two values zero and one + + align:start position:0% +x only takes on two values zero and one + + + align:start position:0% +x only takes on two values zero and one +uh well we have a special name for that + + align:start position:0% +uh well we have a special name for that + + + align:start position:0% +uh well we have a special name for that +type of variable we call it a dummy + + align:start position:0% +type of variable we call it a dummy + + + align:start position:0% +type of variable we call it a dummy +variable or sometimes we call it an inde + + align:start position:0% +variable or sometimes we call it an inde + + + align:start position:0% +variable or sometimes we call it an inde +indicative variable and there's no + + align:start position:0% +indicative variable and there's no + + + align:start position:0% +indicative variable and there's no +problem at all in that there's nothing + + align:start position:0% +problem at all in that there's nothing + + + align:start position:0% +problem at all in that there's nothing +in our assumptions that have that rule + + align:start position:0% +in our assumptions that have that rule + + + align:start position:0% +in our assumptions that have that rule +this out okay so there's you know that + + align:start position:0% +this out okay so there's you know that + + + align:start position:0% +this out okay so there's you know that +that uh you know that is not a problem + + align:start position:0% +that uh you know that is not a problem + + + align:start position:0% +that uh you know that is not a problem +for estimating a a a linear regression + + align:start position:0% +for estimating a a a linear regression + + + align:start position:0% +for estimating a a a linear regression +and in fact dummy variables can be quite + + align:start position:0% +and in fact dummy variables can be quite + + + align:start position:0% +and in fact dummy variables can be quite +useful okay the pictures will look a + + align:start position:0% +useful okay the pictures will look a + + + align:start position:0% +useful okay the pictures will look a +little different I'll show you a picture + + align:start position:0% +little different I'll show you a picture + + + align:start position:0% +little different I'll show you a picture +in a second okay here's what I mean if + + align:start position:0% +in a second okay here's what I mean if + + + align:start position:0% +in a second okay here's what I mean if +we only if our X variable only takes on + + align:start position:0% +we only if our X variable only takes on + + + align:start position:0% +we only if our X variable only takes on +values zero and one uh then you know we + + align:start position:0% +values zero and one uh then you know we + + + align:start position:0% +values zero and one uh then you know we +sort of don't have this nice cloud of + + align:start position:0% +sort of don't have this nice cloud of + + + align:start position:0% +sort of don't have this nice cloud of +data we just have these two you know but + + align:start position:0% +data we just have these two you know but + + + align:start position:0% +data we just have these two you know but +nothing wrong with that right okay and + + align:start position:0% +nothing wrong with that right okay and + + + align:start position:0% +nothing wrong with that right okay and +then we estimate then sort of beta not + + align:start position:0% +then we estimate then sort of beta not + + + align:start position:0% +then we estimate then sort of beta not +hat is interpreted as this the uh sort + + align:start position:0% +hat is interpreted as this the uh sort + + + align:start position:0% +hat is interpreted as this the uh sort +of mean of the group of observations + + align:start position:0% +of mean of the group of observations + + + align:start position:0% +of mean of the group of observations +that have the dummy variable equaling + + align:start position:0% +that have the dummy variable equaling + + + align:start position:0% +that have the dummy variable equaling +zero and beta one hat is the uh the the + + align:start position:0% +zero and beta one hat is the uh the the + + + align:start position:0% +zero and beta one hat is the uh the the +sort of um increment in the mean or the + + align:start position:0% +sort of um increment in the mean or the + + + align:start position:0% +sort of um increment in the mean or the +you know sort of effect of having the + + align:start position:0% +you know sort of effect of having the + + + align:start position:0% +you know sort of effect of having the +dummy variable equal + + align:start position:0% + + + + align:start position:0% + +one okay so dummy variables serve a + + align:start position:0% +one okay so dummy variables serve a + + + align:start position:0% +one okay so dummy variables serve a +number of important roles in linear + + align:start position:0% +number of important roles in linear + + + align:start position:0% +number of important roles in linear +models and we've actually seen one + + align:start position:0% +models and we've actually seen one + + + align:start position:0% +models and we've actually seen one +already uh uh randomized control trials + + align:start position:0% +already uh uh randomized control trials + + + align:start position:0% +already uh uh randomized control trials +so so when Esther was talking about + + align:start position:0% +so so when Esther was talking about + + + align:start position:0% +so so when Esther was talking about +having sort of two groups a treatment a + + align:start position:0% +having sort of two groups a treatment a + + + align:start position:0% +having sort of two groups a treatment a +control group we could just simply have + + align:start position:0% +control group we could just simply have + + + align:start position:0% +control group we could just simply have +done the whole analysis in the linear + + align:start position:0% +done the whole analysis in the linear + + + align:start position:0% +done the whole analysis in the linear +regression framework uh assigning a zero + + align:start position:0% +regression framework uh assigning a zero + + + align:start position:0% +regression framework uh assigning a zero +to one of the groups and a one to the + + align:start position:0% +to one of the groups and a one to the + + + align:start position:0% +to one of the groups and a one to the +other group okay so suppose we have some + + align:start position:0% +other group okay so suppose we have some + + + align:start position:0% +other group okay so suppose we have some +treatment in whose effect we're + + align:start position:0% +treatment in whose effect we're + + + align:start position:0% +treatment in whose effect we're +interested we randomly assign the + + align:start position:0% +interested we randomly assign the + + + align:start position:0% +interested we randomly assign the +treatment to half of the observations + + align:start position:0% +treatment to half of the observations + + + align:start position:0% +treatment to half of the observations +leave the other half untreated we assign + + align:start position:0% +leave the other half untreated we assign + + + align:start position:0% +leave the other half untreated we assign +the treated observations xal 1 and the + + align:start position:0% +the treated observations xal 1 and the + + + align:start position:0% +the treated observations xal 1 and the +untreated xals 0 okay + + align:start position:0% +untreated xals 0 okay + + + align:start position:0% +untreated xals 0 okay +and then if we estimate the regression + + align:start position:0% +and then if we estimate the regression + + + align:start position:0% +and then if we estimate the regression +above beta 1 Hat will be the estimated + + align:start position:0% +above beta 1 Hat will be the estimated + + + align:start position:0% +above beta 1 Hat will be the estimated +effect of the + + align:start position:0% + + + + align:start position:0% + +treatment and by the way X need not be + + align:start position:0% +treatment and by the way X need not be + + + align:start position:0% +treatment and by the way X need not be +randomly assigned half zeros and half + + align:start position:0% +randomly assigned half zeros and half + + + align:start position:0% +randomly assigned half zeros and half +ones or anything like that to be a dummy + + align:start position:0% +ones or anything like that to be a dummy + + + align:start position:0% +ones or anything like that to be a dummy +variable so we can we do use dummy + + align:start position:0% +variable so we can we do use dummy + + + align:start position:0% +variable so we can we do use dummy +variables or can use dummy variables if + + align:start position:0% +variables or can use dummy variables if + + + align:start position:0% +variables or can use dummy variables if +we do have this sort of random + + align:start position:0% +we do have this sort of random + + + align:start position:0% +we do have this sort of random +assignment um variable but we can use it + + align:start position:0% +assignment um variable but we can use it + + + align:start position:0% +assignment um variable but we can use it +for lots of other things too any + + align:start position:0% +for lots of other things too any + + + align:start position:0% +for lots of other things too any +characteristic of the observations that + + align:start position:0% +characteristic of the observations that + + + align:start position:0% +characteristic of the observations that +exists on some but not all observations + + align:start position:0% +exists on some but not all observations + + + align:start position:0% +exists on some but not all observations +can be represented uh with a dummy + + align:start position:0% +can be represented uh with a dummy + + + align:start position:0% +can be represented uh with a dummy +variable okay there's nothing about a + + align:start position:0% +variable okay there's nothing about a + + + align:start position:0% +variable okay there's nothing about a +dummy variable we're we're assuming is + + align:start position:0% +dummy variable we're we're assuming is + + + align:start position:0% +dummy variable we're we're assuming is +randomly assigned or anything like that + + align:start position:0% +randomly assigned or anything like that + + + align:start position:0% +randomly assigned or anything like that +okay and we'll see lots of other uses of + + align:start position:0% +okay and we'll see lots of other uses of + + + align:start position:0% +okay and we'll see lots of other uses of +dummy variables when we get to multiple + + align:start position:0% +dummy variables when we get to multiple + + + align:start position:0% +dummy variables when we get to multiple +regression because we can use them to + + align:start position:0% +regression because we can use them to + + + align:start position:0% +regression because we can use them to +sort of um um multiply we can use them + + align:start position:0% +sort of um um multiply we can use them + + + align:start position:0% +sort of um um multiply we can use them +to interact with uh other explanatory + + align:start position:0% +to interact with uh other explanatory + + + align:start position:0% +to interact with uh other explanatory +variables and shift slopes around and + + align:start position:0% +variables and shift slopes around and + + + align:start position:0% +variables and shift slopes around and +and uh you know Trace out nonlinear + + align:start position:0% +and uh you know Trace out nonlinear + + + align:start position:0% +and uh you know Trace out nonlinear +relationships we can do all kinds of + + align:start position:0% +relationships we can do all kinds of + + + align:start position:0% +relationships we can do all kinds of +tricky things with dummy variables um + + align:start position:0% +tricky things with dummy variables um + + + align:start position:0% +tricky things with dummy variables um +and we'll see that + + align:start position:0% +and we'll see that + + + align:start position:0% +and we'll see that +later + + align:start position:0% +later + + + align:start position:0% +later +okay um another uh sort of practical + + align:start position:0% +okay um another uh sort of practical + + + align:start position:0% +okay um another uh sort of practical +issue that we'll sort of deal with in + + align:start position:0% +issue that we'll sort of deal with in + + + align:start position:0% +issue that we'll sort of deal with in +more detail uh in um multiple regression + + align:start position:0% +more detail uh in um multiple regression + + + align:start position:0% +more detail uh in um multiple regression +you might be thinking well fine the + + align:start position:0% +you might be thinking well fine the + + + align:start position:0% +you might be thinking well fine the +linear model seems pretty useful we can + + align:start position:0% +linear model seems pretty useful we can + + + align:start position:0% +linear model seems pretty useful we can +uh use it for all kinds of stuff but + + align:start position:0% +uh use it for all kinds of stuff but + + + align:start position:0% +uh use it for all kinds of stuff but +isn't it really restrictive I mean maybe + + align:start position:0% +isn't it really restrictive I mean maybe + + + align:start position:0% +isn't it really restrictive I mean maybe +the relationship between these variables + + align:start position:0% +the relationship between these variables + + + align:start position:0% +the relationship between these variables +there is a relationship but it's just + + align:start position:0% +there is a relationship but it's just + + + align:start position:0% +there is a relationship but it's just +not linear and so we're sort of imposing + + align:start position:0% +not linear and so we're sort of imposing + + + align:start position:0% +not linear and so we're sort of imposing +linearity on here and that seems like + + align:start position:0% +linearity on here and that seems like + + + align:start position:0% +linearity on here and that seems like +something we wouldn't often want to do + + align:start position:0% +something we wouldn't often want to do + + + align:start position:0% +something we wouldn't often want to do +well there are a couple things I can say + + align:start position:0% +well there are a couple things I can say + + + align:start position:0% +well there are a couple things I can say +about this one is that the linear model + + align:start position:0% +about this one is that the linear model + + + align:start position:0% +about this one is that the linear model +is actually super flexible okay so for + + align:start position:0% +is actually super flexible okay so for + + + align:start position:0% +is actually super flexible okay so for +instance we can um we can take nonlinear + + align:start position:0% +instance we can um we can take nonlinear + + + align:start position:0% +instance we can um we can take nonlinear +functions + + align:start position:0% +functions + + + align:start position:0% +functions +of both of the variables X variable and + + align:start position:0% +of both of the variables X variable and + + + align:start position:0% +of both of the variables X variable and +Y variable and uh sort of analyze those + + align:start position:0% +Y variable and uh sort of analyze those + + + align:start position:0% +Y variable and uh sort of analyze those +uh the sort of relationships between + + align:start position:0% +uh the sort of relationships between + + + align:start position:0% +uh the sort of relationships between +those nonlinear functions of X and Y + + align:start position:0% +those nonlinear functions of X and Y + + + align:start position:0% +those nonlinear functions of X and Y +within a linear framework um we can also + + align:start position:0% +within a linear framework um we can also + + + align:start position:0% +within a linear framework um we can also +uh create uh interaction variables which + + align:start position:0% +uh create uh interaction variables which + + + align:start position:0% +uh create uh interaction variables which +is sort of the product of two variables + + align:start position:0% +is sort of the product of two variables + + + align:start position:0% +is sort of the product of two variables +and that allows for you know sort of uh + + align:start position:0% +and that allows for you know sort of uh + + + align:start position:0% +and that allows for you know sort of uh +other types of uh nonlinearity and we + + align:start position:0% +other types of uh nonlinearity and we + + + align:start position:0% +other types of uh nonlinearity and we +can do all of this and like I said we + + align:start position:0% +can do all of this and like I said we + + + align:start position:0% +can do all of this and like I said we +can use dummy variables to sort of allow + + align:start position:0% +can use dummy variables to sort of allow + + + align:start position:0% +can use dummy variables to sort of allow +for + + align:start position:0% +for + + + align:start position:0% +for +nonlinear um you know allow for sort of + + align:start position:0% +nonlinear um you know allow for sort of + + + align:start position:0% +nonlinear um you know allow for sort of +nonlinear shapes uh by sort of um you + + align:start position:0% +nonlinear shapes uh by sort of um you + + + align:start position:0% +nonlinear shapes uh by sort of um you +know tricky multiplication we'll show + + align:start position:0% +know tricky multiplication we'll show + + + align:start position:0% +know tricky multiplication we'll show +you examples of that but the point I + + align:start position:0% +you examples of that but the point I + + + align:start position:0% +you examples of that but the point I +want to make now is just that this is + + align:start position:0% +want to make now is just that this is + + + align:start position:0% +want to make now is just that this is +actually it seems like it might be a + + align:start position:0% +actually it seems like it might be a + + + align:start position:0% +actually it seems like it might be a +restrictive framework it's actually a + + align:start position:0% +restrictive framework it's actually a + + + align:start position:0% +restrictive framework it's actually a +super flexible framework um and we'll + + align:start position:0% +super flexible framework um and we'll + + + align:start position:0% +super flexible framework um and we'll +see all kinds of examples about how + + align:start position:0% +see all kinds of examples about how + + + align:start position:0% +see all kinds of examples about how +flexible the linear framework actually + + align:start position:0% +flexible the linear framework actually + + + align:start position:0% +flexible the linear framework actually +is one additional comment I want to make + + align:start position:0% +is one additional comment I want to make + + + align:start position:0% +is one additional comment I want to make +about this is that we can do um the + + align:start position:0% +about this is that we can do um the + + + align:start position:0% +about this is that we can do um the +non-parametric version of a linear + + align:start position:0% +non-parametric version of a linear + + + align:start position:0% +non-parametric version of a linear +regression that Ester talked about uh + + align:start position:0% +regression that Ester talked about uh + + + align:start position:0% +regression that Ester talked about uh +last time a kernel regression and uh + + align:start position:0% +last time a kernel regression and uh + + + align:start position:0% +last time a kernel regression and uh +researchers do um perform they do + + align:start position:0% +researchers do um perform they do + + + align:start position:0% +researchers do um perform they do +estimate kernel regressions and um + + align:start position:0% +estimate kernel regressions and um + + + align:start position:0% +estimate kernel regressions and um +they're useful in a lot of situations + + align:start position:0% +they're useful in a lot of situations + + + align:start position:0% +they're useful in a lot of situations +but there are serious tradeoffs and + + align:start position:0% +but there are serious tradeoffs and + + + align:start position:0% +but there are serious tradeoffs and +there are very good reasons why the + + align:start position:0% +there are very good reasons why the + + + align:start position:0% +there are very good reasons why the +linear regression is the Workhorse that + + align:start position:0% +linear regression is the Workhorse that + + + align:start position:0% +linear regression is the Workhorse that +it is and the tradeoffs mostly uh come + + align:start position:0% +it is and the tradeoffs mostly uh come + + + align:start position:0% +it is and the tradeoffs mostly uh come +in the form of efficiency a linear + + align:start position:0% +in the form of efficiency a linear + + + align:start position:0% +in the form of efficiency a linear +regression is going to be a much much + + align:start position:0% +regression is going to be a much much + + + align:start position:0% +regression is going to be a much much +more efficient way to estimate a + + align:start position:0% +more efficient way to estimate a + + + align:start position:0% +more efficient way to estimate a +relationship than um than a kernel + + align:start position:0% +relationship than um than a kernel + + + align:start position:0% +relationship than um than a kernel +regression so the kernel regression is + + align:start position:0% +regression so the kernel regression is + + + align:start position:0% +regression so the kernel regression is +uh sort of infinitely flexible in some + + align:start position:0% +uh sort of infinitely flexible in some + + + align:start position:0% +uh sort of infinitely flexible in some +sense but you pay for it because it's + + align:start position:0% +sense but you pay for it because it's + + + align:start position:0% +sense but you pay for it because it's +not an an efficient estimator at all + + align:start position:0% + + + + align:start position:0% + +really + + align:start position:0% +really + + + align:start position:0% +really +okay so question + + align:start position:0% +okay so question + + + align:start position:0% +okay so question +questions about those sort of + + align:start position:0% +questions about those sort of + + + align:start position:0% +questions about those sort of +practical issues concerning linear + + align:start position:0% +practical issues concerning linear + + + align:start position:0% +practical issues concerning linear +linear regression okay so let me just + + align:start position:0% +linear regression okay so let me just + + + align:start position:0% +linear regression okay so let me just +get started I have a few minutes now and + + align:start position:0% +get started I have a few minutes now and + + + align:start position:0% +get started I have a few minutes now and +we'll get started on uh a generalization + + align:start position:0% +we'll get started on uh a generalization + + + align:start position:0% +we'll get started on uh a generalization +of the linear model the sort of + + align:start position:0% +of the linear model the sort of + + + align:start position:0% +of the linear model the sort of +multivariant um linear model okay and uh + + align:start position:0% +multivariant um linear model okay and uh + + + align:start position:0% +multivariant um linear model okay and uh +this is um this is what it looks like so + + align:start position:0% +this is um this is what it looks like so + + + align:start position:0% +this is um this is what it looks like so +why + + align:start position:0% +why + + + align:start position:0% +why +might we be interested in sort of this + + align:start position:0% +might we be interested in sort of this + + + align:start position:0% +might we be interested in sort of this +more General linear + + align:start position:0% +more General linear + + + align:start position:0% +more General linear +model I mean maybe the answer is kind of + + align:start position:0% +model I mean maybe the answer is kind of + + + align:start position:0% +model I mean maybe the answer is kind of +obvious but you know I could sort of + + align:start position:0% +obvious but you know I could sort of + + + align:start position:0% +obvious but you know I could sort of +talk about a lot of um you know we could + + align:start position:0% +talk about a lot of um you know we could + + + align:start position:0% +talk about a lot of um you know we could +talk about a lot of uh examples where + + align:start position:0% +talk about a lot of uh examples where + + + align:start position:0% +talk about a lot of uh examples where +you know we're we're primarily + + align:start position:0% +you know we're we're primarily + + + align:start position:0% +you know we're we're primarily +interested in the relationship between + + align:start position:0% +interested in the relationship between + + + align:start position:0% +interested in the relationship between +one particular X variable and are + + align:start position:0% +one particular X variable and are + + + align:start position:0% +one particular X variable and are +dependent or Y variable but there are + + align:start position:0% +dependent or Y variable but there are + + + align:start position:0% +dependent or Y variable but there are +other factors that might come into play + + align:start position:0% +other factors that might come into play + + + align:start position:0% +other factors that might come into play +that we need to account for in our + + align:start position:0% +that we need to account for in our + + + align:start position:0% +that we need to account for in our +analysis so that's one very good reason + + align:start position:0% +analysis so that's one very good reason + + + align:start position:0% +analysis so that's one very good reason +to to consider uh sort of this + + align:start position:0% +to to consider uh sort of this + + + align:start position:0% +to to consider uh sort of this +multivariate um linear model as opposed + + align:start position:0% +multivariate um linear model as opposed + + + align:start position:0% +multivariate um linear model as opposed +to just the bivariate linear model it + + align:start position:0% +to just the bivariate linear model it + + + align:start position:0% +to just the bivariate linear model it +could also be that um we uh you know we + + align:start position:0% +could also be that um we uh you know we + + + align:start position:0% +could also be that um we uh you know we +actually have many variables we we don't + + align:start position:0% +actually have many variables we we don't + + + align:start position:0% +actually have many variables we we don't +have any a priority notion about what x + + align:start position:0% +have any a priority notion about what x + + + align:start position:0% +have any a priority notion about what x +variables might be important uh + + align:start position:0% +variables might be important uh + + + align:start position:0% +variables might be important uh +predictors of why so think back to the + + align:start position:0% +predictors of why so think back to the + + + align:start position:0% +predictors of why so think back to the +example of a firm trying to decide who + + align:start position:0% +example of a firm trying to decide who + + + align:start position:0% +example of a firm trying to decide who +to + + align:start position:0% +to + + + align:start position:0% +to +serve ads on um the that Moby Dick + + align:start position:0% +serve ads on um the that Moby Dick + + + align:start position:0% +serve ads on um the that Moby Dick +t-shirt too well they might not have any + + align:start position:0% +t-shirt too well they might not have any + + + align:start position:0% +t-shirt too well they might not have any +sort of aii reason to think well it's + + align:start position:0% +sort of aii reason to think well it's + + + align:start position:0% +sort of aii reason to think well it's +people who read XKCD who might buy this + + align:start position:0% +people who read XKCD who might buy this + + + align:start position:0% +people who read XKCD who might buy this +t-shirt and what they would like to do + + align:start position:0% +t-shirt and what they would like to do + + + align:start position:0% +t-shirt and what they would like to do +is get sort of the web browsing beh + + align:start position:0% +is get sort of the web browsing beh + + + align:start position:0% +is get sort of the web browsing beh +behavior of lots and lots of people and + + align:start position:0% +behavior of lots and lots of people and + + + align:start position:0% +behavior of lots and lots of people and +see all kinds of uh websites that they + + align:start position:0% +see all kinds of uh websites that they + + + align:start position:0% +see all kinds of uh websites that they +visit figure out which ones actually buy + + align:start position:0% +visit figure out which ones actually buy + + + align:start position:0% +visit figure out which ones actually buy +this t-shirt and then use the results of + + align:start position:0% +this t-shirt and then use the results of + + + align:start position:0% +this t-shirt and then use the results of +that um analysis to figure out who to + + align:start position:0% +that um analysis to figure out who to + + + align:start position:0% +that um analysis to figure out who to +serve ads to in the future okay so + + align:start position:0% +serve ads to in the future okay so + + + align:start position:0% +serve ads to in the future okay so +that's another reason why we want to + + align:start position:0% +that's another reason why we want to + + + align:start position:0% +that's another reason why we want to +consider models that have lots of uh + + align:start position:0% +consider models that have lots of uh + + + align:start position:0% +consider models that have lots of uh +potentially lots of regressors in them + + align:start position:0% +potentially lots of regressors in them + + + align:start position:0% +potentially lots of regressors in them +not just one + + align:start position:0% +not just one + + + align:start position:0% +not just one +okay so as I said before the sort of not + + align:start position:0% +okay so as I said before the sort of not + + + align:start position:0% +okay so as I said before the sort of not +not a we were using for the B variant + + align:start position:0% +not a we were using for the B variant + + + align:start position:0% +not a we were using for the B variant +regression was just it was just sort of + + align:start position:0% +regression was just it was just sort of + + + align:start position:0% +regression was just it was just sort of +not up to the task it was kind of clunky + + align:start position:0% +not up to the task it was kind of clunky + + + align:start position:0% +not up to the task it was kind of clunky +it was a little awkward and it turns out + + align:start position:0% +it was a little awkward and it turns out + + + align:start position:0% +it was a little awkward and it turns out +that uh we can sort of all of the things + + align:start position:0% +that uh we can sort of all of the things + + + align:start position:0% +that uh we can sort of all of the things +that I um can you know say about linear + + align:start position:0% +that I um can you know say about linear + + + align:start position:0% +that I um can you know say about linear +regression can be said much more + + align:start position:0% +regression can be said much more + + + align:start position:0% +regression can be said much more +elegantly using Matrix notation okay so + + align:start position:0% +elegantly using Matrix notation okay so + + + align:start position:0% +elegantly using Matrix notation okay so +what we're going to do I by the way + + align:start position:0% +what we're going to do I by the way + + + align:start position:0% +what we're going to do I by the way +maybe I should take a show of hands how + + align:start position:0% +maybe I should take a show of hands how + + + align:start position:0% +maybe I should take a show of hands how +many people are familiar with some basic + + align:start position:0% +many people are familiar with some basic + + + align:start position:0% +many people are familiar with some basic +Matrix notation and linear algebra + + align:start position:0% + + + + align:start position:0% + +facts yes okay so there might be a + + align:start position:0% +facts yes okay so there might be a + + + align:start position:0% +facts yes okay so there might be a +couple who aren't but it seems like the + + align:start position:0% +couple who aren't but it seems like the + + + align:start position:0% +couple who aren't but it seems like the +vast majority of the class is so I have + + align:start position:0% +vast majority of the class is so I have + + + align:start position:0% +vast majority of the class is so I have +put up on the website also under + + align:start position:0% +put up on the website also under + + + align:start position:0% +put up on the website also under +resources a a separate handout and I + + align:start position:0% +resources a a separate handout and I + + + align:start position:0% +resources a a separate handout and I +forget what it's called maybe it's + + align:start position:0% +forget what it's called maybe it's + + + align:start position:0% +forget what it's called maybe it's +called Matrix notation Etc or something + + align:start position:0% +called Matrix notation Etc or something + + + align:start position:0% +called Matrix notation Etc or something +like that and basically it goes through + + align:start position:0% +like that and basically it goes through + + + align:start position:0% +like that and basically it goes through +in Greater detail than I'm going to do + + align:start position:0% +in Greater detail than I'm going to do + + + align:start position:0% +in Greater detail than I'm going to do +in lecture um you know it it gives you + + align:start position:0% +in lecture um you know it it gives you + + + align:start position:0% +in lecture um you know it it gives you +both a primer for you know uh Matrix + + align:start position:0% +both a primer for you know uh Matrix + + + align:start position:0% +both a primer for you know uh Matrix +notation and reminds you sort of + + align:start position:0% +notation and reminds you sort of + + + align:start position:0% +notation and reminds you sort of +definitions uh you know Matrix algebra + + align:start position:0% +definitions uh you know Matrix algebra + + + align:start position:0% +definitions uh you know Matrix algebra +you know linear algebra kind of + + align:start position:0% +you know linear algebra kind of + + + align:start position:0% +you know linear algebra kind of +definitions reminds you of those but + + align:start position:0% +definitions reminds you of those but + + + align:start position:0% +definitions reminds you of those but +then also sort of goes through uh the + + align:start position:0% +then also sort of goes through uh the + + + align:start position:0% +then also sort of goes through uh the +the um uh linear regression stuff in + + align:start position:0% +the um uh linear regression stuff in + + + align:start position:0% +the um uh linear regression stuff in +more detail that I'm going to do in + + align:start position:0% +more detail that I'm going to do in + + + align:start position:0% +more detail that I'm going to do in +lecture so you can look at those notes + + align:start position:0% +lecture so you can look at those notes + + + align:start position:0% +lecture so you can look at those notes +if you want okay so this is a job for + + align:start position:0% +if you want okay so this is a job for + + + align:start position:0% +if you want okay so this is a job for +Matrix notation we don't have too much + + align:start position:0% +Matrix notation we don't have too much + + + align:start position:0% +Matrix notation we don't have too much +time but I'll just get started here + + align:start position:0% +time but I'll just get started here + + + align:start position:0% +time but I'll just get started here +let's replace this whole parade of x's + + align:start position:0% +let's replace this whole parade of x's + + + align:start position:0% +let's replace this whole parade of x's +with a vector a row Vector okay and + + align:start position:0% +with a vector a row Vector okay and + + + align:start position:0% +with a vector a row Vector okay and +let's um say let's define a new X that's + + align:start position:0% +let's um say let's define a new X that's + + + align:start position:0% +let's um say let's define a new X that's +identically equal to one and that's + + align:start position:0% +identically equal to one and that's + + + align:start position:0% +identically equal to one and that's +called x sub 01 Okay the reason we do + + align:start position:0% +called x sub 01 Okay the reason we do + + + align:start position:0% +called x sub 01 Okay the reason we do +this is because sort of implicitly in + + align:start position:0% +this is because sort of implicitly in + + + align:start position:0% +this is because sort of implicitly in +the byari regression we had beta not + + align:start position:0% +the byari regression we had beta not + + + align:start position:0% +the byari regression we had beta not +time one we never had the one there but + + align:start position:0% +time one we never had the one there but + + + align:start position:0% +time one we never had the one there but +we you know sort of implicitly there was + + align:start position:0% +we you know sort of implicitly there was + + + align:start position:0% +we you know sort of implicitly there was +a one multiplying beta KN and then we + + align:start position:0% +a one multiplying beta KN and then we + + + align:start position:0% +a one multiplying beta KN and then we +had beta 1 * x sub I well here we want + + align:start position:0% +had beta 1 * x sub I well here we want + + + align:start position:0% +had beta 1 * x sub I well here we want +to explicitly have the the the one in + + align:start position:0% +to explicitly have the the the one in + + + align:start position:0% +to explicitly have the the the one in +that first spot so we can do everything + + align:start position:0% +that first spot so we can do everything + + + align:start position:0% +that first spot so we can do everything +in Matrix notation okay and so um let's + + align:start position:0% +in Matrix notation okay and so um let's + + + align:start position:0% +in Matrix notation okay and so um let's +define let's replace this whole parade + + align:start position:0% +define let's replace this whole parade + + + align:start position:0% +define let's replace this whole parade +of x's with a row vector and so for each + + align:start position:0% +of x's with a row vector and so for each + + + align:start position:0% +of x's with a row vector and so for each +observ ation we have a vector of + + align:start position:0% +observ ation we have a vector of + + + align:start position:0% +observ ation we have a vector of +different + + align:start position:0% +different + + + align:start position:0% +different +measures X knot up through X subk for + + align:start position:0% +measures X knot up through X subk for + + + align:start position:0% +measures X knot up through X subk for +each observation okay and then let's + + align:start position:0% +each observation okay and then let's + + + align:start position:0% +each observation okay and then let's +also replace uh uh all of the betas that + + align:start position:0% +also replace uh uh all of the betas that + + + align:start position:0% +also replace uh uh all of the betas that +multiply all of these regressors by a + + align:start position:0% +multiply all of these regressors by a + + + align:start position:0% +multiply all of these regressors by a +vector in this case a column Vector um a + + align:start position:0% +vector in this case a column Vector um a + + + align:start position:0% +vector in this case a column Vector um a +k by k+ 1 by one column Vector of um uh + + align:start position:0% +k by k+ 1 by one column Vector of um uh + + + align:start position:0% +k by k+ 1 by one column Vector of um uh +parameters beta okay + + align:start position:0% + + + + align:start position:0% + +okay and then that lets us uh use a much + + align:start position:0% +okay and then that lets us uh use a much + + + align:start position:0% +okay and then that lets us uh use a much +more condensed notation for our um + + align:start position:0% +more condensed notation for our um + + + align:start position:0% +more condensed notation for our um +multivariate linear model and it's just + + align:start position:0% +multivariate linear model and it's just + + + align:start position:0% +multivariate linear model and it's just +y subi equal x subi beta plus Epson subi + + align:start position:0% +y subi equal x subi beta plus Epson subi + + + align:start position:0% +y subi equal x subi beta plus Epson subi +okay so this is still this is the model + + align:start position:0% +okay so this is still this is the model + + + align:start position:0% +okay so this is still this is the model +for for each individual observation and + + align:start position:0% +for for each individual observation and + + + align:start position:0% +for for each individual observation and +so we can go even further and we can + + align:start position:0% +so we can go even further and we can + + + align:start position:0% +so we can go even further and we can +basically put all the observations into + + align:start position:0% +basically put all the observations into + + + align:start position:0% +basically put all the observations into +um Matrix es or vectors and sort of + + align:start position:0% +um Matrix es or vectors and sort of + + + align:start position:0% +um Matrix es or vectors and sort of +compress our notation even further okay + + align:start position:0% +compress our notation even further okay + + + align:start position:0% +compress our notation even further okay +so now let's let y uh the the entire um + + align:start position:0% +so now let's let y uh the the entire um + + + align:start position:0% +so now let's let y uh the the entire um +set of observations on our outcome + + align:start position:0% +set of observations on our outcome + + + align:start position:0% +set of observations on our outcome +variable across our different + + align:start position:0% +variable across our different + + + align:start position:0% +variable across our different +observations let's put that into a n by1 + + align:start position:0% +observations let's put that into a n by1 + + + align:start position:0% +observations let's put that into a n by1 +column + + align:start position:0% +column + + + align:start position:0% +column +vector and then let's put our errors + + align:start position:0% +vector and then let's put our errors + + + align:start position:0% +vector and then let's put our errors +also into an N by1 column + + align:start position:0% +also into an N by1 column + + + align:start position:0% +also into an N by1 column +vector and then let's take each one of + + align:start position:0% +vector and then let's take each one of + + + align:start position:0% +vector and then let's take each one of +these row vector vors that I defined on + + align:start position:0% +these row vector vors that I defined on + + + align:start position:0% +these row vector vors that I defined on +the previous slide so remember for each + + align:start position:0% +the previous slide so remember for each + + + align:start position:0% +the previous slide so remember for each +observation we had a row Vector that was + + align:start position:0% +observation we had a row Vector that was + + + align:start position:0% +observation we had a row Vector that was +the measures of all of the X's for each + + align:start position:0% +the measures of all of the X's for each + + + align:start position:0% +the measures of all of the X's for each +observation let's stack those up and put + + align:start position:0% +observation let's stack those up and put + + + align:start position:0% +observation let's stack those up and put +those into uh an N by k + one + + align:start position:0% +those into uh an N by k + one + + + align:start position:0% +those into uh an N by k + one +Matrix okay so remember this column here + + align:start position:0% +Matrix okay so remember this column here + + + align:start position:0% +Matrix okay so remember this column here +is identically equal to + + align:start position:0% +is identically equal to + + + align:start position:0% +is identically equal to +one and then these the second column on + + align:start position:0% +one and then these the second column on + + + align:start position:0% +one and then these the second column on +are all measures of are explanatory + + align:start position:0% +are all measures of are explanatory + + + align:start position:0% +are all measures of are explanatory +variables X1 through + + align:start position:0% + + + + align:start position:0% + +XK + + align:start position:0% +XK + + + align:start position:0% +XK +yes or is just + + align:start position:0% +yes or is just + + + align:start position:0% +yes or is just +X yes it is supposed to be + + align:start position:0% +X yes it is supposed to be + + + align:start position:0% +X yes it is supposed to be +X so yes the that the the the I + + align:start position:0% +X so yes the that the the the I + + + align:start position:0% +X so yes the that the the the I +subscript snuck in there and I apologize + + align:start position:0% +subscript snuck in there and I apologize + + + align:start position:0% +subscript snuck in there and I apologize +for + + align:start position:0% +for + + + align:start position:0% +for +it + + align:start position:0% +it + + + align:start position:0% +it +yes so each row is X toi yes so each row + + align:start position:0% +yes so each row is X toi yes so each row + + + align:start position:0% +yes so each row is X toi yes so each row +vector will call X toi this entire + + align:start position:0% +vector will call X toi this entire + + + align:start position:0% +vector will call X toi this entire +Matrix will call X so you're absolutely + + align:start position:0% +Matrix will call X so you're absolutely + + + align:start position:0% +Matrix will call X so you're absolutely +right okay so everyone on board with + + align:start position:0% +right okay so everyone on board with + + + align:start position:0% +right okay so everyone on board with +this + + align:start position:0% +this + + + align:start position:0% +this +structure okay so one more slide and + + align:start position:0% +structure okay so one more slide and + + + align:start position:0% +structure okay so one more slide and +then we'll call it a + + align:start position:0% +then we'll call it a + + + align:start position:0% +then we'll call it a +day then when when we have defined + + align:start position:0% +day then when when we have defined + + + align:start position:0% +day then when when we have defined +everything and sort of created that + + align:start position:0% +everything and sort of created that + + + align:start position:0% +everything and sort of created that +structure uh we now can write the + + align:start position:0% +structure uh we now can write the + + + align:start position:0% +structure uh we now can write the +multiple multivariate linear regression + + align:start position:0% +multiple multivariate linear regression + + + align:start position:0% +multiple multivariate linear regression +model or linear model as yal X beta plus + + align:start position:0% +model or linear model as yal X beta plus + + + align:start position:0% +model or linear model as yal X beta plus +Epsilon uh with all of those Dimensions + + align:start position:0% +Epsilon uh with all of those Dimensions + + + align:start position:0% +Epsilon uh with all of those Dimensions +up there okay so we'll start here next + + align:start position:0% +up there okay so we'll start here next + + + align:start position:0% +up there okay so we'll start here next +time and um see you guys in a couple of + + align:start position:0% + + + + align:start position:0% + +days \ No newline at end of file diff --git a/rOA1VC5aQ7Q.txt b/rOA1VC5aQ7Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..8267f7d7a753bffa1ec9d3f9b28abe34fd11850e --- /dev/null +++ b/rOA1VC5aQ7Q.txt @@ -0,0 +1,499 @@ +PROFESSOR: Last time we talked +about op-amps and the fact + +that they allowed us to +abstract away certain + +components of a circuit and +sample particular voltages + +from a circuit and then modify +those voltages as we would + +like in an LTI fashion. + +Today I'd like to talk to you +about some other interesting + +things that fall out of the fact +that we're only dealing + +with LTI systems. + +In particular, Thevenin/Norton +equivalence and superposition. + +Thevenin/Norton equivalence is +the idea that if you have a + +very complex circuit, but it's +still a LTI circuit, you can + +express it using +a linear curve. + +And superposition is the idea +that because you're also + +dealing with LTI components, +if you're trying to solve a + +circuit, you can take the +individual contributions of + +independent sources to that +circuit and sum them in order + +to find out either the total +current flowing through a + +particular component or the +total voltage drop across a + +particular component. + +At this point, I'll walk +you through both. + +Thevenin/Norton equivalence is +an important concept in that + +you may have a very complicated +circuit. + +And you don't really want +to talk about the entire + +complicated circuit. + +You just want to sample the +voltage drop or current in a + +very particular location. + +Because we're dealing with LTI +systems we can actually + +express that particular sample +as its relationship between I + +and V and possibly whatever +resistive component is + +associated with the voltage +drop across that sample. + +We can solve for this curve by +looking at the location that + +were sampling and finding +the open circuit voltage + +associated with that position. + +Or if we were to leave the two +terminals from where we are + +sampling open, what is the +voltage drop across that + +section of our circuit? + +That's the point right here, +where the current flowing + +through the system is 0. + +And there's a given voltage +associated with it. + +Likewise if we want to find the +other intercept, we can + +close those two terminals by +running a wire across them and + +then look at the current that +flows across that wire. + +That's the close circuit +current. + +The slope is going to tell us +about our resistance, if any. + +If we're only dealing with a +voltage source or a current + +source, then we're only +going to be dealing + +with a straight line. + +Once we've solved for these +values, we tend to express + +them either as a Thevenin +equivalent circuit or a Norton + +equivalent circuit. + +And you can convert +between the two. + +Let's walk through an example. + +Here I've got a simple +circuit. + +And I would like to find the +Thevenin equivalent of that + +circuit, given that I'm sampling +from above this + +resistor and below +this resistor. + +The first thing that I'm +going to do is find the + +open circuit voltage. + +Or if I were sampling from this +point to this point, what + +is the voltage drop across this +section of the circuit? + +Well, I've got 36 Volts. + +There's 12 Ohms of +resistance in the + +section that I'm sampling. + +And there's 6 Ohms of resistance +outside the section + +that I'm sampling. + +So 2/3 of my total voltage +drop across this voltage + +divider is going to be accounted +for inside my + +Thevenin equivalent circuit. + +So my Thevenin equivalent +voltage is 24 Volts. + +Now I want to go after the +short circuit current. + +If I were to draw a wire from +this terminal to this + +terminal, I'm curious what +this value would be. + +As a consequence of connecting +these two terminals, these + +resistors are going to be +completely bypassed. + +We don't actually have to drop +any voltage or put any current + +through these resistors because +there's actually an + +infinitely easier way for +the current to go. + +In this case, we're just going +to follow Ohm's law. + +36 divided by 6 is 6 Amperes. + +But because of the +directionality on this short + +circuit current, current in this +system is going to flow + +in this direction. + +So are short circuit current is + +actually negative 6 Amperes. + +That just leaves Rth. + +Once again we're going +to rely on Ohm's law. + +If we divide our voltage +by our current-- + +you can't have a negative +resistance. + +We're actually going to divide +by the negative of this. + +We'll get out 4 Ohms. + +Let's do it again, this time +with a slightly different + +sample point and +find the Norton + +equivalent of our circuit. + +So if I'm only sampling across +the 9 Ohm resistor-- + +I personally still solve for +the Thevenin equivalent + +voltage first because I +think it's easiest. + +I'll just make note +of it over here. + +The voltage drop across this +resistor is determined by the + +fact that this is a simple +voltage divider. + +The other resistors +in this circuit-- + +7, 2, 9 Ohms. + +So the voltage drop across +this resistor is going to + +represent half of the total +voltage in our circuit. + +That's 18 Volts. + +The short circuit current +associated with connecting + +these two terminals is 36 Volts +divided by the sum of + +these two resistors. + +Once again we're going to end +up bypassing this resistor + +entirely because, think about +it this way, if there was a + +resistor across here with 0 +resistance, all the current + +would sink through it, or it +would represent the location + +for which infinite current +would flow. + +36 divided by 9 is 4. + +And because we're following in +the opposite direction we're + +going to say this is +negative 4 Amperes. + +In this orientation, the Norton +equivalent amperage is + +actually the negative +of this value. + +You sometimes see the arrow +pointing downwards. + +This preserves our property +of short circuit current. + +If this was short circuited, +Isc would still + +be negative 4 Amperes. + +And our Vth-- + +if our Vth was the voltage drop +across these two points-- + +ha, I haven't solved +for Rth yet. + +There are a few ways +to do this. + +But I'm going to +use Vth and In. + +18 over 4, we can reduce +it to 9 over 2. + +And if I were to solve back +out for the voltage drop + +across this resistor just as a +consequence of I Norton, I + +would get 18 Volts, which is +also the Thevenin equivalent + +voltage for this circuit. + +That covers Thevenin/Norton +equivalence. + +And we're going to talk about +superposition really quickly. + +Superposition is yet another +circuit-solving strategy. + +It falls out as a consequence +of only working with LTI + +components. + +And it means that in order to +solve for a given component + +current or component voltage, +you can actually find it by + +taking the linear combination +of every contribution as a + +consequence of independent +sources. + +What do I mean when +I say that? + +Well, if you have a circuit +like this-- + +and you might recognize +it from the + +NVCC lecture earlier-- + +you can actually express it as +a linear combination of just + +the voltage source and just +the current source. + +Note what when I remove the +current source, I end up with + +no connection because if you +have 0 current flowing through + +a system, it's the +same as if the + +connection has been removed. + +Note that when I remove the +voltage source, I no longer + +have a voltage drop across +that connection, but I + +maintain the connection. + +If in this example I was +just looking for I1. + +I1 would be the linear +combination of the + +contribution of I1 in this +particular circuit plus I1 in + +this particular circuit. + +So this is the expression +that I'm looking for. + +In the first circuit, I'm just +going to use V over IR -- + +or V equals IR -- + +and I'm going to have 3 Amperes +in this direction. + +In this circuit I'm actually +going to have to + +use a current divider. + +Identify that I have five parts +total to distribute + +among these two branches. + +Identify that this side is going +to get the inverse of + +this side's contribution to the +total parts, or this side + +is going to get the proportion +of parts equivalent to this + +side's contribution. + +And vice versa. + +That this side is the side +that I'm interested in. + +And so 2/5 of the total current +flowing through this + +current divider is going to +end up in this branch. + +2/5 of 10 is 4. + +It's in the opposite direction +of this current flow. + +So I'm actually going to +contribute negative 4 Amperes + +from this subcircuit. + +This should match the results +from the NVCC lecture. + +That's my super fast coverage +of superposition and also + +Thevenin/Norton equivalence. + +Next time we're going to start +a whole new module. \ No newline at end of file diff --git a/rZS2LGiurKY.txt b/rZS2LGiurKY.txt new file mode 100644 index 0000000000000000000000000000000000000000..f9a7e3bba7aeb3fefbc1e7c870707fbe035a38f8 --- /dev/null +++ b/rZS2LGiurKY.txt @@ -0,0 +1,7731 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so hi everybody I'm Alan Edelman and + + align:start position:0% +so hi everybody I'm Alan Edelman and + + + align:start position:0% +so hi everybody I'm Alan Edelman and +helped a little bit to teach this class + + align:start position:0% +helped a little bit to teach this class + + + align:start position:0% +helped a little bit to teach this class +last year but happy to see that it's + + align:start position:0% +last year but happy to see that it's + + + align:start position:0% +last year but happy to see that it's +going great this year so professor + + align:start position:0% +going great this year so professor + + + align:start position:0% +going great this year so professor +Strang came to teach 1806 some of you + + align:start position:0% +Strang came to teach 1806 some of you + + + align:start position:0% +Strang came to teach 1806 some of you +may know the the introductory linear + + align:start position:0% +may know the the introductory linear + + + align:start position:0% +may know the the introductory linear +algebra course and professor Strang came + + align:start position:0% +algebra course and professor Strang came + + + align:start position:0% +algebra course and professor Strang came +by and gave this great demonstration + + align:start position:0% +by and gave this great demonstration + + + align:start position:0% +by and gave this great demonstration +about the row rank equals the column + + align:start position:0% +about the row rank equals the column + + + align:start position:0% +about the row rank equals the column +rank and I'm wondering if you did that + + align:start position:0% +rank and I'm wondering if you did that + + + align:start position:0% +rank and I'm wondering if you did that +in this class at any time or would they + + align:start position:0% +in this class at any time or would they + + + align:start position:0% +in this class at any time or would they +have seen that it's in the notes well in + + align:start position:0% +have seen that it's in the notes well in + + + align:start position:0% +have seen that it's in the notes well in +in any event just as professor Strang + + align:start position:0% +in any event just as professor Strang + + + align:start position:0% +in any event just as professor Strang +walked out so here I'll just grab this + + align:start position:0% +walked out so here I'll just grab this + + + align:start position:0% +walked out so here I'll just grab this +this is truly I was actually gonna start + + align:start position:0% +this is truly I was actually gonna start + + + align:start position:0% +this is truly I was actually gonna start +writing the code to do the quadrilateral + + align:start position:0% +writing the code to do the quadrilateral + + + align:start position:0% +writing the code to do the quadrilateral +but I didn't have enough time you could + + align:start position:0% +but I didn't have enough time you could + + + align:start position:0% +but I didn't have enough time you could +see me starting but here's the point + + align:start position:0% +see me starting but here's the point + + + align:start position:0% +see me starting but here's the point +five for the triangle which was easy so + + align:start position:0% +five for the triangle which was easy so + + + align:start position:0% +five for the triangle which was easy so +that what's the story with Julia in this + + align:start position:0% +that what's the story with Julia in this + + + align:start position:0% +that what's the story with Julia in this +class have they used it a little or a + + align:start position:0% +class have they used it a little or a + + + align:start position:0% +class have they used it a little or a +lot or in the labs you've used Julia but + + align:start position:0% +lot or in the labs you've used Julia but + + + align:start position:0% +lot or in the labs you've used Julia but +that was just MATLAB so that was but + + align:start position:0% +that was just MATLAB so that was but + + + align:start position:0% +that was just MATLAB so that was but +okay so so so professor Strang showed + + align:start position:0% +okay so so so professor Strang showed + + + align:start position:0% +okay so so so professor Strang showed +this proof where he would he put down a + + align:start position:0% +this proof where he would he put down a + + + align:start position:0% +this proof where he would he put down a +three by three matrix it had rank two + + align:start position:0% +three by three matrix it had rank two + + + align:start position:0% +three by three matrix it had rank two +and he showed the you know took the + + align:start position:0% +and he showed the you know took the + + + align:start position:0% +and he showed the you know took the +columns that were you know the first two + + align:start position:0% +columns that were you know the first two + + + align:start position:0% +columns that were you know the first two +columns were independent and and was + + align:start position:0% +columns were independent and and was + + + align:start position:0% +columns were independent and and was +easy you know it was easy to show the + + align:start position:0% +easy you know it was easy to show the + + + align:start position:0% +easy you know it was easy to show the +row rank equals the column rank after + + align:start position:0% +row rank equals the column rank after + + + align:start position:0% +row rank equals the column rank after +professor Strang Roy went out I asked + + align:start position:0% +professor Strang Roy went out I asked + + + align:start position:0% +professor Strang Roy went out I asked +would that work for the zero matrix so + + align:start position:0% +would that work for the zero matrix so + + + align:start position:0% +would that work for the zero matrix so +so here's the the zero matrix and since + + align:start position:0% +so here's the the zero matrix and since + + + align:start position:0% +so here's the the zero matrix and since +I'm not really telling you the proof + + align:start position:0% +I'm not really telling you the proof + + + align:start position:0% +I'm not really telling you the proof +I'll just say if I were to put a mate if + + align:start position:0% +I'll just say if I were to put a mate if + + + align:start position:0% +I'll just say if I were to put a mate if +I were to make a matrix of the literally + + align:start position:0% +I were to make a matrix of the literally + + + align:start position:0% +I were to make a matrix of the literally +independent columns of this matrix what + + align:start position:0% +independent columns of this matrix what + + + align:start position:0% +independent columns of this matrix what +would I do + + align:start position:0% +would I do + + + align:start position:0% +would I do +so it's zero sort of a might seem tricky + + align:start position:0% +so it's zero sort of a might seem tricky + + + align:start position:0% +so it's zero sort of a might seem tricky +it's not really that tricky but this is + + align:start position:0% +it's not really that tricky but this is + + + align:start position:0% +it's not really that tricky but this is +what I did the moment you walked out so + + align:start position:0% +what I did the moment you walked out so + + + align:start position:0% +what I did the moment you walked out so +so yeah so I've got this three by three + + align:start position:0% +so yeah so I've got this three by three + + + align:start position:0% +so yeah so I've got this three by three +matrix and I need to make a first step + + align:start position:0% +matrix and I need to make a first step + + + align:start position:0% +matrix and I need to make a first step +in and whatever the proof was I needed + + align:start position:0% +in and whatever the proof was I needed + + + align:start position:0% +in and whatever the proof was I needed +to take the columns of the the literally + + align:start position:0% +to take the columns of the the literally + + + align:start position:0% +to take the columns of the the literally +independent columns of this matrix and + + align:start position:0% +independent columns of this matrix and + + + align:start position:0% +independent columns of this matrix and +place them in a matrix of their own what + + align:start position:0% +place them in a matrix of their own what + + + align:start position:0% +place them in a matrix of their own what +would I do it would be an empty matrix + + align:start position:0% +would I do it would be an empty matrix + + + align:start position:0% +would I do it would be an empty matrix +what would be the size of this empty + + align:start position:0% +what would be the size of this empty + + + align:start position:0% +what would be the size of this empty +matrix not exactly zero by zero because + + align:start position:0% +matrix not exactly zero by zero because + + + align:start position:0% +matrix not exactly zero by zero because +where every every column is still in our + + align:start position:0% +where every every column is still in our + + + align:start position:0% +where every every column is still in our +three you see so the right answer I hope + + align:start position:0% +three you see so the right answer I hope + + + align:start position:0% +three you see so the right answer I hope +this makes sense is a three by zero + + align:start position:0% +this makes sense is a three by zero + + + align:start position:0% +this makes sense is a three by zero +empty matrix and that's a concept that + + align:start position:0% +empty matrix and that's a concept that + + + align:start position:0% +empty matrix and that's a concept that +exists in MATLAB and in Julia and in + + align:start position:0% +exists in MATLAB and in Julia and in + + + align:start position:0% +exists in MATLAB and in Julia and in +Python I think I'm sure and in any + + align:start position:0% +Python I think I'm sure and in any + + + align:start position:0% +Python I think I'm sure and in any +computer language so if you had a full + + align:start position:0% +computer language so if you had a full + + + align:start position:0% +computer language so if you had a full +rank 3x3 matrix the linearly independent + + align:start position:0% +rank 3x3 matrix the linearly independent + + + align:start position:0% +rank 3x3 matrix the linearly independent +columns would be three by three if you + + align:start position:0% +columns would be three by three if you + + + align:start position:0% +columns would be three by three if you +had a rank two would be three by two + + align:start position:0% +had a rank two would be three by two + + + align:start position:0% +had a rank two would be three by two +they've had a rank one matrix it'd be + + align:start position:0% +they've had a rank one matrix it'd be + + + align:start position:0% +they've had a rank one matrix it'd be +three by one so if I had no columns + + align:start position:0% +three by one so if I had no columns + + + align:start position:0% +three by one so if I had no columns +three by zero makes sense and to finish + + align:start position:0% +three by zero makes sense and to finish + + + align:start position:0% +three by zero makes sense and to finish +the proof again I'm not telling these + + align:start position:0% +the proof again I'm not telling these + + + align:start position:0% +the proof again I'm not telling these +students it's in the notes apparently + + align:start position:0% +students it's in the notes apparently + + + align:start position:0% +students it's in the notes apparently +the next matrix would be R and of zero + + align:start position:0% +the next matrix would be R and of zero + + + align:start position:0% +the next matrix would be R and of zero +three and of course you multiply and you + + align:start position:0% +three and of course you multiply and you + + + align:start position:0% +three and of course you multiply and you +get a three by three matrix of zeros so + + align:start position:0% +get a three by three matrix of zeros so + + + align:start position:0% +get a three by three matrix of zeros so +it's fun to see that that proof still + + align:start position:0% +it's fun to see that that proof still + + + align:start position:0% +it's fun to see that that proof still +works even for the zero matrix without + + align:start position:0% +works even for the zero matrix without + + + align:start position:0% +works even for the zero matrix without +any real age so that was just today um + + align:start position:0% +any real age so that was just today um + + + align:start position:0% +any real age so that was just today um +let me the other thing is let me can I + + align:start position:0% +let me the other thing is let me can I + + + align:start position:0% +let me the other thing is let me can I +say a word or two about recent stuff + + align:start position:0% +say a word or two about recent stuff + + + align:start position:0% +say a word or two about recent stuff +about Julia so I start to put together a + + align:start position:0% +about Julia so I start to put together a + + + align:start position:0% +about Julia so I start to put together a +talk it's not really ready yet but I'll + + align:start position:0% +talk it's not really ready yet but I'll + + + align:start position:0% +talk it's not really ready yet but I'll +share it with you anyway so Google did + + align:start position:0% +share it with you anyway so Google did + + + align:start position:0% +share it with you anyway so Google did +the Julia world a big favor last week I + + align:start position:0% +the Julia world a big favor last week I + + + align:start position:0% +the Julia world a big favor last week I +mean this is huge so you all know + + align:start position:0% +mean this is huge so you all know + + + align:start position:0% +mean this is huge so you all know +machine learning is hot that's probably + + align:start position:0% +machine learning is hot that's probably + + + align:start position:0% +machine learning is hot that's probably +why you're here in this class I probably + + align:start position:0% +why you're here in this class I probably + + + align:start position:0% +why you're here in this class I probably +don't have to tell you and yet I + + align:start position:0% +don't have to tell you and yet I + + + align:start position:0% +don't have to tell you and yet I +wouldn't be surprised if a number of you + + align:start position:0% +wouldn't be surprised if a number of you + + + align:start position:0% +wouldn't be surprised if a number of you +were sort of wish the whole this whole + + align:start position:0% +were sort of wish the whole this whole + + + align:start position:0% +were sort of wish the whole this whole +class was in Python or something or + + align:start position:0% +class was in Python or something or + + + align:start position:0% +class was in Python or something or +maybe MATLAB or so I don't doubt that + + align:start position:0% +maybe MATLAB or so I don't doubt that + + + align:start position:0% +maybe MATLAB or so I don't doubt that +some of you might have wanted that to + + align:start position:0% +some of you might have wanted that to + + + align:start position:0% +some of you might have wanted that to +happen and we get sort of bombarded with + + align:start position:0% +happen and we get sort of bombarded with + + + align:start position:0% +happen and we get sort of bombarded with +with you know why not Python not so much + + align:start position:0% +with you know why not Python not so much + + + align:start position:0% +with you know why not Python not so much +MATLAB anymore but you know why not + + align:start position:0% +MATLAB anymore but you know why not + + + align:start position:0% +MATLAB anymore but you know why not +Python is sort of the issue that comes + + align:start position:0% +Python is sort of the issue that comes + + + align:start position:0% +Python is sort of the issue that comes +up a lot and I could talk til the cows + + align:start position:0% +up a lot and I could talk til the cows + + + align:start position:0% +up a lot and I could talk til the cows +come home but nobody would believe me + + align:start position:0% +come home but nobody would believe me + + + align:start position:0% +come home but nobody would believe me +but Google came out last week and said + + align:start position:0% +but Google came out last week and said + + + align:start position:0% +but Google came out last week and said +that that when it comes to machine + + align:start position:0% +that that when it comes to machine + + + align:start position:0% +that that when it comes to machine +learning there really are two languages + + align:start position:0% +learning there really are two languages + + + align:start position:0% +learning there really are two languages +that are powerful enough to do machine + + align:start position:0% +that are powerful enough to do machine + + + align:start position:0% +that are powerful enough to do machine +learning to do machine learning kinds of + + align:start position:0% +learning to do machine learning kinds of + + + align:start position:0% +learning to do machine learning kinds of +things that you want to do and in some + + align:start position:0% +things that you want to do and in some + + + align:start position:0% +things that you want to do and in some +sense the the rest of today's lecture + + align:start position:0% +sense the the rest of today's lecture + + + align:start position:0% +sense the the rest of today's lecture +that I'm going to give will will be + + align:start position:0% +that I'm going to give will will be + + + align:start position:0% +that I'm going to give will will be +maybe illustrations of this but if you + + align:start position:0% +maybe illustrations of this but if you + + + align:start position:0% +maybe illustrations of this but if you +want you can go and look at their their + + align:start position:0% +want you can go and look at their their + + + align:start position:0% +want you can go and look at their their +blog here + + align:start position:0% +blog here + + + align:start position:0% +blog here +what they do is they basically sort of + + align:start position:0% +what they do is they basically sort of + + + align:start position:0% +what they do is they basically sort of +start the the race with a whole bunch of + + align:start position:0% +start the the race with a whole bunch of + + + align:start position:0% +start the the race with a whole bunch of +programming languages there's Python + + align:start position:0% +programming languages there's Python + + + align:start position:0% +programming languages there's Python +there's our Java JavaScript they they're + + align:start position:0% +there's our Java JavaScript they they're + + + align:start position:0% +there's our Java JavaScript they they're +you know they they they sort of look at + + align:start position:0% +you know they they they sort of look at + + + align:start position:0% +you know they they they sort of look at +all of these languages and if you read + + align:start position:0% +all of these languages and if you read + + + align:start position:0% +all of these languages and if you read +the blog you'll see but we're gonna + + align:start position:0% +the blog you'll see but we're gonna + + + align:start position:0% +the blog you'll see but we're gonna +filter them out on technical merits and + + align:start position:0% +filter them out on technical merits and + + + align:start position:0% +filter them out on technical merits and +and right away a lot of them disappear + + align:start position:0% +and right away a lot of them disappear + + + align:start position:0% +and right away a lot of them disappear +including Python and Java + + align:start position:0% +including Python and Java + + + align:start position:0% +including Python and Java +and and they actually spend if you go to + + align:start position:0% +and and they actually spend if you go to + + + align:start position:0% +and and they actually spend if you go to +the blog you'll see they spend a great + + align:start position:0% +the blog you'll see they spend a great + + + align:start position:0% +the blog you'll see they spend a great +deal of time on the Python story because + + align:start position:0% +deal of time on the Python story because + + + align:start position:0% +deal of time on the Python story because +they know that people are gonna want to + + align:start position:0% +they know that people are gonna want to + + + align:start position:0% +they know that people are gonna want to +hear that one right I mean if people + + align:start position:0% +hear that one right I mean if people + + + align:start position:0% +hear that one right I mean if people +want to be convinced and so there's + + align:start position:0% +want to be convinced and so there's + + + align:start position:0% +want to be convinced and so there's +actually multiple screens full on the + + align:start position:0% +actually multiple screens full on the + + + align:start position:0% +actually multiple screens full on the +the reason why Python is just not good + + align:start position:0% +the reason why Python is just not good + + + align:start position:0% +the reason why Python is just not good +enough for machine learning so they they + + align:start position:0% +enough for machine learning so they they + + + align:start position:0% +enough for machine learning so they they +leave for languages left julia swift c++ + + align:start position:0% +leave for languages left julia swift c++ + + + align:start position:0% +leave for languages left julia swift c++ +and rust and then sort of they the next + + align:start position:0% +and rust and then sort of they the next + + + align:start position:0% +and rust and then sort of they the next +sort of part of the if you go to the + + align:start position:0% +sort of part of the if you go to the + + + align:start position:0% +sort of part of the if you go to the +next part of of the blog they filter on + + align:start position:0% +next part of of the blog they filter on + + + align:start position:0% +next part of of the blog they filter on +usability and then two more so to bite + + align:start position:0% +usability and then two more so to bite + + + align:start position:0% +usability and then two more so to bite +the dust + + align:start position:0% +the dust + + + align:start position:0% +the dust +so c++ and rust disappeared and then + + align:start position:0% +so c++ and rust disappeared and then + + + align:start position:0% +so c++ and rust disappeared and then +they go on to say that these are the + + align:start position:0% +they go on to say that these are the + + + align:start position:0% +they go on to say that these are the +only two languages they feel are + + align:start position:0% +only two languages they feel are + + + align:start position:0% +only two languages they feel are +appropriate for machine learning and + + align:start position:0% +appropriate for machine learning and + + + align:start position:0% +appropriate for machine learning and +they put this nice quote you know that + + align:start position:0% +they put this nice quote you know that + + + align:start position:0% +they put this nice quote you know that +that you know it shares many common + + align:start position:0% +that you know it shares many common + + + align:start position:0% +that you know it shares many common +values and they actually go on and about + + align:start position:0% +values and they actually go on and about + + + align:start position:0% +values and they actually go on and about +what machine learning really needs and + + align:start position:0% +what machine learning really needs and + + + align:start position:0% +what machine learning really needs and +you know yeah i'd recommend you look at + + align:start position:0% +you know yeah i'd recommend you look at + + + align:start position:0% +you know yeah i'd recommend you look at +it and then finally of course they're + + align:start position:0% +it and then finally of course they're + + + align:start position:0% +it and then finally of course they're +gonna push swift which they which they + + align:start position:0% +gonna push swift which they which they + + + align:start position:0% +gonna push swift which they which they +should so they had some more blahblah + + align:start position:0% +should so they had some more blahblah + + + align:start position:0% +should so they had some more blahblah +about more people are using swift maybe + + align:start position:0% +about more people are using swift maybe + + + align:start position:0% +about more people are using swift maybe +it's true i don't know but so that you + + align:start position:0% +it's true i don't know but so that you + + + align:start position:0% +it's true i don't know but so that you +know they're gonna they really said is + + align:start position:0% +know they're gonna they really said is + + + align:start position:0% +know they're gonna they really said is +they're more familiar with swift and + + align:start position:0% +they're more familiar with swift and + + + align:start position:0% +they're more familiar with swift and +julia which you know if i if I were + + align:start position:0% +julia which you know if i if I were + + + align:start position:0% +julia which you know if i if I were +speaking I'd say I'm more familiar than + + align:start position:0% +speaking I'd say I'm more familiar than + + + align:start position:0% +speaking I'd say I'm more familiar than +Julia than Swift so maybe it's fair and + + align:start position:0% +Julia than Swift so maybe it's fair and + + + align:start position:0% +Julia than Swift so maybe it's fair and +then I started to put a little cartoon + + align:start position:0% +then I started to put a little cartoon + + + align:start position:0% +then I started to put a little cartoon +on the psychology of programming + + align:start position:0% +on the psychology of programming + + + align:start position:0% +on the psychology of programming +languages just because it's it's sort of + + align:start position:0% +languages just because it's it's sort of + + + align:start position:0% +languages just because it's it's sort of +a something that I bump into with all + + align:start position:0% +a something that I bump into with all + + + align:start position:0% +a something that I bump into with all +the time people always say all languages + + align:start position:0% +the time people always say all languages + + + align:start position:0% +the time people always say all languages +are equally good it doesn't really + + align:start position:0% +are equally good it doesn't really + + + align:start position:0% +are equally good it doesn't really +matter but the truth is if you don't + + align:start position:0% +matter but the truth is if you don't + + + align:start position:0% +matter but the truth is if you don't +mention a language if you mention a + + align:start position:0% +mention a language if you mention a + + + align:start position:0% +mention a language if you mention a +language that you're not using yet + + align:start position:0% +language that you're not using yet + + + align:start position:0% +language that you're not using yet +you're gonna tune it out at least until + + align:start position:0% +you're gonna tune it out at least until + + + align:start position:0% +you're gonna tune it out at least until +Google comes along so that that's where + + align:start position:0% +Google comes along so that that's where + + + align:start position:0% +Google comes along so that that's where +we are okay enough about I just put this + + align:start position:0% +we are okay enough about I just put this + + + align:start position:0% +we are okay enough about I just put this +together I know testing it out on you + + align:start position:0% +together I know testing it out on you + + + align:start position:0% +together I know testing it out on you +all right now so now let me do so two + + align:start position:0% +all right now so now let me do so two + + + align:start position:0% +all right now so now let me do so two +more mathematical things so the first + + align:start position:0% +more mathematical things so the first + + + align:start position:0% +more mathematical things so the first +thing I want to do is talk to you about + + align:start position:0% +thing I want to do is talk to you about + + + align:start position:0% +thing I want to do is talk to you about +forward mode automatic + + align:start position:0% +forward mode automatic + + + align:start position:0% +forward mode automatic +differentiation so if you've done any + + align:start position:0% +differentiation so if you've done any + + + align:start position:0% +differentiation so if you've done any +automatic depreciation of course okay so + + align:start position:0% +automatic depreciation of course okay so + + + align:start position:0% +automatic depreciation of course okay so +I think this is pretty fun I hope you'll + + align:start position:0% +I think this is pretty fun I hope you'll + + + align:start position:0% +I think this is pretty fun I hope you'll +like it + + align:start position:0% +like it + + + align:start position:0% +like it +I have a notebook and Julia run forward + + align:start position:0% +I have a notebook and Julia run forward + + + align:start position:0% +I have a notebook and Julia run forward +mode automatic differentiation and the + + align:start position:0% +mode automatic differentiation and the + + + align:start position:0% +mode automatic differentiation and the +this notebook came together because I + + align:start position:0% +this notebook came together because I + + + align:start position:0% +this notebook came together because I +was trying to understand what the big + + align:start position:0% +was trying to understand what the big + + + align:start position:0% +was trying to understand what the big +deal was for a long time and and I had a + + align:start position:0% +deal was for a long time and and I had a + + + align:start position:0% +deal was for a long time and and I had a +little trouble I mean it's it's the + + align:start position:0% +little trouble I mean it's it's the + + + align:start position:0% +little trouble I mean it's it's the +usual story we're on a line-by-line + + align:start position:0% +usual story we're on a line-by-line + + + align:start position:0% +usual story we're on a line-by-line +level it's easy to understand but like + + align:start position:0% +level it's easy to understand but like + + + align:start position:0% +level it's easy to understand but like +what's the big deal part that's that + + align:start position:0% +what's the big deal part that's that + + + align:start position:0% +what's the big deal part that's that +sometimes the harder thing to grasp and + + align:start position:0% +sometimes the harder thing to grasp and + + + align:start position:0% +sometimes the harder thing to grasp and +and and the first notebook I'm gonna + + align:start position:0% +and and the first notebook I'm gonna + + + align:start position:0% +and and the first notebook I'm gonna +show you is sort of the result of my + + align:start position:0% +show you is sort of the result of my + + + align:start position:0% +show you is sort of the result of my +trying to grasp like what was the the + + align:start position:0% +trying to grasp like what was the the + + + align:start position:0% +trying to grasp like what was the the +real picture here and the second thing I + + align:start position:0% +real picture here and the second thing I + + + align:start position:0% +real picture here and the second thing I +think I'll just do on the blackboard + + align:start position:0% +think I'll just do on the blackboard + + + align:start position:0% +think I'll just do on the blackboard +it's not even really ready yet but I'll + + align:start position:0% +it's not even really ready yet but I'll + + + align:start position:0% +it's not even really ready yet but I'll +sort of unleash it on you folks anyway + + align:start position:0% +sort of unleash it on you folks anyway + + + align:start position:0% +sort of unleash it on you folks anyway +is to show you how to do a particular + + align:start position:0% +is to show you how to do a particular + + + align:start position:0% +is to show you how to do a particular +example of backward mode automatically + + align:start position:0% +example of backward mode automatically + + + align:start position:0% +example of backward mode automatically +pronounciation the backpropagation let + + align:start position:0% +pronounciation the backpropagation let + + + align:start position:0% +pronounciation the backpropagation let +you see in a neural net and I I guess + + align:start position:0% +you see in a neural net and I I guess + + + align:start position:0% +you see in a neural net and I I guess +you have seen some their own that's here + + align:start position:0% +you have seen some their own that's here + + + align:start position:0% +you have seen some their own that's here +so actually they might now everybody's + + align:start position:0% +so actually they might now everybody's + + + align:start position:0% +so actually they might now everybody's +seen neural nets I think you know two + + align:start position:0% +seen neural nets I think you know two + + + align:start position:0% +seen neural nets I think you know two +years from now it'll be in height low + + align:start position:0% +years from now it'll be in height low + + + align:start position:0% +years from now it'll be in height low +high schools and three years from there + + align:start position:0% +high schools and three years from there + + + align:start position:0% +high schools and three years from there +will be in kindergartens I don't know + + align:start position:0% +will be in kindergartens I don't know + + + align:start position:0% +will be in kindergartens I don't know +everybody see neural nets seem to be + + align:start position:0% +everybody see neural nets seem to be + + + align:start position:0% +everybody see neural nets seem to be +sort of they're not that hard to + + align:start position:0% +sort of they're not that hard to + + + align:start position:0% +sort of they're not that hard to +understand okay so let me let me start + + align:start position:0% +understand okay so let me let me start + + + align:start position:0% +understand okay so let me let me start +things off and really the two things + + align:start position:0% +things off and really the two things + + + align:start position:0% +things off and really the two things +that I'd left to convince you of is + + align:start position:0% +that I'd left to convince you of is + + + align:start position:0% +that I'd left to convince you of is +let's let me just find here's my ordered + + align:start position:0% +let's let me just find here's my ordered + + + align:start position:0% +let's let me just find here's my ordered +if thing the two things that I really + + align:start position:0% +if thing the two things that I really + + + align:start position:0% +if thing the two things that I really +want to convince you of and maybe you + + align:start position:0% +want to convince you of and maybe you + + + align:start position:0% +want to convince you of and maybe you +already believe some of this is one that + + align:start position:0% +already believe some of this is one that + + + align:start position:0% +already believe some of this is one that +well maybe you don't believe this yet + + align:start position:0% +well maybe you don't believe this yet + + + align:start position:0% +well maybe you don't believe this yet +but that the language matters in a + + align:start position:0% +but that the language matters in a + + + align:start position:0% +but that the language matters in a +mathematical sense that the right the + + align:start position:0% +mathematical sense that the right the + + + align:start position:0% +mathematical sense that the right the +right the right computer language can do + + align:start position:0% +right the right computer language can do + + + align:start position:0% +right the right computer language can do +more for you than just take some + + align:start position:0% +more for you than just take some + + + align:start position:0% +more for you than just take some +algorithm on a blackboard and implement + + align:start position:0% +algorithm on a blackboard and implement + + + align:start position:0% +algorithm on a blackboard and implement +it you could do it could do much more + + align:start position:0% +it you could do it could do much more + + + align:start position:0% +it you could do it could do much more +and this is something that that I hope + + align:start position:0% +and this is something that that I hope + + + align:start position:0% +and this is something that that I hope +to give a few examples of and the other + + align:start position:0% +to give a few examples of and the other + + + align:start position:0% +to give a few examples of and the other +thing that I bet you all are believed + + align:start position:0% +thing that I bet you all are believed + + + align:start position:0% +thing that I bet you all are believed +now because you've been in this class is + + align:start position:0% +now because you've been in this class is + + + align:start position:0% +now because you've been in this class is +that that linear algebra is the basis + + align:start position:0% +that that linear algebra is the basis + + + align:start position:0% +that that linear algebra is the basis +for everything every course should start + + align:start position:0% +for everything every course should start + + + align:start position:0% +for everything every course should start +with linear algebra I mean that's it to + + align:start position:0% +with linear algebra I mean that's it to + + + align:start position:0% +with linear algebra I mean that's it to +me it feels like a unfortunate accident + + align:start position:0% +me it feels like a unfortunate accident + + + align:start position:0% +me it feels like a unfortunate accident +of history that that linear algebra came + + align:start position:0% +of history that that linear algebra came + + + align:start position:0% +of history that that linear algebra came +too late for too many reasons and and so + + align:start position:0% +too late for too many reasons and and so + + + align:start position:0% +too late for too many reasons and and so +very often things that would be better + + align:start position:0% +very often things that would be better + + + align:start position:0% +very often things that would be better +done with linear algebra are + + align:start position:0% +done with linear algebra are + + + align:start position:0% +done with linear algebra are +not and and and I mean it if to me it + + align:start position:0% +not and and and I mean it if to me it + + + align:start position:0% +not and and and I mean it if to me it +feels like doing physics without + + align:start position:0% +feels like doing physics without + + + align:start position:0% +feels like doing physics without +calculus like I just don't get it + + align:start position:0% +calculus like I just don't get it + + + align:start position:0% +calculus like I just don't get it +like I know high schools do that but it + + align:start position:0% +like I know high schools do that but it + + + align:start position:0% +like I know high schools do that but it +just seems wrong you know it to me like + + align:start position:0% +just seems wrong you know it to me like + + + align:start position:0% +just seems wrong you know it to me like +you know all of engineering all it + + align:start position:0% +you know all of engineering all it + + + align:start position:0% +you know all of engineering all it +should all be linear algebra I mean I'm + + align:start position:0% +should all be linear algebra I mean I'm + + + align:start position:0% +should all be linear algebra I mean I'm +I just believe that almost all maybe not + + align:start position:0% +I just believe that almost all maybe not + + + align:start position:0% +I just believe that almost all maybe not +all but quite a lot more than most + + align:start position:0% +all but quite a lot more than most + + + align:start position:0% +all but quite a lot more than most +people realize I would say okay so let + + align:start position:0% +people realize I would say okay so let + + + align:start position:0% +people realize I would say okay so let +me start with automatic differentiation + + align:start position:0% +me start with automatic differentiation + + + align:start position:0% +me start with automatic differentiation +so so I'm gonna start by this story by + + align:start position:0% +so so I'm gonna start by this story by + + + align:start position:0% +so so I'm gonna start by this story by +telling you that I would go to + + align:start position:0% +telling you that I would go to + + + align:start position:0% +telling you that I would go to +conferences I would go to numerical + + align:start position:0% +conferences I would go to numerical + + + align:start position:0% +conferences I would go to numerical +analysis conferences I would hear people + + align:start position:0% +analysis conferences I would hear people + + + align:start position:0% +analysis conferences I would hear people +talk about automatic differentiation I'm + + align:start position:0% +talk about automatic differentiation I'm + + + align:start position:0% +talk about automatic differentiation I'm +gonna be honest I was reading my email I + + align:start position:0% +gonna be honest I was reading my email I + + + align:start position:0% +gonna be honest I was reading my email I +was tuned out like who cares about like + + align:start position:0% +was tuned out like who cares about like + + + align:start position:0% +was tuned out like who cares about like +I know calculus I could you could teach + + align:start position:0% +I know calculus I could you could teach + + + align:start position:0% +I know calculus I could you could teach +a computer to do it I don't you know I'm + + align:start position:0% +a computer to do it I don't you know I'm + + + align:start position:0% +a computer to do it I don't you know I'm +seems pretty easy to me I mean I'm sure + + align:start position:0% +seems pretty easy to me I mean I'm sure + + + align:start position:0% +seems pretty easy to me I mean I'm sure +there are technical details but it + + align:start position:0% +there are technical details but it + + + align:start position:0% +there are technical details but it +didn't seem that interesting to teach a + + align:start position:0% +didn't seem that interesting to teach a + + + align:start position:0% +didn't seem that interesting to teach a +computer to differentiate I sort of + + align:start position:0% +computer to differentiate I sort of + + + align:start position:0% +computer to differentiate I sort of +figured that it was the same calculus + + align:start position:0% +figured that it was the same calculus + + + align:start position:0% +figured that it was the same calculus +that I learned when I took a calculus + + align:start position:0% +that I learned when I took a calculus + + + align:start position:0% +that I learned when I took a calculus +class you know here you know you you've + + align:start position:0% +class you know here you know you you've + + + align:start position:0% +class you know here you know you you've +memorized this table you teach it to a + + align:start position:0% +memorized this table you teach it to a + + + align:start position:0% +memorized this table you teach it to a +computer you know you learn the chain + + align:start position:0% +computer you know you learn the chain + + + align:start position:0% +computer you know you learn the chain +rule and the product rule and the + + align:start position:0% +rule and the product rule and the + + + align:start position:0% +rule and the product rule and the +quotient rule and bump you you did the + + align:start position:0% +quotient rule and bump you you did the + + + align:start position:0% +quotient rule and bump you you did the +computer is doing just what I would do + + align:start position:0% +computer is doing just what I would do + + + align:start position:0% +computer is doing just what I would do +it with paper and pencil so a big deal I + + align:start position:0% +it with paper and pencil so a big deal I + + + align:start position:0% +it with paper and pencil so a big deal I +was I didn't pay attention and in any + + align:start position:0% +was I didn't pay attention and in any + + + align:start position:0% +was I didn't pay attention and in any +event there was said a little there was + + align:start position:0% +event there was said a little there was + + + align:start position:0% +event there was said a little there was +this little neuron in the back of my + + align:start position:0% +this little neuron in the back of my + + + align:start position:0% +this little neuron in the back of my +brain that said hey maybe I'm wrong + + align:start position:0% +brain that said hey maybe I'm wrong + + + align:start position:0% +brain that said hey maybe I'm wrong +maybe it's doing finite differences you + + align:start position:0% +maybe it's doing finite differences you + + + align:start position:0% +maybe it's doing finite differences you +know the sort of thing where you take + + align:start position:0% +know the sort of thing where you take + + + align:start position:0% +know the sort of thing where you take +the the the you take the d-y-by-dx in + + align:start position:0% +the the the you take the d-y-by-dx in + + + align:start position:0% +the the the you take the d-y-by-dx in +some numerical way it's you do the + + align:start position:0% +some numerical way it's you do the + + + align:start position:0% +some numerical way it's you do the +finite differences and in the radical + + align:start position:0% +finite differences and in the radical + + + align:start position:0% +finite differences and in the radical +analysis they're supposed to tell you + + align:start position:0% +analysis they're supposed to tell you + + + align:start position:0% +analysis they're supposed to tell you +you know if H is too big you get + + align:start position:0% +you know if H is too big you get + + + align:start position:0% +you know if H is too big you get +truncation error if you have a t too + + align:start position:0% +truncation error if you have a t too + + + align:start position:0% +truncation error if you have a t too +small you get roundoff error and the + + align:start position:0% +small you get roundoff error and the + + + align:start position:0% +small you get roundoff error and the +truth is nobody ever tells you what's a + + align:start position:0% +truth is nobody ever tells you what's a + + + align:start position:0% +truth is nobody ever tells you what's a +good age but you go to numerical + + align:start position:0% +good age but you go to numerical + + + align:start position:0% +good age but you go to numerical +analysis class hoping somebody would + + align:start position:0% +analysis class hoping somebody would + + + align:start position:0% +analysis class hoping somebody would +tell you but but in any event so I + + align:start position:0% +tell you but but in any event so I + + + align:start position:0% +tell you but but in any event so I +thought maybe it was that kind of a + + align:start position:0% +thought maybe it was that kind of a + + + align:start position:0% +thought maybe it was that kind of a +numerical finite difference and and and + + align:start position:0% +numerical finite difference and and and + + + align:start position:0% +numerical finite difference and and and +and I think the big surprise for me was + + align:start position:0% +and I think the big surprise for me was + + + align:start position:0% +and I think the big surprise for me was +that automatic differentiation was + + align:start position:0% +that automatic differentiation was + + + align:start position:0% +that automatic differentiation was +neither the first nor the second thing + + align:start position:0% +neither the first nor the second thing + + + align:start position:0% +neither the first nor the second thing +that there's actually a third thing + + align:start position:0% +that there's actually a third thing + + + align:start position:0% +that there's actually a third thing +something different + + align:start position:0% +something different + + + align:start position:0% +something different +that's neither the first or the second + + align:start position:0% +that's neither the first or the second + + + align:start position:0% +that's neither the first or the second +that I found that fascinating and and + + align:start position:0% +that I found that fascinating and and + + + align:start position:0% +that I found that fascinating and and +maybe I'll even tell you how how it hit + + align:start position:0% +maybe I'll even tell you how how it hit + + + align:start position:0% +maybe I'll even tell you how how it hit +me in the head that this was the story + + align:start position:0% +me in the head that this was the story + + + align:start position:0% +me in the head that this was the story +because I really wasn't paying attention + + align:start position:0% +because I really wasn't paying attention + + + align:start position:0% +because I really wasn't paying attention +but I loved the singular value + + align:start position:0% +but I loved the singular value + + + align:start position:0% +but I loved the singular value +decomposition I'm glad to see that + + align:start position:0% +decomposition I'm glad to see that + + + align:start position:0% +decomposition I'm glad to see that +people are drawing parabolas and quarter + + align:start position:0% +people are drawing parabolas and quarter + + + align:start position:0% +people are drawing parabolas and quarter +circles and figuring out what the the + + align:start position:0% +circles and figuring out what the the + + + align:start position:0% +circles and figuring out what the the +minimum SVD value is this thing right is + + align:start position:0% +minimum SVD value is this thing right is + + + align:start position:0% +minimum SVD value is this thing right is +is just you know the + + align:start position:0% +is just you know the + + + align:start position:0% +is just you know the +it's justyou know God's gift to mankind + + align:start position:0% +it's justyou know God's gift to mankind + + + align:start position:0% +it's justyou know God's gift to mankind +it's just a good factorization and one + + align:start position:0% +it's just a good factorization and one + + + align:start position:0% +it's just a good factorization and one +of the things that I would I was playing + + align:start position:0% +of the things that I would I was playing + + + align:start position:0% +of the things that I would I was playing +with with with Julia was to calculate + + align:start position:0% +with with with Julia was to calculate + + + align:start position:0% +with with with Julia was to calculate +the the Jacobian matrix for the SVD so + + align:start position:0% +the the Jacobian matrix for the SVD so + + + align:start position:0% +the the Jacobian matrix for the SVD so +so you know all matrix factorizations + + align:start position:0% +so you know all matrix factorizations + + + align:start position:0% +so you know all matrix factorizations +are just changes of variables right so + + align:start position:0% +are just changes of variables right so + + + align:start position:0% +are just changes of variables right so +if you have an if you have a square + + align:start position:0% +if you have an if you have a square + + + align:start position:0% +if you have an if you have a square +matrix n by n the SVD babe I'm sure you + + align:start position:0% +matrix n by n the SVD babe I'm sure you + + + align:start position:0% +matrix n by n the SVD babe I'm sure you +know this is you know the the U matrix + + align:start position:0% +know this is you know the the U matrix + + + align:start position:0% +know this is you know the the U matrix +is really n times n minus one over two + + align:start position:0% +is really n times n minus one over two + + + align:start position:0% +is really n times n minus one over two +variables so is the V and the Sigma has + + align:start position:0% +variables so is the V and the Sigma has + + + align:start position:0% +variables so is the V and the Sigma has +got n variables put it all together you + + align:start position:0% +got n variables put it all together you + + + align:start position:0% +got n variables put it all together you +got N squared so it's just a change of + + align:start position:0% +got N squared so it's just a change of + + + align:start position:0% +got N squared so it's just a change of +variables and every time you change + + align:start position:0% +variables and every time you change + + + align:start position:0% +variables and every time you change +variables you can form that big matrix n + + align:start position:0% +variables you can form that big matrix n + + + align:start position:0% +variables you can form that big matrix n +squared by N squared of the you know + + align:start position:0% +squared by N squared of the you know + + + align:start position:0% +squared by N squared of the you know +dy/dx compute its determinants and get + + align:start position:0% +dy/dx compute its determinants and get + + + align:start position:0% +dy/dx compute its determinants and get +an answer and and I want you to know + + align:start position:0% +an answer and and I want you to know + + + align:start position:0% +an answer and and I want you to know +what that I wanted to actually knew the + + align:start position:0% +what that I wanted to actually knew the + + + align:start position:0% +what that I wanted to actually knew the +theoretical answer for that and I wanted + + align:start position:0% +theoretical answer for that and I wanted + + + align:start position:0% +theoretical answer for that and I wanted +to see a computer confirm that + + align:start position:0% +to see a computer confirm that + + + align:start position:0% +to see a computer confirm that +theoretical answer and I spoke to some + + align:start position:0% +theoretical answer and I spoke to some + + + align:start position:0% +theoretical answer and I spoke to some +people who who wrote Otto Tiffin in non + + align:start position:0% +people who who wrote Otto Tiffin in non + + + align:start position:0% +people who who wrote Otto Tiffin in non +giulia languages and I was surprised by + + align:start position:0% +giulia languages and I was surprised by + + + align:start position:0% +giulia languages and I was surprised by +the answer they said oh yeah we could + + align:start position:0% +the answer they said oh yeah we could + + + align:start position:0% +the answer they said oh yeah we could +teach the answer to our system I said + + align:start position:0% +teach the answer to our system I said + + + align:start position:0% +teach the answer to our system I said +what do you mean you could teach the + + align:start position:0% +what do you mean you could teach the + + + align:start position:0% +what do you mean you could teach the +answer why doesn't just compute the + + align:start position:0% +answer why doesn't just compute the + + + align:start position:0% +answer why doesn't just compute the +answer what you have to teach the answer + + align:start position:0% +answer what you have to teach the answer + + + align:start position:0% +answer what you have to teach the answer +I thought that was all wrong because in + + align:start position:0% +I thought that was all wrong because in + + + align:start position:0% +I thought that was all wrong because in +Julia we didn't have to teach it it + + align:start position:0% +Julia we didn't have to teach it it + + + align:start position:0% +Julia we didn't have to teach it it +actually it would actually calculate it + + align:start position:0% +actually it would actually calculate it + + + align:start position:0% +actually it would actually calculate it +oh and then I started to understand a + + align:start position:0% +oh and then I started to understand a + + + align:start position:0% +oh and then I started to understand a +little bit more about what auto-da-fé + + align:start position:0% +little bit more about what auto-da-fé + + + align:start position:0% +little bit more about what auto-da-fé +was doing and what Julia was doing and + + align:start position:0% +was doing and what Julia was doing and + + + align:start position:0% +was doing and what Julia was doing and +so this is how this notebook came to be + + align:start position:0% +so this is how this notebook came to be + + + align:start position:0% +so this is how this notebook came to be +so let me start I'm saying too much let + + align:start position:0% +so let me start I'm saying too much let + + + align:start position:0% +so let me start I'm saying too much let +me start with an example that that might + + align:start position:0% +me start with an example that that might + + + align:start position:0% +me start with an example that that might +kind of hit home so I'm going to compute + + align:start position:0% +kind of hit home so I'm going to compute + + + align:start position:0% +kind of hit home so I'm going to compute +the square root of x I'm a real simple + + align:start position:0% +the square root of x I'm a real simple + + + align:start position:0% +the square root of x I'm a real simple +example you know square roots pretty + + align:start position:0% +example you know square roots pretty + + + align:start position:0% +example you know square roots pretty +easy I'm gonna take when the oldest + + align:start position:0% +easy I'm gonna take when the oldest + + + align:start position:0% +easy I'm gonna take when the oldest +algorithms known to mankind + + align:start position:0% +algorithms known to mankind + + + align:start position:0% +algorithms known to mankind +the Babylonians square root algorithm it + + align:start position:0% +the Babylonians square root algorithm it + + + align:start position:0% +the Babylonians square root algorithm it +says you know start with a starting + + align:start position:0% +says you know start with a starting + + + align:start position:0% +says you know start with a starting +guess T maybe it's a little bit too low + + align:start position:0% +guess T maybe it's a little bit too low + + + align:start position:0% +guess T maybe it's a little bit too low +for the square root of x get x over T so + + align:start position:0% +for the square root of x get x over T so + + + align:start position:0% +for the square root of x get x over T so +that would be too large go ahead and + + align:start position:0% +that would be too large go ahead and + + + align:start position:0% +that would be too large go ahead and +take the average and repeat okay this is + + align:start position:0% +take the average and repeat okay this is + + + align:start position:0% +take the average and repeat okay this is +equivalent to a Newton's method for + + align:start position:0% +equivalent to a Newton's method for + + + align:start position:0% +equivalent to a Newton's method for +taking the square root and you know it's + + align:start position:0% +taking the square root and you know it's + + + align:start position:0% +taking the square root and you know it's +been known for millennia to mankind so + + align:start position:0% +been known for millennia to mankind so + + + align:start position:0% +been known for millennia to mankind so +it's not a terribly you know it's not + + align:start position:0% +it's not a terribly you know it's not + + + align:start position:0% +it's not a terribly you know it's not +the latest research by any means for + + align:start position:0% +the latest research by any means for + + + align:start position:0% +the latest research by any means for +computing square roots but it it works + + align:start position:0% +computing square roots but it it works + + + align:start position:0% +computing square roots but it it works +very effectively and here's a little + + align:start position:0% +very effectively and here's a little + + + align:start position:0% +very effectively and here's a little +Julia code that actually will well will + + align:start position:0% +Julia code that actually will well will + + + align:start position:0% +Julia code that actually will well will +implement it it probably looks like code + + align:start position:0% +implement it it probably looks like code + + + align:start position:0% +implement it it probably looks like code +in any language so I'm gonna start off + + align:start position:0% +in any language so I'm gonna start off + + + align:start position:0% +in any language so I'm gonna start off +at one so + + align:start position:0% +at one so + + + align:start position:0% +at one so +literally I'm just gonna take one plus + + align:start position:0% +literally I'm just gonna take one plus + + + align:start position:0% +literally I'm just gonna take one plus +the starting value X and divide by two + + align:start position:0% +the starting value X and divide by two + + + align:start position:0% +the starting value X and divide by two +and then I'm gonna repeat okay and you + + align:start position:0% +and then I'm gonna repeat okay and you + + + align:start position:0% +and then I'm gonna repeat okay and you +know you can we we can check that the + + align:start position:0% +know you can we we can check that the + + + align:start position:0% +know you can we we can check that the +algorithm works here's alphas PI and so + + align:start position:0% +algorithm works here's alphas PI and so + + + align:start position:0% +algorithm works here's alphas PI and so +I'll take the Babylonian algorithm and + + align:start position:0% +I'll take the Babylonian algorithm and + + + align:start position:0% +I'll take the Babylonian algorithm and +compare it to Julie's built-in and you + + align:start position:0% +compare it to Julie's built-in and you + + + align:start position:0% +compare it to Julie's built-in and you +see it gives gives the right answer here + + align:start position:0% +see it gives gives the right answer here + + + align:start position:0% +see it gives gives the right answer here +it is with square root of two you know + + align:start position:0% +it is with square root of two you know + + + align:start position:0% +it is with square root of two you know +always good to check your your code + + align:start position:0% +always good to check your your code + + + align:start position:0% +always good to check your your code +works okay even I like to see things + + align:start position:0% +works okay even I like to see things + + + align:start position:0% +works okay even I like to see things +graphically so I ran the algorithm for + + align:start position:0% +graphically so I ran the algorithm for + + + align:start position:0% +graphically so I ran the algorithm for +lots of values of X and you could even I + + align:start position:0% +lots of values of X and you could even I + + + align:start position:0% +lots of values of X and you could even I +love doing this I kind of wished that in + + align:start position:0% +love doing this I kind of wished that in + + + align:start position:0% +love doing this I kind of wished that in +the previous talk I was this is what if + + align:start position:0% +the previous talk I was this is what if + + + align:start position:0% +the previous talk I was this is what if +I'd only worked fast enough I was + + align:start position:0% +I'd only worked fast enough I was + + + align:start position:0% +I'd only worked fast enough I was +actually I went to build a little gooey + + align:start position:0% +actually I went to build a little gooey + + + align:start position:0% +actually I went to build a little gooey +where I could move the points and in + + align:start position:0% +where I could move the points and in + + + align:start position:0% +where I could move the points and in +front of your eyes maybe you have one in + + align:start position:0% +front of your eyes maybe you have one in + + + align:start position:0% +front of your eyes maybe you have one in +MATLAB I bet you do but I wanted to + + align:start position:0% +MATLAB I bet you do but I wanted to + + + align:start position:0% +MATLAB I bet you do but I wanted to +build it but they didn't get there fast + + align:start position:0% +build it but they didn't get there fast + + + align:start position:0% +build it but they didn't get there fast +enough but here this is a sort of thing + + align:start position:0% +enough but here this is a sort of thing + + + align:start position:0% +enough but here this is a sort of thing +and I'd like to see the convergence I + + align:start position:0% +and I'd like to see the convergence I + + + align:start position:0% +and I'd like to see the convergence I +mean so you could see the digits + + align:start position:0% +mean so you could see the digits + + + align:start position:0% +mean so you could see the digits +converging the the the parabola on the + + align:start position:0% +converging the the the parabola on the + + + align:start position:0% +converging the the the parabola on the +bottom the black is the square root of + + align:start position:0% +bottom the black is the square root of + + + align:start position:0% +bottom the black is the square root of +course so there it is there's the + + align:start position:0% +course so there it is there's the + + + align:start position:0% +course so there it is there's the +Babylonian algorithm I would like to get + + align:start position:0% +Babylonian algorithm I would like to get + + + align:start position:0% +Babylonian algorithm I would like to get +the derivative of square root but the + + align:start position:0% +the derivative of square root but the + + + align:start position:0% +the derivative of square root but the +rules of the game are I'm not going to + + align:start position:0% +rules of the game are I'm not going to + + + align:start position:0% +rules of the game are I'm not going to +type method one or method two I'm not + + align:start position:0% +type method one or method two I'm not + + + align:start position:0% +type method one or method two I'm not +going to do you'll never see me type 1/2 + + align:start position:0% +going to do you'll never see me type 1/2 + + + align:start position:0% +going to do you'll never see me type 1/2 +X to the minus 1/2 that's right you all + + align:start position:0% +X to the minus 1/2 that's right you all + + + align:start position:0% +X to the minus 1/2 that's right you all +know that's the derivative I will not + + align:start position:0% +know that's the derivative I will not + + + align:start position:0% +know that's the derivative I will not +type that I will not it's not gonna come + + align:start position:0% +type that I will not it's not gonna come + + + align:start position:0% +type that I will not it's not gonna come +anywhere from Julia ok and the second + + align:start position:0% +anywhere from Julia ok and the second + + + align:start position:0% +anywhere from Julia ok and the second +thing is I'm not gonna do a finite + + align:start position:0% +thing is I'm not gonna do a finite + + + align:start position:0% +thing is I'm not gonna do a finite +difference all right I'm gonna get that + + align:start position:0% +difference all right I'm gonna get that + + + align:start position:0% +difference all right I'm gonna get that +square root but not by by by sort of + + align:start position:0% +square root but not by by by sort of + + + align:start position:0% +square root but not by by by sort of +either the two things that I'm sure you + + align:start position:0% +either the two things that I'm sure you + + + align:start position:0% +either the two things that I'm sure you +would think of alright but here's how + + align:start position:0% +would think of alright but here's how + + + align:start position:0% +would think of alright but here's how +I'm gonna do it and and I'm gonna do a + + align:start position:0% +I'm gonna do it and and I'm gonna do a + + + align:start position:0% +I'm gonna do it and and I'm gonna do a +little bit of Julia code there'll be + + align:start position:0% +little bit of Julia code there'll be + + + align:start position:0% +little bit of Julia code there'll be +eight lines of Julia but I'm not gonna + + align:start position:0% +eight lines of Julia but I'm not gonna + + + align:start position:0% +eight lines of Julia but I'm not gonna +completely say how it works yet I'll + + align:start position:0% +completely say how it works yet I'll + + + align:start position:0% +completely say how it works yet I'll +I'll keep you in suspense for maybe + + align:start position:0% +I'll keep you in suspense for maybe + + + align:start position:0% +I'll keep you in suspense for maybe +about five minutes and then I'll tell + + align:start position:0% +about five minutes and then I'll tell + + + align:start position:0% +about five minutes and then I'll tell +you how it how it works + + align:start position:0% +you how it how it works + + + align:start position:0% +you how it how it works +all right so here's eight lines of Julia + + align:start position:0% +all right so here's eight lines of Julia + + + align:start position:0% +all right so here's eight lines of Julia +code that will get me the square root so + + align:start position:0% +code that will get me the square root so + + + align:start position:0% +code that will get me the square root so +in these three lines I'm gonna create a + + align:start position:0% +in these three lines I'm gonna create a + + + align:start position:0% +in these three lines I'm gonna create a +julia type i'm gonna call it a d4 for a + + align:start position:0% +julia type i'm gonna call it a d4 for a + + + align:start position:0% +julia type i'm gonna call it a d4 for a +dual number which is a name that goes + + align:start position:0% +dual number which is a name that goes + + + align:start position:0% +dual number which is a name that goes +back at least a century maybe more so + + align:start position:0% +back at least a century maybe more so + + + align:start position:0% +back at least a century maybe more so +i'm gonna create a d type and all this + + align:start position:0% +i'm gonna create a d type and all this + + + align:start position:0% +i'm gonna create a d type and all this +is is a pair of floats okay so um it's a + + align:start position:0% +is is a pair of floats okay so um it's a + + + align:start position:0% +is is a pair of floats okay so um it's a +tuple with a pair of floats it's gonna + + align:start position:0% +tuple with a pair of floats it's gonna + + + align:start position:0% +tuple with a pair of floats it's gonna +be it's going to be some sort of + + align:start position:0% +be it's going to be some sort of + + + align:start position:0% +be it's going to be some sort of +numerical function and derivative pair + + align:start position:0% +numerical function and derivative pair + + + align:start position:0% +numerical function and derivative pair +all right so three of my eight lines is + + align:start position:0% +all right so three of my eight lines is + + + align:start position:0% +all right so three of my eight lines is +to create a d-- this means enjoy your + + align:start position:0% +to create a d-- this means enjoy your + + + align:start position:0% +to create a d-- this means enjoy your +language + + align:start position:0% +language + + + align:start position:0% +language +this means to use a subtype of a number + + align:start position:0% +this means to use a subtype of a number + + + align:start position:0% +this means to use a subtype of a number +so we're gonna treat it like a number + + align:start position:0% +so we're gonna treat it like a number + + + align:start position:0% +so we're gonna treat it like a number +right we want to be able to add multiply + + align:start position:0% +right we want to be able to add multiply + + + align:start position:0% +right we want to be able to add multiply +and divide these these ordered pairs but + + align:start position:0% +and divide these these ordered pairs but + + + align:start position:0% +and divide these these ordered pairs but +it's just a pair of numbers right don't + + align:start position:0% +it's just a pair of numbers right don't + + + align:start position:0% +it's just a pair of numbers right don't +get--don't the Julia scare you it's just + + align:start position:0% +get--don't the Julia scare you it's just + + + align:start position:0% +get--don't the Julia scare you it's just +a function derivative numerical pair + + align:start position:0% +a function derivative numerical pair + + + align:start position:0% +a function derivative numerical pair +okay and what's these other five lines + + align:start position:0% +okay and what's these other five lines + + + align:start position:0% +okay and what's these other five lines +well I want to teach it to some rule in + + align:start position:0% +well I want to teach it to some rule in + + + align:start position:0% +well I want to teach it to some rule in +the quotient rule so you all remember + + align:start position:0% +the quotient rule so you all remember + + + align:start position:0% +the quotient rule so you all remember +the sum rule I guess that's the easy one + + align:start position:0% +the sum rule I guess that's the easy one + + + align:start position:0% +the sum rule I guess that's the easy one +the quotient rule is still I still have + + align:start position:0% +the quotient rule is still I still have + + + align:start position:0% +the quotient rule is still I still have +the my teacher from high school you know + + align:start position:0% +the my teacher from high school you know + + + align:start position:0% +the my teacher from high school you know +ringing in the back of my ear you know + + align:start position:0% +ringing in the back of my ear you know + + + align:start position:0% +ringing in the back of my ear you know +the denominator times it was the + + align:start position:0% +the denominator times it was the + + + align:start position:0% +the denominator times it was the +numerator minus the numerator you all + + align:start position:0% +numerator minus the numerator you all + + + align:start position:0% +numerator minus the numerator you all +have that jingle and you're working your + + align:start position:0% +have that jingle and you're working your + + + align:start position:0% +have that jingle and you're working your +brain too I bet you do divided by the + + align:start position:0% +brain too I bet you do divided by the + + + align:start position:0% +brain too I bet you do divided by the +denominator squared + + align:start position:0% +denominator squared + + + align:start position:0% +denominator squared +can't even get it out of my head so up + + align:start position:0% +can't even get it out of my head so up + + + align:start position:0% +can't even get it out of my head so up +so so there's the quotient rule and so + + align:start position:0% +so so there's the quotient rule and so + + + align:start position:0% +so so there's the quotient rule and so +what are we doing in these five lines + + align:start position:0% +what are we doing in these five lines + + + align:start position:0% +what are we doing in these five lines +well first of all I want to overload + + align:start position:0% +well first of all I want to overload + + + align:start position:0% +well first of all I want to overload +plus and divide and a few other things + + align:start position:0% +plus and divide and a few other things + + + align:start position:0% +plus and divide and a few other things +and Julia wants me to say are you sure + + align:start position:0% +and Julia wants me to say are you sure + + + align:start position:0% +and Julia wants me to say are you sure +so the way you say are you sure is that + + align:start position:0% +so the way you say are you sure is that + + + align:start position:0% +so the way you say are you sure is that +I'm going to import plus and divide you + + align:start position:0% +I'm going to import plus and divide you + + + align:start position:0% +I'm going to import plus and divide you +know because it'd be dangerous to play + + align:start position:0% +know because it'd be dangerous to play + + + align:start position:0% +know because it'd be dangerous to play +with plus so here I'm gonna the plus two + + align:start position:0% +with plus so here I'm gonna the plus two + + + align:start position:0% +with plus so here I'm gonna the plus two +dual numbers we're gonna add the + + align:start position:0% +dual numbers we're gonna add the + + + align:start position:0% +dual numbers we're gonna add the +function and the derivatives divide two + + align:start position:0% +function and the derivatives divide two + + + align:start position:0% +function and the derivatives divide two +dual numbers we're gonna divide the + + align:start position:0% +dual numbers we're gonna divide the + + + align:start position:0% +dual numbers we're gonna divide the +function values and denominator times + + align:start position:0% +function values and denominator times + + + align:start position:0% +function values and denominator times +the numerator blah blah but you get it + + align:start position:0% +the numerator blah blah but you get it + + + align:start position:0% +the numerator blah blah but you get it +okay that's six of the eight lines the + + align:start position:0% +okay that's six of the eight lines the + + + align:start position:0% +okay that's six of the eight lines the +seventh line is if I have a dual number + + align:start position:0% +seventh line is if I have a dual number + + + align:start position:0% +seventh line is if I have a dual number +I wanted to to convert it you know how + + align:start position:0% +I wanted to to convert it you know how + + + align:start position:0% +I wanted to to convert it you know how +like the wheels are embedded in the + + align:start position:0% +like the wheels are embedded in the + + + align:start position:0% +like the wheels are embedded in the +complex is you know you just we have to + + align:start position:0% +complex is you know you just we have to + + + align:start position:0% +complex is you know you just we have to +tell Julia to to take a dual number and + + align:start position:0% +tell Julia to to take a dual number and + + + align:start position:0% +tell Julia to to take a dual number and +stick a zero in in and then then dual + + align:start position:0% +stick a zero in in and then then dual + + + align:start position:0% +stick a zero in in and then then dual +numbers and regular numbers can complete + + align:start position:0% +numbers and regular numbers can complete + + + align:start position:0% +numbers and regular numbers can complete +nicely together and this this actually + + align:start position:0% +nicely together and this this actually + + + align:start position:0% +nicely together and this this actually +is the thing that actually says if I + + align:start position:0% +is the thing that actually says if I + + + align:start position:0% +is the thing that actually says if I +have a dual number in a number in + + align:start position:0% +have a dual number in a number in + + + align:start position:0% +have a dual number in a number in +operation promote them so the work as + + align:start position:0% +operation promote them so the work as + + + align:start position:0% +operation promote them so the work as +dual numbers so eight lines of code so + + align:start position:0% +dual numbers so eight lines of code so + + + align:start position:0% +dual numbers so eight lines of code so +the first thing I'm gonna tell you is + + align:start position:0% +the first thing I'm gonna tell you is + + + align:start position:0% +the first thing I'm gonna tell you is +I'm going to remind you you never know I + + align:start position:0% +I'm going to remind you you never know I + + + align:start position:0% +I'm going to remind you you never know I +never typed one-half X to the minus 1/2 + + align:start position:0% +never typed one-half X to the minus 1/2 + + + align:start position:0% +never typed one-half X to the minus 1/2 +do you agree no one I'm not importing + + align:start position:0% +do you agree no one I'm not importing + + + align:start position:0% +do you agree no one I'm not importing +any packages it's not like it's coming + + align:start position:0% +any packages it's not like it's coming + + + align:start position:0% +any packages it's not like it's coming +in from the I'm not sneaking it in from + + align:start position:0% +in from the I'm not sneaking it in from + + + align:start position:0% +in from the I'm not sneaking it in from +the side + + align:start position:0% +the side + + + align:start position:0% +the side +there's no 1/2 X to the minus a house + + align:start position:0% +there's no 1/2 X to the minus a house + + + align:start position:0% +there's no 1/2 X to the minus a house +and there's certainly not any numerical + + align:start position:0% +and there's certainly not any numerical + + + align:start position:0% +and there's certainly not any numerical +derivatives either right just the just + + align:start position:0% +derivatives either right just the just + + + align:start position:0% +derivatives either right just the just +just arguably a rule that almost feels + + align:start position:0% +just arguably a rule that almost feels + + + align:start position:0% +just arguably a rule that almost feels +symbolic the quotient rule in the + + align:start position:0% +symbolic the quotient rule in the + + + align:start position:0% +symbolic the quotient rule in the +addition rule but but no numerical + + align:start position:0% +addition rule but but no numerical + + + align:start position:0% +addition rule but but no numerical +finite differences at all here okay so + + align:start position:0% +finite differences at all here okay so + + + align:start position:0% +finite differences at all here okay so +so first of all let me show you here + + align:start position:0% +so first of all let me show you here + + + align:start position:0% +so first of all let me show you here +that I'm taking the I'm applying the + + align:start position:0% +that I'm taking the I'm applying the + + + align:start position:0% +that I'm taking the I'm applying the +Babylonian algorithm without rewriting + + align:start position:0% +Babylonian algorithm without rewriting + + + align:start position:0% +Babylonian algorithm without rewriting +code to a dual number now before we + + align:start position:0% +code to a dual number now before we + + + align:start position:0% +code to a dual number now before we +applied it to numbers but now I'm gonna + + align:start position:0% +applied it to numbers but now I'm gonna + + + align:start position:0% +applied it to numbers but now I'm gonna +apply it to this dual number they're + + align:start position:0% +apply it to this dual number they're + + + align:start position:0% +apply it to this dual number they're +just invented I'm gonna apply it at 49 + + align:start position:0% +just invented I'm gonna apply it at 49 + + + align:start position:0% +just invented I'm gonna apply it at 49 +one cuz I know the answer and then I'm + + align:start position:0% +one cuz I know the answer and then I'm + + + align:start position:0% +one cuz I know the answer and then I'm +gonna compare it with I'm taking one + + align:start position:0% +gonna compare it with I'm taking one + + + align:start position:0% +gonna compare it with I'm taking one +half of a square root of x just for + + align:start position:0% +half of a square root of x just for + + + align:start position:0% +half of a square root of x just for +comparison purposes right and not not in + + align:start position:0% +comparison purposes right and not not in + + + align:start position:0% +comparison purposes right and not not in +my own algorithm and of course you see + + align:start position:0% +my own algorithm and of course you see + + + align:start position:0% +my own algorithm and of course you see +that I'm getting magically the right + + align:start position:0% +that I'm getting magically the right + + + align:start position:0% +that I'm getting magically the right +answer without ever so you should wonder + + align:start position:0% +answer without ever so you should wonder + + + align:start position:0% +answer without ever so you should wonder +how did I do that how did I get the + + align:start position:0% +how did I do that how did I get the + + + align:start position:0% +how did I do that how did I get the +derivative we could take any number you + + align:start position:0% +derivative we could take any number you + + + align:start position:0% +derivative we could take any number you +like here's a hundred if you prefer to + + align:start position:0% +like here's a hundred if you prefer to + + + align:start position:0% +like here's a hundred if you prefer to +see a number like pi we can do that I + + align:start position:0% +see a number like pi we can do that I + + + align:start position:0% +see a number like pi we can do that I +mean you know we can do it every like + + align:start position:0% +mean you know we can do it every like + + + align:start position:0% +mean you know we can do it every like +it's going to work so there you see that + + align:start position:0% +it's going to work so there you see that + + + align:start position:0% +it's going to work so there you see that +this is the square root of pi and this + + align:start position:0% +this is the square root of pi and this + + + align:start position:0% +this is the square root of pi and this +would be one half over the square root + + align:start position:0% +would be one half over the square root + + + align:start position:0% +would be one half over the square root +of pi numerically so and you see it + + align:start position:0% +of pi numerically so and you see it + + + align:start position:0% +of pi numerically so and you see it +matches these these numbers to enough + + align:start position:0% +matches these these numbers to enough + + + align:start position:0% +matches these these numbers to enough +digits in fact all the digits actually + + align:start position:0% +digits in fact all the digits actually + + + align:start position:0% +digits in fact all the digits actually +yeah so this thing magically worked okay + + align:start position:0% +yeah so this thing magically worked okay + + + align:start position:0% +yeah so this thing magically worked okay +you should all be wondering how did that + + align:start position:0% +you should all be wondering how did that + + + align:start position:0% +you should all be wondering how did that +happen + + align:start position:0% +happen + + + align:start position:0% +happen +right I didn't rewrite any code I + + align:start position:0% +right I didn't rewrite any code I + + + align:start position:0% +right I didn't rewrite any code I +actually wrote a code to just compute a + + align:start position:0% +actually wrote a code to just compute a + + + align:start position:0% +actually wrote a code to just compute a +square root I never could never wrote a + + align:start position:0% +square root I never could never wrote a + + + align:start position:0% +square root I never could never wrote a +code to compute the derivative of square + + align:start position:0% +code to compute the derivative of square + + + align:start position:0% +code to compute the derivative of square +roots and and by the way this is a + + align:start position:0% +roots and and by the way this is a + + + align:start position:0% +roots and and by the way this is a +little bit of the Julia magic that that + + align:start position:0% +little bit of the Julia magic that that + + + align:start position:0% +little bit of the Julia magic that that +we're pushing numerically that very + + align:start position:0% +we're pushing numerically that very + + + align:start position:0% +we're pushing numerically that very +often and in this world people will + + align:start position:0% +often and in this world people will + + + align:start position:0% +often and in this world people will +write a code to do something and then if + + align:start position:0% +write a code to do something and then if + + + align:start position:0% +write a code to do something and then if +you wanted to do something more like get + + align:start position:0% +you wanted to do something more like get + + + align:start position:0% +you wanted to do something more like get +a derivative somebody writes another + + align:start position:0% +a derivative somebody writes another + + + align:start position:0% +a derivative somebody writes another +code with Julia very often you can + + align:start position:0% +code with Julia very often you can + + + align:start position:0% +code with Julia very often you can +actually keep to the original code if + + align:start position:0% +actually keep to the original code if + + + align:start position:0% +actually keep to the original code if +you just use it properly and + + align:start position:0% +you just use it properly and + + + align:start position:0% +you just use it properly and +intelligently you can do magic things + + align:start position:0% +intelligently you can do magic things + + + align:start position:0% +intelligently you can do magic things +without writing new codes and you'll see + + align:start position:0% +without writing new codes and you'll see + + + align:start position:0% +without writing new codes and you'll see +this again in a little bit but here's + + align:start position:0% +this again in a little bit but here's + + + align:start position:0% +this again in a little bit but here's +the derivative of you know this this is + + align:start position:0% +the derivative of you know this this is + + + align:start position:0% +the derivative of you know this this is +the plot of 1/2 of the square root of x + + align:start position:0% +the plot of 1/2 of the square root of x + + + align:start position:0% +the plot of 1/2 of the square root of x +in black and again you could see the + + align:start position:0% +in black and again you could see the + + + align:start position:0% +in black and again you could see the +convergence over here all right well I'm + + align:start position:0% +convergence over here all right well I'm + + + align:start position:0% +convergence over here all right well I'm +still not going to show you why it works + + align:start position:0% +still not going to show you why it works + + + align:start position:0% +still not going to show you why it works +just yet I promise I will and it's + + align:start position:0% +just yet I promise I will and it's + + + align:start position:0% +just yet I promise I will and it's +probably a few more minutes more but + + align:start position:0% +probably a few more minutes more but + + + align:start position:0% +probably a few more minutes more but +what I will do first is is I'd like to + + align:start position:0% +what I will do first is is I'd like to + + + align:start position:0% +what I will do first is is I'd like to +show you something that most people + + align:start position:0% +show you something that most people + + + align:start position:0% +show you something that most people +don't ever look at I never look at it I + + align:start position:0% +don't ever look at I never look at it I + + + align:start position:0% +don't ever look at I never look at it I +want to show you here's the same + + align:start position:0% +want to show you here's the same + + + align:start position:0% +want to show you here's the same +Babylonian code I want to show you the + + align:start position:0% +Babylonian code I want to show you the + + + align:start position:0% +Babylonian code I want to show you the +assembler for the computation of the + + align:start position:0% +assembler for the computation of the + + + align:start position:0% +assembler for the computation of the +derivative so I'm gonna run Babylonian + + align:start position:0% +derivative so I'm gonna run Babylonian + + + align:start position:0% +derivative so I'm gonna run Babylonian +on a dual dual number and we're gonna + + align:start position:0% +on a dual dual number and we're gonna + + + align:start position:0% +on a dual dual number and we're gonna +look here and I don't know if anybody + + align:start position:0% +look here and I don't know if anybody + + + align:start position:0% +look here and I don't know if anybody +here reads assembler I'm betting there's + + align:start position:0% +here reads assembler I'm betting there's + + + align:start position:0% +here reads assembler I'm betting there's +zero or one of you actually + + align:start position:0% +zero or one of you actually + + + align:start position:0% +zero or one of you actually +reads this stuff how many of you read + + align:start position:0% +reads this stuff how many of you read + + + align:start position:0% +reads this stuff how many of you read +assembler okay we have got it wasn't 0-1 + + align:start position:0% +assembler okay we have got it wasn't 0-1 + + + align:start position:0% +assembler okay we have got it wasn't 0-1 +we had a half right there's a half he's + + align:start position:0% +we had a half right there's a half he's + + + align:start position:0% +we had a half right there's a half he's +kind of going like this here's the arrow + + align:start position:0% +kind of going like this here's the arrow + + + align:start position:0% +kind of going like this here's the arrow +here's one he's like this okay + + align:start position:0% +here's one he's like this okay + + + align:start position:0% +here's one he's like this okay +so so I think zero ones like the right + + align:start position:0% +so so I think zero ones like the right + + + align:start position:0% +so so I think zero ones like the right +bit but I'll bet you'll believe me if I + + align:start position:0% +bit but I'll bet you'll believe me if I + + + align:start position:0% +bit but I'll bet you'll believe me if I +tell you that when you have short + + align:start position:0% +tell you that when you have short + + + align:start position:0% +tell you that when you have short +assembler like this and it's not very + + align:start position:0% +assembler like this and it's not very + + + align:start position:0% +assembler like this and it's not very +long then you have efficient code but + + align:start position:0% +long then you have efficient code but + + + align:start position:0% +long then you have efficient code but +it's very tight it'll run very fast + + align:start position:0% +it's very tight it'll run very fast + + + align:start position:0% +it's very tight it'll run very fast +so whatever this thing is doing it's + + align:start position:0% +so whatever this thing is doing it's + + + align:start position:0% +so whatever this thing is doing it's +short and this you won't get from any + + align:start position:0% +short and this you won't get from any + + + align:start position:0% +short and this you won't get from any +other language if you did try to do the + + align:start position:0% +other language if you did try to do the + + + align:start position:0% +other language if you did try to do the +same thing in Python I promise you + + align:start position:0% +same thing in Python I promise you + + + align:start position:0% +same thing in Python I promise you +they'll be screens and screens and + + align:start position:0% +they'll be screens and screens and + + + align:start position:0% +they'll be screens and screens and +screens full of stuff if even if you + + align:start position:0% +screens full of stuff if even if you + + + align:start position:0% +screens full of stuff if even if you +could get it so so here's the Babylonian + + align:start position:0% +could get it so so here's the Babylonian + + + align:start position:0% +could get it so so here's the Babylonian +algorithm on the dual number and here it + + align:start position:0% +algorithm on the dual number and here it + + + align:start position:0% +algorithm on the dual number and here it +is an assembler and it's short so so the + + align:start position:0% +is an assembler and it's short so so the + + + align:start position:0% +is an assembler and it's short so so the +other thing I'm saying is not only does + + align:start position:0% +other thing I'm saying is not only does + + + align:start position:0% +other thing I'm saying is not only does +it work but Julie also makes it + + align:start position:0% +it work but Julie also makes it + + + align:start position:0% +it work but Julie also makes it +efficient so before I finally tell you + + align:start position:0% +efficient so before I finally tell you + + + align:start position:0% +efficient so before I finally tell you +what's really going on and why it works + + align:start position:0% +what's really going on and why it works + + + align:start position:0% +what's really going on and why it works +I'm gonna grab a Python symbolic package + + align:start position:0% +I'm gonna grab a Python symbolic package + + + align:start position:0% +I'm gonna grab a Python symbolic package +which will work nicely with Julia and + + align:start position:0% +which will work nicely with Julia and + + + align:start position:0% +which will work nicely with Julia and +I'm going to run the same code through + + align:start position:0% +I'm going to run the same code through + + + align:start position:0% +I'm going to run the same code through +the Python symbolic and show you what + + align:start position:0% +the Python symbolic and show you what + + + align:start position:0% +the Python symbolic and show you what +the these are the iterations that you + + align:start position:0% +the these are the iterations that you + + + align:start position:0% +the these are the iterations that you +get so this is a Khaleesi the the + + align:start position:0% +get so this is a Khaleesi the the + + + align:start position:0% +get so this is a Khaleesi the the +iterations towards the square root and + + align:start position:0% +iterations towards the square root and + + + align:start position:0% +iterations towards the square root and +here are the iterations of the + + align:start position:0% +here are the iterations of the + + + align:start position:0% +here are the iterations of the +derivative that's actually being + + align:start position:0% +derivative that's actually being + + + align:start position:0% +derivative that's actually being +calculated um and the key point here is + + align:start position:0% +calculated um and the key point here is + + + align:start position:0% +calculated um and the key point here is +of course we're not this is a symbolic + + align:start position:0% +of course we're not this is a symbolic + + + align:start position:0% +of course we're not this is a symbolic +computation we're not doing a symbolic + + align:start position:0% +computation we're not doing a symbolic + + + align:start position:0% +computation we're not doing a symbolic +computation this is mathematically + + align:start position:0% +computation this is mathematically + + + align:start position:0% +computation this is mathematically +equivalent to the function we would get + + align:start position:0% +equivalent to the function we would get + + + align:start position:0% +equivalent to the function we would get +if we were to like plot it or something + + align:start position:0% +if we were to like plot it or something + + + align:start position:0% +if we were to like plot it or something +but of course we're not symbolic + + align:start position:0% +but of course we're not symbolic + + + align:start position:0% +but of course we're not symbolic +computation is very inefficient I mean + + align:start position:0% +computation is very inefficient I mean + + + align:start position:0% +computation is very inefficient I mean +you get these big coefficients I mean + + align:start position:0% +you get these big coefficients I mean + + + align:start position:0% +you get these big coefficients I mean +look at this number what is this five + + align:start position:0% +look at this number what is this five + + + align:start position:0% +look at this number what is this five +million or something anyway you get + + align:start position:0% +million or something anyway you get + + + align:start position:0% +million or something anyway you get +these big numbers these people even + + align:start position:0% +these big numbers these people even + + + align:start position:0% +these big numbers these people even +bigger numbers here look at these huge + + align:start position:0% +bigger numbers here look at these huge + + + align:start position:0% +bigger numbers here look at these huge +numbers right the it takes a lot of + + align:start position:0% +numbers right the it takes a lot of + + + align:start position:0% +numbers right the it takes a lot of +storage I'm dragging these X's along + + align:start position:0% +storage I'm dragging these X's along + + + align:start position:0% +storage I'm dragging these X's along +there's a big drag on memory I mean this + + align:start position:0% +there's a big drag on memory I mean this + + + align:start position:0% +there's a big drag on memory I mean this +is not the way that this is why we do + + align:start position:0% +is not the way that this is why we do + + + align:start position:0% +is not the way that this is why we do +numerical computation but what the + + align:start position:0% +numerical computation but what the + + + align:start position:0% +numerical computation but what the +Babylonian algorithm in the absence of + + align:start position:0% +Babylonian algorithm in the absence of + + + align:start position:0% +Babylonian algorithm in the absence of +any roundoff is equivalent to computing + + align:start position:0% +any roundoff is equivalent to computing + + + align:start position:0% +any roundoff is equivalent to computing +you know above the line it's computing + + align:start position:0% +you know above the line it's computing + + + align:start position:0% +you know above the line it's computing +the square root here and then below here + + align:start position:0% +the square root here and then below here + + + align:start position:0% +the square root here and then below here +this is these are the iterates towards + + align:start position:0% +this is these are the iterates towards + + + align:start position:0% +this is these are the iterates towards +the derivative so it's not actually + + align:start position:0% +the derivative so it's not actually + + + align:start position:0% +the derivative so it's not actually +calculating X 1/2 X to the minus 1/2 + + align:start position:0% +calculating X 1/2 X to the minus 1/2 + + + align:start position:0% +calculating X 1/2 X to the minus 1/2 +it's actually doing something iterative + + align:start position:0% +it's actually doing something iterative + + + align:start position:0% +it's actually doing something iterative +that is approximating 1/2 + + align:start position:0% +that is approximating 1/2 + + + align:start position:0% +that is approximating 1/2 +- all right well let me tell you now let + + align:start position:0% +- all right well let me tell you now let + + + align:start position:0% +- all right well let me tell you now let +me sort of reveal what's going on just + + align:start position:0% +me sort of reveal what's going on just + + + align:start position:0% +me sort of reveal what's going on just +so that I can kind of show you how it's + + align:start position:0% +so that I can kind of show you how it's + + + align:start position:0% +so that I can kind of show you how it's +getting the answer and like I said it + + align:start position:0% +getting the answer and like I said it + + + align:start position:0% +getting the answer and like I said it +was the SVD that sort of convinced me + + align:start position:0% +was the SVD that sort of convinced me + + + align:start position:0% +was the SVD that sort of convinced me +how this was happening cuz the SVD is + + align:start position:0% +how this was happening cuz the SVD is + + + align:start position:0% +how this was happening cuz the SVD is +also an iterative algorithm like this + + align:start position:0% +also an iterative algorithm like this + + + align:start position:0% +also an iterative algorithm like this +Babylonian square root but but it's + + align:start position:0% +Babylonian square root but but it's + + + align:start position:0% +Babylonian square root but but it's +easier to show you the point with the + + align:start position:0% +easier to show you the point with the + + + align:start position:0% +easier to show you the point with the +baloney and square root so I'm gonna do + + align:start position:0% +baloney and square root so I'm gonna do + + + align:start position:0% +baloney and square root so I'm gonna do +something that I would never want to do + + align:start position:0% +something that I would never want to do + + + align:start position:0% +something that I would never want to do +which is explicitly write a derivative + + align:start position:0% +which is explicitly write a derivative + + + align:start position:0% +which is explicitly write a derivative +Babylonian algorithm and what I'm doing + + align:start position:0% +Babylonian algorithm and what I'm doing + + + align:start position:0% +Babylonian algorithm and what I'm doing +is I'm gonna take the derivative spec 2x + + align:start position:0% +is I'm gonna take the derivative spec 2x + + + align:start position:0% +is I'm gonna take the derivative spec 2x +of every line of my code so you know if + + align:start position:0% +of every line of my code so you know if + + + align:start position:0% +of every line of my code so you know if +every even or odd line I never know + + align:start position:0% +every even or odd line I never know + + + align:start position:0% +every even or odd line I never know +what's even or odd anymore but the + + align:start position:0% +what's even or odd anymore but the + + + align:start position:0% +what's even or odd anymore but the +original line of code had one flex over + + align:start position:0% +original line of code had one flex over + + + align:start position:0% +original line of code had one flex over +two now I'm going to take the derivative + + align:start position:0% +two now I'm going to take the derivative + + + align:start position:0% +two now I'm going to take the derivative +or get 1/2 here + + align:start position:0% +or get 1/2 here + + + align:start position:0% +or get 1/2 here +I had this line of code if I take the + + align:start position:0% +I had this line of code if I take the + + + align:start position:0% +I had this line of code if I take the +derivative I'll use the the the the + + align:start position:0% +derivative I'll use the the the the + + + align:start position:0% +derivative I'll use the the the the +quotient rule and this would be the + + align:start position:0% +quotient rule and this would be the + + + align:start position:0% +quotient rule and this would be the +derivative if I run this code what I'm + + align:start position:0% +derivative if I run this code what I'm + + + align:start position:0% +derivative if I run this code what I'm +effectively doing is I'm just using good + + align:start position:0% +effectively doing is I'm just using good + + + align:start position:0% +effectively doing is I'm just using good +old plus and times and divide nothing + + align:start position:0% +old plus and times and divide nothing + + + align:start position:0% +old plus and times and divide nothing +fancy there's not a square root to be + + align:start position:0% +fancy there's not a square root to be + + + align:start position:0% +fancy there's not a square root to be +seen but what I'm doing is as I run my + + align:start position:0% +seen but what I'm doing is as I run my + + + align:start position:0% +seen but what I'm doing is as I run my +algorithm I'm also running I'm actually + + align:start position:0% +algorithm I'm also running I'm actually + + + align:start position:0% +algorithm I'm also running I'm actually +computing the derivative as I go so if I + + align:start position:0% +computing the derivative as I go so if I + + + align:start position:0% +computing the derivative as I go so if I +have this infinite algorithm it's going + + align:start position:0% +have this infinite algorithm it's going + + + align:start position:0% +have this infinite algorithm it's going +to converge to the square root this the + + align:start position:0% +to converge to the square root this the + + + align:start position:0% +to converge to the square root this the +derivative algorithm will converge to + + align:start position:0% +derivative algorithm will converge to + + + align:start position:0% +derivative algorithm will converge to +the derivative of the square roots but + + align:start position:0% +the derivative of the square roots but + + + align:start position:0% +the derivative of the square roots but +I'm not I'm not using anything other + + align:start position:0% +I'm not I'm not using anything other + + + align:start position:0% +I'm not I'm not using anything other +than plus minus times and divide to make + + align:start position:0% +than plus minus times and divide to make + + + align:start position:0% +than plus minus times and divide to make +that happen so if you rewrite any code + + align:start position:0% +that happen so if you rewrite any code + + + align:start position:0% +that happen so if you rewrite any code +at all you could have any code iterative + + align:start position:0% +at all you could have any code iterative + + + align:start position:0% +at all you could have any code iterative +finite it doesn't matter if you just + + align:start position:0% +finite it doesn't matter if you just + + + align:start position:0% +finite it doesn't matter if you just +take the derivatives back to your + + align:start position:0% +take the derivatives back to your + + + align:start position:0% +take the derivatives back to your +variable of every line of your code then + + align:start position:0% +variable of every line of your code then + + + align:start position:0% +variable of every line of your code then +you can get a derivative out and as I + + align:start position:0% +you can get a derivative out and as I + + + align:start position:0% +you can get a derivative out and as I +said it's not a symbolic derivative like + + align:start position:0% +said it's not a symbolic derivative like + + + align:start position:0% +said it's not a symbolic derivative like +you know all of 1801 or whatever + + align:start position:0% +you know all of 1801 or whatever + + + align:start position:0% +you know all of 1801 or whatever +wherever we teach calculus these days + + align:start position:0% +wherever we teach calculus these days + + + align:start position:0% +wherever we teach calculus these days +and it's not a numerical derivative like + + align:start position:0% +and it's not a numerical derivative like + + + align:start position:0% +and it's not a numerical derivative like +in a numerical courses that you know the + + align:start position:0% +in a numerical courses that you know the + + + align:start position:0% +in a numerical courses that you know the +18.3 a X Y Z's whatever it's a different + + align:start position:0% +18.3 a X Y Z's whatever it's a different + + + align:start position:0% +18.3 a X Y Z's whatever it's a different +beast it's the it's it's using the the + + align:start position:0% +beast it's the it's it's using the the + + + align:start position:0% +beast it's the it's it's using the the +quotient rule in the addition rule at + + align:start position:0% +quotient rule in the addition rule at + + + align:start position:0% +quotient rule in the addition rule at +every step of the way to get the answer + + align:start position:0% +every step of the way to get the answer + + + align:start position:0% +every step of the way to get the answer +so and you know here's this d-bob + + align:start position:0% +so and you know here's this d-bob + + + align:start position:0% +so and you know here's this d-bob +learning algorithm you could see it + + align:start position:0% +learning algorithm you could see it + + + align:start position:0% +learning algorithm you could see it +running and I'll get it gives the right + + align:start position:0% +running and I'll get it gives the right + + + align:start position:0% +running and I'll get it gives the right +answer I have to execute the code first + + align:start position:0% +answer I have to execute the code first + + + align:start position:0% +answer I have to execute the code first +to get the right answer but you see it + + align:start position:0% +to get the right answer but you see it + + + align:start position:0% +to get the right answer but you see it +gives it gives the right answer okay oh + + align:start position:0% +gives it gives the right answer okay oh + + + align:start position:0% +gives it gives the right answer okay oh +I was just in Istanbul and I they could + + align:start position:0% +I was just in Istanbul and I they could + + + align:start position:0% +I was just in Istanbul and I they could +challenge me to do sign I forgot about + + align:start position:0% +challenge me to do sign I forgot about + + + align:start position:0% +challenge me to do sign I forgot about +that it's still in the Summa notebook I + + align:start position:0% +that it's still in the Summa notebook I + + + align:start position:0% +that it's still in the Summa notebook I +it in front of everybody it worked I got + + align:start position:0% +it in front of everybody it worked I got + + + align:start position:0% +it in front of everybody it worked I got +a cosign okay but let me pass all of + + align:start position:0% +a cosign okay but let me pass all of + + + align:start position:0% +a cosign okay but let me pass all of +that so so so so let me go back and tell + + align:start position:0% +that so so so so let me go back and tell + + + align:start position:0% +that so so so so let me go back and tell +you then how is this all working well + + align:start position:0% +you then how is this all working well + + + align:start position:0% +you then how is this all working well +what's happening let's go back to the + + align:start position:0% +what's happening let's go back to the + + + align:start position:0% +what's happening let's go back to the +eight lines of code and now maybe you + + align:start position:0% +eight lines of code and now maybe you + + + align:start position:0% +eight lines of code and now maybe you +could see what's happening the where's + + align:start position:0% +could see what's happening the where's + + + align:start position:0% +could see what's happening the where's +my eight lines of code from the very + + align:start position:0% +my eight lines of code from the very + + + align:start position:0% +my eight lines of code from the very +beginning and I could have watched the + + align:start position:0% +beginning and I could have watched the + + + align:start position:0% +beginning and I could have watched the +time I want to show you this one other + + align:start position:0% +time I want to show you this one other + + + align:start position:0% +time I want to show you this one other +thing too so hopefully I'll have enough + + align:start position:0% +thing too so hopefully I'll have enough + + + align:start position:0% +thing too so hopefully I'll have enough +time to do that but here let's see we + + align:start position:0% +time to do that but here let's see we + + + align:start position:0% +time to do that but here let's see we +were mighty Atlantic code where are they + + align:start position:0% +were mighty Atlantic code where are they + + + align:start position:0% +were mighty Atlantic code where are they +here we go you're here the events of + + align:start position:0% +here we go you're here the events of + + + align:start position:0% +here we go you're here the events of +code so what I'm doing is instead of + + align:start position:0% +code so what I'm doing is instead of + + + align:start position:0% +code so what I'm doing is instead of +rewriting all your code by taking the + + align:start position:0% +rewriting all your code by taking the + + + align:start position:0% +rewriting all your code by taking the +derivative of every line the human way + + align:start position:0% +derivative of every line the human way + + + align:start position:0% +derivative of every line the human way +I'm saying that why can't the software + + align:start position:0% +I'm saying that why can't the software + + + align:start position:0% +I'm saying that why can't the software +just do this in some automatic way and + + align:start position:0% +just do this in some automatic way and + + + align:start position:0% +just do this in some automatic way and +this is where the automatic + + align:start position:0% +this is where the automatic + + + align:start position:0% +this is where the automatic +differentiation comes in and in the old + + align:start position:0% +differentiation comes in and in the old + + + align:start position:0% +differentiation comes in and in the old +old days when people in all the + + align:start position:0% +old days when people in all the + + + align:start position:0% +old days when people in all the +numerical code was in Fortran there + + align:start position:0% +numerical code was in Fortran there + + + align:start position:0% +numerical code was in Fortran there +would be these source-to-source + + align:start position:0% +would be these source-to-source + + + align:start position:0% +would be these source-to-source +translators that would actually input + + align:start position:0% +translators that would actually input + + + align:start position:0% +translators that would actually input +code and output derivatives of code the + + align:start position:0% +code and output derivatives of code the + + + align:start position:0% +code and output derivatives of code the +giulia way the more modern way is to let + + align:start position:0% +giulia way the more modern way is to let + + + align:start position:0% +giulia way the more modern way is to let +the JIT compiler kind of do that for you + + align:start position:0% +the JIT compiler kind of do that for you + + + align:start position:0% +the JIT compiler kind of do that for you +so here I need it plus and divide of + + align:start position:0% +so here I need it plus and divide of + + + align:start position:0% +so here I need it plus and divide of +course I would want to add minus and + + align:start position:0% +course I would want to add minus and + + + align:start position:0% +course I would want to add minus and +times but you just add a couple of + + align:start position:0% +times but you just add a couple of + + + align:start position:0% +times but you just add a couple of +things and then bump the you know you + + align:start position:0% +things and then bump the you know you + + + align:start position:0% +things and then bump the you know you +don't have to rewrite the D Babylonian + + align:start position:0% +don't have to rewrite the D Babylonian + + + align:start position:0% +don't have to rewrite the D Babylonian +because the Babylonian with this type + + align:start position:0% +because the Babylonian with this type + + + align:start position:0% +because the Babylonian with this type +will just will do the work for you okay + + align:start position:0% +will just will do the work for you okay + + + align:start position:0% +will just will do the work for you okay +and that's where the magic of a good + + align:start position:0% +and that's where the magic of a good + + + align:start position:0% +and that's where the magic of a good +piece of software will have it so you + + align:start position:0% +piece of software will have it so you + + + align:start position:0% +piece of software will have it so you +don't have to write a translator you + + align:start position:0% +don't have to write a translator you + + + align:start position:0% +don't have to write a translator you +don't have to handwrite it you just give + + align:start position:0% +don't have to handwrite it you just give + + + align:start position:0% +don't have to handwrite it you just give +sort of the rules and you let the + + align:start position:0% +sort of the rules and you let the + + + align:start position:0% +sort of the rules and you let the +computer do it right I mean that's what + + align:start position:0% +computer do it right I mean that's what + + + align:start position:0% +computer do it right I mean that's what +computers are supposed to be good at and + + align:start position:0% +computers are supposed to be good at and + + + align:start position:0% +computers are supposed to be good at and +so that's that's what's happening all + + align:start position:0% +so that's that's what's happening all + + + align:start position:0% +so that's that's what's happening all +right so that's that's forward mode + + align:start position:0% +right so that's that's forward mode + + + align:start position:0% +right so that's that's forward mode +automatic differentiation I've got 10 + + align:start position:0% +automatic differentiation I've got 10 + + + align:start position:0% +automatic differentiation I've got 10 +minutes to go backwards so but let me + + align:start position:0% +minutes to go backwards so but let me + + + align:start position:0% +minutes to go backwards so but let me +see if there's any anybody have any + + align:start position:0% +see if there's any anybody have any + + + align:start position:0% +see if there's any anybody have any +questions about this this it's really + + align:start position:0% +questions about this this it's really + + + align:start position:0% +questions about this this it's really +magic right but it's pretty wonderful + + align:start position:0% +magic right but it's pretty wonderful + + + align:start position:0% +magic right but it's pretty wonderful +magic and and and you know I don't know + + align:start position:0% +magic and and and you know I don't know + + + align:start position:0% +magic and and and you know I don't know +what you've heard about machine learning + + align:start position:0% +what you've heard about machine learning + + + align:start position:0% +what you've heard about machine learning +but to be honest + + align:start position:0% +but to be honest + + + align:start position:0% +but to be honest +machine learning these days it's it's + + align:start position:0% +machine learning these days it's it's + + + align:start position:0% +machine learning these days it's it's +it's it's you know forgetting about + + align:start position:0% +it's it's you know forgetting about + + + align:start position:0% +it's it's you know forgetting about +whether you know humans will be useless + + align:start position:0% +whether you know humans will be useless + + + align:start position:0% +whether you know humans will be useless +which I don't believe by the way but but + + align:start position:0% +which I don't believe by the way but but + + + align:start position:0% +which I don't believe by the way but but +the the the the big thing about machine + + align:start position:0% +the the the the big thing about machine + + + align:start position:0% +the the the the big thing about machine +learning is that it's really just a big + + align:start position:0% +learning is that it's really just a big + + + align:start position:0% +learning is that it's really just a big +optimization that's all it is right + + align:start position:0% +optimization that's all it is right + + + align:start position:0% +optimization that's all it is right +big minimum/maximum problem where you've + + align:start position:0% +big minimum/maximum problem where you've + + + align:start position:0% +big minimum/maximum problem where you've +all known from calculus that what you + + align:start position:0% +all known from calculus that what you + + + align:start position:0% +all known from calculus that what you +need to do is take derivatives you know + + align:start position:0% +need to do is take derivatives you know + + + align:start position:0% +need to do is take derivatives you know +set them to zero right you know in the + + align:start position:0% +set them to zero right you know in the + + + align:start position:0% +set them to zero right you know in the +case of multivariate it's a gradient you + + align:start position:0% +case of multivariate it's a gradient you + + + align:start position:0% +case of multivariate it's a gradient you +set it to zero and so really all of this + + align:start position:0% +set it to zero and so really all of this + + + align:start position:0% +set it to zero and so really all of this +machine learning all the big stories and + + align:start position:0% +machine learning all the big stories and + + + align:start position:0% +machine learning all the big stories and +everything in the end comes down to a + + align:start position:0% +everything in the end comes down to a + + + align:start position:0% +everything in the end comes down to a +automatic differentiation is sort of + + align:start position:0% +automatic differentiation is sort of + + + align:start position:0% +automatic differentiation is sort of +like the the workhorse of the whole + + align:start position:0% +like the the workhorse of the whole + + + align:start position:0% +like the the workhorse of the whole +thing and so if we could have a a + + align:start position:0% +thing and so if we could have a a + + + align:start position:0% +thing and so if we could have a a +language that gives you that workhorse + + align:start position:0% +language that gives you that workhorse + + + align:start position:0% +language that gives you that workhorse +in a good way then machine learning + + align:start position:0% +in a good way then machine learning + + + align:start position:0% +in a good way then machine learning +really sort of benefits from that so so + + align:start position:0% +really sort of benefits from that so so + + + align:start position:0% +really sort of benefits from that so so +I hope you all see the the big picture + + align:start position:0% +I hope you all see the the big picture + + + align:start position:0% +I hope you all see the the big picture +of machine learning it really does come + + align:start position:0% +of machine learning it really does come + + + align:start position:0% +of machine learning it really does come +down to taking derivatives that that's + + align:start position:0% +down to taking derivatives that that's + + + align:start position:0% +down to taking derivatives that that's +that's the end of that's how you + + align:start position:0% +that's the end of that's how you + + + align:start position:0% +that's the end of that's how you +optimize any quick questions otherwise + + align:start position:0% +optimize any quick questions otherwise + + + align:start position:0% +optimize any quick questions otherwise +I'm gonna switch topics and I'm going to + + align:start position:0% +I'm gonna switch topics and I'm going to + + + align:start position:0% +I'm gonna switch topics and I'm going to +move to the blackboard yeah there's a + + align:start position:0% +move to the blackboard yeah there's a + + + align:start position:0% +move to the blackboard yeah there's a +trick that basically lets you go to + + align:start position:0% +trick that basically lets you go to + + + align:start position:0% +trick that basically lets you go to +higher orders yeah you can basically + + align:start position:0% +higher orders yeah you can basically + + + align:start position:0% +higher orders yeah you can basically +make it a combo of two first order + + align:start position:0% +make it a combo of two first order + + + align:start position:0% +make it a combo of two first order +derivatives so yeah it can be done did + + align:start position:0% +derivatives so yeah it can be done did + + + align:start position:0% +derivatives so yeah it can be done did +you have a question oh we're using for + + align:start position:0% +you have a question oh we're using for + + + align:start position:0% +you have a question oh we're using for +using types so so it's the biggest trick + + align:start position:0% +using types so so it's the biggest trick + + + align:start position:0% +using types so so it's the biggest trick +in the world it's not this little thing + + align:start position:0% +in the world it's not this little thing + + + align:start position:0% +in the world it's not this little thing +the idea of making a type to do what you + + align:start position:0% +the idea of making a type to do what you + + + align:start position:0% +the idea of making a type to do what you +did you see chroniker products in this + + align:start position:0% +did you see chroniker products in this + + + align:start position:0% +did you see chroniker products in this +class what no okay um let me see what + + align:start position:0% +class what no okay um let me see what + + + align:start position:0% +class what no okay um let me see what +what would you have seen in this yeah + + align:start position:0% +what would you have seen in this yeah + + + align:start position:0% +what would you have seen in this yeah +did you see tridiagonal matrices your + + align:start position:0% +did you see tridiagonal matrices your + + + align:start position:0% +did you see tridiagonal matrices your +favorite okay so here so here's a + + align:start position:0% +favorite okay so here so here's a + + + align:start position:0% +favorite okay so here so here's a +built-in type let's say n is it doesn't + + align:start position:0% +built-in type let's say n is it doesn't + + + align:start position:0% +built-in type let's say n is it doesn't +have to be four I'm gonna create a + + align:start position:0% +have to be four I'm gonna create a + + + align:start position:0% +have to be four I'm gonna create a +Strang matrix if I could spell it right + + align:start position:0% +Strang matrix if I could spell it right + + + align:start position:0% +Strang matrix if I could spell it right +and it's going to be a sim tri diagonal + + align:start position:0% +and it's going to be a sim tri diagonal + + + align:start position:0% +and it's going to be a sim tri diagonal +which is a julia type and we will create + + align:start position:0% +which is a julia type and we will create + + + align:start position:0% +which is a julia type and we will create +two x ones of N and minus ones of n + + align:start position:0% +two x ones of N and minus ones of n + + + align:start position:0% +two x ones of N and minus ones of n +minus one now here's a type I mean this + + align:start position:0% +minus one now here's a type I mean this + + + align:start position:0% +minus one now here's a type I mean this +is built-in but you could have created + + align:start position:0% +is built-in but you could have created + + + align:start position:0% +is built-in but you could have created +it yourself just as easily and I don't + + align:start position:0% +it yourself just as easily and I don't + + + align:start position:0% +it yourself just as easily and I don't +like calling + + align:start position:0% +like calling + + + align:start position:0% +like calling +this it's certainly not a dense matrix + + align:start position:0% +this it's certainly not a dense matrix + + + align:start position:0% +this it's certainly not a dense matrix +and I don't like calling it a sparse + + align:start position:0% +and I don't like calling it a sparse + + + align:start position:0% +and I don't like calling it a sparse +matrix I prefer to call it a structured + + align:start position:0% +matrix I prefer to call it a structured + + + align:start position:0% +matrix I prefer to call it a structured +matrix though the word sparse it's a + + align:start position:0% +matrix though the word sparse it's a + + + align:start position:0% +matrix though the word sparse it's a +little tricky here but the reason why I + + align:start position:0% +little tricky here but the reason why I + + + align:start position:0% +little tricky here but the reason why I +don't like to call this a sparse matrix + + align:start position:0% +don't like to call this a sparse matrix + + + align:start position:0% +don't like to call this a sparse matrix +is because we're not storing indices in + + align:start position:0% +is because we're not storing indices in + + + align:start position:0% +is because we're not storing indices in +any I mean there's a lot of fancy + + align:start position:0% +any I mean there's a lot of fancy + + + align:start position:0% +any I mean there's a lot of fancy +schemes for storing indices for for + + align:start position:0% +schemes for storing indices for for + + + align:start position:0% +schemes for storing indices for for +sparse matrices well the score store is + + align:start position:0% +sparse matrices well the score store is + + + align:start position:0% +sparse matrices well the score store is +a diagonal vector there's the two's on + + align:start position:0% +a diagonal vector there's the two's on + + + align:start position:0% +a diagonal vector there's the two's on +the diagonal there's a four vector with + + align:start position:0% +the diagonal there's a four vector with + + + align:start position:0% +the diagonal there's a four vector with +four twos and here's a three vector for + + align:start position:0% +four twos and here's a three vector for + + + align:start position:0% +four twos and here's a three vector for +the off diagonal and you know you don't + + align:start position:0% +the off diagonal and you know you don't + + + align:start position:0% +the off diagonal and you know you don't +have it twice by the way most sparse + + align:start position:0% +have it twice by the way most sparse + + + align:start position:0% +have it twice by the way most sparse +matrix structures would would would + + align:start position:0% +matrix structures would would would + + + align:start position:0% +matrix structures would would would +would have you know the the minus ones + + align:start position:0% +would have you know the the minus ones + + + align:start position:0% +would have you know the the minus ones +vector twice the super and the sub but + + align:start position:0% +vector twice the super and the sub but + + + align:start position:0% +vector twice the super and the sub but +really only the quarter information + + align:start position:0% +really only the quarter information + + + align:start position:0% +really only the quarter information +that's needed is stored and in a way one + + align:start position:0% +that's needed is stored and in a way one + + + align:start position:0% +that's needed is stored and in a way one +uses types in julia to basically you + + align:start position:0% +uses types in julia to basically you + + + align:start position:0% +uses types in julia to basically you +only store what you need not more and + + align:start position:0% +only store what you need not more and + + + align:start position:0% +only store what you need not more and +then you define your operations to work + + align:start position:0% +then you define your operations to work + + + align:start position:0% +then you define your operations to work +so for example if i were to take you + + align:start position:0% +so for example if i were to take you + + + align:start position:0% +so for example if i were to take you +know Strang inverse time so anything + + align:start position:0% +know Strang inverse time so anything + + + align:start position:0% +know Strang inverse time so anything +with here's you know terms of random for + + align:start position:0% +with here's you know terms of random for + + + align:start position:0% +with here's you know terms of random for +I'm gonna do a linear solve you would + + align:start position:0% +I'm gonna do a linear solve you would + + + align:start position:0% +I'm gonna do a linear solve you would +want to use a special back Slav that + + align:start position:0% +want to use a special back Slav that + + + align:start position:0% +want to use a special back Slav that +knew that the matrix was a symmetric + + align:start position:0% +knew that the matrix was a symmetric + + + align:start position:0% +knew that the matrix was a symmetric +tri-diagonal so it's a big story of + + align:start position:0% +tri-diagonal so it's a big story of + + + align:start position:0% +tri-diagonal so it's a big story of +being able to create types and use them + + align:start position:0% +being able to create types and use them + + + align:start position:0% +being able to create types and use them +for your own purposes without you know + + align:start position:0% +for your own purposes without you know + + + align:start position:0% +for your own purposes without you know +any wastage and this is a sort of thing + + align:start position:0% +any wastage and this is a sort of thing + + + align:start position:0% +any wastage and this is a sort of thing +that while you can do it in languages + + align:start position:0% +that while you can do it in languages + + + align:start position:0% +that while you can do it in languages +like Python in MATLAB if you were table + + align:start position:0% +like Python in MATLAB if you were table + + + align:start position:0% +like Python in MATLAB if you were table +look at the assembler and that level + + align:start position:0% +look at the assembler and that level + + + align:start position:0% +look at the assembler and that level +never let you Python you just would + + align:start position:0% +never let you Python you just would + + + align:start position:0% +never let you Python you just would +regret it but you would you would see + + align:start position:0% +regret it but you would you would see + + + align:start position:0% +regret it but you would you would see +just how much overhead there is in doing + + align:start position:0% +just how much overhead there is in doing + + + align:start position:0% +just how much overhead there is in doing +this so there'd be no performance gain + + align:start position:0% +this so there'd be no performance gain + + + align:start position:0% +this so there'd be no performance gain +but in a way what this is what you want + + align:start position:0% +but in a way what this is what you want + + + align:start position:0% +but in a way what this is what you want +to do you want to use these things to + + align:start position:0% +to do you want to use these things to + + + align:start position:0% +to do you want to use these things to +match the mathematics and and so that's + + align:start position:0% +match the mathematics and and so that's + + + align:start position:0% +match the mathematics and and so that's +really the nice thing to be able to do + + align:start position:0% +really the nice thing to be able to do + + + align:start position:0% +really the nice thing to be able to do +all right I only have five minutes I + + align:start position:0% +all right I only have five minutes I + + + align:start position:0% +all right I only have five minutes I +don't know if I'm gonna pull this off + + align:start position:0% +don't know if I'm gonna pull this off + + + align:start position:0% +don't know if I'm gonna pull this off +but I'll let me see if I could give you + + align:start position:0% +but I'll let me see if I could give you + + + align:start position:0% +but I'll let me see if I could give you +the main idea in five minutes of her + + align:start position:0% +the main idea in five minutes of her + + + align:start position:0% +the main idea in five minutes of her +immersed mode differentiations but here + + align:start position:0% +immersed mode differentiations but here + + + align:start position:0% +immersed mode differentiations but here +as long as you are familiar with neural + + align:start position:0% +as long as you are familiar with neural + + + align:start position:0% +as long as you are familiar with neural +networks let me see if I can do this + + align:start position:0% +networks let me see if I can do this + + + align:start position:0% +networks let me see if I can do this +very quickly I'm going to start with + + align:start position:0% +very quickly I'm going to start with + + + align:start position:0% +very quickly I'm going to start with +scalars okay I'm gonna do a neural + + align:start position:0% +scalars okay I'm gonna do a neural + + + align:start position:0% +scalars okay I'm gonna do a neural +network of all scalars but only for + + align:start position:0% +network of all scalars but only for + + + align:start position:0% +network of all scalars but only for +simplicity for starters but I think + + align:start position:0% +simplicity for starters but I think + + + align:start position:0% +simplicity for starters but I think +you're gonna see that this can general + + align:start position:0% +you're gonna see that this can general + + + align:start position:0% +you're gonna see that this can general +two vectors and matrices which are real + + align:start position:0% +two vectors and matrices which are real + + + align:start position:0% +two vectors and matrices which are real +neural networks so what I'm going to do + + align:start position:0% +neural networks so what I'm going to do + + + align:start position:0% +neural networks so what I'm going to do +is I want to imagine that we have our + + align:start position:0% +is I want to imagine that we have our + + + align:start position:0% +is I want to imagine that we have our +inputs will have a bunch of scalar + + align:start position:0% +inputs will have a bunch of scalar + + + align:start position:0% +inputs will have a bunch of scalar +weights and biases so here's w1 and I'll + + align:start position:0% +weights and biases so here's w1 and I'll + + + align:start position:0% +weights and biases so here's w1 and I'll +go up to W and B all right so we have a + + align:start position:0% +go up to W and B all right so we have a + + + align:start position:0% +go up to W and B all right so we have a +bunch of weights and biases here okay + + align:start position:0% +bunch of weights and biases here okay + + + align:start position:0% +bunch of weights and biases here okay +and we'll also have an x1 which will + + align:start position:0% +and we'll also have an x1 which will + + + align:start position:0% +and we'll also have an x1 which will +sort of start off our neural network and + + align:start position:0% +sort of start off our neural network and + + + align:start position:0% +sort of start off our neural network and +we're going to compute I'll write in + + align:start position:0% +we're going to compute I'll write in + + + align:start position:0% +we're going to compute I'll write in +sort of Julia like or MATLAB black + + align:start position:0% +sort of Julia like or MATLAB black + + + align:start position:0% +sort of Julia like or MATLAB black +notation for I equals 1 through n I will + + align:start position:0% +notation for I equals 1 through n I will + + + align:start position:0% +notation for I equals 1 through n I will +update X by taking some function of my + + align:start position:0% +update X by taking some function of my + + + align:start position:0% +update X by taking some function of my +current input maybe something like this + + align:start position:0% +current input maybe something like this + + + align:start position:0% +current input maybe something like this +and what function H to use I don't + + align:start position:0% +and what function H to use I don't + + + align:start position:0% +and what function H to use I don't +really care too much in the old days + + align:start position:0% +really care too much in the old days + + + align:start position:0% +really care too much in the old days +people used to talk about the sigmoid + + align:start position:0% +people used to talk about the sigmoid + + + align:start position:0% +people used to talk about the sigmoid +function nowadays it's the maximum of 0 + + align:start position:0% +function nowadays it's the maximum of 0 + + + align:start position:0% +function nowadays it's the maximum of 0 +and T that gets used all the time it's + + align:start position:0% +and T that gets used all the time it's + + + align:start position:0% +and T that gets used all the time it's +got this ridiculous name rel U which I I + + align:start position:0% +got this ridiculous name rel U which I I + + + align:start position:0% +got this ridiculous name rel U which I I +really can't stand but anyway they + + align:start position:0% +really can't stand but anyway they + + + align:start position:0% +really can't stand but anyway they +rectified linear unit but in any event I + + align:start position:0% +rectified linear unit but in any event I + + + align:start position:0% +rectified linear unit but in any event I +mean it it it's just a function that's + + align:start position:0% +mean it it it's just a function that's + + + align:start position:0% +mean it it it's just a function that's +you know T of T is greater than equal to + + align:start position:0% +you know T of T is greater than equal to + + + align:start position:0% +you know T of T is greater than equal to +0 0 if not so so but whatever function + + align:start position:0% +0 0 if not so so but whatever function + + + align:start position:0% +0 0 if not so so but whatever function +and you like and here I'm just gonna + + align:start position:0% +and you like and here I'm just gonna + + + align:start position:0% +and you like and here I'm just gonna +update Taemin ultimately you might also + + align:start position:0% +update Taemin ultimately you might also + + + align:start position:0% +update Taemin ultimately you might also +have some data Y and you would like to + + align:start position:0% +have some data Y and you would like to + + + align:start position:0% +have some data Y and you would like to +if everything is a scalar like I said + + align:start position:0% +if everything is a scalar like I said + + + align:start position:0% +if everything is a scalar like I said +this could be generalized pretty quickly + + align:start position:0% +this could be generalized pretty quickly + + + align:start position:0% +this could be generalized pretty quickly +but what we can do is we we can minimize + + align:start position:0% +but what we can do is we we can minimize + + + align:start position:0% +but what we can do is we we can minimize +say 1/2 Y minus X M squared you know in + + align:start position:0% +say 1/2 Y minus X M squared you know in + + + align:start position:0% +say 1/2 Y minus X M squared you know in +the you're going to want to find the + + align:start position:0% +the you're going to want to find the + + + align:start position:0% +the you're going to want to find the +data that would minimize that ok all + + align:start position:0% +data that would minimize that ok all + + + align:start position:0% +data that would minimize that ok all +this generalizes to matrices and vectors + + align:start position:0% +this generalizes to matrices and vectors + + + align:start position:0% +this generalizes to matrices and vectors +which is what most neural nets do ok and + + align:start position:0% +which is what most neural nets do ok and + + + align:start position:0% +which is what most neural nets do ok and +since since since I'm not going to have + + align:start position:0% +since since since I'm not going to have + + + align:start position:0% +since since since I'm not going to have +a lot of time maybe I can just sort of + + align:start position:0% +a lot of time maybe I can just sort of + + + align:start position:0% +a lot of time maybe I can just sort of +cut to the chase if I were to + + align:start position:0% +cut to the chase if I were to + + + align:start position:0% +cut to the chase if I were to +differentiate the key line here I've got + + align:start position:0% +differentiate the key line here I've got + + + align:start position:0% +differentiate the key line here I've got +a little bit of Julia here but if I were + + align:start position:0% +a little bit of Julia here but if I were + + + align:start position:0% +a little bit of Julia here but if I were +to differentiate the key line what would + + align:start position:0% +to differentiate the key line what would + + + align:start position:0% +to differentiate the key line what would +I write I would write well here actually + + align:start position:0% +I write I would write well here actually + + + align:start position:0% +I write I would write well here actually +let me use the + + align:start position:0% +let me use the + + + align:start position:0% +let me use the +usual notation let me have Delta IB the + + align:start position:0% +usual notation let me have Delta IB the + + + align:start position:0% +usual notation let me have Delta IB the +H prime of WX i plus bi okay so that's + + align:start position:0% +H prime of WX i plus bi okay so that's + + + align:start position:0% +H prime of WX i plus bi okay so that's +that's Delta I and then you can see that + + align:start position:0% +that's Delta I and then you can see that + + + align:start position:0% +that's Delta I and then you can see that +DX I plus one is Delta I and I'll have + + align:start position:0% +DX I plus one is Delta I and I'll have + + + align:start position:0% +DX I plus one is Delta I and I'll have +DWI X I plus D X I WI plus d bi would be + + align:start position:0% +DWI X I plus D X I WI plus d bi would be + + + align:start position:0% +DWI X I plus D X I WI plus d bi would be +the differential this would be how how + + align:start position:0% +the differential this would be how how + + + align:start position:0% +the differential this would be how how +I'm almost done that's the goodness so + + align:start position:0% +I'm almost done that's the goodness so + + + align:start position:0% +I'm almost done that's the goodness so +if I make a little change I like to + + align:start position:0% +if I make a little change I like to + + + align:start position:0% +if I make a little change I like to +think of this as like point 0:01 changes + + align:start position:0% +think of this as like point 0:01 changes + + + align:start position:0% +think of this as like point 0:01 changes +I don't like I don't like infinitesimal + + align:start position:0% +I don't like I don't like infinitesimal + + + align:start position:0% +I don't like I don't like infinitesimal +said like point O once it's how I think + + align:start position:0% +said like point O once it's how I think + + + align:start position:0% +said like point O once it's how I think +of them but you make a little change + + align:start position:0% +of them but you make a little change + + + align:start position:0% +of them but you make a little change +here a little change here a little + + align:start position:0% +here a little change here a little + + + align:start position:0% +here a little change here a little +change here you get a change here you + + align:start position:0% +change here you get a change here you + + + align:start position:0% +change here you get a change here you +you'll get this you know you'll get this + + align:start position:0% +you'll get this you know you'll get this + + + align:start position:0% +you'll get this you know you'll get this +linear this linear function of the + + align:start position:0% +linear this linear function of the + + + align:start position:0% +linear this linear function of the +perturbations here gives you perturb + + align:start position:0% +perturbations here gives you perturb + + + align:start position:0% +perturbations here gives you perturb +ations here ok well I've only got one + + align:start position:0% +ations here ok well I've only got one + + + align:start position:0% +ations here ok well I've only got one +minute so I'm gonna write all this out + + align:start position:0% +minute so I'm gonna write all this out + + + align:start position:0% +minute so I'm gonna write all this out +with linear algebra because everything + + align:start position:0% +with linear algebra because everything + + + align:start position:0% +with linear algebra because everything +is better when written out with linear + + align:start position:0% +is better when written out with linear + + + align:start position:0% +is better when written out with linear +algebra so I'm gonna write down that I'm + + align:start position:0% +algebra so I'm gonna write down that I'm + + + align:start position:0% +algebra so I'm gonna write down that I'm +gonna write down that I'm actually + + align:start position:0% +gonna write down that I'm actually + + + align:start position:0% +gonna write down that I'm actually +interested in the last element but dxd n + + align:start position:0% +interested in the last element but dxd n + + + align:start position:0% +interested in the last element but dxd n +plus 1 is going to equal and I'm gonna + + align:start position:0% +plus 1 is going to equal and I'm gonna + + + align:start position:0% +plus 1 is going to equal and I'm gonna +have a couple of matrices here let me + + align:start position:0% +have a couple of matrices here let me + + + align:start position:0% +have a couple of matrices here let me +just sort of get the structure right + + align:start position:0% +just sort of get the structure right + + + align:start position:0% +just sort of get the structure right +this will be T X 2 DX n plus 1 again + + align:start position:0% +this will be T X 2 DX n plus 1 again + + + align:start position:0% +this will be T X 2 DX n plus 1 again +sorry for the squishing okay but and + + align:start position:0% +sorry for the squishing okay but and + + + align:start position:0% +sorry for the squishing okay but and +here in fact I'd like to use block + + align:start position:0% +here in fact I'd like to use block + + + align:start position:0% +here in fact I'd like to use block +matrices a little bit so here I'm gonna + + align:start position:0% +matrices a little bit so here I'm gonna + + + align:start position:0% +matrices a little bit so here I'm gonna +have DW 1 DB 1 I'm gonna put the bias + + align:start position:0% +have DW 1 DB 1 I'm gonna put the bias + + + align:start position:0% +have DW 1 DB 1 I'm gonna put the bias +together sorry for the mess but and DW + + align:start position:0% +together sorry for the mess but and DW + + + align:start position:0% +together sorry for the mess but and DW +and DB n Julia lets you make block + + align:start position:0% +and DB n Julia lets you make block + + + align:start position:0% +and DB n Julia lets you make block +matrices and you can actually use them + + align:start position:0% +matrices and you can actually use them + + + align:start position:0% +matrices and you can actually use them +directly there'd be a special type right + + align:start position:0% +directly there'd be a special type right + + + align:start position:0% +directly there'd be a special type right +there okay and then what goes here you + + align:start position:0% +there okay and then what goes here you + + + align:start position:0% +there okay and then what goes here you +could actually see what it would be + + align:start position:0% +could actually see what it would be + + + align:start position:0% +could actually see what it would be +would be I hope I'm doing it right but + + align:start position:0% +would be I hope I'm doing it right but + + + align:start position:0% +would be I hope I'm doing it right but +there'd be a delta 1 X 1 and Delta and X + + align:start position:0% +there'd be a delta 1 X 1 and Delta and X + + + align:start position:0% +there'd be a delta 1 X 1 and Delta and X +N and this would be a diagonal matrix + + align:start position:0% +N and this would be a diagonal matrix + + + align:start position:0% +N and this would be a diagonal matrix +okay and then what do I have over here + + align:start position:0% +okay and then what do I have over here + + + align:start position:0% +okay and then what do I have over here +here I'd have the Delta WS and if you + + align:start position:0% +here I'd have the Delta WS and if you + + + align:start position:0% +here I'd have the Delta WS and if you +check you'll see that this will be I'm + + align:start position:0% +check you'll see that this will be I'm + + + align:start position:0% +check you'll see that this will be I'm +not gonna get the indices right and I + + align:start position:0% +not gonna get the indices right and I + + + align:start position:0% +not gonna get the indices right and I +don't have time so I'm just gonna write + + align:start position:0% +don't have time so I'm just gonna write + + + align:start position:0% +don't have time so I'm just gonna write +it like this and now I'm just going to + + align:start position:0% +it like this and now I'm just going to + + + align:start position:0% +it like this and now I'm just going to +give you the end of the story + + align:start position:0% +give you the end of the story + + + align:start position:0% +give you the end of the story +at a time you could write all this as DX + + align:start position:0% +at a time you could write all this as DX + + + align:start position:0% +at a time you could write all this as DX +is equal to a diagonal matrix times the + + align:start position:0% +is equal to a diagonal matrix times the + + + align:start position:0% +is equal to a diagonal matrix times the +derivative of the parameters plus a + + align:start position:0% +derivative of the parameters plus a + + + align:start position:0% +derivative of the parameters plus a +lower triangular matrix times D X again + + align:start position:0% +lower triangular matrix times D X again + + + align:start position:0% +lower triangular matrix times D X again +and so if you want to solve this linear + + align:start position:0% +and so if you want to solve this linear + + + align:start position:0% +and so if you want to solve this linear +algebra just does the back propagation + + align:start position:0% +algebra just does the back propagation + + + align:start position:0% +algebra just does the back propagation +you have I minus L DX is d DP or DX will + + align:start position:0% +you have I minus L DX is d DP or DX will + + + align:start position:0% +you have I minus L DX is d DP or DX will +be I minus L inverse D DP and if I only + + align:start position:0% +be I minus L inverse D DP and if I only + + + align:start position:0% +be I minus L inverse D DP and if I only +want the last element let's say E and as + + align:start position:0% +want the last element let's say E and as + + + align:start position:0% +want the last element let's say E and as +the vector that pulls out the last + + align:start position:0% +the vector that pulls out the last + + + align:start position:0% +the vector that pulls out the last +element then this is all I'm going to + + align:start position:0% +element then this is all I'm going to + + + align:start position:0% +element then this is all I'm going to +need to get all my derivatives and + + align:start position:0% +need to get all my derivatives and + + + align:start position:0% +need to get all my derivatives and +what's the moral of the story I + + align:start position:0% +what's the moral of the story I + + + align:start position:0% +what's the moral of the story I +apologize for going one minute over but + + align:start position:0% +apologize for going one minute over but + + + align:start position:0% +apologize for going one minute over but +the moral the story is instead of back + + align:start position:0% +the moral the story is instead of back + + + align:start position:0% +the moral the story is instead of back +propagating through your own hard work + + align:start position:0% +propagating through your own hard work + + + align:start position:0% +propagating through your own hard work +you probably know that when you solve a + + align:start position:0% +you probably know that when you solve a + + + align:start position:0% +you probably know that when you solve a +lower triangular matrix people over a + + align:start position:0% +lower triangular matrix people over a + + + align:start position:0% +lower triangular matrix people over a +written code that backhauls the lower + + align:start position:0% +written code that backhauls the lower + + + align:start position:0% +written code that backhauls the lower +triangular matrix the back the big back + + align:start position:0% +triangular matrix the back the big back + + + align:start position:0% +triangular matrix the back the big back +piece has already been implemented for + + align:start position:0% +piece has already been implemented for + + + align:start position:0% +piece has already been implemented for +you why do it why reinvent the wheel in + + align:start position:0% +you why do it why reinvent the wheel in + + + align:start position:0% +you why do it why reinvent the wheel in +back propagation at the back of linear + + align:start position:0% +back propagation at the back of linear + + + align:start position:0% +back propagation at the back of linear +algebra already has the back you see I + + align:start position:0% +algebra already has the back you see I + + + align:start position:0% +algebra already has the back you see I +mean so if you just do this and you do + + align:start position:0% +mean so if you just do this and you do + + + align:start position:0% +mean so if you just do this and you do +it in a language to let you get full + + align:start position:0% +it in a language to let you get full + + + align:start position:0% +it in a language to let you get full +full performance you don't need to do + + align:start position:0% +full performance you don't need to do + + + align:start position:0% +full performance you don't need to do +your own back propagation because a + + align:start position:0% +your own back propagation because a + + + align:start position:0% +your own back propagation because a +simple backslash will do it for you so I + + align:start position:0% +simple backslash will do it for you so I + + + align:start position:0% +simple backslash will do it for you so I +apologize for going over I know if + + align:start position:0% +apologize for going over I know if + + + align:start position:0% +apologize for going over I know if +professor Strang got some final words + + align:start position:0% +professor Strang got some final words + + + align:start position:0% +professor Strang got some final words +but but anyway the linear algebra is a + + align:start position:0% +but but anyway the linear algebra is a + + + align:start position:0% +but but anyway the linear algebra is a +secret to everything that's that's the + + align:start position:0% +secret to everything that's that's the + + + align:start position:0% +secret to everything that's that's the +big message + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +since it's our last two minutes or minus + + align:start position:0% +since it's our last two minutes or minus + + + align:start position:0% +since it's our last two minutes or minus +two minutes of 1806 five let me just I + + align:start position:0% +two minutes of 1806 five let me just I + + + align:start position:0% +two minutes of 1806 five let me just I +hope you guys enjoyed it I certainly + + align:start position:0% +hope you guys enjoyed it I certainly + + + align:start position:0% +hope you guys enjoyed it I certainly +enjoyed as you could tell teaching this + + align:start position:0% +enjoyed as you could tell teaching this + + + align:start position:0% +enjoyed as you could tell teaching this +class seeing how it would go and writing + + align:start position:0% +class seeing how it would go and writing + + + align:start position:0% +class seeing how it would go and writing +about it + + align:start position:0% +about it + + + align:start position:0% +about it +so I'll let you know was about the + + align:start position:0% +so I'll let you know was about the + + + align:start position:0% +so I'll let you know was about the +writing and meanwhile I'll get your + + align:start position:0% +writing and meanwhile I'll get your + + + align:start position:0% +writing and meanwhile I'll get your +writing on the projects which I + + align:start position:0% +writing on the projects which I + + + align:start position:0% +writing on the projects which I +appreciate very much and of course + + align:start position:0% +appreciate very much and of course + + + align:start position:0% +appreciate very much and of course +grades are going to come out well and I + + align:start position:0% +grades are going to come out well and I + + + align:start position:0% +grades are going to come out well and I +hope you've enjoyed it so thank you all + + align:start position:0% +hope you've enjoyed it so thank you all + + + align:start position:0% +hope you've enjoyed it so thank you all +right thanks + + align:start position:0% +right thanks + + + align:start position:0% +right thanks +[Applause] \ No newline at end of file diff --git a/sjgFbLjMgZw.txt b/sjgFbLjMgZw.txt new file mode 100644 index 0000000000000000000000000000000000000000..d2542f7764f54e07db53ec8f9e82616461098653 --- /dev/null +++ b/sjgFbLjMgZw.txt @@ -0,0 +1,3979 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Okay, this is this is what we use called + + align:start position:0% +Okay, this is this is what we use called + + + align:start position:0% +Okay, this is this is what we use called +ACE uh competitive excellence and it's + + align:start position:0% +ACE uh competitive excellence and it's + + + align:start position:0% +ACE uh competitive excellence and it's +not only at Pratt and Whitney. United + + align:start position:0% +not only at Pratt and Whitney. United + + + align:start position:0% +not only at Pratt and Whitney. United +Technologies is Otis, Carrier, Sakorski, + + align:start position:0% +Technologies is Otis, Carrier, Sakorski, + + + align:start position:0% +Technologies is Otis, Carrier, Sakorski, +um Fire and Chub. I mean they have a lot + + align:start position:0% +um Fire and Chub. I mean they have a lot + + + align:start position:0% +um Fire and Chub. I mean they have a lot +of different divisions but we all are + + align:start position:0% +of different divisions but we all are + + + align:start position:0% +of different divisions but we all are +working to the ACE competitive + + align:start position:0% +working to the ACE competitive + + + align:start position:0% +working to the ACE competitive +excellence operating system. + + align:start position:0% +excellence operating system. + + + align:start position:0% +excellence operating system. +It defines daily management system. It + + align:start position:0% +It defines daily management system. It + + + align:start position:0% +It defines daily management system. It +defines the human wear. It defines the + + align:start position:0% +defines the human wear. It defines the + + + align:start position:0% +defines the human wear. It defines the +culture, the hardware, and the + + align:start position:0% +culture, the hardware, and the + + + align:start position:0% +culture, the hardware, and the +competency. Which one up here is the + + align:start position:0% +competency. Which one up here is the + + + align:start position:0% +competency. Which one up here is the +hardest one to + + align:start position:0% +hardest one to + + + align:start position:0% +hardest one to +do? + + align:start position:0% +do? + + + align:start position:0% +do? +Culture. All of you guys here are super + + align:start position:0% +Culture. All of you guys here are super + + + align:start position:0% +Culture. All of you guys here are super +smart. You guys could probably write + + align:start position:0% +smart. You guys could probably write + + + align:start position:0% +smart. You guys could probably write +programs and do all kinds of neat things + + align:start position:0% +programs and do all kinds of neat things + + + align:start position:0% +programs and do all kinds of neat things +and really get things going. But the + + align:start position:0% +and really get things going. But the + + + align:start position:0% +and really get things going. But the +hardest part of this is the people. + + align:start position:0% +hardest part of this is the people. + + + align:start position:0% +hardest part of this is the people. +If you don't have the people engaged and + + align:start position:0% +If you don't have the people engaged and + + + align:start position:0% +If you don't have the people engaged and +if they don't see what's in it for them, + + align:start position:0% +if they don't see what's in it for them, + + + align:start position:0% +if they don't see what's in it for them, +it's not going to + + align:start position:0% +it's not going to + + + align:start position:0% +it's not going to +happen. What else does it take? Can I + + align:start position:0% +happen. What else does it take? Can I + + + align:start position:0% +happen. What else does it take? Can I +just walk into Pratt and Whitney, go to + + align:start position:0% +just walk into Pratt and Whitney, go to + + + align:start position:0% +just walk into Pratt and Whitney, go to +my desk, sit down and say, "Boy, I want + + align:start position:0% +my desk, sit down and say, "Boy, I want + + + align:start position:0% +my desk, sit down and say, "Boy, I want +us to be ace gold. I want to be the best + + align:start position:0% +us to be ace gold. I want to be the best + + + align:start position:0% +us to be ace gold. I want to be the best +best company in the world." What does it + + align:start position:0% +best company in the world." What does it + + + align:start position:0% +best company in the world." What does it +take? + + align:start position:0% +take? + + + align:start position:0% +take? +Commitment. Commitment from whom? + + align:start position:0% + + + + align:start position:0% + +sponsorship from your higherups. + + align:start position:0% +sponsorship from your higherups. + + + align:start position:0% +sponsorship from your higherups. +Correct. You have to have sponsorship + + align:start position:0% +Correct. You have to have sponsorship + + + align:start position:0% +Correct. You have to have sponsorship +from the higherups. It has to be part of + + align:start position:0% +from the higherups. It has to be part of + + + align:start position:0% +from the higherups. It has to be part of +the culture. It's a it's a set of tools. + + align:start position:0% +the culture. It's a it's a set of tools. + + + align:start position:0% +the culture. It's a it's a set of tools. +It's a way to to do continuous + + align:start position:0% +It's a way to to do continuous + + + align:start position:0% +It's a way to to do continuous +improvement. And competency is really + + align:start position:0% +improvement. And competency is really + + + align:start position:0% +improvement. And competency is really +just the training part of it. Making + + align:start position:0% +just the training part of it. Making + + + align:start position:0% +just the training part of it. Making +sure that people understand the common + + align:start position:0% +sure that people understand the common + + + align:start position:0% +sure that people understand the common +language across. The really neat thing + + align:start position:0% +language across. The really neat thing + + + align:start position:0% +language across. The really neat thing +about achieving competitive excellence. + + align:start position:0% +about achieving competitive excellence. + + + align:start position:0% +about achieving competitive excellence. +How many of you have ever heard about + + align:start position:0% +How many of you have ever heard about + + + align:start position:0% +How many of you have ever heard about +ACE achieving competitive excellence and + + align:start position:0% +ACE achieving competitive excellence and + + + align:start position:0% +ACE achieving competitive excellence and +you can't raise your hand? No, I know + + align:start position:0% +you can't raise your hand? No, I know + + + align:start position:0% +you can't raise your hand? No, I know +you can't raise your hand in the back. + + align:start position:0% +you can't raise your hand in the back. + + + align:start position:0% +you can't raise your hand in the back. +It is like six sigma lean to United + + align:start position:0% +It is like six sigma lean to United + + + align:start position:0% +It is like six sigma lean to United +Technologies. It's the same. It has the + + align:start position:0% +Technologies. It's the same. It has the + + + align:start position:0% +Technologies. It's the same. It has the +same. We have what we call process + + align:start position:0% +same. We have what we call process + + + align:start position:0% +same. We have what we call process +certification. It talks about the upper + + align:start position:0% +certification. It talks about the upper + + + align:start position:0% +certification. It talks about the upper +and lower control limits for statistical + + align:start position:0% +and lower control limits for statistical + + + align:start position:0% +and lower control limits for statistical +control. It's our six sigma program. So + + align:start position:0% +control. It's our six sigma program. So + + + align:start position:0% +control. It's our six sigma program. So +if you're ever out and about with maybe + + align:start position:0% +if you're ever out and about with maybe + + + align:start position:0% +if you're ever out and about with maybe +Carrie or Sakorski and somebody says + + align:start position:0% +Carrie or Sakorski and somebody says + + + align:start position:0% +Carrie or Sakorski and somebody says +Ace, that's what they're talking + + align:start position:0% +Ace, that's what they're talking + + + align:start position:0% +Ace, that's what they're talking +about. George David. How many of you + + align:start position:0% +about. George David. How many of you + + + align:start position:0% +about. George David. How many of you +ever heard of George + + align:start position:0% +ever heard of George + + + align:start position:0% +ever heard of George +David? Well, nobody back here. Nobody + + align:start position:0% +David? Well, nobody back here. Nobody + + + align:start position:0% +David? Well, nobody back here. Nobody +here. He is our + + align:start position:0% +here. He is our + + + align:start position:0% +here. He is our +CEO and he's retiring this year and + + align:start position:0% +CEO and he's retiring this year and + + + align:start position:0% +CEO and he's retiring this year and +Louis Shenevir is going to be taking + + align:start position:0% +Louis Shenevir is going to be taking + + + align:start position:0% +Louis Shenevir is going to be taking +over. But George David truly believes in + + align:start position:0% +over. But George David truly believes in + + + align:start position:0% +over. But George David truly believes in +ACE achieving competitive excellence. He + + align:start position:0% +ACE achieving competitive excellence. He + + + align:start position:0% +ACE achieving competitive excellence. He +is a he'll go to Wall Street. He talks + + align:start position:0% +is a he'll go to Wall Street. He talks + + + align:start position:0% +is a he'll go to Wall Street. He talks +about it. He believes it. And if you + + align:start position:0% +about it. He believes it. And if you + + + align:start position:0% +about it. He believes it. And if you +just read this comment here, that was in + + align:start position:0% +just read this comment here, that was in + + + align:start position:0% +just read this comment here, that was in +2003, but if you look in articles in + + align:start position:0% +2003, but if you look in articles in + + + align:start position:0% +2003, but if you look in articles in +Business Week, he was named CEO of the + + align:start position:0% +Business Week, he was named CEO of the + + + align:start position:0% +Business Week, he was named CEO of the +decade in + + align:start position:0% +decade in + + + align:start position:0% +decade in +2006. And he is a strong driver behind + + align:start position:0% +2006. And he is a strong driver behind + + + align:start position:0% +2006. And he is a strong driver behind +us. + + align:start position:0% +us. + + + align:start position:0% +us. +And why is why why what what makes it + + align:start position:0% + + + + align:start position:0% + +important good quality delighted + + align:start position:0% +important good quality delighted + + + align:start position:0% +important good quality delighted +customers also looking at employee + + align:start position:0% +customers also looking at employee + + + align:start position:0% +customers also looking at employee +fulfillment also looking at + + align:start position:0% +fulfillment also looking at + + + align:start position:0% +fulfillment also looking at +EHNS environmental health and safety and + + align:start position:0% +EHNS environmental health and safety and + + + align:start position:0% +EHNS environmental health and safety and +it's also looking at even though the + + align:start position:0% +it's also looking at even though the + + + align:start position:0% +it's also looking at even though the +stock market's been doing lousy the + + align:start position:0% +stock market's been doing lousy the + + + align:start position:0% +stock market's been doing lousy the +stockholders it's all plays + + align:start position:0% + + + + align:start position:0% + +together and it's a common language for + + align:start position:0% +together and it's a common language for + + + align:start position:0% +together and it's a common language for +many many years at Pratt. I've been at + + align:start position:0% +many many years at Pratt. I've been at + + + align:start position:0% +many many years at Pratt. I've been at +Pratt for a long time and you'd had the + + align:start position:0% +Pratt for a long time and you'd had the + + + align:start position:0% +Pratt for a long time and you'd had the +flavor of the month TQM work + + align:start position:0% +flavor of the month TQM work + + + align:start position:0% +flavor of the month TQM work +simplification Q+ but if you went + + align:start position:0% +simplification Q+ but if you went + + + align:start position:0% +simplification Q+ but if you went +outside of Prattton Whitney and went to + + align:start position:0% +outside of Prattton Whitney and went to + + + align:start position:0% +outside of Prattton Whitney and went to +another division in United + + align:start position:0% +another division in United + + + align:start position:0% +another division in United +Technologies they didn't know what you + + align:start position:0% +Technologies they didn't know what you + + + align:start position:0% +Technologies they didn't know what you +were talking about. Nobody spoke the + + align:start position:0% +were talking about. Nobody spoke the + + + align:start position:0% +were talking about. Nobody spoke the +same language. So ACE is a common + + align:start position:0% +same language. So ACE is a common + + + align:start position:0% +same language. So ACE is a common +language across all + + align:start position:0% + + + + align:start position:0% + +divisions + + align:start position:0% +divisions + + + align:start position:0% +divisions +culture. I can tell you when I walk into + + align:start position:0% +culture. I can tell you when I walk into + + + align:start position:0% +culture. I can tell you when I walk into +a + + align:start position:0% +a + + + align:start position:0% +a +plant, you can see it. You actually + + align:start position:0% +plant, you can see it. You actually + + + align:start position:0% +plant, you can see it. You actually +truly can see an ACE organization, a + + align:start position:0% +truly can see an ACE organization, a + + + align:start position:0% +truly can see an ACE organization, a +gold organization. And I'll talk about + + align:start position:0% +gold organization. And I'll talk about + + + align:start position:0% +gold organization. And I'll talk about +the different levels coming up here. And + + align:start position:0% +the different levels coming up here. And + + + align:start position:0% +the different levels coming up here. And +top line, leadership is engaged at all + + align:start position:0% +top line, leadership is engaged at all + + + align:start position:0% +top line, leadership is engaged at all +levels. + + align:start position:0% +levels. + + + align:start position:0% +levels. +And I don't see our our friend from the + + align:start position:0% +And I don't see our our friend from the + + + align:start position:0% +And I don't see our our friend from the +army back there. You were talking about + + align:start position:0% +army back there. You were talking about + + + align:start position:0% +army back there. You were talking about +the frozen middle. Yeah, we have the + + align:start position:0% +the frozen middle. Yeah, we have the + + + align:start position:0% +the frozen middle. Yeah, we have the +frozen middle, too. We have lots of + + align:start position:0% +frozen middle, too. We have lots of + + + align:start position:0% +frozen middle, too. We have lots of +excitement down here. Lots of excitement + + align:start position:0% +excitement down here. Lots of excitement + + + align:start position:0% +excitement down here. Lots of excitement +here, but we're having a little problem + + align:start position:0% +here, but we're having a little problem + + + align:start position:0% +here, but we're having a little problem +with the middle part, but we're getting + + align:start position:0% +with the middle part, but we're getting + + + align:start position:0% +with the middle part, but we're getting +there. Pratt uh has been doing this + + align:start position:0% +there. Pratt uh has been doing this + + + align:start position:0% +there. Pratt uh has been doing this +since + + align:start position:0% +since + + + align:start position:0% +since +1996. And at Prattton Whitney right now, + + align:start position:0% +1996. And at Prattton Whitney right now, + + + align:start position:0% +1996. And at Prattton Whitney right now, +we have + + align:start position:0% +we have + + + align:start position:0% +we have +22% gold sites. + + align:start position:0% +22% gold sites. + + + align:start position:0% +22% gold sites. +This is 2008, ladies and gentlemen. So + + align:start position:0% +This is 2008, ladies and gentlemen. So + + + align:start position:0% +This is 2008, ladies and gentlemen. So +that should tell you how long this + + align:start position:0% +that should tell you how long this + + + align:start position:0% +that should tell you how long this +process takes. It's a slow, slow + + align:start position:0% +process takes. It's a slow, slow + + + align:start position:0% +process takes. It's a slow, slow +process, but once you get it going, it's + + align:start position:0% +process, but once you get it going, it's + + + align:start position:0% +process, but once you get it going, it's +amazing. Should look kind of + + align:start position:0% +amazing. Should look kind of + + + align:start position:0% +amazing. Should look kind of +familiar. It's a learning process when + + align:start position:0% +familiar. It's a learning process when + + + align:start position:0% +familiar. It's a learning process when +you first start continuous improvement. + + align:start position:0% +you first start continuous improvement. + + + align:start position:0% +you first start continuous improvement. +A lot of people think, well, I'm going + + align:start position:0% +A lot of people think, well, I'm going + + + align:start position:0% +A lot of people think, well, I'm going +to move the waste paper can from that + + align:start position:0% +to move the waste paper can from that + + + align:start position:0% +to move the waste paper can from that +corner of the room to the other corner + + align:start position:0% +corner of the room to the other corner + + + align:start position:0% +corner of the room to the other corner +of the room and I'm saving steps. You + + align:start position:0% +of the room and I'm saving steps. You + + + align:start position:0% +of the room and I'm saving steps. You +got to think bigger, guys and gals. + + align:start position:0% +got to think bigger, guys and gals. + + + align:start position:0% +got to think bigger, guys and gals. +You've got to think bigger. What is the + + align:start position:0% +You've got to think bigger. What is the + + + align:start position:0% +You've got to think bigger. What is the +customer? What are your objectives for + + align:start position:0% +customer? What are your objectives for + + + align:start position:0% +customer? What are your objectives for +the company? Where are what's your + + align:start position:0% +the company? Where are what's your + + + align:start position:0% +the company? Where are what's your +business strategy? Somebody was talking + + align:start position:0% +business strategy? Somebody was talking + + + align:start position:0% +business strategy? Somebody was talking +earlier today about you need to look at + + align:start position:0% +earlier today about you need to look at + + + align:start position:0% +earlier today about you need to look at +the projects that have the most value. + + align:start position:0% +the projects that have the most value. + + + align:start position:0% +the projects that have the most value. +What is what's going to make some impact + + align:start position:0% +What is what's going to make some impact + + + align:start position:0% +What is what's going to make some impact +to the company? How are you going to + + align:start position:0% +to the company? How are you going to + + + align:start position:0% +to the company? How are you going to +really show some results? And so you + + align:start position:0% +really show some results? And so you + + + align:start position:0% +really show some results? And so you +need to look at the customer business + + align:start position:0% +need to look at the customer business + + + align:start position:0% +need to look at the customer business +strategy. Where are some of the + + align:start position:0% +strategy. Where are some of the + + + align:start position:0% +strategy. Where are some of the +opportunities discrepancy? Here's + + align:start position:0% +opportunities discrepancy? Here's + + + align:start position:0% +opportunities discrepancy? Here's +quality and your + + align:start position:0% +quality and your + + + align:start position:0% +quality and your +processes. And now you ref you referred + + align:start position:0% +processes. And now you ref you referred + + + align:start position:0% +processes. And now you ref you referred +earlier today about they talk about + + align:start position:0% +earlier today about they talk about + + + align:start position:0% +earlier today about they talk about +process flow and looking for problems. + + align:start position:0% +process flow and looking for problems. + + + align:start position:0% +process flow and looking for problems. +You do a value stream map, you see the + + align:start position:0% +You do a value stream map, you see the + + + align:start position:0% +You do a value stream map, you see the +problems. I mean, I'm not quite sure why + + align:start position:0% +problems. I mean, I'm not quite sure why + + + align:start position:0% +problems. I mean, I'm not quite sure why +they separate those two, but it's + + align:start position:0% +they separate those two, but it's + + + align:start position:0% +they separate those two, but it's +interesting. Here's any of you familiar + + align:start position:0% +interesting. Here's any of you familiar + + + align:start position:0% +interesting. Here's any of you familiar +with + + align:start position:0% +with + + + align:start position:0% +with +Deming? I should see a for a few more + + align:start position:0% +Deming? I should see a for a few more + + + align:start position:0% +Deming? I should see a for a few more +hands than just a couple. Plan, do, + + align:start position:0% +hands than just a couple. Plan, do, + + + align:start position:0% +hands than just a couple. Plan, do, +check, act, folks. It's the continuous + + align:start position:0% +check, act, folks. It's the continuous + + + align:start position:0% +check, act, folks. It's the continuous +cycle of improvement. Why do they call + + align:start position:0% +cycle of improvement. Why do they call + + + align:start position:0% +cycle of improvement. Why do they call +it continuous + + align:start position:0% + + + + align:start position:0% + +improvement? Never + + align:start position:0% +improvement? Never + + + align:start position:0% +improvement? Never +ends. You just keep improving. You keep + + align:start position:0% +ends. You just keep improving. You keep + + + align:start position:0% +ends. You just keep improving. You keep +improving. You establish your vision, + + align:start position:0% +improving. You establish your vision, + + + align:start position:0% +improving. You establish your vision, +your goals, your + + align:start position:0% +your goals, your + + + align:start position:0% +your goals, your +strategy. Metrics is perhaps one of the + + align:start position:0% +strategy. Metrics is perhaps one of the + + + align:start position:0% +strategy. Metrics is perhaps one of the +most challenging parts of doing + + align:start position:0% +most challenging parts of doing + + + align:start position:0% +most challenging parts of doing +continuous improvement. I cannot tell + + align:start position:0% +continuous improvement. I cannot tell + + + align:start position:0% +continuous improvement. I cannot tell +you how many projects I walked in on and + + align:start position:0% +you how many projects I walked in on and + + + align:start position:0% +you how many projects I walked in on and +said, "Hey guys, what are you going to + + align:start position:0% +said, "Hey guys, what are you going to + + + align:start position:0% +said, "Hey guys, what are you going to +measure? Is it throughput? Is it, you + + align:start position:0% +measure? Is it throughput? Is it, you + + + align:start position:0% +measure? Is it throughput? Is it, you +know, improving your schedule? What are + + align:start position:0% +know, improving your schedule? What are + + + align:start position:0% +know, improving your schedule? What are +you trying to do? What's your metric? + + align:start position:0% +you trying to do? What's your metric? + + + align:start position:0% +you trying to do? What's your metric? +How you going to measure the + + align:start position:0% +How you going to measure the + + + align:start position:0% +How you going to measure the +improvement?" Very, very key. and + + align:start position:0% +improvement?" Very, very key. and + + + align:start position:0% +improvement?" Very, very key. and +identifying gaps. Now, I've heard you + + align:start position:0% +identifying gaps. Now, I've heard you + + + align:start position:0% +identifying gaps. Now, I've heard you +guys talk about root cause analysis. + + align:start position:0% +guys talk about root cause analysis. + + + align:start position:0% +guys talk about root cause analysis. +Have they gone through root cause five + + align:start position:0% +Have they gone through root cause five + + + align:start position:0% +Have they gone through root cause five +W's fishbone diagram? + + align:start position:0% +W's fishbone diagram? + + + align:start position:0% +W's fishbone diagram? +Okay. Now, does any of this look + + align:start position:0% +Okay. Now, does any of this look + + + align:start position:0% +Okay. Now, does any of this look +familiar? But you see the title, it's + + align:start position:0% +familiar? But you see the title, it's + + + align:start position:0% +familiar? But you see the title, it's +the + + align:start position:0% +the + + + align:start position:0% +the +same 5S, 6S, value stream management, + + align:start position:0% +same 5S, 6S, value stream management, + + + align:start position:0% +same 5S, 6S, value stream management, +process control, and certification. Once + + align:start position:0% +process control, and certification. Once + + + align:start position:0% +process control, and certification. Once +again, that's our six sigma. That's how + + align:start position:0% +again, that's our six sigma. That's how + + + align:start position:0% +again, that's our six sigma. That's how +we do processert to make sure that we + + align:start position:0% +we do processert to make sure that we + + + align:start position:0% +we do processert to make sure that we +have things under control and measuring + + align:start position:0% +have things under control and measuring + + + align:start position:0% +have things under control and measuring +the variation. + + align:start position:0% +the variation. + + + align:start position:0% +the variation. +3P total product maintenance. Yes, we + + align:start position:0% +3P total product maintenance. Yes, we + + + align:start position:0% +3P total product maintenance. Yes, we +did talk about P total maintenance + + align:start position:0% +did talk about P total maintenance + + + align:start position:0% +did talk about P total maintenance +instead of + + align:start position:0% +instead of + + + align:start position:0% +instead of +Okay, these are more for like + + align:start position:0% +Okay, these are more for like + + + align:start position:0% +Okay, these are more for like +manufacturing + + align:start position:0% +manufacturing + + + align:start position:0% +manufacturing +uh + + align:start position:0% +uh + + + align:start position:0% +uh +opportunities, production prep, + + align:start position:0% +opportunities, production prep, + + + align:start position:0% +opportunities, production prep, +preparation process. + + align:start position:0% +preparation process. + + + align:start position:0% +preparation process. +Sounds kind of crazy, but they they did + + align:start position:0% +Sounds kind of crazy, but they they did + + + align:start position:0% +Sounds kind of crazy, but they they did +this at Hamilton Sunstrand in Prattton + + align:start position:0% +this at Hamilton Sunstrand in Prattton + + + align:start position:0% +this at Hamilton Sunstrand in Prattton +Whitney, Canada. And I wish I would have + + align:start position:0% +Whitney, Canada. And I wish I would have + + + align:start position:0% +Whitney, Canada. And I wish I would have +brought you the videos because it's + + align:start position:0% +brought you the videos because it's + + + align:start position:0% +brought you the videos because it's +really cool. What they'll do is they'll + + align:start position:0% +really cool. What they'll do is they'll + + + align:start position:0% +really cool. What they'll do is they'll +they'll just lay it out with cardboard + + align:start position:0% +they'll just lay it out with cardboard + + + align:start position:0% +they'll just lay it out with cardboard +and actually run through the process to + + align:start position:0% +and actually run through the process to + + + align:start position:0% +and actually run through the process to +see where they can improve things. And + + align:start position:0% +see where they can improve things. And + + + align:start position:0% +see where they can improve things. And +it's a way of designing ahead of time + + align:start position:0% +it's a way of designing ahead of time + + + align:start position:0% +it's a way of designing ahead of time +instead of setting up the manufacturing + + align:start position:0% +instead of setting up the manufacturing + + + align:start position:0% +instead of setting up the manufacturing +area and floor without actually thinking + + align:start position:0% +area and floor without actually thinking + + + align:start position:0% +area and floor without actually thinking +about what the flow is going to be. It's + + align:start position:0% +about what the flow is going to be. It's + + + align:start position:0% +about what the flow is going to be. It's +very very useful. Market feedback + + align:start position:0% +very very useful. Market feedback + + + align:start position:0% +very very useful. Market feedback +analysis. Oh, excuse me. + + align:start position:0% + + + + align:start position:0% + +TPM. When you have a machine, you need + + align:start position:0% +TPM. When you have a machine, you need + + + align:start position:0% +TPM. When you have a machine, you need +to keep it working. How do you do that? + + align:start position:0% +to keep it working. How do you do that? + + + align:start position:0% +to keep it working. How do you do that? +You keep ensuring that it's working and + + align:start position:0% +You keep ensuring that it's working and + + + align:start position:0% +You keep ensuring that it's working and +you keep taking care of it. How many of + + align:start position:0% +you keep taking care of it. How many of + + + align:start position:0% +you keep taking care of it. How many of +you change your oil on your car? + + align:start position:0% + + + + align:start position:0% + +I This gentleman here, Harvey, you're + + align:start position:0% +I This gentleman here, Harvey, you're + + + align:start position:0% +I This gentleman here, Harvey, you're +scaring me. you you you're like, "Well, + + align:start position:0% +scaring me. you you you're like, "Well, + + + align:start position:0% +scaring me. you you you're like, "Well, +maybe when was the last time you changed + + align:start position:0% +maybe when was the last time you changed + + + align:start position:0% +maybe when was the last time you changed +oil?" I asked my dad to do it. Oh, okay. + + align:start position:0% +oil?" I asked my dad to do it. Oh, okay. + + + align:start position:0% +oil?" I asked my dad to do it. Oh, okay. +Okay. And setup reduction. That's just a + + align:start position:0% +Okay. And setup reduction. That's just a + + + align:start position:0% +Okay. And setup reduction. That's just a +way of when they're setting up uh + + align:start position:0% +way of when they're setting up uh + + + align:start position:0% +way of when they're setting up uh +machines, if they're like making this + + align:start position:0% +machines, if they're like making this + + + align:start position:0% +machines, if they're like making this +part, what do you have to do to to set + + align:start position:0% +part, what do you have to do to to set + + + align:start position:0% +part, what do you have to do to to set +up the part in the machine and how can + + align:start position:0% +up the part in the machine and how can + + + align:start position:0% +up the part in the machine and how can +you improve on that process? And there's + + align:start position:0% +you improve on that process? And there's + + + align:start position:0% +you improve on that process? And there's +a lot of work that can be done in that + + align:start position:0% +a lot of work that can be done in that + + + align:start position:0% +a lot of work that can be done in that +area. And that's another thing too. + + align:start position:0% +area. And that's another thing too. + + + align:start position:0% +area. And that's another thing too. +Prattton Whitney. Uh we've been in with + + align:start position:0% +Prattton Whitney. Uh we've been in with + + + align:start position:0% +Prattton Whitney. Uh we've been in with +a lean book. We've been written up in + + align:start position:0% +a lean book. We've been written up in + + + align:start position:0% +a lean book. We've been written up in +some books. Jim Walmack has written + + align:start position:0% +some books. Jim Walmack has written + + + align:start position:0% +some books. Jim Walmack has written +about us. First off, we started in the + + align:start position:0% +about us. First off, we started in the + + + align:start position:0% +about us. First off, we started in the +manufacturing floor. Boy, there's lots + + align:start position:0% +manufacturing floor. Boy, there's lots + + + align:start position:0% +manufacturing floor. Boy, there's lots +of things to do in the manufacturing + + align:start position:0% +of things to do in the manufacturing + + + align:start position:0% +of things to do in the manufacturing +floor and they really went out there and + + align:start position:0% +floor and they really went out there and + + + align:start position:0% +floor and they really went out there and +fixed things. But then they realized + + align:start position:0% +fixed things. But then they realized + + + align:start position:0% +fixed things. But then they realized +it's above the floor. That's your + + align:start position:0% +it's above the floor. That's your + + + align:start position:0% +it's above the floor. That's your +opportunities. Now, we're dealing with + + align:start position:0% +opportunities. Now, we're dealing with + + + align:start position:0% +opportunities. Now, we're dealing with +our friends in engineering and that's + + align:start position:0% +our friends in engineering and that's + + + align:start position:0% +our friends in engineering and that's +that's another story, but we're getting + + align:start position:0% +that's another story, but we're getting + + + align:start position:0% +that's another story, but we're getting +there. and uh trying to get them to + + align:start position:0% +there. and uh trying to get them to + + + align:start position:0% +there. and uh trying to get them to +understand how important it is uh to + + align:start position:0% +understand how important it is uh to + + + align:start position:0% +understand how important it is uh to +improve and to design ahead of time + + align:start position:0% +improve and to design ahead of time + + + align:start position:0% +improve and to design ahead of time +instead of waiting until something + + align:start position:0% +instead of waiting until something + + + align:start position:0% +instead of waiting until something +happens and then fixing it. Market + + align:start position:0% +happens and then fixing it. Market + + + align:start position:0% +happens and then fixing it. Market +feedback analysis, that's just a way of + + align:start position:0% +feedback analysis, that's just a way of + + + align:start position:0% +feedback analysis, that's just a way of +getting customer feedback. I think you + + align:start position:0% +getting customer feedback. I think you + + + align:start position:0% +getting customer feedback. I think you +guys are probably going to be filling + + align:start position:0% +guys are probably going to be filling + + + align:start position:0% +guys are probably going to be filling +out a customer feed at the end of the + + align:start position:0% +out a customer feed at the end of the + + + align:start position:0% +out a customer feed at the end of the +class. I hope. Okay. QCPC. This is a way + + align:start position:0% +class. I hope. Okay. QCPC. This is a way + + + align:start position:0% +class. I hope. Okay. QCPC. This is a way +that we collect what we call + + align:start position:0% +that we collect what we call + + + align:start position:0% +that we collect what we call +opportunities. When you're doing a + + align:start position:0% +opportunities. When you're doing a + + + align:start position:0% +opportunities. When you're doing a +process, is there anything that impedes + + align:start position:0% +process, is there anything that impedes + + + align:start position:0% +process, is there anything that impedes +the process? Like if I'm making this + + align:start position:0% +the process? Like if I'm making this + + + align:start position:0% +the process? Like if I'm making this +this book over here and I can't get the + + align:start position:0% +this book over here and I can't get the + + + align:start position:0% +this book over here and I can't get the +printer to fix that label, that would be + + align:start position:0% +printer to fix that label, that would be + + + align:start position:0% +printer to fix that label, that would be +considered a turnback. And you collect + + align:start position:0% +considered a turnback. And you collect + + + align:start position:0% +considered a turnback. And you collect +that data. And like you were saying + + align:start position:0% +that data. And like you were saying + + + align:start position:0% +that data. And like you were saying +before, it is absolutely data driven. + + align:start position:0% +before, it is absolutely data driven. + + + align:start position:0% +before, it is absolutely data driven. +Steve Finger, the president of uh Pratt + + align:start position:0% +Steve Finger, the president of uh Pratt + + + align:start position:0% +Steve Finger, the president of uh Pratt +and Whitney, is absolutely passionate + + align:start position:0% +and Whitney, is absolutely passionate + + + align:start position:0% +and Whitney, is absolutely passionate +about this discussion. + + align:start position:0% +about this discussion. + + + align:start position:0% +about this discussion. +He will say when he's in a meeting with + + align:start position:0% +He will say when he's in a meeting with + + + align:start position:0% +He will say when he's in a meeting with +you and you start waving your hands + + align:start position:0% +you and you start waving your hands + + + align:start position:0% +you and you start waving your hands +about things being wrong, he will say, + + align:start position:0% +about things being wrong, he will say, + + + align:start position:0% +about things being wrong, he will say, +"Show me the data." If you don't have + + align:start position:0% +"Show me the data." If you don't have + + + align:start position:0% +"Show me the data." If you don't have +the data, I don't want to hear the + + align:start position:0% +the data, I don't want to hear the + + + align:start position:0% +the data, I don't want to hear the +discussion. So data is + + align:start position:0% +discussion. So data is + + + align:start position:0% +discussion. So data is +key. Mistake proofing. How many of you + + align:start position:0% +key. Mistake proofing. How many of you + + + align:start position:0% +key. Mistake proofing. How many of you +use computers + + align:start position:0% +use computers + + + align:start position:0% +use computers +here? Okay. How many of you know Bill + + align:start position:0% +here? Okay. How many of you know Bill + + + align:start position:0% +here? Okay. How many of you know Bill +Gates? Mr. + + align:start position:0% +Gates? Mr. + + + align:start position:0% +Gates? Mr. +Gates. Software. Microsoft software. And + + align:start position:0% +Gates. Software. Microsoft software. And + + + align:start position:0% +Gates. Software. Microsoft software. And +some of the things that he's put in + + align:start position:0% +some of the things that he's put in + + + align:start position:0% +some of the things that he's put in +there is mistake proofing to make sure + + align:start position:0% +there is mistake proofing to make sure + + + align:start position:0% +there is mistake proofing to make sure +you don't make mistakes, + + align:start position:0% +you don't make mistakes, + + + align:start position:0% +you don't make mistakes, +errors. This is something very unique to + + align:start position:0% +errors. This is something very unique to + + + align:start position:0% +errors. This is something very unique to +Pratt and Whitney. I'm not sure if this + + align:start position:0% +Pratt and Whitney. I'm not sure if this + + + align:start position:0% +Pratt and Whitney. I'm not sure if this +is across the industry. What happens is + + align:start position:0% +is across the industry. What happens is + + + align:start position:0% +is across the industry. What happens is +like when you're designing an engine, + + align:start position:0% +like when you're designing an engine, + + + align:start position:0% +like when you're designing an engine, +takes years to design an engine. There's + + align:start position:0% +takes years to design an engine. There's + + + align:start position:0% +takes years to design an engine. There's +processes and gates that you go through. + + align:start position:0% +processes and gates that you go through. + + + align:start position:0% +processes and gates that you go through. +The passport + + align:start position:0% +The passport + + + align:start position:0% +The passport +process checks throughout the life cycle + + align:start position:0% +process checks throughout the life cycle + + + align:start position:0% +process checks throughout the life cycle +of that engine to ensure that you don't + + align:start position:0% +of that engine to ensure that you don't + + + align:start position:0% +of that engine to ensure that you don't +go to market at the wrong time that you + + align:start position:0% +go to market at the wrong time that you + + + align:start position:0% +go to market at the wrong time that you +are developing something that's not + + align:start position:0% +are developing something that's not + + + align:start position:0% +are developing something that's not +technically sound. It's a way to + + align:start position:0% +technically sound. It's a way to + + + align:start position:0% +technically sound. It's a way to +actually check the process of developing + + align:start position:0% +actually check the process of developing + + + align:start position:0% +actually check the process of developing +an engine to ensure that it's not any + + align:start position:0% +an engine to ensure that it's not any + + + align:start position:0% +an engine to ensure that it's not any +turnbacks. Decision gates decision + + align:start position:0% +turnbacks. Decision gates decision + + + align:start position:0% +turnbacks. Decision gates decision +gates. And we are big on passport + + align:start position:0% +gates. And we are big on passport + + + align:start position:0% +gates. And we are big on passport +process. In fact, we're in the process + + align:start position:0% +process. In fact, we're in the process + + + align:start position:0% +process. In fact, we're in the process +of doing some continuous + + align:start position:0% +of doing some continuous + + + align:start position:0% +of doing some continuous +improvement ACE competencies. Ido + + align:start position:0% +improvement ACE competencies. Ido + + + align:start position:0% +improvement ACE competencies. Ido +University ACE training high impact ace + + align:start position:0% +University ACE training high impact ace + + + align:start position:0% +University ACE training high impact ace +teams great I high impact ace teams are + + align:start position:0% +teams great I high impact ace teams are + + + align:start position:0% +teams great I high impact ace teams are +looking at the big issues throughout the + + align:start position:0% +looking at the big issues throughout the + + + align:start position:0% +looking at the big issues throughout the +company and working across the value + + align:start position:0% +company and working across the value + + + align:start position:0% +company and working across the value +streams and I know you guys talked about + + align:start position:0% +streams and I know you guys talked about + + + align:start position:0% +streams and I know you guys talked about +value streams and I don't know what + + align:start position:0% +value streams and I don't know what + + + align:start position:0% +value streams and I don't know what +level you talked about value streams are + + align:start position:0% +level you talked about value streams are + + + align:start position:0% +level you talked about value streams are +you talking value streams or you talking + + align:start position:0% +you talking value streams or you talking + + + align:start position:0% +you talking value streams or you talking +enterprise value + + align:start position:0% +enterprise value + + + align:start position:0% +enterprise value +streams lower lower + + align:start position:0% +streams lower lower + + + align:start position:0% +streams lower lower +Okay. Someday think higher because it + + align:start position:0% +Okay. Someday think higher because it + + + align:start position:0% +Okay. Someday think higher because it +really Yeah, I know. really makes and + + align:start position:0% +really Yeah, I know. really makes and + + + align:start position:0% +really Yeah, I know. really makes and +sharing of best practices. Pratt Whitney + + align:start position:0% +sharing of best practices. Pratt Whitney + + + align:start position:0% +sharing of best practices. Pratt Whitney +and I think a lot of organizations + + align:start position:0% +and I think a lot of organizations + + + align:start position:0% +and I think a lot of organizations +suffer from this. We don't really take + + align:start position:0% +suffer from this. We don't really take + + + align:start position:0% +suffer from this. We don't really take +the opportunity to share best practices. + + align:start position:0% +the opportunity to share best practices. + + + align:start position:0% +the opportunity to share best practices. +We really don't stop and say good job. + + align:start position:0% +We really don't stop and say good job. + + + align:start position:0% +We really don't stop and say good job. +Now they have developed a web page where + + align:start position:0% +Now they have developed a web page where + + + align:start position:0% +Now they have developed a web page where +they actually put best practices out + + align:start position:0% +they actually put best practices out + + + align:start position:0% +they actually put best practices out +there. + + align:start position:0% +there. + + + align:start position:0% +there. +qualifying bronze, silver, and gold. + + align:start position:0% +qualifying bronze, silver, and gold. + + + align:start position:0% +qualifying bronze, silver, and gold. +These are different levels of ACE + + align:start position:0% +These are different levels of ACE + + + align:start position:0% +These are different levels of ACE +competency. And there's a Shingo jitsu. + + align:start position:0% +competency. And there's a Shingo jitsu. + + + align:start position:0% +competency. And there's a Shingo jitsu. +Am I I don't even know if I'm + + align:start position:0% +Am I I don't even know if I'm + + + align:start position:0% +Am I I don't even know if I'm +pronouncing that right, but they have + + align:start position:0% +pronouncing that right, but they have + + + align:start position:0% +pronouncing that right, but they have +something similar to this. And this + + align:start position:0% +something similar to this. And this + + + align:start position:0% +something similar to this. And this +actually came from the Olympics. And + + align:start position:0% +actually came from the Olympics. And + + + align:start position:0% +actually came from the Olympics. And +believe me, to get to ace gold, you have + + align:start position:0% +believe me, to get to ace gold, you have + + + align:start position:0% +believe me, to get to ace gold, you have +to be 100% on time + + align:start position:0% +to be 100% on time + + + align:start position:0% +to be 100% on time +delivery, zero escapes. I mean, the + + align:start position:0% +delivery, zero escapes. I mean, the + + + align:start position:0% +delivery, zero escapes. I mean, the +metrics are + + align:start position:0% +metrics are + + + align:start position:0% +metrics are +um what what we call a behag. I mean + + align:start position:0% +um what what we call a behag. I mean + + + align:start position:0% +um what what we call a behag. I mean +they are some very very serious metrics + + align:start position:0% +they are some very very serious metrics + + + align:start position:0% +they are some very very serious metrics +to get to ace gold and this is just the + + align:start position:0% +to get to ace gold and this is just the + + + align:start position:0% +to get to ace gold and this is just the +the progression that organizations go + + align:start position:0% +the progression that organizations go + + + align:start position:0% +the progression that organizations go +through. Steve Finger had put out an + + align:start position:0% +through. Steve Finger had put out an + + + align:start position:0% +through. Steve Finger had put out an +edict about two years ago uh by May of + + align:start position:0% +edict about two years ago uh by May of + + + align:start position:0% +edict about two years ago uh by May of +2008. All of Pratt and Whitney would be + + align:start position:0% +2008. All of Pratt and Whitney would be + + + align:start position:0% +2008. All of Pratt and Whitney would be +gold solid + + align:start position:0% +gold solid + + + align:start position:0% +gold solid +gold. + + align:start position:0% +gold. + + + align:start position:0% +gold. +Well, Steve has good intentions. Steve + + align:start position:0% +Well, Steve has good intentions. Steve + + + align:start position:0% +Well, Steve has good intentions. Steve +is a is a great leader. But we're not at + + align:start position:0% +is a is a great leader. But we're not at + + + align:start position:0% +is a is a great leader. But we're not at +ace gold for all of Pratt and Whitney. + + align:start position:0% +ace gold for all of Pratt and Whitney. + + + align:start position:0% +ace gold for all of Pratt and Whitney. +And I think about a month ago he came to + + align:start position:0% +And I think about a month ago he came to + + + align:start position:0% +And I think about a month ago he came to +the actually I was in a meeting with him + + align:start position:0% +the actually I was in a meeting with him + + + align:start position:0% +the actually I was in a meeting with him +in October. He came to the realization + + align:start position:0% +in October. He came to the realization + + + align:start position:0% +in October. He came to the realization +may not get there but it's making a + + align:start position:0% +may not get there but it's making a + + + align:start position:0% +may not get there but it's making a +great strides to get towards that goal + + align:start position:0% +great strides to get towards that goal + + + align:start position:0% +great strides to get towards that goal +and he's he's still pushing it. In fact, + + align:start position:0% +and he's he's still pushing it. In fact, + + + align:start position:0% +and he's he's still pushing it. In fact, +this morning I just received an email at + + align:start position:0% +this morning I just received an email at + + + align:start position:0% +this morning I just received an email at +how excited he is about ACE and where + + align:start position:0% +how excited he is about ACE and where + + + align:start position:0% +how excited he is about ACE and where +it's going and how it's going to help us + + align:start position:0% +it's going and how it's going to help us + + + align:start position:0% +it's going and how it's going to help us +for + + align:start position:0% + + + + align:start position:0% + +2008. Sure. Yeah. One quick question. Is + + align:start position:0% +2008. Sure. Yeah. One quick question. Is + + + align:start position:0% +2008. Sure. Yeah. One quick question. Is +any part of United Technology the + + align:start position:0% +any part of United Technology the + + + align:start position:0% +any part of United Technology the +technology is not um ACE qualifying yet? + + align:start position:0% +technology is not um ACE qualifying yet? + + + align:start position:0% +technology is not um ACE qualifying yet? +There are different segments of it. We + + align:start position:0% +There are different segments of it. We + + + align:start position:0% +There are different segments of it. We +are about 50 51%. There's parts of them + + align:start position:0% +are about 50 51%. There's parts of them + + + align:start position:0% +are about 50 51%. There's parts of them +that are like at 10, you know, very low. + + align:start position:0% +that are like at 10, you know, very low. + + + align:start position:0% +that are like at 10, you know, very low. +They haven't really gone as far. In + + align:start position:0% +They haven't really gone as far. In + + + align:start position:0% +They haven't really gone as far. In +fact, out of all the divisions, Pratt + + align:start position:0% +fact, out of all the divisions, Pratt + + + align:start position:0% +fact, out of all the divisions, Pratt +and Whitney is the leader. But the other + + align:start position:0% +and Whitney is the leader. But the other + + + align:start position:0% +and Whitney is the leader. But the other +ones are still getting there. Yes. With + + align:start position:0% +ones are still getting there. Yes. With + + + align:start position:0% +ones are still getting there. Yes. With +regard to the different levels, are they + + align:start position:0% +regard to the different levels, are they + + + align:start position:0% +regard to the different levels, are they +based on more like a maturity model for + + align:start position:0% +based on more like a maturity model for + + + align:start position:0% +based on more like a maturity model for +adoption of ACE or is it more about + + align:start position:0% +adoption of ACE or is it more about + + + align:start position:0% +adoption of ACE or is it more about +meeting objectives from the business + + align:start position:0% +meeting objectives from the business + + + align:start position:0% +meeting objectives from the business +perspective? Both. when they come out + + align:start position:0% +perspective? Both. when they come out + + + align:start position:0% +perspective? Both. when they come out +and do an ACE assessment from core core + + align:start position:0% +and do an ACE assessment from core core + + + align:start position:0% +and do an ACE assessment from core core +quality, the ACE office, they will look + + align:start position:0% +quality, the ACE office, they will look + + + align:start position:0% +quality, the ACE office, they will look +for your what we have control towers, + + align:start position:0% +for your what we have control towers, + + + align:start position:0% +for your what we have control towers, +which you guys would probably call data + + align:start position:0% +which you guys would probably call data + + + align:start position:0% +which you guys would probably call data +cards or quality cards or whatever that + + align:start position:0% +cards or quality cards or whatever that + + + align:start position:0% +cards or quality cards or whatever that +actually have certain metrics that are + + align:start position:0% +actually have certain metrics that are + + + align:start position:0% +actually have certain metrics that are +that have to be met. Those have to be + + align:start position:0% +that have to be met. Those have to be + + + align:start position:0% +that have to be met. Those have to be +solid gold for 12 + + align:start position:0% +solid gold for 12 + + + align:start position:0% +solid gold for 12 +months. I mean, it's some really tough + + align:start position:0% +months. I mean, it's some really tough + + + align:start position:0% +months. I mean, it's some really tough +metrics that they're driven by. And then + + align:start position:0% +metrics that they're driven by. And then + + + align:start position:0% +metrics that they're driven by. And then +when they go and do the assessment, they + + align:start position:0% +when they go and do the assessment, they + + + align:start position:0% +when they go and do the assessment, they +randomly walk through the area, they do + + align:start position:0% +randomly walk through the area, they do + + + align:start position:0% +randomly walk through the area, they do +the 6S, which is our 5S, which we have + + align:start position:0% +the 6S, which is our 5S, which we have + + + align:start position:0% +the 6S, which is our 5S, which we have +safety as is the 6S. And they go through + + align:start position:0% +safety as is the 6S. And they go through + + + align:start position:0% +safety as is the 6S. And they go through +and actually see are people engaged? Are + + align:start position:0% +and actually see are people engaged? Are + + + align:start position:0% +and actually see are people engaged? Are +they actually talking it? Are they + + align:start position:0% +they actually talking it? Are they + + + align:start position:0% +they actually talking it? Are they +actually doing it? So it's a twofold. + + align:start position:0% +actually doing it? So it's a twofold. + + + align:start position:0% +actually doing it? So it's a twofold. +And let me tell you, the metric one, + + align:start position:0% +And let me tell you, the metric one, + + + align:start position:0% +And let me tell you, the metric one, +okay, the hard one, the + + align:start position:0% +okay, the hard one, the + + + align:start position:0% +okay, the hard one, the +people, very, very tough. And here's + + align:start position:0% +people, very, very tough. And here's + + + align:start position:0% +people, very, very tough. And here's +George David being quoted in the + + align:start position:0% +George David being quoted in the + + + align:start position:0% +George David being quoted in the +financial times. Uh it talks about six + + align:start position:0% +financial times. Uh it talks about six + + + align:start position:0% +financial times. Uh it talks about six +sigas done by black belts. Um we all + + align:start position:0% +sigas done by black belts. Um we all + + + align:start position:0% +sigas done by black belts. Um we all +he's talking about ace there + + align:start position:0% +he's talking about ace there + + + align:start position:0% +he's talking about ace there +also. And then here I just wanted you + + align:start position:0% +also. And then here I just wanted you + + + align:start position:0% +also. And then here I just wanted you +know what is his secret and how does he + + align:start position:0% +know what is his secret and how does he + + + align:start position:0% +know what is his secret and how does he +maintain this clear consistent mature + + align:start position:0% +maintain this clear consistent mature + + + align:start position:0% +maintain this clear consistent mature +repetitive throughout operating + + align:start position:0% +repetitive throughout operating + + + align:start position:0% +repetitive throughout operating +systems. And here's Louisie. This is the + + align:start position:0% +systems. And here's Louisie. This is the + + + align:start position:0% +systems. And here's Louisie. This is the +gentleman that's going to take uh + + align:start position:0% +gentleman that's going to take uh + + + align:start position:0% +gentleman that's going to take uh +George's place this year. And you can + + align:start position:0% +George's place this year. And you can + + + align:start position:0% +George's place this year. And you can +see in December 13th, this was last + + align:start position:0% +see in December 13th, this was last + + + align:start position:0% +see in December 13th, this was last +2007, talking about their shares, + + align:start position:0% +2007, talking about their shares, + + + align:start position:0% +2007, talking about their shares, +earnings. By the way, today we're at + + align:start position:0% + + + + align:start position:0% + +$74 per share + + align:start position:0% +$74 per share + + + align:start position:0% +$74 per share +UTC. And uh earnings per share. And then + + align:start position:0% +UTC. And uh earnings per share. And then + + + align:start position:0% +UTC. And uh earnings per share. And then +if you look down a little bit further + + align:start position:0% +if you look down a little bit further + + + align:start position:0% +if you look down a little bit further +down his quote here again, he's talking + + align:start position:0% +down his quote here again, he's talking + + + align:start position:0% +down his quote here again, he's talking +about the ACE operating + + align:start position:0% +about the ACE operating + + + align:start position:0% +about the ACE operating +system. George is moving on. Louis + + align:start position:0% +system. George is moving on. Louis + + + align:start position:0% +system. George is moving on. Louis +coming in. it isn't going to stop. So + + align:start position:0% +coming in. it isn't going to stop. So + + + align:start position:0% +coming in. it isn't going to stop. So +that that's the good + + align:start position:0% +that that's the good + + + align:start position:0% +that that's the good +news. Now a lot of people say, you know, + + align:start position:0% +news. Now a lot of people say, you know, + + + align:start position:0% +news. Now a lot of people say, you know, +does this stuff really work? What what + + align:start position:0% +does this stuff really work? What what + + + align:start position:0% +does this stuff really work? What what +are you doing? I think the stock market + + align:start position:0% +are you doing? I think the stock market + + + align:start position:0% +are you doing? I think the stock market +can show you that that it is working for + + align:start position:0% +can show you that that it is working for + + + align:start position:0% +can show you that that it is working for +us. And also here's here's some friends + + align:start position:0% +us. And also here's here's some friends + + + align:start position:0% +us. And also here's here's some friends +from global services engineering. + + align:start position:0% +from global services engineering. + + + align:start position:0% +from global services engineering. +Believe me, if you you get the + + align:start position:0% +Believe me, if you you get the + + + align:start position:0% +Believe me, if you you get the +engineering folks engaged, this is good + + align:start position:0% +engineering folks engaged, this is good + + + align:start position:0% +engineering folks engaged, this is good +stuff. This is talking to some quotes uh + + align:start position:0% +stuff. This is talking to some quotes uh + + + align:start position:0% +stuff. This is talking to some quotes uh +from this group. I just want to show you + + align:start position:0% +from this group. I just want to show you + + + align:start position:0% +from this group. I just want to show you +some numbers + + align:start position:0% +some numbers + + + align:start position:0% +some numbers +here. Cactus wires is is a way that we + + align:start position:0% +here. Cactus wires is is a way that we + + + align:start position:0% +here. Cactus wires is is a way that we +communicate back and forth with our + + align:start position:0% +communicate back and forth with our + + + align:start position:0% +communicate back and forth with our +customers. 70% to + + align:start position:0% +customers. 70% to + + + align:start position:0% +customers. 70% to +98%. Overdue wires reduced from 13 to9 + + align:start position:0% +98%. Overdue wires reduced from 13 to9 + + + align:start position:0% +98%. Overdue wires reduced from 13 to9 +72% in improvement in turn time 40% + + align:start position:0% +72% in improvement in turn time 40% + + + align:start position:0% +72% in improvement in turn time 40% +improvement in turn time for processing + + align:start position:0% +improvement in turn time for processing + + + align:start position:0% +improvement in turn time for processing +with engineering + + align:start position:0% +with engineering + + + align:start position:0% +with engineering +um survey. And I'm not quite sure how + + align:start position:0% +um survey. And I'm not quite sure how + + + align:start position:0% +um survey. And I'm not quite sure how +they do this, but for employee + + align:start position:0% +they do this, but for employee + + + align:start position:0% +they do this, but for employee +fulfillment, 65% employee fulfillment is + + align:start position:0% +fulfillment, 65% employee fulfillment is + + + align:start position:0% +fulfillment, 65% employee fulfillment is +the + + align:start position:0% +the + + + align:start position:0% +the +standard. That's that's what we're being + + align:start position:0% +standard. That's that's what we're being + + + align:start position:0% +standard. That's that's what we're being +told by HR. So, anything above 65% is + + align:start position:0% +told by HR. So, anything above 65% is + + + align:start position:0% +told by HR. So, anything above 65% is +gold, considered gold. And then + + align:start position:0% +gold, considered gold. And then + + + align:start position:0% +gold, considered gold. And then +improvement on the + + align:start position:0% +improvement on the + + + align:start position:0% +improvement on the +website. Here's another one from + + align:start position:0% + + + + align:start position:0% + +engineering. Customer feedback is 6.2. + + align:start position:0% +engineering. Customer feedback is 6.2. + + + align:start position:0% +engineering. Customer feedback is 6.2. +Employee SE survey 71% zero lost time + + align:start position:0% +Employee SE survey 71% zero lost time + + + align:start position:0% +Employee SE survey 71% zero lost time +injuries. Quality assurance data + + align:start position:0% +injuries. Quality assurance data + + + align:start position:0% +injuries. Quality assurance data +delivered 100% on time. Engineering + + align:start position:0% +delivered 100% on time. Engineering + + + align:start position:0% +delivered 100% on time. Engineering +standard work. How many times you go in + + align:start position:0% +standard work. How many times you go in + + + align:start position:0% +standard work. How many times you go in +and improve a process. Everybody has the + + align:start position:0% +and improve a process. Everybody has the + + + align:start position:0% +and improve a process. Everybody has the +cake and the banners and the pictures + + align:start position:0% +cake and the banners and the pictures + + + align:start position:0% +cake and the banners and the pictures +are taken and everybody walks away but + + align:start position:0% +are taken and everybody walks away but + + + align:start position:0% +are taken and everybody walks away but +nobody's written it down. Nobody is + + align:start position:0% +nobody's written it down. Nobody is + + + align:start position:0% +nobody's written it down. Nobody is +going to be able to repeat this process + + align:start position:0% +going to be able to repeat this process + + + align:start position:0% +going to be able to repeat this process +again. So standard work is very very + + align:start position:0% +again. So standard work is very very + + + align:start position:0% +again. So standard work is very very +important. + + align:start position:0% +important. + + + align:start position:0% +important. +procedures, a way to let people know how + + align:start position:0% +procedures, a way to let people know how + + + align:start position:0% +procedures, a way to let people know how +to continue doing the job. Here we go. + + align:start position:0% +to continue doing the job. Here we go. + + + align:start position:0% +to continue doing the job. Here we go. +Moving from a silver to gold is directly + + align:start position:0% +Moving from a silver to gold is directly + + + align:start position:0% +Moving from a silver to gold is directly +attributed to, and I don't want to read + + align:start position:0% +attributed to, and I don't want to read + + + align:start position:0% +attributed to, and I don't want to read +this whole thing, but I just wanted to + + align:start position:0% +this whole thing, but I just wanted to + + + align:start position:0% +this whole thing, but I just wanted to +throw some quotes in here from different + + align:start position:0% +throw some quotes in here from different + + + align:start position:0% +throw some quotes in here from different +people throughout the + + align:start position:0% +people throughout the + + + align:start position:0% +people throughout the +organization. And then this is uh AEDC. + + align:start position:0% +organization. And then this is uh AEDC. + + + align:start position:0% +organization. And then this is uh AEDC. +Remember if you remember AEDC we did + + align:start position:0% +Remember if you remember AEDC we did + + + align:start position:0% +Remember if you remember AEDC we did +some work LI did some work with them a + + align:start position:0% +some work LI did some work with them a + + + align:start position:0% +some work LI did some work with them a +couple years ago but they have really uh + + align:start position:0% +couple years ago but they have really uh + + + align:start position:0% +couple years ago but they have really uh +moved ahead 94 straight months without + + align:start position:0% +moved ahead 94 straight months without + + + align:start position:0% +moved ahead 94 straight months without +loss time injury just goes on and on and + + align:start position:0% +loss time injury just goes on and on and + + + align:start position:0% +loss time injury just goes on and on and +on standard work just some of the data + + align:start position:0% +on standard work just some of the data + + + align:start position:0% +on standard work just some of the data +showing you here what's going + + align:start position:0% +showing you here what's going + + + align:start position:0% +showing you here what's going +on and then that is actually a site + + align:start position:0% +on and then that is actually a site + + + align:start position:0% +on and then that is actually a site +manager Prattton Whitney talking about + + align:start position:0% +manager Prattton Whitney talking about + + + align:start position:0% +manager Prattton Whitney talking about +how ACE has really helped them on their + + align:start position:0% +how ACE has really helped them on their + + + align:start position:0% +how ACE has really helped them on their +journey to improvement + + align:start position:0% +journey to improvement + + + align:start position:0% +journey to improvement +And the journey continues. Like I said, + + align:start position:0% +And the journey continues. Like I said, + + + align:start position:0% +And the journey continues. Like I said, +we are only at + + align:start position:0% +we are only at + + + align:start position:0% +we are only at +22%. You imagine when Prattton Whitney + + align:start position:0% +22%. You imagine when Prattton Whitney + + + align:start position:0% +22%. You imagine when Prattton Whitney +is at 100%. It'll be amazing. Is there + + align:start position:0% +is at 100%. It'll be amazing. Is there + + + align:start position:0% +is at 100%. It'll be amazing. Is there +any questions? + + align:start position:0% +any questions? + + + align:start position:0% +any questions? +Well, I got a question. Sure. Uh, and + + align:start position:0% +Well, I got a question. Sure. Uh, and + + + align:start position:0% +Well, I got a question. Sure. Uh, and +you kind of alluded to it, but let me + + align:start position:0% +you kind of alluded to it, but let me + + + align:start position:0% +you kind of alluded to it, but let me +just put it on the table. When I go into + + align:start position:0% +just put it on the table. When I go into + + + align:start position:0% +just put it on the table. When I go into +organizations and asked, you know, who's + + align:start position:0% +organizations and asked, you know, who's + + + align:start position:0% +organizations and asked, you know, who's +the most difficult, what's the most + + align:start position:0% +the most difficult, what's the most + + + align:start position:0% +the most difficult, what's the most +difficult group of people in your + + align:start position:0% +difficult group of people in your + + + align:start position:0% +difficult group of people in your +organization to buy into the lean + + align:start position:0% +organization to buy into the lean + + + align:start position:0% +organization to buy into the lean +transformation? The answer is always the + + align:start position:0% +transformation? The answer is always the + + + align:start position:0% +transformation? The answer is always the +same. The frozen middle people in the + + align:start position:0% +same. The frozen middle people in the + + + align:start position:0% +same. The frozen middle people in the +middle because they're worried whether + + align:start position:0% +middle because they're worried whether + + + align:start position:0% +middle because they're worried whether +their job really adds value or not and + + align:start position:0% +their job really adds value or not and + + + align:start position:0% +their job really adds value or not and +the engineers because the engineers say + + align:start position:0% +the engineers because the engineers say + + + align:start position:0% +the engineers because the engineers say +it doesn't apply to me. Doesn't apply to + + align:start position:0% +it doesn't apply to me. Doesn't apply to + + + align:start position:0% +it doesn't apply to me. Doesn't apply to +me. Yeah. So, what are you doing at + + align:start position:0% +me. Yeah. So, what are you doing at + + + align:start position:0% +me. Yeah. So, what are you doing at +Prattton Whitney to get the engineers on + + align:start position:0% +Prattton Whitney to get the engineers on + + + align:start position:0% +Prattton Whitney to get the engineers on +board? Well, uh Paul Adams who's the + + align:start position:0% +board? Well, uh Paul Adams who's the + + + align:start position:0% +board? Well, uh Paul Adams who's the +executive there, he's on this working + + align:start position:0% +executive there, he's on this working + + + align:start position:0% +executive there, he's on this working +together team and they all talk across + + align:start position:0% +together team and they all talk across + + + align:start position:0% +together team and they all talk across +to do the cross talk. I now sit in the + + align:start position:0% +to do the cross talk. I now sit in the + + + align:start position:0% +to do the cross talk. I now sit in the +engineering building and I cannot tell + + align:start position:0% +engineering building and I cannot tell + + + align:start position:0% +engineering building and I cannot tell +you how many times I hear them talking + + align:start position:0% +you how many times I hear them talking + + + align:start position:0% +you how many times I hear them talking +about their control towers, their + + align:start position:0% +about their control towers, their + + + align:start position:0% +about their control towers, their +metrics, their + + align:start position:0% +metrics, their + + + align:start position:0% +metrics, their +turnbacks. They're talking it. They were + + align:start position:0% +turnbacks. They're talking it. They were + + + align:start position:0% +turnbacks. They're talking it. They were +perhaps the last group to make that flip + + align:start position:0% +perhaps the last group to make that flip + + + align:start position:0% +perhaps the last group to make that flip +that switch. A lot of push back. And + + align:start position:0% +that switch. A lot of push back. And + + + align:start position:0% +that switch. A lot of push back. And +that's one thing. And and if you + + align:start position:0% +that's one thing. And and if you + + + align:start position:0% +that's one thing. And and if you +remember this George David uh why is he + + align:start position:0% +remember this George David uh why is he + + + align:start position:0% +remember this George David uh why is he +such a great leader? You got to repeat + + align:start position:0% +such a great leader? You got to repeat + + + align:start position:0% +such a great leader? You got to repeat +the same message over and over again for + + align:start position:0% +the same message over and over again for + + + align:start position:0% +the same message over and over again for +people to get it. And and they're + + align:start position:0% +people to get it. And and they're + + + align:start position:0% +people to get it. And and they're +getting it. They have to get it. + + align:start position:0% + + + + align:start position:0% + +Okay. We want to thank you for fighting + + align:start position:0% +Okay. We want to thank you for fighting + + + align:start position:0% +Okay. We want to thank you for fighting +drove two hours to get here this + + align:start position:0% +drove two hours to get here this + + + align:start position:0% +drove two hours to get here this +morning. And let me tell you, + + align:start position:0% +morning. And let me tell you, + + + align:start position:0% +morning. And let me tell you, +Massachusetts drivers. + + align:start position:0% + + + + align:start position:0% + +A little certificate of appreciation. + + align:start position:0% +A little certificate of appreciation. + + + align:start position:0% +A little certificate of appreciation. +Thank you so much. Thanks. Thank you. \ No newline at end of file diff --git a/tQz6iktxQqM.txt b/tQz6iktxQqM.txt new file mode 100644 index 0000000000000000000000000000000000000000..1ee518caefda3dab89b90047f6006cf68b3cdfe7 --- /dev/null +++ b/tQz6iktxQqM.txt @@ -0,0 +1,2043 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Now we consider the process of + + align:start position:0% +Now we consider the process of + + + align:start position:0% +Now we consider the process of +thermopforming. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +In this process, we will make a simple + + align:start position:0% +In this process, we will make a simple + + + align:start position:0% +In this process, we will make a simple +circular part by heating a flat sheet of + + align:start position:0% +circular part by heating a flat sheet of + + + align:start position:0% +circular part by heating a flat sheet of +polystyrene and then pulling it over a + + align:start position:0% +polystyrene and then pulling it over a + + + align:start position:0% +polystyrene and then pulling it over a +tool under + + align:start position:0% + + + + align:start position:0% + +vacuum. After forming, the part is + + align:start position:0% +vacuum. After forming, the part is + + + align:start position:0% +vacuum. After forming, the part is +usually trimmed to a final + + align:start position:0% + + + + align:start position:0% + +shape. To begin the process, the flat + + align:start position:0% +shape. To begin the process, the flat + + + align:start position:0% +shape. To begin the process, the flat +sheet is loaded into the machine and + + align:start position:0% +sheet is loaded into the machine and + + + align:start position:0% +sheet is loaded into the machine and +then clamped into + + align:start position:0% +then clamped into + + + align:start position:0% +then clamped into +place. The sheet is moved into an oven. + + align:start position:0% +place. The sheet is moved into an oven. + + + align:start position:0% +place. The sheet is moved into an oven. +heated for a specified amount of + + align:start position:0% + + + + align:start position:0% + +time. The oven temperature is under + + align:start position:0% +time. The oven temperature is under + + + align:start position:0% +time. The oven temperature is under +feedback control and the timing of + + align:start position:0% +feedback control and the timing of + + + align:start position:0% +feedback control and the timing of +entering and exiting the oven is also + + align:start position:0% +entering and exiting the oven is also + + + align:start position:0% +entering and exiting the oven is also +under program + + align:start position:0% + + + + align:start position:0% + +control. After residing in the oven the + + align:start position:0% +control. After residing in the oven the + + + align:start position:0% +control. After residing in the oven the +desired time, the sheet is moved over + + align:start position:0% +desired time, the sheet is moved over + + + align:start position:0% +desired time, the sheet is moved over +the tool. It comes up to contact the + + align:start position:0% +the tool. It comes up to contact the + + + align:start position:0% +the tool. It comes up to contact the +sheet and the vacuum is applied through + + align:start position:0% +sheet and the vacuum is applied through + + + align:start position:0% +sheet and the vacuum is applied through +the tool. + + align:start position:0% + + + + align:start position:0% + +This draws the sheet onto the tool, + + align:start position:0% +This draws the sheet onto the tool, + + + align:start position:0% +This draws the sheet onto the tool, +taking its form, and at the same time + + align:start position:0% +taking its form, and at the same time + + + align:start position:0% +taking its form, and at the same time +cools the + + align:start position:0% + + + + align:start position:0% + +sheet. The part is then removed from the + + align:start position:0% +sheet. The part is then removed from the + + + align:start position:0% +sheet. The part is then removed from the +clamps and measured using a verier + + align:start position:0% +clamps and measured using a verier + + + align:start position:0% +clamps and measured using a verier +caliper. + + align:start position:0% + + + + align:start position:0% + +We will look at two different thickness + + align:start position:0% +We will look at two different thickness + + + align:start position:0% +We will look at two different thickness +sheets and have two different resonance + + align:start position:0% +sheets and have two different resonance + + + align:start position:0% +sheets and have two different resonance +times in the oven for a total of four + + align:start position:0% +times in the oven for a total of four + + + align:start position:0% +times in the oven for a total of four +different + + align:start position:0% +different + + + align:start position:0% +different +conditions. Run charts for the part + + align:start position:0% +conditions. Run charts for the part + + + align:start position:0% +conditions. Run charts for the part +diameter can then be plotted noting the + + align:start position:0% +diameter can then be plotted noting the + + + align:start position:0% +diameter can then be plotted noting the +effect of thickness and heating time. + + align:start position:0% +effect of thickness and heating time. + + + align:start position:0% +effect of thickness and heating time. +[Music] + + align:start position:0% + + + + align:start position:0% + +Now we consider the process of sheet + + align:start position:0% +Now we consider the process of sheet + + + align:start position:0% +Now we consider the process of sheet +metal shearing. In this process, we take + + align:start position:0% +metal shearing. In this process, we take + + + align:start position:0% +metal shearing. In this process, we take +5-in wide strips of sheet metal and cut + + align:start position:0% +5-in wide strips of sheet metal and cut + + + align:start position:0% +5-in wide strips of sheet metal and cut +off 1-in wide coupons to be used in the + + align:start position:0% +off 1-in wide coupons to be used in the + + + align:start position:0% +off 1-in wide coupons to be used in the +brake forming process. + + align:start position:0% + + + + align:start position:0% + +The key dimensions for the part are the + + align:start position:0% +The key dimensions for the part are the + + + align:start position:0% +The key dimensions for the part are the +average width and the taper along the + + align:start position:0% +average width and the taper along the + + + align:start position:0% +average width and the taper along the +length determined by measuring the width + + align:start position:0% +length determined by measuring the width + + + align:start position:0% +length determined by measuring the width +at each + + align:start position:0% + + + + align:start position:0% + +end. The cutting is done on a simple + + align:start position:0% +end. The cutting is done on a simple + + + align:start position:0% +end. The cutting is done on a simple +treddle shear operated manually. + + align:start position:0% + + + + align:start position:0% + +The cut width is determined by the + + align:start position:0% +The cut width is determined by the + + + align:start position:0% +The cut width is determined by the +location of the back gauge, which can be + + align:start position:0% +location of the back gauge, which can be + + + align:start position:0% +location of the back gauge, which can be +set using the graduations on the gauge. + + align:start position:0% +set using the graduations on the gauge. + + + align:start position:0% +set using the graduations on the gauge. +Note that these can resolve to only + + align:start position:0% +Note that these can resolve to only + + + align:start position:0% +Note that these can resolve to only +about 1/16th of an inch, and sighting + + align:start position:0% +about 1/16th of an inch, and sighting + + + align:start position:0% +about 1/16th of an inch, and sighting +errors are likely to happen. The sheet + + align:start position:0% +errors are likely to happen. The sheet + + + align:start position:0% +errors are likely to happen. The sheet +is inserted into the shear as shown and + + align:start position:0% +is inserted into the shear as shown and + + + align:start position:0% +is inserted into the shear as shown and +pushed into contact with the back + + align:start position:0% +pushed into contact with the back + + + align:start position:0% +pushed into contact with the back +gauge. To ensure a square part, the long + + align:start position:0% +gauge. To ensure a square part, the long + + + align:start position:0% +gauge. To ensure a square part, the long +edge of the sheet should be held flush + + align:start position:0% +edge of the sheet should be held flush + + + align:start position:0% +edge of the sheet should be held flush +to the edge fence as shown. If instead + + align:start position:0% +to the edge fence as shown. If instead + + + align:start position:0% +to the edge fence as shown. If instead +we keep the cut edge of the sheet flush + + align:start position:0% +we keep the cut edge of the sheet flush + + + align:start position:0% +we keep the cut edge of the sheet flush +to the back gauge, we could not + + align:start position:0% +to the back gauge, we could not + + + align:start position:0% +to the back gauge, we could not +eliminate initial tapered edges on the + + align:start position:0% + + + + align:start position:0% + +sheet. As the treddle is pushed down, + + align:start position:0% +sheet. As the treddle is pushed down, + + + align:start position:0% +sheet. As the treddle is pushed down, +notice that a clamp comes down to hold + + align:start position:0% +notice that a clamp comes down to hold + + + align:start position:0% +notice that a clamp comes down to hold +the sheet just before the blade moves to + + align:start position:0% +the sheet just before the blade moves to + + + align:start position:0% +the sheet just before the blade moves to +cut the sheet. + + align:start position:0% + + + + align:start position:0% + +Okay, do it again. + + align:start position:0% + + + + align:start position:0% + +The part falls off at the rear and + + align:start position:0% +The part falls off at the rear and + + + align:start position:0% +The part falls off at the rear and +should be collected and + + align:start position:0% + + + + align:start position:0% + +numbered. The width at each end is then + + align:start position:0% +numbered. The width at each end is then + + + align:start position:0% +numbered. The width at each end is then +measured using a verier + + align:start position:0% + + + + align:start position:0% + +caliper. Both measurements are recorded + + align:start position:0% +caliper. Both measurements are recorded + + + align:start position:0% +caliper. Both measurements are recorded +so we can get an average width and + + align:start position:0% +so we can get an average width and + + + align:start position:0% +so we can get an average width and +taper. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +For this process, we will shear both + + align:start position:0% +For this process, we will shear both + + + align:start position:0% +For this process, we will shear both +aluminum and steel sheets and create a + + align:start position:0% +aluminum and steel sheets and create a + + + align:start position:0% +aluminum and steel sheets and create a +run chart for + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +each + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Here we consider the process of break + + align:start position:0% + + + + align:start position:0% + +forming. The purpose of this process is + + align:start position:0% +forming. The purpose of this process is + + + align:start position:0% +forming. The purpose of this process is +to bend flat coupons of sheet metal to a + + align:start position:0% +to bend flat coupons of sheet metal to a + + + align:start position:0% +to bend flat coupons of sheet metal to a +finite angle. + + align:start position:0% + + + + align:start position:0% + +This is accomplished by applying a + + align:start position:0% +This is accomplished by applying a + + + align:start position:0% +This is accomplished by applying a +three-point load using a punch and die. + + align:start position:0% +three-point load using a punch and die. + + + align:start position:0% +three-point load using a punch and die. +In this case, mounted in a + + align:start position:0% + + + + align:start position:0% + +lathe. The lathe provides a stiff + + align:start position:0% +lathe. The lathe provides a stiff + + + align:start position:0% +lathe. The lathe provides a stiff +foundation and with the tailtock a means + + align:start position:0% +foundation and with the tailtock a means + + + align:start position:0% +foundation and with the tailtock a means +of controlling the displacement of the + + align:start position:0% + + + + align:start position:0% + +punch. Here we see the tooling mounted + + align:start position:0% +punch. Here we see the tooling mounted + + + align:start position:0% +punch. Here we see the tooling mounted +in the lathe and show the punch moving + + align:start position:0% +in the lathe and show the punch moving + + + align:start position:0% +in the lathe and show the punch moving +as the tailtock lead screw is rotated. + + align:start position:0% +as the tailtock lead screw is rotated. + + + align:start position:0% +as the tailtock lead screw is rotated. +Notice that the displacement of the + + align:start position:0% +Notice that the displacement of the + + + align:start position:0% +Notice that the displacement of the +punch is determined by the rotations of + + align:start position:0% +punch is determined by the rotations of + + + align:start position:0% +punch is determined by the rotations of +the hand wheel on the tailtock. + + align:start position:0% + + + + align:start position:0% + +The bend angle is determined by the + + align:start position:0% +The bend angle is determined by the + + + align:start position:0% +The bend angle is determined by the +displacement of the punch relative to + + align:start position:0% +displacement of the punch relative to + + + align:start position:0% +displacement of the punch relative to +the die but will also depend on the + + align:start position:0% +the die but will also depend on the + + + align:start position:0% +the die but will also depend on the +thickness and constitutive properties of + + align:start position:0% +thickness and constitutive properties of + + + align:start position:0% +thickness and constitutive properties of +the + + align:start position:0% +the + + + align:start position:0% +the +sheet. The rotational displacement is + + align:start position:0% +sheet. The rotational displacement is + + + align:start position:0% +sheet. The rotational displacement is +measured using the verier on the lead + + align:start position:0% +measured using the verier on the lead + + + align:start position:0% +measured using the verier on the lead +screw. In this machine, we can resolve + + align:start position:0% +screw. In this machine, we can resolve + + + align:start position:0% +screw. In this machine, we can resolve +one part in 100 per rotation. For a lead + + align:start position:0% +one part in 100 per rotation. For a lead + + + align:start position:0% +one part in 100 per rotation. For a lead +screw ratio of 1 in per 10 revolutions, + + align:start position:0% +screw ratio of 1 in per 10 revolutions, + + + align:start position:0% +screw ratio of 1 in per 10 revolutions, +this gives a displacement of 1,000th of + + align:start position:0% +this gives a displacement of 1,000th of + + + align:start position:0% +this gives a displacement of 1,000th of +an inch per line on the + + align:start position:0% + + + + align:start position:0% + +verier. Here we see the machine being + + align:start position:0% +verier. Here we see the machine being + + + align:start position:0% +verier. Here we see the machine being +cycled while forming + + align:start position:0% + + + + align:start position:0% + +parts. Notice that when the load is + + align:start position:0% +parts. Notice that when the load is + + + align:start position:0% +parts. Notice that when the load is +released, the part shows significant + + align:start position:0% +released, the part shows significant + + + align:start position:0% +released, the part shows significant +spring back. We can show that this + + align:start position:0% +spring back. We can show that this + + + align:start position:0% +spring back. We can show that this +spring back is a function of the + + align:start position:0% +spring back is a function of the + + + align:start position:0% +spring back is a function of the +thickness, yield stress, elastic + + align:start position:0% +thickness, yield stress, elastic + + + align:start position:0% +thickness, yield stress, elastic +modulus, and strain hardening properties + + align:start position:0% +modulus, and strain hardening properties + + + align:start position:0% +modulus, and strain hardening properties +of the sheet as well as the degree of + + align:start position:0% + + + + align:start position:0% + +bending. The specifications call for a + + align:start position:0% +bending. The specifications call for a + + + align:start position:0% +bending. The specifications call for a +depth of either 3/10 of an inch or 6/10 + + align:start position:0% +depth of either 3/10 of an inch or 6/10 + + + align:start position:0% +depth of either 3/10 of an inch or 6/10 +of an inch or three or six full + + align:start position:0% +of an inch or three or six full + + + align:start position:0% +of an inch or three or six full +revolutions of the lead screw. The key + + align:start position:0% +revolutions of the lead screw. The key + + + align:start position:0% +revolutions of the lead screw. The key +is determining the zero angle point + + align:start position:0% +is determining the zero angle point + + + align:start position:0% +is determining the zero angle point +where the punch just touches the sheet + + align:start position:0% +where the punch just touches the sheet + + + align:start position:0% +where the punch just touches the sheet +and then moving three or six revolutions + + align:start position:0% +and then moving three or six revolutions + + + align:start position:0% +and then moving three or six revolutions +further + + align:start position:0% + + + + align:start position:0% + +in. As each part is formed, we can + + align:start position:0% +in. As each part is formed, we can + + + align:start position:0% +in. As each part is formed, we can +measure the resulting angle using a + + align:start position:0% +measure the resulting angle using a + + + align:start position:0% +measure the resulting angle using a +machinist's + + align:start position:0% +machinist's + + + align:start position:0% +machinist's +protractor. This is a difficult + + align:start position:0% +protractor. This is a difficult + + + align:start position:0% +protractor. This is a difficult +measurement and must be made with care. + + align:start position:0% +measurement and must be made with care. + + + align:start position:0% +measurement and must be made with care. +In this case, we can resolve to better + + align:start position:0% +In this case, we can resolve to better + + + align:start position:0% +In this case, we can resolve to better +than onetenth of a degree, but it is + + align:start position:0% +than onetenth of a degree, but it is + + + align:start position:0% +than onetenth of a degree, but it is +important to stay tangent to the flanks + + align:start position:0% +important to stay tangent to the flanks + + + align:start position:0% +important to stay tangent to the flanks +of the + + align:start position:0% +of the + + + align:start position:0% +of the +part. Finally, we record the angle, the + + align:start position:0% +part. Finally, we record the angle, the + + + align:start position:0% +part. Finally, we record the angle, the +material type, and the depth of the + + align:start position:0% +material type, and the depth of the + + + align:start position:0% +material type, and the depth of the +punch on a data + + align:start position:0% + + + + align:start position:0% + +sheet. A run chart for the process is + + align:start position:0% +sheet. A run chart for the process is + + + align:start position:0% +sheet. A run chart for the process is +then plotted. Data is most logically + + align:start position:0% +then plotted. Data is most logically + + + align:start position:0% +then plotted. Data is most logically +grouped by material and depth since each + + align:start position:0% +grouped by material and depth since each + + + align:start position:0% +grouped by material and depth since each +has a strong effect on the final angle. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +Now we consider the process of injection + + align:start position:0% + + + + align:start position:0% + +molding. In this process, we are + + align:start position:0% +molding. In this process, we are + + + align:start position:0% +molding. In this process, we are +manufacturing simple snap rings to a + + align:start position:0% +manufacturing simple snap rings to a + + + align:start position:0% +manufacturing simple snap rings to a +specified diameter. + + align:start position:0% +specified diameter. + + + align:start position:0% +specified diameter. +We start with clear polyropylene pellets + + align:start position:0% +We start with clear polyropylene pellets + + + align:start position:0% +We start with clear polyropylene pellets +which are melted and injected into the + + align:start position:0% +which are melted and injected into the + + + align:start position:0% +which are melted and injected into the +tool under pressure. The injection + + align:start position:0% +tool under pressure. The injection + + + align:start position:0% +tool under pressure. The injection +molding machine is rather + + align:start position:0% +molding machine is rather + + + align:start position:0% +molding machine is rather +complex. It includes a compounding and + + align:start position:0% +complex. It includes a compounding and + + + align:start position:0% +complex. It includes a compounding and +melting screw, an injection barrel, as + + align:start position:0% +melting screw, an injection barrel, as + + + align:start position:0% +melting screw, an injection barrel, as +well as the tooling and tooling + + align:start position:0% + + + + align:start position:0% + +clamp. The pellets move from a hopper + + align:start position:0% +clamp. The pellets move from a hopper + + + align:start position:0% +clamp. The pellets move from a hopper +into a heated barrel with a single + + align:start position:0% +into a heated barrel with a single + + + align:start position:0% +into a heated barrel with a single +screw. During the melting phase, the + + align:start position:0% +screw. During the melting phase, the + + + align:start position:0% +screw. During the melting phase, the +screw rotates and moves rearward, + + align:start position:0% +screw rotates and moves rearward, + + + align:start position:0% +screw rotates and moves rearward, +storing the melted plastic in the nose + + align:start position:0% +storing the melted plastic in the nose + + + align:start position:0% +storing the melted plastic in the nose +of the barrel. The melting is affected + + align:start position:0% +of the barrel. The melting is affected + + + align:start position:0% +of the barrel. The melting is affected +mainly by the mechanical shear on the + + align:start position:0% +mainly by the mechanical shear on the + + + align:start position:0% +mainly by the mechanical shear on the +pellets and not by heat transfer from + + align:start position:0% +pellets and not by heat transfer from + + + align:start position:0% +pellets and not by heat transfer from +the + + align:start position:0% +the + + + align:start position:0% +the +barrel. The barrel is brought into + + align:start position:0% +barrel. The barrel is brought into + + + align:start position:0% +barrel. The barrel is brought into +contact with one tool half to create a + + align:start position:0% +contact with one tool half to create a + + + align:start position:0% +contact with one tool half to create a +flow path into the tool cavity. + + align:start position:0% + + + + align:start position:0% + +During the injection cycle, the screw + + align:start position:0% +During the injection cycle, the screw + + + align:start position:0% +During the injection cycle, the screw +first rotates and then moves backward as + + align:start position:0% +first rotates and then moves backward as + + + align:start position:0% +first rotates and then moves backward as +the plastic is + + align:start position:0% +the plastic is + + + align:start position:0% +the plastic is +melted. It then moves forward at a + + align:start position:0% +melted. It then moves forward at a + + + align:start position:0% +melted. It then moves forward at a +specified velocity to fill the mold. + + align:start position:0% + + + + align:start position:0% + +Once the mold is filled, the screw + + align:start position:0% +Once the mold is filled, the screw + + + align:start position:0% +Once the mold is filled, the screw +piston switches to pressure control and + + align:start position:0% +piston switches to pressure control and + + + align:start position:0% +piston switches to pressure control and +the additional forward motion called + + align:start position:0% +the additional forward motion called + + + align:start position:0% +the additional forward motion called +packing is caused by the plastic + + align:start position:0% +packing is caused by the plastic + + + align:start position:0% +packing is caused by the plastic +compressing in the mold before it + + align:start position:0% +compressing in the mold before it + + + align:start position:0% +compressing in the mold before it +hardens + + align:start position:0% +hardens + + + align:start position:0% +hardens +fully. The two halves of the tool are + + align:start position:0% +fully. The two halves of the tool are + + + align:start position:0% +fully. The two halves of the tool are +brought together under the action of a + + align:start position:0% +brought together under the action of a + + + align:start position:0% +brought together under the action of a +large hydraulic clamping cylinder which + + align:start position:0% +large hydraulic clamping cylinder which + + + align:start position:0% +large hydraulic clamping cylinder which +keeps them closed during injection. The + + align:start position:0% +keeps them closed during injection. The + + + align:start position:0% +keeps them closed during injection. The +tool itself serves to cool the part and + + align:start position:0% +tool itself serves to cool the part and + + + align:start position:0% +tool itself serves to cool the part and +the temperature of the part when the + + align:start position:0% +the temperature of the part when the + + + align:start position:0% +the temperature of the part when the +tool opens depends strongly on the hold + + align:start position:0% +tool opens depends strongly on the hold + + + align:start position:0% +tool opens depends strongly on the hold +time in the tool. This time can also be + + align:start position:0% +time in the tool. This time can also be + + + align:start position:0% +time in the tool. This time can also be +programmed into the + + align:start position:0% +programmed into the + + + align:start position:0% +programmed into the +machine. After the hold time, the tool + + align:start position:0% +machine. After the hold time, the tool + + + align:start position:0% +machine. After the hold time, the tool +separates and the part is + + align:start position:0% +separates and the part is + + + align:start position:0% +separates and the part is +removed. In a production process, the + + align:start position:0% +removed. In a production process, the + + + align:start position:0% +removed. In a production process, the +part would be ejected by a set of + + align:start position:0% +part would be ejected by a set of + + + align:start position:0% +part would be ejected by a set of +actuated pins. But here it is done + + align:start position:0% +actuated pins. But here it is done + + + align:start position:0% +actuated pins. But here it is done +manually. + + align:start position:0% + + + + align:start position:0% + +After the part is removed and cooled, it + + align:start position:0% +After the part is removed and cooled, it + + + align:start position:0% +After the part is removed and cooled, it +can be measured using a verier caliper + + align:start position:0% +can be measured using a verier caliper + + + align:start position:0% +can be measured using a verier caliper +and the diameter + + align:start position:0% + + + + align:start position:0% + +recorded. In this experiment, we will + + align:start position:0% +recorded. In this experiment, we will + + + align:start position:0% +recorded. In this experiment, we will +vary the injection speed and the hold + + align:start position:0% +vary the injection speed and the hold + + + align:start position:0% +vary the injection speed and the hold +time to yield four different production + + align:start position:0% +time to yield four different production + + + align:start position:0% +time to yield four different production +conditions. + + align:start position:0% + + + + align:start position:0% + +A run chart can then be plotted for all + + align:start position:0% +A run chart can then be plotted for all + + + align:start position:0% +A run chart can then be plotted for all +the data keeping track of the machine + + align:start position:0% + + + + align:start position:0% + +settings. Now we consider the process of + + align:start position:0% +settings. Now we consider the process of + + + align:start position:0% +settings. Now we consider the process of +CNC turning. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +The part to be manufactured here is a + + align:start position:0% +The part to be manufactured here is a + + + align:start position:0% +The part to be manufactured here is a +simple cylinder of + + align:start position:0% +simple cylinder of + + + align:start position:0% +simple cylinder of +aluminum. The workpiece is a bar of 0.75 + + align:start position:0% +aluminum. The workpiece is a bar of 0.75 + + + align:start position:0% +aluminum. The workpiece is a bar of 0.75 +in diameter aluminum which is to be + + align:start position:0% +in diameter aluminum which is to be + + + align:start position:0% +in diameter aluminum which is to be +turned to 0.675 in + + align:start position:0% +turned to 0.675 in + + + align:start position:0% +turned to 0.675 in +diameter. After turning, three parts of + + align:start position:0% +diameter. After turning, three parts of + + + align:start position:0% +diameter. After turning, three parts of +0.75 in length will be cut off from the + + align:start position:0% +0.75 in length will be cut off from the + + + align:start position:0% +0.75 in length will be cut off from the +bar. + + align:start position:0% + + + + align:start position:0% + +The workpiece is clamped in the chuck + + align:start position:0% +The workpiece is clamped in the chuck + + + align:start position:0% +The workpiece is clamped in the chuck +with a stick out of 3 + + align:start position:0% + + + + align:start position:0% + +in. The turning and cut off cycles are + + align:start position:0% +in. The turning and cut off cycles are + + + align:start position:0% +in. The turning and cut off cycles are +controlled by the NC controller. So the + + align:start position:0% +controlled by the NC controller. So the + + + align:start position:0% +controlled by the NC controller. So the +only operator intervention is loading of + + align:start position:0% +only operator intervention is loading of + + + align:start position:0% +only operator intervention is loading of +material and changing of + + align:start position:0% +material and changing of + + + align:start position:0% +material and changing of +tools. Note that the machine frame for + + align:start position:0% +tools. Note that the machine frame for + + + align:start position:0% +tools. Note that the machine frame for +this process is massive so as to + + align:start position:0% +this process is massive so as to + + + align:start position:0% +this process is massive so as to +minimize any deflection under machining + + align:start position:0% +minimize any deflection under machining + + + align:start position:0% +minimize any deflection under machining +loads. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +The cycle begins with a single turning + + align:start position:0% +The cycle begins with a single turning + + + align:start position:0% +The cycle begins with a single turning +pass with fixed spindle speed and feed. + + align:start position:0% + + + + align:start position:0% + +Notice that the longitudinal motion is + + align:start position:0% +Notice that the longitudinal motion is + + + align:start position:0% +Notice that the longitudinal motion is +controlled by a servo motor driving the + + align:start position:0% +controlled by a servo motor driving the + + + align:start position:0% +controlled by a servo motor driving the +longaxis lead screw under program + + align:start position:0% + + + + align:start position:0% + +control. During the experiment, the + + align:start position:0% +control. During the experiment, the + + + align:start position:0% +control. During the experiment, the +operator will change the spindle speed + + align:start position:0% +operator will change the spindle speed + + + align:start position:0% +operator will change the spindle speed +once and the feed rate once for a total + + align:start position:0% +once and the feed rate once for a total + + + align:start position:0% +once and the feed rate once for a total +of four different operating conditions. + + align:start position:0% + + + + align:start position:0% + +Heat. Heat. + + align:start position:0% + + + + align:start position:0% + +After turning, we change to a simple cut + + align:start position:0% +After turning, we change to a simple cut + + + align:start position:0% +After turning, we change to a simple cut +off tool and a fast plunge cut motion + + align:start position:0% +off tool and a fast plunge cut motion + + + align:start position:0% +off tool and a fast plunge cut motion +separates the parts. + + align:start position:0% + + + + align:start position:0% + +It is important that each part is + + align:start position:0% +It is important that each part is + + + align:start position:0% +It is important that each part is +captured as it falls so we can tell + + align:start position:0% +captured as it falls so we can tell + + + align:start position:0% +captured as it falls so we can tell +which part of the bar it was made from, + + align:start position:0% +which part of the bar it was made from, + + + align:start position:0% +which part of the bar it was made from, +inner, outer, or + + align:start position:0% + + + + align:start position:0% + +middle. Each part diameter is measured + + align:start position:0% +middle. Each part diameter is measured + + + align:start position:0% +middle. Each part diameter is measured +using a verier caliper and recorded in + + align:start position:0% +using a verier caliper and recorded in + + + align:start position:0% +using a verier caliper and recorded in +order of production. + + align:start position:0% + + + + align:start position:0% + +The spindle speed and feed rate should + + align:start position:0% +The spindle speed and feed rate should + + + align:start position:0% +The spindle speed and feed rate should +also be recorded for each + + align:start position:0% +also be recorded for each + + + align:start position:0% +also be recorded for each +part. Run charts are then created for + + align:start position:0% +part. Run charts are then created for + + + align:start position:0% +part. Run charts are then created for +the part in sequence or by location on + + align:start position:0% +the part in sequence or by location on + + + align:start position:0% +the part in sequence or by location on +the bar. \ No newline at end of file diff --git a/tdjAGitQHDo.txt b/tdjAGitQHDo.txt new file mode 100644 index 0000000000000000000000000000000000000000..c3ec4bd5bbc898e1cf4930d53f986ed6e9163775 --- /dev/null +++ b/tdjAGitQHDo.txt @@ -0,0 +1,313 @@ +PROF. +WAMPLER: Well, + +the Cuba Studio last spring, +which was a level two studio, + +the overview follows my +philosophy about architecture. + +And that is that I don't +believe students should just be + +at MIT inside these walls +designing for people around the + +world. +I think the issue is + +maintaining identities of +people, of cultures, + +being sensitive to climate +conditions, architecture, + +where we are, +where they, in this case, + +may be working. +So the theory behind it is to + +take my students to a place that +they don't know, + +immerse them into that culture +as quickly as possible, + +let them talk to the people, +let them move around the city, + +let them absorb what there is +about that place so that when + +they design, it was a design +project, they are coming from + +the point of sensitivity to the +people and to the culture. + +Not from some Western notion +about what architecture should + +be or not from some intellectual +position, although that is + +important, but they are coming +from understanding the site, + +understanding the buildings, +the people, the culture, + +the history. +So that is central to all my + +work as an overview. +And the Cuba Studio is an + +example of that. +I think the goals of this + +studio, and also working with +Cuba are somewhat similar. + +I go places where I am invited +and where the studio can help, + +because MIT has incredible +researches. + +And let's share them with the +rest of the world if we can. + +So, actually, +the project in Cuba was one + +that they wanted because they +want prototype about how to + +develop areas. +In terms of what I want + +students to get out of this, +I want them to make the most + +beautiful buildings in the +world, but I want those + +buildings to relate to the +people. + +And so I am not just teaching +how to design buildings which, + +of course, is part of the +studio, nor am I teaching just + +that we should be making +beautiful building, + +but we should be making the +best architecture we can make + +and respond to the people's +needs. + +Now, I am critical of our +profession because I think often + +architects are what I call +technocrats. + +They just kind of follow what +somebody tells them to do and + +they are technicians. +My goal for the students is to + +come away, of course, +with open doors into a new way + +of looking at architecture. +There may never be a typical + +week, but I will tell you the +ingredients that go into + +teaching are a combination. +Today I am going to show some + +of my own work, +so it is a combination of + +lecturing and about work that I +have done. + +And, more importantly, +how I have gotten to that work + +not only to work. +It is a combination about + +lectures of particular subjects. +Maybe materials or sunlight, + +issues that I'm concerned +about. + +It is an intense experience, +what we call desk-side crits + +where you sit down with the +student and you look at their + +work. +And it is kind of an + +interesting process. +I have done it for years. + +You quickly see what they are +doing. + +They have sketched something or +they made a model and you have + +to very quickly say what you +think about that. + +We have what we call pinups +which are reviews. + +In my case, they are quite +often, once a week where the + +students put their work up and +we, as a class, + +talk about it. +I encourage my studio class to + +actually engage in the +discussion about the work. + +And, in fact, +just last week I asked them to + +trade models, +exchange models and talk about + +each other's work to get them +out of their own way of + +thinking. +And then there are periods of + +just working in the studio. +And then full scale reviews + +where I invite people in from +other faculty of the school or + +other professions to give them +feedback. + +I think in the studio teaching +it is important to get out of + +the studio and go into what I +call the library of architecture + +forum, everything that is around +us. + +In all my studios, +the site is very important to + +understand. +I tell them when I was in + +school I used to go sleep on the +site for a weekend, + +and I will cookout and so on, +so that I could get to know the + +site as well as my own backyard. +And then I would come back and + +announce to my professor that +the site was too beautiful to + +build on. +And I am glad I am not one of + +my students. +But anyway the point is to + +absorb the site as much as you +can, absorb the outside. + +So I think part of the studio, +or a big part of the studio is + +getting out of here, +getting out of MIT. + +Now, the other side of that is +that I bring people in who know + +about, in this case, +Havana, Cuba to talk, + +to give overviews. +I want my students to know as + +many different views as they +can. + +And then from that they make a +decision. + +I think the teaching of a +studio and the teaching of + +architects is the most important +thing we can do because I think + +the architects are the only ones +that are going to be looking out + +for the physical world. +And the physical world is in + +bad shape. +And, in this generation, + +it may disappear as we know it. +I think of architects as + +caretakers of the physical +world. + +I think we have to be +sensitive, much more sensitive + +than we have been to cultures, +to the land, + +to the forest, +to the water, + +to everything, +materials. + +We are more than technicians. +We are what I call creative + +leaders. +And I think that is a new role + +for us, and I think it is a very +important one that we take very + +seriously. \ No newline at end of file diff --git a/ttCKLZ2fWWE.txt b/ttCKLZ2fWWE.txt new file mode 100644 index 0000000000000000000000000000000000000000..25426b7cf3a35dbf768db7379d312fc98dc234d4 --- /dev/null +++ b/ttCKLZ2fWWE.txt @@ -0,0 +1,955 @@ +align:start position:0% + +here are the differential equations for + + align:start position:0% +here are the differential equations for + + + align:start position:0% +here are the differential equations for +the angular momentum of a tumbling box + + align:start position:0% +the angular momentum of a tumbling box + + + align:start position:0% +the angular momentum of a tumbling box +try throwing a book or a box or any + + align:start position:0% +try throwing a book or a box or any + + + align:start position:0% +try throwing a book or a box or any +rectilinear object whose three + + align:start position:0% +rectilinear object whose three + + + align:start position:0% +rectilinear object whose three +dimensions are all different into the + + align:start position:0% +dimensions are all different into the + + + align:start position:0% +dimensions are all different into the +air with a twist to make a tumble you + + align:start position:0% +air with a twist to make a tumble you + + + align:start position:0% +air with a twist to make a tumble you +can get it to rotate about its longest + + align:start position:0% +can get it to rotate about its longest + + + align:start position:0% +can get it to rotate about its longest +axis or about its shortest axis but you + + align:start position:0% +axis or about its shortest axis but you + + + align:start position:0% +axis or about its shortest axis but you +can't get it to rotate about its middle + + align:start position:0% +can't get it to rotate about its middle + + + align:start position:0% +can't get it to rotate about its middle +axis let's examine that phenomenon + + align:start position:0% +axis let's examine that phenomenon + + + align:start position:0% +axis let's examine that phenomenon +numerically here's the anonymous + + align:start position:0% +numerically here's the anonymous + + + align:start position:0% +numerically here's the anonymous +function defining those three system of + + align:start position:0% +function defining those three system of + + + align:start position:0% +function defining those three system of +three first-order differential equations + + align:start position:0% +three first-order differential equations + + + align:start position:0% +three first-order differential equations +now I'm going to start at with a initial + + align:start position:0% +now I'm going to start at with a initial + + + align:start position:0% +now I'm going to start at with a initial +condition that's near the first critical + + align:start position:0% +condition that's near the first critical + + + align:start position:0% +condition that's near the first critical +point one zero zero is a critical point + + align:start position:0% +point one zero zero is a critical point + + + align:start position:0% +point one zero zero is a critical point +and I'm going to take point two times a + + align:start position:0% +and I'm going to take point two times a + + + align:start position:0% +and I'm going to take point two times a +random number to be this ought to be + + align:start position:0% +random number to be this ought to be + + + align:start position:0% +random number to be this ought to be +near the critical point and then + + align:start position:0% +near the critical point and then + + + align:start position:0% +near the critical point and then +normalize it so that it has length one + + align:start position:0% +normalize it so that it has length one + + + align:start position:0% +normalize it so that it has length one +so this the largest component is the + + align:start position:0% +so this the largest component is the + + + align:start position:0% +so this the largest component is the +first component and the other two are + + align:start position:0% +first component and the other two are + + + align:start position:0% +first component and the other two are +small but not too small under this is an + + align:start position:0% +small but not too small under this is an + + + align:start position:0% +small but not too small under this is an +easy problem numerically there's no + + align:start position:0% +easy problem numerically there's no + + + align:start position:0% +easy problem numerically there's no +stiffness involved here so I'm going to + + align:start position:0% +stiffness involved here so I'm going to + + + align:start position:0% +stiffness involved here so I'm going to +use only e23 + + align:start position:0% + + + + align:start position:0% + +integrate from zero to ten and here's + + align:start position:0% +integrate from zero to ten and here's + + + align:start position:0% +integrate from zero to ten and here's +the solution the blue component is the + + align:start position:0% +the solution the blue component is the + + + align:start position:0% +the solution the blue component is the +is the first one and it stays near one + + align:start position:0% +is the first one and it stays near one + + + align:start position:0% +is the first one and it stays near one +and the other two are periodic rotating + + align:start position:0% +and the other two are periodic rotating + + + align:start position:0% +and the other two are periodic rotating +around zero let's go back and take + + align:start position:0% +around zero let's go back and take + + + align:start position:0% +around zero let's go back and take +another starting condition here it is + + align:start position:0% +another starting condition here it is + + + align:start position:0% +another starting condition here it is +again + + align:start position:0% +again + + + align:start position:0% +again +now the the second the other two + + align:start position:0% +now the the second the other two + + + align:start position:0% +now the the second the other two +components are really small and when we + + align:start position:0% +components are really small and when we + + + align:start position:0% +components are really small and when we +integrate that the blue components a is + + align:start position:0% +integrate that the blue components a is + + + align:start position:0% +integrate that the blue components a is +flat near one and the other two guys + + align:start position:0% +flat near one and the other two guys + + + align:start position:0% +flat near one and the other two guys +hardly move at all now I'm going to go + + align:start position:0% +hardly move at all now I'm going to go + + + align:start position:0% +hardly move at all now I'm going to go +to the third critical point zero zero + + align:start position:0% +to the third critical point zero zero + + + align:start position:0% +to the third critical point zero zero +one do the same thing take a random + + align:start position:0% +one do the same thing take a random + + + align:start position:0% +one do the same thing take a random +number near there + + align:start position:0% +number near there + + + align:start position:0% +number near there +use OD twenty three now that yellow + + align:start position:0% +use OD twenty three now that yellow + + + align:start position:0% +use OD twenty three now that yellow +component stays near one and the other + + align:start position:0% +component stays near one and the other + + + align:start position:0% +component stays near one and the other +two moved periodically around zero run + + align:start position:0% +two moved periodically around zero run + + + align:start position:0% +two moved periodically around zero run +that again third component is near one + + align:start position:0% +that again third component is near one + + + align:start position:0% +that again third component is near one +the other two are not too big and run OD + + align:start position:0% +the other two are not too big and run OD + + + align:start position:0% +the other two are not too big and run OD +e 23 the other component stays there one + + align:start position:0% +e 23 the other component stays there one + + + align:start position:0% +e 23 the other component stays there one +and the other to rotate periodically + + align:start position:0% +and the other to rotate periodically + + + align:start position:0% +and the other to rotate periodically +around zero now we're going to go to the + + align:start position:0% +around zero now we're going to go to the + + + align:start position:0% +around zero now we're going to go to the +mythical middle critical point we're + + align:start position:0% +mythical middle critical point we're + + + align:start position:0% +mythical middle critical point we're +going to try and get the box to rotate + + align:start position:0% +going to try and get the box to rotate + + + align:start position:0% +going to try and get the box to rotate +around its middle axis the second + + align:start position:0% +around its middle axis the second + + + align:start position:0% +around its middle axis the second +component is the one near one and now we + + align:start position:0% +component is the one near one and now we + + + align:start position:0% +component is the one near one and now we +see completely different behavior this + + align:start position:0% + + + + align:start position:0% + +Seanna component doesn't stay near one + + align:start position:0% +Seanna component doesn't stay near one + + + align:start position:0% +Seanna component doesn't stay near one +it goes down there but minus one and + + align:start position:0% +it goes down there but minus one and + + + align:start position:0% +it goes down there but minus one and +comes back up let's integrate over a + + align:start position:0% +comes back up let's integrate over a + + + align:start position:0% +comes back up let's integrate over a +longer period so we can see that + + align:start position:0% +longer period so we can see that + + + align:start position:0% +longer period so we can see that +behavior so it's periodic but it goes + + align:start position:0% +behavior so it's periodic but it goes + + + align:start position:0% +behavior so it's periodic but it goes +down to minus one it comes back to one + + align:start position:0% +down to minus one it comes back to one + + + align:start position:0% +down to minus one it comes back to one +and the other to move in large + + align:start position:0% +and the other to move in large + + + align:start position:0% +and the other to move in large +amplitudes around zero so this is the + + align:start position:0% +amplitudes around zero so this is the + + + align:start position:0% +amplitudes around zero so this is the +instability of that middle middle middle + + align:start position:0% +instability of that middle middle middle + + + align:start position:0% +instability of that middle middle middle +critical value let's do it again same + + align:start position:0% +critical value let's do it again same + + + align:start position:0% +critical value let's do it again same +thing one down 2-1 back + + align:start position:0% +thing one down 2-1 back + + + align:start position:0% +thing one down 2-1 back +it's periodic these solutions are all + + align:start position:0% +it's periodic these solutions are all + + + align:start position:0% +it's periodic these solutions are all +periodic but that middle critical point + + align:start position:0% +periodic but that middle critical point + + + align:start position:0% +periodic but that middle critical point +is unstable now I want to view these in + + align:start position:0% +is unstable now I want to view these in + + + align:start position:0% +is unstable now I want to view these in +a in a different way graphically the + + align:start position:0% +a in a different way graphically the + + + align:start position:0% +a in a different way graphically the +differential equations have these three + + align:start position:0% +differential equations have these three + + + align:start position:0% +differential equations have these three +critical points and the solutions that + + align:start position:0% +critical points and the solutions that + + + align:start position:0% +critical points and the solutions that +start exactly on these initial + + align:start position:0% +start exactly on these initial + + + align:start position:0% +start exactly on these initial +conditions stay there but what happens + + align:start position:0% +conditions stay there but what happens + + + align:start position:0% +conditions stay there but what happens +if you start near these initial + + align:start position:0% +if you start near these initial + + + align:start position:0% +if you start near these initial +conditions well it turns out that X and + + align:start position:0% +conditions well it turns out that X and + + + align:start position:0% +conditions well it turns out that X and +Z are stable critical points but Y is an + + align:start position:0% +Z are stable critical points but Y is an + + + align:start position:0% +Z are stable critical points but Y is an +unstable critical point if the angular + + align:start position:0% +unstable critical point if the angular + + + align:start position:0% +unstable critical point if the angular +momentum is near X or near Z it stays + + align:start position:0% +momentum is near X or near Z it stays + + + align:start position:0% +momentum is near X or near Z it stays +near there but if it starts near Y it + + align:start position:0% +near there but if it starts near Y it + + + align:start position:0% +near there but if it starts near Y it +moves away quickly you can think of X as + + align:start position:0% +moves away quickly you can think of X as + + + align:start position:0% +moves away quickly you can think of X as +the short axis and Z is the long axis + + align:start position:0% +the short axis and Z is the long axis + + + align:start position:0% +the short axis and Z is the long axis +rotation near the short axis is stable + + align:start position:0% +rotation near the short axis is stable + + + align:start position:0% +rotation near the short axis is stable +and rotation near the long axis is + + align:start position:0% +and rotation near the long axis is + + + align:start position:0% +and rotation near the long axis is +stable the rotation near the middle axis + + align:start position:0% +stable the rotation near the middle axis + + + align:start position:0% +stable the rotation near the middle axis +is unstable we can see that in the + + align:start position:0% +is unstable we can see that in the + + + align:start position:0% +is unstable we can see that in the +following graphic it turns out that if a + + align:start position:0% +following graphic it turns out that if a + + + align:start position:0% +following graphic it turns out that if a +solution starts with a initial condition + + align:start position:0% +solution starts with a initial condition + + + align:start position:0% +solution starts with a initial condition +that has norm one + + align:start position:0% +that has norm one + + + align:start position:0% +that has norm one +it stays with norm one so the solution + + align:start position:0% +it stays with norm one so the solution + + + align:start position:0% +it stays with norm one so the solution +lives on the unit sphere here's our unit + + align:start position:0% +lives on the unit sphere here's our unit + + + align:start position:0% +lives on the unit sphere here's our unit +sphere with our three critical points XY + + align:start position:0% +sphere with our three critical points XY + + + align:start position:0% +sphere with our three critical points XY +and z if this were the earth the Z would + + align:start position:0% +and z if this were the earth the Z would + + + align:start position:0% +and z if this were the earth the Z would +be the North Pole X is where where the + + align:start position:0% +be the North Pole X is where where the + + + align:start position:0% +be the North Pole X is where where the +0th meridian crosses the equator that's + + align:start position:0% +0th meridian crosses the equator that's + + + align:start position:0% +0th meridian crosses the equator that's +in the East Atlantic a little off of + + align:start position:0% +in the East Atlantic a little off of + + + align:start position:0% +in the East Atlantic a little off of +West Africa Y would be where the 90th + + align:start position:0% +West Africa Y would be where the 90th + + + align:start position:0% +West Africa Y would be where the 90th +Meridian crosses the equator that's in + + align:start position:0% +Meridian crosses the equator that's in + + + align:start position:0% +Meridian crosses the equator that's in +the Indian Ocean west of Sumatra if we + + align:start position:0% +the Indian Ocean west of Sumatra if we + + + align:start position:0% +the Indian Ocean west of Sumatra if we +start with an initial condition near X + + align:start position:0% +start with an initial condition near X + + + align:start position:0% +start with an initial condition near X +it orbits the solution orbits around + + align:start position:0% +it orbits the solution orbits around + + + align:start position:0% +it orbits the solution orbits around +that's that's stable rotation around the + + align:start position:0% +that's that's stable rotation around the + + + align:start position:0% +that's that's stable rotation around the +short axis if we start with an initial + + align:start position:0% +short axis if we start with an initial + + + align:start position:0% +short axis if we start with an initial +condition Z near Z the solution orbits + + align:start position:0% +condition Z near Z the solution orbits + + + align:start position:0% +condition Z near Z the solution orbits +around Z that's stable rotation around + + align:start position:0% +around Z that's stable rotation around + + + align:start position:0% +around Z that's stable rotation around +the long axis but if we start near y the + + align:start position:0% +the long axis but if we start near y the + + + align:start position:0% +the long axis but if we start near y the +solution takes off goes over to near + + align:start position:0% +solution takes off goes over to near + + + align:start position:0% +solution takes off goes over to near +minus y turns around and comes back to Y + + align:start position:0% +minus y turns around and comes back to Y + + + align:start position:0% +minus y turns around and comes back to Y +periodic but it was clear around the + + align:start position:0% +periodic but it was clear around the + + + align:start position:0% +periodic but it was clear around the +globe that turns out that's a circle + + align:start position:0% +globe that turns out that's a circle + + + align:start position:0% +globe that turns out that's a circle +actually it's an orbit around X if we + + align:start position:0% +actually it's an orbit around X if we + + + align:start position:0% +actually it's an orbit around X if we +come up a little above Y we get an orbit + + align:start position:0% +come up a little above Y we get an orbit + + + align:start position:0% +come up a little above Y we get an orbit +around Z go down a little blow Y we get + + align:start position:0% +around Z go down a little blow Y we get + + + align:start position:0% +around Z go down a little blow Y we get +an orbit around minus Z go to the right + + align:start position:0% +an orbit around minus Z go to the right + + + align:start position:0% +an orbit around minus Z go to the right +of Y we've got an orbit around minus X + + align:start position:0% +of Y we've got an orbit around minus X + + + align:start position:0% +of Y we've got an orbit around minus X +let's zoom in a little bit + + align:start position:0% + + + + align:start position:0% + +and we can see that Y is a classic + + align:start position:0% +and we can see that Y is a classic + + + align:start position:0% +and we can see that Y is a classic +unstable critical point + + align:start position:0% + + + + align:start position:0% + +let's conclude by drawing a few orbits + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/uK5yvoXnkSk.txt b/uK5yvoXnkSk.txt new file mode 100644 index 0000000000000000000000000000000000000000..9509d7909f1b972266a3011c59fdeb601a49a0fc --- /dev/null +++ b/uK5yvoXnkSk.txt @@ -0,0 +1,7739 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common license. Your support + + align:start position:0% +a Creative Common license. Your support + + + align:start position:0% +a Creative Common license. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +All right, we ended the last lecture + + align:start position:0% +All right, we ended the last lecture + + + align:start position:0% +All right, we ended the last lecture +looking at greedy algorithms and so + + align:start position:0% +looking at greedy algorithms and so + + + align:start position:0% +looking at greedy algorithms and so +today I want to discuss the pros and + + align:start position:0% +today I want to discuss the pros and + + + align:start position:0% +today I want to discuss the pros and +cons of greedy. Oh, I should mention in + + align:start position:0% +cons of greedy. Oh, I should mention in + + + align:start position:0% +cons of greedy. Oh, I should mention in +response to popular demand I have put + + align:start position:0% +response to popular demand I have put + + + align:start position:0% +response to popular demand I have put +the PowerPoint up. So if you download + + align:start position:0% +the PowerPoint up. So if you download + + + align:start position:0% +the PowerPoint up. So if you download +the zip file, you'll find the questions + + align:start position:0% +the zip file, you'll find the questions + + + align:start position:0% +the zip file, you'll find the questions +including question one, the first + + align:start position:0% +including question one, the first + + + align:start position:0% +including question one, the first +question plus the code plus the + + align:start position:0% +question plus the code plus the + + + align:start position:0% +question plus the code plus the +PowerPoint. Um we actually do read Piaza + + align:start position:0% +PowerPoint. Um we actually do read Piaza + + + align:start position:0% +PowerPoint. Um we actually do read Piaza +and sometimes at least pay attention. We + + align:start position:0% +and sometimes at least pay attention. We + + + align:start position:0% +and sometimes at least pay attention. We +should pay attention all the time. All + + align:start position:0% +should pay attention all the time. All + + + align:start position:0% +should pay attention all the time. All +right. + + align:start position:0% +right. + + + align:start position:0% +right. +So what are the pros and cons of greedy? + + align:start position:0% +So what are the pros and cons of greedy? + + + align:start position:0% +So what are the pros and cons of greedy? +Uh the pro and it's a big pro is that + + align:start position:0% +Uh the pro and it's a big pro is that + + + align:start position:0% +Uh the pro and it's a big pro is that +it's really easy to implement as you + + align:start position:0% +it's really easy to implement as you + + + align:start position:0% +it's really easy to implement as you +could see. + + align:start position:0% +could see. + + + align:start position:0% +could see. +also enormously important. It's really + + align:start position:0% +also enormously important. It's really + + + align:start position:0% +also enormously important. It's really +fast. We looked at the complexity last + + align:start position:0% +fast. We looked at the complexity last + + + align:start position:0% +fast. We looked at the complexity last +time. It was n login quite quick. Uh the + + align:start position:0% +time. It was n login quite quick. Uh the + + + align:start position:0% +time. It was n login quite quick. Uh the +downside and this can be either a big + + align:start position:0% +downside and this can be either a big + + + align:start position:0% +downside and this can be either a big +problem or not a big problem is that it + + align:start position:0% +problem or not a big problem is that it + + + align:start position:0% +problem or not a big problem is that it +doesn't actually solve the problem in + + align:start position:0% +doesn't actually solve the problem in + + + align:start position:0% +doesn't actually solve the problem in +the sense that we've asked ourselves to + + align:start position:0% +the sense that we've asked ourselves to + + + align:start position:0% +the sense that we've asked ourselves to +optimize something and we get a solution + + align:start position:0% +optimize something and we get a solution + + + align:start position:0% +optimize something and we get a solution +that may or may not be optimal. + + align:start position:0% +that may or may not be optimal. + + + align:start position:0% +that may or may not be optimal. +worse. We don't even know in this case + + align:start position:0% +worse. We don't even know in this case + + + align:start position:0% +worse. We don't even know in this case +how close to optimal it is. Maybe it's + + align:start position:0% +how close to optimal it is. Maybe it's + + + align:start position:0% +how close to optimal it is. Maybe it's +almost optimal, but maybe it's really + + align:start position:0% +almost optimal, but maybe it's really + + + align:start position:0% +almost optimal, but maybe it's really +far away. And that's a big problem with + + align:start position:0% +far away. And that's a big problem with + + + align:start position:0% +far away. And that's a big problem with +many greedy algorithms. There are some + + align:start position:0% +many greedy algorithms. There are some + + + align:start position:0% +many greedy algorithms. There are some +very sophisticated sophisticated greedy + + align:start position:0% +very sophisticated sophisticated greedy + + + align:start position:0% +very sophisticated sophisticated greedy +algorithms we won't be looking at that + + align:start position:0% +algorithms we won't be looking at that + + + align:start position:0% +algorithms we won't be looking at that +give you a bound on how good the + + align:start position:0% +give you a bound on how good the + + + align:start position:0% +give you a bound on how good the +approximation is, but most of them don't + + align:start position:0% +approximation is, but most of them don't + + + align:start position:0% +approximation is, but most of them don't +do that. + + align:start position:0% +do that. + + + align:start position:0% +do that. +Last time we looked at an alternative to + + align:start position:0% +Last time we looked at an alternative to + + + align:start position:0% +Last time we looked at an alternative to +a greedy algorithm that was guaranteed + + align:start position:0% +a greedy algorithm that was guaranteed + + + align:start position:0% +a greedy algorithm that was guaranteed +to find the right solution. It was a + + align:start position:0% +to find the right solution. It was a + + + align:start position:0% +to find the right solution. It was a +brute force algorithm. The basic idea is + + align:start position:0% +brute force algorithm. The basic idea is + + + align:start position:0% +brute force algorithm. The basic idea is +simple that you enumerate all possible + + align:start position:0% +simple that you enumerate all possible + + + align:start position:0% +simple that you enumerate all possible +combinations of + + align:start position:0% +combinations of + + + align:start position:0% +combinations of +items, remove the combination whose + + align:start position:0% +items, remove the combination whose + + + align:start position:0% +items, remove the combination whose +total units exceed the allowable weight + + align:start position:0% +total units exceed the allowable weight + + + align:start position:0% +total units exceed the allowable weight +and then choose the winner from those + + align:start position:0% +and then choose the winner from those + + + align:start position:0% +and then choose the winner from those +that are + + align:start position:0% +that are + + + align:start position:0% +that are +remaining. Now let's talk about how to + + align:start position:0% +remaining. Now let's talk about how to + + + align:start position:0% +remaining. Now let's talk about how to +implement it. And the way I want to + + align:start position:0% +implement it. And the way I want to + + + align:start position:0% +implement it. And the way I want to +implement it is using something called a + + align:start position:0% +implement it is using something called a + + + align:start position:0% +implement it is using something called a +search tree. Um there are lots of + + align:start position:0% +search tree. Um there are lots of + + + align:start position:0% +search tree. Um there are lots of +different ways to implement it. In the + + align:start position:0% +different ways to implement it. In the + + + align:start position:0% +different ways to implement it. In the +second half of today's lecture, you'll + + align:start position:0% +second half of today's lecture, you'll + + + align:start position:0% +second half of today's lecture, you'll +see why I happen to choose this + + align:start position:0% +see why I happen to choose this + + + align:start position:0% +see why I happen to choose this +particular + + align:start position:0% +particular + + + align:start position:0% +particular +approach. So what is a search tree? A + + align:start position:0% +approach. So what is a search tree? A + + + align:start position:0% +approach. So what is a search tree? A +tree is + + align:start position:0% +tree is + + + align:start position:0% +tree is +basically a kind of graph. And we'll + + align:start position:0% +basically a kind of graph. And we'll + + + align:start position:0% +basically a kind of graph. And we'll +hear much more about graphs next week. + + align:start position:0% +hear much more about graphs next week. + + + align:start position:0% +hear much more about graphs next week. +But this is a simple form where you have + + align:start position:0% +But this is a simple form where you have + + + align:start position:0% +But this is a simple form where you have +a + + align:start position:0% +a + + + align:start position:0% +a +root and then children of the root. In + + align:start position:0% +root and then children of the root. In + + + align:start position:0% +root and then children of the root. In +this particular form research see you + + align:start position:0% +this particular form research see you + + + align:start position:0% +this particular form research see you +have two children. So we start with the + + align:start position:0% + + + + align:start position:0% + +root and then we look at our list of + + align:start position:0% +root and then we look at our list of + + + align:start position:0% +root and then we look at our list of +elements to be considered that we might + + align:start position:0% +elements to be considered that we might + + + align:start position:0% +elements to be considered that we might +take and we look at the first element in + + align:start position:0% +take and we look at the first element in + + + align:start position:0% +take and we look at the first element in +that list and then we draw a left + + align:start position:0% +that list and then we draw a left + + + align:start position:0% +that list and then we draw a left +branch which shows the consequence of + + align:start position:0% +branch which shows the consequence of + + + align:start position:0% +branch which shows the consequence of +choosing to take that element and a + + align:start position:0% +choosing to take that element and a + + + align:start position:0% +choosing to take that element and a +right branch which shows the + + align:start position:0% +right branch which shows the + + + align:start position:0% +right branch which shows the +consequences of not taking that element. + + align:start position:0% + + + + align:start position:0% + +and then we consider the second + + align:start position:0% +and then we consider the second + + + align:start position:0% +and then we consider the second +element and so on and so + + align:start position:0% +element and so on and so + + + align:start position:0% +element and so on and so +forth until we get to the bottom of the + + align:start position:0% +forth until we get to the bottom of the + + + align:start position:0% +forth until we get to the bottom of the +tree. So by convention the left element + + align:start position:0% +tree. So by convention the left element + + + align:start position:0% +tree. So by convention the left element +will mean we took it the right direction + + align:start position:0% +will mean we took it the right direction + + + align:start position:0% +will mean we took it the right direction +will mean we didn't take + + align:start position:0% + + + + align:start position:0% + +it and then we apply it recursively to + + align:start position:0% +it and then we apply it recursively to + + + align:start position:0% +it and then we apply it recursively to +the non-leaf children. The leaf means we + + align:start position:0% +the non-leaf children. The leaf means we + + + align:start position:0% +the non-leaf children. The leaf means we +get to the end. We've considered the + + align:start position:0% +get to the end. We've considered the + + + align:start position:0% +get to the end. We've considered the +last element to be considered. Nothing + + align:start position:0% +last element to be considered. Nothing + + + align:start position:0% +last element to be considered. Nothing +else to think about. + + align:start position:0% +else to think about. + + + align:start position:0% +else to think about. +So when we get to the code, we'll see + + align:start position:0% +So when we get to the code, we'll see + + + align:start position:0% +So when we get to the code, we'll see +that in addition to the description + + align:start position:0% +that in addition to the description + + + align:start position:0% +that in addition to the description +being recursive, it's convenient to + + align:start position:0% +being recursive, it's convenient to + + + align:start position:0% +being recursive, it's convenient to +write the code that way + + align:start position:0% +write the code that way + + + align:start position:0% +write the code that way +too. And then finally, we'll choose the + + align:start position:0% +too. And then finally, we'll choose the + + + align:start position:0% +too. And then finally, we'll choose the +node that has the highest value that + + align:start position:0% +node that has the highest value that + + + align:start position:0% +node that has the highest value that +meets our constraints. So let's look at + + align:start position:0% +meets our constraints. So let's look at + + + align:start position:0% +meets our constraints. So let's look at +an example. So my example is I have my + + align:start position:0% +an example. So my example is I have my + + + align:start position:0% +an example. So my example is I have my +backpack that can hold a certain number + + align:start position:0% +backpack that can hold a certain number + + + align:start position:0% +backpack that can hold a certain number +of calories, if you will, and I'm + + align:start position:0% +of calories, if you will, and I'm + + + align:start position:0% +of calories, if you will, and I'm +choosing between to keep it small a + + align:start position:0% +choosing between to keep it small a + + + align:start position:0% +choosing between to keep it small a +beer, a pizza, and a burger. + + align:start position:0% +beer, a pizza, and a burger. + + + align:start position:0% +beer, a pizza, and a burger. +three essential food + + align:start position:0% +three essential food + + + align:start position:0% +three essential food +groups. So the first thing I explore on + + align:start position:0% +groups. So the first thing I explore on + + + align:start position:0% +groups. So the first thing I explore on +the left is take the + + align:start position:0% +the left is take the + + + align:start position:0% +the left is take the +beer and then I have the pizza and the + + align:start position:0% +beer and then I have the pizza and the + + + align:start position:0% +beer and then I have the pizza and the +burger to continue to + + align:start position:0% +burger to continue to + + + align:start position:0% +burger to continue to +consider. I then say all right let's + + align:start position:0% +consider. I then say all right let's + + + align:start position:0% +consider. I then say all right let's +take the pizza. Now I have just the + + align:start position:0% +take the pizza. Now I have just the + + + align:start position:0% +take the pizza. Now I have just the +burger now I taste the burger. So this + + align:start position:0% +burger now I taste the burger. So this + + + align:start position:0% +burger now I taste the burger. So this +traversal or this generation of the tree + + align:start position:0% +traversal or this generation of the tree + + + align:start position:0% +traversal or this generation of the tree +is called + + align:start position:0% +is called + + + align:start position:0% +is called +leftmost depthmost. So, I go all the way + + align:start position:0% +leftmost depthmost. So, I go all the way + + + align:start position:0% +leftmost depthmost. So, I go all the way +down to the bottom of the + + align:start position:0% +down to the bottom of the + + + align:start position:0% +down to the bottom of the +tree. I then back up a level and say, + + align:start position:0% +tree. I then back up a level and say, + + + align:start position:0% +tree. I then back up a level and say, +"All right, I'm now at the + + align:start position:0% +"All right, I'm now at the + + + align:start position:0% +"All right, I'm now at the +bottom. Let's go + + align:start position:0% +bottom. Let's go + + + align:start position:0% +bottom. Let's go +back + + align:start position:0% +back + + + align:start position:0% +back +and see what happens if I make the other + + align:start position:0% +and see what happens if I make the other + + + align:start position:0% +and see what happens if I make the other +choice at the one level up the tree." + + align:start position:0% +choice at the one level up the tree." + + + align:start position:0% +choice at the one level up the tree." +So, I've went up and said, "Well, now + + align:start position:0% +So, I've went up and said, "Well, now + + + align:start position:0% +So, I've went up and said, "Well, now +let's see what happens if + + align:start position:0% +let's see what happens if + + + align:start position:0% +let's see what happens if +I make a different decision as in we + + align:start position:0% +I make a different decision as in we + + + align:start position:0% +I make a different decision as in we +didn't take the + + align:start position:0% +didn't take the + + + align:start position:0% +didn't take the +burger." And then I work my way I this + + align:start position:0% +burger." And then I work my way I this + + + align:start position:0% +burger." And then I work my way I this +is called backtracking up another level. + + align:start position:0% +is called backtracking up another level. + + + align:start position:0% +is called backtracking up another level. +I now say suppose I didn't take the + + align:start position:0% +I now say suppose I didn't take the + + + align:start position:0% +I now say suppose I didn't take the +piece of pizza. Now I have the beer only + + align:start position:0% +piece of pizza. Now I have the beer only + + + align:start position:0% +piece of pizza. Now I have the beer only +and only the burger to think about. so + + align:start position:0% +and only the burger to think about. so + + + align:start position:0% +and only the burger to think about. so +on and so + + align:start position:0% + + + + align:start position:0% + +forth until I've generated the whole + + align:start position:0% +forth until I've generated the whole + + + align:start position:0% +forth until I've generated the whole +tree. You'll notice it will always be + + align:start position:0% +tree. You'll notice it will always be + + + align:start position:0% +tree. You'll notice it will always be +the case that the leftmost leaf of this + + align:start position:0% +the case that the leftmost leaf of this + + + align:start position:0% +the case that the leftmost leaf of this +tree has got all of the possible items + + align:start position:0% +tree has got all of the possible items + + + align:start position:0% +tree has got all of the possible items +in it and the rightmost leaf + + align:start position:0% +in it and the rightmost leaf + + + align:start position:0% +in it and the rightmost leaf +none. And then I just check which of + + align:start position:0% +none. And then I just check which of + + + align:start position:0% +none. And then I just check which of +these leaves meets the + + align:start position:0% +these leaves meets the + + + align:start position:0% +these leaves meets the +constraint and what are the values. And + + align:start position:0% +constraint and what are the values. And + + + align:start position:0% +constraint and what are the values. And +if I compute the + + align:start position:0% +if I compute the + + + align:start position:0% +if I compute the +value and the calories in each one and + + align:start position:0% +value and the calories in each one and + + + align:start position:0% +value and the calories in each one and +if our constraint was 750 calories then + + align:start position:0% +if our constraint was 750 calories then + + + align:start position:0% +if our constraint was 750 calories then +I get to choose the winner which is + + align:start position:0% +I get to choose the winner which is + + + align:start position:0% +I get to choose the winner which is +uh I guess it's the pizza and the + + align:start position:0% +uh I guess it's the pizza and the + + + align:start position:0% +uh I guess it's the pizza and the +burger. Is that + + align:start position:0% +burger. Is that + + + align:start position:0% +burger. Is that +right? the most value under + + align:start position:0% + + + + align:start position:0% + +750. Okay. All right. So, that's the way + + align:start position:0% +750. Okay. All right. So, that's the way + + + align:start position:0% +750. Okay. All right. So, that's the way +I go through and I do that. It's a quite + + align:start position:0% +I go through and I do that. It's a quite + + + align:start position:0% +I go through and I do that. It's a quite +a straightforward + + align:start position:0% +a straightforward + + + align:start position:0% +a straightforward +algorithm. And I don't know why we draw + + align:start position:0% +algorithm. And I don't know why we draw + + + align:start position:0% +algorithm. And I don't know why we draw +our trees with the root at the top and + + align:start position:0% +our trees with the root at the top and + + + align:start position:0% +our trees with the root at the top and +the leaves at the bottom. Uh my only + + align:start position:0% +the leaves at the bottom. Uh my only + + + align:start position:0% +the leaves at the bottom. Uh my only +conjecture is computer scientists don't + + align:start position:0% +conjecture is computer scientists don't + + + align:start position:0% +conjecture is computer scientists don't +spend enough time + + align:start position:0% +spend enough time + + + align:start position:0% +spend enough time +outdoors. Um all right. So now let's + + align:start position:0% +outdoors. Um all right. So now let's + + + align:start position:0% +outdoors. Um all right. So now let's +think of the computational complexity of + + align:start position:0% +think of the computational complexity of + + + align:start position:0% +think of the computational complexity of +this + + align:start position:0% +this + + + align:start position:0% +this +process. Well, the time is going to be + + align:start position:0% +process. Well, the time is going to be + + + align:start position:0% +process. Well, the time is going to be +based on the total number of nodes we + + align:start position:0% +based on the total number of nodes we + + + align:start position:0% +based on the total number of nodes we +generate. So if we know the number of + + align:start position:0% +generate. So if we know the number of + + + align:start position:0% +generate. So if we know the number of +nodes that are in the tree, we then know + + align:start position:0% +nodes that are in the tree, we then know + + + align:start position:0% +nodes that are in the tree, we then know +the complexity of the algorithm, the + + align:start position:0% +the complexity of the algorithm, the + + + align:start position:0% +the complexity of the algorithm, the +asmtoic + + align:start position:0% +asmtoic + + + align:start position:0% +asmtoic +complexity. + + align:start position:0% +complexity. + + + align:start position:0% +complexity. +Well, how many levels do we have in the + + align:start position:0% +Well, how many levels do we have in the + + + align:start position:0% +Well, how many levels do we have in the +tree? Just the number of items, right? + + align:start position:0% +tree? Just the number of items, right? + + + align:start position:0% +tree? Just the number of items, right? +because at each level of the tree, we're + + align:start position:0% +because at each level of the tree, we're + + + align:start position:0% +because at each level of the tree, we're +deciding to take or not take an + + align:start position:0% +deciding to take or not take an + + + align:start position:0% +deciding to take or not take an +item. And so we can only do that for the + + align:start position:0% +item. And so we can only do that for the + + + align:start position:0% +item. And so we can only do that for the +number of items we + + align:start position:0% +number of items we + + + align:start position:0% +number of items we +have. So if we go back, for example, and + + align:start position:0% +have. So if we go back, for example, and + + + align:start position:0% +have. So if we go back, for example, and +we look at the tree, not that tree, that + + align:start position:0% +we look at the tree, not that tree, that + + + align:start position:0% +we look at the tree, not that tree, that +tree, and we count the number of levels, + + align:start position:0% +tree, and we count the number of levels, + + + align:start position:0% +tree, and we count the number of levels, +it's going to be based upon the total + + align:start position:0% +it's going to be based upon the total + + + align:start position:0% +it's going to be based upon the total +number of items. + + align:start position:0% +number of items. + + + align:start position:0% +number of items. +We know that because if you look at say + + align:start position:0% +We know that because if you look at say + + + align:start position:0% +We know that because if you look at say +the leftmost node at the bottom, it's + + align:start position:0% +the leftmost node at the bottom, it's + + + align:start position:0% +the leftmost node at the bottom, it's +we've made three separate + + align:start position:0% +we've made three separate + + + align:start position:0% +we've made three separate +decisions. So here it's counting the + + align:start position:0% +decisions. So here it's counting the + + + align:start position:0% +decisions. So here it's counting the +root. It's one two it's n + one. But we + + align:start position:0% +root. It's one two it's n + one. But we + + + align:start position:0% +root. It's one two it's n + one. But we +don't care about plus one, right? When + + align:start position:0% +don't care about plus one, right? When + + + align:start position:0% +don't care about plus one, right? When +we're doing asmtoic + + align:start position:0% +we're doing asmtoic + + + align:start position:0% +we're doing asmtoic +complexity. All right. So that tells us + + align:start position:0% +complexity. All right. So that tells us + + + align:start position:0% +complexity. All right. So that tells us +how many levels we have in the + + align:start position:0% +how many levels we have in the + + + align:start position:0% +how many levels we have in the +tree. The next question we need to ask + + align:start position:0% +tree. The next question we need to ask + + + align:start position:0% +tree. The next question we need to ask +is how many nodes are there at each + + align:start position:0% +is how many nodes are there at each + + + align:start position:0% +is how many nodes are there at each +level? + + align:start position:0% +level? + + + align:start position:0% +level? +And you can sort of look at this and see + + align:start position:0% +And you can sort of look at this and see + + + align:start position:0% +And you can sort of look at this and see +the deeper we go the more nodes we have + + align:start position:0% +the deeper we go the more nodes we have + + + align:start position:0% +the deeper we go the more nodes we have +at each level. + + align:start position:0% +at each level. + + + align:start position:0% +at each level. +Right? And in fact if we come + + align:start position:0% + + + + align:start position:0% + +here we can see that the number of nodes + + align:start position:0% +here we can see that the number of nodes + + + align:start position:0% +here we can see that the number of nodes +at level I depth I of the tree is 2 to + + align:start position:0% +at level I depth I of the tree is 2 to + + + align:start position:0% +at level I depth I of the tree is 2 to +the + + align:start position:0% +the + + + align:start position:0% +the +I. That makes sense. If you remember + + align:start position:0% +I. That makes sense. If you remember + + + align:start position:0% +I. That makes sense. If you remember +last time we looked at binary numbers + + align:start position:0% +last time we looked at binary numbers + + + align:start position:0% +last time we looked at binary numbers +and we're saying we're representing our + + align:start position:0% +and we're saying we're representing our + + + align:start position:0% +and we're saying we're representing our +choices as either zero or one for what + + align:start position:0% +choices as either zero or one for what + + + align:start position:0% +choices as either zero or one for what +we take. If we have n items to choose + + align:start position:0% +we take. If we have n items to choose + + + align:start position:0% +we take. If we have n items to choose +from then the number of possible choices + + align:start position:0% +from then the number of possible choices + + + align:start position:0% +from then the number of possible choices +is two to the n the size of the power + + align:start position:0% +is two to the n the size of the power + + + align:start position:0% +is two to the n the size of the power +set. And so that will tell us the number + + align:start position:0% +set. And so that will tell us the number + + + align:start position:0% +set. And so that will tell us the number +of nodes at each level. + + align:start position:0% + + + + align:start position:0% + +So if there are n items, the number of + + align:start position:0% +So if there are n items, the number of + + + align:start position:0% +So if there are n items, the number of +nodes in the tree is going to be the sum + + align:start position:0% +nodes in the tree is going to be the sum + + + align:start position:0% +nodes in the tree is going to be the sum +from 0 to n of 2 to the i because we + + align:start position:0% +from 0 to n of 2 to the i because we + + + align:start position:0% +from 0 to n of 2 to the i because we +have that many levels. And if you've + + align:start position:0% +have that many levels. And if you've + + + align:start position:0% +have that many levels. And if you've +studied a little math, you know that's + + align:start position:0% +studied a little math, you know that's + + + align:start position:0% +studied a little math, you know that's +exactly 2 to the n + + + align:start position:0% +exactly 2 to the n + + + + align:start position:0% +exactly 2 to the n + +one. Or if you do what I did, you'd look + + align:start position:0% +one. Or if you do what I did, you'd look + + + align:start position:0% +one. Or if you do what I did, you'd look +it up in Wikipedia and you know it's 2 + + align:start position:0% +it up in Wikipedia and you know it's 2 + + + align:start position:0% +it up in Wikipedia and you know it's 2 +to the n plus + + align:start position:0% +to the n plus + + + align:start position:0% +to the n plus +one. Now there's an obvious + + align:start position:0% +one. Now there's an obvious + + + align:start position:0% +one. Now there's an obvious +optimization, right? We don't need to + + align:start position:0% +optimization, right? We don't need to + + + align:start position:0% +optimization, right? We don't need to +explore the whole tree. You know, if we + + align:start position:0% +explore the whole tree. You know, if we + + + align:start position:0% +explore the whole tree. You know, if we +get to a point where the backpack is + + align:start position:0% +get to a point where the backpack is + + + align:start position:0% +get to a point where the backpack is +over stuffed, there's no point in + + align:start position:0% +over stuffed, there's no point in + + + align:start position:0% +over stuffed, there's no point in +saying, should we take this next item + + align:start position:0% +saying, should we take this next item + + + align:start position:0% +saying, should we take this next item +because we know we can't, right? I + + align:start position:0% +because we know we can't, right? I + + + align:start position:0% +because we know we can't, right? I +generated a bunch of leaves that were + + align:start position:0% +generated a bunch of leaves that were + + + align:start position:0% +generated a bunch of leaves that were +useless because they're the weight was + + align:start position:0% +useless because they're the weight was + + + align:start position:0% +useless because they're the weight was +too high. So you could + + align:start position:0% +too high. So you could + + + align:start position:0% +too high. So you could +always abort early and saying, "Oh, no + + align:start position:0% +always abort early and saying, "Oh, no + + + align:start position:0% +always abort early and saying, "Oh, no +point in generating the rest of this + + align:start position:0% +point in generating the rest of this + + + align:start position:0% +point in generating the rest of this +part of the tree because we know + + align:start position:0% +part of the tree because we know + + + align:start position:0% +part of the tree because we know +everything in it will be too heavy." You + + align:start position:0% +everything in it will be too heavy." You + + + align:start position:0% +everything in it will be too heavy." You +know, adding something cannot reduce the + + align:start position:0% +know, adding something cannot reduce the + + + align:start position:0% +know, adding something cannot reduce the +weight. It's a nice optimization. It's + + align:start position:0% +weight. It's a nice optimization. It's + + + align:start position:0% +weight. It's a nice optimization. It's +one you'll see we actually do in the + + align:start position:0% +one you'll see we actually do in the + + + align:start position:0% +one you'll see we actually do in the +code, but it really doesn't change the + + align:start position:0% +code, but it really doesn't change the + + + align:start position:0% +code, but it really doesn't change the +complexity, right? It's not going to + + align:start position:0% +complexity, right? It's not going to + + + align:start position:0% +complexity, right? It's not going to +change the worst co cost + + align:start position:0% +change the worst co cost + + + align:start position:0% +change the worst co cost +complexity. All right. + + align:start position:0% +complexity. All right. + + + align:start position:0% +complexity. All right. +So exponential as we saw I think in + + align:start position:0% +So exponential as we saw I think in + + + align:start position:0% +So exponential as we saw I think in +Eric's lecture is a big number. We don't + + align:start position:0% +Eric's lecture is a big number. We don't + + + align:start position:0% +Eric's lecture is a big number. We don't +usually like 2 to the n. Does this mean + + align:start position:0% +usually like 2 to the n. Does this mean + + + align:start position:0% +usually like 2 to the n. Does this mean +that brute force is never useful? Well, + + align:start position:0% +that brute force is never useful? Well, + + + align:start position:0% +that brute force is never useful? Well, +let's give it a + + align:start position:0% + + + + align:start position:0% + +try. We'll look at some + + align:start position:0% + + + + align:start position:0% + +code. Here's the implementation. + + align:start position:0% + + + + align:start position:0% + +Um so it's max + + align:start position:0% +Um so it's max + + + align:start position:0% +Um so it's max +valu consider and avail. And then we say + + align:start position:0% +valu consider and avail. And then we say + + + align:start position:0% +valu consider and avail. And then we say +if two consider is empty or avail + + align:start position:0% +if two consider is empty or avail + + + align:start position:0% +if two consider is empty or avail +is zero. A veil is an index. We're going + + align:start position:0% +is zero. A veil is an index. We're going + + + align:start position:0% +is zero. A veil is an index. We're going +to go through the list using that to + + align:start position:0% +to go through the list using that to + + + align:start position:0% +to go through the list using that to +tell us whether or not we still have an + + align:start position:0% +tell us whether or not we still have an + + + align:start position:0% +tell us whether or not we still have an +element to consider. + + align:start position:0% +element to consider. + + + align:start position:0% +element to consider. +then the result will be the tupil zero + + align:start position:0% +then the result will be the tupil zero + + + align:start position:0% +then the result will be the tupil zero +and the empty + + align:start position:0% +and the empty + + + align:start position:0% +and the empty +tupil. Okay, we couldn't take anything. + + align:start position:0% +tupil. Okay, we couldn't take anything. + + + align:start position:0% +tupil. Okay, we couldn't take anything. +This is the base of our recursion, + + align:start position:0% +This is the base of our recursion, + + + align:start position:0% +This is the base of our recursion, +right? Either there's nothing left to + + align:start position:0% +right? Either there's nothing left to + + + align:start position:0% +right? Either there's nothing left to +consider or there's no available weight. + + align:start position:0% +consider or there's no available weight. + + + align:start position:0% +consider or there's no available weight. +The avail is the amount of weight is + + align:start position:0% +The avail is the amount of weight is + + + align:start position:0% +The avail is the amount of weight is +zero or to consider is empty. All right. + + align:start position:0% +zero or to consider is empty. All right. + + + align:start position:0% +zero or to consider is empty. All right. +Well, if neither of those are + + align:start position:0% +Well, if neither of those are + + + align:start position:0% +Well, if neither of those are +true, then we ask whether to consider + + align:start position:0% +true, then we ask whether to consider + + + align:start position:0% +true, then we ask whether to consider +subzero. The first element to look at is + + align:start position:0% +subzero. The first element to look at is + + + align:start position:0% +subzero. The first element to look at is +cost is greater than + + align:start position:0% + + + + align:start position:0% + +availability. If it is, we don't need to + + align:start position:0% +availability. If it is, we don't need to + + + align:start position:0% +availability. If it is, we don't need to +explore the left branch, right? Because + + align:start position:0% +explore the left branch, right? Because + + + align:start position:0% +explore the left branch, right? Because +it means we can't afford to put that + + align:start position:0% +it means we can't afford to put that + + + align:start position:0% +it means we can't afford to put that +thing in the backpack, the knapsack. + + align:start position:0% +thing in the backpack, the knapsack. + + + align:start position:0% +thing in the backpack, the knapsack. +There's just no room for it. So, we'll + + align:start position:0% +There's just no room for it. So, we'll + + + align:start position:0% +There's just no room for it. So, we'll +explore the right branch only. And so + + align:start position:0% +explore the right branch only. And so + + + align:start position:0% +explore the right branch only. And so +the result will be whatever the maximum + + align:start position:0% +the result will be whatever the maximum + + + align:start position:0% +the result will be whatever the maximum +value is of to consider of the remainder + + align:start position:0% +value is of to consider of the remainder + + + align:start position:0% +value is of to consider of the remainder +of the list, the list with the first + + align:start position:0% +of the list, the list with the first + + + align:start position:0% +of the list, the list with the first +element sliced off and availability + + align:start position:0% +element sliced off and availability + + + align:start position:0% +element sliced off and availability +unchanged. All right. So it's a + + align:start position:0% +unchanged. All right. So it's a + + + align:start position:0% +unchanged. All right. So it's a +recursive implementation saying now we + + align:start position:0% +recursive implementation saying now we + + + align:start position:0% +recursive implementation saying now we +only have to consider the right branch + + align:start position:0% +only have to consider the right branch + + + align:start position:0% +only have to consider the right branch +of the tree because we knew we couldn't + + align:start position:0% +of the tree because we knew we couldn't + + + align:start position:0% +of the tree because we knew we couldn't +take this element. It just weighed too + + align:start position:0% +take this element. It just weighed too + + + align:start position:0% +take this element. It just weighed too +much or cost too much or was too + + align:start position:0% +much or cost too much or was too + + + align:start position:0% +much or cost too much or was too +fattening in my case. All right. + + align:start position:0% +fattening in my case. All right. + + + align:start position:0% +fattening in my case. All right. +Otherwise well we now have to consider + + align:start position:0% +Otherwise well we now have to consider + + + align:start position:0% +Otherwise well we now have to consider +both + + align:start position:0% +both + + + align:start position:0% +both +branches. So we'll set next item to two + + align:start position:0% +branches. So we'll set next item to two + + + align:start position:0% +branches. So we'll set next item to two +consider of zero the first one and + + align:start position:0% +consider of zero the first one and + + + align:start position:0% +consider of zero the first one and +explore the left + + align:start position:0% +explore the left + + + align:start position:0% +explore the left +branch. Now there on this branch there + + align:start position:0% +branch. Now there on this branch there + + + align:start position:0% +branch. Now there on this branch there +are two possibilities to think + + align:start position:0% +are two possibilities to think + + + align:start position:0% +are two possibilities to think +about which I'm calling with val and + + align:start position:0% +about which I'm calling with val and + + + align:start position:0% +about which I'm calling with val and +with take. + + align:start position:0% +with take. + + + align:start position:0% +with take. +So I'm going to call max val of two + + align:start position:0% +So I'm going to call max val of two + + + align:start position:0% +So I'm going to call max val of two +consider of everything except the + + align:start position:0% +consider of everything except the + + + align:start position:0% +consider of everything except the +current + + align:start position:0% + + + + align:start position:0% + +element and pass in an available weight + + align:start position:0% +element and pass in an available weight + + + align:start position:0% +element and pass in an available weight +of avail minus whatever. Well, let + + align:start position:0% +of avail minus whatever. Well, let + + + align:start position:0% +of avail minus whatever. Well, let +me widen this so we can see the whole + + align:start position:0% + + + + align:start position:0% + +code. Guess it's not going to let me + + align:start position:0% +code. Guess it's not going to let me + + + align:start position:0% +code. Guess it's not going to let me +widen this window + + align:start position:0% +widen this window + + + align:start position:0% +widen this window +anymore. Shame on it. Let's see what + + align:start position:0% +anymore. Shame on it. Let's see what + + + align:start position:0% +anymore. Shame on it. Let's see what +happens if I get rid of the + + align:start position:0% + + + + align:start position:0% + +console. All right. Well, we'll have to + + align:start position:0% +console. All right. Well, we'll have to + + + align:start position:0% +console. All right. Well, we'll have to +do this + + align:start position:0% + + + + align:start position:0% + +instead. + + align:start position:0% +instead. + + + align:start position:0% +instead. +So, we're going to call max val with + + align:start position:0% +So, we're going to call max val with + + + align:start position:0% +So, we're going to call max val with +everything except the current element + + align:start position:0% +everything except the current element + + + align:start position:0% +everything except the current element +and give it avail minus the cost of that + + align:start position:0% +and give it avail minus the cost of that + + + align:start position:0% +and give it avail minus the cost of that +next item of two consider sub zero. + + align:start position:0% +next item of two consider sub zero. + + + align:start position:0% +next item of two consider sub zero. +Okay? Because we know that the + + align:start position:0% +Okay? Because we know that the + + + align:start position:0% +Okay? Because we know that the +availability available weight has to + + align:start position:0% +availability available weight has to + + + align:start position:0% +availability available weight has to +have that cost subtracted from + + align:start position:0% + + + + align:start position:0% + +it and + + align:start position:0% + + + + align:start position:0% + +then we'll add to with val next item.get + + align:start position:0% +then we'll add to with val next item.get + + + align:start position:0% +then we'll add to with val next item.get +value. So that's the value if we do take + + align:start position:0% +value. So that's the value if we do take + + + align:start position:0% +value. So that's the value if we do take +it. Then we'll explore the right branch. + + align:start position:0% +it. Then we'll explore the right branch. + + + align:start position:0% +it. Then we'll explore the right branch. +What happens if we don't take it? + + align:start position:0% +What happens if we don't take it? + + + align:start position:0% +What happens if we don't take it? +and then we'll choose the better + + align:start position:0% + + + + align:start position:0% + +branch. So it's a pretty simple + + align:start position:0% +branch. So it's a pretty simple + + + align:start position:0% +branch. So it's a pretty simple +recursive algorithm. We just per we go + + align:start position:0% +recursive algorithm. We just per we go + + + align:start position:0% +recursive algorithm. We just per we go +all the way to the bottom and make the + + align:start position:0% +all the way to the bottom and make the + + + align:start position:0% +all the way to the bottom and make the +right choice at the bottom and then + + align:start position:0% +right choice at the bottom and then + + + align:start position:0% +right choice at the bottom and then +percolate back up like so many recursive + + align:start position:0% + + + + align:start position:0% + +algorithms. All right. And then we have + + align:start position:0% +algorithms. All right. And then we have + + + align:start position:0% +algorithms. All right. And then we have +a simple program to test it. + + align:start position:0% + + + + align:start position:0% + +I better start a console now if I'm + + align:start position:0% +I better start a console now if I'm + + + align:start position:0% +I better start a console now if I'm +going to run + + align:start position:0% + + + + align:start position:0% + +it. And we'll test greedies on foods. + + align:start position:0% +it. And we'll test greedies on foods. + + + align:start position:0% +it. And we'll test greedies on foods. +Well, we'll test greedies and then we'll + + align:start position:0% +Well, we'll test greedies and then we'll + + + align:start position:0% +Well, we'll test greedies and then we'll +test maxv val. So, I'm building the same + + align:start position:0% +test maxv val. So, I'm building the same + + + align:start position:0% +test maxv val. So, I'm building the same +thing we did in Monday's lecture, the + + align:start position:0% +thing we did in Monday's lecture, the + + + align:start position:0% +thing we did in Monday's lecture, the +same menu, and I'll run the same test + + align:start position:0% +same menu, and I'll run the same test + + + align:start position:0% +same menu, and I'll run the same test +greetings we looked at last time, and + + align:start position:0% +greetings we looked at last time, and + + + align:start position:0% +greetings we looked at last time, and +we'll see whether or not we get + + align:start position:0% +we'll see whether or not we get + + + align:start position:0% +we'll see whether or not we get +something better when we run the truly + + align:start position:0% +something better when we run the truly + + + align:start position:0% +something better when we run the truly +optimal + + align:start position:0% + + + + align:start position:0% + +one. Well, indeed we do. You remember + + align:start position:0% +one. Well, indeed we do. You remember + + + align:start position:0% +one. Well, indeed we do. You remember +that last time and fortunately this time + + align:start position:0% +that last time and fortunately this time + + + align:start position:0% +that last time and fortunately this time +too the best we did was a value of + + align:start position:0% +too the best we did was a value of + + + align:start position:0% +too the best we did was a value of +318. But now we see we can actually get + + align:start position:0% +318. But now we see we can actually get + + + align:start position:0% +318. But now we see we can actually get +to + + align:start position:0% +to + + + align:start position:0% +to +353 if we use the truly optimal + + align:start position:0% +353 if we use the truly optimal + + + align:start position:0% +353 if we use the truly optimal +algorithm. So we see it ran pretty + + align:start position:0% +algorithm. So we see it ran pretty + + + align:start position:0% +algorithm. So we see it ran pretty +quickly and actually gave us a better + + align:start position:0% +quickly and actually gave us a better + + + align:start position:0% +quickly and actually gave us a better +answer than we got from the greedy + + align:start position:0% +answer than we got from the greedy + + + align:start position:0% +answer than we got from the greedy +algorithm. And it's often the case, and + + align:start position:0% +algorithm. And it's often the case, and + + + align:start position:0% +algorithm. And it's often the case, and +if I have time at the end, I'll show you + + align:start position:0% +if I have time at the end, I'll show you + + + align:start position:0% +if I have time at the end, I'll show you +an optimization program you might want + + align:start position:0% +an optimization program you might want + + + align:start position:0% +an optimization program you might want +to run + + align:start position:0% +to run + + + align:start position:0% +to run +that it works perfectly fine to use this + + align:start position:0% +that it works perfectly fine to use this + + + align:start position:0% +that it works perfectly fine to use this +kind of brute force algorithm on. All + + align:start position:0% +kind of brute force algorithm on. All + + + align:start position:0% +kind of brute force algorithm on. All +right, let's go back to the + + align:start position:0% + + + + align:start position:0% + +PowerPoint. So, I'm just going through + + align:start position:0% +PowerPoint. So, I'm just going through + + + align:start position:0% +PowerPoint. So, I'm just going through +the code again that we just ran. This + + align:start position:0% +the code again that we just ran. This + + + align:start position:0% +the code again that we just ran. This +was the header we + + align:start position:0% +was the header we + + + align:start position:0% +was the header we +saw to consider is the items that + + align:start position:0% +saw to consider is the items that + + + align:start position:0% +saw to consider is the items that +correspond to the nodes higher up the + + align:start position:0% +correspond to the nodes higher up the + + + align:start position:0% +correspond to the nodes higher up the +tree and avail as I said the amount of + + align:start position:0% +tree and avail as I said the amount of + + + align:start position:0% +tree and avail as I said the amount of +space and again here's what the body of + + align:start position:0% +space and again here's what the body of + + + align:start position:0% +space and again here's what the body of +the code look like. Uh I took out the + + align:start position:0% +the code look like. Uh I took out the + + + align:start position:0% +the code look like. Uh I took out the +comments. Uh one of the things you might + + align:start position:0% +comments. Uh one of the things you might + + + align:start position:0% +comments. Uh one of the things you might +think about in your head when you look + + align:start position:0% +think about in your head when you look + + + align:start position:0% +think about in your head when you look +at this code is putting the comments + + align:start position:0% +at this code is putting the comments + + + align:start position:0% +at this code is putting the comments +back in. I always find that for me a + + align:start position:0% +back in. I always find that for me a + + + align:start position:0% +back in. I always find that for me a +really good way to understand code that + + align:start position:0% +really good way to understand code that + + + align:start position:0% +really good way to understand code that +I didn't write is to try and comment it + + align:start position:0% +I didn't write is to try and comment it + + + align:start position:0% +I didn't write is to try and comment it +and that helps me sort of force myself + + align:start position:0% +and that helps me sort of force myself + + + align:start position:0% +and that helps me sort of force myself +to think about what is it really doing. + + align:start position:0% +to think about what is it really doing. + + + align:start position:0% +to think about what is it really doing. +Uh so you'll have both versions. You'll + + align:start position:0% +Uh so you'll have both versions. You'll + + + align:start position:0% +Uh so you'll have both versions. You'll +have the PowerPoint version without the + + align:start position:0% +have the PowerPoint version without the + + + align:start position:0% +have the PowerPoint version without the +comments and the actual code with the + + align:start position:0% +comments and the actual code with the + + + align:start position:0% +comments and the actual code with the +comments and you can think about looking + + align:start position:0% +comments and you can think about looking + + + align:start position:0% +comments and you can think about looking +at this and then looking at the power + + align:start position:0% +at this and then looking at the power + + + align:start position:0% +at this and then looking at the power +the real code and making sure that + + align:start position:0% +the real code and making sure that + + + align:start position:0% +the real code and making sure that +you're understanding + + align:start position:0% +you're understanding + + + align:start position:0% +you're understanding +jobs. All right. + + align:start position:0% +jobs. All right. + + + align:start position:0% +jobs. All right. +um should point out that this doesn't + + align:start position:0% +um should point out that this doesn't + + + align:start position:0% +um should point out that this doesn't +actually build the search tree, right? + + align:start position:0% +actually build the search tree, right? + + + align:start position:0% +actually build the search tree, right? +We've got this local variable + + align:start position:0% + + + + align:start position:0% + +result starting + + align:start position:0% + + + + align:start position:0% + +here that records the best solution + + align:start position:0% +here that records the best solution + + + align:start position:0% +here that records the best solution +found so + + align:start position:0% +found so + + + align:start position:0% +found so +far. Right? So, it's not the picture I + + align:start position:0% +far. Right? So, it's not the picture I + + + align:start position:0% +far. Right? So, it's not the picture I +drew where I generate all the nodes and + + align:start position:0% +drew where I generate all the nodes and + + + align:start position:0% +drew where I generate all the nodes and +then I inspect them. I just keep track + + align:start position:0% +then I inspect them. I just keep track + + + align:start position:0% +then I inspect them. I just keep track +as I generate a node. I say how good is + + align:start position:0% +as I generate a node. I say how good is + + + align:start position:0% +as I generate a node. I say how good is +this? Is it better than the best I found + + align:start position:0% +this? Is it better than the best I found + + + align:start position:0% +this? Is it better than the best I found +so far? If so, it becomes the new + + align:start position:0% +so far? If so, it becomes the new + + + align:start position:0% +so far? If so, it becomes the new +best. And I can do that because every + + align:start position:0% +best. And I can do that because every + + + align:start position:0% +best. And I can do that because every +node I generate is in some sense a legal + + align:start position:0% +node I generate is in some sense a legal + + + align:start position:0% +node I generate is in some sense a legal +solution to the + + align:start position:0% +solution to the + + + align:start position:0% +solution to the +problem. Not probably ne rarely is it + + align:start position:0% +problem. Not probably ne rarely is it + + + align:start position:0% +problem. Not probably ne rarely is it +the final optimal solution, but it's at + + align:start position:0% +the final optimal solution, but it's at + + + align:start position:0% +the final optimal solution, but it's at +least a legal solution. And so if it's + + align:start position:0% +least a legal solution. And so if it's + + + align:start position:0% +least a legal solution. And so if it's +better than something we saw before, we + + align:start position:0% +better than something we saw before, we + + + align:start position:0% +better than something we saw before, we +can make it the new + + align:start position:0% +can make it the new + + + align:start position:0% +can make it the new +best. This is very common and this is in + + align:start position:0% +best. This is very common and this is in + + + align:start position:0% +best. This is very common and this is in +fact what most people do when they use a + + align:start position:0% +fact what most people do when they use a + + + align:start position:0% +fact what most people do when they use a +search tree is they don't actually build + + align:start position:0% +search tree is they don't actually build + + + align:start position:0% +search tree is they don't actually build +the tree in the pictorial way we've + + align:start position:0% +the tree in the pictorial way we've + + + align:start position:0% +the tree in the pictorial way we've +looked at it but play some trick like + + align:start position:0% +looked at it but play some trick like + + + align:start position:0% +looked at it but play some trick like +this of just keeping track of their + + align:start position:0% + + + + align:start position:0% + +results. All right, any questions about + + align:start position:0% +results. All right, any questions about + + + align:start position:0% +results. All right, any questions about +this? + + align:start position:0% + + + + align:start position:0% + +All right. Uh, we did just try it on the + + align:start position:0% +All right. Uh, we did just try it on the + + + align:start position:0% +All right. Uh, we did just try it on the +example from lecture + + align:start position:0% +example from lecture + + + align:start position:0% +example from lecture +one and we saw that it worked great. It + + align:start position:0% +one and we saw that it worked great. It + + + align:start position:0% +one and we saw that it worked great. It +gave us a better answer. It finished + + align:start position:0% +gave us a better answer. It finished + + + align:start position:0% +gave us a better answer. It finished +quickly. But we should not take too much + + align:start position:0% +quickly. But we should not take too much + + + align:start position:0% +quickly. But we should not take too much +solace from the fact that it finished + + align:start position:0% +solace from the fact that it finished + + + align:start position:0% +solace from the fact that it finished +quickly because 2 to the eth is actually + + align:start position:0% +quickly because 2 to the eth is actually + + + align:start position:0% +quickly because 2 to the eth is actually +a pretty tiny number. + + align:start position:0% + + + + align:start position:0% + +um almost any algorithm can is fine on + + align:start position:0% +um almost any algorithm can is fine on + + + align:start position:0% +um almost any algorithm can is fine on +working on something this small. Let's + + align:start position:0% +working on something this small. Let's + + + align:start position:0% +working on something this small. Let's +look now at what happens if we have a + + align:start position:0% +look now at what happens if we have a + + + align:start position:0% +look now at what happens if we have a +bigger + + align:start position:0% + + + + align:start position:0% + +menu. So here's some code to do a bigger + + align:start position:0% +menu. So here's some code to do a bigger + + + align:start position:0% +menu. So here's some code to do a bigger +menu. Since as you will discover if you + + align:start position:0% +menu. Since as you will discover if you + + + align:start position:0% +menu. Since as you will discover if you +haven't already, I'm a pretty lazy + + align:start position:0% +haven't already, I'm a pretty lazy + + + align:start position:0% +haven't already, I'm a pretty lazy +person. I didn't want to write out a + + align:start position:0% +person. I didn't want to write out a + + + align:start position:0% +person. I didn't want to write out a +menu with a hundred items or even 50 + + align:start position:0% +menu with a hundred items or even 50 + + + align:start position:0% +menu with a hundred items or even 50 +items. So, I wrote some code to generate + + align:start position:0% +items. So, I wrote some code to generate + + + align:start position:0% +items. So, I wrote some code to generate +the menus and I used randomness to do + + align:start position:0% +the menus and I used randomness to do + + + align:start position:0% +the menus and I used randomness to do +that. This is a Python library we'll be + + align:start position:0% +that. This is a Python library we'll be + + + align:start position:0% +that. This is a Python library we'll be +using a lot for the rest of the + + align:start position:0% +using a lot for the rest of the + + + align:start position:0% +using a lot for the rest of the +semester. Uh it's used for anytime you + + align:start position:0% +semester. Uh it's used for anytime you + + + align:start position:0% +semester. Uh it's used for anytime you +want to generate things at random and do + + align:start position:0% +want to generate things at random and do + + + align:start position:0% +want to generate things at random and do +many other things and we'll come back to + + align:start position:0% +many other things and we'll come back to + + + align:start position:0% +many other things and we'll come back to +it a lot here. We're just going to use a + + align:start position:0% +it a lot here. We're just going to use a + + + align:start position:0% +it a lot here. We're just going to use a +very small part of + + align:start position:0% +very small part of + + + align:start position:0% +very small part of +it. So to build a large + + align:start position:0% +it. So to build a large + + + align:start position:0% +it. So to build a large +menu of some numbum items, we're going + + align:start position:0% +menu of some numbum items, we're going + + + align:start position:0% +menu of some numbum items, we're going +to and we're going to give the maximum + + align:start position:0% +to and we're going to give the maximum + + + align:start position:0% +to and we're going to give the maximum +value and the maximum cost for each + + align:start position:0% +value and the maximum cost for each + + + align:start position:0% +value and the maximum cost for each +item. We'll assume the minimum is in + + align:start position:0% +item. We'll assume the minimum is in + + + align:start position:0% +item. We'll assume the minimum is in +this case + + align:start position:0% +this case + + + align:start position:0% +this case +one. Items will start empty. And then + + align:start position:0% +one. Items will start empty. And then + + + align:start position:0% +one. Items will start empty. And then +for i in the range number of + + align:start position:0% +for i in the range number of + + + align:start position:0% +for i in the range number of +items, I'm going to call this function + + align:start position:0% + + + + align:start position:0% + +random.rand that takes a range of + + align:start position:0% +random.rand that takes a range of + + + align:start position:0% +random.rand that takes a range of +integers from one to actually in this + + align:start position:0% +integers from one to actually in this + + + align:start position:0% +integers from one to actually in this +case max val minus + + align:start position:0% +case max val minus + + + align:start position:0% +case max val minus +one or one to max val actually rather in + + align:start position:0% +one or one to max val actually rather in + + + align:start position:0% +one or one to max val actually rather in +this case and it just chooses one of + + align:start position:0% +this case and it just chooses one of + + + align:start position:0% +this case and it just chooses one of +them at random. So when you run this, + + align:start position:0% +them at random. So when you run this, + + + align:start position:0% +them at random. So when you run this, +you don't know what it's going to get, + + align:start position:0% +you don't know what it's going to get, + + + align:start position:0% +you don't know what it's going to get, +right? Random.rand might return one. It + + align:start position:0% +right? Random.rand might return one. It + + + align:start position:0% +right? Random.rand might return one. It +might return 23. It might return 54. The + + align:start position:0% +might return 23. It might return 54. The + + + align:start position:0% +might return 23. It might return 54. The +only thing you know is it will be an + + align:start position:0% +only thing you know is it will be an + + + align:start position:0% +only thing you know is it will be an +integer. And then I'm going to build + + align:start position:0% +integer. And then I'm going to build + + + align:start position:0% +integer. And then I'm going to build +menus ranging from five items to 60 + + align:start position:0% +menus ranging from five items to 60 + + + align:start position:0% +menus ranging from five items to 60 +items. + + align:start position:0% + + + + align:start position:0% + +Um, build large menu. The number of + + align:start position:0% +Um, build large menu. The number of + + + align:start position:0% +Um, build large menu. The number of +items + + align:start position:0% +items + + + align:start position:0% +items +uh with a minimum value + + align:start position:0% +uh with a minimum value + + + align:start position:0% +uh with a minimum value +of with a max val of 90 and a max cost + + align:start position:0% +of with a max val of 90 and a max cost + + + align:start position:0% +of with a max val of 90 and a max cost +of + + align:start position:0% +of + + + align:start position:0% +of +250 pleasure and calories. And then I'm + + align:start position:0% +250 pleasure and calories. And then I'm + + + align:start position:0% +250 pleasure and calories. And then I'm +going to test max val on each of these + + align:start position:0% + + + + align:start position:0% + +menus. All right. So building menus of + + align:start position:0% +menus. All right. So building menus of + + + align:start position:0% +menus. All right. So building menus of +various sizes at random and then just + + align:start position:0% +various sizes at random and then just + + + align:start position:0% +various sizes at random and then just +trying to find the optimal value for + + align:start position:0% +trying to find the optimal value for + + + align:start position:0% +trying to find the optimal value for +each of them. All right, let's look at + + align:start position:0% +each of them. All right, let's look at + + + align:start position:0% +each of them. All right, let's look at +the + + align:start position:0% +the + + + align:start position:0% +the +code. It is well let's comment this + + align:start position:0% + + + + align:start position:0% + +out. So we don't need to run that again. + + align:start position:0% + + + + align:start position:0% + +So, build a large menu and then we'll + + align:start position:0% +So, build a large menu and then we'll + + + align:start position:0% +So, build a large menu and then we'll +try it for a bunch of items and see what + + align:start position:0% +try it for a bunch of items and see what + + + align:start position:0% +try it for a bunch of items and see what +we + + align:start position:0% + + + + align:start position:0% + +get. So, it's going along trying to menu + + align:start position:0% +get. So, it's going along trying to menu + + + align:start position:0% +get. So, it's going along trying to menu +with third up to 30 went pretty quickly. + + align:start position:0% +with third up to 30 went pretty quickly. + + + align:start position:0% +with third up to 30 went pretty quickly. +So, that's even two to the 30 didn't + + align:start position:0% +So, that's even two to the 30 didn't + + + align:start position:0% +So, that's even two to the 30 didn't +take too long. But you might notice it's + + align:start position:0% +take too long. But you might notice it's + + + align:start position:0% +take too long. But you might notice it's +kind of bogging down. We got + + align:start position:0% + + + + align:start position:0% + +35. And I guess I could ask the question + + align:start position:0% +35. And I guess I could ask the question + + + align:start position:0% +35. And I guess I could ask the question +now. It was one of the questions I was + + align:start position:0% +now. It was one of the questions I was + + + align:start position:0% +now. It was one of the questions I was +going to ask as a poll, but maybe I + + align:start position:0% +going to ask as a poll, but maybe I + + + align:start position:0% +going to ask as a poll, but maybe I +won't bother. Is uh how much patience do + + align:start position:0% +won't bother. Is uh how much patience do + + + align:start position:0% +won't bother. Is uh how much patience do +we have? When do you think we'll run out + + align:start position:0% +we have? When do you think we'll run out + + + align:start position:0% +we have? When do you think we'll run out +of patience and + + align:start position:0% + + + + align:start position:0% + +quit? + + align:start position:0% +quit? + + + align:start position:0% +quit? +Well, if you're out of patience, raise + + align:start position:0% +Well, if you're out of patience, raise + + + align:start position:0% +Well, if you're out of patience, raise +your hand. + + align:start position:0% + + + + align:start position:0% + +Well, some of you were way more patient + + align:start position:0% +Well, some of you were way more patient + + + align:start position:0% +Well, some of you were way more patient +than I am, so we're going to quit + + align:start position:0% + + + + align:start position:0% + +anyway. All + + align:start position:0% +anyway. All + + + align:start position:0% +anyway. All +right, we were trying to do 40. It might + + align:start position:0% +right, we were trying to do 40. It might + + + align:start position:0% +right, we were trying to do 40. It might +have finished 40. 45. I've never waited + + align:start position:0% +have finished 40. 45. I've never waited + + + align:start position:0% +have finished 40. 45. I've never waited +long enough to get to 45. Uh, it just is + + align:start position:0% +long enough to get to 45. Uh, it just is + + + align:start position:0% +long enough to get to 45. Uh, it just is +too long. + + align:start position:0% + + + + align:start position:0% + +So that raises the question is it + + align:start position:0% + + + + align:start position:0% + +hopeless and in theory yes. As I + + align:start position:0% +hopeless and in theory yes. As I + + + align:start position:0% +hopeless and in theory yes. As I +mentioned last time it is an inherently + + align:start position:0% +mentioned last time it is an inherently + + + align:start position:0% +mentioned last time it is an inherently +exponential problem. The answer is in + + align:start position:0% +exponential problem. The answer is in + + + align:start position:0% +exponential problem. The answer is in +practice no because of something called + + align:start position:0% +practice no because of something called + + + align:start position:0% +practice no because of something called +dynamic programming + + align:start position:0% +dynamic programming + + + align:start position:0% +dynamic programming +uh which is invented by a fellow at uh I + + align:start position:0% +uh which is invented by a fellow at uh I + + + align:start position:0% +uh which is invented by a fellow at uh I +think the Rand Corporation called + + align:start position:0% +think the Rand Corporation called + + + align:start position:0% +think the Rand Corporation called +Richard Bellman a rather remarkable + + align:start position:0% +Richard Bellman a rather remarkable + + + align:start position:0% +Richard Bellman a rather remarkable +mathematician/computer scientist. He + + align:start position:0% +mathematician/computer scientist. He + + + align:start position:0% +mathematician/computer scientist. He +wrote a whole book on it but I'm not + + align:start position:0% +wrote a whole book on it but I'm not + + + align:start position:0% +wrote a whole book on it but I'm not +sure why because it's not that + + align:start position:0% +sure why because it's not that + + + align:start position:0% +sure why because it's not that +complicated. + + align:start position:0% +complicated. + + + align:start position:0% +complicated. +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +so when we talk about dynamic + + align:start position:0% +so when we talk about dynamic + + + align:start position:0% +so when we talk about dynamic +programming, it it's kind of a funny + + align:start position:0% +programming, it it's kind of a funny + + + align:start position:0% +programming, it it's kind of a funny +story in at least to me. I learned it + + align:start position:0% +story in at least to me. I learned it + + + align:start position:0% +story in at least to me. I learned it +and I didn't know anything about the + + align:start position:0% +and I didn't know anything about the + + + align:start position:0% +and I didn't know anything about the +history of it. And I was trying to and I + + align:start position:0% +history of it. And I was trying to and I + + + align:start position:0% +history of it. And I was trying to and I +had all sorts of theories about why it + + align:start position:0% +had all sorts of theories about why it + + + align:start position:0% +had all sorts of theories about why it +was called dynamic programming. You + + align:start position:0% +was called dynamic programming. You + + + align:start position:0% +was called dynamic programming. You +know, how it is, how people try and fit + + align:start position:0% +know, how it is, how people try and fit + + + align:start position:0% +know, how it is, how people try and fit +a theory to data. Um, and then I read a + + align:start position:0% +a theory to data. Um, and then I read a + + + align:start position:0% +a theory to data. Um, and then I read a +history book about it. And this was + + align:start position:0% +history book about it. And this was + + + align:start position:0% +history book about it. And this was +Belman's own description of why he + + align:start position:0% +Belman's own description of why he + + + align:start position:0% +Belman's own description of why he +called it dynamic + + align:start position:0% +called it dynamic + + + align:start position:0% +called it dynamic +programming. Uh, and it turned out, as + + align:start position:0% +programming. Uh, and it turned out, as + + + align:start position:0% +programming. Uh, and it turned out, as +you can see, he basically chose a word + + align:start position:0% +you can see, he basically chose a word + + + align:start position:0% +you can see, he basically chose a word +because it didn't a description that + + align:start position:0% +because it didn't a description that + + + align:start position:0% +because it didn't a description that +didn't mean + + align:start position:0% +didn't mean + + + align:start position:0% +didn't mean +anything because he was doing + + align:start position:0% +anything because he was doing + + + align:start position:0% +anything because he was doing +mathematics and at the time he was being + + align:start position:0% +mathematics and at the time he was being + + + align:start position:0% +mathematics and at the time he was being +funded by a part of the defense + + align:start position:0% +funded by a part of the defense + + + align:start position:0% +funded by a part of the defense +department that didn't approve of + + align:start position:0% +department that didn't approve of + + + align:start position:0% +department that didn't approve of +mathematics and he wanted to conceal + + align:start position:0% +mathematics and he wanted to conceal + + + align:start position:0% +mathematics and he wanted to conceal +that fact. And indeed at the time the + + align:start position:0% +that fact. And indeed at the time the + + + align:start position:0% +that fact. And indeed at the time the +head of defense appropriations in the US + + align:start position:0% +head of defense appropriations in the US + + + align:start position:0% +head of defense appropriations in the US +Congress didn't much like mathematics + + align:start position:0% +Congress didn't much like mathematics + + + align:start position:0% +Congress didn't much like mathematics +and he was afraid that he didn't want to + + align:start position:0% +and he was afraid that he didn't want to + + + align:start position:0% +and he was afraid that he didn't want to +have to go and testify and tell people + + align:start position:0% +have to go and testify and tell people + + + align:start position:0% +have to go and testify and tell people +he was doing math. So he just invented + + align:start position:0% +he was doing math. So he just invented + + + align:start position:0% +he was doing math. So he just invented +something that no one would know what it + + align:start position:0% +something that no one would know what it + + + align:start position:0% +something that no one would know what it +meant and years of students spent time + + align:start position:0% +meant and years of students spent time + + + align:start position:0% +meant and years of students spent time +later trying to figure out what it + + align:start position:0% +later trying to figure out what it + + + align:start position:0% +later trying to figure out what it +actually did mean. Anyway, what's the + + align:start position:0% +actually did mean. Anyway, what's the + + + align:start position:0% +actually did mean. Anyway, what's the +basic + + align:start position:0% +basic + + + align:start position:0% +basic +idea to understand it? I want to + + align:start position:0% +idea to understand it? I want to + + + align:start position:0% +idea to understand it? I want to +temporarily abandon the knapsack problem + + align:start position:0% +temporarily abandon the knapsack problem + + + align:start position:0% +temporarily abandon the knapsack problem +and look at a much simpler problem. Um, + + align:start position:0% +and look at a much simpler problem. Um, + + + align:start position:0% +and look at a much simpler problem. Um, +Fibonacci numbers. Um, so you've seen + + align:start position:0% +Fibonacci numbers. Um, so you've seen + + + align:start position:0% +Fibonacci numbers. Um, so you've seen +this already uh with cute little bunnies + + align:start position:0% +this already uh with cute little bunnies + + + align:start position:0% +this already uh with cute little bunnies +I think when you saw it. + + align:start position:0% +I think when you saw it. + + + align:start position:0% +I think when you saw it. +Um, n equals 0 n equals 1 return one. + + align:start position:0% +Um, n equals 0 n equals 1 return one. + + + align:start position:0% +Um, n equals 0 n equals 1 return one. +Otherwise, fib of n minus one plus fib + + align:start position:0% +Otherwise, fib of n minus one plus fib + + + align:start position:0% +Otherwise, fib of n minus one plus fib +of n + + align:start position:0% +of n + + + align:start position:0% +of n +minus2. Um, and as I think you saw when + + align:start position:0% +minus2. Um, and as I think you saw when + + + align:start position:0% +minus2. Um, and as I think you saw when +you first saw it, it's a takes a long + + align:start position:0% +you first saw it, it's a takes a long + + + align:start position:0% +you first saw it, it's a takes a long +time to run. Uh, fib of 120, for + + align:start position:0% +time to run. Uh, fib of 120, for + + + align:start position:0% +time to run. Uh, fib of 120, for +example, is a very big number. It's + + align:start position:0% +example, is a very big number. It's + + + align:start position:0% +example, is a very big number. It's +shocking how quickly Fibonacci + + align:start position:0% +shocking how quickly Fibonacci + + + align:start position:0% +shocking how quickly Fibonacci +grows. + + align:start position:0% +grows. + + + align:start position:0% +grows. +So, let's think + + align:start position:0% +So, let's think + + + align:start position:0% +So, let's think +about implement implementing + + align:start position:0% +about implement implementing + + + align:start position:0% +about implement implementing +it. If we run Fibonacci, well, maybe + + align:start position:0% +it. If we run Fibonacci, well, maybe + + + align:start position:0% +it. If we run Fibonacci, well, maybe +we'll just do that. + + align:start position:0% + + + + align:start position:0% + +So here's fib of n and let's just try + + align:start position:0% +So here's fib of n and let's just try + + + align:start position:0% +So here's fib of n and let's just try +running it and again we'll test people's + + align:start position:0% + + + + align:start position:0% + +patience and uh we'll see how long we're + + align:start position:0% +patience and uh we'll see how long we're + + + align:start position:0% +patience and uh we'll see how long we're +letting it running. I'm going to try for + + align:start position:0% +letting it running. I'm going to try for + + + align:start position:0% +letting it running. I'm going to try for +I in the range 121. + + align:start position:0% +I in the range 121. + + + align:start position:0% +I in the range 121. +We'll print fib of + + align:start position:0% + + + + align:start position:0% + +I comes clumping + + align:start position:0% +I comes clumping + + + align:start position:0% +I comes clumping +along and it slows down pretty quickly. + + align:start position:0% +along and it slows down pretty quickly. + + + align:start position:0% +along and it slows down pretty quickly. +And if you look at it, it's kind of + + align:start position:0% +And if you look at it, it's kind of + + + align:start position:0% +And if you look at it, it's kind of +surprising it's this slow because these + + align:start position:0% +surprising it's this slow because these + + + align:start position:0% +surprising it's this slow because these +numbers aren't that + + align:start position:0% +numbers aren't that + + + align:start position:0% +numbers aren't that +big, right? + + align:start position:0% +big, right? + + + align:start position:0% +big, right? +These are not enormous numbers, right? + + align:start position:0% +These are not enormous numbers, right? + + + align:start position:0% +These are not enormous numbers, right? +FIB of 35 is not a huge number. Yet, it + + align:start position:0% +FIB of 35 is not a huge number. Yet, it + + + align:start position:0% +FIB of 35 is not a huge number. Yet, it +took a long time to + + align:start position:0% +took a long time to + + + align:start position:0% +took a long time to +compute. So, yeah, the numbers are + + align:start position:0% +compute. So, yeah, the numbers are + + + align:start position:0% +compute. So, yeah, the numbers are +growing pretty quickly, but the + + align:start position:0% +growing pretty quickly, but the + + + align:start position:0% +growing pretty quickly, but the +computation actually seems to be growing + + align:start position:0% +computation actually seems to be growing + + + align:start position:0% +computation actually seems to be growing +faster than the + + align:start position:0% +faster than the + + + align:start position:0% +faster than the +results, right? We're + + align:start position:0% +results, right? We're + + + align:start position:0% +results, right? We're +37. Um, you know, it's going to get + + align:start position:0% +37. Um, you know, it's going to get + + + align:start position:0% +37. Um, you know, it's going to get +slower and slower even though our + + align:start position:0% +slower and slower even though our + + + align:start position:0% +slower and slower even though our +numbers are not that big. + + align:start position:0% +numbers are not that big. + + + align:start position:0% +numbers are not that big. +So the question is what's going on? Why + + align:start position:0% +So the question is what's going on? Why + + + align:start position:0% +So the question is what's going on? Why +is it taking so long for Fibonacci to + + align:start position:0% +is it taking so long for Fibonacci to + + + align:start position:0% +is it taking so long for Fibonacci to +compute these + + align:start position:0% +compute these + + + align:start position:0% +compute these +results? Well, let's kill + + align:start position:0% + + + + align:start position:0% + +it and look at the question and to do + + align:start position:0% +it and look at the question and to do + + + align:start position:0% +it and look at the question and to do +that I want to look at the call tree. + + align:start position:0% +that I want to look at the call tree. + + + align:start position:0% +that I want to look at the call tree. +So this is for Fibonacci of six which is + + align:start position:0% +So this is for Fibonacci of six which is + + + align:start position:0% +So this is for Fibonacci of six which is +only 13 which I think we would most + + align:start position:0% +only 13 which I think we would most + + + align:start position:0% +only 13 which I think we would most +agree most of us agree is not a very big + + align:start position:0% +agree most of us agree is not a very big + + + align:start position:0% +agree most of us agree is not a very big +number and let's look what's going on + + align:start position:0% + + + + align:start position:0% + +here. If you look at this what in some + + align:start position:0% +here. If you look at this what in some + + + align:start position:0% +here. If you look at this what in some +sense seems really stupid about + + align:start position:0% +sense seems really stupid about + + + align:start position:0% +sense seems really stupid about +it. What is it doing that a rational + + align:start position:0% +it. What is it doing that a rational + + + align:start position:0% +it. What is it doing that a rational +person would sort of not want to do if + + align:start position:0% +person would sort of not want to do if + + + align:start position:0% +person would sort of not want to do if +they could avoid it? + + align:start position:0% + + + + align:start position:0% + +Well, it's bad enough to do something + + align:start position:0% +Well, it's bad enough to do something + + + align:start position:0% +Well, it's bad enough to do something +once, but to do the same thing over and + + align:start position:0% +once, but to do the same thing over and + + + align:start position:0% +once, but to do the same thing over and +over again is really + + align:start position:0% +over again is really + + + align:start position:0% +over again is really +wasteful. And if we look at this, we'll + + align:start position:0% +wasteful. And if we look at this, we'll + + + align:start position:0% +wasteful. And if we look at this, we'll +see, for example, that fib 4 is being + + align:start position:0% +see, for example, that fib 4 is being + + + align:start position:0% +see, for example, that fib 4 is being +computed + + align:start position:0% +computed + + + align:start position:0% +computed +here and fib 4 is being computed here. + + align:start position:0% +here and fib 4 is being computed here. + + + align:start position:0% +here and fib 4 is being computed here. +Fib 3 is being computed here and here + + align:start position:0% +Fib 3 is being computed here and here + + + align:start position:0% +Fib 3 is being computed here and here +and + + align:start position:0% + + + + align:start position:0% + +here. And do you think we'll get a + + align:start position:0% +here. And do you think we'll get a + + + align:start position:0% +here. And do you think we'll get a +different answer for fib 3 in one place + + align:start position:0% +different answer for fib 3 in one place + + + align:start position:0% +different answer for fib 3 in one place +than we get it in the other place? You + + align:start position:0% +than we get it in the other place? You + + + align:start position:0% +than we get it in the other place? You +sure hope not, + + align:start position:0% +sure hope not, + + + align:start position:0% +sure hope not, +right? And so you think, well, what + + align:start position:0% +right? And so you think, well, what + + + align:start position:0% +right? And so you think, well, what +should we do about + + align:start position:0% +should we do about + + + align:start position:0% +should we do about +this? How would we go about avoiding + + align:start position:0% +this? How would we go about avoiding + + + align:start position:0% +this? How would we go about avoiding +doing the same work over and over again? + + align:start position:0% +doing the same work over and over again? + + + align:start position:0% +doing the same work over and over again? +And there's kind of an obvious answer. + + align:start position:0% +And there's kind of an obvious answer. + + + align:start position:0% +And there's kind of an obvious answer. +That answer is at the heart of dynamic + + align:start position:0% +That answer is at the heart of dynamic + + + align:start position:0% +That answer is at the heart of dynamic +programming. What's the answer? + + align:start position:0% +programming. What's the answer? + + + align:start position:0% +programming. What's the answer? +Yeah. + + align:start position:0% + + + + align:start position:0% + +Exactly. And I'm really happy that + + align:start position:0% +Exactly. And I'm really happy that + + + align:start position:0% +Exactly. And I'm really happy that +someone in the front row answered the + + align:start position:0% +someone in the front row answered the + + + align:start position:0% +someone in the front row answered the +question because I can throw it that + + align:start position:0% +question because I can throw it that + + + align:start position:0% +question because I can throw it that +far. You store the answer and then look + + align:start position:0% +far. You store the answer and then look + + + align:start position:0% +far. You store the answer and then look +it up when you need + + align:start position:0% +it up when you need + + + align:start position:0% +it up when you need +it because we know that we can look + + align:start position:0% +it because we know that we can look + + + align:start position:0% +it because we know that we can look +things up very quickly. + + align:start position:0% +things up very quickly. + + + align:start position:0% +things up very quickly. +Right. A + + align:start position:0% +Right. A + + + align:start position:0% +Right. A +dictionary, despite what Eric said in + + align:start position:0% +dictionary, despite what Eric said in + + + align:start position:0% +dictionary, despite what Eric said in +his lecture, almost all the time works + + align:start position:0% +his lecture, almost all the time works + + + align:start position:0% +his lecture, almost all the time works +in constant time if you make it big + + align:start position:0% +in constant time if you make it big + + + align:start position:0% +in constant time if you make it big +enough. And it usually is in Python. + + align:start position:0% +enough. And it usually is in Python. + + + align:start position:0% +enough. And it usually is in Python. +We'll see later in the term how to do + + align:start position:0% +We'll see later in the term how to do + + + align:start position:0% +We'll see later in the term how to do +that + + align:start position:0% +that + + + align:start position:0% +that +trick. But so you store it and then you + + align:start position:0% +trick. But so you store it and then you + + + align:start position:0% +trick. But so you store it and then you +never have to compute it + + align:start position:0% +never have to compute it + + + align:start position:0% +never have to compute it +again. And that's the basic trick behind + + align:start position:0% +again. And that's the basic trick behind + + + align:start position:0% +again. And that's the basic trick behind +dynamic programming. And it's something + + align:start position:0% +dynamic programming. And it's something + + + align:start position:0% +dynamic programming. And it's something +called + + align:start position:0% + + + + align:start position:0% + +memoization as in you create a memo and + + align:start position:0% +memoization as in you create a memo and + + + align:start position:0% +memoization as in you create a memo and +you store it in the + + align:start position:0% + + + + align:start position:0% + +memo. All right. So we see this here. + + align:start position:0% +memo. All right. So we see this here. + + + align:start position:0% +memo. All right. So we see this here. +Notice that what we're doing is trading + + align:start position:0% +Notice that what we're doing is trading + + + align:start position:0% +Notice that what we're doing is trading +time for space. + + align:start position:0% +time for space. + + + align:start position:0% +time for space. +It takes some space to store the old + + align:start position:0% + + + + align:start position:0% + +results but negligible relative to the + + align:start position:0% +results but negligible relative to the + + + align:start position:0% +results but negligible relative to the +relevant related to the time we save. + + align:start position:0% +relevant related to the time we save. + + + align:start position:0% +relevant related to the time we save. +All right. So here's the trick. We're + + align:start position:0% +All right. So here's the trick. We're + + + align:start position:0% +All right. So here's the trick. We're +going to create a table to record what + + align:start position:0% +going to create a table to record what + + + align:start position:0% +going to create a table to record what +we've done and then before computing fib + + align:start position:0% +we've done and then before computing fib + + + align:start position:0% +we've done and then before computing fib +of x, we'll check if the value has + + align:start position:0% +of x, we'll check if the value has + + + align:start position:0% +of x, we'll check if the value has +already been computed. If so, we just + + align:start position:0% +already been computed. If so, we just + + + align:start position:0% +already been computed. If so, we just +look it up and return it. Otherwise, + + align:start position:0% +look it up and return it. Otherwise, + + + align:start position:0% +look it up and return it. Otherwise, +we'll compute it. it's the first time + + align:start position:0% +we'll compute it. it's the first time + + + align:start position:0% +we'll compute it. it's the first time +and store it in the + + align:start position:0% + + + + align:start position:0% + +table. So, here's a fast implementation + + align:start position:0% +table. So, here's a fast implementation + + + align:start position:0% +table. So, here's a fast implementation +of Fibonacci that does + + align:start position:0% +of Fibonacci that does + + + align:start position:0% +of Fibonacci that does +that. It looks like the old one except + + align:start position:0% +that. It looks like the old one except + + + align:start position:0% +that. It looks like the old one except +it's got an extra + + align:start position:0% +it's got an extra + + + align:start position:0% +it's got an extra +argument memo which is a + + align:start position:0% +argument memo which is a + + + align:start position:0% +argument memo which is a +dictionary. The first time we call it, + + align:start position:0% +dictionary. The first time we call it, + + + align:start position:0% +dictionary. The first time we call it, +the memo will be empty. + + align:start position:0% + + + + align:start position:0% + +So it tries to return the value in the + + align:start position:0% +So it tries to return the value in the + + + align:start position:0% +So it tries to return the value in the +memo. If it's not there, an exception + + align:start position:0% +memo. If it's not there, an exception + + + align:start position:0% +memo. If it's not there, an exception +will get raised. We know that. And it + + align:start position:0% +will get raised. We know that. And it + + + align:start position:0% +will get raised. We know that. And it +will branch to + + align:start position:0% +will branch to + + + align:start position:0% +will branch to +here, compute the result, and then store + + align:start position:0% +here, compute the result, and then store + + + align:start position:0% +here, compute the result, and then store +it in the + + align:start position:0% +it in the + + + align:start position:0% +it in the +memo and return it. So it's the same old + + align:start position:0% +memo and return it. So it's the same old + + + align:start position:0% +memo and return it. So it's the same old +recursive thing we did before, but with + + align:start position:0% +recursive thing we did before, but with + + + align:start position:0% +recursive thing we did before, but with +the memo. + + align:start position:0% +the memo. + + + align:start position:0% +the memo. +Notice by the way that I'm using + + align:start position:0% +Notice by the way that I'm using + + + align:start position:0% +Notice by the way that I'm using +exceptions not as an error handling + + align:start position:0% +exceptions not as an error handling + + + align:start position:0% +exceptions not as an error handling +mechanism really but just as a flow of + + align:start position:0% +mechanism really but just as a flow of + + + align:start position:0% +mechanism really but just as a flow of +control. To me this is cleaner than + + align:start position:0% +control. To me this is cleaner than + + + align:start position:0% +control. To me this is cleaner than +writing code that says if this is in the + + align:start position:0% +writing code that says if this is in the + + + align:start position:0% +writing code that says if this is in the +keys then do this otherwise do + + align:start position:0% +keys then do this otherwise do + + + align:start position:0% +keys then do this otherwise do +that. It's slightly fewer lines of code + + align:start position:0% +that. It's slightly fewer lines of code + + + align:start position:0% +that. It's slightly fewer lines of code +and for me at least easier to read to + + align:start position:0% +and for me at least easier to read to + + + align:start position:0% +and for me at least easier to read to +use try except for this sort of thing. + + align:start position:0% + + + + align:start position:0% + +All right, let's see what happens if we + + align:start position:0% +All right, let's see what happens if we + + + align:start position:0% +All right, let's see what happens if we +run this + + align:start position:0% +run this + + + align:start position:0% +run this +one. So, we'll get rid of the slow + + align:start position:0% + + + + align:start position:0% + +fib. And we'll run fast fib. + + align:start position:0% + + + + align:start position:0% + +Wow, we're all already done with fib + + align:start position:0% + + + + align:start position:0% + +120. Pretty amazing considering last + + align:start position:0% +120. Pretty amazing considering last + + + align:start position:0% +120. Pretty amazing considering last +time we got stuck around + + align:start position:0% +time we got stuck around + + + align:start position:0% +time we got stuck around +40, right? + + align:start position:0% +40, right? + + + align:start position:0% +40, right? +It really works this memorization trick, + + align:start position:0% +It really works this memorization trick, + + + align:start position:0% +It really works this memorization trick, +you know, in an enormous + + align:start position:0% + + + + align:start position:0% + +difference, when can you use it? Right? + + align:start position:0% +difference, when can you use it? Right? + + + align:start position:0% +difference, when can you use it? Right? +It's not that memoization is a magic + + align:start position:0% +It's not that memoization is a magic + + + align:start position:0% +It's not that memoization is a magic +bullet that will solve all problems. + + align:start position:0% +bullet that will solve all problems. + + + align:start position:0% +bullet that will solve all problems. +um you need the problems it can solve or + + align:start position:0% +um you need the problems it can solve or + + + align:start position:0% +um you need the problems it can solve or +can help with really is the right thing. + + align:start position:0% +can help with really is the right thing. + + + align:start position:0% +can help with really is the right thing. +And by the way, as we'll see, it finds + + align:start position:0% +And by the way, as we'll see, it finds + + + align:start position:0% +And by the way, as we'll see, it finds +an optimal solution, not an + + align:start position:0% +an optimal solution, not an + + + align:start position:0% +an optimal solution, not an +approximation is when problems have two + + align:start position:0% +approximation is when problems have two + + + align:start position:0% +approximation is when problems have two +things called optimal substructure and + + align:start position:0% +things called optimal substructure and + + + align:start position:0% +things called optimal substructure and +overlapping + + align:start position:0% +overlapping + + + align:start position:0% +overlapping +subpros. So what do these + + align:start position:0% +subpros. So what do these + + + align:start position:0% +subpros. So what do these +mean? We have optimal substructure when + + align:start position:0% +mean? We have optimal substructure when + + + align:start position:0% +mean? We have optimal substructure when +a globally optimal solution can be found + + align:start position:0% +a globally optimal solution can be found + + + align:start position:0% +a globally optimal solution can be found +by combining optimal solutions to local + + align:start position:0% +by combining optimal solutions to local + + + align:start position:0% +by combining optimal solutions to local +subpros. So for example when x is + + align:start position:0% +subpros. So for example when x is + + + align:start position:0% +subpros. So for example when x is +greater than one we can solve fib x by + + align:start position:0% +greater than one we can solve fib x by + + + align:start position:0% +greater than one we can solve fib x by +solving fib x -1 and fib + + align:start position:0% +solving fib x -1 and fib + + + align:start position:0% +solving fib x -1 and fib +xus2 and adding those two things + + align:start position:0% +xus2 and adding those two things + + + align:start position:0% +xus2 and adding those two things +together. All right. So there's optimal + + align:start position:0% +together. All right. So there's optimal + + + align:start position:0% +together. All right. So there's optimal +substructure. You solve these two + + align:start position:0% +substructure. You solve these two + + + align:start position:0% +substructure. You solve these two +smaller problems independently of each + + align:start position:0% +smaller problems independently of each + + + align:start position:0% +smaller problems independently of each +other and then combine the solutions in + + align:start position:0% +other and then combine the solutions in + + + align:start position:0% +other and then combine the solutions in +a fast way. All + + align:start position:0% + + + + align:start position:0% + +right. You also have to have something + + align:start position:0% +right. You also have to have something + + + align:start position:0% +right. You also have to have something +called overlapping + + align:start position:0% +called overlapping + + + align:start position:0% +called overlapping +subpros. This is why the memo worked, + + align:start position:0% +subpros. This is why the memo worked, + + + align:start position:0% +subpros. This is why the memo worked, +right? Finding an optimal solution has + + align:start position:0% +right? Finding an optimal solution has + + + align:start position:0% +right? Finding an optimal solution has +to involve solving the same problem + + align:start position:0% +to involve solving the same problem + + + align:start position:0% +to involve solving the same problem +multiple + + align:start position:0% +multiple + + + align:start position:0% +multiple +times. Even if you have optimal + + align:start position:0% +times. Even if you have optimal + + + align:start position:0% +times. Even if you have optimal +substructure, if you don't see the same + + align:start position:0% +substructure, if you don't see the same + + + align:start position:0% +substructure, if you don't see the same +problem more than once, creating a memo, + + align:start position:0% +problem more than once, creating a memo, + + + align:start position:0% +problem more than once, creating a memo, +well, it'll work. You can still create + + align:start position:0% +well, it'll work. You can still create + + + align:start position:0% +well, it'll work. You can still create +the memo. You'll just never find it + + align:start position:0% +the memo. You'll just never find it + + + align:start position:0% +the memo. You'll just never find it +anything in it when you look things up + + align:start position:0% +anything in it when you look things up + + + align:start position:0% +anything in it when you look things up +because you're solving each problem + + align:start position:0% +because you're solving each problem + + + align:start position:0% +because you're solving each problem +once. Okay? So you have to be solving + + align:start position:0% +once. Okay? So you have to be solving + + + align:start position:0% +once. Okay? So you have to be solving +the same problem multiple times and you + + align:start position:0% +the same problem multiple times and you + + + align:start position:0% +the same problem multiple times and you +have to be able to solve it by combining + + align:start position:0% +have to be able to solve it by combining + + + align:start position:0% +have to be able to solve it by combining +solutions to smaller + + align:start position:0% + + + + align:start position:0% + +problems now we've seen things with + + align:start position:0% +problems now we've seen things with + + + align:start position:0% +problems now we've seen things with +optimal scrub structure before + + align:start position:0% +optimal scrub structure before + + + align:start position:0% +optimal scrub structure before +right in some sense right what what + + align:start position:0% +right in some sense right what what + + + align:start position:0% +right in some sense right what what +merge sort work that way right we were + + align:start position:0% +merge sort work that way right we were + + + align:start position:0% +merge sort work that way right we were +combining separate problems did merge + + align:start position:0% +combining separate problems did merge + + + align:start position:0% +combining separate problems did merge +sort have overlapping sub + + align:start position:0% + + + + align:start position:0% + +problems No. Right. Because well, I + + align:start position:0% +problems No. Right. Because well, I + + + align:start position:0% +problems No. Right. Because well, I +guess it might have if the list had the + + align:start position:0% +guess it might have if the list had the + + + align:start position:0% +guess it might have if the list had the +same element many many times, but we + + align:start position:0% +same element many many times, but we + + + align:start position:0% +same element many many times, but we +would expect mostly not, right? Because + + align:start position:0% +would expect mostly not, right? Because + + + align:start position:0% +would expect mostly not, right? Because +each time we're solving a different + + align:start position:0% +each time we're solving a different + + + align:start position:0% +each time we're solving a different +problem because we have different lists + + align:start position:0% +problem because we have different lists + + + align:start position:0% +problem because we have different lists +that we're now sorting and + + align:start position:0% +that we're now sorting and + + + align:start position:0% +that we're now sorting and +merging. So has half of it but not the + + align:start position:0% +merging. So has half of it but not the + + + align:start position:0% +merging. So has half of it but not the +other. So dynamic programming will not + + align:start position:0% +other. So dynamic programming will not + + + align:start position:0% +other. So dynamic programming will not +help us for sorting. You know, cannot be + + align:start position:0% +help us for sorting. You know, cannot be + + + align:start position:0% +help us for sorting. You know, cannot be +used to improve merge + + align:start position:0% +used to improve merge + + + align:start position:0% +used to improve merge +sort. Oh well. + + align:start position:0% +sort. Oh well. + + + align:start position:0% +sort. Oh well. +Nothing is a silver + + align:start position:0% +Nothing is a silver + + + align:start position:0% +Nothing is a silver +bullet. All right. What about the + + align:start position:0% +bullet. All right. What about the + + + align:start position:0% +bullet. All right. What about the +knapsack + + align:start position:0% +knapsack + + + align:start position:0% +knapsack +problem? Does it have these two + + align:start position:0% +problem? Does it have these two + + + align:start position:0% +problem? Does it have these two +properties? + + align:start position:0% +properties? + + + align:start position:0% +properties? +So we can look at it in terms of these + + align:start position:0% +So we can look at it in terms of these + + + align:start position:0% +So we can look at it in terms of these +pictures and it's pretty clear that it + + align:start position:0% +pictures and it's pretty clear that it + + + align:start position:0% +pictures and it's pretty clear that it +does have optimal substructure, right? + + align:start position:0% +does have optimal substructure, right? + + + align:start position:0% +does have optimal substructure, right? +Because we're taking the left branch and + + align:start position:0% +Because we're taking the left branch and + + + align:start position:0% +Because we're taking the left branch and +the right branch and choosing the + + align:start position:0% +the right branch and choosing the + + + align:start position:0% +the right branch and choosing the +winner. + + align:start position:0% + + + + align:start position:0% + +But what about overlapping + + align:start position:0% +But what about overlapping + + + align:start position:0% +But what about overlapping +subpros? Are we ever solving in this + + align:start position:0% +subpros? Are we ever solving in this + + + align:start position:0% +subpros? Are we ever solving in this +case the same + + align:start position:0% +case the same + + + align:start position:0% +case the same +problem at two + + align:start position:0% + + + + align:start position:0% + +nodes? Well, do you do any of these + + align:start position:0% +nodes? Well, do you do any of these + + + align:start position:0% +nodes? Well, do you do any of these +nodes look + + align:start position:0% + + + + align:start position:0% + +identical? Well, in this case, no. So we + + align:start position:0% +identical? Well, in this case, no. So we + + + align:start position:0% +identical? Well, in this case, no. So we +could write a dynamic programming + + align:start position:0% +could write a dynamic programming + + + align:start position:0% +could write a dynamic programming +solution to the knapsack problem and we + + align:start position:0% +solution to the knapsack problem and we + + + align:start position:0% +solution to the knapsack problem and we +will and run it on this example and we + + align:start position:0% +will and run it on this example and we + + + align:start position:0% +will and run it on this example and we +get the right answer we would get zero + + align:start position:0% +get the right answer we would get zero + + + align:start position:0% +get the right answer we would get zero +speed up because at each node if you can + + align:start position:0% +speed up because at each node if you can + + + align:start position:0% +speed up because at each node if you can +see the problems are different. We have + + align:start position:0% +see the problems are different. We have + + + align:start position:0% +see the problems are different. We have +different things in the + + align:start position:0% +different things in the + + + align:start position:0% +different things in the +knapsack or different things to + + align:start position:0% +knapsack or different things to + + + align:start position:0% +knapsack or different things to +consider. Never do we have the same + + align:start position:0% +consider. Never do we have the same + + + align:start position:0% +consider. Never do we have the same +contents and the same things left to + + align:start position:0% +contents and the same things left to + + + align:start position:0% +contents and the same things left to +decide. + + align:start position:0% + + + + align:start position:0% + +So maybe was not a bad answer if that's + + align:start position:0% +So maybe was not a bad answer if that's + + + align:start position:0% +So maybe was not a bad answer if that's +was the answer you gave to this + + align:start position:0% +was the answer you gave to this + + + align:start position:0% +was the answer you gave to this +question. But let's look at a different + + align:start position:0% +question. But let's look at a different + + + align:start position:0% +question. But let's look at a different +menu. So this menu happens to have two + + align:start position:0% +menu. So this menu happens to have two + + + align:start position:0% +menu. So this menu happens to have two +beers in + + align:start position:0% + + + + align:start position:0% + +it. Now if we look at what + + align:start position:0% +it. Now if we look at what + + + align:start position:0% +it. Now if we look at what +happens, do we see two nodes that are + + align:start position:0% +happens, do we see two nodes that are + + + align:start position:0% +happens, do we see two nodes that are +solving the same problem? + + align:start position:0% + + + + align:start position:0% + +The answer + + align:start position:0% +The answer + + + align:start position:0% +The answer +is what? Yes or + + align:start position:0% + + + + align:start position:0% + +no? I haven't drawn the whole tree here. + + align:start position:0% +no? I haven't drawn the whole tree here. + + + align:start position:0% +no? I haven't drawn the whole tree here. +Well, you'll notice the answer is yes. + + align:start position:0% +Well, you'll notice the answer is yes. + + + align:start position:0% +Well, you'll notice the answer is yes. +This + + align:start position:0% +This + + + align:start position:0% +This +node and this + + align:start position:0% +node and this + + + align:start position:0% +node and this +node are solving the same problem. Why + + align:start position:0% +node are solving the same problem. Why + + + align:start position:0% +node are solving the same problem. Why +is it? Well, in this node, we took this + + align:start position:0% +is it? Well, in this node, we took this + + + align:start position:0% +is it? Well, in this node, we took this +beer and still had this one to + + align:start position:0% +beer and still had this one to + + + align:start position:0% +beer and still had this one to +consider. But in this node, we took that + + align:start position:0% +consider. But in this node, we took that + + + align:start position:0% +consider. But in this node, we took that +beer. But it doesn't matter which beer + + align:start position:0% +beer. But it doesn't matter which beer + + + align:start position:0% +beer. But it doesn't matter which beer +we took. We still have a beer in the + + align:start position:0% +we took. We still have a beer in the + + + align:start position:0% +we took. We still have a beer in the +knapsack and a burger and a slice to + + align:start position:0% +knapsack and a burger and a slice to + + + align:start position:0% +knapsack and a burger and a slice to +consider. So, we got there different + + align:start position:0% +consider. So, we got there different + + + align:start position:0% +consider. So, we got there different +ways by choosing different beers, but + + align:start position:0% +ways by choosing different beers, but + + + align:start position:0% +ways by choosing different beers, but +we're in the same place. + + align:start position:0% +we're in the same place. + + + align:start position:0% +we're in the same place. +So in fact we actually in this case do + + align:start position:0% +So in fact we actually in this case do + + + align:start position:0% +So in fact we actually in this case do +have the same problem to solve once more + + align:start position:0% +have the same problem to solve once more + + + align:start position:0% +have the same problem to solve once more +than once. Now here I had two things + + align:start position:0% +than once. Now here I had two things + + + align:start position:0% +than once. Now here I had two things +that were the same. That's not really + + align:start position:0% +that were the same. That's not really + + + align:start position:0% +that were the same. That's not really +necessary. Here's another very small + + align:start position:0% +necessary. Here's another very small + + + align:start position:0% +necessary. Here's another very small +example. + + align:start position:0% +example. + + + align:start position:0% +example. +And the point I want to make + + align:start position:0% +And the point I want to make + + + align:start position:0% +And the point I want to make +here is shown by this. So here I've + + align:start position:0% +here is shown by this. So here I've + + + align:start position:0% +here is shown by this. So here I've +again drawn a search tree. And I'm + + align:start position:0% +again drawn a search tree. And I'm + + + align:start position:0% +again drawn a search tree. And I'm +showing you this because in fact it's + + align:start position:0% +showing you this because in fact it's + + + align:start position:0% +showing you this because in fact it's +exactly this tree that we'll be + + align:start position:0% +exactly this tree that we'll be + + + align:start position:0% +exactly this tree that we'll be +producing in + + align:start position:0% +producing in + + + align:start position:0% +producing in +our dynamic programming solution to the + + align:start position:0% +our dynamic programming solution to the + + + align:start position:0% +our dynamic programming solution to the +knapsack problem. Each node in the tree + + align:start position:0% +knapsack problem. Each node in the tree + + + align:start position:0% +knapsack problem. Each node in the tree +is + + align:start position:0% +is + + + align:start position:0% +is +uh starts with what you've taken + + align:start position:0% +uh starts with what you've taken + + + align:start position:0% +uh starts with what you've taken +initially nothing the empty set. what's + + align:start position:0% +initially nothing the empty set. what's + + + align:start position:0% +initially nothing the empty set. what's +left the total value and the remaining + + align:start position:0% +left the total value and the remaining + + + align:start position:0% +left the total value and the remaining +calories. There's some redundancy here, + + align:start position:0% +calories. There's some redundancy here, + + + align:start position:0% +calories. There's some redundancy here, +by the way. If I know what I've taken, I + + align:start position:0% +by the way. If I know what I've taken, I + + + align:start position:0% +by the way. If I know what I've taken, I +could already always compute + + align:start position:0% +could already always compute + + + align:start position:0% +could already always compute +the the value and what's left, but this + + align:start position:0% +the the value and what's left, but this + + + align:start position:0% +the the value and what's left, but this +is just so it's easier to see. And I've + + align:start position:0% +is just so it's easier to see. And I've + + + align:start position:0% +is just so it's easier to see. And I've +numbered the nodes here in the order in + + align:start position:0% +numbered the nodes here in the order in + + + align:start position:0% +numbered the nodes here in the order in +which they get generated. + + align:start position:0% + + + + align:start position:0% + +Now, the thing that I want you to + + align:start position:0% +Now, the thing that I want you to + + + align:start position:0% +Now, the thing that I want you to +notice is when we ask whether we're + + align:start position:0% +notice is when we ask whether we're + + + align:start position:0% +notice is when we ask whether we're +solving the same + + align:start position:0% +solving the same + + + align:start position:0% +solving the same +problem, we don't actually + + align:start position:0% +problem, we don't actually + + + align:start position:0% +problem, we don't actually +care what we've + + align:start position:0% +care what we've + + + align:start position:0% +care what we've +taken. We don't even care about the + + align:start position:0% +taken. We don't even care about the + + + align:start position:0% +taken. We don't even care about the +value. All we care + + align:start position:0% + + + + align:start position:0% + +is how much room we have left in the + + align:start position:0% +is how much room we have left in the + + + align:start position:0% +is how much room we have left in the +knapsack. + + align:start position:0% +knapsack. + + + align:start position:0% +knapsack. +and which items we have left to + + align:start position:0% +and which items we have left to + + + align:start position:0% +and which items we have left to +consider because what I take next or + + align:start position:0% +consider because what I take next or + + + align:start position:0% +consider because what I take next or +what I take remaining really has nothing + + align:start position:0% +what I take remaining really has nothing + + + align:start position:0% +what I take remaining really has nothing +to do with how much value I already have + + align:start position:0% +to do with how much value I already have + + + align:start position:0% +to do with how much value I already have +because I'm trying to maximize the value + + align:start position:0% +because I'm trying to maximize the value + + + align:start position:0% +because I'm trying to maximize the value +that's left independent of previous + + align:start position:0% +that's left independent of previous + + + align:start position:0% +that's left independent of previous +things done. Right? + + align:start position:0% +things done. Right? + + + align:start position:0% +things done. Right? +Similarly, I don't care why I have 100 + + align:start position:0% +Similarly, I don't care why I have 100 + + + align:start position:0% +Similarly, I don't care why I have 100 +calories left. Whether I used it up on + + align:start position:0% +calories left. Whether I used it up on + + + align:start position:0% +calories left. Whether I used it up on +beers or burger doesn't matter. All that + + align:start position:0% +beers or burger doesn't matter. All that + + + align:start position:0% +beers or burger doesn't matter. All that +matters is all I have is that I just + + align:start position:0% +matters is all I have is that I just + + + align:start position:0% +matters is all I have is that I just +have a hundred left. + + align:start position:0% +have a hundred left. + + + align:start position:0% +have a hundred left. +And so we see in a large complicated + + align:start position:0% +And so we see in a large complicated + + + align:start position:0% +And so we see in a large complicated +problem, it could easily be in a + + align:start position:0% +problem, it could easily be in a + + + align:start position:0% +problem, it could easily be in a +situation where different choices of + + align:start position:0% +situation where different choices of + + + align:start position:0% +situation where different choices of +what to take and what to not take would + + align:start position:0% +what to take and what to not take would + + + align:start position:0% +what to take and what to not take would +leave you in a situation where you have + + align:start position:0% +leave you in a situation where you have + + + align:start position:0% +leave you in a situation where you have +the same number of remaining + + align:start position:0% + + + + align:start position:0% + +calories. And therefore, you're solving + + align:start position:0% +calories. And therefore, you're solving + + + align:start position:0% +calories. And therefore, you're solving +a problem you've already solved. + + align:start position:0% + + + + align:start position:0% + +At each node, we're just given the + + align:start position:0% +At each node, we're just given the + + + align:start position:0% +At each node, we're just given the +remaining weight. Maximize the value by + + align:start position:0% +remaining weight. Maximize the value by + + + align:start position:0% +remaining weight. Maximize the value by +choosing among the remaining items. + + align:start position:0% +choosing among the remaining items. + + + align:start position:0% +choosing among the remaining items. +That's all that + + align:start position:0% +That's all that + + + align:start position:0% +That's all that +matters. And so indeed, you will have + + align:start position:0% +matters. And so indeed, you will have + + + align:start position:0% +matters. And so indeed, you will have +overlapping + + align:start position:0% +overlapping + + + align:start position:0% +overlapping +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +subpros. As we see in this tree for the + + align:start position:0% +subpros. As we see in this tree for the + + + align:start position:0% +subpros. As we see in this tree for the +example we just + + align:start position:0% +example we just + + + align:start position:0% +example we just +saw, the box is around a place where + + align:start position:0% +saw, the box is around a place where + + + align:start position:0% +saw, the box is around a place where +we're actually solving the same + + align:start position:0% +we're actually solving the same + + + align:start position:0% +we're actually solving the same +problem even though we've made different + + align:start position:0% +problem even though we've made different + + + align:start position:0% +problem even though we've made different +decisions about what to take A versus B. + + align:start position:0% +decisions about what to take A versus B. + + + align:start position:0% +decisions about what to take A versus B. +And in fact, we have different amounts + + align:start position:0% +And in fact, we have different amounts + + + align:start position:0% +And in fact, we have different amounts +of value in the NAPSAC 6 versus 7. What + + align:start position:0% +of value in the NAPSAC 6 versus 7. What + + + align:start position:0% +of value in the NAPSAC 6 versus 7. What +matters is we still have C and D to + + align:start position:0% +matters is we still have C and D to + + + align:start position:0% +matters is we still have C and D to +consider and we have two units left. + + align:start position:0% + + + + align:start position:0% + +All right, it's a small and easy step + + align:start position:0% +All right, it's a small and easy step + + + align:start position:0% +All right, it's a small and easy step +and I'm not going to walk you through + + align:start position:0% +and I'm not going to walk you through + + + align:start position:0% +and I'm not going to walk you through +the code because it's kind of boring to + + align:start position:0% +the code because it's kind of boring to + + + align:start position:0% +the code because it's kind of boring to +do so of how do you modify the max val + + align:start position:0% +do so of how do you modify the max val + + + align:start position:0% +do so of how do you modify the max val +we looked at before to use a memo. First + + align:start position:0% +we looked at before to use a memo. First + + + align:start position:0% +we looked at before to use a memo. First +you have to add the third argument which + + align:start position:0% +you have to add the third argument which + + + align:start position:0% +you have to add the third argument which +is initially going to be set to the + + align:start position:0% +is initially going to be set to the + + + align:start position:0% +is initially going to be set to the +empty + + align:start position:0% +empty + + + align:start position:0% +empty +dictionary. The key of the memo will be + + align:start position:0% +dictionary. The key of the memo will be + + + align:start position:0% +dictionary. The key of the memo will be +a + + align:start position:0% +a + + + align:start position:0% +a +tupil. the items left to be considered + + align:start position:0% +tupil. the items left to be considered + + + align:start position:0% +tupil. the items left to be considered +and the available + + align:start position:0% +and the available + + + align:start position:0% +and the available +weight. Because the items left to be + + align:start position:0% +weight. Because the items left to be + + + align:start position:0% +weight. Because the items left to be +considered are in a list, we can + + align:start position:0% +considered are in a list, we can + + + align:start position:0% +considered are in a list, we can +represent the items left to be + + align:start position:0% +represent the items left to be + + + align:start position:0% +represent the items left to be +considered + + align:start position:0% +considered + + + align:start position:0% +considered +by how long the list is because we'll + + align:start position:0% +by how long the list is because we'll + + + align:start position:0% +by how long the list is because we'll +start at the front item and just work + + align:start position:0% +start at the front item and just work + + + align:start position:0% +start at the front item and just work +our way to the + + align:start position:0% + + + + align:start position:0% + +end. And then the function works + + align:start position:0% +end. And then the function works + + + align:start position:0% +end. And then the function works +essentially exactly the same way fast + + align:start position:0% +essentially exactly the same way fast + + + align:start position:0% +essentially exactly the same way fast +fib + + align:start position:0% + + + + align:start position:0% + +worked. + + align:start position:0% + + + + align:start position:0% + +Um I'm not going to run it for you + + align:start position:0% +Um I'm not going to run it for you + + + align:start position:0% +Um I'm not going to run it for you +because we're running out of time. Um + + align:start position:0% +because we're running out of time. Um + + + align:start position:0% +because we're running out of time. Um +you might want to run it yourself + + align:start position:0% +you might want to run it yourself + + + align:start position:0% +you might want to run it yourself +because it is kind of fun to see how + + align:start position:0% +because it is kind of fun to see how + + + align:start position:0% +because it is kind of fun to see how +really fast it is. But more + + align:start position:0% +really fast it is. But more + + + align:start position:0% +really fast it is. But more +interestingly, we can look at this + + align:start position:0% +interestingly, we can look at this + + + align:start position:0% +interestingly, we can look at this +table. If we this column is what we + + align:start position:0% +table. If we this column is what we + + + align:start position:0% +table. If we this column is what we +would get with the original recursive + + align:start position:0% +would get with the original recursive + + + align:start position:0% +would get with the original recursive +implementation where we didn't use a + + align:start position:0% +implementation where we didn't use a + + + align:start position:0% +implementation where we didn't use a +memo and it was there for two to the + + align:start position:0% +memo and it was there for two to the + + + align:start position:0% +memo and it was there for two to the +leng length of items. And as you can + + align:start position:0% +leng length of items. And as you can + + + align:start position:0% +leng length of items. And as you can +see, it + + align:start position:0% +see, it + + + align:start position:0% +see, it +gets really big or as we say at the end + + align:start position:0% +gets really big or as we say at the end + + + align:start position:0% +gets really big or as we say at the end +huge. + + align:start position:0% + + + + align:start position:0% + +But the number of calls grows incredibly + + align:start position:0% +But the number of calls grows incredibly + + + align:start position:0% +But the number of calls grows incredibly +slowly for the dynamic programming + + align:start position:0% +slowly for the dynamic programming + + + align:start position:0% +slowly for the dynamic programming +solution. Right? In the beginning, it's + + align:start position:0% +solution. Right? In the beginning, it's + + + align:start position:0% +solution. Right? In the beginning, it's +worse. Oh well. But by the time we get + + align:start position:0% +worse. Oh well. But by the time we get + + + align:start position:0% +worse. Oh well. But by the time we get +to the last number I wrote, um, we're + + align:start position:0% +to the last number I wrote, um, we're + + + align:start position:0% +to the last number I wrote, um, we're +looking at + + align:start position:0% +looking at + + + align:start position:0% +looking at +43,000 versus some really big number. I + + align:start position:0% +43,000 versus some really big number. I + + + align:start position:0% +43,000 versus some really big number. I +don't know how to + + align:start position:0% +don't know how to + + + align:start position:0% +don't know how to +pronounce, 18 somethings. + + align:start position:0% +pronounce, 18 somethings. + + + align:start position:0% +pronounce, 18 somethings. +So + + align:start position:0% +So + + + align:start position:0% +So +incredible improvement in + + align:start position:0% +incredible improvement in + + + align:start position:0% +incredible improvement in +performance and then at the end you know + + align:start position:0% +performance and then at the end you know + + + align:start position:0% +performance and then at the end you know +it's a number we couldn't fit on the + + align:start position:0% +it's a number we couldn't fit on the + + + align:start position:0% +it's a number we couldn't fit on the +slide and even in tiny font and yet only + + align:start position:0% +slide and even in tiny font and yet only + + + align:start position:0% +slide and even in tiny font and yet only +703,000 calls. How can this be? We know + + align:start position:0% +703,000 calls. How can this be? We know + + + align:start position:0% +703,000 calls. How can this be? We know +the problem is inherently + + align:start position:0% +the problem is inherently + + + align:start position:0% +the problem is inherently +exponential. Have we overturned the laws + + align:start position:0% +exponential. Have we overturned the laws + + + align:start position:0% +exponential. Have we overturned the laws +of the + + align:start position:0% +of the + + + align:start position:0% +of the +universe? Is dynamic programming a + + align:start position:0% +universe? Is dynamic programming a + + + align:start position:0% +universe? Is dynamic programming a +miracle in the lurggical sense? + + align:start position:0% +miracle in the lurggical sense? + + + align:start position:0% +miracle in the lurggical sense? +uh + + align:start position:0% +uh + + + align:start position:0% +uh +no but the thing I want you to carry + + align:start position:0% +no but the thing I want you to carry + + + align:start position:0% +no but the thing I want you to carry +away is that computational complexity + + align:start position:0% +away is that computational complexity + + + align:start position:0% +away is that computational complexity +can be a very subtle + + align:start position:0% +can be a very subtle + + + align:start position:0% +can be a very subtle +notion. The running time of fast maxv + + align:start position:0% +notion. The running time of fast maxv + + + align:start position:0% +notion. The running time of fast maxv +val is governed by the number of + + align:start position:0% +val is governed by the number of + + + align:start position:0% +val is governed by the number of +distinct pairs that we might be able to + + align:start position:0% +distinct pairs that we might be able to + + + align:start position:0% +distinct pairs that we might be able to +use as keys in the memo. The to consider + + align:start position:0% +use as keys in the memo. The to consider + + + align:start position:0% +use as keys in the memo. The to consider +and + + align:start position:0% +and + + + align:start position:0% +and +available. Well, the number of possible + + align:start position:0% +available. Well, the number of possible + + + align:start position:0% +available. Well, the number of possible +values of two consider is small, right? + + align:start position:0% +values of two consider is small, right? + + + align:start position:0% +values of two consider is small, right? +It's bounded by the length of the items. + + align:start position:0% +It's bounded by the length of the items. + + + align:start position:0% +It's bounded by the length of the items. +If I have 100 items, it's 0, one, two, + + align:start position:0% +If I have 100 items, it's 0, one, two, + + + align:start position:0% +If I have 100 items, it's 0, one, two, +up to + + align:start position:0% +up to + + + align:start position:0% +up to +100. The possible values of available + + align:start position:0% +100. The possible values of available + + + align:start position:0% +100. The possible values of available +weight is harder to + + align:start position:0% +weight is harder to + + + align:start position:0% +weight is harder to +characterize, but it's bounded by the + + align:start position:0% +characterize, but it's bounded by the + + + align:start position:0% +characterize, but it's bounded by the +number of distinct sums of weights you + + align:start position:0% +number of distinct sums of weights you + + + align:start position:0% +number of distinct sums of weights you +can get. Right? + + align:start position:0% +can get. Right? + + + align:start position:0% +can get. Right? +If I start with 750 calories + + align:start position:0% +If I start with 750 calories + + + align:start position:0% +If I start with 750 calories +left, what are the possibilities? Well, + + align:start position:0% +left, what are the possibilities? Well, + + + align:start position:0% +left, what are the possibilities? Well, +in fact, in this case, maybe we can say + + align:start position:0% +in fact, in this case, maybe we can say + + + align:start position:0% +in fact, in this case, maybe we can say +only + + align:start position:0% +only + + + align:start position:0% +only +750 because we're using with units. So, + + align:start position:0% +750 because we're using with units. So, + + + align:start position:0% +750 because we're using with units. So, +it's small, but it's actually smaller + + align:start position:0% +it's small, but it's actually smaller + + + align:start position:0% +it's small, but it's actually smaller +than that because it has to do with the + + align:start position:0% +than that because it has to do with the + + + align:start position:0% +than that because it has to do with the +combinations of ways I can add up the + + align:start position:0% +combinations of ways I can add up the + + + align:start position:0% +combinations of ways I can add up the +units I have. All right, I know this is + + align:start position:0% +units I have. All right, I know this is + + + align:start position:0% +units I have. All right, I know this is +complicated. It's not worth my going + + align:start position:0% +complicated. It's not worth my going + + + align:start position:0% +complicated. It's not worth my going +through the details in the lectures. + + align:start position:0% +through the details in the lectures. + + + align:start position:0% +through the details in the lectures. +It's covered in considerable detail in + + align:start position:0% +It's covered in considerable detail in + + + align:start position:0% +It's covered in considerable detail in +the assigned + + align:start position:0% +the assigned + + + align:start position:0% +the assigned +reading. All right, quickly summarizing + + align:start position:0% +reading. All right, quickly summarizing + + + align:start position:0% +reading. All right, quickly summarizing +lectures one and two. Here's what I want + + align:start position:0% +lectures one and two. Here's what I want + + + align:start position:0% +lectures one and two. Here's what I want +you to take away. Many problems of + + align:start position:0% +you to take away. Many problems of + + + align:start position:0% +you to take away. Many problems of +practical importance can be formulated + + align:start position:0% +practical importance can be formulated + + + align:start position:0% +practical importance can be formulated +as optimization + + align:start position:0% +as optimization + + + align:start position:0% +as optimization +problems. Greedy algorithms often + + align:start position:0% +problems. Greedy algorithms often + + + align:start position:0% +problems. Greedy algorithms often +provide an adequate though often not + + align:start position:0% +provide an adequate though often not + + + align:start position:0% +provide an adequate though often not +optimal + + align:start position:0% +optimal + + + align:start position:0% +optimal +solution. Even though finding optim an + + align:start position:0% +solution. Even though finding optim an + + + align:start position:0% +solution. Even though finding optim an +optimal solution is in theory + + align:start position:0% +optimal solution is in theory + + + align:start position:0% +optimal solution is in theory +exponentially hard, dynamic programming + + align:start position:0% +exponentially hard, dynamic programming + + + align:start position:0% +exponentially hard, dynamic programming +really often yields great results. It + + align:start position:0% +really often yields great results. It + + + align:start position:0% +really often yields great results. It +always gives you a correct result and it + + align:start position:0% +always gives you a correct result and it + + + align:start position:0% +always gives you a correct result and it +sometimes, in fact, most of the times it + + align:start position:0% +sometimes, in fact, most of the times it + + + align:start position:0% +sometimes, in fact, most of the times it +gives it to you very quickly. + + align:start position:0% +gives it to you very quickly. + + + align:start position:0% +gives it to you very quickly. +Finally, in the PowerPoint, you'll find + + align:start position:0% +Finally, in the PowerPoint, you'll find + + + align:start position:0% +Finally, in the PowerPoint, you'll find +an interesting optimization problem + + align:start position:0% +an interesting optimization problem + + + align:start position:0% +an interesting optimization problem +having to do with whether or not you + + align:start position:0% +having to do with whether or not you + + + align:start position:0% +having to do with whether or not you +should roll over problem set grades into + + align:start position:0% +should roll over problem set grades into + + + align:start position:0% +should roll over problem set grades into +a quiz. And it's simply a question of + + align:start position:0% +a quiz. And it's simply a question of + + + align:start position:0% +a quiz. And it's simply a question of +solving this optimization problem. \ No newline at end of file diff --git a/uPsMwJ116lQ.txt b/uPsMwJ116lQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..62046a93d78f163d1b1bab26720c601031e8a6ad --- /dev/null +++ b/uPsMwJ116lQ.txt @@ -0,0 +1,339 @@ +align:start position:0% + +Good morning everyone. My name is Sean. + + align:start position:0% +Good morning everyone. My name is Sean. + + + align:start position:0% +Good morning everyone. My name is Sean. +I'll be your TA this semester for the + + align:start position:0% +I'll be your TA this semester for the + + + align:start position:0% +I'll be your TA this semester for the +class 10213 chemical engineering + + align:start position:0% +class 10213 chemical engineering + + + align:start position:0% +class 10213 chemical engineering +thermodynamics. I am a P fourth year PhD + + align:start position:0% +thermodynamics. I am a P fourth year PhD + + + align:start position:0% +thermodynamics. I am a P fourth year PhD +student in the chemical engineering + + align:start position:0% +student in the chemical engineering + + + align:start position:0% +student in the chemical engineering +department and my research is actually + + align:start position:0% +department and my research is actually + + + align:start position:0% +department and my research is actually +related related to what you're going to + + align:start position:0% +related related to what you're going to + + + align:start position:0% +related related to what you're going to +learn in this semester. If you have any + + align:start position:0% +learn in this semester. If you have any + + + align:start position:0% +learn in this semester. If you have any +question coming up, you can email me and + + align:start position:0% +question coming up, you can email me and + + + align:start position:0% +question coming up, you can email me and +my email address is + + align:start position:0% +my email address is + + + align:start position:0% +my email address is +sea + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +shawmitt.edu. You can always come to our + + align:start position:0% +shawmitt.edu. You can always come to our + + + align:start position:0% +shawmitt.edu. You can always come to our +office hour if you have any questions. + + align:start position:0% +office hour if you have any questions. + + + align:start position:0% +office hour if you have any questions. +I'll be happy to answer um any concern + + align:start position:0% +I'll be happy to answer um any concern + + + align:start position:0% +I'll be happy to answer um any concern +and question that you have. I really + + align:start position:0% +and question that you have. I really + + + align:start position:0% +and question that you have. I really +hope that we can all learn together uh + + align:start position:0% +hope that we can all learn together uh + + + align:start position:0% +hope that we can all learn together uh +throughout the semester tackling all the + + align:start position:0% +throughout the semester tackling all the + + + align:start position:0% +throughout the semester tackling all the +difficulty and challenges in this class. + + align:start position:0% +difficulty and challenges in this class. + + + align:start position:0% +difficulty and challenges in this class. +I hope you have a great semester and a + + align:start position:0% +I hope you have a great semester and a + + + align:start position:0% +I hope you have a great semester and a +great learning experience and in 10 to + + align:start position:0% + + + + align:start position:0% + +13. Hello and welcome to 1636 + + align:start position:0% +13. Hello and welcome to 1636 + + + align:start position:0% +13. Hello and welcome to 1636 +communication systems and networks. My + + align:start position:0% +communication systems and networks. My + + + align:start position:0% +communication systems and networks. My +name is Marzier and I will be your TA + + align:start position:0% +name is Marzier and I will be your TA + + + align:start position:0% +name is Marzier and I will be your TA +throughout this semester. + + align:start position:0% +throughout this semester. + + + align:start position:0% +throughout this semester. +Um about me, I am a second year PhD + + align:start position:0% +Um about me, I am a second year PhD + + + align:start position:0% +Um about me, I am a second year PhD +student in aeronautics and astronautics + + align:start position:0% +student in aeronautics and astronautics + + + align:start position:0% +student in aeronautics and astronautics +department and I would like to help you + + align:start position:0% +department and I would like to help you + + + align:start position:0% +department and I would like to help you +if you have any question related to the + + align:start position:0% +if you have any question related to the + + + align:start position:0% +if you have any question related to the +course. But um I also want you to help + + align:start position:0% +course. But um I also want you to help + + + align:start position:0% +course. But um I also want you to help +me if there was anything ambiguous. If + + align:start position:0% +me if there was anything ambiguous. If + + + align:start position:0% +me if there was anything ambiguous. If +you had any problem understanding what I + + align:start position:0% +you had any problem understanding what I + + + align:start position:0% +you had any problem understanding what I +explained or related to my accent or + + align:start position:0% +explained or related to my accent or + + + align:start position:0% +explained or related to my accent or +language barrier, please let me know. I + + align:start position:0% +language barrier, please let me know. I + + + align:start position:0% +language barrier, please let me know. I +will work on it and try to fix it. + + align:start position:0% +will work on it and try to fix it. + + + align:start position:0% +will work on it and try to fix it. +So the information that you need is the + + align:start position:0% +So the information that you need is the + + + align:start position:0% +So the information that you need is the +office hour. It would be on Mondays 3 to + + align:start position:0% +office hour. It would be on Mondays 3 to + + + align:start position:0% +office hour. It would be on Mondays 3 to +4:00 p.m. in room + + align:start position:0% +4:00 p.m. in room + + + align:start position:0% +4:00 p.m. in room +33422. And if you had any question other + + align:start position:0% +33422. And if you had any question other + + + align:start position:0% +33422. And if you had any question other +than this time, please email me at + + align:start position:0% +than this time, please email me at + + + align:start position:0% +than this time, please email me at +marmit.edu. I will try to get back to + + align:start position:0% +marmit.edu. I will try to get back to + + + align:start position:0% +marmit.edu. I will try to get back to +you as soon as possible. Okay. So is + + align:start position:0% +you as soon as possible. Okay. So is + + + align:start position:0% +you as soon as possible. Okay. So is +there any question related to this? \ No newline at end of file diff --git a/uRUAnKCyyig.txt b/uRUAnKCyyig.txt new file mode 100644 index 0000000000000000000000000000000000000000..607f98fdcbe31e5602f625e8b1f7cb00cca2db4c --- /dev/null +++ b/uRUAnKCyyig.txt @@ -0,0 +1,691 @@ +align:start position:0% + +How do we solve problems involving + + align:start position:0% +How do we solve problems involving + + + align:start position:0% +How do we solve problems involving +massive pulleys using Newton's laws? As + + align:start position:0% +massive pulleys using Newton's laws? As + + + align:start position:0% +massive pulleys using Newton's laws? As +a simple example, let's look at this + + align:start position:0% +a simple example, let's look at this + + + align:start position:0% +a simple example, let's look at this +problem consisting of a block of mass m1 + + align:start position:0% +problem consisting of a block of mass m1 + + + align:start position:0% +problem consisting of a block of mass m1 +hanging from a massive pulley that has a + + align:start position:0% +hanging from a massive pulley that has a + + + align:start position:0% +hanging from a massive pulley that has a +moment of inertia i and radius r. We'll + + align:start position:0% +moment of inertia i and radius r. We'll + + + align:start position:0% +moment of inertia i and radius r. We'll +find the acceleration of the block a1 + + align:start position:0% +find the acceleration of the block a1 + + + align:start position:0% +find the acceleration of the block a1 +and the angular acceleration of the + + align:start position:0% +and the angular acceleration of the + + + align:start position:0% +and the angular acceleration of the +massive pulley alpha. + + align:start position:0% +massive pulley alpha. + + + align:start position:0% +massive pulley alpha. +It is critical to remember that the + + align:start position:0% +It is critical to remember that the + + + align:start position:0% +It is critical to remember that the +first step in solving these problems is + + align:start position:0% +first step in solving these problems is + + + align:start position:0% +first step in solving these problems is +to define the positive x and y + + align:start position:0% +to define the positive x and y + + + align:start position:0% +to define the positive x and y +directions and the positive direction of + + align:start position:0% +directions and the positive direction of + + + align:start position:0% +directions and the positive direction of +rotation. In two-dimensional problems, + + align:start position:0% +rotation. In two-dimensional problems, + + + align:start position:0% +rotation. In two-dimensional problems, +you're free to define any direction to + + align:start position:0% +you're free to define any direction to + + + align:start position:0% +you're free to define any direction to +be positive. Here we'll set our positive + + align:start position:0% +be positive. Here we'll set our positive + + + align:start position:0% +be positive. Here we'll set our positive +x and positive y like this. Once we pick + + align:start position:0% +x and positive y like this. Once we pick + + + align:start position:0% +x and positive y like this. Once we pick +x and y, the direction of the positive + + align:start position:0% +x and y, the direction of the positive + + + align:start position:0% +x and y, the direction of the positive +rotation is now also defined by the + + align:start position:0% +rotation is now also defined by the + + + align:start position:0% +rotation is now also defined by the +right- hand rule. + + align:start position:0% +right- hand rule. + + + align:start position:0% +right- hand rule. +You'll see shortly that defining + + align:start position:0% +You'll see shortly that defining + + + align:start position:0% +You'll see shortly that defining +positive directions at the beginning + + align:start position:0% +positive directions at the beginning + + + align:start position:0% +positive directions at the beginning +will save you from a negative sign + + align:start position:0% +will save you from a negative sign + + + align:start position:0% +will save you from a negative sign +nightmare later + + align:start position:0% +nightmare later + + + align:start position:0% +nightmare later +on. Now, let's write down Newton's laws + + align:start position:0% +on. Now, let's write down Newton's laws + + + align:start position:0% +on. Now, let's write down Newton's laws +for the different parts of the system. + + align:start position:0% +for the different parts of the system. + + + align:start position:0% +for the different parts of the system. +First, for the block, we will write down + + align:start position:0% +First, for the block, we will write down + + + align:start position:0% +First, for the block, we will write down +the linear version of Newton's second + + align:start position:0% +the linear version of Newton's second + + + align:start position:0% +the linear version of Newton's second +law. For the sum of forces, we have + + align:start position:0% +law. For the sum of forces, we have + + + align:start position:0% +law. For the sum of forces, we have +gravity pointing down and tension + + align:start position:0% +gravity pointing down and tension + + + align:start position:0% +gravity pointing down and tension +pointing up. According to the convention + + align:start position:0% +pointing up. According to the convention + + + align:start position:0% +pointing up. According to the convention +we just defined, t1 is positive and m1g + + align:start position:0% +we just defined, t1 is positive and m1g + + + align:start position:0% +we just defined, t1 is positive and m1g +is negative. + + align:start position:0% +is negative. + + + align:start position:0% +is negative. +Notice that since the block is + + align:start position:0% +Notice that since the block is + + + align:start position:0% +Notice that since the block is +accelerating, t1 minus m1g is not zero, + + align:start position:0% +accelerating, t1 minus m1g is not zero, + + + align:start position:0% +accelerating, t1 minus m1g is not zero, +but is equal to m1 + + align:start position:0% +but is equal to m1 + + + align:start position:0% +but is equal to m1 +a1. Notice that here we've set the signs + + align:start position:0% +a1. Notice that here we've set the signs + + + align:start position:0% +a1. Notice that here we've set the signs +for tension and weight. But we don't yet + + align:start position:0% +for tension and weight. But we don't yet + + + align:start position:0% +for tension and weight. But we don't yet +know which way the block is + + align:start position:0% +know which way the block is + + + align:start position:0% +know which way the block is +accelerating. So we just start by + + align:start position:0% +accelerating. So we just start by + + + align:start position:0% +accelerating. So we just start by +writing m1 a1. And if in the end we get + + align:start position:0% +writing m1 a1. And if in the end we get + + + align:start position:0% +writing m1 a1. And if in the end we get +that a1 is negative, we'll know that + + align:start position:0% +that a1 is negative, we'll know that + + + align:start position:0% +that a1 is negative, we'll know that +it's actually accelerating in the + + align:start position:0% +it's actually accelerating in the + + + align:start position:0% +it's actually accelerating in the +negative + + align:start position:0% +negative + + + align:start position:0% +negative +direction. Now let's look at the pulley. + + align:start position:0% +direction. Now let's look at the pulley. + + + align:start position:0% +direction. Now let's look at the pulley. +Newton's second law in its rotational + + align:start position:0% +Newton's second law in its rotational + + + align:start position:0% +Newton's second law in its rotational +form is toao is equal to I alpha. For a + + align:start position:0% +form is toao is equal to I alpha. For a + + + align:start position:0% +form is toao is equal to I alpha. For a +normal pulley, the string is always + + align:start position:0% +normal pulley, the string is always + + + align:start position:0% +normal pulley, the string is always +tangential to the side of the pulley. So + + align:start position:0% +tangential to the side of the pulley. So + + + align:start position:0% +tangential to the side of the pulley. So +r and f are perpendicular. So that means + + align:start position:0% +r and f are perpendicular. So that means + + + align:start position:0% +r and f are perpendicular. So that means +the torque is just t1 * r. What's the + + align:start position:0% +the torque is just t1 * r. What's the + + + align:start position:0% +the torque is just t1 * r. What's the +sign of this term? Well, according to + + align:start position:0% +sign of this term? Well, according to + + + align:start position:0% +sign of this term? Well, according to +the positive direction that we defined, + + align:start position:0% +the positive direction that we defined, + + + align:start position:0% +the positive direction that we defined, +this torque is + + align:start position:0% +this torque is + + + align:start position:0% +this torque is +positive. Again we'll leave the sign of + + align:start position:0% +positive. Again we'll leave the sign of + + + align:start position:0% +positive. Again we'll leave the sign of +the I alpha term to be positive and + + align:start position:0% +the I alpha term to be positive and + + + align:start position:0% +the I alpha term to be positive and +alpha will turn out to be either + + align:start position:0% +alpha will turn out to be either + + + align:start position:0% +alpha will turn out to be either +positive or + + align:start position:0% +positive or + + + align:start position:0% +positive or +negative. Finally we need to connect + + align:start position:0% +negative. Finally we need to connect + + + align:start position:0% +negative. Finally we need to connect +these two equations because the block is + + align:start position:0% +these two equations because the block is + + + align:start position:0% +these two equations because the block is +connected to the pulley using an ideal + + align:start position:0% +connected to the pulley using an ideal + + + align:start position:0% +connected to the pulley using an ideal +taut inextensible rope. A1 is going to + + align:start position:0% +taut inextensible rope. A1 is going to + + + align:start position:0% +taut inextensible rope. A1 is going to +be related to alpha. We just need to + + align:start position:0% +be related to alpha. We just need to + + + align:start position:0% +be related to alpha. We just need to +figure out exactly how they're related. + + align:start position:0% +figure out exactly how they're related. + + + align:start position:0% +figure out exactly how they're related. +In other words, we need to write down + + align:start position:0% +In other words, we need to write down + + + align:start position:0% +In other words, we need to write down +the constraint condition. + + align:start position:0% +the constraint condition. + + + align:start position:0% +the constraint condition. +Let's say that the block hypothetically + + align:start position:0% +Let's say that the block hypothetically + + + align:start position:0% +Let's say that the block hypothetically +is moving upwards. In this case, what's + + align:start position:0% +is moving upwards. In this case, what's + + + align:start position:0% +is moving upwards. In this case, what's +happening to the pulley? It must be + + align:start position:0% +happening to the pulley? It must be + + + align:start position:0% +happening to the pulley? It must be +spinning clockwise to pull the rope up + + align:start position:0% +spinning clockwise to pull the rope up + + + align:start position:0% +spinning clockwise to pull the rope up +as the block goes + + align:start position:0% +as the block goes + + + align:start position:0% +as the block goes +in. So, it has a clockwise angular + + align:start position:0% +in. So, it has a clockwise angular + + + align:start position:0% +in. So, it has a clockwise angular +velocity, which according to our + + align:start position:0% +velocity, which according to our + + + align:start position:0% +velocity, which according to our +convention is negative. In fact, if the + + align:start position:0% +convention is negative. In fact, if the + + + align:start position:0% +convention is negative. In fact, if the +pulley rotates a full turn in the + + align:start position:0% +pulley rotates a full turn in the + + + align:start position:0% +pulley rotates a full turn in the +clockwise negative direction, the angle + + align:start position:0% +clockwise negative direction, the angle + + + align:start position:0% +clockwise negative direction, the angle +changes by -2 pi. and 2 pi * r of the + + align:start position:0% +changes by -2 pi. and 2 pi * r of the + + + align:start position:0% +changes by -2 pi. and 2 pi * r of the +rope will be pulled up. So we can write + + align:start position:0% +rope will be pulled up. So we can write + + + align:start position:0% +rope will be pulled up. So we can write +that delta y is equal to r delta theta + + align:start position:0% +that delta y is equal to r delta theta + + + align:start position:0% +that delta y is equal to r delta theta +or taking some derivatives a1 is equal + + align:start position:0% +or taking some derivatives a1 is equal + + + align:start position:0% +or taking some derivatives a1 is equal +to r * + + align:start position:0% +to r * + + + align:start position:0% +to r * +alpha. After setting the sign + + align:start position:0% +alpha. After setting the sign + + + align:start position:0% +alpha. After setting the sign +conventions, writing Newton's laws for + + align:start position:0% +conventions, writing Newton's laws for + + + align:start position:0% +conventions, writing Newton's laws for +different parts of the system, and then + + align:start position:0% +different parts of the system, and then + + + align:start position:0% +different parts of the system, and then +writing down the constraint condition, + + align:start position:0% +writing down the constraint condition, + + + align:start position:0% +writing down the constraint condition, +we have three equations and three + + align:start position:0% +we have three equations and three + + + align:start position:0% +we have three equations and three +unknowns for which we can now solve. \ No newline at end of file diff --git a/uVlkeGHup6E.txt b/uVlkeGHup6E.txt new file mode 100644 index 0000000000000000000000000000000000000000..3939bddc8f5b7c1fa43e0f201d69962923c77419 --- /dev/null +++ b/uVlkeGHup6E.txt @@ -0,0 +1,10339 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Let's move on to our next module of the + + align:start position:0% +Let's move on to our next module of the + + + align:start position:0% +Let's move on to our next module of the +day which is called people the heart of + + align:start position:0% + + + + align:start position:0% + +lean. What people who have studied lean + + align:start position:0% +lean. What people who have studied lean + + + align:start position:0% +lean. What people who have studied lean +and the Toyota production system in + + align:start position:0% +and the Toyota production system in + + + align:start position:0% +and the Toyota production system in +general have found is that there's two + + align:start position:0% +general have found is that there's two + + + align:start position:0% +general have found is that there's two +major aspects of these kinds of systems. + + align:start position:0% +major aspects of these kinds of systems. + + + align:start position:0% +major aspects of these kinds of systems. +One is this kind of just in time + + align:start position:0% +One is this kind of just in time + + + align:start position:0% +One is this kind of just in time +production that we typically see and + + align:start position:0% +production that we typically see and + + + align:start position:0% +production that we typically see and +which we talked about in the New Balance + + align:start position:0% +which we talked about in the New Balance + + + align:start position:0% +which we talked about in the New Balance +plant tour. But the second and equally + + align:start position:0% +plant tour. But the second and equally + + + align:start position:0% +plant tour. But the second and equally +important component of these kinds of + + align:start position:0% +important component of these kinds of + + + align:start position:0% +important component of these kinds of +systems is the respect for human system + + align:start position:0% +systems is the respect for human system + + + align:start position:0% +systems is the respect for human system +that exists. And you heard again in our + + align:start position:0% +that exists. And you heard again in our + + + align:start position:0% +that exists. And you heard again in our +New Balance plant tour, you heard + + align:start position:0% +New Balance plant tour, you heard + + + align:start position:0% +New Balance plant tour, you heard +Claudio talk about the immense respect + + align:start position:0% +Claudio talk about the immense respect + + + align:start position:0% +Claudio talk about the immense respect +that they have for their employees and + + align:start position:0% +that they have for their employees and + + + align:start position:0% +that they have for their employees and +how employee involvement is valued and + + align:start position:0% +how employee involvement is valued and + + + align:start position:0% +how employee involvement is valued and +encouraged in his organization. + + align:start position:0% + + + + align:start position:0% + +Now the trouble is for a lot of folks + + align:start position:0% +Now the trouble is for a lot of folks + + + align:start position:0% +Now the trouble is for a lot of folks +and and engineers in particular you know + + align:start position:0% +and and engineers in particular you know + + + align:start position:0% +and and engineers in particular you know +we we think about the people parts of + + align:start position:0% +we we think about the people parts of + + + align:start position:0% +we we think about the people parts of +the problem and we sometimes see these + + align:start position:0% +the problem and we sometimes see these + + + align:start position:0% +the problem and we sometimes see these +as really challenging and this is a + + align:start position:0% +as really challenging and this is a + + + align:start position:0% +as really challenging and this is a +quote from a gentleman at Northwork + + align:start position:0% +quote from a gentleman at Northwork + + + align:start position:0% +quote from a gentleman at Northwork +Brumman who's fairly high up in their + + align:start position:0% +Brumman who's fairly high up in their + + + align:start position:0% +Brumman who's fairly high up in their +management and he sums it up very nicely + + align:start position:0% +management and he sums it up very nicely + + + align:start position:0% +management and he sums it up very nicely +by saying the soft stuff is the hard + + align:start position:0% +by saying the soft stuff is the hard + + + align:start position:0% +by saying the soft stuff is the hard +stuff the soft stuff which is usually + + align:start position:0% +stuff the soft stuff which is usually + + + align:start position:0% +stuff the soft stuff which is usually +thought of as the people issues is often + + align:start position:0% +thought of as the people issues is often + + + align:start position:0% +thought of as the people issues is often +seen as some of the hardest challenges + + align:start position:0% +seen as some of the hardest challenges + + + align:start position:0% +seen as some of the hardest challenges +in an organization. is very true, but + + align:start position:0% +in an organization. is very true, but + + + align:start position:0% +in an organization. is very true, but +it's one of those important items to + + align:start position:0% +it's one of those important items to + + + align:start position:0% +it's one of those important items to +work on when you think about making an + + align:start position:0% +work on when you think about making an + + + align:start position:0% +work on when you think about making an +organization + + align:start position:0% +organization + + + align:start position:0% +organization +lean. So, in this section on people, we + + align:start position:0% +lean. So, in this section on people, we + + + align:start position:0% +lean. So, in this section on people, we +want to have you achieve the following + + align:start position:0% +want to have you achieve the following + + + align:start position:0% +want to have you achieve the following +three learning objectives. The first is + + align:start position:0% +three learning objectives. The first is + + + align:start position:0% +three learning objectives. The first is +to be able to explain why people are key + + align:start position:0% +to be able to explain why people are key + + + align:start position:0% +to be able to explain why people are key +to improving productivity and + + align:start position:0% +to improving productivity and + + + align:start position:0% +to improving productivity and +organization. The second is to make you + + align:start position:0% +organization. The second is to make you + + + align:start position:0% +organization. The second is to make you +realize that effective communication, + + align:start position:0% +realize that effective communication, + + + align:start position:0% +realize that effective communication, +shared goals and knowledge, and mutual + + align:start position:0% +shared goals and knowledge, and mutual + + + align:start position:0% +shared goals and knowledge, and mutual +respect lead to improved organizational + + align:start position:0% +respect lead to improved organizational + + + align:start position:0% +respect lead to improved organizational +performance. And third, we'd like you to + + align:start position:0% +performance. And third, we'd like you to + + + align:start position:0% +performance. And third, we'd like you to +be able to participate as a member of a + + align:start position:0% +be able to participate as a member of a + + + align:start position:0% +be able to participate as a member of a +team in order to achieve a productive + + align:start position:0% +team in order to achieve a productive + + + align:start position:0% +team in order to achieve a productive +and positive outcome. So to get us + + align:start position:0% +and positive outcome. So to get us + + + align:start position:0% +and positive outcome. So to get us +kicked off on this discussion, I'd like + + align:start position:0% +kicked off on this discussion, I'd like + + + align:start position:0% +kicked off on this discussion, I'd like +you to think and reflect on the most + + align:start position:0% +you to think and reflect on the most + + + align:start position:0% +you to think and reflect on the most +important things that contribute to your + + align:start position:0% +important things that contribute to your + + + align:start position:0% +important things that contribute to your +job satisfaction. So whether you're a + + align:start position:0% +job satisfaction. So whether you're a + + + align:start position:0% +job satisfaction. So whether you're a +student or whether you're currently + + align:start position:0% +student or whether you're currently + + + align:start position:0% +student or whether you're currently +working, think about what it is that + + align:start position:0% +working, think about what it is that + + + align:start position:0% +working, think about what it is that +makes you very satisfied with your job. + + align:start position:0% +makes you very satisfied with your job. + + + align:start position:0% +makes you very satisfied with your job. +And I'd like to ask for some volunteers + + align:start position:0% +And I'd like to ask for some volunteers + + + align:start position:0% +And I'd like to ask for some volunteers +to tell me first of all what's the most + + align:start position:0% +to tell me first of all what's the most + + + align:start position:0% +to tell me first of all what's the most +important thing. Let's start off with + + align:start position:0% +important thing. Let's start off with + + + align:start position:0% +important thing. Let's start off with +that. And I'm going to start to make a + + align:start position:0% +that. And I'm going to start to make a + + + align:start position:0% +that. And I'm going to start to make a +list on the board. Yes. Maybe feeling + + align:start position:0% +list on the board. Yes. Maybe feeling + + + align:start position:0% +list on the board. Yes. Maybe feeling +like you made a difference at the end of + + align:start position:0% +like you made a difference at the end of + + + align:start position:0% +like you made a difference at the end of +the day. + + align:start position:0% + + + + align:start position:0% + +What else? Yes. Uh I felt like I learned + + align:start position:0% +What else? Yes. Uh I felt like I learned + + + align:start position:0% +What else? Yes. Uh I felt like I learned +something. + + align:start position:0% +something. + + + align:start position:0% +something. +Okay. Yeah. Something + + align:start position:0% +Okay. Yeah. Something + + + align:start position:0% +Okay. Yeah. Something +learning. Great. + + align:start position:0% +learning. Great. + + + align:start position:0% +learning. Great. +Having control over the outcomes you're + + align:start position:0% +Having control over the outcomes you're + + + align:start position:0% +Having control over the outcomes you're +responsible for. + + align:start position:0% + + + + align:start position:0% + +Yes. It's okay. Having room for + + align:start position:0% +Yes. It's okay. Having room for + + + align:start position:0% +Yes. It's okay. Having room for +creativity. Creativity. + + align:start position:0% +creativity. Creativity. + + + align:start position:0% +creativity. Creativity. +Feeling respected or valued. + + align:start position:0% + + + + align:start position:0% + +Yes. making connections with individuals + + align:start position:0% +Yes. making connections with individuals + + + align:start position:0% +Yes. making connections with individuals +and with the community at large. + + align:start position:0% +and with the community at large. + + + align:start position:0% +and with the community at large. +Connections. So, it's the relationships + + align:start position:0% +Connections. So, it's the relationships + + + align:start position:0% +Connections. So, it's the relationships +with your co-workers, customers, + + align:start position:0% +with your co-workers, customers, + + + align:start position:0% +with your co-workers, customers, +everybody. Yeah. With my patients and + + align:start position:0% +everybody. Yeah. With my patients and + + + align:start position:0% +everybody. Yeah. With my patients and +the students that I work with, but also + + align:start position:0% +the students that I work with, but also + + + align:start position:0% +the students that I work with, but also +connecting with the needs of the + + align:start position:0% +connecting with the needs of the + + + align:start position:0% +connecting with the needs of the +community in + + align:start position:0% +community in + + + align:start position:0% +community in +general. I guess with my colleagues, + + align:start position:0% +general. I guess with my colleagues, + + + align:start position:0% +general. I guess with my colleagues, +although that second + + align:start position:0% + + + + align:start position:0% + +Yes. Job that need to be worked to my + + align:start position:0% +Yes. Job that need to be worked to my + + + align:start position:0% +Yes. Job that need to be worked to my +full potential. + + align:start position:0% +full potential. + + + align:start position:0% +full potential. +Okay. + + align:start position:0% + + + + align:start position:0% + +Responsibility. + + align:start position:0% + + + + align:start position:0% + +Okay. In the back. Yes. Okay. I I know + + align:start position:0% +Okay. In the back. Yes. Okay. I I know + + + align:start position:0% +Okay. In the back. Yes. Okay. I I know +people are shy about this. The financial + + align:start position:0% +people are shy about this. The financial + + + align:start position:0% +people are shy about this. The financial +incentives. Financial incentives. + + align:start position:0% +incentives. Financial incentives. + + + align:start position:0% +incentives. Financial incentives. +Salary. All right. Good morning. Let's + + align:start position:0% +Salary. All right. Good morning. Let's + + + align:start position:0% +Salary. All right. Good morning. Let's +call that what it is. Salary. Great. We + + align:start position:0% +call that what it is. Salary. Great. We + + + align:start position:0% +call that what it is. Salary. Great. We +We've all got to eat. Go ahead. having + + align:start position:0% +We've all got to eat. Go ahead. having + + + align:start position:0% +We've all got to eat. Go ahead. having +the time to do my job right the first + + align:start position:0% +the time to do my job right the first + + + align:start position:0% +the time to do my job right the first +time and feeling like I didn't walk away + + align:start position:0% +time and feeling like I didn't walk away + + + align:start position:0% +time and feeling like I didn't walk away +making errors throughout the day. So, + + align:start position:0% +making errors throughout the day. So, + + + align:start position:0% +making errors throughout the day. So, +adequate time. What else? + + align:start position:0% +adequate time. What else? + + + align:start position:0% +adequate time. What else? +I don't know. Working hours, your + + align:start position:0% +I don't know. Working hours, your + + + align:start position:0% +I don't know. Working hours, your +hours. So, take a look at the list we + + align:start position:0% +hours. So, take a look at the list we + + + align:start position:0% +hours. So, take a look at the list we +have here and think if if the most + + align:start position:0% +have here and think if if the most + + + align:start position:0% +have here and think if if the most +important thing that contributes to your + + align:start position:0% +important thing that contributes to your + + + align:start position:0% +important thing that contributes to your +own job satisfaction isn't on this list, + + align:start position:0% +own job satisfaction isn't on this list, + + + align:start position:0% +own job satisfaction isn't on this list, +uh, and you'd like to raise your hand + + align:start position:0% +uh, and you'd like to raise your hand + + + align:start position:0% +uh, and you'd like to raise your hand +and tell us about it, that'd be great. + + align:start position:0% +and tell us about it, that'd be great. + + + align:start position:0% +and tell us about it, that'd be great. +We'll add it to the list. Otherwise, we + + align:start position:0% +We'll add it to the list. Otherwise, we + + + align:start position:0% +We'll add it to the list. Otherwise, we +might start to winnow it down. Lack of + + align:start position:0% +might start to winnow it down. Lack of + + + align:start position:0% +might start to winnow it down. Lack of +stress, + + align:start position:0% +stress, + + + align:start position:0% +stress, +stressfree environment, reduce stress. + + align:start position:0% +stressfree environment, reduce stress. + + + align:start position:0% +stressfree environment, reduce stress. +Okay. So, low stress, reduce stress. + + align:start position:0% +Okay. So, low stress, reduce stress. + + + align:start position:0% +Okay. So, low stress, reduce stress. +Susan carpet team. + + align:start position:0% +Susan carpet team. + + + align:start position:0% +Susan carpet team. +Yes. I'm back. It's sort of related to + + align:start position:0% +Yes. I'm back. It's sort of related to + + + align:start position:0% +Yes. I'm back. It's sort of related to +hours, but work family balance. Mhm. + + align:start position:0% + + + + align:start position:0% + +Yes. Feedback. + + align:start position:0% +Yes. Feedback. + + + align:start position:0% +Yes. Feedback. +feedback from your supervisor. + + align:start position:0% + + + + align:start position:0% + +Okay, great. Do we have any one more + + align:start position:0% +Okay, great. Do we have any one more + + + align:start position:0% +Okay, great. Do we have any one more +burning last suggestion? + + align:start position:0% +burning last suggestion? + + + align:start position:0% +burning last suggestion? +Environmental working environment. + + align:start position:0% +Environmental working environment. + + + align:start position:0% +Environmental working environment. +Okay, so take a read through these and + + align:start position:0% +Okay, so take a read through these and + + + align:start position:0% +Okay, so take a read through these and +what I'd like to ask you to do now is + + align:start position:0% +what I'd like to ask you to do now is + + + align:start position:0% +what I'd like to ask you to do now is +each person take a a voting strip of + + align:start position:0% +each person take a a voting strip of + + + align:start position:0% +each person take a a voting strip of +dots. They should be distributed on your + + align:start position:0% +dots. They should be distributed on your + + + align:start position:0% +dots. They should be distributed on your +table. What I'm going to ask you to do + + align:start position:0% +table. What I'm going to ask you to do + + + align:start position:0% +table. What I'm going to ask you to do +is just come up to the board and place + + align:start position:0% +is just come up to the board and place + + + align:start position:0% +is just come up to the board and place +uh one dot next to each of your top + + align:start position:0% +uh one dot next to each of your top + + + align:start position:0% +uh one dot next to each of your top +three items. So, you get to vote for + + align:start position:0% +three items. So, you get to vote for + + + align:start position:0% +three items. So, you get to vote for +three as the most important things that + + align:start position:0% +three as the most important things that + + + align:start position:0% +three as the most important things that +contribute to your job satisfaction. So, + + align:start position:0% +contribute to your job satisfaction. So, + + + align:start position:0% +contribute to your job satisfaction. So, +when you're ready, just head up to the + + align:start position:0% +when you're ready, just head up to the + + + align:start position:0% +when you're ready, just head up to the +board and place your dots on the line. + + align:start position:0% +board and place your dots on the line. + + + align:start position:0% +board and place your dots on the line. +And yes, you do have to vote for three + + align:start position:0% +And yes, you do have to vote for three + + + align:start position:0% +And yes, you do have to vote for three +separate items. You can't put all your + + align:start position:0% +separate items. You can't put all your + + + align:start position:0% +separate items. You can't put all your +three dots on one particular row. + + align:start position:0% +three dots on one particular row. + + + align:start position:0% +three dots on one particular row. +So, go ahead. When you're ready, just + + align:start position:0% +So, go ahead. When you're ready, just + + + align:start position:0% +So, go ahead. When you're ready, just +come on up. + + align:start position:0% + + + + align:start position:0% + +Hey, has everybody had a chance to + + align:start position:0% + + + + align:start position:0% + +vote? Very good. All right, let's see + + align:start position:0% +vote? Very good. All right, let's see + + + align:start position:0% +vote? Very good. All right, let's see +where our our top vote getters were. So, + + align:start position:0% +where our our top vote getters were. So, + + + align:start position:0% +where our our top vote getters were. So, +it looks like work family balance is up + + align:start position:0% +it looks like work family balance is up + + + align:start position:0% +it looks like work family balance is up +there as is making a difference. + + align:start position:0% + + + + align:start position:0% + +Let's see. + + align:start position:0% + + + + align:start position:0% + +So, it looks like salary gets up there + + align:start position:0% +So, it looks like salary gets up there + + + align:start position:0% +So, it looks like salary gets up there +too as our top three + + align:start position:0% +too as our top three + + + align:start position:0% +too as our top three +there. Okay. Excellent. So, I think it's + + align:start position:0% +there. Okay. Excellent. So, I think it's + + + align:start position:0% +there. Okay. Excellent. So, I think it's +I think it's making a difference by + + align:start position:0% +I think it's making a difference by + + + align:start position:0% +I think it's making a difference by +quite a few quite a few lengths there. + + align:start position:0% +quite a few quite a few lengths there. + + + align:start position:0% +quite a few quite a few lengths there. +Work, family, balance, and then + + align:start position:0% +Work, family, balance, and then + + + align:start position:0% +Work, family, balance, and then +salary. So, let's see how some of your + + align:start position:0% +salary. So, let's see how some of your + + + align:start position:0% +salary. So, let's see how some of your +answers as a class compared to some + + align:start position:0% +answers as a class compared to some + + + align:start position:0% +answers as a class compared to some +studies that have been done. And this is + + align:start position:0% +studies that have been done. And this is + + + align:start position:0% +studies that have been done. And this is +just one sample that's actually been + + align:start position:0% +just one sample that's actually been + + + align:start position:0% +just one sample that's actually been +done by Boeing. It's some of their + + align:start position:0% +done by Boeing. It's some of their + + + align:start position:0% +done by Boeing. It's some of their +employee satisfaction surveys. And what + + align:start position:0% +employee satisfaction surveys. And what + + + align:start position:0% +employee satisfaction surveys. And what +you see here on the chart is the um the + + align:start position:0% +you see here on the chart is the um the + + + align:start position:0% +you see here on the chart is the um the +x-axis here. And the placement of these + + align:start position:0% +x-axis here. And the placement of these + + + align:start position:0% +x-axis here. And the placement of these +items shows the correlation or the + + align:start position:0% +items shows the correlation or the + + + align:start position:0% +items shows the correlation or the +strength of association with uh a high + + align:start position:0% +strength of association with uh a high + + + align:start position:0% +strength of association with uh a high +performance work environment. Really the + + align:start position:0% +performance work environment. Really the + + + align:start position:0% +performance work environment. Really the +things that are are making employees + + align:start position:0% +things that are are making employees + + + align:start position:0% +things that are are making employees +perform really well. And you'll see + + align:start position:0% +perform really well. And you'll see + + + align:start position:0% +perform really well. And you'll see +things like encouraged to come up with + + align:start position:0% +things like encouraged to come up with + + + align:start position:0% +things like encouraged to come up with +new and better ways to do things, + + align:start position:0% +new and better ways to do things, + + + align:start position:0% +new and better ways to do things, +involving them in decisions, improving + + align:start position:0% +involving them in decisions, improving + + + align:start position:0% +involving them in decisions, improving +my skills or learning as we called it + + align:start position:0% +my skills or learning as we called it + + + align:start position:0% +my skills or learning as we called it +here in class. Conditions allow me to be + + align:start position:0% +here in class. Conditions allow me to be + + + align:start position:0% +here in class. Conditions allow me to be +productive. We also talked about that. + + align:start position:0% +productive. We also talked about that. + + + align:start position:0% +productive. We also talked about that. +Someone made that suggestion. These are + + align:start position:0% +Someone made that suggestion. These are + + + align:start position:0% +Someone made that suggestion. These are +all things that have a a much higher + + align:start position:0% +all things that have a a much higher + + + align:start position:0% +all things that have a a much higher +correlation with having a high + + align:start position:0% +correlation with having a high + + + align:start position:0% +correlation with having a high +performance work environment than things + + align:start position:0% +performance work environment than things + + + align:start position:0% +performance work environment than things +uh on this side. And notice pay is sort + + align:start position:0% +uh on this side. And notice pay is sort + + + align:start position:0% +uh on this side. And notice pay is sort +of farthest from people's job + + align:start position:0% +of farthest from people's job + + + align:start position:0% +of farthest from people's job +satisfaction. So it just really goes to + + align:start position:0% +satisfaction. So it just really goes to + + + align:start position:0% +satisfaction. So it just really goes to +show you it's not just what you pay + + align:start position:0% +show you it's not just what you pay + + + align:start position:0% +show you it's not just what you pay +people in the job security but it's a + + align:start position:0% +people in the job security but it's a + + + align:start position:0% +people in the job security but it's a +lot of these other important + + align:start position:0% +lot of these other important + + + align:start position:0% +lot of these other important +satisfaction items that contributes to + + align:start position:0% +satisfaction items that contributes to + + + align:start position:0% +satisfaction items that contributes to +people really doing a productive + + align:start position:0% +people really doing a productive + + + align:start position:0% +people really doing a productive +job. Now there are several different + + align:start position:0% +job. Now there are several different + + + align:start position:0% +job. Now there are several different +theories about how workers are + + align:start position:0% +theories about how workers are + + + align:start position:0% +theories about how workers are +productive. They relate to the + + align:start position:0% +productive. They relate to the + + + align:start position:0% +productive. They relate to the +brainstorming that we've been doing. The + + align:start position:0% +brainstorming that we've been doing. The + + + align:start position:0% +brainstorming that we've been doing. The +first is usually called theory X and it + + align:start position:0% +first is usually called theory X and it + + + align:start position:0% +first is usually called theory X and it +was one of the original management + + align:start position:0% +was one of the original management + + + align:start position:0% +was one of the original management +theories and it's based on the premise + + align:start position:0% +theories and it's based on the premise + + + align:start position:0% +theories and it's based on the premise +that workers don't like to work so they + + align:start position:0% +that workers don't like to work so they + + + align:start position:0% +that workers don't like to work so they +must be made to work. So you have to + + align:start position:0% +must be made to work. So you have to + + + align:start position:0% +must be made to work. So you have to +enforce harsh rules and lots of + + align:start position:0% +enforce harsh rules and lots of + + + align:start position:0% +enforce harsh rules and lots of +motivation to get them to overcome this + + align:start position:0% +motivation to get them to overcome this + + + align:start position:0% +motivation to get them to overcome this +general human desire to not work. + + align:start position:0% +general human desire to not work. + + + align:start position:0% +general human desire to not work. +Yes, I have a thought. Um as you get + + align:start position:0% +Yes, I have a thought. Um as you get + + + align:start position:0% +Yes, I have a thought. Um as you get +salary and pay I think why that um + + align:start position:0% +salary and pay I think why that um + + + align:start position:0% +salary and pay I think why that um +example yeah why this one might be a + + align:start position:0% +example yeah why this one might be a + + + align:start position:0% +example yeah why this one might be a +little different. It's because on the + + align:start position:0% +little different. It's because on the + + + align:start position:0% +little different. It's because on the +average I want to guess that bulk of the + + align:start position:0% +average I want to guess that bulk of the + + + align:start position:0% +average I want to guess that bulk of the +work has already been paid good enough + + align:start position:0% +work has already been paid good enough + + + align:start position:0% +work has already been paid good enough +for to take care of themselves and their + + align:start position:0% +for to take care of themselves and their + + + align:start position:0% +for to take care of themselves and their +families and all that. So if you're + + align:start position:0% +families and all that. So if you're + + + align:start position:0% +families and all that. So if you're +paying someone a salary that um he's not + + align:start position:0% +paying someone a salary that um he's not + + + align:start position:0% +paying someone a salary that um he's not +able to um take care of himself or he's + + align:start position:0% +able to um take care of himself or he's + + + align:start position:0% +able to um take care of himself or he's +not able to pay his bills and all that, + + align:start position:0% +not able to pay his bills and all that, + + + align:start position:0% +not able to pay his bills and all that, +I don't think it won't be an issue. And + + align:start position:0% +I don't think it won't be an issue. And + + + align:start position:0% +I don't think it won't be an issue. And +I don't think so I think you might this + + align:start position:0% +I don't think so I think you might this + + + align:start position:0% +I don't think so I think you might this +might not really be a very good example + + align:start position:0% +might not really be a very good example + + + align:start position:0% +might not really be a very good example +because if we look at the average pay um + + align:start position:0% +because if we look at the average pay um + + + align:start position:0% +because if we look at the average pay um +the lowest pay you get might be + + align:start position:0% +the lowest pay you get might be + + + align:start position:0% +the lowest pay you get might be +something very tangible. Sure. And I I + + align:start position:0% +something very tangible. Sure. And I I + + + align:start position:0% +something very tangible. Sure. And I I +think I would agree with you that's a + + align:start position:0% +think I would agree with you that's a + + + align:start position:0% +think I would agree with you that's a +function of of some base level of pay. + + align:start position:0% +function of of some base level of pay. + + + align:start position:0% +function of of some base level of pay. +And perhaps one of the reasons why + + align:start position:0% +And perhaps one of the reasons why + + + align:start position:0% +And perhaps one of the reasons why +salary sometimes shows up in this + + align:start position:0% +salary sometimes shows up in this + + + align:start position:0% +salary sometimes shows up in this +environment is more important than on + + align:start position:0% +environment is more important than on + + + align:start position:0% +environment is more important than on +some of these other surveys that have + + align:start position:0% +some of these other surveys that have + + + align:start position:0% +some of these other surveys that have +been done is because we have a number of + + align:start position:0% +been done is because we have a number of + + + align:start position:0% +been done is because we have a number of +students in the room. Right? Raise your + + align:start position:0% +students in the room. Right? Raise your + + + align:start position:0% +students in the room. Right? Raise your +hand if you're a student. if you're not + + align:start position:0% +hand if you're a student. if you're not + + + align:start position:0% +hand if you're a student. if you're not +being paid much of anything and hence if + + align:start position:0% +being paid much of anything and hence if + + + align:start position:0% +being paid much of anything and hence if +salary is really important to you. But + + align:start position:0% +salary is really important to you. But + + + align:start position:0% +salary is really important to you. But +you know as you s as you suggest when + + align:start position:0% +you know as you s as you suggest when + + + align:start position:0% +you know as you s as you suggest when +you go out in the workforce and you you + + align:start position:0% +you go out in the workforce and you you + + + align:start position:0% +you go out in the workforce and you you +are earning a salary and and putting + + align:start position:0% +are earning a salary and and putting + + + align:start position:0% +are earning a salary and and putting +food on the table is not as as + + align:start position:0% +food on the table is not as as + + + align:start position:0% +food on the table is not as as +concerning for you as it might be when + + align:start position:0% +concerning for you as it might be when + + + align:start position:0% +concerning for you as it might be when +you're not getting salary as a student + + align:start position:0% +you're not getting salary as a student + + + align:start position:0% +you're not getting salary as a student +some of these other items really become + + align:start position:0% +some of these other items really become + + + align:start position:0% +some of these other items really become +important. So after a while if you're + + align:start position:0% +important. So after a while if you're + + + align:start position:0% +important. So after a while if you're +trying to create a high performing work + + align:start position:0% +trying to create a high performing work + + + align:start position:0% +trying to create a high performing work +organization it's not so much increasing + + align:start position:0% +organization it's not so much increasing + + + align:start position:0% +organization it's not so much increasing +people's pay as it is focusing on making + + align:start position:0% +people's pay as it is focusing on making + + + align:start position:0% +people's pay as it is focusing on making +sure there are all these other + + align:start position:0% +sure there are all these other + + + align:start position:0% +sure there are all these other +conditions. And sometimes people think + + align:start position:0% +conditions. And sometimes people think + + + align:start position:0% +conditions. And sometimes people think +it's easier to just pay people more and + + align:start position:0% +it's easier to just pay people more and + + + align:start position:0% +it's easier to just pay people more and +that doing this is harder but it pays + + align:start position:0% +that doing this is harder but it pays + + + align:start position:0% +that doing this is harder but it pays +off much + + align:start position:0% + + + + align:start position:0% + +higher. All right. So back to our our + + align:start position:0% +higher. All right. So back to our our + + + align:start position:0% +higher. All right. So back to our our +worker theories which comes into play a + + align:start position:0% +worker theories which comes into play a + + + align:start position:0% +worker theories which comes into play a +bit with your comment as well. So we + + align:start position:0% +bit with your comment as well. So we + + + align:start position:0% +bit with your comment as well. So we +started out early management theory with + + align:start position:0% +started out early management theory with + + + align:start position:0% +started out early management theory with +theoryax. So then to counter that after + + align:start position:0% +theoryax. So then to counter that after + + + align:start position:0% +theoryax. So then to counter that after +a little while of experimenting with it + + align:start position:0% +a little while of experimenting with it + + + align:start position:0% +a little while of experimenting with it +they really came upon 3y which is + + align:start position:0% +they really came upon 3y which is + + + align:start position:0% +they really came upon 3y which is +reflected in Elton Mayo's work where + + align:start position:0% +reflected in Elton Mayo's work where + + + align:start position:0% +reflected in Elton Mayo's work where +they said no actually workers you know + + align:start position:0% +they said no actually workers you know + + + align:start position:0% +they said no actually workers you know +if you just make them happy then they're + + align:start position:0% +if you just make them happy then they're + + + align:start position:0% +if you just make them happy then they're +going to be really productive. So this + + align:start position:0% +going to be really productive. So this + + + align:start position:0% +going to be really productive. So this +theory out of that was born the whole + + align:start position:0% +theory out of that was born the whole + + + align:start position:0% +theory out of that was born the whole +focus on human resources and human + + align:start position:0% +focus on human resources and human + + + align:start position:0% +focus on human resources and human +relations in the workplace and trying to + + align:start position:0% +relations in the workplace and trying to + + + align:start position:0% +relations in the workplace and trying to +create a happy workplace. So that was + + align:start position:0% +create a happy workplace. So that was + + + align:start position:0% +create a happy workplace. So that was +about 1920 and then around the turn of + + align:start position:0% +about 1920 and then around the turn of + + + align:start position:0% +about 1920 and then around the turn of +this century uh we have expressed by + + align:start position:0% +this century uh we have expressed by + + + align:start position:0% +this century uh we have expressed by +Dick Klene at John Deere his thought is + + align:start position:0% +Dick Klene at John Deere his thought is + + + align:start position:0% +Dick Klene at John Deere his thought is +that a productive worker is a happy + + align:start position:0% +that a productive worker is a happy + + + align:start position:0% +that a productive worker is a happy +worker. So we've got these three + + align:start position:0% +worker. So we've got these three + + + align:start position:0% +worker. So we've got these three +different competing theories. Of those + + align:start position:0% +different competing theories. Of those + + + align:start position:0% +different competing theories. Of those +three which do you think most aligns + + align:start position:0% +three which do you think most aligns + + + align:start position:0% +three which do you think most aligns +with a lean way of thinking? How many + + align:start position:0% +with a lean way of thinking? How many + + + align:start position:0% +with a lean way of thinking? How many +people think it's the first theory? + + align:start position:0% +people think it's the first theory? + + + align:start position:0% +people think it's the first theory? +theory X. How many people think it's the + + align:start position:0% +theory X. How many people think it's the + + + align:start position:0% +theory X. How many people think it's the +middle one? How many people think it's + + align:start position:0% +middle one? How many people think it's + + + align:start position:0% +middle one? How many people think it's +the last one? Very good. That's the way + + align:start position:0% +the last one? Very good. That's the way + + + align:start position:0% +the last one? Very good. That's the way +we we think too. We think that that uh + + align:start position:0% +we we think too. We think that that uh + + + align:start position:0% +we we think too. We think that that uh +Dick Klein's thought about a productive + + align:start position:0% +Dick Klein's thought about a productive + + + align:start position:0% +Dick Klein's thought about a productive +worker being happy worker really is the + + align:start position:0% +worker being happy worker really is the + + + align:start position:0% +worker being happy worker really is the +way that things + + align:start position:0% +way that things + + + align:start position:0% +way that things +are. And to try to illustrate some of + + align:start position:0% +are. And to try to illustrate some of + + + align:start position:0% +are. And to try to illustrate some of +the links between uh employee + + align:start position:0% +the links between uh employee + + + align:start position:0% +the links between uh employee +productivity and company performance, we + + align:start position:0% +productivity and company performance, we + + + align:start position:0% +productivity and company performance, we +want to take a case study here on + + align:start position:0% +want to take a case study here on + + + align:start position:0% +want to take a case study here on +Southwest Airlines. And just to give you + + align:start position:0% +Southwest Airlines. And just to give you + + + align:start position:0% +Southwest Airlines. And just to give you +some brief background on Southwest as a + + align:start position:0% +some brief background on Southwest as a + + + align:start position:0% +some brief background on Southwest as a +company to put them in context, um they + + align:start position:0% +company to put them in context, um they + + + align:start position:0% +company to put them in context, um they +are one of the best well they really are + + align:start position:0% +are one of the best well they really are + + + align:start position:0% +are one of the best well they really are +the best performance of the major US + + align:start position:0% +the best performance of the major US + + + align:start position:0% +the best performance of the major US +domestic airlines and you can see their + + align:start position:0% +domestic airlines and you can see their + + + align:start position:0% +domestic airlines and you can see their +uh profitability metric here uh on the + + align:start position:0% +uh profitability metric here uh on the + + + align:start position:0% +uh profitability metric here uh on the +chart. Southwest is in blue which is far + + align:start position:0% +chart. Southwest is in blue which is far + + + align:start position:0% +chart. Southwest is in blue which is far +above the red which is an aggregate of + + align:start position:0% +above the red which is an aggregate of + + + align:start position:0% +above the red which is an aggregate of +all the major domestic airlines and + + align:start position:0% +all the major domestic airlines and + + + align:start position:0% +all the major domestic airlines and +their profitability over the past couple + + align:start position:0% +their profitability over the past couple + + + align:start position:0% +their profitability over the past couple +of decades. And in addition, Southwest + + align:start position:0% +of decades. And in addition, Southwest + + + align:start position:0% +of decades. And in addition, Southwest +has made an operating profit every year + + align:start position:0% +has made an operating profit every year + + + align:start position:0% +has made an operating profit every year +for over 30 years. Now, this is a big + + align:start position:0% +for over 30 years. Now, this is a big + + + align:start position:0% +for over 30 years. Now, this is a big +achievement for an airline. Um, no one + + align:start position:0% +achievement for an airline. Um, no one + + + align:start position:0% +achievement for an airline. Um, no one +else has this record and many, many + + align:start position:0% +else has this record and many, many + + + align:start position:0% +else has this record and many, many +times, many years, many airlines are at + + align:start position:0% +times, many years, many airlines are at + + + align:start position:0% +times, many years, many airlines are at +a net loss. A few more items about + + align:start position:0% +a net loss. A few more items about + + + align:start position:0% +a net loss. A few more items about +Southwest. You know, they are one of the + + align:start position:0% +Southwest. You know, they are one of the + + + align:start position:0% +Southwest. You know, they are one of the +safest airlines around. Uh, they did + + align:start position:0% +safest airlines around. Uh, they did + + + align:start position:0% +safest airlines around. Uh, they did +have a very homogeneous fleet until they + + align:start position:0% +have a very homogeneous fleet until they + + + align:start position:0% +have a very homogeneous fleet until they +merged with Airran, and that simplifies + + align:start position:0% +merged with Airran, and that simplifies + + + align:start position:0% +merged with Airran, and that simplifies +some of their training and maintenance + + align:start position:0% +some of their training and maintenance + + + align:start position:0% +some of their training and maintenance +and logistics items. They had never laid + + align:start position:0% +and logistics items. They had never laid + + + align:start position:0% +and logistics items. They had never laid +off any employees even after the events + + align:start position:0% +off any employees even after the events + + + align:start position:0% +off any employees even after the events +of 911. + + align:start position:0% +of 911. + + + align:start position:0% +of 911. +They are the most highly unionized US + + align:start position:0% +They are the most highly unionized US + + + align:start position:0% +They are the most highly unionized US +airline. Even though there's some + + align:start position:0% +airline. Even though there's some + + + align:start position:0% +airline. Even though there's some +perceptions out there that there's no + + align:start position:0% +perceptions out there that there's no + + + align:start position:0% +perceptions out there that there's no +unions on Southwest because after all + + align:start position:0% +unions on Southwest because after all + + + align:start position:0% +unions on Southwest because after all +those Southwest employees are so happy + + align:start position:0% +those Southwest employees are so happy + + + align:start position:0% +those Southwest employees are so happy +and the company's doing so good, surely + + align:start position:0% +and the company's doing so good, surely + + + align:start position:0% +and the company's doing so good, surely +they don't have unions. That's not true + + align:start position:0% +they don't have unions. That's not true + + + align:start position:0% +they don't have unions. That's not true +at all. They're highly + + align:start position:0% +at all. They're highly + + + align:start position:0% +at all. They're highly +unionized. They have a pointto-oint + + align:start position:0% +unionized. They have a pointto-oint + + + align:start position:0% +unionized. They have a pointto-oint +which is different than a hub and spoke + + align:start position:0% +which is different than a hub and spoke + + + align:start position:0% +which is different than a hub and spoke +route structure. And many of the other + + align:start position:0% +route structure. And many of the other + + + align:start position:0% +route structure. And many of the other +airlines in the US operate on a hub and + + align:start position:0% +airlines in the US operate on a hub and + + + align:start position:0% +airlines in the US operate on a hub and +spoke root structure. You can think of + + align:start position:0% +spoke root structure. You can think of + + + align:start position:0% +spoke root structure. You can think of +it a little bit more like uh batch and Q + + align:start position:0% +it a little bit more like uh batch and Q + + + align:start position:0% +it a little bit more like uh batch and Q +and continuous flow. little bit + + align:start position:0% +and continuous flow. little bit + + + align:start position:0% +and continuous flow. little bit +different. They consistently offer some + + align:start position:0% +different. They consistently offer some + + + align:start position:0% +different. They consistently offer some +of the lowest fairs that are around. + + align:start position:0% +of the lowest fairs that are around. + + + align:start position:0% +of the lowest fairs that are around. +They're liked by investors and employees + + align:start position:0% +They're liked by investors and employees + + + align:start position:0% +They're liked by investors and employees +and customers, I should say. And so, you + + align:start position:0% +and customers, I should say. And so, you + + + align:start position:0% +and customers, I should say. And so, you +might ask, what makes Southwest so + + align:start position:0% +might ask, what makes Southwest so + + + align:start position:0% +might ask, what makes Southwest so +successful in its business? And + + align:start position:0% +successful in its business? And + + + align:start position:0% +successful in its business? And +Professor Jodie Hofferell in her book, + + align:start position:0% +Professor Jodie Hofferell in her book, + + + align:start position:0% +Professor Jodie Hofferell in her book, +The Southwest Airlines Way, which + + align:start position:0% +The Southwest Airlines Way, which + + + align:start position:0% +The Southwest Airlines Way, which +resulted out of her PhD work here at + + align:start position:0% +resulted out of her PhD work here at + + + align:start position:0% +resulted out of her PhD work here at +MIT, she argues it's because of + + align:start position:0% +MIT, she argues it's because of + + + align:start position:0% +MIT, she argues it's because of +Southwest's organizational competency + + align:start position:0% +Southwest's organizational competency + + + align:start position:0% +Southwest's organizational competency +and characterized by shared goals, + + align:start position:0% +and characterized by shared goals, + + + align:start position:0% +and characterized by shared goals, +shared knowledge, and mutual respect. + + align:start position:0% +shared knowledge, and mutual respect. + + + align:start position:0% +shared knowledge, and mutual respect. +And she calls these three things + + align:start position:0% +And she calls these three things + + + align:start position:0% +And she calls these three things +relational coordination. + + align:start position:0% +relational coordination. + + + align:start position:0% +relational coordination. +And she says shared goals helps the + + align:start position:0% +And she says shared goals helps the + + + align:start position:0% +And she says shared goals helps the +employees to align and prioritize the + + align:start position:0% +employees to align and prioritize the + + + align:start position:0% +employees to align and prioritize the +organization's success over doing their + + align:start position:0% +organization's success over doing their + + + align:start position:0% +organization's success over doing their +job or succeeding at just their job. The + + align:start position:0% +job or succeeding at just their job. The + + + align:start position:0% +job or succeeding at just their job. The +second item of relational coordination + + align:start position:0% +second item of relational coordination + + + align:start position:0% +second item of relational coordination +is this element of shared knowledge. So + + align:start position:0% +is this element of shared knowledge. So + + + align:start position:0% +is this element of shared knowledge. So +if everybody has the same kind of + + align:start position:0% +if everybody has the same kind of + + + align:start position:0% +if everybody has the same kind of +knowledge, then you have visibility of + + align:start position:0% +knowledge, then you have visibility of + + + align:start position:0% +knowledge, then you have visibility of +the overall work process and not just + + align:start position:0% +the overall work process and not just + + + align:start position:0% +the overall work process and not just +your little part on it. So you can help + + align:start position:0% +your little part on it. So you can help + + + align:start position:0% +your little part on it. So you can help +see the linkages between what you're + + align:start position:0% +see the linkages between what you're + + + align:start position:0% +see the linkages between what you're +doing and what someone else is doing and + + align:start position:0% +doing and what someone else is doing and + + + align:start position:0% +doing and what someone else is doing and +be able to create overall a more + + align:start position:0% +be able to create overall a more + + + align:start position:0% +be able to create overall a more +efficient and effective system. + + align:start position:0% +efficient and effective system. + + + align:start position:0% +efficient and effective system. +And lastly, this third element of + + align:start position:0% +And lastly, this third element of + + + align:start position:0% +And lastly, this third element of +relational coordination is mutual + + align:start position:0% +relational coordination is mutual + + + align:start position:0% +relational coordination is mutual +respect. And that helps to reduce some + + align:start position:0% +respect. And that helps to reduce some + + + align:start position:0% +respect. And that helps to reduce some +of the barriers between employees, + + align:start position:0% +of the barriers between employees, + + + align:start position:0% +of the barriers between employees, +employee groups, and helps them + + align:start position:0% +employee groups, and helps them + + + align:start position:0% +employee groups, and helps them +cooperate more effectively to get the + + align:start position:0% +cooperate more effectively to get the + + + align:start position:0% +cooperate more effectively to get the +job done. And all these three elements + + align:start position:0% +job done. And all these three elements + + + align:start position:0% +job done. And all these three elements +of relational coordination really + + align:start position:0% +of relational coordination really + + + align:start position:0% +of relational coordination really +couldn't happen if it weren't for the + + align:start position:0% +couldn't happen if it weren't for the + + + align:start position:0% +couldn't happen if it weren't for the +underlying practice of effective + + align:start position:0% +underlying practice of effective + + + align:start position:0% +underlying practice of effective +communication. + + align:start position:0% +communication. + + + align:start position:0% +communication. +This effective communication is + + align:start position:0% +This effective communication is + + + align:start position:0% +This effective communication is +particularly one where people are + + align:start position:0% +particularly one where people are + + + align:start position:0% +particularly one where people are +communicating about the problem itself + + align:start position:0% +communicating about the problem itself + + + align:start position:0% +communicating about the problem itself +and not really worried about assigning + + align:start position:0% +and not really worried about assigning + + + align:start position:0% +and not really worried about assigning +blame when something bad goes wrong. So + + align:start position:0% +blame when something bad goes wrong. So + + + align:start position:0% +blame when something bad goes wrong. So +if you think in your own work uh + + align:start position:0% +if you think in your own work uh + + + align:start position:0% +if you think in your own work uh +environment, you may be able to think + + align:start position:0% +environment, you may be able to think + + + align:start position:0% +environment, you may be able to think +about some people that you interact with + + align:start position:0% +about some people that you interact with + + + align:start position:0% +about some people that you interact with +perhaps who are very good at thinking + + align:start position:0% +perhaps who are very good at thinking + + + align:start position:0% +perhaps who are very good at thinking +just about the problem and trying to + + align:start position:0% +just about the problem and trying to + + + align:start position:0% +just about the problem and trying to +separate the people out from it. And + + align:start position:0% +separate the people out from it. And + + + align:start position:0% +separate the people out from it. And +then you may also know some people who + + align:start position:0% +then you may also know some people who + + + align:start position:0% +then you may also know some people who +tend to focus more on on blaming some + + align:start position:0% +tend to focus more on on blaming some + + + align:start position:0% +tend to focus more on on blaming some +somebody when something goes wrong and + + align:start position:0% +somebody when something goes wrong and + + + align:start position:0% +somebody when something goes wrong and +not really focusing on what went wrong + + align:start position:0% +not really focusing on what went wrong + + + align:start position:0% +not really focusing on what went wrong +and how we can fix it, but really who + + align:start position:0% +and how we can fix it, but really who + + + align:start position:0% +and how we can fix it, but really who +might be responsible for it. That's not + + align:start position:0% +might be responsible for it. That's not + + + align:start position:0% +might be responsible for it. That's not +as effective communication uh as we + + align:start position:0% +as effective communication uh as we + + + align:start position:0% +as effective communication uh as we +could be. Other elements of what makes + + align:start position:0% +could be. Other elements of what makes + + + align:start position:0% +could be. Other elements of what makes +communication effective frequent, + + align:start position:0% +communication effective frequent, + + + align:start position:0% +communication effective frequent, +timely, open, honest, very very simple + + align:start position:0% +timely, open, honest, very very simple + + + align:start position:0% +timely, open, honest, very very simple +description, not as easy to to achieve, + + align:start position:0% +description, not as easy to to achieve, + + + align:start position:0% +description, not as easy to to achieve, +but very simple to try to understand. + + align:start position:0% + + + + align:start position:0% + +Now when an organization has very high + + align:start position:0% +Now when an organization has very high + + + align:start position:0% +Now when an organization has very high +relational coordination, Professor + + align:start position:0% +relational coordination, Professor + + + align:start position:0% +relational coordination, Professor +Hoffer Gatell found that high uh levels + + align:start position:0% +Hoffer Gatell found that high uh levels + + + align:start position:0% +Hoffer Gatell found that high uh levels +of relational coordination do correlate + + align:start position:0% +of relational coordination do correlate + + + align:start position:0% +of relational coordination do correlate +with performance for the airlines that + + align:start position:0% +with performance for the airlines that + + + align:start position:0% +with performance for the airlines that +she studied. And this graph shows you uh + + align:start position:0% +she studied. And this graph shows you uh + + + align:start position:0% +she studied. And this graph shows you uh +some composite measure of airline + + align:start position:0% +some composite measure of airline + + + align:start position:0% +some composite measure of airline +performance on the X. She took many + + align:start position:0% +performance on the X. She took many + + + align:start position:0% +performance on the X. She took many +different things into account including + + align:start position:0% +different things into account including + + + align:start position:0% +different things into account including +on time departures, fewer lost bags, + + align:start position:0% +on time departures, fewer lost bags, + + + align:start position:0% +on time departures, fewer lost bags, +things like that. And then she has + + align:start position:0% +things like that. And then she has + + + align:start position:0% +things like that. And then she has +relational coordination as measured by + + align:start position:0% +relational coordination as measured by + + + align:start position:0% +relational coordination as measured by +another amalgam of a bunch of different + + align:start position:0% +another amalgam of a bunch of different + + + align:start position:0% +another amalgam of a bunch of different +measures that she created in her + + align:start position:0% +measures that she created in her + + + align:start position:0% +measures that she created in her +research. And each of these dots is a + + align:start position:0% +research. And each of these dots is a + + + align:start position:0% +research. And each of these dots is a +number of different airlines in + + align:start position:0% +number of different airlines in + + + align:start position:0% +number of different airlines in +different locations around the country. + + align:start position:0% +different locations around the country. + + + align:start position:0% +different locations around the country. +There are two here shown from Southwest + + align:start position:0% +There are two here shown from Southwest + + + align:start position:0% +There are two here shown from Southwest +and the others are for three other + + align:start position:0% +and the others are for three other + + + align:start position:0% +and the others are for three other +different airlines. But you see the + + align:start position:0% +different airlines. But you see the + + + align:start position:0% +different airlines. But you see the +general trend as we increase relational + + align:start position:0% +general trend as we increase relational + + + align:start position:0% +general trend as we increase relational +coordination. We tend to see the + + align:start position:0% +coordination. We tend to see the + + + align:start position:0% +coordination. We tend to see the +aggregate performance increase. So we've + + align:start position:0% +aggregate performance increase. So we've + + + align:start position:0% +aggregate performance increase. So we've +seen how relational coordination works + + align:start position:0% +seen how relational coordination works + + + align:start position:0% +seen how relational coordination works +and increases performance in airlines. + + align:start position:0% +and increases performance in airlines. + + + align:start position:0% +and increases performance in airlines. +But you can apply this concept well + + align:start position:0% +But you can apply this concept well + + + align:start position:0% +But you can apply this concept well +beyond the domain of of airlines. And it + + align:start position:0% +beyond the domain of of airlines. And it + + + align:start position:0% +beyond the domain of of airlines. And it +really applies, she says, in any setting + + align:start position:0% +really applies, she says, in any setting + + + align:start position:0% +really applies, she says, in any setting +where there is task interdependence. So + + align:start position:0% +where there is task interdependence. So + + + align:start position:0% +where there is task interdependence. So +there may be handoffs that take place + + align:start position:0% +there may be handoffs that take place + + + align:start position:0% +there may be handoffs that take place +requiring feedback and iterations or + + align:start position:0% +requiring feedback and iterations or + + + align:start position:0% +requiring feedback and iterations or +where there's uncertainty and there has + + align:start position:0% +where there's uncertainty and there has + + + align:start position:0% +where there's uncertainty and there has +to be continual adjustment of plans and + + align:start position:0% +to be continual adjustment of plans and + + + align:start position:0% +to be continual adjustment of plans and +updating or where there are time + + align:start position:0% +updating or where there are time + + + align:start position:0% +updating or where there are time +constraints and so you can't just wait + + align:start position:0% +constraints and so you can't just wait + + + align:start position:0% +constraints and so you can't just wait +while you try to fix a problem. Now, I + + align:start position:0% +while you try to fix a problem. Now, I + + + align:start position:0% +while you try to fix a problem. Now, I +want you to think about what you think + + align:start position:0% +want you to think about what you think + + + align:start position:0% +want you to think about what you think +of when you your careers are going to + + align:start position:0% +of when you your careers are going to + + + align:start position:0% +of when you your careers are going to +unfold and the kinds of industries you + + align:start position:0% +unfold and the kinds of industries you + + + align:start position:0% +unfold and the kinds of industries you +all anticipate being in. And tell me if + + align:start position:0% +all anticipate being in. And tell me if + + + align:start position:0% +all anticipate being in. And tell me if +you think you are ever going to spend + + align:start position:0% +you think you are ever going to spend + + + align:start position:0% +you think you are ever going to spend +your time in an organization that does + + align:start position:0% +your time in an organization that does + + + align:start position:0% +your time in an organization that does +not have one or more of these elements + + align:start position:0% +not have one or more of these elements + + + align:start position:0% +not have one or more of these elements +in it. I suspect not. I suspect you're + + align:start position:0% +in it. I suspect not. I suspect you're + + + align:start position:0% +in it. I suspect not. I suspect you're +all going to find yourself in + + align:start position:0% +all going to find yourself in + + + align:start position:0% +all going to find yourself in +organizations where these are critical + + align:start position:0% +organizations where these are critical + + + align:start position:0% +organizations where these are critical +elements. And so this notion of + + align:start position:0% +elements. And so this notion of + + + align:start position:0% +elements. And so this notion of +relational coordination is one that + + align:start position:0% +relational coordination is one that + + + align:start position:0% +relational coordination is one that +would translate equally well into any + + align:start position:0% +would translate equally well into any + + + align:start position:0% +would translate equally well into any +environment where these items exist. So + + align:start position:0% +environment where these items exist. So + + + align:start position:0% +environment where these items exist. So +one example is healthcare obviously. Uh + + align:start position:0% +one example is healthcare obviously. Uh + + + align:start position:0% +one example is healthcare obviously. Uh +another one that we talk about is + + align:start position:0% +another one that we talk about is + + + align:start position:0% +another one that we talk about is +product + + align:start position:0% +product + + + align:start position:0% +product +development. Product development is done + + align:start position:0% +development. Product development is done + + + align:start position:0% +development. Product development is done +by different kinds of uh engineers + + align:start position:0% +by different kinds of uh engineers + + + align:start position:0% +by different kinds of uh engineers +typically. Lots of handoffs, lots of + + align:start position:0% +typically. Lots of handoffs, lots of + + + align:start position:0% +typically. Lots of handoffs, lots of +uncertainties, lots of time constraints. + + align:start position:0% +uncertainties, lots of time constraints. + + + align:start position:0% +uncertainties, lots of time constraints. +And I'm sure that you can think of many + + align:start position:0% +And I'm sure that you can think of many + + + align:start position:0% +And I'm sure that you can think of many +other situations. Uh any come to + + align:start position:0% + + + + align:start position:0% + +mind? Yes, Fris. government programs + + align:start position:0% +mind? Yes, Fris. government programs + + + align:start position:0% +mind? Yes, Fris. government programs +where the government invests in industry + + align:start position:0% +where the government invests in industry + + + align:start position:0% +where the government invests in industry +to develop something and all of a sudden + + align:start position:0% +to develop something and all of a sudden + + + align:start position:0% +to develop something and all of a sudden +you have standardization everybody. + + align:start position:0% +you have standardization everybody. + + + align:start position:0% +you have standardization everybody. +Excellent. Yeah, great example. There's + + align:start position:0% +Excellent. Yeah, great example. There's + + + align:start position:0% +Excellent. Yeah, great example. There's +lots of different products being + + align:start position:0% +lots of different products being + + + align:start position:0% +lots of different products being +developed under those circumstances. All + + align:start position:0% +developed under those circumstances. All + + + align:start position:0% +developed under those circumstances. All +right. Well, let's look at one + + align:start position:0% +right. Well, let's look at one + + + align:start position:0% +right. Well, let's look at one +particular example translating + + align:start position:0% +particular example translating + + + align:start position:0% +particular example translating +relational coordination into another + + align:start position:0% +relational coordination into another + + + align:start position:0% +relational coordination into another +particular + + align:start position:0% +particular + + + align:start position:0% +particular +environment. Professor Hofferatel then + + align:start position:0% +environment. Professor Hofferatel then + + + align:start position:0% +environment. Professor Hofferatel then +went and said, "Well, let me see if this + + align:start position:0% +went and said, "Well, let me see if this + + + align:start position:0% +went and said, "Well, let me see if this +really does translate into other + + align:start position:0% +really does translate into other + + + align:start position:0% +really does translate into other +environments." And so she went and + + align:start position:0% +environments." And so she went and + + + align:start position:0% +environments." And so she went and +studied healthcare environments to see + + align:start position:0% +studied healthcare environments to see + + + align:start position:0% +studied healthcare environments to see +if these same elements of relational + + align:start position:0% +if these same elements of relational + + + align:start position:0% +if these same elements of relational +coordination correlated with elements of + + align:start position:0% +coordination correlated with elements of + + + align:start position:0% +coordination correlated with elements of +performance. And just as you saw with + + align:start position:0% +performance. And just as you saw with + + + align:start position:0% +performance. And just as you saw with +the airline chart, the same kind of + + align:start position:0% +the airline chart, the same kind of + + + align:start position:0% +the airline chart, the same kind of +pattern starts to appear in the + + align:start position:0% +pattern starts to appear in the + + + align:start position:0% +pattern starts to appear in the +healthcare industry here. So it's not + + align:start position:0% +healthcare industry here. So it's not + + + align:start position:0% +healthcare industry here. So it's not +only do we suspect that these this + + align:start position:0% +only do we suspect that these this + + + align:start position:0% +only do we suspect that these this +notion of relational coordination + + align:start position:0% +notion of relational coordination + + + align:start position:0% +notion of relational coordination +translates. We actually have yet another + + align:start position:0% +translates. We actually have yet another + + + align:start position:0% +translates. We actually have yet another +study in another domain which does show + + align:start position:0% +study in another domain which does show + + + align:start position:0% +study in another domain which does show +that we see increased levels of + + align:start position:0% +that we see increased levels of + + + align:start position:0% +that we see increased levels of +performance with increased instances of + + align:start position:0% +performance with increased instances of + + + align:start position:0% +performance with increased instances of +relational coordination. + + align:start position:0% +relational coordination. + + + align:start position:0% +relational coordination. +So in order to achieve relational + + align:start position:0% +So in order to achieve relational + + + align:start position:0% +So in order to achieve relational +coordination, Professor Hoffer Gretell + + align:start position:0% +coordination, Professor Hoffer Gretell + + + align:start position:0% +coordination, Professor Hoffer Gretell +looked at various practices that were in + + align:start position:0% +looked at various practices that were in + + + align:start position:0% +looked at various practices that were in +place at Southwest Airlines. And she + + align:start position:0% +place at Southwest Airlines. And she + + + align:start position:0% +place at Southwest Airlines. And she +identified and codified 10 different + + align:start position:0% +identified and codified 10 different + + + align:start position:0% +identified and codified 10 different +ones that underlied being able to create + + align:start position:0% +ones that underlied being able to create + + + align:start position:0% +ones that underlied being able to create +a high an environment where there was + + align:start position:0% +a high an environment where there was + + + align:start position:0% +a high an environment where there was +good relational coordination, which then + + align:start position:0% +good relational coordination, which then + + + align:start position:0% +good relational coordination, which then +led to having very good performance + + align:start position:0% +led to having very good performance + + + align:start position:0% +led to having very good performance +outcomes. And you can read them here. + + align:start position:0% +outcomes. And you can read them here. + + + align:start position:0% +outcomes. And you can read them here. +They're in your notes. Lead with + + align:start position:0% +They're in your notes. Lead with + + + align:start position:0% +They're in your notes. Lead with +credibility and caring. hire and + + align:start position:0% +credibility and caring. hire and + + + align:start position:0% +credibility and caring. hire and +training for relational competence and + + align:start position:0% +training for relational competence and + + + align:start position:0% +training for relational competence and +not just for other factors. Bridging the + + align:start position:0% +not just for other factors. Bridging the + + + align:start position:0% +not just for other factors. Bridging the +work family divide, recognizing that + + align:start position:0% +work family divide, recognizing that + + + align:start position:0% +work family divide, recognizing that +that's something important for + + align:start position:0% +that's something important for + + + align:start position:0% +that's something important for +employees. Measuring performance + + align:start position:0% +employees. Measuring performance + + + align:start position:0% +employees. Measuring performance +broadly, making unions your unions your + + align:start position:0% +broadly, making unions your unions your + + + align:start position:0% +broadly, making unions your unions your +partners. Building relationships with + + align:start position:0% +partners. Building relationships with + + + align:start position:0% +partners. Building relationships with +your suppliers. Keeping jobs flexible at + + align:start position:0% +your suppliers. Keeping jobs flexible at + + + align:start position:0% +your suppliers. Keeping jobs flexible at +the + + align:start position:0% +the + + + align:start position:0% +the +boundaries. In addition, creating + + align:start position:0% +boundaries. In addition, creating + + + align:start position:0% +boundaries. In addition, creating +boundary spanners who are crossing + + align:start position:0% +boundary spanners who are crossing + + + align:start position:0% +boundary spanners who are crossing +different parts of the organization. + + align:start position:0% +different parts of the organization. + + + align:start position:0% +different parts of the organization. +using conflicts to build relationships + + align:start position:0% +using conflicts to build relationships + + + align:start position:0% +using conflicts to build relationships +and to learn and grow and investing in + + align:start position:0% +and to learn and grow and investing in + + + align:start position:0% +and to learn and grow and investing in +the frontline leadership. That's not the + + align:start position:0% +the frontline leadership. That's not the + + + align:start position:0% +the frontline leadership. That's not the +leadership at the the seauite of the + + align:start position:0% +leadership at the the seauite of the + + + align:start position:0% +leadership at the the seauite of the +organization, but those who are right + + align:start position:0% +organization, but those who are right + + + align:start position:0% +organization, but those who are right +right on this the front lines of for + + align:start position:0% +right on this the front lines of for + + + align:start position:0% +right on this the front lines of for +Southwest maintaining airplanes, manning + + align:start position:0% +Southwest maintaining airplanes, manning + + + align:start position:0% +Southwest maintaining airplanes, manning +the gates and interacting with customers + + align:start position:0% +the gates and interacting with customers + + + align:start position:0% +the gates and interacting with customers +and so on. And then the outcomes that + + align:start position:0% +and so on. And then the outcomes that + + + align:start position:0% +and so on. And then the outcomes that +Professor Hoffer Gatell found coord + + align:start position:0% +Professor Hoffer Gatell found coord + + + align:start position:0% +Professor Hoffer Gatell found coord +relational coordination leads to is + + align:start position:0% +relational coordination leads to is + + + align:start position:0% +relational coordination leads to is +higher reliability. This was judged for + + align:start position:0% +higher reliability. This was judged for + + + align:start position:0% +higher reliability. This was judged for +airlines by better on-time performance + + align:start position:0% +airlines by better on-time performance + + + align:start position:0% +airlines by better on-time performance +and fewer loss bags as well as greater + + align:start position:0% +and fewer loss bags as well as greater + + + align:start position:0% +and fewer loss bags as well as greater +customer + + align:start position:0% +customer + + + align:start position:0% +customer +satisfaction and shorter turnaround time + + align:start position:0% +satisfaction and shorter turnaround time + + + align:start position:0% +satisfaction and shorter turnaround time +which is really important in an industry + + align:start position:0% +which is really important in an industry + + + align:start position:0% +which is really important in an industry +like air transportation where you have + + align:start position:0% +like air transportation where you have + + + align:start position:0% +like air transportation where you have +very expensive capital assets and the + + align:start position:0% +very expensive capital assets and the + + + align:start position:0% +very expensive capital assets and the +more time they're used the greater + + align:start position:0% +more time they're used the greater + + + align:start position:0% +more time they're used the greater +return you're getting on them and the + + align:start position:0% +return you're getting on them and the + + + align:start position:0% +return you're getting on them and the +more time they sit idle at the gate + + align:start position:0% +more time they sit idle at the gate + + + align:start position:0% +more time they sit idle at the gate +while they're waiting to be cleaned and + + align:start position:0% +while they're waiting to be cleaned and + + + align:start position:0% +while they're waiting to be cleaned and +you're offloading and unloading + + align:start position:0% +you're offloading and unloading + + + align:start position:0% +you're offloading and unloading +passengers. It's not generating any + + align:start position:0% +passengers. It's not generating any + + + align:start position:0% +passengers. It's not generating any +revenue for the organization. + + align:start position:0% +revenue for the organization. + + + align:start position:0% +revenue for the organization. +to turn to an example from health care. + + align:start position:0% +to turn to an example from health care. + + + align:start position:0% +to turn to an example from health care. +This shows you uh reflects back on that + + align:start position:0% +This shows you uh reflects back on that + + + align:start position:0% +This shows you uh reflects back on that +chart that I showed you two slides ago + + align:start position:0% +chart that I showed you two slides ago + + + align:start position:0% +chart that I showed you two slides ago +with the coordination between relational + + align:start position:0% +with the coordination between relational + + + align:start position:0% +with the coordination between relational +coordination and performance and + + align:start position:0% +coordination and performance and + + + align:start position:0% +coordination and performance and +hypothesizes that if we were able to + + align:start position:0% +hypothesizes that if we were able to + + + align:start position:0% +hypothesizes that if we were able to +make a 100% improvement in various work + + align:start position:0% +make a 100% improvement in various work + + + align:start position:0% +make a 100% improvement in various work +practices that underly relational + + align:start position:0% +practices that underly relational + + + align:start position:0% +practices that underly relational +coordination in hospitals. So if we were + + align:start position:0% +coordination in hospitals. So if we were + + + align:start position:0% +coordination in hospitals. So if we were +to double our measure of relational + + align:start position:0% +to double our measure of relational + + + align:start position:0% +to double our measure of relational +coordination + + align:start position:0% +coordination + + + align:start position:0% +coordination +uh our our improvement in these work + + align:start position:0% +uh our our improvement in these work + + + align:start position:0% +uh our our improvement in these work +practices, we would have some kind of + + align:start position:0% +practices, we would have some kind of + + + align:start position:0% +practices, we would have some kind of +almost 50% increase in relational + + align:start position:0% +almost 50% increase in relational + + + align:start position:0% +almost 50% increase in relational +coordination which would then lead to + + align:start position:0% +coordination which would then lead to + + + align:start position:0% +coordination which would then lead to +significant increases in patient + + align:start position:0% +significant increases in patient + + + align:start position:0% +significant increases in patient +satisfaction and decreases in the length + + align:start position:0% +satisfaction and decreases in the length + + + align:start position:0% +satisfaction and decreases in the length +of stay which are all very good things + + align:start position:0% +of stay which are all very good things + + + align:start position:0% +of stay which are all very good things +because these are what uh hospitals and + + align:start position:0% +because these are what uh hospitals and + + + align:start position:0% +because these are what uh hospitals and +healthcare settings tend to measure, + + align:start position:0% +healthcare settings tend to measure, + + + align:start position:0% +healthcare settings tend to measure, +right? Healthcare folks, you're probably + + align:start position:0% +right? Healthcare folks, you're probably + + + align:start position:0% +right? Healthcare folks, you're probably +measured on those. You know, it's also + + align:start position:0% +measured on those. You know, it's also + + + align:start position:0% +measured on those. You know, it's also +interesting to me to note that well, + + align:start position:0% +interesting to me to note that well, + + + align:start position:0% +interesting to me to note that well, +just because we increase our relational + + align:start position:0% +just because we increase our relational + + + align:start position:0% +just because we increase our relational +coordination doesn't necessarily going + + align:start position:0% +coordination doesn't necessarily going + + + align:start position:0% +coordination doesn't necessarily going +to, you know, increase people's freedom + + align:start position:0% +to, you know, increase people's freedom + + + align:start position:0% +to, you know, increase people's freedom +from pain or their mobility. This is a + + align:start position:0% +from pain or their mobility. This is a + + + align:start position:0% +from pain or their mobility. This is a +joint unit that was studied in this + + align:start position:0% +joint unit that was studied in this + + + align:start position:0% +joint unit that was studied in this +particular focus area. Um, because these + + align:start position:0% +particular focus area. Um, because these + + + align:start position:0% +particular focus area. Um, because these +are really more related to the types of + + align:start position:0% +are really more related to the types of + + + align:start position:0% +are really more related to the types of +treatment that you're giving, but these + + align:start position:0% +treatment that you're giving, but these + + + align:start position:0% +treatment that you're giving, but these +are are elements that are really being + + align:start position:0% +are are elements that are really being + + + align:start position:0% +are are elements that are really being +measured in the hospital setting. + + align:start position:0% +measured in the hospital setting. + + + align:start position:0% +measured in the hospital setting. +So just to conclude our discussion about + + align:start position:0% +So just to conclude our discussion about + + + align:start position:0% +So just to conclude our discussion about +Southwest and the power of workforce + + align:start position:0% +Southwest and the power of workforce + + + align:start position:0% +Southwest and the power of workforce +productivity. Some of the benefits that + + align:start position:0% +productivity. Some of the benefits that + + + align:start position:0% +productivity. Some of the benefits that +you see, we've got bigger revenues that + + align:start position:0% +you see, we've got bigger revenues that + + + align:start position:0% +you see, we've got bigger revenues that +are generated from not only satisfied + + align:start position:0% +are generated from not only satisfied + + + align:start position:0% +are generated from not only satisfied +customers, but better utilized capital + + align:start position:0% +customers, but better utilized capital + + + align:start position:0% +customers, but better utilized capital +assets here. And we have reduced costs + + align:start position:0% +assets here. And we have reduced costs + + + align:start position:0% +assets here. And we have reduced costs +from lower employee turnover if they're + + align:start position:0% +from lower employee turnover if they're + + + align:start position:0% +from lower employee turnover if they're +productive and satisfied and not having + + align:start position:0% +productive and satisfied and not having + + + align:start position:0% +productive and satisfied and not having +people sit idle. Wasted human resources. + + align:start position:0% +people sit idle. Wasted human resources. + + + align:start position:0% +people sit idle. Wasted human resources. +It's very bad thing. + + align:start position:0% +It's very bad thing. + + + align:start position:0% +It's very bad thing. +And lastly, increased productivity leads + + align:start position:0% +And lastly, increased productivity leads + + + align:start position:0% +And lastly, increased productivity leads +to happy satisfied employees, which + + align:start position:0% +to happy satisfied employees, which + + + align:start position:0% +to happy satisfied employees, which +leads to more increased productivity, + + align:start position:0% +leads to more increased productivity, + + + align:start position:0% +leads to more increased productivity, +which leads to more happy, satisfied + + align:start position:0% +which leads to more happy, satisfied + + + align:start position:0% +which leads to more happy, satisfied +employees. A very virtuous + + align:start position:0% + + + + align:start position:0% + +circle. So now we'd like to turn from + + align:start position:0% +circle. So now we'd like to turn from + + + align:start position:0% +circle. So now we'd like to turn from +our case example of Southwest and + + align:start position:0% +our case example of Southwest and + + + align:start position:0% +our case example of Southwest and +linking um employee satisfaction + + align:start position:0% +linking um employee satisfaction + + + align:start position:0% +linking um employee satisfaction +essentially and productivity to now + + align:start position:0% +essentially and productivity to now + + + align:start position:0% +essentially and productivity to now +talking about working in teams and + + align:start position:0% +talking about working in teams and + + + align:start position:0% +talking about working in teams and +thinking about how teams can better work + + align:start position:0% +thinking about how teams can better work + + + align:start position:0% +thinking about how teams can better work +together. And to start that off, we want + + align:start position:0% +together. And to start that off, we want + + + align:start position:0% +together. And to start that off, we want +to do some active learning. We're going + + align:start position:0% +to do some active learning. We're going + + + align:start position:0% +to do some active learning. We're going +to have a class debate. So the objective + + align:start position:0% +to have a class debate. So the objective + + + align:start position:0% +to have a class debate. So the objective +here is you're going to have a time + + align:start position:0% +here is you're going to have a time + + + align:start position:0% +here is you're going to have a time +constraint and you're going to have to + + align:start position:0% +constraint and you're going to have to + + + align:start position:0% +constraint and you're going to have to +articulate a clear and concise message, + + align:start position:0% +articulate a clear and concise message, + + + align:start position:0% +articulate a clear and concise message, +you know, on one side of the debate or + + align:start position:0% +you know, on one side of the debate or + + + align:start position:0% +you know, on one side of the debate or +the other. That's your overall + + align:start position:0% +the other. That's your overall + + + align:start position:0% +the other. That's your overall +objective. But while you're doing that, + + align:start position:0% +objective. But while you're doing that, + + + align:start position:0% +objective. But while you're doing that, +we want you to observe a couple things + + align:start position:0% +we want you to observe a couple things + + + align:start position:0% +we want you to observe a couple things +about the team dynamics. We want you to + + align:start position:0% +about the team dynamics. We want you to + + + align:start position:0% +about the team dynamics. We want you to +think about how differing viewpoints in + + align:start position:0% +think about how differing viewpoints in + + + align:start position:0% +think about how differing viewpoints in +your team affect their work. Want you to + + align:start position:0% +your team affect their work. Want you to + + + align:start position:0% +your team affect their work. Want you to +think about the process that's used for + + align:start position:0% +think about the process that's used for + + + align:start position:0% +think about the process that's used for +your group decision- making. And lastly, + + align:start position:0% +your group decision- making. And lastly, + + + align:start position:0% +your group decision- making. And lastly, +we want you to think about how + + align:start position:0% +we want you to think about how + + + align:start position:0% +we want you to think about how +completing the task depends upon the + + align:start position:0% +completing the task depends upon the + + + align:start position:0% +completing the task depends upon the +personal feelings of your group and the + + align:start position:0% +personal feelings of your group and the + + + align:start position:0% +personal feelings of your group and the +process. Okay? So there there's two + + align:start position:0% +process. Okay? So there there's two + + + align:start position:0% +process. Okay? So there there's two +things you're doing. One is you're + + align:start position:0% +things you're doing. One is you're + + + align:start position:0% +things you're doing. One is you're +you're making this argument and two + + align:start position:0% +you're making this argument and two + + + align:start position:0% +you're making this argument and two +you're you're stepping back and + + align:start position:0% +you're you're stepping back and + + + align:start position:0% +you're you're stepping back and +observing the whole process while it + + align:start position:0% +observing the whole process while it + + + align:start position:0% +observing the whole process while it +happens and taking notes on both of + + align:start position:0% +happens and taking notes on both of + + + align:start position:0% +happens and taking notes on both of +those. All right. So here's our + + align:start position:0% +those. All right. So here's our + + + align:start position:0% +those. All right. So here's our +debate. So the early bird may get the + + align:start position:0% +debate. So the early bird may get the + + + align:start position:0% +debate. So the early bird may get the +worm, but it's a second mouse that gets + + align:start position:0% +worm, but it's a second mouse that gets + + + align:start position:0% +worm, but it's a second mouse that gets +the cheese. + + align:start position:0% +the cheese. + + + align:start position:0% +the cheese. +So the bird's proposition here in this + + align:start position:0% +So the bird's proposition here in this + + + align:start position:0% +So the bird's proposition here in this +debate thinking putting in a lean + + align:start position:0% +debate thinking putting in a lean + + + align:start position:0% +debate thinking putting in a lean +context early adopters of lean thinking + + align:start position:0% +context early adopters of lean thinking + + + align:start position:0% +context early adopters of lean thinking +gain the greatest competitive + + align:start position:0% +gain the greatest competitive + + + align:start position:0% +gain the greatest competitive +advantage. But then there's another side + + align:start position:0% +advantage. But then there's another side + + + align:start position:0% +advantage. But then there's another side +of the debate that goes something like + + align:start position:0% +of the debate that goes something like + + + align:start position:0% +of the debate that goes something like +this that the second followers people + + align:start position:0% +this that the second followers people + + + align:start position:0% +this that the second followers people +who are not the first the second + + align:start position:0% +who are not the first the second + + + align:start position:0% +who are not the first the second +followers of lean thinking gain the + + align:start position:0% +followers of lean thinking gain the + + + align:start position:0% +followers of lean thinking gain the +greatest competitive + + align:start position:0% +greatest competitive + + + align:start position:0% +greatest competitive +advantage. So either of those points + + align:start position:0% +advantage. So either of those points + + + align:start position:0% +advantage. So either of those points +could be true. And we're going to assign + + align:start position:0% +could be true. And we're going to assign + + + align:start position:0% +could be true. And we're going to assign +the tables to be various points of view. + + align:start position:0% +the tables to be various points of view. + + + align:start position:0% +the tables to be various points of view. +And you're going to have to argue for + + align:start position:0% +And you're going to have to argue for + + + align:start position:0% +And you're going to have to argue for +one of these two different + + align:start position:0% +one of these two different + + + align:start position:0% +one of these two different +propositions. All right. So I'm going to + + align:start position:0% +propositions. All right. So I'm going to + + + align:start position:0% +propositions. All right. So I'm going to +go and assign tables. I'm actually going + + align:start position:0% +go and assign tables. I'm actually going + + + align:start position:0% +go and assign tables. I'm actually going +to make you birds, mice, birds, mice, + + align:start position:0% +to make you birds, mice, birds, mice, + + + align:start position:0% +to make you birds, mice, birds, mice, +and birds in the + + align:start position:0% + + + + align:start position:0% + +back. And what you have to do is I'm + + align:start position:0% +back. And what you have to do is I'm + + + align:start position:0% +back. And what you have to do is I'm +going to give you eight minutes to work + + align:start position:0% +going to give you eight minutes to work + + + align:start position:0% +going to give you eight minutes to work +on formulating a 60-second or less + + align:start position:0% +on formulating a 60-second or less + + + align:start position:0% +on formulating a 60-second or less +argument. in support of the proposition + + align:start position:0% +argument. in support of the proposition + + + align:start position:0% +argument. in support of the proposition +you've been + + align:start position:0% +you've been + + + align:start position:0% +you've been +assigned. And you also then have to come + + align:start position:0% +assigned. And you also then have to come + + + align:start position:0% +assigned. And you also then have to come +up with a 30- secondond or less rebuttal + + align:start position:0% +up with a 30- secondond or less rebuttal + + + align:start position:0% +up with a 30- secondond or less rebuttal +because the format's going to go, you + + align:start position:0% +because the format's going to go, you + + + align:start position:0% +because the format's going to go, you +get to make your point, the birds make + + align:start position:0% +get to make your point, the birds make + + + align:start position:0% +get to make your point, the birds make +their point, then the mice make their + + align:start position:0% +their point, then the mice make their + + + align:start position:0% +their point, then the mice make their +point, then the birds get to rebutt, and + + align:start position:0% +point, then the birds get to rebutt, and + + + align:start position:0% +point, then the birds get to rebutt, and +then the mice get to rebutt. So, you + + align:start position:0% +then the mice get to rebutt. So, you + + + align:start position:0% +then the mice get to rebutt. So, you +have to write two things, your your + + align:start position:0% +have to write two things, your your + + + align:start position:0% +have to write two things, your your +proposition and then your rebuttal. And + + align:start position:0% +proposition and then your rebuttal. And + + + align:start position:0% +proposition and then your rebuttal. And +they can take no more than 60 seconds. + + align:start position:0% +they can take no more than 60 seconds. + + + align:start position:0% +they can take no more than 60 seconds. +And you have eight minutes in which to + + align:start position:0% +And you have eight minutes in which to + + + align:start position:0% +And you have eight minutes in which to +formulate both. And then we're gonna + + align:start position:0% +formulate both. And then we're gonna + + + align:start position:0% +formulate both. And then we're gonna +have each team do one or the other. You + + align:start position:0% +have each team do one or the other. You + + + align:start position:0% +have each team do one or the other. You +won't know which until we get time and + + align:start position:0% +won't know which until we get time and + + + align:start position:0% +won't know which until we get time and +then we'll kind of roll dice and see who + + align:start position:0% +then we'll kind of roll dice and see who + + + align:start position:0% +then we'll kind of roll dice and see who +gets assigned + + align:start position:0% +gets assigned + + + align:start position:0% +gets assigned +what. All right. Any questions about the + + align:start position:0% +what. All right. Any questions about the + + + align:start position:0% +what. All right. Any questions about the +the tasks being active + + align:start position:0% +the tasks being active + + + align:start position:0% +the tasks being active +view? All right. Great. Go to it. I'll + + align:start position:0% +view? All right. Great. Go to it. I'll + + + align:start position:0% +view? All right. Great. Go to it. I'll +give you eight minutes on the clock. + + align:start position:0% + + + + align:start position:0% + +All right. Time's + + align:start position:0% +All right. Time's + + + align:start position:0% +All right. Time's +up. All right. So now everybody's got + + align:start position:0% +up. All right. So now everybody's got + + + align:start position:0% +up. All right. So now everybody's got +their their proposal or proposition and + + align:start position:0% +their their proposal or proposition and + + + align:start position:0% +their their proposal or proposition and +their rebuttal + + align:start position:0% +their rebuttal + + + align:start position:0% +their rebuttal +formulated. So we're going to have each + + align:start position:0% +formulated. So we're going to have each + + + align:start position:0% +formulated. So we're going to have each +uh each of the birds and the mice are + + align:start position:0% +uh each of the birds and the mice are + + + align:start position:0% +uh each of the birds and the mice are +going to give their proposals and then + + align:start position:0% +going to give their proposals and then + + + align:start position:0% +going to give their proposals and then +we're going to hear the rebuttals. And + + align:start position:0% +we're going to hear the rebuttals. And + + + align:start position:0% +we're going to hear the rebuttals. And +uh since I can't I don't have the right + + align:start position:0% +uh since I can't I don't have the right + + + align:start position:0% +uh since I can't I don't have the right +number of dice to roll for each of the + + align:start position:0% +number of dice to roll for each of the + + + align:start position:0% +number of dice to roll for each of the +situations, I'm just going to pick. So + + align:start position:0% +situations, I'm just going to pick. So + + + align:start position:0% +situations, I'm just going to pick. So +I'm going to ask this table. You guys + + align:start position:0% +I'm going to ask this table. You guys + + + align:start position:0% +I'm going to ask this table. You guys +are birds. Okay. I'm gonna ask you to do + + align:start position:0% +are birds. Okay. I'm gonna ask you to do + + + align:start position:0% +are birds. Okay. I'm gonna ask you to do +your + + align:start position:0% +your + + + align:start position:0% +your +proposition + + align:start position:0% +proposition + + + align:start position:0% +proposition +and and your birds in the back, too. + + align:start position:0% +and and your birds in the back, too. + + + align:start position:0% +and and your birds in the back, too. +I'll ask you to do your proposition. So, + + align:start position:0% +I'll ask you to do your proposition. So, + + + align:start position:0% +I'll ask you to do your proposition. So, +we'll hear the same thing from both + + align:start position:0% +we'll hear the same thing from both + + + align:start position:0% +we'll hear the same thing from both +teams. And I'll ask the remainder birds + + align:start position:0% +teams. And I'll ask the remainder birds + + + align:start position:0% +teams. And I'll ask the remainder birds +that you guys do the + + align:start position:0% +that you guys do the + + + align:start position:0% +that you guys do the +rebuttal. And then I'll ask this team + + align:start position:0% +rebuttal. And then I'll ask this team + + + align:start position:0% +rebuttal. And then I'll ask this team +over here, mice. I'll ask you to do the + + align:start position:0% +over here, mice. I'll ask you to do the + + + align:start position:0% +over here, mice. I'll ask you to do the +proposition. And I'll ask this mouse + + align:start position:0% +proposition. And I'll ask this mouse + + + align:start position:0% +proposition. And I'll ask this mouse +team to do the rebuttal. + + align:start position:0% + + + + align:start position:0% + +All right. So, let's have the birds go + + align:start position:0% +All right. So, let's have the birds go + + + align:start position:0% +All right. So, let's have the birds go +first. So, we'll hear the two bird + + align:start position:0% +first. So, we'll hear the two bird + + + align:start position:0% +first. So, we'll hear the two bird +propositions. Go ahead. And I've got you + + align:start position:0% +propositions. Go ahead. And I've got you + + + align:start position:0% +propositions. Go ahead. And I've got you +on the clock. + + align:start position:0% +on the clock. + + + align:start position:0% +on the clock. +So um I think it's a good idea to start + + align:start position:0% +So um I think it's a good idea to start + + + align:start position:0% +So um I think it's a good idea to start +early because it's a continuous process + + align:start position:0% +early because it's a continuous process + + + align:start position:0% +early because it's a continuous process +and it takes time to implement and to + + align:start position:0% +and it takes time to implement and to + + + align:start position:0% +and it takes time to implement and to +change your company's culture. So we're + + align:start position:0% +change your company's culture. So we're + + + align:start position:0% +change your company's culture. So we're +talking about 5 years earlier. So the + + align:start position:0% +talking about 5 years earlier. So the + + + align:start position:0% +talking about 5 years earlier. So the +sooner you get started, the sooner you + + align:start position:0% +sooner you get started, the sooner you + + + align:start position:0% +sooner you get started, the sooner you +can realize your gains. Um you can use + + align:start position:0% +can realize your gains. Um you can use + + + align:start position:0% +can realize your gains. Um you can use +creativity to kind of create the + + align:start position:0% +creativity to kind of create the + + + align:start position:0% +creativity to kind of create the +standard before other people really + + align:start position:0% +standard before other people really + + + align:start position:0% +standard before other people really +define it for you. + + align:start position:0% +define it for you. + + + align:start position:0% +define it for you. +Um if you start early and you find you + + align:start position:0% +Um if you start early and you find you + + + align:start position:0% +Um if you start early and you find you +run into some challenges then you have + + align:start position:0% +run into some challenges then you have + + + align:start position:0% +run into some challenges then you have +time to go back and change things and + + align:start position:0% +time to go back and change things and + + + align:start position:0% +time to go back and change things and +make it more efficient or um choose a + + align:start position:0% +make it more efficient or um choose a + + + align:start position:0% +make it more efficient or um choose a +different path. Um you can establish a + + align:start position:0% +different path. Um you can establish a + + + align:start position:0% +different path. Um you can establish a +reputation of being innovative which + + align:start position:0% +reputation of being innovative which + + + align:start position:0% +reputation of being innovative which +will not only encourage people to invest + + align:start position:0% +will not only encourage people to invest + + + align:start position:0% +will not only encourage people to invest +in your company but um may also excite + + align:start position:0% +in your company but um may also excite + + + align:start position:0% +in your company but um may also excite +your employees um because they'll just + + align:start position:0% +your employees um because they'll just + + + align:start position:0% +your employees um because they'll just +be exciting about being on the leading + + align:start position:0% +be exciting about being on the leading + + + align:start position:0% +be exciting about being on the leading +edge of something. Um, and then it takes + + align:start position:0% +edge of something. Um, and then it takes + + + align:start position:0% +edge of something. Um, and then it takes +time just to change the culture of the + + align:start position:0% +time just to change the culture of the + + + align:start position:0% +time just to change the culture of the +company. So that's also a good + + align:start position:0% +company. So that's also a good + + + align:start position:0% +company. So that's also a good +advantage, right? + + align:start position:0% +advantage, right? + + + align:start position:0% +advantage, right? +Okay. And just a few seconds of spare. + + align:start position:0% +Okay. And just a few seconds of spare. + + + align:start position:0% +Okay. And just a few seconds of spare. +Good job. Let's have the other + + align:start position:0% +Good job. Let's have the other + + + align:start position:0% +Good job. Let's have the other +proposition for the birds. And please + + align:start position:0% +proposition for the birds. And please + + + align:start position:0% +proposition for the birds. And please +speak up so everybody can hear you. + + align:start position:0% +speak up so everybody can hear you. + + + align:start position:0% +speak up so everybody can hear you. +Okay. Well, I'm going to start with the + + align:start position:0% +Okay. Well, I'm going to start with the + + + align:start position:0% +Okay. Well, I'm going to start with the +um our graph that we have here. So this + + align:start position:0% +um our graph that we have here. So this + + + align:start position:0% +um our graph that we have here. So this +is time and this is productivity. And if + + align:start position:0% +is time and this is productivity. And if + + + align:start position:0% +is time and this is productivity. And if +you start with the this company right + + align:start position:0% +you start with the this company right + + + align:start position:0% +you start with the this company right +here, which would be the early bird who + + align:start position:0% +here, which would be the early bird who + + + align:start position:0% +here, which would be the early bird who +adopting lean and they improve their + + align:start position:0% +adopting lean and they improve their + + + align:start position:0% +adopting lean and they improve their +productivity and their um employee + + align:start position:0% +productivity and their um employee + + + align:start position:0% +productivity and their um employee +satisfaction and their efficiency, + + align:start position:0% +satisfaction and their efficiency, + + + align:start position:0% +satisfaction and their efficiency, +there's virtually no way that this um + + align:start position:0% +there's virtually no way that this um + + + align:start position:0% +there's virtually no way that this um +second company that starts it at a later + + align:start position:0% +second company that starts it at a later + + + align:start position:0% +second company that starts it at a later +time can ever catch up to it. And while + + align:start position:0% +time can ever catch up to it. And while + + + align:start position:0% +time can ever catch up to it. And while +they start their innovations that we're + + align:start position:0% +they start their innovations that we're + + + align:start position:0% +they start their innovations that we're +on moving on to our next innovations um + + align:start position:0% +on moving on to our next innovations um + + + align:start position:0% +on moving on to our next innovations um +after we've already established some + + align:start position:0% +after we've already established some + + + align:start position:0% +after we've already established some +brand loyalty and got um customer + + align:start position:0% +brand loyalty and got um customer + + + align:start position:0% +brand loyalty and got um customer +allegiance, + + align:start position:0% +allegiance, + + + align:start position:0% +allegiance, +we've have the market edge and we also + + align:start position:0% +we've have the market edge and we also + + + align:start position:0% +we've have the market edge and we also +you know that some point the market gets + + align:start position:0% +you know that some point the market gets + + + align:start position:0% +you know that some point the market gets +saturated and we've already reached it + + align:start position:0% +saturated and we've already reached it + + + align:start position:0% +saturated and we've already reached it +like this um graph shows you the same + + align:start position:0% +like this um graph shows you the same + + + align:start position:0% +like this um graph shows you the same +thing that our um colleagues were saying + + align:start position:0% +thing that our um colleagues were saying + + + align:start position:0% +thing that our um colleagues were saying +is that because it takes five years that + + align:start position:0% +is that because it takes five years that + + + align:start position:0% +is that because it takes five years that +we have and it's not just an end street + + align:start position:0% +we have and it's not just an end street + + + align:start position:0% +we have and it's not just an end street +if we have ongoing continuous + + align:start position:0% +if we have ongoing continuous + + + align:start position:0% +if we have ongoing continuous +improvement that it's something that + + align:start position:0% +improvement that it's something that + + + align:start position:0% +improvement that it's something that +continues moving on indefinitely in the + + align:start position:0% +continues moving on indefinitely in the + + + align:start position:0% +continues moving on indefinitely in the +future. Um in our uh patients we have + + align:start position:0% +future. Um in our uh patients we have + + + align:start position:0% +future. Um in our uh patients we have +better recruitment and retention of + + align:start position:0% +better recruitment and retention of + + + align:start position:0% +better recruitment and retention of +satisfied employees. Our end product is + + align:start position:0% +satisfied employees. Our end product is + + + align:start position:0% +satisfied employees. Our end product is +better and we can respond to the + + align:start position:0% +better and we can respond to the + + + align:start position:0% +better and we can respond to the +customer needs quickly. + + align:start position:0% +customer needs quickly. + + + align:start position:0% +customer needs quickly. +Okay. Thank + + align:start position:0% +Okay. Thank + + + align:start position:0% +Okay. Thank +you. All right. Let's go to our + + align:start position:0% +you. All right. Let's go to our + + + align:start position:0% +you. All right. Let's go to our +mice. All + + align:start position:0% +mice. All + + + align:start position:0% +mice. All +right. So, uh, the first to make a move + + align:start position:0% +right. So, uh, the first to make a move + + + align:start position:0% +right. So, uh, the first to make a move +themselves at significant risk of + + align:start position:0% +themselves at significant risk of + + + align:start position:0% +themselves at significant risk of +failure and squandered time and + + align:start position:0% +failure and squandered time and + + + align:start position:0% +failure and squandered time and +resources. Once a plan has been + + align:start position:0% +resources. Once a plan has been + + + align:start position:0% +resources. Once a plan has been +implemented, that is advantages. So, we + + align:start position:0% +implemented, that is advantages. So, we + + + align:start position:0% +implemented, that is advantages. So, we +see that the mistakes and inefficiencies + + align:start position:0% +see that the mistakes and inefficiencies + + + align:start position:0% +see that the mistakes and inefficiencies +of that process can be corrected, + + align:start position:0% +of that process can be corrected, + + + align:start position:0% +of that process can be corrected, +reddrafted and implemented, gaining a + + align:start position:0% +reddrafted and implemented, gaining a + + + align:start position:0% +reddrafted and implemented, gaining a +competitive advantage. Also, by um + + align:start position:0% +competitive advantage. Also, by um + + + align:start position:0% +competitive advantage. Also, by um +starting off later, the standard had + + align:start position:0% +starting off later, the standard had + + + align:start position:0% +starting off later, the standard had +already been established and that way + + align:start position:0% +already been established and that way + + + align:start position:0% +already been established and that way +the um implementation time is less. + + align:start position:0% +the um implementation time is less. + + + align:start position:0% +the um implementation time is less. +Very good. Very efficient. Much less + + align:start position:0% +Very good. Very efficient. Much less + + + align:start position:0% +Very good. Very efficient. Much less +than 60 seconds. + + align:start position:0% +than 60 seconds. + + + align:start position:0% +than 60 seconds. +All right. So now we've heard arguments + + align:start position:0% +All right. So now we've heard arguments + + + align:start position:0% +All right. So now we've heard arguments +on both sides of the case. So let's hear + + align:start position:0% +on both sides of the case. So let's hear + + + align:start position:0% +on both sides of the case. So let's hear +some rebuttals. So the mice just went, + + align:start position:0% +some rebuttals. So the mice just went, + + + align:start position:0% +some rebuttals. So the mice just went, +so let's hear the bird's rebuttal to the + + align:start position:0% +so let's hear the bird's rebuttal to the + + + align:start position:0% +so let's hear the bird's rebuttal to the +mouse's proposition. + + align:start position:0% +mouse's proposition. + + + align:start position:0% +mouse's proposition. +Okay. So So the mice proposed that they + + align:start position:0% +Okay. So So the mice proposed that they + + + align:start position:0% +Okay. So So the mice proposed that they +would learn from the bird's uh mistakes, + + align:start position:0% +would learn from the bird's uh mistakes, + + + align:start position:0% +would learn from the bird's uh mistakes, +but so much of lean is specific to + + align:start position:0% +but so much of lean is specific to + + + align:start position:0% +but so much of lean is specific to +individual enterprises as it relates to + + align:start position:0% +individual enterprises as it relates to + + + align:start position:0% +individual enterprises as it relates to +local politics, the culture of that + + align:start position:0% +local politics, the culture of that + + + align:start position:0% +local politics, the culture of that +enterprise, the physical space that we + + align:start position:0% +enterprise, the physical space that we + + + align:start position:0% +enterprise, the physical space that we +think that it's it's very specific. And + + align:start position:0% +think that it's it's very specific. And + + + align:start position:0% +think that it's it's very specific. And +then the what we learn in say BI might + + align:start position:0% +then the what we learn in say BI might + + + align:start position:0% +then the what we learn in say BI might +not necessarily be directly to we're + + align:start position:0% +not necessarily be directly to we're + + + align:start position:0% +not necessarily be directly to we're +going to miss the mess the burden. And + + align:start position:0% +going to miss the mess the burden. And + + + align:start position:0% +going to miss the mess the burden. And +our second point is that um by being an + + align:start position:0% +our second point is that um by being an + + + align:start position:0% +our second point is that um by being an +early adopter um by not being an early + + align:start position:0% +early adopter um by not being an early + + + align:start position:0% +early adopter um by not being an early +adopter you're kind of adding some more + + align:start position:0% +adopter you're kind of adding some more + + + align:start position:0% +adopter you're kind of adding some more +time. You're kind of just sitting around + + align:start position:0% +time. You're kind of just sitting around + + + align:start position:0% +time. You're kind of just sitting around +and waiting in and existing in a culture + + align:start position:0% +and waiting in and existing in a culture + + + align:start position:0% +and waiting in and existing in a culture +of inefficiency um that is doing harm to + + align:start position:0% +of inefficiency um that is doing harm to + + + align:start position:0% +of inefficiency um that is doing harm to +healthcare patients potentially and + + align:start position:0% +healthcare patients potentially and + + + align:start position:0% +healthcare patients potentially and +that's just unacceptable. you know that + + align:start position:0% +that's just unacceptable. you know that + + + align:start position:0% +that's just unacceptable. you know that +there is uh better better ways of + + align:start position:0% +there is uh better better ways of + + + align:start position:0% +there is uh better better ways of +operating on the table. + + align:start position:0% +operating on the table. + + + align:start position:0% +operating on the table. +Very good. No pun intended. + + align:start position:0% + + + + align:start position:0% + +All right, let's hear the rebuttal to + + align:start position:0% +All right, let's hear the rebuttal to + + + align:start position:0% +All right, let's hear the rebuttal to +the mouse's proposition. + + align:start position:0% +the mouse's proposition. + + + align:start position:0% +the mouse's proposition. +So for the money, it's better to be the + + align:start position:0% +So for the money, it's better to be the + + + align:start position:0% +So for the money, it's better to be the +second adopter because you have an + + align:start position:0% +second adopter because you have an + + + align:start position:0% +second adopter because you have an +easier time getting the buy in. And + + align:start position:0% +easier time getting the buy in. And + + + align:start position:0% +easier time getting the buy in. And +that's one of the biggest hurdles + + align:start position:0% +that's one of the biggest hurdles + + + align:start position:0% +that's one of the biggest hurdles +because people see how it's worked in + + align:start position:0% +because people see how it's worked in + + + align:start position:0% +because people see how it's worked in +other industries, other companies. So + + align:start position:0% +other industries, other companies. So + + + align:start position:0% +other industries, other companies. So +they say, "Oh, we can do this." You can + + align:start position:0% +they say, "Oh, we can do this." You can + + + align:start position:0% +they say, "Oh, we can do this." You can +also pick and choose what you want and + + align:start position:0% +also pick and choose what you want and + + + align:start position:0% +also pick and choose what you want and +what you think will work best for your + + align:start position:0% +what you think will work best for your + + + align:start position:0% +what you think will work best for your +specific situation. You also have more + + align:start position:0% +specific situation. You also have more + + + align:start position:0% +specific situation. You also have more +experts to learn from because you can + + align:start position:0% +experts to learn from because you can + + + align:start position:0% +experts to learn from because you can +tap into the resources and the knowledge + + align:start position:0% +tap into the resources and the knowledge + + + align:start position:0% +tap into the resources and the knowledge +at the other companies and you can see + + align:start position:0% +at the other companies and you can see + + + align:start position:0% +at the other companies and you can see +what failed. And it's always the the + + align:start position:0% +what failed. And it's always the the + + + align:start position:0% +what failed. And it's always the the +first time that takes the most and then + + align:start position:0% +first time that takes the most and then + + + align:start position:0% +first time that takes the most and then +you're starting from a higher point so + + align:start position:0% +you're starting from a higher point so + + + align:start position:0% +you're starting from a higher point so +you can more easily reach and even + + align:start position:0% +you can more easily reach and even + + + align:start position:0% +you can more easily reach and even +surpass the point of the birds. And just + + align:start position:0% +surpass the point of the birds. And just + + + align:start position:0% +surpass the point of the birds. And just +to add to that um they shared with us a + + align:start position:0% +to add to that um they shared with us a + + + align:start position:0% +to add to that um they shared with us a +graph um showing production and all but + + align:start position:0% +graph um showing production and all but + + + align:start position:0% +graph um showing production and all but +I mean today we learned that the US auto + + align:start position:0% +I mean today we learned that the US auto + + + align:start position:0% +I mean today we learned that the US auto +industry and compared to Japan auto + + align:start position:0% +industry and compared to Japan auto + + + align:start position:0% +industry and compared to Japan auto +industry as of 1947 + + align:start position:0% +industry as of 1947 + + + align:start position:0% +industry as of 1947 +Japan and 40 years and five but in the + + align:start position:0% +Japan and 40 years and five but in the + + + align:start position:0% +Japan and 40 years and five but in the +space of um about 40 years the way we + + align:start position:0% +space of um about 40 years the way we + + + align:start position:0% +space of um about 40 years the way we +are protecting the US industry so this + + align:start position:0% +are protecting the US industry so this + + + align:start position:0% +are protecting the US industry so this +is a clear example there's always + + align:start position:0% +is a clear example there's always + + + align:start position:0% +is a clear example there's always +all right and that's actually your 60 + + align:start position:0% +all right and that's actually your 60 + + + align:start position:0% +all right and that's actually your 60 +seconds. Okay, very good. + + align:start position:0% + + + + align:start position:0% + +Excellent. So, I'm glad that this has in + + align:start position:0% +Excellent. So, I'm glad that this has in + + + align:start position:0% +Excellent. So, I'm glad that this has in +inspired some fires in + + align:start position:0% +inspired some fires in + + + align:start position:0% +inspired some fires in +you. So, now that you've heard both + + align:start position:0% +you. So, now that you've heard both + + + align:start position:0% +you. So, now that you've heard both +sides of the argument, you I actually + + align:start position:0% +sides of the argument, you I actually + + + align:start position:0% +sides of the argument, you I actually +would like you to uh to step aside from + + align:start position:0% +would like you to uh to step aside from + + + align:start position:0% +would like you to uh to step aside from +your team propositions regardless of + + align:start position:0% +your team propositions regardless of + + + align:start position:0% +your team propositions regardless of +what you were asked to to argue for your + + align:start position:0% +what you were asked to to argue for your + + + align:start position:0% +what you were asked to to argue for your +teams. And I want you to think about the + + align:start position:0% +teams. And I want you to think about the + + + align:start position:0% +teams. And I want you to think about the +arguments and the rebuttals that you did + + align:start position:0% +arguments and the rebuttals that you did + + + align:start position:0% +arguments and the rebuttals that you did +here and think about which side of the + + align:start position:0% +here and think about which side of the + + + align:start position:0% +here and think about which side of the +argument seemed more convincing to you + + align:start position:0% +argument seemed more convincing to you + + + align:start position:0% +argument seemed more convincing to you +personally. So, if you could take out + + align:start position:0% +personally. So, if you could take out + + + align:start position:0% +personally. So, if you could take out +your green cards and your yellow cards, + + align:start position:0% +your green cards and your yellow cards, + + + align:start position:0% +your green cards and your yellow cards, +and I'd like you to think if you if you + + align:start position:0% +and I'd like you to think if you if you + + + align:start position:0% +and I'd like you to think if you if you +really believe the the bird argument or + + align:start position:0% +really believe the the bird argument or + + + align:start position:0% +really believe the the bird argument or +the mouse argument. So, if you feel you + + align:start position:0% +the mouse argument. So, if you feel you + + + align:start position:0% +the mouse argument. So, if you feel you +believe the bird argument, raise up a + + align:start position:0% +believe the bird argument, raise up a + + + align:start position:0% +believe the bird argument, raise up a +green card. And if you feel you believe + + align:start position:0% +green card. And if you feel you believe + + + align:start position:0% +green card. And if you feel you believe +the mouse argument, raise up the yellow + + align:start position:0% +the mouse argument, raise up the yellow + + + align:start position:0% +the mouse argument, raise up the yellow +card. Just go ahead and raise it up. We + + align:start position:0% +card. Just go ahead and raise it up. We + + + align:start position:0% +card. Just go ahead and raise it up. We +just want to get a sense of the the uh + + align:start position:0% +just want to get a sense of the the uh + + + align:start position:0% +just want to get a sense of the the uh +room. + + align:start position:0% + + + + align:start position:0% + +All right. So, + + align:start position:0% + + + + align:start position:0% + +So, do we have everybody making a + + align:start position:0% +So, do we have everybody making a + + + align:start position:0% +So, do we have everybody making a +decision? Somebody lost the green + + align:start position:0% +decision? Somebody lost the green + + + align:start position:0% +decision? Somebody lost the green +cards. All right. So, it looks like, + + align:start position:0% +cards. All right. So, it looks like, + + + align:start position:0% +cards. All right. So, it looks like, +look around. We've got more green cards + + align:start position:0% +look around. We've got more green cards + + + align:start position:0% +look around. We've got more green cards +than yellow cards, right? We got good, + + align:start position:0% +than yellow cards, right? We got good, + + + align:start position:0% +than yellow cards, right? We got good, +but still we got maybe maybe four to one + + align:start position:0% +but still we got maybe maybe four to one + + + align:start position:0% +but still we got maybe maybe four to one +green to yellow. + + align:start position:0% +green to yellow. + + + align:start position:0% +green to yellow. +So it seems like overall you all feel + + align:start position:0% +So it seems like overall you all feel + + + align:start position:0% +So it seems like overall you all feel +that um the bird argument the early + + align:start position:0% +that um the bird argument the early + + + align:start position:0% +that um the bird argument the early +adopters of lean have the greatest + + align:start position:0% +adopters of lean have the greatest + + + align:start position:0% +adopters of lean have the greatest +competitive advantage and there's no + + align:start position:0% +competitive advantage and there's no + + + align:start position:0% +competitive advantage and there's no +right and wrong to this uh and it's + + align:start position:0% +right and wrong to this uh and it's + + + align:start position:0% +right and wrong to this uh and it's +largely dependent on your context and + + align:start position:0% +largely dependent on your context and + + + align:start position:0% +largely dependent on your context and +situations and there may be + + align:start position:0% +situations and there may be + + + align:start position:0% +situations and there may be +circumstances where it's it's better for + + align:start position:0% +circumstances where it's it's better for + + + align:start position:0% +circumstances where it's it's better for +an organization to wait. The + + align:start position:0% +an organization to wait. The + + + align:start position:0% +an organization to wait. The +organization is say in the middle of a + + align:start position:0% +organization is say in the middle of a + + + align:start position:0% +organization is say in the middle of a +big transition to a new product it just + + align:start position:0% +big transition to a new product it just + + + align:start position:0% +big transition to a new product it just +might not be the right time to start. It + + align:start position:0% +might not be the right time to start. It + + + align:start position:0% +might not be the right time to start. It +may not be advantageous for them to uh + + align:start position:0% +may not be advantageous for them to uh + + + align:start position:0% +may not be advantageous for them to uh +think about being an early adopter. Um, + + align:start position:0% +think about being an early adopter. Um, + + + align:start position:0% +think about being an early adopter. Um, +but there are certainly are lots of + + align:start position:0% +but there are certainly are lots of + + + align:start position:0% +but there are certainly are lots of +advantages for an organization who's + + align:start position:0% +advantages for an organization who's + + + align:start position:0% +advantages for an organization who's +ready to adopt lean to adopt it. So you + + align:start position:0% +ready to adopt lean to adopt it. So you + + + align:start position:0% +ready to adopt lean to adopt it. So you +might say that if you're ready, if + + align:start position:0% +might say that if you're ready, if + + + align:start position:0% +might say that if you're ready, if +you're able, if it's a good time, and if + + align:start position:0% +you're able, if it's a good time, and if + + + align:start position:0% +you're able, if it's a good time, and if +you don't adopt lean, that's not so + + align:start position:0% +you don't adopt lean, that's not so + + + align:start position:0% +you don't adopt lean, that's not so +good, right? But necessarily being an + + align:start position:0% +good, right? But necessarily being an + + + align:start position:0% +good, right? But necessarily being an +early adopter doesn't have to help you, + + align:start position:0% +early adopter doesn't have to help you, + + + align:start position:0% +early adopter doesn't have to help you, +but uh it certainly can be a very good + + align:start position:0% +but uh it certainly can be a very good + + + align:start position:0% +but uh it certainly can be a very good +thing for an + + align:start position:0% +thing for an + + + align:start position:0% +thing for an +organization. So now let's turn from + + align:start position:0% +organization. So now let's turn from + + + align:start position:0% +organization. So now let's turn from +thinking about the outcome of this + + align:start position:0% +thinking about the outcome of this + + + align:start position:0% +thinking about the outcome of this +debate and whether you thought about + + align:start position:0% +debate and whether you thought about + + + align:start position:0% +debate and whether you thought about +yourself as a bird or a mouse. Let's + + align:start position:0% +yourself as a bird or a mouse. Let's + + + align:start position:0% +yourself as a bird or a mouse. Let's +think about the team experience itself + + align:start position:0% +think about the team experience itself + + + align:start position:0% +think about the team experience itself +which was the other element I asked you + + align:start position:0% +which was the other element I asked you + + + align:start position:0% +which was the other element I asked you +to reflect upon as you're going through + + align:start position:0% +to reflect upon as you're going through + + + align:start position:0% +to reflect upon as you're going through +this exercise. So think about this + + align:start position:0% +this exercise. So think about this + + + align:start position:0% +this exercise. So think about this +common dilemma that we find ourselves in + + align:start position:0% +common dilemma that we find ourselves in + + + align:start position:0% +common dilemma that we find ourselves in +when we're working in teams of your + + align:start position:0% +when we're working in teams of your + + + align:start position:0% +when we're working in teams of your +personal views versus the team views. + + align:start position:0% +personal views versus the team views. + + + align:start position:0% +personal views versus the team views. +Think about in your exercise here uh was + + align:start position:0% +Think about in your exercise here uh was + + + align:start position:0% +Think about in your exercise here uh was +there adapting that you did or was there + + align:start position:0% +there adapting that you did or was there + + + align:start position:0% +there adapting that you did or was there +compromising you saw taking place in the + + align:start position:0% +compromising you saw taking place in the + + + align:start position:0% +compromising you saw taking place in the +team? How were the personal feelings, + + align:start position:0% +team? How were the personal feelings, + + + align:start position:0% +team? How were the personal feelings, +attitudes and perceptions of others + + align:start position:0% +attitudes and perceptions of others + + + align:start position:0% +attitudes and perceptions of others +handled? How did you feel it was handled + + align:start position:0% +handled? How did you feel it was handled + + + align:start position:0% +handled? How did you feel it was handled +for you? Did you feel anybody else um + + align:start position:0% +for you? Did you feel anybody else um + + + align:start position:0% +for you? Did you feel anybody else um +maybe being uncomfortable in that + + align:start position:0% +maybe being uncomfortable in that + + + align:start position:0% +maybe being uncomfortable in that +situation? Uh what about the wordings of + + align:start position:0% +situation? Uh what about the wordings of + + + align:start position:0% +situation? Uh what about the wordings of +statements? Did you as a team argue + + align:start position:0% +statements? Did you as a team argue + + + align:start position:0% +statements? Did you as a team argue +about how you worded things? Did that + + align:start position:0% +about how you worded things? Did that + + + align:start position:0% +about how you worded things? Did that +make a difference? What was the process + + align:start position:0% +make a difference? What was the process + + + align:start position:0% +make a difference? What was the process +used for your group to decide and + + align:start position:0% +used for your group to decide and + + + align:start position:0% +used for your group to decide and +discuss and present? Was there a + + align:start position:0% +discuss and present? Was there a + + + align:start position:0% +discuss and present? Was there a +process? Did you think about it? How did + + align:start position:0% +process? Did you think about it? How did + + + align:start position:0% +process? Did you think about it? How did +it unfold? Um and how satisfied were you + + align:start position:0% +it unfold? Um and how satisfied were you + + + align:start position:0% +it unfold? Um and how satisfied were you +with the team outcome? And I'd like to + + align:start position:0% +with the team outcome? And I'd like to + + + align:start position:0% +with the team outcome? And I'd like to +take probably three minutes for each + + align:start position:0% +take probably three minutes for each + + + align:start position:0% +take probably three minutes for each +group to discuss it within their group. + + align:start position:0% +group to discuss it within their group. + + + align:start position:0% +group to discuss it within their group. +and then we'll take one or two minutes + + align:start position:0% +and then we'll take one or two minutes + + + align:start position:0% +and then we'll take one or two minutes +to kind of give some some open + + align:start position:0% +to kind of give some some open + + + align:start position:0% +to kind of give some some open +commentary on these issues as you + + align:start position:0% +commentary on these issues as you + + + align:start position:0% +commentary on these issues as you +discuss them in your group. + + align:start position:0% + + + + align:start position:0% + +If I can have everybody's attention + + align:start position:0% +If I can have everybody's attention + + + align:start position:0% +If I can have everybody's attention +please, we'll get back to sharing our + + align:start position:0% +please, we'll get back to sharing our + + + align:start position:0% +please, we'll get back to sharing our +discussions with the class so we can all + + align:start position:0% +discussions with the class so we can all + + + align:start position:0% +discussions with the class so we can all +benefit from the table discussions. The + + align:start position:0% +benefit from the table discussions. The + + + align:start position:0% +benefit from the table discussions. The +table discussions are a great way to get + + align:start position:0% +table discussions are a great way to get + + + align:start position:0% +table discussions are a great way to get +more people talking at once. So, if we + + align:start position:0% +more people talking at once. So, if we + + + align:start position:0% +more people talking at once. So, if we +just had a class discussion, we would + + align:start position:0% +just had a class discussion, we would + + + align:start position:0% +just had a class discussion, we would +get um oneif the kind of conversation + + align:start position:0% +get um oneif the kind of conversation + + + align:start position:0% +get um oneif the kind of conversation +that we get going on with all the + + align:start position:0% +that we get going on with all the + + + align:start position:0% +that we get going on with all the +tables. So now I'd like to hear though + + align:start position:0% +tables. So now I'd like to hear though + + + align:start position:0% +tables. So now I'd like to hear though +about some of the richness of the the + + align:start position:0% +about some of the richness of the the + + + align:start position:0% +about some of the richness of the the +conversations you had. So first on items + + align:start position:0% +conversations you had. So first on items + + + align:start position:0% +conversations you had. So first on items +of the dilemma of the personal versus + + align:start position:0% +of the dilemma of the personal versus + + + align:start position:0% +of the dilemma of the personal versus +team views, which tables felt that they + + align:start position:0% +team views, which tables felt that they + + + align:start position:0% +team views, which tables felt that they +experience some of those things? Yes. + + align:start position:0% +experience some of those things? Yes. + + + align:start position:0% +experience some of those things? Yes. +Yeah. Well, at the start I sort of had a + + align:start position:0% +Yeah. Well, at the start I sort of had a + + + align:start position:0% +Yeah. Well, at the start I sort of had a +different opinion from the rest of the + + align:start position:0% +different opinion from the rest of the + + + align:start position:0% +different opinion from the rest of the +team, but because we were assigned to a + + align:start position:0% +team, but because we were assigned to a + + + align:start position:0% +team, but because we were assigned to a +particular side of the coin, so we just + + align:start position:0% +particular side of the coin, so we just + + + align:start position:0% +particular side of the coin, so we just +had to work together and within 10 + + align:start position:0% +had to work together and within 10 + + + align:start position:0% +had to work together and within 10 +seconds I was convinced. + + align:start position:0% + + + + align:start position:0% + +I think you came uh to a very similar + + align:start position:0% +I think you came uh to a very similar + + + align:start position:0% +I think you came uh to a very similar +conclusion of saying had it been maybe a + + align:start position:0% +conclusion of saying had it been maybe a + + + align:start position:0% +conclusion of saying had it been maybe a +topic like politics where everybody has + + align:start position:0% +topic like politics where everybody has + + + align:start position:0% +topic like politics where everybody has +a view but you're just meeting people + + align:start position:0% +a view but you're just meeting people + + + align:start position:0% +a view but you're just meeting people +and you want to be respectful of other + + align:start position:0% +and you want to be respectful of other + + + align:start position:0% +and you want to be respectful of other +people's views um we might have had a + + align:start position:0% +people's views um we might have had a + + + align:start position:0% +people's views um we might have had a +little bit more conflict whereas here + + align:start position:0% +little bit more conflict whereas here + + + align:start position:0% +little bit more conflict whereas here +since we were given our conclusion + + align:start position:0% +since we were given our conclusion + + + align:start position:0% +since we were given our conclusion +everyone was just trying to quickly find + + align:start position:0% +everyone was just trying to quickly find + + + align:start position:0% +everyone was just trying to quickly find +ways to support that conclusion + + align:start position:0% +ways to support that conclusion + + + align:start position:0% +ways to support that conclusion +together. Yeah. And this table over here + + align:start position:0% +together. Yeah. And this table over here + + + align:start position:0% +together. Yeah. And this table over here +where you guys had an even split of + + align:start position:0% +where you guys had an even split of + + + align:start position:0% +where you guys had an even split of +yellows and greens in your personal + + align:start position:0% +yellows and greens in your personal + + + align:start position:0% +yellows and greens in your personal +votes. + + align:start position:0% + + + + align:start position:0% + +We were all yellow. + + align:start position:0% + + + + align:start position:0% + +We worked so well together that we were + + align:start position:0% +We worked so well together that we were + + + align:start position:0% +We worked so well together that we were +actually truly convinced. + + align:start position:0% +actually truly convinced. + + + align:start position:0% +actually truly convinced. +Excellent. + + align:start position:0% +Excellent. + + + align:start position:0% +Excellent. +Um, let's talk about the process that + + align:start position:0% +Um, let's talk about the process that + + + align:start position:0% +Um, let's talk about the process that +you used. + + align:start position:0% +you used. + + + align:start position:0% +you used. +We just had a big lecture on process + + align:start position:0% +We just had a big lecture on process + + + align:start position:0% +We just had a big lecture on process +before this, right? and seeing life as a + + align:start position:0% +before this, right? and seeing life as a + + + align:start position:0% +before this, right? and seeing life as a +process. What process did you use? + + align:start position:0% +process. What process did you use? + + + align:start position:0% +process. What process did you use? +We we had a good process. I mean, + + align:start position:0% +We we had a good process. I mean, + + + align:start position:0% +We we had a good process. I mean, +everyone had to give their opinion + + align:start position:0% +everyone had to give their opinion + + + align:start position:0% +everyone had to give their opinion +initially. We had input from everyone + + align:start position:0% +initially. We had input from everyone + + + align:start position:0% +initially. We had input from everyone +before coming to a consensus. So, it + + align:start position:0% +before coming to a consensus. So, it + + + align:start position:0% +before coming to a consensus. So, it +wasn't like someone just came out with a + + align:start position:0% +wasn't like someone just came out with a + + + align:start position:0% +wasn't like someone just came out with a +final solution. I mean, we had to listen + + align:start position:0% +final solution. I mean, we had to listen + + + align:start position:0% +final solution. I mean, we had to listen +to everybody's point of view and maybe + + align:start position:0% +to everybody's point of view and maybe + + + align:start position:0% +to everybody's point of view and maybe +because our group is small made it more + + align:start position:0% +because our group is small made it more + + + align:start position:0% +because our group is small made it more +effective. We were able to come to a + + align:start position:0% +effective. We were able to come to a + + + align:start position:0% +effective. We were able to come to a +very good conclusion based on the + + align:start position:0% +very good conclusion based on the + + + align:start position:0% +very good conclusion based on the +different input from everyone. other + + align:start position:0% +different input from everyone. other + + + align:start position:0% +different input from everyone. other +reflections on process. + + align:start position:0% + + + + align:start position:0% + +Uh I guess it's not explicitly + + align:start position:0% +Uh I guess it's not explicitly + + + align:start position:0% +Uh I guess it's not explicitly +delineated, but we split up our we + + align:start position:0% +delineated, but we split up our we + + + align:start position:0% +delineated, but we split up our we +budgeted our time into three different + + align:start position:0% +budgeted our time into three different + + + align:start position:0% +budgeted our time into three different +sections. One was just anyone who just + + align:start position:0% +sections. One was just anyone who just + + + align:start position:0% +sections. One was just anyone who just +chimed in within their own uh answers + + align:start position:0% +chimed in within their own uh answers + + + align:start position:0% +chimed in within their own uh answers +supporting the case. Two was looking and + + align:start position:0% +supporting the case. Two was looking and + + + align:start position:0% +supporting the case. Two was looking and +anticipating rebuttals. Um and three was + + align:start position:0% +anticipating rebuttals. Um and three was + + + align:start position:0% +anticipating rebuttals. Um and three was +just writing it all in structure. + + align:start position:0% +just writing it all in structure. + + + align:start position:0% +just writing it all in structure. +Excellent. And did you come up with a + + align:start position:0% +Excellent. And did you come up with a + + + align:start position:0% +Excellent. And did you come up with a +written statement? Yeah, we did. + + align:start position:0% +written statement? Yeah, we did. + + + align:start position:0% +written statement? Yeah, we did. +Excellent. Excellent. + + align:start position:0% + + + + align:start position:0% + +How about your satisfaction with the + + align:start position:0% +How about your satisfaction with the + + + align:start position:0% +How about your satisfaction with the +team outcomes? + + align:start position:0% +team outcomes? + + + align:start position:0% +team outcomes? +Anybody uh unsatisfied or satisfied with + + align:start position:0% +Anybody uh unsatisfied or satisfied with + + + align:start position:0% +Anybody uh unsatisfied or satisfied with +the team outcome? + + align:start position:0% +the team outcome? + + + align:start position:0% +the team outcome? +I'm going to hazard to guess that on + + align:start position:0% +I'm going to hazard to guess that on + + + align:start position:0% +I'm going to hazard to guess that on +balance, people seem satisfied because + + align:start position:0% +balance, people seem satisfied because + + + align:start position:0% +balance, people seem satisfied because +there wasn't a lot of storming out of + + align:start position:0% +there wasn't a lot of storming out of + + + align:start position:0% +there wasn't a lot of storming out of +the room and yelling and shouting. But + + align:start position:0% +the room and yelling and shouting. But + + + align:start position:0% +the room and yelling and shouting. But +um if you had any complaints, however + + align:start position:0% +um if you had any complaints, however + + + align:start position:0% +um if you had any complaints, however +small, about your your team outcomes, if + + align:start position:0% +small, about your your team outcomes, if + + + align:start position:0% +small, about your your team outcomes, if +you wanted to voice that now. It was + + align:start position:0% +you wanted to voice that now. It was + + + align:start position:0% +you wanted to voice that now. It was +ironic. We were mice, but by the time + + align:start position:0% +ironic. We were mice, but by the time + + + align:start position:0% +ironic. We were mice, but by the time +you were done, we all pretty much agreed + + align:start position:0% +you were done, we all pretty much agreed + + + align:start position:0% +you were done, we all pretty much agreed +on the bird view. + + align:start position:0% +on the bird view. + + + align:start position:0% +on the bird view. +I think we started out with the bird + + align:start position:0% +I think we started out with the bird + + + align:start position:0% +I think we started out with the bird +view. We forced ourselves to figure out + + align:start position:0% +view. We forced ourselves to figure out + + + align:start position:0% +view. We forced ourselves to figure out +mice view and then we came back to + + align:start position:0% +mice view and then we came back to + + + align:start position:0% +mice view and then we came back to +because as soon as we started talking + + align:start position:0% +because as soon as we started talking + + + align:start position:0% +because as soon as we started talking +about the rebuttal, we realized + + align:start position:0% + + + + align:start position:0% + +which is why good debate teams work on + + align:start position:0% +which is why good debate teams work on + + + align:start position:0% +which is why good debate teams work on +their rebuttals a lot. Yeah. Okay. So + + align:start position:0% +their rebuttals a lot. Yeah. Okay. So + + + align:start position:0% +their rebuttals a lot. Yeah. Okay. So +let's use this exercise then to jump off + + align:start position:0% +let's use this exercise then to jump off + + + align:start position:0% +let's use this exercise then to jump off +into our last segment of slides here in + + align:start position:0% +into our last segment of slides here in + + + align:start position:0% +into our last segment of slides here in +people in our people module focusing on + + align:start position:0% +people in our people module focusing on + + + align:start position:0% +people in our people module focusing on +on team elements and team skills. And + + align:start position:0% +on team elements and team skills. And + + + align:start position:0% +on team elements and team skills. And +this chart is our transition to just + + align:start position:0% +this chart is our transition to just + + + align:start position:0% +this chart is our transition to just +remind us how people are the heart of + + align:start position:0% +remind us how people are the heart of + + + align:start position:0% +remind us how people are the heart of +lean because we have the tasks which are + + align:start position:0% +lean because we have the tasks which are + + + align:start position:0% +lean because we have the tasks which are +what the people are doing and you all + + align:start position:0% +what the people are doing and you all + + + align:start position:0% +what the people are doing and you all +just had a task in your exercise. Um the + + align:start position:0% +just had a task in your exercise. Um the + + + align:start position:0% +just had a task in your exercise. Um the +processes are how people are doing their + + align:start position:0% +processes are how people are doing their + + + align:start position:0% +processes are how people are doing their +tasks and we talked about what your + + align:start position:0% +tasks and we talked about what your + + + align:start position:0% +tasks and we talked about what your +process may or may not have been but + + align:start position:0% +process may or may not have been but + + + align:start position:0% +process may or may not have been but +it's all about the people. The people + + align:start position:0% +it's all about the people. The people + + + align:start position:0% +it's all about the people. The people +are doing the tasks. of people during + + align:start position:0% +are doing the tasks. of people during + + + align:start position:0% +are doing the tasks. of people during +the process and they set within various + + align:start position:0% +the process and they set within various + + + align:start position:0% +the process and they set within various +organization structures that are which + + align:start position:0% +organization structures that are which + + + align:start position:0% +organization structures that are which +enable them to do their processes and + + align:start position:0% +enable them to do their processes and + + + align:start position:0% +enable them to do their processes and +tasks and that's all embedded in a + + align:start position:0% +tasks and that's all embedded in a + + + align:start position:0% +tasks and that's all embedded in a +particular organization's culture which + + align:start position:0% +particular organization's culture which + + + align:start position:0% +particular organization's culture which +has uh attributes about it that further + + align:start position:0% +has uh attributes about it that further + + + align:start position:0% +has uh attributes about it that further +sort of influence and enable a person's + + align:start position:0% +sort of influence and enable a person's + + + align:start position:0% +sort of influence and enable a person's +ability to do their tasks and processes. + + align:start position:0% +ability to do their tasks and processes. + + + align:start position:0% +ability to do their tasks and processes. +Now many of the work that people do are + + align:start position:0% +Now many of the work that people do are + + + align:start position:0% +Now many of the work that people do are +in teams and they're collaborating and + + align:start position:0% +in teams and they're collaborating and + + + align:start position:0% +in teams and they're collaborating and +there's really three elements of + + align:start position:0% +there's really three elements of + + + align:start position:0% +there's really three elements of +collaboration. There's not just the + + align:start position:0% +collaboration. There's not just the + + + align:start position:0% +collaboration. There's not just the +thing you're doing, but there's how + + align:start position:0% +thing you're doing, but there's how + + + align:start position:0% +thing you're doing, but there's how +you're doing it. And then there's this + + align:start position:0% +you're doing it. And then there's this + + + align:start position:0% +you're doing it. And then there's this +thing we called affect, which is the + + align:start position:0% +thing we called affect, which is the + + + align:start position:0% +thing we called affect, which is the +feelings about the work. And this is + + align:start position:0% +feelings about the work. And this is + + + align:start position:0% +feelings about the work. And this is +what the people bring to it. And it's + + align:start position:0% +what the people bring to it. And it's + + + align:start position:0% +what the people bring to it. And it's +based on your prior experiences. It's + + align:start position:0% +based on your prior experiences. It's + + + align:start position:0% +based on your prior experiences. It's +based on the culture that you sit in, + + align:start position:0% +based on the culture that you sit in, + + + align:start position:0% +based on the culture that you sit in, +organizational, national, ethnic, etc. + + align:start position:0% +organizational, national, ethnic, etc. + + + align:start position:0% +organizational, national, ethnic, etc. +on your own biases that you bring to + + align:start position:0% +on your own biases that you bring to + + + align:start position:0% +on your own biases that you bring to +what you're doing. And it's also based + + align:start position:0% +what you're doing. And it's also based + + + align:start position:0% +what you're doing. And it's also based +on your current experience and where you + + align:start position:0% +on your current experience and where you + + + align:start position:0% +on your current experience and where you +are. And it's both the process as well + + align:start position:0% +are. And it's both the process as well + + + align:start position:0% +are. And it's both the process as well +as the feelings or the affect that are + + align:start position:0% +as the feelings or the affect that are + + + align:start position:0% +as the feelings or the affect that are +supporting the task actually getting + + align:start position:0% +supporting the task actually getting + + + align:start position:0% +supporting the task actually getting +done. When you're collaborating in teams + + align:start position:0% +done. When you're collaborating in teams + + + align:start position:0% +done. When you're collaborating in teams +and you're bringing all these elements + + align:start position:0% +and you're bringing all these elements + + + align:start position:0% +and you're bringing all these elements +together of process, task and affect + + align:start position:0% +together of process, task and affect + + + align:start position:0% +together of process, task and affect +there's a lot of benefits to + + align:start position:0% +there's a lot of benefits to + + + align:start position:0% +there's a lot of benefits to +collaboration. You get I think most of + + align:start position:0% +collaboration. You get I think most of + + + align:start position:0% +collaboration. You get I think most of +you would recognize these. You get more + + align:start position:0% +you would recognize these. You get more + + + align:start position:0% +you would recognize these. You get more +ideas, new ideas, multiple areas of + + align:start position:0% +ideas, new ideas, multiple areas of + + + align:start position:0% +ideas, new ideas, multiple areas of +expertise to bring to bear on the + + align:start position:0% +expertise to bring to bear on the + + + align:start position:0% +expertise to bring to bear on the +problem. Work is shared. It should + + align:start position:0% +problem. Work is shared. It should + + + align:start position:0% +problem. Work is shared. It should +result in some stronger problem solving + + align:start position:0% +result in some stronger problem solving + + + align:start position:0% +result in some stronger problem solving +abilities and should improve things like + + align:start position:0% +abilities and should improve things like + + + align:start position:0% +abilities and should improve things like +design work and other kind of creative + + align:start position:0% +design work and other kind of creative + + + align:start position:0% +design work and other kind of creative +tasks. But there's also a lot of + + align:start position:0% +tasks. But there's also a lot of + + + align:start position:0% +tasks. But there's also a lot of +challenges that are involved in + + align:start position:0% +challenges that are involved in + + + align:start position:0% +challenges that are involved in +collaborating with teams and I'm sure + + align:start position:0% +collaborating with teams and I'm sure + + + align:start position:0% +collaborating with teams and I'm sure +you've all run into some of those over + + align:start position:0% +you've all run into some of those over + + + align:start position:0% +you've all run into some of those over +the course of your school and work time. + + align:start position:0% +the course of your school and work time. + + + align:start position:0% +the course of your school and work time. +So what are some of the challenges you + + align:start position:0% +So what are some of the challenges you + + + align:start position:0% +So what are some of the challenges you +run into when you're trying to + + align:start position:0% +run into when you're trying to + + + align:start position:0% +run into when you're trying to +collaborate? + + align:start position:0% +collaborate? + + + align:start position:0% +collaborate? +The workload isn't shared. Not shared + + align:start position:0% +The workload isn't shared. Not shared + + + align:start position:0% +The workload isn't shared. Not shared +evenly in the workload. What else? I + + align:start position:0% +evenly in the workload. What else? I + + + align:start position:0% +evenly in the workload. What else? I +think d I think diversity can bring new + + align:start position:0% +think d I think diversity can bring new + + + align:start position:0% +think d I think diversity can bring new +ideas but if our group size was larger I + + align:start position:0% +ideas but if our group size was larger I + + + align:start position:0% +ideas but if our group size was larger I +mean it's hard to accommodate everyone's + + align:start position:0% +mean it's hard to accommodate everyone's + + + align:start position:0% +mean it's hard to accommodate everyone's +ideas. So somebody might do that oh my + + align:start position:0% +ideas. So somebody might do that oh my + + + align:start position:0% +ideas. So somebody might do that oh my +ideas and get into the process. So it + + align:start position:0% +ideas and get into the process. So it + + + align:start position:0% +ideas and get into the process. So it +can be inefficient and unwieldy. Yeah it + + align:start position:0% +can be inefficient and unwieldy. Yeah it + + + align:start position:0% +can be inefficient and unwieldy. Yeah it +takes time to develop and + + align:start position:0% +takes time to develop and + + + align:start position:0% +takes time to develop and +more time consuming. + + align:start position:0% + + + + align:start position:0% + +Yes. you're talking about how as we go + + align:start position:0% +Yes. you're talking about how as we go + + + align:start position:0% +Yes. you're talking about how as we go +in, people are um that we're working + + align:start position:0% +in, people are um that we're working + + + align:start position:0% +in, people are um that we're working +with may not be skilled, may not know + + align:start position:0% +with may not be skilled, may not know + + + align:start position:0% +with may not be skilled, may not know +how to work in this sort of model that + + align:start position:0% +how to work in this sort of model that + + + align:start position:0% +how to work in this sort of model that +they're used to just being told what to + + align:start position:0% +they're used to just being told what to + + + align:start position:0% +they're used to just being told what to +do. I see that on a micro level with + + align:start position:0% +do. I see that on a micro level with + + + align:start position:0% +do. I see that on a micro level with +patients, but also if you try and ask + + align:start position:0% +patients, but also if you try and ask + + + align:start position:0% +patients, but also if you try and ask +your um staff to, you know, be more of a + + align:start position:0% +your um staff to, you know, be more of a + + + align:start position:0% +your um staff to, you know, be more of a +contributor and be more responsible and + + align:start position:0% +contributor and be more responsible and + + + align:start position:0% +contributor and be more responsible and +also take on more credit, they they may + + align:start position:0% +also take on more credit, they they may + + + align:start position:0% +also take on more credit, they they may +be like, "What are you talking about? I + + align:start position:0% +be like, "What are you talking about? I + + + align:start position:0% +be like, "What are you talking about? I +punch in, I punch out. I'm not, you + + align:start position:0% +punch in, I punch out. I'm not, you + + + align:start position:0% +punch in, I punch out. I'm not, you +know, I'm not a member in that way." And + + align:start position:0% +know, I'm not a member in that way." And + + + align:start position:0% +know, I'm not a member in that way." And +so, we have to retrain them. Yeah. + + align:start position:0% +so, we have to retrain them. Yeah. + + + align:start position:0% +so, we have to retrain them. Yeah. +people just may not have the skills to + + align:start position:0% +people just may not have the skills to + + + align:start position:0% +people just may not have the skills to +collaborate in teams that they need + + align:start position:0% +collaborate in teams that they need + + + align:start position:0% +collaborate in teams that they need +either by training or just by + + align:start position:0% +either by training or just by + + + align:start position:0% +either by training or just by +expectations. Yeah, these are these are + + align:start position:0% +expectations. Yeah, these are these are + + + align:start position:0% +expectations. Yeah, these are these are +some of the common challenges. I'll just + + align:start position:0% +some of the common challenges. I'll just + + + align:start position:0% +some of the common challenges. I'll just +list for you on uh the rest of the slide + + align:start position:0% +list for you on uh the rest of the slide + + + align:start position:0% +list for you on uh the rest of the slide +ones that that we think are prominent as + + align:start position:0% +ones that that we think are prominent as + + + align:start position:0% +ones that that we think are prominent as +well. Different goals and values. We + + align:start position:0% +well. Different goals and values. We + + + align:start position:0% +well. Different goals and values. We +just talked about not being skilled in + + align:start position:0% +just talked about not being skilled in + + + align:start position:0% +just talked about not being skilled in +it or practiced in it. Sometimes you run + + align:start position:0% +it or practiced in it. Sometimes you run + + + align:start position:0% +it or practiced in it. Sometimes you run +into ego issues and people are defensive + + align:start position:0% +into ego issues and people are defensive + + + align:start position:0% +into ego issues and people are defensive +about their particular work or their + + align:start position:0% +about their particular work or their + + + align:start position:0% +about their particular work or their +ideas. There are preconceived notions + + align:start position:0% +ideas. There are preconceived notions + + + align:start position:0% +ideas. There are preconceived notions +that get in the way of teamwork. And + + align:start position:0% +that get in the way of teamwork. And + + + align:start position:0% +that get in the way of teamwork. And +then there's these differing work styles + + align:start position:0% +then there's these differing work styles + + + align:start position:0% +then there's these differing work styles +that you try to bring together in a team + + align:start position:0% +that you try to bring together in a team + + + align:start position:0% +that you try to bring together in a team +and that can be counterproductive to + + align:start position:0% +and that can be counterproductive to + + + align:start position:0% +and that can be counterproductive to +your efficiency. Or maybe somebody + + align:start position:0% +your efficiency. Or maybe somebody + + + align:start position:0% +your efficiency. Or maybe somebody +worked in a bad team situation before + + align:start position:0% +worked in a bad team situation before + + + align:start position:0% +worked in a bad team situation before +and that's just really hindering their + + align:start position:0% +and that's just really hindering their + + + align:start position:0% +and that's just really hindering their +ability to to work together productively + + align:start position:0% +ability to to work together productively + + + align:start position:0% +ability to to work together productively +in future teams. So then with all these + + align:start position:0% +in future teams. So then with all these + + + align:start position:0% +in future teams. So then with all these +challenges, how do you meet them? What + + align:start position:0% +challenges, how do you meet them? What + + + align:start position:0% +challenges, how do you meet them? What +are some of your thoughts? + + align:start position:0% +are some of your thoughts? + + + align:start position:0% +are some of your thoughts? +I think setting out ahead of time what + + align:start position:0% +I think setting out ahead of time what + + + align:start position:0% +I think setting out ahead of time what +the expectations of teamwork are and + + align:start position:0% +the expectations of teamwork are and + + + align:start position:0% +the expectations of teamwork are and +just kind of lay out for people how how + + align:start position:0% +just kind of lay out for people how how + + + align:start position:0% +just kind of lay out for people how how +do you work with a team like kind of the + + align:start position:0% +do you work with a team like kind of the + + + align:start position:0% +do you work with a team like kind of the +respect others listen first speak later + + align:start position:0% +respect others listen first speak later + + + align:start position:0% +respect others listen first speak later +things like that. Excellent. So clear + + align:start position:0% +things like that. Excellent. So clear + + + align:start position:0% +things like that. Excellent. So clear +rules and education. + + align:start position:0% +rules and education. + + + align:start position:0% +rules and education. +I think shared knowledge and shared + + align:start position:0% +I think shared knowledge and shared + + + align:start position:0% +I think shared knowledge and shared +goals can add a lot to the correlational + + align:start position:0% +goals can add a lot to the correlational + + + align:start position:0% +goals can add a lot to the correlational +coordination because these this is how + + align:start position:0% +coordination because these this is how + + + align:start position:0% +coordination because these this is how +you share your goals with others and try + + align:start position:0% +you share your goals with others and try + + + align:start position:0% +you share your goals with others and try +to convince them to came to the same + + align:start position:0% +to convince them to came to the same + + + align:start position:0% +to convince them to came to the same +conclusion otherwise I mean everyone + + align:start position:0% +conclusion otherwise I mean everyone + + + align:start position:0% +conclusion otherwise I mean everyone +believes that I have my own + + align:start position:0% +believes that I have my own + + + align:start position:0% +believes that I have my own +ideas okay + + align:start position:0% +ideas okay + + + align:start position:0% +ideas okay +something important the diagrams you + + align:start position:0% +something important the diagrams you + + + align:start position:0% +something important the diagrams you +always show about collaboration is + + align:start position:0% +always show about collaboration is + + + align:start position:0% +always show about collaboration is +always the puzzle pieces always fit + + align:start position:0% +always the puzzle pieces always fit + + + align:start position:0% +always the puzzle pieces always fit +perfectly which I think is a + + align:start position:0% +perfectly which I think is a + + + align:start position:0% +perfectly which I think is a +misrepresentation we have to accept that + + align:start position:0% +misrepresentation we have to accept that + + + align:start position:0% +misrepresentation we have to accept that +puzzle piece pieces won't fit perfectly. + + align:start position:0% +puzzle piece pieces won't fit perfectly. + + + align:start position:0% +puzzle piece pieces won't fit perfectly. +If there's someone who's going to make a + + align:start position:0% +If there's someone who's going to make a + + + align:start position:0% +If there's someone who's going to make a +decision in the end and if there is a + + align:start position:0% +decision in the end and if there is a + + + align:start position:0% +decision in the end and if there is a +culture of mutual respect, the person + + align:start position:0% +culture of mutual respect, the person + + + align:start position:0% +culture of mutual respect, the person +making decision will respect the people + + align:start position:0% +making decision will respect the people + + + align:start position:0% +making decision will respect the people +that brought in the suggestions and vice + + align:start position:0% +that brought in the suggestions and vice + + + align:start position:0% +that brought in the suggestions and vice +versa. And that's just the nature of + + align:start position:0% +versa. And that's just the nature of + + + align:start position:0% +versa. And that's just the nature of +life. + + align:start position:0% +life. + + + align:start position:0% +life. +Establishing that expectation is + + align:start position:0% +Establishing that expectation is + + + align:start position:0% +Establishing that expectation is +important. + + align:start position:0% +important. + + + align:start position:0% +important. +Yeah. like ongoing training. Starting + + align:start position:0% +Yeah. like ongoing training. Starting + + + align:start position:0% +Yeah. like ongoing training. Starting +off with something small that you can + + align:start position:0% +off with something small that you can + + + align:start position:0% +off with something small that you can +have an obvious um tangible result that + + align:start position:0% +have an obvious um tangible result that + + + align:start position:0% +have an obvious um tangible result that +in with guaranteed success so that they + + align:start position:0% +in with guaranteed success so that they + + + align:start position:0% +in with guaranteed success so that they +can learn the process and feel good + + align:start position:0% +can learn the process and feel good + + + align:start position:0% +can learn the process and feel good +about it and then keep continuously + + align:start position:0% +about it and then keep continuously + + + align:start position:0% +about it and then keep continuously +doing ongoing training over time + + align:start position:0% +doing ongoing training over time + + + align:start position:0% +doing ongoing training over time +to improve their ability to do it and + + align:start position:0% +to improve their ability to do it and + + + align:start position:0% +to improve their ability to do it and +remind them. + + align:start position:0% +remind them. + + + align:start position:0% +remind them. +Excellent. Again, really excellent + + align:start position:0% +Excellent. Again, really excellent + + + align:start position:0% +Excellent. Again, really excellent +ideas. Let me uh spell out some some + + align:start position:0% +ideas. Let me uh spell out some some + + + align:start position:0% +ideas. Let me uh spell out some some +others, some that are duplicate of what + + align:start position:0% +others, some that are duplicate of what + + + align:start position:0% +others, some that are duplicate of what +we just discussed and some which are + + align:start position:0% +we just discussed and some which are + + + align:start position:0% +we just discussed and some which are +new. So along the lines of trying to + + align:start position:0% +new. So along the lines of trying to + + + align:start position:0% +new. So along the lines of trying to +make it explicit and try to train people + + align:start position:0% +make it explicit and try to train people + + + align:start position:0% +make it explicit and try to train people +and set expectations, you may want to + + align:start position:0% +and set expectations, you may want to + + + align:start position:0% +and set expectations, you may want to +try to do those also in writing and not + + align:start position:0% +try to do those also in writing and not + + + align:start position:0% +try to do those also in writing and not +just verbally. Sometimes seeing things + + align:start position:0% +just verbally. Sometimes seeing things + + + align:start position:0% +just verbally. Sometimes seeing things +in writing can really help people + + align:start position:0% +in writing can really help people + + + align:start position:0% +in writing can really help people +understand what's going on. Uh + + align:start position:0% +understand what's going on. Uh + + + align:start position:0% +understand what's going on. Uh +considering alternate ideas or solutions + + align:start position:0% +considering alternate ideas or solutions + + + align:start position:0% +considering alternate ideas or solutions +and not jumping to consensus prematurely + + align:start position:0% +and not jumping to consensus prematurely + + + align:start position:0% +and not jumping to consensus prematurely +can be one way to meet the challenges of + + align:start position:0% +can be one way to meet the challenges of + + + align:start position:0% +can be one way to meet the challenges of +collaboration. Paying careful attention + + align:start position:0% +collaboration. Paying careful attention + + + align:start position:0% +collaboration. Paying careful attention +to process is really important. If + + align:start position:0% +to process is really important. If + + + align:start position:0% +to process is really important. If +people understand the process is very + + align:start position:0% +people understand the process is very + + + align:start position:0% +people understand the process is very +clear and very fair, then when they + + align:start position:0% +clear and very fair, then when they + + + align:start position:0% +clear and very fair, then when they +express opinions that are counter to + + align:start position:0% +express opinions that are counter to + + + align:start position:0% +express opinions that are counter to +what the rest of the group does want to + + align:start position:0% +what the rest of the group does want to + + + align:start position:0% +what the rest of the group does want to +do and the group goes in a different + + align:start position:0% +do and the group goes in a different + + + align:start position:0% +do and the group goes in a different +direction, at least that person has felt + + align:start position:0% +direction, at least that person has felt + + + align:start position:0% +direction, at least that person has felt +that they've had their due process and + + align:start position:0% +that they've had their due process and + + + align:start position:0% +that they've had their due process and +they haven't been shortch + + align:start position:0% +they haven't been shortch + + + align:start position:0% +they haven't been shortch +changed. The next point, voicing + + align:start position:0% +changed. The next point, voicing + + + align:start position:0% +changed. The next point, voicing +disagreements constructively, directly, + + align:start position:0% +disagreements constructively, directly, + + + align:start position:0% +disagreements constructively, directly, +and explicitly is really important + + align:start position:0% +and explicitly is really important + + + align:start position:0% +and explicitly is really important +because you're not all going to agree + + align:start position:0% +because you're not all going to agree + + + align:start position:0% +because you're not all going to agree +except for certain groups in this + + align:start position:0% +except for certain groups in this + + + align:start position:0% +except for certain groups in this +particular exercise where you've all + + align:start position:0% +particular exercise where you've all + + + align:start position:0% +particular exercise where you've all +coalesed on a certain point. But, you + + align:start position:0% +coalesed on a certain point. But, you + + + align:start position:0% +coalesed on a certain point. But, you +know, in your work environments, you're + + align:start position:0% +know, in your work environments, you're + + + align:start position:0% +know, in your work environments, you're +going to have times when you disagree. + + align:start position:0% +going to have times when you disagree. + + + align:start position:0% +going to have times when you disagree. +And learning how to do that productively + + align:start position:0% +And learning how to do that productively + + + align:start position:0% +And learning how to do that productively +so that you're focusing just on the + + align:start position:0% +so that you're focusing just on the + + + align:start position:0% +so that you're focusing just on the +disagreement and not on the person that + + align:start position:0% +disagreement and not on the person that + + + align:start position:0% +disagreement and not on the person that +you're having that disagreement with, + + align:start position:0% +you're having that disagreement with, + + + align:start position:0% +you're having that disagreement with, +will help you get to a solution more + + align:start position:0% +will help you get to a solution more + + + align:start position:0% +will help you get to a solution more +productively. Um, lastly, give positive + + align:start position:0% +productively. Um, lastly, give positive + + + align:start position:0% +productively. Um, lastly, give positive +feedback directly and explicitly too, + + align:start position:0% +feedback directly and explicitly too, + + + align:start position:0% +feedback directly and explicitly too, +right? So, how many times a day do you + + align:start position:0% +right? So, how many times a day do you + + + align:start position:0% +right? So, how many times a day do you +say to a colleague, "That was a great + + align:start position:0% +say to a colleague, "That was a great + + + align:start position:0% +say to a colleague, "That was a great +job." And then think of how many times + + align:start position:0% +job." And then think of how many times + + + align:start position:0% +job." And then think of how many times +you make critical comments about a peers + + align:start position:0% +you make critical comments about a peers + + + align:start position:0% +you make critical comments about a peers +or a colleague's work or suggestions for + + align:start position:0% +or a colleague's work or suggestions for + + + align:start position:0% +or a colleague's work or suggestions for +improvement. Especially at MIT, uh, we + + align:start position:0% +improvement. Especially at MIT, uh, we + + + align:start position:0% +improvement. Especially at MIT, uh, we +have a reputation for being a + + align:start position:0% +have a reputation for being a + + + align:start position:0% +have a reputation for being a +praise-free zone here. Lots of lots of + + align:start position:0% +praise-free zone here. Lots of lots of + + + align:start position:0% +praise-free zone here. Lots of lots of +criticism. Um, it's very important that + + align:start position:0% +criticism. Um, it's very important that + + + align:start position:0% +criticism. Um, it's very important that +you also reinforce the positives in + + align:start position:0% +you also reinforce the positives in + + + align:start position:0% +you also reinforce the positives in +collaboration because that's going to + + align:start position:0% +collaboration because that's going to + + + align:start position:0% +collaboration because that's going to +foster the team being able to work + + align:start position:0% +foster the team being able to work + + + align:start position:0% +foster the team being able to work +productively + + align:start position:0% + + + + align:start position:0% + +together. Now, in organizations, you're + + align:start position:0% +together. Now, in organizations, you're + + + align:start position:0% +together. Now, in organizations, you're +going to find many entities are + + align:start position:0% +going to find many entities are + + + align:start position:0% +going to find many entities are +organized in teams of various sorts. And + + align:start position:0% +organized in teams of various sorts. And + + + align:start position:0% +organized in teams of various sorts. And +this diagram helps orient you to some of + + align:start position:0% +this diagram helps orient you to some of + + + align:start position:0% +this diagram helps orient you to some of +the previous as well as current + + align:start position:0% +the previous as well as current + + + align:start position:0% +the previous as well as current +structures that we find in a lot of the + + align:start position:0% +structures that we find in a lot of the + + + align:start position:0% +structures that we find in a lot of the +uh complex engineering system kinds of + + align:start position:0% +uh complex engineering system kinds of + + + align:start position:0% +uh complex engineering system kinds of +of industries. Usually there's uh the + + align:start position:0% +of industries. Usually there's uh the + + + align:start position:0% +of industries. Usually there's uh the +organization is broken down + + align:start position:0% +organization is broken down + + + align:start position:0% +organization is broken down +functionally. You know there may be a + + align:start position:0% +functionally. You know there may be a + + + align:start position:0% +functionally. You know there may be a +design function, there may be an + + align:start position:0% +design function, there may be an + + + align:start position:0% +design function, there may be an +operations function, there may be a a + + align:start position:0% +operations function, there may be a a + + + align:start position:0% +operations function, there may be a a +maintenance function uh or it may be a + + align:start position:0% +maintenance function uh or it may be a + + + align:start position:0% +maintenance function uh or it may be a +structures function, a thermal function + + align:start position:0% +structures function, a thermal function + + + align:start position:0% +structures function, a thermal function +so on. And it used to be that groups + + align:start position:0% +so on. And it used to be that groups + + + align:start position:0% +so on. And it used to be that groups +worked independently and whenever you + + align:start position:0% +worked independently and whenever you + + + align:start position:0% +worked independently and whenever you +had to collaborate somehow between say + + align:start position:0% +had to collaborate somehow between say + + + align:start position:0% +had to collaborate somehow between say +function one and function two the + + align:start position:0% +function one and function two the + + + align:start position:0% +function one and function two the +interface took place between the top + + align:start position:0% +interface took place between the top + + + align:start position:0% +interface took place between the top +people but it was usually the folks down + + align:start position:0% +people but it was usually the folks down + + + align:start position:0% +people but it was usually the folks down +here who were doing all the work and + + align:start position:0% +here who were doing all the work and + + + align:start position:0% +here who were doing all the work and +needed the answers from these people but + + align:start position:0% +needed the answers from these people but + + + align:start position:0% +needed the answers from these people but +they had to work all the way up through + + align:start position:0% +they had to work all the way up through + + + align:start position:0% +they had to work all the way up through +their bosses to communicate with that + + align:start position:0% +their bosses to communicate with that + + + align:start position:0% +their bosses to communicate with that +person's boss to work all the way down + + align:start position:0% +person's boss to work all the way down + + + align:start position:0% +person's boss to work all the way down +through the chain. So that's kind of the + + align:start position:0% +through the chain. So that's kind of the + + + align:start position:0% +through the chain. So that's kind of the +old style the way organizations worked. + + align:start position:0% +old style the way organizations worked. + + + align:start position:0% +old style the way organizations worked. +And then back a couple decades ago, we + + align:start position:0% +And then back a couple decades ago, we + + + align:start position:0% +And then back a couple decades ago, we +introduced the concepts of integrated + + align:start position:0% +introduced the concepts of integrated + + + align:start position:0% +introduced the concepts of integrated +product and process teams, which really + + align:start position:0% +product and process teams, which really + + + align:start position:0% +product and process teams, which really +took essentially the folks doing the + + align:start position:0% +took essentially the folks doing the + + + align:start position:0% +took essentially the folks doing the +work down here and put them into a team + + align:start position:0% +work down here and put them into a team + + + align:start position:0% +work down here and put them into a team +so that the communication could happen + + align:start position:0% +so that the communication could happen + + + align:start position:0% +so that the communication could happen +directly between people who are doing + + align:start position:0% +directly between people who are doing + + + align:start position:0% +directly between people who are doing +the tasks and not really up and down a + + align:start position:0% +the tasks and not really up and down a + + + align:start position:0% +the tasks and not really up and down a +chain of communications where it really + + align:start position:0% +chain of communications where it really + + + align:start position:0% +chain of communications where it really +didn't matter that this person knew what + + align:start position:0% +didn't matter that this person knew what + + + align:start position:0% +didn't matter that this person knew what +the question was that they were asking, + + align:start position:0% +the question was that they were asking, + + + align:start position:0% +the question was that they were asking, +had to pass it along. They were just + + align:start position:0% +had to pass it along. They were just + + + align:start position:0% +had to pass it along. They were just +relaying it. It's much better if you can + + align:start position:0% +relaying it. It's much better if you can + + + align:start position:0% +relaying it. It's much better if you can +have direct interaction between people. + + align:start position:0% +have direct interaction between people. + + + align:start position:0% +have direct interaction between people. +So this kind of an organization + + align:start position:0% +So this kind of an organization + + + align:start position:0% +So this kind of an organization +structure has helped uh increase the + + align:start position:0% +structure has helped uh increase the + + + align:start position:0% +structure has helped uh increase the +effective communications and the ability + + align:start position:0% +effective communications and the ability + + + align:start position:0% +effective communications and the ability +for uh teams to work together in these + + align:start position:0% +for uh teams to work together in these + + + align:start position:0% +for uh teams to work together in these +complex enterprises that we see today. + + align:start position:0% +complex enterprises that we see today. + + + align:start position:0% +complex enterprises that we see today. +But being on an IP or IPT, you're now + + align:start position:0% +But being on an IP or IPT, you're now + + + align:start position:0% +But being on an IP or IPT, you're now +asking people who are in this part of + + align:start position:0% +asking people who are in this part of + + + align:start position:0% +asking people who are in this part of +the + + align:start position:0% +the + + + align:start position:0% +the +organization to have teamwork and + + align:start position:0% +organization to have teamwork and + + + align:start position:0% +organization to have teamwork and +leadership skills that they might not + + align:start position:0% +leadership skills that they might not + + + align:start position:0% +leadership skills that they might not +have needed to have in our old kind of + + align:start position:0% +have needed to have in our old kind of + + + align:start position:0% +have needed to have in our old kind of +organization where the leadership was + + align:start position:0% +organization where the leadership was + + + align:start position:0% +organization where the leadership was +largely done at the top. So this helps + + align:start position:0% +largely done at the top. So this helps + + + align:start position:0% +largely done at the top. So this helps +us understand why introducing the + + align:start position:0% +us understand why introducing the + + + align:start position:0% +us understand why introducing the +concepts of teamwork and leadership and + + align:start position:0% +concepts of teamwork and leadership and + + + align:start position:0% +concepts of teamwork and leadership and +developing skills around those is really + + align:start position:0% +developing skills around those is really + + + align:start position:0% +developing skills around those is really +important to do really from day one when + + align:start position:0% +important to do really from day one when + + + align:start position:0% +important to do really from day one when +you join an organization and not waiting + + align:start position:0% +you join an organization and not waiting + + + align:start position:0% +you join an organization and not waiting +until you get to be at the top of that + + align:start position:0% +until you get to be at the top of that + + + align:start position:0% +until you get to be at the top of that +org chart. + + align:start position:0% +org chart. + + + align:start position:0% +org chart. +Now teams progress through a number of + + align:start position:0% +Now teams progress through a number of + + + align:start position:0% +Now teams progress through a number of +different stages and there's a lot of + + align:start position:0% +different stages and there's a lot of + + + align:start position:0% +different stages and there's a lot of +literature about this but in essence you + + align:start position:0% +literature about this but in essence you + + + align:start position:0% +literature about this but in essence you +know when you first start out with a + + align:start position:0% +know when you first start out with a + + + align:start position:0% +know when you first start out with a +team there's a lot of challenges we've + + align:start position:0% +team there's a lot of challenges we've + + + align:start position:0% +team there's a lot of challenges we've +just discussed in working together and + + align:start position:0% +just discussed in working together and + + + align:start position:0% +just discussed in working together and +teams take a little while to grow from + + align:start position:0% +teams take a little while to grow from + + + align:start position:0% +teams take a little while to grow from +beginning teams to what we'd really call + + align:start position:0% +beginning teams to what we'd really call + + + align:start position:0% +beginning teams to what we'd really call +high performance ones and the degree of + + align:start position:0% +high performance ones and the degree of + + + align:start position:0% +high performance ones and the degree of +management necessary for those decreases + + align:start position:0% +management necessary for those decreases + + + align:start position:0% +management necessary for those decreases +over time as we get towards a more high + + align:start position:0% +over time as we get towards a more high + + + align:start position:0% +over time as we get towards a more high +performing team and their empowerment + + align:start position:0% +performing team and their empowerment + + + align:start position:0% +performing team and their empowerment +and ability to do things increases as + + align:start position:0% +and ability to do things increases as + + + align:start position:0% +and ability to do things increases as +well. We find that when we look at high + + align:start position:0% +well. We find that when we look at high + + + align:start position:0% +well. We find that when we look at high +performing teams in a lean environment, + + align:start position:0% +performing teams in a lean environment, + + + align:start position:0% +performing teams in a lean environment, +they have these attributes about them + + align:start position:0% +they have these attributes about them + + + align:start position:0% +they have these attributes about them +and we've mentioned most of them so far. + + align:start position:0% +and we've mentioned most of them so far. + + + align:start position:0% +and we've mentioned most of them so far. +They have mutual respect for all people + + align:start position:0% +They have mutual respect for all people + + + align:start position:0% +They have mutual respect for all people +and all jobs. They encourage + + align:start position:0% +and all jobs. They encourage + + + align:start position:0% +and all jobs. They encourage +contribution by all the team members. We + + align:start position:0% +contribution by all the team members. We + + + align:start position:0% +contribution by all the team members. We +heard Clauddio talk about that in our + + align:start position:0% +heard Clauddio talk about that in our + + + align:start position:0% +heard Clauddio talk about that in our +tour today. Different opinions are not + + align:start position:0% +tour today. Different opinions are not + + + align:start position:0% +tour today. Different opinions are not +only valued, but they're sought after + + align:start position:0% +only valued, but they're sought after + + + align:start position:0% +only valued, but they're sought after +and brought out. There's open and honest + + align:start position:0% +and brought out. There's open and honest + + + align:start position:0% +and brought out. There's open and honest +communication and feedback. The goals of + + align:start position:0% +communication and feedback. The goals of + + + align:start position:0% +communication and feedback. The goals of +the team are aligned. + + align:start position:0% +the team are aligned. + + + align:start position:0% +the team are aligned. +There's continuous improvement of both + + align:start position:0% +There's continuous improvement of both + + + align:start position:0% +There's continuous improvement of both +the individuals and the team, always + + align:start position:0% +the individuals and the team, always + + + align:start position:0% +the individuals and the team, always +seeking to do a better job. And there's + + align:start position:0% +seeking to do a better job. And there's + + + align:start position:0% +seeking to do a better job. And there's +a high degree of synergy and cooperation + + align:start position:0% +a high degree of synergy and cooperation + + + align:start position:0% +a high degree of synergy and cooperation +among the members. So if you're striving + + align:start position:0% +among the members. So if you're striving + + + align:start position:0% +among the members. So if you're striving +to put together a team that is high + + align:start position:0% +to put together a team that is high + + + align:start position:0% +to put together a team that is high +performing, you're really trying to work + + align:start position:0% +performing, you're really trying to work + + + align:start position:0% +performing, you're really trying to work +on these seven particular attributes and + + align:start position:0% +on these seven particular attributes and + + + align:start position:0% +on these seven particular attributes and +trying to increase those for your + + align:start position:0% +trying to increase those for your + + + align:start position:0% +trying to increase those for your +team. So lastly, we'll just conclude + + align:start position:0% +team. So lastly, we'll just conclude + + + align:start position:0% +team. So lastly, we'll just conclude +with our chart here. People are the + + align:start position:0% +with our chart here. People are the + + + align:start position:0% +with our chart here. People are the +heart of + + align:start position:0% +heart of + + + align:start position:0% +heart of +lean with our shared goals, our shared + + align:start position:0% +lean with our shared goals, our shared + + + align:start position:0% +lean with our shared goals, our shared +knowledge, mutual respect, + + align:start position:0% +knowledge, mutual respect, + + + align:start position:0% +knowledge, mutual respect, +communication, teamwork, and leadership. + + align:start position:0% +communication, teamwork, and leadership. + + + align:start position:0% +communication, teamwork, and leadership. +All the hallmarks of a high-erforming + + align:start position:0% +All the hallmarks of a high-erforming + + + align:start position:0% +All the hallmarks of a high-erforming +lean + + align:start position:0% +lean + + + align:start position:0% +lean +team. And by way of summary, from what + + align:start position:0% +team. And by way of summary, from what + + + align:start position:0% +team. And by way of summary, from what +you've just heard over the past module + + align:start position:0% +you've just heard over the past module + + + align:start position:0% +you've just heard over the past module +on people, I'd like you to take out one + + align:start position:0% +on people, I'd like you to take out one + + + align:start position:0% +on people, I'd like you to take out one +of your white index cards and take out a + + align:start position:0% +of your white index cards and take out a + + + align:start position:0% +of your white index cards and take out a +pen and write down for us what's the + + align:start position:0% +pen and write down for us what's the + + + align:start position:0% +pen and write down for us what's the +most important thing you learned from + + align:start position:0% +most important thing you learned from + + + align:start position:0% +most important thing you learned from +this module on + + align:start position:0% +this module on + + + align:start position:0% +this module on +people. And on your way out to the + + align:start position:0% +people. And on your way out to the + + + align:start position:0% +people. And on your way out to the +break, you can drop that on the back + + align:start position:0% +break, you can drop that on the back + + + align:start position:0% +break, you can drop that on the back +desk so we can take a look. \ No newline at end of file diff --git a/uXt8qF2Zzfo.txt b/uXt8qF2Zzfo.txt new file mode 100644 index 0000000000000000000000000000000000000000..7bc41885bf10580dcb91812f722d6a6308658b08 --- /dev/null +++ b/uXt8qF2Zzfo.txt @@ -0,0 +1,8787 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +It was um in 2010. Yes, that's right. It + + align:start position:0% +It was um in 2010. Yes, that's right. It + + + align:start position:0% +It was um in 2010. Yes, that's right. It +was in + + align:start position:0% +was in + + + align:start position:0% +was in +2010. We were having our annual + + align:start position:0% +2010. We were having our annual + + + align:start position:0% +2010. We were having our annual +discussion about what we would dump from + + align:start position:0% +discussion about what we would dump from + + + align:start position:0% +discussion about what we would dump from +6034 in order to make room for some + + align:start position:0% +6034 in order to make room for some + + + align:start position:0% +6034 in order to make room for some +other stuff. And we almost killed off + + align:start position:0% +other stuff. And we almost killed off + + + align:start position:0% +other stuff. And we almost killed off +neural nets. + + align:start position:0% +neural nets. + + + align:start position:0% +neural nets. +Now that might seem strange because um + + align:start position:0% +Now that might seem strange because um + + + align:start position:0% +Now that might seem strange because um +you know our heads are stuffed with + + align:start position:0% +you know our heads are stuffed with + + + align:start position:0% +you know our heads are stuffed with +neurons. If you open up your skull and + + align:start position:0% +neurons. If you open up your skull and + + + align:start position:0% +neurons. If you open up your skull and +pluck them all out, you don't think + + align:start position:0% +pluck them all out, you don't think + + + align:start position:0% +pluck them all out, you don't think +anymore. So it would seem that um neural + + align:start position:0% +anymore. So it would seem that um neural + + + align:start position:0% +anymore. So it would seem that um neural +nets uh would + + align:start position:0% +nets uh would + + + align:start position:0% +nets uh would +be a fundamental and unassalable topic. + + align:start position:0% +be a fundamental and unassalable topic. + + + align:start position:0% +be a fundamental and unassalable topic. +But many of us felt that the uh neural + + align:start position:0% +But many of us felt that the uh neural + + + align:start position:0% +But many of us felt that the uh neural +models of the day weren't much + + align:start position:0% +models of the day weren't much + + + align:start position:0% +models of the day weren't much +um in the way of + + align:start position:0% +um in the way of + + + align:start position:0% +um in the way of +um faithful models of what actually goes + + align:start position:0% +um faithful models of what actually goes + + + align:start position:0% +um faithful models of what actually goes +in inside our heads. And besides that, + + align:start position:0% +in inside our heads. And besides that, + + + align:start position:0% +in inside our heads. And besides that, +nobody had ever made a neural net that + + align:start position:0% +nobody had ever made a neural net that + + + align:start position:0% +nobody had ever made a neural net that +was worth darn for doing anything. So, + + align:start position:0% +was worth darn for doing anything. So, + + + align:start position:0% +was worth darn for doing anything. So, +um we almost killed it off. But then we + + align:start position:0% +um we almost killed it off. But then we + + + align:start position:0% +um we almost killed it off. But then we +said, well, the everybody will feel + + align:start position:0% +said, well, the everybody will feel + + + align:start position:0% +said, well, the everybody will feel +cheated if they take a course in + + align:start position:0% +cheated if they take a course in + + + align:start position:0% +cheated if they take a course in +artificial intelligence, don't learn + + align:start position:0% +artificial intelligence, don't learn + + + align:start position:0% +artificial intelligence, don't learn +anything about neural nets, and then + + align:start position:0% +anything about neural nets, and then + + + align:start position:0% +anything about neural nets, and then +they'll go off and invent them + + align:start position:0% +they'll go off and invent them + + + align:start position:0% +they'll go off and invent them +themselves and waste all sorts of time. + + align:start position:0% +themselves and waste all sorts of time. + + + align:start position:0% +themselves and waste all sorts of time. +So, we kept the subject in. Uh, then two + + align:start position:0% +So, we kept the subject in. Uh, then two + + + align:start position:0% +So, we kept the subject in. Uh, then two +years + + align:start position:0% +years + + + align:start position:0% +years +later, Jeff Hinton from the University + + align:start position:0% +later, Jeff Hinton from the University + + + align:start position:0% +later, Jeff Hinton from the University +of + + align:start position:0% +of + + + align:start position:0% +of +Toronto stunned the world uh with some + + align:start position:0% +Toronto stunned the world uh with some + + + align:start position:0% +Toronto stunned the world uh with some +real net work he had done on recognizing + + align:start position:0% +real net work he had done on recognizing + + + align:start position:0% +real net work he had done on recognizing +and classifying pictures. and he + + align:start position:0% +and classifying pictures. and he + + + align:start position:0% +and classifying pictures. and he +published a paper from which I am now + + align:start position:0% +published a paper from which I am now + + + align:start position:0% +published a paper from which I am now +going to show you a couple of + + align:start position:0% +going to show you a couple of + + + align:start position:0% +going to show you a couple of +examples. Uh Jeff's neural net by the + + align:start position:0% +examples. Uh Jeff's neural net by the + + + align:start position:0% +examples. Uh Jeff's neural net by the +way had 60 million parameters in it and + + align:start position:0% +way had 60 million parameters in it and + + + align:start position:0% +way had 60 million parameters in it and +it was its purpose was to determine + + align:start position:0% +it was its purpose was to determine + + + align:start position:0% +it was its purpose was to determine +which of a thousand + + align:start position:0% +which of a thousand + + + align:start position:0% +which of a thousand +categories best characterized a + + align:start position:0% + + + + align:start position:0% + +picture. So there it is. There's a + + align:start position:0% +picture. So there it is. There's a + + + align:start position:0% +picture. So there it is. There's a +sample of things that + + align:start position:0% + + + + align:start position:0% + +um the Toronto neural net uh was able to + + align:start position:0% +um the Toronto neural net uh was able to + + + align:start position:0% +um the Toronto neural net uh was able to +uh recognize or make mistakes on. I'm + + align:start position:0% +uh recognize or make mistakes on. I'm + + + align:start position:0% +uh recognize or make mistakes on. I'm +going to blow that up a little bit. I + + align:start position:0% +going to blow that up a little bit. I + + + align:start position:0% +going to blow that up a little bit. I +think I'm going to look particularly at + + align:start position:0% +think I'm going to look particularly at + + + align:start position:0% +think I'm going to look particularly at +the uh example there labeled + + align:start position:0% +the uh example there labeled + + + align:start position:0% +the uh example there labeled +containership. + + align:start position:0% +containership. + + + align:start position:0% +containership. +So what you see here is that the uh + + align:start position:0% +So what you see here is that the uh + + + align:start position:0% +So what you see here is that the uh +program returned its best estimate of + + align:start position:0% +program returned its best estimate of + + + align:start position:0% +program returned its best estimate of +what it was ranked first five according + + align:start position:0% +what it was ranked first five according + + + align:start position:0% +what it was ranked first five according +to the likelihood of probability or the + + align:start position:0% +to the likelihood of probability or the + + + align:start position:0% +to the likelihood of probability or the +certainty that it felt that a + + align:start position:0% +certainty that it felt that a + + + align:start position:0% +certainty that it felt that a +particular class was characteristic of + + align:start position:0% +particular class was characteristic of + + + align:start position:0% +particular class was characteristic of +the picture. And so you can see this one + + align:start position:0% +the picture. And so you can see this one + + + align:start position:0% +the picture. And so you can see this one +is extremely confident that it's a + + align:start position:0% +is extremely confident that it's a + + + align:start position:0% +is extremely confident that it's a +container + + align:start position:0% +container + + + align:start position:0% +container +ship. It also was uh fairly u moved by + + align:start position:0% +ship. It also was uh fairly u moved by + + + align:start position:0% +ship. It also was uh fairly u moved by +the idea that might be a lifeboat. + + align:start position:0% +the idea that might be a lifeboat. + + + align:start position:0% +the idea that might be a lifeboat. +Now, I'm not sure about you, but I don't + + align:start position:0% +Now, I'm not sure about you, but I don't + + + align:start position:0% +Now, I'm not sure about you, but I don't +think this looks much like a lifeboat, + + align:start position:0% +think this looks much like a lifeboat, + + + align:start position:0% +think this looks much like a lifeboat, +but it does look like a container ship. + + align:start position:0% +but it does look like a container ship. + + + align:start position:0% +but it does look like a container ship. +So, if I look at only the best choice, + + align:start position:0% +So, if I look at only the best choice, + + + align:start position:0% +So, if I look at only the best choice, +it looks pretty good. Here are the other + + align:start position:0% +it looks pretty good. Here are the other + + + align:start position:0% +it looks pretty good. Here are the other +things that it did pretty well on. Got + + align:start position:0% +things that it did pretty well on. Got + + + align:start position:0% +things that it did pretty well on. Got +the right answer as the first choice is + + align:start position:0% +the right answer as the first choice is + + + align:start position:0% +the right answer as the first choice is +this first + + align:start position:0% +this first + + + align:start position:0% +this first +choice. So, over on the left, you see + + align:start position:0% +choice. So, over on the left, you see + + + align:start position:0% +choice. So, over on the left, you see +that it's decided that the picture is a + + align:start position:0% +that it's decided that the picture is a + + + align:start position:0% +that it's decided that the picture is a +picture of a might. Uh the might is not + + align:start position:0% +picture of a might. Uh the might is not + + + align:start position:0% +picture of a might. Uh the might is not +anywhere near the center of the picture, + + align:start position:0% +anywhere near the center of the picture, + + + align:start position:0% +anywhere near the center of the picture, +but somehow it managed to find it. The + + align:start position:0% +but somehow it managed to find it. The + + + align:start position:0% +but somehow it managed to find it. The +container ship. Again, there's a motor + + align:start position:0% +container ship. Again, there's a motor + + + align:start position:0% +container ship. Again, there's a motor +scooter, couple people sitting on it, + + align:start position:0% +scooter, couple people sitting on it, + + + align:start position:0% +scooter, couple people sitting on it, +but it correctly characterized the + + align:start position:0% +but it correctly characterized the + + + align:start position:0% +but it correctly characterized the +picture as a motor scooter. And then on + + align:start position:0% +picture as a motor scooter. And then on + + + align:start position:0% +picture as a motor scooter. And then on +the right, a leopard, and everything + + align:start position:0% +the right, a leopard, and everything + + + align:start position:0% +the right, a leopard, and everything +else is a cat of some sort. So, it seems + + align:start position:0% +else is a cat of some sort. So, it seems + + + align:start position:0% +else is a cat of some sort. So, it seems +to be doing pretty well. In fact, it + + align:start position:0% +to be doing pretty well. In fact, it + + + align:start position:0% +to be doing pretty well. In fact, it +does do pretty well. But anyone who uh + + align:start position:0% +does do pretty well. But anyone who uh + + + align:start position:0% +does do pretty well. But anyone who uh +does this kind of work has an obligation + + align:start position:0% +does this kind of work has an obligation + + + align:start position:0% +does this kind of work has an obligation +to show you some of the stuff it doesn't + + align:start position:0% +to show you some of the stuff it doesn't + + + align:start position:0% +to show you some of the stuff it doesn't +work so well on or doesn't get quite + + align:start position:0% +work so well on or doesn't get quite + + + align:start position:0% +work so well on or doesn't get quite +right. And so, these pictures also + + align:start position:0% +right. And so, these pictures also + + + align:start position:0% +right. And so, these pictures also +occurred in Hinton's paper. + + align:start position:0% +occurred in Hinton's paper. + + + align:start position:0% +occurred in Hinton's paper. +So the first one is characterized as a + + align:start position:0% +So the first one is characterized as a + + + align:start position:0% +So the first one is characterized as a +grill but the right answer was supposed + + align:start position:0% +grill but the right answer was supposed + + + align:start position:0% +grill but the right answer was supposed +to be convertible. Oh no. Yes. Yeah. + + align:start position:0% +to be convertible. Oh no. Yes. Yeah. + + + align:start position:0% +to be convertible. Oh no. Yes. Yeah. +Right answer was + + align:start position:0% +Right answer was + + + align:start position:0% +Right answer was +convertible. In the second case um the + + align:start position:0% +convertible. In the second case um the + + + align:start position:0% +convertible. In the second case um the +characterization is of a mushroom and + + align:start position:0% +characterization is of a mushroom and + + + align:start position:0% +characterization is of a mushroom and +the alleged right answer is agaric. Is + + align:start position:0% +the alleged right answer is agaric. Is + + + align:start position:0% +the alleged right answer is agaric. Is +that pronounced right? It turns out + + align:start position:0% +that pronounced right? It turns out + + + align:start position:0% +that pronounced right? It turns out +that's a kind of mushroom. So no problem + + align:start position:0% +that's a kind of mushroom. So no problem + + + align:start position:0% +that's a kind of mushroom. So no problem +there. In the next case it said it was a + + align:start position:0% +there. In the next case it said it was a + + + align:start position:0% +there. In the next case it said it was a +cherry but it was supposed to be a + + align:start position:0% +cherry but it was supposed to be a + + + align:start position:0% +cherry but it was supposed to be a +dalmatian. Now, I think a dalmatation is + + align:start position:0% +dalmatian. Now, I think a dalmatation is + + + align:start position:0% +dalmatian. Now, I think a dalmatation is +a perfectly legitimate answer for that + + align:start position:0% +a perfectly legitimate answer for that + + + align:start position:0% +a perfectly legitimate answer for that +particular picture. So, hard to fault it + + align:start position:0% +particular picture. So, hard to fault it + + + align:start position:0% +particular picture. So, hard to fault it +for that. And in the last case, it + + align:start position:0% +for that. And in the last case, it + + + align:start position:0% +for that. And in the last case, it +didn't, you know, the the correct answer + + align:start position:0% +didn't, you know, the the correct answer + + + align:start position:0% +didn't, you know, the the correct answer +was not in any of the top + + align:start position:0% +was not in any of the top + + + align:start position:0% +was not in any of the top +five. I I'm not sure if you've ever seen + + align:start position:0% +five. I I'm not sure if you've ever seen + + + align:start position:0% +five. I I'm not sure if you've ever seen +a Madagascar cat, but that's a picture + + align:start position:0% +a Madagascar cat, but that's a picture + + + align:start position:0% +a Madagascar cat, but that's a picture +of one. And it's interesting to compare + + align:start position:0% +of one. And it's interesting to compare + + + align:start position:0% +of one. And it's interesting to compare +that with the uh first choice of the + + align:start position:0% +that with the uh first choice of the + + + align:start position:0% +that with the uh first choice of the +program, squirrel monkey. This is the + + align:start position:0% +program, squirrel monkey. This is the + + + align:start position:0% +program, squirrel monkey. This is the +two side by side. + + align:start position:0% +two side by side. + + + align:start position:0% +two side by side. +So, in a way, it's not surprising that + + align:start position:0% +So, in a way, it's not surprising that + + + align:start position:0% +So, in a way, it's not surprising that +it thought that the Madagascar cat was a + + align:start position:0% +it thought that the Madagascar cat was a + + + align:start position:0% +it thought that the Madagascar cat was a +picture of a squirrel monkey. So, pretty + + align:start position:0% +picture of a squirrel monkey. So, pretty + + + align:start position:0% +picture of a squirrel monkey. So, pretty +impressive. It blew away the + + align:start position:0% +impressive. It blew away the + + + align:start position:0% +impressive. It blew away the +competition. It did so much better that + + align:start position:0% +competition. It did so much better that + + + align:start position:0% +competition. It did so much better that +second place wasn't even close. And for + + align:start position:0% +second place wasn't even close. And for + + + align:start position:0% +second place wasn't even close. And for +the first time, demonstrated that a + + align:start position:0% +the first time, demonstrated that a + + + align:start position:0% +the first time, demonstrated that a +neural net could actually do something. + + align:start position:0% +neural net could actually do something. + + + align:start position:0% +neural net could actually do something. +And since that time, in the three years + + align:start position:0% +And since that time, in the three years + + + align:start position:0% +And since that time, in the three years +since that time, there's been an + + align:start position:0% +since that time, there's been an + + + align:start position:0% +since that time, there's been an +enormous amount of effort put into + + align:start position:0% +enormous amount of effort put into + + + align:start position:0% +enormous amount of effort put into +neural net technology, which some say is + + align:start position:0% +neural net technology, which some say is + + + align:start position:0% +neural net technology, which some say is +the answer. + + align:start position:0% +the answer. + + + align:start position:0% +the answer. +So what we're going to do today and uh + + align:start position:0% +So what we're going to do today and uh + + + align:start position:0% +So what we're going to do today and uh +tomorrow uh is have a look at this stuff + + align:start position:0% +tomorrow uh is have a look at this stuff + + + align:start position:0% +tomorrow uh is have a look at this stuff +and uh ask ourselves why it works when + + align:start position:0% +and uh ask ourselves why it works when + + + align:start position:0% +and uh ask ourselves why it works when +it might not work what needs to be done + + align:start position:0% +it might not work what needs to be done + + + align:start position:0% +it might not work what needs to be done +what has been done and all those kinds + + align:start position:0% +what has been done and all those kinds + + + align:start position:0% +what has been done and all those kinds +of questions will + + align:start position:0% + + + + align:start position:0% + +emerge. + + align:start position:0% +emerge. + + + align:start position:0% +emerge. +So I guess the first thing to do is + + align:start position:0% +So I guess the first thing to do is + + + align:start position:0% +So I guess the first thing to do is +think about what it is that we are being + + align:start position:0% +think about what it is that we are being + + + align:start position:0% +think about what it is that we are being +inspired by. uh we're being inspired by + + align:start position:0% +inspired by. uh we're being inspired by + + + align:start position:0% +inspired by. uh we're being inspired by +those things that are growing that are + + align:start position:0% +those things that are growing that are + + + align:start position:0% +those things that are growing that are +inside our head all 10 to the 11th of + + align:start position:0% +inside our head all 10 to the 11th of + + + align:start position:0% +inside our head all 10 to the 11th of +them. And so if we take one of those 10 + + align:start position:0% +them. And so if we take one of those 10 + + + align:start position:0% +them. And so if we take one of those 10 +to the 11th and look at it + + align:start position:0% +to the 11th and look at it + + + align:start position:0% +to the 11th and look at it +uh you know from uh 70 something or + + align:start position:0% +uh you know from uh 70 something or + + + align:start position:0% +uh you know from uh 70 something or +other approximately what a neuron looks + + align:start position:0% +other approximately what a neuron looks + + + align:start position:0% +other approximately what a neuron looks +like. And by the way I'm going to teach + + align:start position:0% +like. And by the way I'm going to teach + + + align:start position:0% +like. And by the way I'm going to teach +you uh in this lecture how to answer + + align:start position:0% +you uh in this lecture how to answer + + + align:start position:0% +you uh in this lecture how to answer +questions about neurobiology with an 80% + + align:start position:0% +questions about neurobiology with an 80% + + + align:start position:0% +questions about neurobiology with an 80% +probability that you will give the same + + align:start position:0% +probability that you will give the same + + + align:start position:0% +probability that you will give the same +answer as a neurobiologist. Okay. So + + align:start position:0% +answer as a neurobiologist. Okay. So + + + align:start position:0% +answer as a neurobiologist. Okay. So +let's go. + + align:start position:0% +let's go. + + + align:start position:0% +let's go. +So, here's a a neuron. It's got a cell + + align:start position:0% +So, here's a a neuron. It's got a cell + + + align:start position:0% +So, here's a a neuron. It's got a cell +body. In there is a nucleus. And then + + align:start position:0% +body. In there is a nucleus. And then + + + align:start position:0% +body. In there is a nucleus. And then +out here is a long thing which + + align:start position:0% +out here is a long thing which + + + align:start position:0% +out here is a long thing which +divides maybe a little bit but not much. + + align:start position:0% +divides maybe a little bit but not much. + + + align:start position:0% +divides maybe a little bit but not much. +And we call that the + + align:start position:0% + + + + align:start position:0% + +axon. So then over here we got this uh + + align:start position:0% +axon. So then over here we got this uh + + + align:start position:0% +axon. So then over here we got this uh +much more branching type of structure + + align:start position:0% +much more branching type of structure + + + align:start position:0% +much more branching type of structure +that looks maybe a little bit like so. + + align:start position:0% + + + + align:start position:0% + +I don't know, maybe like that. And this + + align:start position:0% +I don't know, maybe like that. And this + + + align:start position:0% +I don't know, maybe like that. And this +stuff branches a whole lot. And that + + align:start position:0% +stuff branches a whole lot. And that + + + align:start position:0% +stuff branches a whole lot. And that +part is called the dendritic + + align:start position:0% + + + + align:start position:0% + +tree. Now, uh there are a couple of + + align:start position:0% +tree. Now, uh there are a couple of + + + align:start position:0% +tree. Now, uh there are a couple of +things we can uh note about this is that + + align:start position:0% +things we can uh note about this is that + + + align:start position:0% +things we can uh note about this is that +these guys are connected axon to + + align:start position:0% +these guys are connected axon to + + + align:start position:0% +these guys are connected axon to +dendrite. So over here there'll be a a + + align:start position:0% +dendrite. So over here there'll be a a + + + align:start position:0% +dendrite. So over here there'll be a a +so-called presaptic thickening and over + + align:start position:0% +so-called presaptic thickening and over + + + align:start position:0% +so-called presaptic thickening and over +here will be some other neurons dendrite + + align:start position:0% +here will be some other neurons dendrite + + + align:start position:0% +here will be some other neurons dendrite +and likewise over here some other + + align:start position:0% +and likewise over here some other + + + align:start position:0% +and likewise over here some other +neurons axon is coming in + + align:start position:0% + + + + align:start position:0% + +here and hitting the dendrite of our of + + align:start position:0% +here and hitting the dendrite of our of + + + align:start position:0% +here and hitting the dendrite of our of +of the one that occupies most of our + + align:start position:0% + + + + align:start position:0% + +So if there's enough uh stimulation from + + align:start position:0% +So if there's enough uh stimulation from + + + align:start position:0% +So if there's enough uh stimulation from +this side in the axonal tree or in the + + align:start position:0% +this side in the axonal tree or in the + + + align:start position:0% +this side in the axonal tree or in the +dendritic tree then a spike will go down + + align:start position:0% +dendritic tree then a spike will go down + + + align:start position:0% +dendritic tree then a spike will go down +that axon. It acts like a transmission + + align:start position:0% +that axon. It acts like a transmission + + + align:start position:0% +that axon. It acts like a transmission +line and then after uh that happens uh + + align:start position:0% +line and then after uh that happens uh + + + align:start position:0% +line and then after uh that happens uh +the act the neuron will go quiet for a + + align:start position:0% +the act the neuron will go quiet for a + + + align:start position:0% +the act the neuron will go quiet for a +while as it's kind of recovering it + + align:start position:0% +while as it's kind of recovering it + + + align:start position:0% +while as it's kind of recovering it +strength. is called the refractory + + align:start position:0% + + + + align:start position:0% + +period. Now, if we look at um that + + align:start position:0% +period. Now, if we look at um that + + + align:start position:0% +period. Now, if we look at um that +connection in a little more + + align:start position:0% +connection in a little more + + + align:start position:0% +connection in a little more +detail, this little piece right here, it + + align:start position:0% +detail, this little piece right here, it + + + align:start position:0% +detail, this little piece right here, it +sort of looks like this. Here's the axon + + align:start position:0% +sort of looks like this. Here's the axon + + + align:start position:0% +sort of looks like this. Here's the axon +coming + + align:start position:0% +coming + + + align:start position:0% +coming +in. It's got a whole bunch of little + + align:start position:0% +in. It's got a whole bunch of little + + + align:start position:0% +in. It's got a whole bunch of little +vesicles in it. And then there's a + + align:start position:0% +vesicles in it. And then there's a + + + align:start position:0% +vesicles in it. And then there's a +dendrite over here. And when a and when + + align:start position:0% +dendrite over here. And when a and when + + + align:start position:0% +dendrite over here. And when a and when +the axon is stimulated, it dumps all + + align:start position:0% +the axon is stimulated, it dumps all + + + align:start position:0% +the axon is stimulated, it dumps all +these vesicles into this inner synaptic + + align:start position:0% +these vesicles into this inner synaptic + + + align:start position:0% +these vesicles into this inner synaptic +space. For a long time, it wasn't known + + align:start position:0% +space. For a long time, it wasn't known + + + align:start position:0% +space. For a long time, it wasn't known +whether those things were actually + + align:start position:0% +whether those things were actually + + + align:start position:0% +whether those things were actually +separated. I think it was Ramoni Kahal + + align:start position:0% +separated. I think it was Ramoni Kahal + + + align:start position:0% +separated. I think it was Ramoni Kahal +who demonstrated that the that one + + align:start position:0% +who demonstrated that the that one + + + align:start position:0% +who demonstrated that the that one +neuron is actually not part of the next + + align:start position:0% +neuron is actually not part of the next + + + align:start position:0% +neuron is actually not part of the next +one. They're actually separated by these + + align:start position:0% +one. They're actually separated by these + + + align:start position:0% +one. They're actually separated by these +synaptic uh by these synaptic + + align:start position:0% +synaptic uh by these synaptic + + + align:start position:0% +synaptic uh by these synaptic +gaps. So, oh, there it is. How can we + + align:start position:0% +gaps. So, oh, there it is. How can we + + + align:start position:0% +gaps. So, oh, there it is. How can we +model that sort of thing? Well, here's + + align:start position:0% +model that sort of thing? Well, here's + + + align:start position:0% +model that sort of thing? Well, here's +what's usually done. Here's what is done + + align:start position:0% +what's usually done. Here's what is done + + + align:start position:0% +what's usually done. Here's what is done +in the neural net + + align:start position:0% + + + + align:start position:0% + +literature. First of all, uh we've got + + align:start position:0% +literature. First of all, uh we've got + + + align:start position:0% +literature. First of all, uh we've got +some kind of binary input because these + + align:start position:0% +some kind of binary input because these + + + align:start position:0% +some kind of binary input because these +things either fire or they don't fire. + + align:start position:0% +things either fire or they don't fire. + + + align:start position:0% +things either fire or they don't fire. +So it's an all ornone kind of situation. + + align:start position:0% +So it's an all ornone kind of situation. + + + align:start position:0% +So it's an all ornone kind of situation. +So over here we have some kind of input + + align:start position:0% +So over here we have some kind of input + + + align:start position:0% +So over here we have some kind of input +value. We'll call it x1 and it's either + + align:start position:0% +value. We'll call it x1 and it's either + + + align:start position:0% +value. We'll call it x1 and it's either +a zero or a one. + + align:start position:0% +a zero or a one. + + + align:start position:0% +a zero or a one. +So it comes in here and then it gets + + align:start position:0% +So it comes in here and then it gets + + + align:start position:0% +So it comes in here and then it gets +multiplied times some kind of weight. + + align:start position:0% +multiplied times some kind of weight. + + + align:start position:0% +multiplied times some kind of weight. +We'll call + + align:start position:0% +We'll call + + + align:start position:0% +We'll call +it + + align:start position:0% +it + + + align:start position:0% +it +W + + align:start position:0% +W + + + align:start position:0% +W +one. So this this part here is sort of + + align:start position:0% +one. So this this part here is sort of + + + align:start position:0% +one. So this this part here is sort of +modeling this this synaptic connection. + + align:start position:0% +modeling this this synaptic connection. + + + align:start position:0% +modeling this this synaptic connection. +It may be more or less strong and if + + align:start position:0% +It may be more or less strong and if + + + align:start position:0% +It may be more or less strong and if +it's more strong this weight goes up and + + align:start position:0% +it's more strong this weight goes up and + + + align:start position:0% +it's more strong this weight goes up and +if it's less strong this weight goes + + align:start position:0% +if it's less strong this weight goes + + + align:start position:0% +if it's less strong this weight goes +down. So that's the that's the that's + + align:start position:0% +down. So that's the that's the that's + + + align:start position:0% +down. So that's the that's the that's +the influence that that reflects the + + align:start position:0% +the influence that that reflects the + + + align:start position:0% +the influence that that reflects the +influence of the synapse on on on + + align:start position:0% +influence of the synapse on on on + + + align:start position:0% +influence of the synapse on on on +whether or not the whole axon decides + + align:start position:0% +whether or not the whole axon decides + + + align:start position:0% +whether or not the whole axon decides +it's + + align:start position:0% +it's + + + align:start position:0% +it's +stimulated. And we got other inputs down + + align:start position:0% +stimulated. And we got other inputs down + + + align:start position:0% +stimulated. And we got other inputs down +here. X subn also + + align:start position:0% +here. X subn also + + + align:start position:0% +here. X subn also +01. It's also multiplied by a + + align:start position:0% +01. It's also multiplied by a + + + align:start position:0% +01. It's also multiplied by a +weight. We'll call that W subn. And now + + align:start position:0% +weight. We'll call that W subn. And now + + + align:start position:0% +weight. We'll call that W subn. And now +we have to somehow uh represent the way + + align:start position:0% +we have to somehow uh represent the way + + + align:start position:0% +we have to somehow uh represent the way +in which these uh these inputs uh are + + align:start position:0% +in which these uh these inputs uh are + + + align:start position:0% +in which these uh these inputs uh are +collected together. How how they have + + align:start position:0% +collected together. How how they have + + + align:start position:0% +collected together. How how they have +collective force and we're going to + + align:start position:0% +collective force and we're going to + + + align:start position:0% +collective force and we're going to +model that very very simply just by + + align:start position:0% +model that very very simply just by + + + align:start position:0% +model that very very simply just by +saying okay we're running through a + + align:start position:0% +saying okay we're running through a + + + align:start position:0% +saying okay we're running through a +summer like + + align:start position:0% +summer like + + + align:start position:0% +summer like +so. But then we have to decide if the + + align:start position:0% +so. But then we have to decide if the + + + align:start position:0% +so. But then we have to decide if the +collective influence of all those + + align:start position:0% +collective influence of all those + + + align:start position:0% +collective influence of all those +uh inputs is sufficient to make the + + align:start position:0% +uh inputs is sufficient to make the + + + align:start position:0% +uh inputs is sufficient to make the +neuron fire. So we're going to do that + + align:start position:0% +neuron fire. So we're going to do that + + + align:start position:0% +neuron fire. So we're going to do that +by running this guy through a + + align:start position:0% +by running this guy through a + + + align:start position:0% +by running this guy through a +threshold box like so. Here is what the + + align:start position:0% +threshold box like so. Here is what the + + + align:start position:0% +threshold box like so. Here is what the +box looks like in terms of the + + align:start position:0% +box looks like in terms of the + + + align:start position:0% +box looks like in terms of the +relationship between the input and the + + align:start position:0% +relationship between the input and the + + + align:start position:0% +relationship between the input and the +output. And what you can see here is + + align:start position:0% +output. And what you can see here is + + + align:start position:0% +output. And what you can see here is +that nothing happens until the input + + align:start position:0% +that nothing happens until the input + + + align:start position:0% +that nothing happens until the input +exceeds some threshold t. If that + + align:start position:0% +exceeds some threshold t. If that + + + align:start position:0% +exceeds some threshold t. If that +happens then the output Z is a one + + align:start position:0% +happens then the output Z is a one + + + align:start position:0% +happens then the output Z is a one +otherwise it's a zero. So binary in + + align:start position:0% +otherwise it's a zero. So binary in + + + align:start position:0% +otherwise it's a zero. So binary in +binary out. We model the synaptic + + align:start position:0% +binary out. We model the synaptic + + + align:start position:0% +binary out. We model the synaptic +weights by these multipliers. We model + + align:start position:0% +weights by these multipliers. We model + + + align:start position:0% +weights by these multipliers. We model +the accumulating accumulative effect of + + align:start position:0% +the accumulating accumulative effect of + + + align:start position:0% +the accumulating accumulative effect of +all that input to the neuron by a + + align:start position:0% +all that input to the neuron by a + + + align:start position:0% +all that input to the neuron by a +summer. We decide if it's going to be + + align:start position:0% +summer. We decide if it's going to be + + + align:start position:0% +summer. We decide if it's going to be +the an all or none one by running it + + align:start position:0% +the an all or none one by running it + + + align:start position:0% +the an all or none one by running it +through this threshold box and seeing if + + align:start position:0% +through this threshold box and seeing if + + + align:start position:0% +through this threshold box and seeing if +the sum + + align:start position:0% +the sum + + + align:start position:0% +the sum +products add up to more than the + + align:start position:0% +products add up to more than the + + + align:start position:0% +products add up to more than the +threshold. If so, we get a + + align:start position:0% +threshold. If so, we get a + + + align:start position:0% +threshold. If so, we get a +one. So what in the end are we in fact + + align:start position:0% +one. So what in the end are we in fact + + + align:start position:0% +one. So what in the end are we in fact +modeling? + + align:start position:0% +modeling? + + + align:start position:0% +modeling? +Well, with this + + align:start position:0% + + + + align:start position:0% + +model we have number one all or + + align:start position:0% + + + + align:start position:0% + +none. Number + + align:start position:0% +none. Number + + + align:start position:0% +none. Number +two cumulative + + align:start position:0% + + + + align:start position:0% + +influence. Number + + align:start position:0% +influence. Number + + + align:start position:0% +influence. Number +three. Oh, I suppose synaptic weight. + + align:start position:0% + + + + align:start position:0% + +But that's not all that there might be + + align:start position:0% +But that's not all that there might be + + + align:start position:0% +But that's not all that there might be +to model in a real neuron. We might want + + align:start position:0% +to model in a real neuron. We might want + + + align:start position:0% +to model in a real neuron. We might want +to deal with the refractory + + align:start position:0% + + + + align:start position:0% + +period. Not noted in these biological + + align:start position:0% +period. Not noted in these biological + + + align:start position:0% +period. Not noted in these biological +models that we build neural nets out of. + + align:start position:0% +models that we build neural nets out of. + + + align:start position:0% +models that we build neural nets out of. +We might want to model axonal + + align:start position:0% + + + + align:start position:0% + +bifurcation. We do get some division in + + align:start position:0% +bifurcation. We do get some division in + + + align:start position:0% +bifurcation. We do get some division in +the axon of the neuron. And it turns out + + align:start position:0% +the axon of the neuron. And it turns out + + + align:start position:0% +the axon of the neuron. And it turns out +that that pulse will either go down one + + align:start position:0% +that that pulse will either go down one + + + align:start position:0% +that that pulse will either go down one +branch or the other. And which branch it + + align:start position:0% +branch or the other. And which branch it + + + align:start position:0% +branch or the other. And which branch it +goes down depends on electrical activity + + align:start position:0% +goes down depends on electrical activity + + + align:start position:0% +goes down depends on electrical activity +in the vicinity of the division. So + + align:start position:0% +in the vicinity of the division. So + + + align:start position:0% +in the vicinity of the division. So +these things might actually be fantastic + + align:start position:0% +these things might actually be fantastic + + + align:start position:0% +these things might actually be fantastic +coincidence detectors, but we're not + + align:start position:0% +coincidence detectors, but we're not + + + align:start position:0% +coincidence detectors, but we're not +modeling them. We don't know how it + + align:start position:0% +modeling them. We don't know how it + + + align:start position:0% +modeling them. We don't know how it +works. So axonal bifurcation might be + + align:start position:0% +works. So axonal bifurcation might be + + + align:start position:0% +works. So axonal bifurcation might be +modeled. We might + + align:start position:0% +modeled. We might + + + align:start position:0% +modeled. We might +also have a look at time + + align:start position:0% + + + + align:start position:0% + +patterns. See what we don't know is we + + align:start position:0% +patterns. See what we don't know is we + + + align:start position:0% +patterns. See what we don't know is we +don't know if the timing of the arrival + + align:start position:0% +don't know if the timing of the arrival + + + align:start position:0% +don't know if the timing of the arrival +of these pulses in the dendritic tree + + align:start position:0% +of these pulses in the dendritic tree + + + align:start position:0% +of these pulses in the dendritic tree +has anything to do with what that neuron + + align:start position:0% +has anything to do with what that neuron + + + align:start position:0% +has anything to do with what that neuron +is going to + + align:start position:0% +is going to + + + align:start position:0% +is going to +recognize. Right? So there a lot of + + align:start position:0% +recognize. Right? So there a lot of + + + align:start position:0% +recognize. Right? So there a lot of +unknowns here. And now I'm going to show + + align:start position:0% +unknowns here. And now I'm going to show + + + align:start position:0% +unknowns here. And now I'm going to show +you how to answer a question about + + align:start position:0% +you how to answer a question about + + + align:start position:0% +you how to answer a question about +neurobiology with 80% probability you'll + + align:start position:0% +neurobiology with 80% probability you'll + + + align:start position:0% +neurobiology with 80% probability you'll +get it right. Just say we don't + + align:start position:0% +get it right. Just say we don't + + + align:start position:0% +get it right. Just say we don't +know. And that'll be with 80% + + align:start position:0% +know. And that'll be with 80% + + + align:start position:0% +know. And that'll be with 80% +probability what the neurobiologist + + align:start position:0% +probability what the neurobiologist + + + align:start position:0% +probability what the neurobiologist +would + + align:start position:0% + + + + align:start position:0% + +say. So this is a model inspired by what + + align:start position:0% +say. So this is a model inspired by what + + + align:start position:0% +say. So this is a model inspired by what +goes on in our heads. But it's far from + + align:start position:0% +goes on in our heads. But it's far from + + + align:start position:0% +goes on in our heads. But it's far from +a it's far from clear if what we're + + align:start position:0% +a it's far from clear if what we're + + + align:start position:0% +a it's far from clear if what we're +modeling is the essence of why those + + align:start position:0% +modeling is the essence of why those + + + align:start position:0% +modeling is the essence of why those +guys make possible what we can do. + + align:start position:0% +guys make possible what we can do. + + + align:start position:0% +guys make possible what we can do. +Nevertheless, that's where we're going + + align:start position:0% +Nevertheless, that's where we're going + + + align:start position:0% +Nevertheless, that's where we're going +to start. That's where we're going to + + align:start position:0% +to start. That's where we're going to + + + align:start position:0% +to start. That's where we're going to +go. So, we've got this model of what + + align:start position:0% +go. So, we've got this model of what + + + align:start position:0% +go. So, we've got this model of what +it's of what a neuron does. So, what + + align:start position:0% +it's of what a neuron does. So, what + + + align:start position:0% +it's of what a neuron does. So, what +about what does a collection of these + + align:start position:0% +about what does a collection of these + + + align:start position:0% +about what does a collection of these +neurons do? Well, we can think of your + + align:start position:0% +neurons do? Well, we can think of your + + + align:start position:0% +neurons do? Well, we can think of your +skull as a big + + align:start position:0% +skull as a big + + + align:start position:0% +skull as a big +box full of neurons. + + align:start position:0% + + + + align:start position:0% + +Uh maybe a better way to think of this + + align:start position:0% +Uh maybe a better way to think of this + + + align:start position:0% +Uh maybe a better way to think of this +is that your head is full of neurons and + + align:start position:0% +is that your head is full of neurons and + + + align:start position:0% +is that your head is full of neurons and +they in turn are full of weights and + + align:start position:0% + + + + align:start position:0% + +thresholds like so. + + align:start position:0% +thresholds like so. + + + align:start position:0% +thresholds like so. +So into this box come a variety of + + align:start position:0% +So into this box come a variety of + + + align:start position:0% +So into this box come a variety of +inputs X1 through + + align:start position:0% +inputs X1 through + + + align:start position:0% +inputs X1 through +X + + align:start position:0% +X + + + align:start position:0% +X +M. And these find their way to the + + align:start position:0% +M. And these find their way to the + + + align:start position:0% +M. And these find their way to the +inside of this gaggle of neurons. And + + align:start position:0% +inside of this gaggle of neurons. And + + + align:start position:0% +inside of this gaggle of neurons. And +out here come a bunch of + + align:start position:0% +out here come a bunch of + + + align:start position:0% +out here come a bunch of +outputs Z1 through Z + + align:start position:0% +outputs Z1 through Z + + + align:start position:0% +outputs Z1 through Z +N. And there a whole bunch of these + + align:start position:0% +N. And there a whole bunch of these + + + align:start position:0% +N. And there a whole bunch of these +maybe like so. And there are a lot of + + align:start position:0% +maybe like so. And there are a lot of + + + align:start position:0% +maybe like so. And there are a lot of +inputs like so. And somehow uh these + + align:start position:0% +inputs like so. And somehow uh these + + + align:start position:0% +inputs like so. And somehow uh these +inputs um through the influence of the + + align:start position:0% +inputs um through the influence of the + + + align:start position:0% +inputs um through the influence of the +weights and the thresholds come out as a + + align:start position:0% +weights and the thresholds come out as a + + + align:start position:0% +weights and the thresholds come out as a +set of + + align:start position:0% +set of + + + align:start position:0% +set of +outputs. So we can we can write that + + align:start position:0% +outputs. So we can we can write that + + + align:start position:0% +outputs. So we can we can write that +down a little fancier by just saying + + align:start position:0% +down a little fancier by just saying + + + align:start position:0% +down a little fancier by just saying +that Z is a vector which is a function + + align:start position:0% +that Z is a vector which is a function + + + align:start position:0% +that Z is a vector which is a function +of um well certainly the input vector + + align:start position:0% +of um well certainly the input vector + + + align:start position:0% +of um well certainly the input vector +but also the weight vector and the + + align:start position:0% +but also the weight vector and the + + + align:start position:0% +but also the weight vector and the +threshold vector. So that's all a neural + + align:start position:0% +threshold vector. So that's all a neural + + + align:start position:0% +threshold vector. So that's all a neural +net is. And when we train a neural net, + + align:start position:0% +net is. And when we train a neural net, + + + align:start position:0% +net is. And when we train a neural net, +all we're going to be able to do is + + align:start position:0% +all we're going to be able to do is + + + align:start position:0% +all we're going to be able to do is +adjust those weights and thresholds so + + align:start position:0% +adjust those weights and thresholds so + + + align:start position:0% +adjust those weights and thresholds so +that what we get out is what we want. So + + align:start position:0% +that what we get out is what we want. So + + + align:start position:0% +that what we get out is what we want. So +a neural net is a function + + align:start position:0% +a neural net is a function + + + align:start position:0% +a neural net is a function +approximator. It's good to think about + + align:start position:0% +approximator. It's good to think about + + + align:start position:0% +approximator. It's good to think about +that. It's a function approximator. + + align:start position:0% +that. It's a function approximator. + + + align:start position:0% +that. It's a function approximator. +So maybe we've got uh some sample data + + align:start position:0% +So maybe we've got uh some sample data + + + align:start position:0% +So maybe we've got uh some sample data +uh that gives us an output vector that's + + align:start position:0% +uh that gives us an output vector that's + + + align:start position:0% +uh that gives us an output vector that's +desired as a function as another + + align:start position:0% +desired as a function as another + + + align:start position:0% +desired as a function as another +function of the input forgetting about + + align:start position:0% +function of the input forgetting about + + + align:start position:0% +function of the input forgetting about +what the weights and the thresholds are. + + align:start position:0% +what the weights and the thresholds are. + + + align:start position:0% +what the weights and the thresholds are. +That's what we want to get out. And so + + align:start position:0% +That's what we want to get out. And so + + + align:start position:0% +That's what we want to get out. And so +how well we're doing can be figured out + + align:start position:0% +how well we're doing can be figured out + + + align:start position:0% +how well we're doing can be figured out +by comparing uh the desired value with + + align:start position:0% +by comparing uh the desired value with + + + align:start position:0% +by comparing uh the desired value with +the actual value. + + align:start position:0% +the actual value. + + + align:start position:0% +the actual value. +So we we might uh think then that we can + + align:start position:0% +So we we might uh think then that we can + + + align:start position:0% +So we we might uh think then that we can +get a handle on how well we're doing by + + align:start position:0% +get a handle on how well we're doing by + + + align:start position:0% +get a handle on how well we're doing by +constructing some performance function + + align:start position:0% +constructing some performance function + + + align:start position:0% +constructing some performance function +which is + + align:start position:0% +which is + + + align:start position:0% +which is +determined by the desired vector + + align:start position:0% +determined by the desired vector + + + align:start position:0% +determined by the desired vector +uh and uh the input + + align:start position:0% +uh and uh the input + + + align:start position:0% +uh and uh the input +vector sorry the the desired vector and + + align:start position:0% +vector sorry the the desired vector and + + + align:start position:0% +vector sorry the the desired vector and +the actual output vector for some + + align:start position:0% +the actual output vector for some + + + align:start position:0% +the actual output vector for some +particular input or for some set of + + align:start position:0% +particular input or for some set of + + + align:start position:0% +particular input or for some set of +inputs. And the question is what what + + align:start position:0% +inputs. And the question is what what + + + align:start position:0% +inputs. And the question is what what +should that function be? How should we + + align:start position:0% +should that function be? How should we + + + align:start position:0% +should that function be? How should we +measure + + align:start position:0% +measure + + + align:start position:0% +measure +performance given that we have what we + + align:start position:0% +performance given that we have what we + + + align:start position:0% +performance given that we have what we +want out of here and what we actually + + align:start position:0% +want out of here and what we actually + + + align:start position:0% +want out of here and what we actually +got out of here? Well, one simple thing + + align:start position:0% +got out of here? Well, one simple thing + + + align:start position:0% +got out of here? Well, one simple thing +to do is just to measure the magnitude + + align:start position:0% +to do is just to measure the magnitude + + + align:start position:0% +to do is just to measure the magnitude +of the + + align:start position:0% +of the + + + align:start position:0% +of the +difference. That makes sense. But of + + align:start position:0% +difference. That makes sense. But of + + + align:start position:0% +difference. That makes sense. But of +course uh that would give us a uh + + align:start position:0% +course uh that would give us a uh + + + align:start position:0% +course uh that would give us a uh +performance + + align:start position:0% +performance + + + align:start position:0% +performance +function that is a function of the + + align:start position:0% +function that is a function of the + + + align:start position:0% +function that is a function of the +distance between those vectors would + + align:start position:0% +distance between those vectors would + + + align:start position:0% +distance between those vectors would +look like + + align:start position:0% + + + + align:start position:0% + +this. But this turns out to be + + align:start position:0% +this. But this turns out to be + + + align:start position:0% +this. But this turns out to be +um mathematically inconvenient in the + + align:start position:0% +um mathematically inconvenient in the + + + align:start position:0% +um mathematically inconvenient in the +end. So how do you think we're going to + + align:start position:0% +end. So how do you think we're going to + + + align:start position:0% +end. So how do you think we're going to +tart it up a little bit? What's that? + + align:start position:0% +tart it up a little bit? What's that? + + + align:start position:0% +tart it up a little bit? What's that? +Well, I don't know. How about just we + + align:start position:0% +Well, I don't know. How about just we + + + align:start position:0% +Well, I don't know. How about just we +square + + align:start position:0% +square + + + align:start position:0% +square +it that way? We're we're we're going to + + align:start position:0% +it that way? We're we're we're going to + + + align:start position:0% +it that way? We're we're we're going to +go from this little sharp point down + + align:start position:0% +go from this little sharp point down + + + align:start position:0% +go from this little sharp point down +there to something looks more like + + align:start position:0% +there to something looks more like + + + align:start position:0% +there to something looks more like +that. So, it's best when uh the + + align:start position:0% +that. So, it's best when uh the + + + align:start position:0% +that. So, it's best when uh the +difference is zero, of course, and it + + align:start position:0% +difference is zero, of course, and it + + + align:start position:0% +difference is zero, of course, and it +gets worse as you move away from + + align:start position:0% +gets worse as you move away from + + + align:start position:0% +gets worse as you move away from +zero. Um but what we're trying to do + + align:start position:0% +zero. Um but what we're trying to do + + + align:start position:0% +zero. Um but what we're trying to do +here is we're trying to get to a minimum + + align:start position:0% +here is we're trying to get to a minimum + + + align:start position:0% +here is we're trying to get to a minimum +value. And and and I I hope you'll + + align:start position:0% +value. And and and I I hope you'll + + + align:start position:0% +value. And and and I I hope you'll +forgive me. I I just don't like that the + + align:start position:0% +forgive me. I I just don't like that the + + + align:start position:0% +forgive me. I I just don't like that the +direction we're going here because I + + align:start position:0% +direction we're going here because I + + + align:start position:0% +direction we're going here because I +like to think in terms of improvement as + + align:start position:0% +like to think in terms of improvement as + + + align:start position:0% +like to think in terms of improvement as +going uphill instead of + + align:start position:0% +going uphill instead of + + + align:start position:0% +going uphill instead of +downhill. So I'm going to dress this up + + align:start position:0% +downhill. So I'm going to dress this up + + + align:start position:0% +downhill. So I'm going to dress this up +just one more step. Put a minus sign out + + align:start position:0% +just one more step. Put a minus sign out + + + align:start position:0% +just one more step. Put a minus sign out +there. And then our performance function + + align:start position:0% +there. And then our performance function + + + align:start position:0% +there. And then our performance function +looks like this. It's always negative + + align:start position:0% +looks like this. It's always negative + + + align:start position:0% +looks like this. It's always negative +and it gets and and the best value it + + align:start position:0% +and it gets and and the best value it + + + align:start position:0% +and it gets and and the best value it +can possibly be is zero. So that's what + + align:start position:0% +can possibly be is zero. So that's what + + + align:start position:0% +can possibly be is zero. So that's what +we're going to use just because I am who + + align:start position:0% +we're going to use just because I am who + + + align:start position:0% +we're going to use just because I am who +I am. It doesn't matter, right? still + + align:start position:0% +I am. It doesn't matter, right? still + + + align:start position:0% +I am. It doesn't matter, right? still +you're you're trying to either minimize + + align:start position:0% +you're you're trying to either minimize + + + align:start position:0% +you're you're trying to either minimize +or maximize some performance + + align:start position:0% +or maximize some performance + + + align:start position:0% +or maximize some performance +function. Okay, so what are we going to + + align:start position:0% +function. Okay, so what are we going to + + + align:start position:0% +function. Okay, so what are we going to +do? I guess what we could + + align:start position:0% +do? I guess what we could + + + align:start position:0% +do? I guess what we could +do is we could treat this thing. Well, + + align:start position:0% +do is we could treat this thing. Well, + + + align:start position:0% +do is we could treat this thing. Well, +we already know what to do. I'm not even + + align:start position:0% +we already know what to do. I'm not even + + + align:start position:0% +we already know what to do. I'm not even +sure why we're devoting a lecture to + + align:start position:0% +sure why we're devoting a lecture to + + + align:start position:0% +sure why we're devoting a lecture to +this because it's clear that what we're + + align:start position:0% +this because it's clear that what we're + + + align:start position:0% +this because it's clear that what we're +trying to do is we're trying to take our + + align:start position:0% +trying to do is we're trying to take our + + + align:start position:0% +trying to do is we're trying to take our +weights and our thresholds and adjust + + align:start position:0% +weights and our thresholds and adjust + + + align:start position:0% +weights and our thresholds and adjust +them so as to maximize performance. So + + align:start position:0% +them so as to maximize performance. So + + + align:start position:0% +them so as to maximize performance. So +we can make a little contour map here + + align:start position:0% +we can make a little contour map here + + + align:start position:0% +we can make a little contour map here +with a simple neural net with just two + + align:start position:0% +with a simple neural net with just two + + + align:start position:0% +with a simple neural net with just two +weights in it. And maybe it looks like + + align:start position:0% +weights in it. And maybe it looks like + + + align:start position:0% +weights in it. And maybe it looks like +this contour + + align:start position:0% + + + + align:start position:0% + +map. And at any given time we've got a + + align:start position:0% +map. And at any given time we've got a + + + align:start position:0% +map. And at any given time we've got a +particular W1 and particular two W2 and + + align:start position:0% +particular W1 and particular two W2 and + + + align:start position:0% +particular W1 and particular two W2 and +we're trying to find a better W1 and W2. + + align:start position:0% +we're trying to find a better W1 and W2. + + + align:start position:0% +we're trying to find a better W1 and W2. +So here we are right + + align:start position:0% +So here we are right + + + align:start position:0% +So here we are right +now and there's the contour map and this + + align:start position:0% +now and there's the contour map and this + + + align:start position:0% +now and there's the contour map and this +is 6034. So what do we + + align:start position:0% +is 6034. So what do we + + + align:start position:0% +is 6034. So what do we +do? a simple simple matter of hill + + align:start position:0% +do? a simple simple matter of hill + + + align:start position:0% +do? a simple simple matter of hill +climbing, right? So, we'll take a step + + align:start position:0% +climbing, right? So, we'll take a step + + + align:start position:0% +climbing, right? So, we'll take a step +in every direction. If we take a step in + + align:start position:0% +in every direction. If we take a step in + + + align:start position:0% +in every direction. If we take a step in +that direction, not so hot. That + + align:start position:0% +that direction, not so hot. That + + + align:start position:0% +that direction, not so hot. That +actually goes pretty bad. These two are + + align:start position:0% +actually goes pretty bad. These two are + + + align:start position:0% +actually goes pretty bad. These two are +really ugly. Ah, but that one that one + + align:start position:0% +really ugly. Ah, but that one that one + + + align:start position:0% +really ugly. Ah, but that one that one +takes us up a hill a little bit. So, + + align:start position:0% +takes us up a hill a little bit. So, + + + align:start position:0% +takes us up a hill a little bit. So, +we're done. Except + + align:start position:0% +we're done. Except + + + align:start position:0% +we're done. Except +that I just mentioned it. Hinton's + + align:start position:0% +that I just mentioned it. Hinton's + + + align:start position:0% +that I just mentioned it. Hinton's +neural net has 60 million parameters in + + align:start position:0% +neural net has 60 million parameters in + + + align:start position:0% +neural net has 60 million parameters in +it. So we're not going to hill climb + + align:start position:0% +it. So we're not going to hill climb + + + align:start position:0% +it. So we're not going to hill climb +with 60 million parameters because that + + align:start position:0% +with 60 million parameters because that + + + align:start position:0% +with 60 million parameters because that +you know it explodes exponentially in + + align:start position:0% +you know it explodes exponentially in + + + align:start position:0% +you know it explodes exponentially in +the number of weights you've got to deal + + align:start position:0% +the number of weights you've got to deal + + + align:start position:0% +the number of weights you've got to deal +with the number of steps you can take. + + align:start position:0% +with the number of steps you can take. + + + align:start position:0% +with the number of steps you can take. +So that so this approach is + + align:start position:0% +So that so this approach is + + + align:start position:0% +So that so this approach is +computationally + + align:start position:0% +computationally + + + align:start position:0% +computationally +intractable. Fortunately you've all + + align:start position:0% +intractable. Fortunately you've all + + + align:start position:0% +intractable. Fortunately you've all +taken 801 1801 or the equivalent + + align:start position:0% +taken 801 1801 or the equivalent + + + align:start position:0% +taken 801 1801 or the equivalent +thereof. So you have a better idea. + + align:start position:0% +thereof. So you have a better idea. + + + align:start position:0% +thereof. So you have a better idea. +Instead of just taking a step in every + + align:start position:0% +Instead of just taking a step in every + + + align:start position:0% +Instead of just taking a step in every +direction, what we're going to do is + + align:start position:0% +direction, what we're going to do is + + + align:start position:0% +direction, what we're going to do is +we're going to take some partial + + align:start position:0% +we're going to take some partial + + + align:start position:0% +we're going to take some partial +derivatives and we're going to see what + + align:start position:0% +derivatives and we're going to see what + + + align:start position:0% +derivatives and we're going to see what +the they suggest to us in terms of how + + align:start position:0% +the they suggest to us in terms of how + + + align:start position:0% +the they suggest to us in terms of how +we're going to get get around in this + + align:start position:0% +we're going to get get around in this + + + align:start position:0% +we're going to get get around in this +space. So we might have the partial of + + align:start position:0% +space. So we might have the partial of + + + align:start position:0% +space. So we might have the partial of +that performance function up there with + + align:start position:0% +that performance function up there with + + + align:start position:0% +that performance function up there with +respect to W1 and we might also take the + + align:start position:0% +respect to W1 and we might also take the + + + align:start position:0% +respect to W1 and we might also take the +partial derivative of that guy with + + align:start position:0% +partial derivative of that guy with + + + align:start position:0% +partial derivative of that guy with +respect to W2. + + align:start position:0% +respect to W2. + + + align:start position:0% +respect to W2. +And these will tell us how much + + align:start position:0% +And these will tell us how much + + + align:start position:0% +And these will tell us how much +improvement we're getting by making a + + align:start position:0% +improvement we're getting by making a + + + align:start position:0% +improvement we're getting by making a +little movement in those directions, + + align:start position:0% +little movement in those directions, + + + align:start position:0% +little movement in those directions, +right? How much how much of changes + + align:start position:0% +right? How much how much of changes + + + align:start position:0% +right? How much how much of changes +given that we're just going right along + + align:start position:0% +given that we're just going right along + + + align:start position:0% +given that we're just going right along +the + + align:start position:0% +the + + + align:start position:0% +the +axis. So maybe what we ought to do is + + align:start position:0% +axis. So maybe what we ought to do is + + + align:start position:0% +axis. So maybe what we ought to do is +if this + + align:start position:0% +if this + + + align:start position:0% +if this +guy is much bigger than this guy, it + + align:start position:0% +guy is much bigger than this guy, it + + + align:start position:0% +guy is much bigger than this guy, it +would suggest that we mostly want to + + align:start position:0% +would suggest that we mostly want to + + + align:start position:0% +would suggest that we mostly want to +move in this direction. Or to put it in + + align:start position:0% +move in this direction. Or to put it in + + + align:start position:0% +move in this direction. Or to put it in +1801 terms, what we're going to do is + + align:start position:0% +1801 terms, what we're going to do is + + + align:start position:0% +1801 terms, what we're going to do is +we're going to follow the gradient. And + + align:start position:0% +we're going to follow the gradient. And + + + align:start position:0% +we're going to follow the gradient. And +so the change in the W vector is going + + align:start position:0% +so the change in the W vector is going + + + align:start position:0% +so the change in the W vector is going +to equal + + align:start position:0% +to equal + + + align:start position:0% +to equal +to this partial derivative time I plus + + align:start position:0% +to this partial derivative time I plus + + + align:start position:0% +to this partial derivative time I plus +this partial derivative time J. So what + + align:start position:0% +this partial derivative time J. So what + + + align:start position:0% +this partial derivative time J. So what +we're going to end up doing in this + + align:start position:0% +we're going to end up doing in this + + + align:start position:0% +we're going to end up doing in this +particular case by following that + + align:start position:0% +particular case by following that + + + align:start position:0% +particular case by following that +formula is moving off in that direction + + align:start position:0% +formula is moving off in that direction + + + align:start position:0% +formula is moving off in that direction +right up right up the steepest part of + + align:start position:0% +right up right up the steepest part of + + + align:start position:0% +right up right up the steepest part of +the + + align:start position:0% +the + + + align:start position:0% +the +hill. And you know how much we move is a + + align:start position:0% +hill. And you know how much we move is a + + + align:start position:0% +hill. And you know how much we move is a +is a question. So, let's just have a + + align:start position:0% +is a question. So, let's just have a + + + align:start position:0% +is a question. So, let's just have a +rate constant R that decides how big our + + align:start position:0% +rate constant R that decides how big our + + + align:start position:0% +rate constant R that decides how big our +step is going to + + align:start position:0% +step is going to + + + align:start position:0% +step is going to +be. And now you think we were + + align:start position:0% +be. And now you think we were + + + align:start position:0% +be. And now you think we were +done. Well, too bad for our side. We're + + align:start position:0% +done. Well, too bad for our side. We're + + + align:start position:0% +done. Well, too bad for our side. We're +not done. Uh there's a reason why we + + align:start position:0% +not done. Uh there's a reason why we + + + align:start position:0% +not done. Uh there's a reason why we +can't use gradient ascent or in the case + + align:start position:0% +can't use gradient ascent or in the case + + + align:start position:0% +can't use gradient ascent or in the case +that I've drawn or gradient descent. If + + align:start position:0% +that I've drawn or gradient descent. If + + + align:start position:0% +that I've drawn or gradient descent. If +we take the performance function the + + align:start position:0% +we take the performance function the + + + align:start position:0% +we take the performance function the +other way, why can't we use it? + + align:start position:0% + + + + align:start position:0% + +Uh the remark is local maxima and that + + align:start position:0% +Uh the remark is local maxima and that + + + align:start position:0% +Uh the remark is local maxima and that +is certainly true but it's not our first + + align:start position:0% + + + + align:start position:0% + +obstacle when does gradient descent work + + align:start position:0% + + + + align:start position:0% + +ah there's something wrong with our + + align:start position:0% +ah there's something wrong with our + + + align:start position:0% +ah there's something wrong with our +function that's right it's nonlinear or + + align:start position:0% +function that's right it's nonlinear or + + + align:start position:0% +function that's right it's nonlinear or +it's rather it's + + align:start position:0% +it's rather it's + + + align:start position:0% +it's rather it's +discontinuous so gradient descent + + align:start position:0% +discontinuous so gradient descent + + + align:start position:0% +discontinuous so gradient descent +requires a continuous space continuous + + align:start position:0% +requires a continuous space continuous + + + align:start position:0% +requires a continuous space continuous +surface + + align:start position:0% +surface + + + align:start position:0% +surface +So too bad for our + + align:start position:0% +So too bad for our + + + align:start position:0% +So too bad for our +side. It + + align:start position:0% +side. It + + + align:start position:0% +side. It +isn't. So what to + + align:start position:0% +isn't. So what to + + + align:start position:0% +isn't. So what to +do? Well, nobody knew what to do for 25 + + align:start position:0% +do? Well, nobody knew what to do for 25 + + + align:start position:0% +do? Well, nobody knew what to do for 25 +years. People were screwing around with + + align:start position:0% +years. People were screwing around with + + + align:start position:0% +years. People were screwing around with +training neural nets for 25 years before + + align:start position:0% +training neural nets for 25 years before + + + align:start position:0% +training neural nets for 25 years before +Paul Werbos sadly at Harvard in 1974 + + align:start position:0% +Paul Werbos sadly at Harvard in 1974 + + + align:start position:0% +Paul Werbos sadly at Harvard in 1974 +gave us the answer. Now I want to tell + + align:start position:0% +gave us the answer. Now I want to tell + + + align:start position:0% +gave us the answer. Now I want to tell +you what the answer is. First part of + + align:start position:0% +you what the answer is. First part of + + + align:start position:0% +you what the answer is. First part of +the answer is those thresholds are + + align:start position:0% +the answer is those thresholds are + + + align:start position:0% +the answer is those thresholds are +annoying. + + align:start position:0% +annoying. + + + align:start position:0% +annoying. +They're just they're just extra baggage + + align:start position:0% +They're just they're just extra baggage + + + align:start position:0% +They're just they're just extra baggage +to deal + + align:start position:0% +to deal + + + align:start position:0% +to deal +with. What we really like instead of Z + + align:start position:0% +with. What we really like instead of Z + + + align:start position:0% +with. What we really like instead of Z +being a function of X, W, and T was like + + align:start position:0% +being a function of X, W, and T was like + + + align:start position:0% +being a function of X, W, and T was like +C prime to be a function FP prime of X + + align:start position:0% +C prime to be a function FP prime of X + + + align:start position:0% +C prime to be a function FP prime of X +and the weights. But we got to account + + align:start position:0% +and the weights. But we got to account + + + align:start position:0% +and the weights. But we got to account +for the threshold somehow. So here's how + + align:start position:0% +for the threshold somehow. So here's how + + + align:start position:0% +for the threshold somehow. So here's how +you do that. What you do is you + + align:start position:0% +you do that. What you do is you + + + align:start position:0% +you do that. What you do is you +say, let us add another input to this + + align:start position:0% +say, let us add another input to this + + + align:start position:0% +say, let us add another input to this +neuron and it's going to have a + + align:start position:0% +neuron and it's going to have a + + + align:start position:0% +neuron and it's going to have a +weight + + align:start position:0% + + + + align:start position:0% + +w. All right? And it's going to be + + align:start position:0% +w. All right? And it's going to be + + + align:start position:0% +w. All right? And it's going to be +connected to an input that's always + + align:start position:0% +connected to an input that's always + + + align:start position:0% +connected to an input that's always +minus + + align:start position:0% +minus + + + align:start position:0% +minus +one. You with me so far? We're just + + align:start position:0% +one. You with me so far? We're just + + + align:start position:0% +one. You with me so far? We're just +going to add another. Now what we're + + align:start position:0% +going to add another. Now what we're + + + align:start position:0% +going to add another. Now what we're +going to do is we're going to say + + align:start position:0% + + + + align:start position:0% + +let w 0 equal + + align:start position:0% +let w 0 equal + + + align:start position:0% +let w 0 equal +t. What's that do to to movement of the + + align:start position:0% + + + + align:start position:0% + +threshold? What it does is it takes that + + align:start position:0% +threshold? What it does is it takes that + + + align:start position:0% +threshold? What it does is it takes that +threshold and moves it back to + + align:start position:0% +threshold and moves it back to + + + align:start position:0% +threshold and moves it back to +zero. So this little trick here takes + + align:start position:0% +zero. So this little trick here takes + + + align:start position:0% +zero. So this little trick here takes +this pink threshold and re redo it so + + align:start position:0% +this pink threshold and re redo it so + + + align:start position:0% +this pink threshold and re redo it so +that the that the new threshold box + + align:start position:0% +that the that the new threshold box + + + align:start position:0% +that the that the new threshold box +looks like this. + + align:start position:0% + + + + align:start position:0% + +Right? Think about it. If if this is t + + align:start position:0% +Right? Think about it. If if this is t + + + align:start position:0% +Right? Think about it. If if this is t +and this is minus one, then this is + + align:start position:0% +and this is minus one, then this is + + + align:start position:0% +and this is minus one, then this is +minus t. And so this thing ought to fire + + align:start position:0% +minus t. And so this thing ought to fire + + + align:start position:0% +minus t. And so this thing ought to fire +if everything's over if the sum is over + + align:start position:0% +if everything's over if the sum is over + + + align:start position:0% +if everything's over if the sum is over +zero. So it makes sense. It gets rid of + + align:start position:0% +zero. So it makes sense. It gets rid of + + + align:start position:0% +zero. So it makes sense. It gets rid of +the it gets rid of the threshold thing + + align:start position:0% +the it gets rid of the threshold thing + + + align:start position:0% +the it gets rid of the threshold thing +for us. So now we can just think about + + align:start position:0% +for us. So now we can just think about + + + align:start position:0% +for us. So now we can just think about +weights. But still we've got that we've + + align:start position:0% +weights. But still we've got that we've + + + align:start position:0% +weights. But still we've got that we've +got that + + align:start position:0% +got that + + + align:start position:0% +got that +uh we've got that step function there. + + align:start position:0% +uh we've got that step function there. + + + align:start position:0% +uh we've got that step function there. +And uh that's not good. + + align:start position:0% +And uh that's not good. + + + align:start position:0% +And uh that's not good. +So what we're going to do is we're going + + align:start position:0% +So what we're going to do is we're going + + + align:start position:0% +So what we're going to do is we're going +to smooth that guy + + align:start position:0% +to smooth that guy + + + align:start position:0% +to smooth that guy +out. So this is trick number + + align:start position:0% +out. So this is trick number + + + align:start position:0% +out. So this is trick number +two. Instead of a step function, we're + + align:start position:0% +two. Instead of a step function, we're + + + align:start position:0% +two. Instead of a step function, we're +going to have this thing we uh lovingly + + align:start position:0% +going to have this thing we uh lovingly + + + align:start position:0% +going to have this thing we uh lovingly +call a sigmoid function because it's + + align:start position:0% +call a sigmoid function because it's + + + align:start position:0% +call a sigmoid function because it's +kind of got an S-type shape. And the + + align:start position:0% +kind of got an S-type shape. And the + + + align:start position:0% +kind of got an S-type shape. And the +function we're going to use is this one. + + align:start position:0% +function we're going to use is this one. + + + align:start position:0% +function we're going to use is this one. +One well better make it a little bit + + align:start position:0% +One well better make it a little bit + + + align:start position:0% +One well better make it a little bit +different. 1 over 1 + e to the minus + + align:start position:0% +different. 1 over 1 + e to the minus + + + align:start position:0% +different. 1 over 1 + e to the minus +whatever the input is. Let's call the + + align:start position:0% +whatever the input is. Let's call the + + + align:start position:0% +whatever the input is. Let's call the +input + + align:start position:0% +input + + + align:start position:0% +input +alpha. Does that make sense? Let's see. + + align:start position:0% +alpha. Does that make sense? Let's see. + + + align:start position:0% +alpha. Does that make sense? Let's see. +If alpha is zero, then it's 1 over 1 + + align:start position:0% +If alpha is zero, then it's 1 over 1 + + + align:start position:0% +If alpha is zero, then it's 1 over 1 +plus 1. So that's + + align:start position:0% +plus 1. So that's + + + align:start position:0% +plus 1. So that's +1/2. If alpha is extremely big, then e + + align:start position:0% +1/2. If alpha is extremely big, then e + + + align:start position:0% +1/2. If alpha is extremely big, then e +to the minus alpha is extremely small + + align:start position:0% +to the minus alpha is extremely small + + + align:start position:0% +to the minus alpha is extremely small +and it becomes + + align:start position:0% +and it becomes + + + align:start position:0% +and it becomes +one. Goes up to an asmtoic value one + + align:start position:0% +one. Goes up to an asmtoic value one + + + align:start position:0% +one. Goes up to an asmtoic value one +here. + + align:start position:0% +here. + + + align:start position:0% +here. +On the other hand, if alpha is extremely + + align:start position:0% +On the other hand, if alpha is extremely + + + align:start position:0% +On the other hand, if alpha is extremely +negative, then e to the minus alpha is + + align:start position:0% +negative, then e to the minus alpha is + + + align:start position:0% +negative, then e to the minus alpha is +extremely positive and it goes to zero + + align:start position:0% +extremely positive and it goes to zero + + + align:start position:0% +extremely positive and it goes to zero +asmtoically. So we got the right look to + + align:start position:0% +asmtoically. So we got the right look to + + + align:start position:0% +asmtoically. So we got the right look to +that function. It's a very convenient + + align:start position:0% +that function. It's a very convenient + + + align:start position:0% +that function. It's a very convenient +function. Did God say that neurons ought + + align:start position:0% +function. Did God say that neurons ought + + + align:start position:0% +function. Did God say that neurons ought +to + + align:start position:0% +to + + + align:start position:0% +to +be has that threshold ought to work like + + align:start position:0% +be has that threshold ought to work like + + + align:start position:0% +be has that threshold ought to work like +that? No. God didn't say so. Who said + + align:start position:0% +that? No. God didn't say so. Who said + + + align:start position:0% +that? No. God didn't say so. Who said +so? The math says so. it has the right + + align:start position:0% +so? The math says so. it has the right + + + align:start position:0% +so? The math says so. it has the right +shape and look and the math and it turns + + align:start position:0% +shape and look and the math and it turns + + + align:start position:0% +shape and look and the math and it turns +out to have the right math. We'll as + + align:start position:0% +out to have the right math. We'll as + + + align:start position:0% +out to have the right math. We'll as +we'll see in a moment. + + align:start position:0% +we'll see in a moment. + + + align:start position:0% +we'll see in a moment. +Okay, so let's see where are we? We + + align:start position:0% +Okay, so let's see where are we? We + + + align:start position:0% +Okay, so let's see where are we? We +decided that what we'd like to do is + + align:start position:0% +decided that what we'd like to do is + + + align:start position:0% +decided that what we'd like to do is +take these partial derivatives. We noted + + align:start position:0% +take these partial derivatives. We noted + + + align:start position:0% +take these partial derivatives. We noted +that it was awkward to have those + + align:start position:0% +that it was awkward to have those + + + align:start position:0% +that it was awkward to have those +thresholds, so we got rid of them. And + + align:start position:0% +thresholds, so we got rid of them. And + + + align:start position:0% +thresholds, so we got rid of them. And +we noted it was impossible to have the + + align:start position:0% +we noted it was impossible to have the + + + align:start position:0% +we noted it was impossible to have the +step function, so we got rid of it. Now + + align:start position:0% +step function, so we got rid of it. Now + + + align:start position:0% +step function, so we got rid of it. Now +we're in a situation where we can + + align:start position:0% +we're in a situation where we can + + + align:start position:0% +we're in a situation where we can +actually take those partial derivatives + + align:start position:0% +actually take those partial derivatives + + + align:start position:0% +actually take those partial derivatives +and see if it gives us a way of training + + align:start position:0% +and see if it gives us a way of training + + + align:start position:0% +and see if it gives us a way of training +the neural net. so as to bring the + + align:start position:0% +the neural net. so as to bring the + + + align:start position:0% +the neural net. so as to bring the +actual output into alignment with what + + align:start position:0% +actual output into alignment with what + + + align:start position:0% +actual output into alignment with what +we + + align:start position:0% +we + + + align:start position:0% +we +desire. All right? So to deal with that, + + align:start position:0% +desire. All right? So to deal with that, + + + align:start position:0% +desire. All right? So to deal with that, +we're going to have to work with the + + align:start position:0% +we're going to have to work with the + + + align:start position:0% +we're going to have to work with the +world's simplest neural net. Now, if + + align:start position:0% +world's simplest neural net. Now, if + + + align:start position:0% +world's simplest neural net. Now, if +we've got one neuron, it's not a net. + + align:start position:0% +we've got one neuron, it's not a net. + + + align:start position:0% +we've got one neuron, it's not a net. +But if we've got two word neurons, we've + + align:start position:0% +But if we've got two word neurons, we've + + + align:start position:0% +But if we've got two word neurons, we've +got a net. Turns out that's the world's + + align:start position:0% +got a net. Turns out that's the world's + + + align:start position:0% +got a net. Turns out that's the world's +simplest neuron. So we're going to look + + align:start position:0% +simplest neuron. So we're going to look + + + align:start position:0% +simplest neuron. So we're going to look +at it. Not 60 million parameters, but + + align:start position:0% +at it. Not 60 million parameters, but + + + align:start position:0% +at it. Not 60 million parameters, but +just a few. Actually, just two + + align:start position:0% +just a few. Actually, just two + + + align:start position:0% +just a few. Actually, just two +parameters. + + align:start position:0% +parameters. + + + align:start position:0% +parameters. +So let's draw it out. We've got an input + + align:start position:0% +So let's draw it out. We've got an input + + + align:start position:0% +So let's draw it out. We've got an input +X that goes into a multiplier and it + + align:start position:0% +X that goes into a multiplier and it + + + align:start position:0% +X that goes into a multiplier and it +gets multiplied times + + align:start position:0% +gets multiplied times + + + align:start position:0% +gets multiplied times +W1. Then that goes into a sigmoid box + + align:start position:0% +W1. Then that goes into a sigmoid box + + + align:start position:0% +W1. Then that goes into a sigmoid box +like so. We'll call this P1, by the way, + + align:start position:0% +like so. We'll call this P1, by the way, + + + align:start position:0% +like so. We'll call this P1, by the way, +product number one. Out here comes Y. Y + + align:start position:0% +product number one. Out here comes Y. Y + + + align:start position:0% +product number one. Out here comes Y. Y +gets multiplied times another weight. + + align:start position:0% +gets multiplied times another weight. + + + align:start position:0% +gets multiplied times another weight. +We'll call that + + align:start position:0% +We'll call that + + + align:start position:0% +We'll call that +W2. The neck produces another product + + align:start position:0% +W2. The neck produces another product + + + align:start position:0% +W2. The neck produces another product +which we'll call P2 and that goes into a + + align:start position:0% +which we'll call P2 and that goes into a + + + align:start position:0% +which we'll call P2 and that goes into a +sigmoid + + align:start position:0% +sigmoid + + + align:start position:0% +sigmoid +box. And then that comes out as Z. And Z + + align:start position:0% +box. And then that comes out as Z. And Z + + + align:start position:0% +box. And then that comes out as Z. And Z +is the number that we use to determine + + align:start position:0% +is the number that we use to determine + + + align:start position:0% +is the number that we use to determine +how well we're doing. And our + + align:start position:0% +how well we're doing. And our + + + align:start position:0% +how well we're doing. And our +performance is actually going to be our + + align:start position:0% +performance is actually going to be our + + + align:start position:0% +performance is actually going to be our +performance function P is going to be 12 + + align:start position:0% +performance function P is going to be 12 + + + align:start position:0% +performance function P is going to be 12 +minus 12 because I like things are going + + align:start position:0% +minus 12 because I like things are going + + + align:start position:0% +minus 12 because I like things are going +in that direction times the difference + + align:start position:0% +in that direction times the difference + + + align:start position:0% +in that direction times the difference +between the desired output and the + + align:start position:0% +between the desired output and the + + + align:start position:0% +between the desired output and the +actual output + + align:start position:0% + + + + align:start position:0% + +squared. Okay. So now let's decide what + + align:start position:0% +squared. Okay. So now let's decide what + + + align:start position:0% +squared. Okay. So now let's decide what +those partial derivatives are going to + + align:start position:0% +those partial derivatives are going to + + + align:start position:0% +those partial derivatives are going to +be. + + align:start position:0% + + + + align:start position:0% + +Oh, let me do it over + + align:start position:0% + + + + align:start position:0% + +here. So, what are we trying to compute? + + align:start position:0% +here. So, what are we trying to compute? + + + align:start position:0% +here. So, what are we trying to compute? +Partial of the performance function P + + align:start position:0% +Partial of the performance function P + + + align:start position:0% +Partial of the performance function P +with respect to + + align:start position:0% + + + + align:start position:0% + +W2. + + align:start position:0% + + + + align:start position:0% + +Okay. Well, let's see. you know, + + align:start position:0% +Okay. Well, let's see. you know, + + + align:start position:0% +Okay. Well, let's see. you know, +partial. We're trying to figure out how + + align:start position:0% +partial. We're trying to figure out how + + + align:start position:0% +partial. We're trying to figure out how +much this wiggles when we wiggle + + align:start position:0% +much this wiggles when we wiggle + + + align:start position:0% +much this wiggles when we wiggle +that, right? But, you know, it goes + + align:start position:0% +that, right? But, you know, it goes + + + align:start position:0% +that, right? But, you know, it goes +through this variable P2. And so, maybe + + align:start position:0% +through this variable P2. And so, maybe + + + align:start position:0% +through this variable P2. And so, maybe +what we can do is figure out how much + + align:start position:0% +what we can do is figure out how much + + + align:start position:0% +what we can do is figure out how much +this wiggles when we wiggle, how much Z + + align:start position:0% +this wiggles when we wiggle, how much Z + + + align:start position:0% +this wiggles when we wiggle, how much Z +wiggles when we wiggle P2, and then how + + align:start position:0% +wiggles when we wiggle P2, and then how + + + align:start position:0% +wiggles when we wiggle P2, and then how +much P2 wiggles when we + + align:start position:0% +much P2 wiggles when we + + + align:start position:0% +much P2 wiggles when we +wiggle + + align:start position:0% +wiggle + + + align:start position:0% +wiggle +W2. And just multiply those together. I + + align:start position:0% +W2. And just multiply those together. I + + + align:start position:0% +W2. And just multiply those together. I +forget what's that called. + + align:start position:0% +forget what's that called. + + + align:start position:0% +forget what's that called. +in 180 something or other the chain + + align:start position:0% +in 180 something or other the chain + + + align:start position:0% +in 180 something or other the chain +rule. So what we're going to do is we're + + align:start position:0% +rule. So what we're going to do is we're + + + align:start position:0% +rule. So what we're going to do is we're +going to rewrite that der that partial + + align:start position:0% +going to rewrite that der that partial + + + align:start position:0% +going to rewrite that der that partial +derivative using chain rule. And all + + align:start position:0% +derivative using chain rule. And all + + + align:start position:0% +derivative using chain rule. And all +it's doing is saying that there's an + + align:start position:0% +it's doing is saying that there's an + + + align:start position:0% +it's doing is saying that there's an +intermediate variable and we can compute + + align:start position:0% +intermediate variable and we can compute + + + align:start position:0% +intermediate variable and we can compute +how much that end wiggles with respect + + align:start position:0% +how much that end wiggles with respect + + + align:start position:0% +how much that end wiggles with respect +to how much that end wiggles by + + align:start position:0% +to how much that end wiggles by + + + align:start position:0% +to how much that end wiggles by +multiplying + + align:start position:0% + + + + align:start position:0% + +the how much of the other guys wiggle. + + align:start position:0% +the how much of the other guys wiggle. + + + align:start position:0% +the how much of the other guys wiggle. +Let me write it down. It makes more + + align:start position:0% +Let me write it down. It makes more + + + align:start position:0% +Let me write it down. It makes more +sense in mathematics. + + align:start position:0% +sense in mathematics. + + + align:start position:0% +sense in mathematics. +So that's going to be equal to the + + align:start position:0% +So that's going to be equal to the + + + align:start position:0% +So that's going to be equal to the +partial of P with respect to + + align:start position:0% +partial of P with respect to + + + align:start position:0% +partial of P with respect to +Z times the partial of P. Oh, sorry. + + align:start position:0% +Z times the partial of P. Oh, sorry. + + + align:start position:0% +Z times the partial of P. Oh, sorry. +Partial of Z with respect to + + align:start position:0% +Partial of Z with respect to + + + align:start position:0% +Partial of Z with respect to +P2. + + align:start position:0% +P2. + + + align:start position:0% +P2. +Ah, keep me on track here. Partial of Z + + align:start position:0% +Ah, keep me on track here. Partial of Z + + + align:start position:0% +Ah, keep me on track here. Partial of Z +with respect + + align:start position:0% +with respect + + + align:start position:0% +with respect +to W2. + + align:start position:0% + + + + align:start position:0% + +Now, I'm going to do something for which + + align:start position:0% +Now, I'm going to do something for which + + + align:start position:0% +Now, I'm going to do something for which +I will hate myself. I'm going to erase + + align:start position:0% +I will hate myself. I'm going to erase + + + align:start position:0% +I will hate myself. I'm going to erase +something on the board. I I don't like + + align:start position:0% +something on the board. I I don't like + + + align:start position:0% +something on the board. I I don't like +to do that. But but you you you know + + align:start position:0% +to do that. But but you you you know + + + align:start position:0% +to do that. But but you you you know +what I'm going to do, don't you? I'm + + align:start position:0% +what I'm going to do, don't you? I'm + + + align:start position:0% +what I'm going to do, don't you? I'm +going to + + align:start position:0% +going to + + + align:start position:0% +going to +say this this this is true by a chain + + align:start position:0% +say this this this is true by a chain + + + align:start position:0% +say this this this is true by a chain +rule. But look, I can take this guy here + + align:start position:0% +rule. But look, I can take this guy here + + + align:start position:0% +rule. But look, I can take this guy here +and screw around with it with a chain + + align:start position:0% +and screw around with it with a chain + + + align:start position:0% +and screw around with it with a chain +rule, too. + + align:start position:0% +rule, too. + + + align:start position:0% +rule, too. +And in fact, what what what I'm going to + + align:start position:0% +And in fact, what what what I'm going to + + + align:start position:0% +And in fact, what what what I'm going to +do is I'm going to replace that with + + align:start position:0% +do is I'm going to replace that with + + + align:start position:0% +do is I'm going to replace that with +partial of Z with respect to P2 and + + align:start position:0% +partial of Z with respect to P2 and + + + align:start position:0% +partial of Z with respect to P2 and +partial of P2 with respect to + + align:start position:0% +partial of P2 with respect to + + + align:start position:0% +partial of P2 with respect to +W2. Right? So, I didn't erase it after + + align:start position:0% +W2. Right? So, I didn't erase it after + + + align:start position:0% +W2. Right? So, I didn't erase it after +all, but you can see what I'm going to + + align:start position:0% +all, but you can see what I'm going to + + + align:start position:0% +all, but you can see what I'm going to +do next. I'm going to do the same thing + + align:start position:0% +do next. I'm going to do the same thing + + + align:start position:0% +do next. I'm going to do the same thing +with the other partial derivative, but + + align:start position:0% +with the other partial derivative, but + + + align:start position:0% +with the other partial derivative, but +this time instead of writing down and + + align:start position:0% +this time instead of writing down and + + + align:start position:0% +this time instead of writing down and +writing over, I'm just going to expand + + align:start position:0% +writing over, I'm just going to expand + + + align:start position:0% +writing over, I'm just going to expand +it all out in one go. I + + align:start position:0% +it all out in one go. I + + + align:start position:0% +it all out in one go. I +think so. Partial of + + align:start position:0% +think so. Partial of + + + align:start position:0% +think so. Partial of +P with respect to W1 is equal to the + + align:start position:0% +P with respect to W1 is equal to the + + + align:start position:0% +P with respect to W1 is equal to the +partial of P with respect to Z. The + + align:start position:0% +partial of P with respect to Z. The + + + align:start position:0% +partial of P with respect to Z. The +partial of Z with respect to + + align:start position:0% +partial of Z with respect to + + + align:start position:0% +partial of Z with respect to +P2. The partial of + + align:start position:0% +P2. The partial of + + + align:start position:0% +P2. The partial of +P2 with respect to what? Y. + + align:start position:0% +P2 with respect to what? Y. + + + align:start position:0% +P2 with respect to what? Y. +partial of y with respect to p1 partial + + align:start position:0% +partial of y with respect to p1 partial + + + align:start position:0% +partial of y with respect to p1 partial +of p1 with respect to + + align:start position:0% +of p1 with respect to + + + align:start position:0% +of p1 with respect to +w1. So that's just kind of going like a + + align:start position:0% +w1. So that's just kind of going like a + + + align:start position:0% +w1. So that's just kind of going like a +zipper down that that string of + + align:start position:0% +zipper down that that string of + + + align:start position:0% +zipper down that that string of +variables expanding each by using a + + align:start position:0% +variables expanding each by using a + + + align:start position:0% +variables expanding each by using a +chain rule until we got to the end. So + + align:start position:0% +chain rule until we got to the end. So + + + align:start position:0% +chain rule until we got to the end. So +there are some expressions that provide + + align:start position:0% +there are some expressions that provide + + + align:start position:0% +there are some expressions that provide +those partial derivatives. + + align:start position:0% + + + + align:start position:0% + +But + + align:start position:0% + + + + align:start position:0% + +now, if you don't if if you'll forgive + + align:start position:0% +now, if you don't if if you'll forgive + + + align:start position:0% +now, if you don't if if you'll forgive +me, it was convenient to write them out + + align:start position:0% +me, it was convenient to write them out + + + align:start position:0% +me, it was convenient to write them out +that way because that that matched the + + align:start position:0% +that way because that that matched the + + + align:start position:0% +that way because that that matched the +intuition in my head, but I'm just going + + align:start position:0% +intuition in my head, but I'm just going + + + align:start position:0% +intuition in my head, but I'm just going +to turn them + + align:start position:0% +to turn them + + + align:start position:0% +to turn them +around. I'm not just a it's just a + + align:start position:0% +around. I'm not just a it's just a + + + align:start position:0% +around. I'm not just a it's just a +product. I'm just going to turn them + + align:start position:0% +product. I'm just going to turn them + + + align:start position:0% +product. I'm just going to turn them +around. So partial + + align:start position:0% +around. So partial + + + align:start position:0% +around. So partial +P2 partial + + align:start position:0% +P2 partial + + + align:start position:0% +P2 partial +W2 times partial of Z partial + + align:start position:0% +W2 times partial of Z partial + + + align:start position:0% +W2 times partial of Z partial +P2 times the partial of + + align:start position:0% +P2 times the partial of + + + align:start position:0% +P2 times the partial of +P with respect to Z. Same thing. And now + + align:start position:0% +P with respect to Z. Same thing. And now + + + align:start position:0% +P with respect to Z. Same thing. And now +this one keep me on track because if + + align:start position:0% +this one keep me on track because if + + + align:start position:0% +this one keep me on track because if +there's a mutation here it will be + + align:start position:0% +there's a mutation here it will be + + + align:start position:0% +there's a mutation here it will be +fatal. partial of P1 partial W1 partial + + align:start position:0% +fatal. partial of P1 partial W1 partial + + + align:start position:0% +fatal. partial of P1 partial W1 partial +of + + align:start position:0% +of + + + align:start position:0% +of +Y partial + + align:start position:0% +Y partial + + + align:start position:0% +Y partial +P1 partial + + align:start position:0% +P1 partial + + + align:start position:0% +P1 partial +P2 partial of + + align:start position:0% +P2 partial of + + + align:start position:0% +P2 partial of +Y partial of + + align:start position:0% +Y partial of + + + align:start position:0% +Y partial of +Z times a partial of + + align:start position:0% +Z times a partial of + + + align:start position:0% +Z times a partial of +P2 partial of performance function with + + align:start position:0% +P2 partial of performance function with + + + align:start position:0% +P2 partial of performance function with +respect to Z. Okay. + + align:start position:0% +respect to Z. Okay. + + + align:start position:0% +respect to Z. Okay. +And now all we have to do is figure it + + align:start position:0% +And now all we have to do is figure it + + + align:start position:0% +And now all we have to do is figure it +out. Figure out what those partials are. + + align:start position:0% +out. Figure out what those partials are. + + + align:start position:0% +out. Figure out what those partials are. +And we uh have solved this little simple + + align:start position:0% +And we uh have solved this little simple + + + align:start position:0% +And we uh have solved this little simple +neural net neural net. So it's going to + + align:start position:0% +neural net neural net. So it's going to + + + align:start position:0% +neural net neural net. So it's going to +be + + align:start position:0% + + + + align:start position:0% + +easy. Oh, where where is my board space? + + align:start position:0% +easy. Oh, where where is my board space? + + + align:start position:0% +easy. Oh, where where is my board space? +Let's see. Partial of P2 with respected + + align:start position:0% +Let's see. Partial of P2 with respected + + + align:start position:0% +Let's see. Partial of P2 with respected +to + + align:start position:0% +to + + + align:start position:0% +to +um what partial that's that's the + + align:start position:0% +um what partial that's that's the + + + align:start position:0% +um what partial that's that's the +product. Partial of Z partial of the + + align:start position:0% +product. Partial of Z partial of the + + + align:start position:0% +product. Partial of Z partial of the +performance function with respect to Z. + + align:start position:0% +performance function with respect to Z. + + + align:start position:0% +performance function with respect to Z. +Oh, now I can see why I wrote it down + + align:start position:0% +Oh, now I can see why I wrote it down + + + align:start position:0% +Oh, now I can see why I wrote it down +this way. Let's see. is going to just be + + align:start position:0% +this way. Let's see. is going to just be + + + align:start position:0% +this way. Let's see. is going to just be +d minus e. We can do that one in our + + align:start position:0% + + + + align:start position:0% + +head. What about the partial of p2 with + + align:start position:0% +head. What about the partial of p2 with + + + align:start position:0% +head. What about the partial of p2 with +respect to + + align:start position:0% + + + + align:start position:0% + +w2? Well, p2 is equal to y * w2. So + + align:start position:0% +w2? Well, p2 is equal to y * w2. So + + + align:start position:0% +w2? Well, p2 is equal to y * w2. So +that's easy. That's just + + align:start position:0% + + + + align:start position:0% + +y. And now all we have to do is figure + + align:start position:0% +y. And now all we have to do is figure + + + align:start position:0% +y. And now all we have to do is figure +out the partial of Z with respect to P2. + + align:start position:0% +out the partial of Z with respect to P2. + + + align:start position:0% +out the partial of Z with respect to P2. +Oh crap. All it's just it's going + + align:start position:0% +Oh crap. All it's just it's going + + + align:start position:0% +Oh crap. All it's just it's going +through this this threshold box. So I + + align:start position:0% +through this this threshold box. So I + + + align:start position:0% +through this this threshold box. So I +don't know exactly what that partial + + align:start position:0% +don't know exactly what that partial + + + align:start position:0% +don't know exactly what that partial +derivative is. So we'll have to figure + + align:start position:0% +derivative is. So we'll have to figure + + + align:start position:0% +derivative is. So we'll have to figure +that out, + + align:start position:0% +that out, + + + align:start position:0% +that out, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +Because uh the function relating them is + + align:start position:0% +Because uh the function relating them is + + + align:start position:0% +Because uh the function relating them is +this is this guy here. And so we have to + + align:start position:0% +this is this guy here. And so we have to + + + align:start position:0% +this is this guy here. And so we have to +figure out the partial of that with + + align:start position:0% +figure out the partial of that with + + + align:start position:0% +figure out the partial of that with +respect to + + align:start position:0% +respect to + + + align:start position:0% +respect to +alpha. All right. So we got to do it. + + align:start position:0% +alpha. All right. So we got to do it. + + + align:start position:0% +alpha. All right. So we got to do it. +There's no qu there's no way around it. + + align:start position:0% +There's no qu there's no way around it. + + + align:start position:0% +There's no qu there's no way around it. +So, uh, we have to destroy + + align:start position:0% +So, uh, we have to destroy + + + align:start position:0% +So, uh, we have to destroy +something. Okay, we're going to + + align:start position:0% +something. Okay, we're going to + + + align:start position:0% +something. Okay, we're going to +destroy our neuron. + + align:start position:0% + + + + align:start position:0% + +So the function we're dealing with is + + align:start position:0% +So the function we're dealing with is + + + align:start position:0% +So the function we're dealing with is +we'll call it beta is equal to 1 / 1 + e + + align:start position:0% +we'll call it beta is equal to 1 / 1 + e + + + align:start position:0% +we'll call it beta is equal to 1 / 1 + e +to the minus alpha. And we want what we + + align:start position:0% +to the minus alpha. And we want what we + + + align:start position:0% +to the minus alpha. And we want what we +want is the + + align:start position:0% +want is the + + + align:start position:0% +want is the +derivative with respect to + + align:start position:0% +derivative with respect to + + + align:start position:0% +derivative with respect to +alpha of beta and that's equal to d by d + + align:start position:0% +alpha of beta and that's equal to d by d + + + align:start position:0% +alpha of beta and that's equal to d by d +alpha + + align:start position:0% +alpha + + + align:start position:0% +alpha +of you know I I can never remember those + + align:start position:0% +of you know I I can never remember those + + + align:start position:0% +of you know I I can never remember those +quotient formulas. Uh so I'm going to + + align:start position:0% +quotient formulas. Uh so I'm going to + + + align:start position:0% +quotient formulas. Uh so I'm going to +rewrite it a little different way. I'm + + align:start position:0% +rewrite it a little different way. I'm + + + align:start position:0% +rewrite it a little different way. I'm +going to write it as 1 minus e to the + + align:start position:0% +going to write it as 1 minus e to the + + + align:start position:0% +going to write it as 1 minus e to the +minus + + align:start position:0% +minus + + + align:start position:0% +minus +alpha to the minus one. So I because I + + align:start position:0% +alpha to the minus one. So I because I + + + align:start position:0% +alpha to the minus one. So I because I +can't remember the formula for + + align:start position:0% +can't remember the formula for + + + align:start position:0% +can't remember the formula for +differentiating + + align:start position:0% +differentiating + + + align:start position:0% +differentiating +quotient. Okay. So let's differentiate + + align:start position:0% +quotient. Okay. So let's differentiate + + + align:start position:0% +quotient. Okay. So let's differentiate +it. So + + align:start position:0% +it. So + + + align:start position:0% +it. So +uh that's equal + + align:start position:0% +uh that's equal + + + align:start position:0% +uh that's equal +to 1 - alpha 1 - e to the minus + + align:start position:0% +to 1 - alpha 1 - e to the minus + + + align:start position:0% +to 1 - alpha 1 - e to the minus +alpha to the minus + + align:start position:0% + + + + align:start position:0% + +2 and we got that minus comes out out of + + align:start position:0% +2 and we got that minus comes out out of + + + align:start position:0% +2 and we got that minus comes out out of +that part of it. Then we got to + + align:start position:0% +that part of it. Then we got to + + + align:start position:0% +that part of it. Then we got to +differentiate the it's got to + + align:start position:0% +differentiate the it's got to + + + align:start position:0% +differentiate the it's got to +differentiate the inside. of that + + align:start position:0% +differentiate the inside. of that + + + align:start position:0% +differentiate the inside. of that +expression and when we differentiate the + + align:start position:0% +expression and when we differentiate the + + + align:start position:0% +expression and when we differentiate the +inside of that expression we get e to + + align:start position:0% +inside of that expression we get e to + + + align:start position:0% +inside of that expression we get e to +the minus alpha. + + align:start position:0% +the minus alpha. + + + align:start position:0% +the minus alpha. +Yeah. + + align:start position:0% + + + + align:start position:0% + +Oh yeah. Sorry. Thank you. That was that + + align:start position:0% +Oh yeah. Sorry. Thank you. That was that + + + align:start position:0% +Oh yeah. Sorry. Thank you. That was that +was one of those fatal mistakes you just + + align:start position:0% +was one of those fatal mistakes you just + + + align:start position:0% +was one of those fatal mistakes you just +prevented. So that's one plus. That's + + align:start position:0% +prevented. So that's one plus. That's + + + align:start position:0% +prevented. So that's one plus. That's +one plus here too. Okay. So so we we've + + align:start position:0% +one plus here too. Okay. So so we we've + + + align:start position:0% +one plus here too. Okay. So so we we've +differentiated that. We've turned that + + align:start position:0% +differentiated that. We've turned that + + + align:start position:0% +differentiated that. We've turned that +into a minus2. We brought the minus sign + + align:start position:0% +into a minus2. We brought the minus sign + + + align:start position:0% +into a minus2. We brought the minus sign +outside. Then we're differentiating the + + align:start position:0% +outside. Then we're differentiating the + + + align:start position:0% +outside. Then we're differentiating the +inside. The derivative of an exponential + + align:start position:0% +inside. The derivative of an exponential + + + align:start position:0% +inside. The derivative of an exponential +is an exponential. Then we got to + + align:start position:0% +is an exponential. Then we got to + + + align:start position:0% +is an exponential. Then we got to +differentiate that guy and that just + + align:start position:0% +differentiate that guy and that just + + + align:start position:0% +differentiate that guy and that just +helps us get rid of the minus sign we + + align:start position:0% +helps us get rid of the minus sign we + + + align:start position:0% +helps us get rid of the minus sign we +introduced. So that's the + + align:start position:0% +introduced. So that's the + + + align:start position:0% +introduced. So that's the +derivative. I'm not sure how much that + + align:start position:0% +derivative. I'm not sure how much that + + + align:start position:0% +derivative. I'm not sure how much that +helps except that I'm going to perform a + + align:start position:0% +helps except that I'm going to perform a + + + align:start position:0% +helps except that I'm going to perform a +polar trick here and rewrite that + + align:start position:0% +polar trick here and rewrite that + + + align:start position:0% +polar trick here and rewrite that +expression thusly. + + align:start position:0% +expression thusly. + + + align:start position:0% +expression thusly. +I'm going to say that's going to be + + align:start position:0% +I'm going to say that's going to be + + + align:start position:0% +I'm going to say that's going to be +um eus + + align:start position:0% +um eus + + + align:start position:0% +um eus +alpha over 1 + e to the minus + + align:start position:0% +alpha over 1 + e to the minus + + + align:start position:0% +alpha over 1 + e to the minus +alpha times 1 / 1 + eus + + align:start position:0% +alpha times 1 / 1 + eus + + + align:start position:0% +alpha times 1 / 1 + eus +alpha that + + align:start position:0% +alpha that + + + align:start position:0% +alpha that +okay I've got a lot of nodding heads + + align:start position:0% +okay I've got a lot of nodding heads + + + align:start position:0% +okay I've got a lot of nodding heads +here so I think I'm safe on safe + + align:start position:0% +here so I think I'm safe on safe + + + align:start position:0% +here so I think I'm safe on safe +ground but now I'm going to perform + + align:start position:0% +ground but now I'm going to perform + + + align:start position:0% +ground but now I'm going to perform +another polar trick + + align:start position:0% + + + + align:start position:0% + +I'm going to add + + align:start position:0% + + + + align:start position:0% + +one, which means I also have to subtract + + align:start position:0% + + + + align:start position:0% + +one. All right, that's legitimate, isn't + + align:start position:0% +one. All right, that's legitimate, isn't + + + align:start position:0% +one. All right, that's legitimate, isn't +it? + + align:start position:0% +it? + + + align:start position:0% +it? +So now I can rewrite this + + align:start position:0% +So now I can rewrite this + + + align:start position:0% +So now I can rewrite this +as 1 + eus alpha over 1 + eus + + align:start position:0% + + + + align:start position:0% + +alpha minus 1 / 1 + eus + + align:start position:0% + + + + align:start position:0% + +alpha times 1 over 1 + e to the minus + + align:start position:0% +alpha times 1 over 1 + e to the minus + + + align:start position:0% +alpha times 1 over 1 + e to the minus +alpha. Any high school kid could do + + align:start position:0% +alpha. Any high school kid could do + + + align:start position:0% +alpha. Any high school kid could do +that. I think I'm on safe ground. + + align:start position:0% +that. I think I'm on safe ground. + + + align:start position:0% +that. I think I'm on safe ground. +Oh, + + align:start position:0% + + + + align:start position:0% + +wait. This is + + align:start position:0% +wait. This is + + + align:start position:0% +wait. This is +beta. This is beta. + + align:start position:0% +beta. This is beta. + + + align:start position:0% +beta. This is beta. +Oh, sorry. Wrong wrong wrong side. + + align:start position:0% +Oh, sorry. Wrong wrong wrong side. + + + align:start position:0% +Oh, sorry. Wrong wrong wrong side. +Better make this beta. And this one. Any + + align:start position:0% +Better make this beta. And this one. Any + + + align:start position:0% +Better make this beta. And this one. Any +high school kid could do it. + + align:start position:0% +high school kid could do it. + + + align:start position:0% +high school kid could do it. +Okay. So, what we've got then is that + + align:start position:0% +Okay. So, what we've got then is that + + + align:start position:0% +Okay. So, what we've got then is that +this is equal to 1 minus beta time + + align:start position:0% +this is equal to 1 minus beta time + + + align:start position:0% +this is equal to 1 minus beta time +beta. That's the derivative. And that's + + align:start position:0% +beta. That's the derivative. And that's + + + align:start position:0% +beta. That's the derivative. And that's +weird because the the derivative of the + + align:start position:0% +weird because the the derivative of the + + + align:start position:0% +weird because the the derivative of the +output with respect to the input is + + align:start position:0% +output with respect to the input is + + + align:start position:0% +output with respect to the input is +given exclusively in terms of the + + align:start position:0% +given exclusively in terms of the + + + align:start position:0% +given exclusively in terms of the +output. + + align:start position:0% +output. + + + align:start position:0% +output. +Strange doesn't really matter, but it's + + align:start position:0% +Strange doesn't really matter, but it's + + + align:start position:0% +Strange doesn't really matter, but it's +a curiosity. And what we get out of this + + align:start position:0% +a curiosity. And what we get out of this + + + align:start position:0% +a curiosity. And what we get out of this +is that that partial derivative there + + align:start position:0% +is that that partial derivative there + + + align:start position:0% +is that that partial derivative there +that's equal + + align:start position:0% + + + + align:start position:0% + +to well the output is + + align:start position:0% +to well the output is + + + align:start position:0% +to well the output is +P2. No, the output is Z. So it's Z * 1 - + + align:start position:0% +P2. No, the output is Z. So it's Z * 1 - + + + align:start position:0% +P2. No, the output is Z. So it's Z * 1 - +Z. + + align:start position:0% +Z. + + + align:start position:0% +Z. +So whenever we see the output derivative + + align:start position:0% +So whenever we see the output derivative + + + align:start position:0% +So whenever we see the output derivative +of one of these sigmoids with respect to + + align:start position:0% +of one of these sigmoids with respect to + + + align:start position:0% +of one of these sigmoids with respect to +its input, we can just write the output + + align:start position:0% +its input, we can just write the output + + + align:start position:0% +its input, we can just write the output +times one minus the output. We've got + + align:start position:0% +times one minus the output. We've got + + + align:start position:0% +times one minus the output. We've got +it. So that's why it's mathematically + + align:start position:0% +it. So that's why it's mathematically + + + align:start position:0% +it. So that's why it's mathematically +convenient. It's mathematically + + align:start position:0% +convenient. It's mathematically + + + align:start position:0% +convenient. It's mathematically +convenient because when we do this + + align:start position:0% +convenient because when we do this + + + align:start position:0% +convenient because when we do this +differentiation, we get a very simple + + align:start position:0% +differentiation, we get a very simple + + + align:start position:0% +differentiation, we get a very simple +expression in terms of the output. We + + align:start position:0% +expression in terms of the output. We + + + align:start position:0% +expression in terms of the output. We +get a very simple expression. That's all + + align:start position:0% +get a very simple expression. That's all + + + align:start position:0% +get a very simple expression. That's all +we really + + align:start position:0% + + + + align:start position:0% + +need. + + align:start position:0% +need. + + + align:start position:0% +need. +So would you like to see a + + align:start position:0% +So would you like to see a + + + align:start position:0% +So would you like to see a +demonstration? This is a demonstration + + align:start position:0% +demonstration? This is a demonstration + + + align:start position:0% +demonstration? This is a demonstration +of world's smallest neural net in + + align:start position:0% + + + + align:start position:0% + +action. Where is neural net? There we + + align:start position:0% + + + + align:start position:0% + +go. So there's our neural net. And what + + align:start position:0% +go. So there's our neural net. And what + + + align:start position:0% +go. So there's our neural net. And what +we're going to do is we're going to + + align:start position:0% +we're going to do is we're going to + + + align:start position:0% +we're going to do is we're going to +train it to do absolutely nothing. What + + align:start position:0% +train it to do absolutely nothing. What + + + align:start position:0% +train it to do absolutely nothing. What +we're going to do is train it to have + + align:start position:0% +we're going to do is train it to have + + + align:start position:0% +we're going to do is train it to have +make the output the same as the + + align:start position:0% +make the output the same as the + + + align:start position:0% +make the output the same as the +input. Not what I call a fantastic leap + + align:start position:0% +input. Not what I call a fantastic leap + + + align:start position:0% +input. Not what I call a fantastic leap +of intelligence, but let's see what + + align:start position:0% +of intelligence, but let's see what + + + align:start position:0% +of intelligence, but let's see what +happens. + + align:start position:0% + + + + align:start position:0% + +Wow. Nothing's + + align:start position:0% + + + + align:start position:0% + +happening. Well, it finally got to the + + align:start position:0% +happening. Well, it finally got to the + + + align:start position:0% +happening. Well, it finally got to the +point where the maximum error, not the + + align:start position:0% +point where the maximum error, not the + + + align:start position:0% +point where the maximum error, not the +performance, but the maximum error went + + align:start position:0% +performance, but the maximum error went + + + align:start position:0% +performance, but the maximum error went +below a threshold that I had previously + + align:start position:0% +below a threshold that I had previously + + + align:start position:0% +below a threshold that I had previously +determined. So if you look at the input + + align:start position:0% +determined. So if you look at the input + + + align:start position:0% +determined. So if you look at the input +here and compare that with the desired + + align:start position:0% +here and compare that with the desired + + + align:start position:0% +here and compare that with the desired +output on the far right, you see it + + align:start position:0% +output on the far right, you see it + + + align:start position:0% +output on the far right, you see it +produces an output which compared with + + align:start position:0% +produces an output which compared with + + + align:start position:0% +produces an output which compared with +the desired output is pretty close. So + + align:start position:0% +the desired output is pretty close. So + + + align:start position:0% +the desired output is pretty close. So +we can test uh the other way like so. + + align:start position:0% +we can test uh the other way like so. + + + align:start position:0% +we can test uh the other way like so. +And we can see that the desired output + + align:start position:0% +And we can see that the desired output + + + align:start position:0% +And we can see that the desired output +is pretty close to the desire actual + + align:start position:0% +is pretty close to the desire actual + + + align:start position:0% +is pretty close to the desire actual +output in that case too. And it took 694 + + align:start position:0% +output in that case too. And it took 694 + + + align:start position:0% +output in that case too. And it took 694 +iterations to get that done. Let's try + + align:start position:0% +iterations to get that done. Let's try + + + align:start position:0% +iterations to get that done. Let's try +it again. + + align:start position:0% + + + + align:start position:0% + +Oh, to 823. Of course, this is all a + + align:start position:0% +Oh, to 823. Of course, this is all a + + + align:start position:0% +Oh, to 823. Of course, this is all a +consequence of just starting off with + + align:start position:0% +consequence of just starting off with + + + align:start position:0% +consequence of just starting off with +random + + align:start position:0% +random + + + align:start position:0% +random +weights. By the way, if you started off + + align:start position:0% +weights. By the way, if you started off + + + align:start position:0% +weights. By the way, if you started off +with the weights, all the weights being + + align:start position:0% +with the weights, all the weights being + + + align:start position:0% +with the weights, all the weights being +the same, what would happen? Nothing, + + align:start position:0% +the same, what would happen? Nothing, + + + align:start position:0% +the same, what would happen? Nothing, +because it'd always stay the same. So, + + align:start position:0% +because it'd always stay the same. So, + + + align:start position:0% +because it'd always stay the same. So, +you got to put some randomization into + + align:start position:0% +you got to put some randomization into + + + align:start position:0% +you got to put some randomization into +the + + align:start position:0% +the + + + align:start position:0% +the +beginning. So that took a long time. + + align:start position:0% +beginning. So that took a long time. + + + align:start position:0% +beginning. So that took a long time. +Maybe the problem is that our rate + + align:start position:0% +Maybe the problem is that our rate + + + align:start position:0% +Maybe the problem is that our rate +constant is too small. So let's try + + align:start position:0% +constant is too small. So let's try + + + align:start position:0% +constant is too small. So let's try +let's crank up the rate constant a + + align:start position:0% +let's crank up the rate constant a + + + align:start position:0% +let's crank up the rate constant a +little more a little bit and see what + + align:start position:0% + + + + align:start position:0% + +happens. Ah that was pretty fast. Let's + + align:start position:0% +happens. Ah that was pretty fast. Let's + + + align:start position:0% +happens. Ah that was pretty fast. Let's +see if it was a consequence of uh random + + align:start position:0% +see if it was a consequence of uh random + + + align:start position:0% +see if it was a consequence of uh random +chance + + align:start position:0% +chance + + + align:start position:0% +chance +uh run. No, it's pretty fast there. 57 + + align:start position:0% +uh run. No, it's pretty fast there. 57 + + + align:start position:0% +uh run. No, it's pretty fast there. 57 +times 57 + + align:start position:0% +times 57 + + + align:start position:0% +times 57 +iterations. Third + + align:start position:0% +iterations. Third + + + align:start position:0% +iterations. Third +try 67. So it looks like my initial rate + + align:start position:0% +try 67. So it looks like my initial rate + + + align:start position:0% +try 67. So it looks like my initial rate +constant was too small. So if uh 0.5 was + + align:start position:0% +constant was too small. So if uh 0.5 was + + + align:start position:0% +constant was too small. So if uh 0.5 was +not as good as 5.0, how why don't we + + align:start position:0% +not as good as 5.0, how why don't we + + + align:start position:0% +not as good as 5.0, how why don't we +crank it up to 50 and see what + + align:start position:0% + + + + align:start position:0% + +happens? Oh, in this case 124. Let's try + + align:start position:0% +happens? Oh, in this case 124. Let's try + + + align:start position:0% +happens? Oh, in this case 124. Let's try +it + + align:start position:0% + + + + align:start position:0% + +again. H in this case 117. So it's + + align:start position:0% +again. H in this case 117. So it's + + + align:start position:0% +again. H in this case 117. So it's +actually gotten worse. + + align:start position:0% +actually gotten worse. + + + align:start position:0% +actually gotten worse. +And not only has it gotten worse, you'll + + align:start position:0% +And not only has it gotten worse, you'll + + + align:start position:0% +And not only has it gotten worse, you'll +see that there's a little bit of uh a + + align:start position:0% +see that there's a little bit of uh a + + + align:start position:0% +see that there's a little bit of uh a +little bit of instability showing up as + + align:start position:0% +little bit of instability showing up as + + + align:start position:0% +little bit of instability showing up as +it courses along its way toward a + + align:start position:0% +it courses along its way toward a + + + align:start position:0% +it courses along its way toward a +solution. So what it looks like is that + + align:start position:0% +solution. So what it looks like is that + + + align:start position:0% +solution. So what it looks like is that +if you've got a rate rate constant too + + align:start position:0% +if you've got a rate rate constant too + + + align:start position:0% +if you've got a rate rate constant too +small, it takes forever. You got a rate + + align:start position:0% +small, it takes forever. You got a rate + + + align:start position:0% +small, it takes forever. You got a rate +constant that's too big, it can sort + + align:start position:0% +constant that's too big, it can sort + + + align:start position:0% +constant that's too big, it can sort +of jump too far. As in my diagram, which + + align:start position:0% +of jump too far. As in my diagram, which + + + align:start position:0% +of jump too far. As in my diagram, which +is somewhere underneath a board, you can + + align:start position:0% +is somewhere underneath a board, you can + + + align:start position:0% +is somewhere underneath a board, you can +you can go all the way across the hill + + align:start position:0% +you can go all the way across the hill + + + align:start position:0% +you can go all the way across the hill +and get to the other side. So you have + + align:start position:0% +and get to the other side. So you have + + + align:start position:0% +and get to the other side. So you have +to be careful about the rate constant. + + align:start position:0% +to be careful about the rate constant. + + + align:start position:0% +to be careful about the rate constant. +So what you really want to do is you + + align:start position:0% +So what you really want to do is you + + + align:start position:0% +So what you really want to do is you +want your rate constant to vary with + + align:start position:0% +want your rate constant to vary with + + + align:start position:0% +want your rate constant to vary with +what's happening in the in as you + + align:start position:0% +what's happening in the in as you + + + align:start position:0% +what's happening in the in as you +progress toward uh an optimal part an + + align:start position:0% +progress toward uh an optimal part an + + + align:start position:0% +progress toward uh an optimal part an +optimal performance. So if you if your + + align:start position:0% +optimal performance. So if you if your + + + align:start position:0% +optimal performance. So if you if your +if your performance is going down when + + align:start position:0% +if your performance is going down when + + + align:start position:0% +if your performance is going down when +you make the jump, you know you've got a + + align:start position:0% +you make the jump, you know you've got a + + + align:start position:0% +you make the jump, you know you've got a +rate constant is too big. If your + + align:start position:0% +rate constant is too big. If your + + + align:start position:0% +rate constant is too big. If your +performance is going up when you make a + + align:start position:0% +performance is going up when you make a + + + align:start position:0% +performance is going up when you make a +jump, maybe you want to increase bump it + + align:start position:0% +jump, maybe you want to increase bump it + + + align:start position:0% +jump, maybe you want to increase bump it +up a little bit until it until it until + + align:start position:0% +up a little bit until it until it until + + + align:start position:0% +up a little bit until it until it until +till it doesn't look so + + align:start position:0% +till it doesn't look so + + + align:start position:0% +till it doesn't look so +good. Okay. So uh is that all there is + + align:start position:0% +good. Okay. So uh is that all there is + + + align:start position:0% +good. Okay. So uh is that all there is +to it? Well, not quite because uh this + + align:start position:0% +to it? Well, not quite because uh this + + + align:start position:0% +to it? Well, not quite because uh this +is the world's simplest neural net. And + + align:start position:0% +is the world's simplest neural net. And + + + align:start position:0% +is the world's simplest neural net. And +maybe we ought to look at the world's + + align:start position:0% +maybe we ought to look at the world's + + + align:start position:0% +maybe we ought to look at the world's +second simplest neural + + align:start position:0% +second simplest neural + + + align:start position:0% +second simplest neural +net. Let's call this + + align:start position:0% +net. Let's call this + + + align:start position:0% +net. Let's call this +uh well, let's call this + + align:start position:0% +uh well, let's call this + + + align:start position:0% +uh well, let's call this +X. What we're going to do is we're going + + align:start position:0% +X. What we're going to do is we're going + + + align:start position:0% +X. What we're going to do is we're going +to have a second + + align:start position:0% +to have a second + + + align:start position:0% +to have a second +input. And I'm just I don't know, maybe + + align:start position:0% +input. And I'm just I don't know, maybe + + + align:start position:0% +input. And I'm just I don't know, maybe +this is screwy. I'm just going to use + + align:start position:0% +this is screwy. I'm just going to use + + + align:start position:0% +this is screwy. I'm just going to use +color coding here to differentiate + + align:start position:0% +color coding here to differentiate + + + align:start position:0% +color coding here to differentiate +between the two inputs and and the and + + align:start position:0% +between the two inputs and and the and + + + align:start position:0% +between the two inputs and and the and +the stuff they go through. + + align:start position:0% + + + + align:start position:0% + +Maybe I'll call this Z2 and this Z1 and + + align:start position:0% +Maybe I'll call this Z2 and this Z1 and + + + align:start position:0% +Maybe I'll call this Z2 and this Z1 and +this X1 and + + align:start position:0% + + + + align:start position:0% + +X2. Now, if I do that, if I've got two + + align:start position:0% +X2. Now, if I do that, if I've got two + + + align:start position:0% +X2. Now, if I do that, if I've got two +inputs and two outputs, then then uh my + + align:start position:0% +inputs and two outputs, then then uh my + + + align:start position:0% +inputs and two outputs, then then uh my +performance function is going to have + + align:start position:0% +performance function is going to have + + + align:start position:0% +performance function is going to have +two numbers in it, the two desired + + align:start position:0% +two numbers in it, the two desired + + + align:start position:0% +two numbers in it, the two desired +values and the two actual values. And + + align:start position:0% +values and the two actual values. And + + + align:start position:0% +values and the two actual values. And +I'm going to have two inputs. But, you + + align:start position:0% +I'm going to have two inputs. But, you + + + align:start position:0% +I'm going to have two inputs. But, you +know, it's the same stuff. I just repeat + + align:start position:0% +know, it's the same stuff. I just repeat + + + align:start position:0% +know, it's the same stuff. I just repeat +the I just repeat what I did in white + + align:start position:0% +the I just repeat what I did in white + + + align:start position:0% +the I just repeat what I did in white +only I make it + + align:start position:0% + + + + align:start position:0% + +orange. Oh, but what happens if + + align:start position:0% +orange. Oh, but what happens if + + + align:start position:0% +orange. Oh, but what happens if +um what happens if I I I do this? + + align:start position:0% + + + + align:start position:0% + +So I put a little cross connections in + + align:start position:0% +So I put a little cross connections in + + + align:start position:0% +So I put a little cross connections in +there. So these these these two streams + + align:start position:0% +there. So these these these two streams + + + align:start position:0% +there. So these these these two streams +are going to interact. And then there + + align:start position:0% +are going to interact. And then there + + + align:start position:0% +are going to interact. And then there +might be some you know this this Y can + + align:start position:0% +might be some you know this this Y can + + + align:start position:0% +might be some you know this this Y can +go into another multiplier + + align:start position:0% +go into another multiplier + + + align:start position:0% +go into another multiplier +here and go into a sum here. And + + align:start position:0% +here and go into a sum here. And + + + align:start position:0% +here and go into a sum here. And +likewise this Y can go up here and into + + align:start position:0% +likewise this Y can go up here and into + + + align:start position:0% +likewise this Y can go up here and into +a + + align:start position:0% +a + + + align:start position:0% +a +multiplier like so. + + align:start position:0% +multiplier like so. + + + align:start position:0% +multiplier like so. +And there are weights all over the + + align:start position:0% + + + + align:start position:0% + +place like so. This guy goes up into + + align:start position:0% +place like so. This guy goes up into + + + align:start position:0% +place like so. This guy goes up into +into + + align:start position:0% +into + + + align:start position:0% +into +here. And now what happens now? We've + + align:start position:0% +here. And now what happens now? We've + + + align:start position:0% +here. And now what happens now? We've +got a disaster on our hands because + + align:start position:0% +got a disaster on our hands because + + + align:start position:0% +got a disaster on our hands because +there are all kinds of paths through + + align:start position:0% +there are all kinds of paths through + + + align:start position:0% +there are all kinds of paths through +this network. And you can + + align:start position:0% +this network. And you can + + + align:start position:0% +this network. And you can +imagine that if this was not just two + + align:start position:0% +imagine that if this was not just two + + + align:start position:0% +imagine that if this was not just two +neurons deep, but three neurons deep, + + align:start position:0% +neurons deep, but three neurons deep, + + + align:start position:0% +neurons deep, but three neurons deep, +what I would find is expressions that + + align:start position:0% +what I would find is expressions that + + + align:start position:0% +what I would find is expressions that +look like that. But, you know, you could + + align:start position:0% +look like that. But, you know, you could + + + align:start position:0% +look like that. But, you know, you could +go this way and then down through here + + align:start position:0% +go this way and then down through here + + + align:start position:0% +go this way and then down through here +and out here. Or you could go this way + + align:start position:0% +and out here. Or you could go this way + + + align:start position:0% +and out here. Or you could go this way +and then back up through here. So, it + + align:start position:0% +and then back up through here. So, it + + + align:start position:0% +and then back up through here. So, it +looks like there is an exponentially + + align:start position:0% +looks like there is an exponentially + + + align:start position:0% +looks like there is an exponentially +growing number of paths through that + + align:start position:0% +growing number of paths through that + + + align:start position:0% +growing number of paths through that +network. And so we're back to an + + align:start position:0% +network. And so we're back to an + + + align:start position:0% +network. And so we're back to an +exponential blow up and it won't + + align:start position:0% + + + + align:start position:0% + +work. Uh yeah, it won't work. Except + + align:start position:0% +work. Uh yeah, it won't work. Except + + + align:start position:0% +work. Uh yeah, it won't work. Except +that we need to let the math sink to us + + align:start position:0% +that we need to let the math sink to us + + + align:start position:0% +that we need to let the math sink to us +a little bit and we need to look at the + + align:start position:0% +a little bit and we need to look at the + + + align:start position:0% +a little bit and we need to look at the +picture. And the reason I turned this + + align:start position:0% +picture. And the reason I turned this + + + align:start position:0% +picture. And the reason I turned this +guy + + align:start position:0% +guy + + + align:start position:0% +guy +around was actually + + align:start position:0% +around was actually + + + align:start position:0% +around was actually +because from the point of view of + + align:start position:0% +because from the point of view of + + + align:start position:0% +because from the point of view of +letting the math sink to us, this piece + + align:start position:0% +letting the math sink to us, this piece + + + align:start position:0% +letting the math sink to us, this piece +here is the same as this piece + + align:start position:0% +here is the same as this piece + + + align:start position:0% +here is the same as this piece +here. So part of what we needed to do to + + align:start position:0% +here. So part of what we needed to do to + + + align:start position:0% +here. So part of what we needed to do to +calculate the partial derivative with + + align:start position:0% +calculate the partial derivative with + + + align:start position:0% +calculate the partial derivative with +respect to W1 has already been done when + + align:start position:0% +respect to W1 has already been done when + + + align:start position:0% +respect to W1 has already been done when +we calculated the partial derivative + + align:start position:0% +we calculated the partial derivative + + + align:start position:0% +we calculated the partial derivative +with respect to + + align:start position:0% + + + + align:start position:0% + +W2. And not only + + align:start position:0% +W2. And not only + + + align:start position:0% +W2. And not only +that, if we calculated the partial with + + align:start position:0% +that, if we calculated the partial with + + + align:start position:0% +that, if we calculated the partial with +respect to these green W's at both + + align:start position:0% +respect to these green W's at both + + + align:start position:0% +respect to these green W's at both +levels, what we would discover is that + + align:start position:0% +levels, what we would discover is that + + + align:start position:0% +levels, what we would discover is that +that sort of repetition occurs over and + + align:start position:0% +that sort of repetition occurs over and + + + align:start position:0% +that sort of repetition occurs over and +over again. And now I'm I'm going to try + + align:start position:0% +over again. And now I'm I'm going to try + + + align:start position:0% +over again. And now I'm I'm going to try +to give you an intuitional idea of + + align:start position:0% +to give you an intuitional idea of + + + align:start position:0% +to give you an intuitional idea of +what's going on here rather than just + + align:start position:0% +what's going on here rather than just + + + align:start position:0% +what's going on here rather than just +write down the math and salute it. And + + align:start position:0% +write down the math and salute it. And + + + align:start position:0% +write down the math and salute it. And +and here's here's here's a way to think + + align:start position:0% +and here's here's here's a way to think + + + align:start position:0% +and here's here's here's a way to think +about it from an intuitional point of + + align:start position:0% +about it from an intuitional point of + + + align:start position:0% +about it from an intuitional point of +view. + + align:start position:0% + + + + align:start position:0% + +Whatever happens to this performance + + align:start position:0% +Whatever happens to this performance + + + align:start position:0% +Whatever happens to this performance +function that's back of this row back + + align:start position:0% +function that's back of this row back + + + align:start position:0% +function that's back of this row back +back of these P's + + align:start position:0% +back of these P's + + + align:start position:0% +back of these P's +here the stuff over there can influence + + align:start position:0% +here the stuff over there can influence + + + align:start position:0% +here the stuff over there can influence +P only only by going through can + + align:start position:0% +P only only by going through can + + + align:start position:0% +P only only by going through can +influence performance only going through + + align:start position:0% +influence performance only going through + + + align:start position:0% +influence performance only going through +this column of + + align:start position:0% +this column of + + + align:start position:0% +this column of +PS and there's a fixed number of those + + align:start position:0% +PS and there's a fixed number of those + + + align:start position:0% +PS and there's a fixed number of those +it depends on the width not the depth of + + align:start position:0% +it depends on the width not the depth of + + + align:start position:0% +it depends on the width not the depth of +the + + align:start position:0% + + + + align:start position:0% + +network + + align:start position:0% + + + + align:start position:0% + +So the influence of that stuff back + + align:start position:0% +So the influence of that stuff back + + + align:start position:0% +So the influence of that stuff back +there on P is going to end up going + + align:start position:0% +there on P is going to end up going + + + align:start position:0% +there on P is going to end up going +through these guys and it's going to end + + align:start position:0% +through these guys and it's going to end + + + align:start position:0% +through these guys and it's going to end +up + + align:start position:0% +up + + + align:start position:0% +up +being so that we're going to discover + + align:start position:0% +being so that we're going to discover + + + align:start position:0% +being so that we're going to discover +that a lot of what we need to compute in + + align:start position:0% +that a lot of what we need to compute in + + + align:start position:0% +that a lot of what we need to compute in +one column has already been computed in + + align:start position:0% +one column has already been computed in + + + align:start position:0% +one column has already been computed in +the column on the + + align:start position:0% +the column on the + + + align:start position:0% +the column on the +right. So it isn't going + + align:start position:0% +right. So it isn't going + + + align:start position:0% +right. So it isn't going +to explode + + align:start position:0% +to explode + + + align:start position:0% +to explode +exponentially because the influence let + + align:start position:0% +exponentially because the influence let + + + align:start position:0% +exponentially because the influence let +me say it one more time. The influence + + align:start position:0% +me say it one more time. The influence + + + align:start position:0% +me say it one more time. The influence +of changes the influences of changes in + + align:start position:0% +of changes the influences of changes in + + + align:start position:0% +of changes the influences of changes in +P on the performance is all we care + + align:start position:0% +P on the performance is all we care + + + align:start position:0% +P on the performance is all we care +about when we come back to this part of + + align:start position:0% +about when we come back to this part of + + + align:start position:0% +about when we come back to this part of +the network because this stuff cannot + + align:start position:0% +the network because this stuff cannot + + + align:start position:0% +the network because this stuff cannot +influence the performance except by + + align:start position:0% +influence the performance except by + + + align:start position:0% +influence the performance except by +going through this column of + + align:start position:0% +going through this column of + + + align:start position:0% +going through this column of +peace. So it's not going to blow up + + align:start position:0% +peace. So it's not going to blow up + + + align:start position:0% +peace. So it's not going to blow up +exponentially. we were going to be able + + align:start position:0% +exponentially. we were going to be able + + + align:start position:0% +exponentially. we were going to be able +to reuse a lot of the computation. So, + + align:start position:0% +to reuse a lot of the computation. So, + + + align:start position:0% +to reuse a lot of the computation. So, +it's the reuse + + align:start position:0% +it's the reuse + + + align:start position:0% +it's the reuse +principle. Have we ever seen the reuse + + align:start position:0% +principle. Have we ever seen the reuse + + + align:start position:0% +principle. Have we ever seen the reuse +principle at work + + align:start position:0% +principle at work + + + align:start position:0% +principle at work +before? Not exactly. But you remember + + align:start position:0% +before? Not exactly. But you remember + + + align:start position:0% +before? Not exactly. But you remember +that little business about the extended + + align:start position:0% +that little business about the extended + + + align:start position:0% +that little business about the extended +list? We we we we know that we've + + align:start position:0% +list? We we we we know that we've + + + align:start position:0% +list? We we we we know that we've +seen how we we know we've seen something + + align:start position:0% +seen how we we know we've seen something + + + align:start position:0% +seen how we we know we've seen something +before. So, we have we can stop + + align:start position:0% +before. So, we have we can stop + + + align:start position:0% +before. So, we have we can stop +computing. It's like that. We're going + + align:start position:0% +computing. It's like that. We're going + + + align:start position:0% +computing. It's like that. We're going +to be able to reuse the computation. So + + align:start position:0% +to be able to reuse the computation. So + + + align:start position:0% +to be able to reuse the computation. So +we've already done so as to prevent an + + align:start position:0% +we've already done so as to prevent an + + + align:start position:0% +we've already done so as to prevent an +exponential blow up. By the way, for + + align:start position:0% +exponential blow up. By the way, for + + + align:start position:0% +exponential blow up. By the way, for +those of you who know about fast for + + align:start position:0% +those of you who know about fast for + + + align:start position:0% +those of you who know about fast for +transform, same kind of idea, reuse of + + align:start position:0% +transform, same kind of idea, reuse of + + + align:start position:0% +transform, same kind of idea, reuse of +partial + + align:start position:0% +partial + + + align:start position:0% +partial +results. So in the end, what can we say + + align:start position:0% +results. So in the end, what can we say + + + align:start position:0% +results. So in the end, what can we say +about this stuff? In the end, what we + + align:start position:0% +about this stuff? In the end, what we + + + align:start position:0% +about this stuff? In the end, what we +can say is that + + align:start position:0% +can say is that + + + align:start position:0% +can say is that +it's + + align:start position:0% + + + + align:start position:0% + +linear in depth. + + align:start position:0% + + + + align:start position:0% + +That is to say, if we increase the + + align:start position:0% +That is to say, if we increase the + + + align:start position:0% +That is to say, if we increase the +number of of layers to so-called depth, + + align:start position:0% +number of of layers to so-called depth, + + + align:start position:0% +number of of layers to so-called depth, +then we're going to increase the amount + + align:start position:0% +then we're going to increase the amount + + + align:start position:0% +then we're going to increase the amount +of computation necessary in a linear way + + align:start position:0% +of computation necessary in a linear way + + + align:start position:0% +of computation necessary in a linear way +because the computation we need in any + + align:start position:0% +because the computation we need in any + + + align:start position:0% +because the computation we need in any +column is going to be + + align:start position:0% +column is going to be + + + align:start position:0% +column is going to be +fixed. What about how it goes with + + align:start position:0% +fixed. What about how it goes with + + + align:start position:0% +fixed. What about how it goes with +respect + + align:start position:0% +respect + + + align:start position:0% +respect +to with respect to the width? + + align:start position:0% + + + + align:start position:0% + +Well, with respect to the width, any + + align:start position:0% +Well, with respect to the width, any + + + align:start position:0% +Well, with respect to the width, any +neuron here can be connected to any + + align:start position:0% +neuron here can be connected to any + + + align:start position:0% +neuron here can be connected to any +neuron in the next row. So, the amount + + align:start position:0% +neuron in the next row. So, the amount + + + align:start position:0% +neuron in the next row. So, the amount +of work we're going to have to do will + + align:start position:0% +of work we're going to have to do will + + + align:start position:0% +of work we're going to have to do will +be proportional to the number of + + align:start position:0% +be proportional to the number of + + + align:start position:0% +be proportional to the number of +connections. So, with respect to width, + + align:start position:0% +connections. So, with respect to width, + + + align:start position:0% +connections. So, with respect to width, +it's going to be W + + align:start position:0% +it's going to be W + + + align:start position:0% +it's going to be W +^2. But the fact is that in the end this + + align:start position:0% +^2. But the fact is that in the end this + + + align:start position:0% +^2. But the fact is that in the end this +stuff is readily computed and this + + align:start position:0% +stuff is readily computed and this + + + align:start position:0% +stuff is readily computed and this +phenomenally enough was overlooked for + + align:start position:0% +phenomenally enough was overlooked for + + + align:start position:0% +phenomenally enough was overlooked for +25 years. So, what did it take? What + + align:start position:0% +25 years. So, what did it take? What + + + align:start position:0% +25 years. So, what did it take? What +what is it in the end? In the end, it's + + align:start position:0% +what is it in the end? In the end, it's + + + align:start position:0% +what is it in the end? In the end, it's +extremely simple idea. All great ideas + + align:start position:0% +extremely simple idea. All great ideas + + + align:start position:0% +extremely simple idea. All great ideas +are simple. How come there aren't more + + align:start position:0% +are simple. How come there aren't more + + + align:start position:0% +are simple. How come there aren't more +of them? Well, because + + align:start position:0% +of them? Well, because + + + align:start position:0% +of them? Well, because +frequently that simplicity involves + + align:start position:0% +frequently that simplicity involves + + + align:start position:0% +frequently that simplicity involves +finding a couple tricks and making a + + align:start position:0% +finding a couple tricks and making a + + + align:start position:0% +finding a couple tricks and making a +couple of + + align:start position:0% +couple of + + + align:start position:0% +couple of +observations. So, usually we we we + + align:start position:0% +observations. So, usually we we we + + + align:start position:0% +observations. So, usually we we we +humans hardly ever go beyond one trick + + align:start position:0% +humans hardly ever go beyond one trick + + + align:start position:0% +humans hardly ever go beyond one trick +or one observation. But if you cascade a + + align:start position:0% +or one observation. But if you cascade a + + + align:start position:0% +or one observation. But if you cascade a +few together, sometimes something + + align:start position:0% +few together, sometimes something + + + align:start position:0% +few together, sometimes something +miraculous falls out that looks in + + align:start position:0% +miraculous falls out that looks in + + + align:start position:0% +miraculous falls out that looks in +retrospect extremely s simple. So, + + align:start position:0% +retrospect extremely s simple. So, + + + align:start position:0% +retrospect extremely s simple. So, +that's why we got the reuse principle at + + align:start position:0% +that's why we got the reuse principle at + + + align:start position:0% +that's why we got the reuse principle at +work. Run a reuse computation. In this + + align:start position:0% +work. Run a reuse computation. In this + + + align:start position:0% +work. Run a reuse computation. In this +case, the miracle was a consequence of + + align:start position:0% +case, the miracle was a consequence of + + + align:start position:0% +case, the miracle was a consequence of +two tricks plus an observation. And the + + align:start position:0% +two tricks plus an observation. And the + + + align:start position:0% +two tricks plus an observation. And the +overall idea is all great ideas are + + align:start position:0% +overall idea is all great ideas are + + + align:start position:0% +overall idea is all great ideas are +simple and easy to overlook for a + + align:start position:0% +simple and easy to overlook for a + + + align:start position:0% +simple and easy to overlook for a +quarter century. \ No newline at end of file diff --git a/uc8kW2iDA3A.txt b/uc8kW2iDA3A.txt new file mode 100644 index 0000000000000000000000000000000000000000..10fa7459befcfceccc793e49684f9a1055b525a9 --- /dev/null +++ b/uc8kW2iDA3A.txt @@ -0,0 +1,1035 @@ +align:start position:0% + +Hi, I'm Mary Bukari, a student in the + + align:start position:0% +Hi, I'm Mary Bukari, a student in the + + + align:start position:0% +Hi, I'm Mary Bukari, a student in the +2016 class of the MIT Sloan MBA program. + + align:start position:0% +2016 class of the MIT Sloan MBA program. + + + align:start position:0% +2016 class of the MIT Sloan MBA program. +I'm 26 years old and a millennial. What + + align:start position:0% +I'm 26 years old and a millennial. What + + + align:start position:0% +I'm 26 years old and a millennial. What +do young workers, millennials today, + + align:start position:0% +do young workers, millennials today, + + + align:start position:0% +do young workers, millennials today, +want from their jobs and careers? And + + align:start position:0% +want from their jobs and careers? And + + + align:start position:0% +want from their jobs and careers? And +how do they want to establish and + + align:start position:0% +how do they want to establish and + + + align:start position:0% +how do they want to establish and +maintain a balance between work and + + align:start position:0% +maintain a balance between work and + + + align:start position:0% +maintain a balance between work and +life? These questions are important to + + align:start position:0% +life? These questions are important to + + + align:start position:0% +life? These questions are important to +lots of people. employers wanting to + + align:start position:0% +lots of people. employers wanting to + + + align:start position:0% +lots of people. employers wanting to +recruit and keep young talented workers, + + align:start position:0% +recruit and keep young talented workers, + + + align:start position:0% +recruit and keep young talented workers, +millennials like me who are about to + + align:start position:0% +millennials like me who are about to + + + align:start position:0% +millennials like me who are about to +enter the + + align:start position:0% +enter the + + + align:start position:0% +enter the +workforce, and hordes of consultants + + align:start position:0% +workforce, and hordes of consultants + + + align:start position:0% +workforce, and hordes of consultants +giving us and business leaders advice + + align:start position:0% +giving us and business leaders advice + + + align:start position:0% +giving us and business leaders advice +about the changing workforce. So, let's + + align:start position:0% +about the changing workforce. So, let's + + + align:start position:0% +about the changing workforce. So, let's +start with what our parents told us when + + align:start position:0% +start with what our parents told us when + + + align:start position:0% +start with what our parents told us when +we were growing up. My parents, like I + + align:start position:0% +we were growing up. My parents, like I + + + align:start position:0% +we were growing up. My parents, like I +would guess many of your parents, if + + align:start position:0% +would guess many of your parents, if + + + align:start position:0% +would guess many of your parents, if +you're a millennial, said that if I + + align:start position:0% +you're a millennial, said that if I + + + align:start position:0% +you're a millennial, said that if I +worked hard in school and got a good + + align:start position:0% +worked hard in school and got a good + + + align:start position:0% +worked hard in school and got a good +education, I would do well in life, even + + align:start position:0% +education, I would do well in life, even + + + align:start position:0% +education, I would do well in life, even +better financially and socially than + + align:start position:0% +better financially and socially than + + + align:start position:0% +better financially and socially than +they did. + + align:start position:0% +they did. + + + align:start position:0% +they did. +But today, many of us are worried that + + align:start position:0% +But today, many of us are worried that + + + align:start position:0% +But today, many of us are worried that +our generation, the millennials, might + + align:start position:0% +our generation, the millennials, might + + + align:start position:0% +our generation, the millennials, might +not achieve that + + align:start position:0% +not achieve that + + + align:start position:0% +not achieve that +goal. And if we ask young people today, + + align:start position:0% +goal. And if we ask young people today, + + + align:start position:0% +goal. And if we ask young people today, +if that's what they really want out of + + align:start position:0% +if that's what they really want out of + + + align:start position:0% +if that's what they really want out of +their careers, we get different + + align:start position:0% +their careers, we get different + + + align:start position:0% +their careers, we get different +answers. For example, the people who + + align:start position:0% +answers. For example, the people who + + + align:start position:0% +answers. For example, the people who +took this course last year said that + + align:start position:0% +took this course last year said that + + + align:start position:0% +took this course last year said that +their top priority was addressing big + + align:start position:0% +their top priority was addressing big + + + align:start position:0% +their top priority was addressing big +important problems at work while also + + align:start position:0% +important problems at work while also + + + align:start position:0% +important problems at work while also +having a sensible work life balance. + + align:start position:0% +having a sensible work life balance. + + + align:start position:0% +having a sensible work life balance. +Doing well financially was also + + align:start position:0% +Doing well financially was also + + + align:start position:0% +Doing well financially was also +important, but these data, like other + + align:start position:0% +important, but these data, like other + + + align:start position:0% +important, but these data, like other +surveys of young professionals, show + + align:start position:0% +surveys of young professionals, show + + + align:start position:0% +surveys of young professionals, show +that it's not at the top of the list. + + align:start position:0% +that it's not at the top of the list. + + + align:start position:0% +that it's not at the top of the list. +Hi, my name is Alen Rivera and I'm a + + align:start position:0% +Hi, my name is Alen Rivera and I'm a + + + align:start position:0% +Hi, my name is Alen Rivera and I'm a +third-year student at Welsley College. + + align:start position:0% +third-year student at Welsley College. + + + align:start position:0% +third-year student at Welsley College. +I'm also a millennial about to enter the + + align:start position:0% +I'm also a millennial about to enter the + + + align:start position:0% +I'm also a millennial about to enter the +workforce. And as you saw, there isn't + + align:start position:0% +workforce. And as you saw, there isn't + + + align:start position:0% +workforce. And as you saw, there isn't +one single most important aspiration. + + align:start position:0% +one single most important aspiration. + + + align:start position:0% +one single most important aspiration. +This extended quote from a young woman + + align:start position:0% +This extended quote from a young woman + + + align:start position:0% +This extended quote from a young woman +in the class illustrates how she sees + + align:start position:0% +in the class illustrates how she sees + + + align:start position:0% +in the class illustrates how she sees +these different aspirations fitting + + align:start position:0% +these different aspirations fitting + + + align:start position:0% +these different aspirations fitting +together. + + align:start position:0% +together. + + + align:start position:0% +together. +My dream includes a job where I do + + align:start position:0% +My dream includes a job where I do + + + align:start position:0% +My dream includes a job where I do +important work, something that gives + + align:start position:0% +important work, something that gives + + + align:start position:0% +important work, something that gives +back to the community. I dream of having + + align:start position:0% +back to the community. I dream of having + + + align:start position:0% +back to the community. I dream of having +a work life balance that melds together. + + align:start position:0% +a work life balance that melds together. + + + align:start position:0% +a work life balance that melds together. +I hope that I'm able to utilize + + align:start position:0% +I hope that I'm able to utilize + + + align:start position:0% +I hope that I'm able to utilize +technology to make work more accessible + + align:start position:0% +technology to make work more accessible + + + align:start position:0% +technology to make work more accessible +and eventually have the option to do + + align:start position:0% +and eventually have the option to do + + + align:start position:0% +and eventually have the option to do +work from home. I do hope to be able to + + align:start position:0% +work from home. I do hope to be able to + + + align:start position:0% +work from home. I do hope to be able to +find a company that has a retirement + + align:start position:0% +find a company that has a retirement + + + align:start position:0% +find a company that has a retirement +plan where the company contributes some + + align:start position:0% +plan where the company contributes some + + + align:start position:0% +plan where the company contributes some +percentage to the plan. In some regards, + + align:start position:0% +percentage to the plan. In some regards, + + + align:start position:0% +percentage to the plan. In some regards, +I hope to have some of the same benefits + + align:start position:0% +I hope to have some of the same benefits + + + align:start position:0% +I hope to have some of the same benefits +that my parents had, health insurance, + + align:start position:0% +that my parents had, health insurance, + + + align:start position:0% +that my parents had, health insurance, +retirement plans, etc. Most importantly, + + align:start position:0% +retirement plans, etc. Most importantly, + + + align:start position:0% +retirement plans, etc. Most importantly, +I want to have passion for my work. I + + align:start position:0% +I want to have passion for my work. I + + + align:start position:0% +I want to have passion for my work. I +want my work to help people and I hope + + align:start position:0% +want my work to help people and I hope + + + align:start position:0% +want my work to help people and I hope +to make a decent decent living while + + align:start position:0% +to make a decent decent living while + + + align:start position:0% +to make a decent decent living while +making the generations before me proud. + + align:start position:0% +making the generations before me proud. + + + align:start position:0% +making the generations before me proud. +All this suggests that even though our + + align:start position:0% +All this suggests that even though our + + + align:start position:0% +All this suggests that even though our +generation shares many of the same + + align:start position:0% +generation shares many of the same + + + align:start position:0% +generation shares many of the same +concerns of prior generations, we care + + align:start position:0% +concerns of prior generations, we care + + + align:start position:0% +concerns of prior generations, we care +more about having an impact and work + + align:start position:0% +more about having an impact and work + + + align:start position:0% +more about having an impact and work +life balance and money. Our generation + + align:start position:0% +life balance and money. Our generation + + + align:start position:0% +life balance and money. Our generation +of workers also looks very different + + align:start position:0% +of workers also looks very different + + + align:start position:0% +of workers also looks very different +than workforces of the past, both in + + align:start position:0% +than workforces of the past, both in + + + align:start position:0% +than workforces of the past, both in +America and around the world. Almost + + align:start position:0% +America and around the world. Almost + + + align:start position:0% +America and around the world. Almost +half of Americans today are people of + + align:start position:0% +half of Americans today are people of + + + align:start position:0% +half of Americans today are people of +color and many millennials here and + + align:start position:0% +color and many millennials here and + + + align:start position:0% +color and many millennials here and +around the world are children of + + align:start position:0% +around the world are children of + + + align:start position:0% +around the world are children of +immigrants or immigrants themselves. We + + align:start position:0% +immigrants or immigrants themselves. We + + + align:start position:0% +immigrants or immigrants themselves. We +will all be working together learning + + align:start position:0% +will all be working together learning + + + align:start position:0% +will all be working together learning +from each other and some of us will be + + align:start position:0% +from each other and some of us will be + + + align:start position:0% +from each other and some of us will be +starting families that blend our diverse + + align:start position:0% +starting families that blend our diverse + + + align:start position:0% +starting families that blend our diverse +backgrounds. So we will want our + + align:start position:0% +backgrounds. So we will want our + + + align:start position:0% +backgrounds. So we will want our +workplaces to embrace who we are and + + align:start position:0% +workplaces to embrace who we are and + + + align:start position:0% +workplaces to embrace who we are and +where we come from. But many millennials + + align:start position:0% +where we come from. But many millennials + + + align:start position:0% +where we come from. But many millennials +are also having a hard time getting + + align:start position:0% +are also having a hard time getting + + + align:start position:0% +are also having a hard time getting +started. In the US, the majority of + + align:start position:0% +started. In the US, the majority of + + + align:start position:0% +started. In the US, the majority of +millennials say we are not earning + + align:start position:0% +millennials say we are not earning + + + align:start position:0% +millennials say we are not earning +enough money to live like we want to. + + align:start position:0% +enough money to live like we want to. + + + align:start position:0% +enough money to live like we want to. +One, more than a third of millennials + + align:start position:0% +One, more than a third of millennials + + + align:start position:0% +One, more than a third of millennials +report that we depend on our families + + align:start position:0% +report that we depend on our families + + + align:start position:0% +report that we depend on our families +for financial support. So many of us + + align:start position:0% +for financial support. So many of us + + + align:start position:0% +for financial support. So many of us +have to start out in debt from student + + align:start position:0% +have to start out in debt from student + + + align:start position:0% +have to start out in debt from student +loans and can't find full-time or career + + align:start position:0% +loans and can't find full-time or career + + + align:start position:0% +loans and can't find full-time or career +building jobs in the fields we studied + + align:start position:0% +building jobs in the fields we studied + + + align:start position:0% +building jobs in the fields we studied +in + + align:start position:0% +in + + + align:start position:0% +in +school. How does all this affect how and + + align:start position:0% +school. How does all this affect how and + + + align:start position:0% +school. How does all this affect how and +where we work? Well, for one thing, we + + align:start position:0% +where we work? Well, for one thing, we + + + align:start position:0% +where we work? Well, for one thing, we +move around from job to job a lot. A + + align:start position:0% +move around from job to job a lot. A + + + align:start position:0% +move around from job to job a lot. A +recent survey said people between age 22 + + align:start position:0% +recent survey said people between age 22 + + + align:start position:0% +recent survey said people between age 22 +and 32 change jobs between 1 and four + + align:start position:0% +and 32 change jobs between 1 and four + + + align:start position:0% +and 32 change jobs between 1 and four +times in the last 5 years. and 66% + + align:start position:0% +times in the last 5 years. and 66% + + + align:start position:0% +times in the last 5 years. and 66% +expect to change jobs again in the next + + align:start position:0% +expect to change jobs again in the next + + + align:start position:0% +expect to change jobs again in the next +few years. Many of us are also sending a + + align:start position:0% +few years. Many of us are also sending a + + + align:start position:0% +few years. Many of us are also sending a +clear message that we want more + + align:start position:0% +clear message that we want more + + + align:start position:0% +clear message that we want more +opportunities, not just for ourselves, + + align:start position:0% +opportunities, not just for ourselves, + + + align:start position:0% +opportunities, not just for ourselves, +but for everyone, regardless of race or + + align:start position:0% +but for everyone, regardless of race or + + + align:start position:0% +but for everyone, regardless of race or +the income bracket in which they were + + align:start position:0% +the income bracket in which they were + + + align:start position:0% +the income bracket in which they were +raised. That's why some are protesting + + align:start position:0% +raised. That's why some are protesting + + + align:start position:0% +raised. That's why some are protesting +against low wages of fast food + + align:start position:0% +against low wages of fast food + + + align:start position:0% +against low wages of fast food +companies, racial injustices, and income + + align:start position:0% +companies, racial injustices, and income + + + align:start position:0% +companies, racial injustices, and income +inequality, as seen by the Occupy Wall + + align:start position:0% +inequality, as seen by the Occupy Wall + + + align:start position:0% +inequality, as seen by the Occupy Wall +Street movement in 2011, and by protests + + align:start position:0% +Street movement in 2011, and by protests + + + align:start position:0% +Street movement in 2011, and by protests +of women and men who are forced to work + + align:start position:0% +of women and men who are forced to work + + + align:start position:0% +of women and men who are forced to work +in unacceptable conditions in garment + + align:start position:0% +in unacceptable conditions in garment + + + align:start position:0% +in unacceptable conditions in garment +factories and global supply + + align:start position:0% +factories and global supply + + + align:start position:0% +factories and global supply +chains. What does this mean for the next + + align:start position:0% +chains. What does this mean for the next + + + align:start position:0% +chains. What does this mean for the next +generations of managers and leaders? + + align:start position:0% +generations of managers and leaders? + + + align:start position:0% +generations of managers and leaders? +Sloan school MBAs who studied data from + + align:start position:0% +Sloan school MBAs who studied data from + + + align:start position:0% +Sloan school MBAs who studied data from +last year's class concluded that as + + align:start position:0% +last year's class concluded that as + + + align:start position:0% +last year's class concluded that as +managers of the future, they will need + + align:start position:0% +managers of the future, they will need + + + align:start position:0% +managers of the future, they will need +to listen to their employees, engage + + align:start position:0% +to listen to their employees, engage + + + align:start position:0% +to listen to their employees, engage +them in solving problems that really + + align:start position:0% +them in solving problems that really + + + align:start position:0% +them in solving problems that really +matter to the organization and to + + align:start position:0% +matter to the organization and to + + + align:start position:0% +matter to the organization and to +society and be flexible in how, when, + + align:start position:0% +society and be flexible in how, when, + + + align:start position:0% +society and be flexible in how, when, +and where people work so they can be + + align:start position:0% +and where people work so they can be + + + align:start position:0% +and where people work so they can be +productive and attend to personal and + + align:start position:0% +productive and attend to personal and + + + align:start position:0% +productive and attend to personal and +family affairs. Those are the messages + + align:start position:0% +family affairs. Those are the messages + + + align:start position:0% +family affairs. Those are the messages +sent by last year's class. Let's see how + + align:start position:0% +sent by last year's class. Let's see how + + + align:start position:0% +sent by last year's class. Let's see how +this year's class can bring our voices + + align:start position:0% +this year's class can bring our voices + + + align:start position:0% +this year's class can bring our voices +into the process of shaping the future + + align:start position:0% +into the process of shaping the future + + + align:start position:0% +into the process of shaping the future +of work. \ No newline at end of file diff --git a/v3dkStu-tMc.txt b/v3dkStu-tMc.txt new file mode 100644 index 0000000000000000000000000000000000000000..5641696159d8f15d72e214a1d5150c55989c40ed --- /dev/null +++ b/v3dkStu-tMc.txt @@ -0,0 +1,3124 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: All right, it +is time to get started. + +Thanks for coming for +this cold and rainy + +Wednesday before Thanksgiving. + +Today we're supposed to talk +about the radial equation. + +That's our main subject today. + +We discussed last +time the states + +of angular momentum from +the abstract viewpoint, + +and now we make contact with +some important problems, + +and differential equations, +and things like that. + +And there's a few concepts +I want to emphasize today. + +And basically, the +main concept is + +that I want you to just become +familiar with what we would + +call the diagram, the key +diagram for the states + +of a theory, of a particle in +a three dimensional potential. + +I think you have to have a good +understanding of what it looks, + +and what is special +about it, and when + +it shows particular properties. + +So to begin with, I'll +have to do a little aside + +on a object that is +covered in many courses. + +I don't know to what +that it's covered, + +but it's the subject +of spherical harmonics. + +So we'll talk about spherical +harmonics for about 15 minutes. + +And then we'll do +the radial equation. + +And for the radial equation, +after we discuss it, + +we'll do three examples. + +And that will be the +end of today's lecture. + +Next time, as you come back +from the holiday next week, + +we are doing the addition of +angular momentum basically. + +And then the last week, +more examples and a few more + +things for emphasis to +understand it all well. + +All right, so in terms +of spherical harmonics, + +I wanted to emphasize that +our algebraic analysis led + +to states that we +called jm, but today I + +will call lm, because they +will refer to orbital angular + +momentum. + +And as you've seen in +one of your problems, + +orbital angular +momentum has to do + +with values of j, +which are integers. + +So half integers values of j +cannot be realized for orbital + +angular momentum. + +It's a very interesting thing. + +So spin states don't have wave +functions in the usual way. + +It's only states of +integer angular momentum + +that have wave functions. + +And those are the +spherical harmonics. + +So I will talk about +lm, and l, as usual, + +will go from 0 to infinity. + +And m goes from l to minus l. + +And you had these states, and +we said that algebraically you + +would have L squared equals h +squared l times l plus 1 lm. + +And Lz lm equal hm lm. + +Now basically, the +spherical harmonics + +are going to be wave +functions for these states. + +And the way we +can approach it is + +that we did a little bit of work +already with constructing the l + +squared operator. + +And in last lecture we derived, +starting from the fact that L + +is r cross p and using +x,y, and z, px, py, pz, + +and passing through spherical +coordinates that L squared is + +the operator minus h squared 1 +over sine theta d d theta sine + +theta d d theta again plus +1 over sine squared theta d + +second d phi squared. + +And we didn't do it, +but Lz, which you know + +is h bar over i x d dy +minus y d dx can also + +be translated into +angular variables. + +And it has a very simple form. + +Also purely angular. + +And you can interpret it Lz is +rotations around the z-axis, + +so they change phi. + +So it will not +surprise you, if you + +do this exercise, that +this is h over i d d phi. + +And you should really check it. + +There's another one that +is a bit more laborious. + +L plus minus, remember, +is Lx plus minus i Lz. + +We have a big attendance today. + +Is equal to-- more people. + +h bar e to the plus minus i phi +i cosine theta over sine theta + +d d phi plus minus d d theta. + +And that takes a bit of algebra. + +You could do it. + +It's done in many books. + +It's probably there +in Griffith's. + +And these are the +representations + +of these operators as +differential operators that + +act and function +on theta and phi + +and don't care about radius. + +So in mathematical physics, +people study these things + +and invent these things +called spherical harmonics + +Ylm's of theta and phi. + +And the way you +could see their done + +is in fact, such that +this L squared viewed + +as this operator, differential +operator, acting on Ylm + +is indeed equal to h squared +l times l plus 1 Ylm. + +And Lz thought also as a +differential operator, the one + +that we've written there. + +On the Ylm is h bar m Ylm. + +So they are constructed +in this way, + +satisfying these equations. + +These are important equations +in mathematical physics, + +and these functions +were invented + +to satisfy those equations. + +Well, these are the properties +of those states over there. + +So we can think +of these functions + +as the wave functions +associated with those states. + +So that's interpretation that +is natural in quantum mechanics. + +And we want to think +of them like that. + +We want to think of the Ylm's +as the wave functions associated + +to the states lm. + +So lm. + +And here you would put a +position state theta phi. + +This is analogous to the +thing that we usually + +call the wave function being a +position state times the state + +side. + +So we want to think of +the Ylm's in this way + +as pretty much the wave +functions associated + +to those states. + +Now there is a little bit of +identities that come once you + +accept that this is what +you think of the Ylm's. + +And then the compatibility +of these equations. + +Top here with these ones makes +in this identification natural. + +Now in order to manipulate +and learn things + +about those spherical +harmonics the way + +we do things in +quantum mechanics, + +we think of the +completeness relation. + +If we have d cube x x x, this +is a completeness relation + +for position states. + +And I want to derive or +suggest a completeness relation + +for these theta phi states. + +For that, I would +pass this integral + +to do it in spherical +coordinates. + +So I would do dr rd +theta r sine theta d phi. + +And I would put r theta +phi position states + +for these things. + +And position states r theta phi. + +Still being equal to 1. + +And we can try to +split this thing. + +It's natural for us to +think of just theta phi, + +because these wave functions +have nothing to do with r, + +so I will simply do +the integrals this way. + +d theta sine theta d phi. + +And think just like a +position state in x, y, z. + +It's a position state in x, +in y, and in z multiplied. + +We'll just split these +things without trying + +to be too rigorous about it. + +Theta and phi like this. + +And you would have the integral +dr r squared r r equal 1. + +And at this point, +I want to think + +of this as the natural way of +setting a completeness relation + +for theta and phi. + +And this doesn't +talk to this one, + +so I will think of this that +in the space of theta and phi, + +objects that just +depend on theta and phi, + +this acts as a complete thing. + +And if objects depend +also in r, this + +will act as a complete thing. + +So I will-- I don't know. + +Maybe the right way +to say is postulate + +that we'll have a completeness +relation of this form. + +d theta sine theta d phi +theta phi theta phi equals 1. + +And then with this we can +do all kinds of things. + +First, this integral +is better written. + +This integral really represents +0 to pi d theta sine theta 0 + +to 2 pi d phi. + +Now this is minus +d cosine theta. + +And when theta is equal +to 0, cosine theta + +is 1 to minus 1 integral +d phi 0 to 2 pi. + +So this integral, really +d theta sine theta d + +phi this is really the +integral from minus 1 to 1. + +Change that order of d cos theta +integral d phi from 0 to 2 pi. + +And this is called the +integral over solid angle. + +That's a definition. + +So we could write the +completeness relation + +in the space theta phi as +integral over solid angle theta + +phi theta phi equals 1. + +Then the key property of +the spherical harmonics, + +or the lm states, is +that they are orthogonal. + +So delta l, l prime, +delta m, m prime. + +So the orthogonality +are of this state + +is guaranteed because +Hermitian operators, + +different eigenvalues, +they have to be orthogonal. + +Eigenstates of Hermitian. + +Operators with +different eigenvalues. + +Here, you introduce a complete +set of states of theta phi. + +So you put l prime m prime +theta phi theta phi lm. + +And this is the integral over +solid angle of Yl prime m + +prime of theta phi star. + +This is in the wrong position. + +And here Ylm of theta +phi being equal delta l + +l prime delta m m prime. + +So this is orthogonality +of the spherical harmonics. + +And this is pretty +much all we need. + +Now there's the standard ways +of constructing these things + +from the quantum mechanical +sort of intuition. + +Basically, you can +try to first build + +Yll, which corresponds +to the state ll. + +Now the kind of +differential equations + +this Yll satisfies +are kind of simple. + +But in particular, +the most important one + +is that L plus kills this state. + +So basically you +use the condition + +that L plus kills this +state to find a differential + +equation for this, which +can be solved easily. + +Not a hard +differential equation. + +Then you find Yll. + +And then you can find Yll +minus 1 and all the other ones + +by applying the +operator L minus. + +The lowering operator of m. + +So in principle, if you +have enough patience, + +you can calculate all the +spherical harmonics that way. + +There's no obstruction. + +But the form is a +little messy, and if you + +want to find the normalizations +so that these things work out + +correctly, well, it takes some +work at the end of the day. + +So we're not going +to do that here. + +We'll just leave it at +that, and if we ever + +need some special harmonics, +we'll just hold the answers. + +And they are in most textbooks. + +So if you do need +them, well, you'll + +have to do with +complicated normalizations. + +So that's really all I wanted to +say about spherical harmonics, + +and we can turn then to +the real subject, which + +is the radial equation. + +So the radial equation. + +So we have a Hamiltonian +H equals p squared vector + +over 2m plus v of r. + +And we've seen that +this is equal to h over + +2m 1 over r d second dr +squared r plus 1 over 2mr + +squared L squared plus v of r. + +So this is what we're +trying to solve. + +And the way we +attempt to solve this + +is by separation of variables. + +So we'll try to write the wave +function, psi, characterized + +by three things. + +Its energy, the value of +l, and the value of m. + +And it's a function of +position, because we're + +trying to solve H +psi equal E psi. + +And that's the energy +that we want to consider. + +So I will write here to begin +with something that will not + +turn out to be exactly +right, but it's + +important to do +it first this way. + +A function of art r that +has labels E, l, and m. + +Because it certainly could +depend on E, could depend on l, + +and could depend on m, +that radial function. + +And then the angular +function will + +be the Ylm's of theta and phi. + +So this is the [INAUDIBLE] +sets for the equation. + +If we have that, we can plug +into the Schrodinger equation, + +and see what we get. + +Well, this operator +will act on this f. + +This will have the +operator L squared, + +but L squared over Ylm, +you know what it is. + +And v of r is multiplicative, +so it's no big problem. + +So what do we have? + +We have minus h squared +over 2m 1 over r. + +Now I can talk +normal derivatives. + +d r squared r times fElm +plus 1 over 2mr squared. + +And now have L squared +acting on this, + +but L squared acting on the +Ylm is just this factor. + +So we have h squared l times +l plus 1 times the fElm. + +Now I didn't put the +Ylm in the first term + +because I'm going to +cancel it throughout. + +So we have this term here plus +v of r fElm equals E fElm. + +That is substituting into the +equation h psi equal E psi. + +So first term here. + +Second term, it acted on +the spherical harmonic. + +v of r is multiplicative. + +E on that. + +But then what you +see immediately + +is that this differential +equation doesn't depend on m. + +It was L squared, but no +Lz in the Hamiltonian. + +So no m dependent. + +So actually we +were overly proven + +in thinking that f +was a function of m. + +What we really have +is that psi Elm + +is equal to a function of E +and l or r Ylm of theta phi. + +And then the +differential equation + +is minus h squared over 2m. + +Let's multiply all by r. + +d second dr squared of r fEl. + +Plus look here. + +The r that I'm multiplying +is going to go into the f. + +Here it's going +to go into the f. + +Here it's going +to go into the f. + +It's an overall thing. + +But here we keep h +squared l times l + +plus 1 over 2mr squared rfEl +plus v of r fEl rfEl equal + +e times rfEl. + +So what you see here is that +this function is quite natural. + +So it suggests the +definition of uEl to be rfEl. + +So that the differential +equation now finally becomes + +minus h squared over 2m d +second dr squared of uEl plus + +there's the u here, the u +here, and this potential + +that has two terms. + +So this will be v of +r plus h squared l + +times l plus 1 over 2mr +squared uEl equals E times eEl. + +And this is the famous +radial equation. + +It's an equation for you. + +And here, this whole +thing is sometimes + +called the effective potential. + +So look what we've got. + +This f, if you wish here, +is now of the form uEl + +of r Ylm over r theta phi. + +f is u over r. + +So this is the way we've +written the solution, + +and u satisfies this equation, +which is a one dimensional + +Schrodinger equation +for the radius r. + +One dimensional equation +with an effective potential + +that depends on L. + +So actually the first +thing you have to notice + +is that the central +potential problem + +has turned into an +infinite collection of one + +dimensional problems. + +One for each value of l. + +For different values of l, you +have a different potential. + +Now they're not +all that different. + +They have different +intensity of this term. + +For l equals 0, well +you have some solutions. + +And for l equal 1, the answer +could be quite different. + +For l equal 2, still different. + +And you have to solve +an infinite number + +of one dimensional problems. + +That's what the Schrodinger +equation has turned into. + +So we filled all +these blackboards. + +Let's see, are there questions? + +Anything so far? + +Yes? + +AUDIENCE: You might +get to this later, + +but what does it mean +in our wave equations, + +in our wave function there, +psi of Elm is equal to fEl, + +and the spherical harmonic +of that one mean that one has + +an independence and +the other doesn't. + +Can they be separated +on the basis of m? + +PROFESSOR: So it is just a fact +that the radial solution is + +independent of n, so it's +an important property. + +n is fairly simple. + +The various state, the +states with angular momentum + +l, but different m's just differ +in their angular dependence, + +not in the radial dependence. + +And practically, +it means that you + +have an infinite set of one +dimensional problems labeled + +by l, and not labeled by m, +which conceivably could have + +happened, but it doesn't happen. + +So just a major simplicity. + +Yes? + +AUDIENCE: Does the +radial equation + +have all the same properties as +a one dimensional Schrodinger + +equation? + +Or does the divergence in +the effect [INAUDIBLE] 0 + +change that? + +PROFESSOR: Well, +it changes things, + +but the most serious +change is the fact + +that, in one +dimensional problems, + +x goes from minus +infinity to infinity. + +And here it goes +from 0 to infinity, + +so we need to worry +about what happens at 0. + +Basically that's the +main complication. + +One dimensional potential, +but it really just + +can't go below 0. + +r is a radial variable, +and we can't forget that. + +Yes? + +AUDIENCE: The potential v of r +will depend on whatever problem + +you're solving, right? + +PROFESSOR: That's right. + +AUDIENCE: Could you find +the v of r [INAUDIBLE]? + +PROFESSOR: Well +that doesn't quite + +make sense as a Hamiltonian. + +You see, if you +have a v of r, it's + +something that is supposed to +be v of r for any wave function. + +That's the definition. + +So it can depend +on some parameter, + +but that parameter cannot be +the l of the particular wave + +function. + +AUDIENCE: [INAUDIBLE] or +something that would interact + +with the-- + +PROFESSOR: If you +have magnetic fields, + +things change, because +then you can split levels + +with respect to m. + +Break degeneracies and +things change indeed. + +We'll take care of those by +using perturbation theory + +mostly. + +Use this solution and +then perturbation theory. + +OK, so let's proceed +a little more on this. + +So the first thing that we +want to talk a little about + +is the normalization and +some boundary conditions, + +because otherwise +we can't really + +understand what's going on. + +And happily the discussion +is not that complicated. + +So we want to normalize. + +So what do we want? + +Integral d cube x psi Elm +of x squared equals 1. + +So clearly we want to go +into angular variables. + +So again, this is r squared +dr integral d solid angle, + +r squared Er. + +And this thing is now uEl +squared absolute value + +over r squared. + +Look at the right +most blackboard. + +uEl of r, I must square it +because the wave function + +is squared. + +Over r squared. + +And then I have Ylm star of +theta phi Ylm of theta phi. + +And if this is supposed +to be normalized, + +this is supposed +to be the number 1. + +Well happily, this +part, this is why + +we needed to talk a little +about spherical harmonics. + +This integral is 1, because +it corresponds precisely + +to l equal l prime +m equal m prime. + +And look how lucky +or nice this is. + +r squared cancels +with r squared, + +so the final condition +is the integral from 0 + +to infinity dr uEl of r +squared is equal to 1, + +which shows that +kind of the u really + +plays a role for wave +function and a line. + +And even though it was +a little complicated, + +there was the r here, +and angular dependence, + +and everything, a +good wave function + +is one that is just +think of psi as being u. + +A one dimensional wave +function psi being u, + +and if you can integrate +it square, you've got it. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Because I +had to square this, + +so there was u over r. + +AUDIENCE: But +that's [INAUDIBLE]. + +PROFESSOR: Oh, I'm sorry. + +That parenthesis is a remnant. + +I tried to erase it a little. + +It's not squared anymore. + +The square is on the +absolute value is r squared. + +So this is good news +for our interpretation. + +So now before I discuss the +peculiarities of the boundary + +conditions, I want to +introduce really the main point + +that we're going to +illustrate in this lecture. + +This is the thing that +should remain in your heads. + +It's a picture, but +it's an important one. + +When you want to +organize the spectrum, + +you'll draw the +following diagram. + +Energy is here and l here. + +And it's a funny +kind of diagram. + +It's not like a curve or a plot. + +It's like a histogram or +kind of thing like that. + +So what will happen is that you +have a one dimensional problem. + +If these potentials are normal, +there will be bound states. + +And let's consider the +case of bound states + +for the purposes of this +graph, just bound states. + +Now you look at +this, and you say OK, + +what am I supposed to do? + +I'm going to have states +for all values of l, + +and m, and probably +some energies. + +So m doesn't affect +the radial equation. + +That's very important. + +But l does, so I have +a different problem + +to solve for different l. + +So I will make my histogram +here and put here l + +equals 0 at this region. + +l equals 1, l equals 2, +l equals 3, and go on. + +Now suppose I fix an l. + +l is fixed. + +Now it's a Schrodinger equation +for a one dimensional problem. + +You would expect that if the +potential suitably grows, which + +is a typical case, +E will be quantized. + +And there will not +be degeneracies, + +because the bound state +spectrum in one dimension + +is not degenerate. + +So I should expect +that for each l there + +are going to be energy values +that are going to appear. + +So for l equals 0, I expect that +there will be some energy here + +for which I've got a state. + +And that line means +I got a state. + +And there's some energy here +that could be called E1, + +0 is the first energy that +is allowed with l equals 0. + +Then there will be +another one here maybe. + +E-- I'll write it down-- 2,0. + +So basically I'm labeling the +energies with En,l which means + +the first solution +with l equals 0, + +the second solution +with l equals 0, + +the third solution E 3,0. + +Then you come to l +equals 1, and you + +must solve the equation again. + +And then for l equal 1, there +will be the lowest energy, + +the ground state energy of +the l equal 1 potential, + +and then higher and higher. + +Since the l equal 1 +potential is higher + +than the l equals 0 +potential, it's higher up. + +The energies should +be higher up, + +at least the first +one should be. + +And therefore the +first one could + +be a little higher than this, +or maybe by some accident + +it just fits here, or +maybe it should fit here. + +Well, we don't know +but know, but there's + +no obvious reason why it +should, so I'll put it here. + +l equals 1. + +And this would be E1,1. + +The first state with l equals 1. + +Then here it could be E2,1. + +The second state with l +equal 1 and higher up. + +And then for l equal-- my +diagram is a little too big. + +E1,1. + +E2,1. + +And then you have states here, +so maybe this one, l equals 2, + +I don't know where it goes. + +It just has to be higher than +this one, so I'll put it here. + +And this will be E1,2. + +Maybe there's an E2,2. + +And here an E1,3. + +But this is the answer +to your problem. + +That's the energy levels +of a central potential. + +So it's a good, +nice little diagram + +in which you put the states, +you put the little line wherever + +you find the state. + +And for l equals 0, +you have those states. + +Now because there's no +degeneracies in the bound + +states of a one +dimensional potential, + +I don't have two lines here +that coincide, because there's + +no two states with +the same energy here. + +It's just one state. + +And this one here. + +I cannot have two things there. + +That's pretty important to. + +So you have a list +of states here. + +And just one state here, one +state, but as you can see, + +you're probably are catching +me in a little wrong play + +of words, because I say +there's one state here. + +Yes, it's one state, +because it's l equals 0. + +One state, one state. + +But this state, +which is one single-- + +this should be called one +single l equal 1 multiplet. + +So this is not really one +state at the end of the day. + +It's one state of the one +dimensional radial equation, + +but you know that l +equals 1 comes accompanied + +with three values of m. + +So there's three states +that are degenerate, + +because they have +the same energy. + +The energy doesn't depend on l. + +So this thing is an +l equal 1 multiplet, + +which means really three states. + +And this is three states. + +And this is three states. + +And this is 1 l equal +2 multiplet, which + +has possibility of m equals +2, 1, 0 minus 1 and minus 2. + +So in this state is just +one l equal 2 multiplet, + +but it really means five states +of the central potential. + +Five degenerate +states, because the m + +doesn't change the energy. + +And this is five states. + +And this is seven states. + +One l equal 3 multiplet, +which contains seven states. + +OK, so questions? + +This is the most +important graph. + +If you have that +picture in your head, + +then you can +understand really where + +you're going with any potential. + +Any confusion here +above the notation? + +Yes? + +AUDIENCE: So normally +when we think about a one + +dimensional problem, we say +that there's no degeneracy. + +Not really. + +No multiple degeneracy, +so should we + +think of the radial equation as +having copies for each m value + +and each having the +same eigenvalue? + +PROFESSOR: I don't +think it's necessary. + +You see, you've got your uEl. + +And you have here you solutions. + +Once the uEl is +good, you're supposed + +to be able to put any Ylm. + +So put l, and now the m's that +are allowed are solutions. + +You're solving the problem. + +So think of a master radial +function as good for a fixed l, + +and therefore it works +for all values of m. + +But don't try to think of +many copies of this equation. + +I don't think it would help you. + +Any other questions? + +Yes? + +AUDIENCE: Sorry to ask, +but if you could just + +review how is degeneracy +built one more time? + +PROFESSOR: Yeah. + +Remember last time we +were talking about, + +for example, what is a +j equal to multiplet. + +Well, these were a collection +of states jm with j + +equals 2 an m sum value. + +And they are all obtained by +acting with angular momentum + +operators in each other. + +And there are five states. + +The 2,2, the 2,1, the 2,0, the +2, minus 1, and the 2, minus 2. + +And all these +states are obtained + +by acting with, say, lowering +operators l minus and this. + +Now all these angular +momentum operators, + +all of the Li's commute +with the Hamiltonian. + +Therefore all of +these states are + +obtained by acting with Li +must have the same energy. + +That's why we say that +this comes in a multiplet. + +So when you get j-- in this case +we'll call it l-- l equals 2. + +You get five states. + +They correspond to the +various values of m. + +So when you did that +radial equation that + +has a solution for +l equals 2, you're + +getting the full multiplet. + +You're getting five states. + +1 l equal 2 multiplet. + +That's why one line here. + +That is equivalent +to five states. + +OK, so that diagram, of course, +is really quite important. + +So now we want to understand +the boundary conditions. + +So we have here this. + +So this probably +shouldn't erase yet. + +Let's do the +boundary conditions. + +So behavior here +at r equals to 0. + +At r going to 0. + +The first claim is that +surprisingly, you would think, + +well, normalization is king. + +If it's normalized, it's good. + +So just any number. + +Just don't let it diverge +near 0, and that will be OK. + +But it turns out +that that's not true. + +It's not right. + +And you need the limit as r goes +to 0 of uEl of r be equal to 0. + +And we'll take this and +explore the simplest case. + +That is corresponds to +saying what if the limit of r + +goes to 0 or uEl of +r was a constant? + +What goes wrong? + +Certainly normalization +doesn't go wrong. + +It can be a constant. + +u could be like that, and +it would be normalized, + +and that doesn't go wrong. + +So let's look at +the wave function. + +What happens with this? + +I actually will +take for simplicity, + +because we'll analyze it later, +the example of l equals 0. + +So let's put even 0. + +l equals 0. + +Well, suppose you look +at the wave function now, + +and how does it look? + +Psi of E0-- if l is equal +to 0, m must be equal to 0-- + +would be this u over +r times a constant. + +So a constant, because +y 0, 0 is a constant. + +And then you uE0 of r over r. + +So when r approaches 0, psi +goes like c prime over r, + +some other constant over r. + +So I'm doing +something very simple. + +I'm saying if uE0 is approaching +the constant at the origin, + +if it's uE0, well, this is +a constant because it's 0,0. + +So this is going to constant. + +So at the end of the +day, the wave function + +looks like 1 over r. + +But this is impossible, because +the Schrodinger equation H + +psi has minus h squared over 2m +Laplacian on psi plus dot dot + +dot. + +And the up Laplacian of 1 over +r is minus 4 pi times a delta + +function at x equals 0. + +So this means that the +Schrodinger equation, + +you think oh I put +psi equals c over r. + +Well, if you calculate the +Laplacian, it seems to be 0. + +But if you're more careful, +as you know for [? emm ?] + +the Laplacian of 1 over r is +minus 4 pi times the delta + +function. + +So in the Schrodinger +equation, the kinetic term + +produces a delta function. + +There's no reason +to believe there's + +a delta function +in the potential. + +We'll not try such +crazy potentials. + +A delta function in a one +dimensional potential, + +you've got the solution. + +A delta function in a +three dimensional potential + +is absolutely crazy. + +It has infinite number +of bound states, + +and they just go +all the way down + +to energies of minus infinity. + +It's a very horrendous +thing, a delta function + +in three dimensions, +for quantum mechanics. + +So this thing, there's no delta +function in the potential. + +And you've got a delta +function from the kinetic term. + +You're not going to +be able to cancel it. + +This is not a solution. + +So you really cannot +approach a constant there. + +It's quite bad. + +So the wave functions +will have to vanish, + +and we can prove that, or at +least under some circumstances + +prove it. + +And as all these +things are, they all + +depend on how crazy +potentials you want to accept. + +So we should say something. + +So I'll say something +about these potentials, + +and we'll prove a result. + +So my statement will be the +centrifugal barrier, which + +is a name for this +part of the potential, + +dominates as r goes to 0. + +If this doesn't happen, +all bets are off. + +So let's assume that v of +r, maybe it's 1 over r, + +but it's not worse +than 1 over r squared. + +It's 1 over r +cubed, for example, + +or something like that. + +You would have to +analyze it from scratch + +if it would be that bad. + +But I will assume that the +centrifugal barrier dominates. + +And then look at the +differential equation. + +Well, what differential +equation do I have? + +Well, I have this and this. + +This thing is less +important than that, + +and this is also less +important, because this is u + +divided by r squared. + +And here is just u. + +So this is certainly +less important than that, + +and this is less +important than that, + +and if I want to have +some variation of u, + +or understand how it +varies, I must keep this. + +So at this order, I should +keep just the kinetic term + +h squared over 2m d +second dr squared u of El. + +And h squared l times l +plus 1 over 2 mr squared. + +And I will try to cancel these +two to explore how the wave + +function looks near or equal 0. + +These are the two most important +terms of the differential + +equation, so I have the +right to keep those, and try + +to balance them out to leading +order, and see what I get. + +So all the h squared +over 2m's go away. + +So this is equivalent to +d second uEl dr squared is + +equal to l times l plus +1 uEl over r squared. + +And this is solved +by a power uEl. + +You can try r to the +s, some number s. + +And then this thing gives +you s times s minus 1. + +Taking two derivatives is +equal to l times l plus 1. + +As you take two derivatives, +you lose two powers of r, + +so it will work out. + +And from here, you see +that the possible solutions + +are s equals l plus 1. + +And s equals 2 minus l. + +So this corresponds +to a uEl that + +goes like r to the +l plus 1, or a uEl + +that goes like 1 +over r to the l. + +This Is far too singular. + +For l equals 0, we argued +that the wave function + +should go like a constant. + +I'm sorry, cannot +go like a constant. + +Must vanish. + +This is not possible. + +It's not a solution. + +It must vanish. + +For l equals 0, uE0 goes +like r and vanishes. + +So that's consistent, +and this is good. + +For l equals 0, this would +be like a constant as well + +and would be fine. + +But for l equals 1 +already, this is 1 over r, + +and this is not normalizable. + +So this time this is not +normalizable for l greater + +or equal than one. + +So this is the answer +[INAUDIBLE] this assumption, + +which is a very +reasonable assumption. + +But if you don't have +that you have to beware. + +OK, this is our +condition for u there. + +And so uEl goes like +this as r goes to 0. + +It would be the whole answer. + +So f, if you care about f still, +which is what appears here, + +goes like u divided by r. + +So fEl goes like cr to the l. + +And when l is equal to 0, +f behaves like a constant. + +u vanishes for l +equal to 0, but f + +goes like a +constant, which means + +that if you take 0 +orbital angular momentum, + +you may have some +probability of finding + +the particle at the origin, +because this f behaves + +like a constant for l equals 0. + +On the other hand, +for any higher l, + +f will also vanish +at the origin. + +And that is intuitively said +that the centrifugal barrier + +prevents the particle +from reaching the origin. + +There's a barrier, +a potential barrier. + +This potential is +1 over r squared. + +Doesn't let you go to +close to the origin. + +But that potential +disappears for l equals 0, + +and therefore the particle +can reach the origin. + +But only for l equals 0 +it can reach the origin. + +OK, one more thing. + +Behavior near infinity +is of interest as well. + +So what happens for +r goes to infinity? + +Well, for r goes to +infinity, you also + +have to be a little +careful what you assume. + +I wish I could tell you it's +always like this, but it's not. + +It's rich in all +kinds of problems. + +So there's two +cases where there's + +an analysis that is simple. + +Suppose v of r is equal to 0 +for r greater than some r0. + +Or r times v of f goes to +0 as r goes to infinity. + +Two possibilities. + +The potential is plane +0 after some distance. + +Or the potential +multiplied by r goes to 0 + +as r goes to infinity. + +And you would say, look, you've +missed the most important case. + +The hydrogen atom, the +potential is 1 over r. + +r times v of r doesn't go to 0. + +And indeed, what I'm +going to write here + +doesn't quite apply to the wave +functions of the hydrogen atom. + +They're a little unusual. + +The potential of the hydrogen +atom is felt quite far away. + +So never the less, if you +have those conditions, + +we can ignore the potential +as we go far away. + +And we'll consider the +following situation. + +Look that the centrifugal +barrier satisfies this as well. + +So the full effective +potential satisfies. + +If v of r satisfies +that, r times 1 + +over r squared of effective +potential also satisfies that. + +So we can ignore +all the potential, + +and we're left +ignore the effective. + +And therefore we're left +with minus h squared + +over 2m d second uEl dr +squared is equal to EuEl. + +And that's a very +trivial equation. + +Yes, Matt? + +AUDIENCE: When you +say v of r goes + +to 0 for r greater +than [INAUDIBLE] 0. + +Are you effectively +[INAUDIBLE] the potential? + +PROFESSOR: Right, there may +be some potentials like this. + +A potential that is like that. + +An attractive potential, and it +vanishes after some distance. + +Or a repulsive potential that +vanishes after some distance. + +AUDIENCE: But say the potential +was a [INAUDIBLE] potential. + +Are you just approximating it +to 0 after it's [INAUDIBLE]? + +PROFESSOR: Well, if I'm in +the [INAUDIBLE] potential, + +unfortunately I'm +neither here nor here, + +so this doesn't apply. + +So the [INAUDIBLE] +potential is an exception. + +The solutions are +a little more-- + +AUDIENCE: The conditions +you're saying. [INAUDIBLE]. + +PROFESSOR: So these +are conditions + +that allow me to say something. + +If they're not +satisfied, I sort of + +have to analyze +them case by case. + +That's the price we have to pay. + +It's a little more complicated +than you would think naively. + +Now here, it's interesting to +consider two possibilities. + +The case when E is less +than 0, or the case when + +E is greater than 0. + +So scattering solutions +or bound state solutions. + +For these ones, if the +energy is less than 0 + +and there's no potential, you're +in the forbidden zone far away, + +so you must have a +decaying exponential. + +El goes like exponential +of minus square root + +of 2m E over h squared r. + +That solves that equation. + +You see, the solution +of these things + +are either exponential +decays or exponential growths + +and oscillatory solutions, +sines and cosines, + +or E to the i things. + +So here we have a decay, +because with energy less than 0, + +the potential is 0. + +So you're in a forbidden region, +so you must decay like that. + +In this hydrogen +atom what happens + +is that there's a power +of r multiplying here. + +Like r to the n, or r to the +k or something like that. + +If E is less than 0, you +have uE equal exponential + +of plus minus ikr, where k +is square root of 2m E over h + +squared. + +And those, again, +solve that equation. + +And they are sort of +wave solutions far away. + +Now with this +information, the behavior + +of the u's near the origin, the +behavior of the u's far away, + +you can then make +qualitative plots + +of how solutions would +look at the origin. + +They grow up like r to the l. + +Then it's a one +dimensional potential, + +so they oscillate maybe, but +then decay exponentially. + +And the kind of +thing you used to do + +in 804 of plotting +how things look, + +it's feasible at this stage. + +So it's about time +to do examples. + +I have three examples. + +Given time, maybe +I'll get to two. + +That's OK. + +The last example is +kind of the cutest, + +but maybe it's OK to +leave it for Monday. + +So are there +questions about this + +before we begin our examples? + +Andrew? + +AUDIENCE: What is consumption +of [INAUDIBLE] [? barrier ?] + +dominates. + +But why is that a +reasonable assumptions? + +PROFESSOR: Well, +potentials that are just + +too singular at the +origin are not common. + +Just doesn't happen. + +So mathematically +you could try them, + +but I actually don't +know of useful examples + +if a potential is very +singular at the origin. + +AUDIENCE: [INAUDIBLE] in +the potential [INAUDIBLE] + +the centrifugal barrier. + +That [INAUDIBLE]. + +PROFESSOR: Right. + +An effective potential, the +potential doesn't blow up-- + +your potential doesn't blow +up more than 1 over r squared + +or something like that. + +So we'll just take it like that. + +OK, our first example +is the free particle. + +You would say come on. + +That's ridiculous. + +Too simple. + +But it's fairly non-trivial +in spherical coordinates. + +And you say, well, so what. + +Free particles, you say +what the momentum is. + +You know the energy. + +How do you label the states? + +You label them by three momenta. + +Or energy and direction. + +So momentum +eigenstates, for example + +But in spherical +coordinates, these will not + +be momentum +eigenstates, and these + +are interesting +because they allow + +us to solve for more +complicated problems, in fact. + +And they allow you to +understand scattering out + +of central potential. + +So these are actually +pretty important. + +You can label these +things by three numbers. + +p1, p2, p3. + +Or energy and theta and phi, +the directions of the momenta. + +What we're going to label +them are by energy l and m. + +So you might say how do we +compare all these infinities, + +but it somehow works out. + +There's the same number of +states really in either way. + +So what do we have? + +It's a potential +that v is equal to 0. + +So let's write the +differential equation. + +v is equal to 0. + +But not v effective. + +So you have minus h squared +over 2m d second uEl + +dr squared plus h +squared over 2m l times + +l plus 1 over r +squared uEl equal EuEl. + +This is actually +quite interesting. + +As you will see, it's a bit +puzzling the first time. + +Well, let's cancel +this h squared over 2m, + +because they're +kind of annoying. + +So we'll put d second uEl over +dr squared with a minus-- I'll + +keep that minus-- plus l times +l plus 1 over r squared uEl. + +And here I'll put k +squared times uEl. + +And k squared is the +same k as before. + +And E is positive because +you have a free particle. + +E is positive. + +And k squared is given by +this, 2m E over h squared. + +So this is the equation +we have to solve. + +And it's kind of interesting, +because on the one hand, + +there is an energy on +the right hand side. + +And then you would say, look, +it looks like this just typical + +one dimensional +Schrodinger equation. + +Therefore that +energy probably is + +quantized because it shows +in the right hand side. + +Why wouldn't it be quantized +if it just shows this way? + +On the other hand, it +shouldn't be quantized. + +So what is it about this +differential equation that + +shows that the energy +never gets quantized? + +Well, the fact is that +the energy in some sense + +doesn't show up in this +differential equation. + +You think it's here, but +it's not really there. + +What does that mean? + +It actually means +that you can define + +a new variable rho +equal kr, scale r. + +And basically chain rule +or your intuition, this k + +goes down here. + +k squared r squared k squared +r squared, it's all rho. + +So chain rule or +changing variables + +will turn this equation into +a minus d second uEl d rho + +squared plus l times +l plus 1 rho squared + +is equal to-- times uEl-- +is equal to uEl here. + +And the energy has +disappeared from the equation + +by rescaling, a trivial +rescaling of coordinates. + +That doesn't mean that +the energy is not there. + +It is there, because +you will find solutions + +that depend on rho, +and then you will + +put rho equal kr and +the energies there. + +But there's no +quantization of energy, + +because the energy doesn't +show in this equation anymore. + +It's kind of a neat thing, or +rather conceptually interesting + +thing that energy is +not there anymore. + +And then you look at this +differential equation, + +and you realize that +it's a nasty one. + +So this equation is +quite easy without this. + +It's a power solution. + +It's quite easy without this, +it's exponentials are this. + +But whenever you have a +differential equation that + +has two derivatives, +a term with 1 + +over x squared +times the function, + +and a term with 1 +times the function, + +you're in Bessel territory. + +All these functions +have Bessel things. + +And then you have another +term like 1 over x d dx. + +That is not a problem, but the +presence of these two things, + +one with 1 over x squared +and one with this, + +complicates this equation. + +So Bessel, without +this, would be + +exponential solution without +this would be powers. + +In the end, the fact is that +this is spherical Bessel, + +and it's a little complicated. + +Not terribly complicated. + +The solutions are +spherical Bessel functions, + +which are not all that bad. + +And let me say what they are. + +So what are the +solutions to this thing? + +In fact, the solutions +that are easier to find + +is that the uEl's are r +times the Bessel function + +jl is called spherical +Bessel functions. + +So it's not capital +j that people + +use for the normal +Bessel, but lower case l. + +Of kr. + +As you know, you solve this, +and the solutions for this + +would be of the +form rho jl for rho. + +But rho is kr, so we don't +care about the constant, + +because this is a +homogeneous linear equation. + +So some number here. + +You could put a +constant if you wish. + +But that's the solution. + +Therefore your +complete solutions + +is like the psi's of +Elm would be u divided + +by r, which is jl of kr +times Ylm's of theta phi. + +These are the +complete solutions. + +This is a second order +differential equation. + +Therefore it has to +have two solutions. + +And this is what is called a +regular solution at the origin. + +The Bessel functions +come in j and n type. + +And the n type is +singular at the origins, + +so we won't care about it. + +So what do we get from here? + +Well, some behavior +that is well known. + +Rho jl of rho behaves like +rho to the l plus 2 over 2l + +plus 1 double factorial +as rho goes to 0. + +So that's a fact about +these Bessel functions. + +They behave that +way, which is good, + +because rho jl +behaves like that, + +so u behaves like r +to the l plus 1, which + +is what we derived +a little time ago. + +So this behavior of +the Bessel function + +is indeed consistent +with our solution. + +Moreover, there's another +behavior that is interesting. + +This Bessel +function, by the time + +it's written like +that, when you go + +far off to infinity +jl of rho, it + +behaves like sine of +rho minus l pi over 2. + +This is as rho goes to infinity. + +So as rho goes to +infinity, this is + +behaving like a +trigonometric function. + +It's consistent with this, +because rho-- this is rho jl + +is what we call u essentially. + +So u behaves like this +with rho equal kr. + +And that's consistent. + +This superposition of +a sine and a cosine. + +But it's kind of interesting +though that this l pi over 2 + +shows up here. + +You see the fact +that this function + +has to vanish at the origin. + +It vanishes at the origin +and begins to vary. + +And by the time you go +far away, you contract. + +And the way it +behaves is this way. + +The face is determined. + +So that actually gives +a lot of opportunity + +to physicists because +the free particle-- + +so for the free +particle, uEl behaves + +like sine of kr minus l pi +over 2 as r goes to infinity. + +So from that people have +asked the following question. + +What if you have a +potential that, for example + +for simplicity, a potential +that is localized. + +Well, if this +potential is localized, + +the solution far +away is supposed + +to be a superposition +of sines and cosines. + +So if there is no +potential, the solution + +is supposed to be this. + +Now another superposition +of sines and cosines, + +at the end of the +day, can always + +be written as some sine of +this thing plus a change + +in this phase So in +general, uEl will + +go like sine of kr minus l pi +over 2 plus a shift, a phase + +shift, delta l that can +depend on the energy. + +So if you haven't tried to +find the radial solutions + +of a problem with +some potential, + +if the potential is 0, +there's no such term. + +But if the potential is +here, it will have an effect + +and will give you a phase shift. + +So if you're doing particle +scattering experiments, + +you're sending +waves from far away + +and you just see how the +wave behaves far away, + +you do have measurement +information on this phase + +shift. + +And from this phase shift, +you can learn something + +about the potential. + +So this is how this +problem of free particle + +suddenly becomes very +important and very interesting. + +For example, as a way +through the behavior at + +infinity learning something +about the potential. + +For example, if the +potential is attractive, + +it pulls the wave function +in and produces some sign + +of delta that the corresponds +to a positive delta. + +If the potential +is repulsive, it + +pushes the wave +function out, repels it + +and produces a delta +that is negative. + +You can track those +signs thinking carefully. + +But the potentials will teach +you something about delta. + +The other case that this is +interesting-- I will just + +introduce it and stop, because +we might as well stop-- + +is a very important case. + +The square well. + +Well, we've studied +in one dimension + +the infinite square well. + +That's one potential that +you now how to solve, + +and sines and +cosines is very easy. + +Now imagine a +spherical square well, + +which is some sort of cavity +in which a particle is + +free to move here, but +the potential becomes + +infinite at the boundary. + +It's a hollow sphere, +so the potential v of r + +is equal to 0 for r less than a. + +And it's infinity +for r greater than a. + +So it's like a bag, a +balloon with solid walls + +impossible to penetrate. + +So this is the most +symmetric simple potential + +you could imagine in the world. + +And we're going to solve it. + +How can we solve this? + +Well, we did 2/3 of the +work already in solving it. + +Why? + +Because inside here +the potential is 0, + +so the particle is free. + +So inside here the solutions +are of the form uEl + +go like rjl of kr. + +And the only thing you will need +is that they vanish at the end. + +So you will fix +this by demanding + +that ka is a number z such-- +well, the jl of ka will be 0. + +So that the wave +function vanishes + +at this point where the +potential becomes infinite. + +So you've solved +most of the problem. + +And we'll discuss it in detail, +because it's an important one. + +But this is the most symmetric +potential, you may think. + +This potential is very +symmetric, very pretty, + +but nothing to write home about. + +If you tried to +look-- and we're going + +to calculate this diagram. + +You would say well +it's so symmetric + +that something pretty +is going to happen here. + +Nothing happens. + +These states will show up. + +And these ones will show +up, and no state ever + +will match another one. + +There's no pattern, or +rhyme, or reason for it. + +On the other hand, +if you would have + +taken a potential v of r +of the form beta r squared, + +that potential will +exhibit enormous amounts + +of degeneracies all over. + +And we will have to +understand why that happens. + +So we'll see you next Monday. + +Enjoy your break. + +Homework will only happen +late after Thanksgiving. + +And just have a great time. + +Thank you for coming today, +and will see you soon. + +[APPLAUSE] \ No newline at end of file diff --git a/vUg50UI1aqs.txt b/vUg50UI1aqs.txt new file mode 100644 index 0000000000000000000000000000000000000000..6557e5add9ea2ede530351fd2e9428412ede4693 --- /dev/null +++ b/vUg50UI1aqs.txt @@ -0,0 +1,251 @@ +align:start position:0% + +So let me summarize what the steps that + + align:start position:0% +So let me summarize what the steps that + + + align:start position:0% +So let me summarize what the steps that +we've taken are to do this differential + + align:start position:0% +we've taken are to do this differential + + + align:start position:0% +we've taken are to do this differential +analysis. So when you're trying to + + align:start position:0% +analysis. So when you're trying to + + + align:start position:0% +analysis. So when you're trying to +analyze + + align:start position:0% +analyze + + + align:start position:0% +analyze +a continuous mass distribution, the + + align:start position:0% +a continuous mass distribution, the + + + align:start position:0% +a continuous mass distribution, the +first step is to pick some arbitrary + + align:start position:0% +first step is to pick some arbitrary + + + align:start position:0% +first step is to pick some arbitrary +mass element, a small but finite size + + align:start position:0% +mass element, a small but finite size + + + align:start position:0% +mass element, a small but finite size +mass element somewhere in the middle of + + align:start position:0% +mass element somewhere in the middle of + + + align:start position:0% +mass element somewhere in the middle of +the mass distribution. You don't want to + + align:start position:0% +the mass distribution. You don't want to + + + align:start position:0% +the mass distribution. You don't want to +pick one of the end points because the + + align:start position:0% +pick one of the end points because the + + + align:start position:0% +pick one of the end points because the +end points are special. You want to pick + + align:start position:0% +end points are special. You want to pick + + + align:start position:0% +end points are special. You want to pick +an arbitrary point somewhere in the + + align:start position:0% +an arbitrary point somewhere in the + + + align:start position:0% +an arbitrary point somewhere in the +middle. Pick a and then pick a small + + align:start position:0% +middle. Pick a and then pick a small + + + align:start position:0% +middle. Pick a and then pick a small +mass element at that point. So small but + + align:start position:0% +mass element at that point. So small but + + + align:start position:0% +mass element at that point. So small but +finite size. Analyze the forces acting + + align:start position:0% +finite size. Analyze the forces acting + + + align:start position:0% +finite size. Analyze the forces acting +on that mass element. So write down + + align:start position:0% +on that mass element. So write down + + + align:start position:0% +on that mass element. So write down +Newton's second law, the equation of + + align:start position:0% +Newton's second law, the equation of + + + align:start position:0% +Newton's second law, the equation of +motion for that mass element. + + align:start position:0% +motion for that mass element. + + + align:start position:0% +motion for that mass element. +That will give you um uh what what the + + align:start position:0% +That will give you um uh what what the + + + align:start position:0% +That will give you um uh what what the +action is what what what the forces are + + align:start position:0% +action is what what what the forces are + + + align:start position:0% +action is what what what the forces are +on that element. Then go to the limit of + + align:start position:0% +on that element. Then go to the limit of + + + align:start position:0% +on that element. Then go to the limit of +an infinite decimally small element. + + align:start position:0% +an infinite decimally small element. + + + align:start position:0% +an infinite decimally small element. +That will give you a differential + + align:start position:0% +That will give you a differential + + + align:start position:0% +That will give you a differential +equation. You can then separate the + + align:start position:0% +equation. You can then separate the + + + align:start position:0% +equation. You can then separate the +differential equation and integrate both + + align:start position:0% +differential equation and integrate both + + + align:start position:0% +differential equation and integrate both +sides to solve the differential + + align:start position:0% +sides to solve the differential + + + align:start position:0% +sides to solve the differential +equation. And then finally, you can + + align:start position:0% +equation. And then finally, you can + + + align:start position:0% +equation. And then finally, you can +apply a boundary condition, something + + align:start position:0% +apply a boundary condition, something + + + align:start position:0% +apply a boundary condition, something +you know about one or the other of the + + align:start position:0% +you know about one or the other of the + + + align:start position:0% +you know about one or the other of the +end points. And that will allow you to + + align:start position:0% +end points. And that will allow you to + + + align:start position:0% +end points. And that will allow you to +solve for the function of interest at + + align:start position:0% +solve for the function of interest at + + + align:start position:0% +solve for the function of interest at +any point along your distribution. \ No newline at end of file diff --git a/vewtUlemzto.txt b/vewtUlemzto.txt new file mode 100644 index 0000000000000000000000000000000000000000..a4602cfa30fd5a361461d9602ca081a291275dfd --- /dev/null +++ b/vewtUlemzto.txt @@ -0,0 +1,752 @@ +align:start position:0% + +today we're going to be doing goodie bag + + align:start position:0% +today we're going to be doing goodie bag + + + align:start position:0% +today we're going to be doing goodie bag + + align:start position:0% + + + align:start position:0% +atoms and reactions our objectives today + + align:start position:0% +atoms and reactions our objectives today + + + align:start position:0% +atoms and reactions our objectives today +are to identify material based on its + + align:start position:0% +are to identify material based on its + + + align:start position:0% +are to identify material based on its +properties + + align:start position:0% +properties + + + align:start position:0% +properties +observe a simple chemical reaction and + + align:start position:0% +observe a simple chemical reaction and + + + align:start position:0% +observe a simple chemical reaction and +identify the limiting reagent + + align:start position:0% +identify the limiting reagent + + + align:start position:0% +identify the limiting reagent +and estimate the number of atoms in a + + align:start position:0% +and estimate the number of atoms in a + + + align:start position:0% +and estimate the number of atoms in a +real object + + align:start position:0% +real object + + + align:start position:0% +real object +to do this goodie bag you'll need + + align:start position:0% +to do this goodie bag you'll need + + + align:start position:0% +to do this goodie bag you'll need +vinegar a plastic cup + + align:start position:0% +vinegar a plastic cup + + + align:start position:0% +vinegar a plastic cup +a ruler metal samples of aluminum copper + + align:start position:0% +a ruler metal samples of aluminum copper + + + align:start position:0% +a ruler metal samples of aluminum copper +iron magnesium and tin but if you can + + align:start position:0% +iron magnesium and tin but if you can + + + align:start position:0% +iron magnesium and tin but if you can +only get copper and magnesium it will + + align:start position:0% +only get copper and magnesium it will + + + align:start position:0% +only get copper and magnesium it will +work + + align:start position:0% +work + + + align:start position:0% +work +and a pipette some conceptual questions + + align:start position:0% +and a pipette some conceptual questions + + + align:start position:0% +and a pipette some conceptual questions +to think about while you're doing this + + align:start position:0% +to think about while you're doing this + + + align:start position:0% +to think about while you're doing this +goodie bag are + + align:start position:0% +goodie bag are + + + align:start position:0% +goodie bag are +how can we tell different metals apart + + align:start position:0% +how can we tell different metals apart + + + align:start position:0% +how can we tell different metals apart +and how can we count + + align:start position:0% +and how can we count + + + align:start position:0% +and how can we count +atoms that are too small to see first we + + align:start position:0% +atoms that are too small to see first we + + + align:start position:0% +atoms that are too small to see first we +have five samples of metal that we would + + align:start position:0% +have five samples of metal that we would + + + align:start position:0% +have five samples of metal that we would +like to identify + + align:start position:0% +like to identify + + + align:start position:0% +like to identify +using their properties the easiest to + + align:start position:0% +using their properties the easiest to + + + align:start position:0% +using their properties the easiest to +identify is copper + + align:start position:0% +identify is copper + + + align:start position:0% +identify is copper +by its orangish color next we're going + + align:start position:0% +by its orangish color next we're going + + + align:start position:0% +by its orangish color next we're going +to try to find out which sample is iron + + align:start position:0% +to try to find out which sample is iron + + + align:start position:0% +to try to find out which sample is iron +by testing how easy they are to bend + + align:start position:0% +by testing how easy they are to bend + + + align:start position:0% +by testing how easy they are to bend +iron will be the most difficult to bend + + align:start position:0% +iron will be the most difficult to bend + + + align:start position:0% +iron will be the most difficult to bend +so this sample bends very easily just + + align:start position:0% +so this sample bends very easily just + + + align:start position:0% +so this sample bends very easily just +with my fingers so it must not be iron + + align:start position:0% +with my fingers so it must not be iron + + + align:start position:0% +with my fingers so it must not be iron +this sample is very difficult i can + + align:start position:0% +this sample is very difficult i can + + + align:start position:0% +this sample is very difficult i can +hardly get it to bend at all + + align:start position:0% +hardly get it to bend at all + + + align:start position:0% +hardly get it to bend at all +with my fingers and this sample also + + align:start position:0% +with my fingers and this sample also + + + align:start position:0% +with my fingers and this sample also +bends fairly easily just using my + + align:start position:0% +bends fairly easily just using my + + + align:start position:0% +bends fairly easily just using my +fingers + + align:start position:0% +fingers + + + align:start position:0% +fingers +so we know that this sample the hardest + + align:start position:0% +so we know that this sample the hardest + + + align:start position:0% +so we know that this sample the hardest +to bend must be iron + + align:start position:0% +to bend must be iron + + + align:start position:0% +to bend must be iron +next we're going to try to compare the + + align:start position:0% +next we're going to try to compare the + + + align:start position:0% +next we're going to try to compare the +density of these different metals + + align:start position:0% +density of these different metals + + + align:start position:0% +density of these different metals +so this metal feels the heaviest and + + align:start position:0% +so this metal feels the heaviest and + + + align:start position:0% +so this metal feels the heaviest and +most dense + + align:start position:0% +most dense + + + align:start position:0% +most dense +this one feels lighter and this sample + + align:start position:0% +this one feels lighter and this sample + + + align:start position:0% +this one feels lighter and this sample +feels light as well + + align:start position:0% +feels light as well + + + align:start position:0% +feels light as well +so we know that tin is the most dense + + align:start position:0% +so we know that tin is the most dense + + + align:start position:0% +so we know that tin is the most dense +metal so this sample must be tin + + align:start position:0% +metal so this sample must be tin + + + align:start position:0% +metal so this sample must be tin +to identify which of these samples is + + align:start position:0% +to identify which of these samples is + + + align:start position:0% +to identify which of these samples is +magnesium and which of them is aluminum + + align:start position:0% +magnesium and which of them is aluminum + + + align:start position:0% +magnesium and which of them is aluminum +we're going to test which one of them + + align:start position:0% +we're going to test which one of them + + + align:start position:0% +we're going to test which one of them +reacts with vinegar + + align:start position:0% +reacts with vinegar + + + align:start position:0% +reacts with vinegar +[Music] + + align:start position:0% + + + + align:start position:0% + +so we're going to place each of these + + align:start position:0% +so we're going to place each of these + + + align:start position:0% +so we're going to place each of these +samples on the lid of our plastic cup + + align:start position:0% +samples on the lid of our plastic cup + + + align:start position:0% +samples on the lid of our plastic cup +to make sure we don't spill any of the + + align:start position:0% +to make sure we don't spill any of the + + + align:start position:0% +to make sure we don't spill any of the +vinegar + + align:start position:0% +vinegar + + + align:start position:0% +vinegar +and use our pipette to put a drop of + + align:start position:0% +and use our pipette to put a drop of + + + align:start position:0% +and use our pipette to put a drop of +vinegar on each of the samples + + align:start position:0% +vinegar on each of the samples + + + align:start position:0% +vinegar on each of the samples +and the one that reacts will be + + align:start position:0% +and the one that reacts will be + + + align:start position:0% +and the one that reacts will be +magnesium because we know magnesium + + align:start position:0% +magnesium because we know magnesium + + + align:start position:0% +magnesium because we know magnesium +reacts with vinegar + + align:start position:0% +reacts with vinegar + + + align:start position:0% +reacts with vinegar +watch closely + + align:start position:0% + + + + align:start position:0% + +it doesn't look like we're getting any + + align:start position:0% +it doesn't look like we're getting any + + + align:start position:0% +it doesn't look like we're getting any +reaction from this metal so it must be + + align:start position:0% +reaction from this metal so it must be + + + align:start position:0% +reaction from this metal so it must be +the aluminum now let's try the other + + align:start position:0% +the aluminum now let's try the other + + + align:start position:0% +the aluminum now let's try the other +you can see that this material is + + align:start position:0% +you can see that this material is + + + align:start position:0% +you can see that this material is +forming tiny bubbles after we put the + + align:start position:0% +forming tiny bubbles after we put the + + + align:start position:0% +forming tiny bubbles after we put the +vinegar on it + + align:start position:0% +vinegar on it + + + align:start position:0% +vinegar on it +so it must be magnesium those bubbles + + align:start position:0% +so it must be magnesium those bubbles + + + align:start position:0% +so it must be magnesium those bubbles +are hydrogen gas + + align:start position:0% + + + + align:start position:0% + +now that the bubbling has stopped on our + + align:start position:0% +now that the bubbling has stopped on our + + + align:start position:0% +now that the bubbling has stopped on our +magnesium we know that the reaction is + + align:start position:0% +magnesium we know that the reaction is + + + align:start position:0% +magnesium we know that the reaction is +over + + align:start position:0% +over + + + align:start position:0% +over +there's still plenty of magnesium left + + align:start position:0% +there's still plenty of magnesium left + + + align:start position:0% +there's still plenty of magnesium left +so this indicates that the acetic acid + + align:start position:0% +so this indicates that the acetic acid + + + align:start position:0% +so this indicates that the acetic acid +inside of the vinegar must be the + + align:start position:0% +inside of the vinegar must be the + + + align:start position:0% +inside of the vinegar must be the +limiting reagent + + align:start position:0% +limiting reagent + + + align:start position:0% +limiting reagent +finally we want to estimate how many + + align:start position:0% +finally we want to estimate how many + + + align:start position:0% +finally we want to estimate how many +atoms are in our sample of copper + + align:start position:0% + + + + align:start position:0% + +to do so we're going to use a ruler + + align:start position:0% +to do so we're going to use a ruler + + + align:start position:0% +to do so we're going to use a ruler +using our ruler we can measure the width + + align:start position:0% +using our ruler we can measure the width + + + align:start position:0% +using our ruler we can measure the width +and the height + + align:start position:0% +and the height + + + align:start position:0% +and the height +of this copper sample so using the + + align:start position:0% +of this copper sample so using the + + + align:start position:0% +of this copper sample so using the +metric side of our ruler + + align:start position:0% +metric side of our ruler + + + align:start position:0% +metric side of our ruler +we align the zero with the edge of our + + align:start position:0% +we align the zero with the edge of our + + + align:start position:0% +we align the zero with the edge of our +material + + align:start position:0% +material + + + align:start position:0% +material +and see that it is about 13 millimeters + + align:start position:0% +and see that it is about 13 millimeters + + + align:start position:0% +and see that it is about 13 millimeters +wide + + align:start position:0% +wide + + + align:start position:0% +wide +and 25 millimeters long today we did + + align:start position:0% +and 25 millimeters long today we did + + + align:start position:0% +and 25 millimeters long today we did +goodie bag one + + align:start position:0% +goodie bag one + + + align:start position:0% +goodie bag one +we identified our metal samples based on + + align:start position:0% +we identified our metal samples based on + + + align:start position:0% +we identified our metal samples based on +their material properties + + align:start position:0% +their material properties + + + align:start position:0% +their material properties +we observed a simple reaction and + + align:start position:0% +we observed a simple reaction and + + + align:start position:0% +we observed a simple reaction and +identified the limiting reagent + + align:start position:0% +identified the limiting reagent + + + align:start position:0% +identified the limiting reagent +and we measured our copper to estimate + + align:start position:0% +and we measured our copper to estimate + + + align:start position:0% +and we measured our copper to estimate +the number of atoms in our sample \ No newline at end of file diff --git a/wnyiasdTE0U.txt b/wnyiasdTE0U.txt new file mode 100644 index 0000000000000000000000000000000000000000..643dd13bff2db3a153d1c93800d6223380ec944a --- /dev/null +++ b/wnyiasdTE0U.txt @@ -0,0 +1,13893 @@ +align:start position:0% + +And generally we get a spectrum. Um + + align:start position:0% + + + + align:start position:0% + +and that spectrum can have sharp lines + + align:start position:0% +and that spectrum can have sharp lines + + + align:start position:0% +and that spectrum can have sharp lines +and it can have broad lines and it can + + align:start position:0% +and it can have broad lines and it can + + + align:start position:0% +and it can have broad lines and it can +have continuum. + + align:start position:0% +have continuum. + + + align:start position:0% +have continuum. +And uh since + + align:start position:0% +And uh since + + + align:start position:0% +And uh since +the topic is dynamics + + align:start position:0% +the topic is dynamics + + + align:start position:0% +the topic is dynamics +uh + + align:start position:0% +uh + + + align:start position:0% +uh +I'm going to be talking mostly about + + align:start position:0% +I'm going to be talking mostly about + + + align:start position:0% +I'm going to be talking mostly about +these broad lines + + align:start position:0% +these broad lines + + + align:start position:0% +these broad lines +that appear in our spectra and what is + + align:start position:0% +that appear in our spectra and what is + + + align:start position:0% +that appear in our spectra and what is +the reason why something + + align:start position:0% +the reason why something + + + align:start position:0% +the reason why something +is neither sharp nor continuum. + + align:start position:0% +is neither sharp nor continuum. + + + align:start position:0% +is neither sharp nor continuum. +we have a a a picture of some kind of a + + align:start position:0% +we have a a a picture of some kind of a + + + align:start position:0% +we have a a a picture of some kind of a +a zeroorder state which is able to + + align:start position:0% +a zeroorder state which is able to + + + align:start position:0% +a zeroorder state which is able to +couple to something which is continuous + + align:start position:0% +couple to something which is continuous + + + align:start position:0% +couple to something which is continuous +and what is the mechanism of that + + align:start position:0% +and what is the mechanism of that + + + align:start position:0% +and what is the mechanism of that +coupling? + + align:start position:0% +coupling? + + + align:start position:0% +coupling? +Well, there's two kinds of photo + + align:start position:0% +Well, there's two kinds of photo + + + align:start position:0% +Well, there's two kinds of photo +fragmentation processes. + + align:start position:0% +fragmentation processes. + + + align:start position:0% +fragmentation processes. +We add a photon to our molecule and it + + align:start position:0% +We add a photon to our molecule and it + + + align:start position:0% +We add a photon to our molecule and it +can break and that's photo dissociation. + + align:start position:0% +can break and that's photo dissociation. + + + align:start position:0% +can break and that's photo dissociation. +Or we can add a photon to our molecule + + align:start position:0% +Or we can add a photon to our molecule + + + align:start position:0% +Or we can add a photon to our molecule +and it can + + align:start position:0% +and it can + + + align:start position:0% +and it can +ionize and that's autoionization or + + align:start position:0% +ionize and that's autoionization or + + + align:start position:0% +ionize and that's autoionization or +ionization. + + align:start position:0% +ionization. + + + align:start position:0% +ionization. +And uh um + + align:start position:0% +And uh um + + + align:start position:0% +And uh um +because the final state in both of these + + align:start position:0% +because the final state in both of these + + + align:start position:0% +because the final state in both of these +processes + + align:start position:0% +processes + + + align:start position:0% +processes +uh is continuous in energy. We can have + + align:start position:0% +uh is continuous in energy. We can have + + + align:start position:0% +uh is continuous in energy. We can have +any translational energy relative + + align:start position:0% +any translational energy relative + + + align:start position:0% +any translational energy relative +translational energy of these guys or + + align:start position:0% +translational energy of these guys or + + + align:start position:0% +translational energy of these guys or +any translational energy of the electron + + align:start position:0% +any translational energy of the electron + + + align:start position:0% +any translational energy of the electron +relative to the ion. So one might expect + + align:start position:0% +relative to the ion. So one might expect + + + align:start position:0% +relative to the ion. So one might expect +that the spectrum will be + + align:start position:0% +that the spectrum will be + + + align:start position:0% +that the spectrum will be +so energy increasing the spectrum will + + align:start position:0% +so energy increasing the spectrum will + + + align:start position:0% +so energy increasing the spectrum will +consist of some lines and then some kind + + align:start position:0% +consist of some lines and then some kind + + + align:start position:0% +consist of some lines and then some kind +of continuum that starts up at the + + align:start position:0% +of continuum that starts up at the + + + align:start position:0% +of continuum that starts up at the +thermodynamic threshold for either + + align:start position:0% +thermodynamic threshold for either + + + align:start position:0% +thermodynamic threshold for either +dissociation or ionization. + + align:start position:0% + + + + align:start position:0% + +And we know in fact we're really + + align:start position:0% +And we know in fact we're really + + + align:start position:0% +And we know in fact we're really +interested in the thermodynamic + + align:start position:0% +interested in the thermodynamic + + + align:start position:0% +interested in the thermodynamic +threshold for both of these processes + + align:start position:0% +threshold for both of these processes + + + align:start position:0% +threshold for both of these processes +because that gives us the the bond + + align:start position:0% +because that gives us the the bond + + + align:start position:0% +because that gives us the the bond +energy and the ionization potential and + + align:start position:0% +energy and the ionization potential and + + + align:start position:0% +energy and the ionization potential and +stuff like that. But + + align:start position:0% +stuff like that. But + + + align:start position:0% +stuff like that. But +uh the continuum doesn't start at + + align:start position:0% +uh the continuum doesn't start at + + + align:start position:0% +uh the continuum doesn't start at +threshold and it has a lot of structure + + align:start position:0% +threshold and it has a lot of structure + + + align:start position:0% +threshold and it has a lot of structure +and that structure is connected with the + + align:start position:0% +and that structure is connected with the + + + align:start position:0% +and that structure is connected with the +internal states of A and B or the + + align:start position:0% +internal states of A and B or the + + + align:start position:0% +internal states of A and B or the +internal states of this ion. This ion + + align:start position:0% +internal states of this ion. This ion + + + align:start position:0% +internal states of this ion. This ion +has rotation, vibration, spin orbit, + + align:start position:0% +has rotation, vibration, spin orbit, + + + align:start position:0% +has rotation, vibration, spin orbit, +electronic structure. And so somehow the + + align:start position:0% +electronic structure. And so somehow the + + + align:start position:0% +electronic structure. And so somehow the +internal states of these things are + + align:start position:0% +internal states of these things are + + + align:start position:0% +internal states of these things are +manifest in uh the structured continuum, + + align:start position:0% +manifest in uh the structured continuum, + + + align:start position:0% +manifest in uh the structured continuum, +the resonances that appear in the + + align:start position:0% +the resonances that appear in the + + + align:start position:0% +the resonances that appear in the +photo fragmentation spectrum. + + align:start position:0% + + + + align:start position:0% + +And so + + align:start position:0% +And so + + + align:start position:0% +And so +uh we're really interested in the quasi + + align:start position:0% +uh we're really interested in the quasi + + + align:start position:0% +uh we're really interested in the quasi +bound + + align:start position:0% + + + + align:start position:0% + +states + + align:start position:0% + + + + align:start position:0% + +which are somehow connected with the + + align:start position:0% +which are somehow connected with the + + + align:start position:0% +which are somehow connected with the +internal states of these things. + + align:start position:0% +internal states of these things. + + + align:start position:0% +internal states of these things. +And another name for a quasi balance + + align:start position:0% +And another name for a quasi balance + + + align:start position:0% +And another name for a quasi balance +state is a resonance. + + align:start position:0% + + + + align:start position:0% + +Okay. So uh we're going to be studying + + align:start position:0% +Okay. So uh we're going to be studying + + + align:start position:0% +Okay. So uh we're going to be studying +uh what gives rise to the widths of + + align:start position:0% +uh what gives rise to the widths of + + + align:start position:0% +uh what gives rise to the widths of +these resonances which is the coupling + + align:start position:0% +these resonances which is the coupling + + + align:start position:0% +these resonances which is the coupling +between the bound state and the + + align:start position:0% +between the bound state and the + + + align:start position:0% +between the bound state and the +underlying continuum of lower + + align:start position:0% +underlying continuum of lower + + + align:start position:0% +underlying continuum of lower +resonances. + + align:start position:0% + + + + align:start position:0% + +And in particular, we're going to talk + + align:start position:0% +And in particular, we're going to talk + + + align:start position:0% +And in particular, we're going to talk +about autoization + + align:start position:0% +about autoization + + + align:start position:0% +about autoization +because + + align:start position:0% +because + + + align:start position:0% +because +last time we talked a lot about + + align:start position:0% +last time we talked a lot about + + + align:start position:0% +last time we talked a lot about +vibrational overlap integrals and that's + + align:start position:0% +vibrational overlap integrals and that's + + + align:start position:0% +vibrational overlap integrals and that's +what's relevant to predisociation + + align:start position:0% +what's relevant to predisociation + + + align:start position:0% +what's relevant to predisociation +and I could have talked at much greater + + align:start position:0% +and I could have talked at much greater + + + align:start position:0% +and I could have talked at much greater +length about that but I think it's much + + align:start position:0% +length about that but I think it's much + + + align:start position:0% +length about that but I think it's much +more fun to talk about autoionization. + + align:start position:0% + + + + align:start position:0% + +Now, autoionization is all about + + align:start position:0% + + + + align:start position:0% + +an electron weakly bound to an ion + + align:start position:0% + + + + align:start position:0% + +and somehow + + align:start position:0% +and somehow + + + align:start position:0% +and somehow +energy gets from the ion into this + + align:start position:0% +energy gets from the ion into this + + + align:start position:0% +energy gets from the ion into this +electron. + + align:start position:0% +electron. + + + align:start position:0% +electron. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +And + + align:start position:0% +And + + + align:start position:0% +And +that's a difficult thing to imagine + + align:start position:0% +that's a difficult thing to imagine + + + align:start position:0% +that's a difficult thing to imagine +because if you imagine a collision + + align:start position:0% +because if you imagine a collision + + + align:start position:0% +because if you imagine a collision +between a light particle and a heavy + + align:start position:0% +between a light particle and a heavy + + + align:start position:0% +between a light particle and a heavy +particle, + + align:start position:0% + + + + align:start position:0% + +no energy, no significant energy is + + align:start position:0% +no energy, no significant energy is + + + align:start position:0% +no energy, no significant energy is +added to or removed from the heavy + + align:start position:0% +added to or removed from the heavy + + + align:start position:0% +added to or removed from the heavy +particle + + align:start position:0% +particle + + + align:start position:0% +particle +unless there's some very special thing. + + align:start position:0% +unless there's some very special thing. + + + align:start position:0% +unless there's some very special thing. +If the light particle somehow gets + + align:start position:0% +If the light particle somehow gets + + + align:start position:0% +If the light particle somehow gets +embedded in the heavy particle + + align:start position:0% +embedded in the heavy particle + + + align:start position:0% +embedded in the heavy particle +uh or heavy particle is really sticky or + + align:start position:0% +uh or heavy particle is really sticky or + + + align:start position:0% +uh or heavy particle is really sticky or +uh heavy particle is + + align:start position:0% +uh heavy particle is + + + align:start position:0% +uh heavy particle is +whatever. Right? So that's what we're + + align:start position:0% +whatever. Right? So that's what we're + + + align:start position:0% +whatever. Right? So that's what we're +going to talk about. What are the + + align:start position:0% +going to talk about. What are the + + + align:start position:0% +going to talk about. What are the +possible mechanisms for exchange of + + align:start position:0% +possible mechanisms for exchange of + + + align:start position:0% +possible mechanisms for exchange of +energy between an electron and a + + align:start position:0% +energy between an electron and a + + + align:start position:0% +energy between an electron and a +molecular ion. + + align:start position:0% +molecular ion. + + + align:start position:0% +molecular ion. +And we're going to try not just to talk + + align:start position:0% +And we're going to try not just to talk + + + align:start position:0% +And we're going to try not just to talk +about it phenomenologically, but we're + + align:start position:0% +about it phenomenologically, but we're + + + align:start position:0% +about it phenomenologically, but we're +going to actually try to bring out what + + align:start position:0% +going to actually try to bring out what + + + align:start position:0% +going to actually try to bring out what +are the specific interactions that + + align:start position:0% +are the specific interactions that + + + align:start position:0% +are the specific interactions that +enable this kind of process to occur, + + align:start position:0% +enable this kind of process to occur, + + + align:start position:0% +enable this kind of process to occur, +this energy transfer process to occur + + align:start position:0% +this energy transfer process to occur + + + align:start position:0% +this energy transfer process to occur +despite the kinematic difficulties. + + align:start position:0% + + + + align:start position:0% + +Okay. Now, I gave you uh uh 21 pages + + align:start position:0% +Okay. Now, I gave you uh uh 21 pages + + + align:start position:0% +Okay. Now, I gave you uh uh 21 pages +from the the book. Some of you have a + + align:start position:0% +from the the book. Some of you have a + + + align:start position:0% +from the the book. Some of you have a +handout consisting of roughly half of + + align:start position:0% +handout consisting of roughly half of + + + align:start position:0% +handout consisting of roughly half of +those pages and I don't quite know why I + + align:start position:0% +those pages and I don't quite know why I + + + align:start position:0% +those pages and I don't quite know why I +chose to + + align:start position:0% +chose to + + + align:start position:0% +chose to +give you those. So this is the complete + + align:start position:0% +give you those. So this is the complete + + + align:start position:0% +give you those. So this is the complete +section you want to see. Okay. In order + + align:start position:0% +section you want to see. Okay. In order + + + align:start position:0% +section you want to see. Okay. In order +to talk about these things, I have to + + align:start position:0% +to talk about these things, I have to + + + align:start position:0% +to talk about these things, I have to +introduce Rberg states. + + align:start position:0% +introduce Rberg states. + + + align:start position:0% +introduce Rberg states. +And I'm going to do it in a + + align:start position:0% +And I'm going to do it in a + + + align:start position:0% +And I'm going to do it in a +in as superficial a way as I can get + + align:start position:0% +in as superficial a way as I can get + + + align:start position:0% +in as superficial a way as I can get +away with + + align:start position:0% +away with + + + align:start position:0% +away with +because that's a topic that would take + + align:start position:0% +because that's a topic that would take + + + align:start position:0% +because that's a topic that would take +many lectures if I did it honestly. + + align:start position:0% +many lectures if I did it honestly. + + + align:start position:0% +many lectures if I did it honestly. +Okay. So, let's uh start out. We have a + + align:start position:0% +Okay. So, let's uh start out. We have a + + + align:start position:0% +Okay. So, let's uh start out. We have a +hydrogen atom. Our picture of Rberg + + align:start position:0% +hydrogen atom. Our picture of Rberg + + + align:start position:0% +hydrogen atom. Our picture of Rberg +states is based on the picture of the + + align:start position:0% +states is based on the picture of the + + + align:start position:0% +states is based on the picture of the +hydrogen atom. And for the hydrogen + + align:start position:0% +hydrogen atom. And for the hydrogen + + + align:start position:0% +hydrogen atom. And for the hydrogen +atom, the energy levels, + + align:start position:0% +atom, the energy levels, + + + align:start position:0% +atom, the energy levels, +and I'm always going to use + + align:start position:0% +and I'm always going to use + + + align:start position:0% +and I'm always going to use +spectroscopic units. So, uh, at least + + align:start position:0% +spectroscopic units. So, uh, at least + + + align:start position:0% +spectroscopic units. So, uh, at least +for now, I'm going to, uh, divide by HC + + align:start position:0% +for now, I'm going to, uh, divide by HC + + + align:start position:0% +for now, I'm going to, uh, divide by HC +explicitly, + + align:start position:0% +explicitly, + + + align:start position:0% +explicitly, +but + + align:start position:0% +but + + + align:start position:0% +but +you won't catch me doing that in real + + align:start position:0% +you won't catch me doing that in real + + + align:start position:0% +you won't catch me doing that in real +life. So, the energy is equal to the + + align:start position:0% +life. So, the energy is equal to the + + + align:start position:0% +life. So, the energy is equal to the +ionization potential minus the Renberg + + align:start position:0% +ionization potential minus the Renberg + + + align:start position:0% +ionization potential minus the Renberg +over N². The river is equal to the + + align:start position:0% +over N². The river is equal to the + + + align:start position:0% +over N². The river is equal to the +ionization potential is equal to 109,737 + + align:start position:0% +ionization potential is equal to 109,737 + + + align:start position:0% +ionization potential is equal to 109,737 +reciprocal centimeters. + + align:start position:0% + + + + align:start position:0% + +Just one of those numbers that I have + + align:start position:0% +Just one of those numbers that I have + + + align:start position:0% +Just one of those numbers that I have +had to look up so many times that I + + align:start position:0% +had to look up so many times that I + + + align:start position:0% +had to look up so many times that I +finally remembered it. I don't have any + + align:start position:0% +finally remembered it. I don't have any + + + align:start position:0% +finally remembered it. I don't have any +more digits, but there are more. + + align:start position:0% +more digits, but there are more. + + + align:start position:0% +more digits, but there are more. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +so and n is an integer 1 2 3 and so + + align:start position:0% +so and n is an integer 1 2 3 and so + + + align:start position:0% +so and n is an integer 1 2 3 and so +these are the energy levels of hydrogen + + align:start position:0% + + + + align:start position:0% + +and in addition the energy levels of + + align:start position:0% +and in addition the energy levels of + + + align:start position:0% +and in addition the energy levels of +hydrogen do not depend on the orbital + + align:start position:0% +hydrogen do not depend on the orbital + + + align:start position:0% +hydrogen do not depend on the orbital +angular momentum. + + align:start position:0% + + + + align:start position:0% + +Hydrogen is an electron bound to a point + + align:start position:0% +Hydrogen is an electron bound to a point + + + align:start position:0% +Hydrogen is an electron bound to a point +nucleus. It's like it's a little bit + + align:start position:0% +nucleus. It's like it's a little bit + + + align:start position:0% +nucleus. It's like it's a little bit +like the inert gas approx the ideal gas + + align:start position:0% +like the inert gas approx the ideal gas + + + align:start position:0% +like the inert gas approx the ideal gas +approximation. Right? we have + + align:start position:0% +approximation. Right? we have + + + align:start position:0% +approximation. Right? we have +non-interacting particles that that + + align:start position:0% +non-interacting particles that that + + + align:start position:0% +non-interacting particles that that +point nucleus + + align:start position:0% +point nucleus + + + align:start position:0% +point nucleus +uh has a very nice property that it uh + + align:start position:0% +uh has a very nice property that it uh + + + align:start position:0% +uh has a very nice property that it uh +no matter how the electron looks at it + + align:start position:0% +no matter how the electron looks at it + + + align:start position:0% +no matter how the electron looks at it +from afar or from close in it has a + + align:start position:0% +from afar or from close in it has a + + + align:start position:0% +from afar or from close in it has a +charge of exactly one and it's round. + + align:start position:0% + + + + align:start position:0% + +So the next step in complexity is the + + align:start position:0% +So the next step in complexity is the + + + align:start position:0% +So the next step in complexity is the +sodium atom and the sodium atom has + + align:start position:0% +sodium atom and the sodium atom has + + + align:start position:0% +sodium atom and the sodium atom has +energy levels which are specified by + + align:start position:0% +energy levels which are specified by + + + align:start position:0% +energy levels which are specified by +three quantum numbers. + + align:start position:0% +three quantum numbers. + + + align:start position:0% +three quantum numbers. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +and again we have an ionization + + align:start position:0% +and again we have an ionization + + + align:start position:0% +and again we have an ionization +potential and we have a formula n minus + + align:start position:0% +potential and we have a formula n minus + + + align:start position:0% +potential and we have a formula n minus +quantum defect + + align:start position:0% +quantum defect + + + align:start position:0% +quantum defect +uh and quantum defect as two quantum + + align:start position:0% +uh and quantum defect as two quantum + + + align:start position:0% +uh and quantum defect as two quantum +numbers l and j. + + align:start position:0% +numbers l and j. + + + align:start position:0% +numbers l and j. +Okay. So what is this? It looks like + + align:start position:0% +Okay. So what is this? It looks like + + + align:start position:0% +Okay. So what is this? It looks like +it's just a budge factor. + + align:start position:0% +it's just a budge factor. + + + align:start position:0% +it's just a budge factor. +It just looks like we're we're trying to + + align:start position:0% +It just looks like we're we're trying to + + + align:start position:0% +It just looks like we're we're trying to +use this formula. + + align:start position:0% +use this formula. + + + align:start position:0% +use this formula. +And in order to use it, we have to say, + + align:start position:0% +And in order to use it, we have to say, + + + align:start position:0% +And in order to use it, we have to say, +well, n isn't quite an integer, + + align:start position:0% +well, n isn't quite an integer, + + + align:start position:0% +well, n isn't quite an integer, +but it's there's still some regularity + + align:start position:0% +but it's there's still some regularity + + + align:start position:0% +but it's there's still some regularity +here. It's saying that n isn't quite an + + align:start position:0% +here. It's saying that n isn't quite an + + + align:start position:0% +here. It's saying that n isn't quite an +integer, but it's difference from an + + align:start position:0% +integer, but it's difference from an + + + align:start position:0% +integer, but it's difference from an +integer is the same for every for all + + align:start position:0% +integer is the same for every for all + + + align:start position:0% +integer is the same for every for all +members of a redberg series with the + + align:start position:0% +members of a redberg series with the + + + align:start position:0% +members of a redberg series with the +same value of l and j. + + align:start position:0% +same value of l and j. + + + align:start position:0% +same value of l and j. +So we might have a uh a p rberg series + + align:start position:0% +So we might have a uh a p rberg series + + + align:start position:0% +So we might have a uh a p rberg series +that's l= 1 and uh and j would be three + + align:start position:0% +that's l= 1 and uh and j would be three + + + align:start position:0% +that's l= 1 and uh and j would be three +halves and for all riberg states of this + + align:start position:0% +halves and for all riberg states of this + + + align:start position:0% +halves and for all riberg states of this +uh with these quantum numbers uh the + + align:start position:0% +uh with these quantum numbers uh the + + + align:start position:0% +uh with these quantum numbers uh the +quantum effect will be the same + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +uh we could have a p rberg series where + + align:start position:0% +uh we could have a p rberg series where + + + align:start position:0% +uh we could have a p rberg series where +j is a half and then this quantum defect + + align:start position:0% +j is a half and then this quantum defect + + + align:start position:0% +j is a half and then this quantum defect +would be a little different + + align:start position:0% +would be a little different + + + align:start position:0% +would be a little different +but again the same for all n + + align:start position:0% +but again the same for all n + + + align:start position:0% +but again the same for all n +well + + align:start position:0% +well + + + align:start position:0% +well +the rimmer constant is the same as for + + align:start position:0% +the rimmer constant is the same as for + + + align:start position:0% +the rimmer constant is the same as for +hydrogen almost there's a slight reduced + + align:start position:0% +hydrogen almost there's a slight reduced + + + align:start position:0% +hydrogen almost there's a slight reduced +mass effect but the ionization potential + + align:start position:0% +mass effect but the ionization potential + + + align:start position:0% +mass effect but the ionization potential +is very different + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +what we learn from sodium which is like + + align:start position:0% +what we learn from sodium which is like + + + align:start position:0% +what we learn from sodium which is like +hydrogen except the nucleus isn't a + + align:start position:0% +hydrogen except the nucleus isn't a + + + align:start position:0% +hydrogen except the nucleus isn't a +point + + align:start position:0% +point + + + align:start position:0% +point +is that we need to introduce these + + align:start position:0% +is that we need to introduce these + + + align:start position:0% +is that we need to introduce these +quantum defects which make the integer + + align:start position:0% +quantum defects which make the integer + + + align:start position:0% +quantum defects which make the integer +the energies not given by integers and + + align:start position:0% +the energies not given by integers and + + + align:start position:0% +the energies not given by integers and +the different L's and J's have different + + align:start position:0% +the different L's and J's have different + + + align:start position:0% +the different L's and J's have different +quantum defects and the quantum defects + + align:start position:0% +quantum defects and the quantum defects + + + align:start position:0% +quantum defects and the quantum defects +S 1/2 is large + + align:start position:0% +S 1/2 is large + + + align:start position:0% +S 1/2 is large +B uh 1/2 is smaller. The three halves is + + align:start position:0% +B uh 1/2 is smaller. The three halves is + + + align:start position:0% +B uh 1/2 is smaller. The three halves is +still a little smaller, + + align:start position:0% +still a little smaller, + + + align:start position:0% +still a little smaller, +but really this is S is much larger than + + align:start position:0% +but really this is S is much larger than + + + align:start position:0% +but really this is S is much larger than +the P's. And then we continue and we + + align:start position:0% +the P's. And then we continue and we + + + align:start position:0% +the P's. And then we continue and we +have delta for faves + + align:start position:0% + + + + align:start position:0% + +uh which is approximately equal to delta + + align:start position:0% +uh which is approximately equal to delta + + + align:start position:0% +uh which is approximately equal to delta +for f. What's the matter with this black + + align:start position:0% +for f. What's the matter with this black + + + align:start position:0% +for f. What's the matter with this black + + align:start position:0% + + + align:start position:0% +which is approximately zero. So what + + align:start position:0% +which is approximately zero. So what + + + align:start position:0% +which is approximately zero. So what +happens is the quantum defects + + align:start position:0% +happens is the quantum defects + + + align:start position:0% +happens is the quantum defects +still thought of as punch factors for + + align:start position:0% +still thought of as punch factors for + + + align:start position:0% +still thought of as punch factors for +the moment are large for s and smaller + + align:start position:0% +the moment are large for s and smaller + + + align:start position:0% +the moment are large for s and smaller +for p and eventually they're so small + + align:start position:0% +for p and eventually they're so small + + + align:start position:0% +for p and eventually they're so small +that they're nearly zero and we get back + + align:start position:0% +that they're nearly zero and we get back + + + align:start position:0% +that they're nearly zero and we get back +to + + align:start position:0% +to + + + align:start position:0% +to +uh a quasi hydrogenic situation. + + align:start position:0% +uh a quasi hydrogenic situation. + + + align:start position:0% +uh a quasi hydrogenic situation. +Well, + + align:start position:0% +Well, + + + align:start position:0% +Well, +these quantum defects + + align:start position:0% +these quantum defects + + + align:start position:0% +these quantum defects +are not such factors. + + align:start position:0% +are not such factors. + + + align:start position:0% +are not such factors. +They are what happens to an electron + + align:start position:0% +They are what happens to an electron + + + align:start position:0% +They are what happens to an electron +which scatters off of this nucleus + + align:start position:0% +which scatters off of this nucleus + + + align:start position:0% +which scatters off of this nucleus +when it scatters off of the nucleus. + + align:start position:0% +when it scatters off of the nucleus. + + + align:start position:0% +when it scatters off of the nucleus. +Uh the nucleus has an effective charge + + align:start position:0% +Uh the nucleus has an effective charge + + + align:start position:0% +Uh the nucleus has an effective charge +which depends on the distance of the + + align:start position:0% +which depends on the distance of the + + + align:start position:0% +which depends on the distance of the +electron from the nucleus because there + + align:start position:0% +electron from the nucleus because there + + + align:start position:0% +electron from the nucleus because there +are electrons around it. There's an + + align:start position:0% +are electrons around it. There's an + + + align:start position:0% +are electrons around it. There's an +inner shell of electrons, two inner + + align:start position:0% +inner shell of electrons, two inner + + + align:start position:0% +inner shell of electrons, two inner +shells. And so as the electron gets in + + align:start position:0% +shells. And so as the electron gets in + + + align:start position:0% +shells. And so as the electron gets in +close, it sees a larger charge means + + align:start position:0% +close, it sees a larger charge means + + + align:start position:0% +close, it sees a larger charge means +it's pulled in. It has higher energy + + align:start position:0% +it's pulled in. It has higher energy + + + align:start position:0% +it's pulled in. It has higher energy +than the corresponding + + align:start position:0% +than the corresponding + + + align:start position:0% +than the corresponding +N and L for hydrogen. higher binding + + align:start position:0% +N and L for hydrogen. higher binding + + + align:start position:0% +N and L for hydrogen. higher binding +energy + + align:start position:0% +energy + + + align:start position:0% +energy +and because the effective potential for + + align:start position:0% +and because the effective potential for + + + align:start position:0% +and because the effective potential for +uh for a sodium has the form of Z of R / + + align:start position:0% +uh for a sodium has the form of Z of R / + + + align:start position:0% +uh for a sodium has the form of Z of R / +R minus I that's the cooling potential. + + align:start position:0% +R minus I that's the cooling potential. + + + align:start position:0% +R minus I that's the cooling potential. +So this is what had been one for + + align:start position:0% +So this is what had been one for + + + align:start position:0% +So this is what had been one for +hydrogen. + + align:start position:0% +hydrogen. + + + align:start position:0% +hydrogen. +But this is a function that it goes from + + align:start position:0% +But this is a function that it goes from + + + align:start position:0% +But this is a function that it goes from +one at long distance up to the char to + + align:start position:0% +one at long distance up to the char to + + + align:start position:0% +one at long distance up to the char to +the the the atomic the atomic number of + + align:start position:0% +the the the atomic the atomic number of + + + align:start position:0% +the the the atomic the atomic number of +sodium which is + + align:start position:0% + + + + align:start position:0% + +23. + + align:start position:0% + + + + align:start position:0% + +It's mass 23. + + align:start position:0% + + + + align:start position:0% + +2 + 8 + 1, right? 11. + + align:start position:0% +2 + 8 + 1, right? 11. + + + align:start position:0% +2 + 8 + 1, right? 11. +Okay. And then we have a repulsion L l + + + align:start position:0% +Okay. And then we have a repulsion L l + + + + align:start position:0% +Okay. And then we have a repulsion L l + + + align:start position:0% + + + align:start position:0% +r². That's the centrifugal barrier. + + align:start position:0% +r². That's the centrifugal barrier. + + + align:start position:0% +r². That's the centrifugal barrier. +Because the electron has angular + + align:start position:0% +Because the electron has angular + + + align:start position:0% +Because the electron has angular +momentum, it can't get in close. + + align:start position:0% +momentum, it can't get in close. + + + align:start position:0% +momentum, it can't get in close. +And so as L increases, + + align:start position:0% +And so as L increases, + + + align:start position:0% +And so as L increases, +even though + + align:start position:0% +even though + + + align:start position:0% +even though +uh the nucleus isn't a point, + + align:start position:0% + + + + align:start position:0% + +the electron doesn't know it. So + + align:start position:0% +the electron doesn't know it. So + + + align:start position:0% +the electron doesn't know it. So +basically we're assuming we have one one + + align:start position:0% +basically we're assuming we have one one + + + align:start position:0% +basically we're assuming we have one one +different electron and the other + + align:start position:0% +different electron and the other + + + align:start position:0% +different electron and the other +electrons are just a core which create + + align:start position:0% +electrons are just a core which create + + + align:start position:0% +electrons are just a core which create +an effective Z. That's right. So + + align:start position:0% +an effective Z. That's right. So + + + align:start position:0% +an effective Z. That's right. So +whenever we can approach a problem by + + align:start position:0% +whenever we can approach a problem by + + + align:start position:0% +whenever we can approach a problem by +making most of the particles inactive + + align:start position:0% +making most of the particles inactive + + + align:start position:0% +making most of the particles inactive +we'll do that and that's always wrong. + + align:start position:0% +we'll do that and that's always wrong. + + + align:start position:0% +we'll do that and that's always wrong. +uh but uh uh its wrongness is usually + + align:start position:0% +uh but uh uh its wrongness is usually + + + align:start position:0% +uh but uh uh its wrongness is usually +much less than other wrongnesses that we + + align:start position:0% +much less than other wrongnesses that we + + + align:start position:0% +much less than other wrongnesses that we +adopt in treating a system. And so the + + align:start position:0% +adopt in treating a system. And so the + + + align:start position:0% +adopt in treating a system. And so the +uh + + align:start position:0% + + + + align:start position:0% + +the the fact of treating the ion core as + + align:start position:0% +the the fact of treating the ion core as + + + align:start position:0% +the the fact of treating the ion core as +passive + + align:start position:0% +passive + + + align:start position:0% +passive +leads to corrections that we will make. + + align:start position:0% +leads to corrections that we will make. + + + align:start position:0% +leads to corrections that we will make. +And in fact when I talk about electronic + + align:start position:0% +And in fact when I talk about electronic + + + align:start position:0% +And in fact when I talk about electronic +autoionization that is one of the things + + align:start position:0% +autoionization that is one of the things + + + align:start position:0% +autoionization that is one of the things +that no longer is one of the assumptions + + align:start position:0% +that no longer is one of the assumptions + + + align:start position:0% +that no longer is one of the assumptions +that we no longer make. the electron + + align:start position:0% +that we no longer make. the electron + + + align:start position:0% +that we no longer make. the electron +comes in, smacks the iron core, and + + align:start position:0% +comes in, smacks the iron core, and + + + align:start position:0% +comes in, smacks the iron core, and +excites one of the electrons. + + align:start position:0% +excites one of the electrons. + + + align:start position:0% +excites one of the electrons. +And this is kind of a neat mechanism + + align:start position:0% +And this is kind of a neat mechanism + + + align:start position:0% +And this is kind of a neat mechanism +because it says, okay, we're + + align:start position:0% +because it says, okay, we're + + + align:start position:0% +because it says, okay, we're +transferring energy, but not to the + + align:start position:0% +transferring energy, but not to the + + + align:start position:0% +transferring energy, but not to the +heavy object, but to an electron, + + align:start position:0% +heavy object, but to an electron, + + + align:start position:0% +heavy object, but to an electron, +another electron. + + align:start position:0% +another electron. + + + align:start position:0% +another electron. +So when we need to open up the core and + + align:start position:0% +So when we need to open up the core and + + + align:start position:0% +So when we need to open up the core and +make them not pass it, we do that. Okay, + + align:start position:0% +make them not pass it, we do that. Okay, + + + align:start position:0% +make them not pass it, we do that. Okay, +good question. + + align:start position:0% +good question. + + + align:start position:0% +good question. +Okay. So + + align:start position:0% +Okay. So + + + align:start position:0% +Okay. So +because of this uh at high orbital + + align:start position:0% +because of this uh at high orbital + + + align:start position:0% +because of this uh at high orbital +angular momentum we get uh a return to + + align:start position:0% +angular momentum we get uh a return to + + + align:start position:0% +angular momentum we get uh a return to +hydrogenic behavior and this leads to + + align:start position:0% +hydrogenic behavior and this leads to + + + align:start position:0% +hydrogenic behavior and this leads to +the distinction between core penetrating + + align:start position:0% +the distinction between core penetrating + + + align:start position:0% +the distinction between core penetrating +riberg states + + align:start position:0% +riberg states + + + align:start position:0% +riberg states +and core non-penetrating riberg states + + align:start position:0% +and core non-penetrating riberg states + + + align:start position:0% +and core non-penetrating riberg states +and the way in which the two experience + + align:start position:0% +and the way in which the two experience + + + align:start position:0% +and the way in which the two experience +dynamics is is different because one can + + align:start position:0% +dynamics is is different because one can + + + align:start position:0% +dynamics is is different because one can +get close and one can and we can use the + + align:start position:0% +get close and one can and we can use the + + + align:start position:0% +get close and one can and we can use the +two different classes of states as + + align:start position:0% +two different classes of states as + + + align:start position:0% +two different classes of states as +different kinds of probes of the + + align:start position:0% +different kinds of probes of the + + + align:start position:0% +different kinds of probes of the +structure of the ion. + + align:start position:0% +structure of the ion. + + + align:start position:0% +structure of the ion. +Okay. The quantum defect is not a punch + + align:start position:0% +Okay. The quantum defect is not a punch + + + align:start position:0% +Okay. The quantum defect is not a punch +factor. + + align:start position:0% +factor. + + + align:start position:0% +factor. +Uh the quantum defect is a phase shift. + + align:start position:0% +Uh the quantum defect is a phase shift. + + + align:start position:0% +Uh the quantum defect is a phase shift. +if a phase shift of the wave function + + align:start position:0% +if a phase shift of the wave function + + + align:start position:0% +if a phase shift of the wave function +scattering off the core relative to what + + align:start position:0% +scattering off the core relative to what + + + align:start position:0% +scattering off the core relative to what +it would have been if it was hydrogen. + + align:start position:0% +it would have been if it was hydrogen. + + + align:start position:0% +it would have been if it was hydrogen. +So since the uh ion core has a higher + + align:start position:0% +So since the uh ion core has a higher + + + align:start position:0% +So since the uh ion core has a higher +charge than hydrogen, + + align:start position:0% +charge than hydrogen, + + + align:start position:0% +charge than hydrogen, +the electron is pulled in, it gets it it + + align:start position:0% +the electron is pulled in, it gets it it + + + align:start position:0% +the electron is pulled in, it gets it it +accumulates some extra phase as it goes + + align:start position:0% +accumulates some extra phase as it goes + + + align:start position:0% +accumulates some extra phase as it goes +by. And so there is a phase shift. And + + align:start position:0% +by. And so there is a phase shift. And + + + align:start position:0% +by. And so there is a phase shift. And +this phase shift can also be thought of + + align:start position:0% +this phase shift can also be thought of + + + align:start position:0% +this phase shift can also be thought of +as for a particular + + align:start position:0% +as for a particular + + + align:start position:0% +as for a particular +value of the orbital angular momentum, + + align:start position:0% +value of the orbital angular momentum, + + + align:start position:0% +value of the orbital angular momentum, +the electron experiences a phase shift, + + align:start position:0% +the electron experiences a phase shift, + + + align:start position:0% +the electron experiences a phase shift, +yet it has to somehow if it's in a + + align:start position:0% +yet it has to somehow if it's in a + + + align:start position:0% +yet it has to somehow if it's in a +bounce state go to infinity with + + align:start position:0% +bounce state go to infinity with + + + align:start position:0% +bounce state go to infinity with +amplitude zero at infinity. And if the + + align:start position:0% +amplitude zero at infinity. And if the + + + align:start position:0% +amplitude zero at infinity. And if the +phase shift is wrong, it won't do that. + + align:start position:0% +phase shift is wrong, it won't do that. + + + align:start position:0% +phase shift is wrong, it won't do that. +And that can't be a solution to the the + + align:start position:0% +And that can't be a solution to the the + + + align:start position:0% +And that can't be a solution to the the +the short equation. + + align:start position:0% +the short equation. + + + align:start position:0% +the short equation. +So there has to be phase shifts + + align:start position:0% +So there has to be phase shifts + + + align:start position:0% +So there has to be phase shifts +because the charge isn't one. Uh the + + align:start position:0% +because the charge isn't one. Uh the + + + align:start position:0% +because the charge isn't one. Uh the +phase shift is going to depend on the + + align:start position:0% +phase shift is going to depend on the + + + align:start position:0% +phase shift is going to depend on the +orbital angular momentum. + + align:start position:0% +orbital angular momentum. + + + align:start position:0% +orbital angular momentum. +And uh uh but the thing that's a little + + align:start position:0% +And uh uh but the thing that's a little + + + align:start position:0% +And uh uh but the thing that's a little +bit unexpected is that all members of a + + align:start position:0% +bit unexpected is that all members of a + + + align:start position:0% +bit unexpected is that all members of a +ritberg series will have the same fascia + + align:start position:0% +ritberg series will have the same fascia + + + align:start position:0% +ritberg series will have the same fascia +the same quantum defect to a very good + + align:start position:0% +the same quantum defect to a very good + + + align:start position:0% +the same quantum defect to a very good +approximation. + + align:start position:0% +approximation. + + + align:start position:0% +approximation. +And this leads to another important + + align:start position:0% +And this leads to another important + + + align:start position:0% +And this leads to another important +aspect of rberg states. If we plot the + + align:start position:0% +aspect of rberg states. If we plot the + + + align:start position:0% +aspect of rberg states. If we plot the +wave function + + align:start position:0% +wave function + + + align:start position:0% +wave function +or the versus r. + + align:start position:0% +or the versus r. + + + align:start position:0% +or the versus r. +So uh s r versus r we have some + + align:start position:0% + + + + align:start position:0% + +some nodes + + align:start position:0% +some nodes + + + align:start position:0% +some nodes +um and if we focus only on the inner + + align:start position:0% +um and if we focus only on the inner + + + align:start position:0% +um and if we focus only on the inner +part of the wave function + + align:start position:0% +part of the wave function + + + align:start position:0% +part of the wave function +the shape + + align:start position:0% +the shape + + + align:start position:0% +the shape +of the inner part of the wave function + + align:start position:0% +of the inner part of the wave function + + + align:start position:0% +of the inner part of the wave function +in particular the position of the + + align:start position:0% +in particular the position of the + + + align:start position:0% +in particular the position of the +anti-node and the first node + + align:start position:0% +anti-node and the first node + + + align:start position:0% +anti-node and the first node +doesn't move as you go along a ritberg + + align:start position:0% +doesn't move as you go along a ritberg + + + align:start position:0% +doesn't move as you go along a ritberg +series the Only thing that happens is + + align:start position:0% +series the Only thing that happens is + + + align:start position:0% +series the Only thing that happens is +that the amplitude here is scaled as n + + align:start position:0% +that the amplitude here is scaled as n + + + align:start position:0% +that the amplitude here is scaled as n +the minus3 halves + + align:start position:0% + + + + align:start position:0% + +and there are many ways of explaining + + align:start position:0% +and there are many ways of explaining + + + align:start position:0% +and there are many ways of explaining +this + + align:start position:0% +this + + + align:start position:0% +this +uh but I don't have time uh one way + + align:start position:0% +uh but I don't have time uh one way + + + align:start position:0% +uh but I don't have time uh one way +which is the least good way but which I + + align:start position:0% +which is the least good way but which I + + + align:start position:0% +which is the least good way but which I +can just say you need this to make the + + align:start position:0% +can just say you need this to make the + + + align:start position:0% +can just say you need this to make the +wave functions orthogonal. + + align:start position:0% + + + + align:start position:0% + +But another way of saying it is that + + align:start position:0% +But another way of saying it is that + + + align:start position:0% +But another way of saying it is that +because the kinetic energy of the + + align:start position:0% +because the kinetic energy of the + + + align:start position:0% +because the kinetic energy of the +electron when it's near the core is so + + align:start position:0% +electron when it's near the core is so + + + align:start position:0% +electron when it's near the core is so +enormous, the deproy wavelength doesn't + + align:start position:0% +enormous, the deproy wavelength doesn't + + + align:start position:0% +enormous, the deproy wavelength doesn't +change much when you change the uh uh + + align:start position:0% +change much when you change the uh uh + + + align:start position:0% +change much when you change the uh uh +the energy relative to the ionization + + align:start position:0% +the energy relative to the ionization + + + align:start position:0% +the energy relative to the ionization +limit because the ionization energy is a + + align:start position:0% +limit because the ionization energy is a + + + align:start position:0% +limit because the ionization energy is a +small fraction of the energy of the + + align:start position:0% +small fraction of the energy of the + + + align:start position:0% +small fraction of the energy of the +electron near the core. And so it's + + align:start position:0% +electron near the core. And so it's + + + align:start position:0% +electron near the core. And so it's +because of that that this deoy + + align:start position:0% +because of that that this deoy + + + align:start position:0% +because of that that this deoy +wavelength or average de wavelength is + + align:start position:0% +wavelength or average de wavelength is + + + align:start position:0% +wavelength or average de wavelength is +independent of n. But this leads to all + + align:start position:0% +independent of n. But this leads to all + + + align:start position:0% +independent of n. But this leads to all +sorts of useful scaling laws for river + + align:start position:0% +sorts of useful scaling laws for river + + + align:start position:0% +sorts of useful scaling laws for river +states. + + align:start position:0% +states. + + + align:start position:0% +states. +So + + align:start position:0% +So + + + align:start position:0% +So +since the only different thing between + + align:start position:0% +since the only different thing between + + + align:start position:0% +since the only different thing between +sodium and hydrogen is this quantum + + align:start position:0% +sodium and hydrogen is this quantum + + + align:start position:0% +sodium and hydrogen is this quantum +defect, + + align:start position:0% +defect, + + + align:start position:0% +defect, +one might suspect that all dynamics is + + align:start position:0% +one might suspect that all dynamics is + + + align:start position:0% +one might suspect that all dynamics is +encoded in the quantum defect. That is + + align:start position:0% +encoded in the quantum defect. That is + + + align:start position:0% +encoded in the quantum defect. That is +correct. + + align:start position:0% +correct. + + + align:start position:0% +correct. +Now for molecules, there are more kinds + + align:start position:0% +Now for molecules, there are more kinds + + + align:start position:0% +Now for molecules, there are more kinds +of quantum defects. And the quantum + + align:start position:0% +of quantum defects. And the quantum + + + align:start position:0% +of quantum defects. And the quantum +defect really isn't a constant, but it's + + align:start position:0% +defect really isn't a constant, but it's + + + align:start position:0% +defect really isn't a constant, but it's +a matrix + + align:start position:0% +a matrix + + + align:start position:0% +a matrix +because sodium is round. Orbital angular + + align:start position:0% +because sodium is round. Orbital angular + + + align:start position:0% +because sodium is round. Orbital angular +momentum is conserved for sodium, + + align:start position:0% +momentum is conserved for sodium, + + + align:start position:0% +momentum is conserved for sodium, +but molecules aren't round. And so you + + align:start position:0% +but molecules aren't round. And so you + + + align:start position:0% +but molecules aren't round. And so you +come in with a Pwave, you can come out + + align:start position:0% +come in with a Pwave, you can come out + + + align:start position:0% +come in with a Pwave, you can come out +with a D-wave. And so there has to the + + align:start position:0% +with a D-wave. And so there has to the + + + align:start position:0% +with a D-wave. And so there has to the +quantum defect has to be + + align:start position:0% +quantum defect has to be + + + align:start position:0% +quantum defect has to be +uh something that allows scattering. And + + align:start position:0% +uh something that allows scattering. And + + + align:start position:0% +uh something that allows scattering. And +so it would it's not just a bunch of + + align:start position:0% +so it would it's not just a bunch of + + + align:start position:0% +so it would it's not just a bunch of +constants which would be diagonal + + align:start position:0% +constants which would be diagonal + + + align:start position:0% +constants which would be diagonal +elements of a matrix but it has off + + align:start position:0% +elements of a matrix but it has off + + + align:start position:0% +elements of a matrix but it has off +diagonal elements too. But we we talk + + align:start position:0% +diagonal elements too. But we we talk + + + align:start position:0% +diagonal elements too. But we we talk +about Igen quantum defects + + align:start position:0% +about Igen quantum defects + + + align:start position:0% +about Igen quantum defects +which are the in a sense the igen values + + align:start position:0% +which are the in a sense the igen values + + + align:start position:0% +which are the in a sense the igen values +of this matrix and each rberg series has + + align:start position:0% +of this matrix and each rberg series has + + + align:start position:0% +of this matrix and each rberg series has +an en quantum defect but it's also + + align:start position:0% +an en quantum defect but it's also + + + align:start position:0% +an en quantum defect but it's also +lmixed. + + align:start position:0% +lmixed. + + + align:start position:0% +lmixed. +Okay. So now + + align:start position:0% +Okay. So now + + + align:start position:0% +Okay. So now +[Music] + + align:start position:0% + + + + align:start position:0% + +so for a molecule AB + + align:start position:0% +so for a molecule AB + + + align:start position:0% +so for a molecule AB +we can have vibrational levels of the + + align:start position:0% +we can have vibrational levels of the + + + align:start position:0% +we can have vibrational levels of the +ion core. Each vibrational level has + + align:start position:0% +ion core. Each vibrational level has + + + align:start position:0% +ion core. Each vibrational level has +rotational levels. + + align:start position:0% +rotational levels. + + + align:start position:0% +rotational levels. +uh we can have if this is say a a double + + align:start position:0% +uh we can have if this is say a a double + + + align:start position:0% +uh we can have if this is say a a double +pi state we could have a double pi + + align:start position:0% +pi state we could have a double pi + + + align:start position:0% +pi state we could have a double pi +1/2 and then a similar manifold states + + align:start position:0% +1/2 and then a similar manifold states + + + align:start position:0% +1/2 and then a similar manifold states +for double pi 3s + + align:start position:0% +for double pi 3s + + + align:start position:0% +for double pi 3s +and then there'll be more excited + + align:start position:0% +and then there'll be more excited + + + align:start position:0% +and then there'll be more excited +states. + + align:start position:0% +states. + + + align:start position:0% +states. +So the ion core has many + + align:start position:0% +So the ion core has many + + + align:start position:0% +So the ion core has many +electronic rotation vibration levels. + + align:start position:0% +electronic rotation vibration levels. + + + align:start position:0% +electronic rotation vibration levels. +And because the ion core has many + + align:start position:0% +And because the ion core has many + + + align:start position:0% +And because the ion core has many +levels, + + align:start position:0% +levels, + + + align:start position:0% +levels, +there's going to be a riberg series of + + align:start position:0% +there's going to be a riberg series of + + + align:start position:0% +there's going to be a riberg series of +the molecule converging to each of the + + align:start position:0% +the molecule converging to each of the + + + align:start position:0% +the molecule converging to each of the +levels of the ion core. + + align:start position:0% +levels of the ion core. + + + align:start position:0% +levels of the ion core. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Well, you might say, well, that that's + + align:start position:0% +Well, you might say, well, that that's + + + align:start position:0% +Well, you might say, well, that that's +that's too bad. That means that life is + + align:start position:0% +that's too bad. That means that life is + + + align:start position:0% +that's too bad. That means that life is +going to become incredibly complicated. + + align:start position:0% + + + + align:start position:0% + +So you could also say that's wonderful. + + align:start position:0% +So you could also say that's wonderful. + + + align:start position:0% +So you could also say that's wonderful. +There are lots of dynamical processes we + + align:start position:0% +There are lots of dynamical processes we + + + align:start position:0% +There are lots of dynamical processes we +can throw. + + align:start position:0% +can throw. + + + align:start position:0% +can throw. +It just depends on, you know, whether + + align:start position:0% +It just depends on, you know, whether + + + align:start position:0% +It just depends on, you know, whether +you're uh whether you have the + + align:start position:0% +you're uh whether you have the + + + align:start position:0% +you're uh whether you have the +disposition of Ryan Tom or of + + align:start position:0% +disposition of Ryan Tom or of + + + align:start position:0% +disposition of Ryan Tom or of +me. + + align:start position:0% +me. + + + align:start position:0% +me. +However, + + align:start position:0% +However, + + + align:start position:0% +However, +there is a nice thing and that is that + + align:start position:0% +there is a nice thing and that is that + + + align:start position:0% +there is a nice thing and that is that +many of the processes associated with + + align:start position:0% +many of the processes associated with + + + align:start position:0% +many of the processes associated with +these huge number of different ribert + + align:start position:0% +these huge number of different ribert + + + align:start position:0% +these huge number of different ribert +series are all related. And so you just + + align:start position:0% +series are all related. And so you just + + + align:start position:0% +series are all related. And so you just +find a way to use these multiplicity of + + align:start position:0% +find a way to use these multiplicity of + + + align:start position:0% +find a way to use these multiplicity of +interactions to determine the small + + align:start position:0% +interactions to determine the small + + + align:start position:0% +interactions to determine the small +number of terms that you need to have + + align:start position:0% +number of terms that you need to have + + + align:start position:0% +number of terms that you need to have +essentially a global description of + + align:start position:0% +essentially a global description of + + + align:start position:0% +essentially a global description of +everything that can happen. So I + + align:start position:0% +everything that can happen. So I + + + align:start position:0% +everything that can happen. So I +mentioned Ridberg scaling rules. That + + align:start position:0% +mentioned Ridberg scaling rules. That + + + align:start position:0% +mentioned Ridberg scaling rules. That +means that basically for a family of + + align:start position:0% +means that basically for a family of + + + align:start position:0% +means that basically for a family of +processes you need one coupling constant + + align:start position:0% +processes you need one coupling constant + + + align:start position:0% +processes you need one coupling constant +and then it scales to describe all + + align:start position:0% +and then it scales to describe all + + + align:start position:0% +and then it scales to describe all +members of the family. + + align:start position:0% +members of the family. + + + align:start position:0% +members of the family. +And so as long as you know they're going + + align:start position:0% +And so as long as you know they're going + + + align:start position:0% +And so as long as you know they're going +to be scaling rules, you can go and + + align:start position:0% +to be scaling rules, you can go and + + + align:start position:0% +to be scaling rules, you can go and +measure the one process that s the one + + align:start position:0% +measure the one process that s the one + + + align:start position:0% +measure the one process that s the one +specific effect that samples what you + + align:start position:0% +specific effect that samples what you + + + align:start position:0% +specific effect that samples what you +need most sensitive. + + align:start position:0% + + + + align:start position:0% + +So because there are a huge number of + + align:start position:0% +So because there are a huge number of + + + align:start position:0% +So because there are a huge number of +interact of states that are tied up. I + + align:start position:0% +interact of states that are tied up. I + + + align:start position:0% +interact of states that are tied up. I +mean each rubric series has an infinite + + align:start position:0% +mean each rubric series has an infinite + + + align:start position:0% +mean each rubric series has an infinite +number of count states and then a + + align:start position:0% +number of count states and then a + + + align:start position:0% +number of count states and then a +continuum associated with it. So there's + + align:start position:0% +continuum associated with it. So there's + + + align:start position:0% +continuum associated with it. So there's +a lot of stuff and there's a lot of + + align:start position:0% +a lot of stuff and there's a lot of + + + align:start position:0% +a lot of stuff and there's a lot of +possibilities for accidental + + align:start position:0% +possibilities for accidental + + + align:start position:0% +possibilities for accidental +degeneracies and when there's an + + align:start position:0% +degeneracies and when there's an + + + align:start position:0% +degeneracies and when there's an +accidental degeneracy then any + + align:start position:0% +accidental degeneracy then any + + + align:start position:0% +accidental degeneracy then any +interaction matrix element between the + + align:start position:0% +interaction matrix element between the + + + align:start position:0% +interaction matrix element between the +accidentally degenerate states leads to + + align:start position:0% +accidentally degenerate states leads to + + + align:start position:0% +accidentally degenerate states leads to +trouble leads to dynamics requires some + + align:start position:0% +trouble leads to dynamics requires some + + + align:start position:0% +trouble leads to dynamics requires some +special treatment. So we want to know + + align:start position:0% +special treatment. So we want to know + + + align:start position:0% +special treatment. So we want to know +what are the quantum numbers that make + + align:start position:0% +what are the quantum numbers that make + + + align:start position:0% +what are the quantum numbers that make +states immune from immune from + + align:start position:0% +states immune from immune from + + + align:start position:0% +states immune from immune from +interaction with each other and what are + + align:start position:0% +interaction with each other and what are + + + align:start position:0% +interaction with each other and what are +the the the quantum numbers which are + + align:start position:0% +the the the quantum numbers which are + + + align:start position:0% +the the the quantum numbers which are +only advisory as opposed to rigorous. + + align:start position:0% +only advisory as opposed to rigorous. + + + align:start position:0% +only advisory as opposed to rigorous. +So we have selection rules and + + align:start position:0% +So we have selection rules and + + + align:start position:0% +So we have selection rules and +propensity rules and the rigorously good + + align:start position:0% +propensity rules and the rigorously good + + + align:start position:0% +propensity rules and the rigorously good +quantum numbers of course are the energy + + align:start position:0% +quantum numbers of course are the energy + + + align:start position:0% +quantum numbers of course are the energy +the total angular momentum the + + align:start position:0% +the total angular momentum the + + + align:start position:0% +the total angular momentum the +projection of the total angular momentum + + align:start position:0% +projection of the total angular momentum + + + align:start position:0% +projection of the total angular momentum +but that these go bad if there's an + + align:start position:0% +but that these go bad if there's an + + + align:start position:0% +but that these go bad if there's an +external field without an external field + + align:start position:0% +external field without an external field + + + align:start position:0% +external field without an external field +uh and parity + + align:start position:0% +uh and parity + + + align:start position:0% +uh and parity +it would be nice if there were more but + + align:start position:0% +it would be nice if there were more but + + + align:start position:0% +it would be nice if there were more but +that's it + + align:start position:0% +that's it + + + align:start position:0% +that's it +uh and then there are a whole host of + + align:start position:0% +uh and then there are a whole host of + + + align:start position:0% +uh and then there are a whole host of +approximate uh approximately good + + align:start position:0% +approximate uh approximately good + + + align:start position:0% +approximate uh approximately good +quantum numbers. Um, and those are the + + align:start position:0% +quantum numbers. Um, and those are the + + + align:start position:0% +quantum numbers. Um, and those are the +ones that we use to label the states + + align:start position:0% +ones that we use to label the states + + + align:start position:0% +ones that we use to label the states +and those get compromised by + + align:start position:0% +and those get compromised by + + + align:start position:0% +and those get compromised by +interactions which we would like to + + align:start position:0% +interactions which we would like to + + + align:start position:0% +interactions which we would like to +ignore but can't quite. So first of all + + align:start position:0% +ignore but can't quite. So first of all + + + align:start position:0% +ignore but can't quite. So first of all +uh the um + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +we want to look at the various terms in + + align:start position:0% +we want to look at the various terms in + + + align:start position:0% +we want to look at the various terms in +our perturbation Hamiltonian to find out + + align:start position:0% +our perturbation Hamiltonian to find out + + + align:start position:0% +our perturbation Hamiltonian to find out +what they destroy and what approximate + + align:start position:0% +what they destroy and what approximate + + + align:start position:0% +what they destroy and what approximate +quantum numbers they still leave us. And + + align:start position:0% +quantum numbers they still leave us. And + + + align:start position:0% +quantum numbers they still leave us. And +so + + align:start position:0% +so + + + align:start position:0% +so +here's our + + align:start position:0% +here's our + + + align:start position:0% +here's our +catch all of all the bad stuff. And if + + align:start position:0% +catch all of all the bad stuff. And if + + + align:start position:0% +catch all of all the bad stuff. And if +we're interested in the electronic + + align:start position:0% +we're interested in the electronic + + + align:start position:0% +we're interested in the electronic +Hamiltonian, we have this operator. + + align:start position:0% +Hamiltonian, we have this operator. + + + align:start position:0% +Hamiltonian, we have this operator. +Okay, this operator destroys all one + + align:start position:0% +Okay, this operator destroys all one + + + align:start position:0% +Okay, this operator destroys all one +electron orbitals or one all one + + align:start position:0% +electron orbitals or one all one + + + align:start position:0% +electron orbitals or one all one +electron quantum numbers but + + align:start position:0% +electron quantum numbers but + + + align:start position:0% +electron quantum numbers but +all many + + align:start position:0% +all many + + + align:start position:0% +all many +electron angular momenta + + align:start position:0% + + + + align:start position:0% + +are concerned + + align:start position:0% + + + + align:start position:0% + +as far as this operator is concerned + + align:start position:0% +as far as this operator is concerned + + + align:start position:0% +as far as this operator is concerned +and they are rigorously conserved. So + + align:start position:0% +and they are rigorously conserved. So + + + align:start position:0% +and they are rigorously conserved. So +total J total S + + align:start position:0% +total J total S + + + align:start position:0% +total J total S +uh uh if we since it's not round total L + + align:start position:0% +uh uh if we since it's not round total L + + + align:start position:0% +uh uh if we since it's not round total L +is not conserved but the projection of + + align:start position:0% +is not conserved but the projection of + + + align:start position:0% +is not conserved but the projection of +total J projection of L the projection + + align:start position:0% +total J projection of L the projection + + + align:start position:0% +total J projection of L the projection +of S those are all conserved as far as + + align:start position:0% +of S those are all conserved as far as + + + align:start position:0% +of S those are all conserved as far as +this is concerned this is a scalar and + + align:start position:0% +this is concerned this is a scalar and + + + align:start position:0% +this is concerned this is a scalar and +so that also means that all of the uh + + align:start position:0% +so that also means that all of the uh + + + align:start position:0% +so that also means that all of the uh +matrix elements of this are independent + + align:start position:0% +matrix elements of this are independent + + + align:start position:0% +matrix elements of this are independent +of projection quantum numbers they + + align:start position:0% +of projection quantum numbers they + + + align:start position:0% +of projection quantum numbers they +depend only on orbital angular momentum + + align:start position:0% +depend only on orbital angular momentum + + + align:start position:0% +depend only on orbital angular momentum +magnitude so lots of things are + + align:start position:0% +magnitude so lots of things are + + + align:start position:0% +magnitude so lots of things are +considered now this is a two electron + + align:start position:0% +considered now this is a two electron + + + align:start position:0% +considered now this is a two electron +operator and that means that we can have + + align:start position:0% +operator and that means that we can have + + + align:start position:0% +operator and that means that we can have +a selection rule the change in the spin + + align:start position:0% +a selection rule the change in the spin + + + align:start position:0% +a selection rule the change in the spin +orbitals + + align:start position:0% +orbitals + + + align:start position:0% +orbitals +this is not spin orbit coupling this is + + align:start position:0% +this is not spin orbit coupling this is + + + align:start position:0% +this is not spin orbit coupling this is +we write a wave function as a product of + + align:start position:0% +we write a wave function as a product of + + + align:start position:0% +we write a wave function as a product of +occupied spin orbitals we specify the + + align:start position:0% +occupied spin orbitals we specify the + + + align:start position:0% +occupied spin orbitals we specify the +orbital quantum number and the spin for + + align:start position:0% +orbital quantum number and the spin for + + + align:start position:0% +orbital quantum number and the spin for +each orbital. + + align:start position:0% +each orbital. + + + align:start position:0% +each orbital. +And so a state is a list of occupied + + align:start position:0% +And so a state is a list of occupied + + + align:start position:0% +And so a state is a list of occupied +spin orbitals. That's like an electronic + + align:start position:0% +spin orbitals. That's like an electronic + + + align:start position:0% +spin orbitals. That's like an electronic +configuration. + + align:start position:0% +configuration. + + + align:start position:0% +configuration. +In an electronic configuration, you only + + align:start position:0% +In an electronic configuration, you only + + + align:start position:0% +In an electronic configuration, you only +specify the orbitals. So it's a little + + align:start position:0% +specify the orbitals. So it's a little + + + align:start position:0% +specify the orbitals. So it's a little +bit more information. + + align:start position:0% +bit more information. + + + align:start position:0% +bit more information. +And because it's a two electron + + align:start position:0% +And because it's a two electron + + + align:start position:0% +And because it's a two electron +operator, the change in the number of + + align:start position:0% +operator, the change in the number of + + + align:start position:0% +operator, the change in the number of +spin orbitals is less than or equal to + + align:start position:0% +spin orbitals is less than or equal to + + + align:start position:0% +spin orbitals is less than or equal to +two. So states differing by three spin + + align:start position:0% +two. So states differing by three spin + + + align:start position:0% +two. So states differing by three spin +orbitals + + align:start position:0% +orbitals + + + align:start position:0% +orbitals +are not going to be coupled. + + align:start position:0% + + + + align:start position:0% + +And now normally we're talking about + + align:start position:0% +And now normally we're talking about + + + align:start position:0% +And now normally we're talking about +rberg states and so different orbitals + + align:start position:0% +rberg states and so different orbitals + + + align:start position:0% +rberg states and so different orbitals +there are different spin orbitals. So if + + align:start position:0% +there are different spin orbitals. So if + + + align:start position:0% +there are different spin orbitals. So if +we had an interaction between two Rberg + + align:start position:0% +we had an interaction between two Rberg + + + align:start position:0% +we had an interaction between two Rberg +states, generally we'd we'd be changing + + align:start position:0% +states, generally we'd we'd be changing + + + align:start position:0% +states, generally we'd we'd be changing +one spin orbital automatically. And then + + align:start position:0% +one spin orbital automatically. And then + + + align:start position:0% +one spin orbital automatically. And then +to make up the difference, there's going + + align:start position:0% +to make up the difference, there's going + + + align:start position:0% +to make up the difference, there's going +to have to be some energy in the core. + + align:start position:0% +to have to be some energy in the core. + + + align:start position:0% +to have to be some energy in the core. +And so uh + + align:start position:0% +And so uh + + + align:start position:0% +And so uh +only states, excited electronic states + + align:start position:0% +only states, excited electronic states + + + align:start position:0% +only states, excited electronic states +of the ion core involving a change of + + align:start position:0% +of the ion core involving a change of + + + align:start position:0% +of the ion core involving a change of +one more spin orbital could possibly + + align:start position:0% +one more spin orbital could possibly + + + align:start position:0% +one more spin orbital could possibly +interact. So there are restrictions on + + align:start position:0% +interact. So there are restrictions on + + + align:start position:0% +interact. So there are restrictions on +which interactions we'd have to worry + + align:start position:0% +which interactions we'd have to worry + + + align:start position:0% +which interactions we'd have to worry +about at the first level of complexity. + + align:start position:0% + + + + align:start position:0% + +Okay. Now for spin orbit + + align:start position:0% + + + + align:start position:0% + +it has a rigorous selection rule delta + + align:start position:0% +it has a rigorous selection rule delta + + + align:start position:0% +it has a rigorous selection rule delta +omega equals z. + + align:start position:0% +omega equals z. + + + align:start position:0% +omega equals z. +It's a one electron operator and so the + + align:start position:0% +It's a one electron operator and so the + + + align:start position:0% +It's a one electron operator and so the +delta spin orbitals is less than or + + align:start position:0% +delta spin orbitals is less than or + + + align:start position:0% +delta spin orbitals is less than or +equal to 1. + + align:start position:0% +equal to 1. + + + align:start position:0% +equal to 1. +Uh + + align:start position:0% +Uh + + + align:start position:0% +Uh +delta s is equal to 0 plus or minus one. + + align:start position:0% +delta s is equal to 0 plus or minus one. + + + align:start position:0% +delta s is equal to 0 plus or minus one. +The char the spin of an electron we know + + align:start position:0% +The char the spin of an electron we know + + + align:start position:0% +The char the spin of an electron we know +is always equal to half. + + align:start position:0% +is always equal to half. + + + align:start position:0% +is always equal to half. +And so we're not going to change the + + align:start position:0% +And so we're not going to change the + + + align:start position:0% +And so we're not going to change the +spin of an electron, but we could change + + align:start position:0% +spin of an electron, but we could change + + + align:start position:0% +spin of an electron, but we could change +the total spin by zero or one with spin + + align:start position:0% +the total spin by zero or one with spin + + + align:start position:0% +the total spin by zero or one with spin +orbit, but not by two + + align:start position:0% + + + + align:start position:0% + +directly. You could do spin orbit in two + + align:start position:0% +directly. You could do spin orbit in two + + + align:start position:0% +directly. You could do spin orbit in two +steps to change the spin by two. But + + align:start position:0% +steps to change the spin by two. But + + + align:start position:0% +steps to change the spin by two. But +that would be a less important process. + + align:start position:0% +that would be a less important process. + + + align:start position:0% +that would be a less important process. +Something that one would only + + align:start position:0% +Something that one would only + + + align:start position:0% +Something that one would only +uh invoke if considering all of the the + + align:start position:0% +uh invoke if considering all of the the + + + align:start position:0% +uh invoke if considering all of the the +normal dynamical mechanisms fail to + + align:start position:0% +normal dynamical mechanisms fail to + + + align:start position:0% +normal dynamical mechanisms fail to +explain + + align:start position:0% +explain + + + align:start position:0% +explain +the observation. So you might have to go + + align:start position:0% +the observation. So you might have to go + + + align:start position:0% +the observation. So you might have to go +beyond that. But we normally don't want + + align:start position:0% +beyond that. But we normally don't want + + + align:start position:0% +beyond that. But we normally don't want +to go. We'd like to know what we have to + + align:start position:0% +to go. We'd like to know what we have to + + + align:start position:0% +to go. We'd like to know what we have to +consider before we start just throwing + + align:start position:0% +consider before we start just throwing + + + align:start position:0% +consider before we start just throwing +the kitchen sink at a problem. + + align:start position:0% +the kitchen sink at a problem. + + + align:start position:0% +the kitchen sink at a problem. +Okay? And + + align:start position:0% +Okay? And + + + align:start position:0% +Okay? And +we can also say all right we have some + + align:start position:0% +we can also say all right we have some + + + align:start position:0% +we can also say all right we have some +Hamiltonian + + align:start position:0% +Hamiltonian + + + align:start position:0% +Hamiltonian +and this Hamiltonian + + align:start position:0% +and this Hamiltonian + + + align:start position:0% +and this Hamiltonian +is + + align:start position:0% +is + + + align:start position:0% +is +an implicit function of uh the inner + + align:start position:0% +an implicit function of uh the inner + + + align:start position:0% +an implicit function of uh the inner +nuclear distance and so we could write + + align:start position:0% +nuclear distance and so we could write + + + align:start position:0% +nuclear distance and so we could write +it as dh dr r + + align:start position:0% +it as dh dr r + + + align:start position:0% +it as dh dr r +e plus in other words we're expressing + + align:start position:0% +e plus in other words we're expressing + + + align:start position:0% +e plus in other words we're expressing +it as a power series. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And so these are still matrices, but the + + align:start position:0% +And so these are still matrices, but the + + + align:start position:0% +And so these are still matrices, but the +important thing to notice is this is the + + align:start position:0% +important thing to notice is this is the + + + align:start position:0% +important thing to notice is this is the +coordinate displacement operator that + + align:start position:0% +coordinate displacement operator that + + + align:start position:0% +coordinate displacement operator that +appears in the harmonic oscillator + + align:start position:0% +appears in the harmonic oscillator + + + align:start position:0% +appears in the harmonic oscillator +problem. + + align:start position:0% +problem. + + + align:start position:0% +problem. +And so when you looked at integrals that + + align:start position:0% +And so when you looked at integrals that + + + align:start position:0% +And so when you looked at integrals that +are not zero for harmonic oscillators, + + align:start position:0% +are not zero for harmonic oscillators, + + + align:start position:0% +are not zero for harmonic oscillators, +this one has a selection rule delta v of + + align:start position:0% +this one has a selection rule delta v of + + + align:start position:0% +this one has a selection rule delta v of +plus and minus one. This one has a + + align:start position:0% +plus and minus one. This one has a + + + align:start position:0% +plus and minus one. This one has a +selection rule delta v of plus and minus + + align:start position:0% +selection rule delta v of plus and minus + + + align:start position:0% +selection rule delta v of plus and minus +2 and zero. + + align:start position:0% +2 and zero. + + + align:start position:0% +2 and zero. +And so the R dependence of the + + align:start position:0% +And so the R dependence of the + + + align:start position:0% +And so the R dependence of the +perturbation Hamiltonian whether it's + + align:start position:0% +perturbation Hamiltonian whether it's + + + align:start position:0% +perturbation Hamiltonian whether it's +explicit or implicit can give rise to + + align:start position:0% +explicit or implicit can give rise to + + + align:start position:0% +explicit or implicit can give rise to +vibrational changes + + align:start position:0% +vibrational changes + + + align:start position:0% +vibrational changes +and each of these terms has an explicit + + align:start position:0% +and each of these terms has an explicit + + + align:start position:0% +and each of these terms has an explicit +R dependence V dependence + + align:start position:0% +R dependence V dependence + + + align:start position:0% +R dependence V dependence +the vibrational selection. So vibration + + align:start position:0% +the vibrational selection. So vibration + + + align:start position:0% +the vibrational selection. So vibration +is a is a propensity rule. Vibrational + + align:start position:0% +is a is a propensity rule. Vibrational + + + align:start position:0% +is a is a propensity rule. Vibrational +propensity rules are in here. And but + + align:start position:0% +propensity rules are in here. And but + + + align:start position:0% +propensity rules are in here. And but +the change in vibration normally tells + + align:start position:0% +the change in vibration normally tells + + + align:start position:0% +the change in vibration normally tells +you uh which derivative of the + + align:start position:0% +you uh which derivative of the + + + align:start position:0% +you uh which derivative of the +Hamiltonian the perturbation Hamiltonian + + align:start position:0% +Hamiltonian the perturbation Hamiltonian + + + align:start position:0% +Hamiltonian the perturbation Hamiltonian +you're dealing with. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +All right, we have internal angular + + align:start position:0% +All right, we have internal angular + + + align:start position:0% +All right, we have internal angular +momentum of Rberg states. And since + + align:start position:0% +momentum of Rberg states. And since + + + align:start position:0% +momentum of Rberg states. And since +we're going to separate the Rberg + + align:start position:0% +we're going to separate the Rberg + + + align:start position:0% +we're going to separate the Rberg +electron from the ion core, we need to + + align:start position:0% +electron from the ion core, we need to + + + align:start position:0% +electron from the ion core, we need to +specify three kinds of angular momentum. + + align:start position:0% +specify three kinds of angular momentum. + + + align:start position:0% +specify three kinds of angular momentum. +the core angular momentum, the Rberg + + align:start position:0% +the core angular momentum, the Rberg + + + align:start position:0% +the core angular momentum, the Rberg +electron angular momentum and the total + + align:start position:0% +electron angular momentum and the total + + + align:start position:0% +electron angular momentum and the total +angular momentum. + + align:start position:0% +angular momentum. + + + align:start position:0% +angular momentum. +So for example, we have J the total + + align:start position:0% +So for example, we have J the total + + + align:start position:0% +So for example, we have J the total +angular momentum + + align:start position:0% +angular momentum + + + align:start position:0% +angular momentum +is equal to J plus the total angular + + align:start position:0% +is equal to J plus the total angular + + + align:start position:0% +is equal to J plus the total angular +momentum of the ion core plus L plus S + + align:start position:0% +momentum of the ion core plus L plus S + + + align:start position:0% +momentum of the ion core plus L plus S +the two angular momentum that the river + + align:start position:0% +the two angular momentum that the river + + + align:start position:0% +the two angular momentum that the river +electron could have. + + align:start position:0% +electron could have. + + + align:start position:0% +electron could have. +And uh uh if we if we don't like J + + align:start position:0% +And uh uh if we if we don't like J + + + align:start position:0% +And uh uh if we if we don't like J +because we only need J when spin orbit + + align:start position:0% +because we only need J when spin orbit + + + align:start position:0% +because we only need J when spin orbit +is important + + align:start position:0% +is important + + + align:start position:0% +is important +when spin orbit is not important we can + + align:start position:0% +when spin orbit is not important we can + + + align:start position:0% +when spin orbit is not important we can +simplify our lines to this N which is J + + align:start position:0% +simplify our lines to this N which is J + + + align:start position:0% +simplify our lines to this N which is J +minus S. + + align:start position:0% + + + + align:start position:0% + +Then we can write this operator + + align:start position:0% +Then we can write this operator + + + align:start position:0% +Then we can write this operator +relationship. + + align:start position:0% + + + + align:start position:0% + +We really like the nuclear rotation and + + align:start position:0% +We really like the nuclear rotation and + + + align:start position:0% +We really like the nuclear rotation and +it happens that the nuclear rotation of + + align:start position:0% +it happens that the nuclear rotation of + + + align:start position:0% +it happens that the nuclear rotation of +the neutral molecule and the ion they + + align:start position:0% +the neutral molecule and the ion they + + + align:start position:0% +the neutral molecule and the ion they +have to be the same. + + align:start position:0% +have to be the same. + + + align:start position:0% +have to be the same. +Um and uh for the ion that's n + + + align:start position:0% +Um and uh for the ion that's n + + + + align:start position:0% +Um and uh for the ion that's n + +minus the unit vector along the inner + + align:start position:0% +minus the unit vector along the inner + + + align:start position:0% +minus the unit vector along the inner +nuclear axis times lambda. + + align:start position:0% + + + + align:start position:0% + +Okay. So this is the orbital angular + + align:start position:0% +Okay. So this is the orbital angular + + + align:start position:0% +Okay. So this is the orbital angular +momentum of the uh uh ion lambda plus. + + align:start position:0% +momentum of the uh uh ion lambda plus. + + + align:start position:0% +momentum of the uh uh ion lambda plus. +So + + align:start position:0% +So + + + align:start position:0% +So +we can uh we can get + + align:start position:0% +we can uh we can get + + + align:start position:0% +we can uh we can get +R+ + + align:start position:0% +R+ + + + align:start position:0% +R+ +this way. + + align:start position:0% +this way. + + + align:start position:0% +this way. +So we have relationships between + + align:start position:0% +So we have relationships between + + + align:start position:0% +So we have relationships between +total angular momenta and ion angular + + align:start position:0% +total angular momenta and ion angular + + + align:start position:0% +total angular momenta and ion angular +moment and reverber electron angular + + align:start position:0% +moment and reverber electron angular + + + align:start position:0% +moment and reverber electron angular +momenta. And so when we specify basis + + align:start position:0% +momenta. And so when we specify basis + + + align:start position:0% +momenta. And so when we specify basis +states we need to specify + + align:start position:0% +states we need to specify + + + align:start position:0% +states we need to specify +total angular momenta + + align:start position:0% +total angular momenta + + + align:start position:0% +total angular momenta +and core angular maver electron angular + + align:start position:0% +and core angular maver electron angular + + + align:start position:0% +and core angular maver electron angular +momenta and then we'll be able to + + align:start position:0% +momenta and then we'll be able to + + + align:start position:0% +momenta and then we'll be able to +evaluate the angular momentum matrix + + align:start position:0% +evaluate the angular momentum matrix + + + align:start position:0% +evaluate the angular momentum matrix +elements + + align:start position:0% +elements + + + align:start position:0% +elements +all of the angular momentum matrix + + align:start position:0% +all of the angular momentum matrix + + + align:start position:0% +all of the angular momentum matrix +elements that we would encounter and + + align:start position:0% +elements that we would encounter and + + + align:start position:0% +elements that we would encounter and +that's a fairly big subject but you know + + align:start position:0% +that's a fairly big subject but you know + + + align:start position:0% +that's a fairly big subject but you know +we're trying to get to focus on the + + align:start position:0% +we're trying to get to focus on the + + + align:start position:0% +we're trying to get to focus on the +specific dynamical processes and I'll + + align:start position:0% +specific dynamical processes and I'll + + + align:start position:0% +specific dynamical processes and I'll +introduce use matrix elements evaluation + + align:start position:0% +introduce use matrix elements evaluation + + + align:start position:0% +introduce use matrix elements evaluation +of matrix elements through specific + + align:start position:0% +of matrix elements through specific + + + align:start position:0% +of matrix elements through specific +examples. + + align:start position:0% +examples. + + + align:start position:0% +examples. +Okay. So now because I want to + + align:start position:0% +Okay. So now because I want to + + + align:start position:0% +Okay. So now because I want to +illustrate things I'm going to say we're + + align:start position:0% +illustrate things I'm going to say we're + + + align:start position:0% +illustrate things I'm going to say we're +going to have an ion core which is + + align:start position:0% +going to have an ion core which is + + + align:start position:0% +going to have an ion core which is +closed shell. In other words it's in a + + align:start position:0% +closed shell. In other words it's in a + + + align:start position:0% +closed shell. In other words it's in a +singlet sigma plus state. There's no + + align:start position:0% +singlet sigma plus state. There's no + + + align:start position:0% +singlet sigma plus state. There's no +spin. There's no orbital matter and + + align:start position:0% +spin. There's no orbital matter and + + + align:start position:0% +spin. There's no orbital matter and +uh uh + + align:start position:0% +uh uh + + + align:start position:0% +uh uh +so all of the occupied orbitals are + + align:start position:0% +so all of the occupied orbitals are + + + align:start position:0% +so all of the occupied orbitals are +completely occupied. None of them are + + align:start position:0% +completely occupied. None of them are + + + align:start position:0% +completely occupied. None of them are +half occupied. + + align:start position:0% +half occupied. + + + align:start position:0% +half occupied. +And usually it also means that uh we've + + align:start position:0% +And usually it also means that uh we've + + + align:start position:0% +And usually it also means that uh we've +gone up and we filled all the bonding + + align:start position:0% +gone up and we filled all the bonding + + + align:start position:0% +gone up and we filled all the bonding +orbitals + + align:start position:0% +orbitals + + + align:start position:0% +orbitals +and we haven't put any electrons in the + + align:start position:0% +and we haven't put any electrons in the + + + align:start position:0% +and we haven't put any electrons in the +antib-bonding orbitals. + + align:start position:0% +antib-bonding orbitals. + + + align:start position:0% +antib-bonding orbitals. +But okay and when that's true R+ + + align:start position:0% +But okay and when that's true R+ + + + align:start position:0% +But okay and when that's true R+ +which is something we want is equal to N + + align:start position:0% +which is something we want is equal to N + + + align:start position:0% +which is something we want is equal to N +plus which is equal to J plus + + align:start position:0% +plus which is equal to J plus + + + align:start position:0% +plus which is equal to J plus +and S plus = 0 + + align:start position:0% +and S plus = 0 + + + align:start position:0% +and S plus = 0 +lambda plus = 0 sigma plus 0. So when we + + align:start position:0% +lambda plus = 0 sigma plus 0. So when we + + + align:start position:0% +lambda plus = 0 sigma plus 0. So when we +have a lot of zero angle ma and equal + + align:start position:0% +have a lot of zero angle ma and equal + + + align:start position:0% +have a lot of zero angle ma and equal +angular momenta you can imagine that the + + align:start position:0% +angular momenta you can imagine that the + + + align:start position:0% +angular momenta you can imagine that the +algebra is going to be simplified. + + align:start position:0% +algebra is going to be simplified. + + + align:start position:0% +algebra is going to be simplified. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Okay, we're going to talk about + + align:start position:0% +Okay, we're going to talk about + + + align:start position:0% +Okay, we're going to talk about +autoionization + + align:start position:0% + + + + align:start position:0% + +in particular mechanisms of + + align:start position:0% +in particular mechanisms of + + + align:start position:0% +in particular mechanisms of +autoionization. + + align:start position:0% +autoionization. + + + align:start position:0% +autoionization. +And there's um + + align:start position:0% +And there's um + + + align:start position:0% +And there's um +several + + align:start position:0% +several + + + align:start position:0% +several +classes + + align:start position:0% + + + + align:start position:0% + +of autoionization that I intend to talk + + align:start position:0% +of autoionization that I intend to talk + + + align:start position:0% +of autoionization that I intend to talk +about. I'm going to talk about + + align:start position:0% +about. I'm going to talk about + + + align:start position:0% +about. I'm going to talk about +rotational autoionization at length. + + align:start position:0% +rotational autoionization at length. + + + align:start position:0% +rotational autoionization at length. +Then I'm going to talk about vibrational + + align:start position:0% + + + + align:start position:0% + +It's been + + align:start position:0% + + + + align:start position:0% + +I doubt that I'm going to have time for + + align:start position:0% +I doubt that I'm going to have time for + + + align:start position:0% +I doubt that I'm going to have time for +all this and so I didn't even bother + + align:start position:0% +all this and so I didn't even bother + + + align:start position:0% +all this and so I didn't even bother +writing any notes about the electronic + + align:start position:0% +writing any notes about the electronic + + + align:start position:0% +writing any notes about the electronic +case. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +the basis of rotational autoionization + + align:start position:0% +the basis of rotational autoionization + + + align:start position:0% +the basis of rotational autoionization +is that the ion core isn't round. And + + align:start position:0% +is that the ion core isn't round. And + + + align:start position:0% +is that the ion core isn't round. And +because it isn't round, the electron can + + align:start position:0% +because it isn't round, the electron can + + + align:start position:0% +because it isn't round, the electron can +exert a torque on it + + align:start position:0% +exert a torque on it + + + align:start position:0% +exert a torque on it +or it can exert a torque on the + + align:start position:0% +or it can exert a torque on the + + + align:start position:0% +or it can exert a torque on the +electron. + + align:start position:0% +electron. + + + align:start position:0% +electron. +If it were round, there wouldn't be any + + align:start position:0% +If it were round, there wouldn't be any + + + align:start position:0% +If it were round, there wouldn't be any +rotationalization. + + align:start position:0% + + + + align:start position:0% + +So, and the the torqus are periodic + + align:start position:0% +So, and the the torqus are periodic + + + align:start position:0% +So, and the the torqus are periodic +because uh if the ion core is rotating, + + align:start position:0% +because uh if the ion core is rotating, + + + align:start position:0% +because uh if the ion core is rotating, +uh the electron if it's stationary feels + + align:start position:0% +uh the electron if it's stationary feels + + + align:start position:0% +uh the electron if it's stationary feels +a torque which varies with the uh uh the + + align:start position:0% +a torque which varies with the uh uh the + + + align:start position:0% +a torque which varies with the uh uh the +phase of the autoionization of the + + align:start position:0% +phase of the autoionization of the + + + align:start position:0% +phase of the autoionization of the +rotation. And the period or or the + + align:start position:0% +rotation. And the period or or the + + + align:start position:0% +rotation. And the period or or the +frequency is the ion rotational constant + + align:start position:0% +frequency is the ion rotational constant + + + align:start position:0% +frequency is the ion rotational constant +* 2 * + + align:start position:0% +* 2 * + + + align:start position:0% +* 2 * +the ion core rotational one. + + align:start position:0% +the ion core rotational one. + + + align:start position:0% +the ion core rotational one. +That's basically the energy separation + + align:start position:0% +That's basically the energy separation + + + align:start position:0% +That's basically the energy separation +between the n minus one and n rotational + + align:start position:0% +between the n minus one and n rotational + + + align:start position:0% +between the n minus one and n rotational +levels. + + align:start position:0% +levels. + + + align:start position:0% +levels. +That's the period. a period I mean the + + align:start position:0% +That's the period. a period I mean the + + + align:start position:0% +That's the period. a period I mean the +frequency the the rotational frequency + + align:start position:0% +frequency the the rotational frequency + + + align:start position:0% +frequency the the rotational frequency +is always given by an energy difference + + align:start position:0% +is always given by an energy difference + + + align:start position:0% +is always given by an energy difference +and + + align:start position:0% +and + + + align:start position:0% +and +normally I like to say if we're + + align:start position:0% +normally I like to say if we're + + + align:start position:0% +normally I like to say if we're +interested in the average frequency at n + + align:start position:0% +interested in the average frequency at n + + + align:start position:0% +interested in the average frequency at n +we take the average between n minus one + + align:start position:0% +we take the average between n minus one + + + align:start position:0% +we take the average between n minus one +and n +1 n + + align:start position:0% +and n +1 n + + + align:start position:0% +and n +1 n +but we really want to know + + align:start position:0% +but we really want to know + + + align:start position:0% +but we really want to know +either the n minus one or n +1 and + + align:start position:0% +either the n minus one or n +1 and + + + align:start position:0% +either the n minus one or n +1 and +frequency cuz those are the resonances + + align:start position:0% +frequency cuz those are the resonances + + + align:start position:0% +frequency cuz those are the resonances +that appear + + align:start position:0% +that appear + + + align:start position:0% +that appear +and in one case you're putting energy + + align:start position:0% +and in one case you're putting energy + + + align:start position:0% +and in one case you're putting energy +into the iron core and the other you're + + align:start position:0% +into the iron core and the other you're + + + align:start position:0% +into the iron core and the other you're +taking it out. + + align:start position:0% + + + + align:start position:0% + +Okay, so we have a torque and it's + + align:start position:0% +Okay, so we have a torque and it's + + + align:start position:0% +Okay, so we have a torque and it's +modulating + + align:start position:0% +modulating + + + align:start position:0% +modulating +and that sounds like a good thing for + + align:start position:0% +and that sounds like a good thing for + + + align:start position:0% +and that sounds like a good thing for +exchanging energy. + + align:start position:0% +exchanging energy. + + + align:start position:0% +exchanging energy. +So the the uh the effectiveness of the + + align:start position:0% +So the the uh the effectiveness of the + + + align:start position:0% +So the the uh the effectiveness of the +torque or the ability to apply torque + + align:start position:0% +torque or the ability to apply torque + + + align:start position:0% +torque or the ability to apply torque +has to do with how not round + + align:start position:0% +has to do with how not round + + + align:start position:0% +has to do with how not round +and I'll show you that that appears as + + align:start position:0% +and I'll show you that that appears as + + + align:start position:0% +and I'll show you that that appears as +the difference in quantum defects for + + align:start position:0% +the difference in quantum defects for + + + align:start position:0% +the difference in quantum defects for +the different values of lambda + + align:start position:0% + + + + align:start position:0% + +and uh we'll we'll play with that a lot. + + align:start position:0% +and uh we'll we'll play with that a lot. + + + align:start position:0% +and uh we'll we'll play with that a lot. +Okay, vibrational. + + align:start position:0% +Okay, vibrational. + + + align:start position:0% +Okay, vibrational. +There's two uh two ways of looking at + + align:start position:0% +There's two uh two ways of looking at + + + align:start position:0% +There's two uh two ways of looking at +the vibrational. + + align:start position:0% +the vibrational. + + + align:start position:0% +the vibrational. +One way is to look at the inner lo + + align:start position:0% + + + + align:start position:0% + +of a river or + + align:start position:0% +of a river or + + + align:start position:0% +of a river or +the inner lover + + align:start position:0% +the inner lover + + + align:start position:0% +the inner lover +series + + align:start position:0% +series + + + align:start position:0% +series +is constant. I told you that. You don't + + align:start position:0% +is constant. I told you that. You don't + + + align:start position:0% +is constant. I told you that. You don't +have to believe it, but it's true. + + align:start position:0% +have to believe it, but it's true. + + + align:start position:0% +have to believe it, but it's true. +Now the if we go to the lowest member of + + align:start position:0% +Now the if we go to the lowest member of + + + align:start position:0% +Now the if we go to the lowest member of +a rberg series that is often a veilance + + align:start position:0% +a rberg series that is often a veilance + + + align:start position:0% +a rberg series that is often a veilance +state + + align:start position:0% +state + + + align:start position:0% +state +and one frequently classifies the + + align:start position:0% +and one frequently classifies the + + + align:start position:0% +and one frequently classifies the +orbitals in a veance state as if we're + + align:start position:0% +orbitals in a veance state as if we're + + + align:start position:0% +orbitals in a veance state as if we're +talking about a a relatively covealent + + align:start position:0% +talking about a a relatively covealent + + + align:start position:0% +talking about a a relatively covealent +molecule the orbitals are either bonding + + align:start position:0% +molecule the orbitals are either bonding + + + align:start position:0% +molecule the orbitals are either bonding +or antib-bonding. + + align:start position:0% + + + + align:start position:0% + +If it's an ionic molecule the orbitals + + align:start position:0% +If it's an ionic molecule the orbitals + + + align:start position:0% +If it's an ionic molecule the orbitals +are shielding or desueling. + + align:start position:0% + + + + align:start position:0% + +So if you occupy a bonding orbital, + + align:start position:0% +So if you occupy a bonding orbital, + + + align:start position:0% +So if you occupy a bonding orbital, +the vibration frequency gets increased. + + align:start position:0% +the vibration frequency gets increased. + + + align:start position:0% +the vibration frequency gets increased. +If you occupy a desaling orbital, + + align:start position:0% +If you occupy a desaling orbital, + + + align:start position:0% +If you occupy a desaling orbital, +the vibrational frequency gets + + align:start position:0% +the vibrational frequency gets + + + align:start position:0% +the vibrational frequency gets +increased. If you shield, vibrational + + align:start position:0% +increased. If you shield, vibrational + + + align:start position:0% +increased. If you shield, vibrational +frequency goes down. + + align:start position:0% +frequency goes down. + + + align:start position:0% +frequency goes down. +If you put it in any bounding or the + + align:start position:0% +If you put it in any bounding or the + + + align:start position:0% +If you put it in any bounding or the +vibr frequency goes down. So you can + + align:start position:0% +vibr frequency goes down. So you can + + + align:start position:0% +vibr frequency goes down. So you can +sort of think of this as a uh as the + + align:start position:0% +sort of think of this as a uh as the + + + align:start position:0% +sort of think of this as a uh as the +Renberg electron goes from outside to + + align:start position:0% +Renberg electron goes from outside to + + + align:start position:0% +Renberg electron goes from outside to +inside + + align:start position:0% +inside + + + align:start position:0% +inside +it's going to turn on an interaction + + align:start position:0% +it's going to turn on an interaction + + + align:start position:0% +it's going to turn on an interaction +which changes the vibrational frequency + + align:start position:0% +which changes the vibrational frequency + + + align:start position:0% +which changes the vibrational frequency +or you can think of that as an impulse. + + align:start position:0% +or you can think of that as an impulse. + + + align:start position:0% +or you can think of that as an impulse. +You have an oscillator and you you hit + + align:start position:0% +You have an oscillator and you you hit + + + align:start position:0% +You have an oscillator and you you hit +it + + align:start position:0% +it + + + align:start position:0% +it +uh because uh you know it's happily + + align:start position:0% +uh because uh you know it's happily + + + align:start position:0% +uh because uh you know it's happily +oscillating and all of a sudden it gets + + align:start position:0% +oscillating and all of a sudden it gets + + + align:start position:0% +oscillating and all of a sudden it gets +an impulse because its vibrational + + align:start position:0% +an impulse because its vibrational + + + align:start position:0% +an impulse because its vibrational +frequency has changed because the + + align:start position:0% +frequency has changed because the + + + align:start position:0% +frequency has changed because the +electron has come in and that can cause + + align:start position:0% +electron has come in and that can cause + + + align:start position:0% +electron has come in and that can cause +a change in the vibration quantum. + + align:start position:0% + + + + align:start position:0% + +Another way of looking at this so I just + + align:start position:0% +Another way of looking at this so I just + + + align:start position:0% +Another way of looking at this so I just +gave you the short range point of view. + + align:start position:0% +gave you the short range point of view. + + + align:start position:0% +gave you the short range point of view. +The long range point of view is that the + + align:start position:0% +The long range point of view is that the + + + align:start position:0% +The long range point of view is that the +ion core has a dipole moment and a + + align:start position:0% +ion core has a dipole moment and a + + + align:start position:0% +ion core has a dipole moment and a +quadripole moment and it's vibrating + + align:start position:0% +quadripole moment and it's vibrating + + + align:start position:0% +quadripole moment and it's vibrating +and so these moments are modulated + + align:start position:0% +and so these moments are modulated + + + align:start position:0% +and so these moments are modulated +and the riber electron at long range + + align:start position:0% +and the riber electron at long range + + + align:start position:0% +and the riber electron at long range +feels that modulation + + align:start position:0% +feels that modulation + + + align:start position:0% +feels that modulation +and so if that modulation frequency is + + align:start position:0% +and so if that modulation frequency is + + + align:start position:0% +and so if that modulation frequency is +is close to the orbital frequency the + + align:start position:0% +is close to the orbital frequency the + + + align:start position:0% +is close to the orbital frequency the +Kepler orbit frequency of the river + + align:start position:0% +Kepler orbit frequency of the river + + + align:start position:0% +Kepler orbit frequency of the river +electron then you have a resonance + + align:start position:0% +electron then you have a resonance + + + align:start position:0% +electron then you have a resonance +And even though the um the nuclei are + + align:start position:0% +And even though the um the nuclei are + + + align:start position:0% +And even though the um the nuclei are +heavy and the electron is light at + + align:start position:0% +heavy and the electron is light at + + + align:start position:0% +heavy and the electron is light at +resonance, it's just the same sort of + + align:start position:0% +resonance, it's just the same sort of + + + align:start position:0% +resonance, it's just the same sort of +thing as you're driving a car. The road + + align:start position:0% +thing as you're driving a car. The road + + + align:start position:0% +thing as you're driving a car. The road +is really heavy. The car is pretty + + align:start position:0% +is really heavy. The car is pretty + + + align:start position:0% +is really heavy. The car is pretty +light. Energy does get transferred + + align:start position:0% +light. Energy does get transferred + + + align:start position:0% +light. Energy does get transferred +resonantly + + align:start position:0% +resonantly + + + align:start position:0% +resonantly +into these destructive vibrations of the + + align:start position:0% +into these destructive vibrations of the + + + align:start position:0% +into these destructive vibrations of the +car. uh and so there is a resonant + + align:start position:0% +car. uh and so there is a resonant + + + align:start position:0% +car. uh and so there is a resonant +coupling and when energy gets + + align:start position:0% +coupling and when energy gets + + + align:start position:0% +coupling and when energy gets +transferred it tends to be transferred + + align:start position:0% +transferred it tends to be transferred + + + align:start position:0% +transferred it tends to be transferred +in quantum and so a vibrational quantum + + align:start position:0% +in quantum and so a vibrational quantum + + + align:start position:0% +in quantum and so a vibrational quantum +will suddenly appear in the electronic + + align:start position:0% +will suddenly appear in the electronic + + + align:start position:0% +will suddenly appear in the electronic +energy or suddenly be removed because of + + align:start position:0% +energy or suddenly be removed because of + + + align:start position:0% +energy or suddenly be removed because of +this resonant coupling. So we have a + + align:start position:0% +this resonant coupling. So we have a + + + align:start position:0% +this resonant coupling. So we have a +short range and a long range interaction + + align:start position:0% +short range and a long range interaction + + + align:start position:0% +short range and a long range interaction +and those are the physical mechanisms + + align:start position:0% +and those are the physical mechanisms + + + align:start position:0% +and those are the physical mechanisms +that will appear when we look at the + + align:start position:0% +that will appear when we look at the + + + align:start position:0% +that will appear when we look at the +quota. + + align:start position:0% +quota. + + + align:start position:0% +quota. +Spin orbit + + align:start position:0% +Spin orbit + + + align:start position:0% +Spin orbit +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +uh spin orbit is kind of esoteric but + + align:start position:0% +uh spin orbit is kind of esoteric but + + + align:start position:0% +uh spin orbit is kind of esoteric but +it's kind of neat because it's a + + align:start position:0% +it's kind of neat because it's a + + + align:start position:0% +it's kind of neat because it's a +different way of understanding. Now this + + align:start position:0% +different way of understanding. Now this + + + align:start position:0% +different way of understanding. Now this +what I'm talking about here is really + + align:start position:0% +what I'm talking about here is really + + + align:start position:0% +what I'm talking about here is really +the essence of this lecture. + + align:start position:0% +the essence of this lecture. + + + align:start position:0% +the essence of this lecture. +The rest is just going to be + + align:start position:0% +The rest is just going to be + + + align:start position:0% +The rest is just going to be +realization. You know, building a model. + + align:start position:0% +realization. You know, building a model. + + + align:start position:0% +realization. You know, building a model. +But you know what you don't see is what + + align:start position:0% +But you know what you don't see is what + + + align:start position:0% +But you know what you don't see is what +is the physical reason for this + + align:start position:0% +is the physical reason for this + + + align:start position:0% +is the physical reason for this +improbable energy transfer process + + align:start position:0% +improbable energy transfer process + + + align:start position:0% +improbable energy transfer process +occurring? + + align:start position:0% +occurring? + + + align:start position:0% +occurring? +Why is the resonance + + align:start position:0% +Why is the resonance + + + align:start position:0% +Why is the resonance +short-lived? + + align:start position:0% +short-lived? + + + align:start position:0% +short-lived? +Why doesn't it live forever? + + align:start position:0% +Why doesn't it live forever? + + + align:start position:0% +Why doesn't it live forever? +So we have states + + align:start position:0% +So we have states + + + align:start position:0% +So we have states +which have good which have approximately + + align:start position:0% +which have good which have approximately + + + align:start position:0% +which have good which have approximately +good quantum numbers embedded in various + + align:start position:0% +good quantum numbers embedded in various + + + align:start position:0% +good quantum numbers embedded in various +continua. + + align:start position:0% +continua. + + + align:start position:0% +continua. +And why do they relax into the + + align:start position:0% +And why do they relax into the + + + align:start position:0% +And why do they relax into the +continuum? It's because of these + + align:start position:0% +continuum? It's because of these + + + align:start position:0% +continuum? It's because of these +mechanism. + + align:start position:0% +mechanism. + + + align:start position:0% +mechanism. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Okay. So for spin arbit + + align:start position:0% +Okay. So for spin arbit + + + align:start position:0% +Okay. So for spin arbit +you have an ion core. + + align:start position:0% +you have an ion core. + + + align:start position:0% +you have an ion core. +Let's say it's a double pi state. So we + + align:start position:0% +Let's say it's a double pi state. So we + + + align:start position:0% +Let's say it's a double pi state. So we +have a double pi + + align:start position:0% +have a double pi + + + align:start position:0% +have a double pi +uh 12 and a pi 3s. + + align:start position:0% +uh 12 and a pi 3s. + + + align:start position:0% +uh 12 and a pi 3s. +And there are riberg series built on + + align:start position:0% +And there are riberg series built on + + + align:start position:0% +And there are riberg series built on +both of these. + + align:start position:0% + + + + align:start position:0% + +So suppose + + align:start position:0% +So suppose + + + align:start position:0% +So suppose +we have an s liber series + + align:start position:0% +we have an s liber series + + + align:start position:0% +we have an s liber series +that can contribute the spin of the + + align:start position:0% +that can contribute the spin of the + + + align:start position:0% +that can contribute the spin of the +electron. And so one one can end up + + align:start position:0% +electron. And so one one can end up + + + align:start position:0% +electron. And so one one can end up +getting a single pi state and a triplet + + align:start position:0% +getting a single pi state and a triplet + + + align:start position:0% +getting a single pi state and a triplet +pi state. + + align:start position:0% + + + + align:start position:0% + +012. + + align:start position:0% +012. + + + align:start position:0% +012. +So these are the projections of J on the + + align:start position:0% +So these are the projections of J on the + + + align:start position:0% +So these are the projections of J on the +inner nuclear axis 012. So you have a + + align:start position:0% +inner nuclear axis 012. So you have a + + + align:start position:0% +inner nuclear axis 012. So you have a +single pi state and a triple pi state + + align:start position:0% +single pi state and a triple pi state + + + align:start position:0% +single pi state and a triple pi state +and there are spin orbit interactions + + align:start position:0% +and there are spin orbit interactions + + + align:start position:0% +and there are spin orbit interactions +that produce these inter uh these + + align:start position:0% +that produce these inter uh these + + + align:start position:0% +that produce these inter uh these +splittings + + align:start position:0% +splittings + + + align:start position:0% +splittings +and produce an interaction between + + align:start position:0% +and produce an interaction between + + + align:start position:0% +and produce an interaction between +triple pi one and single pi. + + align:start position:0% +triple pi one and single pi. + + + align:start position:0% +triple pi one and single pi. +So you stick an electron onto this + + align:start position:0% +So you stick an electron onto this + + + align:start position:0% +So you stick an electron onto this +and the standard angular momentum + + align:start position:0% +and the standard angular momentum + + + align:start position:0% +and the standard angular momentum +coupling says you get a triple state and + + align:start position:0% +coupling says you get a triple state and + + + align:start position:0% +coupling says you get a triple state and +a single state. + + align:start position:0% +a single state. + + + align:start position:0% +a single state. +But now suppose the arinberg electron is + + align:start position:0% +But now suppose the arinberg electron is + + + align:start position:0% +But now suppose the arinberg electron is +so far away + + align:start position:0% +so far away + + + align:start position:0% +so far away +that there is no reason for this + + align:start position:0% +that there is no reason for this + + + align:start position:0% +that there is no reason for this +difference in energy between single pi + + align:start position:0% +difference in energy between single pi + + + align:start position:0% +difference in energy between single pi +and triple pi. That's an exchange + + align:start position:0% +and triple pi. That's an exchange + + + align:start position:0% +and triple pi. That's an exchange +energy. + + align:start position:0% +energy. + + + align:start position:0% +energy. +That's uh um it's basically you how does + + align:start position:0% +That's uh um it's basically you how does + + + align:start position:0% +That's uh um it's basically you how does +an electron interact with one electron + + align:start position:0% +an electron interact with one electron + + + align:start position:0% +an electron interact with one electron +interact with another electron? Uh it's + + align:start position:0% +interact with another electron? Uh it's + + + align:start position:0% +interact with another electron? Uh it's +a electrostatic + + align:start position:0% +a electrostatic + + + align:start position:0% +a electrostatic +uh interaction. But if the rberg + + align:start position:0% +uh interaction. But if the rberg + + + align:start position:0% +uh interaction. But if the rberg +electron never gets close to the other + + align:start position:0% +electron never gets close to the other + + + align:start position:0% +electron never gets close to the other +electron, + + align:start position:0% +electron, + + + align:start position:0% +electron, +uh the exchange splitting goes to zero. + + align:start position:0% +uh the exchange splitting goes to zero. + + + align:start position:0% +uh the exchange splitting goes to zero. +And so if the exchange splitting goes to + + align:start position:0% +And so if the exchange splitting goes to + + + align:start position:0% +And so if the exchange splitting goes to +zero, what you end up getting is a + + align:start position:0% +zero, what you end up getting is a + + + align:start position:0% +zero, what you end up getting is a +pattern + + align:start position:0% +pattern + + + align:start position:0% +pattern +not of two levels but of four levels. + + align:start position:0% +not of two levels but of four levels. + + + align:start position:0% +not of two levels but of four levels. +And so, uh, you add, uh, + + align:start position:0% + + + + align:start position:0% + +so the total omega 21 1 0 this splitting + + align:start position:0% +so the total omega 21 1 0 this splitting + + + align:start position:0% +so the total omega 21 1 0 this splitting +is the same as this. + + align:start position:0% +is the same as this. + + + align:start position:0% +is the same as this. +And so what happens in spin orbit + + align:start position:0% +And so what happens in spin orbit + + + align:start position:0% +And so what happens in spin orbit +autoionization + + align:start position:0% +autoionization + + + align:start position:0% +autoionization +is there is a spin orbit coupling + + align:start position:0% +is there is a spin orbit coupling + + + align:start position:0% +is there is a spin orbit coupling +between two states the sigma pi and the + + align:start position:0% +between two states the sigma pi and the + + + align:start position:0% +between two states the sigma pi and the +triple pi state and it's normally weak + + align:start position:0% +triple pi state and it's normally weak + + + align:start position:0% +triple pi state and it's normally weak +but as the electrostatic + + align:start position:0% +but as the electrostatic + + + align:start position:0% +but as the electrostatic +uh uh splitting between those states + + align:start position:0% +uh uh splitting between those states + + + align:start position:0% +uh uh splitting between those states +gets small the spin orbit can do what it + + align:start position:0% +gets small the spin orbit can do what it + + + align:start position:0% +gets small the spin orbit can do what it +wanted to do. it can destroy singlet and + + align:start position:0% +wanted to do. it can destroy singlet and + + + align:start position:0% +wanted to do. it can destroy singlet and +triplet. And so again, it's a mechanism + + align:start position:0% +triplet. And so again, it's a mechanism + + + align:start position:0% +triplet. And so again, it's a mechanism +where the Rberg electron isn't doing + + align:start position:0% +where the Rberg electron isn't doing + + + align:start position:0% +where the Rberg electron isn't doing +anything. + + align:start position:0% +anything. + + + align:start position:0% +anything. +It's just allowing what the core wanted + + align:start position:0% +It's just allowing what the core wanted + + + align:start position:0% +It's just allowing what the core wanted +to do to happen. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +each one of these mechanisms requires a + + align:start position:0% +each one of these mechanisms requires a + + + align:start position:0% +each one of these mechanisms requires a +different way of thinking about how does + + align:start position:0% +different way of thinking about how does + + + align:start position:0% +different way of thinking about how does +this process occur. The last one, the + + align:start position:0% +this process occur. The last one, the + + + align:start position:0% +this process occur. The last one, the +electrostatic the electronic + + align:start position:0% +electrostatic the electronic + + + align:start position:0% +electrostatic the electronic +the Renberg electron strikes the core + + align:start position:0% +the Renberg electron strikes the core + + + align:start position:0% +the Renberg electron strikes the core +and excites it transfers some energy to + + align:start position:0% +and excites it transfers some energy to + + + align:start position:0% +and excites it transfers some energy to +a core electron excites it to a excited + + align:start position:0% +a core electron excites it to a excited + + + align:start position:0% +a core electron excites it to a excited +electronic state and that's an electron + + align:start position:0% +electronic state and that's an electron + + + align:start position:0% +electronic state and that's an electron +electron collision. We know those can be + + align:start position:0% +electron collision. We know those can be + + + align:start position:0% +electron collision. We know those can be +good. Those can be very efficient in + + align:start position:0% +good. Those can be very efficient in + + + align:start position:0% +good. Those can be very efficient in +transferring energy between two + + align:start position:0% +transferring energy between two + + + align:start position:0% +transferring energy between two +particles of the same mass. + + align:start position:0% +particles of the same mass. + + + align:start position:0% +particles of the same mass. +So if there's enough energy + + align:start position:0% +So if there's enough energy + + + align:start position:0% +So if there's enough energy +for uh the + + align:start position:0% +for uh the + + + align:start position:0% +for uh the +um + + align:start position:0% +um + + + align:start position:0% +um +so what happens is you have states + + align:start position:0% +so what happens is you have states + + + align:start position:0% +so what happens is you have states +converging to an electronically riberg + + align:start position:0% +converging to an electronically riberg + + + align:start position:0% +converging to an electronically riberg +series converging to an electronically + + align:start position:0% +series converging to an electronically + + + align:start position:0% +series converging to an electronically +excited state. + + align:start position:0% +excited state. + + + align:start position:0% +excited state. +And now that red river electron enters + + align:start position:0% +And now that red river electron enters + + + align:start position:0% +And now that red river electron enters +the core and gets the core energy from + + align:start position:0% +the core and gets the core energy from + + + align:start position:0% +the core and gets the core energy from +the excited state and gets blown off + + align:start position:0% +the excited state and gets blown off + + + align:start position:0% +the excited state and gets blown off +because now the core is in the ground + + align:start position:0% +because now the core is in the ground + + + align:start position:0% +because now the core is in the ground +state and the electron has too much + + align:start position:0% +state and the electron has too much + + + align:start position:0% +state and the electron has too much +energy. + + align:start position:0% +energy. + + + align:start position:0% +energy. +So so it's a two-step process. So you + + align:start position:0% +So so it's a two-step process. So you + + + align:start position:0% +So so it's a two-step process. So you +first have to excite the core and then + + align:start position:0% +first have to excite the core and then + + + align:start position:0% +first have to excite the core and then +you have to well if you form the redberg + + align:start position:0% +you have to well if you form the redberg + + + align:start position:0% +you have to well if you form the redberg +state where the core is excited + + align:start position:0% +state where the core is excited + + + align:start position:0% +state where the core is excited +then the electron comes in deexites the + + align:start position:0% +then the electron comes in deexites the + + + align:start position:0% +then the electron comes in deexites the +core and carries that electron away. + + align:start position:0% +core and carries that electron away. + + + align:start position:0% +core and carries that electron away. +So those are the the four + + align:start position:0% +So those are the the four + + + align:start position:0% +So those are the the four +mechanisms that are going to be + + align:start position:0% +mechanisms that are going to be + + + align:start position:0% +mechanisms that are going to be +appearing in autoionization rates. + + align:start position:0% +appearing in autoionization rates. + + + align:start position:0% +appearing in autoionization rates. +And uh now I'm going to do some of the + + align:start position:0% +And uh now I'm going to do some of the + + + align:start position:0% +And uh now I'm going to do some of the +quantum mechanics to show how you + + align:start position:0% +quantum mechanics to show how you + + + align:start position:0% +quantum mechanics to show how you +implement this. But the physical + + align:start position:0% +implement this. But the physical + + + align:start position:0% +implement this. But the physical +mechanisms are are all things where + + align:start position:0% +mechanisms are are all things where + + + align:start position:0% +mechanisms are are all things where +you're you've got a good reason for + + align:start position:0% +you're you've got a good reason for + + + align:start position:0% +you're you've got a good reason for +exchanging energy between a light + + align:start position:0% +exchanging energy between a light + + + align:start position:0% +exchanging energy between a light +particle and a heavy particle. + + align:start position:0% +particle and a heavy particle. + + + align:start position:0% +particle and a heavy particle. +And your expectation of billiard balls + + align:start position:0% +And your expectation of billiard balls + + + align:start position:0% +And your expectation of billiard balls +and ping pong balls, there's no problem + + align:start position:0% +and ping pong balls, there's no problem + + + align:start position:0% +and ping pong balls, there's no problem +with that. You know, those are right. uh + + align:start position:0% +with that. You know, those are right. uh + + + align:start position:0% +with that. You know, those are right. uh +your experience tells you it will never + + align:start position:0% +your experience tells you it will never + + + align:start position:0% +your experience tells you it will never +happen unless there's some kind of + + align:start position:0% +happen unless there's some kind of + + + align:start position:0% +happen unless there's some kind of +internal structure or some kind of + + align:start position:0% +internal structure or some kind of + + + align:start position:0% +internal structure or some kind of +periodic resonance. + + align:start position:0% + + + + align:start position:0% + +Okay, are we all content with it? This + + align:start position:0% +Okay, are we all content with it? This + + + align:start position:0% +Okay, are we all content with it? This +is really the important thing. This is + + align:start position:0% +is really the important thing. This is + + + align:start position:0% +is really the important thing. This is +sort of in fact it's the important what + + align:start position:0% +sort of in fact it's the important what + + + align:start position:0% +sort of in fact it's the important what +I've been leading up to in the four + + align:start position:0% +I've been leading up to in the four + + + align:start position:0% +I've been leading up to in the four +lectures. + + align:start position:0% +lectures. + + + align:start position:0% +lectures. +Molecules are not there. That's right. + + align:start position:0% +Molecules are not there. That's right. + + + align:start position:0% +Molecules are not there. That's right. +There is internal structure and you you + + align:start position:0% +There is internal structure and you you + + + align:start position:0% +There is internal structure and you you +reveal the internal structure as much of + + align:start position:0% +reveal the internal structure as much of + + + align:start position:0% +reveal the internal structure as much of +it as you need and you have a way of + + align:start position:0% +it as you need and you have a way of + + + align:start position:0% +it as you need and you have a way of +deciding what is + + align:start position:0% +deciding what is + + + align:start position:0% +deciding what is +uh + + align:start position:0% +uh + + + align:start position:0% +uh +what is reasonable and what is overly + + align:start position:0% +what is reasonable and what is overly + + + align:start position:0% +what is reasonable and what is overly +esoteric. So you you know you have ideas + + align:start position:0% +esoteric. So you you know you have ideas + + + align:start position:0% +esoteric. So you you know you have ideas +about quantum numbers about mechanisms + + align:start position:0% +about quantum numbers about mechanisms + + + align:start position:0% +about quantum numbers about mechanisms +uh and + + align:start position:0% +uh and + + + align:start position:0% +uh and +uh anything can happen nothing except + + align:start position:0% +uh anything can happen nothing except + + + align:start position:0% +uh anything can happen nothing except +you know energy J MJ and parody are + + align:start position:0% +you know energy J MJ and parody are + + + align:start position:0% +you know energy J MJ and parody are +rigorously conserved but a lot of other + + align:start position:0% +rigorously conserved but a lot of other + + + align:start position:0% +rigorously conserved but a lot of other +things are going to be conserved unless + + align:start position:0% +things are going to be conserved unless + + + align:start position:0% +things are going to be conserved unless +there's a good reason why they won't + + align:start position:0% +there's a good reason why they won't + + + align:start position:0% +there's a good reason why they won't +and you can always make decisions about + + align:start position:0% +and you can always make decisions about + + + align:start position:0% +and you can always make decisions about +what is the hierarchy of probability + + align:start position:0% +what is the hierarchy of probability + + + align:start position:0% +what is the hierarchy of probability +ility for a particular process. And as + + align:start position:0% +ility for a particular process. And as + + + align:start position:0% +ility for a particular process. And as +you go down that hierarchy to the + + align:start position:0% +you go down that hierarchy to the + + + align:start position:0% +you go down that hierarchy to the +improbable things, your best + + align:start position:0% +improbable things, your best + + + align:start position:0% +improbable things, your best +investment of effort is in ruling out + + align:start position:0% +investment of effort is in ruling out + + + align:start position:0% +investment of effort is in ruling out +the more probable things before you + + align:start position:0% +the more probable things before you + + + align:start position:0% +the more probable things before you +start to say, I think it's this really + + align:start position:0% +start to say, I think it's this really + + + align:start position:0% +start to say, I think it's this really +neat thing that I dreamt up some one + + align:start position:0% +neat thing that I dreamt up some one + + + align:start position:0% +neat thing that I dreamt up some one +night and I I'm going to devote my life + + align:start position:0% +night and I I'm going to devote my life + + + align:start position:0% +night and I I'm going to devote my life +to finding that effect. + + align:start position:0% + + + + align:start position:0% + +Okay. So let's try to + + align:start position:0% +Okay. So let's try to + + + align:start position:0% +Okay. So let's try to +uh describe + + align:start position:0% +uh describe + + + align:start position:0% +uh describe +the quantum mechanics of rotational + + align:start position:0% +the quantum mechanics of rotational + + + align:start position:0% +the quantum mechanics of rotational +autoionization. And now what I'm going + + align:start position:0% +autoionization. And now what I'm going + + + align:start position:0% +autoionization. And now what I'm going +to do is I'm going to take the usual + + align:start position:0% +to do is I'm going to take the usual + + + align:start position:0% +to do is I'm going to take the usual +expected quantum mechanical approach to + + align:start position:0% +expected quantum mechanical approach to + + + align:start position:0% +expected quantum mechanical approach to +a problem. And it's going to be sort of + + align:start position:0% +a problem. And it's going to be sort of + + + align:start position:0% +a problem. And it's going to be sort of +backwards. + + align:start position:0% +backwards. + + + align:start position:0% +backwards. +It's going to say that the thing we + + align:start position:0% +It's going to say that the thing we + + + align:start position:0% +It's going to say that the thing we +expected + + align:start position:0% +expected + + + align:start position:0% +expected +to cause the process is the thing that's + + align:start position:0% +to cause the process is the thing that's + + + align:start position:0% +to cause the process is the thing that's +in opposing the process as opposed to + + align:start position:0% +in opposing the process as opposed to + + + align:start position:0% +in opposing the process as opposed to +causing it. + + align:start position:0% +causing it. + + + align:start position:0% +causing it. +And it's just a matter of which basis + + align:start position:0% +And it's just a matter of which basis + + + align:start position:0% +And it's just a matter of which basis +set we choose. And if we choose the + + align:start position:0% +set we choose. And if we choose the + + + align:start position:0% +set we choose. And if we choose the +other basis set, which is the one we are + + align:start position:0% +other basis set, which is the one we are + + + align:start position:0% +other basis set, which is the one we are +normally unaccustomed to using, then the + + align:start position:0% +normally unaccustomed to using, then the + + + align:start position:0% +normally unaccustomed to using, then the +causality gets straightened out. + + align:start position:0% +causality gets straightened out. + + + align:start position:0% +causality gets straightened out. +Okay. So I'm going to approach the + + align:start position:0% +Okay. So I'm going to approach the + + + align:start position:0% +Okay. So I'm going to approach the +problem from the a normal coupling case + + align:start position:0% +problem from the a normal coupling case + + + align:start position:0% +problem from the a normal coupling case +which is case B which for this problem + + align:start position:0% +which is case B which for this problem + + + align:start position:0% +which is case B which for this problem +is is essentially identical to case A + + align:start position:0% +is is essentially identical to case A + + + align:start position:0% +is is essentially identical to case A +which is the one I recommended using all + + align:start position:0% +which is the one I recommended using all + + + align:start position:0% +which is the one I recommended using all +the time + + align:start position:0% +the time + + + align:start position:0% +the time +and the good way of approaching the + + align:start position:0% +and the good way of approaching the + + + align:start position:0% +and the good way of approaching the +problem is case D + + align:start position:0% +problem is case D + + + align:start position:0% +problem is case D +and you'll see that when I'm done okay + + align:start position:0% + + + + align:start position:0% + +we'll be like just to get is done. + + align:start position:0% + + + + align:start position:0% + +So the electronic Hamiltonian + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +uh the river constant over n minus + + align:start position:0% +uh the river constant over n minus + + + align:start position:0% +uh the river constant over n minus +delta. + + align:start position:0% +delta. + + + align:start position:0% +delta. +We could write down. + + align:start position:0% + + + + align:start position:0% + +Okay. So this is just the usual + + align:start position:0% +Okay. So this is just the usual + + + align:start position:0% +Okay. So this is just the usual +uh + + align:start position:0% +uh + + + align:start position:0% +uh +rberg expression with a quantum defect + + align:start position:0% +rberg expression with a quantum defect + + + align:start position:0% +rberg expression with a quantum defect +which is different for each L in lambda. + + align:start position:0% + + + + align:start position:0% + +And this is just saying we only have + + align:start position:0% +And this is just saying we only have + + + align:start position:0% +And this is just saying we only have +diagonal elements in L. + + align:start position:0% + + + + align:start position:0% + +So the electronic Hamiltonian is + + align:start position:0% +So the electronic Hamiltonian is + + + align:start position:0% +So the electronic Hamiltonian is +diagonal but the different lambdas have + + align:start position:0% +diagonal but the different lambdas have + + + align:start position:0% +diagonal but the different lambdas have +different energies + + align:start position:0% +different energies + + + align:start position:0% +different energies +and this is due to the fact that the ion + + align:start position:0% +and this is due to the fact that the ion + + + align:start position:0% +and this is due to the fact that the ion +core isn't round. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +differences in diagonal energies are the + + align:start position:0% +differences in diagonal energies are the + + + align:start position:0% +differences in diagonal energies are the +things that oppose + + align:start position:0% +things that oppose + + + align:start position:0% +things that oppose +the coupling. + + align:start position:0% + + + + align:start position:0% + +This is the not roundness. This is the + + align:start position:0% +This is the not roundness. This is the + + + align:start position:0% +This is the not roundness. This is the +thing that enables the electron to exert + + align:start position:0% +thing that enables the electron to exert + + + align:start position:0% +thing that enables the electron to exert +a torque. + + align:start position:0% +a torque. + + + align:start position:0% +a torque. +And instead of causing a process, it's + + align:start position:0% +And instead of causing a process, it's + + + align:start position:0% +And instead of causing a process, it's +opposing it because it's appearing at + + align:start position:0% +opposing it because it's appearing at + + + align:start position:0% +opposing it because it's appearing at +H0. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now, so we have the electronic part of + + align:start position:0% +Now, so we have the electronic part of + + + align:start position:0% +Now, so we have the electronic part of +the problem and we have the rotational + + align:start position:0% +the problem and we have the rotational + + + align:start position:0% +the problem and we have the rotational +part of the problem. The rotational + + align:start position:0% +part of the problem. The rotational + + + align:start position:0% +part of the problem. The rotational +Hamiltonian + + align:start position:0% +Hamiltonian + + + align:start position:0% +Hamiltonian +is + + align:start position:0% + + + + align:start position:0% + +is just the rotational constant or + + align:start position:0% +is just the rotational constant or + + + align:start position:0% +is just the rotational constant or +rotational constant operator + + align:start position:0% +rotational constant operator + + + align:start position:0% +rotational constant operator +times uh + + align:start position:0% +times uh + + + align:start position:0% +times uh +R +. + + align:start position:0% +R +. + + + align:start position:0% +R +. +This is the core rotation. + + align:start position:0% +This is the core rotation. + + + align:start position:0% +This is the core rotation. +Yeah. Well, R+ is NUS L + + align:start position:0% +Yeah. Well, R+ is NUS L + + + align:start position:0% +Yeah. Well, R+ is NUS L +for our particular example because for + + align:start position:0% +for our particular example because for + + + align:start position:0% +for our particular example because for +the particular example our ion core is + + align:start position:0% +the particular example our ion core is + + + align:start position:0% +the particular example our ion core is +close to. So all we do is remove orbital + + align:start position:0% +close to. So all we do is remove orbital + + + align:start position:0% +close to. So all we do is remove orbital +angular momentum from the total n and we + + align:start position:0% +angular momentum from the total n and we + + + align:start position:0% +angular momentum from the total n and we +have n plus but n plus is r plus. + + align:start position:0% + + + + align:start position:0% + +So r + + + align:start position:0% +So r + + + + align:start position:0% +So r + +angular momentum squar is n^2 + + align:start position:0% +angular momentum squar is n^2 + + + align:start position:0% +angular momentum squar is n^2 ++ l 2 + + align:start position:0% ++ l 2 + + + align:start position:0% ++ l 2 +- 2 l z ^ 2 + + align:start position:0% +- 2 l z ^ 2 + + + align:start position:0% +- 2 l z ^ 2 +- n + + align:start position:0% +- n + + + align:start position:0% +- n ++ + + align:start position:0% + + + + align:start position:0% + +l - n - l + + + align:start position:0% + + + + align:start position:0% + +these are not ion core quantum numbers. + + align:start position:0% +these are not ion core quantum numbers. + + + align:start position:0% +these are not ion core quantum numbers. +These are raising and lowering + + align:start position:0% +These are raising and lowering + + + align:start position:0% +These are raising and lowering +operators. So all I did is I just + + align:start position:0% +operators. So all I did is I just + + + align:start position:0% +operators. So all I did is I just +multiply. So I have n^2 l 2 nil + + align:start position:0% +multiply. So I have n^2 l 2 nil + + + align:start position:0% +multiply. So I have n^2 l 2 nil +2 nil. + + align:start position:0% +2 nil. + + + align:start position:0% +2 nil. +And that since nz is the same as lz + + align:start position:0% +And that since nz is the same as lz + + + align:start position:0% +And that since nz is the same as lz +uh that's why we have that and then this + + align:start position:0% +uh that's why we have that and then this + + + align:start position:0% +uh that's why we have that and then this +is what happens when we take the nx lx + + align:start position:0% +is what happens when we take the nx lx + + + align:start position:0% +is what happens when we take the nx lx +ny ly and we arrange rearrange them into + + align:start position:0% +ny ly and we arrange rearrange them into + + + align:start position:0% +ny ly and we arrange rearrange them into +raising lower algorithms. Okay. So this + + align:start position:0% +raising lower algorithms. Okay. So this + + + align:start position:0% +raising lower algorithms. Okay. So this +gives diagonal elements and this gives + + align:start position:0% +gives diagonal elements and this gives + + + align:start position:0% +gives diagonal elements and this gives +off diagonal elements off diagonal and + + align:start position:0% +off diagonal elements off diagonal and + + + align:start position:0% +off diagonal elements off diagonal and +lambda. + + align:start position:0% + + + + align:start position:0% + +So we can add to the diagonal elements + + align:start position:0% +So we can add to the diagonal elements + + + align:start position:0% +So we can add to the diagonal elements +uh + + align:start position:0% +uh + + + align:start position:0% +uh +b + + align:start position:0% +b + + + align:start position:0% +b +* n n + 1 + + align:start position:0% +* n n + 1 + + + align:start position:0% +* n n + 1 ++ l + 1 - lambda^ 2 + + align:start position:0% ++ l + 1 - lambda^ 2 + + + align:start position:0% ++ l + 1 - lambda^ 2 +lambda 2. + + align:start position:0% + + + + align:start position:0% + +Okay. And then we have off diagonal + + align:start position:0% +Okay. And then we have off diagonal + + + align:start position:0% +Okay. And then we have off diagonal +elements. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Matrix elements of n plus are nn +1 + + align:start position:0% +Matrix elements of n plus are nn +1 + + + align:start position:0% +Matrix elements of n plus are nn +1 +minus lambda lambda plus or minus one. + + align:start position:0% +minus lambda lambda plus or minus one. + + + align:start position:0% +minus lambda lambda plus or minus one. +matrix elements of L L minus + + align:start position:0% +matrix elements of L L minus + + + align:start position:0% +matrix elements of L L minus +uh + + align:start position:0% +uh + + + align:start position:0% +uh +I said it back + + align:start position:0% + + + + align:start position:0% + +I said it a little bit n plus is going + + align:start position:0% +I said it a little bit n plus is going + + + align:start position:0% +I said it a little bit n plus is going +to be this time minus lambda lambda + + align:start position:0% +to be this time minus lambda lambda + + + align:start position:0% +to be this time minus lambda lambda +minus one + + align:start position:0% + + + + align:start position:0% + +matrix elements of l minus are ll + 1 + + align:start position:0% +matrix elements of l minus are ll + 1 + + + align:start position:0% +matrix elements of l minus are ll + 1 +minus lambda lambda + + align:start position:0% +minus lambda lambda + + + align:start position:0% +minus lambda lambda +* lambda minus one + + align:start position:0% +* lambda minus one + + + align:start position:0% +* lambda minus one +the thing that you always remember is an + + align:start position:0% +the thing that you always remember is an + + + align:start position:0% +the thing that you always remember is an +off diagonal matrix element of a of a + + align:start position:0% +off diagonal matrix element of a of a + + + align:start position:0% +off diagonal matrix element of a of a +raising or lowering operator is going to + + align:start position:0% +raising or lowering operator is going to + + + align:start position:0% +raising or lowering operator is going to +have the product of the initial and + + align:start position:0% +have the product of the initial and + + + align:start position:0% +have the product of the initial and +final + + align:start position:0% +final + + + align:start position:0% +final +uh quantum numbers in here. + + align:start position:0% +uh quantum numbers in here. + + + align:start position:0% +uh quantum numbers in here. +So uh you don't really have to remember + + align:start position:0% +So uh you don't really have to remember + + + align:start position:0% +So uh you don't really have to remember +the pluses and minuses. You just know + + align:start position:0% +the pluses and minuses. You just know + + + align:start position:0% +the pluses and minuses. You just know +that it's going to be the initial time + + align:start position:0% +that it's going to be the initial time + + + align:start position:0% +that it's going to be the initial time +to final. Okay. + + align:start position:0% +to final. Okay. + + + align:start position:0% +to final. Okay. +So now let's simplify to the simplest + + align:start position:0% +So now let's simplify to the simplest + + + align:start position:0% +So now let's simplify to the simplest +possible + + align:start position:0% +possible + + + align:start position:0% +possible +case actually could give rise to + + align:start position:0% +case actually could give rise to + + + align:start position:0% +case actually could give rise to +rotational autoization and that's L = 1 + + align:start position:0% + + + + align:start position:0% + +and when you have L= 1 + + align:start position:0% +and when you have L= 1 + + + align:start position:0% +and when you have L= 1 +in other words a P orbital + + align:start position:0% +in other words a P orbital + + + align:start position:0% +in other words a P orbital +you can have a double pi state or a + + align:start position:0% +you can have a double pi state or a + + + align:start position:0% +you can have a double pi state or a +double sigma Yeah. + + align:start position:0% + + + + align:start position:0% + +And uh so we need to be able to write + + align:start position:0% +And uh so we need to be able to write + + + align:start position:0% +And uh so we need to be able to write +the wave functions the basis functions + + align:start position:0% +the wave functions the basis functions + + + align:start position:0% +the wave functions the basis functions +and we have to write them in the par + + align:start position:0% +and we have to write them in the par + + + align:start position:0% +and we have to write them in the par +basis because par is an important + + align:start position:0% +basis because par is an important + + + align:start position:0% +basis because par is an important +quantum number. So we have the pi plus + + align:start position:0% +quantum number. So we have the pi plus + + + align:start position:0% +quantum number. So we have the pi plus +or minus one uh plus and minus + + align:start position:0% +or minus one uh plus and minus + + + align:start position:0% +or minus one uh plus and minus +states 1 2* + + align:start position:0% + + + + align:start position:0% + +lambda = 1 plus or minus + + align:start position:0% +lambda = 1 plus or minus + + + align:start position:0% +lambda = 1 plus or minus +lambda = -1 + + align:start position:0% +lambda = -1 + + + align:start position:0% +lambda = -1 +and sigma + + align:start position:0% +and sigma + + + align:start position:0% +and sigma +is exclusively plus and it's just lambda + + align:start position:0% +is exclusively plus and it's just lambda + + + align:start position:0% +is exclusively plus and it's just lambda +equals z. + + align:start position:0% +equals z. + + + align:start position:0% +equals z. +So we want to calculate matrix elements + + align:start position:0% +So we want to calculate matrix elements + + + align:start position:0% +So we want to calculate matrix elements +of these two states + + align:start position:0% + + + + align:start position:0% + +or for those who had only 561 we want to + + align:start position:0% +or for those who had only 561 we want to + + + align:start position:0% +or for those who had only 561 we want to +calculate integrals + + align:start position:0% +calculate integrals + + + align:start position:0% +calculate integrals +and uh integrals of the operators that + + align:start position:0% +and uh integrals of the operators that + + + align:start position:0% +and uh integrals of the operators that +we've got here. And we know what each of + + align:start position:0% +we've got here. And we know what each of + + + align:start position:0% +we've got here. And we know what each of +these operators does to one of those + + align:start position:0% +these operators does to one of those + + + align:start position:0% +these operators does to one of those +functions. And so the integral is just + + align:start position:0% +functions. And so the integral is just + + + align:start position:0% +functions. And so the integral is just +going to be apply the operator to the + + align:start position:0% +going to be apply the operator to the + + + align:start position:0% +going to be apply the operator to the +function and then take the other + + align:start position:0% +function and then take the other + + + align:start position:0% +function and then take the other +function and find uh uh the terms of + + align:start position:0% +function and find uh uh the terms of + + + align:start position:0% +function and find uh uh the terms of +what the operator produced that have the + + align:start position:0% +what the operator produced that have the + + + align:start position:0% +what the operator produced that have the +same angular momentum + + align:start position:0% +same angular momentum + + + align:start position:0% +same angular momentum +function already there. So when you + + align:start position:0% +function already there. So when you + + + align:start position:0% +function already there. So when you +integrate you either get zero or one. + + align:start position:0% +integrate you either get zero or one. + + + align:start position:0% +integrate you either get zero or one. +All right. So it's you can do it. All + + align:start position:0% +All right. So it's you can do it. All + + + align:start position:0% +All right. So it's you can do it. All +right. So + + align:start position:0% +right. So + + + align:start position:0% +right. So +when we put it all together, + + align:start position:0% +when we put it all together, + + + align:start position:0% +when we put it all together, +uh what we're going to get is a matrix + + align:start position:0% +uh what we're going to get is a matrix + + + align:start position:0% +uh what we're going to get is a matrix +for the rotational Hamiltonian + + align:start position:0% +for the rotational Hamiltonian + + + align:start position:0% +for the rotational Hamiltonian +labeled in this way. + + align:start position:0% + + + + align:start position:0% + +So we have P + + align:start position:0% + + + + align:start position:0% + +X + 2 + + align:start position:0% +X + 2 + + + align:start position:0% +X + 2 +X is equal to N and then + one. + + align:start position:0% +X is equal to N and then + one. + + + align:start position:0% +X is equal to N and then + one. +Okay, just to make the writing less. + + align:start position:0% +Okay, just to make the writing less. + + + align:start position:0% +Okay, just to make the writing less. +P X^ square * 2 + + align:start position:0% +P X^ square * 2 + + + align:start position:0% +P X^ square * 2 + + align:start position:0% + + + + align:start position:0% + +symmetric. So that's the same as that. + + align:start position:0% +symmetric. So that's the same as that. + + + align:start position:0% +symmetric. So that's the same as that. +uh b + + align:start position:0% +uh b + + + align:start position:0% +uh b +x + 2 - 2 + + align:start position:0% +x + 2 - 2 + + + align:start position:0% +x + 2 - 2 + + align:start position:0% + + + align:start position:0% + + align:start position:0% + + + align:start position:0% +v + + align:start position:0% +v + + + align:start position:0% +v +x + + align:start position:0% +x + + + align:start position:0% +x +that's so that's what we get from the + + align:start position:0% +that's so that's what we get from the + + + align:start position:0% +that's so that's what we get from the +rotational Hamiltonian when we evaluate + + align:start position:0% +rotational Hamiltonian when we evaluate + + + align:start position:0% +rotational Hamiltonian when we evaluate +matrix elements of v r 2 + + align:start position:0% +matrix elements of v r 2 + + + align:start position:0% +matrix elements of v r 2 +we get + + align:start position:0% +we get + + + align:start position:0% +we get +this matrix + + align:start position:0% +this matrix + + + align:start position:0% +this matrix +And it's a 2x two and a 1x 1. The pi + + align:start position:0% +And it's a 2x two and a 1x 1. The pi + + + align:start position:0% +And it's a 2x two and a 1x 1. The pi +minus is by itself. + + align:start position:0% +minus is by itself. + + + align:start position:0% +minus is by itself. +The pi plus interacts with the sigma. + + align:start position:0% +The pi plus interacts with the sigma. + + + align:start position:0% +The pi plus interacts with the sigma. +And so this is the only off diagonal + + align:start position:0% +And so this is the only off diagonal + + + align:start position:0% +And so this is the only off diagonal +element in the problem. We have a + + align:start position:0% +element in the problem. We have a + + + align:start position:0% +element in the problem. We have a +difference in diagonal elements + + align:start position:0% +difference in diagonal elements + + + align:start position:0% +difference in diagonal elements +associated with this. We have a small + + align:start position:0% +associated with this. We have a small + + + align:start position:0% +associated with this. We have a small +difference in diagonal elements + + align:start position:0% +difference in diagonal elements + + + align:start position:0% +difference in diagonal elements +associated with that. + + align:start position:0% +associated with that. + + + align:start position:0% +associated with that. +And this is the bad guy. + + align:start position:0% +And this is the bad guy. + + + align:start position:0% +And this is the bad guy. +This is + + align:start position:0% +This is + + + align:start position:0% +This is +this expresses a corololis effect as the + + align:start position:0% +this expresses a corololis effect as the + + + align:start position:0% +this expresses a corololis effect as the +ion rotates and if the electron is in + + align:start position:0% +ion rotates and if the electron is in + + + align:start position:0% +ion rotates and if the electron is in +that rotating coordinate system and + + align:start position:0% +that rotating coordinate system and + + + align:start position:0% +that rotating coordinate system and +trying to move there's a corololis force + + align:start position:0% +trying to move there's a corololis force + + + align:start position:0% +trying to move there's a corololis force +on it. + + align:start position:0% +on it. + + + align:start position:0% +on it. +And so that coralus force gets to be + + align:start position:0% +And so that coralus force gets to be + + + align:start position:0% +And so that coralus force gets to be +large enough that it overcomes + + align:start position:0% +large enough that it overcomes + + + align:start position:0% +large enough that it overcomes +the difference in energy associated with + + align:start position:0% +the difference in energy associated with + + + align:start position:0% +the difference in energy associated with +having the electron on the nucle on the + + align:start position:0% +having the electron on the nucle on the + + + align:start position:0% +having the electron on the nucle on the +inner nuclear axis or perpendicular to + + align:start position:0% +inner nuclear axis or perpendicular to + + + align:start position:0% +inner nuclear axis or perpendicular to +it. + + align:start position:0% +it. + + + align:start position:0% +it. +But that's sort of backwards. + + align:start position:0% +But that's sort of backwards. + + + align:start position:0% +But that's sort of backwards. +It's a perfectly complete model. It + + align:start position:0% +It's a perfectly complete model. It + + + align:start position:0% +It's a perfectly complete model. It +gives all of the relevant coupling + + align:start position:0% +gives all of the relevant coupling + + + align:start position:0% +gives all of the relevant coupling +terms. But the mechanism that I told you + + align:start position:0% +terms. But the mechanism that I told you + + + align:start position:0% +terms. But the mechanism that I told you +ought to be + + align:start position:0% +ought to be + + + align:start position:0% +ought to be +uh the way we look at it is that somehow + + align:start position:0% +uh the way we look at it is that somehow + + + align:start position:0% +uh the way we look at it is that somehow +there is this not round object and it + + align:start position:0% +there is this not round object and it + + + align:start position:0% +there is this not round object and it +can exert a torque on the electron or + + align:start position:0% +can exert a torque on the electron or + + + align:start position:0% +can exert a torque on the electron or +the electron can exert a torque on it + + align:start position:0% +the electron can exert a torque on it + + + align:start position:0% +the electron can exert a torque on it +and all of the basis for that torque + + align:start position:0% +and all of the basis for that torque + + + align:start position:0% +and all of the basis for that torque +appears in the difference between the pi + + align:start position:0% +appears in the difference between the pi + + + align:start position:0% +appears in the difference between the pi +and the sigma quantum defects + + align:start position:0% +and the sigma quantum defects + + + align:start position:0% +and the sigma quantum defects +which are on the diagonal. + + align:start position:0% + + + + align:start position:0% + +And this is a little simplistic, but I'm + + align:start position:0% +And this is a little simplistic, but I'm + + + align:start position:0% +And this is a little simplistic, but I'm +still not it's hard for me to see how + + align:start position:0% +still not it's hard for me to see how + + + align:start position:0% +still not it's hard for me to see how +the rotation of this molecule can + + align:start position:0% +the rotation of this molecule can + + + align:start position:0% +the rotation of this molecule can +somehow come in resonance with this + + align:start position:0% +somehow come in resonance with this + + + align:start position:0% +somehow come in resonance with this +Kepler motion of the electron. I mean to + + align:start position:0% +Kepler motion of the electron. I mean to + + + align:start position:0% +Kepler motion of the electron. I mean to +exert to exert the torque, you would + + align:start position:0% +exert to exert the torque, you would + + + align:start position:0% +exert to exert the torque, you would +think that somehow the rotations would + + align:start position:0% +think that somehow the rotations would + + + align:start position:0% +think that somehow the rotations would +have to be, + + align:start position:0% +have to be, + + + align:start position:0% +have to be, +you know, getting seem like they're + + align:start position:0% +you know, getting seem like they're + + + align:start position:0% +you know, getting seem like they're +going to when the torque becomes + + align:start position:0% +going to when the torque becomes + + + align:start position:0% +going to when the torque becomes +especially damaging. Yeah. But okay, + + align:start position:0% +especially damaging. Yeah. But okay, + + + align:start position:0% +especially damaging. Yeah. But okay, +here here how it works. The radius is so + + align:start position:0% +here here how it works. The radius is so + + + align:start position:0% +here here how it works. The radius is so +huge that you know you have so even + + align:start position:0% +huge that you know you have so even + + + align:start position:0% +huge that you know you have so even +though electron is whizzing and bound + + align:start position:0% +though electron is whizzing and bound + + + align:start position:0% +though electron is whizzing and bound +it's so much no matter how fast it's + + align:start position:0% +it's so much no matter how fast it's + + + align:start position:0% +it's so much no matter how fast it's +moving it's moving orbit. The um + + align:start position:0% +moving it's moving orbit. The um + + + align:start position:0% +moving it's moving orbit. The um +uh the Kepler frequency is the Riddler + + align:start position:0% +uh the Kepler frequency is the Riddler + + + align:start position:0% +uh the Kepler frequency is the Riddler +times + + align:start position:0% +times + + + align:start position:0% +times +uh uh + + align:start position:0% + + + + align:start position:0% + +2 / n cub. + + align:start position:0% +2 / n cub. + + + align:start position:0% +2 / n cub. +Okay, it's basically uh the difference + + align:start position:0% +Okay, it's basically uh the difference + + + align:start position:0% +Okay, it's basically uh the difference +between successive + + align:start position:0% +between successive + + + align:start position:0% +between successive +uh rberg series. So we have Rber series + + align:start position:0% +uh rberg series. So we have Rber series + + + align:start position:0% +uh rberg series. So we have Rber series +with quantum number 1 / n with energy 1 + + align:start position:0% +with quantum number 1 / n with energy 1 + + + align:start position:0% +with quantum number 1 / n with energy 1 +/ n^2 the difference is the derivative + + align:start position:0% +/ n^2 the difference is the derivative + + + align:start position:0% +/ n^2 the difference is the derivative +of that and so that's what we get this + + align:start position:0% +of that and so that's what we get this + + + align:start position:0% +of that and so that's what we get this +okay so that's the Kepler and so as n + + align:start position:0% +okay so that's the Kepler and so as n + + + align:start position:0% +okay so that's the Kepler and so as n +gets as gets large the Kepler frequency + + align:start position:0% +gets as gets large the Kepler frequency + + + align:start position:0% +gets as gets large the Kepler frequency +gets smaller the rotational frequency is + + align:start position:0% +gets smaller the rotational frequency is + + + align:start position:0% +gets smaller the rotational frequency is +b + + align:start position:0% +b + + + align:start position:0% +b +uh 2bn + + align:start position:0% +uh 2bn + + + align:start position:0% +uh 2bn +okay so we pick a particular n uh and + + align:start position:0% +okay so we pick a particular n uh and + + + align:start position:0% +okay so we pick a particular n uh and +that determines and the lowercase n at + + align:start position:0% +that determines and the lowercase n at + + + align:start position:0% +that determines and the lowercase n at +which the resonance occurs. + + align:start position:0% +which the resonance occurs. + + + align:start position:0% +which the resonance occurs. +Okay. So you can for any motion + + align:start position:0% +Okay. So you can for any motion + + + align:start position:0% +Okay. So you can for any motion +one can always go to high enough + + align:start position:0% +one can always go to high enough + + + align:start position:0% +one can always go to high enough +principal quantum number to get + + align:start position:0% +principal quantum number to get + + + align:start position:0% +principal quantum number to get +resonance between the Kepler motion and + + align:start position:0% +resonance between the Kepler motion and + + + align:start position:0% +resonance between the Kepler motion and +that other thing. + + align:start position:0% +that other thing. + + + align:start position:0% +that other thing. +Okay. Uh it turns out that um + + align:start position:0% + + + + align:start position:0% + +for molecules with the usual size + + align:start position:0% +for molecules with the usual size + + + align:start position:0% +for molecules with the usual size +rotation constant that corresponds to + + align:start position:0% +rotation constant that corresponds to + + + align:start position:0% +rotation constant that corresponds to +principal quantum numbers on the order + + align:start position:0% +principal quantum numbers on the order + + + align:start position:0% +principal quantum numbers on the order +of 100 or 200 which are ridiculously + + align:start position:0% +of 100 or 200 which are ridiculously + + + align:start position:0% +of 100 or 200 which are ridiculously +high and difficult to do but for H2 it + + align:start position:0% +high and difficult to do but for H2 it + + + align:start position:0% +high and difficult to do but for H2 it +corresponds to quite low principal + + align:start position:0% +corresponds to quite low principal + + + align:start position:0% +corresponds to quite low principal +function. + + align:start position:0% +function. + + + align:start position:0% +function. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +[Music] + + align:start position:0% + + + + align:start position:0% + +Okay. In order to + + align:start position:0% +Okay. In order to + + + align:start position:0% +Okay. In order to +write a nice Hamiltonian, + + align:start position:0% +write a nice Hamiltonian, + + + align:start position:0% +write a nice Hamiltonian, +I have to do some algebra. So, we're on + + align:start position:0% +I have to do some algebra. So, we're on + + + align:start position:0% +I have to do some algebra. So, we're on +page six. And uh um + + align:start position:0% + + + + align:start position:0% + +we're going to + + align:start position:0% +we're going to + + + align:start position:0% +we're going to +whenever we have a 2x2 problem, we + + align:start position:0% +whenever we have a 2x2 problem, we + + + align:start position:0% +whenever we have a 2x2 problem, we +always want to symmetriize it. We want + + align:start position:0% +always want to symmetriize it. We want + + + align:start position:0% +always want to symmetriize it. We want +to take out an average energy so that + + align:start position:0% +to take out an average energy so that + + + align:start position:0% +to take out an average energy so that +the Hamiltonian has the form of plus + + align:start position:0% +the Hamiltonian has the form of plus + + + align:start position:0% +the Hamiltonian has the form of plus +delta / 2 minus delta over two on the + + align:start position:0% +delta / 2 minus delta over two on the + + + align:start position:0% +delta / 2 minus delta over two on the +diagonal and off diagonal. + + align:start position:0% +diagonal and off diagonal. + + + align:start position:0% +diagonal and off diagonal. +And so that's what this is all about. + + align:start position:0% +And so that's what this is all about. + + + align:start position:0% +And so that's what this is all about. +And uh so I define two quantities out + + align:start position:0% +And uh so I define two quantities out + + + align:start position:0% +And uh so I define two quantities out +there. Define the quantum defect average + + align:start position:0% +there. Define the quantum defect average + + + align:start position:0% +there. Define the quantum defect average +for the p orbital as delta + + align:start position:0% +for the p orbital as delta + + + align:start position:0% +for the p orbital as delta +p sigma magnet plus delta pi / 2. And I + + align:start position:0% +p sigma magnet plus delta pi / 2. And I + + + align:start position:0% +p sigma magnet plus delta pi / 2. And I +define the difference for the P as delta + + align:start position:0% +define the difference for the P as delta + + + align:start position:0% +define the difference for the P as delta +P sigma minus delta P + + align:start position:0% +P sigma minus delta P + + + align:start position:0% +P sigma minus delta P +two. + + align:start position:0% +two. + + + align:start position:0% +two. +And uh then you can express + + align:start position:0% +And uh then you can express + + + align:start position:0% +And uh then you can express +uh 1 / n minus delta sigma squ as + + align:start position:0% +uh 1 / n minus delta sigma squ as + + + align:start position:0% +uh 1 / n minus delta sigma squ as +n - delta t + + align:start position:0% +n - delta t + + + align:start position:0% +n - delta t +r - 2 + + align:start position:0% +r - 2 + + + align:start position:0% +r - 2 +plus + + align:start position:0% +plus + + + align:start position:0% +plus +um n - delta v r - 3 * + + align:start position:0% +um n - delta v r - 3 * + + + align:start position:0% +um n - delta v r - 3 * +2 delta + + align:start position:0% +2 delta + + + align:start position:0% +2 delta +delta t + + align:start position:0% +delta t + + + align:start position:0% +delta t +and similarly 1 over mus delta pi + + align:start position:0% +and similarly 1 over mus delta pi + + + align:start position:0% +and similarly 1 over mus delta pi +as the same thing here the same thing + + align:start position:0% +as the same thing here the same thing + + + align:start position:0% +as the same thing here the same thing +here but this + + align:start position:0% +here but this + + + align:start position:0% +here but this +minus 2 delta delta + + align:start position:0% +minus 2 delta delta + + + align:start position:0% +minus 2 delta delta +okay that's just algebra + + align:start position:0% + + + + align:start position:0% + +And so we've taken out an average term + + align:start position:0% +And so we've taken out an average term + + + align:start position:0% +And so we've taken out an average term +and we produced uh the difference term + + align:start position:0% +and we produced uh the difference term + + + align:start position:0% +and we produced uh the difference term +which is just the same thing with + + align:start position:0% +which is just the same thing with + + + align:start position:0% +which is just the same thing with +opposite sides. + + align:start position:0% +opposite sides. + + + align:start position:0% +opposite sides. +And so when we done that done with that + + align:start position:0% + + + + align:start position:0% + +our full Hamiltonian + + align:start position:0% + + + + align:start position:0% + +that's the form HC + + align:start position:0% +that's the form HC + + + align:start position:0% +that's the form HC +is equal to H bar + + align:start position:0% +is equal to H bar + + + align:start position:0% +is equal to H bar +that's just diagonal + + align:start position:0% +that's just diagonal + + + align:start position:0% +that's just diagonal +plus this big + + align:start position:0% +plus this big + + + align:start position:0% +plus this big +we have B plus + + align:start position:0% +we have B plus + + + align:start position:0% +we have B plus +minus the + + align:start position:0% + + + + align:start position:0% + +U + + align:start position:0% +U + + + align:start position:0% +U +delta delta P over + + align:start position:0% +delta delta P over + + + align:start position:0% +delta delta P over +N - delta P R cubed. + + align:start position:0% +N - delta P R cubed. + + + align:start position:0% +N - delta P R cubed. +We have V X square root + + align:start position:0% +We have V X square root + + + align:start position:0% +We have V X square root +Z. + + align:start position:0% +Z. + + + align:start position:0% +Z. +We have + + align:start position:0% +We have + + + align:start position:0% +We have +t x square root and then we have + + align:start position:0% +t x square root and then we have + + + align:start position:0% +t x square root and then we have +uh + + align:start position:0% +uh + + + align:start position:0% +uh +b minus + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +I got the wrong side minus b + + align:start position:0% +I got the wrong side minus b + + + align:start position:0% +I got the wrong side minus b +and then + + align:start position:0% +and then + + + align:start position:0% +and then +plus okay + + align:start position:0% + + + + align:start position:0% + +same thing. Okay, so this is the same as + + align:start position:0% +same thing. Okay, so this is the same as + + + align:start position:0% +same thing. Okay, so this is the same as +this, but it just has the opposite sign + + align:start position:0% +this, but it just has the opposite sign + + + align:start position:0% +this, but it just has the opposite sign +except now I've got Yeah, that's right. + + align:start position:0% +except now I've got Yeah, that's right. + + + align:start position:0% +except now I've got Yeah, that's right. +Uh remember + + align:start position:0% + + + + align:start position:0% + +delta R + + align:start position:0% +delta R + + + align:start position:0% +delta R +and then over. So then we have zero and + + align:start position:0% +and then over. So then we have zero and + + + align:start position:0% +and then over. So then we have zero and +zero and zero and finally over here we + + align:start position:0% +zero and zero and finally over here we + + + align:start position:0% +zero and zero and finally over here we +have + + align:start position:0% +have + + + align:start position:0% +have +minus B + + align:start position:0% +minus B + + + align:start position:0% +minus B +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +plus. + + align:start position:0% + + + + align:start position:0% + +Okay. So these two have the same + + align:start position:0% +Okay. So these two have the same + + + align:start position:0% +Okay. So these two have the same +diagonal elements. + + align:start position:0% +diagonal elements. + + + align:start position:0% +diagonal elements. +These two have + + align:start position:0% +These two have + + + align:start position:0% +These two have +uh + + align:start position:0% +uh + + + align:start position:0% +uh +diagonal elements which are plus and + + align:start position:0% +diagonal elements which are plus and + + + align:start position:0% +diagonal elements which are plus and +minus. + + align:start position:0% +minus. + + + align:start position:0% +minus. +There's one off diagonal element here. + + align:start position:0% +There's one off diagonal element here. + + + align:start position:0% +There's one off diagonal element here. +So we can solve this 3x3 problem now by + + align:start position:0% +So we can solve this 3x3 problem now by + + + align:start position:0% +So we can solve this 3x3 problem now by +inspection. + + align:start position:0% + + + + align:start position:0% + +And what you end up finding is for a + + align:start position:0% +And what you end up finding is for a + + + align:start position:0% +And what you end up finding is for a +given value of n the pi plus and the + + align:start position:0% +given value of n the pi plus and the + + + align:start position:0% +given value of n the pi plus and the +sigma quick series converge to n is + + align:start position:0% +sigma quick series converge to n is + + + align:start position:0% +sigma quick series converge to n is +equal n + n plus or minus one and the pi + + align:start position:0% +equal n + n plus or minus one and the pi + + + align:start position:0% +equal n + n plus or minus one and the pi +minus + + align:start position:0% +minus + + + align:start position:0% +minus +converges to n + + align:start position:0% +converges to n + + + align:start position:0% +converges to n +is that + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +still got a little ways to go to even + + align:start position:0% +still got a little ways to go to even + + + align:start position:0% +still got a little ways to go to even +finish this first half of the problem. + + align:start position:0% +finish this first half of the problem. + + + align:start position:0% +finish this first half of the problem. +So we have a Hamiltonian matrix that + + align:start position:0% +So we have a Hamiltonian matrix that + + + align:start position:0% +So we have a Hamiltonian matrix that +describes the interaction between pi and + + align:start position:0% +describes the interaction between pi and + + + align:start position:0% +describes the interaction between pi and +sigma. + + align:start position:0% +sigma. + + + align:start position:0% +sigma. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Now suppose we're at n= 1 + + align:start position:0% + + + + align:start position:0% + +and we're + + align:start position:0% +and we're + + + align:start position:0% +and we're +at an energy above n += + + align:start position:0% +at an energy above n += + + + align:start position:0% +at an energy above n += +0. + + align:start position:0% +0. + + + align:start position:0% +0. +Okay. So this is the first ionization + + align:start position:0% +Okay. So this is the first ionization + + + align:start position:0% +Okay. So this is the first ionization +limit. + + align:start position:0% + + + + align:start position:0% + +So there's going to be n + + + align:start position:0% +So there's going to be n + + + + align:start position:0% +So there's going to be n + +1 n + + + align:start position:0% +1 n + + + + align:start position:0% +1 n + +2. + + align:start position:0% +2. + + + align:start position:0% +2. +Okay. So suppose uh we're looking at the + + align:start position:0% +Okay. So suppose uh we're looking at the + + + align:start position:0% +Okay. So suppose uh we're looking at the +free state then equals 1 + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +and uh so there's a rberg series that's + + align:start position:0% +and uh so there's a rberg series that's + + + align:start position:0% +and uh so there's a rberg series that's +converging to this n=2 limit + + align:start position:0% +converging to this n=2 limit + + + align:start position:0% +converging to this n=2 limit +could interact with the continuum + + align:start position:0% +could interact with the continuum + + + align:start position:0% +could interact with the continuum +associated with the n equals0 limit. + + align:start position:0% +associated with the n equals0 limit. + + + align:start position:0% +associated with the n equals0 limit. +These two states have the same parity. + + align:start position:0% +These two states have the same parity. + + + align:start position:0% +These two states have the same parity. +they have the same total angular matter. + + align:start position:0% +they have the same total angular matter. + + + align:start position:0% +they have the same total angular matter. +We know the coupling matrix element + + align:start position:0% +We know the coupling matrix element + + + align:start position:0% +We know the coupling matrix element +between them. + + align:start position:0% +between them. + + + align:start position:0% +between them. +So there is an energy region that is uh + + align:start position:0% +So there is an energy region that is uh + + + align:start position:0% +So there is an energy region that is uh +n +1. So that's 2 * 3 is 6. So it's 6 b + + align:start position:0% + + + + align:start position:0% + +and uh uh what is the n uh what is the + + align:start position:0% +and uh uh what is the n uh what is the + + + align:start position:0% +and uh uh what is the n uh what is the +lowest end that could be above this + + align:start position:0% +lowest end that could be above this + + + align:start position:0% +lowest end that could be above this +limit + + align:start position:0% +limit + + + align:start position:0% +limit +and so we say 6 is equal to the river + + align:start position:0% +and so we say 6 is equal to the river + + + align:start position:0% +and so we say 6 is equal to the river +uh over + + align:start position:0% +uh over + + + align:start position:0% +uh over +n^2 + + align:start position:0% + + + + align:start position:0% + +okay and we solve for n + + align:start position:0% +okay and we solve for n + + + align:start position:0% +okay and we solve for n +and so n minimum + + align:start position:0% +and so n minimum + + + align:start position:0% +and so n minimum +is the square root of the windberg over + + align:start position:0% +is the square root of the windberg over + + + align:start position:0% +is the square root of the windberg over +6b. + + align:start position:0% +6b. + + + align:start position:0% +6b. +Okay, the rberg is 100,000. The b value + + align:start position:0% +Okay, the rberg is 100,000. The b value + + + align:start position:0% +Okay, the rberg is 100,000. The b value +is typically 1. And so one over 100,000 + + align:start position:0% +is typically 1. And so one over 100,000 + + + align:start position:0% +is typically 1. And so one over 100,000 +over 6 is about uh 17,000. Square root + + align:start position:0% +over 6 is about uh 17,000. Square root + + + align:start position:0% +over 6 is about uh 17,000. Square root +of that is about + + align:start position:0% +of that is about + + + align:start position:0% +of that is about +what? + + align:start position:0% + + + + align:start position:0% + +It's not 40. That would be + + align:start position:0% + + + + align:start position:0% + +it's 40 * roughly three. It's so it's a + + align:start position:0% +it's 40 * roughly three. It's so it's a + + + align:start position:0% +it's 40 * roughly three. It's so it's a +little it's a little over 100. + + align:start position:0% +little it's a little over 100. + + + align:start position:0% +little it's a little over 100. +So for ordinary molecules this process + + align:start position:0% +So for ordinary molecules this process + + + align:start position:0% +So for ordinary molecules this process +that starts to occur + + align:start position:0% +that starts to occur + + + align:start position:0% +that starts to occur +uh for reinburgg states going to n= 2 + + align:start position:0% +uh for reinburgg states going to n= 2 + + + align:start position:0% +uh for reinburgg states going to n= 2 +with principal clone numbers 100 or + + align:start position:0% +with principal clone numbers 100 or + + + align:start position:0% +with principal clone numbers 100 or +higher they're very close together + + align:start position:0% +higher they're very close together + + + align:start position:0% +higher they're very close together +for hydrogen it starts much much lower + + align:start position:0% +for hydrogen it starts much much lower + + + align:start position:0% +for hydrogen it starts much much lower +because the rotational constant is what + + align:start position:0% +because the rotational constant is what + + + align:start position:0% +because the rotational constant is what +something like 60 wave numbers + + align:start position:0% +something like 60 wave numbers + + + align:start position:0% +something like 60 wave numbers +so Um + + align:start position:0% + + + + align:start position:0% + +all right so we have a matrix the matrix + + align:start position:0% +all right so we have a matrix the matrix + + + align:start position:0% +all right so we have a matrix the matrix +says that the uh the series with n plus + + align:start position:0% +says that the uh the series with n plus + + + align:start position:0% +says that the uh the series with n plus +of two can interact with the series of n + + align:start position:0% +of two can interact with the series of n + + + align:start position:0% +of two can interact with the series of n +plus equals z and there's this matrix + + align:start position:0% +plus equals z and there's this matrix + + + align:start position:0% +plus equals z and there's this matrix +element we have the energy differences. + + align:start position:0% +element we have the energy differences. + + + align:start position:0% +element we have the energy differences. +So it's a solved problem but it's + + align:start position:0% +So it's a solved problem but it's + + + align:start position:0% +So it's a solved problem but it's +expressed in this peculiar way where the + + align:start position:0% +expressed in this peculiar way where the + + + align:start position:0% +expressed in this peculiar way where the +thing that causes the dynamics is here. + + align:start position:0% +thing that causes the dynamics is here. + + + align:start position:0% +thing that causes the dynamics is here. +And so this is a picture where the + + align:start position:0% +And so this is a picture where the + + + align:start position:0% +And so this is a picture where the +dynamics is essentially caused by + + align:start position:0% +dynamics is essentially caused by + + + align:start position:0% +dynamics is essentially caused by +corololis effects against the + + align:start position:0% +corololis effects against the + + + align:start position:0% +corololis effects against the +non-sericity of the core. And that is a + + align:start position:0% +non-sericity of the core. And that is a + + + align:start position:0% +non-sericity of the core. And that is a +way of looking at it but I don't like + + align:start position:0% +way of looking at it but I don't like + + + align:start position:0% +way of looking at it but I don't like +that one this much. So this way is a + + align:start position:0% +that one this much. So this way is a + + + align:start position:0% +that one this much. So this way is a +case B or a case A picture. Then + + align:start position:0% +case B or a case A picture. Then + + + align:start position:0% +case B or a case A picture. Then +let me just go remember I did a little + + align:start position:0% +let me just go remember I did a little + + + align:start position:0% +let me just go remember I did a little +problem on page 15 of lecture number one + + align:start position:0% +problem on page 15 of lecture number one + + + align:start position:0% +problem on page 15 of lecture number one +which I did as the first page of lecture + + align:start position:0% +which I did as the first page of lecture + + + align:start position:0% +which I did as the first page of lecture +number two. + + align:start position:0% +number two. + + + align:start position:0% +number two. +And if you have + + align:start position:0% +And if you have + + + align:start position:0% +And if you have +uh two terms in the Hamilton, one + + align:start position:0% +uh two terms in the Hamilton, one + + + align:start position:0% +uh two terms in the Hamilton, one +producing a difference in energy and one + + align:start position:0% +producing a difference in energy and one + + + align:start position:0% +producing a difference in energy and one +producing an offdial element, you can + + align:start position:0% +producing an offdial element, you can + + + align:start position:0% +producing an offdial element, you can +always go to an opposite representation + + align:start position:0% +always go to an opposite representation + + + align:start position:0% +always go to an opposite representation +where the roles are reversed. + + align:start position:0% +where the roles are reversed. + + + align:start position:0% +where the roles are reversed. +So in case D + + align:start position:0% +So in case D + + + align:start position:0% +So in case D +picture is precisely that + + align:start position:0% +picture is precisely that + + + align:start position:0% +picture is precisely that +in a case D the wave function is + + align:start position:0% +in a case D the wave function is + + + align:start position:0% +in a case D the wave function is +specified by quantum number n plus l sub + + align:start position:0% +specified by quantum number n plus l sub + + + align:start position:0% +specified by quantum number n plus l sub +r plus. + + align:start position:0% +r plus. + + + align:start position:0% +r plus. +So L sub R is the projection of L on N + + align:start position:0% +So L sub R is the projection of L on N + + + align:start position:0% +So L sub R is the projection of L on N +plus + + align:start position:0% + + + + align:start position:0% + +instead of the projection of L on the + + align:start position:0% +instead of the projection of L on the + + + align:start position:0% +instead of the projection of L on the +inner nuclear axis + + align:start position:0% +inner nuclear axis + + + align:start position:0% +inner nuclear axis +and N - N plus + + align:start position:0% +and N - N plus + + + align:start position:0% +and N - N plus +in the case D limit. So this is not an + + align:start position:0% +in the case D limit. So this is not an + + + align:start position:0% +in the case D limit. So this is not an +operator equation. This is a quantum + + align:start position:0% +operator equation. This is a quantum + + + align:start position:0% +operator equation. This is a quantum +number equation. + + align:start position:0% + + + + align:start position:0% + +The rotational Hamiltonian + + align:start position:0% +The rotational Hamiltonian + + + align:start position:0% +The rotational Hamiltonian +in case D + + align:start position:0% +in case D + + + align:start position:0% +in case D +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +r * n + squ. + + align:start position:0% +r * n + squ. + + + align:start position:0% +r * n + squ. +Well, isn't that nice? + + align:start position:0% +Well, isn't that nice? + + + align:start position:0% +Well, isn't that nice? +This doesn't have you see n plus is + + align:start position:0% +This doesn't have you see n plus is + + + align:start position:0% +This doesn't have you see n plus is +here. + + align:start position:0% +here. + + + align:start position:0% +here. +So + + align:start position:0% +So + + + align:start position:0% +So +in case D, this only has diagonal + + align:start position:0% +in case D, this only has diagonal + + + align:start position:0% +in case D, this only has diagonal +elements. + + align:start position:0% + + + + align:start position:0% + +Now there's going to be several + + align:start position:0% +Now there's going to be several + + + align:start position:0% +Now there's going to be several +different diagonal elements depending on + + align:start position:0% +different diagonal elements depending on + + + align:start position:0% +different diagonal elements depending on +the values of L subar. + + align:start position:0% +the values of L subar. + + + align:start position:0% +the values of L subar. +So let's make a little table. We have n + + align:start position:0% +So let's make a little table. We have n + + + align:start position:0% +So let's make a little table. We have n ++ + + align:start position:0% ++ + + + align:start position:0% ++ +l subar + + align:start position:0% +l subar + + + align:start position:0% +l subar +n + + + align:start position:0% +n + + + + align:start position:0% +n + +squ. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +Well, since n is a good quantum number, + + align:start position:0% +Well, since n is a good quantum number, + + + align:start position:0% +Well, since n is a good quantum number, +what we're interested in is three states + + align:start position:0% +what we're interested in is three states + + + align:start position:0% +what we're interested in is three states +of the same value of n. + + align:start position:0% +of the same value of n. + + + align:start position:0% +of the same value of n. +And n plus can be n + one, n minus one. + + align:start position:0% + + + + align:start position:0% + +Well, since + + align:start position:0% +Well, since + + + align:start position:0% +Well, since +n - n plus is l sub r, we have -1 + + align:start position:0% +n - n plus is l sub r, we have -1 + + + align:start position:0% +n - n plus is l sub r, we have -1 +0 and 1. + + align:start position:0% +0 and 1. + + + align:start position:0% +0 and 1. +And + + align:start position:0% +And + + + align:start position:0% +And +so the matrix element of n + 2 is going + + align:start position:0% +so the matrix element of n + 2 is going + + + align:start position:0% +so the matrix element of n + 2 is going +to be n + one + + align:start position:0% +to be n + one + + + align:start position:0% +to be n + one +and n + 1 + + align:start position:0% +and n + 1 + + + align:start position:0% +and n + 1 +and n + 1 + + align:start position:0% +and n + 1 + + + align:start position:0% +and n + 1 ++ 2 + 2 n + + align:start position:0% + + + + align:start position:0% + +- 2 n. + + align:start position:0% +- 2 n. + + + align:start position:0% +- 2 n. +So that's it. That's how we figure out + + align:start position:0% +So that's it. That's how we figure out + + + align:start position:0% +So that's it. That's how we figure out +what goes on the diagonal. + + align:start position:0% + + + + align:start position:0% + +So we have a term that we want to take + + align:start position:0% +So we have a term that we want to take + + + align:start position:0% +So we have a term that we want to take +out because it's common and then we have + + align:start position:0% +out because it's common and then we have + + + align:start position:0% +out because it's common and then we have +some differences. So as far as the + + align:start position:0% +some differences. So as far as the + + + align:start position:0% +some differences. So as far as the +rotational Hamiltonian is concerned, + + align:start position:0% +rotational Hamiltonian is concerned, + + + align:start position:0% +rotational Hamiltonian is concerned, +it's completely diagonal but there's a + + align:start position:0% +it's completely diagonal but there's a + + + align:start position:0% +it's completely diagonal but there's a +little bit of a difference on diagonal + + align:start position:0% +little bit of a difference on diagonal + + + align:start position:0% +little bit of a difference on diagonal +between uh these two states. Now we also + + align:start position:0% +between uh these two states. Now we also + + + align:start position:0% +between uh these two states. Now we also +I should have put in par plus minus + + align:start position:0% +I should have put in par plus minus + + + align:start position:0% +I should have put in par plus minus +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +the + + align:start position:0% + + + + align:start position:0% + +the par is minus1 to the n + + align:start position:0% +the par is minus1 to the n + + + align:start position:0% +the par is minus1 to the n +for a uh p complex + + align:start position:0% +for a uh p complex + + + align:start position:0% +for a uh p complex +minus + + align:start position:0% +minus + + + align:start position:0% +minus +one n minus -1 + + align:start position:0% + + + + align:start position:0% + +Okay. So, these these are the two things + + align:start position:0% +Okay. So, these these are the two things + + + align:start position:0% +Okay. So, these these are the two things +that can interact. + + align:start position:0% +that can interact. + + + align:start position:0% +that can interact. +All right. + + align:start position:0% + + + + align:start position:0% + +And + + align:start position:0% +And + + + align:start position:0% +And +recall we had this over here. This was + + align:start position:0% +recall we had this over here. This was + + + align:start position:0% +recall we had this over here. This was +the the difference along the diagonal. + + align:start position:0% +the the difference along the diagonal. + + + align:start position:0% +the the difference along the diagonal. +when we go to case D, what had been a + + align:start position:0% +when we go to case D, what had been a + + + align:start position:0% +when we go to case D, what had been a +difference on the diagonal gets moved to + + align:start position:0% +difference on the diagonal gets moved to + + + align:start position:0% +difference on the diagonal gets moved to +the off diagonal. + + align:start position:0% +the off diagonal. + + + align:start position:0% +the off diagonal. +And so what we're going to end up + + align:start position:0% +And so what we're going to end up + + + align:start position:0% +And so what we're going to end up +getting for H1 in case D + + align:start position:0% + + + + align:start position:0% + +is going to be something that looks + + align:start position:0% +is going to be something that looks + + + align:start position:0% +is going to be something that looks +about like this. + + align:start position:0% +about like this. + + + align:start position:0% +about like this. + + align:start position:0% + + + + align:start position:0% + +2 * the redberg delta + + align:start position:0% +2 * the redberg delta + + + align:start position:0% +2 * the redberg delta +delta p 0 + + align:start position:0% + + + + align:start position:0% + +and delta r + + align:start position:0% +and delta r + + + align:start position:0% +and delta r +the third power 0 0. + + align:start position:0% + + + + align:start position:0% + +So we have this + + align:start position:0% +So we have this + + + align:start position:0% +So we have this +anisotropy term + + align:start position:0% +anisotropy term + + + align:start position:0% +anisotropy term +here as the off diagonal term and we + + align:start position:0% +here as the off diagonal term and we + + + align:start position:0% +here as the off diagonal term and we +have the rotation is producing a little + + align:start position:0% +have the rotation is producing a little + + + align:start position:0% +have the rotation is producing a little +tiny bit oops + + align:start position:0% +tiny bit oops + + + align:start position:0% +tiny bit oops +the rotation is producing a little tiny + + align:start position:0% +the rotation is producing a little tiny + + + align:start position:0% +the rotation is producing a little tiny +bit of energy denomin + + align:start position:0% + + + + align:start position:0% + +uh diagonal. + + align:start position:0% +uh diagonal. + + + align:start position:0% +uh diagonal. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +So this is much nicer because now what + + align:start position:0% +So this is much nicer because now what + + + align:start position:0% +So this is much nicer because now what +we have is the + + align:start position:0% +we have is the + + + align:start position:0% +we have is the +this quantum defect difference acting as + + align:start position:0% +this quantum defect difference acting as + + + align:start position:0% +this quantum defect difference acting as +the coupling term and it's fighting + + align:start position:0% +the coupling term and it's fighting + + + align:start position:0% +the coupling term and it's fighting +against the very very small + + align:start position:0% +against the very very small + + + align:start position:0% +against the very very small +energy difference associated + + align:start position:0% +energy difference associated + + + align:start position:0% +energy difference associated +uh with + + align:start position:0% +uh with + + + align:start position:0% +uh with +um + + align:start position:0% + + + + align:start position:0% + +the rotation. + + align:start position:0% + + + + align:start position:0% + +So this is the the formulation of the + + align:start position:0% +So this is the the formulation of the + + + align:start position:0% +So this is the the formulation of the +problem that expresses the + + align:start position:0% +problem that expresses the + + + align:start position:0% +problem that expresses the +causal role of the nonspericity + + align:start position:0% +causal role of the nonspericity + + + align:start position:0% +causal role of the nonspericity +through the difference in quantum defect + + align:start position:0% + + + + align:start position:0% + +and it's overcoming a small + + align:start position:0% +and it's overcoming a small + + + align:start position:0% +and it's overcoming a small +rotational effect associated with the + + align:start position:0% +rotational effect associated with the + + + align:start position:0% +rotational effect associated with the +different values of the overlay + + align:start position:0% +different values of the overlay + + + align:start position:0% +different values of the overlay +projections. That's it. I think I should + + align:start position:0% +projections. That's it. I think I should + + + align:start position:0% +projections. That's it. I think I should +stop because this was a fairly heavy + + align:start position:0% +stop because this was a fairly heavy + + + align:start position:0% +stop because this was a fairly heavy +duty derivation. We're we're out of time + + align:start position:0% +duty derivation. We're we're out of time + + + align:start position:0% +duty derivation. We're we're out of time +and the vibrational autoization would + + align:start position:0% +and the vibrational autoization would + + + align:start position:0% +and the vibrational autoization would +also be fairly heavy duty. So I think + + align:start position:0% +also be fairly heavy duty. So I think + + + align:start position:0% +also be fairly heavy duty. So I think +that's enough. Uh I hope that this was + + align:start position:0% +that's enough. Uh I hope that this was + + + align:start position:0% +that's enough. Uh I hope that this was +useful and gave you the flavor of how we + + align:start position:0% +useful and gave you the flavor of how we + + + align:start position:0% +useful and gave you the flavor of how we +characterize dynamics in even the simple + + align:start position:0% +characterize dynamics in even the simple + + + align:start position:0% +characterize dynamics in even the simple +systems of diatomics and that it will + + align:start position:0% +systems of diatomics and that it will + + + align:start position:0% +systems of diatomics and that it will +give you ideas for how you would carry + + align:start position:0% +give you ideas for how you would carry + + + align:start position:0% +give you ideas for how you would carry +some of these things over to more + + align:start position:0% +some of these things over to more + + + align:start position:0% +some of these things over to more +complicated systems, not necessarily + + align:start position:0% +complicated systems, not necessarily + + + align:start position:0% +complicated systems, not necessarily +even gas phase molecules + + align:start position:0% +even gas phase molecules + + + align:start position:0% +even gas phase molecules +that you want to form a representation, + + align:start position:0% +that you want to form a representation, + + + align:start position:0% +that you want to form a representation, +a zero order picture and then say, okay, + + align:start position:0% +a zero order picture and then say, okay, + + + align:start position:0% +a zero order picture and then say, okay, +what's the what are the possible things + + align:start position:0% +what's the what are the possible things + + + align:start position:0% +what's the what are the possible things +that could spoil that and then work out + + align:start position:0% +that could spoil that and then work out + + + align:start position:0% +that could spoil that and then work out +what would be the consequences. And + + align:start position:0% +what would be the consequences. And + + + align:start position:0% +what would be the consequences. And +often there are two complimentary + + align:start position:0% +often there are two complimentary + + + align:start position:0% +often there are two complimentary +representations. + + align:start position:0% +representations. + + + align:start position:0% +representations. +And one often gives you the insight + + align:start position:0% +And one often gives you the insight + + + align:start position:0% +And one often gives you the insight +and one is often the one that you're + + align:start position:0% +and one is often the one that you're + + + align:start position:0% +and one is often the one that you're +most likely to fall on first, which + + align:start position:0% +most likely to fall on first, which + + + align:start position:0% +most likely to fall on first, which +doesn't give you the insight. + + align:start position:0% + + + + align:start position:0% + +And that's it. So wait till next when I + + align:start position:0% +And that's it. So wait till next when I + + + align:start position:0% +And that's it. So wait till next when I +have to do some more of these things. + + align:start position:0% + + + + align:start position:0% + +I hope that helped. Uh I I wish we had + + align:start position:0% +I hope that helped. Uh I I wish we had + + + align:start position:0% +I hope that helped. Uh I I wish we had +more time. I could do this more + + align:start position:0% +more time. I could do this more + + + align:start position:0% +more time. I could do this more +carefully, but the + + align:start position:0% +carefully, but the + + + align:start position:0% +carefully, but the +the spirit is there. Okay. + + align:start position:0% +the spirit is there. Okay. + + + align:start position:0% +the spirit is there. Okay. +Yes. So if if the the in the red brake + + align:start position:0% +Yes. So if if the the in the red brake + + + align:start position:0% +Yes. So if if the the in the red brake +state the um electron is + + align:start position:0% +state the um electron is + + + align:start position:0% +state the um electron is +you're if it can pick up energy from a + + align:start position:0% +you're if it can pick up energy from a + + + align:start position:0% +you're if it can pick up energy from a +rotation of the ion core and that's + + align:start position:0% +rotation of the ion core and that's + + + align:start position:0% +rotation of the ion core and that's +enough to ionize it that means it's + + align:start position:0% +enough to ionize it that means it's + + + align:start position:0% +enough to ionize it that means it's +really I mean the energy difference + + align:start position:0% +really I mean the energy difference + + + align:start position:0% +really I mean the energy difference +between the ionization and the energy of + + align:start position:0% +between the ionization and the energy of + + + align:start position:0% +between the ionization and the energy of +the electrons really small well that's + + align:start position:0% +the electrons really small well that's + + + align:start position:0% +the electrons really small well that's +that's what I was doing over here right + + align:start position:0% +that's what I was doing over here right + + + align:start position:0% +that's what I was doing over here right +okay so it's on it's on the order of you + + align:start position:0% +okay so it's on it's on the order of you + + + align:start position:0% +okay so it's on it's on the order of you +know the rot rotational + + align:start position:0% +know the rot rotational + + + align:start position:0% +know the rot rotational +uh energy of the ion core. So, well, + + align:start position:0% +uh energy of the ion core. So, well, + + + align:start position:0% +uh energy of the ion core. So, well, +it's even less than that because you're + + align:start position:0% +it's even less than that because you're + + + align:start position:0% +it's even less than that because you're +going to only be able to change the + + align:start position:0% +going to only be able to change the + + + align:start position:0% +going to only be able to change the +rotational energy of the ion core by a + + align:start position:0% +rotational energy of the ion core by a + + + align:start position:0% +rotational energy of the ion core by a +few quant. So, like two. My my question + + align:start position:0% +few quant. So, like two. My my question + + + align:start position:0% +few quant. So, like two. My my question +is this. If you've got this really high + + align:start position:0% +is this. If you've got this really high + + + align:start position:0% +is this. If you've got this really high +energy and you've got so you've got some + + align:start position:0% +energy and you've got so you've got some + + + align:start position:0% +energy and you've got so you've got some +uncertainty in that energy, isn't that + + align:start position:0% +uncertainty in that energy, isn't that + + + align:start position:0% +uncertainty in that energy, isn't that +uncertainty much bigger than the + + align:start position:0% +uncertainty much bigger than the + + + align:start position:0% +uncertainty much bigger than the +separation? Why would you have any + + align:start position:0% +separation? Why would you have any + + + align:start position:0% +separation? Why would you have any +uncertainty? Uh you would + + align:start position:0% +uncertainty? Uh you would + + + align:start position:0% +uncertainty? Uh you would +Well, I mean, how long is the lifetime + + align:start position:0% +Well, I mean, how long is the lifetime + + + align:start position:0% +Well, I mean, how long is the lifetime +of the river? Dave, if it's a any kind + + align:start position:0% +of the river? Dave, if it's a any kind + + + align:start position:0% +of the river? Dave, if it's a any kind +of finite lifetime, you've got + + align:start position:0% +of finite lifetime, you've got + + + align:start position:0% +of finite lifetime, you've got +uncertainty in the energy of the Well, + + align:start position:0% +uncertainty in the energy of the Well, + + + align:start position:0% +uncertainty in the energy of the Well, +that's right. Well, the uncertainty in + + align:start position:0% +that's right. Well, the uncertainty in + + + align:start position:0% +that's right. Well, the uncertainty in +the energy is what gives the width. I + + align:start position:0% +the energy is what gives the width. I + + + align:start position:0% +the energy is what gives the width. I +mean, the lifetime, you have a process. + + align:start position:0% +mean, the lifetime, you have a process. + + + align:start position:0% +mean, the lifetime, you have a process. +You have a continuum. And I didn't, you + + align:start position:0% +You have a continuum. And I didn't, you + + + align:start position:0% +You have a continuum. And I didn't, you +know, I didn't talk about you have state + + align:start position:0% +know, I didn't talk about you have state + + + align:start position:0% +know, I didn't talk about you have state +and a continuum. And there's a coupling + + align:start position:0% +and a continuum. And there's a coupling + + + align:start position:0% +and a continuum. And there's a coupling +matrix element between them. And + + align:start position:0% +matrix element between them. And + + + align:start position:0% +matrix element between them. And +family's golden rule tells you the rate, + + align:start position:0% +family's golden rule tells you the rate, + + + align:start position:0% +family's golden rule tells you the rate, +right? And one over the rate is the + + align:start position:0% +right? And one over the rate is the + + + align:start position:0% +right? And one over the rate is the +lifetime. So, so from a naive point of + + align:start position:0% +lifetime. So, so from a naive point of + + + align:start position:0% +lifetime. So, so from a naive point of +view, before I listen to this, I would + + align:start position:0% +view, before I listen to this, I would + + + align:start position:0% +view, before I listen to this, I would +say, all right, I've got an electron + + align:start position:0% +say, all right, I've got an electron + + + align:start position:0% +say, all right, I've got an electron +with a high energy and there's just an + + align:start position:0% +with a high energy and there's just an + + + align:start position:0% +with a high energy and there's just an +uncertainty. The uncertainty in that + + align:start position:0% +uncertainty. The uncertainty in that + + + align:start position:0% +uncertainty. The uncertainty in that +energy overlaps with the ionization. And + + align:start position:0% +energy overlaps with the ionization. And + + + align:start position:0% +energy overlaps with the ionization. And +I would say, okay, there's some + + align:start position:0% +I would say, okay, there's some + + + align:start position:0% +I would say, okay, there's some +probability it's going to ionize. + + align:start position:0% +probability it's going to ionize. + + + align:start position:0% +probability it's going to ionize. +But what this is saying is like this is + + align:start position:0% +But what this is saying is like this is + + + align:start position:0% +But what this is saying is like this is +the mechanism of how that actually + + align:start position:0% +the mechanism of how that actually + + + align:start position:0% +the mechanism of how that actually +happens. Exactly. And in the zero order + + align:start position:0% +happens. Exactly. And in the zero order + + + align:start position:0% +happens. Exactly. And in the zero order +states, there is no uncertainty in the + + align:start position:0% +states, there is no uncertainty in the + + + align:start position:0% +states, there is no uncertainty in the +energy. You have you have energies that + + align:start position:0% +energy. You have you have energies that + + + align:start position:0% +energy. You have you have energies that +have trivially calculable values. + + align:start position:0% +have trivially calculable values. + + + align:start position:0% +have trivially calculable values. +And so your zero order bound state, your + + align:start position:0% +And so your zero order bound state, your + + + align:start position:0% +And so your zero order bound state, your +resonance state has a definite energy. + + align:start position:0% +resonance state has a definite energy. + + + align:start position:0% +resonance state has a definite energy. +And it's coupling to a continuum which + + align:start position:0% +And it's coupling to a continuum which + + + align:start position:0% +And it's coupling to a continuum which +doesn't have a definite energy, but all + + align:start position:0% +doesn't have a definite energy, but all + + + align:start position:0% +doesn't have a definite energy, but all +that matters is what is the density of + + align:start position:0% +that matters is what is the density of + + + align:start position:0% +that matters is what is the density of +the continuum at the energy of your + + align:start position:0% +the continuum at the energy of your + + + align:start position:0% +the continuum at the energy of your +bound state. And now you you get a + + align:start position:0% +bound state. And now you you get a + + + align:start position:0% +bound state. And now you you get a +coupling rate which is a matrix element + + align:start position:0% +coupling rate which is a matrix element + + + align:start position:0% +coupling rate which is a matrix element +squared times the density of states in + + align:start position:0% +squared times the density of states in + + + align:start position:0% +squared times the density of states in +the continuum. And that gives you uh the + + align:start position:0% +the continuum. And that gives you uh the + + + align:start position:0% +the continuum. And that gives you uh the +length of the width. The rate is the + + align:start position:0% +length of the width. The rate is the + + + align:start position:0% +length of the width. The rate is the +width. Right. Right. Okay. So uh most + + align:start position:0% +width. Right. Right. Okay. So uh most + + + align:start position:0% +width. Right. Right. Okay. So uh most +uh most people approach the dynamics in + + align:start position:0% +uh most people approach the dynamics in + + + align:start position:0% +uh most people approach the dynamics in +a way similar to what you just + + align:start position:0% +a way similar to what you just + + + align:start position:0% +a way similar to what you just +described, but that's kind of a + + align:start position:0% +described, but that's kind of a + + + align:start position:0% +described, but that's kind of a +self-fulfilling + + align:start position:0% +self-fulfilling + + + align:start position:0% +self-fulfilling +closed end. You know that you don't have + + align:start position:0% +closed end. You know that you don't have + + + align:start position:0% +closed end. You know that you don't have +a mechanism at all. + + align:start position:0% +a mechanism at all. + + + align:start position:0% +a mechanism at all. +And as long as + + align:start position:0% +And as long as + + + align:start position:0% +And as long as +uh + + align:start position:0% +uh + + + align:start position:0% +uh +there are not many + + align:start position:0% +there are not many + + + align:start position:0% +there are not many +competing mechanisms that could produce + + align:start position:0% +competing mechanisms that could produce + + + align:start position:0% +competing mechanisms that could produce +the ionization. + + align:start position:0% +the ionization. + + + align:start position:0% +the ionization. +uh then it's usually possible to + + align:start position:0% +uh then it's usually possible to + + + align:start position:0% +uh then it's usually possible to +get the smoking gun to say this is the + + align:start position:0% +get the smoking gun to say this is the + + + align:start position:0% +get the smoking gun to say this is the +uh the mechanism that gives rise to this + + align:start position:0% +uh the mechanism that gives rise to this + + + align:start position:0% +uh the mechanism that gives rise to this +uh this particular observation of + + align:start position:0% +uh this particular observation of + + + align:start position:0% +uh this particular observation of +dynamics + + align:start position:0% +dynamics + + + align:start position:0% +dynamics +and it's very rare uh in datomics + + align:start position:0% +and it's very rare uh in datomics + + + align:start position:0% +and it's very rare uh in datomics +that you have to worry about multiple + + align:start position:0% +that you have to worry about multiple + + + align:start position:0% +that you have to worry about multiple +competing mechanisms. + + align:start position:0% +competing mechanisms. + + + align:start position:0% +competing mechanisms. +It does happen. + + align:start position:0% +It does happen. + + + align:start position:0% +It does happen. +Uh it has happened. + + align:start position:0% + + + + align:start position:0% + +Can I ask another question? Absolutely. + + align:start position:0% +Can I ask another question? Absolutely. + + + align:start position:0% +Can I ask another question? Absolutely. +Um when you ranked the um the mechanisms + + align:start position:0% +Um when you ranked the um the mechanisms + + + align:start position:0% +Um when you ranked the um the mechanisms +that lead to automization, what was the + + align:start position:0% +that lead to automization, what was the + + + align:start position:0% +that lead to automization, what was the +basis of the ranking? Again, I think you + + align:start position:0% +basis of the ranking? Again, I think you + + + align:start position:0% +basis of the ranking? Again, I think you +told us, but I think um because you said + + align:start position:0% +told us, but I think um because you said + + + align:start position:0% +told us, but I think um because you said +the rotational was the most the most uh + + align:start position:0% +the rotational was the most the most uh + + + align:start position:0% +the rotational was the most the most uh +like the most uh effective. + + align:start position:0% +like the most uh effective. + + + align:start position:0% +like the most uh effective. +Well, I didn't really mean to say that. + + align:start position:0% +Well, I didn't really mean to say that. + + + align:start position:0% +Well, I didn't really mean to say that. +Maybe I misunderstood. Um + + align:start position:0% + + + + align:start position:0% + +the rotational is kind of the one of the + + align:start position:0% +the rotational is kind of the one of the + + + align:start position:0% +the rotational is kind of the one of the +easiest to understand because you've got + + align:start position:0% +easiest to understand because you've got + + + align:start position:0% +easiest to understand because you've got +this thing that you can So that's a very + + align:start position:0% +this thing that you can So that's a very + + + align:start position:0% +this thing that you can So that's a very +classical picture. Uh + + align:start position:0% + + + + align:start position:0% + +it really depends on where you are + + align:start position:0% +it really depends on where you are + + + align:start position:0% +it really depends on where you are +relative to the lowest ionization limit. + + align:start position:0% +relative to the lowest ionization limit. + + + align:start position:0% +relative to the lowest ionization limit. +If you're uh um + + align:start position:0% +If you're uh um + + + align:start position:0% +If you're uh um +if you're far above it and nothing much + + align:start position:0% +if you're far above it and nothing much + + + align:start position:0% +if you're far above it and nothing much +has happened until suddenly something + + align:start position:0% +has happened until suddenly something + + + align:start position:0% +has happened until suddenly something +happens then you know that it's either a + + align:start position:0% +happens then you know that it's either a + + + align:start position:0% +happens then you know that it's either a +spin orbit or an electronic process. You + + align:start position:0% +spin orbit or an electronic process. You + + + align:start position:0% +spin orbit or an electronic process. You +know the spin orbit couplings and the + + align:start position:0% +know the spin orbit couplings and the + + + align:start position:0% +know the spin orbit couplings and the +you know you know all the constants of + + align:start position:0% +you know you know all the constants of + + + align:start position:0% +you know you know all the constants of +the ion. So if you're looking at your + + align:start position:0% +the ion. So if you're looking at your + + + align:start position:0% +the ion. So if you're looking at your +spectrum above the lowest threshold and + + align:start position:0% +spectrum above the lowest threshold and + + + align:start position:0% +spectrum above the lowest threshold and +you see things happening near a + + align:start position:0% +you see things happening near a + + + align:start position:0% +you see things happening near a +vibrational level of the ion or near a + + align:start position:0% +vibrational level of the ion or near a + + + align:start position:0% +vibrational level of the ion or near a +spin orbit interval of the ion or near + + align:start position:0% +spin orbit interval of the ion or near + + + align:start position:0% +spin orbit interval of the ion or near +an electronic exitation of the ion, you + + align:start position:0% +an electronic exitation of the ion, you + + + align:start position:0% +an electronic exitation of the ion, you +know the dominant process will be + + align:start position:0% +know the dominant process will be + + + align:start position:0% +know the dominant process will be +spin orbit electronic rotation + + align:start position:0% +spin orbit electronic rotation + + + align:start position:0% +spin orbit electronic rotation +vibration. And so just by looking at + + align:start position:0% +vibration. And so just by looking at + + + align:start position:0% +vibration. And so just by looking at +where it is relative to the threshold, + + align:start position:0% +where it is relative to the threshold, + + + align:start position:0% +where it is relative to the threshold, +it tells you which mechanism to look for + + align:start position:0% +it tells you which mechanism to look for + + + align:start position:0% +it tells you which mechanism to look for +first. + + align:start position:0% +first. + + + align:start position:0% +first. +Um, + + align:start position:0% + + + + align:start position:0% + +it's possible + + align:start position:0% +it's possible + + + align:start position:0% +it's possible +to + + align:start position:0% +to + + + align:start position:0% +to +be very definite about the strength of a + + align:start position:0% +be very definite about the strength of a + + + align:start position:0% +be very definite about the strength of a +rotational and a vibrational + + align:start position:0% +rotational and a vibrational + + + align:start position:0% +rotational and a vibrational +and a spin orbit autoionization process + + align:start position:0% +and a spin orbit autoionization process + + + align:start position:0% +and a spin orbit autoionization process +because all of the relevant stuff that + + align:start position:0% +because all of the relevant stuff that + + + align:start position:0% +because all of the relevant stuff that +determines the coupling constant is + + align:start position:0% +determines the coupling constant is + + + align:start position:0% +determines the coupling constant is +available to you through other kinds of + + align:start position:0% +available to you through other kinds of + + + align:start position:0% +available to you through other kinds of +observations. for electronic autoization + + align:start position:0% +observations. for electronic autoization + + + align:start position:0% +observations. for electronic autoization +that is really uh that's a number. The + + align:start position:0% +that is really uh that's a number. The + + + align:start position:0% +that is really uh that's a number. The +coupling strength is not a number that + + align:start position:0% +coupling strength is not a number that + + + align:start position:0% +coupling strength is not a number that +you can estimate. You have to calculate + + align:start position:0% +you can estimate. You have to calculate + + + align:start position:0% +you can estimate. You have to calculate +it or observe it. But all of the others + + align:start position:0% +it or observe it. But all of the others + + + align:start position:0% +it or observe it. But all of the others +they you know you can get them by a kind + + align:start position:0% +they you know you can get them by a kind + + + align:start position:0% +they you know you can get them by a kind +of a backward loop. + + align:start position:0% +of a backward loop. + + + align:start position:0% +of a backward loop. +So the effectiveness of the mechanism is + + align:start position:0% +So the effectiveness of the mechanism is + + + align:start position:0% +So the effectiveness of the mechanism is +determined by how + + align:start position:0% +determined by how + + + align:start position:0% +determined by how +how close you are to being already + + align:start position:0% +how close you are to being already + + + align:start position:0% +how close you are to being already +ionized. + + align:start position:0% + + + + align:start position:0% + +Um, that's how you decide which + + align:start position:0% +Um, that's how you decide which + + + align:start position:0% +Um, that's how you decide which +mechanism is the most relevant or most + + align:start position:0% +mechanism is the most relevant or most + + + align:start position:0% +mechanism is the most relevant or most +likely to be the most relevant. I said + + align:start position:0% +likely to be the most relevant. I said + + + align:start position:0% +likely to be the most relevant. I said +two different things. I think you're + + align:start position:0% +two different things. I think you're + + + align:start position:0% +two different things. I think you're +conflating them into one. Okay. Uh, + + align:start position:0% +conflating them into one. Okay. Uh, + + + align:start position:0% +conflating them into one. Okay. Uh, +first you look at the energy at which + + align:start position:0% +first you look at the energy at which + + + align:start position:0% +first you look at the energy at which +the process you're interested in turns + + align:start position:0% +the process you're interested in turns + + + align:start position:0% +the process you're interested in turns +on and that will point towards one of + + align:start position:0% +on and that will point towards one of + + + align:start position:0% +on and that will point towards one of +the processes. that + + align:start position:0% + + + + align:start position:0% + +the the strength of the coupling that + + align:start position:0% +the the strength of the coupling that + + + align:start position:0% +the the strength of the coupling that +drives each of the processes for three + + align:start position:0% +drives each of the processes for three + + + align:start position:0% +drives each of the processes for three +of the cases can be deduced from other + + align:start position:0% +of the cases can be deduced from other + + + align:start position:0% +of the cases can be deduced from other +stuff for the fourth case the electronic + + align:start position:0% +stuff for the fourth case the electronic + + + align:start position:0% +stuff for the fourth case the electronic +one I don't know how you estimate that + + align:start position:0% +one I don't know how you estimate that + + + align:start position:0% +one I don't know how you estimate that +out priority you probably have to do the + + align:start position:0% +out priority you probably have to do the + + + align:start position:0% +out priority you probably have to do the +full evidence yes absolutely it would be + + align:start position:0% +full evidence yes absolutely it would be + + + align:start position:0% +full evidence yes absolutely it would be +very easy because uh uh it's basically + + align:start position:0% +very easy because uh uh it's basically + + + align:start position:0% +very easy because uh uh it's basically +uh you probably can get it out of not + + align:start position:0% +uh you probably can get it out of not + + + align:start position:0% +uh you probably can get it out of not +even a full opinion. You probably get it + + align:start position:0% +even a full opinion. You probably get it + + + align:start position:0% +even a full opinion. You probably get it +out of the heart because it's really a + + align:start position:0% +out of the heart because it's really a + + + align:start position:0% +out of the heart because it's really a +one electron process. But whatever, yes, + + align:start position:0% +one electron process. But whatever, yes, + + + align:start position:0% +one electron process. But whatever, yes, +you can get it out of an issue. But uh + + align:start position:0% +you can get it out of an issue. But uh + + + align:start position:0% +you can get it out of an issue. But uh +it generally does not yield itself to + + align:start position:0% +it generally does not yield itself to + + + align:start position:0% +it generally does not yield itself to +semi-impirical + + align:start position:0% +semi-impirical + + + align:start position:0% +semi-impirical +guesses whereas the other ones really + + align:start position:0% +guesses whereas the other ones really + + + align:start position:0% +guesses whereas the other ones really +do. And in my notes you'll see I mean + + align:start position:0% +do. And in my notes you'll see I mean + + + align:start position:0% +do. And in my notes you'll see I mean +for the rotational it was the difference + + align:start position:0% +for the rotational it was the difference + + + align:start position:0% +for the rotational it was the difference +in quantum defects which uh you observe + + align:start position:0% +in quantum defects which uh you observe + + + align:start position:0% +in quantum defects which uh you observe +rberg series and you you know what the + + align:start position:0% +rberg series and you you know what the + + + align:start position:0% +rberg series and you you know what the +difference of the quantity defect is so + + align:start position:0% +difference of the quantity defect is so + + + align:start position:0% +difference of the quantity defect is so +you know what the coupling is for + + align:start position:0% +you know what the coupling is for + + + align:start position:0% +you know what the coupling is for +vibration it comes from the derivative + + align:start position:0% +vibration it comes from the derivative + + + align:start position:0% +vibration it comes from the derivative +of the quantum defect with r which you + + align:start position:0% +of the quantum defect with r which you + + + align:start position:0% +of the quantum defect with r which you +can get either from observation of + + align:start position:0% +can get either from observation of + + + align:start position:0% +can get either from observation of +vibrational perturbations at known + + align:start position:0% +vibrational perturbations at known + + + align:start position:0% +vibrational perturbations at known +places in the redber series or by the + + align:start position:0% +places in the redber series or by the + + + align:start position:0% +places in the redber series or by the +difference in the shape of the ion + + align:start position:0% +difference in the shape of the ion + + + align:start position:0% +difference in the shape of the ion +curve, potential curve from the veance + + align:start position:0% +curve, potential curve from the veance + + + align:start position:0% +curve, potential curve from the veance +terminus + + align:start position:0% +terminus + + + align:start position:0% +terminus +curve because those vertical differences + + align:start position:0% +curve because those vertical differences + + + align:start position:0% +curve because those vertical differences +are what you get the quantum defect from + + align:start position:0% +are what you get the quantum defect from + + + align:start position:0% +are what you get the quantum defect from +as a function of r. And so by uh by + + align:start position:0% +as a function of r. And so by uh by + + + align:start position:0% +as a function of r. And so by uh by +looking at the r dependence of that + + align:start position:0% +looking at the r dependence of that + + + align:start position:0% +looking at the r dependence of that +vertical difference, then that's sort of + + align:start position:0% +vertical difference, then that's sort of + + + align:start position:0% +vertical difference, then that's sort of +telling you is the + + align:start position:0% +telling you is the + + + align:start position:0% +telling you is the +riper orbital bonding or anti-bonding, + + align:start position:0% +riper orbital bonding or anti-bonding, + + + align:start position:0% +riper orbital bonding or anti-bonding, +shielding or dshielding. that's + + align:start position:0% +shielding or dshielding. that's + + + align:start position:0% +shielding or dshielding. that's +determining how the the potential curves + + align:start position:0% +determining how the the potential curves + + + align:start position:0% +determining how the the potential curves +are shifted and so and spin orbit is + + align:start position:0% +are shifted and so and spin orbit is + + + align:start position:0% +are shifted and so and spin orbit is +just the spin orbit splitting in the + + align:start position:0% +just the spin orbit splitting in the + + + align:start position:0% +just the spin orbit splitting in the +ion. So all of three of those things are + + align:start position:0% +ion. So all of three of those things are + + + align:start position:0% +ion. So all of three of those things are +easily obtainable without looking at + + align:start position:0% +easily obtainable without looking at + + + align:start position:0% +easily obtainable without looking at +dynamical processing + + align:start position:0% +dynamical processing + + + align:start position:0% +dynamical processing +looking at autoionization. \ No newline at end of file diff --git a/wqNW2Nd8Xx4.txt b/wqNW2Nd8Xx4.txt new file mode 100644 index 0000000000000000000000000000000000000000..18e4e9f9b2c0b517f9312c802827c10c859c4f57 --- /dev/null +++ b/wqNW2Nd8Xx4.txt @@ -0,0 +1,8931 @@ +align:start position:0% + +The following content is provided by MIT + + align:start position:0% +The following content is provided by MIT + + + align:start position:0% +The following content is provided by MIT +Open Courseware under a Creative Common + + align:start position:0% +Open Courseware under a Creative Common + + + align:start position:0% +Open Courseware under a Creative Common +License. Additional information about + + align:start position:0% +License. Additional information about + + + align:start position:0% +License. Additional information about +our license and MIT Open Courseware in + + align:start position:0% +our license and MIT Open Courseware in + + + align:start position:0% +our license and MIT Open Courseware in +general is available at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +So, we finished the unit on oxidation + + align:start position:0% +So, we finished the unit on oxidation + + + align:start position:0% +So, we finished the unit on oxidation +reduction on Wednesday. And so, now + + align:start position:0% +reduction on Wednesday. And so, now + + + align:start position:0% +reduction on Wednesday. And so, now +we're moving into the next unit, which + + align:start position:0% +we're moving into the next unit, which + + + align:start position:0% +we're moving into the next unit, which +is transition metals. And that's chapter + + align:start position:0% +is transition metals. And that's chapter + + + align:start position:0% +is transition metals. And that's chapter +16 in your book. + + align:start position:0% +16 in your book. + + + align:start position:0% +16 in your book. +And following transition metals, the + + align:start position:0% +And following transition metals, the + + + align:start position:0% +And following transition metals, the +last unit is on kinetics or rates of + + align:start position:0% +last unit is on kinetics or rates of + + + align:start position:0% +last unit is on kinetics or rates of +reaction. So, and that's a little bit of + + align:start position:0% +reaction. So, and that's a little bit of + + + align:start position:0% +reaction. So, and that's a little bit of +a longer unit. So there's only uh two + + align:start position:0% +a longer unit. So there's only uh two + + + align:start position:0% +a longer unit. So there's only uh two +more units coming up in the in the + + align:start position:0% +more units coming up in the in the + + + align:start position:0% +more units coming up in the in the +course. So today I'm going to introduce + + align:start position:0% +course. So today I'm going to introduce + + + align:start position:0% +course. So today I'm going to introduce +you to uh transition metal unit and this + + align:start position:0% +you to uh transition metal unit and this + + + align:start position:0% +you to uh transition metal unit and this +follows nicely from oxidation reduction + + align:start position:0% +follows nicely from oxidation reduction + + + align:start position:0% +follows nicely from oxidation reduction +since you uh saw a lot of electrons + + align:start position:0% +since you uh saw a lot of electrons + + + align:start position:0% +since you uh saw a lot of electrons +being lost and gained and metals are + + align:start position:0% +being lost and gained and metals are + + + align:start position:0% +being lost and gained and metals are +definitely something that uh will gain + + align:start position:0% +definitely something that uh will gain + + + align:start position:0% +definitely something that uh will gain +um and lose electrons. So uh it follows + + align:start position:0% +um and lose electrons. So uh it follows + + + align:start position:0% +um and lose electrons. So uh it follows +nicely from that. + + align:start position:0% +nicely from that. + + + align:start position:0% +nicely from that. +So today's an introduction and on Monday + + align:start position:0% +So today's an introduction and on Monday + + + align:start position:0% +So today's an introduction and on Monday +we're going to uh talk about crystal + + align:start position:0% +we're going to uh talk about crystal + + + align:start position:0% +we're going to uh talk about crystal +field theory which is a topic that most + + align:start position:0% +field theory which is a topic that most + + + align:start position:0% +field theory which is a topic that most +people have not seen in high school. At + + align:start position:0% +people have not seen in high school. At + + + align:start position:0% +people have not seen in high school. At +least that's been true in past years. Um + + align:start position:0% +least that's been true in past years. Um + + + align:start position:0% +least that's been true in past years. Um +it looks a little bit scary sometimes to + + align:start position:0% +it looks a little bit scary sometimes to + + + align:start position:0% +it looks a little bit scary sometimes to +people because it looks different. It's + + align:start position:0% +people because it looks different. It's + + + align:start position:0% +people because it looks different. It's +not something that seems familiar. It's + + align:start position:0% +not something that seems familiar. It's + + + align:start position:0% +not something that seems familiar. It's +actually not that hard. But um I + + align:start position:0% +actually not that hard. But um I + + + align:start position:0% +actually not that hard. But um I +strongly recommend uh coming to being + + align:start position:0% +strongly recommend uh coming to being + + + align:start position:0% +strongly recommend uh coming to being +present in lecture and working the + + align:start position:0% +present in lecture and working the + + + align:start position:0% +present in lecture and working the +problems. That's how you learn how to + + align:start position:0% +problems. That's how you learn how to + + + align:start position:0% +problems. That's how you learn how to +how to do this part. And this uh often + + align:start position:0% +how to do this part. And this uh often + + + align:start position:0% +how to do this part. And this uh often +plays a this particular unit and + + align:start position:0% +plays a this particular unit and + + + align:start position:0% +plays a this particular unit and +transition metals is a dominant uh theme + + align:start position:0% +transition metals is a dominant uh theme + + + align:start position:0% +transition metals is a dominant uh theme +on the on the final exam. So you'll see + + align:start position:0% +on the on the final exam. So you'll see + + + align:start position:0% +on the on the final exam. So you'll see +it there. So people could settle down a + + align:start position:0% +it there. So people could settle down a + + + align:start position:0% +it there. So people could settle down a +little. I can't I'm even having trouble + + align:start position:0% +little. I can't I'm even having trouble + + + align:start position:0% +little. I can't I'm even having trouble +hearing myself. Um, + + align:start position:0% +hearing myself. Um, + + + align:start position:0% +hearing myself. Um, +so that's that's going to be Monday. And + + align:start position:0% +so that's that's going to be Monday. And + + + align:start position:0% +so that's that's going to be Monday. And +then on Wednesday, we're going to talk + + align:start position:0% +then on Wednesday, we're going to talk + + + align:start position:0% +then on Wednesday, we're going to talk +about shapes of of uh coordination + + align:start position:0% +about shapes of of uh coordination + + + align:start position:0% +about shapes of of uh coordination +complexes. And this fits in nicely with + + align:start position:0% +complexes. And this fits in nicely with + + + align:start position:0% +complexes. And this fits in nicely with +the transition metals. So we're going to + + align:start position:0% +the transition metals. So we're going to + + + align:start position:0% +the transition metals. So we're going to +talk about vesper theory. And then the + + align:start position:0% +talk about vesper theory. And then the + + + align:start position:0% +talk about vesper theory. And then the +following Monday, we continue on and + + align:start position:0% +following Monday, we continue on and + + + align:start position:0% +following Monday, we continue on and +talk about how one can use crystal field + + align:start position:0% +talk about how one can use crystal field + + + align:start position:0% +talk about how one can use crystal field +theory to think about what colors + + align:start position:0% +theory to think about what colors + + + align:start position:0% +theory to think about what colors +molecules with transition metals have. + + align:start position:0% +molecules with transition metals have. + + + align:start position:0% +molecules with transition metals have. +Uh so these uh these units, it's a it's + + align:start position:0% +Uh so these uh these units, it's a it's + + + align:start position:0% +Uh so these uh these units, it's a it's +a little bit of a a strange order this + + align:start position:0% +a little bit of a a strange order this + + + align:start position:0% +a little bit of a a strange order this +year because of the Thanksgiving + + align:start position:0% +year because of the Thanksgiving + + + align:start position:0% +year because of the Thanksgiving +holidays, but that's what's coming up. + + align:start position:0% +holidays, but that's what's coming up. + + + align:start position:0% +holidays, but that's what's coming up. +So again, this is a unit that most + + align:start position:0% +So again, this is a unit that most + + + align:start position:0% +So again, this is a unit that most +people haven't seen before uh in high + + align:start position:0% +people haven't seen before uh in high + + + align:start position:0% +people haven't seen before uh in high +school. + + align:start position:0% +school. + + + align:start position:0% +school. +Okay. And as I mentioned before, promise + + align:start position:0% +Okay. And as I mentioned before, promise + + + align:start position:0% +Okay. And as I mentioned before, promise +nine, which is handed out today, you'll + + align:start position:0% +nine, which is handed out today, you'll + + + align:start position:0% +nine, which is handed out today, you'll +see that it's really quite short. It + + align:start position:0% +see that it's really quite short. It + + + align:start position:0% +see that it's really quite short. It +just covers today's lecture and Monday's + + align:start position:0% +just covers today's lecture and Monday's + + + align:start position:0% +just covers today's lecture and Monday's +lecture. Just has a few problems on it. + + align:start position:0% +lecture. Just has a few problems on it. + + + align:start position:0% +lecture. Just has a few problems on it. +So, uh, it should it should, uh, just + + align:start position:0% +So, uh, it should it should, uh, just + + + align:start position:0% +So, uh, it should it should, uh, just +kind of keep you from falling behind + + align:start position:0% +kind of keep you from falling behind + + + align:start position:0% +kind of keep you from falling behind +with the material, but not take too much + + align:start position:0% +with the material, but not take too much + + + align:start position:0% +with the material, but not take too much +time. So, you'll be able to get that + + align:start position:0% +time. So, you'll be able to get that + + + align:start position:0% +time. So, you'll be able to get that +done before Thanksgiving. + + align:start position:0% + + + + align:start position:0% + +All right. So, today there are a lot of + + align:start position:0% +All right. So, today there are a lot of + + + align:start position:0% +All right. So, today there are a lot of +topics. So, that's what happens when you + + align:start position:0% +topics. So, that's what happens when you + + + align:start position:0% +topics. So, that's what happens when you +introduce a new area. So, you need to go + + align:start position:0% +introduce a new area. So, you need to go + + + align:start position:0% +introduce a new area. So, you need to go +through a bunch of different kinds of + + align:start position:0% +through a bunch of different kinds of + + + align:start position:0% +through a bunch of different kinds of +definitions. + + align:start position:0% +definitions. + + + align:start position:0% +definitions. +And so, uh, today we're going to talk + + align:start position:0% +And so, uh, today we're going to talk + + + align:start position:0% +And so, uh, today we're going to talk +about coordination complexes. + + align:start position:0% +about coordination complexes. + + + align:start position:0% +about coordination complexes. +And we're going to talk about + + align:start position:0% +And we're going to talk about + + + align:start position:0% +And we're going to talk about +coordination complex notation, + + align:start position:0% +coordination complex notation, + + + align:start position:0% +coordination complex notation, +coordination number, uh structures just + + align:start position:0% +coordination number, uh structures just + + + align:start position:0% +coordination number, uh structures just +briefly of coordination complexes. + + align:start position:0% +briefly of coordination complexes. + + + align:start position:0% +briefly of coordination complexes. +Again, on Wednesday, we're going to be + + align:start position:0% +Again, on Wednesday, we're going to be + + + align:start position:0% +Again, on Wednesday, we're going to be +coming back next Wednesday and talking + + align:start position:0% +coming back next Wednesday and talking + + + align:start position:0% +coming back next Wednesday and talking +much more about about these structures, + + align:start position:0% +much more about about these structures, + + + align:start position:0% +much more about about these structures, +but we'll give a little introduction + + align:start position:0% +but we'll give a little introduction + + + align:start position:0% +but we'll give a little introduction +today. uh going to introduce something + + align:start position:0% +today. uh going to introduce something + + + align:start position:0% +today. uh going to introduce something +called the chelate effect and talk about + + align:start position:0% +called the chelate effect and talk about + + + align:start position:0% +called the chelate effect and talk about +isomers and also since we're talking + + align:start position:0% +isomers and also since we're talking + + + align:start position:0% +isomers and also since we're talking +about transition metals we're going to + + align:start position:0% +about transition metals we're going to + + + align:start position:0% +about transition metals we're going to +start talking about d electrons and d + + align:start position:0% +start talking about d electrons and d + + + align:start position:0% +start talking about d electrons and d +orbitals. + + align:start position:0% +orbitals. + + + align:start position:0% +orbitals. +So this is again all in uh chapter 16 in + + align:start position:0% +So this is again all in uh chapter 16 in + + + align:start position:0% +So this is again all in uh chapter 16 in +your book. + + align:start position:0% + + + + align:start position:0% + +So here's that relevant part of the + + align:start position:0% +So here's that relevant part of the + + + align:start position:0% +So here's that relevant part of the +periodic table that we'll be talking + + align:start position:0% +periodic table that we'll be talking + + + align:start position:0% +periodic table that we'll be talking +about in the in this unit. So these are + + align:start position:0% +about in the in this unit. So these are + + + align:start position:0% +about in the in this unit. So these are +what are called transition metals + + align:start position:0% +what are called transition metals + + + align:start position:0% +what are called transition metals +and this is a part of the periodic table + + align:start position:0% +and this is a part of the periodic table + + + align:start position:0% +and this is a part of the periodic table +that is near and dear to the hearts of + + align:start position:0% +that is near and dear to the hearts of + + + align:start position:0% +that is near and dear to the hearts of +many faculty members in the chemistry + + align:start position:0% +many faculty members in the chemistry + + + align:start position:0% +many faculty members in the chemistry +department including my own. So we study + + align:start position:0% +department including my own. So we study + + + align:start position:0% +department including my own. So we study +proteins that use these metals to + + align:start position:0% +proteins that use these metals to + + + align:start position:0% +proteins that use these metals to +catalyze reactions. + + align:start position:0% +catalyze reactions. + + + align:start position:0% +catalyze reactions. +And so this uh color scheme is actually + + align:start position:0% +And so this uh color scheme is actually + + + align:start position:0% +And so this uh color scheme is actually +out of a book that was published by uh + + align:start position:0% +out of a book that was published by uh + + + align:start position:0% +out of a book that was published by uh +Steve Liippard uh who's a faculty member + + align:start position:0% +Steve Liippard uh who's a faculty member + + + align:start position:0% +Steve Liippard uh who's a faculty member +in the chemistry department. and I'll + + align:start position:0% +in the chemistry department. and I'll + + + align:start position:0% +in the chemistry department. and I'll +mention him again later in the day. So + + align:start position:0% +mention him again later in the day. So + + + align:start position:0% +mention him again later in the day. So +he does a lot of work on what's what the + + align:start position:0% +he does a lot of work on what's what the + + + align:start position:0% +he does a lot of work on what's what the +area called metals in biology, these + + align:start position:0% +area called metals in biology, these + + + align:start position:0% +area called metals in biology, these +transition metals that play a role in + + align:start position:0% +transition metals that play a role in + + + align:start position:0% +transition metals that play a role in +biological systems. And this book was + + align:start position:0% +biological systems. And this book was + + + align:start position:0% +biological systems. And this book was +also with Jeremy Burke who's the current + + align:start position:0% +also with Jeremy Burke who's the current + + + align:start position:0% +also with Jeremy Burke who's the current +uh head of uh of the general medicine + + align:start position:0% +uh head of uh of the general medicine + + + align:start position:0% +uh head of uh of the general medicine +component of the National Institutes of + + align:start position:0% +component of the National Institutes of + + + align:start position:0% +component of the National Institutes of +Health. And so he is somebody else who's + + align:start position:0% +Health. And so he is somebody else who's + + + align:start position:0% +Health. And so he is somebody else who's +thought a lot about metals and biology + + align:start position:0% +thought a lot about metals and biology + + + align:start position:0% +thought a lot about metals and biology +in his case in particular zinc. + + align:start position:0% +in his case in particular zinc. + + + align:start position:0% +in his case in particular zinc. +So, why are metals important in + + align:start position:0% +So, why are metals important in + + + align:start position:0% +So, why are metals important in +biological systems? Well, proteins, and + + align:start position:0% +biological systems? Well, proteins, and + + + align:start position:0% +biological systems? Well, proteins, and +I've talked some about proteins already, + + align:start position:0% +I've talked some about proteins already, + + + align:start position:0% +I've talked some about proteins already, +are composed of amino acids. You have + + align:start position:0% +are composed of amino acids. You have + + + align:start position:0% +are composed of amino acids. You have +carbon, nitrogen, oxygen, sulfur, and + + align:start position:0% +carbon, nitrogen, oxygen, sulfur, and + + + align:start position:0% +carbon, nitrogen, oxygen, sulfur, and +there's quite a bit of chemistry that + + align:start position:0% +there's quite a bit of chemistry that + + + align:start position:0% +there's quite a bit of chemistry that +these particular elements can do that + + align:start position:0% +these particular elements can do that + + + align:start position:0% +these particular elements can do that +amino acids can do. But there's some + + align:start position:0% +amino acids can do. But there's some + + + align:start position:0% +amino acids can do. But there's some +pretty challenging chemical reactions. + + align:start position:0% +pretty challenging chemical reactions. + + + align:start position:0% +pretty challenging chemical reactions. +We talked in uh the unit on chemical + + align:start position:0% +We talked in uh the unit on chemical + + + align:start position:0% +We talked in uh the unit on chemical +equilibrium about a challenging reaction + + align:start position:0% +equilibrium about a challenging reaction + + + align:start position:0% +equilibrium about a challenging reaction +splitting d nitrogen and I told you + + align:start position:0% +splitting d nitrogen and I told you + + + align:start position:0% +splitting d nitrogen and I told you +about the harbor bosch process and how + + align:start position:0% +about the harbor bosch process and how + + + align:start position:0% +about the harbor bosch process and how +uh we need to do this to get fertilizers + + align:start position:0% +uh we need to do this to get fertilizers + + + align:start position:0% +uh we need to do this to get fertilizers +and so it's an important uh industrial + + align:start position:0% +and so it's an important uh industrial + + + align:start position:0% +and so it's an important uh industrial +process that an enzyme can also do very + + align:start position:0% +process that an enzyme can also do very + + + align:start position:0% +process that an enzyme can also do very +efficiently without the high pressures + + align:start position:0% +efficiently without the high pressures + + + align:start position:0% +efficiently without the high pressures +and temperatures that uh human beings + + align:start position:0% +and temperatures that uh human beings + + + align:start position:0% +and temperatures that uh human beings +seem to need to get this reaction to go. + + align:start position:0% +seem to need to get this reaction to go. + + + align:start position:0% +seem to need to get this reaction to go. +So that is one example of a protein that + + align:start position:0% +So that is one example of a protein that + + + align:start position:0% +So that is one example of a protein that +uses metals to do the chemistry and the + + align:start position:0% +uses metals to do the chemistry and the + + + align:start position:0% +uses metals to do the chemistry and the +active site of that enzyme is full of + + align:start position:0% +active site of that enzyme is full of + + + align:start position:0% +active site of that enzyme is full of +different kinds of metals. So um up here + + align:start position:0% +different kinds of metals. So um up here + + + align:start position:0% +different kinds of metals. So um up here +says global cycling of nitrogen, + + align:start position:0% +says global cycling of nitrogen, + + + align:start position:0% +says global cycling of nitrogen, +hydrogen and carbon. And so often some + + align:start position:0% +hydrogen and carbon. And so often some + + + align:start position:0% +hydrogen and carbon. And so often some +of the most fundamental reactions are + + align:start position:0% +of the most fundamental reactions are + + + align:start position:0% +of the most fundamental reactions are +also very challenging reactions and + + align:start position:0% +also very challenging reactions and + + + align:start position:0% +also very challenging reactions and +require metals to make them go. + + align:start position:0% +require metals to make them go. + + + align:start position:0% +require metals to make them go. +uh radical chemistry reactions making + + align:start position:0% +uh radical chemistry reactions making + + + align:start position:0% +uh radical chemistry reactions making +various products like vitamins or + + align:start position:0% +various products like vitamins or + + + align:start position:0% +various products like vitamins or +deoxyucleotides the building block of + + align:start position:0% +deoxyucleotides the building block of + + + align:start position:0% +deoxyucleotides the building block of +DNA and we have some DNA here with us + + align:start position:0% +DNA and we have some DNA here with us + + + align:start position:0% +DNA and we have some DNA here with us +today in class uh a lot of these + + align:start position:0% +today in class uh a lot of these + + + align:start position:0% +today in class uh a lot of these +reactions are require metals so in this + + align:start position:0% +reactions are require metals so in this + + + align:start position:0% +reactions are require metals so in this +uh orange uh color here those are metals + + align:start position:0% +uh orange uh color here those are metals + + + align:start position:0% +uh orange uh color here those are metals +that are found in biological systems and + + align:start position:0% +that are found in biological systems and + + + align:start position:0% +that are found in biological systems and +but there's also uh some metals in gray + + align:start position:0% +but there's also uh some metals in gray + + + align:start position:0% +but there's also uh some metals in gray +and and some have both orange and gray + + align:start position:0% +and and some have both orange and gray + + + align:start position:0% +and and some have both orange and gray +there are other metals that are used as + + align:start position:0% +there are other metals that are used as + + + align:start position:0% +there are other metals that are used as +drugs or to probiological systems. So + + align:start position:0% +drugs or to probiological systems. So + + + align:start position:0% +drugs or to probiological systems. So +there's a whole area of sort of uh + + align:start position:0% +there's a whole area of sort of uh + + + align:start position:0% +there's a whole area of sort of uh +metals metals in medicine where people + + align:start position:0% +metals metals in medicine where people + + + align:start position:0% +metals metals in medicine where people +are using say looking at the use of gold + + align:start position:0% +are using say looking at the use of gold + + + align:start position:0% +are using say looking at the use of gold +for treating arthritis. So there's a lot + + align:start position:0% +for treating arthritis. So there's a lot + + + align:start position:0% +for treating arthritis. So there's a lot +of relevance of these transition metals + + align:start position:0% +of relevance of these transition metals + + + align:start position:0% +of relevance of these transition metals +or DB block metals uh to to medicine. + + align:start position:0% + + + + align:start position:0% + +So let's uh let's talk about the + + align:start position:0% +So let's uh let's talk about the + + + align:start position:0% +So let's uh let's talk about the +abilities of these metals to form + + align:start position:0% +abilities of these metals to form + + + align:start position:0% +abilities of these metals to form +complexes and this is uh important for + + align:start position:0% +complexes and this is uh important for + + + align:start position:0% +complexes and this is uh important for +their ability to function in all systems + + align:start position:0% +their ability to function in all systems + + + align:start position:0% +their ability to function in all systems +including uh the human body. So uh a key + + align:start position:0% +including uh the human body. So uh a key + + + align:start position:0% +including uh the human body. So uh a key +feature is that they can form complexes + + align:start position:0% +feature is that they can form complexes + + + align:start position:0% +feature is that they can form complexes +and let's look at why and so these + + align:start position:0% +and let's look at why and so these + + + align:start position:0% +and let's look at why and so these +complexes then of the metal and their + + align:start position:0% +complexes then of the metal and their + + + align:start position:0% +complexes then of the metal and their +lians are known as these coordination + + align:start position:0% +lians are known as these coordination + + + align:start position:0% +lians are known as these coordination +complexes. + + align:start position:0% +complexes. + + + align:start position:0% +complexes. +So you have a positive metal ion and it + + align:start position:0% +So you have a positive metal ion and it + + + align:start position:0% +So you have a positive metal ion and it +can attract electron density and that's + + align:start position:0% +can attract electron density and that's + + + align:start position:0% +can attract electron density and that's +usually in the form of a lone pair of + + align:start position:0% +usually in the form of a lone pair of + + + align:start position:0% +usually in the form of a lone pair of +electrons from another atom. And so when + + align:start position:0% +electrons from another atom. And so when + + + align:start position:0% +electrons from another atom. And so when +you bring together this metal and uh + + align:start position:0% +you bring together this metal and uh + + + align:start position:0% +you bring together this metal and uh +this other these other atoms and their + + align:start position:0% +this other these other atoms and their + + + align:start position:0% +this other these other atoms and their +lone pairs then you form this kind of + + align:start position:0% +lone pairs then you form this kind of + + + align:start position:0% +lone pairs then you form this kind of +complex. + + align:start position:0% +complex. + + + align:start position:0% +complex. +And so if we look at uh the different + + align:start position:0% +And so if we look at uh the different + + + align:start position:0% +And so if we look at uh the different +roles that things play you have uh donor + + align:start position:0% +roles that things play you have uh donor + + + align:start position:0% +roles that things play you have uh donor +atoms and uh they're called lians. So + + align:start position:0% +atoms and uh they're called lians. So + + + align:start position:0% +atoms and uh they're called lians. So +you often talk about a lian being + + align:start position:0% +you often talk about a lian being + + + align:start position:0% +you often talk about a lian being +coordinated to a metal + + align:start position:0% +coordinated to a metal + + + align:start position:0% +coordinated to a metal +and uh we mentioned uh lis acids and lis + + align:start position:0% +and uh we mentioned uh lis acids and lis + + + align:start position:0% +and uh we mentioned uh lis acids and lis +bases when we were talking about acid + + align:start position:0% +bases when we were talking about acid + + + align:start position:0% +bases when we were talking about acid +base and we didn't really do much with + + align:start position:0% +base and we didn't really do much with + + + align:start position:0% +base and we didn't really do much with +them when we were talking about acid + + align:start position:0% +them when we were talking about acid + + + align:start position:0% +them when we were talking about acid +base and I said this would come back + + align:start position:0% +base and I said this would come back + + + align:start position:0% +base and I said this would come back +later. So l acids and louis bases are + + align:start position:0% +later. So l acids and louis bases are + + + align:start position:0% +later. So l acids and louis bases are +very relevant in terms of talking about + + align:start position:0% +very relevant in terms of talking about + + + align:start position:0% +very relevant in terms of talking about +how coordination complexes are formed. + + align:start position:0% +how coordination complexes are formed. + + + align:start position:0% +how coordination complexes are formed. +So a leis base is going to uh donate + + align:start position:0% +So a leis base is going to uh donate + + + align:start position:0% +So a leis base is going to uh donate +lone pair electrons + + align:start position:0% +lone pair electrons + + + align:start position:0% +lone pair electrons +and here are some examples. Again these + + align:start position:0% +and here are some examples. Again these + + + align:start position:0% +and here are some examples. Again these +are referred to as lians and so they + + align:start position:0% +are referred to as lians and so they + + + align:start position:0% +are referred to as lians and so they +would be acting as lewis bases typically + + align:start position:0% +would be acting as lewis bases typically + + + align:start position:0% +would be acting as lewis bases typically +by donating their lone pair. So here are + + align:start position:0% +by donating their lone pair. So here are + + + align:start position:0% +by donating their lone pair. So here are +some of the ones that you're going to uh + + align:start position:0% +some of the ones that you're going to uh + + + align:start position:0% +some of the ones that you're going to uh +see uh in this unit and some of these + + align:start position:0% +see uh in this unit and some of these + + + align:start position:0% +see uh in this unit and some of these +will become familiar to you as we go + + align:start position:0% +will become familiar to you as we go + + + align:start position:0% +will become familiar to you as we go +through the next uh next few lectures. + + align:start position:0% +through the next uh next few lectures. + + + align:start position:0% +through the next uh next few lectures. +So they all have these lone pairs and uh + + align:start position:0% +So they all have these lone pairs and uh + + + align:start position:0% +So they all have these lone pairs and uh +the metal is very happy to see these + + align:start position:0% +the metal is very happy to see these + + + align:start position:0% +the metal is very happy to see these +lians coming and uh they will they will + + align:start position:0% +lians coming and uh they will they will + + + align:start position:0% +lians coming and uh they will they will +coordinate and form these coordination + + align:start position:0% +coordinate and form these coordination + + + align:start position:0% +coordinate and form these coordination +complexes. + + align:start position:0% + + + + align:start position:0% + +So then you need an acceptor atom and + + align:start position:0% +So then you need an acceptor atom and + + + align:start position:0% +So then you need an acceptor atom and +that's the transition metal. So that's + + align:start position:0% +that's the transition metal. So that's + + + align:start position:0% +that's the transition metal. So that's +going to act as the lis acid and it's + + align:start position:0% +going to act as the lis acid and it's + + + align:start position:0% +going to act as the lis acid and it's +going to accept that lone pair that is + + align:start position:0% +going to accept that lone pair that is + + + align:start position:0% +going to accept that lone pair that is +being donated by the lian. + + align:start position:0% +being donated by the lian. + + + align:start position:0% +being donated by the lian. +So let's look at some example of some of + + align:start position:0% +So let's look at some example of some of + + + align:start position:0% +So let's look at some example of some of +these metals and we saw some of these on + + align:start position:0% +these metals and we saw some of these on + + + align:start position:0% +these metals and we saw some of these on +the on the last uh on the periodic + + align:start position:0% +the on the last uh on the periodic + + + align:start position:0% +the on the last uh on the periodic +table. So these are all these DB block + + align:start position:0% +table. So these are all these DB block + + + align:start position:0% +table. So these are all these DB block +or transition metals. + + align:start position:0% +or transition metals. + + + align:start position:0% +or transition metals. +So then the coordination complex is the + + align:start position:0% +So then the coordination complex is the + + + align:start position:0% +So then the coordination complex is the +metals surrounded by the lians or the + + align:start position:0% +metals surrounded by the lians or the + + + align:start position:0% +metals surrounded by the lians or the +lis acids surrounded by the L bases. + + align:start position:0% + + + + align:start position:0% + +So here's a here's a picture. we have + + align:start position:0% +So here's a here's a picture. we have + + + align:start position:0% +So here's a here's a picture. we have +cobalt in this in the center here and + + align:start position:0% +cobalt in this in the center here and + + + align:start position:0% +cobalt in this in the center here and +then there there's six uh NH3 groups + + align:start position:0% +then there there's six uh NH3 groups + + + align:start position:0% +then there there's six uh NH3 groups +which are acting as the lians uh and + + align:start position:0% +which are acting as the lians uh and + + + align:start position:0% +which are acting as the lians uh and +their lone pairs are pointing toward + + align:start position:0% +their lone pairs are pointing toward + + + align:start position:0% +their lone pairs are pointing toward +toward the metal and so the again the + + align:start position:0% +toward the metal and so the again the + + + align:start position:0% +toward the metal and so the again the +coordination complex all is meant by + + align:start position:0% +coordination complex all is meant by + + + align:start position:0% +coordination complex all is meant by +that is the metal surrounded by the + + align:start position:0% +that is the metal surrounded by the + + + align:start position:0% +that is the metal surrounded by the +lians and uh in this case there's a + + align:start position:0% +lians and uh in this case there's a + + + align:start position:0% +lians and uh in this case there's a +little bracket on the side with a plus + + align:start position:0% +little bracket on the side with a plus + + + align:start position:0% +little bracket on the side with a plus +three charge and in for this particular + + align:start position:0% +three charge and in for this particular + + + align:start position:0% +three charge and in for this particular +complex you might have like three + + align:start position:0% +complex you might have like three + + + align:start position:0% +complex you might have like three +chloride ions hanging around. So, three + + align:start position:0% +chloride ions hanging around. So, three + + + align:start position:0% +chloride ions hanging around. So, three +negative charge ions to kind of + + align:start position:0% +negative charge ions to kind of + + + align:start position:0% +negative charge ions to kind of +counterbalance the fact that this + + align:start position:0% +counterbalance the fact that this + + + align:start position:0% +counterbalance the fact that this +coordination complex has a plus three + + align:start position:0% +coordination complex has a plus three + + + align:start position:0% +coordination complex has a plus three +overall charge. And so, the charge would + + align:start position:0% +overall charge. And so, the charge would + + + align:start position:0% +overall charge. And so, the charge would +be distributed, but it's indicated that + + align:start position:0% +be distributed, but it's indicated that + + + align:start position:0% +be distributed, but it's indicated that +this this whole complex has this charge + + align:start position:0% +this this whole complex has this charge + + + align:start position:0% +this this whole complex has this charge +by that little bracket and the plus + + align:start position:0% +by that little bracket and the plus + + + align:start position:0% +by that little bracket and the plus +three. + + align:start position:0% +three. + + + align:start position:0% +three. +So, again, here cobalt is acting as the + + align:start position:0% +So, again, here cobalt is acting as the + + + align:start position:0% +So, again, here cobalt is acting as the +Lewis acid. It's accepting the electrons + + align:start position:0% +Lewis acid. It's accepting the electrons + + + align:start position:0% +Lewis acid. It's accepting the electrons +that are being donated by the lians. So, + + align:start position:0% +that are being donated by the lians. So, + + + align:start position:0% +that are being donated by the lians. So, +it's the acceptor atom. + + align:start position:0% +it's the acceptor atom. + + + align:start position:0% +it's the acceptor atom. +And the NH3 groups are acting as the + + align:start position:0% +And the NH3 groups are acting as the + + + align:start position:0% +And the NH3 groups are acting as the +Lewis bases. They're the donor atoms. + + align:start position:0% +Lewis bases. They're the donor atoms. + + + align:start position:0% +Lewis bases. They're the donor atoms. +So, they're donating a lone pair of + + align:start position:0% +So, they're donating a lone pair of + + + align:start position:0% +So, they're donating a lone pair of +electrons. + + align:start position:0% + + + + align:start position:0% + +So, now we can introduce a term called + + align:start position:0% +So, now we can introduce a term called + + + align:start position:0% +So, now we can introduce a term called +coordination number CN. And that's + + align:start position:0% +coordination number CN. And that's + + + align:start position:0% +coordination number CN. And that's +pretty simple. is just the number of + + align:start position:0% +pretty simple. is just the number of + + + align:start position:0% +pretty simple. is just the number of +lians that are bonded to the metal. And + + align:start position:0% +lians that are bonded to the metal. And + + + align:start position:0% +lians that are bonded to the metal. And +so here there are six. So the + + align:start position:0% +so here there are six. So the + + + align:start position:0% +so here there are six. So the +coordination number is six. So that + + align:start position:0% +coordination number is six. So that + + + align:start position:0% +coordination number is six. So that +would be written as CN equals 6. And you + + align:start position:0% +would be written as CN equals 6. And you + + + align:start position:0% +would be written as CN equals 6. And you +have six lians comprising the primary + + align:start position:0% +have six lians comprising the primary + + + align:start position:0% +have six lians comprising the primary +coordination sphere. We also have three + + align:start position:0% +coordination sphere. We also have three + + + align:start position:0% +coordination sphere. We also have three +chlorines hanging around, but they're + + align:start position:0% +chlorines hanging around, but they're + + + align:start position:0% +chlorines hanging around, but they're +not coordinated to the metal. So they + + align:start position:0% +not coordinated to the metal. So they + + + align:start position:0% +not coordinated to the metal. So they +don't get counted in this. So you're + + align:start position:0% +don't get counted in this. So you're + + + align:start position:0% +don't get counted in this. So you're +only interested in the lians that are + + align:start position:0% +only interested in the lians that are + + + align:start position:0% +only interested in the lians that are +actually coordinated in the complex. + + align:start position:0% +actually coordinated in the complex. + + + align:start position:0% +actually coordinated in the complex. +So CN numbers typically range from 2 to + + align:start position:0% +So CN numbers typically range from 2 to + + + align:start position:0% +So CN numbers typically range from 2 to +12, but six is the most common. So + + align:start position:0% +12, but six is the most common. So + + + align:start position:0% +12, but six is the most common. So +you're going to be seeing a lot of + + align:start position:0% +you're going to be seeing a lot of + + + align:start position:0% +you're going to be seeing a lot of +different coordination complexes like + + align:start position:0% +different coordination complexes like + + + align:start position:0% +different coordination complexes like +this. + + align:start position:0% + + + + align:start position:0% + +And let me just show you how that would + + align:start position:0% +And let me just show you how that would + + + align:start position:0% +And let me just show you how that would +be written. So when you're doing a + + align:start position:0% +be written. So when you're doing a + + + align:start position:0% +be written. So when you're doing a +problem in your book, it's most likely + + align:start position:0% +problem in your book, it's most likely + + + align:start position:0% +problem in your book, it's most likely +not going to be drawn. you're going to + + align:start position:0% +not going to be drawn. you're going to + + + align:start position:0% +not going to be drawn. you're going to +see notation for this instead. And so + + align:start position:0% +see notation for this instead. And so + + + align:start position:0% +see notation for this instead. And so +this particular one would be indicated. + + align:start position:0% +this particular one would be indicated. + + + align:start position:0% +this particular one would be indicated. +You have the cobalt and then you have + + align:start position:0% +You have the cobalt and then you have + + + align:start position:0% +You have the cobalt and then you have +your NH3 groups. There are six of them. + + align:start position:0% +your NH3 groups. There are six of them. + + + align:start position:0% +your NH3 groups. There are six of them. +So that's indicated there. Then you have + + align:start position:0% +So that's indicated there. Then you have + + + align:start position:0% +So that's indicated there. Then you have +a bracket around the outside with a plus + + align:start position:0% +a bracket around the outside with a plus + + + align:start position:0% +a bracket around the outside with a plus +three. So that indicates that the charge + + align:start position:0% +three. So that indicates that the charge + + + align:start position:0% +three. So that indicates that the charge +of everything inside equals + three. + + align:start position:0% +of everything inside equals + three. + + + align:start position:0% +of everything inside equals + three. +You also might might see this where + + align:start position:0% +You also might might see this where + + + align:start position:0% +You also might might see this where +outside the bracket you have three + + align:start position:0% +outside the bracket you have three + + + align:start position:0% +outside the bracket you have three +chloride ions. And so you should be able + + align:start position:0% +chloride ions. And so you should be able + + + align:start position:0% +chloride ions. And so you should be able +to think backwards to this and say, + + align:start position:0% +to think backwards to this and say, + + + align:start position:0% +to think backwards to this and say, +well, we have if we have three things + + align:start position:0% +well, we have if we have three things + + + align:start position:0% +well, we have if we have three things +with a negative one charge. And you see + + align:start position:0% +with a negative one charge. And you see + + + align:start position:0% +with a negative one charge. And you see +why oxidation reduction unit was + + align:start position:0% +why oxidation reduction unit was + + + align:start position:0% +why oxidation reduction unit was +important before this because we talked + + align:start position:0% +important before this because we talked + + + align:start position:0% +important before this because we talked +about oxidation numbers and all the + + align:start position:0% +about oxidation numbers and all the + + + align:start position:0% +about oxidation numbers and all the +rules for assigning oxidation numbers. + + align:start position:0% +rules for assigning oxidation numbers. + + + align:start position:0% +rules for assigning oxidation numbers. +You're going to need that knowledge to + + align:start position:0% +You're going to need that knowledge to + + + align:start position:0% +You're going to need that knowledge to +do this unit as well. + + align:start position:0% +do this unit as well. + + + align:start position:0% +do this unit as well. +So uh you should know that that this is + + align:start position:0% +So uh you should know that that this is + + + align:start position:0% +So uh you should know that that this is +going to be minus minus1 for each + + align:start position:0% +going to be minus minus1 for each + + + align:start position:0% +going to be minus minus1 for each +chloride. So that would be three which + + align:start position:0% +chloride. So that would be three which + + + align:start position:0% +chloride. So that would be three which +would mean that if this is minus3 this + + align:start position:0% +would mean that if this is minus3 this + + + align:start position:0% +would mean that if this is minus3 this +bracket would be + three for this one + + align:start position:0% +bracket would be + three for this one + + + align:start position:0% +bracket would be + three for this one +down here is written to be neutral. So + + align:start position:0% +down here is written to be neutral. So + + + align:start position:0% +down here is written to be neutral. So +you'll be seeing this and need to back + + align:start position:0% +you'll be seeing this and need to back + + + align:start position:0% +you'll be seeing this and need to back +calculate. Then you're also going to + + align:start position:0% +calculate. Then you're also going to + + + align:start position:0% +calculate. Then you're also going to +need to calculate what the uh what the + + align:start position:0% +need to calculate what the uh what the + + + align:start position:0% +need to calculate what the uh what the +oxidation numbers of the things within + + align:start position:0% +oxidation numbers of the things within + + + align:start position:0% +oxidation numbers of the things within +the bracket are as well. And we'll talk + + align:start position:0% +the bracket are as well. And we'll talk + + + align:start position:0% +the bracket are as well. And we'll talk +more about that a little later in the + + align:start position:0% +more about that a little later in the + + + align:start position:0% +more about that a little later in the +lecture. So again, the NH3 within the + + align:start position:0% +lecture. So again, the NH3 within the + + + align:start position:0% +lecture. So again, the NH3 within the +brackets means it's bound to the cobalt. + + align:start position:0% +brackets means it's bound to the cobalt. + + + align:start position:0% +brackets means it's bound to the cobalt. +So that would be this picture here. + + align:start position:0% +So that would be this picture here. + + + align:start position:0% +So that would be this picture here. +There's six of them. So you would draw + + align:start position:0% +There's six of them. So you would draw + + + align:start position:0% +There's six of them. So you would draw +them uh as six around. And let me just + + align:start position:0% +them uh as six around. And let me just + + + align:start position:0% +them uh as six around. And let me just +uh mention a little bit about this + + align:start position:0% +uh mention a little bit about this + + + align:start position:0% +uh mention a little bit about this +particular configuration. So here these + + align:start position:0% +particular configuration. So here these + + + align:start position:0% +particular configuration. So here these +uh where there's sort of the thick lines + + align:start position:0% +uh where there's sort of the thick lines + + + align:start position:0% +uh where there's sort of the thick lines +coming out that indicates that it's + + align:start position:0% +coming out that indicates that it's + + + align:start position:0% +coming out that indicates that it's +coming toward you. + + align:start position:0% +coming toward you. + + + align:start position:0% +coming toward you. +So um + + align:start position:0% +So um + + + align:start position:0% +So um +here in this case you'd have two atoms + + align:start position:0% +here in this case you'd have two atoms + + + align:start position:0% +here in this case you'd have two atoms +coming toward you the dashed lines here + + align:start position:0% +coming toward you the dashed lines here + + + align:start position:0% +coming toward you the dashed lines here +are showing that there are two atoms + + align:start position:0% +are showing that there are two atoms + + + align:start position:0% +are showing that there are two atoms +back behind the plane and then when you + + align:start position:0% +back behind the plane and then when you + + + align:start position:0% +back behind the plane and then when you +have the straight line that's in the + + align:start position:0% +have the straight line that's in the + + + align:start position:0% +have the straight line that's in the +plane. So this picture here is showing + + align:start position:0% +plane. So this picture here is showing + + + align:start position:0% +plane. So this picture here is showing +you this type of geometry which is + + align:start position:0% +you this type of geometry which is + + + align:start position:0% +you this type of geometry which is +called what? + + align:start position:0% + + + + align:start position:0% + +Ocahedral geometry, right? + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So, let's talk about ocahedral geometry + + align:start position:0% +So, let's talk about ocahedral geometry + + + align:start position:0% +So, let's talk about ocahedral geometry +and the other geometries that you're + + align:start position:0% +and the other geometries that you're + + + align:start position:0% +and the other geometries that you're +going to see most often in this + + align:start position:0% +going to see most often in this + + + align:start position:0% +going to see most often in this +particular unit. And again, I'm going to + + align:start position:0% +particular unit. And again, I'm going to + + + align:start position:0% +particular unit. And again, I'm going to +do much more on this on on Wednesday, + + align:start position:0% +do much more on this on on Wednesday, + + + align:start position:0% +do much more on this on on Wednesday, +but this is just a very brief uh + + align:start position:0% +but this is just a very brief uh + + + align:start position:0% +but this is just a very brief uh +introduction to the structures that + + align:start position:0% +introduction to the structures that + + + align:start position:0% +introduction to the structures that +you'll see the most in this particular + + align:start position:0% +you'll see the most in this particular + + + align:start position:0% +you'll see the most in this particular +unit. + + align:start position:0% +unit. + + + align:start position:0% +unit. +So for a coordination number of six, + + align:start position:0% +So for a coordination number of six, + + + align:start position:0% +So for a coordination number of six, +you're just going to see one type of + + align:start position:0% +you're just going to see one type of + + + align:start position:0% +you're just going to see one type of +geometry, which is this ocahedral + + align:start position:0% +geometry, which is this ocahedral + + + align:start position:0% +geometry, which is this ocahedral +geometry, which I just showed you. + + align:start position:0% +geometry, which I just showed you. + + + align:start position:0% +geometry, which I just showed you. +For coordination number of five, you'll + + align:start position:0% +For coordination number of five, you'll + + + align:start position:0% +For coordination number of five, you'll +see two different types of geometry in + + align:start position:0% +see two different types of geometry in + + + align:start position:0% +see two different types of geometry in +uh in this unit. And uh let's take a + + align:start position:0% +uh in this unit. And uh let's take a + + + align:start position:0% +uh in this unit. And uh let's take a +look at this. The first one over here, + + align:start position:0% +look at this. The first one over here, + + + align:start position:0% +look at this. The first one over here, +the trigonal byparameal. + + align:start position:0% + + + + align:start position:0% + +So here here is an example of that and + + align:start position:0% +So here here is an example of that and + + + align:start position:0% +So here here is an example of that and +I'll try to have this as it is. Uh three + + align:start position:0% +I'll try to have this as it is. Uh three + + + align:start position:0% +I'll try to have this as it is. Uh three +lians are in the plane you have up and + + align:start position:0% +lians are in the plane you have up and + + + align:start position:0% +lians are in the plane you have up and +down and out here. One lian is pointing + + align:start position:0% +down and out here. One lian is pointing + + + align:start position:0% +down and out here. One lian is pointing +out toward you with the thick line and + + align:start position:0% +out toward you with the thick line and + + + align:start position:0% +out toward you with the thick line and +another lian is going back with the uh + + align:start position:0% +another lian is going back with the uh + + + align:start position:0% +another lian is going back with the uh +with the dashed line here. + + align:start position:0% +with the dashed line here. + + + align:start position:0% +with the dashed line here. +So that's that's one uh there. So let's + + align:start position:0% +So that's that's one uh there. So let's + + + align:start position:0% +So that's that's one uh there. So let's +go. We we talked about uh the geometry + + align:start position:0% +go. We we talked about uh the geometry + + + align:start position:0% +go. We we talked about uh the geometry +and uh I forgot to mention so those are + + align:start position:0% +and uh I forgot to mention so those are + + + align:start position:0% +and uh I forgot to mention so those are +90 degree angles which I think is pretty + + align:start position:0% +90 degree angles which I think is pretty + + + align:start position:0% +90 degree angles which I think is pretty +easy to see when you look at it that you + + align:start position:0% +easy to see when you look at it that you + + + align:start position:0% +easy to see when you look at it that you +would have 90 degrees in between those + + align:start position:0% +would have 90 degrees in between those + + + align:start position:0% +would have 90 degrees in between those +bonds. And what about for this one? What + + align:start position:0% +bonds. And what about for this one? What + + + align:start position:0% +bonds. And what about for this one? What +do we have going for the red? What kind + + align:start position:0% +do we have going for the red? What kind + + + align:start position:0% +do we have going for the red? What kind +of angle is that? + + align:start position:0% +of angle is that? + + + align:start position:0% +of angle is that? +120. And what about from the red to the + + align:start position:0% +120. And what about from the red to the + + + align:start position:0% +120. And what about from the red to the +black? + + align:start position:0% +black? + + + align:start position:0% +black? +90. + + align:start position:0% +90. + + + align:start position:0% +90. +So those are the angles we would see in + + align:start position:0% +So those are the angles we would see in + + + align:start position:0% +So those are the angles we would see in +here. And this is going to become + + align:start position:0% +here. And this is going to become + + + align:start position:0% +here. And this is going to become +important because we're going to be + + align:start position:0% +important because we're going to be + + + align:start position:0% +important because we're going to be +talking about d orbitals and where the + + align:start position:0% +talking about d orbitals and where the + + + align:start position:0% +talking about d orbitals and where the +d- orbitals are for the metal which is + + align:start position:0% +d- orbitals are for the metal which is + + + align:start position:0% +d- orbitals are for the metal which is +in the center of the coordination + + align:start position:0% +in the center of the coordination + + + align:start position:0% +in the center of the coordination +complex. So one of the issues we'll be + + align:start position:0% +complex. So one of the issues we'll be + + + align:start position:0% +complex. So one of the issues we'll be +discussing are where are the atoms with + + align:start position:0% +discussing are where are the atoms with + + + align:start position:0% +discussing are where are the atoms with +respect to those d orbitals. So geometry + + align:start position:0% +respect to those d orbitals. So geometry + + + align:start position:0% +respect to those d orbitals. So geometry +becomes important at this point. + + align:start position:0% +becomes important at this point. + + + align:start position:0% +becomes important at this point. +The other type of complex coordination + + align:start position:0% +The other type of complex coordination + + + align:start position:0% +The other type of complex coordination +complex you might see here the metal is + + align:start position:0% +complex you might see here the metal is + + + align:start position:0% +complex you might see here the metal is +gray in the middle and so then we have + + align:start position:0% +gray in the middle and so then we have + + + align:start position:0% +gray in the middle and so then we have +our lians bonded to it. If you have five + + align:start position:0% +our lians bonded to it. If you have five + + + align:start position:0% +our lians bonded to it. If you have five +lians, you also might see this geometry + + align:start position:0% +lians, you also might see this geometry + + + align:start position:0% +lians, you also might see this geometry +here. So the square parameal geometry + + align:start position:0% +here. So the square parameal geometry + + + align:start position:0% +here. So the square parameal geometry +and what are what are the angles between + + align:start position:0% +and what are what are the angles between + + + align:start position:0% +and what are what are the angles between +all of the atoms here? + + align:start position:0% +all of the atoms here? + + + align:start position:0% +all of the atoms here? +90. + + align:start position:0% +90. + + + align:start position:0% +90. +All right. So now in the case where you + + align:start position:0% +All right. So now in the case where you + + + align:start position:0% +All right. So now in the case where you +have four lians bound to your central + + align:start position:0% +have four lians bound to your central + + + align:start position:0% +have four lians bound to your central +metal, there's two possibilities for the + + align:start position:0% +metal, there's two possibilities for the + + + align:start position:0% +metal, there's two possibilities for the +geometry that you'll see. Uh one is + + align:start position:0% +geometry that you'll see. Uh one is + + + align:start position:0% +geometry that you'll see. Uh one is +square planer. So in this case it's + + align:start position:0% +square planer. So in this case it's + + + align:start position:0% +square planer. So in this case it's +drawn with two lians coming out towards + + align:start position:0% +drawn with two lians coming out towards + + + align:start position:0% +drawn with two lians coming out towards +you and two lians going behind. And what + + align:start position:0% +you and two lians going behind. And what + + + align:start position:0% +you and two lians going behind. And what +would be the geometry between these + + align:start position:0% +would be the geometry between these + + + align:start position:0% +would be the geometry between these +guys? + + align:start position:0% +guys? + + + align:start position:0% +guys? +90 as well. And so this is one of the + + align:start position:0% +90 as well. And so this is one of the + + + align:start position:0% +90 as well. And so this is one of the +easy ones to remember because it's a + + align:start position:0% +easy ones to remember because it's a + + + align:start position:0% +easy ones to remember because it's a +square and it's planer. So that's a an + + align:start position:0% +square and it's planer. So that's a an + + + align:start position:0% +square and it's planer. So that's a an +easy one to remember. + + align:start position:0% + + + + align:start position:0% + +The other that you might see when you + + align:start position:0% +The other that you might see when you + + + align:start position:0% +The other that you might see when you +have four lians is this guy tetrahedral. + + align:start position:0% +have four lians is this guy tetrahedral. + + + align:start position:0% +have four lians is this guy tetrahedral. +And what are the angles here? + + align:start position:0% +And what are the angles here? + + + align:start position:0% +And what are the angles here? +Yep. 109.5. + + align:start position:0% + + + + align:start position:0% + +And then if you have three lians, pretty + + align:start position:0% +And then if you have three lians, pretty + + + align:start position:0% +And then if you have three lians, pretty +much this is all you're going to see in + + align:start position:0% +much this is all you're going to see in + + + align:start position:0% +much this is all you're going to see in +this unit. And so we have the trigonal + + align:start position:0% +this unit. And so we have the trigonal + + + align:start position:0% +this unit. And so we have the trigonal +um trigonal planer. Again, it looks and + + align:start position:0% +um trigonal planer. Again, it looks and + + + align:start position:0% +um trigonal planer. Again, it looks and +it's also quite planer. And what are our + + align:start position:0% +it's also quite planer. And what are our + + + align:start position:0% +it's also quite planer. And what are our +angles here? + + align:start position:0% +angles here? + + + align:start position:0% +angles here? +120. + + align:start position:0% +120. + + + align:start position:0% +120. +And linear + + align:start position:0% +And linear + + + align:start position:0% +And linear +is going to give you what what angle? + + align:start position:0% +is going to give you what what angle? + + + align:start position:0% +is going to give you what what angle? +180. So you'll see this this one as + + align:start position:0% +180. So you'll see this this one as + + + align:start position:0% +180. So you'll see this this one as +well. And this this model is a little + + align:start position:0% +well. And this this model is a little + + + align:start position:0% +well. And this this model is a little +old. So it's not really so linear + + align:start position:0% +old. So it's not really so linear + + + align:start position:0% +old. So it's not really so linear +anymore, but it's still supposed to be. + + align:start position:0% +anymore, but it's still supposed to be. + + + align:start position:0% +anymore, but it's still supposed to be. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So we're going to bring back I'm going + + align:start position:0% +So we're going to bring back I'm going + + + align:start position:0% +So we're going to bring back I'm going +to bring these models to class for a lot + + align:start position:0% +to bring these models to class for a lot + + + align:start position:0% +to bring these models to class for a lot +of the next lectures because thinking + + align:start position:0% +of the next lectures because thinking + + + align:start position:0% +of the next lectures because thinking +about the structure is going to be very + + align:start position:0% +about the structure is going to be very + + + align:start position:0% +about the structure is going to be very +important in thinking about uh the + + align:start position:0% +important in thinking about uh the + + + align:start position:0% +important in thinking about uh the +properties of transition metals. + + align:start position:0% + + + + align:start position:0% + +All right. So what else can transition + + align:start position:0% +All right. So what else can transition + + + align:start position:0% +All right. So what else can transition +metals do? What are some of the other + + align:start position:0% +metals do? What are some of the other + + + align:start position:0% +metals do? What are some of the other +things? Um so when you talk about + + align:start position:0% +things? Um so when you talk about + + + align:start position:0% +things? Um so when you talk about +transition metals and coordination + + align:start position:0% +transition metals and coordination + + + align:start position:0% +transition metals and coordination +complexes, you need to talk about the + + align:start position:0% +complexes, you need to talk about the + + + align:start position:0% +complexes, you need to talk about the +chilate effect. So we've seen so far + + align:start position:0% +chilate effect. So we've seen so far + + + align:start position:0% +chilate effect. So we've seen so far +lians binding at one site but some + + align:start position:0% +lians binding at one site but some + + + align:start position:0% +lians binding at one site but some +ligans can bind a metal at uh more than + + align:start position:0% +ligans can bind a metal at uh more than + + + align:start position:0% +ligans can bind a metal at uh more than +one site and so then you start talking + + align:start position:0% +one site and so then you start talking + + + align:start position:0% +one site and so then you start talking +about chelates. So first a lian that can + + align:start position:0% +about chelates. So first a lian that can + + + align:start position:0% +about chelates. So first a lian that can +bind a metal at one site is called + + align:start position:0% +bind a metal at one site is called + + + align:start position:0% +bind a metal at one site is called +unidentate or monodentate and the dent + + align:start position:0% +unidentate or monodentate and the dent + + + align:start position:0% +unidentate or monodentate and the dent +comes from dentist or tooth. So this + + align:start position:0% +comes from dentist or tooth. So this + + + align:start position:0% +comes from dentist or tooth. So this +would be one. + + align:start position:0% +would be one. + + + align:start position:0% +would be one. +If you have a lian that can bind at more + + align:start position:0% +If you have a lian that can bind at more + + + align:start position:0% +If you have a lian that can bind at more +than one point of attachment + + align:start position:0% +than one point of attachment + + + align:start position:0% +than one point of attachment +then it's called a chelating liant and + + align:start position:0% +then it's called a chelating liant and + + + align:start position:0% +then it's called a chelating liant and +the coordination complex that it forms + + align:start position:0% +the coordination complex that it forms + + + align:start position:0% +the coordination complex that it forms +is called achilate + + align:start position:0% +is called achilate + + + align:start position:0% +is called achilate +and so this is Greek for claws. So it + + align:start position:0% +and so this is Greek for claws. So it + + + align:start position:0% +and so this is Greek for claws. So it +seems like claws are coming down and + + align:start position:0% +seems like claws are coming down and + + + align:start position:0% +seems like claws are coming down and +binding to to the metal. + + align:start position:0% +binding to to the metal. + + + align:start position:0% +binding to to the metal. +So anything above one would be + + align:start position:0% +So anything above one would be + + + align:start position:0% +So anything above one would be +considered a chilate if it has two + + align:start position:0% +considered a chilate if it has two + + + align:start position:0% +considered a chilate if it has two +points of attachment or three or four. + + align:start position:0% +points of attachment or three or four. + + + align:start position:0% +points of attachment or three or four. +Uh so by dentate means two points and + + align:start position:0% +Uh so by dentate means two points and + + + align:start position:0% +Uh so by dentate means two points and +this nomenclature not too challenging. + + align:start position:0% +this nomenclature not too challenging. + + + align:start position:0% +this nomenclature not too challenging. +People are usually pretty good at + + align:start position:0% +People are usually pretty good at + + + align:start position:0% +People are usually pretty good at +guessing what they mean. Uh tridentate + + align:start position:0% +guessing what they mean. Uh tridentate + + + align:start position:0% +guessing what they mean. Uh tridentate +would have how many points of + + align:start position:0% +would have how many points of + + + align:start position:0% +would have how many points of +attachment? + + align:start position:0% +attachment? + + + align:start position:0% +attachment? +Three. Tetraentate. + + align:start position:0% +Three. Tetraentate. + + + align:start position:0% +Three. Tetraentate. +Hexadentate. + + align:start position:0% +Hexadentate. + + + align:start position:0% +Hexadentate. +Six. There are some people, this was a + + align:start position:0% +Six. There are some people, this was a + + + align:start position:0% +Six. There are some people, this was a +question, uh, I think a hexodate on a + + align:start position:0% +question, uh, I think a hexodate on a + + + align:start position:0% +question, uh, I think a hexodate on a +final one year, people got it wrong. + + align:start position:0% +final one year, people got it wrong. + + + align:start position:0% +final one year, people got it wrong. +Don't get something like that wrong. + + align:start position:0% +Don't get something like that wrong. + + + align:start position:0% +Don't get something like that wrong. +Save the things you're going to get + + align:start position:0% +Save the things you're going to get + + + align:start position:0% +Save the things you're going to get +wrong for the really hard part. This is + + align:start position:0% +wrong for the really hard part. This is + + + align:start position:0% +wrong for the really hard part. This is +really not so difficult. Uh, so that + + align:start position:0% +really not so difficult. Uh, so that + + + align:start position:0% +really not so difficult. Uh, so that +that should be some uh, bonus points + + align:start position:0% +that should be some uh, bonus points + + + align:start position:0% +that should be some uh, bonus points +there for you. If you remember the + + align:start position:0% +there for you. If you remember the + + + align:start position:0% +there for you. If you remember the +dentate, and this term actually gets + + align:start position:0% +dentate, and this term actually gets + + + align:start position:0% +dentate, and this term actually gets +used quite a bit, uh, you'll be all set. + + align:start position:0% +used quite a bit, uh, you'll be all set. + + + align:start position:0% +used quite a bit, uh, you'll be all set. +All right. So, what is the chilate + + align:start position:0% +All right. So, what is the chilate + + + align:start position:0% +All right. So, what is the chilate +effect? So chilates are lians that + + align:start position:0% +effect? So chilates are lians that + + + align:start position:0% +effect? So chilates are lians that +combined at more than one point of + + align:start position:0% +combined at more than one point of + + + align:start position:0% +combined at more than one point of +attachment. What's the chilate effect? + + align:start position:0% +attachment. What's the chilate effect? + + + align:start position:0% +attachment. What's the chilate effect? +Well, it turns out that metal chilates + + align:start position:0% +Well, it turns out that metal chilates + + + align:start position:0% +Well, it turns out that metal chilates +are very very stable. And so this is a + + align:start position:0% +are very very stable. And so this is a + + + align:start position:0% +are very very stable. And so this is a +thermodynamic property that they have. + + align:start position:0% +thermodynamic property that they have. + + + align:start position:0% +thermodynamic property that they have. +And uh it's believed or the rationale + + align:start position:0% +And uh it's believed or the rationale + + + align:start position:0% +And uh it's believed or the rationale +for this stability which is observed is + + align:start position:0% +for this stability which is observed is + + + align:start position:0% +for this stability which is observed is +that it's an entropic factor that's + + align:start position:0% +that it's an entropic factor that's + + + align:start position:0% +that it's an entropic factor that's +going on. So the binding of that chilate + + align:start position:0% +going on. So the binding of that chilate + + + align:start position:0% +going on. So the binding of that chilate +at more than one point of attachment is + + align:start position:0% +at more than one point of attachment is + + + align:start position:0% +at more than one point of attachment is +entropically favorable because you're + + align:start position:0% +entropically favorable because you're + + + align:start position:0% +entropically favorable because you're +going to be releasing waters as you do + + align:start position:0% +going to be releasing waters as you do + + + align:start position:0% +going to be releasing waters as you do +this. So we're going to come back and + + align:start position:0% +this. So we're going to come back and + + + align:start position:0% +this. So we're going to come back and +I'm going to explain this uh using an + + align:start position:0% +I'm going to explain this uh using an + + + align:start position:0% +I'm going to explain this uh using an +example in a few minutes. + + align:start position:0% +example in a few minutes. + + + align:start position:0% +example in a few minutes. +So first let me give you some examples + + align:start position:0% +So first let me give you some examples + + + align:start position:0% +So first let me give you some examples +of chelates and then I'll show you how + + align:start position:0% +of chelates and then I'll show you how + + + align:start position:0% +of chelates and then I'll show you how +this chilate effect could work. So there + + align:start position:0% +this chilate effect could work. So there + + + align:start position:0% +this chilate effect could work. So there +are examples of chilates in biological + + align:start position:0% +are examples of chilates in biological + + + align:start position:0% +are examples of chilates in biological +systems and it may not be a surprise to + + align:start position:0% +systems and it may not be a surprise to + + + align:start position:0% +systems and it may not be a surprise to +some of you that one of the chilates is + + align:start position:0% +some of you that one of the chilates is + + + align:start position:0% +some of you that one of the chilates is +vitamin B12 and that would be one that I + + align:start position:0% +vitamin B12 and that would be one that I + + + align:start position:0% +vitamin B12 and that would be one that I +would pick to mention in particular. Uh + + align:start position:0% +would pick to mention in particular. Uh + + + align:start position:0% +would pick to mention in particular. Uh +so here the chilate this is all one + + align:start position:0% +so here the chilate this is all one + + + align:start position:0% +so here the chilate this is all one +lian. This this whole bottom part is + + align:start position:0% +lian. This this whole bottom part is + + + align:start position:0% +lian. This this whole bottom part is +attached. It's one lian. So we have uh + + align:start position:0% +attached. It's one lian. So we have uh + + + align:start position:0% +attached. It's one lian. So we have uh +this called the corin ring. You have + + align:start position:0% +this called the corin ring. You have + + + align:start position:0% +this called the corin ring. You have +cobalt in the middle and it's + + align:start position:0% +cobalt in the middle and it's + + + align:start position:0% +cobalt in the middle and it's +coordinated by this planer part and you + + align:start position:0% +coordinated by this planer part and you + + + align:start position:0% +coordinated by this planer part and you +have four nitrogen lians uh + + align:start position:0% +have four nitrogen lians uh + + + align:start position:0% +have four nitrogen lians uh +coordinating. So it's one ringed system + + align:start position:0% +coordinating. So it's one ringed system + + + align:start position:0% +coordinating. So it's one ringed system +here called the corin ring that is + + align:start position:0% +here called the corin ring that is + + + align:start position:0% +here called the corin ring that is +attaching at four points of attachment. + + align:start position:0% +attaching at four points of attachment. + + + align:start position:0% +attaching at four points of attachment. +You also have an upper liant here and + + align:start position:0% +You also have an upper liant here and + + + align:start position:0% +You also have an upper liant here and +this is this is an adenosil muy and we + + align:start position:0% +this is this is an adenosil muy and we + + + align:start position:0% +this is this is an adenosil muy and we +have a lower liant and we talked about + + align:start position:0% +have a lower liant and we talked about + + + align:start position:0% +have a lower liant and we talked about +this before with buffers effects because + + align:start position:0% +this before with buffers effects because + + + align:start position:0% +this before with buffers effects because +if this lower ligant is detached on the + + align:start position:0% +if this lower ligant is detached on the + + + align:start position:0% +if this lower ligant is detached on the +protein it has to fit into a binding + + align:start position:0% +protein it has to fit into a binding + + + align:start position:0% +protein it has to fit into a binding +site and genetic defects that block that + + align:start position:0% +site and genetic defects that block that + + + align:start position:0% +site and genetic defects that block that +uh impair the activity of the enzyme + + align:start position:0% +uh impair the activity of the enzyme + + + align:start position:0% +uh impair the activity of the enzyme +that was uh mentioned before. So this + + align:start position:0% +that was uh mentioned before. So this + + + align:start position:0% +that was uh mentioned before. So this +actually has six different lians and + + align:start position:0% +actually has six different lians and + + + align:start position:0% +actually has six different lians and +will classify as a keelate or six + + align:start position:0% +will classify as a keelate or six + + + align:start position:0% +will classify as a keelate or six +different points of attachment uh and + + align:start position:0% +different points of attachment uh and + + + align:start position:0% +different points of attachment uh and +classifies as as a chilate. + + align:start position:0% +classifies as as a chilate. + + + align:start position:0% +classifies as as a chilate. +So let me just sort of spin that around + + align:start position:0% +So let me just sort of spin that around + + + align:start position:0% +So let me just sort of spin that around +so you can kind of get a sense of the + + align:start position:0% +so you can kind of get a sense of the + + + align:start position:0% +so you can kind of get a sense of the +geometry here. So again here's the + + align:start position:0% +geometry here. So again here's the + + + align:start position:0% +geometry here. So again here's the +cobalt in the middle, the upper lian and + + align:start position:0% +cobalt in the middle, the upper lian and + + + align:start position:0% +cobalt in the middle, the upper lian and +the lower lian. And if we move that + + align:start position:0% +the lower lian. And if we move that + + + align:start position:0% +the lower lian. And if we move that +around, see if you can get a sense of + + align:start position:0% +around, see if you can get a sense of + + + align:start position:0% +around, see if you can get a sense of +the sort of geometry uh around that + + align:start position:0% +the sort of geometry uh around that + + + align:start position:0% +the sort of geometry uh around that +cobalt. + + align:start position:0% +cobalt. + + + align:start position:0% +cobalt. +So you have four in a plane here, one on + + align:start position:0% +So you have four in a plane here, one on + + + align:start position:0% +So you have four in a plane here, one on +top and one on bottom. So it's sort of a + + align:start position:0% +top and one on bottom. So it's sort of a + + + align:start position:0% +top and one on bottom. So it's sort of a +an ocahedral type coordination of that + + align:start position:0% +an ocahedral type coordination of that + + + align:start position:0% +an ocahedral type coordination of that +metal in the center. + + align:start position:0% +metal in the center. + + + align:start position:0% +metal in the center. +I thought I would just mention um the + + align:start position:0% +I thought I would just mention um the + + + align:start position:0% +I thought I would just mention um the +person who determined the structure of + + align:start position:0% +person who determined the structure of + + + align:start position:0% +person who determined the structure of +uh vitamin B12 and uh that's Dorothy + + align:start position:0% +uh vitamin B12 and uh that's Dorothy + + + align:start position:0% +uh vitamin B12 and uh that's Dorothy +Hodkin. um for her work on this and on + + align:start position:0% +Hodkin. um for her work on this and on + + + align:start position:0% +Hodkin. um for her work on this and on +penicellin she received a Nobel prize + + align:start position:0% +penicellin she received a Nobel prize + + + align:start position:0% +penicellin she received a Nobel prize +because at the time she was studying + + align:start position:0% +because at the time she was studying + + + align:start position:0% +because at the time she was studying +this structure it was really considered + + align:start position:0% +this structure it was really considered + + + align:start position:0% +this structure it was really considered +very large for the technique that she + + align:start position:0% +very large for the technique that she + + + align:start position:0% +very large for the technique that she +used which is X-ray crystalallography + + align:start position:0% +used which is X-ray crystalallography + + + align:start position:0% +used which is X-ray crystalallography +and people didn't think she would be + + align:start position:0% +and people didn't think she would be + + + align:start position:0% +and people didn't think she would be +able to determine where all those atoms + + align:start position:0% +able to determine where all those atoms + + + align:start position:0% +able to determine where all those atoms +were located in something that was that + + align:start position:0% +were located in something that was that + + + align:start position:0% +were located in something that was that +big using crystalallography. Uh since + + align:start position:0% +big using crystalallography. Uh since + + + align:start position:0% +big using crystalallography. Uh since +then we have gone on to solve much + + align:start position:0% +then we have gone on to solve much + + + align:start position:0% +then we have gone on to solve much +larger structures. uh but she really + + align:start position:0% +larger structures. uh but she really + + + align:start position:0% +larger structures. uh but she really +opened the doors for people thinking + + align:start position:0% +opened the doors for people thinking + + + align:start position:0% +opened the doors for people thinking +about this technique as being important + + align:start position:0% +about this technique as being important + + + align:start position:0% +about this technique as being important +in biological systems. Uh she had uh a + + align:start position:0% +in biological systems. Uh she had uh a + + + align:start position:0% +in biological systems. Uh she had uh a +number of graduate students who went on + + align:start position:0% +number of graduate students who went on + + + align:start position:0% +number of graduate students who went on +to do some pretty spectacular things and + + align:start position:0% +to do some pretty spectacular things and + + + align:start position:0% +to do some pretty spectacular things and +really helped to establish the field of + + align:start position:0% +really helped to establish the field of + + + align:start position:0% +really helped to establish the field of +crystalallography. And I'll just mention + + align:start position:0% +crystalallography. And I'll just mention + + + align:start position:0% +crystalallography. And I'll just mention +one of her graduate students who was not + + align:start position:0% +one of her graduate students who was not + + + align:start position:0% +one of her graduate students who was not +as successful as a crystalallographer. + + align:start position:0% +as successful as a crystalallographer. + + + align:start position:0% +as successful as a crystalallographer. +This is what I do. And you know not + + align:start position:0% +This is what I do. And you know not + + + align:start position:0% +This is what I do. And you know not +everybody can do X-ray + + align:start position:0% +everybody can do X-ray + + + align:start position:0% +everybody can do X-ray +crystalallography. it's a bit + + align:start position:0% +crystalallography. it's a bit + + + align:start position:0% +crystalallography. it's a bit +challenging and some people had to sort + + align:start position:0% +challenging and some people had to sort + + + align:start position:0% +challenging and some people had to sort +of find something else to do with their + + align:start position:0% +of find something else to do with their + + + align:start position:0% +of find something else to do with their +lives. So, one of her students um didn't + + align:start position:0% +lives. So, one of her students um didn't + + + align:start position:0% +lives. So, one of her students um didn't +quite cut it as a crystalallographer. + + align:start position:0% +quite cut it as a crystalallographer. + + + align:start position:0% +quite cut it as a crystalallographer. +But, uh the good news is she was still + + align:start position:0% +But, uh the good news is she was still + + + align:start position:0% +But, uh the good news is she was still +able to find a job. So, um and it's + + align:start position:0% +able to find a job. So, um and it's + + + align:start position:0% +able to find a job. So, um and it's +actually kind of interesting that + + align:start position:0% +actually kind of interesting that + + + align:start position:0% +actually kind of interesting that +Dorothy Hodkin was a real socialist. She + + align:start position:0% +Dorothy Hodkin was a real socialist. She + + + align:start position:0% +Dorothy Hodkin was a real socialist. She +was very involved in left-wing issues, + + align:start position:0% +was very involved in left-wing issues, + + + align:start position:0% +was very involved in left-wing issues, +but uh she stayed friends with Margaret + + align:start position:0% +but uh she stayed friends with Margaret + + + align:start position:0% +but uh she stayed friends with Margaret +Thatcher throughout the years, and it + + align:start position:0% +Thatcher throughout the years, and it + + + align:start position:0% +Thatcher throughout the years, and it +would have been very interesting to be + + align:start position:0% +would have been very interesting to be + + + align:start position:0% +would have been very interesting to be +in a living room with the two of them + + align:start position:0% +in a living room with the two of them + + + align:start position:0% +in a living room with the two of them +hearing them talk about politics. + + align:start position:0% +hearing them talk about politics. + + + align:start position:0% +hearing them talk about politics. +Maybe they would talk about + + align:start position:0% +Maybe they would talk about + + + align:start position:0% +Maybe they would talk about +crystalallography. I don't really know + + align:start position:0% +crystalallography. I don't really know + + + align:start position:0% +crystalallography. I don't really know +if they were together. That might have + + align:start position:0% +if they were together. That might have + + + align:start position:0% +if they were together. That might have +been safer. Okay, so that's one example + + align:start position:0% +been safer. Okay, so that's one example + + + align:start position:0% +been safer. Okay, so that's one example +of a keelate. Here is another example of + + align:start position:0% +of a keelate. Here is another example of + + + align:start position:0% +of a keelate. Here is another example of +a chilate and this is called EDTA. + + align:start position:0% +a chilate and this is called EDTA. + + + align:start position:0% +a chilate and this is called EDTA. +And so it has many points for attachment + + align:start position:0% +And so it has many points for attachment + + + align:start position:0% +And so it has many points for attachment +to a metal. So we have a lone pair up + + align:start position:0% +to a metal. So we have a lone pair up + + + align:start position:0% +to a metal. So we have a lone pair up +here on this atom. So we have a donor + + align:start position:0% +here on this atom. So we have a donor + + + align:start position:0% +here on this atom. So we have a donor +here. We have another lone pair. Another + + align:start position:0% +here. We have another lone pair. Another + + + align:start position:0% +here. We have another lone pair. Another +donor site here. Another lone pair. + + align:start position:0% +donor site here. Another lone pair. + + + align:start position:0% +donor site here. Another lone pair. +Another donor site here. Also over here + + align:start position:0% +Another donor site here. Also over here + + + align:start position:0% +Another donor site here. Also over here +and here and here. So there's this lian + + align:start position:0% +and here and here. So there's this lian + + + align:start position:0% +and here and here. So there's this lian +can attach to something in six places. + + align:start position:0% + + + + align:start position:0% + +So here again is uh the free molecule + + align:start position:0% +So here again is uh the free molecule + + + align:start position:0% +So here again is uh the free molecule +and here's what it looks like when it's + + align:start position:0% +and here's what it looks like when it's + + + align:start position:0% +and here's what it looks like when it's +attached to the metal. So see this uh + + align:start position:0% +attached to the metal. So see this uh + + + align:start position:0% +attached to the metal. So see this uh +this oxygen here over here and then if + + align:start position:0% +this oxygen here over here and then if + + + align:start position:0% +this oxygen here over here and then if +you follow it down over here this + + align:start position:0% +you follow it down over here this + + + align:start position:0% +you follow it down over here this +nitrogen is also coordinated. Uh if we + + align:start position:0% +nitrogen is also coordinated. Uh if we + + + align:start position:0% +nitrogen is also coordinated. Uh if we +go over here then this oxygen is is + + align:start position:0% +go over here then this oxygen is is + + + align:start position:0% +go over here then this oxygen is is +coordinated. If we come from this + + align:start position:0% +coordinated. If we come from this + + + align:start position:0% +coordinated. If we come from this +nitrogen over to the other nitrogen it's + + align:start position:0% +nitrogen over to the other nitrogen it's + + + align:start position:0% +nitrogen over to the other nitrogen it's +over here. go down to this oxygen. This + + align:start position:0% +over here. go down to this oxygen. This + + + align:start position:0% +over here. go down to this oxygen. This +oxygen's coordinated down here. And then + + align:start position:0% +oxygen's coordinated down here. And then + + + align:start position:0% +oxygen's coordinated down here. And then +in purple, we have the last + + align:start position:0% +in purple, we have the last + + + align:start position:0% +in purple, we have the last +coordination. + + align:start position:0% +coordination. + + + align:start position:0% +coordination. +So what is the uh geometry around that + + align:start position:0% +So what is the uh geometry around that + + + align:start position:0% +So what is the uh geometry around that +that metal site? + + align:start position:0% +that metal site? + + + align:start position:0% +that metal site? +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +What what is uh you have these six + + align:start position:0% +What what is uh you have these six + + + align:start position:0% +What what is uh you have these six +lians. So what's that going to be? + + align:start position:0% +lians. So what's that going to be? + + + align:start position:0% +lians. So what's that going to be? +It's going to be an ocahedral. + + align:start position:0% +It's going to be an ocahedral. + + + align:start position:0% +It's going to be an ocahedral. +You should have angles around 90. And uh + + align:start position:0% +You should have angles around 90. And uh + + + align:start position:0% +You should have angles around 90. And uh +it's also hexodentate. So you have a + + align:start position:0% +it's also hexodentate. So you have a + + + align:start position:0% +it's also hexodentate. So you have a +lian binding with six points of + + align:start position:0% +lian binding with six points of + + + align:start position:0% +lian binding with six points of +attachment. It would also have a CN + + align:start position:0% +attachment. It would also have a CN + + + align:start position:0% +attachment. It would also have a CN +number then of six. + + align:start position:0% + + + + align:start position:0% + +So uh why is the keelate effect why do + + align:start position:0% +So uh why is the keelate effect why do + + + align:start position:0% +So uh why is the keelate effect why do +why are complexes like that so stable? + + align:start position:0% +why are complexes like that so stable? + + + align:start position:0% +why are complexes like that so stable? +So the keelate effect could be uh viewed + + align:start position:0% +So the keelate effect could be uh viewed + + + align:start position:0% +So the keelate effect could be uh viewed +in in this slide. So before you have the + + align:start position:0% +in in this slide. So before you have the + + + align:start position:0% +in in this slide. So before you have the +EDTA bound we have six water molecules + + align:start position:0% +EDTA bound we have six water molecules + + + align:start position:0% +EDTA bound we have six water molecules +around it. Then we bind one molecule of + + align:start position:0% +around it. Then we bind one molecule of + + + align:start position:0% +around it. Then we bind one molecule of +EDTA and it binds in the hexodentate + + align:start position:0% +EDTA and it binds in the hexodentate + + + align:start position:0% +EDTA and it binds in the hexodentate +complex releasing all six waters. + + align:start position:0% +complex releasing all six waters. + + + align:start position:0% +complex releasing all six waters. +So where is entropy greater? When you + + align:start position:0% +So where is entropy greater? When you + + + align:start position:0% +So where is entropy greater? When you +have one free thing or when you have six + + align:start position:0% +have one free thing or when you have six + + + align:start position:0% +have one free thing or when you have six +free things? + + align:start position:0% +free things? + + + align:start position:0% +free things? +Six. So this is entropically favorable. + + align:start position:0% +Six. So this is entropically favorable. + + + align:start position:0% +Six. So this is entropically favorable. +You're creating disorder. You're binding + + align:start position:0% +You're creating disorder. You're binding + + + align:start position:0% +You're creating disorder. You're binding +one thing and releasing six things. So + + align:start position:0% +one thing and releasing six things. So + + + align:start position:0% +one thing and releasing six things. So +that's why these complexes are really + + align:start position:0% +that's why these complexes are really + + + align:start position:0% +that's why these complexes are really +quite stable. + + align:start position:0% +quite stable. + + + align:start position:0% +quite stable. +So we're getting back to entropy now. + + align:start position:0% +So we're getting back to entropy now. + + + align:start position:0% +So we're getting back to entropy now. +We've been talking about delta G. We had + + align:start position:0% +We've been talking about delta G. We had + + + align:start position:0% +We've been talking about delta G. We had +delta H. Now we have delta S. + + align:start position:0% + + + + align:start position:0% + +So that's the chilate effect. We talk + + align:start position:0% +So that's the chilate effect. We talk + + + align:start position:0% +So that's the chilate effect. We talk +about it due to this entropic effect + + align:start position:0% +about it due to this entropic effect + + + align:start position:0% +about it due to this entropic effect +accompanied by the release of + + align:start position:0% +accompanied by the release of + + + align:start position:0% +accompanied by the release of +non-elating lians usually water uh from + + align:start position:0% +non-elating lians usually water uh from + + + align:start position:0% +non-elating lians usually water uh from +the coordination sphere. So one in this + + align:start position:0% +the coordination sphere. So one in this + + + align:start position:0% +the coordination sphere. So one in this +case one lian binding displacing fix six + + align:start position:0% +case one lian binding displacing fix six + + + align:start position:0% +case one lian binding displacing fix six +things is favorable. + + align:start position:0% + + + + align:start position:0% + +So the keelate effect leads to a lot of + + align:start position:0% +So the keelate effect leads to a lot of + + + align:start position:0% +So the keelate effect leads to a lot of +practical uses. So here um some of the + + align:start position:0% +practical uses. So here um some of the + + + align:start position:0% +practical uses. So here um some of the +uses would be in medicine. + + align:start position:0% +uses would be in medicine. + + + align:start position:0% +uses would be in medicine. +If you discover over Thanksgiving that + + align:start position:0% +If you discover over Thanksgiving that + + + align:start position:0% +If you discover over Thanksgiving that +your uh you know one and a halfyear-old + + align:start position:0% +your uh you know one and a halfyear-old + + + align:start position:0% +your uh you know one and a halfyear-old +uh niece or nephew has discovered paint + + align:start position:0% +uh niece or nephew has discovered paint + + + align:start position:0% +uh niece or nephew has discovered paint +on the window sill is peeling and is + + align:start position:0% +on the window sill is peeling and is + + + align:start position:0% +on the window sill is peeling and is +starting eating the paint off of the + + align:start position:0% +starting eating the paint off of the + + + align:start position:0% +starting eating the paint off of the +window sill. You might want to remember + + align:start position:0% +window sill. You might want to remember + + + align:start position:0% +window sill. You might want to remember +whether uh when that was painted last + + align:start position:0% +whether uh when that was painted last + + + align:start position:0% +whether uh when that was painted last +and if there was lead in that paint and + + align:start position:0% +and if there was lead in that paint and + + + align:start position:0% +and if there was lead in that paint and +uh rush the child to the emergency room. + + align:start position:0% +uh rush the child to the emergency room. + + + align:start position:0% +uh rush the child to the emergency room. +And when you get there, just in case the + + align:start position:0% +And when you get there, just in case the + + + align:start position:0% +And when you get there, just in case the +people there, you know, on Thanksgiving, + + align:start position:0% +people there, you know, on Thanksgiving, + + + align:start position:0% +people there, you know, on Thanksgiving, +it's always dangerous to be in an + + align:start position:0% +it's always dangerous to be in an + + + align:start position:0% +it's always dangerous to be in an +emergency room. Um, you might say, "Give + + align:start position:0% +emergency room. Um, you might say, "Give + + + align:start position:0% +emergency room. Um, you might say, "Give +this kid EDTA." So, uh, that's really + + align:start position:0% +this kid EDTA." So, uh, that's really + + + align:start position:0% +this kid EDTA." So, uh, that's really +what's used. And that will keelate then + + align:start position:0% +what's used. And that will keelate then + + + align:start position:0% +what's used. And that will keelate then +the lead, uh, out of the system before + + align:start position:0% +the lead, uh, out of the system before + + + align:start position:0% +the lead, uh, out of the system before +it can bind to things and do a lot of + + align:start position:0% +it can bind to things and do a lot of + + + align:start position:0% +it can bind to things and do a lot of +damage. So, this is one of the chilators + + align:start position:0% +damage. So, this is one of the chilators + + + align:start position:0% +damage. So, this is one of the chilators +that's used. It's a chilate effect. + + align:start position:0% +that's used. It's a chilate effect. + + + align:start position:0% +that's used. It's a chilate effect. +works pretty well uh if someone's been + + align:start position:0% +works pretty well uh if someone's been + + + align:start position:0% +works pretty well uh if someone's been +exposed to something like lead which is + + align:start position:0% +exposed to something like lead which is + + + align:start position:0% +exposed to something like lead which is +pretty toxic and you want to get it out + + align:start position:0% +pretty toxic and you want to get it out + + + align:start position:0% +pretty toxic and you want to get it out +of their system. So that's uh one use. + + align:start position:0% + + + + align:start position:0% + +It's also in food. It's a food additive. + + align:start position:0% +It's also in food. It's a food additive. + + + align:start position:0% +It's also in food. It's a food additive. +Sometimes it's fun after you take a + + align:start position:0% +Sometimes it's fun after you take a + + + align:start position:0% +Sometimes it's fun after you take a +couple chemistry courses to actually + + align:start position:0% +couple chemistry courses to actually + + + align:start position:0% +couple chemistry courses to actually +start reading the labels of the food + + align:start position:0% +start reading the labels of the food + + + align:start position:0% +start reading the labels of the food +that you're consuming and some of those + + align:start position:0% +that you're consuming and some of those + + + align:start position:0% +that you're consuming and some of those +uh words will actually start making + + align:start position:0% +uh words will actually start making + + + align:start position:0% +uh words will actually start making +sense. Uh so one thing that you'll will + + align:start position:0% +sense. Uh so one thing that you'll will + + + align:start position:0% +sense. Uh so one thing that you'll will +often see is EDTA and it will say EDTA + + align:start position:0% +often see is EDTA and it will say EDTA + + + align:start position:0% +often see is EDTA and it will say EDTA +was added for freshness. So uh one uh + + align:start position:0% +was added for freshness. So uh one uh + + + align:start position:0% +was added for freshness. So uh one uh +thing that EDTA can do. So + + align:start position:0% +thing that EDTA can do. So + + + align:start position:0% +thing that EDTA can do. So +microorganisms, bacteras, other things + + align:start position:0% +microorganisms, bacteras, other things + + + align:start position:0% +microorganisms, bacteras, other things +that you would rather not have consuming + + align:start position:0% +that you would rather not have consuming + + + align:start position:0% +that you would rather not have consuming +your food at the time that you also want + + align:start position:0% +your food at the time that you also want + + + align:start position:0% +your food at the time that you also want +to consume it um need metals for life as + + align:start position:0% +to consume it um need metals for life as + + + align:start position:0% +to consume it um need metals for life as +we all do. So if you add ETA, it's a + + align:start position:0% +we all do. So if you add ETA, it's a + + + align:start position:0% +we all do. So if you add ETA, it's a +good way of preventing other kinds of + + align:start position:0% +good way of preventing other kinds of + + + align:start position:0% +good way of preventing other kinds of +unwanted microorganisms from growing on + + align:start position:0% +unwanted microorganisms from growing on + + + align:start position:0% +unwanted microorganisms from growing on +the food because it'll accelate all the + + align:start position:0% +the food because it'll accelate all the + + + align:start position:0% +the food because it'll accelate all the +metals and the organisms can't live. So + + align:start position:0% +metals and the organisms can't live. So + + + align:start position:0% +metals and the organisms can't live. So +uh added for freshness. It's a more + + align:start position:0% +uh added for freshness. It's a more + + + align:start position:0% +uh added for freshness. It's a more +polite way of saying that this food is + + align:start position:0% +polite way of saying that this food is + + + align:start position:0% +polite way of saying that this food is +less likely to be contaminated with lots + + align:start position:0% +less likely to be contaminated with lots + + + align:start position:0% +less likely to be contaminated with lots +of uh bacteria growing on top of it. + + align:start position:0% +of uh bacteria growing on top of it. + + + align:start position:0% +of uh bacteria growing on top of it. +Another + + align:start position:0% +Another + + + align:start position:0% +Another +thing that it can be used for cleaning, + + align:start position:0% +thing that it can be used for cleaning, + + + align:start position:0% +thing that it can be used for cleaning, +bathtub cleaning, uh or or other kinds, + + align:start position:0% +bathtub cleaning, uh or or other kinds, + + + align:start position:0% +bathtub cleaning, uh or or other kinds, +but bathtubs and showers in particular. + + align:start position:0% +but bathtubs and showers in particular. + + + align:start position:0% +but bathtubs and showers in particular. +There's calcium in tub scum. And uh most + + align:start position:0% +There's calcium in tub scum. And uh most + + + align:start position:0% +There's calcium in tub scum. And uh most +most kinds of cleaners have something + + align:start position:0% +most kinds of cleaners have something + + + align:start position:0% +most kinds of cleaners have something +that chelates out that calcium which + + align:start position:0% +that chelates out that calcium which + + + align:start position:0% +that chelates out that calcium which +allows you to clean. So again, over + + align:start position:0% +allows you to clean. So again, over + + + align:start position:0% +allows you to clean. So again, over +Thanksgiving, one thing that happens uh + + align:start position:0% +Thanksgiving, one thing that happens uh + + + align:start position:0% +Thanksgiving, one thing that happens uh +to a lot of people when they go home is + + align:start position:0% +to a lot of people when they go home is + + + align:start position:0% +to a lot of people when they go home is +that their parents say, "Here, help us + + align:start position:0% +that their parents say, "Here, help us + + + align:start position:0% +that their parents say, "Here, help us +clean to get ready for everyone coming." + + align:start position:0% +clean to get ready for everyone coming." + + + align:start position:0% +clean to get ready for everyone coming." +And so you might be using EDTA then as + + align:start position:0% +And so you might be using EDTA then as + + + align:start position:0% +And so you might be using EDTA then as +well. + + align:start position:0% +well. + + + align:start position:0% +well. +So um I thought I'd tell you a little + + align:start position:0% +So um I thought I'd tell you a little + + + align:start position:0% +So um I thought I'd tell you a little +story about how knowledge from freshman + + align:start position:0% +story about how knowledge from freshman + + + align:start position:0% +story about how knowledge from freshman +chemistry can make somebody money. + + align:start position:0% +chemistry can make somebody money. + + + align:start position:0% +chemistry can make somebody money. +So this is a really kind of fun story. + + align:start position:0% +So this is a really kind of fun story. + + + align:start position:0% +So this is a really kind of fun story. +So, one day, Robert Black, I don't know + + align:start position:0% +So, one day, Robert Black, I don't know + + + align:start position:0% +So, one day, Robert Black, I don't know +if it's around Thanksgiving, it might + + align:start position:0% +if it's around Thanksgiving, it might + + + align:start position:0% +if it's around Thanksgiving, it might +have been. One day, Robert Black had a + + align:start position:0% +have been. One day, Robert Black had a + + + align:start position:0% +have been. One day, Robert Black had a +lifealtering experience. + + align:start position:0% +lifealtering experience. + + + align:start position:0% +lifealtering experience. +So, his wife said to him, + + align:start position:0% +So, his wife said to him, + + + align:start position:0% +So, his wife said to him, +"Could you clean the tub?" Apparently, + + align:start position:0% +"Could you clean the tub?" Apparently, + + + align:start position:0% +"Could you clean the tub?" Apparently, +Robert Black had never cleaned the tub + + align:start position:0% +Robert Black had never cleaned the tub + + + align:start position:0% +Robert Black had never cleaned the tub +before that time. Uh, and so he went to + + align:start position:0% +before that time. Uh, and so he went to + + + align:start position:0% +before that time. Uh, and so he went to +clean it. And apparently, maybe it + + align:start position:0% +clean it. And apparently, maybe it + + + align:start position:0% +clean it. And apparently, maybe it +hadn't been cleaned in a while. And he + + align:start position:0% +hadn't been cleaned in a while. And he + + + align:start position:0% +hadn't been cleaned in a while. And he +discovered that it's really hard. you + + align:start position:0% +discovered that it's really hard. you + + + align:start position:0% +discovered that it's really hard. you +have to scrub a lot to get the tub + + align:start position:0% +have to scrub a lot to get the tub + + + align:start position:0% +have to scrub a lot to get the tub +clean. So, we thought, wouldn't it be + + align:start position:0% +clean. So, we thought, wouldn't it be + + + align:start position:0% +clean. So, we thought, wouldn't it be +nice if one never had to clean a tub? + + align:start position:0% +nice if one never had to clean a tub? + + + align:start position:0% +nice if one never had to clean a tub? +So, we came up with this idea. And uh + + align:start position:0% +So, we came up with this idea. And uh + + + align:start position:0% +So, we came up with this idea. And uh +here is uh one of the products that came + + align:start position:0% +here is uh one of the products that came + + + align:start position:0% +here is uh one of the products that came +out of this sparkling shower available + + align:start position:0% +out of this sparkling shower available + + + align:start position:0% +out of this sparkling shower available +at Lever's. Um, + + align:start position:0% +at Lever's. Um, + + + align:start position:0% +at Lever's. Um, +and what he did was he put the same + + align:start position:0% +and what he did was he put the same + + + align:start position:0% +and what he did was he put the same +ingredients, including EDTA, in that you + + align:start position:0% +ingredients, including EDTA, in that you + + + align:start position:0% +ingredients, including EDTA, in that you +have in most cleaners, but he had sort + + align:start position:0% +have in most cleaners, but he had sort + + + align:start position:0% +have in most cleaners, but he had sort +of a novel pitch, which is every time + + align:start position:0% +of a novel pitch, which is every time + + + align:start position:0% +of a novel pitch, which is every time +you take a shower, just squirt the + + align:start position:0% +you take a shower, just squirt the + + + align:start position:0% +you take a shower, just squirt the +shower or the tub, and then you never + + align:start position:0% +shower or the tub, and then you never + + + align:start position:0% +shower or the tub, and then you never +really have to clean it. So, um, in in + + align:start position:0% +really have to clean it. So, um, in in + + + align:start position:0% +really have to clean it. So, um, in in +this patent, he had a a surfactant, + + align:start position:0% +this patent, he had a a surfactant, + + + align:start position:0% +this patent, he had a a surfactant, +keelating agent, EDTA, and an alcohol. + + align:start position:0% +keelating agent, EDTA, and an alcohol. + + + align:start position:0% +keelating agent, EDTA, and an alcohol. +So, you had a surfactant to sort of + + align:start position:0% +So, you had a surfactant to sort of + + + align:start position:0% +So, you had a surfactant to sort of +break up the water tension. the + + align:start position:0% +break up the water tension. the + + + align:start position:0% +break up the water tension. the +chilating agent to sequester out the + + align:start position:0% +chilating agent to sequester out the + + + align:start position:0% +chilating agent to sequester out the +salts in the in the um scum and an + + align:start position:0% +salts in the in the um scum and an + + + align:start position:0% +salts in the in the um scum and an +alcohol to dissolve um the more oily + + align:start position:0% +alcohol to dissolve um the more oily + + + align:start position:0% +alcohol to dissolve um the more oily +ingredients. And so those together kind + + align:start position:0% +ingredients. And so those together kind + + + align:start position:0% +ingredients. And so those together kind +of got everything loose and ready to go. + + align:start position:0% +of got everything loose and ready to go. + + + align:start position:0% +of got everything loose and ready to go. +And the surfactant kind of helped it run + + align:start position:0% +And the surfactant kind of helped it run + + + align:start position:0% +And the surfactant kind of helped it run +off. So if you squirt your shower every + + align:start position:0% +off. So if you squirt your shower every + + + align:start position:0% +off. So if you squirt your shower every +time you shower, you'll never really + + align:start position:0% +time you shower, you'll never really + + + align:start position:0% +time you shower, you'll never really +have to clean it. So he used all + + align:start position:0% +have to clean it. So he used all + + + align:start position:0% +have to clean it. So he used all +ingredients that were known before, but + + align:start position:0% +ingredients that were known before, but + + + align:start position:0% +ingredients that were known before, but +packaged it slightly differently. And uh + + align:start position:0% +packaged it slightly differently. And uh + + + align:start position:0% +packaged it slightly differently. And uh +so again EDTA is one of one of the + + align:start position:0% +so again EDTA is one of one of the + + + align:start position:0% +so again EDTA is one of one of the +ingredients in these products and so + + align:start position:0% +ingredients in these products and so + + + align:start position:0% +ingredients in these products and so +sales of these project of these + + align:start position:0% +sales of these project of these + + + align:start position:0% +sales of these project of these +particular products have reached $70 + + align:start position:0% +particular products have reached $70 + + + align:start position:0% +particular products have reached $70 +million every year. So um I think that + + align:start position:0% +million every year. So um I think that + + + align:start position:0% +million every year. So um I think that +uh the wife is probably very happy that + + align:start position:0% +uh the wife is probably very happy that + + + align:start position:0% +uh the wife is probably very happy that +one day she insisted that uh he clean + + align:start position:0% +one day she insisted that uh he clean + + + align:start position:0% +one day she insisted that uh he clean +the tub because this turned out to be a + + align:start position:0% +the tub because this turned out to be a + + + align:start position:0% +the tub because this turned out to be a +pretty profitable exercise. It's also an + + align:start position:0% +pretty profitable exercise. It's also an + + + align:start position:0% +pretty profitable exercise. It's also an +example of how some very simple + + align:start position:0% +example of how some very simple + + + align:start position:0% +example of how some very simple +chemistry can yield you quite a bit of + + align:start position:0% +chemistry can yield you quite a bit of + + + align:start position:0% +chemistry can yield you quite a bit of +money. + + align:start position:0% +money. + + + align:start position:0% +money. +All right. So, tub cleaner. There's one + + align:start position:0% +All right. So, tub cleaner. There's one + + + align:start position:0% +All right. So, tub cleaner. There's one +more that I thought of. + + align:start position:0% +more that I thought of. + + + align:start position:0% +more that I thought of. +Anybody a fan of vampire movies? + + align:start position:0% + + + + align:start position:0% + +Not really all that many. It's a little + + align:start position:0% +Not really all that many. It's a little + + + align:start position:0% +Not really all that many. It's a little +surprising. I'm not sure you're all + + align:start position:0% +surprising. I'm not sure you're all + + + align:start position:0% +surprising. I'm not sure you're all +telling the truth. + + align:start position:0% +telling the truth. + + + align:start position:0% +telling the truth. +They're romantic. + + align:start position:0% +They're romantic. + + + align:start position:0% +They're romantic. +So, uh, if any of you happen to, uh, see + + align:start position:0% +So, uh, if any of you happen to, uh, see + + + align:start position:0% +So, uh, if any of you happen to, uh, see +Blade, + + align:start position:0% +Blade, + + + align:start position:0% +Blade, +you might be aware of another use for + + align:start position:0% +you might be aware of another use for + + + align:start position:0% +you might be aware of another use for +EDTA. + + align:start position:0% +EDTA. + + + align:start position:0% +EDTA. +If you remember, you may not have + + align:start position:0% +If you remember, you may not have + + + align:start position:0% +If you remember, you may not have +noticed what they were, what they were + + align:start position:0% +noticed what they were, what they were + + + align:start position:0% +noticed what they were, what they were +mentioning at the time, but they came up + + align:start position:0% +mentioning at the time, but they came up + + + align:start position:0% +mentioning at the time, but they came up +with a great way of killing vampires. + + align:start position:0% +with a great way of killing vampires. + + + align:start position:0% +with a great way of killing vampires. +And there were these darts filled with + + align:start position:0% +And there were these darts filled with + + + align:start position:0% +And there were these darts filled with +EDTA. + + align:start position:0% +EDTA. + + + align:start position:0% +EDTA. +And uh I'm I'm not I think the kind of + + align:start position:0% +And uh I'm I'm not I think the kind of + + + align:start position:0% +And uh I'm I'm not I think the kind of +general premise that you can rationalize + + align:start position:0% +general premise that you can rationalize + + + align:start position:0% +general premise that you can rationalize +this uh Hollywood special feature is + + align:start position:0% +this uh Hollywood special feature is + + + align:start position:0% +this uh Hollywood special feature is +that vampires drink blood. Blood has + + align:start position:0% +that vampires drink blood. Blood has + + + align:start position:0% +that vampires drink blood. Blood has +iron. And if they're pretty much all + + align:start position:0% +iron. And if they're pretty much all + + + align:start position:0% +iron. And if they're pretty much all +blood, if you give them something that + + align:start position:0% +blood, if you give them something that + + + align:start position:0% +blood, if you give them something that +keates out the iron, it could cause some + + align:start position:0% +keates out the iron, it could cause some + + + align:start position:0% +keates out the iron, it could cause some +kind of harmful effect. In the movie, + + align:start position:0% +kind of harmful effect. In the movie, + + + align:start position:0% +kind of harmful effect. In the movie, +they exploded and sort of disintegrated + + align:start position:0% +they exploded and sort of disintegrated + + + align:start position:0% +they exploded and sort of disintegrated +completely. Um, if you take your niece + + align:start position:0% +completely. Um, if you take your niece + + + align:start position:0% +completely. Um, if you take your niece +or nephew to the emergency room for + + align:start position:0% +or nephew to the emergency room for + + + align:start position:0% +or nephew to the emergency room for +eating lead paint, this will not happen. + + align:start position:0% +eating lead paint, this will not happen. + + + align:start position:0% +eating lead paint, this will not happen. +I'm quite sure, but it was really very + + align:start position:0% +I'm quite sure, but it was really very + + + align:start position:0% +I'm quite sure, but it was really very +spectacular. So, uh, here they are of + + align:start position:0% +spectacular. So, uh, here they are of + + + align:start position:0% +spectacular. So, uh, here they are of +the little darts filled with EDTA. So, + + align:start position:0% +the little darts filled with EDTA. So, + + + align:start position:0% +the little darts filled with EDTA. So, +uh, again, more knowledge that could be + + align:start position:0% +uh, again, more knowledge that could be + + + align:start position:0% +uh, again, more knowledge that could be +useful on some occasion perhaps. I'm not + + align:start position:0% +useful on some occasion perhaps. I'm not + + + align:start position:0% +useful on some occasion perhaps. I'm not +really sure. Uh I have a feeling that + + align:start position:0% +really sure. Uh I have a feeling that + + + align:start position:0% +really sure. Uh I have a feeling that +most of you will find the top three more + + align:start position:0% +most of you will find the top three more + + + align:start position:0% +most of you will find the top three more +useful but uh here is the complete list + + align:start position:0% +useful but uh here is the complete list + + + align:start position:0% +useful but uh here is the complete list +that I have been able to come up with + + align:start position:0% +that I have been able to come up with + + + align:start position:0% +that I have been able to come up with +for the uses of chelators. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +So those are some coordination complexes + + align:start position:0% +So those are some coordination complexes + + + align:start position:0% +So those are some coordination complexes +either single single lians bound around + + align:start position:0% +either single single lians bound around + + + align:start position:0% +either single single lians bound around +a central metal or chelating lians bound + + align:start position:0% +a central metal or chelating lians bound + + + align:start position:0% +a central metal or chelating lians bound +around a central metal. + + align:start position:0% +around a central metal. + + + align:start position:0% +around a central metal. +There are other coordination complexes + + align:start position:0% +There are other coordination complexes + + + align:start position:0% +There are other coordination complexes +which have important features and one + + align:start position:0% +which have important features and one + + + align:start position:0% +which have important features and one +thing that we'll talk about are isomers + + align:start position:0% +thing that we'll talk about are isomers + + + align:start position:0% +thing that we'll talk about are isomers +and geometric isomers can have very + + align:start position:0% +and geometric isomers can have very + + + align:start position:0% +and geometric isomers can have very +different properties to them. So it + + align:start position:0% +different properties to them. So it + + + align:start position:0% +different properties to them. So it +seems like it's pretty much almost the + + align:start position:0% +seems like it's pretty much almost the + + + align:start position:0% +seems like it's pretty much almost the +exact same compound but the arrangement + + align:start position:0% +exact same compound but the arrangement + + + align:start position:0% +exact same compound but the arrangement +of the atoms is slightly different and + + align:start position:0% +of the atoms is slightly different and + + + align:start position:0% +of the atoms is slightly different and +that can yield to very different + + align:start position:0% +that can yield to very different + + + align:start position:0% +that can yield to very different +properties for those particular + + align:start position:0% +properties for those particular + + + align:start position:0% +properties for those particular +compounds. + + align:start position:0% +compounds. + + + align:start position:0% +compounds. +So let's look at one example and uh so + + align:start position:0% +So let's look at one example and uh so + + + align:start position:0% +So let's look at one example and uh so +here this is platinum + + align:start position:0% +here this is platinum + + + align:start position:0% +here this is platinum +and it has two NH3 + + align:start position:0% +and it has two NH3 + + + align:start position:0% +and it has two NH3 +uh lians and two chloride lians and so + + align:start position:0% +uh lians and two chloride lians and so + + + align:start position:0% +uh lians and two chloride lians and so +that's in the bracket. So those four + + align:start position:0% +that's in the bracket. So those four + + + align:start position:0% +that's in the bracket. So those four +different um lians are coordinated + + align:start position:0% +different um lians are coordinated + + + align:start position:0% +different um lians are coordinated +centrally to the platinum. So it would + + align:start position:0% +centrally to the platinum. So it would + + + align:start position:0% +centrally to the platinum. So it would +have a CN number of four and there'd be + + align:start position:0% +have a CN number of four and there'd be + + + align:start position:0% +have a CN number of four and there'd be +a couple different uh the the most + + align:start position:0% +a couple different uh the the most + + + align:start position:0% +a couple different uh the the most +common shape that you would see for this + + align:start position:0% +common shape that you would see for this + + + align:start position:0% +common shape that you would see for this +would be uh this one here this square + + align:start position:0% +would be uh this one here this square + + + align:start position:0% +would be uh this one here this square +planer shape. + + align:start position:0% + + + + align:start position:0% + +So depending on how you arrange the four + + align:start position:0% +So depending on how you arrange the four + + + align:start position:0% +So depending on how you arrange the four +different lians 2 NH3 and 2 Cl you get a + + align:start position:0% +different lians 2 NH3 and 2 Cl you get a + + + align:start position:0% +different lians 2 NH3 and 2 Cl you get a +very different result. + + align:start position:0% +very different result. + + + align:start position:0% +very different result. +So we have in this arrangement a + + align:start position:0% +So we have in this arrangement a + + + align:start position:0% +So we have in this arrangement a +compound called cis platinum. You have a + + align:start position:0% +compound called cis platinum. You have a + + + align:start position:0% +compound called cis platinum. You have a +cis arrangement where the chlorides are + + align:start position:0% +cis arrangement where the chlorides are + + + align:start position:0% +cis arrangement where the chlorides are +on one side and the NH3 groups ammonia + + align:start position:0% +on one side and the NH3 groups ammonia + + + align:start position:0% +on one side and the NH3 groups ammonia +groups are on the other side. Or you can + + align:start position:0% +groups are on the other side. Or you can + + + align:start position:0% +groups are on the other side. Or you can +have transplatinum where the lians are + + align:start position:0% +have transplatinum where the lians are + + + align:start position:0% +have transplatinum where the lians are +across from each other. So um here are + + align:start position:0% +across from each other. So um here are + + + align:start position:0% +across from each other. So um here are +these two different + + align:start position:0% +these two different + + + align:start position:0% +these two different +molecules. So here they're cis with + + align:start position:0% +molecules. So here they're cis with + + + align:start position:0% +molecules. So here they're cis with +respect to each other and here they're + + align:start position:0% +respect to each other and here they're + + + align:start position:0% +respect to each other and here they're +trans with respect to each other. One is + + align:start position:0% +trans with respect to each other. One is + + + align:start position:0% +trans with respect to each other. One is +a very potent uh drug that's used in + + align:start position:0% +a very potent uh drug that's used in + + + align:start position:0% +a very potent uh drug that's used in +treatment of cancer. The other has no + + align:start position:0% +treatment of cancer. The other has no + + + align:start position:0% +treatment of cancer. The other has no +known function. + + align:start position:0% +known function. + + + align:start position:0% +known function. +They're composed of identical atoms. So + + align:start position:0% +They're composed of identical atoms. So + + + align:start position:0% +They're composed of identical atoms. So +why is this different? Why are there + + align:start position:0% +why is this different? Why are there + + + align:start position:0% +why is this different? Why are there +different functions with the different + + align:start position:0% +different functions with the different + + + align:start position:0% +different functions with the different +geometries? + + align:start position:0% +geometries? + + + align:start position:0% +geometries? +Well, as it as it turns out, it's real + + align:start position:0% +Well, as it as it turns out, it's real + + + align:start position:0% +Well, as it as it turns out, it's real +important to have the atoms on the same + + align:start position:0% +important to have the atoms on the same + + + align:start position:0% +important to have the atoms on the same +side. + + align:start position:0% + + + + align:start position:0% + +So, as shown in this slide, and I me I + + align:start position:0% +So, as shown in this slide, and I me I + + + align:start position:0% +So, as shown in this slide, and I me I +said I'd mention Steve Liippard again, + + align:start position:0% +said I'd mention Steve Liippard again, + + + align:start position:0% +said I'd mention Steve Liippard again, +and here I am. This has been a subject + + align:start position:0% +and here I am. This has been a subject + + + align:start position:0% +and here I am. This has been a subject +of research in Steve Liippard's + + align:start position:0% +of research in Steve Liippard's + + + align:start position:0% +of research in Steve Liippard's +laboratory here in the chemistry + + align:start position:0% +laboratory here in the chemistry + + + align:start position:0% +laboratory here in the chemistry +department at MIT for a number number of + + align:start position:0% +department at MIT for a number number of + + + align:start position:0% +department at MIT for a number number of +years. So um + + align:start position:0% +years. So um + + + align:start position:0% +years. So um +so if you have a a cancer cell and you + + align:start position:0% +so if you have a a cancer cell and you + + + align:start position:0% +so if you have a a cancer cell and you +want to kill the cancer cell, one thing + + align:start position:0% +want to kill the cancer cell, one thing + + + align:start position:0% +want to kill the cancer cell, one thing +that you can do is give it cy platinum. + + align:start position:0% +that you can do is give it cy platinum. + + + align:start position:0% +that you can do is give it cy platinum. +The cis platinum comes and binds to DNA. + + align:start position:0% +The cis platinum comes and binds to DNA. + + + align:start position:0% +The cis platinum comes and binds to DNA. +So here's a little uh cartoon of DNA + + align:start position:0% +So here's a little uh cartoon of DNA + + + align:start position:0% +So here's a little uh cartoon of DNA +here. There's the actual uh a model of + + align:start position:0% +here. There's the actual uh a model of + + + align:start position:0% +here. There's the actual uh a model of +DNA structure down here in the front of + + align:start position:0% +DNA structure down here in the front of + + + align:start position:0% +DNA structure down here in the front of +the room. When it when it binds, then uh + + align:start position:0% +the room. When it when it binds, then uh + + + align:start position:0% +the room. When it when it binds, then uh +it will can inhibit transcription. And + + align:start position:0% +it will can inhibit transcription. And + + + align:start position:0% +it will can inhibit transcription. And +so this can then lead to cell death. And + + align:start position:0% +so this can then lead to cell death. And + + + align:start position:0% +so this can then lead to cell death. And +so Steve has been really looking at this + + align:start position:0% +so Steve has been really looking at this + + + align:start position:0% +so Steve has been really looking at this +issue, trying to redesign cis platinums + + align:start position:0% +issue, trying to redesign cis platinums + + + align:start position:0% +issue, trying to redesign cis platinums +to see if you get a better drug, looking + + align:start position:0% +to see if you get a better drug, looking + + + align:start position:0% +to see if you get a better drug, looking +at other factors which might have an + + align:start position:0% +at other factors which might have an + + + align:start position:0% +at other factors which might have an +additive effect. This particular drug is + + align:start position:0% +additive effect. This particular drug is + + + align:start position:0% +additive effect. This particular drug is +used often in prostate for prostate + + align:start position:0% +used often in prostate for prostate + + + align:start position:0% +used often in prostate for prostate +cancer and it's really been uh quite + + align:start position:0% +cancer and it's really been uh quite + + + align:start position:0% +cancer and it's really been uh quite +effective. So why does it matter if + + align:start position:0% +effective. So why does it matter if + + + align:start position:0% +effective. So why does it matter if +they're on the same side? Well, if you + + align:start position:0% +they're on the same side? Well, if you + + + align:start position:0% +they're on the same side? Well, if you +look at this uh the complex and the + + align:start position:0% +look at this uh the complex and the + + + align:start position:0% +look at this uh the complex and the +other, you see that only two of these + + align:start position:0% +other, you see that only two of these + + + align:start position:0% +other, you see that only two of these +lians are left. Two of the lians were + + align:start position:0% +lians are left. Two of the lians were + + + align:start position:0% +lians are left. Two of the lians were +gone. and at those sites is actually + + align:start position:0% +gone. and at those sites is actually + + + align:start position:0% +gone. and at those sites is actually +coordinated to the DNA itself. So that's + + align:start position:0% +coordinated to the DNA itself. So that's + + + align:start position:0% +coordinated to the DNA itself. So that's +why it's important that they're on the + + align:start position:0% +why it's important that they're on the + + + align:start position:0% +why it's important that they're on the +same side. You have to have you want to + + align:start position:0% +same side. You have to have you want to + + + align:start position:0% +same side. You have to have you want to +release two chlorides and have it bind + + align:start position:0% +release two chlorides and have it bind + + + align:start position:0% +release two chlorides and have it bind +to DNA this way. If it's on the other + + align:start position:0% +to DNA this way. If it's on the other + + + align:start position:0% +to DNA this way. If it's on the other +side, it really doesn't work as well. So + + align:start position:0% +side, it really doesn't work as well. So + + + align:start position:0% +side, it really doesn't work as well. So +if we go over uh and look at the DNA + + align:start position:0% +if we go over uh and look at the DNA + + + align:start position:0% +if we go over uh and look at the DNA +molecule for a minute, you see that if + + align:start position:0% +molecule for a minute, you see that if + + + align:start position:0% +molecule for a minute, you see that if +you want to have two free sites uh to + + align:start position:0% +you want to have two free sites uh to + + + align:start position:0% +you want to have two free sites uh to +coordinate um to a DNA molecule, of + + align:start position:0% +coordinate um to a DNA molecule, of + + + align:start position:0% +coordinate um to a DNA molecule, of +course, this is the totally wrong scale, + + align:start position:0% +course, this is the totally wrong scale, + + + align:start position:0% +course, this is the totally wrong scale, +but you want these on the same side. If + + align:start position:0% +but you want these on the same side. If + + + align:start position:0% +but you want these on the same side. If +you had uh if I made it on the right + + align:start position:0% +you had uh if I made it on the right + + + align:start position:0% +you had uh if I made it on the right +scale, it would not fit in the room + + align:start position:0% +scale, it would not fit in the room + + + align:start position:0% +scale, it would not fit in the room +really. So uh this is uh more or less + + align:start position:0% +really. So uh this is uh more or less + + + align:start position:0% +really. So uh this is uh more or less +you can imagine. But if you're going + + align:start position:0% +you can imagine. But if you're going + + + align:start position:0% +you can imagine. But if you're going +down here and you want to release just + + align:start position:0% +down here and you want to release just + + + align:start position:0% +down here and you want to release just +the chloride ligans, well, you can't get + + align:start position:0% +the chloride ligans, well, you can't get + + + align:start position:0% +the chloride ligans, well, you can't get +the chloride ligans to be on the right + + align:start position:0% +the chloride ligans to be on the right + + + align:start position:0% +the chloride ligans to be on the right +side for this. + + align:start position:0% +side for this. + + + align:start position:0% +side for this. +So, um, so molecules that have different + + align:start position:0% +So, um, so molecules that have different + + + align:start position:0% +So, um, so molecules that have different +shapes may have different properties and + + align:start position:0% +shapes may have different properties and + + + align:start position:0% +shapes may have different properties and +you're if you're in an environment and + + align:start position:0% +you're if you're in an environment and + + + align:start position:0% +you're if you're in an environment and +you're looking to re react with a + + align:start position:0% +you're looking to re react with a + + + align:start position:0% +you're looking to re react with a +particular molecule, you know, if you + + align:start position:0% +particular molecule, you know, if you + + + align:start position:0% +particular molecule, you know, if you +want to put on show you another kind of + + align:start position:0% +want to put on show you another kind of + + + align:start position:0% +want to put on show you another kind of +view of DNA. DNA is a really beautiful u + + align:start position:0% +view of DNA. DNA is a really beautiful u + + + align:start position:0% +view of DNA. DNA is a really beautiful u +molecule. So here uh you have something + + align:start position:0% +molecule. So here uh you have something + + + align:start position:0% +molecule. So here uh you have something +you can carry around and show your + + align:start position:0% +you can carry around and show your + + + align:start position:0% +you can carry around and show your +friends, but also there's a a smaller uh + + align:start position:0% +friends, but also there's a a smaller uh + + + align:start position:0% +friends, but also there's a a smaller uh +model of DNA and this is actually an + + align:start position:0% +model of DNA and this is actually an + + + align:start position:0% +model of DNA and this is actually an +artist uh in Michigan will carve out + + align:start position:0% +artist uh in Michigan will carve out + + + align:start position:0% +artist uh in Michigan will carve out +within these blocks uh any atomic + + align:start position:0% +within these blocks uh any atomic + + + align:start position:0% +within these blocks uh any atomic +structure uh that you have and you can + + align:start position:0% +structure uh that you have and you can + + + align:start position:0% +structure uh that you have and you can +show the sort of uh bases and the + + align:start position:0% +show the sort of uh bases and the + + + align:start position:0% +show the sort of uh bases and the +detail. That's what DNA looks like sort + + align:start position:0% +detail. That's what DNA looks like sort + + + align:start position:0% +detail. That's what DNA looks like sort +of from the top and then from the side. + + align:start position:0% +of from the top and then from the side. + + + align:start position:0% +of from the top and then from the side. +So it's a really beautiful molecule. + + align:start position:0% +So it's a really beautiful molecule. + + + align:start position:0% +So it's a really beautiful molecule. +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +so this is a nice example. Steve + + align:start position:0% +so this is a nice example. Steve + + + align:start position:0% +so this is a nice example. Steve +Liippard often takes a lot of Europe + + align:start position:0% +Liippard often takes a lot of Europe + + + align:start position:0% +Liippard often takes a lot of Europe +students, so it might be something if + + align:start position:0% +students, so it might be something if + + + align:start position:0% +students, so it might be something if +you're interested in this area that uh + + align:start position:0% +you're interested in this area that uh + + + align:start position:0% +you're interested in this area that uh +you might want to look at his his web + + align:start position:0% +you might want to look at his his web + + + align:start position:0% +you might want to look at his his web +page and see if that type of research + + align:start position:0% +page and see if that type of research + + + align:start position:0% +page and see if that type of research +interests you. + + align:start position:0% + + + + align:start position:0% + +Okay. So again, + + align:start position:0% +Okay. So again, + + + align:start position:0% +Okay. So again, +lost my pointer. + + align:start position:0% +lost my pointer. + + + align:start position:0% +lost my pointer. +So the the cy platinum has the effect + + align:start position:0% +So the the cy platinum has the effect + + + align:start position:0% +So the the cy platinum has the effect +because you need to release chlorides on + + align:start position:0% +because you need to release chlorides on + + + align:start position:0% +because you need to release chlorides on +the same side so that it can bind DNA + + align:start position:0% +the same side so that it can bind DNA + + + align:start position:0% +the same side so that it can bind DNA +over here. Uh this cannot bind DNA + + align:start position:0% +over here. Uh this cannot bind DNA + + + align:start position:0% +over here. Uh this cannot bind DNA +because you don't have the chlorides + + align:start position:0% +because you don't have the chlorides + + + align:start position:0% +because you don't have the chlorides +together so that uh they can't be + + align:start position:0% +together so that uh they can't be + + + align:start position:0% +together so that uh they can't be +released and you won't interact with the + + align:start position:0% +released and you won't interact with the + + + align:start position:0% +released and you won't interact with the +DNA. So again these different isomers + + align:start position:0% +DNA. So again these different isomers + + + align:start position:0% +DNA. So again these different isomers +have really really different properties. + + align:start position:0% + + + + align:start position:0% + +So here uh we look at optical isomers or + + align:start position:0% +So here uh we look at optical isomers or + + + align:start position:0% +So here uh we look at optical isomers or +enantiomers + + align:start position:0% +enantiomers + + + align:start position:0% +enantiomers +and introduce the idea of a mirror plane + + align:start position:0% +and introduce the idea of a mirror plane + + + align:start position:0% +and introduce the idea of a mirror plane +here. So when you have two different + + align:start position:0% +here. So when you have two different + + + align:start position:0% +here. So when you have two different +isomers and if they're not super + + align:start position:0% +isomers and if they're not super + + + align:start position:0% +isomers and if they're not super +imposable that means there is a mirror + + align:start position:0% +imposable that means there is a mirror + + + align:start position:0% +imposable that means there is a mirror +plane and that they are chyro and chyro + + align:start position:0% +plane and that they are chyro and chyro + + + align:start position:0% +plane and that they are chyro and chyro +molecules can have vastly different + + align:start position:0% +molecules can have vastly different + + + align:start position:0% +molecules can have vastly different +properties again if they're in a chyro + + align:start position:0% +properties again if they're in a chyro + + + align:start position:0% +properties again if they're in a chyro +environment such as the human body. So + + align:start position:0% +environment such as the human body. So + + + align:start position:0% +environment such as the human body. So +let's just look at these two. + + align:start position:0% + + + + align:start position:0% + +So um see that there is a mirror plane. + + align:start position:0% +So um see that there is a mirror plane. + + + align:start position:0% +So um see that there is a mirror plane. +So here we have the green uh on top, the + + align:start position:0% +So here we have the green uh on top, the + + + align:start position:0% +So here we have the green uh on top, the +NH3 on top, chloride in gray here on the + + align:start position:0% +NH3 on top, chloride in gray here on the + + + align:start position:0% +NH3 on top, chloride in gray here on the +bottom, and then on the side we have the + + align:start position:0% +bottom, and then on the side we have the + + + align:start position:0% +bottom, and then on the side we have the +oxygens, the black atoms here, more + + align:start position:0% +oxygens, the black atoms here, more + + + align:start position:0% +oxygens, the black atoms here, more +chlorides here. On the other side, + + align:start position:0% +chlorides here. On the other side, + + + align:start position:0% +chlorides here. On the other side, +they're also oxygen pointing out in + + align:start position:0% +they're also oxygen pointing out in + + + align:start position:0% +they're also oxygen pointing out in +front. Another NH3 group sort of + + align:start position:0% +front. Another NH3 group sort of + + + align:start position:0% +front. Another NH3 group sort of +pointing back. And so they're very very + + align:start position:0% +pointing back. And so they're very very + + + align:start position:0% +pointing back. And so they're very very +similar, but if you try to superimpose + + align:start position:0% +similar, but if you try to superimpose + + + align:start position:0% +similar, but if you try to superimpose +them, you'll realize that it doesn't + + align:start position:0% +them, you'll realize that it doesn't + + + align:start position:0% +them, you'll realize that it doesn't +match up. Uh if you try again other + + align:start position:0% +match up. Uh if you try again other + + + align:start position:0% +match up. Uh if you try again other +ways, put another uh green over here. + + align:start position:0% +ways, put another uh green over here. + + + align:start position:0% +ways, put another uh green over here. +No, that's wrong too. And you can uh + + align:start position:0% +No, that's wrong too. And you can uh + + + align:start position:0% +No, that's wrong too. And you can uh +spend maybe not very long convincing + + align:start position:0% +spend maybe not very long convincing + + + align:start position:0% +spend maybe not very long convincing +yourself that in fact these are nons + + align:start position:0% +yourself that in fact these are nons + + + align:start position:0% +yourself that in fact these are nons +superimposable. Uh they are mirror + + align:start position:0% +superimposable. Uh they are mirror + + + align:start position:0% +superimposable. Uh they are mirror +images. So they're chyal compounds. And + + align:start position:0% +images. So they're chyal compounds. And + + + align:start position:0% +images. So they're chyal compounds. And +the idea of chyro compounds will come + + align:start position:0% +the idea of chyro compounds will come + + + align:start position:0% +the idea of chyro compounds will come +back and you'll hear much more about + + align:start position:0% +back and you'll hear much more about + + + align:start position:0% +back and you'll hear much more about +that if you take organic chemistry uh + + align:start position:0% +that if you take organic chemistry uh + + + align:start position:0% +that if you take organic chemistry uh +512 or 513. + + align:start position:0% + + + + align:start position:0% + +Okay. So now we have to get to some + + align:start position:0% +Okay. So now we have to get to some + + + align:start position:0% +Okay. So now we have to get to some +business that we need to think more + + align:start position:0% +business that we need to think more + + + align:start position:0% +business that we need to think more +about the properties of these elements + + align:start position:0% +about the properties of these elements + + + align:start position:0% +about the properties of these elements +and that is we need to count a lot of + + align:start position:0% +and that is we need to count a lot of + + + align:start position:0% +and that is we need to count a lot of +counting in these units oxidation + + align:start position:0% +counting in these units oxidation + + + align:start position:0% +counting in these units oxidation +reduction and also in this unit uh + + align:start position:0% +reduction and also in this unit uh + + + align:start position:0% +reduction and also in this unit uh +counting skills we need to figure out + + align:start position:0% +counting skills we need to figure out + + + align:start position:0% +counting skills we need to figure out +how many de electrons are involved in + + align:start position:0% +how many de electrons are involved in + + + align:start position:0% +how many de electrons are involved in +coordination complexes to be able to + + align:start position:0% +coordination complexes to be able to + + + align:start position:0% +coordination complexes to be able to +rationalize their properties. + + align:start position:0% +rationalize their properties. + + + align:start position:0% +rationalize their properties. +So this is pretty straightforward. One + + align:start position:0% +So this is pretty straightforward. One + + + align:start position:0% +So this is pretty straightforward. One +can figure this out what the d electron + + align:start position:0% +can figure this out what the d electron + + + align:start position:0% +can figure this out what the d electron +count is if you know the group number + + align:start position:0% +count is if you know the group number + + + align:start position:0% +count is if you know the group number +from the periodic table and the + + align:start position:0% +from the periodic table and the + + + align:start position:0% +from the periodic table and the +oxidation number of the metal. So uh we + + align:start position:0% +oxidation number of the metal. So uh we + + + align:start position:0% +oxidation number of the metal. So uh we +know how to calculate oxidation numbers + + align:start position:0% +know how to calculate oxidation numbers + + + align:start position:0% +know how to calculate oxidation numbers +at this point and uh periodic table uh + + align:start position:0% +at this point and uh periodic table uh + + + align:start position:0% +at this point and uh periodic table uh +in your book. So let's uh just take a + + align:start position:0% +in your book. So let's uh just take a + + + align:start position:0% +in your book. So let's uh just take a +look at a couple of examples and uh + + align:start position:0% +look at a couple of examples and uh + + + align:start position:0% +look at a couple of examples and uh +count some d electrons. + + align:start position:0% +count some d electrons. + + + align:start position:0% +count some d electrons. +So suppose we have a complex a + + align:start position:0% +So suppose we have a complex a + + + align:start position:0% +So suppose we have a complex a +coordination complex. It has cobalt in + + align:start position:0% +coordination complex. It has cobalt in + + + align:start position:0% +coordination complex. It has cobalt in +it. It has three ammonia or six ammonial + + align:start position:0% +it. It has three ammonia or six ammonial + + + align:start position:0% +it. It has three ammonia or six ammonial +lians and it has a charge of plus three + + align:start position:0% +lians and it has a charge of plus three + + + align:start position:0% +lians and it has a charge of plus three +for the overall complex. + + align:start position:0% +for the overall complex. + + + align:start position:0% +for the overall complex. +So then we need to figure out what the + + align:start position:0% +So then we need to figure out what the + + + align:start position:0% +So then we need to figure out what the +oxidation number of cobalt is first. So + + align:start position:0% +oxidation number of cobalt is first. So + + + align:start position:0% +oxidation number of cobalt is first. So +what is the overall charge on NH3? + + align:start position:0% +what is the overall charge on NH3? + + + align:start position:0% +what is the overall charge on NH3? +And that's zero. This is a neutral + + align:start position:0% +And that's zero. This is a neutral + + + align:start position:0% +And that's zero. This is a neutral +molecule. And uh if you don't know that, + + align:start position:0% +molecule. And uh if you don't know that, + + + align:start position:0% +molecule. And uh if you don't know that, +it's just something you'll memorize as + + align:start position:0% +it's just something you'll memorize as + + + align:start position:0% +it's just something you'll memorize as +you go through this unit. So what does + + align:start position:0% +you go through this unit. So what does + + + align:start position:0% +you go through this unit. So what does +that leave you for for cobalt + + align:start position:0% +that leave you for for cobalt + + + align:start position:0% +that leave you for for cobalt +plus three? Because it all has to add up + + align:start position:0% +plus three? Because it all has to add up + + + align:start position:0% +plus three? Because it all has to add up +just as it has before. And so we figure + + align:start position:0% +just as it has before. And so we figure + + + align:start position:0% +just as it has before. And so we figure +out the oxidation number first and then + + align:start position:0% +out the oxidation number first and then + + + align:start position:0% +out the oxidation number first and then +second we would figure out the decount. + + align:start position:0% +second we would figure out the decount. + + + align:start position:0% +second we would figure out the decount. +So we need to look at the periodic table + + align:start position:0% +So we need to look at the periodic table + + + align:start position:0% +So we need to look at the periodic table +and see where it is. And uh here we have + + align:start position:0% +and see where it is. And uh here we have + + + align:start position:0% +and see where it is. And uh here we have +cobalt + + align:start position:0% +cobalt + + + align:start position:0% +cobalt +um in group nine. + + align:start position:0% + + + + align:start position:0% + +So we have group number + + align:start position:0% +So we have group number + + + align:start position:0% +So we have group number +nine minus the oxidation number + + align:start position:0% +nine minus the oxidation number + + + align:start position:0% +nine minus the oxidation number +which is three that we just calculated + + align:start position:0% +which is three that we just calculated + + + align:start position:0% +which is three that we just calculated +and we're left with six. And you'll + + align:start position:0% +and we're left with six. And you'll + + + align:start position:0% +and we're left with six. And you'll +often see this written as d to the six + + align:start position:0% +often see this written as d to the six + + + align:start position:0% +often see this written as d to the six +for the uh dount number of uh electrons. + + align:start position:0% +for the uh dount number of uh electrons. + + + align:start position:0% +for the uh dount number of uh electrons. +One year when I had this, I think the + + align:start position:0% +One year when I had this, I think the + + + align:start position:0% +One year when I had this, I think the +first year I actually had uh I think 9 + + align:start position:0% +first year I actually had uh I think 9 + + + align:start position:0% +first year I actually had uh I think 9 +minus 3 equals 5 in the handout and that + + align:start position:0% +minus 3 equals 5 in the handout and that + + + align:start position:0% +minus 3 equals 5 in the handout and that +was rather embarrassing. + + align:start position:0% + + + + align:start position:0% + +Okay. Oh wait, I want to do one more + + align:start position:0% +Okay. Oh wait, I want to do one more + + + align:start position:0% +Okay. Oh wait, I want to do one more +example first. Okay. So let's or two + + align:start position:0% +example first. Okay. So let's or two + + + align:start position:0% +example first. Okay. So let's or two +more examples first. Let's try just a + + align:start position:0% +more examples first. Let's try just a + + + align:start position:0% +more examples first. Let's try just a +couple of more. + + align:start position:0% + + + + align:start position:0% + +All right. So, there's some that'll + + align:start position:0% +All right. So, there's some that'll + + + align:start position:0% +All right. So, there's some that'll +become very familiar to you as you do + + align:start position:0% +become very familiar to you as you do + + + align:start position:0% +become very familiar to you as you do +these. So, let's look at nickel + + align:start position:0% +these. So, let's look at nickel + + + align:start position:0% +these. So, let's look at nickel +with CO lians, four of them written like + + align:start position:0% +with CO lians, four of them written like + + + align:start position:0% +with CO lians, four of them written like +this. So, there's nothing up here. So, + + align:start position:0% +this. So, there's nothing up here. So, + + + align:start position:0% +this. So, there's nothing up here. So, +that means that the overall charge has + + align:start position:0% +that means that the overall charge has + + + align:start position:0% +that means that the overall charge has +to equal zero. + + align:start position:0% +to equal zero. + + + align:start position:0% +to equal zero. +CO, + + align:start position:0% +CO, + + + align:start position:0% +CO, +that's one that you'll uh come across. + + align:start position:0% +that's one that you'll uh come across. + + + align:start position:0% +that's one that you'll uh come across. +And its overall charge is also going to + + align:start position:0% +And its overall charge is also going to + + + align:start position:0% +And its overall charge is also going to +be zero. It's neutral as well. + + align:start position:0% + + + + align:start position:0% + +And so what does that leave for nickel? + + align:start position:0% +And so what does that leave for nickel? + + + align:start position:0% +And so what does that leave for nickel? +Zero. + + align:start position:0% +Zero. + + + align:start position:0% +Zero. +So sometimes not very exciting. All + + align:start position:0% +So sometimes not very exciting. All + + + align:start position:0% +So sometimes not very exciting. All +right. So if your oxidation number + + align:start position:0% +right. So if your oxidation number + + + align:start position:0% +right. So if your oxidation number +is zero, + + align:start position:0% +is zero, + + + align:start position:0% +is zero, +then we want to look up + + align:start position:0% +then we want to look up + + + align:start position:0% +then we want to look up +figure out what the decount is. So we + + align:start position:0% +figure out what the decount is. So we + + + align:start position:0% +figure out what the decount is. So we +have to see where nickel is and it's in + + align:start position:0% +have to see where nickel is and it's in + + + align:start position:0% +have to see where nickel is and it's in +group 10. + + align:start position:0% + + + + align:start position:0% + +So we have 10 minus 0. + + align:start position:0% +So we have 10 minus 0. + + + align:start position:0% +So we have 10 minus 0. +So it is a D10 + + align:start position:0% +So it is a D10 + + + align:start position:0% +So it is a D10 +system. + + align:start position:0% + + + + align:start position:0% + +Let's just try one more. + + align:start position:0% + + + + align:start position:0% + +Cobalt + + align:start position:0% +Cobalt + + + align:start position:0% +Cobalt +again. Two molecules of water. + + align:start position:0% + + + + align:start position:0% + +and one of uh NH3 + + align:start position:0% +and one of uh NH3 + + + align:start position:0% +and one of uh NH3 +and three of chloride to the minus1. + + align:start position:0% + + + + align:start position:0% + +Let's put that up a little bit. All + + align:start position:0% +Let's put that up a little bit. All + + + align:start position:0% +Let's put that up a little bit. All +right. So, what overall this has to be + + align:start position:0% +right. So, what overall this has to be + + + align:start position:0% +right. So, what overall this has to be +minus1. What's the charge on chloride + + align:start position:0% +minus1. What's the charge on chloride + + + align:start position:0% +minus1. What's the charge on chloride +going to be? + + align:start position:0% +going to be? + + + align:start position:0% +going to be? +It'll be minus1. There'll be three of + + align:start position:0% +It'll be minus1. There'll be three of + + + align:start position:0% +It'll be minus1. There'll be three of +them. + + align:start position:0% +them. + + + align:start position:0% +them. +NH3 was what again? + + align:start position:0% +NH3 was what again? + + + align:start position:0% +NH3 was what again? +Zero. You want to guess what water is + + align:start position:0% +Zero. You want to guess what water is + + + align:start position:0% +Zero. You want to guess what water is +going to be? + + align:start position:0% +going to be? + + + align:start position:0% +going to be? +Zero. So, two zeros. And so, what does + + align:start position:0% +Zero. So, two zeros. And so, what does + + + align:start position:0% +Zero. So, two zeros. And so, what does +that leave you for? Cobalt. + + align:start position:0% +that leave you for? Cobalt. + + + align:start position:0% +that leave you for? Cobalt. +Plus two. + + align:start position:0% + + + + align:start position:0% + +All right. So, cobalt we looked up + + align:start position:0% +All right. So, cobalt we looked up + + + align:start position:0% +All right. So, cobalt we looked up +before and it was in nine. So, over here + + align:start position:0% +before and it was in nine. So, over here + + + align:start position:0% +before and it was in nine. So, over here +we have plus two and we have group 9 + + align:start position:0% +we have plus two and we have group 9 + + + align:start position:0% +we have plus two and we have group 9 +minus 2 is seven. And so that's a D7 + + align:start position:0% +minus 2 is seven. And so that's a D7 + + + align:start position:0% +minus 2 is seven. And so that's a D7 +system. So that's how you will you will + + align:start position:0% +system. So that's how you will you will + + + align:start position:0% +system. So that's how you will you will +do those problems + + align:start position:0% +do those problems + + + align:start position:0% +do those problems +and those go into you'll need that on + + align:start position:0% +and those go into you'll need that on + + + align:start position:0% +and those go into you'll need that on +Monday when we start talking about + + align:start position:0% +Monday when we start talking about + + + align:start position:0% +Monday when we start talking about +crystal field theory. + + align:start position:0% +crystal field theory. + + + align:start position:0% +crystal field theory. +Okay. So in the last uh couple of + + align:start position:0% +Okay. So in the last uh couple of + + + align:start position:0% +Okay. So in the last uh couple of +minutes I want to remind you of the + + align:start position:0% +minutes I want to remind you of the + + + align:start position:0% +minutes I want to remind you of the +shapes of d orbitals. + + align:start position:0% +shapes of d orbitals. + + + align:start position:0% +shapes of d orbitals. +So this is leading into what we knew + + align:start position:0% +So this is leading into what we knew + + + align:start position:0% +So this is leading into what we knew +next. Again, we're thinking about the + + align:start position:0% +next. Again, we're thinking about the + + + align:start position:0% +next. Again, we're thinking about the +shapes of the d orbitals and the metals. + + align:start position:0% +shapes of the d orbitals and the metals. + + + align:start position:0% +shapes of the d orbitals and the metals. +And then we're thinking about the shapes + + align:start position:0% +And then we're thinking about the shapes + + + align:start position:0% +And then we're thinking about the shapes +of the coordination complexes, and we're + + align:start position:0% +of the coordination complexes, and we're + + + align:start position:0% +of the coordination complexes, and we're +trying to figure out whether the lians + + align:start position:0% +trying to figure out whether the lians + + + align:start position:0% +trying to figure out whether the lians +are going to be near the d- orbitals or + + align:start position:0% +are going to be near the d- orbitals or + + + align:start position:0% +are going to be near the d- orbitals or +away. And depending on how the lians are + + align:start position:0% +away. And depending on how the lians are + + + align:start position:0% +away. And depending on how the lians are +arranged with respect to the d- orbitals + + align:start position:0% +arranged with respect to the d- orbitals + + + align:start position:0% +arranged with respect to the d- orbitals +changes the properties of the + + align:start position:0% +changes the properties of the + + + align:start position:0% +changes the properties of the +coordination complex. All right. So + + align:start position:0% +coordination complex. All right. So + + + align:start position:0% +coordination complex. All right. So +there are five d orbitals and you should + + align:start position:0% +there are five d orbitals and you should + + + align:start position:0% +there are five d orbitals and you should +be able to draw them. Again, the bar for + + align:start position:0% +be able to draw them. Again, the bar for + + + align:start position:0% +be able to draw them. Again, the bar for +successfully drawing the d- orbitals is + + align:start position:0% +successfully drawing the d- orbitals is + + + align:start position:0% +successfully drawing the d- orbitals is +you have to do as well as I do when I + + align:start position:0% +you have to do as well as I do when I + + + align:start position:0% +you have to do as well as I do when I +try to draw the d- orbitals. Again, it's + + align:start position:0% +try to draw the d- orbitals. Again, it's + + + align:start position:0% +try to draw the d- orbitals. Again, it's +a low bar for drawing. Uh you just kind + + align:start position:0% +a low bar for drawing. Uh you just kind + + + align:start position:0% +a low bar for drawing. Uh you just kind +of need to get some of the general + + align:start position:0% +of need to get some of the general + + + align:start position:0% +of need to get some of the general +features right. So, if we look at dz 2, + + align:start position:0% +features right. So, if we look at dz 2, + + + align:start position:0% +features right. So, if we look at dz 2, +it has a maximum amplitude along the + + align:start position:0% +it has a maximum amplitude along the + + + align:start position:0% +it has a maximum amplitude along the +z-axis. And in this course, we'll always + + align:start position:0% +z-axis. And in this course, we'll always + + + align:start position:0% +z-axis. And in this course, we'll always +try to keep the axis more or less the + + align:start position:0% +try to keep the axis more or less the + + + align:start position:0% +try to keep the axis more or less the +same to help you out. um and uh they + + align:start position:0% +same to help you out. um and uh they + + + align:start position:0% +same to help you out. um and uh they +will be labeled so you know where the + + align:start position:0% +will be labeled so you know where the + + + align:start position:0% +will be labeled so you know where the +z-axis is. So here's the z-axis. Y is uh + + align:start position:0% +z-axis is. So here's the z-axis. Y is uh + + + align:start position:0% +z-axis is. So here's the z-axis. Y is uh +along the plane here and x is coming out + + align:start position:0% +along the plane here and x is coming out + + + align:start position:0% +along the plane here and x is coming out +toward you. So there's x and then you + + align:start position:0% +toward you. So there's x and then you + + + align:start position:0% +toward you. So there's x and then you +have a donut in the uh xy plane. So d + + align:start position:0% +have a donut in the uh xy plane. So d + + + align:start position:0% +have a donut in the uh xy plane. So d +x^2us y^2 has maximum amplitudes along x + + align:start position:0% +x^2us y^2 has maximum amplitudes along x + + + align:start position:0% +x^2us y^2 has maximum amplitudes along x +and y. So it doesn't have anything along + + align:start position:0% +and y. So it doesn't have anything along + + + align:start position:0% +and y. So it doesn't have anything along +z. The orbitals are along y in the plane + + align:start position:0% +z. The orbitals are along y in the plane + + + align:start position:0% +z. The orbitals are along y in the plane +of the board and along x coming out + + align:start position:0% +of the board and along x coming out + + + align:start position:0% +of the board and along x coming out +towards you and also going behind the + + align:start position:0% +towards you and also going behind the + + + align:start position:0% +towards you and also going behind the +screen. + + align:start position:0% + + + + align:start position:0% + +So then we have three more. We have d uh + + align:start position:0% +So then we have three more. We have d uh + + + align:start position:0% +So then we have three more. We have d uh +yz and it has its amplitudes 45 degrees + + align:start position:0% +yz and it has its amplitudes 45 degrees + + + align:start position:0% +yz and it has its amplitudes 45 degrees +off the uh y and the z axis. So here's y + + align:start position:0% +off the uh y and the z axis. So here's y + + + align:start position:0% +off the uh y and the z axis. So here's y +up and down and uh a z up and down and y + + align:start position:0% +up and down and uh a z up and down and y + + + align:start position:0% +up and down and uh a z up and down and y +uh across the plane of the board. And so + + align:start position:0% +uh across the plane of the board. And so + + + align:start position:0% +uh across the plane of the board. And so +these orbitals are drawn to be 45 + + align:start position:0% +these orbitals are drawn to be 45 + + + align:start position:0% +these orbitals are drawn to be 45 +degrees off those axes. dxy is 45° to + + align:start position:0% +degrees off those axes. dxy is 45° to + + + align:start position:0% +degrees off those axes. dxy is 45° to +the x and the z. So these are coming out + + align:start position:0% +the x and the z. So these are coming out + + + align:start position:0% +the x and the z. So these are coming out +towards you and going behind and also + + align:start position:0% +towards you and going behind and also + + + align:start position:0% +towards you and going behind and also +going up. And then d y uh dxy is 45 + + align:start position:0% +going up. And then d y uh dxy is 45 + + + align:start position:0% +going up. And then d y uh dxy is 45 +degrees off of y and x. And you'll need + + align:start position:0% +degrees off of y and x. And you'll need + + + align:start position:0% +degrees off of y and x. And you'll need +to know how to draw these and need to + + align:start position:0% +to know how to draw these and need to + + + align:start position:0% +to know how to draw these and need to +know the shapes and to be able to think + + align:start position:0% +know the shapes and to be able to think + + + align:start position:0% +know the shapes and to be able to think +about them in 3D so that you can imagine + + align:start position:0% +about them in 3D so that you can imagine + + + align:start position:0% +about them in 3D so that you can imagine +where lians are and how those lians are + + align:start position:0% +where lians are and how those lians are + + + align:start position:0% +where lians are and how those lians are +affected by these dorbitals. + + align:start position:0% +affected by these dorbitals. + + + align:start position:0% +affected by these dorbitals. +Have a great weekend. \ No newline at end of file diff --git a/xAuh5VptDQ4.txt b/xAuh5VptDQ4.txt new file mode 100644 index 0000000000000000000000000000000000000000..3ba28f36be051d25c19c76ae21d961d3a7712046 --- /dev/null +++ b/xAuh5VptDQ4.txt @@ -0,0 +1,67 @@ +align:start position:0% + +hi I'm Angie and I'll be presenting the + + align:start position:0% +hi I'm Angie and I'll be presenting the + + + align:start position:0% +hi I'm Angie and I'll be presenting the +recitation for this week in lecture two + + align:start position:0% +recitation for this week in lecture two + + + align:start position:0% +recitation for this week in lecture two +we saw the story of Moneyball and + + align:start position:0% +we saw the story of Moneyball and + + + align:start position:0% +we saw the story of Moneyball and +explored how to build linear regression + + align:start position:0% +explored how to build linear regression + + + align:start position:0% +explored how to build linear regression +models for baseball analytics today + + align:start position:0% +models for baseball analytics today + + + align:start position:0% +models for baseball analytics today +we'll apply the same method linear + + align:start position:0% +we'll apply the same method linear + + + align:start position:0% +we'll apply the same method linear +regression to data from the National + + align:start position:0% +regression to data from the National + + + align:start position:0% +regression to data from the National +Basketball Association the NBA let's get + + align:start position:0% +Basketball Association the NBA let's get + + + align:start position:0% +Basketball Association the NBA let's get +started \ No newline at end of file diff --git a/x_0TWhJ1nh4.txt b/x_0TWhJ1nh4.txt new file mode 100644 index 0000000000000000000000000000000000000000..eea8582a01fdaa88bd2783fce16d5b2e02234916 --- /dev/null +++ b/x_0TWhJ1nh4.txt @@ -0,0 +1,603 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mit.edu. + + align:start position:0% + + + + align:start position:0% + +Now, we're ready to look at two slit + + align:start position:0% +Now, we're ready to look at two slit + + + align:start position:0% +Now, we're ready to look at two slit +defraction patterns. + + align:start position:0% +defraction patterns. + + + align:start position:0% +defraction patterns. +What we have here is a is a slide and on + + align:start position:0% +What we have here is a is a slide and on + + + align:start position:0% +What we have here is a is a slide and on +the slide we have pairs of slits. + + align:start position:0% +the slide we have pairs of slits. + + + align:start position:0% +the slide we have pairs of slits. +The individual width of each slit is 100 + + align:start position:0% +The individual width of each slit is 100 + + + align:start position:0% +The individual width of each slit is 100 +microns + + align:start position:0% +microns + + + align:start position:0% +microns +and the spacing between slits varies + + align:start position:0% +and the spacing between slits varies + + + align:start position:0% +and the spacing between slits varies +anywhere from 150 microns to 2 + + align:start position:0% +anywhere from 150 microns to 2 + + + align:start position:0% +anywhere from 150 microns to 2 +millimeters. + + align:start position:0% +millimeters. + + + align:start position:0% +millimeters. +The only thing we've added to the + + align:start position:0% +The only thing we've added to the + + + align:start position:0% +The only thing we've added to the +previous setup is is this lens in order + + align:start position:0% +previous setup is is this lens in order + + + align:start position:0% +previous setup is is this lens in order +to expand the beam so that we can cover + + align:start position:0% +to expand the beam so that we can cover + + + align:start position:0% +to expand the beam so that we can cover +um both both slits. So let's first look + + align:start position:0% +um both both slits. So let's first look + + + align:start position:0% +um both both slits. So let's first look +at the defraction pattern associated + + align:start position:0% +at the defraction pattern associated + + + align:start position:0% +at the defraction pattern associated +with with a single slit. So now if we + + align:start position:0% +with with a single slit. So now if we + + + align:start position:0% +with with a single slit. So now if we +look at the screen in closeup you can + + align:start position:0% +look at the screen in closeup you can + + + align:start position:0% +look at the screen in closeup you can +see we have a single slit defraction + + align:start position:0% +see we have a single slit defraction + + + align:start position:0% +see we have a single slit defraction +pattern. + + align:start position:0% +pattern. + + + align:start position:0% +pattern. +The as before the circles + + align:start position:0% +The as before the circles + + + align:start position:0% +The as before the circles +are 5cm markers and in addition now + + align:start position:0% +are 5cm markers and in addition now + + + align:start position:0% +are 5cm markers and in addition now +we've added the little squares the two + + align:start position:0% +we've added the little squares the two + + + align:start position:0% +we've added the little squares the two +squares and that denotes the separation + + align:start position:0% +squares and that denotes the separation + + + align:start position:0% +squares and that denotes the separation +between the zeros of the center lobe of + + align:start position:0% +between the zeros of the center lobe of + + + align:start position:0% +between the zeros of the center lobe of +the single slit defraction pattern. Let + + align:start position:0% +the single slit defraction pattern. Let + + + align:start position:0% +the single slit defraction pattern. Let +me remind you that the spacing between + + align:start position:0% +me remind you that the spacing between + + + align:start position:0% +me remind you that the spacing between +the slide here and the screen is about + + align:start position:0% +the slide here and the screen is about + + + align:start position:0% +the slide here and the screen is about +200 cm and we're using six 6,328 + + align:start position:0% +200 cm and we're using six 6,328 + + + align:start position:0% +200 cm and we're using six 6,328 +angstrom light. All right, so you have + + align:start position:0% +angstrom light. All right, so you have + + + align:start position:0% +angstrom light. All right, so you have +all the tools needed then to calculate + + align:start position:0% +all the tools needed then to calculate + + + align:start position:0% +all the tools needed then to calculate +spacings and what have you. So now let's + + align:start position:0% +spacings and what have you. So now let's + + + align:start position:0% +spacings and what have you. So now let's +start + + align:start position:0% +start + + + align:start position:0% +start +by looking at the smallest uh spacing + + align:start position:0% +by looking at the smallest uh spacing + + + align:start position:0% +by looking at the smallest uh spacing +which is 150 microns. So indeed what you + + align:start position:0% +which is 150 microns. So indeed what you + + + align:start position:0% +which is 150 microns. So indeed what you +see is that the single slit defraction + + align:start position:0% +see is that the single slit defraction + + + align:start position:0% +see is that the single slit defraction +pattern now has been modified by the + + align:start position:0% +pattern now has been modified by the + + + align:start position:0% +pattern now has been modified by the +addition of the other loes of the + + align:start position:0% +addition of the other loes of the + + + align:start position:0% +addition of the other loes of the +smaller loes and this is for then for + + align:start position:0% +smaller loes and this is for then for + + + align:start position:0% +smaller loes and this is for then for +150 micron spacing. + + align:start position:0% +150 micron spacing. + + + align:start position:0% +150 micron spacing. +Remember each slit width is 100 microns. + + align:start position:0% +Remember each slit width is 100 microns. + + + align:start position:0% +Remember each slit width is 100 microns. +Now, let's go on and look at 175. Well, + + align:start position:0% +Now, let's go on and look at 175. Well, + + + align:start position:0% +Now, let's go on and look at 175. Well, +175 from 150 is not much of a change. + + align:start position:0% +175 from 150 is not much of a change. + + + align:start position:0% +175 from 150 is not much of a change. +So, you don't expect to see uh much + + align:start position:0% +So, you don't expect to see uh much + + + align:start position:0% +So, you don't expect to see uh much +narrowing of the of the small loes. + + align:start position:0% +narrowing of the of the small loes. + + + align:start position:0% +narrowing of the of the small loes. +Let's go on to 200. + + align:start position:0% +Let's go on to 200. + + + align:start position:0% +Let's go on to 200. +Well, here you're beginning to see that + + align:start position:0% +Well, here you're beginning to see that + + + align:start position:0% +Well, here you're beginning to see that +the the loes under the single slit + + align:start position:0% +the the loes under the single slit + + + align:start position:0% +the the loes under the single slit +defraction pattern are now narrower. And + + align:start position:0% +defraction pattern are now narrower. And + + + align:start position:0% +defraction pattern are now narrower. And +now 300 micron separation. Well, here + + align:start position:0% +now 300 micron separation. Well, here + + + align:start position:0% +now 300 micron separation. Well, here +it's clear they're getting they're + + align:start position:0% +it's clear they're getting they're + + + align:start position:0% +it's clear they're getting they're +getting narrower. In fact, you have + + align:start position:0% +getting narrower. In fact, you have + + + align:start position:0% +getting narrower. In fact, you have +about five of them or so under the uh + + align:start position:0% +about five of them or so under the uh + + + align:start position:0% +about five of them or so under the uh +central lobe of the single slit + + align:start position:0% +central lobe of the single slit + + + align:start position:0% +central lobe of the single slit +defraction pattern. Now, let me go on to + + align:start position:0% +defraction pattern. Now, let me go on to + + + align:start position:0% +defraction pattern. Now, let me go on to +the 2,00 or 2 mm spacing. And at first, + + align:start position:0% +the 2,00 or 2 mm spacing. And at first, + + + align:start position:0% +the 2,00 or 2 mm spacing. And at first, +you think there's no + + align:start position:0% +you think there's no + + + align:start position:0% +you think there's no +little loes under the single thread + + align:start position:0% +little loes under the single thread + + + align:start position:0% +little loes under the single thread +diffraction pattern. But all we have to + + align:start position:0% +diffraction pattern. But all we have to + + + align:start position:0% +diffraction pattern. But all we have to +do here is get the camera to zoom in. + + align:start position:0% +do here is get the camera to zoom in. + + + align:start position:0% +do here is get the camera to zoom in. +And as it zooms in, you begin to see + + align:start position:0% +And as it zooms in, you begin to see + + + align:start position:0% +And as it zooms in, you begin to see +that indeed there is structure there. + + align:start position:0% +that indeed there is structure there. + + + align:start position:0% +that indeed there is structure there. +And if the if your calculations are + + align:start position:0% +And if the if your calculations are + + + align:start position:0% +And if the if your calculations are +correct, you'll be able to show what the + + align:start position:0% +correct, you'll be able to show what the + + + align:start position:0% +correct, you'll be able to show what the +spacing is for a 2 mm + + align:start position:0% +spacing is for a 2 mm + + + align:start position:0% +spacing is for a 2 mm +slit separation. + + align:start position:0% +slit separation. + + + align:start position:0% +slit separation. +Now, in the in the next uh + + align:start position:0% +Now, in the in the next uh + + + align:start position:0% +Now, in the in the next uh +demonstration, we're going to show the + + align:start position:0% +demonstration, we're going to show the + + + align:start position:0% +demonstration, we're going to show the +the franha defraction pattern associated + + align:start position:0% +the franha defraction pattern associated + + + align:start position:0% +the franha defraction pattern associated +with many slits. \ No newline at end of file diff --git a/x_vlxGFrZLY.txt b/x_vlxGFrZLY.txt new file mode 100644 index 0000000000000000000000000000000000000000..0fdb48afc4696d3d91838be5c28b93205cd26ed8 --- /dev/null +++ b/x_vlxGFrZLY.txt @@ -0,0 +1,371 @@ +PROFESSOR: Hi. + +In this clip, we're going to go +through problem two of the + +transcription and translation +unit. + +We're also going to review all +of the information you would + +need to fill out problem +one, the table. + +If you haven't tried these +problems yet on your own, + +please pause the video now and +try them, and then come back + +and watch this explanation. + +OK. + +So here we have, as in problem +two, the double stranded DNA. + +Now, this is a piece of the +eukaryotic genome, and so this + +DNA is in the nucleus +of the cell. + +Now what we're going to do is +we're going to go through + +transcription and translation +with this gene. + +So the first thing we need to +do is we need to figure out + +where we want to start +transcription and in what + +direction we want to go and what +strand we want to use as + +our template. + +So in the problem, we're given +our promoter region and we're + +given that our transcription +starts right here at this + +arrow and moves in +this direction. + +So we know where we're starting +and what direction + +we're moving in. + +All transcription will proceed +reading a template in the + +three prime to five prime +direction and will polymerize + +the RNA made in the five prime +to three prime direction. + +So what we need to do now is +figure out what strand is + +going in the three prime to five +prime direction and the + +direction that we're going +to be transcribed. + +So that means that this strand, +which is going from + +three prime over here down to +five prime at the end, this is + +going to be our template +strand. + +So our template strand is going +to be at the bottom. + +OK. + +So when our RNA polymerase +starts, it's going to be + +reading this template strand +and adding nucleic acid, + +adding nucleotide triphosphates, +or NTPs, one by + +one together to make the RNA. + +Now it's going to add these +together by adding a + +phosphodiester bond in between +all of the monomers. + +So we're going to start +our transcription. + +And basically, what I need +to do is just use the + +complimentary base pair +to my template strand. + +So I'm going to write +it out here. + +So I've done a lot of +transcription here. + +Now where am I going to +stop my transcription? + +I'm not going to stop +just randomly in + +the middle of nowhere. + +What my RNA polymerase is going +to do is it's going to + +stop when it gets to the end of +this terminator sequence. + +So I'm going to keep +transcribing until I get to + +the end of my terminator here. + +OK. + +So this is my RNA strand. + +And as I said before, we're +going to polymerize this mRNA + +in the five prime to three +prime direction. + +OK, we've got our mRNA. + +Since this is a eukaryotic cell +and the mRNA right now is + +in the nucleus, what we need to +do is transport it out of + +the nucleus and into the +cytoplasm where it will be + +translated by a ribosome. + +Now what the ribosome is going +to do is it's going to take + +this mRNA, which is a message +that encodes the sequence of + +amino acids that we need to +put together to make the + +protein, and we're going to take +this message and we're + +going to find a place to +start translation. + +So what the ribosome is going +to do is it's going to start + +at the five prime end of the +template and read towards the + +three prime end of +the template. + +It's going to read until it +gets to a start codon. + +The start codon is AUG. + +So this is where we're going +to start, and AUG encodes + +methionine. + +We're then going to read in +three base pair codons down + +from the five prime end of our +template to the three prime + +end of our template. + +And so we're going to keep +going in this translation + +until we reach what's +called a stop codon. + +Now there are three +stop codons. + +Stop codons are UAA, +UGA, and UAG. + +So if when my ribosome finds any +of these three codons in + +frame, it's going to stop. + +So I get all the way down here +before I hit a stop codon on + +this transcript. + +So what my ribosome is going +to be doing as it's reading + +these codons is it's going to +insert amino acid by amino + +acid, pairing them together +with a peptide bond. + +So we've got methionine bonded +to histidine, tyrosine, + +leucine, and so on +and so forth. + +OK, so this is the protein chain +that's encoded by this + +gene in the DNA. + +And in proteins, we always +synthesize from the N terminus + +to the C terminus. + +OK, so we've gone through both +transcription and translation. + +Now what we want to do is we +want to take into account what + +would happen if we had a +mutation in our sequence. + +So in this case, in this +problem, we're going to insert + +a base pair right here. + +So we're going to insert +an extra T here + +and an extra A here. + +Now, if this is happening in +the DNA, when our DNA is + +transcribed to make our +RNA, what's going to + +happen to the RNA? + +Well, we're going to also add +the corresponding base into + +our RNA, so we're going to +have an extra U here. + +So in addition to only adding +one nucleotide in our RNA, + +this is also going to throw +off our frame that we're + +reading when our ribosome +is reading our RNA. + +So instead of the frame that we +had previously, we're now + +going to have a new frame. + +So it's going to start at the +same start codon and then read + +this codon just as normal, but +then this U will make UUA and + +then will read in codons +of three from there. + +So again, I need to translate +until I hit a stop codon. + +And so the stop codon is going +to be different in this case, + +because this stop codon +is no longer in frame. + +I need to find an in +frame stop codon. + +And the first stop codon that I +hit is going to be this you + +UAG right here. + +And so our new protein sequence +is now going to be N + +terminus, and then the beginning +is going to be very + +similar, and then our amino +acids are going to be + +completely different because +we're reading this in a + +different frame. + +OK, so we can see how this one +mutation, addition of one base + +pair into our DNA, has caused +us to create a completely + +different peptide. + +It's probably not going to +perform the same function. + +OK. + +So we've gone over transcription +and translation. + +You should be able at this +point to answer all of + +question two and you should +also be able to fill in + +all of table one. + +Thank you for watching. \ No newline at end of file diff --git a/yrmqYNvvIzs.txt b/yrmqYNvvIzs.txt new file mode 100644 index 0000000000000000000000000000000000000000..471f08f3d02406699bc699b2dc7ec5ac084284ce --- /dev/null +++ b/yrmqYNvvIzs.txt @@ -0,0 +1,14840 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu now also before I begin + + align:start position:0% +ocw.mit.edu now also before I begin + + + align:start position:0% +ocw.mit.edu now also before I begin +today's lecture I want to comment a bit + + align:start position:0% +today's lecture I want to comment a bit + + + align:start position:0% +today's lecture I want to comment a bit +about what's going on in the news + + align:start position:0% +about what's going on in the news + + + align:start position:0% +about what's going on in the news +because at last uh last time on Monday + + align:start position:0% +because at last uh last time on Monday + + + align:start position:0% +because at last uh last time on Monday +we we said or I said that the Fed was + + align:start position:0% +we we said or I said that the Fed was + + + align:start position:0% +we we said or I said that the Fed was +going to cut + + align:start position:0% +going to cut + + + align:start position:0% +going to cut +rates and uh in fact if you looked at + + align:start position:0% +rates and uh in fact if you looked at + + + align:start position:0% +rates and uh in fact if you looked at +the data on Monday and you looked at + + align:start position:0% +the data on Monday and you looked at + + + align:start position:0% +the data on Monday and you looked at +things like the FED funds future and + + align:start position:0% +things like the FED funds future and + + + align:start position:0% +things like the FED funds future and +other Financial contracts the market had + + align:start position:0% +other Financial contracts the market had + + + align:start position:0% +other Financial contracts the market had +priced in the fact that the Fed was + + align:start position:0% +priced in the fact that the Fed was + + + align:start position:0% +priced in the fact that the Fed was +going to cut at least 25 basis points + + align:start position:0% +going to cut at least 25 basis points + + + align:start position:0% +going to cut at least 25 basis points +and actually a reasonable probability + + align:start position:0% +and actually a reasonable probability + + + align:start position:0% +and actually a reasonable probability +that it was going to cut 50 and of of + + align:start position:0% +that it was going to cut 50 and of of + + + align:start position:0% +that it was going to cut 50 and of of +course they did neither they actually + + align:start position:0% +course they did neither they actually + + + align:start position:0% +course they did neither they actually +held rat + + align:start position:0% +held rat + + + align:start position:0% +held rat +steady but they did do + + align:start position:0% +steady but they did do + + + align:start position:0% +steady but they did do +something who what did they do anybody + + align:start position:0% +something who what did they do anybody + + + align:start position:0% +something who what did they do anybody +no + + align:start position:0% + + + + align:start position:0% + +yeah how how large a loan 85 + + align:start position:0% +yeah how how large a loan 85 + + + align:start position:0% +yeah how how large a loan 85 +billion which even among friends is a + + align:start position:0% +billion which even among friends is a + + + align:start position:0% +billion which even among friends is a +lot of + + align:start position:0% +lot of + + + align:start position:0% +lot of +money now this is yet again an + + align:start position:0% +money now this is yet again an + + + align:start position:0% +money now this is yet again an +extraordinary and unprecedented measure + + align:start position:0% +extraordinary and unprecedented measure + + + align:start position:0% +extraordinary and unprecedented measure +you know we know that that the FED did + + align:start position:0% +you know we know that that the FED did + + + align:start position:0% +you know we know that that the FED did +Back Stop Bear Sterns but the FED didn't + + align:start position:0% +Back Stop Bear Sterns but the FED didn't + + + align:start position:0% +Back Stop Bear Sterns but the FED didn't +spend any direct money on Bear Sterns + + align:start position:0% +spend any direct money on Bear Sterns + + + align:start position:0% +spend any direct money on Bear Sterns +they basically got JP Morgan to buy Bear + + align:start position:0% +they basically got JP Morgan to buy Bear + + + align:start position:0% +they basically got JP Morgan to buy Bear +Sterns and negotiated the + + align:start position:0% +Sterns and negotiated the + + + align:start position:0% +Sterns and negotiated the +deal in this instance the FED is lending + + align:start position:0% +deal in this instance the FED is lending + + + align:start position:0% +deal in this instance the FED is lending +money to AIG lending $85 billion and AIG + + align:start position:0% +money to AIG lending $85 billion and AIG + + + align:start position:0% +money to AIG lending $85 billion and AIG +isn't even a bank + + align:start position:0% +isn't even a bank + + + align:start position:0% +isn't even a bank +so what do you think is going on does + + align:start position:0% +so what do you think is going on does + + + align:start position:0% +so what do you think is going on does +that make sense what does that tell you + + align:start position:0% +that make sense what does that tell you + + + align:start position:0% +that make sense what does that tell you +about what's going on in markets the + + align:start position:0% +about what's going on in markets the + + + align:start position:0% +about what's going on in markets the +fact that the everybody thought the Fed + + align:start position:0% +fact that the everybody thought the Fed + + + align:start position:0% +fact that the everybody thought the Fed +was going to cut rates + + align:start position:0% +was going to cut rates + + + align:start position:0% +was going to cut rates +and they didn't that shows a certain + + align:start position:0% +and they didn't that shows a certain + + + align:start position:0% +and they didn't that shows a certain +kind of restraint in fact I think it was + + align:start position:0% +kind of restraint in fact I think it was + + + align:start position:0% +kind of restraint in fact I think it was +this class that somebody mentioned well + + align:start position:0% +this class that somebody mentioned well + + + align:start position:0% +this class that somebody mentioned well +rates are already down at 2% how much + + align:start position:0% +rates are already down at 2% how much + + + align:start position:0% +rates are already down at 2% how much +more can they cut I mean if they cut 50 + + align:start position:0% +more can they cut I mean if they cut 50 + + + align:start position:0% +more can they cut I mean if they cut 50 +basis points that leaves them very + + align:start position:0% +basis points that leaves them very + + + align:start position:0% +basis points that leaves them very +little flexibility and also if you think + + align:start position:0% +little flexibility and also if you think + + + align:start position:0% +little flexibility and also if you think +that the reason we are in this crisis is + + align:start position:0% +that the reason we are in this crisis is + + + align:start position:0% +that the reason we are in this crisis is +because borrowing has been so low for so + + align:start position:0% +because borrowing has been so low for so + + + align:start position:0% +because borrowing has been so low for so +long that people have been going out and + + align:start position:0% +long that people have been going out and + + + align:start position:0% +long that people have been going out and +making all these bad loans and they + + align:start position:0% +making all these bad loans and they + + + align:start position:0% +making all these bad loans and they +shouldn't be doing that to begin with + + align:start position:0% +shouldn't be doing that to begin with + + + align:start position:0% +shouldn't be doing that to begin with +cutting rates is not going to really + + align:start position:0% +cutting rates is not going to really + + + align:start position:0% +cutting rates is not going to really +help that situation but can only + + align:start position:0% +help that situation but can only + + + align:start position:0% +help that situation but can only +encourage it but nevertheless there was + + align:start position:0% +encourage it but nevertheless there was + + + align:start position:0% +encourage it but nevertheless there was +a crisis certainly over the weekend we + + align:start position:0% +a crisis certainly over the weekend we + + + align:start position:0% +a crisis certainly over the weekend we +had some very bad news Leman Brothers + + align:start position:0% +had some very bad news Leman Brothers + + + align:start position:0% +had some very bad news Leman Brothers +went under and the FED did + + align:start position:0% +went under and the FED did + + + align:start position:0% +went under and the FED did +what nothing so if the FED did nothing + + align:start position:0% +what nothing so if the FED did nothing + + + align:start position:0% +what nothing so if the FED did nothing +for lhan yet they extended an 85 billion + + align:start position:0% +for lhan yet they extended an 85 billion + + + align:start position:0% +for lhan yet they extended an 85 billion +loan for AIG what something's got to be + + align:start position:0% +loan for AIG what something's got to be + + + align:start position:0% +loan for AIG what something's got to be +different right I mean I guess you could + + align:start position:0% +different right I mean I guess you could + + + align:start position:0% +different right I mean I guess you could +see whether or not Ben banki has a + + align:start position:0% +see whether or not Ben banki has a + + + align:start position:0% +see whether or not Ben banki has a +brother-in-law working at AIG but I + + align:start position:0% +brother-in-law working at AIG but I + + + align:start position:0% +brother-in-law working at AIG but I +don't think that's it yeah + + align:start position:0% +don't think that's it yeah + + + align:start position:0% +don't think that's it yeah +report that barley is actually going to + + align:start position:0% +report that barley is actually going to + + + align:start position:0% +report that barley is actually going to +go ahead and buy what changed well + + align:start position:0% +go ahead and buy what changed well + + + align:start position:0% +go ahead and buy what changed well +Barkley's the the announcement is that + + align:start position:0% +Barkley's the the announcement is that + + + align:start position:0% +Barkley's the the announcement is that +Barkley is buying some of the US + + align:start position:0% +Barkley is buying some of the US + + + align:start position:0% +Barkley is buying some of the US +operations of Leman Brothers they are + + align:start position:0% +operations of Leman Brothers they are + + + align:start position:0% +operations of Leman Brothers they are +cherry-picking the operations that they + + align:start position:0% +cherry-picking the operations that they + + + align:start position:0% +cherry-picking the operations that they +want what Leman tried to do over the + + align:start position:0% +want what Leman tried to do over the + + + align:start position:0% +want what Leman tried to do over the +weekend was broker a deal where Barkley + + align:start position:0% +weekend was broker a deal where Barkley + + + align:start position:0% +weekend was broker a deal where Barkley +would buy all of them and assume all + + align:start position:0% +would buy all of them and assume all + + + align:start position:0% +would buy all of them and assume all +their obligations and allow them to keep + + align:start position:0% +their obligations and allow them to keep + + + align:start position:0% +their obligations and allow them to keep +on going as a going business concern + + align:start position:0% +on going as a going business concern + + + align:start position:0% +on going as a going business concern +Barkley's couldn't do that because they + + align:start position:0% +Barkley's couldn't do that because they + + + align:start position:0% +Barkley's couldn't do that because they +couldn't get shareholder approval + + align:start position:0% +couldn't get shareholder approval + + + align:start position:0% +couldn't get shareholder approval +quickly enough and also aens because the + + align:start position:0% +quickly enough and also aens because the + + + align:start position:0% +quickly enough and also aens because the +FED would not back stop any losses that + + align:start position:0% +FED would not back stop any losses that + + + align:start position:0% +FED would not back stop any losses that +Leman had hidden in its books and you + + align:start position:0% +Leman had hidden in its books and you + + + align:start position:0% +Leman had hidden in its books and you +know in a matter of 48 hours it's kind + + align:start position:0% +know in a matter of 48 hours it's kind + + + align:start position:0% +know in a matter of 48 hours it's kind +of hard to figure out all the buried + + align:start position:0% +of hard to figure out all the buried + + + align:start position:0% +of hard to figure out all the buried +bodies in an organization as complex and + + align:start position:0% +bodies in an organization as complex and + + + align:start position:0% +bodies in an organization as complex and +as large as lemman but but Barkley is + + align:start position:0% +as large as lemman but but Barkley is + + + align:start position:0% +as large as lemman but but Barkley is +going ahead and purchasing those units + + align:start position:0% +going ahead and purchasing those units + + + align:start position:0% +going ahead and purchasing those units +that they like and there are many units + + align:start position:0% +that they like and there are many units + + + align:start position:0% +that they like and there are many units +at Leman brothers that are + + align:start position:0% +at Leman brothers that are + + + align:start position:0% +at Leman brothers that are +extraordinarily profitable very good + + align:start position:0% +extraordinarily profitable very good + + + align:start position:0% +extraordinarily profitable very good +businesses with excellent people so + + align:start position:0% +businesses with excellent people so + + + align:start position:0% +businesses with excellent people so +barkle is going ahead with those and by + + align:start position:0% +barkle is going ahead with those and by + + + align:start position:0% +barkle is going ahead with those and by +the way there are all sorts of other + + align:start position:0% +the way there are all sorts of other + + + align:start position:0% +the way there are all sorts of other +sharks that are swimming around Leman + + align:start position:0% +sharks that are swimming around Leman + + + align:start position:0% +sharks that are swimming around Leman +cherry picking various different groups + + align:start position:0% +cherry picking various different groups + + + align:start position:0% +cherry picking various different groups +this is part of the problem with these + + align:start position:0% +this is part of the problem with these + + + align:start position:0% +this is part of the problem with these +this kind of financial distress we're + + align:start position:0% +this kind of financial distress we're + + + align:start position:0% +this kind of financial distress we're +going to actually get to this at about + + align:start position:0% +going to actually get to this at about + + + align:start position:0% +going to actually get to this at about +lecture 18 we're going to talk about + + align:start position:0% +lecture 18 we're going to talk about + + + align:start position:0% +lecture 18 we're going to talk about +financial distress and I'm going to + + align:start position:0% +financial distress and I'm going to + + + align:start position:0% +financial distress and I'm going to +bring you back to Leman brothers and ask + + align:start position:0% +bring you back to Leman brothers and ask + + + align:start position:0% +bring you back to Leman brothers and ask +you to think about the problems that + + align:start position:0% +you to think about the problems that + + + align:start position:0% +you to think about the problems that +this company faces because think about + + align:start position:0% +this company faces because think about + + + align:start position:0% +this company faces because think about +it now that it's been announced that + + align:start position:0% +it now that it's been announced that + + + align:start position:0% +it now that it's been announced that +Leman is liquidating well let me put it + + align:start position:0% +Leman is liquidating well let me put it + + + align:start position:0% +Leman is liquidating well let me put it +to you this way suppose you were working + + align:start position:0% +to you this way suppose you were working + + + align:start position:0% +to you this way suppose you were working +at Leman brothers and suppose that + + align:start position:0% +at Leman brothers and suppose that + + + align:start position:0% +at Leman brothers and suppose that +you've been there 15 years and suppose + + align:start position:0% +you've been there 15 years and suppose + + + align:start position:0% +you've been there 15 years and suppose +that you were running one of the most + + align:start position:0% +that you were running one of the most + + + align:start position:0% +that you were running one of the most +most successful uh proprietary trading + + align:start position:0% +most successful uh proprietary trading + + + align:start position:0% +most successful uh proprietary trading +groups at Leman brothers and now this + + align:start position:0% +groups at Leman brothers and now this + + + align:start position:0% +groups at Leman brothers and now this +news comes up and it's a surprise to + + align:start position:0% +news comes up and it's a surprise to + + + align:start position:0% +news comes up and it's a surprise to +you what is your first reaction what are + + align:start position:0% +you what is your first reaction what are + + + align:start position:0% +you what is your first reaction what are +you going to do yeah right that's + + align:start position:0% +you going to do yeah right that's + + + align:start position:0% +you going to do yeah right that's +certainly one thing you're going to take + + align:start position:0% +certainly one thing you're going to take + + + align:start position:0% +certainly one thing you're going to take +a look at what your positions are and + + align:start position:0% +a look at what your positions are and + + + align:start position:0% +a look at what your positions are and +then after you establish that you're + + align:start position:0% +then after you establish that you're + + + align:start position:0% +then after you establish that you're +okay in terms of your trading positions + + align:start position:0% +okay in terms of your trading positions + + + align:start position:0% +okay in terms of your trading positions +what's the next thing you're going to do + + align:start position:0% +what's the next thing you're going to do + + + align:start position:0% +what's the next thing you're going to do +what are you going to start thinking + + align:start position:0% +what are you going to start thinking + + + align:start position:0% +what are you going to start thinking +about yeah start printing your resume + + align:start position:0% +about yeah start printing your resume + + + align:start position:0% +about yeah start printing your resume +exactly you're going to start looking + + align:start position:0% +exactly you're going to start looking + + + align:start position:0% +exactly you're going to start looking +around so you're going to talk to lots + + align:start position:0% +around so you're going to talk to lots + + + align:start position:0% +around so you're going to talk to lots +of other people about maybe moving your + + align:start position:0% +of other people about maybe moving your + + + align:start position:0% +of other people about maybe moving your +entire group of 15 people that you've + + align:start position:0% +entire group of 15 people that you've + + + align:start position:0% +entire group of 15 people that you've +handpicked and developed over the last + + align:start position:0% +handpicked and developed over the last + + + align:start position:0% +handpicked and developed over the last +15 years and you're going start talking + + align:start position:0% +15 years and you're going start talking + + + align:start position:0% +15 years and you're going start talking +to all sorts of other counterparties to + + align:start position:0% +to all sorts of other counterparties to + + + align:start position:0% +to all sorts of other counterparties to +move your entire group and now Barkley + + align:start position:0% +move your entire group and now Barkley + + + align:start position:0% +move your entire group and now Barkley +decides to buy Leman the operations that + + align:start position:0% +decides to buy Leman the operations that + + + align:start position:0% +decides to buy Leman the operations that +you're part + + align:start position:0% +you're part + + + align:start position:0% +you're part +of but there's no slavery in the United + + align:start position:0% +of but there's no slavery in the United + + + align:start position:0% +of but there's no slavery in the United +States at least not since the 1800s + + align:start position:0% +States at least not since the 1800s + + + align:start position:0% +States at least not since the 1800s +which means that if you want to walk you + + align:start position:0% +which means that if you want to walk you + + + align:start position:0% +which means that if you want to walk you +can so if Leman buys if Barkley buys + + align:start position:0% +can so if Leman buys if Barkley buys + + + align:start position:0% +can so if Leman buys if Barkley buys +Leman and buys the group that you're in + + align:start position:0% +Leman and buys the group that you're in + + + align:start position:0% +Leman and buys the group that you're in +and you're one of the most profitable + + align:start position:0% +and you're one of the most profitable + + + align:start position:0% +and you're one of the most profitable +parts of that you don't have to stay so + + align:start position:0% +parts of that you don't have to stay so + + + align:start position:0% +parts of that you don't have to stay so +in addition to paying for Leman Barkley + + align:start position:0% +in addition to paying for Leman Barkley + + + align:start position:0% +in addition to paying for Leman Barkley +is also going to have to talk talk to + + align:start position:0% +is also going to have to talk talk to + + + align:start position:0% +is also going to have to talk talk to +you and get you to stay which means that + + align:start position:0% +you and get you to stay which means that + + + align:start position:0% +you and get you to stay which means that +they're going to have to pay you an + + align:start position:0% +they're going to have to pay you an + + + align:start position:0% +they're going to have to pay you an +extra bonus and all of your people + + align:start position:0% +extra bonus and all of your people + + + align:start position:0% +extra bonus and all of your people +bonuses to stay so now the price of + + align:start position:0% +bonuses to stay so now the price of + + + align:start position:0% +bonuses to stay so now the price of +having a keep Leeming together has just + + align:start position:0% +having a keep Leeming together has just + + + align:start position:0% +having a keep Leeming together has just +gone up dramatically because you've got + + align:start position:0% +gone up dramatically because you've got + + + align:start position:0% +gone up dramatically because you've got +to keep all of the talent and it's very + + align:start position:0% +to keep all of the talent and it's very + + + align:start position:0% +to keep all of the talent and it's very +hard to do that so the fact that Leman + + align:start position:0% +hard to do that so the fact that Leman + + + align:start position:0% +hard to do that so the fact that Leman +is in trouble has caused all sorts of + + align:start position:0% +is in trouble has caused all sorts of + + + align:start position:0% +is in trouble has caused all sorts of +problems and will create additional + + align:start position:0% +problems and will create additional + + + align:start position:0% +problems and will create additional +amounts of frictions and payments that + + align:start position:0% +amounts of frictions and payments that + + + align:start position:0% +amounts of frictions and payments that +otherwise wouldn't have had to be so + + align:start position:0% +otherwise wouldn't have had to be so + + + align:start position:0% +otherwise wouldn't have had to be so +that's I want you to keep that in the + + align:start position:0% +that's I want you to keep that in the + + + align:start position:0% +that's I want you to keep that in the +back of your mind the costs of financial + + align:start position:0% +back of your mind the costs of financial + + + align:start position:0% +back of your mind the costs of financial +distress we're going to come back to + + align:start position:0% +distress we're going to come back to + + + align:start position:0% +distress we're going to come back to +that uh in about 10 lectures okay so + + align:start position:0% +that uh in about 10 lectures okay so + + + align:start position:0% +that uh in about 10 lectures okay so +yeah question um I Heard a quote with + + align:start position:0% +yeah question um I Heard a quote with + + + align:start position:0% +yeah question um I Heard a quote with +regards to the FED action that the FED + + align:start position:0% +regards to the FED action that the FED + + + align:start position:0% +regards to the FED action that the FED +decided that the problem is not the cost + + align:start position:0% +decided that the problem is not the cost + + + align:start position:0% +decided that the problem is not the cost +of money but the supply of money and so + + align:start position:0% +of money but the supply of money and so + + + align:start position:0% +of money but the supply of money and so +they're they were going to infuse + + align:start position:0% +they're they were going to infuse + + + align:start position:0% +they're they were going to infuse +Capital into the market is that just + + align:start position:0% +Capital into the market is that just + + + align:start position:0% +Capital into the market is that just +referring to the the AIG 85 billion or + + align:start position:0% +referring to the the AIG 85 billion or + + + align:start position:0% +referring to the the AIG 85 billion or +is there some other way that they're + + align:start position:0% +is there some other way that they're + + + align:start position:0% +is there some other way that they're +infusing Capital no I mean that well + + align:start position:0% +infusing Capital no I mean that well + + + align:start position:0% +infusing Capital no I mean that well +that's certainly one way but the other + + align:start position:0% +that's certainly one way but the other + + + align:start position:0% +that's certainly one way but the other +way is that they are they are allowing + + align:start position:0% +way is that they are they are allowing + + + align:start position:0% +way is that they are they are allowing +the other Banks to borrow from them at a + + align:start position:0% +the other Banks to borrow from them at a + + + align:start position:0% +the other Banks to borrow from them at a +lower rate so the discount window that + + align:start position:0% +lower rate so the discount window that + + + align:start position:0% +lower rate so the discount window that +typically Banks go to borrow from the + + align:start position:0% +typically Banks go to borrow from the + + + align:start position:0% +typically Banks go to borrow from the +FED uh they're making more money + + align:start position:0% +FED uh they're making more money + + + align:start position:0% +FED uh they're making more money +available in that way and other central + + align:start position:0% +available in that way and other central + + + align:start position:0% +available in that way and other central +banks are doing the same thing injecting + + align:start position:0% +banks are doing the same thing injecting + + + align:start position:0% +banks are doing the same thing injecting +money into the system in order to calm + + align:start position:0% +money into the system in order to calm + + + align:start position:0% +money into the system in order to calm +the fears of individuals does that lower + + align:start position:0% +the fears of individuals does that lower + + + align:start position:0% +the fears of individuals does that lower +the effective industry well we're going + + align:start position:0% +the effective industry well we're going + + + align:start position:0% +the effective industry well we're going +to see that in a minute we're going to + + align:start position:0% +to see that in a minute we're going to + + + align:start position:0% +to see that in a minute we're going to +actually uh one of the things I want to + + align:start position:0% +actually uh one of the things I want to + + + align:start position:0% +actually uh one of the things I want to +talk about today is exactly what do we + + align:start position:0% +talk about today is exactly what do we + + + align:start position:0% +talk about today is exactly what do we +see from market prices now on Monday I + + align:start position:0% +see from market prices now on Monday I + + + align:start position:0% +see from market prices now on Monday I +claimed that market prices was telling + + align:start position:0% +claimed that market prices was telling + + + align:start position:0% +claimed that market prices was telling +us there's going to be a Fed cut clearly + + align:start position:0% +us there's going to be a Fed cut clearly + + + align:start position:0% +us there's going to be a Fed cut clearly +it was wrong now + + align:start position:0% +it was wrong now + + + align:start position:0% +it was wrong now +that's a very good lesson because what + + align:start position:0% +that's a very good lesson because what + + + align:start position:0% +that's a very good lesson because what +what this is telling us is that market + + align:start position:0% +what this is telling us is that market + + + align:start position:0% +what this is telling us is that market +prices have information but as I told + + align:start position:0% +prices have information but as I told + + + align:start position:0% +prices have information but as I told +you last time they're not a crystal ball + + align:start position:0% +you last time they're not a crystal ball + + + align:start position:0% +you last time they're not a crystal ball +they're not perfect and so they can be + + align:start position:0% +they're not perfect and so they can be + + + align:start position:0% +they're not perfect and so they can be +wrong apparently and this is now very + + align:start position:0% +wrong apparently and this is now very + + + align:start position:0% +wrong apparently and this is now very +speculative apparently the FED decided + + align:start position:0% +speculative apparently the FED decided + + + align:start position:0% +speculative apparently the FED decided +as you pointed out that it's not the + + align:start position:0% +as you pointed out that it's not the + + + align:start position:0% +as you pointed out that it's not the +it's it's not the availability of or the + + align:start position:0% +it's it's not the availability of or the + + + align:start position:0% +it's it's not the availability of or the +rather the the cost of funds that's not + + align:start position:0% +rather the the cost of funds that's not + + + align:start position:0% +rather the the cost of funds that's not +that's important but rather the + + align:start position:0% +that's important but rather the + + + align:start position:0% +that's important but rather the +availability in other words they're + + align:start position:0% +availability in other words they're + + + align:start position:0% +availability in other words they're +worried about a credit crisis uh a + + align:start position:0% +worried about a credit crisis uh a + + + align:start position:0% +worried about a credit crisis uh a +crisis of liquidity and + + align:start position:0% +crisis of liquidity and + + + align:start position:0% +crisis of liquidity and +AIG is a very important player in that + + align:start position:0% +AIG is a very important player in that + + + align:start position:0% +AIG is a very important player in that +respect apparently much more so than + + align:start position:0% +respect apparently much more so than + + + align:start position:0% +respect apparently much more so than +Leman because fed didn't do anything to + + align:start position:0% +Leman because fed didn't do anything to + + + align:start position:0% +Leman because fed didn't do anything to +try to keep Leman from going under but + + align:start position:0% +try to keep Leman from going under but + + + align:start position:0% +try to keep Leman from going under but +an $85 billion loan uh was what they + + align:start position:0% +an $85 billion loan uh was what they + + + align:start position:0% +an $85 billion loan uh was what they +decided was appropriate for AIG the + + align:start position:0% +decided was appropriate for AIG the + + + align:start position:0% +decided was appropriate for AIG the +reason for that the ostensible reason + + align:start position:0% +reason for that the ostensible reason + + + align:start position:0% +reason for that the ostensible reason +who knows what the real reasons may be + + align:start position:0% +who knows what the real reasons may be + + + align:start position:0% +who knows what the real reasons may be +but the the reasons that we think this + + align:start position:0% +but the the reasons that we think this + + + align:start position:0% +but the the reasons that we think this +happened is that AIG provides enormous + + align:start position:0% +happened is that AIG provides enormous + + + align:start position:0% +happened is that AIG provides enormous +amounts of insurance to variety of other + + align:start position:0% +amounts of insurance to variety of other + + + align:start position:0% +amounts of insurance to variety of other +players in the credit markets and if + + align:start position:0% +players in the credit markets and if + + + align:start position:0% +players in the credit markets and if +they go under if they decide that they + + align:start position:0% +they go under if they decide that they + + + align:start position:0% +they go under if they decide that they +can't make good on those insurance + + align:start position:0% +can't make good on those insurance + + + align:start position:0% +can't make good on those insurance +claims what happens is that those + + align:start position:0% +claims what happens is that those + + + align:start position:0% +claims what happens is that those +investors that are holding the paper + + align:start position:0% +investors that are holding the paper + + + align:start position:0% +investors that are holding the paper +that is backed by subprime assets and + + align:start position:0% +that is backed by subprime assets and + + + align:start position:0% +that is backed by subprime assets and +that are insured by AIG once the + + align:start position:0% +that are insured by AIG once the + + + align:start position:0% +that are insured by AIG once the +insurance + + align:start position:0% +insurance + + + align:start position:0% +insurance +disappears they are obligated a number + + align:start position:0% +disappears they are obligated a number + + + align:start position:0% +disappears they are obligated a number +of them to sell those pieces of paper if + + align:start position:0% +of them to sell those pieces of paper if + + + align:start position:0% +of them to sell those pieces of paper if +you're a pension fund you are obligated + + align:start position:0% +you're a pension fund you are obligated + + + align:start position:0% +you're a pension fund you are obligated +to hold only investment grade assets if + + align:start position:0% +to hold only investment grade assets if + + + align:start position:0% +to hold only investment grade assets if +it turns out that for any reason those + + align:start position:0% +it turns out that for any reason those + + + align:start position:0% +it turns out that for any reason those +assets become lower than investment + + align:start position:0% +assets become lower than investment + + + align:start position:0% +assets become lower than investment +grade and we're going to talk about this + + align:start position:0% +grade and we're going to talk about this + + + align:start position:0% +grade and we're going to talk about this +at four o'clock today at that Pro + + align:start position:0% +at four o'clock today at that Pro + + + align:start position:0% +at four o'clock today at that Pro +seminar if it falls below investment + + align:start position:0% +seminar if it falls below investment + + + align:start position:0% +seminar if it falls below investment +grade by law you are obligated to get + + align:start position:0% +grade by law you are obligated to get + + + align:start position:0% +grade by law you are obligated to get +rid of those + + align:start position:0% +rid of those + + + align:start position:0% +rid of those +assets now what do you think would + + align:start position:0% +assets now what do you think would + + + align:start position:0% +assets now what do you think would +happen to the market if everybody all at + + align:start position:0% +happen to the market if everybody all at + + + align:start position:0% +happen to the market if everybody all at +once decided to get rid of those + + align:start position:0% + + + + align:start position:0% + +assets right and and then there'd be a + + align:start position:0% +assets right and and then there'd be a + + + align:start position:0% +assets right and and then there'd be a +mass panic right I just have there's + + align:start position:0% +mass panic right I just have there's + + + align:start position:0% +mass panic right I just have there's +something simple that I don't understand + + align:start position:0% +something simple that I don't understand + + + align:start position:0% +something simple that I don't understand +how can the um interest rate go below + + align:start position:0% +how can the um interest rate go below + + + align:start position:0% +how can the um interest rate go below +the inflation rate well it's not + + align:start position:0% +the inflation rate well it's not + + + align:start position:0% +the inflation rate well it's not +supposed to for any extended period of + + align:start position:0% +supposed to for any extended period of + + + align:start position:0% +supposed to for any extended period of +time but for any short period of time it + + align:start position:0% +time but for any short period of time it + + + align:start position:0% +time but for any short period of time it +certainly can what it says is that the + + align:start position:0% +certainly can what it says is that the + + + align:start position:0% +certainly can what it says is that the +real rate is negative or that the + + align:start position:0% +real rate is negative or that the + + + align:start position:0% +real rate is negative or that the +economy is Contracting so like right now + + align:start position:0% +economy is Contracting so like right now + + + align:start position:0% +economy is Contracting so like right now +$1 a year from now is more valuable than + + align:start position:0% +$1 a year from now is more valuable than + + + align:start position:0% +$1 a year from now is more valuable than +a today right well if you think if you + + align:start position:0% +a today right well if you think if you + + + align:start position:0% +a today right well if you think if you +take inflation into account yes on in + + align:start position:0% +take inflation into account yes on in + + + align:start position:0% +take inflation into account yes on in +real terms not in nominal terms you you + + align:start position:0% +real terms not in nominal terms you you + + + align:start position:0% +real terms not in nominal terms you you +can never have a negative nominal + + align:start position:0% +can never have a negative nominal + + + align:start position:0% +can never have a negative nominal +interest rate right unless you know + + align:start position:0% +interest rate right unless you know + + + align:start position:0% +interest rate right unless you know +somebody's burning dollar bills but let + + align:start position:0% +somebody's burning dollar bills but let + + + align:start position:0% +somebody's burning dollar bills but let +me let me hold off on that because I + + align:start position:0% +me let me hold off on that because I + + + align:start position:0% +me let me hold off on that because I +want to actually that brings us back to + + align:start position:0% +want to actually that brings us back to + + + align:start position:0% +want to actually that brings us back to +the end of last lecture what I want to + + align:start position:0% +the end of last lecture what I want to + + + align:start position:0% +the end of last lecture what I want to +do today is I want to talk about + + align:start position:0% +do today is I want to talk about + + + align:start position:0% +do today is I want to talk about +information specifically contained in + + align:start position:0% +information specifically contained in + + + align:start position:0% +information specifically contained in +interest rates and we're going to + + align:start position:0% +interest rates and we're going to + + + align:start position:0% +interest rates and we're going to +actually take a look at what the + + align:start position:0% +actually take a look at what the + + + align:start position:0% +actually take a look at what the +short-term interest rate is I think it' + + align:start position:0% +short-term interest rate is I think it' + + + align:start position:0% +short-term interest rate is I think it' +be kind of surprised to see what the + + align:start position:0% +be kind of surprised to see what the + + + align:start position:0% +be kind of surprised to see what the +three-month t- Bill rate is as of today + + align:start position:0% +three-month t- Bill rate is as of today + + + align:start position:0% +three-month t- Bill rate is as of today +anybody know what it + + align:start position:0% +anybody know what it + + + align:start position:0% +anybody know what it +is you seen it 2% + + align:start position:0% +is you seen it 2% + + + align:start position:0% +is you seen it 2% +no no it's + + align:start position:0% +no no it's + + + align:start position:0% +no no it's +lower we let me we we'll see in just a + + align:start position:0% +lower we let me we we'll see in just a + + + align:start position:0% +lower we let me we we'll see in just a +minute okay so let + + align:start position:0% + + + + align:start position:0% + +me let me let me start today's lecture + + align:start position:0% +me let me let me start today's lecture + + + align:start position:0% +me let me let me start today's lecture +by going back to where we left off uh + + align:start position:0% +by going back to where we left off uh + + + align:start position:0% +by going back to where we left off uh +last time last time we talked about the + + align:start position:0% +last time last time we talked about the + + + align:start position:0% +last time last time we talked about the +pricing of pure discount bonds bonds + + align:start position:0% +pricing of pure discount bonds bonds + + + align:start position:0% +pricing of pure discount bonds bonds +that that pay only a principal at the + + align:start position:0% +that that pay only a principal at the + + + align:start position:0% +that that pay only a principal at the +end and no intermediate coupon payments + + align:start position:0% +end and no intermediate coupon payments + + + align:start position:0% +end and no intermediate coupon payments +and we saw that the price today is + + align:start position:0% +and we saw that the price today is + + + align:start position:0% +and we saw that the price today is +simply equal to the face value or + + align:start position:0% +simply equal to the face value or + + + align:start position:0% +simply equal to the face value or +principal at the end of the uh maturity + + align:start position:0% +principal at the end of the uh maturity + + + align:start position:0% +principal at the end of the uh maturity +date and then discounted back using the + + align:start position:0% +date and then discounted back using the + + + align:start position:0% +date and then discounted back using the +interest rate and I pointed out at the + + align:start position:0% +interest rate and I pointed out at the + + + align:start position:0% +interest rate and I pointed out at the +end of last lecture that the interest + + align:start position:0% +end of last lecture that the interest + + + align:start position:0% +end of last lecture that the interest +rate can differ depending on the horizon + + align:start position:0% +rate can differ depending on the horizon + + + align:start position:0% +rate can differ depending on the horizon +so a one-year interest rate is not the + + align:start position:0% +so a one-year interest rate is not the + + + align:start position:0% +so a one-year interest rate is not the +same as a five-year interest rate + + align:start position:0% +same as a five-year interest rate + + + align:start position:0% +same as a five-year interest rate +because the market has different + + align:start position:0% +because the market has different + + + align:start position:0% +because the market has different +expectations about how the economy will + + align:start position:0% +expectations about how the economy will + + + align:start position:0% +expectations about how the economy will +do and what the appropriate borrowing + + align:start position:0% +do and what the appropriate borrowing + + + align:start position:0% +do and what the appropriate borrowing +rate or the time rate of preference uh + + align:start position:0% +rate or the time rate of preference uh + + + align:start position:0% +rate or the time rate of preference uh +might be + + align:start position:0% +might be + + + align:start position:0% +might be +so in fact for every Horizon one year + + align:start position:0% +so in fact for every Horizon one year + + + align:start position:0% +so in fact for every Horizon one year +two year 3 year 5 years we have a + + align:start position:0% +two year 3 year 5 years we have a + + + align:start position:0% +two year 3 year 5 years we have a +different interest rate it doesn't have + + align:start position:0% +different interest rate it doesn't have + + + align:start position:0% +different interest rate it doesn't have +to be different but in general it does + + align:start position:0% +to be different but in general it does + + + align:start position:0% +to be different but in general it does +tend to be different how do we find out + + align:start position:0% +tend to be different how do we find out + + + align:start position:0% +tend to be different how do we find out +what these interest rates + + align:start position:0% +what these interest rates + + + align:start position:0% +what these interest rates +are yeah Market exactly the market the + + align:start position:0% +are yeah Market exactly the market the + + + align:start position:0% +are yeah Market exactly the market the +way to do it is not to think about + + align:start position:0% +way to do it is not to think about + + + align:start position:0% +way to do it is not to think about +interest rates at all but rather to + + align:start position:0% +interest rates at all but rather to + + + align:start position:0% +interest rates at all but rather to +auction off pieces of paper that pay + + align:start position:0% +auction off pieces of paper that pay + + + align:start position:0% +auction off pieces of paper that pay +$1,000 in a year $1,000 in two years + + align:start position:0% +$1,000 in a year $1,000 in two years + + + align:start position:0% +$1,000 in a year $1,000 in two years +$11,000 in 3 years and so on and we + + align:start position:0% +$11,000 in 3 years and so on and we + + + align:start position:0% +$11,000 in 3 years and so on and we +auction off each of these pieces of + + align:start position:0% +auction off each of these pieces of + + + align:start position:0% +auction off each of these pieces of +paper and see what the prices we fetch + + align:start position:0% +paper and see what the prices we fetch + + + align:start position:0% +paper and see what the prices we fetch +are for those pieces of paper once we + + align:start position:0% +are for those pieces of paper once we + + + align:start position:0% +are for those pieces of paper once we +have the price and once we know the face + + align:start position:0% +have the price and once we know the face + + + align:start position:0% +have the price and once we know the face +value of + + align:start position:0% +value of + + + align:start position:0% +value of +$1,000 we can back out the interest rate + + align:start position:0% +$1,000 we can back out the interest rate + + + align:start position:0% +$1,000 we can back out the interest rate +we can solve for the interest rate R + + align:start position:0% +we can solve for the interest rate R + + + align:start position:0% +we can solve for the interest rate R +okay so that's how we get the rates and + + align:start position:0% +okay so that's how we get the rates and + + + align:start position:0% +okay so that's how we get the rates and +what I want to do today is to explicate + + align:start position:0% +what I want to do today is to explicate + + + align:start position:0% +what I want to do today is to explicate +what those rates really mean I want to + + align:start position:0% +what those rates really mean I want to + + + align:start position:0% +what those rates really mean I want to +show you how to read the entrails and + + align:start position:0% +show you how to read the entrails and + + + align:start position:0% +show you how to read the entrails and +see that these rates contain en enormous + + align:start position:0% +see that these rates contain en enormous + + + align:start position:0% +see that these rates contain en enormous +amounts of information about the future + + align:start position:0% +amounts of information about the future + + + align:start position:0% +amounts of information about the future +not all of that information is good so + + align:start position:0% +not all of that information is good so + + + align:start position:0% +not all of that information is good so +sometimes it's misleading and incorrect + + align:start position:0% +sometimes it's misleading and incorrect + + + align:start position:0% +sometimes it's misleading and incorrect +but it's always useful in one form or + + align:start position:0% +but it's always useful in one form or + + + align:start position:0% +but it's always useful in one form or +another now to do that I want to develop + + align:start position:0% +another now to do that I want to develop + + + align:start position:0% +another now to do that I want to develop +a little bit of new notation and get you + + align:start position:0% +a little bit of new notation and get you + + + align:start position:0% +a little bit of new notation and get you +to think yet again differently about the + + align:start position:0% +to think yet again differently about the + + + align:start position:0% +to think yet again differently about the +evolution of interest rates over + + align:start position:0% +evolution of interest rates over + + + align:start position:0% +evolution of interest rates over +time I'm going to Define what's called a + + align:start position:0% +time I'm going to Define what's called a + + + align:start position:0% +time I'm going to Define what's called a +spot rate as the rate of an of interest + + align:start position:0% +spot rate as the rate of an of interest + + + align:start position:0% +spot rate as the rate of an of interest +between today and some other point in + + align:start position:0% +between today and some other point in + + + align:start position:0% +between today and some other point in +time and I'm going to talk about future + + align:start position:0% +time and I'm going to talk about future + + + align:start position:0% +time and I'm going to talk about future +spot rates as the interest rates between + + align:start position:0% +spot rates as the interest rates between + + + align:start position:0% +spot rates as the interest rates between +some future date and then another date + + align:start position:0% +some future date and then another date + + + align:start position:0% +some future date and then another date +even beyond that so to be explicit I + + align:start position:0% +even beyond that so to be explicit I + + + align:start position:0% +even beyond that so to be explicit I +wanted to find new notation called + + align:start position:0% +wanted to find new notation called + + + align:start position:0% +wanted to find new notation called +capital r uppercase R is meant to convey + + align:start position:0% +capital r uppercase R is meant to convey + + + align:start position:0% +capital r uppercase R is meant to convey +a + + align:start position:0% +a + + + align:start position:0% +a +one-year spot rate of interest + + align:start position:0% +one-year spot rate of interest + + + align:start position:0% +one-year spot rate of interest +at a particular point in time t Okay so + + align:start position:0% +at a particular point in time t Okay so + + + align:start position:0% +at a particular point in time t Okay so +Capital R1 that denotes the spot rate of + + align:start position:0% +Capital R1 that denotes the spot rate of + + + align:start position:0% +Capital R1 that denotes the spot rate of +interest between today and next year + + align:start position:0% +interest between today and next year + + + align:start position:0% +interest between today and next year +Capital R3 denotes the spot rate of + + align:start position:0% +Capital R3 denotes the spot rate of + + + align:start position:0% +Capital R3 denotes the spot rate of +interest between years two and + + align:start position:0% +interest between years two and + + + align:start position:0% +interest between years two and +three and capital RT denotes the oneyear + + align:start position:0% +three and capital RT denotes the oneyear + + + align:start position:0% +three and capital RT denotes the oneyear +spot rate between dates T minus one and + + align:start position:0% +spot rate between dates T minus one and + + + align:start position:0% +spot rate between dates T minus one and +T okay so these capital RS are always + + align:start position:0% +T okay so these capital RS are always + + + align:start position:0% +T okay so these capital RS are always +oneyear rates unlike the little RS which + + align:start position:0% +oneyear rates unlike the little RS which + + + align:start position:0% +oneyear rates unlike the little RS which +can denote multi-year rates depending on + + align:start position:0% +can denote multi-year rates depending on + + + align:start position:0% +can denote multi-year rates depending on +the + + align:start position:0% +the + + + align:start position:0% +the +application now there's a reason I + + align:start position:0% +application now there's a reason I + + + align:start position:0% +application now there's a reason I +wanted to find the the these big + + align:start position:0% +wanted to find the the these big + + + align:start position:0% +wanted to find the the these big +RS it turns out that if I have a oneyear + + align:start position:0% +RS it turns out that if I have a oneyear + + + align:start position:0% +RS it turns out that if I have a oneyear +dis a pure discount bond that pays off + + align:start position:0% +dis a pure discount bond that pays off + + + align:start position:0% +dis a pure discount bond that pays off +at year T then I can use the one-year + + align:start position:0% +at year T then I can use the one-year + + + align:start position:0% +at year T then I can use the one-year +spot rates to compute today's price + + align:start position:0% +spot rates to compute today's price + + + align:start position:0% +spot rates to compute today's price +right the one-ear spot rate when you + + align:start position:0% +right the one-ear spot rate when you + + + align:start position:0% +right the one-ear spot rate when you +cumulate them when you multiply them + + align:start position:0% +cumulate them when you multiply them + + + align:start position:0% +cumulate them when you multiply them +together that will give you the + + align:start position:0% +together that will give you the + + + align:start position:0% +together that will give you the +accumulated interest over this entire + + align:start position:0% +accumulated interest over this entire + + + align:start position:0% +accumulated interest over this entire +t-year period so if I want to Discount + + align:start position:0% +t-year period so if I want to Discount + + + align:start position:0% +t-year period so if I want to Discount +the face value F and bring it back to + + align:start position:0% +the face value F and bring it back to + + + align:start position:0% +the face value F and bring it back to +year + + align:start position:0% +year + + + align:start position:0% +year +zero I can just assume that there exists + + align:start position:0% +zero I can just assume that there exists + + + align:start position:0% +zero I can just assume that there exists +One + + align:start position:0% +One + + + align:start position:0% +One +Rate or I can say you know what if + + align:start position:0% +Rate or I can say you know what if + + + align:start position:0% +Rate or I can say you know what if +there's multiple rates that differ year + + align:start position:0% +there's multiple rates that differ year + + + align:start position:0% +there's multiple rates that differ year +by year + + align:start position:0% +by year + + + align:start position:0% +by year +I can use those individual + + align:start position:0% +I can use those individual + + + align:start position:0% +I can use those individual +rates okay so I get that first equation + + align:start position:0% +rates okay so I get that first equation + + + align:start position:0% +rates okay so I get that first equation +now we don't observe them so this is a + + align:start position:0% +now we don't observe them so this is a + + + align:start position:0% +now we don't observe them so this is a +pure fiction in terms of what I'm + + align:start position:0% +pure fiction in terms of what I'm + + + align:start position:0% +pure fiction in terms of what I'm +writing down it's a it's a theory so I'm + + align:start position:0% +writing down it's a it's a theory so I'm + + + align:start position:0% +writing down it's a it's a theory so I'm +I'm not telling you that we know what + + align:start position:0% +I'm not telling you that we know what + + + align:start position:0% +I'm not telling you that we know what +those big RS are but I know that they + + align:start position:0% +those big RS are but I know that they + + + align:start position:0% +those big RS are but I know that they +exist and whatever they are this is what + + align:start position:0% +exist and whatever they are this is what + + + align:start position:0% +exist and whatever they are this is what +the price of the bond ought to be today + + align:start position:0% +the price of the bond ought to be today + + + align:start position:0% +the price of the bond ought to be today +any questions about + + align:start position:0% +any questions about + + + align:start position:0% +any questions about +that okay + + align:start position:0% +that okay + + + align:start position:0% +that okay +now what I do observe is the price and F + + align:start position:0% +now what I do observe is the price and F + + + align:start position:0% +now what I do observe is the price and F +those things I get from the marketplace + + align:start position:0% +those things I get from the marketplace + + + align:start position:0% +those things I get from the marketplace +and the contract uh for these bonds + + align:start position:0% +and the contract uh for these bonds + + + align:start position:0% +and the contract uh for these bonds +therefore it turns out that as a very + + align:start position:0% +therefore it turns out that as a very + + + align:start position:0% +therefore it turns out that as a very +simple + + align:start position:0% +simple + + + align:start position:0% +simple +identity this + + align:start position:0% +identity this + + + align:start position:0% +identity this +expression this little r which I'm + + align:start position:0% +expression this little r which I'm + + + align:start position:0% +expression this little r which I'm +adding some little more complicated + + align:start position:0% +adding some little more complicated + + + align:start position:0% +adding some little more complicated +notation to indicate when I begin and + + align:start position:0% +notation to indicate when I begin and + + + align:start position:0% +notation to indicate when I begin and +when I end in terms of my Horizon I can + + align:start position:0% +when I end in terms of my Horizon I can + + + align:start position:0% +when I end in terms of my Horizon I can +simply Define this little r as being + + align:start position:0% +simply Define this little r as being + + + align:start position:0% +simply Define this little r as being +equal to the geometric average of these + + align:start position:0% +equal to the geometric average of these + + + align:start position:0% +equal to the geometric average of these +big RS it's really just terminology at + + align:start position:0% +big RS it's really just terminology at + + + align:start position:0% +big RS it's really just terminology at +this point right I'm simply saying that + + align:start position:0% +this point right I'm simply saying that + + + align:start position:0% +this point right I'm simply saying that +in reality we have one-year interest + + align:start position:0% +in reality we have one-year interest + + + align:start position:0% +in reality we have one-year interest +rates that may change over time and I + + align:start position:0% +rates that may change over time and I + + + align:start position:0% +rates that may change over time and I +know that the price of the bond today is + + align:start position:0% +know that the price of the bond today is + + + align:start position:0% +know that the price of the bond today is +equal to the Future course of one-year + + align:start position:0% +equal to the Future course of one-year + + + align:start position:0% +equal to the Future course of one-year +interest rates uh as discounts over that + + align:start position:0% +interest rates uh as discounts over that + + + align:start position:0% +interest rates uh as discounts over that +uh period when I use those as discount + + align:start position:0% +uh period when I use those as discount + + + align:start position:0% +uh period when I use those as discount +rates I bring back this value F I get + + align:start position:0% +rates I bring back this value F I get + + + align:start position:0% +rates I bring back this value F I get +today's price I can just as well write + + align:start position:0% +today's price I can just as well write + + + align:start position:0% +today's price I can just as well write +that chain of oneyear interest rates as + + align:start position:0% +that chain of oneyear interest rates as + + + align:start position:0% +that chain of oneyear interest rates as +a single number raised to the teeth + + align:start position:0% +a single number raised to the teeth + + + align:start position:0% +a single number raised to the teeth +power I can always do that right you + + align:start position:0% +power I can always do that right you + + + align:start position:0% +power I can always do that right you +could think of this little + + align:start position:0% +could think of this little + + + align:start position:0% +could think of this little +r as an + + align:start position:0% +r as an + + + align:start position:0% +r as an +average a geometric average of the big + + align:start position:0% +average a geometric average of the big + + + align:start position:0% +average a geometric average of the big +RS right so the strict definition is + + align:start position:0% +RS right so the strict definition is + + + align:start position:0% +RS right so the strict definition is +going to be little r is going to be the + + align:start position:0% +going to be little r is going to be the + + + align:start position:0% +going to be little r is going to be the +teth root of the product and then minus + + align:start position:0% +teth root of the product and then minus + + + align:start position:0% +teth root of the product and then minus +one + + align:start position:0% +one + + + align:start position:0% +one +that's what the little r is all right + + align:start position:0% +that's what the little r is all right + + + align:start position:0% +that's what the little r is all right +you take that product and you raise that + + align:start position:0% +you take that product and you raise that + + + align:start position:0% +you take that product and you raise that +to the one over teeth power or take the + + align:start position:0% +to the one over teeth power or take the + + + align:start position:0% +to the one over teeth power or take the +the teeth root and then subtract one + + align:start position:0% +the teeth root and then subtract one + + + align:start position:0% +the teeth root and then subtract one +from that that's what my little r is now + + align:start position:0% +from that that's what my little r is now + + + align:start position:0% +from that that's what my little r is now +why am I going through all of this it's + + align:start position:0% +why am I going through all of this it's + + + align:start position:0% +why am I going through all of this it's +because I want to show you that from a + + align:start position:0% +because I want to show you that from a + + + align:start position:0% +because I want to show you that from a +theoretical + + align:start position:0% +theoretical + + + align:start position:0% +theoretical +perspective the little r which we can + + align:start position:0% +perspective the little r which we can + + + align:start position:0% +perspective the little r which we can +observe contains information about the + + align:start position:0% +observe contains information about the + + + align:start position:0% +observe contains information about the +future course of interest + + align:start position:0% +future course of interest + + + align:start position:0% +future course of interest +rates right within the little r + + align:start position:0% +rates right within the little r + + + align:start position:0% +rates right within the little r +are all the big RS at least today's + + align:start position:0% +are all the big RS at least today's + + + align:start position:0% +are all the big RS at least today's +expectations of what those big RS are + + align:start position:0% +expectations of what those big RS are + + + align:start position:0% +expectations of what those big RS are +going to + + align:start position:0% +going to + + + align:start position:0% +going to +be + + align:start position:0% +be + + + align:start position:0% +be +so it turns out that uh if we look into + + align:start position:0% +so it turns out that uh if we look into + + + align:start position:0% +so it turns out that uh if we look into +the little RS we can actually develop + + align:start position:0% +the little RS we can actually develop + + + align:start position:0% +the little RS we can actually develop +insight about what's going to be + + align:start position:0% +insight about what's going to be + + + align:start position:0% +insight about what's going to be +happening next year 5 years from now 30 + + align:start position:0% +happening next year 5 years from now 30 + + + align:start position:0% +happening next year 5 years from now 30 +years from now now let me give you an + + align:start position:0% +years from now now let me give you an + + + align:start position:0% +years from now now let me give you an +example just to make sure that we + + align:start position:0% +example just to make sure that we + + + align:start position:0% +example just to make sure that we +understand the mechanism by which these + + align:start position:0% +understand the mechanism by which these + + + align:start position:0% +understand the mechanism by which these +little RS and big RS are determined okay + + align:start position:0% +little RS and big RS are determined okay + + + align:start position:0% +little RS and big RS are determined okay +so here's uh a set of + + align:start position:0% +so here's uh a set of + + + align:start position:0% +so here's uh a set of +prices of strips these are treasury + + align:start position:0% +prices of strips these are treasury + + + align:start position:0% +prices of strips these are treasury +securities issued by the US government + + align:start position:0% +securities issued by the US government + + + align:start position:0% +securities issued by the US government +and then a a third party buys them and + + align:start position:0% +and then a a third party buys them and + + + align:start position:0% +and then a a third party buys them and +then takes the coupons and creates + + align:start position:0% +then takes the coupons and creates + + + align:start position:0% +then takes the coupons and creates +separate Securities and sells those + + align:start position:0% +separate Securities and sells those + + + align:start position:0% +separate Securities and sells those +separate Securities each one of which is + + align:start position:0% +separate Securities each one of which is + + + align:start position:0% +separate Securities each one of which is +one of these coupons so from our + + align:start position:0% +one of these coupons so from our + + + align:start position:0% +one of these coupons so from our +perspective they look like pure discount + + align:start position:0% +perspective they look like pure discount + + + align:start position:0% +perspective they look like pure discount +bonds there's no intermediate coupon + + align:start position:0% +bonds there's no intermediate coupon + + + align:start position:0% +bonds there's no intermediate coupon +payment for each one of these strips and + + align:start position:0% +payment for each one of these strips and + + + align:start position:0% +payment for each one of these strips and +the maturity is 3 months 6 months 1 year + + align:start position:0% +the maturity is 3 months 6 months 1 year + + + align:start position:0% +the maturity is 3 months 6 months 1 year +2 years up to 30 years okay and those + + align:start position:0% +2 years up to 30 years okay and those + + + align:start position:0% +2 years up to 30 years okay and those +are the prices so a three-month strip is + + align:start position:0% +are the prices so a three-month strip is + + + align:start position:0% +are the prices so a three-month strip is +currently priced as of August the 1st + + align:start position:0% +currently priced as of August the 1st + + + align:start position:0% +currently priced as of August the 1st +2001 it was priced at uh a little bit + + align:start position:0% +2001 it was priced at uh a little bit + + + align:start position:0% +2001 it was priced at uh a little bit +less than a + + align:start position:0% +less than a + + + align:start position:0% +less than a +dollar okay so how do we figure out what + + align:start position:0% +dollar okay so how do we figure out what + + + align:start position:0% +dollar okay so how do we figure out what +the little r is associated with those + + align:start position:0% +the little r is associated with those + + + align:start position:0% +the little r is associated with those +various prices well let's take an + + align:start position:0% +various prices well let's take an + + + align:start position:0% +various prices well let's take an +example the um uh The Five-Year strip is + + align:start position:0% +example the um uh The Five-Year strip is + + + align:start position:0% +example the um uh The Five-Year strip is +priced at about 80 cents to the dollar + + align:start position:0% +priced at about 80 cents to the dollar + + + align:start position:0% +priced at about 80 cents to the dollar +okay so the price is 797 and that's + + align:start position:0% +okay so the price is 797 and that's + + + align:start position:0% +okay so the price is 797 and that's +equal to a dollar paid five years later + + align:start position:0% +equal to a dollar paid five years later + + + align:start position:0% +equal to a dollar paid five years later +so therefore it's a dollar discounted + + align:start position:0% +so therefore it's a dollar discounted + + + align:start position:0% +so therefore it's a dollar discounted +back five years so I'm going to use my + + align:start position:0% +back five years so I'm going to use my + + + align:start position:0% +back five years so I'm going to use my +little r and the 0 comma 5 indicates + + align:start position:0% +little r and the 0 comma 5 indicates + + + align:start position:0% +little r and the 0 comma 5 indicates +that it's today's spot rate for + + align:start position:0% +that it's today's spot rate for + + + align:start position:0% +that it's today's spot rate for +borrowing over a 5year + + align:start position:0% +borrowing over a 5year + + + align:start position:0% +borrowing over a 5year +horizon and it turns out that when I + + align:start position:0% +horizon and it turns out that when I + + + align:start position:0% +horizon and it turns out that when I +solve for that I get a number that's + + align:start position:0% +solve for that I get a number that's + + + align:start position:0% +solve for that I get a number that's +4.64% that's the the rate of return the + + align:start position:0% +4.64% that's the the rate of return the + + + align:start position:0% +4.64% that's the the rate of return the +cost of capital the yield uh of that + + align:start position:0% +cost of capital the yield uh of that + + + align:start position:0% +cost of capital the yield uh of that +five period + + align:start position:0% +five period + + + align:start position:0% +five period +Horizon + + align:start position:0% +Horizon + + + align:start position:0% +Horizon +okay any questions about this yeah just + + align:start position:0% +okay any questions about this yeah just + + + align:start position:0% +okay any questions about this yeah just +how do we how would we do it maybe if it + + align:start position:0% +how do we how would we do it maybe if it + + + align:start position:0% +how do we how would we do it maybe if it +was one that was less than years Horizon + + align:start position:0% +was one that was less than years Horizon + + + align:start position:0% +was one that was less than years Horizon +so if it's less than a Year's Horizon + + align:start position:0% +so if it's less than a Year's Horizon + + + align:start position:0% +so if it's less than a Year's Horizon +then you basically have to go the other + + align:start position:0% +then you basically have to go the other + + + align:start position:0% +then you basically have to go the other +way in terms of the power + + align:start position:0% +way in terms of the power + + + align:start position:0% +way in terms of the power +right yeah basally exactly that's right + + align:start position:0% +right yeah basally exactly that's right + + + align:start position:0% +right yeah basally exactly that's right +yep that's it it's just a shorter time + + align:start position:0% +yep that's it it's just a shorter time + + + align:start position:0% +yep that's it it's just a shorter time +Horizon than a + + align:start position:0% +Horizon than a + + + align:start position:0% +Horizon than a +year + + align:start position:0% +year + + + align:start position:0% +year +now suppose that we observe a bunch of + + align:start position:0% +now suppose that we observe a bunch of + + + align:start position:0% +now suppose that we observe a bunch of +these as we do with the strips so in + + align:start position:0% +these as we do with the strips so in + + + align:start position:0% +these as we do with the strips so in +other words you you've got a fiveyear + + align:start position:0% +other words you you've got a fiveyear + + + align:start position:0% +other words you you've got a fiveyear +rate youve got a 10-year rate you got a + + align:start position:0% +rate youve got a 10-year rate you got a + + + align:start position:0% +rate youve got a 10-year rate you got a +two-year rate and so + + align:start position:0% +two-year rate and so + + + align:start position:0% +two-year rate and so +on what does that tell us about the + + align:start position:0% +on what does that tell us about the + + + align:start position:0% +on what does that tell us about the +future well let's write down the big RS + + align:start position:0% +future well let's write down the big RS + + + align:start position:0% +future well let's write down the big RS +even though we don't see them we know + + align:start position:0% +even though we don't see them we know + + + align:start position:0% +even though we don't see them we know +that some somehow implicitly they're + + align:start position:0% +that some somehow implicitly they're + + + align:start position:0% +that some somehow implicitly they're +there so what are the relationships + + align:start position:0% +there so what are the relationships + + + align:start position:0% +there so what are the relationships +between the little RS and the big RS + + align:start position:0% +between the little RS and the big RS + + + align:start position:0% +between the little RS and the big RS +well you'll see something really neat + + align:start position:0% +well you'll see something really neat + + + align:start position:0% +well you'll see something really neat +emerge out of this so we'll start with a + + align:start position:0% +emerge out of this so we'll start with a + + + align:start position:0% +emerge out of this so we'll start with a +one-year strip with a one-year strip the + + align:start position:0% +one-year strip with a one-year strip the + + + align:start position:0% +one-year strip with a one-year strip the +little r and the Big R is the same right + + align:start position:0% +little r and the Big R is the same right + + + align:start position:0% +little r and the Big R is the same right +because it's only one year so there's a + + align:start position:0% +because it's only one year so there's a + + + align:start position:0% +because it's only one year so there's a +onee big r a one year little r and when + + align:start position:0% +onee big r a one year little r and when + + + align:start position:0% +onee big r a one year little r and when +you work out the math they're actually + + align:start position:0% +you work out the math they're actually + + + align:start position:0% +you work out the math they're actually +equal to each other + + align:start position:0% +equal to each other + + + align:start position:0% +equal to each other +but now when you go with two years three + + align:start position:0% +but now when you go with two years three + + + align:start position:0% +but now when you go with two years three +years and T years it gets a little bit + + align:start position:0% +years and T years it gets a little bit + + + align:start position:0% +years and T years it gets a little bit +more + + align:start position:0% +more + + + align:start position:0% +more +complicated take a look at what happens + + align:start position:0% +complicated take a look at what happens + + + align:start position:0% +complicated take a look at what happens +if you take the price of the one year + + align:start position:0% +if you take the price of the one year + + + align:start position:0% +if you take the price of the one year +and you divide that into the price of + + align:start position:0% +and you divide that into the price of + + + align:start position:0% +and you divide that into the price of +the + + align:start position:0% +the + + + align:start position:0% +the +two-year so these two Securities the one + + align:start position:0% +two-year so these two Securities the one + + + align:start position:0% +two-year so these two Securities the one +year and the + + align:start position:0% +year and the + + + align:start position:0% +year and the +two-year they have the same F the same + + align:start position:0% +two-year they have the same F the same + + + align:start position:0% +two-year they have the same F the same +face value they pay $1,000 at maturity + + align:start position:0% +face value they pay $1,000 at maturity + + + align:start position:0% +face value they pay $1,000 at maturity +but one of them goes for one year and + + align:start position:0% +but one of them goes for one year and + + + align:start position:0% +but one of them goes for one year and +one of them goes for two years what + + align:start position:0% +one of them goes for two years what + + + align:start position:0% +one of them goes for two years what +happens when you take P 01 and you + + align:start position:0% +happens when you take P 01 and you + + + align:start position:0% +happens when you take P 01 and you +divide that by p02 by the way both of + + align:start position:0% +divide that by p02 by the way both of + + + align:start position:0% +divide that by p02 by the way both of +those + + align:start position:0% +those + + + align:start position:0% +those +prices exist today right for example if + + align:start position:0% +prices exist today right for example if + + + align:start position:0% +prices exist today right for example if +you take a look at the strips the price + + align:start position:0% +you take a look at the strips the price + + + align:start position:0% +you take a look at the strips the price +of p01 is 967 the price of p02 is + + align:start position:0% +of p01 is 967 the price of p02 is + + + align:start position:0% +of p01 is 967 the price of p02 is +927 if I take the price of one divided + + align:start position:0% +927 if I take the price of one divided + + + align:start position:0% +927 if I take the price of one divided +by the price of two + + align:start position:0% +by the price of two + + + align:start position:0% +by the price of two +what do I get yeah R2 exactly I get 1 + + align:start position:0% +what do I get yeah R2 exactly I get 1 + + + align:start position:0% +what do I get yeah R2 exactly I get 1 +plus + + align:start position:0% +plus + + + align:start position:0% +plus +R2 and so if I subtract one from that I + + align:start position:0% +R2 and so if I subtract one from that I + + + align:start position:0% +R2 and so if I subtract one from that I +get + + align:start position:0% +get + + + align:start position:0% +get +R2 so let's just go back I don't have a + + align:start position:0% +R2 so let's just go back I don't have a + + + align:start position:0% +R2 so let's just go back I don't have a +calculator with me but I'm sure all of + + align:start position:0% +calculator with me but I'm sure all of + + + align:start position:0% +calculator with me but I'm sure all of +you do somebody do that division for me + + align:start position:0% +you do somebody do that division for me + + + align:start position:0% +you do somebody do that division for me +will you can you take 0967 and divide + + align:start position:0% +will you can you take 0967 and divide + + + align:start position:0% +will you can you take 0967 and divide +that by 0927 what do you + + align:start position:0% +that by 0927 what do you + + + align:start position:0% +that by 0927 what do you +get 967 ided + + align:start position:0% + + + + align:start position:0% + +927 what's that 1.04 1.04 and then + + align:start position:0% +927 what's that 1.04 1.04 and then + + + align:start position:0% +927 what's that 1.04 1.04 and then +subtract one from that 4% actually can + + align:start position:0% +subtract one from that 4% actually can + + + align:start position:0% +subtract one from that 4% actually can +you give me a few more digits of + + align:start position:0% +you give me a few more digits of + + + align:start position:0% +you give me a few more digits of +accuracy + + align:start position:0% +accuracy + + + align:start position:0% +accuracy +4314 what's that + + align:start position:0% +4314 what's that + + + align:start position:0% +4314 what's that + + align:start position:0% + + + align:start position:0% +4314 so it turns out that in year in + + align:start position:0% +4314 so it turns out that in year in + + + align:start position:0% +4314 so it turns out that in year in +year zero where we have all of these + + align:start position:0% +year zero where we have all of these + + + align:start position:0% +year zero where we have all of these +prices we actually have a + + align:start position:0% +prices we actually have a + + + align:start position:0% +prices we actually have a +forecast for what big R2 is Big R2 in + + align:start position:0% +forecast for what big R2 is Big R2 in + + + align:start position:0% +forecast for what big R2 is Big R2 in +this case is the borrowing cost between + + align:start position:0% +this case is the borrowing cost between + + + align:start position:0% +this case is the borrowing cost between +year 1 and year + + align:start position:0% +year 1 and year + + + align:start position:0% +year 1 and year +two but we're sitting at year zero so + + align:start position:0% +two but we're sitting at year zero so + + + align:start position:0% +two but we're sitting at year zero so +implicit in the price of a two-year Bond + + align:start position:0% +implicit in the price of a two-year Bond + + + align:start position:0% +implicit in the price of a two-year Bond +and a one-year Bond implicit in that is + + align:start position:0% +and a one-year Bond implicit in that is + + + align:start position:0% +and a one-year Bond implicit in that is +a forecast of what the price is going to + + align:start position:0% +a forecast of what the price is going to + + + align:start position:0% +a forecast of what the price is going to +be or what the yield is going to be or + + align:start position:0% +be or what the yield is going to be or + + + align:start position:0% +be or what the yield is going to be or +what the borrowing cost is going to be + + align:start position:0% +what the borrowing cost is going to be + + + align:start position:0% +what the borrowing cost is going to be +between years one and two in this case + + align:start position:0% +between years one and two in this case + + + align:start position:0% +between years one and two in this case +4.3% or + + align:start position:0% +4.3% or + + + align:start position:0% +4.3% or +so and that's a really + + align:start position:0% +so and that's a really + + + align:start position:0% +so and that's a really +uh important + + align:start position:0% +uh important + + + align:start position:0% +uh important +observation if you plot these little RS + + align:start position:0% +observation if you plot these little RS + + + align:start position:0% +observation if you plot these little RS +on a graph as a function of + + align:start position:0% +on a graph as a function of + + + align:start position:0% +on a graph as a function of +time you actually get a sense of where + + align:start position:0% +time you actually get a sense of where + + + align:start position:0% +time you actually get a sense of where +the future big RS are going to + + align:start position:0% +the future big RS are going to + + + align:start position:0% +the future big RS are going to +lie this plot a plot of the RS as a + + align:start position:0% +lie this plot a plot of the RS as a + + + align:start position:0% +lie this plot a plot of the RS as a +function of time is known as the term + + align:start position:0% +function of time is known as the term + + + align:start position:0% +function of time is known as the term +structure of interest rates or the yield + + align:start position:0% +structure of interest rates or the yield + + + align:start position:0% +structure of interest rates or the yield +curve and it gives you a sense of where + + align:start position:0% +curve and it gives you a sense of where + + + align:start position:0% +curve and it gives you a sense of where +future interest rates are going to go if + + align:start position:0% +future interest rates are going to go if + + + align:start position:0% +future interest rates are going to go if +the curve is upward sloping it says that + + align:start position:0% +the curve is upward sloping it says that + + + align:start position:0% +the curve is upward sloping it says that +as you go out into longer maturities + + align:start position:0% +as you go out into longer maturities + + + align:start position:0% +as you go out into longer maturities +your average + + align:start position:0% +your average + + + align:start position:0% +your average +yield the average the geometric average + + align:start position:0% +yield the average the geometric average + + + align:start position:0% +yield the average the geometric average +of all the big + + align:start position:0% +of all the big + + + align:start position:0% +of all the big +RS it's getting bigger As Time grows as + + align:start position:0% +RS it's getting bigger As Time grows as + + + align:start position:0% +RS it's getting bigger As Time grows as +the time Horizon grows if it's downward + + align:start position:0% +the time Horizon grows if it's downward + + + align:start position:0% +the time Horizon grows if it's downward +sloping it + + align:start position:0% +sloping it + + + align:start position:0% +sloping it +suggests that future interest rates + + align:start position:0% +suggests that future interest rates + + + align:start position:0% +suggests that future interest rates +future big RS are + + align:start position:0% +future big RS are + + + align:start position:0% +future big RS are +declining so I want to show you what + + align:start position:0% +declining so I want to show you what + + + align:start position:0% +declining so I want to show you what +this yield curve looks like today now it + + align:start position:0% +this yield curve looks like today now it + + + align:start position:0% +this yield curve looks like today now it +turns out that we don't have a yield + + align:start position:0% +turns out that we don't have a yield + + + align:start position:0% +turns out that we don't have a yield +curve of strips as readily available as + + align:start position:0% +curve of strips as readily available as + + + align:start position:0% +curve of strips as readily available as +a yield curve that includes coupon + + align:start position:0% +a yield curve that includes coupon + + + align:start position:0% +a yield curve that includes coupon +payments so I'm going to come back to + + align:start position:0% +payments so I'm going to come back to + + + align:start position:0% +payments so I'm going to come back to +the distinction a little bit later on we + + align:start position:0% +the distinction a little bit later on we + + + align:start position:0% +the distinction a little bit later on we +haven't talked about coupon bonds yet + + align:start position:0% +haven't talked about coupon bonds yet + + + align:start position:0% +haven't talked about coupon bonds yet +but I just want to show you what the + + align:start position:0% +but I just want to show you what the + + + align:start position:0% +but I just want to show you what the +yield curve is so I I'm on the Bloomberg + + align:start position:0% +yield curve is so I I'm on the Bloomberg + + + align:start position:0% +yield curve is so I I'm on the Bloomberg +website this is uh publicly available so + + align:start position:0% +website this is uh publicly available so + + + align:start position:0% +website this is uh publicly available so +I don't have a particular license for it + + align:start position:0% +I don't have a particular license for it + + + align:start position:0% +I don't have a particular license for it +it's the the public version and if you + + align:start position:0% +it's the the public version and if you + + + align:start position:0% +it's the the public version and if you +click on Market data and then click on + + align:start position:0% +click on Market data and then click on + + + align:start position:0% +click on Market data and then click on +rates and bonds you're going to get this + + align:start position:0% +rates and bonds you're going to get this + + + align:start position:0% +rates and bonds you're going to get this +page right here so these are the + + align:start position:0% +page right here so these are the + + + align:start position:0% +page right here so these are the +different US Treasury Securities the + + align:start position:0% +different US Treasury Securities the + + + align:start position:0% +different US Treasury Securities the +different Horizons these are the coupons + + align:start position:0% +different Horizons these are the coupons + + + align:start position:0% +different Horizons these are the coupons +for less than a year there are no coupon + + align:start position:0% +for less than a year there are no coupon + + + align:start position:0% +for less than a year there are no coupon +payments so these are pure discount + + align:start position:0% +payments so these are pure discount + + + align:start position:0% +payments so these are pure discount +bonds + + align:start position:0% + + + + align:start position:0% + +and there's the + + align:start position:0% +and there's the + + + align:start position:0% +and there's the +graph that's + + align:start position:0% +graph that's + + + align:start position:0% +graph that's +it that graph the green line is showing + + align:start position:0% +it that graph the green line is showing + + + align:start position:0% +it that graph the green line is showing +you the future course of interest + + align:start position:0% +you the future course of interest + + + align:start position:0% +you the future course of interest +rates it's extremely low today the scale + + align:start position:0% +rates it's extremely low today the scale + + + align:start position:0% +rates it's extremely low today the scale +is on the leftand axis and by the way + + align:start position:0% +is on the leftand axis and by the way + + + align:start position:0% +is on the leftand axis and by the way +these are in + + align:start position:0% +these are in + + + align:start position:0% +these are in +percent so where we are today for a + + align:start position:0% +percent so where we are today for a + + + align:start position:0% +percent so where we are today for a +three Monon + + align:start position:0% + + + + align:start position:0% + +rate it's close to zero it's actually + + align:start position:0% +rate it's close to zero it's actually + + + align:start position:0% +rate it's close to zero it's actually +three basis + + align:start position:0% +three basis + + + align:start position:0% +three basis +points three basis points for a + + align:start position:0% +points three basis points for a + + + align:start position:0% +points three basis points for a +three-month t- Bill what ises that + + align:start position:0% +three-month t- Bill what ises that + + + align:start position:0% +three-month t- Bill what ises that +telling + + align:start position:0% + + + + align:start position:0% + +you what's the relationship between + + align:start position:0% +you what's the relationship between + + + align:start position:0% +you what's the relationship between +price + + align:start position:0% +price + + + align:start position:0% +price +and this little + + align:start position:0% +and this little + + + align:start position:0% +and this little +r + + align:start position:0% + + + + align:start position:0% + +yeah well that that's right but how does + + align:start position:0% +yeah well that that's right but how does + + + align:start position:0% +yeah well that that's right but how does +that yield get so + + align:start position:0% +that yield get so + + + align:start position:0% +that yield get so +low yes price is extremely high the + + align:start position:0% +low yes price is extremely high the + + + align:start position:0% +low yes price is extremely high the +price is extremely high that's right + + align:start position:0% +price is extremely high that's right + + + align:start position:0% +price is extremely high that's right +price is equal to the three-month payout + + align:start position:0% +price is equal to the three-month payout + + + align:start position:0% +price is equal to the three-month payout +divided by 1 plus little r if little r + + align:start position:0% +divided by 1 plus little r if little r + + + align:start position:0% +divided by 1 plus little r if little r +ends up being really really tiny it's + + align:start position:0% +ends up being really really tiny it's + + + align:start position:0% +ends up being really really tiny it's +only because the price is really high + + align:start position:0% +only because the price is really high + + + align:start position:0% +only because the price is really high +why would the price be + + align:start position:0% +why would the price be + + + align:start position:0% +why would the price be +high because us treasuries are the only + + align:start position:0% +high because us treasuries are the only + + + align:start position:0% +high because us treasuries are the only +safe thing to own right now at least + + align:start position:0% +safe thing to own right now at least + + + align:start position:0% +safe thing to own right now at least +that's what many people think exactly + + align:start position:0% +that's what many people think exactly + + + align:start position:0% +that's what many people think exactly +there is a a really strong flight to + + align:start position:0% +there is a a really strong flight to + + + align:start position:0% +there is a a really strong flight to +liquidity going on in markets as of + + align:start position:0% +liquidity going on in markets as of + + + align:start position:0% +liquidity going on in markets as of +today and how do you know that it's as + + align:start position:0% +today and how do you know that it's as + + + align:start position:0% +today and how do you know that it's as +of today well take a look at the + + align:start position:0% +of today well take a look at the + + + align:start position:0% +of today well take a look at the +difference between the green line and + + align:start position:0% +difference between the green line and + + + align:start position:0% +difference between the green line and +the Orange Line the orange line was what + + align:start position:0% +the Orange Line the orange line was what + + + align:start position:0% +the Orange Line the orange line was what +it was + + align:start position:0% +it was + + + align:start position:0% +it was +yesterday you see that there's a + + align:start position:0% +yesterday you see that there's a + + + align:start position:0% +yesterday you see that there's a +difference there's a noticeable + + align:start position:0% +difference there's a noticeable + + + align:start position:0% +difference there's a noticeable +difference on the short end that means a + + align:start position:0% +difference on the short end that means a + + + align:start position:0% +difference on the short end that means a +lot of people people are out there + + align:start position:0% +lot of people people are out there + + + align:start position:0% +lot of people people are out there +buying treasury bills now probably as we + + align:start position:0% +buying treasury bills now probably as we + + + align:start position:0% +buying treasury bills now probably as we +speak uh maybe you ought to go and uh + + align:start position:0% +speak uh maybe you ought to go and uh + + + align:start position:0% +speak uh maybe you ought to go and uh +buy some treasury + + align:start position:0% +buy some treasury + + + align:start position:0% +buy some treasury +bills people are scared and they're + + align:start position:0% +bills people are scared and they're + + + align:start position:0% +bills people are scared and they're +scared because all the things that are + + align:start position:0% +scared because all the things that are + + + align:start position:0% +scared because all the things that are +going on in the news and this is exactly + + align:start position:0% +going on in the news and this is exactly + + + align:start position:0% +going on in the news and this is exactly +what the FED is trying to to Stave off + + align:start position:0% +what the FED is trying to to Stave off + + + align:start position:0% +what the FED is trying to to Stave off +so you're absolutely right the FED is + + align:start position:0% +so you're absolutely right the FED is + + + align:start position:0% +so you're absolutely right the FED is +not worried about the cost of borrowing + + align:start position:0% +not worried about the cost of borrowing + + + align:start position:0% +not worried about the cost of borrowing +they're worried about whether or not + + align:start position:0% +they're worried about whether or not + + + align:start position:0% +they're worried about whether or not +there's money out there to be able to + + align:start position:0% +there's money out there to be able to + + + align:start position:0% +there's money out there to be able to +calm the fears of Market participants + + align:start position:0% +calm the fears of Market participants + + + align:start position:0% +calm the fears of Market participants +yeah you think also the jump from two + + align:start position:0% +yeah you think also the jump from two + + + align:start position:0% +yeah you think also the jump from two +days ago to today is prob the didn't cut + + align:start position:0% +days ago to today is prob the didn't cut + + + align:start position:0% +days ago to today is prob the didn't cut +interest R but in not theyed that in the + + align:start position:0% +interest R but in not theyed that in the + + + align:start position:0% +interest R but in not theyed that in the +near future have that's right they might + + align:start position:0% +near future have that's right they might + + + align:start position:0% +near future have that's right they might +have to so that expectation actually is + + align:start position:0% +have to so that expectation actually is + + + align:start position:0% +have to so that expectation actually is +built in to these prices the market + + align:start position:0% +built in to these prices the market + + + align:start position:0% +built in to these prices the market +recognizes that and they're worried but + + align:start position:0% +recognizes that and they're worried but + + + align:start position:0% +recognizes that and they're worried but +think about that if the FED has said + + align:start position:0% +think about that if the FED has said + + + align:start position:0% +think about that if the FED has said +that they're going to be cutting rates + + align:start position:0% +that they're going to be cutting rates + + + align:start position:0% +that they're going to be cutting rates +possibly cutting rates in the future and + + align:start position:0% +possibly cutting rates in the future and + + + align:start position:0% +possibly cutting rates in the future and +yet the rate stays high in going forward + + align:start position:0% +yet the rate stays high in going forward + + + align:start position:0% +yet the rate stays high in going forward +relatively high and rates go down today + + align:start position:0% +relatively high and rates go down today + + + align:start position:0% +relatively high and rates go down today +what that's telling you is that the + + align:start position:0% +what that's telling you is that the + + + align:start position:0% +what that's telling you is that the +market is being driven by a panic + + align:start position:0% +market is being driven by a panic + + + align:start position:0% +market is being driven by a panic +reaction now now rates are going to go + + align:start position:0% +reaction now now rates are going to go + + + align:start position:0% +reaction now now rates are going to go +up so the fact that you see the market + + align:start position:0% +up so the fact that you see the market + + + align:start position:0% +up so the fact that you see the market +uh determining a yield curve that's + + align:start position:0% +uh determining a yield curve that's + + + align:start position:0% +uh determining a yield curve that's +upward sloping that's telling you that + + align:start position:0% +upward sloping that's telling you that + + + align:start position:0% +upward sloping that's telling you that +people expect that rates are going to go + + align:start position:0% +people expect that rates are going to go + + + align:start position:0% +people expect that rates are going to go +up that rates have to go up for one of + + align:start position:0% +up that rates have to go up for one of + + + align:start position:0% +up that rates have to go up for one of +two reasons and in fact you can take a + + align:start position:0% +two reasons and in fact you can take a + + + align:start position:0% +two reasons and in fact you can take a +look at the steepness of the yield curve + + align:start position:0% +look at the steepness of the yield curve + + + align:start position:0% +look at the steepness of the yield curve +as telling you what the Market's + + align:start position:0% +as telling you what the Market's + + + align:start position:0% +as telling you what the Market's +expectations are for how quickly rates + + align:start position:0% +expectations are for how quickly rates + + + align:start position:0% +expectations are for how quickly rates +are going to go up and and where they're + + align:start position:0% +are going to go up and and where they're + + + align:start position:0% +are going to go up and and where they're +going to go up so you have to look at + + align:start position:0% +going to go up so you have to look at + + + align:start position:0% +going to go up so you have to look at +the the um x-axis a little bit + + align:start position:0% +the the um x-axis a little bit + + + align:start position:0% +the the um x-axis a little bit +differently these are denominated in + + align:start position:0% +differently these are denominated in + + + align:start position:0% +differently these are denominated in +years so this is 3 months 6 months one + + align:start position:0% +years so this is 3 months 6 months one + + + align:start position:0% +years so this is 3 months 6 months one +year 2 3 4 5 up to 10 then 15 20 and 30 + + align:start position:0% +year 2 3 4 5 up to 10 then 15 20 and 30 + + + align:start position:0% +year 2 3 4 5 up to 10 then 15 20 and 30 +so these are long long-term rates and + + align:start position:0% +so these are long long-term rates and + + + align:start position:0% +so these are long long-term rates and +you can see that the yield curve really + + align:start position:0% +you can see that the yield curve really + + + align:start position:0% +you can see that the yield curve really +goes up sharply after the first three + + align:start position:0% +goes up sharply after the first three + + + align:start position:0% +goes up sharply after the first three +months there's a big increase in the + + align:start position:0% +months there's a big increase in the + + + align:start position:0% +months there's a big increase in the +slope and then it becomes a little bit + + align:start position:0% +slope and then it becomes a little bit + + + align:start position:0% +slope and then it becomes a little bit +more gradual + + align:start position:0% +more gradual + + + align:start position:0% +more gradual +that's an a uh a sign of a short-term + + align:start position:0% +that's an a uh a sign of a short-term + + + align:start position:0% +that's an a uh a sign of a short-term +flight to Quality or flight to liquidity + + align:start position:0% +flight to Quality or flight to liquidity + + + align:start position:0% +flight to Quality or flight to liquidity +but that the market expects over time as + + align:start position:0% +but that the market expects over time as + + + align:start position:0% +but that the market expects over time as +things calm down that interest rates + + align:start position:0% +things calm down that interest rates + + + align:start position:0% +things calm down that interest rates +will go up for one of two reasons you + + align:start position:0% +will go up for one of two reasons you + + + align:start position:0% +will go up for one of two reasons you +know either there's inflationary + + align:start position:0% +know either there's inflationary + + + align:start position:0% +know either there's inflationary +pressures and that will drive rates up + + align:start position:0% +pressures and that will drive rates up + + + align:start position:0% +pressures and that will drive rates up +or there's going to be some economic + + align:start position:0% +or there's going to be some economic + + + align:start position:0% +or there's going to be some economic +consequences of what's happening today + + align:start position:0% +consequences of what's happening today + + + align:start position:0% +consequences of what's happening today +and that will ultimately cause rates to + + align:start position:0% +and that will ultimately cause rates to + + + align:start position:0% +and that will ultimately cause rates to +go + + align:start position:0% +go + + + align:start position:0% +go +up yeah so what's + + align:start position:0% +up yeah so what's + + + align:start position:0% +up yeah so what's +happening with the interest rates + + align:start position:0% +happening with the interest rates + + + align:start position:0% +happening with the interest rates +outside of the states because what like + + align:start position:0% +outside of the states because what like + + + align:start position:0% +outside of the states because what like +I'm I'm from Argentina right and when we + + align:start position:0% +I'm I'm from Argentina right and when we + + + align:start position:0% +I'm I'm from Argentina right and when we +have crisis like in general interest + + align:start position:0% +have crisis like in general interest + + + align:start position:0% +have crisis like in general interest +rates go up because the probability of + + align:start position:0% +rates go up because the probability of + + + align:start position:0% +rates go up because the probability of +defol increases and now I see here it's + + align:start position:0% +defol increases and now I see here it's + + + align:start position:0% +defol increases and now I see here it's +the other way around because sort + + align:start position:0% +the other way around because sort + + + align:start position:0% +the other way around because sort +of considering it will be that's right + + align:start position:0% +of considering it will be that's right + + + align:start position:0% +of considering it will be that's right +it depends on the nature of the crisis + + align:start position:0% +it depends on the nature of the crisis + + + align:start position:0% +it depends on the nature of the crisis +so in certain countries where there is a + + align:start position:0% +so in certain countries where there is a + + + align:start position:0% +so in certain countries where there is a +financial crisis the typical reaction of + + align:start position:0% +financial crisis the typical reaction of + + + align:start position:0% +financial crisis the typical reaction of +monetary authorities is to flood the + + align:start position:0% +monetary authorities is to flood the + + + align:start position:0% +monetary authorities is to flood the +market with cash because that's their + + align:start position:0% +market with cash because that's their + + + align:start position:0% +market with cash because that's their +reaction to a liquidity crunch they want + + align:start position:0% +reaction to a liquidity crunch they want + + + align:start position:0% +reaction to a liquidity crunch they want +to reduce the prospect of having a kind + + align:start position:0% +to reduce the prospect of having a kind + + + align:start position:0% +to reduce the prospect of having a kind +of run on the banks so they'll flood the + + align:start position:0% +of run on the banks so they'll flood the + + + align:start position:0% +of run on the banks so they'll flood the +market with uh with their currency when + + align:start position:0% +market with uh with their currency when + + + align:start position:0% +market with uh with their currency when +you do that you encourage inflation and + + align:start position:0% +you do that you encourage inflation and + + + align:start position:0% +you do that you encourage inflation and +that's why interest rates go up in those + + align:start position:0% +that's why interest rates go up in those + + + align:start position:0% +that's why interest rates go up in those +kind of economies the US For Better or + + align:start position:0% +kind of economies the US For Better or + + + align:start position:0% +kind of economies the US For Better or +For Worse has shown a certain degree of + + align:start position:0% +For Worse has shown a certain degree of + + + align:start position:0% +For Worse has shown a certain degree of +Monet Ary restraint over the years in + + align:start position:0% +Monet Ary restraint over the years in + + + align:start position:0% +Monet Ary restraint over the years in +that while they do certainly cut + + align:start position:0% +that while they do certainly cut + + + align:start position:0% +that while they do certainly cut +interest rates and Allan Greenspan you + + align:start position:0% +interest rates and Allan Greenspan you + + + align:start position:0% +interest rates and Allan Greenspan you +know was uh uh very active in this + + align:start position:0% +know was uh uh very active in this + + + align:start position:0% +know was uh uh very active in this +respect over the last uh you know 10 or + + align:start position:0% +respect over the last uh you know 10 or + + + align:start position:0% +respect over the last uh you know 10 or +15 years the fact is that there's been + + align:start position:0% +15 years the fact is that there's been + + + align:start position:0% +15 years the fact is that there's been +more measured control of monetary policy + + align:start position:0% +more measured control of monetary policy + + + align:start position:0% +more measured control of monetary policy +in the United States so what that means + + align:start position:0% +in the United States so what that means + + + align:start position:0% +in the United States so what that means +is that this is a symptom more of a + + align:start position:0% +is that this is a symptom more of a + + + align:start position:0% +is that this is a symptom more of a +short-term cash crunch people are just + + align:start position:0% +short-term cash crunch people are just + + + align:start position:0% +short-term cash crunch people are just +putting money in treasury bills for the + + align:start position:0% +putting money in treasury bills for the + + + align:start position:0% +putting money in treasury bills for the +short term without any + + align:start position:0% +short term without any + + + align:start position:0% +short term without any +expectation that the Fed is going to + + align:start position:0% +expectation that the Fed is going to + + + align:start position:0% +expectation that the Fed is going to +dramatically increase the money money + + align:start position:0% +dramatically increase the money money + + + align:start position:0% +dramatically increase the money money +supply if they did that you would then + + align:start position:0% +supply if they did that you would then + + + align:start position:0% +supply if they did that you would then +see interest rates rise because + + align:start position:0% +see interest rates rise because + + + align:start position:0% +see interest rates rise because +inflation would be much more of a + + align:start position:0% +inflation would be much more of a + + + align:start position:0% +inflation would be much more of a +problem okay uh yes I mean I thought for + + align:start position:0% +problem okay uh yes I mean I thought for + + + align:start position:0% +problem okay uh yes I mean I thought for +example the European Central Bank yeah + + align:start position:0% +example the European Central Bank yeah + + + align:start position:0% +example the European Central Bank yeah +normally raises the the interest rates + + align:start position:0% +normally raises the the interest rates + + + align:start position:0% +normally raises the the interest rates +to preventation than that's right they + + align:start position:0% +to preventation than that's right they + + + align:start position:0% +to preventation than that's right they +do raise it and that's one of the + + align:start position:0% +do raise it and that's one of the + + + align:start position:0% +do raise it and that's one of the +reasons why the FED did not cut it it's + + align:start position:0% +reasons why the FED did not cut it it's + + + align:start position:0% +reasons why the FED did not cut it it's +because they are concerned with + + align:start position:0% +because they are concerned with + + + align:start position:0% +because they are concerned with +inflation and so if they ended up + + align:start position:0% +inflation and so if they ended up + + + align:start position:0% +inflation and so if they ended up +cutting interest rates while that might + + align:start position:0% +cutting interest rates while that might + + + align:start position:0% +cutting interest rates while that might +Stave off certain credit crunches that + + align:start position:0% +Stave off certain credit crunches that + + + align:start position:0% +Stave off certain credit crunches that +would actually encourage inflation + + align:start position:0% +would actually encourage inflation + + + align:start position:0% +would actually encourage inflation +inflation does encourage higher interest + + align:start position:0% +inflation does encourage higher interest + + + align:start position:0% +inflation does encourage higher interest +rates but when is + + align:start position:0% +rates but when is + + + align:start position:0% +rates but when is +the inflation causes so I I I I see the + + align:start position:0% +the inflation causes so I I I I see the + + + align:start position:0% +the inflation causes so I I I I see the +confusion and let me make a distinction + + align:start position:0% +confusion and let me make a distinction + + + align:start position:0% +confusion and let me make a distinction +there are two different interest rates + + align:start position:0% +there are two different interest rates + + + align:start position:0% +there are two different interest rates +that are going on there's the market + + align:start position:0% +that are going on there's the market + + + align:start position:0% +that are going on there's the market +rate of interest which is what this is + + align:start position:0% +rate of interest which is what this is + + + align:start position:0% +rate of interest which is what this is +and then there's the fed's stated + + align:start position:0% +and then there's the fed's stated + + + align:start position:0% +and then there's the fed's stated +federal funds rate which is what it + + align:start position:0% +federal funds rate which is what it + + + align:start position:0% +federal funds rate which is what it +charges its other Banks member banks for + + align:start position:0% +charges its other Banks member banks for + + + align:start position:0% +charges its other Banks member banks for +borrowing the FED is able to control + + align:start position:0% +borrowing the FED is able to control + + + align:start position:0% +borrowing the FED is able to control +what it charges to other Banks the FED + + align:start position:0% +what it charges to other Banks the FED + + + align:start position:0% +what it charges to other Banks the FED +cannot control these rates so the + + align:start position:0% +cannot control these rates so the + + + align:start position:0% +cannot control these rates so the +interest rates that you you're thinking + + align:start position:0% +interest rates that you you're thinking + + + align:start position:0% +interest rates that you you're thinking +about that for example when the ECB + + align:start position:0% +about that for example when the ECB + + + align:start position:0% +about that for example when the ECB +raises rates they do so uh so as to + + align:start position:0% +raises rates they do so uh so as to + + + align:start position:0% +raises rates they do so uh so as to +discourage lots of uh borrowing and + + align:start position:0% +discourage lots of uh borrowing and + + + align:start position:0% +discourage lots of uh borrowing and +lending and reduce the amount of money + + align:start position:0% +lending and reduce the amount of money + + + align:start position:0% +lending and reduce the amount of money +that's in the money sub uh that's in uh + + align:start position:0% +that's in the money sub uh that's in uh + + + align:start position:0% +that's in the money sub uh that's in uh +in circulation and that decreases uh + + align:start position:0% +in circulation and that decreases uh + + + align:start position:0% +in circulation and that decreases uh +business activity which then reduces the + + align:start position:0% +business activity which then reduces the + + + align:start position:0% +business activity which then reduces the +pressure inflation okay so that's what + + align:start position:0% +pressure inflation okay so that's what + + + align:start position:0% +pressure inflation okay so that's what +they do in response but they don't + + align:start position:0% +they do in response but they don't + + + align:start position:0% +they do in response but they don't +control the interest rate determined by + + align:start position:0% +control the interest rate determined by + + + align:start position:0% +control the interest rate determined by +the market for treasury bills and in + + align:start position:0% +the market for treasury bills and in + + + align:start position:0% +the market for treasury bills and in +these interest rates these 30-year rates + + align:start position:0% +these interest rates these 30-year rates + + + align:start position:0% +these interest rates these 30-year rates +as opposed to overnight borrowing rates + + align:start position:0% +as opposed to overnight borrowing rates + + + align:start position:0% +as opposed to overnight borrowing rates +and fed funds rates these rates give you + + align:start position:0% +and fed funds rates these rates give you + + + align:start position:0% +and fed funds rates these rates give you +a sense of what the market is expecting + + align:start position:0% +a sense of what the market is expecting + + + align:start position:0% +a sense of what the market is expecting +over time Megan do you have a question + + align:start position:0% + + + + align:start position:0% + +as + + align:start position:0% + + + + align:start position:0% + +much Banks spread + + align:start position:0% +much Banks spread + + + align:start position:0% +much Banks spread +over + + align:start position:0% + + + + align:start position:0% + +Char + + align:start position:0% +Char + + + align:start position:0% +Char +right to save off that + + align:start position:0% +right to save off that + + + align:start position:0% +right to save off that +credit well that's right I think that + + align:start position:0% +credit well that's right I think that + + + align:start position:0% +credit well that's right I think that +when you think about the instruments + + align:start position:0% +when you think about the instruments + + + align:start position:0% +when you think about the instruments +that the FED has for managing monetary + + align:start position:0% +that the FED has for managing monetary + + + align:start position:0% +that the FED has for managing monetary +policy and credit and + + align:start position:0% +policy and credit and + + + align:start position:0% +policy and credit and +liquidity it's actually pretty minimal I + + align:start position:0% +liquidity it's actually pretty minimal I + + + align:start position:0% +liquidity it's actually pretty minimal I +mean they have like one one variable you + + align:start position:0% +mean they have like one one variable you + + + align:start position:0% +mean they have like one one variable you +know imagine flying an airplane and you + + align:start position:0% +know imagine flying an airplane and you + + + align:start position:0% +know imagine flying an airplane and you +get one control you know pick you pick + + align:start position:0% +get one control you know pick you pick + + + align:start position:0% +get one control you know pick you pick +the control you you want to be able to + + align:start position:0% +the control you you want to be able to + + + align:start position:0% +the control you you want to be able to +control the wheels or the the aerons or + + align:start position:0% +control the wheels or the the aerons or + + + align:start position:0% +control the wheels or the the aerons or +the you know it's very very hard to try + + align:start position:0% +the you know it's very very hard to try + + + align:start position:0% +the you know it's very very hard to try +to manage the economy with one variable + + align:start position:0% +to manage the economy with one variable + + + align:start position:0% +to manage the economy with one variable +now the FED has other policy instruments + + align:start position:0% +now the FED has other policy instruments + + + align:start position:0% +now the FED has other policy instruments +that are a little bit more complex like + + align:start position:0% +that are a little bit more complex like + + + align:start position:0% +that are a little bit more complex like +the discount window like moral suasion + + align:start position:0% +the discount window like moral suasion + + + align:start position:0% +the discount window like moral suasion +the New York fed can go to these Banks + + align:start position:0% +the New York fed can go to these Banks + + + align:start position:0% +the New York fed can go to these Banks +and say what are you guys doing are you + + align:start position:0% +and say what are you guys doing are you + + + align:start position:0% +and say what are you guys doing are you +nuts um but what's going on now is that + + align:start position:0% +nuts um but what's going on now is that + + + align:start position:0% +nuts um but what's going on now is that +because the crisis + + align:start position:0% +because the crisis + + + align:start position:0% +because the crisis +has reached such an extraordinary level + + align:start position:0% +has reached such an extraordinary level + + + align:start position:0% +has reached such an extraordinary level +they're not worrying about interest + + align:start position:0% +they're not worrying about interest + + + align:start position:0% +they're not worrying about interest +rates they're actually trying to figure + + align:start position:0% +rates they're actually trying to figure + + + align:start position:0% +rates they're actually trying to figure +out how to Stave off some kind of mass + + align:start position:0% +out how to Stave off some kind of mass + + + align:start position:0% +out how to Stave off some kind of mass +panic and so getting directly involved + + align:start position:0% +panic and so getting directly involved + + + align:start position:0% +panic and so getting directly involved +with AIG getting in discussions with + + align:start position:0% +with AIG getting in discussions with + + + align:start position:0% +with AIG getting in discussions with +Bear Sterns and JB Morgan they really + + align:start position:0% +Bear Sterns and JB Morgan they really + + + align:start position:0% +Bear Sterns and JB Morgan they really +have no choice and and it's it's a + + align:start position:0% +have no choice and and it's it's a + + + align:start position:0% +have no choice and and it's it's a +signal of sort of how desperate times + + align:start position:0% +signal of sort of how desperate times + + + align:start position:0% +signal of sort of how desperate times +are yeah one last question a couple this + + align:start position:0% +are yeah one last question a couple this + + + align:start position:0% +are yeah one last question a couple this +is kind of M my understanding is first + + align:start position:0% +is kind of M my understanding is first + + + align:start position:0% +is kind of M my understanding is first +that the FED is not a federal + + align:start position:0% +that the FED is not a federal + + + align:start position:0% +that the FED is not a federal +organization it's made up of number + + align:start position:0% +organization it's made up of number + + + align:start position:0% +organization it's made up of number +Banks yeah so that it's not a government + + align:start position:0% +Banks yeah so that it's not a government + + + align:start position:0% +Banks yeah so that it's not a government +entity but the government has pointed + + align:start position:0% +entity but the government has pointed + + + align:start position:0% +entity but the government has pointed +representative to it and on the same + + align:start position:0% +representative to it and on the same + + + align:start position:0% +representative to it and on the same +time where does the FED get all their + + align:start position:0% +time where does the FED get all their + + + align:start position:0% +time where does the FED get all their +money from well uh so this is more of a + + align:start position:0% +money from well uh so this is more of a + + + align:start position:0% +money from well uh so this is more of a +question that you probably should be + + align:start position:0% +question that you probably should be + + + align:start position:0% +question that you probably should be +asking your macro instructor but I'm I'm + + align:start position:0% +asking your macro instructor but I'm I'm + + + align:start position:0% +asking your macro instructor but I'm I'm +happy to answer but they may the macro + + align:start position:0% +happy to answer but they may the macro + + + align:start position:0% +happy to answer but they may the macro +folks May disagree with what I'm about + + align:start position:0% +folks May disagree with what I'm about + + + align:start position:0% +folks May disagree with what I'm about +to tell you um the FED is a government + + align:start position:0% +to tell you um the FED is a government + + + align:start position:0% +to tell you um the FED is a government +organization it's you're it's it's + + align:start position:0% +organization it's you're it's it's + + + align:start position:0% +organization it's you're it's it's +separate from the government in the + + align:start position:0% +separate from the government in the + + + align:start position:0% +separate from the government in the +sense that it's not a political uh + + align:start position:0% +sense that it's not a political uh + + + align:start position:0% +sense that it's not a political uh +organization but it does have the full + + align:start position:0% +organization but it does have the full + + + align:start position:0% +organization but it does have the full +backing of the government and it has + + align:start position:0% +backing of the government and it has + + + align:start position:0% +backing of the government and it has +power is granted to it uh as part of the + + align:start position:0% +power is granted to it uh as part of the + + + align:start position:0% +power is granted to it uh as part of the +various uh legal um uh legal proposals + + align:start position:0% +various uh legal um uh legal proposals + + + align:start position:0% +various uh legal um uh legal proposals +that were developed to create the + + align:start position:0% +that were developed to create the + + + align:start position:0% +that were developed to create the +Federal Reserve System um where does the + + align:start position:0% +Federal Reserve System um where does the + + + align:start position:0% +Federal Reserve System um where does the +FED get its money from it get it gets + + align:start position:0% +FED get its money from it get it gets + + + align:start position:0% +FED get its money from it get it gets +its money from the treasury so the FED + + align:start position:0% +its money from the treasury so the FED + + + align:start position:0% +its money from the treasury so the FED +can actually engage in what are called + + align:start position:0% +can actually engage in what are called + + + align:start position:0% +can actually engage in what are called +open market operations and uh can + + align:start position:0% +open market operations and uh can + + + align:start position:0% +open market operations and uh can +actually contract or expand money supply + + align:start position:0% +actually contract or expand money supply + + + align:start position:0% +actually contract or expand money supply +based upon what the treasury will uh + + align:start position:0% +based upon what the treasury will uh + + + align:start position:0% +based upon what the treasury will uh +will allow it to do or will work with it + + align:start position:0% +will allow it to do or will work with it + + + align:start position:0% +will allow it to do or will work with it +to do so and the FED controls the + + align:start position:0% +to do so and the FED controls the + + + align:start position:0% +to do so and the FED controls the +borrowing rate among all of the member + + align:start position:0% +borrowing rate among all of the member + + + align:start position:0% +borrowing rate among all of the member +banks and actually all of the major + + align:start position:0% +banks and actually all of the major + + + align:start position:0% +banks and actually all of the major +banks are members so it's not like you + + align:start position:0% +banks are members so it's not like you + + + align:start position:0% +banks are members so it's not like you +can start up your bank tomorrow in order + + align:start position:0% +can start up your bank tomorrow in order + + + align:start position:0% +can start up your bank tomorrow in order +to start a bank and deal with the public + + align:start position:0% +to start a bank and deal with the public + + + align:start position:0% +to start a bank and deal with the public +you need a bank Charter and the bank + + align:start position:0% +you need a bank Charter and the bank + + + align:start position:0% +you need a bank Charter and the bank +Charter is issued by the government and + + align:start position:0% +Charter is issued by the government and + + + align:start position:0% +Charter is issued by the government and +once you're part of that Network you are + + align:start position:0% +once you're part of that Network you are + + + align:start position:0% +once you're part of that Network you are +part of the uh the Federal Reserve + + align:start position:0% +part of the uh the Federal Reserve + + + align:start position:0% +part of the uh the Federal Reserve +System aren't they losing money from say + + align:start position:0% +System aren't they losing money from say + + + align:start position:0% +System aren't they losing money from say +the Fallout of these Banks AR they in + + align:start position:0% +the Fallout of these Banks AR they in + + + align:start position:0% +the Fallout of these Banks AR they in +essence losing also themselves well + + align:start position:0% +essence losing also themselves well + + + align:start position:0% +essence losing also themselves well +they're they're not trying to make money + + align:start position:0% +they're they're not trying to make money + + + align:start position:0% +they're they're not trying to make money +that's not their objective uh and if + + align:start position:0% +that's not their objective uh and if + + + align:start position:0% +that's not their objective uh and if +they're losing money ultimately it's not + + align:start position:0% +they're losing money ultimately it's not + + + align:start position:0% +they're losing money ultimately it's not +them that is losing money it is who yeah + + align:start position:0% +them that is losing money it is who yeah + + + align:start position:0% +them that is losing money it is who yeah +we're we're losing money it's government + + align:start position:0% +we're we're losing money it's government + + + align:start position:0% +we're we're losing money it's government +sponsored so that's one of the reasons + + align:start position:0% +sponsored so that's one of the reasons + + + align:start position:0% +sponsored so that's one of the reasons +why I think the FED has been so + + align:start position:0% +why I think the FED has been so + + + align:start position:0% +why I think the FED has been so +concerned about uh bailing out Leman + + align:start position:0% +concerned about uh bailing out Leman + + + align:start position:0% +concerned about uh bailing out Leman +brothers and even the bailout of Bear + + align:start position:0% +brothers and even the bailout of Bear + + + align:start position:0% +brothers and even the bailout of Bear +Sterns which did not necessarily cost + + align:start position:0% +Sterns which did not necessarily cost + + + align:start position:0% +Sterns which did not necessarily cost +them anything uh the fact that they were + + align:start position:0% +them anything uh the fact that they were + + + align:start position:0% +them anything uh the fact that they were +willing to provide this back stop + + align:start position:0% +willing to provide this back stop + + + align:start position:0% +willing to provide this back stop +guarantee in order to make the deal + + align:start position:0% +guarantee in order to make the deal + + + align:start position:0% +guarantee in order to make the deal +happen that implicit insurance is a cost + + align:start position:0% +happen that implicit insurance is a cost + + + align:start position:0% +happen that implicit insurance is a cost +that we ultimately end up paying they + + align:start position:0% +that we ultimately end up paying they + + + align:start position:0% +that we ultimately end up paying they +got a huge amount of heat for that and + + align:start position:0% +got a huge amount of heat for that and + + + align:start position:0% +got a huge amount of heat for that and +that's one of the reasons why they + + align:start position:0% +that's one of the reasons why they + + + align:start position:0% +that's one of the reasons why they +decided to back off from the Leman + + align:start position:0% +decided to back off from the Leman + + + align:start position:0% +decided to back off from the Leman +Brothers deal it's because they would + + align:start position:0% +Brothers deal it's because they would + + + align:start position:0% +Brothers deal it's because they would +have gotten huge huge backlash uh from + + align:start position:0% +have gotten huge huge backlash uh from + + + align:start position:0% +have gotten huge huge backlash uh from +that kind of an event now AIG the fact + + align:start position:0% +that kind of an event now AIG the fact + + + align:start position:0% +that kind of an event now AIG the fact +that they went and did something there + + align:start position:0% +that they went and did something there + + + align:start position:0% +that they went and did something there +tells you something about how important + + align:start position:0% +tells you something about how important + + + align:start position:0% +tells you something about how important +AIG is or what repercussions might have + + align:start position:0% +AIG is or what repercussions might have + + + align:start position:0% +AIG is or what repercussions might have +come about if they had let AIG fail so + + align:start position:0% +come about if they had let AIG fail so + + + align:start position:0% +come about if they had let AIG fail so +that says more not about the FED but + + align:start position:0% +that says more not about the FED but + + + align:start position:0% +that says more not about the FED but +more about the situation with AIG and + + align:start position:0% +more about the situation with AIG and + + + align:start position:0% +more about the situation with AIG and +the specific Financial transactions that + + align:start position:0% +the specific Financial transactions that + + + align:start position:0% +the specific Financial transactions that +engaged + + align:start position:0% +engaged + + + align:start position:0% +engaged +in okay let me uh continue on and uh + + align:start position:0% +in okay let me uh continue on and uh + + + align:start position:0% +in okay let me uh continue on and uh +sorry I'm going to uh hold off questions + + align:start position:0% +sorry I'm going to uh hold off questions + + + align:start position:0% +sorry I'm going to uh hold off questions +for a little bit longer but I do want to + + align:start position:0% +for a little bit longer but I do want to + + + align:start position:0% +for a little bit longer but I do want to +cover uh you know some additional + + align:start position:0% +cover uh you know some additional + + + align:start position:0% +cover uh you know some additional +material so this is the expression that + + align:start position:0% +material so this is the expression that + + + align:start position:0% +material so this is the expression that +we just described for getting a sense of + + align:start position:0% +we just described for getting a sense of + + + align:start position:0% +we just described for getting a sense of +future interest rates and we saw given + + align:start position:0% +future interest rates and we saw given + + + align:start position:0% +future interest rates and we saw given +today's uh yield curve you know that + + align:start position:0% +today's uh yield curve you know that + + + align:start position:0% +today's uh yield curve you know that +there is some sense that interest rates + + align:start position:0% +there is some sense that interest rates + + + align:start position:0% +there is some sense that interest rates +are going to rise but it turns out that + + align:start position:0% +are going to rise but it turns out that + + + align:start position:0% +are going to rise but it turns out that +the yield curve contains all sorts of + + align:start position:0% +the yield curve contains all sorts of + + + align:start position:0% +the yield curve contains all sorts of +information not just about oneyear rates + + align:start position:0% +information not just about oneyear rates + + + align:start position:0% +information not just about oneyear rates +but in fact about multi-year rates so + + align:start position:0% +but in fact about multi-year rates so + + + align:start position:0% +but in fact about multi-year rates so +this is a clear example this is one + + align:start position:0% +this is a clear example this is one + + + align:start position:0% +this is a clear example this is one +example um and it turns out that there's + + align:start position:0% +example um and it turns out that there's + + + align:start position:0% +example um and it turns out that there's +another example that makes this a little + + align:start position:0% +another example that makes this a little + + + align:start position:0% +another example that makes this a little +bit clearer which is future rates and + + align:start position:0% +bit clearer which is future rates and + + + align:start position:0% +bit clearer which is future rates and +forward rates these are all very + + align:start position:0% +forward rates these are all very + + + align:start position:0% +forward rates these are all very +confusing terminology unless you sit + + align:start position:0% +confusing terminology unless you sit + + + align:start position:0% +confusing terminology unless you sit +down and read through it carefully so I + + align:start position:0% +down and read through it carefully so I + + + align:start position:0% +down and read through it carefully so I +would encourage you all to do that after + + align:start position:0% +would encourage you all to do that after + + + align:start position:0% +would encourage you all to do that after +this lecture there's a lot of notation + + align:start position:0% +this lecture there's a lot of notation + + + align:start position:0% +this lecture there's a lot of notation +in this lecture not a lot of conceptual + + align:start position:0% +in this lecture not a lot of conceptual + + + align:start position:0% +in this lecture not a lot of conceptual +challenges because all the conceptual + + align:start position:0% +challenges because all the conceptual + + + align:start position:0% +challenges because all the conceptual +challenges we derived when we talked + + align:start position:0% +challenges we derived when we talked + + + align:start position:0% +challenges we derived when we talked +about net pressent value rules so most + + align:start position:0% +about net pressent value rules so most + + + align:start position:0% +about net pressent value rules so most +of this is just lots of notation and + + align:start position:0% +of this is just lots of notation and + + + align:start position:0% +of this is just lots of notation and +terminology so let me describe the + + align:start position:0% +terminology so let me describe the + + + align:start position:0% +terminology so let me describe the +terminology here at date Zero if we + + align:start position:0% +terminology here at date Zero if we + + + align:start position:0% +terminology here at date Zero if we +focus on the price of a bond that + + align:start position:0% +focus on the price of a bond that + + + align:start position:0% +focus on the price of a bond that +matures at time T minus one and at date + + align:start position:0% +matures at time T minus one and at date + + + align:start position:0% +matures at time T minus one and at date +Zero if we focus on the price of a bond + + align:start position:0% +Zero if we focus on the price of a bond + + + align:start position:0% +Zero if we focus on the price of a bond +that + + align:start position:0% +that + + + align:start position:0% +that +matures at dayt and we take the ratio of + + align:start position:0% +matures at dayt and we take the ratio of + + + align:start position:0% +matures at dayt and we take the ratio of +those two then it turns out we're + + align:start position:0% +those two then it turns out we're + + + align:start position:0% +those two then it turns out we're +getting an implicit forecast of the + + align:start position:0% +getting an implicit forecast of the + + + align:start position:0% +getting an implicit forecast of the +future oneyear spot rate between T minus + + align:start position:0% +future oneyear spot rate between T minus + + + align:start position:0% +future oneyear spot rate between T minus +one and T right that's just what we did + + align:start position:0% +one and T right that's just what we did + + + align:start position:0% +one and T right that's just what we did +with + + align:start position:0% +with + + + align:start position:0% +with +R2 so this is true in general and + + align:start position:0% +R2 so this is true in general and + + + align:start position:0% +R2 so this is true in general and +there's a name for this + + align:start position:0% +there's a name for this + + + align:start position:0% +there's a name for this +forecast it's called + + align:start position:0% +forecast it's called + + + align:start position:0% +forecast it's called +today's forward rate between dates T + + align:start position:0% +today's forward rate between dates T + + + align:start position:0% +today's forward rate between dates T +minus one and T it is a + + align:start position:0% +minus one and T it is a + + + align:start position:0% +minus one and T it is a +forecast of the future spot rate between + + align:start position:0% +forecast of the future spot rate between + + + align:start position:0% +forecast of the future spot rate between +dates T minus one and T okay we don't + + align:start position:0% +dates T minus one and T okay we don't + + + align:start position:0% +dates T minus one and T okay we don't +know what that spot rate is going to be + + align:start position:0% +know what that spot rate is going to be + + + align:start position:0% +know what that spot rate is going to be +in general we don't know what future + + align:start position:0% +in general we don't know what future + + + align:start position:0% +in general we don't know what future +interest rates are going to be it's + + align:start position:0% +interest rates are going to be it's + + + align:start position:0% +interest rates are going to be it's +uncertain but today implicit in today's + + align:start position:0% +uncertain but today implicit in today's + + + align:start position:0% +uncertain but today implicit in today's +prices is a forecast of that unknown + + align:start position:0% +prices is a forecast of that unknown + + + align:start position:0% +prices is a forecast of that unknown +future and we're going to call that + + align:start position:0% +future and we're going to call that + + + align:start position:0% +future and we're going to call that +forecast the forward + + align:start position:0% +forecast the forward + + + align:start position:0% +forecast the forward +rate + + align:start position:0% +rate + + + align:start position:0% +rate +so that is really meant to convey that + + align:start position:0% +so that is really meant to convey that + + + align:start position:0% +so that is really meant to convey that +it is a rate that we observe + + align:start position:0% +it is a rate that we observe + + + align:start position:0% +it is a rate that we observe +today and it is meant to capture the + + align:start position:0% +today and it is meant to capture the + + + align:start position:0% +today and it is meant to capture the +Market's best guess about what the + + align:start position:0% +Market's best guess about what the + + + align:start position:0% +Market's best guess about what the +future spot rate will be + + align:start position:0% +future spot rate will be + + + align:start position:0% +future spot rate will be +okay so this is I know a little bit + + align:start position:0% +okay so this is I know a little bit + + + align:start position:0% +okay so this is I know a little bit +confusing and just to give you a summary + + align:start position:0% +confusing and just to give you a summary + + + align:start position:0% +confusing and just to give you a summary +of all the notation and terminology + + align:start position:0% +of all the notation and terminology + + + align:start position:0% +of all the notation and terminology +we've defined today we have a spot rate + + align:start position:0% +we've defined today we have a spot rate + + + align:start position:0% +we've defined today we have a spot rate +right that's a spot rate is the rate + + align:start position:0% +right that's a spot rate is the rate + + + align:start position:0% +right that's a spot rate is the rate +that you have to pay or that you will + + align:start position:0% +that you have to pay or that you will + + + align:start position:0% +that you have to pay or that you will +earn on the spot for a period of time so + + align:start position:0% +earn on the spot for a period of time so + + + align:start position:0% +earn on the spot for a period of time so +you've got the two-year spot rate + + align:start position:0% +you've got the two-year spot rate + + + align:start position:0% +you've got the two-year spot rate +today you've also got future spot rates + + align:start position:0% +today you've also got future spot rates + + + align:start position:0% +today you've also got future spot rates +which you don't know and don't observe + + align:start position:0% +which you don't know and don't observe + + + align:start position:0% +which you don't know and don't observe +you also have a forward rate which you + + align:start position:0% +you also have a forward rate which you + + + align:start position:0% +you also have a forward rate which you +do observe today and the forward rate is + + align:start position:0% +do observe today and the forward rate is + + + align:start position:0% +do observe today and the forward rate is +a rate that applies over some period in + + align:start position:0% +a rate that applies over some period in + + + align:start position:0% +a rate that applies over some period in +the + + align:start position:0% +the + + + align:start position:0% +the +future and it's today's best guess of + + align:start position:0% +future and it's today's best guess of + + + align:start position:0% +future and it's today's best guess of +what that future rate will + + align:start position:0% +what that future rate will + + + align:start position:0% +what that future rate will +be now we can see the implicit + + align:start position:0% +be now we can see the implicit + + + align:start position:0% +be now we can see the implicit +forecasts that are are in the yield + + align:start position:0% +forecasts that are are in the yield + + + align:start position:0% +forecasts that are are in the yield +curve the oneyear spot rate today also + + align:start position:0% +curve the oneyear spot rate today also + + + align:start position:0% +curve the oneyear spot rate today also +happens to be equal to the one-year + + align:start position:0% +happens to be equal to the one-year + + + align:start position:0% +happens to be equal to the one-year +forward + + align:start position:0% +forward + + + align:start position:0% +forward +rate however if you take a look at the + + align:start position:0% +rate however if you take a look at the + + + align:start position:0% +rate however if you take a look at the +2-year spot rate and compare that with + + align:start position:0% +2-year spot rate and compare that with + + + align:start position:0% +2-year spot rate and compare that with +the one-year spot rate you can compute + + align:start position:0% +the one-year spot rate you can compute + + + align:start position:0% +the one-year spot rate you can compute +the the the oneyear forward + + align:start position:0% +the the the oneyear forward + + + align:start position:0% +the the the oneyear forward +rate for borrowing between years one and + + align:start position:0% +rate for borrowing between years one and + + + align:start position:0% +rate for borrowing between years one and +two and similarly if you compare the + + align:start position:0% +two and similarly if you compare the + + + align:start position:0% +two and similarly if you compare the +four-year spot rate with the three-year + + align:start position:0% +four-year spot rate with the three-year + + + align:start position:0% +four-year spot rate with the three-year +spot rate you will be able to figure out + + align:start position:0% +spot rate you will be able to figure out + + + align:start position:0% +spot rate you will be able to figure out +what the forward rate is for borrowing + + align:start position:0% +what the forward rate is for borrowing + + + align:start position:0% +what the forward rate is for borrowing +one year + + align:start position:0% +one year + + + align:start position:0% +one year +between three and four + + align:start position:0% +between three and four + + + align:start position:0% +between three and four +okay now you might think this is + + align:start position:0% +okay now you might think this is + + + align:start position:0% +okay now you might think this is +complicated believe me it gets even more + + align:start position:0% +complicated believe me it gets even more + + + align:start position:0% +complicated believe me it gets even more +complicated when you think about + + align:start position:0% +complicated when you think about + + + align:start position:0% +complicated when you think about +multi-year forward rates so suppose I + + align:start position:0% +multi-year forward rates so suppose I + + + align:start position:0% +multi-year forward rates so suppose I +asked you what is the two-year borrowing + + align:start position:0% +asked you what is the two-year borrowing + + + align:start position:0% +asked you what is the two-year borrowing +rate three years from now then what you + + align:start position:0% +rate three years from now then what you + + + align:start position:0% +rate three years from now then what you +would do is to take a five-year Bond and + + align:start position:0% +would do is to take a five-year Bond and + + + align:start position:0% +would do is to take a five-year Bond and +compare that to a three-year Bond and + + align:start position:0% +compare that to a three-year Bond and + + + align:start position:0% +compare that to a three-year Bond and +that would give you the two-year forward + + align:start position:0% +that would give you the two-year forward + + + align:start position:0% +that would give you the two-year forward +rate today starting in year three okay + + align:start position:0% +rate today starting in year three okay + + + align:start position:0% +rate today starting in year three okay +lots of different rates this is again + + align:start position:0% +lots of different rates this is again + + + align:start position:0% +lots of different rates this is again +why I've told you every time you have a + + align:start position:0% +why I've told you every time you have a + + + align:start position:0% +why I've told you every time you have a +problem like this draw a timeline + + align:start position:0% +problem like this draw a timeline + + + align:start position:0% +problem like this draw a timeline +otherwise you're going to get hopelessly + + align:start position:0% +otherwise you're going to get hopelessly + + + align:start position:0% +otherwise you're going to get hopelessly +confused now um in general you can + + align:start position:0% +confused now um in general you can + + + align:start position:0% +confused now um in general you can +Define forward interest rates between + + align:start position:0% +Define forward interest rates between + + + align:start position:0% +Define forward interest rates between +any two points in time between time T1 + + align:start position:0% +any two points in time between time T1 + + + align:start position:0% +any two points in time between time T1 +and T2 and so the typical forward + + align:start position:0% +and T2 and so the typical forward + + + align:start position:0% +and T2 and so the typical forward +transaction is one where today we agree + + align:start position:0% +transaction is one where today we agree + + + align:start position:0% +transaction is one where today we agree +to do a deal that starts at some point + + align:start position:0% +to do a deal that starts at some point + + + align:start position:0% +to do a deal that starts at some point +T1 in the future and concludes at some + + align:start position:0% +T1 in the future and concludes at some + + + align:start position:0% +T1 in the future and concludes at some +point T2 in the future and that's known + + align:start position:0% +point T2 in the future and that's known + + + align:start position:0% +point T2 in the future and that's known +as a forward transaction it's a + + align:start position:0% +as a forward transaction it's a + + + align:start position:0% +as a forward transaction it's a +transaction that we agree upon today to + + align:start position:0% +transaction that we agree upon today to + + + align:start position:0% +transaction that we agree upon today to +engage in sometime in the + + align:start position:0% +engage in sometime in the + + + align:start position:0% +engage in sometime in the +future + + align:start position:0% +future + + + align:start position:0% +future +okay now I want to work through an + + align:start position:0% +okay now I want to work through an + + + align:start position:0% +okay now I want to work through an +example because this is a bit confusing + + align:start position:0% +example because this is a bit confusing + + + align:start position:0% +example because this is a bit confusing +so let me show you how this might work + + align:start position:0% +so let me show you how this might work + + + align:start position:0% +so let me show you how this might work +and why the whole idea of forward rates + + align:start position:0% +and why the whole idea of forward rates + + + align:start position:0% +and why the whole idea of forward rates +and future spot rates is so + + align:start position:0% +and future spot rates is so + + + align:start position:0% +and future spot rates is so +important a practical example example is + + align:start position:0% +important a practical example example is + + + align:start position:0% +important a practical example example is +that you are the Chief Financial Officer + + align:start position:0% +that you are the Chief Financial Officer + + + align:start position:0% +that you are the Chief Financial Officer +of a multinational company based in the + + align:start position:0% +of a multinational company based in the + + + align:start position:0% +of a multinational company based in the +US and you're going to get 10 million + + align:start position:0% +US and you're going to get 10 million + + + align:start position:0% +US and you're going to get 10 million +dollar a year from now from operations + + align:start position:0% +dollar a year from now from operations + + + align:start position:0% +dollar a year from now from operations +overseas and it's going to come back in + + align:start position:0% +overseas and it's going to come back in + + + align:start position:0% +overseas and it's going to come back in +the form of dollars but it's not going + + align:start position:0% +the form of dollars but it's not going + + + align:start position:0% +the form of dollars but it's not going +to come back today it's going to come + + align:start position:0% +to come back today it's going to come + + + align:start position:0% +to come back today it's going to come +back exactly one year from today now you + + align:start position:0% +back exactly one year from today now you + + + align:start position:0% +back exactly one year from today now you +got to pay dividends two years from + + align:start position:0% +got to pay dividends two years from + + + align:start position:0% +got to pay dividends two years from +today so you're going to use that money + + align:start position:0% +today so you're going to use that money + + + align:start position:0% +today so you're going to use that money +that's going to come in a year from now + + align:start position:0% +that's going to come in a year from now + + + align:start position:0% +that's going to come in a year from now +and then at the end of year two you're + + align:start position:0% +and then at the end of year two you're + + + align:start position:0% +and then at the end of year two you're +going to pay it + + align:start position:0% +going to pay it + + + align:start position:0% +going to pay it +out and so you don't want to take that + + align:start position:0% +out and so you don't want to take that + + + align:start position:0% +out and so you don't want to take that +money next year and fool around with it + + align:start position:0% +money next year and fool around with it + + + align:start position:0% +money next year and fool around with it +you don't you don't know what interest + + align:start position:0% +you don't you don't know what interest + + + align:start position:0% +you don't you don't know what interest +rates are going to be but what you'd + + align:start position:0% +rates are going to be but what you'd + + + align:start position:0% +rates are going to be but what you'd +like to be able to do is to today lock + + align:start position:0% +like to be able to do is to today lock + + + align:start position:0% +like to be able to do is to today lock +in a rate of return between years one + + align:start position:0% +in a rate of return between years one + + + align:start position:0% +in a rate of return between years one +and two because you know that you're + + align:start position:0% +and two because you know that you're + + + align:start position:0% +and two because you know that you're +going to need to get that money invested + + align:start position:0% +going to need to get that money invested + + + align:start position:0% +going to need to get that money invested +in year + + align:start position:0% +in year + + + align:start position:0% +in year +one and you'd like to be able to pay it + + align:start position:0% +one and you'd like to be able to pay it + + + align:start position:0% +one and you'd like to be able to pay it +out in year two and you want to do that + + align:start position:0% +out in year two and you want to do that + + + align:start position:0% +out in year two and you want to do that +all today so how do you do that well you + + align:start position:0% +all today so how do you do that well you + + + align:start position:0% +all today so how do you do that well you +go to the financial Market market and + + align:start position:0% +go to the financial Market market and + + + align:start position:0% +go to the financial Market market and +you look at the yield curve and you see + + align:start position:0% +you look at the yield curve and you see + + + align:start position:0% +you look at the yield curve and you see +what the one-year rate is and what the + + align:start position:0% +what the one-year rate is and what the + + + align:start position:0% +what the one-year rate is and what the +two-year rate is and what you get from + + align:start position:0% +two-year rate is and what you get from + + + align:start position:0% +two-year rate is and what you get from +looking at the newspaper is the one-year + + align:start position:0% +looking at the newspaper is the one-year + + + align:start position:0% +looking at the newspaper is the one-year +rate is + + align:start position:0% +rate is + + + align:start position:0% +rate is +5% and the two-year rate is + + align:start position:0% +5% and the two-year rate is + + + align:start position:0% +5% and the two-year rate is +7% question is 7% a spot rate forward + + align:start position:0% +7% question is 7% a spot rate forward + + + align:start position:0% +7% question is 7% a spot rate forward +rate or future spot + + align:start position:0% +rate or future spot + + + align:start position:0% +rate or future spot +rate it's a spot rate of + + align:start position:0% +rate it's a spot rate of + + + align:start position:0% +rate it's a spot rate of +what exactly it is today's spot rate + + align:start position:0% +what exactly it is today's spot rate + + + align:start position:0% +what exactly it is today's spot rate +between now and two years from now it's + + align:start position:0% +between now and two years from now it's + + + align:start position:0% +between now and two years from now it's +a twoyear spot rate R right what you + + align:start position:0% +a twoyear spot rate R right what you + + + align:start position:0% +a twoyear spot rate R right what you +care about though for the example that I + + align:start position:0% +care about though for the example that I + + + align:start position:0% +care about though for the example that I +just gave you is + + align:start position:0% +just gave you is + + + align:start position:0% +just gave you is +what one rate in one year exactly you + + align:start position:0% +what one rate in one year exactly you + + + align:start position:0% +what one rate in one year exactly you +care about the oneyear spot rate in one + + align:start position:0% +care about the oneyear spot rate in one + + + align:start position:0% +care about the oneyear spot rate in one +year the future oneyear spot rate which + + align:start position:0% +year the future oneyear spot rate which + + + align:start position:0% +year the future oneyear spot rate which +you don't know what it's going to be + + align:start position:0% +you don't know what it's going to be + + + align:start position:0% +you don't know what it's going to be +that's uncertain but you do have the + + align:start position:0% +that's uncertain but you do have the + + + align:start position:0% +that's uncertain but you do have the +what rate what rate do you have + + align:start position:0% +what rate what rate do you have + + + align:start position:0% +what rate what rate do you have +today the forward rate right you have + + align:start position:0% +today the forward rate right you have + + + align:start position:0% +today the forward rate right you have +the forward rate because you've got the + + align:start position:0% +the forward rate because you've got the + + + align:start position:0% +the forward rate because you've got the +2-year spot rate you've got the one-year + + align:start position:0% +2-year spot rate you've got the one-year + + + align:start position:0% +2-year spot rate you've got the one-year +spot rate so so when you compare the two + + align:start position:0% +spot rate so so when you compare the two + + + align:start position:0% +spot rate so so when you compare the two +implicitly in that in those two + + align:start position:0% +implicitly in that in those two + + + align:start position:0% +implicitly in that in those two +rates is the future is the forecast of + + align:start position:0% +rates is the future is the forecast of + + + align:start position:0% +rates is the future is the forecast of +the future onee spot rate or today's + + align:start position:0% +the future onee spot rate or today's + + + align:start position:0% +the future onee spot rate or today's +forward rate between years one and two + + align:start position:0% +forward rate between years one and two + + + align:start position:0% +forward rate between years one and two +all right now let's get to Brass tax how + + align:start position:0% +all right now let's get to Brass tax how + + + align:start position:0% +all right now let's get to Brass tax how +do you go about locking in the rate + + align:start position:0% +do you go about locking in the rate + + + align:start position:0% +do you go about locking in the rate +between years one and + + align:start position:0% +between years one and + + + align:start position:0% +between years one and +two well here's a a really cool + + align:start position:0% +two well here's a a really cool + + + align:start position:0% +two well here's a a really cool +transaction that you can do uh today + + align:start position:0% +transaction that you can do uh today + + + align:start position:0% +transaction that you can do uh today +borrow + + align:start position:0% +borrow + + + align:start position:0% +borrow +$9.52 four million for a + + align:start position:0% +$9.52 four million for a + + + align:start position:0% +$9.52 four million for a +year how do you know you can do + + align:start position:0% + + + + align:start position:0% + +that you're the one year interest rate + + align:start position:0% +that you're the one year interest rate + + + align:start position:0% +that you're the one year interest rate +exactly you've got the one-ear interest + + align:start position:0% +exactly you've got the one-ear interest + + + align:start position:0% +exactly you've got the one-ear interest +rate at 5% so if that's really a market + + align:start position:0% +rate at 5% so if that's really a market + + + align:start position:0% +rate at 5% so if that's really a market +rate that means that you should be able + + align:start position:0% +rate that means that you should be able + + + align:start position:0% +rate that means that you should be able +to borrow at that rate okay so when + + align:start position:0% +to borrow at that rate okay so when + + + align:start position:0% +to borrow at that rate okay so when +you're borrowing money what are you + + align:start position:0% +you're borrowing money what are you + + + align:start position:0% +you're borrowing money what are you +doing you're are you buying a + + align:start position:0% +doing you're are you buying a + + + align:start position:0% +doing you're are you buying a +bond you're selling a bond you're + + align:start position:0% +bond you're selling a bond you're + + + align:start position:0% +bond you're selling a bond you're +issuing a bond right okay so you + + align:start position:0% +issuing a bond right okay so you + + + align:start position:0% +issuing a bond right okay so you +borrowed $9.52 million today now in a + + align:start position:0% +borrowed $9.52 million today now in a + + + align:start position:0% +borrowed $9.52 million today now in a +minute I'll explain to you why that that + + align:start position:0% +minute I'll explain to you why that that + + + align:start position:0% +minute I'll explain to you why that that +number is so weird + + align:start position:0% +number is so weird + + + align:start position:0% +number is so weird +then after you get the money + + align:start position:0% + + + + align:start position:0% + +today I'm going to ask you to put it + + align:start position:0% +today I'm going to ask you to put it + + + align:start position:0% +today I'm going to ask you to put it +into the two-year + + align:start position:0% +into the two-year + + + align:start position:0% +into the two-year +Bond so you got $9.52 million in + + align:start position:0% +Bond so you got $9.52 million in + + + align:start position:0% +Bond so you got $9.52 million in +cash and you put it into a two-year Bond + + align:start position:0% +cash and you put it into a two-year Bond + + + align:start position:0% +cash and you put it into a two-year Bond +so let's take a look at what you've done + + align:start position:0% +so let's take a look at what you've done + + + align:start position:0% +so let's take a look at what you've done +with that + + align:start position:0% + + + + align:start position:0% + +transaction the + + align:start position:0% +transaction the + + + align:start position:0% +transaction the +outcome looks like this in year zero + + align:start position:0% +outcome looks like this in year zero + + + align:start position:0% +outcome looks like this in year zero +you've borrowed + + align:start position:0% +you've borrowed + + + align:start position:0% +you've borrowed +9.52 and then you've taken the proceeds + + align:start position:0% +9.52 and then you've taken the proceeds + + + align:start position:0% +9.52 and then you've taken the proceeds +and youve bought a bond at + + align:start position:0% +and youve bought a bond at + + + align:start position:0% +and youve bought a bond at +9.52 so in fact your net expenditures is + + align:start position:0% +9.52 so in fact your net expenditures is + + + align:start position:0% +9.52 so in fact your net expenditures is +nothing right you borrowed money you + + align:start position:0% +nothing right you borrowed money you + + + align:start position:0% +nothing right you borrowed money you +took that money and you bought something + + align:start position:0% +took that money and you bought something + + + align:start position:0% +took that money and you bought something +else youve loaned it out you borrowed + + align:start position:0% +else youve loaned it out you borrowed + + + align:start position:0% +else youve loaned it out you borrowed +money for one year and you've loaned it + + align:start position:0% +money for one year and you've loaned it + + + align:start position:0% +money for one year and you've loaned it +out for two years that's what you've + + align:start position:0% +out for two years that's what you've + + + align:start position:0% +out for two years that's what you've +done so today you actually have zero in + + align:start position:0% +done so today you actually have zero in + + + align:start position:0% +done so today you actually have zero in +terms of your your assets and + + align:start position:0% +terms of your your assets and + + + align:start position:0% +terms of your your assets and +liabilities okay now let's see what + + align:start position:0% +liabilities okay now let's see what + + + align:start position:0% +liabilities okay now let's see what +happens next year in one year's time + + align:start position:0% +happens next year in one year's time + + + align:start position:0% +happens next year in one year's time +that 9.52 magically turns into + + align:start position:0% +that 9.52 magically turns into + + + align:start position:0% +that 9.52 magically turns into +10 okay so but it's a negative 10 + + align:start position:0% +10 okay so but it's a negative 10 + + + align:start position:0% +10 okay so but it's a negative 10 +meaning you've borrowed + + align:start position:0% +meaning you've borrowed + + + align:start position:0% +meaning you've borrowed +9.52 you got to pay back 9.52 with + + align:start position:0% +9.52 you got to pay back 9.52 with + + + align:start position:0% +9.52 you got to pay back 9.52 with +interest how much much + + align:start position:0% +interest how much much + + + align:start position:0% +interest how much much +interest 5% that's the one-year rate so + + align:start position:0% +interest 5% that's the one-year rate so + + + align:start position:0% +interest 5% that's the one-year rate so +now you actually have to pay back $10 + + align:start position:0% +now you actually have to pay back $10 + + + align:start position:0% +now you actually have to pay back $10 +million well it just so happens you have + + align:start position:0% +million well it just so happens you have + + + align:start position:0% +million well it just so happens you have +$10 million how from the money that's + + align:start position:0% +$10 million how from the money that's + + + align:start position:0% +$10 million how from the money that's +coming in from your subsidiary that + + align:start position:0% +coming in from your subsidiary that + + + align:start position:0% +coming in from your subsidiary that +repatriation amount of money so you take + + align:start position:0% +repatriation amount of money so you take + + + align:start position:0% +repatriation amount of money so you take +that $10 million and you pay it back and + + align:start position:0% +that $10 million and you pay it back and + + + align:start position:0% +that $10 million and you pay it back and +you're done with that part of your + + align:start position:0% +you're done with that part of your + + + align:start position:0% +you're done with that part of your +portfolio what do you have left what you + + align:start position:0% +portfolio what do you have left what you + + + align:start position:0% +portfolio what do you have left what you +have left + + align:start position:0% +have left + + + align:start position:0% +have left +is a bond that will pay you + + align:start position:0% +is a bond that will pay you + + + align:start position:0% +is a bond that will pay you +money in the year after that between + + align:start position:0% +money in the year after that between + + + align:start position:0% +money in the year after that between +years one and two and there you go you + + align:start position:0% +years one and two and there you go you + + + align:start position:0% +years one and two and there you go you +get paid $10.9 million you've done all + + align:start position:0% +get paid $10.9 million you've done all + + + align:start position:0% +get paid $10.9 million you've done all +of this transaction today you've locked + + align:start position:0% +of this transaction today you've locked + + + align:start position:0% +of this transaction today you've locked +in the rates + + align:start position:0% +in the rates + + + align:start position:0% +in the rates +today okay yeah you're locking in the + + align:start position:0% +today okay yeah you're locking in the + + + align:start position:0% +today okay yeah you're locking in the +onee spot rate one year that's right + + align:start position:0% +onee spot rate one year that's right + + + align:start position:0% +onee spot rate one year that's right +you're locking well you're locking in + + align:start position:0% +you're locking well you're locking in + + + align:start position:0% +you're locking well you're locking in +the forward rate which is the forecast + + align:start position:0% +the forward rate which is the forecast + + + align:start position:0% +the forward rate which is the forecast +right it's the it's it's what the market + + align:start position:0% +right it's the it's it's what the market + + + align:start position:0% +right it's the it's it's what the market +expects the future one-year spot rate + + align:start position:0% +expects the future one-year spot rate + + + align:start position:0% +expects the future one-year spot rate +will be now that's a good that's a good + + align:start position:0% +will be now that's a good that's a good + + + align:start position:0% +will be now that's a good that's a good +point that you bring up which is let's + + align:start position:0% +point that you bring up which is let's + + + align:start position:0% +point that you bring up which is let's +say let's say that in year one it turns + + align:start position:0% +say let's say that in year one it turns + + + align:start position:0% +say let's say that in year one it turns +out that at that point in time the + + align:start position:0% +out that at that point in time the + + + align:start position:0% +out that at that point in time the +one-year spot + + align:start position:0% +one-year spot + + + align:start position:0% +one-year spot +rate is + + align:start position:0% +rate is + + + align:start position:0% +rate is +7% are you happy or are you + + align:start position:0% + + + + align:start position:0% + +sad some people say Sad some will say + + align:start position:0% + + + + align:start position:0% + +happy what what if the onee spot rate + + align:start position:0% +happy what what if the onee spot rate + + + align:start position:0% +happy what what if the onee spot rate +one year from now is + + align:start position:0% +one year from now is + + + align:start position:0% +one year from now is +7% and you've done this deal already + + align:start position:0% +7% and you've done this deal already + + + align:start position:0% +7% and you've done this deal already +you're happy you're happy that's right + + align:start position:0% +you're happy you're happy that's right + + + align:start position:0% +you're happy you're happy that's right +because what are you getting on your + + align:start position:0% +because what are you getting on your + + + align:start position:0% +because what are you getting on your +portfolio 9% now wait a minute how do + + align:start position:0% +portfolio 9% now wait a minute how do + + + align:start position:0% +portfolio 9% now wait a minute how do +you get 9% I thought that I told you the + + align:start position:0% +you get 9% I thought that I told you the + + + align:start position:0% +you get 9% I thought that I told you the +two-year rate was + + align:start position:0% + + + + align:start position:0% + +7% I'm I'm purposely confusing you so + + align:start position:0% +7% I'm I'm purposely confusing you so + + + align:start position:0% +7% I'm I'm purposely confusing you so +I'm hoping it works and then I'm going + + align:start position:0% +I'm hoping it works and then I'm going + + + align:start position:0% +I'm hoping it works and then I'm going +to try to UNC confuse you and I hope + + align:start position:0% +to try to UNC confuse you and I hope + + + align:start position:0% +to try to UNC confuse you and I hope +that works + + align:start position:0% +that works + + + align:start position:0% +that works +too 5% is the one-year spot rate 7% is + + align:start position:0% +too 5% is the one-year spot rate 7% is + + + align:start position:0% +too 5% is the one-year spot rate 7% is +the 2-year spot rate + + align:start position:0% + + + + align:start position:0% + +yeah right that's right the year between + + align:start position:0% +yeah right that's right the year between + + + align:start position:0% +yeah right that's right the year between +the rate between years one and two is + + align:start position:0% +the rate between years one and two is + + + align:start position:0% +the rate between years one and two is +around 9% and the reason it's got to be + + align:start position:0% +around 9% and the reason it's got to be + + + align:start position:0% +around 9% and the reason it's got to be +that way is the 7% that I told + + align:start position:0% +that way is the 7% that I told + + + align:start position:0% +that way is the 7% that I told +you that's a two-year rate right that's + + align:start position:0% +you that's a two-year rate right that's + + + align:start position:0% +you that's a two-year rate right that's +the average of two years but you know + + align:start position:0% +the average of two years but you know + + + align:start position:0% +the average of two years but you know +what the rate is the first year + + align:start position:0% +what the rate is the first year + + + align:start position:0% +what the rate is the first year +the first year rate is 5% so if + + align:start position:0% +the first year rate is 5% so if + + + align:start position:0% +the first year rate is 5% so if +something averages to 7% over two years + + align:start position:0% +something averages to 7% over two years + + + align:start position:0% +something averages to 7% over two years +but the first year is five the second + + align:start position:0% +but the first year is five the second + + + align:start position:0% +but the first year is five the second +Year's got to be greater than seven + + align:start position:0% +Year's got to be greater than seven + + + align:start position:0% +Year's got to be greater than seven +otherwise the average can't be seven in + + align:start position:0% +otherwise the average can't be seven in + + + align:start position:0% +otherwise the average can't be seven in +fact the second year rate the ye the + + align:start position:0% +fact the second year rate the ye the + + + align:start position:0% +fact the second year rate the ye the +one-ear rate between years one and two + + align:start position:0% +one-ear rate between years one and two + + + align:start position:0% +one-ear rate between years one and two +is around + + align:start position:0% +is around + + + align:start position:0% +is around +%. and so that's why if when you arrive + + align:start position:0% +%. and so that's why if when you arrive + + + align:start position:0% +%. and so that's why if when you arrive +on at the end of year one ready to + + align:start position:0% +on at the end of year one ready to + + + align:start position:0% +on at the end of year one ready to +borrow for one more year and you've + + align:start position:0% +borrow for one more year and you've + + + align:start position:0% +borrow for one more year and you've +already locked in a 9% rate you are are + + align:start position:0% +already locked in a 9% rate you are are + + + align:start position:0% +already locked in a 9% rate you are are +pretty happy that the rate at that time + + align:start position:0% +pretty happy that the rate at that time + + + align:start position:0% +pretty happy that the rate at that time +is seven however if I told you that the + + align:start position:0% +is seven however if I told you that the + + + align:start position:0% +is seven however if I told you that the +rate at that time was + + align:start position:0% +rate at that time was + + + align:start position:0% +rate at that time was +15 you'd be kicking yourself because you + + align:start position:0% +15 you'd be kicking yourself because you + + + align:start position:0% +15 you'd be kicking yourself because you +locked in a 9% rate and yet it's + + align:start position:0% +locked in a 9% rate and yet it's + + + align:start position:0% +locked in a 9% rate and yet it's +15% okay so there's room for regret as + + align:start position:0% +15% okay so there's room for regret as + + + align:start position:0% +15% okay so there's room for regret as +well as celebration depending on what + + align:start position:0% +well as celebration depending on what + + + align:start position:0% +well as celebration depending on what +Market's going to do but the point is + + align:start position:0% +Market's going to do but the point is + + + align:start position:0% +Market's going to do but the point is +that in year zero I don't know what it's + + align:start position:0% +that in year zero I don't know what it's + + + align:start position:0% +that in year zero I don't know what it's +going to be and I'm not a I'm not a + + align:start position:0% +going to be and I'm not a I'm not a + + + align:start position:0% +going to be and I'm not a I'm not a +hedge fund manager I'm not a Trader I + + align:start position:0% +hedge fund manager I'm not a Trader I + + + align:start position:0% +hedge fund manager I'm not a Trader I +don't care I don't want to make a bet on + + align:start position:0% +don't care I don't want to make a bet on + + + align:start position:0% +don't care I don't want to make a bet on +future interest rates I just want to get + + align:start position:0% +future interest rates I just want to get + + + align:start position:0% +future interest rates I just want to get +this problem solved and right now today + + align:start position:0% +this problem solved and right now today + + + align:start position:0% +this problem solved and right now today +I can actually solve my problem of of + + align:start position:0% +I can actually solve my problem of of + + + align:start position:0% +I can actually solve my problem of of +figuring out how to invest my money + + align:start position:0% +figuring out how to invest my money + + + align:start position:0% +figuring out how to invest my money +between years one and two by doing this + + align:start position:0% +between years one and two by doing this + + + align:start position:0% +between years one and two by doing this +very simple transaction in open markets + + align:start position:0% +very simple transaction in open markets + + + align:start position:0% +very simple transaction in open markets +with Market determined interest rates + + align:start position:0% +with Market determined interest rates + + + align:start position:0% +with Market determined interest rates +and I know as long as these interest + + align:start position:0% +and I know as long as these interest + + + align:start position:0% +and I know as long as these interest +rates are not nuts then I'm getting a + + align:start position:0% +rates are not nuts then I'm getting a + + + align:start position:0% +rates are not nuts then I'm getting a +reasonable deal yeah I mean this is one + + align:start position:0% +reasonable deal yeah I mean this is one + + + align:start position:0% +reasonable deal yeah I mean this is one +of the main things you do right you + + align:start position:0% +of the main things you do right you + + + align:start position:0% +of the main things you do right you +something is it even simpler to just say + + align:start position:0% +something is it even simpler to just say + + + align:start position:0% +something is it even simpler to just say +the + + align:start position:0% + + + + align:start position:0% + +yeah but the problem is that you don't + + align:start position:0% +yeah but the problem is that you don't + + + align:start position:0% +yeah but the problem is that you don't +know what that oneye chill rate will be + + align:start position:0% +know what that oneye chill rate will be + + + align:start position:0% +know what that oneye chill rate will be +whereas right now you know that it's + + align:start position:0% +whereas right now you know that it's + + + align:start position:0% +whereas right now you know that it's +9% right now you know it's 9% and it + + align:start position:0% +9% right now you know it's 9% and it + + + align:start position:0% +9% right now you know it's 9% and it +seems like a pretty good deal go ahead + + align:start position:0% +seems like a pretty good deal go ahead + + + align:start position:0% +seems like a pretty good deal go ahead +and do it if however you think that + + align:start position:0% +and do it if however you think that + + + align:start position:0% +and do it if however you think that +interest rates are going to go + + align:start position:0% +interest rates are going to go + + + align:start position:0% +interest rates are going to go +up much more than the market thinks then + + align:start position:0% +up much more than the market thinks then + + + align:start position:0% +up much more than the market thinks then +you may want to wait waight but now + + align:start position:0% +you may want to wait waight but now + + + align:start position:0% +you may want to wait waight but now +you're becoming an interest rate + + align:start position:0% +you're becoming an interest rate + + + align:start position:0% +you're becoming an interest rate +Speculator you're you're you're taking + + align:start position:0% +Speculator you're you're you're taking + + + align:start position:0% +Speculator you're you're you're taking +risk and as a CFO that's generally not + + align:start position:0% +risk and as a CFO that's generally not + + + align:start position:0% +risk and as a CFO that's generally not +your job and not your level of + + align:start position:0% +your job and not your level of + + + align:start position:0% +your job and not your level of +Competency right you're not there trying + + align:start position:0% +Competency right you're not there trying + + + align:start position:0% +Competency right you're not there trying +to forecast interest + + align:start position:0% +to forecast interest + + + align:start position:0% +to forecast interest +rates + + align:start position:0% +rates + + + align:start position:0% +rates +yeah the is the present value of, that's + + align:start position:0% +yeah the is the present value of, that's + + + align:start position:0% +yeah the is the present value of, that's +right the 9.52 four is the present value + + align:start position:0% +right the 9.52 four is the present value + + + align:start position:0% +right the 9.52 four is the present value +of $10 million today at a rate of 5% + + align:start position:0% + + + + align:start position:0% + +interest okay so the way that I did this + + align:start position:0% +interest okay so the way that I did this + + + align:start position:0% +interest okay so the way that I did this +and you know the this is a good + + align:start position:0% +and you know the this is a good + + + align:start position:0% +and you know the this is a good +illustration of what I've been telling + + align:start position:0% +illustration of what I've been telling + + + align:start position:0% +illustration of what I've been telling +you about Finance not being a spectator + + align:start position:0% +you about Finance not being a spectator + + + align:start position:0% +you about Finance not being a spectator +sport I suspect that all of you + + align:start position:0% +sport I suspect that all of you + + + align:start position:0% +sport I suspect that all of you +understand the lectures that I've given + + align:start position:0% +understand the lectures that I've given + + + align:start position:0% +understand the lectures that I've given +so far about present value and about + + align:start position:0% +so far about present value and about + + + align:start position:0% +so far about present value and about +time value of money and the fact that + + align:start position:0% +time value of money and the fact that + + + align:start position:0% +time value of money and the fact that +You' got to use the right exchange rate + + align:start position:0% +You' got to use the right exchange rate + + + align:start position:0% +You' got to use the right exchange rate +it all is pretty + + align:start position:0% +it all is pretty + + + align:start position:0% +it all is pretty +straightforward but putting it into + + align:start position:0% +straightforward but putting it into + + + align:start position:0% +straightforward but putting it into +practice is not so easy at least for me + + align:start position:0% +practice is not so easy at least for me + + + align:start position:0% +practice is not so easy at least for me +I don't find this example so transparent + + align:start position:0% +I don't find this example so transparent + + + align:start position:0% +I don't find this example so transparent +you have to actually spend some time + + align:start position:0% +you have to actually spend some time + + + align:start position:0% +you have to actually spend some time +thinking about it thinking about where + + align:start position:0% +thinking about it thinking about where + + + align:start position:0% +thinking about it thinking about where +the money's coming from where the + + align:start position:0% +the money's coming from where the + + + align:start position:0% +the money's coming from where the +money's going how much money you have at + + align:start position:0% +money's going how much money you have at + + + align:start position:0% +money's going how much money you have at +any point in time and but when you work + + align:start position:0% +any point in time and but when you work + + + align:start position:0% +any point in time and but when you work +it out it all makes sense and so I would + + align:start position:0% +it out it all makes sense and so I would + + + align:start position:0% +it out it all makes sense and so I would +encourage all of you to spend some time + + align:start position:0% +encourage all of you to spend some time + + + align:start position:0% +encourage all of you to spend some time +working this out okay uh question + + align:start position:0% + + + + align:start position:0% + +yeah yes there there are ways you can + + align:start position:0% +yeah yes there there are ways you can + + + align:start position:0% +yeah yes there there are ways you can +engage in a forward contract of course + + align:start position:0% +engage in a forward contract of course + + + align:start position:0% +engage in a forward contract of course +so you don't have to do this but the + + align:start position:0% +so you don't have to do this but the + + + align:start position:0% +so you don't have to do this but the +fact is doing this is so simple why not + + align:start position:0% +fact is doing this is so simple why not + + + align:start position:0% +fact is doing this is so simple why not +you know and if it's simple most likely + + align:start position:0% +you know and if it's simple most likely + + + align:start position:0% +you know and if it's simple most likely +it'll be cheap if it's complex Flex + + align:start position:0% +it'll be cheap if it's complex Flex + + + align:start position:0% +it'll be cheap if it's complex Flex +that's when you're going to pay for it + + align:start position:0% +that's when you're going to pay for it + + + align:start position:0% +that's when you're going to pay for it +right so I'm happy to structure a + + align:start position:0% +right so I'm happy to structure a + + + align:start position:0% +right so I'm happy to structure a +derivatives product for you let's call + + align:start position:0% +derivatives product for you let's call + + + align:start position:0% +derivatives product for you let's call +it a structured product that we trade + + align:start position:0% +it a structured product that we trade + + + align:start position:0% +it a structured product that we trade +over the counter where I offer you a + + align:start position:0% +over the counter where I offer you a + + + align:start position:0% +over the counter where I offer you a +forward contract one year borrowing with + + align:start position:0% +forward contract one year borrowing with + + + align:start position:0% +forward contract one year borrowing with +certain terms and Privileges and so on + + align:start position:0% +certain terms and Privileges and so on + + + align:start position:0% +certain terms and Privileges and so on +and by the time we're done I'm going to + + align:start position:0% +and by the time we're done I'm going to + + + align:start position:0% +and by the time we're done I'm going to +charge you a transaction fee of oh I + + align:start position:0% +charge you a transaction fee of oh I + + + align:start position:0% +charge you a transaction fee of oh I +don't know maybe + + align:start position:0% +don't know maybe + + + align:start position:0% +don't know maybe +5% versus you buy a two-year Bill and a + + align:start position:0% +5% versus you buy a two-year Bill and a + + + align:start position:0% +5% versus you buy a two-year Bill and a +a two-year Bond and a one-year Bill and + + align:start position:0% +a two-year Bond and a one-year Bill and + + + align:start position:0% +a two-year Bond and a one-year Bill and +you're done right so that that's the + + align:start position:0% +you're done right so that that's the + + + align:start position:0% +you're done right so that that's the +difference it's really the ease with + + align:start position:0% +difference it's really the ease with + + + align:start position:0% +difference it's really the ease with +which you can implement the strategy all + + align:start position:0% +which you can implement the strategy all + + + align:start position:0% +which you can implement the strategy all +of you right now today all of you can do + + align:start position:0% +of you right now today all of you can do + + + align:start position:0% +of you right now today all of you can do +this you can do this you can actually + + align:start position:0% +this you can do this you can actually + + + align:start position:0% +this you can do this you can actually +trade in these markets set up a + + align:start position:0% +trade in these markets set up a + + + align:start position:0% +trade in these markets set up a +brokerage account trade these treasury + + align:start position:0% +brokerage account trade these treasury + + + align:start position:0% +brokerage account trade these treasury +instruments do this yourself in fact you + + align:start position:0% +instruments do this yourself in fact you + + + align:start position:0% +instruments do this yourself in fact you +could do this online so it's very very + + align:start position:0% +could do this online so it's very very + + + align:start position:0% +could do this online so it's very very +simple and yeah that easy to get 10 + + align:start position:0% +simple and yeah that easy to get 10 + + + align:start position:0% +simple and yeah that easy to get 10 +million oh well yeah that's that that's + + align:start position:0% +million oh well yeah that's that that's + + + align:start position:0% +million oh well yeah that's that that's +the hard part yeah there's an old Steve + + align:start position:0% +the hard part yeah there's an old Steve + + + align:start position:0% +the hard part yeah there's an old Steve +Martin joke that says I'm going to show + + align:start position:0% +Martin joke that says I'm going to show + + + align:start position:0% +Martin joke that says I'm going to show +you how to uh make a million dollars and + + align:start position:0% +you how to uh make a million dollars and + + + align:start position:0% +you how to uh make a million dollars and +pay no taxes first get a million + + align:start position:0% +pay no taxes first get a million + + + align:start position:0% +pay no taxes first get a million +so yes that that's the hard part okay um + + align:start position:0% +so yes that that's the hard part okay um + + + align:start position:0% +so yes that that's the hard part okay um +so now this transaction this transaction + + align:start position:0% +so now this transaction this transaction + + + align:start position:0% +so now this transaction this transaction +today locks you in to a 9% rate between + + align:start position:0% +today locks you in to a 9% rate between + + + align:start position:0% +today locks you in to a 9% rate between +years one and two and so going back to + + align:start position:0% +years one and two and so going back to + + + align:start position:0% +years one and two and so going back to +the question that an non-raised should + + align:start position:0% +the question that an non-raised should + + + align:start position:0% +the question that an non-raised should +you do this or should you just wait well + + align:start position:0% +you do this or should you just wait well + + + align:start position:0% +you do this or should you just wait well +it + + align:start position:0% +it + + + align:start position:0% +it +depends do you feel lucky do you do you + + align:start position:0% +depends do you feel lucky do you do you + + + align:start position:0% +depends do you feel lucky do you do you +think do you think you can do better + + align:start position:0% +think do you think you can do better + + + align:start position:0% +think do you think you can do better +than 9% I mean today 9% looks wonderful + + align:start position:0% +than 9% I mean today 9% looks wonderful + + + align:start position:0% +than 9% I mean today 9% looks wonderful +but that's not what the rate you're + + align:start position:0% +but that's not what the rate you're + + + align:start position:0% +but that's not what the rate you're +going to get today in fact if we go back + + align:start position:0% +going to get today in fact if we go back + + + align:start position:0% +going to get today in fact if we go back +to the Bloomberg site you can see what + + align:start position:0% +to the Bloomberg site you can see what + + + align:start position:0% +to the Bloomberg site you can see what +kind of rate you would lock in today + + align:start position:0% +kind of rate you would lock in today + + + align:start position:0% +kind of rate you would lock in today +between years one and years two and I + + align:start position:0% +between years one and years two and I + + + align:start position:0% +between years one and years two and I +promise you it's nowhere near + + align:start position:0% +promise you it's nowhere near + + + align:start position:0% +promise you it's nowhere near +%. and so again you might you might + + align:start position:0% +%. and so again you might you might + + + align:start position:0% +%. and so again you might you might +actually say today in today's low + + align:start position:0% +actually say today in today's low + + + align:start position:0% +actually say today in today's low +interest rate environment you might say + + align:start position:0% +interest rate environment you might say + + + align:start position:0% +interest rate environment you might say +look I think that inflation is going to + + align:start position:0% +look I think that inflation is going to + + + align:start position:0% +look I think that inflation is going to +heat up a great deal over the next year + + align:start position:0% +heat up a great deal over the next year + + + align:start position:0% +heat up a great deal over the next year +and therefore what's implicit in + + align:start position:0% +and therefore what's implicit in + + + align:start position:0% +and therefore what's implicit in +today's forecast of future spot rates is + + align:start position:0% +today's forecast of future spot rates is + + + align:start position:0% +today's forecast of future spot rates is +lower than I think it ought to be so I'm + + align:start position:0% +lower than I think it ought to be so I'm + + + align:start position:0% +lower than I think it ought to be so I'm +going to hold off that's a bet and so + + align:start position:0% +going to hold off that's a bet and so + + + align:start position:0% +going to hold off that's a bet and so +you're going to take some risk that's + + align:start position:0% +you're going to take some risk that's + + + align:start position:0% +you're going to take some risk that's +all and for those people who are good at + + align:start position:0% +all and for those people who are good at + + + align:start position:0% +all and for those people who are good at +taking risks like that they end up doing + + align:start position:0% +taking risks like that they end up doing + + + align:start position:0% +taking risks like that they end up doing +well and for those who don't they end up + + align:start position:0% +well and for those who don't they end up + + + align:start position:0% +well and for those who don't they end up +you know losing out on good + + align:start position:0% +you know losing out on good + + + align:start position:0% +you know losing out on good +opportunities okay there's another + + align:start position:0% +opportunities okay there's another + + + align:start position:0% +opportunities okay there's another +example that I'd like you to look at and + + align:start position:0% +example that I'd like you to look at and + + + align:start position:0% +example that I'd like you to look at and +work through on your own it's very + + align:start position:0% +work through on your own it's very + + + align:start position:0% +work through on your own it's very +similar to the first one but it just + + align:start position:0% +similar to the first one but it just + + + align:start position:0% +similar to the first one but it just +gives you practice thinking about + + align:start position:0% +gives you practice thinking about + + + align:start position:0% +gives you practice thinking about +timelines and moving money back and + + align:start position:0% +timelines and moving money back and + + + align:start position:0% +timelines and moving money back and +forth and trying to understand how to + + align:start position:0% +forth and trying to understand how to + + + align:start position:0% +forth and trying to understand how to +structure the payoffs in order to + + align:start position:0% +structure the payoffs in order to + + + align:start position:0% +structure the payoffs in order to +satisfy certain consumption patterns so + + align:start position:0% +satisfy certain consumption patterns so + + + align:start position:0% +satisfy certain consumption patterns so +if you can look at this example and work + + align:start position:0% +if you can look at this example and work + + + align:start position:0% +if you can look at this example and work +it through that'll give you more + + align:start position:0% +it through that'll give you more + + + align:start position:0% +it through that'll give you more +practice on uh you know how to deal with + + align:start position:0% +practice on uh you know how to deal with + + + align:start position:0% +practice on uh you know how to deal with +these + + align:start position:0% +these + + + align:start position:0% +these +transactions + + align:start position:0% +transactions + + + align:start position:0% +transactions +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +now if there are no more questions about + + align:start position:0% +now if there are no more questions about + + + align:start position:0% +now if there are no more questions about +pure discount bonds I want to turn to + + align:start position:0% +pure discount bonds I want to turn to + + + align:start position:0% +pure discount bonds I want to turn to +the more General case of coupon bonds + + align:start position:0% +the more General case of coupon bonds + + + align:start position:0% +the more General case of coupon bonds +these are bonds that pay off coupons and + + align:start position:0% +these are bonds that pay off coupons and + + + align:start position:0% +these are bonds that pay off coupons and +really the theory behind coupon bonds is + + align:start position:0% +really the theory behind coupon bonds is + + + align:start position:0% +really the theory behind coupon bonds is +virtually identical to that that of + + align:start position:0% +virtually identical to that that of + + + align:start position:0% +virtually identical to that that of +discount Bonds in the sense that you can + + align:start position:0% +discount Bonds in the sense that you can + + + align:start position:0% +discount Bonds in the sense that you can +always look at a coupon + + align:start position:0% +always look at a coupon + + + align:start position:0% +always look at a coupon +Bond as a package of discount bonds + + align:start position:0% +Bond as a package of discount bonds + + + align:start position:0% +Bond as a package of discount bonds +right that's sort of the opposite of a + + align:start position:0% +right that's sort of the opposite of a + + + align:start position:0% +right that's sort of the opposite of a +strip a strip takes a coupon Bond and + + align:start position:0% +strip a strip takes a coupon Bond and + + + align:start position:0% +strip a strip takes a coupon Bond and +breaks it up into what look like little + + align:start position:0% +breaks it up into what look like little + + + align:start position:0% +breaks it up into what look like little +discount bonds well if you think about + + align:start position:0% +discount bonds well if you think about + + + align:start position:0% +discount bonds well if you think about +what a coupon bond is it's really just a + + align:start position:0% +what a coupon bond is it's really just a + + + align:start position:0% +what a coupon bond is it's really just a +collection of discount bonds at + + align:start position:0% +collection of discount bonds at + + + align:start position:0% +collection of discount bonds at +different maturities that's the way to + + align:start position:0% +different maturities that's the way to + + + align:start position:0% +different maturities that's the way to +think about it so here's a simple + + align:start position:0% +think about it so here's a simple + + + align:start position:0% +think about it so here's a simple +example a + + align:start position:0% +example a + + + align:start position:0% +example a +three-year bond with a 5% coupon is + + align:start position:0% +three-year bond with a 5% coupon is + + + align:start position:0% +three-year bond with a 5% coupon is +going to look like this it's going to + + align:start position:0% +going to look like this it's going to + + + align:start position:0% +going to look like this it's going to +pay 50 50 and then 1,50 now as I + + align:start position:0% +pay 50 50 and then 1,50 now as I + + + align:start position:0% +pay 50 50 and then 1,50 now as I +mentioned there are some coupon bonds + + align:start position:0% +mentioned there are some coupon bonds + + + align:start position:0% +mentioned there are some coupon bonds +that pay semiannually so when they say + + align:start position:0% +that pay semiannually so when they say + + + align:start position:0% +that pay semiannually so when they say +that there's a coupon of 3% it's 3% + + align:start position:0% +that there's a coupon of 3% it's 3% + + + align:start position:0% +that there's a coupon of 3% it's 3% +every six months so you have to take + + align:start position:0% +every six months so you have to take + + + align:start position:0% +every six months so you have to take +that into account when you're Computing + + align:start position:0% +that into account when you're Computing + + + align:start position:0% +that into account when you're Computing +the present values of these + + align:start position:0% +the present values of these + + + align:start position:0% +the present values of these +objects how do we do it exactly the same + + align:start position:0% +objects how do we do it exactly the same + + + align:start position:0% +objects how do we do it exactly the same +way as we do for Pure discount bonds + + align:start position:0% +way as we do for Pure discount bonds + + + align:start position:0% +way as we do for Pure discount bonds +take the coupon + + align:start position:0% +take the coupon + + + align:start position:0% +take the coupon +each of them and discount them back to + + align:start position:0% +each of them and discount them back to + + + align:start position:0% +each of them and discount them back to +the present using either the big + + align:start position:0% +the present using either the big + + + align:start position:0% +the present using either the big +RS or the little RS either way you ought + + align:start position:0% +RS or the little RS either way you ought + + + align:start position:0% +RS or the little RS either way you ought +to get the same answer because the + + align:start position:0% +to get the same answer because the + + + align:start position:0% +to get the same answer because the +little RS are simply the uh geometric + + align:start position:0% +little RS are simply the uh geometric + + + align:start position:0% +little RS are simply the uh geometric +averages of the big RS okay however + + align:start position:0% +averages of the big RS okay however + + + align:start position:0% +averages of the big RS okay however +instead of using the little RS for the + + align:start position:0% +instead of using the little RS for the + + + align:start position:0% +instead of using the little RS for the +different uh + + align:start position:0% +different uh + + + align:start position:0% +different uh +payments coupon bonds are often quoted + + align:start position:0% +payments coupon bonds are often quoted + + + align:start position:0% +payments coupon bonds are often quoted +with a single number that is a + + align:start position:0% +with a single number that is a + + + align:start position:0% +with a single number that is a +yield so the theoretically correct way + + align:start position:0% +yield so the theoretically correct way + + + align:start position:0% +yield so the theoretically correct way +to write the price is given up there p 0 + + align:start position:0% +to write the price is given up there p 0 + + + align:start position:0% +to write the price is given up there p 0 +is equal to C all the coupons divided by + + align:start position:0% +is equal to C all the coupons divided by + + + align:start position:0% +is equal to C all the coupons divided by +the appropriate big + + align:start position:0% +the appropriate big + + + align:start position:0% +the appropriate big +RS or we could replace every one of + + align:start position:0% +RS or we could replace every one of + + + align:start position:0% +RS or we could replace every one of +those big RS with the appropriate little + + align:start position:0% +those big RS with the appropriate little + + + align:start position:0% +those big RS with the appropriate little +r by appropriate little r i mean little + + align:start position:0% +r by appropriate little r i mean little + + + align:start position:0% +r by appropriate little r i mean little +r01 little r02 little r03 right each of + + align:start position:0% +r01 little r02 little r03 right each of + + + align:start position:0% +r01 little r02 little r03 right each of +those but we can also calculate an + + align:start position:0% +those but we can also calculate an + + + align:start position:0% +those but we can also calculate an +average of all of those little RS and + + align:start position:0% +average of all of those little RS and + + + align:start position:0% +average of all of those little RS and +just use one variable and to simplify + + align:start position:0% +just use one variable and to simplify + + + align:start position:0% +just use one variable and to simplify +notation I'm going to give it a + + align:start position:0% +notation I'm going to give it a + + + align:start position:0% +notation I'm going to give it a +completely different symbol y and say + + align:start position:0% +completely different symbol y and say + + + align:start position:0% +completely different symbol y and say +what is that single number + + align:start position:0% +what is that single number + + + align:start position:0% +what is that single number +y that will give me the price of the + + align:start position:0% +y that will give me the price of the + + + align:start position:0% +y that will give me the price of the +bond and that Y is known as the + + align:start position:0% +bond and that Y is known as the + + + align:start position:0% +bond and that Y is known as the +particular bonds + + align:start position:0% +particular bonds + + + align:start position:0% +particular bonds +yield it is the single interest rate + + align:start position:0% +yield it is the single interest rate + + + align:start position:0% +yield it is the single interest rate +which if interest rates were constant + + align:start position:0% +which if interest rates were constant + + + align:start position:0% +which if interest rates were constant +throughout time would make the present + + align:start position:0% +throughout time would make the present + + + align:start position:0% +throughout time would make the present +value of all the coupons and principal + + align:start position:0% +value of all the coupons and principal + + + align:start position:0% +value of all the coupons and principal +equal to the current + + align:start position:0% +equal to the current + + + align:start position:0% +equal to the current +price okay so if you think about a + + align:start position:0% +price okay so if you think about a + + + align:start position:0% +price okay so if you think about a +mortgage and you ask the question if the + + align:start position:0% +mortgage and you ask the question if the + + + align:start position:0% +mortgage and you ask the question if the +interest if the mortgage rate is 5% what + + align:start position:0% +interest if the mortgage rate is 5% what + + + align:start position:0% +interest if the mortgage rate is 5% what +is the value of the uh of the loan + + align:start position:0% +is the value of the uh of the loan + + + align:start position:0% +is the value of the uh of the loan +that's exactly this expression right + + align:start position:0% +that's exactly this expression right + + + align:start position:0% +that's exactly this expression right +here okay now obviously when you get a a + + align:start position:0% +here okay now obviously when you get a a + + + align:start position:0% +here okay now obviously when you get a a +fixed rate mortgage of + + align:start position:0% +fixed rate mortgage of + + + align:start position:0% +fixed rate mortgage of +5.89% you know that the interest rate is + + align:start position:0% +5.89% you know that the interest rate is + + + align:start position:0% +5.89% you know that the interest rate is +not really going to be 5.89% forever the + + align:start position:0% +not really going to be 5.89% forever the + + + align:start position:0% +not really going to be 5.89% forever the +interest rate changes every year but + + align:start position:0% +interest rate changes every year but + + + align:start position:0% +interest rate changes every year but +that + + align:start position:0% +that + + + align:start position:0% +that +5.89% is an average of the + + align:start position:0% +5.89% is an average of the + + + align:start position:0% +5.89% is an average of the +30-year period where you're going to be + + align:start position:0% +30-year period where you're going to be + + + align:start position:0% +30-year period where you're going to be +borrowing that mortgage money so you can + + align:start position:0% +borrowing that mortgage money so you can + + + align:start position:0% +borrowing that mortgage money so you can +think of this discount the coupon Bond + + align:start position:0% +think of this discount the coupon Bond + + + align:start position:0% +think of this discount the coupon Bond +exactly the same way we quote this + + align:start position:0% +exactly the same way we quote this + + + align:start position:0% +exactly the same way we quote this +number y as a yield sometimes we talk + + align:start position:0% +number y as a yield sometimes we talk + + + align:start position:0% +number y as a yield sometimes we talk +about yield instead of prices but the + + align:start position:0% +about yield instead of prices but the + + + align:start position:0% +about yield instead of prices but the +way that we figure out yield is we take + + align:start position:0% +way that we figure out yield is we take + + + align:start position:0% +way that we figure out yield is we take +this 30-year bond that pays 5% a year we + + align:start position:0% +this 30-year bond that pays 5% a year we + + + align:start position:0% +this 30-year bond that pays 5% a year we +auction it off and we figure out what + + align:start position:0% +auction it off and we figure out what + + + align:start position:0% +auction it off and we figure out what +the price is given the price we can find + + align:start position:0% +the price is given the price we can find + + + align:start position:0% +the price is given the price we can find +the + + align:start position:0% + + + + align:start position:0% + +yield finding the yield is not so easy + + align:start position:0% +yield finding the yield is not so easy + + + align:start position:0% +yield finding the yield is not so easy +in this case + + align:start position:0% +in this case + + + align:start position:0% +in this case +because in this case unlike just taking + + align:start position:0% +because in this case unlike just taking + + + align:start position:0% +because in this case unlike just taking +a simple geometric average which is what + + align:start position:0% +a simple geometric average which is what + + + align:start position:0% +a simple geometric average which is what +we did to calculate the little RS and + + align:start position:0% +we did to calculate the little RS and + + + align:start position:0% +we did to calculate the little RS and +the big RS in this case in order to find + + align:start position:0% +the big RS in this case in order to find + + + align:start position:0% +the big RS in this case in order to find +the Y + + align:start position:0% +the Y + + + align:start position:0% +the Y +we actually have to solve an equation + + align:start position:0% +we actually have to solve an equation + + + align:start position:0% +we actually have to solve an equation +that can be highly nonlinear in fact + + align:start position:0% +that can be highly nonlinear in fact + + + align:start position:0% +that can be highly nonlinear in fact +it's a polom it's a a teeth order polom + + align:start position:0% +it's a polom it's a a teeth order polom + + + align:start position:0% +it's a polom it's a a teeth order polom +and for those of you high school math + + align:start position:0% +and for those of you high school math + + + align:start position:0% +and for those of you high school math +team jocks you'll remember that um when + + align:start position:0% +team jocks you'll remember that um when + + + align:start position:0% +team jocks you'll remember that um when +you've got uh a teeth order polinomial + + align:start position:0% +you've got uh a teeth order polinomial + + + align:start position:0% +you've got uh a teeth order polinomial +first of all you have a lot of solutions + + align:start position:0% +first of all you have a lot of solutions + + + align:start position:0% +first of all you have a lot of solutions +how many solutions do you typically have + + align:start position:0% +how many solutions do you typically have + + + align:start position:0% +how many solutions do you typically have +t and of those Solutions how many of + + align:start position:0% +t and of those Solutions how many of + + + align:start position:0% +t and of those Solutions how many of +them are guaranteed to be real + + align:start position:0% + + + + align:start position:0% + +numbers right there's no guarantee that + + align:start position:0% +numbers right there's no guarantee that + + + align:start position:0% +numbers right there's no guarantee that +any of them are real now you might ask + + align:start position:0% +any of them are real now you might ask + + + align:start position:0% +any of them are real now you might ask +what do you mean by real well if you're + + align:start position:0% +what do you mean by real well if you're + + + align:start position:0% +what do you mean by real well if you're +asking me you don't need to know don't + + align:start position:0% +asking me you don't need to know don't + + + align:start position:0% +asking me you don't need to know don't +don't uh it means numbers that we + + align:start position:0% +don't uh it means numbers that we + + + align:start position:0% +don't uh it means numbers that we +encounter in reality let's call it that + + align:start position:0% +encounter in reality let's call it that + + + align:start position:0% +encounter in reality let's call it that +put it that way there it turns out that + + align:start position:0% +put it that way there it turns out that + + + align:start position:0% +put it that way there it turns out that +there are numbers that actually don't + + align:start position:0% +there are numbers that actually don't + + + align:start position:0% +there are numbers that actually don't +exist in reality uh they're called + + align:start position:0% +exist in reality uh they're called + + + align:start position:0% +exist in reality uh they're called +complex numbers and uh they are quite + + align:start position:0% +complex numbers and uh they are quite + + + align:start position:0% +complex numbers and uh they are quite +complex so I won't uh talk about them + + align:start position:0% +complex so I won't uh talk about them + + + align:start position:0% +complex so I won't uh talk about them +but these kinds of equations it turns + + align:start position:0% +but these kinds of equations it turns + + + align:start position:0% +but these kinds of equations it turns +out that they're not guaranteed to even + + align:start position:0% +out that they're not guaranteed to even + + + align:start position:0% +out that they're not guaranteed to even +have real solutions now it turns out + + align:start position:0% +have real solutions now it turns out + + + align:start position:0% +have real solutions now it turns out +that for + + align:start position:0% +that for + + + align:start position:0% +that for +bonds where the coupon payments are all + + align:start position:0% +bonds where the coupon payments are all + + + align:start position:0% +bonds where the coupon payments are all +positive and the principal is all + + align:start position:0% +positive and the principal is all + + + align:start position:0% +positive and the principal is all +positive it turns out in that very + + align:start position:0% +positive it turns out in that very + + + align:start position:0% +positive it turns out in that very +restrictive and the price is positive it + + align:start position:0% +restrictive and the price is positive it + + + align:start position:0% +restrictive and the price is positive it +turns out in those cases you actually do + + align:start position:0% +turns out in those cases you actually do + + + align:start position:0% +turns out in those cases you actually do +get uh a real number at at least one + + align:start position:0% +get uh a real number at at least one + + + align:start position:0% +get uh a real number at at least one +real number the problem is that in some + + align:start position:0% +real number the problem is that in some + + + align:start position:0% +real number the problem is that in some +cases you get multiple real numbers and + + align:start position:0% +cases you get multiple real numbers and + + + align:start position:0% +cases you get multiple real numbers and +then it's very very hard to figure out + + align:start position:0% +then it's very very hard to figure out + + + align:start position:0% +then it's very very hard to figure out +which yield is the correct one to use + + align:start position:0% +which yield is the correct one to use + + + align:start position:0% +which yield is the correct one to use +the only reason I'm telling you about + + align:start position:0% +the only reason I'm telling you about + + + align:start position:0% +the only reason I'm telling you about +this is because it turns out as a matter + + align:start position:0% +this is because it turns out as a matter + + + align:start position:0% +this is because it turns out as a matter +of convention very often people will + + align:start position:0% +of convention very often people will + + + align:start position:0% +of convention very often people will +quote why these why little why yields + + align:start position:0% +quote why these why little why yields + + + align:start position:0% +quote why these why little why yields +when they talk about coupon bonds but + + align:start position:0% +when they talk about coupon bonds but + + + align:start position:0% +when they talk about coupon bonds but +the way to think about them is to think + + align:start position:0% +the way to think about them is to think + + + align:start position:0% +the way to think about them is to think +about the price which is the present + + align:start position:0% +about the price which is the present + + + align:start position:0% +about the price which is the present +value of the coupon payments as a + + align:start position:0% +value of the coupon payments as a + + + align:start position:0% +value of the coupon payments as a +present discounted value of the interest + + align:start position:0% +present discounted value of the interest + + + align:start position:0% +present discounted value of the interest +that really applies between today and + + align:start position:0% +that really applies between today and + + + align:start position:0% +that really applies between today and +date T in fact in order to do this + + align:start position:0% +date T in fact in order to do this + + + align:start position:0% +date T in fact in order to do this +present value calculation you need not + + align:start position:0% +present value calculation you need not + + + align:start position:0% +present value calculation you need not +just one interest rate how many interest + + align:start position:0% +just one interest rate how many interest + + + align:start position:0% +just one interest rate how many interest +rates do you + + align:start position:0% +rates do you + + + align:start position:0% +rates do you +need T right you're at year zero and + + align:start position:0% +need T right you're at year zero and + + + align:start position:0% +need T right you're at year zero and +you've got payments for every single + + align:start position:0% +you've got payments for every single + + + align:start position:0% +you've got payments for every single +year between one and T So you need + + align:start position:0% +year between one and T So you need + + + align:start position:0% +year between one and T So you need +interest rates that apply between zero + + align:start position:0% +interest rates that apply between zero + + + align:start position:0% +interest rates that apply between zero +and one 0 and two 0 and three and so on + + align:start position:0% +and one 0 and two 0 and three and so on + + + align:start position:0% +and one 0 and two 0 and three and so on +you need T interest rates or exchange + + align:start position:0% +you need T interest rates or exchange + + + align:start position:0% +you need T interest rates or exchange +rates right or exchange rates between + + align:start position:0% +rates right or exchange rates between + + + align:start position:0% +rates right or exchange rates between +different + + align:start position:0% +different + + + align:start position:0% +different +dates but now the yield is important + + align:start position:0% +dates but now the yield is important + + + align:start position:0% +dates but now the yield is important +because it allows us to quote the pseudo + + align:start position:0% +because it allows us to quote the pseudo + + + align:start position:0% +because it allows us to quote the pseudo +rate of return of this Bond uh in a + + align:start position:0% +rate of return of this Bond uh in a + + + align:start position:0% +rate of return of this Bond uh in a +single number and very often people will + + align:start position:0% +single number and very often people will + + + align:start position:0% +single number and very often people will +plot the Y's as a function of the + + align:start position:0% +plot the Y's as a function of the + + + align:start position:0% +plot the Y's as a function of the +Horizon of these bonds so when I showed + + align:start position:0% +Horizon of these bonds so when I showed + + + align:start position:0% +Horizon of these bonds so when I showed +you that yield curve let me get it get + + align:start position:0% +you that yield curve let me get it get + + + align:start position:0% +you that yield curve let me get it get +that + + align:start position:0% + + + + align:start position:0% + +back whoops I just had + + align:start position:0% + + + + align:start position:0% + +it + + align:start position:0% +it + + + align:start position:0% +it +yeah let's take a look at this again + + align:start position:0% + + + + align:start position:0% + +these uh treasury bonds from years 2 to + + align:start position:0% +these uh treasury bonds from years 2 to + + + align:start position:0% +these uh treasury bonds from years 2 to +years 30 those have coupon payments and + + align:start position:0% +years 30 those have coupon payments and + + + align:start position:0% +years 30 those have coupon payments and +those are the coupon rates and they have + + align:start position:0% +those are the coupon rates and they have + + + align:start position:0% +those are the coupon rates and they have +prices and they have yields so what's + + align:start position:0% +prices and they have yields so what's + + + align:start position:0% +prices and they have yields so what's +plotted here is not the little + + align:start position:0% +plotted here is not the little + + + align:start position:0% +plotted here is not the little +r it's the Y for the coupon + + align:start position:0% +r it's the Y for the coupon + + + align:start position:0% +r it's the Y for the coupon +bonds and so the reason that they're not + + align:start position:0% +bonds and so the reason that they're not + + + align:start position:0% +bonds and so the reason that they're not +the same is because the yields the + + align:start position:0% +the same is because the yields the + + + align:start position:0% +the same is because the yields the +little y they depend on the coupon + + align:start position:0% +little y they depend on the coupon + + + align:start position:0% +little y they depend on the coupon +payments and and really strictly + + align:start position:0% +payments and and really strictly + + + align:start position:0% +payments and and really strictly +speaking we don't care about coupon + + align:start position:0% +speaking we don't care about coupon + + + align:start position:0% +speaking we don't care about coupon +payments when we look at time to + + align:start position:0% +payments when we look at time to + + + align:start position:0% +payments when we look at time to +maturity we just want to know what is + + align:start position:0% +maturity we just want to know what is + + + align:start position:0% +maturity we just want to know what is +the interest rate between 0 and one 0 + + align:start position:0% +the interest rate between 0 and one 0 + + + align:start position:0% +the interest rate between 0 and one 0 +and two 0 and three 0 and five and so on + + align:start position:0% +and two 0 and three 0 and five and so on + + + align:start position:0% +and two 0 and three 0 and five and so on +but this is a reasonable proxy as long + + align:start position:0% +but this is a reasonable proxy as long + + + align:start position:0% +but this is a reasonable proxy as long +as the coupons don't look too crazy and + + align:start position:0% +as the coupons don't look too crazy and + + + align:start position:0% +as the coupons don't look too crazy and +are not too different from each other + + align:start position:0% +are not too different from each other + + + align:start position:0% +are not too different from each other +and you can see that the coupons are all + + align:start position:0% +and you can see that the coupons are all + + + align:start position:0% +and you can see that the coupons are all +sort of in the same neighborhood you + + align:start position:0% +sort of in the same neighborhood you + + + align:start position:0% +sort of in the same neighborhood you +know some of them are 2.3% versus + + align:start position:0% +know some of them are 2.3% versus + + + align:start position:0% +know some of them are 2.3% versus +4.5% but they're not so different so + + align:start position:0% +4.5% but they're not so different so + + + align:start position:0% +4.5% but they're not so different so +this gives us uh an indication of what + + align:start position:0% +this gives us uh an indication of what + + + align:start position:0% +this gives us uh an indication of what +the the strips yield curve would look + + align:start position:0% +the the strips yield curve would look + + + align:start position:0% +the the strips yield curve would look +like all + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +so let me uh go + + align:start position:0% + + + + align:start position:0% + +back here's an example of the historical + + align:start position:0% +back here's an example of the historical + + + align:start position:0% +back here's an example of the historical +yield curve for US Treasury Securities + + align:start position:0% +yield curve for US Treasury Securities + + + align:start position:0% +yield curve for US Treasury Securities +and let me just show you a + + align:start position:0% +and let me just show you a + + + align:start position:0% +and let me just show you a +plot they move around a lot so these + + align:start position:0% +plot they move around a lot so these + + + align:start position:0% +plot they move around a lot so these +yield curves tell us something about the + + align:start position:0% +yield curves tell us something about the + + + align:start position:0% +yield curves tell us something about the +average interest rate across various + + align:start position:0% +average interest rate across various + + + align:start position:0% +average interest rate across various +different maturities so if you look at + + align:start position:0% +different maturities so if you look at + + + align:start position:0% +different maturities so if you look at +the um the yellow line that's a one-year + + align:start position:0% +the um the yellow line that's a one-year + + + align:start position:0% +the um the yellow line that's a one-year +yield curve or or sorry oneyear yield uh + + align:start position:0% +yield curve or or sorry oneyear yield uh + + + align:start position:0% +yield curve or or sorry oneyear yield uh +over time so this is not the yield curve + + align:start position:0% +over time so this is not the yield curve + + + align:start position:0% +over time so this is not the yield curve +anymore this is a plot of the time + + align:start position:0% +anymore this is a plot of the time + + + align:start position:0% +anymore this is a plot of the time +series of oneyear + + align:start position:0% +series of oneyear + + + align:start position:0% +series of oneyear +yields over time and you can see that + + align:start position:0% +yields over time and you can see that + + + align:start position:0% +yields over time and you can see that +starting in the when the sample began in + + align:start position:0% +starting in the when the sample began in + + + align:start position:0% +starting in the when the sample began in +1982 the one-year yield for us treasury + + align:start position:0% +1982 the one-year yield for us treasury + + + align:start position:0% +1982 the one-year yield for us treasury +bills is + + align:start position:0% +bills is + + + align:start position:0% +bills is +12% 12% back in 1982 and there's a point + + align:start position:0% +12% 12% back in 1982 and there's a point + + + align:start position:0% +12% 12% back in 1982 and there's a point +at which one of the longer maturity uh + + align:start position:0% +at which one of the longer maturity uh + + + align:start position:0% +at which one of the longer maturity uh +uh instruments reaches a peak of 16 or + + align:start position:0% +uh instruments reaches a peak of 16 or + + + align:start position:0% +uh instruments reaches a peak of 16 or +17% remember I told you I borrowed I was + + align:start position:0% +17% remember I told you I borrowed I was + + + align:start position:0% +17% remember I told you I borrowed I was +looking to get a house and get a + + align:start position:0% +looking to get a house and get a + + + align:start position:0% +looking to get a house and get a +mortgage at 18% that was a 30-year fixed + + align:start position:0% +mortgage at 18% that was a 30-year fixed + + + align:start position:0% +mortgage at 18% that was a 30-year fixed +rate back in the + + align:start position:0% +rate back in the + + + align:start position:0% +rate back in the +1980s so borrowing rates are very very + + align:start position:0% +1980s so borrowing rates are very very + + + align:start position:0% +1980s so borrowing rates are very very +low by by these historical + + align:start position:0% +low by by these historical + + + align:start position:0% +low by by these historical +standards if borrowing rates are very + + align:start position:0% +standards if borrowing rates are very + + + align:start position:0% +standards if borrowing rates are very +low what does that tell you about credit + + align:start position:0% +low what does that tell you about credit + + + align:start position:0% +low what does that tell you about credit +and about the amount of cash sloshing + + align:start position:0% +and about the amount of cash sloshing + + + align:start position:0% +and about the amount of cash sloshing +around in the + + align:start position:0% +around in the + + + align:start position:0% +around in the +economy yeah Avil exactly lots and lots + + align:start position:0% +economy yeah Avil exactly lots and lots + + + align:start position:0% +economy yeah Avil exactly lots and lots +and lots of money available so for those + + align:start position:0% +and lots of money available so for those + + + align:start position:0% +and lots of money available so for those +of you who are thinking about uh + + align:start position:0% +of you who are thinking about uh + + + align:start position:0% +of you who are thinking about uh +entrepreneurial Ventures you're thinking + + align:start position:0% +entrepreneurial Ventures you're thinking + + + align:start position:0% +entrepreneurial Ventures you're thinking +about raising Capital you might be + + align:start position:0% +about raising Capital you might be + + + align:start position:0% +about raising Capital you might be +depressed by what's going on in Market + + align:start position:0% +depressed by what's going on in Market + + + align:start position:0% +depressed by what's going on in Market +today but look at the interest rate and + + align:start position:0% +today but look at the interest rate and + + + align:start position:0% +today but look at the interest rate and +ask yourself gee would I rather start a + + align:start position:0% +ask yourself gee would I rather start a + + + align:start position:0% +ask yourself gee would I rather start a +company today or back in + + align:start position:0% +company today or back in + + + align:start position:0% +company today or back in +1982 is a heck of a lot more money + + align:start position:0% +1982 is a heck of a lot more money + + + align:start position:0% +1982 is a heck of a lot more money +sloshing around the system + + align:start position:0% +sloshing around the system + + + align:start position:0% +sloshing around the system +today in fact a few years ago I talked + + align:start position:0% +today in fact a few years ago I talked + + + align:start position:0% +today in fact a few years ago I talked +to uh a couple of uh MIT undergraduates + + align:start position:0% +to uh a couple of uh MIT undergraduates + + + align:start position:0% +to uh a couple of uh MIT undergraduates +uh one of them came up and asked me + + align:start position:0% +uh one of them came up and asked me + + + align:start position:0% +uh one of them came up and asked me +whether I'd be willing to advise them on + + align:start position:0% +whether I'd be willing to advise them on + + + align:start position:0% +whether I'd be willing to advise them on +some uh internet company they wanted to + + align:start position:0% +some uh internet company they wanted to + + + align:start position:0% +some uh internet company they wanted to +start and um you know I said well you + + align:start position:0% +start and um you know I said well you + + + align:start position:0% +start and um you know I said well you +know where are you going to get your + + align:start position:0% +know where are you going to get your + + + align:start position:0% +know where are you going to get your +financing and they said oh don't worry + + align:start position:0% +financing and they said oh don't worry + + + align:start position:0% +financing and they said oh don't worry +about that we've already got it all set + + align:start position:0% +about that we've already got it all set + + + align:start position:0% +about that we've already got it all set +you know we got 10 of us and each of us + + align:start position:0% +you know we got 10 of us and each of us + + + align:start position:0% +you know we got 10 of us and each of us +is able to borrow uh you know $1,000 + + align:start position:0% +is able to borrow uh you know $1,000 + + + align:start position:0% +is able to borrow uh you know $1,000 +each on credit cards and we each have 10 + + align:start position:0% +each on credit cards and we each have 10 + + + align:start position:0% +each on credit cards and we each have 10 +credit cards so that that's + + align:start position:0% +credit cards so that that's + + + align:start position:0% +credit cards so that that's +$100,000 and I'm saying $100,000 on + + align:start position:0% +$100,000 and I'm saying $100,000 on + + + align:start position:0% +$100,000 and I'm saying $100,000 on +credit cards I mean you guys are going + + align:start position:0% +credit cards I mean you guys are going + + + align:start position:0% +credit cards I mean you guys are going +to be paying 18% a year or something on + + align:start position:0% +to be paying 18% a year or something on + + + align:start position:0% +to be paying 18% a year or something on +that and they said yeah you know what + + align:start position:0% +that and they said yeah you know what + + + align:start position:0% +that and they said yeah you know what +that's the cheapest Venture financing + + align:start position:0% +that's the cheapest Venture financing + + + align:start position:0% +that's the cheapest Venture financing +you'll ever find and they're right + + align:start position:0% +you'll ever find and they're right + + + align:start position:0% +you'll ever find and they're right +because those are non-recourse loans + + align:start position:0% +because those are non-recourse loans + + + align:start position:0% +because those are non-recourse loans +they don't take a piece of your company + + align:start position:0% +they don't take a piece of your company + + + align:start position:0% +they don't take a piece of your company +and 18% for a venture is actually pretty + + align:start position:0% +and 18% for a venture is actually pretty + + + align:start position:0% +and 18% for a venture is actually pretty +attractive well look at what the + + align:start position:0% +attractive well look at what the + + + align:start position:0% +attractive well look at what the +borrowing rate is now now you can't + + align:start position:0% +borrowing rate is now now you can't + + + align:start position:0% +borrowing rate is now now you can't +borrow at this rate for ventures but it + + align:start position:0% +borrow at this rate for ventures but it + + + align:start position:0% +borrow at this rate for ventures but it +indicates that there's a lot of credit + + align:start position:0% +indicates that there's a lot of credit + + + align:start position:0% +indicates that there's a lot of credit +out there and there's still a lot of + + align:start position:0% +out there and there's still a lot of + + + align:start position:0% +out there and there's still a lot of +credit out there there in fact the + + align:start position:0% +credit out there there in fact the + + + align:start position:0% +credit out there there in fact the +treasury and the FED would argue there's + + align:start position:0% +treasury and the FED would argue there's + + + align:start position:0% +treasury and the FED would argue there's +too much credit out there and that's why + + align:start position:0% +too much credit out there and that's why + + + align:start position:0% +too much credit out there and that's why +we're in the problems that we are today + + align:start position:0% +we're in the problems that we are today + + + align:start position:0% +we're in the problems that we are today +it's because too many people people that + + align:start position:0% +it's because too many people people that + + + align:start position:0% +it's because too many people people that +should not have been leveraging and + + align:start position:0% +should not have been leveraging and + + + align:start position:0% +should not have been leveraging and +borrowing uh have have done so and now + + align:start position:0% +borrowing uh have have done so and now + + + align:start position:0% +borrowing uh have have done so and now +we're feeling the Pains of a + + align:start position:0% +we're feeling the Pains of a + + + align:start position:0% +we're feeling the Pains of a +contraction okay so this is the history + + align:start position:0% +contraction okay so this is the history + + + align:start position:0% +contraction okay so this is the history +of yield curves and at a given point in + + align:start position:0% +of yield curves and at a given point in + + + align:start position:0% +of yield curves and at a given point in +time we can take a look at uh yield + + align:start position:0% +time we can take a look at uh yield + + + align:start position:0% +time we can take a look at uh yield +curves and see how that curve changes + + align:start position:0% +curves and see how that curve changes + + + align:start position:0% +curves and see how that curve changes +day to-day I showed you today's yield + + align:start position:0% +day to-day I showed you today's yield + + + align:start position:0% +day to-day I showed you today's yield +curve which is upward sloping but you + + align:start position:0% +curve which is upward sloping but you + + + align:start position:0% +curve which is upward sloping but you +there was a period uh back in 2000 where + + align:start position:0% +there was a period uh back in 2000 where + + + align:start position:0% +there was a period uh back in 2000 where +this yield curve was actually upward + + align:start position:0% +this yield curve was actually upward + + + align:start position:0% +this yield curve was actually upward +sloping and then downward + + align:start position:0% +sloping and then downward + + + align:start position:0% +sloping and then downward +sloping why would the yield curve be + + align:start position:0% +sloping why would the yield curve be + + + align:start position:0% +sloping why would the yield curve be +downward + + align:start position:0% +downward + + + align:start position:0% +downward +sloping what that tells you is that + + align:start position:0% +sloping what that tells you is that + + + align:start position:0% +sloping what that tells you is that +there's an + + align:start position:0% +there's an + + + align:start position:0% +there's an +expectation of the market participants + + align:start position:0% +expectation of the market participants + + + align:start position:0% +expectation of the market participants +that interest rates in the long run have + + align:start position:0% +that interest rates in the long run have + + + align:start position:0% +that interest rates in the long run have +got to come down uh and that there's + + align:start position:0% +got to come down uh and that there's + + + align:start position:0% +got to come down uh and that there's +going to be some kind of fed policy + + align:start position:0% +going to be some kind of fed policy + + + align:start position:0% +going to be some kind of fed policy +shift possible within three years five + + align:start position:0% +shift possible within three years five + + + align:start position:0% +shift possible within three years five +years 10 years that would make that more + + align:start position:0% +years 10 years that would make that more + + + align:start position:0% +years 10 years that would make that more +likely than not so by looking at these + + align:start position:0% +likely than not so by looking at these + + + align:start position:0% +likely than not so by looking at these +yield curves over different dates you + + align:start position:0% +yield curves over different dates you + + + align:start position:0% +yield curves over different dates you +can get a sense of how the Market's + + align:start position:0% +can get a sense of how the Market's + + + align:start position:0% +can get a sense of how the Market's +expectations are of the future which I + + align:start position:0% +expectations are of the future which I + + + align:start position:0% +expectations are of the future which I +think is a tremendous uh ability to + + align:start position:0% +think is a tremendous uh ability to + + + align:start position:0% +think is a tremendous uh ability to +actually look into the future at least + + align:start position:0% +actually look into the future at least + + + align:start position:0% +actually look into the future at least +look into the future as predicted by all + + align:start position:0% +look into the future as predicted by all + + + align:start position:0% +look into the future as predicted by all +the market + + align:start position:0% + + + + align:start position:0% + +participants uh this is just the yield + + align:start position:0% +participants uh this is just the yield + + + align:start position:0% +participants uh this is just the yield +curve that I told you about this is not + + align:start position:0% +curve that I told you about this is not + + + align:start position:0% +curve that I told you about this is not +in your notes but uh I was able to copy + + align:start position:0% +in your notes but uh I was able to copy + + + align:start position:0% +in your notes but uh I was able to copy +that from Bloomberg this morning but you + + align:start position:0% +that from Bloomberg this morning but you + + + align:start position:0% +that from Bloomberg this morning but you +have that in the public website and + + align:start position:0% +have that in the public website and + + + align:start position:0% +have that in the public website and +now the the the next topic I want to + + align:start position:0% +now the the the next topic I want to + + + align:start position:0% +now the the the next topic I want to +take on very briefly because there's a + + align:start position:0% +take on very briefly because there's a + + + align:start position:0% +take on very briefly because there's a +lot to be said about models of the yield + + align:start position:0% +lot to be said about models of the yield + + + align:start position:0% +lot to be said about models of the yield +curve and I won't take up class time to + + align:start position:0% +curve and I won't take up class time to + + + align:start position:0% +curve and I won't take up class time to +do that this is something that is a more + + align:start position:0% +do that this is something that is a more + + + align:start position:0% +do that this is something that is a more +uh a toic that's more uh significantly + + align:start position:0% +uh a toic that's more uh significantly + + + align:start position:0% +uh a toic that's more uh significantly +focused on in Investments and in uh + + align:start position:0% +focused on in Investments and in uh + + + align:start position:0% +focused on in Investments and in uh +fixed income securities but what one of + + align:start position:0% +fixed income securities but what one of + + + align:start position:0% +fixed income securities but what one of +the things that we'd like to be able to + + align:start position:0% +the things that we'd like to be able to + + + align:start position:0% +the things that we'd like to be able to +do is to try to model that term + + align:start position:0% +do is to try to model that term + + + align:start position:0% +do is to try to model that term +structure of interest rates is there any + + align:start position:0% +structure of interest rates is there any + + + align:start position:0% +structure of interest rates is there any +logic that we can come up with that + + align:start position:0% +logic that we can come up with that + + + align:start position:0% +logic that we can come up with that +explains why the yield curve is upward + + align:start position:0% +explains why the yield curve is upward + + + align:start position:0% +explains why the yield curve is upward +sloping or backward bending or + + align:start position:0% +sloping or backward bending or + + + align:start position:0% +sloping or backward bending or +inverted and it turns out that there are + + align:start position:0% +inverted and it turns out that there are + + + align:start position:0% +inverted and it turns out that there are +a number of theories that have come to + + align:start position:0% +a number of theories that have come to + + + align:start position:0% +a number of theories that have come to +be proposed I'm not going to cover any + + align:start position:0% +be proposed I'm not going to cover any + + + align:start position:0% +be proposed I'm not going to cover any +of these in any depth but I want to at + + align:start position:0% +of these in any depth but I want to at + + + align:start position:0% +of these in any depth but I want to at +least mention the name so that you'll + + align:start position:0% +least mention the name so that you'll + + + align:start position:0% +least mention the name so that you'll +know that there are theories out there + + align:start position:0% +know that there are theories out there + + + align:start position:0% +know that there are theories out there +that will tell you whether or not the + + align:start position:0% +that will tell you whether or not the + + + align:start position:0% +that will tell you whether or not the +yield curve should be so steeply sloped + + align:start position:0% +yield curve should be so steeply sloped + + + align:start position:0% +yield curve should be so steeply sloped +or not there's something called the + + align:start position:0% +or not there's something called the + + + align:start position:0% +or not there's something called the +expectations hypothesis there's + + align:start position:0% +expectations hypothesis there's + + + align:start position:0% +expectations hypothesis there's +something called the liquidity + + align:start position:0% +something called the liquidity + + + align:start position:0% +something called the liquidity +preference hypothesis there's a + + align:start position:0% +preference hypothesis there's a + + + align:start position:0% +preference hypothesis there's a +preferred habitat Model A Market + + align:start position:0% +preferred habitat Model A Market + + + align:start position:0% +preferred habitat Model A Market +segmentation model and then there are a + + align:start position:0% +segmentation model and then there are a + + + align:start position:0% +segmentation model and then there are a +whole slew of extraordinarily + + align:start position:0% +whole slew of extraordinarily + + + align:start position:0% +whole slew of extraordinarily +sophisticated and complex uh + + align:start position:0% +sophisticated and complex uh + + + align:start position:0% +sophisticated and complex uh +mathematical models one of which and + + align:start position:0% +mathematical models one of which and + + + align:start position:0% +mathematical models one of which and +probably the best known of which was + + align:start position:0% +probably the best known of which was + + + align:start position:0% +probably the best known of which was +developed by our very own uh John Cox + + align:start position:0% +developed by our very own uh John Cox + + + align:start position:0% +developed by our very own uh John Cox +and uh Steve Ross the Cox ingol Ross + + align:start position:0% +and uh Steve Ross the Cox ingol Ross + + + align:start position:0% +and uh Steve Ross the Cox ingol Ross +model of the term structure of interest + + align:start position:0% +model of the term structure of interest + + + align:start position:0% +model of the term structure of interest +rates is probably the single best known + + align:start position:0% +rates is probably the single best known + + + align:start position:0% +rates is probably the single best known +yield Curve Model it's a very + + align:start position:0% +yield Curve Model it's a very + + + align:start position:0% +yield Curve Model it's a very +complicated model but it has some pretty + + align:start position:0% +complicated model but it has some pretty + + + align:start position:0% +complicated model but it has some pretty +significant implications for whether the + + align:start position:0% +significant implications for whether the + + + align:start position:0% +significant implications for whether the +yield curve ought to be upward sloping + + align:start position:0% +yield curve ought to be upward sloping + + + align:start position:0% +yield curve ought to be upward sloping +or downward sloping or how it changes + + align:start position:0% +or downward sloping or how it changes + + + align:start position:0% +or downward sloping or how it changes +over time so I'll give you one example + + align:start position:0% +over time so I'll give you one example + + + align:start position:0% +over time so I'll give you one example +of what that theory what these theories + + align:start position:0% +of what that theory what these theories + + + align:start position:0% +of what that theory what these theories +are and I I won't spend much time on it + + align:start position:0% +are and I I won't spend much time on it + + + align:start position:0% +are and I I won't spend much time on it +but I want to at least leave you with + + align:start position:0% +but I want to at least leave you with + + + align:start position:0% +but I want to at least leave you with +some intuition for how you would go + + align:start position:0% +some intuition for how you would go + + + align:start position:0% +some intuition for how you would go +about modeling it + + align:start position:0% +about modeling it + + + align:start position:0% +about modeling it +okay so one model says that the today's + + align:start position:0% +okay so one model says that the today's + + + align:start position:0% +okay so one model says that the today's +forward rates are in fact the best guess + + align:start position:0% +forward rates are in fact the best guess + + + align:start position:0% +forward rates are in fact the best guess +of what future spot rates are likely to + + align:start position:0% +of what future spot rates are likely to + + + align:start position:0% +of what future spot rates are likely to +be and that's known as the expectations + + align:start position:0% +be and that's known as the expectations + + + align:start position:0% +be and that's known as the expectations +hypothesis okay this hypothesis states + + align:start position:0% +hypothesis okay this hypothesis states + + + align:start position:0% +hypothesis okay this hypothesis states +that today's forward rate which is what + + align:start position:0% +that today's forward rate which is what + + + align:start position:0% +that today's forward rate which is what +we do + + align:start position:0% +we do + + + align:start position:0% +we do +observe is equal to the mathematical + + align:start position:0% +observe is equal to the mathematical + + + align:start position:0% +observe is equal to the mathematical +expectation today of the future one-year + + align:start position:0% +expectation today of the future one-year + + + align:start position:0% +expectation today of the future one-year +spot + + align:start position:0% +spot + + + align:start position:0% +spot +rate now you might say well that not + + align:start position:0% +rate now you might say well that not + + + align:start position:0% +rate now you might say well that not +that's not much of a theory I mean what + + align:start position:0% +that's not much of a theory I mean what + + + align:start position:0% +that's not much of a theory I mean what +else could it be well it turns out that + + align:start position:0% +else could it be well it turns out that + + + align:start position:0% +else could it be well it turns out that +there's another theory called the + + align:start position:0% +there's another theory called the + + + align:start position:0% +there's another theory called the +preferred liquidity preference theory + + align:start position:0% +preferred liquidity preference theory + + + align:start position:0% +preferred liquidity preference theory +that says that the longer the term of + + align:start position:0% +that says that the longer the term of + + + align:start position:0% +that says that the longer the term of +borrowing the more you're going to have + + align:start position:0% +borrowing the more you're going to have + + + align:start position:0% +borrowing the more you're going to have +to pay a premium for people to lend to + + align:start position:0% +to pay a premium for people to lend to + + + align:start position:0% +to pay a premium for people to lend to +you so because people would prefer + + align:start position:0% +you so because people would prefer + + + align:start position:0% +you so because people would prefer +liquidity + + align:start position:0% +liquidity + + + align:start position:0% +liquidity +and so the longer you demand the + + align:start position:0% +and so the longer you demand the + + + align:start position:0% +and so the longer you demand the +borrowing for a greater period of time + + align:start position:0% +borrowing for a greater period of time + + + align:start position:0% +borrowing for a greater period of time +the more you have to pay much more so + + align:start position:0% +the more you have to pay much more so + + + align:start position:0% +the more you have to pay much more so +than just linearly so in particular the + + align:start position:0% +than just linearly so in particular the + + + align:start position:0% +than just linearly so in particular the +expectations hypothesis that suggests + + align:start position:0% +expectations hypothesis that suggests + + + align:start position:0% +expectations hypothesis that suggests +that the yield curve is flat right it + + align:start position:0% +that the yield curve is flat right it + + + align:start position:0% +that the yield curve is flat right it +doesn't there's no there's no impact on + + align:start position:0% +doesn't there's no there's no impact on + + + align:start position:0% +doesn't there's no there's no impact on +borrowing for two years three years five + + align:start position:0% +borrowing for two years three years five + + + align:start position:0% +borrowing for two years three years five +years 10 years the future rate is just + + align:start position:0% +years 10 years the future rate is just + + + align:start position:0% +years 10 years the future rate is just +equal to today's uh the today's forward + + align:start position:0% +equal to today's uh the today's forward + + + align:start position:0% +equal to today's uh the today's forward +rate is the expectation of the future + + align:start position:0% +rate is the expectation of the future + + + align:start position:0% +rate is the expectation of the future +okay it's a fair bet liquidity + + align:start position:0% +okay it's a fair bet liquidity + + + align:start position:0% +okay it's a fair bet liquidity +preference says that the yield curve + + align:start position:0% +preference says that the yield curve + + + align:start position:0% +preference says that the yield curve +should be upward + + align:start position:0% +should be upward + + + align:start position:0% +should be upward +sloping because it's going to be more + + align:start position:0% +sloping because it's going to be more + + + align:start position:0% +sloping because it's going to be more +costly for you to borrow over a + + align:start position:0% +costly for you to borrow over a + + + align:start position:0% +costly for you to borrow over a +three-year period than a one-year period + + align:start position:0% +three-year period than a one-year period + + + align:start position:0% +three-year period than a one-year period +simply because it's going to be it's + + align:start position:0% +simply because it's going to be it's + + + align:start position:0% +simply because it's going to be it's +going to entail somebody giving up their + + align:start position:0% +going to entail somebody giving up their + + + align:start position:0% +going to entail somebody giving up their +money for a longer period of time + + align:start position:0% +money for a longer period of time + + + align:start position:0% +money for a longer period of time +they're going to be less liquid you're + + align:start position:0% +they're going to be less liquid you're + + + align:start position:0% +they're going to be less liquid you're +going to have to bribe them to be + + align:start position:0% +going to have to bribe them to be + + + align:start position:0% +going to have to bribe them to be +willing to give up that liquidity + + align:start position:0% +willing to give up that liquidity + + + align:start position:0% +willing to give up that liquidity +so that's the liquidity preference + + align:start position:0% +so that's the liquidity preference + + + align:start position:0% +so that's the liquidity preference +Theory the preferred habitat Theory says + + align:start position:0% +Theory the preferred habitat Theory says + + + align:start position:0% +Theory the preferred habitat Theory says +you know there are preferred maturities + + align:start position:0% +you know there are preferred maturities + + + align:start position:0% +you know there are preferred maturities +that people have and for those + + align:start position:0% +that people have and for those + + + align:start position:0% +that people have and for those +maturities you're going to have + + align:start position:0% +maturities you're going to have + + + align:start position:0% +maturities you're going to have +different rates than for those that + + align:start position:0% +different rates than for those that + + + align:start position:0% +different rates than for those that +people don't prefer so if you want a + + align:start position:0% +people don't prefer so if you want a + + + align:start position:0% +people don't prefer so if you want a +30-year maturity and that's not + + align:start position:0% +30-year maturity and that's not + + + align:start position:0% +30-year maturity and that's not +preferred because it's too far off then + + align:start position:0% +preferred because it's too far off then + + + align:start position:0% +preferred because it's too far off then +you're going to have to pay a premium on + + align:start position:0% +you're going to have to pay a premium on + + + align:start position:0% +you're going to have to pay a premium on +the other hand 10 years is a period that + + align:start position:0% +the other hand 10 years is a period that + + + align:start position:0% +the other hand 10 years is a period that +a number of Pension funds prefer so you + + align:start position:0% +a number of Pension funds prefer so you + + + align:start position:0% +a number of Pension funds prefer so you +may not have to pay as much for those + + align:start position:0% +may not have to pay as much for those + + + align:start position:0% +may not have to pay as much for those +preferred + + align:start position:0% +preferred + + + align:start position:0% +preferred +habitats and to give you a sense of + + align:start position:0% +habitats and to give you a sense of + + + align:start position:0% +habitats and to give you a sense of +where academics is + + align:start position:0% +where academics is + + + align:start position:0% +where academics is +today none of these models work none of + + align:start position:0% +today none of these models work none of + + + align:start position:0% +today none of these models work none of +them can fully explain movements in the + + align:start position:0% +them can fully explain movements in the + + + align:start position:0% +them can fully explain movements in the +yield curve which by the way is a + + align:start position:0% +yield curve which by the way is a + + + align:start position:0% +yield curve which by the way is a +wonderful opportunity for all of you + + align:start position:0% +wonderful opportunity for all of you + + + align:start position:0% +wonderful opportunity for all of you +because if you have a model that does + + align:start position:0% +because if you have a model that does + + + align:start position:0% +because if you have a model that does +work then you can do extraordinarily + + align:start position:0% +work then you can do extraordinarily + + + align:start position:0% +work then you can do extraordinarily +well you can turn very very small + + align:start position:0% +well you can turn very very small + + + align:start position:0% +well you can turn very very small +forecast power into enormous ounts of + + align:start position:0% +forecast power into enormous ounts of + + + align:start position:0% +forecast power into enormous ounts of +wealth very very quickly uh on Wall + + align:start position:0% +wealth very very quickly uh on Wall + + + align:start position:0% +wealth very very quickly uh on Wall +Street + + align:start position:0% + + + + align:start position:0% + +yes does + + align:start position:0% +yes does + + + align:start position:0% +yes does +he you can't patent it right so does he + + align:start position:0% +he you can't patent it right so does he + + + align:start position:0% +he you can't patent it right so does he +gain anything out of that besides + + align:start position:0% +gain anything out of that besides + + + align:start position:0% +gain anything out of that besides +besides notoriety uh well that's a good + + align:start position:0% +besides notoriety uh well that's a good + + + align:start position:0% +besides notoriety uh well that's a good +question the question has to do with um + + align:start position:0% +question the question has to do with um + + + align:start position:0% +question the question has to do with um +I guess the difference between academic + + align:start position:0% +I guess the difference between academic + + + align:start position:0% +I guess the difference between academic +Endeavors and business endeavors um as + + align:start position:0% +Endeavors and business endeavors um as + + + align:start position:0% +Endeavors and business endeavors um as +an academic what you're trying to do is + + align:start position:0% +an academic what you're trying to do is + + + align:start position:0% +an academic what you're trying to do is +to make a name for yourself and to put + + align:start position:0% +to make a name for yourself and to put + + + align:start position:0% +to make a name for yourself and to put +out research ideas that will have an + + align:start position:0% +out research ideas that will have an + + + align:start position:0% +out research ideas that will have an +impact uh on with your colleagues and + + align:start position:0% +impact uh on with your colleagues and + + + align:start position:0% +impact uh on with your colleagues and +the particular area that you're in so uh + + align:start position:0% +the particular area that you're in so uh + + + align:start position:0% +the particular area that you're in so uh +if you're asking did Professor GX get + + align:start position:0% +if you're asking did Professor GX get + + + align:start position:0% +if you're asking did Professor GX get +rich off of this the answer is no + + align:start position:0% +rich off of this the answer is no + + + align:start position:0% +rich off of this the answer is no +probably not neither did Black schs + + align:start position:0% +probably not neither did Black schs + + + align:start position:0% +probably not neither did Black schs +actually when they published their black + + align:start position:0% +actually when they published their black + + + align:start position:0% +actually when they published their black +shows option pricing formula that was + + align:start position:0% +shows option pricing formula that was + + + align:start position:0% +shows option pricing formula that was +the same year that the Chicago Board + + align:start position:0% +the same year that the Chicago Board + + + align:start position:0% +the same year that the Chicago Board +options exchange started trading and + + align:start position:0% +options exchange started trading and + + + align:start position:0% +options exchange started trading and +everybody just used the options pricing + + align:start position:0% +everybody just used the options pricing + + + align:start position:0% +everybody just used the options pricing +formula almost from the very start did + + align:start position:0% +formula almost from the very start did + + + align:start position:0% +formula almost from the very start did +they make any money off of that no they + + align:start position:0% +they make any money off of that no they + + + align:start position:0% +they make any money off of that no they +didn't and you're right you can't patent + + align:start position:0% +didn't and you're right you can't patent + + + align:start position:0% +didn't and you're right you can't patent +it so very often in financial uh + + align:start position:0% +it so very often in financial uh + + + align:start position:0% +it so very often in financial uh +Financial firms when they have good + + align:start position:0% +Financial firms when they have good + + + align:start position:0% +Financial firms when they have good +ideas so for example I do believe there + + align:start position:0% +ideas so for example I do believe there + + + align:start position:0% +ideas so for example I do believe there +are term structure models out there that + + align:start position:0% +are term structure models out there that + + + align:start position:0% +are term structure models out there that +work reasonably well they are not + + align:start position:0% +work reasonably well they are not + + + align:start position:0% +work reasonably well they are not +published they're kept as the the + + align:start position:0% +published they're kept as the the + + + align:start position:0% +published they're kept as the the +coca-colas uh of financial markets + + align:start position:0% +coca-colas uh of financial markets + + + align:start position:0% +coca-colas uh of financial markets +they're Trade Secrets and so if you go + + align:start position:0% +they're Trade Secrets and so if you go + + + align:start position:0% +they're Trade Secrets and so if you go +there to work and ultimately work with + + align:start position:0% +there to work and ultimately work with + + + align:start position:0% +there to work and ultimately work with +the right people you will learn such + + align:start position:0% +the right people you will learn such + + + align:start position:0% +the right people you will learn such +Trade Secrets which by the way is one of + + align:start position:0% +Trade Secrets which by the way is one of + + + align:start position:0% +Trade Secrets which by the way is one of +the reasons why when Barkley's acquires + + align:start position:0% +the reasons why when Barkley's acquires + + + align:start position:0% +the reasons why when Barkley's acquires +Leman and wants to keep all of these + + align:start position:0% +Leman and wants to keep all of these + + + align:start position:0% +Leman and wants to keep all of these +really really terrific people together + + align:start position:0% +really really terrific people together + + + align:start position:0% +really really terrific people together +they're going to have to offer Premia to + + align:start position:0% +they're going to have to offer Premia to + + + align:start position:0% +they're going to have to offer Premia to +do that and so that's part of the cost + + align:start position:0% +do that and so that's part of the cost + + + align:start position:0% +do that and so that's part of the cost +of financial distress when you disturb + + align:start position:0% +of financial distress when you disturb + + + align:start position:0% +of financial distress when you disturb +the the status + + align:start position:0% +the the status + + + align:start position:0% +the the status +quo okay so that's a few models of the + + align:start position:0% +quo okay so that's a few models of the + + + align:start position:0% +quo okay so that's a few models of the +term structure of interest rates and um + + align:start position:0% +term structure of interest rates and um + + + align:start position:0% +term structure of interest rates and um +I want to talk about one last topic on + + align:start position:0% +I want to talk about one last topic on + + + align:start position:0% +I want to talk about one last topic on +coupon bonds before uh concluding this + + align:start position:0% +coupon bonds before uh concluding this + + + align:start position:0% +coupon bonds before uh concluding this +lecture next lecture on Monday we're + + align:start position:0% +lecture next lecture on Monday we're + + + align:start position:0% +lecture next lecture on Monday we're +going to take up measures of interest + + align:start position:0% +going to take up measures of interest + + + align:start position:0% +going to take up measures of interest +rate risk we're going to look explicitly + + align:start position:0% +rate risk we're going to look explicitly + + + align:start position:0% +rate risk we're going to look explicitly +as what happens when interest rates + + align:start position:0% +as what happens when interest rates + + + align:start position:0% +as what happens when interest rates +bounce around before we get to that + + align:start position:0% +bounce around before we get to that + + + align:start position:0% +bounce around before we get to that +though I want to talk about another way + + align:start position:0% +though I want to talk about another way + + + align:start position:0% +though I want to talk about another way +to Value coupon bonds and it's exactly + + align:start position:0% +to Value coupon bonds and it's exactly + + + align:start position:0% +to Value coupon bonds and it's exactly +the idea that I said before of using + + align:start position:0% +the idea that I said before of using + + + align:start position:0% +the idea that I said before of using +pure discount bonds to do so if I have a + + align:start position:0% +pure discount bonds to do so if I have a + + + align:start position:0% +pure discount bonds to do so if I have a +pure discount Bond I I can use that to + + align:start position:0% +pure discount Bond I I can use that to + + + align:start position:0% +pure discount Bond I I can use that to +price coupon bonds by building up a + + align:start position:0% +price coupon bonds by building up a + + + align:start position:0% +price coupon bonds by building up a +package of discount bonds so the example + + align:start position:0% +package of discount bonds so the example + + + align:start position:0% +package of discount bonds so the example +of the strips is given here you've got a + + align:start position:0% +of the strips is given here you've got a + + + align:start position:0% +of the strips is given here you've got a +three-year 5% Bond and it turns out that + + align:start position:0% +three-year 5% Bond and it turns out that + + + align:start position:0% +three-year 5% Bond and it turns out that +you can show that that 3-year 5% bond is + + align:start position:0% +you can show that that 3-year 5% bond is + + + align:start position:0% +you can show that that 3-year 5% bond is +going to be identical to 51-year strips + + align:start position:0% +going to be identical to 51-year strips + + + align:start position:0% +going to be identical to 51-year strips +52-year strips and 1,50 threeyear strips + + align:start position:0% +52-year strips and 1,50 threeyear strips + + + align:start position:0% +52-year strips and 1,50 threeyear strips +each strip paying a dollar in years one + + align:start position:0% +each strip paying a dollar in years one + + + align:start position:0% +each strip paying a dollar in years one +two and + + align:start position:0% +two and + + + align:start position:0% +two and +three any question about that claim + + align:start position:0% +three any question about that claim + + + align:start position:0% +three any question about that claim +anybody want to argue with me that + + align:start position:0% +anybody want to argue with me that + + + align:start position:0% +anybody want to argue with me that +that's not true it's pretty obvious + + align:start position:0% +that's not true it's pretty obvious + + + align:start position:0% +that's not true it's pretty obvious +right well this actually has a very + + align:start position:0% +right well this actually has a very + + + align:start position:0% +right well this actually has a very +dramatic + + align:start position:0% +dramatic + + + align:start position:0% +dramatic +implication and let me tell you what + + align:start position:0% +implication and let me tell you what + + + align:start position:0% +implication and let me tell you what +that implication is the implication is + + align:start position:0% +that implication is the implication is + + + align:start position:0% +that implication is the implication is +that the + + align:start position:0% +that the + + + align:start position:0% +that the +price of a three-year 5% Bond better be + + align:start position:0% +price of a three-year 5% Bond better be + + + align:start position:0% +price of a three-year 5% Bond better be +equal to the cost of 51-year strips 52e + + align:start position:0% +equal to the cost of 51-year strips 52e + + + align:start position:0% +equal to the cost of 51-year strips 52e +strips and 1,5 three-year strips the + + align:start position:0% +strips and 1,5 three-year strips the + + + align:start position:0% +strips and 1,5 three-year strips the +price of this three-year Bond better be + + align:start position:0% +price of this three-year Bond better be + + + align:start position:0% +price of this three-year Bond better be +equal to what it costs to put that + + align:start position:0% +equal to what it costs to put that + + + align:start position:0% +equal to what it costs to put that +portfolio of strips together + + align:start position:0% +portfolio of strips together + + + align:start position:0% +portfolio of strips together +today + + align:start position:0% +today + + + align:start position:0% +today +why why should it be equal yes + + align:start position:0% +why why should it be equal yes + + + align:start position:0% +why why should it be equal yes +what is arbitrage we haven't defined + + align:start position:0% +what is arbitrage we haven't defined + + + align:start position:0% +what is arbitrage we haven't defined +that I + + align:start position:0% + + + + align:start position:0% + +can are or the other until they make + + align:start position:0% +can are or the other until they make + + + align:start position:0% +can are or the other until they make +money exactly there's there's a way to + + align:start position:0% +money exactly there's there's a way to + + + align:start position:0% +money exactly there's there's a way to +make money if the price of that + + align:start position:0% +make money if the price of that + + + align:start position:0% +make money if the price of that +three-year bond is anything other than + + align:start position:0% +three-year bond is anything other than + + + align:start position:0% +three-year bond is anything other than +the cost of that package of strips so + + align:start position:0% +the cost of that package of strips so + + + align:start position:0% +the cost of that package of strips so +let's do an example suppose that the + + align:start position:0% +let's do an example suppose that the + + + align:start position:0% +let's do an example suppose that the +price of a three-year bond is greater + + align:start position:0% +price of a three-year bond is greater + + + align:start position:0% +price of a three-year bond is greater +than the cost of these strips tell tell + + align:start position:0% +than the cost of these strips tell tell + + + align:start position:0% +than the cost of these strips tell tell +me what to + + align:start position:0% +me what to + + + align:start position:0% +me what to +do yeah buy those strips package them as + + align:start position:0% +do yeah buy those strips package them as + + + align:start position:0% +do yeah buy those strips package them as +a bond and then sell it uh then sell the + + align:start position:0% +a bond and then sell it uh then sell the + + + align:start position:0% +a bond and then sell it uh then sell the +bond of the market just keep doing that + + align:start position:0% +bond of the market just keep doing that + + + align:start position:0% +bond of the market just keep doing that +over and over again okay so let's let's + + align:start position:0% +over and over again okay so let's let's + + + align:start position:0% +over and over again okay so let's let's +talk about this slowly I first buy those + + align:start position:0% +talk about this slowly I first buy those + + + align:start position:0% +talk about this slowly I first buy those +strips I buy the portfolio of strips and + + align:start position:0% +strips I buy the portfolio of strips and + + + align:start position:0% +strips I buy the portfolio of strips and +then I take this Bond that's trading in + + align:start position:0% +then I take this Bond that's trading in + + + align:start position:0% +then I take this Bond that's trading in +the Open Marketplace and I sell + + align:start position:0% +the Open Marketplace and I sell + + + align:start position:0% +the Open Marketplace and I sell +it how do I sell something I don't + + align:start position:0% +it how do I sell something I don't + + + align:start position:0% +it how do I sell something I don't +own short sell it yes Short Selling + + align:start position:0% +own short sell it yes Short Selling + + + align:start position:0% +own short sell it yes Short Selling +which you can read about in bre Myers + + align:start position:0% +which you can read about in bre Myers + + + align:start position:0% +which you can read about in bre Myers +and Allen is when if you don't own the + + align:start position:0% +and Allen is when if you don't own the + + + align:start position:0% +and Allen is when if you don't own the +security you can borrow it from the + + align:start position:0% +security you can borrow it from the + + + align:start position:0% +security you can borrow it from the +broker and then sell it and you'll + + align:start position:0% +broker and then sell it and you'll + + + align:start position:0% +broker and then sell it and you'll +collect the money from selling it now + + align:start position:0% +collect the money from selling it now + + + align:start position:0% +collect the money from selling it now +the broker obviously is going to want to + + align:start position:0% +the broker obviously is going to want to + + + align:start position:0% +the broker obviously is going to want to +keep you to keep that money uh in that + + align:start position:0% +keep you to keep that money uh in that + + + align:start position:0% +keep you to keep that money uh in that +brokerage firm so that you don't run + + align:start position:0% +brokerage firm so that you don't run + + + align:start position:0% +brokerage firm so that you don't run +away with it because you've borrowed the + + align:start position:0% +away with it because you've borrowed the + + + align:start position:0% +away with it because you've borrowed the +security at some point you've got to pay + + align:start position:0% +security at some point you've got to pay + + + align:start position:0% +security at some point you've got to pay +it back you've got to return that + + align:start position:0% +it back you've got to return that + + + align:start position:0% +it back you've got to return that +security right so the transaction is you + + align:start position:0% +security right so the transaction is you + + + align:start position:0% +security right so the transaction is you +buy these strips you short sell the bond + + align:start position:0% +buy these strips you short sell the bond + + + align:start position:0% +buy these strips you short sell the bond +and and what have you done have you made + + align:start position:0% +and and what have you done have you made + + + align:start position:0% +and and what have you done have you made +money or lost money on day one you've + + align:start position:0% +money or lost money on day one you've + + + align:start position:0% +money or lost money on day one you've +made money why because buying costs less + + align:start position:0% +made money why because buying costs less + + + align:start position:0% +made money why because buying costs less +than the amount of money you get from + + align:start position:0% +than the amount of money you get from + + + align:start position:0% +than the amount of money you get from +selling and how do you know that CU I + + align:start position:0% +selling and how do you know that CU I + + + align:start position:0% +selling and how do you know that CU I +just assumed that it's more expensive + + align:start position:0% +just assumed that it's more expensive + + + align:start position:0% +just assumed that it's more expensive +for you to get the three-year Bond than + + align:start position:0% +for you to get the three-year Bond than + + + align:start position:0% +for you to get the three-year Bond than +the package of strips so you've made + + align:start position:0% +the package of strips so you've made + + + align:start position:0% +the package of strips so you've made +money + + align:start position:0% +money + + + align:start position:0% +money +today but you have no further + + align:start position:0% +today but you have no further + + + align:start position:0% +today but you have no further +obligations because what you end up + + align:start position:0% +obligations because what you end up + + + align:start position:0% +obligations because what you end up +getting from the strips you've bought + + align:start position:0% +getting from the strips you've bought + + + align:start position:0% +getting from the strips you've bought +the strips so you're going to get their + + align:start position:0% +the strips so you're going to get their + + + align:start position:0% +the strips so you're going to get their +coupons or their face value you're going + + align:start position:0% +coupons or their face value you're going + + + align:start position:0% +coupons or their face value you're going +to use those to pay the coupons of the + + align:start position:0% +to use those to pay the coupons of the + + + align:start position:0% +to use those to pay the coupons of the +bonds that you + + align:start position:0% +bonds that you + + + align:start position:0% +bonds that you +sold and therefore you have no further + + align:start position:0% +sold and therefore you have no further + + + align:start position:0% +sold and therefore you have no further +obligations but you have a pile of money + + align:start position:0% +obligations but you have a pile of money + + + align:start position:0% +obligations but you have a pile of money +in front of you that's pretty cool and + + align:start position:0% +in front of you that's pretty cool and + + + align:start position:0% +in front of you that's pretty cool and +if you do that a lot that pile of money + + align:start position:0% +if you do that a lot that pile of money + + + align:start position:0% +if you do that a lot that pile of money +grows so obviously we know it's not easy + + align:start position:0% +grows so obviously we know it's not easy + + + align:start position:0% +grows so obviously we know it's not easy +to do that and if it's not easy to do + + align:start position:0% +to do that and if it's not easy to do + + + align:start position:0% +to do that and if it's not easy to do +that that means that our assumption that + + align:start position:0% +that that means that our assumption that + + + align:start position:0% +that that means that our assumption that +the bond was greater than the cost of + + align:start position:0% +the bond was greater than the cost of + + + align:start position:0% +the bond was greater than the cost of +the strips can't be true if you reverse + + align:start position:0% +the strips can't be true if you reverse + + + align:start position:0% +the strips can't be true if you reverse +the logic you get the same kind of + + align:start position:0% +the logic you get the same kind of + + + align:start position:0% +the logic you get the same kind of +argument in Reverse therefore the only + + align:start position:0% +argument in Reverse therefore the only + + + align:start position:0% +argument in Reverse therefore the only +thing that can be is that the prices are + + align:start position:0% +thing that can be is that the prices are + + + align:start position:0% +thing that can be is that the prices are +equal to each other next time what we're + + align:start position:0% +equal to each other next time what we're + + + align:start position:0% +equal to each other next time what we're +going to do is show that a little bit of + + align:start position:0% +going to do is show that a little bit of + + + align:start position:0% +going to do is show that a little bit of +linear algebra is going to allow you to + + align:start position:0% +linear algebra is going to allow you to + + + align:start position:0% +linear algebra is going to allow you to +make tons of money by comparing all + + align:start position:0% +make tons of money by comparing all + + + align:start position:0% +make tons of money by comparing all +sorts of bonds and looking at these kind + + align:start position:0% +sorts of bonds and looking at these kind + + + align:start position:0% +sorts of bonds and looking at these kind +of relationships okay I'll see you at 4 + + align:start position:0% +of relationships okay I'll see you at 4 + + + align:start position:0% +of relationships okay I'll see you at 4 +o'cl if if you're interested \ No newline at end of file diff --git a/z1lAn4GMaFs.txt b/z1lAn4GMaFs.txt new file mode 100644 index 0000000000000000000000000000000000000000..d81d3b884452f12f2f4e3f33fa531f4644cc535c --- /dev/null +++ b/z1lAn4GMaFs.txt @@ -0,0 +1,883 @@ +align:start position:0% + +before we get going with our discussion + + align:start position:0% +before we get going with our discussion + + + align:start position:0% +before we get going with our discussion +of inference methods it is worth looking + + align:start position:0% +of inference methods it is worth looking + + + align:start position:0% +of inference methods it is worth looking +at the big picture for some perspective + + align:start position:0% +at the big picture for some perspective + + + align:start position:0% +at the big picture for some perspective +so far we have concentrated on ways to + + align:start position:0% +so far we have concentrated on ways to + + + align:start position:0% +so far we have concentrated on ways to +analyze probability models this part of + + align:start position:0% +analyze probability models this part of + + + align:start position:0% +analyze probability models this part of +the picture if our model has been + + align:start position:0% +the picture if our model has been + + + align:start position:0% +the picture if our model has been +selected in a careful way then it should + + align:start position:0% +selected in a careful way then it should + + + align:start position:0% +selected in a careful way then it should +also be relevant to the real world and + + align:start position:0% +also be relevant to the real world and + + + align:start position:0% +also be relevant to the real world and +help us make predictions or decisions + + align:start position:0% +help us make predictions or decisions + + + align:start position:0% +help us make predictions or decisions +but how do we know that this is the case + + align:start position:0% +but how do we know that this is the case + + + align:start position:0% +but how do we know that this is the case +this is why we need to look at data that + + align:start position:0% +this is why we need to look at data that + + + align:start position:0% +this is why we need to look at data that +are generated by the real world and then + + align:start position:0% +are generated by the real world and then + + + align:start position:0% +are generated by the real world and then +use these to come up with the model this + + align:start position:0% +use these to come up with the model this + + + align:start position:0% +use these to come up with the model this +is what the field of inference and + + align:start position:0% +is what the field of inference and + + + align:start position:0% +is what the field of inference and +statistics is all about this field has + + align:start position:0% +statistics is all about this field has + + + align:start position:0% +statistics is all about this field has +undergone a radical transformation in + + align:start position:0% +undergone a radical transformation in + + + align:start position:0% +undergone a radical transformation in +recent years + + align:start position:0% +recent years + + + align:start position:0% +recent years +I will exaggerate a little but in the + + align:start position:0% +I will exaggerate a little but in the + + + align:start position:0% +I will exaggerate a little but in the +past as the distinction might be called + + align:start position:0% +past as the distinction might be called + + + align:start position:0% +past as the distinction might be called +to look at problems such as this one + + align:start position:0% +to look at problems such as this one + + + align:start position:0% +to look at problems such as this one +you're given data on a few patients and + + align:start position:0% +you're given data on a few patients and + + + align:start position:0% +you're given data on a few patients and +you need to figure out whether a certain + + align:start position:0% +you need to figure out whether a certain + + + align:start position:0% +you need to figure out whether a certain +treatment is effective or not but today + + align:start position:0% +treatment is effective or not but today + + + align:start position:0% +treatment is effective or not but today +as the distinction lives in a dreamland + + align:start position:0% +as the distinction lives in a dreamland + + + align:start position:0% +as the distinction lives in a dreamland +there are tones of data that are + + align:start position:0% +there are tones of data that are + + + align:start position:0% +there are tones of data that are +generated everywhere these allow us to + + align:start position:0% +generated everywhere these allow us to + + + align:start position:0% +generated everywhere these allow us to +build quite detailed large models + + align:start position:0% +build quite detailed large models + + + align:start position:0% +build quite detailed large models +involving thousands of parameters and we + + align:start position:0% +involving thousands of parameters and we + + + align:start position:0% +involving thousands of parameters and we +do have the computational power to do + + align:start position:0% +do have the computational power to do + + + align:start position:0% +do have the computational power to do +all that in this landscape the + + align:start position:0% +all that in this landscape the + + + align:start position:0% +all that in this landscape the +opportunities for a statistician are + + align:start position:0% +opportunities for a statistician are + + + align:start position:0% +opportunities for a statistician are +endless so let me give you a small + + align:start position:0% +endless so let me give you a small + + + align:start position:0% +endless so let me give you a small +representative sample in a somewhat + + align:start position:0% +representative sample in a somewhat + + + align:start position:0% +representative sample in a somewhat +traditional setting one designs a data + + align:start position:0% +traditional setting one designs a data + + + align:start position:0% +traditional setting one designs a data +collection method and then uses these + + align:start position:0% +collection method and then uses these + + + align:start position:0% +collection method and then uses these +data to make a simple prediction this is + + align:start position:0% +data to make a simple prediction this is + + + align:start position:0% +data to make a simple prediction this is +the case for example in polling where + + align:start position:0% +the case for example in polling where + + + align:start position:0% +the case for example in polling where +the purpose is to predict the outcome of + + align:start position:0% +the purpose is to predict the outcome of + + + align:start position:0% +the purpose is to predict the outcome of +an election another field is marketing + + align:start position:0% +an election another field is marketing + + + align:start position:0% +an election another field is marketing +and advertising where the situation is + + align:start position:0% +and advertising where the situation is + + + align:start position:0% +and advertising where the situation is +somewhat similar except now we want to + + align:start position:0% +somewhat similar except now we want to + + + align:start position:0% +somewhat similar except now we want to +make predictions not for a population as + + align:start position:0% +make predictions not for a population as + + + align:start position:0% +make predictions not for a population as +a whole but for each individual consumer + + align:start position:0% +a whole but for each individual consumer + + + align:start position:0% +a whole but for each individual consumer +and the particular application has to do + + align:start position:0% +and the particular application has to do + + + align:start position:0% +and the particular application has to do +with so-called recommendation systems + + align:start position:0% +with so-called recommendation systems + + + align:start position:0% +with so-called recommendation systems +you collect ratings that people give to + + align:start position:0% +you collect ratings that people give to + + + align:start position:0% +you collect ratings that people give to +movies as in a famous competition that + + align:start position:0% +movies as in a famous competition that + + + align:start position:0% +movies as in a famous competition that +was announced by Netflix so you have + + align:start position:0% +was announced by Netflix so you have + + + align:start position:0% +was announced by Netflix so you have +data for + + align:start position:0% +data for + + + align:start position:0% +data for +every movie and the people who have + + align:start position:0% +every movie and the people who have + + + align:start position:0% +every movie and the people who have +watched them you make a note of what + + align:start position:0% +watched them you make a note of what + + + align:start position:0% +watched them you make a note of what +rating that person gave to a particular + + align:start position:0% +rating that person gave to a particular + + + align:start position:0% +rating that person gave to a particular +movie and now after you collect huge + + align:start position:0% +movie and now after you collect huge + + + align:start position:0% +movie and now after you collect huge +amounts of data of this kind you try to + + align:start position:0% +amounts of data of this kind you try to + + + align:start position:0% +amounts of data of this kind you try to +use this information to yes whether for + + align:start position:0% +use this information to yes whether for + + + align:start position:0% +use this information to yes whether for +example this person is interested in + + align:start position:0% +example this person is interested in + + + align:start position:0% +example this person is interested in +this particular movie or not this is a + + align:start position:0% +this particular movie or not this is a + + + align:start position:0% +this particular movie or not this is a +quite difficult problem a quite + + align:start position:0% +quite difficult problem a quite + + + align:start position:0% +quite difficult problem a quite +complicated one and it gave the + + align:start position:0% +complicated one and it gave the + + + align:start position:0% +complicated one and it gave the +community an opportunity to develop + + align:start position:0% +community an opportunity to develop + + + align:start position:0% +community an opportunity to develop +fancier and fancier combinations of + + align:start position:0% +fancier and fancier combinations of + + + align:start position:0% +fancier and fancier combinations of +methods in order to come up with good + + align:start position:0% +methods in order to come up with good + + + align:start position:0% +methods in order to come up with good +predictions of unknown entries in this + + align:start position:0% +predictions of unknown entries in this + + + align:start position:0% +predictions of unknown entries in this +table another field is of course finance + + align:start position:0% +table another field is of course finance + + + align:start position:0% +table another field is of course finance +the markets are truly uncertain and + + align:start position:0% +the markets are truly uncertain and + + + align:start position:0% +the markets are truly uncertain and +there are quite complete historical data + + align:start position:0% +there are quite complete historical data + + + align:start position:0% +there are quite complete historical data +lots of them how do we use these data to + + align:start position:0% +lots of them how do we use these data to + + + align:start position:0% +lots of them how do we use these data to +make predictions coming now to the + + align:start position:0% +make predictions coming now to the + + + align:start position:0% +make predictions coming now to the +Natural Sciences a revolution has been + + align:start position:0% +Natural Sciences a revolution has been + + + align:start position:0% +Natural Sciences a revolution has been +taking place in the life sciences there + + align:start position:0% +taking place in the life sciences there + + + align:start position:0% +taking place in the life sciences there +are tons of genomic data to be processed + + align:start position:0% +are tons of genomic data to be processed + + + align:start position:0% +are tons of genomic data to be processed +to find out what combination of genes + + align:start position:0% +to find out what combination of genes + + + align:start position:0% +to find out what combination of genes +causes what disease or we may want to + + align:start position:0% +causes what disease or we may want to + + + align:start position:0% +causes what disease or we may want to +find out the details of the chemical + + align:start position:0% +find out the details of the chemical + + + align:start position:0% +find out the details of the chemical +reactions inside the living cell and + + align:start position:0% +reactions inside the living cell and + + + align:start position:0% +reactions inside the living cell and +there is an upcoming new frontier in + + align:start position:0% +there is an upcoming new frontier in + + + align:start position:0% +there is an upcoming new frontier in +neuroscience where there will be vast + + align:start position:0% +neuroscience where there will be vast + + + align:start position:0% +neuroscience where there will be vast +amounts of data that will be generated + + align:start position:0% +amounts of data that will be generated + + + align:start position:0% +amounts of data that will be generated +these will consist of brain measurements + + align:start position:0% +these will consist of brain measurements + + + align:start position:0% +these will consist of brain measurements +of measurements of what each neuron is + + align:start position:0% +of measurements of what each neuron is + + + align:start position:0% +of measurements of what each neuron is +doing and hopefully these will lead us + + align:start position:0% +doing and hopefully these will lead us + + + align:start position:0% +doing and hopefully these will lead us +one day to finding out what the brain + + align:start position:0% +one day to finding out what the brain + + + align:start position:0% +one day to finding out what the brain +really does and how it works in the + + align:start position:0% +really does and how it works in the + + + align:start position:0% +really does and how it works in the +sciences the list is endless it goes on + + align:start position:0% +sciences the list is endless it goes on + + + align:start position:0% +sciences the list is endless it goes on +and on in modeling climate and the + + align:start position:0% +and on in modeling climate and the + + + align:start position:0% +and on in modeling climate and the +environment scientists are using huge + + align:start position:0% +environment scientists are using huge + + + align:start position:0% +environment scientists are using huge +models these days which they try to + + align:start position:0% +models these days which they try to + + + align:start position:0% +models these days which they try to +calibrate using lots of available data + + align:start position:0% +calibrate using lots of available data + + + align:start position:0% +calibrate using lots of available data +and in physics as well scientists use + + align:start position:0% +and in physics as well scientists use + + + align:start position:0% +and in physics as well scientists use +fancy inference methods trying to find + + align:start position:0% +fancy inference methods trying to find + + + align:start position:0% +fancy inference methods trying to find +needles in a haystack like rare + + align:start position:0% +needles in a haystack like rare + + + align:start position:0% +needles in a haystack like rare +particles or remote planets + + align:start position:0% +particles or remote planets + + + align:start position:0% +particles or remote planets +finally engineering is a fight against + + align:start position:0% +finally engineering is a fight against + + + align:start position:0% +finally engineering is a fight against +noise engineers try to make devices that + + align:start position:0% +noise engineers try to make devices that + + + align:start position:0% +noise engineers try to make devices that +will work in uncertain environments the + + align:start position:0% +will work in uncertain environments the + + + align:start position:0% +will work in uncertain environments the +field of signal processing is a prime + + align:start position:0% +field of signal processing is a prime + + + align:start position:0% +field of signal processing is a prime +example where the generic question is to + + align:start position:0% +example where the generic question is to + + + align:start position:0% +example where the generic question is to +recover the content of a signal for + + align:start position:0% +recover the content of a signal for + + + align:start position:0% +recover the content of a signal for +example the content of a radio + + align:start position:0% +example the content of a radio + + + align:start position:0% +example the content of a radio +transmission when a signal is received + + align:start position:0% +transmission when a signal is received + + + align:start position:0% +transmission when a signal is received +after it gets corrupted by noise I could + + align:start position:0% +after it gets corrupted by noise I could + + + align:start position:0% +after it gets corrupted by noise I could +go on and on for hours generating lists + + align:start position:0% +go on and on for hours generating lists + + + align:start position:0% +go on and on for hours generating lists +of this kind but we have to stop + + align:start position:0% +of this kind but we have to stop + + + align:start position:0% +of this kind but we have to stop +somewhere the bottom line is that the + + align:start position:0% +somewhere the bottom line is that the + + + align:start position:0% +somewhere the bottom line is that the +opportunities and the needs are vast for + + align:start position:0% +opportunities and the needs are vast for + + + align:start position:0% +opportunities and the needs are vast for +this reason we will look into the core + + align:start position:0% +this reason we will look into the core + + + align:start position:0% +this reason we will look into the core +methodologies that come into play + + align:start position:0% +methodologies that come into play + + + align:start position:0% +methodologies that come into play +fortunately for us the fundamental + + align:start position:0% +fortunately for us the fundamental + + + align:start position:0% +fortunately for us the fundamental +concepts and approaches turn out to be + + align:start position:0% +concepts and approaches turn out to be + + + align:start position:0% +concepts and approaches turn out to be +the same independent of the particular + + align:start position:0% +the same independent of the particular + + + align:start position:0% +the same independent of the particular +application \ No newline at end of file diff --git a/zC78xmSbhAY.txt b/zC78xmSbhAY.txt new file mode 100644 index 0000000000000000000000000000000000000000..abbeefbeccb2bb078891767d2145b2ec8509405c --- /dev/null +++ b/zC78xmSbhAY.txt @@ -0,0 +1,12083 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Okay. So uh uh first uh I was say I + + align:start position:0% +Okay. So uh uh first uh I was say I + + + align:start position:0% +Okay. So uh uh first uh I was say I +think you should start thinking about + + align:start position:0% +think you should start thinking about + + + align:start position:0% +think you should start thinking about +the um project + + align:start position:0% +the um project + + + align:start position:0% +the um project +and what uh I'm looking for uh is a u + + align:start position:0% +and what uh I'm looking for uh is a u + + + align:start position:0% +and what uh I'm looking for uh is a u +short report paper type report. I want + + align:start position:0% +short report paper type report. I want + + + align:start position:0% +short report paper type report. I want +to limit to only five pages. Okay. And + + align:start position:0% +to limit to only five pages. Okay. And + + + align:start position:0% +to limit to only five pages. Okay. And +uh uh it could be uh anything related to + + align:start position:0% +uh uh it could be uh anything related to + + + align:start position:0% +uh uh it could be uh anything related to +this subject right. So if you happen to + + align:start position:0% +this subject right. So if you happen to + + + align:start position:0% +this subject right. So if you happen to +be work on something you want to extend + + align:start position:0% +be work on something you want to extend + + + align:start position:0% +be work on something you want to extend +and apply the knowledge that you you + + align:start position:0% +and apply the knowledge that you you + + + align:start position:0% +and apply the knowledge that you you +learn in this subject you're welcome to + + align:start position:0% +learn in this subject you're welcome to + + + align:start position:0% +learn in this subject you're welcome to +do so. And in fact uh uh I + + align:start position:0% +do so. And in fact uh uh I + + + align:start position:0% +do so. And in fact uh uh I +um wrote a paper u based on term paper + + align:start position:0% +um wrote a paper u based on term paper + + + align:start position:0% +um wrote a paper u based on term paper +uh I was working on when I was a + + align:start position:0% +uh I was working on when I was a + + + align:start position:0% +uh I was working on when I was a +graduate student. I thought that that's + + align:start position:0% +graduate student. I thought that that's + + + align:start position:0% +graduate student. I thought that that's +that was a good experience. In fact, + + align:start position:0% +that was a good experience. In fact, + + + align:start position:0% +that was a good experience. In fact, +that turns out to be the first paper on + + align:start position:0% +that turns out to be the first paper on + + + align:start position:0% +that turns out to be the first paper on +thermal conductivity of quantum wells. + + align:start position:0% +thermal conductivity of quantum wells. + + + align:start position:0% +thermal conductivity of quantum wells. +Um I was taking a long linear optics + + align:start position:0% +Um I was taking a long linear optics + + + align:start position:0% +Um I was taking a long linear optics +course. I spend uh the whole semester + + align:start position:0% +course. I spend uh the whole semester + + + align:start position:0% +course. I spend uh the whole semester +and uh at the end I went to professor I + + align:start position:0% +and uh at the end I went to professor I + + + align:start position:0% +and uh at the end I went to professor I +don't understand what you talk + + align:start position:0% +don't understand what you talk + + + align:start position:0% +don't understand what you talk +uh and he want a term paper and I said + + align:start position:0% +uh and he want a term paper and I said + + + align:start position:0% +uh and he want a term paper and I said +how about uh um he was talking about + + align:start position:0% +how about uh um he was talking about + + + align:start position:0% +how about uh um he was talking about +double site the fman diagram so I I + + align:start position:0% +double site the fman diagram so I I + + + align:start position:0% +double site the fman diagram so I I +still don't quite understand what what + + align:start position:0% +still don't quite understand what what + + + align:start position:0% +still don't quite understand what what +say the fman diagram but uh so I said + + align:start position:0% +say the fman diagram but uh so I said + + + align:start position:0% +say the fman diagram but uh so I said +how about I worked on a paper on quantum + + align:start position:0% +how about I worked on a paper on quantum + + + align:start position:0% +how about I worked on a paper on quantum +wells thermal connectivity quantum wells + + align:start position:0% +wells thermal connectivity quantum wells + + + align:start position:0% +wells thermal connectivity quantum wells +said fine that's fine so I wrote the + + align:start position:0% +said fine that's fine so I wrote the + + + align:start position:0% +said fine that's fine so I wrote the +term paper and uh I continued to work on + + align:start position:0% +term paper and uh I continued to work on + + + align:start position:0% +term paper and uh I continued to work on +it and uh I eventually actually + + align:start position:0% +it and uh I eventually actually + + + align:start position:0% +it and uh I eventually actually +published a paper on the thermal + + align:start position:0% +published a paper on the thermal + + + align:start position:0% +published a paper on the thermal +conductivity of quantum wells + + align:start position:0% +conductivity of quantum wells + + + align:start position:0% +conductivity of quantum wells +and uh uh looking back at there because + + align:start position:0% +and uh uh looking back at there because + + + align:start position:0% +and uh uh looking back at there because +that was a I was doing pretty much a + + align:start position:0% +that was a I was doing pretty much a + + + align:start position:0% +that was a I was doing pretty much a +boardman equation. So completely forgot + + align:start position:0% +boardman equation. So completely forgot + + + align:start position:0% +boardman equation. So completely forgot +the quantization. + + align:start position:0% +the quantization. + + + align:start position:0% +the quantization. +But uh uh um it turns out that most of + + align:start position:0% +But uh uh um it turns out that most of + + + align:start position:0% +But uh uh um it turns out that most of +the stuff were correct. Not that + + align:start position:0% +the stuff were correct. Not that + + + align:start position:0% +the stuff were correct. Not that +everything was correct. And uh uh so uh + + align:start position:0% +everything was correct. And uh uh so uh + + + align:start position:0% +everything was correct. And uh uh so uh +what I want to say is I encourage you to + + align:start position:0% +what I want to say is I encourage you to + + + align:start position:0% +what I want to say is I encourage you to +think about subject relative research + + align:start position:0% +think about subject relative research + + + align:start position:0% +think about subject relative research +uh uh you can expand it. uh or if you uh + + align:start position:0% +uh uh you can expand it. uh or if you uh + + + align:start position:0% +uh uh you can expand it. uh or if you uh +uh you're not say you don't have a + + align:start position:0% +uh you're not say you don't have a + + + align:start position:0% +uh you're not say you don't have a +subject, you can uh do a literature + + align:start position:0% +subject, you can uh do a literature + + + align:start position:0% +subject, you can uh do a literature +review. Let me say you're interested in + + align:start position:0% +review. Let me say you're interested in + + + align:start position:0% +review. Let me say you're interested in +a specific topic. Let's say + + align:start position:0% +a specific topic. Let's say + + + align:start position:0% +a specific topic. Let's say +metamaterials or plasmonics or any any + + align:start position:0% +metamaterials or plasmonics or any any + + + align:start position:0% +metamaterials or plasmonics or any any +of the thing that we mentioned or you + + align:start position:0% +of the thing that we mentioned or you + + + align:start position:0% +of the thing that we mentioned or you +read, right? You're going to apply the + + align:start position:0% +read, right? You're going to apply the + + + align:start position:0% +read, right? You're going to apply the +knowledge. you can do a a literature + + align:start position:0% +knowledge. you can do a a literature + + + align:start position:0% +knowledge. you can do a a literature +review and expand on it and maybe you + + align:start position:0% +review and expand on it and maybe you + + + align:start position:0% +review and expand on it and maybe you +say okay based on that maybe this is a a + + align:start position:0% +say okay based on that maybe this is a a + + + align:start position:0% +say okay based on that maybe this is a a +interesting problem that I can continue + + align:start position:0% +interesting problem that I can continue + + + align:start position:0% +interesting problem that I can continue +working on you can work after this uh + + align:start position:0% +working on you can work after this uh + + + align:start position:0% +working on you can work after this uh +semester + + align:start position:0% +semester + + + align:start position:0% +semester +uh you can always you're always welcome + + align:start position:0% +uh you can always you're always welcome + + + align:start position:0% +uh you can always you're always welcome +to discuss with me and if you really + + align:start position:0% +to discuss with me and if you really + + + align:start position:0% +to discuss with me and if you really +don't say don't have a a topic come talk + + align:start position:0% +don't say don't have a a topic come talk + + + align:start position:0% +don't say don't have a a topic come talk +to me I think I can always figure + + align:start position:0% +to me I think I can always figure + + + align:start position:0% +to me I think I can always figure +something uh we can negotiate and say + + align:start position:0% +something uh we can negotiate and say + + + align:start position:0% +something uh we can negotiate and say +what you would be interested. + + align:start position:0% +what you would be interested. + + + align:start position:0% +what you would be interested. +Okay. Uh so uh that's on the term paper. + + align:start position:0% +Okay. Uh so uh that's on the term paper. + + + align:start position:0% +Okay. Uh so uh that's on the term paper. +Uh my uh uh so now you have uh all + + align:start position:0% +Uh my uh uh so now you have uh all + + + align:start position:0% +Uh my uh uh so now you have uh all +turned in. I say your first uh qu first + + align:start position:0% +turned in. I say your first uh qu first + + + align:start position:0% +turned in. I say your first uh qu first +midterm and redo it. Any questions + + align:start position:0% +midterm and redo it. Any questions + + + align:start position:0% +midterm and redo it. Any questions +on those + + align:start position:0% +on those + + + align:start position:0% +on those +first midterm? + + align:start position:0% +first midterm? + + + align:start position:0% +first midterm? +I think say when I was uh looking at + + align:start position:0% +I think say when I was uh looking at + + + align:start position:0% +I think say when I was uh looking at +where uh or + + align:start position:0% +where uh or + + + align:start position:0% +where uh or +most mistakes made I think uh uh one of + + align:start position:0% +most mistakes made I think uh uh one of + + + align:start position:0% +most mistakes made I think uh uh one of +this is the um the depths of the eval + + align:start position:0% +this is the um the depths of the eval + + + align:start position:0% +this is the um the depths of the eval +way right and uh uh probably uh because + + align:start position:0% +way right and uh uh probably uh because + + + align:start position:0% +way right and uh uh probably uh because +unless you go back you written down and + + align:start position:0% +unless you go back you written down and + + + align:start position:0% +unless you go back you written down and +it may not be easy to figure out what's + + align:start position:0% +it may not be easy to figure out what's + + + align:start position:0% +it may not be easy to figure out what's +the depths but say the kay is you should + + align:start position:0% +the depths but say the kay is you should + + + align:start position:0% +the depths but say the kay is you should +be able to write down the plane wave + + align:start position:0% +be able to write down the plane wave + + + align:start position:0% +be able to write down the plane wave +expressions, right? And if you have the + + align:start position:0% +expressions, right? And if you have the + + + align:start position:0% +expressions, right? And if you have the +plane wave expression and you use your + + align:start position:0% +plane wave expression and you use your + + + align:start position:0% +plane wave expression and you use your +snail law and you can find the angle + + align:start position:0% +snail law and you can find the angle + + + align:start position:0% +snail law and you can find the angle +when the angle cosine theta or sin theta + + align:start position:0% +when the angle cosine theta or sin theta + + + align:start position:0% +when the angle cosine theta or sin theta +is larger than one. So you use your + + align:start position:0% +is larger than one. So you use your + + + align:start position:0% +is larger than one. So you use your +cosine theta one square root of 1 minus + + align:start position:0% +cosine theta one square root of 1 minus + + + align:start position:0% +cosine theta one square root of 1 minus +that sin theta squared and they plug in + + align:start position:0% +that sin theta squared and they plug in + + + align:start position:0% +that sin theta squared and they plug in +the plan wave. you should be able to + + align:start position:0% +the plan wave. you should be able to + + + align:start position:0% +the plan wave. you should be able to +find out what's the uh penetration depth + + align:start position:0% +find out what's the uh penetration depth + + + align:start position:0% +find out what's the uh penetration depth +of the evallescent wave. + + align:start position:0% +of the evallescent wave. + + + align:start position:0% +of the evallescent wave. +And there was another question about the + + align:start position:0% +And there was another question about the + + + align:start position:0% +And there was another question about the +uh what's the number of molecules + + align:start position:0% +uh what's the number of molecules + + + align:start position:0% +uh what's the number of molecules +having certain speed right that's a gas + + align:start position:0% +having certain speed right that's a gas + + + align:start position:0% +having certain speed right that's a gas +molecule + + align:start position:0% +molecule + + + align:start position:0% +molecule +and uh so there I would guess uh + + align:start position:0% +and uh so there I would guess uh + + + align:start position:0% +and uh so there I would guess uh +probably you might be get stuck in + + align:start position:0% +probably you might be get stuck in + + + align:start position:0% +probably you might be get stuck in +what's the total number of you need to + + align:start position:0% +what's the total number of you need to + + + align:start position:0% +what's the total number of you need to +start with the total number of molecules + + align:start position:0% +start with the total number of molecules + + + align:start position:0% +start with the total number of molecules +all right per unit volume and that's the + + align:start position:0% +all right per unit volume and that's the + + + align:start position:0% +all right per unit volume and that's the +first that you need to given temperature + + align:start position:0% +first that you need to given temperature + + + align:start position:0% +first that you need to given temperature +given pressure you could use the ideal + + align:start position:0% +given pressure you could use the ideal + + + align:start position:0% +given pressure you could use the ideal +gas four to find out what's local + + align:start position:0% +gas four to find out what's local + + + align:start position:0% +gas four to find out what's local +density and and then use a maxwell + + align:start position:0% +density and and then use a maxwell + + + align:start position:0% +density and and then use a maxwell +velocity distribution to say what's the + + align:start position:0% +velocity distribution to say what's the + + + align:start position:0% +velocity distribution to say what's the +total number what's the number of + + align:start position:0% +total number what's the number of + + + align:start position:0% +total number what's the number of +molecules that have a certain velocity + + align:start position:0% +molecules that have a certain velocity + + + align:start position:0% +molecules that have a certain velocity +and uh uh then I think it's a matter of + + align:start position:0% +and uh uh then I think it's a matter of + + + align:start position:0% +and uh uh then I think it's a matter of +time um most of you couldn't finish the + + align:start position:0% +time um most of you couldn't finish the + + + align:start position:0% +time um most of you couldn't finish the +last problem uh where uh we're looking + + align:start position:0% +last problem uh where uh we're looking + + + align:start position:0% +last problem uh where uh we're looking +at the uh fullon uh say the equivalent + + align:start position:0% +at the uh fullon uh say the equivalent + + + align:start position:0% +at the uh fullon uh say the equivalent +of a fullon distribution + + align:start position:0% +of a fullon distribution + + + align:start position:0% +of a fullon distribution +uh to the black body radiation where is + + align:start position:0% +uh to the black body radiation where is + + + align:start position:0% +uh to the black body radiation where is +the peak w displacements no right so uh + + align:start position:0% +the peak w displacements no right so uh + + + align:start position:0% +the peak w displacements no right so uh +you find out that in many case a low + + align:start position:0% +you find out that in many case a low + + + align:start position:0% +you find out that in many case a low +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +yeah you do have a peak but at high + + align:start position:0% +yeah you do have a peak but at high + + + align:start position:0% +yeah you do have a peak but at high +temperature that wavelength peak + + align:start position:0% +temperature that wavelength peak + + + align:start position:0% +temperature that wavelength peak +wavelength too short compared two times + + align:start position:0% +wavelength too short compared two times + + + align:start position:0% +wavelength too short compared two times +the lattice constant so you actually + + align:start position:0% +the lattice constant so you actually + + + align:start position:0% +the lattice constant so you actually +never reach that peak + + align:start position:0% +never reach that peak + + + align:start position:0% +never reach that peak +it will be uh you you should uh uh + + align:start position:0% +it will be uh you you should uh uh + + + align:start position:0% +it will be uh you you should uh uh +continue to try that out + + align:start position:0% +continue to try that out + + + align:start position:0% +continue to try that out +and for many years um I haven't done + + align:start position:0% +and for many years um I haven't done + + + align:start position:0% +and for many years um I haven't done +that myself until this time I said I + + align:start position:0% +that myself until this time I said I + + + align:start position:0% +that myself until this time I said I +have to make a problem out of it uh this + + align:start position:0% +have to make a problem out of it uh this + + + align:start position:0% +have to make a problem out of it uh this +is the optical absorption right that's + + align:start position:0% +is the optical absorption right that's + + + align:start position:0% +is the optical absorption right that's +the second long l long longer problem uh + + align:start position:0% +the second long l long longer problem uh + + + align:start position:0% +the second long l long longer problem uh +what's the optical absorption for a + + align:start position:0% +what's the optical absorption for a + + + align:start position:0% +what's the optical absorption for a +direct gap semiconductor + + align:start position:0% +direct gap semiconductor + + + align:start position:0% +direct gap semiconductor +and it's a matter of joint dens of + + align:start position:0% +and it's a matter of joint dens of + + + align:start position:0% +and it's a matter of joint dens of +states + + align:start position:0% +states + + + align:start position:0% +states +so uh if I have + + align:start position:0% +so uh if I have + + + align:start position:0% +so uh if I have +right so I have a semiconductor + + align:start position:0% +right so I have a semiconductor + + + align:start position:0% +right so I have a semiconductor +dispersion and I have a photon this is + + align:start position:0% +dispersion and I have a photon this is + + + align:start position:0% +dispersion and I have a photon this is +the nift electron uh from from the + + align:start position:0% +the nift electron uh from from the + + + align:start position:0% +the nift electron uh from from the +valance band to conduction band and then + + align:start position:0% +valance band to conduction band and then + + + align:start position:0% +valance band to conduction band and then +you need to say this is my photon energy + + align:start position:0% +you need to say this is my photon energy + + + align:start position:0% +you need to say this is my photon energy +h omega mu and how is it related to k so + + align:start position:0% +h omega mu and how is it related to k so + + + align:start position:0% +h omega mu and how is it related to k so +you you need to f first write down + + align:start position:0% +you you need to f first write down + + + align:start position:0% +you you need to f first write down +because you know this parabola this + + align:start position:0% +because you know this parabola this + + + align:start position:0% +because you know this parabola this +parabola and the difference of these two + + align:start position:0% +parabola and the difference of these two + + + align:start position:0% +parabola and the difference of these two +energy gives you the photon energy + + align:start position:0% +energy gives you the photon energy + + + align:start position:0% +energy gives you the photon energy +Right. So once you have photon energy or + + align:start position:0% +Right. So once you have photon energy or + + + align:start position:0% +Right. So once you have photon energy or +frequency versus K and you can use the + + align:start position:0% +frequency versus K and you can use the + + + align:start position:0% +frequency versus K and you can use the +um normal way we do dens of states + + align:start position:0% +um normal way we do dens of states + + + align:start position:0% +um normal way we do dens of states +because the absorption depends on how + + align:start position:0% +because the absorption depends on how + + + align:start position:0% +because the absorption depends on how +many states you have and this is in fact + + align:start position:0% +many states you have and this is in fact + + + align:start position:0% +many states you have and this is in fact +called the joint dens of states between + + align:start position:0% +called the joint dens of states between + + + align:start position:0% +called the joint dens of states between +the balance band and conduction band. + + align:start position:0% +the balance band and conduction band. + + + align:start position:0% +the balance band and conduction band. +And then it turns out it's same as your + + align:start position:0% +And then it turns out it's same as your + + + align:start position:0% +And then it turns out it's same as your +bulk material that's the square root of + + align:start position:0% +bulk material that's the square root of + + + align:start position:0% +bulk material that's the square root of +E months is the bank gap right. So uh + + align:start position:0% +E months is the bank gap right. So uh + + + align:start position:0% +E months is the bank gap right. So uh +the absorption of the uh light u for uh + + align:start position:0% +the absorption of the uh light u for uh + + + align:start position:0% +the absorption of the uh light u for uh +um typical semiconductor this is uh this + + align:start position:0% +um typical semiconductor this is uh this + + + align:start position:0% +um typical semiconductor this is uh this +curve of absorption is a reflection of + + align:start position:0% +curve of absorption is a reflection of + + + align:start position:0% +curve of absorption is a reflection of +the joint densel states and of course + + align:start position:0% +the joint densel states and of course + + + align:start position:0% +the joint densel states and of course +you have the population right we didn't + + align:start position:0% +you have the population right we didn't + + + align:start position:0% +you have the population right we didn't +say okay you have to say how many + + align:start position:0% +say okay you have to say how many + + + align:start position:0% +say okay you have to say how many +electrons here how many amplitates here + + align:start position:0% +electrons here how many amplitates here + + + align:start position:0% +electrons here how many amplitates here +if I do it I really need to say this is + + align:start position:0% +if I do it I really need to say this is + + + align:start position:0% +if I do it I really need to say this is +a f And here f for the number of + + align:start position:0% +a f And here f for the number of + + + align:start position:0% +a f And here f for the number of +electron here here is empty. So so + + align:start position:0% +electron here here is empty. So so + + + align:start position:0% +electron here here is empty. So so +that's a one month f and that's a + + align:start position:0% +that's a one month f and that's a + + + align:start position:0% +that's a one month f and that's a +different f because there if you + + align:start position:0% +different f because there if you + + + align:start position:0% +different f because there if you +chemical potential is here and you say + + align:start position:0% +chemical potential is here and you say + + + align:start position:0% +chemical potential is here and you say +the uh say fmy dro is say energy minus + + align:start position:0% +the uh say fmy dro is say energy minus + + + align:start position:0% +the uh say fmy dro is say energy minus +mu and here is the balance band energy + + align:start position:0% +mu and here is the balance band energy + + + align:start position:0% +mu and here is the balance band energy +minus mu there right. So + + align:start position:0% +minus mu there right. So + + + align:start position:0% +minus mu there right. So +uh basically + + align:start position:0% +uh basically + + + align:start position:0% +uh basically +uh if you force yourself going through + + align:start position:0% +uh if you force yourself going through + + + align:start position:0% +uh if you force yourself going through +those problems many times you can + + align:start position:0% +those problems many times you can + + + align:start position:0% +those problems many times you can +understand + + align:start position:0% +understand + + + align:start position:0% +understand +uh a lot of the basics that you say and + + align:start position:0% +uh a lot of the basics that you say and + + + align:start position:0% +uh a lot of the basics that you say and +I let I did not do this before and uh uh + + align:start position:0% +I let I did not do this before and uh uh + + + align:start position:0% +I let I did not do this before and uh uh +uh I this time I said okay I give you + + align:start position:0% +uh I this time I said okay I give you + + + align:start position:0% +uh I this time I said okay I give you +problems I have first do it myself. + + align:start position:0% +problems I have first do it myself. + + + align:start position:0% +problems I have first do it myself. +Any questions? + + align:start position:0% + + + + align:start position:0% + +Okay. Uh so if not let's come back and + + align:start position:0% +Okay. Uh so if not let's come back and + + + align:start position:0% +Okay. Uh so if not let's come back and +uh uh if we think what we're talking the + + align:start position:0% +uh uh if we think what we're talking the + + + align:start position:0% +uh uh if we think what we're talking the +last time we talk about this whip to + + align:start position:0% +last time we talk about this whip to + + + align:start position:0% +last time we talk about this whip to +particle transition and from that I say + + align:start position:0% +particle transition and from that I say + + + align:start position:0% +particle transition and from that I say +from now on I'm going to neglect the + + align:start position:0% +from now on I'm going to neglect the + + + align:start position:0% +from now on I'm going to neglect the +phase of the energy carriers uh the plan + + align:start position:0% +phase of the energy carriers uh the plan + + + align:start position:0% +phase of the energy carriers uh the plan +wave. I'm not no longer carrying the + + align:start position:0% +wave. I'm not no longer carrying the + + + align:start position:0% +wave. I'm not no longer carrying the +face. I'm just look at the the + + align:start position:0% +face. I'm just look at the the + + + align:start position:0% +face. I'm just look at the the +trajectory and treat them as billables + + align:start position:0% +trajectory and treat them as billables + + + align:start position:0% +trajectory and treat them as billables +right so um look at the trajectory and + + align:start position:0% +right so um look at the trajectory and + + + align:start position:0% +right so um look at the trajectory and +uh for that we say we discuss briefly + + align:start position:0% +uh for that we say we discuss briefly + + + align:start position:0% +uh for that we say we discuss briefly +the novel equation which is a n particle + + align:start position:0% +the novel equation which is a n particle + + + align:start position:0% +the novel equation which is a n particle +distribution function and that I say uh + + align:start position:0% +distribution function and that I say uh + + + align:start position:0% +distribution function and that I say uh +it's of course that n is huge the number + + align:start position:0% +it's of course that n is huge the number + + + align:start position:0% +it's of course that n is huge the number +of particle in my system + + align:start position:0% +of particle in my system + + + align:start position:0% +of particle in my system +and we say okay from this no equation + + align:start position:0% +and we say okay from this no equation + + + align:start position:0% +and we say okay from this no equation +there are generally two approach one is + + align:start position:0% +there are generally two approach one is + + + align:start position:0% +there are generally two approach one is +the borsman equation that's the uh say + + align:start position:0% +the borsman equation that's the uh say + + + align:start position:0% +the borsman equation that's the uh say +long developed and the other is the + + align:start position:0% +long developed and the other is the + + + align:start position:0% +long developed and the other is the +linear response theory uh which I hope I + + align:start position:0% +linear response theory uh which I hope I + + + align:start position:0% +linear response theory uh which I hope I +have will have time at the end to cover + + align:start position:0% +have will have time at the end to cover + + + align:start position:0% +have will have time at the end to cover +some if you do molecular dynamics you + + align:start position:0% +some if you do molecular dynamics you + + + align:start position:0% +some if you do molecular dynamics you +should really dive into linear response + + align:start position:0% +should really dive into linear response + + + align:start position:0% +should really dive into linear response +theory that's the analysis I I comment a + + align:start position:0% +theory that's the analysis I I comment a + + + align:start position:0% +theory that's the analysis I I comment a +lot of people in fact say any + + align:start position:0% +lot of people in fact say any + + + align:start position:0% +lot of people in fact say any +undergraduate student come in can + + align:start position:0% +undergraduate student come in can + + + align:start position:0% +undergraduate student come in can +conceptually understand equal ma f equal + + align:start position:0% +conceptually understand equal ma f equal + + + align:start position:0% +conceptually understand equal ma f equal +ma do a simulation. But the K is you + + align:start position:0% +ma do a simulation. But the K is you + + + align:start position:0% +ma do a simulation. But the K is you +have to really understand that the the + + align:start position:0% +have to really understand that the the + + + align:start position:0% +have to really understand that the the +basis for that + + align:start position:0% +basis for that + + + align:start position:0% +basis for that +and uh so we move on and say okay from f + + align:start position:0% +and uh so we move on and say okay from f + + + align:start position:0% +and uh so we move on and say okay from f +to n and to f of one that's a one + + align:start position:0% +to n and to f of one that's a one + + + align:start position:0% +to n and to f of one that's a one +particle distribution function that's a + + align:start position:0% +particle distribution function that's a + + + align:start position:0% +particle distribution function that's a +boardsman equation + + align:start position:0% +boardsman equation + + + align:start position:0% +boardsman equation +and uh uh the fn is just the + + align:start position:0% +and uh uh the fn is just the + + + align:start position:0% +and uh uh the fn is just the +multiplication of f1 for n particles + + align:start position:0% +multiplication of f1 for n particles + + + align:start position:0% +multiplication of f1 for n particles +and uh uh we uh uh the because of the + + align:start position:0% +and uh uh we uh uh the because of the + + + align:start position:0% +and uh uh we uh uh the because of the +one particle now this particle will + + align:start position:0% +one particle now this particle will + + + align:start position:0% +one particle now this particle will +interact with the rest of the particle + + align:start position:0% +interact with the rest of the particle + + + align:start position:0% +interact with the rest of the particle +in the system. So uh the borsman + + align:start position:0% +in the system. So uh the borsman + + + align:start position:0% +in the system. So uh the borsman +equation uh which you roughly can show + + align:start position:0% +equation uh which you roughly can show + + + align:start position:0% +equation uh which you roughly can show +from no equation the left hand side is + + align:start position:0% +from no equation the left hand side is + + + align:start position:0% +from no equation the left hand side is +dfdt. + + align:start position:0% +dfdt. + + + align:start position:0% +dfdt. +The first derivative because here is + + align:start position:0% +The first derivative because here is + + + align:start position:0% +The first derivative because here is +still a function in phase space right f + + align:start position:0% +still a function in phase space right f + + + align:start position:0% +still a function in phase space right f +is the distribution function still a + + align:start position:0% +is the distribution function still a + + + align:start position:0% +is the distribution function still a +function in phase space. So the first + + align:start position:0% +function in phase space. So the first + + + align:start position:0% +function in phase space. So the first +derivative is gradient is with respect + + align:start position:0% +derivative is gradient is with respect + + + align:start position:0% +derivative is gradient is with respect +to space. The second gradient is with + + align:start position:0% +to space. The second gradient is with + + + align:start position:0% +to space. The second gradient is with +respect to the momentum + + align:start position:0% +respect to the momentum + + + align:start position:0% +respect to the momentum +right and uh uh it's actually + + align:start position:0% +right and uh uh it's actually + + + align:start position:0% +right and uh uh it's actually +interesting to comment the f it looks + + align:start position:0% +interesting to comment the f it looks + + + align:start position:0% +interesting to comment the f it looks +like it's a function of xyz vx wy vz + + align:start position:0% +like it's a function of xyz vx wy vz + + + align:start position:0% +like it's a function of xyz vx wy vz +looks like it has direction vx vy vz if + + align:start position:0% +looks like it has direction vx vy vz if + + + align:start position:0% +looks like it has direction vx vy vz if +a particle is going certain direction I + + align:start position:0% +a particle is going certain direction I + + + align:start position:0% +a particle is going certain direction I +have different f right so but uh + + align:start position:0% +have different f right so but uh + + + align:start position:0% +have different f right so but uh +uh Say uh the question is is a vector or + + align:start position:0% +uh Say uh the question is is a vector or + + + align:start position:0% +uh Say uh the question is is a vector or +scalar? + + align:start position:0% +scalar? + + + align:start position:0% +scalar? +What do you think? + + align:start position:0% +What do you think? + + + align:start position:0% +What do you think? +It's a scalar in high dimensional space. + + align:start position:0% +It's a scalar in high dimensional space. + + + align:start position:0% +It's a scalar in high dimensional space. +Right? And if you just think about any + + align:start position:0% +Right? And if you just think about any + + + align:start position:0% +Right? And if you just think about any +point in space and particle going + + align:start position:0% +point in space and particle going + + + align:start position:0% +point in space and particle going +specific direction have specific + + align:start position:0% +specific direction have specific + + + align:start position:0% +specific direction have specific +distribution. So that looks like it has + + align:start position:0% +distribution. So that looks like it has + + + align:start position:0% +distribution. So that looks like it has +direction properties but that direction + + align:start position:0% +direction properties but that direction + + + align:start position:0% +direction properties but that direction +property is really the way coordinate + + align:start position:0% +property is really the way coordinate + + + align:start position:0% +property is really the way coordinate +the higher dimensional coordinate space + + align:start position:0% +the higher dimensional coordinate space + + + align:start position:0% +the higher dimensional coordinate space +say face space coordinate + + align:start position:0% +say face space coordinate + + + align:start position:0% +say face space coordinate +okay and also uh there are different + + align:start position:0% +okay and also uh there are different + + + align:start position:0% +okay and also uh there are different +ways to write this force term dpdt + + align:start position:0% +ways to write this force term dpdt + + + align:start position:0% +ways to write this force term dpdt +is the uh if you look at think about the + + align:start position:0% +is the uh if you look at think about the + + + align:start position:0% +is the uh if you look at think about the +len's law dpdt gives you the f the force + + align:start position:0% +len's law dpdt gives you the f the force + + + align:start position:0% +len's law dpdt gives you the f the force +and the force you can write f say + + align:start position:0% +and the force you can write f say + + + align:start position:0% +and the force you can write f say +because p is the ma m so I can put them + + align:start position:0% +because p is the ma m so I can put them + + + align:start position:0% +because p is the ma m so I can put them +m out and f uh say d d d d d d d d d d d + + align:start position:0% +m out and f uh say d d d d d d d d d d d + + + align:start position:0% +m out and f uh say d d d d d d d d d d d +d d d d d d d d d dive with respect to V + + align:start position:0% +d d d d d d d d d dive with respect to V + + + align:start position:0% +d d d d d d d d d dive with respect to V +or P is a function of H K right so by I + + align:start position:0% +or P is a function of H K right so by I + + + align:start position:0% +or P is a function of H K right so by I +can use different variables rather than + + align:start position:0% +can use different variables rather than + + + align:start position:0% +can use different variables rather than +using P I can use V I can use K and a + + align:start position:0% +using P I can use V I can use K and a + + + align:start position:0% +using P I can use V I can use K and a +different way of writing this term and + + align:start position:0% +different way of writing this term and + + + align:start position:0% +different way of writing this term and +that's uh most of time I say when you + + align:start position:0% +that's uh most of time I say when you + + + align:start position:0% +that's uh most of time I say when you +deal with electrons you have to keep + + align:start position:0% +deal with electrons you have to keep + + + align:start position:0% +deal with electrons you have to keep +this term. That's the uh important + + align:start position:0% +this term. That's the uh important + + + align:start position:0% +this term. That's the uh important +driving force for the electron motion. + + align:start position:0% +driving force for the electron motion. + + + align:start position:0% +driving force for the electron motion. +But when we deal photon or fon we do not + + align:start position:0% +But when we deal photon or fon we do not + + + align:start position:0% +But when we deal photon or fon we do not +need uh this term or even say the + + align:start position:0% +need uh this term or even say the + + + align:start position:0% +need uh this term or even say the +molecules there's no direct force on + + align:start position:0% +molecules there's no direct force on + + + align:start position:0% +molecules there's no direct force on +them. + + align:start position:0% +them. + + + align:start position:0% +them. +uh but the complication is really on + + align:start position:0% +uh but the complication is really on + + + align:start position:0% +uh but the complication is really on +this left hand side right hand side + + align:start position:0% +this left hand side right hand side + + + align:start position:0% +this left hand side right hand side +where I say the now the particle + + align:start position:0% +where I say the now the particle + + + align:start position:0% +where I say the now the particle +interact with the rest of the particle + + align:start position:0% +interact with the rest of the particle + + + align:start position:0% +interact with the rest of the particle +and that's the collision term so uh + + align:start position:0% +and that's the collision term so uh + + + align:start position:0% +and that's the collision term so uh +let's move on and try to write down this + + align:start position:0% +let's move on and try to write down this + + + align:start position:0% +let's move on and try to write down this +collision term because so far it looks + + align:start position:0% +collision term because so far it looks + + + align:start position:0% +collision term because so far it looks +all + + align:start position:0% +all + + + align:start position:0% +all +pretty simple on the uh right hand left + + align:start position:0% +pretty simple on the uh right hand left + + + align:start position:0% +pretty simple on the uh right hand left +hand side you can say it's a first order + + align:start position:0% +hand side you can say it's a first order + + + align:start position:0% +hand side you can say it's a first order +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +Right. And uh + + align:start position:0% +Right. And uh + + + align:start position:0% +Right. And uh +so let's look at the collision term + + align:start position:0% +so let's look at the collision term + + + align:start position:0% +so let's look at the collision term +df + + align:start position:0% +df + + + align:start position:0% +df +dt. This is not a derivative just a + + align:start position:0% +dt. This is not a derivative just a + + + align:start position:0% +dt. This is not a derivative just a +symbol how we can uh express it and uh + + align:start position:0% +symbol how we can uh express it and uh + + + align:start position:0% +symbol how we can uh express it and uh +uh normally I can start just consider + + align:start position:0% +uh normally I can start just consider + + + align:start position:0% +uh normally I can start just consider +the two particle coalition and uh so if + + align:start position:0% +the two particle coalition and uh so if + + + align:start position:0% +the two particle coalition and uh so if +I have two particles interact with each + + align:start position:0% +I have two particles interact with each + + + align:start position:0% +I have two particles interact with each +other and this initially this particle + + align:start position:0% +other and this initially this particle + + + align:start position:0% +other and this initially this particle +has a energy and momentum of a vector + + align:start position:0% +has a energy and momentum of a vector + + + align:start position:0% +has a energy and momentum of a vector +right hk is momentum and this other + + align:start position:0% +right hk is momentum and this other + + + align:start position:0% +right hk is momentum and this other +particle has a E1 + + align:start position:0% +particle has a E1 + + + align:start position:0% +particle has a E1 +K1 + + align:start position:0% +K1 + + + align:start position:0% +K1 +and uh when they get close to the + + align:start position:0% +and uh when they get close to the + + + align:start position:0% +and uh when they get close to the +interaction range what is close to + + align:start position:0% +interaction range what is close to + + + align:start position:0% +interaction range what is close to +interaction range it means if you think + + align:start position:0% +interaction range it means if you think + + + align:start position:0% +interaction range it means if you think +about two gas say atoms it's the + + align:start position:0% +about two gas say atoms it's the + + + align:start position:0% +about two gas say atoms it's the +electron when the electrostatic + + align:start position:0% +electron when the electrostatic + + + align:start position:0% +electron when the electrostatic +potential can interact with each other + + align:start position:0% +potential can interact with each other + + + align:start position:0% +potential can interact with each other +right so uh you have uh electrons you + + align:start position:0% +right so uh you have uh electrons you + + + align:start position:0% +right so uh you have uh electrons you +have nuclei so you have that that's + + align:start position:0% +have nuclei so you have that that's + + + align:start position:0% +have nuclei so you have that that's +where they start to interact so if you + + align:start position:0% +where they start to interact so if you + + + align:start position:0% +where they start to interact so if you +think about The + + align:start position:0% +think about The + + + align:start position:0% +think about The +gas molecules in this room we see the + + align:start position:0% +gas molecules in this room we see the + + + align:start position:0% +gas molecules in this room we see the +average mean free pass about 100 + + align:start position:0% +average mean free pass about 100 + + + align:start position:0% +average mean free pass about 100 +nanometer + + align:start position:0% +nanometer + + + align:start position:0% +nanometer +right and the the atomic size is a few + + align:start position:0% +right and the the atomic size is a few + + + align:start position:0% +right and the the atomic size is a few +unstron + + align:start position:0% +unstron + + + align:start position:0% +unstron +so there is actually a very large space + + align:start position:0% +so there is actually a very large space + + + align:start position:0% +so there is actually a very large space +in between them most time they do not + + align:start position:0% +in between them most time they do not + + + align:start position:0% +in between them most time they do not +interact they will just travel freely + + align:start position:0% +interact they will just travel freely + + + align:start position:0% +interact they will just travel freely +and when they're getting really close to + + align:start position:0% +and when they're getting really close to + + + align:start position:0% +and when they're getting really close to +each other you got this collision right + + align:start position:0% +each other you got this collision right + + + align:start position:0% +each other you got this collision right +so uh due to the collision you'll have + + align:start position:0% +so uh due to the collision you'll have + + + align:start position:0% +so uh due to the collision you'll have +the energy change maybe right and you + + align:start position:0% +the energy change maybe right and you + + + align:start position:0% +the energy change maybe right and you +change the direction. So that's the + + align:start position:0% +change the direction. So that's the + + + align:start position:0% +change the direction. So that's the +final state for this first first + + align:start position:0% +final state for this first first + + + align:start position:0% +final state for this first first +particle and you have the energy change + + align:start position:0% +particle and you have the energy change + + + align:start position:0% +particle and you have the energy change +of second particle and momentum change + + align:start position:0% +of second particle and momentum change + + + align:start position:0% +of second particle and momentum change +of the second particle + + align:start position:0% +of the second particle + + + align:start position:0% +of the second particle +right and uh in a typical problem + + align:start position:0% +right and uh in a typical problem + + + align:start position:0% +right and uh in a typical problem +what do you want to say okay what's the + + align:start position:0% +what do you want to say okay what's the + + + align:start position:0% +what do you want to say okay what's the +first what's the rate of what's the + + align:start position:0% +first what's the rate of what's the + + + align:start position:0% +first what's the rate of what's the +probability what's the rate right and + + align:start position:0% +probability what's the rate right and + + + align:start position:0% +probability what's the rate right and +the way uh uh to do this is a + + align:start position:0% +the way uh uh to do this is a + + + align:start position:0% +the way uh uh to do this is a +approximate method. So if you have + + align:start position:0% +approximate method. So if you have + + + align:start position:0% +approximate method. So if you have +originally if you solve a m metal for + + align:start position:0% +originally if you solve a m metal for + + + align:start position:0% +originally if you solve a m metal for +example if I have photon comes in and + + align:start position:0% +example if I have photon comes in and + + + align:start position:0% +example if I have photon comes in and +getting absorbed by the uh materials + + align:start position:0% +getting absorbed by the uh materials + + + align:start position:0% +getting absorbed by the uh materials +getting absorbed by material right so + + align:start position:0% +getting absorbed by material right so + + + align:start position:0% +getting absorbed by material right so +originally the material has a certain + + align:start position:0% +originally the material has a certain + + + align:start position:0% +originally the material has a certain +energy and that's a quantum mechanable + + align:start position:0% +energy and that's a quantum mechanable + + + align:start position:0% +energy and that's a quantum mechanable +energy levels that's what we did in the + + align:start position:0% +energy levels that's what we did in the + + + align:start position:0% +energy levels that's what we did in the +second chapter right so we original + + align:start position:0% +second chapter right so we original + + + align:start position:0% +second chapter right so we original +problem this system before interaction + + align:start position:0% +problem this system before interaction + + + align:start position:0% +problem this system before interaction +action has energy and correspondingly we + + align:start position:0% +action has energy and correspondingly we + + + align:start position:0% +action has energy and correspondingly we +can write the uh shinger equation. Uh + + align:start position:0% +can write the uh shinger equation. Uh + + + align:start position:0% +can write the uh shinger equation. Uh +essentially we can write the hamiltonian + + align:start position:0% +essentially we can write the hamiltonian + + + align:start position:0% +essentially we can write the hamiltonian +which is the kinetic energy. So uh h bar + + align:start position:0% +which is the kinetic energy. So uh h bar + + + align:start position:0% +which is the kinetic energy. So uh h bar +squar uh 2m k so is the operator that's + + align:start position:0% +squar uh 2m k so is the operator that's + + + align:start position:0% +squar uh 2m k so is the operator that's +the first term in the shinger equation + + align:start position:0% +the first term in the shinger equation + + + align:start position:0% +the first term in the shinger equation +right and plus u0 + + align:start position:0% +right and plus u0 + + + align:start position:0% +right and plus u0 +right so when we show solve the + + align:start position:0% +right so when we show solve the + + + align:start position:0% +right so when we show solve the +shroinger equation we say this one + + align:start position:0% +shroinger equation we say this one + + + align:start position:0% +shroinger equation we say this one +equals mass i h bar ih bar deep side dt + + align:start position:0% +equals mass i h bar ih bar deep side dt + + + align:start position:0% +equals mass i h bar ih bar deep side dt +we solve for the energy states + + align:start position:0% +we solve for the energy states + + + align:start position:0% +we solve for the energy states +Right. So now uh what I have so this is + + align:start position:0% +Right. So now uh what I have so this is + + + align:start position:0% +Right. So now uh what I have so this is +we did a steady state problem + + align:start position:0% +we did a steady state problem + + + align:start position:0% +we did a steady state problem +now during uh uh photon comes in what it + + align:start position:0% +now during uh uh photon comes in what it + + + align:start position:0% +now during uh uh photon comes in what it +does is to create a perturbation you + + align:start position:0% +does is to create a perturbation you + + + align:start position:0% +does is to create a perturbation you +treat as a small perturbation + + align:start position:0% +treat as a small perturbation + + + align:start position:0% +treat as a small perturbation +to the original homatian h. So uh let's + + align:start position:0% +to the original homatian h. So uh let's + + + align:start position:0% +to the original homatian h. So uh let's +say this is your h0 + + align:start position:0% +say this is your h0 + + + align:start position:0% +say this is your h0 +and the small perturbation let's say uh + + align:start position:0% +and the small perturbation let's say uh + + + align:start position:0% +and the small perturbation let's say uh +the now the interaction uh hamiltonian h + + align:start position:0% +the now the interaction uh hamiltonian h + + + align:start position:0% +the now the interaction uh hamiltonian h +is h0 plus a small perturbation which + + align:start position:0% +is h0 plus a small perturbation which + + + align:start position:0% +is h0 plus a small perturbation which +could be a function r and t + + align:start position:0% +could be a function r and t + + + align:start position:0% +could be a function r and t +right this is the interaction term + + align:start position:0% +right this is the interaction term + + + align:start position:0% +right this is the interaction term +this is the original unperturbed where I + + align:start position:0% +this is the original unperturbed where I + + + align:start position:0% +this is the original unperturbed where I +already have suppose You already have + + align:start position:0% +already have suppose You already have + + + align:start position:0% +already have suppose You already have +the short equation solution. You know + + align:start position:0% +the short equation solution. You know + + + align:start position:0% +the short equation solution. You know +the energy level. You know the wave + + align:start position:0% +the energy level. You know the wave + + + align:start position:0% +the energy level. You know the wave +function the state quantum states of the + + align:start position:0% +function the state quantum states of the + + + align:start position:0% +function the state quantum states of the +original system. Right? And due to this + + align:start position:0% +original system. Right? And due to this + + + align:start position:0% +original system. Right? And due to this +perturbation you go back to the short + + align:start position:0% +perturbation you go back to the short + + + align:start position:0% +perturbation you go back to the short +equation. You solve using perturbation + + align:start position:0% +equation. You solve using perturbation + + + align:start position:0% +equation. You solve using perturbation +method. + + align:start position:0% +method. + + + align:start position:0% +method. +We're not going to do it. And with that + + align:start position:0% +We're not going to do it. And with that + + + align:start position:0% +We're not going to do it. And with that +you can find the rate of perturbing due + + align:start position:0% +you can find the rate of perturbing due + + + align:start position:0% +you can find the rate of perturbing due +to this perturbation. The system + + align:start position:0% +to this perturbation. The system + + + align:start position:0% +to this perturbation. The system +changing from one state to the other. + + align:start position:0% +changing from one state to the other. + + + align:start position:0% +changing from one state to the other. +And this rate + + align:start position:0% +And this rate + + + align:start position:0% +And this rate +is a transition rate. + + align:start position:0% + + + + align:start position:0% + +This is a farmer initial state to a + + align:start position:0% +This is a farmer initial state to a + + + align:start position:0% +This is a farmer initial state to a +final state. Right? And this is a 2 pi + + align:start position:0% +final state. Right? And this is a 2 pi + + + align:start position:0% +final state. Right? And this is a 2 pi +hbar. + + align:start position:0% +hbar. + + + align:start position:0% +hbar. +And uh uh we have the integration of the + + align:start position:0% +And uh uh we have the integration of the + + + align:start position:0% +And uh uh we have the integration of the +final state wave function complex + + align:start position:0% +final state wave function complex + + + align:start position:0% +final state wave function complex +conjugate the perturbation. So this is + + align:start position:0% +conjugate the perturbation. So this is + + + align:start position:0% +conjugate the perturbation. So this is +the + + align:start position:0% +the + + + align:start position:0% +the +the unperturbed system the wave function + + align:start position:0% +the unperturbed system the wave function + + + align:start position:0% +the unperturbed system the wave function +let's suppose you start with a certain + + align:start position:0% +let's suppose you start with a certain + + + align:start position:0% +let's suppose you start with a certain +initial state wave function and the + + align:start position:0% +initial state wave function and the + + + align:start position:0% +initial state wave function and the +final state wave function that's suppose + + align:start position:0% +final state wave function that's suppose + + + align:start position:0% +final state wave function that's suppose +you already had solving the original + + align:start position:0% +you already had solving the original + + + align:start position:0% +you already had solving the original +problem and now given this perturbation + + align:start position:0% +problem and now given this perturbation + + + align:start position:0% +problem and now given this perturbation +hamiltonian and I have the initial state + + align:start position:0% +hamiltonian and I have the initial state + + + align:start position:0% +hamiltonian and I have the initial state +wave function and I interact integrate + + align:start position:0% +wave function and I interact integrate + + + align:start position:0% +wave function and I interact integrate +over the volume of that interaction + + align:start position:0% +over the volume of that interaction + + + align:start position:0% +over the volume of that interaction +and there's a square and then a delta + + align:start position:0% +and there's a square and then a delta + + + align:start position:0% +and there's a square and then a delta +function either + + align:start position:0% + + + + align:start position:0% + +the energy conservation delta function + + align:start position:0% +the energy conservation delta function + + + align:start position:0% +the energy conservation delta function +is zero when uh the ei does not equal ef + + align:start position:0% +is zero when uh the ei does not equal ef + + + align:start position:0% +is zero when uh the ei does not equal ef +right so only when ei equals ef this is + + align:start position:0% +right so only when ei equals ef this is + + + align:start position:0% +right so only when ei equals ef this is +non zero + + align:start position:0% +non zero + + + align:start position:0% +non zero +So essentially what this gives us is the + + align:start position:0% +So essentially what this gives us is the + + + align:start position:0% +So essentially what this gives us is the +energy conservation + + align:start position:0% +energy conservation + + + align:start position:0% +energy conservation +of the uh system. And if you do this, if + + align:start position:0% +of the uh system. And if you do this, if + + + align:start position:0% +of the uh system. And if you do this, if +you say when you do the uh wave function + + align:start position:0% +you say when you do the uh wave function + + + align:start position:0% +you say when you do the uh wave function +for plan wave, you have wave vector, + + align:start position:0% +for plan wave, you have wave vector, + + + align:start position:0% +for plan wave, you have wave vector, +right? For each quantum state, you have + + align:start position:0% +right? For each quantum state, you have + + + align:start position:0% +right? For each quantum state, you have +wave vector. And if you do your + + align:start position:0% +wave vector. And if you do your + + + align:start position:0% +wave vector. And if you do your +integration of this, you'll also find a + + align:start position:0% +integration of this, you'll also find a + + + align:start position:0% +integration of this, you'll also find a +corresponding conservation in w vector. + + align:start position:0% +corresponding conservation in w vector. + + + align:start position:0% +corresponding conservation in w vector. +That's your momentum conservation. + + align:start position:0% +That's your momentum conservation. + + + align:start position:0% +That's your momentum conservation. +So uh what do you have uh essentially + + align:start position:0% +So uh what do you have uh essentially + + + align:start position:0% +So uh what do you have uh essentially +you'll get the momentum energy + + align:start position:0% +you'll get the momentum energy + + + align:start position:0% +you'll get the momentum energy +conservation from this transition rate + + align:start position:0% +conservation from this transition rate + + + align:start position:0% +conservation from this transition rate +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +so the uh you you have for example the + + align:start position:0% +so the uh you you have for example the + + + align:start position:0% +so the uh you you have for example the +initial energy so this is the two + + align:start position:0% +initial energy so this is the two + + + align:start position:0% +initial energy so this is the two +particle interacting so this is + + align:start position:0% +particle interacting so this is + + + align:start position:0% +particle interacting so this is +initially E is function K and the + + align:start position:0% +initially E is function K and the + + + align:start position:0% +initially E is function K and the +incoming one E1 K1 + + align:start position:0% +incoming one E1 K1 + + + align:start position:0% +incoming one E1 K1 +equals + + align:start position:0% +equals + + + align:start position:0% +equals +E uh prime K prime it goes scatter into + + align:start position:0% +E uh prime K prime it goes scatter into + + + align:start position:0% +E uh prime K prime it goes scatter into +another uh state and E1 prime + + align:start position:0% +another uh state and E1 prime + + + align:start position:0% +another uh state and E1 prime +K1 U prime + + align:start position:0% +K1 U prime + + + align:start position:0% +K1 U prime +and so that's the energy conservation + + align:start position:0% +and so that's the energy conservation + + + align:start position:0% +and so that's the energy conservation +this is the delta function the initial + + align:start position:0% +this is the delta function the initial + + + align:start position:0% +this is the delta function the initial +of the two system two two particles and + + align:start position:0% +of the two system two two particles and + + + align:start position:0% +of the two system two two particles and +the final of the two particles + + align:start position:0% +the final of the two particles + + + align:start position:0% +the final of the two particles +and uh uh the corresponding uh energy + + align:start position:0% +and uh uh the corresponding uh energy + + + align:start position:0% +and uh uh the corresponding uh energy +conservation is K + K1 prime equals K + + align:start position:0% +conservation is K + K1 prime equals K + + + align:start position:0% +conservation is K + K1 prime equals K +prime that's the final plus K1 prime + + align:start position:0% +prime that's the final plus K1 prime + + + align:start position:0% +prime that's the final plus K1 prime +final and uh let's see just wait hold on + + align:start position:0% +final and uh let's see just wait hold on + + + align:start position:0% +final and uh let's see just wait hold on +this and because hk hk that gives me + + align:start position:0% +this and because hk hk that gives me + + + align:start position:0% +this and because hk hk that gives me +momentum and later on I'll make a say a + + align:start position:0% +momentum and later on I'll make a say a + + + align:start position:0% +momentum and later on I'll make a say a +modification to this form here you can + + align:start position:0% +modification to this form here you can + + + align:start position:0% +modification to this form here you can +see this is a simple momentum + + align:start position:0% +see this is a simple momentum + + + align:start position:0% +see this is a simple momentum +conservation + + align:start position:0% +conservation + + + align:start position:0% +conservation +But later on we'll add say in crystal + + align:start position:0% +But later on we'll add say in crystal + + + align:start position:0% +But later on we'll add say in crystal +you add reciprocal latice G and that's + + align:start position:0% +you add reciprocal latice G and that's + + + align:start position:0% +you add reciprocal latice G and that's +soal clan process but basically those + + align:start position:0% +soal clan process but basically those + + + align:start position:0% +soal clan process but basically those +transition rate also give you I say uh + + align:start position:0% +transition rate also give you I say uh + + + align:start position:0% +transition rate also give you I say uh +in the doing the math also you actually + + align:start position:0% +in the doing the math also you actually + + + align:start position:0% +in the doing the math also you actually +get the energy and momentum conservation + + align:start position:0% +get the energy and momentum conservation + + + align:start position:0% +get the energy and momentum conservation +and uh uh most of the time you can say + + align:start position:0% +and uh uh most of the time you can say + + + align:start position:0% +and uh uh most of the time you can say +uh people do not like to write those + + align:start position:0% +uh people do not like to write those + + + align:start position:0% +uh people do not like to write those +integr That's why the direct if you read + + align:start position:0% +integr That's why the direct if you read + + + align:start position:0% +integr That's why the direct if you read +the quantum mechanics book they will + + align:start position:0% +the quantum mechanics book they will + + + align:start position:0% +the quantum mechanics book they will +write direct notation and uh uh the + + align:start position:0% +write direct notation and uh uh the + + + align:start position:0% +write direct notation and uh uh the +direct notation for this is your initial + + align:start position:0% +direct notation for this is your initial + + + align:start position:0% +direct notation for this is your initial +state interacting that's the like a wave + + align:start position:0% +state interacting that's the like a wave + + + align:start position:0% +state interacting that's the like a wave +function here interaction with perturbed + + align:start position:0% +function here interaction with perturbed + + + align:start position:0% +function here interaction with perturbed +honia and goes to final state so that + + align:start position:0% +honia and goes to final state so that + + + align:start position:0% +honia and goes to final state so that +represent this integral and you have + + align:start position:0% +represent this integral and you have + + + align:start position:0% +represent this integral and you have +this integration + + align:start position:0% +this integration + + + align:start position:0% +this integration +okay and uh you also Write this as a + + align:start position:0% +okay and uh you also Write this as a + + + align:start position:0% +okay and uh you also Write this as a +matrix form fi + + align:start position:0% +matrix form fi + + + align:start position:0% +matrix form fi +squar. + + align:start position:0% +squar. + + + align:start position:0% +squar. +So there are three different ways to do + + align:start position:0% +So there are three different ways to do + + + align:start position:0% +So there are three different ways to do +quantum mechanics. One is a matrix due + + align:start position:0% +quantum mechanics. One is a matrix due + + + align:start position:0% +quantum mechanics. One is a matrix due +to Heisenberg + + align:start position:0% +to Heisenberg + + + align:start position:0% +to Heisenberg +drotation + + align:start position:0% +drotation + + + align:start position:0% +drotation +dac and shinger is the shroinger + + align:start position:0% +dac and shinger is the shroinger + + + align:start position:0% +dac and shinger is the shroinger +equation. + + align:start position:0% +equation. + + + align:start position:0% +equation. +Okay they are all equivalent. + + align:start position:0% +Okay they are all equivalent. + + + align:start position:0% +Okay they are all equivalent. +Okay + + align:start position:0% +Okay + + + align:start position:0% +Okay +so this is the famous firmy golden rule. + + align:start position:0% +so this is the famous firmy golden rule. + + + align:start position:0% +so this is the famous firmy golden rule. +Next time you you heard from me golden + + align:start position:0% +Next time you you heard from me golden + + + align:start position:0% +Next time you you heard from me golden +rule, you now at least you have said. + + align:start position:0% + + + + align:start position:0% + +So that gives you the uh transition rate + + align:start position:0% +So that gives you the uh transition rate + + + align:start position:0% +So that gives you the uh transition rate +from the initial initial to final this + + align:start position:0% +from the initial initial to final this + + + align:start position:0% +from the initial initial to final this +uh uh given the uh uh interaction + + align:start position:0% +uh uh given the uh uh interaction + + + align:start position:0% +uh uh given the uh uh interaction +hamiltonian. This is by solving the time + + align:start position:0% +hamiltonian. This is by solving the time + + + align:start position:0% +hamiltonian. This is by solving the time +dependent shorting equation using the + + align:start position:0% +dependent shorting equation using the + + + align:start position:0% +dependent shorting equation using the +perturbation method. + + align:start position:0% + + + + align:start position:0% + +Okay, so that's the first step, right? + + align:start position:0% +Okay, so that's the first step, right? + + + align:start position:0% +Okay, so that's the first step, right? +We say we're dealing with the collision + + align:start position:0% +We say we're dealing with the collision + + + align:start position:0% +We say we're dealing with the collision +and uh now coming back to the BMAN + + align:start position:0% +and uh now coming back to the BMAN + + + align:start position:0% +and uh now coming back to the BMAN +equation. I'm looking at one particle + + align:start position:0% +equation. I'm looking at one particle + + + align:start position:0% +equation. I'm looking at one particle +and this particle can collide with many + + align:start position:0% +and this particle can collide with many + + + align:start position:0% +and this particle can collide with many +particles in the system. + + align:start position:0% +particles in the system. + + + align:start position:0% +particles in the system. +Right. So I have to count all that + + align:start position:0% +Right. So I have to count all that + + + align:start position:0% +Right. So I have to count all that +possibilities + + align:start position:0% + + + + align:start position:0% + +and so the now I can start write the df + + align:start position:0% +and so the now I can start write the df + + + align:start position:0% +and so the now I can start write the df +uh dt this collision term + + align:start position:0% + + + + align:start position:0% + +df dt this collision first if this + + align:start position:0% +df dt this collision first if this + + + align:start position:0% +df dt this collision first if this +particle is collide to other states then + + align:start position:0% +particle is collide to other states then + + + align:start position:0% +particle is collide to other states then +I have a loss right you go if from + + align:start position:0% +I have a loss right you go if from + + + align:start position:0% +I have a loss right you go if from +original E K states to E prime K prime + + align:start position:0% +original E K states to E prime K prime + + + align:start position:0% +original E K states to E prime K prime +states then this F because F is + + align:start position:0% +states then this F because F is + + + align:start position:0% +states then this F because F is +representing the uh one particle at a + + align:start position:0% +representing the uh one particle at a + + + align:start position:0% +representing the uh one particle at a +specific state so I lose a particle in + + align:start position:0% +specific state so I lose a particle in + + + align:start position:0% +specific state so I lose a particle in +that state so my first term is going out + + align:start position:0% +that state so my first term is going out + + + align:start position:0% +that state so my first term is going out +that's a loss so I have a negative sign + + align:start position:0% +that's a loss so I have a negative sign + + + align:start position:0% +that's a loss so I have a negative sign +so it's going out + + align:start position:0% + + + + align:start position:0% + +right and uh of First that depends on + + align:start position:0% +right and uh of First that depends on + + + align:start position:0% +right and uh of First that depends on +say the rate really depend say first I + + align:start position:0% +say the rate really depend say first I + + + align:start position:0% +say the rate really depend say first I +have the rate here collision rate uh of + + align:start position:0% +have the rate here collision rate uh of + + + align:start position:0% +have the rate here collision rate uh of +uh two quantum states but then I need to + + align:start position:0% +uh two quantum states but then I need to + + + align:start position:0% +uh two quantum states but then I need to +say each quantum states how many + + align:start position:0% +say each quantum states how many + + + align:start position:0% +say each quantum states how many +particles I have + + align:start position:0% +particles I have + + + align:start position:0% +particles I have +right so I need to say um + + align:start position:0% +right so I need to say um + + + align:start position:0% +right so I need to say um +uh f really the initial t r okay k and + + align:start position:0% +uh f really the initial t r okay k and + + + align:start position:0% +uh f really the initial t r okay k and +if we collide either with the other one + + align:start position:0% +if we collide either with the other one + + + align:start position:0% +if we collide either with the other one +T + + align:start position:0% +T + + + align:start position:0% +T +R uh uh at the same location K1 + + align:start position:0% +R uh uh at the same location K1 + + + align:start position:0% +R uh uh at the same location K1 +right so say how many in K how many in + + align:start position:0% +right so say how many in K how many in + + + align:start position:0% +right so say how many in K how many in +K1 and what's the rate of going from K + + align:start position:0% +K1 and what's the rate of going from K + + + align:start position:0% +K1 and what's the rate of going from K +K1 + + align:start position:0% +K1 + + + align:start position:0% +K1 +to K prime K1 K1 prime so this is where + + align:start position:0% +to K prime K1 K1 prime so this is where + + + align:start position:0% +to K prime K1 K1 prime so this is where +the forming golden rule tells me Those + + align:start position:0% +the forming golden rule tells me Those + + + align:start position:0% +the forming golden rule tells me Those +are how many to start with. + + align:start position:0% +are how many to start with. + + + align:start position:0% +are how many to start with. +Okay. So this is the loss. + + align:start position:0% +Okay. So this is the loss. + + + align:start position:0% +Okay. So this is the loss. +And now because I'm counting one + + align:start position:0% +And now because I'm counting one + + + align:start position:0% +And now because I'm counting one +specific so I need to really say sum up + + align:start position:0% +specific so I need to really say sum up + + + align:start position:0% +specific so I need to really say sum up +all other possibility. + + align:start position:0% +all other possibility. + + + align:start position:0% +all other possibility. +So I need to sum up K1. I need to sum up + + align:start position:0% +So I need to sum up K1. I need to sum up + + + align:start position:0% +So I need to sum up K1. I need to sum up +K prime. I need to sum up K1 prime. + + align:start position:0% +K prime. I need to sum up K1 prime. + + + align:start position:0% +K prime. I need to sum up K1 prime. +That summation is actually because each + + align:start position:0% +That summation is actually because each + + + align:start position:0% +That summation is actually because each +K is a V vector is vector right is + + align:start position:0% +K is a V vector is vector right is + + + align:start position:0% +K is a V vector is vector right is +actually each of this K is three + + align:start position:0% +actually each of this K is three + + + align:start position:0% +actually each of this K is three +summation. + + align:start position:0% +summation. + + + align:start position:0% +summation. +So I have really + + align:start position:0% + + + + align:start position:0% + +uh uh nine summation K1 is a vector + + align:start position:0% +uh uh nine summation K1 is a vector + + + align:start position:0% +uh uh nine summation K1 is a vector +K prime is a vector and K one prime is a + + align:start position:0% +K prime is a vector and K one prime is a + + + align:start position:0% +K prime is a vector and K one prime is a +vector. + + align:start position:0% +vector. + + + align:start position:0% +vector. +This is a loss. + + align:start position:0% +This is a loss. + + + align:start position:0% +This is a loss. +And then there's a gain that's going + + align:start position:0% +And then there's a gain that's going + + + align:start position:0% +And then there's a gain that's going +from uh uh uh the reverse. See how many + + align:start position:0% +from uh uh uh the reverse. See how many + + + align:start position:0% +from uh uh uh the reverse. See how many +k prime k1 prime they scatter and + + align:start position:0% +k prime k1 prime they scatter and + + + align:start position:0% +k prime k1 prime they scatter and +scatter back into the current state + + align:start position:0% +scatter back into the current state + + + align:start position:0% +scatter back into the current state +of k. + + align:start position:0% +of k. + + + align:start position:0% +of k. +So the gain is from + + align:start position:0% +So the gain is from + + + align:start position:0% +So the gain is from +uh + + align:start position:0% +uh + + + align:start position:0% +uh +t + + align:start position:0% +t + + + align:start position:0% +t +uh r. So here this is where the borman + + align:start position:0% +uh r. So here this is where the borman + + + align:start position:0% +uh r. So here this is where the borman +equation where the molecular chaos + + align:start position:0% +equation where the molecular chaos + + + align:start position:0% +equation where the molecular chaos +uh assumption we we used before right so + + align:start position:0% +uh assumption we we used before right so + + + align:start position:0% +uh assumption we we used before right so +it's only interacting at r point so I'm + + align:start position:0% +it's only interacting at r point so I'm + + + align:start position:0% +it's only interacting at r point so I'm +not writing at different r mentioned + + align:start position:0% +not writing at different r mentioned + + + align:start position:0% +not writing at different r mentioned +that there are modification people try + + align:start position:0% +that there are modification people try + + + align:start position:0% +that there are modification people try +to consider final size of the atom or + + align:start position:0% +to consider final size of the atom or + + + align:start position:0% +to consider final size of the atom or +molecule like ansk equation in that case + + align:start position:0% +molecule like ansk equation in that case + + + align:start position:0% +molecule like ansk equation in that case +you have to add two different r point + + align:start position:0% +you have to add two different r point + + + align:start position:0% +you have to add two different r point +that becomes a lot more complicated + + align:start position:0% +that becomes a lot more complicated + + + align:start position:0% +that becomes a lot more complicated +So uh here I have k prime + + align:start position:0% +So uh here I have k prime + + + align:start position:0% +So uh here I have k prime +that's the from uh the uh initial state + + align:start position:0% +that's the from uh the uh initial state + + + align:start position:0% +that's the from uh the uh initial state +k prime and t r same and k1 prime + + align:start position:0% +k prime and t r same and k1 prime + + + align:start position:0% +k prime and t r same and k1 prime +right and they will interact and going + + align:start position:0% +right and they will interact and going + + + align:start position:0% +right and they will interact and going +from k prime k1 prime + + align:start position:0% +from k prime k1 prime + + + align:start position:0% +from k prime k1 prime +going to k1. + + align:start position:0% + + + + align:start position:0% + +But what I care is really just this one + + align:start position:0% +But what I care is really just this one + + + align:start position:0% +But what I care is really just this one +specific quantum state in K. So I need + + align:start position:0% +specific quantum state in K. So I need + + + align:start position:0% +specific quantum state in K. So I need +to sum again all those uh + + align:start position:0% +to sum again all those uh + + + align:start position:0% +to sum again all those uh +other states. So this is a k1 + + align:start position:0% +other states. So this is a k1 + + + align:start position:0% +other states. So this is a k1 +k prime k1 prime. So this is summation + + align:start position:0% +k prime k1 prime. So this is summation + + + align:start position:0% +k prime k1 prime. So this is summation +index is same. So this is out this is + + align:start position:0% +index is same. So this is out this is + + + align:start position:0% +index is same. So this is out this is +in. It's I'm doing the number balance + + align:start position:0% +in. It's I'm doing the number balance + + + align:start position:0% +in. It's I'm doing the number balance +and you put in that summation into left + + align:start position:0% +and you put in that summation into left + + + align:start position:0% +and you put in that summation into left +hand side + + align:start position:0% +hand side + + + align:start position:0% +hand side +a right hand side of the boardsman + + align:start position:0% +a right hand side of the boardsman + + + align:start position:0% +a right hand side of the boardsman +equation you get the full boardsman + + align:start position:0% +equation you get the full boardsman + + + align:start position:0% +equation you get the full boardsman +equation. + + align:start position:0% +equation. + + + align:start position:0% +equation. +Okay. Now you can say this was just a a + + align:start position:0% +Okay. Now you can say this was just a a + + + align:start position:0% +Okay. Now you can say this was just a a +starter. The real thing is the + + align:start position:0% +starter. The real thing is the + + + align:start position:0% +starter. The real thing is the +complication + + align:start position:0% +complication + + + align:start position:0% +complication +is on the right hand side. + + align:start position:0% +is on the right hand side. + + + align:start position:0% +is on the right hand side. +And uh most time we do not write this as + + align:start position:0% +And uh most time we do not write this as + + + align:start position:0% +And uh most time we do not write this as +a summation. You can use what you learn + + align:start position:0% +a summation. You can use what you learn + + + align:start position:0% +a summation. You can use what you learn +how to change a summation into + + align:start position:0% +how to change a summation into + + + align:start position:0% +how to change a summation into +integration. + + align:start position:0% +integration. + + + align:start position:0% +integration. +Right? K is a sum in the quantum states. + + align:start position:0% +Right? K is a sum in the quantum states. + + + align:start position:0% +Right? K is a sum in the quantum states. +Now you need to convert that summation + + align:start position:0% +Now you need to convert that summation + + + align:start position:0% +Now you need to convert that summation +into integration. As long as all the + + align:start position:0% +into integration. As long as all the + + + align:start position:0% +into integration. As long as all the +assumption we made say apply here. So if + + align:start position:0% +assumption we made say apply here. So if + + + align:start position:0% +assumption we made say apply here. So if +you convert this summation into + + align:start position:0% +you convert this summation into + + + align:start position:0% +you convert this summation into +integration, what do you have in terms + + align:start position:0% +integration, what do you have in terms + + + align:start position:0% +integration, what do you have in terms +of number of integrations? + + align:start position:0% + + + + align:start position:0% + +Line. Each of this is a vector, + + align:start position:0% +Line. Each of this is a vector, + + + align:start position:0% +Line. Each of this is a vector, +right? So you have a line listed the + + align:start position:0% +right? So you have a line listed the + + + align:start position:0% +right? So you have a line listed the +integrals + + align:start position:0% + + + + align:start position:0% + +and of course so when you convert state + + align:start position:0% +and of course so when you convert state + + + align:start position:0% +and of course so when you convert state +you you do 2 L say uh the distance is 2 + + align:start position:0% +you you do 2 L say uh the distance is 2 + + + align:start position:0% +you you do 2 L say uh the distance is 2 +pi / so you you have that distance you + + align:start position:0% +pi / so you you have that distance you + + + align:start position:0% +pi / so you you have that distance you +have all this constant from converting + + align:start position:0% +have all this constant from converting + + + align:start position:0% +have all this constant from converting +summation into integration and you have + + align:start position:0% +summation into integration and you have + + + align:start position:0% +summation into integration and you have +a lineless integral and this line less + + align:start position:0% +a lineless integral and this line less + + + align:start position:0% +a lineless integral and this line less +integr is dk1 + + align:start position:0% +integr is dk1 + + + align:start position:0% +integr is dk1 +vector. So I can write the three. This + + align:start position:0% +vector. So I can write the three. This + + + align:start position:0% +vector. So I can write the three. This +is DK1 X, DK1 Y, DK1 Z, + + align:start position:0% +is DK1 X, DK1 Y, DK1 Z, + + + align:start position:0% +is DK1 X, DK1 Y, DK1 Z, +right? And D K prime + + align:start position:0% +right? And D K prime + + + align:start position:0% +right? And D K prime +and DK1 prime. + + align:start position:0% + + + + align:start position:0% + +So this is a from converting summation + + align:start position:0% +So this is a from converting summation + + + align:start position:0% +So this is a from converting summation +to integration. + + align:start position:0% +to integration. + + + align:start position:0% +to integration. +The second comment is + + align:start position:0% +The second comment is + + + align:start position:0% +The second comment is +uh this W. + + align:start position:0% +uh this W. + + + align:start position:0% +uh this W. +Uh it turns out one could argue that + + align:start position:0% +Uh it turns out one could argue that + + + align:start position:0% +Uh it turns out one could argue that +this W equals this W. That's a detail + + align:start position:0% +this W equals this W. That's a detail + + + align:start position:0% +this W equals this W. That's a detail +balance + + align:start position:0% +balance + + + align:start position:0% +balance +and the equilibrium in everything say is + + align:start position:0% +and the equilibrium in everything say is + + + align:start position:0% +and the equilibrium in everything say is +the same scatter out equals scatter in + + align:start position:0% +the same scatter out equals scatter in + + + align:start position:0% +the same scatter out equals scatter in +otherwise you have this one state either + + align:start position:0% +otherwise you have this one state either + + + align:start position:0% +otherwise you have this one state either +will be depleted completed or it goes to + + align:start position:0% +will be depleted completed or it goes to + + + align:start position:0% +will be depleted completed or it goes to +blow to infinite. Right? That's the + + align:start position:0% +blow to infinite. Right? That's the + + + align:start position:0% +blow to infinite. Right? That's the +detail balance. So because of that you + + align:start position:0% +detail balance. So because of that you + + + align:start position:0% +detail balance. So because of that you +have the equality. So rather than + + align:start position:0% +have the equality. So rather than + + + align:start position:0% +have the equality. So rather than +writing two terms you can split write + + align:start position:0% +writing two terms you can split write + + + align:start position:0% +writing two terms you can split write +into combine into one term. So at the + + align:start position:0% +into combine into one term. So at the + + + align:start position:0% +into combine into one term. So at the +end what I can write this scattering + + align:start position:0% +end what I can write this scattering + + + align:start position:0% +end what I can write this scattering +term df dt + + align:start position:0% +term df dt + + + align:start position:0% +term df dt +say equals I put a negative sign the + + align:start position:0% +say equals I put a negative sign the + + + align:start position:0% +say equals I put a negative sign the +first term in the front. I have then W + + align:start position:0% +first term in the front. I have then W + + + align:start position:0% +first term in the front. I have then W +and F TR + + align:start position:0% +and F TR + + + align:start position:0% +and F TR +K + + align:start position:0% +K + + + align:start position:0% +K +and F T R + + align:start position:0% +and F T R + + + align:start position:0% +and F T R +K1. So this is the first term minus let + + align:start position:0% +K1. So this is the first term minus let + + + align:start position:0% +K1. So this is the first term minus let +me write this here. The second term is + + align:start position:0% +me write this here. The second term is + + + align:start position:0% +me write this here. The second term is +say f so + + align:start position:0% +say f so + + + align:start position:0% +say f so +minus f t + + align:start position:0% +minus f t + + + align:start position:0% +minus f t +r + + align:start position:0% +r + + + align:start position:0% +r +k prime + + align:start position:0% +k prime + + + align:start position:0% +k prime +and f t + + align:start position:0% +and f t + + + align:start position:0% +and f t +r k1 prime let me just made uh another + + align:start position:0% +r k1 prime let me just made uh another + + + align:start position:0% +r k1 prime let me just made uh another +comment + + align:start position:0% +comment + + + align:start position:0% +comment +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +here I'm writing two fixed particles + + align:start position:0% +here I'm writing two fixed particles + + + align:start position:0% +here I'm writing two fixed particles +when you do a real problem whether for + + align:start position:0% +when you do a real problem whether for + + + align:start position:0% +when you do a real problem whether for +example when your electron interact with + + align:start position:0% +example when your electron interact with + + + align:start position:0% +example when your electron interact with +the folon at the end the electron the + + align:start position:0% +the folon at the end the electron the + + + align:start position:0% +the folon at the end the electron the +fon may be absorbed right so you don't + + align:start position:0% +fon may be absorbed right so you don't + + + align:start position:0% +fon may be absorbed right so you don't +have a fullon coming out so for each of + + align:start position:0% +have a fullon coming out so for each of + + + align:start position:0% +have a fullon coming out so for each of +this specific case you need to carefully + + align:start position:0% +this specific case you need to carefully + + + align:start position:0% +this specific case you need to carefully +write down this f here I'm just writing + + align:start position:0% +write down this f here I'm just writing + + + align:start position:0% +write down this f here I'm just writing +a generic way of if I have two particle + + align:start position:0% +a generic way of if I have two particle + + + align:start position:0% +a generic way of if I have two particle +comes in collide with each other I have + + align:start position:0% +comes in collide with each other I have + + + align:start position:0% +comes in collide with each other I have +two particle goes up. But say when you + + align:start position:0% +two particle goes up. But say when you + + + align:start position:0% +two particle goes up. But say when you +actually like you have photon getting + + align:start position:0% +actually like you have photon getting + + + align:start position:0% +actually like you have photon getting +absorbed, photon disappeared, right? So + + align:start position:0% +absorbed, photon disappeared, right? So + + + align:start position:0% +absorbed, photon disappeared, right? So +you need to do each of this case just + + align:start position:0% +you need to do each of this case just + + + align:start position:0% +you need to do each of this case just +using the same idea do your detail + + align:start position:0% +using the same idea do your detail + + + align:start position:0% +using the same idea do your detail +expression and so you read different + + align:start position:0% +expression and so you read different + + + align:start position:0% +expression and so you read different +papers different problem this will be + + align:start position:0% +papers different problem this will be + + + align:start position:0% +papers different problem this will be +different expressions. + + align:start position:0% +different expressions. + + + align:start position:0% +different expressions. +Okay. So now go to solve this. Yes, + + align:start position:0% +Okay. So now go to solve this. Yes, + + + align:start position:0% +Okay. So now go to solve this. Yes, +never mind. Um I was just wondering + + align:start position:0% +never mind. Um I was just wondering + + + align:start position:0% +never mind. Um I was just wondering +what's the point of having an integral + + align:start position:0% +what's the point of having an integral + + + align:start position:0% +what's the point of having an integral +representation of this when we're + + align:start position:0% +representation of this when we're + + + align:start position:0% +representation of this when we're +probably going to be doing this + + align:start position:0% +probably going to be doing this + + + align:start position:0% +probably going to be doing this +numerically and then because this also + + align:start position:0% +numerically and then because this also + + + align:start position:0% +numerically and then because this also +has to have the assumption that these + + align:start position:0% +has to have the assumption that these + + + align:start position:0% +has to have the assumption that these +functions are slowly varying right for + + align:start position:0% +functions are slowly varying right for + + + align:start position:0% +functions are slowly varying right for +like every infant decimal step. Uh yeah + + align:start position:0% +like every infant decimal step. Uh yeah + + + align:start position:0% +like every infant decimal step. Uh yeah +so so so integral equ uh uh uh that's + + align:start position:0% +so so so integral equ uh uh uh that's + + + align:start position:0% +so so so integral equ uh uh uh that's +true say um you can do a go back to + + align:start position:0% +true say um you can do a go back to + + + align:start position:0% +true say um you can do a go back to +summation but in the uh remember in the + + align:start position:0% +summation but in the uh remember in the + + + align:start position:0% +summation but in the uh remember in the +past + + align:start position:0% +past + + + align:start position:0% +past +right before computer was very powerful + + align:start position:0% +right before computer was very powerful + + + align:start position:0% +right before computer was very powerful +people always try to say whether I can + + align:start position:0% +people always try to say whether I can + + + align:start position:0% +people always try to say whether I can +solve it numeric say analytically + + align:start position:0% +solve it numeric say analytically + + + align:start position:0% +solve it numeric say analytically +right but say uh so so that's the um and + + align:start position:0% +right but say uh so so that's the um and + + + align:start position:0% +right but say uh so so that's the um and +and in fact I say most of time this + + align:start position:0% +and in fact I say most of time this + + + align:start position:0% +and in fact I say most of time this +function doesn't change that rapidly. So + + align:start position:0% +function doesn't change that rapidly. So + + + align:start position:0% +function doesn't change that rapidly. So +that's a valid approximation. + + align:start position:0% +that's a valid approximation. + + + align:start position:0% +that's a valid approximation. +The + + align:start position:0% +The + + + align:start position:0% +The +it's not as bad as say the line + + align:start position:0% +it's not as bad as say the line + + + align:start position:0% +it's not as bad as say the line +integral. + + align:start position:0% +integral. + + + align:start position:0% +integral. +The reason is that you see when you have + + align:start position:0% +The reason is that you see when you have + + + align:start position:0% +The reason is that you see when you have +coalition you have this delta functions, + + align:start position:0% +coalition you have this delta functions, + + + align:start position:0% +coalition you have this delta functions, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +So it's those delta function in energy + + align:start position:0% +So it's those delta function in energy + + + align:start position:0% +So it's those delta function in energy +conservation + + align:start position:0% +conservation + + + align:start position:0% +conservation +and the the delta in momentum + + align:start position:0% +and the the delta in momentum + + + align:start position:0% +and the the delta in momentum +conservation. This is also delta + + align:start position:0% +conservation. This is also delta + + + align:start position:0% +conservation. This is also delta +function, right? will significantly + + align:start position:0% +function, right? will significantly + + + align:start position:0% +function, right? will significantly +constrain + + align:start position:0% +constrain + + + align:start position:0% +constrain +what are the possible values you have to + + align:start position:0% +what are the possible values you have to + + + align:start position:0% +what are the possible values you have to +consider. + + align:start position:0% +consider. + + + align:start position:0% +consider. +Okay. So that's the see that will allow + + align:start position:0% +Okay. So that's the see that will allow + + + align:start position:0% +Okay. So that's the see that will allow +you to simplify and uh make this still + + align:start position:0% +you to simplify and uh make this still + + + align:start position:0% +you to simplify and uh make this still +uh uh say trackable. But I have to say + + align:start position:0% +uh uh say trackable. But I have to say + + + align:start position:0% +uh uh say trackable. But I have to say +that + + align:start position:0% +that + + + align:start position:0% +that +solving full BSman equation now I'm not + + align:start position:0% +solving full BSman equation now I'm not + + + align:start position:0% +solving full BSman equation now I'm not +going to write combine the left hand + + align:start position:0% +going to write combine the left hand + + + align:start position:0% +going to write combine the left hand +side to the right hand side + + align:start position:0% +side to the right hand side + + + align:start position:0% +side to the right hand side +right uh left hand side to right hand + + align:start position:0% +right uh left hand side to right hand + + + align:start position:0% +right uh left hand side to right hand +side what you really have is a + + align:start position:0% +side what you really have is a + + + align:start position:0% +side what you really have is a +differential on the left integral + + align:start position:0% +differential on the left integral + + + align:start position:0% +differential on the left integral +equation on the right + + align:start position:0% +equation on the right + + + align:start position:0% +equation on the right +so even so even though you are solving + + align:start position:0% +so even so even though you are solving + + + align:start position:0% +so even so even though you are solving +one specific state with K you have to + + align:start position:0% +one specific state with K you have to + + + align:start position:0% +one specific state with K you have to +consider all the other K in your system, + + align:start position:0% +consider all the other K in your system, + + + align:start position:0% +consider all the other K in your system, +all the quantum state in your system + + align:start position:0% +all the quantum state in your system + + + align:start position:0% +all the quantum state in your system +to solve this distribution functions + + align:start position:0% +to solve this distribution functions + + + align:start position:0% +to solve this distribution functions +and uh in transport of course if your + + align:start position:0% +and uh in transport of course if your + + + align:start position:0% +and uh in transport of course if your +temperature is changing you say as a + + align:start position:0% +temperature is changing you say as a + + + align:start position:0% +temperature is changing you say as a +function R. So every point you consider + + align:start position:0% +function R. So every point you consider + + + align:start position:0% +function R. So every point you consider +all the K and you swap you you so the + + align:start position:0% +all the K and you swap you you so the + + + align:start position:0% +all the K and you swap you you so the +the the way that people some people try + + align:start position:0% +the the way that people some people try + + + align:start position:0% +the the way that people some people try +to swap there for each of this field + + align:start position:0% +to swap there for each of this field + + + align:start position:0% +to swap there for each of this field +there are not many + + align:start position:0% +there are not many + + + align:start position:0% +there are not many +twice it's pretty complicated problem + + align:start position:0% +twice it's pretty complicated problem + + + align:start position:0% +twice it's pretty complicated problem +right and say you typically do a + + align:start position:0% +right and say you typically do a + + + align:start position:0% +right and say you typically do a +iterative solution + + align:start position:0% +iterative solution + + + align:start position:0% +iterative solution +because say this one is for specific K + + align:start position:0% +because say this one is for specific K + + + align:start position:0% +because say this one is for specific K +but this integration involves all other + + align:start position:0% +but this integration involves all other + + + align:start position:0% +but this integration involves all other +states + + align:start position:0% +states + + + align:start position:0% +states +right your solution has to meet those + + align:start position:0% +right your solution has to meet those + + + align:start position:0% +right your solution has to meet those +all those requirements + + align:start position:0% + + + + align:start position:0% + +okay so it's a integral differential + + align:start position:0% +okay so it's a integral differential + + + align:start position:0% +okay so it's a integral differential +equation + + align:start position:0% +equation + + + align:start position:0% +equation +and the integration + + align:start position:0% +and the integration + + + align:start position:0% +and the integration +is in k space the differentiation in + + align:start position:0% +is in k space the differentiation in + + + align:start position:0% +is in k space the differentiation in +both uh say uh real space r + + align:start position:0% +both uh say uh real space r + + + align:start position:0% +both uh say uh real space r +and p k space + + align:start position:0% +and p k space + + + align:start position:0% +and p k space +Okay. + + align:start position:0% + + + + align:start position:0% + +But this is very hard + + align:start position:0% +But this is very hard + + + align:start position:0% +But this is very hard +and uh uh this equation the boardsman + + align:start position:0% +and uh uh this equation the boardsman + + + align:start position:0% +and uh uh this equation the boardsman +equation is used by electrical engineer. + + align:start position:0% +equation is used by electrical engineer. + + + align:start position:0% +equation is used by electrical engineer. +It's the foundation you can derive all + + align:start position:0% +It's the foundation you can derive all + + + align:start position:0% +It's the foundation you can derive all +the electrical the equation electrical + + align:start position:0% +the electrical the equation electrical + + + align:start position:0% +the electrical the equation electrical +engineer use + + align:start position:0% +engineer use + + + align:start position:0% +engineer use +and uh it's used lot of the past + + align:start position:0% +and uh it's used lot of the past + + + align:start position:0% +and uh it's used lot of the past +literature is on gas dynamics rarified + + align:start position:0% +literature is on gas dynamics rarified + + + align:start position:0% +literature is on gas dynamics rarified +gas dynamics lot of studies in rarified + + align:start position:0% +gas dynamics lot of studies in rarified + + + align:start position:0% +gas dynamics lot of studies in rarified +gas dynamics do you know the reason + + align:start position:0% + + + + align:start position:0% + +why there are so many study in gas + + align:start position:0% +why there are so many study in gas + + + align:start position:0% +why there are so many study in gas +dynamics + + align:start position:0% + + + + align:start position:0% + +this is due to Apollo project. + + align:start position:0% +this is due to Apollo project. + + + align:start position:0% +this is due to Apollo project. +Why? Because say uh uh when you try to + + align:start position:0% +Why? Because say uh uh when you try to + + + align:start position:0% +Why? Because say uh uh when you try to +send the spaceship through the + + align:start position:0% +send the spaceship through the + + + align:start position:0% +send the spaceship through the +atmosphere, when you go outside the say + + align:start position:0% +atmosphere, when you go outside the say + + + align:start position:0% +atmosphere, when you go outside the say +go to outer atmosphere, the pressure is + + align:start position:0% +go to outer atmosphere, the pressure is + + + align:start position:0% +go to outer atmosphere, the pressure is +very low. The molecule mean free pass is + + align:start position:0% +very low. The molecule mean free pass is + + + align:start position:0% +very low. The molecule mean free pass is +very long. + + align:start position:0% +very long. + + + align:start position:0% +very long. +So it's in the rarified gas flow regime. + + align:start position:0% +So it's in the rarified gas flow regime. + + + align:start position:0% +So it's in the rarified gas flow regime. +So a lot of study in rarified gas + + align:start position:0% +So a lot of study in rarified gas + + + align:start position:0% +So a lot of study in rarified gas +dynamics + + align:start position:0% +dynamics + + + align:start position:0% +dynamics +and in 1960 + + align:start position:0% +and in 1960 + + + align:start position:0% +and in 1960 +uh region let's say time time scale lot + + align:start position:0% +uh region let's say time time scale lot + + + align:start position:0% +uh region let's say time time scale lot +of study in neutron + + align:start position:0% +of study in neutron + + + align:start position:0% +of study in neutron +you go to look at the neutron transport + + align:start position:0% +you go to look at the neutron transport + + + align:start position:0% +you go to look at the neutron transport +right there a lot of work they're just + + align:start position:0% +right there a lot of work they're just + + + align:start position:0% +right there a lot of work they're just +solving neutron boards my equation so + + align:start position:0% +solving neutron boards my equation so + + + align:start position:0% +solving neutron boards my equation so +you got the neutron boards my equation + + align:start position:0% +you got the neutron boards my equation + + + align:start position:0% +you got the neutron boards my equation +you got the gas boards my equation you + + align:start position:0% +you got the gas boards my equation you + + + align:start position:0% +you got the gas boards my equation you +got the electron boards my equation + + align:start position:0% +got the electron boards my equation + + + align:start position:0% +got the electron boards my equation +right you can do electron + + align:start position:0% +right you can do electron + + + align:start position:0% +right you can do electron +and a phong and photon I teach another + + align:start position:0% +and a phong and photon I teach another + + + align:start position:0% +and a phong and photon I teach another +course radiation transfer at the end we + + align:start position:0% +course radiation transfer at the end we + + + align:start position:0% +course radiation transfer at the end we +solve this equation for the photons + + align:start position:0% +solve this equation for the photons + + + align:start position:0% +solve this equation for the photons +that's when you completely ignore the + + align:start position:0% +that's when you completely ignore the + + + align:start position:0% +that's when you completely ignore the +phase of the particles + + align:start position:0% +phase of the particles + + + align:start position:0% +phase of the particles +of those waves + + align:start position:0% +of those waves + + + align:start position:0% +of those waves +so this is a uh uh that's why really + + align:start position:0% +so this is a uh uh that's why really + + + align:start position:0% +so this is a uh uh that's why really +there are not many equations if you + + align:start position:0% +there are not many equations if you + + + align:start position:0% +there are not many equations if you +start from here you can derive all the + + align:start position:0% +start from here you can derive all the + + + align:start position:0% +start from here you can derive all the +equations every field or most field use + + align:start position:0% +equations every field or most field use + + + align:start position:0% +equations every field or most field use +in in this transport regime, right? But + + align:start position:0% +in in this transport regime, right? But + + + align:start position:0% +in in this transport regime, right? But +it's a molecular chaos assumption. + + align:start position:0% +it's a molecular chaos assumption. + + + align:start position:0% +it's a molecular chaos assumption. +So this is only valid when the particles + + align:start position:0% +So this is only valid when the particles + + + align:start position:0% +So this is only valid when the particles +are dilute. That's why so far I've been + + align:start position:0% +are dilute. That's why so far I've been + + + align:start position:0% +are dilute. That's why so far I've been +doing electron full on photon molecules + + align:start position:0% +doing electron full on photon molecules + + + align:start position:0% +doing electron full on photon molecules +more on a parallel path. I can't deal + + align:start position:0% +more on a parallel path. I can't deal + + + align:start position:0% +more on a parallel path. I can't deal +you can't use words equation for liquid. + + align:start position:0% +you can't use words equation for liquid. + + + align:start position:0% +you can't use words equation for liquid. +That's not right. + + align:start position:0% +That's not right. + + + align:start position:0% +That's not right. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now moving on. This is a hard equation + + align:start position:0% +Now moving on. This is a hard equation + + + align:start position:0% +Now moving on. This is a hard equation +to solve. So there's a creative way to + + align:start position:0% +to solve. So there's a creative way to + + + align:start position:0% +to solve. So there's a creative way to +make it simple. + + align:start position:0% +make it simple. + + + align:start position:0% +make it simple. +And uh that creative way + + align:start position:0% +And uh that creative way + + + align:start position:0% +And uh that creative way +now we have Borsman equation right. So + + align:start position:0% +now we have Borsman equation right. So + + + align:start position:0% +now we have Borsman equation right. So +we do relaxation time approximation + + align:start position:0% + + + + align:start position:0% + +I say I can't deal with this nasty in + + align:start position:0% +I say I can't deal with this nasty in + + + align:start position:0% +I say I can't deal with this nasty in +integers. So what I'm going to write + + align:start position:0% +integers. So what I'm going to write + + + align:start position:0% +integers. So what I'm going to write +is + + align:start position:0% + + + + align:start position:0% + +you will be happy. Forget about that + + align:start position:0% +you will be happy. Forget about that + + + align:start position:0% +you will be happy. Forget about that +line integral. Okay. And this is the + + align:start position:0% +line integral. Okay. And this is the + + + align:start position:0% +line integral. Okay. And this is the +relaxation time. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And now you will feel that we can + + align:start position:0% +And now you will feel that we can + + + align:start position:0% +And now you will feel that we can +probably do something. And this + + align:start position:0% +probably do something. And this + + + align:start position:0% +probably do something. And this +relaxation time approximation uh again + + align:start position:0% +relaxation time approximation uh again + + + align:start position:0% +relaxation time approximation uh again +there are different field has a + + align:start position:0% +there are different field has a + + + align:start position:0% +there are different field has a +different name. You put in this + + align:start position:0% +different name. You put in this + + + align:start position:0% +different name. You put in this +relaxation time on the right hand side + + align:start position:0% +relaxation time on the right hand side + + + align:start position:0% +relaxation time on the right hand side +of Borsma equation. You go to verify gas + + align:start position:0% +of Borsma equation. You go to verify gas + + + align:start position:0% +of Borsma equation. You go to verify gas +dynamic or gas dynamic book. You will + + align:start position:0% +dynamic or gas dynamic book. You will + + + align:start position:0% +dynamic or gas dynamic book. You will +not be called Borsman equation. + + align:start position:0% +not be called Borsman equation. + + + align:start position:0% +not be called Borsman equation. +it'll be called a crook equation right + + align:start position:0% +it'll be called a crook equation right + + + align:start position:0% +it'll be called a crook equation right +so in the gas dynamic that will be crook + + align:start position:0% +so in the gas dynamic that will be crook + + + align:start position:0% +so in the gas dynamic that will be crook +equation + + align:start position:0% + + + + align:start position:0% + +and in other field people don't call the + + align:start position:0% +and in other field people don't call the + + + align:start position:0% +and in other field people don't call the +crook equation so I remember once I was + + align:start position:0% +crook equation so I remember once I was + + + align:start position:0% +crook equation so I remember once I was +given a seminar and uh say uh uh uh a + + align:start position:0% +given a seminar and uh say uh uh uh a + + + align:start position:0% +given a seminar and uh say uh uh uh a +question was ah you're not so boring + + align:start position:0% +question was ah you're not so boring + + + align:start position:0% +question was ah you're not so boring +equation you're solving crook equation + + align:start position:0% +equation you're solving crook equation + + + align:start position:0% +equation you're solving crook equation +because I I need I know who is crook + + align:start position:0% +because I I need I know who is crook + + + align:start position:0% +because I I need I know who is crook +okay what is a crook equation Okay. + + align:start position:0% +okay what is a crook equation Okay. + + + align:start position:0% +okay what is a crook equation Okay. +So uh uh the uh why it's a relaxation + + align:start position:0% +So uh uh the uh why it's a relaxation + + + align:start position:0% +So uh uh the uh why it's a relaxation +time and uh if you put in the right hand + + align:start position:0% +time and uh if you put in the right hand + + + align:start position:0% +time and uh if you put in the right hand +side and let's forget the spatial + + align:start position:0% +side and let's forget the spatial + + + align:start position:0% +side and let's forget the spatial +dependence then what I have is df dt + + align:start position:0% +dependence then what I have is df dt + + + align:start position:0% +dependence then what I have is df dt +equals so if your system is uniformly + + align:start position:0% +equals so if your system is uniformly + + + align:start position:0% +equals so if your system is uniformly +disturbed from equilibrium f0 is the + + align:start position:0% +disturbed from equilibrium f0 is the + + + align:start position:0% +disturbed from equilibrium f0 is the +equilibrium distribution + + align:start position:0% +equilibrium distribution + + + align:start position:0% +equilibrium distribution +okay then you can say here if If you + + align:start position:0% +okay then you can say here if If you + + + align:start position:0% +okay then you can say here if If you +solve this system will return f uh uh to + + align:start position:0% +solve this system will return f uh uh to + + + align:start position:0% +solve this system will return f uh uh to +equilibrium f0= + + align:start position:0% +equilibrium f0= + + + align:start position:0% +equilibrium f0= +c exponential t over to top. So you can + + align:start position:0% +c exponential t over to top. So you can + + + align:start position:0% +c exponential t over to top. So you can +say this uh exponentially relax back to + + align:start position:0% +say this uh exponentially relax back to + + + align:start position:0% +say this uh exponentially relax back to +equilibrium. + + align:start position:0% +equilibrium. + + + align:start position:0% +equilibrium. +That's why toao is called the relaxation + + align:start position:0% +That's why toao is called the relaxation + + + align:start position:0% +That's why toao is called the relaxation +time. + + align:start position:0% +time. + + + align:start position:0% +time. +Right? And uh + + align:start position:0% +Right? And uh + + + align:start position:0% +Right? And uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +typically we call this Borisma equation + + align:start position:0% +typically we call this Borisma equation + + + align:start position:0% +typically we call this Borisma equation +under relaxation time approximation. + + align:start position:0% +under relaxation time approximation. + + + align:start position:0% +under relaxation time approximation. +Uh um sometimes people also call the + + align:start position:0% +Uh um sometimes people also call the + + + align:start position:0% +Uh um sometimes people also call the +linearized Borisma equation but there + + align:start position:0% +linearized Borisma equation but there + + + align:start position:0% +linearized Borisma equation but there +some uh uh confusion there I think. So + + align:start position:0% +some uh uh confusion there I think. So + + + align:start position:0% +some uh uh confusion there I think. So +now let's go to discuss + + align:start position:0% +now let's go to discuss + + + align:start position:0% +now let's go to discuss +what's the relaxation time right? What's + + align:start position:0% +what's the relaxation time right? What's + + + align:start position:0% +what's the relaxation time right? What's +this scatter? + + align:start position:0% +this scatter? + + + align:start position:0% +this scatter? +And uh + + align:start position:0% + + + + align:start position:0% + +let's look at a different relaxation + + align:start position:0% +let's look at a different relaxation + + + align:start position:0% +let's look at a different relaxation +times different process scattering + + align:start position:0% + + + + align:start position:0% + +in general when I + + align:start position:0% + + + + align:start position:0% + +think about the uh uh scattering and uh + + align:start position:0% +think about the uh uh scattering and uh + + + align:start position:0% +think about the uh uh scattering and uh +relaxation process. Of course we can say + + align:start position:0% +relaxation process. Of course we can say + + + align:start position:0% +relaxation process. Of course we can say +we we mentioned before photon absorption + + align:start position:0% + + + + align:start position:0% + +right so if I have uh before we say okay + + align:start position:0% +right so if I have uh before we say okay + + + align:start position:0% +right so if I have uh before we say okay +this is my the problem you worked on + + align:start position:0% +this is my the problem you worked on + + + align:start position:0% +this is my the problem you worked on +right + + align:start position:0% +right + + + align:start position:0% +right +this is my semiconductor with a bank gap + + align:start position:0% +this is my semiconductor with a bank gap + + + align:start position:0% +this is my semiconductor with a bank gap +with vector so you know it's a 3D + + align:start position:0% +with vector so you know it's a 3D + + + align:start position:0% +with vector so you know it's a 3D +and uh if I have photon comes in excite + + align:start position:0% +and uh if I have photon comes in excite + + + align:start position:0% +and uh if I have photon comes in excite +from here to here and the photon + + align:start position:0% +from here to here and the photon + + + align:start position:0% +from here to here and the photon +momentum is very small. + + align:start position:0% +momentum is very small. + + + align:start position:0% +momentum is very small. +So when I do my energy conservation, + + align:start position:0% +So when I do my energy conservation, + + + align:start position:0% +So when I do my energy conservation, +this is the electron initial energy and + + align:start position:0% +this is the electron initial energy and + + + align:start position:0% +this is the electron initial energy and +this is the final energy and final + + align:start position:0% +this is the final energy and final + + + align:start position:0% +this is the final energy and final +initial energy you also have the photon + + align:start position:0% +initial energy you also have the photon + + + align:start position:0% +initial energy you also have the photon +energy right it's a two particle so + + align:start position:0% +energy right it's a two particle so + + + align:start position:0% +energy right it's a two particle so +initial have electron at e uh certain + + align:start position:0% +initial have electron at e uh certain + + + align:start position:0% +initial have electron at e uh certain +energy + + align:start position:0% +energy + + + align:start position:0% +energy +and initially my photon has energy h new + + align:start position:0% +and initially my photon has energy h new + + + align:start position:0% +and initially my photon has energy h new +right and finally the electron has + + align:start position:0% +right and finally the electron has + + + align:start position:0% +right and finally the electron has +energy EF so uh I have my energy + + align:start position:0% +energy EF so uh I have my energy + + + align:start position:0% +energy EF so uh I have my energy +conservation + + align:start position:0% +conservation + + + align:start position:0% +conservation +is E F mass EI. This is the initial + + align:start position:0% +is E F mass EI. This is the initial + + + align:start position:0% +is E F mass EI. This is the initial +electron energy that equals H bar omega + + align:start position:0% +electron energy that equals H bar omega + + + align:start position:0% +electron energy that equals H bar omega +or H new + + align:start position:0% + + + + align:start position:0% + +that's a photon energy + + align:start position:0% +that's a photon energy + + + align:start position:0% +that's a photon energy +and the momentum is KF + + align:start position:0% +and the momentum is KF + + + align:start position:0% +and the momentum is KF +uh equals KI. So the final momentum of + + align:start position:0% +uh equals KI. So the final momentum of + + + align:start position:0% +uh equals KI. So the final momentum of +the electron plus the photon h bar k of + + align:start position:0% +the electron plus the photon h bar k of + + + align:start position:0% +the electron plus the photon h bar k of +the photon + + align:start position:0% + + + + align:start position:0% + +right and of course the photon + + align:start position:0% +right and of course the photon + + + align:start position:0% +right and of course the photon +wavelength is micron typically right if + + align:start position:0% +wavelength is micron typically right if + + + align:start position:0% +wavelength is micron typically right if +one micron is 1.1 about one electron + + align:start position:0% +one micron is 1.1 about one electron + + + align:start position:0% +one micron is 1.1 about one electron +volt + + align:start position:0% +volt + + + align:start position:0% +volt +the band gap is typically electron volt + + align:start position:0% +the band gap is typically electron volt + + + align:start position:0% +the band gap is typically electron volt +few electron volts or 0.1 electron volt + + align:start position:0% +few electron volts or 0.1 electron volt + + + align:start position:0% +few electron volts or 0.1 electron volt +Right? So you can say that the + + align:start position:0% +Right? So you can say that the + + + align:start position:0% +Right? So you can say that the +wavelength lambda is of the order one + + align:start position:0% +wavelength lambda is of the order one + + + align:start position:0% +wavelength lambda is of the order one +micron + + align:start position:0% +micron + + + align:start position:0% +micron +and here the zoom boundary is pi / a. A + + align:start position:0% +and here the zoom boundary is pi / a. A + + + align:start position:0% +and here the zoom boundary is pi / a. A +a is latis constant right lattice + + align:start position:0% +a is latis constant right lattice + + + align:start position:0% +a is latis constant right lattice +constant is armstrong. So you can see + + align:start position:0% +constant is armstrong. So you can see + + + align:start position:0% +constant is armstrong. So you can see +that say lambda is really doesn't shift + + align:start position:0% +that say lambda is really doesn't shift + + + align:start position:0% +that say lambda is really doesn't shift +this the photon momentum does not shift + + align:start position:0% +this the photon momentum does not shift + + + align:start position:0% +this the photon momentum does not shift +the k much. It's just a very little + + align:start position:0% +the k much. It's just a very little + + + align:start position:0% +the k much. It's just a very little +change. So it's essentially a vertical + + align:start position:0% +change. So it's essentially a vertical + + + align:start position:0% +change. So it's essentially a vertical +transition in this case and that's the + + align:start position:0% +transition in this case and that's the + + + align:start position:0% +transition in this case and that's the +homework problem you did. uh no the the + + align:start position:0% +homework problem you did. uh no the the + + + align:start position:0% +homework problem you did. uh no the the +midterm problem you did right + + align:start position:0% +midterm problem you did right + + + align:start position:0% +midterm problem you did right +and of course you can extend this if you + + align:start position:0% +and of course you can extend this if you + + + align:start position:0% +and of course you can extend this if you +do a indirect gap semiconductor like + + align:start position:0% +do a indirect gap semiconductor like + + + align:start position:0% +do a indirect gap semiconductor like +silicon and uh say silicon I have a + + align:start position:0% +silicon and uh say silicon I have a + + + align:start position:0% +silicon and uh say silicon I have a +valance band here conduction band is not + + align:start position:0% +valance band here conduction band is not + + + align:start position:0% +valance band here conduction band is not +a minimum is somewhere here + + align:start position:0% + + + + align:start position:0% + +right this is a silicon uh or indirect + + align:start position:0% +right this is a silicon uh or indirect + + + align:start position:0% +right this is a silicon uh or indirect +gap in general + + align:start position:0% +gap in general + + + align:start position:0% +gap in general +And uh now when the energy of the photon + + align:start position:0% +And uh now when the energy of the photon + + + align:start position:0% +And uh now when the energy of the photon +is right at the gap you can say there's + + align:start position:0% +is right at the gap you can say there's + + + align:start position:0% +is right at the gap you can say there's +no enough momentum + + align:start position:0% +no enough momentum + + + align:start position:0% +no enough momentum +right the photon cannot lift the + + align:start position:0% +right the photon cannot lift the + + + align:start position:0% +right the photon cannot lift the +electron from here to here alone + + align:start position:0% +electron from here to here alone + + + align:start position:0% +electron from here to here alone +because the momentum K is not enough. + + align:start position:0% +because the momentum K is not enough. + + + align:start position:0% +because the momentum K is not enough. +So what it does is you will interact you + + align:start position:0% +So what it does is you will interact you + + + align:start position:0% +So what it does is you will interact you +actually have three particle + + align:start position:0% +actually have three particle + + + align:start position:0% +actually have three particle +right electron interact with the photon + + align:start position:0% +right electron interact with the photon + + + align:start position:0% +right electron interact with the photon +and interact with the fon + + align:start position:0% +and interact with the fon + + + align:start position:0% +and interact with the fon +very small energy + + align:start position:0% +very small energy + + + align:start position:0% +very small energy +mini eay to tens of mill + + align:start position:0% +mini eay to tens of mill + + + align:start position:0% +mini eay to tens of mill +and uh the wave vector on the other hand + + align:start position:0% +and uh the wave vector on the other hand + + + align:start position:0% +and uh the wave vector on the other hand +the momentum is large + + align:start position:0% +the momentum is large + + + align:start position:0% +the momentum is large +so you can write your uh in that case + + align:start position:0% +so you can write your uh in that case + + + align:start position:0% +so you can write your uh in that case +you say okay my uh uh the uh say + + align:start position:0% +you say okay my uh uh the uh say + + + align:start position:0% +you say okay my uh uh the uh say +indirect gap. If this transition happen, + + align:start position:0% +indirect gap. If this transition happen, + + + align:start position:0% +indirect gap. If this transition happen, +you will involve say both electron + + align:start position:0% +you will involve say both electron + + + align:start position:0% +you will involve say both electron +photon and photon and ef= ei plus h bar + + align:start position:0% +photon and photon and ef= ei plus h bar + + + align:start position:0% +photon and photon and ef= ei plus h bar +omega photon + + align:start position:0% +omega photon + + + align:start position:0% +omega photon +and it could be plus minus h bar omega + + align:start position:0% +and it could be plus minus h bar omega + + + align:start position:0% +and it could be plus minus h bar omega +of folon. + + align:start position:0% +of folon. + + + align:start position:0% +of folon. +So what that plus minus means if it's a + + align:start position:0% +So what that plus minus means if it's a + + + align:start position:0% +So what that plus minus means if it's a +plus it absorb a fon get in if it's a + + align:start position:0% +plus it absorb a fon get in if it's a + + + align:start position:0% +plus it absorb a fon get in if it's a +minus a fullon emitted + + align:start position:0% +minus a fullon emitted + + + align:start position:0% +minus a fullon emitted +right so that's your energy conservation + + align:start position:0% +right so that's your energy conservation + + + align:start position:0% +right so that's your energy conservation +now you have three particles involved + + align:start position:0% +now you have three particles involved + + + align:start position:0% +now you have three particles involved +and uh uh kf + + align:start position:0% +and uh uh kf + + + align:start position:0% +and uh uh kf +uh equals ki + + align:start position:0% +uh equals ki + + + align:start position:0% +uh equals ki +plus + + align:start position:0% +plus + + + align:start position:0% +plus +h bar k photon which you can neglect + + align:start position:0% +h bar k photon which you can neglect + + + align:start position:0% +h bar k photon which you can neglect +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And in the case of Fon this energy is + + align:start position:0% +And in the case of Fon this energy is + + + align:start position:0% +And in the case of Fon this energy is +still you you should carry it if in your + + align:start position:0% +still you you should carry it if in your + + + align:start position:0% +still you you should carry it if in your +analysis but this one is pretty small + + align:start position:0% +analysis but this one is pretty small + + + align:start position:0% +analysis but this one is pretty small +and plus minus H baron. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +uh now if you can do this problem + + align:start position:0% +uh now if you can do this problem + + + align:start position:0% +uh now if you can do this problem +you should be able to do this problem + + align:start position:0% +you should be able to do this problem + + + align:start position:0% +you should be able to do this problem +using the joint densor. Try to write + + align:start position:0% +using the joint densor. Try to write + + + align:start position:0% +using the joint densor. Try to write +down this joint of states joint density + + align:start position:0% +down this joint of states joint density + + + align:start position:0% +down this joint of states joint density +of states and say if you have an + + align:start position:0% +of states and say if you have an + + + align:start position:0% +of states and say if you have an +indirect gap semiconductor how the + + align:start position:0% +indirect gap semiconductor how the + + + align:start position:0% +indirect gap semiconductor how the +absorption would change near the band + + align:start position:0% +absorption would change near the band + + + align:start position:0% +absorption would change near the band +gap right + + align:start position:0% +gap right + + + align:start position:0% +gap right +so those are the things now you can + + align:start position:0% +so those are the things now you can + + + align:start position:0% +so those are the things now you can +apply + + align:start position:0% +apply + + + align:start position:0% +apply +and uh of course uh what I say the what + + align:start position:0% +and uh of course uh what I say the what + + + align:start position:0% +and uh of course uh what I say the what +the general behavior is for direct gap + + align:start position:0% +the general behavior is for direct gap + + + align:start position:0% +the general behavior is for direct gap +this is your energy gap eg G + + align:start position:0% +this is your energy gap eg G + + + align:start position:0% +this is your energy gap eg G +and you have a very sharp rise + + align:start position:0% +and you have a very sharp rise + + + align:start position:0% +and you have a very sharp rise +in the absorption by the indirect gap it + + align:start position:0% +in the absorption by the indirect gap it + + + align:start position:0% +in the absorption by the indirect gap it +could be lower full on right absorption + + align:start position:0% +could be lower full on right absorption + + + align:start position:0% +could be lower full on right absorption +or higher but the rate will be much + + align:start position:0% +or higher but the rate will be much + + + align:start position:0% +or higher but the rate will be much +smaller + + align:start position:0% +smaller + + + align:start position:0% +smaller +okay and uh that's the we mentioned + + align:start position:0% +okay and uh that's the we mentioned + + + align:start position:0% +okay and uh that's the we mentioned +before this is a problem of silicon when + + align:start position:0% +before this is a problem of silicon when + + + align:start position:0% +before this is a problem of silicon when +you try to use as a solar cell Because + + align:start position:0% +you try to use as a solar cell Because + + + align:start position:0% +you try to use as a solar cell Because +this absorption is not very strong which + + align:start position:0% +this absorption is not very strong which + + + align:start position:0% +this absorption is not very strong which +purely means you can have to use very + + align:start position:0% +purely means you can have to use very + + + align:start position:0% +purely means you can have to use very +thick material to absorb the photon to + + align:start position:0% +thick material to absorb the photon to + + + align:start position:0% +thick material to absorb the photon to +capture it and uh that is the cost of + + align:start position:0% +capture it and uh that is the cost of + + + align:start position:0% +capture it and uh that is the cost of +the materials. + + align:start position:0% +the materials. + + + align:start position:0% +the materials. +Yes. + + align:start position:0% +Yes. + + + align:start position:0% +Yes. +You actually have that three body + + align:start position:0% +You actually have that three body + + + align:start position:0% +You actually have that three body +interaction. + + align:start position:0% +interaction. + + + align:start position:0% +interaction. +Oh yeah. + + align:start position:0% +Oh yeah. + + + align:start position:0% +Oh yeah. +Or is it typical that you absorb first + + align:start position:0% +Or is it typical that you absorb first + + + align:start position:0% +Or is it typical that you absorb first +and the photon has to provide the + + align:start position:0% +and the photon has to provide the + + + align:start position:0% +and the photon has to provide the +vertical gap and then it'll dissipate + + align:start position:0% +vertical gap and then it'll dissipate + + + align:start position:0% +vertical gap and then it'll dissipate +some of that energy? Oh, that's a this + + align:start position:0% +some of that energy? Oh, that's a this + + + align:start position:0% +some of that energy? Oh, that's a this +is a very good question. Uh it's a rate + + align:start position:0% +is a very good question. Uh it's a rate + + + align:start position:0% +is a very good question. Uh it's a rate +problem. + + align:start position:0% +problem. + + + align:start position:0% +problem. +It's a rate, right? So whether it happen + + align:start position:0% +It's a rate, right? So whether it happen + + + align:start position:0% +It's a rate, right? So whether it happen +if you have absorb and uh uh uh uh I + + align:start position:0% +if you have absorb and uh uh uh uh I + + + align:start position:0% +if you have absorb and uh uh uh uh I +think say you probably can have some + + align:start position:0% +think say you probably can have some + + + align:start position:0% +think say you probably can have some +mismatch due to the uncertainty + + align:start position:0% +mismatch due to the uncertainty + + + align:start position:0% +mismatch due to the uncertainty +principle. + + align:start position:0% +principle. + + + align:start position:0% +principle. +But I do not uh say so you sometimes you + + align:start position:0% +But I do not uh say so you sometimes you + + + align:start position:0% +But I do not uh say so you sometimes you +can say you raise that to virtual state + + align:start position:0% +can say you raise that to virtual state + + + align:start position:0% +can say you raise that to virtual state +and then you need the other send to come + + align:start position:0% +and then you need the other send to come + + + align:start position:0% +and then you need the other send to come +in but say that's very short. So you you + + align:start position:0% +in but say that's very short. So you you + + + align:start position:0% +in but say that's very short. So you you +almost instantaneous you have to have + + align:start position:0% +almost instantaneous you have to have + + + align:start position:0% +almost instantaneous you have to have +that. So that that's a lot of reason why + + align:start position:0% +that. So that that's a lot of reason why + + + align:start position:0% +that. So that that's a lot of reason why +this one is smaller right the scatter + + align:start position:0% +this one is smaller right the scatter + + + align:start position:0% +this one is smaller right the scatter +matrix will be weaker + + align:start position:0% +matrix will be weaker + + + align:start position:0% +matrix will be weaker +and uh the that's in this region is + + align:start position:0% +and uh the that's in this region is + + + align:start position:0% +and uh the that's in this region is +smaller. + + align:start position:0% +smaller. + + + align:start position:0% +smaller. +Yes. If you were to provide a lattice + + align:start position:0% +Yes. If you were to provide a lattice + + + align:start position:0% +Yes. If you were to provide a lattice +vibration for like indirect + + align:start position:0% +vibration for like indirect + + + align:start position:0% +vibration for like indirect +semiconductor + + align:start position:0% +semiconductor + + + align:start position:0% +semiconductor +right + + align:start position:0% +right + + + align:start position:0% +right +could you theoretically convert it from + + align:start position:0% +could you theoretically convert it from + + + align:start position:0% +could you theoretically convert it from +indirect to direct + + align:start position:0% +indirect to direct + + + align:start position:0% +indirect to direct +how uh oh see could you what's the + + align:start position:0% +how uh oh see could you what's the + + + align:start position:0% +how uh oh see could you what's the +question again + + align:start position:0% +question again + + + align:start position:0% +question again +you basically providing the phone + + align:start position:0% +you basically providing the phone + + + align:start position:0% +you basically providing the phone +right + + align:start position:0% +right + + + align:start position:0% +right +well uh you you don't have see this is + + align:start position:0% +well uh you you don't have see this is + + + align:start position:0% +well uh you you don't have see this is +you can't shift this one + + align:start position:0% +you can't shift this one + + + align:start position:0% +you can't shift this one +there are some idea how to shift it the + + align:start position:0% +there are some idea how to shift it the + + + align:start position:0% +there are some idea how to shift it the +idea to shift it is using quantum size + + align:start position:0% +idea to shift it is using quantum size + + + align:start position:0% +idea to shift it is using quantum size +Okay, that's the uh first problem uh uh + + align:start position:0% +Okay, that's the uh first problem uh uh + + + align:start position:0% +Okay, that's the uh first problem uh uh +I give say in the quiz the short + + align:start position:0% +I give say in the quiz the short + + + align:start position:0% +I give say in the quiz the short +problem. Now when you use very small so + + align:start position:0% +problem. Now when you use very small so + + + align:start position:0% +problem. Now when you use very small so +what happens is this one will rise + + align:start position:0% +what happens is this one will rise + + + align:start position:0% +what happens is this one will rise +right the next the first level will + + align:start position:0% +right the next the first level will + + + align:start position:0% +right the next the first level will +become here rather than at the bottom + + align:start position:0% +become here rather than at the bottom + + + align:start position:0% +become here rather than at the bottom +and if it's small enough this one rise + + align:start position:0% +and if it's small enough this one rise + + + align:start position:0% +and if it's small enough this one rise +here and be lower than that + + align:start position:0% +here and be lower than that + + + align:start position:0% +here and be lower than that +depends on the effective mass it's if + + align:start position:0% +depends on the effective mass it's if + + + align:start position:0% +depends on the effective mass it's if +this is a sharp this is a very very see + + align:start position:0% +this is a sharp this is a very very see + + + align:start position:0% +this is a sharp this is a very very see +the the flat means a large effective + + align:start position:0% +the the flat means a large effective + + + align:start position:0% +the the flat means a large effective +mass that means you need a much smaller + + align:start position:0% +mass that means you need a much smaller + + + align:start position:0% +mass that means you need a much smaller +diameter to raise it so you have to look + + align:start position:0% +diameter to raise it so you have to look + + + align:start position:0% +diameter to raise it so you have to look +at the effective mass of each band + + align:start position:0% +at the effective mass of each band + + + align:start position:0% +at the effective mass of each band +and uh of course when you make small + + align:start position:0% +and uh of course when you make small + + + align:start position:0% +and uh of course when you make small +this will also going down and the some + + align:start position:0% +this will also going down and the some + + + align:start position:0% +this will also going down and the some +of the you say this is the first problem + + align:start position:0% +of the you say this is the first problem + + + align:start position:0% +of the you say this is the first problem +is you have to consider what's going up + + align:start position:0% +is you have to consider what's going up + + + align:start position:0% +is you have to consider what's going up +for the conduction band what's goes down + + align:start position:0% +for the conduction band what's goes down + + + align:start position:0% +for the conduction band what's goes down +you multiply when the effective mass is + + align:start position:0% +you multiply when the effective mass is + + + align:start position:0% +you multiply when the effective mass is +same you multiply by a factor of two + + align:start position:0% +same you multiply by a factor of two + + + align:start position:0% +same you multiply by a factor of two +that's how you enlarge the band gap + + align:start position:0% +that's how you enlarge the band gap + + + align:start position:0% +that's how you enlarge the band gap +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +uh this is a photon Maybe I can make one + + align:start position:0% +uh this is a photon Maybe I can make one + + + align:start position:0% +uh this is a photon Maybe I can make one +more comment related to Wy question, + + align:start position:0% +more comment related to Wy question, + + + align:start position:0% +more comment related to Wy question, +right? Some people say, okay, let me + + align:start position:0% +right? Some people say, okay, let me + + + align:start position:0% +right? Some people say, okay, let me +develop a intermediate band gap solar + + align:start position:0% +develop a intermediate band gap solar + + + align:start position:0% +develop a intermediate band gap solar +shell, + + align:start position:0% +shell, + + + align:start position:0% +shell, +right? What does that mean? + + align:start position:0% +right? What does that mean? + + + align:start position:0% +right? What does that mean? +This is a band gap, right? And some of + + align:start position:0% +This is a band gap, right? And some of + + + align:start position:0% +This is a band gap, right? And some of +the infrared photon is not absorbed + + align:start position:0% +the infrared photon is not absorbed + + + align:start position:0% +the infrared photon is not absorbed +because there's not enough energy. So + + align:start position:0% +because there's not enough energy. So + + + align:start position:0% +because there's not enough energy. So +the idea is okay let me develop a energy + + align:start position:0% +the idea is okay let me develop a energy + + + align:start position:0% +the idea is okay let me develop a energy +level in the gap by putting out other + + align:start position:0% +level in the gap by putting out other + + + align:start position:0% +level in the gap by putting out other +atoms or quantum dots in the region + + align:start position:0% +atoms or quantum dots in the region + + + align:start position:0% +atoms or quantum dots in the region +right + + align:start position:0% +right + + + align:start position:0% +right +and then the infrared photon now can go + + align:start position:0% +and then the infrared photon now can go + + + align:start position:0% +and then the infrared photon now can go +from here to here the first photon + + align:start position:0% +from here to here the first photon + + + align:start position:0% +from here to here the first photon +and then the second photon go from here + + align:start position:0% +and then the second photon go from here + + + align:start position:0% +and then the second photon go from here +to here + + align:start position:0% +to here + + + align:start position:0% +to here +it's a nice idea + + align:start position:0% +it's a nice idea + + + align:start position:0% +it's a nice idea +but it's hard to do why + + align:start position:0% +but it's hard to do why + + + align:start position:0% +but it's hard to do why +this is a matter of the time residual + + align:start position:0% +this is a matter of the time residual + + + align:start position:0% +this is a matter of the time residual +time Right? You leave the electron to + + align:start position:0% +time Right? You leave the electron to + + + align:start position:0% +time Right? You leave the electron to +here and it has a tendency to get lost. + + align:start position:0% +here and it has a tendency to get lost. + + + align:start position:0% +here and it has a tendency to get lost. +The competition this is all red. Right? + + align:start position:0% +The competition this is all red. Right? + + + align:start position:0% +The competition this is all red. Right? +If it relax back or interact with the + + align:start position:0% +If it relax back or interact with the + + + align:start position:0% +If it relax back or interact with the +phong and become heat, then you lost. + + align:start position:0% +phong and become heat, then you lost. + + + align:start position:0% +phong and become heat, then you lost. +So you have say the uh say if you can + + align:start position:0% +So you have say the uh say if you can + + + align:start position:0% +So you have say the uh say if you can +stay there long enough wait for the next + + align:start position:0% +stay there long enough wait for the next + + + align:start position:0% +stay there long enough wait for the next +photon to come to lift it. + + align:start position:0% +photon to come to lift it. + + + align:start position:0% +photon to come to lift it. +You can go to calculate + + align:start position:0% +You can go to calculate + + + align:start position:0% +You can go to calculate +roughly back of envelope. If I have + + align:start position:0% +roughly back of envelope. If I have + + + align:start position:0% +roughly back of envelope. If I have +certain photon density coming in, how + + align:start position:0% +certain photon density coming in, how + + + align:start position:0% +certain photon density coming in, how +long it takes for the lex photon to come + + align:start position:0% +long it takes for the lex photon to come + + + align:start position:0% +long it takes for the lex photon to come +in with that certain energy, right? So, + + align:start position:0% +in with that certain energy, right? So, + + + align:start position:0% +in with that certain energy, right? So, +and the other way is say uh uh there are + + align:start position:0% +and the other way is say uh uh there are + + + align:start position:0% +and the other way is say uh uh there are +also the so-called two photon + + align:start position:0% +also the so-called two photon + + + align:start position:0% +also the so-called two photon +absorption. + + align:start position:0% +absorption. + + + align:start position:0% +absorption. +What happens is is two photon comes in + + align:start position:0% +What happens is is two photon comes in + + + align:start position:0% +What happens is is two photon comes in +at same time + + align:start position:0% +at same time + + + align:start position:0% +at same time +and same place and then you get that + + align:start position:0% +and same place and then you get that + + + align:start position:0% +and same place and then you get that +transition. But you can see in that case + + align:start position:0% +transition. But you can see in that case + + + align:start position:0% +transition. But you can see in that case +what they need it's a very high flux + + align:start position:0% +what they need it's a very high flux + + + align:start position:0% +what they need it's a very high flux +right because they need to come at the + + align:start position:0% +right because they need to come at the + + + align:start position:0% +right because they need to come at the +same time same location so you need a + + align:start position:0% +same time same location so you need a + + + align:start position:0% +same time same location so you need a +lot of them so long linear optics this + + align:start position:0% +lot of them so long linear optics this + + + align:start position:0% +lot of them so long linear optics this +two photon absorption they require very + + align:start position:0% +two photon absorption they require very + + + align:start position:0% +two photon absorption they require very +high intensity you use lasers to do that + + align:start position:0% +high intensity you use lasers to do that + + + align:start position:0% +high intensity you use lasers to do that +and uh uh in fact many times you need a + + align:start position:0% +and uh uh in fact many times you need a + + + align:start position:0% +and uh uh in fact many times you need a +very high fre uh intensity lasers to get + + align:start position:0% +very high fre uh intensity lasers to get + + + align:start position:0% +very high fre uh intensity lasers to get +a nonlinear regime. + + align:start position:0% +a nonlinear regime. + + + align:start position:0% +a nonlinear regime. +So it's all related to the rate the time + + align:start position:0% +So it's all related to the rate the time + + + align:start position:0% +So it's all related to the rate the time +when you think about what's possible + + align:start position:0% +when you think about what's possible + + + align:start position:0% +when you think about what's possible +right there's a concept there you this + + align:start position:0% +right there's a concept there you this + + + align:start position:0% +right there's a concept there you this +rate concept is very important right how + + align:start position:0% +rate concept is very important right how + + + align:start position:0% +rate concept is very important right how +fast is the process + + align:start position:0% +fast is the process + + + align:start position:0% +fast is the process +and uh you can dream for example uh I + + align:start position:0% +and uh you can dream for example uh I + + + align:start position:0% +and uh you can dream for example uh I +have say uh some electron comes photon + + align:start position:0% +have say uh some electron comes photon + + + align:start position:0% +have say uh some electron comes photon +comes in right I can lift the electron + + align:start position:0% +comes in right I can lift the electron + + + align:start position:0% +comes in right I can lift the electron +say sometimes I can have absorption + + align:start position:0% +say sometimes I can have absorption + + + align:start position:0% +say sometimes I can have absorption +from here to here + + align:start position:0% +from here to here + + + align:start position:0% +from here to here +free carrier absorption and I say okay + + align:start position:0% +free carrier absorption and I say okay + + + align:start position:0% +free carrier absorption and I say okay +uh or I have a high energy photon comes + + align:start position:0% +uh or I have a high energy photon comes + + + align:start position:0% +uh or I have a high energy photon comes +in right because the solar spectrum have + + align:start position:0% +in right because the solar spectrum have + + + align:start position:0% +in right because the solar spectrum have +a lot of photon like that you raise + + align:start position:0% +a lot of photon like that you raise + + + align:start position:0% +a lot of photon like that you raise +electron here + + align:start position:0% +electron here + + + align:start position:0% +electron here +isn't it good if you take this electron + + align:start position:0% +isn't it good if you take this electron + + + align:start position:0% +isn't it good if you take this electron +energy out rather than go back to here + + align:start position:0% +energy out rather than go back to here + + + align:start position:0% +energy out rather than go back to here +most solar cell this electron will go + + align:start position:0% +most solar cell this electron will go + + + align:start position:0% +most solar cell this electron will go +here then you take it out + + align:start position:0% +here then you take it out + + + align:start position:0% +here then you take it out +from here to here is about pec + + align:start position:0% +from here to here is about pec + + + align:start position:0% +from here to here is about pec +okay time scale. So you look at how long + + align:start position:0% +okay time scale. So you look at how long + + + align:start position:0% +okay time scale. So you look at how long +it takes how one picoscond how much + + align:start position:0% +it takes how one picoscond how much + + + align:start position:0% +it takes how one picoscond how much +electron will travel + + align:start position:0% +electron will travel + + + align:start position:0% +electron will travel +you'll say that's very hard right so + + align:start position:0% +you'll say that's very hard right so + + + align:start position:0% +you'll say that's very hard right so +it's this rate process those are the uh + + align:start position:0% +it's this rate process those are the uh + + + align:start position:0% +it's this rate process those are the uh +very important getting this order right + + align:start position:0% + + + + align:start position:0% + +so this is a we say okay energy + + align:start position:0% +so this is a we say okay energy + + + align:start position:0% +so this is a we say okay energy +transport energy conversion what is it + + align:start position:0% +transport energy conversion what is it + + + align:start position:0% +transport energy conversion what is it +this is energy conversion you say Right? + + align:start position:0% +this is energy conversion you say Right? + + + align:start position:0% +this is energy conversion you say Right? +The energy is going from photon to + + align:start position:0% +The energy is going from photon to + + + align:start position:0% +The energy is going from photon to +electron + + align:start position:0% +electron + + + align:start position:0% +electron +and there are of course many competing + + align:start position:0% +and there are of course many competing + + + align:start position:0% +and there are of course many competing +process if you do a device and the other + + align:start position:0% +process if you do a device and the other + + + align:start position:0% +process if you do a device and the other +process you electron full once you get + + align:start position:0% +process you electron full once you get + + + align:start position:0% +process you electron full once you get +the electron and + + align:start position:0% +the electron and + + + align:start position:0% +the electron and +full on fullon. + + align:start position:0% + + + + align:start position:0% + +So uh + + align:start position:0% +So uh + + + align:start position:0% +So uh +let's look at solon + + align:start position:0% + + + + align:start position:0% + +so far when we talk about full on we did + + align:start position:0% +so far when we talk about full on we did + + + align:start position:0% +so far when we talk about full on we did +dispersion we did the sprint mass + + align:start position:0% +dispersion we did the sprint mass + + + align:start position:0% +dispersion we did the sprint mass +springs right + + align:start position:0% +springs right + + + align:start position:0% +springs right +that's the idea harmonic oscillator and + + align:start position:0% +that's the idea harmonic oscillator and + + + align:start position:0% +that's the idea harmonic oscillator and +they do not interact if I just have + + align:start position:0% +they do not interact if I just have + + + align:start position:0% +they do not interact if I just have +harmonic oscillator photon is a harmonic + + align:start position:0% +harmonic oscillator photon is a harmonic + + + align:start position:0% +harmonic oscillator photon is a harmonic +oscillator photon do not interact. + + align:start position:0% +oscillator photon do not interact. + + + align:start position:0% +oscillator photon do not interact. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +so it's the unharmonic term that will + + align:start position:0% +so it's the unharmonic term that will + + + align:start position:0% +so it's the unharmonic term that will +cause that interaction and for photon + + align:start position:0% +cause that interaction and for photon + + + align:start position:0% +cause that interaction and for photon +folong in fact it's hard to get a photon + + align:start position:0% +folong in fact it's hard to get a photon + + + align:start position:0% +folong in fact it's hard to get a photon +talk to each other interact with each + + align:start position:0% +talk to each other interact with each + + + align:start position:0% +talk to each other interact with each +other like I say nonlinear objects you + + align:start position:0% +other like I say nonlinear objects you + + + align:start position:0% +other like I say nonlinear objects you +need a very large flux to get them + + align:start position:0% +need a very large flux to get them + + + align:start position:0% +need a very large flux to get them +together right but with a phong which is + + align:start position:0% +together right but with a phong which is + + + align:start position:0% +together right but with a phong which is +in the sol in solid the lattice say this + + align:start position:0% +in the sol in solid the lattice say this + + + align:start position:0% +in the sol in solid the lattice say this +is the potential we draw before and the + + align:start position:0% +is the potential we draw before and the + + + align:start position:0% +is the potential we draw before and the +harmonic approximation is approxim made + + align:start position:0% +harmonic approximation is approxim made + + + align:start position:0% +harmonic approximation is approxim made +this point up by parabola, right? So + + align:start position:0% +this point up by parabola, right? So + + + align:start position:0% +this point up by parabola, right? So +here is the potential, here is the + + align:start position:0% +here is the potential, here is the + + + align:start position:0% +here is the potential, here is the +distance and uh but say if you write + + align:start position:0% +distance and uh but say if you write + + + align:start position:0% +distance and uh but say if you write +down the higher order term, right? This + + align:start position:0% +down the higher order term, right? This + + + align:start position:0% +down the higher order term, right? This +is the minimum and the first order is + + align:start position:0% +is the minimum and the first order is + + + align:start position:0% +is the minimum and the first order is +gone 12 k x - x0 squar. So that's a + + align:start position:0% +gone 12 k x - x0 squar. So that's a + + + align:start position:0% +gone 12 k x - x0 squar. So that's a +harmonic term, + + align:start position:0% +harmonic term, + + + align:start position:0% +harmonic term, +right? And then you have unharmonic. The + + align:start position:0% +right? And then you have unharmonic. The + + + align:start position:0% +right? And then you have unharmonic. The +next term is unharmonic. So you expand + + align:start position:0% +next term is unharmonic. So you expand + + + align:start position:0% +next term is unharmonic. So you expand +your potential using tailor expansion is + + align:start position:0% +your potential using tailor expansion is + + + align:start position:0% +your potential using tailor expansion is +dx² + + align:start position:0% +dx² + + + align:start position:0% +dx² +uh say uh x0 and x - x0 cubic + + align:start position:0% +uh say uh x0 and x - x0 cubic + + + align:start position:0% +uh say uh x0 and x - x0 cubic +right zer first order g second order + + align:start position:0% +right zer first order g second order + + + align:start position:0% +right zer first order g second order +third order + + align:start position:0% +third order + + + align:start position:0% +third order +you can write fourth order + + align:start position:0% +you can write fourth order + + + align:start position:0% +you can write fourth order +now you do your spring constant your + + align:start position:0% +now you do your spring constant your + + + align:start position:0% +now you do your spring constant your +force is df du dx + + align:start position:0% +force is df du dx + + + align:start position:0% +force is df du dx +Right? Of course, you get your spring + + align:start position:0% +Right? Of course, you get your spring + + + align:start position:0% +Right? Of course, you get your spring +term, harmonica spring term. That's what + + align:start position:0% +term, harmonica spring term. That's what + + + align:start position:0% +term, harmonica spring term. That's what +we use when do the full on dispersion. + + align:start position:0% +we use when do the full on dispersion. + + + align:start position:0% +we use when do the full on dispersion. +But if you go to your next term, your + + align:start position:0% +But if you go to your next term, your + + + align:start position:0% +But if you go to your next term, your +higher order term, you'll get the x - x0 + + align:start position:0% +higher order term, you'll get the x - x0 + + + align:start position:0% +higher order term, you'll get the x - x0 +squar, + + align:start position:0% +squar, + + + align:start position:0% +squar, +right? That's the third order term. So + + align:start position:0% +right? That's the third order term. So + + + align:start position:0% +right? That's the third order term. So +that gives you + + align:start position:0% +that gives you + + + align:start position:0% +that gives you +not a sprint linear sprint along linear + + align:start position:0% +not a sprint linear sprint along linear + + + align:start position:0% +not a sprint linear sprint along linear +sprint. + + align:start position:0% +sprint. + + + align:start position:0% +sprint. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +Now if you have two phonons + + align:start position:0% +Now if you have two phonons + + + align:start position:0% +Now if you have two phonons +each one has one specific frequency + + align:start position:0% +each one has one specific frequency + + + align:start position:0% +each one has one specific frequency +you do there's product + + align:start position:0% +you do there's product + + + align:start position:0% +you do there's product +of the two for right omega 1 sin omega + + align:start position:0% +of the two for right omega 1 sin omega + + + align:start position:0% +of the two for right omega 1 sin omega +1* omega t1 t * sin omega 2 2t what do + + align:start position:0% +1* omega t1 t * sin omega 2 2t what do + + + align:start position:0% +1* omega t1 t * sin omega 2 2t what do +you get you got plus minus + + align:start position:0% +you get you got plus minus + + + align:start position:0% +you get you got plus minus +right that's a long linear term so you + + align:start position:0% +right that's a long linear term so you + + + align:start position:0% +right that's a long linear term so you +start to have the two sine waves + + align:start position:0% +start to have the two sine waves + + + align:start position:0% +start to have the two sine waves +interact with each + + align:start position:0% +interact with each + + + align:start position:0% +interact with each +If you have those nonlinear term + + align:start position:0% +If you have those nonlinear term + + + align:start position:0% +If you have those nonlinear term +otherwise it's just a linear ship + + align:start position:0% +otherwise it's just a linear ship + + + align:start position:0% +otherwise it's just a linear ship +position they will never change + + align:start position:0% +position they will never change + + + align:start position:0% +position they will never change +frequency. + + align:start position:0% +frequency. + + + align:start position:0% +frequency. +So this is the source of full on full on + + align:start position:0% +So this is the source of full on full on + + + align:start position:0% +So this is the source of full on full on +interaction + + align:start position:0% +interaction + + + align:start position:0% +interaction +and uh the unharmonic force term gives + + align:start position:0% +and uh the unharmonic force term gives + + + align:start position:0% +and uh the unharmonic force term gives +you the part because of this you can say + + align:start position:0% +you the part because of this you can say + + + align:start position:0% +you the part because of this you can say +if I have omega 1 comes in + + align:start position:0% +if I have omega 1 comes in + + + align:start position:0% +if I have omega 1 comes in +omega 2 comes in it can go omega 3 + + align:start position:0% +omega 2 comes in it can go omega 3 + + + align:start position:0% +omega 2 comes in it can go omega 3 +that's a sum so what it means is two + + align:start position:0% +that's a sum so what it means is two + + + align:start position:0% +that's a sum so what it means is two +fullon becomes one + + align:start position:0% +fullon becomes one + + + align:start position:0% +fullon becomes one +or you can have one fon split into two, + + align:start position:0% +or you can have one fon split into two, + + + align:start position:0% +or you can have one fon split into two, +right? So you have the uh omega 1 omega + + align:start position:0% +right? So you have the uh omega 1 omega + + + align:start position:0% +right? So you have the uh omega 1 omega +2 omega 3 and then in the process you + + align:start position:0% +2 omega 3 and then in the process you + + + align:start position:0% +2 omega 3 and then in the process you +have energy and momentum conservation. + + align:start position:0% +have energy and momentum conservation. + + + align:start position:0% +have energy and momentum conservation. +This is h omega 1 plus h omega 2 = h + + align:start position:0% +This is h omega 1 plus h omega 2 = h + + + align:start position:0% +This is h omega 1 plus h omega 2 = h +omega 3. That's for the this one is the + + align:start position:0% +omega 3. That's for the this one is the + + + align:start position:0% +omega 3. That's for the this one is the +uh say absorption process. And in follow + + align:start position:0% +uh say absorption process. And in follow + + + align:start position:0% +uh say absorption process. And in follow +language we don't call that absorption. + + align:start position:0% +language we don't call that absorption. + + + align:start position:0% +language we don't call that absorption. +We say that uh anhilation I don't I okay + + align:start position:0% +We say that uh anhilation I don't I okay + + + align:start position:0% +We say that uh anhilation I don't I okay +I say + + align:start position:0% +I say + + + align:start position:0% +I say +maybe I should not pronounce the h + + align:start position:0% +maybe I should not pronounce the h + + + align:start position:0% +maybe I should not pronounce the h +right. Annulation, + + align:start position:0% + + + + align:start position:0% + +right? Annelation, you agree? + + align:start position:0% +right? Annelation, you agree? + + + align:start position:0% +right? Annelation, you agree? +And here is a creation, right? One + + align:start position:0% +And here is a creation, right? One + + + align:start position:0% +And here is a creation, right? One +becomes two. + + align:start position:0% +becomes two. + + + align:start position:0% +becomes two. +So this is a creation process. + + align:start position:0% + + + + align:start position:0% + +So uh create uh say for this you can + + align:start position:0% +So uh create uh say for this you can + + + align:start position:0% +So uh create uh say for this you can +write the corresponding + + align:start position:0% +write the corresponding + + + align:start position:0% +write the corresponding +energy conservation. + + align:start position:0% +energy conservation. + + + align:start position:0% +energy conservation. +Now momentum conservation is interesting + + align:start position:0% +Now momentum conservation is interesting + + + align:start position:0% +Now momentum conservation is interesting +and normally I would write h bar k1 + + align:start position:0% +and normally I would write h bar k1 + + + align:start position:0% +and normally I would write h bar k1 +plus h bar k2 + + align:start position:0% +plus h bar k2 + + + align:start position:0% +plus h bar k2 +equals h bar k3. + + align:start position:0% +equals h bar k3. + + + align:start position:0% +equals h bar k3. +This is a law more and in fact this is + + align:start position:0% +This is a law more and in fact this is + + + align:start position:0% +This is a law more and in fact this is +called normal process. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +But normal process that scattering + + align:start position:0% +But normal process that scattering + + + align:start position:0% +But normal process that scattering +actually do not create a resistance for + + align:start position:0% +actually do not create a resistance for + + + align:start position:0% +actually do not create a resistance for +heat flow. + + align:start position:0% + + + + align:start position:0% + +Why is that? + + align:start position:0% +Why is that? + + + align:start position:0% +Why is that? +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Let's think about the vector uh format + + align:start position:0% +Let's think about the vector uh format + + + align:start position:0% +Let's think about the vector uh format +we just did. + + align:start position:0% +we just did. + + + align:start position:0% +we just did. +Right. + + align:start position:0% + + + + align:start position:0% + +So what I have if I draw that as a + + align:start position:0% +So what I have if I draw that as a + + + align:start position:0% +So what I have if I draw that as a +momentum conservation. So this is a uh h + + align:start position:0% +momentum conservation. So this is a uh h + + + align:start position:0% +momentum conservation. So this is a uh h +bar k1 + + align:start position:0% +bar k1 + + + align:start position:0% +bar k1 +h har k k2 + + align:start position:0% + + + + align:start position:0% + +and this is when they combine they form + + align:start position:0% +and this is when they combine they form + + + align:start position:0% +and this is when they combine they form +h bar k3. + + align:start position:0% +h bar k3. + + + align:start position:0% +h bar k3. +Right? That's a long process. Now + + align:start position:0% +Right? That's a long process. Now + + + align:start position:0% +Right? That's a long process. Now +originally I have h bar k1 is carrying a + + align:start position:0% +originally I have h bar k1 is carrying a + + + align:start position:0% +originally I have h bar k1 is carrying a +heat h bar omega 1 and h bar k2 is + + align:start position:0% +heat h bar omega 1 and h bar k2 is + + + align:start position:0% +heat h bar omega 1 and h bar k2 is +carrying heat h bar omega 2. Now if it's + + align:start position:0% +carrying heat h bar omega 2. Now if it's + + + align:start position:0% +carrying heat h bar omega 2. Now if it's +a normal process this final one is + + align:start position:0% +a normal process this final one is + + + align:start position:0% +a normal process this final one is +carrying a energy of omega 1 plus omega + + align:start position:0% +carrying a energy of omega 1 plus omega + + + align:start position:0% +carrying a energy of omega 1 plus omega +2 that's the same as the original right + + align:start position:0% +2 that's the same as the original right + + + align:start position:0% +2 that's the same as the original right +and also the direction is the sum of the + + align:start position:0% +and also the direction is the sum of the + + + align:start position:0% +and also the direction is the sum of the +two. + + align:start position:0% +two. + + + align:start position:0% +two. +So essentially the lat effect is if I + + align:start position:0% +So essentially the lat effect is if I + + + align:start position:0% +So essentially the lat effect is if I +have heat flow this create a lat heat + + align:start position:0% +have heat flow this create a lat heat + + + align:start position:0% +have heat flow this create a lat heat +flow in this direction. This final one + + align:start position:0% +flow in this direction. This final one + + + align:start position:0% +flow in this direction. This final one +is still carrying that same heat mount + + align:start position:0% +is still carrying that same heat mount + + + align:start position:0% +is still carrying that same heat mount +of heat flow in the same direction. + + align:start position:0% +of heat flow in the same direction. + + + align:start position:0% +of heat flow in the same direction. +Right? So this normal process actually + + align:start position:0% +Right? So this normal process actually + + + align:start position:0% +Right? So this normal process actually +do not create a resistance + + align:start position:0% + + + + align:start position:0% + +and what happens is if I think about the + + align:start position:0% +and what happens is if I think about the + + + align:start position:0% +and what happens is if I think about the +uh dispersion + + align:start position:0% + + + + align:start position:0% + +So full on dispersion + + align:start position:0% +So full on dispersion + + + align:start position:0% +So full on dispersion +right transverse non shunior + + align:start position:0% +right transverse non shunior + + + align:start position:0% +right transverse non shunior +and uh so you have to consider + + align:start position:0% +and uh so you have to consider + + + align:start position:0% +and uh so you have to consider +phone on from each different branches + + align:start position:0% +phone on from each different branches + + + align:start position:0% +phone on from each different branches +whether they can satisfy the energy + + align:start position:0% +whether they can satisfy the energy + + + align:start position:0% +whether they can satisfy the energy +conservation + + align:start position:0% +conservation + + + align:start position:0% +conservation +right this is a k + + align:start position:0% +right this is a k + + + align:start position:0% +right this is a k +and a specific direction + + align:start position:0% +and a specific direction + + + align:start position:0% +and a specific direction +omega + + align:start position:0% +omega + + + align:start position:0% +omega +and sometimes say when this one go + + align:start position:0% +and sometimes say when this one go + + + align:start position:0% +and sometimes say when this one go +beyond h k1 Let's see. + + align:start position:0% +beyond h k1 Let's see. + + + align:start position:0% +beyond h k1 Let's see. +Uh here is K2. K1 K2 go beyond the brino + + align:start position:0% +Uh here is K2. K1 K2 go beyond the brino + + + align:start position:0% +Uh here is K2. K1 K2 go beyond the brino +zone get a much larger K + + align:start position:0% + + + + align:start position:0% + +and in that case the crystal symmetry + + align:start position:0% +and in that case the crystal symmetry + + + align:start position:0% +and in that case the crystal symmetry +the reciprocal lice here this point the + + align:start position:0% +the reciprocal lice here this point the + + + align:start position:0% +the reciprocal lice here this point the +G + + align:start position:0% +G + + + align:start position:0% +G +right it could be another direction G + + align:start position:0% +right it could be another direction G + + + align:start position:0% +right it could be another direction G +I'm just drawing on the same branch but + + align:start position:0% +I'm just drawing on the same branch but + + + align:start position:0% +I'm just drawing on the same branch but +it could be completely different branch + + align:start position:0% +it could be completely different branch + + + align:start position:0% +it could be completely different branch +two phonons interact right and the uh uh + + align:start position:0% +two phonons interact right and the uh uh + + + align:start position:0% +two phonons interact right and the uh uh +if you do the wave analysis. So what's + + align:start position:0% +if you do the wave analysis. So what's + + + align:start position:0% +if you do the wave analysis. So what's +another allowable process is h bar k1 + + align:start position:0% +another allowable process is h bar k1 + + + align:start position:0% +another allowable process is h bar k1 +plus h bar k2 + + align:start position:0% +plus h bar k2 + + + align:start position:0% +plus h bar k2 +each of course h bar k3 + + align:start position:0% +each of course h bar k3 + + + align:start position:0% +each of course h bar k3 +plus h bar g. This is g is the + + align:start position:0% +plus h bar g. This is g is the + + + align:start position:0% +plus h bar g. This is g is the +reciprocal lattice vector. + + align:start position:0% + + + + align:start position:0% + +Right? In chapter + + align:start position:0% +Right? In chapter + + + align:start position:0% +Right? In chapter +uh four we talked about the fial + + align:start position:0% +uh four we talked about the fial + + + align:start position:0% +uh four we talked about the fial +transform of crystal latice point into + + align:start position:0% +transform of crystal latice point into + + + align:start position:0% +transform of crystal latice point into +fial space. + + align:start position:0% +fial space. + + + align:start position:0% +fial space. +This fer space has a corresponding lice + + align:start position:0% +This fer space has a corresponding lice + + + align:start position:0% +This fer space has a corresponding lice +constant g and that g is that g. + + align:start position:0% +constant g and that g is that g. + + + align:start position:0% +constant g and that g is that g. +Okay. And this process + + align:start position:0% +Okay. And this process + + + align:start position:0% +Okay. And this process +by adding another ve uh vector g it + + align:start position:0% +by adding another ve uh vector g it + + + align:start position:0% +by adding another ve uh vector g it +could go completely different random + + align:start position:0% +could go completely different random + + + align:start position:0% +could go completely different random +directions. + + align:start position:0% +directions. + + + align:start position:0% +directions. +That's not the original heat flow + + align:start position:0% +That's not the original heat flow + + + align:start position:0% +That's not the original heat flow +direction. + + align:start position:0% +direction. + + + align:start position:0% +direction. +So it's this process. It still has the + + align:start position:0% +So it's this process. It still has the + + + align:start position:0% +So it's this process. It still has the +energy conservation + + align:start position:0% +energy conservation + + + align:start position:0% +energy conservation +but the direction + + align:start position:0% +but the direction + + + align:start position:0% +but the direction +change due to the crystal say momentum + + align:start position:0% +change due to the crystal say momentum + + + align:start position:0% +change due to the crystal say momentum +here. This create a resistance and this + + align:start position:0% +here. This create a resistance and this + + + align:start position:0% +here. This create a resistance and this +is called the clamp + + align:start position:0% + + + + align:start position:0% + +process. + + align:start position:0% + + + + align:start position:0% + +It's a German word + + align:start position:0% +It's a German word + + + align:start position:0% +It's a German word +I think. I'm not see but this + + align:start position:0% +I think. I'm not see but this + + + align:start position:0% +I think. I'm not see but this +explanation come from Paris. Paris uh uh + + align:start position:0% +explanation come from Paris. Paris uh uh + + + align:start position:0% +explanation come from Paris. Paris uh uh +see was um Paris I think is he's he's a + + align:start position:0% +see was um Paris I think is he's he's a + + + align:start position:0% +see was um Paris I think is he's he's a +British guy. So I don't know why where + + align:start position:0% +British guy. So I don't know why where + + + align:start position:0% +British guy. So I don't know why where +this is clamp. Okay. But see I remember + + align:start position:0% +this is clamp. Okay. But see I remember + + + align:start position:0% +this is clamp. Okay. But see I remember +when I was a student I actually heard a + + align:start position:0% +when I was a student I actually heard a + + + align:start position:0% +when I was a student I actually heard a +talk seminar given by Paris. He was in + + align:start position:0% +talk seminar given by Paris. He was in + + + align:start position:0% +talk seminar given by Paris. He was in +the ' 90s at Berkeley and he told an + + align:start position:0% +the ' 90s at Berkeley and he told an + + + align:start position:0% +the ' 90s at Berkeley and he told an +interesting story + + align:start position:0% +interesting story + + + align:start position:0% +interesting story +and he say he know uh Landal and uh uh + + align:start position:0% +and he say he know uh Landal and uh uh + + + align:start position:0% +and he say he know uh Landal and uh uh +I'm not sure say the Nishious Land book + + align:start position:0% +I'm not sure say the Nishious Land book + + + align:start position:0% +I'm not sure say the Nishious Land book +that's if you read through that book uh + + align:start position:0% +that's if you read through that book uh + + + align:start position:0% +that's if you read through that book uh +you understand everything + + align:start position:0% +you understand everything + + + align:start position:0% +you understand everything +uh uh say Nandal he say Nandal was + + align:start position:0% +uh uh say Nandal he say Nandal was + + + align:start position:0% +uh uh say Nandal he say Nandal was +timing people he say he's a ser say he + + align:start position:0% +timing people he say he's a ser say he + + + align:start position:0% +timing people he say he's a ser say he +he he considered consider himself as a + + align:start position:0% +he he considered consider himself as a + + + align:start position:0% +he he considered consider himself as a +third rate scientist. + + align:start position:0% +third rate scientist. + + + align:start position:0% +third rate scientist. +Okay. And uh uh so uh people ask him who + + align:start position:0% +Okay. And uh uh so uh people ask him who + + + align:start position:0% +Okay. And uh uh so uh people ask him who +is the first rate? He say Einstein's + + align:start position:0% +is the first rate? He say Einstein's + + + align:start position:0% +is the first rate? He say Einstein's +first rate. Who is the second rate? + + align:start position:0% +first rate. Who is the second rate? + + + align:start position:0% +first rate. Who is the second rate? +Heisenberg or Dag those are first second + + align:start position:0% +Heisenberg or Dag those are first second + + + align:start position:0% +Heisenberg or Dag those are first second +rate. So he's third rate. + + align:start position:0% +rate. So he's third rate. + + + align:start position:0% +rate. So he's third rate. +Okay. Now I'm trying to read myself. + + align:start position:0% + + + + align:start position:0% + +Okay. Um so this incline process create + + align:start position:0% +Okay. Um so this incline process create + + + align:start position:0% +Okay. Um so this incline process create +resistant for the heat flow. Okay. + + align:start position:0% +resistant for the heat flow. Okay. + + + align:start position:0% +resistant for the heat flow. Okay. +And uh there are diff uh different so + + align:start position:0% +And uh there are diff uh different so + + + align:start position:0% +And uh there are diff uh different so +people have used those kind of uh so use + + align:start position:0% +people have used those kind of uh so use + + + align:start position:0% +people have used those kind of uh so use +the uh uh firm golden rule and derive + + align:start position:0% +the uh uh firm golden rule and derive + + + align:start position:0% +the uh uh firm golden rule and derive +some expressions + + align:start position:0% +some expressions + + + align:start position:0% +some expressions +but those for example for incl process + + align:start position:0% +but those for example for incl process + + + align:start position:0% +but those for example for incl process +the relaxation time uh is uh one + + align:start position:0% +the relaxation time uh is uh one + + + align:start position:0% +the relaxation time uh is uh one +expression that's used is uh the by + + align:start position:0% +expression that's used is uh the by + + + align:start position:0% +expression that's used is uh the by +temperature and KT KBT that's in the + + align:start position:0% +temperature and KT KBT that's in the + + + align:start position:0% +temperature and KT KBT that's in the +exponent G cubic omega square. + + align:start position:0% +exponent G cubic omega square. + + + align:start position:0% +exponent G cubic omega square. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +but I want to caution you this were + + align:start position:0% +but I want to caution you this were + + + align:start position:0% +but I want to caution you this were +actually uh uh done in the 50s. A lot of + + align:start position:0% +actually uh uh done in the 50s. A lot of + + + align:start position:0% +actually uh uh done in the 50s. A lot of +approximation made in those derivation + + align:start position:0% +approximation made in those derivation + + + align:start position:0% +approximation made in those derivation +and uh one for example common + + align:start position:0% +and uh one for example common + + + align:start position:0% +and uh one for example common +approximation is the B model which is a + + align:start position:0% +approximation is the B model which is a + + + align:start position:0% +approximation is the B model which is a +linear approximation to the dispersion + + align:start position:0% +linear approximation to the dispersion + + + align:start position:0% +linear approximation to the dispersion +right you know it's not going to be + + align:start position:0% +right you know it's not going to be + + + align:start position:0% +right you know it's not going to be +valid when you go to high frequency + + align:start position:0% +valid when you go to high frequency + + + align:start position:0% +valid when you go to high frequency +highway vectors + + align:start position:0% +highway vectors + + + align:start position:0% +highway vectors +and uh uh so there there are different + + align:start position:0% +and uh uh so there there are different + + + align:start position:0% +and uh uh so there there are different +former process their expression clamp + + align:start position:0% +former process their expression clamp + + + align:start position:0% +former process their expression clamp +process their approximation and also + + align:start position:0% +process their approximation and also + + + align:start position:0% +process their approximation and also +there are unknown constants + + align:start position:0% +there are unknown constants + + + align:start position:0% +there are unknown constants +And this constants is the scattering + + align:start position:0% +And this constants is the scattering + + + align:start position:0% +And this constants is the scattering +matrix. And if you don't know, so + + align:start position:0% +matrix. And if you don't know, so + + + align:start position:0% +matrix. And if you don't know, so +typically people use this as a fading + + align:start position:0% +typically people use this as a fading + + + align:start position:0% +typically people use this as a fading +parameter. + + align:start position:0% + + + + align:start position:0% + +And that's uh full on fullon scattering. + + align:start position:0% +And that's uh full on fullon scattering. + + + align:start position:0% +And that's uh full on fullon scattering. +Now there are say for what other scatter + + align:start position:0% +Now there are say for what other scatter + + + align:start position:0% +Now there are say for what other scatter +fullon are the impurities, right? You + + align:start position:0% +fullon are the impurities, right? You + + + align:start position:0% +fullon are the impurities, right? You +have say uh harmonica oscillator, you + + align:start position:0% +have say uh harmonica oscillator, you + + + align:start position:0% +have say uh harmonica oscillator, you +have silicon + + align:start position:0% +have silicon + + + align:start position:0% +have silicon +and then you dope it. You do boron, you + + align:start position:0% +and then you dope it. You do boron, you + + + align:start position:0% +and then you dope it. You do boron, you +dope phosphor, right? those has a + + align:start position:0% +dope phosphor, right? those has a + + + align:start position:0% +dope phosphor, right? those has a +different mass + + align:start position:0% +different mass + + + align:start position:0% +different mass +and uh uh the uh when so when there are + + align:start position:0% +and uh uh the uh when so when there are + + + align:start position:0% +and uh uh the uh when so when there are +waves comes in say a different mass + + align:start position:0% +waves comes in say a different mass + + + align:start position:0% +waves comes in say a different mass +they'll be scattered + + align:start position:0% +they'll be scattered + + + align:start position:0% +they'll be scattered +and this scattering is typically so + + align:start position:0% +and this scattering is typically so + + + align:start position:0% +and this scattering is typically so +impurity scattered + + align:start position:0% + + + + align:start position:0% + +and remember last time I say full on + + align:start position:0% +and remember last time I say full on + + + align:start position:0% +and remember last time I say full on +full-on scattering is a is you can tra + + align:start position:0% +full-on scattering is a is you can tra + + + align:start position:0% +full-on scattering is a is you can tra +the complete face randomizing because + + align:start position:0% +the complete face randomizing because + + + align:start position:0% +the complete face randomizing because +pop up here pop up + + align:start position:0% +pop up here pop up + + + align:start position:0% +pop up here pop up +you can't fix the position, right? + + align:start position:0% +you can't fix the position, right? + + + align:start position:0% +you can't fix the position, right? +But when you have impur scatter, those + + align:start position:0% +But when you have impur scatter, those + + + align:start position:0% +But when you have impur scatter, those +impur atoms are fixed. It's just you + + align:start position:0% +impur atoms are fixed. It's just you + + + align:start position:0% +impur atoms are fixed. It's just you +can't you normally don't know where they + + align:start position:0% +can't you normally don't know where they + + + align:start position:0% +can't you normally don't know where they +are, right? And the impur scattering + + align:start position:0% +are, right? And the impur scattering + + + align:start position:0% +are, right? And the impur scattering +form is typically + + align:start position:0% +form is typically + + + align:start position:0% +form is typically +written as a fourth power inverse. Here + + align:start position:0% +written as a fourth power inverse. Here + + + align:start position:0% +written as a fourth power inverse. Here +you can say I write humorous. + + align:start position:0% +you can say I write humorous. + + + align:start position:0% +you can say I write humorous. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So in fact this is a result not derived + + align:start position:0% +So in fact this is a result not derived + + + align:start position:0% +So in fact this is a result not derived +it's a result from light + + align:start position:0% +it's a result from light + + + align:start position:0% +it's a result from light +and if you look at the sky it's a blue + + align:start position:0% +and if you look at the sky it's a blue + + + align:start position:0% +and if you look at the sky it's a blue +sky + + align:start position:0% +sky + + + align:start position:0% +sky +and that's because the light is + + align:start position:0% +and that's because the light is + + + align:start position:0% +and that's because the light is +scattered by the density fluctuation of + + align:start position:0% +scattered by the density fluctuation of + + + align:start position:0% +scattered by the density fluctuation of +the gas or small particles + + align:start position:0% +the gas or small particles + + + align:start position:0% +the gas or small particles +and uh so when you have small atoms or + + align:start position:0% +and uh so when you have small atoms or + + + align:start position:0% +and uh so when you have small atoms or +small particles you can say the higher + + align:start position:0% +small particles you can say the higher + + + align:start position:0% +small particles you can say the higher +frequency + + align:start position:0% +frequency + + + align:start position:0% +frequency +uh this tile towel + + align:start position:0% +uh this tile towel + + + align:start position:0% +uh this tile towel +is the this is a towel right towel + + align:start position:0% +is the this is a towel right towel + + + align:start position:0% +is the this is a towel right towel +itself is smaller + + align:start position:0% +itself is smaller + + + align:start position:0% +itself is smaller +the left at the relaxation time that + + align:start position:0% +the left at the relaxation time that + + + align:start position:0% +the left at the relaxation time that +means is scatter more often + + align:start position:0% +means is scatter more often + + + align:start position:0% +means is scatter more often +right so that's why the sky is blue + + align:start position:0% +right so that's why the sky is blue + + + align:start position:0% +right so that's why the sky is blue +right that's the relay scatter this is + + align:start position:0% +right that's the relay scatter this is + + + align:start position:0% +right that's the relay scatter this is +relay scatter + + align:start position:0% + + + + align:start position:0% + +acoustical wave waves + + align:start position:0% +acoustical wave waves + + + align:start position:0% +acoustical wave waves +and uh say optical waves they all have + + align:start position:0% +and uh say optical waves they all have + + + align:start position:0% +and uh say optical waves they all have +those characteristics but say it's not + + align:start position:0% +those characteristics but say it's not + + + align:start position:0% +those characteristics but say it's not +completely sure what in what regime this + + align:start position:0% +completely sure what in what regime this + + + align:start position:0% +completely sure what in what regime this +is applicable for acoustic for atomic + + align:start position:0% +is applicable for acoustic for atomic + + + align:start position:0% +is applicable for acoustic for atomic +waves and this is still uh uh some + + align:start position:0% +waves and this is still uh uh some + + + align:start position:0% +waves and this is still uh uh some +debate there right + + align:start position:0% +debate there right + + + align:start position:0% +debate there right +and finally this is a boundary there's + + align:start position:0% +and finally this is a boundary there's + + + align:start position:0% +and finally this is a boundary there's +also boundary if the there's no + + align:start position:0% +also boundary if the there's no + + + align:start position:0% +also boundary if the there's no +scattering hits boundary there's + + align:start position:0% +scattering hits boundary there's + + + align:start position:0% +scattering hits boundary there's +boundary scattering and that's the one + + align:start position:0% +boundary scattering and that's the one + + + align:start position:0% +boundary scattering and that's the one +that will actually solve borsman + + align:start position:0% +that will actually solve borsman + + + align:start position:0% +that will actually solve borsman +equation using this as a boundary + + align:start position:0% +equation using this as a boundary + + + align:start position:0% +equation using this as a boundary +condition of bourgeman equation. We we + + align:start position:0% +condition of bourgeman equation. We we + + + align:start position:0% +condition of bourgeman equation. We we +can trade more rigorously. + + align:start position:0% +can trade more rigorously. + + + align:start position:0% +can trade more rigorously. +But typically in the past people would + + align:start position:0% +But typically in the past people would + + + align:start position:0% +But typically in the past people would +do is when you have different relaxation + + align:start position:0% +do is when you have different relaxation + + + align:start position:0% +do is when you have different relaxation +time you patch them together + + align:start position:0% +time you patch them together + + + align:start position:0% +time you patch them together +right particularly if they are all + + align:start position:0% +right particularly if they are all + + + align:start position:0% +right particularly if they are all +randomly distribute in the volume and + + align:start position:0% +randomly distribute in the volume and + + + align:start position:0% +randomly distribute in the volume and +you do this uh total to equals the + + align:start position:0% +you do this uh total to equals the + + + align:start position:0% +you do this uh total to equals the +different process inverse. So it's a + + align:start position:0% +different process inverse. So it's a + + + align:start position:0% +different process inverse. So it's a +more resistive one + + align:start position:0% +more resistive one + + + align:start position:0% +more resistive one +the more frequently scatter one that + + align:start position:0% +the more frequently scatter one that + + + align:start position:0% +the more frequently scatter one that +will be dominant + + align:start position:0% +will be dominant + + + align:start position:0% +will be dominant +right because this is all inverse and + + align:start position:0% +right because this is all inverse and + + + align:start position:0% +right because this is all inverse and +this is the mathem rule. + + align:start position:0% + + + + align:start position:0% + +Okay. So that's you put all this + + align:start position:0% +Okay. So that's you put all this + + + align:start position:0% +Okay. So that's you put all this +different process together. + + align:start position:0% +different process together. + + + align:start position:0% +different process together. +One final comment. So here is a fullon + + align:start position:0% +One final comment. So here is a fullon + + + align:start position:0% +One final comment. So here is a fullon +fullon scatter and then you have + + align:start position:0% +fullon scatter and then you have + + + align:start position:0% +fullon scatter and then you have +electron fullon scatter. + + align:start position:0% + + + + align:start position:0% + +Right? We have electron has certain + + align:start position:0% +Right? We have electron has certain + + + align:start position:0% +Right? We have electron has certain +energy interact with the folon get into + + align:start position:0% +energy interact with the folon get into + + + align:start position:0% +energy interact with the folon get into +a different energy + + align:start position:0% + + + + align:start position:0% + +E prime and also in the process you have + + align:start position:0% +E prime and also in the process you have + + + align:start position:0% +E prime and also in the process you have +the energy momentum conservation + + align:start position:0% +the energy momentum conservation + + + align:start position:0% +the energy momentum conservation +and this scattering of course you deal + + align:start position:0% +and this scattering of course you deal + + + align:start position:0% +and this scattering of course you deal +with electron transport that's very + + align:start position:0% +with electron transport that's very + + + align:start position:0% +with electron transport that's very +important right electrical engineer + + align:start position:0% +important right electrical engineer + + + align:start position:0% +important right electrical engineer +always try to improve their mobility + + align:start position:0% +always try to improve their mobility + + + align:start position:0% +always try to improve their mobility +try to make a faster device you want to + + align:start position:0% +try to make a faster device you want to + + + align:start position:0% +try to make a faster device you want to +reduce the full-on scatter + + align:start position:0% +reduce the full-on scatter + + + align:start position:0% +reduce the full-on scatter +and uh um + + align:start position:0% +and uh um + + + align:start position:0% +and uh um +so the uh the uh one thing I want to + + align:start position:0% +so the uh the uh one thing I want to + + + align:start position:0% +so the uh the uh one thing I want to +comment here is of course the energy + + align:start position:0% +comment here is of course the energy + + + align:start position:0% +comment here is of course the energy +change process if the there's energy + + align:start position:0% +change process if the there's energy + + + align:start position:0% +change process if the there's energy +change is elastic + + align:start position:0% +change is elastic + + + align:start position:0% +change is elastic +right the energy is not conserved say + + align:start position:0% +right the energy is not conserved say + + + align:start position:0% +right the energy is not conserved say +the the particle energy change during + + align:start position:0% +the the particle energy change during + + + align:start position:0% +the the particle energy change during +this scatter + + align:start position:0% +this scatter + + + align:start position:0% +this scatter +and the impurity scattering like The + + align:start position:0% +and the impurity scattering like The + + + align:start position:0% +and the impurity scattering like The +relay scatter + + align:start position:0% +relay scatter + + + align:start position:0% +relay scatter +we typically these are the elastic + + align:start position:0% +we typically these are the elastic + + + align:start position:0% +we typically these are the elastic +scatter + + align:start position:0% +scatter + + + align:start position:0% +scatter +elastic scatter frequency doesn't change + + align:start position:0% +elastic scatter frequency doesn't change + + + align:start position:0% +elastic scatter frequency doesn't change +and in fact rigorously speaking + + align:start position:0% +and in fact rigorously speaking + + + align:start position:0% +and in fact rigorously speaking +rigorously speaking + + align:start position:0% +rigorously speaking + + + align:start position:0% +rigorously speaking +for all inelastic scattering process + + align:start position:0% +for all inelastic scattering process + + + align:start position:0% +for all inelastic scattering process +where the energy change that + + align:start position:0% +where the energy change that + + + align:start position:0% +where the energy change that +approximation the relaxation time + + align:start position:0% +approximation the relaxation time + + + align:start position:0% +approximation the relaxation time +approximation is not valid. We do it all + + align:start position:0% +approximation is not valid. We do it all + + + align:start position:0% +approximation is not valid. We do it all +the time but this actual regression not + + align:start position:0% +the time but this actual regression not + + + align:start position:0% +the time but this actual regression not +valid. + + align:start position:0% +valid. + + + align:start position:0% +valid. +So you go once we go to chapter eight we + + align:start position:0% +So you go once we go to chapter eight we + + + align:start position:0% +So you go once we go to chapter eight we +have one more step let's suppose you + + align:start position:0% +have one more step let's suppose you + + + align:start position:0% +have one more step let's suppose you +split this say into two terms rather + + align:start position:0% +split this say into two terms rather + + + align:start position:0% +split this say into two terms rather +than just relaxation term. So that's + + align:start position:0% +than just relaxation term. So that's + + + align:start position:0% +than just relaxation term. So that's +when we deal with the electron fall for + + align:start position:0% +when we deal with the electron fall for + + + align:start position:0% +when we deal with the electron fall for +long and the line equilibrium between + + align:start position:0% +long and the line equilibrium between + + + align:start position:0% +long and the line equilibrium between +electron fall. + + align:start position:0% + + + + align:start position:0% + +Okay. So uh I think uh uh I will stop on + + align:start position:0% +Okay. So uh I think uh uh I will stop on + + + align:start position:0% +Okay. So uh I think uh uh I will stop on +this topic and now I think uh we come to + + align:start position:0% +this topic and now I think uh we come to + + + align:start position:0% +this topic and now I think uh we come to +the stage. I would say you should pick + + align:start position:0% +the stage. I would say you should pick + + + align:start position:0% +the stage. I would say you should pick +up the + + align:start position:0% +up the + + + align:start position:0% +up the +as I said at the beginning any journal + + align:start position:0% +as I said at the beginning any journal + + + align:start position:0% +as I said at the beginning any journal +and uh you should not be say you were + + align:start position:0% +and uh you should not be say you were + + + align:start position:0% +and uh you should not be say you were +say that you should not be afraid of + + align:start position:0% +say that you should not be afraid of + + + align:start position:0% +say that you should not be afraid of +reading right I'm I'm sure that you + + align:start position:0% +reading right I'm I'm sure that you + + + align:start position:0% +reading right I'm I'm sure that you +can't understand everything but what I'm + + align:start position:0% +can't understand everything but what I'm + + + align:start position:0% +can't understand everything but what I'm +hoping is uh uh uh there are always + + align:start position:0% +hoping is uh uh uh there are always + + + align:start position:0% +hoping is uh uh uh there are always +things that help you to to get some idea + + align:start position:0% +things that help you to to get some idea + + + align:start position:0% +things that help you to to get some idea +of of those different uh many many u + + align:start position:0% +of of those different uh many many u + + + align:start position:0% +of of those different uh many many u +papers + + align:start position:0% +papers + + + align:start position:0% +papers +So, um, let's take a quick look. + + align:start position:0% + + + + align:start position:0% + +So say all the I think I have covered + + align:start position:0% +So say all the I think I have covered + + + align:start position:0% +So say all the I think I have covered +most of the basic concepts + + align:start position:0% +most of the basic concepts + + + align:start position:0% +most of the basic concepts +and uh uh + + align:start position:0% + + + + align:start position:0% + +the rest is if you read paper of course + + align:start position:0% +the rest is if you read paper of course + + + align:start position:0% +the rest is if you read paper of course +say the concept need time to digest + + align:start position:0% +say the concept need time to digest + + + align:start position:0% +say the concept need time to digest +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +I was I was quickly look at uh let's say + + align:start position:0% +I was I was quickly look at uh let's say + + + align:start position:0% +I was I was quickly look at uh let's say +nano letter now you can look at all I + + align:start position:0% +nano letter now you can look at all I + + + align:start position:0% +nano letter now you can look at all I +would say you should look at all the + + align:start position:0% +would say you should look at all the + + + align:start position:0% +would say you should look at all the +nano journals + + align:start position:0% + + + + align:start position:0% + +uh this is a two + + align:start position:0% + + + + align:start position:0% + +Okay. So, uh uh + + align:start position:0% +Okay. So, uh uh + + + align:start position:0% +Okay. So, uh uh +silicon l wire this is more the uh uh + + align:start position:0% +silicon l wire this is more the uh uh + + + align:start position:0% +silicon l wire this is more the uh uh +device related right. Uh I thought uh we + + align:start position:0% +device related right. Uh I thought uh we + + + align:start position:0% +device related right. Uh I thought uh we +can look at the current issue. + + align:start position:0% +can look at the current issue. + + + align:start position:0% +can look at the current issue. +Where is the current issue? + + align:start position:0% + + + + align:start position:0% + +More materials. So rel make how to make + + align:start position:0% +More materials. So rel make how to make + + + align:start position:0% +More materials. So rel make how to make +a material. So that that's relatively + + align:start position:0% +a material. So that that's relatively + + + align:start position:0% +a material. So that that's relatively +easy, right? Um + + align:start position:0% +easy, right? Um + + + align:start position:0% +easy, right? Um +uh + + align:start position:0% + + + + align:start position:0% + +okay for example if you go to next one + + align:start position:0% +okay for example if you go to next one + + + align:start position:0% +okay for example if you go to next one +this paper by David Smith uh he was a + + align:start position:0% +this paper by David Smith uh he was a + + + align:start position:0% +this paper by David Smith uh he was a +guy first who did the negative + + align:start position:0% +guy first who did the negative + + + align:start position:0% +guy first who did the negative +refraction experiment and the surface + + align:start position:0% +refraction experiment and the surface + + + align:start position:0% +refraction experiment and the surface +plasmas right if you look at the title + + align:start position:0% +plasmas right if you look at the title + + + align:start position:0% +plasmas right if you look at the title +lowquality tone surface plasma resonance + + align:start position:0% +lowquality tone surface plasma resonance + + + align:start position:0% +lowquality tone surface plasma resonance +you heard the surface plasma you can + + align:start position:0% +you heard the surface plasma you can + + + align:start position:0% +you heard the surface plasma you can +read and see what what it means what's + + align:start position:0% +read and see what what it means what's + + + align:start position:0% +read and see what what it means what's +it doing + + align:start position:0% +it doing + + + align:start position:0% +it doing +and um + + align:start position:0% + + + + align:start position:0% + +if I look at this one right + + align:start position:0% +if I look at this one right + + + align:start position:0% +if I look at this one right +uh I didn't open but you can go to check + + align:start position:0% +uh I didn't open but you can go to check + + + align:start position:0% +uh I didn't open but you can go to check +whether I guessed it right uh so if I + + align:start position:0% +whether I guessed it right uh so if I + + + align:start position:0% +whether I guessed it right uh so if I +look at this uh electric breakdown on + + align:start position:0% +look at this uh electric breakdown on + + + align:start position:0% +look at this uh electric breakdown on +off state electric sustainable graphin + + align:start position:0% +off state electric sustainable graphin + + + align:start position:0% +off state electric sustainable graphin +junction + + align:start position:0% +junction + + + align:start position:0% +junction +uh probably there okay breakdown Of + + align:start position:0% +uh probably there okay breakdown Of + + + align:start position:0% +uh probably there okay breakdown Of +course they they uh it can um create the + + align:start position:0% +course they they uh it can um create the + + + align:start position:0% +course they they uh it can um create the +gaps but there also could be tunnel + + align:start position:0% +gaps but there also could be tunnel + + + align:start position:0% +gaps but there also could be tunnel +phenomena if you have very small gaps + + align:start position:0% +phenomena if you have very small gaps + + + align:start position:0% +phenomena if you have very small gaps +right electron tunnel I don't know + + align:start position:0% +right electron tunnel I don't know + + + align:start position:0% +right electron tunnel I don't know +whether the paper will deal with those + + align:start position:0% +whether the paper will deal with those + + + align:start position:0% +whether the paper will deal with those +issues right and uh + + align:start position:0% + + + + align:start position:0% + +it's where I stopped + + align:start position:0% + + + + align:start position:0% + +water. you have to wait when we do the + + align:start position:0% +water. you have to wait when we do the + + + align:start position:0% +water. you have to wait when we do the +linear more Einstein treatment linear + + align:start position:0% +linear more Einstein treatment linear + + + align:start position:0% +linear more Einstein treatment linear +response theory and uh uh when you look + + align:start position:0% +response theory and uh uh when you look + + + align:start position:0% +response theory and uh uh when you look +at battery one concept I'll go into not + + align:start position:0% +at battery one concept I'll go into not + + + align:start position:0% +at battery one concept I'll go into not +directly on battery but you have to + + align:start position:0% +directly on battery but you have to + + + align:start position:0% +directly on battery but you have to +understand what is electrochemical + + align:start position:0% +understand what is electrochemical + + + align:start position:0% +understand what is electrochemical +potential okay and uh uh + + align:start position:0% +potential okay and uh uh + + + align:start position:0% +potential okay and uh uh +conducting graphin + + align:start position:0% +conducting graphin + + + align:start position:0% +conducting graphin +uh nano nano cubes so I I I guess say my + + align:start position:0% +uh nano nano cubes so I I I guess say my + + + align:start position:0% +uh nano nano cubes so I I I guess say my +message to you is now you go to this uh + + align:start position:0% +message to you is now you go to this uh + + + align:start position:0% +message to you is now you go to this uh +journal + + align:start position:0% +journal + + + align:start position:0% +journal +and try to say read through the title + + align:start position:0% +and try to say read through the title + + + align:start position:0% +and try to say read through the title +and guess what is doing uh you uh and + + align:start position:0% +and guess what is doing uh you uh and + + + align:start position:0% +and guess what is doing uh you uh and +and you pull out a few papers + + align:start position:0% +and you pull out a few papers + + + align:start position:0% +and you pull out a few papers +and you try to read through uh uh the + + align:start position:0% +and you try to read through uh uh the + + + align:start position:0% +and you try to read through uh uh the +the the content + + align:start position:0% +the the content + + + align:start position:0% +the the content +not of your say concern does this help + + align:start position:0% +not of your say concern does this help + + + align:start position:0% +not of your say concern does this help +you pass the call and say the call is + + align:start position:0% +you pass the call and say the call is + + + align:start position:0% +you pass the call and say the call is +asking to read papers + + align:start position:0% +asking to read papers + + + align:start position:0% +asking to read papers +Right. And you sit there, we'll ask you + + align:start position:0% +Right. And you sit there, we'll ask you + + + align:start position:0% +Right. And you sit there, we'll ask you +questions. + + align:start position:0% +questions. + + + align:start position:0% +questions. +So that's I think uh it should help but + + align:start position:0% +So that's I think uh it should help but + + + align:start position:0% +So that's I think uh it should help but +uh not guarantee. + + align:start position:0% +uh not guarantee. + + + align:start position:0% +uh not guarantee. +Okay. \ No newline at end of file diff --git a/z_YXJLMpxoM.txt b/z_YXJLMpxoM.txt new file mode 100644 index 0000000000000000000000000000000000000000..761834b979d527f3bd60566a78f222a3b11bd881 --- /dev/null +++ b/z_YXJLMpxoM.txt @@ -0,0 +1,1795 @@ +align:start position:0% + +so what is Creole and and when I like to + + align:start position:0% +so what is Creole and and when I like to + + + align:start position:0% +so what is Creole and and when I like to +do is to look at same what happens in + + align:start position:0% +do is to look at same what happens in + + + align:start position:0% +do is to look at same what happens in +the history of of learning French by by + + align:start position:0% +the history of of learning French by by + + + align:start position:0% +the history of of learning French by by +address and by children we saw examples + + align:start position:0% +address and by children we saw examples + + + align:start position:0% +address and by children we saw examples +of that before but what we find there so + + align:start position:0% +of that before but what we find there so + + + align:start position:0% +of that before but what we find there so +this is actually very reverse fact which + + align:start position:0% +this is actually very reverse fact which + + + align:start position:0% +this is actually very reverse fact which +is that when when you have people + + align:start position:0% +is that when when you have people + + + align:start position:0% +is that when when you have people +learning French often so in the case of + + align:start position:0% +learning French often so in the case of + + + align:start position:0% +learning French often so in the case of +the object pronouns they do produce + + align:start position:0% +the object pronouns they do produce + + + align:start position:0% +the object pronouns they do produce +structures of that sort right in its + + align:start position:0% +structures of that sort right in its + + + align:start position:0% +structures of that sort right in its +have to be in it have to be in a Creole + + align:start position:0% +have to be in it have to be in a Creole + + + align:start position:0% +have to be in it have to be in a Creole +environment it happens in Marseille + + align:start position:0% +environment it happens in Marseille + + + align:start position:0% +environment it happens in Marseille +depends in in all kinds of varieties + + align:start position:0% +depends in in all kinds of varieties + + + align:start position:0% +depends in in all kinds of varieties +where you have second language learning + + align:start position:0% +where you have second language learning + + + align:start position:0% +where you have second language learning +so so delia is that often as you learn + + align:start position:0% +so so delia is that often as you learn + + + align:start position:0% +so so delia is that often as you learn +the language you might see particular + + align:start position:0% +the language you might see particular + + + align:start position:0% +the language you might see particular +order like subject verb object object in + + align:start position:0% +order like subject verb object object in + + + align:start position:0% +order like subject verb object object in +that order is the dominant order often + + align:start position:0% +that order is the dominant order often + + + align:start position:0% +that order is the dominant order often +you take that order in a new applied to + + align:start position:0% +you take that order in a new applied to + + + align:start position:0% +you take that order in a new applied to +all the elements that that might fit it + + align:start position:0% +all the elements that that might fit it + + + align:start position:0% +all the elements that that might fit it +right you over terrorized children do + + align:start position:0% +right you over terrorized children do + + + align:start position:0% +right you over terrorized children do +that all the time when children see + + align:start position:0% +that all the time when children see + + + align:start position:0% +that all the time when children see +things like oh I have one foot and you + + align:start position:0% +things like oh I have one foot and you + + + align:start position:0% +things like oh I have one foot and you +have two two foods right saying food and + + align:start position:0% +have two two foods right saying food and + + + align:start position:0% +have two two foods right saying food and +foods instead of saying foot and feet + + align:start position:0% +foods instead of saying foot and feet + + + align:start position:0% +foods instead of saying foot and feet +it's a mystic that you know almost every + + align:start position:0% +it's a mystic that you know almost every + + + align:start position:0% +it's a mystic that you know almost every +children every child will get to do in + + align:start position:0% +children every child will get to do in + + + align:start position:0% +children every child will get to do in +the in the path of learning French + + align:start position:0% +the in the path of learning French + + + align:start position:0% +the in the path of learning French +learning English because what do they do + + align:start position:0% +learning English because what do they do + + + align:start position:0% +learning English because what do they do +do they real scientist right the after + + align:start position:0% +do they real scientist right the after + + + align:start position:0% +do they real scientist right the after +hypothesis about say cool ok s Multipure + + align:start position:0% +hypothesis about say cool ok s Multipure + + + align:start position:0% +hypothesis about say cool ok s Multipure +so why should you bother to say feet if + + align:start position:0% +so why should you bother to say feet if + + + align:start position:0% +so why should you bother to say feet if +you have to pro well-behaved girl like s + + align:start position:0% +you have to pro well-behaved girl like s + + + align:start position:0% +you have to pro well-behaved girl like s +if you say I don't know if you see table + + align:start position:0% +if you say I don't know if you see table + + + align:start position:0% +if you say I don't know if you see table +tables if you say pan pans why would you + + align:start position:0% +tables if you say pan pans why would you + + + align:start position:0% +tables if you say pan pans why would you +say food feet you fine I posit it's + + align:start position:0% +say food feet you fine I posit it's + + + align:start position:0% +say food feet you fine I posit it's +right and children do that right so in + + align:start position:0% +right and children do that right so in + + + align:start position:0% +right and children do that right so in +the same here if you know that your + + align:start position:0% +the same here if you know that your + + + align:start position:0% +the same here if you know that your +language has public order you say you + + align:start position:0% +language has public order you say you + + + align:start position:0% +language has public order you say you +know Caraballo + + align:start position:0% +know Caraballo + + + align:start position:0% +know Caraballo +hit the ball why would you say when you + + align:start position:0% +hit the ball why would you say when you + + + align:start position:0% +hit the ball why would you say when you +have a pronoun why would you put it + + align:start position:0% +have a pronoun why would you put it + + + align:start position:0% +have a pronoun why would you put it +before the verb it seems to be a natural + + align:start position:0% +before the verb it seems to be a natural + + + align:start position:0% +before the verb it seems to be a natural +hypothesis if you learn to assume that a + + align:start position:0% +hypothesis if you learn to assume that a + + + align:start position:0% +hypothesis if you learn to assume that a +pronoun like a full noun will come after + + align:start position:0% +pronoun like a full noun will come after + + + align:start position:0% +pronoun like a full noun will come after +the affirmance what you see you know and + + align:start position:0% +the affirmance what you see you know and + + + align:start position:0% +the affirmance what you see you know and +this is so the contrast is between + + align:start position:0% +this is so the contrast is between + + + align:start position:0% +this is so the contrast is between +standard french where you get the + + align:start position:0% +standard french where you get the + + + align:start position:0% +standard french where you get the +pronoun before the verb and this is l2 f + + align:start position:0% +pronoun before the verb and this is l2 f + + + align:start position:0% +pronoun before the verb and this is l2 f +ends is a learner's french + + align:start position:0% +ends is a learner's french + + + align:start position:0% +ends is a learner's french +and I'd open his french where you get + + align:start position:0% +and I'd open his french where you get + + + align:start position:0% +and I'd open his french where you get +the pronoun after this right so not to + + align:start position:0% +the pronoun after this right so not to + + + align:start position:0% +the pronoun after this right so not to +make a long story short it go ahead big + + align:start position:0% +make a long story short it go ahead big + + + align:start position:0% +make a long story short it go ahead big +I don't know maybe just our topic I'm + + align:start position:0% +I don't know maybe just our topic I'm + + + align:start position:0% +I don't know maybe just our topic I'm +like why like if it's like the most + + align:start position:0% +like why like if it's like the most + + + align:start position:0% +like why like if it's like the most +natural thing to assume that a the + + align:start position:0% +natural thing to assume that a the + + + align:start position:0% +natural thing to assume that a the +object follows the variable like how is + + align:start position:0% +object follows the variable like how is + + + align:start position:0% +object follows the variable like how is +house never + + align:start position:0% +house never + + + align:start position:0% +house never +how did French ever develop this weird + + align:start position:0% +how did French ever develop this weird + + + align:start position:0% +how did French ever develop this weird +name in there that's that's a that's a + + align:start position:0% +name in there that's that's a that's a + + + align:start position:0% +name in there that's that's a that's a +good question that's exactly it means + + align:start position:0% +good question that's exactly it means + + + align:start position:0% +good question that's exactly it means +that as you learn a language there other + + align:start position:0% +that as you learn a language there other + + + align:start position:0% +that as you learn a language there other +there are other factors in that learning + + align:start position:0% +there are other factors in that learning + + + align:start position:0% +there are other factors in that learning +right so although the learner might have + + align:start position:0% +right so although the learner might have + + + align:start position:0% +right so although the learner might have +a natural tendency to do that but since + + align:start position:0% +a natural tendency to do that but since + + + align:start position:0% +a natural tendency to do that but since +in the case of French there are norms + + align:start position:0% +in the case of French there are norms + + + align:start position:0% +in the case of French there are norms +yeah books there is TV so eventually the + + align:start position:0% +yeah books there is TV so eventually the + + + align:start position:0% +yeah books there is TV so eventually the +learner will come will move towards a + + align:start position:0% +learner will come will move towards a + + + align:start position:0% +learner will come will move towards a +different set of patterns you know but + + align:start position:0% +different set of patterns you know but + + + align:start position:0% +different set of patterns you know but +then languages do change and in English + + align:start position:0% +then languages do change and in English + + + align:start position:0% +then languages do change and in English +change often days there is a path + + align:start position:0% +change often days there is a path + + + align:start position:0% +change often days there is a path +towards more general think of examples + + align:start position:0% +towards more general think of examples + + + align:start position:0% +towards more general think of examples +so Steven Pinker a very good linguist + + align:start position:0% +so Steven Pinker a very good linguist + + + align:start position:0% +so Steven Pinker a very good linguist +was at MIT no mati and he has a whole + + align:start position:0% +was at MIT no mati and he has a whole + + + align:start position:0% +was at MIT no mati and he has a whole +book on how the patterns of regular + + align:start position:0% +book on how the patterns of regular + + + align:start position:0% +book on how the patterns of regular +verbs change in English right things + + align:start position:0% +verbs change in English right things + + + align:start position:0% +verbs change in English right things +like go went or Shine's shown so many of + + align:start position:0% +like go went or Shine's shown so many of + + + align:start position:0% +like go went or Shine's shown so many of +these over time become regular so you go + + align:start position:0% +these over time become regular so you go + + + align:start position:0% +these over time become regular so you go +from shine shown to shine shine well it + + align:start position:0% +from shine shown to shine shine well it + + + align:start position:0% +from shine shown to shine shine well it +hasn't happened yet right but what you + + align:start position:0% +hasn't happened yet right but what you + + + align:start position:0% +hasn't happened yet right but what you +should is that over time there is a + + align:start position:0% +should is that over time there is a + + + align:start position:0% +should is that over time there is a +movement of verbs going from being + + align:start position:0% +movement of verbs going from being + + + align:start position:0% +movement of verbs going from being +irregular to being regular and one could + + align:start position:0% +irregular to being regular and one could + + + align:start position:0% +irregular to being regular and one could +explain that because of the fact that + + align:start position:0% +explain that because of the fact that + + + align:start position:0% +explain that because of the fact that +there's a tendency to make all these + + align:start position:0% +there's a tendency to make all these + + + align:start position:0% +there's a tendency to make all these +verbs fit the same the same pattern the + + align:start position:0% +verbs fit the same the same pattern the + + + align:start position:0% +verbs fit the same the same pattern the +regular pattern right very same time + + align:start position:0% +regular pattern right very same time + + + align:start position:0% +regular pattern right very same time +there's also prescriptive norms no + + align:start position:0% +there's also prescriptive norms no + + + align:start position:0% +there's also prescriptive norms no +there's a pastiche language there's a + + align:start position:0% +there's a pastiche language there's a + + + align:start position:0% +there's a pastiche language there's a +language called tony crock what he + + align:start position:0% +language called tony crock what he + + + align:start position:0% +language called tony crock what he +argued that very often changes okay in a + + align:start position:0% +argued that very often changes okay in a + + + align:start position:0% +argued that very often changes okay in a +different direction because why because + + align:start position:0% +different direction because why because + + + align:start position:0% +different direction because why because +people use language to show that they're + + align:start position:0% +people use language to show that they're + + + align:start position:0% +people use language to show that they're +fancy they are sophisticated so they + + align:start position:0% +fancy they are sophisticated so they + + + align:start position:0% +fancy they are sophisticated so they +will use the more the irregular pattern + + align:start position:0% +will use the more the irregular pattern + + + align:start position:0% +will use the more the irregular pattern +to show off exactly who whom cakes right + + align:start position:0% +to show off exactly who whom cakes right + + + align:start position:0% +to show off exactly who whom cakes right +so how many of you hear people saying + + align:start position:0% +so how many of you hear people saying + + + align:start position:0% +so how many of you hear people saying +whom in all the wrong places + + align:start position:0% +whom in all the wrong places + + + align:start position:0% +whom in all the wrong places +because right because because whom when + + align:start position:0% +because right because because whom when + + + align:start position:0% +because right because because whom when +you see whom when you say john and i it + + align:start position:0% +you see whom when you say john and i it + + + align:start position:0% +you see whom when you say john and i it +makes sound fancier than John and me but + + align:start position:0% +makes sound fancier than John and me but + + + align:start position:0% +makes sound fancier than John and me but +what you find is that often people we + + align:start position:0% +what you find is that often people we + + + align:start position:0% +what you find is that often people we +will see John and I + + align:start position:0% +will see John and I + + + align:start position:0% +will see John and I +and I in the wrong place they will say + + align:start position:0% +and I in the wrong place they will say + + + align:start position:0% +and I in the wrong place they will say +you know I just had a good talk with + + align:start position:0% +you know I just had a good talk with + + + align:start position:0% +you know I just had a good talk with +Mary and no no my dad went went to see + + align:start position:0% +Mary and no no my dad went went to see + + + align:start position:0% +Mary and no no my dad went went to see +Mary and I so but Marian high in that + + align:start position:0% +Mary and I so but Marian high in that + + + align:start position:0% +Mary and I so but Marian high in that +particular context is not it's not + + align:start position:0% +particular context is not it's not + + + align:start position:0% +particular context is not it's not +correctly Mary and me because it is the + + align:start position:0% +correctly Mary and me because it is the + + + align:start position:0% +correctly Mary and me because it is the +object right so why would you see Mary + + align:start position:0% +object right so why would you see Mary + + + align:start position:0% +object right so why would you see Mary +and I in object position but because + + align:start position:0% +and I in object position but because + + + align:start position:0% +and I in object position but because +Mary and I sound fancier people would + + align:start position:0% +Mary and I sound fancier people would + + + align:start position:0% +Mary and I sound fancier people would +tend to use it or the home thing earlier + + align:start position:0% +tend to use it or the home thing earlier + + + align:start position:0% +tend to use it or the home thing earlier +that cases we have to go see whom which + + align:start position:0% +that cases we have to go see whom which + + + align:start position:0% +that cases we have to go see whom which +grammatically is not correct but because + + align:start position:0% +grammatically is not correct but because + + + align:start position:0% +grammatically is not correct but because +it sound fancy so whom should I say is + + align:start position:0% +it sound fancy so whom should I say is + + + align:start position:0% +it sound fancy so whom should I say is +calling you know I hear that all the + + align:start position:0% +calling you know I hear that all the + + + align:start position:0% +calling you know I hear that all the +time because they you know whom whom + + align:start position:0% +time because they you know whom whom + + + align:start position:0% +time because they you know whom whom +calls you who told you it should be who + + align:start position:0% +calls you who told you it should be who + + + align:start position:0% +calls you who told you it should be who +called you right because it's but + + align:start position:0% +called you right because it's but + + + align:start position:0% +called you right because it's but +because I came to the gram of the + + align:start position:0% +because I came to the gram of the + + + align:start position:0% +because I came to the gram of the +language in that in that particular + + align:start position:0% +language in that in that particular + + + align:start position:0% +language in that in that particular +environment it's a subject so you don't + + align:start position:0% +environment it's a subject so you don't + + + align:start position:0% +environment it's a subject so you don't +expect to get home because whom is whom + + align:start position:0% +expect to get home because whom is whom + + + align:start position:0% +expect to get home because whom is whom +it's for who technically you know in + + align:start position:0% +it's for who technically you know in + + + align:start position:0% +it's for who technically you know in +terms of grammar like him is for he or + + align:start position:0% +terms of grammar like him is for he or + + + align:start position:0% +terms of grammar like him is for he or +like her is for she right this is + + align:start position:0% +like her is for she right this is + + + align:start position:0% +like her is for she right this is +basically the function of the of the + + align:start position:0% +basically the function of the of the + + + align:start position:0% +basically the function of the of the +Ehrmann home it makes it an acquisitive + + align:start position:0% +Ehrmann home it makes it an acquisitive + + + align:start position:0% +Ehrmann home it makes it an acquisitive +form but yet people now use whom even + + align:start position:0% +form but yet people now use whom even + + + align:start position:0% +form but yet people now use whom even +when it's a subject why because it + + align:start position:0% +when it's a subject why because it + + + align:start position:0% +when it's a subject why because it +sounds fancy + + align:start position:0% +sounds fancy + + + align:start position:0% +sounds fancy +itself in fact it's a language that call + + align:start position:0% +itself in fact it's a language that call + + + align:start position:0% +itself in fact it's a language that call +it to various a grammar various you get + + align:start position:0% +it to various a grammar various you get + + + align:start position:0% +it to various a grammar various you get +infected because you want to sound fancy + + align:start position:0% +infected because you want to sound fancy + + + align:start position:0% +infected because you want to sound fancy +so let's talk about identity that's one + + align:start position:0% +so let's talk about identity that's one + + + align:start position:0% +so let's talk about identity that's one +place where identity might be a role in + + align:start position:0% +place where identity might be a role in + + + align:start position:0% +place where identity might be a role in +language change because by using those + + align:start position:0% +language change because by using those + + + align:start position:0% +language change because by using those +forms you want to project yourself as + + align:start position:0% +forms you want to project yourself as + + + align:start position:0% +forms you want to project yourself as +being as being superior as being you + + align:start position:0% +being as being superior as being you + + + align:start position:0% +being as being superior as being you +know sophisticated know and then you + + align:start position:0% +know sophisticated know and then you + + + align:start position:0% +know sophisticated know and then you +would use it second in creation Creole + + align:start position:0% +would use it second in creation Creole + + + align:start position:0% +would use it second in creation Creole +people use often the rounded vowels from + + align:start position:0% +people use often the rounded vowels from + + + align:start position:0% +people use often the rounded vowels from +French to show that they know French but + + align:start position:0% +French to show that they know French but + + + align:start position:0% +French to show that they know French but +they use the rounded vowels like instead + + align:start position:0% +they use the rounded vowels like instead + + + align:start position:0% +they use the rounded vowels like instead +of e way doesn't belong and they produce + + align:start position:0% +of e way doesn't belong and they produce + + + align:start position:0% +of e way doesn't belong and they produce +all kinds of weird sentences where you + + align:start position:0% +all kinds of weird sentences where you + + + align:start position:0% +all kinds of weird sentences where you +get all these news where even in French + + align:start position:0% +get all these news where even in French + + + align:start position:0% +get all these news where even in French +you have eat because they perceive that + + align:start position:0% +you have eat because they perceive that + + + align:start position:0% +you have eat because they perceive that +the e is the French is a marker of a + + align:start position:0% +the e is the French is a marker of a + + + align:start position:0% +the e is the French is a marker of a +French not Creole and therefore they + + align:start position:0% +French not Creole and therefore they + + + align:start position:0% +French not Creole and therefore they +want to use it all over the place + + align:start position:0% +want to use it all over the place + + + align:start position:0% +want to use it all over the place +you see and it's called a pro correction + + align:start position:0% +you see and it's called a pro correction + + + align:start position:0% +you see and it's called a pro correction +you are correcting yourself but as you + + align:start position:0% +you are correcting yourself but as you + + + align:start position:0% +you are correcting yourself but as you +ever correct you sound stupid really you + + align:start position:0% +ever correct you sound stupid really you + + + align:start position:0% +ever correct you sound stupid really you +know many know and then there are all + + align:start position:0% +know many know and then there are all + + + align:start position:0% +know many know and then there are all +these jokes about it actually because + + align:start position:0% +these jokes about it actually because + + + align:start position:0% +these jokes about it actually because +people are aware that people who use all + + align:start position:0% +people are aware that people who use all + + + align:start position:0% +people are aware that people who use all +these views is really not really know + + align:start position:0% +these views is really not really know + + + align:start position:0% +these views is really not really know +where to use the e + + align:start position:0% +where to use the e + + + align:start position:0% +where to use the e +chef's society and I'm speaking in a + + align:start position:0% +chef's society and I'm speaking in a + + + align:start position:0% +chef's society and I'm speaking in a +particular way that actually creates all + + align:start position:0% +particular way that actually creates all + + + align:start position:0% +particular way that actually creates all +kinds of weird patterns and eventually + + align:start position:0% +kinds of weird patterns and eventually + + + align:start position:0% +kinds of weird patterns and eventually +can become part of the language that's + + align:start position:0% +can become part of the language that's + + + align:start position:0% +can become part of the language that's +that that's one driving force in + + align:start position:0% +that that's one driving force in + + + align:start position:0% +that that's one driving force in +language change it is desired to sound + + align:start position:0% +language change it is desired to sound + + + align:start position:0% +language change it is desired to sound +better than your exact you know people + + align:start position:0% +better than your exact you know people + + + align:start position:0% +better than your exact you know people +who vote for Trombley might put four on + + align:start position:0% +who vote for Trombley might put four on + + + align:start position:0% +who vote for Trombley might put four on +them because they believe in some but + + align:start position:0% +them because they believe in some but + + + align:start position:0% +them because they believe in some but +because it might mean something for the + + align:start position:0% +because it might mean something for the + + + align:start position:0% +because it might mean something for the +identity it's like so language has this + + align:start position:0% +identity it's like so language has this + + + align:start position:0% +identity it's like so language has this +power of also establishing status yeah + + align:start position:0% +power of also establishing status yeah + + + align:start position:0% +power of also establishing status yeah +the next part that I was going to talk + + align:start position:0% +the next part that I was going to talk + + + align:start position:0% +the next part that I was going to talk +about how to do with so why why does + + align:start position:0% +about how to do with so why why does + + + align:start position:0% +about how to do with so why why does +language learning by adults have this + + align:start position:0% +language learning by adults have this + + + align:start position:0% +language learning by adults have this +effect on say verb order on conjugation + + align:start position:0% +effect on say verb order on conjugation + + + align:start position:0% +effect on say verb order on conjugation +and and the deposit image very very very + + align:start position:0% +and and the deposit image very very very + + + align:start position:0% +and and the deposit image very very very +quickly which is that you know this is + + align:start position:0% +quickly which is that you know this is + + + align:start position:0% +quickly which is that you know this is +something which is universal that we + + align:start position:0% +something which is universal that we + + + align:start position:0% +something which is universal that we +know in many context of language + + align:start position:0% +know in many context of language + + + align:start position:0% +know in many context of language +learning that that adults do have this + + align:start position:0% +learning that that adults do have this + + + align:start position:0% +learning that that adults do have this +effect + + align:start position:0% +effect + + + align:start position:0% +effect +santoprene they learn say if you need to + + align:start position:0% +santoprene they learn say if you need to + + + align:start position:0% +santoprene they learn say if you need to +learn say Italian or or any other + + align:start position:0% +learn say Italian or or any other + + + align:start position:0% +learn say Italian or or any other +languages and have lots of markers on + + align:start position:0% +languages and have lots of markers on + + + align:start position:0% +languages and have lots of markers on +reverb for conjugation often in the + + align:start position:0% +reverb for conjugation often in the + + + align:start position:0% +reverb for conjugation often in the +first stages of learning you you you + + align:start position:0% +first stages of learning you you you + + + align:start position:0% +first stages of learning you you you +don't have these you drop these and it's + + align:start position:0% +don't have these you drop these and it's + + + align:start position:0% +don't have these you drop these and it's +a because you're trying to speak a + + align:start position:0% +a because you're trying to speak a + + + align:start position:0% +a because you're trying to speak a +language and these are to be memorized + + align:start position:0% +language and these are to be memorized + + + align:start position:0% +language and these are to be memorized +and at first you will not memorize it + + align:start position:0% +and at first you will not memorize it + + + align:start position:0% +and at first you will not memorize it +properly so it seems that it's a general + + align:start position:0% +properly so it seems that it's a general + + + align:start position:0% +properly so it seems that it's a general +phenomenon and the point is that so the + + align:start position:0% +phenomenon and the point is that so the + + + align:start position:0% +phenomenon and the point is that so the +key maybe the key paragraph here is this + + align:start position:0% +key maybe the key paragraph here is this + + + align:start position:0% +key maybe the key paragraph here is this +one that maybe the way to understand + + align:start position:0% +one that maybe the way to understand + + + align:start position:0% +one that maybe the way to understand +language change and which I in my view + + align:start position:0% +language change and which I in my view + + + align:start position:0% +language change and which I in my view +include formation is to consider the + + align:start position:0% +include formation is to consider the + + + align:start position:0% +include formation is to consider the +effect of both language learning by + + align:start position:0% +effect of both language learning by + + + align:start position:0% +effect of both language learning by +adults and by children and it has the + + align:start position:0% +adults and by children and it has the + + + align:start position:0% +adults and by children and it has the +case then that that's what is it to + + align:start position:0% +case then that that's what is it to + + + align:start position:0% +case then that that's what is it to +drive all kinds of language change not + + align:start position:0% +drive all kinds of language change not + + + align:start position:0% +drive all kinds of language change not +just what what you see in the case of + + align:start position:0% +just what what you see in the case of + + + align:start position:0% +just what what you see in the case of +Korea formation okay so yeah so so this + + align:start position:0% +Korea formation okay so yeah so so this + + + align:start position:0% +Korea formation okay so yeah so so this +is another part of the conclusion just + + align:start position:0% +is another part of the conclusion just + + + align:start position:0% +is another part of the conclusion just +to recapitulate that basically to those + + align:start position:0% +to recapitulate that basically to those + + + align:start position:0% +to recapitulate that basically to those +of you were asking so what's my theory + + align:start position:0% +of you were asking so what's my theory + + + align:start position:0% +of you were asking so what's my theory +of close formation I don't need one you + + align:start position:0% +of close formation I don't need one you + + + align:start position:0% +of close formation I don't need one you +say nothing in one because cross + + align:start position:0% +say nothing in one because cross + + + align:start position:0% +say nothing in one because cross +formation is just + + align:start position:0% +formation is just + + + align:start position:0% +formation is just +linguist change so whatever linguist + + align:start position:0% +linguist change so whatever linguist + + + align:start position:0% +linguist change so whatever linguist +understand about the whaling leaders + + align:start position:0% +understand about the whaling leaders + + + align:start position:0% +understand about the whaling leaders +change to meet applies to crew of + + align:start position:0% +change to meet applies to crew of + + + align:start position:0% +change to meet applies to crew of +formation so I have one paper that came + + align:start position:0% +formation so I have one paper that came + + + align:start position:0% +formation so I have one paper that came +out earlier this year with Eric abou my + + align:start position:0% +out earlier this year with Eric abou my + + + align:start position:0% +out earlier this year with Eric abou my +my colleague from the B'nai from West + + align:start position:0% +my colleague from the B'nai from West + + + align:start position:0% +my colleague from the B'nai from West +Africa and and the paper is called a new + + align:start position:0% +Africa and and the paper is called a new + + + align:start position:0% +Africa and and the paper is called a new +theory of realization right it's known + + align:start position:0% +theory of realization right it's known + + + align:start position:0% +theory of realization right it's known +instance that it's it should be the + + align:start position:0% +instance that it's it should be the + + + align:start position:0% +instance that it's it should be the +default theory that Creoles like other + + align:start position:0% +default theory that Creoles like other + + + align:start position:0% +default theory that Creoles like other +languages so therefore you don't need to + + align:start position:0% +languages so therefore you don't need to + + + align:start position:0% +languages so therefore you don't need to +have a special theory for them so it + + align:start position:0% +have a special theory for them so it + + + align:start position:0% +have a special theory for them so it +should be the new liabilities that + + align:start position:0% +should be the new liabilities that + + + align:start position:0% +should be the new liabilities that +Creoles don't need a theory whatever + + align:start position:0% +Creoles don't need a theory whatever + + + align:start position:0% +Creoles don't need a theory whatever +theory applies to French or English + + align:start position:0% +theory applies to French or English + + + align:start position:0% +theory applies to French or English +should apply to Creole \ No newline at end of file diff --git a/z_eiVf-x0NI.txt b/z_eiVf-x0NI.txt new file mode 100644 index 0000000000000000000000000000000000000000..35a31af78974445db74ffae9e83428344a31c0fe --- /dev/null +++ b/z_eiVf-x0NI.txt @@ -0,0 +1,17387 @@ +align:start position:0% + +uh welcome to class so um you know this + + align:start position:0% +uh welcome to class so um you know this + + + align:start position:0% +uh welcome to class so um you know this +is 14271 I I should say that uh you know + + align:start position:0% +is 14271 I I should say that uh you know + + + align:start position:0% +is 14271 I I should say that uh you know +uh syllabus has a bunch of basic + + align:start position:0% +uh syllabus has a bunch of basic + + + align:start position:0% +uh syllabus has a bunch of basic +information uh you'll notice the course + + align:start position:0% +information uh you'll notice the course + + + align:start position:0% +information uh you'll notice the course +is listed as co-taught by me and Tobias + + align:start position:0% +is listed as co-taught by me and Tobias + + + align:start position:0% +is listed as co-taught by me and Tobias +uh you know Co permitting I'm going to + + align:start position:0% +uh you know Co permitting I'm going to + + + align:start position:0% +uh you know Co permitting I'm going to +be doing most of the lecturing in this + + align:start position:0% +be doing most of the lecturing in this + + + align:start position:0% +be doing most of the lecturing in this +class I think the plan is I'll be doing + + align:start position:0% +class I think the plan is I'll be doing + + + align:start position:0% +class I think the plan is I'll be doing +21 of the lectures Tobias will be doing + + align:start position:0% +21 of the lectures Tobias will be doing + + + align:start position:0% +21 of the lectures Tobias will be doing +four Shan terroll will be doing two um + + align:start position:0% +four Shan terroll will be doing two um + + + align:start position:0% +four Shan terroll will be doing two um +and uh you know it's a basic course in + + align:start position:0% +and uh you know it's a basic course in + + + align:start position:0% +and uh you know it's a basic course in +industrial + + align:start position:0% +industrial + + + align:start position:0% +industrial +organization uh you know I think these + + align:start position:0% +organization uh you know I think these + + + align:start position:0% +organization uh you know I think these +days you know my primary responsibility + + align:start position:0% +days you know my primary responsibility + + + align:start position:0% +days you know my primary responsibility +in this class is to teach students who + + align:start position:0% +in this class is to teach students who + + + align:start position:0% +in this class is to teach students who +are going to write their thesis and + + align:start position:0% +are going to write their thesis and + + + align:start position:0% +are going to write their thesis and +industrial organization what they need + + align:start position:0% +industrial organization what they need + + + align:start position:0% +industrial organization what they need +to do to write an IO thesis but you know + + align:start position:0% +to do to write an IO thesis but you know + + + align:start position:0% +to do to write an IO thesis but you know +the course has also traditionally been + + align:start position:0% +the course has also traditionally been + + + align:start position:0% +the course has also traditionally been +useful for many students in other fields + + align:start position:0% +useful for many students in other fields + + + align:start position:0% +useful for many students in other fields +I think that's for two reasons you know + + align:start position:0% +I think that's for two reasons you know + + + align:start position:0% +I think that's for two reasons you know +one sort of IO has always been at the + + align:start position:0% +one sort of IO has always been at the + + + align:start position:0% +one sort of IO has always been at the +front in economics and sort of linking + + align:start position:0% +front in economics and sort of linking + + + align:start position:0% +front in economics and sort of linking +Theory and empirics together uh and then + + align:start position:0% +Theory and empirics together uh and then + + + align:start position:0% +Theory and empirics together uh and then +also you know in recent years IO has + + align:start position:0% +also you know in recent years IO has + + + align:start position:0% +also you know in recent years IO has +developed a lot of techniques for what's + + align:start position:0% +developed a lot of techniques for what's + + + align:start position:0% +developed a lot of techniques for what's +referred to as structural empirical + + align:start position:0% +referred to as structural empirical + + + align:start position:0% +referred to as structural empirical +industrial organization which have + + align:start position:0% +industrial organization which have + + + align:start position:0% +industrial organization which have +become very very popular in other fields + + align:start position:0% +become very very popular in other fields + + + align:start position:0% +become very very popular in other fields +um anyway so you know my goal here is + + align:start position:0% +um anyway so you know my goal here is + + + align:start position:0% +um anyway so you know my goal here is +really to sort of teach the basics of IO + + align:start position:0% +really to sort of teach the basics of IO + + + align:start position:0% +really to sort of teach the basics of IO +Theory and how IO people think about + + align:start position:0% +Theory and how IO people think about + + + align:start position:0% +Theory and how IO people think about +empirical work which is sometimes + + align:start position:0% +empirical work which is sometimes + + + align:start position:0% +empirical work which is sometimes +different from how empirical work is + + align:start position:0% +different from how empirical work is + + + align:start position:0% +different from how empirical work is +done in different fields um the way I'm + + align:start position:0% +done in different fields um the way I'm + + + align:start position:0% +done in different fields um the way I'm +going to do that is is um you'll see on + + align:start position:0% +going to do that is is um you'll see on + + + align:start position:0% +going to do that is is um you'll see on +the syllabus we've got you know 12 + + align:start position:0% +the syllabus we've got you know 12 + + + align:start position:0% +the syllabus we've got you know 12 +topics or whatever we're going to cover + + align:start position:0% +topics or whatever we're going to cover + + + align:start position:0% +topics or whatever we're going to cover +uh almost all of them are going to get + + align:start position:0% +uh almost all of them are going to get + + + align:start position:0% +uh almost all of them are going to get +covered in two lectures and typically + + align:start position:0% +covered in two lectures and typically + + + align:start position:0% +covered in two lectures and typically +like in the first part of the semester + + align:start position:0% +like in the first part of the semester + + + align:start position:0% +like in the first part of the semester +the pattern is going to be on Wednesday + + align:start position:0% +the pattern is going to be on Wednesday + + + align:start position:0% +the pattern is going to be on Wednesday +I'm going to explain the theory of a + + align:start position:0% +I'm going to explain the theory of a + + + align:start position:0% +I'm going to explain the theory of a +topic I'm going to go over the basic + + align:start position:0% +topic I'm going to go over the basic + + + align:start position:0% +topic I'm going to go over the basic +theory on a topic and then on the Monday + + align:start position:0% +theory on a topic and then on the Monday + + + align:start position:0% +theory on a topic and then on the Monday +I'm going to go over the empirical work + + align:start position:0% +I'm going to go over the empirical work + + + align:start position:0% +I'm going to go over the empirical work +on a topic and you know my basic view of + + align:start position:0% +on a topic and you know my basic view of + + + align:start position:0% +on a topic and you know my basic view of +IO is IO is just an inherently + + align:start position:0% +IO is IO is just an inherently + + + align:start position:0% +IO is IO is just an inherently +theoretical field um you know there are + + align:start position:0% +theoretical field um you know there are + + + align:start position:0% +theoretical field um you know there are +many fields in which empirical work and + + align:start position:0% +many fields in which empirical work and + + + align:start position:0% +many fields in which empirical work and +natural experiments testing policies are + + align:start position:0% +natural experiments testing policies are + + + align:start position:0% +natural experiments testing policies are +what you want to do in studying that + + align:start position:0% +what you want to do in studying that + + + align:start position:0% +what you want to do in studying that +field in IO you know the questions we + + align:start position:0% +field in IO you know the questions we + + + align:start position:0% +field in IO you know the questions we +get asked are should Facebook be + + align:start position:0% +get asked are should Facebook be + + + align:start position:0% +get asked are should Facebook be +required to divest itself of + + align:start position:0% +required to divest itself of + + + align:start position:0% +required to divest itself of +Instagram or is it okay for Google to be + + align:start position:0% +Instagram or is it okay for Google to be + + + align:start position:0% +Instagram or is it okay for Google to be +paying Apple 12 billion doll a year to + + align:start position:0% +paying Apple 12 billion doll a year to + + + align:start position:0% +paying Apple 12 billion doll a year to +make Google the default search engine on + + align:start position:0% +make Google the default search engine on + + + align:start position:0% +make Google the default search engine on +iPhones and these are not things that + + align:start position:0% +iPhones and these are not things that + + + align:start position:0% +iPhones and these are not things that +can be addressed with natural + + align:start position:0% +can be addressed with natural + + + align:start position:0% +can be addressed with natural +experiments you you can't create a + + align:start position:0% +experiments you you can't create a + + + align:start position:0% +experiments you you can't create a +hundred different worlds and have break + + align:start position:0% +hundred different worlds and have break + + + align:start position:0% +hundred different worlds and have break +up Facebook and Instagram in half of + + align:start position:0% +up Facebook and Instagram in half of + + + align:start position:0% +up Facebook and Instagram in half of +them and not break up Facebook and + + align:start position:0% +them and not break up Facebook and + + + align:start position:0% +them and not break up Facebook and +Instagram in the other half of them and + + align:start position:0% +Instagram in the other half of them and + + + align:start position:0% +Instagram in the other half of them and +then do a comparison of means 10 years + + align:start position:0% +then do a comparison of means 10 years + + + align:start position:0% +then do a comparison of means 10 years +later and see which was the right + + align:start position:0% +later and see which was the right + + + align:start position:0% +later and see which was the right +decision you know it's a one-time + + align:start position:0% +decision you know it's a one-time + + + align:start position:0% +decision you know it's a one-time +decision that will get made or not and + + align:start position:0% +decision that will get made or not and + + + align:start position:0% +decision that will get made or not and +so you know you basically to make + + align:start position:0% +so you know you basically to make + + + align:start position:0% +so you know you basically to make +decisions like that you need to have + + align:start position:0% +decisions like that you need to have + + + align:start position:0% +decisions like that you need to have +sort of a theoretical understanding of + + align:start position:0% +sort of a theoretical understanding of + + + align:start position:0% +sort of a theoretical understanding of +how the world works and how firms + + align:start position:0% +how the world works and how firms + + + align:start position:0% +how the world works and how firms +competing with other firms work and what + + align:start position:0% +competing with other firms work and what + + + align:start position:0% +competing with other firms work and what +would what do you think would happen on + + align:start position:0% +would what do you think would happen on + + + align:start position:0% +would what do you think would happen on +the two different Market structures and + + align:start position:0% +the two different Market structures and + + + align:start position:0% +the two different Market structures and +then you know you may never find out if + + align:start position:0% +then you know you may never find out if + + + align:start position:0% +then you know you may never find out if +you were right or wrong um while I I + + align:start position:0% +you were right or wrong um while I I + + + align:start position:0% +you were right or wrong um while I I +think you know iio is inherently a + + align:start position:0% +think you know iio is inherently a + + + align:start position:0% +think you know iio is inherently a +theoretical field almost all students + + align:start position:0% +theoretical field almost all students + + + align:start position:0% +theoretical field almost all students +getting good jobs in I/O in the last you + + align:start position:0% +getting good jobs in I/O in the last you + + + align:start position:0% +getting good jobs in I/O in the last you +know 15 20 years are doing empirical IO + + align:start position:0% +know 15 20 years are doing empirical IO + + + align:start position:0% +know 15 20 years are doing empirical IO +uh and in part this is because you know + + align:start position:0% +uh and in part this is because you know + + + align:start position:0% +uh and in part this is because you know +what happens is you know people in IO + + align:start position:0% +what happens is you know people in IO + + + align:start position:0% +what happens is you know people in IO +make up models and the question is you + + align:start position:0% +make up models and the question is you + + + align:start position:0% +make up models and the question is you +can make up you know you can make up + + align:start position:0% +can make up you know you can make up + + + align:start position:0% +can make up you know you can make up +models that predict all kinds of things + + align:start position:0% +models that predict all kinds of things + + + align:start position:0% +models that predict all kinds of things +then you have to ask which models + + align:start position:0% +then you have to ask which models + + + align:start position:0% +then you have to ask which models +assumptions are correct in terms of how + + align:start position:0% +assumptions are correct in terms of how + + + align:start position:0% +assumptions are correct in terms of how +people behave how firms + + align:start position:0% +people behave how firms + + + align:start position:0% +people behave how firms +behave and how large are those effects + + align:start position:0% +behave and how large are those effects + + + align:start position:0% +behave and how large are those effects +empirically uh and so what typically + + align:start position:0% +empirically uh and so what typically + + + align:start position:0% +empirically uh and so what typically +happens there's a lot of play in IO + + align:start position:0% +happens there's a lot of play in IO + + + align:start position:0% +happens there's a lot of play in IO +between you develop a theory you then do + + align:start position:0% +between you develop a theory you then do + + + align:start position:0% +between you develop a theory you then do +empirical work that tries to examine the + + align:start position:0% +empirical work that tries to examine the + + + align:start position:0% +empirical work that tries to examine the +theory in places where it should or + + align:start position:0% +theory in places where it should or + + + align:start position:0% +theory in places where it should or +shouldn't work and you find out how + + align:start position:0% +shouldn't work and you find out how + + + align:start position:0% +shouldn't work and you find out how +important are the effects the different + + align:start position:0% +important are the effects the different + + + align:start position:0% +important are the effects the different +models predict um are the assumptions of + + align:start position:0% +models predict um are the assumptions of + + + align:start position:0% +models predict um are the assumptions of +models good or should we be looking at + + align:start position:0% +models good or should we be looking at + + + align:start position:0% +models good or should we be looking at +what you know in some sense in any good + + align:start position:0% +what you know in some sense in any good + + + align:start position:0% +what you know in some sense in any good +IO empirical work something doesn't fit + + align:start position:0% +IO empirical work something doesn't fit + + + align:start position:0% +IO empirical work something doesn't fit +and then what doesn't fit gives you the + + align:start position:0% +and then what doesn't fit gives you the + + + align:start position:0% +and then what doesn't fit gives you the +idea of how do you refine the model what + + align:start position:0% +idea of how do you refine the model what + + + align:start position:0% +idea of how do you refine the model what +else should be added to the model to get + + align:start position:0% +else should be added to the model to get + + + align:start position:0% +else should be added to the model to get +a better predictive model so let me go + + align:start position:0% +a better predictive model so let me go + + + align:start position:0% +a better predictive model so let me go +ahead and get started uh and I'm going + + align:start position:0% +ahead and get started uh and I'm going + + + align:start position:0% +ahead and get started uh and I'm going +to get started I should say you know + + align:start position:0% +to get started I should say you know + + + align:start position:0% +to get started I should say you know +right normally when you design a class + + align:start position:0% +right normally when you design a class + + + align:start position:0% +right normally when you design a class +you want to sort of have the first class + + align:start position:0% +you want to sort of have the first class + + + align:start position:0% +you want to sort of have the first class +be really exciting and have something + + align:start position:0% +be really exciting and have something + + + align:start position:0% +be really exciting and have something +intriguing whatever for students to to + + align:start position:0% +intriguing whatever for students to to + + + align:start position:0% +intriguing whatever for students to to +get hooked on the class you know that's + + align:start position:0% +get hooked on the class you know that's + + + align:start position:0% +get hooked on the class you know that's +not the case with iio you know I I just + + align:start position:0% +not the case with iio you know I I just + + + align:start position:0% +not the case with iio you know I I just +I have to start at square one I have to + + align:start position:0% +I have to start at square one I have to + + + align:start position:0% +I have to start at square one I have to +start with Monopoly pricing I'm sure + + align:start position:0% +start with Monopoly pricing I'm sure + + + align:start position:0% +start with Monopoly pricing I'm sure +many of you have seen Monopoly pricing + + align:start position:0% +many of you have seen Monopoly pricing + + + align:start position:0% +many of you have seen Monopoly pricing +in your undergraduate intermediate micro + + align:start position:0% +in your undergraduate intermediate micro + + + align:start position:0% +in your undergraduate intermediate micro +or principal classes but I'm sort of + + align:start position:0% +or principal classes but I'm sort of + + + align:start position:0% +or principal classes but I'm sort of +gonna start with the beginning with with + + align:start position:0% +gonna start with the beginning with with + + + align:start position:0% +gonna start with the beginning with with +monopolies pricing and then sort of + + align:start position:0% +monopolies pricing and then sort of + + + align:start position:0% +monopolies pricing and then sort of +build from there um so anyway first + + align:start position:0% +build from there um so anyway first + + + align:start position:0% +build from there um so anyway first +class so this is 1401 um Monopoly sell + + align:start position:0% +class so this is 1401 um Monopoly sell + + + align:start position:0% +class so this is 1401 um Monopoly sell +over a single product in in this cost + + align:start position:0% +over a single product in in this cost + + + align:start position:0% +over a single product in in this cost +I'm generally going to be putting uh + + align:start position:0% +I'm generally going to be putting uh + + + align:start position:0% +I'm generally going to be putting uh +quantity on the x axis and price on the + + align:start position:0% +quantity on the x axis and price on the + + + align:start position:0% +quantity on the x axis and price on the +Y AIS um so you know monopolis has this + + align:start position:0% +Y AIS um so you know monopolis has this + + + align:start position:0% +Y AIS um so you know monopolis has this +downwards uh facing this inverse demand + + align:start position:0% +downwards uh facing this inverse demand + + + align:start position:0% +downwards uh facing this inverse demand +curve P of x if it sells X + + align:start position:0% +curve P of x if it sells X + + + align:start position:0% +curve P of x if it sells X +units monopolis has a total cost + + align:start position:0% +units monopolis has a total cost + + + align:start position:0% +units monopolis has a total cost +function C of X so if they produce X + + align:start position:0% +function C of X so if they produce X + + + align:start position:0% +function C of X so if they produce X +units the total cost of production is c + + align:start position:0% +units the total cost of production is c + + + align:start position:0% +units the total cost of production is c +ofx what does the monopolis do you've + + align:start position:0% +ofx what does the monopolis do you've + + + align:start position:0% +ofx what does the monopolis do you've +seen this many times you maximize overx + + align:start position:0% +seen this many times you maximize overx + + + align:start position:0% +seen this many times you maximize overx +x * P of x minus C ofx + + align:start position:0% +x * P of x minus C ofx + + + align:start position:0% +x * P of x minus C ofx +I take the first order condition and I + + align:start position:0% +I take the first order condition and I + + + align:start position:0% +I take the first order condition and I +get this familiar equation marginal + + align:start position:0% +get this familiar equation marginal + + + align:start position:0% +get this familiar equation marginal +revenue minus marginal cost equals zero + + align:start position:0% +revenue minus marginal cost equals zero + + + align:start position:0% +revenue minus marginal cost equals zero +so monopolis sets marginal revenue equal + + align:start position:0% +so monopolis sets marginal revenue equal + + + align:start position:0% +so monopolis sets marginal revenue equal +to marginal cost okay um why am I + + align:start position:0% +to marginal cost okay um why am I + + + align:start position:0% +to marginal cost okay um why am I +starting here well even in iio we do + + align:start position:0% +starting here well even in iio we do + + + align:start position:0% +starting here well even in iio we do +things a little differently the way + + align:start position:0% +things a little differently the way + + + align:start position:0% +things a little differently the way +people typically think about this first + + align:start position:0% +people typically think about this first + + + align:start position:0% +people typically think about this first +order condition is I've got instead of + + align:start position:0% +order condition is I've got instead of + + + align:start position:0% +order condition is I've got instead of +putting marginal revenue on the left and + + align:start position:0% +putting marginal revenue on the left and + + + align:start position:0% +putting marginal revenue on the left and +marginal cost on the right I'm going to + + align:start position:0% +marginal cost on the right I'm going to + + + align:start position:0% +marginal cost on the right I'm going to +take price minus marginal cost and move + + align:start position:0% +take price minus marginal cost and move + + + align:start position:0% +take price minus marginal cost and move +the minus x p Prime at X to the other + + align:start position:0% +the minus x p Prime at X to the other + + + align:start position:0% +the minus x p Prime at X to the other +side and then I divide both sides by P + + align:start position:0% +side and then I divide both sides by P + + + align:start position:0% +side and then I divide both sides by P +of X and I get price minus marginal cost + + align:start position:0% +of X and I get price minus marginal cost + + + align:start position:0% +of X and I get price minus marginal cost +over price equals this okay and you know + + align:start position:0% +over price equals this okay and you know + + + align:start position:0% +over price equals this okay and you know +what's over here on the right side P + + align:start position:0% +what's over here on the right side P + + + align:start position:0% +what's over here on the right side P +Prime at x x over P of + + align:start position:0% +Prime at x x over P of + + + align:start position:0% +Prime at x x over P of +X you know so you can think of that as X + + align:start position:0% +X you know so you can think of that as X + + + align:start position:0% +X you know so you can think of that as X +over uh P of x 1 over P Prime at + + align:start position:0% +over uh P of x 1 over P Prime at + + + align:start position:0% +over uh P of x 1 over P Prime at +X and then if you think about the + + align:start position:0% +X and then if you think about the + + + align:start position:0% +X and then if you think about the +inverse function theorem 1/ P Prime at X + + align:start position:0% +inverse function theorem 1/ P Prime at X + + + align:start position:0% +inverse function theorem 1/ P Prime at X +is kind of like uh you know DQ + + align:start position:0% +is kind of like uh you know DQ + + + align:start position:0% +is kind of like uh you know DQ +DP right because the p is the in you + + align:start position:0% +DP right because the p is the in you + + + align:start position:0% +DP right because the p is the in you +know uh you know if you think about p is + + align:start position:0% +know uh you know if you think about p is + + + align:start position:0% +know uh you know if you think about p is +the inverse function of Q so this is + + align:start position:0% +the inverse function of Q so this is + + + align:start position:0% +the inverse function of Q so this is +like X over P Prime at X and so if I + + align:start position:0% +like X over P Prime at X and so if I + + + align:start position:0% +like X over P Prime at X and so if I +divide by this D qdp * p over Q This is + + align:start position:0% +divide by this D qdp * p over Q This is + + + align:start position:0% +divide by this D qdp * p over Q This is +the elasticity of + + align:start position:0% +the elasticity of + + + align:start position:0% +the elasticity of +demand so what a monopolis does is it + + align:start position:0% +demand so what a monopolis does is it + + + align:start position:0% +demand so what a monopolis does is it +sets its price so that price minus + + align:start position:0% +sets its price so that price minus + + + align:start position:0% +sets its price so that price minus +marginal cost over price is the negative + + align:start position:0% +marginal cost over price is the negative + + + align:start position:0% +marginal cost over price is the negative +of one over the elasticity of demand and + + align:start position:0% +of one over the elasticity of demand and + + + align:start position:0% +of one over the elasticity of demand and +you know I start here because you know + + align:start position:0% +you know I start here because you know + + + align:start position:0% +you know I start here because you know +in in macroeconomics they seem to have + + align:start position:0% +in in macroeconomics they seem to have + + + align:start position:0% +in in macroeconomics they seem to have +this thing that when demand goes up + + align:start position:0% +this thing that when demand goes up + + + align:start position:0% +this thing that when demand goes up +price goes up and when demand goes down + + align:start position:0% +price goes up and when demand goes down + + + align:start position:0% +price goes up and when demand goes down +price goes down that that doesn't happen + + align:start position:0% +price goes down that that doesn't happen + + + align:start position:0% +price goes down that that doesn't happen +in IO like like when you think about + + align:start position:0% +in IO like like when you think about + + + align:start position:0% +in IO like like when you think about +firms with Market power pricing is based + + align:start position:0% +firms with Market power pricing is based + + + align:start position:0% +firms with Market power pricing is based +on demand elasticities not demand + + align:start position:0% +on demand elasticities not demand + + + align:start position:0% +on demand elasticities not demand +levels um and on this left side you know + + align:start position:0% +levels um and on this left side you know + + + align:start position:0% +levels um and on this left side you know +this is something that uh um in iio we + + align:start position:0% +this is something that uh um in iio we + + + align:start position:0% +this is something that uh um in iio we +call it the learner index uh ignoring + + align:start position:0% +call it the learner index uh ignoring + + + align:start position:0% +call it the learner index uh ignoring +the marginal versus average this is like + + align:start position:0% +the marginal versus average this is like + + + align:start position:0% +the marginal versus average this is like +what accountants would call the gross + + align:start position:0% +what accountants would call the gross + + + align:start position:0% +what accountants would call the gross +margin this is the markup that you're + + align:start position:0% +margin this is the markup that you're + + + align:start position:0% +margin this is the markup that you're +charging as a fraction of the price so + + align:start position:0% +charging as a fraction of the price so + + + align:start position:0% +charging as a fraction of the price so +if you're you know if you're if you + + align:start position:0% +if you're you know if you're if you + + + align:start position:0% +if you're you know if you're if you +charge double your marginal cost that's + + align:start position:0% +charge double your marginal cost that's + + + align:start position:0% +charge double your marginal cost that's +a 50% markup because 50% of your price + + align:start position:0% +a 50% markup because 50% of your price + + + align:start position:0% +a 50% markup because 50% of your price +is markup 50% is cost so this says the + + align:start position:0% +is markup 50% is cost so this says the + + + align:start position:0% +is markup 50% is cost so this says the +learner index is negative of one over + + align:start position:0% +learner index is negative of one over + + + align:start position:0% +learner index is negative of one over +the elasticity of + + align:start position:0% +the elasticity of + + + align:start position:0% +the elasticity of +demand so if for instance the elasticity + + align:start position:0% +demand so if for instance the elasticity + + + align:start position:0% +demand so if for instance the elasticity +of demand is you know if Epsilon is -2 + + align:start position:0% +of demand is you know if Epsilon is -2 + + + align:start position:0% +of demand is you know if Epsilon is -2 +then this would say you do price minus + + align:start position:0% +then this would say you do price minus + + + align:start position:0% +then this would say you do price minus +marginal cost over price is one half so + + align:start position:0% +marginal cost over price is one half so + + + align:start position:0% +marginal cost over price is one half so +if you're a monopolist your last demand + + align:start position:0% +if you're a monopolist your last demand + + + align:start position:0% +if you're a monopolist your last demand +is two your margin is 50% you double + + align:start position:0% +is two your margin is 50% you double + + + align:start position:0% +is two your margin is 50% you double +your marginal cost when you think of + + align:start position:0% +your marginal cost when you think of + + + align:start position:0% +your marginal cost when you think of +your Monopoly price if your elasticity + + align:start position:0% +your Monopoly price if your elasticity + + + align:start position:0% +your Monopoly price if your elasticity +is four you do uh your + + align:start position:0% +is four you do uh your + + + align:start position:0% +is four you do uh your +25% uh learner index 20 learner index is + + align:start position:0% +25% uh learner index 20 learner index is + + + align:start position:0% +25% uh learner index 20 learner index is +is 1/4 which means you're sort of + + align:start position:0% +is 1/4 which means you're sort of + + + align:start position:0% +is 1/4 which means you're sort of +raising your price by 1/3 over of + + align:start position:0% + + + + align:start position:0% + +cost in 1401 you certainly also did a + + align:start position:0% +cost in 1401 you certainly also did a + + + align:start position:0% +cost in 1401 you certainly also did a +diagram like this um you know so what + + align:start position:0% +diagram like this um you know so what + + + align:start position:0% +diagram like this um you know so what +happens you know firm sets marginal + + align:start position:0% +happens you know firm sets marginal + + + align:start position:0% +happens you know firm sets marginal +revenue equal to marginal cost they have + + align:start position:0% +revenue equal to marginal cost they have + + + align:start position:0% +revenue equal to marginal cost they have +this Monopoly price they earn a profit + + align:start position:0% +this Monopoly price they earn a profit + + + align:start position:0% +this Monopoly price they earn a profit +on all the units they sell at a cost + + align:start position:0% +on all the units they sell at a cost + + + align:start position:0% +on all the units they sell at a cost +that's greater than a cost of producing + + align:start position:0% +that's greater than a cost of producing + + + align:start position:0% +that's greater than a cost of producing +them and so this is the + + align:start position:0% +them and so this is the + + + align:start position:0% +them and so this is the +profit this is the difference between + + align:start position:0% +profit this is the difference between + + + align:start position:0% +profit this is the difference between +the consumer willingness to pay for each + + align:start position:0% +the consumer willingness to pay for each + + + align:start position:0% +the consumer willingness to pay for each +unit and the price that they've paid so + + align:start position:0% +unit and the price that they've paid so + + + align:start position:0% +unit and the price that they've paid so +this is consumer Surplus this is dead + + align:start position:0% +this is consumer Surplus this is dead + + + align:start position:0% +this is consumer Surplus this is dead +weight + + align:start position:0% +weight + + + align:start position:0% +weight +loss um typically you know a lot of um + + align:start position:0% +loss um typically you know a lot of um + + + align:start position:0% +loss um typically you know a lot of um +IO is about Market power is a bad thing + + align:start position:0% +IO is about Market power is a bad thing + + + align:start position:0% +IO is about Market power is a bad thing +we want to prevent Market power why do + + align:start position:0% +we want to prevent Market power why do + + + align:start position:0% +we want to prevent Market power why do +we want to prevent Market power um you + + align:start position:0% +we want to prevent Market power um you + + + align:start position:0% +we want to prevent Market power um you +know classic explanation for why you + + align:start position:0% +know classic explanation for why you + + + align:start position:0% +know classic explanation for why you +want to prevent Market power is this + + align:start position:0% +want to prevent Market power is this + + + align:start position:0% +want to prevent Market power is this +triangle you have these this dead weight + + align:start position:0% +triangle you have these this dead weight + + + align:start position:0% +triangle you have these this dead weight +loss is a social + + align:start position:0% +loss is a social + + + align:start position:0% +loss is a social +inefficiency you know people are willing + + align:start position:0% +inefficiency you know people are willing + + + align:start position:0% +inefficiency you know people are willing +to pay more than the cost of producing + + align:start position:0% +to pay more than the cost of producing + + + align:start position:0% +to pay more than the cost of producing +the goods and yet those goods don't get + + align:start position:0% +the goods and yet those goods don't get + + + align:start position:0% +the goods and yet those goods don't get +produced and sold to them that's sort of + + align:start position:0% +produced and sold to them that's sort of + + + align:start position:0% +produced and sold to them that's sort of +socially wasteful that we have these + + align:start position:0% +socially wasteful that we have these + + + align:start position:0% +socially wasteful that we have these +opportunities for gains from trade that + + align:start position:0% +opportunities for gains from trade that + + + align:start position:0% +opportunities for gains from trade that +aren't realized okay + + align:start position:0% +aren't realized okay + + + align:start position:0% +aren't realized okay +um while people often focus on dead + + align:start position:0% +um while people often focus on dead + + + align:start position:0% +um while people often focus on dead +weight loss there a lot of other reasons + + align:start position:0% +weight loss there a lot of other reasons + + + align:start position:0% +weight loss there a lot of other reasons +why you might think monopolies are also + + align:start position:0% +why you might think monopolies are also + + + align:start position:0% +why you might think monopolies are also +a bad idea so many of these are harder + + align:start position:0% +a bad idea so many of these are harder + + + align:start position:0% +a bad idea so many of these are harder +to um harder to actually sort of explain + + align:start position:0% +to um harder to actually sort of explain + + + align:start position:0% +to um harder to actually sort of explain +economically to realize think they + + align:start position:0% +economically to realize think they + + + align:start position:0% +economically to realize think they +should recurring but one thing you hear + + align:start position:0% +should recurring but one thing you hear + + + align:start position:0% +should recurring but one thing you hear +people talk about is productive + + align:start position:0% +people talk about is productive + + + align:start position:0% +people talk about is productive +inefficiency um you know certainly the + + align:start position:0% +inefficiency um you know certainly the + + + align:start position:0% +inefficiency um you know certainly the +question is like you know are monopolis + + align:start position:0% +question is like you know are monopolis + + + align:start position:0% +question is like you know are monopolis +going to produce things at the lowest + + align:start position:0% +going to produce things at the lowest + + + align:start position:0% +going to produce things at the lowest +cost possible + + align:start position:0% +cost possible + + + align:start position:0% +cost possible +nor your basic intuition should be yes + + align:start position:0% +nor your basic intuition should be yes + + + align:start position:0% +nor your basic intuition should be yes +you know monopolist gets all the extra + + align:start position:0% +you know monopolist gets all the extra + + + align:start position:0% +you know monopolist gets all the extra +money they make from cost savings so + + align:start position:0% +money they make from cost savings so + + + align:start position:0% +money they make from cost savings so +monopolists ought to want to produce in + + align:start position:0% +monopolists ought to want to produce in + + + align:start position:0% +monopolists ought to want to produce in +the most efficient technology possible + + align:start position:0% +the most efficient technology possible + + + align:start position:0% +the most efficient technology possible +um you know there lots of discussions + + align:start position:0% +um you know there lots of discussions + + + align:start position:0% +um you know there lots of discussions +like if you think about the old Soviet + + align:start position:0% +like if you think about the old Soviet + + + align:start position:0% +like if you think about the old Soviet +Union why they were making you know they + + align:start position:0% +Union why they were making you know they + + + align:start position:0% +Union why they were making you know they +had factories making things out of + + align:start position:0% +had factories making things out of + + + align:start position:0% +had factories making things out of +titanium that could have been made out + + align:start position:0% +titanium that could have been made out + + + align:start position:0% +titanium that could have been made out +of steel and they cost five times as + + align:start position:0% +of steel and they cost five times as + + + align:start position:0% +of steel and they cost five times as +much as they cost in the west why did + + align:start position:0% +much as they cost in the west why did + + + align:start position:0% +much as they cost in the west why did +that happen well one thing that you hear + + align:start position:0% +that happen well one thing that you hear + + + align:start position:0% +that happen well one thing that you hear +is that when you have them if you have a + + align:start position:0% +is that when you have them if you have a + + + align:start position:0% +is that when you have them if you have a +firm that's a monopoly they don't have + + align:start position:0% +firm that's a monopoly they don't have + + + align:start position:0% +firm that's a monopoly they don't have +anyone to compare themselves to they + + align:start position:0% +anyone to compare themselves to they + + + align:start position:0% +anyone to compare themselves to they +don't realize their better Production + + align:start position:0% +don't realize their better Production + + + align:start position:0% +don't realize their better Production +Technologies you know employees can be + + align:start position:0% +Technologies you know employees can be + + + align:start position:0% +Technologies you know employees can be +lazy in figuring out how to produce + + align:start position:0% +lazy in figuring out how to produce + + + align:start position:0% +lazy in figuring out how to produce +things and no one ever catches them so + + align:start position:0% +things and no one ever catches them so + + + align:start position:0% +things and no one ever catches them so +productive efficiency could be a cost of + + align:start position:0% +productive efficiency could be a cost of + + + align:start position:0% +productive efficiency could be a cost of +Monopoly uh quality distortions again + + align:start position:0% +Monopoly uh quality distortions again + + + align:start position:0% +Monopoly uh quality distortions again +you know this is more an informal + + align:start position:0% +you know this is more an informal + + + align:start position:0% +you know this is more an informal +complaint but you know people look at + + align:start position:0% +complaint but you know people look at + + + align:start position:0% +complaint but you know people look at +Microsoft Windows and are often like + + align:start position:0% +Microsoft Windows and are often like + + + align:start position:0% +Microsoft Windows and are often like +thinking of 30 different criticisms of + + align:start position:0% +thinking of 30 different criticisms of + + + align:start position:0% +thinking of 30 different criticisms of +Microsoft Windows and why does it suck + + align:start position:0% +Microsoft Windows and why does it suck + + + align:start position:0% +Microsoft Windows and why does it suck +in so many ways why can't Excel do this + + align:start position:0% +in so many ways why can't Excel do this + + + align:start position:0% +in so many ways why can't Excel do this +why can't Excel do this is it because + + align:start position:0% +why can't Excel do this is it because + + + align:start position:0% +why can't Excel do this is it because +Microsoft is a monopoly and has no + + align:start position:0% +Microsoft is a monopoly and has no + + + align:start position:0% +Microsoft is a monopoly and has no +incentive to improve the quality of its + + align:start position:0% +incentive to improve the quality of its + + + align:start position:0% +incentive to improve the quality of its +products because you know you've got got + + align:start position:0% +products because you know you've got got + + + align:start position:0% +products because you know you've got got +to buy them You' got to put Windows on + + align:start position:0% +to buy them You' got to put Windows on + + + align:start position:0% +to buy them You' got to put Windows on +your computer anyway even if you don't + + align:start position:0% +your computer anyway even if you don't + + + align:start position:0% +your computer anyway even if you don't +like it um rent seeking uh is an + + align:start position:0% +like it um rent seeking uh is an + + + align:start position:0% +like it um rent seeking uh is an +important thing you know like sometimes + + align:start position:0% +important thing you know like sometimes + + + align:start position:0% +important thing you know like sometimes +we have monopolies for regulatory + + align:start position:0% +we have monopolies for regulatory + + + align:start position:0% +we have monopolies for regulatory +reasons or for capacity constraints so + + align:start position:0% +reasons or for capacity constraints so + + + align:start position:0% +reasons or for capacity constraints so +for instance you know there's a limited + + align:start position:0% +for instance you know there's a limited + + + align:start position:0% +for instance you know there's a limited +number of licenses to provide cell phone + + align:start position:0% +number of licenses to provide cell phone + + + align:start position:0% +number of licenses to provide cell phone +service uh in every city um in the old + + align:start position:0% +service uh in every city um in the old + + + align:start position:0% +service uh in every city um in the old +days when cell phone service first + + align:start position:0% +days when cell phone service first + + + align:start position:0% +days when cell phone service first +started these were actually sort of like + + align:start position:0% +started these were actually sort of like + + + align:start position:0% +started these were actually sort of like +when United States first adopted cell + + align:start position:0% +when United States first adopted cell + + + align:start position:0% +when United States first adopted cell +phon you know cell phones there were + + align:start position:0% +phon you know cell phones there were + + + align:start position:0% +phon you know cell phones there were +going to be two licenses in every city + + align:start position:0% +going to be two licenses in every city + + + align:start position:0% +going to be two licenses in every city +uh and they had what Ty people refer to + + align:start position:0% +uh and they had what Ty people refer to + + + align:start position:0% +uh and they had what Ty people refer to +as a beauty + + align:start position:0% +as a beauty + + + align:start position:0% +as a beauty +contest to to allocate those licenses + + align:start position:0% +contest to to allocate those licenses + + + align:start position:0% +contest to to allocate those licenses +that is firms didn't have to pay for + + align:start position:0% +that is firms didn't have to pay for + + + align:start position:0% +that is firms didn't have to pay for +them you just had to apply to produce uh + + align:start position:0% +them you just had to apply to produce uh + + + align:start position:0% +them you just had to apply to produce uh +to provide cell phone service and the + + align:start position:0% +to provide cell phone service and the + + + align:start position:0% +to provide cell phone service and the +government would pick the firm that + + align:start position:0% +government would pick the firm that + + + align:start position:0% +government would pick the firm that +seemed best do the you know socially + + align:start position:0% +seemed best do the you know socially + + + align:start position:0% +seemed best do the you know socially +efficient to provide the cell phone + + align:start position:0% +efficient to provide the cell phone + + + align:start position:0% +efficient to provide the cell phone +service and would award those licenses + + align:start position:0% +service and would award those licenses + + + align:start position:0% +service and would award those licenses +those winning parties um often these + + align:start position:0% +those winning parties um often these + + + align:start position:0% +those winning parties um often these +winning parties were perhaps not the + + align:start position:0% +winning parties were perhaps not the + + + align:start position:0% +winning parties were perhaps not the +ones you would think so for instance I I + + align:start position:0% +ones you would think so for instance I I + + + align:start position:0% +ones you would think so for instance I I +don't know if the story is true there's + + align:start position:0% +don't know if the story is true there's + + + align:start position:0% +don't know if the story is true there's +a story that like Washington DC one of + + align:start position:0% +a story that like Washington DC one of + + + align:start position:0% +a story that like Washington DC one of +the two licenses went to kathern Graham + + align:start position:0% +the two licenses went to kathern Graham + + + align:start position:0% +the two licenses went to kathern Graham +who's the editor of the Washington Post + + align:start position:0% +who's the editor of the Washington Post + + + align:start position:0% +who's the editor of the Washington Post +why would she know more than anyone else + + align:start position:0% +why would she know more than anyone else + + + align:start position:0% +why would she know more than anyone else +about running a cell phone company well + + align:start position:0% +about running a cell phone company well + + + align:start position:0% +about running a cell phone company well +she ran a newspaper that would write + + align:start position:0% +she ran a newspaper that would write + + + align:start position:0% +she ran a newspaper that would write +stories about the politicians so when + + align:start position:0% +stories about the politicians so when + + + align:start position:0% +stories about the politicians so when +they're thinking of who to give the + + align:start position:0% +they're thinking of who to give the + + + align:start position:0% +they're thinking of who to give the +license to they give it to her but in + + align:start position:0% +license to they give it to her but in + + + align:start position:0% +license to they give it to her but in +general you know in many situations + + align:start position:0% +general you know in many situations + + + align:start position:0% +general you know in many situations +you're going to find that if there are + + align:start position:0% +you're going to find that if there are + + + align:start position:0% +you're going to find that if there are +Monopoly rents to be given out someone + + align:start position:0% +Monopoly rents to be given out someone + + + align:start position:0% +Monopoly rents to be given out someone +has the power to give out the Monopoly + + align:start position:0% +has the power to give out the Monopoly + + + align:start position:0% +has the power to give out the Monopoly +rents and then when someone has the + + align:start position:0% +rents and then when someone has the + + + align:start position:0% +rents and then when someone has the +power to give out the Monopoly rents + + align:start position:0% +power to give out the Monopoly rents + + + align:start position:0% +power to give out the Monopoly rents +those people you know may take bribes + + align:start position:0% +those people you know may take bribes + + + align:start position:0% +those people you know may take bribes +from the people who are giving them it + + align:start position:0% +from the people who are giving them it + + + align:start position:0% +from the people who are giving them it +may be that you have something akin to a + + align:start position:0% +may be that you have something akin to a + + + align:start position:0% +may be that you have something akin to a +political campaign where you're doing + + align:start position:0% +political campaign where you're doing + + + align:start position:0% +political campaign where you're doing +advertising or lobbying and you have all + + align:start position:0% +advertising or lobbying and you have all + + + align:start position:0% +advertising or lobbying and you have all +these socially wasteful expenditures to + + align:start position:0% +these socially wasteful expenditures to + + + align:start position:0% +these socially wasteful expenditures to +try to be the one who earns these + + align:start position:0% +try to be the one who earns these + + + align:start position:0% +try to be the one who earns these +profits you know if you imagine like you + + align:start position:0% +profits you know if you imagine like you + + + align:start position:0% +profits you know if you imagine like you +know a bidding game where like you know + + align:start position:0% +know a bidding game where like you know + + + align:start position:0% +know a bidding game where like you know +if uh everybody is going to give a bribe + + align:start position:0% +if uh everybody is going to give a bribe + + + align:start position:0% +if uh everybody is going to give a bribe +to the politician and the biggest bribe + + align:start position:0% +to the politician and the biggest bribe + + + align:start position:0% +to the politician and the biggest bribe +wins what's your bribe going to be you + + align:start position:0% +wins what's your bribe going to be you + + + align:start position:0% +wins what's your bribe going to be you +know you're will to pay a bribe equal to + + align:start position:0% +know you're will to pay a bribe equal to + + + align:start position:0% +know you're will to pay a bribe equal to +the discounted value of all future + + align:start position:0% +the discounted value of all future + + + align:start position:0% +the discounted value of all future +profits that you're going to earn in + + align:start position:0% +profits that you're going to earn in + + + align:start position:0% +profits that you're going to earn in +that game you'd ECT all of the sort of + + align:start position:0% +that game you'd ECT all of the sort of + + + align:start position:0% +that game you'd ECT all of the sort of +profits would also then get dissipated + + align:start position:0% +profits would also then get dissipated + + + align:start position:0% +profits would also then get dissipated +socially well actually you know if it + + align:start position:0% +socially well actually you know if it + + + align:start position:0% +socially well actually you know if it +now if it's a bribe you believe in sort + + align:start position:0% +now if it's a bribe you believe in sort + + + align:start position:0% +now if it's a bribe you believe in sort +of efficient markets it's sort of like + + align:start position:0% +of efficient markets it's sort of like + + + align:start position:0% +of efficient markets it's sort of like +it's just a transfer and so it's just a + + align:start position:0% +it's just a transfer and so it's just a + + + align:start position:0% +it's just a transfer and so it's just a +transfer of wealth from consumers to the + + align:start position:0% +transfer of wealth from consumers to the + + + align:start position:0% +transfer of wealth from consumers to the +one person who's taking the bribe um but + + align:start position:0% +one person who's taking the bribe um but + + + align:start position:0% +one person who's taking the bribe um but +you know if if the bribes are given in a + + align:start position:0% +you know if if the bribes are given in a + + + align:start position:0% +you know if if the bribes are given in a +socially wasteful way all of this could + + align:start position:0% +socially wasteful way all of this could + + + align:start position:0% +socially wasteful way all of this could +also be a loss of Monopoly power uh and + + align:start position:0% +also be a loss of Monopoly power uh and + + + align:start position:0% +also be a loss of Monopoly power uh and +then my final comment on BR brings up + + align:start position:0% +then my final comment on BR brings up + + + align:start position:0% +then my final comment on BR brings up +this sort of equity concern another + + align:start position:0% +this sort of equity concern another + + + align:start position:0% +this sort of equity concern another +problem with Monopoly is that in a + + align:start position:0% +problem with Monopoly is that in a + + + align:start position:0% +problem with Monopoly is that in a +competitive market the consumers will be + + align:start position:0% +competitive market the consumers will be + + + align:start position:0% +competitive market the consumers will be +paying this in Monopoly they're paying + + align:start position:0% +paying this in Monopoly they're paying + + + align:start position:0% +paying this in Monopoly they're paying +this consumers paying more it's a + + align:start position:0% +this consumers paying more it's a + + + align:start position:0% +this consumers paying more it's a +transfer from consumers to firms if you + + align:start position:0% +transfer from consumers to firms if you + + + align:start position:0% +transfer from consumers to firms if you +believe that the consumers have a higher + + align:start position:0% +believe that the consumers have a higher + + + align:start position:0% +believe that the consumers have a higher +marginal utility of income than the + + align:start position:0% +marginal utility of income than the + + + align:start position:0% +marginal utility of income than the +shareholders of the firm that's also a + + align:start position:0% +shareholders of the firm that's also a + + + align:start position:0% +shareholders of the firm that's also a +sort of concern we should be worried + + align:start position:0% +sort of concern we should be worried + + + align:start position:0% +sort of concern we should be worried +about I should say that in IO I + + align:start position:0% +about I should say that in IO I + + + align:start position:0% +about I should say that in IO I +mentioned that today I'm never going to + + align:start position:0% +mentioned that today I'm never going to + + + align:start position:0% +mentioned that today I'm never going to +mention it again pretty much uh Jean may + + align:start position:0% +mention it again pretty much uh Jean may + + + align:start position:0% +mention it again pretty much uh Jean may +talk about it when he gives his his uh + + align:start position:0% +talk about it when he gives his his uh + + + align:start position:0% +talk about it when he gives his his uh +guest lectures but uh in IO all these + + align:start position:0% +guest lectures but uh in IO all these + + + align:start position:0% +guest lectures but uh in IO all these +income effects you see in Public Finance + + align:start position:0% +income effects you see in Public Finance + + + align:start position:0% +income effects you see in Public Finance +whatever those are all going to + + align:start position:0% +whatever those are all going to + + + align:start position:0% +whatever those are all going to +disappear here so so in IO pretty much + + align:start position:0% +disappear here so so in IO pretty much + + + align:start position:0% +disappear here so so in IO pretty much +everybody has uh quasi linear + + align:start position:0% +everybody has uh quasi linear + + + align:start position:0% +everybody has uh quasi linear +preferences and everyone has you know + + align:start position:0% +preferences and everyone has you know + + + align:start position:0% +preferences and everyone has you know +preferences that look like V minus P + + align:start position:0% +preferences that look like V minus P + + + align:start position:0% +preferences that look like V minus P +where everybody's got a marginal utility + + align:start position:0% +where everybody's got a marginal utility + + + align:start position:0% +where everybody's got a marginal utility +of income of one that's constant and + + align:start position:0% +of income of one that's constant and + + + align:start position:0% +of income of one that's constant and +everyone has some value from buying the + + align:start position:0% +everyone has some value from buying the + + + align:start position:0% +everyone has some value from buying the +good and we just do additively separable + + align:start position:0% +good and we just do additively separable + + + align:start position:0% +good and we just do additively separable +utility and don't really worry about + + align:start position:0% +utility and don't really worry about + + + align:start position:0% +utility and don't really worry about +income effects and stuff um and it's + + align:start position:0% +income effects and stuff um and it's + + + align:start position:0% +income effects and stuff um and it's +it's you know obviously that's not to + + align:start position:0% +it's you know obviously that's not to + + + align:start position:0% +it's you know obviously that's not to +say that Equity concerns and transfers + + align:start position:0% +say that Equity concerns and transfers + + + align:start position:0% +say that Equity concerns and transfers +across consumers aren't important but + + align:start position:0% +across consumers aren't important but + + + align:start position:0% +across consumers aren't important but +it's + + align:start position:0% +it's + + + align:start position:0% +it's +just you know I think people in iow have + + align:start position:0% +just you know I think people in iow have + + + align:start position:0% +just you know I think people in iow have +made the decision that you don't want to + + align:start position:0% +made the decision that you don't want to + + + align:start position:0% +made the decision that you don't want to +sort of be every single model talking + + align:start position:0% +sort of be every single model talking + + + align:start position:0% +sort of be every single model talking +about the incentive to distort what you + + align:start position:0% +about the incentive to distort what you + + + align:start position:0% +about the incentive to distort what you +have the firms doing in order to sort of + + align:start position:0% +have the firms doing in order to sort of + + + align:start position:0% +have the firms doing in order to sort of +benefit the consumers with lower + + align:start position:0% +benefit the consumers with lower + + + align:start position:0% +benefit the consumers with lower +marginal utilities of income instead of + + align:start position:0% +marginal utilities of income instead of + + + align:start position:0% +marginal utilities of income instead of +higher marginal utilities of income so + + align:start position:0% +higher marginal utilities of income so + + + align:start position:0% +higher marginal utilities of income so +we just do this and you can think about + + align:start position:0% +we just do this and you can think about + + + align:start position:0% +we just do this and you can think about +sort of equity concerns on top of it but + + align:start position:0% +sort of equity concerns on top of it but + + + align:start position:0% +sort of equity concerns on top of it but +for pretty much all semester I'm going + + align:start position:0% +for pretty much all semester I'm going + + + align:start position:0% +for pretty much all semester I'm going +to have that kind of + + align:start position:0% +to have that kind of + + + align:start position:0% +to have that kind of +utility okay okay um that's your basic + + align:start position:0% +utility okay okay um that's your basic + + + align:start position:0% +utility okay okay um that's your basic +Monopoly pricing model what are some of + + align:start position:0% +Monopoly pricing model what are some of + + + align:start position:0% +Monopoly pricing model what are some of +other things you need to know um first + + align:start position:0% +other things you need to know um first + + + align:start position:0% +other things you need to know um first +of all most fir in the real world sell + + align:start position:0% +of all most fir in the real world sell + + + align:start position:0% +of all most fir in the real world sell +multiple Goods instead of a single good + + align:start position:0% +multiple Goods instead of a single good + + + align:start position:0% +multiple Goods instead of a single good +um so the way I'm going to think about + + align:start position:0% +um so the way I'm going to think about + + + align:start position:0% +um so the way I'm going to think about +this is you know simplest example + + align:start position:0% +this is you know simplest example + + + align:start position:0% +this is you know simplest example +suppose the monopolist has two goods to + + align:start position:0% +suppose the monopolist has two goods to + + + align:start position:0% +suppose the monopolist has two goods to +sell um now I'm putting price as the + + align:start position:0% +sell um now I'm putting price as the + + + align:start position:0% +sell um now I'm putting price as the +argument so demand for good one is a + + align:start position:0% +argument so demand for good one is a + + + align:start position:0% +argument so demand for good one is a +function of P1 and P2 demand for good to + + align:start position:0% +function of P1 and P2 demand for good to + + + align:start position:0% +function of P1 and P2 demand for good to +is also a function of P1 and + + align:start position:0% +is also a function of P1 and + + + align:start position:0% +is also a function of P1 and +P2 um let me stick with constant + + align:start position:0% +P2 um let me stick with constant + + + align:start position:0% +P2 um let me stick with constant +marginal costs here so the total cost of + + align:start position:0% +marginal costs here so the total cost of + + + align:start position:0% +marginal costs here so the total cost of +producing X1 units of good one and X2 + + align:start position:0% +producing X1 units of good one and X2 + + + align:start position:0% +producing X1 units of good one and X2 +units of good two is just C1 X1 plus C2 + + align:start position:0% + + + + align:start position:0% + +X2 so what's the monopolis problem it's + + align:start position:0% +X2 so what's the monopolis problem it's + + + align:start position:0% +X2 so what's the monopolis problem it's +now maximizing over the two + + align:start position:0% +now maximizing over the two + + + align:start position:0% +now maximizing over the two +prices uh price one minus marginal cost + + align:start position:0% +prices uh price one minus marginal cost + + + align:start position:0% +prices uh price one minus marginal cost +one times number of units of good one + + align:start position:0% +one times number of units of good one + + + align:start position:0% +one times number of units of good one +plus P2 minus C2 DX * + + align:start position:0% +plus P2 minus C2 DX * + + + align:start position:0% +plus P2 minus C2 DX * +X2 what do the first order conditions + + align:start position:0% +X2 what do the first order conditions + + + align:start position:0% +X2 what do the first order conditions +look like well if I differentiate think + + align:start position:0% +look like well if I differentiate think + + + align:start position:0% +look like well if I differentiate think +about differentiating with respect to + + align:start position:0% +about differentiating with respect to + + + align:start position:0% +about differentiating with respect to +the price of good one if I differentiate + + align:start position:0% +the price of good one if I differentiate + + + align:start position:0% +the price of good one if I differentiate +with respect to p 1 I'm going to get P1 + + align:start position:0% +with respect to p 1 I'm going to get P1 + + + align:start position:0% +with respect to p 1 I'm going to get P1 +- C1 dx1 + + align:start position:0% +- C1 dx1 + + + align:start position:0% +- C1 dx1 +dp1 plus this times der of that which is + + align:start position:0% +dp1 plus this times der of that which is + + + align:start position:0% +dp1 plus this times der of that which is +X1 of P1 + + align:start position:0% +X1 of P1 + + + align:start position:0% +X1 of P1 +P2 uh but now I'm going to get a extra + + align:start position:0% +P2 uh but now I'm going to get a extra + + + align:start position:0% +P2 uh but now I'm going to get a extra +term that I wasn't getting before which + + align:start position:0% +term that I wasn't getting before which + + + align:start position:0% +term that I wasn't getting before which +is dx2 dp1 * P2 minus + + align:start position:0% + + + + align:start position:0% + +C2 so one way to think about what we're + + align:start position:0% +C2 so one way to think about what we're + + + align:start position:0% +C2 so one way to think about what we're +getting is if I now do the same thing if + + align:start position:0% +getting is if I now do the same thing if + + + align:start position:0% +getting is if I now do the same thing if +I divide by X I get price Minus cost + + align:start position:0% +I divide by X I get price Minus cost + + + align:start position:0% +I divide by X I get price Minus cost +plus um X1 over dx1 dp1 plus P2 minus C2 + + align:start position:0% +plus um X1 over dx1 dp1 plus P2 minus C2 + + + align:start position:0% +plus um X1 over dx1 dp1 plus P2 minus C2 +* dx2 dp1 over dx1 dp1 equals 0 so this + + align:start position:0% +* dx2 dp1 over dx1 dp1 equals 0 so this + + + align:start position:0% +* dx2 dp1 over dx1 dp1 equals 0 so this +is the same first order condition I had + + align:start position:0% +is the same first order condition I had + + + align:start position:0% +is the same first order condition I had +before but with the addition of this + + align:start position:0% +before but with the addition of this + + + align:start position:0% +before but with the addition of this +extra term uh people in IO refer to this + + align:start position:0% +extra term uh people in IO refer to this + + + align:start position:0% +extra term uh people in IO refer to this +as the diversion ratio this is when I + + align:start position:0% +as the diversion ratio this is when I + + + align:start position:0% +as the diversion ratio this is when I +raise the price of good + + align:start position:0% +raise the price of good + + + align:start position:0% +raise the price of good +one I'm going to sell fewer units of + + align:start position:0% +one I'm going to sell fewer units of + + + align:start position:0% +one I'm going to sell fewer units of +good two + + align:start position:0% +good two + + + align:start position:0% +good two +when I sell fewer units of good two + + align:start position:0% +when I sell fewer units of good two + + + align:start position:0% +when I sell fewer units of good two +sorry I'm when I sell PR price of good + + align:start position:0% +sorry I'm when I sell PR price of good + + + align:start position:0% +sorry I'm when I sell PR price of good +one I'm going to sell fewer units of + + align:start position:0% +one I'm going to sell fewer units of + + + align:start position:0% +one I'm going to sell fewer units of +good one but when I sell fer units of + + align:start position:0% +good one but when I sell fer units of + + + align:start position:0% +good one but when I sell fer units of +good + + align:start position:0% +good + + + align:start position:0% +good +one that's going to affect my sales of + + align:start position:0% +one that's going to affect my sales of + + + align:start position:0% +one that's going to affect my sales of +good two um and so it can either raise + + align:start position:0% +good two um and so it can either raise + + + align:start position:0% +good two um and so it can either raise +my sales of good two or lower my sales + + align:start position:0% +my sales of good two or lower my sales + + + align:start position:0% +my sales of good two or lower my sales +of good two but I have to take in that + + align:start position:0% +of good two but I have to take in that + + + align:start position:0% +of good two but I have to take in that +account for every unit that I of of + + align:start position:0% +account for every unit that I of of + + + align:start position:0% +account for every unit that I of of +goods that I don't sell it gets diverted + + align:start position:0% +goods that I don't sell it gets diverted + + + align:start position:0% +goods that I don't sell it gets diverted +possibly to a sale of the another good + + align:start position:0% +possibly to a sale of the another good + + + align:start position:0% +possibly to a sale of the another good +and I have to take the profits I would + + align:start position:0% +and I have to take the profits I would + + + align:start position:0% +and I have to take the profits I would +earn on those goods into account when + + align:start position:0% +earn on those goods into account when + + + align:start position:0% +earn on those goods into account when +I'm doing the first one + + align:start position:0% +I'm doing the first one + + + align:start position:0% +I'm doing the first one +okay and so this gives me a different + + align:start position:0% +okay and so this gives me a different + + + align:start position:0% +okay and so this gives me a different +markup formula um price minus marginal + + align:start position:0% +markup formula um price minus marginal + + + align:start position:0% +markup formula um price minus marginal +cost over price is minus one over + + align:start position:0% +cost over price is minus one over + + + align:start position:0% +cost over price is minus one over +Epsilon the elasticity of the + + align:start position:0% +Epsilon the elasticity of the + + + align:start position:0% +Epsilon the elasticity of the +good plus this other effect which comes + + align:start position:0% +good plus this other effect which comes + + + align:start position:0% +good plus this other effect which comes +from thinking about the effect of my + + align:start position:0% +from thinking about the effect of my + + + align:start position:0% +from thinking about the effect of my +change in price of good one on sales of + + align:start position:0% +change in price of good one on sales of + + + align:start position:0% +change in price of good one on sales of +good to + + align:start position:0% + + + + align:start position:0% + +I should say before I go to the next + + align:start position:0% +I should say before I go to the next + + + align:start position:0% +I should say before I go to the next +page you know one way you can also think + + align:start position:0% +page you know one way you can also think + + + align:start position:0% +page you know one way you can also think +about this is just you have to think + + align:start position:0% +about this is just you have to think + + + align:start position:0% +about this is just you have to think +about your pricing as a system so for + + align:start position:0% +about your pricing as a system so for + + + align:start position:0% +about your pricing as a system so for +instance like if + + align:start position:0% +instance like if + + + align:start position:0% +instance like if +you're the worst thing in the world you + + align:start position:0% +you're the worst thing in the world you + + + align:start position:0% +you're the worst thing in the world you +could do is like imagine you're sort of + + align:start position:0% +could do is like imagine you're sort of + + + align:start position:0% +could do is like imagine you're sort of +uh + + align:start position:0% +uh + + + align:start position:0% +uh +advising + + align:start position:0% +advising + + + align:start position:0% +advising +um apple on selling both blue iPhones + + align:start position:0% +um apple on selling both blue iPhones + + + align:start position:0% +um apple on selling both blue iPhones +and silver iPhones and you do a study of + + align:start position:0% +and silver iPhones and you do a study of + + + align:start position:0% +and silver iPhones and you do a study of +the price elasticity of blue iPhones by + + align:start position:0% +the price elasticity of blue iPhones by + + + align:start position:0% +the price elasticity of blue iPhones by +raising the price of blue iPhones by $20 + + align:start position:0% +raising the price of blue iPhones by $20 + + + align:start position:0% +raising the price of blue iPhones by $20 +and lowering it by $20 and seeing what + + align:start position:0% +and lowering it by $20 and seeing what + + + align:start position:0% +and lowering it by $20 and seeing what +that does to sales holding all other + + align:start position:0% +that does to sales holding all other + + + align:start position:0% +that does to sales holding all other +prices fixed you'll find that the blue + + align:start position:0% +prices fixed you'll find that the blue + + + align:start position:0% +prices fixed you'll find that the blue +iPhone is incredibly price sensitive uh + + align:start position:0% +iPhone is incredibly price sensitive uh + + + align:start position:0% +iPhone is incredibly price sensitive uh +price because people switch and buy the + + align:start position:0% +price because people switch and buy the + + + align:start position:0% +price because people switch and buy the +silver + + align:start position:0% +silver + + + align:start position:0% +silver +one that does not mean that you want to + + align:start position:0% +one that does not mean that you want to + + + align:start position:0% +one that does not mean that you want to +have a really really low mark up on the + + align:start position:0% +have a really really low mark up on the + + + align:start position:0% +have a really really low mark up on the +blue iPhone you have to think of it as a + + align:start position:0% +blue iPhone you have to think of it as a + + + align:start position:0% +blue iPhone you have to think of it as a +system and like what's the sort of + + align:start position:0% +system and like what's the sort of + + + align:start position:0% +system and like what's the sort of +equilibrium solution to blue iPhone + + align:start position:0% +equilibrium solution to blue iPhone + + + align:start position:0% +equilibrium solution to blue iPhone +silver iPhone red iPhone green iPhone + + align:start position:0% +silver iPhone red iPhone green iPhone + + + align:start position:0% +silver iPhone red iPhone green iPhone +whatever and think of all those things + + align:start position:0% +whatever and think of all those things + + + align:start position:0% +whatever and think of all those things +as a system if you look at each one + + align:start position:0% +as a system if you look at each one + + + align:start position:0% +as a system if you look at each one +individually You' get it terribly wrong + + align:start position:0% +individually You' get it terribly wrong + + + align:start position:0% +individually You' get it terribly wrong +okay and so in general anytime you're + + align:start position:0% +okay and so in general anytime you're + + + align:start position:0% +okay and so in general anytime you're +doing pricing of multiple Goods you know + + align:start position:0% +doing pricing of multiple Goods you know + + + align:start position:0% +doing pricing of multiple Goods you know +if there are very strong diversion + + align:start position:0% +if there are very strong diversion + + + align:start position:0% +if there are very strong diversion +ratios between them you always want to + + align:start position:0% +ratios between them you always want to + + + align:start position:0% +ratios between them you always want to +make sure you're thinking of it as a + + align:start position:0% +make sure you're thinking of it as a + + + align:start position:0% +make sure you're thinking of it as a +system not in terms of like each one + + align:start position:0% +system not in terms of like each one + + + align:start position:0% +system not in terms of like each one +individually is its Epsilon um but you + + align:start position:0% +individually is its Epsilon um but you + + + align:start position:0% +individually is its Epsilon um but you +know when these diversion ratios are + + align:start position:0% +know when these diversion ratios are + + + align:start position:0% +know when these diversion ratios are +smaller you can sort of think of it as + + align:start position:0% +smaller you can sort of think of it as + + + align:start position:0% +smaller you can sort of think of it as +it is like one over Epsilon pricing with + + align:start position:0% +it is like one over Epsilon pricing with + + + align:start position:0% +it is like one over Epsilon pricing with +some increase or decrease based on + + align:start position:0% +some increase or decrease based on + + + align:start position:0% +some increase or decrease based on +whether there is effect of changing + + align:start position:0% +whether there is effect of changing + + + align:start position:0% +whether there is effect of changing +sales on the other + + align:start position:0% + + + + align:start position:0% + +products so you know if I if I'm uh okay + + align:start position:0% +products so you know if I if I'm uh okay + + + align:start position:0% +products so you know if I if I'm uh okay +anyway + + align:start position:0% + + + + align:start position:0% + +um okay so what does this formula look + + align:start position:0% +um okay so what does this formula look + + + align:start position:0% +um okay so what does this formula look +like so my price is inverse + + align:start position:0% +like so my price is inverse + + + align:start position:0% +like so my price is inverse +elasticity minus price Minus cost over + + align:start position:0% +elasticity minus price Minus cost over + + + align:start position:0% +elasticity minus price Minus cost over +price dxi + + align:start position:0% +price dxi + + + align:start position:0% +price dxi +DPI if you think about the normal case + + align:start position:0% +DPI if you think about the normal case + + + align:start position:0% +DPI if you think about the normal case +in the normal case goods are sold at + + align:start position:0% +in the normal case goods are sold at + + + align:start position:0% +in the normal case goods are sold at +positive markups right so this would be + + align:start position:0% +positive markups right so this would be + + + align:start position:0% +positive markups right so this would be +a positive number this would be a + + align:start position:0% +a positive number this would be a + + + align:start position:0% +a positive number this would be a +positive number dxid DPI is a negative + + align:start position:0% +positive number dxid DPI is a negative + + + align:start position:0% +positive number dxid DPI is a negative +number so this is negative there's a + + align:start position:0% +number so this is negative there's a + + + align:start position:0% +number so this is negative there's a +negative sign this is positive so you + + align:start position:0% +negative sign this is positive so you + + + align:start position:0% +negative sign this is positive so you +can think of the whole thing in blue as + + align:start position:0% +can think of the whole thing in blue as + + + align:start position:0% +can think of the whole thing in blue as +a positive number + + align:start position:0% +a positive number + + + align:start position:0% +a positive number +normally and so whether you price above + + align:start position:0% +normally and so whether you price above + + + align:start position:0% +normally and so whether you price above +or below the inverse elasticity is + + align:start position:0% +or below the inverse elasticity is + + + align:start position:0% +or below the inverse elasticity is +typically going to depend on whether + + align:start position:0% +typically going to depend on whether + + + align:start position:0% +typically going to depend on whether +this is a positive number or a negative + + align:start position:0% +this is a positive number or a negative + + + align:start position:0% +this is a positive number or a negative +number + + align:start position:0% +number + + + align:start position:0% +number +okay you know standard case we're + + align:start position:0% +okay you know standard case we're + + + align:start position:0% +okay you know standard case we're +dealing with Monopoly pricing is often + + align:start position:0% +dealing with Monopoly pricing is often + + + align:start position:0% +dealing with Monopoly pricing is often +the substitutes case the substitutes + + align:start position:0% +the substitutes case the substitutes + + + align:start position:0% +the substitutes case the substitutes +case is when I raise the price of the + + align:start position:0% +case is when I raise the price of the + + + align:start position:0% +case is when I raise the price of the +blue iPhone sales of the silver iPhone + + align:start position:0% +blue iPhone sales of the silver iPhone + + + align:start position:0% +blue iPhone sales of the silver iPhone +go up these goods are substitutes for + + align:start position:0% +go up these goods are substitutes for + + + align:start position:0% +go up these goods are substitutes for +consumers um so when that's the case you + + align:start position:0% +consumers um so when that's the case you + + + align:start position:0% +consumers um so when that's the case you +know margins for both products are + + align:start position:0% +know margins for both products are + + + align:start position:0% +know margins for both products are +positive and you're just your margin + + align:start position:0% +positive and you're just your margin + + + align:start position:0% +positive and you're just your margin +exceeds the single product learner index + + align:start position:0% +exceeds the single product learner index + + + align:start position:0% +exceeds the single product learner index +formula and the amount by which it + + align:start position:0% +formula and the amount by which it + + + align:start position:0% +formula and the amount by which it +exceeds that single index learner + + align:start position:0% +exceeds that single index learner + + + align:start position:0% +exceeds that single index learner +formula depends + + align:start position:0% +formula depends + + + align:start position:0% +formula depends +on you know what is DX minus I over D + + align:start position:0% +on you know what is DX minus I over D + + + align:start position:0% +on you know what is DX minus I over D +DPI you know how large is the diversion + + align:start position:0% +DPI you know how large is the diversion + + + align:start position:0% +DPI you know how large is the diversion +ratio this divided by this is the + + align:start position:0% +ratio this divided by this is the + + + align:start position:0% +ratio this divided by this is the +diversion ratio so the larger is the + + align:start position:0% +diversion ratio so the larger is the + + + align:start position:0% +diversion ratio so the larger is the +diversion ratio the larger is the markup + + align:start position:0% +diversion ratio the larger is the markup + + + align:start position:0% +diversion ratio the larger is the markup +you're earning on the on the other + + align:start position:0% +you're earning on the on the other + + + align:start position:0% +you're earning on the on the other +second product you're selling the more + + align:start position:0% +second product you're selling the more + + + align:start position:0% +second product you're selling the more +you the learner index formula + + align:start position:0% +you the learner index formula + + + align:start position:0% +you the learner index formula +okay you know the other more interesting + + align:start position:0% +okay you know the other more interesting + + + align:start position:0% +okay you know the other more interesting +case is this sort of uh compliments case + + align:start position:0% +case is this sort of uh compliments case + + + align:start position:0% +case is this sort of uh compliments case +um so you know sometimes you have firm + + align:start position:0% +um so you know sometimes you have firm + + + align:start position:0% +um so you know sometimes you have firm +selling compliments like you know uh + + align:start position:0% +selling compliments like you know uh + + + align:start position:0% +selling compliments like you know uh +hamburgers and french fries at + + align:start position:0% +hamburgers and french fries at + + + align:start position:0% +hamburgers and french fries at +McDonald's um if your price of + + align:start position:0% +McDonald's um if your price of + + + align:start position:0% +McDonald's um if your price of +hamburgers is lower more people come to + + align:start position:0% +hamburgers is lower more people come to + + + align:start position:0% +hamburgers is lower more people come to +McDonald's more people buy french fries + + align:start position:0% +McDonald's more people buy french fries + + + align:start position:0% +McDonald's more people buy french fries +if your price for hamburgers is higher + + align:start position:0% +if your price for hamburgers is higher + + + align:start position:0% +if your price for hamburgers is higher +there could be an income effect where + + align:start position:0% +there could be an income effect where + + + align:start position:0% +there could be an income effect where +people feel like I've spent too much + + align:start position:0% +people feel like I've spent too much + + + align:start position:0% +people feel like I've spent too much +already I don't want to also buy the + + align:start position:0% +already I don't want to also buy the + + + align:start position:0% +already I don't want to also buy the +fries but typically it's like the effect + + align:start position:0% +fries but typically it's like the effect + + + align:start position:0% +fries but typically it's like the effect +it's going to be people don't come to + + align:start position:0% +it's going to be people don't come to + + + align:start position:0% +it's going to be people don't come to +your restaurant then they don't buy + + align:start position:0% +your restaurant then they don't buy + + + align:start position:0% +your restaurant then they don't buy +fries at all um uh you know in the Apple + + align:start position:0% +fries at all um uh you know in the Apple + + + align:start position:0% +fries at all um uh you know in the Apple +case if I don't sell them this iPhone + + align:start position:0% +case if I don't sell them this iPhone + + + align:start position:0% +case if I don't sell them this iPhone +I'm not going to sell them my my uh + + align:start position:0% +I'm not going to sell them my my uh + + + align:start position:0% +I'm not going to sell them my my uh +earbuds that I sell for a huge profit if + + align:start position:0% +earbuds that I sell for a huge profit if + + + align:start position:0% +earbuds that I sell for a huge profit if +I don't sell them my iPhone I'm not + + align:start position:0% +I don't sell them my iPhone I'm not + + + align:start position:0% +I don't sell them my iPhone I'm not +going to sell them the 17th charger that + + align:start position:0% +going to sell them the 17th charger that + + + align:start position:0% +going to sell them the 17th charger that +they've had to buy from me because I + + align:start position:0% +they've had to buy from me because I + + + align:start position:0% +they've had to buy from me because I +keep changing the way my charger + + align:start position:0% +keep changing the way my charger + + + align:start position:0% +keep changing the way my charger +connector Works um and so you know the + + align:start position:0% +connector Works um and so you know the + + + align:start position:0% +connector Works um and so you know the +compliment case is the higher the price + + align:start position:0% +compliment case is the higher the price + + + align:start position:0% +compliment case is the higher the price +of my iPhone I sell fewer if I sell if I + + align:start position:0% +of my iPhone I sell fewer if I sell if I + + + align:start position:0% +of my iPhone I sell fewer if I sell if I +raise the price of the iPhone I sell + + align:start position:0% +raise the price of the iPhone I sell + + + align:start position:0% +raise the price of the iPhone I sell +fewer earbuds okay uh and so in this + + align:start position:0% +fewer earbuds okay uh and so in this + + + align:start position:0% +fewer earbuds okay uh and so in this +case you know now this becomes it this + + align:start position:0% +case you know now this becomes it this + + + align:start position:0% +case you know now this becomes it this +becomes a negative number you set price + + align:start position:0% +becomes a negative number you set price + + + align:start position:0% +becomes a negative number you set price +below the elasticity of demand you know + + align:start position:0% +below the elasticity of demand you know + + + align:start position:0% +below the elasticity of demand you know +very easily if this diversion ratio is + + align:start position:0% +very easily if this diversion ratio is + + + align:start position:0% +very easily if this diversion ratio is +large like you know you can often think + + align:start position:0% +large like you know you can often think + + + align:start position:0% +large like you know you can often think +of like the diversion ratio is in some + + align:start position:0% +of like the diversion ratio is in some + + + align:start position:0% +of like the diversion ratio is in some +sense uh one uh for every for every + + align:start position:0% +sense uh one uh for every for every + + + align:start position:0% +sense uh one uh for every for every +iPhone I sell I don't sell that's + + align:start position:0% +iPhone I sell I don't sell that's + + + align:start position:0% +iPhone I sell I don't sell that's +exactly one pair of your buds don't sell + + align:start position:0% +exactly one pair of your buds don't sell + + + align:start position:0% +exactly one pair of your buds don't sell +or that's one charger I don't sell so if + + align:start position:0% +or that's one charger I don't sell so if + + + align:start position:0% +or that's one charger I don't sell so if +this is a large you know if this is a + + align:start position:0% +this is a large you know if this is a + + + align:start position:0% +this is a large you know if this is a +large number if this if this diversion + + align:start position:0% +large number if this if this diversion + + + align:start position:0% +large number if this if this diversion +ratio is one the margin is high in the + + align:start position:0% +ratio is one the margin is high in the + + + align:start position:0% +ratio is one the margin is high in the +competing good uh you can very easily + + align:start position:0% +competing good uh you can very easily + + + align:start position:0% +competing good uh you can very easily +end up with pricing one good below cost + + align:start position:0% +end up with pricing one good below cost + + + align:start position:0% +end up with pricing one good below cost +or even having a negative price like you + + align:start position:0% +or even having a negative price like you + + + align:start position:0% +or even having a negative price like you +know you may have thought like you know + + align:start position:0% +know you may have thought like you know + + + align:start position:0% +know you may have thought like you know +you go into the store to buy an inkjet + + align:start position:0% +you go into the store to buy an inkjet + + + align:start position:0% +you go into the store to buy an inkjet +printer and it's like remarkable that I + + align:start position:0% +printer and it's like remarkable that I + + + align:start position:0% +printer and it's like remarkable that I +can get this I can get this phenomenally + + align:start position:0% +can get this I can get this phenomenally + + + align:start position:0% +can get this I can get this phenomenally +complicated piece of electronics with + + align:start position:0% +complicated piece of electronics with + + + align:start position:0% +complicated piece of electronics with +all kinds of chips in it and hardware + + align:start position:0% +all kinds of chips in it and hardware + + + align:start position:0% +all kinds of chips in it and hardware +and precision stuff and it's only $99 + + align:start position:0% +and precision stuff and it's only $99 + + + align:start position:0% +and precision stuff and it's only $99 +and then you get really pissed off when + + align:start position:0% +and then you get really pissed off when + + + align:start position:0% +and then you get really pissed off when +you like sort of thing runs out of ink + + align:start position:0% +you like sort of thing runs out of ink + + + align:start position:0% +you like sort of thing runs out of ink +seven days later and it's like $59 for + + align:start position:0% +seven days later and it's like $59 for + + + align:start position:0% +seven days later and it's like $59 for +ink and you're think to yourself how can + + align:start position:0% +ink and you're think to yourself how can + + + align:start position:0% +ink and you're think to yourself how can +it be that it only cost $99 to produce + + align:start position:0% +it be that it only cost $99 to produce + + + align:start position:0% +it be that it only cost $99 to produce +this printer and yet it cost $59 to get + + align:start position:0% +this printer and yet it cost $59 to get + + + align:start position:0% +this printer and yet it cost $59 to get +a bottle of ink this big you know you + + align:start position:0% +a bottle of ink this big you know you + + + align:start position:0% +a bottle of ink this big you know you +would think the ink should only cost 50 + + align:start position:0% +would think the ink should only cost 50 + + + align:start position:0% +would think the ink should only cost 50 +cents and you the answer is yes + + align:start position:0% +cents and you the answer is yes + + + align:start position:0% +cents and you the answer is yes +obviously yes the ink only costs 50 + + align:start position:0% +obviously yes the ink only costs 50 + + + align:start position:0% +obviously yes the ink only costs 50 +cents but they're sort of pricing the + + align:start position:0% +cents but they're sort of pricing the + + + align:start position:0% +cents but they're sort of pricing the +printer way below the cost of producing + + align:start position:0% +printer way below the cost of producing + + + align:start position:0% +printer way below the cost of producing +the printer to get you to buy the ink um + + align:start position:0% +the printer to get you to buy the ink um + + + align:start position:0% +the printer to get you to buy the ink um +you know guess you know newspapers these + + align:start position:0% +you know guess you know newspapers these + + + align:start position:0% +you know guess you know newspapers these +examples no longer resonate you know + + align:start position:0% +examples no longer resonate you know + + + align:start position:0% +examples no longer resonate you know +there was a time when people had these + + align:start position:0% +there was a time when people had these + + + align:start position:0% +there was a time when people had these +things called newspapers and instead of + + align:start position:0% +things called newspapers and instead of + + + align:start position:0% +things called newspapers and instead of +reading news on your phone you got like + + align:start position:0% +reading news on your phone you got like + + + align:start position:0% +reading news on your phone you got like +this big piece of paper delivered to + + align:start position:0% +this big piece of paper delivered to + + + align:start position:0% +this big piece of paper delivered to +your house every day um the way + + align:start position:0% +your house every day um the way + + + align:start position:0% +your house every day um the way +newspapers used to work is the newspaper + + align:start position:0% +newspapers used to work is the newspaper + + + align:start position:0% +newspapers used to work is the newspaper +would only cost 50 cents and if you + + align:start position:0% +would only cost 50 cents and if you + + + align:start position:0% +would only cost 50 cents and if you +think about how much does it cost to + + align:start position:0% +think about how much does it cost to + + + align:start position:0% +think about how much does it cost to +produce and get a newspaper to your + + align:start position:0% +produce and get a newspaper to your + + + align:start position:0% +produce and get a newspaper to your +house every morning the answer was way + + align:start position:0% +house every morning the answer was way + + + align:start position:0% +house every morning the answer was way +more than 50 cents you know it cost a + + align:start position:0% +more than 50 cents you know it cost a + + + align:start position:0% +more than 50 cents you know it cost a +dollar $150 or something like that how + + align:start position:0% +dollar $150 or something like that how + + + align:start position:0% +dollar $150 or something like that how +did newspapers work newspapers worked + + align:start position:0% +did newspapers work newspapers worked + + + align:start position:0% +did newspapers work newspapers worked +because they sold them for 50 cents even + + align:start position:0% +because they sold them for 50 cents even + + + align:start position:0% +because they sold them for 50 cents even +though it cost a $150 to produce it + + align:start position:0% +though it cost a $150 to produce it + + + align:start position:0% +though it cost a $150 to produce it +because they were full of ads and they + + align:start position:0% +because they were full of ads and they + + + align:start position:0% +because they were full of ads and they +were full of classified ads that you + + align:start position:0% +were full of classified ads that you + + + align:start position:0% +were full of classified ads that you +know now go to you know wherever they + + align:start position:0% +know now go to you know wherever they + + + align:start position:0% +know now go to you know wherever they +were full of real estate ads they're now + + align:start position:0% +were full of real estate ads they're now + + + align:start position:0% +were full of real estate ads they're now +on Zillow they were full of ads for + + align:start position:0% +on Zillow they were full of ads for + + + align:start position:0% +on Zillow they were full of ads for +local car dealers they were full of ads + + align:start position:0% +local car dealers they were full of ads + + + align:start position:0% +local car dealers they were full of ads +for all kind you know all kinds of + + align:start position:0% +for all kind you know all kinds of + + + align:start position:0% +for all kind you know all kinds of +things um you know whatever eBay + + align:start position:0% +things um you know whatever eBay + + + align:start position:0% +things um you know whatever eBay +everything that was sold on eBay was + + align:start position:0% +everything that was sold on eBay was + + + align:start position:0% +everything that was sold on eBay was +sold through the newspaper you know the + + align:start position:0% +sold through the newspaper you know the + + + align:start position:0% +sold through the newspaper you know the +newspapers are sort of selling the + + align:start position:0% +newspapers are sort of selling the + + + align:start position:0% +newspapers are sort of selling the +newspaper below cost because the you + + align:start position:0% +newspaper below cost because the you + + + align:start position:0% +newspaper below cost because the you +know the cost of printing an ad was + + align:start position:0% +know the cost of printing an ad was + + + align:start position:0% +know the cost of printing an ad was +essentially zero and so the cost of + + align:start position:0% +essentially zero and so the cost of + + + align:start position:0% +essentially zero and so the cost of +producing ad was Zero they charge you + + align:start position:0% +producing ad was Zero they charge you + + + align:start position:0% +producing ad was Zero they charge you +you know $100 or $1,000 to list your + + align:start position:0% +you know $100 or $1,000 to list your + + + align:start position:0% +you know $100 or $1,000 to list your +house in the + + align:start position:0% +house in the + + + align:start position:0% +house in the +newspaper price Minus cost was huge on + + align:start position:0% +newspaper price Minus cost was huge on + + + align:start position:0% +newspaper price Minus cost was huge on +the ads that made the margin on the + + align:start position:0% +the ads that made the margin on the + + + align:start position:0% +the ads that made the margin on the +newspaper negative um you know in some + + align:start position:0% +newspaper negative um you know in some + + + align:start position:0% +newspaper negative um you know in some +Industries like um uh some Industries it + + align:start position:0% +Industries like um uh some Industries it + + + align:start position:0% +Industries like um uh some Industries it +even becomes like there's like a zero + + align:start position:0% +even becomes like there's like a zero + + + align:start position:0% +even becomes like there's like a zero +lower bound that becomes important like + + align:start position:0% +lower bound that becomes important like + + + align:start position:0% +lower bound that becomes important like +you know Google in some sense would like + + align:start position:0% +you know Google in some sense would like + + + align:start position:0% +you know Google in some sense would like +to pay you to use Google you know every + + align:start position:0% +to pay you to use Google you know every + + + align:start position:0% +to pay you to use Google you know every +time you do it you know Google's ad + + align:start position:0% +time you do it you know Google's ad + + + align:start position:0% +time you do it you know Google's ad +revenue is something like six or eight + + align:start position:0% +revenue is something like six or eight + + + align:start position:0% +revenue is something like six or eight +cents a search + + align:start position:0% +cents a search + + + align:start position:0% +cents a search +um every time you do a search on Google + + align:start position:0% +um every time you do a search on Google + + + align:start position:0% +um every time you do a search on Google +Google is making money + + align:start position:0% +Google is making money + + + align:start position:0% +Google is making money +um the marginal cost of doing a running + + align:start position:0% +um the marginal cost of doing a running + + + align:start position:0% +um the marginal cost of doing a running +a search for you on Google is very very + + align:start position:0% +a search for you on Google is very very + + + align:start position:0% +a search for you on Google is very very +small so when Google does the price + + align:start position:0% +small so when Google does the price + + + align:start position:0% +small so when Google does the price +search of you know it costs them a + + align:start position:0% +search of you know it costs them a + + + align:start position:0% +search of you know it costs them a +thousandth of a cent to run the search + + align:start position:0% +thousandth of a cent to run the search + + + align:start position:0% +thousandth of a cent to run the search +for you they're making eight cents + + align:start position:0% +for you they're making eight cents + + + align:start position:0% +for you they're making eight cents +profit on the on every search they want + + align:start position:0% +profit on the on every search they want + + + align:start position:0% +profit on the on every search they want +to sort of like set the price of having + + align:start position:0% +to sort of like set the price of having + + + align:start position:0% +to sort of like set the price of having +Google on your phone negative that's why + + align:start position:0% +Google on your phone negative that's why + + + align:start position:0% +Google on your phone negative that's why +Google is willing to pay Apple billions + + align:start position:0% +Google is willing to pay Apple billions + + + align:start position:0% +Google is willing to pay Apple billions +and billions of dollars to put Google + + align:start position:0% +and billions of dollars to put Google + + + align:start position:0% +and billions of dollars to put Google +there and make Google the default in + + align:start position:0% +there and make Google the default in + + + align:start position:0% +there and make Google the default in +some sense they want to have a negative + + align:start position:0% +some sense they want to have a negative + + + align:start position:0% +some sense they want to have a negative +price to get as many people to use it as + + align:start position:0% +price to get as many people to use it as + + + align:start position:0% +price to get as many people to use it as +possible + + align:start position:0% + + + + align:start position:0% + +okay okay any questions on multi-product + + align:start position:0% +okay okay any questions on multi-product + + + align:start position:0% +okay okay any questions on multi-product +pricing okay so um product quality um so + + align:start position:0% +pricing okay so um product quality um so + + + align:start position:0% +pricing okay so um product quality um so +as I said you know people often get + + align:start position:0% +as I said you know people often get + + + align:start position:0% +as I said you know people often get +frustrated with their Microsoft and + + align:start position:0% +frustrated with their Microsoft and + + + align:start position:0% +frustrated with their Microsoft and +other products and sort of think of like + + align:start position:0% +other products and sort of think of like + + + align:start position:0% +other products and sort of think of like +this thing is so bad because their + + align:start position:0% +this thing is so bad because their + + + align:start position:0% +this thing is so bad because their +Monopoly I have no choice + + align:start position:0% + + + + align:start position:0% + +um okay you know may maybe they get + + align:start position:0% +um okay you know may maybe they get + + + align:start position:0% +um okay you know may maybe they get +frustrated with the sort of Sloan + + align:start position:0% +frustrated with the sort of Sloan + + + align:start position:0% +frustrated with the sort of Sloan +cafeteria and are like you know this is + + align:start position:0% +cafeteria and are like you know this is + + + align:start position:0% +cafeteria and are like you know this is +the this place is closer than everywhere + + align:start position:0% +the this place is closer than everywhere + + + align:start position:0% +the this place is closer than everywhere +else and yet still people like walk + + align:start position:0% +else and yet still people like walk + + + align:start position:0% +else and yet still people like walk +across the brother's Market to get their + + align:start position:0% +across the brother's Market to get their + + + align:start position:0% +across the brother's Market to get their +lunch anyway you know because the you + + align:start position:0% +lunch anyway you know because the you + + + align:start position:0% +lunch anyway you know because the you +know it's it's I don't know not + + align:start position:0% +know it's it's I don't know not + + + align:start position:0% +know it's it's I don't know not +necessarily the price of the food at the + + align:start position:0% +necessarily the price of the food at the + + + align:start position:0% +necessarily the price of the food at the +Salone cafet although it's also high but + + align:start position:0% +Salone cafet although it's also high but + + + align:start position:0% +Salone cafet although it's also high but +the you know does SL have cafeteria have + + align:start position:0% +the you know does SL have cafeteria have + + + align:start position:0% +the you know does SL have cafeteria have +the opt the optimal product quality um + + align:start position:0% +the opt the optimal product quality um + + + align:start position:0% +the opt the optimal product quality um +you know basic reason is going to be in + + align:start position:0% +you know basic reason is going to be in + + + align:start position:0% +you know basic reason is going to be in +some sense you know while we may think + + align:start position:0% +some sense you know while we may think + + + align:start position:0% +some sense you know while we may think +the monopolis often provide lowquality + + align:start position:0% +the monopolis often provide lowquality + + + align:start position:0% +the monopolis often provide lowquality +products at least the sort of profit + + align:start position:0% +products at least the sort of profit + + + align:start position:0% +products at least the sort of profit +maximizing Theory tells us they ought to + + align:start position:0% +maximizing Theory tells us they ought to + + + align:start position:0% +maximizing Theory tells us they ought to +do pretty well on this Dimension so + + align:start position:0% +do pretty well on this Dimension so + + + align:start position:0% +do pretty well on this Dimension so +let's suppose you have a monopolist it + + align:start position:0% +let's suppose you have a monopolist it + + + align:start position:0% +let's suppose you have a monopolist it +has a product that's a variable quality + + align:start position:0% +has a product that's a variable quality + + + align:start position:0% +has a product that's a variable quality +S and S is a choice variable as well as + + align:start position:0% +S and S is a choice variable as well as + + + align:start position:0% +S and S is a choice variable as well as +the + + align:start position:0% +the + + + align:start position:0% +the +price so suppose that has a constant + + align:start position:0% +price so suppose that has a constant + + + align:start position:0% +price so suppose that has a constant +marginal cost C of s so you know you + + align:start position:0% +marginal cost C of s so you know you + + + align:start position:0% +marginal cost C of s so you know you +could think of this as either the + + align:start position:0% +could think of this as either the + + + align:start position:0% +could think of this as either the +quality of the food you're providing at + + align:start position:0% +quality of the food you're providing at + + + align:start position:0% +quality of the food you're providing at +a lunch or like s could be the speed or + + align:start position:0% +a lunch or like s could be the speed or + + + align:start position:0% +a lunch or like s could be the speed or +the quality of the camera in an iPhone + + align:start position:0% +the quality of the camera in an iPhone + + + align:start position:0% +the quality of the camera in an iPhone +uh the unit cost of producing this or + + align:start position:0% +uh the unit cost of producing this or + + + align:start position:0% +uh the unit cost of producing this or +the UN of producing the iPhone is going + + align:start position:0% +the UN of producing the iPhone is going + + + align:start position:0% +the UN of producing the iPhone is going +to be CFS and the higher quality you + + align:start position:0% +to be CFS and the higher quality you + + + align:start position:0% +to be CFS and the higher quality you +make it the more expensive it's going to + + align:start position:0% +make it the more expensive it's going to + + + align:start position:0% +make it the more expensive it's going to +be to + + align:start position:0% +be to + + + align:start position:0% +be to +produce and then I will do this as a + + align:start position:0% +produce and then I will do this as a + + + align:start position:0% +produce and then I will do this as a +constant marginal cost so if you produce + + align:start position:0% +constant marginal cost so if you produce + + + align:start position:0% +constant marginal cost so if you produce +a 100 iPhones it's just 100 times the + + align:start position:0% +a 100 iPhones it's just 100 times the + + + align:start position:0% +a 100 iPhones it's just 100 times the +cost of producing one if you produce 100 + + align:start position:0% +cost of producing one if you produce 100 + + + align:start position:0% +cost of producing one if you produce 100 +lunches 100 times the cost of one lunch + + align:start position:0% +lunches 100 times the cost of one lunch + + + align:start position:0% +lunches 100 times the cost of one lunch +um something we're going to do all the + + align:start position:0% +um something we're going to do all the + + + align:start position:0% +um something we're going to do all the +time in IO is take consumer + + align:start position:0% +time in IO is take consumer + + + align:start position:0% +time in IO is take consumer +heterogeneity very seriously so I'm + + align:start position:0% +heterogeneity very seriously so I'm + + + align:start position:0% +heterogeneity very seriously so I'm +going to think about massive consumers + + align:start position:0% +going to think about massive consumers + + + align:start position:0% +going to think about massive consumers +who have types Theta distributed uniform + + align:start position:0% +who have types Theta distributed uniform + + + align:start position:0% +who have types Theta distributed uniform +on 01 the the uniform 01 here is without + + align:start position:0% +on 01 the the uniform 01 here is without + + + align:start position:0% +on 01 the the uniform 01 here is without +loss of generality I do that a lot it's + + align:start position:0% +loss of generality I do that a lot it's + + + align:start position:0% +loss of generality I do that a lot it's +just I index consumers by their + + align:start position:0% +just I index consumers by their + + + align:start position:0% +just I index consumers by their +percentile within the distribution of + + align:start position:0% +percentile within the distribution of + + + align:start position:0% +percentile within the distribution of +consumers um here it's indexing within + + align:start position:0% +consumers um here it's indexing within + + + align:start position:0% +consumers um here it's indexing within +their distribution of consumers in terms + + align:start position:0% +their distribution of consumers in terms + + + align:start position:0% +their distribution of consumers in terms +of How High their valuation is for the + + align:start position:0% +of How High their valuation is for the + + + align:start position:0% +of How High their valuation is for the +good that people are buying okay so + + align:start position:0% +good that people are buying okay so + + + align:start position:0% +good that people are buying okay so +consumers are going to get they're only + + align:start position:0% +consumers are going to get they're only + + + align:start position:0% +consumers are going to get they're only +consumers are going to either buy one + + align:start position:0% +consumers are going to either buy one + + + align:start position:0% +consumers are going to either buy one +they either want one launch or one phone + + align:start position:0% +they either want one launch or one phone + + + align:start position:0% +they either want one launch or one phone +it's a unit demand case and they're + + align:start position:0% +it's a unit demand case and they're + + + align:start position:0% +it's a unit demand case and they're +going to get utility V of s Theta minus + + align:start position:0% +going to get utility V of s Theta minus + + + align:start position:0% +going to get utility V of s Theta minus +P if they buy one unit of a quality s + + align:start position:0% +P if they buy one unit of a quality s + + + align:start position:0% +P if they buy one unit of a quality s +good and their type is + + align:start position:0% +good and their type is + + + align:start position:0% +good and their type is +Theta and I'm going to assume that we've + + align:start position:0% +Theta and I'm going to assume that we've + + + align:start position:0% +Theta and I'm going to assume that we've +ordered the qualities and the type so + + align:start position:0% +ordered the qualities and the type so + + + align:start position:0% +ordered the qualities and the type so +that utility is increasing in quality + + align:start position:0% +that utility is increasing in quality + + + align:start position:0% +that utility is increasing in quality +for everyone regardless of theta and the + + align:start position:0% +for everyone regardless of theta and the + + + align:start position:0% +for everyone regardless of theta and the +high Theta people have a higher + + align:start position:0% +high Theta people have a higher + + + align:start position:0% +high Theta people have a higher +willingness to pay than the low Theta + + align:start position:0% +willingness to pay than the low Theta + + + align:start position:0% +willingness to pay than the low Theta +people again for Anye equality okay that + + align:start position:0% +people again for Anye equality okay that + + + align:start position:0% +people again for Anye equality okay that +doesn't fit all products but assume that + + align:start position:0% +doesn't fit all products but assume that + + + align:start position:0% +doesn't fit all products but assume that +there are these high types and low types + + align:start position:0% +there are these high types and low types + + + align:start position:0% +there are these high types and low types +and the high types are willing to pay + + align:start position:0% +and the high types are willing to pay + + + align:start position:0% +and the high types are willing to pay +more for everything as if they're + + align:start position:0% +more for everything as if they're + + + align:start position:0% +more for everything as if they're +wealthier people with a lower marginal + + align:start position:0% +wealthier people with a lower marginal + + + align:start position:0% +wealthier people with a lower marginal +utility of income okay um now imagine + + align:start position:0% +utility of income okay um now imagine + + + align:start position:0% +utility of income okay um now imagine +that in equilibrium the firm is going to + + align:start position:0% +that in equilibrium the firm is going to + + + align:start position:0% +that in equilibrium the firm is going to +sell Q units given that the high Theta + + align:start position:0% +sell Q units given that the high Theta + + + align:start position:0% +sell Q units given that the high Theta +people have the highest willingness to + + align:start position:0% +people have the highest willingness to + + + align:start position:0% +people have the highest willingness to +pay if you're going to sell let me put + + align:start position:0% + + + + align:start position:0% + +my you know theta's uniform 01 + + align:start position:0% +my you know theta's uniform 01 + + + align:start position:0% +my you know theta's uniform 01 +here if I'm going to + + align:start position:0% +here if I'm going to + + + align:start position:0% +here if I'm going to +sell Q + + align:start position:0% +sell Q + + + align:start position:0% +sell Q +units what's going to have to happen in + + align:start position:0% +units what's going to have to happen in + + + align:start position:0% +units what's going to have to happen in +equilibrium is everyone whose type is + + align:start position:0% +equilibrium is everyone whose type is + + + align:start position:0% +equilibrium is everyone whose type is +above one minus Q buys the good and + + align:start position:0% +above one minus Q buys the good and + + + align:start position:0% +above one minus Q buys the good and +everyone whose type is below one minus Q + + align:start position:0% +everyone whose type is below one minus Q + + + align:start position:0% +everyone whose type is below one minus Q +doesn't buy the good because if someone + + align:start position:0% +doesn't buy the good because if someone + + + align:start position:0% +doesn't buy the good because if someone +here is willing to buy the good anyone + + align:start position:0% +here is willing to buy the good anyone + + + align:start position:0% +here is willing to buy the good anyone +with a higher type is strictly willing + + align:start position:0% +with a higher type is strictly willing + + + align:start position:0% +with a higher type is strictly willing +to buy the good at the same price so if + + align:start position:0% +to buy the good at the same price so if + + + align:start position:0% +to buy the good at the same price so if +you're going to sell the good this is + + align:start position:0% +you're going to sell the good this is + + + align:start position:0% +you're going to sell the good this is +how it's going to look in characteristic + + align:start position:0% +how it's going to look in characteristic + + + align:start position:0% +how it's going to look in characteristic +space um so therefore what's your + + align:start position:0% +space um so therefore what's your + + + align:start position:0% +space um so therefore what's your +maximization problem I'm going to + + align:start position:0% +maximization problem I'm going to + + + align:start position:0% +maximization problem I'm going to +maximize I'm going to set it over + + align:start position:0% +maximize I'm going to set it over + + + align:start position:0% +maximize I'm going to set it over +maximize over the quantity that I'm + + align:start position:0% +maximize over the quantity that I'm + + + align:start position:0% +maximize over the quantity that I'm +going to sell and the + + align:start position:0% +going to sell and the + + + align:start position:0% +going to sell and the +quality if I'm going to sell to everyone + + align:start position:0% +quality if I'm going to sell to everyone + + + align:start position:0% +quality if I'm going to sell to everyone +in this + + align:start position:0% +in this + + + align:start position:0% +in this +interval um it's got to be that this + + align:start position:0% +interval um it's got to be that this + + + align:start position:0% +interval um it's got to be that this +person is just indifferent between + + align:start position:0% +person is just indifferent between + + + align:start position:0% +person is just indifferent between +buying and not buying this person is + + align:start position:0% +buying and not buying this person is + + + align:start position:0% +buying and not buying this person is +willing to pay V of s 1 minus Q because + + align:start position:0% +willing to pay V of s 1 minus Q because + + + align:start position:0% +willing to pay V of s 1 minus Q because +1 minus Q is their type so if I'm going + + align:start position:0% +1 minus Q is their type so if I'm going + + + align:start position:0% +1 minus Q is their type so if I'm going +to sell to these people and not to these + + align:start position:0% +to sell to these people and not to these + + + align:start position:0% +to sell to these people and not to these +people it must be that this is the price + + align:start position:0% +people it must be that this is the price + + + align:start position:0% +people it must be that this is the price +I'm + + align:start position:0% +I'm + + + align:start position:0% +I'm +charging so if I'm going to sell Q units + + align:start position:0% +charging so if I'm going to sell Q units + + + align:start position:0% +charging so if I'm going to sell Q units +my profit is Q * V of S1 minus Q minus C + + align:start position:0% +my profit is Q * V of S1 minus Q minus C + + + align:start position:0% +my profit is Q * V of S1 minus Q minus C +of + + align:start position:0% + + + + align:start position:0% + +s i now want to differentiate that with + + align:start position:0% +s i now want to differentiate that with + + + align:start position:0% +s i now want to differentiate that with +respect to S to say what is the optimal + + align:start position:0% +respect to S to say what is the optimal + + + align:start position:0% +respect to S to say what is the optimal +quality to + + align:start position:0% +quality to + + + align:start position:0% +quality to +choose um notice the Q um this Q drops + + align:start position:0% +choose um notice the Q um this Q drops + + + align:start position:0% +choose um notice the Q um this Q drops +out of the first order condition so I + + align:start position:0% +out of the first order condition so I + + + align:start position:0% +out of the first order condition so I +just get + + align:start position:0% +just get + + + align:start position:0% +just get +DVDs evaluated at the Monopoly level of + + align:start position:0% +DVDs evaluated at the Monopoly level of + + + align:start position:0% +DVDs evaluated at the Monopoly level of +s and and 1 minus Q equals + + align:start position:0% +s and and 1 minus Q equals + + + align:start position:0% +s and and 1 minus Q equals +dcds so what this says is that + + align:start position:0% +dcds so what this says is that + + + align:start position:0% +dcds so what this says is that +the effect on the unit c cost of + + align:start position:0% +the effect on the unit c cost of + + + align:start position:0% +the effect on the unit c cost of +increasing + + align:start position:0% +increasing + + + align:start position:0% +increasing +quality is exactly what the effect on of + + align:start position:0% +quality is exactly what the effect on of + + + align:start position:0% +quality is exactly what the effect on of +that quality increase is on the + + align:start position:0% +that quality increase is on the + + + align:start position:0% +that quality increase is on the +valuation of the marginal + + align:start position:0% +valuation of the marginal + + + align:start position:0% +valuation of the marginal +consumer okay so the monopolist is + + align:start position:0% +consumer okay so the monopolist is + + + align:start position:0% +consumer okay so the monopolist is +choosing optimally choosing quality + + align:start position:0% +choosing optimally choosing quality + + + align:start position:0% +choosing optimally choosing quality +optimally from the perspective of the + + align:start position:0% +optimally from the perspective of the + + + align:start position:0% +optimally from the perspective of the +marginal consumer and that's because the + + align:start position:0% +marginal consumer and that's because the + + + align:start position:0% +marginal consumer and that's because the +marginal consumer if you raise the + + align:start position:0% +marginal consumer if you raise the + + + align:start position:0% +marginal consumer if you raise the +quality that person will be willing to + + align:start position:0% +quality that person will be willing to + + + align:start position:0% +quality that person will be willing to +pay more you can charge them more and so + + align:start position:0% +pay more you can charge them more and so + + + align:start position:0% +pay more you can charge them more and so +you're improving quality if and only if + + align:start position:0% +you're improving quality if and only if + + + align:start position:0% +you're improving quality if and only if +the amount that the sort of uh uh + + align:start position:0% +the amount that the sort of uh uh + + + align:start position:0% +the amount that the sort of uh uh +marginal consumer is willing to pay for + + align:start position:0% +marginal consumer is willing to pay for + + + align:start position:0% +marginal consumer is willing to pay for +that Improvement in quality matches the + + align:start position:0% +that Improvement in quality matches the + + + align:start position:0% +that Improvement in quality matches the +cost of implementing that Improvement in + + align:start position:0% + + + + align:start position:0% + +quality so some sense it's a partial + + align:start position:0% +quality so some sense it's a partial + + + align:start position:0% +quality so some sense it's a partial +optimality + + align:start position:0% +optimality + + + align:start position:0% +optimality +theorem uh what would a social planner + + align:start position:0% +theorem uh what would a social planner + + + align:start position:0% +theorem uh what would a social planner +do well social planner would be choosing + + align:start position:0% +do well social planner would be choosing + + + align:start position:0% +do well social planner would be choosing +so let me sort of say so this would be + + align:start position:0% +so let me sort of say so this would be + + + align:start position:0% +so let me sort of say so this would be +like what the monopolis ended up doing + + align:start position:0% +like what the monopolis ended up doing + + + align:start position:0% +like what the monopolis ended up doing +uh what would the social planner end up + + align:start position:0% +uh what would the social planner end up + + + align:start position:0% +uh what would the social planner end up +doing it's maximizing over q and s + + align:start position:0% +doing it's maximizing over q and s + + + align:start position:0% +doing it's maximizing over q and s +integral over all types from 1us Q to 1 + + align:start position:0% +integral over all types from 1us Q to 1 + + + align:start position:0% +integral over all types from 1us Q to 1 +1 V of s Theta minus C of s d + + align:start position:0% +1 V of s Theta minus C of s d + + + align:start position:0% +1 V of s Theta minus C of s d +Theta um maximize that I I differentiate + + align:start position:0% +Theta um maximize that I I differentiate + + + align:start position:0% +Theta um maximize that I I differentiate +with respect to S under the integral + + align:start position:0% +with respect to S under the integral + + + align:start position:0% +with respect to S under the integral +sign so I get the integral from 1us Q to + + align:start position:0% +sign so I get the integral from 1us Q to + + + align:start position:0% +sign so I get the integral from 1us Q to +one of DVDs minus + + align:start position:0% +one of DVDs minus + + + align:start position:0% +one of DVDs minus +dcds D + + align:start position:0% +dcds D + + + align:start position:0% +dcds D +Theta + + align:start position:0% +Theta + + + align:start position:0% +Theta +the integral from 1 minus Q to one of + + align:start position:0% +the integral from 1 minus Q to one of + + + align:start position:0% +the integral from 1 minus Q to one of +dcds is just you know that's a constant + + align:start position:0% +dcds is just you know that's a constant + + + align:start position:0% +dcds is just you know that's a constant +function so it's just Q * dcds so I've + + align:start position:0% +function so it's just Q * dcds so I've + + + align:start position:0% +function so it's just Q * dcds so I've +divided both sides by q and I get get + + align:start position:0% +divided both sides by q and I get get + + + align:start position:0% +divided both sides by q and I get get +this + + align:start position:0% +this + + + align:start position:0% +this +expression + + align:start position:0% +expression + + + align:start position:0% +expression +the effect on the marginal cost of + + align:start position:0% +the effect on the marginal cost of + + + align:start position:0% +the effect on the marginal cost of +increasing + + align:start position:0% +increasing + + + align:start position:0% +increasing +quality is equal to this is just an + + align:start position:0% +quality is equal to this is just an + + + align:start position:0% +quality is equal to this is just an +average across consumers of + + align:start position:0% +average across consumers of + + + align:start position:0% +average across consumers of +DVDs so what the monopolist is doing is + + align:start position:0% +DVDs so what the monopolist is doing is + + + align:start position:0% +DVDs so what the monopolist is doing is +instead of equating the Bene the cost of + + align:start position:0% +instead of equating the Bene the cost of + + + align:start position:0% +instead of equating the Bene the cost of +the quality improvement to the benefit + + align:start position:0% +the quality improvement to the benefit + + + align:start position:0% +the quality improvement to the benefit +for the marginal consumer it's equating + + align:start position:0% +for the marginal consumer it's equating + + + align:start position:0% +for the marginal consumer it's equating +the benefit for the average + + align:start position:0% +the benefit for the average + + + align:start position:0% +the benefit for the average +consumer so there are two reasons in + + align:start position:0% +consumer so there are two reasons in + + + align:start position:0% +consumer so there are two reasons in +which the monopolist is not not doing + + align:start position:0% +which the monopolist is not not doing + + + align:start position:0% +which the monopolist is not not doing +what we want + + align:start position:0% +what we want + + + align:start position:0% +what we want +socially + + align:start position:0% +socially + + + align:start position:0% +socially +um first is that monopolist is focusing + + align:start position:0% +um first is that monopolist is focusing + + + align:start position:0% +um first is that monopolist is focusing +on the marginal consumer rather than the + + align:start position:0% +on the marginal consumer rather than the + + + align:start position:0% +on the marginal consumer rather than the +average + + align:start position:0% +average + + + align:start position:0% +average +consumer but the other thing the + + align:start position:0% +consumer but the other thing the + + + align:start position:0% +consumer but the other thing the +monopolist is doing is you know + + align:start position:0% +monopolist is doing is you know + + + align:start position:0% +monopolist is doing is you know +typically like in this case um you know + + align:start position:0% +typically like in this case um you know + + + align:start position:0% +typically like in this case um you know +the monopolist is choosing this + + align:start position:0% +the monopolist is choosing this + + + align:start position:0% +the monopolist is choosing this +quantity you know the competitive + + align:start position:0% +quantity you know the competitive + + + align:start position:0% +quantity you know the competitive +quantity that the social planner might + + align:start position:0% +quantity that the social planner might + + + align:start position:0% +quantity that the social planner might +choose might be down here the social + + align:start position:0% +choose might be down here the social + + + align:start position:0% +choose might be down here the social +planner is going to serve many you know + + align:start position:0% +planner is going to serve many you know + + + align:start position:0% +planner is going to serve many you know +the with a social planner there would be + + align:start position:0% +the with a social planner there would be + + + align:start position:0% +the with a social planner there would be +many more iPhones sold than there are + + align:start position:0% +many more iPhones sold than there are + + + align:start position:0% +many more iPhones sold than there are +with apple as an iPhone monopolist + + align:start position:0% +with apple as an iPhone monopolist + + + align:start position:0% +with apple as an iPhone monopolist +okay and so you know notice that these + + align:start position:0% +okay and so you know notice that these + + + align:start position:0% +okay and so you know notice that these +effects often go in opposite directions + + align:start position:0% +effects often go in opposite directions + + + align:start position:0% +effects often go in opposite directions +um one is that the monopolist is + + align:start position:0% +um one is that the monopolist is + + + align:start position:0% +um one is that the monopolist is +focusing on the marginal consumer rather + + align:start position:0% +focusing on the marginal consumer rather + + + align:start position:0% +focusing on the marginal consumer rather +than the average consumer because you're + + align:start position:0% +than the average consumer because you're + + + align:start position:0% +than the average consumer because you're +focusing on the marginal consumer you + + align:start position:0% +focusing on the marginal consumer you + + + align:start position:0% +focusing on the marginal consumer you +may make uh the quality too low it may + + align:start position:0% +may make uh the quality too low it may + + + align:start position:0% +may make uh the quality too low it may +be that you know everyone the average + + align:start position:0% +be that you know everyone the average + + + align:start position:0% +be that you know everyone the average +consumer wishes that their iPhone worked + + align:start position:0% +consumer wishes that their iPhone worked + + + align:start position:0% +consumer wishes that their iPhone worked +had a camera that was as good as the + + align:start position:0% +had a camera that was as good as the + + + align:start position:0% +had a camera that was as good as the +camera on the Google pixel but it + + align:start position:0% +camera on the Google pixel but it + + + align:start position:0% +camera on the Google pixel but it +doesn't have a camera that's that good + + align:start position:0% +doesn't have a camera that's that good + + + align:start position:0% +doesn't have a camera that's that good +good because the marginal consumer is + + align:start position:0% +good because the marginal consumer is + + + align:start position:0% +good because the marginal consumer is +not willing to pay as much for the + + align:start position:0% +not willing to pay as much for the + + + align:start position:0% +not willing to pay as much for the +camera Improvement so the camera you + + align:start position:0% +camera Improvement so the camera you + + + align:start position:0% +camera Improvement so the camera you +make the the camera lower than the + + align:start position:0% +make the the camera lower than the + + + align:start position:0% +make the the camera lower than the +average iPhone consumer wishes worse + + align:start position:0% +average iPhone consumer wishes worse + + + align:start position:0% +average iPhone consumer wishes worse +than the iPhone camera average iPhone + + align:start position:0% +than the iPhone camera average iPhone + + + align:start position:0% +than the iPhone camera average iPhone +consumer wants the camera to be but the + + align:start position:0% +consumer wants the camera to be but the + + + align:start position:0% +consumer wants the camera to be but the +second effect is because only wealthy + + align:start position:0% +second effect is because only wealthy + + + align:start position:0% +second effect is because only wealthy +people and graduate students have + + align:start position:0% +people and graduate students have + + + align:start position:0% +people and graduate students have +iPhones um you know because relatively + + align:start position:0% +iPhones um you know because relatively + + + align:start position:0% +iPhones um you know because relatively +wealthy people have iPhones all these + + align:start position:0% +wealthy people have iPhones all these + + + align:start position:0% +wealthy people have iPhones all these +people are not actually getting iPhones + + align:start position:0% +people are not actually getting iPhones + + + align:start position:0% +people are not actually getting iPhones +at all and so it could be that the + + align:start position:0% +at all and so it could be that the + + + align:start position:0% +at all and so it could be that the +average you know with a social planner + + align:start position:0% +average you know with a social planner + + + align:start position:0% +average you know with a social planner +you'd have this many iPhones sold the + + align:start position:0% +you'd have this many iPhones sold the + + + align:start position:0% +you'd have this many iPhones sold the +average consumer would be somewhere down + + align:start position:0% +average consumer would be somewhere down + + + align:start position:0% +average consumer would be somewhere down +here and serving the average consumer + + align:start position:0% +here and serving the average consumer + + + align:start position:0% +here and serving the average consumer +the iPhone would be even worse than it + + align:start position:0% +the iPhone would be even worse than it + + + align:start position:0% +the iPhone would be even worse than it +is today um because you know it's it's + + align:start position:0% +is today um because you know it's it's + + + align:start position:0% +is today um because you know it's it's +because apple is only serving the high + + align:start position:0% +because apple is only serving the high + + + align:start position:0% +because apple is only serving the high +high end of the Theta distribution their + + align:start position:0% +high end of the Theta distribution their + + + align:start position:0% +high end of the Theta distribution their +marginal consumer is higher than the + + align:start position:0% +marginal consumer is higher than the + + + align:start position:0% +marginal consumer is higher than the +marginal consumer would be if they were + + align:start position:0% +marginal consumer would be if they were + + + align:start position:0% +marginal consumer would be if they were +serving everyone with a $300 + + align:start position:0% + + + + align:start position:0% + +iPhone but you know one Coral are of + + align:start position:0% +iPhone but you know one Coral are of + + + align:start position:0% +iPhone but you know one Coral are of +this analysis is if you have a + + align:start position:0% +this analysis is if you have a + + + align:start position:0% +this analysis is if you have a +homogeneous population model which + + align:start position:0% +homogeneous population model which + + + align:start position:0% +homogeneous population model which +people often do not thinking about it to + + align:start position:0% +people often do not thinking about it to + + + align:start position:0% +people often do not thinking about it to +just to simplify things you make all the + + align:start position:0% +just to simplify things you make all the + + + align:start position:0% +just to simplify things you make all the +consumers identical if all consumers are + + align:start position:0% +consumers identical if all consumers are + + + align:start position:0% +consumers identical if all consumers are +identical two things happen one is the + + align:start position:0% +identical two things happen one is the + + + align:start position:0% +identical two things happen one is the +marginal consumer is the average + + align:start position:0% +marginal consumer is the average + + + align:start position:0% +marginal consumer is the average +consumer because marginal and average + + align:start position:0% +consumer because marginal and average + + + align:start position:0% +consumer because marginal and average +are the same when all consumers are + + align:start position:0% +are the same when all consumers are + + + align:start position:0% +are the same when all consumers are +identical the second is in a homogeneous + + align:start position:0% +identical the second is in a homogeneous + + + align:start position:0% +identical the second is in a homogeneous +population model you're always making an + + align:start position:0% +population model you're always making an + + + align:start position:0% +population model you're always making an +all or none sales decision if everyone's + + align:start position:0% +all or none sales decision if everyone's + + + align:start position:0% +all or none sales decision if everyone's +identical you either sell to everyone or + + align:start position:0% +identical you either sell to everyone or + + + align:start position:0% +identical you either sell to everyone or +you sell to no one uh and typically you + + align:start position:0% +you sell to no one uh and typically you + + + align:start position:0% +you sell to no one uh and typically you +sell to everyone um with those two + + align:start position:0% +sell to everyone um with those two + + + align:start position:0% +sell to everyone um with those two +choices so in a homogeneous population + + align:start position:0% +choices so in a homogeneous population + + + align:start position:0% +choices so in a homogeneous population +model uh there's a strong optimal + + align:start position:0% +model uh there's a strong optimal + + + align:start position:0% +model uh there's a strong optimal +quality theorem that is if you sort of + + align:start position:0% +quality theorem that is if you sort of + + + align:start position:0% +quality theorem that is if you sort of +analyze something that's a homogeneous + + align:start position:0% +analyze something that's a homogeneous + + + align:start position:0% +analyze something that's a homogeneous +population model you assume the + + align:start position:0% +population model you assume the + + + align:start position:0% +population model you assume the +monopolist is maximizing its profits + + align:start position:0% +monopolist is maximizing its profits + + + align:start position:0% +monopolist is maximizing its profits +you're going to assume it's choosing the + + align:start position:0% +you're going to assume it's choosing the + + + align:start position:0% +you're going to assume it's choosing the +socially optimal quality because there's + + align:start position:0% +socially optimal quality because there's + + + align:start position:0% +socially optimal quality because there's +no scope for those two to be + + align:start position:0% + + + + align:start position:0% + +different questions on + + align:start position:0% +different questions on + + + align:start position:0% +different questions on +that okay and this sort of optimal + + align:start position:0% +that okay and this sort of optimal + + + align:start position:0% +that okay and this sort of optimal +quality reasoning this will come in a + + align:start position:0% +quality reasoning this will come in a + + + align:start position:0% +quality reasoning this will come in a +few a few different times later in the + + align:start position:0% +few a few different times later in the + + + align:start position:0% +few a few different times later in the +class + + align:start position:0% +class + + + align:start position:0% +class +um okay um durable goods um so you know + + align:start position:0% +um okay um durable goods um so you know + + + align:start position:0% +um okay um durable goods um so you know +in many cases people are selling durable + + align:start position:0% +in many cases people are selling durable + + + align:start position:0% +in many cases people are selling durable +goods that provide services over many + + align:start position:0% +goods that provide services over many + + + align:start position:0% +goods that provide services over many +periods you know you're selling washing + + align:start position:0% +periods you know you're selling washing + + + align:start position:0% +periods you know you're selling washing +machines you're selling cars you're + + align:start position:0% +machines you're selling cars you're + + + align:start position:0% +machines you're selling cars you're +selling phones you know consumers are + + align:start position:0% +selling phones you know consumers are + + + align:start position:0% +selling phones you know consumers are +buying it today and they're consu + + align:start position:0% +buying it today and they're consu + + + align:start position:0% +buying it today and they're consu +they're using that same product in in + + align:start position:0% +they're using that same product in in + + + align:start position:0% +they're using that same product in in +multiple periods + + align:start position:0% +multiple periods + + + align:start position:0% +multiple periods +um you know one intuition you'll have + + align:start position:0% +um you know one intuition you'll have + + + align:start position:0% +um you know one intuition you'll have +have sometimes is that this is a + + align:start position:0% +have sometimes is that this is a + + + align:start position:0% +have sometimes is that this is a +potential Advantage firms can use this + + align:start position:0% +potential Advantage firms can use this + + + align:start position:0% +potential Advantage firms can use this +sort of durable goods nature the fact + + align:start position:0% +sort of durable goods nature the fact + + + align:start position:0% +sort of durable goods nature the fact +people buy it at different times to sort + + align:start position:0% +people buy it at different times to sort + + + align:start position:0% +people buy it at different times to sort +of move down the demand curve and sell + + align:start position:0% +of move down the demand curve and sell + + + align:start position:0% +of move down the demand curve and sell +the goods first to the people who have + + align:start position:0% +the goods first to the people who have + + + align:start position:0% +the goods first to the people who have +high values that you know like you have + + align:start position:0% +high values that you know like you have + + + align:start position:0% +high values that you know like you have +a you know whatever whatever new Xbox is + + align:start position:0% +a you know whatever whatever new Xbox is + + + align:start position:0% +a you know whatever whatever new Xbox is +coming out there's some number of people + + align:start position:0% +coming out there's some number of people + + + align:start position:0% +coming out there's some number of people +who line up outside the store sleeping + + align:start position:0% +who line up outside the store sleeping + + + align:start position:0% +who line up outside the store sleeping +on the curb to buy the Xbox they do not + + align:start position:0% +on the curb to buy the Xbox they do not + + + align:start position:0% +on the curb to buy the Xbox they do not +get it at the best possible price you + + align:start position:0% +get it at the best possible price you + + + align:start position:0% +get it at the best possible price you +know they all pay full price and then + + align:start position:0% +know they all pay full price and then + + + align:start position:0% +know they all pay full price and then +you know 14 months later at Christmas + + align:start position:0% +you know 14 months later at Christmas + + + align:start position:0% +you know 14 months later at Christmas +that same Xbox is selling for much much + + align:start position:0% +that same Xbox is selling for much much + + + align:start position:0% +that same Xbox is selling for much much +less and that you know maybe what uh + + align:start position:0% +less and that you know maybe what uh + + + align:start position:0% +less and that you know maybe what uh +Microsoft has done is they've sort of + + align:start position:0% +Microsoft has done is they've sort of + + + align:start position:0% +Microsoft has done is they've sort of +walked down that demand curve first + + align:start position:0% +walked down that demand curve first + + + align:start position:0% +walked down that demand curve first +selling you the high value people then + + align:start position:0% +selling you the high value people then + + + align:start position:0% +selling you the high value people then +waiting for the high value people to buy + + align:start position:0% +waiting for the high value people to buy + + + align:start position:0% +waiting for the high value people to buy +then selling to the next highest value + + align:start position:0% +then selling to the next highest value + + + align:start position:0% +then selling to the next highest value +people and sort of in some sense trying + + align:start position:0% +people and sort of in some sense trying + + + align:start position:0% +people and sort of in some sense trying +to sort of uh discriminate between + + align:start position:0% +to sort of uh discriminate between + + + align:start position:0% +to sort of uh discriminate between +people by based on when they want to buy + + align:start position:0% +people by based on when they want to buy + + + align:start position:0% +people by based on when they want to buy +the good okay + + align:start position:0% +the good okay + + + align:start position:0% +the good okay +um you know while while sort of some + + align:start position:0% +um you know while while sort of some + + + align:start position:0% +um you know while while sort of some +somewhat appealing when you first hear + + align:start position:0% +somewhat appealing when you first hear + + + align:start position:0% +somewhat appealing when you first hear +the idea you know if you think about + + align:start position:0% +the idea you know if you think about + + + align:start position:0% +the idea you know if you think about +rational forward-looking + + align:start position:0% +rational forward-looking + + + align:start position:0% +rational forward-looking +consumers a durbo Goods monopolist is + + align:start position:0% +consumers a durbo Goods monopolist is + + + align:start position:0% +consumers a durbo Goods monopolist is +competing with itself uh and you're + + align:start position:0% +competing with itself uh and you're + + + align:start position:0% +competing with itself uh and you're +competing with your future self and if + + align:start position:0% +competing with your future self and if + + + align:start position:0% +competing with your future self and if +consumers think your future self your + + align:start position:0% +consumers think your future self your + + + align:start position:0% +consumers think your future self your +future self is going to lower the prices + + align:start position:0% +future self is going to lower the prices + + + align:start position:0% +future self is going to lower the prices +of the Xbox they're going to be hesitant + + align:start position:0% +of the Xbox they're going to be hesitant + + + align:start position:0% +of the Xbox they're going to be hesitant +to buy it on the first day that it comes + + align:start position:0% +to buy it on the first day that it comes + + + align:start position:0% +to buy it on the first day that it comes +out because they're going to think why + + align:start position:0% +out because they're going to think why + + + align:start position:0% +out because they're going to think why +don't I just wait a month and get it + + align:start position:0% +don't I just wait a month and get it + + + align:start position:0% +don't I just wait a month and get it +when the price drops or why don't I + + align:start position:0% +when the price drops or why don't I + + + align:start position:0% +when the price drops or why don't I +waste three months and get it when the + + align:start position:0% +waste three months and get it when the + + + align:start position:0% +waste three months and get it when the +price drops or whatever and then the + + align:start position:0% +price drops or whatever and then the + + + align:start position:0% +price drops or whatever and then the +consumers who would nor might have + + align:start position:0% +consumers who would nor might have + + + align:start position:0% +consumers who would nor might have +bought it 6 months out are going to + + align:start position:0% +bought it 6 months out are going to + + + align:start position:0% +bought it 6 months out are going to +think why don't I wait till Christmas + + align:start position:0% +think why don't I wait till Christmas + + + align:start position:0% +think why don't I wait till Christmas +you know or whatever where it's the day + + align:start position:0% +you know or whatever where it's the day + + + align:start position:0% +you know or whatever where it's the day +for Thanksgiving I can get that thing at + + align:start position:0% +for Thanksgiving I can get that thing at + + + align:start position:0% +for Thanksgiving I can get that thing at +Half Price seven month 14 months after + + align:start position:0% +Half Price seven month 14 months after + + + align:start position:0% +Half Price seven month 14 months after +it comes out or + + align:start position:0% +it comes out or + + + align:start position:0% +it comes out or +whatever okay um so first thing I want + + align:start position:0% +whatever okay um so first thing I want + + + align:start position:0% +whatever okay um so first thing I want +to do is just think about let's suppose + + align:start position:0% +to do is just think about let's suppose + + + align:start position:0% +to do is just think about let's suppose +you do have this model with commitment + + align:start position:0% +you do have this model with commitment + + + align:start position:0% +you do have this model with commitment +power and with the forward-looking + + align:start position:0% +power and with the forward-looking + + + align:start position:0% +power and with the forward-looking +consumers what would you do um so simple + + align:start position:0% +consumers what would you do um so simple + + + align:start position:0% +consumers what would you do um so simple +simplest model with commitment power you + + align:start position:0% +simplest model with commitment power you + + + align:start position:0% +simplest model with commitment power you +know I'm often going to do this you know + + align:start position:0% +know I'm often going to do this you know + + + align:start position:0% +know I'm often going to do this you know +in in you know I know in some subjects + + align:start position:0% +in in you know I know in some subjects + + + align:start position:0% +in in you know I know in some subjects +especially like macro these days + + align:start position:0% +especially like macro these days + + + align:start position:0% +especially like macro these days +everything has to be an infinite Horizon + + align:start position:0% +everything has to be an infinite Horizon + + + align:start position:0% +everything has to be an infinite Horizon +dynamic programming model um there's + + align:start position:0% +dynamic programming model um there's + + + align:start position:0% +dynamic programming model um there's +certainly plenty of infinite Horizon + + align:start position:0% +certainly plenty of infinite Horizon + + + align:start position:0% +certainly plenty of infinite Horizon +dynamic programming models in IO often + + align:start position:0% +dynamic programming models in IO often + + + align:start position:0% +dynamic programming models in IO often +though in class and I'm just going to + + align:start position:0% +though in class and I'm just going to + + + align:start position:0% +though in class and I'm just going to +use two period versions because I think + + align:start position:0% +use two period versions because I think + + + align:start position:0% +use two period versions because I think +you two period versions give you a lot + + align:start position:0% +you two period versions give you a lot + + + align:start position:0% +you two period versions give you a lot +of the intuition with much less + + align:start position:0% +of the intuition with much less + + + align:start position:0% +of the intuition with much less +complication than the bment equations + + align:start position:0% +complication than the bment equations + + + align:start position:0% +complication than the bment equations +would so my symol mod of commitment + + align:start position:0% +would so my symol mod of commitment + + + align:start position:0% +would so my symol mod of commitment +power there are just two periods + + align:start position:0% +power there are just two periods + + + align:start position:0% +power there are just two periods +consumers can buy the good either T + + align:start position:0% +consumers can buy the good either T + + + align:start position:0% +consumers can buy the good either T +equals 1 or t equals 2 so think about it + + align:start position:0% +equals 1 or t equals 2 so think about it + + + align:start position:0% +equals 1 or t equals 2 so think about it +there's T equals 1 there's T equals 2 + + align:start position:0% +there's T equals 1 there's T equals 2 + + + align:start position:0% +there's T equals 1 there's T equals 2 +then the world ends and everything goes + + align:start position:0% +then the world ends and everything goes + + + align:start position:0% +then the world ends and everything goes +away um good is perfectly durable + + align:start position:0% +away um good is perfectly durable + + + align:start position:0% +away um good is perfectly durable +consumers again are going to have types + + align:start position:0% +consumers again are going to have types + + + align:start position:0% +consumers again are going to have types +Theta on distributed on 01 here I'm + + align:start position:0% +Theta on distributed on 01 here I'm + + + align:start position:0% +Theta on distributed on 01 here I'm +going to make Theta the actual value so + + align:start position:0% +going to make Theta the actual value so + + + align:start position:0% +going to make Theta the actual value so +then I'm going to want Theta to have a + + align:start position:0% +then I'm going to want Theta to have a + + + align:start position:0% +then I'm going to want Theta to have a +distribution capital F of + + align:start position:0% +distribution capital F of + + + align:start position:0% +distribution capital F of +theta uh and so the consumer's utility + + align:start position:0% +theta uh and so the consumer's utility + + + align:start position:0% +theta uh and so the consumer's utility +is going to be 2 Theta minus P if they + + align:start position:0% +is going to be 2 Theta minus P if they + + + align:start position:0% +is going to be 2 Theta minus P if they +buy it at t equal 1 Theta minus P if + + align:start position:0% +buy it at t equal 1 Theta minus P if + + + align:start position:0% +buy it at t equal 1 Theta minus P if +they buy it at T equals 2 and zero if + + align:start position:0% +they buy it at T equals 2 and zero if + + + align:start position:0% +they buy it at T equals 2 and zero if +they don't buy so the reasoning is like + + align:start position:0% +they don't buy so the reasoning is like + + + align:start position:0% +they don't buy so the reasoning is like +a type Theta consumer gets utility Theta + + align:start position:0% +a type Theta consumer gets utility Theta + + + align:start position:0% +a type Theta consumer gets utility Theta +every period they have the good and so + + align:start position:0% +every period they have the good and so + + + align:start position:0% +every period they have the good and so +they buy it to equals one they get to + + align:start position:0% +they buy it to equals one they get to + + + align:start position:0% +they buy it to equals one they get to +enjoy the Xbox in two periods if they + + align:start position:0% +enjoy the Xbox in two periods if they + + + align:start position:0% +enjoy the Xbox in two periods if they +buy it at to equals two they only get to + + align:start position:0% +buy it at to equals two they only get to + + + align:start position:0% +buy it at to equals two they only get to +enjoy it for one + + align:start position:0% + + + + align:start position:0% + +period I'm going to have a constant + + align:start position:0% +period I'm going to have a constant + + + align:start position:0% +period I'm going to have a constant +marginal cost of producing the good and + + align:start position:0% +marginal cost of producing the good and + + + align:start position:0% +marginal cost of producing the good and +I'm going to assume the monopolist has + + align:start position:0% +I'm going to assume the monopolist has + + + align:start position:0% +I'm going to assume the monopolist has +commitment power and can set the prices + + align:start position:0% +commitment power and can set the prices + + + align:start position:0% +commitment power and can set the prices +P1 and P2 that it's going to charge in + + align:start position:0% +P1 and P2 that it's going to charge in + + + align:start position:0% +P1 and P2 that it's going to charge in +the two + + align:start position:0% +the two + + + align:start position:0% +the two +periods okay basic observation in this + + align:start position:0% +periods okay basic observation in this + + + align:start position:0% +periods okay basic observation in this +model is that in this model you TP as + + align:start position:0% +model is that in this model you TP as + + + align:start position:0% +model is that in this model you TP as +I've written it you don't want to walk + + align:start position:0% +I've written it you don't want to walk + + + align:start position:0% +I've written it you don't want to walk +down the demand curve in this model what + + align:start position:0% +down the demand curve in this model what + + + align:start position:0% +down the demand curve in this model what +you want to do is sell the good at the + + align:start position:0% +you want to do is sell the good at the + + + align:start position:0% +you want to do is sell the good at the +Monopoly price at T equals 1 and commit + + align:start position:0% +Monopoly price at T equals 1 and commit + + + align:start position:0% +Monopoly price at T equals 1 and commit +to make no sales at all at T equals + + align:start position:0% + + + + align:start position:0% + +2 so in this model you know and you know + + align:start position:0% +2 so in this model you know and you know + + + align:start position:0% +2 so in this model you know and you know +obviously there's some firms that fit + + align:start position:0% +obviously there's some firms that fit + + + align:start position:0% +obviously there's some firms that fit +this like if you look at Apple's iPhone + + align:start position:0% +this like if you look at Apple's iPhone + + + align:start position:0% +this like if you look at Apple's iPhone +pricing it seems like that iPhone comes + + align:start position:0% +pricing it seems like that iPhone comes + + + align:start position:0% +pricing it seems like that iPhone comes +out and it's $9.99 and everyone knows + + align:start position:0% +out and it's $9.99 and everyone knows + + + align:start position:0% +out and it's $9.99 and everyone knows +that the iPhone 14 is coming out + + align:start position:0% +that the iPhone 14 is coming out + + + align:start position:0% +that the iPhone 14 is coming out +literally next week and the iPhone 13 + + align:start position:0% +literally next week and the iPhone 13 + + + align:start position:0% +literally next week and the iPhone 13 +price still has not dropped right + + align:start position:0% +price still has not dropped right + + + align:start position:0% +price still has not dropped right +they've sort of set it at the Monopoly + + align:start position:0% +they've sort of set it at the Monopoly + + + align:start position:0% +they've sort of set it at the Monopoly +price iPhone 13s and they're going to + + align:start position:0% +price iPhone 13s and they're going to + + + align:start position:0% +price iPhone 13s and they're going to +keep it there and never never sell + + align:start position:0% +keep it there and never never sell + + + align:start position:0% +keep it there and never never sell +another one until the 14 comes + + align:start position:0% +another one until the 14 comes + + + align:start position:0% +another one until the 14 comes +out okay + + align:start position:0% +out okay + + + align:start position:0% +out okay +um why does this happen well again I'm + + align:start position:0% +um why does this happen well again I'm + + + align:start position:0% +um why does this happen well again I'm +going to think of my Theta line + + align:start position:0% +going to think of my Theta line + + + align:start position:0% +going to think of my Theta line +so you know suppose we've got our + + align:start position:0% +so you know suppose we've got our + + + align:start position:0% +so you know suppose we've got our +consumers they're ranged by + + align:start position:0% + + + + align:start position:0% + +Theta what's going to happen in + + align:start position:0% +Theta what's going to happen in + + + align:start position:0% +Theta what's going to happen in +equilibrium if I have some policy that + + align:start position:0% +equilibrium if I have some policy that + + + align:start position:0% +equilibrium if I have some policy that +involves selling the goods in both in + + align:start position:0% +involves selling the goods in both in + + + align:start position:0% +involves selling the goods in both in +both + + align:start position:0% +both + + + align:start position:0% +both +periods I'm going to have some high + + align:start position:0% +periods I'm going to have some high + + + align:start position:0% +periods I'm going to have some high +types who buy at T equals + + align:start position:0% +types who buy at T equals + + + align:start position:0% +types who buy at T equals +1 some intermediate types who buy at T + + align:start position:0% +1 some intermediate types who buy at T + + + align:start position:0% +1 some intermediate types who buy at T +equals + + align:start position:0% +equals + + + align:start position:0% +equals +2 and some lower types who don't + + align:start position:0% +2 and some lower types who don't + + + align:start position:0% +2 and some lower types who don't +buy okay why is that what's going to + + align:start position:0% +buy okay why is that what's going to + + + align:start position:0% +buy okay why is that what's going to +happen well again it's a revealed + + align:start position:0% +happen well again it's a revealed + + + align:start position:0% +happen well again it's a revealed +preference argument right if this person + + align:start position:0% +preference argument right if this person + + + align:start position:0% +preference argument right if this person +is willing to buy the phone at T equals + + align:start position:0% +is willing to buy the phone at T equals + + + align:start position:0% +is willing to buy the phone at T equals +2 this person gets a higher value they + + align:start position:0% +2 this person gets a higher value they + + + align:start position:0% +2 this person gets a higher value they +strictly prefer buying it at T equals 2 + + align:start position:0% +strictly prefer buying it at T equals 2 + + + align:start position:0% +strictly prefer buying it at T equals 2 +so if anyone is buying it everyone + + align:start position:0% +so if anyone is buying it everyone + + + align:start position:0% +so if anyone is buying it everyone +higher is buying it so the people buying + + align:start position:0% +higher is buying it so the people buying + + + align:start position:0% +higher is buying it so the people buying +it have to have to be above everyone who + + align:start position:0% +it have to have to be above everyone who + + + align:start position:0% +it have to have to be above everyone who +never buys it and + + align:start position:0% +never buys it and + + + align:start position:0% +never buys it and +then buying it t equals 1 you know if + + align:start position:0% +then buying it t equals 1 you know if + + + align:start position:0% +then buying it t equals 1 you know if +you buy it t equals one you may pay a + + align:start position:0% +you buy it t equals one you may pay a + + + align:start position:0% +you buy it t equals one you may pay a +high price for getting the Xbox in the + + align:start position:0% +high price for getting the Xbox in the + + + align:start position:0% +high price for getting the Xbox in the +first day or you can wait and get it + + align:start position:0% +first day or you can wait and get it + + + align:start position:0% +first day or you can wait and get it +later at a lower price again if you + + align:start position:0% +later at a lower price again if you + + + align:start position:0% +later at a lower price again if you +prefer buying it at tals one then anyone + + align:start position:0% +prefer buying it at tals one then anyone + + + align:start position:0% +prefer buying it at tals one then anyone +who's a strictly higher value strictly + + align:start position:0% +who's a strictly higher value strictly + + + align:start position:0% +who's a strictly higher value strictly +prefers getting a tal one relative + + align:start position:0% +prefers getting a tal one relative + + + align:start position:0% +prefers getting a tal one relative +equals 2 because they're getting the + + align:start position:0% +equals 2 because they're getting the + + + align:start position:0% +equals 2 because they're getting the +extra period of enjoyment of the good + + align:start position:0% +extra period of enjoyment of the good + + + align:start position:0% +extra period of enjoyment of the good +that extra period of enjoyment is + + align:start position:0% +that extra period of enjoyment is + + + align:start position:0% +that extra period of enjoyment is +increasing in + + align:start position:0% +increasing in + + + align:start position:0% +increasing in +Theta okay so if I do want you know I'm + + align:start position:0% +Theta okay so if I do want you know I'm + + + align:start position:0% +Theta okay so if I do want you know I'm +often in iow it often makes sense to + + align:start position:0% +often in iow it often makes sense to + + + align:start position:0% +often in iow it often makes sense to +think about the choices not in price + + align:start position:0% +think about the choices not in price + + + align:start position:0% +think about the choices not in price +space but in this Theta space um so if I + + align:start position:0% +space but in this Theta space um so if I + + + align:start position:0% +space but in this Theta space um so if I +want to implement this policy how do I + + align:start position:0% +want to implement this policy how do I + + + align:start position:0% +want to implement this policy how do I +do it well for this to be the cut off + + align:start position:0% +do it well for this to be the cut off + + + align:start position:0% +do it well for this to be the cut off +between people who buy it tals 2 and buy + + align:start position:0% +between people who buy it tals 2 and buy + + + align:start position:0% +between people who buy it tals 2 and buy +it and don't buy obviously you're going + + align:start position:0% +it and don't buy obviously you're going + + + align:start position:0% +it and don't buy obviously you're going +to have to have P2 + + align:start position:0% +to have to have P2 + + + align:start position:0% +to have to have P2 +equals Theta 2 hat right in the second + + align:start position:0% +equals Theta 2 hat right in the second + + + align:start position:0% +equals Theta 2 hat right in the second +period you're selling it at a price of + + align:start position:0% +period you're selling it at a price of + + + align:start position:0% +period you're selling it at a price of +theta 2 hat so the people who have + + align:start position:0% +theta 2 hat so the people who have + + + align:start position:0% +theta 2 hat so the people who have +utilities values above the2 hat buy at + + align:start position:0% +utilities values above the2 hat buy at + + + align:start position:0% +utilities values above the2 hat buy at +the second period the people who don't + + align:start position:0% +the second period the people who don't + + + align:start position:0% +the second period the people who don't +utilities B that uh don't buy what about + + align:start position:0% +utilities B that uh don't buy what about + + + align:start position:0% +utilities B that uh don't buy what about +in the first period you know in the + + align:start position:0% +in the first period you know in the + + + align:start position:0% +in the first period you know in the +first period you can't sell to this guy + + align:start position:0% +first period you can't sell to this guy + + + align:start position:0% +first period you can't sell to this guy +at a price of 2 Theta one hat because + + align:start position:0% +at a price of 2 Theta one hat because + + + align:start position:0% +at a price of 2 Theta one hat because +he'd be getting zero utility buying at a + + align:start position:0% +he'd be getting zero utility buying at a + + + align:start position:0% +he'd be getting zero utility buying at a +price of 2 Theta one hat he would just + + align:start position:0% +price of 2 Theta one hat he would just + + + align:start position:0% +price of 2 Theta one hat he would just +wait until the second period and buy it + + align:start position:0% +wait until the second period and buy it + + + align:start position:0% +wait until the second period and buy it +at this low price and get positive + + align:start position:0% +at this low price and get positive + + + align:start position:0% +at this low price and get positive +utility by by buying in the second + + align:start position:0% +utility by by buying in the second + + + align:start position:0% +utility by by buying in the second +period so what you can do the best you + + align:start position:0% +period so what you can do the best you + + + align:start position:0% +period so what you can do the best you +can do is to sort of chart is set a + + align:start position:0% +can do is to sort of chart is set a + + + align:start position:0% +can do is to sort of chart is set a +price so that the utility he gets from + + align:start position:0% +price so that the utility he gets from + + + align:start position:0% +price so that the utility he gets from +buying in the first period exactly + + align:start position:0% +buying in the first period exactly + + + align:start position:0% +buying in the first period exactly +matches the utility he could get from + + align:start position:0% +matches the utility he could get from + + + align:start position:0% +matches the utility he could get from +waiting and buying it in the second + + align:start position:0% +waiting and buying it in the second + + + align:start position:0% +waiting and buying it in the second +period And so what it tells you is that + + align:start position:0% +period And so what it tells you is that + + + align:start position:0% +period And so what it tells you is that +P1 is going to be Theta 1 Hat bigger + + align:start position:0% +P1 is going to be Theta 1 Hat bigger + + + align:start position:0% +P1 is going to be Theta 1 Hat bigger +than + + align:start position:0% +than + + + align:start position:0% +than +P2 so P1 is going to be Theta 1 Hat plus + + align:start position:0% +P2 so P1 is going to be Theta 1 Hat plus + + + align:start position:0% +P2 so P1 is going to be Theta 1 Hat plus +Theta 2 hat which would make sense you + + align:start position:0% +Theta 2 hat which would make sense you + + + align:start position:0% +Theta 2 hat which would make sense you +know he's getting the one extra utility + + align:start position:0% +know he's getting the one extra utility + + + align:start position:0% +know he's getting the one extra utility +of En period of enjoyment + + align:start position:0% + + + + align:start position:0% + +so you'd think about what's his marginal + + align:start position:0% +so you'd think about what's his marginal + + + align:start position:0% +so you'd think about what's his marginal +what's his incremental benefit from + + align:start position:0% +what's his incremental benefit from + + + align:start position:0% +what's his incremental benefit from +buying it early versus late it's Theta + + align:start position:0% +buying it early versus late it's Theta + + + align:start position:0% +buying it early versus late it's Theta +one hat is his incremental utility + + align:start position:0% +one hat is his incremental utility + + + align:start position:0% +one hat is his incremental utility +that's what you're charging him + + align:start position:0% +that's what you're charging him + + + align:start position:0% +that's what you're charging him +okay so monopolis problem looks like + + align:start position:0% +okay so monopolis problem looks like + + + align:start position:0% +okay so monopolis problem looks like +this um maximize over Theta 1 + + align:start position:0% +this um maximize over Theta 1 + + + align:start position:0% +this um maximize over Theta 1 +constrained by Theta 1 hat at least + + align:start position:0% +constrained by Theta 1 hat at least + + + align:start position:0% +constrained by Theta 1 hat at least +Theta 2 hat the price you get at T the + + align:start position:0% +Theta 2 hat the price you get at T the + + + align:start position:0% +Theta 2 hat the price you get at T the +price Minus cost at t equal 1 times the + + align:start position:0% +price Minus cost at t equal 1 times the + + + align:start position:0% +price Minus cost at t equal 1 times the +number of units you sell at t equal 1 + + align:start position:0% +number of units you sell at t equal 1 + + + align:start position:0% +number of units you sell at t equal 1 +which is 1 US capital F of theta 1 Hat + + align:start position:0% +which is 1 US capital F of theta 1 Hat + + + align:start position:0% +which is 1 US capital F of theta 1 Hat +plus profits you get from second period + + align:start position:0% +plus profits you get from second period + + + align:start position:0% +plus profits you get from second period +sales times the mass of people who buy + + align:start position:0% +sales times the mass of people who buy + + + align:start position:0% +sales times the mass of people who buy +the good in the second period which + + align:start position:0% +the good in the second period which + + + align:start position:0% +the good in the second period which +again is the number of people with types + + align:start position:0% +again is the number of people with types + + + align:start position:0% +again is the number of people with types +between Theta 2 hat and Theta 1 hat so + + align:start position:0% +between Theta 2 hat and Theta 1 hat so + + + align:start position:0% +between Theta 2 hat and Theta 1 hat so +that's what my profit function looks + + align:start position:0% +that's what my profit function looks + + + align:start position:0% +that's what my profit function looks +like notice that I've got two different + + align:start position:0% +like notice that I've got two different + + + align:start position:0% +like notice that I've got two different +terms that involve Theta 2 hat minus C + + align:start position:0% +terms that involve Theta 2 hat minus C + + + align:start position:0% +terms that involve Theta 2 hat minus C +it's here and it's here so if I group + + align:start position:0% +it's here and it's here so if I group + + + align:start position:0% +it's here and it's here so if I group +those together it becomes my my profit + + align:start position:0% +those together it becomes my my profit + + + align:start position:0% +those together it becomes my my profit +function looks like Theta 1 Hat * 1 - F + + align:start position:0% +function looks like Theta 1 Hat * 1 - F + + + align:start position:0% +function looks like Theta 1 Hat * 1 - F +of theta 1 Hat plus Theta 2 hat minus + + align:start position:0% +of theta 1 Hat plus Theta 2 hat minus + + + align:start position:0% +of theta 1 Hat plus Theta 2 hat minus +c times this plus this and then these + + align:start position:0% +c times this plus this and then these + + + align:start position:0% +c times this plus this and then these +things + + align:start position:0% +things + + + align:start position:0% +things +cancel and so my profit function is + + align:start position:0% +cancel and so my profit function is + + + align:start position:0% +cancel and so my profit function is +Theta 1 Hat * 1 - F of theta 1 Hat plus + + align:start position:0% +Theta 1 Hat * 1 - F of theta 1 Hat plus + + + align:start position:0% +Theta 1 Hat * 1 - F of theta 1 Hat plus +Theta 2 hat minus C * 1 - F of theta 2 + + align:start position:0% +Theta 2 hat minus C * 1 - F of theta 2 + + + align:start position:0% +Theta 2 hat minus C * 1 - F of theta 2 +hat that's my profit function + + align:start position:0% + + + + align:start position:0% + +okay um let's assume that the constraint + + align:start position:0% +okay um let's assume that the constraint + + + align:start position:0% +okay um let's assume that the constraint +was not binding um so if the constraints + + align:start position:0% +was not binding um so if the constraints + + + align:start position:0% +was not binding um so if the constraints +not binding that's I actually want to + + align:start position:0% +not binding that's I actually want to + + + align:start position:0% +not binding that's I actually want to +walk down my demand curve and set a high + + align:start position:0% +walk down my demand curve and set a high + + + align:start position:0% +walk down my demand curve and set a high +price and then set a lower price in the + + align:start position:0% +price and then set a lower price in the + + + align:start position:0% +price and then set a lower price in the +second period um this is just two + + align:start position:0% +second period um this is just two + + + align:start position:0% +second period um this is just two +separate maximization problems right I + + align:start position:0% +separate maximization problems right I + + + align:start position:0% +separate maximization problems right I +maximize this with respect to Theta one + + align:start position:0% +maximize this with respect to Theta one + + + align:start position:0% +maximize this with respect to Theta one +hat I maximized this with respect to + + align:start position:0% +hat I maximized this with respect to + + + align:start position:0% +hat I maximized this with respect to +Theta 2 hat + + align:start position:0% + + + + align:start position:0% + +well now let me go back to 121 for those + + align:start position:0% +well now let me go back to 121 for those + + + align:start position:0% +well now let me go back to 121 for those +of you who have taken it um 121 last + + align:start position:0% +of you who have taken it um 121 last + + + align:start position:0% +of you who have taken it um 121 last +year pague did a lot of this sort of + + align:start position:0% +year pague did a lot of this sort of + + + align:start position:0% +year pague did a lot of this sort of +functions with increasing differences + + align:start position:0% +functions with increasing differences + + + align:start position:0% +functions with increasing differences +stuff um if you look at this function + + align:start position:0% +stuff um if you look at this function + + + align:start position:0% +stuff um if you look at this function +Theta minus C1 minus F of theta this is + + align:start position:0% +Theta minus C1 minus F of theta this is + + + align:start position:0% +Theta minus C1 minus F of theta this is +like the Monopoly profit function this + + align:start position:0% +like the Monopoly profit function this + + + align:start position:0% +like the Monopoly profit function this +thing has increasing differences in C + + align:start position:0% +thing has increasing differences in C + + + align:start position:0% +thing has increasing differences in C +and and and + + align:start position:0% +and and and + + + align:start position:0% +and and and +Theta which means that you know this is + + align:start position:0% +Theta which means that you know this is + + + align:start position:0% +Theta which means that you know this is +very general theorem when a monopolis + + align:start position:0% +very general theorem when a monopolis + + + align:start position:0% +very general theorem when a monopolis +marginal cost is higher it sets a higher + + align:start position:0% +marginal cost is higher it sets a higher + + + align:start position:0% +marginal cost is higher it sets a higher +price + + align:start position:0% + + + + align:start position:0% + +this is basically the Monopoly pricing + + align:start position:0% +this is basically the Monopoly pricing + + + align:start position:0% +this is basically the Monopoly pricing +problem with a cost of zero this is a + + align:start position:0% +problem with a cost of zero this is a + + + align:start position:0% +problem with a cost of zero this is a +monopoly pricing problem with the cost + + align:start position:0% +monopoly pricing problem with the cost + + + align:start position:0% +monopoly pricing problem with the cost +of + + align:start position:0% +of + + + align:start position:0% +of +C so the maximizer of this is larger + + align:start position:0% +C so the maximizer of this is larger + + + align:start position:0% +C so the maximizer of this is larger +than the maximizer of + + align:start position:0% +than the maximizer of + + + align:start position:0% +than the maximizer of +this so if I ignore the constraint you + + align:start position:0% +this so if I ignore the constraint you + + + align:start position:0% +this so if I ignore the constraint you +know this is the Monopoly price when + + align:start position:0% +know this is the Monopoly price when + + + align:start position:0% +know this is the Monopoly price when +your cost is C this is the Monopoly + + align:start position:0% +your cost is C this is the Monopoly + + + align:start position:0% +your cost is C this is the Monopoly +price when your cost is zero this tells + + align:start position:0% +price when your cost is zero this tells + + + align:start position:0% +price when your cost is zero this tells +you that Theta 2 hat would be bigger + + align:start position:0% +you that Theta 2 hat would be bigger + + + align:start position:0% +you that Theta 2 hat would be bigger +than Theta 1 hat so if I assume this + + align:start position:0% +than Theta 1 hat so if I assume this + + + align:start position:0% +than Theta 1 hat so if I assume this +constraint is non-binding I get the + + align:start position:0% +constraint is non-binding I get the + + + align:start position:0% +constraint is non-binding I get the +contradiction that if if that constraint + + align:start position:0% +contradiction that if if that constraint + + + align:start position:0% +contradiction that if if that constraint +is not binding I find that Theta 2 hat + + align:start position:0% +is not binding I find that Theta 2 hat + + + align:start position:0% +is not binding I find that Theta 2 hat +is strictly greater than Theta 1 hat and + + align:start position:0% +is strictly greater than Theta 1 hat and + + + align:start position:0% +is strictly greater than Theta 1 hat and +that contradicts the Assumption the + + align:start position:0% +that contradicts the Assumption the + + + align:start position:0% +that contradicts the Assumption the +constraint is not binding okay you know + + align:start position:0% +constraint is not binding okay you know + + + align:start position:0% +constraint is not binding okay you know +why is this in in some sense what's + + align:start position:0% +why is this in in some sense what's + + + align:start position:0% +why is this in in some sense what's +going on here + + align:start position:0% +going on here + + + align:start position:0% +going on here +is you know almost imagine with the this + + align:start position:0% +is you know almost imagine with the this + + + align:start position:0% +is you know almost imagine with the this +durable good I'm instead of selling + + align:start position:0% +durable good I'm instead of selling + + + align:start position:0% +durable good I'm instead of selling +those Xboxes in the first period I rent + + align:start position:0% +those Xboxes in the first period I rent + + + align:start position:0% +those Xboxes in the first period I rent +them to people I get all those people l + + align:start position:0% +them to people I get all those people l + + + align:start position:0% +them to people I get all those people l +in line I give them a one period rental + + align:start position:0% +in line I give them a one period rental + + + align:start position:0% +in line I give them a one period rental +on the Xbox and then I take them all + + align:start position:0% +on the Xbox and then I take them all + + + align:start position:0% +on the Xbox and then I take them all +back and then I rent them again in the + + align:start position:0% +back and then I rent them again in the + + + align:start position:0% +back and then I rent them again in the +second period okay + + align:start position:0% +second period okay + + + align:start position:0% +second period okay +you know anyone that I'm selling it to + + align:start position:0% +you know anyone that I'm selling it to + + + align:start position:0% +you know anyone that I'm selling it to +in the first per all these people who + + align:start position:0% +in the first per all these people who + + + align:start position:0% +in the first per all these people who +get in the first period they're going to + + align:start position:0% +get in the first period they're going to + + + align:start position:0% +get in the first period they're going to +rent it back for me in the second period + + align:start position:0% +rent it back for me in the second period + + + align:start position:0% +rent it back for me in the second period +at a price of theta 2 + + align:start position:0% + + + + align:start position:0% + +hat when I'm selling extra units in the + + align:start position:0% +hat when I'm selling extra units in the + + + align:start position:0% +hat when I'm selling extra units in the +first period any extra units I sell in + + align:start position:0% +first period any extra units I sell in + + + align:start position:0% +first period any extra units I sell in +the first period were units that I were + + align:start position:0% +the first period were units that I were + + + align:start position:0% +the first period were units that I were +go I was going to sell in the second + + align:start position:0% +go I was going to sell in the second + + + align:start position:0% +go I was going to sell in the second +period anyway so the cost of selling + + align:start position:0% +period anyway so the cost of selling + + + align:start position:0% +period anyway so the cost of selling +them one period early is zero right I'm + + align:start position:0% +them one period early is zero right I'm + + + align:start position:0% +them one period early is zero right I'm +already producing them to sell in the + + align:start position:0% +already producing them to sell in the + + + align:start position:0% +already producing them to sell in the +second period so given that I'm + + align:start position:0% +second period so given that I'm + + + align:start position:0% +second period so given that I'm +producing them to sell in the second + + align:start position:0% +producing them to sell in the second + + + align:start position:0% +producing them to sell in the second +period there's zero cost to me of + + align:start position:0% +period there's zero cost to me of + + + align:start position:0% +period there's zero cost to me of +selling them in the first period + + align:start position:0% +selling them in the first period + + + align:start position:0% +selling them in the first period +instead um so it's as if those sort of + + align:start position:0% +instead um so it's as if those sort of + + + align:start position:0% +instead um so it's as if those sort of +units I'm going to sell anyway have a + + align:start position:0% +units I'm going to sell anyway have a + + + align:start position:0% +units I'm going to sell anyway have a +marginal cost of zero instead of a + + align:start position:0% +marginal cost of zero instead of a + + + align:start position:0% +marginal cost of zero instead of a +marginal cost of c and so because I'm + + align:start position:0% +marginal cost of c and so because I'm + + + align:start position:0% +marginal cost of c and so because I'm +I'm going to produce them and sell them + + align:start position:0% +I'm going to produce them and sell them + + + align:start position:0% +I'm going to produce them and sell them +anyway they have no cost so that makes + + align:start position:0% +anyway they have no cost so that makes + + + align:start position:0% +anyway they have no cost so that makes +me even more want to sell them rather + + align:start position:0% +me even more want to sell them rather + + + align:start position:0% +me even more want to sell them rather +than less want to sell them so this + + align:start position:0% +than less want to sell them so this + + + align:start position:0% +than less want to sell them so this +doesn't make any + + align:start position:0% +doesn't make any + + + align:start position:0% +doesn't make any +sense okay so this would say is that you + + align:start position:0% +sense okay so this would say is that you + + + align:start position:0% +sense okay so this would say is that you +know like monopolis selling durable + + align:start position:0% +know like monopolis selling durable + + + align:start position:0% +know like monopolis selling durable +goods this whole idea it's it's a + + align:start position:0% +goods this whole idea it's it's a + + + align:start position:0% +goods this whole idea it's it's a +strictly bad idea to walk down your + + align:start position:0% +strictly bad idea to walk down your + + + align:start position:0% +strictly bad idea to walk down your +demand curve because you're sort of + + align:start position:0% +demand curve because you're sort of + + + align:start position:0% +demand curve because you're sort of +taking these Goods that you're going to + + align:start position:0% +taking these Goods that you're going to + + + align:start position:0% +taking these Goods that you're going to +produce anyway they really have no cost + + align:start position:0% +produce anyway they really have no cost + + + align:start position:0% +produce anyway they really have no cost +to selling to people early and you're + + align:start position:0% +to selling to people early and you're + + + align:start position:0% +to selling to people early and you're +you know losing those people's enjoyment + + align:start position:0% +you know losing those people's enjoyment + + + align:start position:0% +you know losing those people's enjoyment +it it doesn't make any sense you know + + align:start position:0% +it it doesn't make any sense you know + + + align:start position:0% +it it doesn't make any sense you know +the these ones you have to be hesitant + + align:start position:0% +the these ones you have to be hesitant + + + align:start position:0% +the these ones you have to be hesitant +to produce because they have a cost + + align:start position:0% +to produce because they have a cost + + + align:start position:0% +to produce because they have a cost +these ones have no cost of + + align:start position:0% +these ones have no cost of + + + align:start position:0% +these ones have no cost of +production okay so mon you know so in + + align:start position:0% +production okay so mon you know so in + + + align:start position:0% +production okay so mon you know so in +some sense you know someone at Apple saw + + align:start position:0% +some sense you know someone at Apple saw + + + align:start position:0% +some sense you know someone at Apple saw +this lecture they realized this is what + + align:start position:0% +this lecture they realized this is what + + + align:start position:0% +this lecture they realized this is what +you do you do not bring out the new + + align:start position:0% +you do you do not bring out the new + + + align:start position:0% +you do you do not bring out the new +iPhone and then sort of make its price + + align:start position:0% +iPhone and then sort of make its price + + + align:start position:0% +iPhone and then sort of make its price +go down and people wait for the the + + align:start position:0% +go down and people wait for the the + + + align:start position:0% +go down and people wait for the the +price cut you just sort of bring it out + + align:start position:0% +price cut you just sort of bring it out + + + align:start position:0% +price cut you just sort of bring it out +you fix the price forever and that's the + + align:start position:0% +you fix the price forever and that's the + + + align:start position:0% +you fix the price forever and that's the +optimal Monopoly pricing policy with + + align:start position:0% +optimal Monopoly pricing policy with + + + align:start position:0% +optimal Monopoly pricing policy with +durable + + align:start position:0% +durable + + + align:start position:0% +durable +goods okay + + align:start position:0% +goods okay + + + align:start position:0% +goods okay +um + + align:start position:0% + + + + align:start position:0% + +um wait simple numerical example there I + + align:start position:0% +um wait simple numerical example there I + + + align:start position:0% +um wait simple numerical example there I +don't need to go over it so you know + + align:start position:0% +don't need to go over it so you know + + + align:start position:0% +don't need to go over it so you know +where would price drops come from in + + align:start position:0% +where would price drops come from in + + + align:start position:0% +where would price drops come from in +real life + + align:start position:0% +real life + + + align:start position:0% +real life +um you know obviously we need to do + + align:start position:0% +um you know obviously we need to do + + + align:start position:0% +um you know obviously we need to do +something different from this model to + + align:start position:0% +something different from this model to + + + align:start position:0% +something different from this model to +get prices of new Goods to come out you + + align:start position:0% +get prices of new Goods to come out you + + + align:start position:0% +get prices of new Goods to come out you +know I I think we do often have the view + + align:start position:0% +know I I think we do often have the view + + + align:start position:0% +know I I think we do often have the view +that there are many new things the new + + align:start position:0% +that there are many new things the new + + + align:start position:0% +that there are many new things the new +product comes out it's got a really high + + align:start position:0% +product comes out it's got a really high + + + align:start position:0% +product comes out it's got a really high +price and then if you wait for it the + + align:start position:0% +price and then if you wait for it the + + + align:start position:0% +price and then if you wait for it the +price will decline over time why why + + align:start position:0% +price will decline over time why why + + + align:start position:0% +price will decline over time why why +does that happen um you know one thing + + align:start position:0% +does that happen um you know one thing + + + align:start position:0% +does that happen um you know one thing +you can get is different + + align:start position:0% +you can get is different + + + align:start position:0% +you can get is different +preferences suppose that people get + + align:start position:0% +preferences suppose that people get + + + align:start position:0% +preferences suppose that people get +utility not from enjoying the good for + + align:start position:0% +utility not from enjoying the good for + + + align:start position:0% +utility not from enjoying the good for +instance but from having the Xbox before + + align:start position:0% +instance but from having the Xbox before + + + align:start position:0% +instance but from having the Xbox before +any of their friend do like I'm the one + + align:start position:0% +any of their friend do like I'm the one + + + align:start position:0% +any of their friend do like I'm the one +guy who has the brand new Xbox everyone + + align:start position:0% +guy who has the brand new Xbox everyone + + + align:start position:0% +guy who has the brand new Xbox everyone +has to come to my house to play it I + + align:start position:0% +has to come to my house to play it I + + + align:start position:0% +has to come to my house to play it I +somehow get status in my friend group + + align:start position:0% +somehow get status in my friend group + + + align:start position:0% +somehow get status in my friend group +out of being the guy with the new Xbox + + align:start position:0% +out of being the guy with the new Xbox + + + align:start position:0% +out of being the guy with the new Xbox +um you know fashion clothing you know + + align:start position:0% +um you know fashion clothing you know + + + align:start position:0% +um you know fashion clothing you know +right like clothes come out fashion + + align:start position:0% +right like clothes come out fashion + + + align:start position:0% +right like clothes come out fashion +designers introduce it someone has a + + align:start position:0% +designers introduce it someone has a + + + align:start position:0% +designers introduce it someone has a +copy some number months later but the + + align:start position:0% +copy some number months later but the + + + align:start position:0% +copy some number months later but the +people who wear the $3,000 dresses get + + align:start position:0% +people who wear the $3,000 dresses get + + + align:start position:0% +people who wear the $3,000 dresses get +utility from knowing that they have the + + align:start position:0% +utility from knowing that they have the + + + align:start position:0% +utility from knowing that they have the +genuine $3,000 dress that no one else + + align:start position:0% +genuine $3,000 dress that no one else + + + align:start position:0% +genuine $3,000 dress that no one else +has because it's just it's just the new + + align:start position:0% +has because it's just it's just the new + + + align:start position:0% +has because it's just it's just the new +good that comes out out so if you you + + align:start position:0% +good that comes out out so if you you + + + align:start position:0% +good that comes out out so if you you +know give people preferences for owning + + align:start position:0% +know give people preferences for owning + + + align:start position:0% +know give people preferences for owning +Goods that other people don't have then + + align:start position:0% +Goods that other people don't have then + + + align:start position:0% +Goods that other people don't have then +it can make total sense to sort of have + + align:start position:0% +it can make total sense to sort of have + + + align:start position:0% +it can make total sense to sort of have +some set of people like in some sense + + align:start position:0% +some set of people like in some sense + + + align:start position:0% +some set of people like in some sense +you know some almost that's like Ping + + align:start position:0% +you know some almost that's like Ping + + + align:start position:0% +you know some almost that's like Ping +back to an optimal quality theorem like + + align:start position:0% +back to an optimal quality theorem like + + + align:start position:0% +back to an optimal quality theorem like +if there are people out there who have a + + align:start position:0% +if there are people out there who have a + + + align:start position:0% +if there are people out there who have a +high willingness to pay for things that + + align:start position:0% +high willingness to pay for things that + + + align:start position:0% +high willingness to pay for things that +other people don't have you create a + + align:start position:0% +other people don't have you create a + + + align:start position:0% +other people don't have you create a +high quality product which is a product + + align:start position:0% +high quality product which is a product + + + align:start position:0% +high quality product which is a product +other people don't have and sell it to + + align:start position:0% +other people don't have and sell it to + + + align:start position:0% +other people don't have and sell it to +them okay and then maybe once you've + + align:start position:0% +them okay and then maybe once you've + + + align:start position:0% +them okay and then maybe once you've +sold it to people that who have those + + align:start position:0% +sold it to people that who have those + + + align:start position:0% +sold it to people that who have those +preferences then you can sell it to the + + align:start position:0% +preferences then you can sell it to the + + + align:start position:0% +preferences then you can sell it to the +other people later um but so that would + + align:start position:0% +other people later um but so that would + + + align:start position:0% +other people later um but so that would +be one way you can get early adopters um + + align:start position:0% +be one way you can get early adopters um + + + align:start position:0% +be one way you can get early adopters um +you know I I think another thing that + + align:start position:0% +you know I I think another thing that + + + align:start position:0% +you know I I think another thing that +often comes up in the tech sector is + + align:start position:0% +often comes up in the tech sector is + + + align:start position:0% +often comes up in the tech sector is +just costs that are changing over time + + align:start position:0% +just costs that are changing over time + + + align:start position:0% +just costs that are changing over time +or Capa you know costs that are changing + + align:start position:0% +or Capa you know costs that are changing + + + align:start position:0% +or Capa you know costs that are changing +over time because of technological + + align:start position:0% +over time because of technological + + + align:start position:0% +over time because of technological +improvements because of learning by + + align:start position:0% +improvements because of learning by + + + align:start position:0% +improvements because of learning by +doing because of capacity constraints of + + align:start position:0% +doing because of capacity constraints of + + + align:start position:0% +doing because of capacity constraints of +the factories early on it's very costly + + align:start position:0% +the factories early on it's very costly + + + align:start position:0% +the factories early on it's very costly +to produce Goods the costs are high + + align:start position:0% +to produce Goods the costs are high + + + align:start position:0% +to produce Goods the costs are high +therefore you set a high price as the + + align:start position:0% +therefore you set a high price as the + + + align:start position:0% +therefore you set a high price as the +sort of Technology becomes you know + + align:start position:0% +sort of Technology becomes you know + + + align:start position:0% +sort of Technology becomes you know +level changes it becomes cheaper and + + align:start position:0% +level changes it becomes cheaper and + + + align:start position:0% +level changes it becomes cheaper and +cheaper to produce that good you get + + align:start position:0% +cheaper to produce that good you get + + + align:start position:0% +cheaper to produce that good you get +better at producing it um your costs go + + align:start position:0% +better at producing it um your costs go + + + align:start position:0% +better at producing it um your costs go +down you drop your price as a result + + align:start position:0% +down you drop your price as a result + + + align:start position:0% +down you drop your price as a result +okay um third explanation is uh you know + + align:start position:0% +okay um third explanation is uh you know + + + align:start position:0% +okay um third explanation is uh you know +firms may have a commitment problem that + + align:start position:0% +firms may have a commitment problem that + + + align:start position:0% +firms may have a commitment problem that +is you if you think about like what this + + align:start position:0% +is you if you think about like what this + + + align:start position:0% +is you if you think about like what this +this you know how is this pricing + + align:start position:0% +this you know how is this pricing + + + align:start position:0% +this you know how is this pricing +supposed to go um I bring out my new + + align:start position:0% +supposed to go um I bring out my new + + + align:start position:0% +supposed to go um I bring out my new +phone I price it at + + align:start position:0% +phone I price it at + + + align:start position:0% +phone I price it at +$11,000 everyone everyone who wants that + + align:start position:0% +$11,000 everyone everyone who wants that + + + align:start position:0% +$11,000 everyone everyone who wants that +new phone comes out and buys at $1,000 + + align:start position:0% +new phone comes out and buys at $1,000 + + + align:start position:0% +new phone comes out and buys at $1,000 +and then I'm supposed to sell you know + + align:start position:0% +and then I'm supposed to sell you know + + + align:start position:0% +and then I'm supposed to sell you know +in this example without phones that + + align:start position:0% +in this example without phones that + + + align:start position:0% +in this example without phones that +break I sell + + align:start position:0% +break I sell + + + align:start position:0% +break I sell +none for the next two years or whatever + + align:start position:0% +none for the next two years or whatever + + + align:start position:0% +none for the next two years or whatever +until I my new product comes out so I S + + align:start position:0% +until I my new product comes out so I S + + + align:start position:0% +until I my new product comes out so I S +I sell a whole bunch of phones I keep + + align:start position:0% +I sell a whole bunch of phones I keep + + + align:start position:0% +I sell a whole bunch of phones I keep +the price high no one buy everyone + + align:start position:0% +the price high no one buy everyone + + + align:start position:0% +the price high no one buy everyone +bought it at T equals one no one buys it + + align:start position:0% +bought it at T equals one no one buys it + + + align:start position:0% +bought it at T equals one no one buys it +at T equals 2 you know if you imagine + + align:start position:0% +at T equals 2 you know if you imagine + + + align:start position:0% +at T equals 2 you know if you imagine +the firm sitting there at T equals 2 + + align:start position:0% +the firm sitting there at T equals 2 + + + align:start position:0% +the firm sitting there at T equals 2 +they must be thinking like once everyone + + align:start position:0% +they must be thinking like once everyone + + + align:start position:0% +they must be thinking like once everyone +has already bought the product um if + + align:start position:0% +has already bought the product um if + + + align:start position:0% +has already bought the product um if +this was not like any repeated game like + + align:start position:0% +this was not like any repeated game like + + + align:start position:0% +this was not like any repeated game like +imagine this was the last iPhone that + + align:start position:0% +imagine this was the last iPhone that + + + align:start position:0% +imagine this was the last iPhone that +was ever going to exist why keep selling + + align:start position:0% +was ever going to exist why keep selling + + + align:start position:0% +was ever going to exist why keep selling +zero why not take all those people who + + align:start position:0% +zero why not take all those people who + + + align:start position:0% +zero why not take all those people who +have low values um you know the other + + align:start position:0% +have low values um you know the other + + + align:start position:0% +have low values um you know the other +people you know other people are going + + align:start position:0% +people you know other people are going + + + align:start position:0% +people you know other people are going +to be disappointed when you cut the + + align:start position:0% +to be disappointed when you cut the + + + align:start position:0% +to be disappointed when you cut the +price and wish they had bought it later + + align:start position:0% +price and wish they had bought it later + + + align:start position:0% +price and wish they had bought it later +but it's too late for them to actually + + align:start position:0% +but it's too late for them to actually + + + align:start position:0% +but it's too late for them to actually +buy it later once you've already sold + + align:start position:0% +buy it later once you've already sold + + + align:start position:0% +buy it later once you've already sold +the phones it is optimal for you then in + + align:start position:0% +the phones it is optimal for you then in + + + align:start position:0% +the phones it is optimal for you then in +the second period to go ahead and cut + + align:start position:0% +the second period to go ahead and cut + + + align:start position:0% +the second period to go ahead and cut +the price and sell to more + + align:start position:0% +the price and sell to more + + + align:start position:0% +the price and sell to more +people um and so if you don't have some + + align:start position:0% +people um and so if you don't have some + + + align:start position:0% +people um and so if you don't have some +way to commit yourself not to lower the + + align:start position:0% +way to commit yourself not to lower the + + + align:start position:0% +way to commit yourself not to lower the +price after all the early adopters have + + align:start position:0% +price after all the early adopters have + + + align:start position:0% +price after all the early adopters have +bought you're going to want to lower the + + align:start position:0% +bought you're going to want to lower the + + + align:start position:0% +bought you're going to want to lower the +price and then once you're going to want + + align:start position:0% +price and then once you're going to want + + + align:start position:0% +price and then once you're going to want +to lower the price in equili you will + + align:start position:0% +to lower the price in equili you will + + + align:start position:0% +to lower the price in equili you will +lower the price and then you'll be in + + align:start position:0% +lower the price and then you'll be in + + + align:start position:0% +lower the price and then you'll be in +the position of every in the first + + align:start position:0% +the position of every in the first + + + align:start position:0% +the position of every in the first +period thinking you're going to lower + + align:start position:0% +period thinking you're going to lower + + + align:start position:0% +period thinking you're going to lower +the price and not buy it because the + + align:start position:0% +the price and not buy it because the + + + align:start position:0% +the price and not buy it because the +price is too high given what you're + + align:start position:0% +price is too high given what you're + + + align:start position:0% +price is too high given what you're +going to lower it to and so on um so you + + align:start position:0% +going to lower it to and so on um so you + + + align:start position:0% +going to lower it to and so on um so you +know firms could be lowering prices + + align:start position:0% +know firms could be lowering prices + + + align:start position:0% +know firms could be lowering prices +because they lack the ability to + + align:start position:0% +because they lack the ability to + + + align:start position:0% +because they lack the ability to +commit um commit to a pricing structure + + align:start position:0% +commit um commit to a pricing structure + + + align:start position:0% +commit um commit to a pricing structure +okay so this for instance like if you + + align:start position:0% +okay so this for instance like if you + + + align:start position:0% +okay so this for instance like if you +think about Apple versus some company + + align:start position:0% +think about Apple versus some company + + + align:start position:0% +think about Apple versus some company +that's a new startup that may never have + + align:start position:0% +that's a new startup that may never have + + + align:start position:0% +that's a new startup that may never have +a second phone you could imagine that + + align:start position:0% +a second phone you could imagine that + + + align:start position:0% +a second phone you could imagine that +sort of Apple is able to commit because + + align:start position:0% +sort of Apple is able to commit because + + + align:start position:0% +sort of Apple is able to commit because +they have some reputation a new entrant + + align:start position:0% +they have some reputation a new entrant + + + align:start position:0% +they have some reputation a new entrant +is not able to commit because no one + + align:start position:0% +is not able to commit because no one + + + align:start position:0% +is not able to commit because no one +knows if they're going to be around you + + align:start position:0% +knows if they're going to be around you + + + align:start position:0% +knows if they're going to be around you +know like we don't know that they're a + + align:start position:0% +know like we don't know that they're a + + + align:start position:0% +know like we don't know that they're a +firm that's not going to cut the price + + align:start position:0% +firm that's not going to cut the price + + + align:start position:0% +firm that's not going to cut the price +and so it may be that that's sort of a + + align:start position:0% +and so it may be that that's sort of a + + + align:start position:0% +and so it may be that that's sort of a +disadvantage that you get if you're not + + align:start position:0% +disadvantage that you get if you're not + + + align:start position:0% +disadvantage that you get if you're not +someone who's known to be there for a + + align:start position:0% +someone who's known to be there for a + + + align:start position:0% +someone who's known to be there for a +long time and known to have this + + align:start position:0% +long time and known to have this + + + align:start position:0% +long time and known to have this +reputation for high + + align:start position:0% +reputation for high + + + align:start position:0% +reputation for high +pricing okay um I put on the slides I I + + align:start position:0% +pricing okay um I put on the slides I I + + + align:start position:0% +pricing okay um I put on the slides I I +don't want to take the time some sense I + + align:start position:0% +don't want to take the time some sense I + + + align:start position:0% +don't want to take the time some sense I +I think that um you know overtime people + + align:start position:0% +I think that um you know overtime people + + + align:start position:0% +I think that um you know overtime people +in IO believe less and less in + + align:start position:0% +in IO believe less and less in + + + align:start position:0% +in IO believe less and less in +commitment problems and in firms being + + align:start position:0% +commitment problems and in firms being + + + align:start position:0% +commitment problems and in firms being +unable to exploit their Monopoly power + + align:start position:0% +unable to exploit their Monopoly power + + + align:start position:0% +unable to exploit their Monopoly power +because they have these sort of severe + + align:start position:0% +because they have these sort of severe + + + align:start position:0% +because they have these sort of severe +commitment problems but anyway you know + + align:start position:0% +commitment problems but anyway you know + + + align:start position:0% +commitment problems but anyway you know +I put on the slide a simple numerical + + align:start position:0% +I put on the slide a simple numerical + + + align:start position:0% +I put on the slide a simple numerical +example of you know imagine Theta was + + align:start position:0% +example of you know imagine Theta was + + + align:start position:0% +example of you know imagine Theta was +uniform + + align:start position:0% +uniform + + + align:start position:0% +uniform +01 cost was Zero D of p is 1 minus P + + align:start position:0% +01 cost was Zero D of p is 1 minus P + + + align:start position:0% +01 cost was Zero D of p is 1 minus P +what is it that you + + align:start position:0% +what is it that you + + + align:start position:0% +what is it that you +do uh and without worrying out the + + align:start position:0% +do uh and without worrying out the + + + align:start position:0% +do uh and without worrying out the +algebra you can look at it afterwards + + align:start position:0% +algebra you can look at it afterwards + + + align:start position:0% +algebra you can look at it afterwards +what you do is do I have on the next + + align:start position:0% +what you do is do I have on the next + + + align:start position:0% +what you do is do I have on the next +slide yeah you know whereas + + align:start position:0% +slide yeah you know whereas + + + align:start position:0% +slide yeah you know whereas +in this model if you were a monopolist + + align:start position:0% +in this model if you were a monopolist + + + align:start position:0% +in this model if you were a monopolist +with d ofp as 1 minus p in two periods + + align:start position:0% +with d ofp as 1 minus p in two periods + + + align:start position:0% +with d ofp as 1 minus p in two periods +you know the Monopoly price is one half + + align:start position:0% +you know the Monopoly price is one half + + + align:start position:0% +you know the Monopoly price is one half +per period so you'd set a price of one + + align:start position:0% +per period so you'd set a price of one + + + align:start position:0% +per period so you'd set a price of one +and so what you get instead of setting a + + align:start position:0% +and so what you get instead of setting a + + + align:start position:0% +and so what you get instead of setting a +price of one and then sticking to it and + + align:start position:0% +price of one and then sticking to it and + + + align:start position:0% +price of one and then sticking to it and +selling to half the consumers the + + align:start position:0% +selling to half the consumers the + + + align:start position:0% +selling to half the consumers the +solution turns out to be a set a price + + align:start position:0% +solution turns out to be a set a price + + + align:start position:0% +solution turns out to be a set a price +of 9/10 in the first period and then + + align:start position:0% +of 9/10 in the first period and then + + + align:start position:0% +of 9/10 in the first period and then +drop it to 3/10 in the first period you + + align:start position:0% +drop it to 3/10 in the first period you + + + align:start position:0% +drop it to 3/10 in the first period you +sell to some people but less than half + + align:start position:0% +sell to some people but less than half + + + align:start position:0% +sell to some people but less than half +in the first period even though your + + align:start position:0% +in the first period even though your + + + align:start position:0% +in the first period even though your +price is lower and then you sell to some + + align:start position:0% +price is lower and then you sell to some + + + align:start position:0% +price is lower and then you sell to some +people in the second per + + align:start position:0% +people in the second per + + + align:start position:0% +people in the second per +period so two things that come out in + + align:start position:0% +period so two things that come out in + + + align:start position:0% +period so two things that come out in +this sort of simple algebraic example is + + align:start position:0% +this sort of simple algebraic example is + + + align:start position:0% +this sort of simple algebraic example is +you know you get a deep decreasing price + + align:start position:0% +you know you get a deep decreasing price + + + align:start position:0% +you know you get a deep decreasing price +sequence this is the commitment problem + + align:start position:0% +sequence this is the commitment problem + + + align:start position:0% +sequence this is the commitment problem +you the price sequence has to go down + + align:start position:0% +you the price sequence has to go down + + + align:start position:0% +you the price sequence has to go down +because what if your price didn't go + + align:start position:0% +because what if your price didn't go + + + align:start position:0% +because what if your price didn't go +down no one would buy in the second + + align:start position:0% +down no one would buy in the second + + + align:start position:0% +down no one would buy in the second +period and then the second period you + + align:start position:0% +period and then the second period you + + + align:start position:0% +period and then the second period you +would be getting zero profits instead of + + align:start position:0% +would be getting zero profits instead of + + + align:start position:0% +would be getting zero profits instead of +positive profits so in a problem with + + align:start position:0% +positive profits so in a problem with + + + align:start position:0% +positive profits so in a problem with +commitment you always get P2 less than 1 + + align:start position:0% +commitment you always get P2 less than 1 + + + align:start position:0% +commitment you always get P2 less than 1 +half P1 and you always get profits are + + align:start position:0% +half P1 and you always get profits are + + + align:start position:0% +half P1 and you always get profits are +lower without commitment than with + + align:start position:0% +lower without commitment than with + + + align:start position:0% +lower without commitment than with +commit commment because you know if the + + align:start position:0% +commit commment because you know if the + + + align:start position:0% +commit commment because you know if the +prits were better with this sort of 9/10 + + align:start position:0% +prits were better with this sort of 9/10 + + + align:start position:0% +prits were better with this sort of 9/10 +310 thing that's what you would have + + align:start position:0% +310 thing that's what you would have + + + align:start position:0% +310 thing that's what you would have +chosen when you had commitment power so + + align:start position:0% +chosen when you had commitment power so + + + align:start position:0% +chosen when you had commitment power so +commitment power is always the best you + + align:start position:0% +commitment power is always the best you + + + align:start position:0% +commitment power is always the best you +can do when you have commitment power + + align:start position:0% +can do when you have commitment power + + + align:start position:0% +can do when you have commitment power +not so what you do in these sort of + + align:start position:0% +not so what you do in these sort of + + + align:start position:0% +not so what you do in these sort of +problems with a self-control problem is + + align:start position:0% +problems with a self-control problem is + + + align:start position:0% +problems with a self-control problem is +always you earn lower profits and you do + + align:start position:0% +always you earn lower profits and you do + + + align:start position:0% +always you earn lower profits and you do +walk down your demand + + align:start position:0% +walk down your demand + + + align:start position:0% +walk down your demand +curve + + align:start position:0% +curve + + + align:start position:0% +curve +okay so you know firms lacking this + + align:start position:0% +okay so you know firms lacking this + + + align:start position:0% +okay so you know firms lacking this +ability to commit is sort of one + + align:start position:0% +ability to commit is sort of one + + + align:start position:0% +ability to commit is sort of one +explanation and it's it's firms are + + align:start position:0% +explanation and it's it's firms are + + + align:start position:0% +explanation and it's it's firms are +worse off because they don't they can't + + align:start position:0% +worse off because they don't they can't + + + align:start position:0% +worse off because they don't they can't +commit to doing what they would like to + + align:start position:0% + + + + align:start position:0% + +do okay um the coast conjecture is you + + align:start position:0% +do okay um the coast conjecture is you + + + align:start position:0% +do okay um the coast conjecture is you +know even more extreme commitment + + align:start position:0% +know even more extreme commitment + + + align:start position:0% +know even more extreme commitment +problem you know I think like in the + + align:start position:0% +problem you know I think like in the + + + align:start position:0% +problem you know I think like in the +1970s or whatever this was something the + + align:start position:0% +1970s or whatever this was something the + + + align:start position:0% +1970s or whatever this was something the +quote Chicago School of of uh economics + + align:start position:0% +quote Chicago School of of uh economics + + + align:start position:0% +quote Chicago School of of uh economics +took seriously that even monopolist has + + align:start position:0% +took seriously that even monopolist has + + + align:start position:0% +took seriously that even monopolist has +no Market power and has to price a + + align:start position:0% +no Market power and has to price a + + + align:start position:0% +no Market power and has to price a +marginal cost because commitment power + + align:start position:0% +marginal cost because commitment power + + + align:start position:0% +marginal cost because commitment power +is so severe so the coast conjecture is + + align:start position:0% +is so severe so the coast conjecture is + + + align:start position:0% +is so severe so the coast conjecture is +let's take the extreme version of this + + align:start position:0% +let's take the extreme version of this + + + align:start position:0% +let's take the extreme version of this +where I set a price at T equals zero I + + align:start position:0% +where I set a price at T equals zero I + + + align:start position:0% +where I set a price at T equals zero I +set a price at delta T which think of as + + align:start position:0% +set a price at delta T which think of as + + + align:start position:0% +set a price at delta T which think of as +one day later 2 delta T 3 delta T and so + + align:start position:0% +one day later 2 delta T 3 delta T and so + + + align:start position:0% +one day later 2 delta T 3 delta T and so +on and assume that consumers have + + align:start position:0% +on and assume that consumers have + + + align:start position:0% +on and assume that consumers have +utility Theta e to the minus RT if they + + align:start position:0% +utility Theta e to the minus RT if they + + + align:start position:0% +utility Theta e to the minus RT if they +purchase uh at time T So consumers are + + align:start position:0% +purchase uh at time T So consumers are + + + align:start position:0% +purchase uh at time T So consumers are +discounting firms are setting their + + align:start position:0% +discounting firms are setting their + + + align:start position:0% +discounting firms are setting their +prices over and over and over again uh + + align:start position:0% +prices over and over and over again uh + + + align:start position:0% +prices over and over and over again uh +and the consumers have this kind of + + align:start position:0% +and the consumers have this kind of + + + align:start position:0% +and the consumers have this kind of +discounted expected utility and our + + align:start position:0% +discounted expected utility and our + + + align:start position:0% +discounted expected utility and our +forward looking uh the the coast + + align:start position:0% +forward looking uh the the coast + + + align:start position:0% +forward looking uh the the coast +conjecture says that under some + + align:start position:0% +conjecture says that under some + + + align:start position:0% +conjecture says that under some +conditions the monopolis monopolis + + align:start position:0% +conditions the monopolis monopolis + + + align:start position:0% +conditions the monopolis monopolis +profits go to zero as delta T goes to + + align:start position:0% +profits go to zero as delta T goes to + + + align:start position:0% +profits go to zero as delta T goes to +zero so if you look at if you make this + + align:start position:0% +zero so if you look at if you make this + + + align:start position:0% +zero so if you look at if you make this +sort of severe commitment problem that + + align:start position:0% +sort of severe commitment problem that + + + align:start position:0% +sort of severe commitment problem that +every day I'm going to choose a new + + align:start position:0% +every day I'm going to choose a new + + + align:start position:0% +every day I'm going to choose a new +price every day I'm going to choose a + + align:start position:0% +price every day I'm going to choose a + + + align:start position:0% +price every day I'm going to choose a +new price with no ability to commit to + + align:start position:0% +new price with no ability to commit to + + + align:start position:0% +new price with no ability to commit to +that price uh the theorem is that you + + align:start position:0% +that price uh the theorem is that you + + + align:start position:0% +that price uh the theorem is that you +know actually the the more often you can + + align:start position:0% +know actually the the more often you can + + + align:start position:0% +know actually the the more often you can +change your price the more severe this + + align:start position:0% +change your price the more severe this + + + align:start position:0% +change your price the more severe this +commitment uh problem gets and in the + + align:start position:0% +commitment uh problem gets and in the + + + align:start position:0% +commitment uh problem gets and in the +limit as delta T goes to zero what you + + align:start position:0% +limit as delta T goes to zero what you + + + align:start position:0% +limit as delta T goes to zero what you +do is basically you do almost like that + + align:start position:0% +do is basically you do almost like that + + + align:start position:0% +do is basically you do almost like that +you just sort of start may you start + + align:start position:0% +you just sort of start may you start + + + align:start position:0% +you just sort of start may you start +your price out closer to one but then it + + align:start position:0% +your price out closer to one but then it + + + align:start position:0% +your price out closer to one but then it +just it drops to zero and it goes to + + align:start position:0% +just it drops to zero and it goes to + + + align:start position:0% +just it drops to zero and it goes to +zero almost instantly and in the limit + + align:start position:0% +zero almost instantly and in the limit + + + align:start position:0% +zero almost instantly and in the limit +as Delta goes to zero and in fact your + + align:start position:0% +as Delta goes to zero and in fact your + + + align:start position:0% +as Delta goes to zero and in fact your +price goes to zero instantly and the + + align:start position:0% +price goes to zero instantly and the + + + align:start position:0% +price goes to zero instantly and the +monopolis ears zero profits at + + align:start position:0% +monopolis ears zero profits at + + + align:start position:0% +monopolis ears zero profits at +all + + align:start position:0% + + + + align:start position:0% + +um why does this happen you + + align:start position:0% +um why does this happen you + + + align:start position:0% +um why does this happen you +know again it's the example the argument + + align:start position:0% +know again it's the example the argument + + + align:start position:0% +know again it's the example the argument +is really this there's nothing else that + + align:start position:0% +is really this there's nothing else that + + + align:start position:0% +is really this there's nothing else that +could happen in this model so you know + + align:start position:0% +could happen in this model so you know + + + align:start position:0% +could happen in this model so you know +suppose you know right like I I did this + + align:start position:0% +suppose you know right like I I did this + + + align:start position:0% +suppose you know right like I I did this +example where if if I have commitment + + align:start position:0% +example where if if I have commitment + + + align:start position:0% +example where if if I have commitment +power I just set the price at one and + + align:start position:0% +power I just set the price at one and + + + align:start position:0% +power I just set the price at one and +never change it so if I put time on this + + align:start position:0% +never change it so if I put time on this + + + align:start position:0% +never change it so if I put time on this +axis and P of t on this axis this is + + align:start position:0% +axis and P of t on this axis this is + + + align:start position:0% +axis and P of t on this axis this is +what the monopolis wants to do and when + + align:start position:0% +what the monopolis wants to do and when + + + align:start position:0% +what the monopolis wants to do and when +you + + align:start position:0% +you + + + align:start position:0% +you +have no when you had two periods I think + + align:start position:0% +have no when you had two periods I think + + + align:start position:0% +have no when you had two periods I think +I showed you that you know this is some + + align:start position:0% +I showed you that you know this is some + + + align:start position:0% +I showed you that you know this is some +sense that's what the monopolis does it + + align:start position:0% +sense that's what the monopolis does it + + + align:start position:0% +sense that's what the monopolis does it +sets the price here and then drops the + + align:start position:0% +sets the price here and then drops the + + + align:start position:0% +sets the price here and then drops the +price down if you have three periods the + + align:start position:0% +price down if you have three periods the + + + align:start position:0% +price down if you have three periods the +monopolis is going to do something like + + align:start position:0% +monopolis is going to do something like + + + align:start position:0% +monopolis is going to do something like +this set the price here set the price + + align:start position:0% +this set the price here set the price + + + align:start position:0% +this set the price here set the price +here set the price + + align:start position:0% +here set the price + + + align:start position:0% +here set the price +here um imagine the prices didn't go to + + align:start position:0% +here um imagine the prices didn't go to + + + align:start position:0% +here um imagine the prices didn't go to +zero if prices didn't go to zero it must + + align:start position:0% +zero if prices didn't go to zero it must + + + align:start position:0% +zero if prices didn't go to zero it must +be when you do this thing in + + align:start position:0% +be when you do this thing in + + + align:start position:0% +be when you do this thing in +very rapidly you get sort of some smooth + + align:start position:0% +very rapidly you get sort of some smooth + + + align:start position:0% +very rapidly you get sort of some smooth +curve like you know this is what the + + align:start position:0% +curve like you know this is what the + + + align:start position:0% +curve like you know this is what the +monopolis + + align:start position:0% +monopolis + + + align:start position:0% +monopolis +does when it's changing prices every + + align:start position:0% +does when it's changing prices every + + + align:start position:0% +does when it's changing prices every +second it just sort of drops its price + + align:start position:0% +second it just sort of drops its price + + + align:start position:0% +second it just sort of drops its price +smoothly over + + align:start position:0% +smoothly over + + + align:start position:0% +smoothly over +time but dropping your price smoothly + + align:start position:0% +time but dropping your price smoothly + + + align:start position:0% +time but dropping your price smoothly +over + + align:start position:0% +over + + + align:start position:0% +over +time ju at a finite slope just isn't + + align:start position:0% +time ju at a finite slope just isn't + + + align:start position:0% +time ju at a finite slope just isn't +going to ever be optimal and why is that + + align:start position:0% +going to ever be optimal and why is that + + + align:start position:0% +going to ever be optimal and why is that +the reason is that imagine this was what + + align:start position:0% +the reason is that imagine this was what + + + align:start position:0% +the reason is that imagine this was what +you were going to do and you decide at + + align:start position:0% +you were going to do and you decide at + + + align:start position:0% +you were going to do and you decide at +this time to sort of instead of charging + + align:start position:0% +this time to sort of instead of charging + + + align:start position:0% +this time to sort of instead of charging +this price I'm just going to jump ahead + + align:start position:0% +this price I'm just going to jump ahead + + + align:start position:0% +this price I'm just going to jump ahead +one period and charge this price instead + + align:start position:0% +one period and charge this price instead + + + align:start position:0% +one period and charge this price instead +and then follow the same path so I just + + align:start position:0% +and then follow the same path so I just + + + align:start position:0% +and then follow the same path so I just +ex sort of say okay at this one period + + align:start position:0% +ex sort of say okay at this one period + + + align:start position:0% +ex sort of say okay at this one period +I'm just going to jump ahead and charge + + align:start position:0% +I'm just going to jump ahead and charge + + + align:start position:0% +I'm just going to jump ahead and charge +that price instead of this price + + align:start position:0% +that price instead of this price + + + align:start position:0% +that price instead of this price +if I jump ahead one period I move all + + align:start position:0% +if I jump ahead one period I move all + + + align:start position:0% +if I jump ahead one period I move all +future sales back by delta + + align:start position:0% +future sales back by delta + + + align:start position:0% +future sales back by delta +T the gain from moving those things + + align:start position:0% +T the gain from moving those things + + + align:start position:0% +T the gain from moving those things +ahead uh is first order in delta + + align:start position:0% +ahead uh is first order in delta + + + align:start position:0% +ahead uh is first order in delta +T because I've just it's got an e to the + + align:start position:0% +T because I've just it's got an e to the + + + align:start position:0% +T because I've just it's got an e to the +minus delta T in it I just move sales + + align:start position:0% +minus delta T in it I just move sales + + + align:start position:0% +minus delta T in it I just move sales +forward one + + align:start position:0% +forward one + + + align:start position:0% +forward one +period what have I lost by dropping the + + align:start position:0% +period what have I lost by dropping the + + + align:start position:0% +period what have I lost by dropping the +price from this to this well I you know + + align:start position:0% +price from this to this well I you know + + + align:start position:0% +price from this to this well I you know +I could have earned this price on this + + align:start position:0% +I could have earned this price on this + + + align:start position:0% +I could have earned this price on this +tiny tiny number of units I sell in that + + align:start position:0% +tiny tiny number of units I sell in that + + + align:start position:0% +tiny tiny number of units I sell in that +period I now get this price on those + + align:start position:0% +period I now get this price on those + + + align:start position:0% +period I now get this price on those +units and + + align:start position:0% +units and + + + align:start position:0% +units and +so + + align:start position:0% +so + + + align:start position:0% +so +my loss from having jump forward is this + + align:start position:0% +my loss from having jump forward is this + + + align:start position:0% +my loss from having jump forward is this +thing times this + + align:start position:0% +thing times this + + + align:start position:0% +thing times this +thing that's second order in delta T + + align:start position:0% +thing that's second order in delta T + + + align:start position:0% +thing that's second order in delta T +because the number of products I'm + + align:start position:0% +because the number of products I'm + + + align:start position:0% +because the number of products I'm +selling each delta T unit interval is + + align:start position:0% +selling each delta T unit interval is + + + align:start position:0% +selling each delta T unit interval is +like a delta T proportional delta T and + + align:start position:0% +like a delta T proportional delta T and + + + align:start position:0% +like a delta T proportional delta T and +the price drops are proportional to + + align:start position:0% +the price drops are proportional to + + + align:start position:0% +the price drops are proportional to +Delta so the gain from moving things + + align:start position:0% +Delta so the gain from moving things + + + align:start position:0% +Delta so the gain from moving things +forward would be first order the loss + + align:start position:0% +forward would be first order the loss + + + align:start position:0% +forward would be first order the loss +from moving things forward would be + + align:start position:0% +from moving things forward would be + + + align:start position:0% +from moving things forward would be +second ORD You' always want to move + + align:start position:0% +second ORD You' always want to move + + + align:start position:0% +second ORD You' always want to move +things forward and so what must be the + + align:start position:0% +things forward and so what must be the + + + align:start position:0% +things forward and so what must be the +case is it's not the case that these + + align:start position:0% +case is it's not the case that these + + + align:start position:0% +case is it's not the case that these +things are both of order Delta it's got + + align:start position:0% +things are both of order Delta it's got + + + align:start position:0% +things are both of order Delta it's got +to be that like this thing is falling at + + align:start position:0% +to be that like this thing is falling at + + + align:start position:0% +to be that like this thing is falling at +nearly infinite rate so that the loss + + align:start position:0% +nearly infinite rate so that the loss + + + align:start position:0% +nearly infinite rate so that the loss +and gains both become first + + align:start position:0% +and gains both become first + + + align:start position:0% +and gains both become first +order okay so anyway so the coast + + align:start position:0% +order okay so anyway so the coast + + + align:start position:0% +order okay so anyway so the coast +conjecture says there's some conditions + + align:start position:0% +conjecture says there's some conditions + + + align:start position:0% +conjecture says there's some conditions +under which this + + align:start position:0% +under which this + + + align:start position:0% +under which this +happens you know there's a big + + align:start position:0% +happens you know there's a big + + + align:start position:0% +happens you know there's a big +literature on the coast conjecture like + + align:start position:0% +literature on the coast conjecture like + + + align:start position:0% +literature on the coast conjecture like +you know like if you read The fudenberg + + align:start position:0% +you know like if you read The fudenberg + + + align:start position:0% +you know like if you read The fudenberg +tooll Game Theory textbook not the io + + align:start position:0% +tooll Game Theory textbook not the io + + + align:start position:0% +tooll Game Theory textbook not the io +textbook it's got like you know know + + align:start position:0% +textbook it's got like you know know + + + align:start position:0% +textbook it's got like you know know +pages and pages and Pages proving + + align:start position:0% +pages and pages and Pages proving + + + align:start position:0% +pages and pages and Pages proving +versions of the coast theorem I I think + + align:start position:0% +versions of the coast theorem I I think + + + align:start position:0% +versions of the coast theorem I I think +in IO right now um you I should say it's + + align:start position:0% +in IO right now um you I should say it's + + + align:start position:0% +in IO right now um you I should say it's +Coast conjecture even though it's a + + align:start position:0% +Coast conjecture even though it's a + + + align:start position:0% +Coast conjecture even though it's a +theorem whereas the coast theorem is + + align:start position:0% +theorem whereas the coast theorem is + + + align:start position:0% +theorem whereas the coast theorem is +really a conjecture but the coast + + align:start position:0% +really a conjecture but the coast + + + align:start position:0% +really a conjecture but the coast +conjecture is true it's a theorem people + + align:start position:0% +conjecture is true it's a theorem people + + + align:start position:0% +conjecture is true it's a theorem people +have proved it under various + + align:start position:0% +have proved it under various + + + align:start position:0% +have proved it under various +assumptions why isn't it true there's + + align:start position:0% +assumptions why isn't it true there's + + + align:start position:0% +assumptions why isn't it true there's +more of a literature in IO unlike why it + + align:start position:0% +more of a literature in IO unlike why it + + + align:start position:0% +more of a literature in IO unlike why it +doesn't happen uh and I don't think + + align:start position:0% +doesn't happen uh and I don't think + + + align:start position:0% +doesn't happen uh and I don't think +anyone believes it should happen these + + align:start position:0% +anyone believes it should happen these + + + align:start position:0% +anyone believes it should happen these +days why wouldn't it happen first of all + + align:start position:0% +days why wouldn't it happen first of all + + + align:start position:0% +days why wouldn't it happen first of all +you know firms don't change their price + + align:start position:0% +you know firms don't change their price + + + align:start position:0% +you know firms don't change their price +every day it takes time to change your + + align:start position:0% +every day it takes time to change your + + + align:start position:0% +every day it takes time to change your +price in particular it takes time after + + align:start position:0% +price in particular it takes time after + + + align:start position:0% +price in particular it takes time after +you change your price for All consumers + + align:start position:0% +you change your price for All consumers + + + align:start position:0% +you change your price for All consumers +who are supposed to buy at that price to + + align:start position:0% +who are supposed to buy at that price to + + + align:start position:0% +who are supposed to buy at that price to +buy at that price so if you decide I'm + + align:start position:0% +buy at that price so if you decide I'm + + + align:start position:0% +buy at that price so if you decide I'm +going to sell my phone for my Xbox at$ + + align:start position:0% +going to sell my phone for my Xbox at$ + + + align:start position:0% +going to sell my phone for my Xbox at$ +3.99 instead of + + align:start position:0% +3.99 instead of + + + align:start position:0% +3.99 instead of +$459 you're going to have to wait a + + align:start position:0% +$459 you're going to have to wait a + + + align:start position:0% +$459 you're going to have to wait a +month for all the 399 consumers to get + + align:start position:0% +month for all the 399 consumers to get + + + align:start position:0% +month for all the 399 consumers to get +around to coming in and buying it so + + align:start position:0% +around to coming in and buying it so + + + align:start position:0% +around to coming in and buying it so +it's not like the consumers buy + + align:start position:0% +it's not like the consumers buy + + + align:start position:0% +it's not like the consumers buy +instantly it's also costly if you you + + align:start position:0% +instantly it's also costly if you you + + + align:start position:0% +instantly it's also costly if you you +know you're not going to change your + + align:start position:0% +know you're not going to change your + + + align:start position:0% +know you're not going to change your +price every day um firms like apple can + + align:start position:0% +price every day um firms like apple can + + + align:start position:0% +price every day um firms like apple can +have reput ations for not buying their + + align:start position:0% +have reput ations for not buying their + + + align:start position:0% +have reput ations for not buying their +goods um you can also have inflows of + + align:start position:0% +goods um you can also have inflows of + + + align:start position:0% +goods um you can also have inflows of +new high willingness to pay customers so + + align:start position:0% +new high willingness to pay customers so + + + align:start position:0% +new high willingness to pay customers so +even if Apple didn't have this + + align:start position:0% +even if Apple didn't have this + + + align:start position:0% +even if Apple didn't have this +reputation there are people who are very + + align:start position:0% +reputation there are people who are very + + + align:start position:0% +reputation there are people who are very +high value iPhone users whose phones + + align:start position:0% +high value iPhone users whose phones + + + align:start position:0% +high value iPhone users whose phones +break and then when their phones break + + align:start position:0% +break and then when their phones break + + + align:start position:0% +break and then when their phones break +those new high Theta people show up + + align:start position:0% +those new high Theta people show up + + + align:start position:0% +those new high Theta people show up +wanting to buy a new iPhone so in some + + align:start position:0% +wanting to buy a new iPhone so in some + + + align:start position:0% +wanting to buy a new iPhone so in some +sense there's always high Theta people + + align:start position:0% +sense there's always high Theta people + + + align:start position:0% +sense there's always high Theta people +showing up in the market and with high + + align:start position:0% +showing up in the market and with high + + + align:start position:0% +showing up in the market and with high +Theta people showing up in the market + + align:start position:0% +Theta people showing up in the market + + + align:start position:0% +Theta people showing up in the market +that gives you another reason to keep + + align:start position:0% +that gives you another reason to keep + + + align:start position:0% +that gives you another reason to keep +your prices + + align:start position:0% +your prices + + + align:start position:0% +your prices +High um + + align:start position:0% + + + + align:start position:0% + +uh consumers not being all rational and + + align:start position:0% +uh consumers not being all rational and + + + align:start position:0% +uh consumers not being all rational and +forward-looking again that argument that + + align:start position:0% +forward-looking again that argument that + + + align:start position:0% +forward-looking again that argument that +I gave you was all the consu the + + align:start position:0% +I gave you was all the consu the + + + align:start position:0% +I gave you was all the consu the +consumers are anticipating the future + + align:start position:0% +consumers are anticipating the future + + + align:start position:0% +consumers are anticipating the future +price drops you know if you have some + + align:start position:0% +price drops you know if you have some + + + align:start position:0% +price drops you know if you have some +consumers who don't realize the price is + + align:start position:0% +consumers who don't realize the price is + + + align:start position:0% +consumers who don't realize the price is +going to drop um then you're going to + + align:start position:0% +going to drop um then you're going to + + + align:start position:0% +going to drop um then you're going to +want to exploit the consumers who don't + + align:start position:0% +want to exploit the consumers who don't + + + align:start position:0% +want to exploit the consumers who don't +understand that the prices are going to + + align:start position:0% +understand that the prices are going to + + + align:start position:0% +understand that the prices are going to +drop that's going to change that sort of + + align:start position:0% +drop that's going to change that sort of + + + align:start position:0% +drop that's going to change that sort of +first order condition I gave you um + + align:start position:0% +first order condition I gave you um + + + align:start position:0% +first order condition I gave you um +there are also many strategic reasons so + + align:start position:0% +there are also many strategic reasons so + + + align:start position:0% +there are also many strategic reasons so +for instance um + + align:start position:0% +for instance um + + + align:start position:0% +for instance um +you know you can rent the good rather + + align:start position:0% +you know you can rent the good rather + + + align:start position:0% +you know you can rent the good rather +than selling the good um you know like + + align:start position:0% +than selling the good um you know like + + + align:start position:0% +than selling the good um you know like +in the old days um it used to be that + + align:start position:0% +in the old days um it used to be that + + + align:start position:0% +in the old days um it used to be that +like AT&T when they were phone monopis + + align:start position:0% +like AT&T when they were phone monopis + + + align:start position:0% +like AT&T when they were phone monopis +the United States didn't sell telephones + + align:start position:0% +the United States didn't sell telephones + + + align:start position:0% +the United States didn't sell telephones +they only rented telephones and you had + + align:start position:0% +they only rented telephones and you had + + + align:start position:0% +they only rented telephones and you had +to rent your phone from AT&T they didn't + + align:start position:0% +to rent your phone from AT&T they didn't + + + align:start position:0% +to rent your phone from AT&T they didn't +offer sales as an option when Xerox + + align:start position:0% +offer sales as an option when Xerox + + + align:start position:0% +offer sales as an option when Xerox +first started selling copy machines they + + align:start position:0% +first started selling copy machines they + + + align:start position:0% +first started selling copy machines they +didn't sell copy machines they rented + + align:start position:0% +didn't sell copy machines they rented + + + align:start position:0% +didn't sell copy machines they rented +copy machines if you rent them instead + + align:start position:0% +copy machines if you rent them instead + + + align:start position:0% +copy machines if you rent them instead +of selling them you don't face this + + align:start position:0% +of selling them you don't face this + + + align:start position:0% +of selling them you don't face this +commitment problem because just every + + align:start position:0% +commitment problem because just every + + + align:start position:0% +commitment problem because just every +month you're renting to your current set + + align:start position:0% +month you're renting to your current set + + + align:start position:0% +month you're renting to your current set +of consumers you're setting your optimal + + align:start position:0% +of consumers you're setting your optimal + + + align:start position:0% +of consumers you're setting your optimal +price to keep renting it that is the + + align:start position:0% +price to keep renting it that is the + + + align:start position:0% +price to keep renting it that is the +Monopoly price okay um the other thing + + align:start position:0% +Monopoly price okay um the other thing + + + align:start position:0% +Monopoly price okay um the other thing +you can do is of a tricky thing that + + align:start position:0% +you can do is of a tricky thing that + + + align:start position:0% +you can do is of a tricky thing that +seems like it's favorable to your + + align:start position:0% +seems like it's favorable to your + + + align:start position:0% +seems like it's favorable to your +customers you can sort of say I have + + align:start position:0% +customers you can sort of say I have + + + align:start position:0% +customers you can sort of say I have +this very customer friendly policy if I + + align:start position:0% +this very customer friendly policy if I + + + align:start position:0% +this very customer friendly policy if I +ever sell this iPhone to any customer at + + align:start position:0% +ever sell this iPhone to any customer at + + + align:start position:0% +ever sell this iPhone to any customer at +a lower price than I sold it to you uh + + align:start position:0% +a lower price than I sold it to you uh + + + align:start position:0% +a lower price than I sold it to you uh +I'm going to rebate you the difference + + align:start position:0% +I'm going to rebate you the difference + + + align:start position:0% +I'm going to rebate you the difference +automatically it's going to come back to + + align:start position:0% +automatically it's going to come back to + + + align:start position:0% +automatically it's going to come back to +your credit card it's a best price + + align:start position:0% +your credit card it's a best price + + + align:start position:0% +your credit card it's a best price +guarantee that you're never never have + + align:start position:0% +guarantee that you're never never have + + + align:start position:0% +guarantee that you're never never have +to worry about I bought my iPhone and + + align:start position:0% +to worry about I bought my iPhone and + + + align:start position:0% +to worry about I bought my iPhone and +got ripped and got ripped off and + + align:start position:0% +got ripped and got ripped off and + + + align:start position:0% +got ripped and got ripped off and +someone else paid less than me again I + + align:start position:0% +someone else paid less than me again I + + + align:start position:0% +someone else paid less than me again I +adopt that most favored customer policy + + align:start position:0% +adopt that most favored customer policy + + + align:start position:0% +adopt that most favored customer policy +I commit to it then once I've sold my + + align:start position:0% +I commit to it then once I've sold my + + + align:start position:0% +I commit to it then once I've sold my +phone to all the high value customers I + + align:start position:0% +phone to all the high value customers I + + + align:start position:0% +phone to all the high value customers I +don't want to cut the price because I + + align:start position:0% +don't want to cut the price because I + + + align:start position:0% +don't want to cut the price because I +cut the price I'm cutting the price for + + align:start position:0% +cut the price I'm cutting the price for + + + align:start position:0% +cut the price I'm cutting the price for +everyone that's back to the same thing + + align:start position:0% +everyone that's back to the same thing + + + align:start position:0% +everyone that's back to the same thing +as the rental + + align:start position:0% +as the rental + + + align:start position:0% +as the rental +problem + + align:start position:0% +problem + + + align:start position:0% +problem +um okay um and you know firms can also + + align:start position:0% +um okay um and you know firms can also + + + align:start position:0% +um okay um and you know firms can also +sort of strategically I can just build a + + align:start position:0% +sort of strategically I can just build a + + + align:start position:0% +sort of strategically I can just build a +factory that only produces so many + + align:start position:0% +factory that only produces so many + + + align:start position:0% +factory that only produces so many +phones per month I build a factory that + + align:start position:0% +phones per month I build a factory that + + + align:start position:0% +phones per month I build a factory that +only produces enough phones to sell to + + align:start position:0% +only produces enough phones to sell to + + + align:start position:0% +only produces enough phones to sell to +everyone at one size I'm not tempted to + + align:start position:0% +everyone at one size I'm not tempted to + + + align:start position:0% +everyone at one size I'm not tempted to +to raise my price so I I I think the + + align:start position:0% +to raise my price so I I I think the + + + align:start position:0% +to raise my price so I I I think the +general view in IO is that there are you + + align:start position:0% +general view in IO is that there are you + + + align:start position:0% +general view in IO is that there are you +know enough reasons why you know the + + align:start position:0% +know enough reasons why you know the + + + align:start position:0% +know enough reasons why you know the +consumer not being rational the inflows + + align:start position:0% +consumer not being rational the inflows + + + align:start position:0% +consumer not being rational the inflows +of high willingness to pay customers are + + align:start position:0% +of high willingness to pay customers are + + + align:start position:0% +of high willingness to pay customers are +such that the extreme coting shouldn't + + align:start position:0% +such that the extreme coting shouldn't + + + align:start position:0% +such that the extreme coting shouldn't +happen and if you were in a situation + + align:start position:0% +happen and if you were in a situation + + + align:start position:0% +happen and if you were in a situation +where the extreme Coast problem were + + align:start position:0% +where the extreme Coast problem were + + + align:start position:0% +where the extreme Coast problem were +there firms would come up with a way + + align:start position:0% +there firms would come up with a way + + + align:start position:0% +there firms would come up with a way +around it um obviously there are sort of + + align:start position:0% +around it um obviously there are sort of + + + align:start position:0% +around it um obviously there are sort of +some antitrust concerns with some of + + align:start position:0% +some antitrust concerns with some of + + + align:start position:0% +some antitrust concerns with some of +these but you know there are ways to + + align:start position:0% +these but you know there are ways to + + + align:start position:0% +these but you know there are ways to +avoid the coast conjecture I think we + + align:start position:0% +avoid the coast conjecture I think we + + + align:start position:0% +avoid the coast conjecture I think we +don't you know we don't necessarily + + align:start position:0% +don't you know we don't necessarily + + + align:start position:0% +don't you know we don't necessarily +think of that that this is so important + + align:start position:0% +think of that that this is so important + + + align:start position:0% +think of that that this is so important +um and I I should say that you know this + + align:start position:0% +um and I I should say that you know this + + + align:start position:0% +um and I I should say that you know this +is a you know something you'll get later + + align:start position:0% +is a you know something you'll get later + + + align:start position:0% +is a you know something you'll get later +in the class we start doing sort of a + + align:start position:0% +in the class we start doing sort of a + + + align:start position:0% +in the class we start doing sort of a +lot of people in iio are doing sort of + + align:start position:0% +lot of people in iio are doing sort of + + + align:start position:0% +lot of people in iio are doing sort of +structural models of dynamic situations + + align:start position:0% +structural models of dynamic situations + + + align:start position:0% +structural models of dynamic situations +where you're always assuming firms + + align:start position:0% +where you're always assuming firms + + + align:start position:0% +where you're always assuming firms +follow these Markov perfect strategies + + align:start position:0% +follow these Markov perfect strategies + + + align:start position:0% +follow these Markov perfect strategies +this Markov maximization is in some + + align:start position:0% +this Markov maximization is in some + + + align:start position:0% +this Markov maximization is in some +sense always a firm with commitment + + align:start position:0% +sense always a firm with commitment + + + align:start position:0% +sense always a firm with commitment +problems where it's every period the + + align:start position:0% +problems where it's every period the + + + align:start position:0% +problems where it's every period the +firm is choosing the optimal action + + align:start position:0% +firm is choosing the optimal action + + + align:start position:0% +firm is choosing the optimal action +given that state you know our skepticism + + align:start position:0% +given that state you know our skepticism + + + align:start position:0% +given that state you know our skepticism +of the coast conjecture sort of some + + align:start position:0% +of the coast conjecture sort of some + + + align:start position:0% +of the coast conjecture sort of some +sense should translate to skepticism of + + align:start position:0% +sense should translate to skepticism of + + + align:start position:0% +sense should translate to skepticism of +some of those models or at least think + + align:start position:0% +some of those models or at least think + + + align:start position:0% +some of those models or at least think +about are do we really think the firms + + align:start position:0% +about are do we really think the firms + + + align:start position:0% +about are do we really think the firms +lack commitment power and are always + + align:start position:0% +lack commitment power and are always + + + align:start position:0% +lack commitment power and are always +going to be maximizing period by period + + align:start position:0% +going to be maximizing period by period + + + align:start position:0% +going to be maximizing period by period +what's optimal for + + align:start position:0% +what's optimal for + + + align:start position:0% +what's optimal for +them okay um okay so then the final + + align:start position:0% +them okay um okay so then the final + + + align:start position:0% +them okay um okay so then the final +topic I want to talk about today and + + align:start position:0% +topic I want to talk about today and + + + align:start position:0% +topic I want to talk about today and +I'll I'll see if I have time to finish + + align:start position:0% +I'll I'll see if I have time to finish + + + align:start position:0% +I'll I'll see if I have time to finish +it is uh this is a more recent Topic in + + align:start position:0% +it is uh this is a more recent Topic in + + + align:start position:0% +it is uh this is a more recent Topic in +IO and if you wanted to do IO theory on + + align:start position:0% +IO and if you wanted to do IO theory on + + + align:start position:0% +IO and if you wanted to do IO theory on +Monopoly pricing as a thesis topic um + + align:start position:0% +Monopoly pricing as a thesis topic um + + + align:start position:0% +Monopoly pricing as a thesis topic um +you know this would be the active area + + align:start position:0% +you know this would be the active area + + + align:start position:0% +you know this would be the active area +of IO Monopoly pricing you could work on + + align:start position:0% +of IO Monopoly pricing you could work on + + + align:start position:0% +of IO Monopoly pricing you could work on +today uh so I'll sort of give an + + align:start position:0% +today uh so I'll sort of give an + + + align:start position:0% +today uh so I'll sort of give an +overview of information design and + + align:start position:0% +overview of information design and + + + align:start position:0% +overview of information design and +obviously I would say if you really want + + align:start position:0% +obviously I would say if you really want + + + align:start position:0% +obviously I would say if you really want +to study information design uh uh + + align:start position:0% +to study information design uh uh + + + align:start position:0% +to study information design uh uh +Stephen and Ian in the 281 class do a + + align:start position:0% +Stephen and Ian in the 281 class do a + + + align:start position:0% +Stephen and Ian in the 281 class do a +lot of information design and you would + + align:start position:0% +lot of information design and you would + + + align:start position:0% +lot of information design and you would +want to know information design at the + + align:start position:0% +want to know information design at the + + + align:start position:0% +want to know information design at the +level at which they teach it but um you + + align:start position:0% +level at which they teach it but um you + + + align:start position:0% +level at which they teach it but um you +I think basics for this I'm going to + + align:start position:0% +I think basics for this I'm going to + + + align:start position:0% +I think basics for this I'm going to +cover here as well so you motivating + + align:start position:0% +cover here as well so you motivating + + + align:start position:0% +cover here as well so you motivating +lure for this is that you know it is an + + align:start position:0% +lure for this is that you know it is an + + + align:start position:0% +lure for this is that you know it is an +interesting observation that when you + + align:start position:0% +interesting observation that when you + + + align:start position:0% +interesting observation that when you +look at Goods there are some goods for + + align:start position:0% +look at Goods there are some goods for + + + align:start position:0% +look at Goods there are some goods for +which you seem to get an awful lot of + + align:start position:0% +which you seem to get an awful lot of + + + align:start position:0% +which you seem to get an awful lot of +information about what you're buying and + + align:start position:0% +information about what you're buying and + + + align:start position:0% +information about what you're buying and +some for which you seem to get very + + align:start position:0% +some for which you seem to get very + + + align:start position:0% +some for which you seem to get very +little information about what you're + + align:start position:0% +little information about what you're + + + align:start position:0% +little information about what you're +buying so an example of a good where you + + align:start position:0% +buying so an example of a good where you + + + align:start position:0% +buying so an example of a good where you +seem to get a lot of information is you + + align:start position:0% +seem to get a lot of information is you + + + align:start position:0% +seem to get a lot of information is you +want to buy a new laptop + + align:start position:0% +want to buy a new laptop + + + align:start position:0% +want to buy a new laptop +computer you know you can get on the + + align:start position:0% +computer you know you can get on the + + + align:start position:0% +computer you know you can get on the +site and the firms that are selling you + + align:start position:0% +site and the firms that are selling you + + + align:start position:0% +site and the firms that are selling you +laptop computers you know they're going + + align:start position:0% +laptop computers you know they're going + + + align:start position:0% +laptop computers you know they're going +to tell you exactly how many pixels are + + align:start position:0% +to tell you exactly how many pixels are + + + align:start position:0% +to tell you exactly how many pixels are +in the screen they're going to tell you + + align:start position:0% +in the screen they're going to tell you + + + align:start position:0% +in the screen they're going to tell you +what processor is in it what the + + align:start position:0% +what processor is in it what the + + + align:start position:0% +what processor is in it what the +processor speed is what the um you know + + align:start position:0% +processor speed is what the um you know + + + align:start position:0% +processor speed is what the um you know +what the battery life is what the + + align:start position:0% +what the battery life is what the + + + align:start position:0% +what the battery life is what the +battery power is how much the laptop + + align:start position:0% +battery power is how much the laptop + + + align:start position:0% +battery power is how much the laptop +weighs what it's made out of you can get + + align:start position:0% +weighs what it's made out of you can get + + + align:start position:0% +weighs what it's made out of you can get +a tremendous amount of information about + + align:start position:0% +a tremendous amount of information about + + + align:start position:0% +a tremendous amount of information about +every laptop top that you're considering + + align:start position:0% +every laptop top that you're considering + + + align:start position:0% +every laptop top that you're considering +buying uh I don't know how many of you + + align:start position:0% +buying uh I don't know how many of you + + + align:start position:0% +buying uh I don't know how many of you +moved here recently and tried to buy a + + align:start position:0% +moved here recently and tried to buy a + + + align:start position:0% +moved here recently and tried to buy a +mattress in the United States you try to + + align:start position:0% +mattress in the United States you try to + + + align:start position:0% +mattress in the United States you try to +buy a mattress in the United States and + + align:start position:0% +buy a mattress in the United States and + + + align:start position:0% +buy a mattress in the United States and +just you know there are lots of these + + align:start position:0% +just you know there are lots of these + + + align:start position:0% +just you know there are lots of these +mattress stores and they sell really + + align:start position:0% +mattress stores and they sell really + + + align:start position:0% +mattress stores and they sell really +expensive like it's often like you know + + align:start position:0% +expensive like it's often like you know + + + align:start position:0% +expensive like it's often like you know +this mattress is $1,200 or this one is + + align:start position:0% +this mattress is $1,200 or this one is + + + align:start position:0% +this mattress is $1,200 or this one is +$300 + + align:start position:0% +$300 + + + align:start position:0% +$300 +and it's just impossible to figure out + + align:start position:0% +and it's just impossible to figure out + + + align:start position:0% +and it's just impossible to figure out +like what makes mattress a different + + align:start position:0% +like what makes mattress a different + + + align:start position:0% +like what makes mattress a different +from mattress B and you might even think + + align:start position:0% +from mattress B and you might even think + + + align:start position:0% +from mattress B and you might even think +okay I'll go to four different stores + + align:start position:0% +okay I'll go to four different stores + + + align:start position:0% +okay I'll go to four different stores +all of whom sell cely pasture + + align:start position:0% +all of whom sell cely pasture + + + align:start position:0% +all of whom sell cely pasture +Posturepedic mattresses and comparison + + align:start position:0% +Posturepedic mattresses and comparison + + + align:start position:0% +Posturepedic mattresses and comparison +shop and you'll you see that like this + + align:start position:0% +shop and you'll you see that like this + + + align:start position:0% +shop and you'll you see that like this +store has the Cy Posturepedic Ruby and + + align:start position:0% +store has the Cy Posturepedic Ruby and + + + align:start position:0% +store has the Cy Posturepedic Ruby and +diamond and emerald and this store has + + align:start position:0% +diamond and emerald and this store has + + + align:start position:0% +diamond and emerald and this store has +the C poster Pedic gold and platinum and + + align:start position:0% +the C poster Pedic gold and platinum and + + + align:start position:0% +the C poster Pedic gold and platinum and +bronze and this one has a Seely P + + align:start position:0% +bronze and this one has a Seely P + + + align:start position:0% +bronze and this one has a Seely P +Posturepedic cloud and Mountain and + + align:start position:0% +Posturepedic cloud and Mountain and + + + align:start position:0% +Posturepedic cloud and Mountain and +Valley or something and like they just + + align:start position:0% +Valley or something and like they just + + + align:start position:0% +Valley or something and like they just +every different store like even if it's + + align:start position:0% +every different store like even if it's + + + align:start position:0% +every different store like even if it's +the same brand of mattress they have all + + align:start position:0% +the same brand of mattress they have all + + + align:start position:0% +the same brand of mattress they have all +different names on them and no one + + align:start position:0% +different names on them and no one + + + align:start position:0% +different names on them and no one +giving you any attribute like the coils + + align:start position:0% +giving you any attribute like the coils + + + align:start position:0% +giving you any attribute like the coils +in this one are 73 Ms thick and the + + align:start position:0% +in this one are 73 Ms thick and the + + + align:start position:0% +in this one are 73 Ms thick and the +memory foam has this compression per + + align:start position:0% +memory foam has this compression per + + + align:start position:0% +memory foam has this compression per +unit thing + + align:start position:0% +unit thing + + + align:start position:0% +unit thing +and you know right given that you can't + + align:start position:0% +and you know right given that you can't + + + align:start position:0% +and you know right given that you can't +actually sleep on them in the store it + + align:start position:0% +actually sleep on them in the store it + + + align:start position:0% +actually sleep on them in the store it +just seems like there's no information + + align:start position:0% +just seems like there's no information + + + align:start position:0% +just seems like there's no information +whatsoever to compare these matches and + + align:start position:0% +whatsoever to compare these matches and + + + align:start position:0% +whatsoever to compare these matches and +figure out which do I want to pay $100 + + align:start position:0% +figure out which do I want to pay $100 + + + align:start position:0% +figure out which do I want to pay $100 +for this one instead of that one um + + align:start position:0% +for this one instead of that one um + + + align:start position:0% +for this one instead of that one um +wholesale used cars are almost one of + + align:start position:0% +wholesale used cars are almost one of + + + align:start position:0% +wholesale used cars are almost one of +the most interesting examples of + + align:start position:0% +the most interesting examples of + + + align:start position:0% +the most interesting examples of +explicit lack of information so you know + + align:start position:0% +explicit lack of information so you know + + + align:start position:0% +explicit lack of information so you know +you turn your car into a dealer um like + + align:start position:0% +you turn your car into a dealer um like + + + align:start position:0% +you turn your car into a dealer um like +let's suppose that you had a car U you + + align:start position:0% +let's suppose that you had a car U you + + + align:start position:0% +let's suppose that you had a car U you +know I I I you know I have my Honda + + align:start position:0% +know I I I you know I have my Honda + + + align:start position:0% +know I I I you know I have my Honda +Civic I decide I want to buy a Toyota I + + align:start position:0% +Civic I decide I want to buy a Toyota I + + + align:start position:0% +Civic I decide I want to buy a Toyota I +turn in my old Honda Civic to the Toyota + + align:start position:0% +turn in my old Honda Civic to the Toyota + + + align:start position:0% +turn in my old Honda Civic to the Toyota +dealer when I buy my Toyota and then my + + align:start position:0% +dealer when I buy my Toyota and then my + + + align:start position:0% +dealer when I buy my Toyota and then my +Toyota dealer doesn't want to have a + + align:start position:0% +Toyota dealer doesn't want to have a + + + align:start position:0% +Toyota dealer doesn't want to have a +Honda so he takes and sells it at the + + align:start position:0% +Honda so he takes and sells it at the + + + align:start position:0% +Honda so he takes and sells it at the +wholesale level to some Honda dealer + + align:start position:0% +wholesale level to some Honda dealer + + + align:start position:0% +wholesale level to some Honda dealer +somewhere who wants to have a used Honda + + align:start position:0% +somewhere who wants to have a used Honda + + + align:start position:0% +somewhere who wants to have a used Honda +on their + + align:start position:0% +on their + + + align:start position:0% +on their +lot um you go to see these wholesale + + align:start position:0% +lot um you go to see these wholesale + + + align:start position:0% +lot um you go to see these wholesale +used car auctions and it's a remarkable + + align:start position:0% +used car auctions and it's a remarkable + + + align:start position:0% +used car auctions and it's a remarkable +thing like they have these giant parking + + align:start position:0% +thing like they have these giant parking + + + align:start position:0% +thing like they have these giant parking +lots uh in the middle of nowhere with + + align:start position:0% +lots uh in the middle of nowhere with + + + align:start position:0% +lots uh in the middle of nowhere with +like you know some big building next to + + align:start position:0% +like you know some big building next to + + + align:start position:0% +like you know some big building next to +them all the used car dealers show up + + align:start position:0% +them all the used car dealers show up + + + align:start position:0% +them all the used car dealers show up +with cars to sell and have their cars + + align:start position:0% +with cars to sell and have their cars + + + align:start position:0% +with cars to sell and have their cars +listed for sale and then a bunch of + + align:start position:0% +listed for sale and then a bunch of + + + align:start position:0% +listed for sale and then a bunch of +people have the cars listed to + + align:start position:0% +people have the cars listed to + + + align:start position:0% +people have the cars listed to +buy and the rules for the wholesale used + + align:start position:0% +buy and the rules for the wholesale used + + + align:start position:0% +buy and the rules for the wholesale used +car auction is they drive the like you + + align:start position:0% +car auction is they drive the like you + + + align:start position:0% +car auction is they drive the like you +know 2013 Honda Civic 63,000 miles up + + align:start position:0% +know 2013 Honda Civic 63,000 miles up + + + align:start position:0% +know 2013 Honda Civic 63,000 miles up +there all the buyers are allowed to look + + align:start position:0% +there all the buyers are allowed to look + + + align:start position:0% +there all the buyers are allowed to look +at the car from the inside a guy who + + align:start position:0% +at the car from the inside a guy who + + + align:start position:0% +at the car from the inside a guy who +works um at the auction house starts the + + align:start position:0% +works um at the auction house starts the + + + align:start position:0% +works um at the auction house starts the +engine you can hear the car that the car + + align:start position:0% +engine you can hear the car that the car + + + align:start position:0% +engine you can hear the car that the car +runs you can look at it from the outside + + align:start position:0% +runs you can look at it from the outside + + + align:start position:0% +runs you can look at it from the outside +you may not open the hood and look under + + align:start position:0% +you may not open the hood and look under + + + align:start position:0% +you may not open the hood and look under +the hood you may not look under it with + + align:start position:0% +the hood you may not look under it with + + + align:start position:0% +the hood you may not look under it with +the mirror and see whether the M the + + align:start position:0% +the mirror and see whether the M the + + + align:start position:0% +the mirror and see whether the M the +muffler is rusted out you may not like + + align:start position:0% +muffler is rusted out you may not like + + + align:start position:0% +muffler is rusted out you may not like +have your mechanic try out all the parts + + align:start position:0% +have your mechanic try out all the parts + + + align:start position:0% +have your mechanic try out all the parts +it's like the car is wheeled up there + + align:start position:0% +it's like the car is wheeled up there + + + align:start position:0% +it's like the car is wheeled up there +everything stays closed except for the + + align:start position:0% +everything stays closed except for the + + + align:start position:0% +everything stays closed except for the +guy from the dealer turns it on runs the + + align:start position:0% +guy from the dealer turns it on runs the + + + align:start position:0% +guy from the dealer turns it on runs the +thing they then auction off in 45 + + align:start position:0% +thing they then auction off in 45 + + + align:start position:0% +thing they then auction off in 45 +seconds and move on to the next car so + + align:start position:0% +seconds and move on to the next car so + + + align:start position:0% +seconds and move on to the next car so +basically they provide no information + + align:start position:0% +basically they provide no information + + + align:start position:0% +basically they provide no information +whatsoever on the car that's being sold + + align:start position:0% +whatsoever on the car that's being sold + + + align:start position:0% +whatsoever on the car that's being sold +other than Honda Civic 2013 6300 miles + + align:start position:0% +other than Honda Civic 2013 6300 miles + + + align:start position:0% +other than Honda Civic 2013 6300 miles +here's what the the engine turns on + + align:start position:0% +here's what the the engine turns on + + + align:start position:0% +here's what the the engine turns on +here's what it sounds like this is what + + align:start position:0% +here's what it sounds like this is what + + + align:start position:0% +here's what it sounds like this is what +it looks like from the outside and then + + align:start position:0% +it looks like from the outside and then + + + align:start position:0% +it looks like from the outside and then +the next one is + + align:start position:0% +the next one is + + + align:start position:0% +the next one is +sold and is clearly an intentional + + align:start position:0% +sold and is clearly an intentional + + + align:start position:0% +sold and is clearly an intentional +design to provide zero information to + + align:start position:0% +design to provide zero information to + + + align:start position:0% +design to provide zero information to +the buyers um okay um these examples + + align:start position:0% +the buyers um okay um these examples + + + align:start position:0% +the buyers um okay um these examples +these are ones we think of is these are + + align:start position:0% +these are ones we think of is these are + + + align:start position:0% +these are ones we think of is these are +clearly pure Monopoly pricing decisions + + align:start position:0% +clearly pure Monopoly pricing decisions + + + align:start position:0% +clearly pure Monopoly pricing decisions +that that somehow the mon the ma + + align:start position:0% +that that somehow the mon the ma + + + align:start position:0% +that that somehow the mon the ma +Mattress Firm the laptop firm the used + + align:start position:0% +Mattress Firm the laptop firm the used + + + align:start position:0% +Mattress Firm the laptop firm the used +car firms they've decided that providing + + align:start position:0% +car firms they've decided that providing + + + align:start position:0% +car firms they've decided that providing +this information to their consumers is + + align:start position:0% +this information to their consumers is + + + align:start position:0% +this information to their consumers is +what maximizes their profits because + + align:start position:0% +what maximizes their profits because + + + align:start position:0% +what maximizes their profits because +they're controlling the information flow + + align:start position:0% +they're controlling the information flow + + + align:start position:0% +they're controlling the information flow +okay um there are other examples now I + + align:start position:0% +okay um there are other examples now I + + + align:start position:0% +okay um there are other examples now I +guess which is caus view on another side + + align:start position:0% +guess which is caus view on another side + + + align:start position:0% +guess which is caus view on another side +which is is that they're now like plenty + + align:start position:0% +which is is that they're now like plenty + + + align:start position:0% +which is is that they're now like plenty +of intermediaries that make fir make + + align:start position:0% +of intermediaries that make fir make + + + align:start position:0% +of intermediaries that make fir make +money by providing information about + + align:start position:0% +money by providing information about + + + align:start position:0% +money by providing information about +products and helping consumers find + + align:start position:0% +products and helping consumers find + + + align:start position:0% +products and helping consumers find +products they want so for instance you + + align:start position:0% +products they want so for instance you + + + align:start position:0% +products they want so for instance you +know Yelp helps people find restaurants + + align:start position:0% +know Yelp helps people find restaurants + + + align:start position:0% +know Yelp helps people find restaurants +Amazon sells many things that are not + + align:start position:0% +Amazon sells many things that are not + + + align:start position:0% +Amazon sells many things that are not +Amazon products helping you to find + + align:start position:0% +Amazon products helping you to find + + + align:start position:0% +Amazon products helping you to find +what's the best phone for me to buy + + align:start position:0% +what's the best phone for me to buy + + + align:start position:0% +what's the best phone for me to buy +what's the best you know tent for me to + + align:start position:0% +what's the best you know tent for me to + + + align:start position:0% +what's the best you know tent for me to +buy what's the best uh you know what's + + align:start position:0% +buy what's the best uh you know what's + + + align:start position:0% +buy what's the best uh you know what's +the best shirt for me to buy what are + + align:start position:0% +the best shirt for me to buy what are + + + align:start position:0% +the best shirt for me to buy what are +the best pair of hiking boots whatever + + align:start position:0% +the best pair of hiking boots whatever + + + align:start position:0% +the best pair of hiking boots whatever +Amazon is sort of selling these products + + align:start position:0% +Amazon is sort of selling these products + + + align:start position:0% +Amazon is sort of selling these products +that they don't make and just providing + + align:start position:0% +that they don't make and just providing + + + align:start position:0% +that they don't make and just providing +you information about + + align:start position:0% +you information about + + + align:start position:0% +you information about +them one concern that you can think + + align:start position:0% +them one concern that you can think + + + align:start position:0% +them one concern that you can think +about you know like what what does + + align:start position:0% +about you know like what what does + + + align:start position:0% +about you know like what what does +Amazon want you to do Amazon wants you + + align:start position:0% +Amazon want you to do Amazon wants you + + + align:start position:0% +Amazon want you to do Amazon wants you +to buy products from + + align:start position:0% +to buy products from + + + align:start position:0% +to buy products from +Amazon uh Amazon therefore wants to + + align:start position:0% +Amazon uh Amazon therefore wants to + + + align:start position:0% +Amazon uh Amazon therefore wants to +provide you with consumer surplus when + + align:start position:0% +provide you with consumer surplus when + + + align:start position:0% +provide you with consumer surplus when +you're buying these thirdparty products + + align:start position:0% +you're buying these thirdparty products + + + align:start position:0% +you're buying these thirdparty products +that you buy the third party products + + align:start position:0% +that you buy the third party products + + + align:start position:0% +that you buy the third party products +you get consumer surplus you keep coming + + align:start position:0% +you get consumer surplus you keep coming + + + align:start position:0% +you get consumer surplus you keep coming +back to Amazon as a place to start your + + align:start position:0% +back to Amazon as a place to start your + + + align:start position:0% +back to Amazon as a place to start your +shopping + + align:start position:0% +shopping + + + align:start position:0% +shopping +trips what information what information + + align:start position:0% +trips what information what information + + + align:start position:0% +trips what information what information +problem they have is that let's suppose + + align:start position:0% +problem they have is that let's suppose + + + align:start position:0% +problem they have is that let's suppose +they provide you with some number of + + align:start position:0% +they provide you with some number of + + + align:start position:0% +they provide you with some number of +information about the good if they + + align:start position:0% +information about the good if they + + + align:start position:0% +information about the good if they +provide you with information that let + + align:start position:0% +provide you with information that let + + + align:start position:0% +provide you with information that let +you figure out yes this is the perfect + + align:start position:0% +you figure out yes this is the perfect + + + align:start position:0% +you figure out yes this is the perfect +pair of hiking boots for + + align:start position:0% +pair of hiking boots for + + + align:start position:0% +pair of hiking boots for +me then the hiking boot company knowing + + align:start position:0% +me then the hiking boot company knowing + + + align:start position:0% +me then the hiking boot company knowing +that Amazon is selling it only to the + + align:start position:0% +that Amazon is selling it only to the + + + align:start position:0% +that Amazon is selling it only to the +consumers for whom it's the perfect + + align:start position:0% +consumers for whom it's the perfect + + + align:start position:0% +consumers for whom it's the perfect +product will set a really high price and + + align:start position:0% +product will set a really high price and + + + align:start position:0% +product will set a really high price and +the consumer surplus will be low so + + align:start position:0% +the consumer surplus will be low so + + + align:start position:0% +the consumer surplus will be low so +sometimes Amazon has this problem of if + + align:start position:0% +sometimes Amazon has this problem of if + + + align:start position:0% +sometimes Amazon has this problem of if +they provide information let you figure + + align:start position:0% +they provide information let you figure + + + align:start position:0% +they provide information let you figure +out + + align:start position:0% +out + + + align:start position:0% +out +exactly how good the product is for you + + align:start position:0% +exactly how good the product is for you + + + align:start position:0% +exactly how good the product is for you +and what is is you know in some sense + + align:start position:0% +and what is is you know in some sense + + + align:start position:0% +and what is is you know in some sense +trying to maximize the The Profit + + align:start position:0% +trying to maximize the The Profit + + + align:start position:0% +trying to maximize the The Profit +maximizing set of information then it + + align:start position:0% +maximizing set of information then it + + + align:start position:0% +maximizing set of information then it +maybe the monopolis then just raises the + + align:start position:0% +maybe the monopolis then just raises the + + + align:start position:0% +maybe the monopolis then just raises the +price and extracts all that Surplus and + + align:start position:0% +price and extracts all that Surplus and + + + align:start position:0% +price and extracts all that Surplus and +then the consumers get no Surplus and + + align:start position:0% +then the consumers get no Surplus and + + + align:start position:0% +then the consumers get no Surplus and +then Amazon isn't the place to start + + align:start position:0% +then Amazon isn't the place to start + + + align:start position:0% +then Amazon isn't the place to start +shopping because it's the place where + + align:start position:0% +shopping because it's the place where + + + align:start position:0% +shopping because it's the place where +yes you found what you wanted but yes + + align:start position:0% +yes you found what you wanted but yes + + + align:start position:0% +yes you found what you wanted but yes +you also paid a super premium price and + + align:start position:0% +you also paid a super premium price and + + + align:start position:0% +you also paid a super premium price and +therefore you didn't get any surplus + + align:start position:0% +therefore you didn't get any surplus + + + align:start position:0% +therefore you didn't get any surplus +anyway okay um so you know these kinds + + align:start position:0% +anyway okay um so you know these kinds + + + align:start position:0% +anyway okay um so you know these kinds +of I think it's sort of the platform + + align:start position:0% +of I think it's sort of the platform + + + align:start position:0% +of I think it's sort of the platform +application and the the developments in + + align:start position:0% +application and the the developments in + + + align:start position:0% +application and the the developments in +theory where this growth of what we call + + align:start position:0% +theory where this growth of what we call + + + align:start position:0% +theory where this growth of what we call +information design thinking + + align:start position:0% +information design thinking + + + align:start position:0% +information design thinking +about how would a firm that controls + + align:start position:0% +about how would a firm that controls + + + align:start position:0% +about how would a firm that controls +information products want to provide + + align:start position:0% +information products want to provide + + + align:start position:0% +information products want to provide +that information either to maximize its + + align:start position:0% +that information either to maximize its + + + align:start position:0% +that information either to maximize its +profit selling them directly or to + + align:start position:0% +profit selling them directly or to + + + align:start position:0% +profit selling them directly or to +maximize the consumer surplus of the + + align:start position:0% +maximize the consumer surplus of the + + + align:start position:0% +maximize the consumer surplus of the +consumers who it's not selling them who + + align:start position:0% +consumers who it's not selling them who + + + align:start position:0% +consumers who it's not selling them who +who are it's if it's an intermediary it + + align:start position:0% +who are it's if it's an intermediary it + + + align:start position:0% +who are it's if it's an intermediary it +wants to maximize a consumer surplus + + align:start position:0% +wants to maximize a consumer surplus + + + align:start position:0% +wants to maximize a consumer surplus +rather than the profit or it might want + + align:start position:0% +rather than the profit or it might want + + + align:start position:0% +rather than the profit or it might want +to do something in + + align:start position:0% +to do something in + + + align:start position:0% +to do something in +between so to think about an example for + + align:start position:0% +between so to think about an example for + + + align:start position:0% +between so to think about an example for +illustration um let's assume that we + + align:start position:0% +illustration um let's assume that we + + + align:start position:0% +illustration um let's assume that we +have a new product maybe this this uh + + align:start position:0% +have a new product maybe this this uh + + + align:start position:0% +have a new product maybe this this uh +new product is uh you know uh cover has + + align:start position:0% +new product is uh you know uh cover has + + + align:start position:0% +new product is uh you know uh cover has +a new fried cauliflower sandwich with + + align:start position:0% +a new fried cauliflower sandwich with + + + align:start position:0% +a new fried cauliflower sandwich with +some kind of Chinese + + align:start position:0% +some kind of Chinese + + + align:start position:0% +some kind of Chinese +sauce on it or indo-chinese + + align:start position:0% +sauce on it or indo-chinese + + + align:start position:0% +sauce on it or indo-chinese +uh fried cauliflower sandwich which I + + align:start position:0% +uh fried cauliflower sandwich which I + + + align:start position:0% +uh fried cauliflower sandwich which I +think they do have um so suppose that + + align:start position:0% +think they do have um so suppose that + + + align:start position:0% +think they do have um so suppose that +fully informed consumers if they really + + align:start position:0% +fully informed consumers if they really + + + align:start position:0% +fully informed consumers if they really +understood what the sandwich tasted like + + align:start position:0% +understood what the sandwich tasted like + + + align:start position:0% +understood what the sandwich tasted like +would have values V distributed uniform + + align:start position:0% +would have values V distributed uniform + + + align:start position:0% +would have values V distributed uniform +01 or maybe in this case uniform + + align:start position:0% +01 or maybe in this case uniform + + + align:start position:0% +01 or maybe in this case uniform +018 um suppose that the monopolis has a + + align:start position:0% +018 um suppose that the monopolis has a + + + align:start position:0% +018 um suppose that the monopolis has a +constant marginal cost of a third so $6 + + align:start position:0% +constant marginal cost of a third so $6 + + + align:start position:0% +constant marginal cost of a third so $6 +in this example + + align:start position:0% +in this example + + + align:start position:0% +in this example +okay um what are you going to do do if + + align:start position:0% +okay um what are you going to do do if + + + align:start position:0% +okay um what are you going to do do if +consumers are fully informed they have + + align:start position:0% +consumers are fully informed they have + + + align:start position:0% +consumers are fully informed they have +values uniform 01 you have a cost of a + + align:start position:0% +values uniform 01 you have a cost of a + + + align:start position:0% +values uniform 01 you have a cost of a +third you know you maximize P minus A3 + + align:start position:0% +third you know you maximize P minus A3 + + + align:start position:0% +third you know you maximize P minus A3 +times 1 minus P Monopoly price is 2/3 so + + align:start position:0% +times 1 minus P Monopoly price is 2/3 so + + + align:start position:0% +times 1 minus P Monopoly price is 2/3 so +we get this situation of the your cost + + align:start position:0% +we get this situation of the your cost + + + align:start position:0% +we get this situation of the your cost +is 1/3 you set a price of 2/3 onethird + + align:start position:0% +is 1/3 you set a price of 2/3 onethird + + + align:start position:0% +is 1/3 you set a price of 2/3 onethird +of the people buy okay so if I multiply + + align:start position:0% +of the people buy okay so if I multiply + + + align:start position:0% +of the people buy okay so if I multiply +by 18 uh I have a cost of $6 I set the + + align:start position:0% +by 18 uh I have a cost of $6 I set the + + + align:start position:0% +by 18 uh I have a cost of $6 I set the +price at + + align:start position:0% +price at + + + align:start position:0% +price at +$12 uh a third of the people buy my + + align:start position:0% +$12 uh a third of the people buy my + + + align:start position:0% +$12 uh a third of the people buy my +sandwich I make $6 each I make $2 in off + + align:start position:0% +sandwich I make $6 each I make $2 in off + + + align:start position:0% +sandwich I make $6 each I make $2 in off +it + + align:start position:0% +it + + + align:start position:0% +it +okay so that's clearly one thing that + + align:start position:0% +okay so that's clearly one thing that + + + align:start position:0% +okay so that's clearly one thing that +cover could do is just tell everybody + + align:start position:0% +cover could do is just tell everybody + + + align:start position:0% +cover could do is just tell everybody +everything about the sandwich somehow + + align:start position:0% +everything about the sandwich somehow + + + align:start position:0% +everything about the sandwich somehow +convey to them what it tastes like I + + align:start position:0% +convey to them what it tastes like I + + + align:start position:0% +convey to them what it tastes like I +don't quite how they do that but they + + align:start position:0% +don't quite how they do that but they + + + align:start position:0% +don't quite how they do that but they +convey it people get these values you + + align:start position:0% +convey it people get these values you + + + align:start position:0% +convey it people get these values you +know maybe they give free sandwiches to + + align:start position:0% +know maybe they give free sandwiches to + + + align:start position:0% +know maybe they give free sandwiches to +everyone's they all learn their values + + align:start position:0% +everyone's they all learn their values + + + align:start position:0% +everyone's they all learn their values +um they learn their learn their v's and + + align:start position:0% +um they learn their learn their v's and + + + align:start position:0% +um they learn their learn their v's and +then they Monopoly price relative to + + align:start position:0% +then they Monopoly price relative to + + + align:start position:0% +then they Monopoly price relative to +those values + + align:start position:0% +those values + + + align:start position:0% +those values +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um what else could you do um imagine + + align:start position:0% +um what else could you do um imagine + + + align:start position:0% +um what else could you do um imagine +that you + + align:start position:0% +that you + + + align:start position:0% +that you +know consumers learn their + + align:start position:0% +know consumers learn their + + + align:start position:0% +know consumers learn their +values not you know like consumers have + + align:start position:0% +values not you know like consumers have + + + align:start position:0% +values not you know like consumers have +to learn their value somewhere like I + + align:start position:0% +to learn their value somewhere like I + + + align:start position:0% +to learn their value somewhere like I +know there's a new Clover sandwich how + + align:start position:0% +know there's a new Clover sandwich how + + + align:start position:0% +know there's a new Clover sandwich how +would I know whether I like it or not + + align:start position:0% +would I know whether I like it or not + + + align:start position:0% +would I know whether I like it or not +you know I know that I'm rational so I + + align:start position:0% +you know I know that I'm rational so I + + + align:start position:0% +you know I know that I'm rational so I +know that V is distributed uniform + + align:start position:0% +know that V is distributed uniform + + + align:start position:0% +know that V is distributed uniform +018 but I don't know whether I'm one of + + align:start position:0% +018 but I don't know whether I'm one of + + + align:start position:0% +018 but I don't know whether I'm one of +the people who's going to like this + + align:start position:0% +the people who's going to like this + + + align:start position:0% +the people who's going to like this +sandwich or one people who's not going + + align:start position:0% +sandwich or one people who's not going + + + align:start position:0% +sandwich or one people who's not going +to like the sandwich Imagine One Thing + + align:start position:0% +to like the sandwich Imagine One Thing + + + align:start position:0% +to like the sandwich Imagine One Thing +Clover could do is provide no + + align:start position:0% +Clover could do is provide no + + + align:start position:0% +Clover could do is provide no +information whatsoever about this + + align:start position:0% +information whatsoever about this + + + align:start position:0% +information whatsoever about this +sandwich don't even tell you it's got + + align:start position:0% +sandwich don't even tell you it's got + + + align:start position:0% +sandwich don't even tell you it's got +cauliflower don't even tell you what the + + align:start position:0% +cauliflower don't even tell you what the + + + align:start position:0% +cauliflower don't even tell you what the +spice is say this is the new Clover + + align:start position:0% +spice is say this is the new Clover + + + align:start position:0% +spice is say this is the new Clover +sandwich if you're rational you're going + + align:start position:0% +sandwich if you're rational you're going + + + align:start position:0% +sandwich if you're rational you're going +to know that okay there's a new sandwich + + align:start position:0% +to know that okay there's a new sandwich + + + align:start position:0% +to know that okay there's a new sandwich +out there + + align:start position:0% +out there + + + align:start position:0% +out there +um I my value must be somewhere between + + align:start position:0% +um I my value must be somewhere between + + + align:start position:0% +um I my value must be somewhere between +0 and 18 for that sandwich I don't know + + align:start position:0% +0 and 18 for that sandwich I don't know + + + align:start position:0% +0 and 18 for that sandwich I don't know +what that I don't know what that value + + align:start position:0% +what that I don't know what that value + + + align:start position:0% +what that I don't know what that value +is okay um or uniform 01 you know so + + align:start position:0% +is okay um or uniform 01 you know so + + + align:start position:0% +is okay um or uniform 01 you know so +here I would think on average that + + align:start position:0% +here I would think on average that + + + align:start position:0% +here I would think on average that +sandwich is worth $9 me not knowing it's + + align:start position:0% +sandwich is worth $9 me not knowing it's + + + align:start position:0% +sandwich is worth $9 me not knowing it's +it's just in a brown paper bag they've + + align:start position:0% +it's just in a brown paper bag they've + + + align:start position:0% +it's just in a brown paper bag they've +kept all it's a secret sandwich um you + + align:start position:0% +kept all it's a secret sandwich um you + + + align:start position:0% +kept all it's a secret sandwich um you +know my value is a half or nine in that + + align:start position:0% +know my value is a half or nine in that + + + align:start position:0% +know my value is a half or nine in that +example okay U so what the monopolis can + + align:start position:0% +example okay U so what the monopolis can + + + align:start position:0% +example okay U so what the monopolis can +do is sell these sandwiches in the brown + + align:start position:0% +do is sell these sandwiches in the brown + + + align:start position:0% +do is sell these sandwiches in the brown +paper bags to everyone at a price of + + align:start position:0% +paper bags to everyone at a price of + + + align:start position:0% +paper bags to everyone at a price of +nine and so instead of you know selling + + align:start position:0% +nine and so instead of you know selling + + + align:start position:0% +nine and so instead of you know selling +it to the I had the previous example I'd + + align:start position:0% +it to the I had the previous example I'd + + + align:start position:0% +it to the I had the previous example I'd +sell it to oneir of the people at a + + align:start position:0% +sell it to oneir of the people at a + + + align:start position:0% +sell it to oneir of the people at a +price of 12 and earn 1/3 * 12 - 6 is $2 + + align:start position:0% +price of 12 and earn 1/3 * 12 - 6 is $2 + + + align:start position:0% +price of 12 and earn 1/3 * 12 - 6 is $2 +profit now every everyone is willing to + + align:start position:0% +profit now every everyone is willing to + + + align:start position:0% +profit now every everyone is willing to +buy the sandwich in the paper + + align:start position:0% +buy the sandwich in the paper + + + align:start position:0% +buy the sandwich in the paper +bag they're only willing to pay $9 for + + align:start position:0% +bag they're only willing to pay $9 for + + + align:start position:0% +bag they're only willing to pay $9 for +it because they don't know whether + + align:start position:0% +it because they don't know whether + + + align:start position:0% +it because they don't know whether +they's someone who likes the sandwich or + + align:start position:0% +they's someone who likes the sandwich or + + + align:start position:0% +they's someone who likes the sandwich or +someone who hates the sandwich but I get + + align:start position:0% +someone who hates the sandwich but I get + + + align:start position:0% +someone who hates the sandwich but I get +a third * 9 - 6 is + + align:start position:0% +a third * 9 - 6 is + + + align:start position:0% +a third * 9 - 6 is +three so I've made more money by hiding + + align:start position:0% +three so I've made more money by hiding + + + align:start position:0% +three so I've made more money by hiding +what my product + + align:start position:0% +what my product + + + align:start position:0% +what my product +is + + align:start position:0% +is + + + align:start position:0% +is +okay and how have I made more money by + + align:start position:0% +okay and how have I made more money by + + + align:start position:0% +okay and how have I made more money by +hiding what my product is well social + + align:start position:0% +hiding what my product is well social + + + align:start position:0% +hiding what my product is well social +surplus has gone down there are all + + align:start position:0% +surplus has gone down there are all + + + align:start position:0% +surplus has gone down there are all +these people with low values for the + + align:start position:0% +these people with low values for the + + + align:start position:0% +these people with low values for the +sandwich values below six who should not + + align:start position:0% +sandwich values below six who should not + + + align:start position:0% +sandwich values below six who should not +that sandwich should not be sold to them + + align:start position:0% +that sandwich should not be sold to them + + + align:start position:0% +that sandwich should not be sold to them +there's this inefficient production that + + align:start position:0% +there's this inefficient production that + + + align:start position:0% +there's this inefficient production that +there + + align:start position:0% +there + + + align:start position:0% +there +people who don't even like the sandwich + + align:start position:0% +people who don't even like the sandwich + + + align:start position:0% +people who don't even like the sandwich +it's being produced and sold to but I've + + align:start position:0% +it's being produced and sold to but I've + + + align:start position:0% +it's being produced and sold to but I've +eliminated the Monopoly dead weight loss + + align:start position:0% +eliminated the Monopoly dead weight loss + + + align:start position:0% +eliminated the Monopoly dead weight loss +that came from these people with values + + align:start position:0% +that came from these people with values + + + align:start position:0% +that came from these people with values +between six and 12 not getting a + + align:start position:0% +between six and 12 not getting a + + + align:start position:0% +between six and 12 not getting a +sandwich because I was Monopoly pricing + + align:start position:0% +sandwich because I was Monopoly pricing + + + align:start position:0% +sandwich because I was Monopoly pricing +at 12 and so because I'm extracting all + + align:start position:0% +at 12 and so because I'm extracting all + + + align:start position:0% +at 12 and so because I'm extracting all +the consumer surplus or I've driven + + align:start position:0% +the consumer surplus or I've driven + + + align:start position:0% +the consumer surplus or I've driven +consumer surplus to zero total social + + align:start position:0% +consumer surplus to zero total social + + + align:start position:0% +consumer surplus to zero total social +Surplus has gone down but because + + align:start position:0% +Surplus has gone down but because + + + align:start position:0% +Surplus has gone down but because +consumer surplus went down even faster + + align:start position:0% +consumer surplus went down even faster + + + align:start position:0% +consumer surplus went down even faster +than social surplus went up + + align:start position:0% +than social surplus went up + + + align:start position:0% +than social surplus went up +um uh suppressing information is + + align:start position:0% +um uh suppressing information is + + + align:start position:0% +um uh suppressing information is +transferred Surplus and the monopolis is + + align:start position:0% +transferred Surplus and the monopolis is + + + align:start position:0% +transferred Surplus and the monopolis is +better off so this is just an extreme + + align:start position:0% +better off so this is just an extreme + + + align:start position:0% +better off so this is just an extreme +example where I hide information about + + align:start position:0% +example where I hide information about + + + align:start position:0% +example where I hide information about +my product my profits go up and it goes + + align:start position:0% +my product my profits go up and it goes + + + align:start position:0% +my product my profits go up and it goes +up because I've made consumers + + align:start position:0% +up because I've made consumers + + + align:start position:0% +up because I've made consumers +homogeneous by making them homogeneous I + + align:start position:0% +homogeneous by making them homogeneous I + + + align:start position:0% +homogeneous by making them homogeneous I +can extract all their Surplus and that's + + align:start position:0% +can extract all their Surplus and that's + + + align:start position:0% +can extract all their Surplus and that's +sort of a you know it's a socially was + + align:start position:0% +sort of a you know it's a socially was + + + align:start position:0% +sort of a you know it's a socially was +but it's a it's a transfer from the + + align:start position:0% +but it's a it's a transfer from the + + + align:start position:0% +but it's a it's a transfer from the +consumers to monopolis and it makes the + + align:start position:0% +consumers to monopolis and it makes the + + + align:start position:0% +consumers to monopolis and it makes the +monopis better + + align:start position:0% +monopis better + + + align:start position:0% +monopis better +off + + align:start position:0% + + + + align:start position:0% + +okay so anyway that's one thing cover + + align:start position:0% +okay so anyway that's one thing cover + + + align:start position:0% +okay so anyway that's one thing cover +could do here + + align:start position:0% +could do here + + + align:start position:0% +could do here +um second observation is that you can + + align:start position:0% +um second observation is that you can + + + align:start position:0% +um second observation is that you can +also have examples like this + + align:start position:0% +also have examples like this + + + align:start position:0% +also have examples like this +where um + + align:start position:0% +where um + + + align:start position:0% +where um +providing less than full information + + align:start position:0% +providing less than full information + + + align:start position:0% +providing less than full information +actually makes the consumer surplus go + + align:start position:0% +actually makes the consumer surplus go + + + align:start position:0% +actually makes the consumer surplus go +up so here's an example of again this is + + align:start position:0% +up so here's an example of again this is + + + align:start position:0% +up so here's an example of again this is +like think about Amazon trying to or or + + align:start position:0% +like think about Amazon trying to or or + + + align:start position:0% +like think about Amazon trying to or or +Yelp trying to sell through + + align:start position:0% +Yelp trying to sell through + + + align:start position:0% +Yelp trying to sell through +Clover provide information about Clover + + align:start position:0% +Clover provide information about Clover + + + align:start position:0% +Clover provide information about Clover +sandwiches to people um + + align:start position:0% +sandwiches to people um + + + align:start position:0% +sandwiches to people um +and uh make and and give the consumers + + align:start position:0% +and uh make and and give the consumers + + + align:start position:0% +and uh make and and give the consumers +more Surplus by using the platform so + + align:start position:0% +more Surplus by using the platform so + + + align:start position:0% +more Surplus by using the platform so +suppose what happens here is that um so + + align:start position:0% +suppose what happens here is that um so + + + align:start position:0% +suppose what happens here is that um so +think of uh Yelp as as the firm uh + + align:start position:0% +think of uh Yelp as as the firm uh + + + align:start position:0% +think of uh Yelp as as the firm uh +designing the information structure and + + align:start position:0% +designing the information structure and + + + align:start position:0% +designing the information structure and +suppose that Yelp because they've read + + align:start position:0% +suppose that Yelp because they've read + + + align:start position:0% +suppose that Yelp because they've read +all your reviews that you've ever + + align:start position:0% +all your reviews that you've ever + + + align:start position:0% +all your reviews that you've ever +written of restaurants in the past they + + align:start position:0% +written of restaurants in the past they + + + align:start position:0% +written of restaurants in the past they +know how much you're going to like the + + align:start position:0% +know how much you're going to like the + + + align:start position:0% +know how much you're going to like the +Clover sandwich like they've done they + + align:start position:0% +Clover sandwich like they've done they + + + align:start position:0% +Clover sandwich like they've done they +right they've got enough sort of things + + align:start position:0% +right they've got enough sort of things + + + align:start position:0% +right they've got enough sort of things +of people who both ate this sandwich and + + align:start position:0% +of people who both ate this sandwich and + + + align:start position:0% +of people who both ate this sandwich and +had the same tastes as you at all + + align:start position:0% +had the same tastes as you at all + + + align:start position:0% +had the same tastes as you at all +previous + + align:start position:0% +previous + + + align:start position:0% +previous +restaurants that Yelp knows whether or + + align:start position:0% +restaurants that Yelp knows whether or + + + align:start position:0% +restaurants that Yelp knows whether or +not you're going to like this sandwich + + align:start position:0% +not you're going to like this sandwich + + + align:start position:0% +not you're going to like this sandwich +uh you know because they know sort of in + + align:start position:0% +uh you know because they know sort of in + + + align:start position:0% +uh you know because they know sort of in +some sense they imply know what it + + align:start position:0% +some sense they imply know what it + + + align:start position:0% +some sense they imply know what it +tastes like relative to your + + align:start position:0% + + + + align:start position:0% + +tastes and so suppose what Yelp does it + + align:start position:0% +tastes and so suppose what Yelp does it + + + align:start position:0% +tastes and so suppose what Yelp does it +commits to this partial information + + align:start position:0% +commits to this partial information + + + align:start position:0% +commits to this partial information +policy if your value is between 0 and A3 + + align:start position:0% +policy if your value is between 0 and A3 + + + align:start position:0% +policy if your value is between 0 and A3 +or 0 and $6 it tells you you are someone + + align:start position:0% +or 0 and $6 it tells you you are someone + + + align:start position:0% +or 0 and $6 it tells you you are someone +who are who is going to have a low value + + align:start position:0% +who are who is going to have a low value + + + align:start position:0% +who are who is going to have a low value +for that + + align:start position:0% +for that + + + align:start position:0% +for that +sandwich if your value is between 1/3 + + align:start position:0% +sandwich if your value is between 1/3 + + + align:start position:0% +sandwich if your value is between 1/3 +and 7 9ths so that's between $6 and + + align:start position:0% +and 7 9ths so that's between $6 and + + + align:start position:0% +and 7 9ths so that's between $6 and +$14 uh it's going to tell you have a + + align:start position:0% +$14 uh it's going to tell you have a + + + align:start position:0% +$14 uh it's going to tell you have a +medium value for that + + align:start position:0% +medium value for that + + + align:start position:0% +medium value for that +sandwich and if your value is between $4 + + align:start position:0% +sandwich and if your value is between $4 + + + align:start position:0% +sandwich and if your value is between $4 +and $18 it's going to tell you you have + + align:start position:0% +and $18 it's going to tell you you have + + + align:start position:0% +and $18 it's going to tell you you have +the high value for that sandwich so it's + + align:start position:0% +the high value for that sandwich so it's + + + align:start position:0% +the high value for that sandwich so it's +like it's taken the sandwich it's + + align:start position:0% +like it's taken the sandwich it's + + + align:start position:0% +like it's taken the sandwich it's +wrapped in a paper bag and not told you + + align:start position:0% +wrapped in a paper bag and not told you + + + align:start position:0% +wrapped in a paper bag and not told you +what it is but it says based on what we + + align:start position:0% +what it is but it says based on what we + + + align:start position:0% +what it is but it says based on what we +know about you your value for this + + align:start position:0% +know about you your value for this + + + align:start position:0% +know about you your value for this +sandwich is low your value for that + + align:start position:0% +sandwich is low your value for that + + + align:start position:0% +sandwich is low your value for that +sandwich is medium your value for that + + align:start position:0% +sandwich is medium your value for that + + + align:start position:0% +sandwich is medium your value for that +sandwich is + + align:start position:0% +sandwich is + + + align:start position:0% +sandwich is +high and then it sends you into cover + + align:start position:0% +high and then it sends you into cover + + + align:start position:0% +high and then it sends you into cover +with that knowledge of you know it you + + align:start position:0% +with that knowledge of you know it you + + + align:start position:0% +with that knowledge of you know it you +know you only can buy from cover Through + + align:start position:0% +know you only can buy from cover Through + + + align:start position:0% +know you only can buy from cover Through +Yelp in this example I mean it's more + + align:start position:0% +Yelp in this example I mean it's more + + + align:start position:0% +Yelp in this example I mean it's more +plausible with Amazon um and so all + + align:start position:0% +plausible with Amazon um and so all + + + align:start position:0% +plausible with Amazon um and so all +you're provided with is the information + + align:start position:0% +you're provided with is the information + + + align:start position:0% +you're provided with is the information +of my value is low my value is medium or + + align:start position:0% +of my value is low my value is medium or + + + align:start position:0% +of my value is low my value is medium or +my value is high so now what does cover + + align:start position:0% +my value is high so now what does cover + + + align:start position:0% +my value is high so now what does cover +do when it's in this world well the + + align:start position:0% +do when it's in this world well the + + + align:start position:0% +do when it's in this world well the +people who are told the value is low + + align:start position:0% +people who are told the value is low + + + align:start position:0% +people who are told the value is low +think that the value is is + + align:start position:0% +think that the value is is + + + align:start position:0% +think that the value is is +one6 or um or three those who think that + + align:start position:0% +one6 or um or three those who think that + + + align:start position:0% +one6 or um or three those who think that +their value is medium are think their + + align:start position:0% +their value is medium are think their + + + align:start position:0% +their value is medium are think their +value is 5 9ths you know halfway between + + align:start position:0% +value is 5 9ths you know halfway between + + + align:start position:0% +value is 5 9ths you know halfway between +3 9th and 7 9ths and those who are told + + align:start position:0% +3 9th and 7 9ths and those who are told + + + align:start position:0% +3 9th and 7 9ths and those who are told +value is high in expectation think their + + align:start position:0% +value is high in expectation think their + + + align:start position:0% +value is high in expectation think their +utility is going to be + + align:start position:0% +utility is going to be + + + align:start position:0% +utility is going to be +89s so cover is facing this strange + + align:start position:0% +89s so cover is facing this strange + + + align:start position:0% +89s so cover is facing this strange +population + + align:start position:0% +population + + + align:start position:0% +population +where we now have sort of three point + + align:start position:0% +where we now have sort of three point + + + align:start position:0% +where we now have sort of three point +instead of having sort of cons with + + align:start position:0% +instead of having sort of cons with + + + align:start position:0% +instead of having sort of cons with +values uniform on 0 to + + align:start position:0% +values uniform on 0 to + + + align:start position:0% +values uniform on 0 to +18 we now just have three point masses + + align:start position:0% +18 we now just have three point masses + + + align:start position:0% +18 we now just have three point masses +we have a point mass of + + align:start position:0% +we have a point mass of + + + align:start position:0% +we have a point mass of +1/3 on people who think it's worth $3 to + + align:start position:0% +1/3 on people who think it's worth $3 to + + + align:start position:0% +1/3 on people who think it's worth $3 to +them uh we have a point Mass that's like + + align:start position:0% +them uh we have a point Mass that's like + + + align:start position:0% +them uh we have a point Mass that's like +uh this big uh four 9ths of the people + + align:start position:0% +uh this big uh four 9ths of the people + + + align:start position:0% +uh this big uh four 9ths of the people +who think the thing is worth 10 and then + + align:start position:0% +who think the thing is worth 10 and then + + + align:start position:0% +who think the thing is worth 10 and then +we have a smaller Point Mass uh 2 9ths + + align:start position:0% +we have a smaller Point Mass uh 2 9ths + + + align:start position:0% +we have a smaller Point Mass uh 2 9ths +who think the thing is worth + + align:start position:0% + + + + align:start position:0% + +16 okay so what does cover do if it's + + align:start position:0% +16 okay so what does cover do if it's + + + align:start position:0% +16 okay so what does cover do if it's +faced with this demand like there's some + + align:start position:0% +faced with this demand like there's some + + + align:start position:0% +faced with this demand like there's some +people who think it's worth three some + + align:start position:0% +people who think it's worth three some + + + align:start position:0% +people who think it's worth three some +who think it's worth 10 some who think + + align:start position:0% +who think it's worth 10 some who think + + + align:start position:0% +who think it's worth 10 some who think +it's worth + + align:start position:0% +it's worth + + + align:start position:0% +it's worth +16 well obviously you're going to price + + align:start position:0% +16 well obviously you're going to price + + + align:start position:0% +16 well obviously you're going to price +the good either at 10 or 16 in this + + align:start position:0% +the good either at 10 or 16 in this + + + align:start position:0% +the good either at 10 or 16 in this +example because you know everyone has a + + align:start position:0% +example because you know everyone has a + + + align:start position:0% +example because you know everyone has a +value of if I price more than 10 only + + align:start position:0% +value of if I price more than 10 only + + + align:start position:0% +value of if I price more than 10 only +these people buy so I might as well + + align:start position:0% +these people buy so I might as well + + + align:start position:0% +these people buy so I might as well +charge 16 so I basically have two + + align:start position:0% +charge 16 so I basically have two + + + align:start position:0% +charge 16 so I basically have two +choices I can price it at + + align:start position:0% +choices I can price it at + + + align:start position:0% +choices I can price it at +10 and earn 10 minus 6 and sell it to + + align:start position:0% +10 and earn 10 minus 6 and sell it to + + + align:start position:0% +10 and earn 10 minus 6 and sell it to +2/3 of the people + + align:start position:0% +2/3 of the people + + + align:start position:0% +2/3 of the people +or I can price it at + + align:start position:0% +or I can price it at + + + align:start position:0% +or I can price it at +16 and get 16 minus 6 and then sell it + + align:start position:0% +16 and get 16 minus 6 and then sell it + + + align:start position:0% +16 and get 16 minus 6 and then sell it +to 29ths of the + + align:start position:0% + + + + align:start position:0% + +people and I think the way I did these + + align:start position:0% +people and I think the way I did these + + + align:start position:0% +people and I think the way I did these +numbers you know selling to both groups + + align:start position:0% +numbers you know selling to both groups + + + align:start position:0% +numbers you know selling to both groups +at 10 is better for them than selling to + + align:start position:0% +at 10 is better for them than selling to + + + align:start position:0% +at 10 is better for them than selling to +only the high types at + + align:start position:0% +only the high types at + + + align:start position:0% +only the high types at +16 so what happens is I get them to sell + + align:start position:0% +16 so what happens is I get them to sell + + + align:start position:0% +16 so what happens is I get them to sell +the sandwich to um both the medium and + + align:start position:0% +the sandwich to um both the medium and + + + align:start position:0% +the sandwich to um both the medium and +the high + + align:start position:0% +the high + + + align:start position:0% +the high +types and if you look at what I've done + + align:start position:0% +types and if you look at what I've done + + + align:start position:0% +types and if you look at what I've done +you know I've worked out the + + align:start position:0% +you know I've worked out the + + + align:start position:0% +you know I've worked out the +calculations + + align:start position:0% +calculations + + + align:start position:0% +calculations +here I've gotten them to sell the + + align:start position:0% +here I've gotten them to sell the + + + align:start position:0% +here I've gotten them to sell the +sandwich you know instead of having the + + align:start position:0% +sandwich you know instead of having the + + + align:start position:0% +sandwich you know instead of having the +Monopoly price of + + align:start position:0% +Monopoly price of + + + align:start position:0% +Monopoly price of +12 you the Monopoly price would sell it + + align:start position:0% +12 you the Monopoly price would sell it + + + align:start position:0% +12 you the Monopoly price would sell it +at 12 and everyone with a value uh above + + align:start position:0% +at 12 and everyone with a value uh above + + + align:start position:0% +at 12 and everyone with a value uh above +above 12 + + align:start position:0% +above 12 + + + align:start position:0% +above 12 +buys here I've gotten them to sell the + + align:start position:0% +buys here I've gotten them to sell the + + + align:start position:0% +buys here I've gotten them to sell the +good at a price of 10 instead of + + align:start position:0% +good at a price of 10 instead of + + + align:start position:0% +good at a price of 10 instead of +12 and so by getting them to co by by + + align:start position:0% +12 and so by getting them to co by by + + + align:start position:0% +12 and so by getting them to co by by +some sense creating this extra mass of + + align:start position:0% +some sense creating this extra mass of + + + align:start position:0% +some sense creating this extra mass of +consumers who think it's worth 10 I've + + align:start position:0% +consumers who think it's worth 10 I've + + + align:start position:0% +consumers who think it's worth 10 I've +shifted down where the Monopoly price is + + align:start position:0% +shifted down where the Monopoly price is + + + align:start position:0% +shifted down where the Monopoly price is +and gotten Clover to sell the good at 10 + + align:start position:0% +and gotten Clover to sell the good at 10 + + + align:start position:0% +and gotten Clover to sell the good at 10 +instead of 12 and it turns out if you + + align:start position:0% +instead of 12 and it turns out if you + + + align:start position:0% +instead of 12 and it turns out if you +work out the algebra here um you know + + align:start position:0% +work out the algebra here um you know + + + align:start position:0% +work out the algebra here um you know +the profit uh of the monopolist is I + + align:start position:0% +the profit uh of the monopolist is I + + + align:start position:0% +the profit uh of the monopolist is I +believe lower um nope uh so actually + + align:start position:0% +believe lower um nope uh so actually + + + align:start position:0% +believe lower um nope uh so actually +sorry it's here so um consumer surplus + + align:start position:0% +sorry it's here so um consumer surplus + + + align:start position:0% +sorry it's here so um consumer surplus +is higher than it is under Monopoly + + align:start position:0% +is higher than it is under Monopoly + + + align:start position:0% +is higher than it is under Monopoly +pricing and actually in this example the + + align:start position:0% +pricing and actually in this example the + + + align:start position:0% +pricing and actually in this example the +profit of the monopolist is also higher + + align:start position:0% +profit of the monopolist is also higher + + + align:start position:0% +profit of the monopolist is also higher +so this was the no information treatment + + align:start position:0% +so this was the no information treatment + + + align:start position:0% +so this was the no information treatment +this was the sort of full information + + align:start position:0% +this was the sort of full information + + + align:start position:0% +this was the sort of full information +treatment this one I've actually bumped + + align:start position:0% +treatment this one I've actually bumped + + + align:start position:0% +treatment this one I've actually bumped +up consumer surplus and profits + + align:start position:0% +up consumer surplus and profits + + + align:start position:0% +up consumer surplus and profits +relatively monopolist is done okay uh + + align:start position:0% +relatively monopolist is done okay uh + + + align:start position:0% +relatively monopolist is done okay uh +anyway so I am out of time now so why + + align:start position:0% +anyway so I am out of time now so why + + + align:start position:0% +anyway so I am out of time now so why +don't I leave it there I will do sort of + + align:start position:0% +don't I leave it there I will do sort of + + + align:start position:0% +don't I leave it there I will do sort of +my uh final slides on information design + + align:start position:0% +my uh final slides on information design + + + align:start position:0% +my uh final slides on information design +uh next time and I should say jumping + + align:start position:0% +uh next time and I should say jumping + + + align:start position:0% +uh next time and I should say jumping +ahead um you know as I said I'm going to + + align:start position:0% +ahead um you know as I said I'm going to + + + align:start position:0% +ahead um you know as I said I'm going to +do sort of theory on Wednesdays and + + align:start position:0% +do sort of theory on Wednesdays and + + + align:start position:0% +do sort of theory on Wednesdays and +empir work on Mondays for the immediate + + align:start position:0% +empir work on Mondays for the immediate + + + align:start position:0% +empir work on Mondays for the immediate +future um so in Monday's class I'm going + + align:start position:0% +future um so in Monday's class I'm going + + + align:start position:0% +future um so in Monday's class I'm going +to talk about two empirical papers on + + align:start position:0% +to talk about two empirical papers on + + + align:start position:0% +to talk about two empirical papers on +Monopoly pricing chaler ghouls be and + + align:start position:0% +Monopoly pricing chaler ghouls be and + + + align:start position:0% +Monopoly pricing chaler ghouls be and +Jens cow Shapiro um so you know be + + align:start position:0% +Jens cow Shapiro um so you know be + + + align:start position:0% +Jens cow Shapiro um so you know be +useful for you to sort of I I will + + align:start position:0% +useful for you to sort of I I will + + + align:start position:0% +useful for you to sort of I I will +discuss what's in the papers but + + align:start position:0% +discuss what's in the papers but + + + align:start position:0% +discuss what's in the papers but +probably useful for you to like try to + + align:start position:0% +probably useful for you to like try to + + + align:start position:0% +probably useful for you to like try to +look at the papers beforehand try to + + align:start position:0% +look at the papers beforehand try to + + + align:start position:0% +look at the papers beforehand try to +read what's in them get some sense for + + align:start position:0% +read what's in them get some sense for + + + align:start position:0% +read what's in them get some sense for +reading IO papers I will say that jent + + align:start position:0% +reading IO papers I will say that jent + + + align:start position:0% +reading IO papers I will say that jent +cow Shapiro is a bit difficult paper to + + align:start position:0% +cow Shapiro is a bit difficult paper to + + + align:start position:0% +cow Shapiro is a bit difficult paper to +read if you haven't done a lot of + + align:start position:0% +read if you haven't done a lot of + + + align:start position:0% +read if you haven't done a lot of +econometrics um we are sort of covering + + align:start position:0% +econometrics um we are sort of covering + + + align:start position:0% +econometrics um we are sort of covering +the sort of demand estimation in week + + align:start position:0% +the sort of demand estimation in week + + + align:start position:0% +the sort of demand estimation in week +four of this course course and in the + + align:start position:0% +four of this course course and in the + + + align:start position:0% +four of this course course and in the +first 3 weeks of this course you may be + + align:start position:0% +first 3 weeks of this course you may be + + + align:start position:0% +first 3 weeks of this course you may be +reading papers on demand estimation that + + align:start position:0% +reading papers on demand estimation that + + + align:start position:0% +reading papers on demand estimation that +are harder to read I would just in the + + align:start position:0% +are harder to read I would just in the + + + align:start position:0% +are harder to read I would just in the +first 3 weeks skim through them if you + + align:start position:0% +first 3 weeks skim through them if you + + + align:start position:0% +first 3 weeks skim through them if you +haven't done GMM estimation and things + + align:start position:0% +haven't done GMM estimation and things + + + align:start position:0% +haven't done GMM estimation and things +and have trouble reading those papers + + align:start position:0% +and have trouble reading those papers + + + align:start position:0% +and have trouble reading those papers +okay okay thanks uh hope you enjoy the + + align:start position:0% +okay okay thanks uh hope you enjoy the + + + align:start position:0% +okay okay thanks uh hope you enjoy the +course and I will see you on Monday \ No newline at end of file diff --git a/zrB6pocJSI8.txt b/zrB6pocJSI8.txt new file mode 100644 index 0000000000000000000000000000000000000000..9338f152ac8502a3c405653529a397b256a4685d --- /dev/null +++ b/zrB6pocJSI8.txt @@ -0,0 +1,1251 @@ +align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +hi my name is amit gandhi and i'm a + + align:start position:0% +hi my name is amit gandhi and i'm a + + + align:start position:0% +hi my name is amit gandhi and i'm a +graduate researcher at mit + + align:start position:0% +graduate researcher at mit + + + align:start position:0% +graduate researcher at mit +welcome to this course on exploring + + align:start position:0% +welcome to this course on exploring + + + align:start position:0% +welcome to this course on exploring +fairness and machine learning for + + align:start position:0% +fairness and machine learning for + + + align:start position:0% +fairness and machine learning for +international development + + align:start position:0% +international development + + + align:start position:0% +international development +in this video we will examine bias in + + align:start position:0% +in this video we will examine bias in + + + align:start position:0% +in this video we will examine bias in +machine learning models through a + + align:start position:0% +machine learning models through a + + + align:start position:0% +machine learning models through a +pulmonary health diagnostic case study + + align:start position:0% +pulmonary health diagnostic case study + + + align:start position:0% +pulmonary health diagnostic case study +in particular we will explore the + + align:start position:0% +in particular we will explore the + + + align:start position:0% +in particular we will explore the +influence of representative data + + align:start position:0% +influence of representative data + + + align:start position:0% +influence of representative data +on accuracy when building a model + + align:start position:0% +on accuracy when building a model + + + align:start position:0% +on accuracy when building a model +pulmonary diseases including asthma copd + + align:start position:0% +pulmonary diseases including asthma copd + + + align:start position:0% +pulmonary diseases including asthma copd +allergic rhinitis and others can have + + align:start position:0% +allergic rhinitis and others can have + + + align:start position:0% +allergic rhinitis and others can have +significant detrimental health impacts + + align:start position:0% +significant detrimental health impacts + + + align:start position:0% +significant detrimental health impacts +if undetected + + align:start position:0% +if undetected + + + align:start position:0% +if undetected +in remote areas with limited access to + + align:start position:0% +in remote areas with limited access to + + + align:start position:0% +in remote areas with limited access to +healthcare they can often go undiagnosed + + align:start position:0% +healthcare they can often go undiagnosed + + + align:start position:0% +healthcare they can often go undiagnosed +and untreated + + align:start position:0% +and untreated + + + align:start position:0% +and untreated +the motivation for this work was to + + align:start position:0% +the motivation for this work was to + + + align:start position:0% +the motivation for this work was to +develop the screening tool for community + + align:start position:0% +develop the screening tool for community + + + align:start position:0% +develop the screening tool for community +healthcare workers to determine if + + align:start position:0% +healthcare workers to determine if + + + align:start position:0% +healthcare workers to determine if +patients who were presenting symptoms of + + align:start position:0% +patients who were presenting symptoms of + + + align:start position:0% +patients who were presenting symptoms of +pulmonary disease + + align:start position:0% +pulmonary disease + + + align:start position:0% +pulmonary disease +actually have pulmonary disease + + align:start position:0% + + + + align:start position:0% + +to develop the tool data was collected + + align:start position:0% +to develop the tool data was collected + + + align:start position:0% +to develop the tool data was collected +from 303 patients who sought medical + + align:start position:0% +from 303 patients who sought medical + + + align:start position:0% +from 303 patients who sought medical +care at health clinics between 2015 + + align:start position:0% +care at health clinics between 2015 + + + align:start position:0% +care at health clinics between 2015 +and 2018 in pune india + + align:start position:0% +and 2018 in pune india + + + align:start position:0% +and 2018 in pune india +patient data was collected at health + + align:start position:0% +patient data was collected at health + + + align:start position:0% +patient data was collected at health +clinics from two exams administered by + + align:start position:0% +clinics from two exams administered by + + + align:start position:0% +clinics from two exams administered by +researchers + + align:start position:0% +researchers + + + align:start position:0% +researchers +a mobile health diagnostic kit developed + + align:start position:0% +a mobile health diagnostic kit developed + + + align:start position:0% +a mobile health diagnostic kit developed +by dr fletcher's group + + align:start position:0% +by dr fletcher's group + + + align:start position:0% +by dr fletcher's group +and a set of measurements from a + + align:start position:0% +and a set of measurements from a + + + align:start position:0% +and a set of measurements from a +pulmonary function test lab + + align:start position:0% +pulmonary function test lab + + + align:start position:0% +pulmonary function test lab +health diagnoses were performed by + + align:start position:0% +health diagnoses were performed by + + + align:start position:0% +health diagnoses were performed by +medical staff with a focus on asthma + + align:start position:0% +medical staff with a focus on asthma + + + align:start position:0% +medical staff with a focus on asthma +allergic rhinitis and copd + + align:start position:0% + + + + align:start position:0% + +the overall disease distribution among + + align:start position:0% +the overall disease distribution among + + + align:start position:0% +the overall disease distribution among +the patients as shown in the plot + + align:start position:0% +the patients as shown in the plot + + + align:start position:0% +the patients as shown in the plot +the data included 175 patients with + + align:start position:0% +the data included 175 patients with + + + align:start position:0% +the data included 175 patients with +pulmonary diseases + + align:start position:0% +pulmonary diseases + + + align:start position:0% +pulmonary diseases +and 87 healthy patients patients may + + align:start position:0% +and 87 healthy patients patients may + + + align:start position:0% +and 87 healthy patients patients may +also have multiple pulmonary diseases + + align:start position:0% +also have multiple pulmonary diseases + + + align:start position:0% +also have multiple pulmonary diseases +for example asthma and copd + + align:start position:0% + + + + align:start position:0% + +the exploration of representative + + align:start position:0% +the exploration of representative + + + align:start position:0% +the exploration of representative +sampling on accuracy was conducted + + align:start position:0% +sampling on accuracy was conducted + + + align:start position:0% +sampling on accuracy was conducted +across + + align:start position:0% +across + + + align:start position:0% +across +two protected variables gender and + + align:start position:0% +two protected variables gender and + + + align:start position:0% +two protected variables gender and +income + + align:start position:0% +income + + + align:start position:0% +income +the population distributions for the two + + align:start position:0% +the population distributions for the two + + + align:start position:0% +the population distributions for the two +variables can be seen in the slides for + + align:start position:0% +variables can be seen in the slides for + + + align:start position:0% +variables can be seen in the slides for +income considerations patients were + + align:start position:0% +income considerations patients were + + + align:start position:0% +income considerations patients were +categorized as either low income + + align:start position:0% +categorized as either low income + + + align:start position:0% +categorized as either low income +or high income + + align:start position:0% + + + + align:start position:0% + +the overall approach to the bi study was + + align:start position:0% +the overall approach to the bi study was + + + align:start position:0% +the overall approach to the bi study was +to divide the data set into a larger + + align:start position:0% +to divide the data set into a larger + + + align:start position:0% +to divide the data set into a larger +training data superset + + align:start position:0% +training data superset + + + align:start position:0% +training data superset +in a test data set a logistic regression + + align:start position:0% +in a test data set a logistic regression + + + align:start position:0% +in a test data set a logistic regression +model with l2 regularization was used to + + align:start position:0% +model with l2 regularization was used to + + + align:start position:0% +model with l2 regularization was used to +make predictions on disease + + align:start position:0% +make predictions on disease + + + align:start position:0% +make predictions on disease +to train the model training data subsets + + align:start position:0% +to train the model training data subsets + + + align:start position:0% +to train the model training data subsets +were randomly sampled from the superset + + align:start position:0% +were randomly sampled from the superset + + + align:start position:0% +were randomly sampled from the superset +that intentionally introduced imbalances + + align:start position:0% +that intentionally introduced imbalances + + + align:start position:0% +that intentionally introduced imbalances +along protected variables + + align:start position:0% +along protected variables + + + align:start position:0% +along protected variables +for example with regards to income + + align:start position:0% +for example with regards to income + + + align:start position:0% +for example with regards to income +trading data subsets range from 50 + + align:start position:0% +trading data subsets range from 50 + + + align:start position:0% +trading data subsets range from 50 +high income and 50 low income to 87.5 + + align:start position:0% +high income and 50 low income to 87.5 + + + align:start position:0% +high income and 50 low income to 87.5 +high income and 12.5 percent low income + + align:start position:0% +high income and 12.5 percent low income + + + align:start position:0% +high income and 12.5 percent low income +to account for stochastic error this + + align:start position:0% +to account for stochastic error this + + + align:start position:0% +to account for stochastic error this +process was run a thousand times for + + align:start position:0% +process was run a thousand times for + + + align:start position:0% +process was run a thousand times for +each test + + align:start position:0% +each test + + + align:start position:0% +each test +the area under the curve of the receiver + + align:start position:0% +the area under the curve of the receiver + + + align:start position:0% +the area under the curve of the receiver +operating characteristic curve + + align:start position:0% +operating characteristic curve + + + align:start position:0% +operating characteristic curve +was used as a metric for accuracy + + align:start position:0% + + + + align:start position:0% + +starting with gender bias analysis our + + align:start position:0% +starting with gender bias analysis our + + + align:start position:0% +starting with gender bias analysis our +training data sets and test data set + + align:start position:0% +training data sets and test data set + + + align:start position:0% +training data sets and test data set +were divided as + + align:start position:0% +were divided as + + + align:start position:0% +were divided as +shown male female representativeness was + + align:start position:0% +shown male female representativeness was + + + align:start position:0% +shown male female representativeness was +varied from 5050 + + align:start position:0% +varied from 5050 + + + align:start position:0% +varied from 5050 +to 87.5 to 12.5 + + align:start position:0% + + + + align:start position:0% + +the results for predictive accuracy for + + align:start position:0% +the results for predictive accuracy for + + + align:start position:0% +the results for predictive accuracy for +allergic rhinitis asthma and copd are + + align:start position:0% +allergic rhinitis asthma and copd are + + + align:start position:0% +allergic rhinitis asthma and copd are +shown on the slide + + align:start position:0% +shown on the slide + + + align:start position:0% +shown on the slide +the data shows no significant decrease + + align:start position:0% +the data shows no significant decrease + + + align:start position:0% +the data shows no significant decrease +in algorithm accuracy + + align:start position:0% +in algorithm accuracy + + + align:start position:0% +in algorithm accuracy +as gender imbalances are introduced in + + align:start position:0% +as gender imbalances are introduced in + + + align:start position:0% +as gender imbalances are introduced in +the data + + align:start position:0% +the data + + + align:start position:0% +the data +this may be surprising considering how + + align:start position:0% +this may be surprising considering how + + + align:start position:0% +this may be surprising considering how +we have highlighted the principle of + + align:start position:0% +we have highlighted the principle of + + + align:start position:0% +we have highlighted the principle of +representativeness and data + + align:start position:0% +representativeness and data + + + align:start position:0% +representativeness and data +throughout this course however it is + + align:start position:0% +throughout this course however it is + + + align:start position:0% +throughout this course however it is +important to note that protected + + align:start position:0% +important to note that protected + + + align:start position:0% +important to note that protected +variables do not necessarily affect + + align:start position:0% +variables do not necessarily affect + + + align:start position:0% +variables do not necessarily affect +outcome variables + + align:start position:0% +outcome variables + + + align:start position:0% +outcome variables +and the lack of representativeness may + + align:start position:0% +and the lack of representativeness may + + + align:start position:0% +and the lack of representativeness may +not always introduce bias or unfairness + + align:start position:0% +not always introduce bias or unfairness + + + align:start position:0% +not always introduce bias or unfairness +into models + + align:start position:0% +into models + + + align:start position:0% +into models +looking at our results we also notice + + align:start position:0% +looking at our results we also notice + + + align:start position:0% +looking at our results we also notice +that our algorithm is more accurate at + + align:start position:0% +that our algorithm is more accurate at + + + align:start position:0% +that our algorithm is more accurate at +predicting copd + + align:start position:0% +predicting copd + + + align:start position:0% +predicting copd +in women than men exploring the results + + align:start position:0% +in women than men exploring the results + + + align:start position:0% +in women than men exploring the results +further + + align:start position:0% +further + + + align:start position:0% +further +we look at other variables in their + + align:start position:0% +we look at other variables in their + + + align:start position:0% +we look at other variables in their +correlation with gender + + align:start position:0% +correlation with gender + + + align:start position:0% +correlation with gender +in our data set we found that smoking + + align:start position:0% +in our data set we found that smoking + + + align:start position:0% +in our data set we found that smoking +heavily correlated with gender + + align:start position:0% +heavily correlated with gender + + + align:start position:0% +heavily correlated with gender +55 percent of men reported that they + + align:start position:0% +55 percent of men reported that they + + + align:start position:0% +55 percent of men reported that they +were non-smokers + + align:start position:0% +were non-smokers + + + align:start position:0% +were non-smokers +whereas a hundred percent of women + + align:start position:0% +whereas a hundred percent of women + + + align:start position:0% +whereas a hundred percent of women +reported that they were non-smokers + + align:start position:0% +reported that they were non-smokers + + + align:start position:0% +reported that they were non-smokers +as a result the population of women was + + align:start position:0% +as a result the population of women was + + + align:start position:0% +as a result the population of women was +more homogeneous + + align:start position:0% +more homogeneous + + + align:start position:0% +more homogeneous +allowing for higher predictive accuracy + + align:start position:0% + + + + align:start position:0% + +moving on to the income bias analysis + + align:start position:0% +moving on to the income bias analysis + + + align:start position:0% +moving on to the income bias analysis +the training data sets and test data + + align:start position:0% +the training data sets and test data + + + align:start position:0% +the training data sets and test data +sets were divided as shown + + align:start position:0% +sets were divided as shown + + + align:start position:0% +sets were divided as shown +similar to the gender study + + align:start position:0% +similar to the gender study + + + align:start position:0% +similar to the gender study +representativeness based on income was + + align:start position:0% +representativeness based on income was + + + align:start position:0% +representativeness based on income was +varied for the training data set + + align:start position:0% +varied for the training data set + + + align:start position:0% +varied for the training data set +the results for predictive accuracy for + + align:start position:0% +the results for predictive accuracy for + + + align:start position:0% +the results for predictive accuracy for +allergic rhinitis asthma and copd + + align:start position:0% +allergic rhinitis asthma and copd + + + align:start position:0% +allergic rhinitis asthma and copd +are shown on the slide again we see very + + align:start position:0% +are shown on the slide again we see very + + + align:start position:0% +are shown on the slide again we see very +little difference in accuracy as we + + align:start position:0% +little difference in accuracy as we + + + align:start position:0% +little difference in accuracy as we +change representativeness within the + + align:start position:0% +change representativeness within the + + + align:start position:0% +change representativeness within the +sample + + align:start position:0% +sample + + + align:start position:0% +sample +copd is the most sensitive to + + align:start position:0% +copd is the most sensitive to + + + align:start position:0% +copd is the most sensitive to +socioeconomic status with a four percent + + align:start position:0% +socioeconomic status with a four percent + + + align:start position:0% +socioeconomic status with a four percent +difference in model accuracy + + align:start position:0% +difference in model accuracy + + + align:start position:0% +difference in model accuracy +for high income and low income + + align:start position:0% +for high income and low income + + + align:start position:0% +for high income and low income +populations asthma and allergic rhinitis + + align:start position:0% +populations asthma and allergic rhinitis + + + align:start position:0% +populations asthma and allergic rhinitis +show no difference in performance + + align:start position:0% + + + + align:start position:0% + +in summary we found that + + align:start position:0% +in summary we found that + + + align:start position:0% +in summary we found that +representativeness across the protected + + align:start position:0% +representativeness across the protected + + + align:start position:0% +representativeness across the protected +variables of gender and income + + align:start position:0% +variables of gender and income + + + align:start position:0% +variables of gender and income +do not play a large role in model + + align:start position:0% +do not play a large role in model + + + align:start position:0% +do not play a large role in model +accuracy for this example on pulmonary + + align:start position:0% +accuracy for this example on pulmonary + + + align:start position:0% +accuracy for this example on pulmonary +diseases in india + + align:start position:0% +diseases in india + + + align:start position:0% +diseases in india +as part of building a machine learning + + align:start position:0% +as part of building a machine learning + + + align:start position:0% +as part of building a machine learning +model it is always important to check + + align:start position:0% +model it is always important to check + + + align:start position:0% +model it is always important to check +what effects + + align:start position:0% +what effects + + + align:start position:0% +what effects +if any protected attributes may have on + + align:start position:0% +if any protected attributes may have on + + + align:start position:0% +if any protected attributes may have on +the model + + align:start position:0% +the model + + + align:start position:0% +the model +in the real world it will be impossible + + align:start position:0% +in the real world it will be impossible + + + align:start position:0% +in the real world it will be impossible +to find perfectly balanced data sets + + align:start position:0% +to find perfectly balanced data sets + + + align:start position:0% +to find perfectly balanced data sets +and tests such as the one described can + + align:start position:0% +and tests such as the one described can + + + align:start position:0% +and tests such as the one described can +be used to check for the effect of + + align:start position:0% +be used to check for the effect of + + + align:start position:0% +be used to check for the effect of +representativeness across protected + + align:start position:0% +representativeness across protected + + + align:start position:0% +representativeness across protected +variables on data and model accuracy + + align:start position:0% +variables on data and model accuracy + + + align:start position:0% +variables on data and model accuracy +it is important to understand these + + align:start position:0% +it is important to understand these + + + align:start position:0% +it is important to understand these +tradeoffs so that you can make informed + + align:start position:0% +tradeoffs so that you can make informed + + + align:start position:0% +tradeoffs so that you can make informed +decisions when building models + + align:start position:0% + + + + align:start position:0% + +thank you for taking the time to watch + + align:start position:0% +thank you for taking the time to watch + + + align:start position:0% +thank you for taking the time to watch +this case study and we hope that you'll + + align:start position:0% +this case study and we hope that you'll + + + align:start position:0% +this case study and we hope that you'll +watch the other content in this series + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/zx_DA70lYww.txt b/zx_DA70lYww.txt new file mode 100644 index 0000000000000000000000000000000000000000..4e3c3d91fe17d0681804de8c19386d9cc1d5737b --- /dev/null +++ b/zx_DA70lYww.txt @@ -0,0 +1,12339 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common license. Your support + + align:start position:0% +a Creative Common license. Your support + + + align:start position:0% +a Creative Common license. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Okay, I think we'll make a start. Uh + + align:start position:0% +Okay, I think we'll make a start. Uh + + + align:start position:0% +Okay, I think we'll make a start. Uh +since it's almost 10, can everyone hear + + align:start position:0% +since it's almost 10, can everyone hear + + + align:start position:0% +since it's almost 10, can everyone hear +me in Singapore? + + align:start position:0% +me in Singapore? + + + align:start position:0% +me in Singapore? +uh wave if you can. + + align:start position:0% +uh wave if you can. + + + align:start position:0% +uh wave if you can. +No. Oh, yes, you can. Excellent. Right. + + align:start position:0% +No. Oh, yes, you can. Excellent. Right. + + + align:start position:0% +No. Oh, yes, you can. Excellent. Right. +Um I think that there's a couple of + + align:start position:0% +Um I think that there's a couple of + + + align:start position:0% +Um I think that there's a couple of +announcements before uh we start. Um I'm + + align:start position:0% +announcements before uh we start. Um I'm + + + align:start position:0% +announcements before uh we start. Um I'm +going to have office hours tomorrow + + align:start position:0% +going to have office hours tomorrow + + + align:start position:0% +going to have office hours tomorrow +between 5 and 6 uh in case you have any + + align:start position:0% +between 5 and 6 uh in case you have any + + + align:start position:0% +between 5 and 6 uh in case you have any +questions about the current problem set + + align:start position:0% +questions about the current problem set + + + align:start position:0% +questions about the current problem set +which is due on Thursday at 5:00 p.m. + + align:start position:0% +which is due on Thursday at 5:00 p.m. + + + align:start position:0% +which is due on Thursday at 5:00 p.m. +MIT time. And uh we are uh marking the + + align:start position:0% +MIT time. And uh we are uh marking the + + + align:start position:0% +MIT time. And uh we are uh marking the +quizzes as fast as we can. So you'll + + align:start position:0% +quizzes as fast as we can. So you'll + + + align:start position:0% +quizzes as fast as we can. So you'll +have them back soon. Uh if you have any + + align:start position:0% +have them back soon. Uh if you have any + + + align:start position:0% +have them back soon. Uh if you have any +comments about the quiz uh how you found + + align:start position:0% +comments about the quiz uh how you found + + + align:start position:0% +comments about the quiz uh how you found +the questions and so forth, then I'd be + + align:start position:0% +the questions and so forth, then I'd be + + + align:start position:0% +the questions and so forth, then I'd be +delighted to hear them. + + align:start position:0% +delighted to hear them. + + + align:start position:0% +delighted to hear them. +Uh any questions? + + align:start position:0% +Uh any questions? + + + align:start position:0% +Uh any questions? +Okay. Singapore. No. So uh anyway, today + + align:start position:0% +Okay. Singapore. No. So uh anyway, today + + + align:start position:0% +Okay. Singapore. No. So uh anyway, today +uh I'm going to uh introduce a tool + + align:start position:0% +uh I'm going to uh introduce a tool + + + align:start position:0% +uh I'm going to uh introduce a tool +that's going to be very helpful to us as + + align:start position:0% +that's going to be very helpful to us as + + + align:start position:0% +that's going to be very helpful to us as +we look to uh have ways of studying a + + align:start position:0% +we look to uh have ways of studying a + + + align:start position:0% +we look to uh have ways of studying a +process and understanding exactly how + + align:start position:0% +process and understanding exactly how + + + align:start position:0% +process and understanding exactly how +its inputs relate to its outputs. So + + align:start position:0% +its inputs relate to its outputs. So + + + align:start position:0% +its inputs relate to its outputs. So +that by doing that we can eventually + + align:start position:0% +that by doing that we can eventually + + + align:start position:0% +that by doing that we can eventually +model the process, control it better and + + align:start position:0% +model the process, control it better and + + + align:start position:0% +model the process, control it better and +uh improve its performance. + + align:start position:0% +uh improve its performance. + + + align:start position:0% +uh improve its performance. +And uh that technique is called the + + align:start position:0% +And uh that technique is called the + + + align:start position:0% +And uh that technique is called the +analysis of variance or ANOVA. + + align:start position:0% +analysis of variance or ANOVA. + + + align:start position:0% +analysis of variance or ANOVA. +I want first to quickly review the tools + + align:start position:0% +I want first to quickly review the tools + + + align:start position:0% +I want first to quickly review the tools +that we've looked at in the in the + + align:start position:0% +that we've looked at in the in the + + + align:start position:0% +that we've looked at in the in the +course so far uh so that we can put + + align:start position:0% +course so far uh so that we can put + + + align:start position:0% +course so far uh so that we can put +ANOVA into perspective + + align:start position:0% +ANOVA into perspective + + + align:start position:0% +ANOVA into perspective +and uh we talked for the first couple of + + align:start position:0% +and uh we talked for the first couple of + + + align:start position:0% +and uh we talked for the first couple of +lectures about uh a systems view of + + align:start position:0% +lectures about uh a systems view of + + + align:start position:0% +lectures about uh a systems view of +manufacturing processes. We talked about + + align:start position:0% +manufacturing processes. We talked about + + + align:start position:0% +manufacturing processes. We talked about +uh a variety of parameters that were + + align:start position:0% +uh a variety of parameters that were + + + align:start position:0% +uh a variety of parameters that were +important in determining the outputs. + + align:start position:0% +important in determining the outputs. + + + align:start position:0% +important in determining the outputs. +Some of which we have control over, some + + align:start position:0% +Some of which we have control over, some + + + align:start position:0% +Some of which we have control over, some +of which we don't, some of which are + + align:start position:0% +of which we don't, some of which are + + + align:start position:0% +of which we don't, some of which are +actually disturbances or inherent + + align:start position:0% +actually disturbances or inherent + + + align:start position:0% +actually disturbances or inherent +properties of the equipment or the + + align:start position:0% +properties of the equipment or the + + + align:start position:0% +properties of the equipment or the +material that we're processing. And uh + + align:start position:0% +material that we're processing. And uh + + + align:start position:0% +material that we're processing. And uh +so we we have this idea that there must + + align:start position:0% +so we we have this idea that there must + + + align:start position:0% +so we we have this idea that there must +be some relationship between the inputs + + align:start position:0% +be some relationship between the inputs + + + align:start position:0% +be some relationship between the inputs +and the outputs. uh but we've actually + + align:start position:0% +and the outputs. uh but we've actually + + + align:start position:0% +and the outputs. uh but we've actually +focused on developing tools that just + + align:start position:0% +focused on developing tools that just + + + align:start position:0% +focused on developing tools that just +focus on the output on interpreting the + + align:start position:0% +focus on the output on interpreting the + + + align:start position:0% +focus on the output on interpreting the +output the geometry uh some other + + align:start position:0% +output the geometry uh some other + + + align:start position:0% +output the geometry uh some other +property and + + align:start position:0% +property and + + + align:start position:0% +property and +uh that's fine that's an important tool + + align:start position:0% +uh that's fine that's an important tool + + + align:start position:0% +uh that's fine that's an important tool +um and here here are some of the tools + + align:start position:0% +um and here here are some of the tools + + + align:start position:0% +um and here here are some of the tools +we've looked at uh for statistical + + align:start position:0% +we've looked at uh for statistical + + + align:start position:0% +we've looked at uh for statistical +testing purposes there are of course the + + align:start position:0% +testing purposes there are of course the + + + align:start position:0% +testing purposes there are of course the +t and the f tests and we looked at + + align:start position:0% +t and the f tests and we looked at + + + align:start position:0% +t and the f tests and we looked at +control charts which are essentially + + align:start position:0% +control charts which are essentially + + + align:start position:0% +control charts which are essentially +running hypothesis tests tests that a + + align:start position:0% +running hypothesis tests tests that a + + + align:start position:0% +running hypothesis tests tests that a +process is in control. We're testing the + + align:start position:0% +process is in control. We're testing the + + + align:start position:0% +process is in control. We're testing the +hypothesis that the process uh mean or + + align:start position:0% +hypothesis that the process uh mean or + + + align:start position:0% +hypothesis that the process uh mean or +uh variation is uh of a certain value. + + align:start position:0% +uh variation is uh of a certain value. + + + align:start position:0% +uh variation is uh of a certain value. +We looked at cumulative sum charts and + + align:start position:0% +We looked at cumulative sum charts and + + + align:start position:0% +We looked at cumulative sum charts and +we looked at uh moving average charts. + + align:start position:0% +we looked at uh moving average charts. + + + align:start position:0% +we looked at uh moving average charts. +Then briefly two lectures ago we looked + + align:start position:0% +Then briefly two lectures ago we looked + + + align:start position:0% +Then briefly two lectures ago we looked +at kai squared and tsquare charts. So + + align:start position:0% +at kai squared and tsquare charts. So + + + align:start position:0% +at kai squared and tsquare charts. So +let's look at the properties of those + + align:start position:0% +let's look at the properties of those + + + align:start position:0% +let's look at the properties of those +things just to remind ourselves. Um the + + align:start position:0% +things just to remind ourselves. Um the + + + align:start position:0% +things just to remind ourselves. Um the +key thing with the hypothesis tests and + + align:start position:0% +key thing with the hypothesis tests and + + + align:start position:0% +key thing with the hypothesis tests and +with the control charts is that what + + align:start position:0% +with the control charts is that what + + + align:start position:0% +with the control charts is that what +we're doing is we're interpreting + + align:start position:0% +we're doing is we're interpreting + + + align:start position:0% +we're doing is we're interpreting +changes in one particular specific + + align:start position:0% +changes in one particular specific + + + align:start position:0% +changes in one particular specific +output variable. So whether that be + + align:start position:0% +output variable. So whether that be + + + align:start position:0% +output variable. So whether that be +diameter or threshold voltage or + + align:start position:0% +diameter or threshold voltage or + + + align:start position:0% +diameter or threshold voltage or +something all these hypothesis tests are + + align:start position:0% +something all these hypothesis tests are + + + align:start position:0% +something all these hypothesis tests are +comparing uh sample means sample + + align:start position:0% +comparing uh sample means sample + + + align:start position:0% +comparing uh sample means sample +variances based on one output variable. + + align:start position:0% +variances based on one output variable. + + + align:start position:0% +variances based on one output variable. +And with the kai squared of the tep + + align:start position:0% +And with the kai squared of the tep + + + align:start position:0% +And with the kai squared of the tep +squared charts, uh we introduced the + + align:start position:0% +squared charts, uh we introduced the + + + align:start position:0% +squared charts, uh we introduced the +ability to look at two outputs which + + align:start position:0% +ability to look at two outputs which + + + align:start position:0% +ability to look at two outputs which +might have different dimensions uh and + + align:start position:0% +might have different dimensions uh and + + + align:start position:0% +might have different dimensions uh and +which we expect to be somehow + + align:start position:0% +which we expect to be somehow + + + align:start position:0% +which we expect to be somehow +interdependent. So uh we're uh allowing + + align:start position:0% +interdependent. So uh we're uh allowing + + + align:start position:0% +interdependent. So uh we're uh allowing +ourselves to to interpret two different + + align:start position:0% +ourselves to to interpret two different + + + align:start position:0% +ourselves to to interpret two different +outputs. + + align:start position:0% + + + + align:start position:0% + +Thinking about the number of samples + + align:start position:0% +Thinking about the number of samples + + + align:start position:0% +Thinking about the number of samples +that you can interpret with any one of + + align:start position:0% +that you can interpret with any one of + + + align:start position:0% +that you can interpret with any one of +these given tests. Well, with a T or an + + align:start position:0% +these given tests. Well, with a T or an + + + align:start position:0% +these given tests. Well, with a T or an +F test, you're taking two samples and + + align:start position:0% +F test, you're taking two samples and + + + align:start position:0% +F test, you're taking two samples and +you're comparing them. So, in the case + + align:start position:0% +you're comparing them. So, in the case + + + align:start position:0% +you're comparing them. So, in the case +of a T test, you're asking the question, + + align:start position:0% +of a T test, you're asking the question, + + + align:start position:0% +of a T test, you're asking the question, +is there uh evidence that uh there's a a + + align:start position:0% +is there uh evidence that uh there's a a + + + align:start position:0% +is there uh evidence that uh there's a a +significant difference between uh the + + align:start position:0% +significant difference between uh the + + + align:start position:0% +significant difference between uh the +means of the underlying distributions of + + align:start position:0% +means of the underlying distributions of + + + align:start position:0% +means of the underlying distributions of +the two samples you've taken? And uh + + align:start position:0% +the two samples you've taken? And uh + + + align:start position:0% +the two samples you've taken? And uh +with the F test, we're saying, is there + + align:start position:0% +with the F test, we're saying, is there + + + align:start position:0% +with the F test, we're saying, is there +a significant difference between the + + align:start position:0% +a significant difference between the + + + align:start position:0% +a significant difference between the +underlying variances of of two + + align:start position:0% +underlying variances of of two + + + align:start position:0% +underlying variances of of two +distributions? with a control chart. + + align:start position:0% +distributions? with a control chart. + + + align:start position:0% +distributions? with a control chart. +Well, that's just a running hypothesis + + align:start position:0% +Well, that's just a running hypothesis + + + align:start position:0% +Well, that's just a running hypothesis +test. So, you take many samples and + + align:start position:0% +test. So, you take many samples and + + + align:start position:0% +test. So, you take many samples and +you're constantly uh doing uh doing a + + align:start position:0% +you're constantly uh doing uh doing a + + + align:start position:0% +you're constantly uh doing uh doing a +hypothesis test to see whether the + + align:start position:0% +hypothesis test to see whether the + + + align:start position:0% +hypothesis test to see whether the +process is at the place where where you + + align:start position:0% +process is at the place where where you + + + align:start position:0% +process is at the place where where you +want it to be. Uh so some predetermined + + align:start position:0% +want it to be. Uh so some predetermined + + + align:start position:0% +want it to be. Uh so some predetermined +operating point that you're content is + + align:start position:0% +operating point that you're content is + + + align:start position:0% +operating point that you're content is +optimal, I suppose. + + align:start position:0% +optimal, I suppose. + + + align:start position:0% +optimal, I suppose. +Um and with with with the kai square and + + align:start position:0% +Um and with with with the kai square and + + + align:start position:0% +Um and with with with the kai square and +the tsquare charts again the same is + + align:start position:0% +the tsquare charts again the same is + + + align:start position:0% +the tsquare charts again the same is +true many samples. + + align:start position:0% +true many samples. + + + align:start position:0% +true many samples. +But when we come to ask well how many + + align:start position:0% +But when we come to ask well how many + + + align:start position:0% +But when we come to ask well how many +inputs were we dealing with with these + + align:start position:0% +inputs were we dealing with with these + + + align:start position:0% +inputs were we dealing with with these +things we don't necessarily have any + + align:start position:0% +things we don't necessarily have any + + + align:start position:0% +things we don't necessarily have any +idea. We might be told that uh some + + align:start position:0% +idea. We might be told that uh some + + + align:start position:0% +idea. We might be told that uh some +input to the process was changed here + + align:start position:0% +input to the process was changed here + + + align:start position:0% +input to the process was changed here +are some samples. Is there evidence that + + align:start position:0% +are some samples. Is there evidence that + + + align:start position:0% +are some samples. Is there evidence that +the input has had an effect on the + + align:start position:0% +the input has had an effect on the + + + align:start position:0% +the input has had an effect on the +output? uh but sometimes we might just + + align:start position:0% +output? uh but sometimes we might just + + + align:start position:0% +output? uh but sometimes we might just +have samples and have no clear + + align:start position:0% +have samples and have no clear + + + align:start position:0% +have samples and have no clear +understanding of what the relevant + + align:start position:0% +understanding of what the relevant + + + align:start position:0% +understanding of what the relevant +inputs were. So there's nothing inherent + + align:start position:0% +inputs were. So there's nothing inherent + + + align:start position:0% +inputs were. So there's nothing inherent +in these tools that allows us to to get + + align:start position:0% +in these tools that allows us to to get + + + align:start position:0% +in these tools that allows us to to get +the the relationship between inputs and + + align:start position:0% +the the relationship between inputs and + + + align:start position:0% +the the relationship between inputs and +outputs. And similarly, we don't know, + + align:start position:0% +outputs. And similarly, we don't know, + + + align:start position:0% +outputs. And similarly, we don't know, +you know, how how many levels or + + align:start position:0% +you know, how how many levels or + + + align:start position:0% +you know, how how many levels or +different values any given input to a + + align:start position:0% +different values any given input to a + + + align:start position:0% +different values any given input to a +process might take. How many voltages + + align:start position:0% +process might take. How many voltages + + + align:start position:0% +process might take. How many voltages +could we could we set a particular + + align:start position:0% +could we could we set a particular + + + align:start position:0% +could we could we set a particular +control voltage to? And uh so I've said + + align:start position:0% +control voltage to? And uh so I've said + + + align:start position:0% +control voltage to? And uh so I've said +that they're unknown, but in a sense I' + + align:start position:0% +that they're unknown, but in a sense I' + + + align:start position:0% +that they're unknown, but in a sense I' +I've put I've put two with a question + + align:start position:0% +I've put I've put two with a question + + + align:start position:0% +I've put I've put two with a question +mark because you might think in in a + + align:start position:0% +mark because you might think in in a + + + align:start position:0% +mark because you might think in in a +very clearly defined t test say you + + align:start position:0% +very clearly defined t test say you + + + align:start position:0% +very clearly defined t test say you +might say well an operator varies one + + align:start position:0% +might say well an operator varies one + + + align:start position:0% +might say well an operator varies one +input uh and here are some samples did + + align:start position:0% +input uh and here are some samples did + + + align:start position:0% +input uh and here are some samples did +the output change? So in that case you'd + + align:start position:0% +the output change? So in that case you'd + + + align:start position:0% +the output change? So in that case you'd +have two samples two values for a + + align:start position:0% +have two samples two values for a + + + align:start position:0% +have two samples two values for a +particular input and that might be the + + align:start position:0% +particular input and that might be the + + + align:start position:0% +particular input and that might be the +most uh sort of precisely defined type + + align:start position:0% +most uh sort of precisely defined type + + + align:start position:0% +most uh sort of precisely defined type +of test you can do. We've also talked + + align:start position:0% +of test you can do. We've also talked + + + align:start position:0% +of test you can do. We've also talked +about uh yield modeling where we're + + align:start position:0% +about uh yield modeling where we're + + + align:start position:0% +about uh yield modeling where we're +starting to to to try to get some + + align:start position:0% +starting to to to try to get some + + + align:start position:0% +starting to to to try to get some +physical concept of the link between uh + + align:start position:0% +physical concept of the link between uh + + + align:start position:0% +physical concept of the link between uh +the properties of the process, the + + align:start position:0% +the properties of the process, the + + + align:start position:0% +the properties of the process, the +actual nature of the process and what + + align:start position:0% +actual nature of the process and what + + + align:start position:0% +actual nature of the process and what +comes out at the other end in terms of + + align:start position:0% +comes out at the other end in terms of + + + align:start position:0% +comes out at the other end in terms of +of yield and and process capability. uh + + align:start position:0% +of yield and and process capability. uh + + + align:start position:0% +of yield and and process capability. uh +where we're uh trying to ask questions + + align:start position:0% +where we're uh trying to ask questions + + + align:start position:0% +where we're uh trying to ask questions +about uh how well the process performs + + align:start position:0% +about uh how well the process performs + + + align:start position:0% +about uh how well the process performs +based on being centered at a particular + + align:start position:0% +based on being centered at a particular + + + align:start position:0% +based on being centered at a particular +output mean. But those tools again uh + + align:start position:0% +output mean. But those tools again uh + + + align:start position:0% +output mean. But those tools again uh +don't necessarily let us model the + + align:start position:0% +don't necessarily let us model the + + + align:start position:0% +don't necessarily let us model the +process or indeed give us any insight + + align:start position:0% +process or indeed give us any insight + + + align:start position:0% +process or indeed give us any insight +with which to improve it. So we need we + + align:start position:0% +with which to improve it. So we need we + + + align:start position:0% +with which to improve it. So we need we +need some tools that will start letting + + align:start position:0% +need some tools that will start letting + + + align:start position:0% +need some tools that will start letting +us do that especially if we + + align:start position:0% +us do that especially if we + + + align:start position:0% +us do that especially if we +look at some typical data. Now you'll + + align:start position:0% +look at some typical data. Now you'll + + + align:start position:0% +look at some typical data. Now you'll +recall this this set of data this was + + align:start position:0% +recall this this set of data this was + + + align:start position:0% +recall this this set of data this was +used in problem set two. This is from an + + align:start position:0% +used in problem set two. This is from an + + + align:start position:0% +used in problem set two. This is from an +injection molding experiment done uh at + + align:start position:0% +injection molding experiment done uh at + + + align:start position:0% +injection molding experiment done uh at +MIT for the course a couple of years + + align:start position:0% +MIT for the course a couple of years + + + align:start position:0% +MIT for the course a couple of years +ago. And uh so + + align:start position:0% +ago. And uh so + + + align:start position:0% +ago. And uh so +what we've got here is uh an output + + align:start position:0% +what we've got here is uh an output + + + align:start position:0% +what we've got here is uh an output +which is diameter. We've got one output + + align:start position:0% +which is diameter. We've got one output + + + align:start position:0% +which is diameter. We've got one output +that we've measured uh but we've got uh + + align:start position:0% +that we've measured uh but we've got uh + + + align:start position:0% +that we've measured uh but we've got uh +two input parameters that we think are + + align:start position:0% +two input parameters that we think are + + + align:start position:0% +two input parameters that we think are +relevant. There may be others and in + + align:start position:0% +relevant. There may be others and in + + + align:start position:0% +relevant. There may be others and in +fact there almost certainly are because + + align:start position:0% +fact there almost certainly are because + + + align:start position:0% +fact there almost certainly are because +when uh we look at + + align:start position:0% +when uh we look at + + + align:start position:0% +when uh we look at +uh when when we look at the the sample + + align:start position:0% +uh when when we look at the the sample + + + align:start position:0% +uh when when we look at the the sample +of of parts with a given combination of + + align:start position:0% +of of parts with a given combination of + + + align:start position:0% +of of parts with a given combination of +these input parameters velocity and hold + + align:start position:0% +these input parameters velocity and hold + + + align:start position:0% +these input parameters velocity and hold +time uh we see that there is substantial + + align:start position:0% +time uh we see that there is substantial + + + align:start position:0% +time uh we see that there is substantial +variation and that is either due to uh + + align:start position:0% +variation and that is either due to uh + + + align:start position:0% +variation and that is either due to uh +inherent random variation in properties + + align:start position:0% +inherent random variation in properties + + + align:start position:0% +inherent random variation in properties +of the materials or some input variable + + align:start position:0% +of the materials or some input variable + + + align:start position:0% +of the materials or some input variable +that we haven't fully controlled. + + align:start position:0% +that we haven't fully controlled. + + + align:start position:0% +that we haven't fully controlled. +But uh we've got two input uh parameters + + align:start position:0% +But uh we've got two input uh parameters + + + align:start position:0% +But uh we've got two input uh parameters +and two values that we happen to have + + align:start position:0% +and two values that we happen to have + + + align:start position:0% +and two values that we happen to have +chosen for each of them. Now, we could + + align:start position:0% +chosen for each of them. Now, we could + + + align:start position:0% +chosen for each of them. Now, we could +start to look for significant + + align:start position:0% +start to look for significant + + + align:start position:0% +start to look for significant +differences between the means for each + + align:start position:0% +differences between the means for each + + + align:start position:0% +differences between the means for each +setting uh by + + align:start position:0% +setting uh by + + + align:start position:0% +setting uh by +uh by doing a whole raft of t tests or f + + align:start position:0% +uh by doing a whole raft of t tests or f + + + align:start position:0% +uh by doing a whole raft of t tests or f +tests. But, you know, that would become + + align:start position:0% +tests. But, you know, that would become + + + align:start position:0% +tests. But, you know, that would become +uh tedious quite quickly, especially if + + align:start position:0% +uh tedious quite quickly, especially if + + + align:start position:0% +uh tedious quite quickly, especially if +you're starting to look at uh many + + align:start position:0% +you're starting to look at uh many + + + align:start position:0% +you're starting to look at uh many +variables, many settings. So we need a + + align:start position:0% +variables, many settings. So we need a + + + align:start position:0% +variables, many settings. So we need a +more systematic way of uh of going about + + align:start position:0% +more systematic way of uh of going about + + + align:start position:0% +more systematic way of uh of going about +this and eventually uh being able to say + + align:start position:0% +this and eventually uh being able to say + + + align:start position:0% +this and eventually uh being able to say +which of the inputs is is is important + + align:start position:0% +which of the inputs is is is important + + + align:start position:0% +which of the inputs is is is important +in determining the value of the output. + + align:start position:0% + + + + align:start position:0% + +Eventually once we have those tools well + + align:start position:0% +Eventually once we have those tools well + + + align:start position:0% +Eventually once we have those tools well +there are a few aims that we might have + + align:start position:0% +there are a few aims that we might have + + + align:start position:0% +there are a few aims that we might have +and uh first among those is developing a + + align:start position:0% +and uh first among those is developing a + + + align:start position:0% +and uh first among those is developing a +process model. So uh we want to be able + + align:start position:0% +process model. So uh we want to be able + + + align:start position:0% +process model. So uh we want to be able +to relate inputs and uh disturbances so + + align:start position:0% +to relate inputs and uh disturbances so + + + align:start position:0% +to relate inputs and uh disturbances so +inputs that we can't control to uh to + + align:start position:0% +inputs that we can't control to uh to + + + align:start position:0% +inputs that we can't control to uh to +the outputs and uh we want to know which + + align:start position:0% +the outputs and uh we want to know which + + + align:start position:0% +the outputs and uh we want to know which +inputs are relevant which inputs when + + align:start position:0% +inputs are relevant which inputs when + + + align:start position:0% +inputs are relevant which inputs when +they vary by a reasonable amount + + align:start position:0% +they vary by a reasonable amount + + + align:start position:0% +they vary by a reasonable amount +actually have a significant effect on + + align:start position:0% +actually have a significant effect on + + + align:start position:0% +actually have a significant effect on +the output that we're interested in uh + + align:start position:0% +the output that we're interested in uh + + + align:start position:0% +the output that we're interested in uh +understanding. + + align:start position:0% +understanding. + + + align:start position:0% +understanding. +Once we've done that, we can think about + + align:start position:0% +Once we've done that, we can think about + + + align:start position:0% +Once we've done that, we can think about +optimizing the the process target that + + align:start position:0% +optimizing the the process target that + + + align:start position:0% +optimizing the the process target that +we might have is to maximize CPK, + + align:start position:0% +we might have is to maximize CPK, + + + align:start position:0% +we might have is to maximize CPK, +minimize the cost associated with uh + + align:start position:0% +minimize the cost associated with uh + + + align:start position:0% +minimize the cost associated with uh +deviation from our target output value. + + align:start position:0% +deviation from our target output value. + + + align:start position:0% +deviation from our target output value. +Uh we might have particular models that + + align:start position:0% +Uh we might have particular models that + + + align:start position:0% +Uh we might have particular models that +allow us to uh look at the impact of say + + align:start position:0% +allow us to uh look at the impact of say + + + align:start position:0% +allow us to uh look at the impact of say +a candidate process change to the mean + + align:start position:0% +a candidate process change to the mean + + + align:start position:0% +a candidate process change to the mean +output to the variance of the output. + + align:start position:0% +output to the variance of the output. + + + align:start position:0% +output to the variance of the output. +These are all saying essentially the + + align:start position:0% +These are all saying essentially the + + + align:start position:0% +These are all saying essentially the +same thing. Uh that if we can model a + + align:start position:0% +same thing. Uh that if we can model a + + + align:start position:0% +same thing. Uh that if we can model a +process, we can control it better. + + align:start position:0% + + + + align:start position:0% + +If you had uh perfect understanding of + + align:start position:0% +If you had uh perfect understanding of + + + align:start position:0% +If you had uh perfect understanding of +the physics surrounding the process that + + align:start position:0% +the physics surrounding the process that + + + align:start position:0% +the physics surrounding the process that +you had, you could work forward from + + align:start position:0% +you had, you could work forward from + + + align:start position:0% +you had, you could work forward from +first principles and you could uh you + + align:start position:0% +first principles and you could uh you + + + align:start position:0% +first principles and you could uh you +could think about every physical + + align:start position:0% +could think about every physical + + + align:start position:0% +could think about every physical +phenomenon going on in your system and + + align:start position:0% +phenomenon going on in your system and + + + align:start position:0% +phenomenon going on in your system and +predict what the output would be. But we + + align:start position:0% +predict what the output would be. But we + + + align:start position:0% +predict what the output would be. But we +don't we don't have uh understanding of + + align:start position:0% +don't we don't have uh understanding of + + + align:start position:0% +don't we don't have uh understanding of +all the variables that are at play. And + + align:start position:0% +all the variables that are at play. And + + + align:start position:0% +all the variables that are at play. And +uh what this means is that to get + + align:start position:0% +uh what this means is that to get + + + align:start position:0% +uh what this means is that to get +control of a process, we we need to work + + align:start position:0% +control of a process, we we need to work + + + align:start position:0% +control of a process, we we need to work +backwards from the physical output. We + + align:start position:0% +backwards from the physical output. We + + + align:start position:0% +backwards from the physical output. We +need to take measurements of what the + + align:start position:0% +need to take measurements of what the + + + align:start position:0% +need to take measurements of what the +process is doing and model backwards to + + align:start position:0% +process is doing and model backwards to + + + align:start position:0% +process is doing and model backwards to +understand what the inputs do. Um + + align:start position:0% +understand what the inputs do. Um + + + align:start position:0% +understand what the inputs do. Um +so + + align:start position:0% +so + + + align:start position:0% +so +when we're doing this kind of empirical + + align:start position:0% +when we're doing this kind of empirical + + + align:start position:0% +when we're doing this kind of empirical +modeling uh there are some questions we + + align:start position:0% +modeling uh there are some questions we + + + align:start position:0% +modeling uh there are some questions we +need to ask ourselves. + + align:start position:0% +need to ask ourselves. + + + align:start position:0% +need to ask ourselves. +What are we trying to achieve? Do we + + align:start position:0% +What are we trying to achieve? Do we + + + align:start position:0% +What are we trying to achieve? Do we +want to minimize uh quality loss, + + align:start position:0% +want to minimize uh quality loss, + + + align:start position:0% +want to minimize uh quality loss, +maximize CPK? Uh do we just want to + + align:start position:0% +maximize CPK? Uh do we just want to + + + align:start position:0% +maximize CPK? Uh do we just want to +reduce the variance for some specific + + align:start position:0% +reduce the variance for some specific + + + align:start position:0% +reduce the variance for some specific +reason? Uh we need to define our system + + align:start position:0% +reason? Uh we need to define our system + + + align:start position:0% +reason? Uh we need to define our system +very carefully. What what is the output? + + align:start position:0% +very carefully. What what is the output? + + + align:start position:0% +very carefully. What what is the output? +Are there multiple outputs? Are there + + align:start position:0% +Are there multiple outputs? Are there + + + align:start position:0% +Are there multiple outputs? Are there +multiple inputs? + + align:start position:0% +multiple inputs? + + + align:start position:0% +multiple inputs? +uh what do we want to vary? What does it + + align:start position:0% +uh what do we want to vary? What does it + + + align:start position:0% +uh what do we want to vary? What does it +cost us least to vary either in + + align:start position:0% +cost us least to vary either in + + + align:start position:0% +cost us least to vary either in +exploring the process space or actually + + align:start position:0% +exploring the process space or actually + + + align:start position:0% +exploring the process space or actually +uh what does it cost us least to uh + + align:start position:0% +uh what does it cost us least to uh + + + align:start position:0% +uh what does it cost us least to uh +least to control in the factory and uh + + align:start position:0% +least to control in the factory and uh + + + align:start position:0% +least to control in the factory and uh +we need to come up with some sort of + + align:start position:0% +we need to come up with some sort of + + + align:start position:0% +we need to come up with some sort of +model some sort of form for the model + + align:start position:0% +model some sort of form for the model + + + align:start position:0% +model some sort of form for the model +that we can use. We haven't yet + + align:start position:0% +that we can use. We haven't yet + + + align:start position:0% +that we can use. We haven't yet +described any particular model. this + + align:start position:0% +described any particular model. this + + + align:start position:0% +described any particular model. this +function fi we've been talking about in + + align:start position:0% +function fi we've been talking about in + + + align:start position:0% +function fi we've been talking about in +previous lectures + + align:start position:0% +previous lectures + + + align:start position:0% +previous lectures +uh hasn't hasn't been specific to any + + align:start position:0% +uh hasn't hasn't been specific to any + + + align:start position:0% +uh hasn't hasn't been specific to any +particular process. What's also + + align:start position:0% +particular process. What's also + + + align:start position:0% +particular process. What's also +important is to is to think about how + + align:start position:0% +important is to is to think about how + + + align:start position:0% +important is to is to think about how +easy it is to collect data from the + + align:start position:0% +easy it is to collect data from the + + + align:start position:0% +easy it is to collect data from the +process. If you have 20 variables and + + align:start position:0% +process. If you have 20 variables and + + + align:start position:0% +process. If you have 20 variables and +they can v each vary over a factor of + + align:start position:0% +they can v each vary over a factor of + + + align:start position:0% +they can v each vary over a factor of +10, one needs to start thinking about uh + + align:start position:0% +10, one needs to start thinking about uh + + + align:start position:0% +10, one needs to start thinking about uh +how one can simplify the process of + + align:start position:0% +how one can simplify the process of + + + align:start position:0% +how one can simplify the process of +doing these experiments and working + + align:start position:0% +doing these experiments and working + + + align:start position:0% +doing these experiments and working +towards a model + + align:start position:0% +towards a model + + + align:start position:0% +towards a model +especially if there's a lot of + + align:start position:0% +especially if there's a lot of + + + align:start position:0% +especially if there's a lot of +measurement uh of the outputs involved a + + align:start position:0% +measurement uh of the outputs involved a + + + align:start position:0% +measurement uh of the outputs involved a +lot of laborious + + align:start position:0% +lot of laborious + + + align:start position:0% +lot of laborious +measurement. So going back to that chart + + align:start position:0% +measurement. So going back to that chart + + + align:start position:0% +measurement. So going back to that chart +of of the tools we have so far, what + + align:start position:0% +of of the tools we have so far, what + + + align:start position:0% +of of the tools we have so far, what +we're going to do today is uh add add a + + align:start position:0% +we're going to do today is uh add add a + + + align:start position:0% +we're going to do today is uh add add a +new one and that is the analysis of + + align:start position:0% +new one and that is the analysis of + + + align:start position:0% +new one and that is the analysis of +variance. + + align:start position:0% + + + + align:start position:0% + +Now, the key uh advantage of of this is + + align:start position:0% +Now, the key uh advantage of of this is + + + align:start position:0% +Now, the key uh advantage of of this is +that we're now starting to be specific + + align:start position:0% +that we're now starting to be specific + + + align:start position:0% +that we're now starting to be specific +about uh looking at + + align:start position:0% +about uh looking at + + + align:start position:0% +about uh looking at +the uh the actual inputs that we're + + align:start position:0% +the uh the actual inputs that we're + + + align:start position:0% +the uh the actual inputs that we're +interested in and how they impact the + + align:start position:0% +interested in and how they impact the + + + align:start position:0% +interested in and how they impact the +outputs. And uh so we might just be + + align:start position:0% +outputs. And uh so we might just be + + + align:start position:0% +outputs. And uh so we might just be +interested in uh + + align:start position:0% +interested in uh + + + align:start position:0% +interested in uh +we might just be interested in studying + + align:start position:0% +we might just be interested in studying + + + align:start position:0% +we might just be interested in studying +one input but equally there are ANOVA + + align:start position:0% +one input but equally there are ANOVA + + + align:start position:0% +one input but equally there are ANOVA +techniques that will let us study + + align:start position:0% +techniques that will let us study + + + align:start position:0% +techniques that will let us study +multiple input parameters. Was there a + + align:start position:0% +multiple input parameters. Was there a + + + align:start position:0% +multiple input parameters. Was there a +question in Singapore? + + align:start position:0% +question in Singapore? + + + align:start position:0% +question in Singapore? +Yeah I I have a I have a question. + + align:start position:0% +Yeah I I have a I have a question. + + + align:start position:0% +Yeah I I have a I have a question. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +what is a kai square chart and why do + + align:start position:0% +what is a kai square chart and why do + + + align:start position:0% +what is a kai square chart and why do +does it have true outputs? + + align:start position:0% + + + + align:start position:0% + +Right. Well, this uh I think we covered + + align:start position:0% +Right. Well, this uh I think we covered + + + align:start position:0% +Right. Well, this uh I think we covered +in in lecture two two lectures ago + + align:start position:0% +in in lecture two two lectures ago + + + align:start position:0% +in in lecture two two lectures ago +certainly the tsquare chart. What that + + align:start position:0% +certainly the tsquare chart. What that + + + align:start position:0% +certainly the tsquare chart. What that +does is if you have uh two output + + align:start position:0% +does is if you have uh two output + + + align:start position:0% +does is if you have uh two output +variables that you are maintaining + + align:start position:0% +variables that you are maintaining + + + align:start position:0% +variables that you are maintaining +control charts for uh but they are + + align:start position:0% +control charts for uh but they are + + + align:start position:0% +control charts for uh but they are +functionally interdependent. You might + + align:start position:0% +functionally interdependent. You might + + + align:start position:0% +functionally interdependent. You might +not know exactly how but you know that + + align:start position:0% +not know exactly how but you know that + + + align:start position:0% +not know exactly how but you know that +there's some relationship between them. + + align:start position:0% +there's some relationship between them. + + + align:start position:0% +there's some relationship between them. +uh a part that is out of specification + + align:start position:0% +uh a part that is out of specification + + + align:start position:0% +uh a part that is out of specification +may not uh may not uh trigger + + align:start position:0% +may not uh may not uh trigger + + + align:start position:0% +may not uh may not uh trigger +an an outofc control alarm on one of + + align:start position:0% +an an outofc control alarm on one of + + + align:start position:0% +an an outofc control alarm on one of +those control charts. But if you uh plot + + align:start position:0% +those control charts. But if you uh plot + + + align:start position:0% +those control charts. But if you uh plot +both of them together + + align:start position:0% +both of them together + + + align:start position:0% +both of them together +uh and look at the results in + + align:start position:0% +uh and look at the results in + + + align:start position:0% +uh and look at the results in +conjunction with one another, that + + align:start position:0% +conjunction with one another, that + + + align:start position:0% +conjunction with one another, that +allows you to infer more about whether + + align:start position:0% +allows you to infer more about whether + + + align:start position:0% +allows you to infer more about whether +the process is in or out of control. Um + + align:start position:0% +the process is in or out of control. Um + + + align:start position:0% +the process is in or out of control. Um +so uh it's covered in Montgomery. We we + + align:start position:0% +so uh it's covered in Montgomery. We we + + + align:start position:0% +so uh it's covered in Montgomery. We we +may have a problem set question about it + + align:start position:0% +may have a problem set question about it + + + align:start position:0% +may have a problem set question about it +as well to help you develop + + align:start position:0% +as well to help you develop + + + align:start position:0% +as well to help you develop +understanding. Uh + + align:start position:0% +understanding. Uh + + + align:start position:0% +understanding. Uh +anyway I'm sorry I want to focus on + + align:start position:0% +anyway I'm sorry I want to focus on + + + align:start position:0% +anyway I'm sorry I want to focus on +ANOVA today. So + + align:start position:0% + + + + align:start position:0% + +um anyway, so we have the option of + + align:start position:0% +um anyway, so we have the option of + + + align:start position:0% +um anyway, so we have the option of +looking at more than one more than one + + align:start position:0% +looking at more than one more than one + + + align:start position:0% +looking at more than one more than one +input and taking uh more than one uh + + align:start position:0% +input and taking uh more than one uh + + + align:start position:0% +input and taking uh more than one uh +input value for each input. And when we + + align:start position:0% +input value for each input. And when we + + + align:start position:0% +input value for each input. And when we +have different levels for an input, + + align:start position:0% +have different levels for an input, + + + align:start position:0% +have different levels for an input, +we're going to refer to those as + + align:start position:0% +we're going to refer to those as + + + align:start position:0% +we're going to refer to those as +treatments. So a variable may be treated + + align:start position:0% +treatments. So a variable may be treated + + + align:start position:0% +treatments. So a variable may be treated +in one of a number of ways. + + align:start position:0% + + + + align:start position:0% + +the outputs. Uh well, we're dealing in + + align:start position:0% +the outputs. Uh well, we're dealing in + + + align:start position:0% +the outputs. Uh well, we're dealing in +this particular case with one particular + + align:start position:0% +this particular case with one particular + + + align:start position:0% +this particular case with one particular +quantity that we're going to measure and + + align:start position:0% +quantity that we're going to measure and + + + align:start position:0% +quantity that we're going to measure and +analyze and uh we we're going to have uh + + align:start position:0% +analyze and uh we we're going to have uh + + + align:start position:0% +analyze and uh we we're going to have uh +two or more uh samples + + align:start position:0% +two or more uh samples + + + align:start position:0% +two or more uh samples +um that we are able to deal with. So + + align:start position:0% +um that we are able to deal with. So + + + align:start position:0% +um that we are able to deal with. So +this is what we're going to do. We're + + align:start position:0% +this is what we're going to do. We're + + + align:start position:0% +this is what we're going to do. We're +going to look first for uh the ANOVA + + align:start position:0% +going to look first for uh the ANOVA + + + align:start position:0% +going to look first for uh the ANOVA +technique applied to one input variable + + align:start position:0% +technique applied to one input variable + + + align:start position:0% +technique applied to one input variable +and then uh we're going to + + align:start position:0% +and then uh we're going to + + + align:start position:0% +and then uh we're going to +uh work through an example of that. Then + + align:start position:0% +uh work through an example of that. Then + + + align:start position:0% +uh work through an example of that. Then +we'll look at uh multi- variable + + align:start position:0% +we'll look at uh multi- variable + + + align:start position:0% +we'll look at uh multi- variable +analysis of variance where you have in + + align:start position:0% +analysis of variance where you have in + + + align:start position:0% +analysis of variance where you have in +this in this particular case we're going + + align:start position:0% +this in this particular case we're going + + + align:start position:0% +this in this particular case we're going +to look at two input variables and how + + align:start position:0% +to look at two input variables and how + + + align:start position:0% +to look at two input variables and how +we uh look at the interactions of those + + align:start position:0% +we uh look at the interactions of those + + + align:start position:0% +we uh look at the interactions of those +two variables in setting the output. + + align:start position:0% + + + + align:start position:0% + +So here we're we're going to start with + + align:start position:0% +So here we're we're going to start with + + + align:start position:0% +So here we're we're going to start with +the single variable ANOVA and uh this is + + align:start position:0% +the single variable ANOVA and uh this is + + + align:start position:0% +the single variable ANOVA and uh this is +a diagram that shows to you uh what + + align:start position:0% +a diagram that shows to you uh what + + + align:start position:0% +a diagram that shows to you uh what +might happen to the uh the output of a + + align:start position:0% +might happen to the uh the output of a + + + align:start position:0% +might happen to the uh the output of a +process uh which the output being uh + + align:start position:0% +process uh which the output being uh + + + align:start position:0% +process uh which the output being uh +being this axis + + align:start position:0% +being this axis + + + align:start position:0% +being this axis +um as we vary one particular input + + align:start position:0% +um as we vary one particular input + + + align:start position:0% +um as we vary one particular input +parameter. So we're assuming we have + + align:start position:0% +parameter. So we're assuming we have + + + align:start position:0% +parameter. So we're assuming we have +good control over this and we can + + align:start position:0% +good control over this and we can + + + align:start position:0% +good control over this and we can +command that that input parameter to be + + align:start position:0% +command that that input parameter to be + + + align:start position:0% +command that that input parameter to be +whatever we choose. In this particular + + align:start position:0% +whatever we choose. In this particular + + + align:start position:0% +whatever we choose. In this particular +case we're saying well that there there + + align:start position:0% +case we're saying well that there there + + + align:start position:0% +case we're saying well that there there +are three possible values we might be + + align:start position:0% +are three possible values we might be + + + align:start position:0% +are three possible values we might be +interested in uh a b and c. And so these + + align:start position:0% +interested in uh a b and c. And so these + + + align:start position:0% +interested in uh a b and c. And so these +are the three treatments and what we've + + align:start position:0% +are the three treatments and what we've + + + align:start position:0% +are the three treatments and what we've +shown here schematically is the + + align:start position:0% +shown here schematically is the + + + align:start position:0% +shown here schematically is the +distribution of the output variable + + align:start position:0% +distribution of the output variable + + + align:start position:0% +distribution of the output variable +under each of those three conditions. + + align:start position:0% + + + + align:start position:0% + +We're assuming that the uh the variation + + align:start position:0% +We're assuming that the uh the variation + + + align:start position:0% +We're assuming that the uh the variation +in the output for each particular + + align:start position:0% +in the output for each particular + + + align:start position:0% +in the output for each particular +treatment uh is normally distributed + + align:start position:0% +treatment uh is normally distributed + + + align:start position:0% +treatment uh is normally distributed +but that uh the mean of the output uh is + + align:start position:0% +but that uh the mean of the output uh is + + + align:start position:0% +but that uh the mean of the output uh is +determined directly by the value of this + + align:start position:0% +determined directly by the value of this + + + align:start position:0% +determined directly by the value of this +input parameter. So there's a onetoone + + align:start position:0% +input parameter. So there's a onetoone + + + align:start position:0% +input parameter. So there's a onetoone +deterministic relationship between the + + align:start position:0% +deterministic relationship between the + + + align:start position:0% +deterministic relationship between the +mean and uh the value of the input. So + + align:start position:0% +mean and uh the value of the input. So + + + align:start position:0% +mean and uh the value of the input. So +these TOAO values TOAO one, TOAO two and + + align:start position:0% +these TOAO values TOAO one, TOAO two and + + + align:start position:0% +these TOAO values TOAO one, TOAO two and +TOA 3 these are + + align:start position:0% +TOA 3 these are + + + align:start position:0% +TOA 3 these are +uh these are actually + + align:start position:0% +uh these are actually + + + align:start position:0% +uh these are actually +uh determined directly by the + + align:start position:0% +uh determined directly by the + + + align:start position:0% +uh determined directly by the +populations. But then if we imagine + + align:start position:0% +populations. But then if we imagine + + + align:start position:0% +populations. But then if we imagine +doing experiments under these three + + align:start position:0% +doing experiments under these three + + + align:start position:0% +doing experiments under these three +conditions uh we're going to take uh + + align:start position:0% +conditions uh we're going to take uh + + + align:start position:0% +conditions uh we're going to take uh +we're going to set the input to the + + align:start position:0% +we're going to set the input to the + + + align:start position:0% +we're going to set the input to the +value for sample A say and then we're + + align:start position:0% +value for sample A say and then we're + + + align:start position:0% +value for sample A say and then we're +going to take a a number of a number of + + align:start position:0% +going to take a a number of a number of + + + align:start position:0% +going to take a a number of a number of +output parts measure them and those + + align:start position:0% +output parts measure them and those + + + align:start position:0% +output parts measure them and those +outputs will have they will have a + + align:start position:0% +outputs will have they will have a + + + align:start position:0% +outputs will have they will have a +sample mean Y1 + + align:start position:0% +sample mean Y1 + + + align:start position:0% +sample mean Y1 +uh and there will be uh + + align:start position:0% +uh and there will be uh + + + align:start position:0% +uh and there will be uh +for each of these uh samples a sample + + align:start position:0% +for each of these uh samples a sample + + + align:start position:0% +for each of these uh samples a sample +mean we can take all the data together + + align:start position:0% +mean we can take all the data together + + + align:start position:0% +mean we can take all the data together +and come up with a grand average for the + + align:start position:0% +and come up with a grand average for the + + + align:start position:0% +and come up with a grand average for the +collected data. + + align:start position:0% +collected data. + + + align:start position:0% +collected data. +Then the the differences between those + + align:start position:0% +Then the the differences between those + + + align:start position:0% +Then the the differences between those +individual treatment sample means and + + align:start position:0% +individual treatment sample means and + + + align:start position:0% +individual treatment sample means and +the grand mean will uh be estimators for + + align:start position:0% +the grand mean will uh be estimators for + + + align:start position:0% +the grand mean will uh be estimators for +the values of of tow uh the effects of + + align:start position:0% +the values of of tow uh the effects of + + + align:start position:0% +the values of of tow uh the effects of +the treatments the different treatments + + align:start position:0% +the treatments the different treatments + + + align:start position:0% +the treatments the different treatments +that we're doing. + + align:start position:0% +that we're doing. + + + align:start position:0% +that we're doing. +So here's what we're doing. We're uh + + align:start position:0% +So here's what we're doing. We're uh + + + align:start position:0% +So here's what we're doing. We're uh +considering multiple settings for some + + align:start position:0% +considering multiple settings for some + + + align:start position:0% +considering multiple settings for some +variable of interest. And uh there are + + align:start position:0% +variable of interest. And uh there are + + + align:start position:0% +variable of interest. And uh there are +these real uh effects + + align:start position:0% +these real uh effects + + + align:start position:0% +these real uh effects +uh deltas between uh the the output the + + align:start position:0% +uh deltas between uh the the output the + + + align:start position:0% +uh deltas between uh the the output the +output mean uh for different conditions + + align:start position:0% +output mean uh for different conditions + + + align:start position:0% +output mean uh for different conditions +and uh we've we've observed these + + align:start position:0% +and uh we've we've observed these + + + align:start position:0% +and uh we've we've observed these +samples. So the the question is based on + + align:start position:0% +samples. So the the question is based on + + + align:start position:0% +samples. So the the question is based on +based on these observations + + align:start position:0% +based on these observations + + + align:start position:0% +based on these observations +uh we want to be able to uh + + align:start position:0% +uh we want to be able to uh + + + align:start position:0% +uh we want to be able to uh +see whether the observed differences in + + align:start position:0% +see whether the observed differences in + + + align:start position:0% +see whether the observed differences in +sample means are real. Uh so we're going + + align:start position:0% +sample means are real. Uh so we're going + + + align:start position:0% +sample means are real. Uh so we're going +to do some kind of hypothesis test that + + align:start position:0% +to do some kind of hypothesis test that + + + align:start position:0% +to do some kind of hypothesis test that +says uh the null hypothesis is going to + + align:start position:0% +says uh the null hypothesis is going to + + + align:start position:0% +says uh the null hypothesis is going to +be changing the input variable doesn't + + align:start position:0% +be changing the input variable doesn't + + + align:start position:0% +be changing the input variable doesn't +make a blind of difference to the output + + align:start position:0% +make a blind of difference to the output + + + align:start position:0% +make a blind of difference to the output +mean. And uh the alternate hypothesis is + + align:start position:0% +mean. And uh the alternate hypothesis is + + + align:start position:0% +mean. And uh the alternate hypothesis is +there is a significant difference which + + align:start position:0% +there is a significant difference which + + + align:start position:0% +there is a significant difference which +later we want to model somehow probably + + align:start position:0% +later we want to model somehow probably + + + align:start position:0% +later we want to model somehow probably +what's important uh in ANOVA is this + + align:start position:0% +what's important uh in ANOVA is this + + + align:start position:0% +what's important uh in ANOVA is this +assumption that the variance of the + + align:start position:0% +assumption that the variance of the + + + align:start position:0% +assumption that the variance of the +output for each uh + + align:start position:0% +output for each uh + + + align:start position:0% +output for each uh +for each treatment is equivalent and + + align:start position:0% +for each treatment is equivalent and + + + align:start position:0% +for each treatment is equivalent and +here we've written it as sigma subzero + + align:start position:0% +here we've written it as sigma subzero + + + align:start position:0% +here we've written it as sigma subzero +squared. So the width of each of those + + align:start position:0% +squared. So the width of each of those + + + align:start position:0% +squared. So the width of each of those +uh those subpopuls + + align:start position:0% +uh those subpopuls + + + align:start position:0% +uh those subpopuls +is uh has to be assumed to be to be + + align:start position:0% +is uh has to be assumed to be to be + + + align:start position:0% +is uh has to be assumed to be to be +equal and that that when one's doing an + + align:start position:0% +equal and that that when one's doing an + + + align:start position:0% +equal and that that when one's doing an +over that's something that one needs to + + align:start position:0% +over that's something that one needs to + + + align:start position:0% +over that's something that one needs to +check and we'll we'll talk about that a + + align:start position:0% +check and we'll we'll talk about that a + + + align:start position:0% +check and we'll we'll talk about that a +little later. + + align:start position:0% + + + + align:start position:0% + +Now I'm going to uh describe uh the + + align:start position:0% +Now I'm going to uh describe uh the + + + align:start position:0% +Now I'm going to uh describe uh the +underlying assumption that allows uh the + + align:start position:0% +underlying assumption that allows uh the + + + align:start position:0% +underlying assumption that allows uh the +analysis of variance to be done in this + + align:start position:0% +analysis of variance to be done in this + + + align:start position:0% +analysis of variance to be done in this +way. And uh this underlying assumption + + align:start position:0% +way. And uh this underlying assumption + + + align:start position:0% +way. And uh this underlying assumption +is that you can uh model the uh + + align:start position:0% +is that you can uh model the uh + + + align:start position:0% +is that you can uh model the uh +the value of uh sample part as the sum + + align:start position:0% +the value of uh sample part as the sum + + + align:start position:0% +the value of uh sample part as the sum +of three quantities. + + align:start position:0% +of three quantities. + + + align:start position:0% +of three quantities. +First quantity is the the process mean + + align:start position:0% +First quantity is the the process mean + + + align:start position:0% +First quantity is the the process mean +uh around which uh + + align:start position:0% +uh around which uh + + + align:start position:0% +uh around which uh +the output means of all the possible + + align:start position:0% +the output means of all the possible + + + align:start position:0% +the output means of all the possible +treatments center. + + align:start position:0% +treatments center. + + + align:start position:0% +treatments center. +Second is uh the the effect of the + + align:start position:0% +Second is uh the the effect of the + + + align:start position:0% +Second is uh the the effect of the +treatment. So that's how far is the + + align:start position:0% +treatment. So that's how far is the + + + align:start position:0% +treatment. So that's how far is the +output mean offset when you have this + + align:start position:0% +output mean offset when you have this + + + align:start position:0% +output mean offset when you have this +particular treatment tow taking place or + + align:start position:0% +particular treatment tow taking place or + + + align:start position:0% +particular treatment tow taking place or +there's a certain voltage setting on the + + align:start position:0% +there's a certain voltage setting on the + + + align:start position:0% +there's a certain voltage setting on the +input or whatever. And the third is this + + align:start position:0% +input or whatever. And the third is this + + + align:start position:0% +input or whatever. And the third is this +uh this residual term which we write + + align:start position:0% +uh this residual term which we write + + + align:start position:0% +uh this residual term which we write +with with epsilon and that is describing + + align:start position:0% +with with epsilon and that is describing + + + align:start position:0% +with with epsilon and that is describing +the the random variation in the output + + align:start position:0% +the the random variation in the output + + + align:start position:0% +the the random variation in the output +beyond the the systematic effect of the + + align:start position:0% +beyond the the systematic effect of the + + + align:start position:0% +beyond the the systematic effect of the +treatment. Sometimes we take this mu and + + align:start position:0% +treatment. Sometimes we take this mu and + + + align:start position:0% +treatment. Sometimes we take this mu and +the tao subt together we write it as as + + align:start position:0% +the tao subt together we write it as as + + + align:start position:0% +the tao subt together we write it as as +a mu subt that's the output mean for a + + align:start position:0% +a mu subt that's the output mean for a + + + align:start position:0% +a mu subt that's the output mean for a +particular treatment. + + align:start position:0% + + + + align:start position:0% + +So at the bottom of this graph, I've uh + + align:start position:0% +So at the bottom of this graph, I've uh + + + align:start position:0% +So at the bottom of this graph, I've uh +I've just sketched that out to show what + + align:start position:0% +I've just sketched that out to show what + + + align:start position:0% +I've just sketched that out to show what +I mean. uh here is the sort of the the + + align:start position:0% +I mean. uh here is the sort of the the + + + align:start position:0% +I mean. uh here is the sort of the the +process overall process mean uh here is + + align:start position:0% +process overall process mean uh here is + + + align:start position:0% +process overall process mean uh here is +the output mean for a particular + + align:start position:0% +the output mean for a particular + + + align:start position:0% +the output mean for a particular +treatment and say if we take this uh + + align:start position:0% +treatment and say if we take this uh + + + align:start position:0% +treatment and say if we take this uh +this particular sample for example then + + align:start position:0% +this particular sample for example then + + + align:start position:0% +this particular sample for example then +there's a residual there's a difference + + align:start position:0% +there's a residual there's a difference + + + align:start position:0% +there's a residual there's a difference +between the treatment mean and the + + align:start position:0% +between the treatment mean and the + + + align:start position:0% +between the treatment mean and the +actual value of that sample uh which is + + align:start position:0% +actual value of that sample uh which is + + + align:start position:0% +actual value of that sample uh which is +uh epsilon subti sorry that squared + + align:start position:0% +uh epsilon subti sorry that squared + + + align:start position:0% +uh epsilon subti sorry that squared +shouldn't be there so + + align:start position:0% +shouldn't be there so + + + align:start position:0% +shouldn't be there so +uh the sum of these three quantities uh + + align:start position:0% +uh the sum of these three quantities uh + + + align:start position:0% +uh the sum of these three quantities uh +is is thought of as giving us the the + + align:start position:0% +is is thought of as giving us the the + + + align:start position:0% +is is thought of as giving us the the +output uh the output quantity. + + align:start position:0% + + + + align:start position:0% + +Now I'm going to describe the uh the + + align:start position:0% +Now I'm going to describe the uh the + + + align:start position:0% +Now I'm going to describe the uh the +three steps that one is going to go + + align:start position:0% +three steps that one is going to go + + + align:start position:0% +three steps that one is going to go +through to test this hypothesis that + + align:start position:0% +through to test this hypothesis that + + + align:start position:0% +through to test this hypothesis that +changing the value of the input has no + + align:start position:0% +changing the value of the input has no + + + align:start position:0% +changing the value of the input has no +effect on the the the treatment means. + + align:start position:0% +effect on the the the treatment means. + + + align:start position:0% +effect on the the the treatment means. +And uh the first step is to uh come up + + align:start position:0% +And uh the first step is to uh come up + + + align:start position:0% +And uh the first step is to uh come up +with an estimate of the uh the + + align:start position:0% +with an estimate of the uh the + + + align:start position:0% +with an estimate of the uh the +underlying population variance that + + align:start position:0% +underlying population variance that + + + align:start position:0% +underlying population variance that +involves looking at each uh treatment + + align:start position:0% +involves looking at each uh treatment + + + align:start position:0% +involves looking at each uh treatment +sample in turn. So looking at this + + align:start position:0% +sample in turn. So looking at this + + + align:start position:0% +sample in turn. So looking at this +sample then this sample and looking at + + align:start position:0% +sample then this sample and looking at + + + align:start position:0% +sample then this sample and looking at +the uh sample variance individually for + + align:start position:0% +the uh sample variance individually for + + + align:start position:0% +the uh sample variance individually for +each sample and then uh taking a pulled + + align:start position:0% +each sample and then uh taking a pulled + + + align:start position:0% +each sample and then uh taking a pulled +estimate of the uh the random component + + align:start position:0% +estimate of the uh the random component + + + align:start position:0% +estimate of the uh the random component +of of variation based on all those + + align:start position:0% +of of variation based on all those + + + align:start position:0% +of of variation based on all those +sample + + align:start position:0% +sample + + + align:start position:0% +sample +variances. + + align:start position:0% +variances. + + + align:start position:0% +variances. +That's the first step. Second step is to + + align:start position:0% +That's the first step. Second step is to + + + align:start position:0% +That's the first step. Second step is to +uh try to look at uh the between group + + align:start position:0% +uh try to look at uh the between group + + + align:start position:0% +uh try to look at uh the between group +variation and that means uh looking at + + align:start position:0% +variation and that means uh looking at + + + align:start position:0% +variation and that means uh looking at +the sample means which I've denoted with + + align:start position:0% +the sample means which I've denoted with + + + align:start position:0% +the sample means which I've denoted with +these uh these horizontal lines here and + + align:start position:0% +these uh these horizontal lines here and + + + align:start position:0% +these uh these horizontal lines here and +uh looking looking at the variance of + + align:start position:0% +uh looking looking at the variance of + + + align:start position:0% +uh looking looking at the variance of +those and making an inference from that + + align:start position:0% +those and making an inference from that + + + align:start position:0% +those and making an inference from that +about how much variation there is in the + + align:start position:0% +about how much variation there is in the + + + align:start position:0% +about how much variation there is in the +output as we change uh the input + + align:start position:0% +output as we change uh the input + + + align:start position:0% +output as we change uh the input +setting. + + align:start position:0% +setting. + + + align:start position:0% +setting. +Once we've got those two estimates + + align:start position:0% +Once we've got those two estimates + + + align:start position:0% +Once we've got those two estimates +within group variation between group + + align:start position:0% +within group variation between group + + + align:start position:0% +within group variation between group +variation we want to compare those uh + + align:start position:0% +variation we want to compare those uh + + + align:start position:0% +variation we want to compare those uh +those estimates and uh infer from that + + align:start position:0% +those estimates and uh infer from that + + + align:start position:0% +those estimates and uh infer from that +whether uh there is a difference between + + align:start position:0% +whether uh there is a difference between + + + align:start position:0% +whether uh there is a difference between +the the the the different treatments. + + align:start position:0% +the the the the different treatments. + + + align:start position:0% +the the the the different treatments. +If there is a difference then we're + + align:start position:0% +If there is a difference then we're + + + align:start position:0% +If there is a difference then we're +going to expect the second estimate that + + align:start position:0% +going to expect the second estimate that + + + align:start position:0% +going to expect the second estimate that +we make to be larger than the first + + align:start position:0% +we make to be larger than the first + + + align:start position:0% +we make to be larger than the first +estimate. And just by looking at this uh + + align:start position:0% +estimate. And just by looking at this uh + + + align:start position:0% +estimate. And just by looking at this uh +this schematic in the top right of of + + align:start position:0% +this schematic in the top right of of + + + align:start position:0% +this schematic in the top right of of +the view graph, uh you you can perhaps + + align:start position:0% +the view graph, uh you you can perhaps + + + align:start position:0% +the view graph, uh you you can perhaps +see intuitively how that might be the + + align:start position:0% +see intuitively how that might be the + + + align:start position:0% +see intuitively how that might be the +the var the variance associated with um + + align:start position:0% +the var the variance associated with um + + + align:start position:0% +the var the variance associated with um +uh the uh the between group uh changes + + align:start position:0% +uh the uh the between group uh changes + + + align:start position:0% +uh the uh the between group uh changes +is is going to be larger if there's a + + align:start position:0% +is is going to be larger if there's a + + + align:start position:0% +is is going to be larger if there's a +significant impact of the input on the + + align:start position:0% +significant impact of the input on the + + + align:start position:0% +significant impact of the input on the +output. Um but if not then those two + + align:start position:0% +output. Um but if not then those two + + + align:start position:0% +output. Um but if not then those two +variances estimates should be equal. + + align:start position:0% +variances estimates should be equal. + + + align:start position:0% +variances estimates should be equal. +There's no effect uh had by the input. + + align:start position:0% + + + + align:start position:0% + +I'm going to go through each of those + + align:start position:0% +I'm going to go through each of those + + + align:start position:0% +I'm going to go through each of those +steps in turn and go through the + + align:start position:0% +steps in turn and go through the + + + align:start position:0% +steps in turn and go through the +mechanics of how uh we're going to do + + align:start position:0% +mechanics of how uh we're going to do + + + align:start position:0% +mechanics of how uh we're going to do +that. + + align:start position:0% +that. + + + align:start position:0% +that. +I've already said that we're assuming uh + + align:start position:0% +I've already said that we're assuming uh + + + align:start position:0% +I've already said that we're assuming uh +that uh the the output for each group + + align:start position:0% +that uh the the output for each group + + + align:start position:0% +that uh the the output for each group +and by group I mean uh the the the parts + + align:start position:0% +and by group I mean uh the the the parts + + + align:start position:0% +and by group I mean uh the the the parts +sampled for a given treatment. So for a + + align:start position:0% +sampled for a given treatment. So for a + + + align:start position:0% +sampled for a given treatment. So for a +given setting of the input variable, + + align:start position:0% +given setting of the input variable, + + + align:start position:0% +given setting of the input variable, +we're saying that that that variation + + align:start position:0% +we're saying that that that variation + + + align:start position:0% +we're saying that that that variation +has is described by a variance of sigma + + align:start position:0% +has is described by a variance of sigma + + + align:start position:0% +has is described by a variance of sigma +n squared and it's the same for each + + align:start position:0% +n squared and it's the same for each + + + align:start position:0% +n squared and it's the same for each +group which may be true or may not be uh + + align:start position:0% +group which may be true or may not be uh + + + align:start position:0% +group which may be true or may not be uh +in which case we need to go back and + + align:start position:0% +in which case we need to go back and + + + align:start position:0% +in which case we need to go back and +think again. + + align:start position:0% + + + + align:start position:0% + +So the second bullet point here is uh is + + align:start position:0% +So the second bullet point here is uh is + + + align:start position:0% +So the second bullet point here is uh is +is + + align:start position:0% +is + + + align:start position:0% +is +giving us the sum of the square + + align:start position:0% +giving us the sum of the square + + + align:start position:0% +giving us the sum of the square +deviations for the teeth uh teeth group + + align:start position:0% +deviations for the teeth uh teeth group + + + align:start position:0% +deviations for the teeth uh teeth group +and uh so this is just saying we have uh + + align:start position:0% +and uh so this is just saying we have uh + + + align:start position:0% +and uh so this is just saying we have uh +we have a sampled value for the output y + + align:start position:0% +we have a sampled value for the output y + + + align:start position:0% +we have a sampled value for the output y +subti + + align:start position:0% +subti + + + align:start position:0% +subti +we've taken uh a mean for the group y + + align:start position:0% +we've taken uh a mean for the group y + + + align:start position:0% +we've taken uh a mean for the group y +bar subt + + align:start position:0% +bar subt + + + align:start position:0% +bar subt +which is here + + align:start position:0% +which is here + + + align:start position:0% +which is here +and uh we're summing the squares of the + + align:start position:0% +and uh we're summing the squares of the + + + align:start position:0% +and uh we're summing the squares of the +deviations between these values and the + + align:start position:0% +deviations between these values and the + + + align:start position:0% +deviations between these values and the +sample mean. + + align:start position:0% +sample mean. + + + align:start position:0% +sample mean. +Once we've done that, it's a simple step + + align:start position:0% +Once we've done that, it's a simple step + + + align:start position:0% +Once we've done that, it's a simple step +to go to the the group variance. Uh so + + align:start position:0% +to go to the the group variance. Uh so + + + align:start position:0% +to go to the the group variance. Uh so +this is an unbiased estimate of the of + + align:start position:0% +this is an unbiased estimate of the of + + + align:start position:0% +this is an unbiased estimate of the of +the group variance the sum of the + + align:start position:0% +the group variance the sum of the + + + align:start position:0% +the group variance the sum of the +squares divided by the uh the number of + + align:start position:0% +squares divided by the uh the number of + + + align:start position:0% +squares divided by the uh the number of +degrees of freedom in uh in that + + align:start position:0% +degrees of freedom in uh in that + + + align:start position:0% +degrees of freedom in uh in that +treatment. So that's the number of uh + + align:start position:0% +treatment. So that's the number of uh + + + align:start position:0% +treatment. So that's the number of uh +the number of parts sampled minus one + + align:start position:0% +the number of parts sampled minus one + + + align:start position:0% +the number of parts sampled minus one +and the minus one is because well the + + align:start position:0% +and the minus one is because well the + + + align:start position:0% +and the minus one is because well the +the the value of the mean y bar subt is + + align:start position:0% +the the value of the mean y bar subt is + + + align:start position:0% +the the value of the mean y bar subt is +dependent on all the individual y + + align:start position:0% +dependent on all the individual y + + + align:start position:0% +dependent on all the individual y +subtis. So uh + + align:start position:0% +subtis. So uh + + + align:start position:0% +subtis. So uh +that there's one less degree of freedom + + align:start position:0% +that there's one less degree of freedom + + + align:start position:0% +that there's one less degree of freedom +than there are data points. + + align:start position:0% + + + + align:start position:0% + +Once we've got each of those group + + align:start position:0% +Once we've got each of those group + + + align:start position:0% +Once we've got each of those group +variances based on the data, we're going + + align:start position:0% +variances based on the data, we're going + + + align:start position:0% +variances based on the data, we're going +to take a a pulled estimate of the + + align:start position:0% +to take a a pulled estimate of the + + + align:start position:0% +to take a a pulled estimate of the +common within group variance. So + + align:start position:0% +common within group variance. So + + + align:start position:0% +common within group variance. So +inherent in this again is the assumption + + align:start position:0% +inherent in this again is the assumption + + + align:start position:0% +inherent in this again is the assumption +that the v the variance uh could be + + align:start position:0% +that the v the variance uh could be + + + align:start position:0% +that the v the variance uh could be +modeled as being equal for each group. + + align:start position:0% +modeled as being equal for each group. + + + align:start position:0% +modeled as being equal for each group. +And uh actually well there that should + + align:start position:0% +And uh actually well there that should + + + align:start position:0% +And uh actually well there that should +be a up to um + + align:start position:0% +be a up to um + + + align:start position:0% +be a up to um +but what we're doing this is effectively + + align:start position:0% +but what we're doing this is effectively + + + align:start position:0% +but what we're doing this is effectively +taking a weighted average based on the + + align:start position:0% +taking a weighted average based on the + + + align:start position:0% +taking a weighted average based on the +number of data points that we have for + + align:start position:0% +number of data points that we have for + + + align:start position:0% +number of data points that we have for +each uh for each group. So we might take + + align:start position:0% +each uh for each group. So we might take + + + align:start position:0% +each uh for each group. So we might take +more samples for a particular treatment + + align:start position:0% +more samples for a particular treatment + + + align:start position:0% +more samples for a particular treatment +uh but we can deal with that uh by uh + + align:start position:0% +uh but we can deal with that uh by uh + + + align:start position:0% +uh but we can deal with that uh by uh +using the correct number of degrees of + + align:start position:0% +using the correct number of degrees of + + + align:start position:0% +using the correct number of degrees of +freedom for each treatment. And what we + + align:start position:0% +freedom for each treatment. And what we + + + align:start position:0% +freedom for each treatment. And what we +get out of that is this poolled estimate + + align:start position:0% +get out of that is this poolled estimate + + + align:start position:0% +get out of that is this poolled estimate +of common variance uh + + align:start position:0% +of common variance uh + + + align:start position:0% +of common variance uh +s subr squ. + + align:start position:0% + + + + align:start position:0% + +So that was the within group variance + + align:start position:0% +So that was the within group variance + + + align:start position:0% +So that was the within group variance +and now we're going to talk about uh the + + align:start position:0% +and now we're going to talk about uh the + + + align:start position:0% +and now we're going to talk about uh the +between group variance. As I said, we're + + align:start position:0% +between group variance. As I said, we're + + + align:start position:0% +between group variance. As I said, we're +testing the hypothesis that varying the + + align:start position:0% +testing the hypothesis that varying the + + + align:start position:0% +testing the hypothesis that varying the +input uh does not uh cause the uh the + + align:start position:0% +input uh does not uh cause the uh the + + + align:start position:0% +input uh does not uh cause the uh the +output mean to vary. + + align:start position:0% +output mean to vary. + + + align:start position:0% +output mean to vary. +If that were true, then uh what what + + align:start position:0% +If that were true, then uh what what + + + align:start position:0% +If that were true, then uh what what +I've sketched on the bottom left here + + align:start position:0% +I've sketched on the bottom left here + + + align:start position:0% +I've sketched on the bottom left here +would be the case. You would have, you + + align:start position:0% +would be the case. You would have, you + + + align:start position:0% +would be the case. You would have, you +know, three populations that looked + + align:start position:0% +know, three populations that looked + + + align:start position:0% +know, three populations that looked +absolutely identical and uh it wouldn't + + align:start position:0% +absolutely identical and uh it wouldn't + + + align:start position:0% +absolutely identical and uh it wouldn't +matter what value you chose for the + + align:start position:0% +matter what value you chose for the + + + align:start position:0% +matter what value you chose for the +input, you get the same output. However, + + align:start position:0% +input, you get the same output. However, + + + align:start position:0% +input, you get the same output. However, +when you sample, we know that of course + + align:start position:0% +when you sample, we know that of course + + + align:start position:0% +when you sample, we know that of course +because there's random variation in the + + align:start position:0% +because there's random variation in the + + + align:start position:0% +because there's random variation in the +output, the sample mean will not always + + align:start position:0% +output, the sample mean will not always + + + align:start position:0% +output, the sample mean will not always +be the same and that will vary. That + + align:start position:0% +be the same and that will vary. That + + + align:start position:0% +be the same and that will vary. That +will sample mean will itself be normally + + align:start position:0% +will sample mean will itself be normally + + + align:start position:0% +will sample mean will itself be normally +distributed with a variance of uh sigma + + align:start position:0% +distributed with a variance of uh sigma + + + align:start position:0% +distributed with a variance of uh sigma +squar over n where n is the number of + + align:start position:0% +squar over n where n is the number of + + + align:start position:0% +squar over n where n is the number of +samples in uh in the number of data + + align:start position:0% +samples in uh in the number of data + + + align:start position:0% +samples in uh in the number of data +points in the sample. + + align:start position:0% +points in the sample. + + + align:start position:0% +points in the sample. +So this is looking a little bit on on + + align:start position:0% +So this is looking a little bit on on + + + align:start position:0% +So this is looking a little bit on on +the bottom right a little bit like a + + align:start position:0% +the bottom right a little bit like a + + + align:start position:0% +the bottom right a little bit like a +control chart where the the y- axis is + + align:start position:0% +control chart where the the y- axis is + + + align:start position:0% +control chart where the the y- axis is +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the could be thought of as um + + align:start position:0% + + + + align:start position:0% + +as as uh + + align:start position:0% +as as uh + + + align:start position:0% +as as uh +being linked to uh + + align:start position:0% +being linked to uh + + + align:start position:0% +being linked to uh +sigma squared uh divided by the sample + + align:start position:0% +sigma squared uh divided by the sample + + + align:start position:0% +sigma squared uh divided by the sample +size. And uh so what this all means is + + align:start position:0% +size. And uh so what this all means is + + + align:start position:0% +size. And uh so what this all means is +that if the uh if the hypothesis was + + align:start position:0% +that if the uh if the hypothesis was + + + align:start position:0% +that if the uh if the hypothesis was +true, inputs don't affect the output + + align:start position:0% +true, inputs don't affect the output + + + align:start position:0% +true, inputs don't affect the output +mean uh then we could form a second + + align:start position:0% +mean uh then we could form a second + + + align:start position:0% +mean uh then we could form a second +estimate of the uh + + align:start position:0% +estimate of the uh + + + align:start position:0% +estimate of the uh +uh the within group variation + + align:start position:0% +uh the within group variation + + + align:start position:0% +uh the within group variation +uh by looking at it this way + + align:start position:0% +uh by looking at it this way + + + align:start position:0% +uh by looking at it this way +where we're taking uh the treatment mean + + align:start position:0% +where we're taking uh the treatment mean + + + align:start position:0% +where we're taking uh the treatment mean +which are these values here. We're + + align:start position:0% +which are these values here. We're + + + align:start position:0% +which are these values here. We're +subtracting uh the grand mean of all the + + align:start position:0% +subtracting uh the grand mean of all the + + + align:start position:0% +subtracting uh the grand mean of all the +data from each treatment mean in turn. + + align:start position:0% +data from each treatment mean in turn. + + + align:start position:0% +data from each treatment mean in turn. +We're taking the square of those + + align:start position:0% +We're taking the square of those + + + align:start position:0% +We're taking the square of those +deviations. And this n subt here is + + align:start position:0% +deviations. And this n subt here is + + + align:start position:0% +deviations. And this n subt here is +accounting for the fact that + + align:start position:0% +accounting for the fact that + + + align:start position:0% +accounting for the fact that +because of the central limit theorem uh + + align:start position:0% +because of the central limit theorem uh + + + align:start position:0% +because of the central limit theorem uh +the variance of the sample mean is + + align:start position:0% +the variance of the sample mean is + + + align:start position:0% +the variance of the sample mean is +inversely proportional to the sample + + align:start position:0% +inversely proportional to the sample + + + align:start position:0% +inversely proportional to the sample +size + + align:start position:0% +size + + + align:start position:0% +size +and uh k is the number of different + + align:start position:0% +and uh k is the number of different + + + align:start position:0% +and uh k is the number of different +treatments. So in this case k is three. + + align:start position:0% +treatments. So in this case k is three. + + + align:start position:0% +treatments. So in this case k is three. +So we're making this estimate s subt^2 + + align:start position:0% +So we're making this estimate s subt^2 + + + align:start position:0% +So we're making this estimate s subt^2 +which in the case I've sketched here we + + align:start position:0% +which in the case I've sketched here we + + + align:start position:0% +which in the case I've sketched here we +would expect to be equal to s subr 2. + + align:start position:0% +would expect to be equal to s subr 2. + + + align:start position:0% +would expect to be equal to s subr 2. +However, uh and uh + + align:start position:0% + + + + align:start position:0% + +if that isn't the case, if there is a + + align:start position:0% +if that isn't the case, if there is a + + + align:start position:0% +if that isn't the case, if there is a +significant relationship between the + + align:start position:0% +significant relationship between the + + + align:start position:0% +significant relationship between the +input and the output, + + align:start position:0% +input and the output, + + + align:start position:0% +input and the output, +uh then s subt^ 2 will be larger than s + + align:start position:0% +uh then s subt^ 2 will be larger than s + + + align:start position:0% +uh then s subt^ 2 will be larger than s +subr squ. And uh that's the the quantity + + align:start position:0% +subr squ. And uh that's the the quantity + + + align:start position:0% +subr squ. And uh that's the the quantity +by which it's larger. + + align:start position:0% +by which it's larger. + + + align:start position:0% +by which it's larger. +This sum here and this value to subt is + + align:start position:0% +This sum here and this value to subt is + + + align:start position:0% +This sum here and this value to subt is +the is the real difference the actual + + align:start position:0% +the is the real difference the actual + + + align:start position:0% +the is the real difference the actual +systematic change in treatment uh output + + align:start position:0% +systematic change in treatment uh output + + + align:start position:0% +systematic change in treatment uh output +mean that occurs when we vary the input. + + align:start position:0% + + + + align:start position:0% + +So we're causing an an inflation in the + + align:start position:0% +So we're causing an an inflation in the + + + align:start position:0% +So we're causing an an inflation in the +value of S subt^ squ based on the uh the + + align:start position:0% +value of S subt^ squ based on the uh the + + + align:start position:0% +value of S subt^ squ based on the uh the +fact that changing the input changes the + + align:start position:0% +fact that changing the input changes the + + + align:start position:0% +fact that changing the input changes the +output mean. So we've got these two + + align:start position:0% +output mean. So we've got these two + + + align:start position:0% +output mean. So we've got these two +estimates uh the within group variation + + align:start position:0% +estimates uh the within group variation + + + align:start position:0% +estimates uh the within group variation +and the the between group variation. we + + align:start position:0% +and the the between group variation. we + + + align:start position:0% +and the the between group variation. we +want to look at them and compare them + + align:start position:0% +want to look at them and compare them + + + align:start position:0% +want to look at them and compare them +and say uh is there is there a + + align:start position:0% +and say uh is there is there a + + + align:start position:0% +and say uh is there is there a +significant impact on the output when we + + align:start position:0% +significant impact on the output when we + + + align:start position:0% +significant impact on the output when we +go through these different treatments. + + align:start position:0% +go through these different treatments. + + + align:start position:0% +go through these different treatments. +So we're comparing two variances and uh + + align:start position:0% +So we're comparing two variances and uh + + + align:start position:0% +So we're comparing two variances and uh +that means that what we're interested in + + align:start position:0% +that means that what we're interested in + + + align:start position:0% +that means that what we're interested in +doing is an F test. + + align:start position:0% + + + + align:start position:0% + +So we're asking ourselves + + align:start position:0% +So we're asking ourselves + + + align:start position:0% +So we're asking ourselves +how big is the chance that if the null + + align:start position:0% +how big is the chance that if the null + + + align:start position:0% +how big is the chance that if the null +hypothesis were true, we would observe + + align:start position:0% +hypothesis were true, we would observe + + + align:start position:0% +hypothesis were true, we would observe +these two variances. + + align:start position:0% + + + + align:start position:0% + +We're going to make the test statistic + + align:start position:0% +We're going to make the test statistic + + + align:start position:0% +We're going to make the test statistic +the ratio s subt ^ 2 / s subr 2. So + + align:start position:0% +the ratio s subt ^ 2 / s subr 2. So + + + align:start position:0% +the ratio s subt ^ 2 / s subr 2. So +that's going to usually be value greater + + align:start position:0% +that's going to usually be value greater + + + align:start position:0% +that's going to usually be value greater +than one. And uh + + align:start position:0% +than one. And uh + + + align:start position:0% +than one. And uh +we reject the null hypothesis if that + + align:start position:0% +we reject the null hypothesis if that + + + align:start position:0% +we reject the null hypothesis if that +value is significantly greater than one + + align:start position:0% + + + + align:start position:0% + +it's worth remembering here. Go ahead. + + align:start position:0% +it's worth remembering here. Go ahead. + + + align:start position:0% +it's worth remembering here. Go ahead. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Right. Well, we're going to do an F test + + align:start position:0% +Right. Well, we're going to do an F test + + + align:start position:0% +Right. Well, we're going to do an F test +at a chosen level of significance to + + align:start position:0% +at a chosen level of significance to + + + align:start position:0% +at a chosen level of significance to +work that out. + + align:start position:0% +work that out. + + + align:start position:0% +work that out. +And that's exactly what this slide says. + + align:start position:0% +And that's exactly what this slide says. + + + align:start position:0% +And that's exactly what this slide says. +So, good question. um we have this f F + + align:start position:0% +So, good question. um we have this f F + + + align:start position:0% +So, good question. um we have this f F +statistic and uh we're now going to + + align:start position:0% +statistic and uh we're now going to + + + align:start position:0% +statistic and uh we're now going to +interpret that. We're going to pick a + + align:start position:0% +interpret that. We're going to pick a + + + align:start position:0% +interpret that. We're going to pick a +particular significance level which we + + align:start position:0% +particular significance level which we + + + align:start position:0% +particular significance level which we +want to say is it at the 5% level is it + + align:start position:0% +want to say is it at the 5% level is it + + + align:start position:0% +want to say is it at the 5% level is it +significant that there's a a + + align:start position:0% +significant that there's a a + + + align:start position:0% +significant that there's a a +relationship between the the treatment + + align:start position:0% +relationship between the the treatment + + + align:start position:0% +relationship between the the treatment +that's chosen and the output mean. + + align:start position:0% +that's chosen and the output mean. + + + align:start position:0% +that's chosen and the output mean. +It's important to remember that this is + + align:start position:0% +It's important to remember that this is + + + align:start position:0% +It's important to remember that this is +a a one-sided F test that we're + + align:start position:0% +a a one-sided F test that we're + + + align:start position:0% +a a one-sided F test that we're +interested in doing. uh the possibility + + align:start position:0% +interested in doing. uh the possibility + + + align:start position:0% +interested in doing. uh the possibility +we're considering is that sigma subt is + + align:start position:0% +we're considering is that sigma subt is + + + align:start position:0% +we're considering is that sigma subt is +greater than sigma subr 2. The the case + + align:start position:0% +greater than sigma subr 2. The the case + + + align:start position:0% +greater than sigma subr 2. The the case +where the real value of uh + + align:start position:0% +where the real value of uh + + + align:start position:0% +where the real value of uh +the between group variance is less than + + align:start position:0% +the between group variance is less than + + + align:start position:0% +the between group variance is less than +the real value of the within group + + align:start position:0% +the real value of the within group + + + align:start position:0% +the real value of the within group +variance is not something that has a + + align:start position:0% +variance is not something that has a + + + align:start position:0% +variance is not something that has a +physical meaning. So, it's a one-sided F + + align:start position:0% +physical meaning. So, it's a one-sided F + + + align:start position:0% +physical meaning. So, it's a one-sided F +test uh where the statistic we're + + align:start position:0% +test uh where the statistic we're + + + align:start position:0% +test uh where the statistic we're +expecting to be bigger than one, much + + align:start position:0% +expecting to be bigger than one, much + + + align:start position:0% +expecting to be bigger than one, much +bigger than one. And uh here are the uh + + align:start position:0% +bigger than one. And uh here are the uh + + + align:start position:0% +bigger than one. And uh here are the uh +the degrees of freedom that we need to + + align:start position:0% +the degrees of freedom that we need to + + + align:start position:0% +the degrees of freedom that we need to +use uh for that evaluation. + + align:start position:0% +use uh for that evaluation. + + + align:start position:0% +use uh for that evaluation. +And + + align:start position:0% + + + + align:start position:0% + +that's uh based on what we've learned so + + align:start position:0% +that's uh based on what we've learned so + + + align:start position:0% +that's uh based on what we've learned so +far, fairly straightforward test to do. + + align:start position:0% +far, fairly straightforward test to do. + + + align:start position:0% +far, fairly straightforward test to do. +uh + + align:start position:0% +uh + + + align:start position:0% +uh +we can also make this this additional + + align:start position:0% +we can also make this this additional + + + align:start position:0% +we can also make this this additional +estimate which is the sum based on the + + align:start position:0% +estimate which is the sum based on the + + + align:start position:0% +estimate which is the sum based on the +sum of the squared deviations from the + + align:start position:0% +sum of the squared deviations from the + + + align:start position:0% +sum of the squared deviations from the +grand mean among all samples and that + + align:start position:0% +grand mean among all samples and that + + + align:start position:0% +grand mean among all samples and that +can be useful in a number of ways + + align:start position:0% +can be useful in a number of ways + + + align:start position:0% +can be useful in a number of ways +although it's not central to uh + + align:start position:0% +although it's not central to uh + + + align:start position:0% +although it's not central to uh +evaluating this fstistic and testing the + + align:start position:0% +evaluating this fstistic and testing the + + + align:start position:0% +evaluating this fstistic and testing the +hypothesis that we've described. + + align:start position:0% + + + + align:start position:0% + +This slide is pretty important. So this + + align:start position:0% +This slide is pretty important. So this + + + align:start position:0% +This slide is pretty important. So this +shows you uh how one usually would lay + + align:start position:0% +shows you uh how one usually would lay + + + align:start position:0% +shows you uh how one usually would lay +out an ANOVA analysis and uh we would we + + align:start position:0% +out an ANOVA analysis and uh we would we + + + align:start position:0% +out an ANOVA analysis and uh we would we +would put real quantities in the spaces + + align:start position:0% +would put real quantities in the spaces + + + align:start position:0% +would put real quantities in the spaces +shown by expressions here. We'd evaluate + + align:start position:0% +shown by expressions here. We'd evaluate + + + align:start position:0% +shown by expressions here. We'd evaluate +the sum of squares between treatments + + align:start position:0% +the sum of squares between treatments + + + align:start position:0% +the sum of squares between treatments +and within treatments and uh we'd figure + + align:start position:0% +and within treatments and uh we'd figure + + + align:start position:0% +and within treatments and uh we'd figure +out what the number of degrees of + + align:start position:0% +out what the number of degrees of + + + align:start position:0% +out what the number of degrees of +freedom was. We'd look at the uh the + + align:start position:0% +freedom was. We'd look at the uh the + + + align:start position:0% +freedom was. We'd look at the uh the +estimates of our variances. We take + + align:start position:0% +estimates of our variances. We take + + + align:start position:0% +estimates of our variances. We take +their ratio and we would then use uh f + + align:start position:0% +their ratio and we would then use uh f + + + align:start position:0% +their ratio and we would then use uh f +tables to uh find the probability that + + align:start position:0% +tables to uh find the probability that + + + align:start position:0% +tables to uh find the probability that +by chance that uh value of f sub0 uh was + + align:start position:0% +by chance that uh value of f sub0 uh was + + + align:start position:0% +by chance that uh value of f sub0 uh was +observed if the null hypothesis + + align:start position:0% +observed if the null hypothesis + + + align:start position:0% +observed if the null hypothesis +uh of zero treatment effect were true. + + align:start position:0% + + + + align:start position:0% + +And uh + + align:start position:0% + + + + align:start position:0% + +it's worth remembering this word + + align:start position:0% +it's worth remembering this word + + + align:start position:0% +it's worth remembering this word +residual. So I I before when I + + align:start position:0% +residual. So I I before when I + + + align:start position:0% +residual. So I I before when I +highlighted that quantity epsilon which + + align:start position:0% +highlighted that quantity epsilon which + + + align:start position:0% +highlighted that quantity epsilon which +is the variation associated with with + + align:start position:0% +is the variation associated with with + + + align:start position:0% +is the variation associated with with +randomness the thing that we're not + + align:start position:0% +randomness the thing that we're not + + + align:start position:0% +randomness the thing that we're not +trying to model in looking at looking at + + align:start position:0% +trying to model in looking at looking at + + + align:start position:0% +trying to model in looking at looking at +these different treatments uh that is uh + + align:start position:0% +these different treatments uh that is uh + + + align:start position:0% +these different treatments uh that is uh +accounted for by this sum of squares + + align:start position:0% +accounted for by this sum of squares + + + align:start position:0% +accounted for by this sum of squares +within treatments. + + align:start position:0% + + + + align:start position:0% + +What I'm going to do now is work through + + align:start position:0% +What I'm going to do now is work through + + + align:start position:0% +What I'm going to do now is work through +a very simple example to show how this + + align:start position:0% +a very simple example to show how this + + + align:start position:0% +a very simple example to show how this +single variable ANOVA can be done and uh + + align:start position:0% +single variable ANOVA can be done and uh + + + align:start position:0% +single variable ANOVA can be done and uh +it'll hopefully give you a feel for uh + + align:start position:0% +it'll hopefully give you a feel for uh + + + align:start position:0% +it'll hopefully give you a feel for uh +for the steps that have to be gone + + align:start position:0% +for the steps that have to be gone + + + align:start position:0% +for the steps that have to be gone +through. This sort of thing is automated + + align:start position:0% +through. This sort of thing is automated + + + align:start position:0% +through. This sort of thing is automated +in a number of programs. There are + + align:start position:0% +in a number of programs. There are + + + align:start position:0% +in a number of programs. There are +macros available in Excel to do it. But + + align:start position:0% +macros available in Excel to do it. But + + + align:start position:0% +macros available in Excel to do it. But +it's worth uh knowing exactly what the + + align:start position:0% +it's worth uh knowing exactly what the + + + align:start position:0% +it's worth uh knowing exactly what the +steps are so that uh so so that you + + align:start position:0% +steps are so that uh so so that you + + + align:start position:0% +steps are so that uh so so that you +understand what's going on. + + align:start position:0% +understand what's going on. + + + align:start position:0% +understand what's going on. +What we've got here are uh three samples + + align:start position:0% +What we've got here are uh three samples + + + align:start position:0% +What we've got here are uh three samples +for each of three treatments of a + + align:start position:0% +for each of three treatments of a + + + align:start position:0% +for each of three treatments of a +particular variable. So this is the + + align:start position:0% +particular variable. So this is the + + + align:start position:0% +particular variable. So this is the +output + + align:start position:0% +output + + + align:start position:0% +output +that we've measured and some arbitrary + + align:start position:0% +that we've measured and some arbitrary + + + align:start position:0% +that we've measured and some arbitrary +quantity and uh here are the treatments. + + align:start position:0% + + + + align:start position:0% + +So uh for each particular treatment we + + align:start position:0% +So uh for each particular treatment we + + + align:start position:0% +So uh for each particular treatment we +have three samples. We eval evaluate a + + align:start position:0% +have three samples. We eval evaluate a + + + align:start position:0% +have three samples. We eval evaluate a +sample mean. Here it's 11. Here it's + + align:start position:0% +sample mean. Here it's 11. Here it's + + + align:start position:0% +sample mean. Here it's 11. Here it's +eight. And uh we take the grand average + + align:start position:0% +eight. And uh we take the grand average + + + align:start position:0% +eight. And uh we take the grand average +of all samples. And uh we know that as + + align:start position:0% +of all samples. And uh we know that as + + + align:start position:0% +of all samples. And uh we know that as +well. + + align:start position:0% + + + + align:start position:0% + +We can also evaluate the sum of squared + + align:start position:0% +We can also evaluate the sum of squared + + + align:start position:0% +We can also evaluate the sum of squared +deviations of the sample values from the + + align:start position:0% +deviations of the sample values from the + + + align:start position:0% +deviations of the sample values from the +sample mean. And in this case, sum of + + align:start position:0% +sample mean. And in this case, sum of + + + align:start position:0% +sample mean. And in this case, sum of +squares for treatment one uh is + + align:start position:0% +squares for treatment one uh is + + + align:start position:0% +squares for treatment one uh is +the square of that difference plus the + + align:start position:0% +the square of that difference plus the + + + align:start position:0% +the square of that difference plus the +square of that difference plus uh zero + + align:start position:0% +square of that difference plus uh zero + + + align:start position:0% +square of that difference plus uh zero +because that particular sample lies on + + align:start position:0% +because that particular sample lies on + + + align:start position:0% +because that particular sample lies on +the mean. We do that for each particular + + align:start position:0% +the mean. We do that for each particular + + + align:start position:0% +the mean. We do that for each particular +treatment and evaluate these sums of + + align:start position:0% +treatment and evaluate these sums of + + + align:start position:0% +treatment and evaluate these sums of +squares. + + align:start position:0% +squares. + + + align:start position:0% +squares. +We know that there are two degrees of + + align:start position:0% +We know that there are two degrees of + + + align:start position:0% +We know that there are two degrees of +freedom for each particular sample. So + + align:start position:0% +freedom for each particular sample. So + + + align:start position:0% +freedom for each particular sample. So +we can go straight to estimates of the + + align:start position:0% +we can go straight to estimates of the + + + align:start position:0% +we can go straight to estimates of the +within group variances + + align:start position:0% +within group variances + + + align:start position:0% +within group variances +uh for each for each group or treatment + + align:start position:0% +uh for each for each group or treatment + + + align:start position:0% +uh for each for each group or treatment +and based on that we can evaluate that + + align:start position:0% +and based on that we can evaluate that + + + align:start position:0% +and based on that we can evaluate that +pulled estimate of within group variance + + align:start position:0% +pulled estimate of within group variance + + + align:start position:0% +pulled estimate of within group variance +which is the thing that's meant to be + + align:start position:0% +which is the thing that's meant to be + + + align:start position:0% +which is the thing that's meant to be +excluding + + align:start position:0% +excluding + + + align:start position:0% +excluding +uh the effect of the treatments. + + align:start position:0% + + + + align:start position:0% + +Now what we're going to do is uh make + + align:start position:0% +Now what we're going to do is uh make + + + align:start position:0% +Now what we're going to do is uh make +the second estimate the the uh the + + align:start position:0% +the second estimate the the uh the + + + align:start position:0% +the second estimate the the uh the +between group variance estimate. And + + align:start position:0% +between group variance estimate. And + + + align:start position:0% +between group variance estimate. And +here uh what we're doing is uh looking + + align:start position:0% +here uh what we're doing is uh looking + + + align:start position:0% +here uh what we're doing is uh looking +purely at + + align:start position:0% +purely at + + + align:start position:0% +purely at +we're interested purely in the uh sample + + align:start position:0% +we're interested purely in the uh sample + + + align:start position:0% +we're interested purely in the uh sample +means that we've evaluated. + + align:start position:0% +means that we've evaluated. + + + align:start position:0% +means that we've evaluated. +Take this value, this value and this + + align:start position:0% +Take this value, this value and this + + + align:start position:0% +Take this value, this value and this +value. + + align:start position:0% +value. + + + align:start position:0% +value. +That sample mean is 11. + + align:start position:0% +That sample mean is 11. + + + align:start position:0% +That sample mean is 11. +The grand average for all samples is 10. + + align:start position:0% +The grand average for all samples is 10. + + + align:start position:0% +The grand average for all samples is 10. +We're looking at that + + align:start position:0% +We're looking at that + + + align:start position:0% +We're looking at that +difference + + align:start position:0% +difference + + + align:start position:0% +difference +and we're squaring that deviation here + + align:start position:0% +and we're squaring that deviation here + + + align:start position:0% +and we're squaring that deviation here +and then we're scaling it by + + align:start position:0% +and then we're scaling it by + + + align:start position:0% +and then we're scaling it by +the number of the number of samples for + + align:start position:0% +the number of the number of samples for + + + align:start position:0% +the number of the number of samples for +that particular treatment which is + + align:start position:0% +that particular treatment which is + + + align:start position:0% +that particular treatment which is +three. Three samples. And that's again + + align:start position:0% +three. Three samples. And that's again + + + align:start position:0% +three. Three samples. And that's again +uh dealing with the fact that the uh the + + align:start position:0% +uh dealing with the fact that the uh the + + + align:start position:0% +uh dealing with the fact that the uh the +standard deviation of a sample mean is + + align:start position:0% +standard deviation of a sample mean is + + + align:start position:0% +standard deviation of a sample mean is +inversely proportional to the number of + + align:start position:0% +inversely proportional to the number of + + + align:start position:0% +inversely proportional to the number of +data points in the sample. + + align:start position:0% +data points in the sample. + + + align:start position:0% +data points in the sample. +So we do we do this for each treatment + + align:start position:0% +So we do we do this for each treatment + + + align:start position:0% +So we do we do this for each treatment +t= 1 2 and three and we evaluate + + align:start position:0% +t= 1 2 and three and we evaluate + + + align:start position:0% +t= 1 2 and three and we evaluate +uh our estimate of the between group + + align:start position:0% +uh our estimate of the between group + + + align:start position:0% +uh our estimate of the between group +variance. + + align:start position:0% +variance. + + + align:start position:0% +variance. +So this this estimate in a sense is + + align:start position:0% +So this this estimate in a sense is + + + align:start position:0% +So this this estimate in a sense is +uh + + align:start position:0% +uh + + + align:start position:0% +uh +trying to uh look + + align:start position:0% +trying to uh look + + + align:start position:0% +trying to uh look +uh well folded into that estimate will + + align:start position:0% +uh well folded into that estimate will + + + align:start position:0% +uh well folded into that estimate will +be the effect of the random variation + + align:start position:0% +be the effect of the random variation + + + align:start position:0% +be the effect of the random variation +within the group and the effect of + + align:start position:0% +within the group and the effect of + + + align:start position:0% +within the group and the effect of +changing the treatment. + + align:start position:0% +changing the treatment. + + + align:start position:0% +changing the treatment. +We have these two estimates sigma subr 2 + + align:start position:0% +We have these two estimates sigma subr 2 + + + align:start position:0% +We have these two estimates sigma subr 2 +sigma subt. + + align:start position:0% +sigma subt. + + + align:start position:0% +sigma subt. +Now, we're going to do the F test to see + + align:start position:0% +Now, we're going to do the F test to see + + + align:start position:0% +Now, we're going to do the F test to see +whether there's a significant uh + + align:start position:0% +whether there's a significant uh + + + align:start position:0% +whether there's a significant uh +evidence that changing the input changes + + align:start position:0% +evidence that changing the input changes + + + align:start position:0% +evidence that changing the input changes +the output. + + align:start position:0% +the output. + + + align:start position:0% +the output. +Here's how we might lay it out in Excel. + + align:start position:0% +Here's how we might lay it out in Excel. + + + align:start position:0% +Here's how we might lay it out in Excel. +We've evaluated the sums of squares + + align:start position:0% +We've evaluated the sums of squares + + + align:start position:0% +We've evaluated the sums of squares +between groups within squares within + + align:start position:0% +between groups within squares within + + + align:start position:0% +between groups within squares within +groups, sorry. Uh we've got the degrees + + align:start position:0% +groups, sorry. Uh we've got the degrees + + + align:start position:0% +groups, sorry. Uh we've got the degrees +of freedom here. The mean squared value + + align:start position:0% +of freedom here. The mean squared value + + + align:start position:0% +of freedom here. The mean squared value +is just taken from over here. And uh the + + align:start position:0% +is just taken from over here. And uh the + + + align:start position:0% +is just taken from over here. And uh the +f statistic is just uh the between group + + align:start position:0% +f statistic is just uh the between group + + + align:start position:0% +f statistic is just uh the between group +estimate divided by the within group + + align:start position:0% +estimate divided by the within group + + + align:start position:0% +estimate divided by the within group +estimate. So four and a half. + + align:start position:0% +estimate. So four and a half. + + + align:start position:0% +estimate. So four and a half. +Then we can go to the tables and say you + + align:start position:0% +Then we can go to the tables and say you + + + align:start position:0% +Then we can go to the tables and say you +know the 5% level what's the critical + + align:start position:0% +know the 5% level what's the critical + + + align:start position:0% +know the 5% level what's the critical +value of f uh turns out to be 5.14. + + align:start position:0% +value of f uh turns out to be 5.14. + + + align:start position:0% +value of f uh turns out to be 5.14. +So in this case we would the 5% level uh + + align:start position:0% +So in this case we would the 5% level uh + + + align:start position:0% +So in this case we would the 5% level uh +reject accept accept the null hypothesis + + align:start position:0% +reject accept accept the null hypothesis + + + align:start position:0% +reject accept accept the null hypothesis +that there was no uh significant + + align:start position:0% +that there was no uh significant + + + align:start position:0% +that there was no uh significant +effective inputs on outputs. + + align:start position:0% +effective inputs on outputs. + + + align:start position:0% +effective inputs on outputs. +Um is the ratio always larger than one + + align:start position:0% +Um is the ratio always larger than one + + + align:start position:0% +Um is the ratio always larger than one +or can it be smaller? + + align:start position:0% +or can it be smaller? + + + align:start position:0% +or can it be smaller? +There's a chance that it will be smaller + + align:start position:0% +There's a chance that it will be smaller + + + align:start position:0% +There's a chance that it will be smaller +than one. There's even even if the the + + align:start position:0% +than one. There's even even if the the + + + align:start position:0% +than one. There's even even if the the +actual output means were unaffected by + + align:start position:0% +actual output means were unaffected by + + + align:start position:0% +actual output means were unaffected by +the by the input. Uh but again that + + align:start position:0% +the by the input. Uh but again that + + + align:start position:0% +the by the input. Uh but again that +would be so if this is this is the value + + align:start position:0% +would be so if this is this is the value + + + align:start position:0% +would be so if this is this is the value +of + + align:start position:0% +of + + + align:start position:0% +of +f and this is the pdf I forget it's this + + align:start position:0% +f and this is the pdf I forget it's this + + + align:start position:0% +f and this is the pdf I forget it's this +would be what the f distribution looks + + align:start position:0% +would be what the f distribution looks + + + align:start position:0% +would be what the f distribution looks +like. So there are there are values of f + + align:start position:0% +like. So there are there are values of f + + + align:start position:0% +like. So there are there are values of f +that are less than one down here. + + align:start position:0% +that are less than one down here. + + + align:start position:0% +that are less than one down here. +But uh + + align:start position:0% +But uh + + + align:start position:0% +But uh +the 5% level + + align:start position:0% +the 5% level + + + align:start position:0% +the 5% level +you would only reject the hypothesis + + align:start position:0% +you would only reject the hypothesis + + + align:start position:0% +you would only reject the hypothesis +that + + align:start position:0% +that + + + align:start position:0% +that +uh and and so frit here is 5.14 + + align:start position:0% +uh and and so frit here is 5.14 + + + align:start position:0% +uh and and so frit here is 5.14 +the 5% level. You would reject the + + align:start position:0% +the 5% level. You would reject the + + + align:start position:0% +the 5% level. You would reject the +hypothesis that uh there was no + + align:start position:0% +hypothesis that uh there was no + + + align:start position:0% +hypothesis that uh there was no +significant impact of inputs on outputs. + + align:start position:0% +significant impact of inputs on outputs. + + + align:start position:0% +significant impact of inputs on outputs. +if you this particular variable input + + align:start position:0% +if you this particular variable input + + + align:start position:0% +if you this particular variable input +obviously if uh if the if the value of f + + align:start position:0% +obviously if uh if the if the value of f + + + align:start position:0% +obviously if uh if the if the value of f +were were greater than that so yeah + + align:start position:0% +were were greater than that so yeah + + + align:start position:0% +were were greater than that so yeah +there's a there's a small chance that f + + align:start position:0% +there's a there's a small chance that f + + + align:start position:0% +there's a there's a small chance that f +will be less less than one + + align:start position:0% +will be less less than one + + + align:start position:0% +will be less less than one +um + + align:start position:0% + + + + align:start position:0% + +I think that's right is that right + + align:start position:0% +I think that's right is that right + + + align:start position:0% +I think that's right is that right +yeah certainly if the observed f + + align:start position:0% +yeah certainly if the observed f + + + align:start position:0% +yeah certainly if the observed f +tell you that + + align:start position:0% +tell you that + + + align:start position:0% +tell you that +treatments are not having an effect. + + align:start position:0% +treatments are not having an effect. + + + align:start position:0% +treatments are not having an effect. +Your treatment deltas are so small that + + align:start position:0% +Your treatment deltas are so small that + + + align:start position:0% +Your treatment deltas are so small that +you got lucky + + align:start position:0% +you got lucky + + + align:start position:0% +you got lucky +sample with zero treatment effects in + + align:start position:0% +sample with zero treatment effects in + + + align:start position:0% +sample with zero treatment effects in +that case. + + align:start position:0% + + + + align:start position:0% + +So if you observe actually observe an F + + align:start position:0% +So if you observe actually observe an F + + + align:start position:0% +So if you observe actually observe an F +less than one exactly as Hayden said you + + align:start position:0% +less than one exactly as Hayden said you + + + align:start position:0% +less than one exactly as Hayden said you +would reject the alternative hypothesis + + align:start position:0% +would reject the alternative hypothesis + + + align:start position:0% +would reject the alternative hypothesis +just have to say yeah. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Well, that uh is the whole example. + + align:start position:0% +Well, that uh is the whole example. + + + align:start position:0% +Well, that uh is the whole example. +That's what you would do if you had nine + + align:start position:0% +That's what you would do if you had nine + + + align:start position:0% +That's what you would do if you had nine +data points and you could all write it + + align:start position:0% +data points and you could all write it + + + align:start position:0% +data points and you could all write it +down on on one bit of paper. Uh + + align:start position:0% +down on on one bit of paper. Uh + + + align:start position:0% +down on on one bit of paper. Uh +obviously uh not everything is that uh + + align:start position:0% +obviously uh not everything is that uh + + + align:start position:0% +obviously uh not everything is that uh +uh simple. + + align:start position:0% +uh simple. + + + align:start position:0% +uh simple. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Yeah. Can I go back to previous slide? + + align:start position:0% +Yeah. Can I go back to previous slide? + + + align:start position:0% +Yeah. Can I go back to previous slide? +So the p value means if the alpha is + + align:start position:0% +So the p value means if the alpha is + + + align:start position:0% +So the p value means if the alpha is +larger than 0064 you will reject null + + align:start position:0% +larger than 0064 you will reject null + + + align:start position:0% +larger than 0064 you will reject null +hypothesis right? + + align:start position:0% +hypothesis right? + + + align:start position:0% +hypothesis right? +Yeah the p value is the + + align:start position:0% +Yeah the p value is the + + + align:start position:0% +Yeah the p value is the +the level of significance at which you + + align:start position:0% +the level of significance at which you + + + align:start position:0% +the level of significance at which you +would just reject the null hypothesis. + + align:start position:0% +would just reject the null hypothesis. + + + align:start position:0% +would just reject the null hypothesis. +So that's that's the level of + + align:start position:0% +So that's that's the level of + + + align:start position:0% +So that's that's the level of +significance for which f is equal to + + align:start position:0% +significance for which f is equal to + + + align:start position:0% +significance for which f is equal to +frit and in this case it's 6.4%. + + align:start position:0% +frit and in this case it's 6.4%. + + + align:start position:0% +frit and in this case it's 6.4%. +So if the level of significance is 5% + + align:start position:0% +So if the level of significance is 5% + + + align:start position:0% +So if the level of significance is 5% +uh that's a more stringent + + align:start position:0% +uh that's a more stringent + + + align:start position:0% +uh that's a more stringent +uh + + align:start position:0% +uh + + + align:start position:0% +uh +places a more stringent requirement to + + align:start position:0% +places a more stringent requirement to + + + align:start position:0% +places a more stringent requirement to +reject the null hypothesis than uh than + + align:start position:0% +reject the null hypothesis than uh than + + + align:start position:0% +reject the null hypothesis than uh than +6.4%. So you keep the null hypothesis at + + align:start position:0% +6.4%. So you keep the null hypothesis at + + + align:start position:0% +6.4%. So you keep the null hypothesis at +the 5% level. + + align:start position:0% +the 5% level. + + + align:start position:0% +the 5% level. +So in fact this is a good example where + + align:start position:0% +So in fact this is a good example where + + + align:start position:0% +So in fact this is a good example where +if I ask you just directly the question + + align:start position:0% +if I ask you just directly the question + + + align:start position:0% +if I ask you just directly the question +did the treatment have an effect + + align:start position:0% +did the treatment have an effect + + + align:start position:0% +did the treatment have an effect +your answer is dependent on what level + + align:start position:0% +your answer is dependent on what level + + + align:start position:0% +your answer is dependent on what level +of confidence you want to believe that + + align:start position:0% +of confidence you want to believe that + + + align:start position:0% +of confidence you want to believe that +the evidence tells you there was an + + align:start position:0% +the evidence tells you there was an + + + align:start position:0% +the evidence tells you there was an +effect. If I asked you I want to be 95% + + align:start position:0% +effect. If I asked you I want to be 95% + + + align:start position:0% +effect. If I asked you I want to be 95% +confident there was an effect. Your + + align:start position:0% +confident there was an effect. Your + + + align:start position:0% +confident there was an effect. Your +answer would be I don't have enough + + align:start position:0% +answer would be I don't have enough + + + align:start position:0% +answer would be I don't have enough +evidence. No there's no effect. If I + + align:start position:0% +evidence. No there's no effect. If I + + + align:start position:0% +evidence. No there's no effect. If I +asked you instead, 90% confident that + + align:start position:0% +asked you instead, 90% confident that + + + align:start position:0% +asked you instead, 90% confident that +there's an effect, your answer is yes, + + align:start position:0% +there's an effect, your answer is yes, + + + align:start position:0% +there's an effect, your answer is yes, +there is an effect to 90% confidence. + + align:start position:0% +there is an effect to 90% confidence. + + + align:start position:0% +there is an effect to 90% confidence. +So, you're right at that interesting + + align:start position:0% +So, you're right at that interesting + + + align:start position:0% +So, you're right at that interesting +point with that 6.4. + + align:start position:0% +point with that 6.4. + + + align:start position:0% +point with that 6.4. +What is it? + + align:start position:0% +What is it? + + + align:start position:0% +What is it? +Yes, 6.4. + + align:start position:0% +Yes, 6.4. + + + align:start position:0% +Yes, 6.4. +6.4%. + + align:start position:0% +6.4%. + + + align:start position:0% +6.4%. +And if you just look at the scatter of + + align:start position:0% +And if you just look at the scatter of + + + align:start position:0% +And if you just look at the scatter of +the data, it's kind of fuzzy. You don't + + align:start position:0% +the data, it's kind of fuzzy. You don't + + + align:start position:0% +the data, it's kind of fuzzy. You don't +have a lot of data. have three data + + align:start position:0% +have a lot of data. have three data + + + align:start position:0% +have a lot of data. have three data +points in the example. + + align:start position:0% +points in the example. + + + align:start position:0% +points in the example. +So that whole idea of confidence there + + align:start position:0% +So that whole idea of confidence there + + + align:start position:0% +So that whole idea of confidence there +we talked way back about + + align:start position:0% +we talked way back about + + + align:start position:0% +we talked way back about +early in the term very important. + + align:start position:0% + + + + align:start position:0% + +Okay. Any more questions from anyone? + + align:start position:0% +Okay. Any more questions from anyone? + + + align:start position:0% +Okay. Any more questions from anyone? +Right. + + align:start position:0% + + + + align:start position:0% + +Well, we uh we mentioned at the start + + align:start position:0% +Well, we uh we mentioned at the start + + + align:start position:0% +Well, we uh we mentioned at the start +that uh in inherent in doing this + + align:start position:0% +that uh in inherent in doing this + + + align:start position:0% +that uh in inherent in doing this +analysis is the assumption that + + align:start position:0% +analysis is the assumption that + + + align:start position:0% +analysis is the assumption that +the within group variance is the same + + align:start position:0% +the within group variance is the same + + + align:start position:0% +the within group variance is the same +for every group. And uh this actually + + align:start position:0% +for every group. And uh this actually + + + align:start position:0% +for every group. And uh this actually +should be a a sigma not a three + + align:start position:0% +should be a a sigma not a three + + + align:start position:0% +should be a a sigma not a three +quarters. Um + + align:start position:0% + + + + align:start position:0% + +it's important to check that to make + + align:start position:0% +it's important to check that to make + + + align:start position:0% +it's important to check that to make +sure that the uh the ANOVA is is valid. + + align:start position:0% +sure that the uh the ANOVA is is valid. + + + align:start position:0% +sure that the uh the ANOVA is is valid. +And there are ways of looking at the + + align:start position:0% +And there are ways of looking at the + + + align:start position:0% +And there are ways of looking at the +problem differently if if you can't + + align:start position:0% +problem differently if if you can't + + + align:start position:0% +problem differently if if you can't +really make that assumption. + + align:start position:0% +really make that assumption. + + + align:start position:0% +really make that assumption. +But what we also want to do is uh try to + + align:start position:0% +But what we also want to do is uh try to + + + align:start position:0% +But what we also want to do is uh try to +uh + + align:start position:0% +uh + + + align:start position:0% +uh +try to make sure that the analysis we're + + align:start position:0% +try to make sure that the analysis we're + + + align:start position:0% +try to make sure that the analysis we're +doing really does uh + + align:start position:0% +doing really does uh + + + align:start position:0% +doing really does uh +capture uh as much as possible of the + + align:start position:0% +capture uh as much as possible of the + + + align:start position:0% +capture uh as much as possible of the +treatment effect + + align:start position:0% +treatment effect + + + align:start position:0% +treatment effect +and there are various ways of doing + + align:start position:0% +and there are various ways of doing + + + align:start position:0% +and there are various ways of doing +that. We can take the residuals in other + + align:start position:0% +that. We can take the residuals in other + + + align:start position:0% +that. We can take the residuals in other +words the difference between the sample + + align:start position:0% +words the difference between the sample + + + align:start position:0% +words the difference between the sample +value and the sample mean. We can plot + + align:start position:0% +value and the sample mean. We can plot + + + align:start position:0% +value and the sample mean. We can plot +those residuals uh either against the + + align:start position:0% +those residuals uh either against the + + + align:start position:0% +those residuals uh either against the +time order in which the samples were + + align:start position:0% +time order in which the samples were + + + align:start position:0% +time order in which the samples were +taken. Uh we could look at the + + align:start position:0% +taken. Uh we could look at the + + + align:start position:0% +taken. Uh we could look at the +distribution of those residuals do a + + align:start position:0% +distribution of those residuals do a + + + align:start position:0% +distribution of those residuals do a +norm QQ norm plot or some other kind of + + align:start position:0% +norm QQ norm plot or some other kind of + + + align:start position:0% +norm QQ norm plot or some other kind of +plot and uh we can we can make checks + + align:start position:0% +plot and uh we can we can make checks + + + align:start position:0% +plot and uh we can we can make checks +that this underlying assumption is uh is + + align:start position:0% +that this underlying assumption is uh is + + + align:start position:0% +that this underlying assumption is uh is +reasonable. + + align:start position:0% + + + + align:start position:0% + +So that's all I'm going to say about + + align:start position:0% +So that's all I'm going to say about + + + align:start position:0% +So that's all I'm going to say about +this. But uh I think um it's uh it's an + + align:start position:0% +this. But uh I think um it's uh it's an + + + align:start position:0% +this. But uh I think um it's uh it's an +important thing to to bear in mind. + + align:start position:0% +important thing to to bear in mind. + + + align:start position:0% +important thing to to bear in mind. +So ANOVA for one variable + + align:start position:0% +So ANOVA for one variable + + + align:start position:0% +So ANOVA for one variable +uh though it takes uh takes quite a lot + + align:start position:0% +uh though it takes uh takes quite a lot + + + align:start position:0% +uh though it takes uh takes quite a lot +of effort to get it conceptually uh the + + align:start position:0% +of effort to get it conceptually uh the + + + align:start position:0% +of effort to get it conceptually uh the +actual mechanics of doing it are fairly + + align:start position:0% +actual mechanics of doing it are fairly + + + align:start position:0% +actual mechanics of doing it are fairly +straightforward. + + align:start position:0% +straightforward. + + + align:start position:0% +straightforward. +It's not always the case that there's + + align:start position:0% +It's not always the case that there's + + + align:start position:0% +It's not always the case that there's +only one input variable that we're + + align:start position:0% +only one input variable that we're + + + align:start position:0% +only one input variable that we're +interested in in changing. Uh we might + + align:start position:0% +interested in in changing. Uh we might + + + align:start position:0% +interested in in changing. Uh we might +of course want to do it with two or more + + align:start position:0% +of course want to do it with two or more + + + align:start position:0% +of course want to do it with two or more +input variables. Uh there are good + + align:start position:0% +input variables. Uh there are good + + + align:start position:0% +input variables. Uh there are good +reasons why we'd be interested in uh + + align:start position:0% +reasons why we'd be interested in uh + + + align:start position:0% +reasons why we'd be interested in uh +exploiting + + align:start position:0% +exploiting + + + align:start position:0% +exploiting +a number of inputs to achieve the output + + align:start position:0% +a number of inputs to achieve the output + + + align:start position:0% +a number of inputs to achieve the output +we want. If we have uh if we have + + align:start position:0% +we want. If we have uh if we have + + + align:start position:0% +we want. If we have uh if we have +several variables we can control. We can + + align:start position:0% +several variables we can control. We can + + + align:start position:0% +several variables we can control. We can +do things like controlling the output + + align:start position:0% +do things like controlling the output + + + align:start position:0% +do things like controlling the output +mean and the output variance uh to be + + align:start position:0% +mean and the output variance uh to be + + + align:start position:0% +mean and the output variance uh to be +what we want them to be. Uh or we can uh + + align:start position:0% +what we want them to be. Uh or we can uh + + + align:start position:0% +what we want them to be. Uh or we can uh +control the output + + align:start position:0% +control the output + + + align:start position:0% +control the output +uh to improve CPK while at the same time + + align:start position:0% +uh to improve CPK while at the same time + + + align:start position:0% +uh to improve CPK while at the same time +reducing sensitivity to some other + + align:start position:0% +reducing sensitivity to some other + + + align:start position:0% +reducing sensitivity to some other +disturbance. + + align:start position:0% +disturbance. + + + align:start position:0% +disturbance. +And + + align:start position:0% +And + + + align:start position:0% +And +that is uh that is why we need to be + + align:start position:0% +that is uh that is why we need to be + + + align:start position:0% +that is uh that is why we need to be +able to uh to do analysis of variance + + align:start position:0% +able to uh to do analysis of variance + + + align:start position:0% +able to uh to do analysis of variance +for uh multiple inputs. + + align:start position:0% + + + + align:start position:0% + +One way of modeling the effect of these + + align:start position:0% +One way of modeling the effect of these + + + align:start position:0% +One way of modeling the effect of these +multiple inputs would be to have this + + align:start position:0% +multiple inputs would be to have this + + + align:start position:0% +multiple inputs would be to have this +simple additive model uh where we're + + align:start position:0% +simple additive model uh where we're + + + align:start position:0% +simple additive model uh where we're +saying that the uh the output + + align:start position:0% +saying that the uh the output + + + align:start position:0% +saying that the uh the output +uh value + + align:start position:0% +uh value + + + align:start position:0% +uh value +is the sum of four quantities. + + align:start position:0% +is the sum of four quantities. + + + align:start position:0% +is the sum of four quantities. +uh process mean as we mentioned before + + align:start position:0% +uh process mean as we mentioned before + + + align:start position:0% +uh process mean as we mentioned before +then two separate treatment effects + + align:start position:0% +then two separate treatment effects + + + align:start position:0% +then two separate treatment effects +to subt as we described uh for the one + + align:start position:0% +to subt as we described uh for the one + + + align:start position:0% +to subt as we described uh for the one +variable case and then an equivalent + + align:start position:0% +variable case and then an equivalent + + + align:start position:0% +variable case and then an equivalent +value for another input + + align:start position:0% +value for another input + + + align:start position:0% +value for another input +beta subq + + align:start position:0% +beta subq + + + align:start position:0% +beta subq +and uh there in this case we would say + + align:start position:0% +and uh there in this case we would say + + + align:start position:0% +and uh there in this case we would say +that there were there were k possible + + align:start position:0% +that there were there were k possible + + + align:start position:0% +that there were there were k possible +treatments for the first the first + + align:start position:0% +treatments for the first the first + + + align:start position:0% +treatments for the first the first +variable and n possible treatments for + + align:start position:0% +variable and n possible treatments for + + + align:start position:0% +variable and n possible treatments for +the second. So you could have any one of + + align:start position:0% +the second. So you could have any one of + + + align:start position:0% +the second. So you could have any one of +the treatments for the first variable + + align:start position:0% +the treatments for the first variable + + + align:start position:0% +the treatments for the first variable +and any one of the treatments for the + + align:start position:0% +and any one of the treatments for the + + + align:start position:0% +and any one of the treatments for the +second variable in combination. The + + align:start position:0% +second variable in combination. The + + + align:start position:0% +second variable in combination. The +fourth quantity is is again this + + align:start position:0% +fourth quantity is is again this + + + align:start position:0% +fourth quantity is is again this +residual this random variation that's + + align:start position:0% +residual this random variation that's + + + align:start position:0% +residual this random variation that's +not something we're trying to account + + align:start position:0% +not something we're trying to account + + + align:start position:0% +not something we're trying to account +for uh with these two uh with these two + + align:start position:0% +for uh with these two uh with these two + + + align:start position:0% +for uh with these two uh with these two +input variables. + + align:start position:0% +input variables. + + + align:start position:0% +input variables. +And uh again this is this is what we + + align:start position:0% +And uh again this is this is what we + + + align:start position:0% +And uh again this is this is what we +call a fixed effects model. So we're + + align:start position:0% +call a fixed effects model. So we're + + + align:start position:0% +call a fixed effects model. So we're +saying that there's a deterministic + + align:start position:0% +saying that there's a deterministic + + + align:start position:0% +saying that there's a deterministic +relationship between the input values + + align:start position:0% +relationship between the input values + + + align:start position:0% +relationship between the input values +and the value of uh of toao subt and + + align:start position:0% +and the value of uh of toao subt and + + + align:start position:0% +and the value of uh of toao subt and +beta subq. There are cases in which + + align:start position:0% +beta subq. There are cases in which + + + align:start position:0% +beta subq. There are cases in which +there's a there's a probabilistic + + align:start position:0% +there's a there's a probabilistic + + + align:start position:0% +there's a there's a probabilistic +relationship between the input and those + + align:start position:0% +relationship between the input and those + + + align:start position:0% +relationship between the input and those +treatment effects. There are ways of + + align:start position:0% +treatment effects. There are ways of + + + align:start position:0% +treatment effects. There are ways of +dealing with that uh that we won't + + align:start position:0% +dealing with that uh that we won't + + + align:start position:0% +dealing with that uh that we won't +describe here. + + align:start position:0% + + + + align:start position:0% + +The model that is up on the board now is + + align:start position:0% +The model that is up on the board now is + + + align:start position:0% +The model that is up on the board now is +uh is pretty simple. it assumes that the + + align:start position:0% +uh is pretty simple. it assumes that the + + + align:start position:0% +uh is pretty simple. it assumes that the +effects of these two inputs are + + align:start position:0% +effects of these two inputs are + + + align:start position:0% +effects of these two inputs are +additive. There are plenty of cases, + + align:start position:0% +additive. There are plenty of cases, + + + align:start position:0% +additive. There are plenty of cases, +plenty of processes where that simply + + align:start position:0% +plenty of processes where that simply + + + align:start position:0% +plenty of processes where that simply +isn't realistic and uh there's some + + align:start position:0% +isn't realistic and uh there's some + + + align:start position:0% +isn't realistic and uh there's some +synergism between the two inputs. An + + align:start position:0% +synergism between the two inputs. An + + + align:start position:0% +synergism between the two inputs. An +example that I can think of that's been + + align:start position:0% +example that I can think of that's been + + + align:start position:0% +example that I can think of that's been +relevant in my research is in modeling + + align:start position:0% +relevant in my research is in modeling + + + align:start position:0% +relevant in my research is in modeling +the etching rates in a in a silicon + + align:start position:0% +the etching rates in a in a silicon + + + align:start position:0% +the etching rates in a in a silicon +plasma etching chamber where there are + + align:start position:0% +plasma etching chamber where there are + + + align:start position:0% +plasma etching chamber where there are +uh I guess you could you could think of + + align:start position:0% +uh I guess you could you could think of + + + align:start position:0% +uh I guess you could you could think of +it as there be there being two really + + align:start position:0% +it as there be there being two really + + + align:start position:0% +it as there be there being two really +important input quantities which are the + + align:start position:0% +important input quantities which are the + + + align:start position:0% +important input quantities which are the +flux of of ions of reactant uh onto the + + align:start position:0% +flux of of ions of reactant uh onto the + + + align:start position:0% +flux of of ions of reactant uh onto the +surface of the wafer. the flux of uh + + align:start position:0% +surface of the wafer. the flux of uh + + + align:start position:0% +surface of the wafer. the flux of uh +uncharged florine radicals which are the + + align:start position:0% +uncharged florine radicals which are the + + + align:start position:0% +uncharged florine radicals which are the +the chemical species that are + + align:start position:0% +the chemical species that are + + + align:start position:0% +the chemical species that are +responsible for chemical etching of the + + align:start position:0% +responsible for chemical etching of the + + + align:start position:0% +responsible for chemical etching of the +silicon. So you have these two fluxes + + align:start position:0% +silicon. So you have these two fluxes + + + align:start position:0% +silicon. So you have these two fluxes +approaching the surface of the wafer. + + align:start position:0% +approaching the surface of the wafer. + + + align:start position:0% +approaching the surface of the wafer. +And it's not just the case that the rate + + align:start position:0% +And it's not just the case that the rate + + + align:start position:0% +And it's not just the case that the rate +of removal of silicon is + + align:start position:0% +of removal of silicon is + + + align:start position:0% +of removal of silicon is +proportional to some weighted sum of + + align:start position:0% +proportional to some weighted sum of + + + align:start position:0% +proportional to some weighted sum of +those two fluxes. You can't really have + + align:start position:0% +those two fluxes. You can't really have + + + align:start position:0% +those two fluxes. You can't really have +etching unless you have a substantial + + align:start position:0% +etching unless you have a substantial + + + align:start position:0% +etching unless you have a substantial +flux of both ions and these florine + + align:start position:0% +flux of both ions and these florine + + + align:start position:0% +flux of both ions and these florine +neutrals. So that the ions provide the + + align:start position:0% +neutrals. So that the ions provide the + + + align:start position:0% +neutrals. So that the ions provide the +energy for the reaction to occur. And + + align:start position:0% +energy for the reaction to occur. And + + + align:start position:0% +energy for the reaction to occur. And +that uh means that that the model I just + + align:start position:0% +that uh means that that the model I just + + + align:start position:0% +that uh means that that the model I just +described wouldn't wouldn't get us very + + align:start position:0% +described wouldn't wouldn't get us very + + + align:start position:0% +described wouldn't wouldn't get us very +far. We need to be able to deal with an + + align:start position:0% +far. We need to be able to deal with an + + + align:start position:0% +far. We need to be able to deal with an +interaction between those two those two + + align:start position:0% +interaction between those two those two + + + align:start position:0% +interaction between those two those two +inputs. + + align:start position:0% + + + + align:start position:0% + +This is uh how we can represent it. We + + align:start position:0% +This is uh how we can represent it. We + + + align:start position:0% +This is uh how we can represent it. We +can add in a fifth term which uh is + + align:start position:0% +can add in a fifth term which uh is + + + align:start position:0% +can add in a fifth term which uh is +specific to the combination of + + align:start position:0% +specific to the combination of + + + align:start position:0% +specific to the combination of +treatments + + align:start position:0% +treatments + + + align:start position:0% +treatments +uh t and q. + + align:start position:0% + + + + align:start position:0% + +Let's look at how we might incorporate + + align:start position:0% +Let's look at how we might incorporate + + + align:start position:0% +Let's look at how we might incorporate +that into uh anova. + + align:start position:0% + + + + align:start position:0% + +Here we uh look at the uh + + align:start position:0% + + + + align:start position:0% + +the within group variance for a + + align:start position:0% +the within group variance for a + + + align:start position:0% +the within group variance for a +particular + + align:start position:0% +particular + + + align:start position:0% +particular +uh + + align:start position:0% +uh + + + align:start position:0% +uh +for a partic for for particular input + + align:start position:0% +for a partic for for particular input + + + align:start position:0% +for a partic for for particular input +variable. Uh so this is for the the + + align:start position:0% +variable. Uh so this is for the the + + + align:start position:0% +variable. Uh so this is for the the +first input variable uh the treatments + + align:start position:0% +first input variable uh the treatments + + + align:start position:0% +first input variable uh the treatments +toao and that then we have the + + align:start position:0% +toao and that then we have the + + + align:start position:0% +toao and that then we have the +equivalent expression for uh what + + align:start position:0% +equivalent expression for uh what + + + align:start position:0% +equivalent expression for uh what +happens with the with the second + + align:start position:0% +happens with the with the second + + + align:start position:0% +happens with the with the second +variable. Then we have this this + + align:start position:0% +variable. Then we have this this + + + align:start position:0% +variable. Then we have this this +interaction term + + align:start position:0% +interaction term + + + align:start position:0% +interaction term +uh which is an estimate of the variance + + align:start position:0% +uh which is an estimate of the variance + + + align:start position:0% +uh which is an estimate of the variance +that's to do with uh that can't be + + align:start position:0% +that's to do with uh that can't be + + + align:start position:0% +that's to do with uh that can't be +explained by this additive idea and + + align:start position:0% +explained by this additive idea and + + + align:start position:0% +explained by this additive idea and +finally the residuals. So taking the the + + align:start position:0% +finally the residuals. So taking the the + + + align:start position:0% +finally the residuals. So taking the the +actual value of the uh of the outputs + + align:start position:0% +actual value of the uh of the outputs + + + align:start position:0% +actual value of the uh of the outputs +uh minus the grand mean squaring those + + align:start position:0% +uh minus the grand mean squaring those + + + align:start position:0% +uh minus the grand mean squaring those +residuals. + + align:start position:0% +residuals. + + + align:start position:0% +residuals. +And uh + + align:start position:0% +And uh + + + align:start position:0% +And uh +what this leads us to is uh a two-way + + align:start position:0% +what this leads us to is uh a two-way + + + align:start position:0% +what this leads us to is uh a two-way +ANOVA table + + align:start position:0% +ANOVA table + + + align:start position:0% +ANOVA table +where we can evaluate three F statistics + + align:start position:0% +where we can evaluate three F statistics + + + align:start position:0% +where we can evaluate three F statistics +and apply three F tests to look for + + align:start position:0% +and apply three F tests to look for + + + align:start position:0% +and apply three F tests to look for +significant + + align:start position:0% +significant + + + align:start position:0% +significant +uh relationships between uh factor one + + align:start position:0% +uh relationships between uh factor one + + + align:start position:0% +uh relationships between uh factor one +and the output, factor two and the + + align:start position:0% +and the output, factor two and the + + + align:start position:0% +and the output, factor two and the +output and uh for a significant amount + + align:start position:0% +output and uh for a significant amount + + + align:start position:0% +output and uh for a significant amount +of interaction between those two factors + + align:start position:0% +of interaction between those two factors + + + align:start position:0% +of interaction between those two factors +in setting the output. Karina, you had a + + align:start position:0% +in setting the output. Karina, you had a + + + align:start position:0% +in setting the output. Karina, you had a +question. + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% + + + + align:start position:0% + +Yeah. Um, this is + + align:start position:0% +Yeah. Um, this is + + + align:start position:0% +Yeah. Um, this is +this sorry, this is between groups, + + align:start position:0% +this sorry, this is between groups, + + + align:start position:0% +this sorry, this is between groups, +isn't it? Oh right. Yes. Karina was + + align:start position:0% +isn't it? Oh right. Yes. Karina was + + + align:start position:0% +isn't it? Oh right. Yes. Karina was +asking are these are these estimates uh + + align:start position:0% +asking are these are these estimates uh + + + align:start position:0% +asking are these are these estimates uh +within group estimates or between group + + align:start position:0% +within group estimates or between group + + + align:start position:0% +within group estimates or between group +uh estimates and uh yes absolutely + + align:start position:0% +uh estimates and uh yes absolutely + + + align:start position:0% +uh estimates and uh yes absolutely +you're right. These are actually between + + align:start position:0% +you're right. These are actually between + + + align:start position:0% +you're right. These are actually between +between group estimates. So we're taking + + align:start position:0% +between group estimates. So we're taking + + + align:start position:0% +between group estimates. So we're taking +uh taking a sample mean and looking at + + align:start position:0% +uh taking a sample mean and looking at + + + align:start position:0% +uh taking a sample mean and looking at +its deviation from the grand mean for + + align:start position:0% +its deviation from the grand mean for + + + align:start position:0% +its deviation from the grand mean for +all data and we're making an estimate + + align:start position:0% +all data and we're making an estimate + + + align:start position:0% +all data and we're making an estimate +based on that of the the between group + + align:start position:0% +based on that of the the between group + + + align:start position:0% +based on that of the the between group +mean. So this is this is folding into it + + align:start position:0% +mean. So this is this is folding into it + + + align:start position:0% +mean. So this is this is folding into it +some of the uh the effect of varying the + + align:start position:0% +some of the uh the effect of varying the + + + align:start position:0% +some of the uh the effect of varying the +input + + align:start position:0% +input + + + align:start position:0% +input +question in Singapore. + + align:start position:0% +question in Singapore. + + + align:start position:0% +question in Singapore. +Yes. Uh for SI square shouldn't it be yt + + align:start position:0% +Yes. Uh for SI square shouldn't it be yt + + + align:start position:0% +Yes. Uh for SI square shouldn't it be yt +ytq minus yt minus yq + y instead of + + align:start position:0% +ytq minus yt minus yq + y instead of + + + align:start position:0% +ytq minus yt minus yq + y instead of +minus y? + + align:start position:0% +minus y? + + + align:start position:0% +minus y? +Um + + align:start position:0% +Um + + + align:start position:0% +Um +according to a slide you show just + + align:start position:0% +according to a slide you show just + + + align:start position:0% +according to a slide you show just +before this slide. + + align:start position:0% +before this slide. + + + align:start position:0% +before this slide. +Did I show? Oh yeah. Okay. + + align:start position:0% +Did I show? Oh yeah. Okay. + + + align:start position:0% +Did I show? Oh yeah. Okay. +Yes, I'm sorry. That's that's a mistake. + + align:start position:0% +Yes, I'm sorry. That's that's a mistake. + + + align:start position:0% +Yes, I'm sorry. That's that's a mistake. +Yeah, you're quite right. Thank you very + + align:start position:0% +Yeah, you're quite right. Thank you very + + + align:start position:0% +Yeah, you're quite right. Thank you very +much. + + align:start position:0% +much. + + + align:start position:0% +much. +Absolutely. + + align:start position:0% + + + + align:start position:0% + +Anyway, we have these estimates of the + + align:start position:0% +Anyway, we have these estimates of the + + + align:start position:0% +Anyway, we have these estimates of the +the between between group variances and + + align:start position:0% +the between between group variances and + + + align:start position:0% +the between between group variances and +the the interaction + + align:start position:0% +the the interaction + + + align:start position:0% +the the interaction +uh variance and uh we have these three F + + align:start position:0% +uh variance and uh we have these three F + + + align:start position:0% +uh variance and uh we have these three F +statistics that we can uh use separately + + align:start position:0% +statistics that we can uh use separately + + + align:start position:0% +statistics that we can uh use separately +to test separate null hypotheses that + + align:start position:0% +to test separate null hypotheses that + + + align:start position:0% +to test separate null hypotheses that +there's no impact of factor one on the + + align:start position:0% +there's no impact of factor one on the + + + align:start position:0% +there's no impact of factor one on the +output, no input of factor two on the + + align:start position:0% +output, no input of factor two on the + + + align:start position:0% +output, no input of factor two on the +output and uh get test the hypothesis + + align:start position:0% +output and uh get test the hypothesis + + + align:start position:0% +output and uh get test the hypothesis +that there's no uh importance in any + + align:start position:0% +that there's no uh importance in any + + + align:start position:0% +that there's no uh importance in any +interaction between those factors. + + align:start position:0% + + + + align:start position:0% + +So now I I want to uh + + align:start position:0% +So now I I want to uh + + + align:start position:0% +So now I I want to uh +give an example of where this uh this + + align:start position:0% +give an example of where this uh this + + + align:start position:0% +give an example of where this uh this +analysis + + align:start position:0% +analysis + + + align:start position:0% +analysis +could be could be relevant and useful. + + align:start position:0% +could be could be relevant and useful. + + + align:start position:0% +could be could be relevant and useful. +Now we often think about uh the + + align:start position:0% +Now we often think about uh the + + + align:start position:0% +Now we often think about uh the +relationship between inputs and outputs + + align:start position:0% +relationship between inputs and outputs + + + align:start position:0% +relationship between inputs and outputs +being uh + + align:start position:0% +being uh + + + align:start position:0% +being uh +described where we're we're varying some + + align:start position:0% +described where we're we're varying some + + + align:start position:0% +described where we're we're varying some +input over time and the the output is + + align:start position:0% +input over time and the the output is + + + align:start position:0% +input over time and the the output is +changing over time. The output mean + + align:start position:0% +changing over time. The output mean + + + align:start position:0% +changing over time. The output mean +could be shifting over time. So we have + + align:start position:0% +could be shifting over time. So we have + + + align:start position:0% +could be shifting over time. So we have +a machine and we're trying different + + align:start position:0% +a machine and we're trying different + + + align:start position:0% +a machine and we're trying different +settings for it. But in fact uh a lot of + + align:start position:0% +settings for it. But in fact uh a lot of + + + align:start position:0% +settings for it. But in fact uh a lot of +cases in uh semiconductor + + align:start position:0% +cases in uh semiconductor + + + align:start position:0% +cases in uh semiconductor +uh process control we're interested in + + align:start position:0% +uh process control we're interested in + + + align:start position:0% +uh process control we're interested in +spatial variations. And uh you can think + + align:start position:0% +spatial variations. And uh you can think + + + align:start position:0% +spatial variations. And uh you can think +of uh the case I'm going to show you. + + align:start position:0% +of uh the case I'm going to show you. + + + align:start position:0% +of uh the case I'm going to show you. +This is for uh a metal etching process + + align:start position:0% +This is for uh a metal etching process + + + align:start position:0% +This is for uh a metal etching process +where we're uh + + align:start position:0% +where we're uh + + + align:start position:0% +where we're uh +some work that uh we've started with uh + + align:start position:0% +some work that uh we've started with uh + + + align:start position:0% +some work that uh we've started with uh +with one of our collaborators. The idea + + align:start position:0% +with one of our collaborators. The idea + + + align:start position:0% +with one of our collaborators. The idea +is that we want to be able to model and + + align:start position:0% +is that we want to be able to model and + + + align:start position:0% +is that we want to be able to model and +we're etching a metal layer to form + + align:start position:0% +we're etching a metal layer to form + + + align:start position:0% +we're etching a metal layer to form +interconnect wires to be able to model + + align:start position:0% +interconnect wires to be able to model + + + align:start position:0% +interconnect wires to be able to model +how uniformly + + align:start position:0% +how uniformly + + + align:start position:0% +how uniformly +uh that etches across a wafer depending + + align:start position:0% +uh that etches across a wafer depending + + + align:start position:0% +uh that etches across a wafer depending +on how densely the features are packed + + align:start position:0% +on how densely the features are packed + + + align:start position:0% +on how densely the features are packed +uh what their individual sizes are and + + align:start position:0% +uh what their individual sizes are and + + + align:start position:0% +uh what their individual sizes are and +where they're situated on the wafer. + + align:start position:0% +where they're situated on the wafer. + + + align:start position:0% +where they're situated on the wafer. +One problem that you can encounter when + + align:start position:0% +One problem that you can encounter when + + + align:start position:0% +One problem that you can encounter when +processing these metal layers is that + + align:start position:0% +processing these metal layers is that + + + align:start position:0% +processing these metal layers is that +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +the metal when you're you're masking a a + + align:start position:0% +the metal when you're you're masking a a + + + align:start position:0% +the metal when you're you're masking a a +blanket layer of the metal with + + align:start position:0% +blanket layer of the metal with + + + align:start position:0% +blanket layer of the metal with +photoresist and then applying a plasma + + align:start position:0% +photoresist and then applying a plasma + + + align:start position:0% +photoresist and then applying a plasma +to the to the wafer to etch the exposed + + align:start position:0% +to the to the wafer to etch the exposed + + + align:start position:0% +to the to the wafer to etch the exposed +metal away. But as that process happens, + + align:start position:0% +metal away. But as that process happens, + + + align:start position:0% +metal away. But as that process happens, +you can uh you can get sideways etching + + align:start position:0% +you can uh you can get sideways etching + + + align:start position:0% +you can uh you can get sideways etching +of the metal and uh + + align:start position:0% +of the metal and uh + + + align:start position:0% +of the metal and uh +imagine + + align:start position:0% +imagine + + + align:start position:0% +imagine +you have uh you have a photoresist + + align:start position:0% +you have uh you have a photoresist + + + align:start position:0% +you have uh you have a photoresist +layer. This is a cross-section I'm + + align:start position:0% +layer. This is a cross-section I'm + + + align:start position:0% +layer. This is a cross-section I'm +sketching here. And uh + + align:start position:0% +sketching here. And uh + + + align:start position:0% +sketching here. And uh +you're etching a trench into the metal + + align:start position:0% +you're etching a trench into the metal + + + align:start position:0% +you're etching a trench into the metal +down to some insulating layer. + + align:start position:0% + + + + align:start position:0% + +etchants have to enter this gap. + + align:start position:0% +etchants have to enter this gap. + + + align:start position:0% +etchants have to enter this gap. +Depending on the size of the gap, that + + align:start position:0% +Depending on the size of the gap, that + + + align:start position:0% +Depending on the size of the gap, that +transport process will + + align:start position:0% +transport process will + + + align:start position:0% +transport process will +will vary. It will be harder in narrower + + align:start position:0% +will vary. It will be harder in narrower + + + align:start position:0% +will vary. It will be harder in narrower +gaps than in wider gaps for the reactant + + align:start position:0% +gaps than in wider gaps for the reactant + + + align:start position:0% +gaps than in wider gaps for the reactant +to get in, for the products to get out. + + align:start position:0% +to get in, for the products to get out. + + + align:start position:0% +to get in, for the products to get out. +But also, there's going to be some some + + align:start position:0% +But also, there's going to be some some + + + align:start position:0% +But also, there's going to be some some +lateral etching of the metal. And the + + align:start position:0% +lateral etching of the metal. And the + + + align:start position:0% +lateral etching of the metal. And the +rate at which that lateral etching + + align:start position:0% +rate at which that lateral etching + + + align:start position:0% +rate at which that lateral etching +happens will depend on uh the the + + align:start position:0% +happens will depend on uh the the + + + align:start position:0% +happens will depend on uh the the +availability of reactants in the region + + align:start position:0% +availability of reactants in the region + + + align:start position:0% +availability of reactants in the region +of that feature which might vary across + + align:start position:0% +of that feature which might vary across + + + align:start position:0% +of that feature which might vary across +the wafer. If there is this lateral + + align:start position:0% +the wafer. If there is this lateral + + + align:start position:0% +the wafer. If there is this lateral +etching, if it varies, then it's going + + align:start position:0% +etching, if it varies, then it's going + + + align:start position:0% +etching, if it varies, then it's going +to affect the final width of the wire, + + align:start position:0% +to affect the final width of the wire, + + + align:start position:0% +to affect the final width of the wire, +its final resistance, and therefore uh + + align:start position:0% +its final resistance, and therefore uh + + + align:start position:0% +its final resistance, and therefore uh +the speed at which an individual + + align:start position:0% +the speed at which an individual + + + align:start position:0% +the speed at which an individual +uh + + align:start position:0% +uh + + + align:start position:0% +uh +capacitor parasitic or otherwise in the + + align:start position:0% +capacitor parasitic or otherwise in the + + + align:start position:0% +capacitor parasitic or otherwise in the +circuit will charge. So you might find + + align:start position:0% +circuit will charge. So you might find + + + align:start position:0% +circuit will charge. So you might find +that if you can't reduce variation in + + align:start position:0% +that if you can't reduce variation in + + + align:start position:0% +that if you can't reduce variation in +this lateral etching process, the uh + + align:start position:0% +this lateral etching process, the uh + + + align:start position:0% +this lateral etching process, the uh +the the the circuit properties of the + + align:start position:0% +the the the circuit properties of the + + + align:start position:0% +the the the circuit properties of the +devices produced will vary substantially + + align:start position:0% +devices produced will vary substantially + + + align:start position:0% +devices produced will vary substantially +across the wafer. + + align:start position:0% + + + + align:start position:0% + +So there there are several + + align:start position:0% +So there there are several + + + align:start position:0% +So there there are several +things that can affect the availability + + align:start position:0% +things that can affect the availability + + + align:start position:0% +things that can affect the availability +of reactants at a given feature. + + align:start position:0% +of reactants at a given feature. + + + align:start position:0% +of reactants at a given feature. +Firstly, there is the position in the + + align:start position:0% +Firstly, there is the position in the + + + align:start position:0% +Firstly, there is the position in the +chamber and uh what I've sketched in the + + align:start position:0% +chamber and uh what I've sketched in the + + + align:start position:0% +chamber and uh what I've sketched in the +top left is a plan view of uh of a + + align:start position:0% +top left is a plan view of uh of a + + + align:start position:0% +top left is a plan view of uh of a +wafer. This is say maybe one of several + + align:start position:0% +wafer. This is say maybe one of several + + + align:start position:0% +wafer. This is say maybe one of several +wafers sitting in a in a large uh plasma + + align:start position:0% +wafers sitting in a in a large uh plasma + + + align:start position:0% +wafers sitting in a in a large uh plasma +plasma etching chamber. The gases flow + + align:start position:0% +plasma etching chamber. The gases flow + + + align:start position:0% +plasma etching chamber. The gases flow +through this chamber with some uh some + + align:start position:0% +through this chamber with some uh some + + + align:start position:0% +through this chamber with some uh some +path some velocity distribution. + + align:start position:0% +path some velocity distribution. + + + align:start position:0% +path some velocity distribution. +uh the design of the chamber will have + + align:start position:0% +uh the design of the chamber will have + + + align:start position:0% +uh the design of the chamber will have +an impact on the density of reactants + + align:start position:0% +an impact on the density of reactants + + + align:start position:0% +an impact on the density of reactants +uh and how it varies across the wafer. + + align:start position:0% +uh and how it varies across the wafer. + + + align:start position:0% +uh and how it varies across the wafer. +So you might find that there there's + + align:start position:0% +So you might find that there there's + + + align:start position:0% +So you might find that there there's +greater availability of reactants at the + + align:start position:0% +greater availability of reactants at the + + + align:start position:0% +greater availability of reactants at the +center of the wafer. That's because + + align:start position:0% +center of the wafer. That's because + + + align:start position:0% +center of the wafer. That's because +there's an inlet above the center. + + align:start position:0% +there's an inlet above the center. + + + align:start position:0% +there's an inlet above the center. +And uh so that's one thing that can + + align:start position:0% +And uh so that's one thing that can + + + align:start position:0% +And uh so that's one thing that can +affect the the amount of lateral metal + + align:start position:0% +affect the the amount of lateral metal + + + align:start position:0% +affect the the amount of lateral metal +etching. Then you have the uh + + align:start position:0% +etching. Then you have the uh + + + align:start position:0% +etching. Then you have the uh +the actual geometry of the pattern that + + align:start position:0% +the actual geometry of the pattern that + + + align:start position:0% +the actual geometry of the pattern that +is being etched. If you're trying to + + align:start position:0% +is being etched. If you're trying to + + + align:start position:0% +is being etched. If you're trying to +etch a large amount of metal in a given + + align:start position:0% +etch a large amount of metal in a given + + + align:start position:0% +etch a large amount of metal in a given +region of the wafer that will act as a + + align:start position:0% +region of the wafer that will act as a + + + align:start position:0% +region of the wafer that will act as a +as a sink for reactants, there'll be a + + align:start position:0% +as a sink for reactants, there'll be a + + + align:start position:0% +as a sink for reactants, there'll be a +lot of competition for these reactants. + + align:start position:0% +lot of competition for these reactants. + + + align:start position:0% +lot of competition for these reactants. +The concentration locally the surface is + + align:start position:0% +The concentration locally the surface is + + + align:start position:0% +The concentration locally the surface is +likely to be to be depressed and that's + + align:start position:0% +likely to be to be depressed and that's + + + align:start position:0% +likely to be to be depressed and that's +going to reduce the lateral etching rate + + align:start position:0% +going to reduce the lateral etching rate + + + align:start position:0% +going to reduce the lateral etching rate +for any individual feature. So we have + + align:start position:0% +for any individual feature. So we have + + + align:start position:0% +for any individual feature. So we have +this what we're going to call pattern + + align:start position:0% +this what we're going to call pattern + + + align:start position:0% +this what we're going to call pattern +density effect density of exposed metal + + align:start position:0% +density effect density of exposed metal + + + align:start position:0% +density effect density of exposed metal +for etching. Finally the thing that that + + align:start position:0% +for etching. Finally the thing that that + + + align:start position:0% +for etching. Finally the thing that that +can affect uh the availability of + + align:start position:0% +can affect uh the availability of + + + align:start position:0% +can affect uh the availability of +reactants for this lateral etching is + + align:start position:0% +reactants for this lateral etching is + + + align:start position:0% +reactants for this lateral etching is +the size of the feature. As I mentioned + + align:start position:0% +the size of the feature. As I mentioned + + + align:start position:0% +the size of the feature. As I mentioned +narrower features uh provide a greater + + align:start position:0% +narrower features uh provide a greater + + + align:start position:0% +narrower features uh provide a greater +impediment to to the transport of + + align:start position:0% +impediment to to the transport of + + + align:start position:0% +impediment to to the transport of +reactants to to the to the sidewall of + + align:start position:0% +reactants to to the to the sidewall of + + + align:start position:0% +reactants to to the to the sidewall of +the feature. + + align:start position:0% +the feature. + + + align:start position:0% +the feature. +So in a way you could think of these uh + + align:start position:0% +So in a way you could think of these uh + + + align:start position:0% +So in a way you could think of these uh +of these phenomena as being being input + + align:start position:0% +of these phenomena as being being input + + + align:start position:0% +of these phenomena as being being input +variables. What some of them you can + + align:start position:0% +variables. What some of them you can + + + align:start position:0% +variables. What some of them you can +control. You could you could if you + + align:start position:0% +control. You could you could if you + + + align:start position:0% +control. You could you could if you +wanted to you could place constraints on + + align:start position:0% +wanted to you could place constraints on + + + align:start position:0% +wanted to you could place constraints on +what kind of density of features were + + align:start position:0% +what kind of density of features were + + + align:start position:0% +what kind of density of features were +available, what the smallest feature + + align:start position:0% +available, what the smallest feature + + + align:start position:0% +available, what the smallest feature +available was to the designer these + + align:start position:0% +available was to the designer these + + + align:start position:0% +available was to the designer these +chips. uh and to an extent you can + + align:start position:0% +chips. uh and to an extent you can + + + align:start position:0% +chips. uh and to an extent you can +control the the tool related variation. + + align:start position:0% +control the the tool related variation. + + + align:start position:0% +control the the tool related variation. +You can uh choose a process that will + + align:start position:0% +You can uh choose a process that will + + + align:start position:0% +You can uh choose a process that will +give a more uniform distribution of + + align:start position:0% +give a more uniform distribution of + + + align:start position:0% +give a more uniform distribution of +gases in the chamber. You could redesign + + align:start position:0% +gases in the chamber. You could redesign + + + align:start position:0% +gases in the chamber. You could redesign +the chamber uh and and some of that + + align:start position:0% +the chamber uh and and some of that + + + align:start position:0% +the chamber uh and and some of that +variation you don't have an easy way to + + align:start position:0% +variation you don't have an easy way to + + + align:start position:0% +variation you don't have an easy way to +control some some of that you you don't + + align:start position:0% +control some some of that you you don't + + + align:start position:0% +control some some of that you you don't +have complete control over all the + + align:start position:0% +have complete control over all the + + + align:start position:0% +have complete control over all the +inputs. What I'm saying is that this is + + align:start position:0% +inputs. What I'm saying is that this is + + + align:start position:0% +inputs. What I'm saying is that this is +a case where you have multiple + + align:start position:0% +a case where you have multiple + + + align:start position:0% +a case where you have multiple +geometrical input variations where + + align:start position:0% +geometrical input variations where + + + align:start position:0% +geometrical input variations where +you're trying to manufacture many + + align:start position:0% +you're trying to manufacture many + + + align:start position:0% +you're trying to manufacture many +identical chips. + + align:start position:0% +identical chips. + + + align:start position:0% +identical chips. +Each square in this graph + + align:start position:0% +Each square in this graph + + + align:start position:0% +Each square in this graph +is + + align:start position:0% +is + + + align:start position:0% +is +uh is one chip and they're they're all + + align:start position:0% +uh is one chip and they're they're all + + + align:start position:0% +uh is one chip and they're they're all +supposed to be identical to one another. + + align:start position:0% +supposed to be identical to one another. + + + align:start position:0% +supposed to be identical to one another. +But because of the effects I described + + align:start position:0% +But because of the effects I described + + + align:start position:0% +But because of the effects I described +uh that they will they will not in fact + + align:start position:0% +uh that they will they will not in fact + + + align:start position:0% +uh that they will they will not in fact +be identical. + + align:start position:0% +be identical. + + + align:start position:0% +be identical. +So you can think of this as being uh a + + align:start position:0% +So you can think of this as being uh a + + + align:start position:0% +So you can think of this as being uh a +wafer as being many interdependent + + align:start position:0% +wafer as being many interdependent + + + align:start position:0% +wafer as being many interdependent +samples + + align:start position:0% +samples + + + align:start position:0% +samples +uh of the output of a process + + align:start position:0% +uh of the output of a process + + + align:start position:0% +uh of the output of a process +uh where the uh the input is varying uh + + align:start position:0% +uh where the uh the input is varying uh + + + align:start position:0% +uh where the uh the input is varying uh +in in an in some cases an uncontrolled + + align:start position:0% +in in an in some cases an uncontrolled + + + align:start position:0% +in in an in some cases an uncontrolled +way in some cases a way you can control. + + align:start position:0% +way in some cases a way you can control. + + + align:start position:0% +way in some cases a way you can control. +So this would be a really meaty problem + + align:start position:0% +So this would be a really meaty problem + + + align:start position:0% +So this would be a really meaty problem +for uh multivariate ANOVA to deal with. + + align:start position:0% + + + + align:start position:0% + +What we've got uh within each within + + align:start position:0% +What we've got uh within each within + + + align:start position:0% +What we've got uh within each within +each chip, this is actually a test chip + + align:start position:0% +each chip, this is actually a test chip + + + align:start position:0% +each chip, this is actually a test chip +that was designed to do some experiments + + align:start position:0% +that was designed to do some experiments + + + align:start position:0% +that was designed to do some experiments +and build a model. So it's not actually + + align:start position:0% +and build a model. So it's not actually + + + align:start position:0% +and build a model. So it's not actually +a product, but within each chip uh what + + align:start position:0% +a product, but within each chip uh what + + + align:start position:0% +a product, but within each chip uh what +we have is many copies of actually the + + align:start position:0% +we have is many copies of actually the + + + align:start position:0% +we have is many copies of actually the +same sorts of features. In fact, what + + align:start position:0% +same sorts of features. In fact, what + + + align:start position:0% +same sorts of features. In fact, what +they are is is just snake snakeshaped + + align:start position:0% +they are is is just snake snakeshaped + + + align:start position:0% +they are is is just snake snakeshaped +wires which have a total length uh that + + align:start position:0% +wires which have a total length uh that + + + align:start position:0% +wires which have a total length uh that +that amplifies any resistance variations + + align:start position:0% +that amplifies any resistance variations + + + align:start position:0% +that amplifies any resistance variations +caused by the lateral etching. You can + + align:start position:0% +caused by the lateral etching. You can + + + align:start position:0% +caused by the lateral etching. You can +go into the chip and you can probe the + + align:start position:0% +go into the chip and you can probe the + + + align:start position:0% +go into the chip and you can probe the +resistance of these wires. As the + + align:start position:0% +resistance of these wires. As the + + + align:start position:0% +resistance of these wires. As the +lateral etching gets faster, + + align:start position:0% +lateral etching gets faster, + + + align:start position:0% +lateral etching gets faster, +uh the resistance gets higher because + + align:start position:0% +uh the resistance gets higher because + + + align:start position:0% +uh the resistance gets higher because +the wires are narrower. So you have many + + align:start position:0% +the wires are narrower. So you have many + + + align:start position:0% +the wires are narrower. So you have many +of these snake features within each of + + align:start position:0% +of these snake features within each of + + + align:start position:0% +of these snake features within each of +these individual squares. And what we do + + align:start position:0% +these individual squares. And what we do + + + align:start position:0% +these individual squares. And what we do +is we surround surrounded those those + + align:start position:0% +is we surround surrounded those those + + + align:start position:0% +is we surround surrounded those those +same features by a different amount of + + align:start position:0% +same features by a different amount of + + + align:start position:0% +same features by a different amount of +padding metal uh which is not + + align:start position:0% +padding metal uh which is not + + + align:start position:0% +padding metal uh which is not +electrically connected to these snakes + + align:start position:0% +electrically connected to these snakes + + + align:start position:0% +electrically connected to these snakes +but is sitting right next to the snake + + align:start position:0% +but is sitting right next to the snake + + + align:start position:0% +but is sitting right next to the snake +structures so that they're perturbing uh + + align:start position:0% +structures so that they're perturbing uh + + + align:start position:0% +structures so that they're perturbing uh +the uh the transport of of etchent gas. + + align:start position:0% +the uh the transport of of etchent gas. + + + align:start position:0% +the uh the transport of of etchent gas. +So in areas where there's a larger + + align:start position:0% +So in areas where there's a larger + + + align:start position:0% +So in areas where there's a larger +amount of metal exposed for etching, + + align:start position:0% +amount of metal exposed for etching, + + + align:start position:0% +amount of metal exposed for etching, +there's going to be greater competition + + align:start position:0% +there's going to be greater competition + + + align:start position:0% +there's going to be greater competition +for reactants locally and there's going + + align:start position:0% +for reactants locally and there's going + + + align:start position:0% +for reactants locally and there's going +to be a lower a lower etch rate + + align:start position:0% +to be a lower a lower etch rate + + + align:start position:0% +to be a lower a lower etch rate +including a lower lateral etch rate. + + align:start position:0% + + + + align:start position:0% + +It's not necessarily true of course that + + align:start position:0% +It's not necessarily true of course that + + + align:start position:0% +It's not necessarily true of course that +uh that pattern density effects are + + align:start position:0% +uh that pattern density effects are + + + align:start position:0% +uh that pattern density effects are +confined to one of these squares. You + + align:start position:0% +confined to one of these squares. You + + + align:start position:0% +confined to one of these squares. You +may find that the length the lengths + + align:start position:0% +may find that the length the lengths + + + align:start position:0% +may find that the length the lengths +over which uh competition for reactants + + align:start position:0% +over which uh competition for reactants + + + align:start position:0% +over which uh competition for reactants +occur uh are larger than the diameter of + + align:start position:0% +occur uh are larger than the diameter of + + + align:start position:0% +occur uh are larger than the diameter of +one of these these patches. And uh that + + align:start position:0% +one of these these patches. And uh that + + + align:start position:0% +one of these these patches. And uh that +is something that would need to be + + align:start position:0% +is something that would need to be + + + align:start position:0% +is something that would need to be +modeled and dealt with uh + + align:start position:0% +modeled and dealt with uh + + + align:start position:0% +modeled and dealt with uh +in understanding in understanding the + + align:start position:0% +in understanding in understanding the + + + align:start position:0% +in understanding in understanding the +process. + + align:start position:0% + + + + align:start position:0% + +So I'm not I'm not going to go through + + align:start position:0% +So I'm not I'm not going to go through + + + align:start position:0% +So I'm not I'm not going to go through +the analysis of variance for this + + align:start position:0% +the analysis of variance for this + + + align:start position:0% +the analysis of variance for this +problem. I just wanted to highlight the + + align:start position:0% +problem. I just wanted to highlight the + + + align:start position:0% +problem. I just wanted to highlight the +fact that uh that there are these uh + + align:start position:0% +fact that uh that there are these uh + + + align:start position:0% +fact that uh that there are these uh +these complicated + + align:start position:0% +these complicated + + + align:start position:0% +these complicated +uh sets of geometrical input uh input + + align:start position:0% +uh sets of geometrical input uh input + + + align:start position:0% +uh sets of geometrical input uh input +variables that that we want to try to + + align:start position:0% +variables that that we want to try to + + + align:start position:0% +variables that that we want to try to +understand often in semiconductor + + align:start position:0% +understand often in semiconductor + + + align:start position:0% +understand often in semiconductor +manufacturing processes. And uh very + + align:start position:0% +manufacturing processes. And uh very + + + align:start position:0% +manufacturing processes. And uh very +often we want to just go beyond finding + + align:start position:0% +often we want to just go beyond finding + + + align:start position:0% +often we want to just go beyond finding +a functional relationship between some + + align:start position:0% +a functional relationship between some + + + align:start position:0% +a functional relationship between some +geometrical property and the performance + + align:start position:0% +geometrical property and the performance + + + align:start position:0% +geometrical property and the performance +of the product. We want to uh build a + + align:start position:0% +of the product. We want to uh build a + + + align:start position:0% +of the product. We want to uh build a +physical model that will that will work + + align:start position:0% +physical model that will that will work + + + align:start position:0% +physical model that will that will work +as far back as the uh the settings on + + align:start position:0% +as far back as the uh the settings on + + + align:start position:0% +as far back as the uh the settings on +the machine, the flow rates of gases, + + align:start position:0% +the machine, the flow rates of gases, + + + align:start position:0% +the machine, the flow rates of gases, +the amount of electrical power that's + + align:start position:0% +the amount of electrical power that's + + + align:start position:0% +the amount of electrical power that's +going into generating the the plasma in + + align:start position:0% +going into generating the the plasma in + + + align:start position:0% +going into generating the the plasma in +the chamber to try to to work back with + + align:start position:0% +the chamber to try to to work back with + + + align:start position:0% +the chamber to try to to work back with +enough detail that we can start to uh + + align:start position:0% +enough detail that we can start to uh + + + align:start position:0% +enough detail that we can start to uh +decide what good input variable values + + align:start position:0% +decide what good input variable values + + + align:start position:0% +decide what good input variable values +would be. + + align:start position:0% + + + + align:start position:0% + +I'm just going to show you a little bit + + align:start position:0% +I'm just going to show you a little bit + + + align:start position:0% +I'm just going to show you a little bit +of + + align:start position:0% +of + + + align:start position:0% +of +little bit of data from from one of + + align:start position:0% +little bit of data from from one of + + + align:start position:0% +little bit of data from from one of +these test wafers. Can see that we've + + align:start position:0% +these test wafers. Can see that we've + + + align:start position:0% +these test wafers. Can see that we've +identified a clear relationship between + + align:start position:0% +identified a clear relationship between + + + align:start position:0% +identified a clear relationship between +uh + + align:start position:0% +uh + + + align:start position:0% +uh +between the pattern density, the amount + + align:start position:0% +between the pattern density, the amount + + + align:start position:0% +between the pattern density, the amount +of padding metal wi within one of those + + align:start position:0% +of padding metal wi within one of those + + + align:start position:0% +of padding metal wi within one of those +uh those sets of features and the + + align:start position:0% +uh those sets of features and the + + + align:start position:0% +uh those sets of features and the +average resistance of one of one of the + + align:start position:0% +average resistance of one of one of the + + + align:start position:0% +average resistance of one of one of the +snakes. There are several hundred snakes + + align:start position:0% +snakes. There are several hundred snakes + + + align:start position:0% +snakes. There are several hundred snakes +within the within that uh uh within each + + align:start position:0% +within the within that uh uh within each + + + align:start position:0% +within the within that uh uh within each +within each given patch of features. And + + align:start position:0% +within each given patch of features. And + + + align:start position:0% +within each given patch of features. And +what we've done here is just average the + + align:start position:0% +what we've done here is just average the + + + align:start position:0% +what we've done here is just average the +resistance of all of them uh to give a + + align:start position:0% +resistance of all of them uh to give a + + + align:start position:0% +resistance of all of them uh to give a +quick estimate of the the effect of + + align:start position:0% +quick estimate of the the effect of + + + align:start position:0% +quick estimate of the the effect of +local pattern density and input variable + + align:start position:0% +local pattern density and input variable + + + align:start position:0% +local pattern density and input variable +on uh on one important output. So we can + + align:start position:0% +on uh on one important output. So we can + + + align:start position:0% +on uh on one important output. So we can +see that the patent density has a has an + + align:start position:0% +see that the patent density has a has an + + + align:start position:0% +see that the patent density has a has an +effect that we could think of inventing + + align:start position:0% +effect that we could think of inventing + + + align:start position:0% +effect that we could think of inventing +a functional model for + + align:start position:0% +a functional model for + + + align:start position:0% +a functional model for +but what we also have is the the wafer + + align:start position:0% +but what we also have is the the wafer + + + align:start position:0% +but what we also have is the the wafer +scale non-uniformity. This is to do with + + align:start position:0% +scale non-uniformity. This is to do with + + + align:start position:0% +scale non-uniformity. This is to do with +the the way gases flow around the + + align:start position:0% +the the way gases flow around the + + + align:start position:0% +the the way gases flow around the +chamber approach the wafer transported + + align:start position:0% +chamber approach the wafer transported + + + align:start position:0% +chamber approach the wafer transported +across the wafer. And this this graph + + align:start position:0% +across the wafer. And this this graph + + + align:start position:0% +across the wafer. And this this graph +shows you uh a subset of the data we + + align:start position:0% +shows you uh a subset of the data we + + + align:start position:0% +shows you uh a subset of the data we +have down in the bottom left is a + + align:start position:0% +have down in the bottom left is a + + + align:start position:0% +have down in the bottom left is a +diagram of the wafer. And what we've + + align:start position:0% +diagram of the wafer. And what we've + + + align:start position:0% +diagram of the wafer. And what we've +done on this graph is plotted the + + align:start position:0% +done on this graph is plotted the + + + align:start position:0% +done on this graph is plotted the +resistance of a of a particular of a + + align:start position:0% +resistance of a of a particular of a + + + align:start position:0% +resistance of a of a particular of a +particular uh test feature, a resistive + + align:start position:0% +particular uh test feature, a resistive + + + align:start position:0% +particular uh test feature, a resistive +snake uh + + align:start position:0% +snake uh + + + align:start position:0% +snake uh +uh within + + align:start position:0% +uh within + + + align:start position:0% +uh within +uh within each within each chip on the + + align:start position:0% +uh within each within each chip on the + + + align:start position:0% +uh within each within each chip on the +wafer as a function of location. We + + align:start position:0% +wafer as a function of location. We + + + align:start position:0% +wafer as a function of location. We +slice up the wafer uh and the x-axis + + align:start position:0% +slice up the wafer uh and the x-axis + + + align:start position:0% +slice up the wafer uh and the x-axis +corresponds to uh each slice of the + + align:start position:0% +corresponds to uh each slice of the + + + align:start position:0% +corresponds to uh each slice of the +wafer being uh concatenated. The first + + align:start position:0% +wafer being uh concatenated. The first + + + align:start position:0% +wafer being uh concatenated. The first +slice is here, second slice is here and + + align:start position:0% +slice is here, second slice is here and + + + align:start position:0% +slice is here, second slice is here and +so forth. + + align:start position:0% +so forth. + + + align:start position:0% +so forth. +What we see is that uh the resistances + + align:start position:0% +What we see is that uh the resistances + + + align:start position:0% +What we see is that uh the resistances +that result tend to be larger in the + + align:start position:0% +that result tend to be larger in the + + + align:start position:0% +that result tend to be larger in the +center of the wafer. Here's here's a + + align:start position:0% +center of the wafer. Here's here's a + + + align:start position:0% +center of the wafer. Here's here's a +central part of the wafer and here's + + align:start position:0% +central part of the wafer and here's + + + align:start position:0% +central part of the wafer and here's +here's an edge. + + align:start position:0% +here's an edge. + + + align:start position:0% +here's an edge. +Um, + + align:start position:0% + + + + align:start position:0% + +so that relationship is clear. But then + + align:start position:0% +so that relationship is clear. But then + + + align:start position:0% +so that relationship is clear. But then +if we look within each chip, if we look + + align:start position:0% +if we look within each chip, if we look + + + align:start position:0% +if we look within each chip, if we look +at the features that are near this 5% + + align:start position:0% +at the features that are near this 5% + + + align:start position:0% +at the features that are near this 5% +local metal density, then we see we see + + align:start position:0% +local metal density, then we see we see + + + align:start position:0% +local metal density, then we see we see +this amount of variation. And if we look + + align:start position:0% +this amount of variation. And if we look + + + align:start position:0% +this amount of variation. And if we look +in the region where there's a much + + align:start position:0% +in the region where there's a much + + + align:start position:0% +in the region where there's a much +higher uh amount of metal density, + + align:start position:0% +higher uh amount of metal density, + + + align:start position:0% +higher uh amount of metal density, +therefore less of the metal is being + + align:start position:0% +therefore less of the metal is being + + + align:start position:0% +therefore less of the metal is being +etched away. We see that the uh the + + align:start position:0% +etched away. We see that the uh the + + + align:start position:0% +etched away. We see that the uh the +resistance is higher. + + align:start position:0% +resistance is higher. + + + align:start position:0% +resistance is higher. +And uh I'm sorry, by pattern density, we + + align:start position:0% +And uh I'm sorry, by pattern density, we + + + align:start position:0% +And uh I'm sorry, by pattern density, we +mean that the the proportion of the chip + + align:start position:0% +mean that the the proportion of the chip + + + align:start position:0% +mean that the the proportion of the chip +that is open for etching. And uh we see + + align:start position:0% +that is open for etching. And uh we see + + + align:start position:0% +that is open for etching. And uh we see +that the resistance is higher because + + align:start position:0% +that the resistance is higher because + + + align:start position:0% +that the resistance is higher because +there's more + + align:start position:0% +there's more + + + align:start position:0% +there's more +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh there's more lateral etching. + + align:start position:0% +uh there's more lateral etching. + + + align:start position:0% +uh there's more lateral etching. +And uh but what this gives us an + + align:start position:0% +And uh but what this gives us an + + + align:start position:0% +And uh but what this gives us an +indication of is that there is there + + align:start position:0% +indication of is that there is there + + + align:start position:0% +indication of is that there is there +must be an interaction because the size + + align:start position:0% +must be an interaction because the size + + + align:start position:0% +must be an interaction because the size +of the wafer scale non-uniformity + + align:start position:0% +of the wafer scale non-uniformity + + + align:start position:0% +of the wafer scale non-uniformity +depends on the local pattern density. + + align:start position:0% +depends on the local pattern density. + + + align:start position:0% +depends on the local pattern density. +It's not as if we're taking the 5% + + align:start position:0% +It's not as if we're taking the 5% + + + align:start position:0% +It's not as if we're taking the 5% +variation pattern and we're shifting it + + align:start position:0% +variation pattern and we're shifting it + + + align:start position:0% +variation pattern and we're shifting it +up when we uh when we change to 85% + + align:start position:0% +up when we uh when we change to 85% + + + align:start position:0% +up when we uh when we change to 85% +pattern density. Uh there is a change in + + align:start position:0% +pattern density. Uh there is a change in + + + align:start position:0% +pattern density. Uh there is a change in +the in the shape + + align:start position:0% +the in the shape + + + align:start position:0% +the in the shape +uh of the location dependence as we + + align:start position:0% +uh of the location dependence as we + + + align:start position:0% +uh of the location dependence as we +change the local pattern density. And + + align:start position:0% +change the local pattern density. And + + + align:start position:0% +change the local pattern density. And +that is uh an example of one of those + + align:start position:0% +that is uh an example of one of those + + + align:start position:0% +that is uh an example of one of those +interaction effects that we would need + + align:start position:0% +interaction effects that we would need + + + align:start position:0% +interaction effects that we would need +to capture. So either through some + + align:start position:0% +to capture. So either through some + + + align:start position:0% +to capture. So either through some +multiplicative + + align:start position:0% +multiplicative + + + align:start position:0% +multiplicative +uh model or + + align:start position:0% +uh model or + + + align:start position:0% +uh model or +something more more physically based. + + align:start position:0% + + + + align:start position:0% + +Anyway, that is uh + + align:start position:0% +Anyway, that is uh + + + align:start position:0% +Anyway, that is uh +the end of today's lecture. Next time + + align:start position:0% +the end of today's lecture. Next time + + + align:start position:0% +the end of today's lecture. Next time +we're going to use these uh these + + align:start position:0% +we're going to use these uh these + + + align:start position:0% +we're going to use these uh these +techniques and over uh as the basis for + + align:start position:0% +techniques and over uh as the basis for + + + align:start position:0% +techniques and over uh as the basis for +uh starting to build real models where + + align:start position:0% +uh starting to build real models where + + + align:start position:0% +uh starting to build real models where +we're actually fleshing out the + + align:start position:0% +we're actually fleshing out the + + + align:start position:0% +we're actually fleshing out the +functional relationship between inputs + + align:start position:0% +functional relationship between inputs + + + align:start position:0% +functional relationship between inputs +and outputs + + align:start position:0% +and outputs + + + align:start position:0% +and outputs +and designing uh experiments that will + + align:start position:0% +and designing uh experiments that will + + + align:start position:0% +and designing uh experiments that will +give us that information as efficiently + + align:start position:0% +give us that information as efficiently + + + align:start position:0% +give us that information as efficiently +as possible. + + align:start position:0% +as possible. + + + align:start position:0% +as possible. +Uh okay. Are there any questions from + + align:start position:0% +Uh okay. Are there any questions from + + + align:start position:0% +Uh okay. Are there any questions from +either side? + + align:start position:0% +either side? + + + align:start position:0% +either side? +Hello. + + align:start position:0% +Hello. + + + align:start position:0% +Hello. +Yeah, I have one question. As for the + + align:start position:0% +Yeah, I have one question. As for the + + + align:start position:0% +Yeah, I have one question. As for the +monova, + + align:start position:0% +monova, + + + align:start position:0% +monova, +you have like three uh parameters K, N, + + align:start position:0% +you have like three uh parameters K, N, + + + align:start position:0% +you have like three uh parameters K, N, +and M, right? So, does M always equal to + + align:start position:0% +and M, right? So, does M always equal to + + + align:start position:0% +and M, right? So, does M always equal to +N multiply by K? + + align:start position:0% +N multiply by K? + + + align:start position:0% +N multiply by K? +Actually, + + align:start position:0% +Actually, + + + align:start position:0% +Actually, +yeah, m in that case was the number of + + align:start position:0% +yeah, m in that case was the number of + + + align:start position:0% +yeah, m in that case was the number of +samples uh per + + align:start position:0% +samples uh per + + + align:start position:0% +samples uh per +combination of treatments. So actually + + align:start position:0% +combination of treatments. So actually + + + align:start position:0% +combination of treatments. So actually +in manover the quantity that I termed m + + align:start position:0% +in manover the quantity that I termed m + + + align:start position:0% +in manover the quantity that I termed m +is a bit like n in the single variable + + align:start position:0% +is a bit like n in the single variable + + + align:start position:0% +is a bit like n in the single variable +an over. I know that's confusing. Uh but + + align:start position:0% +an over. I know that's confusing. Uh but + + + align:start position:0% +an over. I know that's confusing. Uh but +here m m is the the number of replicates + + align:start position:0% +here m m is the the number of replicates + + + align:start position:0% +here m m is the the number of replicates +for a given combination of input + + align:start position:0% +for a given combination of input + + + align:start position:0% +for a given combination of input +variables t and q. + + align:start position:0% + + + + align:start position:0% + +Does that make sense? + + align:start position:0% +Does that make sense? + + + align:start position:0% +Does that make sense? +So we we have a combination of inputs T + + align:start position:0% +So we we have a combination of inputs T + + + align:start position:0% +So we we have a combination of inputs T +and Q. We keep them constant. We sample + + align:start position:0% +and Q. We keep them constant. We sample + + + align:start position:0% +and Q. We keep them constant. We sample +a few a few parts for that combination + + align:start position:0% +a few a few parts for that combination + + + align:start position:0% +a few a few parts for that combination +of inputs and there are m of those + + align:start position:0% +of inputs and there are m of those + + + align:start position:0% +of inputs and there are m of those +parts. + + align:start position:0% +parts. + + + align:start position:0% +parts. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Thanks. + + align:start position:0% +Thanks. + + + align:start position:0% +Thanks. +Anyone else? + + align:start position:0% + + + + align:start position:0% + +Okay. Well, thank you. Uh the problem + + align:start position:0% +Okay. Well, thank you. Uh the problem + + + align:start position:0% +Okay. Well, thank you. Uh the problem +set is due on Thursday. + + align:start position:0% +set is due on Thursday. + + + align:start position:0% +set is due on Thursday. +Uh let me know if you have any questions + + align:start position:0% +Uh let me know if you have any questions + + + align:start position:0% +Uh let me know if you have any questions +about it. + + align:start position:0% +about it. + + + align:start position:0% +about it. +I'm sure you will. Oh, hello. + + align:start position:0% +I'm sure you will. Oh, hello. + + + align:start position:0% +I'm sure you will. Oh, hello. +Can I check one thing with you? + + align:start position:0% +Can I check one thing with you? + + + align:start position:0% +Can I check one thing with you? +Sure. + + align:start position:0% +Sure. + + + align:start position:0% +Sure. +For the quiz, I'm not sure which + + align:start position:0% +For the quiz, I'm not sure which + + + align:start position:0% +For the quiz, I'm not sure which +question. I think probably the last + + align:start position:0% +question. I think probably the last + + + align:start position:0% +question. I think probably the last +section of problem one, I think I needed + + align:start position:0% +section of problem one, I think I needed + + + align:start position:0% +section of problem one, I think I needed +a if table with alpha equal to 0.025, + + align:start position:0% +a if table with alpha equal to 0.025, + + + align:start position:0% +a if table with alpha equal to 0.025, +but we were not provided with that. + + align:start position:0% +but we were not provided with that. + + + align:start position:0% +but we were not provided with that. +Yes, + + align:start position:0% +Yes, + + + align:start position:0% +Yes, +I'm not sure whether I'm wrong or + + align:start position:0% +I'm not sure whether I'm wrong or + + + align:start position:0% +I'm not sure whether I'm wrong or +about 10 people asked me. They said + + align:start position:0% +about 10 people asked me. They said + + + align:start position:0% +about 10 people asked me. They said +about that. Well, you know, I I actually + + align:start position:0% +about that. Well, you know, I I actually + + + align:start position:0% +about that. Well, you know, I I actually +I actually think that a one-sided F test + + align:start position:0% +I actually think that a one-sided F test + + + align:start position:0% +I actually think that a one-sided F test +would have been appropriate in that + + align:start position:0% +would have been appropriate in that + + + align:start position:0% +would have been appropriate in that +case. Uh in which case the the uh the + + align:start position:0% +case. Uh in which case the the uh the + + + align:start position:0% +case. Uh in which case the the uh the +table the the 05 table would have been + + align:start position:0% +table the the 05 table would have been + + + align:start position:0% +table the the 05 table would have been +appropriate to do a one-sided 5% deaf + + align:start position:0% +appropriate to do a one-sided 5% deaf + + + align:start position:0% +appropriate to do a one-sided 5% deaf +test. + + align:start position:0% +test. + + + align:start position:0% +test. +It was also possible to answer that + + align:start position:0% +It was also possible to answer that + + + align:start position:0% +It was also possible to answer that +question by looking at the confidence + + align:start position:0% +question by looking at the confidence + + + align:start position:0% +question by looking at the confidence +intervals from part B and seeing whether + + align:start position:0% +intervals from part B and seeing whether + + + align:start position:0% +intervals from part B and seeing whether +they over overlapped. And I think they + + align:start position:0% +they over overlapped. And I think they + + + align:start position:0% +they over overlapped. And I think they +didn't overlap, did they? So they didn't + + align:start position:0% +didn't overlap, did they? So they didn't + + + align:start position:0% +didn't overlap, did they? So they didn't +overlap. So we said there was a + + align:start position:0% +overlap. So we said there was a + + + align:start position:0% +overlap. So we said there was a +significant difference. But anyway, + + align:start position:0% +significant difference. But anyway, + + + align:start position:0% +significant difference. But anyway, +we'll publish solutions. + + align:start position:0% +we'll publish solutions. + + + align:start position:0% +we'll publish solutions. +Thanks. Anyone else? + + align:start position:0% +Thanks. Anyone else? + + + align:start position:0% +Thanks. Anyone else? +No. Good. + + align:start position:0% +No. Good. + + + align:start position:0% +No. Good. +Um, one question. + + align:start position:0% +Um, one question. + + + align:start position:0% +Um, one question. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +I'm sorry. + + align:start position:0% +I'm sorry. + + + align:start position:0% +I'm sorry. +It's okay. + + align:start position:0% +It's okay. + + + align:start position:0% +It's okay. +Um, for the MANOVA + + align:start position:0% +Um, for the MANOVA + + + align:start position:0% +Um, for the MANOVA +um there are Okay. For ANOV there's a + + align:start position:0% +um there are Okay. For ANOV there's a + + + align:start position:0% +um there are Okay. For ANOV there's a +term uh that is the zero mean normal uh + + align:start position:0% +term uh that is the zero mean normal uh + + + align:start position:0% +term uh that is the zero mean normal uh +residual and for manover there's a same + + align:start position:0% +residual and for manover there's a same + + + align:start position:0% +residual and for manover there's a same +term but this u in the second line the + + align:start position:0% +term but this u in the second line the + + + align:start position:0% +term but this u in the second line the +term disappeared. + + align:start position:0% +term disappeared. + + + align:start position:0% +term disappeared. +So do you know what I'm talking about? + + align:start position:0% +So do you know what I'm talking about? + + + align:start position:0% +So do you know what I'm talking about? +Um previous slide + + align:start position:0% +Um previous slide + + + align:start position:0% +Um previous slide +on the previous this slide this slide + + align:start position:0% +on the previous this slide this slide + + + align:start position:0% +on the previous this slide this slide +no previous previous slide two slides + + align:start position:0% +no previous previous slide two slides + + + align:start position:0% +no previous previous slide two slides +ago. Oh yeah, this one. + + align:start position:0% +ago. Oh yeah, this one. + + + align:start position:0% +ago. Oh yeah, this one. +This one. + + align:start position:0% +This one. + + + align:start position:0% +This one. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +the term disappear or something like + + align:start position:0% +the term disappear or something like + + + align:start position:0% +the term disappear or something like +that. + + align:start position:0% +that. + + + align:start position:0% +that. +The the last term on the + + align:start position:0% +The the last term on the + + + align:start position:0% +The the last term on the +Yeah. Oh, you mean you mean the term + + align:start position:0% +Yeah. Oh, you mean you mean the term + + + align:start position:0% +Yeah. Oh, you mean you mean the term +there's a term uh there's a term here, + + align:start position:0% +there's a term uh there's a term here, + + + align:start position:0% +there's a term uh there's a term here, +but there isn't a term here. Is that + + align:start position:0% +but there isn't a term here. Is that + + + align:start position:0% +but there isn't a term here. Is that +what you mean? + + align:start position:0% +what you mean? + + + align:start position:0% +what you mean? +Oh, yeah. Yeah. + + align:start position:0% +Oh, yeah. Yeah. + + + align:start position:0% +Oh, yeah. Yeah. +Yeah. All right. Well, the second line + + align:start position:0% +Yeah. All right. Well, the second line + + + align:start position:0% +Yeah. All right. Well, the second line +is uh an estimate of uh of the value of + + align:start position:0% +is uh an estimate of uh of the value of + + + align:start position:0% +is uh an estimate of uh of the value of +the output for the combination of inputs + + align:start position:0% +the output for the combination of inputs + + + align:start position:0% +the output for the combination of inputs +t and q. And what an estimate is not + + align:start position:0% +t and q. And what an estimate is not + + + align:start position:0% +t and q. And what an estimate is not +trying to make any predictions about + + align:start position:0% +trying to make any predictions about + + + align:start position:0% +trying to make any predictions about +what what a residual will be. It's + + align:start position:0% +what what a residual will be. It's + + + align:start position:0% +what what a residual will be. It's +really dealing just with uh means for a + + align:start position:0% +really dealing just with uh means for a + + + align:start position:0% +really dealing just with uh means for a +given treatment. And it it's saying, you + + align:start position:0% +given treatment. And it it's saying, you + + + align:start position:0% +given treatment. And it it's saying, you +know, if if say you set your machine to + + align:start position:0% +know, if if say you set your machine to + + + align:start position:0% +know, if if say you set your machine to +input one having value T, input two + + align:start position:0% +input one having value T, input two + + + align:start position:0% +input one having value T, input two +having value Q, + + align:start position:0% +having value Q, + + + align:start position:0% +having value Q, +you know, what's your best estimate of + + align:start position:0% +you know, what's your best estimate of + + + align:start position:0% +you know, what's your best estimate of +what the output will be. And that that + + align:start position:0% +what the output will be. And that that + + + align:start position:0% +what the output will be. And that that +that estimate has to be the the mean + + align:start position:0% +that estimate has to be the the mean + + + align:start position:0% +that estimate has to be the the mean +output. There's no point making it + + align:start position:0% +output. There's no point making it + + + align:start position:0% +output. There's no point making it +anything other than the mean. And so so + + align:start position:0% +anything other than the mean. And so so + + + align:start position:0% +anything other than the mean. And so so +the residual that epsilon term is is + + align:start position:0% +the residual that epsilon term is is + + + align:start position:0% +the residual that epsilon term is is +present in real data because there's + + align:start position:0% +present in real data because there's + + + align:start position:0% +present in real data because there's +random variation in the output around + + align:start position:0% +random variation in the output around + + + align:start position:0% +random variation in the output around +the the expected mean. + + align:start position:0% +the the expected mean. + + + align:start position:0% +the the expected mean. +Another way to say that is your best + + align:start position:0% +Another way to say that is your best + + + align:start position:0% +Another way to say that is your best +estimate of epsilon. + + align:start position:0% +estimate of epsilon. + + + align:start position:0% +estimate of epsilon. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +So you could put + + align:start position:0% +So you could put + + + align:start position:0% +So you could put +you could put a plus zero there. That's + + align:start position:0% +you could put a plus zero there. That's + + + align:start position:0% +you could put a plus zero there. That's +your best guess. + + align:start position:0% + + + + align:start position:0% + +Okay. Did you hear that in Singapore? + + align:start position:0% +Okay. Did you hear that in Singapore? + + + align:start position:0% +Okay. Did you hear that in Singapore? +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Yeah. Good. Good. Okay. + + align:start position:0% +Yeah. Good. Good. Okay. + + + align:start position:0% +Yeah. Good. Good. Okay. +Thank you. + + align:start position:0% + + + + align:start position:0% + +Anyone else? + + align:start position:0% + + + + align:start position:0% + +Okay. See you next time. \ No newline at end of file